LMFDB - Embedded newform 1638.2.bj.i.127.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 $ x^16 - 2x^15 + 2x^14 + 18x^13 + 143x^12 - 148x^11 + 172x^10 + 1612x^9 + 6655x^8 + 478x^7 + 1106x^6 + 11266x^5 + 55249x^4 + 8856x^3 + 288x^2 + 7488*x + 97344
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.8
Root			$-1.41701 - 1.41701i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.i.1135.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.18381i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.18381i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(1.59191 + 2.75726i) q^{10} +(3.49326 - 2.01684i) q^{11} +(-0.333648 - 3.59008i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.23249 - 2.13473i) q^{17} +(0.595420 + 0.343766i) q^{19} +(2.75726 + 1.59191i) q^{20} +(2.01684 - 3.49326i) q^{22} +(2.89543 + 5.01503i) q^{23} -5.13667 q^{25} +(-2.08399 - 2.94228i) q^{26} +(0.866025 - 0.500000i) q^{28} +(0.940078 + 1.62826i) q^{29} +4.17543i q^{31} +(-0.866025 - 0.500000i) q^{32} -2.46497i q^{34} +(-1.59191 + 2.75726i) q^{35} +(-0.322768 + 0.186350i) q^{37} +0.687532 q^{38} +3.18381 q^{40} +(6.83868 - 3.94832i) q^{41} +(2.48320 - 4.30103i) q^{43} -4.03367i q^{44} +(5.01503 + 2.89543i) q^{46} +11.8723i q^{47} +(0.500000 + 0.866025i) q^{49} +(-4.44848 + 2.56833i) q^{50} +(-3.27592 - 1.50609i) q^{52} +9.59637 q^{53} +(6.42123 + 11.1219i) q^{55} +(0.500000 - 0.866025i) q^{56} +(1.62826 + 0.940078i) q^{58} +(2.23154 + 1.28838i) q^{59} +(-6.79497 + 11.7692i) q^{61} +(2.08771 + 3.61603i) q^{62} -1.00000 q^{64} +(11.4301 - 1.06227i) q^{65} +(7.46491 - 4.30987i) q^{67} +(-1.23249 - 2.13473i) q^{68} +3.18381i q^{70} +(-9.08320 - 5.24419i) q^{71} +16.5347i q^{73} +(-0.186350 + 0.322768i) q^{74} +(0.595420 - 0.343766i) q^{76} +4.03367 q^{77} -13.2874 q^{79} +(2.75726 - 1.59191i) q^{80} +(3.94832 - 6.83868i) q^{82} -9.39302i q^{83} +(6.79658 + 3.92401i) q^{85} -4.96640i q^{86} +(-2.01684 - 3.49326i) q^{88} +(7.55214 - 4.36023i) q^{89} +(1.50609 - 3.27592i) q^{91} +5.79086 q^{92} +(5.93616 + 10.2817i) q^{94} +(-1.09449 + 1.89571i) q^{95} +(-5.32679 - 3.07542i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 2 q^{10} + 12 q^{11} + 10 q^{13} + 16 q^{14} - 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{23} - 20 q^{25} + 2 q^{26} - 16 q^{29} - 2 q^{35} - 6 q^{37} + 4 q^{40} - 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} + 24 q^{50} - 4 q^{52} + 40 q^{53} + 20 q^{55} + 8 q^{56} + 6 q^{58} - 6 q^{59} - 2 q^{61} + 14 q^{62} - 16 q^{64} + 52 q^{65} - 30 q^{67} - 6 q^{68} - 12 q^{71} - 24 q^{74} - 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} - 30 q^{89} + 4 q^{91} + 24 q^{92} - 8 q^{94} + 40 q^{95} - 24 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^10 + 12 * q^11 + 10 * q^13 + 16 * q^14 - 8 * q^16 + 6 * q^17 - 4 * q^22 + 12 * q^23 - 20 * q^25 + 2 * q^26 - 16 * q^29 - 2 * q^35 - 6 * q^37 + 4 * q^40 - 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 + 24 * q^50 - 4 * q^52 + 40 * q^53 + 20 * q^55 + 8 * q^56 + 6 * q^58 - 6 * q^59 - 2 * q^61 + 14 * q^62 - 16 * q^64 + 52 * q^65 - 30 * q^67 - 6 * q^68 - 12 * q^71 - 24 * q^74 - 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 - 30 * q^89 + 4 * q^91 + 24 * q^92 - 8 * q^94 + 40 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			3.18381i			1.42384i	0.702258	+	0.711922i	$0.252175\pi$
$5$			3.18381i			1.42384i	−0.702258	+	0.711922i	$0.747825\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.59191	+	2.75726i	0.503405	+	0.871923i
$11$	3.49326	−	2.01684i	1.05326	−	0.608099i	0.129698	−	0.991553i	$-0.458599\pi$
$11$	3.49326	−	2.01684i	1.05326	−	0.608099i	0.923560	+	0.383455i	$0.125266\pi$
$12$		0			0
$13$	−0.333648	−	3.59008i	−0.0925372	−	0.995709i
$13$	−0.333648	−	3.59008i	−0.0925372	−	0.995709i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.23249	−	2.13473i	0.298922	−	0.517748i	−0.676968	−	0.736013i	$-0.736706\pi$
$17$	1.23249	−	2.13473i	0.298922	−	0.517748i	0.975890	+	0.218265i	$0.0700397\pi$
$18$		0			0
$19$	0.595420	+	0.343766i	0.136599	+	0.0788653i	0.566742	−	0.823895i	$-0.308204\pi$
$19$	0.595420	+	0.343766i	0.136599	+	0.0788653i	−0.430143	+	0.902761i	$0.641537\pi$
$20$	2.75726	+	1.59191i	0.616543	+	0.355961i
$21$		0			0
$22$	2.01684	−	3.49326i	0.429991	−	0.744766i
$23$	2.89543	+	5.01503i	0.603739	+	1.04571i	0.992249	+	0.124262i	$0.0396564\pi$
$23$	2.89543	+	5.01503i	0.603739	+	1.04571i	−0.388510	+	0.921444i	$0.627010\pi$
$24$		0			0
$25$	−5.13667			−1.02733
$26$	−2.08399	−	2.94228i	−0.408704	−	0.577028i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	0.940078	+	1.62826i	0.174568	+	0.302361i	0.940012	−	0.341142i	$-0.110814\pi$
$29$	0.940078	+	1.62826i	0.174568	+	0.302361i	−0.765444	+	0.643503i	$0.777480\pi$
$30$		0			0
$31$			4.17543i			0.749929i	0.927039	+	0.374964i	$0.122345\pi$
$31$			4.17543i			0.749929i	−0.927039	+	0.374964i	$0.877655\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	2.46497i		−	0.422739i
$35$	−1.59191	+	2.75726i	−0.269081	+	0.466063i
$36$		0			0
$37$	−0.322768	+	0.186350i	−0.0530628	+	0.0306358i	−0.526297	−	0.850301i	$-0.676420\pi$
$37$	−0.322768	+	0.186350i	−0.0530628	+	0.0306358i	0.473234	+	0.880937i	$0.343087\pi$
$38$	0.687532			0.111532
$39$		0			0
$40$	3.18381			0.503405
$41$	6.83868	−	3.94832i	1.06802	−	0.616623i	0.140382	−	0.990097i	$-0.455167\pi$
$41$	6.83868	−	3.94832i	1.06802	−	0.616623i	0.927641	+	0.373474i	$0.121834\pi$
$42$		0			0
$43$	2.48320	−	4.30103i	0.378684	−	0.655900i	−0.612187	−	0.790713i	$-0.709710\pi$
$43$	2.48320	−	4.30103i	0.378684	−	0.655900i	0.990871	+	0.134813i	$0.0430433\pi$
$44$		−	4.03367i		−	0.608099i
$45$		0			0
$46$	5.01503	+	2.89543i	0.739426	+	0.426908i
$47$			11.8723i			1.73176i	0.500254	+	0.865879i	$0.333240\pi$
$47$			11.8723i			1.73176i	−0.500254	+	0.865879i	$0.666760\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−4.44848	+	2.56833i	−0.629111	+	0.363217i
$51$		0			0
$52$	−3.27592	−	1.50609i	−0.454289	−	0.208858i
$53$	9.59637			1.31816			0.659081	−	0.752072i	$-0.270945\pi$
$53$	9.59637			1.31816			0.659081	+	0.752072i	$0.270945\pi$
$54$		0			0
$55$	6.42123	+	11.1219i	0.865838	+	1.49968i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	1.62826	+	0.940078i	0.213801	+	0.123438i
$59$	2.23154	+	1.28838i	0.290522	+	0.167733i	0.638177	−	0.769889i	$-0.279689\pi$
$59$	2.23154	+	1.28838i	0.290522	+	0.167733i	−0.347655	+	0.937623i	$0.613022\pi$
$60$		0			0
$61$	−6.79497	+	11.7692i	−0.870006	+	1.50690i	−0.00801784	+	0.999968i	$0.502552\pi$
$61$	−6.79497	+	11.7692i	−0.870006	+	1.50690i	−0.861989	+	0.506928i	$0.830781\pi$
$62$	2.08771	+	3.61603i	0.265140	+	0.459236i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	11.4301	−	1.06227i	1.41774	−	0.131759i
$66$		0			0
$67$	7.46491	−	4.30987i	0.911984	−	0.526534i	0.0309151	−	0.999522i	$-0.490158\pi$
$67$	7.46491	−	4.30987i	0.911984	−	0.526534i	0.881069	+	0.472988i	$0.156825\pi$
$68$	−1.23249	−	2.13473i	−0.149461	−	0.258874i
$69$		0			0
$70$			3.18381i			0.380538i
$71$	−9.08320	−	5.24419i	−1.07798	−	0.622371i	−0.147627	−	0.989043i	$-0.547164\pi$
$71$	−9.08320	−	5.24419i	−1.07798	−	0.622371i	−0.930350	+	0.366672i	$0.880497\pi$
$72$		0			0
$73$			16.5347i			1.93524i	0.252406	+	0.967621i	$0.418778\pi$
$73$			16.5347i			1.93524i	−0.252406	+	0.967621i	$0.581222\pi$
$74$	−0.186350	+	0.322768i	−0.0216628	+	0.0375211i
$75$		0			0
$76$	0.595420	−	0.343766i	0.0682993	−	0.0394326i
$77$	4.03367			0.459680
$78$		0			0
$79$	−13.2874			−1.49495			−0.747477	−	0.664288i	$-0.768735\pi$
$79$	−13.2874			−1.49495			−0.747477	+	0.664288i	$0.768735\pi$
$80$	2.75726	−	1.59191i	0.308271	−	0.177981i
$81$		0			0
$82$	3.94832	−	6.83868i	0.436019	−	0.755206i
$83$		−	9.39302i		−	1.03102i	−0.856884	−	0.515509i	$-0.827603\pi$
$83$		−	9.39302i		−	1.03102i	0.856884	−	0.515509i	$-0.172397\pi$
$84$		0			0
$85$	6.79658	+	3.92401i	0.737192	+	0.425618i
$86$		−	4.96640i		−	0.535540i
$87$		0			0
$88$	−2.01684	−	3.49326i	−0.214995	−	0.372383i
$89$	7.55214	−	4.36023i	0.800525	−	0.462183i	−0.0431297	−	0.999069i	$-0.513733\pi$
$89$	7.55214	−	4.36023i	0.800525	−	0.462183i	0.843655	+	0.536886i	$0.180400\pi$
$90$		0			0
$91$	1.50609	−	3.27592i	0.157881	−	0.343410i
$92$	5.79086			0.603739
$93$		0			0
$94$	5.93616	+	10.2817i	0.612269	+	1.06048i
$95$	−1.09449	+	1.89571i	−0.112292	+	0.194495i
$96$		0			0
$97$	−5.32679	−	3.07542i	−0.540854	−	0.312262i	0.204571	−	0.978852i	$-0.434420\pi$
$97$	−5.32679	−	3.07542i	−0.540854	−	0.312262i	−0.745425	+	0.666590i	$0.767753\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$		0			0
$100$	−2.56833	+	4.44848i	−0.256833	+	0.444848i
$101$	3.54879	+	6.14668i	0.353117	+	0.611617i	0.986794	−	0.161981i	$-0.0517883\pi$
$101$	3.54879	+	6.14668i	0.353117	+	0.611617i	−0.633677	+	0.773598i	$0.718455\pi$
$102$		0			0
$103$	−8.44343			−0.831956			−0.415978	−	0.909375i	$-0.636561\pi$
$103$	−8.44343			−0.831956			−0.415978	+	0.909375i	$0.636561\pi$
$104$	−3.59008	+	0.333648i	−0.352036	+	0.0327168i
$105$		0			0
$106$	8.31070	−	4.79818i	0.807206	−	0.466041i
$107$	−5.42496	−	9.39631i	−0.524451	−	0.908376i	−0.999595	−	0.0284677i	$-0.990937\pi$
$107$	−5.42496	−	9.39631i	−0.524451	−	0.908376i	0.475144	−	0.879908i	$-0.342396\pi$
$108$		0			0
$109$		−	14.9645i		−	1.43334i	−0.697414	−	0.716669i	$-0.745666\pi$
$109$		−	14.9645i		−	1.43334i	0.697414	−	0.716669i	$-0.254334\pi$
$110$	11.1219	+	6.42123i	1.06043	+	0.612240i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	4.75100	−	8.22897i	0.446936	−	0.774117i	−0.551248	−	0.834341i	$-0.685848\pi$
$113$	4.75100	−	8.22897i	0.446936	−	0.774117i	0.998185	+	0.0602246i	$0.0191817\pi$
$114$		0			0
$115$	−15.9669	+	9.21851i	−1.48892	+	0.859630i
$116$	1.88016			0.174568
$117$		0			0
$118$	2.57677			0.237211
$119$	2.13473	−	1.23249i	0.195690	−	0.112982i
$120$		0			0
$121$	2.63525	−	4.56440i	0.239569	−	0.414945i
$122$			13.5899i			1.23037i
$123$		0			0
$124$	3.61603	+	2.08771i	0.324729	+	0.187482i
$125$		−	0.435119i		−	0.0389182i
$126$		0			0
$127$	−4.28578	−	7.42319i	−0.380302	−	0.658702i	0.610803	−	0.791782i	$-0.290847\pi$
$127$	−4.28578	−	7.42319i	−0.380302	−	0.658702i	−0.991105	+	0.133080i	$0.957513\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	9.36766	−	6.63503i	0.821598	−	0.581930i
$131$	9.45294			0.825907			0.412953	−	0.910752i	$-0.364497\pi$
$131$	9.45294			0.825907			0.412953	+	0.910752i	$0.364497\pi$
$132$		0			0
$133$	0.343766	+	0.595420i	0.0298083	+	0.0516295i
$134$	4.30987	−	7.46491i	0.372316	−	0.644870i
$135$		0			0
$136$	−2.13473	−	1.23249i	−0.183051	−	0.105685i
$137$	−6.77434	−	3.91117i	−0.578771	−	0.334153i	0.181874	−	0.983322i	$-0.441784\pi$
$137$	−6.77434	−	3.91117i	−0.578771	−	0.334153i	−0.760645	+	0.649168i	$0.775117\pi$
$138$		0			0
$139$	1.33554	−	2.31322i	0.113279	−	0.196205i	−0.803812	−	0.594884i	$-0.797198\pi$
$139$	1.33554	−	2.31322i	0.113279	−	0.196205i	0.917090	+	0.398679i	$0.130531\pi$
$140$	1.59191	+	2.75726i	0.134541	+	0.233031i
$141$		0			0
$142$	−10.4884			−0.880165
$143$	−8.40612	−	11.8682i	−0.702955	−	0.992467i
$144$		0			0
$145$	−5.18408	+	2.99303i	−0.430515	+	0.248558i
$146$	8.26736	+	14.3195i	0.684212	+	1.18509i
$147$		0			0
$148$			0.372701i			0.0306358i
$149$	3.71910	+	2.14722i	0.304680	+	0.175907i	0.644543	−	0.764568i	$-0.277047\pi$
$149$	3.71910	+	2.14722i	0.304680	+	0.175907i	−0.339863	+	0.940475i	$0.610381\pi$
$150$		0			0
$151$		−	23.9425i		−	1.94841i	−0.225656	−	0.974207i	$-0.572452\pi$
$151$		−	23.9425i		−	1.94841i	0.225656	−	0.974207i	$-0.427548\pi$
$152$	0.343766	−	0.595420i	0.0278831	−	0.0482949i
$153$		0			0
$154$	3.49326	−	2.01684i	0.281495	−	0.162521i
$155$	−13.2938			−1.06778
$156$		0			0
$157$	−21.1640			−1.68907			−0.844535	−	0.535501i	$-0.820123\pi$
$157$	−21.1640			−1.68907			−0.844535	+	0.535501i	$0.820123\pi$
$158$	−11.5073	+	6.64372i	−0.915469	+	0.528546i
$159$		0			0
$160$	1.59191	−	2.75726i	0.125851	−	0.217981i
$161$			5.79086i			0.456384i
$162$		0			0
$163$	2.97609	+	1.71825i	0.233105	+	0.134583i	0.612004	−	0.790855i	$-0.290364\pi$
$163$	2.97609	+	1.71825i	0.233105	+	0.134583i	−0.378898	+	0.925438i	$0.623697\pi$
$164$		−	7.89663i		−	0.616623i
$165$		0			0
$166$	−4.69651	−	8.13460i	−0.364520	−	0.631367i
$167$	1.29715	−	0.748912i	0.100377	−	0.0579526i	−0.448971	−	0.893546i	$-0.648209\pi$
$167$	1.29715	−	0.748912i	0.100377	−	0.0579526i	0.549348	+	0.835594i	$0.314876\pi$
$168$		0			0
$169$	−12.7774	+	2.39564i	−0.982874	+	0.184280i
$170$	7.84801			0.601915
$171$		0			0
$172$	−2.48320	−	4.30103i	−0.189342	−	0.327950i
$173$	−4.11216	+	7.12246i	−0.312641	+	0.541511i	−0.978933	−	0.204180i	$-0.934547\pi$
$173$	−4.11216	+	7.12246i	−0.312641	+	0.541511i	0.666292	+	0.745691i	$0.267880\pi$
$174$		0			0
$175$	−4.44848	−	2.56833i	−0.336274	−	0.194148i
$176$	−3.49326	−	2.01684i	−0.263315	−	0.152025i
$177$		0			0
$178$	4.36023	−	7.55214i	0.326813	−	0.566057i
$179$	4.56957	+	7.91473i	0.341546	+	0.591575i	0.984720	−	0.174145i	$-0.0557162\pi$
$179$	4.56957	+	7.91473i	0.341546	+	0.591575i	−0.643174	+	0.765720i	$0.722383\pi$
$180$		0			0
$181$	3.97003			0.295090			0.147545	−	0.989055i	$-0.452863\pi$
$181$	3.97003			0.295090			0.147545	+	0.989055i	$0.452863\pi$
$182$	−0.333648	−	3.59008i	−0.0247316	−	0.266114i
$183$		0			0
$184$	5.01503	−	2.89543i	0.369713	−	0.213454i
$185$	−0.593305	−	1.02763i	−0.0436206	−	0.0755532i
$186$		0			0
$187$		−	9.94289i		−	0.727096i
$188$	10.2817	+	5.93616i	0.749873	+	0.432939i
$189$		0			0
$190$			2.18897i			0.158805i
$191$	−7.22054	+	12.5063i	−0.522460	+	0.904927i	0.477198	+	0.878796i	$0.341652\pi$
$191$	−7.22054	+	12.5063i	−0.522460	+	0.904927i	−0.999659	+	0.0261318i	$0.991681\pi$
$192$		0			0
$193$	−3.55466	+	2.05228i	−0.255870	+	0.147727i	−0.622449	−	0.782660i	$-0.713862\pi$
$193$	−3.55466	+	2.05228i	−0.255870	+	0.147727i	0.366579	+	0.930387i	$0.380529\pi$
$194$	−6.15085			−0.441605
$195$		0			0
$196$	1.00000			0.0714286
$197$	−15.8433	+	9.14716i	−1.12879	+	0.651708i	−0.943631	−	0.331000i	$-0.892614\pi$
$197$	−15.8433	+	9.14716i	−1.12879	+	0.651708i	−0.185161	+	0.982708i	$0.559281\pi$
$198$		0			0
$199$	8.69290	−	15.0566i	0.616224	−	1.06733i	−0.373945	−	0.927451i	$-0.621995\pi$
$199$	8.69290	−	15.0566i	0.616224	−	1.06733i	0.990169	−	0.139880i	$-0.0446716\pi$
$200$			5.13667i			0.363217i
$201$		0			0
$202$	6.14668	+	3.54879i	0.432479	+	0.249692i
$203$			1.88016i			0.131961i
$204$		0			0
$205$	12.5707	+	21.7731i	0.877976	+	1.52070i
$206$	−7.31223	+	4.22172i	−0.509467	+	0.294141i
$207$		0			0
$208$	−2.94228	+	2.08399i	−0.204010	+	0.144499i
$209$	2.77328			0.191832
$210$		0			0
$211$	2.51818	+	4.36161i	0.173359	+	0.300266i	0.939592	−	0.342297i	$-0.111205\pi$
$211$	2.51818	+	4.36161i	0.173359	+	0.300266i	−0.766233	+	0.642562i	$0.777871\pi$
$212$	4.79818	−	8.31070i	0.329541	−	0.570781i
$213$		0			0
$214$	−9.39631	−	5.42496i	−0.642319	−	0.370843i
$215$	13.6937	+	7.90604i	0.933900	+	0.539187i
$216$		0			0
$217$	−2.08771	+	3.61603i	−0.141723	+	0.245472i
$218$	−7.48224	−	12.9596i	−0.506761	−	0.877736i
$219$		0			0
$220$	12.8425			0.865838
$221$	−8.07506	−	3.71248i	−0.543188	−	0.249728i
$222$		0			0
$223$	4.39565	−	2.53783i	0.294355	−	0.169946i	−0.345549	−	0.938401i	$-0.612307\pi$
$223$	4.39565	−	2.53783i	0.294355	−	0.169946i	0.639904	+	0.768455i	$0.278974\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$		−	9.50200i		−	0.632064i
$227$	−23.7848	−	13.7322i	−1.57865	−	0.911436i	−0.995048	−	0.0993983i	$-0.968308\pi$
$227$	−23.7848	−	13.7322i	−1.57865	−	0.911436i	−0.583605	−	0.812037i	$-0.698358\pi$
$228$		0			0
$229$		−	27.6832i		−	1.82936i	−0.404181	−	0.914679i	$-0.632443\pi$
$229$		−	27.6832i		−	1.82936i	0.404181	−	0.914679i	$-0.367557\pi$
$230$	−9.21851	+	15.9669i	−0.607850	+	1.05283i
$231$		0			0
$232$	1.62826	−	0.940078i	0.106901	−	0.0617191i
$233$	27.1843			1.78090			0.890451	−	0.455078i	$-0.150389\pi$
$233$	27.1843			1.78090			0.890451	+	0.455078i	$0.150389\pi$
$234$		0			0
$235$	−37.7993			−2.46575
$236$	2.23154	−	1.28838i	0.145261	−	0.0838666i
$237$		0			0
$238$	1.23249	−	2.13473i	0.0798902	−	0.138374i
$239$		−	3.65168i		−	0.236207i	−0.993001	−	0.118104i	$-0.962318\pi$
$239$		−	3.65168i		−	0.236207i	0.993001	−	0.118104i	$-0.0376815\pi$
$240$		0			0
$241$	−0.107048	−	0.0618044i	−0.00689559	−	0.00398117i	0.496548	−	0.868009i	$-0.334601\pi$
$241$	−0.107048	−	0.0618044i	−0.00689559	−	0.00398117i	−0.503444	+	0.864028i	$0.667934\pi$
$242$		−	5.27051i		−	0.338801i
$243$		0			0
$244$	6.79497	+	11.7692i	0.435003	+	0.753448i
$245$	−2.75726	+	1.59191i	−0.176155	+	0.101703i
$246$		0			0
$247$	1.03549	−	2.25230i	0.0658864	−	0.143311i
$248$	4.17543			0.265140
$249$		0			0
$250$	−0.217559	−	0.376824i	−0.0137597	−	0.0238324i
$251$	7.54462	−	13.0677i	0.476212	−	0.824824i	−0.523416	−	0.852077i	$-0.675343\pi$
$251$	7.54462	−	13.0677i	0.476212	−	0.824824i	0.999629	+	0.0272533i	$0.00867608\pi$
$252$		0			0
$253$	20.2290	+	11.6792i	1.27179	+	0.734266i
$254$	−7.42319	−	4.28578i	−0.465773	−	0.268914i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.94509	+	6.83309i	0.246088	+	0.426237i	0.962437	−	0.271506i	$-0.0875215\pi$
$257$	3.94509	+	6.83309i	0.246088	+	0.426237i	−0.716349	+	0.697742i	$0.754188\pi$
$258$		0			0
$259$	−0.372701			−0.0231585
$260$	4.79512	−	10.4299i	0.297381	−	0.646837i
$261$		0			0
$262$	8.18648	−	4.72647i	0.505763	−	0.292002i
$263$	−4.45634	−	7.71861i	−0.274790	−	0.475950i	0.695292	−	0.718727i	$-0.255275\pi$
$263$	−4.45634	−	7.71861i	−0.274790	−	0.475950i	−0.970082	+	0.242777i	$0.921942\pi$
$264$		0			0
$265$			30.5530i			1.87686i
$266$	0.595420	+	0.343766i	0.0365075	+	0.0210776i
$267$		0			0
$268$		−	8.61974i		−	0.526534i
$269$	−7.21199	+	12.4915i	−0.439723	+	0.761622i	−0.997668	−	0.0682557i	$-0.978257\pi$
$269$	−7.21199	+	12.4915i	−0.439723	+	0.761622i	0.557945	+	0.829878i	$0.311590\pi$
$270$		0			0
$271$	−16.2356	+	9.37361i	−0.986240	+	0.569406i	−0.904148	−	0.427219i	$-0.859493\pi$
$271$	−16.2356	+	9.37361i	−0.986240	+	0.569406i	−0.0820919	+	0.996625i	$0.526160\pi$
$272$	−2.46497			−0.149461
$273$		0			0
$274$	−7.82233			−0.472564
$275$	−17.9437	+	10.3598i	−1.08205	+	0.624720i
$276$		0			0
$277$	−9.70728	+	16.8135i	−0.583254	+	1.01023i	0.411836	+	0.911258i	$0.364887\pi$
$277$	−9.70728	+	16.8135i	−0.583254	+	1.01023i	−0.995091	+	0.0989680i	$0.968446\pi$
$278$		−	2.67107i		−	0.160200i
$279$		0			0
$280$	2.75726	+	1.59191i	0.164778	+	0.0951346i
$281$		−	19.4085i		−	1.15781i	−0.815394	−	0.578906i	$-0.803480\pi$
$281$		−	19.4085i		−	1.15781i	0.815394	−	0.578906i	$-0.196520\pi$
$282$		0			0
$283$	6.70552	+	11.6143i	0.398602	+	0.690398i	0.993554	−	0.113363i	$-0.0361622\pi$
$283$	6.70552	+	11.6143i	0.398602	+	0.690398i	−0.594952	+	0.803761i	$0.702829\pi$
$284$	−9.08320	+	5.24419i	−0.538989	+	0.311185i
$285$		0			0
$286$	−13.2140	−	6.07509i	−0.781361	−	0.359227i
$287$	7.89663			0.466123
$288$		0			0
$289$	5.46196	+	9.46039i	0.321292	+	0.556493i
$290$	−2.99303	+	5.18408i	−0.175757	+	0.304420i
$291$		0			0
$292$	14.3195	+	8.26736i	0.837985	+	0.483811i
$293$	2.01398	+	1.16277i	0.117658	+	0.0679299i	0.557674	−	0.830060i	$-0.311694\pi$
$293$	2.01398	+	1.16277i	0.117658	+	0.0679299i	−0.440016	+	0.897990i	$0.645027\pi$
$294$		0			0
$295$	−4.10197	+	7.10482i	−0.238826	+	0.413659i
$296$	0.186350	+	0.322768i	0.0108314	+	0.0187605i
$297$		0			0
$298$	4.29444			0.248770
$299$	17.0383	−	12.0681i	0.985351	−	0.697915i
$300$		0			0
$301$	4.30103	−	2.48320i	0.247907	−	0.143129i
$302$	−11.9713	−	20.7348i	−0.688868	−	1.19316i
$303$		0			0
$304$		−	0.687532i		−	0.0394326i
$305$	−37.4710	−	21.6339i	−2.14558	−	1.23875i
$306$		0			0
$307$			7.09575i			0.404976i	0.979285	+	0.202488i	$0.0649027\pi$
$307$			7.09575i			0.404976i	−0.979285	+	0.202488i	$0.935097\pi$
$308$	2.01684	−	3.49326i	0.114920	−	0.199047i
$309$		0			0
$310$	−11.5128	+	6.64689i	−0.653880	+	0.377518i
$311$	−12.0586			−0.683780			−0.341890	−	0.939740i	$-0.611067\pi$
$311$	−12.0586			−0.683780			−0.341890	+	0.939740i	$0.611067\pi$
$312$		0			0
$313$	−11.4098			−0.644921			−0.322461	−	0.946583i	$-0.604510\pi$
$313$	−11.4098			−0.644921			−0.322461	+	0.946583i	$0.604510\pi$
$314$	−18.3285	+	10.5820i	−1.03434	+	0.597176i
$315$		0			0
$316$	−6.64372	+	11.5073i	−0.373739	+	0.647334i
$317$			6.67694i			0.375014i	0.982263	+	0.187507i	$0.0600408\pi$
$317$			6.67694i			0.375014i	−0.982263	+	0.187507i	$0.939959\pi$
$318$		0			0
$319$	6.56788	+	3.79197i	0.367731	+	0.212309i
$320$		−	3.18381i		−	0.177981i
$321$		0			0
$322$	2.89543	+	5.01503i	0.161356	+	0.279477i
$323$	1.46769	−	0.847373i	0.0816646	−	0.0471491i
$324$		0			0
$325$	1.71384	+	18.4410i	0.0950665	+	1.02293i
$326$	3.43649			0.190330
$327$		0			0
$328$	−3.94832	−	6.83868i	−0.218009	−	0.377603i
$329$	−5.93616	+	10.2817i	−0.327271	+	0.566851i
$330$		0			0
$331$	−1.10741	−	0.639361i	−0.0608685	−	0.0351424i	0.469257	−	0.883062i	$-0.344522\pi$
$331$	−1.10741	−	0.639361i	−0.0608685	−	0.0351424i	−0.530125	+	0.847919i	$0.677855\pi$
$332$	−8.13460	−	4.69651i	−0.446444	−	0.257755i
$333$		0			0
$334$	0.748912	−	1.29715i	0.0409787	−	0.0709771i
$335$	13.7218	+	23.7669i	0.749703	+	1.29852i
$336$		0			0
$337$	−10.9634			−0.597214			−0.298607	−	0.954376i	$-0.596522\pi$
$337$	−10.9634			−0.597214			−0.298607	+	0.954376i	$0.596522\pi$
$338$	−9.86770	+	8.46337i	−0.536732	+	0.460347i
$339$		0			0
$340$	6.79658	−	3.92401i	0.368596	−	0.212809i
$341$	8.42115	+	14.5859i	0.456031	+	0.789869i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−4.30103	−	2.48320i	−0.231896	−	0.133885i
$345$		0			0
$346$			8.22431i			0.442142i
$347$	−12.1257	+	21.0023i	−0.650942	+	1.12746i	0.331953	+	0.943296i	$0.392293\pi$
$347$	−12.1257	+	21.0023i	−0.650942	+	1.12746i	−0.982895	+	0.184169i	$0.941041\pi$
$348$		0			0
$349$	−0.792668	+	0.457647i	−0.0424305	+	0.0244973i	−0.521065	−	0.853517i	$-0.674465\pi$
$349$	−0.792668	+	0.457647i	−0.0424305	+	0.0244973i	0.478635	+	0.878014i	$0.341132\pi$
$350$	−5.13667			−0.274566
$351$		0			0
$352$	−4.03367			−0.214995
$353$	−10.2702	+	5.92948i	−0.546625	+	0.315594i	−0.747760	−	0.663969i	$-0.768871\pi$
$353$	−10.2702	+	5.92948i	−0.546625	+	0.315594i	0.201134	+	0.979564i	$0.435537\pi$
$354$		0			0
$355$	16.6965	−	28.9192i	0.886159	−	1.53487i
$356$		−	8.72046i		−	0.462183i
$357$		0			0
$358$	7.91473	+	4.56957i	0.418306	+	0.241509i
$359$			6.14816i			0.324488i	0.986751	+	0.162244i	$0.0518731\pi$
$359$			6.14816i			0.324488i	−0.986751	+	0.162244i	$0.948127\pi$
$360$		0			0
$361$	−9.26365	−	16.0451i	−0.487561	−	0.844480i
$362$	3.43815	−	1.98502i	0.180705	−	0.104330i
$363$		0			0
$364$	−2.08399	−	2.94228i	−0.109231	−	0.154217i
$365$	−52.6435			−2.75549
$366$		0			0
$367$	−9.27627	−	16.0670i	−0.484217	−	0.838689i	0.515618	−	0.856818i	$-0.327562\pi$
$367$	−9.27627	−	16.0670i	−0.484217	−	0.838689i	−0.999836	+	0.0181296i	$0.994229\pi$
$368$	2.89543	−	5.01503i	0.150935	−	0.261427i
$369$		0			0
$370$	−1.02763	−	0.593305i	−0.0534242	−	0.0308445i
$371$	8.31070	+	4.79818i	0.431470	+	0.249109i
$372$		0			0
$373$	12.0745	−	20.9137i	0.625195	−	1.08287i	−0.363308	−	0.931669i	$-0.618353\pi$
$373$	12.0745	−	20.9137i	0.625195	−	1.08287i	0.988503	−	0.151201i	$-0.0483140\pi$
$374$	−4.97144	−	8.61079i	−0.257067	−	0.445254i
$375$		0			0
$376$	11.8723			0.612269
$377$	5.53194	−	3.91822i	0.284909	−	0.201799i
$378$		0			0
$379$	13.4253	−	7.75109i	0.689610	−	0.398147i	−0.113856	−	0.993497i	$-0.536320\pi$
$379$	13.4253	−	7.75109i	0.689610	−	0.398147i	0.803466	+	0.595351i	$0.202987\pi$
$380$	1.09449	+	1.89571i	0.0561460	+	0.0972477i
$381$		0			0
$382$			14.4411i			0.738870i
$383$	−4.10975	−	2.37277i	−0.209998	−	0.121243i	0.391312	−	0.920258i	$-0.372021\pi$
$383$	−4.10975	−	2.37277i	−0.209998	−	0.121243i	−0.601311	+	0.799015i	$0.705355\pi$
$384$		0			0
$385$			12.8425i			0.654512i
$386$	−2.05228	+	3.55466i	−0.104459	+	0.180927i
$387$		0			0
$388$	−5.32679	+	3.07542i	−0.270427	+	0.156131i
$389$	0.255450			0.0129519			0.00647593	−	0.999979i	$-0.497939\pi$
$389$	0.255450			0.0129519			0.00647593	+	0.999979i	$0.497939\pi$
$390$		0			0
$391$	14.2743			0.721883
$392$	0.866025	−	0.500000i	0.0437409	−	0.0252538i
$393$		0			0
$394$	−9.14716	+	15.8433i	−0.460827	+	0.798176i
$395$		−	42.3047i		−	2.12858i
$396$		0			0
$397$	5.10155	+	2.94538i	0.256040	+	0.147825i	0.622527	−	0.782599i	$-0.286106\pi$
$397$	5.10155	+	2.94538i	0.256040	+	0.147825i	−0.366487	+	0.930423i	$0.619440\pi$
$398$		−	17.3858i		−	0.871472i
$399$		0			0
$400$	2.56833	+	4.44848i	0.128417	+	0.222424i
$401$	−9.14301	+	5.27872i	−0.456580	+	0.263607i	−0.710605	−	0.703591i	$-0.751579\pi$
$401$	−9.14301	+	5.27872i	−0.456580	+	0.263607i	0.254025	+	0.967198i	$0.418245\pi$
$402$		0			0
$403$	14.9901	−	1.39312i	0.746711	−	0.0693963i
$404$	7.09757			0.353117
$405$		0			0
$406$	0.940078	+	1.62826i	0.0466553	+	0.0808093i
$407$	−0.751677	+	1.30194i	−0.0372592	+	0.0645349i
$408$		0			0
$409$	2.15730	+	1.24552i	0.106672	+	0.0615869i	0.552387	−	0.833588i	$-0.313717\pi$
$409$	2.15730	+	1.24552i	0.106672	+	0.0615869i	−0.445715	+	0.895175i	$0.647051\pi$
$410$	21.7731	+	12.5707i	1.07530	+	0.620823i
$411$		0			0
$412$	−4.22172	+	7.31223i	−0.207989	+	0.360248i
$413$	1.28838	+	2.23154i	0.0633972	+	0.109807i
$414$		0			0
$415$	29.9056			1.46801
$416$	−1.50609	+	3.27592i	−0.0738423	+	0.160615i
$417$		0			0
$418$	2.40173	−	1.38664i	0.117472	−	0.0678227i
$419$	8.30873	+	14.3911i	0.405908	+	0.703053i	0.994427	−	0.105430i	$-0.0336220\pi$
$419$	8.30873	+	14.3911i	0.405908	+	0.703053i	−0.588519	+	0.808484i	$0.700289\pi$
$420$		0			0
$421$			38.3927i			1.87114i	0.353137	+	0.935572i	$0.385115\pi$
$421$			38.3927i			1.87114i	−0.353137	+	0.935572i	$0.614885\pi$
$422$	4.36161	+	2.51818i	0.212320	+	0.122583i
$423$		0			0
$424$		−	9.59637i		−	0.466041i
$425$	−6.33087	+	10.9654i	−0.307092	+	0.531899i
$426$		0			0
$427$	−11.7692	+	6.79497i	−0.569553	+	0.328832i
$428$	−10.8499			−0.524451
$429$		0			0
$430$	15.8121			0.762526
$431$	21.5077	−	12.4175i	1.03599	−	0.598130i	0.117296	−	0.993097i	$-0.462577\pi$
$431$	21.5077	−	12.4175i	1.03599	−	0.598130i	0.918695	+	0.394967i	$0.129244\pi$
$432$		0			0
$433$	11.5166	−	19.9473i	0.553450	−	0.958604i	−0.444572	−	0.895743i	$-0.646644\pi$
$433$	11.5166	−	19.9473i	0.553450	−	0.958604i	0.998022	−	0.0628608i	$-0.0200224\pi$
$434$			4.17543i			0.200427i
$435$		0			0
$436$	−12.9596	−	7.48224i	−0.620653	−	0.358334i
$437$			3.98140i			0.190456i
$438$		0			0
$439$	1.05272	+	1.82337i	0.0502437	+	0.0870247i	0.890053	−	0.455856i	$-0.150667\pi$
$439$	1.05272	+	1.82337i	0.0502437	+	0.0870247i	−0.839810	+	0.542881i	$0.817334\pi$
$440$	11.1219	−	6.42123i	0.530216	−	0.306120i
$441$		0			0
$442$	−8.84945	+	0.822432i	−0.420925	+	0.0391191i
$443$	−36.8615			−1.75134			−0.875670	−	0.482910i	$-0.839580\pi$
$443$	−36.8615			−1.75134			−0.875670	+	0.482910i	$0.839580\pi$
$444$		0			0
$445$	13.8822	+	24.0446i	0.658077	+	1.13982i
$446$	2.53783	−	4.39565i	0.120170	−	0.208140i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	−27.0644	−	15.6257i	−1.27725	−	0.737421i	−0.300908	−	0.953653i	$-0.597290\pi$
$449$	−27.0644	−	15.6257i	−1.27725	−	0.737421i	−0.976342	+	0.216232i	$0.930623\pi$
$450$		0			0
$451$	15.9262	−	27.5850i	0.749936	−	1.29893i
$452$	−4.75100	−	8.22897i	−0.223468	−	0.387058i
$453$		0			0
$454$	−27.4643			−1.28896
$455$	10.4299	+	4.79512i	0.488963	+	0.224799i
$456$		0			0
$457$	9.93318	−	5.73492i	0.464654	−	0.268268i	−0.249345	−	0.968415i	$-0.580215\pi$
$457$	9.93318	−	5.73492i	0.464654	−	0.268268i	0.713999	+	0.700146i	$0.246882\pi$
$458$	−13.8416	−	23.9744i	−0.646776	−	1.12025i
$459$		0			0
$460$			18.4370i			0.859630i
$461$	−13.6364	−	7.87297i	−0.635110	−	0.366681i	0.147619	−	0.989044i	$-0.452839\pi$
$461$	−13.6364	−	7.87297i	−0.635110	−	0.366681i	−0.782728	+	0.622364i	$0.786173\pi$
$462$		0			0
$463$		−	18.5070i		−	0.860093i	−0.902807	−	0.430046i	$-0.858497\pi$
$463$		−	18.5070i		−	0.860093i	0.902807	−	0.430046i	$-0.141503\pi$
$464$	0.940078	−	1.62826i	0.0436420	−	0.0755902i
$465$		0			0
$466$	23.5423	−	13.5922i	1.09058	−	0.629644i
$467$	−11.7992			−0.546001			−0.273000	−	0.962014i	$-0.588016\pi$
$467$	−11.7992			−0.546001			−0.273000	+	0.962014i	$0.588016\pi$
$468$		0			0
$469$	8.61974			0.398023
$470$	−32.7351	+	18.8996i	−1.50996	+	0.871775i
$471$		0			0
$472$	1.28838	−	2.23154i	0.0593026	−	0.102715i
$473$		−	20.0328i		−	0.921110i
$474$		0			0
$475$	−3.05847	−	1.76581i	−0.140332	−	0.0810209i
$476$		−	2.46497i		−	0.112982i
$477$		0			0
$478$	−1.82584	−	3.16245i	−0.0835120	−	0.144647i
$479$	7.04158	−	4.06546i	0.321738	−	0.185755i	−0.330429	−	0.943831i	$-0.607193\pi$
$479$	7.04158	−	4.06546i	0.321738	−	0.185755i	0.652167	+	0.758075i	$0.273860\pi$
$480$		0			0
$481$	0.776704	+	1.09659i	0.0354147	+	0.0500002i
$482$	−0.123609			−0.00563022
$483$		0			0
$484$	−2.63525	−	4.56440i	−0.119784	−	0.207473i
$485$	9.79157	−	16.9595i	0.444612	−	0.770091i
$486$		0			0
$487$	−28.1884	−	16.2746i	−1.27734	−	0.737473i	−0.300982	−	0.953630i	$-0.597314\pi$
$487$	−28.1884	−	16.2746i	−1.27734	−	0.737473i	−0.976359	+	0.216157i	$0.930648\pi$
$488$	11.7692	+	6.79497i	0.532768	+	0.307594i
$489$		0			0
$490$	−1.59191	+	2.75726i	−0.0719150	+	0.124560i
$491$	10.6268	+	18.4062i	0.479583	+	0.830661i	0.999726	−	0.0234177i	$-0.00745477\pi$
$491$	10.6268	+	18.4062i	0.479583	+	0.830661i	−0.520143	+	0.854079i	$0.674121\pi$
$492$		0			0
$493$	4.63453			0.208729
$494$	−0.229393	−	2.46829i	−0.0103209	−	0.111054i
$495$		0			0
$496$	3.61603	−	2.08771i	0.162364	−	0.0937411i
$497$	−5.24419	−	9.08320i	−0.235234	−	0.407437i
$498$		0			0
$499$		−	34.0619i		−	1.52482i	−0.647095	−	0.762409i	$-0.724016\pi$
$499$		−	34.0619i		−	1.52482i	0.647095	−	0.762409i	$-0.275984\pi$
$500$	−0.376824	−	0.217559i	−0.0168521	−	0.00972955i
$501$		0			0
$502$		−	15.0892i		−	0.673466i
$503$	2.96436	−	5.13442i	0.132174	−	0.228933i	−0.792340	−	0.610080i	$-0.791137\pi$
$503$	2.96436	−	5.13442i	0.132174	−	0.228933i	0.924514	+	0.381147i	$0.124471\pi$
$504$		0			0
$505$	−19.5699	+	11.2987i	−0.870848	+	0.502784i
$506$	23.3584			1.03841
$507$		0			0
$508$	−8.57157			−0.380302
$509$	−32.6711	+	18.8626i	−1.44812	+	0.836072i	−0.998369	−	0.0570827i	$-0.981820\pi$
$509$	−32.6711	+	18.8626i	−1.44812	+	0.836072i	−0.449750	+	0.893155i	$0.648487\pi$
$510$		0			0
$511$	−8.26736	+	14.3195i	−0.365727	+	0.633457i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	6.83309	+	3.94509i	0.301395	+	0.174010i
$515$		−	26.8823i		−	1.18458i
$516$		0			0
$517$	23.9445	+	41.4732i	1.05308	+	1.82399i
$518$	−0.322768	+	0.186350i	−0.0141816	+	0.00818777i
$519$		0			0
$520$	−1.06227	−	11.4301i	−0.0465837	−	0.501245i
$521$	16.7098			0.732070			0.366035	−	0.930601i	$-0.380715\pi$
$521$	16.7098			0.732070			0.366035	+	0.930601i	$0.380715\pi$
$522$		0			0
$523$	−14.3349	−	24.8287i	−0.626821	−	1.08569i	−0.988186	−	0.153261i	$-0.951023\pi$
$523$	−14.3349	−	24.8287i	−0.626821	−	1.08569i	0.361365	−	0.932424i	$-0.382311\pi$
$524$	4.72647	−	8.18648i	0.206477	−	0.357628i
$525$		0			0
$526$	−7.71861	−	4.45634i	−0.336547	−	0.194306i
$527$	8.91340	+	5.14616i	0.388274	+	0.224170i
$528$		0			0
$529$	−5.26703	+	9.12277i	−0.229001	+	0.396642i
$530$	15.2765	+	26.4597i	0.663570	+	1.14934i
$531$		0			0
$532$	0.687532			0.0298083
$533$	−16.4565	−	23.2341i	−0.712809	−	1.00638i
$534$		0			0
$535$	29.9161	−	17.2721i	1.29339	−	0.746737i
$536$	−4.30987	−	7.46491i	−0.186158	−	0.322435i
$537$		0			0
$538$			14.4240i			0.621862i
$539$	3.49326	+	2.01684i	0.150465	+	0.0868713i
$540$		0			0
$541$		−	8.03625i		−	0.345505i	−0.984965	−	0.172753i	$-0.944734\pi$
$541$		−	8.03625i		−	0.345505i	0.984965	−	0.172753i	$-0.0552661\pi$
$542$	−9.37361	+	16.2356i	−0.402631	+	0.697377i
$543$		0			0
$544$	−2.13473	+	1.23249i	−0.0915257	+	0.0528424i
$545$	47.6441			2.04085
$546$		0			0
$547$	25.2164			1.07817			0.539087	−	0.842250i	$-0.318769\pi$
$547$	25.2164			1.07817			0.539087	+	0.842250i	$0.318769\pi$
$548$	−6.77434	+	3.91117i	−0.289385	+	0.167077i
$549$		0			0
$550$	−10.3598	+	17.9437i	−0.441744	+	0.765123i
$551$			1.29267i			0.0550695i
$552$		0			0
$553$	−11.5073	−	6.64372i	−0.489339	−	0.282520i
$554$			19.4146i			0.824846i
$555$		0			0
$556$	−1.33554	−	2.31322i	−0.0566394	−	0.0981023i
$557$	−18.8958	+	10.9095i	−0.800639	+	0.462249i	−0.843695	−	0.536824i	$-0.819624\pi$
$557$	−18.8958	+	10.9095i	−0.800639	+	0.462249i	0.0430556	+	0.999073i	$0.486291\pi$
$558$		0			0
$559$	−16.2695	−	7.47986i	−0.688128	−	0.316364i
$560$	3.18381			0.134541
$561$		0			0
$562$	−9.70424	−	16.8082i	−0.409349	−	0.709013i
$563$	−10.7185	+	18.5650i	−0.451732	+	0.782422i	−0.998494	−	0.0548657i	$-0.982527\pi$
$563$	−10.7185	+	18.5650i	−0.451732	+	0.782422i	0.546762	+	0.837288i	$0.315860\pi$
$564$		0			0
$565$	26.1995	+	15.1263i	1.10222	+	0.636368i
$566$	11.6143	+	6.70552i	0.488185	+	0.281854i
$567$		0			0
$568$	−5.24419	+	9.08320i	−0.220041	+	0.381123i
$569$	19.9983	+	34.6381i	0.838373	+	1.45210i	0.891254	+	0.453504i	$0.149826\pi$
$569$	19.9983	+	34.6381i	0.838373	+	1.45210i	−0.0528815	+	0.998601i	$0.516841\pi$
$570$		0			0
$571$	24.1693			1.01145			0.505726	−	0.862694i	$-0.331225\pi$
$571$	24.1693			1.01145			0.505726	+	0.862694i	$0.331225\pi$
$572$	−14.4812	+	1.34583i	−0.605490	+	0.0562718i
$573$		0			0
$574$	6.83868	−	3.94832i	0.285441	−	0.164800i
$575$	−14.8729	−	25.7605i	−0.620241	−	1.07429i
$576$		0			0
$577$		−	23.0573i		−	0.959887i	−0.877300	−	0.479943i	$-0.840657\pi$
$577$		−	23.0573i		−	0.959887i	0.877300	−	0.479943i	$-0.159343\pi$
$578$	9.46039	+	5.46196i	0.393500	+	0.227187i
$579$		0			0
$580$			5.98606i			0.248558i
$581$	4.69651	−	8.13460i	0.194844	−	0.337480i
$582$		0			0
$583$	33.5226	−	19.3543i	1.38837	−	0.801573i
$584$	16.5347			0.684212
$585$		0			0
$586$	2.32554			0.0960674
$587$	−31.2097	+	18.0189i	−1.28816	+	0.743720i	−0.978326	−	0.207070i	$-0.933607\pi$
$587$	−31.2097	+	18.0189i	−1.28816	+	0.743720i	−0.309835	+	0.950790i	$0.600274\pi$
$588$		0			0
$589$	−1.43537	+	2.48613i	−0.0591434	+	0.102439i
$590$			8.20394i			0.337751i
$591$		0			0
$592$	0.322768	+	0.186350i	0.0132657	+	0.00765896i
$593$		−	16.5198i		−	0.678386i	−0.940717	−	0.339193i	$-0.889846\pi$
$593$		−	16.5198i		−	0.678386i	0.940717	−	0.339193i	$-0.110154\pi$
$594$		0			0
$595$	3.92401	+	6.79658i	0.160869	+	0.278632i
$596$	3.71910	−	2.14722i	0.152340	−	0.0879536i
$597$		0			0
$598$	8.72157	−	18.9704i	0.356652	−	0.775758i
$599$	−5.57909			−0.227956			−0.113978	−	0.993483i	$-0.536359\pi$
$599$	−5.57909			−0.227956			−0.113978	+	0.993483i	$0.536359\pi$
$600$		0			0
$601$	−18.7171	−	32.4190i	−0.763486	−	1.32240i	−0.941043	−	0.338286i	$-0.890153\pi$
$601$	−18.7171	−	32.4190i	−0.763486	−	1.32240i	0.177557	−	0.984111i	$-0.443181\pi$
$602$	2.48320	−	4.30103i	0.101208	−	0.175297i
$603$		0			0
$604$	−20.7348	−	11.9713i	−0.843688	−	0.487104i
$605$	14.5322	+	8.39016i	0.590817	+	0.341108i
$606$		0			0
$607$	−1.72160	+	2.98191i	−0.0698778	+	0.121032i	−0.898847	−	0.438262i	$-0.855594\pi$
$607$	−1.72160	+	2.98191i	−0.0698778	+	0.121032i	0.828970	+	0.559294i	$0.188928\pi$
$608$	−0.343766	−	0.595420i	−0.0139415	−	0.0241475i
$609$		0			0
$610$	−43.2678			−1.75186
$611$	42.6226	−	3.96117i	1.72433	−	0.160252i
$612$		0			0
$613$	−34.3407	+	19.8266i	−1.38701	+	0.800790i	−0.992977	−	0.118307i	$-0.962253\pi$
$613$	−34.3407	+	19.8266i	−1.38701	+	0.800790i	−0.394032	+	0.919097i	$0.628920\pi$
$614$	3.54788	+	6.14510i	0.143181	+	0.247996i
$615$		0			0
$616$		−	4.03367i		−	0.162521i
$617$	−15.6609	−	9.04183i	−0.630485	−	0.364010i	0.150455	−	0.988617i	$-0.451926\pi$
$617$	−15.6609	−	9.04183i	−0.630485	−	0.364010i	−0.780940	+	0.624606i	$0.785259\pi$
$618$		0			0
$619$			23.5906i			0.948187i	0.880475	+	0.474093i	$0.157224\pi$
$619$			23.5906i			0.948187i	−0.880475	+	0.474093i	$0.842776\pi$
$620$	−6.64689	+	11.5128i	−0.266946	+	0.462363i
$621$		0			0
$622$	−10.4430	+	6.02929i	−0.418728	+	0.241753i
$623$	8.72046			0.349378
$624$		0			0
$625$	−24.2980			−0.971920
$626$	−9.88120	+	5.70491i	−0.394932	+	0.228014i
$627$		0			0
$628$	−10.5820	+	18.3285i	−0.422267	+	0.731388i
$629$			0.918697i			0.0366309i
$630$		0			0
$631$	−42.3081	−	24.4266i	−1.68426	−	0.972406i	−0.958775	−	0.284166i	$-0.908283\pi$
$631$	−42.3081	−	24.4266i	−1.68426	−	0.972406i	−0.725482	−	0.688241i	$-0.758383\pi$
$632$			13.2874i			0.528546i
$633$		0			0
$634$	3.33847	+	5.78240i	0.132588	+	0.229648i
$635$	23.6341	−	13.6451i	0.937889	−	0.541491i
$636$		0			0
$637$	2.94228	−	2.08399i	0.116577	−	0.0825706i
$638$	7.58393			0.300251
$639$		0			0
$640$	−1.59191	−	2.75726i	−0.0629256	−	0.108990i
$641$	3.62675	−	6.28172i	0.143248	−	0.248113i	−0.785470	−	0.618900i	$-0.787579\pi$
$641$	3.62675	−	6.28172i	0.143248	−	0.248113i	0.928718	+	0.370787i	$0.120912\pi$
$642$		0			0
$643$	33.0001	+	19.0526i	1.30140	+	0.751361i	0.980644	−	0.195802i	$-0.0627308\pi$
$643$	33.0001	+	19.0526i	1.30140	+	0.751361i	0.320753	+	0.947163i	$0.396064\pi$
$644$	5.01503	+	2.89543i	0.197620	+	0.114096i
$645$		0			0
$646$	0.847373	−	1.46769i	0.0333395	−	0.0577456i
$647$	−16.2780	−	28.1943i	−0.639953	−	1.10843i	−0.985443	−	0.170009i	$-0.945620\pi$
$647$	−16.2780	−	28.1943i	−0.639953	−	1.10843i	0.345489	−	0.938423i	$-0.387713\pi$
$648$		0			0
$649$	10.3938			0.407993
$650$	10.7047	+	15.1135i	0.419875	+	0.592800i
$651$		0			0
$652$	2.97609	−	1.71825i	0.116553	−	0.0672917i
$653$	14.0997	+	24.4214i	0.551763	+	0.955682i	0.998148	+	0.0608403i	$0.0193780\pi$
$653$	14.0997	+	24.4214i	0.551763	+	0.955682i	−0.446384	+	0.894841i	$0.647289\pi$
$654$		0			0
$655$			30.0964i			1.17596i
$656$	−6.83868	−	3.94832i	−0.267006	−	0.154156i
$657$		0			0
$658$			11.8723i			0.462832i
$659$	−12.5440	+	21.7268i	−0.488644	+	0.846356i	−0.999915	−	0.0130635i	$-0.995842\pi$
$659$	−12.5440	+	21.7268i	−0.488644	+	0.846356i	0.511271	+	0.859420i	$0.329175\pi$
$660$		0			0
$661$	−0.853782	+	0.492931i	−0.0332083	+	0.0191728i	−0.516512	−	0.856280i	$-0.672770\pi$
$661$	−0.853782	+	0.492931i	−0.0332083	+	0.0191728i	0.483304	+	0.875453i	$0.339437\pi$
$662$	−1.27872			−0.0496989
$663$		0			0
$664$	−9.39302			−0.364520
$665$	−1.89571	+	1.09449i	−0.0735123	+	0.0424424i
$666$		0			0
$667$	−5.44386	+	9.42904i	−0.210787	+	0.365094i
$668$		−	1.49782i		−	0.0579526i
$669$		0			0
$670$	23.7669	+	13.7218i	0.918195	+	0.530120i
$671$			54.8173i			2.11620i
$672$		0			0
$673$	20.9713	+	36.3233i	0.808383	+	1.40016i	0.913984	+	0.405751i	$0.132990\pi$
$673$	20.9713	+	36.3233i	0.808383	+	1.40016i	−0.105601	+	0.994409i	$0.533677\pi$
$674$	−9.49457	+	5.48170i	−0.365717	+	0.211147i
$675$		0			0
$676$	−4.31399	+	12.2633i	−0.165923	+	0.471667i
$677$	25.0312			0.962027			0.481013	−	0.876713i	$-0.340269\pi$
$677$	25.0312			0.962027			0.481013	+	0.876713i	$0.340269\pi$
$678$		0			0
$679$	−3.07542	−	5.32679i	−0.118024	−	0.204423i
$680$	3.92401	−	6.79658i	0.150479	−	0.260637i
$681$		0			0
$682$	14.5859	+	8.42115i	0.558522	+	0.322463i
$683$	18.2859	+	10.5573i	0.699689	+	0.403966i	0.807232	−	0.590235i	$-0.200965\pi$
$683$	18.2859	+	10.5573i	0.699689	+	0.403966i	−0.107542	+	0.994200i	$0.534298\pi$
$684$		0			0
$685$	12.4524	−	21.5682i	0.475782	−	0.824079i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−4.96640			−0.189342
$689$	−3.20181	−	34.4517i	−0.121979	−	1.31251i
$690$		0			0
$691$	−42.7299	+	24.6701i	−1.62552	+	0.938495i	−0.640114	+	0.768280i	$0.721113\pi$
$691$	−42.7299	+	24.6701i	−1.62552	+	0.938495i	−0.985407	+	0.170216i	$0.945554\pi$
$692$	4.11216	+	7.12246i	0.156321	+	0.270755i
$693$		0			0
$694$			24.2514i			0.920571i
$695$	7.36485	+	4.25210i	0.279365	+	0.161291i
$696$		0			0
$697$		−	19.4650i		−	0.737289i
$698$	−0.457647	+	0.792668i	−0.0173222	+	0.0300029i
$699$		0			0
$700$	−4.44848	+	2.56833i	−0.168137	+	0.0970739i
$701$	26.1837			0.988946			0.494473	−	0.869193i	$-0.335361\pi$
$701$	26.1837			0.988946			0.494473	+	0.869193i	$0.335361\pi$
$702$		0			0
$703$	−0.256244			−0.00966441
$704$	−3.49326	+	2.01684i	−0.131657	+	0.0760124i
$705$		0			0
$706$	−5.92948	+	10.2702i	−0.223159	+	0.386523i
$707$			7.09757i			0.266932i
$708$		0			0
$709$	19.3232	+	11.1562i	0.725697	+	0.418981i	0.816846	−	0.576856i	$-0.195721\pi$
$709$	19.3232	+	11.1562i	0.725697	+	0.418981i	−0.0911490	+	0.995837i	$0.529054\pi$
$710$		−	33.3930i		−	1.25322i
$711$		0			0
$712$	−4.36023	−	7.55214i	−0.163406	−	0.283028i
$713$	−20.9399	+	12.0897i	−0.784206	+	0.452761i
$714$		0			0
$715$	37.7861	−	26.7635i	1.41312	−	1.00090i
$716$	9.13914			0.341546
$717$		0			0
$718$	3.07408	+	5.32446i	0.114724	+	0.198707i
$719$	−1.77486	+	3.07415i	−0.0661912	+	0.114647i	−0.897222	−	0.441580i	$-0.854418\pi$
$719$	−1.77486	+	3.07415i	−0.0661912	+	0.114647i	0.831031	+	0.556227i	$0.187751\pi$
$720$		0			0
$721$	−7.31223	−	4.22172i	−0.272322	−	0.157225i
$722$	−16.0451	−	9.26365i	−0.597137	−	0.344757i
$723$		0			0
$724$	1.98502	−	3.43815i	0.0737726	−	0.127778i
$725$	−4.82887	−	8.36384i	−0.179340	−	0.310625i
$726$		0			0
$727$	−0.112332			−0.00416615			−0.00208307	−	0.999998i	$-0.500663\pi$
$727$	−0.112332			−0.00416615			−0.00208307	+	0.999998i	$0.500663\pi$
$728$	−3.27592	−	1.50609i	−0.121414	−	0.0558195i
$729$		0			0
$730$	−45.5906	+	26.3217i	−1.68738	+	0.974211i
$731$	−6.12102	−	10.6019i	−0.226394	−	0.392126i
$732$		0			0
$733$			36.6154i			1.35242i	0.736708	+	0.676211i	$0.236379\pi$
$733$			36.6154i			1.35242i	−0.736708	+	0.676211i	$0.763621\pi$
$734$	−16.0670	−	9.27627i	−0.593042	−	0.342393i
$735$		0			0
$736$		−	5.79086i		−	0.213454i
$737$	17.3846	−	30.1110i	0.640370	−	1.10915i
$738$		0			0
$739$	39.4611	−	22.7829i	1.45160	−	0.838081i	0.453026	−	0.891497i	$-0.350344\pi$
$739$	39.4611	−	22.7829i	1.45160	−	0.838081i	0.998572	+	0.0534162i	$0.0170110\pi$
$740$	−1.18661			−0.0436206
$741$		0			0
$742$	9.59637			0.352294
$743$	−0.246449	+	0.142287i	−0.00904132	+	0.00522001i	−0.504514	−	0.863404i	$-0.668328\pi$
$743$	−0.246449	+	0.142287i	−0.00904132	+	0.00522001i	0.495473	+	0.868624i	$0.334995\pi$
$744$		0			0
$745$	−6.83635	+	11.8409i	−0.250464	+	0.433817i
$746$		−	24.1491i		−	0.884160i
$747$		0			0
$748$	−8.61079	−	4.97144i	−0.314842	−	0.181774i
$749$		−	10.8499i		−	0.396448i
$750$		0			0
$751$	0.0384437	+	0.0665865i	0.00140283	+	0.00242977i	0.866726	−	0.498785i	$-0.166220\pi$
$751$	0.0384437	+	0.0665865i	0.00140283	+	0.00242977i	−0.865323	+	0.501214i	$0.832887\pi$
$752$	10.2817	−	5.93616i	0.374936	−	0.216470i
$753$		0			0
$754$	2.83169	−	6.15925i	0.103124	−	0.224307i
$755$	76.2285			2.77424
$756$		0			0
$757$	−12.1791	−	21.0948i	−0.442656	−	0.766702i	0.555230	−	0.831697i	$-0.312630\pi$
$757$	−12.1791	−	21.0948i	−0.442656	−	0.766702i	−0.997886	+	0.0649946i	$0.979297\pi$
$758$	7.75109	−	13.4253i	0.281532	−	0.487628i
$759$		0			0
$760$	1.89571	+	1.09449i	0.0687645	+	0.0397012i
$761$	27.6551	+	15.9667i	1.00249	+	0.578791i	0.908986	−	0.416828i	$-0.136858\pi$
$761$	27.6551	+	15.9667i	1.00249	+	0.578791i	0.0935094	+	0.995618i	$0.470191\pi$
$762$		0			0
$763$	7.48224	−	12.9596i	0.270875	−	0.469170i
$764$	7.22054	+	12.5063i	0.261230	+	0.452464i
$765$		0			0
$766$	−4.74553			−0.171463
$767$	3.88085	−	8.44129i	0.140129	−	0.304797i
$768$		0			0
$769$	−14.0798	+	8.12896i	−0.507730	+	0.293138i	−0.731900	−	0.681412i	$-0.761366\pi$
$769$	−14.0798	+	8.12896i	−0.507730	+	0.293138i	0.224170	+	0.974550i	$0.428033\pi$
$770$	6.42123	+	11.1219i	0.231405	+	0.400805i
$771$		0			0
$772$			4.10457i			0.147727i
$773$	11.0350	+	6.37105i	0.396900	+	0.229151i	0.685146	−	0.728406i	$-0.259739\pi$
$773$	11.0350	+	6.37105i	0.396900	+	0.229151i	−0.288245	+	0.957557i	$0.593072\pi$
$774$		0			0
$775$		−	21.4478i		−	0.770427i
$776$	−3.07542	+	5.32679i	−0.110401	+	0.191221i
$777$		0			0
$778$	0.221227	−	0.127725i	0.00793136	−	0.00457917i
$779$	5.42918			0.194521
$780$		0			0
$781$	−42.3067			−1.51385
$782$	12.3619	−	7.13715i	0.442061	−	0.255224i
$783$		0			0
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$		−	67.3821i		−	2.40497i
$786$		0			0
$787$	−24.7761	−	14.3045i	−0.883173	−	0.509900i	−0.0114696	−	0.999934i	$-0.503651\pi$
$787$	−24.7761	−	14.3045i	−0.883173	−	0.509900i	−0.871703	+	0.490034i	$0.836984\pi$
$788$			18.2943i			0.651708i
$789$		0			0
$790$	−21.1524	−	36.6370i	−0.752568	−	1.30349i
$791$	8.22897	−	4.75100i	0.292589	−	0.168926i
$792$		0			0
$793$	44.5196	+	20.4677i	1.58094	+	0.726830i
$794$	5.89077			0.209055
$795$		0			0
$796$	−8.69290	−	15.0566i	−0.308112	−	0.533665i
$797$	−4.14067	+	7.17185i	−0.146670	+	0.254040i	−0.929995	−	0.367573i	$-0.880189\pi$
$797$	−4.14067	+	7.17185i	−0.146670	+	0.254040i	0.783325	+	0.621613i	$0.213522\pi$
$798$		0			0
$799$	25.3442	+	14.6325i	0.896613	+	0.517660i
$800$	4.44848	+	2.56833i	0.157278	+	0.0908043i
$801$		0			0
$802$	−5.27872	+	9.14301i	−0.186398	+	0.322851i
$803$	33.3478	+	57.7601i	1.17682	+	2.03831i
$804$		0			0
$805$	−18.4370			−0.649819
$806$	12.2853	−	8.70154i	0.432730	−	0.306499i
$807$		0			0
$808$	6.14668	−	3.54879i	0.216239	−	0.124846i
$809$	10.3018	+	17.8433i	0.362193	+	0.627337i	0.988321	−	0.152383i	$-0.0486948\pi$
$809$	10.3018	+	17.8433i	0.362193	+	0.627337i	−0.626129	+	0.779720i	$0.715361\pi$
$810$		0			0
$811$		−	19.1892i		−	0.673826i	−0.941536	−	0.336913i	$-0.890617\pi$
$811$		−	19.1892i		−	0.673826i	0.941536	−	0.336913i	$-0.109383\pi$
$812$	1.62826	+	0.940078i	0.0571408	+	0.0329903i
$813$		0			0
$814$			1.50335i			0.0526925i
$815$	−5.47057	+	9.47531i	−0.191626	+	0.331906i
$816$		0			0
$817$	2.95709	−	1.70728i	0.103456	−	0.0597301i
$818$	2.49104			0.0870971
$819$		0			0
$820$	25.1414			0.877976
$821$	−19.1914	+	11.0801i	−0.669783	+	0.386699i	−0.795994	−	0.605304i	$-0.793052\pi$
$821$	−19.1914	+	11.0801i	−0.669783	+	0.386699i	0.126211	+	0.992003i	$0.459718\pi$
$822$		0			0
$823$	4.40969	−	7.63781i	0.153712	−	0.266237i	−0.778877	−	0.627176i	$-0.784210\pi$
$823$	4.40969	−	7.63781i	0.153712	−	0.266237i	0.932589	+	0.360939i	$0.117544\pi$
$824$			8.44343i			0.294141i
$825$		0			0
$826$	2.23154	+	1.28838i	0.0776454	+	0.0448286i
$827$		−	48.9775i		−	1.70312i	−0.524260	−	0.851558i	$-0.675658\pi$
$827$		−	48.9775i		−	1.70312i	0.524260	−	0.851558i	$-0.324342\pi$
$828$		0			0
$829$	−3.10592	−	5.37962i	−0.107873	−	0.186842i	0.807035	−	0.590503i	$-0.201071\pi$
$829$	−3.10592	−	5.37962i	−0.107873	−	0.186842i	−0.914908	+	0.403661i	$0.867737\pi$
$830$	25.8990	−	14.9528i	0.898969	−	0.519020i
$831$		0			0
$832$	0.333648	+	3.59008i	0.0115672	+	0.124464i
$833$	2.46497			0.0854062
$834$		0			0
$835$	2.38440	+	4.12990i	0.0825154	+	0.142921i
$836$	1.38664	−	2.40173i	0.0479579	−	0.0830655i
$837$		0			0
$838$	14.3911	+	8.30873i	0.497134	+	0.287020i
$839$	1.46160	+	0.843857i	0.0504601	+	0.0291332i	0.525018	−	0.851091i	$-0.324059\pi$
$839$	1.46160	+	0.843857i	0.0504601	+	0.0291332i	−0.474558	+	0.880224i	$0.657392\pi$
$840$		0			0
$841$	12.7325	−	22.0533i	0.439052	−	0.760460i
$842$	19.1963	+	33.2490i	0.661549	+	1.14584i
$843$		0			0
$844$	5.03636			0.173359
$845$	−7.62728	−	40.6807i	−0.262386	−	1.39946i
$846$		0			0
$847$	4.56440	−	2.63525i	0.156834	−	0.0905484i
$848$	−4.79818	−	8.31070i	−0.164770	−	0.285391i
$849$		0			0
$850$			12.6617i			0.434294i
$851$	−1.86911	−	1.07913i	−0.0640722	−	0.0369921i
$852$		0			0
$853$			22.1066i			0.756914i	0.925619	+	0.378457i	$0.123545\pi$
$853$			22.1066i			0.756914i	−0.925619	+	0.378457i	$0.876455\pi$
$854$	−6.79497	+	11.7692i	−0.232519	+	0.402735i
$855$		0			0
$856$	−9.39631	+	5.42496i	−0.321159	+	0.185421i
$857$	5.43662			0.185711			0.0928556	−	0.995680i	$-0.470400\pi$
$857$	5.43662			0.185711			0.0928556	+	0.995680i	$0.470400\pi$
$858$		0			0
$859$	−53.9329			−1.84017			−0.920083	−	0.391724i	$-0.871879\pi$
$859$	−53.9329			−1.84017			−0.920083	+	0.391724i	$0.871879\pi$
$860$	13.6937	−	7.90604i	0.466950	−	0.269594i
$861$		0			0
$862$	12.4175	−	21.5077i	0.422942	−	0.732557i
$863$		−	26.9278i		−	0.916633i	−0.888789	−	0.458316i	$-0.848453\pi$
$863$		−	26.9278i		−	0.916633i	0.888789	−	0.458316i	$-0.151547\pi$
$864$		0			0
$865$	−22.6766	−	13.0923i	−0.771027	−	0.445153i
$866$		−	23.0331i		−	0.782697i
$867$		0			0
$868$	2.08771	+	3.61603i	0.0708616	+	0.122736i
$869$	−46.4165	+	26.7986i	−1.57457	+	0.909080i
$870$		0			0
$871$	−17.9634	−	25.3617i	−0.608668	−	0.859347i
$872$	−14.9645			−0.506761
$873$		0			0
$874$	1.99070	+	3.44799i	0.0673364	+	0.116630i
$875$	0.217559	−	0.376824i	0.00735485	−	0.0127390i
$876$		0			0
$877$	42.6890	+	24.6465i	1.44150	+	0.832253i	0.997950	−	0.0639940i	$-0.0203839\pi$
$877$	42.6890	+	24.6465i	1.44150	+	0.832253i	0.443555	+	0.896247i	$0.353717\pi$
$878$	1.82337	+	1.05272i	0.0615357	+	0.0355277i
$879$		0			0
$880$	6.42123	−	11.1219i	0.216460	−	0.374919i
$881$	8.61337	+	14.9188i	0.290192	+	0.502627i	0.973855	−	0.227171i	$-0.0729475\pi$
$881$	8.61337	+	14.9188i	0.290192	+	0.502627i	−0.683663	+	0.729798i	$0.739614\pi$
$882$		0			0
$883$	−24.2874			−0.817335			−0.408667	−	0.912683i	$-0.634006\pi$
$883$	−24.2874			−0.817335			−0.408667	+	0.912683i	$0.634006\pi$
$884$	−7.25263	+	5.13697i	−0.243932	+	0.172775i
$885$		0			0
$886$	−31.9230	+	18.4307i	−1.07247	+	0.619192i
$887$	−19.9927	−	34.6283i	−0.671289	−	1.16271i	−0.977539	−	0.210755i	$-0.932408\pi$
$887$	−19.9927	−	34.6283i	−0.671289	−	1.16271i	0.306250	−	0.951951i	$-0.400926\pi$
$888$		0			0
$889$		−	8.57157i		−	0.287481i
$890$	24.0446	+	13.8822i	0.805977	+	0.465331i
$891$		0			0
$892$		−	5.07566i		−	0.169946i
$893$	−4.08130	+	7.06902i	−0.136576	+	0.236556i
$894$		0			0
$895$	−25.1990	+	14.5487i	−0.842310	+	0.486308i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−31.2513			−1.04287
$899$	−6.79869	+	3.92523i	−0.226749	+	0.130914i
$900$		0			0
$901$	11.8274	−	20.4856i	0.394027	−	0.682476i
$902$		−	31.8524i		−	1.06057i
$903$		0			0
$904$	−8.22897	−	4.75100i	−0.273692	−	0.158016i
$905$			12.6398i			0.420163i
$906$		0			0
$907$	−15.0476	−	26.0632i	−0.499648	−	0.865416i	0.500352	−	0.865822i	$-0.333204\pi$
$907$	−15.0476	−	26.0632i	−0.499648	−	0.865416i	−1.00000		0.000406499i	$0.999871\pi$
$908$	−23.7848	+	13.7322i	−0.789327	+	0.455718i
$909$		0			0
$910$	11.4301	−	1.06227i	0.378906	−	0.0352140i
$911$	20.2884			0.672184			0.336092	−	0.941829i	$-0.390895\pi$
$911$	20.2884			0.672184			0.336092	+	0.941829i	$0.390895\pi$
$912$		0			0
$913$	−18.9442	−	32.8123i	−0.626961	−	1.08593i
$914$	5.73492	−	9.93318i	0.189694	−	0.328560i
$915$		0			0
$916$	−23.9744	−	13.8416i	−0.792135	−	0.457339i
$917$	8.18648	+	4.72647i	0.270341	+	0.156082i
$918$		0			0
$919$	9.47940	−	16.4188i	0.312697	−	0.541606i	−0.666249	−	0.745730i	$-0.732101\pi$
$919$	9.47940	−	16.4188i	0.312697	−	0.541606i	0.978945	+	0.204123i	$0.0654344\pi$
$920$	9.21851	+	15.9669i	0.303925	+	0.526414i
$921$		0			0
$922$	−15.7459			−0.518565
$923$	−15.7965	+	34.3591i	−0.519947	+	1.13094i
$924$		0			0
$925$	1.65795	−	0.957220i	0.0545132	−	0.0314732i
$926$	−9.25349	−	16.0275i	−0.304089	−	0.526697i
$927$		0			0
$928$		−	1.88016i		−	0.0617191i
$929$	38.9321	+	22.4774i	1.27732	+	0.737461i	0.976355	−	0.216174i	$-0.0693580\pi$
$929$	38.9321	+	22.4774i	1.27732	+	0.737461i	0.300965	+	0.953635i	$0.402691\pi$
$930$		0			0
$931$			0.687532i			0.0225329i
$932$	13.5922	−	23.5423i	0.445226	−	0.771154i
$933$		0			0
$934$	−10.2184	+	5.89959i	−0.334356	+	0.193040i
$935$	31.6563			1.03527
$936$		0			0
$937$	50.2773			1.64249			0.821244	−	0.570577i	$-0.193280\pi$
$937$	50.2773			1.64249			0.821244	+	0.570577i	$0.193280\pi$
$938$	7.46491	−	4.30987i	0.243738	−	0.140722i
$939$		0			0
$940$	−18.8996	+	32.7351i	−0.616438	+	1.06770i
$941$			26.1622i			0.852862i	0.904520	+	0.426431i	$0.140229\pi$
$941$			26.1622i			0.852862i	−0.904520	+	0.426431i	$0.859771\pi$
$942$		0			0
$943$	39.6019	+	22.8641i	1.28961	+	0.744559i
$944$		−	2.57677i		−	0.0838666i
$945$		0			0
$946$	−10.0164	−	17.3489i	−0.325662	−	0.564062i
$947$	−29.4303	+	16.9916i	−0.956358	+	0.552153i	−0.895050	−	0.445966i	$-0.852860\pi$
$947$	−29.4303	+	16.9916i	−0.956358	+	0.552153i	−0.0613076	+	0.998119i	$0.519527\pi$
$948$		0			0
$949$	59.3610	−	5.51677i	1.92694	−	0.179082i
$950$	−3.53162			−0.114581
$951$		0			0
$952$	−1.23249	−	2.13473i	−0.0399451	−	0.0691869i
$953$	9.86552	−	17.0876i	0.319576	−	0.553521i	−0.660824	−	0.750541i	$-0.729793\pi$
$953$	9.86552	−	17.0876i	0.319576	−	0.553521i	0.980400	+	0.197020i	$0.0631263\pi$
$954$		0			0
$955$	−39.8179	−	22.9889i	−1.28848	−	0.743902i
$956$	−3.16245	−	1.82584i	−0.102281	−	0.0590519i
$957$		0			0
$958$	4.06546	−	7.04158i	0.131349	−	0.227503i
$959$	−3.91117	−	6.77434i	−0.126298	−	0.218755i
$960$		0			0
$961$	13.5658			0.437607
$962$	1.22094	+	0.561322i	0.0393647	+	0.0180978i
$963$		0			0
$964$	−0.107048	+	0.0618044i	−0.00344779	+	0.00199058i
$965$	−6.53409	−	11.3174i	−0.210340	−	0.364319i
$966$		0			0
$967$		−	40.0777i		−	1.28881i	−0.764683	−	0.644406i	$-0.777105\pi$
$967$		−	40.0777i		−	1.28881i	0.764683	−	0.644406i	$-0.222895\pi$
$968$	−4.56440	−	2.63525i	−0.146705	−	0.0847003i
$969$		0			0
$970$		−	19.5831i		−	0.628777i
$971$	20.4682	−	35.4519i	0.656855	−	1.13771i	−0.324570	−	0.945862i	$-0.605220\pi$
$971$	20.4682	−	35.4519i	0.656855	−	1.13771i	0.981425	−	0.191845i	$-0.0614470\pi$
$972$		0			0
$973$	2.31322	−	1.33554i	0.0741583	−	0.0428153i
$974$	−32.5492			−1.04294
$975$		0			0
$976$	13.5899			0.435003
$977$	−51.3639	+	29.6549i	−1.64328	+	0.948746i	−0.663618	+	0.748072i	$0.730980\pi$
$977$	−51.3639	+	29.6549i	−1.64328	+	0.948746i	−0.979658	+	0.200674i	$0.935687\pi$
$978$		0			0
$979$	17.5877	−	30.4628i	0.562106	−	0.973597i
$980$			3.18381i			0.101703i
$981$		0			0
$982$	18.4062	+	10.6268i	0.587366	+	0.339116i
$983$			26.5688i			0.847412i	0.905800	+	0.423706i	$0.139271\pi$
$983$			26.5688i			0.847412i	−0.905800	+	0.423706i	$0.860729\pi$
$984$		0			0
$985$	−29.1228	−	50.4422i	−0.927931	−	1.60722i
$986$	4.01362	−	2.31727i	0.127820	−	0.0737968i
$987$		0			0
$988$	−1.43281	−	2.02291i	−0.0455837	−	0.0643573i
$989$	28.7597			0.914506
$990$		0			0
$991$	17.0282	+	29.4937i	0.540918	+	0.936898i	0.998852	+	0.0479116i	$0.0152566\pi$
$991$	17.0282	+	29.4937i	0.540918	+	0.936898i	−0.457933	+	0.888987i	$0.651410\pi$
$992$	2.08771	−	3.61603i	0.0662850	−	0.114809i
$993$		0			0
$994$	−9.08320	−	5.24419i	−0.288102	−	0.166336i
$995$	47.9372	+	27.6766i	1.51971	+	0.877407i
$996$		0			0
$997$	6.03595	−	10.4546i	0.191160	−	0.331100i	−0.754475	−	0.656329i	$-0.772108\pi$
$997$	6.03595	−	10.4546i	0.191160	−	0.331100i	0.945635	+	0.325230i	$0.105442\pi$
$998$	−17.0309	−	29.4984i	−0.539105	−	0.933757i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.i.127.8	yes	16
3.2	odd	2		1638.2.bj.h.127.1	✓	16
13.4	even	6	inner	1638.2.bj.i.1135.5	yes	16
39.17	odd	6		1638.2.bj.h.1135.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bj.h.127.1	✓	16	3.2	odd	2
1638.2.bj.h.1135.4	yes	16	39.17	odd	6
1638.2.bj.i.127.8	yes	16	1.1	even	1	trivial
1638.2.bj.i.1135.5	yes	16	13.4	even	6	inner

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.18381i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.18381i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(1.59191 + 2.75726i) q^{10} +(3.49326 - 2.01684i) q^{11} +(-0.333648 - 3.59008i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.23249 - 2.13473i) q^{17} +(0.595420 + 0.343766i) q^{19} +(2.75726 + 1.59191i) q^{20} +(2.01684 - 3.49326i) q^{22} +(2.89543 + 5.01503i) q^{23} -5.13667 q^{25} +(-2.08399 - 2.94228i) q^{26} +(0.866025 - 0.500000i) q^{28} +(0.940078 + 1.62826i) q^{29} +4.17543i q^{31} +(-0.866025 - 0.500000i) q^{32} -2.46497i q^{34} +(-1.59191 + 2.75726i) q^{35} +(-0.322768 + 0.186350i) q^{37} +0.687532 q^{38} +3.18381 q^{40} +(6.83868 - 3.94832i) q^{41} +(2.48320 - 4.30103i) q^{43} -4.03367i q^{44} +(5.01503 + 2.89543i) q^{46} +11.8723i q^{47} +(0.500000 + 0.866025i) q^{49} +(-4.44848 + 2.56833i) q^{50} +(-3.27592 - 1.50609i) q^{52} +9.59637 q^{53} +(6.42123 + 11.1219i) q^{55} +(0.500000 - 0.866025i) q^{56} +(1.62826 + 0.940078i) q^{58} +(2.23154 + 1.28838i) q^{59} +(-6.79497 + 11.7692i) q^{61} +(2.08771 + 3.61603i) q^{62} -1.00000 q^{64} +(11.4301 - 1.06227i) q^{65} +(7.46491 - 4.30987i) q^{67} +(-1.23249 - 2.13473i) q^{68} +3.18381i q^{70} +(-9.08320 - 5.24419i) q^{71} +16.5347i q^{73} +(-0.186350 + 0.322768i) q^{74} +(0.595420 - 0.343766i) q^{76} +4.03367 q^{77} -13.2874 q^{79} +(2.75726 - 1.59191i) q^{80} +(3.94832 - 6.83868i) q^{82} -9.39302i q^{83} +(6.79658 + 3.92401i) q^{85} -4.96640i q^{86} +(-2.01684 - 3.49326i) q^{88} +(7.55214 - 4.36023i) q^{89} +(1.50609 - 3.27592i) q^{91} +5.79086 q^{92} +(5.93616 + 10.2817i) q^{94} +(-1.09449 + 1.89571i) q^{95} +(-5.32679 - 3.07542i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 2 q^{10} + 12 q^{11} + 10 q^{13} + 16 q^{14} - 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{23} - 20 q^{25} + 2 q^{26} - 16 q^{29} - 2 q^{35} - 6 q^{37} + 4 q^{40} - 12 q^{41} - 6 q^{43} + 6 q^{46} + 8 q^{49} + 24 q^{50} - 4 q^{52} + 40 q^{53} + 20 q^{55} + 8 q^{56} + 6 q^{58} - 6 q^{59} - 2 q^{61} + 14 q^{62} - 16 q^{64} + 52 q^{65} - 30 q^{67} - 6 q^{68} - 12 q^{71} - 24 q^{74} - 8 q^{77} - 16 q^{79} + 2 q^{82} + 6 q^{85} + 4 q^{88} - 30 q^{89} + 4 q^{91} + 24 q^{92} - 8 q^{94} + 40 q^{95} - 24 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^10 + 12 * q^11 + 10 * q^13 + 16 * q^14 - 8 * q^16 + 6 * q^17 - 4 * q^22 + 12 * q^23 - 20 * q^25 + 2 * q^26 - 16 * q^29 - 2 * q^35 - 6 * q^37 + 4 * q^40 - 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 + 24 * q^50 - 4 * q^52 + 40 * q^53 + 20 * q^55 + 8 * q^56 + 6 * q^58 - 6 * q^59 - 2 * q^61 + 14 * q^62 - 16 * q^64 + 52 * q^65 - 30 * q^67 - 6 * q^68 - 12 * q^71 - 24 * q^74 - 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 - 30 * q^89 + 4 * q^91 + 24 * q^92 - 8 * q^94 + 40 * q^95 - 24 * q^97

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