LMFDB - Embedded newform 324.3.f.a.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(55,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (of order $6$, degree $2$, not 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.a.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +4.00000 q^{4} +(-1.00000 - 1.73205i) q^{5} +(6.00000 + 3.46410i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q-2.00000 q^{2} +4.00000 q^{4} +(-1.00000 - 1.73205i) q^{5} +(6.00000 + 3.46410i) q^{7} -8.00000 q^{8} +(2.00000 + 3.46410i) q^{10} +(6.00000 + 3.46410i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-12.0000 - 6.92820i) q^{14} +16.0000 q^{16} -10.0000 q^{17} +20.7846i q^{19} +(-4.00000 - 6.92820i) q^{20} +(-12.0000 - 6.92820i) q^{22} +(24.0000 - 13.8564i) q^{23} +(10.5000 - 18.1865i) q^{25} +(2.00000 + 3.46410i) q^{26} +(24.0000 + 13.8564i) q^{28} +(-13.0000 + 22.5167i) q^{29} +(6.00000 - 3.46410i) q^{31} -32.0000 q^{32} +20.0000 q^{34} -13.8564i q^{35} +26.0000 q^{37} -41.5692i q^{38} +(8.00000 + 13.8564i) q^{40} +(29.0000 + 50.2295i) q^{41} +(42.0000 + 24.2487i) q^{43} +(24.0000 + 13.8564i) q^{44} +(-48.0000 + 27.7128i) q^{46} +(60.0000 + 34.6410i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-21.0000 + 36.3731i) q^{50} +(-4.00000 - 6.92820i) q^{52} +74.0000 q^{53} -13.8564i q^{55} +(-48.0000 - 27.7128i) q^{56} +(26.0000 - 45.0333i) q^{58} +(78.0000 - 45.0333i) q^{59} +(-13.0000 + 22.5167i) q^{61} +(-12.0000 + 6.92820i) q^{62} +64.0000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(6.00000 - 3.46410i) q^{67} -40.0000 q^{68} +27.7128i q^{70} -46.0000 q^{73} -52.0000 q^{74} +83.1384i q^{76} +(24.0000 + 41.5692i) q^{77} +(-102.000 - 58.8897i) q^{79} +(-16.0000 - 27.7128i) q^{80} +(-58.0000 - 100.459i) q^{82} +(42.0000 + 24.2487i) q^{83} +(10.0000 + 17.3205i) q^{85} +(-84.0000 - 48.4974i) q^{86} +(-48.0000 - 27.7128i) q^{88} -82.0000 q^{89} -13.8564i q^{91} +(96.0000 - 55.4256i) q^{92} +(-120.000 - 69.2820i) q^{94} +(36.0000 - 20.7846i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(1.00000 + 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 8 q^{4} - 2 q^{5} + 12 q^{7} - 16 q^{8}+O(q^{10}) $ 2 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 + 12 * q^7 - 16 * q^8	$ 2 q - 4 q^{2} + 8 q^{4} - 2 q^{5} + 12 q^{7} - 16 q^{8} + 4 q^{10} + 12 q^{11} - 2 q^{13} - 24 q^{14} + 32 q^{16} - 20 q^{17} - 8 q^{20} - 24 q^{22} + 48 q^{23} + 21 q^{25} + 4 q^{26} + 48 q^{28} - 26 q^{29} + 12 q^{31} - 64 q^{32} + 40 q^{34} + 52 q^{37} + 16 q^{40} + 58 q^{41} + 84 q^{43} + 48 q^{44} - 96 q^{46} + 120 q^{47} - q^{49} - 42 q^{50} - 8 q^{52} + 148 q^{53} - 96 q^{56} + 52 q^{58} + 156 q^{59} - 26 q^{61} - 24 q^{62} + 128 q^{64} - 4 q^{65} + 12 q^{67} - 80 q^{68} - 92 q^{73} - 104 q^{74} + 48 q^{77} - 204 q^{79} - 32 q^{80} - 116 q^{82} + 84 q^{83} + 20 q^{85} - 168 q^{86} - 96 q^{88} - 164 q^{89} + 192 q^{92} - 240 q^{94} + 72 q^{95} - 2 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 + 12 * q^7 - 16 * q^8 + 4 * q^10 + 12 * q^11 - 2 * q^13 - 24 * q^14 + 32 * q^16 - 20 * q^17 - 8 * q^20 - 24 * q^22 + 48 * q^23 + 21 * q^25 + 4 * q^26 + 48 * q^28 - 26 * q^29 + 12 * q^31 - 64 * q^32 + 40 * q^34 + 52 * q^37 + 16 * q^40 + 58 * q^41 + 84 * q^43 + 48 * q^44 - 96 * q^46 + 120 * q^47 - q^49 - 42 * q^50 - 8 * q^52 + 148 * q^53 - 96 * q^56 + 52 * q^58 + 156 * q^59 - 26 * q^61 - 24 * q^62 + 128 * q^64 - 4 * q^65 + 12 * q^67 - 80 * q^68 - 92 * q^73 - 104 * q^74 + 48 * q^77 - 204 * q^79 - 32 * q^80 - 116 * q^82 + 84 * q^83 + 20 * q^85 - 168 * q^86 - 96 * q^88 - 164 * q^89 + 192 * q^92 - 240 * q^94 + 72 * q^95 - 2 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.00000			−1.00000
$2$	−2.00000			−1.00000
$3$		0			0
$3$		0			0
$4$	4.00000			1.00000
$5$	−1.00000	−	1.73205i	−0.200000	−	0.346410i	0.748528	−	0.663103i	$-0.230761\pi$
$5$	−1.00000	−	1.73205i	−0.200000	−	0.346410i	−0.948528	+	0.316693i	$0.897428\pi$
$6$		0			0
$7$	6.00000	+	3.46410i	0.857143	+	0.494872i	0.863054	−	0.505111i	$-0.168548\pi$
$7$	6.00000	+	3.46410i	0.857143	+	0.494872i	−0.00591161	+	0.999983i	$0.501882\pi$
$8$	−8.00000			−1.00000
$9$		0			0
$10$	2.00000	+	3.46410i	0.200000	+	0.346410i
$11$	6.00000	+	3.46410i	0.545455	+	0.314918i	0.747287	−	0.664502i	$-0.231356\pi$
$11$	6.00000	+	3.46410i	0.545455	+	0.314918i	−0.201832	+	0.979420i	$0.564690\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.0769231	−	0.133235i	0.824998	−	0.565136i	$-0.191176\pi$
$13$	−1.00000	−	1.73205i	−0.0769231	−	0.133235i	−0.901921	+	0.431901i	$0.857843\pi$
$14$	−12.0000	−	6.92820i	−0.857143	−	0.494872i
$15$		0			0
$16$	16.0000			1.00000
$17$	−10.0000			−0.588235			−0.294118	−	0.955769i	$-0.595026\pi$
$17$	−10.0000			−0.588235			−0.294118	+	0.955769i	$0.595026\pi$
$18$		0			0
$19$			20.7846i			1.09393i	0.837157	+	0.546963i	$0.184216\pi$
$19$			20.7846i			1.09393i	−0.837157	+	0.546963i	$0.815784\pi$
$20$	−4.00000	−	6.92820i	−0.200000	−	0.346410i
$21$		0			0
$22$	−12.0000	−	6.92820i	−0.545455	−	0.314918i
$23$	24.0000	−	13.8564i	1.04348	−	0.602452i	0.122662	−	0.992449i	$-0.460857\pi$
$23$	24.0000	−	13.8564i	1.04348	−	0.602452i	0.920817	+	0.389996i	$0.127524\pi$
$24$		0			0
$25$	10.5000	−	18.1865i	0.420000	−	0.727461i
$26$	2.00000	+	3.46410i	0.0769231	+	0.133235i
$27$		0			0
$28$	24.0000	+	13.8564i	0.857143	+	0.494872i
$29$	−13.0000	+	22.5167i	−0.448276	+	0.776437i	−0.998274	−	0.0587293i	$-0.981295\pi$
$29$	−13.0000	+	22.5167i	−0.448276	+	0.776437i	0.549998	+	0.835166i	$0.314628\pi$
$30$		0			0
$31$	6.00000	−	3.46410i	0.193548	−	0.111745i	−0.400094	−	0.916474i	$-0.631023\pi$
$31$	6.00000	−	3.46410i	0.193548	−	0.111745i	0.593643	+	0.804729i	$0.297689\pi$
$32$	−32.0000			−1.00000
$33$		0			0
$34$	20.0000			0.588235
$35$		−	13.8564i		−	0.395897i
$36$		0			0
$37$	26.0000			0.702703			0.351351	−	0.936244i	$-0.385722\pi$
$37$	26.0000			0.702703			0.351351	+	0.936244i	$0.385722\pi$
$38$		−	41.5692i		−	1.09393i
$39$		0			0
$40$	8.00000	+	13.8564i	0.200000	+	0.346410i
$41$	29.0000	+	50.2295i	0.707317	+	1.22511i	0.965849	+	0.259106i	$0.0834280\pi$
$41$	29.0000	+	50.2295i	0.707317	+	1.22511i	−0.258532	+	0.966003i	$0.583239\pi$
$42$		0			0
$43$	42.0000	+	24.2487i	0.976744	+	0.563924i	0.901286	−	0.433225i	$-0.142625\pi$
$43$	42.0000	+	24.2487i	0.976744	+	0.563924i	0.0754586	+	0.997149i	$0.475958\pi$
$44$	24.0000	+	13.8564i	0.545455	+	0.314918i
$45$		0			0
$46$	−48.0000	+	27.7128i	−1.04348	+	0.602452i
$47$	60.0000	+	34.6410i	1.27660	+	0.737043i	0.976221	−	0.216778i	$-0.0695549\pi$
$47$	60.0000	+	34.6410i	1.27660	+	0.737043i	0.300375	+	0.953821i	$0.402888\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0102041	−	0.0176740i
$50$	−21.0000	+	36.3731i	−0.420000	+	0.727461i
$51$		0			0
$52$	−4.00000	−	6.92820i	−0.0769231	−	0.133235i
$53$	74.0000			1.39623			0.698113	−	0.715987i	$-0.254023\pi$
$53$	74.0000			1.39623			0.698113	+	0.715987i	$0.254023\pi$
$54$		0			0
$55$		−	13.8564i		−	0.251935i
$56$	−48.0000	−	27.7128i	−0.857143	−	0.494872i
$57$		0			0
$58$	26.0000	−	45.0333i	0.448276	−	0.776437i
$59$	78.0000	−	45.0333i	1.32203	−	0.763277i	0.337981	−	0.941153i	$-0.390256\pi$
$59$	78.0000	−	45.0333i	1.32203	−	0.763277i	0.984053	+	0.177876i	$0.0569227\pi$
$60$		0			0
$61$	−13.0000	+	22.5167i	−0.213115	+	0.369126i	−0.952688	−	0.303951i	$-0.901694\pi$
$61$	−13.0000	+	22.5167i	−0.213115	+	0.369126i	0.739573	+	0.673076i	$0.235027\pi$
$62$	−12.0000	+	6.92820i	−0.193548	+	0.111745i
$63$		0			0
$64$	64.0000			1.00000
$65$	−2.00000	+	3.46410i	−0.0307692	+	0.0532939i
$66$		0			0
$67$	6.00000	−	3.46410i	0.0895522	−	0.0517030i	−0.454555	−	0.890719i	$-0.650202\pi$
$67$	6.00000	−	3.46410i	0.0895522	−	0.0517030i	0.544107	+	0.839016i	$0.316868\pi$
$68$	−40.0000			−0.588235
$69$		0			0
$70$			27.7128i			0.395897i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	−46.0000			−0.630137			−0.315068	−	0.949069i	$-0.602027\pi$
$73$	−46.0000			−0.630137			−0.315068	+	0.949069i	$0.602027\pi$
$74$	−52.0000			−0.702703
$75$		0			0
$76$			83.1384i			1.09393i
$77$	24.0000	+	41.5692i	0.311688	+	0.539860i
$78$		0			0
$79$	−102.000	−	58.8897i	−1.29114	−	0.745440i	−0.312283	−	0.949989i	$-0.601094\pi$
$79$	−102.000	−	58.8897i	−1.29114	−	0.745440i	−0.978856	+	0.204550i	$0.934427\pi$
$80$	−16.0000	−	27.7128i	−0.200000	−	0.346410i
$81$		0			0
$82$	−58.0000	−	100.459i	−0.707317	−	1.22511i
$83$	42.0000	+	24.2487i	0.506024	+	0.292153i	0.731198	−	0.682165i	$-0.238962\pi$
$83$	42.0000	+	24.2487i	0.506024	+	0.292153i	−0.225174	+	0.974319i	$0.572295\pi$
$84$		0			0
$85$	10.0000	+	17.3205i	0.117647	+	0.203771i
$86$	−84.0000	−	48.4974i	−0.976744	−	0.563924i
$87$		0			0
$88$	−48.0000	−	27.7128i	−0.545455	−	0.314918i
$89$	−82.0000			−0.921348			−0.460674	−	0.887569i	$-0.652392\pi$
$89$	−82.0000			−0.921348			−0.460674	+	0.887569i	$0.652392\pi$
$90$		0			0
$91$		−	13.8564i		−	0.152268i
$92$	96.0000	−	55.4256i	1.04348	−	0.602452i
$93$		0			0
$94$	−120.000	−	69.2820i	−1.27660	−	0.737043i
$95$	36.0000	−	20.7846i	0.378947	−	0.218785i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.0103093	+	0.0178562i	−0.871134	−	0.491045i	$-0.836615\pi$
$97$	−1.00000	+	1.73205i	−0.0103093	+	0.0178562i	0.860825	+	0.508902i	$0.169948\pi$
$98$	1.00000	+	1.73205i	0.0102041	+	0.0176740i
$99$		0			0
$100$	42.0000	−	72.7461i	0.420000	−	0.727461i
$101$	−37.0000	+	64.0859i	−0.366337	+	0.634514i	−0.988990	−	0.147984i	$-0.952721\pi$
$101$	−37.0000	+	64.0859i	−0.366337	+	0.634514i	0.622653	+	0.782498i	$0.286055\pi$
$102$		0			0
$103$	−66.0000	+	38.1051i	−0.640777	+	0.369953i	−0.784914	−	0.619605i	$-0.787293\pi$
$103$	−66.0000	+	38.1051i	−0.640777	+	0.369953i	0.144137	+	0.989558i	$0.453959\pi$
$104$	8.00000	+	13.8564i	0.0769231	+	0.133235i
$105$		0			0
$106$	−148.000			−1.39623
$107$		−	20.7846i		−	0.194249i	−0.995272	−	0.0971243i	$-0.969036\pi$
$107$		−	20.7846i		−	0.194249i	0.995272	−	0.0971243i	$-0.0309645\pi$
$108$		0			0
$109$	−46.0000			−0.422018			−0.211009	−	0.977484i	$-0.567675\pi$
$109$	−46.0000			−0.422018			−0.211009	+	0.977484i	$0.567675\pi$
$110$			27.7128i			0.251935i
$111$		0			0
$112$	96.0000	+	55.4256i	0.857143	+	0.494872i
$113$	−55.0000	−	95.2628i	−0.486726	−	0.843034i	0.513158	−	0.858294i	$-0.328476\pi$
$113$	−55.0000	−	95.2628i	−0.486726	−	0.843034i	−0.999884	+	0.0152607i	$0.995142\pi$
$114$		0			0
$115$	−48.0000	−	27.7128i	−0.417391	−	0.240981i
$116$	−52.0000	+	90.0666i	−0.448276	+	0.776437i
$117$		0			0
$118$	−156.000	+	90.0666i	−1.32203	+	0.763277i
$119$	−60.0000	−	34.6410i	−0.504202	−	0.291101i
$120$		0			0
$121$	−36.5000	−	63.2199i	−0.301653	−	0.522478i
$122$	26.0000	−	45.0333i	0.213115	−	0.369126i
$123$		0			0
$124$	24.0000	−	13.8564i	0.193548	−	0.111745i
$125$	−92.0000			−0.736000
$126$		0			0
$127$		−	145.492i		−	1.14561i	−0.819692	−	0.572804i	$-0.805856\pi$
$127$		−	145.492i		−	1.14561i	0.819692	−	0.572804i	$-0.194144\pi$
$128$	−128.000			−1.00000
$129$		0			0
$130$	4.00000	−	6.92820i	0.0307692	−	0.0532939i
$131$	−102.000	+	58.8897i	−0.778626	+	0.449540i	−0.835943	−	0.548816i	$-0.815079\pi$
$131$	−102.000	+	58.8897i	−0.778626	+	0.449540i	0.0573171	+	0.998356i	$0.481745\pi$
$132$		0			0
$133$	−72.0000	+	124.708i	−0.541353	+	0.937652i
$134$	−12.0000	+	6.92820i	−0.0895522	+	0.0517030i
$135$		0			0
$136$	80.0000			0.588235
$137$	5.00000	−	8.66025i	0.0364964	−	0.0632135i	−0.847200	−	0.531274i	$-0.821714\pi$
$137$	5.00000	−	8.66025i	0.0364964	−	0.0632135i	0.883697	+	0.468060i	$0.155047\pi$
$138$		0			0
$139$	42.0000	−	24.2487i	0.302158	−	0.174451i	−0.341254	−	0.939971i	$-0.610852\pi$
$139$	42.0000	−	24.2487i	0.302158	−	0.174451i	0.643412	+	0.765520i	$0.277518\pi$
$140$		−	55.4256i		−	0.395897i
$141$		0			0
$142$		0			0
$143$		−	13.8564i		−	0.0968979i
$144$		0			0
$145$	52.0000			0.358621
$146$	92.0000			0.630137
$147$		0			0
$148$	104.000			0.702703
$149$	−1.00000	−	1.73205i	−0.00671141	−	0.0116245i	0.862650	−	0.505801i	$-0.168803\pi$
$149$	−1.00000	−	1.73205i	−0.00671141	−	0.0116245i	−0.869362	+	0.494176i	$0.835470\pi$
$150$		0			0
$151$	78.0000	+	45.0333i	0.516556	+	0.298234i	0.735525	−	0.677498i	$-0.236936\pi$
$151$	78.0000	+	45.0333i	0.516556	+	0.298234i	−0.218968	+	0.975732i	$0.570269\pi$
$152$		−	166.277i		−	1.09393i
$153$		0			0
$154$	−48.0000	−	83.1384i	−0.311688	−	0.539860i
$155$	−12.0000	−	6.92820i	−0.0774194	−	0.0446981i
$156$		0			0
$157$	107.000	+	185.329i	0.681529	+	1.18044i	0.974514	+	0.224325i	$0.0720179\pi$
$157$	107.000	+	185.329i	0.681529	+	1.18044i	−0.292986	+	0.956117i	$0.594649\pi$
$158$	204.000	+	117.779i	1.29114	+	0.745440i
$159$		0			0
$160$	32.0000	+	55.4256i	0.200000	+	0.346410i
$161$	192.000			1.19255
$162$		0			0
$163$			20.7846i			0.127513i	0.997965	+	0.0637565i	$0.0203081\pi$
$163$			20.7846i			0.127513i	−0.997965	+	0.0637565i	$0.979692\pi$
$164$	116.000	+	200.918i	0.707317	+	1.22511i
$165$		0			0
$166$	−84.0000	−	48.4974i	−0.506024	−	0.292153i
$167$	−84.0000	+	48.4974i	−0.502994	+	0.290404i	−0.729949	−	0.683501i	$-0.760456\pi$
$167$	−84.0000	+	48.4974i	−0.502994	+	0.290404i	0.226955	+	0.973905i	$0.427123\pi$
$168$		0			0
$169$	82.5000	−	142.894i	0.488166	−	0.845528i
$170$	−20.0000	−	34.6410i	−0.117647	−	0.203771i
$171$		0			0
$172$	168.000	+	96.9948i	0.976744	+	0.563924i
$173$	167.000	−	289.252i	0.965318	−	1.67198i	0.256559	−	0.966528i	$-0.417411\pi$
$173$	167.000	−	289.252i	0.965318	−	1.67198i	0.708758	−	0.705451i	$-0.249256\pi$
$174$		0			0
$175$	126.000	−	72.7461i	0.720000	−	0.415692i
$176$	96.0000	+	55.4256i	0.545455	+	0.314918i
$177$		0			0
$178$	164.000			0.921348
$179$			187.061i			1.04504i	0.852628	+	0.522518i	$0.175007\pi$
$179$			187.061i			1.04504i	−0.852628	+	0.522518i	$0.824993\pi$
$180$		0			0
$181$	2.00000			0.0110497			0.00552486	−	0.999985i	$-0.498241\pi$
$181$	2.00000			0.0110497			0.00552486	+	0.999985i	$0.498241\pi$
$182$			27.7128i			0.152268i
$183$		0			0
$184$	−192.000	+	110.851i	−1.04348	+	0.602452i
$185$	−26.0000	−	45.0333i	−0.140541	−	0.243423i
$186$		0			0
$187$	−60.0000	−	34.6410i	−0.320856	−	0.185246i
$188$	240.000	+	138.564i	1.27660	+	0.737043i
$189$		0			0
$190$	−72.0000	+	41.5692i	−0.378947	+	0.218785i
$191$	−192.000	−	110.851i	−1.00524	−	0.580373i	−0.0954424	−	0.995435i	$-0.530427\pi$
$191$	−192.000	−	110.851i	−1.00524	−	0.580373i	−0.909793	+	0.415062i	$0.863760\pi$
$192$		0			0
$193$	−145.000	−	251.147i	−0.751295	−	1.30128i	−0.947195	−	0.320658i	$-0.896096\pi$
$193$	−145.000	−	251.147i	−0.751295	−	1.30128i	0.195900	−	0.980624i	$-0.437237\pi$
$194$	2.00000	−	3.46410i	0.0103093	−	0.0178562i
$195$		0			0
$196$	−2.00000	−	3.46410i	−0.0102041	−	0.0176740i
$197$	26.0000			0.131980			0.0659898	−	0.997820i	$-0.478980\pi$
$197$	26.0000			0.131980			0.0659898	+	0.997820i	$0.478980\pi$
$198$		0			0
$199$			394.908i			1.98446i	0.124416	+	0.992230i	$0.460294\pi$
$199$			394.908i			1.98446i	−0.124416	+	0.992230i	$0.539706\pi$
$200$	−84.0000	+	145.492i	−0.420000	+	0.727461i
$201$		0			0
$202$	74.0000	−	128.172i	0.366337	−	0.634514i
$203$	−156.000	+	90.0666i	−0.768473	+	0.443678i
$204$		0			0
$205$	58.0000	−	100.459i	0.282927	−	0.490044i
$206$	132.000	−	76.2102i	0.640777	−	0.369953i
$207$		0			0
$208$	−16.0000	−	27.7128i	−0.0769231	−	0.133235i
$209$	−72.0000	+	124.708i	−0.344498	+	0.596687i
$210$		0			0
$211$	−210.000	+	121.244i	−0.995261	+	0.574614i	−0.906843	−	0.421469i	$-0.861514\pi$
$211$	−210.000	+	121.244i	−0.995261	+	0.574614i	−0.0884181	+	0.996083i	$0.528181\pi$
$212$	296.000			1.39623
$213$		0			0
$214$			41.5692i			0.194249i
$215$		−	96.9948i		−	0.451139i
$216$		0			0
$217$	48.0000			0.221198
$218$	92.0000			0.422018
$219$		0			0
$220$		−	55.4256i		−	0.251935i
$221$	10.0000	+	17.3205i	0.0452489	+	0.0783733i
$222$		0			0
$223$	294.000	+	169.741i	1.31839	+	0.761170i	0.983469	−	0.181077i	$-0.0579585\pi$
$223$	294.000	+	169.741i	1.31839	+	0.761170i	0.334917	+	0.942248i	$0.391292\pi$
$224$	−192.000	−	110.851i	−0.857143	−	0.494872i
$225$		0			0
$226$	110.000	+	190.526i	0.486726	+	0.843034i
$227$	−246.000	−	142.028i	−1.08370	−	0.625675i	−0.151808	−	0.988410i	$-0.548510\pi$
$227$	−246.000	−	142.028i	−1.08370	−	0.625675i	−0.931892	+	0.362735i	$0.881843\pi$
$228$		0			0
$229$	71.0000	+	122.976i	0.310044	+	0.537011i	0.978372	−	0.206855i	$-0.0663230\pi$
$229$	71.0000	+	122.976i	0.310044	+	0.537011i	−0.668328	+	0.743867i	$0.732990\pi$
$230$	96.0000	+	55.4256i	0.417391	+	0.240981i
$231$		0			0
$232$	104.000	−	180.133i	0.448276	−	0.776437i
$233$	−82.0000			−0.351931			−0.175966	−	0.984396i	$-0.556305\pi$
$233$	−82.0000			−0.351931			−0.175966	+	0.984396i	$0.556305\pi$
$234$		0			0
$235$		−	138.564i		−	0.589634i
$236$	312.000	−	180.133i	1.32203	−	0.763277i
$237$		0			0
$238$	120.000	+	69.2820i	0.504202	+	0.291101i
$239$	−336.000	+	193.990i	−1.40586	+	0.811672i	−0.994985	−	0.100021i	$-0.968109\pi$
$239$	−336.000	+	193.990i	−1.40586	+	0.811672i	−0.410872	+	0.911693i	$0.634776\pi$
$240$		0			0
$241$	23.0000	−	39.8372i	0.0954357	−	0.165299i	−0.814355	−	0.580368i	$-0.802909\pi$
$241$	23.0000	−	39.8372i	0.0954357	−	0.165299i	0.909790	+	0.415068i	$0.136242\pi$
$242$	73.0000	+	126.440i	0.301653	+	0.522478i
$243$		0			0
$244$	−52.0000	+	90.0666i	−0.213115	+	0.369126i
$245$	−1.00000	+	1.73205i	−0.00408163	+	0.00706960i
$246$		0			0
$247$	36.0000	−	20.7846i	0.145749	−	0.0841482i
$248$	−48.0000	+	27.7128i	−0.193548	+	0.111745i
$249$		0			0
$250$	184.000			0.736000
$251$		−	145.492i		−	0.579650i	−0.957080	−	0.289825i	$-0.906403\pi$
$251$		−	145.492i		−	0.579650i	0.957080	−	0.289825i	$-0.0935972\pi$
$252$		0			0
$253$	192.000			0.758893
$254$			290.985i			1.14561i
$255$		0			0
$256$	256.000			1.00000
$257$	−127.000	−	219.970i	−0.494163	−	0.855916i	0.505814	−	0.862643i	$-0.331192\pi$
$257$	−127.000	−	219.970i	−0.494163	−	0.855916i	−0.999977	+	0.00672644i	$0.997859\pi$
$258$		0			0
$259$	156.000	+	90.0666i	0.602317	+	0.347748i
$260$	−8.00000	+	13.8564i	−0.0307692	+	0.0532939i
$261$		0			0
$262$	204.000	−	117.779i	0.778626	−	0.449540i
$263$	132.000	+	76.2102i	0.501901	+	0.289773i	0.729498	−	0.683983i	$-0.239754\pi$
$263$	132.000	+	76.2102i	0.501901	+	0.289773i	−0.227597	+	0.973755i	$0.573087\pi$
$264$		0			0
$265$	−74.0000	−	128.172i	−0.279245	−	0.483667i
$266$	144.000	−	249.415i	0.541353	−	0.937652i
$267$		0			0
$268$	24.0000	−	13.8564i	0.0895522	−	0.0517030i
$269$	−262.000			−0.973978			−0.486989	−	0.873408i	$-0.661905\pi$
$269$	−262.000			−0.973978			−0.486989	+	0.873408i	$0.661905\pi$
$270$		0			0
$271$			20.7846i			0.0766960i	0.999264	+	0.0383480i	$0.0122095\pi$
$271$			20.7846i			0.0766960i	−0.999264	+	0.0383480i	$0.987790\pi$
$272$	−160.000			−0.588235
$273$		0			0
$274$	−10.0000	+	17.3205i	−0.0364964	+	0.0632135i
$275$	126.000	−	72.7461i	0.458182	−	0.264531i
$276$		0			0
$277$	−145.000	+	251.147i	−0.523466	+	0.906669i	0.476161	+	0.879358i	$0.342028\pi$
$277$	−145.000	+	251.147i	−0.523466	+	0.906669i	−0.999627	+	0.0273112i	$0.991305\pi$
$278$	−84.0000	+	48.4974i	−0.302158	+	0.174451i
$279$		0			0
$280$			110.851i			0.395897i
$281$	113.000	−	195.722i	0.402135	−	0.696519i	−0.591848	−	0.806049i	$-0.701601\pi$
$281$	113.000	−	195.722i	0.402135	−	0.696519i	0.993983	+	0.109531i	$0.0349348\pi$
$282$		0			0
$283$	258.000	−	148.956i	0.911661	−	0.526348i	0.0306956	−	0.999529i	$-0.490228\pi$
$283$	258.000	−	148.956i	0.911661	−	0.526348i	0.880965	+	0.473181i	$0.156894\pi$
$284$		0			0
$285$		0			0
$286$			27.7128i			0.0968979i
$287$			401.836i			1.40012i
$288$		0			0
$289$	−189.000			−0.653979
$290$	−104.000			−0.358621
$291$		0			0
$292$	−184.000			−0.630137
$293$	−181.000	−	313.501i	−0.617747	−	1.06997i	−0.989896	−	0.141797i	$-0.954712\pi$
$293$	−181.000	−	313.501i	−0.617747	−	1.06997i	0.372148	−	0.928173i	$-0.378621\pi$
$294$		0			0
$295$	−156.000	−	90.0666i	−0.528814	−	0.305311i
$296$	−208.000			−0.702703
$297$		0			0
$298$	2.00000	+	3.46410i	0.00671141	+	0.0116245i
$299$	−48.0000	−	27.7128i	−0.160535	−	0.0926850i
$300$		0			0
$301$	168.000	+	290.985i	0.558140	+	0.966726i
$302$	−156.000	−	90.0666i	−0.516556	−	0.298234i
$303$		0			0
$304$			332.554i			1.09393i
$305$	52.0000			0.170492
$306$		0			0
$307$			145.492i			0.473916i	0.971520	+	0.236958i	$0.0761504\pi$
$307$			145.492i			0.473916i	−0.971520	+	0.236958i	$0.923850\pi$
$308$	96.0000	+	166.277i	0.311688	+	0.539860i
$309$		0			0
$310$	24.0000	+	13.8564i	0.0774194	+	0.0446981i
$311$	204.000	−	117.779i	0.655949	−	0.378712i	−0.134783	−	0.990875i	$-0.543034\pi$
$311$	204.000	−	117.779i	0.655949	−	0.378712i	0.790732	+	0.612163i	$0.209700\pi$
$312$		0			0
$313$	239.000	−	413.960i	0.763578	−	1.32256i	−0.177417	−	0.984136i	$-0.556774\pi$
$313$	239.000	−	413.960i	0.763578	−	1.32256i	0.940995	−	0.338421i	$-0.109893\pi$
$314$	−214.000	−	370.659i	−0.681529	−	1.18044i
$315$		0			0
$316$	−408.000	−	235.559i	−1.29114	−	0.745440i
$317$	−85.0000	+	147.224i	−0.268139	+	0.464430i	−0.968381	−	0.249475i	$-0.919742\pi$
$317$	−85.0000	+	147.224i	−0.268139	+	0.464430i	0.700242	+	0.713905i	$0.253075\pi$
$318$		0			0
$319$	−156.000	+	90.0666i	−0.489028	+	0.282341i
$320$	−64.0000	−	110.851i	−0.200000	−	0.346410i
$321$		0			0
$322$	−384.000			−1.19255
$323$		−	207.846i		−	0.643486i
$324$		0			0
$325$	−42.0000			−0.129231
$326$		−	41.5692i		−	0.127513i
$327$		0			0
$328$	−232.000	−	401.836i	−0.707317	−	1.22511i
$329$	240.000	+	415.692i	0.729483	+	1.26350i
$330$		0			0
$331$	−354.000	−	204.382i	−1.06949	−	0.617468i	−0.141445	−	0.989946i	$-0.545175\pi$
$331$	−354.000	−	204.382i	−1.06949	−	0.617468i	−0.928041	+	0.372478i	$0.878508\pi$
$332$	168.000	+	96.9948i	0.506024	+	0.292153i
$333$		0			0
$334$	168.000	−	96.9948i	0.502994	−	0.290404i
$335$	−12.0000	−	6.92820i	−0.0358209	−	0.0206812i
$336$		0			0
$337$	−169.000	−	292.717i	−0.501484	−	0.868595i	−0.999999	−	0.00171405i	$-0.999454\pi$
$337$	−169.000	−	292.717i	−0.501484	−	0.868595i	0.498515	−	0.866881i	$-0.333879\pi$
$338$	−165.000	+	285.788i	−0.488166	+	0.845528i
$339$		0			0
$340$	40.0000	+	69.2820i	0.117647	+	0.203771i
$341$	48.0000			0.140762
$342$		0			0
$343$		−	346.410i		−	1.00994i
$344$	−336.000	−	193.990i	−0.976744	−	0.563924i
$345$		0			0
$346$	−334.000	+	578.505i	−0.965318	+	1.67198i
$347$	−174.000	+	100.459i	−0.501441	+	0.289507i	−0.729308	−	0.684185i	$-0.760158\pi$
$347$	−174.000	+	100.459i	−0.501441	+	0.289507i	0.227867	+	0.973692i	$0.426825\pi$
$348$		0			0
$349$	−253.000	+	438.209i	−0.724928	+	1.25561i	0.234075	+	0.972219i	$0.424794\pi$
$349$	−253.000	+	438.209i	−0.724928	+	1.25561i	−0.959003	+	0.283394i	$0.908540\pi$
$350$	−252.000	+	145.492i	−0.720000	+	0.415692i
$351$		0			0
$352$	−192.000	−	110.851i	−0.545455	−	0.314918i
$353$	89.0000	−	154.153i	0.252125	−	0.436693i	−0.711986	−	0.702194i	$-0.752204\pi$
$353$	89.0000	−	154.153i	0.252125	−	0.436693i	0.964111	+	0.265501i	$0.0855374\pi$
$354$		0			0
$355$		0			0
$356$	−328.000			−0.921348
$357$		0			0
$358$		−	374.123i		−	1.04504i
$359$		−	166.277i		−	0.463167i	−0.972815	−	0.231583i	$-0.925609\pi$
$359$		−	166.277i		−	0.463167i	0.972815	−	0.231583i	$-0.0743906\pi$
$360$		0			0
$361$	−71.0000			−0.196676
$362$	−4.00000			−0.0110497
$363$		0			0
$364$		−	55.4256i		−	0.152268i
$365$	46.0000	+	79.6743i	0.126027	+	0.218286i
$366$		0			0
$367$	−174.000	−	100.459i	−0.474114	−	0.273730i	0.243846	−	0.969814i	$-0.421591\pi$
$367$	−174.000	−	100.459i	−0.474114	−	0.273730i	−0.717960	+	0.696084i	$0.754924\pi$
$368$	384.000	−	221.703i	1.04348	−	0.602452i
$369$		0			0
$370$	52.0000	+	90.0666i	0.140541	+	0.243423i
$371$	444.000	+	256.344i	1.19677	+	0.690953i
$372$		0			0
$373$	155.000	+	268.468i	0.415550	+	0.719753i	0.995486	−	0.0949088i	$-0.0302559\pi$
$373$	155.000	+	268.468i	0.415550	+	0.719753i	−0.579936	+	0.814662i	$0.696923\pi$
$374$	120.000	+	69.2820i	0.320856	+	0.185246i
$375$		0			0
$376$	−480.000	−	277.128i	−1.27660	−	0.737043i
$377$	52.0000			0.137931
$378$		0			0
$379$		−	436.477i		−	1.15165i	−0.817572	−	0.575827i	$-0.804680\pi$
$379$		−	436.477i		−	1.15165i	0.817572	−	0.575827i	$-0.195320\pi$
$380$	144.000	−	83.1384i	0.378947	−	0.218785i
$381$		0			0
$382$	384.000	+	221.703i	1.00524	+	0.580373i
$383$	528.000	−	304.841i	1.37859	−	0.795929i	0.386600	−	0.922247i	$-0.373649\pi$
$383$	528.000	−	304.841i	1.37859	−	0.795929i	0.991990	+	0.126318i	$0.0403160\pi$
$384$		0			0
$385$	48.0000	−	83.1384i	0.124675	−	0.215944i
$386$	290.000	+	502.295i	0.751295	+	1.30128i
$387$		0			0
$388$	−4.00000	+	6.92820i	−0.0103093	+	0.0178562i
$389$	−289.000	+	500.563i	−0.742931	+	1.28679i	0.208225	+	0.978081i	$0.433231\pi$
$389$	−289.000	+	500.563i	−0.742931	+	1.28679i	−0.951155	+	0.308713i	$0.900102\pi$
$390$		0			0
$391$	−240.000	+	138.564i	−0.613811	+	0.354384i
$392$	4.00000	+	6.92820i	0.0102041	+	0.0176740i
$393$		0			0
$394$	−52.0000			−0.131980
$395$			235.559i			0.596352i
$396$		0			0
$397$	26.0000			0.0654912			0.0327456	−	0.999464i	$-0.489575\pi$
$397$	26.0000			0.0654912			0.0327456	+	0.999464i	$0.489575\pi$
$398$		−	789.815i		−	1.98446i
$399$		0			0
$400$	168.000	−	290.985i	0.420000	−	0.727461i
$401$	125.000	+	216.506i	0.311721	+	0.539916i	0.978735	−	0.205129i	$-0.0657613\pi$
$401$	125.000	+	216.506i	0.311721	+	0.539916i	−0.667014	+	0.745045i	$0.732428\pi$
$402$		0			0
$403$	−12.0000	−	6.92820i	−0.0297767	−	0.0171916i
$404$	−148.000	+	256.344i	−0.366337	+	0.634514i
$405$		0			0
$406$	312.000	−	180.133i	0.768473	−	0.443678i
$407$	156.000	+	90.0666i	0.383292	+	0.221294i
$408$		0			0
$409$	−145.000	−	251.147i	−0.354523	−	0.614052i	0.632513	−	0.774550i	$-0.282023\pi$
$409$	−145.000	−	251.147i	−0.354523	−	0.614052i	−0.987036	+	0.160497i	$0.948690\pi$
$410$	−116.000	+	200.918i	−0.282927	+	0.490044i
$411$		0			0
$412$	−264.000	+	152.420i	−0.640777	+	0.369953i
$413$	624.000			1.51090
$414$		0			0
$415$		−	96.9948i		−	0.233723i
$416$	32.0000	+	55.4256i	0.0769231	+	0.133235i
$417$		0			0
$418$	144.000	−	249.415i	0.344498	−	0.596687i
$419$	294.000	−	169.741i	0.701671	−	0.405110i	−0.106299	−	0.994334i	$-0.533900\pi$
$419$	294.000	−	169.741i	0.701671	−	0.405110i	0.807969	+	0.589225i	$0.200567\pi$
$420$		0			0
$421$	−337.000	+	583.701i	−0.800475	+	1.38646i	0.118829	+	0.992915i	$0.462086\pi$
$421$	−337.000	+	583.701i	−0.800475	+	1.38646i	−0.919304	+	0.393549i	$0.871247\pi$
$422$	420.000	−	242.487i	0.995261	−	0.574614i
$423$		0			0
$424$	−592.000			−1.39623
$425$	−105.000	+	181.865i	−0.247059	+	0.427918i
$426$		0			0
$427$	−156.000	+	90.0666i	−0.365340	+	0.210929i
$428$		−	83.1384i		−	0.194249i
$429$		0			0
$430$			193.990i			0.451139i
$431$		−	540.400i		−	1.25383i	−0.779088	−	0.626914i	$-0.784318\pi$
$431$		−	540.400i		−	1.25383i	0.779088	−	0.626914i	$-0.215682\pi$
$432$		0			0
$433$	−334.000			−0.771363			−0.385681	−	0.922632i	$-0.626034\pi$
$433$	−334.000			−0.771363			−0.385681	+	0.922632i	$0.626034\pi$
$434$	−96.0000			−0.221198
$435$		0			0
$436$	−184.000			−0.422018
$437$	288.000	+	498.831i	0.659039	+	1.14149i
$438$		0			0
$439$	−102.000	−	58.8897i	−0.232346	−	0.134145i	0.379308	−	0.925271i	$-0.376162\pi$
$439$	−102.000	−	58.8897i	−0.232346	−	0.134145i	−0.611654	+	0.791125i	$0.709496\pi$
$440$			110.851i			0.251935i
$441$		0			0
$442$	−20.0000	−	34.6410i	−0.0452489	−	0.0783733i
$443$	−66.0000	−	38.1051i	−0.148984	−	0.0860161i	0.423655	−	0.905824i	$-0.360747\pi$
$443$	−66.0000	−	38.1051i	−0.148984	−	0.0860161i	−0.572639	+	0.819808i	$0.694080\pi$
$444$		0			0
$445$	82.0000	+	142.028i	0.184270	+	0.319164i
$446$	−588.000	−	339.482i	−1.31839	−	0.761170i
$447$		0			0
$448$	384.000	+	221.703i	0.857143	+	0.494872i
$449$	−394.000			−0.877506			−0.438753	−	0.898608i	$-0.644580\pi$
$449$	−394.000			−0.877506			−0.438753	+	0.898608i	$0.644580\pi$
$450$		0			0
$451$			401.836i			0.890988i
$452$	−220.000	−	381.051i	−0.486726	−	0.843034i
$453$		0			0
$454$	492.000	+	284.056i	1.08370	+	0.625675i
$455$	−24.0000	+	13.8564i	−0.0527473	+	0.0304536i
$456$		0			0
$457$	239.000	−	413.960i	0.522976	−	0.905821i	−0.476667	−	0.879084i	$-0.658155\pi$
$457$	239.000	−	413.960i	0.522976	−	0.905821i	0.999643	−	0.0267367i	$-0.00851158\pi$
$458$	−142.000	−	245.951i	−0.310044	−	0.537011i
$459$		0			0
$460$	−192.000	−	110.851i	−0.417391	−	0.240981i
$461$	71.0000	−	122.976i	0.154013	−	0.266758i	−0.778686	−	0.627414i	$-0.784114\pi$
$461$	71.0000	−	122.976i	0.154013	−	0.266758i	0.932699	+	0.360655i	$0.117447\pi$
$462$		0			0
$463$	546.000	−	315.233i	1.17927	−	0.680849i	0.223421	−	0.974722i	$-0.428278\pi$
$463$	546.000	−	315.233i	1.17927	−	0.680849i	0.955845	+	0.293873i	$0.0949442\pi$
$464$	−208.000	+	360.267i	−0.448276	+	0.776437i
$465$		0			0
$466$	164.000			0.351931
$467$		−	20.7846i		−	0.0445067i	−0.999752	−	0.0222533i	$-0.992916\pi$
$467$		−	20.7846i		−	0.0445067i	0.999752	−	0.0222533i	$-0.00708404\pi$
$468$		0			0
$469$	48.0000			0.102345
$470$			277.128i			0.589634i
$471$		0			0
$472$	−624.000	+	360.267i	−1.32203	+	0.763277i
$473$	168.000	+	290.985i	0.355180	+	0.615189i
$474$		0			0
$475$	378.000	+	218.238i	0.795789	+	0.459449i
$476$	−240.000	−	138.564i	−0.504202	−	0.291101i
$477$		0			0
$478$	672.000	−	387.979i	1.40586	−	0.811672i
$479$	636.000	+	367.195i	1.32777	+	0.766586i	0.984954	−	0.172818i	$-0.0552872\pi$
$479$	636.000	+	367.195i	1.32777	+	0.766586i	0.342812	+	0.939404i	$0.388620\pi$
$480$		0			0
$481$	−26.0000	−	45.0333i	−0.0540541	−	0.0936244i
$482$	−46.0000	+	79.6743i	−0.0954357	+	0.165299i
$483$		0			0
$484$	−146.000	−	252.879i	−0.301653	−	0.522478i
$485$	4.00000			0.00824742
$486$		0			0
$487$			103.923i			0.213394i	0.994292	+	0.106697i	$0.0340275\pi$
$487$			103.923i			0.213394i	−0.994292	+	0.106697i	$0.965972\pi$
$488$	104.000	−	180.133i	0.213115	−	0.369126i
$489$		0			0
$490$	2.00000	−	3.46410i	0.00408163	−	0.00706960i
$491$	798.000	−	460.726i	1.62525	−	0.938341i	0.639772	−	0.768565i	$-0.279029\pi$
$491$	798.000	−	460.726i	1.62525	−	0.938341i	0.985483	−	0.169776i	$-0.0543045\pi$
$492$		0			0
$493$	130.000	−	225.167i	0.263692	−	0.456727i
$494$	−72.0000	+	41.5692i	−0.145749	+	0.0841482i
$495$		0			0
$496$	96.0000	−	55.4256i	0.193548	−	0.111745i
$497$		0			0
$498$		0			0
$499$	−66.0000	+	38.1051i	−0.132265	+	0.0763630i	−0.564672	−	0.825315i	$-0.690997\pi$
$499$	−66.0000	+	38.1051i	−0.132265	+	0.0763630i	0.432408	+	0.901678i	$0.357664\pi$
$500$	−368.000			−0.736000
$501$		0			0
$502$			290.985i			0.579650i
$503$			581.969i			1.15700i	0.815684	+	0.578498i	$0.196361\pi$
$503$			581.969i			1.15700i	−0.815684	+	0.578498i	$0.803639\pi$
$504$		0			0
$505$	148.000			0.293069
$506$	−384.000			−0.758893
$507$		0			0
$508$		−	581.969i		−	1.14561i
$509$	−421.000	−	729.193i	−0.827112	−	1.43260i	−0.900294	−	0.435281i	$-0.856649\pi$
$509$	−421.000	−	729.193i	−0.827112	−	1.43260i	0.0731825	−	0.997319i	$-0.476684\pi$
$510$		0			0
$511$	−276.000	−	159.349i	−0.540117	−	0.311837i
$512$	−512.000			−1.00000
$513$		0			0
$514$	254.000	+	439.941i	0.494163	+	0.855916i
$515$	132.000	+	76.2102i	0.256311	+	0.147981i
$516$		0			0
$517$	240.000	+	415.692i	0.464217	+	0.804047i
$518$	−312.000	−	180.133i	−0.602317	−	0.347748i
$519$		0			0
$520$	16.0000	−	27.7128i	0.0307692	−	0.0532939i
$521$	326.000			0.625720			0.312860	−	0.949799i	$-0.398713\pi$
$521$	326.000			0.625720			0.312860	+	0.949799i	$0.398713\pi$
$522$		0			0
$523$			311.769i			0.596117i	0.954548	+	0.298058i	$0.0963390\pi$
$523$			311.769i			0.596117i	−0.954548	+	0.298058i	$0.903661\pi$
$524$	−408.000	+	235.559i	−0.778626	+	0.449540i
$525$		0			0
$526$	−264.000	−	152.420i	−0.501901	−	0.289773i
$527$	−60.0000	+	34.6410i	−0.113852	+	0.0657325i
$528$		0			0
$529$	119.500	−	206.980i	0.225898	−	0.391267i
$530$	148.000	+	256.344i	0.279245	+	0.483667i
$531$		0			0
$532$	−288.000	+	498.831i	−0.541353	+	0.937652i
$533$	58.0000	−	100.459i	0.108818	−	0.188478i
$534$		0			0
$535$	−36.0000	+	20.7846i	−0.0672897	+	0.0388497i
$536$	−48.0000	+	27.7128i	−0.0895522	+	0.0517030i
$537$		0			0
$538$	524.000			0.973978
$539$		−	6.92820i		−	0.0128538i
$540$		0			0
$541$	530.000			0.979667			0.489834	−	0.871816i	$-0.337058\pi$
$541$	530.000			0.979667			0.489834	+	0.871816i	$0.337058\pi$
$542$		−	41.5692i		−	0.0766960i
$543$		0			0
$544$	320.000			0.588235
$545$	46.0000	+	79.6743i	0.0844037	+	0.146191i
$546$		0			0
$547$	294.000	+	169.741i	0.537477	+	0.310313i	0.744056	−	0.668117i	$-0.232900\pi$
$547$	294.000	+	169.741i	0.537477	+	0.310313i	−0.206579	+	0.978430i	$0.566233\pi$
$548$	20.0000	−	34.6410i	0.0364964	−	0.0632135i
$549$		0			0
$550$	−252.000	+	145.492i	−0.458182	+	0.264531i
$551$	−468.000	−	270.200i	−0.849365	−	0.490381i
$552$		0			0
$553$	−408.000	−	706.677i	−0.737794	−	1.27790i
$554$	290.000	−	502.295i	0.523466	−	0.906669i
$555$		0			0
$556$	168.000	−	96.9948i	0.302158	−	0.174451i
$557$	−766.000			−1.37522			−0.687612	−	0.726078i	$-0.741341\pi$
$557$	−766.000			−1.37522			−0.687612	+	0.726078i	$0.741341\pi$
$558$		0			0
$559$		−	96.9948i		−	0.173515i
$560$		−	221.703i		−	0.395897i
$561$		0			0
$562$	−226.000	+	391.443i	−0.402135	+	0.696519i
$563$	−426.000	+	245.951i	−0.756661	+	0.436858i	−0.828096	−	0.560587i	$-0.810576\pi$
$563$	−426.000	+	245.951i	−0.756661	+	0.436858i	0.0714348	+	0.997445i	$0.477242\pi$
$564$		0			0
$565$	−110.000	+	190.526i	−0.194690	+	0.337213i
$566$	−516.000	+	297.913i	−0.911661	+	0.526348i
$567$		0			0
$568$		0			0
$569$	−211.000	+	365.463i	−0.370826	+	0.642289i	−0.989693	−	0.143206i	$-0.954259\pi$
$569$	−211.000	+	365.463i	−0.370826	+	0.642289i	0.618867	+	0.785496i	$0.287592\pi$
$570$		0			0
$571$	−246.000	+	142.028i	−0.430823	+	0.248736i	−0.699697	−	0.714439i	$-0.746682\pi$
$571$	−246.000	+	142.028i	−0.430823	+	0.248736i	0.268874	+	0.963175i	$0.413348\pi$
$572$		−	55.4256i		−	0.0968979i
$573$		0			0
$574$		−	803.672i		−	1.40012i
$575$		−	581.969i		−	1.01212i
$576$		0			0
$577$	−46.0000			−0.0797227			−0.0398614	−	0.999205i	$-0.512692\pi$
$577$	−46.0000			−0.0797227			−0.0398614	+	0.999205i	$0.512692\pi$
$578$	378.000			0.653979
$579$		0			0
$580$	208.000			0.358621
$581$	168.000	+	290.985i	0.289157	+	0.500834i
$582$		0			0
$583$	444.000	+	256.344i	0.761578	+	0.439697i
$584$	368.000			0.630137
$585$		0			0
$586$	362.000	+	627.002i	0.617747	+	1.06997i
$587$	546.000	+	315.233i	0.930153	+	0.537024i	0.886860	−	0.462038i	$-0.152882\pi$
$587$	546.000	+	315.233i	0.930153	+	0.537024i	0.0432933	+	0.999062i	$0.486215\pi$
$588$		0			0
$589$	72.0000	+	124.708i	0.122241	+	0.211728i
$590$	312.000	+	180.133i	0.528814	+	0.305311i
$591$		0			0
$592$	416.000			0.702703
$593$	−82.0000			−0.138280			−0.0691400	−	0.997607i	$-0.522026\pi$
$593$	−82.0000			−0.138280			−0.0691400	+	0.997607i	$0.522026\pi$
$594$		0			0
$595$			138.564i			0.232881i
$596$	−4.00000	−	6.92820i	−0.00671141	−	0.0116245i
$597$		0			0
$598$	96.0000	+	55.4256i	0.160535	+	0.0926850i
$599$	−48.0000	+	27.7128i	−0.0801336	+	0.0462651i	−0.539531	−	0.841965i	$-0.681399\pi$
$599$	−48.0000	+	27.7128i	−0.0801336	+	0.0462651i	0.459398	+	0.888231i	$0.348065\pi$
$600$		0			0
$601$	167.000	−	289.252i	0.277870	−	0.481285i	−0.692985	−	0.720952i	$-0.743705\pi$
$601$	167.000	−	289.252i	0.277870	−	0.481285i	0.970855	+	0.239667i	$0.0770381\pi$
$602$	−336.000	−	581.969i	−0.558140	−	0.966726i
$603$		0			0
$604$	312.000	+	180.133i	0.516556	+	0.298234i
$605$	−73.0000	+	126.440i	−0.120661	+	0.208991i
$606$		0			0
$607$	−318.000	+	183.597i	−0.523888	+	0.302467i	−0.738524	−	0.674227i	$-0.764477\pi$
$607$	−318.000	+	183.597i	−0.523888	+	0.302467i	0.214636	+	0.976694i	$0.431143\pi$
$608$		−	665.108i		−	1.09393i
$609$		0			0
$610$	−104.000			−0.170492
$611$		−	138.564i		−	0.226782i
$612$		0			0
$613$	−214.000			−0.349103			−0.174551	−	0.984648i	$-0.555848\pi$
$613$	−214.000			−0.349103			−0.174551	+	0.984648i	$0.555848\pi$
$614$		−	290.985i		−	0.473916i
$615$		0			0
$616$	−192.000	−	332.554i	−0.311688	−	0.539860i
$617$	−559.000	−	968.216i	−0.905997	−	1.56923i	−0.819574	−	0.572974i	$-0.805790\pi$
$617$	−559.000	−	968.216i	−0.905997	−	1.56923i	−0.0864231	−	0.996259i	$-0.527544\pi$
$618$		0			0
$619$	582.000	+	336.018i	0.940226	+	0.542840i	0.890031	−	0.455900i	$-0.150682\pi$
$619$	582.000	+	336.018i	0.940226	+	0.542840i	0.0501950	+	0.998739i	$0.484016\pi$
$620$	−48.0000	−	27.7128i	−0.0774194	−	0.0446981i
$621$		0			0
$622$	−408.000	+	235.559i	−0.655949	+	0.378712i
$623$	−492.000	−	284.056i	−0.789727	−	0.455949i
$624$		0			0
$625$	−170.500	−	295.315i	−0.272800	−	0.472503i
$626$	−478.000	+	827.920i	−0.763578	+	1.32256i
$627$		0			0
$628$	428.000	+	741.318i	0.681529	+	1.18044i
$629$	−260.000			−0.413355
$630$		0			0
$631$		−	145.492i		−	0.230574i	−0.993332	−	0.115287i	$-0.963221\pi$
$631$		−	145.492i		−	0.230574i	0.993332	−	0.115287i	$-0.0367788\pi$
$632$	816.000	+	471.118i	1.29114	+	0.745440i
$633$		0			0
$634$	170.000	−	294.449i	0.268139	−	0.464430i
$635$	−252.000	+	145.492i	−0.396850	+	0.229122i
$636$		0			0
$637$	−1.00000	+	1.73205i	−0.00156986	+	0.00271908i
$638$	312.000	−	180.133i	0.489028	−	0.282341i
$639$		0			0
$640$	128.000	+	221.703i	0.200000	+	0.346410i
$641$	5.00000	−	8.66025i	0.00780031	−	0.0135105i	−0.862099	−	0.506740i	$-0.830850\pi$
$641$	5.00000	−	8.66025i	0.00780031	−	0.0135105i	0.869899	+	0.493230i	$0.164184\pi$
$642$		0			0
$643$	1050.00	−	606.218i	1.63297	−	0.942796i	0.649800	−	0.760105i	$-0.274853\pi$
$643$	1050.00	−	606.218i	1.63297	−	0.942796i	0.983170	−	0.182691i	$-0.0584807\pi$
$644$	768.000			1.19255
$645$		0			0
$646$			415.692i			0.643486i
$647$			332.554i			0.513993i	0.966412	+	0.256997i	$0.0827330\pi$
$647$			332.554i			0.513993i	−0.966412	+	0.256997i	$0.917267\pi$
$648$		0			0
$649$	624.000			0.961479
$650$	84.0000			0.129231
$651$		0			0
$652$			83.1384i			0.127513i
$653$	335.000	+	580.237i	0.513017	+	0.888571i	0.999886	+	0.0150964i	$0.00480550\pi$
$653$	335.000	+	580.237i	0.513017	+	0.888571i	−0.486869	+	0.873475i	$0.661861\pi$
$654$		0			0
$655$	204.000	+	117.779i	0.311450	+	0.179816i
$656$	464.000	+	803.672i	0.707317	+	1.22511i
$657$		0			0
$658$	−480.000	−	831.384i	−0.729483	−	1.26350i
$659$	−714.000	−	412.228i	−1.08346	−	0.625536i	−0.151632	−	0.988437i	$-0.548453\pi$
$659$	−714.000	−	412.228i	−1.08346	−	0.625536i	−0.931828	+	0.362901i	$0.881786\pi$
$660$		0			0
$661$	611.000	+	1058.28i	0.924357	+	1.60103i	0.792592	+	0.609752i	$0.208731\pi$
$661$	611.000	+	1058.28i	0.924357	+	1.60103i	0.131765	+	0.991281i	$0.457936\pi$
$662$	708.000	+	408.764i	1.06949	+	0.617468i
$663$		0			0
$664$	−336.000	−	193.990i	−0.506024	−	0.292153i
$665$	288.000			0.433083
$666$		0			0
$667$			720.533i			1.08026i
$668$	−336.000	+	193.990i	−0.502994	+	0.290404i
$669$		0			0
$670$	24.0000	+	13.8564i	0.0358209	+	0.0206812i
$671$	−156.000	+	90.0666i	−0.232489	+	0.134227i
$672$		0			0
$673$	167.000	−	289.252i	0.248143	−	0.429796i	−0.714868	−	0.699260i	$-0.753513\pi$
$673$	167.000	−	289.252i	0.248143	−	0.429796i	0.963010	+	0.269464i	$0.0868465\pi$
$674$	338.000	+	585.433i	0.501484	+	0.868595i
$675$		0			0
$676$	330.000	−	571.577i	0.488166	−	0.845528i
$677$	503.000	−	871.222i	0.742984	−	1.28689i	−0.208147	−	0.978098i	$-0.566743\pi$
$677$	503.000	−	871.222i	0.742984	−	1.28689i	0.951131	−	0.308788i	$-0.0999234\pi$
$678$		0			0
$679$	−12.0000	+	6.92820i	−0.0176730	+	0.0102035i
$680$	−80.0000	−	138.564i	−0.117647	−	0.203771i
$681$		0			0
$682$	−96.0000			−0.140762
$683$			187.061i			0.273882i	0.990579	+	0.136941i	$0.0437271\pi$
$683$			187.061i			0.273882i	−0.990579	+	0.136941i	$0.956273\pi$
$684$		0			0
$685$	−20.0000			−0.0291971
$686$			692.820i			1.00994i
$687$		0			0
$688$	672.000	+	387.979i	0.976744	+	0.563924i
$689$	−74.0000	−	128.172i	−0.107402	−	0.186026i
$690$		0			0
$691$	−858.000	−	495.367i	−1.24168	−	0.716884i	−0.272243	−	0.962229i	$-0.587765\pi$
$691$	−858.000	−	495.367i	−1.24168	−	0.716884i	−0.969436	+	0.245345i	$0.921099\pi$
$692$	668.000	−	1157.01i	0.965318	−	1.67198i
$693$		0			0
$694$	348.000	−	200.918i	0.501441	−	0.289507i
$695$	−84.0000	−	48.4974i	−0.120863	−	0.0697805i
$696$		0			0
$697$	−290.000	−	502.295i	−0.416069	−	0.720652i
$698$	506.000	−	876.418i	0.724928	−	1.25561i
$699$		0			0
$700$	504.000	−	290.985i	0.720000	−	0.415692i
$701$	1034.00			1.47504			0.737518	−	0.675328i	$-0.235998\pi$
$701$	1034.00			1.47504			0.737518	+	0.675328i	$0.235998\pi$
$702$		0			0
$703$			540.400i			0.768705i
$704$	384.000	+	221.703i	0.545455	+	0.314918i
$705$		0			0
$706$	−178.000	+	308.305i	−0.252125	+	0.436693i
$707$	−444.000	+	256.344i	−0.628006	+	0.362579i
$708$		0			0
$709$	−265.000	+	458.993i	−0.373766	+	0.647381i	−0.990141	−	0.140071i	$-0.955267\pi$
$709$	−265.000	+	458.993i	−0.373766	+	0.647381i	0.616376	+	0.787452i	$0.288600\pi$
$710$		0			0
$711$		0			0
$712$	656.000			0.921348
$713$	96.0000	−	166.277i	0.134642	−	0.233207i
$714$		0			0
$715$	−24.0000	+	13.8564i	−0.0335664	+	0.0193796i
$716$			748.246i			1.04504i
$717$		0			0
$718$			332.554i			0.463167i
$719$			706.677i			0.982861i	0.870917	+	0.491430i	$0.163526\pi$
$719$			706.677i			0.982861i	−0.870917	+	0.491430i	$0.836474\pi$
$720$		0			0
$721$	−528.000			−0.732316
$722$	142.000			0.196676
$723$		0			0
$724$	8.00000			0.0110497
$725$	273.000	+	472.850i	0.376552	+	0.652207i
$726$		0			0
$727$	−210.000	−	121.244i	−0.288858	−	0.166772i	0.348569	−	0.937283i	$-0.386668\pi$
$727$	−210.000	−	121.244i	−0.288858	−	0.166772i	−0.637427	+	0.770511i	$0.720001\pi$
$728$			110.851i			0.152268i
$729$		0			0
$730$	−92.0000	−	159.349i	−0.126027	−	0.218286i
$731$	−420.000	−	242.487i	−0.574555	−	0.331720i
$732$		0			0
$733$	−97.0000	−	168.009i	−0.132333	−	0.229207i	0.792243	−	0.610206i	$-0.208913\pi$
$733$	−97.0000	−	168.009i	−0.132333	−	0.229207i	−0.924575	+	0.380999i	$0.875580\pi$
$734$	348.000	+	200.918i	0.474114	+	0.273730i
$735$		0			0
$736$	−768.000	+	443.405i	−1.04348	+	0.602452i
$737$	48.0000			0.0651289
$738$		0			0
$739$		−	1351.00i		−	1.82815i	−0.405550	−	0.914073i	$-0.632920\pi$
$739$		−	1351.00i		−	1.82815i	0.405550	−	0.914073i	$-0.367080\pi$
$740$	−104.000	−	180.133i	−0.140541	−	0.243423i
$741$		0			0
$742$	−888.000	−	512.687i	−1.19677	−	0.690953i
$743$	−588.000	+	339.482i	−0.791386	+	0.456907i	−0.840450	−	0.541889i	$-0.817709\pi$
$743$	−588.000	+	339.482i	−0.791386	+	0.456907i	0.0490641	+	0.998796i	$0.484376\pi$
$744$		0			0
$745$	−2.00000	+	3.46410i	−0.00268456	+	0.00464980i
$746$	−310.000	−	536.936i	−0.415550	−	0.719753i
$747$		0			0
$748$	−240.000	−	138.564i	−0.320856	−	0.185246i
$749$	72.0000	−	124.708i	0.0961282	−	0.166499i
$750$		0			0
$751$	−570.000	+	329.090i	−0.758988	+	0.438202i	−0.828932	−	0.559349i	$-0.811051\pi$
$751$	−570.000	+	329.090i	−0.758988	+	0.438202i	0.0699443	+	0.997551i	$0.477718\pi$
$752$	960.000	+	554.256i	1.27660	+	0.737043i
$753$		0			0
$754$	−104.000			−0.137931
$755$		−	180.133i		−	0.238587i
$756$		0			0
$757$	−1006.00			−1.32893			−0.664465	−	0.747319i	$-0.731341\pi$
$757$	−1006.00			−1.32893			−0.664465	+	0.747319i	$0.731341\pi$
$758$			872.954i			1.15165i
$759$		0			0
$760$	−288.000	+	166.277i	−0.378947	+	0.218785i
$761$	−379.000	−	656.447i	−0.498029	−	0.862611i	0.501969	−	0.864886i	$-0.332609\pi$
$761$	−379.000	−	656.447i	−0.498029	−	0.862611i	−0.999997	+	0.00227453i	$0.999276\pi$
$762$		0			0
$763$	−276.000	−	159.349i	−0.361730	−	0.208845i
$764$	−768.000	−	443.405i	−1.00524	−	0.580373i
$765$		0			0
$766$	−1056.00	+	609.682i	−1.37859	+	0.795929i
$767$	−156.000	−	90.0666i	−0.203390	−	0.117427i
$768$		0			0
$769$	−1.00000	−	1.73205i	−0.00130039	−	0.00225234i	0.865374	−	0.501126i	$-0.167081\pi$
$769$	−1.00000	−	1.73205i	−0.00130039	−	0.00225234i	−0.866675	+	0.498873i	$0.833747\pi$
$770$	−96.0000	+	166.277i	−0.124675	+	0.215944i
$771$		0			0
$772$	−580.000	−	1004.59i	−0.751295	−	1.30128i
$773$	−262.000			−0.338939			−0.169470	−	0.985535i	$-0.554205\pi$
$773$	−262.000			−0.338939			−0.169470	+	0.985535i	$0.554205\pi$
$774$		0			0
$775$		−	145.492i		−	0.187732i
$776$	8.00000	−	13.8564i	0.0103093	−	0.0178562i
$777$		0			0
$778$	578.000	−	1001.13i	0.742931	−	1.28679i
$779$	−1044.00	+	602.754i	−1.34018	+	0.773753i
$780$		0			0
$781$		0			0
$782$	480.000	−	277.128i	0.613811	−	0.354384i
$783$		0			0
$784$	−8.00000	−	13.8564i	−0.0102041	−	0.0176740i
$785$	214.000	−	370.659i	0.272611	−	0.472177i
$786$		0			0
$787$	−1254.00	+	723.997i	−1.59339	+	0.919946i	−0.600673	+	0.799495i	$0.705101\pi$
$787$	−1254.00	+	723.997i	−1.59339	+	0.919946i	−0.992719	+	0.120451i	$0.961566\pi$
$788$	104.000			0.131980
$789$		0			0
$790$		−	471.118i		−	0.596352i
$791$		−	762.102i		−	0.963467i
$792$		0			0
$793$	52.0000			0.0655738
$794$	−52.0000			−0.0654912
$795$		0			0
$796$			1579.63i			1.98446i
$797$	−433.000	−	749.978i	−0.543287	−	0.941001i	−0.998713	−	0.0507272i	$-0.983846\pi$
$797$	−433.000	−	749.978i	−0.543287	−	0.941001i	0.455425	−	0.890274i	$-0.349487\pi$
$798$		0			0
$799$	−600.000	−	346.410i	−0.750939	−	0.433555i
$800$	−336.000	+	581.969i	−0.420000	+	0.727461i
$801$		0			0
$802$	−250.000	−	433.013i	−0.311721	−	0.539916i
$803$	−276.000	−	159.349i	−0.343711	−	0.198442i
$804$		0			0
$805$	−192.000	−	332.554i	−0.238509	−	0.413110i
$806$	24.0000	+	13.8564i	0.0297767	+	0.0171916i
$807$		0			0
$808$	296.000	−	512.687i	0.366337	−	0.634514i
$809$	−10.0000			−0.0123609			−0.00618047	−	0.999981i	$-0.501967\pi$
$809$	−10.0000			−0.0123609			−0.00618047	+	0.999981i	$0.501967\pi$
$810$		0			0
$811$		−	436.477i		−	0.538196i	−0.963113	−	0.269098i	$-0.913274\pi$
$811$		−	436.477i		−	0.538196i	0.963113	−	0.269098i	$-0.0867255\pi$
$812$	−624.000	+	360.267i	−0.768473	+	0.443678i
$813$		0			0
$814$	−312.000	−	180.133i	−0.383292	−	0.221294i
$815$	36.0000	−	20.7846i	0.0441718	−	0.0255026i
$816$		0			0
$817$	−504.000	+	872.954i	−0.616891	+	1.06849i
$818$	290.000	+	502.295i	0.354523	+	0.614052i
$819$		0			0
$820$	232.000	−	401.836i	0.282927	−	0.490044i
$821$	419.000	−	725.729i	0.510353	−	0.883958i	−0.489575	−	0.871961i	$-0.662848\pi$
$821$	419.000	−	725.729i	0.510353	−	0.883958i	0.999928	−	0.0119964i	$-0.00381867\pi$
$822$		0			0
$823$	762.000	−	439.941i	0.925881	−	0.534558i	0.0403744	−	0.999185i	$-0.487145\pi$
$823$	762.000	−	439.941i	0.925881	−	0.534558i	0.885506	+	0.464627i	$0.153812\pi$
$824$	528.000	−	304.841i	0.640777	−	0.369953i
$825$		0			0
$826$	−1248.00			−1.51090
$827$			727.461i			0.879639i	0.898086	+	0.439819i	$0.144958\pi$
$827$			727.461i			0.879639i	−0.898086	+	0.439819i	$0.855042\pi$
$828$		0			0
$829$	1298.00			1.56574			0.782871	−	0.622184i	$-0.213754\pi$
$829$	1298.00			1.56574			0.782871	+	0.622184i	$0.213754\pi$
$830$			193.990i			0.233723i
$831$		0			0
$832$	−64.0000	−	110.851i	−0.0769231	−	0.133235i
$833$	5.00000	+	8.66025i	0.00600240	+	0.0103965i
$834$		0			0
$835$	168.000	+	96.9948i	0.201198	+	0.116161i
$836$	−288.000	+	498.831i	−0.344498	+	0.596687i
$837$		0			0
$838$	−588.000	+	339.482i	−0.701671	+	0.405110i
$839$	168.000	+	96.9948i	0.200238	+	0.115608i	0.596767	−	0.802415i	$-0.296452\pi$
$839$	168.000	+	96.9948i	0.200238	+	0.115608i	−0.396528	+	0.918023i	$0.629785\pi$
$840$		0			0
$841$	82.5000	+	142.894i	0.0980975	+	0.169910i
$842$	674.000	−	1167.40i	0.800475	−	1.38646i
$843$		0			0
$844$	−840.000	+	484.974i	−0.995261	+	0.574614i
$845$	−330.000			−0.390533
$846$		0			0
$847$		−	505.759i		−	0.597118i
$848$	1184.00			1.39623
$849$		0			0
$850$	210.000	−	363.731i	0.247059	−	0.427918i
$851$	624.000	−	360.267i	0.733255	−	0.423345i
$852$		0			0
$853$	−253.000	+	438.209i	−0.296600	+	0.513727i	−0.975356	−	0.220638i	$-0.929186\pi$
$853$	−253.000	+	438.209i	−0.296600	+	0.513727i	0.678756	+	0.734364i	$0.262520\pi$
$854$	312.000	−	180.133i	0.365340	−	0.210929i
$855$		0			0
$856$			166.277i			0.194249i
$857$	−499.000	+	864.293i	−0.582264	+	1.00851i	0.412947	+	0.910755i	$0.364500\pi$
$857$	−499.000	+	864.293i	−0.582264	+	1.00851i	−0.995210	+	0.0977552i	$0.968834\pi$
$858$		0			0
$859$	438.000	−	252.879i	0.509895	−	0.294388i	−0.222895	−	0.974842i	$-0.571551\pi$
$859$	438.000	−	252.879i	0.509895	−	0.294388i	0.732791	+	0.680454i	$0.238217\pi$
$860$		−	387.979i		−	0.451139i
$861$		0			0
$862$			1080.80i			1.25383i
$863$		−	166.277i		−	0.192673i	−0.995349	−	0.0963365i	$-0.969287\pi$
$863$		−	166.277i		−	0.192673i	0.995349	−	0.0963365i	$-0.0307125\pi$
$864$		0			0
$865$	−668.000			−0.772254
$866$	668.000			0.771363
$867$		0			0
$868$	192.000			0.221198
$869$	−408.000	−	706.677i	−0.469505	−	0.813207i
$870$		0			0
$871$	−12.0000	−	6.92820i	−0.0137773	−	0.00795431i
$872$	368.000			0.422018
$873$		0			0
$874$	−576.000	−	997.661i	−0.659039	−	1.14149i
$875$	−552.000	−	318.697i	−0.630857	−	0.364226i
$876$		0			0
$877$	323.000	+	559.452i	0.368301	+	0.637916i	0.989300	−	0.145895i	$-0.0466062\pi$
$877$	323.000	+	559.452i	0.368301	+	0.637916i	−0.620999	+	0.783811i	$0.713273\pi$
$878$	204.000	+	117.779i	0.232346	+	0.134145i
$879$		0			0
$880$		−	221.703i		−	0.251935i
$881$	−898.000			−1.01930			−0.509648	−	0.860383i	$-0.670224\pi$
$881$	−898.000			−1.01930			−0.509648	+	0.860383i	$0.670224\pi$
$882$		0			0
$883$		−	727.461i		−	0.823852i	−0.911217	−	0.411926i	$-0.864856\pi$
$883$		−	727.461i		−	0.823852i	0.911217	−	0.411926i	$-0.135144\pi$
$884$	40.0000	+	69.2820i	0.0452489	+	0.0783733i
$885$		0			0
$886$	132.000	+	76.2102i	0.148984	+	0.0860161i
$887$	−732.000	+	422.620i	−0.825254	+	0.476460i	−0.852225	−	0.523176i	$-0.824747\pi$
$887$	−732.000	+	422.620i	−0.825254	+	0.476460i	0.0269711	+	0.999636i	$0.491414\pi$
$888$		0			0
$889$	504.000	−	872.954i	0.566929	−	0.981950i
$890$	−164.000	−	284.056i	−0.184270	−	0.319164i
$891$		0			0
$892$	1176.00	+	678.964i	1.31839	+	0.761170i
$893$	−720.000	+	1247.08i	−0.806271	+	1.39650i
$894$		0			0
$895$	324.000	−	187.061i	0.362011	−	0.209007i
$896$	−768.000	−	443.405i	−0.857143	−	0.494872i
$897$		0			0
$898$	788.000			0.877506
$899$			180.133i			0.200371i
$900$		0			0
$901$	−740.000			−0.821310
$902$		−	803.672i		−	0.890988i
$903$		0			0
$904$	440.000	+	762.102i	0.486726	+	0.843034i
$905$	−2.00000	−	3.46410i	−0.00220994	−	0.00382774i
$906$		0			0
$907$	−1182.00	−	682.428i	−1.30320	−	0.752401i	−0.322246	−	0.946656i	$-0.604438\pi$
$907$	−1182.00	−	682.428i	−1.30320	−	0.752401i	−0.980951	+	0.194255i	$0.937771\pi$
$908$	−984.000	−	568.113i	−1.08370	−	0.625675i
$909$		0			0
$910$	48.0000	−	27.7128i	0.0527473	−	0.0304536i
$911$	−336.000	−	193.990i	−0.368825	−	0.212941i	0.304120	−	0.952634i	$-0.401638\pi$
$911$	−336.000	−	193.990i	−0.368825	−	0.212941i	−0.672945	+	0.739692i	$0.734971\pi$
$912$		0			0
$913$	168.000	+	290.985i	0.184009	+	0.318713i
$914$	−478.000	+	827.920i	−0.522976	+	0.905821i
$915$		0			0
$916$	284.000	+	491.902i	0.310044	+	0.537011i
$917$	−816.000			−0.889858
$918$		0			0
$919$			602.754i			0.655880i	0.944699	+	0.327940i	$0.106354\pi$
$919$			602.754i			0.655880i	−0.944699	+	0.327940i	$0.893646\pi$
$920$	384.000	+	221.703i	0.417391	+	0.240981i
$921$		0			0
$922$	−142.000	+	245.951i	−0.154013	+	0.266758i
$923$		0			0
$924$		0			0
$925$	273.000	−	472.850i	0.295135	−	0.511189i
$926$	−1092.00	+	630.466i	−1.17927	+	0.680849i
$927$		0			0
$928$	416.000	−	720.533i	0.448276	−	0.776437i
$929$	797.000	−	1380.44i	0.857912	−	1.48595i	−0.0160055	−	0.999872i	$-0.505095\pi$
$929$	797.000	−	1380.44i	0.857912	−	1.48595i	0.873917	−	0.486075i	$-0.161572\pi$
$930$		0			0
$931$	18.0000	−	10.3923i	0.0193340	−	0.0111625i
$932$	−328.000			−0.351931
$933$		0			0
$934$			41.5692i			0.0445067i
$935$			138.564i			0.148197i
$936$		0			0
$937$	674.000			0.719317			0.359658	−	0.933084i	$-0.382893\pi$
$937$	674.000			0.719317			0.359658	+	0.933084i	$0.382893\pi$
$938$	−96.0000			−0.102345
$939$		0			0
$940$		−	554.256i		−	0.589634i
$941$	215.000	+	372.391i	0.228480	+	0.395740i	0.957358	−	0.288904i	$-0.0932910\pi$
$941$	215.000	+	372.391i	0.228480	+	0.395740i	−0.728878	+	0.684644i	$0.759958\pi$
$942$		0			0
$943$	1392.00	+	803.672i	1.47614	+	0.852250i
$944$	1248.00	−	720.533i	1.32203	−	0.763277i
$945$		0			0
$946$	−336.000	−	581.969i	−0.355180	−	0.615189i
$947$	−66.0000	−	38.1051i	−0.0696938	−	0.0402377i	0.464748	−	0.885443i	$-0.346145\pi$
$947$	−66.0000	−	38.1051i	−0.0696938	−	0.0402377i	−0.534442	+	0.845205i	$0.679478\pi$
$948$		0			0
$949$	46.0000	+	79.6743i	0.0484721	+	0.0839561i
$950$	−756.000	−	436.477i	−0.795789	−	0.459449i
$951$		0			0
$952$	480.000	+	277.128i	0.504202	+	0.291101i
$953$	−730.000			−0.766002			−0.383001	−	0.923748i	$-0.625109\pi$
$953$	−730.000			−0.766002			−0.383001	+	0.923748i	$0.625109\pi$
$954$		0			0
$955$			443.405i			0.464298i
$956$	−1344.00	+	775.959i	−1.40586	+	0.811672i
$957$		0			0
$958$	−1272.00	−	734.390i	−1.32777	−	0.766586i
$959$	60.0000	−	34.6410i	0.0625652	−	0.0361220i
$960$		0			0
$961$	−456.500	+	790.681i	−0.475026	+	0.822769i
$962$	52.0000	+	90.0666i	0.0540541	+	0.0936244i
$963$		0			0
$964$	92.0000	−	159.349i	0.0954357	−	0.165299i
$965$	−290.000	+	502.295i	−0.300518	+	0.520513i
$966$		0			0
$967$	798.000	−	460.726i	0.825233	−	0.476448i	−0.0269849	−	0.999636i	$-0.508591\pi$
$967$	798.000	−	460.726i	0.825233	−	0.476448i	0.852218	+	0.523188i	$0.175257\pi$
$968$	292.000	+	505.759i	0.301653	+	0.522478i
$969$		0			0
$970$	−8.00000			−0.00824742
$971$		−	1475.71i		−	1.51978i	−0.650051	−	0.759890i	$-0.725253\pi$
$971$		−	1475.71i		−	1.51978i	0.650051	−	0.759890i	$-0.274747\pi$
$972$		0			0
$973$	336.000			0.345324
$974$		−	207.846i		−	0.213394i
$975$		0			0
$976$	−208.000	+	360.267i	−0.213115	+	0.369126i
$977$	173.000	+	299.645i	0.177073	+	0.306699i	0.940877	−	0.338749i	$-0.110004\pi$
$977$	173.000	+	299.645i	0.177073	+	0.306699i	−0.763804	+	0.645448i	$0.776671\pi$
$978$		0			0
$979$	−492.000	−	284.056i	−0.502554	−	0.290149i
$980$	−4.00000	+	6.92820i	−0.00408163	+	0.00706960i
$981$		0			0
$982$	−1596.00	+	921.451i	−1.62525	+	0.938341i
$983$	636.000	+	367.195i	0.646999	+	0.373545i	0.787306	−	0.616563i	$-0.211475\pi$
$983$	636.000	+	367.195i	0.646999	+	0.373545i	−0.140307	+	0.990108i	$0.544809\pi$
$984$		0			0
$985$	−26.0000	−	45.0333i	−0.0263959	−	0.0457191i
$986$	−260.000	+	450.333i	−0.263692	+	0.456727i
$987$		0			0
$988$	144.000	−	83.1384i	0.145749	−	0.0841482i
$989$	1344.00			1.35895
$990$		0			0
$991$			976.877i			0.985748i	0.870101	+	0.492874i	$0.164054\pi$
$991$			976.877i			0.985748i	−0.870101	+	0.492874i	$0.835946\pi$
$992$	−192.000	+	110.851i	−0.193548	+	0.111745i
$993$		0			0
$994$		0			0
$995$	684.000	−	394.908i	0.687437	−	0.396892i
$996$		0			0
$997$	−229.000	+	396.640i	−0.229689	+	0.397833i	−0.957716	−	0.287715i	$-0.907104\pi$
$997$	−229.000	+	396.640i	−0.229689	+	0.397833i	0.728027	+	0.685549i	$0.240438\pi$
$998$	132.000	−	76.2102i	0.132265	−	0.0763630i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.a.55.1		2
3.2	odd	2		324.3.f.j.55.1		2
4.3	odd	2		324.3.f.g.55.1		2
9.2	odd	6		12.3.d.a.7.1	✓	2
9.4	even	3		324.3.f.g.271.1		2
9.5	odd	6		324.3.f.d.271.1		2
9.7	even	3		36.3.d.c.19.2		2
12.11	even	2		324.3.f.d.55.1		2
36.7	odd	6		36.3.d.c.19.1		2
36.11	even	6		12.3.d.a.7.2	yes	2
36.23	even	6		324.3.f.j.271.1		2
36.31	odd	6	inner	324.3.f.a.271.1		2
45.2	even	12		300.3.f.a.199.3		4
45.7	odd	12		900.3.f.c.199.2		4
45.29	odd	6		300.3.c.b.151.2		2
45.34	even	6		900.3.c.e.451.1		2
45.38	even	12		300.3.f.a.199.2		4
45.43	odd	12		900.3.f.c.199.3		4
63.20	even	6		588.3.g.b.295.1		2
72.11	even	6		192.3.g.b.127.2		2
72.29	odd	6		192.3.g.b.127.1		2
72.43	odd	6		576.3.g.e.127.2		2
72.61	even	6		576.3.g.e.127.1		2
144.11	even	12		768.3.b.c.127.1		4
144.29	odd	12		768.3.b.c.127.2		4
144.43	odd	12		2304.3.b.l.127.3		4
144.61	even	12		2304.3.b.l.127.2		4
144.83	even	12		768.3.b.c.127.4		4
144.101	odd	12		768.3.b.c.127.3		4
144.115	odd	12		2304.3.b.l.127.1		4
144.133	even	12		2304.3.b.l.127.4		4
180.7	even	12		900.3.f.c.199.4		4
180.43	even	12		900.3.f.c.199.1		4
180.47	odd	12		300.3.f.a.199.1		4
180.79	odd	6		900.3.c.e.451.2		2
180.83	odd	12		300.3.f.a.199.4		4
180.119	even	6		300.3.c.b.151.1		2
252.83	odd	6		588.3.g.b.295.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.3.d.a.7.1	✓	2	9.2	odd	6
12.3.d.a.7.2	yes	2	36.11	even	6
36.3.d.c.19.1		2	36.7	odd	6
36.3.d.c.19.2		2	9.7	even	3
192.3.g.b.127.1		2	72.29	odd	6
192.3.g.b.127.2		2	72.11	even	6
300.3.c.b.151.1		2	180.119	even	6
300.3.c.b.151.2		2	45.29	odd	6
300.3.f.a.199.1		4	180.47	odd	12
300.3.f.a.199.2		4	45.38	even	12
300.3.f.a.199.3		4	45.2	even	12
300.3.f.a.199.4		4	180.83	odd	12
324.3.f.a.55.1		2	1.1	even	1	trivial
324.3.f.a.271.1		2	36.31	odd	6	inner
324.3.f.d.55.1		2	12.11	even	2
324.3.f.d.271.1		2	9.5	odd	6
324.3.f.g.55.1		2	4.3	odd	2
324.3.f.g.271.1		2	9.4	even	3
324.3.f.j.55.1		2	3.2	odd	2
324.3.f.j.271.1		2	36.23	even	6
576.3.g.e.127.1		2	72.61	even	6
576.3.g.e.127.2		2	72.43	odd	6
588.3.g.b.295.1		2	63.20	even	6
588.3.g.b.295.2		2	252.83	odd	6
768.3.b.c.127.1		4	144.11	even	12
768.3.b.c.127.2		4	144.29	odd	12
768.3.b.c.127.3		4	144.101	odd	12
768.3.b.c.127.4		4	144.83	even	12
900.3.c.e.451.1		2	45.34	even	6
900.3.c.e.451.2		2	180.79	odd	6
900.3.f.c.199.1		4	180.43	even	12
900.3.f.c.199.2		4	45.7	odd	12
900.3.f.c.199.3		4	45.43	odd	12
900.3.f.c.199.4		4	180.7	even	12
2304.3.b.l.127.1		4	144.115	odd	12
2304.3.b.l.127.2		4	144.61	even	12
2304.3.b.l.127.3		4	144.43	odd	12
2304.3.b.l.127.4		4	144.133	even	12

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +4.00000 q^{4} +(-1.00000 - 1.73205i) q^{5} +(6.00000 + 3.46410i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q-2.00000 q^{2} +4.00000 q^{4} +(-1.00000 - 1.73205i) q^{5} +(6.00000 + 3.46410i) q^{7} -8.00000 q^{8} +(2.00000 + 3.46410i) q^{10} +(6.00000 + 3.46410i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-12.0000 - 6.92820i) q^{14} +16.0000 q^{16} -10.0000 q^{17} +20.7846i q^{19} +(-4.00000 - 6.92820i) q^{20} +(-12.0000 - 6.92820i) q^{22} +(24.0000 - 13.8564i) q^{23} +(10.5000 - 18.1865i) q^{25} +(2.00000 + 3.46410i) q^{26} +(24.0000 + 13.8564i) q^{28} +(-13.0000 + 22.5167i) q^{29} +(6.00000 - 3.46410i) q^{31} -32.0000 q^{32} +20.0000 q^{34} -13.8564i q^{35} +26.0000 q^{37} -41.5692i q^{38} +(8.00000 + 13.8564i) q^{40} +(29.0000 + 50.2295i) q^{41} +(42.0000 + 24.2487i) q^{43} +(24.0000 + 13.8564i) q^{44} +(-48.0000 + 27.7128i) q^{46} +(60.0000 + 34.6410i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-21.0000 + 36.3731i) q^{50} +(-4.00000 - 6.92820i) q^{52} +74.0000 q^{53} -13.8564i q^{55} +(-48.0000 - 27.7128i) q^{56} +(26.0000 - 45.0333i) q^{58} +(78.0000 - 45.0333i) q^{59} +(-13.0000 + 22.5167i) q^{61} +(-12.0000 + 6.92820i) q^{62} +64.0000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(6.00000 - 3.46410i) q^{67} -40.0000 q^{68} +27.7128i q^{70} -46.0000 q^{73} -52.0000 q^{74} +83.1384i q^{76} +(24.0000 + 41.5692i) q^{77} +(-102.000 - 58.8897i) q^{79} +(-16.0000 - 27.7128i) q^{80} +(-58.0000 - 100.459i) q^{82} +(42.0000 + 24.2487i) q^{83} +(10.0000 + 17.3205i) q^{85} +(-84.0000 - 48.4974i) q^{86} +(-48.0000 - 27.7128i) q^{88} -82.0000 q^{89} -13.8564i q^{91} +(96.0000 - 55.4256i) q^{92} +(-120.000 - 69.2820i) q^{94} +(36.0000 - 20.7846i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(1.00000 + 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 8 q^{4} - 2 q^{5} + 12 q^{7} - 16 q^{8}+O(q^{10}) \) 2 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 + 12 * q^7 - 16 * q^8	\( 2 q - 4 q^{2} + 8 q^{4} - 2 q^{5} + 12 q^{7} - 16 q^{8} + 4 q^{10} + 12 q^{11} - 2 q^{13} - 24 q^{14} + 32 q^{16} - 20 q^{17} - 8 q^{20} - 24 q^{22} + 48 q^{23} + 21 q^{25} + 4 q^{26} + 48 q^{28} - 26 q^{29} + 12 q^{31} - 64 q^{32} + 40 q^{34} + 52 q^{37} + 16 q^{40} + 58 q^{41} + 84 q^{43} + 48 q^{44} - 96 q^{46} + 120 q^{47} - q^{49} - 42 q^{50} - 8 q^{52} + 148 q^{53} - 96 q^{56} + 52 q^{58} + 156 q^{59} - 26 q^{61} - 24 q^{62} + 128 q^{64} - 4 q^{65} + 12 q^{67} - 80 q^{68} - 92 q^{73} - 104 q^{74} + 48 q^{77} - 204 q^{79} - 32 q^{80} - 116 q^{82} + 84 q^{83} + 20 q^{85} - 168 q^{86} - 96 q^{88} - 164 q^{89} + 192 q^{92} - 240 q^{94} + 72 q^{95} - 2 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 + 12 * q^7 - 16 * q^8 + 4 * q^10 + 12 * q^11 - 2 * q^13 - 24 * q^14 + 32 * q^16 - 20 * q^17 - 8 * q^20 - 24 * q^22 + 48 * q^23 + 21 * q^25 + 4 * q^26 + 48 * q^28 - 26 * q^29 + 12 * q^31 - 64 * q^32 + 40 * q^34 + 52 * q^37 + 16 * q^40 + 58 * q^41 + 84 * q^43 + 48 * q^44 - 96 * q^46 + 120 * q^47 - q^49 - 42 * q^50 - 8 * q^52 + 148 * q^53 - 96 * q^56 + 52 * q^58 + 156 * q^59 - 26 * q^61 - 24 * q^62 + 128 * q^64 - 4 * q^65 + 12 * q^67 - 80 * q^68 - 92 * q^73 - 104 * q^74 + 48 * q^77 - 204 * q^79 - 32 * q^80 - 116 * q^82 + 84 * q^83 + 20 * q^85 - 168 * q^86 - 96 * q^88 - 164 * q^89 + 192 * q^92 - 240 * q^94 + 72 * q^95 - 2 * q^97 + 2 * q^98

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