LMFDB - Embedded newform 891.2.k.a.809.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(161,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("891.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			809.16
Character	$\chi$	$=$	891.809
Dual form			891.2.k.a.728.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.474113 + 1.45917i) q^{2} +(-0.286362 + 0.208054i) q^{4} +(-2.65673 - 0.863223i) q^{5} +(-1.55356 - 2.13829i) q^{7} +(2.04313 + 1.48442i) q^{8} +O(q^{10})$	\(q+(0.474113 + 1.45917i) q^{2} +(-0.286362 + 0.208054i) q^{4} +(-2.65673 - 0.863223i) q^{5} +(-1.55356 - 2.13829i) q^{7} +(2.04313 + 1.48442i) q^{8} -4.28588i q^{10} +(2.31825 + 2.37186i) q^{11} +(-3.77297 + 1.22591i) q^{13} +(2.38356 - 3.28070i) q^{14} +(-1.41611 + 4.35835i) q^{16} +(-0.950349 + 2.92487i) q^{17} +(-3.46908 + 4.77479i) q^{19} +(0.940383 - 0.305549i) q^{20} +(-2.36183 + 4.50726i) q^{22} +7.86539i q^{23} +(2.26795 + 1.64777i) q^{25} +(-3.57763 - 4.92418i) q^{26} +(0.889760 + 0.289101i) q^{28} +(-1.44342 + 1.04870i) q^{29} +(-0.106433 - 0.327568i) q^{31} -1.98006 q^{32} -4.71846 q^{34} +(2.28156 + 7.02191i) q^{35} +(-0.830542 + 0.603424i) q^{37} +(-8.61197 - 2.79820i) q^{38} +(-4.14666 - 5.70739i) q^{40} +(-0.801475 - 0.582306i) q^{41} -7.86473i q^{43} +(-1.15733 - 0.196887i) q^{44} +(-11.4770 + 3.72909i) q^{46} +(-2.41446 + 3.32322i) q^{47} +(0.00438399 - 0.0134925i) q^{49} +(-1.32910 + 4.09056i) q^{50} +(0.825379 - 1.13604i) q^{52} +(-0.543068 + 0.176453i) q^{53} +(-4.11152 - 8.30254i) q^{55} -6.67495i q^{56} +(-2.21458 - 1.60899i) q^{58} +(3.16215 + 4.35233i) q^{59} +(-2.92236 - 0.949534i) q^{61} +(0.427516 - 0.310608i) q^{62} +(1.89345 + 5.82744i) q^{64} +11.0820 q^{65} +12.3825 q^{67} +(-0.336388 - 1.03530i) q^{68} +(-9.16445 + 6.65836i) q^{70} +(-6.04945 - 1.96559i) q^{71} +(2.35594 + 3.24267i) q^{73} +(-1.27427 - 0.925811i) q^{74} -2.08908i q^{76} +(1.47017 - 8.64191i) q^{77} +(-2.81422 + 0.914396i) q^{79} +(7.52445 - 10.3565i) q^{80} +(0.469694 - 1.44557i) q^{82} +(-1.42306 + 4.37972i) q^{83} +(5.04963 - 6.95022i) q^{85} +(11.4760 - 3.72877i) q^{86} +(1.21566 + 8.28729i) q^{88} -13.1208i q^{89} +(8.48287 + 6.16317i) q^{91} +(-1.63643 - 2.25235i) q^{92} +(-5.99387 - 1.94753i) q^{94} +(13.3381 - 9.69070i) q^{95} +(3.40521 + 10.4802i) q^{97} +0.0217664 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7}+O(q^{10}) $ 80 * q - 10 * q^4 + 10 * q^7	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58} + 10 q^{61} - 8 q^{64} - 20 q^{67} - 60 q^{70} - 20 q^{73} + 10 q^{79} - 2 q^{82} + 10 q^{85} + 118 q^{88} + 52 q^{91} + 10 q^{94} - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.474113	+	1.45917i	0.335249	+	1.03179i	0.966599	+	0.256292i	$0.0825009\pi$
$2$	0.474113	+	1.45917i	0.335249	+	1.03179i	−0.631351	+	0.775498i	$0.717499\pi$
$3$		0			0
$3$		0			0
$4$	−0.286362	+	0.208054i	−0.143181	+	0.104027i
$5$	−2.65673	−	0.863223i	−1.18812	−	0.386045i	−0.352745	−	0.935719i	$-0.614752\pi$
$5$	−2.65673	−	0.863223i	−1.18812	−	0.386045i	−0.835379	+	0.549675i	$0.814752\pi$
$6$		0			0
$7$	−1.55356	−	2.13829i	−0.587189	−	0.808197i	0.407271	−	0.913307i	$-0.366480\pi$
$7$	−1.55356	−	2.13829i	−0.587189	−	0.808197i	−0.994461	+	0.105110i	$0.966480\pi$
$8$	2.04313	+	1.48442i	0.722357	+	0.524823i
$9$		0			0
$10$		−	4.28588i		−	1.35531i
$11$	2.31825	+	2.37186i	0.698980	+	0.715141i
$11$	2.31825	+	2.37186i	0.698980	+	0.715141i
$12$		0			0
$13$	−3.77297	+	1.22591i	−1.04643	+	0.340007i	−0.781267	−	0.624196i	$-0.785427\pi$
$13$	−3.77297	+	1.22591i	−1.04643	+	0.340007i	−0.265165	+	0.964203i	$0.585427\pi$
$14$	2.38356	−	3.28070i	0.637035	−	0.876803i
$15$		0			0
$16$	−1.41611	+	4.35835i	−0.354028	+	1.08959i
$17$	−0.950349	+	2.92487i	−0.230493	+	0.709386i	0.767194	+	0.641415i	$0.221652\pi$
$17$	−0.950349	+	2.92487i	−0.230493	+	0.709386i	−0.997687	+	0.0679706i	$0.978348\pi$
$18$		0			0
$19$	−3.46908	+	4.77479i	−0.795863	+	1.09541i	0.197491	+	0.980305i	$0.436721\pi$
$19$	−3.46908	+	4.77479i	−0.795863	+	1.09541i	−0.993353	+	0.115106i	$0.963279\pi$
$20$	0.940383	−	0.305549i	0.210276	−	0.0683228i
$21$		0			0
$22$	−2.36183	+	4.50726i	−0.503543	+	0.960950i
$23$			7.86539i			1.64005i	0.572329	+	0.820024i	$0.306040\pi$
$23$			7.86539i			1.64005i	−0.572329	+	0.820024i	$0.693960\pi$
$24$		0			0
$25$	2.26795	+	1.64777i	0.453591	+	0.329553i
$26$	−3.57763	−	4.92418i	−0.701631	−	0.965712i
$27$		0			0
$28$	0.889760	+	0.289101i	0.168149	+	0.0546349i
$29$	−1.44342	+	1.04870i	−0.268036	+	0.194739i	−0.713682	−	0.700470i	$-0.752974\pi$
$29$	−1.44342	+	1.04870i	−0.268036	+	0.194739i	0.445646	+	0.895209i	$0.352974\pi$
$30$		0			0
$31$	−0.106433	−	0.327568i	−0.0191160	−	0.0588329i	0.941044	−	0.338286i	$-0.109847\pi$
$31$	−0.106433	−	0.327568i	−0.0191160	−	0.0588329i	−0.960159	+	0.279453i	$0.909847\pi$
$32$	−1.98006			−0.350029
$33$		0			0
$34$	−4.71846			−0.809210
$35$	2.28156	+	7.02191i	0.385653	+	1.18692i
$36$		0			0
$37$	−0.830542	+	0.603424i	−0.136540	+	0.0992023i	−0.653959	−	0.756530i	$-0.726893\pi$
$37$	−0.830542	+	0.603424i	−0.136540	+	0.0992023i	0.517419	+	0.855732i	$0.326893\pi$
$38$	−8.61197	−	2.79820i	−1.39705	−	0.453928i
$39$		0			0
$40$	−4.14666	−	5.70739i	−0.655645	−	0.902417i
$41$	−0.801475	−	0.582306i	−0.125169	−	0.0909409i	0.523439	−	0.852063i	$-0.324649\pi$
$41$	−0.801475	−	0.582306i	−0.125169	−	0.0909409i	−0.648609	+	0.761122i	$0.724649\pi$
$42$		0			0
$43$		−	7.86473i		−	1.19936i	−0.800240	−	0.599680i	$-0.795295\pi$
$43$		−	7.86473i		−	1.19936i	0.800240	−	0.599680i	$-0.204705\pi$
$44$	−1.15733	−	0.196887i	−0.174475	−	0.0296819i
$45$		0			0
$46$	−11.4770	+	3.72909i	−1.69218	+	0.549824i
$47$	−2.41446	+	3.32322i	−0.352185	+	0.484741i	−0.947951	−	0.318417i	$-0.896849\pi$
$47$	−2.41446	+	3.32322i	−0.352185	+	0.484741i	0.595765	+	0.803158i	$0.296849\pi$
$48$		0			0
$49$	0.00438399	−	0.0134925i	0.000626285	−	0.00192751i
$50$	−1.32910	+	4.09056i	−0.187964	+	0.578493i
$51$		0			0
$52$	0.825379	−	1.13604i	0.114459	−	0.157540i
$53$	−0.543068	+	0.176453i	−0.0745961	+	0.0242377i	−0.346077	−	0.938206i	$-0.612487\pi$
$53$	−0.543068	+	0.176453i	−0.0745961	+	0.0242377i	0.271481	+	0.962444i	$0.412487\pi$
$54$		0			0
$55$	−4.11152	−	8.30254i	−0.554398	−	1.11951i
$56$		−	6.67495i		−	0.891977i
$57$		0			0
$58$	−2.21458	−	1.60899i	−0.290789	−	0.211270i
$59$	3.16215	+	4.35233i	0.411677	+	0.566625i	0.963627	−	0.267253i	$-0.0861158\pi$
$59$	3.16215	+	4.35233i	0.411677	+	0.566625i	−0.551949	+	0.833878i	$0.686116\pi$
$60$		0			0
$61$	−2.92236	−	0.949534i	−0.374170	−	0.121575i	0.115894	−	0.993262i	$-0.463027\pi$
$61$	−2.92236	−	0.949534i	−0.374170	−	0.121575i	−0.490064	+	0.871686i	$0.663027\pi$
$62$	0.427516	−	0.310608i	0.0542945	−	0.0394473i
$63$		0			0
$64$	1.89345	+	5.82744i	0.236681	+	0.728430i
$65$	11.0820			1.37455
$66$		0			0
$67$	12.3825			1.51276			0.756380	−	0.654133i	$-0.226966\pi$
$67$	12.3825			1.51276			0.756380	+	0.654133i	$0.226966\pi$
$68$	−0.336388	−	1.03530i	−0.0407931	−	0.125548i
$69$		0			0
$70$	−9.16445	+	6.65836i	−1.09536	+	0.795826i
$71$	−6.04945	−	1.96559i	−0.717938	−	0.233272i	−0.0728088	−	0.997346i	$-0.523196\pi$
$71$	−6.04945	−	1.96559i	−0.717938	−	0.233272i	−0.645129	+	0.764074i	$0.723196\pi$
$72$		0			0
$73$	2.35594	+	3.24267i	0.275742	+	0.379526i	0.924318	−	0.381624i	$-0.124635\pi$
$73$	2.35594	+	3.24267i	0.275742	+	0.379526i	−0.648576	+	0.761150i	$0.724635\pi$
$74$	−1.27427	−	0.925811i	−0.148131	−	0.107623i
$75$		0			0
$76$		−	2.08908i		−	0.239633i
$77$	1.47017	−	8.64191i	0.167542	−	0.984837i
$78$		0			0
$79$	−2.81422	+	0.914396i	−0.316624	+	0.102878i	−0.463018	−	0.886349i	$-0.653233\pi$
$79$	−2.81422	+	0.914396i	−0.316624	+	0.102878i	0.146393	+	0.989226i	$0.453233\pi$
$80$	7.52445	−	10.3565i	0.841259	−	1.15789i
$81$		0			0
$82$	0.469694	−	1.44557i	0.0518690	−	0.159636i
$83$	−1.42306	+	4.37972i	−0.156201	+	0.480736i	−0.998281	−	0.0586165i	$-0.981331\pi$
$83$	−1.42306	+	4.37972i	−0.156201	+	0.480736i	0.842080	+	0.539353i	$0.181331\pi$
$84$		0			0
$85$	5.04963	−	6.95022i	0.547709	−	0.753857i
$86$	11.4760	−	3.72877i	1.23749	−	0.402084i
$87$		0			0
$88$	1.21566	+	8.28729i	0.129590	+	0.883428i
$89$		−	13.1208i		−	1.39080i	−0.718622	−	0.695401i	$-0.755227\pi$
$89$		−	13.1208i		−	1.39080i	0.718622	−	0.695401i	$-0.244773\pi$
$90$		0			0
$91$	8.48287	+	6.16317i	0.889246	+	0.646075i
$92$	−1.63643	−	2.25235i	−0.170610	−	0.234824i
$93$		0			0
$94$	−5.99387	−	1.94753i	−0.618221	−	0.200872i
$95$	13.3381	−	9.69070i	1.36846	−	0.994245i
$96$		0			0
$97$	3.40521	+	10.4802i	0.345747	+	1.06410i	0.961183	+	0.275912i	$0.0889798\pi$
$97$	3.40521	+	10.4802i	0.345747	+	1.06410i	−0.615436	+	0.788187i	$0.711020\pi$
$98$	0.0217664			0.00219874
$99$		0			0
$100$	−0.992281			−0.0992281
$101$	−2.96402	−	9.12230i	−0.294931	−	0.907703i	−0.983245	−	0.182290i	$-0.941649\pi$
$101$	−2.96402	−	9.12230i	−0.294931	−	0.907703i	0.688314	−	0.725413i	$-0.258351\pi$
$102$		0			0
$103$	−11.8120	+	8.58192i	−1.16387	+	0.845602i	−0.990263	−	0.139212i	$-0.955543\pi$
$103$	−11.8120	+	8.58192i	−1.16387	+	0.845602i	−0.173609	+	0.984815i	$0.555543\pi$
$104$	−9.52845	−	3.09598i	−0.934342	−	0.303586i
$105$		0			0
$106$	−0.514951	−	0.708769i	−0.0500165	−	0.0688418i
$107$	3.05515	+	2.21970i	0.295353	+	0.214586i	0.725586	−	0.688131i	$-0.241569\pi$
$107$	3.05515	+	2.21970i	0.295353	+	0.214586i	−0.430234	+	0.902718i	$0.641569\pi$
$108$		0			0
$109$		−	17.8297i		−	1.70777i	−0.520460	−	0.853886i	$-0.674240\pi$
$109$		−	17.8297i		−	1.70777i	0.520460	−	0.853886i	$-0.325760\pi$
$110$	10.1655	−	9.93576i	0.969242	−	0.947338i
$111$		0			0
$112$	11.5194	−	3.74288i	1.08848	−	0.353669i
$113$	−7.31262	+	10.0650i	−0.687913	+	0.946831i	−0.999995	−	0.00322418i	$-0.998974\pi$
$113$	−7.31262	+	10.0650i	−0.687913	+	0.946831i	0.312082	+	0.950055i	$0.398974\pi$
$114$		0			0
$115$	6.78958	−	20.8962i	0.633132	−	1.94858i
$116$	0.195153	−	0.600618i	0.0181195	−	0.0557660i
$117$		0			0
$118$	−4.85157	+	6.67762i	−0.446624	+	0.614725i
$119$	7.73064	−	2.51184i	0.708667	−	0.230260i
$120$		0			0
$121$	−0.251401	+	10.9971i	−0.0228546	+	0.999739i
$122$		−	4.71442i		−	0.426823i
$123$		0			0
$124$	0.0986303	+	0.0716591i	0.00885726	+	0.00643517i
$125$	3.60679	+	4.96432i	0.322601	+	0.444022i
$126$		0			0
$127$	5.84705	+	1.89982i	0.518842	+	0.168582i	0.556719	−	0.830701i	$-0.312060\pi$
$127$	5.84705	+	1.89982i	0.518842	+	0.168582i	−0.0378780	+	0.999282i	$0.512060\pi$
$128$	−10.8093	+	7.85344i	−0.955419	+	0.694153i
$129$		0			0
$130$	5.25411	+	16.1705i	0.460816	+	1.41825i
$131$	−6.54248			−0.571619			−0.285810	−	0.958286i	$-0.592262\pi$
$131$	−6.54248			−0.571619			−0.285810	+	0.958286i	$0.592262\pi$
$132$		0			0
$133$	15.5993			1.35263
$134$	5.87069	+	18.0681i	0.507151	+	1.56085i
$135$		0			0
$136$	−6.28344	+	4.56519i	−0.538801	+	0.391462i
$137$	6.12533	+	1.99024i	0.523323	+	0.170038i	0.558753	−	0.829334i	$-0.311280\pi$
$137$	6.12533	+	1.99024i	0.523323	+	0.170038i	−0.0354301	+	0.999372i	$0.511280\pi$
$138$		0			0
$139$	−11.9595	−	16.4608i	−1.01439	−	1.39618i	−0.916065	−	0.401030i	$-0.868652\pi$
$139$	−11.9595	−	16.4608i	−1.01439	−	1.39618i	−0.0983228	−	0.995155i	$-0.531348\pi$
$140$	−2.11429	−	1.53612i	−0.178690	−	0.129826i
$141$		0			0
$142$		−	9.75909i		−	0.818965i
$143$	−11.6544	−	6.10696i	−0.974588	−	0.510690i
$144$		0			0
$145$	4.74003	−	1.54013i	0.393638	−	0.127901i
$146$	−3.61463	+	4.97512i	−0.299149	+	0.411744i
$147$		0			0
$148$	0.112291	−	0.345596i	0.00923025	−	0.0284078i
$149$	−1.61519	+	4.97103i	−0.132321	+	0.407243i	−0.995164	−	0.0982299i	$-0.968682\pi$
$149$	−1.61519	+	4.97103i	−0.132321	+	0.407243i	0.862842	+	0.505473i	$0.168682\pi$
$150$		0			0
$151$	−2.12847	+	2.92959i	−0.173212	+	0.238407i	−0.886793	−	0.462167i	$-0.847072\pi$
$151$	−2.12847	+	2.92959i	−0.173212	+	0.238407i	0.713581	+	0.700573i	$0.247072\pi$
$152$	−14.1756	+	4.60594i	−1.14979	+	0.373591i
$153$		0			0
$154$	13.3070	−	1.95201i	1.07231	−	0.157298i
$155$			0.962133i			0.0772803i
$156$		0			0
$157$	8.56332	+	6.22162i	0.683427	+	0.496539i	0.874493	−	0.485038i	$-0.161194\pi$
$157$	8.56332	+	6.22162i	0.683427	+	0.496539i	−0.191066	+	0.981577i	$0.561194\pi$
$158$	−2.66852	−	3.67290i	−0.212296	−	0.292200i
$159$		0			0
$160$	5.26048	+	1.70923i	0.415878	+	0.135127i
$161$	16.8185	−	12.2193i	1.32548	−	0.963019i
$162$		0			0
$163$	−4.87570	−	15.0059i	−0.381894	−	1.17535i	−0.938708	−	0.344712i	$-0.887977\pi$
$163$	−4.87570	−	15.0059i	−0.381894	−	1.17535i	0.556814	−	0.830637i	$-0.312023\pi$
$164$	0.350664			0.0273822
$165$		0			0
$166$	−7.06544			−0.548385
$167$	−1.91668	−	5.89892i	−0.148317	−	0.456472i	0.849106	−	0.528223i	$-0.177141\pi$
$167$	−1.91668	−	5.89892i	−0.148317	−	0.456472i	−0.997423	+	0.0717505i	$0.977141\pi$
$168$		0			0
$169$	2.21520	−	1.60944i	0.170400	−	0.123803i
$170$	12.5357	+	4.07308i	0.961441	+	0.312391i
$171$		0			0
$172$	1.63629	+	2.25216i	0.124766	+	0.171726i
$173$	−11.9163	−	8.65769i	−0.905979	−	0.658232i	0.0340156	−	0.999421i	$-0.489170\pi$
$173$	−11.9163	−	8.65769i	−0.905979	−	0.658232i	−0.939995	+	0.341189i	$0.889170\pi$
$174$		0			0
$175$		−	7.40943i		−	0.560101i
$176$	−13.6203	+	6.74494i	−1.02667	+	0.508419i
$177$		0			0
$178$	19.1455	−	6.22074i	1.43501	−	0.466264i
$179$	−7.32242	+	10.0784i	−0.547303	+	0.753299i	−0.989643	−	0.143549i	$-0.954149\pi$
$179$	−7.32242	+	10.0784i	−0.547303	+	0.753299i	0.442340	+	0.896848i	$0.354149\pi$
$180$		0			0
$181$	0.342305	−	1.05351i	0.0254433	−	0.0783064i	−0.937529	−	0.347908i	$-0.886892\pi$
$181$	0.342305	−	1.05351i	0.0254433	−	0.0783064i	0.962972	+	0.269602i	$0.0868921\pi$
$182$	−4.97127	+	15.3000i	−0.368495	+	1.13411i
$183$		0			0
$184$	−11.6756	+	16.0701i	−0.860735	+	1.18470i
$185$	2.72741	−	0.886190i	0.200523	−	0.0651540i
$186$		0			0
$187$	−9.14053	+	4.52651i	−0.668421	+	0.331011i
$188$		−	1.45398i		−	0.106043i
$189$		0			0
$190$	20.4642	+	14.8681i	1.48463	+	1.07864i
$191$	11.5046	+	15.8348i	0.832445	+	1.14576i	0.987463	+	0.157851i	$0.0504565\pi$
$191$	11.5046	+	15.8348i	0.832445	+	1.14576i	−0.155018	+	0.987912i	$0.549544\pi$
$192$		0			0
$193$	9.04885	+	2.94015i	0.651351	+	0.211637i	0.616010	−	0.787739i	$-0.288748\pi$
$193$	9.04885	+	2.94015i	0.651351	+	0.211637i	0.0353411	+	0.999375i	$0.488748\pi$
$194$	−13.6779	+	9.93756i	−0.982015	+	0.713475i
$195$		0			0
$196$	0.00155177	+	0.00477586i	0.000110841	+	0.000341133i
$197$	−0.576409			−0.0410674			−0.0205337	−	0.999789i	$-0.506537\pi$
$197$	−0.576409			−0.0410674			−0.0205337	+	0.999789i	$0.506537\pi$
$198$		0			0
$199$	21.9796			1.55809			0.779047	−	0.626965i	$-0.215703\pi$
$199$	21.9796			1.55809			0.779047	+	0.626965i	$0.215703\pi$
$200$	2.18775	+	6.73321i	0.154698	+	0.476110i
$201$		0			0
$202$	11.9057	−	8.65001i	0.837683	−	0.608613i
$203$	4.48486	+	1.45722i	0.314776	+	0.102277i
$204$		0			0
$205$	1.62664	+	2.23888i	0.113610	+	0.156370i
$206$	−18.1227	−	13.1669i	−1.26267	−	0.917384i
$207$		0			0
$208$		−	18.1799i		−	1.26055i
$209$	−19.3673	+	2.84099i	−1.33967	+	0.196516i
$210$		0			0
$211$	22.8739	−	7.43218i	1.57471	−	0.511653i	0.614019	−	0.789291i	$-0.289552\pi$
$211$	22.8739	−	7.43218i	1.57471	−	0.511653i	0.960686	+	0.277638i	$0.0895516\pi$
$212$	0.118802	−	0.163517i	0.00815936	−	0.0112304i
$213$		0			0
$214$	−1.79043	+	5.51037i	−0.122391	+	0.376681i
$215$	−6.78901	+	20.8944i	−0.463007	+	1.42499i
$216$		0			0
$217$	−0.535084	+	0.736479i	−0.0363238	+	0.0499955i
$218$	26.0165	−	8.45328i	1.76206	−	0.572528i
$219$		0			0
$220$	2.90476	+	1.52211i	0.195839	+	0.102621i
$221$		−	12.2005i		−	0.820694i
$222$		0			0
$223$	−3.88850	−	2.82516i	−0.260393	−	0.189187i	0.449927	−	0.893065i	$-0.351450\pi$
$223$	−3.88850	−	2.82516i	−0.260393	−	0.189187i	−0.710320	+	0.703878i	$0.751450\pi$
$224$	3.07614	+	4.23394i	0.205533	+	0.282892i
$225$		0			0
$226$	−18.1535	−	5.89843i	−1.20755	−	0.392358i
$227$	2.31921	−	1.68500i	0.153931	−	0.111838i	−0.508154	−	0.861266i	$-0.669672\pi$
$227$	2.31921	−	1.68500i	0.153931	−	0.111838i	0.662085	+	0.749429i	$0.269672\pi$
$228$		0			0
$229$	−3.69600	−	11.3751i	−0.244239	−	0.751690i	−0.995761	−	0.0919815i	$-0.970680\pi$
$229$	−3.69600	−	11.3751i	−0.244239	−	0.751690i	0.751522	−	0.659708i	$-0.229320\pi$
$230$	33.7101			2.22278
$231$		0			0
$232$	−4.50582			−0.295821
$233$	0.512177	+	1.57632i	0.0335538	+	0.103268i	0.966431	−	0.256927i	$-0.0827101\pi$
$233$	0.512177	+	1.57632i	0.0335538	+	0.103268i	−0.932877	+	0.360195i	$0.882710\pi$
$234$		0			0
$235$	9.28324	−	6.74467i	0.605572	−	0.439974i
$236$	−1.81104	−	0.588443i	−0.117889	−	0.0383044i
$237$		0			0
$238$	7.33040	+	10.0894i	0.475159	+	0.654001i
$239$	−3.24986	−	2.36116i	−0.210216	−	0.152731i	0.477696	−	0.878525i	$-0.341472\pi$
$239$	−3.24986	−	2.36116i	−0.210216	−	0.152731i	−0.687911	+	0.725795i	$0.741472\pi$
$240$		0			0
$241$			15.5948i			1.00455i	0.864708	+	0.502274i	$0.167503\pi$
$241$			15.5948i			1.00455i	−0.864708	+	0.502274i	$0.832497\pi$
$242$	−16.1659	+	4.84705i	−1.03918	+	0.311580i
$243$		0			0
$244$	1.03441	−	0.336100i	0.0662213	−	0.0215166i
$245$	−0.0232941	+	0.0320616i	−0.00148821	+	0.00204834i
$246$		0			0
$247$	7.23528	−	22.2679i	0.460370	−	1.41687i
$248$	0.268792	−	0.827257i	0.0170683	−	0.0525308i
$249$		0			0
$250$	−5.53377	+	7.61657i	−0.349986	+	0.481714i
$251$	22.7610	−	7.39551i	1.43666	−	0.466800i	0.515808	−	0.856704i	$-0.327492\pi$
$251$	22.7610	−	7.39551i	1.43666	−	0.466800i	0.920856	+	0.389904i	$0.127492\pi$
$252$		0			0
$253$	−18.6556	+	18.2340i	−1.17287	+	1.14636i
$254$			9.43257i			0.591852i
$255$		0			0
$256$	−6.67012	−	4.84613i	−0.416883	−	0.302883i
$257$	10.3527	+	14.2492i	0.645782	+	0.888843i	0.998907	−	0.0467329i	$-0.0148810\pi$
$257$	10.3527	+	14.2492i	0.645782	+	0.888843i	−0.353125	+	0.935576i	$0.614881\pi$
$258$		0			0
$259$	2.58059	+	0.838484i	0.160350	+	0.0521009i
$260$	−3.17346	+	2.30565i	−0.196809	+	0.142990i
$261$		0			0
$262$	−3.10188	−	9.54659i	−0.191635	−	0.589791i
$263$	4.58957			0.283005			0.141502	−	0.989938i	$-0.454807\pi$
$263$	4.58957			0.283005			0.141502	+	0.989938i	$0.454807\pi$
$264$		0			0
$265$	1.59510			0.0979862
$266$	7.39583	+	22.7620i	0.453467	+	1.39563i
$267$		0			0
$268$	−3.54587	+	2.57623i	−0.216599	+	0.157368i
$269$	7.71837	+	2.50785i	0.470597	+	0.152906i	0.534709	−	0.845036i	$-0.320421\pi$
$269$	7.71837	+	2.50785i	0.470597	+	0.152906i	−0.0641114	+	0.997943i	$0.520421\pi$
$270$		0			0
$271$	2.83543	+	3.90264i	0.172240	+	0.237068i	0.886406	−	0.462908i	$-0.153194\pi$
$271$	2.83543	+	3.90264i	0.172240	+	0.237068i	−0.714166	+	0.699976i	$0.753194\pi$
$272$	−11.4018	−	8.28390i	−0.691336	−	0.502285i
$273$		0			0
$274$			9.88151i			0.596964i
$275$	1.34943	+	9.19920i	0.0813738	+	0.554732i
$276$		0			0
$277$	10.4010	−	3.37949i	0.624935	−	0.203054i	0.0206050	−	0.999788i	$-0.493441\pi$
$277$	10.4010	−	3.37949i	0.624935	−	0.203054i	0.604330	+	0.796734i	$0.293441\pi$
$278$	18.3489	−	25.2552i	1.10050	−	1.51470i
$279$		0			0
$280$	−5.76197	+	17.7335i	−0.344343	+	1.05978i
$281$	−1.29149	+	3.97481i	−0.0770440	+	0.237117i	−0.982160	−	0.188048i	$-0.939784\pi$
$281$	−1.29149	+	3.97481i	−0.0770440	+	0.237117i	0.905116	+	0.425165i	$0.139784\pi$
$282$		0			0
$283$	6.60735	−	9.09423i	0.392766	−	0.540596i	−0.566144	−	0.824306i	$-0.691565\pi$
$283$	6.60735	−	9.09423i	0.392766	−	0.540596i	0.958910	+	0.283710i	$0.0915654\pi$
$284$	2.14128	−	0.695745i	0.127062	−	0.0412849i
$285$		0			0
$286$	3.38560	−	19.9011i	0.200195	−	1.17678i
$287$			2.61843i			0.154561i
$288$		0			0
$289$	6.10157	+	4.43305i	0.358916	+	0.260768i
$290$	4.49462	+	6.18632i	0.263933	+	0.363273i
$291$		0			0
$292$	−1.34930	−	0.438416i	−0.0789621	−	0.0256563i
$293$	−22.4499	+	16.3108i	−1.31154	+	0.952887i	−0.311540	+	0.950233i	$0.600845\pi$
$293$	−22.4499	+	16.3108i	−1.31154	+	0.952887i	−0.999996	+	0.00265376i	$0.999155\pi$
$294$		0			0
$295$	−4.64394	−	14.2926i	−0.270381	−	0.832147i
$296$	−2.59265			−0.150695
$297$		0			0
$298$	−8.01937			−0.464550
$299$	−9.64227	−	29.6759i	−0.557627	−	1.71620i
$300$		0			0
$301$	−16.8171	+	12.2183i	−0.969319	+	0.704251i
$302$	−5.28391	−	1.71685i	−0.304055	−	0.0987934i
$303$		0			0
$304$	−15.8976	−	21.8811i	−0.911787	−	1.25497i
$305$	6.94426	+	5.04530i	0.397627	+	0.288893i
$306$		0			0
$307$			29.0972i			1.66067i	0.557266	+	0.830334i	$0.311850\pi$
$307$			29.0972i			1.66067i	−0.557266	+	0.830334i	$0.688150\pi$
$308$	1.37698	+	2.78059i	0.0784610	+	0.158439i
$309$		0			0
$310$	−1.40392	+	0.456160i	−0.0797371	+	0.0259081i
$311$	12.5777	−	17.3117i	0.713217	−	0.981659i	−0.286505	−	0.958079i	$-0.592493\pi$
$311$	12.5777	−	17.3117i	0.713217	−	0.981659i	0.999722	−	0.0235804i	$-0.00750658\pi$
$312$		0			0
$313$	−1.04383	+	3.21257i	−0.0590006	+	0.181585i	−0.976213	−	0.216813i	$-0.930434\pi$
$313$	−1.04383	+	3.21257i	−0.0590006	+	0.181585i	0.917213	+	0.398398i	$0.130434\pi$
$314$	−5.01842	+	15.4451i	−0.283206	+	0.871617i
$315$		0			0
$316$	0.615642	−	0.847359i	0.0346326	−	0.0476677i
$317$	−18.5995	+	6.04334i	−1.04465	+	0.339428i	−0.780567	−	0.625072i	$-0.785070\pi$
$317$	−18.5995	+	6.04334i	−1.04465	+	0.339428i	−0.264084	+	0.964500i	$0.585070\pi$
$318$		0			0
$319$	−5.83358	−	0.992416i	−0.326618	−	0.0555646i
$320$		−	17.1164i		−	0.956835i
$321$		0			0
$322$	25.8040	+	18.7477i	1.43800	+	1.04477i
$323$	−10.6688	−	14.6843i	−0.593628	−	0.817059i
$324$		0			0
$325$	−10.5769	−	3.43665i	−0.586702	−	0.190631i
$326$	19.5845	−	14.2289i	1.08468	−	0.788069i
$327$		0			0
$328$	−0.773133	−	2.37946i	−0.0426891	−	0.131384i
$329$	10.8570			0.598566
$330$		0			0
$331$	30.9746			1.70252			0.851259	−	0.524746i	$-0.175840\pi$
$331$	30.9746			1.70252			0.851259	+	0.524746i	$0.175840\pi$
$332$	−0.503709	−	1.55026i	−0.0276446	−	0.0850815i
$333$		0			0
$334$	7.69882	−	5.59352i	0.421260	−	0.306064i
$335$	−32.8968	−	10.6888i	−1.79735	−	0.583993i
$336$		0			0
$337$	17.4907	+	24.0738i	0.952777	+	1.31138i	0.950283	+	0.311388i	$0.100794\pi$
$337$	17.4907	+	24.0738i	0.952777	+	1.31138i	0.00249373	+	0.999997i	$0.499206\pi$
$338$	3.39870	+	2.46930i	0.184865	+	0.134312i
$339$		0			0
$340$			3.04088i			0.164915i
$341$	0.530204	−	1.01183i	0.0287122	−	0.0547936i
$342$		0			0
$343$	−17.6316	+	5.72886i	−0.952018	+	0.309329i
$344$	11.6746	−	16.0687i	0.629452	−	0.866366i
$345$		0			0
$346$	6.98338	−	21.4926i	0.375429	−	1.15545i
$347$	−8.34186	+	25.6736i	−0.447815	+	1.37823i	0.431553	+	0.902088i	$0.357966\pi$
$347$	−8.34186	+	25.6736i	−0.447815	+	1.37823i	−0.879367	+	0.476144i	$0.842034\pi$
$348$		0			0
$349$	−14.3466	+	19.7464i	−0.767955	+	1.05700i	0.228555	+	0.973531i	$0.426600\pi$
$349$	−14.3466	+	19.7464i	−0.767955	+	1.05700i	−0.996510	+	0.0834687i	$0.973400\pi$
$350$	10.8116	−	3.51291i	0.577906	−	0.187773i
$351$		0			0
$352$	−4.59029	−	4.69642i	−0.244663	−	0.250320i
$353$		−	0.846486i		−	0.0450539i	−0.999746	−	0.0225270i	$-0.992829\pi$
$353$		−	0.846486i		−	0.0450539i	0.999746	−	0.0225270i	$-0.00717116\pi$
$354$		0			0
$355$	14.3750	+	10.4440i	0.762945	+	0.554312i
$356$	2.72984	+	3.75730i	0.144681	+	0.199136i
$357$		0			0
$358$	−18.1778	−	5.90634i	−0.960728	−	0.312160i
$359$	−19.5043	+	14.1707i	−1.02940	+	0.747902i	−0.968188	−	0.250223i	$-0.919496\pi$
$359$	−19.5043	+	14.1707i	−1.02940	+	0.747902i	−0.0612103	+	0.998125i	$0.519496\pi$
$360$		0			0
$361$	−4.89271	−	15.0582i	−0.257511	−	0.792537i
$362$	1.69954			0.0893256
$363$		0			0
$364$	−3.71145			−0.194533
$365$	−3.45994	−	10.6486i	−0.181102	−	0.557373i
$366$		0			0
$367$	5.19427	−	3.77386i	0.271139	−	0.196994i	−0.443905	−	0.896074i	$-0.646407\pi$
$367$	5.19427	−	3.77386i	0.271139	−	0.196994i	0.715043	+	0.699080i	$0.246407\pi$
$368$	−34.2801	−	11.1383i	−1.78697	−	0.580623i
$369$		0			0
$370$	2.58620	+	3.55961i	0.134450	+	0.185055i
$371$	1.22099	+	0.887104i	0.0633909	+	0.0460562i
$372$		0			0
$373$		−	29.6760i		−	1.53657i	−0.640109	−	0.768284i	$-0.721111\pi$
$373$		−	29.6760i		−	1.53657i	0.640109	−	0.768284i	$-0.278889\pi$
$374$	−10.9386	−	11.1915i	−0.565621	−	0.578699i
$375$		0			0
$376$	−9.86614	+	3.20570i	−0.508807	+	0.165321i
$377$	4.16035	−	5.72623i	0.214269	−	0.294916i
$378$		0			0
$379$	8.27226	−	25.4594i	0.424917	−	1.30776i	−0.478156	−	0.878275i	$-0.658695\pi$
$379$	8.27226	−	25.4594i	0.424917	−	1.30776i	0.903073	−	0.429486i	$-0.141305\pi$
$380$	−1.80334	+	5.55010i	−0.0925093	+	0.284714i
$381$		0			0
$382$	−17.6511	+	24.2947i	−0.903110	+	1.24302i
$383$	9.69520	−	3.15016i	0.495402	−	0.160966i	−0.0506513	−	0.998716i	$-0.516130\pi$
$383$	9.69520	−	3.15016i	0.495402	−	0.160966i	0.546053	+	0.837751i	$0.316130\pi$
$384$		0			0
$385$	−11.3657	+	21.6901i	−0.579251	+	1.10543i
$386$			14.5978i			0.743008i
$387$		0			0
$388$	−3.15556	−	2.29265i	−0.160199	−	0.116392i
$389$	8.69286	+	11.9647i	0.440746	+	0.606634i	0.970378	−	0.241593i	$-0.0776700\pi$
$389$	8.69286	+	11.9647i	0.440746	+	0.606634i	−0.529632	+	0.848227i	$0.677670\pi$
$390$		0			0
$391$	−23.0053	−	7.47487i	−1.16343	−	0.378020i
$392$	0.0289858	−	0.0210594i	0.00146400	−	0.00106366i
$393$		0			0
$394$	−0.273283	−	0.841079i	−0.0137678	−	0.0423730i
$395$	8.26594			0.415904
$396$		0			0
$397$	8.81189			0.442256			0.221128	−	0.975245i	$-0.429026\pi$
$397$	8.81189			0.442256			0.221128	+	0.975245i	$0.429026\pi$
$398$	10.4208	+	32.0720i	0.522349	+	1.60763i
$399$		0			0
$400$	−10.3932	+	7.55111i	−0.519660	+	0.377555i
$401$	0.155398	+	0.0504918i	0.00776019	+	0.00252144i	0.312895	−	0.949788i	$-0.398701\pi$
$401$	0.155398	+	0.0504918i	0.00776019	+	0.00252144i	−0.305134	+	0.952309i	$0.598701\pi$
$402$		0			0
$403$	0.803137	+	1.10542i	0.0400071	+	0.0550651i
$404$	2.74672	+	1.99561i	0.136654	+	0.0992851i
$405$		0			0
$406$			7.23507i			0.359070i
$407$	−3.35664	−	0.571036i	−0.166383	−	0.0283052i
$408$		0			0
$409$	−10.7391	+	3.48936i	−0.531016	+	0.172538i	−0.562239	−	0.826975i	$-0.690060\pi$
$409$	−10.7391	+	3.48936i	−0.531016	+	0.172538i	0.0312226	+	0.999512i	$0.490060\pi$
$410$	−2.49570	+	3.43503i	−0.123254	+	0.169644i
$411$		0			0
$412$	1.59701	−	4.91508i	0.0786788	−	0.242148i
$413$	4.39395	−	13.5232i	0.216212	−	0.665432i
$414$		0			0
$415$	7.56134	−	10.4073i	0.371172	−	0.510874i
$416$	7.47071	−	2.42738i	0.366282	−	0.119012i
$417$		0			0
$418$	−13.3278	−	26.9133i	−0.651884	−	1.31637i
$419$		−	22.0175i		−	1.07562i	−0.843065	−	0.537812i	$-0.819251\pi$
$419$		−	22.0175i		−	1.07562i	0.843065	−	0.537812i	$-0.180749\pi$
$420$		0			0
$421$	−7.96431	−	5.78641i	−0.388157	−	0.282012i	0.376543	−	0.926399i	$-0.377113\pi$
$421$	−7.96431	−	5.78641i	−0.388157	−	0.282012i	−0.764700	+	0.644387i	$0.777113\pi$
$422$	21.6897	+	29.8532i	1.05584	+	1.45323i
$423$		0			0
$424$	−1.37149	−	0.445625i	−0.0666055	−	0.0216414i
$425$	−6.97485	+	5.06752i	−0.338330	+	0.245811i
$426$		0			0
$427$	2.50968	+	7.72401i	0.121452	+	0.373791i
$428$	−1.33670			−0.0646117
$429$		0			0
$430$	−33.7073			−1.62551
$431$	−6.08766	−	18.7359i	−0.293232	−	0.902476i	−0.983809	−	0.179218i	$-0.942643\pi$
$431$	−6.08766	−	18.7359i	−0.293232	−	0.902476i	0.690577	−	0.723259i	$-0.257357\pi$
$432$		0			0
$433$	−11.7898	+	8.56581i	−0.566583	+	0.411647i	−0.833862	−	0.551973i	$-0.813875\pi$
$433$	−11.7898	+	8.56581i	−0.566583	+	0.411647i	0.267279	+	0.963619i	$0.413875\pi$
$434$	−1.32834	−	0.431604i	−0.0637623	−	0.0207176i
$435$		0			0
$436$	3.70954	+	5.10574i	0.177655	+	0.244521i
$437$	−37.5556	−	27.2857i	−1.79653	−	1.30525i
$438$		0			0
$439$		−	11.4796i		−	0.547890i	−0.961745	−	0.273945i	$-0.911671\pi$
$439$		−	11.4796i		−	0.547890i	0.961745	−	0.273945i	$-0.0883286\pi$
$440$	3.92409	−	23.0665i	0.187074	−	1.09965i
$441$		0			0
$442$	17.8026	−	5.78442i	0.846783	−	0.275137i
$443$	5.54096	−	7.62648i	0.263259	−	0.362345i	−0.656841	−	0.754030i	$-0.728108\pi$
$443$	5.54096	−	7.62648i	0.263259	−	0.362345i	0.920100	+	0.391685i	$0.128108\pi$
$444$		0			0
$445$	−11.3262	+	34.8584i	−0.536912	+	1.65244i
$446$	2.27880	−	7.01344i	0.107904	−	0.332096i
$447$		0			0
$448$	9.51917	−	13.1020i	0.449738	−	0.619012i
$449$	−0.636449	+	0.206795i	−0.0300359	+	0.00975924i	−0.323996	−	0.946058i	$-0.605027\pi$
$449$	−0.636449	+	0.206795i	−0.0300359	+	0.00975924i	0.293961	+	0.955818i	$0.405027\pi$
$450$		0			0
$451$	−0.476877	−	3.25092i	−0.0224553	−	0.153080i
$452$		−	4.40364i		−	0.207130i
$453$		0			0
$454$	3.55828	+	2.58524i	0.166998	+	0.121331i
$455$	−17.2165	−	23.6964i	−0.807121	−	1.11091i
$456$		0			0
$457$	−22.1609	−	7.20052i	−1.03664	−	0.336826i	−0.259231	−	0.965815i	$-0.583469\pi$
$457$	−22.1609	−	7.20052i	−1.03664	−	0.336826i	−0.777414	+	0.628989i	$0.783469\pi$
$458$	14.8459	−	10.7862i	0.693705	−	0.504006i
$459$		0			0
$460$	2.40326	+	7.39648i	0.112053	+	0.344863i
$461$	20.3122			0.946035			0.473017	−	0.881053i	$-0.343165\pi$
$461$	20.3122			0.946035			0.473017	+	0.881053i	$0.343165\pi$
$462$		0			0
$463$	−34.6656			−1.61105			−0.805524	−	0.592563i	$-0.798116\pi$
$463$	−34.6656			−1.61105			−0.805524	+	0.592563i	$0.798116\pi$
$464$	−2.52657	−	7.77599i	−0.117293	−	0.360991i
$465$		0			0
$466$	−2.05729	+	1.49471i	−0.0953021	+	0.0692410i
$467$	−23.4499	−	7.61935i	−1.08513	−	0.352581i	−0.288770	−	0.957399i	$-0.593246\pi$
$467$	−23.4499	−	7.61935i	−1.08513	−	0.352581i	−0.796364	+	0.604817i	$0.793246\pi$
$468$		0			0
$469$	−19.2369	−	26.4773i	−0.888276	−	1.22261i
$470$	14.2429	+	10.3481i	0.656977	+	0.477322i
$471$		0			0
$472$			13.5864i			0.625364i
$473$	18.6540	−	18.2324i	0.857712	−	0.838328i
$474$		0			0
$475$	−15.7354	+	5.11276i	−0.721992	+	0.234589i
$476$	−1.69116	+	2.32769i	−0.0775144	+	0.106689i
$477$		0			0
$478$	1.90453	−	5.86155i	0.0871114	−	0.268101i
$479$	3.78875	−	11.6606i	0.173113	−	0.532786i	−0.826430	−	0.563040i	$-0.809632\pi$
$479$	3.78875	−	11.6606i	0.173113	−	0.532786i	0.999542	+	0.0302542i	$0.00963167\pi$
$480$		0			0
$481$	2.39386	−	3.29487i	0.109151	−	0.150233i
$482$	−22.7555	+	7.39369i	−1.03648	+	0.336774i
$483$		0			0
$484$	−2.21601	−	3.20147i	−0.100728	−	0.145521i
$485$		−	30.7823i		−	1.39775i
$486$		0			0
$487$	−2.20321	−	1.60073i	−0.0998371	−	0.0725359i	0.536747	−	0.843743i	$-0.319653\pi$
$487$	−2.20321	−	1.60073i	−0.0998371	−	0.0725359i	−0.636584	+	0.771208i	$0.719653\pi$
$488$	−4.56127	−	6.27805i	−0.206479	−	0.284194i
$489$		0			0
$490$	−0.0578275	−	0.0187893i	−0.00261238	−	0.000848813i
$491$	8.45619	−	6.14378i	0.381623	−	0.277265i	−0.380391	−	0.924826i	$-0.624211\pi$
$491$	8.45619	−	6.14378i	0.381623	−	0.277265i	0.762014	+	0.647561i	$0.224211\pi$
$492$		0			0
$493$	−1.69558	−	5.21845i	−0.0763649	−	0.235027i
$494$	35.9230			1.61625
$495$		0			0
$496$	1.57837			0.0708711
$497$	5.19518	+	15.9891i	0.233036	+	0.717210i
$498$		0			0
$499$	8.89922	−	6.46566i	0.398384	−	0.289443i	−0.370499	−	0.928833i	$-0.620813\pi$
$499$	8.89922	−	6.46566i	0.398384	−	0.289443i	0.768882	+	0.639390i	$0.220813\pi$
$500$	−2.06570	−	0.671186i	−0.0923808	−	0.0300163i
$501$		0			0
$502$	21.5826	+	29.7059i	0.963279	+	1.32584i
$503$	6.64248	+	4.82604i	0.296173	+	0.215183i	0.725941	−	0.687757i	$-0.241405\pi$
$503$	6.64248	+	4.82604i	0.296173	+	0.215183i	−0.429768	+	0.902940i	$0.641405\pi$
$504$		0			0
$505$			26.7941i			1.19232i
$506$	−35.4513	−	18.5767i	−1.57600	−	0.825835i
$507$		0			0
$508$	−2.06964	+	0.672466i	−0.0918254	+	0.0298359i
$509$	12.9861	−	17.8738i	0.575599	−	0.792244i	−0.417605	−	0.908629i	$-0.637131\pi$
$509$	12.9861	−	17.8738i	0.575599	−	0.792244i	0.993204	+	0.116385i	$0.0371305\pi$
$510$		0			0
$511$	3.27368	−	10.0754i	0.144819	−	0.445708i
$512$	−4.34866	+	13.3838i	−0.192186	+	0.591486i
$513$		0			0
$514$	−15.8837	+	21.8621i	−0.700601	+	0.964295i
$515$	38.7894	−	12.6034i	1.70926	−	0.555374i
$516$		0			0
$517$	−13.4795	+	1.97731i	−0.592829	+	0.0869622i
$518$			4.16306i			0.182914i
$519$		0			0
$520$	22.6420	+	16.4503i	0.992916	+	0.721396i
$521$	14.3440	+	19.7428i	0.628422	+	0.864949i	0.997932	−	0.0642780i	$-0.0204744\pi$
$521$	14.3440	+	19.7428i	0.628422	+	0.864949i	−0.369510	+	0.929227i	$0.620474\pi$
$522$		0			0
$523$	−11.4006	−	3.70428i	−0.498513	−	0.161977i	0.0489586	−	0.998801i	$-0.484410\pi$
$523$	−11.4006	−	3.70428i	−0.498513	−	0.161977i	−0.547472	+	0.836824i	$0.684410\pi$
$524$	1.87352	−	1.36119i	0.0818450	−	0.0594639i
$525$		0			0
$526$	2.17598	+	6.69696i	0.0948770	+	0.292001i
$527$	1.05924			0.0461413
$528$		0			0
$529$	−38.8644			−1.68976
$530$	0.756258	+	2.32752i	0.0328498	+	0.101101i
$531$		0			0
$532$	−4.46705	+	3.24550i	−0.193671	+	0.140710i
$533$	3.73780	+	1.21448i	0.161902	+	0.0526051i
$534$		0			0
$535$	−6.20060	−	8.53440i	−0.268075	−	0.368974i
$536$	25.2991	+	18.3808i	1.09275	+	0.793931i
$537$		0			0
$538$			12.4514i			0.536819i
$539$	0.0421656	−	0.0208809i	0.00181620	−	0.000899406i
$540$		0			0
$541$	13.9239	−	4.52415i	0.598635	−	0.194508i	0.00600328	−	0.999982i	$-0.498089\pi$
$541$	13.9239	−	4.52415i	0.598635	−	0.194508i	0.592631	+	0.805474i	$0.298089\pi$
$542$	−4.35030	+	5.98768i	−0.186861	+	0.257193i
$543$		0			0
$544$	1.88175	−	5.79143i	0.0806794	−	0.248306i
$545$	−15.3910	+	47.3685i	−0.659276	+	2.02904i
$546$		0			0
$547$	3.83972	−	5.28493i	0.164175	−	0.225967i	−0.719001	−	0.695009i	$-0.755401\pi$
$547$	3.83972	−	5.28493i	0.164175	−	0.225967i	0.883176	+	0.469041i	$0.155401\pi$
$548$	−2.16814	+	0.704472i	−0.0926184	+	0.0300936i
$549$		0			0
$550$	−12.7834	+	6.33051i	−0.545087	+	0.269934i
$551$		−	10.5300i		−	0.448595i
$552$		0			0
$553$	6.32729	+	4.59705i	0.269064	+	0.195486i
$554$	9.86250	+	13.5746i	0.419018	+	0.576728i
$555$		0			0
$556$	6.84947	+	2.22553i	0.290482	+	0.0943834i
$557$	−31.9814	+	23.2358i	−1.35509	+	0.984533i	−0.356354	+	0.934351i	$0.615980\pi$
$557$	−31.9814	+	23.2358i	−1.35509	+	0.984533i	−0.998740	+	0.0501824i	$0.984020\pi$
$558$		0			0
$559$	9.64146	+	29.6734i	0.407790	+	1.25505i
$560$	−33.8349			−1.42978
$561$		0			0
$562$	−6.41223			−0.270484
$563$	11.8302	+	36.4095i	0.498582	+	1.53448i	0.811298	+	0.584632i	$0.198761\pi$
$563$	11.8302	+	36.4095i	0.498582	+	1.53448i	−0.312716	+	0.949847i	$0.601239\pi$
$564$		0			0
$565$	28.1159	−	20.4274i	1.18285	−	0.859387i
$566$	16.4027	+	5.32955i	0.689456	+	0.224018i
$567$		0			0
$568$	−9.44208	−	12.9959i	−0.396181	−	0.545296i
$569$	20.0131	+	14.5404i	0.838992	+	0.609564i	0.922089	−	0.386978i	$-0.126481\pi$
$569$	20.0131	+	14.5404i	0.838992	+	0.609564i	−0.0830967	+	0.996541i	$0.526481\pi$
$570$		0			0
$571$			33.7881i			1.41399i	0.707220	+	0.706994i	$0.249949\pi$
$571$			33.7881i			1.41399i	−0.707220	+	0.706994i	$0.750051\pi$
$572$	4.60795	−	0.675941i	0.192668	−	0.0282625i
$573$		0			0
$574$	−3.82074	+	1.24143i	−0.159475	+	0.0518164i
$575$	−12.9603	+	17.8383i	−0.540483	+	0.743911i
$576$		0			0
$577$	−1.28480	+	3.95422i	−0.0534871	+	0.164616i	−0.974232	−	0.225549i	$-0.927582\pi$
$577$	−1.28480	+	3.95422i	−0.0534871	+	0.164616i	0.920745	+	0.390166i	$0.127582\pi$
$578$	−3.57574	+	11.0050i	−0.148731	+	0.457748i
$579$		0			0
$580$	−1.03693	+	1.42722i	−0.0430564	+	0.0592620i
$581$	11.5759	−	3.76124i	0.480249	−	0.156042i
$582$		0			0
$583$	−1.67749	−	0.879014i	−0.0694745	−	0.0364051i
$584$			10.1224i			0.418869i
$585$		0			0
$586$	−34.4440	−	25.0251i	−1.42287	−	1.03378i
$587$	−4.74153	−	6.52615i	−0.195704	−	0.269363i	0.699876	−	0.714265i	$-0.253239\pi$
$587$	−4.74153	−	6.52615i	−0.195704	−	0.269363i	−0.895580	+	0.444902i	$0.853239\pi$
$588$		0			0
$589$	1.93329	+	0.628164i	0.0796598	+	0.0258831i
$590$	18.6536	−	13.5526i	0.767955	−	0.557952i
$591$		0			0
$592$	−1.45379	−	4.47431i	−0.0597504	−	0.183893i
$593$	−3.24653			−0.133319			−0.0666596	−	0.997776i	$-0.521234\pi$
$593$	−3.24653			−0.133319			−0.0666596	+	0.997776i	$0.521234\pi$
$594$		0			0
$595$	−22.7065			−0.930874
$596$	−0.571717	−	1.75956i	−0.0234184	−	0.0720745i
$597$		0			0
$598$	38.7306	−	28.1395i	1.58381	−	1.15071i
$599$	−14.7524	−	4.79336i	−0.602769	−	0.195851i	−0.00829381	−	0.999966i	$-0.502640\pi$
$599$	−14.7524	−	4.79336i	−0.602769	−	0.195851i	−0.594475	+	0.804114i	$0.702640\pi$
$600$		0			0
$601$	7.54413	+	10.3836i	0.307731	+	0.423556i	0.934672	−	0.355511i	$-0.115693\pi$
$601$	7.54413	+	10.3836i	0.307731	+	0.423556i	−0.626941	+	0.779067i	$0.715693\pi$
$602$	−25.8018	−	18.7461i	−1.05160	−	0.764034i
$603$		0			0
$604$		−	1.28176i		−	0.0521541i
$605$	10.1609	−	28.9993i	0.413098	−	1.17899i
$606$		0			0
$607$	−8.64905	+	2.81025i	−0.351054	+	0.114064i	−0.479236	−	0.877686i	$-0.659086\pi$
$607$	−8.64905	+	2.81025i	−0.351054	+	0.114064i	0.128181	+	0.991751i	$0.459086\pi$
$608$	6.86901	−	9.45437i	0.278575	−	0.383426i
$609$		0			0
$610$	−4.06959	+	12.5249i	−0.164773	+	0.507119i
$611$	5.03571	−	15.4983i	0.203723	−	0.626995i
$612$		0			0
$613$	−2.23663	+	3.07846i	−0.0903368	+	0.124338i	−0.851793	−	0.523878i	$-0.824485\pi$
$613$	−2.23663	+	3.07846i	−0.0903368	+	0.124338i	0.761456	+	0.648216i	$0.224485\pi$
$614$	−42.4579	+	13.7954i	−1.71346	+	0.556737i
$615$		0			0
$616$	15.8320	−	15.4742i	0.637890	−	0.623474i
$617$			37.5594i			1.51209i	0.654522	+	0.756043i	$0.272870\pi$
$617$			37.5594i			1.51209i	−0.654522	+	0.756043i	$0.727130\pi$
$618$		0			0
$619$	−23.7866	−	17.2820i	−0.956063	−	0.694620i	−0.00382996	−	0.999993i	$-0.501219\pi$
$619$	−23.7866	−	17.2820i	−0.956063	−	0.694620i	−0.952233	+	0.305372i	$0.901219\pi$
$620$	−0.200176	−	0.275518i	−0.00803925	−	0.0110651i
$621$		0			0
$622$	31.2241	+	10.1453i	1.25197	+	0.406790i
$623$	−28.0560	+	20.3839i	−1.12404	+	0.816664i
$624$		0			0
$625$	−9.62835	−	29.6330i	−0.385134	−	1.18532i
$626$	−5.18258			−0.207138
$627$		0			0
$628$	−3.74665			−0.149507
$629$	−0.975634	−	3.00269i	−0.0389011	−	0.119725i
$630$		0			0
$631$	2.62503	−	1.90720i	0.104501	−	0.0759243i	−0.534308	−	0.845290i	$-0.679428\pi$
$631$	2.62503	−	1.90720i	0.104501	−	0.0759243i	0.638808	+	0.769366i	$0.279428\pi$
$632$	−7.10718	−	2.30926i	−0.282709	−	0.0918576i
$633$		0			0
$634$	−17.6365	−	24.2746i	−0.700436	−	0.964067i
$635$	−13.8940	−	10.0946i	−0.551368	−	0.400592i
$636$		0			0
$637$			0.0562813i			0.00222995i
$638$	−1.31767	−	8.98271i	−0.0521672	−	0.355629i
$639$		0			0
$640$	35.4967	−	11.5336i	1.40313	−	0.455905i
$641$	17.3005	−	23.8122i	0.683330	−	0.940524i	−0.316637	−	0.948547i	$-0.602554\pi$
$641$	17.3005	−	23.8122i	0.683330	−	0.940524i	0.999968	+	0.00802302i	$0.00255383\pi$
$642$		0			0
$643$	−5.12392	+	15.7698i	−0.202068	+	0.621901i	0.797753	+	0.602984i	$0.206022\pi$
$643$	−5.12392	+	15.7698i	−0.202068	+	0.621901i	−0.999821	+	0.0189167i	$0.993978\pi$
$644$	−2.27389	+	6.99831i	−0.0896038	+	0.275772i
$645$		0			0
$646$	16.3687	−	22.5296i	0.644020	−	0.886417i
$647$	40.6801	−	13.2178i	1.59930	−	0.519643i	0.632364	−	0.774671i	$-0.282085\pi$
$647$	40.6801	−	13.2178i	1.59930	−	0.519643i	0.966934	+	0.255028i	$0.0820846\pi$
$648$		0			0
$649$	−2.99243	+	17.5900i	−0.117463	+	0.690467i
$650$		−	17.0629i		−	0.669262i
$651$		0			0
$652$	4.51825	+	3.28270i	0.176948	+	0.128560i
$653$	18.9767	+	26.1191i	0.742614	+	1.02212i	0.998464	+	0.0554038i	$0.0176446\pi$
$653$	18.9767	+	26.1191i	0.742614	+	1.02212i	−0.255850	+	0.966716i	$0.582355\pi$
$654$		0			0
$655$	17.3816	+	5.64762i	0.679154	+	0.220671i
$656$	3.67287	−	2.66850i	0.143402	−	0.104187i
$657$		0			0
$658$	5.14745	+	15.8422i	0.200668	+	0.617594i
$659$	−5.39201			−0.210043			−0.105022	−	0.994470i	$-0.533491\pi$
$659$	−5.39201			−0.210043			−0.105022	+	0.994470i	$0.533491\pi$
$660$		0			0
$661$	6.97111			0.271145			0.135572	−	0.990767i	$-0.456713\pi$
$661$	6.97111			0.271145			0.135572	+	0.990767i	$0.456713\pi$
$662$	14.6855	+	45.1972i	0.570767	+	1.75664i
$663$		0			0
$664$	−9.40885	+	6.83593i	−0.365134	+	0.265286i
$665$	−41.4430	−	13.4657i	−1.60709	−	0.522176i
$666$		0			0
$667$	−8.24847	−	11.3530i	−0.319382	−	0.439592i
$668$	1.77616	+	1.29046i	0.0687217	+	0.0499292i
$669$		0			0
$670$		−	53.0698i		−	2.05027i
$671$	−4.52262	−	9.13269i	−0.174594	−	0.352563i
$672$		0			0
$673$	9.00133	−	2.92471i	0.346976	−	0.112739i	−0.130344	−	0.991469i	$-0.541608\pi$
$673$	9.00133	−	2.92471i	0.346976	−	0.112739i	0.477320	+	0.878730i	$0.341608\pi$
$674$	−26.8353	+	36.9356i	−1.03366	+	1.42271i
$675$		0			0
$676$	−0.299499	+	0.921763i	−0.0115192	+	0.0354524i
$677$	−12.3857	+	38.1192i	−0.476021	+	1.46504i	0.368555	+	0.929606i	$0.379852\pi$
$677$	−12.3857	+	38.1192i	−0.476021	+	1.46504i	−0.844576	+	0.535435i	$0.820148\pi$
$678$		0			0
$679$	17.1194	−	23.5628i	0.656982	−	0.904258i
$680$	20.6342	−	6.70444i	0.791284	−	0.257104i
$681$		0			0
$682$	1.72781	+	0.293937i	0.0661612	+	0.0112554i
$683$			18.6808i			0.714802i	0.933951	+	0.357401i	$0.116337\pi$
$683$			18.6808i			0.714802i	−0.933951	+	0.357401i	$0.883663\pi$
$684$		0			0
$685$	−14.5553	−	10.5751i	−0.556130	−	0.404052i
$686$	−16.7188	−	23.0114i	−0.638326	−	0.878580i
$687$		0			0
$688$	34.2772	+	11.1373i	1.30681	+	0.424607i
$689$	1.83266	−	1.33151i	0.0698188	−	0.0507263i
$690$		0			0
$691$	2.50085	+	7.69683i	0.0951369	+	0.292801i	0.987289	−	0.158933i	$-0.0508054\pi$
$691$	2.50085	+	7.69683i	0.0951369	+	0.292801i	−0.892152	+	0.451734i	$0.850805\pi$
$692$	5.21365			0.198193
$693$		0			0
$694$	−41.4172			−1.57217
$695$	17.5637	+	54.0554i	0.666228	+	2.05044i
$696$		0			0
$697$	2.46485	−	1.79082i	0.0933629	−	0.0678321i
$698$	−35.6153	−	11.5721i	−1.34806	−	0.438010i
$699$		0			0
$700$	1.54156	+	2.12178i	0.0582657	+	0.0801958i
$701$	−13.7719	−	10.0059i	−0.520157	−	0.377916i	0.296506	−	0.955031i	$-0.404179\pi$
$701$	−13.7719	−	10.0059i	−0.520157	−	0.377916i	−0.816663	+	0.577115i	$0.804179\pi$
$702$		0			0
$703$		−	6.05899i		−	0.228519i
$704$	−9.43236	+	18.0005i	−0.355495	+	0.678419i
$705$		0			0
$706$	1.23517	−	0.401331i	0.0464862	−	0.0151043i
$707$	−14.9013	+	20.5099i	−0.560423	+	0.771356i
$708$		0			0
$709$	−10.7031	+	32.9409i	−0.401965	+	1.23712i	0.521438	+	0.853289i	$0.325396\pi$
$709$	−10.7031	+	32.9409i	−0.401965	+	1.23712i	−0.923403	+	0.383832i	$0.874604\pi$
$710$	−8.42427	+	25.9272i	−0.316157	+	0.973032i
$711$		0			0
$712$	19.4768	−	26.8076i	0.729925	−	1.00466i
$713$	2.57645	−	0.837138i	0.0964887	−	0.0313511i
$714$		0			0
$715$	25.6908	+	26.2848i	0.960782	+	0.982997i
$716$		−	4.40955i		−	0.164793i
$717$		0			0
$718$	−29.9248	−	21.7416i	−1.11678	−	0.811390i
$719$	−18.8375	−	25.9276i	−0.702521	−	0.966937i	−0.999926	−	0.0121856i	$-0.996121\pi$
$719$	−18.8375	−	25.9276i	−0.702521	−	0.966937i	0.297405	−	0.954751i	$-0.403879\pi$
$720$		0			0
$721$	36.7012	+	11.9250i	1.36683	+	0.444109i
$722$	19.6528	−	14.2786i	0.731401	−	0.531394i
$723$		0			0
$724$	0.121163	+	0.372902i	0.00450299	+	0.0138588i
$725$	−5.00162			−0.185756
$726$		0			0
$727$	43.0819			1.59782			0.798910	−	0.601451i	$-0.205410\pi$
$727$	43.0819			1.59782			0.798910	+	0.601451i	$0.205410\pi$
$728$	8.18289	+	25.1844i	0.303278	+	0.933394i
$729$		0			0
$730$	13.8977	−	10.0973i	0.514378	−	0.373717i
$731$	23.0033	+	7.47424i	0.850809	+	0.276445i
$732$		0			0
$733$	20.2620	+	27.8883i	0.748395	+	1.03008i	0.998091	+	0.0617534i	$0.0196692\pi$
$733$	20.2620	+	27.8883i	0.748395	+	1.03008i	−0.249696	+	0.968324i	$0.580331\pi$
$734$	7.96937	+	5.79009i	0.294155	+	0.213716i
$735$		0			0
$736$		−	15.5740i		−	0.574064i
$737$	28.7057	+	29.3694i	1.05739	+	1.08184i
$738$		0			0
$739$	0.742336	−	0.241200i	0.0273073	−	0.00887267i	−0.295332	−	0.955395i	$-0.595430\pi$
$739$	0.742336	−	0.241200i	0.0273073	−	0.00887267i	0.322639	+	0.946522i	$0.395430\pi$
$740$	−0.596652	+	0.821221i	−0.0219334	+	0.0301887i
$741$		0			0
$742$	−0.715547	+	2.20223i	−0.0262686	+	0.0808463i
$743$	6.96153	−	21.4254i	0.255394	−	0.786022i	−0.738358	−	0.674409i	$-0.764398\pi$
$743$	6.96153	−	21.4254i	0.255394	−	0.786022i	0.993752	−	0.111613i	$-0.0356016\pi$
$744$		0			0
$745$	8.58222	−	11.8124i	0.314428	−	0.432773i
$746$	43.3024	−	14.0698i	1.58541	−	0.515132i
$747$		0			0
$748$	1.67574	−	3.19795i	0.0612712	−	0.116928i
$749$		−	9.98121i		−	0.364706i
$750$		0			0
$751$	−0.899212	−	0.653316i	−0.0328127	−	0.0238398i	0.571258	−	0.820771i	$-0.306456\pi$
$751$	−0.899212	−	0.653316i	−0.0328127	−	0.0238398i	−0.604071	+	0.796931i	$0.706456\pi$
$752$	−11.0646	−	15.2291i	−0.403484	−	0.555348i
$753$		0			0
$754$	10.3280	+	3.35578i	0.376124	+	0.122210i
$755$	8.18365	−	5.94577i	0.297834	−	0.216389i
$756$		0			0
$757$	16.0853	+	49.5054i	0.584629	+	1.79930i	0.600753	+	0.799434i	$0.294867\pi$
$757$	16.0853	+	49.5054i	0.584629	+	1.79930i	−0.0161240	+	0.999870i	$0.505133\pi$
$758$	41.0716			1.49179
$759$		0			0
$760$	41.6367			1.51032
$761$	−15.3157	−	47.1369i	−0.555194	−	1.70871i	−0.695430	−	0.718594i	$-0.744786\pi$
$761$	−15.3157	−	47.1369i	−0.555194	−	1.70871i	0.140236	−	0.990118i	$-0.455214\pi$
$762$		0			0
$763$	−38.1249	+	27.6994i	−1.38022	+	1.00279i
$764$	−6.58898	−	2.14089i	−0.238381	−	0.0774546i
$765$		0			0
$766$	9.19325	+	12.6534i	0.332166	+	0.457187i
$767$	−17.2663	−	12.5447i	−0.623449	−	0.452962i
$768$		0			0
$769$			40.9106i			1.47527i	0.675197	+	0.737637i	$0.264059\pi$
$769$			40.9106i			1.47527i	−0.675197	+	0.737637i	$0.735941\pi$
$770$	−37.0382	−	6.30098i	−1.33476	−	0.227072i
$771$		0			0
$772$	−3.20296	+	1.04070i	−0.115277	+	0.0374558i
$773$	−21.1418	+	29.0992i	−0.760417	+	1.04662i	0.236762	+	0.971568i	$0.423914\pi$
$773$	−21.1418	+	29.0992i	−0.760417	+	1.04662i	−0.997179	+	0.0750568i	$0.976086\pi$
$774$		0			0
$775$	0.298369	−	0.918285i	0.0107177	−	0.0329858i
$776$	−8.59970	+	26.4671i	−0.308711	+	0.950115i
$777$		0			0
$778$	−13.3371	+	18.3570i	−0.478159	+	0.658130i
$779$	5.56077	−	1.80680i	0.199235	−	0.0647355i
$780$		0			0
$781$	−9.36207	−	18.9051i	−0.335001	−	0.676479i
$782$		−	37.1126i		−	1.32714i
$783$		0			0
$784$	0.0525970	+	0.0382139i	0.00187846	+	0.00136478i
$785$	−17.3798	−	23.9212i	−0.620310	−	0.853784i
$786$		0			0
$787$	−20.5278	−	6.66990i	−0.731739	−	0.237756i	−0.0806336	−	0.996744i	$-0.525694\pi$
$787$	−20.5278	−	6.66990i	−0.731739	−	0.237756i	−0.651105	+	0.758987i	$0.725694\pi$
$788$	0.165062	−	0.119924i	0.00588008	−	0.00427213i
$789$		0			0
$790$	3.91899	+	12.0614i	0.139431	+	0.429126i
$791$	32.8823			1.16916
$792$		0			0
$793$	12.1900			0.432881
$794$	4.17783	+	12.8580i	0.148266	+	0.456315i
$795$		0			0
$796$	−6.29413	+	4.57296i	−0.223090	+	0.162084i
$797$	33.9142	+	11.0194i	1.20130	+	0.390327i	0.840240	−	0.542214i	$-0.182414\pi$
$797$	33.9142	+	11.0194i	1.20130	+	0.390327i	0.361063	+	0.932541i	$0.382414\pi$
$798$		0			0
$799$	−7.42542	−	10.2202i	−0.262692	−	0.361565i
$800$	−4.49069	−	3.26268i	−0.158770	−	0.115353i
$801$		0			0
$802$			0.250691i			0.00885219i
$803$	−2.22949	+	13.1053i	−0.0786769	+	0.462476i
$804$		0			0
$805$	−55.2301	+	17.9453i	−1.94660	+	0.632490i
$806$	−1.23222	+	1.69601i	−0.0434032	+	0.0597394i
$807$		0			0
$808$	7.48548	−	23.0380i	0.263338	−	0.810472i
$809$	−11.2240	+	34.5440i	−0.394615	+	1.21450i	0.534646	+	0.845076i	$0.320445\pi$
$809$	−11.2240	+	34.5440i	−0.394615	+	1.21450i	−0.929261	+	0.369424i	$0.879555\pi$
$810$		0			0
$811$	10.9328	−	15.0477i	0.383902	−	0.528396i	−0.572711	−	0.819757i	$-0.694108\pi$
$811$	10.9328	−	15.0477i	0.383902	−	0.528396i	0.956613	+	0.291361i	$0.0941082\pi$
$812$	−1.58748	+	0.515802i	−0.0557095	+	0.0181011i
$813$		0			0
$814$	−0.758190	−	5.16865i	−0.0265745	−	0.181161i
$815$			44.0752i			1.54389i
$816$		0			0
$817$	37.5524	+	27.2834i	1.31379	+	0.954526i
$818$	−10.1831	−	14.0159i	−0.356045	−	0.490054i
$819$		0			0
$820$	−0.931617	−	0.302701i	−0.0325335	−	0.0105708i
$821$	−1.19626	+	0.869131i	−0.0417496	+	0.0303329i	−0.608464	−	0.793581i	$-0.708214\pi$
$821$	−1.19626	+	0.869131i	−0.0417496	+	0.0303329i	0.566715	+	0.823914i	$0.308214\pi$
$822$		0			0
$823$	−8.13633	−	25.0410i	−0.283614	−	0.872876i	−0.986811	−	0.161880i	$-0.948244\pi$
$823$	−8.13633	−	25.0410i	−0.283614	−	0.872876i	0.703196	−	0.710996i	$-0.251756\pi$
$824$	−36.8727			−1.28452
$825$		0			0
$826$	21.8159			0.759071
$827$	−12.8224	−	39.4633i	−0.445879	−	1.37227i	−0.881517	−	0.472152i	$-0.843477\pi$
$827$	−12.8224	−	39.4633i	−0.445879	−	1.37227i	0.435639	−	0.900122i	$-0.356523\pi$
$828$		0			0
$829$	−24.3273	+	17.6748i	−0.844922	+	0.613871i	−0.923741	−	0.383017i	$-0.874885\pi$
$829$	−24.3273	+	17.6748i	−0.844922	+	0.613871i	0.0788195	+	0.996889i	$0.474885\pi$
$830$	18.7709	+	6.09905i	0.651549	+	0.211701i
$831$		0			0
$832$	−14.2879	−	19.6655i	−0.495342	−	0.681780i
$833$	0.0352977	+	0.0256452i	0.00122299	+	0.000888555i
$834$		0			0
$835$			17.3263i			0.599603i
$836$	4.95499	−	4.84301i	0.171372	−	0.167499i
$837$		0			0
$838$	32.1273	−	10.4388i	1.10982	−	0.360602i
$839$	−25.7547	+	35.4483i	−0.889152	+	1.22381i	0.0846495	+	0.996411i	$0.473023\pi$
$839$	−25.7547	+	35.4483i	−0.889152	+	1.22381i	−0.973801	+	0.227401i	$0.926977\pi$
$840$		0			0
$841$	−7.97782	+	24.5532i	−0.275097	+	0.846662i
$842$	4.66737	−	14.3647i	0.160848	−	0.495040i
$843$		0			0
$844$	−5.00393	+	6.88731i	−0.172242	+	0.237071i
$845$	−7.27448	+	2.36362i	−0.250250	+	0.0813110i
$846$		0			0
$847$	23.9056	−	16.5471i	0.821406	−	0.568565i
$848$		−	2.61675i		−	0.0898597i
$849$		0			0
$850$	−10.7013	−	7.77492i	−0.367050	−	0.266677i
$851$	−4.74617	−	6.53254i	−0.162697	−	0.223933i
$852$		0			0
$853$	22.5087	+	7.31352i	0.770683	+	0.250410i	0.667857	−	0.744289i	$-0.267212\pi$
$853$	22.5087	+	7.31352i	0.770683	+	0.250410i	0.102826	+	0.994699i	$0.467212\pi$
$854$	−10.0808	+	7.32411i	−0.344957	+	0.250626i
$855$		0			0
$856$	2.94711	+	9.07028i	0.100730	+	0.310016i
$857$	13.6018			0.464630			0.232315	−	0.972641i	$-0.425370\pi$
$857$	13.6018			0.464630			0.232315	+	0.972641i	$0.425370\pi$
$858$		0			0
$859$	42.8744			1.46286			0.731428	−	0.681919i	$-0.238854\pi$
$859$	42.8744			1.46286			0.731428	+	0.681919i	$0.238854\pi$
$860$	−2.40306	−	7.39586i	−0.0819437	−	0.252197i
$861$		0			0
$862$	24.4526	−	17.7659i	0.832860	−	0.605108i
$863$	44.3529	+	14.4111i	1.50979	+	0.490561i	0.942856	−	0.333202i	$-0.108129\pi$
$863$	44.3529	+	14.4111i	1.50979	+	0.490561i	0.566935	+	0.823762i	$0.308129\pi$
$864$		0			0
$865$	24.1848	+	33.2875i	0.822308	+	1.13181i
$866$	−18.0887	−	13.1422i	−0.614679	−	0.446590i
$867$		0			0
$868$		−	0.322226i		−	0.0109371i
$869$	−8.69289	−	4.55512i	−0.294886	−	0.154522i
$870$		0			0
$871$	−46.7186	+	15.1798i	−1.58300	+	0.514348i
$872$	26.4668	−	36.4284i	0.896278	−	1.23362i
$873$		0			0
$874$	22.0089	−	67.7365i	0.744463	−	2.29122i
$875$	5.01179	−	15.4247i	0.169430	−	0.521450i
$876$		0			0
$877$	22.1769	−	30.5239i	0.748862	−	1.03072i	−0.249198	−	0.968453i	$-0.580167\pi$
$877$	22.1769	−	30.5239i	0.748862	−	1.03072i	0.998060	−	0.0622672i	$-0.0198331\pi$
$878$	16.7506	−	5.44261i	0.565307	−	0.183679i
$879$		0			0
$880$	42.0077	−	6.16212i	1.41608	−	0.207725i
$881$			26.0806i			0.878678i	0.898321	+	0.439339i	$0.144787\pi$
$881$			26.0806i			0.878678i	−0.898321	+	0.439339i	$0.855213\pi$
$882$		0			0
$883$	−37.3267	−	27.1194i	−1.25614	−	0.912642i	−0.257582	−	0.966256i	$-0.582926\pi$
$883$	−37.3267	−	27.1194i	−1.25614	−	0.912642i	−0.998562	+	0.0536143i	$0.982926\pi$
$884$	2.53836	+	3.49376i	0.0853744	+	0.117508i
$885$		0			0
$886$	13.7554	+	4.46939i	0.462121	+	0.150152i
$887$	17.2176	−	12.5093i	0.578109	−	0.420021i	−0.259933	−	0.965627i	$-0.583700\pi$
$887$	17.2176	−	12.5093i	0.578109	−	0.420021i	0.838042	+	0.545606i	$0.183700\pi$
$888$		0			0
$889$	−5.02136	−	15.4541i	−0.168411	−	0.518315i
$890$	−56.2342			−1.88497
$891$		0			0
$892$	1.70131			0.0569640
$893$	−7.49170	−	23.0571i	−0.250700	−	0.771575i
$894$		0			0
$895$	28.1536	−	20.4548i	0.941071	−	0.683728i
$896$	33.5858	+	10.9127i	1.12202	+	0.364568i
$897$		0			0
$898$	−0.603497	−	0.830643i	−0.0201390	−	0.0277189i
$899$	0.497149	+	0.361200i	0.0165808	+	0.0120467i
$900$		0			0
$901$		−	1.75610i		−	0.0585040i
$902$	4.51755	−	2.23715i	0.150418	−	0.0744889i
$903$		0			0
$904$	−29.8813	+	9.70903i	−0.993838	+	0.322918i
$905$	−1.81882	+	2.50339i	−0.0604596	+	0.0832155i
$906$		0			0
$907$	0.393638	−	1.21149i	0.0130705	−	0.0402270i	−0.944309	−	0.329061i	$-0.893268\pi$
$907$	0.393638	−	1.21149i	0.0130705	−	0.0402270i	0.957379	+	0.288834i	$0.0932677\pi$
$908$	−0.313562	+	0.965043i	−0.0104059	+	0.0320261i
$909$		0			0
$910$	26.4146	−	36.3566i	0.875636	−	1.20521i
$911$	24.8900	−	8.08724i	0.824641	−	0.267942i	0.133855	−	0.991001i	$-0.457264\pi$
$911$	24.8900	−	8.08724i	0.824641	−	0.267942i	0.690786	+	0.723059i	$0.257264\pi$
$912$		0			0
$913$	−13.6871	+	6.77801i	−0.452976	+	0.224319i
$914$		−	35.7505i		−	1.18252i
$915$		0			0
$916$	3.42504	+	2.48844i	0.113166	+	0.0822203i
$917$	10.1641	+	13.9897i	0.335649	+	0.461981i
$918$		0			0
$919$	−44.7124	−	14.5279i	−1.47493	−	0.479233i	−0.542333	−	0.840163i	$-0.682459\pi$
$919$	−44.7124	−	14.5279i	−1.47493	−	0.479233i	−0.932593	+	0.360931i	$0.882459\pi$
$920$	44.8909	−	32.6151i	1.48001	−	1.07529i
$921$		0			0
$922$	9.63030	+	29.6390i	0.317157	+	0.976109i
$923$	25.2340			0.830587
$924$		0			0
$925$	−2.87793			−0.0946258
$926$	−16.4354	−	50.5831i	−0.540102	−	1.66226i
$927$		0			0
$928$	2.85806	−	2.07650i	0.0938203	−	0.0681644i
$929$	−6.71970	−	2.18336i	−0.220466	−	0.0716338i	0.196701	−	0.980463i	$-0.436977\pi$
$929$	−6.71970	−	2.18336i	−0.220466	−	0.0716338i	−0.417167	+	0.908830i	$0.636977\pi$
$930$		0			0
$931$	0.0492156	+	0.0677394i	0.00161298	+	0.00222007i
$932$	−0.474628	−	0.344838i	−0.0155470	−	0.0112955i
$933$		0			0
$934$		−	37.8299i		−	1.23783i
$935$	28.1913	−	4.13538i	0.921953	−	0.135241i
$936$		0			0
$937$	−30.3985	+	9.87708i	−0.993076	+	0.322670i	−0.760095	−	0.649811i	$-0.774848\pi$
$937$	−30.3985	+	9.87708i	−0.993076	+	0.322670i	−0.232981	+	0.972481i	$0.574848\pi$
$938$	29.5144	−	40.6231i	0.963680	−	1.32639i
$939$		0			0
$940$	−1.25511	+	3.86284i	−0.0409372	+	0.125992i
$941$	9.63537	−	29.6546i	0.314104	−	0.966713i	−0.662018	−	0.749488i	$-0.730300\pi$
$941$	9.63537	−	29.6546i	0.314104	−	0.966713i	0.976122	−	0.217224i	$-0.0697003\pi$
$942$		0			0
$943$	4.58007	−	6.30392i	0.149147	−	0.205284i
$944$	−23.4469	+	7.61837i	−0.763132	+	0.247957i
$945$		0			0
$946$	35.4484	+	18.5751i	1.15253	+	0.603930i
$947$		−	27.2044i		−	0.884024i	−0.897009	−	0.442012i	$-0.854265\pi$
$947$		−	27.2044i		−	0.884024i	0.897009	−	0.442012i	$-0.145735\pi$
$948$		0			0
$949$	−12.8641	−	9.34633i	−0.417587	−	0.303395i
$950$	−14.9208	−	20.5367i	−0.484094	−	0.666298i
$951$		0			0
$952$	19.5234	+	6.34353i	0.632756	+	0.205595i
$953$	1.81421	−	1.31810i	0.0587681	−	0.0426975i	−0.558013	−	0.829832i	$-0.688436\pi$
$953$	1.81421	−	1.31810i	0.0587681	−	0.0426975i	0.616781	+	0.787134i	$0.288436\pi$
$954$		0			0
$955$	−16.8957	−	51.9996i	−0.546732	−	1.68267i
$956$	1.42189			0.0459871
$957$		0			0
$958$	18.8111			0.607759
$959$	−5.26034	−	16.1897i	−0.169865	−	0.522792i
$960$		0			0
$961$	24.9836	−	18.1516i	0.805921	−	0.585536i
$962$	5.94274	+	1.93091i	0.191602	+	0.0622551i
$963$		0			0
$964$	−3.24456	−	4.46576i	−0.104500	−	0.143832i
$965$	−21.5023	−	15.6223i	−0.692184	−	0.502901i
$966$		0			0
$967$			3.90894i			0.125703i	0.998023	+	0.0628516i	$0.0200195\pi$
$967$			3.90894i			0.125703i	−0.998023	+	0.0628516i	$0.979981\pi$
$968$	−16.8380	+	22.0954i	−0.541195	+	0.710174i
$969$		0			0
$970$	44.9167	−	14.5943i	1.44219	−	0.468595i
$971$	8.82768	−	12.1503i	0.283294	−	0.389920i	−0.643528	−	0.765423i	$-0.722530\pi$
$971$	8.82768	−	12.1503i	0.283294	−	0.389920i	0.926821	+	0.375502i	$0.122530\pi$
$972$		0			0
$973$	−16.6182	+	51.1455i	−0.532754	+	1.63965i
$974$	1.29116	−	3.97379i	0.0413715	−	0.127328i
$975$		0			0
$976$	8.27679	−	11.3920i	0.264934	−	0.364650i
$977$	15.0640	−	4.89460i	0.481941	−	0.156592i	−0.0579628	−	0.998319i	$-0.518460\pi$
$977$	15.0640	−	4.89460i	0.481941	−	0.156592i	0.539904	+	0.841727i	$0.318460\pi$
$978$		0			0
$979$	31.1206	−	30.4173i	0.994620	−	0.972142i
$980$		−	0.0140277i		−	0.000448098i
$981$		0			0
$982$	12.9740	+	9.42618i	0.414018	+	0.300801i
$983$	12.8845	+	17.7340i	0.410952	+	0.565627i	0.963450	−	0.267887i	$-0.0863254\pi$
$983$	12.8845	+	17.7340i	0.410952	+	0.565627i	−0.552498	+	0.833514i	$0.686325\pi$
$984$		0			0
$985$	1.53136	+	0.497569i	0.0487932	+	0.0158539i
$986$	6.81071	−	4.94827i	0.216897	−	0.157585i
$987$		0			0
$988$	2.56102	+	7.88201i	0.0814770	+	0.250760i
$989$	61.8592			1.96701
$990$		0			0
$991$	29.5878			0.939888			0.469944	−	0.882696i	$-0.344274\pi$
$991$	29.5878			0.939888			0.469944	+	0.882696i	$0.344274\pi$
$992$	0.210744	+	0.648604i	0.00669114	+	0.0205932i
$993$		0			0
$994$	−20.8677	+	15.1613i	−0.661885	+	0.480887i
$995$	−58.3938	−	18.9733i	−1.85121	−	0.601494i
$996$		0			0
$997$	−21.7735	−	29.9687i	−0.689575	−	0.949118i	0.310424	−	0.950598i	$-0.399529\pi$
$997$	−21.7735	−	29.9687i	−0.689575	−	0.949118i	−0.999999	+	0.00148017i	$0.999529\pi$
$998$	13.6537	+	9.92003i	0.432202	+	0.314013i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.809.16		80
3.2	odd	2	inner	891.2.k.a.809.5		80
9.2	odd	6		99.2.p.a.50.3	yes	80
9.4	even	3		99.2.p.a.83.3	yes	80
9.5	odd	6		297.2.t.a.116.8		80
9.7	even	3		297.2.t.a.17.8		80
11.2	odd	10	inner	891.2.k.a.728.5		80
33.2	even	10	inner	891.2.k.a.728.16		80
99.2	even	30		99.2.p.a.68.3	yes	80
99.13	odd	30		99.2.p.a.2.3	✓	80
99.68	even	30		297.2.t.a.35.8		80
99.79	odd	30		297.2.t.a.233.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.3	✓	80	99.13	odd	30
99.2.p.a.50.3	yes	80	9.2	odd	6
99.2.p.a.68.3	yes	80	99.2	even	30
99.2.p.a.83.3	yes	80	9.4	even	3
297.2.t.a.17.8		80	9.7	even	3
297.2.t.a.35.8		80	99.68	even	30
297.2.t.a.116.8		80	9.5	odd	6
297.2.t.a.233.8		80	99.79	odd	30
891.2.k.a.728.5		80	11.2	odd	10	inner
891.2.k.a.728.16		80	33.2	even	10	inner
891.2.k.a.809.5		80	3.2	odd	2	inner
891.2.k.a.809.16		80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.474113 + 1.45917i) q^{2} +(-0.286362 + 0.208054i) q^{4} +(-2.65673 - 0.863223i) q^{5} +(-1.55356 - 2.13829i) q^{7} +(2.04313 + 1.48442i) q^{8} +O(q^{10})\)	\(q+(0.474113 + 1.45917i) q^{2} +(-0.286362 + 0.208054i) q^{4} +(-2.65673 - 0.863223i) q^{5} +(-1.55356 - 2.13829i) q^{7} +(2.04313 + 1.48442i) q^{8} -4.28588i q^{10} +(2.31825 + 2.37186i) q^{11} +(-3.77297 + 1.22591i) q^{13} +(2.38356 - 3.28070i) q^{14} +(-1.41611 + 4.35835i) q^{16} +(-0.950349 + 2.92487i) q^{17} +(-3.46908 + 4.77479i) q^{19} +(0.940383 - 0.305549i) q^{20} +(-2.36183 + 4.50726i) q^{22} +7.86539i q^{23} +(2.26795 + 1.64777i) q^{25} +(-3.57763 - 4.92418i) q^{26} +(0.889760 + 0.289101i) q^{28} +(-1.44342 + 1.04870i) q^{29} +(-0.106433 - 0.327568i) q^{31} -1.98006 q^{32} -4.71846 q^{34} +(2.28156 + 7.02191i) q^{35} +(-0.830542 + 0.603424i) q^{37} +(-8.61197 - 2.79820i) q^{38} +(-4.14666 - 5.70739i) q^{40} +(-0.801475 - 0.582306i) q^{41} -7.86473i q^{43} +(-1.15733 - 0.196887i) q^{44} +(-11.4770 + 3.72909i) q^{46} +(-2.41446 + 3.32322i) q^{47} +(0.00438399 - 0.0134925i) q^{49} +(-1.32910 + 4.09056i) q^{50} +(0.825379 - 1.13604i) q^{52} +(-0.543068 + 0.176453i) q^{53} +(-4.11152 - 8.30254i) q^{55} -6.67495i q^{56} +(-2.21458 - 1.60899i) q^{58} +(3.16215 + 4.35233i) q^{59} +(-2.92236 - 0.949534i) q^{61} +(0.427516 - 0.310608i) q^{62} +(1.89345 + 5.82744i) q^{64} +11.0820 q^{65} +12.3825 q^{67} +(-0.336388 - 1.03530i) q^{68} +(-9.16445 + 6.65836i) q^{70} +(-6.04945 - 1.96559i) q^{71} +(2.35594 + 3.24267i) q^{73} +(-1.27427 - 0.925811i) q^{74} -2.08908i q^{76} +(1.47017 - 8.64191i) q^{77} +(-2.81422 + 0.914396i) q^{79} +(7.52445 - 10.3565i) q^{80} +(0.469694 - 1.44557i) q^{82} +(-1.42306 + 4.37972i) q^{83} +(5.04963 - 6.95022i) q^{85} +(11.4760 - 3.72877i) q^{86} +(1.21566 + 8.28729i) q^{88} -13.1208i q^{89} +(8.48287 + 6.16317i) q^{91} +(-1.63643 - 2.25235i) q^{92} +(-5.99387 - 1.94753i) q^{94} +(13.3381 - 9.69070i) q^{95} +(3.40521 + 10.4802i) q^{97} +0.0217664 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7}+O(q^{10}) \) 80 * q - 10 * q^4 + 10 * q^7	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58} + 10 q^{61} - 8 q^{64} - 20 q^{67} - 60 q^{70} - 20 q^{73} + 10 q^{79} - 2 q^{82} + 10 q^{85} + 118 q^{88} + 52 q^{91} + 10 q^{94} - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

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