LMFDB - Embedded newform 784.2.x.n.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.1
Character	$\chi$	$=$	784.165
Dual form			784.2.x.n.765.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21510 - 0.723563i) q^{2} +(-0.608516 - 2.27101i) q^{3} +(0.952912 + 1.75840i) q^{4} +(-0.400455 + 1.49452i) q^{5} +(-0.903818 + 3.19980i) q^{6} +(0.114433 - 2.82611i) q^{8} +(-2.18914 + 1.26390i) q^{9} +O(q^{10})$	\(q+(-1.21510 - 0.723563i) q^{2} +(-0.608516 - 2.27101i) q^{3} +(0.952912 + 1.75840i) q^{4} +(-0.400455 + 1.49452i) q^{5} +(-0.903818 + 3.19980i) q^{6} +(0.114433 - 2.82611i) q^{8} +(-2.18914 + 1.26390i) q^{9} +(1.56797 - 1.52623i) q^{10} +(-1.75187 + 0.469413i) q^{11} +(3.41348 - 3.23409i) q^{12} +(1.49861 - 1.49861i) q^{13} +3.63776 q^{15} +(-2.18392 + 3.35119i) q^{16} +(2.44112 - 4.22814i) q^{17} +(3.57452 + 0.0482225i) q^{18} +(-7.02361 - 1.88197i) q^{19} +(-3.00955 + 0.719985i) q^{20} +(2.46834 + 0.697210i) q^{22} +(-6.87807 + 3.97105i) q^{23} +(-6.48777 + 1.45986i) q^{24} +(2.25691 + 1.30303i) q^{25} +(-2.90528 + 0.736612i) q^{26} +(-0.785033 - 0.785033i) q^{27} +(-4.18002 + 4.18002i) q^{29} +(-4.42022 - 2.63215i) q^{30} +(-4.73710 + 8.20490i) q^{31} +(5.07847 - 2.49182i) q^{32} +(2.13209 + 3.69289i) q^{33} +(-6.02552 + 3.37129i) q^{34} +(-4.30849 - 2.64499i) q^{36} +(-0.449796 + 1.67866i) q^{37} +(7.17263 + 7.36880i) q^{38} +(-4.31528 - 2.49143i) q^{39} +(4.17785 + 1.30275i) q^{40} -10.6111i q^{41} +(2.27704 + 2.27704i) q^{43} +(-2.49480 - 2.63318i) q^{44} +(-1.01227 - 3.77784i) q^{45} +(11.2308 + 0.151510i) q^{46} +(-0.930171 - 1.61110i) q^{47} +(8.93956 + 2.92045i) q^{48} +(-1.79953 - 3.21632i) q^{50} +(-11.0876 - 2.97092i) q^{51} +(4.06318 + 1.20710i) q^{52} +(-8.15297 + 2.18458i) q^{53} +(0.385868 + 1.52191i) q^{54} -2.80619i q^{55} +17.0959i q^{57} +(8.10363 - 2.05461i) q^{58} +(-3.73991 + 1.00211i) q^{59} +(3.46646 + 6.39662i) q^{60} +(5.17474 + 1.38657i) q^{61} +(11.6928 - 6.54214i) q^{62} +(-7.97381 - 0.646803i) q^{64} +(1.63957 + 2.83982i) q^{65} +(0.0813471 - 6.02991i) q^{66} +(0.173571 + 0.647776i) q^{67} +(9.76092 + 0.263409i) q^{68} +(13.2037 + 13.2037i) q^{69} -1.50161i q^{71} +(3.32141 + 6.33138i) q^{72} +(8.75126 + 5.05254i) q^{73} +(1.76116 - 1.71428i) q^{74} +(1.58583 - 5.91838i) q^{75} +(-3.38363 - 14.1437i) q^{76} +(3.44077 + 6.14970i) q^{78} +(3.90884 + 6.77031i) q^{79} +(-4.13386 - 4.60591i) q^{80} +(-5.09681 + 8.82794i) q^{81} +(-7.67778 + 12.8935i) q^{82} +(-8.73286 + 8.73286i) q^{83} +(5.34147 + 5.34147i) q^{85} +(-1.11924 - 4.41440i) q^{86} +(12.0365 + 6.94928i) q^{87} +(1.12614 + 5.00471i) q^{88} +(3.69289 - 2.13209i) q^{89} +(-1.50350 + 5.32288i) q^{90} +(-13.5369 - 8.31031i) q^{92} +(21.5160 + 5.76521i) q^{93} +(-0.0354895 + 2.63068i) q^{94} +(5.62528 - 9.74327i) q^{95} +(-8.74928 - 10.0170i) q^{96} -12.3413 q^{97} +(3.24180 - 3.24180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{4}+O(q^{10}) $ 40 * q + 8 * q^4	$ 40 q + 8 q^{4} - 4 q^{11} - 32 q^{15} - 16 q^{18} - 8 q^{29} - 8 q^{30} + 40 q^{32} + 80 q^{36} + 20 q^{37} + 120 q^{43} - 56 q^{44} + 64 q^{46} - 112 q^{50} + 16 q^{51} - 28 q^{53} + 72 q^{58} + 24 q^{60} - 64 q^{64} - 16 q^{65} - 12 q^{67} - 16 q^{72} + 16 q^{74} - 176 q^{78} + 72 q^{79} - 12 q^{81} + 64 q^{85} + 40 q^{86} - 80 q^{88} - 48 q^{92} - 48 q^{93} - 64 q^{95} - 216 q^{99}+O(q^{100}) $ 40 * q + 8 * q^4 - 4 * q^11 - 32 * q^15 - 16 * q^18 - 8 * q^29 - 8 * q^30 + 40 * q^32 + 80 * q^36 + 20 * q^37 + 120 * q^43 - 56 * q^44 + 64 * q^46 - 112 * q^50 + 16 * q^51 - 28 * q^53 + 72 * q^58 + 24 * q^60 - 64 * q^64 - 16 * q^65 - 12 * q^67 - 16 * q^72 + 16 * q^74 - 176 * q^78 + 72 * q^79 - 12 * q^81 + 64 * q^85 + 40 * q^86 - 80 * q^88 - 48 * q^92 - 48 * q^93 - 64 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.21510	−	0.723563i	−0.859202	−	0.511637i
$2$	−1.21510	−	0.723563i	−0.859202	−	0.511637i
$3$	−0.608516	−	2.27101i	−0.351327	−	1.31117i	−0.885044	−	0.465508i	$-0.845872\pi$
$3$	−0.608516	−	2.27101i	−0.351327	−	1.31117i	0.533717	−	0.845663i	$-0.320795\pi$
$4$	0.952912	+	1.75840i	0.476456	+	0.879198i
$5$	−0.400455	+	1.49452i	−0.179089	+	0.668369i	0.816730	+	0.577020i	$0.195784\pi$
$5$	−0.400455	+	1.49452i	−0.179089	+	0.668369i	−0.995819	+	0.0913488i	$0.970882\pi$
$6$	−0.903818	+	3.19980i	−0.368982	+	1.30631i
$7$		0			0
$7$		0			0
$8$	0.114433	−	2.82611i	0.0404583	−	0.999181i
$9$	−2.18914	+	1.26390i	−0.729713	+	0.421300i
$10$	1.56797	−	1.52623i	0.495835	−	0.482635i
$11$	−1.75187	+	0.469413i	−0.528210	+	0.141533i	−0.513062	−	0.858352i	$-0.671489\pi$
$11$	−1.75187	+	0.469413i	−0.528210	+	0.141533i	−0.0151484	+	0.999885i	$0.504822\pi$
$12$	3.41348	−	3.23409i	0.985387	−	0.933601i
$13$	1.49861	−	1.49861i	0.415638	−	0.415638i	−0.468059	−	0.883697i	$-0.655046\pi$
$13$	1.49861	−	1.49861i	0.415638	−	0.415638i	0.883697	+	0.468059i	$0.155046\pi$
$14$		0			0
$15$	3.63776			0.939264
$16$	−2.18392	+	3.35119i	−0.545980	+	0.837798i
$17$	2.44112	−	4.22814i	0.592058	−	1.02547i	−0.401897	−	0.915685i	$-0.631649\pi$
$17$	2.44112	−	4.22814i	0.592058	−	1.02547i	0.993955	−	0.109790i	$-0.0350178\pi$
$18$	3.57452	+	0.0482225i	0.842523	+	0.0113661i
$19$	−7.02361	−	1.88197i	−1.61133	−	0.431754i	−0.662890	−	0.748717i	$-0.730670\pi$
$19$	−7.02361	−	1.88197i	−1.61133	−	0.431754i	−0.948438	+	0.316963i	$0.897337\pi$
$20$	−3.00955	+	0.719985i	−0.672957	+	0.160994i
$21$		0			0
$22$	2.46834	+	0.697210i	0.526253	+	0.148646i
$23$	−6.87807	+	3.97105i	−1.43418	+	0.828022i	−0.997436	−	0.0715658i	$-0.977200\pi$
$23$	−6.87807	+	3.97105i	−1.43418	+	0.828022i	−0.436740	+	0.899588i	$0.643867\pi$
$24$	−6.48777	+	1.45986i	−1.32431	+	0.297992i
$25$	2.25691	+	1.30303i	0.451382	+	0.260605i
$26$	−2.90528	+	0.736612i	−0.569773	+	0.144461i
$27$	−0.785033	−	0.785033i	−0.151080	−	0.151080i
$28$		0			0
$29$	−4.18002	+	4.18002i	−0.776211	+	0.776211i	−0.979184	−	0.202974i	$-0.934939\pi$
$29$	−4.18002	+	4.18002i	−0.776211	+	0.776211i	0.202974	+	0.979184i	$0.434939\pi$
$30$	−4.42022	−	2.63215i	−0.807018	−	0.480562i
$31$	−4.73710	+	8.20490i	−0.850808	+	1.47364i	0.0296718	+	0.999560i	$0.490554\pi$
$31$	−4.73710	+	8.20490i	−0.850808	+	1.47364i	−0.880480	+	0.474083i	$0.842780\pi$
$32$	5.07847	−	2.49182i	0.897755	−	0.440495i
$33$	2.13209	+	3.69289i	0.371149	+	0.642849i
$34$	−6.02552	+	3.37129i	−1.03337	+	0.578171i
$35$		0			0
$36$	−4.30849	−	2.64499i	−0.718082	−	0.440831i
$37$	−0.449796	+	1.67866i	−0.0739461	+	0.275971i	−0.992992	−	0.118179i	$-0.962294\pi$
$37$	−0.449796	+	1.67866i	−0.0739461	+	0.275971i	0.919046	+	0.394150i	$0.128961\pi$
$38$	7.17263	+	7.36880i	1.16355	+	1.19538i
$39$	−4.31528	−	2.49143i	−0.690998	−	0.398948i
$40$	4.17785	+	1.30275i	0.660576	+	0.205983i
$41$		−	10.6111i		−	1.65717i	−0.559863	−	0.828585i	$-0.689146\pi$
$41$		−	10.6111i		−	1.65717i	0.559863	−	0.828585i	$-0.310854\pi$
$42$		0			0
$43$	2.27704	+	2.27704i	0.347245	+	0.347245i	0.859083	−	0.511837i	$-0.171035\pi$
$43$	2.27704	+	2.27704i	0.347245	+	0.347245i	−0.511837	+	0.859083i	$0.671035\pi$
$44$	−2.49480	−	2.63318i	−0.376105	−	0.396967i
$45$	−1.01227	−	3.77784i	−0.150900	−	0.563167i
$46$	11.2308	+	0.151510i	1.65589	+	0.0223390i
$47$	−0.930171	−	1.61110i	−0.135679	−	0.235004i	0.790177	−	0.612878i	$-0.209988\pi$
$47$	−0.930171	−	1.61110i	−0.135679	−	0.235004i	−0.925857	+	0.377875i	$0.876655\pi$
$48$	8.93956	+	2.92045i	1.29031	+	0.421531i
$49$		0			0
$50$	−1.79953	−	3.21632i	−0.254493	−	0.454856i
$51$	−11.0876	−	2.97092i	−1.55258	−	0.416012i
$52$	4.06318	+	1.20710i	0.563462	+	0.167395i
$53$	−8.15297	+	2.18458i	−1.11990	+	0.300075i	−0.770842	−	0.637027i	$-0.780164\pi$
$53$	−8.15297	+	2.18458i	−1.11990	+	0.300075i	−0.349055	+	0.937102i	$0.613497\pi$
$54$	0.385868	+	1.52191i	0.0525101	+	0.207106i
$55$		−	2.80619i		−	0.378386i
$56$		0			0
$57$			17.0959i			2.26441i
$58$	8.10363	−	2.05461i	1.06406	−	0.269784i
$59$	−3.73991	+	1.00211i	−0.486895	+	0.130463i	−0.493911	−	0.869512i	$-0.664433\pi$
$59$	−3.73991	+	1.00211i	−0.486895	+	0.130463i	0.00701626	+	0.999975i	$0.497767\pi$
$60$	3.46646	+	6.39662i	0.447518	+	0.825800i
$61$	5.17474	+	1.38657i	0.662558	+	0.177532i	0.574400	−	0.818575i	$-0.305235\pi$
$61$	5.17474	+	1.38657i	0.662558	+	0.177532i	0.0881577	+	0.996107i	$0.471902\pi$
$62$	11.6928	−	6.54214i	1.48499	−	0.830852i
$63$		0			0
$64$	−7.97381	−	0.646803i	−0.996726	−	0.0808503i
$65$	1.63957	+	2.83982i	0.203364	+	0.352236i
$66$	0.0813471	−	6.02991i	0.0100131	−	0.742230i
$67$	0.173571	+	0.647776i	0.0212051	+	0.0791384i	0.975718	−	0.219033i	$-0.0702901\pi$
$67$	0.173571	+	0.647776i	0.0212051	+	0.0791384i	−0.954512	+	0.298171i	$0.903623\pi$
$68$	9.76092	+	0.263409i	1.18369	+	0.0319431i
$69$	13.2037	+	13.2037i	1.58954	+	1.58954i
$70$		0			0
$71$		−	1.50161i		−	0.178208i	−0.996022	−	0.0891041i	$-0.971600\pi$
$71$		−	1.50161i		−	0.178208i	0.996022	−	0.0891041i	$-0.0284004\pi$
$72$	3.32141	+	6.33138i	0.391432	+	0.746160i
$73$	8.75126	+	5.05254i	1.02426	+	0.591355i	0.915334	−	0.402695i	$-0.131926\pi$
$73$	8.75126	+	5.05254i	1.02426	+	0.591355i	0.108923	+	0.994050i	$0.465260\pi$
$74$	1.76116	−	1.71428i	0.204731	−	0.199281i
$75$	1.58583	−	5.91838i	0.183115	−	0.683396i
$76$	−3.38363	−	14.1437i	−0.388129	−	1.62239i
$77$		0			0
$78$	3.44077	+	6.14970i	0.389590	+	0.696317i
$79$	3.90884	+	6.77031i	0.439779	+	0.761720i	0.997672	−	0.0681931i	$-0.0217234\pi$
$79$	3.90884	+	6.77031i	0.439779	+	0.761720i	−0.557893	+	0.829913i	$0.688390\pi$
$80$	−4.13386	−	4.60591i	−0.462179	−	0.514956i
$81$	−5.09681	+	8.82794i	−0.566313	+	0.980882i
$82$	−7.67778	+	12.8935i	−0.847869	+	1.42384i
$83$	−8.73286	+	8.73286i	−0.958556	+	0.958556i	−0.999175	−	0.0406187i	$-0.987067\pi$
$83$	−8.73286	+	8.73286i	−0.958556	+	0.958556i	0.0406187	+	0.999175i	$0.487067\pi$
$84$		0			0
$85$	5.34147	+	5.34147i	0.579364	+	0.579364i
$86$	−1.11924	−	4.41440i	−0.120690	−	0.476018i
$87$	12.0365	+	6.94928i	1.29045	+	0.745041i
$88$	1.12614	+	5.00471i	0.120047	+	0.533504i
$89$	3.69289	−	2.13209i	0.391445	−	0.226001i	−0.291341	−	0.956619i	$-0.594101\pi$
$89$	3.69289	−	2.13209i	0.391445	−	0.226001i	0.682786	+	0.730618i	$0.260768\pi$
$90$	−1.50350	+	5.32288i	−0.158483	+	0.561080i
$91$		0			0
$92$	−13.5369	−	8.31031i	−1.41132	−	0.866409i
$93$	21.5160	+	5.76521i	2.23111	+	0.597824i
$94$	−0.0354895	+	2.63068i	−0.00366046	+	0.271334i
$95$	5.62528	−	9.74327i	0.577142	−	0.999639i
$96$	−8.74928	−	10.0170i	−0.892970	−	1.02235i
$97$	−12.3413			−1.25307			−0.626535	−	0.779393i	$-0.715528\pi$
$97$	−12.3413			−1.25307			−0.626535	+	0.779393i	$0.715528\pi$
$98$		0			0
$99$	3.24180	−	3.24180i	0.325813	−	0.325813i
$100$	−0.140603	+	5.21021i	−0.0140603	+	0.521021i
$101$	−13.7062	+	3.67256i	−1.36382	+	0.365433i	−0.865216	−	0.501399i	$-0.832819\pi$
$101$	−13.7062	+	3.67256i	−1.36382	+	0.365433i	−0.498600	+	0.866832i	$0.666152\pi$
$102$	11.3229	+	11.6326i	1.12113	+	1.15179i
$103$	7.37016	−	4.25517i	0.726204	−	0.419274i	−0.0908279	−	0.995867i	$-0.528951\pi$
$103$	7.37016	−	4.25517i	0.726204	−	0.419274i	0.817032	+	0.576593i	$0.195618\pi$
$104$	−4.06374	−	4.40672i	−0.398482	−	0.432114i
$105$		0			0
$106$	11.4873	+	3.24472i	1.11575	+	0.315155i
$107$	1.09550	−	4.08845i	0.105906	−	0.395246i	−0.892541	−	0.450967i	$-0.851079\pi$
$107$	1.09550	−	4.08845i	0.105906	−	0.395246i	0.998446	+	0.0557213i	$0.0177458\pi$
$108$	0.632332	−	2.12847i	0.0608462	−	0.204812i
$109$	−1.54355	−	5.76060i	−0.147845	−	0.551765i	−0.999612	−	0.0278449i	$-0.991136\pi$
$109$	−1.54355	−	5.76060i	−0.147845	−	0.551765i	0.851767	−	0.523920i	$-0.175531\pi$
$110$	−2.03045	+	3.40978i	−0.193596	+	0.325110i
$111$	4.08598			0.387824
$112$		0			0
$113$	−12.4238			−1.16874			−0.584368	−	0.811489i	$-0.698657\pi$
$113$	−12.4238			−1.16874			−0.584368	+	0.811489i	$0.698657\pi$
$114$	12.3700	−	20.7732i	1.15856	−	1.94559i
$115$	−3.18046	−	11.8696i	−0.296579	−	1.10685i
$116$	−11.3333	−	3.36694i	−1.05227	−	0.312613i
$117$	−1.38657	+	5.17474i	−0.128188	+	0.478405i
$118$	5.26944	+	1.48841i	0.485091	+	0.137019i
$119$		0			0
$120$	0.416280	−	10.2807i	0.0380010	−	0.938495i
$121$	−6.67757	+	3.85529i	−0.607051	+	0.350481i
$122$	−5.28453	−	5.42907i	−0.478439	−	0.491525i
$123$	−24.0979	+	6.45701i	−2.17283	+	0.582209i
$124$	−18.9415	−	0.511157i	−1.70100	−	0.0459033i
$125$	−8.32150	+	8.32150i	−0.744298	+	0.744298i
$126$		0			0
$127$	18.3696			1.63004			0.815018	−	0.579436i	$-0.196727\pi$
$127$	18.3696			1.63004			0.815018	+	0.579436i	$0.196727\pi$
$128$	9.22093	+	6.55548i	0.815023	+	0.579428i
$129$	3.78558	−	6.55681i	0.333301	−	0.577295i
$130$	0.0625556	−	4.63698i	0.00548649	−	0.406690i
$131$	−1.16578	−	0.312371i	−0.101855	−	0.0272920i	0.207532	−	0.978228i	$-0.433457\pi$
$131$	−1.16578	−	0.312371i	−0.101855	−	0.0272920i	−0.309387	+	0.950936i	$0.600124\pi$
$132$	−4.46187	+	7.26805i	−0.388356	+	0.632603i
$133$		0			0
$134$	0.257802	−	0.912699i	0.0222707	−	0.0788452i
$135$	1.48762	−	0.858876i	0.128034	−	0.0739202i
$136$	−11.6699	−	7.38271i	−1.00068	−	0.633062i
$137$	6.76016	+	3.90298i	0.577560	+	0.333454i	0.760163	−	0.649733i	$-0.225119\pi$
$137$	6.76016	+	3.90298i	0.577560	+	0.333454i	−0.182603	+	0.983187i	$0.558452\pi$
$138$	−6.49005	−	25.5975i	−0.552470	−	2.17901i
$139$	0.0436953	+	0.0436953i	0.00370618	+	0.00370618i	0.708957	−	0.705251i	$-0.249166\pi$
$139$	0.0436953	+	0.0436953i	0.00370618	+	0.00370618i	−0.705251	+	0.708957i	$0.749166\pi$
$140$		0			0
$141$	−3.09281	+	3.09281i	−0.260462	+	0.260462i
$142$	−1.08651	+	1.82460i	−0.0911779	+	0.153117i
$143$	−1.92190	+	3.32883i	−0.160718	+	0.278371i
$144$	0.545327	−	10.0965i	0.0454439	−	0.841373i
$145$	−4.57321	−	7.92103i	−0.379784	−	0.657805i
$146$	−6.97778	−	12.4714i	−0.577485	−	1.03214i
$147$		0			0
$148$	−3.38037	+	0.808697i	−0.277865	+	0.0664745i
$149$	5.90459	−	22.0362i	0.483723	−	1.80528i	−0.102020	−	0.994782i	$-0.532530\pi$
$149$	5.90459	−	22.0362i	0.483723	−	1.80528i	0.585743	−	0.810497i	$-0.300803\pi$
$150$	−6.20925	+	6.04395i	−0.506984	+	0.493487i
$151$	−7.18049	−	4.14566i	−0.584340	−	0.337369i	0.178516	−	0.983937i	$-0.442870\pi$
$151$	−7.18049	−	4.14566i	−0.584340	−	0.337369i	−0.762856	+	0.646568i	$0.776204\pi$
$152$	−6.12240	+	19.6342i	−0.496592	+	1.59254i
$153$			12.3413i			0.997736i
$154$		0			0
$155$	−10.3654	−	10.3654i	−0.832567	−	0.832567i
$156$	0.268838	−	9.96209i	0.0215243	−	0.797605i
$157$	−0.0985155	−	0.367665i	−0.00786239	−	0.0293428i	0.961883	−	0.273461i	$-0.0881683\pi$
$157$	−0.0985155	−	0.367665i	−0.00786239	−	0.0293428i	−0.969746	+	0.244118i	$0.921502\pi$
$158$	0.149137	−	11.0549i	0.0118647	−	0.879478i
$159$	9.92244	+	17.1862i	0.786900	+	1.36295i
$160$	1.69036	+	8.58772i	0.133635	+	0.678919i
$161$		0			0
$162$	12.5807	−	7.03892i	0.988432	−	0.553030i
$163$	−19.3374	−	5.18143i	−1.51462	−	0.405841i	−0.596653	−	0.802500i	$-0.703503\pi$
$163$	−19.3374	−	5.18143i	−1.51462	−	0.405841i	−0.917966	+	0.396659i	$0.870170\pi$
$164$	18.6585	−	10.1114i	1.45698	−	0.789569i
$165$	−6.37289	+	1.70761i	−0.496129	+	0.132937i
$166$	16.9300	−	4.29248i	1.31403	−	0.333161i
$167$			0.242171i			0.0187397i	0.999956	+	0.00936987i	$0.00298256\pi$
$167$			0.242171i			0.0187397i	−0.999956	+	0.00936987i	$0.997017\pi$
$168$		0			0
$169$			8.50836i			0.654489i
$170$	−2.62550	−	10.3553i	−0.201367	−	0.794215i
$171$	17.7543	−	4.75725i	1.35770	−	0.363796i
$172$	−1.83412	+	6.17376i	−0.139851	+	0.470745i
$173$	−7.45806	−	1.99838i	−0.567026	−	0.151934i	−0.0360938	−	0.999348i	$-0.511492\pi$
$173$	−7.45806	−	1.99838i	−0.567026	−	0.151934i	−0.530932	+	0.847414i	$0.678158\pi$
$174$	−9.59725	−	17.1532i	−0.727566	−	1.30038i
$175$		0			0
$176$	2.25286	−	6.89603i	0.169815	−	0.519808i
$177$	4.55160	+	7.88360i	0.342119	+	0.592568i
$178$	−6.02991	−	0.0813471i	−0.451961	−	0.00609722i
$179$	−2.37369	−	8.85874i	−0.177418	−	0.662133i	−0.996127	−	0.0879245i	$-0.971977\pi$
$179$	−2.37369	−	8.85874i	−0.177418	−	0.662133i	0.818709	−	0.574208i	$-0.194690\pi$
$180$	5.67834	−	5.37992i	0.423238	−	0.400996i
$181$	−9.82011	−	9.82011i	−0.729923	−	0.729923i	0.240681	−	0.970604i	$-0.422629\pi$
$181$	−9.82011	−	9.82011i	−0.729923	−	0.729923i	−0.970604	+	0.240681i	$0.922629\pi$
$182$		0			0
$183$		−	12.5957i		−	0.931098i
$184$	10.4356	+	19.8926i	0.769320	+	1.46650i
$185$	−2.32867	−	1.34446i	−0.171207	−	0.0988465i
$186$	−21.9725	−	22.5735i	−1.61111	−	1.65517i
$187$	−2.29179	+	8.55306i	−0.167592	+	0.625462i
$188$	1.94659	−	3.17085i	0.141969	−	0.231258i
$189$		0			0
$190$	−13.8851	+	7.76875i	−1.00733	+	0.563605i
$191$	3.22457	+	5.58512i	0.233322	+	0.404125i	0.958784	−	0.284137i	$-0.0917072\pi$
$191$	3.22457	+	5.58512i	0.233322	+	0.404125i	−0.725462	+	0.688262i	$0.758374\pi$
$192$	3.38330	+	18.5022i	0.244168	+	1.33528i
$193$	3.97562	−	6.88598i	0.286172	−	0.495664i	−0.686721	−	0.726921i	$-0.740951\pi$
$193$	3.97562	−	6.88598i	0.286172	−	0.495664i	0.972893	+	0.231257i	$0.0742839\pi$
$194$	14.9959	+	8.92972i	1.07664	+	0.641117i
$195$	5.45156	−	5.45156i	0.390394	−	0.390394i
$196$		0			0
$197$	−9.02399	−	9.02399i	−0.642933	−	0.642933i	0.308343	−	0.951275i	$-0.400226\pi$
$197$	−9.02399	−	9.02399i	−0.642933	−	0.642933i	−0.951275	+	0.308343i	$0.900226\pi$
$198$	−6.28475	+	1.59345i	−0.446638	+	0.113241i
$199$	−3.84721	−	2.22119i	−0.272722	−	0.157456i	0.357402	−	0.933951i	$-0.383663\pi$
$199$	−3.84721	−	2.22119i	−0.272722	−	0.157456i	−0.630124	+	0.776495i	$0.716996\pi$
$200$	3.94076	−	6.22916i	0.278654	−	0.440468i
$201$	1.36549	−	0.788365i	0.0963141	−	0.0556070i
$202$	19.3116	+	5.45478i	1.35876	+	0.383797i
$203$		0			0
$204$	−5.34147	−	22.3275i	−0.373978	−	1.56324i
$205$	15.8584	+	4.24925i	1.10760	+	0.296781i
$206$	−12.0343	−	0.162350i	−0.838472	−	0.0113115i
$207$	10.0380	−	17.3864i	0.697691	−	1.20844i
$208$	1.74929	+	8.29495i	0.121291	+	0.575151i
$209$	13.1879			0.912227
$210$		0			0
$211$	18.1613	−	18.1613i	1.25027	−	1.25027i	0.294675	−	0.955598i	$-0.404789\pi$
$211$	18.1613	−	18.1613i	1.25027	−	1.25027i	0.955598	−	0.294675i	$-0.0952113\pi$
$212$	−11.6104	−	12.2544i	−0.797407	−	0.841639i
$213$	−3.41018	+	0.913754i	−0.233661	+	0.0626094i
$214$	−4.28939	+	4.17520i	−0.293217	+	0.285411i
$215$	−4.31493	+	2.49123i	−0.294276	+	0.169900i
$216$	−2.30842	+	2.12876i	−0.157068	+	0.144844i
$217$		0			0
$218$	−2.29260	+	8.11653i	−0.155275	+	0.549721i
$219$	6.14911	−	22.9488i	0.415518	−	1.55074i
$220$	4.93439	−	2.67405i	0.332676	−	0.180284i
$221$	−2.67804	−	9.99459i	−0.180145	−	0.672309i
$222$	−4.96485	−	2.95646i	−0.333219	−	0.198425i
$223$	14.6202			0.979044			0.489522	−	0.871991i	$-0.337171\pi$
$223$	14.6202			0.979044			0.489522	+	0.871991i	$0.337171\pi$
$224$		0			0
$225$	−6.58758			−0.439172
$226$	15.0961	+	8.98943i	1.00418	+	0.597968i
$227$	−1.57679	−	5.88466i	−0.104655	−	0.390579i	0.893651	−	0.448763i	$-0.148135\pi$
$227$	−1.57679	−	5.88466i	−0.104655	−	0.390579i	−0.998306	+	0.0581847i	$0.981469\pi$
$228$	−30.0614	+	16.2909i	−1.99087	+	1.07889i
$229$	0.702394	−	2.62137i	0.0464155	−	0.173225i	−0.938827	−	0.344389i	$-0.888086\pi$
$229$	0.702394	−	2.62137i	0.0464155	−	0.173225i	0.985243	+	0.171164i	$0.0547528\pi$
$230$	−4.72387	+	16.7240i	−0.311483	+	1.10275i
$231$		0			0
$232$	11.3349	+	12.2915i	0.744171	+	0.806979i
$233$	0.544147	−	0.314164i	0.0356483	−	0.0205815i	−0.482070	−	0.876133i	$-0.660115\pi$
$233$	0.544147	−	0.314164i	0.0356483	−	0.0205815i	0.517718	+	0.855551i	$0.326782\pi$
$234$	5.42907	−	5.28453i	0.354909	−	0.345461i
$235$	2.78031	−	0.744983i	0.181368	−	0.0485973i
$236$	−5.32591	−	5.62133i	−0.346687	−	0.365918i
$237$	12.9969	−	12.9969i	0.844238	−	0.844238i
$238$		0			0
$239$	5.13936			0.332438			0.166219	−	0.986089i	$-0.446844\pi$
$239$	5.13936			0.332438			0.166219	+	0.986089i	$0.446844\pi$
$240$	−7.94456	+	12.1908i	−0.512819	+	0.786914i
$241$	−11.2792	+	19.5362i	−0.726559	+	1.25844i	0.231769	+	0.972771i	$0.425549\pi$
$241$	−11.2792	+	19.5362i	−0.726559	+	1.25844i	−0.958329	+	0.285667i	$0.907785\pi$
$242$	10.9034	+	0.147094i	0.700899	+	0.00945554i
$243$	19.9328	+	5.34097i	1.27869	+	0.342623i
$244$	2.49294	+	10.4205i	0.159594	+	0.667106i
$245$		0			0
$246$	33.9533	+	9.59047i	2.16478	+	0.611466i
$247$	−13.3460	+	7.70529i	−0.849183	+	0.490276i
$248$	22.6459	+	14.3265i	1.43801	+	0.909733i
$249$	25.1465	+	14.5184i	1.59360	+	0.920064i
$250$	16.1325	−	4.09028i	1.02031	−	0.258692i
$251$	−1.77457	−	1.77457i	−0.112010	−	0.112010i	0.648880	−	0.760890i	$-0.275238\pi$
$251$	−1.77457	−	1.77457i	−0.112010	−	0.112010i	−0.760890	+	0.648880i	$0.775238\pi$
$252$		0			0
$253$	10.1854	−	10.1854i	0.640353	−	0.640353i
$254$	−22.3208	−	13.2915i	−1.40053	−	0.833986i
$255$	8.88019	−	15.3809i	0.556099	−	0.963192i
$256$	−6.46100	−	14.6375i	−0.403813	−	0.914842i
$257$	−10.1818	−	17.6355i	−0.635126	−	1.10007i	−0.986488	−	0.163831i	$-0.947615\pi$
$257$	−10.1818	−	17.6355i	−0.635126	−	1.10007i	0.351363	−	0.936239i	$-0.385718\pi$
$258$	−9.34410	+	5.22804i	−0.581738	+	0.325484i
$259$		0			0
$260$	−3.43116	+	5.58911i	−0.212792	+	0.346622i
$261$	3.86752	−	14.4338i	0.239393	−	0.893428i
$262$	1.19052	+	1.22308i	0.0735504	+	0.0755620i
$263$	9.97007	+	5.75622i	0.614781	+	0.354944i	0.774834	−	0.632164i	$-0.217833\pi$
$263$	9.97007	+	5.75622i	0.614781	+	0.354944i	−0.160053	+	0.987108i	$0.551167\pi$
$264$	10.6805	−	5.60293i	0.657339	−	0.344837i
$265$		−	13.0596i		−	0.802244i
$266$		0			0
$267$	−7.08919	−	7.08919i	−0.433851	−	0.433851i
$268$	−0.973649	+	0.922480i	−0.0594751	+	0.0563494i
$269$	7.44120	+	27.7709i	0.453698	+	1.69322i	0.691888	+	0.722005i	$0.256779\pi$
$269$	7.44120	+	27.7709i	0.453698	+	1.69322i	−0.238190	+	0.971219i	$0.576554\pi$
$270$	−2.42905	−	0.0327693i	−0.147827	−	0.00199428i
$271$	−8.05308	−	13.9484i	−0.489190	−	0.847302i	0.510733	−	0.859740i	$-0.329374\pi$
$271$	−8.05308	−	13.9484i	−0.489190	−	0.847302i	−0.999923	+	0.0124376i	$0.996041\pi$
$272$	8.83812	+	17.4146i	0.535890	+	1.05591i
$273$		0			0
$274$	−5.39018	−	9.63390i	−0.325633	−	0.582005i
$275$	−4.56548	−	1.22332i	−0.275309	−	0.0737687i
$276$	−10.6354	+	35.7994i	−0.640177	+	2.15487i
$277$	−5.15211	+	1.38050i	−0.309560	+	0.0829464i	−0.410255	−	0.911971i	$-0.634560\pi$
$277$	−5.15211	+	1.38050i	−0.309560	+	0.0829464i	0.100694	+	0.994917i	$0.467894\pi$
$278$	−0.0214776	−	0.0847102i	−0.00128814	−	0.00508058i
$279$		−	23.9489i		−	1.43378i
$280$		0			0
$281$			1.98190i			0.118231i	0.998251	+	0.0591153i	$0.0188279\pi$
$281$			1.98190i			0.118231i	−0.998251	+	0.0591153i	$0.981172\pi$
$282$	5.99591	−	1.52022i	0.357051	−	0.0905275i
$283$	−15.2130	+	4.07631i	−0.904320	+	0.242312i	−0.680870	−	0.732404i	$-0.738398\pi$
$283$	−15.2130	+	4.07631i	−0.904320	+	0.242312i	−0.223449	+	0.974716i	$0.571732\pi$
$284$	2.64042	−	1.43090i	0.156680	−	0.0849084i
$285$	−25.5502	−	6.84615i	−1.51346	−	0.405531i
$286$	4.74392	−	2.65423i	0.280514	−	0.156948i
$287$		0			0
$288$	−7.96807	+	11.8736i	−0.469523	+	0.699659i
$289$	−3.41812	−	5.92036i	−0.201066	−	0.348256i
$290$	−0.174485	+	12.9338i	−0.0102461	+	0.759499i
$291$	7.50989	+	28.0273i	0.440238	+	1.64299i
$292$	−0.545195	+	20.2028i	−0.0319051	+	1.18228i
$293$	−11.6089	−	11.6089i	−0.678198	−	0.678198i	0.281394	−	0.959592i	$-0.409203\pi$
$293$	−11.6089	−	11.6089i	−0.678198	−	0.678198i	−0.959592	+	0.281394i	$0.909203\pi$
$294$		0			0
$295$		−	5.99066i		−	0.348790i
$296$	4.69262	+	1.46327i	0.272753	+	0.0850508i
$297$	1.74378	+	1.00677i	0.101185	+	0.0584190i
$298$	−23.1193	+	22.5038i	−1.33926	+	1.30361i
$299$	−4.35647	+	16.2586i	−0.251941	+	0.940256i
$300$	11.9180	−	2.85119i	0.688087	−	0.164613i
$301$		0			0
$302$	5.72533	+	10.2329i	0.329456	+	0.588837i
$303$	16.6809	+	28.8921i	0.958291	+	1.65981i
$304$	21.6459	−	19.4274i	1.24147	−	1.11424i
$305$	−4.14450	+	7.17849i	−0.237313	+	0.411039i
$306$	8.92972	−	14.9959i	0.510478	−	0.857257i
$307$	−0.828728	+	0.828728i	−0.0472980	+	0.0472980i	−0.730360	−	0.683062i	$-0.760648\pi$
$307$	−0.828728	+	0.828728i	−0.0472980	+	0.0472980i	0.683062	+	0.730360i	$0.260648\pi$
$308$		0			0
$309$	−14.1484	−	14.1484i	−0.804875	−	0.804875i
$310$	5.09491	+	20.0949i	0.289371	+	1.14131i
$311$	−26.0005	−	15.0114i	−1.47435	−	0.851217i	−0.474768	−	0.880111i	$-0.657468\pi$
$311$	−26.0005	−	15.0114i	−1.47435	−	0.851217i	−0.999582	+	0.0288939i	$0.990802\pi$
$312$	−7.53487	+	11.9104i	−0.426578	+	0.674292i
$313$	−9.71444	+	5.60863i	−0.549093	+	0.317019i	−0.748756	−	0.662846i	$-0.769348\pi$
$313$	−9.71444	+	5.60863i	−0.549093	+	0.317019i	0.199663	+	0.979865i	$0.436015\pi$
$314$	−0.146323	+	0.518030i	−0.00825749	+	0.0292341i
$315$		0			0
$316$	−8.18011	+	13.3248i	−0.460167	+	0.749579i
$317$	15.5922	+	4.17793i	0.875747	+	0.234656i	0.668571	−	0.743648i	$-0.266906\pi$
$317$	15.5922	+	4.17793i	0.875747	+	0.234656i	0.207176	+	0.978304i	$0.433573\pi$
$318$	0.378578	−	28.0623i	0.0212296	−	1.57366i
$319$	5.36071	−	9.28503i	0.300142	−	0.519862i
$320$	4.15981	−	11.6580i	0.232540	−	0.651701i
$321$	−9.95157			−0.555442
$322$		0			0
$323$	−25.1027	+	25.1027i	−1.39675	+	1.39675i
$324$	−20.3798	−	0.549973i	−1.13221	−	0.0305540i
$325$	5.33494	−	1.42949i	0.295929	−	0.0792939i
$326$	19.7476	+	20.2877i	1.09372	+	1.12363i
$327$	−12.1431	+	7.01084i	−0.671517	+	0.387700i
$328$	−29.9881	−	1.21426i	−1.65581	−	0.0670463i
$329$		0			0
$330$	8.97923	+	2.53628i	0.494290	+	0.139618i
$331$	5.60899	−	20.9330i	0.308298	−	1.15058i	−0.621771	−	0.783199i	$-0.713587\pi$
$331$	5.60899	−	20.9330i	0.308298	−	1.15058i	0.930069	−	0.367385i	$-0.119747\pi$
$332$	−23.6775	−	7.03419i	−1.29947	−	0.386051i
$333$	−1.13699	−	4.24332i	−0.0623069	−	0.232533i
$334$	0.175226	−	0.294260i	0.00958793	−	0.0161012i
$335$	−1.03762			−0.0566912
$336$		0			0
$337$	15.1140			0.823314			0.411657	−	0.911339i	$-0.364950\pi$
$337$	15.1140			0.823314			0.411657	+	0.911339i	$0.364950\pi$
$338$	6.15634	−	10.3385i	0.334861	−	0.562339i
$339$	7.56010	+	28.2147i	0.410609	+	1.53241i
$340$	−4.30248	+	14.4824i	−0.233335	+	0.785418i
$341$	4.44731	−	16.5976i	0.240836	−	0.898811i
$342$	−25.0153	−	7.06585i	−1.35267	−	0.382077i
$343$		0			0
$344$	6.69574	−	6.17460i	0.361010	−	0.332912i
$345$	−25.0207	+	14.4457i	−1.34707	+	0.777731i
$346$	7.61630	+	7.82461i	0.409455	+	0.420654i
$347$	17.9787	−	4.81739i	0.965149	−	0.258611i	0.258371	−	0.966046i	$-0.416814\pi$
$347$	17.9787	−	4.81739i	0.965149	−	0.258611i	0.706778	+	0.707435i	$0.250148\pi$
$348$	−0.749863	+	27.7870i	−0.0401969	+	1.48954i
$349$	−11.3593	+	11.3593i	−0.608051	+	0.608051i	−0.942436	−	0.334386i	$-0.891471\pi$
$349$	−11.3593	+	11.3593i	−0.608051	+	0.608051i	0.334386	+	0.942436i	$0.391471\pi$
$350$		0			0
$351$	−2.35291			−0.125589
$352$	−7.72715	+	6.74925i	−0.411858	+	0.359736i
$353$	6.46116	−	11.1911i	0.343893	−	0.595640i	−0.641259	−	0.767324i	$-0.721588\pi$
$353$	6.46116	−	11.1911i	0.343893	−	0.595640i	0.985152	+	0.171685i	$0.0549210\pi$
$354$	0.173660	−	12.8727i	0.00922994	−	0.684176i
$355$	2.24418	+	0.601327i	0.119109	+	0.0319151i
$356$	7.26805	+	4.46187i	0.385206	+	0.236478i
$357$		0			0
$358$	−3.52560	+	12.4817i	−0.186334	+	0.659679i
$359$	9.86513	−	5.69564i	0.520662	−	0.300604i	−0.216544	−	0.976273i	$-0.569478\pi$
$359$	9.86513	−	5.69564i	0.520662	−	0.300604i	0.737205	+	0.675669i	$0.236145\pi$
$360$	−10.7924	+	2.42848i	−0.568811	+	0.127992i
$361$	29.3348	+	16.9365i	1.54394	+	0.891394i
$362$	4.82689	+	19.0378i	0.253696	+	1.00061i
$363$	12.8188	+	12.8188i	0.672814	+	0.672814i
$364$		0			0
$365$	−11.0556	+	11.0556i	−0.578676	+	0.578676i
$366$	−9.11376	+	15.3049i	−0.476384	+	0.800001i
$367$	13.4301	−	23.2616i	0.701044	−	1.21424i	−0.267056	−	0.963681i	$-0.586051\pi$
$367$	13.4301	−	23.2616i	0.701044	−	1.21424i	0.968100	−	0.250564i	$-0.0806159\pi$
$368$	1.71336	−	31.7222i	0.0893153	−	1.65363i
$369$	13.4113	+	23.2291i	0.698166	+	1.20926i
$370$	1.85675	+	3.31858i	0.0965280	+	0.172525i
$371$		0			0
$372$	10.3654	+	43.3275i	0.537419	+	2.24642i
$373$	−3.30994	+	12.3529i	−0.171382	+	0.639607i	0.825757	+	0.564025i	$0.190748\pi$
$373$	−3.30994	+	12.3529i	−0.171382	+	0.639607i	−0.997140	+	0.0755816i	$0.975919\pi$
$374$	8.97342	−	8.73453i	0.464005	−	0.451652i
$375$	23.9620	+	13.8345i	1.23739	+	0.714409i
$376$	−4.65960	+	2.44440i	−0.240300	+	0.126060i
$377$			12.5284i			0.645246i
$378$		0			0
$379$	−13.0659	−	13.0659i	−0.671149	−	0.671149i	0.286832	−	0.957981i	$-0.407398\pi$
$379$	−13.0659	−	13.0659i	−0.671149	−	0.671149i	−0.957981	+	0.286832i	$0.907398\pi$
$380$	22.4929	+	0.606997i	1.15386	+	0.0311383i
$381$	−11.1782	−	41.7175i	−0.572676	−	2.13725i
$382$	0.123029	−	9.11963i	0.00629472	−	0.466601i
$383$	−7.95002	−	13.7698i	−0.406227	−	0.703606i	0.588236	−	0.808689i	$-0.299822\pi$
$383$	−7.95002	−	13.7698i	−0.406227	−	0.703606i	−0.994463	+	0.105083i	$0.966489\pi$
$384$	9.27651	−	24.9300i	0.473390	−	1.27220i
$385$		0			0
$386$	−9.81321	+	5.49051i	−0.499479	+	0.279459i
$387$	−7.86271	−	2.10681i	−0.399684	−	0.107095i
$388$	−11.7602	−	21.7009i	−0.597033	−	1.10170i
$389$	18.7561	−	5.02567i	0.950970	−	0.254812i	0.250196	−	0.968195i	$-0.419505\pi$
$389$	18.7561	−	5.02567i	0.950970	−	0.254812i	0.700774	+	0.713384i	$0.252838\pi$
$390$	−10.5687	+	2.67961i	−0.535168	+	0.135688i
$391$			38.7752i			1.96095i
$392$		0			0
$393$			2.83759i			0.143138i
$394$	4.43557	+	17.4944i	0.223461	+	0.881357i
$395$	−11.6837	+	3.13063i	−0.587869	+	0.157519i
$396$	8.78953	+	2.61122i	0.441690	+	0.131219i
$397$	34.5788	+	9.26535i	1.73546	+	0.465015i	0.981429	−	0.191826i	$-0.0614409\pi$
$397$	34.5788	+	9.26535i	1.73546	+	0.465015i	0.754029	+	0.656841i	$0.228108\pi$
$398$	3.06756	+	5.48266i	0.153763	+	0.274821i
$399$		0			0
$400$	−9.29560	+	4.71763i	−0.464780	+	0.235882i
$401$	−13.1203	−	22.7251i	−0.655197	−	1.13483i	−0.981844	−	0.189689i	$-0.939252\pi$
$401$	−13.1203	−	22.7251i	−0.655197	−	1.13483i	0.326647	−	0.945146i	$-0.394081\pi$
$402$	−2.22963	−	0.0300790i	−0.111204	−	0.00150021i
$403$	5.19686	+	19.3949i	0.258874	+	0.966131i
$404$	−19.5186	−	20.6013i	−0.971087	−	1.02495i
$405$	−11.1525	−	11.1525i	−0.554171	−	0.554171i
$406$		0			0
$407$		−	3.15195i		−	0.156236i
$408$	−9.66495	+	30.9949i	−0.478486	+	1.53448i
$409$	−21.9760	−	12.6879i	−1.08664	−	0.627374i	−0.153963	−	0.988077i	$-0.549204\pi$
$409$	−21.9760	−	12.6879i	−1.08664	−	0.627374i	−0.932681	+	0.360703i	$0.882537\pi$
$410$	−16.1949	−	16.6378i	−0.799809	−	0.821684i
$411$	4.75006	−	17.7275i	0.234303	−	0.874431i
$412$	14.5054	+	8.90488i	0.714629	+	0.438712i
$413$		0			0
$414$	−24.7773	+	13.8629i	−1.21774	+	0.681326i
$415$	−9.55430	−	16.5485i	−0.469002	−	0.812336i
$416$	3.87637	−	11.3449i	0.190055	−	0.556228i
$417$	0.0726433	−	0.125822i	0.00355736	−	0.00616152i
$418$	−16.0246	−	9.54229i	−0.783787	−	0.466729i
$419$	12.8188	−	12.8188i	0.626241	−	0.626241i	−0.320879	−	0.947120i	$-0.603978\pi$
$419$	12.8188	−	12.8188i	0.626241	−	0.626241i	0.947120	+	0.320879i	$0.103978\pi$
$420$		0			0
$421$	5.55169	+	5.55169i	0.270573	+	0.270573i	0.829331	−	0.558758i	$-0.188722\pi$
$421$	5.55169	+	5.55169i	0.270573	+	0.270573i	−0.558758	+	0.829331i	$0.688722\pi$
$422$	−35.2085	+	8.92683i	−1.71392	+	0.434551i
$423$	4.07254	+	2.35128i	0.198014	+	0.114323i
$424$	5.24090	+	23.2912i	0.254521	+	1.13112i
$425$	11.0188	−	6.36168i	0.534488	−	0.308587i
$426$	4.80485	+	1.35718i	0.232796	+	0.0657556i
$427$		0			0
$428$	8.23304	−	1.96962i	0.397959	−	0.0952050i
$429$	8.72934	+	2.33902i	0.421456	+	0.112929i
$430$	7.04561	+	0.0950495i	0.339770	+	0.00458369i
$431$	13.7035	−	23.7352i	0.660076	−	1.14329i	−0.320519	−	0.947242i	$-0.603857\pi$
$431$	13.7035	−	23.7352i	0.660076	−	1.14329i	0.980595	−	0.196043i	$-0.0628093\pi$
$432$	4.34525	−	0.916350i	0.209061	−	0.0440879i
$433$	32.7756			1.57510			0.787548	−	0.616253i	$-0.211350\pi$
$433$	32.7756			1.57510			0.787548	+	0.616253i	$0.211350\pi$
$434$		0			0
$435$	−15.2059	+	15.2059i	−0.729067	+	0.729067i
$436$	8.65855	−	8.20351i	0.414670	−	0.392877i
$437$	55.7823	−	14.9468i	2.66843	−	0.715003i
$438$	−24.0767	+	23.4357i	−1.15043	+	1.11980i
$439$	−11.1535	+	6.43948i	−0.532328	+	0.307340i	−0.741964	−	0.670440i	$-0.766105\pi$
$439$	−11.1535	+	6.43948i	−0.532328	+	0.307340i	0.209636	+	0.977779i	$0.432772\pi$
$440$	−7.93059	−	0.321121i	−0.378076	−	0.0153089i
$441$		0			0
$442$	−3.97764	+	14.0821i	−0.189197	+	0.669818i
$443$	−1.95738	+	7.30506i	−0.0929981	+	0.347074i	−0.996708	−	0.0810709i	$-0.974166\pi$
$443$	−1.95738	+	7.30506i	−0.0929981	+	0.347074i	0.903710	+	0.428145i	$0.140833\pi$
$444$	3.89358	+	7.18477i	0.184781	+	0.340974i
$445$	1.70761	+	6.37289i	0.0809485	+	0.302104i
$446$	−17.7650	−	10.5787i	−0.841197	−	0.500915i
$447$	−53.6377			−2.53697
$448$		0			0
$449$	−15.8168			−0.746441			−0.373220	−	0.927743i	$-0.621747\pi$
$449$	−15.8168			−0.746441			−0.373220	+	0.927743i	$0.621747\pi$
$450$	8.00453	+	4.76653i	0.377337	+	0.224696i
$451$	4.98098	+	18.5893i	0.234545	+	0.875334i
$452$	−11.8388	−	21.8460i	−0.556851	−	1.02755i
$453$	−5.04540	+	18.8297i	−0.237054	+	0.884696i
$454$	−2.34198	+	8.29133i	−0.109914	+	0.389132i
$455$		0			0
$456$	48.3150	+	1.95635i	2.26256	+	0.0916143i
$457$	−23.4823	+	13.5575i	−1.09845	+	0.634193i	−0.935814	−	0.352493i	$-0.885334\pi$
$457$	−23.4823	+	13.5575i	−1.09845	+	0.634193i	−0.162639	+	0.986686i	$0.552001\pi$
$458$	−2.75020	+	2.67699i	−0.128509	+	0.125087i
$459$	−5.23559	+	1.40287i	−0.244376	+	0.0654805i
$460$	17.8408	−	16.9032i	0.831832	−	0.788116i
$461$	6.31691	−	6.31691i	0.294208	−	0.294208i	−0.544532	−	0.838740i	$-0.683293\pi$
$461$	6.31691	−	6.31691i	0.294208	−	0.294208i	0.838740	+	0.544532i	$0.183293\pi$
$462$		0			0
$463$	2.89508			0.134546			0.0672730	−	0.997735i	$-0.478570\pi$
$463$	2.89508			0.134546			0.0672730	+	0.997735i	$0.478570\pi$
$464$	−4.87924	−	23.1369i	−0.226513	−	1.07410i
$465$	−17.2324	+	29.8474i	−0.799134	+	1.38414i
$466$	−0.888508	−	0.0119865i	−0.0411593	−	0.000555264i
$467$	1.31802	+	0.353162i	0.0609906	+	0.0163424i	0.289185	−	0.957273i	$-0.406616\pi$
$467$	1.31802	+	0.353162i	0.0609906	+	0.0163424i	−0.228195	+	0.973616i	$0.573282\pi$
$468$	−10.4205	+	2.49294i	−0.481689	+	0.115236i
$469$		0			0
$470$	−3.91739	−	1.10651i	−0.180696	−	0.0510394i
$471$	−0.775024	+	0.447460i	−0.0357112	+	0.0206179i
$472$	2.40409	+	10.6841i	0.110657	+	0.491775i
$473$	−5.05796	−	2.92022i	−0.232565	−	0.134272i
$474$	−25.1965	+	6.38838i	−1.15731	+	0.293428i
$475$	−13.3994	−	13.3994i	−0.614806	−	0.614806i
$476$		0			0
$477$	15.0869	−	15.0869i	0.690781	−	0.690781i
$478$	−6.24482	−	3.71866i	−0.285631	−	0.170087i
$479$	−6.00343	+	10.3983i	−0.274304	+	0.475108i	−0.969959	−	0.243267i	$-0.921781\pi$
$479$	−6.00343	+	10.3983i	−0.274304	+	0.475108i	0.695655	+	0.718376i	$0.255114\pi$
$480$	18.4742	−	9.06461i	0.843229	−	0.413741i
$481$	1.84159	+	3.18972i	0.0839691	+	0.145439i
$482$	27.8410	−	15.5771i	1.26812	−	0.709518i
$483$		0			0
$484$	−13.1423	−	8.06805i	−0.597376	−	0.366730i
$485$	4.94214	−	18.4443i	0.224411	−	0.837513i
$486$	−20.3557	−	20.9124i	−0.923352	−	0.948605i
$487$	−13.8361	−	7.98829i	−0.626975	−	0.361984i	0.152605	−	0.988287i	$-0.451234\pi$
$487$	−13.8361	−	7.98829i	−0.626975	−	0.361984i	−0.779579	+	0.626303i	$0.784567\pi$
$488$	4.51076	−	14.4657i	0.204192	−	0.654833i
$489$			47.0684i			2.12851i
$490$		0			0
$491$	17.5557	+	17.5557i	0.792277	+	0.792277i	0.981864	−	0.189587i	$-0.0607150\pi$
$491$	17.5557	+	17.5557i	0.792277	+	0.792277i	−0.189587	+	0.981864i	$0.560715\pi$
$492$	−34.3171	−	36.2207i	−1.54714	−	1.63295i
$493$	7.46979	+	27.8777i	0.336423	+	1.25555i
$494$	21.7919	+	0.293986i	0.980463	+	0.0132270i
$495$	3.54674	+	6.14313i	0.159414	+	0.276113i
$496$	−17.1508	−	33.7938i	−0.770092	−	1.51738i
$497$		0			0
$498$	−20.0505	−	35.8363i	−0.898484	−	1.60586i
$499$	11.8528	+	3.17596i	0.530606	+	0.142175i	0.514168	−	0.857689i	$-0.328101\pi$
$499$	11.8528	+	3.17596i	0.530606	+	0.142175i	0.0164379	+	0.999865i	$0.494767\pi$
$500$	−22.5622	−	6.70284i	−1.00901	−	0.299760i
$501$	0.549973	−	0.147365i	0.0245710	−	0.00658378i
$502$	0.872259	+	3.44029i	0.0389308	+	0.153548i
$503$			34.4831i			1.53753i	0.639533	+	0.768764i	$0.279128\pi$
$503$			34.4831i			1.53753i	−0.639533	+	0.768764i	$0.720872\pi$
$504$		0			0
$505$		−	21.9548i		−	0.976977i
$506$	−19.7461	+	5.00647i	−0.877821	+	0.222565i
$507$	19.3226	−	5.17748i	0.858147	−	0.229940i
$508$	17.5046	+	32.3010i	0.776640	+	1.43312i
$509$	17.1380	+	4.59211i	0.759628	+	0.203542i	0.617784	−	0.786347i	$-0.288030\pi$
$509$	17.1380	+	4.59211i	0.759628	+	0.203542i	0.141843	+	0.989889i	$0.454697\pi$
$510$	−21.9194	+	12.2639i	−0.970606	+	0.543056i
$511$		0			0
$512$	−2.74041	+	22.4609i	−0.121110	+	0.992639i
$513$	4.03636	+	6.99118i	0.178210	+	0.308668i
$514$	−0.388475	+	28.7960i	−0.0171349	+	1.27014i
$515$	3.40800	+	12.7188i	0.150175	+	0.560459i
$516$	15.1368	+	0.408483i	0.666360	+	0.0179825i
$517$	2.38581	+	2.38581i	0.104928	+	0.104928i
$518$		0			0
$519$			18.1534i			0.796847i
$520$	8.21326	−	4.30863i	0.360175	−	0.188946i
$521$	6.31273	+	3.64466i	0.276566	+	0.159675i	0.631868	−	0.775076i	$-0.282289\pi$
$521$	6.31273	+	3.64466i	0.276566	+	0.159675i	−0.355302	+	0.934752i	$0.615622\pi$
$522$	−15.1432	+	14.7400i	−0.662798	+	0.645153i
$523$	7.28876	−	27.2020i	0.318715	−	1.18946i	−0.601766	−	0.798673i	$-0.705536\pi$
$523$	7.28876	−	27.2020i	0.318715	−	1.18946i	0.920481	−	0.390788i	$-0.127797\pi$
$524$	−0.561617	−	2.34757i	−0.0245344	−	0.102554i
$525$		0			0
$526$	−7.94959	−	14.2083i	−0.346619	−	0.619513i
$527$	23.1276	+	40.0583i	1.00746	+	1.74496i
$528$	−17.0319	−	0.919918i	−0.741218	−	0.0400343i
$529$	20.0385	−	34.7078i	0.871241	−	1.50903i
$530$	−9.44944	+	15.8686i	−0.410458	+	0.689290i
$531$	6.92062	−	6.92062i	0.300330	−	0.300330i
$532$		0			0
$533$	−15.9018	−	15.9018i	−0.688784	−	0.688784i
$534$	3.48456	+	13.7435i	0.150792	+	0.594740i
$535$	5.67157	+	3.27448i	0.245203	+	0.141568i
$536$	1.85055	−	0.416404i	0.0799316	−	0.0179859i
$537$	−18.6739	+	10.7814i	−0.805838	+	0.465251i
$538$	11.0523	−	39.1285i	0.476497	−	1.68695i
$539$		0			0
$540$	2.92781	+	1.79739i	0.125993	+	0.0773472i
$541$	−40.0586	−	10.7337i	−1.72225	−	0.461476i	−0.743877	−	0.668316i	$-0.767015\pi$
$541$	−40.0586	−	10.7337i	−1.72225	−	0.461476i	−0.978375	+	0.206840i	$0.933682\pi$
$542$	−0.307255	+	22.7755i	−0.0131977	+	0.978291i
$543$	−16.3259	+	28.2773i	−0.700612	+	1.21350i
$544$	1.86140	−	27.5553i	0.0798068	−	1.18142i
$545$	9.22744			0.395260
$546$		0			0
$547$	8.27618	−	8.27618i	0.353864	−	0.353864i	−0.507681	−	0.861545i	$-0.669497\pi$
$547$	8.27618	−	8.27618i	0.353864	−	0.353864i	0.861545	+	0.507681i	$0.169497\pi$
$548$	−0.421152	+	15.6062i	−0.0179907	+	0.666666i
$549$	−13.0807	+	3.50497i	−0.558271	+	0.149588i
$550$	4.66234	+	4.78986i	0.198803	+	0.204240i
$551$	37.2255	−	21.4922i	1.58586	−	0.915597i
$552$	38.8262	−	35.8043i	1.65255	−	1.52393i
$553$		0			0
$554$	7.25919	+	2.05044i	0.308413	+	0.0871147i
$555$	−1.63625	+	6.10657i	−0.0694549	+	0.259209i
$556$	−0.0351959	+	0.118471i	−0.00149264	+	0.00502430i
$557$	−4.44611	−	16.5931i	−0.188388	−	0.703073i	−0.993880	−	0.110466i	$-0.964766\pi$
$557$	−4.44611	−	16.5931i	−0.188388	−	0.703073i	0.805492	−	0.592606i	$-0.201901\pi$
$558$	−17.3285	+	29.1002i	−0.733575	+	1.23191i
$559$	6.82477			0.288657
$560$		0			0
$561$	20.8187			0.878967
$562$	1.43403	−	2.40820i	0.0604911	−	0.101584i
$563$	7.70019	+	28.7375i	0.324524	+	1.21114i	0.914789	+	0.403931i	$0.132356\pi$
$563$	7.70019	+	28.7375i	0.324524	+	1.21114i	−0.590265	+	0.807209i	$0.700977\pi$
$564$	−8.38557	−	2.49121i	−0.353096	−	0.104899i
$565$	4.97518	−	18.5676i	0.209308	−	0.781146i
$566$	21.4347	+	6.05447i	0.900969	+	0.254488i
$567$		0			0
$568$	−4.24371	−	0.171834i	−0.178062	−	0.00721000i
$569$	0.0913759	−	0.0527559i	0.00383068	−	0.00221164i	−0.498083	−	0.867129i	$-0.665963\pi$
$569$	0.0913759	−	0.0527559i	0.00383068	−	0.00221164i	0.501914	+	0.864917i	$0.332629\pi$
$570$	26.0923	+	26.8059i	1.09289	+	1.12278i
$571$	−32.1882	+	8.62480i	−1.34703	+	0.360937i	−0.859039	−	0.511910i	$-0.828938\pi$
$571$	−32.1882	+	8.62480i	−1.34703	+	0.360937i	−0.487995	+	0.872847i	$0.662271\pi$
$572$	−7.68481	−	0.207383i	−0.321318	−	0.00867113i
$573$	10.7217	−	10.7217i	0.447904	−	0.447904i
$574$		0			0
$575$	−20.6975			−0.863147
$576$	18.2733	−	8.66215i	0.761386	−	0.360923i
$577$	19.0200	−	32.9435i	0.791811	−	1.37146i	−0.133033	−	0.991112i	$-0.542472\pi$
$577$	19.0200	−	32.9435i	0.791811	−	1.37146i	0.924844	−	0.380346i	$-0.124195\pi$
$578$	−0.130414	+	9.66702i	−0.00542450	+	0.402095i
$579$	−18.0574	−	4.83847i	−0.750440	−	0.201080i
$580$	9.57045	−	15.5896i	0.397391	−	0.647321i
$581$		0			0
$582$	11.1543	−	39.4897i	0.462361	−	1.63690i
$583$	13.2575	−	7.65423i	0.549070	−	0.317006i
$584$	15.2805	−	24.1539i	0.632311	−	0.999494i
$585$	−7.17849	−	4.14450i	−0.296794	−	0.171354i
$586$	5.70613	+	22.5057i	0.235718	+	0.929700i
$587$	0.198475	+	0.198475i	0.00819196	+	0.00819196i	0.711191	−	0.702999i	$-0.248156\pi$
$587$	0.198475	+	0.198475i	0.00819196	+	0.00819196i	−0.702999	+	0.711191i	$0.748156\pi$
$588$		0			0
$589$	48.7129	−	48.7129i	2.00718	−	2.00718i
$590$	−4.33463	+	7.27923i	−0.178454	+	0.299681i
$591$	−15.0024	+	25.9849i	−0.617115	+	1.06887i
$592$	−4.64321	−	5.17342i	−0.190835	−	0.212626i
$593$	21.2989	+	36.8908i	0.874641	+	1.51492i	0.857145	+	0.515075i	$0.172236\pi$
$593$	21.2989	+	36.8908i	0.874641	+	1.51492i	0.0174959	+	0.999847i	$0.494431\pi$
$594$	−1.39040	−	2.48506i	−0.0570487	−	0.101963i
$595$		0			0
$596$	44.3750	−	10.6160i	1.81767	−	0.434847i
$597$	−2.70326	+	10.0887i	−0.110637	+	0.412903i
$598$	17.0576	−	16.6035i	0.697538	−	0.678968i
$599$	28.0505	+	16.1950i	1.14611	+	0.661708i	0.947937	−	0.318458i	$-0.103165\pi$
$599$	28.0505	+	16.1950i	1.14611	+	0.661708i	0.198175	+	0.980167i	$0.436498\pi$
$600$	−16.5445	−	5.15898i	−0.675428	−	0.210615i
$601$		−	0.122467i		−	0.00499552i	−0.999997	−	0.00249776i	$-0.999205\pi$
$601$		−	0.122467i		−	0.00499552i	0.999997	−	0.00249776i	$-0.000795062\pi$
$602$		0			0
$603$	−1.19869	−	1.19869i	−0.0488146	−	0.0488146i
$604$	0.447338	−	16.5766i	0.0182019	−	0.674492i
$605$	−3.08774	−	11.5236i	−0.125535	−	0.468501i
$606$	0.636437	−	47.1764i	0.0258535	−	1.91641i
$607$	−5.95755	−	10.3188i	−0.241809	−	0.418826i	0.719420	−	0.694575i	$-0.244408\pi$
$607$	−5.95755	−	10.3188i	−0.241809	−	0.418826i	−0.961230	+	0.275749i	$0.911074\pi$
$608$	−40.3587	+	7.94401i	−1.63676	+	0.322172i
$609$		0			0
$610$	10.2301	−	5.72373i	0.414203	−	0.231747i
$611$	−3.80837	−	1.02045i	−0.154070	−	0.0412829i
$612$	−21.7009	+	11.7602i	−0.877208	+	0.475377i
$613$	−35.1329	+	9.41382i	−1.41900	+	0.380221i	−0.885130	−	0.465344i	$-0.845931\pi$
$613$	−35.1329	+	9.41382i	−1.41900	+	0.380221i	−0.533873	+	0.845565i	$0.679264\pi$
$614$	1.60662	−	0.407346i	0.0648380	−	0.0164392i
$615$		−	38.6005i		−	1.55652i
$616$		0			0
$617$		−	2.53102i		−	0.101895i	−0.998701	−	0.0509475i	$-0.983776\pi$
$617$		−	2.53102i		−	0.101895i	0.998701	−	0.0509475i	$-0.0162241\pi$
$618$	6.95439	+	27.4289i	0.279747	+	1.10335i
$619$	−24.6845	+	6.61419i	−0.992153	+	0.265847i	−0.718155	−	0.695883i	$-0.755013\pi$
$619$	−24.6845	+	6.61419i	−0.992153	+	0.265847i	−0.273999	+	0.961730i	$0.588346\pi$
$620$	8.34915	−	28.1037i	0.335310	−	1.12867i
$621$	8.51692	+	2.28210i	0.341772	+	0.0915776i
$622$	20.7313	+	37.0532i	0.831251	+	1.48570i
$623$		0			0
$624$	17.7735	−	9.02027i	0.711509	−	0.361100i
$625$	−2.58911	−	4.48448i	−0.103565	−	0.179379i
$626$	15.8622	+	0.213990i	0.633980	+	0.00855277i
$627$	−8.02506	−	29.9499i	−0.320490	−	1.19609i
$628$	0.552624	−	0.523581i	0.0220521	−	0.0208932i
$629$	5.99962	+	5.99962i	0.239220	+	0.239220i
$630$		0			0
$631$			40.8187i			1.62497i	0.582985	+	0.812483i	$0.301885\pi$
$631$			40.8187i			1.62497i	−0.582985	+	0.812483i	$0.698115\pi$
$632$	19.5810	−	10.2721i	0.778889	−	0.408601i
$633$	−52.2959	−	30.1931i	−2.07858	−	1.20007i
$634$	−15.9231	−	16.3585i	−0.632385	−	0.649681i
$635$	−7.35618	+	27.4536i	−0.291921	+	1.08946i
$636$	−20.7649	+	33.8245i	−0.823381	+	1.34123i
$637$		0			0
$638$	−13.2321	+	7.40338i	−0.523863	+	0.293102i
$639$	1.89788	+	3.28723i	0.0750791	+	0.130041i
$640$	−13.4899	+	11.1557i	−0.533233	+	0.440967i
$641$	−16.5926	+	28.7392i	−0.655369	+	1.13513i	0.326433	+	0.945220i	$0.394153\pi$
$641$	−16.5926	+	28.7392i	−0.655369	+	1.13513i	−0.981801	+	0.189911i	$0.939180\pi$
$642$	12.0921	+	7.20059i	0.477237	+	0.284185i
$643$	3.62191	−	3.62191i	0.142834	−	0.142834i	−0.632074	−	0.774908i	$-0.717796\pi$
$643$	3.62191	−	3.62191i	0.142834	−	0.142834i	0.774908	+	0.632074i	$0.217796\pi$
$644$		0			0
$645$	8.28332	+	8.28332i	0.326155	+	0.326155i
$646$	48.6656	−	12.3388i	1.91472	−	0.485463i
$647$	12.2945	+	7.09823i	0.483346	+	0.279060i	0.721810	−	0.692091i	$-0.243310\pi$
$647$	12.2945	+	7.09823i	0.483346	+	0.279060i	−0.238464	+	0.971151i	$0.576644\pi$
$648$	24.3655	+	15.4144i	0.957167	+	0.605534i
$649$	6.08145	−	3.51113i	0.238718	−	0.137824i
$650$	−7.51678	−	2.12320i	−0.294832	−	0.0832786i
$651$		0			0
$652$	−9.31579	−	38.9402i	−0.364834	−	1.52502i
$653$	−8.49640	−	2.27660i	−0.332490	−	0.0890904i	0.0887120	−	0.996057i	$-0.471725\pi$
$653$	−8.49640	−	2.27660i	−0.332490	−	0.0890904i	−0.421202	+	0.906967i	$0.638392\pi$
$654$	19.8278	+	0.267489i	0.775330	+	0.0104597i
$655$	0.933687	−	1.61719i	0.0364822	−	0.0631890i
$656$	35.5597	+	23.1737i	1.38837	+	0.904781i
$657$	−25.5436			−0.996552
$658$		0			0
$659$	−4.19659	+	4.19659i	−0.163476	+	0.163476i	−0.784105	−	0.620629i	$-0.786877\pi$
$659$	−4.19659	+	4.19659i	−0.163476	+	0.163476i	0.620629	+	0.784105i	$0.286877\pi$
$660$	−9.07546	−	9.57886i	−0.353262	−	0.372857i
$661$	31.0300	−	8.31447i	1.20693	−	0.323395i	0.401372	−	0.915915i	$-0.368534\pi$
$661$	31.0300	−	8.31447i	1.20693	−	0.323395i	0.805556	+	0.592520i	$0.201867\pi$
$662$	−21.9618	+	21.3772i	−0.853571	+	0.830847i
$663$	−21.0682	+	12.1637i	−0.818222	+	0.472401i
$664$	23.6807	+	25.6794i	0.918990	+	0.996553i
$665$		0			0
$666$	−1.68876	+	5.97873i	−0.0654380	+	0.231671i
$667$	12.1514	−	45.3496i	0.470503	−	1.75594i
$668$	−0.425832	+	0.230767i	−0.0164759	+	0.00892866i
$669$	−8.89666	−	33.2028i	−0.343965	−	1.28369i
$670$	1.26081	+	0.750784i	0.0487092	+	0.0290053i
$671$	−9.71637			−0.375096
$672$		0			0
$673$	13.6167			0.524885			0.262443	−	0.964948i	$-0.415472\pi$
$673$	13.6167			0.524885			0.262443	+	0.964948i	$0.415472\pi$
$674$	−18.3650	−	10.9360i	−0.707393	−	0.421238i
$675$	−0.748828	−	2.79467i	−0.0288224	−	0.107567i
$676$	−14.9611	+	8.10772i	−0.575426	+	0.311835i
$677$	−0.636069	+	2.37384i	−0.0244461	+	0.0912342i	−0.977071	−	0.212913i	$-0.931705\pi$
$677$	−0.636069	+	2.37384i	−0.0244461	+	0.0912342i	0.952625	+	0.304147i	$0.0983715\pi$
$678$	11.2289	−	39.7538i	0.431242	−	1.52673i
$679$		0			0
$680$	15.7068	−	14.4844i	0.602330	−	0.555450i
$681$	−12.4047	+	7.16183i	−0.475347	+	0.274442i
$682$	−17.4133	+	16.9498i	−0.666791	+	0.649039i
$683$	9.13560	−	2.44788i	0.349564	−	0.0936654i	−0.0797647	−	0.996814i	$-0.525417\pi$
$683$	9.13560	−	2.44788i	0.349564	−	0.0936654i	0.429329	+	0.903148i	$0.358750\pi$
$684$	25.2834	+	26.6858i	0.966735	+	1.02036i
$685$	−8.54021	+	8.54021i	−0.326305	+	0.326305i
$686$		0			0
$687$	−6.38059			−0.243435
$688$	−12.6037	+	2.65793i	−0.480511	+	0.101333i
$689$	−8.94426	+	15.4919i	−0.340749	+	0.590195i
$690$	40.8550	+	0.551158i	1.55532	+	0.0209822i
$691$	−4.14329	−	1.11019i	−0.157618	−	0.0422337i	0.179147	−	0.983822i	$-0.442666\pi$
$691$	−4.14329	−	1.11019i	−0.157618	−	0.0422337i	−0.336765	+	0.941589i	$0.609333\pi$
$692$	−3.59293	−	15.0185i	−0.136583	−	0.570918i
$693$		0			0
$694$	−25.3316	−	7.15517i	−0.961573	−	0.271607i
$695$	−0.0828013	+	0.0478054i	−0.00314083	+	0.00181336i
$696$	21.0168	−	33.2213i	0.796640	−	1.25925i
$697$	−44.8651	−	25.9029i	−1.69939	−	0.981141i
$698$	22.0219	−	5.58347i	0.833539	−	0.211337i
$699$	−1.04459	−	1.04459i	−0.0395101	−	0.0395101i
$700$		0			0
$701$	−4.63375	+	4.63375i	−0.175014	+	0.175014i	−0.789178	−	0.614164i	$-0.789493\pi$
$701$	−4.63375	+	4.63375i	−0.175014	+	0.175014i	0.614164	+	0.789178i	$0.289493\pi$
$702$	2.85901	+	1.70248i	0.107906	+	0.0642560i
$703$	6.31839	−	10.9438i	0.238303	−	0.412752i
$704$	14.2727	−	2.60990i	0.537924	−	0.0983641i
$705$	−3.38373	−	5.86080i	−0.127439	−	0.220730i
$706$	−15.9484	+	8.92314i	−0.600225	+	0.335827i
$707$		0			0
$708$	−9.52522	+	15.5159i	−0.357980	+	0.583123i
$709$	2.78632	−	10.3987i	0.104642	−	0.390530i	−0.893662	−	0.448741i	$-0.851873\pi$
$709$	2.78632	−	10.3987i	0.104642	−	0.390530i	0.998304	+	0.0582103i	$0.0185394\pi$
$710$	−2.29180	−	2.35448i	−0.0860096	−	0.0883619i
$711$	−17.1140	−	9.88077i	−0.641825	−	0.370558i
$712$	−5.60293	−	10.6805i	−0.209979	−	0.400268i
$713$		−	75.2451i		−	2.81795i
$714$		0			0
$715$	−4.20537	−	4.20537i	−0.157272	−	0.157272i
$716$	13.3153	−	12.6155i	0.497614	−	0.471463i
$717$	−3.12739	−	11.6716i	−0.116794	−	0.435883i
$718$	−16.1082	−	0.217310i	−0.601154	−	0.00810992i
$719$	−12.9391	−	22.4112i	−0.482548	−	0.835798i	0.517251	−	0.855834i	$-0.326955\pi$
$719$	−12.9391	−	22.4112i	−0.482548	−	0.835798i	−0.999799	+	0.0200355i	$0.993622\pi$
$720$	14.8710	+	4.85818i	0.554209	+	0.181054i
$721$		0			0
$722$	−23.3900	−	41.8051i	−0.870486	−	1.55582i
$723$	51.2306	+	13.7272i	1.90529	+	0.510520i
$724$	7.90995	−	26.6253i	0.293971	−	0.989523i
$725$	−14.8806	+	3.98724i	−0.552652	+	0.148083i
$726$	−6.30086	−	24.8513i	−0.233847	−	0.922320i
$727$			2.94733i			0.109310i	0.998505	+	0.0546552i	$0.0174060\pi$
$727$			2.94733i			0.109310i	−0.998505	+	0.0546552i	$0.982594\pi$
$728$		0			0
$729$		−	17.9368i		−	0.664324i
$730$	21.4330	−	5.43418i	0.793272	−	0.201128i
$731$	15.1862	−	4.06912i	0.561681	−	0.150502i
$732$	22.1482	−	12.0026i	0.818620	−	0.443627i
$733$	−33.8363	−	9.06642i	−1.24977	−	0.334876i	−0.427525	−	0.904004i	$-0.640614\pi$
$733$	−33.8363	−	9.06642i	−1.24977	−	0.334876i	−0.822249	+	0.569128i	$0.807281\pi$
$734$	−33.1501	+	18.5475i	−1.22359	+	0.684601i
$735$		0			0
$736$	−25.0349	+	37.3057i	−0.922799	+	1.37511i
$737$	−0.608149	−	1.05335i	−0.0224015	−	0.0388005i
$738$	0.511692	−	37.9295i	0.0188356	−	1.39620i
$739$	0.943006	+	3.51934i	0.0346890	+	0.129461i	0.981099	−	0.193507i	$-0.0619861\pi$
$739$	0.943006	+	3.51934i	0.0346890	+	0.129461i	−0.946410	+	0.322968i	$0.895319\pi$
$740$	0.145074	−	5.37587i	0.00533302	−	0.197621i
$741$	25.6201	+	25.6201i	0.941177	+	0.941177i
$742$		0			0
$743$			9.54797i			0.350281i	0.984543	+	0.175140i	$0.0560379\pi$
$743$			9.54797i			0.350281i	−0.984543	+	0.175140i	$0.943962\pi$
$744$	18.7553	−	60.1470i	0.687601	−	2.20510i
$745$	30.5690	+	17.6490i	1.11996	+	0.646611i
$746$	12.9600	−	12.6149i	0.474498	−	0.461866i
$747$	8.07998	−	30.1549i	0.295631	−	1.10331i
$748$	−17.2236	+	4.12045i	−0.629755	+	0.150658i
$749$		0			0
$750$	−19.1060	−	34.1482i	−0.697653	−	1.24692i
$751$	−14.9233	−	25.8480i	−0.544560	−	0.943206i	−0.998634	−	0.0522419i	$-0.983363\pi$
$751$	−14.9233	−	25.8480i	−0.544560	−	0.943206i	0.454074	−	0.890964i	$-0.349970\pi$
$752$	7.43053	+	0.401335i	0.270964	+	0.0146352i
$753$	−2.95022	+	5.10994i	−0.107512	+	0.186216i
$754$	9.06510	−	15.2232i	0.330131	−	0.554396i
$755$	9.07122	−	9.07122i	0.330135	−	0.330135i
$756$		0			0
$757$	32.3321	+	32.3321i	1.17513	+	1.17513i	0.980970	+	0.194161i	$0.0621986\pi$
$757$	32.3321	+	32.3321i	1.17513	+	1.17513i	0.194161	+	0.980970i	$0.437801\pi$
$758$	6.42229	+	25.3303i	0.233268	+	0.920037i
$759$	−29.3293	−	16.9333i	−1.06459	−	0.614639i
$760$	−26.8918	−	17.0126i	−0.975470	−	0.617113i
$761$	−30.3673	+	17.5326i	−1.10081	+	0.635556i	−0.936435	−	0.350842i	$-0.885896\pi$
$761$	−30.3673	+	17.5326i	−1.10081	+	0.635556i	−0.164380	+	0.986397i	$0.552562\pi$
$762$	−16.6027	+	58.7789i	−0.601454	+	2.12934i
$763$		0			0
$764$	−6.74812	+	10.9922i	−0.244138	+	0.397684i
$765$	−18.4443	−	4.94214i	−0.666856	−	0.178683i
$766$	−0.303323	+	22.4840i	−0.0109595	+	0.812380i
$767$	−4.10289	+	7.10642i	−0.148147	+	0.256598i
$768$	−29.3103	+	23.5802i	−1.05764	+	0.850876i
$769$	−2.64747			−0.0954704			−0.0477352	−	0.998860i	$-0.515200\pi$
$769$	−2.64747			−0.0954704			−0.0477352	+	0.998860i	$0.515200\pi$
$770$		0			0
$771$	−33.8546	+	33.8546i	−1.21924	+	1.21924i
$772$	15.8967	+	0.428990i	0.572135	+	0.0154397i
$773$	−40.8781	+	10.9533i	−1.47028	+	0.393961i	−0.903029	−	0.429581i	$-0.858661\pi$
$773$	−40.8781	+	10.9533i	−1.47028	+	0.393961i	−0.567255	+	0.823542i	$0.691995\pi$
$774$	8.02953	+	8.24914i	0.288615	+	0.296509i
$775$	−21.3824	+	12.3451i	−0.768078	+	0.443450i
$776$	−1.41226	+	34.8779i	−0.0506971	+	1.25204i
$777$		0			0
$778$	−26.4268	−	7.46453i	−0.947446	−	0.267616i
$779$	−19.9697	+	74.5280i	−0.715490	+	2.67024i
$780$	14.7809	+	4.39115i	0.529240	+	0.157228i
$781$	0.704875	+	2.63063i	0.0252224	+	0.0941313i
$782$	28.0564	−	47.1156i	1.00329	−	1.68485i
$783$	6.56291			0.234539
$784$		0			0
$785$	0.588933			0.0210199
$786$	2.05318	−	3.44795i	0.0732345	−	0.122984i
$787$	−7.77480	−	29.0159i	−0.277142	−	1.03431i	−0.954393	−	0.298555i	$-0.903495\pi$
$787$	−7.77480	−	29.0159i	−0.277142	−	1.03431i	0.677251	−	0.735752i	$-0.263171\pi$
$788$	7.26869	−	24.4668i	0.258936	−	0.871594i
$789$	7.00551	−	26.1449i	0.249403	−	0.930784i
$790$	16.4620	+	4.64986i	0.585691	+	0.165435i
$791$		0			0
$792$	−8.79073	−	9.53267i	−0.312365	−	0.338729i
$793$	9.83282	−	5.67698i	0.349174	−	0.201595i
$794$	−35.3124	−	36.2782i	−1.25319	−	1.28747i
$795$	−29.6585	+	7.94698i	−1.05188	+	0.281850i
$796$	0.239678	−	8.88152i	0.00849515	−	0.314797i
$797$	−14.9534	+	14.9534i	−0.529676	+	0.529676i	−0.920476	−	0.390800i	$-0.872198\pi$
$797$	−14.9534	+	14.9534i	−0.529676	+	0.529676i	0.390800	+	0.920476i	$0.372198\pi$
$798$		0			0
$799$	−9.08263			−0.321320
$800$	14.7085	+	0.993582i	0.520025	+	0.0351284i
$801$	−5.38949	+	9.33487i	−0.190428	+	0.329832i
$802$	−0.500589	+	37.1065i	−0.0176764	+	1.31028i
$803$	−17.7028	−	4.74346i	−0.624719	−	0.167393i
$804$	2.68745	+	1.64983i	0.0947790	+	0.0581849i
$805$		0			0
$806$	7.71880	−	27.3270i	0.271883	−	0.962551i
$807$	58.5401	−	33.7981i	2.06071	−	1.18975i
$808$	8.81062	+	39.1555i	0.309957	+	1.37748i
$809$	−38.5669	−	22.2666i	−1.35594	−	0.782853i	−0.366867	−	0.930273i	$-0.619570\pi$
$809$	−38.5669	−	22.2666i	−1.35594	−	0.782853i	−0.989074	+	0.147420i	$0.952903\pi$
$810$	5.48179	+	21.6208i	0.192611	+	0.759679i
$811$	5.06726	+	5.06726i	0.177935	+	0.177935i	0.790455	−	0.612520i	$-0.209844\pi$
$811$	5.06726	+	5.06726i	0.177935	+	0.177935i	−0.612520	+	0.790455i	$0.709844\pi$
$812$		0			0
$813$	−26.7765	+	26.7765i	−0.939092	+	0.939092i
$814$	−2.28063	+	3.82991i	−0.0799362	+	0.134238i
$815$	15.4875	−	26.8251i	0.542503	−	0.939642i
$816$	34.1706	−	30.6686i	1.19621	−	1.07361i
$817$	−11.7077	−	20.2784i	−0.409602	−	0.709451i
$818$	17.5225	+	31.3180i	0.612659	+	1.09501i
$819$		0			0
$820$	7.63981	+	31.9346i	0.266794	+	1.11520i
$821$	−0.662191	+	2.47133i	−0.0231106	+	0.0862500i	−0.976518	−	0.215436i	$-0.930883\pi$
$821$	−0.662191	+	2.47133i	−0.0231106	+	0.0862500i	0.953407	+	0.301686i	$0.0975494\pi$
$822$	−18.5987	+	18.1036i	−0.648704	+	0.631435i
$823$	−42.0582	−	24.2823i	−1.46606	−	0.846428i	−0.466776	−	0.884376i	$-0.654585\pi$
$823$	−42.0582	−	24.2823i	−1.46606	−	0.846428i	−0.999280	+	0.0379480i	$0.987918\pi$
$824$	−11.1822	−	21.3158i	−0.389550	−	0.742572i
$825$			11.1127i			0.386893i
$826$		0			0
$827$	12.3701	+	12.3701i	0.430151	+	0.430151i	0.888680	−	0.458529i	$-0.151623\pi$
$827$	12.3701	+	12.3701i	0.430151	+	0.430151i	−0.458529	+	0.888680i	$0.651623\pi$
$828$	40.1375	+	1.08315i	1.39487	+	0.0376422i
$829$	−2.56971	−	9.59030i	−0.0892498	−	0.333085i	0.906835	−	0.421485i	$-0.138491\pi$
$829$	−2.56971	−	9.59030i	−0.0892498	−	0.333085i	−0.996085	+	0.0884006i	$0.971824\pi$
$830$	−0.364532	+	27.0212i	−0.0126531	+	0.937919i
$831$	6.27029	+	10.8605i	0.217514	+	0.376745i
$832$	−12.9189	+	10.9803i	−0.447882	+	0.380673i
$833$		0			0
$834$	−0.179309	+	0.100323i	−0.00620895	+	0.00347392i
$835$	−0.361928	−	0.0969784i	−0.0125251	−	0.00335608i
$836$	12.5669	+	23.1896i	0.434636	+	0.802028i
$837$	10.1599	−	2.72234i	0.351177	−	0.0940977i
$838$	−24.8513	+	6.30086i	−0.858476	+	0.217660i
$839$			3.24523i			0.112038i	0.998430	+	0.0560190i	$0.0178407\pi$
$839$			3.24523i			0.112038i	−0.998430	+	0.0560190i	$0.982159\pi$
$840$		0			0
$841$		−	5.94516i		−	0.205006i
$842$	−2.72883	−	10.7628i	−0.0940418	−	0.370912i
$843$	4.50093	−	1.20602i	0.155020	−	0.0415376i
$844$	49.2408	+	14.6286i	1.69494	+	0.503538i
$845$	−12.7159	−	3.40721i	−0.437440	−	0.117212i
$846$	−3.24722	−	5.80378i	−0.111642	−	0.199538i
$847$		0			0
$848$	10.4845	−	32.0931i	0.360038	−	1.10208i
$849$	18.5147	+	32.0685i	0.635424	+	1.10059i
$850$	−17.9919	−	0.242722i	−0.617118	−	0.00832529i
$851$	−3.57233	−	13.3321i	−0.122458	−	0.457019i
$852$	−4.85634	−	5.12572i	−0.166375	−	0.175604i
$853$	−17.1348	−	17.1348i	−0.586685	−	0.586685i	0.350047	−	0.936732i	$-0.386166\pi$
$853$	−17.1348	−	17.1348i	−0.586685	−	0.586685i	−0.936732	+	0.350047i	$0.886166\pi$
$854$		0			0
$855$			28.4392i			0.972599i
$856$	−11.4291	−	3.56385i	−0.390637	−	0.121810i
$857$	6.12761	+	3.53778i	0.209315	+	0.120848i	0.600993	−	0.799254i	$-0.294772\pi$
$857$	6.12761	+	3.53778i	0.209315	+	0.120848i	−0.391678	+	0.920102i	$0.628105\pi$
$858$	−8.91455	−	9.15836i	−0.304338	−	0.312661i
$859$	−12.1272	+	45.2594i	−0.413775	+	1.54423i	0.373500	+	0.927630i	$0.378157\pi$
$859$	−12.1272	+	45.2594i	−0.413775	+	1.54423i	−0.787276	+	0.616601i	$0.788509\pi$
$860$	−8.49231	−	5.21344i	−0.289585	−	0.177777i
$861$		0			0
$862$	−33.8250	+	18.9252i	−1.15209	+	0.644594i
$863$	7.63479	+	13.2238i	0.259891	+	0.450145i	0.966213	−	0.257747i	$-0.0829799\pi$
$863$	7.63479	+	13.2238i	0.259891	+	0.450145i	−0.706321	+	0.707891i	$0.749647\pi$
$864$	−5.94292	−	2.03061i	−0.202182	−	0.0690827i
$865$	5.97324	−	10.3459i	0.203096	−	0.351773i
$866$	−39.8255	−	23.7153i	−1.35333	−	0.805877i
$867$	−11.3652	+	11.3652i	−0.385984	+	0.385984i
$868$		0			0
$869$	−10.0259	−	10.0259i	−0.340104	−	0.340104i
$870$	29.4790	−	7.47418i	0.999433	−	0.253398i
$871$	1.23088	+	0.710646i	0.0417066	+	0.0240793i
$872$	−16.4567	+	3.70303i	−0.557295	+	0.125401i
$873$	27.0168	−	15.5982i	0.914382	−	0.527918i
$874$	−78.5958	−	22.2002i	−2.65854	−	0.750934i
$875$		0			0
$876$	46.2126	−	11.0556i	1.56138	−	0.373534i
$877$	7.37580	+	1.97634i	0.249063	+	0.0667362i	0.381191	−	0.924496i	$-0.375514\pi$
$877$	7.37580	+	1.97634i	0.249063	+	0.0667362i	−0.132128	+	0.991233i	$0.542181\pi$
$878$	18.2119	+	0.245690i	0.614623	+	0.00829163i
$879$	−19.2997	+	33.4281i	−0.650964	+	1.12750i
$880$	9.40407	+	6.12848i	0.317011	+	0.206591i
$881$	8.36445			0.281805			0.140903	−	0.990023i	$-0.455000\pi$
$881$	8.36445			0.281805			0.140903	+	0.990023i	$0.455000\pi$
$882$		0			0
$883$	1.09301	−	1.09301i	0.0367828	−	0.0367828i	−0.688476	−	0.725259i	$-0.741720\pi$
$883$	1.09301	−	1.09301i	0.0367828	−	0.0367828i	0.725259	+	0.688476i	$0.241720\pi$
$884$	15.0225	−	14.2330i	0.505262	−	0.478708i
$885$	−13.6049	+	3.64542i	−0.457323	+	0.122539i
$886$	7.66408	−	7.46005i	0.257480	−	0.250625i
$887$	33.4773	−	19.3281i	1.12406	−	0.648974i	0.181623	−	0.983368i	$-0.441865\pi$
$887$	33.4773	−	19.3281i	1.12406	−	0.648974i	0.942433	+	0.334394i	$0.108532\pi$
$888$	0.467572	−	11.5474i	0.0156907	−	0.387506i
$889$		0			0
$890$	2.53628	−	8.97923i	0.0850163	−	0.300984i
$891$	4.78502	−	17.8580i	0.160304	−	0.598264i
$892$	13.9318	+	25.7082i	0.466471	+	0.860774i
$893$	3.50111	+	13.0663i	0.117160	+	0.437248i
$894$	65.1749	+	38.8103i	2.17977	+	1.29801i
$895$	14.1901			0.474323
$896$		0			0
$897$	39.5744			1.32135
$898$	19.2189	+	11.4445i	0.641344	+	0.381907i
$899$	−14.4955	−	54.0978i	−0.483451	−	1.80426i
$900$	−6.27738	−	11.5836i	−0.209246	−	0.386119i
$901$	−10.6656	+	39.8047i	−0.355324	+	1.32609i
$902$	7.39815	−	26.1918i	0.246331	−	0.872090i
$903$		0			0
$904$	−1.42170	+	35.1111i	−0.0472850	+	1.16778i
$905$	18.6088	−	10.7438i	0.618579	−	0.357136i
$906$	19.7551	−	19.2292i	0.656320	−	0.638847i
$907$	47.1464	−	12.6328i	1.56547	−	0.419467i	0.631081	−	0.775717i	$-0.282612\pi$
$907$	47.1464	−	12.6328i	1.56547	−	0.419467i	0.934391	+	0.356250i	$0.115945\pi$
$908$	8.84503	−	8.38019i	0.293533	−	0.278106i
$909$	25.3630	−	25.3630i	0.841237	−	0.841237i
$910$		0			0
$911$	14.2220			0.471196			0.235598	−	0.971851i	$-0.424295\pi$
$911$	14.2220			0.471196			0.235598	+	0.971851i	$0.424295\pi$
$912$	−57.2918	−	37.3361i	−1.89712	−	1.23632i
$913$	11.1996	−	19.3982i	0.370651	−	0.641986i
$914$	38.3429	+	0.517268i	1.26827	+	0.0171097i
$915$	18.8244	+	5.04399i	0.622317	+	0.166749i
$916$	5.27873	−	1.26285i	0.174414	−	0.0417257i
$917$		0			0
$918$	7.37681	+	2.08366i	0.243471	+	0.0687710i
$919$	−18.8177	+	10.8644i	−0.620738	+	0.358383i	−0.777156	−	0.629308i	$-0.783339\pi$
$919$	−18.8177	+	10.8644i	−0.620738	+	0.358383i	0.156418	+	0.987691i	$0.450005\pi$
$920$	−33.9088	+	7.63004i	−1.11794	+	0.251555i
$921$	2.38635	+	1.37776i	0.0786329	+	0.0453987i
$922$	−12.2463	+	3.10496i	−0.403311	+	0.102256i
$923$	−2.25032	−	2.25032i	−0.0740702	−	0.0740702i
$924$		0			0
$925$	−3.20249	+	3.20249i	−0.105297	+	0.105297i
$926$	−3.51780	−	2.09478i	−0.115602	−	0.0688386i
$927$	−10.7562	+	18.6303i	−0.353280	+	0.611899i
$928$	−10.8123	+	31.6440i	−0.354930	+	1.03876i
$929$	−16.2809	−	28.1994i	−0.534160	−	0.925193i	−0.999203	−	0.0399047i	$-0.987295\pi$
$929$	−16.2809	−	28.1994i	−0.534160	−	0.925193i	0.465043	−	0.885288i	$-0.346039\pi$
$930$	42.5355	−	23.7987i	1.39479	−	0.780390i
$931$		0			0
$932$	1.07095	+	0.657457i	0.0350801	+	0.0215357i
$933$	−18.2693	+	68.1821i	−0.598111	+	2.23218i
$934$	−1.34598	−	1.38279i	−0.0440418	−	0.0452464i
$935$	−11.8650	−	6.85023i	−0.388025	−	0.224027i
$936$	14.4657	+	4.51076i	0.472827	+	0.147439i
$937$		−	25.2755i		−	0.825714i	−0.910796	−	0.412857i	$-0.864531\pi$
$937$		−	25.2755i		−	0.825714i	0.910796	−	0.412857i	$-0.135469\pi$
$938$		0			0
$939$	18.6487	+	18.6487i	0.608577	+	0.608577i
$940$	3.95937	+	4.17899i	0.129140	+	0.136304i
$941$	9.87914	+	36.8695i	0.322051	+	1.20191i	0.917243	+	0.398327i	$0.130409\pi$
$941$	9.87914	+	36.8695i	0.322051	+	1.20191i	−0.595193	+	0.803583i	$0.702924\pi$
$942$	1.26549	+	0.0170723i	0.0412320	+	0.000556244i
$943$	42.1371	+	72.9836i	1.37217	+	2.37667i
$944$	4.80941	−	14.7217i	0.156533	−	0.479150i
$945$		0			0
$946$	4.03294	+	7.20810i	0.131122	+	0.234355i
$947$	45.5247	+	12.1983i	1.47936	+	0.396392i	0.906128	−	0.423004i	$-0.139024\pi$
$947$	45.5247	+	12.1983i	1.47936	+	0.396392i	0.573228	+	0.819396i	$0.305691\pi$
$948$	35.2386	+	10.4688i	1.14450	+	0.340011i
$949$	20.6865	−	5.54292i	0.671511	−	0.179931i
$950$	6.58622	+	25.9768i	0.213685	+	0.842800i
$951$		−	37.9525i		−	1.23070i
$952$		0			0
$953$		−	0.698407i		−	0.0226236i	−0.999936	−	0.0113118i	$-0.996399\pi$
$953$		−	0.698407i		−	0.0226236i	0.999936	−	0.0113118i	$-0.00360074\pi$
$954$	−29.2483	+	7.41568i	−0.946950	+	0.240092i
$955$	−9.63835	+	2.58259i	−0.311890	+	0.0835706i
$956$	4.89736	+	9.03704i	0.158392	+	0.292279i
$957$	−24.3485	−	6.52417i	−0.787076	−	0.210896i
$958$	14.8185	−	8.29100i	0.478765	−	0.267870i
$959$		0			0
$960$	−29.0068	−	2.35291i	−0.936189	−	0.0759398i
$961$	−29.3802	−	50.8880i	−0.947749	−	1.64155i
$962$	0.0702634	−	5.20832i	0.00226538	−	0.167923i
$963$	2.76920	+	10.3348i	0.0892362	+	0.333034i
$964$	−45.1005	−	1.21709i	−1.45259	−	0.0391998i
$965$	8.69917	+	8.69917i	0.280036	+	0.280036i
$966$		0			0
$967$		−	21.7169i		−	0.698368i	−0.937054	−	0.349184i	$-0.886459\pi$
$967$		−	21.7169i		−	0.698368i	0.937054	−	0.349184i	$-0.113541\pi$
$968$	10.1314	+	19.3127i	0.325634	+	0.620734i
$969$	72.2840	+	41.7332i	2.32210	+	1.34066i
$970$	−19.3508	+	18.8356i	−0.621317	+	0.604776i
$971$	−11.4079	+	42.5750i	−0.366098	+	1.36630i	0.499828	+	0.866125i	$0.333397\pi$
$971$	−11.4079	+	42.5750i	−0.366098	+	1.36630i	−0.865926	+	0.500172i	$0.833270\pi$
$972$	9.60262	+	40.1392i	0.308004	+	1.28746i
$973$		0			0
$974$	11.0322	+	19.7178i	0.353493	+	0.631800i
$975$	−6.49279	−	11.2458i	−0.207936	−	0.360155i
$976$	−15.9479	+	14.3134i	−0.510479	+	0.458161i
$977$	−13.4986	+	23.3803i	−0.431860	+	0.748003i	−0.997034	−	0.0769687i	$-0.975476\pi$
$977$	−13.4986	+	23.3803i	−0.431860	+	0.748003i	0.565174	+	0.824972i	$0.308809\pi$
$978$	34.0570	−	57.1926i	1.08902	−	1.82882i
$979$	−5.46864	+	5.46864i	−0.174778	+	0.174778i
$980$		0			0
$981$	10.6599	+	10.6599i	0.340343	+	0.340343i
$982$	−8.62917	−	34.0345i	−0.275368	−	1.08608i
$983$	36.3269	+	20.9734i	1.15865	+	0.668946i	0.950980	−	0.309253i	$-0.100079\pi$
$983$	36.3269	+	20.9734i	1.15865	+	0.668946i	0.207669	+	0.978199i	$0.433412\pi$
$984$	15.4906	+	68.8422i	0.493823	+	2.19461i
$985$	17.1002	−	9.87281i	0.544858	−	0.314574i
$986$	11.0947	−	39.2789i	0.353329	−	1.25089i
$987$		0			0
$988$	−26.2665	−	16.1250i	−0.835648	−	0.513005i
$989$	−24.7039	−	6.61939i	−0.785538	−	0.210484i
$990$	0.135321	−	10.0308i	0.00430079	−	0.318799i
$991$	−22.3707	+	38.7473i	−0.710630	+	1.23085i	0.253991	+	0.967207i	$0.418257\pi$
$991$	−22.3707	+	38.7473i	−0.710630	+	1.23085i	−0.964621	+	0.263641i	$0.915077\pi$
$992$	−3.61213	+	53.4723i	−0.114685	+	1.69775i
$993$	−50.9524			−1.61692
$994$		0			0
$995$	4.86024	−	4.86024i	0.154080	−	0.154080i
$996$	−1.56661	+	58.0523i	−0.0496398	+	1.83946i
$997$	−52.3690	+	14.0322i	−1.65854	+	0.444405i	−0.961986	−	0.273097i	$-0.911952\pi$
$997$	−52.3690	+	14.0322i	−1.65854	+	0.444405i	−0.696556	+	0.717502i	$0.745285\pi$
$998$	−12.1043	−	12.4354i	−0.383156	−	0.393635i
$999$	1.67091	−	0.964701i	0.0528653	−	0.0305218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.n.165.1		40
7.2	even	3	inner	784.2.x.n.373.6		40
7.3	odd	6		784.2.m.i.197.10	yes	20
7.4	even	3		784.2.m.i.197.9	✓	20
7.5	odd	6	inner	784.2.x.n.373.5		40
7.6	odd	2	inner	784.2.x.n.165.2		40
16.13	even	4	inner	784.2.x.n.557.6		40
112.13	odd	4	inner	784.2.x.n.557.5		40
112.45	odd	12		784.2.m.i.589.10	yes	20
112.61	odd	12	inner	784.2.x.n.765.2		40
112.93	even	12	inner	784.2.x.n.765.1		40
112.109	even	12		784.2.m.i.589.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.i.197.9	✓	20	7.4	even	3
784.2.m.i.197.10	yes	20	7.3	odd	6
784.2.m.i.589.9	yes	20	112.109	even	12
784.2.m.i.589.10	yes	20	112.45	odd	12
784.2.x.n.165.1		40	1.1	even	1	trivial
784.2.x.n.165.2		40	7.6	odd	2	inner
784.2.x.n.373.5		40	7.5	odd	6	inner
784.2.x.n.373.6		40	7.2	even	3	inner
784.2.x.n.557.5		40	112.13	odd	4	inner
784.2.x.n.557.6		40	16.13	even	4	inner
784.2.x.n.765.1		40	112.93	even	12	inner
784.2.x.n.765.2		40	112.61	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.21510 - 0.723563i) q^{2} +(-0.608516 - 2.27101i) q^{3} +(0.952912 + 1.75840i) q^{4} +(-0.400455 + 1.49452i) q^{5} +(-0.903818 + 3.19980i) q^{6} +(0.114433 - 2.82611i) q^{8} +(-2.18914 + 1.26390i) q^{9} +O(q^{10})\)	\(q+(-1.21510 - 0.723563i) q^{2} +(-0.608516 - 2.27101i) q^{3} +(0.952912 + 1.75840i) q^{4} +(-0.400455 + 1.49452i) q^{5} +(-0.903818 + 3.19980i) q^{6} +(0.114433 - 2.82611i) q^{8} +(-2.18914 + 1.26390i) q^{9} +(1.56797 - 1.52623i) q^{10} +(-1.75187 + 0.469413i) q^{11} +(3.41348 - 3.23409i) q^{12} +(1.49861 - 1.49861i) q^{13} +3.63776 q^{15} +(-2.18392 + 3.35119i) q^{16} +(2.44112 - 4.22814i) q^{17} +(3.57452 + 0.0482225i) q^{18} +(-7.02361 - 1.88197i) q^{19} +(-3.00955 + 0.719985i) q^{20} +(2.46834 + 0.697210i) q^{22} +(-6.87807 + 3.97105i) q^{23} +(-6.48777 + 1.45986i) q^{24} +(2.25691 + 1.30303i) q^{25} +(-2.90528 + 0.736612i) q^{26} +(-0.785033 - 0.785033i) q^{27} +(-4.18002 + 4.18002i) q^{29} +(-4.42022 - 2.63215i) q^{30} +(-4.73710 + 8.20490i) q^{31} +(5.07847 - 2.49182i) q^{32} +(2.13209 + 3.69289i) q^{33} +(-6.02552 + 3.37129i) q^{34} +(-4.30849 - 2.64499i) q^{36} +(-0.449796 + 1.67866i) q^{37} +(7.17263 + 7.36880i) q^{38} +(-4.31528 - 2.49143i) q^{39} +(4.17785 + 1.30275i) q^{40} -10.6111i q^{41} +(2.27704 + 2.27704i) q^{43} +(-2.49480 - 2.63318i) q^{44} +(-1.01227 - 3.77784i) q^{45} +(11.2308 + 0.151510i) q^{46} +(-0.930171 - 1.61110i) q^{47} +(8.93956 + 2.92045i) q^{48} +(-1.79953 - 3.21632i) q^{50} +(-11.0876 - 2.97092i) q^{51} +(4.06318 + 1.20710i) q^{52} +(-8.15297 + 2.18458i) q^{53} +(0.385868 + 1.52191i) q^{54} -2.80619i q^{55} +17.0959i q^{57} +(8.10363 - 2.05461i) q^{58} +(-3.73991 + 1.00211i) q^{59} +(3.46646 + 6.39662i) q^{60} +(5.17474 + 1.38657i) q^{61} +(11.6928 - 6.54214i) q^{62} +(-7.97381 - 0.646803i) q^{64} +(1.63957 + 2.83982i) q^{65} +(0.0813471 - 6.02991i) q^{66} +(0.173571 + 0.647776i) q^{67} +(9.76092 + 0.263409i) q^{68} +(13.2037 + 13.2037i) q^{69} -1.50161i q^{71} +(3.32141 + 6.33138i) q^{72} +(8.75126 + 5.05254i) q^{73} +(1.76116 - 1.71428i) q^{74} +(1.58583 - 5.91838i) q^{75} +(-3.38363 - 14.1437i) q^{76} +(3.44077 + 6.14970i) q^{78} +(3.90884 + 6.77031i) q^{79} +(-4.13386 - 4.60591i) q^{80} +(-5.09681 + 8.82794i) q^{81} +(-7.67778 + 12.8935i) q^{82} +(-8.73286 + 8.73286i) q^{83} +(5.34147 + 5.34147i) q^{85} +(-1.11924 - 4.41440i) q^{86} +(12.0365 + 6.94928i) q^{87} +(1.12614 + 5.00471i) q^{88} +(3.69289 - 2.13209i) q^{89} +(-1.50350 + 5.32288i) q^{90} +(-13.5369 - 8.31031i) q^{92} +(21.5160 + 5.76521i) q^{93} +(-0.0354895 + 2.63068i) q^{94} +(5.62528 - 9.74327i) q^{95} +(-8.74928 - 10.0170i) q^{96} -12.3413 q^{97} +(3.24180 - 3.24180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{4}+O(q^{10}) \) 40 * q + 8 * q^4	\( 40 q + 8 q^{4} - 4 q^{11} - 32 q^{15} - 16 q^{18} - 8 q^{29} - 8 q^{30} + 40 q^{32} + 80 q^{36} + 20 q^{37} + 120 q^{43} - 56 q^{44} + 64 q^{46} - 112 q^{50} + 16 q^{51} - 28 q^{53} + 72 q^{58} + 24 q^{60} - 64 q^{64} - 16 q^{65} - 12 q^{67} - 16 q^{72} + 16 q^{74} - 176 q^{78} + 72 q^{79} - 12 q^{81} + 64 q^{85} + 40 q^{86} - 80 q^{88} - 48 q^{92} - 48 q^{93} - 64 q^{95} - 216 q^{99}+O(q^{100}) \) 40 * q + 8 * q^4 - 4 * q^11 - 32 * q^15 - 16 * q^18 - 8 * q^29 - 8 * q^30 + 40 * q^32 + 80 * q^36 + 20 * q^37 + 120 * q^43 - 56 * q^44 + 64 * q^46 - 112 * q^50 + 16 * q^51 - 28 * q^53 + 72 * q^58 + 24 * q^60 - 64 * q^64 - 16 * q^65 - 12 * q^67 - 16 * q^72 + 16 * q^74 - 176 * q^78 + 72 * q^79 - 12 * q^81 + 64 * q^85 + 40 * q^86 - 80 * q^88 - 48 * q^92 - 48 * q^93 - 64 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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