LMFDB - Embedded newform 27.3.d.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,3,Mod(8,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("27.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	27.d (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:	$0.735696713773$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	27.17
Dual form			27.3.d.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.00000 - 1.73205i) q^{7} +8.66025i q^{8} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.00000 - 1.73205i) q^{7} +8.66025i q^{8} -6.00000 q^{10} +(1.50000 - 0.866025i) q^{11} +(2.00000 - 3.46410i) q^{13} +(-3.00000 - 1.73205i) q^{14} +(5.50000 + 9.52628i) q^{16} -15.5885i q^{17} +11.0000 q^{19} +(3.00000 - 1.73205i) q^{20} +(1.50000 - 2.59808i) q^{22} +(24.0000 + 13.8564i) q^{23} +(-6.50000 - 11.2583i) q^{25} -6.92820i q^{26} +2.00000 q^{28} +(-39.0000 + 22.5167i) q^{29} +(-16.0000 + 27.7128i) q^{31} +(-13.5000 - 7.79423i) q^{32} +(-13.5000 - 23.3827i) q^{34} +6.92820i q^{35} -34.0000 q^{37} +(16.5000 - 9.52628i) q^{38} +(15.0000 - 25.9808i) q^{40} +(10.5000 + 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +1.73205i q^{44} +48.0000 q^{46} +(42.0000 - 24.2487i) q^{47} +(22.5000 - 38.9711i) q^{49} +(-19.5000 - 11.2583i) q^{50} +(2.00000 + 3.46410i) q^{52} -6.00000 q^{55} +(15.0000 - 8.66025i) q^{56} +(-39.0000 + 67.5500i) q^{58} +(-43.5000 - 25.1147i) q^{59} +(-28.0000 - 48.4974i) q^{61} +55.4256i q^{62} -71.0000 q^{64} +(-12.0000 + 6.92820i) q^{65} +(15.5000 - 26.8468i) q^{67} +(13.5000 + 7.79423i) q^{68} +(6.00000 + 10.3923i) q^{70} +31.1769i q^{71} +65.0000 q^{73} +(-51.0000 + 29.4449i) q^{74} +(-5.50000 + 9.52628i) q^{76} +(-3.00000 - 1.73205i) q^{77} +(-19.0000 - 32.9090i) q^{79} -38.1051i q^{80} +21.0000 q^{82} +(42.0000 - 24.2487i) q^{83} +(-27.0000 + 46.7654i) q^{85} +(91.5000 + 52.8275i) q^{86} +(7.50000 + 12.9904i) q^{88} -124.708i q^{89} -8.00000 q^{91} +(-24.0000 + 13.8564i) q^{92} +(42.0000 - 72.7461i) q^{94} +(-33.0000 - 19.0526i) q^{95} +(57.5000 + 99.5929i) q^{97} -77.9423i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} - q^{4} - 6 q^{5} - 2 q^{7}+O(q^{10}) $ 2 * q + 3 * q^2 - q^4 - 6 * q^5 - 2 * q^7	$ 2 q + 3 q^{2} - q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{10} + 3 q^{11} + 4 q^{13} - 6 q^{14} + 11 q^{16} + 22 q^{19} + 6 q^{20} + 3 q^{22} + 48 q^{23} - 13 q^{25} + 4 q^{28} - 78 q^{29} - 32 q^{31} - 27 q^{32} - 27 q^{34} - 68 q^{37} + 33 q^{38} + 30 q^{40} + 21 q^{41} + 61 q^{43} + 96 q^{46} + 84 q^{47} + 45 q^{49} - 39 q^{50} + 4 q^{52} - 12 q^{55} + 30 q^{56} - 78 q^{58} - 87 q^{59} - 56 q^{61} - 142 q^{64} - 24 q^{65} + 31 q^{67} + 27 q^{68} + 12 q^{70} + 130 q^{73} - 102 q^{74} - 11 q^{76} - 6 q^{77} - 38 q^{79} + 42 q^{82} + 84 q^{83} - 54 q^{85} + 183 q^{86} + 15 q^{88} - 16 q^{91} - 48 q^{92} + 84 q^{94} - 66 q^{95} + 115 q^{97}+O(q^{100}) $ 2 * q + 3 * q^2 - q^4 - 6 * q^5 - 2 * q^7 - 12 * q^10 + 3 * q^11 + 4 * q^13 - 6 * q^14 + 11 * q^16 + 22 * q^19 + 6 * q^20 + 3 * q^22 + 48 * q^23 - 13 * q^25 + 4 * q^28 - 78 * q^29 - 32 * q^31 - 27 * q^32 - 27 * q^34 - 68 * q^37 + 33 * q^38 + 30 * q^40 + 21 * q^41 + 61 * q^43 + 96 * q^46 + 84 * q^47 + 45 * q^49 - 39 * q^50 + 4 * q^52 - 12 * q^55 + 30 * q^56 - 78 * q^58 - 87 * q^59 - 56 * q^61 - 142 * q^64 - 24 * q^65 + 31 * q^67 + 27 * q^68 + 12 * q^70 + 130 * q^73 - 102 * q^74 - 11 * q^76 - 6 * q^77 - 38 * q^79 + 42 * q^82 + 84 * q^83 - 54 * q^85 + 183 * q^86 + 15 * q^88 - 16 * q^91 - 48 * q^92 + 84 * q^94 - 66 * q^95 + 115 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.50000	−	0.866025i	0.750000	−	0.433013i	−0.0756939	−	0.997131i	$-0.524117\pi$
$2$	1.50000	−	0.866025i	0.750000	−	0.433013i	0.825694	+	0.564118i	$0.190784\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$5$	−3.00000	−	1.73205i	−0.600000	−	0.346410i	0.169042	−	0.985609i	$-0.445933\pi$
$5$	−3.00000	−	1.73205i	−0.600000	−	0.346410i	−0.769042	+	0.639199i	$0.779266\pi$
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.142857	−	0.247436i	0.785714	−	0.618590i	$-0.212296\pi$
$7$	−1.00000	−	1.73205i	−0.142857	−	0.247436i	−0.928571	+	0.371154i	$0.878962\pi$
$8$			8.66025i			1.08253i
$9$		0			0
$10$	−6.00000			−0.600000
$11$	1.50000	−	0.866025i	0.136364	−	0.0787296i	−0.430266	−	0.902702i	$-0.641580\pi$
$11$	1.50000	−	0.866025i	0.136364	−	0.0787296i	0.566630	+	0.823972i	$0.308247\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.153846	−	0.266469i	−0.778792	−	0.627282i	$-0.784167\pi$
$13$	2.00000	−	3.46410i	0.153846	−	0.266469i	0.932638	+	0.360813i	$0.117501\pi$
$14$	−3.00000	−	1.73205i	−0.214286	−	0.123718i
$15$		0			0
$16$	5.50000	+	9.52628i	0.343750	+	0.595392i
$17$		−	15.5885i		−	0.916968i	−0.888703	−	0.458484i	$-0.848393\pi$
$17$		−	15.5885i		−	0.916968i	0.888703	−	0.458484i	$-0.151607\pi$
$18$		0			0
$19$	11.0000			0.578947			0.289474	−	0.957186i	$-0.406520\pi$
$19$	11.0000			0.578947			0.289474	+	0.957186i	$0.406520\pi$
$20$	3.00000	−	1.73205i	0.150000	−	0.0866025i
$21$		0			0
$22$	1.50000	−	2.59808i	0.0681818	−	0.118094i
$23$	24.0000	+	13.8564i	1.04348	+	0.602452i	0.920817	−	0.389996i	$-0.127524\pi$
$23$	24.0000	+	13.8564i	1.04348	+	0.602452i	0.122662	+	0.992449i	$0.460857\pi$
$24$		0			0
$25$	−6.50000	−	11.2583i	−0.260000	−	0.450333i
$26$		−	6.92820i		−	0.266469i
$27$		0			0
$28$	2.00000			0.0714286
$29$	−39.0000	+	22.5167i	−1.34483	+	0.776437i	−0.987511	−	0.157547i	$-0.949641\pi$
$29$	−39.0000	+	22.5167i	−1.34483	+	0.776437i	−0.357316	+	0.933984i	$0.616308\pi$
$30$		0			0
$31$	−16.0000	+	27.7128i	−0.516129	+	0.893962i	0.483696	+	0.875236i	$0.339294\pi$
$31$	−16.0000	+	27.7128i	−0.516129	+	0.893962i	−0.999825	+	0.0187254i	$0.994039\pi$
$32$	−13.5000	−	7.79423i	−0.421875	−	0.243570i
$33$		0			0
$34$	−13.5000	−	23.3827i	−0.397059	−	0.687726i
$35$			6.92820i			0.197949i
$36$		0			0
$37$	−34.0000			−0.918919			−0.459459	−	0.888199i	$-0.651957\pi$
$37$	−34.0000			−0.918919			−0.459459	+	0.888199i	$0.651957\pi$
$38$	16.5000	−	9.52628i	0.434211	−	0.250692i
$39$		0			0
$40$	15.0000	−	25.9808i	0.375000	−	0.649519i
$41$	10.5000	+	6.06218i	0.256098	+	0.147858i	0.622553	−	0.782578i	$-0.286095\pi$
$41$	10.5000	+	6.06218i	0.256098	+	0.147858i	−0.366456	+	0.930436i	$0.619429\pi$
$42$		0			0
$43$	30.5000	+	52.8275i	0.709302	+	1.22855i	0.965116	+	0.261822i	$0.0843232\pi$
$43$	30.5000	+	52.8275i	0.709302	+	1.22855i	−0.255814	+	0.966726i	$0.582343\pi$
$44$			1.73205i			0.0393648i
$45$		0			0
$46$	48.0000			1.04348
$47$	42.0000	−	24.2487i	0.893617	−	0.515930i	0.0184931	−	0.999829i	$-0.494113\pi$
$47$	42.0000	−	24.2487i	0.893617	−	0.515930i	0.875124	+	0.483899i	$0.160780\pi$
$48$		0			0
$49$	22.5000	−	38.9711i	0.459184	−	0.795329i
$50$	−19.5000	−	11.2583i	−0.390000	−	0.225167i
$51$		0			0
$52$	2.00000	+	3.46410i	0.0384615	+	0.0666173i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$	−6.00000			−0.109091
$56$	15.0000	−	8.66025i	0.267857	−	0.154647i
$57$		0			0
$58$	−39.0000	+	67.5500i	−0.672414	+	1.16465i
$59$	−43.5000	−	25.1147i	−0.737288	−	0.425674i	0.0837943	−	0.996483i	$-0.473296\pi$
$59$	−43.5000	−	25.1147i	−0.737288	−	0.425674i	−0.821082	+	0.570810i	$0.806629\pi$
$60$		0			0
$61$	−28.0000	−	48.4974i	−0.459016	−	0.795040i	0.539893	−	0.841734i	$-0.318465\pi$
$61$	−28.0000	−	48.4974i	−0.459016	−	0.795040i	−0.998909	+	0.0466940i	$0.985131\pi$
$62$			55.4256i			0.893962i
$63$		0			0
$64$	−71.0000			−1.10938
$65$	−12.0000	+	6.92820i	−0.184615	+	0.106588i
$66$		0			0
$67$	15.5000	−	26.8468i	0.231343	−	0.400698i	−0.726860	−	0.686785i	$-0.759021\pi$
$67$	15.5000	−	26.8468i	0.231343	−	0.400698i	0.958204	+	0.286087i	$0.0923546\pi$
$68$	13.5000	+	7.79423i	0.198529	+	0.114621i
$69$		0			0
$70$	6.00000	+	10.3923i	0.0857143	+	0.148461i
$71$			31.1769i			0.439111i	0.975600	+	0.219556i	$0.0704608\pi$
$71$			31.1769i			0.439111i	−0.975600	+	0.219556i	$0.929539\pi$
$72$		0			0
$73$	65.0000			0.890411			0.445205	−	0.895428i	$-0.353131\pi$
$73$	65.0000			0.890411			0.445205	+	0.895428i	$0.353131\pi$
$74$	−51.0000	+	29.4449i	−0.689189	+	0.397904i
$75$		0			0
$76$	−5.50000	+	9.52628i	−0.0723684	+	0.125346i
$77$	−3.00000	−	1.73205i	−0.0389610	−	0.0224942i
$78$		0			0
$79$	−19.0000	−	32.9090i	−0.240506	−	0.416569i	0.720352	−	0.693608i	$-0.243980\pi$
$79$	−19.0000	−	32.9090i	−0.240506	−	0.416569i	−0.960859	+	0.277039i	$0.910647\pi$
$80$		−	38.1051i		−	0.476314i
$81$		0			0
$82$	21.0000			0.256098
$83$	42.0000	−	24.2487i	0.506024	−	0.292153i	−0.225174	−	0.974319i	$-0.572295\pi$
$83$	42.0000	−	24.2487i	0.506024	−	0.292153i	0.731198	+	0.682165i	$0.238962\pi$
$84$		0			0
$85$	−27.0000	+	46.7654i	−0.317647	+	0.550181i
$86$	91.5000	+	52.8275i	1.06395	+	0.614274i
$87$		0			0
$88$	7.50000	+	12.9904i	0.0852273	+	0.147618i
$89$		−	124.708i		−	1.40121i	−0.713549	−	0.700605i	$-0.752914\pi$
$89$		−	124.708i		−	1.40121i	0.713549	−	0.700605i	$-0.247086\pi$
$90$		0			0
$91$	−8.00000			−0.0879121
$92$	−24.0000	+	13.8564i	−0.260870	+	0.150613i
$93$		0			0
$94$	42.0000	−	72.7461i	0.446809	−	0.773895i
$95$	−33.0000	−	19.0526i	−0.347368	−	0.200553i
$96$		0			0
$97$	57.5000	+	99.5929i	0.592784	+	1.02673i	0.993856	+	0.110685i	$0.0353044\pi$
$97$	57.5000	+	99.5929i	0.592784	+	1.02673i	−0.401072	+	0.916047i	$0.631362\pi$
$98$		−	77.9423i		−	0.795329i
$99$		0			0
$100$	13.0000			0.130000
$101$	−39.0000	+	22.5167i	−0.386139	+	0.222937i	−0.680486	−	0.732761i	$-0.738231\pi$
$101$	−39.0000	+	22.5167i	−0.386139	+	0.222937i	0.294347	+	0.955699i	$0.404898\pi$
$102$		0			0
$103$	20.0000	−	34.6410i	0.194175	−	0.336321i	−0.752455	−	0.658644i	$-0.771130\pi$
$103$	20.0000	−	34.6410i	0.194175	−	0.336321i	0.946630	+	0.322323i	$0.104464\pi$
$104$	30.0000	+	17.3205i	0.288462	+	0.166543i
$105$		0			0
$106$		0			0
$107$			140.296i			1.31118i	0.755118	+	0.655589i	$0.227580\pi$
$107$			140.296i			1.31118i	−0.755118	+	0.655589i	$0.772420\pi$
$108$		0			0
$109$	−52.0000			−0.477064			−0.238532	−	0.971135i	$-0.576666\pi$
$109$	−52.0000			−0.477064			−0.238532	+	0.971135i	$0.576666\pi$
$110$	−9.00000	+	5.19615i	−0.0818182	+	0.0472377i
$111$		0			0
$112$	11.0000	−	19.0526i	0.0982143	−	0.170112i
$113$	78.0000	+	45.0333i	0.690265	+	0.398525i	0.803711	−	0.595019i	$-0.202856\pi$
$113$	78.0000	+	45.0333i	0.690265	+	0.398525i	−0.113446	+	0.993544i	$0.536189\pi$
$114$		0			0
$115$	−48.0000	−	83.1384i	−0.417391	−	0.722943i
$116$		−	45.0333i		−	0.388218i
$117$		0			0
$118$	−87.0000			−0.737288
$119$	−27.0000	+	15.5885i	−0.226891	+	0.130995i
$120$		0			0
$121$	−59.0000	+	102.191i	−0.487603	+	0.844554i
$122$	−84.0000	−	48.4974i	−0.688525	−	0.397520i
$123$		0			0
$124$	−16.0000	−	27.7128i	−0.129032	−	0.223490i
$125$			131.636i			1.05309i
$126$		0			0
$127$	−16.0000			−0.125984			−0.0629921	−	0.998014i	$-0.520064\pi$
$127$	−16.0000			−0.125984			−0.0629921	+	0.998014i	$0.520064\pi$
$128$	−52.5000	+	30.3109i	−0.410156	+	0.236804i
$129$		0			0
$130$	−12.0000	+	20.7846i	−0.0923077	+	0.159882i
$131$	−138.000	−	79.6743i	−1.05344	−	0.608201i	−0.129826	−	0.991537i	$-0.541442\pi$
$131$	−138.000	−	79.6743i	−1.05344	−	0.608201i	−0.923609	+	0.383336i	$0.874775\pi$
$132$		0			0
$133$	−11.0000	−	19.0526i	−0.0827068	−	0.143252i
$134$		−	53.6936i		−	0.400698i
$135$		0			0
$136$	135.000			0.992647
$137$	163.500	−	94.3968i	1.19343	−	0.689028i	0.234348	−	0.972153i	$-0.424705\pi$
$137$	163.500	−	94.3968i	1.19343	−	0.689028i	0.959083	+	0.283125i	$0.0913712\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.0179856	+	0.0311520i	−0.874878	−	0.484343i	$-0.839059\pi$
$139$	−2.50000	+	4.33013i	−0.0179856	+	0.0311520i	0.856893	+	0.515495i	$0.172392\pi$
$140$	−6.00000	−	3.46410i	−0.0428571	−	0.0247436i
$141$		0			0
$142$	27.0000	+	46.7654i	0.190141	+	0.329334i
$143$		−	6.92820i		−	0.0484490i
$144$		0			0
$145$	156.000			1.07586
$146$	97.5000	−	56.2917i	0.667808	−	0.385559i
$147$		0			0
$148$	17.0000	−	29.4449i	0.114865	−	0.198952i
$149$	132.000	+	76.2102i	0.885906	+	0.511478i	0.872601	−	0.488433i	$-0.162431\pi$
$149$	132.000	+	76.2102i	0.885906	+	0.511478i	0.0133049	+	0.999911i	$0.495765\pi$
$150$		0			0
$151$	−10.0000	−	17.3205i	−0.0662252	−	0.114705i	0.831012	−	0.556255i	$-0.187762\pi$
$151$	−10.0000	−	17.3205i	−0.0662252	−	0.114705i	−0.897237	+	0.441550i	$0.854429\pi$
$152$			95.2628i			0.626729i
$153$		0			0
$154$	−6.00000			−0.0389610
$155$	96.0000	−	55.4256i	0.619355	−	0.357585i
$156$		0			0
$157$	20.0000	−	34.6410i	0.127389	−	0.220643i	−0.795276	−	0.606248i	$-0.792674\pi$
$157$	20.0000	−	34.6410i	0.127389	−	0.220643i	0.922664	+	0.385605i	$0.126007\pi$
$158$	−57.0000	−	32.9090i	−0.360759	−	0.208285i
$159$		0			0
$160$	27.0000	+	46.7654i	0.168750	+	0.292284i
$161$		−	55.4256i		−	0.344259i
$162$		0			0
$163$	−106.000			−0.650307			−0.325153	−	0.945661i	$-0.605416\pi$
$163$	−106.000			−0.650307			−0.325153	+	0.945661i	$0.605416\pi$
$164$	−10.5000	+	6.06218i	−0.0640244	+	0.0369645i
$165$		0			0
$166$	42.0000	−	72.7461i	0.253012	−	0.438230i
$167$	−165.000	−	95.2628i	−0.988024	−	0.570436i	−0.0833409	−	0.996521i	$-0.526559\pi$
$167$	−165.000	−	95.2628i	−0.988024	−	0.570436i	−0.904683	+	0.426085i	$0.859892\pi$
$168$		0			0
$169$	76.5000	+	132.502i	0.452663	+	0.784035i
$170$			93.5307i			0.550181i
$171$		0			0
$172$	−61.0000			−0.354651
$173$	−201.000	+	116.047i	−1.16185	+	0.670794i	−0.951747	−	0.306885i	$-0.900713\pi$
$173$	−201.000	+	116.047i	−1.16185	+	0.670794i	−0.210103	+	0.977679i	$0.567380\pi$
$174$		0			0
$175$	−13.0000	+	22.5167i	−0.0742857	+	0.128667i
$176$	16.5000	+	9.52628i	0.0937500	+	0.0541266i
$177$		0			0
$178$	−108.000	−	187.061i	−0.606742	−	1.05091i
$179$		−	62.3538i		−	0.348345i	−0.984715	−	0.174173i	$-0.944275\pi$
$179$		−	62.3538i		−	0.348345i	0.984715	−	0.174173i	$-0.0557251\pi$
$180$		0			0
$181$	−232.000			−1.28177			−0.640884	−	0.767638i	$-0.721432\pi$
$181$	−232.000			−1.28177			−0.640884	+	0.767638i	$0.721432\pi$
$182$	−12.0000	+	6.92820i	−0.0659341	+	0.0380671i
$183$		0			0
$184$	−120.000	+	207.846i	−0.652174	+	1.12960i
$185$	102.000	+	58.8897i	0.551351	+	0.318323i
$186$		0			0
$187$	−13.5000	−	23.3827i	−0.0721925	−	0.125041i
$188$			48.4974i			0.257965i
$189$		0			0
$190$	−66.0000			−0.347368
$191$	−201.000	+	116.047i	−1.05236	+	0.607578i	−0.923308	−	0.384060i	$-0.874525\pi$
$191$	−201.000	+	116.047i	−1.05236	+	0.607578i	−0.129048	+	0.991638i	$0.541192\pi$
$192$		0			0
$193$	132.500	−	229.497i	0.686528	−	1.18910i	−0.286425	−	0.958103i	$-0.592467\pi$
$193$	132.500	−	229.497i	0.686528	−	1.18910i	0.972954	−	0.231000i	$-0.0741996\pi$
$194$	172.500	+	99.5929i	0.889175	+	0.513366i
$195$		0			0
$196$	22.5000	+	38.9711i	0.114796	+	0.198832i
$197$		−	124.708i		−	0.633034i	−0.948587	−	0.316517i	$-0.897487\pi$
$197$		−	124.708i		−	0.633034i	0.948587	−	0.316517i	$-0.102513\pi$
$198$		0			0
$199$	290.000			1.45729			0.728643	−	0.684893i	$-0.240151\pi$
$199$	290.000			1.45729			0.728643	+	0.684893i	$0.240151\pi$
$200$	97.5000	−	56.2917i	0.487500	−	0.281458i
$201$		0			0
$202$	−39.0000	+	67.5500i	−0.193069	+	0.334406i
$203$	78.0000	+	45.0333i	0.384236	+	0.221839i
$204$		0			0
$205$	−21.0000	−	36.3731i	−0.102439	−	0.177430i
$206$		−	69.2820i		−	0.336321i
$207$		0			0
$208$	44.0000			0.211538
$209$	16.5000	−	9.52628i	0.0789474	−	0.0455803i
$210$		0			0
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	−0.732893	−	0.680344i	$-0.761830\pi$
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	0.955642	+	0.294532i	$0.0951637\pi$
$212$		0			0
$213$		0			0
$214$	121.500	+	210.444i	0.567757	+	0.983384i
$215$		−	211.310i		−	0.982838i
$216$		0			0
$217$	64.0000			0.294931
$218$	−78.0000	+	45.0333i	−0.357798	+	0.206575i
$219$		0			0
$220$	3.00000	−	5.19615i	0.0136364	−	0.0236189i
$221$	−54.0000	−	31.1769i	−0.244344	−	0.141072i
$222$		0			0
$223$	26.0000	+	45.0333i	0.116592	+	0.201943i	0.918415	−	0.395618i	$-0.129470\pi$
$223$	26.0000	+	45.0333i	0.116592	+	0.201943i	−0.801823	+	0.597562i	$0.796136\pi$
$224$			31.1769i			0.139183i
$225$		0			0
$226$	156.000			0.690265
$227$	163.500	−	94.3968i	0.720264	−	0.415845i	−0.0945856	−	0.995517i	$-0.530153\pi$
$227$	163.500	−	94.3968i	0.720264	−	0.415845i	0.814850	+	0.579672i	$0.196819\pi$
$228$		0			0
$229$	−133.000	+	230.363i	−0.580786	+	1.00595i	0.414600	+	0.910004i	$0.363921\pi$
$229$	−133.000	+	230.363i	−0.580786	+	1.00595i	−0.995386	+	0.0959473i	$0.969412\pi$
$230$	−144.000	−	83.1384i	−0.626087	−	0.361471i
$231$		0			0
$232$	−195.000	−	337.750i	−0.840517	−	1.45582i
$233$		−	202.650i		−	0.869742i	−0.900493	−	0.434871i	$-0.856794\pi$
$233$		−	202.650i		−	0.869742i	0.900493	−	0.434871i	$-0.143206\pi$
$234$		0			0
$235$	−168.000			−0.714894
$236$	43.5000	−	25.1147i	0.184322	−	0.106418i
$237$		0			0
$238$	−27.0000	+	46.7654i	−0.113445	+	0.196493i
$239$	348.000	+	200.918i	1.45607	+	0.840661i	0.998815	−	0.0486764i	$-0.0155003\pi$
$239$	348.000	+	200.918i	1.45607	+	0.840661i	0.457252	+	0.889337i	$0.348834\pi$
$240$		0			0
$241$	−59.5000	−	103.057i	−0.246888	−	0.427623i	0.715773	−	0.698333i	$-0.246075\pi$
$241$	−59.5000	−	103.057i	−0.246888	−	0.427623i	−0.962661	+	0.270711i	$0.912741\pi$
$242$			204.382i			0.844554i
$243$		0			0
$244$	56.0000			0.229508
$245$	−135.000	+	77.9423i	−0.551020	+	0.318132i
$246$		0			0
$247$	22.0000	−	38.1051i	0.0890688	−	0.154272i
$248$	−240.000	−	138.564i	−0.967742	−	0.558726i
$249$		0			0
$250$	114.000	+	197.454i	0.456000	+	0.789815i
$251$			389.711i			1.55264i	0.630342	+	0.776318i	$0.282915\pi$
$251$			389.711i			1.55264i	−0.630342	+	0.776318i	$0.717085\pi$
$252$		0			0
$253$	48.0000			0.189723
$254$	−24.0000	+	13.8564i	−0.0944882	+	0.0545528i
$255$		0			0
$256$	89.5000	−	155.019i	0.349609	−	0.605541i
$257$	−151.500	−	87.4686i	−0.589494	−	0.340345i	0.175403	−	0.984497i	$-0.443877\pi$
$257$	−151.500	−	87.4686i	−0.589494	−	0.340345i	−0.764897	+	0.644152i	$0.777210\pi$
$258$		0			0
$259$	34.0000	+	58.8897i	0.131274	+	0.227373i
$260$		−	13.8564i		−	0.0532939i
$261$		0			0
$262$	−276.000			−1.05344
$263$	−39.0000	+	22.5167i	−0.148289	+	0.0856147i	−0.572309	−	0.820038i	$-0.693952\pi$
$263$	−39.0000	+	22.5167i	−0.148289	+	0.0856147i	0.424020	+	0.905653i	$0.360619\pi$
$264$		0			0
$265$		0			0
$266$	−33.0000	−	19.0526i	−0.124060	−	0.0716262i
$267$		0			0
$268$	15.5000	+	26.8468i	0.0578358	+	0.100175i
$269$			187.061i			0.695396i	0.937607	+	0.347698i	$0.113037\pi$
$269$			187.061i			0.695396i	−0.937607	+	0.347698i	$0.886963\pi$
$270$		0			0
$271$	−268.000			−0.988930			−0.494465	−	0.869198i	$-0.664636\pi$
$271$	−268.000			−0.988930			−0.494465	+	0.869198i	$0.664636\pi$
$272$	148.500	−	85.7365i	0.545956	−	0.315208i
$273$		0			0
$274$	163.500	−	283.190i	0.596715	−	1.03354i
$275$	−19.5000	−	11.2583i	−0.0709091	−	0.0409394i
$276$		0			0
$277$	−28.0000	−	48.4974i	−0.101083	−	0.175081i	0.811048	−	0.584979i	$-0.198897\pi$
$277$	−28.0000	−	48.4974i	−0.101083	−	0.175081i	−0.912131	+	0.409899i	$0.865564\pi$
$278$			8.66025i			0.0311520i
$279$		0			0
$280$	−60.0000			−0.214286
$281$	42.0000	−	24.2487i	0.149466	−	0.0862943i	−0.423402	−	0.905942i	$-0.639164\pi$
$281$	42.0000	−	24.2487i	0.149466	−	0.0862943i	0.572868	+	0.819648i	$0.305831\pi$
$282$		0			0
$283$	−187.000	+	323.894i	−0.660777	+	1.14450i	0.319634	+	0.947541i	$0.396440\pi$
$283$	−187.000	+	323.894i	−0.660777	+	1.14450i	−0.980412	+	0.196959i	$0.936893\pi$
$284$	−27.0000	−	15.5885i	−0.0950704	−	0.0548889i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.0209790	−	0.0363367i
$287$		−	24.2487i		−	0.0844903i
$288$		0			0
$289$	46.0000			0.159170
$290$	234.000	−	135.100i	0.806897	−	0.465862i
$291$		0			0
$292$	−32.5000	+	56.2917i	−0.111301	+	0.192780i
$293$	−219.000	−	126.440i	−0.747440	−	0.431535i	0.0773280	−	0.997006i	$-0.475361\pi$
$293$	−219.000	−	126.440i	−0.747440	−	0.431535i	−0.824768	+	0.565471i	$0.808694\pi$
$294$		0			0
$295$	87.0000	+	150.688i	0.294915	+	0.510808i
$296$		−	294.449i		−	0.994759i
$297$		0			0
$298$	264.000			0.885906
$299$	96.0000	−	55.4256i	0.321070	−	0.185370i
$300$		0			0
$301$	61.0000	−	105.655i	0.202658	−	0.351014i
$302$	−30.0000	−	17.3205i	−0.0993377	−	0.0573527i
$303$		0			0
$304$	60.5000	+	104.789i	0.199013	+	0.344701i
$305$			193.990i			0.636032i
$306$		0			0
$307$	533.000			1.73616			0.868078	−	0.496428i	$-0.165355\pi$
$307$	533.000			1.73616			0.868078	+	0.496428i	$0.165355\pi$
$308$	3.00000	−	1.73205i	0.00974026	−	0.00562354i
$309$		0			0
$310$	96.0000	−	166.277i	0.309677	−	0.536377i
$311$	213.000	+	122.976i	0.684887	+	0.395420i	0.801694	−	0.597735i	$-0.203932\pi$
$311$	213.000	+	122.976i	0.684887	+	0.395420i	−0.116806	+	0.993155i	$0.537266\pi$
$312$		0			0
$313$	−77.5000	−	134.234i	−0.247604	−	0.428862i	0.715257	−	0.698862i	$-0.246310\pi$
$313$	−77.5000	−	134.234i	−0.247604	−	0.428862i	−0.962860	+	0.269999i	$0.912976\pi$
$314$		−	69.2820i		−	0.220643i
$315$		0			0
$316$	38.0000			0.120253
$317$	42.0000	−	24.2487i	0.132492	−	0.0764944i	−0.432289	−	0.901735i	$-0.642294\pi$
$317$	42.0000	−	24.2487i	0.132492	−	0.0764944i	0.564781	+	0.825241i	$0.308961\pi$
$318$		0			0
$319$	−39.0000	+	67.5500i	−0.122257	+	0.211755i
$320$	213.000	+	122.976i	0.665625	+	0.384299i
$321$		0			0
$322$	−48.0000	−	83.1384i	−0.149068	−	0.258194i
$323$		−	171.473i		−	0.530876i
$324$		0			0
$325$	−52.0000			−0.160000
$326$	−159.000	+	91.7987i	−0.487730	+	0.281591i
$327$		0			0
$328$	−52.5000	+	90.9327i	−0.160061	+	0.277234i
$329$	−84.0000	−	48.4974i	−0.255319	−	0.147409i
$330$		0			0
$331$	−1.00000	−	1.73205i	−0.00302115	−	0.00523278i	0.864511	−	0.502614i	$-0.167628\pi$
$331$	−1.00000	−	1.73205i	−0.00302115	−	0.00523278i	−0.867532	+	0.497381i	$0.834295\pi$
$332$			48.4974i			0.146077i
$333$		0			0
$334$	−330.000			−0.988024
$335$	−93.0000	+	53.6936i	−0.277612	+	0.160279i
$336$		0			0
$337$	−38.5000	+	66.6840i	−0.114243	+	0.197875i	−0.917477	−	0.397789i	$-0.869778\pi$
$337$	−38.5000	+	66.6840i	−0.114243	+	0.197875i	0.803234	+	0.595664i	$0.203111\pi$
$338$	229.500	+	132.502i	0.678994	+	0.392017i
$339$		0			0
$340$	−27.0000	−	46.7654i	−0.0794118	−	0.137545i
$341$			55.4256i			0.162538i
$342$		0			0
$343$	−188.000			−0.548105
$344$	−457.500	+	264.138i	−1.32994	+	0.767842i
$345$		0			0
$346$	−201.000	+	348.142i	−0.580925	+	1.00619i
$347$	−97.5000	−	56.2917i	−0.280980	−	0.162224i	0.352887	−	0.935666i	$-0.385200\pi$
$347$	−97.5000	−	56.2917i	−0.280980	−	0.162224i	−0.633867	+	0.773442i	$0.718533\pi$
$348$		0			0
$349$	−208.000	−	360.267i	−0.595989	−	1.03228i	−0.993407	−	0.114645i	$-0.963427\pi$
$349$	−208.000	−	360.267i	−0.595989	−	1.03228i	0.397418	−	0.917638i	$-0.369906\pi$
$350$			45.0333i			0.128667i
$351$		0			0
$352$	−27.0000			−0.0767045
$353$	1.50000	−	0.866025i	0.00424929	−	0.00245333i	−0.497874	−	0.867249i	$-0.665886\pi$
$353$	1.50000	−	0.866025i	0.00424929	−	0.00245333i	0.502123	+	0.864796i	$0.332552\pi$
$354$		0			0
$355$	54.0000	−	93.5307i	0.152113	−	0.263467i
$356$	108.000	+	62.3538i	0.303371	+	0.175151i
$357$		0			0
$358$	−54.0000	−	93.5307i	−0.150838	−	0.261259i
$359$		−	592.361i		−	1.65003i	−0.565110	−	0.825016i	$-0.691166\pi$
$359$		−	592.361i		−	1.65003i	0.565110	−	0.825016i	$-0.308834\pi$
$360$		0			0
$361$	−240.000			−0.664820
$362$	−348.000	+	200.918i	−0.961326	+	0.555022i
$363$		0			0
$364$	4.00000	−	6.92820i	0.0109890	−	0.0190335i
$365$	−195.000	−	112.583i	−0.534247	−	0.308447i
$366$		0			0
$367$	179.000	+	310.037i	0.487738	+	0.844788i	0.999901	−	0.0141011i	$-0.00448865\pi$
$367$	179.000	+	310.037i	0.487738	+	0.844788i	−0.512162	+	0.858889i	$0.671155\pi$
$368$			304.841i			0.828372i
$369$		0			0
$370$	204.000			0.551351
$371$		0			0
$372$		0			0
$373$	290.000	−	502.295i	0.777480	−	1.34663i	−0.155910	−	0.987771i	$-0.549831\pi$
$373$	290.000	−	502.295i	0.777480	−	1.34663i	0.933390	−	0.358863i	$-0.116836\pi$
$374$	−40.5000	−	23.3827i	−0.108289	−	0.0625206i
$375$		0			0
$376$	210.000	+	363.731i	0.558511	+	0.967369i
$377$			180.133i			0.477807i
$378$		0			0
$379$	83.0000			0.218997			0.109499	−	0.993987i	$-0.465075\pi$
$379$	83.0000			0.218997			0.109499	+	0.993987i	$0.465075\pi$
$380$	33.0000	−	19.0526i	0.0868421	−	0.0501383i
$381$		0			0
$382$	−201.000	+	348.142i	−0.526178	+	0.911367i
$383$	483.000	+	278.860i	1.26110	+	0.728094i	0.973287	−	0.229593i	$-0.0737395\pi$
$383$	483.000	+	278.860i	1.26110	+	0.728094i	0.287810	+	0.957688i	$0.407073\pi$
$384$		0			0
$385$	6.00000	+	10.3923i	0.0155844	+	0.0269930i
$386$		−	458.993i		−	1.18910i
$387$		0			0
$388$	−115.000			−0.296392
$389$	447.000	−	258.076i	1.14910	−	0.663433i	0.200432	−	0.979708i	$-0.435765\pi$
$389$	447.000	−	258.076i	1.14910	−	0.663433i	0.948668	+	0.316274i	$0.102432\pi$
$390$		0			0
$391$	216.000	−	374.123i	0.552430	−	0.956836i
$392$	337.500	+	194.856i	0.860969	+	0.497081i
$393$		0			0
$394$	−108.000	−	187.061i	−0.274112	−	0.474775i
$395$			131.636i			0.333255i
$396$		0			0
$397$	362.000			0.911839			0.455919	−	0.890021i	$-0.349311\pi$
$397$	362.000			0.911839			0.455919	+	0.890021i	$0.349311\pi$
$398$	435.000	−	251.147i	1.09296	−	0.631024i
$399$		0			0
$400$	71.5000	−	123.842i	0.178750	−	0.309604i
$401$	−340.500	−	196.588i	−0.849127	−	0.490244i	0.0112291	−	0.999937i	$-0.496426\pi$
$401$	−340.500	−	196.588i	−0.849127	−	0.490244i	−0.860356	+	0.509693i	$0.829759\pi$
$402$		0			0
$403$	64.0000	+	110.851i	0.158809	+	0.275065i
$404$		−	45.0333i		−	0.111469i
$405$		0			0
$406$	156.000			0.384236
$407$	−51.0000	+	29.4449i	−0.125307	+	0.0723461i
$408$		0			0
$409$	−110.500	+	191.392i	−0.270171	+	0.467950i	−0.968905	−	0.247431i	$-0.920414\pi$
$409$	−110.500	+	191.392i	−0.270171	+	0.467950i	0.698734	+	0.715381i	$0.253747\pi$
$410$	−63.0000	−	36.3731i	−0.153659	−	0.0887148i
$411$		0			0
$412$	20.0000	+	34.6410i	0.0485437	+	0.0840801i
$413$			100.459i			0.243242i
$414$		0			0
$415$	−168.000			−0.404819
$416$	−54.0000	+	31.1769i	−0.129808	+	0.0749445i
$417$		0			0
$418$	16.5000	−	28.5788i	0.0394737	−	0.0683704i
$419$	−678.000	−	391.443i	−1.61814	−	0.934233i	−0.987401	−	0.158236i	$-0.949419\pi$
$419$	−678.000	−	391.443i	−1.61814	−	0.934233i	−0.630737	−	0.775997i	$-0.717247\pi$
$420$		0			0
$421$	341.000	+	590.629i	0.809976	+	1.40292i	0.912880	+	0.408229i	$0.133853\pi$
$421$	341.000	+	590.629i	0.809976	+	1.40292i	−0.102903	+	0.994691i	$0.532813\pi$
$422$		−	162.813i		−	0.385812i
$423$		0			0
$424$		0			0
$425$	−175.500	+	101.325i	−0.412941	+	0.238412i
$426$		0			0
$427$	−56.0000	+	96.9948i	−0.131148	+	0.227154i
$428$	−121.500	−	70.1481i	−0.283879	−	0.163897i
$429$		0			0
$430$	−183.000	−	316.965i	−0.425581	−	0.737129i
$431$			280.592i			0.651026i	0.945538	+	0.325513i	$0.105537\pi$
$431$			280.592i			0.651026i	−0.945538	+	0.325513i	$0.894463\pi$
$432$		0			0
$433$	−295.000			−0.681293			−0.340647	−	0.940191i	$-0.610646\pi$
$433$	−295.000			−0.681293			−0.340647	+	0.940191i	$0.610646\pi$
$434$	96.0000	−	55.4256i	0.221198	−	0.127709i
$435$		0			0
$436$	26.0000	−	45.0333i	0.0596330	−	0.103287i
$437$	264.000	+	152.420i	0.604119	+	0.348788i
$438$		0			0
$439$	−406.000	−	703.213i	−0.924829	−	1.60185i	−0.791836	−	0.610734i	$-0.790874\pi$
$439$	−406.000	−	703.213i	−0.924829	−	1.60185i	−0.132993	−	0.991117i	$-0.542459\pi$
$440$		−	51.9615i		−	0.118094i
$441$		0			0
$442$	−108.000			−0.244344
$443$	−79.5000	+	45.8993i	−0.179458	+	0.103610i	−0.587038	−	0.809559i	$-0.699706\pi$
$443$	−79.5000	+	45.8993i	−0.179458	+	0.103610i	0.407580	+	0.913170i	$0.366373\pi$
$444$		0			0
$445$	−216.000	+	374.123i	−0.485393	+	0.840726i
$446$	78.0000	+	45.0333i	0.174888	+	0.100972i
$447$		0			0
$448$	71.0000	+	122.976i	0.158482	+	0.274499i
$449$			639.127i			1.42344i	0.702461	+	0.711722i	$0.252085\pi$
$449$			639.127i			1.42344i	−0.702461	+	0.711722i	$0.747915\pi$
$450$		0			0
$451$	21.0000			0.0465632
$452$	−78.0000	+	45.0333i	−0.172566	+	0.0996312i
$453$		0			0
$454$	163.500	−	283.190i	0.360132	−	0.623767i
$455$	24.0000	+	13.8564i	0.0527473	+	0.0304536i
$456$		0			0
$457$	−32.5000	−	56.2917i	−0.0711160	−	0.123176i	0.828275	−	0.560322i	$-0.189323\pi$
$457$	−32.5000	−	56.2917i	−0.0711160	−	0.123176i	−0.899391	+	0.437146i	$0.855989\pi$
$458$			460.726i			1.00595i
$459$		0			0
$460$	96.0000			0.208696
$461$	690.000	−	398.372i	1.49675	−	0.864147i	0.496753	−	0.867892i	$-0.334525\pi$
$461$	690.000	−	398.372i	1.49675	−	0.864147i	0.999993	+	0.00374501i	$0.00119208\pi$
$462$		0			0
$463$	−367.000	+	635.663i	−0.792657	+	1.37292i	0.131660	+	0.991295i	$0.457969\pi$
$463$	−367.000	+	635.663i	−0.792657	+	1.37292i	−0.924317	+	0.381627i	$0.875364\pi$
$464$	−429.000	−	247.683i	−0.924569	−	0.533800i
$465$		0			0
$466$	−175.500	−	303.975i	−0.376609	−	0.652307i
$467$			202.650i			0.433940i	0.976178	+	0.216970i	$0.0696174\pi$
$467$			202.650i			0.433940i	−0.976178	+	0.216970i	$0.930383\pi$
$468$		0			0
$469$	−62.0000			−0.132196
$470$	−252.000	+	145.492i	−0.536170	+	0.309558i
$471$		0			0
$472$	217.500	−	376.721i	0.460805	−	0.798138i
$473$	91.5000	+	52.8275i	0.193446	+	0.111686i
$474$		0			0
$475$	−71.5000	−	123.842i	−0.150526	−	0.260719i
$476$		−	31.1769i		−	0.0654977i
$477$		0			0
$478$	696.000			1.45607
$479$	−525.000	+	303.109i	−1.09603	+	0.632795i	−0.935176	−	0.354183i	$-0.884759\pi$
$479$	−525.000	+	303.109i	−1.09603	+	0.632795i	−0.160857	+	0.986978i	$0.551426\pi$
$480$		0			0
$481$	−68.0000	+	117.779i	−0.141372	+	0.244864i
$482$	−178.500	−	103.057i	−0.370332	−	0.213811i
$483$		0			0
$484$	−59.0000	−	102.191i	−0.121901	−	0.211138i
$485$		−	398.372i		−	0.821385i
$486$		0			0
$487$	−106.000			−0.217659			−0.108830	−	0.994060i	$-0.534710\pi$
$487$	−106.000			−0.217659			−0.108830	+	0.994060i	$0.534710\pi$
$488$	420.000	−	242.487i	0.860656	−	0.496900i
$489$		0			0
$490$	−135.000	+	233.827i	−0.275510	+	0.477198i
$491$	199.500	+	115.181i	0.406314	+	0.234585i	0.689205	−	0.724567i	$-0.257960\pi$
$491$	199.500	+	115.181i	0.406314	+	0.234585i	−0.282891	+	0.959152i	$0.591293\pi$
$492$		0			0
$493$	351.000	+	607.950i	0.711968	+	1.23316i
$494$		−	76.2102i		−	0.154272i
$495$		0			0
$496$	−352.000			−0.709677
$497$	54.0000	−	31.1769i	0.108652	−	0.0627302i
$498$		0			0
$499$	393.500	−	681.562i	0.788577	−	1.36586i	−0.138261	−	0.990396i	$-0.544151\pi$
$499$	393.500	−	681.562i	0.788577	−	1.36586i	0.926839	−	0.375460i	$-0.122515\pi$
$500$	−114.000	−	65.8179i	−0.228000	−	0.131636i
$501$		0			0
$502$	337.500	+	584.567i	0.672311	+	1.16448i
$503$		−	623.538i		−	1.23964i	−0.784745	−	0.619819i	$-0.787206\pi$
$503$		−	623.538i		−	1.23964i	0.784745	−	0.619819i	$-0.212794\pi$
$504$		0			0
$505$	156.000			0.308911
$506$	72.0000	−	41.5692i	0.142292	−	0.0821526i
$507$		0			0
$508$	8.00000	−	13.8564i	0.0157480	−	0.0272764i
$509$	186.000	+	107.387i	0.365422	+	0.210977i	0.671457	−	0.741044i	$-0.265669\pi$
$509$	186.000	+	107.387i	0.365422	+	0.210977i	−0.306034	+	0.952020i	$0.599002\pi$
$510$		0			0
$511$	−65.0000	−	112.583i	−0.127202	−	0.220320i
$512$		−	552.524i		−	1.07915i
$513$		0			0
$514$	−303.000			−0.589494
$515$	−120.000	+	69.2820i	−0.233010	+	0.134528i
$516$		0			0
$517$	42.0000	−	72.7461i	0.0812379	−	0.140708i
$518$	102.000	+	58.8897i	0.196911	+	0.113687i
$519$		0			0
$520$	−60.0000	−	103.923i	−0.115385	−	0.199852i
$521$			202.650i			0.388963i	0.980906	+	0.194482i	$0.0623025\pi$
$521$			202.650i			0.388963i	−0.980906	+	0.194482i	$0.937698\pi$
$522$		0			0
$523$	−250.000			−0.478011			−0.239006	−	0.971018i	$-0.576821\pi$
$523$	−250.000			−0.478011			−0.239006	+	0.971018i	$0.576821\pi$
$524$	138.000	−	79.6743i	0.263359	−	0.152050i
$525$		0			0
$526$	−39.0000	+	67.5500i	−0.0741445	+	0.128422i
$527$	432.000	+	249.415i	0.819734	+	0.473274i
$528$		0			0
$529$	119.500	+	206.980i	0.225898	+	0.391267i
$530$		0			0
$531$		0			0
$532$	22.0000			0.0413534
$533$	42.0000	−	24.2487i	0.0787992	−	0.0454948i
$534$		0			0
$535$	243.000	−	420.888i	0.454206	−	0.786707i
$536$	232.500	+	134.234i	0.433769	+	0.250436i
$537$		0			0
$538$	162.000	+	280.592i	0.301115	+	0.521547i
$539$		−	77.9423i		−	0.144605i
$540$		0			0
$541$	650.000			1.20148			0.600739	−	0.799445i	$-0.294873\pi$
$541$	650.000			1.20148			0.600739	+	0.799445i	$0.294873\pi$
$542$	−402.000	+	232.095i	−0.741697	+	0.428219i
$543$		0			0
$544$	−121.500	+	210.444i	−0.223346	+	0.386846i
$545$	156.000	+	90.0666i	0.286239	+	0.165260i
$546$		0			0
$547$	−311.500	−	539.534i	−0.569470	−	0.986351i	−0.996618	−	0.0821692i	$-0.973815\pi$
$547$	−311.500	−	539.534i	−0.569470	−	0.986351i	0.427149	−	0.904181i	$-0.359518\pi$
$548$			188.794i			0.344514i
$549$		0			0
$550$	−39.0000			−0.0709091
$551$	−429.000	+	247.683i	−0.778584	+	0.449516i
$552$		0			0
$553$	−38.0000	+	65.8179i	−0.0687161	+	0.119020i
$554$	−84.0000	−	48.4974i	−0.151625	−	0.0875405i
$555$		0			0
$556$	−2.50000	−	4.33013i	−0.00449640	−	0.00778800i
$557$		−	530.008i		−	0.951540i	−0.879570	−	0.475770i	$-0.842170\pi$
$557$		−	530.008i		−	0.951540i	0.879570	−	0.475770i	$-0.157830\pi$
$558$		0			0
$559$	244.000			0.436494
$560$	−66.0000	+	38.1051i	−0.117857	+	0.0680449i
$561$		0			0
$562$	42.0000	−	72.7461i	0.0747331	−	0.129442i
$563$	−97.5000	−	56.2917i	−0.173179	−	0.0999852i	0.410905	−	0.911678i	$-0.365213\pi$
$563$	−97.5000	−	56.2917i	−0.173179	−	0.0999852i	−0.584084	+	0.811693i	$0.698546\pi$
$564$		0			0
$565$	−156.000	−	270.200i	−0.276106	−	0.478230i
$566$			647.787i			1.14450i
$567$		0			0
$568$	−270.000			−0.475352
$569$	−565.500	+	326.492i	−0.993849	+	0.573799i	−0.906423	−	0.422372i	$-0.861198\pi$
$569$	−565.500	+	326.492i	−0.993849	+	0.573799i	−0.0874263	+	0.996171i	$0.527864\pi$
$570$		0			0
$571$	−272.500	+	471.984i	−0.477233	+	0.826592i	−0.999660	−	0.0260926i	$-0.991694\pi$
$571$	−272.500	+	471.984i	−0.477233	+	0.826592i	0.522427	+	0.852684i	$0.325027\pi$
$572$	6.00000	+	3.46410i	0.0104895	+	0.00605612i
$573$		0			0
$574$	−21.0000	−	36.3731i	−0.0365854	−	0.0633677i
$575$		−	360.267i		−	0.626551i
$576$		0			0
$577$	−871.000			−1.50953			−0.754766	−	0.655994i	$-0.772250\pi$
$577$	−871.000			−1.50953			−0.754766	+	0.655994i	$0.772250\pi$
$578$	69.0000	−	39.8372i	0.119377	−	0.0689224i
$579$		0			0
$580$	−78.0000	+	135.100i	−0.134483	+	0.232931i
$581$	−84.0000	−	48.4974i	−0.144578	−	0.0834723i
$582$		0			0
$583$		0			0
$584$			562.917i			0.963898i
$585$		0			0
$586$	−438.000			−0.747440
$587$	1.50000	−	0.866025i	0.00255537	−	0.00147534i	−0.498722	−	0.866762i	$-0.666197\pi$
$587$	1.50000	−	0.866025i	0.00255537	−	0.00147534i	0.501277	+	0.865287i	$0.332864\pi$
$588$		0			0
$589$	−176.000	+	304.841i	−0.298812	+	0.517557i
$590$	261.000	+	150.688i	0.442373	+	0.255404i
$591$		0			0
$592$	−187.000	−	323.894i	−0.315878	−	0.547117i
$593$		−	187.061i		−	0.315449i	−0.987483	−	0.157725i	$-0.949584\pi$
$593$		−	187.061i		−	0.315449i	0.987483	−	0.157725i	$-0.0504159\pi$
$594$		0			0
$595$	108.000			0.181513
$596$	−132.000	+	76.2102i	−0.221477	+	0.127870i
$597$		0			0
$598$	96.0000	−	166.277i	0.160535	−	0.278055i
$599$	−489.000	−	282.324i	−0.816361	−	0.471326i	0.0327992	−	0.999462i	$-0.489558\pi$
$599$	−489.000	−	282.324i	−0.816361	−	0.471326i	−0.849160	+	0.528136i	$0.822891\pi$
$600$		0			0
$601$	−230.500	−	399.238i	−0.383527	−	0.664289i	0.608036	−	0.793909i	$-0.291958\pi$
$601$	−230.500	−	399.238i	−0.383527	−	0.664289i	−0.991564	+	0.129620i	$0.958624\pi$
$602$		−	211.310i		−	0.351014i
$603$		0			0
$604$	20.0000			0.0331126
$605$	354.000	−	204.382i	0.585124	−	0.337821i
$606$		0			0
$607$	56.0000	−	96.9948i	0.0922570	−	0.159794i	−0.816204	−	0.577765i	$-0.803925\pi$
$607$	56.0000	−	96.9948i	0.0922570	−	0.159794i	0.908461	+	0.417971i	$0.137259\pi$
$608$	−148.500	−	85.7365i	−0.244243	−	0.141014i
$609$		0			0
$610$	168.000	+	290.985i	0.275410	+	0.477024i
$611$		−	193.990i		−	0.317495i
$612$		0			0
$613$	902.000			1.47145			0.735726	−	0.677279i	$-0.236841\pi$
$613$	902.000			1.47145			0.735726	+	0.677279i	$0.236841\pi$
$614$	799.500	−	461.592i	1.30212	−	0.751778i
$615$		0			0
$616$	15.0000	−	25.9808i	0.0243506	−	0.0421766i
$617$	307.500	+	177.535i	0.498379	+	0.287739i	0.728044	−	0.685530i	$-0.240430\pi$
$617$	307.500	+	177.535i	0.498379	+	0.287739i	−0.229665	+	0.973270i	$0.573763\pi$
$618$		0			0
$619$	399.500	+	691.954i	0.645396	+	1.11786i	0.984210	+	0.177005i	$0.0566409\pi$
$619$	399.500	+	691.954i	0.645396	+	1.11786i	−0.338814	+	0.940853i	$0.610026\pi$
$620$			110.851i			0.178792i
$621$		0			0
$622$	426.000			0.684887
$623$	−216.000	+	124.708i	−0.346709	+	0.200173i
$624$		0			0
$625$	65.5000	−	113.449i	0.104800	−	0.181519i
$626$	−232.500	−	134.234i	−0.371406	−	0.214431i
$627$		0			0
$628$	20.0000	+	34.6410i	0.0318471	+	0.0551609i
$629$			530.008i			0.842619i
$630$		0			0
$631$	830.000			1.31537			0.657686	−	0.753292i	$-0.271535\pi$
$631$	830.000			1.31537			0.657686	+	0.753292i	$0.271535\pi$
$632$	285.000	−	164.545i	0.450949	−	0.260356i
$633$		0			0
$634$	42.0000	−	72.7461i	0.0662461	−	0.114742i
$635$	48.0000	+	27.7128i	0.0755906	+	0.0436422i
$636$		0			0
$637$	−90.0000	−	155.885i	−0.141287	−	0.244717i
$638$			135.100i			0.211755i
$639$		0			0
$640$	210.000			0.328125
$641$	325.500	−	187.928i	0.507800	−	0.293179i	−0.224129	−	0.974560i	$-0.571954\pi$
$641$	325.500	−	187.928i	0.507800	−	0.293179i	0.731929	+	0.681381i	$0.238620\pi$
$642$		0			0
$643$	6.50000	−	11.2583i	0.0101089	−	0.0175091i	−0.860927	−	0.508729i	$-0.830116\pi$
$643$	6.50000	−	11.2583i	0.0101089	−	0.0175091i	0.871036	+	0.491220i	$0.163449\pi$
$644$	48.0000	+	27.7128i	0.0745342	+	0.0430323i
$645$		0			0
$646$	−148.500	−	257.210i	−0.229876	−	0.398157i
$647$		−	467.654i		−	0.722803i	−0.932410	−	0.361402i	$-0.882298\pi$
$647$		−	467.654i		−	0.722803i	0.932410	−	0.361402i	$-0.117702\pi$
$648$		0			0
$649$	−87.0000			−0.134052
$650$	−78.0000	+	45.0333i	−0.120000	+	0.0692820i
$651$		0			0
$652$	53.0000	−	91.7987i	0.0812883	−	0.140796i
$653$	−327.000	−	188.794i	−0.500766	−	0.289117i	0.228264	−	0.973599i	$-0.426695\pi$
$653$	−327.000	−	188.794i	−0.500766	−	0.289117i	−0.729030	+	0.684482i	$0.760028\pi$
$654$		0			0
$655$	276.000	+	478.046i	0.421374	+	0.729841i
$656$			133.368i			0.203305i
$657$		0			0
$658$	−168.000			−0.255319
$659$	852.000	−	491.902i	1.29287	−	0.746438i	0.313706	−	0.949520i	$-0.398429\pi$
$659$	852.000	−	491.902i	1.29287	−	0.746438i	0.979162	+	0.203082i	$0.0650959\pi$
$660$		0			0
$661$	191.000	−	330.822i	0.288956	−	0.500487i	−0.684605	−	0.728915i	$-0.740025\pi$
$661$	191.000	−	330.822i	0.288956	−	0.500487i	0.973561	+	0.228428i	$0.0733585\pi$
$662$	−3.00000	−	1.73205i	−0.00453172	−	0.00261639i
$663$		0			0
$664$	210.000	+	363.731i	0.316265	+	0.547787i
$665$			76.2102i			0.114602i
$666$		0			0
$667$	−1248.00			−1.87106
$668$	165.000	−	95.2628i	0.247006	−	0.142609i
$669$		0			0
$670$	−93.0000	+	161.081i	−0.138806	+	0.240419i
$671$	−84.0000	−	48.4974i	−0.125186	−	0.0722763i
$672$		0			0
$673$	−289.000	−	500.563i	−0.429421	−	0.743778i	0.567401	−	0.823441i	$-0.307949\pi$
$673$	−289.000	−	500.563i	−0.429421	−	0.743778i	−0.996822	+	0.0796633i	$0.974615\pi$
$674$			133.368i			0.197875i
$675$		0			0
$676$	−153.000			−0.226331
$677$	−606.000	+	349.874i	−0.895126	+	0.516801i	−0.875616	−	0.483009i	$-0.839544\pi$
$677$	−606.000	+	349.874i	−0.895126	+	0.516801i	−0.0195100	+	0.999810i	$0.506211\pi$
$678$		0			0
$679$	115.000	−	199.186i	0.169367	−	0.293352i
$680$	−405.000	−	233.827i	−0.595588	−	0.343863i
$681$		0			0
$682$	48.0000	+	83.1384i	0.0703812	+	0.121904i
$683$			1044.43i			1.52918i	0.644520	+	0.764588i	$0.277057\pi$
$683$			1044.43i			1.52918i	−0.644520	+	0.764588i	$0.722943\pi$
$684$		0			0
$685$	−654.000			−0.954745
$686$	−282.000	+	162.813i	−0.411079	+	0.237336i
$687$		0			0
$688$	−335.500	+	581.103i	−0.487645	+	0.844627i
$689$		0			0
$690$		0			0
$691$	−91.0000	−	157.617i	−0.131693	−	0.228099i	0.792636	−	0.609695i	$-0.208708\pi$
$691$	−91.0000	−	157.617i	−0.131693	−	0.228099i	−0.924329	+	0.381596i	$0.875375\pi$
$692$		−	232.095i		−	0.335397i
$693$		0			0
$694$	−195.000			−0.280980
$695$	15.0000	−	8.66025i	0.0215827	−	0.0124608i
$696$		0			0
$697$	94.5000	−	163.679i	0.135581	−	0.234833i
$698$	−624.000	−	360.267i	−0.893983	−	0.516141i
$699$		0			0
$700$	−13.0000	−	22.5167i	−0.0185714	−	0.0321667i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	−374.000			−0.532006
$704$	−106.500	+	61.4878i	−0.151278	+	0.0873406i
$705$		0			0
$706$	1.50000	−	2.59808i	0.00212465	−	0.00367999i
$707$	78.0000	+	45.0333i	0.110325	+	0.0636964i
$708$		0			0
$709$	350.000	+	606.218i	0.493653	+	0.855032i	0.999973	−	0.00731341i	$-0.00232795\pi$
$709$	350.000	+	606.218i	0.493653	+	0.855032i	−0.506320	+	0.862346i	$0.668995\pi$
$710$		−	187.061i		−	0.263467i
$711$		0			0
$712$	1080.00			1.51685
$713$	−768.000	+	443.405i	−1.07714	+	0.621886i
$714$		0			0
$715$	−12.0000	+	20.7846i	−0.0167832	+	0.0290694i
$716$	54.0000	+	31.1769i	0.0754190	+	0.0435432i
$717$		0			0
$718$	−513.000	−	888.542i	−0.714485	−	1.23752i
$719$			592.361i			0.823868i	0.911214	+	0.411934i	$0.135147\pi$
$719$			592.361i			0.823868i	−0.911214	+	0.411934i	$0.864853\pi$
$720$		0			0
$721$	−80.0000			−0.110957
$722$	−360.000	+	207.846i	−0.498615	+	0.287875i
$723$		0			0
$724$	116.000	−	200.918i	0.160221	−	0.277511i
$725$	507.000	+	292.717i	0.699310	+	0.403747i
$726$		0			0
$727$	332.000	+	575.041i	0.456671	+	0.790978i	0.998783	−	0.0493289i	$-0.0157082\pi$
$727$	332.000	+	575.041i	0.456671	+	0.790978i	−0.542111	+	0.840307i	$0.682375\pi$
$728$		−	69.2820i		−	0.0951676i
$729$		0			0
$730$	−390.000			−0.534247
$731$	823.500	−	475.448i	1.12654	−	0.650408i
$732$		0			0
$733$	335.000	−	580.237i	0.457026	−	0.791592i	−0.541776	−	0.840523i	$-0.682248\pi$
$733$	335.000	−	580.237i	0.457026	−	0.791592i	0.998802	+	0.0489306i	$0.0155813\pi$
$734$	537.000	+	310.037i	0.731608	+	0.422394i
$735$		0			0
$736$	−216.000	−	374.123i	−0.293478	−	0.508319i
$737$		−	53.6936i		−	0.0728542i
$738$		0			0
$739$	317.000			0.428958			0.214479	−	0.976729i	$-0.431195\pi$
$739$	317.000			0.428958			0.214479	+	0.976729i	$0.431195\pi$
$740$	−102.000	+	58.8897i	−0.137838	+	0.0795807i
$741$		0			0
$742$		0			0
$743$	537.000	+	310.037i	0.722746	+	0.417277i	0.815762	−	0.578387i	$-0.196318\pi$
$743$	537.000	+	310.037i	0.722746	+	0.417277i	−0.0930168	+	0.995665i	$0.529651\pi$
$744$		0			0
$745$	−264.000	−	457.261i	−0.354362	−	0.613774i
$746$		−	1004.59i		−	1.34663i
$747$		0			0
$748$	27.0000			0.0360963
$749$	243.000	−	140.296i	0.324433	−	0.187311i
$750$		0			0
$751$	−655.000	+	1134.49i	−0.872170	+	1.51064i	−0.0124237	+	0.999923i	$0.503955\pi$
$751$	−655.000	+	1134.49i	−0.872170	+	1.51064i	−0.859747	+	0.510721i	$0.829379\pi$
$752$	462.000	+	266.736i	0.614362	+	0.354702i
$753$		0			0
$754$	156.000	+	270.200i	0.206897	+	0.358355i
$755$			69.2820i			0.0917643i
$756$		0			0
$757$	218.000			0.287979			0.143989	−	0.989579i	$-0.454007\pi$
$757$	218.000			0.287979			0.143989	+	0.989579i	$0.454007\pi$
$758$	124.500	−	71.8801i	0.164248	−	0.0948286i
$759$		0			0
$760$	165.000	−	285.788i	0.217105	−	0.376037i
$761$	−570.000	−	329.090i	−0.749014	−	0.432444i	0.0763232	−	0.997083i	$-0.475682\pi$
$761$	−570.000	−	329.090i	−0.749014	−	0.432444i	−0.825338	+	0.564639i	$0.809015\pi$
$762$		0			0
$763$	52.0000	+	90.0666i	0.0681520	+	0.118043i
$764$		−	232.095i		−	0.303789i
$765$		0			0
$766$	966.000			1.26110
$767$	−174.000	+	100.459i	−0.226858	+	0.130976i
$768$		0			0
$769$	−511.000	+	885.078i	−0.664499	+	1.15095i	0.314921	+	0.949118i	$0.398022\pi$
$769$	−511.000	+	885.078i	−0.664499	+	1.15095i	−0.979421	+	0.201829i	$0.935312\pi$
$770$	18.0000	+	10.3923i	0.0233766	+	0.0134965i
$771$		0			0
$772$	132.500	+	229.497i	0.171632	+	0.297276i
$773$		−	1184.72i		−	1.53263i	−0.642465	−	0.766315i	$-0.722088\pi$
$773$		−	1184.72i		−	1.53263i	0.642465	−	0.766315i	$-0.277912\pi$
$774$		0			0
$775$	416.000			0.536774
$776$	−862.500	+	497.965i	−1.11147	+	0.641707i
$777$		0			0
$778$	447.000	−	774.227i	0.574550	−	0.995150i
$779$	115.500	+	66.6840i	0.148267	+	0.0856020i
$780$		0			0
$781$	27.0000	+	46.7654i	0.0345711	+	0.0598788i
$782$		−	748.246i		−	0.956836i
$783$		0			0
$784$	495.000			0.631378
$785$	−120.000	+	69.2820i	−0.152866	+	0.0882574i
$786$		0			0
$787$	65.0000	−	112.583i	0.0825921	−	0.143054i	−0.821771	−	0.569819i	$-0.807013\pi$
$787$	65.0000	−	112.583i	0.0825921	−	0.143054i	0.904363	+	0.426765i	$0.140347\pi$
$788$	108.000	+	62.3538i	0.137056	+	0.0791292i
$789$		0			0
$790$	114.000	+	197.454i	0.144304	+	0.249942i
$791$		−	180.133i		−	0.227729i
$792$		0			0
$793$	−224.000			−0.282472
$794$	543.000	−	313.501i	0.683879	−	0.394838i
$795$		0			0
$796$	−145.000	+	251.147i	−0.182161	+	0.315512i
$797$	−273.000	−	157.617i	−0.342535	−	0.197762i	0.318858	−	0.947803i	$-0.396701\pi$
$797$	−273.000	−	157.617i	−0.342535	−	0.197762i	−0.661392	+	0.750040i	$0.730034\pi$
$798$		0			0
$799$	−378.000	−	654.715i	−0.473091	−	0.819418i
$800$			202.650i			0.253312i
$801$		0			0
$802$	−681.000			−0.849127
$803$	97.5000	−	56.2917i	0.121420	−	0.0701017i
$804$		0			0
$805$	−96.0000	+	166.277i	−0.119255	+	0.206555i
$806$	192.000	+	110.851i	0.238213	+	0.137533i
$807$		0			0
$808$	−195.000	−	337.750i	−0.241337	−	0.418007i
$809$			140.296i			0.173419i	0.996234	+	0.0867096i	$0.0276352\pi$
$809$			140.296i			0.173419i	−0.996234	+	0.0867096i	$0.972365\pi$
$810$		0			0
$811$	299.000			0.368681			0.184340	−	0.982862i	$-0.440985\pi$
$811$	299.000			0.368681			0.184340	+	0.982862i	$0.440985\pi$
$812$	−78.0000	+	45.0333i	−0.0960591	+	0.0554598i
$813$		0			0
$814$	−51.0000	+	88.3346i	−0.0626536	+	0.108519i
$815$	318.000	+	183.597i	0.390184	+	0.225273i
$816$		0			0
$817$	335.500	+	581.103i	0.410649	+	0.711264i
$818$			382.783i			0.467950i
$819$		0			0
$820$	42.0000			0.0512195
$821$	−525.000	+	303.109i	−0.639464	+	0.369195i	−0.784408	−	0.620245i	$-0.787033\pi$
$821$	−525.000	+	303.109i	−0.639464	+	0.369195i	0.144944	+	0.989440i	$0.453700\pi$
$822$		0			0
$823$	407.000	−	704.945i	0.494532	−	0.856555i	−0.505448	−	0.862857i	$-0.668673\pi$
$823$	407.000	−	704.945i	0.494532	−	0.856555i	0.999980	+	0.00630221i	$0.00200607\pi$
$824$	300.000	+	173.205i	0.364078	+	0.210200i
$825$		0			0
$826$	87.0000	+	150.688i	0.105327	+	0.182432i
$827$			1434.14i			1.73415i	0.498182	+	0.867073i	$0.334001\pi$
$827$			1434.14i			1.73415i	−0.498182	+	0.867073i	$0.665999\pi$
$828$		0			0
$829$	−718.000			−0.866104			−0.433052	−	0.901369i	$-0.642563\pi$
$829$	−718.000			−0.866104			−0.433052	+	0.901369i	$0.642563\pi$
$830$	−252.000	+	145.492i	−0.303614	+	0.175292i
$831$		0			0
$832$	−142.000	+	245.951i	−0.170673	+	0.295614i
$833$	−607.500	−	350.740i	−0.729292	−	0.421057i
$834$		0			0
$835$	330.000	+	571.577i	0.395210	+	0.684523i
$836$			19.0526i			0.0227901i
$837$		0			0
$838$	−1356.00			−1.61814
$839$	690.000	−	398.372i	0.822408	−	0.474817i	−0.0288384	−	0.999584i	$-0.509181\pi$
$839$	690.000	−	398.372i	0.822408	−	0.474817i	0.851246	+	0.524767i	$0.175847\pi$
$840$		0			0
$841$	593.500	−	1027.97i	0.705707	−	1.22232i
$842$	1023.00	+	590.629i	1.21496	+	0.701460i
$843$		0			0
$844$	47.0000	+	81.4064i	0.0556872	+	0.0964531i
$845$		−	530.008i		−	0.627228i
$846$		0			0
$847$	236.000			0.278630
$848$		0			0
$849$		0			0
$850$	−175.500	+	303.975i	−0.206471	+	0.357618i
$851$	−816.000	−	471.118i	−0.958872	−	0.553605i
$852$		0			0
$853$	−712.000	−	1233.22i	−0.834701	−	1.44574i	−0.894274	−	0.447521i	$-0.852307\pi$
$853$	−712.000	−	1233.22i	−0.834701	−	1.44574i	0.0595725	−	0.998224i	$-0.481026\pi$
$854$			193.990i			0.227154i
$855$		0			0
$856$	−1215.00			−1.41939
$857$	−606.000	+	349.874i	−0.707118	+	0.408255i	−0.809993	−	0.586440i	$-0.800529\pi$
$857$	−606.000	+	349.874i	−0.707118	+	0.408255i	0.102875	+	0.994694i	$0.467196\pi$
$858$		0			0
$859$	−155.500	+	269.334i	−0.181024	+	0.313544i	−0.942230	−	0.334968i	$-0.891275\pi$
$859$	−155.500	+	269.334i	−0.181024	+	0.313544i	0.761205	+	0.648511i	$0.224608\pi$
$860$	183.000	+	105.655i	0.212791	+	0.122855i
$861$		0			0
$862$	243.000	+	420.888i	0.281903	+	0.488270i
$863$			1028.84i			1.19216i	0.802923	+	0.596082i	$0.203277\pi$
$863$			1028.84i			1.19216i	−0.802923	+	0.596082i	$0.796723\pi$
$864$		0			0
$865$	804.000			0.929480
$866$	−442.500	+	255.477i	−0.510970	+	0.295009i
$867$		0			0
$868$	−32.0000	+	55.4256i	−0.0368664	+	0.0638544i
$869$	−57.0000	−	32.9090i	−0.0655926	−	0.0378699i
$870$		0			0
$871$	−62.0000	−	107.387i	−0.0711825	−	0.123292i
$872$		−	450.333i		−	0.516437i
$873$		0			0
$874$	528.000			0.604119
$875$	228.000	−	131.636i	0.260571	−	0.150441i
$876$		0			0
$877$	−52.0000	+	90.0666i	−0.0592930	+	0.102699i	−0.894148	−	0.447771i	$-0.852218\pi$
$877$	−52.0000	+	90.0666i	−0.0592930	+	0.102699i	0.834855	+	0.550470i	$0.185551\pi$
$878$	−1218.00	−	703.213i	−1.38724	−	0.800926i
$879$		0			0
$880$	−33.0000	−	57.1577i	−0.0375000	−	0.0649519i
$881$		−	62.3538i		−	0.0707762i	−0.999374	−	0.0353881i	$-0.988733\pi$
$881$		−	62.3538i		−	0.0707762i	0.999374	−	0.0353881i	$-0.0112667\pi$
$882$		0			0
$883$	119.000			0.134768			0.0673839	−	0.997727i	$-0.478535\pi$
$883$	119.000			0.134768			0.0673839	+	0.997727i	$0.478535\pi$
$884$	54.0000	−	31.1769i	0.0610860	−	0.0352680i
$885$		0			0
$886$	−79.5000	+	137.698i	−0.0897291	+	0.155415i
$887$	−1029.00	−	594.093i	−1.16009	−	0.669778i	−0.208765	−	0.977966i	$-0.566944\pi$
$887$	−1029.00	−	594.093i	−1.16009	−	0.669778i	−0.951326	+	0.308188i	$0.900278\pi$
$888$		0			0
$889$	16.0000	+	27.7128i	0.0179978	+	0.0311730i
$890$			748.246i			0.840726i
$891$		0			0
$892$	−52.0000			−0.0582960
$893$	462.000	−	266.736i	0.517357	−	0.298696i
$894$		0			0
$895$	−108.000	+	187.061i	−0.120670	+	0.209007i
$896$	105.000	+	60.6218i	0.117188	+	0.0676582i
$897$		0			0
$898$	553.500	+	958.690i	0.616370	+	1.06758i
$899$		−	1441.07i		−	1.60297i
$900$		0			0
$901$		0			0
$902$	31.5000	−	18.1865i	0.0349224	−	0.0201625i
$903$		0			0
$904$	−390.000	+	675.500i	−0.431416	+	0.747234i
$905$	696.000	+	401.836i	0.769061	+	0.444017i
$906$		0			0
$907$	−347.500	−	601.888i	−0.383131	−	0.663603i	0.608377	−	0.793648i	$-0.291821\pi$
$907$	−347.500	−	601.888i	−0.383131	−	0.663603i	−0.991508	+	0.130046i	$0.958488\pi$
$908$			188.794i			0.207922i
$909$		0			0
$910$	48.0000			0.0527473
$911$	1500.00	−	866.025i	1.64654	−	0.950632i	0.668110	−	0.744062i	$-0.267103\pi$
$911$	1500.00	−	866.025i	1.64654	−	0.950632i	0.978432	−	0.206569i	$-0.0662299\pi$
$912$		0			0
$913$	42.0000	−	72.7461i	0.0460022	−	0.0796781i
$914$	−97.5000	−	56.2917i	−0.106674	−	0.0615882i
$915$		0			0
$916$	−133.000	−	230.363i	−0.145197	−	0.251488i
$917$			318.697i			0.347543i
$918$		0			0
$919$	56.0000			0.0609358			0.0304679	−	0.999536i	$-0.490300\pi$
$919$	56.0000			0.0609358			0.0304679	+	0.999536i	$0.490300\pi$
$920$	720.000	−	415.692i	0.782609	−	0.451839i
$921$		0			0
$922$	690.000	−	1195.12i	0.748373	−	1.29622i
$923$	108.000	+	62.3538i	0.117010	+	0.0675556i
$924$		0			0
$925$	221.000	+	382.783i	0.238919	+	0.413820i
$926$			1271.33i			1.37292i
$927$		0			0
$928$	702.000			0.756466
$929$	690.000	−	398.372i	0.742734	−	0.428818i	−0.0803285	−	0.996768i	$-0.525597\pi$
$929$	690.000	−	398.372i	0.742734	−	0.428818i	0.823063	+	0.567951i	$0.192264\pi$
$930$		0			0
$931$	247.500	−	428.683i	0.265843	−	0.460454i
$932$	175.500	+	101.325i	0.188305	+	0.108718i
$933$		0			0
$934$	175.500	+	303.975i	0.187901	+	0.325455i
$935$			93.5307i			0.100033i
$936$		0			0
$937$	470.000			0.501601			0.250800	−	0.968039i	$-0.419306\pi$
$937$	470.000			0.501601			0.250800	+	0.968039i	$0.419306\pi$
$938$	−93.0000	+	53.6936i	−0.0991471	+	0.0572426i
$939$		0			0
$940$	84.0000	−	145.492i	0.0893617	−	0.154779i
$941$	348.000	+	200.918i	0.369819	+	0.213515i	0.673380	−	0.739297i	$-0.264842\pi$
$941$	348.000	+	200.918i	0.369819	+	0.213515i	−0.303560	+	0.952812i	$0.598175\pi$
$942$		0			0
$943$	168.000	+	290.985i	0.178155	+	0.308573i
$944$		−	552.524i		−	0.585301i
$945$		0			0
$946$	183.000			0.193446
$947$	1.50000	−	0.866025i	0.00158395	−	0.000914494i	−0.499208	−	0.866482i	$-0.666376\pi$
$947$	1.50000	−	0.866025i	0.00158395	−	0.000914494i	0.500792	+	0.865568i	$0.333042\pi$
$948$		0			0
$949$	130.000	−	225.167i	0.136986	−	0.237267i
$950$	−214.500	−	123.842i	−0.225789	−	0.130360i
$951$		0			0
$952$	−135.000	−	233.827i	−0.141807	−	0.245616i
$953$		−	826.188i		−	0.866934i	−0.901169	−	0.433467i	$-0.857290\pi$
$953$		−	826.188i		−	0.866934i	0.901169	−	0.433467i	$-0.142710\pi$
$954$		0			0
$955$	804.000			0.841885
$956$	−348.000	+	200.918i	−0.364017	+	0.210165i
$957$		0			0
$958$	−525.000	+	909.327i	−0.548017	+	0.949193i
$959$	−327.000	−	188.794i	−0.340980	−	0.196865i
$960$		0			0
$961$	−31.5000	−	54.5596i	−0.0327784	−	0.0567738i
$962$			235.559i			0.244864i
$963$		0			0
$964$	119.000			0.123444
$965$	−795.000	+	458.993i	−0.823834	+	0.475641i
$966$		0			0
$967$	−601.000	+	1040.96i	−0.621510	+	1.07649i	0.367695	+	0.929946i	$0.380147\pi$
$967$	−601.000	+	1040.96i	−0.621510	+	1.07649i	−0.989205	+	0.146540i	$0.953186\pi$
$968$	−885.000	−	510.955i	−0.914256	−	0.527846i
$969$		0			0
$970$	−345.000	−	597.558i	−0.355670	−	0.616039i
$971$			187.061i			0.192648i	0.995350	+	0.0963241i	$0.0307085\pi$
$971$			187.061i			0.192648i	−0.995350	+	0.0963241i	$0.969291\pi$
$972$		0			0
$973$	10.0000			0.0102775
$974$	−159.000	+	91.7987i	−0.163244	+	0.0942492i
$975$		0			0
$976$	308.000	−	533.472i	0.315574	−	0.546590i
$977$	361.500	+	208.712i	0.370010	+	0.213626i	0.673463	−	0.739221i	$-0.264806\pi$
$977$	361.500	+	208.712i	0.370010	+	0.213626i	−0.303453	+	0.952847i	$0.598139\pi$
$978$		0			0
$979$	−108.000	−	187.061i	−0.110317	−	0.191074i
$980$		−	155.885i		−	0.159066i
$981$		0			0
$982$	399.000			0.406314
$983$	−1011.00	+	583.701i	−1.02848	+	0.593796i	−0.916550	−	0.399920i	$-0.869038\pi$
$983$	−1011.00	+	583.701i	−1.02848	+	0.593796i	−0.111934	+	0.993716i	$0.535705\pi$
$984$		0			0
$985$	−216.000	+	374.123i	−0.219289	+	0.379820i
$986$	1053.00	+	607.950i	1.06795	+	0.616582i
$987$		0			0
$988$	22.0000	+	38.1051i	0.0222672	+	0.0385679i
$989$			1690.48i			1.70928i
$990$		0			0
$991$	−1420.00			−1.43290			−0.716448	−	0.697640i	$-0.754233\pi$
$991$	−1420.00			−1.43290			−0.716448	+	0.697640i	$0.754233\pi$
$992$	432.000	−	249.415i	0.435484	−	0.251427i
$993$		0			0
$994$	54.0000	−	93.5307i	0.0543260	−	0.0940953i
$995$	−870.000	−	502.295i	−0.874372	−	0.504819i
$996$		0			0
$997$	−262.000	−	453.797i	−0.262788	−	0.455163i	0.704193	−	0.710008i	$-0.251309\pi$
$997$	−262.000	−	453.797i	−0.262788	−	0.455163i	−0.966982	+	0.254845i	$0.917975\pi$
$998$		−	1363.12i		−	1.36586i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.3.d.a.17.1		2
3.2	odd	2		9.3.d.a.5.1	yes	2
4.3	odd	2		432.3.q.a.17.1		2
5.2	odd	4		675.3.i.a.449.2		4
5.3	odd	4		675.3.i.a.449.1		4
5.4	even	2		675.3.j.a.476.1		2
8.3	odd	2		1728.3.q.b.449.1		2
8.5	even	2		1728.3.q.a.449.1		2
9.2	odd	6	inner	27.3.d.a.8.1		2
9.4	even	3		81.3.b.a.80.2		2
9.5	odd	6		81.3.b.a.80.1		2
9.7	even	3		9.3.d.a.2.1	✓	2
12.11	even	2		144.3.q.a.113.1		2
15.2	even	4		225.3.i.a.149.1		4
15.8	even	4		225.3.i.a.149.2		4
15.14	odd	2		225.3.j.a.176.1		2
21.2	odd	6		441.3.n.b.410.1		2
21.5	even	6		441.3.n.a.410.1		2
21.11	odd	6		441.3.j.a.275.1		2
21.17	even	6		441.3.j.b.275.1		2
21.20	even	2		441.3.r.a.50.1		2
24.5	odd	2		576.3.q.b.257.1		2
24.11	even	2		576.3.q.a.257.1		2
36.7	odd	6		144.3.q.a.65.1		2
36.11	even	6		432.3.q.a.305.1		2
36.23	even	6		1296.3.e.a.161.1		2
36.31	odd	6		1296.3.e.a.161.2		2
45.2	even	12		675.3.i.a.224.1		4
45.7	odd	12		225.3.i.a.74.2		4
45.29	odd	6		675.3.j.a.251.1		2
45.34	even	6		225.3.j.a.101.1		2
45.38	even	12		675.3.i.a.224.2		4
45.43	odd	12		225.3.i.a.74.1		4
63.16	even	3		441.3.j.a.263.1		2
63.25	even	3		441.3.n.b.128.1		2
63.34	odd	6		441.3.r.a.344.1		2
63.52	odd	6		441.3.n.a.128.1		2
63.61	odd	6		441.3.j.b.263.1		2
72.11	even	6		1728.3.q.b.1601.1		2
72.29	odd	6		1728.3.q.a.1601.1		2
72.43	odd	6		576.3.q.a.65.1		2
72.61	even	6		576.3.q.b.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.3.d.a.2.1	✓	2	9.7	even	3
9.3.d.a.5.1	yes	2	3.2	odd	2
27.3.d.a.8.1		2	9.2	odd	6	inner
27.3.d.a.17.1		2	1.1	even	1	trivial
81.3.b.a.80.1		2	9.5	odd	6
81.3.b.a.80.2		2	9.4	even	3
144.3.q.a.65.1		2	36.7	odd	6
144.3.q.a.113.1		2	12.11	even	2
225.3.i.a.74.1		4	45.43	odd	12
225.3.i.a.74.2		4	45.7	odd	12
225.3.i.a.149.1		4	15.2	even	4
225.3.i.a.149.2		4	15.8	even	4
225.3.j.a.101.1		2	45.34	even	6
225.3.j.a.176.1		2	15.14	odd	2
432.3.q.a.17.1		2	4.3	odd	2
432.3.q.a.305.1		2	36.11	even	6
441.3.j.a.263.1		2	63.16	even	3
441.3.j.a.275.1		2	21.11	odd	6
441.3.j.b.263.1		2	63.61	odd	6
441.3.j.b.275.1		2	21.17	even	6
441.3.n.a.128.1		2	63.52	odd	6
441.3.n.a.410.1		2	21.5	even	6
441.3.n.b.128.1		2	63.25	even	3
441.3.n.b.410.1		2	21.2	odd	6
441.3.r.a.50.1		2	21.20	even	2
441.3.r.a.344.1		2	63.34	odd	6
576.3.q.a.65.1		2	72.43	odd	6
576.3.q.a.257.1		2	24.11	even	2
576.3.q.b.65.1		2	72.61	even	6
576.3.q.b.257.1		2	24.5	odd	2
675.3.i.a.224.1		4	45.2	even	12
675.3.i.a.224.2		4	45.38	even	12
675.3.i.a.449.1		4	5.3	odd	4
675.3.i.a.449.2		4	5.2	odd	4
675.3.j.a.251.1		2	45.29	odd	6
675.3.j.a.476.1		2	5.4	even	2
1296.3.e.a.161.1		2	36.23	even	6
1296.3.e.a.161.2		2	36.31	odd	6
1728.3.q.a.449.1		2	8.5	even	2
1728.3.q.a.1601.1		2	72.29	odd	6
1728.3.q.b.449.1		2	8.3	odd	2
1728.3.q.b.1601.1		2	72.11	even	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.00000 - 1.73205i) q^{7} +8.66025i q^{8} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.00000 - 1.73205i) q^{7} +8.66025i q^{8} -6.00000 q^{10} +(1.50000 - 0.866025i) q^{11} +(2.00000 - 3.46410i) q^{13} +(-3.00000 - 1.73205i) q^{14} +(5.50000 + 9.52628i) q^{16} -15.5885i q^{17} +11.0000 q^{19} +(3.00000 - 1.73205i) q^{20} +(1.50000 - 2.59808i) q^{22} +(24.0000 + 13.8564i) q^{23} +(-6.50000 - 11.2583i) q^{25} -6.92820i q^{26} +2.00000 q^{28} +(-39.0000 + 22.5167i) q^{29} +(-16.0000 + 27.7128i) q^{31} +(-13.5000 - 7.79423i) q^{32} +(-13.5000 - 23.3827i) q^{34} +6.92820i q^{35} -34.0000 q^{37} +(16.5000 - 9.52628i) q^{38} +(15.0000 - 25.9808i) q^{40} +(10.5000 + 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +1.73205i q^{44} +48.0000 q^{46} +(42.0000 - 24.2487i) q^{47} +(22.5000 - 38.9711i) q^{49} +(-19.5000 - 11.2583i) q^{50} +(2.00000 + 3.46410i) q^{52} -6.00000 q^{55} +(15.0000 - 8.66025i) q^{56} +(-39.0000 + 67.5500i) q^{58} +(-43.5000 - 25.1147i) q^{59} +(-28.0000 - 48.4974i) q^{61} +55.4256i q^{62} -71.0000 q^{64} +(-12.0000 + 6.92820i) q^{65} +(15.5000 - 26.8468i) q^{67} +(13.5000 + 7.79423i) q^{68} +(6.00000 + 10.3923i) q^{70} +31.1769i q^{71} +65.0000 q^{73} +(-51.0000 + 29.4449i) q^{74} +(-5.50000 + 9.52628i) q^{76} +(-3.00000 - 1.73205i) q^{77} +(-19.0000 - 32.9090i) q^{79} -38.1051i q^{80} +21.0000 q^{82} +(42.0000 - 24.2487i) q^{83} +(-27.0000 + 46.7654i) q^{85} +(91.5000 + 52.8275i) q^{86} +(7.50000 + 12.9904i) q^{88} -124.708i q^{89} -8.00000 q^{91} +(-24.0000 + 13.8564i) q^{92} +(42.0000 - 72.7461i) q^{94} +(-33.0000 - 19.0526i) q^{95} +(57.5000 + 99.5929i) q^{97} -77.9423i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} - q^{4} - 6 q^{5} - 2 q^{7}+O(q^{10}) \) 2 * q + 3 * q^2 - q^4 - 6 * q^5 - 2 * q^7	\( 2 q + 3 q^{2} - q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{10} + 3 q^{11} + 4 q^{13} - 6 q^{14} + 11 q^{16} + 22 q^{19} + 6 q^{20} + 3 q^{22} + 48 q^{23} - 13 q^{25} + 4 q^{28} - 78 q^{29} - 32 q^{31} - 27 q^{32} - 27 q^{34} - 68 q^{37} + 33 q^{38} + 30 q^{40} + 21 q^{41} + 61 q^{43} + 96 q^{46} + 84 q^{47} + 45 q^{49} - 39 q^{50} + 4 q^{52} - 12 q^{55} + 30 q^{56} - 78 q^{58} - 87 q^{59} - 56 q^{61} - 142 q^{64} - 24 q^{65} + 31 q^{67} + 27 q^{68} + 12 q^{70} + 130 q^{73} - 102 q^{74} - 11 q^{76} - 6 q^{77} - 38 q^{79} + 42 q^{82} + 84 q^{83} - 54 q^{85} + 183 q^{86} + 15 q^{88} - 16 q^{91} - 48 q^{92} + 84 q^{94} - 66 q^{95} + 115 q^{97}+O(q^{100}) \) 2 * q + 3 * q^2 - q^4 - 6 * q^5 - 2 * q^7 - 12 * q^10 + 3 * q^11 + 4 * q^13 - 6 * q^14 + 11 * q^16 + 22 * q^19 + 6 * q^20 + 3 * q^22 + 48 * q^23 - 13 * q^25 + 4 * q^28 - 78 * q^29 - 32 * q^31 - 27 * q^32 - 27 * q^34 - 68 * q^37 + 33 * q^38 + 30 * q^40 + 21 * q^41 + 61 * q^43 + 96 * q^46 + 84 * q^47 + 45 * q^49 - 39 * q^50 + 4 * q^52 - 12 * q^55 + 30 * q^56 - 78 * q^58 - 87 * q^59 - 56 * q^61 - 142 * q^64 - 24 * q^65 + 31 * q^67 + 27 * q^68 + 12 * q^70 + 130 * q^73 - 102 * q^74 - 11 * q^76 - 6 * q^77 - 38 * q^79 + 42 * q^82 + 84 * q^83 - 54 * q^85 + 183 * q^86 + 15 * q^88 - 16 * q^91 - 48 * q^92 + 84 * q^94 - 66 * q^95 + 115 * q^97

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