LMFDB - Embedded newform 165.2.p.b.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(41,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("165.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.p (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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	165.41
Dual form			165.2.p.b.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.09233 + 1.52016i) q^{2} +(1.72815 - 0.116121i) q^{3} +(1.44890 - 4.45925i) q^{4} +(-0.587785 + 0.809017i) q^{5} +(-3.43934 + 2.87004i) q^{6} +(0.326781 + 0.106178i) q^{7} +(2.14883 + 6.61341i) q^{8} +(2.97303 - 0.401348i) q^{9} +O(q^{10})$	\(q+(-2.09233 + 1.52016i) q^{2} +(1.72815 - 0.116121i) q^{3} +(1.44890 - 4.45925i) q^{4} +(-0.587785 + 0.809017i) q^{5} +(-3.43934 + 2.87004i) q^{6} +(0.326781 + 0.106178i) q^{7} +(2.14883 + 6.61341i) q^{8} +(2.97303 - 0.401348i) q^{9} -2.58626i q^{10} +(2.88296 - 1.63967i) q^{11} +(1.98611 - 7.87451i) q^{12} +(3.76304 + 5.17938i) q^{13} +(-0.845141 + 0.274603i) q^{14} +(-0.921840 + 1.46636i) q^{15} +(-6.96300 - 5.05891i) q^{16} +(-0.839822 - 0.610166i) q^{17} +(-5.61044 + 5.35925i) q^{18} +(-5.97625 + 1.94180i) q^{19} +(2.75597 + 3.79326i) q^{20} +(0.577058 + 0.145545i) q^{21} +(-3.53953 + 7.81331i) q^{22} +1.43997i q^{23} +(4.48146 + 11.1795i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-15.7470 - 5.11651i) q^{26} +(5.09125 - 1.03882i) q^{27} +(0.946945 - 1.30336i) q^{28} +(1.36614 - 4.20456i) q^{29} +(-0.300318 - 4.46945i) q^{30} +(0.974590 - 0.708081i) q^{31} +8.35174 q^{32} +(4.79180 - 3.16838i) q^{33} +2.68473 q^{34} +(-0.277977 + 0.201962i) q^{35} +(2.51791 - 13.8390i) q^{36} +(0.0967394 - 0.297733i) q^{37} +(9.55241 - 13.1478i) q^{38} +(7.10454 + 8.51379i) q^{39} +(-6.61341 - 2.14883i) q^{40} +(0.390553 + 1.20200i) q^{41} +(-1.42865 + 0.572694i) q^{42} -10.6620i q^{43} +(-3.13458 - 15.2316i) q^{44} +(-1.42281 + 2.64114i) q^{45} +(-2.18899 - 3.01289i) q^{46} +(-8.00954 + 2.60246i) q^{47} +(-12.6206 - 7.93404i) q^{48} +(-5.56761 - 4.04510i) q^{49} +(2.09233 + 1.52016i) q^{50} +(-1.52219 - 0.956941i) q^{51} +(28.5484 - 9.27593i) q^{52} +(0.614788 + 0.846183i) q^{53} +(-9.07338 + 9.91309i) q^{54} +(-0.368041 + 3.29614i) q^{55} +2.38930i q^{56} +(-10.1024 + 4.04970i) q^{57} +(3.53320 + 10.8741i) q^{58} +(7.13553 + 2.31847i) q^{59} +(5.20321 + 6.23532i) q^{60} +(2.01712 - 2.77633i) q^{61} +(-0.962761 + 2.96307i) q^{62} +(1.01415 + 0.184517i) q^{63} +(-3.54858 + 2.57819i) q^{64} -6.40206 q^{65} +(-5.20957 + 13.9136i) q^{66} -7.66699 q^{67} +(-3.93770 + 2.86091i) q^{68} +(0.167210 + 2.48849i) q^{69} +(0.274603 - 0.845141i) q^{70} +(5.34932 - 7.36271i) q^{71} +(9.04282 + 18.7995i) q^{72} +(-3.99770 - 1.29893i) q^{73} +(0.250193 + 0.770015i) q^{74} +(-0.644466 - 1.60769i) q^{75} +29.4631i q^{76} +(1.11619 - 0.229708i) q^{77} +(-27.8074 - 7.01357i) q^{78} +(-2.88184 - 3.96651i) q^{79} +(8.18550 - 2.65963i) q^{80} +(8.67784 - 2.38644i) q^{81} +(-2.64440 - 1.92127i) q^{82} +(-10.7041 - 7.77699i) q^{83} +(1.48512 - 2.36236i) q^{84} +(0.987270 - 0.320783i) q^{85} +(16.2081 + 22.3085i) q^{86} +(1.87267 - 7.42476i) q^{87} +(17.0388 + 15.5429i) q^{88} +4.84619i q^{89} +(-1.03799 - 7.68903i) q^{90} +(0.679756 + 2.09207i) q^{91} +(6.42119 + 2.08637i) q^{92} +(1.60202 - 1.33684i) q^{93} +(12.8024 - 17.6210i) q^{94} +(1.94180 - 5.97625i) q^{95} +(14.4331 - 0.969809i) q^{96} +(-8.10068 + 5.88549i) q^{97} +17.7985 q^{98} +(7.91306 - 6.03187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.09233	+	1.52016i	−1.47950	+	1.07492i	−0.501781	+	0.864995i	$0.667322\pi$
$2$	−2.09233	+	1.52016i	−1.47950	+	1.07492i	−0.977718	+	0.209924i	$0.932678\pi$
$3$	1.72815	−	0.116121i	0.997750	−	0.0670422i
$3$	1.72815	−	0.116121i	0.997750	−	0.0670422i
$4$	1.44890	−	4.45925i	0.724449	−	2.22962i
$5$	−0.587785	+	0.809017i	−0.262866	+	0.361803i
$5$	−0.587785	+	0.809017i	−0.262866	+	0.361803i
$6$	−3.43934	+	2.87004i	−1.40410	+	1.17169i
$7$	0.326781	+	0.106178i	0.123512	+	0.0401314i	0.370121	−	0.928984i	$-0.379316\pi$
$7$	0.326781	+	0.106178i	0.123512	+	0.0401314i	−0.246609	+	0.969115i	$0.579316\pi$
$8$	2.14883	+	6.61341i	0.759725	+	2.33819i
$9$	2.97303	−	0.401348i	0.991011	−	0.133783i
$10$		−	2.58626i		−	0.817847i
$11$	2.88296	−	1.63967i	0.869246	−	0.494380i
$11$	2.88296	−	1.63967i	0.869246	−	0.494380i
$12$	1.98611	−	7.87451i	0.573340	−	2.27318i
$13$	3.76304	+	5.17938i	1.04368	+	1.43650i	0.894163	+	0.447741i	$0.147771\pi$
$13$	3.76304	+	5.17938i	1.04368	+	1.43650i	0.149515	+	0.988759i	$0.452229\pi$
$14$	−0.845141	+	0.274603i	−0.225873	+	0.0733907i
$15$	−0.921840	+	1.46636i	−0.238018	+	0.378612i
$16$	−6.96300	−	5.05891i	−1.74075	−	1.26473i
$17$	−0.839822	−	0.610166i	−0.203687	−	0.147987i	0.481266	−	0.876575i	$-0.340177\pi$
$17$	−0.839822	−	0.610166i	−0.203687	−	0.147987i	−0.684953	+	0.728588i	$0.740177\pi$
$18$	−5.61044	+	5.35925i	−1.32239	+	1.26319i
$19$	−5.97625	+	1.94180i	−1.37105	+	0.445480i	−0.899716	−	0.436477i	$-0.856226\pi$
$19$	−5.97625	+	1.94180i	−1.37105	+	0.445480i	−0.471331	+	0.881957i	$0.656226\pi$
$20$	2.75597	+	3.79326i	0.616253	+	0.848199i
$21$	0.577058	+	0.145545i	0.125924	+	0.0317606i
$22$	−3.53953	+	7.81331i	−0.754630	+	1.66580i
$23$			1.43997i			0.300255i	0.988667	+	0.150127i	$0.0479684\pi$
$23$			1.43997i			0.300255i	−0.988667	+	0.150127i	$0.952032\pi$
$24$	4.48146	+	11.1795i	0.914774	+	2.28200i
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$	−15.7470	−	5.11651i	−3.08824	−	1.00343i
$27$	5.09125	−	1.03882i	0.979812	−	0.199921i
$28$	0.946945	−	1.30336i	0.178956	−	0.246312i
$29$	1.36614	−	4.20456i	0.253686	−	0.780767i	−0.740399	−	0.672168i	$-0.765363\pi$
$29$	1.36614	−	4.20456i	0.253686	−	0.780767i	0.994086	−	0.108599i	$-0.0346365\pi$
$30$	−0.300318	−	4.46945i	−0.0548302	−	0.816007i
$31$	0.974590	−	0.708081i	0.175041	−	0.127175i	−0.496815	−	0.867857i	$-0.665497\pi$
$31$	0.974590	−	0.708081i	0.175041	−	0.127175i	0.671856	+	0.740681i	$0.265497\pi$
$32$	8.35174			1.47639
$33$	4.79180	−	3.16838i	0.834146	−	0.551543i
$34$	2.68473			0.460428
$35$	−0.277977	+	0.201962i	−0.0469866	+	0.0341378i
$36$	2.51791	−	13.8390i	0.419651	−	2.30650i
$37$	0.0967394	−	0.297733i	0.0159039	−	0.0489471i	−0.942790	−	0.333388i	$-0.891808\pi$
$37$	0.0967394	−	0.297733i	0.0159039	−	0.0489471i	0.958694	+	0.284441i	$0.0918080\pi$
$38$	9.55241	−	13.1478i	1.54961	−	2.13285i
$39$	7.10454	+	8.51379i	1.13764	+	1.36330i
$40$	−6.61341	−	2.14883i	−1.04567	−	0.339760i
$41$	0.390553	+	1.20200i	0.0609941	+	0.187720i	0.976911	−	0.213648i	$-0.0685346\pi$
$41$	0.390553	+	1.20200i	0.0609941	+	0.187720i	−0.915917	+	0.401369i	$0.868535\pi$
$42$	−1.42865	+	0.572694i	−0.220445	+	0.0883686i
$43$		−	10.6620i		−	1.62595i	−0.582300	−	0.812974i	$-0.697847\pi$
$43$		−	10.6620i		−	1.62595i	0.582300	−	0.812974i	$-0.302153\pi$
$44$	−3.13458	−	15.2316i	−0.472556	−	2.29624i
$45$	−1.42281	+	2.64114i	−0.212100	+	0.393718i
$46$	−2.18899	−	3.01289i	−0.322750	−	0.444227i
$47$	−8.00954	+	2.60246i	−1.16831	+	0.379607i	−0.828012	−	0.560710i	$-0.810528\pi$
$47$	−8.00954	+	2.60246i	−1.16831	+	0.379607i	−0.340299	+	0.940317i	$0.610528\pi$
$48$	−12.6206	−	7.93404i	−1.82162	−	1.14518i
$49$	−5.56761	−	4.04510i	−0.795372	−	0.577872i
$50$	2.09233	+	1.52016i	0.295900	+	0.214984i
$51$	−1.52219	−	0.956941i	−0.213150	−	0.133999i
$52$	28.5484	−	9.27593i	3.95895	−	1.28634i
$53$	0.614788	+	0.846183i	0.0844476	+	0.116232i	0.849151	−	0.528151i	$-0.177114\pi$
$53$	0.614788	+	0.846183i	0.0844476	+	0.116232i	−0.764703	+	0.644383i	$0.777114\pi$
$54$	−9.07338	+	9.91309i	−1.23473	+	1.34900i
$55$	−0.368041	+	3.29614i	−0.0496266	+	0.444452i
$56$			2.38930i			0.319283i
$57$	−10.1024	+	4.04970i	−1.33810	+	0.536396i
$58$	3.53320	+	10.8741i	0.463932	+	1.42784i
$59$	7.13553	+	2.31847i	0.928966	+	0.301839i	0.734140	−	0.678998i	$-0.237586\pi$
$59$	7.13553	+	2.31847i	0.928966	+	0.301839i	0.194826	+	0.980838i	$0.437586\pi$
$60$	5.20321	+	6.23532i	0.671732	+	0.804976i
$61$	2.01712	−	2.77633i	0.258266	−	0.355472i	−0.660119	−	0.751161i	$-0.729494\pi$
$61$	2.01712	−	2.77633i	0.258266	−	0.355472i	0.918385	+	0.395689i	$0.129494\pi$
$62$	−0.962761	+	2.96307i	−0.122271	+	0.376311i
$63$	1.01415	+	0.184517i	0.127770	+	0.0232469i
$64$	−3.54858	+	2.57819i	−0.443572	+	0.322274i
$65$	−6.40206			−0.794078
$66$	−5.20957	+	13.9136i	−0.641254	+	1.71265i
$67$	−7.66699			−0.936672			−0.468336	−	0.883550i	$-0.655146\pi$
$67$	−7.66699			−0.936672			−0.468336	+	0.883550i	$0.655146\pi$
$68$	−3.93770	+	2.86091i	−0.477516	+	0.346936i
$69$	0.167210	+	2.48849i	0.0201298	+	0.299579i
$70$	0.274603	−	0.845141i	0.0328213	−	0.101014i
$71$	5.34932	−	7.36271i	0.634848	−	0.873793i	−0.363480	−	0.931602i	$-0.618412\pi$
$71$	5.34932	−	7.36271i	0.634848	−	0.873793i	0.998328	+	0.0578092i	$0.0184115\pi$
$72$	9.04282	+	18.7995i	1.06571	+	2.21554i
$73$	−3.99770	−	1.29893i	−0.467895	−	0.152028i	0.0655743	−	0.997848i	$-0.479112\pi$
$73$	−3.99770	−	1.29893i	−0.467895	−	0.152028i	−0.533469	+	0.845819i	$0.679112\pi$
$74$	0.250193	+	0.770015i	0.0290844	+	0.0895125i
$75$	−0.644466	−	1.60769i	−0.0744165	−	0.185640i
$76$			29.4631i			3.37965i
$77$	1.11619	−	0.229708i	0.127202	−	0.0261776i
$78$	−27.8074	−	7.01357i	−3.14857	−	0.794130i
$79$	−2.88184	−	3.96651i	−0.324232	−	0.446268i	0.615521	−	0.788120i	$-0.288946\pi$
$79$	−2.88184	−	3.96651i	−0.324232	−	0.446268i	−0.939754	+	0.341853i	$0.888946\pi$
$80$	8.18550	−	2.65963i	0.915166	−	0.297356i
$81$	8.67784	−	2.38644i	0.964204	−	0.265160i
$82$	−2.64440	−	1.92127i	−0.292025	−	0.212168i
$83$	−10.7041	−	7.77699i	−1.17493	−	0.853636i	−0.183338	−	0.983050i	$-0.558690\pi$
$83$	−10.7041	−	7.77699i	−1.17493	−	0.853636i	−0.991591	+	0.129414i	$0.958690\pi$
$84$	1.48512	−	2.36236i	0.162040	−	0.257755i
$85$	0.987270	−	0.320783i	0.107084	−	0.0347938i
$86$	16.2081	+	22.3085i	1.74776	+	2.40559i
$87$	1.87267	−	7.42476i	0.200771	−	0.796018i
$88$	17.0388	+	15.5429i	1.81634	+	1.65687i
$89$			4.84619i			0.513695i	0.966452	+	0.256847i	$0.0826838\pi$
$89$			4.84619i			0.513695i	−0.966452	+	0.256847i	$0.917316\pi$
$90$	−1.03799	−	7.68903i	−0.109414	−	0.810495i
$91$	0.679756	+	2.09207i	0.0712578	+	0.219309i
$92$	6.42119	+	2.08637i	0.669456	+	0.217519i
$93$	1.60202	−	1.33684i	0.166122	−	0.138624i
$94$	12.8024	−	17.6210i	1.32047	−	1.81747i
$95$	1.94180	−	5.97625i	0.199225	−	0.613151i
$96$	14.4331	−	0.969809i	1.47307	−	0.0989807i
$97$	−8.10068	+	5.88549i	−0.822499	+	0.597581i	−0.917427	−	0.397903i	$-0.869738\pi$
$97$	−8.10068	+	5.88549i	−0.822499	+	0.597581i	0.0949280	+	0.995484i	$0.469738\pi$
$98$	17.7985			1.79792
$99$	7.91306	−	6.03187i	0.795293	−	0.606226i
$100$	−4.68873			−0.468873
$101$	−12.8346	+	9.32488i	−1.27709	+	0.927860i	−0.999461	−	0.0328278i	$-0.989549\pi$
$101$	−12.8346	+	9.32488i	−1.27709	+	0.927860i	−0.277629	+	0.960688i	$0.589549\pi$
$102$	4.63964	−	0.311753i	0.459392	−	0.0308681i
$103$	−3.17626	+	9.77553i	−0.312966	+	0.963212i	0.663617	+	0.748073i	$0.269021\pi$
$103$	−3.17626	+	9.77553i	−0.312966	+	0.963212i	−0.976583	+	0.215139i	$0.930979\pi$
$104$	−26.1672	+	36.0161i	−2.56591	+	3.53167i
$105$	−0.456935	+	0.381300i	−0.0445923	+	0.0372111i
$106$	−2.57268	−	0.835913i	−0.249880	−	0.0811910i
$107$	−4.43495	−	13.6494i	−0.428743	−	1.31954i	−0.899364	−	0.437200i	$-0.855970\pi$
$107$	−4.43495	−	13.6494i	−0.428743	−	1.31954i	0.470621	−	0.882335i	$-0.344030\pi$
$108$	2.74434	−	24.2083i	0.264074	−	2.32945i
$109$			6.28546i			0.602038i	0.953618	+	0.301019i	$0.0973267\pi$
$109$			6.28546i			0.602038i	−0.953618	+	0.301019i	$0.902673\pi$
$110$	−4.24061	−	7.45609i	−0.404327	−	0.710910i
$111$	0.132608	−	0.525763i	0.0125866	−	0.0499032i
$112$	−1.73823	−	2.39247i	−0.164248	−	0.226067i
$113$	−3.87264	+	1.25830i	−0.364307	+	0.118371i	−0.485450	−	0.874264i	$-0.661344\pi$
$113$	−3.87264	+	1.25830i	−0.364307	+	0.118371i	0.121143	+	0.992635i	$0.461344\pi$
$114$	14.9813	−	23.8306i	1.40313	−	2.23194i
$115$	−1.16496	−	0.846394i	−0.108633	−	0.0789267i
$116$	−16.7698	−	12.1839i	−1.55703	−	1.13125i
$117$	13.2664	+	13.8882i	1.22648	+	1.28396i
$118$	−18.4543	+	5.99617i	−1.69886	+	0.551992i
$119$	−0.209652	−	0.288561i	−0.0192188	−	0.0264524i
$120$	−11.6785	−	2.94555i	−1.06610	−	0.268891i
$121$	5.62295	−	9.45423i	0.511178	−	0.859475i
$122$			8.87534i			0.803535i
$123$	0.814512	+	2.03189i	0.0734420	+	0.183209i
$124$	−1.74543	−	5.37187i	−0.156744	−	0.482409i
$125$	0.951057	+	0.309017i	0.0850651	+	0.0276393i
$126$	−2.40242	+	1.15560i	−0.214024	+	0.102949i
$127$	0.832442	−	1.14576i	0.0738673	−	0.101670i	−0.770485	−	0.637459i	$-0.779986\pi$
$127$	0.832442	−	1.14576i	0.0738673	−	0.101670i	0.844352	+	0.535789i	$0.179986\pi$
$128$	−1.65615	+	5.09711i	−0.146385	+	0.450525i
$129$	−1.23808	−	18.4257i	−0.109007	−	1.62229i
$130$	13.3952	−	9.73218i	1.17484	−	0.853569i
$131$	−1.64724			−0.143920			−0.0719600	−	0.997408i	$-0.522925\pi$
$131$	−1.64724			−0.143920			−0.0719600	+	0.997408i	$0.522925\pi$
$132$	−7.18574	−	25.9585i	−0.625439	−	2.25940i
$133$	−2.15910			−0.187218
$134$	16.0419	−	11.6551i	1.38580	−	1.00685i
$135$	−2.15214	+	4.72951i	−0.185227	+	0.407052i
$136$	2.23065	−	6.86523i	0.191277	−	0.588689i
$137$	−4.67962	+	6.44094i	−0.399807	+	0.550287i	−0.960696	−	0.277604i	$-0.910460\pi$
$137$	−4.67962	+	6.44094i	−0.399807	+	0.550287i	0.560889	+	0.827891i	$0.310460\pi$
$138$	−4.13278	−	4.95255i	−0.351805	−	0.421589i
$139$	−4.62440	−	1.50256i	−0.392237	−	0.127445i	0.106257	−	0.994339i	$-0.466113\pi$
$139$	−4.62440	−	1.50256i	−0.392237	−	0.127445i	−0.498494	+	0.866893i	$0.666113\pi$
$140$	0.497839	+	1.53219i	0.0420750	+	0.129494i
$141$	−13.5395	+	5.42752i	−1.14023	+	0.457079i
$142$			23.5370i			1.97518i
$143$	19.3412	+	8.76180i	1.61739	+	0.732699i
$144$	−22.7316	−	12.2457i	−1.89430	−	1.02048i
$145$	2.59856	+	3.57661i	0.215799	+	0.297021i
$146$	10.3391	−	3.35937i	0.855668	−	0.278023i
$147$	−10.0914	−	6.34405i	−0.832325	−	0.523248i
$148$	−1.18750	−	0.862770i	−0.0976120	−	0.0709193i
$149$	12.5759	+	9.13689i	1.03025	+	0.748524i	0.968360	−	0.249559i	$-0.0802857\pi$
$149$	12.5759	+	9.13689i	1.03025	+	0.748524i	0.0618947	+	0.998083i	$0.480286\pi$
$150$	3.79239	+	2.38412i	0.309647	+	0.194662i
$151$	13.5706	−	4.40934i	1.10436	−	0.358827i	0.300579	−	0.953757i	$-0.402820\pi$
$151$	13.5706	−	4.40934i	1.10436	−	0.358827i	0.803778	+	0.594930i	$0.202820\pi$
$152$	−25.6839	−	35.3508i	−2.08324	−	2.86733i
$153$	−2.74171	−	1.47698i	−0.221654	−	0.119407i
$154$	−1.98625	+	2.17742i	−0.160057	+	0.175462i
$155$			1.20466i			0.0967605i
$156$	48.2589	−	19.3453i	3.86380	−	1.54886i
$157$	3.88491	+	11.9565i	0.310049	+	0.954233i	0.977745	+	0.209799i	$0.0672809\pi$
$157$	3.88491	+	11.9565i	0.310049	+	0.954233i	−0.667695	+	0.744435i	$0.732719\pi$
$158$	12.0595	+	3.91837i	0.959403	+	0.311729i
$159$	1.16071	+	1.39095i	0.0920501	+	0.110309i
$160$	−4.90903	+	6.75670i	−0.388093	+	0.534164i
$161$	−0.152893	+	0.470556i	−0.0120496	+	0.0370850i
$162$	−14.5291	+	18.1850i	−1.14151	+	1.42875i
$163$	17.8774	−	12.9887i	1.40027	−	1.01736i	0.405621	−	0.914041i	$-0.367055\pi$
$163$	17.8774	−	12.9887i	1.40027	−	1.01736i	0.994649	−	0.103314i	$-0.0329447\pi$
$164$	5.92588			0.462733
$165$	−0.253282	+	5.73898i	−0.0197180	+	0.446779i
$166$	34.2188			2.65589
$167$	8.36009	−	6.07396i	0.646923	−	0.470017i	−0.215299	−	0.976548i	$-0.569072\pi$
$167$	8.36009	−	6.07396i	0.646923	−	0.470017i	0.862222	+	0.506531i	$0.169072\pi$
$168$	0.277446	+	4.12907i	0.0214054	+	0.318565i
$169$	−8.64827	+	26.6166i	−0.665251	+	2.04743i
$170$	−1.57805	+	2.17200i	−0.121031	+	0.166584i
$171$	−16.9883	+	8.17160i	−1.29912	+	0.624898i
$172$	−47.5447	−	15.4482i	−3.62525	−	1.17792i
$173$	−1.95823	−	6.02681i	−0.148882	−	0.458210i	0.848608	−	0.529022i	$-0.177441\pi$
$173$	−1.95823	−	6.02681i	−0.148882	−	0.458210i	−0.997490	+	0.0708117i	$0.977441\pi$
$174$	7.36862	+	18.3818i	0.558613	+	1.39352i
$175$		−	0.343598i		−	0.0259736i
$176$	−28.3690	−	3.16763i	−2.13840	−	0.238769i
$177$	12.6005	+	3.17810i	0.947112	+	0.238880i
$178$	−7.36700	−	10.1398i	−0.552180	−	0.760011i
$179$	−11.0655	+	3.59539i	−0.827073	+	0.268732i	−0.691812	−	0.722078i	$-0.743187\pi$
$179$	−11.0655	+	3.59539i	−0.827073	+	0.268732i	−0.135261	+	0.990810i	$0.543187\pi$
$180$	9.71600	+	10.1714i	0.724188	+	0.758131i
$181$	−9.94123	−	7.22272i	−0.738926	−	0.536861i	0.153449	−	0.988157i	$-0.450962\pi$
$181$	−9.94123	−	7.22272i	−0.738926	−	0.536861i	−0.892374	+	0.451296i	$0.850962\pi$
$182$	−4.60257	−	3.34396i	−0.341165	−	0.247871i
$183$	3.16351	−	5.03215i	0.233853	−	0.371987i
$184$	−9.52313	+	3.09425i	−0.702054	+	0.228111i
$185$	0.184009	+	0.253267i	0.0135286	+	0.0186206i
$186$	−1.31973	+	5.23244i	−0.0967669	+	0.383661i
$187$	−3.42165	−	0.382055i	−0.250216	−	0.0279386i
$188$			39.4872i			2.87990i
$189$	1.77403	+	0.201110i	0.129041	+	0.0146286i
$190$	5.02200	+	15.4561i	0.364334	+	1.12131i
$191$	7.08007	+	2.30045i	0.512296	+	0.166455i	0.553746	−	0.832686i	$-0.313198\pi$
$191$	7.08007	+	2.30045i	0.512296	+	0.166455i	−0.0414503	+	0.999141i	$0.513198\pi$
$192$	−5.83311	+	4.86758i	−0.420969	+	0.351287i
$193$	−1.99565	+	2.74678i	−0.143650	+	0.197717i	−0.874779	−	0.484522i	$-0.838994\pi$
$193$	−1.99565	+	2.74678i	−0.143650	+	0.197717i	0.731129	+	0.682239i	$0.238994\pi$
$194$	8.00236	−	24.6287i	0.574536	−	1.76824i
$195$	−11.0637	+	0.743411i	−0.792291	+	0.0532367i
$196$	−26.1050	+	18.9664i	−1.86464	+	1.35474i
$197$	−1.79814			−0.128112			−0.0640560	−	0.997946i	$-0.520404\pi$
$197$	−1.79814			−0.128112			−0.0640560	+	0.997946i	$0.520404\pi$
$198$	−7.38728	+	24.6498i	−0.524991	+	1.75178i
$199$	13.8199			0.979665			0.489833	−	0.871817i	$-0.337058\pi$
$199$	13.8199			0.979665			0.489833	+	0.871817i	$0.337058\pi$
$200$	5.62570	−	4.08731i	0.397797	−	0.289017i
$201$	−13.2497	+	0.890295i	−0.934565	+	0.0627966i
$202$	12.6788	−	39.0214i	0.892079	−	2.74554i
$203$	0.892860	−	1.22892i	0.0626665	−	0.0862530i
$204$	−6.47274	+	5.40133i	−0.453182	+	0.378169i
$205$	−1.20200	−	0.390553i	−0.0839511	−	0.0272774i
$206$	−8.21464	−	25.2820i	−0.572341	−	1.76148i
$207$	0.577930	+	4.28108i	0.0401689	+	0.297556i
$208$		−	55.1009i		−	3.82056i
$209$	−14.0454	+	15.3972i	−0.971540	+	1.06505i
$210$	0.376418	−	1.49242i	0.0259753	−	0.102987i
$211$	7.24013	+	9.96518i	0.498431	+	0.686032i	0.981915	−	0.189322i	$-0.0606289\pi$
$211$	7.24013	+	9.96518i	0.498431	+	0.686032i	−0.483484	+	0.875353i	$0.660629\pi$
$212$	4.66411	−	1.51546i	0.320332	−	0.104082i
$213$	8.38949	−	13.3451i	0.574838	−	0.914388i
$214$	30.0287	+	21.8171i	2.05272	+	1.49139i
$215$	8.62578	+	6.26700i	0.588273	+	0.427406i
$216$	17.8104	+	31.4383i	1.21184	+	2.13911i
$217$	0.393660	−	0.127908i	0.0267234	−	0.00868295i
$218$	−9.55493	−	13.1512i	−0.647141	−	0.890714i
$219$	−7.05947	−	1.78054i	−0.477035	−	0.120318i
$220$	14.1651	+	6.41696i	0.955008	+	0.432631i
$221$		−	6.64583i		−	0.447047i
$222$	0.521787	+	1.30165i	0.0350200	+	0.0873612i
$223$	−5.06838	−	15.5989i	−0.339404	−	1.04458i	−0.964512	−	0.264040i	$-0.914945\pi$
$223$	−5.06838	−	15.5989i	−0.339404	−	1.04458i	0.625108	−	0.780538i	$-0.285055\pi$
$224$	2.72919	+	0.886769i	0.182352	+	0.0592497i
$225$	−1.30042	−	2.70350i	−0.0866948	−	0.180233i
$226$	6.19001	−	8.51982i	0.411753	−	0.566730i
$227$	5.56345	−	17.1225i	0.369259	−	1.13646i	−0.578012	−	0.816028i	$-0.696171\pi$
$227$	5.56345	−	17.1225i	0.369259	−	1.13646i	0.947271	−	0.320434i	$-0.103829\pi$
$228$	3.42127	+	50.9167i	0.226579	+	3.37204i
$229$	−15.6528	+	11.3724i	−1.03437	+	0.751510i	−0.969178	−	0.246363i	$-0.920765\pi$
$229$	−15.6528	+	11.3724i	−1.03437	+	0.751510i	−0.0651875	+	0.997873i	$0.520765\pi$
$230$	3.72414			0.245562
$231$	1.90228	−	0.526583i	0.125161	−	0.0346466i
$232$	30.7421			2.01832
$233$	−5.53801	+	4.02360i	−0.362807	+	0.263595i	−0.754222	−	0.656619i	$-0.771986\pi$
$233$	−5.53801	+	4.02360i	−0.362807	+	0.263595i	0.391415	+	0.920214i	$0.371986\pi$
$234$	−48.8699	−	8.89152i	−3.19472	−	0.581257i
$235$	2.60246	−	8.00954i	0.169766	−	0.522485i
$236$	20.6773	−	28.4599i	1.34598	−	1.85258i
$237$	−5.44086	−	6.52010i	−0.353422	−	0.423526i
$238$	0.877321	+	0.285059i	0.0568683	+	0.0184776i
$239$	−0.0459608	−	0.141453i	−0.00297296	−	0.00914982i	0.949559	−	0.313588i	$-0.101531\pi$
$239$	−0.0459608	−	0.141453i	−0.00297296	−	0.00914982i	−0.952532	+	0.304439i	$0.901531\pi$
$240$	13.8370	−	5.54675i	0.893172	−	0.358041i
$241$			0.703420i			0.0453112i	0.999743	+	0.0226556i	$0.00721212\pi$
$241$			0.703420i			0.0453112i	−0.999743	+	0.0226556i	$0.992788\pi$
$242$	2.60692	+	28.3291i	0.167579	+	1.82107i
$243$	14.7195	−	5.13181i	0.944258	−	0.329206i
$244$	−9.45773	−	13.0175i	−0.605469	−	0.833357i
$245$	6.54511	−	2.12664i	0.418152	−	0.135866i
$246$	−4.79302	−	3.01318i	−0.305592	−	0.192113i
$247$	−32.5462	−	23.6462i	−2.07086	−	1.50457i
$248$	6.77706	+	4.92382i	0.430343	+	0.312663i
$249$	−19.4014	−	12.1969i	−1.22951	−	0.772945i
$250$	−2.45968	+	0.799198i	−0.155564	+	0.0505457i
$251$	1.94054	+	2.67093i	0.122486	+	0.168587i	0.865857	−	0.500292i	$-0.166774\pi$
$251$	1.94054	+	2.67093i	0.122486	+	0.168587i	−0.743371	+	0.668880i	$0.766774\pi$
$252$	2.29220	−	4.25498i	0.144395	−	0.268039i
$253$	2.36108	+	4.15139i	0.148440	+	0.260995i
$254$			3.66275i			0.229821i
$255$	1.66890	−	0.669005i	0.104511	−	0.0418947i
$256$	−6.99411	−	21.5257i	−0.437132	−	1.34535i
$257$	22.8885	+	7.43694i	1.42775	+	0.463903i	0.918055	−	0.396453i	$-0.129759\pi$
$257$	22.8885	+	7.43694i	1.42775	+	0.463903i	0.509693	+	0.860356i	$0.329759\pi$
$258$	30.6005	+	36.6704i	1.90510	+	2.28300i
$259$	0.0632253	−	0.0870221i	0.00392863	−	0.00540729i
$260$	−9.27593	+	28.5484i	−0.575269	+	1.77050i
$261$	2.37410	−	13.0486i	0.146953	−	0.807687i
$262$	3.44656	−	2.50408i	0.212929	−	0.154702i
$263$	−6.66938			−0.411252			−0.205626	−	0.978631i	$-0.565923\pi$
$263$	−6.66938			−0.411252			−0.205626	+	0.978631i	$0.565923\pi$
$264$	31.2505	+	24.8819i	1.92334	+	1.53137i
$265$	−1.04594			−0.0642516
$266$	4.51755	−	3.28219i	0.276989	−	0.201244i
$267$	0.562742	+	8.37496i	0.0344392	+	0.512539i
$268$	−11.1087	+	34.1890i	−0.678571	+	2.08843i
$269$	11.0090	−	15.1526i	0.671230	−	0.923869i	−0.328557	−	0.944484i	$-0.606562\pi$
$269$	11.0090	−	15.1526i	0.671230	−	0.923869i	0.999787	+	0.0206150i	$0.00656243\pi$
$270$	−2.68666	−	13.1673i	−0.163505	−	0.801336i
$271$	20.9067	+	6.79300i	1.26999	+	0.412646i	0.865045	−	0.501694i	$-0.167290\pi$
$271$	20.9067	+	6.79300i	1.26999	+	0.412646i	0.404947	+	0.914340i	$0.367290\pi$
$272$	2.76090	+	8.49717i	0.167404	+	0.515217i
$273$	1.41766	+	3.53649i	0.0858004	+	0.214038i
$274$		−	20.5904i		−	1.24391i
$275$	−2.45031	−	2.23517i	−0.147759	−	0.134786i
$276$	11.3391	+	2.85994i	0.682532	+	0.172148i
$277$	14.1319	+	19.4509i	0.849105	+	1.16869i	0.984059	+	0.177841i	$0.0569112\pi$
$277$	14.1319	+	19.4509i	0.849105	+	1.16869i	−0.134955	+	0.990852i	$0.543089\pi$
$278$	11.9599	−	3.88601i	0.717307	−	0.233067i
$279$	2.61330	−	2.49630i	0.156454	−	0.149449i
$280$	−1.93298	−	1.40439i	−0.115518	−	0.0839286i
$281$	4.84319	+	3.51878i	0.288920	+	0.209913i	0.722799	−	0.691058i	$-0.242855\pi$
$281$	4.84319	+	3.51878i	0.288920	+	0.209913i	−0.433878	+	0.900971i	$0.642855\pi$
$282$	20.0784	−	31.9384i	1.19565	−	1.90191i
$283$	−2.49111	+	0.809412i	−0.148081	+	0.0481145i	−0.382120	−	0.924113i	$-0.624806\pi$
$283$	−2.49111	+	0.809412i	−0.148081	+	0.0481145i	0.234038	+	0.972227i	$0.424806\pi$
$284$	−25.0815	−	34.5218i	−1.48831	−	2.04849i
$285$	2.66177	−	10.5534i	0.157669	−	0.625127i
$286$	−53.7874	+	11.0692i	−3.18052	+	0.654536i
$287$			0.434258i			0.0256334i
$288$	24.8300	−	3.35196i	1.46312	−	0.197516i
$289$	−4.92029	−	15.1431i	−0.289429	−	0.890771i
$290$	−10.8741	−	3.53320i	−0.638547	−	0.207477i
$291$	−13.3158	+	11.1117i	−0.780586	+	0.651378i
$292$	−11.5845	+	15.9447i	−0.677932	+	0.933094i
$293$	−1.70408	+	5.24463i	−0.0995536	+	0.306395i	−0.988414	−	0.151784i	$-0.951498\pi$
$293$	−1.70408	+	5.24463i	−0.0995536	+	0.306395i	0.888860	+	0.458179i	$0.151498\pi$
$294$	30.7585	−	2.06677i	1.79387	−	0.120536i
$295$	−6.06984	+	4.41000i	−0.353400	+	0.256760i
$296$	2.17691			0.126530
$297$	12.9746	−	11.3429i	0.752861	−	0.658180i
$298$	−40.2024			−2.32886
$299$	−7.45816	+	5.41867i	−0.431316	+	0.313370i
$300$	−8.10285	+	0.544458i	−0.467818	+	0.0314343i
$301$	1.13207	−	3.48416i	0.0652515	−	0.200824i
$302$	−21.6911	+	29.8553i	−1.24818	+	1.71798i
$303$	−21.0974	+	17.6052i	−1.21201	+	1.01139i
$304$	51.4360	+	16.7126i	2.95006	+	0.958532i
$305$	1.06046	+	3.26377i	0.0607219	+	0.186883i
$306$	7.98180	−	1.07751i	0.456289	−	0.0615974i
$307$		−	1.81322i		−	0.103486i	−0.998660	−	0.0517429i	$-0.983522\pi$
$307$		−	1.81322i		−	0.103486i	0.998660	−	0.0517429i	$-0.0164776\pi$
$308$	0.592929	−	5.31021i	0.0337852	−	0.302577i
$309$	−4.35393	+	17.2625i	−0.247687	+	0.982027i
$310$	−1.83128	−	2.52054i	−0.104010	−	0.143157i
$311$	−9.42208	+	3.06142i	−0.534277	+	0.173597i	−0.563715	−	0.825969i	$-0.690628\pi$
$311$	−9.42208	+	3.06142i	−0.534277	+	0.173597i	0.0294377	+	0.999567i	$0.490628\pi$
$312$	−41.0388	+	65.2799i	−2.32336	+	3.69575i
$313$	9.58966	+	6.96730i	0.542040	+	0.393815i	0.824842	−	0.565363i	$-0.191264\pi$
$313$	9.58966	+	6.96730i	0.542040	+	0.393815i	−0.282802	+	0.959178i	$0.591264\pi$
$314$	−26.3044	−	19.1112i	−1.48444	−	1.07851i
$315$	−0.745377	+	0.712005i	−0.0419972	+	0.0401169i
$316$	−21.8632	+	7.10377i	−1.22990	+	0.399618i
$317$	10.4979	+	14.4492i	0.589622	+	0.811545i	0.994709	−	0.102733i	$-0.0327587\pi$
$317$	10.4979	+	14.4492i	0.589622	+	0.811545i	−0.405087	+	0.914278i	$0.632759\pi$
$318$	−4.54305	−	1.14585i	−0.254761	−	0.0642558i
$319$	−2.95555	−	14.3616i	−0.165479	−	0.804096i
$320$		−	4.38629i		−	0.245201i
$321$	−9.24926	−	23.0732i	−0.516243	−	1.28782i
$322$	−0.395420	−	1.21698i	−0.0220359	−	0.0678196i
$323$	6.20381	+	2.01574i	0.345189	+	0.112159i
$324$	1.93156	−	42.1544i	0.107309	−	2.34191i
$325$	3.76304	−	5.17938i	0.208736	−	0.287300i
$326$	−17.6605	+	54.3533i	−0.978123	+	3.01035i
$327$	0.729871	+	10.8622i	0.0403619	+	0.600683i
$328$	−7.11007	+	5.16577i	−0.392588	+	0.285232i
$329$	−2.89369			−0.159534
$330$	−8.19424	−	12.3928i	−0.451078	−	0.682204i
$331$	−2.70288			−0.148564			−0.0742819	−	0.997237i	$-0.523666\pi$
$331$	−2.70288			−0.148564			−0.0742819	+	0.997237i	$0.523666\pi$
$332$	−50.1887	+	36.4642i	−2.75446	+	2.00123i
$333$	0.168115	−	0.923997i	0.00921263	−	0.0506347i
$334$	−8.25862	+	25.4174i	−0.451892	+	1.39078i
$335$	4.50654	−	6.20273i	0.246219	−	0.338891i
$336$	−3.28175	−	3.93272i	−0.179034	−	0.214547i
$337$	20.4286	+	6.63765i	1.11282	+	0.361576i	0.807022	−	0.590522i	$-0.201078\pi$
$337$	20.4286	+	6.63765i	1.11282	+	0.361576i	0.305794	+	0.952098i	$0.401078\pi$
$338$	−22.3667	−	68.8375i	−1.21659	−	3.74426i
$339$	−6.54640	+	2.62422i	−0.355552	+	0.142528i
$340$		−	4.86726i		−	0.263964i
$341$	1.64869	−	3.63938i	0.0892813	−	0.197083i
$342$	23.1228	−	42.9226i	1.25034	−	2.32099i
$343$	−2.80362	−	3.85886i	−0.151381	−	0.208359i
$344$	70.5125	−	22.9109i	3.80178	−	1.23527i
$345$	−2.11152	−	1.32742i	−0.113680	−	0.0714661i
$346$	13.2590	+	9.63323i	0.712809	+	0.517886i
$347$	8.61224	+	6.25716i	0.462329	+	0.335902i	0.794444	−	0.607337i	$-0.207762\pi$
$347$	8.61224	+	6.25716i	0.462329	+	0.335902i	−0.332115	+	0.943239i	$0.607762\pi$
$348$	−30.3955	−	19.1084i	−1.62937	−	1.02432i
$349$	10.9696	−	3.56423i	0.587188	−	0.190789i	−0.000329875	−	1.00000i	$-0.500105\pi$
$349$	10.9696	−	3.56423i	0.587188	−	0.190789i	0.587518	+	0.809211i	$0.300105\pi$
$350$	0.522326	+	0.718920i	0.0279195	+	0.0384279i
$351$	24.5390	+	22.4604i	1.30980	+	1.19885i
$352$	24.0778	−	13.6941i	1.28335	−	0.729899i
$353$		−	20.3210i		−	1.08158i	−0.841159	−	0.540788i	$-0.818126\pi$
$353$		−	20.3210i		−	1.08158i	0.841159	−	0.540788i	$-0.181874\pi$
$354$	−31.1956	+	12.5052i	−1.65803	+	0.664645i
$355$	2.81230	+	8.65538i	0.149262	+	0.459380i
$356$	21.6103	+	7.02163i	1.14535	+	0.372146i
$357$	−0.395819	−	0.474333i	−0.0209490	−	0.0251044i
$358$	17.6870	−	24.3441i	0.934788	−	1.28663i
$359$	−8.53369	+	26.2640i	−0.450391	+	1.38616i	0.426072	+	0.904689i	$0.359897\pi$
$359$	−8.53369	+	26.2640i	−0.450391	+	1.38616i	−0.876462	+	0.481471i	$0.840103\pi$
$360$	−20.5243	−	3.73425i	−1.08173	−	0.196812i
$361$	16.5737	−	12.0415i	0.872298	−	0.633762i
$362$	31.7800			1.67032
$363$	8.61950	−	16.9913i	0.452406	−	0.891812i
$364$	10.3140			0.540599
$365$	3.40064	−	2.47071i	0.177998	−	0.129323i
$366$	1.03061	+	15.3380i	0.0538708	+	0.801727i
$367$	6.18172	−	19.0254i	0.322683	−	0.993117i	−0.649792	−	0.760112i	$-0.725144\pi$
$367$	6.18172	−	19.0254i	0.322683	−	0.993117i	0.972475	−	0.233005i	$-0.0748560\pi$
$368$	7.28470	−	10.0265i	0.379741	−	0.522669i
$369$	1.64354	+	3.41683i	0.0855595	+	0.177873i
$370$	−0.770015	−	0.250193i	−0.0400312	−	0.0130069i
$371$	0.111055	+	0.341794i	0.00576571	+	0.0177450i
$372$	−3.64015	−	9.08075i	−0.188733	−	0.470815i
$373$		−	15.2941i		−	0.791896i	−0.918273	−	0.395948i	$-0.870416\pi$
$373$		−	15.2941i		−	0.791896i	0.918273	−	0.395948i	$-0.129584\pi$
$374$	7.73999	−	4.40208i	0.400225	−	0.227626i
$375$	1.67946	+	0.423592i	0.0867267	+	0.0218742i
$376$	−34.4222	−	47.3782i	−1.77519	−	2.44334i
$377$	26.9178	−	8.74613i	1.38634	−	0.450449i
$378$	−4.01756	+	2.27602i	−0.206641	+	0.117066i
$379$	−10.8709	−	7.89820i	−0.558402	−	0.405703i	0.272471	−	0.962164i	$-0.412159\pi$
$379$	−10.8709	−	7.89820i	−0.558402	−	0.405703i	−0.830874	+	0.556461i	$0.812159\pi$
$380$	−23.8361	−	17.3180i	−1.22277	−	0.888392i
$381$	1.30554	−	2.07671i	0.0668849	−	0.106393i
$382$	−18.3109	+	5.94957i	−0.936866	+	0.304406i
$383$	13.6188	+	18.7447i	0.695888	+	0.957807i	0.999987	+	0.00516677i	$0.00164464\pi$
$383$	13.6188	+	18.7447i	0.695888	+	0.957807i	−0.304099	+	0.952640i	$0.598355\pi$
$384$	−2.27021	+	9.00090i	−0.115851	+	0.459326i
$385$	−0.470245	+	1.03804i	−0.0239659	+	0.0529034i
$386$		−	8.78087i		−	0.446934i
$387$	−4.27919	−	31.6986i	−0.217524	−	1.61133i
$388$	14.5078	+	44.6504i	0.736522	+	2.26678i
$389$	−33.2537	−	10.8048i	−1.68603	−	0.547824i	−0.699962	−	0.714180i	$-0.746800\pi$
$389$	−33.2537	−	10.8048i	−1.68603	−	0.547824i	−0.986066	+	0.166356i	$0.946800\pi$
$390$	22.0189	−	18.3742i	1.11497	−	0.930412i
$391$	0.878622	−	1.20932i	0.0444338	−	0.0611579i
$392$	14.7881	−	45.5131i	0.746912	−	2.29876i
$393$	−2.84668	+	0.191278i	−0.143596	+	0.00964872i
$394$	3.76229	−	2.73346i	0.189541	−	0.137710i
$395$	4.90288			0.246691
$396$	−15.4324	−	44.0259i	−0.775506	−	2.21238i
$397$	−32.1740			−1.61477			−0.807385	−	0.590026i	$-0.799118\pi$
$397$	−32.1740			−1.61477			−0.807385	+	0.590026i	$0.799118\pi$
$398$	−28.9157	+	21.0085i	−1.44941	+	1.05306i
$399$	−3.73126	+	0.250716i	−0.186797	+	0.0125515i
$400$	−2.65963	+	8.18550i	−0.132981	+	0.409275i
$401$	−5.72923	+	7.88561i	−0.286104	+	0.393788i	−0.927744	−	0.373218i	$-0.878254\pi$
$401$	−5.72923	+	7.88561i	−0.286104	+	0.393788i	0.641640	+	0.767006i	$0.278254\pi$
$402$	26.3694	−	22.0046i	1.31519	−	1.09749i
$403$	7.33483	+	2.38323i	0.365374	+	0.118717i
$404$	22.9859	+	70.7435i	1.14359	+	3.51962i
$405$	−3.17003	+	8.42323i	−0.157520	+	0.418554i
$406$			3.92859i			0.194973i
$407$	−0.209289	−	1.01698i	−0.0103741	−	0.0504096i
$408$	3.05771	−	12.1232i	0.151379	−	0.600188i
$409$	14.2554	+	19.6209i	0.704884	+	0.970190i	0.999892	+	0.0146948i	$0.00467768\pi$
$409$	14.2554	+	19.6209i	0.704884	+	0.970190i	−0.295008	+	0.955495i	$0.595322\pi$
$410$	3.10868	−	1.01007i	0.153527	−	0.0498838i
$411$	−7.33918	+	11.6743i	−0.362015	+	0.575853i
$412$	38.9894	+	28.3275i	1.92087	+	1.39560i
$413$	2.08559	+	1.51527i	0.102625	+	0.0745614i
$414$	−7.71717	−	8.07888i	−0.379278	−	0.397055i
$415$	12.5834	−	4.08861i	0.617697	−	0.200702i
$416$	31.4279	+	43.2568i	1.54088	+	2.12084i
$417$	−8.16616	−	2.05967i	−0.399898	−	0.100862i
$418$	5.98123	−	53.5674i	0.292552	−	2.62007i
$419$		−	8.02852i		−	0.392219i	−0.980582	−	0.196109i	$-0.937169\pi$
$419$		−	8.02852i		−	0.392219i	0.980582	−	0.196109i	$-0.0628307\pi$
$420$	1.03826	+	2.59005i	0.0506619	+	0.126381i
$421$	−2.40846	−	7.41249i	−0.117381	−	0.361263i	0.875055	−	0.484024i	$-0.160825\pi$
$421$	−2.40846	−	7.41249i	−0.117381	−	0.361263i	−0.992436	+	0.122761i	$0.960825\pi$
$422$	−30.2974	−	9.84423i	−1.47486	−	0.479210i
$423$	−22.7681	+	10.9518i	−1.10702	+	0.532495i
$424$	−4.27508	+	5.88415i	−0.207616	+	0.285760i
$425$	−0.320783	+	0.987270i	−0.0155603	+	0.0478896i
$426$	2.73313	+	40.6756i	0.132421	+	1.97074i
$427$	0.953941	−	0.693079i	0.0461644	−	0.0335404i
$428$	−67.2918			−3.25267
$429$	34.4419	+	12.8958i	1.66287	+	0.622617i
$430$	−27.5748			−1.32978
$431$	−3.37302	+	2.45064i	−0.162473	+	0.118043i	−0.666051	−	0.745906i	$-0.732017\pi$
$431$	−3.37302	+	2.45064i	−0.162473	+	0.118043i	0.503578	+	0.863950i	$0.332017\pi$
$432$	−40.7057	−	18.5229i	−1.95845	−	0.891183i
$433$	−5.26721	+	16.2108i	−0.253126	+	0.779042i	0.741067	+	0.671431i	$0.234320\pi$
$433$	−5.26721	+	16.2108i	−0.253126	+	0.779042i	−0.994193	+	0.107611i	$0.965680\pi$
$434$	−0.629224	+	0.866053i	−0.0302037	+	0.0415719i
$435$	4.90603	+	5.87919i	0.235226	+	0.281885i
$436$	28.0284	+	9.10699i	1.34232	+	0.436145i
$437$	−2.79614	−	8.60564i	−0.133758	−	0.411663i
$438$	17.4774	−	7.00609i	0.835104	−	0.334764i
$439$			16.2398i			0.775082i	0.921852	+	0.387541i	$0.126675\pi$
$439$			16.2398i			0.775082i	−0.921852	+	0.387541i	$0.873325\pi$
$440$	−22.5896	+	4.64883i	−1.07692	+	0.221624i
$441$	−18.1762	−	9.79167i	−0.865532	−	0.466270i
$442$	10.1028	+	13.9053i	0.480539	+	0.661405i
$443$	−26.9383	+	8.75278i	−1.27988	+	0.415857i	−0.868537	−	0.495625i	$-0.834939\pi$
$443$	−26.9383	+	8.75278i	−1.27988	+	0.415857i	−0.411340	+	0.911482i	$0.634939\pi$
$444$	−2.15237	−	1.35311i	−0.102147	−	0.0642156i
$445$	−3.92065	−	2.84852i	−0.185856	−	0.135033i
$446$	34.3176	+	24.9332i	1.62498	+	1.18062i
$447$	22.7940	+	14.3296i	1.07812	+	0.677769i
$448$	−1.43336	+	0.465726i	−0.0677197	+	0.0220035i
$449$	−11.9291	−	16.4190i	−0.562971	−	0.774863i	0.428730	−	0.903433i	$-0.358961\pi$
$449$	−11.9291	−	16.4190i	−0.562971	−	0.774863i	−0.991700	+	0.128570i	$0.958961\pi$
$450$	6.83067	+	3.67975i	0.322001	+	0.173465i
$451$	3.09683	+	2.82494i	0.145824	+	0.133021i
$452$			19.0922i			0.898022i
$453$	22.9400	−	9.19584i	1.07782	−	0.432058i
$454$	14.3885	+	44.2833i	0.675286	+	2.07832i
$455$	−2.09207	−	0.679756i	−0.0980779	−	0.0318674i
$456$	−48.4906	−	58.1092i	−2.27078	−	2.72121i
$457$	3.02454	−	4.16292i	0.141482	−	0.194733i	−0.732395	−	0.680879i	$-0.761598\pi$
$457$	3.02454	−	4.16292i	0.141482	−	0.194733i	0.873878	+	0.486146i	$0.161598\pi$
$458$	15.4628	−	47.5896i	0.722529	−	2.22372i
$459$	−4.90960	−	2.23409i	−0.229160	−	0.104278i
$460$	−5.46219	+	3.96852i	−0.254676	+	0.185033i
$461$	−18.6807			−0.870045			−0.435023	−	0.900420i	$-0.643260\pi$
$461$	−18.6807			−0.870045			−0.435023	+	0.900420i	$0.643260\pi$
$462$	−3.17970	+	3.99357i	−0.147933	+	0.185798i
$463$	−0.0692314			−0.00321746			−0.00160873	−	0.999999i	$-0.500512\pi$
$463$	−0.0692314			−0.00321746			−0.00160873	+	0.999999i	$0.500512\pi$
$464$	−30.7830	+	22.3651i	−1.42906	+	1.03827i
$465$	0.139886	+	2.08184i	0.00648704	+	0.0965428i
$466$	5.47080	−	16.8374i	0.253430	−	0.779977i
$467$	11.0390	−	15.1939i	0.510826	−	0.703091i	−0.473233	−	0.880938i	$-0.656913\pi$
$467$	11.0390	−	15.1939i	0.510826	−	0.703091i	0.984058	+	0.177846i	$0.0569130\pi$
$468$	81.1524	−	39.0355i	3.75127	−	1.80442i
$469$	−2.50543	−	0.814063i	−0.115690	−	0.0375899i
$470$	6.73063	+	20.7147i	0.310461	+	0.955499i
$471$	8.10211	+	20.2116i	0.373326	+	0.931300i
$472$			52.1722i			2.40142i
$473$	−17.4823	−	30.7383i	−0.803835	−	1.41335i
$474$	21.2957	+	5.37119i	0.978143	+	0.246707i
$475$	3.69353	+	5.08370i	0.169471	+	0.233256i
$476$	−1.59053	+	0.516795i	−0.0729018	+	0.0236872i
$477$	2.16740	+	2.26899i	0.0992384	+	0.103890i
$478$	0.311197	+	0.226098i	0.0142338	+	0.0103415i
$479$	−3.92837	−	2.85413i	−0.179492	−	0.130408i	0.494412	−	0.869228i	$-0.335384\pi$
$479$	−3.92837	−	2.85413i	−0.179492	−	0.130408i	−0.673903	+	0.738820i	$0.735384\pi$
$480$	−7.69897	+	12.2467i	−0.351408	+	0.558981i
$481$	1.90611	−	0.619332i	0.0869110	−	0.0282391i
$482$	−1.06931	−	1.47178i	−0.0487059	−	0.0670379i
$483$	−0.209581	+	0.830947i	−0.00953628	+	0.0378094i
$484$	−34.0117	−	38.7724i	−1.54598	−	1.76238i
$485$		−	10.0130i		−	0.454666i
$486$	−22.9969	+	33.1135i	−1.04316	+	1.50206i
$487$	0.907924	+	2.79430i	0.0411420	+	0.126622i	0.969518	−	0.245021i	$-0.0787947\pi$
$487$	0.907924	+	2.79430i	0.0411420	+	0.126622i	−0.928376	+	0.371643i	$0.878795\pi$
$488$	22.6954	+	7.37420i	1.02737	+	0.333814i
$489$	29.3867	−	24.5225i	1.32891	−	1.10894i
$490$	−10.4617	+	14.3993i	−0.472611	+	0.650493i
$491$	7.02352	−	21.6162i	0.316967	−	0.975525i	−0.657970	−	0.753044i	$-0.728585\pi$
$491$	7.02352	−	21.6162i	0.316967	−	0.975525i	0.974937	−	0.222480i	$-0.0714154\pi$
$492$	10.2408	−	0.688116i	0.461692	−	0.0310227i
$493$	−3.71280	+	2.69750i	−0.167216	+	0.121489i
$494$	104.043			4.68113
$495$	0.228703	+	9.94725i	0.0102794	+	0.447095i
$496$	−10.3682			−0.465545
$497$	2.52981	−	1.83802i	0.113478	−	0.0824463i
$498$	59.1354	−	3.97350i	2.64992	−	0.178057i
$499$	−9.84087	+	30.2871i	−0.440538	+	1.35584i	0.446766	+	0.894651i	$0.352576\pi$
$499$	−9.84087	+	30.2871i	−0.440538	+	1.35584i	−0.887304	+	0.461185i	$0.847424\pi$
$500$	2.75597	−	3.79326i	0.123251	−	0.169640i
$501$	13.7422	−	11.4675i	0.613957	−	0.512331i
$502$	−8.12049	−	2.63851i	−0.362435	−	0.117762i
$503$	10.7659	+	33.1341i	0.480028	+	1.47738i	0.839054	+	0.544048i	$0.183109\pi$
$503$	10.7659	+	33.1341i	0.480028	+	1.47738i	−0.359026	+	0.933328i	$0.616891\pi$
$504$	0.958940	+	7.10346i	0.0427146	+	0.316413i
$505$		−	15.8644i		−	0.705958i
$506$	−11.2509	−	5.09683i	−0.500165	−	0.226582i
$507$	−11.8548	+	47.0019i	−0.526490	+	2.08743i
$508$	−3.90310	−	5.37215i	−0.173172	−	0.238351i
$509$	22.1952	−	7.21166i	0.983785	−	0.319651i	0.227417	−	0.973797i	$-0.426972\pi$
$509$	22.1952	−	7.21166i	0.983785	−	0.319651i	0.756368	+	0.654146i	$0.226972\pi$
$510$	−2.47490	+	3.93679i	−0.109590	+	0.174324i
$511$	−1.16846	−	0.848932i	−0.0516894	−	0.0375546i
$512$	38.6848	+	28.1061i	1.70964	+	1.24213i
$513$	−28.4094	+	16.0945i	−1.25431	+	0.710588i
$514$	−59.1957	+	19.2338i	−2.61101	+	0.848368i
$515$	−6.04161	−	8.31556i	−0.266225	−	0.366428i
$516$	−83.9585	−	21.1760i	−3.69607	−	0.932221i
$517$	−18.8240	+	20.6358i	−0.827880	+	0.907561i
$518$			0.278191i			0.0122230i
$519$	−4.08396	−	10.1879i	−0.179266	−	0.447198i
$520$	−13.7569	−	42.3395i	−0.603281	−	1.85671i
$521$	22.2491	+	7.22917i	0.974750	+	0.316716i	0.752732	−	0.658327i	$-0.228736\pi$
$521$	22.2491	+	7.22917i	0.974750	+	0.316716i	0.222018	+	0.975043i	$0.428736\pi$
$522$	14.8686	+	30.9109i	0.650781	+	1.35293i
$523$	−19.2610	+	26.5105i	−0.842223	+	1.15922i	0.143300	+	0.989679i	$0.454229\pi$
$523$	−19.2610	+	26.5105i	−0.842223	+	1.15922i	−0.985523	+	0.169542i	$0.945771\pi$
$524$	−2.38668	+	7.34545i	−0.104263	+	0.320888i
$525$	−0.0398988	−	0.593790i	−0.00174133	−	0.0259151i
$526$	13.9545	−	10.1386i	0.608446	−	0.442062i
$527$	−1.25053			−0.0544739
$528$	−49.3939	−	2.17993i	−2.14959	−	0.0948694i
$529$	20.9265			0.909847
$530$	2.18845	−	1.59000i	0.0950601	−	0.0690652i
$531$	22.1447	+	4.02906i	0.960997	+	0.174846i
$532$	−3.12832	+	9.62798i	−0.135630	+	0.417426i
$533$	−4.75593	+	6.54598i	−0.206002	+	0.283538i
$534$	−13.9087	−	16.6677i	−0.601890	−	0.721281i
$535$	13.6494	+	4.43495i	0.590114	+	0.191740i
$536$	−16.4750	−	50.7050i	−0.711614	−	2.19012i
$537$	−18.7054	+	7.49832i	−0.807196	+	0.323577i
$538$			48.4396i			2.08838i
$539$	−22.6838	−	2.53284i	−0.977062	−	0.109097i
$540$	17.9718	+	16.4495i	0.773385	+	0.707874i
$541$	7.84300	+	10.7950i	0.337197	+	0.464112i	0.943620	−	0.331030i	$-0.107396\pi$
$541$	7.84300	+	10.7950i	0.337197	+	0.464112i	−0.606423	+	0.795142i	$0.707396\pi$
$542$	−54.0702	+	17.5685i	−2.32251	+	0.754630i
$543$	−18.0187	−	11.3276i	−0.773255	−	0.486114i
$544$	−7.01398	−	5.09595i	−0.300722	−	0.218487i
$545$	−5.08504	−	3.69450i	−0.217819	−	0.158255i
$546$	−8.34225	−	5.24443i	−0.357015	−	0.224441i
$547$	38.4223	−	12.4842i	1.64282	−	0.533784i	0.665653	−	0.746261i	$-0.268153\pi$
$547$	38.4223	−	12.4842i	1.64282	−	0.533784i	0.977166	+	0.212477i	$0.0681530\pi$
$548$	21.9415	+	30.1999i	0.937294	+	1.29007i
$549$	4.88269	−	9.06368i	0.208388	−	0.386828i
$550$	8.52467	+	0.951849i	0.363493	+	0.0405870i
$551$			27.7803i			1.18348i
$552$	−16.0981	+	6.45318i	−0.685182	+	0.274665i
$553$	−0.520576	−	1.60217i	−0.0221372	−	0.0681312i
$554$	−59.1372	−	19.2148i	−2.51250	−	0.816360i
$555$	0.347406	+	0.416317i	0.0147466	+	0.0176717i
$556$	−13.4006	+	18.4443i	−0.568311	+	0.782213i
$557$	3.94803	−	12.1508i	0.167283	−	0.514845i	−0.831914	−	0.554905i	$-0.812755\pi$
$557$	3.94803	−	12.1508i	0.167283	−	0.514845i	0.999197	+	0.0400595i	$0.0127548\pi$
$558$	−1.67309	+	9.19571i	−0.0708277	+	0.389286i
$559$	55.2228	−	40.1217i	2.33567	−	1.69697i
$560$	2.95726			0.124967
$561$	−5.95750	−	0.262926i	−0.251526	−	0.0111008i
$562$	−15.4827			−0.653097
$563$	−4.97644	+	3.61559i	−0.209732	+	0.152379i	−0.687692	−	0.726002i	$-0.741376\pi$
$563$	−4.97644	+	3.61559i	−0.209732	+	0.152379i	0.477961	+	0.878381i	$0.341376\pi$
$564$	4.58528	+	68.2400i	0.193075	+	2.87342i
$565$	1.25830	−	3.87264i	0.0529370	−	0.162923i
$566$	3.98178	−	5.48046i	0.167367	−	0.230361i
$567$	3.08914	+	0.141548i	0.129732	+	0.00594446i
$568$	60.1874	+	19.5561i	2.52541	+	0.820555i
$569$	4.29218	+	13.2100i	0.179937	+	0.553791i	0.999824	−	0.0187347i	$-0.00596379\pi$
$569$	4.29218	+	13.2100i	0.179937	+	0.553791i	−0.819887	+	0.572525i	$0.805964\pi$
$570$	10.4736	+	26.1274i	0.438689	+	1.09436i
$571$			2.43098i			0.101733i	0.998705	+	0.0508667i	$0.0161984\pi$
$571$			2.43098i			0.101733i	−0.998705	+	0.0508667i	$0.983802\pi$
$572$	67.0944	−	73.5521i	2.80536	−	3.07537i
$573$	12.5026	+	3.15340i	0.522303	+	0.131735i
$574$	−0.660144	−	0.908610i	−0.0275539	−	0.0379246i
$575$	1.36949	−	0.444976i	0.0571119	−	0.0185568i
$576$	−9.51529	+	9.08927i	−0.396470	+	0.378720i
$577$	23.7436	+	17.2507i	0.988458	+	0.718157i	0.959583	−	0.281426i	$-0.0908074\pi$
$577$	23.7436	+	17.2507i	0.988458	+	0.718157i	0.0288753	+	0.999583i	$0.490807\pi$
$578$	33.3149	+	24.2047i	1.38572	+	1.00678i
$579$	−3.12983	+	4.97859i	−0.130071	+	0.206903i
$580$	19.7140	−	6.40548i	0.818581	−	0.265973i
$581$	−2.67216	−	3.67791i	−0.110860	−	0.152585i
$582$	10.9694	−	43.4915i	0.454697	−	1.80278i
$583$	3.15987	+	1.43146i	0.130869	+	0.0592852i
$584$		−	29.2296i		−	1.20953i
$585$	−19.0335	+	2.56946i	−0.786940	+	0.106234i
$586$	−4.40720	−	13.5640i	−0.182060	−	0.560322i
$587$	−35.2864	−	11.4652i	−1.45642	−	0.473221i	−0.529449	−	0.848342i	$-0.677601\pi$
$587$	−35.2864	−	11.4652i	−1.45642	−	0.473221i	−0.926976	+	0.375121i	$0.877601\pi$
$588$	−42.9111	+	35.8082i	−1.76962	+	1.47670i
$589$	−4.44944	+	6.12413i	−0.183336	+	0.252340i
$590$	5.99617	−	18.4543i	0.246858	−	0.759752i
$591$	−3.10746	+	0.208801i	−0.127824	+	0.00858891i
$592$	−2.17980	+	1.58372i	−0.0895894	+	0.0650905i
$593$	−26.8923			−1.10433			−0.552167	−	0.833733i	$-0.686199\pi$
$593$	−26.8923			−1.10433			−0.552167	+	0.833733i	$0.686199\pi$
$594$	−9.90401	+	43.4565i	−0.406367	+	1.78304i
$595$	0.356681			0.0146225
$596$	58.9648	−	42.8404i	2.41529	−	1.75481i
$597$	23.8829	−	1.60477i	0.977461	−	0.0656789i
$598$	7.36763	−	22.6752i	0.301285	−	0.927260i
$599$	−17.0491	+	23.4661i	−0.696607	+	0.958798i	0.303375	+	0.952871i	$0.401886\pi$
$599$	−17.0491	+	23.4661i	−0.696607	+	0.958798i	−0.999982	+	0.00592654i	$0.998114\pi$
$600$	9.24746	−	7.71677i	0.377526	−	0.315036i
$601$	−36.4391	−	11.8398i	−1.48638	−	0.482954i	−0.550368	−	0.834922i	$-0.685513\pi$
$601$	−36.4391	−	11.8398i	−1.48638	−	0.482954i	−0.936012	+	0.351968i	$0.885513\pi$
$602$	2.92783	+	9.01093i	0.119329	+	0.367258i
$603$	−22.7942	+	3.07713i	−0.928252	+	0.125311i
$604$		−	66.9032i		−	2.72225i
$605$	4.34354	+	10.1061i	0.176590	+	0.410872i
$606$	17.3798	−	68.9073i	0.706005	−	2.79917i
$607$	−2.90963	−	4.00476i	−0.118098	−	0.162548i	0.745875	−	0.666086i	$-0.232032\pi$
$607$	−2.90963	−	4.00476i	−0.118098	−	0.162548i	−0.863973	+	0.503538i	$0.832032\pi$
$608$	−49.9121	+	16.2174i	−2.02420	+	0.657704i
$609$	1.40030	−	2.22744i	0.0567429	−	0.0902603i
$610$	−7.18030	−	5.21679i	−0.290722	−	0.211222i
$611$	−43.6193	−	31.6913i	−1.76465	−	1.28209i
$612$	−10.5587	+	10.0860i	−0.426810	+	0.407700i
$613$	−12.9618	+	4.21156i	−0.523524	+	0.170103i	−0.558844	−	0.829273i	$-0.688755\pi$
$613$	−12.9618	+	4.21156i	−0.523524	+	0.170103i	0.0353200	+	0.999376i	$0.488755\pi$
$614$	2.75639	+	3.79385i	0.111239	+	0.153107i
$615$	−2.12259	−	0.535358i	−0.0855910	−	0.0215877i
$616$	3.91766	+	6.88825i	0.157847	+	0.277536i
$617$		−	36.9450i		−	1.48735i	−0.668541	−	0.743675i	$-0.733081\pi$
$617$		−	36.9450i		−	1.48735i	0.668541	−	0.743675i	$-0.266919\pi$
$618$	−17.1319	−	42.7374i	−0.689147	−	1.71915i
$619$	−13.5450	−	41.6872i	−0.544420	−	1.67555i	−0.722365	−	0.691511i	$-0.756945\pi$
$619$	−13.5450	−	41.6872i	−0.544420	−	1.67555i	0.177946	−	0.984040i	$-0.443055\pi$
$620$	5.37187	+	1.74543i	0.215740	+	0.0700981i
$621$	1.49587	+	7.33126i	0.0600274	+	0.294193i
$622$	15.0602	−	20.7286i	0.603860	−	0.831141i
$623$	−0.514557	+	1.58364i	−0.0206153	+	0.0634473i
$624$	−6.39834	−	95.2228i	−0.256139	−	3.81196i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−30.6561			−1.22527
$627$	−22.4847	+	28.2398i	−0.897951	+	1.12779i
$628$	58.9459			2.35220
$629$	−0.262911	+	0.191016i	−0.0104829	+	0.00761630i
$630$	0.477207	−	2.62284i	0.0190124	−	0.104497i
$631$	−14.7108	+	45.2751i	−0.585626	+	1.80237i	0.0111134	+	0.999938i	$0.496462\pi$
$631$	−14.7108	+	45.2751i	−0.585626	+	1.80237i	−0.596740	+	0.802435i	$0.703538\pi$
$632$	20.0396	−	27.5822i	0.797133	−	1.09716i
$633$	13.6692	+	16.3806i	0.543303	+	0.651072i
$634$	−43.9302	−	14.2738i	−1.74469	−	0.566884i
$635$	0.437641	+	1.34692i	0.0173672	+	0.0534509i
$636$	7.88432	−	3.16055i	0.312634	−	0.125324i
$637$		−	44.0586i		−	1.74567i
$638$	28.0160	+	25.5563i	1.10916	+	1.01178i
$639$	12.9487	−	24.0365i	0.512242	−	0.950870i
$640$	−3.15019	−	4.33586i	−0.124522	−	0.171390i
$641$	16.6525	−	5.41073i	0.657735	−	0.213711i	0.0389133	−	0.999243i	$-0.487610\pi$
$641$	16.6525	−	5.41073i	0.657735	−	0.213711i	0.618822	+	0.785532i	$0.287610\pi$
$642$	54.4276	+	34.2164i	2.14809	+	1.35041i
$643$	1.16824	+	0.848773i	0.0460708	+	0.0334724i	0.610582	−	0.791953i	$-0.290935\pi$
$643$	1.16824	+	0.848773i	0.0460708	+	0.0334724i	−0.564512	+	0.825425i	$0.690935\pi$
$644$	1.87680	+	1.36357i	0.0739563	+	0.0537324i
$645$	15.6344	+	9.82870i	0.615604	+	0.387005i
$646$	−16.0447	+	5.21322i	−0.631268	+	0.205112i
$647$	3.75419	+	5.16720i	0.147592	+	0.203144i	0.876412	−	0.481562i	$-0.159931\pi$
$647$	3.75419	+	5.16720i	0.147592	+	0.203144i	−0.728819	+	0.684706i	$0.759931\pi$
$648$	34.4297	+	52.2621i	1.35253	+	2.05305i
$649$	24.3730	−	5.01585i	0.956724	−	0.196889i
$650$			16.5574i			0.649434i
$651$	0.665452	−	0.266756i	0.0260811	−	0.0104550i
$652$	−32.0174	−	98.5393i	−1.25390	−	3.85910i
$653$	34.3191	+	11.1510i	1.34301	+	0.436371i	0.890336	−	0.455304i	$-0.150470\pi$
$653$	34.3191	+	11.1510i	1.34301	+	0.436371i	0.452676	+	0.891675i	$0.350470\pi$
$654$	−18.0395	−	21.6178i	−0.705401	−	0.845324i
$655$	0.968223	−	1.33265i	0.0378316	−	0.0520708i
$656$	3.36138	−	10.3453i	0.131240	−	0.403915i
$657$	−12.4066	−	2.25729i	−0.484028	−	0.0880654i
$658$	6.05454	−	4.39888i	0.236031	−	0.171486i
$659$	8.47258			0.330045			0.165022	−	0.986290i	$-0.447230\pi$
$659$	8.47258			0.330045			0.165022	+	0.986290i	$0.447230\pi$
$660$	25.2245	+	9.44464i	0.981864	+	0.367632i
$661$	−32.3320			−1.25757			−0.628784	−	0.777580i	$-0.716447\pi$
$661$	−32.3320			−1.25757			−0.628784	+	0.777580i	$0.716447\pi$
$662$	5.65531	−	4.10882i	0.219800	−	0.159694i
$663$	−0.771717	−	11.4850i	−0.0299710	−	0.446041i
$664$	28.4312	−	87.5021i	1.10334	−	3.39574i
$665$	1.26909	−	1.74675i	0.0492132	−	0.0677361i
$666$	1.05288	+	2.18887i	0.0407981	+	0.0848168i
$667$	6.05445	+	1.96721i	0.234429	+	0.0761706i
$668$	−14.9724	−	46.0803i	−0.579299	−	1.78290i
$669$	−10.5703	−	26.3687i	−0.408671	−	1.01947i
$670$			19.8288i			0.766054i
$671$	1.26302	−	11.3115i	0.0487582	−	0.436674i
$672$	4.81944	+	1.21556i	0.185914	+	0.0468911i
$673$	20.5832	+	28.3304i	0.793425	+	1.09206i	0.993673	+	0.112310i	$0.0358250\pi$
$673$	20.5832	+	28.3304i	0.793425	+	1.09206i	−0.200249	+	0.979745i	$0.564175\pi$
$674$	−52.8336	+	17.1667i	−2.03507	+	0.661236i
$675$	−2.56126	−	4.52106i	−0.0985830	−	0.174015i
$676$	106.160	+	77.1295i	4.08307	+	2.96652i
$677$	−31.7013	−	23.0323i	−1.21838	−	0.885205i	−0.222415	−	0.974952i	$-0.571394\pi$
$677$	−31.7013	−	23.0323i	−1.21838	−	0.885205i	−0.995965	+	0.0897472i	$0.971394\pi$
$678$	9.70797	−	15.4423i	0.372832	−	0.593060i
$679$	−3.27206	+	1.06316i	−0.125570	+	0.0408002i
$680$	4.24295	+	5.83991i	0.162710	+	0.223950i
$681$	7.62622	−	30.2364i	0.292237	−	1.15866i
$682$	2.08286	+	10.1210i	0.0797569	+	0.387555i
$683$		−	10.2237i		−	0.391199i	−0.980684	−	0.195599i	$-0.937335\pi$
$683$		−	10.2237i		−	0.391199i	0.980684	−	0.195599i	$-0.0626652\pi$
$684$	11.8249	+	87.5946i	0.452138	+	3.34926i
$685$	−2.46022	−	7.57178i	−0.0940002	−	0.289303i
$686$	11.7322	+	3.81202i	0.447937	+	0.145544i
$687$	−25.7299	+	21.4709i	−0.981655	+	0.819166i
$688$	−53.9384	+	74.2398i	−2.05638	+	2.83037i
$689$	−2.06923	+	6.36844i	−0.0788314	+	0.242618i
$690$	6.43589	−	0.432449i	0.245010	−	0.0164631i
$691$	11.1476	−	8.09924i	0.424076	−	0.308110i	−0.355199	−	0.934791i	$-0.615587\pi$
$691$	11.1476	−	8.09924i	0.424076	−	0.308110i	0.779276	+	0.626681i	$0.215587\pi$
$692$	−29.7123			−1.12949
$693$	3.22629	−	1.13091i	0.122557	−	0.0429598i
$694$	−27.5315			−1.04508
$695$	3.93375	−	2.85804i	0.149216	−	0.108412i
$696$	53.1271	−	3.56979i	2.01378	−	0.135312i
$697$	0.405424	−	1.24777i	0.0153565	−	0.0472625i
$698$	−17.5337	+	24.1331i	−0.663662	+	0.913452i
$699$	−9.10332	+	7.59648i	−0.344319	+	0.287325i
$700$	−1.53219	−	0.497839i	−0.0579113	−	0.0188165i
$701$	7.07221	+	21.7660i	0.267114	+	0.822091i	0.991199	+	0.132381i	$0.0422622\pi$
$701$	7.07221	+	21.7660i	0.267114	+	0.822091i	−0.724085	+	0.689710i	$0.757738\pi$
$702$	−85.4871	−	9.69113i	−3.22650	−	0.365768i
$703$			1.96718i			0.0741935i
$704$	−6.00303	+	13.2513i	−0.226248	+	0.499429i
$705$	3.56737	−	14.1439i	0.134355	−	0.532691i
$706$	30.8912	+	42.5181i	1.16261	+	1.60019i
$707$	−5.18420	+	1.68445i	−0.194972	+	0.0633502i
$708$	32.4288	−	51.5841i	1.21875	−	1.93865i
$709$	−15.1938	−	11.0389i	−0.570614	−	0.414575i	0.264714	−	0.964327i	$-0.414722\pi$
$709$	−15.1938	−	11.0389i	−0.570614	−	0.414575i	−0.835328	+	0.549752i	$0.814722\pi$
$710$	−19.0419	−	13.8347i	−0.714628	−	0.519208i
$711$	−10.1598	−	10.6359i	−0.381021	−	0.398879i
$712$	−32.0498	+	10.4136i	−1.20112	+	0.390267i
$713$	1.01962	+	1.40338i	0.0381849	+	0.0525571i
$714$	1.54925	+	0.390751i	0.0579791	+	0.0146235i
$715$	−18.4569	+	10.4973i	−0.690249	+	0.392576i
$716$			54.5531i			2.03875i
$717$	−0.0958529	−	0.239115i	−0.00357969	−	0.00892992i
$718$	−22.0703	−	67.9254i	−0.823657	−	2.53495i
$719$	29.6530	+	9.63483i	1.10587	+	0.359319i	0.804359	−	0.594144i	$-0.202509\pi$
$719$	29.6530	+	9.63483i	1.10587	+	0.359319i	0.301510	+	0.953463i	$0.402509\pi$
$720$	23.2683	−	11.1924i	0.867159	−	0.417116i
$721$	−2.07589	+	2.85721i	−0.0773100	+	0.106408i
$722$	−16.3725	+	50.3894i	−0.609322	+	1.87530i
$723$	0.0816814	+	1.21562i	0.00303777	+	0.0452093i
$724$	−46.6117	+	33.8654i	−1.73231	+	1.25860i
$725$	−4.42093			−0.164189
$726$	7.79476	+	48.6544i	0.289291	+	1.80573i
$727$	−20.4713			−0.759238			−0.379619	−	0.925143i	$-0.623945\pi$
$727$	−20.4713			−0.759238			−0.379619	+	0.925143i	$0.623945\pi$
$728$	−12.3751	+	8.99101i	−0.458650	+	0.333229i
$729$	24.8417	−	10.5778i	0.920063	−	0.391771i
$730$	−3.35937	+	10.3391i	−0.124336	+	0.382666i
$731$	−6.50562	+	8.95422i	−0.240619	+	0.331184i
$732$	−17.8560	−	21.3979i	−0.659977	−	0.790890i
$733$	−30.2050	−	9.81419i	−1.11565	−	0.362495i	−0.307541	−	0.951535i	$-0.599506\pi$
$733$	−30.2050	−	9.81419i	−1.11565	−	0.362495i	−0.808104	+	0.589039i	$0.799506\pi$
$734$	15.9875	+	49.2046i	0.590111	+	1.81617i
$735$	11.0640	−	4.43518i	0.408102	−	0.163594i
$736$			12.0263i			0.443294i
$737$	−22.1037	+	12.5713i	−0.814199	+	0.463072i
$738$	−8.63297	−	4.65066i	−0.317784	−	0.171193i
$739$	−21.9294	−	30.1833i	−0.806687	−	1.11031i	−0.991826	−	0.127598i	$-0.959273\pi$
$739$	−21.9294	−	30.1833i	−0.806687	−	1.11031i	0.185139	−	0.982712i	$-0.440727\pi$
$740$	1.39599	−	0.453585i	0.0513177	−	0.0166741i
$741$	−58.9906	−	37.0850i	−2.16707	−	1.36235i
$742$	−0.751947	−	0.546321i	−0.0276048	−	0.0200561i
$743$	−2.24511	−	1.63117i	−0.0823653	−	0.0598419i	0.545841	−	0.837889i	$-0.316210\pi$
$743$	−2.24511	−	1.63117i	−0.0823653	−	0.0598419i	−0.628206	+	0.778047i	$0.716210\pi$
$744$	12.2836	+	7.72216i	0.450337	+	0.283108i
$745$	−14.7838	+	4.80355i	−0.541637	+	0.175988i
$746$	23.2495	+	32.0002i	0.851224	+	1.17161i
$747$	−34.9449	−	18.8252i	−1.27857	−	0.688777i
$748$	−6.66130	+	14.7044i	−0.243561	+	0.537647i
$749$		−	4.93125i		−	0.180184i
$750$	−4.15790	+	1.66676i	−0.151825	+	0.0608613i
$751$	5.67999	+	17.4812i	0.207266	+	0.637898i	0.999613	+	0.0278276i	$0.00885895\pi$
$751$	5.67999	+	17.4812i	0.207266	+	0.637898i	−0.792347	+	0.610071i	$0.791141\pi$
$752$	68.9360	+	22.3987i	2.51384	+	0.816795i
$753$	3.66370	+	4.39043i	0.133513	+	0.159996i
$754$	−43.0253	+	59.2193i	−1.56689	+	2.15664i
$755$	−4.40934	+	13.5706i	−0.160472	+	0.493883i
$756$	3.46718	−	7.61943i	0.126100	−	0.277116i
$757$	−22.8001	+	16.5653i	−0.828684	+	0.602074i	−0.919187	−	0.393822i	$-0.871153\pi$
$757$	−22.8001	+	16.5653i	−0.828684	+	0.602074i	0.0905024	+	0.995896i	$0.471153\pi$
$758$	34.7521			1.26225
$759$	4.56237	+	6.90007i	0.165604	+	0.250456i
$760$	43.6960			1.58502
$761$	42.2988	−	30.7319i	1.53333	−	1.11403i	0.578979	−	0.815343i	$-0.303451\pi$
$761$	42.2988	−	30.7319i	1.53333	−	1.11403i	0.954351	−	0.298687i	$-0.0965485\pi$
$762$	0.425320	+	6.32980i	0.0154077	+	0.229304i
$763$	−0.667375	+	2.05397i	−0.0241606	+	0.0743587i
$764$	20.5166	−	28.2387i	0.742264	−	1.02164i
$765$	2.80644	−	1.34994i	0.101467	−	0.0488071i
$766$	−56.9899	−	18.5171i	−2.05913	−	0.669052i
$767$	14.8430	+	45.6821i	0.535950	+	1.64948i
$768$	−14.5865	−	36.3875i	−0.526344	−	1.31302i
$769$			15.8942i			0.573161i	0.958056	+	0.286580i	$0.0925185\pi$
$769$			15.8942i			0.573161i	−0.958056	+	0.286580i	$0.907481\pi$
$770$	−0.594083	−	2.88677i	−0.0214093	−	0.104032i
$771$	40.4185	+	10.1943i	1.45564	+	0.367140i
$772$	9.35706	+	12.8789i	0.336768	+	0.463522i
$773$	−21.9001	+	7.11579i	−0.787693	+	0.255937i	−0.675122	−	0.737707i	$-0.735909\pi$
$773$	−21.9001	+	7.11579i	−0.787693	+	0.255937i	−0.112572	+	0.993644i	$0.535909\pi$
$774$	57.1406	+	59.8188i	2.05388	+	2.15014i
$775$	−0.974590	−	0.708081i	−0.0350083	−	0.0254350i
$776$	−56.3301	−	40.9262i	−2.02213	−	1.46917i
$777$	0.0991579	−	0.157729i	0.00355727	−	0.00565851i
$778$	86.0026	−	27.9439i	3.08334	−	1.00184i
$779$	−4.66808	−	6.42506i	−0.167251	−	0.230202i
$780$	−12.7152	+	50.4131i	−0.455277	+	1.80508i
$781$	3.34947	−	29.9975i	0.119853	−	1.07340i
$782$			3.86594i			0.138246i
$783$	2.58760	−	22.8256i	0.0924732	−	0.815722i
$784$	18.3034	+	56.3321i	0.653693	+	2.01186i
$785$	−11.9565	−	3.88491i	−0.426746	−	0.138658i
$786$	5.66542	−	4.72765i	0.202079	−	0.168630i
$787$	10.4882	−	14.4357i	0.373863	−	0.514578i	−0.580083	−	0.814558i	$-0.696980\pi$
$787$	10.4882	−	14.4357i	0.373863	−	0.514578i	0.953946	+	0.299979i	$0.0969798\pi$
$788$	−2.60532	+	8.01834i	−0.0928106	+	0.285642i
$789$	−11.5257	+	0.774452i	−0.410326	+	0.0275712i
$790$	−10.2584	+	7.45318i	−0.364978	+	0.265172i
$791$	−1.39911			−0.0497466
$792$	56.8950	+	39.3709i	2.02168	+	1.39898i
$793$	21.9701			0.780182
$794$	67.3186	−	48.9098i	2.38905	−	1.73575i
$795$	−1.80755	+	0.121455i	−0.0641070	+	0.00430757i
$796$	20.0236	−	61.6263i	0.709717	−	2.18429i
$797$	−5.80882	+	7.99515i	−0.205759	+	0.283203i	−0.899408	−	0.437110i	$-0.856002\pi$
$797$	−5.80882	+	7.99515i	−0.205759	+	0.283203i	0.693649	+	0.720313i	$0.256002\pi$
$798$	7.42589	−	6.19671i	0.262874	−	0.219361i
$799$	8.31452	+	2.70155i	0.294146	+	0.0955740i
$800$	−2.58083	−	7.94298i	−0.0912461	−	0.280827i
$801$	1.94501	+	14.4079i	0.0687235	+	0.509077i
$802$		−	25.2086i		−	0.890148i
$803$	−13.6550	+	2.81014i	−0.481876	+	0.0991678i
$804$	−15.2275	+	60.3738i	−0.537032	+	2.12922i
$805$	−0.290820	−	0.400279i	−0.0102500	−	0.0141080i
$806$	−18.9698	+	6.16365i	−0.668182	+	0.217105i
$807$	17.2657	−	27.4644i	0.607782	−	0.966791i
$808$	−89.2486	−	64.8429i	−3.13976	−	2.28117i
$809$	33.2460	+	24.1546i	1.16887	+	0.849232i	0.990873	−	0.134799i	$-0.0430390\pi$
$809$	33.2460	+	24.1546i	1.16887	+	0.849232i	0.177995	+	0.984031i	$0.443039\pi$
$810$	−6.17196	−	22.4431i	−0.216860	−	0.788571i
$811$	−7.29069	+	2.36889i	−0.256011	+	0.0831829i	−0.434211	−	0.900811i	$-0.642973\pi$
$811$	−7.29069	+	2.36889i	−0.256011	+	0.0831829i	0.178200	+	0.983994i	$0.442973\pi$
$812$	−4.18638	−	5.76206i	−0.146913	−	0.202209i
$813$	36.9188	+	9.31166i	1.29480	+	0.326574i
$814$	1.98387	+	1.80969i	0.0695346	+	0.0634296i
$815$			22.0977i			0.774050i
$816$	5.75796	+	14.3638i	0.201569	+	0.502835i
$817$	20.7036	+	63.7191i	0.724327	+	2.22925i
$818$	−59.6539	−	19.3827i	−2.08575	−	0.677701i
$819$	2.86059	+	5.94698i	0.0999569	+	0.207804i
$820$	−3.48314	+	4.79413i	−0.121637	+	0.167418i
$821$	−3.90848	+	12.0291i	−0.136407	+	0.419817i	−0.995806	−	0.0914878i	$-0.970838\pi$
$821$	−3.90848	+	12.0291i	−0.136407	+	0.419817i	0.859399	+	0.511305i	$0.170838\pi$
$822$	−2.39096	−	35.5833i	−0.0833944	−	1.24111i
$823$	10.4729	−	7.60904i	0.365064	−	0.265234i	−0.390097	−	0.920774i	$-0.627559\pi$
$823$	10.4729	−	7.60904i	0.365064	−	0.265234i	0.755161	+	0.655539i	$0.227559\pi$
$824$	−71.4749			−2.48995
$825$	−4.49405	−	3.57820i	−0.156463	−	0.124577i
$826$	−6.66718			−0.231981
$827$	−18.7178	+	13.5993i	−0.650881	+	0.472892i	−0.863571	−	0.504227i	$-0.831777\pi$
$827$	−18.7178	+	13.5993i	−0.650881	+	0.472892i	0.212690	+	0.977120i	$0.431777\pi$
$828$	19.9278	+	3.62572i	0.692538	+	0.126002i
$829$	6.12785	−	18.8596i	0.212829	−	0.655020i	−0.786472	−	0.617627i	$-0.788094\pi$
$829$	6.12785	−	18.8596i	0.212829	−	0.655020i	0.999301	−	0.0373940i	$-0.0119056\pi$
$830$	−20.1133	+	27.6836i	−0.698143	+	0.960911i
$831$	26.6808	+	31.9732i	0.925546	+	1.10914i
$832$	−26.7069	−	8.67759i	−0.925894	−	0.300841i
$833$	2.20761	+	6.79433i	0.0764892	+	0.235410i
$834$	20.2173	−	8.10441i	0.700068	−	0.280633i
$835$			10.3336i			0.357610i
$836$	48.3098	+	84.9409i	1.67083	+	2.93774i
$837$	4.22631	−	4.61744i	0.146083	−	0.159602i
$838$	12.2047	+	16.7983i	0.421603	+	0.580287i
$839$	37.0142	−	12.0266i	1.27787	−	0.415206i	0.410042	−	0.912067i	$-0.365514\pi$
$839$	37.0142	−	12.0266i	1.27787	−	0.415206i	0.867830	+	0.496861i	$0.165514\pi$
$840$	−3.50357	−	2.20255i	−0.120885	−	0.0759952i
$841$	7.64954	+	5.55771i	0.263777	+	0.191645i
$842$	16.3075	+	11.8481i	0.561993	+	0.408312i
$843$	8.77838	+	5.51860i	0.302343	+	0.190071i
$844$	54.9274	−	17.8470i	1.89068	−	0.614319i
$845$	−16.4500	−	22.6415i	−0.565897	−	0.778890i
$846$	30.9898	−	57.5260i	1.06545	−	1.97779i
$847$	2.84130	−	2.49243i	0.0976283	−	0.0856410i
$848$		−	9.00213i		−	0.309134i
$849$	−4.21104	+	1.68806i	−0.144522	+	0.0579340i
$850$	−0.829629	−	2.55333i	−0.0284560	−	0.0875787i
$851$	0.428728	+	0.139302i	0.0146966	+	0.00477521i
$852$	−47.3534	−	56.7464i	−1.62230	−	1.94410i
$853$	12.9430	−	17.8145i	0.443158	−	0.609955i	−0.527752	−	0.849399i	$-0.676965\pi$
$853$	12.9430	−	17.8145i	0.443158	−	0.609955i	0.970910	+	0.239443i	$0.0769649\pi$
$854$	−0.942363	+	2.90029i	−0.0322470	+	0.0992460i
$855$	3.37448	−	18.5469i	0.115405	−	0.634292i
$856$	80.7390	−	58.6604i	2.75960	−	2.00497i
$857$	27.7089			0.946519			0.473260	−	0.880923i	$-0.343077\pi$
$857$	27.7089			0.946519			0.473260	+	0.880923i	$0.343077\pi$
$858$	−91.6676	+	25.3751i	−3.12948	+	0.866292i
$859$	−18.3305			−0.625428			−0.312714	−	0.949847i	$-0.601238\pi$
$859$	−18.3305			−0.625428			−0.312714	+	0.949847i	$0.601238\pi$
$860$	40.4440	−	29.3843i	1.37913	−	1.00199i
$861$	0.0504263	+	0.750465i	0.00171852	+	0.0255758i
$862$	3.33208	−	10.2551i	0.113491	−	0.349290i
$863$	9.71810	−	13.3758i	0.330808	−	0.455318i	−0.610921	−	0.791692i	$-0.709201\pi$
$863$	9.71810	−	13.3758i	0.330808	−	0.455318i	0.941729	+	0.336374i	$0.109201\pi$
$864$	42.5208	−	8.67597i	1.44659	−	0.295163i
$865$	6.02681	+	1.95823i	0.204918	+	0.0665818i
$866$	−13.6224	−	41.9254i	−0.462907	−	1.42468i
$867$	−10.2614	−	25.5983i	−0.348497	−	0.869362i
$868$		−	1.94075i		−	0.0658734i
$869$	−14.8120	−	6.71004i	−0.502463	−	0.227622i
$870$	−19.2023	−	4.84321i	−0.651021	−	0.164200i
$871$	−28.8512	−	39.7102i	−0.977585	−	1.34553i
$872$	−41.5683	+	13.5064i	−1.40768	+	0.457383i
$873$	−21.7214	+	20.7489i	−0.735160	+	0.702245i
$874$	18.9324	+	13.7552i	0.640399	+	0.465277i
$875$	0.277977	+	0.201962i	0.00939733	+	0.00682756i
$876$	−18.1683	+	28.9001i	−0.613850	+	0.976444i
$877$	−14.3845	+	4.67381i	−0.485731	+	0.157823i	−0.541637	−	0.840613i	$-0.682195\pi$
$877$	−14.3845	+	4.67381i	−0.485731	+	0.157823i	0.0559062	+	0.998436i	$0.482195\pi$
$878$	−24.6871	−	33.9789i	−0.833150	−	1.14673i
$879$	−2.33591	+	9.26141i	−0.0787883	+	0.312380i
$880$	19.2376	−	21.0891i	0.648498	−	0.710915i
$881$			42.7951i			1.44180i	0.693037	+	0.720902i	$0.256272\pi$
$881$			42.7951i			1.44180i	−0.693037	+	0.720902i	$0.743728\pi$
$882$	52.9154	−	7.14339i	1.78176	−	0.240530i
$883$	0.462002	+	1.42190i	0.0155476	+	0.0478506i	0.958529	−	0.284994i	$-0.0919916\pi$
$883$	0.462002	+	1.42190i	0.0155476	+	0.0478506i	−0.942982	+	0.332845i	$0.891992\pi$
$884$	−29.6354	−	9.62913i	−0.996747	−	0.323863i
$885$	−9.97753	+	8.32599i	−0.335391	+	0.279875i
$886$	43.0580	−	59.2643i	1.44656	−	1.99102i
$887$	1.32702	−	4.08415i	0.0445570	−	0.137132i	−0.926303	−	0.376779i	$-0.877032\pi$
$887$	1.32702	−	4.08415i	0.0445570	−	0.137132i	0.970860	+	0.239647i	$0.0770316\pi$
$888$	3.76204	−	0.252784i	0.126246	−	0.00848287i
$889$	0.393680	−	0.286026i	0.0132036	−	0.00959299i
$890$	12.5335			0.420123
$891$	21.1049	−	21.1088i	0.707041	−	0.707172i
$892$	−76.9028			−2.57490
$893$	42.8136	−	31.1059i	1.43270	−	1.04092i
$894$	−69.4759	+	4.66832i	−2.32362	+	0.156132i
$895$	3.59539	−	11.0655i	0.120181	−	0.369878i
$896$	−1.08240	+	1.48979i	−0.0361604	+	0.0497705i
$897$	−12.2596	+	10.2303i	−0.409337	+	0.341581i
$898$	49.9193	+	16.2198i	1.66583	+	0.541261i
$899$	−1.64574	−	5.06506i	−0.0548884	−	0.168929i
$900$	−13.9397	+	1.88181i	−0.464658	+	0.0627271i
$901$		−	1.08577i		−	0.0361721i
$902$	−10.7739	−	1.20300i	−0.358733	−	0.0400555i
$903$	1.55181	−	6.15262i	0.0516411	−	0.204746i
$904$	−16.6433	−	22.9075i	−0.553547	−	0.761892i
$905$	11.6866	−	3.79721i	0.388476	−	0.126224i
$906$	−34.0188	+	54.1133i	−1.13020	+	1.79779i
$907$	−21.8243	−	15.8563i	−0.724664	−	0.526499i	0.163207	−	0.986592i	$-0.447816\pi$
$907$	−21.8243	−	15.8563i	−0.724664	−	0.526499i	−0.887871	+	0.460092i	$0.847816\pi$
$908$	−68.2927	−	49.6176i	−2.26637	−	1.64662i
$909$	−34.4151	+	32.8743i	−1.14148	+	1.09037i
$910$	5.41064	−	1.75802i	0.179361	−	0.0582779i
$911$	−31.0611	−	42.7519i	−1.02910	−	1.41643i	−0.905622	−	0.424085i	$-0.860596\pi$
$911$	−31.0611	−	42.7519i	−1.02910	−	1.41643i	−0.123477	−	0.992347i	$-0.539404\pi$
$912$	90.8301	+	22.9091i	3.00768	+	0.758597i
$913$	−43.6113	−	4.86955i	−1.44332	−	0.161159i
$914$			13.3080i			0.440189i
$915$	2.21163	+	5.51715i	0.0731143	+	0.182391i
$916$	28.0331	+	86.2771i	0.926241	+	2.85068i
$917$	−0.538287	−	0.174900i	−0.0177758	−	0.00577571i
$918$	13.6687	−	2.78896i	0.451133	−	0.0920494i
$919$	10.5444	−	14.5131i	0.347826	−	0.478742i	−0.598881	−	0.800838i	$-0.704388\pi$
$919$	10.5444	−	14.5131i	0.347826	−	0.478742i	0.946707	+	0.322097i	$0.104388\pi$
$920$	3.09425	−	9.52313i	0.102014	−	0.313968i
$921$	−0.210552	−	3.13352i	−0.00693792	−	0.103253i
$922$	39.0860	−	28.3977i	1.28723	−	0.935228i
$923$	58.2639			1.91778
$924$	0.408047	−	9.24572i	0.0134238	−	0.304162i
$925$	−0.313055			−0.0102932
$926$	0.144855	−	0.105243i	0.00476022	−	0.00345850i
$927$	−5.51974	+	30.3378i	−0.181292	+	0.996423i
$928$	11.4097	−	35.1154i	0.374541	−	1.15272i
$929$	−25.0579	+	34.4893i	−0.822125	+	1.13156i	0.167214	+	0.985921i	$0.446523\pi$
$929$	−25.0579	+	34.4893i	−0.822125	+	1.13156i	−0.989338	+	0.145637i	$0.953477\pi$
$930$	−3.45742	−	4.14323i	−0.113373	−	0.135862i
$931$	41.1282	+	13.3634i	1.34792	+	0.437967i
$932$	9.91823	+	30.5252i	0.324882	+	0.999885i
$933$	−15.9273	+	6.38470i	−0.521437	+	0.209026i
$934$			48.5718i			1.58932i
$935$	2.32028	−	2.54361i	0.0758814	−	0.0831848i
$936$	−63.3410	+	117.579i	−2.07037	+	3.84320i
$937$	10.4456	+	14.3772i	0.341244	+	0.469681i	0.944804	−	0.327636i	$-0.106252\pi$
$937$	10.4456	+	14.3772i	0.341244	+	0.469681i	−0.603561	+	0.797317i	$0.706252\pi$
$938$	6.47969	−	2.10538i	0.211569	−	0.0687430i
$939$	17.3815	+	10.9270i	0.567222	+	0.356589i
$940$	−31.9458	−	23.2100i	−1.04196	−	0.757027i
$941$	19.5304	+	14.1897i	0.636673	+	0.462570i	0.858705	−	0.512469i	$-0.171269\pi$
$941$	19.5304	+	14.1897i	0.636673	+	0.462570i	−0.222033	+	0.975039i	$0.571269\pi$
$942$	−47.6772	−	29.9727i	−1.55341	−	0.976563i
$943$	−1.73084	+	0.562385i	−0.0563640	+	0.0183138i
$944$	−37.9557	−	52.2415i	−1.23535	−	1.70032i
$945$	−1.20545	+	1.31701i	−0.0392132	+	0.0428422i
$946$	83.3059	+	37.7387i	2.70851	+	1.22699i
$947$		−	3.73716i		−	0.121442i	−0.998155	−	0.0607208i	$-0.980660\pi$
$947$		−	3.73716i		−	0.121442i	0.998155	−	0.0607208i	$-0.0193399\pi$
$948$	−36.9580	+	14.8152i	−1.20034	+	0.481174i
$949$	−8.31583	−	25.5935i	−0.269943	−	0.830800i
$950$	−15.4561	−	5.02200i	−0.501463	−	0.162935i
$951$	19.8199	+	23.7513i	0.642704	+	0.770190i
$952$	1.45787	−	2.00658i	0.0472498	−	0.0650337i
$953$	13.4150	−	41.2870i	0.434553	−	1.33742i	−0.458991	−	0.888441i	$-0.651789\pi$
$953$	13.4150	−	41.2870i	0.434553	−	1.33742i	0.893544	−	0.448976i	$-0.148211\pi$
$954$	−7.98414	−	1.45266i	−0.258496	−	0.0470315i
$955$	−6.02267	+	4.37572i	−0.194889	+	0.141595i
$956$	−0.697366			−0.0225544
$957$	−6.77533	−	24.4759i	−0.219015	−	0.791193i
$958$	12.5582			0.405736
$959$	−2.21310	+	1.60791i	−0.0714646	+	0.0519221i
$960$	−0.509338	−	7.58018i	−0.0164388	−	0.244649i
$961$	−9.13108	+	28.1026i	−0.294551	+	0.906535i
$962$	−3.04671	+	4.19344i	−0.0982300	+	0.135202i
$963$	−18.6634	−	38.8001i	−0.601420	−	1.25032i
$964$	3.13672	+	1.01918i	0.101027	+	0.0328257i
$965$	−1.04917	−	3.22903i	−0.0337741	−	0.103946i
$966$	−0.824664	−	2.05721i	−0.0265331	−	0.0661897i
$967$			16.0366i			0.515702i	0.966185	+	0.257851i	$0.0830144\pi$
$967$			16.0366i			0.515702i	−0.966185	+	0.257851i	$0.916986\pi$
$968$	74.6075	+	16.8714i	2.39797	+	0.542268i
$969$	10.9552	+	2.76312i	0.351932	+	0.0887642i
$970$	15.2214	+	20.9504i	0.488729	+	0.672678i
$971$	33.4238	−	10.8600i	1.07262	−	0.348515i	0.281112	−	0.959675i	$-0.409297\pi$
$971$	33.4238	−	10.8600i	1.07262	−	0.348515i	0.791507	+	0.611160i	$0.209297\pi$
$972$	−1.55695	−	73.0735i	−0.0499392	−	2.34383i
$973$	−1.35163	−	0.982017i	−0.0433313	−	0.0314820i
$974$	−6.14748	−	4.46640i	−0.196978	−	0.143113i
$975$	5.90167	−	9.38772i	0.189005	−	0.300648i
$976$	−28.0904	+	9.12713i	−0.899152	+	0.292152i
$977$	10.3438	+	14.2370i	0.330928	+	0.455483i	0.941764	−	0.336273i	$-0.109167\pi$
$977$	10.3438	+	14.2370i	0.330928	+	0.455483i	−0.610836	+	0.791757i	$0.709167\pi$
$978$	−24.2085	+	95.9816i	−0.774101	+	3.06915i
$979$	7.94615	+	13.9714i	0.253960	+	0.446527i
$980$		−	32.2676i		−	1.03075i
$981$	2.52266	+	18.6869i	0.0805422	+	0.596626i
$982$	18.1646	+	55.9050i	0.579657	+	1.78400i
$983$	12.8725	+	4.18252i	0.410568	+	0.133402i	0.507017	−	0.861936i	$-0.330748\pi$
$983$	12.8725	+	4.18252i	0.410568	+	0.133402i	−0.0964483	+	0.995338i	$0.530748\pi$
$984$	−11.6875	+	9.75287i	−0.372582	+	0.310910i
$985$	1.05692	−	1.45472i	0.0336762	−	0.0463514i
$986$	3.66773	−	11.2881i	0.116804	−	0.359487i
$987$	−5.00074	+	0.336017i	−0.159175	+	0.0106955i
$988$	−152.600	+	110.871i	−4.85486	+	3.52726i
$989$	15.3531			0.488199
$990$	−15.6000	−	20.4652i	−0.495800	−	0.650427i
$991$	−35.6910			−1.13376			−0.566881	−	0.823800i	$-0.691850\pi$
$991$	−35.6910			−1.13376			−0.566881	+	0.823800i	$0.691850\pi$
$992$	8.13952	−	5.91371i	0.258430	−	0.187760i
$993$	−4.67100	+	0.313860i	−0.148230	+	0.00996005i
$994$	−2.49911	+	7.69146i	−0.0792669	+	0.243958i
$995$	−8.12312	+	11.1805i	−0.257520	+	0.354446i
$996$	−82.4995	+	68.8437i	−2.61410	+	2.18140i
$997$	41.2595	+	13.4060i	1.30670	+	0.424574i	0.877908	−	0.478828i	$-0.158938\pi$
$997$	41.2595	+	13.4060i	1.30670	+	0.424574i	0.428795	+	0.903402i	$0.358938\pi$
$998$	−25.4510	−	78.3302i	−0.805638	−	2.47950i
$999$	0.183233	−	1.61633i	0.00579724	−	0.0511384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.p.b.41.1	✓	48
3.2	odd	2	inner	165.2.p.b.41.12	yes	48
5.2	odd	4		825.2.bs.h.74.2		48
5.3	odd	4		825.2.bs.g.74.11		48
5.4	even	2		825.2.bi.e.701.12		48
11.7	odd	10	inner	165.2.p.b.161.12	yes	48
15.2	even	4		825.2.bs.g.74.12		48
15.8	even	4		825.2.bs.h.74.1		48
15.14	odd	2		825.2.bi.e.701.1		48
33.29	even	10	inner	165.2.p.b.161.1	yes	48
55.7	even	20		825.2.bs.h.524.1		48
55.18	even	20		825.2.bs.g.524.12		48
55.29	odd	10		825.2.bi.e.326.1		48
165.29	even	10		825.2.bi.e.326.12		48
165.62	odd	20		825.2.bs.g.524.11		48
165.128	odd	20		825.2.bs.h.524.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.p.b.41.1	✓	48	1.1	even	1	trivial
165.2.p.b.41.12	yes	48	3.2	odd	2	inner
165.2.p.b.161.1	yes	48	33.29	even	10	inner
165.2.p.b.161.12	yes	48	11.7	odd	10	inner
825.2.bi.e.326.1		48	55.29	odd	10
825.2.bi.e.326.12		48	165.29	even	10
825.2.bi.e.701.1		48	15.14	odd	2
825.2.bi.e.701.12		48	5.4	even	2
825.2.bs.g.74.11		48	5.3	odd	4
825.2.bs.g.74.12		48	15.2	even	4
825.2.bs.g.524.11		48	165.62	odd	20
825.2.bs.g.524.12		48	55.18	even	20
825.2.bs.h.74.1		48	15.8	even	4
825.2.bs.h.74.2		48	5.2	odd	4
825.2.bs.h.524.1		48	55.7	even	20
825.2.bs.h.524.2		48	165.128	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.09233 + 1.52016i) q^{2} +(1.72815 - 0.116121i) q^{3} +(1.44890 - 4.45925i) q^{4} +(-0.587785 + 0.809017i) q^{5} +(-3.43934 + 2.87004i) q^{6} +(0.326781 + 0.106178i) q^{7} +(2.14883 + 6.61341i) q^{8} +(2.97303 - 0.401348i) q^{9} +O(q^{10})\)	\(q+(-2.09233 + 1.52016i) q^{2} +(1.72815 - 0.116121i) q^{3} +(1.44890 - 4.45925i) q^{4} +(-0.587785 + 0.809017i) q^{5} +(-3.43934 + 2.87004i) q^{6} +(0.326781 + 0.106178i) q^{7} +(2.14883 + 6.61341i) q^{8} +(2.97303 - 0.401348i) q^{9} -2.58626i q^{10} +(2.88296 - 1.63967i) q^{11} +(1.98611 - 7.87451i) q^{12} +(3.76304 + 5.17938i) q^{13} +(-0.845141 + 0.274603i) q^{14} +(-0.921840 + 1.46636i) q^{15} +(-6.96300 - 5.05891i) q^{16} +(-0.839822 - 0.610166i) q^{17} +(-5.61044 + 5.35925i) q^{18} +(-5.97625 + 1.94180i) q^{19} +(2.75597 + 3.79326i) q^{20} +(0.577058 + 0.145545i) q^{21} +(-3.53953 + 7.81331i) q^{22} +1.43997i q^{23} +(4.48146 + 11.1795i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-15.7470 - 5.11651i) q^{26} +(5.09125 - 1.03882i) q^{27} +(0.946945 - 1.30336i) q^{28} +(1.36614 - 4.20456i) q^{29} +(-0.300318 - 4.46945i) q^{30} +(0.974590 - 0.708081i) q^{31} +8.35174 q^{32} +(4.79180 - 3.16838i) q^{33} +2.68473 q^{34} +(-0.277977 + 0.201962i) q^{35} +(2.51791 - 13.8390i) q^{36} +(0.0967394 - 0.297733i) q^{37} +(9.55241 - 13.1478i) q^{38} +(7.10454 + 8.51379i) q^{39} +(-6.61341 - 2.14883i) q^{40} +(0.390553 + 1.20200i) q^{41} +(-1.42865 + 0.572694i) q^{42} -10.6620i q^{43} +(-3.13458 - 15.2316i) q^{44} +(-1.42281 + 2.64114i) q^{45} +(-2.18899 - 3.01289i) q^{46} +(-8.00954 + 2.60246i) q^{47} +(-12.6206 - 7.93404i) q^{48} +(-5.56761 - 4.04510i) q^{49} +(2.09233 + 1.52016i) q^{50} +(-1.52219 - 0.956941i) q^{51} +(28.5484 - 9.27593i) q^{52} +(0.614788 + 0.846183i) q^{53} +(-9.07338 + 9.91309i) q^{54} +(-0.368041 + 3.29614i) q^{55} +2.38930i q^{56} +(-10.1024 + 4.04970i) q^{57} +(3.53320 + 10.8741i) q^{58} +(7.13553 + 2.31847i) q^{59} +(5.20321 + 6.23532i) q^{60} +(2.01712 - 2.77633i) q^{61} +(-0.962761 + 2.96307i) q^{62} +(1.01415 + 0.184517i) q^{63} +(-3.54858 + 2.57819i) q^{64} -6.40206 q^{65} +(-5.20957 + 13.9136i) q^{66} -7.66699 q^{67} +(-3.93770 + 2.86091i) q^{68} +(0.167210 + 2.48849i) q^{69} +(0.274603 - 0.845141i) q^{70} +(5.34932 - 7.36271i) q^{71} +(9.04282 + 18.7995i) q^{72} +(-3.99770 - 1.29893i) q^{73} +(0.250193 + 0.770015i) q^{74} +(-0.644466 - 1.60769i) q^{75} +29.4631i q^{76} +(1.11619 - 0.229708i) q^{77} +(-27.8074 - 7.01357i) q^{78} +(-2.88184 - 3.96651i) q^{79} +(8.18550 - 2.65963i) q^{80} +(8.67784 - 2.38644i) q^{81} +(-2.64440 - 1.92127i) q^{82} +(-10.7041 - 7.77699i) q^{83} +(1.48512 - 2.36236i) q^{84} +(0.987270 - 0.320783i) q^{85} +(16.2081 + 22.3085i) q^{86} +(1.87267 - 7.42476i) q^{87} +(17.0388 + 15.5429i) q^{88} +4.84619i q^{89} +(-1.03799 - 7.68903i) q^{90} +(0.679756 + 2.09207i) q^{91} +(6.42119 + 2.08637i) q^{92} +(1.60202 - 1.33684i) q^{93} +(12.8024 - 17.6210i) q^{94} +(1.94180 - 5.97625i) q^{95} +(14.4331 - 0.969809i) q^{96} +(-8.10068 + 5.88549i) q^{97} +17.7985 q^{98} +(7.91306 - 6.03187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

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