LMFDB - Embedded newform 150.2.h.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(19,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("150.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.h (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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	150.19
Dual form			150.2.h.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.06909 + 0.847859i) q^{5} +(0.809017 + 0.587785i) q^{6} -4.07768i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.06909 + 0.847859i) q^{5} +(0.809017 + 0.587785i) q^{6} -4.07768i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.70582 - 1.44575i) q^{10} +(-1.01484 - 3.12334i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(-5.15688 - 1.67557i) q^{13} +(1.26007 + 3.87811i) q^{14} +(1.90211 + 1.17557i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.03353 - 2.79892i) q^{17} -1.00000i q^{18} +(1.32292 + 0.961158i) q^{19} +(-1.17557 + 1.90211i) q^{20} +(-3.29892 + 2.39680i) q^{21} +(1.93033 + 2.65688i) q^{22} +(-0.581542 + 0.188954i) q^{23} +1.00000 q^{24} +(3.56227 - 3.50859i) q^{25} +5.42226 q^{26} +(0.951057 - 0.309017i) q^{27} +(-2.39680 - 3.29892i) q^{28} +(-3.78173 + 2.74759i) q^{29} +(-2.17229 - 0.530249i) q^{30} +(6.71737 + 4.88046i) q^{31} +1.00000i q^{32} +(-1.93033 + 2.65688i) q^{33} +(-1.06909 + 3.29032i) q^{34} +(3.45730 + 8.43710i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.28350 + 0.741955i) q^{37} +(-1.55519 - 0.505311i) q^{38} +(1.67557 + 5.15688i) q^{39} +(0.530249 - 2.17229i) q^{40} +(0.905972 - 2.78829i) q^{41} +(2.39680 - 3.29892i) q^{42} +8.64114i q^{43} +(-2.65688 - 1.93033i) q^{44} +(-0.166977 - 2.22982i) q^{45} +(0.494689 - 0.359413i) q^{46} +(-4.06430 - 5.59403i) q^{47} +(-0.951057 + 0.309017i) q^{48} -9.62750 q^{49} +(-2.30371 + 4.43767i) q^{50} -3.45965 q^{51} +(-5.15688 + 1.67557i) q^{52} +(3.99557 + 5.49942i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(4.74794 + 5.60205i) q^{55} +(3.29892 + 2.39680i) q^{56} -1.63522i q^{57} +(2.74759 - 3.78173i) q^{58} +(4.38081 - 13.4828i) q^{59} +(2.22982 - 0.166977i) q^{60} +(-3.88998 - 11.9721i) q^{61} +(-7.89675 - 2.56581i) q^{62} +(3.87811 + 1.26007i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(12.0907 - 0.905395i) q^{65} +(1.01484 - 3.12334i) q^{66} +(6.39169 - 8.79741i) q^{67} -3.45965i q^{68} +(0.494689 + 0.359413i) q^{69} +(-5.89529 - 6.95579i) q^{70} +(7.33541 - 5.32949i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-8.65537 + 2.81230i) q^{73} -2.40102 q^{74} +(-4.93236 - 0.819639i) q^{75} +1.63522 q^{76} +(-12.7360 + 4.13818i) q^{77} +(-3.18712 - 4.38670i) q^{78} +(-3.31375 + 2.40758i) q^{79} +(0.166977 + 2.22982i) q^{80} +(-0.809017 - 0.587785i) q^{81} +2.93179i q^{82} +(4.19156 - 5.76919i) q^{83} +(-1.26007 + 3.87811i) q^{84} +(-1.83447 + 7.51536i) q^{85} +(-2.67026 - 8.21821i) q^{86} +(4.44569 + 1.44449i) q^{87} +(3.12334 + 1.01484i) q^{88} +(-1.48423 - 4.56799i) q^{89} +(0.847859 + 2.06909i) q^{90} +(-6.83245 + 21.0281i) q^{91} +(-0.359413 + 0.494689i) q^{92} -8.30313i q^{93} +(5.59403 + 4.06430i) q^{94} +(-3.55217 - 0.867073i) q^{95} +(0.809017 - 0.587785i) q^{96} +(8.67557 + 11.9409i) q^{97} +(9.15630 - 2.97506i) q^{98} +3.28408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	$ 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} - 20 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} - 8 q^{19} - 2 q^{21} - 10 q^{23} + 8 q^{24} - 10 q^{25} + 4 q^{26} - 10 q^{28} - 22 q^{29} - 10 q^{30} + 24 q^{31} + 8 q^{34} + 10 q^{35} - 2 q^{36} - 20 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} + 10 q^{42} + 10 q^{46} + 10 q^{47} + 8 q^{49} - 20 q^{50} - 12 q^{51} - 20 q^{52} - 30 q^{53} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 30 q^{58} - 20 q^{59} + 10 q^{60} + 10 q^{62} + 10 q^{63} + 2 q^{64} + 20 q^{65} - 10 q^{66} + 10 q^{67} + 10 q^{69} - 10 q^{70} + 20 q^{71} - 20 q^{73} - 4 q^{74} - 20 q^{75} - 12 q^{76} - 20 q^{77} + 16 q^{79} - 2 q^{81} + 70 q^{83} + 2 q^{84} + 20 q^{85} - 18 q^{86} - 30 q^{87} + 10 q^{88} - 34 q^{89} - 10 q^{90} - 24 q^{91} + 30 q^{92} + 30 q^{94} + 30 q^{95} + 2 q^{96} + 60 q^{97} + 20 q^{98} + 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 - 20 * q^13 - 2 * q^14 - 2 * q^16 + 10 * q^17 - 8 * q^19 - 2 * q^21 - 10 * q^23 + 8 * q^24 - 10 * q^25 + 4 * q^26 - 10 * q^28 - 22 * q^29 - 10 * q^30 + 24 * q^31 + 8 * q^34 + 10 * q^35 - 2 * q^36 - 20 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 + 10 * q^42 + 10 * q^46 + 10 * q^47 + 8 * q^49 - 20 * q^50 - 12 * q^51 - 20 * q^52 - 30 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 30 * q^58 - 20 * q^59 + 10 * q^60 + 10 * q^62 + 10 * q^63 + 2 * q^64 + 20 * q^65 - 10 * q^66 + 10 * q^67 + 10 * q^69 - 10 * q^70 + 20 * q^71 - 20 * q^73 - 4 * q^74 - 20 * q^75 - 12 * q^76 - 20 * q^77 + 16 * q^79 - 2 * q^81 + 70 * q^83 + 2 * q^84 + 20 * q^85 - 18 * q^86 - 30 * q^87 + 10 * q^88 - 34 * q^89 - 10 * q^90 - 24 * q^91 + 30 * q^92 + 30 * q^94 + 30 * q^95 + 2 * q^96 + 60 * q^97 + 20 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−2.06909	+	0.847859i	−0.925325	+	0.379174i
$5$	−2.06909	+	0.847859i	−0.925325	+	0.379174i
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$		−	4.07768i		−	1.54122i	−0.637307	−	0.770610i	$-0.719952\pi$
$7$		−	4.07768i		−	1.54122i	0.637307	−	0.770610i	$-0.280048\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	1.70582	−	1.44575i	0.539427	−	0.457185i
$11$	−1.01484	−	3.12334i	−0.305985	−	0.941724i	−0.979308	−	0.202376i	$-0.935134\pi$
$11$	−1.01484	−	3.12334i	−0.305985	−	0.941724i	0.673323	−	0.739348i	$-0.264866\pi$
$12$	−0.951057	−	0.309017i	−0.274546	−	0.0892055i
$13$	−5.15688	−	1.67557i	−1.43026	−	0.464720i	−0.511413	−	0.859335i	$-0.670878\pi$
$13$	−5.15688	−	1.67557i	−1.43026	−	0.464720i	−0.918847	+	0.394615i	$0.870878\pi$
$14$	1.26007	+	3.87811i	0.336769	+	1.03647i
$15$	1.90211	+	1.17557i	0.491123	+	0.303531i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	2.03353	−	2.79892i	0.493204	−	0.678837i	−0.487771	−	0.872972i	$-0.662190\pi$
$17$	2.03353	−	2.79892i	0.493204	−	0.678837i	0.980975	+	0.194135i	$0.0621899\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.32292	+	0.961158i	0.303499	+	0.220505i	0.729102	−	0.684405i	$-0.239938\pi$
$19$	1.32292	+	0.961158i	0.303499	+	0.220505i	−0.425603	+	0.904910i	$0.639938\pi$
$20$	−1.17557	+	1.90211i	−0.262866	+	0.425325i
$21$	−3.29892	+	2.39680i	−0.719882	+	0.523025i
$22$	1.93033	+	2.65688i	0.411548	+	0.566448i
$23$	−0.581542	+	0.188954i	−0.121260	+	0.0393997i	−0.369018	−	0.929422i	$-0.620306\pi$
$23$	−0.581542	+	0.188954i	−0.121260	+	0.0393997i	0.247758	+	0.968822i	$0.420306\pi$
$24$	1.00000			0.204124
$25$	3.56227	−	3.50859i	0.712454	−	0.701719i
$26$	5.42226			1.06339
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	−2.39680	−	3.29892i	−0.452953	−	0.623436i
$29$	−3.78173	+	2.74759i	−0.702249	+	0.510214i	−0.880664	−	0.473741i	$-0.842903\pi$
$29$	−3.78173	+	2.74759i	−0.702249	+	0.510214i	0.178415	+	0.983955i	$0.442903\pi$
$30$	−2.17229	−	0.530249i	−0.396604	−	0.0968097i
$31$	6.71737	+	4.88046i	1.20648	+	0.876556i	0.994906	−	0.100807i	$-0.0321424\pi$
$31$	6.71737	+	4.88046i	1.20648	+	0.876556i	0.211570	+	0.977363i	$0.432142\pi$
$32$			1.00000i			0.176777i
$33$	−1.93033	+	2.65688i	−0.336028	+	0.462503i
$34$	−1.06909	+	3.29032i	−0.183348	+	0.564286i
$35$	3.45730	+	8.43710i	0.584390	+	1.42613i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	2.28350	+	0.741955i	0.375406	+	0.121977i	0.490642	−	0.871361i	$-0.336762\pi$
$37$	2.28350	+	0.741955i	0.375406	+	0.121977i	−0.115236	+	0.993338i	$0.536762\pi$
$38$	−1.55519	−	0.505311i	−0.252285	−	0.0819722i
$39$	1.67557	+	5.15688i	0.268306	+	0.825761i
$40$	0.530249	−	2.17229i	0.0838397	−	0.343469i
$41$	0.905972	−	2.78829i	0.141489	−	0.435458i	−0.855054	−	0.518539i	$-0.826476\pi$
$41$	0.905972	−	2.78829i	0.141489	−	0.435458i	0.996543	+	0.0830809i	$0.0264760\pi$
$42$	2.39680	−	3.29892i	0.369835	−	0.509034i
$43$			8.64114i			1.31776i	0.752247	+	0.658881i	$0.228970\pi$
$43$			8.64114i			1.31776i	−0.752247	+	0.658881i	$0.771030\pi$
$44$	−2.65688	−	1.93033i	−0.400539	−	0.291009i
$45$	−0.166977	−	2.22982i	−0.0248915	−	0.332403i
$46$	0.494689	−	0.359413i	0.0729379	−	0.0529925i
$47$	−4.06430	−	5.59403i	−0.592839	−	0.815973i	0.402190	−	0.915556i	$-0.368249\pi$
$47$	−4.06430	−	5.59403i	−0.592839	−	0.815973i	−0.995029	+	0.0995832i	$0.968249\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	−9.62750			−1.37536
$50$	−2.30371	+	4.43767i	−0.325793	+	0.627582i
$51$	−3.45965			−0.484448
$52$	−5.15688	+	1.67557i	−0.715130	+	0.232360i
$53$	3.99557	+	5.49942i	0.548833	+	0.755404i	0.989853	−	0.142093i	$-0.0453833\pi$
$53$	3.99557	+	5.49942i	0.548833	+	0.755404i	−0.441020	+	0.897497i	$0.645383\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	4.74794	+	5.60205i	0.640213	+	0.755380i
$56$	3.29892	+	2.39680i	0.440836	+	0.320286i
$57$		−	1.63522i		−	0.216590i
$58$	2.74759	−	3.78173i	0.360776	−	0.496565i
$59$	4.38081	−	13.4828i	0.570333	−	1.75531i	−0.0812131	−	0.996697i	$-0.525879\pi$
$59$	4.38081	−	13.4828i	0.570333	−	1.75531i	0.651546	−	0.758609i	$-0.274121\pi$
$60$	2.22982	−	0.166977i	0.287869	−	0.0215567i
$61$	−3.88998	−	11.9721i	−0.498061	−	1.53287i	−0.812131	−	0.583475i	$-0.801693\pi$
$61$	−3.88998	−	11.9721i	−0.498061	−	1.53287i	0.314070	−	0.949400i	$-0.398307\pi$
$62$	−7.89675	−	2.56581i	−1.00289	−	0.325858i
$63$	3.87811	+	1.26007i	0.488596	+	0.158754i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	12.0907	−	0.905395i	1.49967	−	0.112300i
$66$	1.01484	−	3.12334i	0.124918	−	0.384457i
$67$	6.39169	−	8.79741i	0.780869	−	1.07477i	−0.214316	−	0.976764i	$-0.568752\pi$
$67$	6.39169	−	8.79741i	0.780869	−	1.07477i	0.995185	−	0.0980099i	$-0.0312477\pi$
$68$		−	3.45965i		−	0.419544i
$69$	0.494689	+	0.359413i	0.0595536	+	0.0432682i
$70$	−5.89529	−	6.95579i	−0.704622	−	0.831376i
$71$	7.33541	−	5.32949i	0.870553	−	0.632494i	−0.0601825	−	0.998187i	$-0.519168\pi$
$71$	7.33541	−	5.32949i	0.870553	−	0.632494i	0.930735	+	0.365694i	$0.119168\pi$
$72$	−0.587785	−	0.809017i	−0.0692712	−	0.0953436i
$73$	−8.65537	+	2.81230i	−1.01303	+	0.329155i	−0.768062	−	0.640375i	$-0.778779\pi$
$73$	−8.65537	+	2.81230i	−1.01303	+	0.329155i	−0.244972	+	0.969530i	$0.578779\pi$
$74$	−2.40102			−0.279113
$75$	−4.93236	−	0.819639i	−0.569540	−	0.0946437i
$76$	1.63522			0.187573
$77$	−12.7360	+	4.13818i	−1.45140	+	0.471589i
$78$	−3.18712	−	4.38670i	−0.360871	−	0.496696i
$79$	−3.31375	+	2.40758i	−0.372826	+	0.270874i	−0.758382	−	0.651810i	$-0.774010\pi$
$79$	−3.31375	+	2.40758i	−0.372826	+	0.270874i	0.385556	+	0.922685i	$0.374010\pi$
$80$	0.166977	+	2.22982i	0.0186686	+	0.249302i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$			2.93179i			0.323762i
$83$	4.19156	−	5.76919i	0.460083	−	0.633250i	−0.514443	−	0.857525i	$-0.672001\pi$
$83$	4.19156	−	5.76919i	0.460083	−	0.633250i	0.974526	+	0.224274i	$0.0720012\pi$
$84$	−1.26007	+	3.87811i	−0.137485	+	0.423136i
$85$	−1.83447	+	7.51536i	−0.198977	+	0.815155i
$86$	−2.67026	−	8.21821i	−0.287942	−	0.886193i
$87$	4.44569	+	1.44449i	0.476628	+	0.154866i
$88$	3.12334	+	1.01484i	0.332950	+	0.108182i
$89$	−1.48423	−	4.56799i	−0.157328	−	0.484206i	0.841061	−	0.540940i	$-0.181931\pi$
$89$	−1.48423	−	4.56799i	−0.157328	−	0.484206i	−0.998389	+	0.0567336i	$0.981931\pi$
$90$	0.847859	+	2.06909i	0.0893722	+	0.218101i
$91$	−6.83245	+	21.0281i	−0.716235	+	2.20434i
$92$	−0.359413	+	0.494689i	−0.0374714	+	0.0515749i
$93$		−	8.30313i		−	0.860994i
$94$	5.59403	+	4.06430i	0.576980	+	0.419200i
$95$	−3.55217	−	0.867073i	−0.364445	−	0.0889599i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	8.67557	+	11.9409i	0.880871	+	1.21241i	0.976179	+	0.216967i	$0.0696163\pi$
$97$	8.67557	+	11.9409i	0.880871	+	1.21241i	−0.0953083	+	0.995448i	$0.530384\pi$
$98$	9.15630	−	2.97506i	0.924926	−	0.300527i
$99$	3.28408			0.330062
$100$	0.819639	−	4.93236i	0.0819639	−	0.493236i
$101$	−11.4846			−1.14276			−0.571381	−	0.820685i	$-0.693592\pi$
$101$	−11.4846			−1.14276			−0.571381	+	0.820685i	$0.693592\pi$
$102$	3.29032	−	1.06909i	0.325790	−	0.105856i
$103$	−8.20248	−	11.2897i	−0.808214	−	1.11241i	−0.991596	−	0.129370i	$-0.958705\pi$
$103$	−8.20248	−	11.2897i	−0.808214	−	1.11241i	0.183382	−	0.983042i	$-0.441295\pi$
$104$	4.38670	−	3.18712i	0.430151	−	0.312523i
$105$	4.79360	−	7.75621i	0.467808	−	0.756929i
$106$	−5.49942	−	3.99557i	−0.534151	−	0.388084i
$107$			8.35405i			0.807616i	0.914844	+	0.403808i	$0.132314\pi$
$107$			8.35405i			0.807616i	−0.914844	+	0.403808i	$0.867686\pi$
$108$	0.587785	−	0.809017i	0.0565597	−	0.0778477i
$109$	−0.164593	+	0.506564i	−0.0157651	+	0.0485201i	−0.958630	−	0.284656i	$-0.908120\pi$
$109$	−0.164593	+	0.506564i	−0.0157651	+	0.0485201i	0.942864	+	0.333176i	$0.108120\pi$
$110$	−6.24669	−	3.86067i	−0.595598	−	0.368100i
$111$	−0.741955	−	2.28350i	−0.0704233	−	0.216740i
$112$	−3.87811	−	1.26007i	−0.366447	−	0.119066i
$113$	16.3840	+	5.32350i	1.54128	+	0.500792i	0.951729	−	0.306938i	$-0.0993046\pi$
$113$	16.3840	+	5.32350i	1.54128	+	0.500792i	0.589551	+	0.807731i	$0.299305\pi$
$114$	0.505311	+	1.55519i	0.0473267	+	0.145657i
$115$	1.04306	−	0.884029i	0.0972655	−	0.0824362i
$116$	−1.44449	+	4.44569i	−0.134118	+	0.412772i
$117$	3.18712	−	4.38670i	0.294650	−	0.405551i
$118$			14.1766i			1.30506i
$119$	−11.4131	−	8.29210i	−1.04624	−	0.760135i
$120$	−2.06909	+	0.847859i	−0.188881	+	0.0773986i
$121$	0.173797	−	0.126271i	0.0157997	−	0.0114792i
$122$	7.39919	+	10.1841i	0.669891	+	0.922026i
$123$	−2.78829	+	0.905972i	−0.251412	+	0.0816887i
$124$	8.30313			0.745643
$125$	−4.39587	+	10.2799i	−0.393179	+	0.919462i
$126$	−4.07768			−0.363269
$127$	−1.09148	+	0.354643i	−0.0968532	+	0.0314695i	−0.357043	−	0.934088i	$-0.616215\pi$
$127$	−1.09148	+	0.354643i	−0.0968532	+	0.0314695i	0.260190	+	0.965558i	$0.416215\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	6.99083	−	5.07914i	0.615508	−	0.447193i
$130$	−11.2191	+	4.59731i	−0.983984	+	0.403211i
$131$	5.35494	+	3.89059i	0.467864	+	0.339923i	0.796608	−	0.604496i	$-0.206626\pi$
$131$	5.35494	+	3.89059i	0.467864	+	0.339923i	−0.328745	+	0.944419i	$0.606626\pi$
$132$			3.28408i			0.285842i
$133$	3.91930	−	5.39445i	0.339846	−	0.467758i
$134$	−3.36031	+	10.3420i	−0.290287	+	0.893410i
$135$	−1.70582	+	1.44575i	−0.146814	+	0.124430i
$136$	1.06909	+	3.29032i	0.0916738	+	0.282143i
$137$	−7.05850	−	2.29345i	−0.603049	−	0.195942i	−0.00844901	−	0.999964i	$-0.502689\pi$
$137$	−7.05850	−	2.29345i	−0.603049	−	0.195942i	−0.594600	+	0.804022i	$0.702689\pi$
$138$	−0.581542	−	0.188954i	−0.0495041	−	0.0160849i
$139$	−1.63798	−	5.04119i	−0.138932	−	0.427588i	0.857249	−	0.514902i	$-0.172172\pi$
$139$	−1.63798	−	5.04119i	−0.138932	−	0.427588i	−0.996181	+	0.0873138i	$0.972172\pi$
$140$	7.75621	+	4.79360i	0.655520	+	0.405134i
$141$	−2.13673	+	6.57617i	−0.179945	+	0.553814i
$142$	−5.32949	+	7.33541i	−0.447240	+	0.615574i
$143$			17.8071i			1.48911i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$	5.49517	−	8.89138i	0.456349	−	0.738389i
$146$	7.36269	−	5.34931i	0.609341	−	0.442712i
$147$	5.65890	+	7.78881i	0.466739	+	0.642411i
$148$	2.28350	−	0.741955i	0.187703	−	0.0609883i
$149$	4.79296			0.392655			0.196327	−	0.980538i	$-0.437098\pi$
$149$	4.79296			0.392655			0.196327	+	0.980538i	$0.437098\pi$
$150$	4.94424	−	0.744661i	0.403695	−	0.0608013i
$151$	6.93533			0.564389			0.282195	−	0.959357i	$-0.408938\pi$
$151$	6.93533			0.564389			0.282195	+	0.959357i	$0.408938\pi$
$152$	−1.55519	+	0.505311i	−0.126142	+	0.0409861i
$153$	2.03353	+	2.79892i	0.164401	+	0.226279i
$154$	10.8339	−	7.87129i	0.873020	−	0.634286i
$155$	−18.0368	−	4.40272i	−1.44875	−	0.353635i
$156$	4.38670	+	3.18712i	0.351217	+	0.255174i
$157$			7.51609i			0.599849i	0.953963	+	0.299925i	$0.0969615\pi$
$157$			7.51609i			0.599849i	−0.953963	+	0.299925i	$0.903038\pi$
$158$	2.40758	−	3.31375i	0.191537	−	0.263628i
$159$	2.10059	−	6.46496i	0.166588	−	0.512705i
$160$	−0.847859	−	2.06909i	−0.0670291	−	0.163576i
$161$	0.770497	+	2.37134i	0.0607236	+	0.186888i
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	7.95766	+	2.58560i	0.623292	+	0.202520i	0.603601	−	0.797286i	$-0.293732\pi$
$163$	7.95766	+	2.58560i	0.623292	+	0.202520i	0.0196905	+	0.999806i	$0.493732\pi$
$164$	−0.905972	−	2.78829i	−0.0707445	−	0.217729i
$165$	1.74138	−	7.13397i	0.135566	−	0.555379i
$166$	−2.20363	+	6.78209i	−0.171035	+	0.526392i
$167$	5.25731	−	7.23607i	0.406823	−	0.559944i	−0.555617	−	0.831438i	$-0.687518\pi$
$167$	5.25731	−	7.23607i	0.406823	−	0.559944i	0.962440	+	0.271495i	$0.0875179\pi$
$168$		−	4.07768i		−	0.314600i
$169$	13.2686	+	9.64021i	1.02066	+	0.741555i
$170$	−0.577684	−	7.71441i	−0.0443063	−	0.591668i
$171$	−1.32292	+	0.961158i	−0.101166	+	0.0735016i
$172$	5.07914	+	6.99083i	0.387280	+	0.533046i
$173$	−2.22457	+	0.722807i	−0.169131	+	0.0549540i	−0.392358	−	0.919812i	$-0.628341\pi$
$173$	−2.22457	+	0.722807i	−0.169131	+	0.0549540i	0.223228	+	0.974766i	$0.428341\pi$
$174$	−4.67447			−0.354371
$175$	−14.3069	−	14.5258i	−1.08150	−	1.09805i
$176$	−3.28408			−0.247547
$177$	−13.4828	+	4.38081i	−1.01343	+	0.329282i
$178$	2.82318	+	3.88577i	0.211606	+	0.291251i
$179$	4.87811	−	3.54415i	0.364607	−	0.264902i	−0.390364	−	0.920661i	$-0.627651\pi$
$179$	4.87811	−	3.54415i	0.364607	−	0.264902i	0.754971	+	0.655758i	$0.227651\pi$
$180$	−1.44575	−	1.70582i	−0.107760	−	0.127144i
$181$	−13.4112	−	9.74379i	−0.996844	−	0.724250i	−0.0354351	−	0.999372i	$-0.511282\pi$
$181$	−13.4112	−	9.74379i	−0.996844	−	0.724250i	−0.961409	+	0.275122i	$0.911282\pi$
$182$		−	22.1103i		−	1.63892i
$183$	−7.39919	+	10.1841i	−0.546964	+	0.752831i
$184$	0.188954	−	0.581542i	0.0139299	−	0.0428718i
$185$	−5.35385	+	0.400916i	−0.393623	+	0.0294759i
$186$	2.56581	+	7.89675i	0.188134	+	0.579017i
$187$	−10.8057	−	3.51098i	−0.790189	−	0.256748i
$188$	−6.57617	−	2.13673i	−0.479617	−	0.155837i
$189$	−1.26007	−	3.87811i	−0.0916569	−	0.282091i
$190$	3.64625	−	0.273045i	0.264527	−	0.0198088i
$191$	3.08029	−	9.48015i	0.222882	−	0.685960i	−0.775618	−	0.631203i	$-0.782562\pi$
$191$	3.08029	−	9.48015i	0.222882	−	0.685960i	0.998500	−	0.0547570i	$-0.0174384\pi$
$192$	−0.587785	+	0.809017i	−0.0424197	+	0.0583858i
$193$		−	25.0735i		−	1.80483i	−0.430867	−	0.902416i	$-0.641792\pi$
$193$		−	25.0735i		−	1.80483i	0.430867	−	0.902416i	$-0.358208\pi$
$194$	−11.9409	−	8.67557i	−0.857307	−	0.622870i
$195$	−7.83921	−	9.24940i	−0.561377	−	0.662363i
$196$	−7.78881	+	5.65890i	−0.556344	+	0.404207i
$197$	15.7749	+	21.7123i	1.12391	+	1.54694i	0.799141	+	0.601143i	$0.205288\pi$
$197$	15.7749	+	21.7123i	1.12391	+	1.54694i	0.324773	+	0.945792i	$0.394712\pi$
$198$	−3.12334	+	1.01484i	−0.221966	+	0.0721213i
$199$	4.06114			0.287887			0.143943	−	0.989586i	$-0.454022\pi$
$199$	4.06114			0.287887			0.143943	+	0.989586i	$0.454022\pi$
$200$	0.744661	+	4.94424i	0.0526555	+	0.349610i
$201$	−10.8742			−0.767006
$202$	10.9225	−	3.54894i	0.768506	−	0.249703i
$203$	11.2038	+	15.4207i	0.786352	+	1.08232i
$204$	−2.79892	+	2.03353i	−0.195963	+	0.142376i
$205$	0.489542	+	6.53737i	0.0341911	+	0.456590i
$206$	11.2897	+	8.20248i	0.786594	+	0.571494i
$207$		−	0.611469i		−	0.0425001i
$208$	−3.18712	+	4.38670i	−0.220987	+	0.304163i
$209$	1.65948	−	5.10736i	0.114789	−	0.353283i
$210$	−2.16219	+	8.85790i	−0.149205	+	0.611253i
$211$	−1.34573	−	4.14173i	−0.0926438	−	0.285128i	0.893989	−	0.448090i	$-0.147895\pi$
$211$	−1.34573	−	4.14173i	−0.0926438	−	0.285128i	−0.986632	+	0.162961i	$0.947895\pi$
$212$	6.46496	+	2.10059i	0.444015	+	0.144269i
$213$	−8.62329	−	2.80188i	−0.590858	−	0.191981i
$214$	−2.58154	−	7.94517i	−0.176471	−	0.543121i
$215$	−7.32647	−	17.8793i	−0.499661	−	1.21936i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	19.9010	−	27.3913i	1.35097	−	1.85944i
$218$		−	0.532633i		−	0.0360745i
$219$	7.36269	+	5.34931i	0.497525	+	0.361473i
$220$	7.13397	+	1.74138i	0.480972	+	0.117404i
$221$	−15.1764	+	11.0263i	−1.02088	+	0.741711i
$222$	1.41128	+	1.94246i	0.0947191	+	0.130370i
$223$	−0.344164	+	0.111826i	−0.0230469	+	0.00748840i	−0.320518	−	0.947243i	$-0.603857\pi$
$223$	−0.344164	+	0.111826i	−0.0230469	+	0.00748840i	0.297471	+	0.954731i	$0.403857\pi$
$224$	4.07768			0.272452
$225$	2.23607	+	4.47214i	0.149071	+	0.298142i
$226$	−17.2272			−1.14594
$227$	−12.2284	+	3.97323i	−0.811624	+	0.263713i	−0.685286	−	0.728274i	$-0.740323\pi$
$227$	−12.2284	+	3.97323i	−0.811624	+	0.263713i	−0.126339	+	0.991987i	$0.540323\pi$
$228$	−0.961158	−	1.32292i	−0.0636543	−	0.0876126i
$229$	−13.3769	+	9.71886i	−0.883968	+	0.642240i	−0.934298	−	0.356492i	$-0.883973\pi$
$229$	−13.3769	+	9.71886i	−0.883968	+	0.642240i	0.0503302	+	0.998733i	$0.483973\pi$
$230$	−0.718826	+	1.16308i	−0.0473980	+	0.0766915i
$231$	10.8339	+	7.87129i	0.712818	+	0.517893i
$232$		−	4.67447i		−	0.306894i
$233$	6.50714	−	8.95631i	0.426297	−	0.586747i	−0.540801	−	0.841150i	$-0.681879\pi$
$233$	6.50714	−	8.95631i	0.426297	−	0.586747i	0.967098	+	0.254403i	$0.0818789\pi$
$234$	−1.67557	+	5.15688i	−0.109535	+	0.337116i
$235$	13.1523	+	8.12860i	0.857965	+	0.530251i
$236$	−4.38081	−	13.4828i	−0.285167	−	0.877653i
$237$	3.89555	+	1.26574i	0.253043	+	0.0822187i
$238$	13.4169	+	4.35941i	0.869688	+	0.282579i
$239$	1.72654	+	5.31375i	0.111681	+	0.343718i	0.991240	−	0.132071i	$-0.0421626\pi$
$239$	1.72654	+	5.31375i	0.111681	+	0.343718i	−0.879560	+	0.475789i	$0.842163\pi$
$240$	1.70582	−	1.44575i	0.110110	−	0.0933225i
$241$	−4.59014	+	14.1270i	−0.295677	+	0.909999i	0.687317	+	0.726358i	$0.258788\pi$
$241$	−4.59014	+	14.1270i	−0.295677	+	0.909999i	−0.982993	+	0.183641i	$0.941212\pi$
$242$	−0.126271	+	0.173797i	−0.00811700	+	0.0111721i
$243$			1.00000i			0.0641500i
$244$	−10.1841	−	7.39919i	−0.651971	−	0.473684i
$245$	19.9202	−	8.16276i	1.27265	−	0.521500i
$246$	2.37186	−	1.72326i	0.151225	−	0.109871i
$247$	−5.21165	−	7.17322i	−0.331609	−	0.456421i
$248$	−7.89675	+	2.56581i	−0.501444	+	0.162929i
$249$	−7.13111			−0.451916
$250$	1.00406	−	11.1352i	0.0635021	−	0.704250i
$251$	−12.6802			−0.800368			−0.400184	−	0.916435i	$-0.631054\pi$
$251$	−12.6802			−0.800368			−0.400184	+	0.916435i	$0.631054\pi$
$252$	3.87811	−	1.26007i	0.244298	−	0.0793772i
$253$	1.18034	+	1.62460i	0.0742073	+	0.102138i
$254$	0.928468	−	0.674572i	0.0582573	−	0.0423264i
$255$	7.15833	−	2.93329i	0.448272	−	0.183690i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			19.1916i			1.19714i	0.801071	+	0.598570i	$0.204264\pi$
$257$			19.1916i			1.19714i	−0.801071	+	0.598570i	$0.795736\pi$
$258$	−5.07914	+	6.99083i	−0.316213	+	0.435230i
$259$	3.02546	−	9.31140i	0.187993	−	0.578582i
$260$	9.24940	−	7.83921i	0.573623	−	0.486167i
$261$	−1.44449	−	4.44569i	−0.0894118	−	0.275181i
$262$	−6.29511	−	2.04541i	−0.388913	−	0.126366i
$263$	−28.0323	−	9.10825i	−1.72855	−	0.561639i	−0.735309	−	0.677732i	$-0.762963\pi$
$263$	−28.0323	−	9.10825i	−1.72855	−	0.561639i	−0.993238	+	0.116093i	$0.962963\pi$
$264$	−1.01484	−	3.12334i	−0.0624589	−	0.192229i
$265$	−12.9299	−	7.99113i	−0.794279	−	0.490891i
$266$	−2.06050	+	6.34156i	−0.126337	+	0.388826i
$267$	−2.82318	+	3.88577i	−0.172776	+	0.237805i
$268$		−	10.8742i		−	0.664247i
$269$	17.7191	+	12.8737i	1.08035	+	0.784922i	0.977744	−	0.209800i	$-0.0672814\pi$
$269$	17.7191	+	12.8737i	1.08035	+	0.784922i	0.102608	+	0.994722i	$0.467281\pi$
$270$	1.17557	−	1.90211i	0.0715429	−	0.115759i
$271$	12.2025	−	8.86562i	0.741248	−	0.538548i	−0.151854	−	0.988403i	$-0.548524\pi$
$271$	12.2025	−	8.86562i	0.741248	−	0.538548i	0.893102	+	0.449855i	$0.148524\pi$
$272$	−2.03353	−	2.79892i	−0.123301	−	0.169709i
$273$	21.0281	−	6.83245i	1.27268	−	0.413518i
$274$	7.42175			0.448364
$275$	−14.5737	−	7.56555i	−0.878825	−	0.456220i
$276$	0.611469			0.0368061
$277$	−2.45721	+	0.798395i	−0.147639	+	0.0479709i	−0.381904	−	0.924202i	$-0.624732\pi$
$277$	−2.45721	+	0.798395i	−0.147639	+	0.0479709i	0.234265	+	0.972173i	$0.424732\pi$
$278$	3.11563	+	4.28829i	0.186863	+	0.257195i
$279$	−6.71737	+	4.88046i	−0.402159	+	0.292185i
$280$	−8.85790	−	2.16219i	−0.529361	−	0.129215i
$281$	14.8843	+	10.8141i	0.887923	+	0.645113i	0.935336	−	0.353762i	$-0.115098\pi$
$281$	14.8843	+	10.8141i	0.887923	+	0.645113i	−0.0474130	+	0.998875i	$0.515098\pi$
$282$		−	6.91460i		−	0.411758i
$283$	2.04234	−	2.81105i	0.121405	−	0.167099i	−0.743989	−	0.668192i	$-0.767068\pi$
$283$	2.04234	−	2.81105i	0.121405	−	0.167099i	0.865394	+	0.501093i	$0.167068\pi$
$284$	2.80188	−	8.62329i	0.166261	−	0.511698i
$285$	1.38644	+	3.38342i	0.0821254	+	0.200416i
$286$	−5.50271	−	16.9356i	−0.325382	−	1.00142i
$287$	−11.3698	−	3.69427i	−0.671137	−	0.218066i
$288$	−0.951057	−	0.309017i	−0.0560415	−	0.0182090i
$289$	1.55461	+	4.78460i	0.0914477	+	0.281447i
$290$	−2.47863	+	10.1543i	−0.145550	+	0.596281i
$291$	4.56102	−	14.0374i	0.267372	−	0.822885i
$292$	−5.34931	+	7.36269i	−0.313045	+	0.430869i
$293$		−	15.8625i		−	0.926699i	−0.886176	−	0.463349i	$-0.846647\pi$
$293$		−	15.8625i		−	0.926699i	0.886176	−	0.463349i	$-0.153353\pi$
$294$	−7.78881	−	5.65890i	−0.454253	−	0.330034i
$295$	2.36717	+	31.6114i	0.137822	+	1.84048i
$296$	−1.94246	+	1.41128i	−0.112903	+	0.0820291i
$297$	−1.93033	−	2.65688i	−0.112009	−	0.154168i
$298$	−4.55838	+	1.48111i	−0.264060	+	0.0857982i
$299$	3.31555			0.191743
$300$	−4.47214	+	2.23607i	−0.258199	+	0.129099i
$301$	35.2358			2.03096
$302$	−6.59589	+	2.14314i	−0.379551	+	0.123324i
$303$	6.75049	+	9.29125i	0.387806	+	0.533769i
$304$	1.32292	−	0.961158i	0.0758747	−	0.0551262i
$305$	18.1994	+	21.4733i	1.04210	+	1.22956i
$306$	−2.79892	−	2.03353i	−0.160003	−	0.116249i
$307$		−	25.4122i		−	1.45035i	−0.688565	−	0.725175i	$-0.741759\pi$
$307$		−	25.4122i		−	1.45035i	0.688565	−	0.725175i	$-0.258241\pi$
$308$	−7.87129	+	10.8339i	−0.448508	+	0.617319i
$309$	−4.31230	+	13.2719i	−0.245318	+	0.755012i
$310$	18.5145	−	1.38644i	1.05155	−	0.0787443i
$311$	5.69968	+	17.5418i	0.323199	+	0.994704i	0.972247	+	0.233957i	$0.0751675\pi$
$311$	5.69968	+	17.5418i	0.323199	+	0.994704i	−0.649048	+	0.760748i	$0.724833\pi$
$312$	−5.15688	−	1.67557i	−0.291951	−	0.0948605i
$313$	20.8396	+	6.77121i	1.17793	+	0.382731i	0.831596	−	0.555381i	$-0.187428\pi$
$313$	20.8396	+	6.77121i	1.17793	+	0.382731i	0.346330	+	0.938113i	$0.387428\pi$
$314$	−2.32260	−	7.14823i	−0.131072	−	0.403398i
$315$	−9.09252	+	0.680881i	−0.512305	+	0.0383633i
$316$	−1.26574	+	3.89555i	−0.0712035	+	0.219142i
$317$	−3.40134	+	4.68155i	−0.191039	+	0.262942i	−0.893782	−	0.448501i	$-0.851958\pi$
$317$	−3.40134	+	4.68155i	−0.191039	+	0.262942i	0.702744	+	0.711443i	$0.251958\pi$
$318$			6.79766i			0.381194i
$319$	12.4195	+	9.02329i	0.695358	+	0.505207i
$320$	1.44575	+	1.70582i	0.0808196	+	0.0953582i
$321$	6.75856	−	4.91038i	0.377226	−	0.274071i
$322$	−1.46557	−	2.01719i	−0.0816731	−	0.112413i
$323$	5.38040	−	1.74820i	0.299374	−	0.0972724i
$324$	−1.00000			−0.0555556
$325$	−24.2491	+	12.1245i	−1.34510	+	0.672549i
$326$	−8.36717			−0.463415
$327$	0.506564	−	0.164593i	0.0280131	−	0.00910200i
$328$	1.72326	+	2.37186i	0.0951511	+	0.130964i
$329$	−22.8107	+	16.5729i	−1.25759	+	0.913695i
$330$	0.548367	+	7.32292i	0.0301866	+	0.403114i
$331$	6.18384	+	4.49282i	0.339895	+	0.246948i	0.744617	−	0.667492i	$-0.232632\pi$
$331$	6.18384	+	4.49282i	0.339895	+	0.246948i	−0.404723	+	0.914439i	$0.632632\pi$
$332$		−	7.13111i		−	0.391370i
$333$	−1.41128	+	1.94246i	−0.0773378	+	0.106446i
$334$	−2.76393	+	8.50651i	−0.151236	+	0.465455i
$335$	−5.76603	+	23.6219i	−0.315032	+	1.29060i
$336$	1.26007	+	3.87811i	0.0687426	+	0.211568i
$337$	3.50849	+	1.13998i	0.191119	+	0.0620985i	0.403013	−	0.915194i	$-0.367963\pi$
$337$	3.50849	+	1.13998i	0.191119	+	0.0620985i	−0.211893	+	0.977293i	$0.567963\pi$
$338$	−15.5982	−	5.06816i	−0.848430	−	0.275671i
$339$	−5.32350	−	16.3840i	−0.289133	−	0.889859i
$340$	2.93329	+	7.15833i	0.159080	+	0.388215i
$341$	8.42632	−	25.9335i	0.456311	−	1.40438i
$342$	0.961158	−	1.32292i	0.0519735	−	0.0715354i
$343$			10.7141i			0.578508i
$344$	−6.99083	−	5.07914i	−0.376920	−	0.273849i
$345$	−1.32829	−	0.324231i	−0.0715126	−	0.0174560i
$346$	1.89233	−	1.37486i	0.101732	−	0.0739129i
$347$	−2.13673	−	2.94095i	−0.114706	−	0.157879i	0.747804	−	0.663920i	$-0.231108\pi$
$347$	−2.13673	−	2.94095i	−0.114706	−	0.157879i	−0.862509	+	0.506041i	$0.831108\pi$
$348$	4.44569	−	1.44449i	0.238314	−	0.0774329i
$349$	−12.2270			−0.654496			−0.327248	−	0.944938i	$-0.606121\pi$
$349$	−12.2270			−0.654496			−0.327248	+	0.944938i	$0.606121\pi$
$350$	18.0954	+	9.39378i	0.967241	+	0.502119i
$351$	−5.42226			−0.289419
$352$	3.12334	−	1.01484i	0.166475	−	0.0540910i
$353$	−9.20711	−	12.6725i	−0.490045	−	0.674489i	0.490351	−	0.871525i	$-0.336868\pi$
$353$	−9.20711	−	12.6725i	−0.490045	−	0.674489i	−0.980396	+	0.197036i	$0.936868\pi$
$354$	11.4691	−	8.33280i	0.609577	−	0.442883i
$355$	−10.6590	+	17.2466i	−0.565719	+	0.915353i
$356$	−3.88577	−	2.82318i	−0.205945	−	0.149628i
$357$			14.1074i			0.746640i
$358$	−3.54415	+	4.87811i	−0.187314	+	0.257816i
$359$	−2.18529	+	6.72564i	−0.115335	+	0.354966i	−0.992017	−	0.126105i	$-0.959752\pi$
$359$	−2.18529	+	6.72564i	−0.115335	+	0.354966i	0.876681	+	0.481071i	$0.159752\pi$
$360$	1.90211	+	1.17557i	0.100250	+	0.0619580i
$361$	−5.04503	−	15.5270i	−0.265528	−	0.817211i
$362$	15.7658	+	5.12261i	0.828631	+	0.269238i
$363$	−0.204311	−	0.0663845i	−0.0107235	−	0.00348428i
$364$	6.83245	+	21.0281i	0.358117	+	1.10217i
$365$	15.5243	−	13.1574i	0.812579	−	0.688691i
$366$	3.88998	−	11.9721i	0.203333	−	0.625794i
$367$	−15.7219	+	21.6393i	−0.820676	+	1.12956i	0.168912	+	0.985631i	$0.445975\pi$
$367$	−15.7219	+	21.6393i	−0.820676	+	1.12956i	−0.989588	+	0.143932i	$0.954025\pi$
$368$			0.611469i			0.0318751i
$369$	2.37186	+	1.72326i	0.123474	+	0.0897093i
$370$	4.96792	−	2.03572i	0.258270	−	0.105832i
$371$	22.4249	−	16.2927i	1.16424	−	0.845872i
$372$	−4.88046	−	6.71737i	−0.253040	−	0.348280i
$373$	−11.3031	+	3.67261i	−0.585254	+	0.190161i	−0.586653	−	0.809839i	$-0.699555\pi$
$373$	−11.3031	+	3.67261i	−0.585254	+	0.190161i	0.00139899	+	0.999999i	$0.499555\pi$
$374$	11.3618			0.587503
$375$	10.9004	−	2.48604i	0.562896	−	0.128379i
$376$	6.91460			0.356593
$377$	24.1057	−	7.83241i	1.24151	−	0.403390i
$378$	2.39680	+	3.29892i	0.123278	+	0.169678i
$379$	−3.90398	+	2.83641i	−0.200534	+	0.145696i	−0.683520	−	0.729931i	$-0.739552\pi$
$379$	−3.90398	+	2.83641i	−0.200534	+	0.145696i	0.482987	+	0.875628i	$0.339552\pi$
$380$	−3.38342	+	1.38644i	−0.173566	+	0.0711226i
$381$	0.928468	+	0.674572i	0.0475669	+	0.0345594i
$382$			9.96802i			0.510008i
$383$	−2.82343	+	3.88612i	−0.144271	+	0.198572i	−0.875037	−	0.484056i	$-0.839163\pi$
$383$	−2.82343	+	3.88612i	−0.144271	+	0.198572i	0.730766	+	0.682628i	$0.239163\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$	22.8434	−	19.3606i	1.16421	−	0.986708i
$386$	7.74814	+	23.8463i	0.394370	+	1.21375i
$387$	−8.21821	−	2.67026i	−0.417755	−	0.135737i
$388$	14.0374	+	4.56102i	0.712639	+	0.231551i
$389$	4.15372	+	12.7838i	0.210602	+	0.648166i	0.999437	+	0.0335605i	$0.0106846\pi$
$389$	4.15372	+	12.7838i	0.210602	+	0.648166i	−0.788835	+	0.614605i	$0.789315\pi$
$390$	10.3138	+	6.37425i	0.522257	+	0.322773i
$391$	−0.653716	+	2.01193i	−0.0330599	+	0.101748i
$392$	5.65890	−	7.78881i	0.285818	−	0.393394i
$393$		−	6.61907i		−	0.333888i
$394$	−21.7123	−	15.7749i	−1.09385	−	0.794727i
$395$	4.81516	−	7.79110i	0.242277	−	0.392013i
$396$	2.65688	−	1.93033i	0.133513	−	0.0970029i
$397$	−0.0509156	−	0.0700793i	−0.00255538	−	0.00351718i	0.807737	−	0.589542i	$-0.200692\pi$
$397$	−0.0509156	−	0.0700793i	−0.00255538	−	0.00351718i	−0.810293	+	0.586025i	$0.800692\pi$
$398$	−3.86237	+	1.25496i	−0.193603	+	0.0629055i
$399$	−6.66791			−0.333813
$400$	−2.23607	−	4.47214i	−0.111803	−	0.223607i
$401$	0.321141			0.0160370			0.00801851	−	0.999968i	$-0.497448\pi$
$401$	0.321141			0.0160370			0.00801851	+	0.999968i	$0.497448\pi$
$402$	10.3420	−	3.36031i	0.515811	−	0.167597i
$403$	−26.4631	−	36.4233i	−1.31822	−	1.81438i
$404$	−9.29125	+	6.75049i	−0.462257	+	0.335850i
$405$	2.17229	+	0.530249i	0.107942	+	0.0263483i
$406$	−15.4207	−	11.2038i	−0.765316	−	0.556035i
$407$		−	7.88513i		−	0.390851i
$408$	2.03353	−	2.79892i	0.100675	−	0.138567i
$409$	−7.48890	+	23.0485i	−0.370302	+	1.13967i	0.576291	+	0.817244i	$0.304499\pi$
$409$	−7.48890	+	23.0485i	−0.370302	+	1.13967i	−0.946594	+	0.322429i	$0.895501\pi$
$410$	−2.48574	−	6.06613i	−0.122762	−	0.299585i
$411$	2.29345	+	7.05850i	0.113127	+	0.348170i
$412$	−13.2719	−	4.31230i	−0.653859	−	0.212452i
$413$	−54.9784	−	17.8636i	−2.70531	−	0.879009i
$414$	0.188954	+	0.581542i	0.00928661	+	0.0285812i
$415$	−3.78126	+	15.4908i	−0.185615	+	0.760414i
$416$	1.67557	−	5.15688i	0.0821516	−	0.252837i
$417$	−3.11563	+	4.28829i	−0.152573	+	0.209999i
$418$			5.37019i			0.262665i
$419$	18.4661	+	13.4164i	0.902128	+	0.655434i	0.939012	−	0.343885i	$-0.111743\pi$
$419$	18.4661	+	13.4164i	0.902128	+	0.655434i	−0.0368836	+	0.999320i	$0.511743\pi$
$420$	−0.680881	−	9.09252i	−0.0332236	−	0.443670i
$421$	31.6567	−	22.9999i	1.54285	−	1.12095i	0.594339	−	0.804215i	$-0.297414\pi$
$421$	31.6567	−	22.9999i	1.54285	−	1.12095i	0.948514	−	0.316734i	$-0.102586\pi$
$422$	2.55973	+	3.52316i	0.124606	+	0.171505i
$423$	6.57617	−	2.13673i	0.319745	−	0.103891i
$424$	−6.79766			−0.330124
$425$	−2.57627	−	17.1053i	−0.124967	−	0.829730i
$426$	9.06706			0.439301
$427$	−48.8186	+	15.8621i	−2.36250	+	0.767622i
$428$	4.91038	+	6.75856i	0.237352	+	0.326688i
$429$	14.4063	−	10.4668i	0.695541	−	0.505340i
$430$	12.4929	+	14.7402i	0.602461	+	0.710837i
$431$	−19.9676	−	14.5073i	−0.961806	−	0.698793i	−0.00823646	−	0.999966i	$-0.502622\pi$
$431$	−19.9676	−	14.5073i	−0.961806	−	0.698793i	−0.953569	+	0.301173i	$0.902622\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−11.6839	+	16.0815i	−0.561493	+	0.772829i	−0.991515	−	0.129990i	$-0.958506\pi$
$433$	−11.6839	+	16.0815i	−0.561493	+	0.772829i	0.430023	+	0.902818i	$0.358506\pi$
$434$	−10.4626	+	32.2004i	−0.502219	+	1.54567i
$435$	−10.4233	+	0.780532i	−0.499757	+	0.0374236i
$436$	0.164593	+	0.506564i	0.00788256	+	0.0242600i
$437$	−0.950949	−	0.308982i	−0.0454901	−	0.0147806i
$438$	−8.65537	−	2.81230i	−0.413569	−	0.134377i
$439$	−1.56742	−	4.82402i	−0.0748088	−	0.230238i	0.906659	−	0.421864i	$-0.138624\pi$
$439$	−1.56742	−	4.82402i	−0.0748088	−	0.230238i	−0.981468	+	0.191626i	$0.938624\pi$
$440$	−7.32292	+	0.548367i	−0.349107	+	0.0261424i
$441$	2.97506	−	9.15630i	0.141670	−	0.436014i
$442$	11.0263	−	15.1764i	0.524469	−	0.721870i
$443$		−	10.1873i		−	0.484015i	−0.970274	−	0.242008i	$-0.922194\pi$
$443$		−	10.1873i		−	0.484015i	0.970274	−	0.242008i	$-0.0778059\pi$
$444$	−1.94246	−	1.41128i	−0.0921852	−	0.0669765i
$445$	6.94402	+	8.19318i	0.329178	+	0.388394i
$446$	0.292763	−	0.212705i	0.0138627	−	0.0100719i
$447$	−2.81723	−	3.87759i	−0.133251	−	0.183404i
$448$	−3.87811	+	1.26007i	−0.183223	+	0.0595329i
$449$	−10.3653			−0.489169			−0.244585	−	0.969628i	$-0.578652\pi$
$449$	−10.3653			−0.489169			−0.244585	+	0.969628i	$0.578652\pi$
$450$	−3.50859	−	3.56227i	−0.165397	−	0.167927i
$451$	−9.62822			−0.453375
$452$	16.3840	−	5.32350i	0.770640	−	0.250396i
$453$	−4.07649	−	5.61080i	−0.191530	−	0.263618i
$454$	10.4021	−	7.55754i	0.488193	−	0.354693i
$455$	−3.69192	−	49.3020i	−0.173080	−	2.31131i
$456$	1.32292	+	0.961158i	0.0619514	+	0.0450104i
$457$		−	4.06165i		−	0.189996i	−0.995477	−	0.0949980i	$-0.969716\pi$
$457$		−	4.06165i		−	0.189996i	0.995477	−	0.0949980i	$-0.0302845\pi$
$458$	9.71886	−	13.3769i	0.454133	−	0.625060i
$459$	1.06909	−	3.29032i	0.0499009	−	0.153579i
$460$	0.324231	−	1.32829i	0.0151173	−	0.0619317i
$461$	2.08929	+	6.43019i	0.0973081	+	0.299484i	0.987848	−	0.155421i	$-0.0496734\pi$
$461$	2.08929	+	6.43019i	0.0973081	+	0.299484i	−0.890540	+	0.454905i	$0.849673\pi$
$462$	−12.7360	−	4.13818i	−0.592533	−	0.192526i
$463$	9.24602	+	3.00421i	0.429699	+	0.139618i	0.515878	−	0.856662i	$-0.327466\pi$
$463$	9.24602	+	3.00421i	0.429699	+	0.139618i	−0.0861791	+	0.996280i	$0.527466\pi$
$464$	1.44449	+	4.44569i	0.0670589	+	0.206386i
$465$	7.03988	+	17.1799i	0.326467	+	0.796700i
$466$	−3.42101	+	10.5288i	−0.158475	+	0.487736i
$467$	22.5722	−	31.0679i	1.04452	−	1.43765i	0.151046	−	0.988527i	$-0.451736\pi$
$467$	22.5722	−	31.0679i	1.04452	−	1.43765i	0.893469	−	0.449125i	$-0.148264\pi$
$468$		−	5.42226i		−	0.250644i
$469$	−35.8730	−	26.0633i	−1.65646	−	1.20349i
$470$	−15.0205	−	3.66646i	−0.692844	−	0.169121i
$471$	6.08064	−	4.41785i	0.280181	−	0.203564i
$472$	8.33280	+	11.4691i	0.383548	+	0.527909i
$473$	26.9893	−	8.76934i	1.24097	−	0.403215i
$474$	−4.09602			−0.188137
$475$	8.08492	−	1.21768i	0.370961	−	0.0558712i
$476$	−14.1074			−0.646610
$477$	−6.46496	+	2.10059i	−0.296010	+	0.0961795i
$478$	−3.28408	−	4.52015i	−0.150210	−	0.206747i
$479$	6.85832	−	4.98286i	0.313364	−	0.227673i	−0.419974	−	0.907536i	$-0.637961\pi$
$479$	6.85832	−	4.98286i	0.313364	−	0.227673i	0.733339	+	0.679863i	$0.237961\pi$
$480$	−1.17557	+	1.90211i	−0.0536572	+	0.0868192i
$481$	−10.5325	−	7.65234i	−0.480243	−	0.348917i
$482$		−	14.8540i		−	0.676581i
$483$	1.46557	−	2.01719i	0.0666858	−	0.0917851i
$484$	0.0663845	−	0.204311i	0.00301748	−	0.00928684i
$485$	−28.0747	−	17.3511i	−1.27481	−	0.787875i
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	27.5559	+	8.95344i	1.24868	+	0.405719i	0.857446	−	0.514574i	$-0.172050\pi$
$487$	27.5559	+	8.95344i	1.24868	+	0.405719i	0.391229	+	0.920293i	$0.372050\pi$
$488$	11.9721	+	3.88998i	0.541953	+	0.176091i
$489$	−2.58560	−	7.95766i	−0.116925	−	0.359858i
$490$	−16.4228	+	13.9189i	−0.741906	+	0.628793i
$491$	−3.16018	+	9.72603i	−0.142617	+	0.438930i	−0.996697	−	0.0812121i	$-0.974121\pi$
$491$	−3.16018	+	9.72603i	−0.142617	+	0.438930i	0.854080	+	0.520142i	$0.174121\pi$
$492$	−1.72326	+	2.37186i	−0.0776906	+	0.106932i
$493$			16.1720i			0.728352i
$494$	7.17322	+	5.21165i	0.322738	+	0.234483i
$495$	−6.79506	+	2.78444i	−0.305415	+	0.125151i
$496$	6.71737	−	4.88046i	0.301619	−	0.219139i
$497$	−21.7320	−	29.9115i	−0.974811	−	1.34171i
$498$	6.78209	−	2.20363i	0.303913	−	0.0987472i
$499$	23.0007			1.02965			0.514827	−	0.857294i	$-0.327856\pi$
$499$	23.0007			1.02965			0.514827	+	0.857294i	$0.327856\pi$
$500$	2.48604	+	10.9004i	0.111179	+	0.487483i
$501$	−8.94427			−0.399601
$502$	12.0596	−	3.91840i	0.538246	−	0.174887i
$503$	11.1980	+	15.4127i	0.499293	+	0.687217i	0.982068	−	0.188527i	$-0.0603713\pi$
$503$	11.1980	+	15.4127i	0.499293	+	0.687217i	−0.482775	+	0.875744i	$0.660371\pi$
$504$	−3.29892	+	2.39680i	−0.146945	+	0.106762i
$505$	23.7627	−	9.73734i	1.05743	−	0.433306i
$506$	−1.62460	−	1.18034i	−0.0722222	−	0.0524725i
$507$		−	16.4009i		−	0.728390i
$508$	−0.674572	+	0.928468i	−0.0299293	+	0.0411941i
$509$	7.33006	−	22.5596i	0.324899	−	0.999937i	−0.646587	−	0.762840i	$-0.723804\pi$
$509$	7.33006	−	22.5596i	0.324899	−	0.999937i	0.971486	−	0.237097i	$-0.0761958\pi$
$510$	−5.90154	+	5.00177i	−0.261324	+	0.221482i
$511$	11.4677	+	35.2938i	0.507300	+	1.56131i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	1.55519	+	0.505311i	0.0686632	+	0.0223100i
$514$	−5.93053	−	18.2523i	−0.261585	−	0.805074i
$515$	26.5438	+	16.4050i	1.16966	+	0.722889i
$516$	2.67026	−	8.21821i	0.117552	−	0.361787i
$517$	−13.3475	+	18.3712i	−0.587022	+	0.807966i
$518$			9.79059i			0.430174i
$519$	1.89233	+	1.37486i	0.0830642	+	0.0603497i
$520$	−6.37425	+	10.3138i	−0.279529	+	0.452288i
$521$	−23.6577	+	17.1883i	−1.03646	+	0.753034i	−0.969592	−	0.244728i	$-0.921301\pi$
$521$	−23.6577	+	17.1883i	−1.03646	+	0.753034i	−0.0668706	+	0.997762i	$0.521301\pi$
$522$	2.74759	+	3.78173i	0.120259	+	0.165522i
$523$	−18.3703	+	5.96888i	−0.803278	+	0.261001i	−0.681748	−	0.731587i	$-0.738780\pi$
$523$	−18.3703	+	5.96888i	−0.803278	+	0.261001i	−0.121530	+	0.992588i	$0.538780\pi$
$524$	6.61907			0.289156
$525$	−3.34223	+	20.1126i	−0.145867	+	0.877786i
$526$	29.4749			1.28517
$527$	27.3200	−	8.87680i	1.19008	−	0.386679i
$528$	1.93033	+	2.65688i	0.0840070	+	0.115626i
$529$	−18.3049	+	13.2993i	−0.795865	+	0.578230i
$530$	14.7665	+	3.60445i	0.641415	+	0.156567i
$531$	11.4691	+	8.33280i	0.497717	+	0.361613i
$532$		−	6.66791i		−	0.289091i
$533$	−9.34397	+	12.8609i	−0.404732	+	0.557066i
$534$	1.48423	−	4.56799i	0.0642290	−	0.197676i
$535$	−7.08305	−	17.2853i	−0.306227	−	0.747308i
$536$	3.36031	+	10.3420i	0.145143	+	0.446705i
$537$	−5.73456	−	1.86327i	−0.247464	−	0.0804061i
$538$	−20.8300	−	6.76809i	−0.898047	−	0.291793i
$539$	9.77034	+	30.0700i	0.420838	+	1.29521i
$540$	−0.530249	+	2.17229i	−0.0228183	+	0.0934804i
$541$	−9.95316	+	30.6327i	−0.427920	+	1.31700i	0.472250	+	0.881464i	$0.343442\pi$
$541$	−9.95316	+	30.6327i	−0.427920	+	1.31700i	−0.900170	+	0.435538i	$0.856558\pi$
$542$	−8.86562	+	12.2025i	−0.380811	+	0.524141i
$543$			16.5771i			0.711392i
$544$	2.79892	+	2.03353i	0.120003	+	0.0871869i
$545$	−0.0889378	−	1.18768i	−0.00380968	−	0.0508746i
$546$	−17.8876	+	12.9961i	−0.765518	+	0.556181i
$547$	−13.0871	−	18.0129i	−0.559564	−	0.770174i	0.431707	−	0.902014i	$-0.357912\pi$
$547$	−13.0871	−	18.0129i	−0.559564	−	0.770174i	−0.991271	+	0.131840i	$0.957912\pi$
$548$	−7.05850	+	2.29345i	−0.301524	+	0.0979712i
$549$	12.5882			0.537253
$550$	16.1983	+	2.69176i	0.690696	+	0.114777i
$551$	−7.64379			−0.325637
$552$	−0.581542	+	0.188954i	−0.0247521	+	0.00804244i
$553$	9.81736	+	13.5124i	0.417476	+	0.574607i
$554$	2.09023	−	1.51864i	0.0888052	−	0.0645208i
$555$	3.47126	+	4.09570i	0.147347	+	0.173853i
$556$	−4.28829	−	3.11563i	−0.181864	−	0.132132i
$557$			15.1565i			0.642202i	0.947045	+	0.321101i	$0.104053\pi$
$557$			15.1565i			0.642202i	−0.947045	+	0.321101i	$0.895947\pi$
$558$	4.88046	−	6.71737i	0.206606	−	0.284369i
$559$	14.4788	−	44.5613i	0.612390	−	1.88474i
$560$	9.09252	−	0.680881i	0.384229	−	0.0287725i
$561$	3.51098	+	10.8057i	0.148234	+	0.456216i
$562$	−17.4975	−	5.68529i	−0.738089	−	0.239820i
$563$	19.8019	+	6.43403i	0.834551	+	0.271162i	0.694961	−	0.719047i	$-0.255421\pi$
$563$	19.8019	+	6.43403i	0.834551	+	0.271162i	0.139590	+	0.990209i	$0.455421\pi$
$564$	2.13673	+	6.57617i	0.0899725	+	0.276907i
$565$	−38.4136	+	2.87655i	−1.61607	+	0.121018i
$566$	−1.07372	+	3.30458i	−0.0451320	+	0.138902i
$567$	−2.39680	+	3.29892i	−0.100656	+	0.138541i
$568$			9.06706i			0.380445i
$569$	11.9375	+	8.67311i	0.500446	+	0.363596i	0.809187	−	0.587551i	$-0.199908\pi$
$569$	11.9375	+	8.67311i	0.500446	+	0.363596i	−0.308741	+	0.951146i	$0.599908\pi$
$570$	−2.36411	−	2.78939i	−0.0990218	−	0.116835i
$571$	4.08805	−	2.97014i	0.171080	−	0.124297i	−0.498951	−	0.866630i	$-0.666281\pi$
$571$	4.08805	−	2.97014i	0.171080	−	0.124297i	0.670030	+	0.742334i	$0.266281\pi$
$572$	10.4668	+	14.4063i	0.437638	+	0.602356i
$573$	−9.48015	+	3.08029i	−0.396039	+	0.128681i
$574$	11.9549			0.498988
$575$	−1.40865	+	2.71350i	−0.0587446	+	0.113161i
$576$	1.00000			0.0416667
$577$	5.22817	−	1.69873i	0.217651	−	0.0707193i	−0.198162	−	0.980169i	$-0.563497\pi$
$577$	5.22817	−	1.69873i	0.217651	−	0.0707193i	0.415813	+	0.909450i	$0.363497\pi$
$578$	−2.95704	−	4.07002i	−0.122997	−	0.169291i
$579$	−20.2849	+	14.7378i	−0.843012	+	0.612484i
$580$	−0.780532	−	10.4233i	−0.0324098	−	0.432802i
$581$	−23.5249	−	17.0919i	−0.975978	−	0.709090i
$582$			14.7598i			0.611812i
$583$	13.1218	−	18.0605i	0.543447	−	0.747991i
$584$	2.81230	−	8.65537i	0.116374	−	0.358162i
$585$	−2.87515	+	11.7787i	−0.118873	+	0.486990i
$586$	4.90179	+	15.0862i	0.202491	+	0.623204i
$587$	40.3229	+	13.1017i	1.66430	+	0.540765i	0.981767	−	0.190088i	$-0.0608774\pi$
$587$	40.3229	+	13.1017i	1.66430	+	0.540765i	0.682535	+	0.730853i	$0.260877\pi$
$588$	9.15630	+	2.97506i	0.377599	+	0.122689i
$589$	4.19566	+	12.9129i	0.172879	+	0.532067i
$590$	−12.0198	−	29.3327i	−0.494846	−	1.20761i
$591$	8.29335	−	25.5243i	0.341143	−	1.04993i
$592$	1.41128	−	1.94246i	0.0580033	−	0.0798348i
$593$		−	6.76110i		−	0.277645i	−0.990317	−	0.138822i	$-0.955668\pi$
$593$		−	6.76110i		−	0.277645i	0.990317	−	0.138822i	$-0.0443317\pi$
$594$	2.65688	+	1.93033i	0.109013	+	0.0792025i
$595$	30.6452	+	7.48041i	1.25633	+	0.306667i
$596$	3.87759	−	2.81723i	0.158832	−	0.115398i
$597$	−2.38708	−	3.28553i	−0.0976966	−	0.134468i
$598$	−3.15327	+	1.02456i	−0.128947	+	0.0418974i
$599$	−11.7740			−0.481074			−0.240537	−	0.970640i	$-0.577324\pi$
$599$	−11.7740			−0.481074			−0.240537	+	0.970640i	$0.577324\pi$
$600$	3.56227	−	3.50859i	0.145429	−	0.143238i
$601$	22.4353			0.915154			0.457577	−	0.889170i	$-0.348717\pi$
$601$	22.4353			0.915154			0.457577	+	0.889170i	$0.348717\pi$
$602$	−33.5113	+	10.8885i	−1.36582	+	0.443781i
$603$	6.39169	+	8.79741i	0.260290	+	0.358258i
$604$	5.61080	−	4.07649i	0.228300	−	0.165870i
$605$	−0.252542	+	0.408621i	−0.0102673	+	0.0166128i
$606$	−9.29125	−	6.75049i	−0.377431	−	0.274220i
$607$			33.0837i			1.34283i	0.741083	+	0.671413i	$0.234312\pi$
$607$			33.0837i			1.34283i	−0.741083	+	0.671413i	$0.765688\pi$
$608$	−0.961158	+	1.32292i	−0.0389801	+	0.0536515i
$609$	5.89018	−	18.1281i	0.238682	−	0.734588i
$610$	−23.9443	−	14.7984i	−0.969475	−	0.599169i
$611$	11.5859	+	35.6577i	0.468715	+	1.44256i
$612$	3.29032	+	1.06909i	0.133003	+	0.0432154i
$613$	14.5411	+	4.72470i	0.587311	+	0.190829i	0.587573	−	0.809171i	$-0.300084\pi$
$613$	14.5411	+	4.72470i	0.587311	+	0.190829i	−0.000262331		1.00000i	$0.500084\pi$
$614$	7.85279	+	24.1684i	0.316913	+	0.975358i
$615$	5.00110	−	4.23862i	0.201664	−	0.170918i
$616$	4.13818	−	12.7360i	0.166732	−	0.513149i
$617$	−6.25460	+	8.60872i	−0.251801	+	0.346574i	−0.916141	−	0.400856i	$-0.868713\pi$
$617$	−6.25460	+	8.60872i	−0.251801	+	0.346574i	0.664340	+	0.747430i	$0.268713\pi$
$618$		−	13.9549i		−	0.561348i
$619$	23.3120	+	16.9371i	0.936987	+	0.680761i	0.947693	−	0.319182i	$-0.103408\pi$
$619$	23.3120	+	16.9371i	0.936987	+	0.680761i	−0.0107068	+	0.999943i	$0.503408\pi$
$620$	−17.1799	+	7.03988i	−0.689962	+	0.282728i
$621$	−0.494689	+	0.359413i	−0.0198512	+	0.0144227i
$622$	−10.8414	−	14.9219i	−0.434702	−	0.598316i
$623$	−18.6268	+	6.05223i	−0.746268	+	0.242477i
$624$	5.42226			0.217064
$625$	0.379550	−	24.9971i	0.0151820	−	0.999885i
$626$	−21.9121			−0.875783
$627$	−5.10736	+	1.65948i	−0.203968	+	0.0662733i
$628$	4.41785	+	6.08064i	0.176291	+	0.242644i
$629$	6.72024	−	4.88254i	0.267954	−	0.194680i
$630$	8.43710	−	3.45730i	0.336142	−	0.137742i
$631$	−16.3555	−	11.8830i	−0.651102	−	0.473053i	0.212544	−	0.977151i	$-0.431825\pi$
$631$	−16.3555	−	11.8830i	−0.651102	−	0.473053i	−0.863646	+	0.504098i	$0.831825\pi$
$632$		−	4.09602i		−	0.162931i
$633$	−2.55973	+	3.52316i	−0.101740	+	0.140033i
$634$	1.78819	−	5.50349i	0.0710182	−	0.218572i
$635$	1.95768	−	1.65921i	0.0776883	−	0.0658437i
$636$	−2.10059	−	6.46496i	−0.0832939	−	0.256352i
$637$	49.6478	+	16.1316i	1.96712	+	0.639156i
$638$	−14.6000	−	4.74383i	−0.578019	−	0.187810i
$639$	2.80188	+	8.62329i	0.110841	+	0.341132i
$640$	−1.90211	−	1.17557i	−0.0751876	−	0.0464685i
$641$	−15.4707	+	47.6138i	−0.611055	+	1.88063i	−0.163002	+	0.986626i	$0.552118\pi$
$641$	−15.4707	+	47.6138i	−0.611055	+	1.88063i	−0.448053	+	0.894007i	$0.647882\pi$
$642$	−4.91038	+	6.75856i	−0.193797	+	0.266739i
$643$			11.8080i			0.465660i	0.972517	+	0.232830i	$0.0747986\pi$
$643$			11.8080i			0.465660i	−0.972517	+	0.232830i	$0.925201\pi$
$644$	2.01719	+	1.46557i	0.0794883	+	0.0577516i
$645$	−10.1583	+	16.4364i	−0.399982	+	0.647184i
$646$	−4.57684	+	3.32527i	−0.180073	+	0.130831i
$647$	−17.0969	−	23.5319i	−0.672148	−	0.925133i	0.327658	−	0.944796i	$-0.393740\pi$
$647$	−17.0969	−	23.5319i	−0.672148	−	0.925133i	−0.999807	+	0.0196636i	$0.993740\pi$
$648$	0.951057	−	0.309017i	0.0373610	−	0.0121393i
$649$	−46.5571			−1.82753
$650$	19.3156	−	19.0245i	0.757619	−	0.746202i
$651$	−33.8575			−1.32698
$652$	7.95766	−	2.58560i	0.311646	−	0.101260i
$653$	−14.5845	−	20.0738i	−0.570735	−	0.785549i	0.421906	−	0.906639i	$-0.361361\pi$
$653$	−14.5845	−	20.0738i	−0.570735	−	0.785549i	−0.992642	+	0.121090i	$0.961361\pi$
$654$	−0.430909	+	0.313074i	−0.0168499	+	0.0122422i
$655$	−14.3785	−	3.50976i	−0.561816	−	0.137137i
$656$	−2.37186	−	1.72326i	−0.0926057	−	0.0672820i
$657$		−	9.10079i		−	0.355056i
$658$	16.5729	−	22.8107i	0.646080	−	0.889253i
$659$	−5.92361	+	18.2310i	−0.230751	+	0.710179i	0.766906	+	0.641760i	$0.221795\pi$
$659$	−5.92361	+	18.2310i	−0.230751	+	0.710179i	−0.997657	+	0.0684190i	$0.978205\pi$
$660$	−2.78444	−	6.79506i	−0.108384	−	0.264497i
$661$	−14.1363	−	43.5071i	−0.549839	−	1.69223i	−0.709198	−	0.705010i	$-0.750943\pi$
$661$	−14.1363	−	43.5071i	−0.549839	−	1.69223i	0.159359	−	0.987221i	$-0.449057\pi$
$662$	−7.26954	−	2.36202i	−0.282539	−	0.0918024i
$663$	17.8410	+	5.79689i	0.692886	+	0.225132i
$664$	2.20363	+	6.78209i	0.0855176	+	0.263196i
$665$	−3.53565	+	14.4846i	−0.137107	+	0.561690i
$666$	0.741955	−	2.28350i	0.0287502	−	0.0884839i
$667$	1.68007	−	2.31241i	0.0650524	−	0.0895370i
$668$		−	8.94427i		−	0.346064i
$669$	0.292763	+	0.212705i	0.0113189	+	0.00822365i
$670$	−1.81575	−	24.2475i	−0.0701484	−	0.936764i
$671$	−33.4454	+	24.2995i	−1.29115	+	0.938072i
$672$	−2.39680	−	3.29892i	−0.0924587	−	0.127258i
$673$	20.2139	−	6.56790i	0.779189	−	0.253174i	0.107695	−	0.994184i	$-0.465653\pi$
$673$	20.2139	−	6.56790i	0.779189	−	0.253174i	0.671494	+	0.741010i	$0.265653\pi$
$674$	−3.68904			−0.142097
$675$	2.30371	−	4.43767i	0.0886697	−	0.170806i
$676$	16.4009			0.630804
$677$	41.2313	−	13.3968i	1.58465	−	0.514883i	0.621398	−	0.783495i	$-0.286565\pi$
$677$	41.2313	−	13.3968i	1.58465	−	0.514883i	0.963248	+	0.268613i	$0.0865652\pi$
$678$	10.1259	+	13.9371i	0.388883	+	0.535251i
$679$	48.6912	−	35.3762i	1.86860	−	1.35762i
$680$	−5.00177	−	5.90154i	−0.191809	−	0.226314i
$681$	10.4021	+	7.55754i	0.398608	+	0.289605i
$682$			27.2681i			1.04415i
$683$	−9.15838	+	12.6054i	−0.350436	+	0.482334i	−0.947453	−	0.319895i	$-0.896352\pi$
$683$	−9.15838	+	12.6054i	−0.350436	+	0.482334i	0.597017	+	0.802228i	$0.296352\pi$
$684$	−0.505311	+	1.55519i	−0.0193210	+	0.0594640i
$685$	16.5492	−	1.23927i	0.632313	−	0.0473499i
$686$	−3.31085	−	10.1897i	−0.126409	−	0.389046i
$687$	15.7254	+	5.10951i	0.599963	+	0.194940i
$688$	8.21821	+	2.67026i	0.313316	+	0.101803i
$689$	−11.3900	−	35.0547i	−0.433923	−	1.33548i
$690$	1.36347	−	0.102102i	0.0519064	−	0.00388694i
$691$	7.89660	−	24.3032i	0.300401	−	0.924539i	−0.680953	−	0.732328i	$-0.738434\pi$
$691$	7.89660	−	24.3032i	0.300401	−	0.924539i	0.981354	−	0.192212i	$-0.0615660\pi$
$692$	−1.37486	+	1.89233i	−0.0522643	+	0.0719357i
$693$		−	13.3914i		−	0.508699i
$694$	2.94095	+	2.13673i	0.111637	+	0.0811091i
$695$	7.66335	+	9.04190i	0.290688	+	0.342979i
$696$	−3.78173	+	2.74759i	−0.143346	+	0.104147i
$697$	−5.96188	−	8.20582i	−0.225822	−	0.310818i
$698$	11.6286	−	3.77835i	0.440148	−	0.143013i
$699$	−11.0706			−0.418729
$700$	−20.1126	−	3.34223i	−0.760185	−	0.126324i
$701$	24.7063			0.933146			0.466573	−	0.884483i	$-0.345489\pi$
$701$	24.7063			0.933146			0.466573	+	0.884483i	$0.345489\pi$
$702$	5.15688	−	1.67557i	0.194634	−	0.0632403i
$703$	2.30776	+	3.17636i	0.0870387	+	0.119799i
$704$	−2.65688	+	1.93033i	−0.100135	+	0.0727522i
$705$	−1.15458	−	15.4183i	−0.0434841	−	0.580688i
$706$	12.6725	+	9.20711i	0.476936	+	0.346514i
$707$			46.8307i			1.76125i
$708$	−8.33280	+	11.4691i	−0.313166	+	0.431036i
$709$	6.22394	−	19.1553i	0.233745	−	0.719393i	−0.763541	−	0.645760i	$-0.776541\pi$
$709$	6.22394	−	19.1553i	0.233745	−	0.719393i	0.997285	−	0.0736329i	$-0.0234593\pi$
$710$	4.80780	−	19.6963i	0.180433	−	0.739188i
$711$	−1.26574	−	3.89555i	−0.0474690	−	0.146094i
$712$	4.56799	+	1.48423i	0.171193	+	0.0556239i
$713$	−4.82862	−	1.56891i	−0.180833	−	0.0587563i
$714$	−4.35941	−	13.4169i	−0.163147	−	0.502115i
$715$	−15.0979	−	36.8446i	−0.564631	−	1.37791i
$716$	1.86327	−	5.73456i	0.0696337	−	0.214311i
$717$	3.28408	−	4.52015i	0.122646	−	0.168808i
$718$		−	7.07176i		−	0.263916i
$719$	−21.0273	−	15.2772i	−0.784187	−	0.569745i	0.122046	−	0.992524i	$-0.461055\pi$
$719$	−21.0273	−	15.2772i	−0.784187	−	0.569745i	−0.906233	+	0.422779i	$0.861055\pi$
$720$	−2.17229	−	0.530249i	−0.0809564	−	0.0197612i
$721$	−46.0360	+	33.4471i	−1.71447	+	1.24564i
$722$	9.59621	+	13.2081i	0.357134	+	0.491553i
$723$	14.1270	−	4.59014i	0.525388	−	0.170709i
$724$	−16.5771			−0.616084
$725$	−3.83138	+	23.0562i	−0.142294	+	0.856286i
$726$	0.214825			0.00797290
$727$	32.6799	−	10.6183i	1.21203	−	0.393812i	0.367856	−	0.929883i	$-0.380092\pi$
$727$	32.6799	−	10.6183i	1.21203	−	0.393812i	0.844173	+	0.536071i	$0.180092\pi$
$728$	−12.9961	−	17.8876i	−0.481667	−	0.662958i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−10.6986	+	17.3107i	−0.395974	+	0.640699i
$731$	24.1858	+	17.5720i	0.894545	+	0.649925i
$732$			12.5882i			0.465275i
$733$	18.9570	−	26.0920i	0.700192	−	0.963731i	−0.299761	−	0.954014i	$-0.596907\pi$
$733$	18.9570	−	26.0920i	0.700192	−	0.963731i	0.999953	−	0.00971697i	$-0.00309306\pi$
$734$	8.26549	−	25.4385i	0.305085	−	0.938954i
$735$	−18.3126	−	11.3178i	−0.675470	−	0.417464i
$736$	−0.188954	−	0.581542i	−0.00696495	−	0.0214359i
$737$	−33.9639	−	11.0355i	−1.25107	−	0.406499i
$738$	−2.78829	−	0.905972i	−0.102639	−	0.0333493i
$739$	−12.7515	−	39.2451i	−0.469071	−	1.44365i	−0.853789	−	0.520619i	$-0.825701\pi$
$739$	−12.7515	−	39.2451i	−0.469071	−	1.44365i	0.384718	−	0.923034i	$-0.374299\pi$
$740$	−4.09570	+	3.47126i	−0.150561	+	0.127606i
$741$	−2.73993	+	8.43263i	−0.100654	+	0.309780i
$742$	−16.2927	+	22.4249i	−0.598122	+	0.823244i
$743$		−	7.06997i		−	0.259372i	−0.991555	−	0.129686i	$-0.958603\pi$
$743$		−	7.06997i		−	0.259372i	0.991555	−	0.129686i	$-0.0413969\pi$
$744$	6.71737	+	4.88046i	0.246271	+	0.178926i
$745$	−9.91707	+	4.06375i	−0.363333	+	0.148884i
$746$	9.61502	−	6.98572i	0.352031	−	0.255765i
$747$	4.19156	+	5.76919i	0.153361	+	0.211083i
$748$	−10.8057	+	3.51098i	−0.395095	+	0.128374i
$749$	34.0652			1.24471
$750$	−9.59871	+	5.73279i	−0.350495	+	0.209332i
$751$	−4.57240			−0.166849			−0.0834246	−	0.996514i	$-0.526586\pi$
$751$	−4.57240			−0.166849			−0.0834246	+	0.996514i	$0.526586\pi$
$752$	−6.57617	+	2.13673i	−0.239808	+	0.0779185i
$753$	7.45324	+	10.2585i	0.271611	+	0.373841i
$754$	−20.5055	+	14.8981i	−0.746767	+	0.542558i
$755$	−14.3498	+	5.88018i	−0.522244	+	0.214002i
$756$	−3.29892	−	2.39680i	−0.119980	−	0.0871709i
$757$			21.1871i			0.770058i	0.922904	+	0.385029i	$0.125809\pi$
$757$			21.1871i			0.770058i	−0.922904	+	0.385029i	$0.874191\pi$
$758$	2.83641	−	3.90398i	0.103023	−	0.141799i
$759$	0.620541	−	1.90983i	0.0225242	−	0.0693224i
$760$	2.78939	−	2.36411i	0.101182	−	0.0857554i
$761$	−9.84246	−	30.2920i	−0.356789	−	1.09808i	−0.954965	−	0.296718i	$-0.904108\pi$
$761$	−9.84246	−	30.2920i	−0.356789	−	1.09808i	0.598176	−	0.801365i	$-0.295892\pi$
$762$	−1.09148	−	0.354643i	−0.0395402	−	0.0128474i
$763$	2.06561	+	0.671157i	0.0747801	+	0.0242975i
$764$	−3.08029	−	9.48015i	−0.111441	−	0.342980i
$765$	−6.58064	−	4.06706i	−0.237924	−	0.147045i
$766$	1.48437	−	4.56841i	0.0536324	−	0.165063i
$767$	−45.1826	+	62.1885i	−1.63145	+	2.24550i
$768$			1.00000i			0.0360844i
$769$	−7.38487	−	5.36542i	−0.266305	−	0.193482i	0.446617	−	0.894725i	$-0.352629\pi$
$769$	−7.38487	−	5.36542i	−0.266305	−	0.193482i	−0.712922	+	0.701243i	$0.752629\pi$
$770$	−15.7426	+	25.4720i	−0.567323	+	0.917948i
$771$	15.5263	−	11.2805i	0.559167	−	0.406259i
$772$	−14.7378	−	20.2849i	−0.530427	−	0.730069i
$773$	37.1998	−	12.0870i	1.33798	−	0.434738i	0.449351	−	0.893355i	$-0.351655\pi$
$773$	37.1998	−	12.0870i	1.33798	−	0.434738i	0.888634	+	0.458618i	$0.151655\pi$
$774$	8.64114			0.310599
$775$	41.0526	−	6.18302i	1.47465	−	0.222101i
$776$	−14.7598			−0.529845
$777$	−9.31140	+	3.02546i	−0.334045	+	0.108538i
$778$	−7.90084	−	10.8746i	−0.283259	−	0.389872i
$779$	3.87852	−	2.81791i	0.138962	−	0.100962i
$780$	−11.7787	−	2.87515i	−0.421746	−	0.102947i
$781$	−24.0901	−	17.5025i	−0.862010	−	0.626287i
$782$		−	2.11547i		−	0.0756491i
$783$	−2.74759	+	3.78173i	−0.0981908	+	0.135148i
$784$	−2.97506	+	9.15630i	−0.106252	+	0.327011i
$785$	−6.37258	−	15.5515i	−0.227447	−	0.555056i
$786$	2.04541	+	6.29511i	0.0729572	+	0.224539i
$787$	−25.7764	−	8.37524i	−0.918828	−	0.298545i	−0.188842	−	0.982008i	$-0.560473\pi$
$787$	−25.7764	−	8.37524i	−0.918828	−	0.298545i	−0.729986	+	0.683462i	$0.760473\pi$
$788$	25.5243	+	8.29335i	0.909266	+	0.295438i
$789$	9.10825	+	28.0323i	0.324262	+	0.997977i
$790$	−2.17191	+	8.89774i	−0.0772731	+	0.316567i
$791$	21.7075	−	66.8089i	0.771831	−	2.37545i
$792$	−1.93033	+	2.65688i	−0.0685914	+	0.0944080i
$793$			68.2568i			2.42387i
$794$	0.0700793	+	0.0509156i	0.00248702	+	0.00180693i
$795$	1.13506	+	15.1576i	0.0402563	+	0.537584i
$796$	3.28553	−	2.38708i	0.116453	−	0.0846077i
$797$	−7.78292	−	10.7123i	−0.275685	−	0.379448i	0.648614	−	0.761118i	$-0.275349\pi$
$797$	−7.78292	−	10.7123i	−0.275685	−	0.379448i	−0.924299	+	0.381670i	$0.875349\pi$
$798$	6.34156	−	2.06050i	0.224489	−	0.0729408i
$799$	−23.9221			−0.846303
$800$	3.50859	+	3.56227i	0.124047	+	0.125945i
$801$	4.80307			0.169708
$802$	−0.305423	+	0.0992381i	−0.0107849	+	0.00350422i
$803$	17.5676	+	24.1797i	0.619946	+	0.853282i
$804$	−8.79741	+	6.39169i	−0.310261	+	0.225418i
$805$	−3.60479	−	4.25325i	−0.127052	−	0.149908i
$806$	36.4233	+	26.4631i	1.28296	+	0.932123i
$807$		−	21.9020i		−	0.770987i
$808$	6.75049	−	9.29125i	0.237481	−	0.326865i
$809$	2.32740	−	7.16299i	0.0818269	−	0.251837i	−0.901770	−	0.432215i	$-0.857732\pi$
$809$	2.32740	−	7.16299i	0.0818269	−	0.251837i	0.983597	+	0.180378i	$0.0577321\pi$
$810$	−2.22982	+	0.166977i	−0.0783481	+	0.00586699i
$811$	−8.28844	−	25.5092i	−0.291046	−	0.895749i	−0.984521	−	0.175267i	$-0.943921\pi$
$811$	−8.28844	−	25.5092i	−0.291046	−	0.895749i	0.693475	−	0.720481i	$-0.256079\pi$
$812$	18.1281	+	5.89018i	0.636172	+	0.206705i
$813$	−14.3449	−	4.66093i	−0.503097	−	0.163466i
$814$	2.43664	+	7.49920i	0.0854042	+	0.262847i
$815$	−18.6573	+	1.39713i	−0.653538	+	0.0489393i
$816$	−1.06909	+	3.29032i	−0.0374257	+	0.115184i
$817$	−8.30550	+	11.4315i	−0.290573	+	0.399939i
$818$		−	24.2346i		−	0.847343i
$819$	−17.8876	−	12.9961i	−0.625043	−	0.454120i
$820$	4.23862	+	5.00110i	0.148019	+	0.174646i
$821$	−30.1027	+	21.8709i	−1.05059	+	0.763298i	−0.972325	−	0.233634i	$-0.924938\pi$
$821$	−30.1027	+	21.8709i	−1.05059	+	0.763298i	−0.0782654	+	0.996933i	$0.524938\pi$
$822$	−4.36240	−	6.00432i	−0.152156	−	0.209425i
$823$	17.0656	−	5.54495i	0.594870	−	0.193285i	0.00391871	−	0.999992i	$-0.498753\pi$
$823$	17.0656	−	5.54495i	0.594870	−	0.193285i	0.590951	+	0.806707i	$0.298753\pi$
$824$	13.9549			0.486142
$825$	2.44553	+	16.2373i	0.0851423	+	0.565309i
$826$	57.8077			2.01139
$827$	16.0984	−	5.23070i	0.559798	−	0.181889i	−0.0154325	−	0.999881i	$-0.504913\pi$
$827$	16.0984	−	5.23070i	0.559798	−	0.181889i	0.575230	+	0.817992i	$0.304913\pi$
$828$	−0.359413	−	0.494689i	−0.0124905	−	0.0171916i
$829$	41.6780	−	30.2809i	1.44754	−	1.05170i	0.461138	−	0.887328i	$-0.347441\pi$
$829$	41.6780	−	30.2809i	1.44754	−	1.05170i	0.986399	−	0.164369i	$-0.0525589\pi$
$830$	−1.19073	−	15.9011i	−0.0413310	−	0.551936i
$831$	2.09023	+	1.51864i	0.0725091	+	0.0526810i
$832$			5.42226i			0.187983i
$833$	−19.5778	+	26.9466i	−0.678331	+	0.933643i
$834$	1.63798	−	5.04119i	0.0567187	−	0.174562i
$835$	−4.74269	+	19.4295i	−0.164128	+	0.672387i
$836$	−1.65948	−	5.10736i	−0.0573943	−	0.176642i
$837$	7.89675	+	2.56581i	0.272951	+	0.0886873i
$838$	−21.7082	−	7.05342i	−0.749897	−	0.243656i
$839$	−6.86327	−	21.1230i	−0.236946	−	0.729246i	−0.996857	−	0.0792188i	$-0.974757\pi$
$839$	−6.86327	−	21.1230i	−0.236946	−	0.729246i	0.759911	−	0.650027i	$-0.225243\pi$
$840$	3.45730	+	8.43710i	0.119288	+	0.291107i
$841$	−2.20925	+	6.79938i	−0.0761811	+	0.234461i
$842$	−22.9999	+	31.6567i	−0.792630	+	1.09096i
$843$		−	18.3980i		−	0.633661i
$844$	−3.52316	−	2.55973i	−0.121272	−	0.0881095i
$845$	−35.6275	−	8.69656i	−1.22562	−	0.299171i
$846$	−5.59403	+	4.06430i	−0.192327	+	0.139733i
$847$	−0.514893	−	0.708689i	−0.0176919	−	0.0243508i
$848$	6.46496	−	2.10059i	0.222008	−	0.0721347i
$849$	−3.47464			−0.119249
$850$	7.73601	+	15.4720i	0.265343	+	0.530686i
$851$	−1.46815			−0.0503275
$852$	−8.62329	+	2.80188i	−0.295429	+	0.0959907i
$853$	20.8778	+	28.7359i	0.714843	+	0.983897i	0.999679	+	0.0253210i	$0.00806080\pi$
$853$	20.8778	+	28.7359i	0.714843	+	0.983897i	−0.284836	+	0.958576i	$0.591939\pi$
$854$	41.5276	−	30.1715i	1.42104	−	1.03245i
$855$	1.92232	−	3.11037i	0.0657418	−	0.106373i
$856$	−6.75856	−	4.91038i	−0.231003	−	0.167833i
$857$		−	35.9714i		−	1.22876i	−0.789010	−	0.614380i	$-0.789406\pi$
$857$		−	35.9714i		−	1.22876i	0.789010	−	0.614380i	$-0.210594\pi$
$858$	−10.4668	+	14.4063i	−0.357330	+	0.491822i
$859$	−14.5608	+	44.8137i	−0.496809	+	1.52902i	0.317308	+	0.948322i	$0.397221\pi$
$859$	−14.5608	+	44.8137i	−0.496809	+	1.52902i	−0.814118	+	0.580700i	$0.802779\pi$
$860$	−16.4364	−	10.1583i	−0.560478	−	0.346394i
$861$	3.69427	+	11.3698i	0.125900	+	0.387481i
$862$	23.4733	+	7.62695i	0.799505	+	0.259775i
$863$	38.4902	+	12.5062i	1.31022	+	0.425716i	0.879125	−	0.476590i	$-0.158128\pi$
$863$	38.4902	+	12.5062i	1.31022	+	0.425716i	0.431095	+	0.902307i	$0.358128\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	3.99000	−	3.38167i	0.135664	−	0.114980i
$866$	6.14259	−	18.9050i	0.208734	−	0.642417i
$867$	2.95704	−	4.07002i	0.100427	−	0.138225i
$868$		−	33.8575i		−	1.14920i
$869$	10.8826	+	7.90669i	0.369168	+	0.268216i
$870$	9.67191	−	3.96329i	0.327908	−	0.134368i
$871$	−47.7018	+	34.6574i	−1.61631	+	1.17432i
$872$	−0.313074	−	0.430909i	−0.0106020	−	0.0145924i
$873$	−14.0374	+	4.56102i	−0.475093	+	0.154367i
$874$	0.999887			0.0338217
$875$	41.9182	+	17.9250i	1.41709	+	0.605974i
$876$	9.10079			0.307487
$877$	−12.9166	+	4.19687i	−0.436164	+	0.141718i	−0.518865	−	0.854856i	$-0.673645\pi$
$877$	−12.9166	+	4.19687i	−0.436164	+	0.141718i	0.0827012	+	0.996574i	$0.473645\pi$
$878$	2.98141	+	4.10355i	0.100618	+	0.138488i
$879$	−12.8331	+	9.32376i	−0.432848	+	0.314483i
$880$	6.79506	−	2.78444i	0.229061	−	0.0938633i
$881$	−24.3625	−	17.7004i	−0.820793	−	0.596341i	0.0961468	−	0.995367i	$-0.469348\pi$
$881$	−24.3625	−	17.7004i	−0.820793	−	0.596341i	−0.916939	+	0.399026i	$0.869348\pi$
$882$			9.62750i			0.324175i
$883$	2.80047	−	3.85451i	0.0942433	−	0.129715i	−0.759291	−	0.650751i	$-0.774454\pi$
$883$	2.80047	−	3.85451i	0.0942433	−	0.129715i	0.853535	+	0.521036i	$0.174454\pi$
$884$	−5.79689	+	17.8410i	−0.194970	+	0.600057i
$885$	24.1827	−	20.4958i	0.812894	−	0.688958i
$886$	3.14806	+	9.68874i	0.105761	+	0.325500i
$887$	38.4028	+	12.4778i	1.28944	+	0.418965i	0.871896	−	0.489692i	$-0.162891\pi$
$887$	38.4028	+	12.4778i	1.28944	+	0.418965i	0.417545	+	0.908656i	$0.362891\pi$
$888$	2.28350	+	0.741955i	0.0766293	+	0.0248984i
$889$	1.44612	+	4.45071i	0.0485014	+	0.149272i
$890$	−9.13599	−	5.64635i	−0.306239	−	0.189266i
$891$	−1.01484	+	3.12334i	−0.0339983	+	0.104636i
$892$	−0.212705	+	0.292763i	−0.00712189	+	0.00980244i
$893$		−	11.3069i		−	0.378371i
$894$	3.87759	+	2.81723i	0.129686	+	0.0942223i
$895$	−7.08831	+	11.4691i	−0.236936	+	0.383370i
$896$	3.29892	−	2.39680i	0.110209	−	0.0800715i
$897$	−1.94883	−	2.68233i	−0.0650695	−	0.0895605i
$898$	9.85800	−	3.20306i	0.328966	−	0.106887i
$899$	−38.8128			−1.29448
$900$	4.43767	+	2.30371i	0.147922	+	0.0767902i
$901$	23.5175			0.783482
$902$	9.15698	−	2.97528i	0.304894	−	0.0990661i
$903$	−20.7111	−	28.5064i	−0.689223	−	0.948633i
$904$	−13.9371	+	10.1259i	−0.463541	+	0.336782i
$905$	36.0103	+	8.79000i	1.19702	+	0.292189i
$906$	5.61080	+	4.07649i	0.186406	+	0.135432i
$907$		−	22.3227i		−	0.741214i	−0.928790	−	0.370607i	$-0.879150\pi$
$907$		−	22.3227i		−	0.741214i	0.928790	−	0.370607i	$-0.120850\pi$
$908$	−7.55754	+	10.4021i	−0.250806	+	0.345204i
$909$	3.54894	−	10.9225i	0.117711	−	0.362277i
$910$	18.7464	+	45.7481i	0.621436	+	1.51654i
$911$	0.241832	+	0.744283i	0.00801226	+	0.0246592i	0.954983	−	0.296661i	$-0.0958733\pi$
$911$	0.241832	+	0.744283i	0.00801226	+	0.0246592i	−0.946970	+	0.321321i	$0.895873\pi$
$912$	−1.55519	−	0.505311i	−0.0514974	−	0.0167325i
$913$	−22.2729	−	7.23691i	−0.737126	−	0.239507i
$914$	1.25512	+	3.86286i	0.0415156	+	0.127772i
$915$	6.67490	−	27.3453i	0.220665	−	0.904008i
$916$	−5.10951	+	15.7254i	−0.168823	+	0.519583i
$917$	15.8646	−	21.8358i	0.523896	−	0.721080i
$918$			3.45965i			0.114185i
$919$	−1.59426	−	1.15830i	−0.0525897	−	0.0382087i	0.561180	−	0.827694i	$-0.310348\pi$
$919$	−1.59426	−	1.15830i	−0.0525897	−	0.0382087i	−0.613770	+	0.789485i	$0.710348\pi$
$920$	0.102102	+	1.36347i	0.00336619	+	0.0449523i
$921$	−20.5589	+	14.9369i	−0.677438	+	0.492188i
$922$	−3.97407	−	5.46984i	−0.130879	−	0.180140i
$923$	−46.7577	+	15.1925i	−1.53905	+	0.500067i
$924$	13.3914			0.440546
$925$	10.7377	−	5.36884i	0.353053	−	0.176526i
$926$	−9.72184			−0.319480
$927$	13.2719	−	4.31230i	0.435906	−	0.141634i
$928$	−2.74759	−	3.78173i	−0.0901940	−	0.124141i
$929$	−19.1823	+	13.9368i	−0.629352	+	0.457251i	−0.856176	−	0.516685i	$-0.827166\pi$
$929$	−19.1823	+	13.9368i	−0.629352	+	0.457251i	0.226824	+	0.973936i	$0.427166\pi$
$930$	−12.0042	−	14.1636i	−0.393634	−	0.464444i
$931$	−12.7364	−	9.25355i	−0.417419	−	0.303273i
$932$		−	11.0706i		−	0.362630i
$933$	10.8414	−	14.9219i	0.354932	−	0.488523i
$934$	−11.8669	+	36.5225i	−0.388296	+	1.19505i
$935$	25.3347	−	1.89716i	0.828535	−	0.0620437i
$936$	1.67557	+	5.15688i	0.0547677	+	0.168558i
$937$	−16.8801	−	5.48469i	−0.551450	−	0.179177i	0.0200205	−	0.999800i	$-0.493627\pi$
$937$	−16.8801	−	5.48469i	−0.551450	−	0.179177i	−0.571471	+	0.820623i	$0.693627\pi$
$938$	42.1713	+	13.7023i	1.37694	+	0.447395i
$939$	−6.77121	−	20.8396i	−0.220970	−	0.680076i
$940$	15.4183	−	1.15458i	0.502891	−	0.0376583i
$941$	15.3815	−	47.3393i	0.501422	−	1.54322i	−0.305281	−	0.952262i	$-0.598750\pi$
$941$	15.3815	−	47.3393i	0.501422	−	1.54322i	0.806703	−	0.590956i	$-0.201250\pi$
$942$	−4.41785	+	6.08064i	−0.143941	+	0.198118i
$943$			1.79270i			0.0583783i
$944$	−11.4691	−	8.33280i	−0.373288	−	0.271210i
$945$	5.89529	+	6.95579i	0.191774	+	0.226272i
$946$	−22.9584	+	16.6803i	−0.746443	+	0.542323i
$947$	−2.65398	−	3.65289i	−0.0862428	−	0.118703i	0.763716	−	0.645553i	$-0.223373\pi$
$947$	−2.65398	−	3.65289i	−0.0862428	−	0.118703i	−0.849958	+	0.526850i	$0.823373\pi$
$948$	3.89555	−	1.26574i	0.126522	−	0.0411093i
$949$	49.3469			1.60187
$950$	−7.31293	+	3.65646i	−0.237263	+	0.118631i
$951$	5.78671			0.187647
$952$	13.4169	−	4.35941i	0.434844	−	0.141289i
$953$	5.48579	+	7.55054i	0.177702	+	0.244586i	0.888572	−	0.458738i	$-0.151698\pi$
$953$	5.48579	+	7.55054i	0.177702	+	0.244586i	−0.710869	+	0.703324i	$0.751698\pi$
$954$	5.49942	−	3.99557i	0.178050	−	0.129361i
$955$	1.66444	+	22.2269i	0.0538599	+	0.719247i
$956$	4.52015	+	3.28408i	0.146192	+	0.106215i
$957$		−	15.3513i		−	0.496238i
$958$	−4.98286	+	6.85832i	−0.160989	+	0.221582i
$959$	−9.35195	+	28.7823i	−0.301990	+	0.929430i
$960$	0.530249	−	2.17229i	0.0171137	−	0.0701103i
$961$	11.7247	+	36.0850i	0.378217	+	1.16403i
$962$	12.3817	+	4.02307i	0.399204	+	0.129709i
$963$	−7.94517	−	2.58154i	−0.256030	−	0.0831890i
$964$	4.59014	+	14.1270i	0.147838	+	0.454999i
$965$	21.2588	+	51.8794i	0.684345	+	1.67006i
$966$	−0.770497	+	2.37134i	−0.0247903	+	0.0762968i
$967$	−13.0799	+	18.0029i	−0.420620	+	0.578934i	−0.965769	−	0.259405i	$-0.916473\pi$
$967$	−13.0799	+	18.0029i	−0.420620	+	0.578934i	0.545148	+	0.838340i	$0.316473\pi$
$968$			0.214825i			0.00690473i
$969$	−4.57684	−	3.32527i	−0.147029	−	0.106823i
$970$	32.0625	+	7.82635i	1.02946	+	0.251289i
$971$	−3.55705	+	2.58435i	−0.114151	+	0.0829357i	−0.643396	−	0.765533i	$-0.722475\pi$
$971$	−3.55705	+	2.58435i	−0.114151	+	0.0829357i	0.529245	+	0.848469i	$0.322475\pi$
$972$	0.587785	+	0.809017i	0.0188532	+	0.0259492i
$973$	−20.5564	+	6.67917i	−0.659007	+	0.214124i
$974$	−28.9739			−0.928385
$975$	24.0622	+	12.4913i	0.770608	+	0.400042i
$976$	−12.5882			−0.402940
$977$	−14.1016	+	4.58190i	−0.451151	+	0.146588i	−0.525775	−	0.850624i	$-0.676225\pi$
$977$	−14.1016	+	4.58190i	−0.451151	+	0.146588i	0.0746235	+	0.997212i	$0.476225\pi$
$978$	4.91810	+	6.76919i	0.157264	+	0.216455i
$979$	−12.7612	+	9.27153i	−0.407849	+	0.296319i
$980$	11.3178	−	18.3126i	0.361534	−	0.584975i
$981$	−0.430909	−	0.313074i	−0.0137579	−	0.00999569i
$982$		−	10.2266i		−	0.326343i
$983$	10.6096	−	14.6028i	0.338393	−	0.465758i	−0.605578	−	0.795786i	$-0.707058\pi$
$983$	10.6096	−	14.6028i	0.338393	−	0.465758i	0.943971	+	0.330028i	$0.107058\pi$
$984$	0.905972	−	2.78829i	0.0288813	−	0.0888876i
$985$	−51.0486	−	31.5498i	−1.62654	−	1.00526i
$986$	−4.99744	−	15.3805i	−0.159151	−	0.489816i
$987$	26.8156	+	8.71290i	0.853549	+	0.277335i
$988$	−8.43263	−	2.73993i	−0.268278	−	0.0871687i
$989$	−1.63278	−	5.02519i	−0.0519195	−	0.159792i
$990$	5.60205	−	4.74794i	0.178045	−	0.150900i
$991$	−17.0781	+	52.5608i	−0.542502	+	1.66965i	0.184353	+	0.982860i	$0.440981\pi$
$991$	−17.0781	+	52.5608i	−0.542502	+	1.66965i	−0.726856	+	0.686790i	$0.759019\pi$
$992$	−4.88046	+	6.71737i	−0.154955	+	0.213277i
$993$		−	7.64365i		−	0.242564i
$994$	29.9115	+	21.7320i	0.948734	+	0.689296i
$995$	−8.40287	+	3.44327i	−0.266389	+	0.109159i
$996$	−5.76919	+	4.19156i	−0.182804	+	0.132815i
$997$	−9.56346	−	13.1630i	−0.302878	−	0.416875i	0.630266	−	0.776379i	$-0.282946\pi$
$997$	−9.56346	−	13.1630i	−0.302878	−	0.416875i	−0.933144	+	0.359504i	$0.882946\pi$
$998$	−21.8750	+	7.10761i	−0.692440	+	0.224987i
$999$	2.40102			0.0759648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.h.a.19.1	✓	8
3.2	odd	2		450.2.l.a.19.2		8
5.2	odd	4		750.2.g.e.151.2		8
5.3	odd	4		750.2.g.c.151.1		8
5.4	even	2		750.2.h.c.349.2		8
25.2	odd	20		3750.2.a.m.1.4		4
25.3	odd	20		750.2.g.c.601.1		8
25.4	even	10	inner	150.2.h.a.79.1	yes	8
25.11	even	5		3750.2.c.e.1249.5		8
25.14	even	10		3750.2.c.e.1249.4		8
25.21	even	5		750.2.h.c.649.2		8
25.22	odd	20		750.2.g.e.601.2		8
25.23	odd	20		3750.2.a.o.1.1		4
75.29	odd	10		450.2.l.a.379.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.19.1	✓	8	1.1	even	1	trivial
150.2.h.a.79.1	yes	8	25.4	even	10	inner
450.2.l.a.19.2		8	3.2	odd	2
450.2.l.a.379.2		8	75.29	odd	10
750.2.g.c.151.1		8	5.3	odd	4
750.2.g.c.601.1		8	25.3	odd	20
750.2.g.e.151.2		8	5.2	odd	4
750.2.g.e.601.2		8	25.22	odd	20
750.2.h.c.349.2		8	5.4	even	2
750.2.h.c.649.2		8	25.21	even	5
3750.2.a.m.1.4		4	25.2	odd	20
3750.2.a.o.1.1		4	25.23	odd	20
3750.2.c.e.1249.4		8	25.14	even	10
3750.2.c.e.1249.5		8	25.11	even	5

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.06909 + 0.847859i) q^{5} +(0.809017 + 0.587785i) q^{6} -4.07768i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.06909 + 0.847859i) q^{5} +(0.809017 + 0.587785i) q^{6} -4.07768i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.70582 - 1.44575i) q^{10} +(-1.01484 - 3.12334i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(-5.15688 - 1.67557i) q^{13} +(1.26007 + 3.87811i) q^{14} +(1.90211 + 1.17557i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.03353 - 2.79892i) q^{17} -1.00000i q^{18} +(1.32292 + 0.961158i) q^{19} +(-1.17557 + 1.90211i) q^{20} +(-3.29892 + 2.39680i) q^{21} +(1.93033 + 2.65688i) q^{22} +(-0.581542 + 0.188954i) q^{23} +1.00000 q^{24} +(3.56227 - 3.50859i) q^{25} +5.42226 q^{26} +(0.951057 - 0.309017i) q^{27} +(-2.39680 - 3.29892i) q^{28} +(-3.78173 + 2.74759i) q^{29} +(-2.17229 - 0.530249i) q^{30} +(6.71737 + 4.88046i) q^{31} +1.00000i q^{32} +(-1.93033 + 2.65688i) q^{33} +(-1.06909 + 3.29032i) q^{34} +(3.45730 + 8.43710i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.28350 + 0.741955i) q^{37} +(-1.55519 - 0.505311i) q^{38} +(1.67557 + 5.15688i) q^{39} +(0.530249 - 2.17229i) q^{40} +(0.905972 - 2.78829i) q^{41} +(2.39680 - 3.29892i) q^{42} +8.64114i q^{43} +(-2.65688 - 1.93033i) q^{44} +(-0.166977 - 2.22982i) q^{45} +(0.494689 - 0.359413i) q^{46} +(-4.06430 - 5.59403i) q^{47} +(-0.951057 + 0.309017i) q^{48} -9.62750 q^{49} +(-2.30371 + 4.43767i) q^{50} -3.45965 q^{51} +(-5.15688 + 1.67557i) q^{52} +(3.99557 + 5.49942i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(4.74794 + 5.60205i) q^{55} +(3.29892 + 2.39680i) q^{56} -1.63522i q^{57} +(2.74759 - 3.78173i) q^{58} +(4.38081 - 13.4828i) q^{59} +(2.22982 - 0.166977i) q^{60} +(-3.88998 - 11.9721i) q^{61} +(-7.89675 - 2.56581i) q^{62} +(3.87811 + 1.26007i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(12.0907 - 0.905395i) q^{65} +(1.01484 - 3.12334i) q^{66} +(6.39169 - 8.79741i) q^{67} -3.45965i q^{68} +(0.494689 + 0.359413i) q^{69} +(-5.89529 - 6.95579i) q^{70} +(7.33541 - 5.32949i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-8.65537 + 2.81230i) q^{73} -2.40102 q^{74} +(-4.93236 - 0.819639i) q^{75} +1.63522 q^{76} +(-12.7360 + 4.13818i) q^{77} +(-3.18712 - 4.38670i) q^{78} +(-3.31375 + 2.40758i) q^{79} +(0.166977 + 2.22982i) q^{80} +(-0.809017 - 0.587785i) q^{81} +2.93179i q^{82} +(4.19156 - 5.76919i) q^{83} +(-1.26007 + 3.87811i) q^{84} +(-1.83447 + 7.51536i) q^{85} +(-2.67026 - 8.21821i) q^{86} +(4.44569 + 1.44449i) q^{87} +(3.12334 + 1.01484i) q^{88} +(-1.48423 - 4.56799i) q^{89} +(0.847859 + 2.06909i) q^{90} +(-6.83245 + 21.0281i) q^{91} +(-0.359413 + 0.494689i) q^{92} -8.30313i q^{93} +(5.59403 + 4.06430i) q^{94} +(-3.55217 - 0.867073i) q^{95} +(0.809017 - 0.587785i) q^{96} +(8.67557 + 11.9409i) q^{97} +(9.15630 - 2.97506i) q^{98} +3.28408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	\( 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} - 20 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} - 8 q^{19} - 2 q^{21} - 10 q^{23} + 8 q^{24} - 10 q^{25} + 4 q^{26} - 10 q^{28} - 22 q^{29} - 10 q^{30} + 24 q^{31} + 8 q^{34} + 10 q^{35} - 2 q^{36} - 20 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} + 10 q^{42} + 10 q^{46} + 10 q^{47} + 8 q^{49} - 20 q^{50} - 12 q^{51} - 20 q^{52} - 30 q^{53} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 30 q^{58} - 20 q^{59} + 10 q^{60} + 10 q^{62} + 10 q^{63} + 2 q^{64} + 20 q^{65} - 10 q^{66} + 10 q^{67} + 10 q^{69} - 10 q^{70} + 20 q^{71} - 20 q^{73} - 4 q^{74} - 20 q^{75} - 12 q^{76} - 20 q^{77} + 16 q^{79} - 2 q^{81} + 70 q^{83} + 2 q^{84} + 20 q^{85} - 18 q^{86} - 30 q^{87} + 10 q^{88} - 34 q^{89} - 10 q^{90} - 24 q^{91} + 30 q^{92} + 30 q^{94} + 30 q^{95} + 2 q^{96} + 60 q^{97} + 20 q^{98} + 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 - 20 * q^13 - 2 * q^14 - 2 * q^16 + 10 * q^17 - 8 * q^19 - 2 * q^21 - 10 * q^23 + 8 * q^24 - 10 * q^25 + 4 * q^26 - 10 * q^28 - 22 * q^29 - 10 * q^30 + 24 * q^31 + 8 * q^34 + 10 * q^35 - 2 * q^36 - 20 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 + 10 * q^42 + 10 * q^46 + 10 * q^47 + 8 * q^49 - 20 * q^50 - 12 * q^51 - 20 * q^52 - 30 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 30 * q^58 - 20 * q^59 + 10 * q^60 + 10 * q^62 + 10 * q^63 + 2 * q^64 + 20 * q^65 - 10 * q^66 + 10 * q^67 + 10 * q^69 - 10 * q^70 + 20 * q^71 - 20 * q^73 - 4 * q^74 - 20 * q^75 - 12 * q^76 - 20 * q^77 + 16 * q^79 - 2 * q^81 + 70 * q^83 + 2 * q^84 + 20 * q^85 - 18 * q^86 - 30 * q^87 + 10 * q^88 - 34 * q^89 - 10 * q^90 - 24 * q^91 + 30 * q^92 + 30 * q^94 + 30 * q^95 + 2 * q^96 + 60 * q^97 + 20 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more