LMFDB - Embedded newform 432.2.u.e.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	432.193
Dual form			432.2.u.e.385.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.747543 + 1.56243i) q^{3} +(-0.738874 + 4.19036i) q^{5} +(2.50342 - 2.10062i) q^{7} +(-1.88236 + 2.33596i) q^{9} +O(q^{10})$	\(q+(0.747543 + 1.56243i) q^{3} +(-0.738874 + 4.19036i) q^{5} +(2.50342 - 2.10062i) q^{7} +(-1.88236 + 2.33596i) q^{9} +(-0.0777898 - 0.441168i) q^{11} +(2.92225 - 1.06361i) q^{13} +(-7.09948 + 1.97804i) q^{15} +(-1.84197 + 3.19039i) q^{17} +(1.19355 + 2.06728i) q^{19} +(5.15347 + 2.34111i) q^{21} +(-5.22990 - 4.38841i) q^{23} +(-12.3147 - 4.48220i) q^{25} +(-5.05692 - 1.19482i) q^{27} +(0.616884 + 0.224527i) q^{29} +(3.54095 + 2.97121i) q^{31} +(0.631141 - 0.451333i) q^{33} +(6.95263 + 12.0423i) q^{35} +(-0.459466 + 0.795819i) q^{37} +(3.84632 + 3.77071i) q^{39} +(2.96657 - 1.07974i) q^{41} +(-0.522237 - 2.96175i) q^{43} +(-8.39770 - 9.61375i) q^{45} +(6.99323 - 5.86802i) q^{47} +(0.638970 - 3.62378i) q^{49} +(-6.36170 - 0.492995i) q^{51} +10.8975 q^{53} +1.90613 q^{55} +(-2.33775 + 3.41021i) q^{57} +(-0.976197 + 5.53629i) q^{59} +(9.68089 - 8.12323i) q^{61} +(0.194631 + 9.80200i) q^{63} +(2.29775 + 13.0312i) q^{65} +(-8.22644 + 2.99418i) q^{67} +(2.94700 - 11.4519i) q^{69} +(4.81781 - 8.34470i) q^{71} +(7.57074 + 13.1129i) q^{73} +(-2.20268 - 22.5915i) q^{75} +(-1.12146 - 0.941020i) q^{77} +(-3.69745 - 1.34576i) q^{79} +(-1.91345 - 8.79424i) q^{81} +(9.79861 + 3.56640i) q^{83} +(-12.0079 - 10.0758i) q^{85} +(0.110339 + 1.13168i) q^{87} +(-3.11383 - 5.39332i) q^{89} +(5.08137 - 8.80119i) q^{91} +(-1.99529 + 7.75358i) q^{93} +(-9.54454 + 3.47393i) q^{95} +(-0.477635 - 2.70880i) q^{97} +(1.17698 + 0.648722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q + 3 * q^7 + 6 * q^9	$ 24 q + 3 q^{7} + 6 q^{9} - 6 q^{11} + 12 q^{13} + 3 q^{15} + 6 q^{17} - 9 q^{19} - 18 q^{21} - 24 q^{23} - 24 q^{25} - 9 q^{29} + 27 q^{31} + 21 q^{33} + 18 q^{35} + 15 q^{37} + 15 q^{39} - 6 q^{41} - 39 q^{43} - 69 q^{45} + 36 q^{47} + 3 q^{49} + 36 q^{51} - 18 q^{53} + 54 q^{55} + 27 q^{57} + 30 q^{59} + 12 q^{61} - 18 q^{63} - 18 q^{65} - 54 q^{67} - 57 q^{69} + 36 q^{73} + 51 q^{75} - 24 q^{77} + 45 q^{79} + 18 q^{81} - 33 q^{83} - 57 q^{85} - 90 q^{87} + 9 q^{89} - 39 q^{91} + 42 q^{93} - 87 q^{95} + 57 q^{97} + 24 q^{99}+O(q^{100}) $ 24 * q + 3 * q^7 + 6 * q^9 - 6 * q^11 + 12 * q^13 + 3 * q^15 + 6 * q^17 - 9 * q^19 - 18 * q^21 - 24 * q^23 - 24 * q^25 - 9 * q^29 + 27 * q^31 + 21 * q^33 + 18 * q^35 + 15 * q^37 + 15 * q^39 - 6 * q^41 - 39 * q^43 - 69 * q^45 + 36 * q^47 + 3 * q^49 + 36 * q^51 - 18 * q^53 + 54 * q^55 + 27 * q^57 + 30 * q^59 + 12 * q^61 - 18 * q^63 - 18 * q^65 - 54 * q^67 - 57 * q^69 + 36 * q^73 + 51 * q^75 - 24 * q^77 + 45 * q^79 + 18 * q^81 - 33 * q^83 - 57 * q^85 - 90 * q^87 + 9 * q^89 - 39 * q^91 + 42 * q^93 - 87 * q^95 + 57 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{9}\right)$

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
$3$	0.747543	+	1.56243i	0.431594	+	0.902068i
$3$	0.747543	+	1.56243i	0.431594	+	0.902068i
$4$		0			0
$5$	−0.738874	+	4.19036i	−0.330434	+	1.87399i	0.137916	+	0.990444i	$0.455959\pi$
$5$	−0.738874	+	4.19036i	−0.330434	+	1.87399i	−0.468351	+	0.883543i	$0.655152\pi$
$6$		0			0
$7$	2.50342	−	2.10062i	0.946202	−	0.793958i	−0.0324515	−	0.999473i	$-0.510331\pi$
$7$	2.50342	−	2.10062i	0.946202	−	0.793958i	0.978654	+	0.205515i	$0.0658870\pi$
$8$		0			0
$9$	−1.88236	+	2.33596i	−0.627453	+	0.778654i
$10$		0			0
$11$	−0.0777898	−	0.441168i	−0.0234545	−	0.133017i	0.970832	−	0.239760i	$-0.0770688\pi$
$11$	−0.0777898	−	0.441168i	−0.0234545	−	0.133017i	−0.994287	+	0.106743i	$0.965958\pi$
$12$		0			0
$13$	2.92225	−	1.06361i	0.810487	−	0.294993i	0.0966617	−	0.995317i	$-0.469184\pi$
$13$	2.92225	−	1.06361i	0.810487	−	0.294993i	0.713825	+	0.700324i	$0.246961\pi$
$14$		0			0
$15$	−7.09948	+	1.97804i	−1.83308	+	0.510727i
$16$		0			0
$17$	−1.84197	+	3.19039i	−0.446744	+	0.773783i	−0.998172	−	0.0604394i	$-0.980750\pi$
$17$	−1.84197	+	3.19039i	−0.446744	+	0.773783i	0.551428	+	0.834222i	$0.314083\pi$
$18$		0			0
$19$	1.19355	+	2.06728i	0.273818	+	0.474267i	0.969836	−	0.243757i	$-0.0783800\pi$
$19$	1.19355	+	2.06728i	0.273818	+	0.474267i	−0.696018	+	0.718024i	$0.745047\pi$
$20$		0			0
$21$	5.15347	+	2.34111i	1.12458	+	0.510871i
$22$		0			0
$23$	−5.22990	−	4.38841i	−1.09051	−	0.915047i	−0.0937598	−	0.995595i	$-0.529889\pi$
$23$	−5.22990	−	4.38841i	−1.09051	−	0.915047i	−0.996751	+	0.0805478i	$0.974333\pi$
$24$		0			0
$25$	−12.3147	−	4.48220i	−2.46295	−	0.896439i
$26$		0			0
$27$	−5.05692	−	1.19482i	−0.973204	−	0.229943i
$28$		0			0
$29$	0.616884	+	0.224527i	0.114552	+	0.0416937i	0.398660	−	0.917099i	$-0.369475\pi$
$29$	0.616884	+	0.224527i	0.114552	+	0.0416937i	−0.284108	+	0.958792i	$0.591697\pi$
$30$		0			0
$31$	3.54095	+	2.97121i	0.635973	+	0.533645i	0.902779	−	0.430105i	$-0.141524\pi$
$31$	3.54095	+	2.97121i	0.635973	+	0.533645i	−0.266805	+	0.963750i	$0.585968\pi$
$32$		0			0
$33$	0.631141	−	0.451333i	0.109868	−	0.0785669i
$34$		0			0
$35$	6.95263	+	12.0423i	1.17521	+	2.03552i
$36$		0			0
$37$	−0.459466	+	0.795819i	−0.0755358	+	0.130832i	−0.901319	−	0.433156i	$-0.857400\pi$
$37$	−0.459466	+	0.795819i	−0.0755358	+	0.130832i	0.825783	+	0.563987i	$0.190733\pi$
$38$		0			0
$39$	3.84632	+	3.77071i	0.615905	+	0.603797i
$40$		0			0
$41$	2.96657	−	1.07974i	0.463300	−	0.168627i	−0.0998149	−	0.995006i	$-0.531825\pi$
$41$	2.96657	−	1.07974i	0.463300	−	0.168627i	0.563115	+	0.826379i	$0.309603\pi$
$42$		0			0
$43$	−0.522237	−	2.96175i	−0.0796404	−	0.451663i	−0.998385	−	0.0568107i	$-0.981907\pi$
$43$	−0.522237	−	2.96175i	−0.0796404	−	0.451663i	0.918745	−	0.394852i	$-0.129204\pi$
$44$		0			0
$45$	−8.39770	−	9.61375i	−1.25186	−	1.43313i
$46$		0			0
$47$	6.99323	−	5.86802i	1.02007	−	0.855939i	0.0304320	−	0.999537i	$-0.490312\pi$
$47$	6.99323	−	5.86802i	1.02007	−	0.855939i	0.989636	+	0.143598i	$0.0458672\pi$
$48$		0			0
$49$	0.638970	−	3.62378i	0.0912814	−	0.517682i
$50$		0			0
$51$	−6.36170	−	0.492995i	−0.890817	−	0.0690332i
$52$		0			0
$53$	10.8975			1.49689			0.748445	−	0.663197i	$-0.230801\pi$
$53$	10.8975			1.49689			0.748445	+	0.663197i	$0.230801\pi$
$54$		0			0
$55$	1.90613			0.257022
$56$		0			0
$57$	−2.33775	+	3.41021i	−0.309643	+	0.451693i
$58$		0			0
$59$	−0.976197	+	5.53629i	−0.127090	+	0.720763i	0.852955	+	0.521985i	$0.174808\pi$
$59$	−0.976197	+	5.53629i	−0.127090	+	0.720763i	−0.980045	+	0.198778i	$0.936303\pi$
$60$		0			0
$61$	9.68089	−	8.12323i	1.23951	−	1.04007i	0.241949	−	0.970289i	$-0.422213\pi$
$61$	9.68089	−	8.12323i	1.23951	−	1.04007i	0.997562	−	0.0697841i	$-0.0222310\pi$
$62$		0			0
$63$	0.194631	+	9.80200i	0.0245212	+	1.23494i
$64$		0			0
$65$	2.29775	+	13.0312i	0.285000	+	1.61632i
$66$		0			0
$67$	−8.22644	+	2.99418i	−1.00502	+	0.365797i	−0.791518	−	0.611145i	$-0.790709\pi$
$67$	−8.22644	+	2.99418i	−1.00502	+	0.365797i	−0.213502	+	0.976943i	$0.568487\pi$
$68$		0			0
$69$	2.94700	−	11.4519i	0.354777	−	1.37864i
$70$		0			0
$71$	4.81781	−	8.34470i	0.571769	−	0.990333i	−0.424615	−	0.905374i	$-0.639591\pi$
$71$	4.81781	−	8.34470i	0.571769	−	0.990333i	0.996384	−	0.0849594i	$-0.0270761\pi$
$72$		0			0
$73$	7.57074	+	13.1129i	0.886088	+	1.53475i	0.844462	+	0.535615i	$0.179920\pi$
$73$	7.57074	+	13.1129i	0.886088	+	1.53475i	0.0416255	+	0.999133i	$0.486746\pi$
$74$		0			0
$75$	−2.20268	−	22.5915i	−0.254344	−	2.60864i
$76$		0			0
$77$	−1.12146	−	0.941020i	−0.127803	−	0.107239i
$78$		0			0
$79$	−3.69745	−	1.34576i	−0.415996	−	0.151410i	0.125538	−	0.992089i	$-0.459934\pi$
$79$	−3.69745	−	1.34576i	−0.415996	−	0.151410i	−0.541534	+	0.840679i	$0.682156\pi$
$80$		0			0
$81$	−1.91345	−	8.79424i	−0.212605	−	0.977138i
$82$		0			0
$83$	9.79861	+	3.56640i	1.07554	+	0.391464i	0.818245	−	0.574870i	$-0.194947\pi$
$83$	9.79861	+	3.56640i	1.07554	+	0.391464i	0.257293	+	0.966334i	$0.417170\pi$
$84$		0			0
$85$	−12.0079	−	10.0758i	−1.30244	−	1.09288i
$86$		0			0
$87$	0.110339	+	1.13168i	0.0118296	+	0.121329i
$88$		0			0
$89$	−3.11383	−	5.39332i	−0.330066	−	0.571691i	0.652459	−	0.757824i	$-0.273738\pi$
$89$	−3.11383	−	5.39332i	−0.330066	−	0.571691i	−0.982524	+	0.186134i	$0.940404\pi$
$90$		0			0
$91$	5.08137	−	8.80119i	0.532672	−	0.922615i
$92$		0			0
$93$	−1.99529	+	7.75358i	−0.206902	+	0.804009i
$94$		0			0
$95$	−9.54454	+	3.47393i	−0.979249	+	0.356417i
$96$		0			0
$97$	−0.477635	−	2.70880i	−0.0484965	−	0.275037i	0.950911	−	0.309466i	$-0.100150\pi$
$97$	−0.477635	−	2.70880i	−0.0484965	−	0.275037i	−0.999407	+	0.0344281i	$0.989039\pi$
$98$		0			0
$99$	1.17698	+	0.648722i	0.118291	+	0.0651990i
$100$		0			0
$101$	−10.7431	+	9.01449i	−1.06897	+	0.896976i	−0.994959	−	0.100281i	$-0.968026\pi$
$101$	−10.7431	+	9.01449i	−1.06897	+	0.896976i	−0.0740148	+	0.997257i	$0.523581\pi$
$102$		0			0
$103$	0.468473	−	2.65684i	0.0461600	−	0.261786i	−0.952990	−	0.303001i	$-0.902012\pi$
$103$	0.468473	−	2.65684i	0.0461600	−	0.261786i	0.999150	+	0.0412144i	$0.0131227\pi$
$104$		0			0
$105$	−13.6178	+	19.8651i	−1.32897	+	1.93864i
$106$		0			0
$107$	−5.44650			−0.526533			−0.263267	−	0.964723i	$-0.584800\pi$
$107$	−5.44650			−0.526533			−0.263267	+	0.964723i	$0.584800\pi$
$108$		0			0
$109$	10.8789			1.04201			0.521004	−	0.853554i	$-0.325558\pi$
$109$	10.8789			1.04201			0.521004	+	0.853554i	$0.325558\pi$
$110$		0			0
$111$	−1.58688	−	0.122974i	−0.150620	−	0.0116722i
$112$		0			0
$113$	0.969989	−	5.50108i	0.0912489	−	0.517498i	−0.904584	−	0.426296i	$-0.859818\pi$
$113$	0.969989	−	5.50108i	0.0912489	−	0.517498i	0.995832	−	0.0912018i	$-0.0290708\pi$
$114$		0			0
$115$	22.2533	−	18.6727i	2.07513	−	1.74124i
$116$		0			0
$117$	−3.01617	+	8.82837i	−0.278845	+	0.816183i
$118$		0			0
$119$	2.09056	+	11.8561i	0.191641	+	1.08685i
$120$		0			0
$121$	10.1480	−	3.69358i	0.922549	−	0.335780i
$122$		0			0
$123$	3.90466	+	3.82789i	0.352071	+	0.345150i
$124$		0			0
$125$	17.2435	−	29.8667i	1.54231	−	2.67136i
$126$		0			0
$127$	−9.34394	−	16.1842i	−0.829140	−	1.43611i	−0.898713	−	0.438536i	$-0.855497\pi$
$127$	−9.34394	−	16.1842i	−0.829140	−	1.43611i	0.0695732	−	0.997577i	$-0.477836\pi$
$128$		0			0
$129$	4.23713	−	3.02999i	0.373058	−	0.266776i
$130$		0			0
$131$	−6.83720	−	5.73709i	−0.597369	−	0.501252i	0.293230	−	0.956042i	$-0.405270\pi$
$131$	−6.83720	−	5.73709i	−0.597369	−	0.501252i	−0.890599	+	0.454790i	$0.849714\pi$
$132$		0			0
$133$	7.33051	+	2.66809i	0.635636	+	0.231352i
$134$		0			0
$135$	8.74314	−	20.3075i	0.752490	−	1.74779i
$136$		0			0
$137$	0.128660	+	0.0468284i	0.0109922	+	0.00400082i	0.347510	−	0.937676i	$-0.387027\pi$
$137$	0.128660	+	0.0468284i	0.0109922	+	0.00400082i	−0.336518	+	0.941677i	$0.609249\pi$
$138$		0			0
$139$	−1.79487	−	1.50608i	−0.152239	−	0.127744i	0.563487	−	0.826125i	$-0.309460\pi$
$139$	−1.79487	−	1.50608i	−0.152239	−	0.127744i	−0.715726	+	0.698381i	$0.753904\pi$
$140$		0			0
$141$	14.3961	+	6.53983i	1.21237	+	0.550753i
$142$		0			0
$143$	−0.696553	−	1.20646i	−0.0582487	−	0.100890i
$144$		0			0
$145$	−1.39665	+	2.41907i	−0.115985	+	0.200893i
$146$		0			0
$147$	6.13955	−	1.71058i	0.506381	−	0.141087i
$148$		0			0
$149$	−1.48012	+	0.538720i	−0.121256	+	0.0441337i	−0.401936	−	0.915668i	$-0.631662\pi$
$149$	−1.48012	+	0.538720i	−0.121256	+	0.0441337i	0.280679	+	0.959802i	$0.409440\pi$
$150$		0			0
$151$	1.98500	+	11.2575i	0.161537	+	0.916121i	0.952564	+	0.304339i	$0.0984357\pi$
$151$	1.98500	+	11.2575i	0.161537	+	0.916121i	−0.791027	+	0.611781i	$0.790453\pi$
$152$		0			0
$153$	−3.98538	−	10.3082i	−0.322199	−	0.833372i
$154$		0			0
$155$	−15.0668	+	12.6425i	−1.21019	+	1.01547i
$156$		0			0
$157$	−2.76188	+	15.6634i	−0.220422	+	1.25008i	0.650824	+	0.759229i	$0.274424\pi$
$157$	−2.76188	+	15.6634i	−0.220422	+	1.25008i	−0.871246	+	0.490847i	$0.836687\pi$
$158$		0			0
$159$	8.14636	+	17.0266i	0.646049	+	1.35030i
$160$		0			0
$161$	−22.3110			−1.75835
$162$		0			0
$163$	0.653800			0.0512095			0.0256048	−	0.999672i	$-0.491849\pi$
$163$	0.653800			0.0512095			0.0256048	+	0.999672i	$0.491849\pi$
$164$		0			0
$165$	1.42491	+	2.97819i	0.110929	+	0.231852i
$166$		0			0
$167$	1.51321	−	8.58184i	0.117096	−	0.664083i	−0.868596	−	0.495522i	$-0.834977\pi$
$167$	1.51321	−	8.58184i	0.117096	−	0.664083i	0.985691	−	0.168561i	$-0.0539120\pi$
$168$		0			0
$169$	−2.55030	+	2.13996i	−0.196177	+	0.164612i
$170$		0			0
$171$	−7.07578	−	1.10329i	−0.541098	−	0.0843706i
$172$		0			0
$173$	−0.142550	−	0.808440i	−0.0108379	−	0.0614645i	0.978909	−	0.204296i	$-0.0654905\pi$
$173$	−0.142550	−	0.808440i	−0.0108379	−	0.0614645i	−0.989747	+	0.142831i	$0.954379\pi$
$174$		0			0
$175$	−40.2443	+	14.6477i	−3.04218	+	1.10726i
$176$		0			0
$177$	−9.37980	+	2.61337i	−0.705029	+	0.196433i
$178$		0			0
$179$	2.69134	−	4.66154i	0.201160	−	0.348420i	−0.747742	−	0.663989i	$-0.768862\pi$
$179$	2.69134	−	4.66154i	0.201160	−	0.348420i	0.948903	+	0.315569i	$0.102195\pi$
$180$		0			0
$181$	−3.35283	−	5.80727i	−0.249214	−	0.431651i	0.714094	−	0.700050i	$-0.246839\pi$
$181$	−3.35283	−	5.80727i	−0.249214	−	0.431651i	−0.963308	+	0.268399i	$0.913506\pi$
$182$		0			0
$183$	19.9288	+	9.05323i	1.47318	+	0.669234i
$184$		0			0
$185$	−2.99528	−	2.51334i	−0.220217	−	0.184784i
$186$		0			0
$187$	1.55078	+	0.564439i	0.113405	+	0.0412759i
$188$		0			0
$189$	−15.1694	+	7.63151i	−1.10341	+	0.555111i
$190$		0			0
$191$	3.59589	+	1.30880i	0.260189	+	0.0947011i	0.468821	−	0.883293i	$-0.344679\pi$
$191$	3.59589	+	1.30880i	0.260189	+	0.0947011i	−0.208632	+	0.977994i	$0.566901\pi$
$192$		0			0
$193$	−5.45247	−	4.57517i	−0.392477	−	0.329328i	0.425100	−	0.905146i	$-0.360239\pi$
$193$	−5.45247	−	4.57517i	−0.392477	−	0.329328i	−0.817577	+	0.575819i	$0.804683\pi$
$194$		0			0
$195$	−18.6426	+	13.3314i	−1.33502	+	0.954682i
$196$		0			0
$197$	−0.381405	−	0.660612i	−0.0271740	−	0.0470667i	0.852119	−	0.523349i	$-0.175317\pi$
$197$	−0.381405	−	0.660612i	−0.0271740	−	0.0470667i	−0.879293	+	0.476282i	$0.841984\pi$
$198$		0			0
$199$	−12.3620	+	21.4116i	−0.876318	+	1.51783i	−0.0209652	+	0.999780i	$0.506674\pi$
$199$	−12.3620	+	21.4116i	−0.876318	+	1.51783i	−0.855352	+	0.518047i	$0.826659\pi$
$200$		0			0
$201$	−10.8278	−	10.6149i	−0.763735	−	0.748720i
$202$		0			0
$203$	2.01596	−	0.733750i	0.141493	−	0.0514992i
$204$		0			0
$205$	2.33259	+	13.2288i	0.162915	+	0.923938i
$206$		0			0
$207$	20.0957	−	3.95630i	1.39675	−	0.274982i
$208$		0			0
$209$	0.819173	−	0.687367i	0.0566634	−	0.0475462i
$210$		0			0
$211$	0.332793	−	1.88736i	0.0229104	−	0.129931i	−0.971207	−	0.238236i	$-0.923431\pi$
$211$	0.332793	−	1.88736i	0.0229104	−	0.129931i	0.994118	+	0.108304i	$0.0345421\pi$
$212$		0			0
$213$	16.6395	+	1.28947i	1.14012	+	0.0883527i
$214$		0			0
$215$	12.7967			0.872726
$216$		0			0
$217$	15.1058			1.02545
$218$		0			0
$219$	−14.8285	+	21.6312i	−1.00202	+	1.46170i
$220$		0			0
$221$	−1.98937	+	11.2823i	−0.133819	+	0.758927i
$222$		0			0
$223$	−4.01598	+	3.36981i	−0.268930	+	0.225659i	−0.767273	−	0.641321i	$-0.778387\pi$
$223$	−4.01598	+	3.36981i	−0.268930	+	0.225659i	0.498343	+	0.866980i	$0.333942\pi$
$224$		0			0
$225$	33.6510	−	20.3296i	2.24340	−	1.35531i
$226$		0			0
$227$	1.48616	+	8.42844i	0.0986400	+	0.559415i	0.993571	+	0.113211i	$0.0361135\pi$
$227$	1.48616	+	8.42844i	0.0986400	+	0.559415i	−0.894931	+	0.446204i	$0.852775\pi$
$228$		0			0
$229$	−16.0491	+	5.84138i	−1.06055	+	0.386009i	−0.812636	−	0.582772i	$-0.801968\pi$
$229$	−16.0491	+	5.84138i	−1.06055	+	0.386009i	−0.247916	+	0.968781i	$0.579746\pi$
$230$		0			0
$231$	0.631933	−	2.45566i	0.0415782	−	0.161571i
$232$		0			0
$233$	5.43258	−	9.40951i	0.355900	−	0.616437i	−0.631371	−	0.775481i	$-0.717508\pi$
$233$	5.43258	−	9.40951i	0.355900	−	0.616437i	0.987272	+	0.159043i	$0.0508409\pi$
$234$		0			0
$235$	19.4220	+	33.6399i	1.26695	+	2.19443i
$236$		0			0
$237$	−0.661348	−	6.78302i	−0.0429592	−	0.440605i
$238$		0			0
$239$	−2.15450	−	1.80784i	−0.139363	−	0.116939i	0.570441	−	0.821338i	$-0.306772\pi$
$239$	−2.15450	−	1.80784i	−0.139363	−	0.116939i	−0.709804	+	0.704399i	$0.751217\pi$
$240$		0			0
$241$	−13.3528	−	4.86004i	−0.860132	−	0.313063i	−0.125968	−	0.992034i	$-0.540204\pi$
$241$	−13.3528	−	4.86004i	−0.860132	−	0.313063i	−0.734164	+	0.678972i	$0.762426\pi$
$242$		0			0
$243$	12.3100	−	9.56369i	0.789686	−	0.613511i
$244$		0			0
$245$	14.7128	+	5.35503i	0.939967	+	0.342120i
$246$		0			0
$247$	5.68663	+	4.77165i	0.361831	+	0.303613i
$248$		0			0
$249$	1.75264	+	17.9757i	0.111069	+	1.13916i
$250$		0			0
$251$	−2.84170	−	4.92197i	−0.179366	−	0.310672i	0.762297	−	0.647227i	$-0.224071\pi$
$251$	−2.84170	−	4.92197i	−0.179366	−	0.310672i	−0.941664	+	0.336555i	$0.890738\pi$
$252$		0			0
$253$	−1.52919	+	2.64864i	−0.0961395	+	0.166519i
$254$		0			0
$255$	6.76633	−	26.2936i	0.423724	−	1.64657i
$256$		0			0
$257$	7.52172	−	2.73768i	0.469192	−	0.170772i	−0.0965942	−	0.995324i	$-0.530795\pi$
$257$	7.52172	−	2.73768i	0.469192	−	0.170772i	0.565786	+	0.824552i	$0.308573\pi$
$258$		0			0
$259$	0.521474	+	2.95743i	0.0324028	+	0.183766i
$260$		0			0
$261$	−1.68568	+	1.01838i	−0.104341	+	0.0630359i
$262$		0			0
$263$	−7.37015	+	6.18429i	−0.454463	+	0.381339i	−0.841089	−	0.540897i	$-0.818085\pi$
$263$	−7.37015	+	6.18429i	−0.454463	+	0.381339i	0.386626	+	0.922237i	$0.373640\pi$
$264$		0			0
$265$	−8.05189	+	45.6646i	−0.494624	+	2.80515i
$266$		0			0
$267$	6.09895	−	8.89688i	0.373249	−	0.544480i
$268$		0			0
$269$	−17.9793			−1.09622			−0.548108	−	0.836408i	$-0.684652\pi$
$269$	−17.9793			−1.09622			−0.548108	+	0.836408i	$0.684652\pi$
$270$		0			0
$271$	13.9040			0.844606			0.422303	−	0.906455i	$-0.361222\pi$
$271$	13.9040			0.844606			0.422303	+	0.906455i	$0.361222\pi$
$272$		0			0
$273$	17.5498	+	1.36001i	1.06216	+	0.0823113i
$274$		0			0
$275$	−1.01944	+	5.78153i	−0.0614745	+	0.348639i
$276$		0			0
$277$	−0.191155	+	0.160398i	−0.0114854	+	0.00963739i	−0.648512	−	0.761204i	$-0.724608\pi$
$277$	−0.191155	+	0.160398i	−0.0114854	+	0.00963739i	0.637027	+	0.770842i	$0.280164\pi$
$278$		0			0
$279$	−13.6060	+	2.67864i	−0.814568	+	0.160366i
$280$		0			0
$281$	−0.0563729	−	0.319707i	−0.00336293	−	0.0190721i	0.983080	−	0.183176i	$-0.0586378\pi$
$281$	−0.0563729	−	0.319707i	−0.00336293	−	0.0190721i	−0.986443	+	0.164104i	$0.947527\pi$
$282$		0			0
$283$	4.88992	−	1.77979i	0.290676	−	0.105797i	−0.192567	−	0.981284i	$-0.561681\pi$
$283$	4.88992	−	1.77979i	0.290676	−	0.105797i	0.483243	+	0.875487i	$0.339459\pi$
$284$		0			0
$285$	−12.5627	−	12.3157i	−0.744151	−	0.729521i
$286$		0			0
$287$	5.15843	−	8.93466i	0.304493	−	0.527396i
$288$		0			0
$289$	1.71428	+	2.96922i	0.100840	+	0.174660i
$290$		0			0
$291$	3.87526	−	2.77122i	0.227172	−	0.162452i
$292$		0			0
$293$	−11.2312	−	9.42409i	−0.656134	−	0.550561i	0.252792	−	0.967521i	$-0.418651\pi$
$293$	−11.2312	−	9.42409i	−0.656134	−	0.550561i	−0.908925	+	0.416959i	$0.863096\pi$
$294$		0			0
$295$	−22.4778	−	8.18123i	−1.30871	−	0.476330i
$296$		0			0
$297$	−0.133739	+	2.32389i	−0.00776031	+	0.134846i
$298$		0			0
$299$	−19.9507	−	7.26145i	−1.15378	−	0.419940i
$300$		0			0
$301$	−7.52888	−	6.31748i	−0.433957	−	0.364134i
$302$		0			0
$303$	−22.1154	−	10.0465i	−1.27050	−	0.577158i
$304$		0			0
$305$	26.8863	+	46.5685i	1.53951	+	2.66650i
$306$		0			0
$307$	16.2761	−	28.1910i	0.928924	−	1.60894i	0.143799	−	0.989607i	$-0.454068\pi$
$307$	16.2761	−	28.1910i	0.928924	−	1.60894i	0.785125	−	0.619337i	$-0.212598\pi$
$308$		0			0
$309$	4.50132	−	1.25415i	0.256071	−	0.0713459i
$310$		0			0
$311$	4.59167	−	1.67123i	0.260369	−	0.0947667i	−0.208537	−	0.978014i	$-0.566870\pi$
$311$	4.59167	−	1.67123i	0.260369	−	0.0947667i	0.468907	+	0.883248i	$0.344648\pi$
$312$		0			0
$313$	−4.76503	−	27.0238i	−0.269335	−	1.52748i	−0.756400	−	0.654110i	$-0.773043\pi$
$313$	−4.76503	−	27.0238i	−0.269335	−	1.52748i	0.487065	−	0.873366i	$-0.338068\pi$
$314$		0			0
$315$	−41.2177	−	6.42687i	−2.32236	−	0.362113i
$316$		0			0
$317$	−5.39218	+	4.52458i	−0.302855	+	0.254126i	−0.781532	−	0.623866i	$-0.785561\pi$
$317$	−5.39218	+	4.52458i	−0.302855	+	0.254126i	0.478676	+	0.877991i	$0.341117\pi$
$318$		0			0
$319$	0.0510670	−	0.289615i	0.00285920	−	0.0162153i
$320$		0			0
$321$	−4.07149	−	8.50976i	−0.227249	−	0.474969i
$322$		0			0
$323$	−8.79391			−0.489306
$324$		0			0
$325$	−40.7540			−2.26063
$326$		0			0
$327$	8.13243	+	16.9975i	0.449724	+	0.939962i
$328$		0			0
$329$	5.18052	−	29.3802i	0.285611	−	1.61978i
$330$		0			0
$331$	−19.5884	+	16.4366i	−1.07667	+	0.903437i	−0.995640	−	0.0932742i	$-0.970267\pi$
$331$	−19.5884	+	16.4366i	−1.07667	+	0.903437i	−0.0810340	+	0.996711i	$0.525822\pi$
$332$		0			0
$333$	−0.994123	−	2.57131i	−0.0544776	−	0.140907i
$334$		0			0
$335$	−6.46840	−	36.6841i	−0.353406	−	2.00427i
$336$		0			0
$337$	5.71951	−	2.08173i	0.311562	−	0.113399i	−0.181507	−	0.983390i	$-0.558097\pi$
$337$	5.71951	−	2.08173i	0.311562	−	0.113399i	0.493068	+	0.869991i	$0.335875\pi$
$338$		0			0
$339$	9.32015	−	2.59676i	0.506201	−	0.141036i
$340$		0			0
$341$	1.03535	−	1.79328i	0.0560675	−	0.0971117i
$342$		0			0
$343$	5.42537	+	9.39701i	0.292942	+	0.507391i
$344$		0			0
$345$	45.8100	+	20.8105i	2.46633	+	1.12040i
$346$		0			0
$347$	−0.919185	−	0.771288i	−0.0493444	−	0.0414049i	0.617782	−	0.786349i	$-0.288031\pi$
$347$	−0.919185	−	0.771288i	−0.0493444	−	0.0414049i	−0.667126	+	0.744945i	$0.732476\pi$
$348$		0			0
$349$	16.9776	+	6.17933i	0.908789	+	0.330772i	0.753769	−	0.657139i	$-0.228234\pi$
$349$	16.9776	+	6.17933i	0.908789	+	0.330772i	0.155020	+	0.987911i	$0.450456\pi$
$350$		0			0
$351$	−16.0484	+	1.88704i	−0.856600	+	0.100723i
$352$		0			0
$353$	−28.4476	−	10.3541i	−1.51411	−	0.551092i	−0.554443	−	0.832222i	$-0.687069\pi$
$353$	−28.4476	−	10.3541i	−1.51411	−	0.551092i	−0.959670	+	0.281130i	$0.909291\pi$
$354$		0			0
$355$	31.4075	+	26.3541i	1.66694	+	1.39873i
$356$		0			0
$357$	−16.9616	+	12.1293i	−0.897702	+	0.641952i
$358$		0			0
$359$	−13.1618	−	22.7968i	−0.694651	−	1.20317i	−0.970298	−	0.241912i	$-0.922225\pi$
$359$	−13.1618	−	22.7968i	−0.694651	−	1.20317i	0.275647	−	0.961259i	$-0.411108\pi$
$360$		0			0
$361$	6.65090	−	11.5197i	0.350047	−	0.606299i
$362$		0			0
$363$	13.3571	+	13.0945i	0.701064	+	0.687281i
$364$		0			0
$365$	−60.5416	+	22.0353i	−3.16889	+	1.15338i
$366$		0			0
$367$	−5.44262	−	30.8666i	−0.284102	−	1.61122i	−0.708474	−	0.705736i	$-0.750616\pi$
$367$	−5.44262	−	30.8666i	−0.284102	−	1.61122i	0.424372	−	0.905488i	$-0.360495\pi$
$368$		0			0
$369$	−3.06191	+	8.96226i	−0.159397	+	0.466556i
$370$		0			0
$371$	27.2810	−	22.8915i	1.41636	−	1.18847i
$372$		0			0
$373$	3.17738	−	18.0198i	0.164519	−	0.933032i	−0.785041	−	0.619444i	$-0.787358\pi$
$373$	3.17738	−	18.0198i	0.164519	−	0.933032i	0.949559	−	0.313588i	$-0.101531\pi$
$374$		0			0
$375$	59.5548	+	4.61515i	3.07540	+	0.238325i
$376$		0			0
$377$	2.04150			0.105143
$378$		0			0
$379$	−12.4008			−0.636989			−0.318494	−	0.947925i	$-0.603177\pi$
$379$	−12.4008			−0.636989			−0.318494	+	0.947925i	$0.603177\pi$
$380$		0			0
$381$	18.3016	−	26.6976i	0.937620	−	1.36776i
$382$		0			0
$383$	6.27560	−	35.5907i	0.320668	−	1.81860i	−0.217847	−	0.975983i	$-0.569903\pi$
$383$	6.27560	−	35.5907i	0.320668	−	1.81860i	0.538515	−	0.842616i	$-0.318986\pi$
$384$		0			0
$385$	4.77183	−	4.00404i	0.243195	−	0.204065i
$386$		0			0
$387$	7.90158	+	4.35516i	0.401660	+	0.221385i
$388$		0			0
$389$	−0.965471	−	5.47546i	−0.0489513	−	0.277617i	0.950501	−	0.310723i	$-0.100571\pi$
$389$	−0.965471	−	5.47546i	−0.0489513	−	0.277617i	−0.999452	+	0.0331063i	$0.989460\pi$
$390$		0			0
$391$	23.6341	−	8.60210i	1.19523	−	0.435027i
$392$		0			0
$393$	3.85269	−	14.9714i	0.194343	−	0.755205i
$394$		0			0
$395$	8.37119	−	14.4993i	0.421200	−	0.729540i
$396$		0			0
$397$	11.5692	+	20.0385i	0.580642	+	1.00570i	0.995403	+	0.0957711i	$0.0305317\pi$
$397$	11.5692	+	20.0385i	0.580642	+	1.00570i	−0.414762	+	0.909930i	$0.636135\pi$
$398$		0			0
$399$	1.31118	+	13.4479i	0.0656409	+	0.673237i
$400$		0			0
$401$	2.26522	+	1.90074i	0.113120	+	0.0949186i	0.697593	−	0.716494i	$-0.254254\pi$
$401$	2.26522	+	1.90074i	0.113120	+	0.0949186i	−0.584473	+	0.811413i	$0.698699\pi$
$402$		0			0
$403$	13.5078	+	4.91642i	0.672869	+	0.244904i
$404$		0			0
$405$	38.2649	−	1.52019i	1.90140	−	0.0755389i
$406$		0			0
$407$	0.386831	+	0.140795i	0.0191745	+	0.00697896i
$408$		0			0
$409$	−12.0732	−	10.1306i	−0.596983	−	0.500928i	0.293492	−	0.955962i	$-0.405183\pi$
$409$	−12.0732	−	10.1306i	−0.596983	−	0.500928i	−0.890474	+	0.455034i	$0.849627\pi$
$410$		0			0
$411$	0.0230129	+	0.236028i	0.00113514	+	0.0116424i
$412$		0			0
$413$	9.18578	+	15.9102i	0.452003	+	0.782892i
$414$		0			0
$415$	−22.1845	+	38.4246i	−1.08899	+	1.88619i
$416$		0			0
$417$	1.01139	−	3.93021i	0.0495281	−	0.192463i
$418$		0			0
$419$	−21.4427	+	7.80450i	−1.04754	+	0.381275i	−0.807735	−	0.589546i	$-0.799307\pi$
$419$	−21.4427	+	7.80450i	−1.04754	+	0.381275i	−0.239808	+	0.970820i	$0.577085\pi$
$420$		0			0
$421$	−2.58652	−	14.6689i	−0.126059	−	0.714918i	−0.980673	−	0.195654i	$-0.937317\pi$
$421$	−2.58652	−	14.6689i	−0.126059	−	0.714918i	0.854614	−	0.519264i	$-0.173794\pi$
$422$		0			0
$423$	0.543697	+	27.3817i	0.0264354	+	1.33134i
$424$		0			0
$425$	36.9833	−	31.0327i	1.79396	−	1.50531i
$426$		0			0
$427$	7.17151	−	40.6717i	0.347054	−	1.96824i
$428$		0			0
$429$	1.36431	−	1.99020i	0.0658695	−	0.0960876i
$430$		0			0
$431$	−35.9676			−1.73250			−0.866249	−	0.499613i	$-0.833476\pi$
$431$	−35.9676			−1.73250			−0.866249	+	0.499613i	$0.833476\pi$
$432$		0			0
$433$	12.5784			0.604478			0.302239	−	0.953232i	$-0.402266\pi$
$433$	12.5784			0.604478			0.302239	+	0.953232i	$0.402266\pi$
$434$		0			0
$435$	−4.82368	−	0.373807i	−0.231278	−	0.0179227i
$436$		0			0
$437$	2.82995	−	16.0495i	0.135375	−	0.767750i
$438$		0			0
$439$	−22.0648	+	18.5146i	−1.05310	+	0.883652i	−0.993416	−	0.114566i	$-0.963452\pi$
$439$	−22.0648	+	18.5146i	−1.05310	+	0.883652i	−0.0596796	+	0.998218i	$0.519008\pi$
$440$		0			0
$441$	7.26224	+	8.31386i	0.345821	+	0.395898i
$442$		0			0
$443$	6.19494	+	35.1332i	0.294330	+	1.66923i	0.669911	+	0.742441i	$0.266332\pi$
$443$	6.19494	+	35.1332i	0.294330	+	1.66923i	−0.375581	+	0.926790i	$0.622557\pi$
$444$		0			0
$445$	24.9007	−	9.06311i	1.18041	−	0.429633i
$446$		0			0
$447$	−1.94817	−	1.90987i	−0.0921451	−	0.0903336i
$448$		0			0
$449$	−0.270764	+	0.468978i	−0.0127782	+	0.0221324i	−0.872344	−	0.488893i	$-0.837401\pi$
$449$	−0.270764	+	0.468978i	−0.0127782	+	0.0221324i	0.859566	+	0.511025i	$0.170734\pi$
$450$		0			0
$451$	−0.707116	−	1.22476i	−0.0332968	−	0.0576717i
$452$		0			0
$453$	−16.1051	+	11.5169i	−0.756685	+	0.541110i
$454$		0			0
$455$	33.1257	+	27.7957i	1.55296	+	1.30308i
$456$		0			0
$457$	9.80433	+	3.56848i	0.458627	+	0.166927i	0.560994	−	0.827820i	$-0.310419\pi$
$457$	9.80433	+	3.56848i	0.458627	+	0.166927i	−0.102366	+	0.994747i	$0.532641\pi$
$458$		0			0
$459$	13.1266	−	13.9327i	0.612699	−	0.650323i
$460$		0			0
$461$	28.0910	+	10.2243i	1.30833	+	0.476192i	0.899700	−	0.436510i	$-0.143785\pi$
$461$	28.0910	+	10.2243i	1.30833	+	0.476192i	0.408627	+	0.912701i	$0.366008\pi$
$462$		0			0
$463$	−10.0459	−	8.42955i	−0.466875	−	0.391754i	0.378778	−	0.925487i	$-0.376344\pi$
$463$	−10.0459	−	8.42955i	−0.466875	−	0.391754i	−0.845653	+	0.533733i	$0.820789\pi$
$464$		0			0
$465$	−31.0160	−	14.0899i	−1.43833	−	0.653403i
$466$		0			0
$467$	14.3462	+	24.8483i	0.663862	+	1.14984i	0.979592	+	0.200994i	$0.0644172\pi$
$467$	14.3462	+	24.8483i	0.663862	+	1.14984i	−0.315730	+	0.948849i	$0.602249\pi$
$468$		0			0
$469$	−14.3046	+	24.7763i	−0.660525	+	1.14406i
$470$		0			0
$471$	−26.5376	+	7.39383i	−1.22279	+	0.340690i
$472$		0			0
$473$	−1.26600	+	0.460788i	−0.0582110	+	0.0211871i
$474$		0			0
$475$	−5.43223	−	30.8077i	−0.249248	−	1.41356i
$476$		0			0
$477$	−20.5131	+	25.4562i	−0.939228	+	1.16556i
$478$		0			0
$479$	−14.8636	+	12.4720i	−0.679134	+	0.569861i	−0.915753	−	0.401741i	$-0.868405\pi$
$479$	−14.8636	+	12.4720i	−0.679134	+	0.569861i	0.236619	+	0.971603i	$0.423961\pi$
$480$		0			0
$481$	−0.496233	+	2.81428i	−0.0226263	+	0.128320i
$482$		0			0
$483$	−16.6784	−	34.8593i	−0.758895	−	1.58615i
$484$		0			0
$485$	11.7038			0.531441
$486$		0			0
$487$	35.4942			1.60839			0.804197	−	0.594363i	$-0.202596\pi$
$487$	35.4942			1.60839			0.804197	+	0.594363i	$0.202596\pi$
$488$		0			0
$489$	0.488743	+	1.02151i	0.0221017	+	0.0461945i
$490$		0			0
$491$	−3.26186	+	18.4989i	−0.147206	+	0.834845i	0.818364	+	0.574700i	$0.194881\pi$
$491$	−3.26186	+	18.4989i	−0.147206	+	0.834845i	−0.965570	+	0.260145i	$0.916230\pi$
$492$		0			0
$493$	−1.85261	+	1.55453i	−0.0834375	+	0.0700124i
$494$		0			0
$495$	−3.58802	+	4.45265i	−0.161270	+	0.200132i
$496$		0			0
$497$	−5.46801	−	31.0106i	−0.245274	−	1.39102i
$498$		0			0
$499$	−2.17650	+	0.792183i	−0.0974337	+	0.0354630i	−0.390277	−	0.920697i	$-0.627621\pi$
$499$	−2.17650	+	0.792183i	−0.0974337	+	0.0354630i	0.292843	+	0.956160i	$0.405399\pi$
$500$		0			0
$501$	14.5397	−	4.05101i	0.649585	−	0.180986i
$502$		0			0
$503$	15.4981	−	26.8434i	0.691025	−	1.19689i	−0.280478	−	0.959861i	$-0.590493\pi$
$503$	15.4981	−	26.8434i	0.691025	−	1.19689i	0.971502	−	0.237029i	$-0.0761738\pi$
$504$		0			0
$505$	−29.8362	−	51.6779i	−1.32769	−	2.29963i
$506$		0			0
$507$	−5.24998	−	2.38495i	−0.233160	−	0.105919i
$508$		0			0
$509$	−14.9656	−	12.5576i	−0.663339	−	0.556608i	0.247746	−	0.968825i	$-0.420310\pi$
$509$	−14.9656	−	12.5576i	−0.663339	−	0.556608i	−0.911086	+	0.412217i	$0.864754\pi$
$510$		0			0
$511$	46.4979	+	16.9238i	2.05694	+	0.748667i
$512$		0			0
$513$	−3.56564	−	11.8801i	−0.157427	−	0.524521i
$514$		0			0
$515$	10.7870	+	3.92614i	0.475331	+	0.173006i
$516$		0			0
$517$	−3.13278	−	2.62872i	−0.137780	−	0.115611i
$518$		0			0
$519$	1.15657	−	0.827067i	0.0507676	−	0.0363042i
$520$		0			0
$521$	−7.21348	−	12.4941i	−0.316028	−	0.547377i	0.663627	−	0.748064i	$-0.269016\pi$
$521$	−7.21348	−	12.4941i	−0.316028	−	0.547377i	−0.979656	+	0.200686i	$0.935683\pi$
$522$		0			0
$523$	−6.49050	+	11.2419i	−0.283810	+	0.491573i	−0.972320	−	0.233654i	$-0.924932\pi$
$523$	−6.49050	+	11.2419i	−0.283810	+	0.491573i	0.688510	+	0.725227i	$0.258265\pi$
$524$		0			0
$525$	−52.9703	−	51.9290i	−2.31181	−	2.26637i
$526$		0			0
$527$	−16.0016	+	5.82412i	−0.697043	+	0.253703i
$528$		0			0
$529$	4.09984	+	23.2514i	0.178254	+	1.01093i
$530$		0			0
$531$	−11.0950	−	12.7016i	−0.481482	−	0.551204i
$532$		0			0
$533$	7.52063	−	6.31056i	0.325755	−	0.273341i
$534$		0			0
$535$	4.02428	−	22.8228i	0.173985	−	0.986716i
$536$		0			0
$537$	9.29521	+	0.720325i	0.401118	+	0.0310843i
$538$		0			0
$539$	−1.64840			−0.0710016
$540$		0			0
$541$	−5.86904			−0.252330			−0.126165	−	0.992009i	$-0.540267\pi$
$541$	−5.86904			−0.252330			−0.126165	+	0.992009i	$0.540267\pi$
$542$		0			0
$543$	6.56705	−	9.57973i	0.281819	−	0.411106i
$544$		0			0
$545$	−8.03812	+	45.5864i	−0.344315	+	1.95271i
$546$		0			0
$547$	−31.4121	+	26.3579i	−1.34309	+	1.12698i	−0.362265	+	0.932075i	$0.617996\pi$
$547$	−31.4121	+	26.3579i	−1.34309	+	1.12698i	−0.980822	+	0.194908i	$0.937559\pi$
$548$		0			0
$549$	0.752651	+	37.9050i	0.0321224	+	1.61775i
$550$		0			0
$551$	0.272118	+	1.54326i	0.0115926	+	0.0657449i
$552$		0			0
$553$	−12.0832	+	4.39793i	−0.513830	+	0.187019i
$554$		0			0
$555$	1.68781	−	6.55874i	0.0716435	−	0.278403i
$556$		0			0
$557$	−5.57237	+	9.65164i	−0.236109	+	0.408953i	−0.959594	−	0.281387i	$-0.909206\pi$
$557$	−5.57237	+	9.65164i	−0.236109	+	0.408953i	0.723485	+	0.690340i	$0.242539\pi$
$558$		0			0
$559$	−4.67626	−	8.09953i	−0.197785	−	0.342573i
$560$		0			0
$561$	0.277382	+	2.84493i	0.0117111	+	0.120113i
$562$		0			0
$563$	−0.0339154	−	0.0284584i	−0.00142936	−	0.00119938i	0.642073	−	0.766644i	$-0.278075\pi$
$563$	−0.0339154	−	0.0284584i	−0.00142936	−	0.00119938i	−0.643502	+	0.765444i	$0.722519\pi$
$564$		0			0
$565$	22.3348	+	8.12921i	0.939633	+	0.341998i
$566$		0			0
$567$	−23.2635	−	17.9962i	−0.976974	−	0.755771i
$568$		0			0
$569$	−0.197941	−	0.0720447i	−0.00829813	−	0.00302027i	0.337868	−	0.941194i	$-0.390294\pi$
$569$	−0.197941	−	0.0720447i	−0.00829813	−	0.00302027i	−0.346166	+	0.938173i	$0.612517\pi$
$570$		0			0
$571$	−20.3725	−	17.0945i	−0.852561	−	0.715384i	0.107791	−	0.994174i	$-0.465622\pi$
$571$	−20.3725	−	17.0945i	−0.852561	−	0.715384i	−0.960352	+	0.278790i	$0.910067\pi$
$572$		0			0
$573$	0.643181	+	6.59669i	0.0268693	+	0.275581i
$574$		0			0
$575$	44.7351	+	77.4836i	1.86558	+	3.23129i
$576$		0			0
$577$	16.8850	−	29.2457i	0.702932	−	1.21751i	−0.264501	−	0.964385i	$-0.585207\pi$
$577$	16.8850	−	29.2457i	0.702932	−	1.21751i	0.967433	−	0.253128i	$-0.0814595\pi$
$578$		0			0
$579$	3.07241	−	11.9392i	0.127685	−	0.496177i
$580$		0			0
$581$	32.0216	−	11.6549i	1.32848	−	0.483528i
$582$		0			0
$583$	−0.847716	−	4.80764i	−0.0351088	−	0.199112i
$584$		0			0
$585$	−34.7655	−	19.1619i	−1.43738	−	0.792246i
$586$		0			0
$587$	−26.4661	+	22.2077i	−1.09237	+	0.916610i	−0.996889	−	0.0788214i	$-0.974884\pi$
$587$	−26.4661	+	22.2077i	−1.09237	+	0.916610i	−0.0954840	+	0.995431i	$0.530440\pi$
$588$		0			0
$589$	−1.91604	+	10.8664i	−0.0789491	+	0.447743i
$590$		0			0
$591$	0.747042	−	1.08975i	0.0307292	−	0.0448264i
$592$		0			0
$593$	−14.3387			−0.588819			−0.294410	−	0.955679i	$-0.595123\pi$
$593$	−14.3387			−0.588819			−0.294410	+	0.955679i	$0.595123\pi$
$594$		0			0
$595$	−51.2262			−2.10007
$596$		0			0
$597$	−42.6952	−	3.30863i	−1.74740	−	0.135413i
$598$		0			0
$599$	−1.57484	+	8.93134i	−0.0643461	+	0.364925i	0.935584	+	0.353104i	$0.114874\pi$
$599$	−1.57484	+	8.93134i	−0.0643461	+	0.364925i	−0.999930	+	0.0118207i	$0.996237\pi$
$600$		0			0
$601$	−22.8402	+	19.1652i	−0.931669	+	0.781764i	−0.976116	−	0.217248i	$-0.930292\pi$
$601$	−22.8402	+	19.1652i	−0.931669	+	0.781764i	0.0444469	+	0.999012i	$0.485847\pi$
$602$		0			0
$603$	8.49083	−	24.8528i	0.345773	−	1.01208i
$604$		0			0
$605$	7.97933	+	45.2531i	0.324406	+	1.83980i
$606$		0			0
$607$	−3.82422	+	1.39190i	−0.155220	+	0.0564955i	−0.418462	−	0.908234i	$-0.637431\pi$
$607$	−3.82422	+	1.39190i	−0.155220	+	0.0564955i	0.263242	+	0.964730i	$0.415208\pi$
$608$		0			0
$609$	2.65345	+	2.60129i	0.107523	+	0.105409i
$610$		0			0
$611$	14.1947	−	24.5859i	0.574256	−	0.994640i
$612$		0			0
$613$	0.739746	+	1.28128i	0.0298780	+	0.0517503i	0.880578	−	0.473902i	$-0.157155\pi$
$613$	0.739746	+	1.28128i	0.0298780	+	0.0517503i	−0.850700	+	0.525652i	$0.823821\pi$
$614$		0			0
$615$	−18.9253	+	13.5336i	−0.763142	+	0.545727i
$616$		0			0
$617$	37.6795	+	31.6169i	1.51692	+	1.27285i	0.848686	+	0.528897i	$0.177394\pi$
$617$	37.6795	+	31.6169i	1.51692	+	1.27285i	0.668234	+	0.743951i	$0.267050\pi$
$618$		0			0
$619$	−28.0078	−	10.1940i	−1.12573	−	0.409731i	−0.288988	−	0.957333i	$-0.593319\pi$
$619$	−28.0078	−	10.1940i	−1.12573	−	0.409731i	−0.836739	+	0.547601i	$0.815541\pi$
$620$		0			0
$621$	21.2038	+	28.4406i	0.850881	+	1.14128i
$622$		0			0
$623$	−19.1245	−	6.96075i	−0.766208	−	0.278877i
$624$		0			0
$625$	62.2161	+	52.2055i	2.48864	+	2.08822i
$626$		0			0
$627$	1.68633	+	0.766061i	0.0673455	+	0.0305935i
$628$		0			0
$629$	−1.69265	−	2.93175i	−0.0674903	−	0.116897i
$630$		0			0
$631$	11.9954	−	20.7766i	0.477527	−	0.827102i	−0.522141	−	0.852859i	$-0.674866\pi$
$631$	11.9954	−	20.7766i	0.477527	−	0.827102i	0.999668	+	0.0257576i	$0.00819981\pi$
$632$		0			0
$633$	3.19764	−	0.890918i	0.127095	−	0.0354108i
$634$		0			0
$635$	74.7215	−	27.1964i	2.96523	−	1.07926i
$636$		0			0
$637$	−1.98706	−	11.2692i	−0.0787303	−	0.446502i
$638$		0			0
$639$	10.4240	+	26.9620i	0.412369	+	1.06660i
$640$		0			0
$641$	−10.0053	+	8.39545i	−0.395186	+	0.331600i	−0.818629	−	0.574322i	$-0.805266\pi$
$641$	−10.0053	+	8.39545i	−0.395186	+	0.331600i	0.423443	+	0.905923i	$0.360821\pi$
$642$		0			0
$643$	0.133099	−	0.754842i	0.00524891	−	0.0297681i	−0.982071	−	0.188512i	$-0.939633\pi$
$643$	0.133099	−	0.754842i	0.00524891	−	0.0297681i	0.987320	+	0.158744i	$0.0507446\pi$
$644$		0			0
$645$	9.56607	+	19.9939i	0.376663	+	0.787258i
$646$		0			0
$647$	−30.1269			−1.18441			−0.592205	−	0.805787i	$-0.701742\pi$
$647$	−30.1269			−1.18441			−0.592205	+	0.805787i	$0.701742\pi$
$648$		0			0
$649$	2.51837			0.0988546
$650$		0			0
$651$	11.2923	+	23.6018i	0.442579	+	0.925027i
$652$		0			0
$653$	4.36398	−	24.7494i	0.170776	−	0.968517i	−0.772132	−	0.635463i	$-0.780809\pi$
$653$	4.36398	−	24.7494i	0.170776	−	0.968517i	0.942907	−	0.333055i	$-0.108079\pi$
$654$		0			0
$655$	29.0923	−	24.4114i	1.13673	−	0.953831i
$656$		0			0
$657$	−44.8821	−	6.99823i	−1.75102	−	0.273027i
$658$		0			0
$659$	1.29268	+	7.33115i	0.0503557	+	0.285581i	0.999579	−	0.0290226i	$-0.00923948\pi$
$659$	1.29268	+	7.33115i	0.0503557	+	0.285581i	−0.949223	+	0.314604i	$0.898128\pi$
$660$		0			0
$661$	23.0728	−	8.39782i	0.897428	−	0.326637i	0.148207	−	0.988956i	$-0.452650\pi$
$661$	23.0728	−	8.39782i	0.897428	−	0.326637i	0.749222	+	0.662319i	$0.230428\pi$
$662$		0			0
$663$	−19.1149	+	5.32573i	−0.742359	+	0.206834i
$664$		0			0
$665$	−16.5966	+	28.7461i	−0.643587	+	1.11473i
$666$		0			0
$667$	−2.24093	−	3.88140i	−0.0867690	−	0.150288i
$668$		0			0
$669$	−8.26720	−	3.75560i	−0.319628	−	0.145200i
$670$		0			0
$671$	−4.33678	−	3.63899i	−0.167420	−	0.140482i
$672$		0			0
$673$	41.2582	+	15.0168i	1.59039	+	0.578854i	0.977430	−	0.211261i	$-0.0677570\pi$
$673$	41.2582	+	15.0168i	1.59039	+	0.578854i	0.612959	+	0.790115i	$0.289979\pi$
$674$		0			0
$675$	56.9192	+	37.3799i	2.19082	+	1.43875i
$676$		0			0
$677$	15.7725	+	5.74072i	0.606187	+	0.220634i	0.626834	−	0.779153i	$-0.284350\pi$
$677$	15.7725	+	5.74072i	0.606187	+	0.220634i	−0.0206471	+	0.999787i	$0.506573\pi$
$678$		0			0
$679$	−6.88588	−	5.77794i	−0.264256	−	0.221737i
$680$		0			0
$681$	−12.0579	+	8.62264i	−0.462058	+	0.330420i
$682$		0			0
$683$	−5.52500	−	9.56957i	−0.211408	−	0.366170i	0.740747	−	0.671784i	$-0.234472\pi$
$683$	−5.52500	−	9.56957i	−0.211408	−	0.366170i	−0.952155	+	0.305614i	$0.901138\pi$
$684$		0			0
$685$	−0.291292	+	0.504532i	−0.0111297	+	0.0192772i
$686$		0			0
$687$	−21.1241	−	20.7088i	−0.805935	−	0.790091i
$688$		0			0
$689$	31.8453	−	11.5907i	1.21321	−	0.441572i
$690$		0			0
$691$	6.26508	+	35.5311i	0.238335	+	1.35167i	0.835475	+	0.549528i	$0.185193\pi$
$691$	6.26508	+	35.5311i	0.238335	+	1.35167i	−0.597140	+	0.802137i	$0.703696\pi$
$692$		0			0
$693$	4.30919	−	0.848360i	0.163692	−	0.0322265i
$694$		0			0
$695$	7.63719	−	6.40836i	0.289695	−	0.243083i
$696$		0			0
$697$	−2.01954	+	11.4534i	−0.0764954	+	0.433827i
$698$		0			0
$699$	18.7628	+	1.45401i	0.709673	+	0.0549955i
$700$		0			0
$701$	−31.0966			−1.17450			−0.587251	−	0.809405i	$-0.699790\pi$
$701$	−31.0966			−1.17450			−0.587251	+	0.809405i	$0.699790\pi$
$702$		0			0
$703$	−2.19358			−0.0827323
$704$		0			0
$705$	−38.0411	+	55.4928i	−1.43271	+	2.08998i
$706$		0			0
$707$	−7.95835	+	45.1341i	−0.299305	+	1.69744i
$708$		0			0
$709$	−11.4631	+	9.61868i	−0.430506	+	0.361237i	−0.832143	−	0.554562i	$-0.812886\pi$
$709$	−11.4631	+	9.61868i	−0.430506	+	0.361237i	0.401637	+	0.915799i	$0.368441\pi$
$710$		0			0
$711$	10.1036	−	6.10391i	0.378914	−	0.228914i
$712$		0			0
$713$	−5.47994	−	31.0783i	−0.205225	−	1.16389i
$714$		0			0
$715$	5.57019	−	2.02738i	0.208313	−	0.0758198i
$716$		0			0
$717$	1.21404	−	4.71768i	0.0453390	−	0.176185i
$718$		0			0
$719$	−12.2915	+	21.2894i	−0.458394	+	0.793961i	−0.998876	−	0.0473940i	$-0.984908\pi$
$719$	−12.2915	+	21.2894i	−0.458394	+	0.793961i	0.540483	+	0.841355i	$0.318242\pi$
$720$		0			0
$721$	−4.40822	−	7.63526i	−0.164171	−	0.284352i
$722$		0			0
$723$	−2.38837	−	24.4959i	−0.0888243	−	0.911014i
$724$		0			0
$725$	−6.59038	−	5.52999i	−0.244761	−	0.205379i
$726$		0			0
$727$	−7.45848	−	2.71466i	−0.276620	−	0.100681i	0.199985	−	0.979799i	$-0.435911\pi$
$727$	−7.45848	−	2.71466i	−0.276620	−	0.100681i	−0.476605	+	0.879118i	$0.658133\pi$
$728$		0			0
$729$	24.1448	+	12.0842i	0.894253	+	0.447563i
$730$		0			0
$731$	10.4111	+	3.78933i	0.385068	+	0.140153i
$732$		0			0
$733$	−37.0486	−	31.0875i	−1.36842	−	1.14824i	−0.973280	−	0.229621i	$-0.926251\pi$
$733$	−37.0486	−	31.0875i	−1.36842	−	1.14824i	−0.395141	−	0.918620i	$-0.629304\pi$
$734$		0			0
$735$	2.63162	+	26.9908i	0.0970687	+	0.995571i
$736$		0			0
$737$	1.96087	+	3.39633i	0.0722295	+	0.125105i
$738$		0			0
$739$	22.1883	−	38.4313i	0.816211	−	1.41372i	−0.0922433	−	0.995736i	$-0.529404\pi$
$739$	22.1883	−	38.4313i	0.816211	−	1.41372i	0.908455	−	0.417983i	$-0.137263\pi$
$740$		0			0
$741$	−3.20435	+	12.4520i	−0.117715	+	0.457434i
$742$		0			0
$743$	9.06438	−	3.29916i	0.332540	−	0.121035i	−0.170354	−	0.985383i	$-0.554491\pi$
$743$	9.06438	−	3.29916i	0.332540	−	0.121035i	0.502894	+	0.864348i	$0.332269\pi$
$744$		0			0
$745$	−1.16381	−	6.60029i	−0.0426387	−	0.241816i
$746$		0			0
$747$	−26.7755	+	16.1759i	−0.979664	+	0.591847i
$748$		0			0
$749$	−13.6349	+	11.4410i	−0.498207	+	0.418045i
$750$		0			0
$751$	−5.67193	+	32.1671i	−0.206972	+	1.17380i	0.687335	+	0.726341i	$0.258781\pi$
$751$	−5.67193	+	32.1671i	−0.206972	+	1.17380i	−0.894307	+	0.447455i	$0.852331\pi$
$752$		0			0
$753$	5.56593	−	8.11933i	0.202834	−	0.295885i
$754$		0			0
$755$	−48.6396			−1.77018
$756$		0			0
$757$	6.18068			0.224641			0.112320	−	0.993672i	$-0.464172\pi$
$757$	6.18068			0.224641			0.112320	+	0.993672i	$0.464172\pi$
$758$		0			0
$759$	−5.28144	−	0.409281i	−0.191704	−	0.0148560i
$760$		0			0
$761$	−7.17373	+	40.6842i	−0.260047	+	1.47480i	0.522729	+	0.852499i	$0.324914\pi$
$761$	−7.17373	+	40.6842i	−0.260047	+	1.47480i	−0.782776	+	0.622303i	$0.786197\pi$
$762$		0			0
$763$	27.2344	−	22.8524i	0.985950	−	0.827311i
$764$		0			0
$765$	46.1399	−	9.08368i	1.66819	−	0.328421i
$766$		0			0
$767$	3.03577	+	17.2167i	0.109615	+	0.621659i
$768$		0			0
$769$	−37.1345	+	13.5159i	−1.33911	+	0.487394i	−0.909531	−	0.415637i	$-0.863559\pi$
$769$	−37.1345	+	13.5159i	−1.33911	+	0.487394i	−0.429575	+	0.903031i	$0.641336\pi$
$770$		0			0
$771$	9.90024	+	9.70561i	0.356549	+	0.349539i
$772$		0			0
$773$	24.4912	−	42.4200i	0.880887	−	1.52574i	0.0305304	−	0.999534i	$-0.490280\pi$
$773$	24.4912	−	42.4200i	0.880887	−	1.52574i	0.850357	−	0.526207i	$-0.176386\pi$
$774$		0			0
$775$	−30.2883	−	52.4609i	−1.08799	−	1.88445i
$776$		0			0
$777$	−4.23094	+	3.02557i	−0.151784	+	0.108542i
$778$		0			0
$779$	5.77287	+	4.84401i	0.206834	+	0.173555i
$780$		0			0
$781$	−4.05619	−	1.47633i	−0.145142	−	0.0528273i
$782$		0			0
$783$	−2.85126	−	1.87248i	−0.101896	−	0.0669170i
$784$		0			0
$785$	−63.5947	−	23.1466i	−2.26979	−	0.826136i
$786$		0			0
$787$	12.8473	+	10.7801i	0.457956	+	0.384271i	0.842378	−	0.538887i	$-0.181155\pi$
$787$	12.8473	+	10.7801i	0.457956	+	0.384271i	−0.384422	+	0.923157i	$0.625599\pi$
$788$		0			0
$789$	−15.1720	−	6.89230i	−0.540137	−	0.245372i
$790$		0			0
$791$	−9.12737	−	15.8091i	−0.324532	−	0.562106i
$792$		0			0
$793$	19.6500	−	34.0348i	0.697793	−	1.20861i
$794$		0			0
$795$	−77.3667	+	21.5557i	−2.74391	+	0.764502i
$796$		0			0
$797$	35.7705	−	13.0194i	1.26706	−	0.461171i	0.380925	−	0.924606i	$-0.375606\pi$
$797$	35.7705	−	13.0194i	1.26706	−	0.461171i	0.886131	+	0.463435i	$0.153383\pi$
$798$		0			0
$799$	5.83993	+	33.1199i	0.206602	+	1.17170i
$800$		0			0
$801$	18.4599	+	2.87836i	0.652250	+	0.101702i
$802$		0			0
$803$	5.19606	−	4.36001i	0.183365	−	0.153862i
$804$		0			0
$805$	16.4850	−	93.4911i	0.581020	−	3.29513i
$806$		0			0
$807$	−13.4403	−	28.0913i	−0.473120	−	0.988861i
$808$		0			0
$809$	11.6040			0.407975			0.203987	−	0.978974i	$-0.434610\pi$
$809$	11.6040			0.407975			0.203987	+	0.978974i	$0.434610\pi$
$810$		0			0
$811$	15.8966			0.558206			0.279103	−	0.960261i	$-0.409963\pi$
$811$	15.8966			0.558206			0.279103	+	0.960261i	$0.409963\pi$
$812$		0			0
$813$	10.3938	+	21.7239i	0.364527	+	0.761892i
$814$		0			0
$815$	−0.483075	+	2.73966i	−0.0169214	+	0.0959660i
$816$		0			0
$817$	5.49946	−	4.61460i	0.192402	−	0.161444i
$818$		0			0
$819$	10.9943	+	28.4369i	0.384172	+	0.993665i
$820$		0			0
$821$	−1.50664	−	8.54460i	−0.0525822	−	0.298208i	0.947164	−	0.320751i	$-0.103935\pi$
$821$	−1.50664	−	8.54460i	−0.0525822	−	0.298208i	−0.999746	+	0.0225421i	$0.992824\pi$
$822$		0			0
$823$	34.4688	−	12.5456i	1.20151	−	0.437313i	0.337757	−	0.941234i	$-0.390332\pi$
$823$	34.4688	−	12.5456i	1.20151	−	0.437313i	0.863750	+	0.503921i	$0.168110\pi$
$824$		0			0
$825$	−9.79530	+	2.72914i	−0.341028	+	0.0950165i
$826$		0			0
$827$	−20.7686	+	35.9723i	−0.722195	+	1.25088i	0.237924	+	0.971284i	$0.423533\pi$
$827$	−20.7686	+	35.9723i	−0.722195	+	1.25088i	−0.960118	+	0.279594i	$0.909800\pi$
$828$		0			0
$829$	−2.16199	−	3.74469i	−0.0750892	−	0.130058i	0.826036	−	0.563618i	$-0.190591\pi$
$829$	−2.16199	−	3.74469i	−0.0750892	−	0.130058i	−0.901125	+	0.433559i	$0.857257\pi$
$830$		0			0
$831$	−0.393507	−	0.178761i	−0.0136506	−	0.00620116i
$832$		0			0
$833$	10.3843	+	8.71346i	0.359794	+	0.301903i
$834$		0			0
$835$	34.8429	+	12.6818i	1.20579	+	0.438871i
$836$		0			0
$837$	−14.3562	−	19.2559i	−0.496224	−	0.665583i
$838$		0			0
$839$	3.22589	+	1.17413i	0.111370	+	0.0405353i	0.397104	−	0.917774i	$-0.370015\pi$
$839$	3.22589	+	1.17413i	0.111370	+	0.0405353i	−0.285734	+	0.958309i	$0.592237\pi$
$840$		0			0
$841$	−21.8852	−	18.3638i	−0.754661	−	0.633235i
$842$		0			0
$843$	0.457377	−	0.327073i	0.0157529	−	0.0112650i
$844$		0			0
$845$	−7.08284	−	12.2678i	−0.243657	−	0.422026i
$846$		0			0
$847$	17.6460	−	30.5637i	0.606323	−	1.05018i
$848$		0			0
$849$	6.43622	+	6.30969i	0.220890	+	0.216548i
$850$		0			0
$851$	5.89535	−	2.14573i	0.202090	−	0.0735547i
$852$		0			0
$853$	5.94820	+	33.7339i	0.203663	+	1.15503i	0.899531	+	0.436858i	$0.143909\pi$
$853$	5.94820	+	33.7339i	0.203663	+	1.15503i	−0.695868	+	0.718170i	$0.744980\pi$
$854$		0			0
$855$	9.85129	−	28.8349i	0.336907	−	0.986132i
$856$		0			0
$857$	−38.2448	+	32.0912i	−1.30642	+	1.09621i	−0.317419	+	0.948286i	$0.602816\pi$
$857$	−38.2448	+	32.0912i	−1.30642	+	1.09621i	−0.988998	+	0.147928i	$0.952740\pi$
$858$		0			0
$859$	−7.81774	+	44.3366i	−0.266738	+	1.51275i	0.497303	+	0.867577i	$0.334324\pi$
$859$	−7.81774	+	44.3366i	−0.266738	+	1.51275i	−0.764041	+	0.645168i	$0.776787\pi$
$860$		0			0
$861$	17.8159	+	1.38063i	0.607165	+	0.0470517i
$862$		0			0
$863$	−11.6044			−0.395017			−0.197508	−	0.980301i	$-0.563285\pi$
$863$	−11.6044			−0.395017			−0.197508	+	0.980301i	$0.563285\pi$
$864$		0			0
$865$	3.49298			0.118765
$866$		0			0
$867$	−3.35769	+	4.89805i	−0.114033	+	0.166347i
$868$		0			0
$869$	−0.306083	+	1.73588i	−0.0103832	+	0.0588858i
$870$		0			0
$871$	−20.8551	+	17.4995i	−0.706648	+	0.592948i
$872$		0			0
$873$	7.22675	+	3.98320i	0.244588	+	0.134811i
$874$		0			0
$875$	−19.5707	−	110.991i	−0.661609	−	3.75217i
$876$		0			0
$877$	46.0763	−	16.7704i	1.55589	−	0.566297i	0.586098	−	0.810240i	$-0.300664\pi$
$877$	46.0763	−	16.7704i	1.55589	−	0.566297i	0.969789	+	0.243944i	$0.0784413\pi$
$878$		0			0
$879$	6.32866	−	24.5928i	0.213461	−	0.829496i
$880$		0			0
$881$	−3.65857	+	6.33683i	−0.123260	+	0.213493i	−0.921052	−	0.389441i	$-0.872668\pi$
$881$	−3.65857	+	6.33683i	−0.123260	+	0.213493i	0.797791	+	0.602934i	$0.206002\pi$
$882$		0			0
$883$	−16.6276	−	28.7998i	−0.559562	−	0.969191i	−0.997533	−	0.0702011i	$-0.977636\pi$
$883$	−16.6276	−	28.7998i	−0.559562	−	0.969191i	0.437970	−	0.898989i	$-0.355697\pi$
$884$		0			0
$885$	−4.02050	−	41.2357i	−0.135148	−	1.38612i
$886$		0			0
$887$	41.5414	+	34.8574i	1.39483	+	1.17040i	0.963342	+	0.268276i	$0.0864539\pi$
$887$	41.5414	+	34.8574i	1.39483	+	1.17040i	0.431483	+	0.902121i	$0.357990\pi$
$888$		0			0
$889$	−57.3885	−	20.8877i	−1.92475	−	0.700551i
$890$		0			0
$891$	−3.73089	+	1.52825i	−0.124990	+	0.0511984i
$892$		0			0
$893$	20.4776	+	7.45324i	0.685257	+	0.249413i
$894$		0			0
$895$	17.5450	+	14.7220i	0.586464	+	0.492102i
$896$		0			0
$897$	−3.56849	−	36.5997i	−0.119148	−	1.22203i
$898$		0			0
$899$	1.51724	+	2.62793i	0.0506027	+	0.0876464i
$900$		0			0
$901$	−20.0729	+	34.7673i	−0.668726	+	1.15827i
$902$		0			0
$903$	4.24245	−	16.4859i	0.141180	−	0.548617i
$904$		0			0
$905$	26.8119	−	9.75872i	0.891257	−	0.324391i
$906$		0			0
$907$	5.09827	+	28.9137i	0.169285	+	0.960065i	0.944535	+	0.328410i	$0.106513\pi$
$907$	5.09827	+	28.9137i	0.169285	+	0.960065i	−0.775250	+	0.631655i	$0.782376\pi$
$908$		0			0
$909$	−0.835231	−	42.0639i	−0.0277029	−	1.39517i
$910$		0			0
$911$	39.9203	−	33.4971i	1.32262	−	1.10981i	0.336876	−	0.941549i	$-0.390630\pi$
$911$	39.9203	−	33.4971i	1.32262	−	1.10981i	0.985743	−	0.168260i	$-0.0538148\pi$
$912$		0			0
$913$	0.811150	−	4.60026i	0.0268452	−	0.152246i
$914$		0			0
$915$	−52.6612	+	76.8198i	−1.74092	+	2.53959i
$916$		0			0
$917$	−29.1678			−0.963205
$918$		0			0
$919$	−9.28501			−0.306284			−0.153142	−	0.988204i	$-0.548939\pi$
$919$	−9.28501			−0.306284			−0.153142	+	0.988204i	$0.548939\pi$
$920$		0			0
$921$	56.2134	+	4.35621i	1.85229	+	0.143542i
$922$		0			0
$923$	5.20334	−	29.5096i	0.171270	−	0.971320i
$924$		0			0
$925$	9.22522	−	7.74088i	0.303323	−	0.254518i
$926$		0			0
$927$	5.32445	+	6.09546i	0.174878	+	0.200201i
$928$		0			0
$929$	−1.29489	−	7.34369i	−0.0424840	−	0.240939i	0.956170	−	0.292813i	$-0.0945915\pi$
$929$	−1.29489	−	7.34369i	−0.0424840	−	0.240939i	−0.998654	+	0.0518747i	$0.983480\pi$
$930$		0			0
$931$	8.25401	−	3.00421i	0.270514	−	0.0984591i
$932$		0			0
$933$	6.04364	+	5.92483i	0.197860	+	0.193970i
$934$		0			0
$935$	−3.51104	+	6.08129i	−0.114823	+	0.198880i
$936$		0			0
$937$	2.86863	+	4.96862i	0.0937142	+	0.162318i	0.909071	−	0.416641i	$-0.136793\pi$
$937$	2.86863	+	4.96862i	0.0937142	+	0.162318i	−0.815357	+	0.578958i	$0.803459\pi$
$938$		0			0
$939$	38.6607	−	27.6465i	1.26164	−	0.902208i
$940$		0			0
$941$	29.0530	+	24.3784i	0.947101	+	0.794712i	0.978807	−	0.204786i	$-0.0656497\pi$
$941$	29.0530	+	24.3784i	0.947101	+	0.794712i	−0.0317063	+	0.999497i	$0.510094\pi$
$942$		0			0
$943$	−20.2532	−	7.37157i	−0.659536	−	0.240051i
$944$		0			0
$945$	−20.7705	−	69.2041i	−0.675665	−	2.25121i
$946$		0			0
$947$	4.83043	+	1.75813i	0.156968	+	0.0571317i	0.419309	−	0.907844i	$-0.362272\pi$
$947$	4.83043	+	1.75813i	0.156968	+	0.0571317i	−0.262341	+	0.964975i	$0.584495\pi$
$948$		0			0
$949$	36.0706	+	30.2668i	1.17090	+	0.982504i
$950$		0			0
$951$	−11.1002	−	5.04258i	−0.359949	−	0.163517i
$952$		0			0
$953$	30.0392	+	52.0294i	0.973065	+	1.68540i	0.686179	+	0.727433i	$0.259287\pi$
$953$	30.0392	+	52.0294i	0.973065	+	1.68540i	0.286886	+	0.957965i	$0.407380\pi$
$954$		0			0
$955$	−8.14123	+	14.1010i	−0.263444	+	0.456298i
$956$		0			0
$957$	0.490678	−	0.136711i	0.0158614	−	0.00441925i
$958$		0			0
$959$	0.420458	−	0.153034i	0.0135773	−	0.00494174i
$960$		0			0
$961$	−1.67286	−	9.48724i	−0.0539631	−	0.306040i
$962$		0			0
$963$	10.2523	−	12.7228i	0.330375	−	0.409987i
$964$		0			0
$965$	23.2003	−	19.4674i	0.746844	−	0.626676i
$966$		0			0
$967$	2.08729	−	11.8376i	0.0671229	−	0.380673i	−0.932678	−	0.360710i	$-0.882534\pi$
$967$	2.08729	−	11.8376i	0.0671229	−	0.380673i	0.999801	−	0.0199623i	$-0.00635461\pi$
$968$		0			0
$969$	−6.57383	−	13.7399i	−0.211182	−	0.441388i
$970$		0			0
$971$	32.2162			1.03387			0.516933	−	0.856026i	$-0.327074\pi$
$971$	32.2162			1.03387			0.516933	+	0.856026i	$0.327074\pi$
$972$		0			0
$973$	−7.65700			−0.245472
$974$		0			0
$975$	−30.4654	−	63.6752i	−0.975673	−	2.03924i
$976$		0			0
$977$	6.16085	−	34.9399i	0.197103	−	1.11783i	−0.712289	−	0.701887i	$-0.752341\pi$
$977$	6.16085	−	34.9399i	0.197103	−	1.11783i	0.909392	−	0.415941i	$-0.136548\pi$
$978$		0			0
$979$	−2.13713	+	1.79327i	−0.0683031	+	0.0573131i
$980$		0			0
$981$	−20.4780	+	25.4127i	−0.653811	+	0.811364i
$982$		0			0
$983$	5.04146	+	28.5915i	0.160798	+	0.911928i	0.953292	+	0.302049i	$0.0976707\pi$
$983$	5.04146	+	28.5915i	0.160798	+	0.911928i	−0.792495	+	0.609879i	$0.791218\pi$
$984$		0			0
$985$	3.05001	−	1.11011i	0.0971815	−	0.0353712i
$986$		0			0
$987$	49.7771	−	13.8688i	1.58442	−	0.441448i
$988$		0			0
$989$	−10.2661	+	17.7815i	−0.326444	+	0.565418i
$990$		0			0
$991$	−3.77456	−	6.53773i	−0.119903	−	0.207678i	0.799826	−	0.600232i	$-0.204925\pi$
$991$	−3.77456	−	6.53773i	−0.119903	−	0.207678i	−0.919729	+	0.392554i	$0.871592\pi$
$992$		0			0
$993$	−40.3241	−	18.3184i	−1.27965	−	0.581315i
$994$		0			0
$995$	−80.5883	−	67.6216i	−2.55482	−	2.14375i
$996$		0			0
$997$	−21.5063	−	7.82764i	−0.681110	−	0.247904i	−0.0217859	−	0.999763i	$-0.506935\pi$
$997$	−21.5063	−	7.82764i	−0.681110	−	0.247904i	−0.659324	+	0.751859i	$0.729157\pi$
$998$		0			0
$999$	3.27434	−	3.47541i	0.103596	−	0.109957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.e.193.3		24
4.3	odd	2		216.2.q.a.193.2	yes	24
12.11	even	2		648.2.q.a.145.4		24
27.7	even	9	inner	432.2.u.e.385.3		24
108.7	odd	18		216.2.q.a.169.2	✓	24
108.47	even	18		648.2.q.a.505.4		24
108.67	odd	18		5832.2.a.h.1.1		12
108.95	even	18		5832.2.a.i.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.169.2	✓	24	108.7	odd	18
216.2.q.a.193.2	yes	24	4.3	odd	2
432.2.u.e.193.3		24	1.1	even	1	trivial
432.2.u.e.385.3		24	27.7	even	9	inner
648.2.q.a.145.4		24	12.11	even	2
648.2.q.a.505.4		24	108.47	even	18
5832.2.a.h.1.1		12	108.67	odd	18
5832.2.a.i.1.12		12	108.95	even	18

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.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.747543 + 1.56243i) q^{3} +(-0.738874 + 4.19036i) q^{5} +(2.50342 - 2.10062i) q^{7} +(-1.88236 + 2.33596i) q^{9} +O(q^{10})\)	\(q+(0.747543 + 1.56243i) q^{3} +(-0.738874 + 4.19036i) q^{5} +(2.50342 - 2.10062i) q^{7} +(-1.88236 + 2.33596i) q^{9} +(-0.0777898 - 0.441168i) q^{11} +(2.92225 - 1.06361i) q^{13} +(-7.09948 + 1.97804i) q^{15} +(-1.84197 + 3.19039i) q^{17} +(1.19355 + 2.06728i) q^{19} +(5.15347 + 2.34111i) q^{21} +(-5.22990 - 4.38841i) q^{23} +(-12.3147 - 4.48220i) q^{25} +(-5.05692 - 1.19482i) q^{27} +(0.616884 + 0.224527i) q^{29} +(3.54095 + 2.97121i) q^{31} +(0.631141 - 0.451333i) q^{33} +(6.95263 + 12.0423i) q^{35} +(-0.459466 + 0.795819i) q^{37} +(3.84632 + 3.77071i) q^{39} +(2.96657 - 1.07974i) q^{41} +(-0.522237 - 2.96175i) q^{43} +(-8.39770 - 9.61375i) q^{45} +(6.99323 - 5.86802i) q^{47} +(0.638970 - 3.62378i) q^{49} +(-6.36170 - 0.492995i) q^{51} +10.8975 q^{53} +1.90613 q^{55} +(-2.33775 + 3.41021i) q^{57} +(-0.976197 + 5.53629i) q^{59} +(9.68089 - 8.12323i) q^{61} +(0.194631 + 9.80200i) q^{63} +(2.29775 + 13.0312i) q^{65} +(-8.22644 + 2.99418i) q^{67} +(2.94700 - 11.4519i) q^{69} +(4.81781 - 8.34470i) q^{71} +(7.57074 + 13.1129i) q^{73} +(-2.20268 - 22.5915i) q^{75} +(-1.12146 - 0.941020i) q^{77} +(-3.69745 - 1.34576i) q^{79} +(-1.91345 - 8.79424i) q^{81} +(9.79861 + 3.56640i) q^{83} +(-12.0079 - 10.0758i) q^{85} +(0.110339 + 1.13168i) q^{87} +(-3.11383 - 5.39332i) q^{89} +(5.08137 - 8.80119i) q^{91} +(-1.99529 + 7.75358i) q^{93} +(-9.54454 + 3.47393i) q^{95} +(-0.477635 - 2.70880i) q^{97} +(1.17698 + 0.648722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q + 3 * q^7 + 6 * q^9	\( 24 q + 3 q^{7} + 6 q^{9} - 6 q^{11} + 12 q^{13} + 3 q^{15} + 6 q^{17} - 9 q^{19} - 18 q^{21} - 24 q^{23} - 24 q^{25} - 9 q^{29} + 27 q^{31} + 21 q^{33} + 18 q^{35} + 15 q^{37} + 15 q^{39} - 6 q^{41} - 39 q^{43} - 69 q^{45} + 36 q^{47} + 3 q^{49} + 36 q^{51} - 18 q^{53} + 54 q^{55} + 27 q^{57} + 30 q^{59} + 12 q^{61} - 18 q^{63} - 18 q^{65} - 54 q^{67} - 57 q^{69} + 36 q^{73} + 51 q^{75} - 24 q^{77} + 45 q^{79} + 18 q^{81} - 33 q^{83} - 57 q^{85} - 90 q^{87} + 9 q^{89} - 39 q^{91} + 42 q^{93} - 87 q^{95} + 57 q^{97} + 24 q^{99}+O(q^{100}) \) 24 * q + 3 * q^7 + 6 * q^9 - 6 * q^11 + 12 * q^13 + 3 * q^15 + 6 * q^17 - 9 * q^19 - 18 * q^21 - 24 * q^23 - 24 * q^25 - 9 * q^29 + 27 * q^31 + 21 * q^33 + 18 * q^35 + 15 * q^37 + 15 * q^39 - 6 * q^41 - 39 * q^43 - 69 * q^45 + 36 * q^47 + 3 * q^49 + 36 * q^51 - 18 * q^53 + 54 * q^55 + 27 * q^57 + 30 * q^59 + 12 * q^61 - 18 * q^63 - 18 * q^65 - 54 * q^67 - 57 * q^69 + 36 * q^73 + 51 * q^75 - 24 * q^77 + 45 * q^79 + 18 * q^81 - 33 * q^83 - 57 * q^85 - 90 * q^87 + 9 * q^89 - 39 * q^91 + 42 * q^93 - 87 * q^95 + 57 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

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