LMFDB - Embedded newform 546.2.bd.a.121.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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, 2, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 $ x^16 + 26x^14 + 249x^12 + 1144x^10 + 2766x^8 + 3554x^6 + 2260x^4 + 564*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.5
Root			$1.38609i$ of defining polynomial
Character	$\chi$	$=$	546.121
Dual form			546.2.bd.a.361.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.80406 - 2.19627i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.227820 + 2.63592i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.80406 - 2.19627i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.227820 + 2.63592i) q^{7} -1.00000i q^{8} +1.00000 q^{9} -4.39255 q^{10} +0.981333i q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.727736 + 3.53135i) q^{13} +(1.12066 + 2.39669i) q^{14} +(3.80406 + 2.19627i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.83830 + 4.91608i) q^{17} +(0.866025 - 0.500000i) q^{18} +0.602893i q^{19} +(-3.80406 + 2.19627i) q^{20} +(0.227820 - 2.63592i) q^{21} +(0.490667 + 0.849860i) q^{22} +(-2.32686 - 4.03024i) q^{23} +1.00000i q^{24} +(7.14723 + 12.3794i) q^{25} +(2.39591 + 2.69437i) q^{26} -1.00000 q^{27} +(2.16887 + 1.51526i) q^{28} +(-1.58902 + 2.75226i) q^{29} +4.39255 q^{30} +(-5.23622 + 3.02313i) q^{31} +(-0.866025 - 0.500000i) q^{32} -0.981333i q^{33} +5.67660i q^{34} +(6.65585 - 9.52685i) q^{35} +(0.500000 - 0.866025i) q^{36} +(0.124767 - 0.0720340i) q^{37} +(0.301447 + 0.522121i) q^{38} +(-0.727736 - 3.53135i) q^{39} +(-2.19627 + 3.80406i) q^{40} +(-8.37436 - 4.83494i) q^{41} +(-1.12066 - 2.39669i) q^{42} +(-3.17681 - 5.50239i) q^{43} +(0.849860 + 0.490667i) q^{44} +(-3.80406 - 2.19627i) q^{45} +(-4.03024 - 2.32686i) q^{46} +(8.79254 + 5.07637i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-6.89620 - 1.20103i) q^{49} +(12.3794 + 7.14723i) q^{50} +(2.83830 - 4.91608i) q^{51} +(3.42210 + 1.13543i) q^{52} +(2.74644 + 4.75697i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(2.15528 - 3.73305i) q^{55} +(2.63592 + 0.227820i) q^{56} -0.602893i q^{57} +3.17804i q^{58} +(-7.63468 - 4.40789i) q^{59} +(3.80406 - 2.19627i) q^{60} -1.62525 q^{61} +(-3.02313 + 5.23622i) q^{62} +(-0.227820 + 2.63592i) q^{63} -1.00000 q^{64} +(4.98745 - 15.0317i) q^{65} +(-0.490667 - 0.849860i) q^{66} -10.9188i q^{67} +(2.83830 + 4.91608i) q^{68} +(2.32686 + 4.03024i) q^{69} +(1.00071 - 11.5784i) q^{70} +(-11.1654 + 6.44637i) q^{71} -1.00000i q^{72} +(4.77913 - 2.75923i) q^{73} +(0.0720340 - 0.124767i) q^{74} +(-7.14723 - 12.3794i) q^{75} +(0.522121 + 0.301447i) q^{76} +(-2.58672 - 0.223568i) q^{77} +(-2.39591 - 2.69437i) q^{78} +(-6.75613 + 11.7020i) q^{79} +4.39255i q^{80} +1.00000 q^{81} -9.66987 q^{82} -7.90170i q^{83} +(-2.16887 - 1.51526i) q^{84} +(21.5941 - 12.4674i) q^{85} +(-5.50239 - 3.17681i) q^{86} +(1.58902 - 2.75226i) q^{87} +0.981333 q^{88} +(1.25701 - 0.725734i) q^{89} -4.39255 q^{90} +(-9.47415 + 1.11375i) q^{91} -4.65372 q^{92} +(5.23622 - 3.02313i) q^{93} +10.1527 q^{94} +(1.32412 - 2.29344i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-0.165011 + 0.0952691i) q^{97} +(-6.57280 + 2.40797i) q^{98} +0.981333i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−3.80406	−	2.19627i	−1.70123	−	0.982203i	−0.944524	−	0.328443i	$-0.893476\pi$
$5$	−3.80406	−	2.19627i	−1.70123	−	0.982203i	−0.756702	−	0.653760i	$-0.773190\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.227820	+	2.63592i	−0.0861080	+	0.996286i
$7$	−0.227820	+	2.63592i	−0.0861080	+	0.996286i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	−4.39255			−1.38904
$11$			0.981333i			0.295883i	0.988996	+	0.147942i	$0.0472648\pi$
$11$			0.981333i			0.295883i	−0.988996	+	0.147942i	$0.952735\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.727736	+	3.53135i	0.201838	+	0.979419i
$13$	0.727736	+	3.53135i	0.201838	+	0.979419i
$14$	1.12066	+	2.39669i	0.299510	+	0.640542i
$15$	3.80406	+	2.19627i	0.982203	+	0.567075i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.83830	+	4.91608i	−0.688389	+	1.19233i	0.283970	+	0.958833i	$0.408349\pi$
$17$	−2.83830	+	4.91608i	−0.688389	+	1.19233i	−0.972359	+	0.233492i	$0.924985\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$			0.602893i			0.138313i	0.997606	+	0.0691566i	$0.0220308\pi$
$19$			0.602893i			0.138313i	−0.997606	+	0.0691566i	$0.977969\pi$
$20$	−3.80406	+	2.19627i	−0.850613	+	0.491102i
$21$	0.227820	−	2.63592i	0.0497145	−	0.575206i
$22$	0.490667	+	0.849860i	0.104610	+	0.181191i
$23$	−2.32686	−	4.03024i	−0.485184	−	0.840364i	0.514671	−	0.857388i	$-0.327914\pi$
$23$	−2.32686	−	4.03024i	−0.485184	−	0.840364i	−0.999855	+	0.0170241i	$0.994581\pi$
$24$			1.00000i			0.204124i
$25$	7.14723	+	12.3794i	1.42945	+	2.47587i
$26$	2.39591	+	2.69437i	0.469877	+	0.528409i
$27$	−1.00000			−0.192450
$28$	2.16887	+	1.51526i	0.409877	+	0.286357i
$29$	−1.58902	+	2.75226i	−0.295074	+	0.511083i	−0.975002	−	0.222196i	$-0.928678\pi$
$29$	−1.58902	+	2.75226i	−0.295074	+	0.511083i	0.679928	+	0.733279i	$0.262011\pi$
$30$	4.39255			0.801965
$31$	−5.23622	+	3.02313i	−0.940453	+	0.542971i	−0.890102	−	0.455761i	$-0.849367\pi$
$31$	−5.23622	+	3.02313i	−0.940453	+	0.542971i	−0.0503510	+	0.998732i	$0.516034\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		−	0.981333i		−	0.170828i
$34$			5.67660i			0.973529i
$35$	6.65585	−	9.52685i	1.12504	−	1.61033i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	0.124767	−	0.0720340i	0.0205115	−	0.0118423i	−0.489709	−	0.871886i	$-0.662897\pi$
$37$	0.124767	−	0.0720340i	0.0205115	−	0.0118423i	0.510221	+	0.860044i	$0.329564\pi$
$38$	0.301447	+	0.522121i	0.0489011	+	0.0846992i
$39$	−0.727736	−	3.53135i	−0.116531	−	0.565468i
$40$	−2.19627	+	3.80406i	−0.347261	+	0.601474i
$41$	−8.37436	−	4.83494i	−1.30785	−	0.755090i	−0.326117	−	0.945329i	$-0.605740\pi$
$41$	−8.37436	−	4.83494i	−1.30785	−	0.755090i	−0.981738	+	0.190239i	$0.939074\pi$
$42$	−1.12066	−	2.39669i	−0.172922	−	0.369817i
$43$	−3.17681	−	5.50239i	−0.484458	−	0.839106i	0.515382	−	0.856960i	$-0.327650\pi$
$43$	−3.17681	−	5.50239i	−0.484458	−	0.839106i	−0.999841	+	0.0178540i	$0.994317\pi$
$44$	0.849860	+	0.490667i	0.128121	+	0.0739708i
$45$	−3.80406	−	2.19627i	−0.567075	−	0.327401i
$46$	−4.03024	−	2.32686i	−0.594227	−	0.343077i
$47$	8.79254	+	5.07637i	1.28252	+	0.740465i	0.977309	−	0.211819i	$-0.0679386\pi$
$47$	8.79254	+	5.07637i	1.28252	+	0.740465i	0.305214	+	0.952284i	$0.401272\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−6.89620	−	1.20103i	−0.985171	−	0.171576i
$50$	12.3794	+	7.14723i	1.75071	+	1.01077i
$51$	2.83830	−	4.91608i	0.397442	−	0.688389i
$52$	3.42210	+	1.13543i	0.474560	+	0.157456i
$53$	2.74644	+	4.75697i	0.377252	+	0.653420i	0.990661	−	0.136345i	$-0.0435356\pi$
$53$	2.74644	+	4.75697i	0.377252	+	0.653420i	−0.613409	+	0.789765i	$0.710202\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	2.15528	−	3.73305i	0.290617	−	0.503364i
$56$	2.63592	+	0.227820i	0.352240	+	0.0304438i
$57$		−	0.602893i		−	0.0798552i
$58$			3.17804i			0.417297i
$59$	−7.63468	−	4.40789i	−0.993951	−	0.573858i	−0.0874982	−	0.996165i	$-0.527887\pi$
$59$	−7.63468	−	4.40789i	−0.993951	−	0.573858i	−0.906453	+	0.422307i	$0.861221\pi$
$60$	3.80406	−	2.19627i	0.491102	−	0.283538i
$61$	−1.62525			−0.208091			−0.104046	−	0.994573i	$-0.533179\pi$
$61$	−1.62525			−0.208091			−0.104046	+	0.994573i	$0.533179\pi$
$62$	−3.02313	+	5.23622i	−0.383938	+	0.665001i
$63$	−0.227820	+	2.63592i	−0.0287027	+	0.332095i
$64$	−1.00000			−0.125000
$65$	4.98745	−	15.0317i	0.618617	−	1.86446i
$66$	−0.490667	−	0.849860i	−0.0603969	−	0.104610i
$67$		−	10.9188i		−	1.33394i	−0.745085	−	0.666969i	$-0.767591\pi$
$67$		−	10.9188i		−	1.33394i	0.745085	−	0.666969i	$-0.232409\pi$
$68$	2.83830	+	4.91608i	0.344195	+	0.596163i
$69$	2.32686	+	4.03024i	0.280121	+	0.485184i
$70$	1.00071	−	11.5784i	0.119608	−	1.38389i
$71$	−11.1654	+	6.44637i	−1.32509	+	0.765043i	−0.984536	−	0.175181i	$-0.943949\pi$
$71$	−11.1654	+	6.44637i	−1.32509	+	0.765043i	−0.340557	+	0.940224i	$0.610616\pi$
$72$		−	1.00000i		−	0.117851i
$73$	4.77913	−	2.75923i	0.559355	−	0.322944i	−0.193531	−	0.981094i	$-0.561994\pi$
$73$	4.77913	−	2.75923i	0.559355	−	0.322944i	0.752887	+	0.658150i	$0.228661\pi$
$74$	0.0720340	−	0.124767i	0.00837378	−	0.0145038i
$75$	−7.14723	−	12.3794i	−0.825291	−	1.42945i
$76$	0.522121	+	0.301447i	0.0598914	+	0.0345783i
$77$	−2.58672	−	0.223568i	−0.294784	−	0.0254779i
$78$	−2.39591	−	2.69437i	−0.271283	−	0.305077i
$79$	−6.75613	+	11.7020i	−0.760124	+	1.31657i	0.182662	+	0.983176i	$0.441529\pi$
$79$	−6.75613	+	11.7020i	−0.760124	+	1.31657i	−0.942786	+	0.333398i	$0.891805\pi$
$80$			4.39255i			0.491102i
$81$	1.00000			0.111111
$82$	−9.66987			−1.06786
$83$		−	7.90170i		−	0.867324i	−0.901076	−	0.433662i	$-0.857221\pi$
$83$		−	7.90170i		−	0.867324i	0.901076	−	0.433662i	$-0.142779\pi$
$84$	−2.16887	−	1.51526i	−0.236643	−	0.165328i
$85$	21.5941	−	12.4674i	2.34221	−	1.35228i
$86$	−5.50239	−	3.17681i	−0.593338	−	0.342564i
$87$	1.58902	−	2.75226i	0.170361	−	0.295074i
$88$	0.981333			0.104610
$89$	1.25701	−	0.725734i	0.133243	−	0.0769277i	−0.431897	−	0.901923i	$-0.642156\pi$
$89$	1.25701	−	0.725734i	0.133243	−	0.0769277i	0.565140	+	0.824995i	$0.308822\pi$
$90$	−4.39255			−0.463015
$91$	−9.47415	+	1.11375i	−0.993161	+	0.116752i
$92$	−4.65372			−0.485184
$93$	5.23622	−	3.02313i	0.542971	−	0.313484i
$94$	10.1527			1.04718
$95$	1.32412	−	2.29344i	0.135852	−	0.235302i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−0.165011	+	0.0952691i	−0.0167543	+	0.00967311i	−0.508354	−	0.861148i	$-0.669746\pi$
$97$	−0.165011	+	0.0952691i	−0.0167543	+	0.00967311i	0.491599	+	0.870821i	$0.336412\pi$
$98$	−6.57280	+	2.40797i	−0.663953	+	0.243242i
$99$			0.981333i			0.0986277i
$100$	14.2945			1.42945
$101$	11.6026			1.15450			0.577251	−	0.816566i	$-0.304125\pi$
$101$	11.6026			1.15450			0.577251	+	0.816566i	$0.304125\pi$
$102$		−	5.67660i		−	0.562067i
$103$	−4.08281	+	7.07164i	−0.402292	+	0.696790i	−0.994002	−	0.109361i	$-0.965120\pi$
$103$	−4.08281	+	7.07164i	−0.402292	+	0.696790i	0.591710	+	0.806151i	$0.298453\pi$
$104$	3.53135	−	0.727736i	0.346277	−	0.0713604i
$105$	−6.65585	+	9.52685i	−0.649544	+	0.929725i
$106$	4.75697	+	2.74644i	0.462038	+	0.266758i
$107$	5.93197	+	10.2745i	0.573466	+	0.993271i	0.996206	+	0.0870209i	$0.0277347\pi$
$107$	5.93197	+	10.2745i	0.573466	+	0.993271i	−0.422741	+	0.906251i	$0.638932\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−6.66746	+	3.84946i	−0.638627	+	0.368711i	−0.784085	−	0.620653i	$-0.786868\pi$
$109$	−6.66746	+	3.84946i	−0.638627	+	0.368711i	0.145459	+	0.989364i	$0.453534\pi$
$110$		−	4.31055i		−	0.410995i
$111$	−0.124767	+	0.0720340i	−0.0118423	+	0.00683716i
$112$	2.39669	−	1.12066i	0.226466	−	0.105893i
$113$	8.88358	+	15.3868i	0.835697	+	1.44747i	0.893462	+	0.449139i	$0.148269\pi$
$113$	8.88358	+	15.3868i	0.835697	+	1.44747i	−0.0577654	+	0.998330i	$0.518398\pi$
$114$	−0.301447	−	0.522121i	−0.0282331	−	0.0489011i
$115$			20.4417i			1.90620i
$116$	1.58902	+	2.75226i	0.147537	+	0.255541i
$117$	0.727736	+	3.53135i	0.0672792	+	0.326473i
$118$	−8.81577			−0.811558
$119$	−12.3118	−	8.60153i	−1.12862	−	0.788501i
$120$	2.19627	−	3.80406i	0.200491	−	0.347261i
$121$	10.0370			0.912453
$122$	−1.40750	+	0.812623i	−0.127429	+	0.0735714i
$123$	8.37436	+	4.83494i	0.755090	+	0.435952i
$124$			6.04627i			0.542971i
$125$		−	40.8263i		−	3.65162i
$126$	1.12066	+	2.39669i	0.0998367	+	0.213514i
$127$	0.800233	−	1.38604i	0.0710092	−	0.122992i	−0.828335	−	0.560234i	$-0.810711\pi$
$127$	0.800233	−	1.38604i	0.0710092	−	0.122992i	0.899344	+	0.437242i	$0.144045\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	3.17681	+	5.50239i	0.279702	+	0.484458i
$130$	−3.19661	−	15.5116i	−0.280362	−	1.36046i
$131$	6.92324	−	11.9914i	0.604886	−	1.04769i	−0.387184	−	0.922003i	$-0.626552\pi$
$131$	6.92324	−	11.9914i	0.604886	−	1.04769i	0.992070	−	0.125691i	$-0.0401146\pi$
$132$	−0.849860	−	0.490667i	−0.0739708	−	0.0427070i
$133$	−1.58918	−	0.137351i	−0.137799	−	0.0119099i
$134$	−5.45938	−	9.45592i	−0.471619	−	0.816867i
$135$	3.80406	+	2.19627i	0.327401	+	0.189025i
$136$	4.91608	+	2.83830i	0.421551	+	0.243382i
$137$	−4.54533	−	2.62425i	−0.388334	−	0.224205i	0.293104	−	0.956081i	$-0.405312\pi$
$137$	−4.54533	−	2.62425i	−0.388334	−	0.224205i	−0.681438	+	0.731876i	$0.738645\pi$
$138$	4.03024	+	2.32686i	0.343077	+	0.198076i
$139$	−2.40712	−	4.16925i	−0.204169	−	0.353631i	0.745699	−	0.666283i	$-0.232116\pi$
$139$	−2.40712	−	4.16925i	−0.204169	−	0.353631i	−0.949868	+	0.312652i	$0.898783\pi$
$140$	−4.92257	−	10.5276i	−0.416033	−	0.889741i
$141$	−8.79254	−	5.07637i	−0.740465	−	0.427508i
$142$	−6.44637	+	11.1654i	−0.540967	+	0.936983i
$143$	−3.46543	+	0.714152i	−0.289794	+	0.0597204i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	12.0894	−	6.97984i	1.00397	−	0.579645i
$146$	2.75923	−	4.77913i	0.228356	−	0.395524i
$147$	6.89620	+	1.20103i	0.568789	+	0.0990596i
$148$		−	0.144068i		−	0.0118423i
$149$			5.64708i			0.462627i	0.972879	+	0.231313i	$0.0743023\pi$
$149$			5.64708i			0.462627i	−0.972879	+	0.231313i	$0.925698\pi$
$150$	−12.3794	−	7.14723i	−1.01077	−	0.583569i
$151$	−5.61817	+	3.24365i	−0.457200	+	0.263964i	−0.710866	−	0.703327i	$-0.751697\pi$
$151$	−5.61817	+	3.24365i	−0.457200	+	0.263964i	0.253666	+	0.967292i	$0.418364\pi$
$152$	0.602893			0.0489011
$153$	−2.83830	+	4.91608i	−0.229463	+	0.397442i
$154$	−2.35195	+	1.09974i	−0.189525	+	0.0886200i
$155$	26.5585			2.13323
$156$	−3.42210	−	1.13543i	−0.273988	−	0.0909075i
$157$	−2.90214	−	5.02666i	−0.231616	−	0.401171i	0.726668	−	0.686989i	$-0.241068\pi$
$157$	−2.90214	−	5.02666i	−0.231616	−	0.401171i	−0.958284	+	0.285818i	$0.907735\pi$
$158$			13.5123i			1.07498i
$159$	−2.74644	−	4.75697i	−0.217807	−	0.377252i
$160$	2.19627	+	3.80406i	0.173631	+	0.300737i
$161$	11.1535	−	5.21526i	0.879021	−	0.411020i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$		−	10.3050i		−	0.807147i	−0.914947	−	0.403574i	$-0.867768\pi$
$163$		−	10.3050i		−	0.807147i	0.914947	−	0.403574i	$-0.132232\pi$
$164$	−8.37436	+	4.83494i	−0.653927	+	0.377545i
$165$	−2.15528	+	3.73305i	−0.167788	+	0.290617i
$166$	−3.95085	−	6.84307i	−0.306645	−	0.531126i
$167$	−11.3642	−	6.56115i	−0.879391	−	0.507717i	−0.00893375	−	0.999960i	$-0.502844\pi$
$167$	−11.3642	−	6.56115i	−0.879391	−	0.507717i	−0.870458	+	0.492243i	$0.836177\pi$
$168$	−2.63592	−	0.227820i	−0.203366	−	0.0175767i
$169$	−11.9408	+	5.13978i	−0.918523	+	0.395367i
$170$	12.4674	−	21.5941i	0.956204	−	1.65619i
$171$			0.602893i			0.0461044i
$172$	−6.35361			−0.484458
$173$	−7.81220			−0.593951			−0.296975	−	0.954885i	$-0.595978\pi$
$173$	−7.81220			−0.593951			−0.296975	+	0.954885i	$0.595978\pi$
$174$		−	3.17804i		−	0.240927i
$175$	−34.2593	+	16.0193i	−2.58976	+	1.21094i
$176$	0.849860	−	0.490667i	0.0640606	−	0.0369854i
$177$	7.63468	+	4.40789i	0.573858	+	0.331317i
$178$	0.725734	−	1.25701i	0.0543961	−	0.0942168i
$179$	−13.3246			−0.995927			−0.497963	−	0.867198i	$-0.665919\pi$
$179$	−13.3246			−0.995927			−0.497963	+	0.867198i	$0.665919\pi$
$180$	−3.80406	+	2.19627i	−0.283538	+	0.163701i
$181$	22.5285			1.67453			0.837267	−	0.546794i	$-0.184152\pi$
$181$	22.5285			1.67453			0.837267	+	0.546794i	$0.184152\pi$
$182$	−7.64798	+	5.70161i	−0.566906	+	0.422631i
$183$	1.62525			0.120142
$184$	−4.03024	+	2.32686i	−0.297113	+	0.171539i
$185$	−0.632825			−0.0465262
$186$	3.02313	−	5.23622i	0.221667	−	0.383938i
$187$	−4.82432	−	2.78532i	−0.352789	−	0.203683i
$188$	8.79254	−	5.07637i	0.641262	−	0.370233i
$189$	0.227820	−	2.63592i	0.0165715	−	0.191735i
$190$		−	2.64824i		−	0.192123i
$191$	−1.71117			−0.123816			−0.0619079	−	0.998082i	$-0.519718\pi$
$191$	−1.71117			−0.123816			−0.0619079	+	0.998082i	$0.519718\pi$
$192$	1.00000			0.0721688
$193$			5.08473i			0.366007i	0.983112	+	0.183003i	$0.0585819\pi$
$193$			5.08473i			0.366007i	−0.983112	+	0.183003i	$0.941418\pi$
$194$	−0.0952691	+	0.165011i	−0.00683992	+	0.0118471i
$195$	−4.98745	+	15.0317i	−0.357159	+	1.07645i
$196$	−4.48822	+	5.37176i	−0.320587	+	0.383697i
$197$	−17.1710	−	9.91366i	−1.22338	−	0.706319i	−0.257744	−	0.966213i	$-0.582979\pi$
$197$	−17.1710	−	9.91366i	−1.22338	−	0.706319i	−0.965637	+	0.259894i	$0.916312\pi$
$198$	0.490667	+	0.849860i	0.0348702	+	0.0603969i
$199$	−8.89416	+	15.4051i	−0.630491	+	1.09204i	0.356961	+	0.934119i	$0.383813\pi$
$199$	−8.89416	+	15.4051i	−0.630491	+	1.09204i	−0.987452	+	0.157922i	$0.949520\pi$
$200$	12.3794	−	7.14723i	0.875353	−	0.505385i
$201$			10.9188i			0.770150i
$202$	10.0482	−	5.80131i	0.706986	−	0.408178i
$203$	−6.89275	−	4.81556i	−0.483776	−	0.337986i
$204$	−2.83830	−	4.91608i	−0.198721	−	0.344195i
$205$	21.2377	+	36.7847i	1.48330	+	2.56916i
$206$			8.16563i			0.568926i
$207$	−2.32686	−	4.03024i	−0.161728	−	0.280121i
$208$	2.69437	−	2.39591i	0.186821	−	0.166127i
$209$	−0.591639			−0.0409245
$210$	−1.00071	+	11.5784i	−0.0690556	+	0.798987i
$211$	−1.33521	+	2.31265i	−0.0919196	+	0.159209i	−0.908319	−	0.418278i	$-0.862634\pi$
$211$	−1.33521	+	2.31265i	−0.0919196	+	0.159209i	0.816399	+	0.577488i	$0.195967\pi$
$212$	5.49288			0.377252
$213$	11.1654	−	6.44637i	0.765043	−	0.441698i
$214$	10.2745	+	5.93197i	0.702349	+	0.405501i
$215$			27.9085i			1.90335i
$216$			1.00000i			0.0680414i
$217$	−6.77584	−	14.4910i	−0.459974	−	0.983714i
$218$	−3.84946	+	6.66746i	−0.260718	+	0.451577i
$219$	−4.77913	+	2.75923i	−0.322944	+	0.186452i
$220$	−2.15528	−	3.73305i	−0.145309	−	0.251682i
$221$	−19.4259	−	6.44541i	−1.30673	−	0.433565i
$222$	−0.0720340	+	0.124767i	−0.00483460	+	0.00837378i
$223$	−1.18976	−	0.686910i	−0.0796724	−	0.0459989i	0.459635	−	0.888108i	$-0.347980\pi$
$223$	−1.18976	−	0.686910i	−0.0796724	−	0.0459989i	−0.539307	+	0.842109i	$0.681314\pi$
$224$	1.51526	−	2.16887i	0.101243	−	0.144914i
$225$	7.14723	+	12.3794i	0.476482	+	0.825291i
$226$	15.3868	+	8.88358i	1.02352	+	0.590927i
$227$	15.3078	+	8.83797i	1.01601	+	0.586596i	0.912947	−	0.408078i	$-0.133801\pi$
$227$	15.3078	+	8.83797i	1.01601	+	0.586596i	0.103068	+	0.994674i	$0.467134\pi$
$228$	−0.522121	−	0.301447i	−0.0345783	−	0.0199638i
$229$	18.7520	+	10.8265i	1.23917	+	0.715433i	0.968924	−	0.247359i	$-0.0795627\pi$
$229$	18.7520	+	10.8265i	1.23917	+	0.715433i	0.270243	+	0.962792i	$0.412896\pi$
$230$	10.2208	+	17.7030i	0.673943	+	1.16730i
$231$	2.58672	+	0.223568i	0.170194	+	0.0147097i
$232$	2.75226	+	1.58902i	0.180695	+	0.104324i
$233$	11.8049	−	20.4467i	0.773364	−	1.33951i	−0.162346	−	0.986734i	$-0.551906\pi$
$233$	11.8049	−	20.4467i	0.773364	−	1.33951i	0.935710	−	0.352771i	$-0.114761\pi$
$234$	2.39591	+	2.69437i	0.156626	+	0.176136i
$235$	−22.2982	−	38.6216i	−1.45457	−	2.51940i
$236$	−7.63468	+	4.40789i	−0.496976	+	0.286929i
$237$	6.75613	−	11.7020i	0.438858	−	0.760124i
$238$	−14.9631	−	1.29325i	−0.969914	−	0.0838286i
$239$			8.99248i			0.581675i	0.956772	+	0.290838i	$0.0939340\pi$
$239$			8.99248i			0.581675i	−0.956772	+	0.290838i	$0.906066\pi$
$240$		−	4.39255i		−	0.283538i
$241$	10.1652	+	5.86888i	0.654798	+	0.378048i	0.790292	−	0.612730i	$-0.209929\pi$
$241$	10.1652	+	5.86888i	0.654798	+	0.378048i	−0.135494	+	0.990778i	$0.543262\pi$
$242$	8.69228	−	5.01849i	0.558761	−	0.322601i
$243$	−1.00000			−0.0641500
$244$	−0.812623	+	1.40750i	−0.0520229	+	0.0901062i
$245$	23.5957	+	19.7147i	1.50748	+	1.25953i
$246$	9.66987			0.616529
$247$	−2.12902	+	0.438747i	−0.135467	+	0.0279168i
$248$	3.02313	+	5.23622i	0.191969	+	0.332500i
$249$			7.90170i			0.500750i
$250$	−20.4132	−	35.3566i	−1.29104	−	2.23615i
$251$	1.69099	+	2.92888i	0.106734	+	0.184869i	0.914445	−	0.404709i	$-0.132627\pi$
$251$	1.69099	+	2.92888i	0.106734	+	0.184869i	−0.807711	+	0.589578i	$0.799294\pi$
$252$	2.16887	+	1.51526i	0.136626	+	0.0954524i
$253$	3.95501	−	2.28343i	0.248649	−	0.143558i
$254$		−	1.60047i		−	0.100422i
$255$	−21.5941	+	12.4674i	−1.35228	+	0.780737i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.2504	+	17.7542i	0.639401	+	1.10747i	0.985564	+	0.169300i	$0.0541508\pi$
$257$	10.2504	+	17.7542i	0.639401	+	1.10747i	−0.346164	+	0.938174i	$0.612516\pi$
$258$	5.50239	+	3.17681i	0.342564	+	0.197779i
$259$	0.161452	+	0.345286i	0.0100321	+	0.0214550i
$260$	−10.5241	−	11.8351i	−0.652680	−	0.733983i
$261$	−1.58902	+	2.75226i	−0.0983579	+	0.170361i
$262$		−	13.8465i		−	0.855438i
$263$	11.4554			0.706368			0.353184	−	0.935554i	$-0.385099\pi$
$263$	11.4554			0.706368			0.353184	+	0.935554i	$0.385099\pi$
$264$	−0.981333			−0.0603969
$265$		−	24.1277i		−	1.48215i
$266$	−1.44495	+	0.675641i	−0.0885954	+	0.0414262i
$267$	−1.25701	+	0.725734i	−0.0769277	+	0.0444142i
$268$	−9.45592	−	5.45938i	−0.577612	−	0.333485i
$269$	−4.58177	+	7.93587i	−0.279356	+	0.483858i	−0.971225	−	0.238165i	$-0.923454\pi$
$269$	−4.58177	+	7.93587i	−0.279356	+	0.483858i	0.691869	+	0.722023i	$0.256788\pi$
$270$	4.39255			0.267322
$271$	10.0048	−	5.77628i	0.607749	−	0.350884i	−0.164335	−	0.986405i	$-0.552548\pi$
$271$	10.0048	−	5.77628i	0.607749	−	0.350884i	0.772084	+	0.635520i	$0.219214\pi$
$272$	5.67660			0.344195
$273$	9.47415	−	1.11375i	0.573402	−	0.0674070i
$274$	−5.24850			−0.317073
$275$	−12.1483	+	7.01381i	−0.732569	+	0.422949i
$276$	4.65372			0.280121
$277$	−4.61536	+	7.99404i	−0.277310	+	0.480315i	−0.970715	−	0.240233i	$-0.922776\pi$
$277$	−4.61536	+	7.99404i	−0.277310	+	0.480315i	0.693405	+	0.720548i	$0.256110\pi$
$278$	−4.16925	−	2.40712i	−0.250055	−	0.144369i
$279$	−5.23622	+	3.02313i	−0.313484	+	0.180990i
$280$	−9.52685	−	6.65585i	−0.569338	−	0.397763i
$281$			28.4923i			1.69971i	0.527018	+	0.849854i	$0.323310\pi$
$281$			28.4923i			1.69971i	−0.527018	+	0.849854i	$0.676690\pi$
$282$	−10.1527			−0.604587
$283$	−1.06274			−0.0631736			−0.0315868	−	0.999501i	$-0.510056\pi$
$283$	−1.06274			−0.0631736			−0.0315868	+	0.999501i	$0.510056\pi$
$284$			12.8927i			0.765043i
$285$	−1.32412	+	2.29344i	−0.0784340	+	0.135852i
$286$	−2.64407	+	2.35119i	−0.156347	+	0.139029i
$287$	14.6524	−	20.9727i	0.864902	−	1.23798i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−7.61191	−	13.1842i	−0.447760	−	0.775542i
$290$	6.97984	−	12.0894i	0.409871	−	0.709917i
$291$	0.165011	−	0.0952691i	0.00967311	−	0.00558477i
$292$		−	5.51847i		−	0.322944i
$293$	−7.92143	+	4.57344i	−0.462775	+	0.267183i	−0.713210	−	0.700950i	$-0.752760\pi$
$293$	−7.92143	+	4.57344i	−0.462775	+	0.267183i	0.250436	+	0.968133i	$0.419426\pi$
$294$	6.57280	−	2.40797i	0.383333	−	0.140436i
$295$	19.3618	+	33.5357i	1.12729	+	1.95252i
$296$	−0.0720340	−	0.124767i	−0.00418689	−	0.00725191i
$297$		−	0.981333i		−	0.0569427i
$298$	2.82354	+	4.89051i	0.163563	+	0.283300i
$299$	12.5388	−	11.1499i	0.725140	−	0.644816i
$300$	−14.2945			−0.825291
$301$	15.2276	−	7.12026i	0.877705	−	0.410405i
$302$	−3.24365	+	5.61817i	−0.186651	+	0.323289i
$303$	−11.6026			−0.666553
$304$	0.522121	−	0.301447i	0.0299457	−	0.0172892i
$305$	6.18253	+	3.56948i	0.354011	+	0.204388i
$306$			5.67660i			0.324510i
$307$		−	4.67641i		−	0.266897i	−0.991056	−	0.133448i	$-0.957395\pi$
$307$		−	4.67641i		−	0.266897i	0.991056	−	0.133448i	$-0.0426050\pi$
$308$	−1.48698	+	2.12838i	−0.0847283	+	0.121276i
$309$	4.08281	−	7.07164i	0.232263	−	0.402292i
$310$	23.0003	−	13.2793i	1.30633	−	0.754211i
$311$	−0.384467	−	0.665917i	−0.0218011	−	0.0377607i	0.854919	−	0.518761i	$-0.173607\pi$
$311$	−0.384467	−	0.665917i	−0.0218011	−	0.0377607i	−0.876720	+	0.481001i	$0.840273\pi$
$312$	−3.53135	+	0.727736i	−0.199923	+	0.0412000i
$313$	4.77117	−	8.26391i	0.269682	−	0.467104i	−0.699097	−	0.715027i	$-0.746415\pi$
$313$	4.77117	−	8.26391i	0.269682	−	0.467104i	0.968780	+	0.247923i	$0.0797479\pi$
$314$	−5.02666	−	2.90214i	−0.283671	−	0.163777i
$315$	6.65585	−	9.52685i	0.375015	−	0.536777i
$316$	6.75613	+	11.7020i	0.380062	+	0.658287i
$317$	0.258436	+	0.149208i	0.0145152	+	0.00838036i	0.507240	−	0.861805i	$-0.330666\pi$
$317$	0.258436	+	0.149208i	0.0145152	+	0.00838036i	−0.492725	+	0.870185i	$0.663999\pi$
$318$	−4.75697	−	2.74644i	−0.266758	−	0.154013i
$319$	−2.70089	−	1.55936i	−0.151221	−	0.0873073i
$320$	3.80406	+	2.19627i	0.212653	+	0.122775i
$321$	−5.93197	−	10.2745i	−0.331090	−	0.573466i
$322$	7.05160	−	10.0933i	0.392970	−	0.562478i
$323$	−2.96387	−	1.71119i	−0.164914	−	0.0952133i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−38.5145	+	34.2482i	−2.13640	+	1.89975i
$326$	−5.15248	−	8.92436i	−0.285370	−	0.494275i
$327$	6.66746	−	3.84946i	0.368711	−	0.212876i
$328$	−4.83494	+	8.37436i	−0.266965	+	0.462396i
$329$	−15.3841	+	22.0200i	−0.848150	+	1.21400i
$330$			4.31055i			0.237288i
$331$		−	18.4561i		−	1.01444i	−0.861817	−	0.507219i	$-0.830674\pi$
$331$		−	18.4561i		−	1.01444i	0.861817	−	0.507219i	$-0.169326\pi$
$332$	−6.84307	−	3.95085i	−0.375562	−	0.216831i
$333$	0.124767	−	0.0720340i	0.00683716	−	0.00394744i
$334$	−13.1223			−0.718020
$335$	−23.9806	+	41.5356i	−1.31020	+	2.26933i
$336$	−2.39669	+	1.12066i	−0.130750	+	0.0611372i
$337$	12.4534			0.678378			0.339189	−	0.940718i	$-0.389847\pi$
$337$	12.4534			0.678378			0.339189	+	0.940718i	$0.389847\pi$
$338$	−7.77115	+	10.4216i	−0.422695	+	0.566859i
$339$	−8.88358	−	15.3868i	−0.482490	−	0.835697i
$340$		−	24.9347i		−	1.35228i
$341$	−2.96670	−	5.13848i	−0.160656	−	0.278264i
$342$	0.301447	+	0.522121i	0.0163004	+	0.0282331i
$343$	4.73693	−	17.9042i	0.255770	−	0.966738i
$344$	−5.50239	+	3.17681i	−0.296669	+	0.171282i
$345$		−	20.4417i		−	1.10054i
$346$	−6.76557	+	3.90610i	−0.363719	+	0.209993i
$347$	6.33684	−	10.9757i	0.340179	−	0.589208i	−0.644286	−	0.764784i	$-0.722846\pi$
$347$	6.33684	−	10.9757i	0.340179	−	0.589208i	0.984466	+	0.175576i	$0.0561788\pi$
$348$	−1.58902	−	2.75226i	−0.0851804	−	0.147537i
$349$	−21.4958	−	12.4106i	−1.15064	−	0.664324i	−0.201600	−	0.979468i	$-0.564614\pi$
$349$	−21.4958	−	12.4106i	−1.15064	−	0.664324i	−0.949044	+	0.315144i	$0.897947\pi$
$350$	−21.6598	+	31.0028i	−1.15777	+	1.65717i
$351$	−0.727736	−	3.53135i	−0.0388437	−	0.188489i
$352$	0.490667	−	0.849860i	0.0261526	−	0.0452977i
$353$			33.8635i			1.80237i	0.433435	+	0.901185i	$0.357301\pi$
$353$			33.8635i			1.80237i	−0.433435	+	0.901185i	$0.642699\pi$
$354$	8.81577			0.468553
$355$	56.6319			3.00571
$356$		−	1.45147i		−	0.0769277i
$357$	12.3118	+	8.60153i	0.651610	+	0.455241i
$358$	−11.5394	+	6.66230i	−0.609878	+	0.352113i
$359$	−28.4048	−	16.3995i	−1.49915	−	0.865533i	−0.499148	−	0.866517i	$-0.666354\pi$
$359$	−28.4048	−	16.3995i	−1.49915	−	0.865533i	−1.00000		0.000983725i	$0.999687\pi$
$360$	−2.19627	+	3.80406i	−0.115754	+	0.200491i
$361$	18.6365			0.980869
$362$	19.5103	−	11.2643i	1.02544	−	0.592037i
$363$	−10.0370			−0.526805
$364$	−3.77254	+	8.76173i	−0.197735	+	0.459239i
$365$	−24.2401			−1.26879
$366$	1.40750	−	0.812623i	0.0735714	−	0.0424765i
$367$	28.6163			1.49376			0.746879	−	0.664960i	$-0.231552\pi$
$367$	28.6163			1.49376			0.746879	+	0.664960i	$0.231552\pi$
$368$	−2.32686	+	4.03024i	−0.121296	+	0.210091i
$369$	−8.37436	−	4.83494i	−0.435952	−	0.251697i
$370$	−0.548043	+	0.316413i	−0.0284914	+	0.0164495i
$371$	−13.1647	+	6.15567i	−0.683478	+	0.319586i
$372$		−	6.04627i		−	0.313484i
$373$	−1.27810			−0.0661773			−0.0330887	−	0.999452i	$-0.510534\pi$
$373$	−1.27810			−0.0661773			−0.0330887	+	0.999452i	$0.510534\pi$
$374$	−5.57064			−0.288051
$375$			40.8263i			2.10826i
$376$	5.07637	−	8.79254i	0.261794	−	0.453440i
$377$	−10.8756	−	3.60846i	−0.560121	−	0.185845i
$378$	−1.12066	−	2.39669i	−0.0576407	−	0.123272i
$379$	5.23684	+	3.02349i	0.268999	+	0.155306i	0.628432	−	0.777864i	$-0.283697\pi$
$379$	5.23684	+	3.02349i	0.268999	+	0.155306i	−0.359434	+	0.933171i	$0.617030\pi$
$380$	−1.32412	−	2.29344i	−0.0679258	−	0.117651i
$381$	−0.800233	+	1.38604i	−0.0409972	+	0.0710092i
$382$	−1.48191	+	0.855584i	−0.0758213	+	0.0437755i
$383$			15.0504i			0.769038i	0.923117	+	0.384519i	$0.125633\pi$
$383$			15.0504i			0.769038i	−0.923117	+	0.384519i	$0.874367\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	9.34901	+	6.53161i	0.476470	+	0.332882i
$386$	2.54236	+	4.40350i	0.129403	+	0.224132i
$387$	−3.17681	−	5.50239i	−0.161486	−	0.279702i
$388$			0.190538i			0.00967311i
$389$	3.16331	+	5.47902i	0.160386	+	0.277797i	0.935007	−	0.354628i	$-0.115393\pi$
$389$	3.16331	+	5.47902i	0.160386	+	0.277797i	−0.774621	+	0.632426i	$0.782059\pi$
$390$	3.19661	+	15.5116i	0.161867	+	0.785460i
$391$	26.4173			1.33598
$392$	−1.20103	+	6.89620i	−0.0606614	+	0.348310i
$393$	−6.92324	+	11.9914i	−0.349231	+	0.604886i
$394$	−19.8273			−0.998886
$395$	51.4014	−	29.6766i	2.58629	−	1.49319i
$396$	0.849860	+	0.490667i	0.0427070	+	0.0246569i
$397$			34.5131i			1.73216i	0.499903	+	0.866081i	$0.333369\pi$
$397$			34.5131i			1.73216i	−0.499903	+	0.866081i	$0.666631\pi$
$398$			17.7883i			0.891648i
$399$	1.58918	+	0.137351i	0.0795586	+	0.00687617i
$400$	7.14723	−	12.3794i	0.357361	−	0.618968i
$401$	8.39525	−	4.84700i	0.419239	−	0.242048i	−0.275513	−	0.961297i	$-0.588848\pi$
$401$	8.39525	−	4.84700i	0.419239	−	0.242048i	0.694752	+	0.719250i	$0.255514\pi$
$402$	5.45938	+	9.45592i	0.272289	+	0.471619i
$403$	−14.4863	−	16.2909i	−0.721615	−	0.811506i
$404$	5.80131	−	10.0482i	0.288626	−	0.499914i
$405$	−3.80406	−	2.19627i	−0.189025	−	0.109134i
$406$	−8.37708	−	0.724022i	−0.415747	−	0.0359326i
$407$	0.0706894	+	0.122438i	0.00350394	+	0.00606900i
$408$	−4.91608	−	2.83830i	−0.243382	−	0.140517i
$409$	−15.7864	−	9.11425i	−0.780585	−	0.450671i	0.0560527	−	0.998428i	$-0.482149\pi$
$409$	−15.7864	−	9.11425i	−0.780585	−	0.450671i	−0.836638	+	0.547757i	$0.815482\pi$
$410$	36.7847	+	21.2377i	1.81667	+	1.04885i
$411$	4.54533	+	2.62425i	0.224205	+	0.129445i
$412$	4.08281	+	7.07164i	0.201146	+	0.348395i
$413$	13.3582	−	19.1202i	0.657314	−	0.940846i
$414$	−4.03024	−	2.32686i	−0.198076	−	0.114359i
$415$	−17.3543	+	30.0585i	−0.851889	+	1.47551i
$416$	1.13543	−	3.42210i	0.0556693	−	0.167782i
$417$	2.40712	+	4.16925i	0.117877	+	0.204169i
$418$	−0.512375	+	0.295820i	−0.0250611	+	0.0144690i
$419$	−11.1427	+	19.2997i	−0.544356	+	0.942853i	0.454291	+	0.890853i	$0.349893\pi$
$419$	−11.1427	+	19.2997i	−0.544356	+	0.942853i	−0.998647	+	0.0519993i	$0.983441\pi$
$420$	4.92257	+	10.5276i	0.240197	+	0.513692i
$421$		−	13.4386i		−	0.654957i	−0.944859	−	0.327479i	$-0.893801\pi$
$421$		−	13.4386i		−	0.654957i	0.944859	−	0.327479i	$-0.106199\pi$
$422$			2.67042i			0.129994i
$423$	8.79254	+	5.07637i	0.427508	+	0.246822i
$424$	4.75697	−	2.74644i	0.231019	−	0.133379i
$425$	−81.1440			−3.93606
$426$	6.44637	−	11.1654i	0.312328	−	0.540967i
$427$	0.370264	−	4.28403i	0.0179183	−	0.207319i
$428$	11.8639			0.573466
$429$	3.46543	−	0.714152i	0.167312	−	0.0344796i
$430$	13.9543	+	24.1695i	0.672934	+	1.16556i
$431$		−	1.57361i		−	0.0757983i	−0.999282	−	0.0378991i	$-0.987933\pi$
$431$		−	1.57361i		−	0.0757983i	0.999282	−	0.0378991i	$-0.0120666\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−11.5299	−	19.9703i	−0.554091	−	0.959713i	−0.997974	−	0.0636284i	$-0.979733\pi$
$433$	−11.5299	−	19.9703i	−0.554091	−	0.959713i	0.443883	−	0.896085i	$-0.353601\pi$
$434$	−13.1136	−	9.16167i	−0.629471	−	0.439774i
$435$	−12.0894	+	6.97984i	−0.579645	+	0.334658i
$436$			7.69892i			0.368711i
$437$	2.42981	−	1.40285i	0.116233	−	0.0671074i
$438$	−2.75923	+	4.77913i	−0.131841	+	0.228356i
$439$	−11.8889	−	20.5923i	−0.567429	−	0.982815i	−0.996819	−	0.0796962i	$-0.974605\pi$
$439$	−11.8889	−	20.5923i	−0.567429	−	0.982815i	0.429391	−	0.903119i	$-0.358728\pi$
$440$	−3.73305	−	2.15528i	−0.177966	−	0.102749i
$441$	−6.89620	−	1.20103i	−0.328390	−	0.0571921i
$442$	−20.0460	+	4.13107i	−0.953493	+	0.196495i
$443$	11.2447	−	19.4764i	0.534252	−	0.925351i	−0.464947	−	0.885338i	$-0.653927\pi$
$443$	11.2447	−	19.4764i	0.534252	−	0.925351i	0.999199	−	0.0400129i	$-0.0127399\pi$
$444$			0.144068i			0.00683716i
$445$	−6.37564			−0.302234
$446$	−1.37382			−0.0650523
$447$		−	5.64708i		−	0.267098i
$448$	0.227820	−	2.63592i	0.0107635	−	0.124536i
$449$	−6.93155	+	4.00193i	−0.327120	+	0.188863i	−0.654562	−	0.756008i	$-0.727147\pi$
$449$	−6.93155	+	4.00193i	−0.327120	+	0.188863i	0.327442	+	0.944871i	$0.393814\pi$
$450$	12.3794	+	7.14723i	0.583569	+	0.336924i
$451$	4.74468	−	8.21803i	0.223418	−	0.386972i
$452$	17.7672			0.835697
$453$	5.61817	−	3.24365i	0.263964	−	0.152400i
$454$	17.6759			0.829573
$455$	38.4863	+	16.5711i	1.80427	+	0.776864i
$456$	−0.602893			−0.0282331
$457$	1.35918	−	0.784724i	0.0635799	−	0.0367079i	−0.467873	−	0.883796i	$-0.654980\pi$
$457$	1.35918	−	0.784724i	0.0635799	−	0.0367079i	0.531453	+	0.847088i	$0.321646\pi$
$458$	21.6529			1.01178
$459$	2.83830	−	4.91608i	0.132481	−	0.229463i
$460$	17.7030	+	10.2208i	0.825408	+	0.476549i
$461$	−12.7749	+	7.37561i	−0.594988	+	0.343516i	−0.767067	−	0.641567i	$-0.778285\pi$
$461$	−12.7749	+	7.37561i	−0.594988	+	0.343516i	0.172080	+	0.985083i	$0.444951\pi$
$462$	2.35195	−	1.09974i	0.109423	−	0.0511648i
$463$		−	33.6875i		−	1.56559i	−0.622278	−	0.782797i	$-0.713793\pi$
$463$		−	33.6875i		−	1.56559i	0.622278	−	0.782797i	$-0.286207\pi$
$464$	3.17804			0.147537
$465$	−26.5585			−1.23162
$466$		−	23.6098i		−	1.09370i
$467$	−2.56456	+	4.44196i	−0.118674	+	0.205549i	−0.919242	−	0.393692i	$-0.871198\pi$
$467$	−2.56456	+	4.44196i	−0.118674	+	0.205549i	0.800569	+	0.599241i	$0.204531\pi$
$468$	3.42210	+	1.13543i	0.158187	+	0.0524855i
$469$	28.7810	+	2.48752i	1.32898	+	0.114863i
$470$	−38.6216	−	22.2982i	−1.78148	−	1.02854i
$471$	2.90214	+	5.02666i	0.133724	+	0.231616i
$472$	−4.40789	+	7.63468i	−0.202889	+	0.351415i
$473$	5.39968	−	3.11750i	0.248277	−	0.143343i
$474$		−	13.5123i		−	0.620639i
$475$	−7.46343	+	4.30902i	−0.342446	+	0.197711i
$476$	−13.6050	+	6.36157i	−0.623586	+	0.291582i
$477$	2.74644	+	4.75697i	0.125751	+	0.217807i
$478$	4.49624	+	7.78772i	0.205653	+	0.356202i
$479$			10.6497i			0.486596i	0.969952	+	0.243298i	$0.0782293\pi$
$479$			10.6497i			0.486596i	−0.969952	+	0.243298i	$0.921771\pi$
$480$	−2.19627	−	3.80406i	−0.100246	−	0.173631i
$481$	0.345174	+	0.388172i	0.0157386	+	0.0176991i
$482$	11.7378			0.534640
$483$	−11.1535	+	5.21526i	−0.507503	+	0.237303i
$484$	5.01849	−	8.69228i	0.228113	−	0.395104i
$485$	0.836947			0.0380038
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−12.9208	−	7.45980i	−0.585495	−	0.338036i	0.177819	−	0.984063i	$-0.443096\pi$
$487$	−12.9208	−	7.45980i	−0.585495	−	0.338036i	−0.763314	+	0.646027i	$0.776429\pi$
$488$			1.62525i			0.0735714i
$489$			10.3050i			0.466007i
$490$	30.2919	+	5.27560i	1.36845	+	0.238327i
$491$	−14.2618	+	24.7022i	−0.643628	+	1.11480i	0.340989	+	0.940067i	$0.389238\pi$
$491$	−14.2618	+	24.7022i	−0.643628	+	1.11480i	−0.984617	+	0.174728i	$0.944095\pi$
$492$	8.37436	−	4.83494i	0.377545	−	0.217976i
$493$	−9.02024	−	15.6235i	−0.406251	−	0.703648i
$494$	−1.62442	+	1.44448i	−0.0730859	+	0.0649902i
$495$	2.15528	−	3.73305i	0.0968724	−	0.167788i
$496$	5.23622	+	3.02313i	0.235113	+	0.135743i
$497$	−14.4484	−	30.8999i	−0.648100	−	1.38605i
$498$	3.95085	+	6.84307i	0.177042	+	0.306645i
$499$	−30.5466	−	17.6361i	−1.36745	−	0.789500i	−0.376851	−	0.926274i	$-0.622993\pi$
$499$	−30.5466	−	17.6361i	−1.36745	−	0.789500i	−0.990602	+	0.136774i	$0.956327\pi$
$500$	−35.3566	−	20.4132i	−1.58120	−	0.912904i
$501$	11.3642	+	6.56115i	0.507717	+	0.293130i
$502$	2.92888	+	1.69099i	0.130722	+	0.0754725i
$503$	−3.66511	−	6.34815i	−0.163419	−	0.283050i	0.772674	−	0.634803i	$-0.218919\pi$
$503$	−3.66511	−	6.34815i	−0.163419	−	0.283050i	−0.936093	+	0.351753i	$0.885586\pi$
$504$	2.63592	+	0.227820i	0.117413	+	0.0101479i
$505$	−44.1370	−	25.4825i	−1.96407	−	1.13396i
$506$	2.28343	−	3.95501i	0.101511	−	0.175822i
$507$	11.9408	−	5.13978i	0.530310	−	0.228265i
$508$	−0.800233	−	1.38604i	−0.0355046	−	0.0614958i
$509$	13.1097	−	7.56890i	0.581078	−	0.335486i	−0.180483	−	0.983578i	$-0.557766\pi$
$509$	13.1097	−	7.56890i	0.581078	−	0.335486i	0.761562	+	0.648092i	$0.224433\pi$
$510$	−12.4674	+	21.5941i	−0.552064	+	0.956204i
$511$	6.18435	+	13.2260i	0.273579	+	0.585086i
$512$			1.00000i			0.0441942i
$513$		−	0.602893i		−	0.0266184i
$514$	17.7542	+	10.2504i	0.783103	+	0.452125i
$515$	31.0625	−	17.9340i	1.36878	−	0.790264i
$516$	6.35361			0.279702
$517$	−4.98161	+	8.62841i	−0.219091	+	0.379477i
$518$	0.312464	+	0.218301i	0.0137289	+	0.00959157i
$519$	7.81220			0.342918
$520$	−15.0317	−	4.98745i	−0.659186	−	0.218714i
$521$	−4.32817	−	7.49661i	−0.189620	−	0.328432i	0.755503	−	0.655145i	$-0.227392\pi$
$521$	−4.32817	−	7.49661i	−0.189620	−	0.328432i	−0.945124	+	0.326713i	$0.894059\pi$
$522$			3.17804i			0.139099i
$523$	0.0208312	+	0.0360807i	0.000910886	+	0.00157770i	0.866480	−	0.499211i	$-0.166377\pi$
$523$	0.0208312	+	0.0360807i	0.000910886	+	0.00157770i	−0.865570	+	0.500789i	$0.833043\pi$
$524$	−6.92324	−	11.9914i	−0.302443	−	0.523847i
$525$	34.2593	−	16.0193i	1.49520	−	0.699139i
$526$	9.92064	−	5.72768i	0.432560	−	0.249739i
$527$		−	34.3223i		−	1.49510i
$528$	−0.849860	+	0.490667i	−0.0369854	+	0.0213535i
$529$	0.671428	−	1.16295i	0.0291925	−	0.0505629i
$530$	−12.0639	−	20.8952i	−0.524020	−	0.907630i
$531$	−7.63468	−	4.40789i	−0.331317	−	0.191286i
$532$	−0.913540	+	1.30760i	−0.0396070	+	0.0566915i
$533$	10.9795	−	33.0913i	0.475575	−	1.43334i
$534$	−0.725734	+	1.25701i	−0.0314056	+	0.0543961i
$535$		−	52.1129i		−	2.25304i
$536$	−10.9188			−0.471619
$537$	13.3246			0.574999
$538$			9.16355i			0.395069i
$539$	1.17861	−	6.76747i	0.0507665	−	0.291495i
$540$	3.80406	−	2.19627i	0.163701	−	0.0945125i
$541$	3.82785	+	2.21001i	0.164572	+	0.0950157i	0.580024	−	0.814599i	$-0.303043\pi$
$541$	3.82785	+	2.21001i	0.164572	+	0.0950157i	−0.415452	+	0.909615i	$0.636377\pi$
$542$	5.77628	−	10.0048i	0.248113	−	0.429744i
$543$	−22.5285			−0.966793
$544$	4.91608	−	2.83830i	0.210775	−	0.121691i
$545$	33.8179			1.44860
$546$	7.64798	−	5.70161i	0.327304	−	0.244006i
$547$	−11.5643			−0.494453			−0.247227	−	0.968958i	$-0.579519\pi$
$547$	−11.5643			−0.494453			−0.247227	+	0.968958i	$0.579519\pi$
$548$	−4.54533	+	2.62425i	−0.194167	+	0.112102i
$549$	−1.62525			−0.0693638
$550$	−7.01381	+	12.1483i	−0.299070	+	0.518004i
$551$	−1.65932	−	0.958010i	−0.0706895	−	0.0408126i
$552$	4.03024	−	2.32686i	0.171539	−	0.0990378i
$553$	−29.3063	−	20.4746i	−1.24623	−	0.870669i
$554$			9.23072i			0.392176i
$555$	0.632825			0.0268619
$556$	−4.81424			−0.204169
$557$		−	10.0106i		−	0.424165i	−0.977252	−	0.212082i	$-0.931976\pi$
$557$		−	10.0106i		−	0.424165i	0.977252	−	0.212082i	$-0.0680245\pi$
$558$	−3.02313	+	5.23622i	−0.127979	+	0.221667i
$559$	17.1190	−	15.2227i	0.724055	−	0.643851i
$560$	−11.5784	−	1.00071i	−0.489277	−	0.0422878i
$561$	4.82432	+	2.78532i	0.203683	+	0.117596i
$562$	14.2461	+	24.6751i	0.600938	+	1.04085i
$563$	−9.60167	+	16.6306i	−0.404662	+	0.700895i	−0.994282	−	0.106786i	$-0.965944\pi$
$563$	−9.60167	+	16.6306i	−0.404662	+	0.700895i	0.589620	+	0.807681i	$0.299277\pi$
$564$	−8.79254	+	5.07637i	−0.370233	+	0.213754i
$565$		−	78.0430i		−	3.28329i
$566$	−0.920363	+	0.531372i	−0.0386857	+	0.0223352i
$567$	−0.227820	+	2.63592i	−0.00956755	+	0.110698i
$568$	6.44637	+	11.1654i	0.270484	+	0.468491i
$569$	−4.51268	−	7.81619i	−0.189181	−	0.327672i	0.755796	−	0.654807i	$-0.227250\pi$
$569$	−4.51268	−	7.81619i	−0.189181	−	0.327672i	−0.944978	+	0.327135i	$0.893917\pi$
$570$			2.64824i			0.110922i
$571$	7.99270	+	13.8438i	0.334484	+	0.579343i	0.983386	−	0.181529i	$-0.0581046\pi$
$571$	7.99270	+	13.8438i	0.334484	+	0.579343i	−0.648901	+	0.760872i	$0.724771\pi$
$572$	−1.11424	+	3.35822i	−0.0465887	+	0.140414i
$573$	1.71117			0.0714850
$574$	2.20299	−	25.4891i	0.0919512	−	1.06389i
$575$	33.2612	−	57.6101i	1.38709	−	2.40251i
$576$	−1.00000			−0.0416667
$577$	37.5246	−	21.6648i	1.56217	−	0.901919i	0.565132	−	0.825000i	$-0.308825\pi$
$577$	37.5246	−	21.6648i	1.56217	−	0.901919i	0.997037	−	0.0769186i	$-0.0245082\pi$
$578$	−13.1842	−	7.61191i	−0.548391	−	0.316614i
$579$		−	5.08473i		−	0.211314i
$580$		−	13.9597i		−	0.579645i
$581$	20.8283	+	1.80017i	0.864103	+	0.0746836i
$582$	0.0952691	−	0.165011i	0.00394903	−	0.00683992i
$583$	−4.66817	+	2.69517i	−0.193336	+	0.111623i
$584$	−2.75923	−	4.77913i	−0.114178	−	0.197762i
$585$	4.98745	−	15.0317i	0.206206	−	0.621486i
$586$	−4.57344	+	7.92143i	−0.188927	+	0.327231i
$587$	2.71747	+	1.56893i	0.112162	+	0.0647567i	0.555032	−	0.831829i	$-0.312706\pi$
$587$	2.71747	+	1.56893i	0.112162	+	0.0647567i	−0.442870	+	0.896586i	$0.646040\pi$
$588$	4.48822	−	5.37176i	0.185091	−	0.221528i
$589$	−1.82263	−	3.15688i	−0.0751001	−	0.130077i
$590$	33.5357	+	19.3618i	1.38064	+	0.797115i
$591$	17.1710	+	9.91366i	0.706319	+	0.407794i
$592$	−0.124767	−	0.0720340i	−0.00512787	−	0.00296058i
$593$	28.1879	+	16.2743i	1.15754	+	0.668304i	0.950713	−	0.310074i	$-0.100354\pi$
$593$	28.1879	+	16.2743i	1.15754	+	0.668304i	0.206825	+	0.978378i	$0.433687\pi$
$594$	−0.490667	−	0.849860i	−0.0201323	−	0.0348702i
$595$	27.9435	+	59.7608i	1.14557	+	2.44995i
$596$	4.89051	+	2.82354i	0.200323	+	0.115657i
$597$	8.89416	−	15.4051i	0.364014	−	0.630491i
$598$	5.28400	−	15.9255i	0.216079	−	0.651243i
$599$	11.2690	+	19.5185i	0.460440	+	0.797505i	0.998983	−	0.0450931i	$-0.0143584\pi$
$599$	11.2690	+	19.5185i	0.460440	+	0.797505i	−0.538543	+	0.842598i	$0.681025\pi$
$600$	−12.3794	+	7.14723i	−0.505385	+	0.291784i
$601$	0.165055	−	0.285884i	0.00673275	−	0.0116615i	−0.862639	−	0.505819i	$-0.831190\pi$
$601$	0.165055	−	0.285884i	0.00673275	−	0.0116615i	0.869372	+	0.494158i	$0.164524\pi$
$602$	9.62737	−	13.7801i	0.392383	−	0.561637i
$603$		−	10.9188i		−	0.444646i
$604$			6.48730i			0.263964i
$605$	−38.1813	−	22.0440i	−1.55229	−	0.896214i
$606$	−10.0482	+	5.80131i	−0.408178	+	0.235662i
$607$	−6.12259			−0.248508			−0.124254	−	0.992250i	$-0.539654\pi$
$607$	−6.12259			−0.248508			−0.124254	+	0.992250i	$0.539654\pi$
$608$	0.301447	−	0.522121i	0.0122253	−	0.0211748i
$609$	6.89275	+	4.81556i	0.279308	+	0.195136i
$610$	7.13897			0.289048
$611$	−11.5278	+	34.7437i	−0.466364	+	1.40558i
$612$	2.83830	+	4.91608i	0.114732	+	0.198721i
$613$			28.7907i			1.16284i	0.813602	+	0.581422i	$0.197503\pi$
$613$			28.7907i			1.16284i	−0.813602	+	0.581422i	$0.802497\pi$
$614$	−2.33820	−	4.04989i	−0.0943623	−	0.163440i
$615$	−21.2377	−	36.7847i	−0.856386	−	1.48330i
$616$	−0.223568	+	2.58672i	−0.00900780	+	0.104222i
$617$	13.7454	−	7.93589i	0.553368	−	0.319487i	−0.197112	−	0.980381i	$-0.563156\pi$
$617$	13.7454	−	7.93589i	0.553368	−	0.319487i	0.750479	+	0.660894i	$0.229823\pi$
$618$		−	8.16563i		−	0.328470i
$619$	−26.6026	+	15.3590i	−1.06925	+	0.617330i	−0.927976	−	0.372641i	$-0.878452\pi$
$619$	−26.6026	+	15.3590i	−1.06925	+	0.617330i	−0.141271	+	0.989971i	$0.545119\pi$
$620$	13.2793	−	23.0003i	0.533308	−	0.923716i
$621$	2.32686	+	4.03024i	0.0933737	+	0.161728i
$622$	−0.665917	−	0.384467i	−0.0267008	−	0.0154157i
$623$	1.62661	+	3.47872i	0.0651687	+	0.139372i
$624$	−2.69437	+	2.39591i	−0.107861	+	0.0959132i
$625$	−53.9296	+	93.4088i	−2.15718	+	3.73635i
$626$		−	9.54234i		−	0.381389i
$627$	0.591639			0.0236278
$628$	−5.80428			−0.231616
$629$			0.817817i			0.0326085i
$630$	1.00071	−	11.5784i	0.0398693	−	0.461295i
$631$	33.3375	−	19.2474i	1.32715	−	0.766228i	0.342288	−	0.939595i	$-0.388798\pi$
$631$	33.3375	−	19.2474i	1.32715	−	0.766228i	0.984857	+	0.173367i	$0.0554648\pi$
$632$	11.7020	+	6.75613i	0.465479	+	0.268745i
$633$	1.33521	−	2.31265i	0.0530698	−	0.0919196i
$634$	0.298416			0.0118516
$635$	−6.08826	+	3.51506i	−0.241605	+	0.139491i
$636$	−5.49288			−0.217807
$637$	−0.777346	−	25.2269i	−0.0307996	−	0.999526i
$638$	−3.11872			−0.123471
$639$	−11.1654	+	6.44637i	−0.441698	+	0.255014i
$640$	4.39255			0.173631
$641$	−10.4041	+	18.0204i	−0.410936	+	0.711762i	−0.994992	−	0.0999508i	$-0.968131\pi$
$641$	−10.4041	+	18.0204i	−0.410936	+	0.711762i	0.584056	+	0.811713i	$0.301465\pi$
$642$	−10.2745	−	5.93197i	−0.405501	−	0.234116i
$643$	33.7170	−	19.4665i	1.32967	−	0.767684i	0.344420	−	0.938816i	$-0.388076\pi$
$643$	33.7170	−	19.4665i	1.32967	−	0.767684i	0.985248	+	0.171132i	$0.0547423\pi$
$644$	1.06021	−	12.2669i	0.0417782	−	0.483382i
$645$		−	27.9085i		−	1.09890i
$646$	−3.42239			−0.134652
$647$	−12.6312			−0.496583			−0.248291	−	0.968685i	$-0.579869\pi$
$647$	−12.6312			−0.496583			−0.248291	+	0.968685i	$0.579869\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	4.32561	−	7.49217i	0.169795	−	0.294093i
$650$	−16.2304	+	48.9171i	−0.636609	+	1.91869i
$651$	6.77584	+	14.4910i	0.265566	+	0.567948i
$652$	−8.92436	−	5.15248i	−0.349505	−	0.201787i
$653$	23.4644	+	40.6415i	0.918232	+	1.59042i	0.802100	+	0.597190i	$0.203716\pi$
$653$	23.4644	+	40.6415i	0.918232	+	1.59042i	0.116132	+	0.993234i	$0.462951\pi$
$654$	3.84946	−	6.66746i	0.150526	−	0.260718i
$655$	−52.6728	+	30.4106i	−2.05809	+	1.18824i
$656$			9.66987i			0.377545i
$657$	4.77913	−	2.75923i	0.186452	−	0.107648i
$658$	−2.31300	+	26.7619i	−0.0901702	+	1.04329i
$659$	−2.74654	−	4.75715i	−0.106990	−	0.185312i	0.807559	−	0.589786i	$-0.200788\pi$
$659$	−2.74654	−	4.75715i	−0.106990	−	0.185312i	−0.914550	+	0.404474i	$0.867455\pi$
$660$	2.15528	+	3.73305i	0.0838940	+	0.145309i
$661$			26.3471i			1.02478i	0.858752	+	0.512392i	$0.171240\pi$
$661$			26.3471i			1.02478i	−0.858752	+	0.512392i	$0.828760\pi$
$662$	−9.22804	−	15.9834i	−0.358658	−	0.621214i
$663$	19.4259	+	6.44541i	0.754440	+	0.250319i
$664$	−7.90170			−0.306645
$665$	5.74367	+	4.01277i	0.222730	+	0.155608i
$666$	0.0720340	−	0.124767i	0.00279126	−	0.00483460i
$667$	14.7897			0.572660
$668$	−11.3642	+	6.56115i	−0.439696	+	0.253858i
$669$	1.18976	+	0.686910i	0.0459989	+	0.0265575i
$670$			47.9611i			1.85290i
$671$		−	1.59491i		−	0.0615708i
$672$	−1.51526	+	2.16887i	−0.0584524	+	0.0836659i
$673$	−10.3282	+	17.8890i	−0.398123	+	0.689570i	−0.993494	−	0.113881i	$-0.963672\pi$
$673$	−10.3282	+	17.8890i	−0.398123	+	0.689570i	0.595371	+	0.803451i	$0.297005\pi$
$674$	10.7849	−	6.22668i	0.415420	−	0.239843i
$675$	−7.14723	−	12.3794i	−0.275097	−	0.476482i
$676$	−1.51922	+	12.9109i	−0.0584317	+	0.496574i
$677$	−18.4908	+	32.0270i	−0.710659	+	1.23090i	0.253951	+	0.967217i	$0.418270\pi$
$677$	−18.4908	+	32.0270i	−0.710659	+	1.23090i	−0.964610	+	0.263681i	$0.915063\pi$
$678$	−15.3868	−	8.88358i	−0.590927	−	0.341172i
$679$	−0.213529	−	0.456660i	−0.00819450	−	0.0175250i
$680$	−12.4674	−	21.5941i	−0.478102	−	0.828097i
$681$	−15.3078	−	8.83797i	−0.586596	−	0.338672i
$682$	−5.13848	−	2.96670i	−0.196763	−	0.113601i
$683$	−3.97206	−	2.29327i	−0.151986	−	0.0877494i	0.422078	−	0.906559i	$-0.361301\pi$
$683$	−3.97206	−	2.29327i	−0.151986	−	0.0877494i	−0.574065	+	0.818810i	$0.694634\pi$
$684$	0.522121	+	0.301447i	0.0199638	+	0.0115261i
$685$	11.5271	+	19.9656i	0.440429	+	0.762846i
$686$	−4.84982	−	17.8740i	−0.185167	−	0.682432i
$687$	−18.7520	−	10.8265i	−0.715433	−	0.413056i
$688$	−3.17681	+	5.50239i	−0.121115	+	0.209777i
$689$	−14.7998	+	13.1604i	−0.563828	+	0.501373i
$690$	−10.2208	−	17.7030i	−0.389101	−	0.673943i
$691$	18.3754	−	10.6091i	0.699035	−	0.403588i	−0.107953	−	0.994156i	$-0.534430\pi$
$691$	18.3754	−	10.6091i	0.699035	−	0.403588i	0.806988	+	0.590568i	$0.201096\pi$
$692$	−3.90610	+	6.76557i	−0.148488	+	0.257188i
$693$	−2.58672	−	0.223568i	−0.0982614	−	0.00849263i
$694$		−	12.6737i		−	0.481086i
$695$			21.1468i			0.802142i
$696$	−2.75226	−	1.58902i	−0.104324	−	0.0602317i
$697$	47.5379	−	27.4460i	1.80063	−	1.03959i
$698$	−24.8212			−0.939497
$699$	−11.8049	+	20.4467i	−0.446502	+	0.773364i
$700$	−3.25657	+	37.6791i	−0.123087	+	1.42414i
$701$	−2.29081			−0.0865226			−0.0432613	−	0.999064i	$-0.513775\pi$
$701$	−2.29081			−0.0865226			−0.0432613	+	0.999064i	$0.513775\pi$
$702$	−2.39591	−	2.69437i	−0.0904278	−	0.101692i
$703$	0.0434288	+	0.0752209i	0.00163795	+	0.00283701i
$704$		−	0.981333i		−	0.0369854i
$705$	22.2982	+	38.6216i	0.839799	+	1.45457i
$706$	16.9317	+	29.3266i	0.637234	+	1.10372i
$707$	−2.64331	+	30.5836i	−0.0994119	+	1.15021i
$708$	7.63468	−	4.40789i	0.286929	−	0.165659i
$709$			27.7725i			1.04302i	0.853245	+	0.521510i	$0.174631\pi$
$709$			27.7725i			1.04302i	−0.853245	+	0.521510i	$0.825369\pi$
$710$	49.0447	−	28.3160i	1.84061	−	1.06268i
$711$	−6.75613	+	11.7020i	−0.253375	+	0.438858i
$712$	−0.725734	−	1.25701i	−0.0271980	−	0.0471084i
$713$	24.3679	+	14.0688i	0.912586	+	0.526882i
$714$	14.9631	+	1.29325i	0.559980	+	0.0483985i
$715$	14.7511	+	4.89435i	0.551662	+	0.183038i
$716$	−6.66230	+	11.5394i	−0.248982	+	0.431249i
$717$		−	8.99248i		−	0.335830i
$718$	−32.7990			−1.22405
$719$	5.63262			0.210061			0.105031	−	0.994469i	$-0.466506\pi$
$719$	5.63262			0.210061			0.105031	+	0.994469i	$0.466506\pi$
$720$			4.39255i			0.163701i
$721$	−17.7102	−	12.3731i	−0.659561	−	0.460797i
$722$	16.1397	−	9.31826i	0.600657	−	0.346790i
$723$	−10.1652	−	5.86888i	−0.378048	−	0.218266i
$724$	11.2643	−	19.5103i	0.418633	−	0.725094i
$725$	−45.4284			−1.68717
$726$	−8.69228	+	5.01849i	−0.322601	+	0.186254i
$727$	39.3859			1.46074			0.730372	−	0.683050i	$-0.239347\pi$
$727$	39.3859			1.46074			0.730372	+	0.683050i	$0.239347\pi$
$728$	1.11375	+	9.47415i	0.0412782	+	0.351135i
$729$	1.00000			0.0370370
$730$	−20.9926	+	12.1201i	−0.776969	+	0.448584i
$731$	36.0669			1.33398
$732$	0.812623	−	1.40750i	0.0300354	−	0.0520229i
$733$	−28.6445	−	16.5379i	−1.05801	−	0.610842i	−0.133128	−	0.991099i	$-0.542502\pi$
$733$	−28.6445	−	16.5379i	−1.05801	−	0.610842i	−0.924881	+	0.380257i	$0.875835\pi$
$734$	24.7824	−	14.3081i	0.914736	−	0.528123i
$735$	−23.5957	−	19.7147i	−0.870341	−	0.727189i
$736$			4.65372i			0.171539i
$737$	10.7149			0.394690
$738$	−9.66987			−0.355953
$739$			32.6531i			1.20117i	0.799563	+	0.600583i	$0.205065\pi$
$739$			32.6531i			1.20117i	−0.799563	+	0.600583i	$0.794935\pi$
$740$	−0.316413	+	0.548043i	−0.0116316	+	0.0201464i
$741$	2.12902	−	0.438747i	0.0782117	−	0.0161178i
$742$	−8.32314	+	11.9133i	−0.305552	+	0.437352i
$743$	16.9528	+	9.78772i	0.621939	+	0.359077i	0.777624	−	0.628730i	$-0.216425\pi$
$743$	16.9528	+	9.78772i	0.621939	+	0.359077i	−0.155684	+	0.987807i	$0.549758\pi$
$744$	−3.02313	−	5.23622i	−0.110833	−	0.191969i
$745$	12.4025	−	21.4818i	0.454393	−	0.787032i
$746$	−1.10686	+	0.639048i	−0.0405252	+	0.0233972i
$747$		−	7.90170i		−	0.289108i
$748$	−4.82432	+	2.78532i	−0.176394	+	0.101841i
$749$	−28.4342	+	13.2955i	−1.03896	+	0.485807i
$750$	20.4132	+	35.3566i	0.745383	+	1.29104i
$751$	−22.7884	−	39.4707i	−0.831560	−	1.44030i	−0.896800	−	0.442435i	$-0.854115\pi$
$751$	−22.7884	−	39.4707i	−0.831560	−	1.44030i	0.0652400	−	0.997870i	$-0.479219\pi$
$752$		−	10.1527i		−	0.370233i
$753$	−1.69099	−	2.92888i	−0.0616230	−	0.106734i
$754$	−11.2228	+	2.31278i	−0.408709	+	0.0842263i
$755$	28.4958			1.03707
$756$	−2.16887	−	1.51526i	−0.0788809	−	0.0551095i
$757$	−21.5003	+	37.2396i	−0.781441	+	1.35350i	0.149661	+	0.988737i	$0.452182\pi$
$757$	−21.5003	+	37.2396i	−0.781441	+	1.35350i	−0.931102	+	0.364759i	$0.881151\pi$
$758$	6.04698			0.219636
$759$	−3.95501	+	2.28343i	−0.143558	+	0.0828831i
$760$	−2.29344	−	1.32412i	−0.0831918	−	0.0480308i
$761$		−	43.1591i		−	1.56452i	−0.622954	−	0.782258i	$-0.714068\pi$
$761$		−	43.1591i		−	1.56452i	0.622954	−	0.782258i	$-0.285932\pi$
$762$			1.60047i			0.0579788i
$763$	−8.62790	−	18.4519i	−0.312351	−	0.668004i
$764$	−0.855584	+	1.48191i	−0.0309539	+	0.0536138i
$765$	21.5941	−	12.4674i	0.780737	−	0.450759i
$766$	7.52518	+	13.0340i	0.271896	+	0.470937i
$767$	10.0097	−	30.1685i	0.361431	−	1.08932i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−11.5961	−	6.69499i	−0.418165	−	0.241428i	0.276127	−	0.961121i	$-0.410949\pi$
$769$	−11.5961	−	6.69499i	−0.418165	−	0.241428i	−0.694292	+	0.719694i	$0.744282\pi$
$770$	11.3623	+	0.982031i	0.409468	+	0.0353899i
$771$	−10.2504	−	17.7542i	−0.369158	−	0.639401i
$772$	4.40350	+	2.54236i	0.158486	+	0.0915016i
$773$	−19.2378	−	11.1070i	−0.691936	−	0.399489i	0.112401	−	0.993663i	$-0.464146\pi$
$773$	−19.2378	−	11.1070i	−0.691936	−	0.399489i	−0.804337	+	0.594174i	$0.797479\pi$
$774$	−5.50239	−	3.17681i	−0.197779	−	0.114188i
$775$	−74.8490	−	43.2141i	−2.68865	−	1.55229i
$776$	0.0952691	+	0.165011i	0.00341996	+	0.00592355i
$777$	−0.161452	−	0.345286i	−0.00579205	−	0.0123871i
$778$	5.47902	+	3.16331i	0.196432	+	0.113410i
$779$	2.91495	−	5.04884i	0.104439	−	0.180894i
$780$	10.5241	+	11.8351i	0.376825	+	0.423766i
$781$	−6.32604	−	10.9570i	−0.226363	−	0.392073i
$782$	22.8781	−	13.2087i	0.818119	−	0.472341i
$783$	1.58902	−	2.75226i	0.0567870	−	0.0983579i
$784$	2.40797	+	6.57280i	0.0859990	+	0.234743i
$785$			25.4956i			0.909976i
$786$			13.8465i			0.493887i
$787$	3.01131	+	1.73858i	0.107342	+	0.0619737i	0.552710	−	0.833374i	$-0.313594\pi$
$787$	3.01131	+	1.73858i	0.107342	+	0.0619737i	−0.445368	+	0.895348i	$0.646927\pi$
$788$	−17.1710	+	9.91366i	−0.611690	+	0.353160i
$789$	−11.4554			−0.407822
$790$	29.6766	−	51.4014i	1.05585	−	1.82878i
$791$	−42.5823	+	19.9110i	−1.51405	+	0.707954i
$792$	0.981333			0.0348702
$793$	−1.18275	−	5.73931i	−0.0420007	−	0.203809i
$794$	17.2565	+	29.8892i	0.612412	+	1.06073i
$795$			24.1277i			0.855722i
$796$	8.89416	+	15.4051i	0.315245	+	0.546021i
$797$	16.2271	+	28.1062i	0.574794	+	0.995573i	0.996064	+	0.0886373i	$0.0282512\pi$
$797$	16.2271	+	28.1062i	0.574794	+	0.995573i	−0.421270	+	0.906935i	$0.638415\pi$
$798$	1.44495	−	0.675641i	0.0511506	−	0.0239174i
$799$	−49.9117	+	28.8166i	−1.76575	+	1.01946i
$800$		−	14.2945i		−	0.505385i
$801$	1.25701	−	0.725734i	0.0444142	−	0.0256426i
$802$	4.84700	−	8.39525i	0.171153	−	0.296447i
$803$	2.70773	+	4.68992i	0.0955536	+	0.165504i
$804$	9.45592	+	5.45938i	0.333485	+	0.192537i
$805$	−53.8828	−	4.65703i	−1.89912	−	0.164139i
$806$	−20.6910	−	6.86514i	−0.728808	−	0.241814i
$807$	4.58177	−	7.93587i	0.161286	−	0.279356i
$808$		−	11.6026i		−	0.408178i
$809$	−14.4849			−0.509263			−0.254631	−	0.967038i	$-0.581954\pi$
$809$	−14.4849			−0.509263			−0.254631	+	0.967038i	$0.581954\pi$
$810$	−4.39255			−0.154338
$811$			0.508283i			0.0178482i	0.999960	+	0.00892411i	$0.00284067\pi$
$811$			0.508283i			0.0178482i	−0.999960	+	0.00892411i	$0.997159\pi$
$812$	−7.61677	+	3.56152i	−0.267296	+	0.124985i
$813$	−10.0048	+	5.77628i	−0.350884	+	0.202583i
$814$	0.122438	+	0.0706894i	0.00429143	+	0.00247766i
$815$	−22.6325	+	39.2007i	−0.792782	+	1.37314i
$816$	−5.67660			−0.198721
$817$	3.31735	−	1.91527i	0.116059	−	0.0670070i
$818$	−18.2285			−0.637345
$819$	−9.47415	+	1.11375i	−0.331054	+	0.0389174i
$820$	42.4754			1.48330
$821$	29.9340	−	17.2824i	1.04470	−	0.603160i	0.123542	−	0.992339i	$-0.460575\pi$
$821$	29.9340	−	17.2824i	1.04470	−	0.603160i	0.921162	+	0.389179i	$0.127241\pi$
$822$	5.24850			0.183062
$823$	−21.5776	+	37.3735i	−0.752149	+	1.30276i	0.194631	+	0.980877i	$0.437649\pi$
$823$	−21.5776	+	37.3735i	−0.752149	+	1.30276i	−0.946779	+	0.321883i	$0.895684\pi$
$824$	7.07164	+	4.08281i	0.246352	+	0.142232i
$825$	12.1483	−	7.01381i	0.422949	−	0.244190i
$826$	2.00841	−	23.2377i	0.0698816	−	0.808543i
$827$			45.8647i			1.59487i	0.603404	+	0.797435i	$0.293810\pi$
$827$			45.8647i			1.59487i	−0.603404	+	0.797435i	$0.706190\pi$
$828$	−4.65372			−0.161728
$829$	50.3599			1.74907			0.874536	−	0.484960i	$-0.161166\pi$
$829$	50.3599			1.74907			0.874536	+	0.484960i	$0.161166\pi$
$830$			34.7086i			1.20475i
$831$	4.61536	−	7.99404i	0.160105	−	0.277310i
$832$	−0.727736	−	3.53135i	−0.0252297	−	0.122427i
$833$	25.4779	−	30.4934i	0.882756	−	1.05653i
$834$	4.16925	+	2.40712i	0.144369	+	0.0833517i
$835$	28.8201	+	49.9180i	0.997362	+	1.72748i
$836$	−0.295820	+	0.512375i	−0.0102311	+	0.0177208i
$837$	5.23622	−	3.02313i	0.180990	−	0.104495i
$838$			22.2854i			0.769836i
$839$	−15.4290	+	8.90791i	−0.532667	+	0.307535i	−0.742102	−	0.670287i	$-0.766171\pi$
$839$	−15.4290	+	8.90791i	−0.532667	+	0.307535i	0.209435	+	0.977823i	$0.432838\pi$
$840$	9.52685	+	6.65585i	0.328708	+	0.229649i
$841$	9.45003	+	16.3679i	0.325863	+	0.564411i
$842$	−6.71930	−	11.6382i	−0.231562	−	0.401078i
$843$		−	28.4923i		−	0.981327i
$844$	1.33521	+	2.31265i	0.0459598	+	0.0796047i
$845$	56.7118	+	6.67326i	1.95095	+	0.229567i
$846$	10.1527			0.349059
$847$	−2.28663	+	26.4567i	−0.0785695	+	0.909064i
$848$	2.74644	−	4.75697i	0.0943131	−	0.163355i
$849$	1.06274			0.0364733
$850$	−70.2727	+	40.5720i	−2.41033	+	1.39161i
$851$	−0.580629	−	0.335226i	−0.0199037	−	0.0114914i
$852$		−	12.8927i		−	0.441698i
$853$		−	0.0212438i		−	0.000727374i	−1.00000		0.000363687i	$-0.999884\pi$
$853$		−	0.0212438i		−	0.000727374i	1.00000		0.000363687i	$-0.000115765\pi$
$854$	−1.82136	−	3.89521i	−0.0623255	−	0.133291i
$855$	1.32412	−	2.29344i	0.0452839	−	0.0784340i
$856$	10.2745	−	5.93197i	0.351174	−	0.202751i
$857$	−24.1424	−	41.8159i	−0.824690	−	1.42841i	−0.902156	−	0.431410i	$-0.858016\pi$
$857$	−24.1424	−	41.8159i	−0.824690	−	1.42841i	0.0774656	−	0.996995i	$-0.475317\pi$
$858$	2.64407	−	2.35119i	0.0902671	−	0.0802682i
$859$	−20.1110	+	34.8334i	−0.686180	+	1.18850i	0.286884	+	0.957965i	$0.407381\pi$
$859$	−20.1110	+	34.8334i	−0.686180	+	1.18850i	−0.973064	+	0.230534i	$0.925953\pi$
$860$	24.1695	+	13.9543i	0.824173	+	0.475836i
$861$	−14.6524	+	20.9727i	−0.499352	+	0.714747i
$862$	−0.786807	−	1.36279i	−0.0267987	−	0.0464168i
$863$	−34.8461	−	20.1184i	−1.18617	−	0.684838i	−0.228739	−	0.973488i	$-0.573460\pi$
$863$	−34.8461	−	20.1184i	−1.18617	−	0.684838i	−0.957435	+	0.288650i	$0.906794\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	29.7181	+	17.1577i	1.01044	+	0.583380i
$866$	−19.9703	−	11.5299i	−0.678620	−	0.391801i
$867$	7.61191	+	13.1842i	0.258514	+	0.447760i
$868$	−15.9375	−	1.37746i	−0.540954	−	0.0467541i
$869$	−11.4835	−	6.63002i	−0.389552	−	0.224908i
$870$	−6.97984	+	12.0894i	−0.236639	+	0.409871i
$871$	38.5579	−	7.94598i	1.30648	−	0.269239i
$872$	3.84946	+	6.66746i	0.130359	+	0.225789i
$873$	−0.165011	+	0.0952691i	−0.00558477	+	0.00322437i
$874$	1.40285	−	2.42981i	0.0474521	−	0.0821894i
$875$	107.615	+	9.30106i	3.63805	+	0.314433i
$876$			5.51847i			0.186452i
$877$		−	0.0386569i		−	0.00130535i	−1.00000		0.000652676i	$-0.999792\pi$
$877$		−	0.0386569i		−	0.00130535i	1.00000		0.000652676i	$-0.000207753\pi$
$878$	−20.5923	−	11.8889i	−0.694955	−	0.401233i
$879$	7.92143	−	4.57344i	0.267183	−	0.154258i
$880$	−4.31055			−0.145309
$881$	9.26662	−	16.0503i	0.312200	−	0.540747i	−0.666638	−	0.745382i	$-0.732267\pi$
$881$	9.26662	−	16.0503i	0.312200	−	0.540747i	0.978838	+	0.204635i	$0.0656007\pi$
$882$	−6.57280	+	2.40797i	−0.221318	+	0.0810806i
$883$	−17.2118			−0.579224			−0.289612	−	0.957144i	$-0.593526\pi$
$883$	−17.2118			−0.579224			−0.289612	+	0.957144i	$0.593526\pi$
$884$	−15.2949	+	13.6006i	−0.514421	+	0.457439i
$885$	−19.3618	−	33.5357i	−0.650841	−	1.12729i
$886$		−	22.4894i		−	0.755546i
$887$	−16.5895	−	28.7339i	−0.557021	−	0.964789i	−0.997743	−	0.0671450i	$-0.978611\pi$
$887$	−16.5895	−	28.7339i	−0.557021	−	0.964789i	0.440722	−	0.897644i	$-0.354722\pi$
$888$	0.0720340	+	0.124767i	0.00241730	+	0.00418689i
$889$	3.47120	+	2.42512i	0.116420	+	0.0813360i
$890$	−5.52147	+	3.18782i	−0.185080	+	0.106856i
$891$			0.981333i			0.0328759i
$892$	−1.18976	+	0.686910i	−0.0398362	+	0.0229995i
$893$	−3.06051	+	5.30096i	−0.102416	+	0.177390i
$894$	−2.82354	−	4.89051i	−0.0944333	−	0.163563i
$895$	50.6875	+	29.2644i	1.69430	+	0.978202i
$896$	−1.12066	−	2.39669i	−0.0374388	−	0.0800677i
$897$	−12.5388	+	11.1499i	−0.418660	+	0.372285i
$898$	−4.00193	+	6.93155i	−0.133546	+	0.231309i
$899$		−	19.2153i		−	0.640866i
$900$	14.2945			0.476482
$901$	−31.1809			−1.03879
$902$		−	9.48937i		−	0.315961i
$903$	−15.2276	+	7.12026i	−0.506743	+	0.236948i
$904$	15.3868	−	8.88358i	0.511758	−	0.295463i
$905$	−85.6999	−	49.4788i	−2.84876	−	1.64473i
$906$	3.24365	−	5.61817i	0.107763	−	0.186651i
$907$	1.77405			0.0589064			0.0294532	−	0.999566i	$-0.490623\pi$
$907$	1.77405			0.0589064			0.0294532	+	0.999566i	$0.490623\pi$
$908$	15.3078	−	8.83797i	0.508007	−	0.293298i
$909$	11.6026			0.384834
$910$	41.6156	−	4.89218i	1.37955	−	0.162174i
$911$	−4.41204			−0.146177			−0.0730887	−	0.997325i	$-0.523286\pi$
$911$	−4.41204			−0.146177			−0.0730887	+	0.997325i	$0.523286\pi$
$912$	−0.522121	+	0.301447i	−0.0172892	+	0.00998190i
$913$	7.75420			0.256627
$914$	0.784724	−	1.35918i	0.0259564	−	0.0449578i
$915$	−6.18253	−	3.56948i	−0.204388	−	0.118004i
$916$	18.7520	−	10.8265i	0.619583	−	0.357717i
$917$	30.0312	+	20.9810i	0.991716	+	0.692854i
$918$		−	5.67660i		−	0.187356i
$919$	−20.7402			−0.684156			−0.342078	−	0.939672i	$-0.611131\pi$
$919$	−20.7402			−0.684156			−0.342078	+	0.939672i	$0.611131\pi$
$920$	20.4417			0.673943
$921$			4.67641i			0.154093i
$922$	−7.37561	+	12.7749i	−0.242903	+	0.420720i
$923$	−30.8898	−	34.7378i	−1.01675	−	1.14341i
$924$	1.48698	−	2.12838i	0.0489179	−	0.0700186i
$925$	1.78347	+	1.02969i	0.0586401	+	0.0338559i
$926$	−16.8438	−	29.1743i	−0.553521	−	0.958726i
$927$	−4.08281	+	7.07164i	−0.134097	+	0.232263i
$928$	2.75226	−	1.58902i	0.0903475	−	0.0521622i
$929$			12.4433i			0.408250i	0.978945	+	0.204125i	$0.0654349\pi$
$929$			12.4433i			0.408250i	−0.978945	+	0.204125i	$0.934565\pi$
$930$	−23.0003	+	13.2793i	−0.754211	+	0.435444i
$931$	0.724095	−	4.15767i	0.0237313	−	0.136262i
$932$	−11.8049	−	20.4467i	−0.386682	−	0.669753i
$933$	0.384467	+	0.665917i	0.0125869	+	0.0218011i
$934$			5.12913i			0.167830i
$935$	12.2346	+	21.1910i	0.400116	+	0.693021i
$936$	3.53135	−	0.727736i	0.115426	−	0.0237868i
$937$	−11.3834			−0.371879			−0.185939	−	0.982561i	$-0.559533\pi$
$937$	−11.3834			−0.371879			−0.185939	+	0.982561i	$0.559533\pi$
$938$	26.1689	−	12.2363i	0.854443	−	0.399528i
$939$	−4.77117	+	8.26391i	−0.155701	+	0.269682i
$940$	−44.5964			−1.45457
$941$	−24.5840	+	14.1936i	−0.801415	+	0.462697i	−0.843966	−	0.536397i	$-0.819785\pi$
$941$	−24.5840	+	14.1936i	−0.801415	+	0.462697i	0.0425509	+	0.999094i	$0.486452\pi$
$942$	5.02666	+	2.90214i	0.163777	+	0.0945569i
$943$			45.0009i			1.46543i
$944$			8.81577i			0.286929i
$945$	−6.65585	+	9.52685i	−0.216515	+	0.309908i
$946$	3.11750	−	5.39968i	0.101359	−	0.175559i
$947$	−16.4793	+	9.51432i	−0.535505	+	0.309174i	−0.743255	−	0.669008i	$-0.766719\pi$
$947$	−16.4793	+	9.51432i	−0.535505	+	0.309174i	0.207750	+	0.978182i	$0.433386\pi$
$948$	−6.75613	−	11.7020i	−0.219429	−	0.380062i
$949$	13.2218	+	14.8688i	0.429196	+	0.482661i
$950$	−4.30902	+	7.46343i	−0.139803	+	0.242146i
$951$	−0.258436	−	0.149208i	−0.00838036	−	0.00483840i
$952$	−8.60153	+	12.3118i	−0.278777	+	0.399028i
$953$	0.195153	+	0.338014i	0.00632162	+	0.0109494i	0.869169	−	0.494515i	$-0.164654\pi$
$953$	0.195153	+	0.338014i	0.00632162	+	0.0109494i	−0.862847	+	0.505465i	$0.831321\pi$
$954$	4.75697	+	2.74644i	0.154013	+	0.0889192i
$955$	6.50938	+	3.75819i	0.210638	+	0.121612i
$956$	7.78772	+	4.49624i	0.251873	+	0.145419i
$957$	2.70089	+	1.55936i	0.0873073	+	0.0504069i
$958$	5.32484	+	9.22289i	0.172038	+	0.297978i
$959$	7.95284	−	11.3833i	0.256811	−	0.367586i
$960$	−3.80406	−	2.19627i	−0.122775	−	0.0708844i
$961$	2.77869	−	4.81282i	0.0896350	−	0.155252i
$962$	0.493015	+	0.163580i	0.0158955	+	0.00527402i
$963$	5.93197	+	10.2745i	0.191155	+	0.331090i
$964$	10.1652	−	5.86888i	0.327399	−	0.189024i
$965$	11.1674	−	19.3426i	0.359493	−	0.622660i
$966$	−7.05160	+	10.0933i	−0.226882	+	0.324747i
$967$		−	15.1319i		−	0.486608i	−0.969950	−	0.243304i	$-0.921769\pi$
$967$		−	15.1319i		−	0.486608i	0.969950	−	0.243304i	$-0.0782313\pi$
$968$		−	10.0370i		−	0.322601i
$969$	2.96387	+	1.71119i	0.0952133	+	0.0549714i
$970$	0.724818	−	0.418474i	0.0232725	−	0.0134364i
$971$	−44.5142			−1.42853			−0.714264	−	0.699876i	$-0.753238\pi$
$971$	−44.5142			−1.42853			−0.714264	+	0.699876i	$0.753238\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	11.5382	−	5.39514i	0.369898	−	0.172960i
$974$	−14.9196			−0.478055
$975$	38.5145	−	34.2482i	1.23345	−	1.09682i
$976$	0.812623	+	1.40750i	0.0260114	+	0.0450531i
$977$			51.6873i			1.65362i	0.562479	+	0.826812i	$0.309848\pi$
$977$			51.6873i			1.65362i	−0.562479	+	0.826812i	$0.690152\pi$
$978$	5.15248	+	8.92436i	0.164758	+	0.285370i
$979$	0.712187	+	1.23354i	0.0227616	+	0.0394242i
$980$	28.8713	−	10.5771i	0.922260	−	0.337874i
$981$	−6.66746	+	3.84946i	−0.212876	+	0.122904i
$982$			28.5237i			0.910227i
$983$	22.3994	−	12.9323i	0.714431	−	0.412477i	−0.0982685	−	0.995160i	$-0.531330\pi$
$983$	22.3994	−	12.9323i	0.714431	−	0.412477i	0.812700	+	0.582683i	$0.197997\pi$
$984$	4.83494	−	8.37436i	0.154132	−	0.266965i
$985$	43.5462	+	75.4243i	1.38750	+	2.40322i
$986$	−15.6235	−	9.02024i	−0.497554	−	0.287263i
$987$	15.3841	−	22.0200i	0.489680	−	0.700903i
$988$	−0.684546	+	2.06316i	−0.0217783	+	0.0656380i
$989$	−14.7840	+	25.6066i	−0.470103	+	0.814242i
$990$		−	4.31055i		−	0.136998i
$991$	−19.7160			−0.626300			−0.313150	−	0.949704i	$-0.601384\pi$
$991$	−19.7160			−0.626300			−0.313150	+	0.949704i	$0.601384\pi$
$992$	6.04627			0.191969
$993$			18.4561i			0.585686i
$994$	−27.9626	−	19.5359i	−0.886921	−	0.619640i
$995$	67.6678	−	39.0680i	2.14521	−	1.23854i
$996$	6.84307	+	3.95085i	0.216831	+	0.125187i
$997$	−2.84179	+	4.92212i	−0.0900004	+	0.155885i	−0.907511	−	0.420028i	$-0.862020\pi$
$997$	−2.84179	+	4.92212i	−0.0900004	+	0.155885i	0.817511	+	0.575913i	$0.195353\pi$
$998$	−35.2722			−1.11652
$999$	−0.124767	+	0.0720340i	−0.00394744	+	0.00227905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bd.a.121.5	✓	16
3.2	odd	2		1638.2.cr.a.667.4		16
7.4	even	3		546.2.bm.a.277.8	yes	16
13.10	even	6		546.2.bm.a.205.4	yes	16
21.11	odd	6		1638.2.dt.a.1369.1		16
39.23	odd	6		1638.2.dt.a.1297.5		16
91.88	even	6	inner	546.2.bd.a.361.5	yes	16
273.179	odd	6		1638.2.cr.a.361.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.5	✓	16	1.1	even	1	trivial
546.2.bd.a.361.5	yes	16	91.88	even	6	inner
546.2.bm.a.205.4	yes	16	13.10	even	6
546.2.bm.a.277.8	yes	16	7.4	even	3
1638.2.cr.a.361.4		16	273.179	odd	6
1638.2.cr.a.667.4		16	3.2	odd	2
1638.2.dt.a.1297.5		16	39.23	odd	6
1638.2.dt.a.1369.1		16	21.11	odd	6

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.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.80406 - 2.19627i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.227820 + 2.63592i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.80406 - 2.19627i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.227820 + 2.63592i) q^{7} -1.00000i q^{8} +1.00000 q^{9} -4.39255 q^{10} +0.981333i q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.727736 + 3.53135i) q^{13} +(1.12066 + 2.39669i) q^{14} +(3.80406 + 2.19627i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.83830 + 4.91608i) q^{17} +(0.866025 - 0.500000i) q^{18} +0.602893i q^{19} +(-3.80406 + 2.19627i) q^{20} +(0.227820 - 2.63592i) q^{21} +(0.490667 + 0.849860i) q^{22} +(-2.32686 - 4.03024i) q^{23} +1.00000i q^{24} +(7.14723 + 12.3794i) q^{25} +(2.39591 + 2.69437i) q^{26} -1.00000 q^{27} +(2.16887 + 1.51526i) q^{28} +(-1.58902 + 2.75226i) q^{29} +4.39255 q^{30} +(-5.23622 + 3.02313i) q^{31} +(-0.866025 - 0.500000i) q^{32} -0.981333i q^{33} +5.67660i q^{34} +(6.65585 - 9.52685i) q^{35} +(0.500000 - 0.866025i) q^{36} +(0.124767 - 0.0720340i) q^{37} +(0.301447 + 0.522121i) q^{38} +(-0.727736 - 3.53135i) q^{39} +(-2.19627 + 3.80406i) q^{40} +(-8.37436 - 4.83494i) q^{41} +(-1.12066 - 2.39669i) q^{42} +(-3.17681 - 5.50239i) q^{43} +(0.849860 + 0.490667i) q^{44} +(-3.80406 - 2.19627i) q^{45} +(-4.03024 - 2.32686i) q^{46} +(8.79254 + 5.07637i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-6.89620 - 1.20103i) q^{49} +(12.3794 + 7.14723i) q^{50} +(2.83830 - 4.91608i) q^{51} +(3.42210 + 1.13543i) q^{52} +(2.74644 + 4.75697i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(2.15528 - 3.73305i) q^{55} +(2.63592 + 0.227820i) q^{56} -0.602893i q^{57} +3.17804i q^{58} +(-7.63468 - 4.40789i) q^{59} +(3.80406 - 2.19627i) q^{60} -1.62525 q^{61} +(-3.02313 + 5.23622i) q^{62} +(-0.227820 + 2.63592i) q^{63} -1.00000 q^{64} +(4.98745 - 15.0317i) q^{65} +(-0.490667 - 0.849860i) q^{66} -10.9188i q^{67} +(2.83830 + 4.91608i) q^{68} +(2.32686 + 4.03024i) q^{69} +(1.00071 - 11.5784i) q^{70} +(-11.1654 + 6.44637i) q^{71} -1.00000i q^{72} +(4.77913 - 2.75923i) q^{73} +(0.0720340 - 0.124767i) q^{74} +(-7.14723 - 12.3794i) q^{75} +(0.522121 + 0.301447i) q^{76} +(-2.58672 - 0.223568i) q^{77} +(-2.39591 - 2.69437i) q^{78} +(-6.75613 + 11.7020i) q^{79} +4.39255i q^{80} +1.00000 q^{81} -9.66987 q^{82} -7.90170i q^{83} +(-2.16887 - 1.51526i) q^{84} +(21.5941 - 12.4674i) q^{85} +(-5.50239 - 3.17681i) q^{86} +(1.58902 - 2.75226i) q^{87} +0.981333 q^{88} +(1.25701 - 0.725734i) q^{89} -4.39255 q^{90} +(-9.47415 + 1.11375i) q^{91} -4.65372 q^{92} +(5.23622 - 3.02313i) q^{93} +10.1527 q^{94} +(1.32412 - 2.29344i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-0.165011 + 0.0952691i) q^{97} +(-6.57280 + 2.40797i) q^{98} +0.981333i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

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