LMFDB - Embedded newform 405.3.l.j.298.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(28,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("405.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 256x^{12} + 15630x^{8} + 235936x^{4} + 28561 $ x^16 + 256x^12 + 15630x^8 + 235936*x^4 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			298.4
Root			$-1.96165 + 1.96165i$ of defining polynomial
Character	$\chi$	$=$	405.298
Dual form			405.3.l.j.352.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.718015 + 2.67967i) q^{2} +(-3.20097 + 1.84808i) q^{4} +(-4.53891 + 2.09721i) q^{5} +(2.21431 + 8.26391i) q^{7} +(0.596019 + 0.596019i) q^{8} +(-8.87884 - 10.6569i) q^{10} +(-0.222725 + 0.385771i) q^{11} +(0.975029 - 3.63886i) q^{13} +(-20.5546 + 11.8672i) q^{14} +(-8.56151 + 14.8290i) q^{16} +(-14.8395 + 14.8395i) q^{17} -29.1331i q^{19} +(10.6531 - 15.1014i) q^{20} +(-1.19366 - 0.319839i) q^{22} +(-5.32743 + 19.8822i) q^{23} +(16.2034 - 19.0381i) q^{25} +10.4510 q^{26} +(-22.3603 - 22.3603i) q^{28} +(-34.7292 - 20.0509i) q^{29} +(-7.64656 - 13.2442i) q^{31} +(-42.6273 - 11.4220i) q^{32} +(-50.4198 - 29.1099i) q^{34} +(-27.3817 - 32.8653i) q^{35} +(6.61115 - 6.61115i) q^{37} +(78.0669 - 20.9180i) q^{38} +(-3.95526 - 1.45530i) q^{40} +(21.2181 + 36.7507i) q^{41} +(-35.1195 + 9.41025i) q^{43} -1.64645i q^{44} -57.1029 q^{46} +(19.3932 + 72.3764i) q^{47} +(-20.9538 + 12.0977i) q^{49} +(62.6501 + 29.7501i) q^{50} +(3.60387 + 13.4498i) q^{52} +(-44.8558 - 44.8558i) q^{53} +(0.201884 - 2.21808i) q^{55} +(-3.60568 + 6.24522i) q^{56} +(28.7937 - 107.459i) q^{58} +(61.3077 - 35.3960i) q^{59} +(-53.5057 + 92.6746i) q^{61} +(29.9998 - 29.9998i) q^{62} -53.9361i q^{64} +(3.20589 + 18.5613i) q^{65} +(122.430 + 32.8051i) q^{67} +(20.0762 - 74.9253i) q^{68} +(68.4075 - 96.9716i) q^{70} +71.1649 q^{71} +(77.9049 + 77.9049i) q^{73} +(22.4626 + 12.9688i) q^{74} +(53.8403 + 93.2542i) q^{76} +(-3.68115 - 0.986362i) q^{77} +(-58.2435 - 33.6269i) q^{79} +(7.76041 - 85.2627i) q^{80} +(-83.2449 + 83.2449i) q^{82} +(-31.0330 + 8.31528i) q^{83} +(36.2335 - 98.4766i) q^{85} +(-50.4327 - 87.3520i) q^{86} +(-0.362675 + 0.0971784i) q^{88} +104.971i q^{89} +32.2302 q^{91} +(-19.6910 - 73.4880i) q^{92} +(-180.020 + 103.935i) q^{94} +(61.0983 + 132.232i) q^{95} +(38.5827 + 143.993i) q^{97} +(-47.4628 - 47.4628i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 12 q^{5} - 20 q^{7} - 56 q^{10} + 22 q^{13} - 168 q^{14} + 16 q^{16} - 96 q^{20} - 16 q^{22} + 36 q^{23} + 46 q^{25} + 176 q^{28} - 252 q^{29} - 160 q^{31} - 114 q^{32} + 4 q^{37} + 192 q^{38}+ \cdots - 152 q^{97}+O(q^{100}) $ 16 * q - 6 * q^2 + 12 * q^5 - 20 * q^7 - 56 * q^10 + 22 * q^13 - 168 * q^14 + 16 * q^16 - 96 * q^20 - 16 * q^22 + 36 * q^23 + 46 * q^25 + 176 * q^28 - 252 * q^29 - 160 * q^31 - 114 * q^32 + 4 * q^37 + 192 * q^38 + 264 * q^40 - 128 * q^43 - 16 * q^46 + 204 * q^47 + 540 * q^50 + 154 * q^52 - 364 * q^55 - 246 * q^58 + 36 * q^59 - 4 * q^61 + 24 * q^65 - 44 * q^67 + 966 * q^68 + 18 * q^70 + 364 * q^73 + 288 * q^74 + 456 * q^76 - 204 * q^77 + 32 * q^82 + 12 * q^83 - 32 * q^85 - 420 * q^88 + 224 * q^91 - 960 * q^92 + 114 * q^95 - 152 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.718015	+	2.67967i	0.359007	+	1.33983i	0.875366	+	0.483461i	$0.160621\pi$
$2$	0.718015	+	2.67967i	0.359007	+	1.33983i	−0.516358	+	0.856373i	$0.672713\pi$
$3$		0			0
$3$		0			0
$4$	−3.20097	+	1.84808i	−0.800243	+	0.462021i
$5$	−4.53891	+	2.09721i	−0.907782	+	0.419443i
$5$	−4.53891	+	2.09721i	−0.907782	+	0.419443i
$6$		0			0
$7$	2.21431	+	8.26391i	0.316330	+	1.18056i	0.922745	+	0.385410i	$0.125940\pi$
$7$	2.21431	+	8.26391i	0.316330	+	1.18056i	−0.606416	+	0.795148i	$0.707393\pi$
$8$	0.596019	+	0.596019i	0.0745024	+	0.0745024i
$9$		0			0
$10$	−8.87884	−	10.6569i	−0.887884	−	1.06569i
$11$	−0.222725	+	0.385771i	−0.0202477	+	0.0350700i	−0.875972	−	0.482362i	$-0.839779\pi$
$11$	−0.222725	+	0.385771i	−0.0202477	+	0.0350700i	0.855724	+	0.517433i	$0.173112\pi$
$12$		0			0
$13$	0.975029	−	3.63886i	0.0750023	−	0.279912i	−0.918232	−	0.396044i	$-0.870383\pi$
$13$	0.975029	−	3.63886i	0.0750023	−	0.279912i	0.993234	+	0.116132i	$0.0370495\pi$
$14$	−20.5546	+	11.8672i	−1.46819	+	0.847658i
$15$		0			0
$16$	−8.56151	+	14.8290i	−0.535095	+	0.926811i
$17$	−14.8395	+	14.8395i	−0.872910	+	0.872910i	−0.992789	−	0.119878i	$-0.961750\pi$
$17$	−14.8395	+	14.8395i	−0.872910	+	0.872910i	0.119878	+	0.992789i	$0.461750\pi$
$18$		0			0
$19$		−	29.1331i		−	1.53332i	−0.642054	−	0.766660i	$-0.721917\pi$
$19$		−	29.1331i		−	1.53332i	0.642054	−	0.766660i	$-0.278083\pi$
$20$	10.6531	−	15.1014i	0.532655	−	0.755070i
$21$		0			0
$22$	−1.19366	−	0.319839i	−0.0542571	−	0.0145381i
$23$	−5.32743	+	19.8822i	−0.231627	+	0.864445i	0.748013	+	0.663684i	$0.231008\pi$
$23$	−5.32743	+	19.8822i	−0.231627	+	0.864445i	−0.979640	+	0.200761i	$0.935659\pi$
$24$		0			0
$25$	16.2034	−	19.0381i	0.648136	−	0.761525i
$26$	10.4510			0.401962
$27$		0			0
$28$	−22.3603	−	22.3603i	−0.798583	−	0.798583i
$29$	−34.7292	−	20.0509i	−1.19756	−	0.691410i	−0.237547	−	0.971376i	$-0.576343\pi$
$29$	−34.7292	−	20.0509i	−1.19756	−	0.691410i	−0.960010	+	0.279966i	$0.909677\pi$
$30$		0			0
$31$	−7.64656	−	13.2442i	−0.246663	−	0.427234i	0.715935	−	0.698167i	$-0.246001\pi$
$31$	−7.64656	−	13.2442i	−0.246663	−	0.427234i	−0.962598	+	0.270934i	$0.912668\pi$
$32$	−42.6273	−	11.4220i	−1.33210	−	0.356936i
$33$		0			0
$34$	−50.4198	−	29.1099i	−1.48294	−	0.856174i
$35$	−27.3817	−	32.8653i	−0.782335	−	0.939007i
$36$		0			0
$37$	6.61115	−	6.61115i	0.178680	−	0.178680i	−0.612100	−	0.790780i	$-0.709675\pi$
$37$	6.61115	−	6.61115i	0.178680	−	0.178680i	0.790780	+	0.612100i	$0.209675\pi$
$38$	78.0669	−	20.9180i	2.05439	−	0.550473i
$39$		0			0
$40$	−3.95526	−	1.45530i	−0.0988814	−	0.0363824i
$41$	21.2181	+	36.7507i	0.517513	+	0.896360i	0.999793	+	0.0203423i	$0.00647560\pi$
$41$	21.2181	+	36.7507i	0.517513	+	0.896360i	−0.482280	+	0.876017i	$0.660191\pi$
$42$		0			0
$43$	−35.1195	+	9.41025i	−0.816733	+	0.218843i	−0.642918	−	0.765935i	$-0.722276\pi$
$43$	−35.1195	+	9.41025i	−0.816733	+	0.218843i	−0.173816	+	0.984778i	$0.555610\pi$
$44$		−	1.64645i		−	0.0374194i
$45$		0			0
$46$	−57.1029			−1.24137
$47$	19.3932	+	72.3764i	0.412622	+	1.53992i	0.789552	+	0.613683i	$0.210313\pi$
$47$	19.3932	+	72.3764i	0.412622	+	1.53992i	−0.376931	+	0.926241i	$0.623021\pi$
$48$		0			0
$49$	−20.9538	+	12.0977i	−0.427628	+	0.246891i
$50$	62.6501	+	29.7501i	1.25300	+	0.595001i
$51$		0			0
$52$	3.60387	+	13.4498i	0.0693052	+	0.258650i
$53$	−44.8558	−	44.8558i	−0.846336	−	0.846336i	0.143338	−	0.989674i	$-0.454216\pi$
$53$	−44.8558	−	44.8558i	−0.846336	−	0.846336i	−0.989674	+	0.143338i	$0.954216\pi$
$54$		0			0
$55$	0.201884	−	2.21808i	0.00367062	−	0.0403287i
$56$	−3.60568	+	6.24522i	−0.0643871	+	0.111522i
$57$		0			0
$58$	28.7937	−	107.459i	0.496443	−	1.85275i
$59$	61.3077	−	35.3960i	1.03911	−	0.599932i	0.119531	−	0.992830i	$-0.461861\pi$
$59$	61.3077	−	35.3960i	1.03911	−	0.599932i	0.919582	+	0.392898i	$0.128528\pi$
$60$		0			0
$61$	−53.5057	+	92.6746i	−0.877143	+	1.51926i	−0.0226804	+	0.999743i	$0.507220\pi$
$61$	−53.5057	+	92.6746i	−0.877143	+	1.51926i	−0.854462	+	0.519513i	$0.826113\pi$
$62$	29.9998	−	29.9998i	0.483868	−	0.483868i
$63$		0			0
$64$		−	53.9361i		−	0.842751i
$65$	3.20589	+	18.5613i	0.0493214	+	0.285558i
$66$		0			0
$67$	122.430	+	32.8051i	1.82732	+	0.489629i	0.997643	−	0.0686169i	$-0.0218586\pi$
$67$	122.430	+	32.8051i	1.82732	+	0.489629i	0.829676	+	0.558246i	$0.188525\pi$
$68$	20.0762	−	74.9253i	0.295238	−	1.10184i
$69$		0			0
$70$	68.4075	−	96.9716i	0.977250	−	1.38531i
$71$	71.1649			1.00232			0.501161	−	0.865354i	$-0.332906\pi$
$71$	71.1649			1.00232			0.501161	+	0.865354i	$0.332906\pi$
$72$		0			0
$73$	77.9049	+	77.9049i	1.06719	+	1.06719i	0.997574	+	0.0696171i	$0.0221777\pi$
$73$	77.9049	+	77.9049i	1.06719	+	1.06719i	0.0696171	+	0.997574i	$0.477822\pi$
$74$	22.4626	+	12.9688i	0.303549	+	0.175254i
$75$		0			0
$76$	53.8403	+	93.2542i	0.708425	+	1.22703i
$77$	−3.68115	−	0.986362i	−0.0478072	−	0.0128099i
$78$		0			0
$79$	−58.2435	−	33.6269i	−0.737259	−	0.425657i	0.0838129	−	0.996482i	$-0.473290\pi$
$79$	−58.2435	−	33.6269i	−0.737259	−	0.425657i	−0.821072	+	0.570825i	$0.806624\pi$
$80$	7.76041	−	85.2627i	0.0970051	−	1.06578i
$81$		0			0
$82$	−83.2449	+	83.2449i	−1.01518	+	1.01518i
$83$	−31.0330	+	8.31528i	−0.373892	+	0.100184i	−0.440871	−	0.897570i	$-0.645331\pi$
$83$	−31.0330	+	8.31528i	−0.373892	+	0.100184i	0.0669793	+	0.997754i	$0.478664\pi$
$84$		0			0
$85$	36.2335	−	98.4766i	0.426276	−	1.15855i
$86$	−50.4327	−	87.3520i	−0.586427	−	1.01572i
$87$		0			0
$88$	−0.362675	+	0.0971784i	−0.00412130	+	0.00110430i
$89$			104.971i			1.17945i	0.807603	+	0.589727i	$0.200765\pi$
$89$			104.971i			1.17945i	−0.807603	+	0.589727i	$0.799235\pi$
$90$		0			0
$91$	32.2302			0.354178
$92$	−19.6910	−	73.4880i	−0.214033	−	0.798782i
$93$		0			0
$94$	−180.020	+	103.935i	−1.91511	+	1.10569i
$95$	61.0983	+	132.232i	0.643139	+	1.39192i
$96$		0			0
$97$	38.5827	+	143.993i	0.397760	+	1.48446i	0.817028	+	0.576598i	$0.195620\pi$
$97$	38.5827	+	143.993i	0.397760	+	1.48446i	−0.419268	+	0.907863i	$0.637713\pi$
$98$	−47.4628	−	47.4628i	−0.484315	−	0.484315i
$99$		0			0
$100$	−16.6826	+	90.8857i	−0.166826	+	0.908857i
$101$	−3.08602	+	5.34514i	−0.0305546	+	0.0529222i	−0.880898	−	0.473305i	$-0.843061\pi$
$101$	−3.08602	+	5.34514i	−0.0305546	+	0.0529222i	0.850344	+	0.526228i	$0.176394\pi$
$102$		0			0
$103$	5.06141	−	18.8895i	0.0491399	−	0.183393i	−0.936994	−	0.349347i	$-0.886404\pi$
$103$	5.06141	−	18.8895i	0.0491399	−	0.183393i	0.986134	+	0.165954i	$0.0530703\pi$
$104$	2.74997	−	1.58769i	0.0264420	−	0.0152663i
$105$		0			0
$106$	87.9915	−	152.406i	0.830109	−	1.43779i
$107$	−47.8849	+	47.8849i	−0.447522	+	0.447522i	−0.894530	−	0.447008i	$-0.852490\pi$
$107$	−47.8849	+	47.8849i	−0.447522	+	0.447522i	0.447008	+	0.894530i	$0.352490\pi$
$108$		0			0
$109$		−	60.2436i		−	0.552694i	−0.961058	−	0.276347i	$-0.910876\pi$
$109$		−	60.2436i		−	0.552694i	0.961058	−	0.276347i	$-0.0891239\pi$
$110$	6.08867	−	1.05163i	0.0553515	−	0.00956028i
$111$		0			0
$112$	−141.503	−	37.9156i	−1.26342	−	0.338532i
$113$	20.7967	−	77.6142i	0.184041	−	0.686851i	−0.810793	−	0.585334i	$-0.800964\pi$
$113$	20.7967	−	77.6142i	0.184041	−	0.686851i	0.994834	−	0.101518i	$-0.0323698\pi$
$114$		0			0
$115$	−17.5166	−	101.416i	−0.152318	−	0.881881i
$116$	148.223			1.27778
$117$		0			0
$118$	138.869	+	138.869i	1.17686	+	1.17686i
$119$	−155.491	−	89.7729i	−1.30665	−	0.754394i
$120$		0			0
$121$	60.4008	+	104.617i	0.499180	+	0.864605i
$122$	−286.755	−	76.8358i	−2.35045	−	0.629802i
$123$		0			0
$124$	48.9529	+	28.2630i	0.394781	+	0.227927i
$125$	−33.6187	+	120.394i	−0.268950	+	0.963154i
$126$		0			0
$127$	113.537	−	113.537i	0.893994	−	0.893994i	−0.100902	−	0.994896i	$-0.532173\pi$
$127$	113.537	−	113.537i	0.893994	−	0.893994i	0.994896	+	0.100902i	$0.0321730\pi$
$128$	−25.9785	+	6.96092i	−0.202957	+	0.0543822i
$129$		0			0
$130$	−47.4362	+	21.9180i	−0.364894	+	0.168600i
$131$	39.6983	+	68.7595i	0.303041	+	0.524882i	0.976823	−	0.214048i	$-0.0686649\pi$
$131$	39.6983	+	68.7595i	0.303041	+	0.524882i	−0.673783	+	0.738930i	$0.735332\pi$
$132$		0			0
$133$	240.753	−	64.5096i	1.81017	−	0.485034i
$134$			351.627i			2.62408i
$135$		0			0
$136$	−17.6892			−0.130068
$137$	−25.5439	−	95.3311i	−0.186452	−	0.695848i	−0.994315	−	0.106478i	$-0.966043\pi$
$137$	−25.5439	−	95.3311i	−0.186452	−	0.695848i	0.807863	−	0.589370i	$-0.200624\pi$
$138$		0			0
$139$	−74.3143	+	42.9054i	−0.534635	+	0.308672i	−0.742902	−	0.669400i	$-0.766551\pi$
$139$	−74.3143	+	42.9054i	−0.534635	+	0.308672i	0.208267	+	0.978072i	$0.433218\pi$
$140$	148.386	+	54.5971i	1.05990	+	0.389979i
$141$		0			0
$142$	51.0975	+	190.698i	0.359841	+	1.34295i
$143$	1.18660	+	1.18660i	0.00829791	+	0.00829791i
$144$		0			0
$145$	199.683	+	18.1747i	1.37713	+	0.125343i
$146$	−152.822	+	264.696i	−1.04673	+	1.81299i
$147$		0			0
$148$	−8.94417	+	33.3801i	−0.0604335	+	0.225541i
$149$	−117.167	+	67.6464i	−0.786356	+	0.454003i	−0.838678	−	0.544627i	$-0.816671\pi$
$149$	−117.167	+	67.6464i	−0.786356	+	0.454003i	0.0523222	+	0.998630i	$0.483338\pi$
$150$		0			0
$151$	−72.1025	+	124.885i	−0.477500	+	0.827054i	−0.999667	−	0.0257891i	$-0.991790\pi$
$151$	−72.1025	+	124.885i	−0.477500	+	0.827054i	0.522168	+	0.852843i	$0.325123\pi$
$152$	17.3639	−	17.3639i	0.114236	−	0.114236i
$153$		0			0
$154$		−	10.5725i		−	0.0686525i
$155$	62.4831	+	44.0779i	0.403116	+	0.284374i
$156$		0			0
$157$	−62.0546	−	16.6275i	−0.395252	−	0.105907i	0.0557181	−	0.998447i	$-0.482255\pi$
$157$	−62.0546	−	16.6275i	−0.395252	−	0.105907i	−0.450970	+	0.892539i	$0.648922\pi$
$158$	48.2892	−	180.218i	0.305628	−	1.14062i
$159$		0			0
$160$	217.436	−	37.5553i	1.35897	−	0.234721i
$161$	−176.101			−1.09380
$162$		0			0
$163$	−18.1117	−	18.1117i	−0.111115	−	0.111115i	0.649364	−	0.760478i	$-0.275035\pi$
$163$	−18.1117	−	18.1117i	−0.111115	−	0.111115i	−0.760478	+	0.649364i	$0.775035\pi$
$164$	−135.837	−	78.4254i	−0.828273	−	0.478204i
$165$		0			0
$166$	−44.5644	−	77.1878i	−0.268460	−	0.464987i
$167$	−42.3880	−	11.3578i	−0.253821	−	0.0680110i	0.129665	−	0.991558i	$-0.458610\pi$
$167$	−42.3880	−	11.3578i	−0.253821	−	0.0680110i	−0.383486	+	0.923547i	$0.625276\pi$
$168$		0			0
$169$	134.068	+	77.4040i	0.793300	+	0.458012i
$170$	289.901	+	26.3861i	1.70530	+	0.155212i
$171$		0			0
$172$	95.0258	−	95.0258i	0.552475	−	0.552475i
$173$	77.8985	−	20.8728i	0.450280	−	0.120652i	−0.0265503	−	0.999647i	$-0.508452\pi$
$173$	77.8985	−	20.8728i	0.450280	−	0.120652i	0.476831	+	0.878995i	$0.341786\pi$
$174$		0			0
$175$	193.209	+	91.7471i	1.10405	+	0.524269i
$176$	−3.81372	−	6.60556i	−0.0216689	−	0.0375316i
$177$		0			0
$178$	−281.288	+	75.3710i	−1.58027	+	0.423433i
$179$			55.1405i			0.308047i	0.988067	+	0.154024i	$0.0492232\pi$
$179$			55.1405i			0.308047i	−0.988067	+	0.154024i	$0.950777\pi$
$180$		0			0
$181$	−180.687			−0.998270			−0.499135	−	0.866524i	$-0.666349\pi$
$181$	−180.687			−0.998270			−0.499135	+	0.866524i	$0.666349\pi$
$182$	23.1418	+	86.3663i	0.127153	+	0.474540i
$183$		0			0
$184$	−15.0254	+	8.67494i	−0.0816600	+	0.0471464i
$185$	−16.1424	+	43.8724i	−0.0872564	+	0.237148i
$186$		0			0
$187$	−2.41951	−	9.02975i	−0.0129386	−	0.0482874i
$188$	−195.835	−	195.835i	−1.04167	−	1.04167i
$189$		0			0
$190$	−310.469	+	258.668i	−1.63405	+	1.36141i
$191$	95.1445	−	164.795i	0.498139	−	0.862802i	−0.501859	−	0.864949i	$-0.667350\pi$
$191$	95.1445	−	164.795i	0.498139	−	0.862802i	0.999998	+	0.00214785i	$0.000683684\pi$
$192$		0			0
$193$	2.35869	−	8.80274i	0.0122212	−	0.0456101i	−0.959546	−	0.281552i	$-0.909151\pi$
$193$	2.35869	−	8.80274i	0.0122212	−	0.0456101i	0.971767	+	0.235942i	$0.0758175\pi$
$194$	−358.150	+	206.778i	−1.84613	+	1.06587i
$195$		0			0
$196$	44.7150	−	77.4486i	0.228138	−	0.395146i
$197$	116.112	−	116.112i	0.589403	−	0.589403i	−0.348067	−	0.937470i	$-0.613162\pi$
$197$	116.112	−	116.112i	0.589403	−	0.589403i	0.937470	+	0.348067i	$0.113162\pi$
$198$		0			0
$199$			281.684i			1.41550i	0.706465	+	0.707748i	$0.250289\pi$
$199$			281.684i			1.41550i	−0.706465	+	0.707748i	$0.749711\pi$
$200$	21.0046	−	1.68955i	0.105023	−	0.00844775i
$201$		0			0
$202$	−16.5390	−	4.43162i	−0.0818763	−	0.0219387i
$203$	88.7977	−	331.397i	0.437427	−	1.63250i
$204$		0			0
$205$	−173.381	−	122.310i	−0.845761	−	0.596632i
$206$	54.2516			0.263357
$207$		0			0
$208$	45.6128	+	45.6128i	0.219292	+	0.219292i
$209$	11.2387	+	6.48865i	0.0537736	+	0.0310462i
$210$		0			0
$211$	120.426	+	208.584i	0.570739	+	0.988548i	0.996490	+	0.0837081i	$0.0266763\pi$
$211$	120.426	+	208.584i	0.570739	+	0.988548i	−0.425752	+	0.904840i	$0.639990\pi$
$212$	226.479	+	60.6850i	1.06830	+	0.286250i
$213$		0			0
$214$	−162.698	−	93.9335i	−0.760269	−	0.438942i
$215$	139.669	−	116.365i	0.649624	−	0.541235i
$216$		0			0
$217$	92.5173	−	92.5173i	0.426347	−	0.426347i
$218$	161.433	−	43.2558i	0.740518	−	0.198421i
$219$		0			0
$220$	3.45297	+	7.47311i	0.0156953	+	0.0339687i
$221$	39.5298	+	68.4677i	0.178868	+	0.309809i
$222$		0			0
$223$	−73.6750	+	19.7412i	−0.330381	+	0.0885253i	−0.420197	−	0.907433i	$-0.638039\pi$
$223$	−73.6750	+	19.7412i	−0.330381	+	0.0885253i	0.0898156	+	0.995958i	$0.471372\pi$
$224$		−	377.560i		−	1.68554i
$225$		0			0
$226$	222.913			0.986339
$227$	−2.17831	−	8.12957i	−0.00959608	−	0.0358131i	0.960962	−	0.276681i	$-0.0892346\pi$
$227$	−2.17831	−	8.12957i	−0.00959608	−	0.0358131i	−0.970558	+	0.240868i	$0.922568\pi$
$228$		0			0
$229$	187.477	−	108.240i	0.818678	−	0.472664i	−0.0312821	−	0.999511i	$-0.509959\pi$
$229$	187.477	−	108.240i	0.818678	−	0.472664i	0.849961	+	0.526846i	$0.176626\pi$
$230$	259.185	−	119.757i	1.12689	−	0.520683i
$231$		0			0
$232$	−8.74853	−	32.6499i	−0.0377092	−	0.140733i
$233$	−85.0860	−	85.0860i	−0.365176	−	0.365176i	0.500538	−	0.865714i	$-0.333135\pi$
$233$	−85.0860	−	85.0860i	−0.365176	−	0.365176i	−0.865714	+	0.500538i	$0.833135\pi$
$234$		0			0
$235$	−239.813	−	287.838i	−1.02048	−	1.22484i
$236$	−130.829	+	226.603i	−0.554362	+	0.960183i
$237$		0			0
$238$	128.917	−	481.123i	0.541666	−	2.02153i
$239$	231.345	−	133.567i	0.967971	−	0.558858i	0.0693536	−	0.997592i	$-0.477906\pi$
$239$	231.345	−	133.567i	0.967971	−	0.558858i	0.898617	+	0.438734i	$0.144573\pi$
$240$		0			0
$241$	141.000	−	244.219i	0.585063	−	1.01336i	−0.409805	−	0.912173i	$-0.634403\pi$
$241$	141.000	−	244.219i	0.585063	−	1.01336i	0.994868	−	0.101186i	$-0.0322636\pi$
$242$	−236.971	+	236.971i	−0.979218	+	0.979218i
$243$		0			0
$244$		−	395.532i		−	1.62103i
$245$	69.7359	−	98.8547i	0.284636	−	0.403489i
$246$		0			0
$247$	−106.011	−	28.4056i	−0.429195	−	0.115002i
$248$	3.33632	−	12.4513i	0.0134529	−	0.0502069i
$249$		0			0
$250$	−346.755	−	3.64219i	−1.38702	−	0.0145688i
$251$	−29.8384			−0.118878			−0.0594390	−	0.998232i	$-0.518931\pi$
$251$	−29.8384			−0.118878			−0.0594390	+	0.998232i	$0.518931\pi$
$252$		0			0
$253$	−6.48343	−	6.48343i	−0.0256262	−	0.0256262i
$254$	385.763	+	222.721i	1.51875	+	0.876853i
$255$		0			0
$256$	−145.178	−	251.456i	−0.567102	−	0.982249i
$257$	151.242	+	40.5253i	0.588492	+	0.157686i	0.540764	−	0.841174i	$-0.318135\pi$
$257$	151.242	+	40.5253i	0.588492	+	0.157686i	0.0477280	+	0.998860i	$0.484802\pi$
$258$		0			0
$259$	69.2731	+	39.9948i	0.267464	+	0.154420i
$260$	−44.5648	−	53.4894i	−0.171403	−	0.205729i
$261$		0			0
$262$	−155.749	+	155.749i	−0.594461	+	0.594461i
$263$	−26.9567	+	7.22301i	−0.102497	+	0.0274639i	−0.309703	−	0.950833i	$-0.600230\pi$
$263$	−26.9567	+	7.22301i	−0.102497	+	0.0274639i	0.207206	+	0.978297i	$0.433563\pi$
$264$		0			0
$265$	297.669	+	109.524i	1.12328	+	0.413299i
$266$	345.728	+	598.819i	1.29973	+	2.25120i
$267$		0			0
$268$	−452.523	+	121.253i	−1.68852	+	0.452437i
$269$		−	100.763i		−	0.374584i	−0.982304	−	0.187292i	$-0.940029\pi$
$269$		−	100.763i		−	0.374584i	0.982304	−	0.187292i	$-0.0599711\pi$
$270$		0			0
$271$	−342.248			−1.26291			−0.631453	−	0.775414i	$-0.717541\pi$
$271$	−342.248			−1.26291			−0.631453	+	0.775414i	$0.717541\pi$
$272$	−93.0058	−	347.103i	−0.341933	−	1.27611i
$273$		0			0
$274$	237.115	−	136.898i	0.865383	−	0.499629i
$275$	3.73545	+	10.4911i	0.0135835	+	0.0381493i
$276$		0			0
$277$	−58.9481	−	219.997i	−0.212809	−	0.794214i	−0.986926	−	0.161172i	$-0.948473\pi$
$277$	−58.9481	−	219.997i	−0.212809	−	0.794214i	0.774117	−	0.633042i	$-0.218194\pi$
$278$	−168.331	−	168.331i	−0.605507	−	0.605507i
$279$		0			0
$280$	3.26829	−	35.9083i	0.0116725	−	0.128244i
$281$	254.834	−	441.385i	0.906882	−	1.57077i	0.0885115	−	0.996075i	$-0.471789\pi$
$281$	254.834	−	441.385i	0.906882	−	1.57077i	0.818371	−	0.574691i	$-0.194878\pi$
$282$		0			0
$283$	−93.3222	+	348.283i	−0.329761	+	1.23068i	0.579678	+	0.814845i	$0.303178\pi$
$283$	−93.3222	+	348.283i	−0.329761	+	1.23068i	−0.909439	+	0.415838i	$0.863488\pi$
$284$	−227.797	+	131.519i	−0.802102	+	0.463094i
$285$		0			0
$286$	−2.32770	+	4.03170i	−0.00813881	+	0.0140968i
$287$	−256.721	+	256.721i	−0.894500	+	0.894500i
$288$		0			0
$289$		−	151.420i		−	0.523945i
$290$	94.6735	+	548.135i	0.326460	+	1.89012i
$291$		0			0
$292$	−393.346	−	105.397i	−1.34708	−	0.360948i
$293$	51.3251	−	191.548i	0.175171	−	0.653747i	−0.821352	−	0.570422i	$-0.806780\pi$
$293$	51.3251	−	191.548i	0.175171	−	0.653747i	0.996522	−	0.0833245i	$-0.0265538\pi$
$294$		0			0
$295$	−204.037	+	289.235i	−0.691651	+	0.980456i
$296$	7.88075			0.0266241
$297$		0			0
$298$	−265.398	−	265.398i	−0.890596	−	0.890596i
$299$	67.1542	+	38.7715i	0.224596	+	0.129671i
$300$		0			0
$301$	−155.531	−	269.387i	−0.516714	−	0.894975i
$302$	−386.421	−	103.541i	−1.27954	−	0.342852i
$303$		0			0
$304$	432.014	+	249.423i	1.42110	+	0.820471i
$305$	48.4992	−	532.855i	0.159014	−	1.74706i
$306$		0			0
$307$	123.104	−	123.104i	0.400990	−	0.400990i	−0.477592	−	0.878582i	$-0.658490\pi$
$307$	123.104	−	123.104i	0.400990	−	0.400990i	0.878582	+	0.477592i	$0.158490\pi$
$308$	13.6061	−	3.64576i	0.0441758	−	0.0118369i
$309$		0			0
$310$	−73.2504	+	199.082i	−0.236292	+	0.642201i
$311$	−124.009	−	214.790i	−0.398742	−	0.690642i	0.594829	−	0.803852i	$-0.297220\pi$
$311$	−124.009	−	214.790i	−0.398742	−	0.690642i	−0.993571	+	0.113211i	$0.963887\pi$
$312$		0			0
$313$	−174.262	+	46.6933i	−0.556747	+	0.149180i	−0.526211	−	0.850354i	$-0.676388\pi$
$313$	−174.262	+	46.6933i	−0.556747	+	0.149180i	−0.0305356	+	0.999534i	$0.509721\pi$
$314$		−	178.224i		−	0.567594i
$315$		0			0
$316$	248.581			0.786649
$317$	86.1891	+	321.662i	0.271890	+	1.01471i	0.957897	+	0.287112i	$0.0926951\pi$
$317$	86.1891	+	321.662i	0.271890	+	1.01471i	−0.686007	+	0.727595i	$0.740638\pi$
$318$		0			0
$319$	15.4701	−	8.93166i	0.0484956	−	0.0279989i
$320$	113.115	+	244.811i	0.353486	+	0.765034i
$321$		0			0
$322$	−126.443	−	471.893i	−0.392681	−	1.46551i
$323$	432.319	+	432.319i	1.33845	+	1.33845i
$324$		0			0
$325$	−53.4782	−	77.5246i	−0.164548	−	0.238537i
$326$	35.5288	−	61.5377i	0.108984	−	0.188766i
$327$		0			0
$328$	−9.25778	+	34.5505i	−0.0282249	+	0.105337i
$329$	−555.170	+	320.527i	−1.68745	+	0.974247i
$330$		0			0
$331$	−8.88086	+	15.3821i	−0.0268304	+	0.0464716i	−0.879129	−	0.476584i	$-0.841875\pi$
$331$	−8.88086	+	15.3821i	−0.0268304	+	0.0464716i	0.852298	+	0.523056i	$0.175208\pi$
$332$	83.9686	−	83.9686i	0.252918	−	0.252918i
$333$		0			0
$334$		−	121.741i		−	0.364494i
$335$	−624.500	+	107.863i	−1.86418	+	0.321979i
$336$		0			0
$337$	267.126	+	71.5761i	0.792657	+	0.212392i	0.632358	−	0.774677i	$-0.282087\pi$
$337$	267.126	+	71.5761i	0.792657	+	0.212392i	0.160300	+	0.987068i	$0.448754\pi$
$338$	−111.154	+	414.834i	−0.328859	+	1.22732i
$339$		0			0
$340$	66.0104	+	382.183i	0.194148	+	1.12407i
$341$	6.81232			0.0199775
$342$		0			0
$343$	150.058	+	150.058i	0.437488	+	0.437488i
$344$	−26.5406	−	15.3232i	−0.0771529	−	0.0445443i
$345$		0			0
$346$	111.865	+	193.755i	0.323308	+	0.559986i
$347$	−305.488	−	81.8553i	−0.880369	−	0.235894i	−0.209803	−	0.977744i	$-0.567282\pi$
$347$	−305.488	−	81.8553i	−0.880369	−	0.235894i	−0.670566	+	0.741850i	$0.733949\pi$
$348$		0			0
$349$	585.272	+	337.907i	1.67700	+	0.968215i	0.963559	+	0.267497i	$0.0861967\pi$
$349$	585.272	+	337.907i	1.67700	+	0.968215i	0.713439	+	0.700718i	$0.247137\pi$
$350$	−107.125	+	583.611i	−0.306072	+	1.66746i
$351$		0			0
$352$	13.9004	−	13.9004i	0.0394898	−	0.0394898i
$353$	401.068	−	107.466i	1.13617	−	0.304436i	0.358761	−	0.933430i	$-0.383199\pi$
$353$	401.068	−	107.466i	1.13617	−	0.304436i	0.777411	+	0.628993i	$0.216533\pi$
$354$		0			0
$355$	−323.011	+	149.248i	−0.909890	+	0.420417i
$356$	−193.996	−	336.010i	−0.544932	−	0.943850i
$357$		0			0
$358$	−147.758	+	39.5917i	−0.412732	+	0.110591i
$359$			206.110i			0.574122i	0.957912	+	0.287061i	$0.0926783\pi$
$359$			206.110i			0.574122i	−0.957912	+	0.287061i	$0.907322\pi$
$360$		0			0
$361$	−487.736			−1.35107
$362$	−129.736	−	484.181i	−0.358386	−	1.33752i
$363$		0			0
$364$	−103.168	+	59.5641i	−0.283429	+	0.163638i
$365$	−516.987	−	190.220i	−1.41640	−	0.521151i
$366$		0			0
$367$	−47.8780	−	178.683i	−0.130458	−	0.486875i	0.869518	−	0.493902i	$-0.164430\pi$
$367$	−47.8780	−	178.683i	−0.130458	−	0.486875i	−0.999975	+	0.00702710i	$0.997763\pi$
$368$	−249.222	−	249.222i	−0.677234	−	0.677234i
$369$		0			0
$370$	−129.154	−	11.7553i	−0.349065	−	0.0317711i
$371$	271.360	−	470.009i	0.731428	−	1.26687i
$372$		0			0
$373$	63.0242	−	235.210i	0.168966	−	0.630589i	−0.828535	−	0.559937i	$-0.810825\pi$
$373$	63.0242	−	235.210i	0.168966	−	0.630589i	0.997501	−	0.0706518i	$-0.0225079\pi$
$374$	22.4595	−	12.9670i	0.0600521	−	0.0346711i
$375$		0			0
$376$	−31.5790	+	54.6965i	−0.0839867	+	0.145469i
$377$	−106.824	+	106.824i	−0.283354	+	0.283354i
$378$		0			0
$379$			240.778i			0.635297i	0.948208	+	0.317649i	$0.102893\pi$
$379$			240.778i			0.635297i	−0.948208	+	0.317649i	$0.897107\pi$
$380$	−439.950	−	310.358i	−1.15776	−	0.816730i
$381$		0			0
$382$	509.911	+	136.630i	1.33485	+	0.357671i
$383$	−43.8384	+	163.607i	−0.114461	+	0.427173i	−0.999246	−	0.0388260i	$-0.987638\pi$
$383$	−43.8384	+	163.607i	−0.114461	+	0.427173i	0.884785	+	0.465999i	$0.154305\pi$
$384$		0			0
$385$	18.7770	−	3.24315i	0.0487715	−	0.00842378i
$386$	25.2820			0.0654974
$387$		0			0
$388$	−389.613	−	389.613i	−1.00416	−	1.00416i
$389$	128.012	+	73.9079i	0.329080	+	0.189995i	0.655433	−	0.755254i	$-0.272486\pi$
$389$	128.012	+	73.9079i	0.329080	+	0.189995i	−0.326352	+	0.945248i	$0.605820\pi$
$390$		0			0
$391$	−215.986	−	374.098i	−0.552393	−	0.956772i
$392$	−19.6993	−	5.27841i	−0.0502533	−	0.0134653i
$393$		0			0
$394$	394.513	+	227.772i	1.00130	+	0.578102i
$395$	334.884	+	30.4804i	0.847809	+	0.0771656i
$396$		0			0
$397$	154.690	−	154.690i	0.389647	−	0.389647i	−0.484915	−	0.874561i	$-0.661149\pi$
$397$	154.690	−	154.690i	0.389647	−	0.389647i	0.874561	+	0.484915i	$0.161149\pi$
$398$	−754.819	+	202.253i	−1.89653	+	0.508174i
$399$		0			0
$400$	143.590	+	403.275i	0.358976	+	1.00819i
$401$	354.459	+	613.941i	0.883937	+	1.53102i	0.846927	+	0.531709i	$0.178450\pi$
$401$	354.459	+	613.941i	0.883937	+	1.53102i	0.0370100	+	0.999315i	$0.488217\pi$
$402$		0			0
$403$	−55.6495	+	14.9112i	−0.138088	+	0.0370006i
$404$		−	22.8129i		−	0.0564675i
$405$		0			0
$406$	951.793			2.34432
$407$	1.07792	+	4.02286i	0.00264845	+	0.00988417i
$408$		0			0
$409$	−145.092	+	83.7690i	−0.354749	+	0.204814i	−0.666775	−	0.745259i	$-0.732326\pi$
$409$	−145.092	+	83.7690i	−0.354749	+	0.204814i	0.312026	+	0.950074i	$0.398992\pi$
$410$	203.259	−	552.423i	0.495753	−	1.34737i
$411$		0			0
$412$	18.7078	+	69.8185i	0.0454073	+	0.169462i
$413$	428.263	+	428.263i	1.03696	+	1.03696i
$414$		0			0
$415$	123.417	−	102.825i	0.297391	−	0.247772i
$416$	−83.1258	+	143.978i	−0.199822	+	0.346101i
$417$		0			0
$418$	−9.31790	+	34.7749i	−0.0222916	+	0.0831935i
$419$	122.306	−	70.6136i	0.291901	−	0.168529i	−0.346898	−	0.937903i	$-0.612765\pi$
$419$	122.306	−	70.6136i	0.291901	−	0.168529i	0.638799	+	0.769374i	$0.279432\pi$
$420$		0			0
$421$	288.169	−	499.124i	0.684488	−	1.18557i	−0.289110	−	0.957296i	$-0.593359\pi$
$421$	288.169	−	499.124i	0.684488	−	1.18557i	0.973597	−	0.228272i	$-0.0733075\pi$
$422$	−472.467	+	472.467i	−1.11959	+	1.11959i
$423$		0			0
$424$		−	53.4698i		−	0.126108i
$425$	42.0658	+	522.966i	0.0989784	+	1.23051i
$426$		0			0
$427$	−884.333	−	236.956i	−2.07104	−	0.554933i
$428$	64.7830	−	241.773i	0.151362	−	0.564891i
$429$		0			0
$430$	412.105	+	290.715i	0.958384	+	0.676081i
$431$	−449.009			−1.04179			−0.520893	−	0.853622i	$-0.674401\pi$
$431$	−449.009			−1.04179			−0.520893	+	0.853622i	$0.674401\pi$
$432$		0			0
$433$	542.261	+	542.261i	1.25233	+	1.25233i	0.954671	+	0.297663i	$0.0962072\pi$
$433$	542.261	+	542.261i	1.25233	+	1.25233i	0.297663	+	0.954671i	$0.403793\pi$
$434$	314.344	+	181.487i	0.724296	+	0.418173i
$435$		0			0
$436$	111.335	+	192.838i	0.255356	+	0.442290i
$437$	579.230	+	155.204i	1.32547	+	0.355158i
$438$		0			0
$439$	−397.439	−	229.462i	−0.905328	−	0.522692i	−0.0264032	−	0.999651i	$-0.508405\pi$
$439$	−397.439	−	229.462i	−0.905328	−	0.522692i	−0.878925	+	0.476960i	$0.841739\pi$
$440$	1.44234	−	1.20169i	0.00327805	−	0.00273111i
$441$		0			0
$442$	−155.088	+	155.088i	−0.350877	+	0.350877i
$443$	−228.006	+	61.0941i	−0.514687	+	0.137910i	−0.506808	−	0.862059i	$-0.669175\pi$
$443$	−228.006	+	61.0941i	−0.514687	+	0.137910i	−0.00787902	+	0.999969i	$0.502508\pi$
$444$		0			0
$445$	−220.147	−	476.455i	−0.494713	−	1.07069i
$446$	−105.799	−	183.250i	−0.237219	−	0.410875i
$447$		0			0
$448$	445.723	−	119.431i	0.994917	−	0.266587i
$449$		−	267.125i		−	0.594933i	−0.954732	−	0.297467i	$-0.903858\pi$
$449$		−	267.125i		−	0.594933i	0.954732	−	0.297467i	$-0.0961417\pi$
$450$		0			0
$451$	−18.9031			−0.0419138
$452$	76.8679	+	286.875i	0.170062	+	0.634679i
$453$		0			0
$454$	20.2205	−	11.6743i	0.0445385	−	0.0257143i
$455$	−146.290	+	67.5936i	−0.321516	+	0.148557i
$456$		0			0
$457$	−22.5974	−	84.3345i	−0.0494472	−	0.184539i	0.936785	−	0.349905i	$-0.113786\pi$
$457$	−22.5974	−	84.3345i	−0.0494472	−	0.184539i	−0.986232	+	0.165366i	$0.947120\pi$
$458$	424.659	+	424.659i	0.927203	+	0.927203i
$459$		0			0
$460$	243.496	+	292.259i	0.529339	+	0.635346i
$461$	−228.251	+	395.342i	−0.495121	+	0.857574i	−0.999984	−	0.00562496i	$-0.998210\pi$
$461$	−228.251	+	395.342i	−0.495121	+	0.857574i	0.504863	+	0.863199i	$0.331543\pi$
$462$		0			0
$463$	−191.397	+	714.304i	−0.413385	+	1.54277i	0.374663	+	0.927161i	$0.377758\pi$
$463$	−191.397	+	714.304i	−0.413385	+	1.54277i	−0.788048	+	0.615613i	$0.788908\pi$
$464$	594.668	−	343.332i	1.28161	−	0.739939i
$465$		0			0
$466$	166.909	−	289.095i	0.358174	−	0.620376i
$467$	200.076	−	200.076i	0.428428	−	0.428428i	−0.459664	−	0.888093i	$-0.652030\pi$
$467$	200.076	−	200.076i	0.428428	−	0.428428i	0.888093	+	0.459664i	$0.152030\pi$
$468$		0			0
$469$			1084.39i			2.31214i
$470$	599.122	−	849.291i	1.27473	−	1.80700i
$471$		0			0
$472$	57.6372	+	15.4439i	0.122113	+	0.0327200i
$473$	4.19179	−	15.6440i	0.00886214	−	0.0330739i
$474$		0			0
$475$	−554.639	−	472.055i	−1.16766	−	0.993799i
$476$	663.631			1.39418
$477$		0			0
$478$	524.025	+	524.025i	1.09629	+	1.09629i
$479$	−457.227	−	263.980i	−0.954545	−	0.551107i	−0.0600553	−	0.998195i	$-0.519128\pi$
$479$	−457.227	−	263.980i	−0.954545	−	0.551107i	−0.894490	+	0.447088i	$0.852461\pi$
$480$		0			0
$481$	−17.6110	−	30.5031i	−0.0366133	−	0.0634161i
$482$	755.667	+	202.480i	1.56777	+	0.420084i
$483$		0			0
$484$	−386.683	−	223.251i	−0.798931	−	0.461263i
$485$	−477.107	−	572.654i	−0.983726	−	1.18073i
$486$		0			0
$487$	2.96411	−	2.96411i	0.00608646	−	0.00608646i	−0.704057	−	0.710143i	$-0.748630\pi$
$487$	2.96411	−	2.96411i	0.00608646	−	0.00608646i	0.710143	+	0.704057i	$0.248630\pi$
$488$	−87.1263	+	23.3454i	−0.178537	+	0.0478390i
$489$		0			0
$490$	314.969	+	115.890i	0.642794	+	0.236510i
$491$	−395.412	−	684.874i	−0.805320	−	1.39486i	−0.916075	−	0.401008i	$-0.868660\pi$
$491$	−395.412	−	684.874i	−0.805320	−	1.39486i	0.110754	−	0.993848i	$-0.464673\pi$
$492$		0			0
$493$	812.907	−	217.818i	1.64890	−	0.441821i
$494$		−	304.470i		−	0.616337i
$495$		0			0
$496$	261.865			0.527953
$497$	157.581	+	588.100i	0.317064	+	1.18330i
$498$		0			0
$499$	509.165	−	293.967i	1.02037	−	0.589112i	0.106160	−	0.994349i	$-0.466144\pi$
$499$	509.165	−	293.967i	1.02037	−	0.589112i	0.914212	+	0.405237i	$0.132811\pi$
$500$	−114.886	−	447.509i	−0.229772	−	0.895018i
$501$		0			0
$502$	−21.4244	−	79.9569i	−0.0426780	−	0.159277i
$503$	−282.741	−	282.741i	−0.562109	−	0.562109i	0.367797	−	0.929906i	$-0.380112\pi$
$503$	−282.741	−	282.741i	−0.562109	−	0.562109i	−0.929906	+	0.367797i	$0.880112\pi$
$504$		0			0
$505$	2.79726	−	30.7332i	0.00553913	−	0.0608577i
$506$	12.7182	−	22.0286i	0.0251348	−	0.0435348i
$507$		0			0
$508$	−153.603	+	573.256i	−0.302369	+	1.12846i
$509$	453.850	−	262.030i	0.891651	−	0.514795i	0.0171685	−	0.999853i	$-0.494535\pi$
$509$	453.850	−	262.030i	0.891651	−	0.514795i	0.874482	+	0.485058i	$0.161201\pi$
$510$		0			0
$511$	−471.294	+	816.305i	−0.922297	+	1.59747i
$512$	493.507	−	493.507i	0.963882	−	0.963882i
$513$		0			0
$514$			434.377i			0.845092i
$515$	16.6419	+	96.3524i	0.0323144	+	0.187092i
$516$		0			0
$517$	−32.2400	−	8.63869i	−0.0623599	−	0.0167093i
$518$	−57.4338	+	214.346i	−0.110876	+	0.413795i
$519$		0			0
$520$	−9.15211	+	12.9737i	−0.0176002	+	0.0249493i
$521$	149.033			0.286051			0.143026	−	0.989719i	$-0.454317\pi$
$521$	149.033			0.286051			0.143026	+	0.989719i	$0.454317\pi$
$522$		0			0
$523$	−529.426	−	529.426i	−1.01229	−	1.01229i	−0.999924	−	0.0123638i	$-0.996064\pi$
$523$	−529.426	−	529.426i	−1.01229	−	1.01229i	−0.0123638	−	0.999924i	$-0.503936\pi$
$524$	−254.147	−	146.732i	−0.485012	−	0.280022i
$525$		0			0
$526$	−38.7105	−	67.0486i	−0.0735942	−	0.127469i
$527$	310.009	+	83.0665i	0.588252	+	0.157622i
$528$		0			0
$529$	91.2061	+	52.6578i	0.172412	+	0.0995422i
$530$	−79.7581	+	876.293i	−0.150487	+	1.65338i
$531$		0			0
$532$	−651.425	+	651.425i	−1.22448	+	1.22448i
$533$	154.419	−	41.3764i	0.289717	−	0.0776294i
$534$		0			0
$535$	116.920	−	317.770i	0.218543	−	0.593963i
$536$	53.4184	+	92.5233i	0.0996611	+	0.172618i
$537$		0			0
$538$	270.012	−	72.3495i	0.501881	−	0.134479i
$539$		−	10.7778i		−	0.0199959i
$540$		0			0
$541$	−95.0214			−0.175640			−0.0878202	−	0.996136i	$-0.527990\pi$
$541$	−95.0214			−0.175640			−0.0878202	+	0.996136i	$0.527990\pi$
$542$	−245.739	−	917.110i	−0.453393	−	1.69208i
$543$		0			0
$544$	802.063	−	463.071i	1.47438	−	0.851234i
$545$	126.344	+	273.440i	0.231823	+	0.501726i
$546$		0			0
$547$	160.148	+	597.679i	0.292774	+	1.09265i	0.942969	+	0.332881i	$0.108021\pi$
$547$	160.148	+	597.679i	0.292774	+	1.09265i	−0.650194	+	0.759768i	$0.725313\pi$
$548$	257.945	+	257.945i	0.470703	+	0.470703i
$549$		0			0
$550$	−25.4304	+	17.5425i	−0.0462371	+	0.0318954i
$551$	−584.144	+	1011.77i	−1.06015	+	1.83624i
$552$		0			0
$553$	148.920	−	555.779i	0.269296	−	1.00502i
$554$	547.194	−	315.923i	0.987715	−	0.570257i
$555$		0			0
$556$	158.585	−	274.678i	0.285226	−	0.494025i
$557$	591.236	−	591.236i	1.06147	−	1.06147i	0.0634822	−	0.997983i	$-0.479779\pi$
$557$	591.236	−	591.236i	1.06147	−	1.06147i	0.997983	−	0.0634822i	$-0.0202206\pi$
$558$		0			0
$559$			136.970i			0.245027i
$560$	721.787	−	124.666i	1.28891	−	0.222619i
$561$		0			0
$562$	1365.74	+	365.949i	2.43014	+	0.651155i
$563$	192.769	−	719.424i	0.342396	−	1.27784i	−0.553228	−	0.833030i	$-0.686604\pi$
$563$	192.769	−	719.424i	0.342396	−	1.27784i	0.895624	−	0.444811i	$-0.146729\pi$
$564$		0			0
$565$	68.3793	+	395.899i	0.121025	+	0.700706i
$566$	−1000.29			−1.76730
$567$		0			0
$568$	42.4156	+	42.4156i	0.0746754	+	0.0746754i
$569$	−511.784	−	295.479i	−0.899444	−	0.519294i	−0.0224244	−	0.999749i	$-0.507139\pi$
$569$	−511.784	−	295.479i	−0.899444	−	0.519294i	−0.877020	+	0.480454i	$0.840472\pi$
$570$		0			0
$571$	190.304	+	329.617i	0.333283	+	0.577262i	0.983153	−	0.182782i	$-0.0585104\pi$
$571$	190.304	+	329.617i	0.333283	+	0.577262i	−0.649871	+	0.760045i	$0.725177\pi$
$572$	−5.99122	−	1.60534i	−0.0104742	−	0.00280654i
$573$		0			0
$574$	−872.258	−	503.598i	−1.51961	−	0.877349i
$575$	292.198	+	423.584i	0.508170	+	0.736667i
$576$		0			0
$577$	−156.284	+	156.284i	−0.270856	+	0.270856i	−0.829445	−	0.558589i	$-0.811343\pi$
$577$	−156.284	+	156.284i	−0.270856	+	0.270856i	0.558589	+	0.829445i	$0.311343\pi$
$578$	405.755	−	108.722i	0.701999	−	0.188100i
$579$		0			0
$580$	−672.770	+	310.855i	−1.15995	+	0.535956i
$581$	−137.433	−	238.042i	−0.236546	−	0.409710i
$582$		0			0
$583$	27.2945	−	7.31355i	0.0468174	−	0.0125447i
$584$			92.8656i			0.159017i
$585$		0			0
$586$	550.137			0.938800
$587$	262.569	+	979.920i	0.447306	+	1.66937i	0.709774	+	0.704429i	$0.248797\pi$
$587$	262.569	+	979.920i	0.447306	+	1.66937i	−0.262468	+	0.964941i	$0.584536\pi$
$588$		0			0
$589$	−385.845	+	222.768i	−0.655085	+	0.378214i
$590$	−921.554	−	339.077i	−1.56196	−	0.574706i
$591$		0			0
$592$	41.4352	+	154.638i	0.0699918	+	0.261213i
$593$	−336.299	−	336.299i	−0.567115	−	0.567115i	0.364204	−	0.931319i	$-0.381341\pi$
$593$	−336.299	−	336.299i	−0.567115	−	0.567115i	−0.931319	+	0.364204i	$0.881341\pi$
$594$		0			0
$595$	894.033	+	81.3728i	1.50258	+	0.136761i
$596$	250.032	−	433.069i	0.419517	−	0.726625i
$597$		0			0
$598$	−55.6770	+	207.789i	−0.0931054	+	0.347474i
$599$	−370.646	+	213.993i	−0.618775	+	0.357250i	−0.776392	−	0.630250i	$-0.782952\pi$
$599$	−370.646	+	213.993i	−0.618775	+	0.357250i	0.157617	+	0.987500i	$0.449619\pi$
$600$		0			0
$601$	−8.50753	+	14.7355i	−0.0141556	+	0.0245183i	−0.873016	−	0.487691i	$-0.837839\pi$
$601$	−8.50753	+	14.7355i	−0.0141556	+	0.0245183i	0.858861	+	0.512209i	$0.171173\pi$
$602$	610.195	−	610.195i	1.01361	−	1.01361i
$603$		0			0
$604$		−	533.005i		−	0.882459i
$605$	−493.558	−	348.175i	−0.815799	−	0.575496i
$606$		0			0
$607$	−286.306	−	76.7156i	−0.471675	−	0.126385i	0.0151488	−	0.999885i	$-0.495178\pi$
$607$	−286.306	−	76.7156i	−0.471675	−	0.126385i	−0.486823	+	0.873500i	$0.661844\pi$
$608$	−332.757	+	1241.86i	−0.547297	+	2.04254i
$609$		0			0
$610$	1462.70	−	252.636i	2.39786	−	0.414157i
$611$	282.277			0.461991
$612$		0			0
$613$	−229.232	−	229.232i	−0.373951	−	0.373951i	0.494963	−	0.868914i	$-0.335181\pi$
$613$	−229.232	−	229.232i	−0.373951	−	0.373951i	−0.868914	+	0.494963i	$0.835181\pi$
$614$	418.268	+	241.487i	0.681219	+	0.393302i
$615$		0			0
$616$	−1.60615	−	2.78193i	−0.00260738	−	0.00451612i
$617$	−122.674	−	32.8703i	−0.198823	−	0.0532744i	0.158033	−	0.987434i	$-0.449485\pi$
$617$	−122.674	−	32.8703i	−0.198823	−	0.0532744i	−0.356856	+	0.934159i	$0.616151\pi$
$618$		0			0
$619$	−1002.57	−	578.835i	−1.61966	−	0.935112i	−0.987007	−	0.160679i	$-0.948632\pi$
$619$	−1002.57	−	578.835i	−1.61966	−	0.935112i	−0.632655	−	0.774433i	$-0.718035\pi$
$620$	−281.466	−	25.6184i	−0.453978	−	0.0413200i
$621$		0			0
$622$	486.525	−	486.525i	0.782194	−	0.782194i
$623$	−867.474	+	232.439i	−1.39241	+	0.373096i
$624$		0			0
$625$	−99.9000	−	616.964i	−0.159840	−	0.987143i
$626$	−250.245	−	433.437i	−0.399753	−	0.692392i
$627$		0			0
$628$	229.364	−	61.4579i	0.365229	−	0.0978628i
$629$			196.212i			0.311943i
$630$		0			0
$631$	−1139.80			−1.80634			−0.903169	−	0.429285i	$-0.858766\pi$
$631$	−1139.80			−1.80634			−0.903169	+	0.429285i	$0.858766\pi$
$632$	−14.6720	−	54.7565i	−0.0232151	−	0.0866400i
$633$		0			0
$634$	−800.062	+	461.916i	−1.26193	+	0.728574i
$635$	−277.223	+	753.447i	−0.436572	+	1.18653i
$636$		0			0
$637$	23.5912	+	88.0434i	0.0370348	+	0.138216i
$638$	35.0416	+	35.0416i	0.0549242	+	0.0549242i
$639$		0			0
$640$	103.316	−	86.0774i	0.161431	−	0.134496i
$641$	381.384	−	660.576i	0.594983	−	1.03054i	−0.398566	−	0.917139i	$-0.630492\pi$
$641$	381.384	−	660.576i	0.594983	−	1.03054i	0.993549	−	0.113401i	$-0.0361745\pi$
$642$		0			0
$643$	−117.821	+	439.713i	−0.183236	+	0.683846i	0.811765	+	0.583984i	$0.198507\pi$
$643$	−117.821	+	439.713i	−0.183236	+	0.683846i	−0.995001	+	0.0998621i	$0.968160\pi$
$644$	563.696	−	325.450i	0.875304	−	0.505357i
$645$		0			0
$646$	−848.061	+	1468.88i	−1.31279	+	2.27381i
$647$	−19.2194	+	19.2194i	−0.0297054	+	0.0297054i	−0.721803	−	0.692098i	$-0.756687\pi$
$647$	−19.2194	+	19.2194i	−0.0297054	+	0.0297054i	0.692098	+	0.721803i	$0.256687\pi$
$648$		0			0
$649$			31.5343i			0.0485890i
$650$	169.342	−	198.968i	0.260526	−	0.306104i
$651$		0			0
$652$	91.4468	+	24.5031i	0.140256	+	0.0375814i
$653$	−328.534	+	1226.11i	−0.503115	+	1.87765i	−0.0243595	+	0.999703i	$0.507755\pi$
$653$	−328.534	+	1226.11i	−0.503115	+	1.87765i	−0.478756	+	0.877948i	$0.658912\pi$
$654$		0			0
$655$	−324.390	−	228.837i	−0.495253	−	0.349370i
$656$	−726.634			−1.10767
$657$		0			0
$658$	−1257.53	−	1257.53i	−1.91114	−	1.91114i
$659$	680.526	+	392.902i	1.03266	+	0.596209i	0.917747	−	0.397166i	$-0.130006\pi$
$659$	680.526	+	392.902i	1.03266	+	0.596209i	0.114918	+	0.993375i	$0.463339\pi$
$660$		0			0
$661$	−184.105	−	318.880i	−0.278526	−	0.482421i	0.692493	−	0.721425i	$-0.256512\pi$
$661$	−184.105	−	318.880i	−0.278526	−	0.482421i	−0.971019	+	0.239004i	$0.923179\pi$
$662$	−47.5955	−	12.7532i	−0.0718966	−	0.0192646i
$663$		0			0
$664$	−23.4524	−	13.5402i	−0.0353198	−	0.0203919i
$665$	−957.466	+	797.713i	−1.43980	+	1.19957i
$666$		0			0
$667$	583.673	−	583.673i	0.875072	−	0.875072i
$668$	156.673	−	41.9805i	0.234541	−	0.0628450i
$669$		0			0
$670$	−737.437	−	1596.00i	−1.10065	−	2.38210i
$671$	−23.8341	−	41.2819i	−0.0355203	−	0.0615229i
$672$		0			0
$673$	797.751	−	213.757i	1.18537	−	0.317618i	0.388313	−	0.921528i	$-0.373058\pi$
$673$	797.751	−	213.757i	1.18537	−	0.317618i	0.797053	+	0.603910i	$0.206391\pi$
$674$			767.200i			1.13828i
$675$		0			0
$676$	−572.196			−0.846444
$677$	186.692	+	696.745i	0.275764	+	1.02917i	0.955328	+	0.295549i	$0.0955024\pi$
$677$	186.692	+	696.745i	0.275764	+	1.02917i	−0.679564	+	0.733616i	$0.737831\pi$
$678$		0			0
$679$	−1104.51	+	637.688i	−1.62667	+	0.939158i
$680$	80.2898	−	37.0981i	0.118073	−	0.0545560i
$681$		0			0
$682$	4.89134	+	18.2547i	0.00717206	+	0.0267665i
$683$	264.640	+	264.640i	0.387467	+	0.387467i	0.873783	−	0.486316i	$-0.161660\pi$
$683$	264.640	+	264.640i	0.387467	+	0.387467i	−0.486316	+	0.873783i	$0.661660\pi$
$684$		0			0
$685$	315.871	+	379.128i	0.461126	+	0.553472i
$686$	−294.362	+	509.851i	−0.429100	+	0.743223i
$687$		0			0
$688$	161.132	−	601.353i	0.234203	−	0.874059i
$689$	−206.960	+	119.488i	−0.300377	+	0.173423i
$690$		0			0
$691$	−242.016	+	419.184i	−0.350240	+	0.606633i	−0.986291	−	0.165013i	$-0.947233\pi$
$691$	−242.016	+	419.184i	−0.350240	+	0.606633i	0.636051	+	0.771647i	$0.280567\pi$
$692$	−210.776	+	210.776i	−0.304590	+	0.304590i
$693$		0			0
$694$		−	877.380i		−	1.26424i
$695$	247.324	−	350.597i	0.355862	−	0.504456i
$696$		0			0
$697$	−860.227	−	230.497i	−1.23418	−	0.330699i
$698$	−485.244	+	1810.96i	−0.695193	+	2.59449i
$699$		0			0
$700$	−788.012	+	63.3854i	−1.12573	+	0.0905505i
$701$	−394.513			−0.562787			−0.281393	−	0.959593i	$-0.590797\pi$
$701$	−394.513			−0.562787			−0.281393	+	0.959593i	$0.590797\pi$
$702$		0			0
$703$	−192.603	−	192.603i	−0.273973	−	0.273973i
$704$	20.8069	+	12.0129i	0.0295553	+	0.0170638i
$705$		0			0
$706$	575.946	+	997.568i	0.815788	+	1.41299i
$707$	−51.0052	−	13.6668i	−0.0721431	−	0.0193307i
$708$		0			0
$709$	−97.8826	−	56.5126i	−0.138057	−	0.0797074i	0.429380	−	0.903124i	$-0.358732\pi$
$709$	−97.8826	−	56.5126i	−0.138057	−	0.0797074i	−0.567438	+	0.823416i	$0.692065\pi$
$710$	−631.862	−	758.400i	−0.889946	−	1.06817i
$711$		0			0
$712$	−62.5649	+	62.5649i	−0.0878721	+	0.0878721i
$713$	304.061	−	81.4730i	0.426454	−	0.114268i
$714$		0			0
$715$	−7.87443	−	2.89732i	−0.0110132	−	0.00405220i
$716$	−101.904	−	176.503i	−0.142324	−	0.246513i
$717$		0			0
$718$	−552.306	+	147.990i	−0.769229	+	0.206114i
$719$		−	242.271i		−	0.336955i	−0.985705	−	0.168478i	$-0.946115\pi$
$719$		−	242.271i		−	0.336955i	0.985705	−	0.168478i	$-0.0538851\pi$
$720$		0			0
$721$	167.308			0.232050
$722$	−350.201	−	1306.97i	−0.485043	−	1.81021i
$723$		0			0
$724$	578.374	−	333.924i	0.798859	−	0.461221i
$725$	−944.461	+	336.285i	−1.30271	+	0.463842i
$726$		0			0
$727$	108.815	+	406.101i	0.149676	+	0.558599i	0.999503	+	0.0315363i	$0.0100400\pi$
$727$	108.815	+	406.101i	0.149676	+	0.558599i	−0.849826	+	0.527063i	$0.823293\pi$
$728$	19.2098	+	19.2098i	0.0263871	+	0.0263871i
$729$		0			0
$730$	138.523	−	1521.93i	0.189757	−	2.08484i
$731$	381.512	−	660.799i	0.521905	−	0.903965i
$732$		0			0
$733$	37.6903	−	140.662i	0.0514193	−	0.191899i	−0.935439	−	0.353489i	$-0.884995\pi$
$733$	37.6903	−	140.662i	0.0514193	−	0.191899i	0.986858	+	0.161589i	$0.0516620\pi$
$734$	444.434	−	256.594i	0.605496	−	0.349583i
$735$		0			0
$736$	454.188	−	786.676i	0.617103	−	1.06885i
$737$	−39.9235	+	39.9235i	−0.0541703	+	0.0541703i
$738$		0			0
$739$		−	951.239i		−	1.28720i	−0.765363	−	0.643599i	$-0.777441\pi$
$739$		−	951.239i		−	1.28720i	0.765363	−	0.643599i	$-0.222559\pi$
$740$	−29.4084	−	170.267i	−0.0397411	−	0.230091i
$741$		0			0
$742$	1454.31	+	389.681i	1.95998	+	0.525176i
$743$	−35.8827	+	133.916i	−0.0482943	+	0.180237i	−0.985860	−	0.167572i	$-0.946407\pi$
$743$	−35.8827	+	133.916i	−0.0482943	+	0.180237i	0.937566	+	0.347809i	$0.113074\pi$
$744$		0			0
$745$	389.942	−	552.765i	0.523412	−	0.741967i
$746$	675.536			0.905544
$747$		0			0
$748$	24.4325	+	24.4325i	0.0326638	+	0.0326638i
$749$	−501.748	−	289.684i	−0.669891	−	0.386762i
$750$		0			0
$751$	−72.3063	−	125.238i	−0.0962800	−	0.166762i	0.813862	−	0.581058i	$-0.197361\pi$
$751$	−72.3063	−	125.238i	−0.0962800	−	0.166762i	−0.910142	+	0.414296i	$0.864028\pi$
$752$	−1239.30	−	332.070i	−1.64801	−	0.441583i
$753$		0			0
$754$	−362.955	−	209.552i	−0.481373	−	0.277921i
$755$	65.3558	−	718.056i	0.0865640	−	0.951068i
$756$		0			0
$757$	−509.399	+	509.399i	−0.672918	+	0.672918i	−0.958388	−	0.285470i	$-0.907850\pi$
$757$	−509.399	+	509.399i	−0.672918	+	0.672918i	0.285470	+	0.958388i	$0.407850\pi$
$758$	−645.204	+	172.882i	−0.851193	+	0.228076i
$759$		0			0
$760$	−42.3973	+	115.229i	−0.0557859	+	0.151617i
$761$	−324.207	−	561.542i	−0.426027	−	0.737900i	0.570489	−	0.821305i	$-0.306754\pi$
$761$	−324.207	−	561.542i	−0.426027	−	0.737900i	−0.996516	+	0.0834050i	$0.973420\pi$
$762$		0			0
$763$	497.848	−	133.398i	0.652487	−	0.174833i
$764$			703.340i			0.920601i
$765$		0			0
$766$	−469.889			−0.613433
$767$	−69.0243	−	257.602i	−0.0899926	−	0.335857i
$768$		0			0
$769$	360.970	−	208.406i	0.469402	−	0.271009i	−0.246587	−	0.969121i	$-0.579309\pi$
$769$	360.970	−	208.406i	0.469402	−	0.271009i	0.715989	+	0.698111i	$0.245976\pi$
$770$	22.1728	+	47.9876i	0.0287958	+	0.0623215i
$771$		0			0
$772$	8.71810	+	32.5364i	0.0112929	+	0.0421456i
$773$	114.629	+	114.629i	0.148292	+	0.148292i	0.777354	−	0.629063i	$-0.216561\pi$
$773$	114.629	+	114.629i	0.148292	+	0.148292i	−0.629063	+	0.777354i	$0.716561\pi$
$774$		0			0
$775$	−376.046	−	69.0254i	−0.485220	−	0.0890650i
$776$	−62.8264	+	108.818i	−0.0809618	+	0.140230i
$777$		0			0
$778$	−106.134	+	396.097i	−0.136419	+	0.509122i
$779$	1070.66	−	618.147i	1.37441	−	0.793513i
$780$		0			0
$781$	−15.8502	+	27.4533i	−0.0202947	+	0.0351515i
$782$	847.377	−	847.377i	1.08360	−	1.08360i
$783$		0			0
$784$		−	414.297i		−	0.528440i
$785$	316.531	−	54.6711i	0.403225	−	0.0696447i
$786$		0			0
$787$	917.219	+	245.768i	1.16546	+	0.312285i	0.789146	−	0.614206i	$-0.210524\pi$
$787$	917.219	+	245.768i	1.16546	+	0.312285i	0.376317	+	0.926491i	$0.377190\pi$
$788$	−157.087	+	586.257i	−0.199349	+	0.743981i
$789$		0			0
$790$	158.775	+	919.265i	0.200981	+	1.16363i
$791$	687.447			0.869085
$792$		0			0
$793$	285.060	+	285.060i	0.359471	+	0.359471i
$794$	525.587	+	303.448i	0.661948	+	0.382176i
$795$		0			0
$796$	−520.575	−	901.662i	−0.653988	−	1.13274i
$797$	−265.785	−	71.2169i	−0.333482	−	0.0893563i	0.0881926	−	0.996103i	$-0.471891\pi$
$797$	−265.785	−	71.2169i	−0.333482	−	0.0893563i	−0.421675	+	0.906747i	$0.638558\pi$
$798$		0			0
$799$	−1361.81	−	786.243i	−1.70440	−	0.984034i
$800$	−908.160	+	626.469i	−1.13520	+	0.783087i
$801$		0			0
$802$	−1390.65	+	1390.65i	−1.73398	+	1.73398i
$803$	−47.4048	+	12.7021i	−0.0590346	+	0.0158183i
$804$		0			0
$805$	799.308	−	369.322i	0.992930	−	0.458785i
$806$	−79.9144	−	138.416i	−0.0991494	−	0.171732i
$807$		0			0
$808$	−5.02513	+	1.34648i	−0.00621922	+	0.00166644i
$809$		−	724.904i		−	0.896049i	−0.894021	−	0.448025i	$-0.852128\pi$
$809$		−	724.904i		−	0.896049i	0.894021	−	0.448025i	$-0.147872\pi$
$810$		0			0
$811$	331.996			0.409366			0.204683	−	0.978828i	$-0.434384\pi$
$811$	331.996			0.409366			0.204683	+	0.978828i	$0.434384\pi$
$812$	328.211	+	1224.90i	0.404200	+	1.50850i
$813$		0			0
$814$	−10.0060	+	5.77694i	−0.0122923	+	0.00709698i
$815$	120.191	+	44.2232i	0.147474	+	0.0542616i
$816$		0			0
$817$	274.149	+	1023.14i	0.335556	+	1.25231i
$818$	−328.652	−	328.652i	−0.401775	−	0.401775i
$819$		0			0
$820$	781.026	+	71.0871i	0.952470	+	0.0866916i
$821$	359.807	−	623.204i	0.438254	−	0.759079i	−0.559301	−	0.828965i	$-0.688930\pi$
$821$	359.807	−	623.204i	0.438254	−	0.759079i	0.997555	+	0.0698862i	$0.0222636\pi$
$822$		0			0
$823$	106.313	−	396.767i	0.129178	−	0.482099i	−0.870776	−	0.491680i	$-0.836383\pi$
$823$	106.313	−	396.767i	0.129178	−	0.482099i	0.999954	+	0.00958090i	$0.00304974\pi$
$824$	14.2752	−	8.24177i	0.0173242	−	0.0100022i
$825$		0			0
$826$	−840.104	+	1455.10i	−1.01708	+	1.76163i
$827$	−185.364	+	185.364i	−0.224140	+	0.224140i	−0.810239	−	0.586099i	$-0.800663\pi$
$827$	−185.364	+	185.364i	−0.224140	+	0.224140i	0.586099	+	0.810239i	$0.300663\pi$
$828$		0			0
$829$		−	601.887i		−	0.726040i	−0.931781	−	0.363020i	$-0.881746\pi$
$829$		−	601.887i		−	0.726040i	0.931781	−	0.363020i	$-0.118254\pi$
$830$	364.153	+	256.887i	0.438738	+	0.309503i
$831$		0			0
$832$	−196.266	−	52.5892i	−0.235896	−	0.0632082i
$833$	131.420	−	490.466i	0.157767	−	0.588795i
$834$		0			0
$835$	216.215	−	37.3445i	0.258940	−	0.0447240i
$836$	−47.9663			−0.0573759
$837$		0			0
$838$	277.039	+	277.039i	0.330595	+	0.330595i
$839$	145.550	+	84.0331i	0.173480	+	0.100159i	0.584226	−	0.811591i	$-0.301398\pi$
$839$	145.550	+	84.0331i	0.173480	+	0.100159i	−0.410746	+	0.911750i	$0.634732\pi$
$840$		0			0
$841$	383.576	+	664.374i	0.456095	+	0.789980i
$842$	1544.40	+	413.820i	1.83420	+	0.491472i
$843$		0			0
$844$	−770.960	−	445.114i	−0.913459	−	0.527386i
$845$	−770.854	−	70.1613i	−0.912253	−	0.0830311i
$846$		0			0
$847$	−730.801	+	730.801i	−0.862811	+	0.862811i
$848$	1049.20	−	281.132i	1.23726	−	0.331524i
$849$		0			0
$850$	−1371.17	+	488.219i	−1.61314	+	0.574376i
$851$	96.2240	+	166.665i	0.113072	+	0.195846i
$852$		0			0
$853$	−435.758	+	116.761i	−0.510854	+	0.136883i	−0.505033	−	0.863100i	$-0.668520\pi$
$853$	−435.758	+	116.761i	−0.510854	+	0.136883i	−0.00582116	+	0.999983i	$0.501853\pi$
$854$		−	2539.86i		−	2.97407i
$855$		0			0
$856$	−57.0806			−0.0666830
$857$	249.230	+	930.139i	0.290817	+	1.08534i	0.944483	+	0.328560i	$0.106563\pi$
$857$	249.230	+	930.139i	0.290817	+	1.08534i	−0.653667	+	0.756783i	$0.726770\pi$
$858$		0			0
$859$	285.314	−	164.726i	0.332147	−	0.191765i	−0.324647	−	0.945835i	$-0.605246\pi$
$859$	285.314	−	164.726i	0.332147	−	0.191765i	0.656794	+	0.754070i	$0.271912\pi$
$860$	−232.024	+	630.603i	−0.269795	+	0.733259i
$861$		0			0
$862$	−322.395	−	1203.20i	−0.374009	−	1.39582i
$863$	271.802	+	271.802i	0.314950	+	0.314950i	0.846824	−	0.531874i	$-0.178512\pi$
$863$	271.802	+	271.802i	0.314950	+	0.314950i	−0.531874	+	0.846824i	$0.678512\pi$
$864$		0			0
$865$	−309.799	+	258.110i	−0.358150	+	0.298393i
$866$	−1063.73	+	1842.43i	−1.22832	+	2.12752i
$867$		0			0
$868$	−125.166	+	467.125i	−0.144200	+	0.538162i
$869$	25.9445	−	14.9791i	0.0298556	−	0.0172371i
$870$		0			0
$871$	238.746	−	413.521i	0.274106	−	0.474766i
$872$	35.9064	−	35.9064i	0.0411770	−	0.0411770i
$873$		0			0
$874$			1663.58i			1.90341i
$875$	−1069.37	−	11.2323i	−1.22214	−	0.0128369i
$876$		0			0
$877$	703.795	+	188.581i	0.802503	+	0.215030i	0.636682	−	0.771126i	$-0.280306\pi$
$877$	703.795	+	188.581i	0.802503	+	0.215030i	0.165820	+	0.986156i	$0.446973\pi$
$878$	329.514	−	1229.76i	0.375300	−	1.40064i
$879$		0			0
$880$	31.1634	+	21.9838i	0.0354130	+	0.0249816i
$881$	1330.41			1.51011			0.755055	−	0.655661i	$-0.227610\pi$
$881$	1330.41			1.51011			0.755055	+	0.655661i	$0.227610\pi$
$882$		0			0
$883$	−678.846	−	678.846i	−0.768795	−	0.768795i	0.209099	−	0.977894i	$-0.432947\pi$
$883$	−678.846	−	678.846i	−0.768795	−	0.768795i	−0.977894	+	0.209099i	$0.932947\pi$
$884$	−253.068	−	146.109i	−0.286276	−	0.165281i
$885$		0			0
$886$	−327.424	−	567.115i	−0.369553	−	0.640084i
$887$	1097.46	+	294.062i	1.23727	+	0.331525i	0.817405	−	0.576063i	$-0.195412\pi$
$887$	1097.46	+	294.062i	1.23727	+	0.331525i	0.419862	+	0.907588i	$0.362079\pi$
$888$		0			0
$889$	1189.67	+	686.855i	1.33821	+	0.772615i
$890$	1118.67	−	932.024i	1.25694	−	1.04722i
$891$		0			0
$892$	199.348	−	199.348i	0.223485	−	0.223485i
$893$	2108.55	−	564.984i	2.36120	−	0.632681i
$894$		0			0
$895$	−115.641	−	250.278i	−0.129208	−	0.279640i
$896$	−115.049	−	199.270i	−0.128403	−	0.222400i
$897$		0			0
$898$	715.806	−	191.800i	0.797112	−	0.213585i
$899$			613.282i			0.682182i
$900$		0			0
$901$	1331.27			1.47755
$902$	−13.5727	−	50.6541i	−0.0150474	−	0.0561576i
$903$		0			0
$904$	58.6547	−	33.8643i	0.0648836	−	0.0374605i
$905$	820.122	−	378.939i	0.906212	−	0.418717i
$906$		0			0
$907$	−395.159	−	1474.75i	−0.435677	−	1.62597i	−0.739442	−	0.673220i	$-0.764911\pi$
$907$	−395.159	−	1474.75i	−0.435677	−	1.62597i	0.303765	−	0.952747i	$-0.401756\pi$
$908$	21.9968	+	21.9968i	0.0242256	+	0.0242256i
$909$		0			0
$910$	−286.167	−	343.475i	−0.314469	−	0.377445i
$911$	896.264	−	1552.38i	0.983825	−	1.70403i	0.336778	−	0.941584i	$-0.390663\pi$
$911$	896.264	−	1552.38i	0.983825	−	1.70403i	0.647047	−	0.762451i	$-0.276004\pi$
$912$		0			0
$913$	3.70404	−	13.8237i	0.00405700	−	0.0151409i
$914$	209.763	−	121.107i	0.229500	−	0.132502i
$915$		0			0
$916$	−400.073	+	692.947i	−0.436761	+	0.756493i
$917$	−480.318	+	480.318i	−0.523793	+	0.523793i
$918$		0			0
$919$			1164.78i			1.26744i	0.773563	+	0.633719i	$0.218473\pi$
$919$			1164.78i			1.26744i	−0.773563	+	0.633719i	$0.781527\pi$
$920$	50.0059	−	70.8863i	0.0543542	−	0.0770503i
$921$		0			0
$922$	−1223.27	−	327.775i	−1.32676	−	0.355504i
$923$	69.3879	−	258.959i	0.0751765	−	0.280562i
$924$		0			0
$925$	−18.7408	−	232.987i	−0.0202603	−	0.251878i
$926$	−2051.52			−2.21547
$927$		0			0
$928$	1251.39	+	1251.39i	1.34848	+	1.34848i
$929$	−712.499	−	411.361i	−0.766952	−	0.442800i	0.0648339	−	0.997896i	$-0.479348\pi$
$929$	−712.499	−	411.361i	−0.766952	−	0.442800i	−0.831786	+	0.555096i	$0.812682\pi$
$930$		0			0
$931$	352.442	+	610.447i	0.378563	+	0.655690i
$932$	429.604	+	115.112i	0.460948	+	0.123511i
$933$		0			0
$934$	679.795	+	392.480i	0.727832	+	0.420214i
$935$	29.9193	+	35.9110i	0.0319992	+	0.0384075i
$936$		0			0
$937$	857.665	−	857.665i	0.915331	−	0.915331i	−0.0813546	−	0.996685i	$-0.525925\pi$
$937$	857.665	−	857.665i	0.915331	−	0.915331i	0.996685	+	0.0813546i	$0.0259246\pi$
$938$	−2905.82	+	778.611i	−3.09788	+	0.830076i
$939$		0			0
$940$	1299.58	+	478.169i	1.38254	+	0.508690i
$941$	−84.0785	−	145.628i	−0.0893501	−	0.154759i	0.817886	−	0.575380i	$-0.195146\pi$
$941$	−84.0785	−	145.628i	−0.0893501	−	0.154759i	−0.907237	+	0.420621i	$0.861812\pi$
$942$		0			0
$943$	−843.724	+	226.075i	−0.894723	+	0.239740i
$944$			1212.17i			1.28408i
$945$		0			0
$946$	44.9304			0.0474952
$947$	207.131	+	773.022i	0.218723	+	0.816285i	0.984823	+	0.173564i	$0.0555282\pi$
$947$	207.131	+	773.022i	0.218723	+	0.816285i	−0.766100	+	0.642722i	$0.777805\pi$
$948$		0			0
$949$	359.445	−	207.525i	0.378762	−	0.218678i
$950$	866.711	−	1825.19i	0.912327	−	1.92125i
$951$		0			0
$952$	−39.1694	−	146.182i	−0.0411443	−	0.153553i
$953$	387.854	+	387.854i	0.406982	+	0.406982i	0.880685	−	0.473703i	$-0.157083\pi$
$953$	387.854	+	387.854i	0.406982	+	0.406982i	−0.473703	+	0.880685i	$0.657083\pi$
$954$		0			0
$955$	−86.2418	+	947.528i	−0.0903055	+	0.992176i
$956$	−493.686	+	855.089i	−0.516408	+	0.894445i
$957$		0			0
$958$	379.083	−	1414.76i	0.395703	−	1.47678i
$959$	731.246	−	422.185i	0.762509	−	0.440235i
$960$		0			0
$961$	363.560	−	629.705i	0.378314	−	0.655260i
$962$	69.0933	−	69.0933i	0.0718225	−	0.0718225i
$963$		0			0
$964$			1042.32i			1.08124i
$965$	7.75536	+	44.9015i	0.00803664	+	0.0465301i
$966$		0			0
$967$	1290.63	+	345.824i	1.33468	+	0.357626i	0.854457	−	0.519522i	$-0.173890\pi$
$967$	1290.63	+	345.824i	1.33468	+	0.357626i	0.480220	+	0.877148i	$0.340557\pi$
$968$	−26.3538	+	98.3539i	−0.0272250	+	0.101605i
$969$		0			0
$970$	1191.95	−	1689.66i	1.22882	−	1.74192i
$971$	1177.49			1.21266			0.606328	−	0.795215i	$-0.292642\pi$
$971$	1177.49			1.21266			0.606328	+	0.795215i	$0.292642\pi$
$972$		0			0
$973$	−519.121	−	519.121i	−0.533526	−	0.533526i
$974$	10.0711	+	5.81455i	0.0103399	+	0.00596976i
$975$		0			0
$976$	−916.180	−	1586.87i	−0.938709	−	1.62589i
$977$	349.893	+	93.7536i	0.358130	+	0.0959607i	0.433398	−	0.901203i	$-0.357314\pi$
$977$	349.893	+	93.7536i	0.358130	+	0.0959607i	−0.0752677	+	0.997163i	$0.523981\pi$
$978$		0			0
$979$	−40.4949	−	23.3797i	−0.0413635	−	0.0238812i
$980$	−40.5310	+	445.309i	−0.0413581	+	0.454397i
$981$		0			0
$982$	1551.32	−	1551.32i	1.57976	−	1.57976i
$983$	656.940	−	176.027i	0.668301	−	0.179071i	0.0913119	−	0.995822i	$-0.470894\pi$
$983$	656.940	−	176.027i	0.668301	−	0.179071i	0.576990	+	0.816751i	$0.304227\pi$
$984$		0			0
$985$	−283.511	+	770.535i	−0.287828	+	0.782269i
$986$	1167.36	+	2021.92i	1.18393	+	2.05063i
$987$		0			0
$988$	391.835	−	104.992i	0.396594	−	0.106267i
$989$		−	748.387i		−	0.756711i
$990$		0			0
$991$	809.023			0.816370			0.408185	−	0.912899i	$-0.366162\pi$
$991$	809.023			0.816370			0.408185	+	0.912899i	$0.366162\pi$
$992$	174.677	+	651.905i	0.176086	+	0.657162i
$993$		0			0
$994$	−1462.77	+	844.529i	−1.47160	+	0.849627i
$995$	−590.751	−	1278.54i	−0.593719	−	1.28496i
$996$		0			0
$997$	27.6300	+	103.117i	0.0277131	+	0.103427i	0.978397	−	0.206734i	$-0.0662836\pi$
$997$	27.6300	+	103.117i	0.0277131	+	0.103427i	−0.950684	+	0.310161i	$0.899617\pi$
$998$	1153.32	+	1153.32i	1.15563	+	1.15563i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.j.298.4		16
3.2	odd	2		405.3.l.m.298.1		16
5.2	odd	4		405.3.l.m.217.1		16
9.2	odd	6		405.3.g.f.163.2	yes	16
9.4	even	3		405.3.l.m.28.1		16
9.5	odd	6	inner	405.3.l.j.28.4		16
9.7	even	3		405.3.g.f.163.7	yes	16
15.2	even	4	inner	405.3.l.j.217.4		16
45.2	even	12		405.3.g.f.82.2	✓	16
45.7	odd	12		405.3.g.f.82.7	yes	16
45.22	odd	12	inner	405.3.l.j.352.4		16
45.32	even	12		405.3.l.m.352.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.g.f.82.2	✓	16	45.2	even	12
405.3.g.f.82.7	yes	16	45.7	odd	12
405.3.g.f.163.2	yes	16	9.2	odd	6
405.3.g.f.163.7	yes	16	9.7	even	3
405.3.l.j.28.4		16	9.5	odd	6	inner
405.3.l.j.217.4		16	15.2	even	4	inner
405.3.l.j.298.4		16	1.1	even	1	trivial
405.3.l.j.352.4		16	45.22	odd	12	inner
405.3.l.m.28.1		16	9.4	even	3
405.3.l.m.217.1		16	5.2	odd	4
405.3.l.m.298.1		16	3.2	odd	2
405.3.l.m.352.1		16	45.32	even	12

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.718015 + 2.67967i) q^{2} +(-3.20097 + 1.84808i) q^{4} +(-4.53891 + 2.09721i) q^{5} +(2.21431 + 8.26391i) q^{7} +(0.596019 + 0.596019i) q^{8} +(-8.87884 - 10.6569i) q^{10} +(-0.222725 + 0.385771i) q^{11} +(0.975029 - 3.63886i) q^{13} +(-20.5546 + 11.8672i) q^{14} +(-8.56151 + 14.8290i) q^{16} +(-14.8395 + 14.8395i) q^{17} -29.1331i q^{19} +(10.6531 - 15.1014i) q^{20} +(-1.19366 - 0.319839i) q^{22} +(-5.32743 + 19.8822i) q^{23} +(16.2034 - 19.0381i) q^{25} +10.4510 q^{26} +(-22.3603 - 22.3603i) q^{28} +(-34.7292 - 20.0509i) q^{29} +(-7.64656 - 13.2442i) q^{31} +(-42.6273 - 11.4220i) q^{32} +(-50.4198 - 29.1099i) q^{34} +(-27.3817 - 32.8653i) q^{35} +(6.61115 - 6.61115i) q^{37} +(78.0669 - 20.9180i) q^{38} +(-3.95526 - 1.45530i) q^{40} +(21.2181 + 36.7507i) q^{41} +(-35.1195 + 9.41025i) q^{43} -1.64645i q^{44} -57.1029 q^{46} +(19.3932 + 72.3764i) q^{47} +(-20.9538 + 12.0977i) q^{49} +(62.6501 + 29.7501i) q^{50} +(3.60387 + 13.4498i) q^{52} +(-44.8558 - 44.8558i) q^{53} +(0.201884 - 2.21808i) q^{55} +(-3.60568 + 6.24522i) q^{56} +(28.7937 - 107.459i) q^{58} +(61.3077 - 35.3960i) q^{59} +(-53.5057 + 92.6746i) q^{61} +(29.9998 - 29.9998i) q^{62} -53.9361i q^{64} +(3.20589 + 18.5613i) q^{65} +(122.430 + 32.8051i) q^{67} +(20.0762 - 74.9253i) q^{68} +(68.4075 - 96.9716i) q^{70} +71.1649 q^{71} +(77.9049 + 77.9049i) q^{73} +(22.4626 + 12.9688i) q^{74} +(53.8403 + 93.2542i) q^{76} +(-3.68115 - 0.986362i) q^{77} +(-58.2435 - 33.6269i) q^{79} +(7.76041 - 85.2627i) q^{80} +(-83.2449 + 83.2449i) q^{82} +(-31.0330 + 8.31528i) q^{83} +(36.2335 - 98.4766i) q^{85} +(-50.4327 - 87.3520i) q^{86} +(-0.362675 + 0.0971784i) q^{88} +104.971i q^{89} +32.2302 q^{91} +(-19.6910 - 73.4880i) q^{92} +(-180.020 + 103.935i) q^{94} +(61.0983 + 132.232i) q^{95} +(38.5827 + 143.993i) q^{97} +(-47.4628 - 47.4628i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 12 q^{5} - 20 q^{7} - 56 q^{10} + 22 q^{13} - 168 q^{14} + 16 q^{16} - 96 q^{20} - 16 q^{22} + 36 q^{23} + 46 q^{25} + 176 q^{28} - 252 q^{29} - 160 q^{31} - 114 q^{32} + 4 q^{37} + 192 q^{38}+ \cdots - 152 q^{97}+O(q^{100}) \) 16 * q - 6 * q^2 + 12 * q^5 - 20 * q^7 - 56 * q^10 + 22 * q^13 - 168 * q^14 + 16 * q^16 - 96 * q^20 - 16 * q^22 + 36 * q^23 + 46 * q^25 + 176 * q^28 - 252 * q^29 - 160 * q^31 - 114 * q^32 + 4 * q^37 + 192 * q^38 + 264 * q^40 - 128 * q^43 - 16 * q^46 + 204 * q^47 + 540 * q^50 + 154 * q^52 - 364 * q^55 - 246 * q^58 + 36 * q^59 - 4 * q^61 + 24 * q^65 - 44 * q^67 + 966 * q^68 + 18 * q^70 + 364 * q^73 + 288 * q^74 + 456 * q^76 - 204 * q^77 + 32 * q^82 + 12 * q^83 - 32 * q^85 - 420 * q^88 + 224 * q^91 - 960 * q^92 + 114 * q^95 - 152 * q^97

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