LMFDB - Embedded newform 189.2.p.c.26.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(26,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$-1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	189.26
Dual form			189.2.p.c.80.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.93649 - 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +(-2.00000 + 1.73205i) q^{7} -2.23607i q^{8} +(-3.87298 + 2.23607i) q^{11} +1.73205i q^{13} +(5.80948 - 1.11803i) q^{14} +(0.500000 - 0.866025i) q^{16} +(3.87298 + 6.70820i) q^{17} +(-3.00000 - 1.73205i) q^{19} +10.0000 q^{22} +(3.87298 + 2.23607i) q^{23} +(2.50000 + 4.33013i) q^{25} +(1.93649 - 3.35410i) q^{26} +(-7.50000 - 2.59808i) q^{28} -4.47214i q^{29} +(-1.50000 + 0.866025i) q^{31} +(-5.80948 + 3.35410i) q^{32} -17.3205i q^{34} +(-2.50000 + 4.33013i) q^{37} +(3.87298 + 6.70820i) q^{38} -7.74597 q^{41} -7.00000 q^{43} +(-11.6190 - 6.70820i) q^{44} +(-5.00000 - 8.66025i) q^{46} +(3.87298 - 6.70820i) q^{47} +(1.00000 - 6.92820i) q^{49} -11.1803i q^{50} +(-4.50000 + 2.59808i) q^{52} +(-3.87298 + 2.23607i) q^{53} +(3.87298 + 4.47214i) q^{56} +(-5.00000 + 8.66025i) q^{58} +(-3.87298 - 6.70820i) q^{59} +(7.50000 + 4.33013i) q^{61} +3.87298 q^{62} +13.0000 q^{64} +(0.500000 + 0.866025i) q^{67} +(-11.6190 + 20.1246i) q^{68} +8.94427i q^{71} +(6.00000 - 3.46410i) q^{73} +(9.68246 - 5.59017i) q^{74} -10.3923i q^{76} +(3.87298 - 11.1803i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(15.0000 + 8.66025i) q^{82} +7.74597 q^{83} +(13.5554 + 7.82624i) q^{86} +(5.00000 + 8.66025i) q^{88} +(7.74597 - 13.4164i) q^{89} +(-3.00000 - 3.46410i) q^{91} +13.4164i q^{92} +(-15.0000 + 8.66025i) q^{94} -1.73205i q^{97} +(-9.68246 + 12.2984i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{4} - 8 q^{7} + 2 q^{16} - 12 q^{19} + 40 q^{22} + 10 q^{25} - 30 q^{28} - 6 q^{31} - 10 q^{37} - 28 q^{43} - 20 q^{46} + 4 q^{49} - 18 q^{52} - 20 q^{58} + 30 q^{61} + 52 q^{64} + 2 q^{67} + 24 q^{73}+ \cdots - 60 q^{94}+O(q^{100}) $ 4 * q + 6 * q^4 - 8 * q^7 + 2 * q^16 - 12 * q^19 + 40 * q^22 + 10 * q^25 - 30 * q^28 - 6 * q^31 - 10 * q^37 - 28 * q^43 - 20 * q^46 + 4 * q^49 - 18 * q^52 - 20 * q^58 + 30 * q^61 + 52 * q^64 + 2 * q^67 + 24 * q^73 - 22 * q^79 + 60 * q^82 + 20 * q^88 - 12 * q^91 - 60 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.93649	−	1.11803i	−1.36931	−	0.790569i	−0.378467	−	0.925615i	$-0.623549\pi$
$2$	−1.93649	−	1.11803i	−1.36931	−	0.790569i	−0.990839	+	0.135045i	$0.956882\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	+	2.59808i	0.750000	+	1.29904i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$		−	2.23607i		−	0.790569i
$9$		0			0
$10$		0			0
$11$	−3.87298	+	2.23607i	−1.16775	+	0.674200i	−0.953149	−	0.302502i	$-0.902178\pi$
$11$	−3.87298	+	2.23607i	−1.16775	+	0.674200i	−0.214600	+	0.976702i	$0.568845\pi$
$12$		0			0
$13$			1.73205i			0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$13$			1.73205i			0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	5.80948	−	1.11803i	1.55265	−	0.298807i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.87298	+	6.70820i	0.939336	+	1.62698i	0.766712	+	0.641991i	$0.221891\pi$
$17$	3.87298	+	6.70820i	0.939336	+	1.62698i	0.172624	+	0.984988i	$0.444775\pi$
$18$		0			0
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$		0			0
$22$	10.0000			2.13201
$23$	3.87298	+	2.23607i	0.807573	+	0.466252i	0.846112	−	0.533005i	$-0.178937\pi$
$23$	3.87298	+	2.23607i	0.807573	+	0.466252i	−0.0385394	+	0.999257i	$0.512271\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	1.93649	−	3.35410i	0.379777	−	0.657794i
$27$		0			0
$28$	−7.50000	−	2.59808i	−1.41737	−	0.490990i
$29$		−	4.47214i		−	0.830455i	−0.909718	−	0.415227i	$-0.863702\pi$
$29$		−	4.47214i		−	0.830455i	0.909718	−	0.415227i	$-0.136298\pi$
$30$		0			0
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	0.359211	+	0.933257i	$0.383046\pi$
$32$	−5.80948	+	3.35410i	−1.02698	+	0.592927i
$33$		0			0
$34$		−	17.3205i		−	2.97044i
$35$		0			0
$36$		0			0
$37$	−2.50000	+	4.33013i	−0.410997	+	0.711868i	−0.994999	−	0.0998840i	$-0.968153\pi$
$37$	−2.50000	+	4.33013i	−0.410997	+	0.711868i	0.584002	+	0.811752i	$0.301486\pi$
$38$	3.87298	+	6.70820i	0.628281	+	1.08821i
$39$		0			0
$40$		0			0
$41$	−7.74597			−1.20972			−0.604858	−	0.796333i	$-0.706770\pi$
$41$	−7.74597			−1.20972			−0.604858	+	0.796333i	$0.706770\pi$
$42$		0			0
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$	−11.6190	−	6.70820i	−1.75162	−	1.01130i
$45$		0			0
$46$	−5.00000	−	8.66025i	−0.737210	−	1.27688i
$47$	3.87298	−	6.70820i	0.564933	−	0.978492i	−0.432123	−	0.901815i	$-0.642235\pi$
$47$	3.87298	−	6.70820i	0.564933	−	0.978492i	0.997056	−	0.0766776i	$-0.0244312\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		−	11.1803i		−	1.58114i
$51$		0			0
$52$	−4.50000	+	2.59808i	−0.624038	+	0.360288i
$53$	−3.87298	+	2.23607i	−0.531995	+	0.307148i	−0.741829	−	0.670590i	$-0.766041\pi$
$53$	−3.87298	+	2.23607i	−0.531995	+	0.307148i	0.209833	+	0.977737i	$0.432708\pi$
$54$		0			0
$55$		0			0
$56$	3.87298	+	4.47214i	0.517549	+	0.597614i
$57$		0			0
$58$	−5.00000	+	8.66025i	−0.656532	+	1.13715i
$59$	−3.87298	−	6.70820i	−0.504219	−	0.873334i	−0.999988	−	0.00487911i	$-0.998447\pi$
$59$	−3.87298	−	6.70820i	−0.504219	−	0.873334i	0.495769	−	0.868455i	$-0.334886\pi$
$60$		0			0
$61$	7.50000	+	4.33013i	0.960277	+	0.554416i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	7.50000	+	4.33013i	0.960277	+	0.554416i	0.0640184	+	0.997949i	$0.479608\pi$
$62$	3.87298			0.491869
$63$		0			0
$64$	13.0000			1.62500
$65$		0			0
$66$		0			0
$67$	0.500000	+	0.866025i	0.0610847	+	0.105802i	0.894951	−	0.446165i	$-0.147211\pi$
$67$	0.500000	+	0.866025i	0.0610847	+	0.105802i	−0.833866	+	0.551967i	$0.813877\pi$
$68$	−11.6190	+	20.1246i	−1.40900	+	2.44047i
$69$		0			0
$70$		0			0
$71$			8.94427i			1.06149i	0.847532	+	0.530745i	$0.178088\pi$
$71$			8.94427i			1.06149i	−0.847532	+	0.530745i	$0.821912\pi$
$72$		0			0
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	−0.105937	−	0.994373i	$-0.533784\pi$
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	0.808184	+	0.588930i	$0.200451\pi$
$74$	9.68246	−	5.59017i	1.12556	−	0.649844i
$75$		0			0
$76$		−	10.3923i		−	1.19208i
$77$	3.87298	−	11.1803i	0.441367	−	1.27412i
$78$		0			0
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	0.370907	+	0.928670i	$0.379047\pi$
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	−0.989705	+	0.143120i	$0.954286\pi$
$80$		0			0
$81$		0			0
$82$	15.0000	+	8.66025i	1.65647	+	0.956365i
$83$	7.74597			0.850230			0.425115	−	0.905139i	$-0.360234\pi$
$83$	7.74597			0.850230			0.425115	+	0.905139i	$0.360234\pi$
$84$		0			0
$85$		0			0
$86$	13.5554	+	7.82624i	1.46172	+	0.843925i
$87$		0			0
$88$	5.00000	+	8.66025i	0.533002	+	0.923186i
$89$	7.74597	−	13.4164i	0.821071	−	1.42214i	−0.0838147	−	0.996481i	$-0.526710\pi$
$89$	7.74597	−	13.4164i	0.821071	−	1.42214i	0.904886	−	0.425655i	$-0.139956\pi$
$90$		0			0
$91$	−3.00000	−	3.46410i	−0.314485	−	0.363137i
$92$			13.4164i			1.39876i
$93$		0			0
$94$	−15.0000	+	8.66025i	−1.54713	+	0.893237i
$95$		0			0
$96$		0			0
$97$		−	1.73205i		−	0.175863i	−0.996127	−	0.0879316i	$-0.971974\pi$
$97$		−	1.73205i		−	0.175863i	0.996127	−	0.0879316i	$-0.0280257\pi$
$98$	−9.68246	+	12.2984i	−0.978076	+	1.24232i
$99$		0			0
$100$	−7.50000	+	12.9904i	−0.750000	+	1.29904i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−4.50000	−	2.59808i	−0.443398	−	0.255996i	0.261640	−	0.965166i	$-0.415737\pi$
$103$	−4.50000	−	2.59808i	−0.443398	−	0.255996i	−0.705038	+	0.709170i	$0.749070\pi$
$104$	3.87298			0.379777
$105$		0			0
$106$	10.0000			0.971286
$107$	3.87298	+	2.23607i	0.374415	+	0.216169i	0.675386	−	0.737465i	$-0.263977\pi$
$107$	3.87298	+	2.23607i	0.374415	+	0.216169i	−0.300970	+	0.953634i	$0.597310\pi$
$108$		0			0
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	0.888977	−	0.457951i	$-0.151417\pi$
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	−0.841086	+	0.540901i	$0.818083\pi$
$110$		0			0
$111$		0			0
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$			8.94427i			0.841406i	0.907198	+	0.420703i	$0.138217\pi$
$113$			8.94427i			0.841406i	−0.907198	+	0.420703i	$0.861783\pi$
$114$		0			0
$115$		0			0
$116$	11.6190	−	6.70820i	1.07879	−	0.622841i
$117$		0			0
$118$			17.3205i			1.59448i
$119$	−19.3649	−	6.70820i	−1.77518	−	0.614940i
$120$		0			0
$121$	4.50000	−	7.79423i	0.409091	−	0.708566i
$122$	−9.68246	−	16.7705i	−0.876609	−	1.51833i
$123$		0			0
$124$	−4.50000	−	2.59808i	−0.404112	−	0.233314i
$125$		0			0
$126$		0			0
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	−13.5554	−	7.82624i	−1.19814	−	0.691748i
$129$		0			0
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$	9.00000	−	1.73205i	0.780399	−	0.150188i
$134$		−	2.23607i		−	0.193167i
$135$		0			0
$136$	15.0000	−	8.66025i	1.28624	−	0.742611i
$137$	−3.87298	+	2.23607i	−0.330891	+	0.191040i	−0.656237	−	0.754555i	$-0.727853\pi$
$137$	−3.87298	+	2.23607i	−0.330891	+	0.191040i	0.325345	+	0.945595i	$0.394519\pi$
$138$		0			0
$139$		−	8.66025i		−	0.734553i	−0.930112	−	0.367277i	$-0.880290\pi$
$139$		−	8.66025i		−	0.734553i	0.930112	−	0.367277i	$-0.119710\pi$
$140$		0			0
$141$		0			0
$142$	10.0000	−	17.3205i	0.839181	−	1.45350i
$143$	−3.87298	−	6.70820i	−0.323875	−	0.560968i
$144$		0			0
$145$		0			0
$146$	−15.4919			−1.28212
$147$		0			0
$148$	−15.0000			−1.23299
$149$	15.4919	+	8.94427i	1.26915	+	0.732743i	0.974827	−	0.222963i	$-0.0715729\pi$
$149$	15.4919	+	8.94427i	1.26915	+	0.732743i	0.294322	+	0.955706i	$0.404906\pi$
$150$		0			0
$151$	6.50000	+	11.2583i	0.528962	+	0.916190i	0.999430	+	0.0337724i	$0.0107521\pi$
$151$	6.50000	+	11.2583i	0.528962	+	0.916190i	−0.470467	+	0.882418i	$0.655915\pi$
$152$	−3.87298	+	6.70820i	−0.314140	+	0.544107i
$153$		0			0
$154$	−20.0000	+	17.3205i	−1.61165	+	1.39573i
$155$		0			0
$156$		0			0
$157$	12.0000	−	6.92820i	0.957704	−	0.552931i	0.0622385	−	0.998061i	$-0.480176\pi$
$157$	12.0000	−	6.92820i	0.957704	−	0.552931i	0.895466	+	0.445130i	$0.146843\pi$
$158$	21.3014	−	12.2984i	1.69465	−	0.978406i
$159$		0			0
$160$		0			0
$161$	−11.6190	+	2.23607i	−0.915702	+	0.176227i
$162$		0			0
$163$	6.50000	−	11.2583i	0.509119	−	0.881820i	−0.490825	−	0.871258i	$-0.663305\pi$
$163$	6.50000	−	11.2583i	0.509119	−	0.881820i	0.999944	−	0.0105623i	$-0.00336213\pi$
$164$	−11.6190	−	20.1246i	−0.907288	−	1.57147i
$165$		0			0
$166$	−15.0000	−	8.66025i	−1.16423	−	0.672166i
$167$	−7.74597			−0.599401			−0.299700	−	0.954033i	$-0.596887\pi$
$167$	−7.74597			−0.599401			−0.299700	+	0.954033i	$0.596887\pi$
$168$		0			0
$169$	10.0000			0.769231
$170$		0			0
$171$		0			0
$172$	−10.5000	−	18.1865i	−0.800617	−	1.38671i
$173$	−7.74597	+	13.4164i	−0.588915	+	1.02003i	0.405460	+	0.914113i	$0.367111\pi$
$173$	−7.74597	+	13.4164i	−0.588915	+	1.02003i	−0.994375	+	0.105918i	$0.966222\pi$
$174$		0			0
$175$	−12.5000	−	4.33013i	−0.944911	−	0.327327i
$176$			4.47214i			0.337100i
$177$		0			0
$178$	−30.0000	+	17.3205i	−2.24860	+	1.29823i
$179$	7.74597	−	4.47214i	0.578961	−	0.334263i	−0.181760	−	0.983343i	$-0.558179\pi$
$179$	7.74597	−	4.47214i	0.578961	−	0.334263i	0.760720	+	0.649080i	$0.224846\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	1.93649	+	10.0623i	0.143542	+	0.745868i
$183$		0			0
$184$	5.00000	−	8.66025i	0.368605	−	0.638442i
$185$		0			0
$186$		0			0
$187$	−30.0000	−	17.3205i	−2.19382	−	1.26660i
$188$	23.2379			1.69480
$189$		0			0
$190$		0			0
$191$	15.4919	+	8.94427i	1.12096	+	0.647185i	0.941645	−	0.336607i	$-0.109280\pi$
$191$	15.4919	+	8.94427i	1.12096	+	0.647185i	0.179312	+	0.983792i	$0.442613\pi$
$192$		0			0
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$	−1.93649	+	3.35410i	−0.139032	+	0.240810i
$195$		0			0
$196$	19.5000	−	7.79423i	1.39286	−	0.556731i
$197$			8.94427i			0.637253i	0.947880	+	0.318626i	$0.103222\pi$
$197$			8.94427i			0.637253i	−0.947880	+	0.318626i	$0.896778\pi$
$198$		0			0
$199$	19.5000	−	11.2583i	1.38232	−	0.798082i	0.389885	−	0.920864i	$-0.372515\pi$
$199$	19.5000	−	11.2583i	1.38232	−	0.798082i	0.992434	+	0.122782i	$0.0391815\pi$
$200$	9.68246	−	5.59017i	0.684653	−	0.395285i
$201$		0			0
$202$		0			0
$203$	7.74597	+	8.94427i	0.543660	+	0.627765i
$204$		0			0
$205$		0			0
$206$	5.80948	+	10.0623i	0.404765	+	0.701074i
$207$		0			0
$208$	1.50000	+	0.866025i	0.104006	+	0.0600481i
$209$	15.4919			1.07160
$210$		0			0
$211$	−19.0000			−1.30801			−0.654007	−	0.756489i	$-0.726913\pi$
$211$	−19.0000			−1.30801			−0.654007	+	0.756489i	$0.726913\pi$
$212$	−11.6190	−	6.70820i	−0.797993	−	0.460721i
$213$		0			0
$214$	−5.00000	−	8.66025i	−0.341793	−	0.592003i
$215$		0			0
$216$		0			0
$217$	1.50000	−	4.33013i	0.101827	−	0.293948i
$218$		−	2.23607i		−	0.151446i
$219$		0			0
$220$		0			0
$221$	−11.6190	+	6.70820i	−0.781575	+	0.451243i
$222$		0			0
$223$			24.2487i			1.62381i	0.583787	+	0.811907i	$0.301570\pi$
$223$			24.2487i			1.62381i	−0.583787	+	0.811907i	$0.698430\pi$
$224$	5.80948	−	16.7705i	0.388162	−	1.12053i
$225$		0			0
$226$	10.0000	−	17.3205i	0.665190	−	1.15214i
$227$	11.6190	+	20.1246i	0.771177	+	1.33572i	0.936918	+	0.349548i	$0.113665\pi$
$227$	11.6190	+	20.1246i	0.771177	+	1.33572i	−0.165742	+	0.986169i	$0.553002\pi$
$228$		0			0
$229$	22.5000	+	12.9904i	1.48684	+	0.858429i	0.999888	−	0.0149989i	$-0.00477447\pi$
$229$	22.5000	+	12.9904i	1.48684	+	0.858429i	0.486954	+	0.873427i	$0.338108\pi$
$230$		0			0
$231$		0			0
$232$	−10.0000			−0.656532
$233$	−7.74597	−	4.47214i	−0.507455	−	0.292979i	0.224332	−	0.974513i	$-0.427980\pi$
$233$	−7.74597	−	4.47214i	−0.507455	−	0.292979i	−0.731787	+	0.681533i	$0.761313\pi$
$234$		0			0
$235$		0			0
$236$	11.6190	−	20.1246i	0.756329	−	1.31000i
$237$		0			0
$238$	30.0000	+	34.6410i	1.94461	+	2.24544i
$239$			8.94427i			0.578557i	0.957245	+	0.289278i	$0.0934153\pi$
$239$			8.94427i			0.578557i	−0.957245	+	0.289278i	$0.906585\pi$
$240$		0			0
$241$	13.5000	−	7.79423i	0.869611	−	0.502070i	0.00239235	−	0.999997i	$-0.499238\pi$
$241$	13.5000	−	7.79423i	0.869611	−	0.502070i	0.867219	+	0.497927i	$0.165905\pi$
$242$	−17.4284	+	10.0623i	−1.12034	+	0.646830i
$243$		0			0
$244$			25.9808i			1.66325i
$245$		0			0
$246$		0			0
$247$	3.00000	−	5.19615i	0.190885	−	0.330623i
$248$	1.93649	+	3.35410i	0.122967	+	0.212986i
$249$		0			0
$250$		0			0
$251$	−23.2379			−1.46676			−0.733382	−	0.679817i	$-0.762059\pi$
$251$	−23.2379			−1.46676			−0.733382	+	0.679817i	$0.762059\pi$
$252$		0			0
$253$	−20.0000			−1.25739
$254$	1.93649	+	1.11803i	0.121506	+	0.0701517i
$255$		0			0
$256$	4.50000	+	7.79423i	0.281250	+	0.487139i
$257$	11.6190	−	20.1246i	0.724770	−	1.25534i	−0.234298	−	0.972165i	$-0.575279\pi$
$257$	11.6190	−	20.1246i	0.724770	−	1.25534i	0.959069	−	0.283174i	$-0.0913874\pi$
$258$		0			0
$259$	−2.50000	−	12.9904i	−0.155342	−	0.807183i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.87298	+	2.23607i	−0.238818	+	0.137882i	−0.614634	−	0.788813i	$-0.710696\pi$
$263$	−3.87298	+	2.23607i	−0.238818	+	0.137882i	0.375815	+	0.926695i	$0.377363\pi$
$264$		0			0
$265$		0			0
$266$	−19.3649	−	6.70820i	−1.18734	−	0.411306i
$267$		0			0
$268$	−1.50000	+	2.59808i	−0.0916271	+	0.158703i
$269$	−7.74597	−	13.4164i	−0.472280	−	0.818013i	0.527217	−	0.849731i	$-0.323236\pi$
$269$	−7.74597	−	13.4164i	−0.472280	−	0.818013i	−0.999497	+	0.0317179i	$0.989902\pi$
$270$		0			0
$271$	1.50000	+	0.866025i	0.0911185	+	0.0526073i	0.544867	−	0.838523i	$-0.316580\pi$
$271$	1.50000	+	0.866025i	0.0911185	+	0.0526073i	−0.453748	+	0.891130i	$0.649914\pi$
$272$	7.74597			0.469668
$273$		0			0
$274$	10.0000			0.604122
$275$	−19.3649	−	11.1803i	−1.16775	−	0.674200i
$276$		0			0
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	0.781094	−	0.624413i	$-0.214662\pi$
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−9.68246	+	16.7705i	−0.580715	+	1.00583i
$279$		0			0
$280$		0			0
$281$		−	17.8885i		−	1.06714i	−0.845756	−	0.533571i	$-0.820850\pi$
$281$		−	17.8885i		−	1.06714i	0.845756	−	0.533571i	$-0.179150\pi$
$282$		0			0
$283$	−10.5000	+	6.06218i	−0.624160	+	0.360359i	−0.778487	−	0.627661i	$-0.784012\pi$
$283$	−10.5000	+	6.06218i	−0.624160	+	0.360359i	0.154327	+	0.988020i	$0.450679\pi$
$284$	−23.2379	+	13.4164i	−1.37892	+	0.796117i
$285$		0			0
$286$			17.3205i			1.02418i
$287$	15.4919	−	13.4164i	0.914460	−	0.791946i
$288$		0			0
$289$	−21.5000	+	37.2391i	−1.26471	+	2.19053i
$290$		0			0
$291$		0			0
$292$	18.0000	+	10.3923i	1.05337	+	0.608164i
$293$	−7.74597			−0.452524			−0.226262	−	0.974066i	$-0.572651\pi$
$293$	−7.74597			−0.452524			−0.226262	+	0.974066i	$0.572651\pi$
$294$		0			0
$295$		0			0
$296$	9.68246	+	5.59017i	0.562781	+	0.324922i
$297$		0			0
$298$	−20.0000	−	34.6410i	−1.15857	−	2.00670i
$299$	−3.87298	+	6.70820i	−0.223980	+	0.387945i
$300$		0			0
$301$	14.0000	−	12.1244i	0.806947	−	0.698836i
$302$		−	29.0689i		−	1.67273i
$303$		0			0
$304$	−3.00000	+	1.73205i	−0.172062	+	0.0993399i
$305$		0			0
$306$		0			0
$307$		−	5.19615i		−	0.296560i	−0.988945	−	0.148280i	$-0.952626\pi$
$307$		−	5.19615i		−	0.296560i	0.988945	−	0.148280i	$-0.0473737\pi$
$308$	34.8569	−	6.70820i	1.98615	−	0.382235i
$309$		0			0
$310$		0			0
$311$	7.74597	+	13.4164i	0.439233	+	0.760775i	0.997631	−	0.0687991i	$-0.0219168\pi$
$311$	7.74597	+	13.4164i	0.439233	+	0.760775i	−0.558397	+	0.829574i	$0.688583\pi$
$312$		0			0
$313$	12.0000	+	6.92820i	0.678280	+	0.391605i	0.799207	−	0.601056i	$-0.205253\pi$
$313$	12.0000	+	6.92820i	0.678280	+	0.391605i	−0.120927	+	0.992661i	$0.538587\pi$
$314$	−30.9839			−1.74852
$315$		0			0
$316$	−33.0000			−1.85640
$317$	3.87298	+	2.23607i	0.217528	+	0.125590i	0.604805	−	0.796373i	$-0.293251\pi$
$317$	3.87298	+	2.23607i	0.217528	+	0.125590i	−0.387277	+	0.921963i	$0.626584\pi$
$318$		0			0
$319$	10.0000	+	17.3205i	0.559893	+	0.969762i
$320$		0			0
$321$		0			0
$322$	25.0000	+	8.66025i	1.39320	+	0.482617i
$323$		−	26.8328i		−	1.49302i
$324$		0			0
$325$	−7.50000	+	4.33013i	−0.416025	+	0.240192i
$326$	−25.1744	+	14.5344i	−1.39428	+	0.804988i
$327$		0			0
$328$			17.3205i			0.956365i
$329$	3.87298	+	20.1246i	0.213524	+	1.10951i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	11.6190	+	20.1246i	0.637673	+	1.10448i
$333$		0			0
$334$	15.0000	+	8.66025i	0.820763	+	0.473868i
$335$		0			0
$336$		0			0
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$	−19.3649	−	11.1803i	−1.05331	−	0.608130i
$339$		0			0
$340$		0			0
$341$	3.87298	−	6.70820i	0.209734	−	0.363270i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$			15.6525i			0.843925i
$345$		0			0
$346$	30.0000	−	17.3205i	1.61281	−	0.931156i
$347$	7.74597	−	4.47214i	0.415825	−	0.240077i	−0.277464	−	0.960736i	$-0.589494\pi$
$347$	7.74597	−	4.47214i	0.415825	−	0.240077i	0.693290	+	0.720659i	$0.256161\pi$
$348$		0			0
$349$		−	22.5167i		−	1.20529i	−0.798010	−	0.602645i	$-0.794114\pi$
$349$		−	22.5167i		−	1.20529i	0.798010	−	0.602645i	$-0.205886\pi$
$350$	19.3649	+	22.3607i	1.03510	+	1.19523i
$351$		0			0
$352$	15.0000	−	25.9808i	0.799503	−	1.38478i
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$		0			0
$356$	46.4758			2.46321
$357$		0			0
$358$	−20.0000			−1.05703
$359$	3.87298	+	2.23607i	0.204408	+	0.118015i	0.598710	−	0.800966i	$-0.295680\pi$
$359$	3.87298	+	2.23607i	0.204408	+	0.118015i	−0.394302	+	0.918981i	$0.629014\pi$
$360$		0			0
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$		0			0
$363$		0			0
$364$	4.50000	−	12.9904i	0.235864	−	0.680881i
$365$		0			0
$366$		0			0
$367$	−9.00000	+	5.19615i	−0.469796	+	0.271237i	−0.716154	−	0.697942i	$-0.754099\pi$
$367$	−9.00000	+	5.19615i	−0.469796	+	0.271237i	0.246358	+	0.969179i	$0.420766\pi$
$368$	3.87298	−	2.23607i	0.201893	−	0.116563i
$369$		0			0
$370$		0			0
$371$	3.87298	−	11.1803i	0.201075	−	0.580454i
$372$		0			0
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	−0.890753	−	0.454488i	$-0.849822\pi$
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	0.838975	+	0.544170i	$0.183156\pi$
$374$	38.7298	+	67.0820i	2.00267	+	3.46873i
$375$		0			0
$376$	−15.0000	−	8.66025i	−0.773566	−	0.446619i
$377$	7.74597			0.398938
$378$		0			0
$379$	17.0000			0.873231			0.436616	−	0.899648i	$-0.356177\pi$
$379$	17.0000			0.873231			0.436616	+	0.899648i	$0.356177\pi$
$380$		0			0
$381$		0			0
$382$	−20.0000	−	34.6410i	−1.02329	−	1.77239i
$383$	11.6190	−	20.1246i	0.593701	−	1.02832i	−0.400028	−	0.916503i	$-0.631000\pi$
$383$	11.6190	−	20.1246i	0.593701	−	1.02832i	0.993729	−	0.111817i	$-0.0356670\pi$
$384$		0			0
$385$		0			0
$386$		−	15.6525i		−	0.796690i
$387$		0			0
$388$	4.50000	−	2.59808i	0.228453	−	0.131897i
$389$	7.74597	−	4.47214i	0.392736	−	0.226746i	−0.290609	−	0.956842i	$-0.593858\pi$
$389$	7.74597	−	4.47214i	0.392736	−	0.226746i	0.683345	+	0.730096i	$0.260525\pi$
$390$		0			0
$391$			34.6410i			1.75187i
$392$	−15.4919	−	2.23607i	−0.782461	−	0.112938i
$393$		0			0
$394$	10.0000	−	17.3205i	0.503793	−	0.872595i
$395$		0			0
$396$		0			0
$397$	−25.5000	−	14.7224i	−1.27981	−	0.738898i	−0.302995	−	0.952992i	$-0.597987\pi$
$397$	−25.5000	−	14.7224i	−1.27981	−	0.738898i	−0.976813	+	0.214094i	$0.931320\pi$
$398$	−50.3488			−2.52376
$399$		0			0
$400$	5.00000			0.250000
$401$	−19.3649	−	11.1803i	−0.967038	−	0.558320i	−0.0687059	−	0.997637i	$-0.521887\pi$
$401$	−19.3649	−	11.1803i	−0.967038	−	0.558320i	−0.898332	+	0.439317i	$0.855220\pi$
$402$		0			0
$403$	−1.50000	−	2.59808i	−0.0747203	−	0.129419i
$404$		0			0
$405$		0			0
$406$	−5.00000	−	25.9808i	−0.248146	−	1.28940i
$407$		−	22.3607i		−	1.10838i
$408$		0			0
$409$	−19.5000	+	11.2583i	−0.964213	+	0.556689i	−0.897467	−	0.441081i	$-0.854595\pi$
$409$	−19.5000	+	11.2583i	−0.964213	+	0.556689i	−0.0667458	+	0.997770i	$0.521262\pi$
$410$		0			0
$411$		0			0
$412$		−	15.5885i		−	0.767988i
$413$	19.3649	+	6.70820i	0.952885	+	0.330089i
$414$		0			0
$415$		0			0
$416$	−5.80948	−	10.0623i	−0.284833	−	0.493345i
$417$		0			0
$418$	−30.0000	−	17.3205i	−1.46735	−	0.847174i
$419$	15.4919			0.756830			0.378415	−	0.925636i	$-0.376469\pi$
$419$	15.4919			0.756830			0.378415	+	0.925636i	$0.376469\pi$
$420$		0			0
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$	36.7933	+	21.2426i	1.79107	+	1.03408i
$423$		0			0
$424$	5.00000	+	8.66025i	0.242821	+	0.420579i
$425$	−19.3649	+	33.5410i	−0.939336	+	1.62698i
$426$		0			0
$427$	−22.5000	+	4.33013i	−1.08885	+	0.209550i
$428$			13.4164i			0.648507i
$429$		0			0
$430$		0			0
$431$	−27.1109	+	15.6525i	−1.30589	+	0.753953i	−0.981407	−	0.191940i	$-0.938522\pi$
$431$	−27.1109	+	15.6525i	−1.30589	+	0.753953i	−0.324479	+	0.945893i	$0.605189\pi$
$432$		0			0
$433$			15.5885i			0.749133i	0.927200	+	0.374567i	$0.122209\pi$
$433$			15.5885i			0.749133i	−0.927200	+	0.374567i	$0.877791\pi$
$434$	−7.74597	+	6.70820i	−0.371818	+	0.322004i
$435$		0			0
$436$	−1.50000	+	2.59808i	−0.0718370	+	0.124425i
$437$	−7.74597	−	13.4164i	−0.370540	−	0.641794i
$438$		0			0
$439$	3.00000	+	1.73205i	0.143182	+	0.0826663i	0.569880	−	0.821728i	$-0.306990\pi$
$439$	3.00000	+	1.73205i	0.143182	+	0.0826663i	−0.426698	+	0.904394i	$0.640323\pi$
$440$		0			0
$441$		0			0
$442$	30.0000			1.42695
$443$	−30.9839	−	17.8885i	−1.47209	−	0.849910i	−0.472580	−	0.881288i	$-0.656677\pi$
$443$	−30.9839	−	17.8885i	−1.47209	−	0.849910i	−0.999508	+	0.0313772i	$0.990011\pi$
$444$		0			0
$445$		0			0
$446$	27.1109	−	46.9574i	1.28374	−	2.22350i
$447$		0			0
$448$	−26.0000	+	22.5167i	−1.22838	+	1.06381i
$449$			8.94427i			0.422106i	0.977475	+	0.211053i	$0.0676893\pi$
$449$			8.94427i			0.422106i	−0.977475	+	0.211053i	$0.932311\pi$
$450$		0			0
$451$	30.0000	−	17.3205i	1.41264	−	0.815591i
$452$	−23.2379	+	13.4164i	−1.09302	+	0.631055i
$453$		0			0
$454$		−	51.9615i		−	2.43868i
$455$		0			0
$456$		0			0
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	−0.965512	−	0.260358i	$-0.916159\pi$
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	0.708233	+	0.705979i	$0.249493\pi$
$458$	−29.0474	−	50.3115i	−1.35729	−	2.35090i
$459$		0			0
$460$		0			0
$461$	7.74597			0.360766			0.180383	−	0.983596i	$-0.442266\pi$
$461$	7.74597			0.360766			0.180383	+	0.983596i	$0.442266\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	−3.87298	−	2.23607i	−0.179799	−	0.103807i
$465$		0			0
$466$	10.0000	+	17.3205i	0.463241	+	0.802357i
$467$	−15.4919	+	26.8328i	−0.716881	+	1.24167i	0.245348	+	0.969435i	$0.421098\pi$
$467$	−15.4919	+	26.8328i	−0.716881	+	1.24167i	−0.962229	+	0.272240i	$0.912236\pi$
$468$		0			0
$469$	−2.50000	−	0.866025i	−0.115439	−	0.0399893i
$470$		0			0
$471$		0			0
$472$	−15.0000	+	8.66025i	−0.690431	+	0.398621i
$473$	27.1109	−	15.6525i	1.24656	−	0.719702i
$474$		0			0
$475$		−	17.3205i		−	0.794719i
$476$	−11.6190	−	60.3738i	−0.532554	−	2.76723i
$477$		0			0
$478$	10.0000	−	17.3205i	0.457389	−	0.792222i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	−7.50000	−	4.33013i	−0.341971	−	0.197437i
$482$	−34.8569			−1.58769
$483$		0			0
$484$	27.0000			1.22727
$485$		0			0
$486$		0			0
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.819181	+	0.573535i	$0.194428\pi$
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.0871056	+	0.996199i	$0.472238\pi$
$488$	9.68246	−	16.7705i	0.438304	−	0.759165i
$489$		0			0
$490$		0			0
$491$			22.3607i			1.00912i	0.863376	+	0.504562i	$0.168346\pi$
$491$			22.3607i			1.00912i	−0.863376	+	0.504562i	$0.831654\pi$
$492$		0			0
$493$	30.0000	−	17.3205i	1.35113	−	0.780076i
$494$	−11.6190	+	6.70820i	−0.522761	+	0.301816i
$495$		0			0
$496$			1.73205i			0.0777714i
$497$	−15.4919	−	17.8885i	−0.694908	−	0.802411i
$498$		0			0
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	−0.276683	−	0.960961i	$-0.589235\pi$
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	0.970558	−	0.240866i	$-0.0774314\pi$
$500$		0			0
$501$		0			0
$502$	45.0000	+	25.9808i	2.00845	+	1.15958i
$503$	23.2379			1.03613			0.518063	−	0.855342i	$-0.326653\pi$
$503$	23.2379			1.03613			0.518063	+	0.855342i	$0.326653\pi$
$504$		0			0
$505$		0			0
$506$	38.7298	+	22.3607i	1.72175	+	0.994053i
$507$		0			0
$508$	−1.50000	−	2.59808i	−0.0665517	−	0.115271i
$509$	−11.6190	+	20.1246i	−0.515001	+	0.892008i	0.484848	+	0.874599i	$0.338875\pi$
$509$	−11.6190	+	20.1246i	−0.515001	+	0.892008i	−0.999848	+	0.0174091i	$0.994458\pi$
$510$		0			0
$511$	−6.00000	+	17.3205i	−0.265424	+	0.766214i
$512$			11.1803i			0.494106i
$513$		0			0
$514$	−45.0000	+	25.9808i	−1.98486	+	1.14596i
$515$		0			0
$516$		0			0
$517$			34.6410i			1.52351i
$518$	−9.68246	+	27.9508i	−0.425423	+	1.22809i
$519$		0			0
$520$		0			0
$521$	3.87298	+	6.70820i	0.169678	+	0.293892i	0.938307	−	0.345804i	$-0.112394\pi$
$521$	3.87298	+	6.70820i	0.169678	+	0.293892i	−0.768628	+	0.639696i	$0.779060\pi$
$522$		0			0
$523$	−16.5000	−	9.52628i	−0.721495	−	0.416555i	0.0938079	−	0.995590i	$-0.470096\pi$
$523$	−16.5000	−	9.52628i	−0.721495	−	0.416555i	−0.815303	+	0.579035i	$0.803429\pi$
$524$		0			0
$525$		0			0
$526$	10.0000			0.436021
$527$	−11.6190	−	6.70820i	−0.506129	−	0.292214i
$528$		0			0
$529$	−1.50000	−	2.59808i	−0.0652174	−	0.112960i
$530$		0			0
$531$		0			0
$532$	18.0000	+	20.7846i	0.780399	+	0.901127i
$533$		−	13.4164i		−	0.581129i
$534$		0			0
$535$		0			0
$536$	1.93649	−	1.11803i	0.0836437	−	0.0482917i
$537$		0			0
$538$			34.6410i			1.49348i
$539$	11.6190	+	29.0689i	0.500464	+	1.25209i
$540$		0			0
$541$	−7.00000	+	12.1244i	−0.300954	+	0.521267i	−0.976352	−	0.216186i	$-0.930638\pi$
$541$	−7.00000	+	12.1244i	−0.300954	+	0.521267i	0.675399	+	0.737453i	$0.263972\pi$
$542$	−1.93649	−	3.35410i	−0.0831794	−	0.144071i
$543$		0			0
$544$	−45.0000	−	25.9808i	−1.92936	−	1.11392i
$545$		0			0
$546$		0			0
$547$	11.0000			0.470326			0.235163	−	0.971956i	$-0.424438\pi$
$547$	11.0000			0.470326			0.235163	+	0.971956i	$0.424438\pi$
$548$	−11.6190	−	6.70820i	−0.496337	−	0.286560i
$549$		0			0
$550$	25.0000	+	43.3013i	1.06600	+	1.84637i
$551$	−7.74597	+	13.4164i	−0.329989	+	0.571558i
$552$		0			0
$553$	−5.50000	−	28.5788i	−0.233884	−	1.21530i
$554$			11.1803i			0.475007i
$555$		0			0
$556$	22.5000	−	12.9904i	0.954213	−	0.550915i
$557$	30.9839	−	17.8885i	1.31283	−	0.757962i	0.330265	−	0.943888i	$-0.392862\pi$
$557$	30.9839	−	17.8885i	1.31283	−	0.757962i	0.982564	+	0.185926i	$0.0595286\pi$
$558$		0			0
$559$		−	12.1244i		−	0.512806i
$560$		0			0
$561$		0			0
$562$	−20.0000	+	34.6410i	−0.843649	+	1.46124i
$563$	−3.87298	−	6.70820i	−0.163227	−	0.282717i	0.772797	−	0.634653i	$-0.218857\pi$
$563$	−3.87298	−	6.70820i	−0.163227	−	0.282717i	−0.936024	+	0.351936i	$0.885524\pi$
$564$		0			0
$565$		0			0
$566$	27.1109			1.13956
$567$		0			0
$568$	20.0000			0.839181
$569$	15.4919	+	8.94427i	0.649456	+	0.374963i	0.788248	−	0.615358i	$-0.210989\pi$
$569$	15.4919	+	8.94427i	0.649456	+	0.374963i	−0.138792	+	0.990322i	$0.544322\pi$
$570$		0			0
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	0.983444	−	0.181210i	$-0.0580014\pi$
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	−0.648655	+	0.761083i	$0.724668\pi$
$572$	11.6190	−	20.1246i	0.485813	−	0.841452i
$573$		0			0
$574$	−45.0000	+	8.66025i	−1.87826	+	0.361472i
$575$			22.3607i			0.932505i
$576$		0			0
$577$	−34.5000	+	19.9186i	−1.43625	+	0.829222i	−0.997587	−	0.0694283i	$-0.977883\pi$
$577$	−34.5000	+	19.9186i	−1.43625	+	0.829222i	−0.438667	+	0.898650i	$0.644549\pi$
$578$	83.2691	−	48.0755i	3.46354	−	1.99968i
$579$		0			0
$580$		0			0
$581$	−15.4919	+	13.4164i	−0.642714	+	0.556606i
$582$		0			0
$583$	10.0000	−	17.3205i	0.414158	−	0.717342i
$584$	−7.74597	−	13.4164i	−0.320530	−	0.555175i
$585$		0			0
$586$	15.0000	+	8.66025i	0.619644	+	0.357752i
$587$	30.9839			1.27884			0.639421	−	0.768857i	$-0.279174\pi$
$587$	30.9839			1.27884			0.639421	+	0.768857i	$0.279174\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$		0			0
$591$		0			0
$592$	2.50000	+	4.33013i	0.102749	+	0.177967i
$593$	−15.4919	+	26.8328i	−0.636177	+	1.10189i	0.350087	+	0.936717i	$0.386152\pi$
$593$	−15.4919	+	26.8328i	−0.636177	+	1.10189i	−0.986264	+	0.165174i	$0.947181\pi$
$594$		0			0
$595$		0			0
$596$			53.6656i			2.19823i
$597$		0			0
$598$	15.0000	−	8.66025i	0.613396	−	0.354144i
$599$	7.74597	−	4.47214i	0.316492	−	0.182727i	−0.333336	−	0.942808i	$-0.608174\pi$
$599$	7.74597	−	4.47214i	0.316492	−	0.182727i	0.649828	+	0.760082i	$0.274841\pi$
$600$		0			0
$601$		−	43.3013i		−	1.76630i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$		−	43.3013i		−	1.76630i	0.469095	−	0.883148i	$-0.344580\pi$
$602$	−40.6663	+	7.82624i	−1.65744	+	0.318974i
$603$		0			0
$604$	−19.5000	+	33.7750i	−0.793444	+	1.37428i
$605$		0			0
$606$		0			0
$607$	27.0000	+	15.5885i	1.09590	+	0.632716i	0.935140	−	0.354278i	$-0.115273\pi$
$607$	27.0000	+	15.5885i	1.09590	+	0.632716i	0.160756	+	0.986994i	$0.448607\pi$
$608$	23.2379			0.942421
$609$		0			0
$610$		0			0
$611$	11.6190	+	6.70820i	0.470052	+	0.271385i
$612$		0			0
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	0.534697	−	0.845044i	$-0.320426\pi$
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	−0.999178	+	0.0405396i	$0.987092\pi$
$614$	−5.80948	+	10.0623i	−0.234451	+	0.406082i
$615$		0			0
$616$	−25.0000	−	8.66025i	−1.00728	−	0.348932i
$617$			22.3607i			0.900207i	0.892976	+	0.450104i	$0.148613\pi$
$617$			22.3607i			0.900207i	−0.892976	+	0.450104i	$0.851387\pi$
$618$		0			0
$619$	4.50000	−	2.59808i	0.180870	−	0.104425i	−0.406831	−	0.913503i	$-0.633366\pi$
$619$	4.50000	−	2.59808i	0.180870	−	0.104425i	0.587701	+	0.809078i	$0.300033\pi$
$620$		0			0
$621$		0			0
$622$		−	34.6410i		−	1.38898i
$623$	7.74597	+	40.2492i	0.310336	+	1.61255i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−15.4919	−	26.8328i	−0.619182	−	1.07246i
$627$		0			0
$628$	36.0000	+	20.7846i	1.43656	+	0.829396i
$629$	−38.7298			−1.54426
$630$		0			0
$631$	29.0000			1.15447			0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000			1.15447			0.577236	+	0.816577i	$0.304131\pi$
$632$	21.3014	+	12.2984i	0.847325	+	0.489203i
$633$		0			0
$634$	−5.00000	−	8.66025i	−0.198575	−	0.343943i
$635$		0			0
$636$		0			0
$637$	12.0000	+	1.73205i	0.475457	+	0.0686264i
$638$		−	44.7214i		−	1.77054i
$639$		0			0
$640$		0			0
$641$	−3.87298	+	2.23607i	−0.152974	+	0.0883194i	−0.574533	−	0.818481i	$-0.694816\pi$
$641$	−3.87298	+	2.23607i	−0.152974	+	0.0883194i	0.421559	+	0.906801i	$0.361483\pi$
$642$		0			0
$643$		−	19.0526i		−	0.751360i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$		−	19.0526i		−	0.751360i	0.926750	−	0.375680i	$-0.122591\pi$
$644$	−23.2379	−	26.8328i	−0.915702	−	1.05736i
$645$		0			0
$646$	−30.0000	+	51.9615i	−1.18033	+	2.04440i
$647$	−7.74597	−	13.4164i	−0.304525	−	0.527453i	0.672630	−	0.739979i	$-0.265165\pi$
$647$	−7.74597	−	13.4164i	−0.304525	−	0.527453i	−0.977156	+	0.212525i	$0.931831\pi$
$648$		0			0
$649$	30.0000	+	17.3205i	1.17760	+	0.679889i
$650$	19.3649			0.759555
$651$		0			0
$652$	39.0000			1.52736
$653$	−19.3649	−	11.1803i	−0.757808	−	0.437521i	0.0707003	−	0.997498i	$-0.477477\pi$
$653$	−19.3649	−	11.1803i	−0.757808	−	0.437521i	−0.828508	+	0.559977i	$0.810810\pi$
$654$		0			0
$655$		0			0
$656$	−3.87298	+	6.70820i	−0.151215	+	0.261911i
$657$		0			0
$658$	15.0000	−	43.3013i	0.584761	−	1.68806i
$659$		−	17.8885i		−	0.696839i	−0.937339	−	0.348419i	$-0.886719\pi$
$659$		−	17.8885i		−	0.696839i	0.937339	−	0.348419i	$-0.113281\pi$
$660$		0			0
$661$	−24.0000	+	13.8564i	−0.933492	+	0.538952i	−0.887914	−	0.460009i	$-0.847846\pi$
$661$	−24.0000	+	13.8564i	−0.933492	+	0.538952i	−0.0455776	+	0.998961i	$0.514513\pi$
$662$	−7.74597	+	4.47214i	−0.301056	+	0.173814i
$663$		0			0
$664$		−	17.3205i		−	0.672166i
$665$		0			0
$666$		0			0
$667$	10.0000	−	17.3205i	0.387202	−	0.670653i
$668$	−11.6190	−	20.1246i	−0.449551	−	0.778645i
$669$		0			0
$670$		0			0
$671$	−38.7298			−1.49515
$672$		0			0
$673$	2.00000			0.0770943			0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000			0.0770943			0.0385472	+	0.999257i	$0.487727\pi$
$674$	19.3649	+	11.1803i	0.745909	+	0.430651i
$675$		0			0
$676$	15.0000	+	25.9808i	0.576923	+	0.999260i
$677$	15.4919	−	26.8328i	0.595403	−	1.03127i	−0.398086	−	0.917348i	$-0.630326\pi$
$677$	15.4919	−	26.8328i	0.595403	−	1.03127i	0.993490	−	0.113921i	$-0.0363411\pi$
$678$		0			0
$679$	3.00000	+	3.46410i	0.115129	+	0.132940i
$680$		0			0
$681$		0			0
$682$	−15.0000	+	8.66025i	−0.574380	+	0.331618i
$683$	30.9839	−	17.8885i	1.18556	−	0.684486i	0.228269	−	0.973598i	$-0.426693\pi$
$683$	30.9839	−	17.8885i	1.18556	−	0.684486i	0.957295	+	0.289112i	$0.0933600\pi$
$684$		0			0
$685$		0			0
$686$	−1.93649	−	41.3673i	−0.0739356	−	1.57941i
$687$		0			0
$688$	−3.50000	+	6.06218i	−0.133436	+	0.231118i
$689$	−3.87298	−	6.70820i	−0.147549	−	0.255562i
$690$		0			0
$691$	−28.5000	−	16.4545i	−1.08419	−	0.625958i	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−28.5000	−	16.4545i	−1.08419	−	0.625958i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	−46.4758			−1.76674
$693$		0			0
$694$	−20.0000			−0.759190
$695$		0			0
$696$		0			0
$697$	−30.0000	−	51.9615i	−1.13633	−	1.96818i
$698$	−25.1744	+	43.6033i	−0.952865	+	1.65041i
$699$		0			0
$700$	−7.50000	−	38.9711i	−0.283473	−	1.47297i
$701$			8.94427i			0.337820i	0.985631	+	0.168910i	$0.0540248\pi$
$701$			8.94427i			0.337820i	−0.985631	+	0.168910i	$0.945975\pi$
$702$		0			0
$703$	15.0000	−	8.66025i	0.565736	−	0.326628i
$704$	−50.3488	+	29.0689i	−1.89759	+	1.09557i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	−0.950628	−	0.310334i	$-0.899559\pi$
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	0.744071	+	0.668101i	$0.232892\pi$
$710$		0			0
$711$		0			0
$712$	−30.0000	−	17.3205i	−1.12430	−	0.649113i
$713$	−7.74597			−0.290089
$714$		0			0
$715$		0			0
$716$	23.2379	+	13.4164i	0.868441	+	0.501395i
$717$		0			0
$718$	−5.00000	−	8.66025i	−0.186598	−	0.323198i
$719$	7.74597	−	13.4164i	0.288876	−	0.500348i	−0.684666	−	0.728857i	$-0.740052\pi$
$719$	7.74597	−	13.4164i	0.288876	−	0.500348i	0.973542	+	0.228509i	$0.0733852\pi$
$720$		0			0
$721$	13.5000	−	2.59808i	0.502766	−	0.0967574i
$722$			15.6525i			0.582525i
$723$		0			0
$724$		0			0
$725$	19.3649	−	11.1803i	0.719195	−	0.415227i
$726$		0			0
$727$			19.0526i			0.706620i	0.935506	+	0.353310i	$0.114944\pi$
$727$			19.0526i			0.706620i	−0.935506	+	0.353310i	$0.885056\pi$
$728$	−7.74597	+	6.70820i	−0.287085	+	0.248623i
$729$		0			0
$730$		0			0
$731$	−27.1109	−	46.9574i	−1.00273	−	1.73678i
$732$		0			0
$733$	31.5000	+	18.1865i	1.16348	+	0.671735i	0.952135	−	0.305677i	$-0.0988827\pi$
$733$	31.5000	+	18.1865i	1.16348	+	0.671735i	0.211344	+	0.977412i	$0.432216\pi$
$734$	23.2379			0.857727
$735$		0			0
$736$	−30.0000			−1.10581
$737$	−3.87298	−	2.23607i	−0.142663	−	0.0823666i
$738$		0			0
$739$	−11.5000	−	19.9186i	−0.423034	−	0.732717i	0.573200	−	0.819415i	$-0.305702\pi$
$739$	−11.5000	−	19.9186i	−0.423034	−	0.732717i	−0.996235	+	0.0866983i	$0.972368\pi$
$740$		0			0
$741$		0			0
$742$	−20.0000	+	17.3205i	−0.734223	+	0.635856i
$743$		−	31.3050i		−	1.14847i	−0.818691	−	0.574234i	$-0.805300\pi$
$743$		−	31.3050i		−	1.14847i	0.818691	−	0.574234i	$-0.194700\pi$
$744$		0			0
$745$		0			0
$746$	3.87298	−	2.23607i	0.141800	−	0.0818683i
$747$		0			0
$748$		−	103.923i		−	3.79980i
$749$	−11.6190	+	2.23607i	−0.424547	+	0.0817041i
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	−3.87298	−	6.70820i	−0.141233	−	0.244623i
$753$		0			0
$754$	−15.0000	−	8.66025i	−0.546268	−	0.315388i
$755$		0			0
$756$		0			0
$757$	−25.0000			−0.908640			−0.454320	−	0.890838i	$-0.650118\pi$
$757$	−25.0000			−0.908640			−0.454320	+	0.890838i	$0.650118\pi$
$758$	−32.9204	−	19.0066i	−1.19572	−	0.690350i
$759$		0			0
$760$		0			0
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$		0			0
$763$	−2.50000	−	0.866025i	−0.0905061	−	0.0313522i
$764$			53.6656i			1.94155i
$765$		0			0
$766$	−45.0000	+	25.9808i	−1.62592	+	0.938723i
$767$	11.6190	−	6.70820i	0.419536	−	0.242219i
$768$		0			0
$769$		−	34.6410i		−	1.24919i	−0.780950	−	0.624593i	$-0.785265\pi$
$769$		−	34.6410i		−	1.24919i	0.780950	−	0.624593i	$-0.214735\pi$
$770$		0			0
$771$		0			0
$772$	−10.5000	+	18.1865i	−0.377903	+	0.654548i
$773$	15.4919	+	26.8328i	0.557206	+	0.965109i	0.997728	+	0.0673675i	$0.0214600\pi$
$773$	15.4919	+	26.8328i	0.557206	+	0.965109i	−0.440522	+	0.897742i	$0.645207\pi$
$774$		0			0
$775$	−7.50000	−	4.33013i	−0.269408	−	0.155543i
$776$	−3.87298			−0.139032
$777$		0			0
$778$	−20.0000			−0.717035
$779$	23.2379	+	13.4164i	0.832584	+	0.480693i
$780$		0			0
$781$	−20.0000	−	34.6410i	−0.715656	−	1.23955i
$782$	38.7298	−	67.0820i	1.38498	−	2.39885i
$783$		0			0
$784$	−5.50000	−	4.33013i	−0.196429	−	0.154647i
$785$		0			0
$786$		0			0
$787$	16.5000	−	9.52628i	0.588161	−	0.339575i	−0.176209	−	0.984353i	$-0.556383\pi$
$787$	16.5000	−	9.52628i	0.588161	−	0.339575i	0.764370	+	0.644778i	$0.223050\pi$
$788$	−23.2379	+	13.4164i	−0.827816	+	0.477940i
$789$		0			0
$790$		0			0
$791$	−15.4919	−	17.8885i	−0.550830	−	0.636043i
$792$		0			0
$793$	−7.50000	+	12.9904i	−0.266333	+	0.461302i
$794$	32.9204	+	57.0197i	1.16830	+	2.02355i
$795$		0			0
$796$	58.5000	+	33.7750i	2.07348	+	1.19712i
$797$	38.7298			1.37188			0.685941	−	0.727658i	$-0.259391\pi$
$797$	38.7298			1.37188			0.685941	+	0.727658i	$0.259391\pi$
$798$		0			0
$799$	60.0000			2.12265
$800$	−29.0474	−	16.7705i	−1.02698	−	0.592927i
$801$		0			0
$802$	25.0000	+	43.3013i	0.882781	+	1.52902i
$803$	−15.4919	+	26.8328i	−0.546698	+	0.946910i
$804$		0			0
$805$		0			0
$806$			6.70820i			0.236286i
$807$		0			0
$808$		0			0
$809$	−3.87298	+	2.23607i	−0.136167	+	0.0786160i	−0.566536	−	0.824037i	$-0.691717\pi$
$809$	−3.87298	+	2.23607i	−0.136167	+	0.0786160i	0.430369	+	0.902653i	$0.358383\pi$
$810$		0			0
$811$		−	10.3923i		−	0.364923i	−0.983213	−	0.182462i	$-0.941593\pi$
$811$		−	10.3923i		−	0.364923i	0.983213	−	0.182462i	$-0.0584065\pi$
$812$	−11.6190	+	33.5410i	−0.407745	+	1.17706i
$813$		0			0
$814$	−25.0000	+	43.3013i	−0.876250	+	1.51771i
$815$		0			0
$816$		0			0
$817$	21.0000	+	12.1244i	0.734697	+	0.424178i
$818$	50.3488			1.76040
$819$		0			0
$820$		0			0
$821$	−19.3649	−	11.1803i	−0.675840	−	0.390197i	0.122446	−	0.992475i	$-0.460926\pi$
$821$	−19.3649	−	11.1803i	−0.675840	−	0.390197i	−0.798286	+	0.602279i	$0.794260\pi$
$822$		0			0
$823$	21.5000	+	37.2391i	0.749443	+	1.29807i	0.948090	+	0.318002i	$0.103012\pi$
$823$	21.5000	+	37.2391i	0.749443	+	1.29807i	−0.198647	+	0.980071i	$0.563655\pi$
$824$	−5.80948	+	10.0623i	−0.202383	+	0.350537i
$825$		0			0
$826$	−30.0000	−	34.6410i	−1.04383	−	1.20532i
$827$			8.94427i			0.311023i	0.987834	+	0.155511i	$0.0497025\pi$
$827$			8.94427i			0.311023i	−0.987834	+	0.155511i	$0.950297\pi$
$828$		0			0
$829$	−12.0000	+	6.92820i	−0.416777	+	0.240626i	−0.693698	−	0.720266i	$-0.744020\pi$
$829$	−12.0000	+	6.92820i	−0.416777	+	0.240626i	0.276920	+	0.960893i	$0.410686\pi$
$830$		0			0
$831$		0			0
$832$			22.5167i			0.780625i
$833$	50.3488	−	20.1246i	1.74448	−	0.697276i
$834$		0			0
$835$		0			0
$836$	23.2379	+	40.2492i	0.803700	+	1.39205i
$837$		0			0
$838$	−30.0000	−	17.3205i	−1.03633	−	0.598327i
$839$	7.74597			0.267420			0.133710	−	0.991020i	$-0.457311\pi$
$839$	7.74597			0.267420			0.133710	+	0.991020i	$0.457311\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$	65.8407	+	38.0132i	2.26902	+	1.31002i
$843$		0			0
$844$	−28.5000	−	49.3634i	−0.981010	−	1.69916i
$845$		0			0
$846$		0			0
$847$	4.50000	+	23.3827i	0.154622	+	0.803439i
$848$			4.47214i			0.153574i
$849$		0			0
$850$	75.0000	−	43.3013i	2.57248	−	1.48522i
$851$	−19.3649	+	11.1803i	−0.663821	+	0.383257i
$852$		0			0
$853$			13.8564i			0.474434i	0.971457	+	0.237217i	$0.0762353\pi$
$853$			13.8564i			0.474434i	−0.971457	+	0.237217i	$0.923765\pi$
$854$	48.4123	+	16.7705i	1.65663	+	0.573875i
$855$		0			0
$856$	5.00000	−	8.66025i	0.170896	−	0.296001i
$857$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$	4.50000	+	2.59808i	0.153538	+	0.0886452i	0.574801	−	0.818293i	$-0.305080\pi$
$859$	4.50000	+	2.59808i	0.153538	+	0.0886452i	−0.421263	+	0.906939i	$0.638413\pi$
$860$		0			0
$861$		0			0
$862$	70.0000			2.38421
$863$	−30.9839	−	17.8885i	−1.05470	−	0.608933i	−0.130741	−	0.991417i	$-0.541736\pi$
$863$	−30.9839	−	17.8885i	−1.05470	−	0.608933i	−0.923962	+	0.382483i	$0.875069\pi$
$864$		0			0
$865$		0			0
$866$	17.4284	−	30.1869i	0.592242	−	1.02579i
$867$		0			0
$868$	13.5000	−	2.59808i	0.458220	−	0.0881845i
$869$		−	49.1935i		−	1.66878i
$870$		0			0
$871$	−1.50000	+	0.866025i	−0.0508256	+	0.0293442i
$872$	1.93649	−	1.11803i	0.0655779	−	0.0378614i
$873$		0			0
$874$			34.6410i			1.17175i
$875$		0			0
$876$		0			0
$877$	12.5000	−	21.6506i	0.422095	−	0.731090i	−0.574049	−	0.818821i	$-0.694628\pi$
$877$	12.5000	−	21.6506i	0.422095	−	0.731090i	0.996144	+	0.0877308i	$0.0279615\pi$
$878$	−3.87298	−	6.70820i	−0.130707	−	0.226391i
$879$		0			0
$880$		0			0
$881$	23.2379			0.782905			0.391452	−	0.920198i	$-0.371973\pi$
$881$	23.2379			0.782905			0.391452	+	0.920198i	$0.371973\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	−34.8569	−	20.1246i	−1.17236	−	0.676864i
$885$		0			0
$886$	40.0000	+	69.2820i	1.34383	+	2.32758i
$887$	−11.6190	+	20.1246i	−0.390126	+	0.675718i	−0.992466	−	0.122522i	$-0.960902\pi$
$887$	−11.6190	+	20.1246i	−0.390126	+	0.675718i	0.602340	+	0.798240i	$0.294235\pi$
$888$		0			0
$889$	2.00000	−	1.73205i	0.0670778	−	0.0580911i
$890$		0			0
$891$		0			0
$892$	−63.0000	+	36.3731i	−2.10940	+	1.21786i
$893$	−23.2379	+	13.4164i	−0.777627	+	0.448963i
$894$		0			0
$895$		0			0
$896$	40.6663	−	7.82624i	1.35857	−	0.261456i
$897$		0			0
$898$	10.0000	−	17.3205i	0.333704	−	0.577993i
$899$	3.87298	+	6.70820i	0.129171	+	0.223731i
$900$		0			0
$901$	−30.0000	−	17.3205i	−0.999445	−	0.577030i
$902$	−77.4597			−2.57912
$903$		0			0
$904$	20.0000			0.665190
$905$		0			0
$906$		0			0
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	0.821531	−	0.570164i	$-0.193120\pi$
$907$	−2.50000	−	4.33013i	−0.0830111	−	0.143780i	−0.904542	+	0.426385i	$0.859787\pi$
$908$	−34.8569	+	60.3738i	−1.15677	+	2.00358i
$909$		0			0
$910$		0			0
$911$		−	4.47214i		−	0.148168i	−0.997252	−	0.0740842i	$-0.976397\pi$
$911$		−	4.47214i		−	0.148168i	0.997252	−	0.0740842i	$-0.0236034\pi$
$912$		0			0
$913$	−30.0000	+	17.3205i	−0.992855	+	0.573225i
$914$	21.3014	−	12.2984i	0.704588	−	0.406794i
$915$		0			0
$916$			77.9423i			2.57529i
$917$		0			0
$918$		0			0
$919$	6.50000	−	11.2583i	0.214415	−	0.371378i	−0.738676	−	0.674060i	$-0.764549\pi$
$919$	6.50000	−	11.2583i	0.214415	−	0.371378i	0.953092	+	0.302682i	$0.0978821\pi$
$920$		0			0
$921$		0			0
$922$	−15.0000	−	8.66025i	−0.493999	−	0.285210i
$923$	−15.4919			−0.509923
$924$		0			0
$925$	−25.0000			−0.821995
$926$	−15.4919	−	8.94427i	−0.509097	−	0.293927i
$927$		0			0
$928$	15.0000	+	25.9808i	0.492399	+	0.852860i
$929$	15.4919	−	26.8328i	0.508274	−	0.880356i	−0.491680	−	0.870776i	$-0.663617\pi$
$929$	15.4919	−	26.8328i	0.508274	−	0.880356i	0.999954	−	0.00958031i	$-0.00304955\pi$
$930$		0			0
$931$	−15.0000	+	19.0526i	−0.491605	+	0.624422i
$932$		−	26.8328i		−	0.878938i
$933$		0			0
$934$	60.0000	−	34.6410i	1.96326	−	1.13349i
$935$		0			0
$936$		0			0
$937$		−	46.7654i		−	1.52776i	−0.645359	−	0.763879i	$-0.723292\pi$
$937$		−	46.7654i		−	1.52776i	0.645359	−	0.763879i	$-0.276708\pi$
$938$	3.87298	+	4.47214i	0.126457	+	0.146020i
$939$		0			0
$940$		0			0
$941$	19.3649	+	33.5410i	0.631278	+	1.09341i	0.987291	+	0.158925i	$0.0508027\pi$
$941$	19.3649	+	33.5410i	0.631278	+	1.09341i	−0.356012	+	0.934481i	$0.615864\pi$
$942$		0			0
$943$	−30.0000	−	17.3205i	−0.976934	−	0.564033i
$944$	−7.74597			−0.252110
$945$		0			0
$946$	−70.0000			−2.27590
$947$	3.87298	+	2.23607i	0.125855	+	0.0726624i	0.561606	−	0.827405i	$-0.310184\pi$
$947$	3.87298	+	2.23607i	0.125855	+	0.0726624i	−0.435751	+	0.900067i	$0.643517\pi$
$948$		0			0
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$	−19.3649	+	33.5410i	−0.628281	+	1.08821i
$951$		0			0
$952$	−15.0000	+	43.3013i	−0.486153	+	1.40340i
$953$		−	58.1378i		−	1.88327i	−0.336640	−	0.941634i	$-0.609290\pi$
$953$		−	58.1378i		−	1.88327i	0.336640	−	0.941634i	$-0.390710\pi$
$954$		0			0
$955$		0			0
$956$	−23.2379	+	13.4164i	−0.751567	+	0.433918i
$957$		0			0
$958$		0			0
$959$	3.87298	−	11.1803i	0.125065	−	0.361032i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$	9.68246	+	16.7705i	0.312175	+	0.540703i
$963$		0			0
$964$	40.5000	+	23.3827i	1.30442	+	0.753106i
$965$		0			0
$966$		0			0
$967$	−25.0000			−0.803946			−0.401973	−	0.915652i	$-0.631675\pi$
$967$	−25.0000			−0.803946			−0.401973	+	0.915652i	$0.631675\pi$
$968$	−17.4284	−	10.0623i	−0.560171	−	0.323415i
$969$		0			0
$970$		0			0
$971$	30.9839	−	53.6656i	0.994320	−	1.72221i	0.404984	−	0.914324i	$-0.367277\pi$
$971$	30.9839	−	53.6656i	0.994320	−	1.72221i	0.589336	−	0.807888i	$-0.299390\pi$
$972$		0			0
$973$	15.0000	+	17.3205i	0.480878	+	0.555270i
$974$		−	89.4427i		−	2.86593i
$975$		0			0
$976$	7.50000	−	4.33013i	0.240069	−	0.138604i
$977$	−50.3488	+	29.0689i	−1.61080	+	0.929996i	−0.621615	+	0.783323i	$0.713523\pi$
$977$	−50.3488	+	29.0689i	−1.61080	+	0.929996i	−0.989185	+	0.146673i	$0.953143\pi$
$978$		0			0
$979$			69.2820i			2.21426i
$980$		0			0
$981$		0			0
$982$	25.0000	−	43.3013i	0.797782	−	1.38180i
$983$	23.2379	+	40.2492i	0.741174	+	1.28375i	0.951961	+	0.306219i	$0.0990639\pi$
$983$	23.2379	+	40.2492i	0.741174	+	1.28375i	−0.210787	+	0.977532i	$0.567603\pi$
$984$		0			0
$985$		0			0
$986$	−77.4597			−2.46682
$987$		0			0
$988$	18.0000			0.572656
$989$	−27.1109	−	15.6525i	−0.862076	−	0.497720i
$990$		0			0
$991$	24.5000	+	42.4352i	0.778268	+	1.34800i	0.932939	+	0.360034i	$0.117235\pi$
$991$	24.5000	+	42.4352i	0.778268	+	1.34800i	−0.154671	+	0.987966i	$0.549432\pi$
$992$	5.80948	−	10.0623i	0.184451	−	0.319479i
$993$		0			0
$994$	10.0000	+	51.9615i	0.317181	+	1.64812i
$995$		0			0
$996$		0			0
$997$	−40.5000	+	23.3827i	−1.28265	+	0.740537i	−0.977332	−	0.211714i	$-0.932095\pi$
$997$	−40.5000	+	23.3827i	−1.28265	+	0.740537i	−0.305316	+	0.952251i	$0.598762\pi$
$998$	−60.0312	+	34.6591i	−1.90026	+	1.09711i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.p.c.26.1	✓	4
3.2	odd	2	inner	189.2.p.c.26.2	yes	4
7.2	even	3		1323.2.c.b.1322.4		4
7.3	odd	6	inner	189.2.p.c.80.2	yes	4
7.5	odd	6		1323.2.c.b.1322.3		4
9.2	odd	6		567.2.i.c.215.1		4
9.4	even	3		567.2.s.e.26.2		4
9.5	odd	6		567.2.s.e.26.1		4
9.7	even	3		567.2.i.c.215.2		4
21.2	odd	6		1323.2.c.b.1322.2		4
21.5	even	6		1323.2.c.b.1322.1		4
21.17	even	6	inner	189.2.p.c.80.1	yes	4
63.31	odd	6		567.2.i.c.269.2		4
63.38	even	6		567.2.s.e.458.2		4
63.52	odd	6		567.2.s.e.458.1		4
63.59	even	6		567.2.i.c.269.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.c.26.1	✓	4	1.1	even	1	trivial
189.2.p.c.26.2	yes	4	3.2	odd	2	inner
189.2.p.c.80.1	yes	4	21.17	even	6	inner
189.2.p.c.80.2	yes	4	7.3	odd	6	inner
567.2.i.c.215.1		4	9.2	odd	6
567.2.i.c.215.2		4	9.7	even	3
567.2.i.c.269.1		4	63.59	even	6
567.2.i.c.269.2		4	63.31	odd	6
567.2.s.e.26.1		4	9.5	odd	6
567.2.s.e.26.2		4	9.4	even	3
567.2.s.e.458.1		4	63.52	odd	6
567.2.s.e.458.2		4	63.38	even	6
1323.2.c.b.1322.1		4	21.5	even	6
1323.2.c.b.1322.2		4	21.2	odd	6
1323.2.c.b.1322.3		4	7.5	odd	6
1323.2.c.b.1322.4		4	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93649 - 1.11803i) q^{2} +(1.50000 + 2.59808i) q^{4} +(-2.00000 + 1.73205i) q^{7} -2.23607i q^{8} +(-3.87298 + 2.23607i) q^{11} +1.73205i q^{13} +(5.80948 - 1.11803i) q^{14} +(0.500000 - 0.866025i) q^{16} +(3.87298 + 6.70820i) q^{17} +(-3.00000 - 1.73205i) q^{19} +10.0000 q^{22} +(3.87298 + 2.23607i) q^{23} +(2.50000 + 4.33013i) q^{25} +(1.93649 - 3.35410i) q^{26} +(-7.50000 - 2.59808i) q^{28} -4.47214i q^{29} +(-1.50000 + 0.866025i) q^{31} +(-5.80948 + 3.35410i) q^{32} -17.3205i q^{34} +(-2.50000 + 4.33013i) q^{37} +(3.87298 + 6.70820i) q^{38} -7.74597 q^{41} -7.00000 q^{43} +(-11.6190 - 6.70820i) q^{44} +(-5.00000 - 8.66025i) q^{46} +(3.87298 - 6.70820i) q^{47} +(1.00000 - 6.92820i) q^{49} -11.1803i q^{50} +(-4.50000 + 2.59808i) q^{52} +(-3.87298 + 2.23607i) q^{53} +(3.87298 + 4.47214i) q^{56} +(-5.00000 + 8.66025i) q^{58} +(-3.87298 - 6.70820i) q^{59} +(7.50000 + 4.33013i) q^{61} +3.87298 q^{62} +13.0000 q^{64} +(0.500000 + 0.866025i) q^{67} +(-11.6190 + 20.1246i) q^{68} +8.94427i q^{71} +(6.00000 - 3.46410i) q^{73} +(9.68246 - 5.59017i) q^{74} -10.3923i q^{76} +(3.87298 - 11.1803i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(15.0000 + 8.66025i) q^{82} +7.74597 q^{83} +(13.5554 + 7.82624i) q^{86} +(5.00000 + 8.66025i) q^{88} +(7.74597 - 13.4164i) q^{89} +(-3.00000 - 3.46410i) q^{91} +13.4164i q^{92} +(-15.0000 + 8.66025i) q^{94} -1.73205i q^{97} +(-9.68246 + 12.2984i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{4} - 8 q^{7} + 2 q^{16} - 12 q^{19} + 40 q^{22} + 10 q^{25} - 30 q^{28} - 6 q^{31} - 10 q^{37} - 28 q^{43} - 20 q^{46} + 4 q^{49} - 18 q^{52} - 20 q^{58} + 30 q^{61} + 52 q^{64} + 2 q^{67} + 24 q^{73}+ \cdots - 60 q^{94}+O(q^{100}) \) 4 * q + 6 * q^4 - 8 * q^7 + 2 * q^16 - 12 * q^19 + 40 * q^22 + 10 * q^25 - 30 * q^28 - 6 * q^31 - 10 * q^37 - 28 * q^43 - 20 * q^46 + 4 * q^49 - 18 * q^52 - 20 * q^58 + 30 * q^61 + 52 * q^64 + 2 * q^67 + 24 * q^73 - 22 * q^79 + 60 * q^82 + 20 * q^88 - 12 * q^91 - 60 * q^94

Introduction

L-functions

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