LMFDB - Embedded newform 567.2.s.e.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(26,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("567.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.s (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:	$4.52751779461$
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:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.2
Root			$1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	567.26
Dual form			567.2.s.e.458.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93649 - 1.11803i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-0.500000 - 2.59808i) q^{7} -2.23607i q^{8} +O(q^{10})$	\(q+(1.93649 - 1.11803i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-0.500000 - 2.59808i) q^{7} -2.23607i q^{8} -4.47214i q^{11} +(1.50000 - 0.866025i) q^{13} +(-3.87298 - 4.47214i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.87298 + 6.70820i) q^{17} +(-3.00000 - 1.73205i) q^{19} +(-5.00000 - 8.66025i) q^{22} -4.47214i q^{23} -5.00000 q^{25} +(1.93649 - 3.35410i) q^{26} +(-7.50000 - 2.59808i) q^{28} +(3.87298 + 2.23607i) q^{29} +(1.50000 + 0.866025i) q^{31} +(5.80948 + 3.35410i) q^{32} +(15.0000 + 8.66025i) q^{34} +(-2.50000 + 4.33013i) q^{37} -7.74597 q^{38} +(3.87298 + 6.70820i) q^{41} +(3.50000 - 6.06218i) q^{43} +(-11.6190 - 6.70820i) q^{44} +(-5.00000 - 8.66025i) q^{46} +(3.87298 + 6.70820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-9.68246 + 5.59017i) q^{50} -5.19615i q^{52} +(-3.87298 + 2.23607i) q^{53} +(-5.80948 + 1.11803i) q^{56} +10.0000 q^{58} +(-3.87298 + 6.70820i) q^{59} +(-7.50000 + 4.33013i) q^{61} +3.87298 q^{62} +13.0000 q^{64} +(0.500000 - 0.866025i) q^{67} +23.2379 q^{68} +8.94427i q^{71} +(6.00000 - 3.46410i) q^{73} +11.1803i q^{74} +(-9.00000 + 5.19615i) q^{76} +(-11.6190 + 2.23607i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(15.0000 + 8.66025i) q^{82} +(-3.87298 + 6.70820i) q^{83} -15.6525i q^{86} -10.0000 q^{88} +(7.74597 - 13.4164i) q^{89} +(-3.00000 - 3.46410i) q^{91} +(-11.6190 - 6.70820i) q^{92} +(15.0000 + 8.66025i) q^{94} +(1.50000 + 0.866025i) q^{97} +(-9.68246 + 12.2984i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{4} - 2 q^{7}+O(q^{10}) $ 4 * q + 6 * q^4 - 2 * q^7	$ 4 q + 6 q^{4} - 2 q^{7} + 6 q^{13} + 2 q^{16} - 12 q^{19} - 20 q^{22} - 20 q^{25} - 30 q^{28} + 6 q^{31} + 60 q^{34} - 10 q^{37} + 14 q^{43} - 20 q^{46} - 26 q^{49} + 40 q^{58} - 30 q^{61} + 52 q^{64} + 2 q^{67} + 24 q^{73} - 36 q^{76} - 22 q^{79} + 60 q^{82} - 40 q^{88} - 12 q^{91} + 60 q^{94} + 6 q^{97}+O(q^{100}) $ 4 * q + 6 * q^4 - 2 * q^7 + 6 * q^13 + 2 * q^16 - 12 * q^19 - 20 * q^22 - 20 * q^25 - 30 * q^28 + 6 * q^31 + 60 * q^34 - 10 * q^37 + 14 * q^43 - 20 * q^46 - 26 * q^49 + 40 * q^58 - 30 * q^61 + 52 * q^64 + 2 * q^67 + 24 * q^73 - 36 * q^76 - 22 * q^79 + 60 * q^82 - 40 * q^88 - 12 * q^91 + 60 * q^94 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.93649	−	1.11803i	1.36931	−	0.790569i	0.378467	−	0.925615i	$-0.376451\pi$
$2$	1.93649	−	1.11803i	1.36931	−	0.790569i	0.990839	+	0.135045i	$0.0431180\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	−	2.59808i	0.750000	−	1.29904i
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$		−	2.23607i		−	0.790569i
$9$		0			0
$10$		0			0
$11$		−	4.47214i		−	1.34840i	−0.738549	−	0.674200i	$-0.764489\pi$
$11$		−	4.47214i		−	1.34840i	0.738549	−	0.674200i	$-0.235511\pi$
$12$		0			0
$13$	1.50000	−	0.866025i	0.416025	−	0.240192i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	1.50000	−	0.866025i	0.416025	−	0.240192i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−3.87298	−	4.47214i	−1.03510	−	1.19523i
$15$		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
$22$	−5.00000	−	8.66025i	−1.06600	−	1.84637i
$23$		−	4.47214i		−	0.932505i	−0.884652	−	0.466252i	$-0.845604\pi$
$23$		−	4.47214i		−	0.932505i	0.884652	−	0.466252i	$-0.154396\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$	1.93649	−	3.35410i	0.379777	−	0.657794i
$27$		0			0
$28$	−7.50000	−	2.59808i	−1.41737	−	0.490990i
$29$	3.87298	+	2.23607i	0.719195	+	0.415227i	0.814456	−	0.580225i	$-0.197035\pi$
$29$	3.87298	+	2.23607i	0.719195	+	0.415227i	−0.0952614	+	0.995452i	$0.530369\pi$
$30$		0			0
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	5.80948	+	3.35410i	1.02698	+	0.592927i
$33$		0			0
$34$	15.0000	+	8.66025i	2.57248	+	1.48522i
$35$		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	$0.301486\pi$
$38$	−7.74597			−1.25656
$39$		0			0
$40$		0			0
$41$	3.87298	+	6.70820i	0.604858	+	1.04765i	0.992074	+	0.125656i	$0.0401036\pi$
$41$	3.87298	+	6.70820i	0.604858	+	1.04765i	−0.387215	+	0.921989i	$0.626563\pi$
$42$		0			0
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	−0.465478	−	0.885059i	$-0.654118\pi$
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	0.999223	−	0.0394140i	$-0.0125491\pi$
$44$	−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	0.997056	+	0.0766776i	$0.0244312\pi$
$47$	3.87298	+	6.70820i	0.564933	+	0.978492i	−0.432123	+	0.901815i	$0.642235\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−9.68246	+	5.59017i	−1.36931	+	0.790569i
$51$		0			0
$52$		−	5.19615i		−	0.720577i
$53$	−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
$56$	−5.80948	+	1.11803i	−0.776324	+	0.149404i
$57$		0			0
$58$	10.0000			1.31306
$59$	−3.87298	+	6.70820i	−0.504219	+	0.873334i	0.495769	+	0.868455i	$0.334886\pi$
$59$	−3.87298	+	6.70820i	−0.504219	+	0.873334i	−0.999988	+	0.00487911i	$0.998447\pi$
$60$		0			0
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−7.50000	+	4.33013i	−0.960277	+	0.554416i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	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	−0.833866	−	0.551967i	$-0.813877\pi$
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	0.894951	+	0.446165i	$0.147211\pi$
$68$	23.2379			2.81801
$69$		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	$0.200451\pi$
$74$			11.1803i			1.29969i
$75$		0			0
$76$	−9.00000	+	5.19615i	−1.03237	+	0.596040i
$77$	−11.6190	+	2.23607i	−1.32410	+	0.254824i
$78$		0			0
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$		0			0
$81$		0			0
$82$	15.0000	+	8.66025i	1.65647	+	0.956365i
$83$	−3.87298	+	6.70820i	−0.425115	+	0.736321i	−0.996431	−	0.0844091i	$-0.973100\pi$
$83$	−3.87298	+	6.70820i	−0.425115	+	0.736321i	0.571316	+	0.820730i	$0.306433\pi$
$84$		0			0
$85$		0			0
$86$		−	15.6525i		−	1.68785i
$87$		0			0
$88$	−10.0000			−1.06600
$89$	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
$92$	−11.6190	−	6.70820i	−1.21136	−	0.699379i
$93$		0			0
$94$	15.0000	+	8.66025i	1.54713	+	0.893237i
$95$		0			0
$96$		0			0
$97$	1.50000	+	0.866025i	0.152302	+	0.0879316i	0.574214	−	0.818705i	$-0.305308\pi$
$97$	1.50000	+	0.866025i	0.152302	+	0.0879316i	−0.421912	+	0.906637i	$0.638641\pi$
$98$	−9.68246	+	12.2984i	−0.978076	+	1.24232i
$99$		0			0
$100$	−7.50000	+	12.9904i	−0.750000	+	1.29904i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$			5.19615i			0.511992i	0.966678	+	0.255996i	$0.0824034\pi$
$103$			5.19615i			0.511992i	−0.966678	+	0.255996i	$0.917597\pi$
$104$	−1.93649	−	3.35410i	−0.189889	−	0.328897i
$105$		0			0
$106$	−5.00000	+	8.66025i	−0.485643	+	0.841158i
$107$	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
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	7.74597	−	4.47214i	0.728679	−	0.420703i	−0.0892596	−	0.996008i	$-0.528450\pi$
$113$	7.74597	−	4.47214i	0.728679	−	0.420703i	0.817939	+	0.575305i	$0.195117\pi$
$114$		0			0
$115$		0			0
$116$	11.6190	−	6.70820i	1.07879	−	0.622841i
$117$		0			0
$118$			17.3205i			1.59448i
$119$	15.4919	−	13.4164i	1.42014	−	1.22988i
$120$		0			0
$121$	−9.00000			−0.818182
$122$	−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			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−3.00000	+	8.66025i	−0.260133	+	0.750939i
$134$		−	2.23607i		−	0.193167i
$135$		0			0
$136$	15.0000	−	8.66025i	1.28624	−	0.742611i
$137$		−	4.47214i		−	0.382080i	−0.981582	−	0.191040i	$-0.938814\pi$
$137$		−	4.47214i		−	0.382080i	0.981582	−	0.191040i	$-0.0611861\pi$
$138$		0			0
$139$	−7.50000	+	4.33013i	−0.636142	+	0.367277i	−0.783127	−	0.621862i	$-0.786376\pi$
$139$	−7.50000	+	4.33013i	−0.636142	+	0.367277i	0.146985	+	0.989139i	$0.453043\pi$
$140$		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
$146$	7.74597	−	13.4164i	0.641061	−	1.11035i
$147$		0			0
$148$	7.50000	+	12.9904i	0.616496	+	1.06780i
$149$		−	17.8885i		−	1.46549i	−0.680505	−	0.732743i	$-0.738240\pi$
$149$		−	17.8885i		−	1.46549i	0.680505	−	0.732743i	$-0.261760\pi$
$150$		0			0
$151$	−13.0000			−1.05792			−0.528962	−	0.848645i	$-0.677419\pi$
$151$	−13.0000			−1.05792			−0.528962	+	0.848645i	$0.677419\pi$
$152$	−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	$-0.519824\pi$
$157$	−12.0000	−	6.92820i	−0.957704	−	0.552931i	−0.895466	+	0.445130i	$0.853157\pi$
$158$	−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	$-0.00336213\pi$
$164$	23.2379			1.81458
$165$		0			0
$166$			17.3205i			1.34433i
$167$	3.87298	+	6.70820i	0.299700	+	0.519096i	0.976067	−	0.217468i	$-0.0697799\pi$
$167$	3.87298	+	6.70820i	0.299700	+	0.519096i	−0.676367	+	0.736565i	$0.736447\pi$
$168$		0			0
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$		0			0
$171$		0			0
$172$	−10.5000	−	18.1865i	−0.800617	−	1.38671i
$173$	−7.74597	−	13.4164i	−0.588915	−	1.02003i	−0.994375	−	0.105918i	$-0.966222\pi$
$173$	−7.74597	−	13.4164i	−0.588915	−	1.02003i	0.405460	−	0.914113i	$-0.367111\pi$
$174$		0			0
$175$	2.50000	+	12.9904i	0.188982	+	0.981981i
$176$	3.87298	−	2.23607i	0.291937	−	0.168550i
$177$		0			0
$178$		−	34.6410i		−	2.59645i
$179$	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			$\pi$
$182$	−9.68246	−	3.35410i	−0.717712	−	0.248623i
$183$		0			0
$184$	−10.0000			−0.737210
$185$		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	$-0.890720\pi$
$191$	−15.4919	+	8.94427i	−1.12096	+	0.647185i	−0.179312	+	0.983792i	$0.557387\pi$
$192$		0			0
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$	3.87298			0.278064
$195$		0			0
$196$	−3.00000	+	20.7846i	−0.214286	+	1.48461i
$197$			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	$0.0391815\pi$
$200$			11.1803i			0.790569i
$201$		0			0
$202$		0			0
$203$	3.87298	−	11.1803i	0.271830	−	0.784706i
$204$		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
$209$	−7.74597	+	13.4164i	−0.535800	+	0.928032i
$210$		0			0
$211$	9.50000	+	16.4545i	0.654007	+	1.13277i	0.982142	+	0.188142i	$0.0602466\pi$
$211$	9.50000	+	16.4545i	0.654007	+	1.13277i	−0.328135	+	0.944631i	$0.606420\pi$
$212$			13.4164i			0.921443i
$213$		0			0
$214$	10.0000			0.683586
$215$		0			0
$216$		0			0
$217$	1.50000	−	4.33013i	0.101827	−	0.293948i
$218$	1.93649	+	1.11803i	0.131156	+	0.0757228i
$219$		0			0
$220$		0			0
$221$	11.6190	+	6.70820i	0.781575	+	0.451243i
$222$		0			0
$223$	−21.0000	−	12.1244i	−1.40626	−	0.811907i	−0.411239	−	0.911528i	$-0.634904\pi$
$223$	−21.0000	−	12.1244i	−1.40626	−	0.811907i	−0.995025	+	0.0996209i	$0.968237\pi$
$224$	5.80948	−	16.7705i	0.388162	−	1.12053i
$225$		0			0
$226$	10.0000	−	17.3205i	0.665190	−	1.15214i
$227$	−23.2379			−1.54235			−0.771177	−	0.636621i	$-0.780332\pi$
$227$	−23.2379			−1.54235			−0.771177	+	0.636621i	$0.780332\pi$
$228$		0			0
$229$		−	25.9808i		−	1.71686i	−0.512933	−	0.858429i	$-0.671441\pi$
$229$		−	25.9808i		−	1.71686i	0.512933	−	0.858429i	$-0.328559\pi$
$230$		0			0
$231$		0			0
$232$	5.00000	−	8.66025i	0.328266	−	0.568574i
$233$	−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
$238$	15.0000	−	43.3013i	0.972306	−	2.80680i
$239$	7.74597	−	4.47214i	0.501045	−	0.289278i	−0.228100	−	0.973638i	$-0.573251\pi$
$239$	7.74597	−	4.47214i	0.501045	−	0.289278i	0.729145	+	0.684359i	$0.239918\pi$
$240$		0			0
$241$			15.5885i			1.00414i	0.864827	+	0.502070i	$0.167428\pi$
$241$			15.5885i			1.00414i	−0.864827	+	0.502070i	$0.832572\pi$
$242$	−17.4284	+	10.0623i	−1.12034	+	0.646830i
$243$		0			0
$244$			25.9808i			1.66325i
$245$		0			0
$246$		0			0
$247$	−6.00000			−0.381771
$248$	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
$257$	−23.2379			−1.44954			−0.724770	−	0.688991i	$-0.758054\pi$
$257$	−23.2379			−1.44954			−0.724770	+	0.688991i	$0.758054\pi$
$258$		0			0
$259$	12.5000	+	4.33013i	0.776712	+	0.269061i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	4.47214i		−	0.275764i	−0.990449	−	0.137882i	$-0.955971\pi$
$263$		−	4.47214i		−	0.275764i	0.990449	−	0.137882i	$-0.0440294\pi$
$264$		0			0
$265$		0			0
$266$	3.87298	+	20.1246i	0.237468	+	1.23392i
$267$		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	$0.649914\pi$
$272$	−3.87298	+	6.70820i	−0.234834	+	0.406745i
$273$		0			0
$274$	−5.00000	−	8.66025i	−0.302061	−	0.523185i
$275$			22.3607i			1.34840i
$276$		0			0
$277$	5.00000			0.300421			0.150210	−	0.988654i	$-0.452005\pi$
$277$	5.00000			0.300421			0.150210	+	0.988654i	$0.452005\pi$
$278$	−9.68246	+	16.7705i	−0.580715	+	1.00583i
$279$		0			0
$280$		0			0
$281$	15.4919	+	8.94427i	0.924171	+	0.533571i	0.884963	−	0.465661i	$-0.154183\pi$
$281$	15.4919	+	8.94427i	0.924171	+	0.533571i	0.0392078	+	0.999231i	$0.487517\pi$
$282$		0			0
$283$	10.5000	+	6.06218i	0.624160	+	0.360359i	0.778487	−	0.627661i	$-0.215988\pi$
$283$	10.5000	+	6.06218i	0.624160	+	0.360359i	−0.154327	+	0.988020i	$0.549321\pi$
$284$	23.2379	+	13.4164i	1.37892	+	0.796117i
$285$		0			0
$286$	−15.0000	−	8.66025i	−0.886969	−	0.512092i
$287$	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
$292$		−	20.7846i		−	1.21633i
$293$	3.87298	+	6.70820i	0.226262	+	0.391897i	0.956697	−	0.291084i	$-0.0940161\pi$
$293$	3.87298	+	6.70820i	0.226262	+	0.391897i	−0.730435	+	0.682982i	$0.760683\pi$
$294$		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
$301$	−17.5000	−	6.06218i	−1.00868	−	0.349418i
$302$	−25.1744	+	14.5344i	−1.44862	+	0.836363i
$303$		0			0
$304$		−	3.46410i		−	0.198680i
$305$		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	$-0.0473737\pi$
$308$	−11.6190	+	33.5410i	−0.662051	+	1.91118i
$309$		0			0
$310$		0			0
$311$	7.74597	−	13.4164i	0.439233	−	0.760775i	−0.558397	−	0.829574i	$-0.688583\pi$
$311$	7.74597	−	13.4164i	0.439233	−	0.760775i	0.997631	+	0.0687991i	$0.0219168\pi$
$312$		0			0
$313$	−12.0000	+	6.92820i	−0.678280	+	0.391605i	−0.799207	−	0.601056i	$-0.794747\pi$
$313$	−12.0000	+	6.92820i	−0.678280	+	0.391605i	0.120927	+	0.992661i	$0.461413\pi$
$314$	−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	$-0.706749\pi$
$317$	−3.87298	+	2.23607i	−0.217528	+	0.125590i	0.387277	+	0.921963i	$0.373416\pi$
$318$		0			0
$319$	10.0000	−	17.3205i	0.559893	−	0.969762i
$320$		0			0
$321$		0			0
$322$	−20.0000	+	17.3205i	−1.11456	+	0.965234i
$323$		−	26.8328i		−	1.49302i
$324$		0			0
$325$	−7.50000	+	4.33013i	−0.416025	+	0.240192i
$326$		−	29.0689i		−	1.60998i
$327$		0			0
$328$	15.0000	−	8.66025i	0.828236	−	0.478183i
$329$	15.4919	−	13.4164i	0.854098	−	0.739671i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	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
$337$	5.00000	+	8.66025i	0.272367	+	0.471754i	0.969468	−	0.245220i	$-0.0788601\pi$
$337$	5.00000	+	8.66025i	0.272367	+	0.471754i	−0.697100	+	0.716974i	$0.745527\pi$
$338$			22.3607i			1.21626i
$339$		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
$344$	−13.5554	−	7.82624i	−0.730860	−	0.421962i
$345$		0			0
$346$	−30.0000	−	17.3205i	−1.61281	−	0.931156i
$347$	−7.74597	−	4.47214i	−0.415825	−	0.240077i	0.277464	−	0.960736i	$-0.410506\pi$
$347$	−7.74597	−	4.47214i	−0.415825	−	0.240077i	−0.693290	+	0.720659i	$0.743839\pi$
$348$		0			0
$349$	19.5000	+	11.2583i	1.04381	+	0.602645i	0.920910	−	0.389774i	$-0.127447\pi$
$349$	19.5000	+	11.2583i	1.04381	+	0.602645i	0.122901	+	0.992419i	$0.460780\pi$
$350$	19.3649	+	22.3607i	1.03510	+	1.19523i
$351$		0			0
$352$	15.0000	−	25.9808i	0.799503	−	1.38478i
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$		0			0
$355$		0			0
$356$	−23.2379	−	40.2492i	−1.23161	−	2.13320i
$357$		0			0
$358$	10.0000	−	17.3205i	0.528516	−	0.915417i
$359$	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
$364$	−13.5000	+	2.59808i	−0.707592	+	0.136176i
$365$		0			0
$366$		0			0
$367$		−	10.3923i		−	0.542474i	−0.962513	−	0.271237i	$-0.912567\pi$
$367$		−	10.3923i		−	0.542474i	0.962513	−	0.271237i	$-0.0874327\pi$
$368$	3.87298	−	2.23607i	0.201893	−	0.116563i
$369$		0			0
$370$		0			0
$371$	7.74597	+	8.94427i	0.402151	+	0.464363i
$372$		0			0
$373$	2.00000			0.103556			0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000			0.103556			0.0517780	+	0.998659i	$0.483511\pi$
$374$	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
$383$	−23.2379			−1.18740			−0.593701	−	0.804686i	$-0.702334\pi$
$383$	−23.2379			−1.18740			−0.593701	+	0.804686i	$0.702334\pi$
$384$		0			0
$385$		0			0
$386$		−	15.6525i		−	0.796690i
$387$		0			0
$388$	4.50000	−	2.59808i	0.228453	−	0.131897i
$389$			8.94427i			0.453493i	0.973954	+	0.226746i	$0.0728088\pi$
$389$			8.94427i			0.453493i	−0.973954	+	0.226746i	$0.927191\pi$
$390$		0			0
$391$	30.0000	−	17.3205i	1.51717	−	0.875936i
$392$	5.80948	+	14.5344i	0.293423	+	0.734100i
$393$		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	$0.931320\pi$
$398$	25.1744	−	43.6033i	1.26188	−	2.18564i
$399$		0			0
$400$	−2.50000	−	4.33013i	−0.125000	−	0.216506i
$401$			22.3607i			1.11664i	0.829626	+	0.558320i	$0.188554\pi$
$401$			22.3607i			1.11664i	−0.829626	+	0.558320i	$0.811446\pi$
$402$		0			0
$403$	3.00000			0.149441
$404$		0			0
$405$		0			0
$406$	−5.00000	−	25.9808i	−0.248146	−	1.28940i
$407$	19.3649	+	11.1803i	0.959883	+	0.554189i
$408$		0			0
$409$	19.5000	+	11.2583i	0.964213	+	0.556689i	0.897467	−	0.441081i	$-0.145405\pi$
$409$	19.5000	+	11.2583i	0.964213	+	0.556689i	0.0667458	+	0.997770i	$0.478738\pi$
$410$		0			0
$411$		0			0
$412$	13.5000	+	7.79423i	0.665097	+	0.383994i
$413$	19.3649	+	6.70820i	0.952885	+	0.330089i
$414$		0			0
$415$		0			0
$416$	11.6190			0.569666
$417$		0			0
$418$			34.6410i			1.69435i
$419$	−7.74597	−	13.4164i	−0.378415	−	0.655434i	0.612417	−	0.790535i	$-0.290198\pi$
$419$	−7.74597	−	13.4164i	−0.378415	−	0.655434i	−0.990832	+	0.135101i	$0.956864\pi$
$420$		0			0
$421$	17.0000	−	29.4449i	0.828529	−	1.43505i	−0.0706626	−	0.997500i	$-0.522511\pi$
$421$	17.0000	−	29.4449i	0.828529	−	1.43505i	0.899192	−	0.437555i	$-0.144155\pi$
$422$	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
$427$	15.0000	+	17.3205i	0.725901	+	0.838198i
$428$	11.6190	−	6.70820i	0.561623	−	0.324253i
$429$		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	$0.877791\pi$
$434$	−1.93649	−	10.0623i	−0.0929546	−	0.483006i
$435$		0			0
$436$	3.00000			0.143674
$437$	−7.74597	+	13.4164i	−0.370540	+	0.641794i
$438$		0			0
$439$	−3.00000	+	1.73205i	−0.143182	+	0.0826663i	−0.569880	−	0.821728i	$-0.693010\pi$
$439$	−3.00000	+	1.73205i	−0.143182	+	0.0826663i	0.426698	+	0.904394i	$0.359677\pi$
$440$		0			0
$441$		0			0
$442$	30.0000			1.42695
$443$	30.9839	−	17.8885i	1.47209	−	0.849910i	0.472580	−	0.881288i	$-0.343323\pi$
$443$	30.9839	−	17.8885i	1.47209	−	0.849910i	0.999508	+	0.0313772i	$0.00998932\pi$
$444$		0			0
$445$		0			0
$446$	−54.2218			−2.56748
$447$		0			0
$448$	−6.50000	−	33.7750i	−0.307096	−	1.59572i
$449$			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
$452$		−	26.8328i		−	1.26211i
$453$		0			0
$454$	−45.0000	+	25.9808i	−2.11195	+	1.21934i
$455$		0			0
$456$		0			0
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	0.708233	−	0.705979i	$-0.249493\pi$
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	−0.965512	+	0.260358i	$0.916159\pi$
$458$	−29.0474	−	50.3115i	−1.35729	−	2.35090i
$459$		0			0
$460$		0			0
$461$	−3.87298	+	6.70820i	−0.180383	+	0.312432i	−0.942011	−	0.335582i	$-0.891067\pi$
$461$	−3.87298	+	6.70820i	−0.180383	+	0.312432i	0.761628	+	0.648014i	$0.224400\pi$
$462$		0			0
$463$	−4.00000	−	6.92820i	−0.185896	−	0.321981i	0.757982	−	0.652275i	$-0.226185\pi$
$463$	−4.00000	−	6.92820i	−0.185896	−	0.321981i	−0.943878	+	0.330294i	$0.892852\pi$
$464$			4.47214i			0.207614i
$465$		0			0
$466$	−20.0000			−0.926482
$467$	−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
$475$	15.0000	+	8.66025i	0.688247	+	0.397360i
$476$	−11.6190	−	60.3738i	−0.532554	−	2.76723i
$477$		0			0
$478$	10.0000	−	17.3205i	0.457389	−	0.792222i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$			8.66025i			0.394874i
$482$	17.4284	+	30.1869i	0.793843	+	1.37498i
$483$		0			0
$484$	−13.5000	+	23.3827i	−0.613636	+	1.06285i
$485$		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
$491$	19.3649	−	11.1803i	0.873926	−	0.504562i	0.00527540	−	0.999986i	$-0.498321\pi$
$491$	19.3649	−	11.1803i	0.873926	−	0.504562i	0.868651	+	0.495424i	$0.164987\pi$
$492$		0			0
$493$			34.6410i			1.56015i
$494$	−11.6190	+	6.70820i	−0.522761	+	0.301816i
$495$		0			0
$496$			1.73205i			0.0777714i
$497$	23.2379	−	4.47214i	1.04236	−	0.200603i
$498$		0			0
$499$	−31.0000			−1.38775			−0.693875	−	0.720095i	$-0.744098\pi$
$499$	−31.0000			−1.38775			−0.693875	+	0.720095i	$0.744098\pi$
$500$		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
$509$	23.2379			1.03000			0.515001	−	0.857190i	$-0.327792\pi$
$509$	23.2379			1.03000			0.515001	+	0.857190i	$0.327792\pi$
$510$		0			0
$511$	−12.0000	−	13.8564i	−0.530849	−	0.612971i
$512$			11.1803i			0.494106i
$513$		0			0
$514$	−45.0000	+	25.9808i	−1.98486	+	1.14596i
$515$		0			0
$516$		0			0
$517$	30.0000	−	17.3205i	1.31940	−	0.761755i
$518$	29.0474	−	5.59017i	1.27627	−	0.245618i
$519$		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
$526$	−5.00000	−	8.66025i	−0.218010	−	0.377605i
$527$			13.4164i			0.584428i
$528$		0			0
$529$	3.00000			0.130435
$530$		0			0
$531$		0			0
$532$	18.0000	+	20.7846i	0.780399	+	0.901127i
$533$	11.6190	+	6.70820i	0.503273	+	0.290565i
$534$		0			0
$535$		0			0
$536$	−1.93649	−	1.11803i	−0.0836437	−	0.0482917i
$537$		0			0
$538$	−30.0000	−	17.3205i	−1.29339	−	0.746740i
$539$	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	$0.263972\pi$
$542$	3.87298			0.166359
$543$		0			0
$544$			51.9615i			2.22783i
$545$		0			0
$546$		0			0
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	−0.959320	−	0.282321i	$-0.908896\pi$
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	0.724157	+	0.689635i	$0.242229\pi$
$548$	−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
$553$	−22.0000	+	19.0526i	−0.935535	+	0.810197i
$554$	9.68246	−	5.59017i	0.411368	−	0.237504i
$555$		0			0
$556$			25.9808i			1.10183i
$557$	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
$562$	40.0000			1.68730
$563$	−3.87298	+	6.70820i	−0.163227	+	0.282717i	−0.936024	−	0.351936i	$-0.885524\pi$
$563$	−3.87298	+	6.70820i	−0.163227	+	0.282717i	0.772797	+	0.634653i	$0.218857\pi$
$564$		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	$-0.789011\pi$
$569$	−15.4919	+	8.94427i	−0.649456	+	0.374963i	0.138792	+	0.990322i	$0.455678\pi$
$570$		0			0
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	0.983444	+	0.181210i	$0.0580014\pi$
$572$	−23.2379			−0.971625
$573$		0			0
$574$	15.0000	−	43.3013i	0.626088	−	1.80736i
$575$			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	$0.644549\pi$
$578$			96.1509i			3.99935i
$579$		0			0
$580$		0			0
$581$	19.3649	+	6.70820i	0.803392	+	0.278303i
$582$		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
$587$	−15.4919	+	26.8328i	−0.639421	+	1.10751i	0.346140	+	0.938183i	$0.387492\pi$
$587$	−15.4919	+	26.8328i	−0.639421	+	1.10751i	−0.985560	+	0.169326i	$0.945841\pi$
$588$		0			0
$589$	−3.00000	−	5.19615i	−0.123613	−	0.214104i
$590$		0			0
$591$		0			0
$592$	−5.00000			−0.205499
$593$	−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
$596$	−46.4758	−	26.8328i	−1.90372	−	1.09911i
$597$		0			0
$598$	−15.0000	−	8.66025i	−0.613396	−	0.354144i
$599$	−7.74597	−	4.47214i	−0.316492	−	0.182727i	0.333336	−	0.942808i	$-0.391826\pi$
$599$	−7.74597	−	4.47214i	−0.316492	−	0.182727i	−0.649828	+	0.760082i	$0.725159\pi$
$600$		0			0
$601$	37.5000	+	21.6506i	1.52966	+	0.883148i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$	37.5000	+	21.6506i	1.52966	+	0.883148i	0.530281	+	0.847822i	$0.322086\pi$
$602$	−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
$607$		−	31.1769i		−	1.26543i	−0.774384	−	0.632716i	$-0.781940\pi$
$607$		−	31.1769i		−	1.26543i	0.774384	−	0.632716i	$-0.218060\pi$
$608$	−11.6190	−	20.1246i	−0.471211	−	0.816161i
$609$		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
$616$	5.00000	+	25.9808i	0.201456	+	1.04679i
$617$	19.3649	−	11.1803i	0.779602	−	0.450104i	−0.0566871	−	0.998392i	$-0.518054\pi$
$617$	19.3649	−	11.1803i	0.779602	−	0.450104i	0.836289	+	0.548288i	$0.184720\pi$
$618$		0			0
$619$			5.19615i			0.208851i	0.994533	+	0.104425i	$0.0333004\pi$
$619$			5.19615i			0.208851i	−0.994533	+	0.104425i	$0.966700\pi$
$620$		0			0
$621$		0			0
$622$		−	34.6410i		−	1.38898i
$623$	−38.7298	−	13.4164i	−1.55168	−	0.537517i
$624$		0			0
$625$	25.0000			1.00000
$626$	−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
$637$	−7.50000	+	9.52628i	−0.297161	+	0.377445i
$638$		−	44.7214i		−	1.77054i
$639$		0			0
$640$		0			0
$641$		−	4.47214i		−	0.176639i	−0.996092	−	0.0883194i	$-0.971850\pi$
$641$		−	4.47214i		−	0.176639i	0.996092	−	0.0883194i	$-0.0281496\pi$
$642$		0			0
$643$	−16.5000	+	9.52628i	−0.650696	+	0.375680i	−0.788723	−	0.614749i	$-0.789257\pi$
$643$	−16.5000	+	9.52628i	−0.650696	+	0.375680i	0.138027	+	0.990429i	$0.455924\pi$
$644$	−11.6190	+	33.5410i	−0.457851	+	1.32170i
$645$		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
$650$	−9.68246	+	16.7705i	−0.379777	+	0.657794i
$651$		0			0
$652$	−19.5000	−	33.7750i	−0.763679	−	1.32273i
$653$			22.3607i			0.875041i	0.899208	+	0.437521i	$0.144143\pi$
$653$			22.3607i			0.875041i	−0.899208	+	0.437521i	$0.855857\pi$
$654$		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
$659$	15.4919	+	8.94427i	0.603480	+	0.348419i	0.770409	−	0.637549i	$-0.220052\pi$
$659$	15.4919	+	8.94427i	0.603480	+	0.348419i	−0.166929	+	0.985969i	$0.553385\pi$
$660$		0			0
$661$	24.0000	+	13.8564i	0.933492	+	0.538952i	0.887914	−	0.460009i	$-0.152154\pi$
$661$	24.0000	+	13.8564i	0.933492	+	0.538952i	0.0455776	+	0.998961i	$0.485487\pi$
$662$	7.74597	+	4.47214i	0.301056	+	0.173814i
$663$		0			0
$664$	15.0000	+	8.66025i	0.582113	+	0.336083i
$665$		0			0
$666$		0			0
$667$	10.0000	−	17.3205i	0.387202	−	0.670653i
$668$	23.2379			0.899101
$669$		0			0
$670$		0			0
$671$	19.3649	+	33.5410i	0.747574	+	1.29484i
$672$		0			0
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	−0.884655	−	0.466246i	$-0.845606\pi$
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	0.846108	+	0.533011i	$0.178940\pi$
$674$	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	0.993490	+	0.113921i	$0.0363411\pi$
$677$	15.4919	+	26.8328i	0.595403	+	1.03127i	−0.398086	+	0.917348i	$0.630326\pi$
$678$		0			0
$679$	1.50000	−	4.33013i	0.0575647	−	0.166175i
$680$		0			0
$681$		0			0
$682$		−	17.3205i		−	0.663237i
$683$	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
$686$	36.7933	+	19.0066i	1.40478	+	0.725675i
$687$		0			0
$688$	7.00000			0.266872
$689$	−3.87298	+	6.70820i	−0.147549	+	0.255562i
$690$		0			0
$691$	28.5000	−	16.4545i	1.08419	−	0.625958i	0.152167	−	0.988355i	$-0.451375\pi$
$691$	28.5000	−	16.4545i	1.08419	−	0.625958i	0.932024	+	0.362397i	$0.118041\pi$
$692$	−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
$698$	50.3488			1.90573
$699$		0			0
$700$	37.5000	+	12.9904i	1.41737	+	0.490990i
$701$			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
$704$		−	58.1378i		−	2.19115i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	0.744071	−	0.668101i	$-0.232892\pi$
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	−0.950628	+	0.310334i	$0.899559\pi$
$710$		0			0
$711$		0			0
$712$	−30.0000	−	17.3205i	−1.12430	−	0.649113i
$713$	3.87298	−	6.70820i	0.145044	−	0.251224i
$714$		0			0
$715$		0			0
$716$		−	26.8328i		−	1.00279i
$717$		0			0
$718$	10.0000			0.373197
$719$	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
$722$	−13.5554	−	7.82624i	−0.504481	−	0.291262i
$723$		0			0
$724$		0			0
$725$	−19.3649	−	11.1803i	−0.719195	−	0.415227i
$726$		0			0
$727$	−16.5000	−	9.52628i	−0.611951	−	0.353310i	0.161778	−	0.986827i	$-0.448277\pi$
$727$	−16.5000	−	9.52628i	−0.611951	−	0.353310i	−0.773729	+	0.633517i	$0.781611\pi$
$728$	−7.74597	+	6.70820i	−0.287085	+	0.248623i
$729$		0			0
$730$		0			0
$731$	54.2218			2.00546
$732$		0			0
$733$		−	36.3731i		−	1.34347i	−0.740792	−	0.671735i	$-0.765549\pi$
$733$		−	36.3731i		−	1.34347i	0.740792	−	0.671735i	$-0.234451\pi$
$734$	−11.6190	−	20.1246i	−0.428863	−	0.742813i
$735$		0			0
$736$	15.0000	−	25.9808i	0.552907	−	0.957664i
$737$	−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
$742$	25.0000	+	8.66025i	0.917779	+	0.317928i
$743$	−27.1109	+	15.6525i	−0.994602	+	0.574234i	−0.906647	−	0.421891i	$-0.861367\pi$
$743$	−27.1109	+	15.6525i	−0.994602	+	0.574234i	−0.0879552	+	0.996124i	$0.528033\pi$
$744$		0			0
$745$		0			0
$746$	3.87298	−	2.23607i	0.141800	−	0.0818683i
$747$		0			0
$748$		−	103.923i		−	3.79980i
$749$	3.87298	−	11.1803i	0.141516	−	0.408521i
$750$		0			0
$751$	−16.0000			−0.583848			−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000			−0.583848			−0.291924	+	0.956441i	$0.594295\pi$
$752$	−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			−	1.00000i	$-0.5\pi$
$761$		0			0				1.00000i	$0.5\pi$
$762$		0			0
$763$	2.00000	−	1.73205i	0.0724049	−	0.0627044i
$764$			53.6656i			1.94155i
$765$		0			0
$766$	−45.0000	+	25.9808i	−1.62592	+	0.938723i
$767$			13.4164i			0.484438i
$768$		0			0
$769$	−30.0000	+	17.3205i	−1.08183	+	0.624593i	−0.931389	−	0.364026i	$-0.881402\pi$
$769$	−30.0000	+	17.3205i	−1.08183	+	0.624593i	−0.150439	+	0.988619i	$0.548069\pi$
$770$		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
$776$	1.93649	−	3.35410i	0.0695160	−	0.120405i
$777$		0			0
$778$	10.0000	+	17.3205i	0.358517	+	0.620970i
$779$		−	26.8328i		−	0.961385i
$780$		0			0
$781$	40.0000			1.43131
$782$	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	$-0.443617\pi$
$787$	−16.5000	−	9.52628i	−0.588161	−	0.339575i	−0.764370	+	0.644778i	$0.776950\pi$
$788$	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
$794$	−65.8407			−2.33660
$795$		0			0
$796$		−	67.5500i		−	2.39425i
$797$	−19.3649	−	33.5410i	−0.685941	−	1.18808i	−0.973140	−	0.230213i	$-0.926058\pi$
$797$	−19.3649	−	33.5410i	−0.685941	−	1.18808i	0.287200	−	0.957871i	$-0.407276\pi$
$798$		0			0
$799$	−30.0000	+	51.9615i	−1.06132	+	1.83827i
$800$	−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
$806$	5.80948	−	3.35410i	0.204630	−	0.118143i
$807$		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	$-0.0584065\pi$
$812$	−23.2379	−	26.8328i	−0.815490	−	0.941647i
$813$		0			0
$814$	50.0000			1.75250
$815$		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	$-0.539074\pi$
$821$	19.3649	−	11.1803i	0.675840	−	0.390197i	0.798286	+	0.602279i	$0.205740\pi$
$822$		0			0
$823$	21.5000	−	37.2391i	0.749443	−	1.29807i	−0.198647	−	0.980071i	$-0.563655\pi$
$823$	21.5000	−	37.2391i	0.749443	−	1.29807i	0.948090	−	0.318002i	$-0.103012\pi$
$824$	11.6190			0.404765
$825$		0			0
$826$	45.0000	−	8.66025i	1.56575	−	0.301329i
$827$			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
$832$	19.5000	−	11.2583i	0.676041	−	0.390312i
$833$	−42.6028	−	33.5410i	−1.47610	−	1.16213i
$834$		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
$839$	−3.87298	+	6.70820i	−0.133710	+	0.231593i	−0.925104	−	0.379714i	$-0.876022\pi$
$839$	−3.87298	+	6.70820i	−0.133710	+	0.231593i	0.791394	+	0.611307i	$0.209356\pi$
$840$		0			0
$841$	−4.50000	−	7.79423i	−0.155172	−	0.268767i
$842$		−	76.0263i		−	2.62004i
$843$		0			0
$844$	57.0000			1.96202
$845$		0			0
$846$		0			0
$847$	4.50000	+	23.3827i	0.154622	+	0.803439i
$848$	−3.87298	−	2.23607i	−0.132999	−	0.0767869i
$849$		0			0
$850$	−75.0000	−	43.3013i	−2.57248	−	1.48522i
$851$	19.3649	+	11.1803i	0.663821	+	0.383257i
$852$		0			0
$853$	−12.0000	−	6.92820i	−0.410872	−	0.237217i	0.280292	−	0.959915i	$-0.409569\pi$
$853$	−12.0000	−	6.92820i	−0.410872	−	0.237217i	−0.691164	+	0.722698i	$0.742902\pi$
$854$	48.4123	+	16.7705i	1.65663	+	0.573875i
$855$		0			0
$856$	5.00000	−	8.66025i	0.170896	−	0.296001i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$		−	5.19615i		−	0.177290i	−0.996063	−	0.0886452i	$-0.971746\pi$
$859$		−	5.19615i		−	0.177290i	0.996063	−	0.0886452i	$-0.0282537\pi$
$860$		0			0
$861$		0			0
$862$	−35.0000	+	60.6218i	−1.19210	+	2.06479i
$863$	−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
$868$	−9.00000	−	10.3923i	−0.305480	−	0.352738i
$869$	−42.6028	+	24.5967i	−1.44520	+	0.834388i
$870$		0			0
$871$		−	1.73205i		−	0.0586883i
$872$	1.93649	−	1.11803i	0.0655779	−	0.0378614i
$873$		0			0
$874$			34.6410i			1.17175i
$875$		0			0
$876$		0			0
$877$	−25.0000			−0.844190			−0.422095	−	0.906552i	$-0.638705\pi$
$877$	−25.0000			−0.844190			−0.422095	+	0.906552i	$0.638705\pi$
$878$	−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
$887$	23.2379			0.780252			0.390126	−	0.920761i	$-0.372431\pi$
$887$	23.2379			0.780252			0.390126	+	0.920761i	$0.372431\pi$
$888$		0			0
$889$	0.500000	+	2.59808i	0.0167695	+	0.0871367i
$890$		0			0
$891$		0			0
$892$	−63.0000	+	36.3731i	−2.10940	+	1.21786i
$893$		−	26.8328i		−	0.897926i
$894$		0			0
$895$		0			0
$896$	−27.1109	−	31.3050i	−0.905711	−	1.04583i
$897$		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
$902$	38.7298	−	67.0820i	1.28956	−	2.23359i
$903$		0			0
$904$	−10.0000	−	17.3205i	−0.332595	−	0.576072i
$905$		0			0
$906$		0			0
$907$	5.00000			0.166022			0.0830111	−	0.996549i	$-0.473546\pi$
$907$	5.00000			0.166022			0.0830111	+	0.996549i	$0.473546\pi$
$908$	−34.8569	+	60.3738i	−1.15677	+	2.00358i
$909$		0			0
$910$		0			0
$911$	3.87298	+	2.23607i	0.128318	+	0.0740842i	0.562785	−	0.826603i	$-0.309730\pi$
$911$	3.87298	+	2.23607i	0.128318	+	0.0740842i	−0.434467	+	0.900688i	$0.643063\pi$
$912$		0			0
$913$	30.0000	+	17.3205i	0.992855	+	0.573225i
$914$	−21.3014	−	12.2984i	−0.704588	−	0.406794i
$915$		0			0
$916$	−67.5000	−	38.9711i	−2.23026	−	1.28764i
$917$		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
$922$			17.3205i			0.570421i
$923$	7.74597	+	13.4164i	0.254962	+	0.441606i
$924$		0			0
$925$	12.5000	−	21.6506i	0.410997	−	0.711868i
$926$	−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	0.999954	+	0.00958031i	$0.00304955\pi$
$929$	15.4919	+	26.8328i	0.508274	+	0.880356i	−0.491680	+	0.870776i	$0.663617\pi$
$930$		0			0
$931$	24.0000	+	3.46410i	0.786568	+	0.113531i
$932$	−23.2379	+	13.4164i	−0.761183	+	0.439469i
$933$		0			0
$934$			69.2820i			2.26698i
$935$		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	$-0.276708\pi$
$938$	−5.80948	+	1.11803i	−0.189686	+	0.0365051i
$939$		0			0
$940$		0			0
$941$	19.3649	−	33.5410i	0.631278	−	1.09341i	−0.356012	−	0.934481i	$-0.615864\pi$
$941$	19.3649	−	33.5410i	0.631278	−	1.09341i	0.987291	−	0.158925i	$-0.0508027\pi$
$942$		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	$-0.689816\pi$
$947$	−3.87298	+	2.23607i	−0.125855	+	0.0726624i	0.435751	+	0.900067i	$0.356483\pi$
$948$		0			0
$949$	6.00000	−	10.3923i	0.194768	−	0.337348i
$950$	38.7298			1.25656
$951$		0			0
$952$	−30.0000	−	34.6410i	−0.972306	−	1.12272i
$953$		−	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
$956$		−	26.8328i		−	0.867835i
$957$		0			0
$958$		0			0
$959$	−11.6190	+	2.23607i	−0.375195	+	0.0722064i
$960$		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
$967$	12.5000	+	21.6506i	0.401973	+	0.696237i	0.993964	−	0.109707i	$-0.0349913\pi$
$967$	12.5000	+	21.6506i	0.401973	+	0.696237i	−0.591991	+	0.805945i	$0.701658\pi$
$968$			20.1246i			0.646830i
$969$		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
$974$	77.4597	+	44.7214i	2.48197	+	1.43296i
$975$		0			0
$976$	−7.50000	−	4.33013i	−0.240069	−	0.138604i
$977$	50.3488	+	29.0689i	1.61080	+	0.929996i	0.989185	+	0.146673i	$0.0468566\pi$
$977$	50.3488	+	29.0689i	1.61080	+	0.929996i	0.621615	+	0.783323i	$0.286477\pi$
$978$		0			0
$979$	−60.0000	−	34.6410i	−1.91761	−	1.10713i
$980$		0			0
$981$		0			0
$982$	25.0000	−	43.3013i	0.797782	−	1.38180i
$983$	−46.4758			−1.48235			−0.741174	−	0.671313i	$-0.765731\pi$
$983$	−46.4758			−1.48235			−0.741174	+	0.671313i	$0.765731\pi$
$984$		0			0
$985$		0			0
$986$	38.7298	+	67.0820i	1.23341	+	2.13633i
$987$		0			0
$988$	−9.00000	+	15.5885i	−0.286328	+	0.495935i
$989$	−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
$994$	40.0000	−	34.6410i	1.26872	−	1.09875i
$995$		0			0
$996$		0			0
$997$		−	46.7654i		−	1.48107i	−0.672015	−	0.740537i	$-0.734571\pi$
$997$		−	46.7654i		−	1.48107i	0.672015	−	0.740537i	$-0.265429\pi$
$998$	−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	567.2.s.e.26.2		4
3.2	odd	2	inner	567.2.s.e.26.1		4
7.3	odd	6		567.2.i.c.269.2		4
9.2	odd	6		189.2.p.c.26.2	yes	4
9.4	even	3		567.2.i.c.215.2		4
9.5	odd	6		567.2.i.c.215.1		4
9.7	even	3		189.2.p.c.26.1	✓	4
21.17	even	6		567.2.i.c.269.1		4
63.2	odd	6		1323.2.c.b.1322.2		4
63.16	even	3		1323.2.c.b.1322.4		4
63.31	odd	6	inner	567.2.s.e.458.1		4
63.38	even	6		189.2.p.c.80.1	yes	4
63.47	even	6		1323.2.c.b.1322.1		4
63.52	odd	6		189.2.p.c.80.2	yes	4
63.59	even	6	inner	567.2.s.e.458.2		4
63.61	odd	6		1323.2.c.b.1322.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.c.26.1	✓	4	9.7	even	3
189.2.p.c.26.2	yes	4	9.2	odd	6
189.2.p.c.80.1	yes	4	63.38	even	6
189.2.p.c.80.2	yes	4	63.52	odd	6
567.2.i.c.215.1		4	9.5	odd	6
567.2.i.c.215.2		4	9.4	even	3
567.2.i.c.269.1		4	21.17	even	6
567.2.i.c.269.2		4	7.3	odd	6
567.2.s.e.26.1		4	3.2	odd	2	inner
567.2.s.e.26.2		4	1.1	even	1	trivial
567.2.s.e.458.1		4	63.31	odd	6	inner
567.2.s.e.458.2		4	63.59	even	6	inner
1323.2.c.b.1322.1		4	63.47	even	6
1323.2.c.b.1322.2		4	63.2	odd	6
1323.2.c.b.1322.3		4	63.61	odd	6
1323.2.c.b.1322.4		4	63.16	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.93649 - 1.11803i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-0.500000 - 2.59808i) q^{7} -2.23607i q^{8} +O(q^{10})\)	\(q+(1.93649 - 1.11803i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-0.500000 - 2.59808i) q^{7} -2.23607i q^{8} -4.47214i q^{11} +(1.50000 - 0.866025i) q^{13} +(-3.87298 - 4.47214i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.87298 + 6.70820i) q^{17} +(-3.00000 - 1.73205i) q^{19} +(-5.00000 - 8.66025i) q^{22} -4.47214i q^{23} -5.00000 q^{25} +(1.93649 - 3.35410i) q^{26} +(-7.50000 - 2.59808i) q^{28} +(3.87298 + 2.23607i) q^{29} +(1.50000 + 0.866025i) q^{31} +(5.80948 + 3.35410i) q^{32} +(15.0000 + 8.66025i) q^{34} +(-2.50000 + 4.33013i) q^{37} -7.74597 q^{38} +(3.87298 + 6.70820i) q^{41} +(3.50000 - 6.06218i) q^{43} +(-11.6190 - 6.70820i) q^{44} +(-5.00000 - 8.66025i) q^{46} +(3.87298 + 6.70820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-9.68246 + 5.59017i) q^{50} -5.19615i q^{52} +(-3.87298 + 2.23607i) q^{53} +(-5.80948 + 1.11803i) q^{56} +10.0000 q^{58} +(-3.87298 + 6.70820i) q^{59} +(-7.50000 + 4.33013i) q^{61} +3.87298 q^{62} +13.0000 q^{64} +(0.500000 - 0.866025i) q^{67} +23.2379 q^{68} +8.94427i q^{71} +(6.00000 - 3.46410i) q^{73} +11.1803i q^{74} +(-9.00000 + 5.19615i) q^{76} +(-11.6190 + 2.23607i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(15.0000 + 8.66025i) q^{82} +(-3.87298 + 6.70820i) q^{83} -15.6525i q^{86} -10.0000 q^{88} +(7.74597 - 13.4164i) q^{89} +(-3.00000 - 3.46410i) q^{91} +(-11.6190 - 6.70820i) q^{92} +(15.0000 + 8.66025i) q^{94} +(1.50000 + 0.866025i) q^{97} +(-9.68246 + 12.2984i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{4} - 2 q^{7}+O(q^{10}) \) 4 * q + 6 * q^4 - 2 * q^7	\( 4 q + 6 q^{4} - 2 q^{7} + 6 q^{13} + 2 q^{16} - 12 q^{19} - 20 q^{22} - 20 q^{25} - 30 q^{28} + 6 q^{31} + 60 q^{34} - 10 q^{37} + 14 q^{43} - 20 q^{46} - 26 q^{49} + 40 q^{58} - 30 q^{61} + 52 q^{64} + 2 q^{67} + 24 q^{73} - 36 q^{76} - 22 q^{79} + 60 q^{82} - 40 q^{88} - 12 q^{91} + 60 q^{94} + 6 q^{97}+O(q^{100}) \) 4 * q + 6 * q^4 - 2 * q^7 + 6 * q^13 + 2 * q^16 - 12 * q^19 - 20 * q^22 - 20 * q^25 - 30 * q^28 + 6 * q^31 + 60 * q^34 - 10 * q^37 + 14 * q^43 - 20 * q^46 - 26 * q^49 + 40 * q^58 - 30 * q^61 + 52 * q^64 + 2 * q^67 + 24 * q^73 - 36 * q^76 - 22 * q^79 + 60 * q^82 - 40 * q^88 - 12 * q^91 + 60 * q^94 + 6 * q^97

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