LMFDB - Embedded newform 546.2.bk.b.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(25,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("546.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bk (of order $6$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.5
Root			$-1.75780 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.25
Dual form			546.2.bk.b.415.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.294342 + 0.169938i) q^{5} +1.00000i q^{6} +(-0.420136 - 2.61218i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.294342 + 0.169938i) q^{5} +1.00000i q^{6} +(-0.420136 - 2.61218i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.169938 + 0.294342i) q^{10} +(0.571683 + 0.330062i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.660123 - 3.54461i) q^{13} +(-1.66994 - 2.05215i) q^{14} -0.339877i q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.27230 - 5.66780i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(5.27341 - 3.04461i) q^{19} +0.339877i q^{20} +(2.47228 + 0.942242i) q^{21} +0.660123 q^{22} +(3.71455 + 6.43378i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.44224 + 4.23009i) q^{25} +(-1.20062 - 3.39978i) q^{26} +1.00000 q^{27} +(-2.47228 - 0.942242i) q^{28} -3.56424 q^{29} +(-0.169938 - 0.294342i) q^{30} +(-3.46410 - 2.00000i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.571683 + 0.330062i) q^{33} -6.54461i q^{34} +(0.567573 + 0.697477i) q^{35} -1.00000 q^{36} +(3.06972 - 1.77230i) q^{37} +(3.04461 - 5.27341i) q^{38} +(2.73966 + 2.34399i) q^{39} +(0.169938 + 0.294342i) q^{40} +0.864853i q^{41} +(2.61218 - 0.420136i) q^{42} -5.08921 q^{43} +(0.571683 - 0.330062i) q^{44} +(0.294342 + 0.169938i) q^{45} +(6.43378 + 3.71455i) q^{46} +(8.18283 - 4.72436i) q^{47} +1.00000 q^{48} +(-6.64697 + 2.19494i) q^{49} +4.88448i q^{50} +(3.27230 + 5.66780i) q^{51} +(-2.73966 - 2.34399i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.866025 - 0.500000i) q^{54} -0.224361 q^{55} +(-2.61218 + 0.420136i) q^{56} +6.08921i q^{57} +(-3.08672 + 1.78212i) q^{58} +(3.38106 + 1.95206i) q^{59} +(-0.294342 - 0.169938i) q^{60} +(-0.932427 - 1.61501i) q^{61} -4.00000 q^{62} +(-2.05215 + 1.66994i) q^{63} -1.00000 q^{64} +(0.408063 + 1.15551i) q^{65} +(-0.330062 + 0.571683i) q^{66} +(-6.45078 - 3.72436i) q^{67} +(-3.27230 - 5.66780i) q^{68} -7.42909 q^{69} +(0.840272 + 0.320246i) q^{70} -0.884484i q^{71} +(-0.866025 + 0.500000i) q^{72} +(-8.72051 - 5.03479i) q^{73} +(1.77230 - 3.06972i) q^{74} +(-2.44224 - 4.23009i) q^{75} -6.08921i q^{76} +(0.621996 - 1.63201i) q^{77} +(3.54461 + 0.660123i) q^{78} +(6.22436 + 10.7809i) q^{79} +(0.294342 + 0.169938i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.432427 + 0.748985i) q^{82} +16.2939i q^{83} +(2.05215 - 1.66994i) q^{84} +2.22436i q^{85} +(-4.40739 + 2.54461i) q^{86} +(1.78212 - 3.08672i) q^{87} +(0.330062 - 0.571683i) q^{88} +(-3.85848 + 2.22770i) q^{89} +0.339877 q^{90} +(-9.53649 - 0.235144i) q^{91} +7.42909 q^{92} +(3.46410 - 2.00000i) q^{93} +(4.72436 - 8.18283i) q^{94} +(-1.03479 + 1.79231i) q^{95} +(0.866025 - 0.500000i) q^{96} +16.1088i q^{97} +(-4.65898 + 5.22436i) q^{98} -0.660123i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9} + 6 q^{12} + 12 q^{13} - 18 q^{14} - 6 q^{16} + 18 q^{17} + 12 q^{22} - 6 q^{25} + 12 q^{27} + 12 q^{29} + 24 q^{35} - 12 q^{36} - 6 q^{38} - 6 q^{39} + 6 q^{42} + 24 q^{43} + 12 q^{48} - 18 q^{49} + 18 q^{51} + 6 q^{52} - 18 q^{53} + 48 q^{55} - 6 q^{56} + 6 q^{61} - 48 q^{62} - 12 q^{64} - 12 q^{65} - 6 q^{66} - 18 q^{68} - 6 q^{75} - 24 q^{77} + 24 q^{79} - 6 q^{81} - 12 q^{82} - 6 q^{87} + 6 q^{88} - 24 q^{91} + 6 q^{94} + 24 q^{95}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9 + 6 * q^12 + 12 * q^13 - 18 * q^14 - 6 * q^16 + 18 * q^17 + 12 * q^22 - 6 * q^25 + 12 * q^27 + 12 * q^29 + 24 * q^35 - 12 * q^36 - 6 * q^38 - 6 * q^39 + 6 * q^42 + 24 * q^43 + 12 * q^48 - 18 * q^49 + 18 * q^51 + 6 * q^52 - 18 * q^53 + 48 * q^55 - 6 * q^56 + 6 * q^61 - 48 * q^62 - 12 * q^64 - 12 * q^65 - 6 * q^66 - 18 * q^68 - 6 * q^75 - 24 * q^77 + 24 * q^79 - 6 * q^81 - 12 * q^82 - 6 * q^87 + 6 * q^88 - 24 * q^91 + 6 * q^94 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.294342	+	0.169938i	−0.131634	+	0.0759988i	−0.564371	−	0.825521i	$-0.690881\pi$
$5$	−0.294342	+	0.169938i	−0.131634	+	0.0759988i	0.432737	+	0.901520i	$0.357548\pi$
$6$			1.00000i			0.408248i
$7$	−0.420136	−	2.61218i	−0.158796	−	0.987311i
$7$	−0.420136	−	2.61218i	−0.158796	−	0.987311i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.169938	+	0.294342i	−0.0537393	+	0.0930791i
$11$	0.571683	+	0.330062i	0.172369	+	0.0995173i	0.583702	−	0.811968i	$-0.301603\pi$
$11$	0.571683	+	0.330062i	0.172369	+	0.0995173i	−0.411333	+	0.911485i	$0.634937\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.660123	−	3.54461i	0.183085	−	0.983097i
$13$	0.660123	−	3.54461i	0.183085	−	0.983097i
$14$	−1.66994	−	2.05215i	−0.446310	−	0.548459i
$15$		−	0.339877i		−	0.0877558i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.27230	−	5.66780i	0.793650	−	1.37464i	−0.130043	−	0.991508i	$-0.541511\pi$
$17$	3.27230	−	5.66780i	0.793650	−	1.37464i	0.923693	−	0.383134i	$-0.125155\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	5.27341	−	3.04461i	1.20980	−	0.698481i	0.247088	−	0.968993i	$-0.420526\pi$
$19$	5.27341	−	3.04461i	1.20980	−	0.698481i	0.962716	+	0.270512i	$0.0871931\pi$
$20$			0.339877i			0.0759988i
$21$	2.47228	+	0.942242i	0.539496	+	0.205614i
$22$	0.660123			0.140739
$23$	3.71455	+	6.43378i	0.774536	+	1.34154i	0.935055	+	0.354503i	$0.115350\pi$
$23$	3.71455	+	6.43378i	0.774536	+	1.34154i	−0.160519	+	0.987033i	$0.551317\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−2.44224	+	4.23009i	−0.488448	+	0.846017i
$26$	−1.20062	−	3.39978i	−0.235461	−	0.666752i
$27$	1.00000			0.192450
$28$	−2.47228	−	0.942242i	−0.467217	−	0.178067i
$29$	−3.56424			−0.661862			−0.330931	−	0.943655i	$-0.607363\pi$
$29$	−3.56424			−0.661862			−0.330931	+	0.943655i	$0.607363\pi$
$30$	−0.169938	−	0.294342i	−0.0310264	−	0.0537393i
$31$	−3.46410	−	2.00000i	−0.622171	−	0.359211i	0.155543	−	0.987829i	$-0.450287\pi$
$31$	−3.46410	−	2.00000i	−0.622171	−	0.359211i	−0.777714	+	0.628619i	$0.783621\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.571683	+	0.330062i	−0.0995173	+	0.0574563i
$34$		−	6.54461i		−	1.12239i
$35$	0.567573	+	0.697477i	0.0959374	+	0.117895i
$36$	−1.00000			−0.166667
$37$	3.06972	−	1.77230i	0.504659	−	0.291365i	−0.225977	−	0.974133i	$-0.572557\pi$
$37$	3.06972	−	1.77230i	0.504659	−	0.291365i	0.730635	+	0.682768i	$0.239224\pi$
$38$	3.04461	−	5.27341i	0.493900	−	0.855461i
$39$	2.73966	+	2.34399i	0.438696	+	0.375338i
$40$	0.169938	+	0.294342i	0.0268696	+	0.0465396i
$41$			0.864853i			0.135067i	0.997717	+	0.0675337i	$0.0215130\pi$
$41$			0.864853i			0.135067i	−0.997717	+	0.0675337i	$0.978487\pi$
$42$	2.61218	−	0.420136i	0.403068	−	0.0648284i
$43$	−5.08921			−0.776098			−0.388049	−	0.921639i	$-0.626851\pi$
$43$	−5.08921			−0.776098			−0.388049	+	0.921639i	$0.626851\pi$
$44$	0.571683	−	0.330062i	0.0861845	−	0.0497587i
$45$	0.294342	+	0.169938i	0.0438779	+	0.0253329i
$46$	6.43378	+	3.71455i	0.948609	+	0.547680i
$47$	8.18283	−	4.72436i	1.19359	−	0.689119i	0.234470	−	0.972123i	$-0.424664\pi$
$47$	8.18283	−	4.72436i	1.19359	−	0.689119i	0.959119	+	0.283004i	$0.0913311\pi$
$48$	1.00000			0.144338
$49$	−6.64697	+	2.19494i	−0.949567	+	0.313563i
$50$			4.88448i			0.690770i
$51$	3.27230	+	5.66780i	0.458214	+	0.793650i
$52$	−2.73966	−	2.34399i	−0.379922	−	0.325052i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−0.224361			−0.0302528
$56$	−2.61218	+	0.420136i	−0.349067	+	0.0561430i
$57$			6.08921i			0.806536i
$58$	−3.08672	+	1.78212i	−0.405306	+	0.234004i
$59$	3.38106	+	1.95206i	0.440177	+	0.254136i	0.703673	−	0.710524i	$-0.251542\pi$
$59$	3.38106	+	1.95206i	0.440177	+	0.254136i	−0.263496	+	0.964661i	$0.584876\pi$
$60$	−0.294342	−	0.169938i	−0.0379994	−	0.0219390i
$61$	−0.932427	−	1.61501i	−0.119385	−	0.206781i	0.800139	−	0.599814i	$-0.204759\pi$
$61$	−0.932427	−	1.61501i	−0.119385	−	0.206781i	−0.919524	+	0.393034i	$0.871426\pi$
$62$	−4.00000			−0.508001
$63$	−2.05215	+	1.66994i	−0.258546	+	0.210392i
$64$	−1.00000			−0.125000
$65$	0.408063	+	1.15551i	0.0506140	+	0.143323i
$66$	−0.330062	+	0.571683i	−0.0406278	+	0.0703694i
$67$	−6.45078	−	3.72436i	−0.788088	−	0.455003i	0.0512007	−	0.998688i	$-0.483695\pi$
$67$	−6.45078	−	3.72436i	−0.788088	−	0.455003i	−0.839289	+	0.543685i	$0.817029\pi$
$68$	−3.27230	−	5.66780i	−0.396825	−	0.687321i
$69$	−7.42909			−0.894357
$70$	0.840272	+	0.320246i	0.100432	+	0.0382767i
$71$		−	0.884484i		−	0.104969i	−0.998622	−	0.0524845i	$-0.983286\pi$
$71$		−	0.884484i		−	0.104969i	0.998622	−	0.0524845i	$-0.0167140\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−8.72051	−	5.03479i	−1.02066	−	0.589278i	−0.106364	−	0.994327i	$-0.533921\pi$
$73$	−8.72051	−	5.03479i	−1.02066	−	0.589278i	−0.914295	+	0.405049i	$0.867254\pi$
$74$	1.77230	−	3.06972i	0.206026	−	0.356848i
$75$	−2.44224	−	4.23009i	−0.282006	−	0.488448i
$76$		−	6.08921i		−	0.698481i
$77$	0.621996	−	1.63201i	0.0708830	−	0.185985i
$78$	3.54461	+	0.660123i	0.401348	+	0.0747442i
$79$	6.22436	+	10.7809i	0.700295	+	1.21295i	0.968363	+	0.249547i	$0.0802817\pi$
$79$	6.22436	+	10.7809i	0.700295	+	1.21295i	−0.268067	+	0.963400i	$0.586385\pi$
$80$	0.294342	+	0.169938i	0.0329084	+	0.0189997i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.432427	+	0.748985i	0.0477535	+	0.0827115i
$83$			16.2939i			1.78849i	0.447575	+	0.894246i	$0.352288\pi$
$83$			16.2939i			1.78849i	−0.447575	+	0.894246i	$0.647712\pi$
$84$	2.05215	−	1.66994i	0.223908	−	0.182205i
$85$			2.22436i			0.241266i
$86$	−4.40739	+	2.54461i	−0.475261	+	0.274392i
$87$	1.78212	−	3.08672i	0.191063	−	0.330931i
$88$	0.330062	−	0.571683i	0.0351847	−	0.0609417i
$89$	−3.85848	+	2.22770i	−0.408998	+	0.236135i	−0.690359	−	0.723467i	$-0.742548\pi$
$89$	−3.85848	+	2.22770i	−0.408998	+	0.236135i	0.281361	+	0.959602i	$0.409214\pi$
$90$	0.339877			0.0358262
$91$	−9.53649	−	0.235144i	−0.999696	−	0.0246498i
$92$	7.42909			0.774536
$93$	3.46410	−	2.00000i	0.359211	−	0.207390i
$94$	4.72436	−	8.18283i	0.487281	−	0.843995i
$95$	−1.03479	+	1.79231i	−0.106167	+	0.183887i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$			16.1088i			1.63561i	0.575499	+	0.817803i	$0.304808\pi$
$97$			16.1088i			1.63561i	−0.575499	+	0.817803i	$0.695192\pi$
$98$	−4.65898	+	5.22436i	−0.470628	+	0.527740i
$99$		−	0.660123i		−	0.0663449i
$100$	2.44224	+	4.23009i	0.244224	+	0.423009i
$101$	−1.39764	+	2.42077i	−0.139070	+	0.240876i	−0.927145	−	0.374703i	$-0.877745\pi$
$101$	−1.39764	+	2.42077i	−0.139070	+	0.240876i	0.788075	+	0.615579i	$0.211078\pi$
$102$	5.66780	+	3.27230i	0.561195	+	0.324006i
$103$	3.76897	+	6.52804i	0.371367	+	0.643227i	0.989776	−	0.142629i	$-0.0455557\pi$
$103$	3.76897	+	6.52804i	0.371367	+	0.643227i	−0.618409	+	0.785857i	$0.712222\pi$
$104$	−3.54461	−	0.660123i	−0.347577	−	0.0647304i
$105$	−0.887820	+	0.142794i	−0.0866423	+	0.0139353i
$106$			3.00000i			0.291386i
$107$	1.86485	+	3.23002i	0.180282	+	0.312258i	0.941977	−	0.335679i	$-0.108966\pi$
$107$	1.86485	+	3.23002i	0.180282	+	0.312258i	−0.761694	+	0.647936i	$0.775632\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−12.4790	−	7.20473i	−1.19527	−	0.690088i	−0.235771	−	0.971809i	$-0.575762\pi$
$109$	−12.4790	−	7.20473i	−1.19527	−	0.690088i	−0.959496	+	0.281721i	$0.909095\pi$
$110$	−0.194302	+	0.112180i	−0.0185260	+	0.0106960i
$111$			3.54461i			0.336439i
$112$	−2.05215	+	1.66994i	−0.193910	+	0.157794i
$113$	15.5576			1.46353			0.731766	−	0.681556i	$-0.238696\pi$
$113$	15.5576			1.46353			0.731766	+	0.681556i	$0.238696\pi$
$114$	3.04461	+	5.27341i	0.285154	+	0.493900i
$115$	−2.18669	−	1.26249i	−0.203910	−	0.117728i
$116$	−1.78212	+	3.08672i	−0.165466	+	0.286595i
$117$	−3.39978	+	1.20062i	−0.314310	+	0.110997i
$118$	3.90411			0.359403
$119$	−16.1801	−	6.16660i	−1.48323	−	0.565292i
$120$	−0.339877			−0.0310264
$121$	−5.28212	−	9.14890i	−0.480193	−	0.831718i
$122$	−1.61501	−	0.932427i	−0.146216	−	0.0844179i
$123$	−0.748985	−	0.432427i	−0.0675337	−	0.0389906i
$124$	−3.46410	+	2.00000i	−0.311086	+	0.179605i
$125$		−	3.35951i		−	0.300483i
$126$	−0.942242	+	2.47228i	−0.0839416	+	0.220248i
$127$	14.4028			1.27804			0.639020	−	0.769190i	$-0.279340\pi$
$127$	14.4028			1.27804			0.639020	+	0.769190i	$0.279340\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.54461	−	4.40739i	0.224040	−	0.388049i
$130$	0.931146	+	0.796667i	0.0816669	+	0.0698723i
$131$	10.3365	+	17.9034i	0.903108	+	1.56423i	0.823437	+	0.567407i	$0.192053\pi$
$131$	10.3365	+	17.9034i	0.903108	+	1.56423i	0.0796705	+	0.996821i	$0.474613\pi$
$132$			0.660123i			0.0574563i
$133$	−10.1686	−	12.4960i	−0.881730	−	1.08354i
$134$	−7.44872			−0.643472
$135$	−0.294342	+	0.169938i	−0.0253329	+	0.0146260i
$136$	−5.66780	−	3.27230i	−0.486009	−	0.280598i
$137$	12.3187	+	7.11218i	1.05245	+	0.607635i	0.923335	−	0.383995i	$-0.125452\pi$
$137$	12.3187	+	7.11218i	1.05245	+	0.607635i	0.129119	+	0.991629i	$0.458785\pi$
$138$	−6.43378	+	3.71455i	−0.547680	+	0.316203i
$139$	9.42909			0.799765			0.399883	−	0.916566i	$-0.369051\pi$
$139$	9.42909			0.799765			0.399883	+	0.916566i	$0.369051\pi$
$140$	0.887820	−	0.142794i	0.0750345	−	0.0120683i
$141$			9.44872i			0.795726i
$142$	−0.442242	−	0.765985i	−0.0371121	−	0.0642801i
$143$	1.54732	−	1.80851i	0.129393	−	0.151235i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.04910	−	0.605701i	0.0871234	−	0.0503007i
$146$	−10.0696			−0.833365
$147$	1.42261	−	6.85392i	0.117335	−	0.565302i
$148$		−	3.54461i		−	0.291365i
$149$	−7.02247	+	4.05442i	−0.575303	+	0.332151i	−0.759264	−	0.650782i	$-0.774441\pi$
$149$	−7.02247	+	4.05442i	−0.575303	+	0.332151i	0.183962	+	0.982933i	$0.441108\pi$
$150$	−4.23009	−	2.44224i	−0.345385	−	0.199408i
$151$	4.59047	+	2.65031i	0.373567	+	0.215679i	0.675016	−	0.737803i	$-0.264137\pi$
$151$	4.59047	+	2.65031i	0.373567	+	0.215679i	−0.301449	+	0.953482i	$0.597470\pi$
$152$	−3.04461	−	5.27341i	−0.246950	−	0.427730i
$153$	−6.54461			−0.529100
$154$	−0.277341	−	1.72436i	−0.0223488	−	0.138953i
$155$	1.35951			0.109198
$156$	3.39978	−	1.20062i	0.272200	−	0.0961265i
$157$	11.5281	−	19.9673i	0.920044	−	1.59356i	0.120700	−	0.992689i	$-0.461486\pi$
$157$	11.5281	−	19.9673i	0.920044	−	1.59356i	0.799344	−	0.600874i	$-0.205181\pi$
$158$	10.7809	+	6.22436i	0.857683	+	0.495184i
$159$	−1.50000	−	2.59808i	−0.118958	−	0.206041i
$160$	0.339877			0.0268696
$161$	15.2456	−	12.4061i	1.20152	−	0.977740i
$162$			1.00000i			0.0785674i
$163$	−11.7470	+	6.78212i	−0.920094	+	0.531217i	−0.883665	−	0.468120i	$-0.844932\pi$
$163$	−11.7470	+	6.78212i	−0.920094	+	0.531217i	−0.0364290	+	0.999336i	$0.511598\pi$
$164$	0.748985	+	0.432427i	0.0584859	+	0.0337668i
$165$	0.112180	−	0.194302i	0.00873322	−	0.0151264i
$166$	8.14697	+	14.1110i	0.632328	+	1.09522i
$167$			15.7034i			1.21517i	0.794256	+	0.607583i	$0.207861\pi$
$167$			15.7034i			1.21517i	−0.794256	+	0.607583i	$0.792139\pi$
$168$	0.942242	−	2.47228i	0.0726955	−	0.190741i
$169$	−12.1285	−	4.67975i	−0.932960	−	0.359981i
$170$	1.11218	+	1.92635i	0.0853003	+	0.147745i
$171$	−5.27341	−	3.04461i	−0.403268	−	0.232827i
$172$	−2.54461	+	4.40739i	−0.194024	+	0.336060i
$173$	−6.80175	−	11.7810i	−0.517127	−	0.895691i	−0.999802	−	0.0198913i	$-0.993668\pi$
$173$	−6.80175	−	11.7810i	−0.517127	−	0.895691i	0.482675	−	0.875800i	$-0.339665\pi$
$174$		−	3.56424i		−	0.270204i
$175$	12.0758	+	4.60236i	0.912846	+	0.347906i
$176$		−	0.660123i		−	0.0497587i
$177$	−3.38106	+	1.95206i	−0.254136	+	0.146726i
$178$	−2.22770	+	3.85848i	−0.166973	+	0.289206i
$179$	−0.224361	+	0.388604i	−0.0167695	+	0.0290456i	−0.874288	−	0.485407i	$-0.838671\pi$
$179$	−0.224361	+	0.388604i	−0.0167695	+	0.0290456i	0.857519	+	0.514453i	$0.172005\pi$
$180$	0.294342	−	0.169938i	0.0219390	−	0.0126665i
$181$	−15.9041			−1.18214			−0.591072	−	0.806619i	$-0.701295\pi$
$181$	−15.9041			−1.18214			−0.591072	+	0.806619i	$0.701295\pi$
$182$	−8.37642	+	4.56461i	−0.620901	+	0.338351i
$183$	1.86485			0.137854
$184$	6.43378	−	3.71455i	0.474305	−	0.273840i
$185$	−0.602365	+	1.04333i	−0.0442868	+	0.0767069i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	3.74144	−	2.16012i	0.273601	−	0.157964i
$188$		−	9.44872i		−	0.689119i
$189$	−0.420136	−	2.61218i	−0.0305604	−	0.190008i
$190$			2.06958i			0.150143i
$191$	5.20473	+	9.01486i	0.376601	+	0.652292i	0.990565	−	0.137042i	$-0.0437594\pi$
$191$	5.20473	+	9.01486i	0.376601	+	0.652292i	−0.613964	+	0.789334i	$0.710426\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	6.66786	+	3.84969i	0.479963	+	0.277107i	0.720401	−	0.693558i	$-0.243958\pi$
$193$	6.66786	+	3.84969i	0.479963	+	0.277107i	−0.240438	+	0.970665i	$0.577291\pi$
$194$	8.05442	+	13.9507i	0.578274	+	1.00160i
$195$	−1.20473	−	0.224361i	−0.0862725	−	0.0160668i
$196$	−1.42261	+	6.85392i	−0.101615	+	0.489565i
$197$		−	8.98037i		−	0.639825i	−0.947447	−	0.319912i	$-0.896347\pi$
$197$		−	8.98037i		−	0.639825i	0.947447	−	0.319912i	$-0.103653\pi$
$198$	−0.330062	−	0.571683i	−0.0234565	−	0.0406278i
$199$	10.2973	−	17.8354i	0.729955	−	1.26432i	−0.226947	−	0.973907i	$-0.572874\pi$
$199$	10.2973	−	17.8354i	0.729955	−	1.26432i	0.956902	−	0.290412i	$-0.0937922\pi$
$200$	4.23009	+	2.44224i	0.299112	+	0.172693i
$201$	6.45078	−	3.72436i	0.455003	−	0.262696i
$202$			2.79527i			0.196675i
$203$	1.49746	+	9.31043i	0.105101	+	0.653464i
$204$	6.54461			0.458214
$205$	−0.146972	−	0.254563i	−0.0102650	−	0.0177794i
$206$	6.52804	+	3.76897i	0.454830	+	0.262596i
$207$	3.71455	−	6.43378i	0.258179	−	0.447179i
$208$	−3.39978	+	1.20062i	−0.235732	+	0.0832480i
$209$	4.01963			0.278044
$210$	−0.697477	+	0.567573i	−0.0481305	+	0.0391663i
$211$	15.3898			1.05948			0.529740	−	0.848160i	$-0.322290\pi$
$211$	15.3898			1.05948			0.529740	+	0.848160i	$0.322290\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$	0.765985	+	0.442242i	0.0524845	+	0.0303019i
$214$	3.23002	+	1.86485i	0.220800	+	0.127479i
$215$	1.49797	−	0.864853i	0.102161	−	0.0589825i
$216$		−	1.00000i		−	0.0680414i
$217$	−3.76897	+	9.88913i	−0.255854	+	0.671318i
$218$	−14.4095			−0.975932
$219$	8.72051	−	5.03479i	0.589278	−	0.340220i
$220$	−0.112180	+	0.194302i	−0.00756319	+	0.0130998i
$221$	−17.9300	−	15.3405i	−1.20610	−	1.03191i
$222$	1.77230	+	3.06972i	0.118949	+	0.206026i
$223$		−	18.0196i		−	1.20668i	−0.797483	−	0.603342i	$-0.793835\pi$
$223$		−	18.0196i		−	1.20668i	0.797483	−	0.603342i	$-0.206165\pi$
$224$	−0.942242	+	2.47228i	−0.0629562	+	0.165186i
$225$	4.88448			0.325632
$226$	13.4732	−	7.77878i	0.896227	−	0.517437i
$227$	−0.200080	−	0.115516i	−0.0132798	−	0.00766709i	0.493345	−	0.869833i	$-0.335774\pi$
$227$	−0.200080	−	0.115516i	−0.0132798	−	0.00766709i	−0.506625	+	0.862166i	$0.669107\pi$
$228$	5.27341	+	3.04461i	0.349240	+	0.201634i
$229$	5.75084	−	3.32025i	0.380026	−	0.219408i	−0.297804	−	0.954627i	$-0.596254\pi$
$229$	5.75084	−	3.32025i	0.380026	−	0.219408i	0.677830	+	0.735219i	$0.262921\pi$
$230$	−2.52498			−0.166492
$231$	1.10236	+	1.35467i	0.0725303	+	0.0891307i
$232$			3.56424i			0.234004i
$233$	14.7592	+	25.5636i	0.966904	+	1.67473i	0.704410	+	0.709794i	$0.251212\pi$
$233$	14.7592	+	25.5636i	0.966904	+	1.67473i	0.262495	+	0.964933i	$0.415455\pi$
$234$	−2.34399	+	2.73966i	−0.153231	+	0.179097i
$235$	−1.60570	+	2.78116i	−0.104744	+	0.181423i
$236$	3.38106	−	1.95206i	0.220088	−	0.127068i
$237$	−12.4487			−0.808631
$238$	−17.0957	+	2.74962i	−1.10815	+	0.178232i
$239$		−	15.0236i		−	0.971799i	−0.874015	−	0.485900i	$-0.838492\pi$
$239$		−	15.0236i		−	0.971799i	0.874015	−	0.485900i	$-0.161508\pi$
$240$	−0.294342	+	0.169938i	−0.0189997	+	0.0109695i
$241$	3.85271	+	2.22436i	0.248175	+	0.143284i	0.618928	−	0.785448i	$-0.287567\pi$
$241$	3.85271	+	2.22436i	0.248175	+	0.143284i	−0.370754	+	0.928731i	$0.620901\pi$
$242$	−9.14890	−	5.28212i	−0.588113	−	0.339547i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.86485			−0.119385
$245$	1.58348	−	1.77564i	0.101165	−	0.113441i
$246$	−0.864853			−0.0551410
$247$	−7.31083	−	20.7020i	−0.465177	−	1.31724i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$	−14.1110	−	8.14697i	−0.894246	−	0.516293i
$250$	−1.67975	−	2.90942i	−0.106237	−	0.184008i
$251$	−24.3961			−1.53987			−0.769935	−	0.638123i	$-0.779711\pi$
$251$	−24.3961			−1.53987			−0.769935	+	0.638123i	$0.779711\pi$
$252$	0.420136	+	2.61218i	0.0264661	+	0.164552i
$253$			4.90411i			0.308319i
$254$	12.4732	−	7.20139i	0.782637	−	0.451856i
$255$	−1.92635	−	1.11218i	−0.120633	−	0.0696474i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.22436	−	15.9771i	−0.575400	−	0.996622i	−0.995998	−	0.0893747i	$-0.971513\pi$
$257$	−9.22436	−	15.9771i	−0.575400	−	0.996622i	0.420598	−	0.907247i	$-0.361820\pi$
$258$		−	5.08921i		−	0.316841i
$259$	−5.91928	−	7.27405i	−0.367806	−	0.451988i
$260$	1.20473	+	0.224361i	0.0747142	+	0.0139143i
$261$	1.78212	+	3.08672i	0.110310	+	0.191063i
$262$	17.9034	+	10.3365i	1.10608	+	0.638594i
$263$	3.15031	−	5.45649i	0.194256	−	0.336462i	−0.752400	−	0.658706i	$-0.771104\pi$
$263$	3.15031	−	5.45649i	0.194256	−	0.336462i	0.946656	+	0.322245i	$0.104437\pi$
$264$	0.330062	+	0.571683i	0.0203139	+	0.0351847i
$265$		−	1.01963i		−	0.0626354i
$266$	−15.0543	−	5.73751i	−0.923036	−	0.351789i
$267$		−	4.45539i		−	0.272666i
$268$	−6.45078	+	3.72436i	−0.394044	+	0.227502i
$269$	4.94759	−	8.56947i	0.301660	−	0.522490i	−0.674852	−	0.737953i	$-0.735793\pi$
$269$	4.94759	−	8.56947i	0.301660	−	0.522490i	0.976512	+	0.215463i	$0.0691260\pi$
$270$	−0.169938	+	0.294342i	−0.0103421	+	0.0179131i
$271$	−10.9980	+	6.34969i	−0.668080	+	0.385716i	−0.795349	−	0.606152i	$-0.792712\pi$
$271$	−10.9980	+	6.34969i	−0.668080	+	0.385716i	0.127269	+	0.991868i	$0.459379\pi$
$272$	−6.54461			−0.396825
$273$	4.97189	−	8.14127i	0.300912	−	0.492732i
$274$	14.2244			0.859325
$275$	−2.79238	+	1.61218i	−0.168387	+	0.0972181i
$276$	−3.71455	+	6.43378i	−0.223589	+	0.387268i
$277$	−14.0216	+	24.2862i	−0.842479	+	1.45922i	0.0453142	+	0.998973i	$0.485571\pi$
$277$	−14.0216	+	24.2862i	−0.842479	+	1.45922i	−0.887793	+	0.460243i	$0.847762\pi$
$278$	8.16583	−	4.71455i	0.489754	−	0.282760i
$279$			4.00000i			0.239474i
$280$	0.697477	−	0.567573i	0.0416822	−	0.0339190i
$281$			1.82157i			0.108666i	0.998523	+	0.0543330i	$0.0173032\pi$
$281$			1.82157i			0.108666i	−0.998523	+	0.0543330i	$0.982697\pi$
$282$	4.72436	+	8.18283i	0.281332	+	0.487281i
$283$	−4.49018	+	7.77723i	−0.266914	+	0.462308i	−0.968063	−	0.250706i	$-0.919337\pi$
$283$	−4.49018	+	7.77723i	−0.266914	+	0.462308i	0.701149	+	0.713014i	$0.252671\pi$
$284$	−0.765985	−	0.442242i	−0.0454529	−	0.0262422i
$285$	−1.03479	−	1.79231i	−0.0612958	−	0.106167i
$286$	0.435763	−	2.33988i	0.0257672	−	0.138360i
$287$	2.25915	−	0.363356i	0.133354	−	0.0214482i
$288$			1.00000i			0.0589256i
$289$	−12.9159	−	22.3711i	−0.759761	−	1.31594i
$290$	0.605701	−	1.04910i	0.0355680	−	0.0616056i
$291$	−13.9507	−	8.05442i	−0.817803	−	0.472159i
$292$	−8.72051	+	5.03479i	−0.510330	+	0.294639i
$293$			2.80194i			0.163691i	0.996645	+	0.0818456i	$0.0260814\pi$
$293$			2.80194i			0.163691i	−0.996645	+	0.0818456i	$0.973919\pi$
$294$	−2.19494	−	6.64697i	−0.128012	−	0.387659i
$295$	−1.32692			−0.0772562
$296$	−1.77230	−	3.06972i	−0.103013	−	0.178424i
$297$	0.571683	+	0.330062i	0.0331724	+	0.0191521i
$298$	−4.05442	+	7.02247i	−0.234866	+	0.406800i
$299$	25.2573	−	8.91951i	1.46067	−	0.515829i
$300$	−4.88448			−0.282006
$301$	2.13816	+	13.2939i	0.123242	+	0.766250i
$302$	5.30062			0.305016
$303$	−1.39764	−	2.42077i	−0.0802920	−	0.139070i
$304$	−5.27341	−	3.04461i	−0.302451	−	0.174620i
$305$	0.548905	+	0.316910i	0.0314302	+	0.0181462i
$306$	−5.66780	+	3.27230i	−0.324006	+	0.187065i
$307$			9.21769i			0.526081i	0.964785	+	0.263041i	$0.0847253\pi$
$307$			9.21769i			0.526081i	−0.964785	+	0.263041i	$0.915275\pi$
$308$	−1.10236	−	1.35467i	−0.0628131	−	0.0771895i
$309$	−7.53793			−0.428818
$310$	1.17737	−	0.679754i	0.0668700	−	0.0386074i
$311$	5.73418	−	9.93188i	0.325155	−	0.563185i	−0.656388	−	0.754423i	$-0.727917\pi$
$311$	5.73418	−	9.93188i	0.325155	−	0.563185i	0.981544	+	0.191238i	$0.0612501\pi$
$312$	2.34399	−	2.73966i	0.132702	−	0.155103i
$313$	11.2821	+	19.5412i	0.637703	+	1.10453i	0.985936	+	0.167126i	$0.0534486\pi$
$313$	11.2821	+	19.5412i	0.637703	+	1.10453i	−0.348233	+	0.937408i	$0.613218\pi$
$314$		−	23.0562i		−	1.30114i
$315$	0.320246	−	0.840272i	0.0180438	−	0.0473439i
$316$	12.4487			0.700295
$317$	−10.9354	+	6.31357i	−0.614195	+	0.354606i	−0.774605	−	0.632445i	$-0.782052\pi$
$317$	−10.9354	+	6.31357i	−0.614195	+	0.354606i	0.160410	+	0.987050i	$0.448718\pi$
$318$	−2.59808	−	1.50000i	−0.145693	−	0.0841158i
$319$	−2.03762	−	1.17642i	−0.114085	−	0.0658667i
$320$	0.294342	−	0.169938i	0.0164542	−	0.00949985i
$321$	−3.72971			−0.208172
$322$	7.00000	−	18.3668i	0.390095	−	1.02354i
$323$		−	39.8515i		−	2.21740i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	13.3818	+	11.4492i	0.742290	+	0.635085i
$326$	−6.78212	+	11.7470i	−0.375627	+	0.650605i
$327$	12.4790	−	7.20473i	0.690088	−	0.398422i
$328$	0.864853			0.0477535
$329$	−15.7788	−	19.3902i	−0.869912	−	1.06901i
$330$		−	0.224361i		−	0.0123506i
$331$	23.2278	−	13.4106i	1.27672	−	0.737113i	0.300474	−	0.953790i	$-0.402855\pi$
$331$	23.2278	−	13.4106i	1.27672	−	0.737113i	0.976243	+	0.216677i	$0.0695219\pi$
$332$	14.1110	+	8.14697i	0.774440	+	0.447123i
$333$	−3.06972	−	1.77230i	−0.168220	−	0.0971216i
$334$	7.85170	+	13.5995i	0.429626	+	0.744134i
$335$	2.53165			0.138319
$336$	−0.420136	−	2.61218i	−0.0229203	−	0.142506i
$337$	9.81892			0.534871			0.267435	−	0.963576i	$-0.413824\pi$
$337$	9.81892			0.534871			0.267435	+	0.963576i	$0.413824\pi$
$338$	−12.8434	+	2.01145i	−0.698591	+	0.109409i
$339$	−7.77878	+	13.4732i	−0.422485	+	0.731766i
$340$	1.92635	+	1.11218i	0.104471	+	0.0603164i
$341$	−1.32025	−	2.28673i	−0.0714953	−	0.123834i
$342$	−6.08921			−0.329267
$343$	8.52621	+	16.4409i	0.460372	+	0.887726i
$344$			5.08921i			0.274392i
$345$	2.18669	−	1.26249i	0.117728	−	0.0679701i
$346$	−11.7810	−	6.80175i	−0.633349	−	0.365664i
$347$	−9.54794	+	16.5375i	−0.512560	+	0.887781i	0.487334	+	0.873216i	$0.337970\pi$
$347$	−9.54794	+	16.5375i	−0.512560	+	0.887781i	−0.999894	+	0.0145648i	$0.995364\pi$
$348$	−1.78212	−	3.08672i	−0.0955316	−	0.165466i
$349$		−	0.416132i		−	0.0222750i	−0.999938	−	0.0111375i	$-0.996455\pi$
$349$		−	0.416132i		−	0.0222750i	0.999938	−	0.0111375i	$-0.00354525\pi$
$350$	12.7592	−	2.05215i	0.682005	−	0.109692i
$351$	0.660123	−	3.54461i	0.0352348	−	0.189197i
$352$	−0.330062	−	0.571683i	−0.0175923	−	0.0304708i
$353$	−14.2790	−	8.24399i	−0.759995	−	0.438783i	0.0692989	−	0.997596i	$-0.477924\pi$
$353$	−14.2790	−	8.24399i	−0.759995	−	0.438783i	−0.829294	+	0.558813i	$0.811257\pi$
$354$	−1.95206	+	3.38106i	−0.103751	+	0.179701i
$355$	0.150308	+	0.260341i	0.00797751	+	0.0138175i
$356$			4.45539i			0.236135i
$357$	13.4305	−	10.9291i	0.710817	−	0.578429i
$358$			0.448721i			0.0237157i
$359$	21.1937	−	12.2362i	1.11856	−	0.645801i	0.177527	−	0.984116i	$-0.443190\pi$
$359$	21.1937	−	12.2362i	1.11856	−	0.645801i	0.941033	+	0.338315i	$0.109857\pi$
$360$	0.169938	−	0.294342i	0.00895654	−	0.0155132i
$361$	9.03926	−	15.6565i	0.475751	−	0.824024i
$362$	−13.7734	+	7.95206i	−0.723912	+	0.417951i
$363$	10.5642			0.554479
$364$	−4.97189	+	8.14127i	−0.260598	+	0.426719i
$365$	3.42242			0.179138
$366$	1.61501	−	0.932427i	0.0844179	−	0.0487387i
$367$	6.24399	−	10.8149i	0.325934	−	0.564534i	−0.655767	−	0.754963i	$-0.727655\pi$
$367$	6.24399	−	10.8149i	0.325934	−	0.564534i	0.981701	+	0.190429i	$0.0609880\pi$
$368$	3.71455	−	6.43378i	0.193634	−	0.335384i
$369$	0.748985	−	0.432427i	0.0389906	−	0.0225112i
$370$			1.20473i			0.0626309i
$371$	7.41685	+	2.82673i	0.385064	+	0.146756i
$372$		−	4.00000i		−	0.207390i
$373$	3.91393	+	6.77913i	0.202656	+	0.351010i	0.949383	−	0.314120i	$-0.101709\pi$
$373$	3.91393	+	6.77913i	0.202656	+	0.351010i	−0.746728	+	0.665130i	$0.768376\pi$
$374$	2.16012	−	3.74144i	0.111697	−	0.193465i
$375$	2.90942	+	1.67975i	0.150242	+	0.0867421i
$376$	−4.72436	−	8.18283i	−0.243640	−	0.421997i
$377$	−2.35284	+	12.6338i	−0.121177	+	0.650675i
$378$	−1.66994	−	2.05215i	−0.0858924	−	0.105551i
$379$			8.67975i			0.445849i	0.974836	+	0.222925i	$0.0715603\pi$
$379$			8.67975i			0.445849i	−0.974836	+	0.222925i	$0.928440\pi$
$380$	1.03479	+	1.79231i	0.0530837	+	0.0919436i
$381$	−7.20139	+	12.4732i	−0.368939	+	0.639020i
$382$	9.01486	+	5.20473i	0.461240	+	0.266297i
$383$	−20.2844	+	11.7112i	−1.03648	+	0.598415i	−0.918836	−	0.394640i	$-0.870869\pi$
$383$	−20.2844	+	11.7112i	−1.03648	+	0.598415i	−0.117649	+	0.993055i	$0.537536\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	0.0942619	+	0.586070i	0.00480403	+	0.0298689i
$386$	7.69938			0.391888
$387$	2.54461	+	4.40739i	0.129350	+	0.224040i
$388$	13.9507	+	8.05442i	0.708238	+	0.408901i
$389$	15.0957	−	26.1465i	0.765382	−	1.32568i	−0.174662	−	0.984628i	$-0.555883\pi$
$389$	15.0957	−	26.1465i	0.765382	−	1.32568i	0.940044	−	0.341052i	$-0.110783\pi$
$390$	−1.15551	+	0.408063i	−0.0585114	+	0.0206631i
$391$	48.6205			2.45884
$392$	2.19494	+	6.64697i	0.110861	+	0.335723i
$393$	−20.6731			−1.04282
$394$	−4.49018	−	7.77723i	−0.226212	−	0.391811i
$395$	−3.66418	−	2.11552i	−0.184365	−	0.106443i
$396$	−0.571683	−	0.330062i	−0.0287282	−	0.0165862i
$397$	7.35659	−	4.24733i	0.369216	−	0.213167i	−0.303900	−	0.952704i	$-0.598289\pi$
$397$	7.35659	−	4.24733i	0.369216	−	0.213167i	0.673116	+	0.739537i	$0.264955\pi$
$398$		−	20.5946i		−	1.03231i
$399$	15.9061	−	2.55830i	0.796302	−	0.128075i
$400$	4.88448			0.244224
$401$	−17.4693	+	10.0859i	−0.872373	+	0.503665i	−0.868136	−	0.496326i	$-0.834682\pi$
$401$	−17.4693	+	10.0859i	−0.872373	+	0.503665i	−0.00423681	+	0.999991i	$0.501349\pi$
$402$	3.72436	−	6.45078i	0.185754	−	0.321736i
$403$	−9.37595	+	10.9586i	−0.467049	+	0.545888i
$404$	1.39764	+	2.42077i	0.0695349	+	0.120438i
$405$		−	0.339877i		−	0.0168886i
$406$	5.95206	+	7.31434i	0.295396	+	0.363004i
$407$	2.33988			0.115983
$408$	5.66780	−	3.27230i	0.280598	−	0.162003i
$409$	−3.72444	−	2.15031i	−0.184162	−	0.106326i	0.405085	−	0.914279i	$-0.367242\pi$
$409$	−3.72444	−	2.15031i	−0.184162	−	0.106326i	−0.589247	+	0.807953i	$0.700575\pi$
$410$	−0.254563	−	0.146972i	−0.0125720	−	0.00725842i
$411$	−12.3187	+	7.11218i	−0.607635	+	0.350818i
$412$	7.53793			0.371367
$413$	3.67862	−	9.65207i	0.181013	−	0.474947i
$414$		−	7.42909i		−	0.365120i
$415$	−2.76897	−	4.79599i	−0.135923	−	0.235426i
$416$	−2.34399	+	2.73966i	−0.114923	+	0.134323i
$417$	−4.71455	+	8.16583i	−0.230872	+	0.399883i
$418$	3.48110	−	2.00982i	0.170266	−	0.0983033i
$419$	−32.8974			−1.60715			−0.803573	−	0.595207i	$-0.797070\pi$
$419$	−32.8974			−1.60715			−0.803573	+	0.595207i	$0.797070\pi$
$420$	−0.320246	+	0.840272i	−0.0156264	+	0.0410011i
$421$			21.7230i			1.05872i	0.848399	+	0.529358i	$0.177567\pi$
$421$			21.7230i			1.05872i	−0.848399	+	0.529358i	$0.822433\pi$
$422$	13.3280	−	7.69491i	0.648796	−	0.374583i
$423$	−8.18283	−	4.72436i	−0.397863	−	0.229706i
$424$	2.59808	+	1.50000i	0.126174	+	0.0728464i
$425$	15.9835	+	27.6843i	0.775314	+	1.34288i
$426$	0.884484			0.0428534
$427$	−3.82695	+	3.11419i	−0.185199	+	0.150706i
$428$	3.72971			0.180282
$429$	0.792557	+	2.24427i	0.0382650	+	0.108355i
$430$	0.864853	−	1.49797i	0.0417069	−	0.0722385i
$431$	5.25063	+	3.03146i	0.252914	+	0.146020i	0.621098	−	0.783733i	$-0.286687\pi$
$431$	5.25063	+	3.03146i	0.252914	+	0.146020i	−0.368184	+	0.929753i	$0.620020\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	11.1392			0.535314			0.267657	−	0.963514i	$-0.413751\pi$
$433$	11.1392			0.535314			0.267657	+	0.963514i	$0.413751\pi$
$434$	1.68054	+	10.4487i	0.0806687	+	0.501555i
$435$			1.21140i			0.0580823i
$436$	−12.4790	+	7.20473i	−0.597634	+	0.345044i
$437$	39.1767	+	22.6187i	1.87407	+	1.08200i
$438$	5.03479	−	8.72051i	0.240572	−	0.416682i
$439$	−5.81156	−	10.0659i	−0.277371	−	0.480420i	0.693360	−	0.720592i	$-0.256130\pi$
$439$	−5.81156	−	10.0659i	−0.277371	−	0.480420i	−0.970731	+	0.240171i	$0.922796\pi$
$440$			0.224361i			0.0106960i
$441$	5.22436	+	4.65898i	0.248779	+	0.221856i
$442$	−23.1981	−	4.32025i	−1.10342	−	0.205493i
$443$	2.33654	+	4.04701i	0.111012	+	0.192279i	0.916179	−	0.400770i	$-0.131257\pi$
$443$	2.33654	+	4.04701i	0.111012	+	0.192279i	−0.805166	+	0.593049i	$0.797924\pi$
$444$	3.06972	+	1.77230i	0.145682	+	0.0841098i
$445$	0.757143	−	1.31141i	0.0358920	−	0.0621668i
$446$	−9.00982	−	15.6055i	−0.426627	−	0.738940i
$447$		−	8.10884i		−	0.383535i
$448$	0.420136	+	2.61218i	0.0198496	+	0.123414i
$449$		−	36.6271i		−	1.72854i	−0.503026	−	0.864271i	$-0.667780\pi$
$449$		−	36.6271i		−	1.72854i	0.503026	−	0.864271i	$-0.332220\pi$
$450$	4.23009	−	2.44224i	0.199408	−	0.115128i
$451$	−0.285455	+	0.494422i	−0.0134415	+	0.0232814i
$452$	7.77878	−	13.4732i	0.365883	−	0.633728i
$453$	−4.59047	+	2.65031i	−0.215679	+	0.124522i
$454$	−0.231033			−0.0108429
$455$	2.84695	−	1.55140i	0.133467	−	0.0727309i
$456$	6.08921			0.285154
$457$	−27.1388	+	15.6686i	−1.26950	+	0.732947i	−0.974894	−	0.222672i	$-0.928522\pi$
$457$	−27.1388	+	15.6686i	−1.26950	+	0.732947i	−0.294607	+	0.955618i	$0.595189\pi$
$458$	3.32025	−	5.75084i	0.155145	−	0.268719i
$459$	3.27230	−	5.66780i	0.152738	−	0.264550i
$460$	−2.18669	+	1.26249i	−0.101955	+	0.0588638i
$461$		−	0.601231i		−	0.0280021i	−0.999902	−	0.0140011i	$-0.995543\pi$
$461$		−	0.601231i		−	0.0280021i	0.999902	−	0.0140011i	$-0.00445682\pi$
$462$	1.63201	+	0.621996i	0.0759280	+	0.0289379i
$463$			10.5013i			0.488038i	0.969770	+	0.244019i	$0.0784659\pi$
$463$			10.5013i			0.488038i	−0.969770	+	0.244019i	$0.921534\pi$
$464$	1.78212	+	3.08672i	0.0827328	+	0.143297i
$465$	−0.679754	+	1.17737i	−0.0315228	+	0.0545991i
$466$	25.5636	+	14.7592i	1.18421	+	0.683705i
$467$	−13.6109	−	23.5747i	−0.629835	−	1.09091i	−0.987584	−	0.157089i	$-0.949789\pi$
$467$	−13.6109	−	23.5747i	−0.629835	−	1.09091i	0.357749	−	0.933818i	$-0.383544\pi$
$468$	−0.660123	+	3.54461i	−0.0305142	+	0.163850i
$469$	−7.01850	+	18.4153i	−0.324084	+	0.850341i
$470$			3.21140i			0.148131i
$471$	11.5281	+	19.9673i	0.531188	+	0.920044i
$472$	1.95206	−	3.38106i	0.0898507	−	0.155626i
$473$	−2.90942	−	1.67975i	−0.133775	−	0.0772352i
$474$	−10.7809	+	6.22436i	−0.495184	+	0.285894i
$475$			29.7427i			1.36469i
$476$	−13.4305	+	10.9291i	−0.615586	+	0.500934i
$477$	3.00000			0.137361
$478$	−7.51182	−	13.0109i	−0.343583	−	0.595103i
$479$	−25.0031	−	14.4356i	−1.14242	−	0.659578i	−0.195393	−	0.980725i	$-0.562598\pi$
$479$	−25.0031	−	14.4356i	−1.14242	−	0.659578i	−0.947029	+	0.321147i	$0.895932\pi$
$480$	−0.169938	+	0.294342i	−0.00775659	+	0.0134348i
$481$	−4.25573	−	12.0509i	−0.194044	−	0.549473i
$482$	4.44872			0.202634
$483$	3.12123	+	19.4061i	0.142021	+	0.883009i
$484$	−10.5642			−0.480193
$485$	−2.73751	−	4.74151i	−0.124304	−	0.215301i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	3.39262	+	1.95873i	0.153734	+	0.0887585i	0.574894	−	0.818228i	$-0.305043\pi$
$487$	3.39262	+	1.95873i	0.153734	+	0.0887585i	−0.421159	+	0.906987i	$0.638377\pi$
$488$	−1.61501	+	0.932427i	−0.0731081	+	0.0422090i
$489$		−	13.5642i		−	0.613396i
$490$	0.483513	−	2.32949i	0.0218429	−	0.105236i
$491$	−13.4202			−0.605643			−0.302821	−	0.953047i	$-0.597929\pi$
$491$	−13.4202			−0.605643			−0.302821	+	0.953047i	$0.597929\pi$
$492$	−0.748985	+	0.432427i	−0.0337668	+	0.0194953i
$493$	−11.6633	+	20.2014i	−0.525287	+	0.909824i
$494$	−16.6824	−	14.2730i	−0.750575	−	0.642174i
$495$	0.112180	+	0.194302i	0.00504213	+	0.00873322i
$496$			4.00000i			0.179605i
$497$	−2.31043	+	0.371603i	−0.103637	+	0.0166687i
$498$	−16.2939			−0.730149
$499$	−28.3900	+	16.3910i	−1.27091	+	0.733760i	−0.975159	−	0.221505i	$-0.928903\pi$
$499$	−28.3900	+	16.3910i	−1.27091	+	0.733760i	−0.295751	+	0.955265i	$0.595570\pi$
$500$	−2.90942	−	1.67975i	−0.130113	−	0.0751209i
$501$	−13.5995	−	7.85170i	−0.607583	−	0.350788i
$502$	−21.1277	+	12.1981i	−0.942973	+	0.544426i
$503$	22.8582			1.01920			0.509598	−	0.860413i	$-0.329794\pi$
$503$	22.8582			1.01920			0.509598	+	0.860413i	$0.329794\pi$
$504$	1.66994	+	2.05215i	0.0743850	+	0.0914099i
$505$		−	0.950048i		−	0.0422766i
$506$	2.45206	+	4.24709i	0.109007	+	0.188806i
$507$	10.1170	−	8.16369i	0.449313	−	0.362562i
$508$	7.20139	−	12.4732i	0.319510	−	0.553408i
$509$	−28.4445	+	16.4224i	−1.26078	+	0.727911i	−0.973225	−	0.229854i	$-0.926175\pi$
$509$	−28.4445	+	16.4224i	−1.26078	+	0.727911i	−0.287553	+	0.957765i	$0.592842\pi$
$510$	−2.22436			−0.0984963
$511$	−9.48798	+	24.8949i	−0.419724	+	1.10128i
$512$			1.00000i			0.0441942i
$513$	5.27341	−	3.04461i	0.232827	−	0.134423i
$514$	−15.9771	−	9.22436i	−0.704718	−	0.406869i
$515$	−2.21873	−	1.28098i	−0.0977690	−	0.0564469i
$516$	−2.54461	−	4.40739i	−0.112020	−	0.194024i
$517$	6.23732			0.274317
$518$	−8.76327	−	3.33988i	−0.385036	−	0.146746i
$519$	13.6035			0.597127
$520$	1.15551	−	0.408063i	0.0506723	−	0.0178947i
$521$	−1.40946	+	2.44126i	−0.0617496	+	0.106953i	−0.895248	−	0.445569i	$-0.853001\pi$
$521$	−1.40946	+	2.44126i	−0.0617496	+	0.106953i	0.833498	+	0.552523i	$0.186335\pi$
$522$	3.08672	+	1.78212i	0.135102	+	0.0780012i
$523$	2.81490	+	4.87555i	0.123087	+	0.213193i	0.920984	−	0.389601i	$-0.127387\pi$
$523$	2.81490	+	4.87555i	0.123087	+	0.213193i	−0.797897	+	0.602794i	$0.794054\pi$
$524$	20.6731			0.903108
$525$	−10.0237	+	8.15679i	−0.437469	+	0.355991i
$526$		−	6.30062i		−	0.274720i
$527$	−22.6712	+	13.0892i	−0.987572	+	0.570175i
$528$	0.571683	+	0.330062i	0.0248793	+	0.0143641i
$529$	−16.0957	+	27.8786i	−0.699813	+	1.21211i
$530$	−0.509815	−	0.883026i	−0.0221450	−	0.0383562i
$531$		−	3.90411i		−	0.169424i
$532$	−15.9061	+	2.55830i	−0.689618	+	0.110916i
$533$	3.06556	+	0.570909i	0.132784	+	0.0247288i
$534$	−2.22770	−	3.85848i	−0.0964019	−	0.166973i
$535$	−1.09781	−	0.633820i	−0.0474624	−	0.0274024i
$536$	−3.72436	+	6.45078i	−0.160868	+	0.278631i
$537$	−0.224361	−	0.388604i	−0.00968187	−	0.0167695i
$538$		−	9.89517i		−	0.426611i
$539$	−4.52443	−	0.939099i	−0.194881	−	0.0404498i
$540$			0.339877i			0.0146260i
$541$	21.4015	−	12.3562i	0.920123	−	0.531233i	0.0364488	−	0.999336i	$-0.488395\pi$
$541$	21.4015	−	12.3562i	0.920123	−	0.531233i	0.883674	+	0.468102i	$0.155062\pi$
$542$	−6.34969	+	10.9980i	−0.272743	+	0.472404i
$543$	7.95206	−	13.7734i	0.341255	−	0.591072i
$544$	−5.66780	+	3.27230i	−0.243005	+	0.140299i
$545$	4.89744			0.209783
$546$	0.235144	−	9.53649i	0.0100632	−	0.408124i
$547$	18.1874			0.777636			0.388818	−	0.921315i	$-0.372884\pi$
$547$	18.1874			0.777636			0.388818	+	0.921315i	$0.372884\pi$
$548$	12.3187	−	7.11218i	0.526227	−	0.303817i
$549$	−0.932427	+	1.61501i	−0.0397950	+	0.0689270i
$550$	−1.61218	+	2.79238i	−0.0687436	+	0.119067i
$551$	−18.7957	+	10.8517i	−0.800724	+	0.462298i
$552$			7.42909i			0.316203i
$553$	25.5466	−	20.7886i	1.08635	−	0.884021i
$554$			28.0433i			1.19144i
$555$	−0.602365	−	1.04333i	−0.0255690	−	0.0442868i
$556$	4.71455	−	8.16583i	0.199941	−	0.346308i
$557$	23.0713	+	13.3202i	0.977564	+	0.564397i	0.901534	−	0.432709i	$-0.142442\pi$
$557$	23.0713	+	13.3202i	0.977564	+	0.564397i	0.0760303	+	0.997106i	$0.475775\pi$
$558$	2.00000	+	3.46410i	0.0846668	+	0.146647i
$559$	−3.35951	+	18.0393i	−0.142092	+	0.762979i
$560$	0.320246	−	0.840272i	0.0135329	−	0.0355080i
$561$			4.32025i			0.182401i
$562$	0.910786	+	1.57753i	0.0384192	+	0.0665440i
$563$	−13.8386	+	23.9691i	−0.583225	+	1.01018i	0.411869	+	0.911243i	$0.364876\pi$
$563$	−13.8386	+	23.9691i	−0.583225	+	1.01018i	−0.995094	+	0.0989328i	$0.968457\pi$
$564$	8.18283	+	4.72436i	0.344559	+	0.198931i
$565$	−4.57925	+	2.64383i	−0.192650	+	0.111227i
$566$			8.98037i			0.377473i
$567$	2.47228	+	0.942242i	0.103826	+	0.0395704i
$568$	−0.884484			−0.0371121
$569$	10.1949	+	17.6581i	0.427393	+	0.740266i	0.996641	−	0.0818997i	$-0.0260987\pi$
$569$	10.1949	+	17.6581i	0.427393	+	0.740266i	−0.569248	+	0.822166i	$0.692765\pi$
$570$	−1.79231	−	1.03479i	−0.0750717	−	0.0433426i
$571$	−19.1022	+	33.0859i	−0.799401	+	1.38460i	0.120606	+	0.992700i	$0.461516\pi$
$571$	−19.1022	+	33.0859i	−0.799401	+	1.38460i	−0.920007	+	0.391903i	$0.871817\pi$
$572$	−0.792557	−	2.24427i	−0.0331385	−	0.0938378i
$573$	−10.4095			−0.434861
$574$	1.77481	−	1.44425i	0.0740789	−	0.0602819i
$575$	−36.2873			−1.51328
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−9.83762	−	5.67975i	−0.409546	−	0.236451i	0.281049	−	0.959693i	$-0.409318\pi$
$577$	−9.83762	−	5.67975i	−0.409546	−	0.236451i	−0.690594	+	0.723242i	$0.742651\pi$
$578$	−22.3711	−	12.9159i	−0.930514	−	0.537232i
$579$	−6.66786	+	3.84969i	−0.277107	+	0.159988i
$580$		−	1.21140i		−	0.0503007i
$581$	42.5627	−	6.84567i	1.76580	−	0.284006i
$582$	−16.1088			−0.667733
$583$	−1.71505	+	0.990185i	−0.0710301	+	0.0410093i
$584$	−5.03479	+	8.72051i	−0.208341	+	0.360857i
$585$	0.796667	−	0.931146i	0.0329381	−	0.0384982i
$586$	1.40097	+	2.42655i	0.0578736	+	0.100240i
$587$			37.2347i			1.53684i	0.639946	+	0.768420i	$0.278957\pi$
$587$			37.2347i			1.53684i	−0.639946	+	0.768420i	$0.721043\pi$
$588$	−5.22436	−	4.65898i	−0.215449	−	0.192133i
$589$	−24.3569			−1.00361
$590$	−1.14914	+	0.663459i	−0.0473095	+	0.0273142i
$591$	7.77723	+	4.49018i	0.319912	+	0.184702i
$592$	−3.06972	−	1.77230i	−0.126165	−	0.0728412i
$593$	20.9674	−	12.1055i	0.861026	−	0.497114i	−0.00332968	−	0.999994i	$-0.501060\pi$
$593$	20.9674	−	12.1055i	0.861026	−	0.497114i	0.864356	+	0.502881i	$0.167727\pi$
$594$	0.660123			0.0270852
$595$	5.81043	−	0.934534i	0.238204	−	0.0383121i
$596$			8.10884i			0.332151i
$597$	10.2973	+	17.8354i	0.421440	+	0.729955i
$598$	17.4137	−	20.3532i	0.712099	−	0.832303i
$599$	3.23952	−	5.61102i	0.132363	−	0.229260i	−0.792224	−	0.610231i	$-0.791077\pi$
$599$	3.23952	−	5.61102i	0.132363	−	0.229260i	0.924587	+	0.380971i	$0.124410\pi$
$600$	−4.23009	+	2.44224i	−0.172693	+	0.0997041i
$601$	41.4354			1.69018			0.845092	−	0.534621i	$-0.179546\pi$
$601$	41.4354			1.69018			0.845092	+	0.534621i	$0.179546\pi$
$602$	8.49867	+	10.4438i	0.346380	+	0.425658i
$603$			7.44872i			0.303335i
$604$	4.59047	−	2.65031i	0.186783	−	0.107839i
$605$	3.10950	+	1.79527i	0.126419	+	0.0729881i
$606$	−2.42077	−	1.39764i	−0.0983373	−	0.0567750i
$607$	4.20139	+	7.27703i	0.170529	+	0.295365i	0.938605	−	0.344994i	$-0.112119\pi$
$607$	4.20139	+	7.27703i	0.170529	+	0.295365i	−0.768076	+	0.640359i	$0.778786\pi$
$608$	−6.08921			−0.246950
$609$	−8.81180	−	3.35837i	−0.357072	−	0.136088i
$610$	0.633820			0.0256626
$611$	−11.3443	−	32.1236i	−0.458942	−	1.29958i
$612$	−3.27230	+	5.66780i	−0.132275	+	0.229107i
$613$	−40.6144	−	23.4487i	−1.64040	−	0.947085i	−0.980691	−	0.195563i	$-0.937347\pi$
$613$	−40.6144	−	23.4487i	−1.64040	−	0.947085i	−0.659708	−	0.751522i	$-0.729320\pi$
$614$	4.60884	+	7.98275i	0.185998	+	0.322158i
$615$	0.293944			0.0118529
$616$	−1.63201	−	0.621996i	−0.0657556	−	0.0250609i
$617$			32.6271i			1.31352i	0.754100	+	0.656760i	$0.228073\pi$
$617$			32.6271i			1.31352i	−0.754100	+	0.656760i	$0.771927\pi$
$618$	−6.52804	+	3.76897i	−0.262596	+	0.151610i
$619$	4.72995	+	2.73084i	0.190113	+	0.109762i	0.592035	−	0.805912i	$-0.298325\pi$
$619$	4.72995	+	2.73084i	0.190113	+	0.109762i	−0.401923	+	0.915674i	$0.631658\pi$
$620$	0.679754	−	1.17737i	0.0272996	−	0.0472842i
$621$	3.71455	+	6.43378i	0.149060	+	0.258179i
$622$		−	11.4684i		−	0.459839i
$623$	7.44023	+	9.14312i	0.298087	+	0.366311i
$624$	0.660123	−	3.54461i	0.0264261	−	0.141898i
$625$	−11.6403	−	20.1616i	−0.465612	−	0.806464i
$626$	19.5412	+	11.2821i	0.781024	+	0.450924i
$627$	−2.00982	+	3.48110i	−0.0802643	+	0.139022i
$628$	−11.5281	−	19.9673i	−0.460022	−	0.796782i
$629$		−	23.1981i		−	0.924967i
$630$	−0.142794	−	0.887820i	−0.00568907	−	0.0353716i
$631$		−	41.8845i		−	1.66739i	−0.552221	−	0.833697i	$-0.686220\pi$
$631$		−	41.8845i		−	1.66739i	0.552221	−	0.833697i	$-0.313780\pi$
$632$	10.7809	−	6.22436i	0.428842	−	0.247592i
$633$	−7.69491	+	13.3280i	−0.305845	+	0.529740i
$634$	−6.31357	+	10.9354i	−0.250744	+	0.434301i
$635$	−4.23935	+	2.44759i	−0.168233	+	0.0971295i
$636$	−3.00000			−0.118958
$637$	3.39238	+	25.0098i	0.134411	+	0.990926i
$638$	−2.35284			−0.0931497
$639$	−0.765985	+	0.442242i	−0.0303019	+	0.0174948i
$640$	0.169938	−	0.294342i	0.00671741	−	0.0116349i
$641$	−3.30842	+	5.73035i	−0.130675	+	0.226335i	−0.923937	−	0.382545i	$-0.875048\pi$
$641$	−3.30842	+	5.73035i	−0.130675	+	0.226335i	0.793262	+	0.608880i	$0.208381\pi$
$642$	−3.23002	+	1.86485i	−0.127479	+	0.0735999i
$643$		−	23.7427i		−	0.936319i	−0.883644	−	0.468160i	$-0.844917\pi$
$643$		−	23.7427i		−	0.936319i	0.883644	−	0.468160i	$-0.155083\pi$
$644$	−3.12123	−	19.4061i	−0.122994	−	0.764708i
$645$			1.72971i			0.0681071i
$646$	−19.9258	−	34.5124i	−0.783968	−	1.35787i
$647$	−19.5642	+	33.8863i	−0.769150	+	1.33221i	0.168875	+	0.985637i	$0.445987\pi$
$647$	−19.5642	+	33.8863i	−0.769150	+	1.33221i	−0.938025	+	0.346569i	$0.887347\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	1.28860	+	2.23192i	0.0505819	+	0.0876104i
$650$	17.3136	+	3.22436i	0.679094	+	0.126470i
$651$	−6.67975	−	8.20859i	−0.261800	−	0.321720i
$652$			13.5642i			0.531217i
$653$	−2.75714	−	4.77551i	−0.107895	−	0.186880i	0.807022	−	0.590521i	$-0.201078\pi$
$653$	−2.75714	−	4.77551i	−0.107895	−	0.186880i	−0.914917	+	0.403641i	$0.867744\pi$
$654$	7.20473	−	12.4790i	0.281727	−	0.487966i
$655$	−6.08496	−	3.51315i	−0.237759	−	0.137270i
$656$	0.748985	−	0.432427i	0.0292429	−	0.0168834i
$657$			10.0696i			0.392852i
$658$	−23.3599	−	8.90298i	−0.910664	−	0.347074i
$659$	−49.2217			−1.91741			−0.958703	−	0.284410i	$-0.908202\pi$
$659$	−49.2217			−1.91741			−0.958703	+	0.284410i	$0.908202\pi$
$660$	−0.112180	−	0.194302i	−0.00436661	−	0.00756319i
$661$	10.6731	+	6.16213i	0.415137	+	0.239679i	0.692994	−	0.720943i	$-0.256291\pi$
$661$	10.6731	+	6.16213i	0.415137	+	0.239679i	−0.277858	+	0.960622i	$0.589624\pi$
$662$	13.4106	−	23.2278i	0.521218	−	0.902775i
$663$	22.2502	−	7.85759i	0.864127	−	0.305163i
$664$	16.2939			0.632328
$665$	5.11659	+	1.95005i	0.198413	+	0.0756196i
$666$	−3.54461			−0.137351
$667$	−13.2395	−	22.9315i	−0.512636	−	0.887912i
$668$	13.5995	+	7.85170i	0.526182	+	0.303791i
$669$	15.6055	+	9.00982i	0.603342	+	0.348340i
$670$	2.19247	−	1.26582i	0.0847026	−	0.0489031i
$671$		−	1.23103i		−	0.0475235i
$672$	−1.66994	−	2.05215i	−0.0644193	−	0.0791633i
$673$	6.79527			0.261938			0.130969	−	0.991386i	$-0.458191\pi$
$673$	6.79527			0.261938			0.130969	+	0.991386i	$0.458191\pi$
$674$	8.50343	−	4.90946i	0.327540	−	0.189105i
$675$	−2.44224	+	4.23009i	−0.0940019	+	0.162816i
$676$	−10.1170	+	8.16369i	−0.389116	+	0.313988i
$677$	−8.34636	−	14.4563i	−0.320777	−	0.555601i	0.659872	−	0.751378i	$-0.270611\pi$
$677$	−8.34636	−	14.4563i	−0.320777	−	0.555601i	−0.980648	+	0.195777i	$0.937277\pi$
$678$			15.5576i			0.597485i
$679$	42.0792	−	6.76790i	1.61485	−	0.259728i
$680$	2.22436			0.0853003
$681$	0.200080	−	0.115516i	0.00766709	−	0.00442659i
$682$	−2.28673	−	1.32025i	−0.0875636	−	0.0505548i
$683$	18.8069	+	10.8582i	0.719627	+	0.415477i	0.814615	−	0.580002i	$-0.196948\pi$
$683$	18.8069	+	10.8582i	0.719627	+	0.415477i	−0.0949885	+	0.995478i	$0.530281\pi$
$684$	−5.27341	+	3.04461i	−0.201634	+	0.116413i
$685$	−4.83453			−0.184718
$686$	15.6044	+	9.97514i	0.595778	+	0.380853i
$687$			6.64049i			0.253351i
$688$	2.54461	+	4.40739i	0.0970122	+	0.168030i
$689$	8.21897	+	7.03196i	0.313118	+	0.267896i
$690$	1.26249	−	2.18669i	0.0480621	−	0.0832460i
$691$	40.6461	−	23.4670i	1.54625	−	0.892728i	0.547827	−	0.836592i	$-0.315455\pi$
$691$	40.6461	−	23.4670i	1.54625	−	0.892728i	0.998423	−	0.0561358i	$-0.0178780\pi$
$692$	−13.6035			−0.517127
$693$	−1.72436	+	0.277341i	−0.0655030	+	0.0105353i
$694$			19.0959i			0.724870i
$695$	−2.77538	+	1.60236i	−0.105276	+	0.0607812i
$696$	−3.08672	−	1.78212i	−0.117002	−	0.0675510i
$697$	4.90181	+	2.83006i	0.185669	+	0.107196i
$698$	−0.208066	−	0.360381i	−0.00787541	−	0.0136406i
$699$	−29.5183			−1.11648
$700$	10.0237	−	8.15679i	0.378859	−	0.308298i
$701$	−7.32251			−0.276568			−0.138284	−	0.990393i	$-0.544159\pi$
$701$	−7.32251			−0.276568			−0.138284	+	0.990393i	$0.544159\pi$
$702$	−1.20062	−	3.39978i	−0.0453145	−	0.128316i
$703$	10.7919	−	18.6922i	0.407026	−	0.704989i
$704$	−0.571683	−	0.330062i	−0.0215461	−	0.0124397i
$705$	−1.60570	−	2.78116i	−0.0604742	−	0.104744i
$706$	−16.4880			−0.620533
$707$	6.91070	+	2.63382i	0.259904	+	0.0990550i
$708$			3.90411i			0.146726i
$709$	−5.75661	+	3.32358i	−0.216194	+	0.124820i	−0.604187	−	0.796843i	$-0.706502\pi$
$709$	−5.75661	+	3.32358i	−0.216194	+	0.124820i	0.387993	+	0.921662i	$0.373169\pi$
$710$	0.260341	+	0.150308i	0.00977041	+	0.00564095i
$711$	6.22436	−	10.7809i	0.233432	−	0.404316i
$712$	2.22770	+	3.85848i	0.0834865	+	0.144603i
$713$		−	29.7164i		−	1.11289i
$714$	6.16660	−	16.1801i	0.230779	−	0.605526i
$715$	−0.148106	+	0.795270i	−0.00553884	+	0.0297414i
$716$	0.224361	+	0.388604i	0.00838475	+	0.0145228i
$717$	13.0109	+	7.51182i	0.485900	+	0.280534i
$718$	12.2362	−	21.1937i	0.456650	−	0.790942i
$719$	2.43576	+	4.21886i	0.0908386	+	0.157337i	0.907864	−	0.419264i	$-0.137712\pi$
$719$	2.43576	+	4.21886i	0.0908386	+	0.157337i	−0.817026	+	0.576601i	$0.804379\pi$
$720$		−	0.339877i		−	0.0126665i
$721$	15.4689	−	12.5879i	0.576094	−	0.468797i
$722$		−	18.0785i		−	0.672813i
$723$	−3.85271	+	2.22436i	−0.143284	+	0.0827249i
$724$	−7.95206	+	13.7734i	−0.295536	+	0.511883i
$725$	8.70473	−	15.0770i	0.323286	−	0.559947i
$726$	9.14890	−	5.28212i	0.339547	−	0.196038i
$727$	−4.98931			−0.185043			−0.0925216	−	0.995711i	$-0.529493\pi$
$727$	−4.98931			−0.185043			−0.0925216	+	0.995711i	$0.529493\pi$
$728$	−0.235144	+	9.53649i	−0.00871503	+	0.353446i
$729$	1.00000			0.0370370
$730$	2.96390	−	1.71121i	0.109699	−	0.0633347i
$731$	−16.6535	+	28.8446i	−0.615950	+	1.06686i
$732$	0.932427	−	1.61501i	0.0344635	−	0.0596925i
$733$	6.46582	−	3.73304i	0.238820	−	0.137883i	−0.375814	−	0.926695i	$-0.622637\pi$
$733$	6.46582	−	3.73304i	0.238820	−	0.137883i	0.614634	+	0.788812i	$0.289304\pi$
$734$		−	12.4880i		−	0.460940i
$735$	0.746010	+	2.25915i	0.0275170	+	0.0833301i
$736$		−	7.42909i		−	0.273840i
$737$	−2.45854	−	4.25831i	−0.0905614	−	0.156857i
$738$	0.432427	−	0.748985i	0.0159178	−	0.0275705i
$739$	−1.26585	−	0.730840i	−0.0465651	−	0.0268844i	0.476537	−	0.879155i	$-0.341892\pi$
$739$	−1.26585	−	0.730840i	−0.0465651	−	0.0268844i	−0.523102	+	0.852270i	$0.675225\pi$
$740$	0.602365	+	1.04333i	0.0221434	+	0.0383535i
$741$	21.5839	+	4.01963i	0.792903	+	0.147665i
$742$	7.83654	−	1.26041i	0.287688	−	0.0462710i
$743$			5.67975i			0.208370i	0.994558	+	0.104185i	$0.0332234\pi$
$743$			5.67975i			0.208370i	−0.994558	+	0.104185i	$0.966777\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	1.37800	−	2.38677i	0.0504862	−	0.0874446i
$746$	6.77913	+	3.91393i	0.248201	+	0.143299i
$747$	14.1110	−	8.14697i	0.516293	−	0.298082i
$748$		−	4.32025i		−	0.157964i
$749$	7.65390	−	6.22838i	0.279668	−	0.227580i
$750$	3.35951			0.122672
$751$	−2.19806	−	3.80715i	−0.0802083	−	0.138925i	0.823131	−	0.567851i	$-0.192225\pi$
$751$	−2.19806	−	3.80715i	−0.0802083	−	0.138925i	−0.903339	+	0.428927i	$0.858892\pi$
$752$	−8.18283	−	4.72436i	−0.298397	−	0.172280i
$753$	12.1981	−	21.1277i	0.444522	−	0.769935i
$754$	4.27929	+	12.1176i	0.155843	+	0.441298i
$755$	−1.80156			−0.0655654
$756$	−2.47228	−	0.942242i	−0.0899160	−	0.0342690i
$757$	21.0326			0.764442			0.382221	−	0.924071i	$-0.375159\pi$
$757$	21.0326			0.764442			0.382221	+	0.924071i	$0.375159\pi$
$758$	4.33988	+	7.51689i	0.157631	+	0.273026i
$759$	−4.24709	−	2.45206i	−0.154160	−	0.0890040i
$760$	1.79231	+	1.03479i	0.0650140	+	0.0375358i
$761$	−10.9130	+	6.30062i	−0.395595	+	0.228397i	−0.684582	−	0.728936i	$-0.740015\pi$
$761$	−10.9130	+	6.30062i	−0.395595	+	0.228397i	0.288986	+	0.957333i	$0.406682\pi$
$762$			14.4028i			0.521758i
$763$	−13.5772	+	35.6243i	−0.491528	+	1.28968i
$764$	10.4095			0.376601
$765$	1.92635	−	1.11218i	0.0696474	−	0.0402110i
$766$	−11.7112	+	20.2844i	−0.423143	+	0.732906i
$767$	9.15119	−	10.6959i	0.330430	−	0.386208i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	34.4398i		−	1.24193i	−0.783838	−	0.620965i	$-0.786741\pi$
$769$		−	34.4398i		−	1.24193i	0.783838	−	0.620965i	$-0.213259\pi$
$770$	0.374668	+	0.460421i	0.0135021	+	0.0165924i
$771$	18.4487			0.664414
$772$	6.66786	−	3.84969i	0.239982	−	0.138553i
$773$	−14.5471	−	8.39877i	−0.523223	−	0.302083i	0.215030	−	0.976608i	$-0.431015\pi$
$773$	−14.5471	−	8.39877i	−0.523223	−	0.302083i	−0.738252	+	0.674525i	$0.764349\pi$
$774$	4.40739	+	2.54461i	0.158420	+	0.0914640i
$775$	16.9203	−	9.76897i	0.607797	−	0.350912i
$776$	16.1088			0.578274
$777$	9.25915	−	1.48922i	0.332170	−	0.0534253i
$778$		−	30.1914i		−	1.08241i
$779$	2.63314	+	4.56073i	0.0943419	+	0.163405i
$780$	−0.796667	+	0.931146i	−0.0285253	+	0.0333404i
$781$	0.291934	−	0.505645i	0.0104462	−	0.0180934i
$782$	42.1066	−	24.3102i	1.50573	−	0.869332i
$783$	−3.56424			−0.127375
$784$	5.22436	+	4.65898i	0.186584	+	0.166392i
$785$			7.83628i			0.279689i
$786$	−17.9034	+	10.3365i	−0.638594	+	0.368692i
$787$	−31.9974	−	18.4737i	−1.14058	−	0.658516i	−0.194008	−	0.981000i	$-0.562149\pi$
$787$	−31.9974	−	18.4737i	−1.14058	−	0.658516i	−0.946575	+	0.322484i	$0.895482\pi$
$788$	−7.77723	−	4.49018i	−0.277052	−	0.159956i
$789$	3.15031	+	5.45649i	0.112154	+	0.194256i
$790$	−4.23103			−0.150533
$791$	−6.53629	−	40.6392i	−0.232404	−	1.44496i
$792$	−0.660123			−0.0234565
$793$	−6.34009	+	2.23898i	−0.225143	+	0.0795085i
$794$	4.24733	−	7.35659i	0.150732	−	0.261075i
$795$	0.883026	+	0.509815i	0.0313177	+	0.0180813i
$796$	−10.2973	−	17.8354i	−0.364977	−	0.632159i
$797$	38.7819			1.37373			0.686863	−	0.726787i	$-0.258987\pi$
$797$	38.7819			1.37373			0.686863	+	0.726787i	$0.258987\pi$
$798$	12.4960	−	10.1686i	0.442352	−	0.359965i
$799$		−	61.8382i		−	2.18768i
$800$	4.23009	−	2.44224i	0.149556	−	0.0863463i
$801$	3.85848	+	2.22770i	0.136333	+	0.0787118i
$802$	−10.0859	+	17.4693i	−0.356145	+	0.616861i
$803$	−3.32358	−	5.75661i	−0.117287	−	0.203146i
$804$		−	7.44872i		−	0.262696i
$805$	−2.37914	+	6.24245i	−0.0838536	+	0.220018i
$806$	−2.64049	+	14.1784i	−0.0930074	+	0.499414i
$807$	4.94759	+	8.56947i	0.174163	+	0.301660i
$808$	2.42077	+	1.39764i	0.0851626	+	0.0491686i
$809$	−1.06090	+	1.83754i	−0.0372993	+	0.0646043i	−0.884072	−	0.467350i	$-0.845209\pi$
$809$	−1.06090	+	1.83754i	−0.0372993	+	0.0646043i	0.846773	+	0.531954i	$0.178542\pi$
$810$	−0.169938	−	0.294342i	−0.00597103	−	0.0103421i
$811$		−	3.66680i		−	0.128759i	−0.997926	−	0.0643793i	$-0.979493\pi$
$811$		−	3.66680i		−	0.128759i	0.997926	−	0.0643793i	$-0.0205067\pi$
$812$	8.81180	+	3.35837i	0.309234	+	0.117856i
$813$		−	12.6994i		−	0.445387i
$814$	2.02639	−	1.16994i	0.0710250	−	0.0410063i
$815$	2.30509	−	3.99253i	0.0807436	−	0.139852i
$816$	3.27230	−	5.66780i	0.114554	−	0.198413i
$817$	−26.8375	+	15.4947i	−0.938926	+	0.542089i
$818$	−4.30062			−0.150367
$819$	4.56461	+	8.37642i	0.159500	+	0.292696i
$820$	−0.293944			−0.0102650
$821$	−18.6261	+	10.7538i	−0.650057	+	0.375310i	−0.788478	−	0.615063i	$-0.789131\pi$
$821$	−18.6261	+	10.7538i	−0.650057	+	0.375310i	0.138421	+	0.990373i	$0.455797\pi$
$822$	−7.11218	+	12.3187i	−0.248066	+	0.429663i
$823$	17.9770	−	31.1371i	0.626640	−	1.08537i	−0.361581	−	0.932341i	$-0.617763\pi$
$823$	17.9770	−	31.1371i	0.626640	−	1.08537i	0.988221	−	0.153032i	$-0.0489037\pi$
$824$	6.52804	−	3.76897i	0.227415	−	0.131298i
$825$		−	3.22436i		−	0.112258i
$826$	−1.64026	−	10.1983i	−0.0570719	−	0.354843i
$827$			32.8778i			1.14327i	0.820507	+	0.571637i	$0.193691\pi$
$827$			32.8778i			1.14327i	−0.820507	+	0.571637i	$0.806309\pi$
$828$	−3.71455	−	6.43378i	−0.129089	−	0.223589i
$829$	4.91280	−	8.50921i	0.170628	−	0.295537i	−0.768011	−	0.640436i	$-0.778754\pi$
$829$	4.91280	−	8.50921i	0.170628	−	0.295537i	0.938640	+	0.344899i	$0.112087\pi$
$830$	−4.79599	−	2.76897i	−0.166471	−	0.0961123i
$831$	−14.0216	−	24.2862i	−0.486405	−	0.842479i
$832$	−0.660123	+	3.54461i	−0.0228857	+	0.122887i
$833$	−9.31043	+	44.8562i	−0.322587	+	1.55417i
$834$			9.42909i			0.326503i
$835$	−2.66861	−	4.62217i	−0.0923511	−	0.159957i
$836$	2.00982	−	3.48110i	0.0695109	−	0.120396i
$837$	−3.46410	−	2.00000i	−0.119737	−	0.0691301i
$838$	−28.4900	+	16.4487i	−0.984171	+	0.568212i
$839$			42.6008i			1.47074i	0.677663	+	0.735372i	$0.262993\pi$
$839$			42.6008i			1.47074i	−0.677663	+	0.735372i	$0.737007\pi$
$840$	0.142794	+	0.887820i	0.00492688	+	0.0306327i
$841$	−16.2962			−0.561938
$842$	10.8615	+	18.8127i	0.374313	+	0.648328i
$843$	−1.57753	−	0.910786i	−0.0543330	−	0.0313691i
$844$	7.69491	−	13.3280i	0.264870	−	0.458768i
$845$	4.36519	−	0.683646i	0.150167	−	0.0235181i
$846$	−9.44872			−0.324854
$847$	−21.6794	+	17.6416i	−0.744912	+	0.606173i
$848$	3.00000			0.103020
$849$	−4.49018	−	7.77723i	−0.154103	−	0.266914i
$850$	27.6843	+	15.9835i	0.949562	+	0.548230i
$851$	22.8052	+	13.1666i	0.781753	+	0.451345i
$852$	0.765985	−	0.442242i	0.0262422	−	0.0151510i
$853$		−	47.7490i		−	1.63489i	−0.576005	−	0.817446i	$-0.695389\pi$
$853$		−	47.7490i		−	1.63489i	0.576005	−	0.817446i	$-0.304611\pi$
$854$	−1.75714	+	4.61044i	−0.0601282	+	0.157766i
$855$	2.06958			0.0707782
$856$	3.23002	−	1.86485i	0.110400	−	0.0637394i
$857$	3.44671	−	5.96988i	0.117737	−	0.203927i	−0.801133	−	0.598486i	$-0.795769\pi$
$857$	3.44671	−	5.96988i	0.117737	−	0.203927i	0.918871	+	0.394559i	$0.129103\pi$
$858$	1.80851	+	1.54732i	0.0617416	+	0.0528246i
$859$	−14.3898	−	24.9239i	−0.490975	−	0.850393i	0.508971	−	0.860783i	$-0.330026\pi$
$859$	−14.3898	−	24.9239i	−0.490975	−	0.850393i	−0.999946	+	0.0103904i	$0.996693\pi$
$860$		−	1.72971i		−	0.0589825i
$861$	−0.814901	+	2.13816i	−0.0277717	+	0.0728683i
$862$	6.06291			0.206504
$863$	42.0668	−	24.2873i	1.43197	−	0.826748i	0.434699	−	0.900576i	$-0.356855\pi$
$863$	42.0668	−	24.2873i	1.43197	−	0.826748i	0.997271	+	0.0738274i	$0.0235214\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	4.00408	+	2.31176i	0.136143	+	0.0786021i
$866$	9.64680	−	5.56958i	0.327812	−	0.189262i
$867$	25.8319			0.877297
$868$	6.67975	+	8.20859i	0.226726	+	0.278618i
$869$			8.21769i			0.278766i
$870$	0.605701	+	1.04910i	0.0205352	+	0.0355680i
$871$	−17.4597	+	20.4069i	−0.591600	+	0.691463i
$872$	−7.20473	+	12.4790i	−0.243983	+	0.422591i
$873$	13.9507	−	8.05442i	0.472159	−	0.272601i
$874$	45.2373			1.53018
$875$	−8.77564	+	1.41145i	−0.296671	+	0.0477157i
$876$		−	10.0696i		−	0.340220i
$877$	−7.99779	+	4.61753i	−0.270066	+	0.155923i	−0.628918	−	0.777472i	$-0.716502\pi$
$877$	−7.99779	+	4.61753i	−0.270066	+	0.155923i	0.358852	+	0.933395i	$0.383168\pi$
$878$	−10.0659	−	5.81156i	−0.339709	−	0.196131i
$879$	−2.42655	−	1.40097i	−0.0818456	−	0.0472536i
$880$	0.112180	+	0.194302i	0.00378160	+	0.00654992i
$881$	−14.9108			−0.502357			−0.251179	−	0.967941i	$-0.580818\pi$
$881$	−14.9108			−0.502357			−0.251179	+	0.967941i	$0.580818\pi$
$882$	6.85392	+	1.42261i	0.230783	+	0.0479018i
$883$	−37.9171			−1.27601			−0.638006	−	0.770032i	$-0.720240\pi$
$883$	−37.9171			−1.27601			−0.638006	+	0.770032i	$0.720240\pi$
$884$	−22.2502	+	7.85759i	−0.748356	+	0.264279i
$885$	0.663459	−	1.14914i	0.0223019	−	0.0386281i
$886$	4.04701	+	2.33654i	0.135962	+	0.0784976i
$887$	−5.56424	−	9.63754i	−0.186829	−	0.323597i	0.757362	−	0.652995i	$-0.226488\pi$
$887$	−5.56424	−	9.63754i	−0.186829	−	0.323597i	−0.944191	+	0.329398i	$0.893154\pi$
$888$	3.54461			0.118949
$889$	−6.05113	−	37.6227i	−0.202948	−	1.26182i
$890$		−	1.51429i		−	0.0507590i
$891$	−0.571683	+	0.330062i	−0.0191521	+	0.0110575i
$892$	−15.6055	−	9.00982i	−0.522509	−	0.301671i
$893$	28.7676	−	49.8270i	0.962672	−	1.66740i
$894$	−4.05442	−	7.02247i	−0.135600	−	0.234866i
$895$		−	0.152510i		−	0.00509785i
$896$	1.66994	+	2.05215i	0.0557887	+	0.0685574i
$897$	−4.90411	+	26.3332i	−0.163744	+	0.879240i
$898$	−18.3136	−	31.7200i	−0.611132	−	1.05851i
$899$	12.3469	+	7.12847i	0.411792	+	0.237748i
$900$	2.44224	−	4.23009i	0.0814081	−	0.141003i
$901$	9.81691	+	17.0034i	0.327049	+	0.566465i
$902$			0.570909i			0.0190092i
$903$	−12.5820	−	4.79527i	−0.418702	−	0.159577i
$904$		−	15.5576i		−	0.517437i
$905$	4.68125	−	2.70272i	0.155610	−	0.0898415i
$906$	−2.65031	+	4.59047i	−0.0880506	+	0.152508i
$907$	6.05442	−	10.4866i	0.201034	−	0.348201i	−0.747828	−	0.663893i	$-0.768903\pi$
$907$	6.05442	−	10.4866i	0.201034	−	0.348201i	0.948862	+	0.315692i	$0.102237\pi$
$908$	−0.200080	+	0.115516i	−0.00663989	+	0.00383354i
$909$	2.79527			0.0927133
$910$	1.68983	−	2.76703i	0.0560173	−	0.0917262i
$911$	−46.4354			−1.53847			−0.769236	−	0.638964i	$-0.779363\pi$
$911$	−46.4354			−1.53847			−0.769236	+	0.638964i	$0.779363\pi$
$912$	5.27341	−	3.04461i	0.174620	−	0.100817i
$913$	−5.37800	+	9.31498i	−0.177986	+	0.308281i
$914$	−15.6686	+	27.1388i	−0.518272	+	0.897673i
$915$	−0.548905	+	0.316910i	−0.0181462	+	0.0104767i
$916$		−	6.64049i		−	0.219408i
$917$	42.4242	−	34.5228i	1.40097	−	1.14004i
$918$		−	6.54461i		−	0.216004i
$919$	−18.3898	−	31.8521i	−0.606624	−	1.05070i	−0.991792	−	0.127858i	$-0.959190\pi$
$919$	−18.3898	−	31.8521i	−0.606624	−	1.05070i	0.385168	−	0.922846i	$-0.374143\pi$
$920$	−1.26249	+	2.18669i	−0.0416230	+	0.0720931i
$921$	−7.98275	−	4.60884i	−0.263041	−	0.151867i
$922$	−0.300616	−	0.520681i	−0.00990025	−	0.0171477i
$923$	−3.13515	−	0.583868i	−0.103195	−	0.0192183i
$924$	1.72436	−	0.277341i	0.0567273	−	0.00912386i
$925$			17.3136i			0.569267i
$926$	5.25066	+	9.09442i	0.172548	+	0.298861i
$927$	3.76897	−	6.52804i	0.123789	−	0.214409i
$928$	3.08672	+	1.78212i	0.101327	+	0.0585009i
$929$	3.58462	−	2.06958i	0.117608	−	0.0679008i	−0.440042	−	0.897977i	$-0.645037\pi$
$929$	3.58462	−	2.06958i	0.117608	−	0.0679008i	0.557650	+	0.830076i	$0.311703\pi$
$930$			1.35951i			0.0445800i
$931$	−28.3695	+	31.8122i	−0.929773	+	1.04260i
$932$	29.5183			0.966904
$933$	5.73418	+	9.93188i	0.187728	+	0.325155i
$934$	−23.5747	−	13.6109i	−0.771387	−	0.445361i
$935$	−0.734176	+	1.27163i	−0.0240101	+	0.0415867i
$936$	1.20062	+	3.39978i	0.0392435	+	0.111125i
$937$	45.2939			1.47969			0.739844	−	0.672778i	$-0.234899\pi$
$937$	45.2939			1.47969			0.739844	+	0.672778i	$0.234899\pi$
$938$	3.12947	+	19.4574i	0.102181	+	0.635307i
$939$	−22.5642			−0.736356
$940$	1.60570	+	2.78116i	0.0523722	+	0.0907113i
$941$	−41.4781	−	23.9474i	−1.35215	−	0.780663i	−0.363598	−	0.931556i	$-0.618452\pi$
$941$	−41.4781	−	23.9474i	−1.35215	−	0.780663i	−0.988550	+	0.150893i	$0.951785\pi$
$942$	19.9673	+	11.5281i	0.650569	+	0.375606i
$943$	−5.56428	+	3.21254i	−0.181198	+	0.104615i
$944$		−	3.90411i		−	0.127068i
$945$	0.567573	+	0.697477i	0.0184632	+	0.0226889i
$946$	−3.35951			−0.109227
$947$	18.5809	−	10.7277i	0.603799	−	0.348603i	−0.166736	−	0.986002i	$-0.553323\pi$
$947$	18.5809	−	10.7277i	0.603799	−	0.348603i	0.770534	+	0.637398i	$0.219989\pi$
$948$	−6.22436	+	10.7809i	−0.202158	+	0.350148i
$949$	−23.6030	+	27.5872i	−0.766185	+	0.895519i
$950$	14.8713	+	25.7579i	0.482490	+	0.835697i
$951$		−	12.6271i		−	0.409463i
$952$	−6.16660	+	16.1801i	−0.199861	+	0.524401i
$953$	48.0433			1.55627			0.778137	−	0.628094i	$-0.216165\pi$
$953$	48.0433			1.55627			0.778137	+	0.628094i	$0.216165\pi$
$954$	2.59808	−	1.50000i	0.0841158	−	0.0485643i
$955$	−3.06394	−	1.76897i	−0.0991468	−	0.0572424i
$956$	−13.0109	−	7.51182i	−0.420801	−	0.242950i
$957$	2.03762	−	1.17642i	0.0658667	−	0.0380282i
$958$	−28.8711			−0.932784
$959$	13.4028	−	35.1666i	0.432799	−	1.13559i
$960$			0.339877i			0.0109695i
$961$	−7.50000	−	12.9904i	−0.241935	−	0.419045i
$962$	−9.71101	−	8.30851i	−0.313096	−	0.267877i
$963$	1.86485	−	3.23002i	0.0600940	−	0.104086i
$964$	3.85271	−	2.22436i	0.124087	−	0.0716418i
$965$	−2.61684			−0.0842392
$966$	12.4061	+	15.2456i	0.399160	+	0.490519i
$967$		−	4.91481i		−	0.158049i	−0.996873	−	0.0790247i	$-0.974819\pi$
$967$		−	4.91481i		−	0.158049i	0.996873	−	0.0790247i	$-0.0251806\pi$
$968$	−9.14890	+	5.28212i	−0.294057	+	0.169774i
$969$	34.5124	+	19.9258i	1.10870	+	0.640107i
$970$	−4.74151	−	2.73751i	−0.152241	−	0.0878962i
$971$	−15.0792	−	26.1180i	−0.483915	−	0.838165i	0.515915	−	0.856640i	$-0.327452\pi$
$971$	−15.0792	−	26.1180i	−0.483915	−	0.838165i	−0.999829	+	0.0184751i	$0.994119\pi$
$972$	−1.00000			−0.0320750
$973$	−3.96150	−	24.6305i	−0.127000	−	0.789617i
$974$	3.91746			0.125523
$975$	−16.6062	+	5.86441i	−0.531823	+	0.187811i
$976$	−0.932427	+	1.61501i	−0.0298462	+	0.0516952i
$977$	−29.7995	−	17.2047i	−0.953369	−	0.550428i	−0.0592434	−	0.998244i	$-0.518869\pi$
$977$	−29.7995	−	17.2047i	−0.953369	−	0.550428i	−0.894126	+	0.447815i	$0.852202\pi$
$978$	−6.78212	−	11.7470i	−0.216868	−	0.375627i
$979$	−2.94111			−0.0939982
$980$	−0.746010	−	2.25915i	−0.0238304	−	0.0721660i
$981$			14.4095i			0.460059i
$982$	−11.6222	+	6.71008i	−0.370879	+	0.214127i
$983$	17.2772	+	9.97502i	0.551059	+	0.318154i	0.749549	−	0.661949i	$-0.230270\pi$
$983$	17.2772	+	9.97502i	0.551059	+	0.318154i	−0.198490	+	0.980103i	$0.563604\pi$
$984$	−0.432427	+	0.748985i	−0.0137853	+	0.0238768i
$985$	1.52611	+	2.64330i	0.0486259	+	0.0842225i
$986$			23.3265i			0.742868i
$987$	24.6818	−	3.96975i	0.785629	−	0.126358i
$988$	−21.5839	−	4.01963i	−0.686674	−	0.127881i
$989$	−18.9041	−	32.7429i	−0.601116	−	1.04116i
$990$	0.194302	+	0.112180i	0.00617532	+	0.00356532i
$991$	11.9474	−	20.6935i	0.379521	−	0.657351i	−0.611471	−	0.791267i	$-0.709422\pi$
$991$	11.9474	−	20.6935i	0.379521	−	0.657351i	0.990993	+	0.133916i	$0.0427553\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$			26.8212i			0.851145i
$994$	−1.81509	+	1.47703i	−0.0575712	+	0.0468487i
$995$			6.99961i			0.221903i
$996$	−14.1110	+	8.14697i	−0.447123	+	0.258147i
$997$	−3.07273	+	5.32212i	−0.0973142	+	0.168553i	−0.910572	−	0.413350i	$-0.864359\pi$
$997$	−3.07273	+	5.32212i	−0.0973142	+	0.168553i	0.813258	+	0.581903i	$0.197692\pi$
$998$	−16.3910	+	28.3900i	−0.518847	+	0.898669i
$999$	3.06972	−	1.77230i	0.0971216	−	0.0560732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bk.b.25.5	yes	12
3.2	odd	2		1638.2.dm.c.1117.2		12
7.2	even	3	inner	546.2.bk.b.415.2	yes	12
7.3	odd	6		3822.2.c.j.883.5		6
7.4	even	3		3822.2.c.k.883.5		6
13.12	even	2	inner	546.2.bk.b.25.2	✓	12
21.2	odd	6		1638.2.dm.c.415.5		12
39.38	odd	2		1638.2.dm.c.1117.5		12
91.25	even	6		3822.2.c.k.883.2		6
91.38	odd	6		3822.2.c.j.883.2		6
91.51	even	6	inner	546.2.bk.b.415.5	yes	12
273.233	odd	6		1638.2.dm.c.415.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.b.25.2	✓	12	13.12	even	2	inner
546.2.bk.b.25.5	yes	12	1.1	even	1	trivial
546.2.bk.b.415.2	yes	12	7.2	even	3	inner
546.2.bk.b.415.5	yes	12	91.51	even	6	inner
1638.2.dm.c.415.2		12	273.233	odd	6
1638.2.dm.c.415.5		12	21.2	odd	6
1638.2.dm.c.1117.2		12	3.2	odd	2
1638.2.dm.c.1117.5		12	39.38	odd	2
3822.2.c.j.883.2		6	91.38	odd	6
3822.2.c.j.883.5		6	7.3	odd	6
3822.2.c.k.883.2		6	91.25	even	6
3822.2.c.k.883.5		6	7.4	even	3

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.294342 + 0.169938i) q^{5} +1.00000i q^{6} +(-0.420136 - 2.61218i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.294342 + 0.169938i) q^{5} +1.00000i q^{6} +(-0.420136 - 2.61218i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.169938 + 0.294342i) q^{10} +(0.571683 + 0.330062i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.660123 - 3.54461i) q^{13} +(-1.66994 - 2.05215i) q^{14} -0.339877i q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.27230 - 5.66780i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(5.27341 - 3.04461i) q^{19} +0.339877i q^{20} +(2.47228 + 0.942242i) q^{21} +0.660123 q^{22} +(3.71455 + 6.43378i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.44224 + 4.23009i) q^{25} +(-1.20062 - 3.39978i) q^{26} +1.00000 q^{27} +(-2.47228 - 0.942242i) q^{28} -3.56424 q^{29} +(-0.169938 - 0.294342i) q^{30} +(-3.46410 - 2.00000i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.571683 + 0.330062i) q^{33} -6.54461i q^{34} +(0.567573 + 0.697477i) q^{35} -1.00000 q^{36} +(3.06972 - 1.77230i) q^{37} +(3.04461 - 5.27341i) q^{38} +(2.73966 + 2.34399i) q^{39} +(0.169938 + 0.294342i) q^{40} +0.864853i q^{41} +(2.61218 - 0.420136i) q^{42} -5.08921 q^{43} +(0.571683 - 0.330062i) q^{44} +(0.294342 + 0.169938i) q^{45} +(6.43378 + 3.71455i) q^{46} +(8.18283 - 4.72436i) q^{47} +1.00000 q^{48} +(-6.64697 + 2.19494i) q^{49} +4.88448i q^{50} +(3.27230 + 5.66780i) q^{51} +(-2.73966 - 2.34399i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.866025 - 0.500000i) q^{54} -0.224361 q^{55} +(-2.61218 + 0.420136i) q^{56} +6.08921i q^{57} +(-3.08672 + 1.78212i) q^{58} +(3.38106 + 1.95206i) q^{59} +(-0.294342 - 0.169938i) q^{60} +(-0.932427 - 1.61501i) q^{61} -4.00000 q^{62} +(-2.05215 + 1.66994i) q^{63} -1.00000 q^{64} +(0.408063 + 1.15551i) q^{65} +(-0.330062 + 0.571683i) q^{66} +(-6.45078 - 3.72436i) q^{67} +(-3.27230 - 5.66780i) q^{68} -7.42909 q^{69} +(0.840272 + 0.320246i) q^{70} -0.884484i q^{71} +(-0.866025 + 0.500000i) q^{72} +(-8.72051 - 5.03479i) q^{73} +(1.77230 - 3.06972i) q^{74} +(-2.44224 - 4.23009i) q^{75} -6.08921i q^{76} +(0.621996 - 1.63201i) q^{77} +(3.54461 + 0.660123i) q^{78} +(6.22436 + 10.7809i) q^{79} +(0.294342 + 0.169938i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.432427 + 0.748985i) q^{82} +16.2939i q^{83} +(2.05215 - 1.66994i) q^{84} +2.22436i q^{85} +(-4.40739 + 2.54461i) q^{86} +(1.78212 - 3.08672i) q^{87} +(0.330062 - 0.571683i) q^{88} +(-3.85848 + 2.22770i) q^{89} +0.339877 q^{90} +(-9.53649 - 0.235144i) q^{91} +7.42909 q^{92} +(3.46410 - 2.00000i) q^{93} +(4.72436 - 8.18283i) q^{94} +(-1.03479 + 1.79231i) q^{95} +(0.866025 - 0.500000i) q^{96} +16.1088i q^{97} +(-4.65898 + 5.22436i) q^{98} -0.660123i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9} + 6 q^{12} + 12 q^{13} - 18 q^{14} - 6 q^{16} + 18 q^{17} + 12 q^{22} - 6 q^{25} + 12 q^{27} + 12 q^{29} + 24 q^{35} - 12 q^{36} - 6 q^{38} - 6 q^{39} + 6 q^{42} + 24 q^{43} + 12 q^{48} - 18 q^{49} + 18 q^{51} + 6 q^{52} - 18 q^{53} + 48 q^{55} - 6 q^{56} + 6 q^{61} - 48 q^{62} - 12 q^{64} - 12 q^{65} - 6 q^{66} - 18 q^{68} - 6 q^{75} - 24 q^{77} + 24 q^{79} - 6 q^{81} - 12 q^{82} - 6 q^{87} + 6 q^{88} - 24 q^{91} + 6 q^{94} + 24 q^{95}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9 + 6 * q^12 + 12 * q^13 - 18 * q^14 - 6 * q^16 + 18 * q^17 + 12 * q^22 - 6 * q^25 + 12 * q^27 + 12 * q^29 + 24 * q^35 - 12 * q^36 - 6 * q^38 - 6 * q^39 + 6 * q^42 + 24 * q^43 + 12 * q^48 - 18 * q^49 + 18 * q^51 + 6 * q^52 - 18 * q^53 + 48 * q^55 - 6 * q^56 + 6 * q^61 - 48 * q^62 - 12 * q^64 - 12 * q^65 - 6 * q^66 - 18 * q^68 - 6 * q^75 - 24 * q^77 + 24 * q^79 - 6 * q^81 - 12 * q^82 - 6 * q^87 + 6 * q^88 - 24 * q^91 + 6 * q^94 + 24 * q^95

Introduction

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