LMFDB - Embedded newform 432.2.be.a.239.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.1
Character	$\chi$	$=$	432.239
Dual form			432.2.be.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72868 - 0.107984i) q^{3} +(0.902279 + 0.159096i) q^{5} +(-2.30964 - 2.75253i) q^{7} +(2.97668 + 0.373339i) q^{9} +O(q^{10})$	\(q+(-1.72868 - 0.107984i) q^{3} +(0.902279 + 0.159096i) q^{5} +(-2.30964 - 2.75253i) q^{7} +(2.97668 + 0.373339i) q^{9} +(0.316002 + 1.79214i) q^{11} +(-4.18526 + 1.52331i) q^{13} +(-1.54257 - 0.372458i) q^{15} +(-3.92200 - 2.26437i) q^{17} +(0.794277 - 0.458576i) q^{19} +(3.69541 + 5.00764i) q^{21} +(-5.68258 - 4.76825i) q^{23} +(-3.90967 - 1.42300i) q^{25} +(-5.10542 - 0.966817i) q^{27} +(3.02791 - 8.31913i) q^{29} +(-3.84549 + 4.58288i) q^{31} +(-0.352746 - 3.13216i) q^{33} +(-1.64603 - 2.85100i) q^{35} +(-3.15380 + 5.46255i) q^{37} +(7.39948 - 2.18138i) q^{39} +(-1.16283 - 3.19486i) q^{41} +(0.919062 - 0.162055i) q^{43} +(2.62640 + 0.810434i) q^{45} +(0.999632 - 0.838791i) q^{47} +(-1.02641 + 5.82105i) q^{49} +(6.53538 + 4.33789i) q^{51} -2.53299i q^{53} +1.66728i q^{55} +(-1.42257 + 0.706963i) q^{57} +(-2.13801 + 12.1253i) q^{59} +(-2.66045 + 2.23238i) q^{61} +(-5.84744 - 9.05567i) q^{63} +(-4.01863 + 0.708592i) q^{65} +(0.986708 + 2.71096i) q^{67} +(9.30847 + 8.85641i) q^{69} +(4.44194 - 7.69367i) q^{71} +(-0.528554 - 0.915482i) q^{73} +(6.60491 + 2.88210i) q^{75} +(4.20306 - 5.00901i) q^{77} +(3.99634 - 10.9798i) q^{79} +(8.72124 + 2.22262i) q^{81} +(15.7994 + 5.75052i) q^{83} +(-3.17849 - 2.66707i) q^{85} +(-6.13263 + 14.0542i) q^{87} +(13.1352 - 7.58359i) q^{89} +(13.8594 + 8.00174i) q^{91} +(7.14251 - 7.50709i) q^{93} +(0.789617 - 0.287397i) q^{95} +(1.86037 + 10.5507i) q^{97} +(0.271563 + 5.45260i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^5 - 12 * q^9	$ 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) $ 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{18}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.72868	−	0.107984i	−0.998055	−	0.0623444i
$3$	−1.72868	−	0.107984i	−0.998055	−	0.0623444i
$4$		0			0
$5$	0.902279	+	0.159096i	0.403511	+	0.0711499i	0.371721	−	0.928345i	$-0.378768\pi$
$5$	0.902279	+	0.159096i	0.403511	+	0.0711499i	0.0317906	+	0.999495i	$0.489879\pi$
$6$		0			0
$7$	−2.30964	−	2.75253i	−0.872963	−	1.04036i	−0.998832	−	0.0483102i	$-0.984616\pi$
$7$	−2.30964	−	2.75253i	−0.872963	−	1.04036i	0.125869	−	0.992047i	$-0.459828\pi$
$8$		0			0
$9$	2.97668	+	0.373339i	0.992226	+	0.124446i
$10$		0			0
$11$	0.316002	+	1.79214i	0.0952783	+	0.540350i	0.994662	+	0.103189i	$0.0329048\pi$
$11$	0.316002	+	1.79214i	0.0952783	+	0.540350i	−0.899383	+	0.437161i	$0.855984\pi$
$12$		0			0
$13$	−4.18526	+	1.52331i	−1.16078	+	0.422491i	−0.849377	−	0.527786i	$-0.823022\pi$
$13$	−4.18526	+	1.52331i	−1.16078	+	0.422491i	−0.311406	+	0.950277i	$0.600800\pi$
$14$		0			0
$15$	−1.54257	−	0.372458i	−0.398290	−	0.0961682i
$16$		0			0
$17$	−3.92200	−	2.26437i	−0.951226	−	0.549190i	−0.0577643	−	0.998330i	$-0.518397\pi$
$17$	−3.92200	−	2.26437i	−0.951226	−	0.549190i	−0.893461	+	0.449140i	$0.851731\pi$
$18$		0			0
$19$	0.794277	−	0.458576i	0.182220	−	0.105205i	−0.406115	−	0.913822i	$-0.633117\pi$
$19$	0.794277	−	0.458576i	0.182220	−	0.105205i	0.588335	+	0.808617i	$0.299784\pi$
$20$		0			0
$21$	3.69541	+	5.00764i	0.806405	+	1.09276i
$22$		0			0
$23$	−5.68258	−	4.76825i	−1.18490	−	0.994248i	−0.999934	−	0.0115034i	$-0.996338\pi$
$23$	−5.68258	−	4.76825i	−1.18490	−	0.994248i	−0.184965	−	0.982745i	$-0.559217\pi$
$24$		0			0
$25$	−3.90967	−	1.42300i	−0.781934	−	0.284601i
$26$		0			0
$27$	−5.10542	−	0.966817i	−0.982538	−	0.186064i
$28$		0			0
$29$	3.02791	−	8.31913i	0.562270	−	1.54482i	−0.254031	−	0.967196i	$-0.581757\pi$
$29$	3.02791	−	8.31913i	0.562270	−	1.54482i	0.816301	−	0.577627i	$-0.196021\pi$
$30$		0			0
$31$	−3.84549	+	4.58288i	−0.690671	+	0.823110i	−0.991437	−	0.130588i	$-0.958313\pi$
$31$	−3.84549	+	4.58288i	−0.690671	+	0.823110i	0.300766	+	0.953698i	$0.402758\pi$
$32$		0			0
$33$	−0.352746	−	3.13216i	−0.0614052	−	0.545239i
$34$		0			0
$35$	−1.64603	−	2.85100i	−0.278229	−	0.481907i
$36$		0			0
$37$	−3.15380	+	5.46255i	−0.518482	+	0.898037i	0.481287	+	0.876563i	$0.340169\pi$
$37$	−3.15380	+	5.46255i	−0.518482	+	0.898037i	−0.999769	+	0.0214743i	$0.993164\pi$
$38$		0			0
$39$	7.39948	−	2.18138i	1.18487	−	0.349300i
$40$		0			0
$41$	−1.16283	−	3.19486i	−0.181604	−	0.498953i	0.815169	−	0.579223i	$-0.196644\pi$
$41$	−1.16283	−	3.19486i	−0.181604	−	0.498953i	−0.996773	+	0.0802698i	$0.974422\pi$
$42$		0			0
$43$	0.919062	−	0.162055i	0.140156	−	0.0247132i	−0.103130	−	0.994668i	$-0.532886\pi$
$43$	0.919062	−	0.162055i	0.140156	−	0.0247132i	0.243286	+	0.969955i	$0.421775\pi$
$44$		0			0
$45$	2.62640	+	0.810434i	0.391520	+	0.120812i
$46$		0			0
$47$	0.999632	−	0.838791i	0.145811	−	0.122350i	−0.566964	−	0.823742i	$-0.691882\pi$
$47$	0.999632	−	0.838791i	0.145811	−	0.122350i	0.712776	+	0.701392i	$0.247438\pi$
$48$		0			0
$49$	−1.02641	+	5.82105i	−0.146630	+	0.831579i
$50$		0			0
$51$	6.53538	+	4.33789i	0.915136	+	0.607426i
$52$		0			0
$53$		−	2.53299i		−	0.347934i	−0.984752	−	0.173967i	$-0.944341\pi$
$53$		−	2.53299i		−	0.347934i	0.984752	−	0.173967i	$-0.0556585\pi$
$54$		0			0
$55$			1.66728i			0.224816i
$56$		0			0
$57$	−1.42257	+	0.706963i	−0.188424	+	0.0936395i
$58$		0			0
$59$	−2.13801	+	12.1253i	−0.278346	+	1.57858i	0.449785	+	0.893137i	$0.351501\pi$
$59$	−2.13801	+	12.1253i	−0.278346	+	1.57858i	−0.728130	+	0.685439i	$0.759610\pi$
$60$		0			0
$61$	−2.66045	+	2.23238i	−0.340636	+	0.285827i	−0.797017	−	0.603957i	$-0.793590\pi$
$61$	−2.66045	+	2.23238i	−0.340636	+	0.285827i	0.456381	+	0.889784i	$0.349145\pi$
$62$		0			0
$63$	−5.84744	−	9.05567i	−0.736709	−	1.14091i
$64$		0			0
$65$	−4.01863	+	0.708592i	−0.498449	+	0.0878901i
$66$		0			0
$67$	0.986708	+	2.71096i	0.120546	+	0.331196i	0.985259	−	0.171069i	$-0.0547222\pi$
$67$	0.986708	+	2.71096i	0.120546	+	0.331196i	−0.864713	+	0.502266i	$0.832500\pi$
$68$		0			0
$69$	9.30847	+	8.85641i	1.12061	+	1.06619i
$70$		0			0
$71$	4.44194	−	7.69367i	0.527161	−	0.913070i	−0.472337	−	0.881418i	$-0.656590\pi$
$71$	4.44194	−	7.69367i	0.527161	−	0.913070i	0.999499	−	0.0316527i	$-0.0100770\pi$
$72$		0			0
$73$	−0.528554	−	0.915482i	−0.0618625	−	0.107149i	0.833435	−	0.552617i	$-0.186371\pi$
$73$	−0.528554	−	0.915482i	−0.0618625	−	0.107149i	−0.895298	+	0.445468i	$0.853037\pi$
$74$		0			0
$75$	6.60491	+	2.88210i	0.762669	+	0.332796i
$76$		0			0
$77$	4.20306	−	5.00901i	0.478983	−	0.570829i
$78$		0			0
$79$	3.99634	−	10.9798i	0.449623	−	1.23533i	−0.483364	−	0.875420i	$-0.660585\pi$
$79$	3.99634	−	10.9798i	0.449623	−	1.23533i	0.932987	−	0.359910i	$-0.117193\pi$
$80$		0			0
$81$	8.72124	+	2.22262i	0.969026	+	0.246958i
$82$		0			0
$83$	15.7994	+	5.75052i	1.73421	+	0.631201i	0.998916	−	0.0465461i	$-0.0148214\pi$
$83$	15.7994	+	5.75052i	1.73421	+	0.631201i	0.735295	+	0.677747i	$0.237044\pi$
$84$		0			0
$85$	−3.17849	−	2.66707i	−0.344755	−	0.289284i
$86$		0			0
$87$	−6.13263	+	14.0542i	−0.657487	+	1.50676i
$88$		0			0
$89$	13.1352	−	7.58359i	1.39232	−	0.803859i	0.398752	−	0.917059i	$-0.369444\pi$
$89$	13.1352	−	7.58359i	1.39232	−	0.803859i	0.993572	+	0.113200i	$0.0361102\pi$
$90$		0			0
$91$	13.8594	+	8.00174i	1.45286	+	0.838811i
$92$		0			0
$93$	7.14251	−	7.50709i	0.740644	−	0.778449i
$94$		0			0
$95$	0.789617	−	0.287397i	0.0810130	−	0.0294863i
$96$		0			0
$97$	1.86037	+	10.5507i	0.188892	+	1.07126i	0.920852	+	0.389912i	$0.127495\pi$
$97$	1.86037	+	10.5507i	0.188892	+	1.07126i	−0.731960	+	0.681347i	$0.761394\pi$
$98$		0			0
$99$	0.271563	+	5.45260i	0.0272931	+	0.548007i
$100$		0			0
$101$	−2.54770	−	3.03623i	−0.253506	−	0.302116i	0.624250	−	0.781225i	$-0.285405\pi$
$101$	−2.54770	−	3.03623i	−0.253506	−	0.302116i	−0.877756	+	0.479108i	$0.840960\pi$
$102$		0			0
$103$	−2.32334	−	0.409667i	−0.228925	−	0.0403657i	0.0580087	−	0.998316i	$-0.481525\pi$
$103$	−2.32334	−	0.409667i	−0.228925	−	0.0403657i	−0.286934	+	0.957950i	$0.592636\pi$
$104$		0			0
$105$	2.53759	+	5.10622i	0.247644	+	0.498316i
$106$		0			0
$107$	7.73225			0.747504			0.373752	−	0.927529i	$-0.378071\pi$
$107$	7.73225			0.747504			0.373752	+	0.927529i	$0.378071\pi$
$108$		0			0
$109$	−15.5672			−1.49107			−0.745533	−	0.666469i	$-0.767805\pi$
$109$	−15.5672			−1.49107			−0.745533	+	0.666469i	$0.767805\pi$
$110$		0			0
$111$	6.04179	−	9.10244i	0.573461	−	0.863966i
$112$		0			0
$113$	−9.66087	−	1.70347i	−0.908818	−	0.160249i	−0.300352	−	0.953829i	$-0.597104\pi$
$113$	−9.66087	−	1.70347i	−0.908818	−	0.160249i	−0.608467	+	0.793579i	$0.708215\pi$
$114$		0			0
$115$	−4.36866	−	5.20636i	−0.407379	−	0.485496i
$116$		0			0
$117$	−13.0269	+	2.97189i	−1.20434	+	0.274751i
$118$		0			0
$119$	2.82569	+	16.0253i	0.259031	+	1.46904i
$120$		0			0
$121$	7.22471	−	2.62958i	0.656792	−	0.239053i
$122$		0			0
$123$	1.66518	+	5.64846i	0.150144	+	0.509305i
$124$		0			0
$125$	−7.26847	−	4.19645i	−0.650112	−	0.375342i
$126$		0			0
$127$	16.7402	−	9.66498i	1.48546	−	0.857628i	0.485593	−	0.874185i	$-0.338604\pi$
$127$	16.7402	−	9.66498i	1.48546	−	0.857628i	0.999863	+	0.0165567i	$0.00527040\pi$
$128$		0			0
$129$	−1.60627	+	0.180899i	−0.141424	+	0.0159272i
$130$		0			0
$131$	−13.4142	−	11.2558i	−1.17200	−	0.983427i	−0.172004	−	0.985096i	$-0.555024\pi$
$131$	−13.4142	−	11.2558i	−1.17200	−	0.983427i	−0.999999	+	0.00166932i	$0.999469\pi$
$132$		0			0
$133$	−3.09674	−	1.12712i	−0.268521	−	0.0977338i
$134$		0			0
$135$	−4.45269	−	1.68459i	−0.383227	−	0.144986i
$136$		0			0
$137$	−5.50764	+	15.1321i	−0.470549	+	1.29282i	0.446762	+	0.894653i	$0.352577\pi$
$137$	−5.50764	+	15.1321i	−0.470549	+	1.29282i	−0.917312	+	0.398170i	$0.869645\pi$
$138$		0			0
$139$	−10.6052	+	12.6388i	−0.899525	+	1.07201i	0.0975235	+	0.995233i	$0.468908\pi$
$139$	−10.6052	+	12.6388i	−0.899525	+	1.07201i	−0.997048	+	0.0767785i	$0.975537\pi$
$140$		0			0
$141$	−1.81862	+	1.34206i	−0.153156	+	0.113022i
$142$		0			0
$143$	−4.05254	−	7.01921i	−0.338890	−	0.586975i
$144$		0			0
$145$	4.05556	−	7.02444i	0.336796	−	0.583348i
$146$		0			0
$147$	2.40291	−	9.95191i	0.198189	−	0.820820i
$148$		0			0
$149$	−2.32731	−	6.39423i	−0.190661	−	0.523836i	0.807123	−	0.590384i	$-0.201024\pi$
$149$	−2.32731	−	6.39423i	−0.190661	−	0.523836i	−0.997783	+	0.0665481i	$0.978801\pi$
$150$		0			0
$151$	−14.6770	+	2.58795i	−1.19440	+	0.210604i	−0.735275	−	0.677769i	$-0.762947\pi$
$151$	−14.6770	+	2.58795i	−1.19440	+	0.210604i	−0.459121	+	0.888374i	$0.651836\pi$
$152$		0			0
$153$	−10.8292	−	8.20454i	−0.875487	−	0.663298i
$154$		0			0
$155$	−4.19882	+	3.52323i	−0.337258	+	0.282993i
$156$		0			0
$157$	1.99263	−	11.3007i	0.159029	−	0.901897i	−0.795981	−	0.605322i	$-0.793044\pi$
$157$	1.99263	−	11.3007i	0.159029	−	0.901897i	0.955009	−	0.296575i	$-0.0958446\pi$
$158$		0			0
$159$	−0.273522	+	4.37874i	−0.0216917	+	0.347257i
$160$		0			0
$161$			26.6544i			2.10066i
$162$		0			0
$163$			3.48604i			0.273047i	0.990637	+	0.136524i	$0.0435930\pi$
$163$			3.48604i			0.273047i	−0.990637	+	0.136524i	$0.956407\pi$
$164$		0			0
$165$	0.180039	−	2.88220i	0.0140160	−	0.224379i
$166$		0			0
$167$	−0.759638	+	4.30812i	−0.0587826	+	0.333372i	−0.999990	−	0.00445650i	$-0.998581\pi$
$167$	−0.759638	+	4.30812i	−0.0587826	+	0.333372i	0.941208	+	0.337829i	$0.109693\pi$
$168$		0			0
$169$	5.23738	−	4.39469i	0.402876	−	0.338053i
$170$		0			0
$171$	2.53551	−	1.06850i	0.193895	−	0.0817102i
$172$		0			0
$173$	10.3347	−	1.82229i	0.785732	−	0.138546i	0.233634	−	0.972325i	$-0.424938\pi$
$173$	10.3347	−	1.82229i	0.785732	−	0.138546i	0.552098	+	0.833779i	$0.313827\pi$
$174$		0			0
$175$	5.11309	+	14.0481i	0.386513	+	1.06194i
$176$		0			0
$177$	5.00527	−	20.7299i	0.376219	−	1.55815i
$178$		0			0
$179$	12.6163	−	21.8521i	0.942988	−	1.63330i	0.183257	−	0.983065i	$-0.441336\pi$
$179$	12.6163	−	21.8521i	0.942988	−	1.63330i	0.759731	−	0.650238i	$-0.225331\pi$
$180$		0			0
$181$	1.92076	+	3.32686i	0.142769	+	0.247283i	0.928538	−	0.371236i	$-0.121066\pi$
$181$	1.92076	+	3.32686i	0.142769	+	0.247283i	−0.785769	+	0.618520i	$0.787733\pi$
$182$		0			0
$183$	4.84013	−	3.57179i	0.357793	−	0.264034i
$184$		0			0
$185$	−3.71468	+	4.42698i	−0.273109	+	0.325478i
$186$		0			0
$187$	2.81870	−	7.74432i	0.206124	−	0.566321i
$188$		0			0
$189$	9.13050	+	16.2858i	0.664146	+	1.18462i
$190$		0			0
$191$	−9.28905	−	3.38094i	−0.672132	−	0.244636i	−0.0166663	−	0.999861i	$-0.505305\pi$
$191$	−9.28905	−	3.38094i	−0.672132	−	0.244636i	−0.655465	+	0.755225i	$0.727528\pi$
$192$		0			0
$193$	7.95376	+	6.67400i	0.572524	+	0.480405i	0.882482	−	0.470345i	$-0.155871\pi$
$193$	7.95376	+	6.67400i	0.572524	+	0.480405i	−0.309958	+	0.950750i	$0.600315\pi$
$194$		0			0
$195$	7.02344	−	0.790984i	0.502959	−	0.0566436i
$196$		0			0
$197$	11.0769	−	6.39528i	0.789200	−	0.455645i	−0.0504809	−	0.998725i	$-0.516075\pi$
$197$	11.0769	−	6.39528i	0.789200	−	0.455645i	0.839681	+	0.543080i	$0.182742\pi$
$198$		0			0
$199$	6.79765	+	3.92463i	0.481873	+	0.278209i	0.721197	−	0.692730i	$-0.243592\pi$
$199$	6.79765	+	3.92463i	0.481873	+	0.278209i	−0.239324	+	0.970940i	$0.576926\pi$
$200$		0			0
$201$	−1.41296	−	4.79293i	−0.0996628	−	0.338067i
$202$		0			0
$203$	−29.8920	+	10.8798i	−2.09801	+	0.763613i
$204$		0			0
$205$	−0.540911	−	3.06766i	−0.0377788	−	0.214254i
$206$		0			0
$207$	−15.1350	−	16.3151i	−1.05196	−	1.13398i
$208$		0			0
$209$	1.07283	+	1.27854i	0.0742089	+	0.0884387i
$210$		0			0
$211$	−28.3624	−	5.00106i	−1.95255	−	0.344287i	−0.999084	−	0.0427907i	$-0.986375\pi$
$211$	−28.3624	−	5.00106i	−1.95255	−	0.344287i	−0.953467	−	0.301497i	$-0.902514\pi$
$212$		0			0
$213$	−8.50949	+	12.8202i	−0.583061	+	0.878429i
$214$		0			0
$215$	0.855033			0.0583127
$216$		0			0
$217$	21.4962			1.45926
$218$		0			0
$219$	0.814844	+	1.63965i	0.0550620	+	0.110797i
$220$		0			0
$221$	19.8640	+	3.50255i	1.33620	+	0.235607i
$222$		0			0
$223$	−15.0617	−	17.9499i	−1.00861	−	1.20201i	−0.979294	−	0.202443i	$-0.935112\pi$
$223$	−15.0617	−	17.9499i	−1.00861	−	1.20201i	−0.0293149	−	0.999570i	$-0.509333\pi$
$224$		0			0
$225$	−11.1066	−	5.69545i	−0.740438	−	0.379697i
$226$		0			0
$227$	0.871006	+	4.93972i	0.0578107	+	0.327861i	0.999973	−	0.00729519i	$-0.00232215\pi$
$227$	0.871006	+	4.93972i	0.0578107	+	0.327861i	−0.942163	+	0.335156i	$0.891211\pi$
$228$		0			0
$229$	−9.01670	+	3.28181i	−0.595840	+	0.216868i	−0.622296	−	0.782782i	$-0.713800\pi$
$229$	−9.01670	+	3.28181i	−0.595840	+	0.216868i	0.0264559	+	0.999650i	$0.491578\pi$
$230$		0			0
$231$	−7.80664	+	8.20512i	−0.513639	+	0.539857i
$232$		0			0
$233$	−18.7009	−	10.7969i	−1.22513	−	0.707332i	−0.259126	−	0.965843i	$-0.583435\pi$
$233$	−18.7009	−	10.7969i	−1.22513	−	0.707332i	−0.966008	+	0.258512i	$0.916768\pi$
$234$		0			0
$235$	1.03540	−	0.597786i	0.0675417	−	0.0389952i
$236$		0			0
$237$	−8.09404	+	18.5491i	−0.525764	+	1.20490i
$238$		0			0
$239$	8.27842	+	6.94642i	0.535486	+	0.449326i	0.869991	−	0.493068i	$-0.164125\pi$
$239$	8.27842	+	6.94642i	0.535486	+	0.449326i	−0.334505	+	0.942394i	$0.608569\pi$
$240$		0			0
$241$	12.1965	+	4.43917i	0.785646	+	0.285952i	0.703525	−	0.710670i	$-0.251608\pi$
$241$	12.1965	+	4.43917i	0.785646	+	0.285952i	0.0821214	+	0.996622i	$0.473830\pi$
$242$		0			0
$243$	−14.8362	−	4.78395i	−0.951745	−	0.306891i
$244$		0			0
$245$	−1.85221	+	5.08891i	−0.118334	+	0.325119i
$246$		0			0
$247$	−2.62571	+	3.12919i	−0.167070	+	0.199106i
$248$		0			0
$249$	−26.6912	−	11.6469i	−1.69149	−	0.738092i
$250$		0			0
$251$	−9.36454	−	16.2199i	−0.591085	−	1.02379i	−0.994087	−	0.108590i	$-0.965367\pi$
$251$	−9.36454	−	16.2199i	−0.591085	−	1.02379i	0.403002	−	0.915199i	$-0.367967\pi$
$252$		0			0
$253$	6.74965	−	11.6907i	0.424347	−	0.734991i
$254$		0			0
$255$	5.20659	+	4.95374i	0.326050	+	0.310215i
$256$		0			0
$257$	9.97322	+	27.4012i	0.622113	+	1.70924i	0.701756	+	0.712417i	$0.252399\pi$
$257$	9.97322	+	27.4012i	0.622113	+	1.70924i	−0.0796439	+	0.996823i	$0.525378\pi$
$258$		0			0
$259$	22.3200	−	3.93561i	1.38689	−	0.244547i
$260$		0			0
$261$	12.1190	−	23.6329i	0.750146	−	1.46284i
$262$		0			0
$263$	6.74060	−	5.65604i	0.415643	−	0.348766i	−0.410859	−	0.911699i	$-0.634771\pi$
$263$	6.74060	−	5.65604i	0.415643	−	0.348766i	0.826503	+	0.562932i	$0.190327\pi$
$264$		0			0
$265$	0.402989	−	2.28547i	0.0247554	−	0.140395i
$266$		0			0
$267$	−23.5254	+	11.6912i	−1.43973	+	0.715491i
$268$		0			0
$269$			20.0940i			1.22515i	0.790412	+	0.612575i	$0.209866\pi$
$269$			20.0940i			1.22515i	−0.790412	+	0.612575i	$0.790134\pi$
$270$		0			0
$271$		−	9.14240i		−	0.555361i	−0.960673	−	0.277681i	$-0.910434\pi$
$271$		−	9.14240i		−	0.555361i	0.960673	−	0.277681i	$-0.0895657\pi$
$272$		0			0
$273$	−23.0945	−	15.3291i	−1.39774	−	0.927757i
$274$		0			0
$275$	1.31475	−	7.45634i	0.0792826	−	0.449634i
$276$		0			0
$277$	11.2006	−	9.39839i	0.672977	−	0.564694i	−0.240968	−	0.970533i	$-0.577465\pi$
$277$	11.2006	−	9.39839i	0.672977	−	0.564694i	0.913945	+	0.405839i	$0.133021\pi$
$278$		0			0
$279$	−13.1578	+	12.2061i	−0.787735	+	0.730760i
$280$		0			0
$281$	4.33423	−	0.764241i	0.258558	−	0.0455908i	−0.0428663	−	0.999081i	$-0.513649\pi$
$281$	4.33423	−	0.764241i	0.258558	−	0.0455908i	0.301425	+	0.953490i	$0.402538\pi$
$282$		0			0
$283$	−4.34262	−	11.9313i	−0.258142	−	0.709239i	−0.999282	−	0.0378888i	$-0.987937\pi$
$283$	−4.34262	−	11.9313i	−0.258142	−	0.709239i	0.741140	−	0.671351i	$-0.234285\pi$
$284$		0			0
$285$	−1.39603	+	0.411552i	−0.0826937	+	0.0243782i
$286$		0			0
$287$	−6.10820	+	10.5797i	−0.360556	+	0.624501i
$288$		0			0
$289$	1.75474	+	3.03931i	0.103220	+	0.178783i
$290$		0			0
$291$	−2.07669	−	18.4397i	−0.121737	−	1.08095i
$292$		0			0
$293$	−13.6489	+	16.2661i	−0.797376	+	0.950276i	−0.999577	−	0.0290682i	$-0.990746\pi$
$293$	−13.6489	+	16.2661i	−0.797376	+	0.950276i	0.202201	+	0.979344i	$0.435190\pi$
$294$		0			0
$295$	−3.85817	+	10.6002i	−0.224631	+	0.617169i
$296$		0			0
$297$	0.119346	−	9.45513i	0.00692517	−	0.548642i
$298$		0			0
$299$	31.0466	+	11.3000i	1.79547	+	0.653498i
$300$		0			0
$301$	−2.56877	−	2.15545i	−0.148061	−	0.124238i
$302$		0			0
$303$	4.07630	+	5.52379i	0.234177	+	0.317333i
$304$		0			0
$305$	−2.75563	+	1.59096i	−0.157787	+	0.0910983i
$306$		0			0
$307$	1.24710	+	0.720015i	0.0711759	+	0.0410934i	0.535166	−	0.844747i	$-0.320249\pi$
$307$	1.24710	+	0.720015i	0.0711759	+	0.0410934i	−0.463990	+	0.885841i	$0.653583\pi$
$308$		0			0
$309$	3.97207	+	0.959066i	0.225963	+	0.0545594i
$310$		0			0
$311$	−8.32511	+	3.03009i	−0.472073	+	0.171821i	−0.567091	−	0.823655i	$-0.691931\pi$
$311$	−8.32511	+	3.03009i	−0.472073	+	0.171821i	0.0950180	+	0.995476i	$0.469709\pi$
$312$		0			0
$313$	−5.38779	−	30.5557i	−0.304536	−	1.72711i	−0.625681	−	0.780079i	$-0.715179\pi$
$313$	−5.38779	−	30.5557i	−0.304536	−	1.72711i	0.321145	−	0.947030i	$-0.395932\pi$
$314$		0			0
$315$	−3.83530	−	9.10104i	−0.216095	−	0.512785i
$316$		0			0
$317$	1.05369	+	1.25574i	0.0591813	+	0.0705295i	0.794823	−	0.606841i	$-0.207564\pi$
$317$	1.05369	+	1.25574i	0.0591813	+	0.0705295i	−0.735642	+	0.677371i	$0.763119\pi$
$318$		0			0
$319$	15.8659	+	2.79758i	0.888318	+	0.156634i
$320$		0			0
$321$	−13.3666	−	0.834957i	−0.746050	−	0.0466027i
$322$		0			0
$323$	−4.15354			−0.231109
$324$		0			0
$325$	18.5307			1.02790
$326$		0			0
$327$	26.9107	+	1.68100i	1.48817	+	0.0929597i
$328$		0			0
$329$	−4.61759	−	0.814205i	−0.254576	−	0.0448886i
$330$		0			0
$331$	−4.17455	−	4.97503i	−0.229454	−	0.273452i	0.639017	−	0.769193i	$-0.279341\pi$
$331$	−4.17455	−	4.97503i	−0.229454	−	0.273452i	−0.868471	+	0.495740i	$0.834897\pi$
$332$		0			0
$333$	−11.4272	+	15.0828i	−0.626209	+	0.826533i
$334$		0			0
$335$	0.458983	+	2.60302i	0.0250769	+	0.142218i
$336$		0			0
$337$	19.8793	−	7.23548i	1.08290	−	0.394142i	0.261911	−	0.965092i	$-0.415647\pi$
$337$	19.8793	−	7.23548i	1.08290	−	0.394142i	0.820985	+	0.570950i	$0.193425\pi$
$338$		0			0
$339$	16.5166	+	3.98798i	0.897060	+	0.216597i
$340$		0			0
$341$	−9.42834	−	5.44346i	−0.510573	−	0.294780i
$342$		0			0
$343$	−3.38918	+	1.95675i	−0.182999	+	0.105654i
$344$		0			0
$345$	6.98981	+	9.47189i	0.376319	+	0.509949i
$346$		0			0
$347$	7.60026	+	6.37737i	0.408003	+	0.342355i	0.823577	−	0.567204i	$-0.191975\pi$
$347$	7.60026	+	6.37737i	0.408003	+	0.342355i	−0.415574	+	0.909559i	$0.636419\pi$
$348$		0			0
$349$	−10.6407	−	3.87290i	−0.569583	−	0.207311i	0.0411427	−	0.999153i	$-0.486900\pi$
$349$	−10.6407	−	3.87290i	−0.569583	−	0.207311i	−0.610726	+	0.791842i	$0.709122\pi$
$350$		0			0
$351$	22.8403	−	3.73075i	1.21912	−	0.199133i
$352$		0			0
$353$	3.15842	−	8.67769i	0.168106	−	0.461867i	−0.826821	−	0.562464i	$-0.809853\pi$
$353$	3.15842	−	8.67769i	0.168106	−	0.461867i	0.994927	+	0.100598i	$0.0320755\pi$
$354$		0			0
$355$	5.23190	−	6.23514i	0.277680	−	0.330927i
$356$		0			0
$357$	−3.15425	−	28.0078i	−0.166941	−	1.48233i
$358$		0			0
$359$	8.31565	+	14.4031i	0.438883	+	0.760168i	0.997604	−	0.0691878i	$-0.0220408\pi$
$359$	8.31565	+	14.4031i	0.438883	+	0.760168i	−0.558720	+	0.829356i	$0.688707\pi$
$360$		0			0
$361$	−9.07942	+	15.7260i	−0.477864	+	0.827685i
$362$		0			0
$363$	−12.7732	+	3.76556i	−0.670418	+	0.197640i
$364$		0			0
$365$	−0.331253	−	0.910110i	−0.0173386	−	0.0476374i
$366$		0			0
$367$	−15.0549	+	2.65459i	−0.785860	+	0.138568i	−0.552158	−	0.833740i	$-0.686195\pi$
$367$	−15.0549	+	2.65459i	−0.785860	+	0.138568i	−0.233703	+	0.972308i	$0.575084\pi$
$368$		0			0
$369$	−2.26862	−	9.94420i	−0.118100	−	0.517675i
$370$		0			0
$371$	−6.97213	+	5.85032i	−0.361975	+	0.303733i
$372$		0			0
$373$	−3.27227	+	18.5580i	−0.169432	+	0.960896i	0.774945	+	0.632029i	$0.217778\pi$
$373$	−3.27227	+	18.5580i	−0.169432	+	0.960896i	−0.944376	+	0.328866i	$0.893333\pi$
$374$		0			0
$375$	12.1117	+	8.03920i	0.625446	+	0.415143i
$376$		0			0
$377$			39.4302i			2.03076i
$378$		0			0
$379$			27.7620i			1.42604i	0.701144	+	0.713019i	$0.252673\pi$
$379$			27.7620i			1.42604i	−0.701144	+	0.713019i	$0.747327\pi$
$380$		0			0
$381$	−29.9822	+	14.9000i	−1.53603	+	0.763350i
$382$		0			0
$383$	5.46348	−	30.9849i	0.279171	−	1.58325i	−0.446224	−	0.894921i	$-0.647231\pi$
$383$	5.46348	−	30.9849i	0.279171	−	1.58325i	0.725394	−	0.688333i	$-0.241657\pi$
$384$		0			0
$385$	4.58924	−	3.85083i	0.233889	−	0.196256i
$386$		0			0
$387$	2.79626	−	0.139265i	0.142142	−	0.00707926i
$388$		0			0
$389$	−9.58341	+	1.68981i	−0.485898	+	0.0856769i	−0.411230	−	0.911532i	$-0.634901\pi$
$389$	−9.58341	+	1.68981i	−0.485898	+	0.0856769i	−0.0746678	+	0.997208i	$0.523790\pi$
$390$		0			0
$391$	11.4900	+	31.5685i	0.581075	+	1.59649i
$392$		0			0
$393$	21.9734	+	20.9063i	1.10841	+	1.05458i
$394$		0			0
$395$	5.35266	−	9.27108i	0.269322	−	0.466479i
$396$		0			0
$397$	−8.72266	−	15.1081i	−0.437778	−	0.758253i	0.559740	−	0.828668i	$-0.310901\pi$
$397$	−8.72266	−	15.1081i	−0.437778	−	0.758253i	−0.997518	+	0.0704151i	$0.977568\pi$
$398$		0			0
$399$	5.23156	+	2.28283i	0.261906	+	0.114284i
$400$		0			0
$401$	6.59597	−	7.86077i	0.329387	−	0.392548i	−0.575780	−	0.817605i	$-0.695301\pi$
$401$	6.59597	−	7.86077i	0.329387	−	0.392548i	0.905167	+	0.425057i	$0.139746\pi$
$402$		0			0
$403$	9.11325	−	25.0385i	0.453963	−	1.24725i
$404$		0			0
$405$	7.51537	+	3.39294i	0.373442	+	0.168596i
$406$		0			0
$407$	−10.7863	−	3.92587i	−0.534655	−	0.194598i
$408$		0			0
$409$	−5.65802	−	4.74764i	−0.279771	−	0.234756i	0.492094	−	0.870542i	$-0.336232\pi$
$409$	−5.65802	−	4.74764i	−0.279771	−	0.234756i	−0.771865	+	0.635786i	$0.780676\pi$
$410$		0			0
$411$	11.1550	−	25.5639i	0.550234	−	1.26097i
$412$		0			0
$413$	38.3132	−	22.1201i	1.88527	−	1.08846i
$414$		0			0
$415$	13.3406	+	7.70219i	0.654864	+	0.378086i
$416$		0			0
$417$	19.6979	−	20.7033i	0.964609	−	1.01385i
$418$		0			0
$419$	−15.7103	+	5.71807i	−0.767496	+	0.279346i	−0.695949	−	0.718091i	$-0.745016\pi$
$419$	−15.7103	+	5.71807i	−0.767496	+	0.279346i	−0.0715474	+	0.997437i	$0.522794\pi$
$420$		0			0
$421$	1.99066	+	11.2896i	0.0970187	+	0.550221i	0.994110	+	0.108375i	$0.0345648\pi$
$421$	1.99066	+	11.2896i	0.0970187	+	0.550221i	−0.897091	+	0.441845i	$0.854324\pi$
$422$		0			0
$423$	3.28874	−	2.12361i	0.159904	−	0.103253i
$424$		0			0
$425$	12.1115	+	14.4340i	0.587495	+	0.700150i
$426$		0			0
$427$	12.2894	+	2.16695i	0.594725	+	0.104866i
$428$		0			0
$429$	6.24759	+	12.5716i	0.301637	+	0.606961i
$430$		0			0
$431$	16.5555			0.797449			0.398724	−	0.917071i	$-0.369453\pi$
$431$	16.5555			0.797449			0.398724	+	0.917071i	$0.369453\pi$
$432$		0			0
$433$	−4.88427			−0.234723			−0.117361	−	0.993089i	$-0.537444\pi$
$433$	−4.88427			−0.234723			−0.117361	+	0.993089i	$0.537444\pi$
$434$		0			0
$435$	−7.76930	+	11.7051i	−0.372509	+	0.561216i
$436$		0			0
$437$	−6.70014	−	1.18142i	−0.320511	−	0.0565148i
$438$		0			0
$439$	19.5417	+	23.2889i	0.932677	+	1.11152i	0.993552	+	0.113375i	$0.0361662\pi$
$439$	19.5417	+	23.2889i	0.932677	+	1.11152i	−0.0608757	+	0.998145i	$0.519389\pi$
$440$		0			0
$441$	−5.22851	+	16.9442i	−0.248977	+	0.806867i
$442$		0			0
$443$	−0.340783	−	1.93268i	−0.0161911	−	0.0918243i	0.975641	−	0.219372i	$-0.0704007\pi$
$443$	−0.340783	−	1.93268i	−0.0161911	−	0.0918243i	−0.991832	+	0.127547i	$0.959290\pi$
$444$		0			0
$445$	13.0581	−	4.75276i	0.619013	−	0.225302i
$446$		0			0
$447$	3.33270	+	11.3049i	0.157631	+	0.534703i
$448$		0			0
$449$	−25.2445	−	14.5749i	−1.19136	−	0.687834i	−0.232747	−	0.972537i	$-0.574771\pi$
$449$	−25.2445	−	14.5749i	−1.19136	−	0.687834i	−0.958616	+	0.284704i	$0.908105\pi$
$450$		0			0
$451$	5.35817	−	3.09354i	0.252307	−	0.145669i
$452$		0			0
$453$	25.6513	−	2.88886i	1.20520	−	0.135731i
$454$		0			0
$455$	11.2320	+	9.42478i	0.526565	+	0.441841i
$456$		0			0
$457$	28.2232	+	10.2724i	1.32023	+	0.480523i	0.903531	−	0.428523i	$-0.140966\pi$
$457$	28.2232	+	10.2724i	1.32023	+	0.480523i	0.416695	+	0.909046i	$0.363188\pi$
$458$		0			0
$459$	17.8342	+	15.3524i	0.832431	+	0.716589i
$460$		0			0
$461$	−0.669179	+	1.83856i	−0.0311668	+	0.0856301i	−0.954300	−	0.298850i	$-0.903397\pi$
$461$	−0.669179	+	1.83856i	−0.0311668	+	0.0856301i	0.923133	+	0.384480i	$0.125619\pi$
$462$		0			0
$463$	−13.0605	+	15.5649i	−0.606974	+	0.723363i	−0.978772	−	0.204950i	$-0.934297\pi$
$463$	−13.0605	+	15.5649i	−0.606974	+	0.723363i	0.371799	+	0.928313i	$0.378741\pi$
$464$		0			0
$465$	7.63888	−	5.63714i	0.354245	−	0.261416i
$466$		0			0
$467$	0.632284	+	1.09515i	0.0292586	+	0.0506774i	0.880284	−	0.474447i	$-0.157352\pi$
$467$	0.632284	+	1.09515i	0.0292586	+	0.0506774i	−0.851025	+	0.525125i	$0.824019\pi$
$468$		0			0
$469$	5.18304	−	8.97729i	0.239330	−	0.414533i
$470$		0			0
$471$	−4.66491	+	19.3202i	−0.214948	+	0.890228i
$472$		0			0
$473$	0.580852	+	1.59588i	0.0267076	+	0.0733785i
$474$		0			0
$475$	−3.75791	+	0.662622i	−0.172425	+	0.0304032i
$476$		0			0
$477$	0.945665	−	7.53991i	0.0432990	−	0.345229i
$478$		0			0
$479$	5.46294	−	4.58395i	0.249608	−	0.209446i	−0.509395	−	0.860533i	$-0.670131\pi$
$479$	5.46294	−	4.58395i	0.249608	−	0.209446i	0.759004	+	0.651086i	$0.225686\pi$
$480$		0			0
$481$	4.87834	−	27.6664i	0.222433	−	1.26148i
$482$		0			0
$483$	2.87824	−	46.0770i	0.130964	−	2.09657i
$484$		0			0
$485$			9.81563i			0.445705i
$486$		0			0
$487$		−	35.3831i		−	1.60336i	−0.597752	−	0.801681i	$-0.703939\pi$
$487$		−	35.3831i		−	1.60336i	0.597752	−	0.801681i	$-0.296061\pi$
$488$		0			0
$489$	0.376435	−	6.02625i	0.0170230	−	0.272516i
$490$		0			0
$491$	−0.202915	+	1.15079i	−0.00915741	+	0.0519343i	−0.989044	−	0.147621i	$-0.952839\pi$
$491$	−0.202915	+	1.15079i	−0.00915741	+	0.0519343i	0.979887	+	0.199555i	$0.0639496\pi$
$492$		0			0
$493$	−30.7131	+	25.7713i	−1.38325	+	1.16068i
$494$		0			0
$495$	−0.622462	+	4.96297i	−0.0279776	+	0.223069i
$496$		0			0
$497$	−31.4363	+	5.54307i	−1.41011	+	0.248641i
$498$		0			0
$499$	−9.12958	−	25.0833i	−0.408696	−	1.12288i	−0.957877	−	0.287180i	$-0.907282\pi$
$499$	−9.12958	−	25.0833i	−0.408696	−	1.12288i	0.549180	−	0.835704i	$-0.314940\pi$
$500$		0			0
$501$	1.77838	−	7.36534i	0.0794521	−	0.329059i
$502$		0			0
$503$	−11.9257	+	20.6560i	−0.531742	+	0.921005i	0.467571	+	0.883956i	$0.345129\pi$
$503$	−11.9257	+	20.6560i	−0.531742	+	0.921005i	−0.999313	+	0.0370494i	$0.988204\pi$
$504$		0			0
$505$	−1.81568	−	3.14486i	−0.0807969	−	0.139944i
$506$		0			0
$507$	−9.52832	+	7.03146i	−0.423168	+	0.312278i
$508$		0			0
$509$	13.0480	−	15.5500i	0.578343	−	0.689242i	−0.394978	−	0.918691i	$-0.629248\pi$
$509$	13.0480	−	15.5500i	0.578343	−	0.689242i	0.973321	+	0.229449i	$0.0736923\pi$
$510$		0			0
$511$	−1.29912	+	3.56929i	−0.0574695	+	0.157896i
$512$		0			0
$513$	−4.49847	+	1.57330i	−0.198612	+	0.0694629i
$514$		0			0
$515$	−2.03112	−	0.739267i	−0.0895018	−	0.0325760i
$516$		0			0
$517$	1.81912	+	1.52642i	0.0800046	+	0.0671319i
$518$		0			0
$519$	−18.0622	+	2.03417i	−0.792841	+	0.0892902i
$520$		0			0
$521$	28.4047	−	16.3995i	1.24443	−	0.718474i	0.274439	−	0.961604i	$-0.411508\pi$
$521$	28.4047	−	16.3995i	1.24443	−	0.718474i	0.969993	+	0.243131i	$0.0781745\pi$
$522$		0			0
$523$	−30.4619	−	17.5872i	−1.33201	−	0.769034i	−0.346399	−	0.938087i	$-0.612596\pi$
$523$	−30.4619	−	17.5872i	−1.33201	−	0.769034i	−0.985607	+	0.169053i	$0.945929\pi$
$524$		0			0
$525$	−7.32193	−	24.8368i	−0.319555	−	1.08397i
$526$		0			0
$527$	25.4594	−	9.26646i	1.10903	−	0.403653i
$528$		0			0
$529$	5.56158	+	31.5413i	0.241808	+	1.37136i
$530$		0			0
$531$	−10.8910	+	35.2948i	−0.472630	+	1.53167i
$532$		0			0
$533$	9.73354	+	11.6000i	0.421606	+	0.502451i
$534$		0			0
$535$	6.97664	+	1.23017i	0.301626	+	0.0531849i
$536$		0			0
$537$	−24.1693	+	36.4130i	−1.04298	+	1.57134i
$538$		0			0
$539$	−10.7565			−0.463315
$540$		0			0
$541$	−35.1137			−1.50965			−0.754827	−	0.655924i	$-0.772279\pi$
$541$	−35.1137			−1.50965			−0.754827	+	0.655924i	$0.772279\pi$
$542$		0			0
$543$	−2.96114	−	5.95849i	−0.127075	−	0.255703i
$544$		0			0
$545$	−14.0459	−	2.47668i	−0.601662	−	0.106089i
$546$		0			0
$547$	9.15157	+	10.9064i	0.391293	+	0.466324i	0.925345	−	0.379127i	$-0.123776\pi$
$547$	9.15157	+	10.9064i	0.391293	+	0.466324i	−0.534052	+	0.845452i	$0.679331\pi$
$548$		0			0
$549$	−8.75274	+	5.65184i	−0.373558	+	0.241214i
$550$		0			0
$551$	−1.40995	−	7.99622i	−0.0600659	−	0.340650i
$552$		0			0
$553$	−39.4524	+	14.3595i	−1.67769	+	0.610629i
$554$		0			0
$555$	6.89954	−	7.25172i	0.292869	−	0.307818i
$556$		0			0
$557$	−21.0603	−	12.1592i	−0.892352	−	0.515200i	−0.0176411	−	0.999844i	$-0.505616\pi$
$557$	−21.0603	−	12.1592i	−0.892352	−	0.515200i	−0.874711	+	0.484645i	$0.838949\pi$
$558$		0			0
$559$	−3.59966	+	2.07826i	−0.152249	+	0.0879012i
$560$		0			0
$561$	−5.70890	+	13.0831i	−0.241030	+	0.552369i
$562$		0			0
$563$	5.33375	+	4.47555i	0.224791	+	0.188622i	0.748227	−	0.663443i	$-0.230906\pi$
$563$	5.33375	+	4.47555i	0.224791	+	0.188622i	−0.523436	+	0.852065i	$0.675350\pi$
$564$		0			0
$565$	−8.44578	−	3.07401i	−0.355317	−	0.129325i
$566$		0			0
$567$	−14.0251	−	29.1389i	−0.589000	−	1.22372i
$568$		0			0
$569$	6.42509	−	17.6528i	0.269354	−	0.740043i	−0.729098	−	0.684410i	$-0.760060\pi$
$569$	6.42509	−	17.6528i	0.269354	−	0.740043i	0.998451	−	0.0556334i	$-0.0177178\pi$
$570$		0			0
$571$	17.2113	−	20.5116i	0.720269	−	0.858383i	−0.274388	−	0.961619i	$-0.588475\pi$
$571$	17.2113	−	20.5116i	0.720269	−	0.858383i	0.994657	+	0.103236i	$0.0329197\pi$
$572$		0			0
$573$	15.6927	+	6.84763i	0.655573	+	0.286064i
$574$		0			0
$575$	15.4318	+	26.7286i	0.643549	+	1.11466i
$576$		0			0
$577$	−4.84104	+	8.38493i	−0.201535	+	0.349069i	−0.949023	−	0.315206i	$-0.897926\pi$
$577$	−4.84104	+	8.38493i	−0.201535	+	0.349069i	0.747488	+	0.664275i	$0.231260\pi$
$578$		0			0
$579$	−13.0288	−	12.3961i	−0.541460	−	0.515164i
$580$		0			0
$581$	−20.6626	−	56.7699i	−0.857228	−	2.35521i
$582$		0			0
$583$	4.53948	−	0.800433i	0.188006	−	0.0331505i
$584$		0			0
$585$	−12.2267	+	0.608942i	−0.505512	+	0.0251767i
$586$		0			0
$587$	6.78871	−	5.69641i	0.280200	−	0.235116i	−0.491846	−	0.870682i	$-0.663678\pi$
$587$	6.78871	−	5.69641i	0.280200	−	0.235116i	0.772046	+	0.635566i	$0.219233\pi$
$588$		0			0
$589$	−0.952788	+	5.40353i	−0.0392589	+	0.222648i
$590$		0			0
$591$	−19.8391	+	9.85927i	−0.816072	+	0.405556i
$592$		0			0
$593$		−	6.46963i		−	0.265676i	−0.991138	−	0.132838i	$-0.957591\pi$
$593$		−	6.46963i		−	0.265676i	0.991138	−	0.132838i	$-0.0424090\pi$
$594$		0			0
$595$			14.9088i			0.611203i
$596$		0			0
$597$	−11.3272	−	7.51846i	−0.463590	−	0.307710i
$598$		0			0
$599$	−0.995333	+	5.64481i	−0.0406682	+	0.230641i	−0.998367	−	0.0571331i	$-0.981804\pi$
$599$	−0.995333	+	5.64481i	−0.0406682	+	0.230641i	0.957698	+	0.287774i	$0.0929152\pi$
$600$		0			0
$601$	−13.9437	+	11.7002i	−0.568777	+	0.477260i	−0.881240	−	0.472670i	$-0.843290\pi$
$601$	−13.9437	+	11.7002i	−0.568777	+	0.477260i	0.312463	+	0.949930i	$0.398846\pi$
$602$		0			0
$603$	1.92501	+	8.43803i	0.0783923	+	0.343623i
$604$		0			0
$605$	6.93706	−	1.22319i	0.282032	−	0.0497298i
$606$		0			0
$607$	−12.4668	−	34.2523i	−0.506012	−	1.39026i	−0.885318	−	0.464985i	$-0.846060\pi$
$607$	−12.4668	−	34.2523i	−0.506012	−	1.39026i	0.379307	−	0.925271i	$-0.376163\pi$
$608$		0			0
$609$	52.8486	−	15.5799i	2.14153	−	0.631328i
$610$		0			0
$611$	−2.90599	+	5.03331i	−0.117564	+	0.203626i
$612$		0			0
$613$	9.95224	+	17.2378i	0.401967	+	0.696228i	0.993963	−	0.109713i	$-0.0349932\pi$
$613$	9.95224	+	17.2378i	0.401967	+	0.696228i	−0.591996	+	0.805941i	$0.701660\pi$
$614$		0			0
$615$	0.603805	+	5.36141i	0.0243478	+	0.216193i
$616$		0			0
$617$	10.3239	−	12.3036i	0.415625	−	0.495323i	−0.517093	−	0.855929i	$-0.672986\pi$
$617$	10.3239	−	12.3036i	0.415625	−	0.495323i	0.932718	+	0.360607i	$0.117430\pi$
$618$		0			0
$619$	−11.8156	+	32.4631i	−0.474909	+	1.30480i	0.438855	+	0.898558i	$0.355384\pi$
$619$	−11.8156	+	32.4631i	−0.474909	+	1.30480i	−0.913764	+	0.406245i	$0.866838\pi$
$620$		0			0
$621$	24.4019	+	29.8379i	0.979214	+	1.19735i
$622$		0			0
$623$	−51.2115	−	18.6395i	−2.05175	−	0.746775i
$624$		0			0
$625$	10.0454	+	8.42910i	0.401816	+	0.337164i
$626$		0			0
$627$	−1.71651	−	2.32604i	−0.0685509	−	0.0928932i
$628$		0			0
$629$	24.7385	−	14.2828i	0.986387	−	0.569491i
$630$		0			0
$631$	−26.9199	−	15.5422i	−1.07166	−	0.618725i	−0.143028	−	0.989719i	$-0.545684\pi$
$631$	−26.9199	−	15.5422i	−1.07166	−	0.618725i	−0.928635	+	0.370994i	$0.879017\pi$
$632$		0			0
$633$	48.4896	+	11.7079i	1.92729	+	0.465348i
$634$		0			0
$635$	16.6420	−	6.05720i	0.660418	−	0.240373i
$636$		0			0
$637$	−4.57149	−	25.9262i	−0.181129	−	1.02723i
$638$		0			0
$639$	16.0946	−	21.2432i	0.636692	−	0.840369i
$640$		0			0
$641$	−23.7440	−	28.2970i	−0.937831	−	1.11766i	−0.992873	−	0.119179i	$-0.961974\pi$
$641$	−23.7440	−	28.2970i	−0.937831	−	1.11766i	0.0550422	−	0.998484i	$-0.482471\pi$
$642$		0			0
$643$	−0.700721	−	0.123556i	−0.0276337	−	0.00487257i	0.159814	−	0.987147i	$-0.448910\pi$
$643$	−0.700721	−	0.123556i	−0.0276337	−	0.00487257i	−0.187448	+	0.982275i	$0.560022\pi$
$644$		0			0
$645$	−1.47808	−	0.0923296i	−0.0581993	−	0.00363547i
$646$		0			0
$647$	−33.2439			−1.30695			−0.653476	−	0.756947i	$-0.726690\pi$
$647$	−33.2439			−1.30695			−0.653476	+	0.756947i	$0.726690\pi$
$648$		0			0
$649$	−22.4058			−0.879504
$650$		0			0
$651$	−37.1601	−	2.32124i	−1.45642	−	0.0909766i
$652$		0			0
$653$	5.33170	+	0.940122i	0.208645	+	0.0367898i	0.276994	−	0.960872i	$-0.410662\pi$
$653$	5.33170	+	0.940122i	0.208645	+	0.0367898i	−0.0683484	+	0.997662i	$0.521773\pi$
$654$		0			0
$655$	−10.3126	−	12.2900i	−0.402945	−	0.480212i
$656$		0			0
$657$	−1.23155	−	2.92242i	−0.0480473	−	0.114015i
$658$		0			0
$659$	−3.94718	−	22.3856i	−0.153760	−	0.872017i	−0.959911	−	0.280307i	$-0.909564\pi$
$659$	−3.94718	−	22.3856i	−0.153760	−	0.872017i	0.806150	−	0.591711i	$-0.201547\pi$
$660$		0			0
$661$	1.00411	−	0.365468i	0.0390555	−	0.0142150i	−0.322419	−	0.946597i	$-0.604496\pi$
$661$	1.00411	−	0.365468i	0.0390555	−	0.0142150i	0.361474	+	0.932382i	$0.382274\pi$
$662$		0			0
$663$	−33.9603	−	8.19978i	−1.31891	−	0.318453i
$664$		0			0
$665$	−2.61480	−	1.50966i	−0.101398	−	0.0585419i
$666$		0			0
$667$	−56.8740	+	32.8362i	−2.20217	+	1.27142i
$668$		0			0
$669$	24.0987	+	32.6561i	0.931708	+	1.26256i
$670$		0			0
$671$	−4.84145	−	4.06246i	−0.186902	−	0.156829i
$672$		0			0
$673$	−16.4390	−	5.98331i	−0.633677	−	0.230640i	0.00515388	−	0.999987i	$-0.498359\pi$
$673$	−16.4390	−	5.98331i	−0.633677	−	0.230640i	−0.638831	+	0.769347i	$0.720582\pi$
$674$		0			0
$675$	18.5847	+	11.0450i	0.715325	+	0.425120i
$676$		0			0
$677$	−0.164509	+	0.451985i	−0.00632259	+	0.0173712i	−0.942814	−	0.333320i	$-0.891831\pi$
$677$	−0.164509	+	0.451985i	−0.00632259	+	0.0173712i	0.936491	+	0.350691i	$0.114053\pi$
$678$		0			0
$679$	24.7442	−	29.4890i	0.949597	−	1.13169i
$680$		0			0
$681$	−0.972282	−	8.63325i	−0.0372579	−	0.330827i
$682$		0			0
$683$	−20.5853	−	35.6548i	−0.787675	−	1.36429i	−0.927388	−	0.374101i	$-0.877951\pi$
$683$	−20.5853	−	35.6548i	−0.787675	−	1.36429i	0.139713	−	0.990192i	$-0.455382\pi$
$684$		0			0
$685$	−7.37688	+	12.7771i	−0.281856	+	0.488189i
$686$		0			0
$687$	15.9414	−	4.69955i	0.608202	−	0.179299i
$688$		0			0
$689$	3.85854	+	10.6013i	0.146999	+	0.403876i
$690$		0			0
$691$	10.6791	−	1.88301i	0.406251	−	0.0716330i	0.0332112	−	0.999448i	$-0.489427\pi$
$691$	10.6791	−	1.88301i	0.406251	−	0.0716330i	0.373040	+	0.927815i	$0.378315\pi$
$692$		0			0
$693$	14.3812	−	13.3410i	0.546297	−	0.506784i
$694$		0			0
$695$	−11.5797	+	9.71650i	−0.439242	+	0.368568i
$696$		0			0
$697$	−2.67371	+	15.1633i	−0.101274	+	0.574353i
$698$		0			0
$699$	31.1619	+	20.6839i	1.17865	+	0.782336i
$700$		0			0
$701$			26.1415i			0.987349i	0.869647	+	0.493675i	$0.164347\pi$
$701$			26.1415i			0.987349i	−0.869647	+	0.493675i	$0.835653\pi$
$702$		0			0
$703$			5.78503i			0.218187i
$704$		0			0
$705$	−1.85442	+	0.921575i	−0.0698415	+	0.0347085i
$706$		0			0
$707$	−2.47303	+	14.0252i	−0.0930077	+	0.527473i
$708$		0			0
$709$	1.19849	−	1.00565i	0.0450101	−	0.0377680i	−0.620005	−	0.784598i	$-0.712869\pi$
$709$	1.19849	−	1.00565i	0.0450101	−	0.0377680i	0.665015	+	0.746830i	$0.268425\pi$
$710$		0			0
$711$	15.9950	−	31.1915i	0.599860	−	1.16977i
$712$		0			0
$713$	43.7046	−	7.70630i	1.63675	−	0.288603i
$714$		0			0
$715$	−2.53979	−	6.97802i	−0.0949828	−	0.260963i
$716$		0			0
$717$	−13.5606	−	12.9021i	−0.506432	−	0.481837i
$718$		0			0
$719$	−14.4301	+	24.9937i	−0.538153	+	0.932109i	0.460850	+	0.887478i	$0.347545\pi$
$719$	−14.4301	+	24.9937i	−0.538153	+	0.932109i	−0.999004	+	0.0446310i	$0.985789\pi$
$720$		0			0
$721$	4.23846	+	7.34123i	0.157848	+	0.273402i
$722$		0			0
$723$	−20.6045	−	8.99093i	−0.766291	−	0.334376i
$724$		0			0
$725$	−23.6763	+	28.2163i	−0.879315	+	1.04793i
$726$		0			0
$727$	−13.9968	+	38.4560i	−0.519114	+	1.42625i	0.352385	+	0.935855i	$0.385371\pi$
$727$	−13.9968	+	38.4560i	−0.519114	+	1.42625i	−0.871499	+	0.490398i	$0.836851\pi$
$728$		0			0
$729$	25.1305	+	9.87200i	0.930760	+	0.365630i
$730$		0			0
$731$	−3.97152	−	1.44552i	−0.146892	−	0.0534643i
$732$		0			0
$733$	1.89373	+	1.58903i	0.0699466	+	0.0586922i	0.677091	−	0.735900i	$-0.263240\pi$
$733$	1.89373	+	1.58903i	0.0699466	+	0.0586922i	−0.607144	+	0.794592i	$0.707685\pi$
$734$		0			0
$735$	3.75141	−	8.59710i	0.138373	−	0.317109i
$736$		0			0
$737$	−4.54661	+	2.62499i	−0.167477	+	0.0966926i
$738$		0			0
$739$	9.69724	+	5.59870i	0.356719	+	0.205952i	0.667640	−	0.744484i	$-0.267304\pi$
$739$	9.69724	+	5.59870i	0.356719	+	0.205952i	−0.310922	+	0.950436i	$0.600638\pi$
$740$		0			0
$741$	4.87691	−	5.12585i	0.179158	−	0.188303i
$742$		0			0
$743$	41.9122	−	15.2548i	1.53761	−	0.559645i	0.572140	−	0.820156i	$-0.306113\pi$
$743$	41.9122	−	15.2548i	1.53761	−	0.559645i	0.965471	+	0.260511i	$0.0838911\pi$
$744$		0			0
$745$	−1.08258	−	6.13964i	−0.0396628	−	0.224939i
$746$		0			0
$747$	44.8829	+	23.0160i	1.64218	+	0.842111i
$748$		0			0
$749$	−17.8587	−	21.2832i	−0.652544	−	0.777671i
$750$		0			0
$751$	11.5655	+	2.03931i	0.422032	+	0.0744156i	0.380631	−	0.924727i	$-0.375707\pi$
$751$	11.5655	+	2.03931i	0.422032	+	0.0744156i	0.0414009	+	0.999143i	$0.486818\pi$
$752$		0			0
$753$	14.4368	+	29.0502i	0.526107	+	1.05865i
$754$		0			0
$755$	−13.6545			−0.496937
$756$		0			0
$757$	5.35502			0.194632			0.0973158	−	0.995254i	$-0.468974\pi$
$757$	5.35502			0.194632			0.0973158	+	0.995254i	$0.468974\pi$
$758$		0			0
$759$	−12.9304	+	19.4807i	−0.469344	+	0.707105i
$760$		0			0
$761$	13.3535	+	2.35458i	0.484064	+	0.0853536i	0.410354	−	0.911926i	$-0.365405\pi$
$761$	13.3535	+	2.35458i	0.484064	+	0.0853536i	0.0737099	+	0.997280i	$0.476516\pi$
$762$		0			0
$763$	35.9547	+	42.8491i	1.30165	+	1.55124i
$764$		0			0
$765$	−8.46562	−	9.12566i	−0.306075	−	0.329939i
$766$		0			0
$767$	−9.52242	−	54.0043i	−0.343835	−	1.94998i
$768$		0			0
$769$	−16.2757	+	5.92388i	−0.586917	+	0.213620i	−0.618373	−	0.785885i	$-0.712208\pi$
$769$	−16.2757	+	5.92388i	−0.586917	+	0.213620i	0.0314556	+	0.999505i	$0.489986\pi$
$770$		0			0
$771$	−14.2816	−	48.4449i	−0.514341	−	1.74470i
$772$		0			0
$773$	−43.8577	−	25.3213i	−1.57745	−	0.910743i	−0.995213	−	0.0977249i	$-0.968843\pi$
$773$	−43.8577	−	25.3213i	−1.57745	−	0.910743i	−0.582239	−	0.813018i	$-0.697823\pi$
$774$		0			0
$775$	21.5561	−	12.4454i	0.774316	−	0.447052i
$776$		0			0
$777$	−39.0091	+	4.39323i	−1.39944	+	0.157606i
$778$		0			0
$779$	−2.38870	−	2.00436i	−0.0855840	−	0.0718135i
$780$		0			0
$781$	15.1918	+	5.52936i	0.543605	+	0.197856i
$782$		0			0
$783$	−23.5018	+	39.5452i	−0.839887	+	1.41323i
$784$		0			0
$785$	3.59581	−	9.87940i	0.128340	−	0.352611i
$786$		0			0
$787$	−3.42817	+	4.08553i	−0.122201	+	0.145634i	−0.823676	−	0.567060i	$-0.808081\pi$
$787$	−3.42817	+	4.08553i	−0.122201	+	0.145634i	0.701475	+	0.712694i	$0.252525\pi$
$788$		0			0
$789$	−12.2631	+	9.04961i	−0.436579	+	0.322175i
$790$		0			0
$791$	17.6243	+	30.5262i	0.626649	+	1.08539i
$792$		0			0
$793$	7.73407	−	13.3958i	0.274645	−	0.475699i
$794$		0			0
$795$	−0.943434	+	3.90733i	−0.0334601	+	0.138579i
$796$		0			0
$797$	7.46871	+	20.5201i	0.264555	+	0.726860i	0.998846	+	0.0480248i	$0.0152927\pi$
$797$	7.46871	+	20.5201i	0.264555	+	0.726860i	−0.734291	+	0.678835i	$0.762485\pi$
$798$		0			0
$799$	−5.81990	+	1.02620i	−0.205893	+	0.0363045i
$800$		0			0
$801$	41.9304	−	17.6700i	1.48154	−	0.624340i
$802$		0			0
$803$	1.47365	−	1.23654i	0.0520038	−	0.0436364i
$804$		0			0
$805$	−4.24061	+	24.0497i	−0.149462	+	0.847640i
$806$		0			0
$807$	2.16982	−	34.7361i	0.0763813	−	1.22277i
$808$		0			0
$809$		−	35.0378i		−	1.23186i	−0.787799	−	0.615932i	$-0.788779\pi$
$809$		−	35.0378i		−	1.23186i	0.787799	−	0.615932i	$-0.211221\pi$
$810$		0			0
$811$		−	27.1844i		−	0.954573i	−0.878748	−	0.477287i	$-0.841620\pi$
$811$		−	27.1844i		−	0.954573i	0.878748	−	0.477287i	$-0.158380\pi$
$812$		0			0
$813$	−0.987230	+	15.8043i	−0.0346237	+	0.554281i
$814$		0			0
$815$	−0.554615	+	3.14538i	−0.0194273	+	0.110178i
$816$		0			0
$817$	0.655675	−	0.550177i	0.0229392	−	0.0192483i
$818$		0			0
$819$	38.2677	+	28.9929i	1.33718	+	1.01309i
$820$		0			0
$821$	−6.62706	+	1.16853i	−0.231286	+	0.0407820i	−0.288090	−	0.957603i	$-0.593020\pi$
$821$	−6.62706	+	1.16853i	−0.231286	+	0.0407820i	0.0568037	+	0.998385i	$0.481909\pi$
$822$		0			0
$823$	0.0376566	+	0.103461i	0.00131263	+	0.00360641i	0.940347	−	0.340216i	$-0.110500\pi$
$823$	0.0376566	+	0.103461i	0.00131263	+	0.00360641i	−0.939035	+	0.343823i	$0.888278\pi$
$824$		0			0
$825$	−3.07795	+	12.7477i	−0.107161	+	0.443817i
$826$		0			0
$827$	−10.7113	+	18.5526i	−0.372470	+	0.645137i	−0.989945	−	0.141454i	$-0.954822\pi$
$827$	−10.7113	+	18.5526i	−0.372470	+	0.645137i	0.617475	+	0.786590i	$0.288156\pi$
$828$		0			0
$829$	7.92370	+	13.7242i	0.275201	+	0.476663i	0.970186	−	0.242362i	$-0.0779221\pi$
$829$	7.92370	+	13.7242i	0.275201	+	0.476663i	−0.694985	+	0.719025i	$0.744589\pi$
$830$		0			0
$831$	−20.3771	+	15.0373i	−0.706873	+	0.521640i
$832$		0			0
$833$	17.2066	−	20.5060i	0.596173	−	0.710492i
$834$		0			0
$835$	−1.37081	+	3.76627i	−0.0474389	+	0.130337i
$836$		0			0
$837$	24.0636	−	19.6796i	0.831761	−	0.680227i
$838$		0			0
$839$	−4.96451	−	1.80693i	−0.171394	−	0.0623822i	0.254898	−	0.966968i	$-0.417958\pi$
$839$	−4.96451	−	1.80693i	−0.171394	−	0.0623822i	−0.426292	+	0.904586i	$0.640180\pi$
$840$		0			0
$841$	−37.8243	−	31.7384i	−1.30429	−	1.09443i
$842$		0			0
$843$	−7.57502	+	0.853104i	−0.260898	+	0.0293825i
$844$		0			0
$845$	5.42476	−	3.13198i	0.186617	−	0.107744i
$846$		0			0
$847$	−23.9245	−	13.8128i	−0.822056	−	0.474614i
$848$		0			0
$849$	6.21863	+	21.0943i	0.213423	+	0.723953i
$850$		0			0
$851$	43.9685	−	16.0032i	1.50722	−	0.548584i
$852$		0			0
$853$	0.220692	+	1.25161i	0.00755634	+	0.0428541i	0.988353	−	0.152180i	$-0.0486293\pi$
$853$	0.220692	+	1.25161i	0.00755634	+	0.0428541i	−0.980796	+	0.195034i	$0.937518\pi$
$854$		0			0
$855$	2.45773	−	0.560694i	0.0840527	−	0.0191753i
$856$		0			0
$857$	−15.6352	−	18.6333i	−0.534087	−	0.636500i	0.429764	−	0.902941i	$-0.358597\pi$
$857$	−15.6352	−	18.6333i	−0.534087	−	0.636500i	−0.963851	+	0.266441i	$0.914152\pi$
$858$		0			0
$859$	−7.06237	−	1.24529i	−0.240965	−	0.0424887i	0.0518612	−	0.998654i	$-0.483485\pi$
$859$	−7.06237	−	1.24529i	−0.240965	−	0.0424887i	−0.292826	+	0.956166i	$0.594596\pi$
$860$		0			0
$861$	11.7016	−	17.6294i	0.398789	−	0.600808i
$862$		0			0
$863$	38.1184			1.29757			0.648783	−	0.760973i	$-0.275278\pi$
$863$	38.1184			1.29757			0.648783	+	0.760973i	$0.275278\pi$
$864$		0			0
$865$	9.61469			0.326909
$866$		0			0
$867$	−2.70520	−	5.44348i	−0.0918734	−	0.184870i
$868$		0			0
$869$	20.9403	+	3.69233i	0.710350	+	0.125254i
$870$		0			0
$871$	−8.25927	−	9.84301i	−0.279855	−	0.333518i
$872$		0			0
$873$	1.59874	+	32.1005i	0.0541093	+	1.08644i
$874$		0			0
$875$	5.23673	+	29.6990i	0.177034	+	1.00401i
$876$		0			0
$877$	−4.23247	+	1.54049i	−0.142921	+	0.0520188i	−0.412490	−	0.910962i	$-0.635341\pi$
$877$	−4.23247	+	1.54049i	−0.142921	+	0.0520188i	0.269569	+	0.962981i	$0.413119\pi$
$878$		0			0
$879$	25.3510	−	26.6450i	0.855069	−	0.898715i
$880$		0			0
$881$	−20.5813	−	11.8826i	−0.693401	−	0.400335i	0.111484	−	0.993766i	$-0.464440\pi$
$881$	−20.5813	−	11.8826i	−0.693401	−	0.400335i	−0.804885	+	0.593431i	$0.797773\pi$
$882$		0			0
$883$	−4.93969	+	2.85193i	−0.166234	+	0.0959751i	−0.580809	−	0.814040i	$-0.697264\pi$
$883$	−4.93969	+	2.85193i	−0.166234	+	0.0959751i	0.414575	+	0.910015i	$0.363930\pi$
$884$		0			0
$885$	7.81419	−	17.9078i	0.262671	−	0.601964i
$886$		0			0
$887$	−1.84014	−	1.54406i	−0.0617857	−	0.0518444i	0.611372	−	0.791343i	$-0.290618\pi$
$887$	−1.84014	−	1.54406i	−0.0617857	−	0.0518444i	−0.673158	+	0.739499i	$0.735062\pi$
$888$		0			0
$889$	−65.2671	−	23.7553i	−2.18899	−	0.796726i
$890$		0			0
$891$	−1.22731	+	16.3320i	−0.0411165	+	0.547143i
$892$		0			0
$893$	0.409335	−	1.12464i	0.0136979	−	0.0376346i
$894$		0			0
$895$	14.8600	−	17.7095i	0.496716	−	0.591963i
$896$		0			0
$897$	−52.4495	−	22.8867i	−1.75124	−	0.764165i
$898$		0			0
$899$	26.4817	+	45.8677i	0.883216	+	1.52977i
$900$		0			0
$901$	−5.73564	+	9.93442i	−0.191082	+	0.330963i
$902$		0			0
$903$	4.20783	+	4.00348i	0.140028	+	0.133227i
$904$		0			0
$905$	1.20377	+	3.30734i	0.0400147	+	0.109940i
$906$		0			0
$907$	45.9266	−	8.09809i	1.52497	−	0.268893i	0.652584	−	0.757717i	$-0.273685\pi$
$907$	45.9266	−	8.09809i	1.52497	−	0.268893i	0.872382	+	0.488824i	$0.162574\pi$
$908$		0			0
$909$	−6.45015	−	9.98905i	−0.213938	−	0.331316i
$910$		0			0
$911$	−27.6584	+	23.2082i	−0.916365	+	0.768922i	−0.973319	−	0.229455i	$-0.926306\pi$
$911$	−27.6584	+	23.2082i	−0.916365	+	0.768922i	0.0569539	+	0.998377i	$0.481861\pi$
$912$		0			0
$913$	−5.31307	+	30.1319i	−0.175837	+	0.997221i
$914$		0			0
$915$	4.93540	−	2.45271i	0.163159	−	0.0810840i
$916$		0			0
$917$			62.9199i			2.07780i
$918$		0			0
$919$		−	23.9024i		−	0.788468i	−0.919010	−	0.394234i	$-0.871010\pi$
$919$		−	23.9024i		−	0.788468i	0.919010	−	0.394234i	$-0.128990\pi$
$920$		0			0
$921$	−2.07809	−	1.37934i	−0.0684755	−	0.0454509i
$922$		0			0
$923$	−6.87085	+	38.9665i	−0.226157	+	1.28260i
$924$		0			0
$925$	20.1035	−	16.8689i	0.661000	−	0.554645i
$926$		0			0
$927$	−6.76288	−	2.08684i	−0.222122	−	0.0685408i
$928$		0			0
$929$	11.3439	−	2.00024i	0.372181	−	0.0656256i	0.0155709	−	0.999879i	$-0.495043\pi$
$929$	11.3439	−	2.00024i	0.372181	−	0.0656256i	0.356611	+	0.934253i	$0.383932\pi$
$930$		0			0
$931$	1.85414	+	5.09421i	0.0607671	+	0.166956i
$932$		0			0
$933$	14.7187	−	4.33909i	0.481867	−	0.142055i
$934$		0			0
$935$	3.77535	−	6.53909i	0.123467	−	0.213851i
$936$		0			0
$937$	−17.1278	−	29.6661i	−0.559539	−	0.969150i	−0.997535	−	0.0701733i	$-0.977645\pi$
$937$	−17.1278	−	29.6661i	−0.559539	−	0.969150i	0.437996	−	0.898977i	$-0.355689\pi$
$938$		0			0
$939$	6.01426	+	53.4028i	0.196268	+	1.74274i
$940$		0			0
$941$	−16.8452	+	20.0754i	−0.549139	+	0.654439i	−0.967211	−	0.253975i	$-0.918262\pi$
$941$	−16.8452	+	20.0754i	−0.549139	+	0.654439i	0.418071	+	0.908414i	$0.362706\pi$
$942$		0			0
$943$	−8.62599	+	23.6997i	−0.280901	+	0.771769i
$944$		0			0
$945$	5.64725	+	16.1469i	0.183705	+	0.525260i
$946$		0			0
$947$	−7.77710	−	2.83063i	−0.252722	−	0.0919832i	0.212553	−	0.977150i	$-0.431822\pi$
$947$	−7.77710	−	2.83063i	−0.252722	−	0.0919832i	−0.465275	+	0.885166i	$0.654044\pi$
$948$		0			0
$949$	3.60670	+	3.02638i	0.117078	+	0.0982405i
$950$		0			0
$951$	−1.68590	−	2.28456i	−0.0546690	−	0.0740819i
$952$		0			0
$953$	25.1053	−	14.4946i	0.813241	−	0.469525i	−0.0348391	−	0.999393i	$-0.511092\pi$
$953$	25.1053	−	14.4946i	0.813241	−	0.469525i	0.848080	+	0.529868i	$0.177759\pi$
$954$		0			0
$955$	−7.84341	−	4.52840i	−0.253807	−	0.146535i
$956$		0			0
$957$	−27.1249	−	6.54938i	−0.876824	−	0.211711i
$958$		0			0
$959$	54.3722	−	19.7899i	1.75577	−	0.639048i
$960$		0			0
$961$	−0.831882	−	4.71784i	−0.0268349	−	0.152188i
$962$		0			0
$963$	23.0164	+	2.88675i	0.741694	+	0.0930241i
$964$		0			0
$965$	6.11470	+	7.28721i	0.196839	+	0.234584i
$966$		0			0
$967$	37.9337	+	6.68873i	1.21986	+	0.215095i	0.746267	−	0.665646i	$-0.231844\pi$
$967$	37.9337	+	6.68873i	1.21986	+	0.215095i	0.473597	+	0.880741i	$0.342955\pi$
$968$		0			0
$969$	7.18015	+	0.448515i	0.230660	+	0.0144084i
$970$		0			0
$971$	36.9077			1.18442			0.592212	−	0.805783i	$-0.298255\pi$
$971$	36.9077			1.18442			0.592212	+	0.805783i	$0.298255\pi$
$972$		0			0
$973$	59.2830			1.90053
$974$		0			0
$975$	−32.0336	−	2.00101i	−1.02590	−	0.0640836i
$976$		0			0
$977$	−43.6838	−	7.70263i	−1.39757	−	0.246429i	−0.576424	−	0.817151i	$-0.695552\pi$
$977$	−43.6838	−	7.70263i	−1.39757	−	0.246429i	−0.821144	+	0.570722i	$0.806663\pi$
$978$		0			0
$979$	17.7416	+	21.1436i	0.567023	+	0.675752i
$980$		0			0
$981$	−46.3385	−	5.81184i	−1.47948	−	0.185558i
$982$		0			0
$983$	−6.09294	−	34.5548i	−0.194335	−	1.10213i	−0.913363	−	0.407146i	$-0.866524\pi$
$983$	−6.09294	−	34.5548i	−0.194335	−	1.10213i	0.719028	−	0.694981i	$-0.244587\pi$
$984$		0			0
$985$	11.0120	−	4.00802i	0.350870	−	0.127706i
$986$		0			0
$987$	7.89442	+	1.90613i	0.251282	+	0.0606727i
$988$		0			0
$989$	−5.99536	−	3.46142i	−0.190641	−	0.110067i
$990$		0			0
$991$	5.19698	−	3.00048i	0.165088	−	0.0953134i	−0.415180	−	0.909739i	$-0.636281\pi$
$991$	5.19698	−	3.00048i	0.165088	−	0.0953134i	0.580267	+	0.814426i	$0.302948\pi$
$992$		0			0
$993$	6.67924	+	9.05103i	0.211959	+	0.287226i
$994$		0			0
$995$	5.50898	+	4.62258i	0.174646	+	0.146546i
$996$		0			0
$997$	51.5630	+	18.7674i	1.63302	+	0.594369i	0.985798	−	0.167936i	$-0.0537103\pi$
$997$	51.5630	+	18.7674i	1.63302	+	0.594369i	0.647218	+	0.762305i	$0.275933\pi$
$998$		0			0
$999$	21.3828	−	24.8394i	0.676520	−	0.785885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.a.239.1	yes	36
4.3	odd	2	inner	432.2.be.a.239.6	yes	36
27.20	odd	18	inner	432.2.be.a.47.6	yes	36
108.47	even	18	inner	432.2.be.a.47.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.a.47.1	✓	36	108.47	even	18	inner
432.2.be.a.47.6	yes	36	27.20	odd	18	inner
432.2.be.a.239.1	yes	36	1.1	even	1	trivial
432.2.be.a.239.6	yes	36	4.3	odd	2	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72868 - 0.107984i) q^{3} +(0.902279 + 0.159096i) q^{5} +(-2.30964 - 2.75253i) q^{7} +(2.97668 + 0.373339i) q^{9} +O(q^{10})\)	\(q+(-1.72868 - 0.107984i) q^{3} +(0.902279 + 0.159096i) q^{5} +(-2.30964 - 2.75253i) q^{7} +(2.97668 + 0.373339i) q^{9} +(0.316002 + 1.79214i) q^{11} +(-4.18526 + 1.52331i) q^{13} +(-1.54257 - 0.372458i) q^{15} +(-3.92200 - 2.26437i) q^{17} +(0.794277 - 0.458576i) q^{19} +(3.69541 + 5.00764i) q^{21} +(-5.68258 - 4.76825i) q^{23} +(-3.90967 - 1.42300i) q^{25} +(-5.10542 - 0.966817i) q^{27} +(3.02791 - 8.31913i) q^{29} +(-3.84549 + 4.58288i) q^{31} +(-0.352746 - 3.13216i) q^{33} +(-1.64603 - 2.85100i) q^{35} +(-3.15380 + 5.46255i) q^{37} +(7.39948 - 2.18138i) q^{39} +(-1.16283 - 3.19486i) q^{41} +(0.919062 - 0.162055i) q^{43} +(2.62640 + 0.810434i) q^{45} +(0.999632 - 0.838791i) q^{47} +(-1.02641 + 5.82105i) q^{49} +(6.53538 + 4.33789i) q^{51} -2.53299i q^{53} +1.66728i q^{55} +(-1.42257 + 0.706963i) q^{57} +(-2.13801 + 12.1253i) q^{59} +(-2.66045 + 2.23238i) q^{61} +(-5.84744 - 9.05567i) q^{63} +(-4.01863 + 0.708592i) q^{65} +(0.986708 + 2.71096i) q^{67} +(9.30847 + 8.85641i) q^{69} +(4.44194 - 7.69367i) q^{71} +(-0.528554 - 0.915482i) q^{73} +(6.60491 + 2.88210i) q^{75} +(4.20306 - 5.00901i) q^{77} +(3.99634 - 10.9798i) q^{79} +(8.72124 + 2.22262i) q^{81} +(15.7994 + 5.75052i) q^{83} +(-3.17849 - 2.66707i) q^{85} +(-6.13263 + 14.0542i) q^{87} +(13.1352 - 7.58359i) q^{89} +(13.8594 + 8.00174i) q^{91} +(7.14251 - 7.50709i) q^{93} +(0.789617 - 0.287397i) q^{95} +(1.86037 + 10.5507i) q^{97} +(0.271563 + 5.45260i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^5 - 12 * q^9	\( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) \) 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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