LMFDB - Embedded newform 450.2.p.h.407.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(257,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("450.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.p (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.1
Root			$0.500000 - 1.00333i$ of defining polynomial
Character	$\chi$	$=$	450.407
Dual form			450.2.p.h.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-1.45865 + 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.27970 + 1.16721i) q^{6} +(-1.94786 + 0.521929i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.45865 + 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.27970 + 1.16721i) q^{6} +(-1.94786 + 0.521929i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +(-1.70563 - 0.984748i) q^{11} +(0.796225 - 1.53819i) q^{12} +(3.92790 + 1.05248i) q^{13} +(1.00829 + 1.74641i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.35877 - 2.35877i) q^{17} +(-2.95680 - 0.507306i) q^{18} -3.70753i q^{19} +(2.35376 - 2.58061i) q^{21} +(-0.509743 + 1.90239i) q^{22} +(1.62200 - 6.05338i) q^{23} +(-1.69185 - 0.370982i) q^{24} -4.06647i q^{26} +(0.713876 + 5.14688i) q^{27} +(1.42594 - 1.42594i) q^{28} +(3.74863 - 6.49281i) q^{29} +(3.48837 + 6.04204i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.40767 - 0.156660i) q^{33} +(-2.88889 - 1.66790i) q^{34} +(0.275255 + 2.98735i) q^{36} +(-4.26692 - 4.26692i) q^{37} +(-3.58120 + 0.959578i) q^{38} +(-6.71243 + 2.13346i) q^{39} +(6.13601 - 3.54263i) q^{41} +(-3.10188 - 1.60565i) q^{42} +(-2.43757 - 9.09714i) q^{43} +1.96950 q^{44} -6.26692 q^{46} +(-2.00837 - 7.49533i) q^{47} +(0.0795432 + 1.73022i) q^{48} +(-2.54041 + 1.46671i) q^{49} +(-1.23752 + 5.64369i) q^{51} +(-3.92790 + 1.05248i) q^{52} +(7.03027 + 7.03027i) q^{53} +(4.78674 - 2.02166i) q^{54} +(-1.74641 - 1.00829i) q^{56} +(3.46282 + 5.40797i) q^{57} +(-7.24179 - 1.94043i) q^{58} +(-1.34967 - 2.33769i) q^{59} +(-4.37353 + 7.57518i) q^{61} +(4.93330 - 4.93330i) q^{62} +(-1.02302 + 5.96261i) q^{63} +1.00000i q^{64} +(-1.03329 - 3.25101i) q^{66} +(-2.19259 + 8.18285i) q^{67} +(-0.863368 + 3.22213i) q^{68} +(3.28793 + 10.3447i) q^{69} -5.68481i q^{71} +(2.81431 - 1.03906i) q^{72} +(-1.14928 + 1.14928i) q^{73} +(-3.01717 + 5.22589i) q^{74} +(1.85376 + 3.21081i) q^{76} +(3.83631 + 1.02794i) q^{77} +(3.79807 + 5.93153i) q^{78} +(10.0535 + 5.80440i) q^{79} +(-5.84847 - 6.84072i) q^{81} +(-5.01003 - 5.01003i) q^{82} +(1.64569 - 0.440961i) q^{83} +(-0.748114 + 3.41176i) q^{84} +(-8.15627 + 4.70902i) q^{86} +(0.596356 + 12.9719i) q^{87} +(-0.509743 - 1.90239i) q^{88} +2.04989 q^{89} -8.20034 q^{91} +(1.62200 + 6.05338i) q^{92} +(-10.7315 - 5.55506i) q^{93} +(-6.72013 + 3.87987i) q^{94} +(1.65068 - 0.524648i) q^{96} +(9.71905 - 2.60421i) q^{97} +(2.07424 + 2.07424i) q^{98} +(-4.82426 + 3.41127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 8 q^{16} + 24 q^{21} - 8 q^{22} + 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{36} - 24 q^{38} + 24 q^{41} - 24 q^{42} - 32 q^{46} - 48 q^{47} - 48 q^{51} + 24 q^{56} - 24 q^{57} - 16 q^{58} - 24 q^{61} + 48 q^{63} - 48 q^{66} + 16 q^{67} + 24 q^{68} + 24 q^{72} - 16 q^{73} + 16 q^{76} + 72 q^{77} + 24 q^{81} + 16 q^{82} - 48 q^{83} - 48 q^{86} + 48 q^{87} - 8 q^{88} + 24 q^{92} - 72 q^{93} + 48 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 8 * q^16 + 24 * q^21 - 8 * q^22 + 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^36 - 24 * q^38 + 24 * q^41 - 24 * q^42 - 32 * q^46 - 48 * q^47 - 48 * q^51 + 24 * q^56 - 24 * q^57 - 16 * q^58 - 24 * q^61 + 48 * q^63 - 48 * q^66 + 16 * q^67 + 24 * q^68 + 24 * q^72 - 16 * q^73 + 16 * q^76 + 72 * q^77 + 24 * q^81 + 16 * q^82 - 48 * q^83 - 48 * q^86 + 48 * q^87 - 8 * q^88 + 24 * q^92 - 72 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−1.45865	+	0.933998i	−0.842150	+	0.539244i
$3$	−1.45865	+	0.933998i	−0.842150	+	0.539244i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	1.27970	+	1.16721i	0.522435	+	0.476510i
$7$	−1.94786	+	0.521929i	−0.736223	+	0.197270i	−0.607399	−	0.794397i	$-0.707787\pi$
$7$	−1.94786	+	0.521929i	−0.736223	+	0.197270i	−0.128824	+	0.991667i	$0.541120\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.25529	−	2.72474i	0.418432	−	0.908248i
$10$		0			0
$11$	−1.70563	−	0.984748i	−0.514268	−	0.296913i	0.220318	−	0.975428i	$-0.429290\pi$
$11$	−1.70563	−	0.984748i	−0.514268	−	0.296913i	−0.734586	+	0.678515i	$0.762624\pi$
$12$	0.796225	−	1.53819i	0.229850	−	0.444037i
$13$	3.92790	+	1.05248i	1.08940	+	0.291905i	0.758443	−	0.651739i	$-0.225960\pi$
$13$	3.92790	+	1.05248i	1.08940	+	0.291905i	0.330961	+	0.943644i	$0.392627\pi$
$14$	1.00829	+	1.74641i	0.269476	+	0.466747i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.35877	−	2.35877i	0.572085	−	0.572085i	−0.360626	−	0.932711i	$-0.617437\pi$
$17$	2.35877	−	2.35877i	0.572085	−	0.572085i	0.932711	+	0.360626i	$0.117437\pi$
$18$	−2.95680	−	0.507306i	−0.696923	−	0.119573i
$19$		−	3.70753i		−	0.850565i	−0.905061	−	0.425282i	$-0.860175\pi$
$19$		−	3.70753i		−	0.850565i	0.905061	−	0.425282i	$-0.139825\pi$
$20$		0			0
$21$	2.35376	−	2.58061i	0.513633	−	0.563135i
$22$	−0.509743	+	1.90239i	−0.108678	+	0.405590i
$23$	1.62200	−	6.05338i	0.338210	−	1.26222i	−0.562137	−	0.827044i	$-0.690021\pi$
$23$	1.62200	−	6.05338i	0.338210	−	1.26222i	0.900347	−	0.435173i	$-0.143313\pi$
$24$	−1.69185	−	0.370982i	−0.345348	−	0.0757264i
$25$		0			0
$26$		−	4.06647i		−	0.797499i
$27$	0.713876	+	5.14688i	0.137386	+	0.990518i
$28$	1.42594	−	1.42594i	0.269476	−	0.269476i
$29$	3.74863	−	6.49281i	0.696103	−	1.20569i	−0.273705	−	0.961814i	$-0.588249\pi$
$29$	3.74863	−	6.49281i	0.696103	−	1.20569i	0.969808	−	0.243872i	$-0.0784175\pi$
$30$		0			0
$31$	3.48837	+	6.04204i	0.626530	+	1.08518i	0.988243	+	0.152892i	$0.0488587\pi$
$31$	3.48837	+	6.04204i	0.626530	+	1.08518i	−0.361713	+	0.932289i	$0.617808\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	3.40767	−	0.156660i	0.593199	−	0.0272710i
$34$	−2.88889	−	1.66790i	−0.495440	−	0.286042i
$35$		0			0
$36$	0.275255	+	2.98735i	0.0458759	+	0.497891i
$37$	−4.26692	−	4.26692i	−0.701478	−	0.701478i	0.263250	−	0.964728i	$-0.415206\pi$
$37$	−4.26692	−	4.26692i	−0.701478	−	0.701478i	−0.964728	+	0.263250i	$0.915206\pi$
$38$	−3.58120	+	0.959578i	−0.580947	+	0.155664i
$39$	−6.71243	+	2.13346i	−1.07485	+	0.341627i
$40$		0			0
$41$	6.13601	−	3.54263i	0.958284	−	0.553266i	0.0626396	−	0.998036i	$-0.480048\pi$
$41$	6.13601	−	3.54263i	0.958284	−	0.553266i	0.895644	+	0.444771i	$0.146715\pi$
$42$	−3.10188	−	1.60565i	−0.478630	−	0.247757i
$43$	−2.43757	−	9.09714i	−0.371726	−	1.38730i	−0.858070	−	0.513533i	$-0.828336\pi$
$43$	−2.43757	−	9.09714i	−0.371726	−	1.38730i	0.486344	−	0.873767i	$-0.338330\pi$
$44$	1.96950			0.296913
$45$		0			0
$46$	−6.26692			−0.924007
$47$	−2.00837	−	7.49533i	−0.292951	−	1.09331i	−0.942831	−	0.333270i	$-0.891848\pi$
$47$	−2.00837	−	7.49533i	−0.292951	−	1.09331i	0.649881	−	0.760036i	$-0.274819\pi$
$48$	0.0795432	+	1.73022i	0.0114811	+	0.249736i
$49$	−2.54041	+	1.46671i	−0.362916	+	0.209530i
$50$		0			0
$51$	−1.23752	+	5.64369i	−0.173288	+	0.790274i
$52$	−3.92790	+	1.05248i	−0.544702	+	0.145953i
$53$	7.03027	+	7.03027i	0.965682	+	0.965682i	0.999430	−	0.0337485i	$-0.0107445\pi$
$53$	7.03027	+	7.03027i	0.965682	+	0.965682i	−0.0337485	+	0.999430i	$0.510745\pi$
$54$	4.78674	−	2.02166i	0.651393	−	0.275113i
$55$		0			0
$56$	−1.74641	−	1.00829i	−0.233373	−	0.134738i
$57$	3.46282	+	5.40797i	0.458662	+	0.716303i
$58$	−7.24179	−	1.94043i	−0.950894	−	0.254791i
$59$	−1.34967	−	2.33769i	−0.175712	−	0.304341i	0.764696	−	0.644392i	$-0.222889\pi$
$59$	−1.34967	−	2.33769i	−0.175712	−	0.304341i	−0.940407	+	0.340050i	$0.889556\pi$
$60$		0			0
$61$	−4.37353	+	7.57518i	−0.559973	+	0.969902i	0.437524	+	0.899207i	$0.355855\pi$
$61$	−4.37353	+	7.57518i	−0.559973	+	0.969902i	−0.997498	+	0.0706960i	$0.977478\pi$
$62$	4.93330	−	4.93330i	0.626530	−	0.626530i
$63$	−1.02302	+	5.96261i	−0.128889	+	0.751218i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−1.03329	−	3.25101i	−0.127189	−	0.400171i
$67$	−2.19259	+	8.18285i	−0.267867	+	0.999694i	0.692605	+	0.721317i	$0.256463\pi$
$67$	−2.19259	+	8.18285i	−0.267867	+	0.999694i	−0.960472	+	0.278377i	$0.910204\pi$
$68$	−0.863368	+	3.22213i	−0.104699	+	0.390741i
$69$	3.28793	+	10.3447i	0.395820	+	1.24535i
$70$		0			0
$71$		−	5.68481i		−	0.674663i	−0.941386	−	0.337332i	$-0.890476\pi$
$71$		−	5.68481i		−	0.674663i	0.941386	−	0.337332i	$-0.109524\pi$
$72$	2.81431	−	1.03906i	0.331670	−	0.122454i
$73$	−1.14928	+	1.14928i	−0.134513	+	0.134513i	−0.771157	−	0.636645i	$-0.780322\pi$
$73$	−1.14928	+	1.14928i	−0.134513	+	0.134513i	0.636645	+	0.771157i	$0.280322\pi$
$74$	−3.01717	+	5.22589i	−0.350739	+	0.607498i
$75$		0			0
$76$	1.85376	+	3.21081i	0.212641	+	0.368305i
$77$	3.83631	+	1.02794i	0.437188	+	0.117144i
$78$	3.79807	+	5.93153i	0.430047	+	0.671614i
$79$	10.0535	+	5.80440i	1.13111	+	0.653046i	0.944214	−	0.329334i	$-0.106824\pi$
$79$	10.0535	+	5.80440i	1.13111	+	0.653046i	0.186895	+	0.982380i	$0.440158\pi$
$80$		0			0
$81$	−5.84847	−	6.84072i	−0.649830	−	0.760080i
$82$	−5.01003	−	5.01003i	−0.553266	−	0.553266i
$83$	1.64569	−	0.440961i	0.180638	−	0.0484017i	−0.167366	−	0.985895i	$-0.553526\pi$
$83$	1.64569	−	0.440961i	0.180638	−	0.0484017i	0.348004	+	0.937493i	$0.386860\pi$
$84$	−0.748114	+	3.41176i	−0.0816259	+	0.372253i
$85$		0			0
$86$	−8.15627	+	4.70902i	−0.879513	+	0.507787i
$87$	0.596356	+	12.9719i	0.0639361	+	1.39074i
$88$	−0.509743	−	1.90239i	−0.0543388	−	0.202795i
$89$	2.04989			0.217288			0.108644	−	0.994081i	$-0.465349\pi$
$89$	2.04989			0.217288			0.108644	+	0.994081i	$0.465349\pi$
$90$		0			0
$91$	−8.20034			−0.859629
$92$	1.62200	+	6.05338i	0.169105	+	0.631109i
$93$	−10.7315	−	5.55506i	−1.11281	−	0.576033i
$94$	−6.72013	+	3.87987i	−0.693128	+	0.400178i
$95$		0			0
$96$	1.65068	−	0.524648i	0.168472	−	0.0535466i
$97$	9.71905	−	2.60421i	0.986820	−	0.264418i	0.270906	−	0.962606i	$-0.412677\pi$
$97$	9.71905	−	2.60421i	0.986820	−	0.264418i	0.715914	+	0.698188i	$0.246010\pi$
$98$	2.07424	+	2.07424i	0.209530	+	0.209530i
$99$	−4.82426	+	3.41127i	−0.484856	+	0.342845i
$100$		0			0
$101$	−4.09014	−	2.36144i	−0.406984	−	0.234972i	0.282509	−	0.959265i	$-0.408833\pi$
$101$	−4.09014	−	2.36144i	−0.406984	−	0.234972i	−0.689493	+	0.724292i	$0.742167\pi$
$102$	5.77168	−	0.265340i	0.571481	−	0.0262726i
$103$	3.86872	+	1.03662i	0.381196	+	0.102141i	0.444329	−	0.895864i	$-0.353442\pi$
$103$	3.86872	+	1.03662i	0.381196	+	0.102141i	−0.0631321	+	0.998005i	$0.520109\pi$
$104$	2.03323	+	3.52166i	0.199375	+	0.345327i
$105$		0			0
$106$	4.97115	−	8.61029i	0.482841	−	0.836305i
$107$	−5.40296	+	5.40296i	−0.522324	+	0.522324i	−0.918273	−	0.395949i	$-0.870416\pi$
$107$	−5.40296	+	5.40296i	−0.522324	+	0.522324i	0.395949	+	0.918273i	$0.370416\pi$
$108$	−3.19168	−	4.10039i	−0.307119	−	0.394560i
$109$		−	4.35357i		−	0.416996i	−0.978023	−	0.208498i	$-0.933142\pi$
$109$		−	4.35357i		−	0.416996i	0.978023	−	0.208498i	$-0.0668575\pi$
$110$		0			0
$111$	10.2092	+	2.23863i	0.969017	+	0.212481i
$112$	−0.521929	+	1.94786i	−0.0493176	+	0.184056i
$113$	−0.767544	+	2.86451i	−0.0722045	+	0.269471i	−0.992585	−	0.121553i	$-0.961212\pi$
$113$	−0.767544	+	2.86451i	−0.0722045	+	0.269471i	0.920380	+	0.391024i	$0.127879\pi$
$114$	4.32745	−	4.74451i	0.405303	−	0.444364i
$115$		0			0
$116$			7.49726i			0.696103i
$117$	7.79841	−	9.38136i	0.720964	−	0.867307i
$118$	−1.90872	+	1.90872i	−0.175712	+	0.175712i
$119$	−3.36345	+	5.82566i	−0.308327	+	0.534037i
$120$		0			0
$121$	−3.56054	−	6.16704i	−0.323686	−	0.560640i
$122$	8.44902	+	2.26391i	0.764938	+	0.204965i
$123$	−5.64146	+	10.8985i	−0.508673	+	0.982681i
$124$	−6.04204	−	3.48837i	−0.542591	−	0.313265i
$125$		0			0
$126$	6.02421	−	0.555073i	0.536680	−	0.0494498i
$127$	3.41734	+	3.41734i	0.303240	+	0.303240i	0.842280	−	0.539040i	$-0.181213\pi$
$127$	3.41734	+	3.41734i	0.303240	+	0.303240i	−0.539040	+	0.842280i	$0.681213\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	12.0523	+	10.9928i	1.06114	+	0.967863i
$130$		0			0
$131$	−0.411267	+	0.237445i	−0.0359326	+	0.0207457i	−0.517859	−	0.855466i	$-0.673271\pi$
$131$	−0.411267	+	0.237445i	−0.0359326	+	0.0207457i	0.481926	+	0.876212i	$0.339937\pi$
$132$	−2.87280	+	1.83951i	−0.250045	+	0.160108i
$133$	1.93506	+	7.22176i	0.167791	+	0.626206i
$134$	8.47151			0.731827
$135$		0			0
$136$	3.33580			0.286042
$137$	−2.54985	−	9.51618i	−0.217849	−	0.813022i	−0.985144	−	0.171728i	$-0.945065\pi$
$137$	−2.54985	−	9.51618i	−0.217849	−	0.813022i	0.767296	−	0.641293i	$-0.221602\pi$
$138$	9.14122	−	5.85329i	0.778152	−	0.498265i
$139$	−0.608318	+	0.351212i	−0.0515968	+	0.0297894i	−0.525577	−	0.850746i	$-0.676150\pi$
$139$	−0.608318	+	0.351212i	−0.0515968	+	0.0297894i	0.473980	+	0.880536i	$0.342817\pi$
$140$		0			0
$141$	9.93012	+	9.05722i	0.836267	+	0.762755i
$142$	−5.49111	+	1.47134i	−0.460803	+	0.123472i
$143$	−5.66314	−	5.66314i	−0.473575	−	0.473575i
$144$	−1.73205	−	2.44949i	−0.144338	−	0.204124i
$145$		0			0
$146$	1.40757	+	0.812661i	0.116491	+	0.0672563i
$147$	2.33566	−	4.51215i	0.192642	−	0.372156i
$148$	5.82872	+	1.56180i	0.479118	+	0.128379i
$149$	−4.05609	−	7.02536i	−0.332288	−	0.575540i	0.650672	−	0.759359i	$-0.274487\pi$
$149$	−4.05609	−	7.02536i	−0.332288	−	0.575540i	−0.982960	+	0.183819i	$0.941154\pi$
$150$		0			0
$151$	4.61739	−	7.99755i	0.375758	−	0.650832i	−0.614682	−	0.788775i	$-0.710716\pi$
$151$	4.61739	−	7.99755i	0.375758	−	0.650832i	0.990440	+	0.137943i	$0.0440491\pi$
$152$	2.62162	−	2.62162i	0.212641	−	0.212641i
$153$	−3.46609	−	9.38798i	−0.280217	−	0.758973i
$154$		−	3.97164i		−	0.320044i
$155$		0			0
$156$	4.74641	−	5.20385i	0.380017	−	0.416641i
$157$	2.80938	−	10.4848i	0.224213	−	0.836775i	−0.758505	−	0.651667i	$-0.774070\pi$
$157$	2.80938	−	10.4848i	0.224213	−	0.836775i	0.982718	−	0.185108i	$-0.0592635\pi$
$158$	3.00458	−	11.2132i	0.239031	−	0.892077i
$159$	−16.8209	−	3.68841i	−1.33399	−	0.292510i
$160$		0			0
$161$			12.6377i			0.995993i
$162$	−5.09393	+	7.41970i	−0.400217	+	0.582946i
$163$	−9.68197	+	9.68197i	−0.758351	+	0.758351i	−0.976022	−	0.217671i	$-0.930154\pi$
$163$	−9.68197	+	9.68197i	−0.758351	+	0.758351i	0.217671	+	0.976022i	$0.430154\pi$
$164$	−3.54263	+	6.13601i	−0.276633	+	0.479142i
$165$		0			0
$166$	−0.851871	−	1.47548i	−0.0661180	−	0.114520i
$167$	−4.93579	−	1.32254i	−0.381943	−	0.102341i	0.0627387	−	0.998030i	$-0.480017\pi$
$167$	−4.93579	−	1.32254i	−0.381943	−	0.102341i	−0.444682	+	0.895689i	$0.646683\pi$
$168$	3.48913	−	0.160405i	0.269192	−	0.0123755i
$169$	3.06239	+	1.76807i	0.235568	+	0.136005i
$170$		0			0
$171$	−10.1021	−	4.65404i	−0.772524	−	0.355903i
$172$	6.65957	+	6.65957i	0.507787	+	0.507787i
$173$	7.16239	−	1.91916i	0.544546	−	0.145911i	0.0239492	−	0.999713i	$-0.492376\pi$
$173$	7.16239	−	1.91916i	0.544546	−	0.145911i	0.520597	+	0.853802i	$0.325709\pi$
$174$	12.3756	−	3.93342i	0.938190	−	0.298192i
$175$		0			0
$176$	−1.70563	+	0.984748i	−0.128567	+	0.0742282i
$177$	4.15208	+	2.14928i	0.312090	+	0.161550i
$178$	−0.530550	−	1.98004i	−0.0397664	−	0.148410i
$179$	−2.73426			−0.204369			−0.102184	−	0.994765i	$-0.532583\pi$
$179$	−2.73426			−0.204369			−0.102184	+	0.994765i	$0.532583\pi$
$180$		0			0
$181$	−22.7081			−1.68788			−0.843941	−	0.536437i	$-0.819770\pi$
$181$	−22.7081			−1.68788			−0.843941	+	0.536437i	$0.819770\pi$
$182$	2.12240	+	7.92092i	0.157323	+	0.587138i
$183$	−0.695770	−	15.1344i	−0.0514328	−	1.11877i
$184$	5.42731	−	3.13346i	0.400107	−	0.231002i
$185$		0			0
$186$	−2.58824	+	11.8036i	−0.189779	+	0.865484i
$187$	−6.34598	+	1.70040i	−0.464064	+	0.124346i
$188$	5.48696	+	5.48696i	0.400178	+	0.400178i
$189$	−4.07684	−	9.65283i	−0.296546	−	0.702140i
$190$		0			0
$191$	−1.11154	−	0.641749i	−0.0804283	−	0.0464353i	0.459246	−	0.888309i	$-0.348119\pi$
$191$	−1.11154	−	0.641749i	−0.0804283	−	0.0464353i	−0.539675	+	0.841874i	$0.681453\pi$
$192$	−0.933998	−	1.45865i	−0.0674055	−	0.105269i
$193$	5.28063	+	1.41494i	0.380108	+	0.101850i	0.443814	−	0.896119i	$-0.353625\pi$
$193$	5.28063	+	1.41494i	0.380108	+	0.101850i	−0.0637057	+	0.997969i	$0.520292\pi$
$194$	−5.03095	−	8.71386i	−0.361201	−	0.625619i
$195$		0			0
$196$	1.46671	−	2.54041i	0.104765	−	0.181458i
$197$	−12.0386	+	12.0386i	−0.857716	+	0.857716i	−0.991069	−	0.133353i	$-0.957426\pi$
$197$	−12.0386	+	12.0386i	−0.857716	+	0.857716i	0.133353	+	0.991069i	$0.457426\pi$
$198$	4.54364	+	3.77698i	0.322903	+	0.268418i
$199$		−	4.43831i		−	0.314623i	−0.987549	−	0.157312i	$-0.949717\pi$
$199$		−	4.43831i		−	0.314623i	0.987549	−	0.157312i	$-0.0502827\pi$
$200$		0			0
$201$	−4.44456	−	13.9838i	−0.313495	−	0.986338i
$202$	−1.22237	+	4.56196i	−0.0860058	+	0.320978i
$203$	−3.91303	+	14.6036i	−0.274641	+	1.02497i
$204$	−1.75012	−	5.50634i	−0.122533	−	0.385521i
$205$		0			0
$206$		−	4.00520i		−	0.279055i
$207$	−14.4578	−	12.0183i	−1.00489	−	0.835331i
$208$	2.87542	−	2.87542i	0.199375	−	0.199375i
$209$	−3.65098	+	6.32368i	−0.252543	+	0.437418i
$210$		0			0
$211$	12.0425	+	20.8582i	0.829038	+	1.43594i	0.898794	+	0.438372i	$0.144445\pi$
$211$	12.0425	+	20.8582i	0.829038	+	1.43594i	−0.0697556	+	0.997564i	$0.522222\pi$
$212$	−9.60353	−	2.57326i	−0.659573	−	0.176732i
$213$	5.30960	+	8.29213i	0.363808	+	0.568167i
$214$	6.61725	+	3.82047i	0.452346	+	0.261162i
$215$		0			0
$216$	−3.13461	+	4.14418i	−0.213283	+	0.281976i
$217$	−9.94838	−	9.94838i	−0.675340	−	0.675340i
$218$	−4.20523	+	1.12679i	−0.284814	+	0.0763156i
$219$	0.602965	−	2.74981i	0.0407446	−	0.185815i
$220$		0			0
$221$	11.7476	−	6.78245i	0.790226	−	0.456237i
$222$	−0.479991	−	10.4408i	−0.0322149	−	0.700738i
$223$	−4.34272	−	16.2073i	−0.290810	−	1.08532i	−0.944488	−	0.328546i	$-0.893441\pi$
$223$	−4.34272	−	16.2073i	−0.290810	−	1.08532i	0.653678	−	0.756773i	$-0.273225\pi$
$224$	2.01658			0.134738
$225$		0			0
$226$	2.96556			0.197266
$227$	−1.92533	−	7.18543i	−0.127789	−	0.476914i	0.872135	−	0.489265i	$-0.162735\pi$
$227$	−1.92533	−	7.18543i	−0.127789	−	0.476914i	−0.999924	+	0.0123515i	$0.996068\pi$
$228$	−5.70288	−	2.95203i	−0.377682	−	0.195503i
$229$	7.74183	−	4.46975i	0.511595	−	0.295369i	−0.221894	−	0.975071i	$-0.571224\pi$
$229$	7.74183	−	4.46975i	0.511595	−	0.295369i	0.733489	+	0.679701i	$0.237891\pi$
$230$		0			0
$231$	−6.55591	+	2.08371i	−0.431347	+	0.137098i
$232$	7.24179	−	1.94043i	0.475447	−	0.127396i
$233$	−15.0591	−	15.0591i	−0.986558	−	0.986558i	0.0133533	−	0.999911i	$-0.495749\pi$
$233$	−15.0591	−	15.0591i	−0.986558	−	0.986558i	−0.999911	+	0.0133533i	$0.995749\pi$
$234$	−11.0801	−	5.10461i	−0.724327	−	0.333699i
$235$		0			0
$236$	2.33769	+	1.34967i	0.152171	+	0.0878558i
$237$	−20.0858	+	0.923401i	−1.30471	+	0.0599814i
$238$	6.49768	+	1.74105i	0.421182	+	0.112855i
$239$	−5.42731	−	9.40038i	−0.351064	−	0.608060i	0.635372	−	0.772206i	$-0.280847\pi$
$239$	−5.42731	−	9.40038i	−0.351064	−	0.608060i	−0.986436	+	0.164146i	$0.947513\pi$
$240$		0			0
$241$	11.6659	−	20.2059i	0.751467	−	1.30158i	−0.195645	−	0.980675i	$-0.562680\pi$
$241$	11.6659	−	20.2059i	0.751467	−	1.30158i	0.947112	−	0.320904i	$-0.103987\pi$
$242$	−5.03537	+	5.03537i	−0.323686	+	0.323686i
$243$	14.9201	+	4.51572i	0.957122	+	0.289684i
$244$		−	8.74707i		−	0.559973i
$245$		0			0
$246$	11.9872	+	2.62850i	0.764277	+	0.167587i
$247$	3.90209	−	14.5628i	0.248284	−	0.926609i
$248$	−1.80571	+	6.73901i	−0.114663	+	0.427928i
$249$	−1.98862	+	2.18027i	−0.126024	+	0.138169i
$250$		0			0
$251$			13.3860i			0.844914i	0.906383	+	0.422457i	$0.138832\pi$
$251$			13.3860i			0.844914i	−0.906383	+	0.422457i	$0.861168\pi$
$252$	−2.09534	−	5.67528i	−0.131994	−	0.357509i
$253$	−8.72759	+	8.72759i	−0.548699	+	0.548699i
$254$	2.41643	−	4.18538i	0.151620	−	0.262614i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.29595	+	1.95494i	0.455109	+	0.121946i	0.479089	−	0.877766i	$-0.340967\pi$
$257$	7.29595	+	1.95494i	0.455109	+	0.121946i	−0.0239802	+	0.999712i	$0.507634\pi$
$258$	7.49889	−	14.4867i	0.466860	−	0.901905i
$259$	10.5384	+	6.08436i	0.654825	+	0.378063i
$260$		0			0
$261$	−12.9856	−	18.3645i	−0.803790	−	1.13673i
$262$	0.335798	+	0.335798i	0.0207457	+	0.0207457i
$263$	−10.7695	+	2.88569i	−0.664078	+	0.177939i	−0.575086	−	0.818093i	$-0.695031\pi$
$263$	−10.7695	+	2.88569i	−0.664078	+	0.177939i	−0.0889923	+	0.996032i	$0.528365\pi$
$264$	2.52036	+	2.29881i	0.155117	+	0.141482i
$265$		0			0
$266$	6.47485	−	3.73826i	0.396998	−	0.229207i
$267$	−2.99006	+	1.91459i	−0.182989	+	0.117171i
$268$	−2.19259	−	8.18285i	−0.133934	−	0.499847i
$269$	−13.4707			−0.821326			−0.410663	−	0.911787i	$-0.634703\pi$
$269$	−13.4707			−0.821326			−0.410663	+	0.911787i	$0.634703\pi$
$270$		0			0
$271$	20.4402			1.24165			0.620827	−	0.783947i	$-0.286797\pi$
$271$	20.4402			1.24165			0.620827	+	0.783947i	$0.286797\pi$
$272$	−0.863368	−	3.22213i	−0.0523494	−	0.195371i
$273$	11.9614	−	7.65910i	0.723936	−	0.463550i
$274$	−8.53197	+	4.92594i	−0.515435	+	0.297587i
$275$		0			0
$276$	−8.01977	−	7.31480i	−0.482733	−	0.440299i
$277$	23.4121	−	6.27326i	1.40670	−	0.376924i	0.525953	−	0.850514i	$-0.323709\pi$
$277$	23.4121	−	6.27326i	1.40670	−	0.376924i	0.880745	+	0.473590i	$0.157042\pi$
$278$	0.496689	+	0.496689i	0.0297894	+	0.0297894i
$279$	20.8419	−	1.92038i	1.24777	−	0.114970i
$280$		0			0
$281$	19.5424	+	11.2828i	1.16580	+	0.673076i	0.952687	−	0.303952i	$-0.0983062\pi$
$281$	19.5424	+	11.2828i	1.16580	+	0.673076i	0.213114	+	0.977027i	$0.431640\pi$
$282$	6.17850	−	11.9359i	0.367924	−	0.710775i
$283$	2.05136	+	0.549660i	0.121941	+	0.0326739i	0.319273	−	0.947663i	$-0.396561\pi$
$283$	2.05136	+	0.549660i	0.121941	+	0.0326739i	−0.197333	+	0.980337i	$0.563228\pi$
$284$	2.84241	+	4.92319i	0.168666	+	0.292138i
$285$		0			0
$286$	−4.00444	+	6.93590i	−0.236788	+	0.410128i
$287$	−10.1031	+	10.1031i	−0.596368	+	0.596368i
$288$	−1.91774	+	2.30701i	−0.113004	+	0.135942i
$289$			5.87245i			0.345438i
$290$		0			0
$291$	−11.7443	+	12.8762i	−0.688464	+	0.754816i
$292$	0.420664	−	1.56994i	0.0246175	−	0.0918738i
$293$	0.946406	−	3.53204i	0.0552896	−	0.206344i	−0.932755	−	0.360510i	$-0.882603\pi$
$293$	0.946406	−	3.53204i	0.0552896	−	0.206344i	0.988045	+	0.154167i	$0.0492692\pi$
$294$	−4.96292	−	1.08824i	−0.289443	−	0.0634677i
$295$		0			0
$296$		−	6.03434i		−	0.350739i
$297$	3.85077	−	9.48168i	0.223444	−	0.550183i
$298$	−5.73618	+	5.73618i	−0.332288	+	0.332288i
$299$	12.7421	−	22.0700i	0.736895	−	1.27634i
$300$		0			0
$301$	9.49611	+	16.4477i	0.547347	+	0.948032i
$302$	−8.92011	−	2.39014i	−0.513295	−	0.137537i
$303$	8.17164	−	0.375673i	0.469449	−	0.0215819i
$304$	−3.21081	−	1.85376i	−0.184153	−	0.106321i
$305$		0			0
$306$	−8.17100	+	5.77777i	−0.467105	+	0.330293i
$307$	10.5436	+	10.5436i	0.601754	+	0.601754i	0.940778	−	0.339024i	$-0.110097\pi$
$307$	10.5436	+	10.5436i	0.601754	+	0.601754i	−0.339024	+	0.940778i	$0.610097\pi$
$308$	−3.83631	+	1.02794i	−0.218594	+	0.0585721i
$309$	−6.61130	+	2.10132i	−0.376104	+	0.119540i
$310$		0			0
$311$	−9.08436	+	5.24485i	−0.515127	+	0.297408i	−0.734938	−	0.678134i	$-0.762789\pi$
$311$	−9.08436	+	5.24485i	−0.515127	+	0.297408i	0.219812	+	0.975542i	$0.429456\pi$
$312$	−6.25499	−	3.23782i	−0.354119	−	0.183306i
$313$	4.56901	+	17.0518i	0.258256	+	0.963824i	0.966250	+	0.257606i	$0.0829337\pi$
$313$	4.56901	+	17.0518i	0.258256	+	0.963824i	−0.707994	+	0.706218i	$0.750400\pi$
$314$	−10.8546			−0.612562
$315$		0			0
$316$	−11.6088			−0.653046
$317$	6.00131	+	22.3972i	0.337067	+	1.25795i	0.901611	+	0.432549i	$0.142386\pi$
$317$	6.00131	+	22.3972i	0.337067	+	1.25795i	−0.564543	+	0.825403i	$0.690948\pi$
$318$	0.790843	+	17.2024i	0.0443483	+	0.964663i
$319$	−12.7876	+	7.38291i	−0.715966	+	0.413363i
$320$		0			0
$321$	2.83465	−	12.9274i	0.158215	−	0.721535i
$322$	12.2071	−	3.27089i	0.680276	−	0.182279i
$323$	−8.74518	−	8.74518i	−0.486595	−	0.486595i
$324$	8.48528	+	3.00000i	0.471405	+	0.166667i
$325$		0			0
$326$	11.8579	+	6.84619i	0.656751	+	0.379175i
$327$	4.06623	+	6.35032i	0.224863	+	0.351173i
$328$	6.84383	+	1.83380i	0.377887	+	0.101255i
$329$	7.82405	+	13.5517i	0.431354	+	0.747127i
$330$		0			0
$331$	12.9130	−	22.3659i	0.709761	−	1.22934i	−0.255185	−	0.966892i	$-0.582136\pi$
$331$	12.9130	−	22.3659i	0.709761	−	1.22934i	0.964946	−	0.262450i	$-0.0845303\pi$
$332$	−1.20473	+	1.20473i	−0.0661180	+	0.0661180i
$333$	−16.9825	+	6.27003i	−0.930636	+	0.343595i
$334$			5.10991i			0.279602i
$335$		0			0
$336$	−1.05799	−	3.32872i	−0.0577182	−	0.181597i
$337$	−8.30344	+	30.9889i	−0.452317	+	1.68807i	0.243541	+	0.969891i	$0.421691\pi$
$337$	−8.30344	+	30.9889i	−0.452317	+	1.68807i	−0.695858	+	0.718180i	$0.744976\pi$
$338$	0.915220	−	3.41565i	0.0497814	−	0.185787i
$339$	−1.55588	−	4.89519i	−0.0845035	−	0.265870i
$340$		0			0
$341$		−	13.7407i		−	0.744099i
$342$	−1.88085	+	10.9624i	−0.101705	+	0.592779i
$343$	14.1644	−	14.1644i	0.764806	−	0.764806i
$344$	4.70902	−	8.15627i	0.253894	−	0.439757i
$345$		0			0
$346$	−3.70753	−	6.42162i	−0.199318	−	0.345229i
$347$	14.3001	+	3.83170i	0.767670	+	0.205696i	0.621342	−	0.783540i	$-0.286588\pi$
$347$	14.3001	+	3.83170i	0.767670	+	0.205696i	0.146328	+	0.989236i	$0.453255\pi$
$348$	−7.00242	−	10.9358i	−0.375369	−	0.586223i
$349$	−13.3741	−	7.72151i	−0.715897	−	0.413323i	0.0973439	−	0.995251i	$-0.468965\pi$
$349$	−13.3741	−	7.72151i	−0.715897	−	0.413323i	−0.813241	+	0.581928i	$0.802299\pi$
$350$		0			0
$351$	−2.61295	+	20.9678i	−0.139469	+	1.11918i
$352$	1.39264	+	1.39264i	0.0742282	+	0.0742282i
$353$	20.1446	−	5.39774i	1.07219	−	0.287293i	0.320798	−	0.947148i	$-0.396049\pi$
$353$	20.1446	−	5.39774i	1.07219	−	0.287293i	0.751393	+	0.659855i	$0.229382\pi$
$354$	1.00140	−	4.56688i	0.0532240	−	0.242727i
$355$		0			0
$356$	−1.77526	+	1.02494i	−0.0940883	+	0.0543219i
$357$	−0.535079	−	11.6390i	−0.0283194	−	0.616003i
$358$	0.707680	+	2.64110i	0.0374020	+	0.139586i
$359$	3.39466			0.179163			0.0895815	−	0.995979i	$-0.471447\pi$
$359$	3.39466			0.179163			0.0895815	+	0.995979i	$0.471447\pi$
$360$		0			0
$361$	5.25425			0.276540
$362$	5.87729	+	21.9344i	0.308904	+	1.15284i
$363$	10.9536	+	5.66999i	0.574914	+	0.297597i
$364$	7.10170	−	4.10017i	0.372230	−	0.214907i
$365$		0			0
$366$	−14.4386	+	4.58913i	−0.754718	+	0.239878i
$367$	21.2279	−	5.68801i	1.10809	−	0.296912i	0.342035	−	0.939687i	$-0.388884\pi$
$367$	21.2279	−	5.68801i	1.10809	−	0.296912i	0.766054	+	0.642776i	$0.222217\pi$
$368$	−4.43138	−	4.43138i	−0.231002	−	0.231002i
$369$	−1.95025	−	21.1661i	−0.101526	−	1.10186i
$370$		0			0
$371$	−17.3633	−	10.0247i	−0.901458	−	0.520457i
$372$	12.0713	−	0.554953i	0.625869	−	0.0287730i
$373$	−1.42207	−	0.381044i	−0.0736322	−	0.0197297i	0.221815	−	0.975089i	$-0.428802\pi$
$373$	−1.42207	−	0.381044i	−0.0736322	−	0.0197297i	−0.295447	+	0.955359i	$0.595469\pi$
$374$	3.28492	+	5.68965i	0.169859	+	0.294205i
$375$		0			0
$376$	3.87987	−	6.72013i	0.200089	−	0.346564i
$377$	21.5578	−	21.5578i	1.11028	−	1.11028i
$378$	−8.26875	+	6.43626i	−0.425299	+	0.331045i
$379$			30.1323i			1.54779i	0.633314	+	0.773895i	$0.281694\pi$
$379$			30.1323i			1.54779i	−0.633314	+	0.773895i	$0.718306\pi$
$380$		0			0
$381$	−8.17649	−	1.79290i	−0.418894	−	0.0918531i
$382$	−0.332194	+	1.23976i	−0.0169965	+	0.0634318i
$383$	4.43826	−	16.5638i	0.226785	−	0.846372i	−0.754897	−	0.655843i	$-0.772313\pi$
$383$	4.43826	−	16.5638i	0.226785	−	0.846372i	0.981682	−	0.190528i	$-0.0610201\pi$
$384$	−1.16721	+	1.27970i	−0.0595638	+	0.0653043i
$385$		0			0
$386$		−	5.46691i		−	0.278258i
$387$	−27.8472	−	4.77783i	−1.41556	−	0.242871i
$388$	−7.11484	+	7.11484i	−0.361201	+	0.361201i
$389$	−15.1070	+	26.1660i	−0.765953	+	1.32667i	0.173789	+	0.984783i	$0.444399\pi$
$389$	−15.1070	+	26.1660i	−0.765953	+	1.32667i	−0.939741	+	0.341886i	$0.888934\pi$
$390$		0			0
$391$	−10.4526	−	18.1044i	−0.528610	−	0.915580i
$392$	−2.83346	−	0.759224i	−0.143112	−	0.0383466i
$393$	0.378120	−	0.730471i	0.0190736	−	0.0368474i
$394$	14.7442	+	8.51258i	0.742803	+	0.428858i
$395$		0			0
$396$	2.47230	−	5.36637i	0.124238	−	0.269670i
$397$	2.16969	+	2.16969i	0.108893	+	0.108893i	0.759454	−	0.650561i	$-0.225466\pi$
$397$	2.16969	+	2.16969i	0.108893	+	0.108893i	−0.650561	+	0.759454i	$0.725466\pi$
$398$	−4.28708	+	1.14872i	−0.214892	+	0.0575801i
$399$	−9.56768	−	8.72664i	−0.478983	−	0.436878i
$400$		0			0
$401$	−12.3209	+	7.11346i	−0.615275	+	0.355229i	−0.775027	−	0.631928i	$-0.782264\pi$
$401$	−12.3209	+	7.11346i	−0.615275	+	0.355229i	0.159752	+	0.987157i	$0.448931\pi$
$402$	−12.3569	+	7.91238i	−0.616308	+	0.394633i
$403$	7.34287	+	27.4040i	0.365774	+	1.36509i
$404$	4.72288			0.234972
$405$		0			0
$406$	15.1188			0.750333
$407$	3.07596	+	11.4796i	0.152470	+	0.569025i
$408$	−4.86575	+	3.11563i	−0.240890	+	0.154247i
$409$	10.2963	−	5.94456i	0.509118	−	0.293939i	−0.223353	−	0.974738i	$-0.571700\pi$
$409$	10.2963	−	5.94456i	0.509118	−	0.293939i	0.732471	+	0.680798i	$0.238367\pi$
$410$		0			0
$411$	12.6074	+	11.4992i	0.621878	+	0.567212i
$412$	−3.86872	+	1.03662i	−0.190598	+	0.0510706i
$413$	3.84907	+	3.84907i	0.189401	+	0.189401i
$414$	−7.86684	+	17.0758i	−0.386634	+	0.839228i
$415$		0			0
$416$	−3.52166	−	2.03323i	−0.172664	−	0.0996874i
$417$	0.559288	−	1.08046i	0.0273885	−	0.0529104i
$418$	7.05315	+	1.88989i	0.344981	+	0.0924373i
$419$	19.6354	+	34.0095i	0.959251	+	1.66147i	0.724325	+	0.689458i	$0.242151\pi$
$419$	19.6354	+	34.0095i	0.959251	+	1.66147i	0.234926	+	0.972013i	$0.424515\pi$
$420$		0			0
$421$	−12.2493	+	21.2163i	−0.596992	+	1.03402i	0.396270	+	0.918134i	$0.370304\pi$
$421$	−12.2493	+	21.2163i	−0.596992	+	1.03402i	−0.993262	+	0.115887i	$0.963029\pi$
$422$	17.0306	−	17.0306i	0.829038	−	0.829038i
$423$	−22.9440	−	3.93656i	−1.11557	−	0.191402i
$424$			9.94230i			0.482841i
$425$		0			0
$426$	6.63535	−	7.27484i	0.321484	−	0.352467i
$427$	4.56534	−	17.0381i	0.220932	−	0.824531i
$428$	1.97762	−	7.38058i	0.0955920	−	0.356754i
$429$	13.5499	+	2.97115i	0.654194	+	0.143449i
$430$		0			0
$431$			6.10703i			0.294165i	0.989124	+	0.147083i	$0.0469883\pi$
$431$			6.10703i			0.294165i	−0.989124	+	0.147083i	$0.953012\pi$
$432$	4.81427	+	1.95521i	0.231627	+	0.0940699i
$433$	−10.2605	+	10.2605i	−0.493088	+	0.493088i	−0.909278	−	0.416190i	$-0.863365\pi$
$433$	−10.2605	+	10.2605i	−0.493088	+	0.493088i	0.416190	+	0.909278i	$0.363365\pi$
$434$	−7.03457	+	12.1842i	−0.337670	+	0.584862i
$435$		0			0
$436$	2.17679	+	3.77030i	0.104249	+	0.180565i
$437$	−22.4431	−	6.01360i	−1.07360	−	0.287670i
$438$	−2.81217	+	0.129283i	−0.134371	+	0.00617740i
$439$	−1.96604	−	1.13510i	−0.0938342	−	0.0541752i	0.452349	−	0.891841i	$-0.350586\pi$
$439$	−1.96604	−	1.13510i	−0.0938342	−	0.0541752i	−0.546183	+	0.837666i	$0.683920\pi$
$440$		0			0
$441$	0.807438	+	8.76313i	0.0384494	+	0.417292i
$442$	−9.59184	−	9.59184i	−0.456237	−	0.456237i
$443$	−26.8719	+	7.20031i	−1.27672	+	0.342097i	−0.832603	−	0.553870i	$-0.813150\pi$
$443$	−26.8719	+	7.20031i	−1.27672	+	0.342097i	−0.444120	+	0.895967i	$0.646484\pi$
$444$	−9.96076	+	3.16590i	−0.472717	+	0.150247i
$445$		0			0
$446$	−14.5310	+	8.38950i	−0.688065	+	0.397254i
$447$	12.4781	+	6.45913i	0.590193	+	0.305506i
$448$	−0.521929	−	1.94786i	−0.0246588	−	0.0920279i
$449$	−11.7712			−0.555516			−0.277758	−	0.960651i	$-0.589591\pi$
$449$	−11.7712			−0.555516			−0.277758	+	0.960651i	$0.589591\pi$
$450$		0			0
$451$	−13.9544			−0.657086
$452$	−0.767544	−	2.86451i	−0.0361022	−	0.134735i
$453$	0.734564	+	15.9782i	0.0345128	+	0.750723i
$454$	−6.44228	+	3.71945i	−0.302351	+	0.174562i
$455$		0			0
$456$	−1.37542	+	6.27260i	−0.0644102	+	0.293741i
$457$	−37.5970	+	10.0741i	−1.75871	+	0.471246i	−0.986451	−	0.164058i	$-0.947542\pi$
$457$	−37.5970	+	10.0741i	−1.75871	+	0.471246i	−0.772263	+	0.635303i	$0.780875\pi$
$458$	−6.32118	−	6.32118i	−0.295369	−	0.295369i
$459$	13.8242	+	10.4564i	0.645256	+	0.488064i
$460$		0			0
$461$	−2.62200	−	1.51381i	−0.122119	−	0.0705053i	0.437696	−	0.899123i	$-0.355795\pi$
$461$	−2.62200	−	1.51381i	−0.122119	−	0.0705053i	−0.559815	+	0.828618i	$0.689128\pi$
$462$	3.70950	+	5.79322i	0.172582	+	0.269525i
$463$	6.60350	+	1.76940i	0.306891	+	0.0822311i	0.408978	−	0.912544i	$-0.365885\pi$
$463$	6.60350	+	1.76940i	0.306891	+	0.0822311i	−0.102087	+	0.994775i	$0.532552\pi$
$464$	−3.74863	−	6.49281i	−0.174026	−	0.301421i
$465$		0			0
$466$	−10.6484	+	18.4436i	−0.493279	+	0.854384i
$467$	−8.05359	+	8.05359i	−0.372676	+	0.372676i	−0.868451	−	0.495775i	$-0.834884\pi$
$467$	−8.05359	+	8.05359i	−0.372676	+	0.372676i	0.495775	+	0.868451i	$0.334884\pi$
$468$	−2.06294	+	12.0237i	−0.0953595	+	0.555796i
$469$		−	17.0835i		−	0.788841i
$470$		0			0
$471$	5.69485	+	17.9175i	0.262405	+	0.825596i
$472$	0.698639	−	2.60736i	0.0321575	−	0.120013i
$473$	−4.80079	+	17.9168i	−0.220740	+	0.823814i
$474$	6.09053	+	19.1624i	0.279747	+	0.880159i
$475$		0			0
$476$		−	6.72689i		−	0.308327i
$477$	27.9808	−	10.3306i	1.28115	−	0.473007i
$478$	−7.67538	+	7.67538i	−0.351064	+	0.351064i
$479$	16.5711	−	28.7020i	0.757154	−	1.31143i	−0.187142	−	0.982333i	$-0.559922\pi$
$479$	16.5711	−	28.7020i	0.757154	−	1.31143i	0.944296	−	0.329097i	$-0.106744\pi$
$480$		0			0
$481$	−12.2692	−	21.2509i	−0.559428	−	0.968958i
$482$	−22.5368	−	6.03872i	−1.02652	−	0.275056i
$483$	−11.8036	−	18.4340i	−0.537083	−	0.838775i
$484$	6.16704	+	3.56054i	0.280320	+	0.161843i
$485$		0			0
$486$	0.500258	−	15.5804i	0.0226921	−	0.706743i
$487$	14.8248	+	14.8248i	0.671777	+	0.671777i	0.958126	−	0.286349i	$-0.0924415\pi$
$487$	14.8248	+	14.8248i	0.671777	+	0.671777i	−0.286349	+	0.958126i	$0.592442\pi$
$488$	−8.44902	+	2.26391i	−0.382469	+	0.102482i
$489$	5.07962	−	23.1655i	0.229709	−	1.04758i
$490$		0			0
$491$	16.1505	−	9.32449i	0.728861	−	0.420808i	−0.0891441	−	0.996019i	$-0.528413\pi$
$491$	16.1505	−	9.32449i	0.728861	−	0.420808i	0.818005	+	0.575210i	$0.195080\pi$
$492$	−0.563584	−	12.2591i	−0.0254083	−	0.552682i
$493$	−6.47289	−	24.1572i	−0.291524	−	1.08798i
$494$	−15.0765			−0.678325
$495$		0			0
$496$	6.97674			0.313265
$497$	2.96707	+	11.0732i	0.133091	+	0.496703i
$498$	2.62068	+	1.35656i	0.117435	+	0.0607890i
$499$	−19.6189	+	11.3270i	−0.878263	+	0.507065i	−0.870085	−	0.492901i	$-0.835936\pi$
$499$	−19.6189	+	11.3270i	−0.878263	+	0.507065i	−0.00817742	+	0.999967i	$0.502603\pi$
$500$		0			0
$501$	8.43482	−	2.68090i	0.376840	−	0.119774i
$502$	12.9298	−	3.46454i	0.577087	−	0.154630i
$503$	9.64801	+	9.64801i	0.430183	+	0.430183i	0.888691	−	0.458507i	$-0.151616\pi$
$503$	9.64801	+	9.64801i	0.430183	+	0.430183i	−0.458507	+	0.888691i	$0.651616\pi$
$504$	−4.93958	+	3.49281i	−0.220027	+	0.155582i
$505$		0			0
$506$	10.6891	+	6.17134i	0.475187	+	0.274349i
$507$	−6.11831	+	0.281276i	−0.271724	+	0.0124919i
$508$	−4.66818	−	1.25084i	−0.207117	−	0.0554968i
$509$	13.5882	+	23.5355i	0.602286	+	1.04319i	0.992474	+	0.122455i	$0.0390768\pi$
$509$	13.5882	+	23.5355i	0.602286	+	1.04319i	−0.390188	+	0.920735i	$0.627590\pi$
$510$		0			0
$511$	1.63879	−	2.83847i	0.0724959	−	0.125567i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	19.0822	−	2.64671i	0.842499	−	0.116855i
$514$		−	7.55332i		−	0.333163i
$515$		0			0
$516$	−15.9340	−	3.49393i	−0.701454	−	0.153812i
$517$	−3.95547	+	14.7620i	−0.173961	+	0.649233i
$518$	3.14949	−	11.7541i	0.138381	−	0.516444i
$519$	−8.65490	+	9.48903i	−0.379908	+	0.416522i
$520$		0			0
$521$			18.3542i			0.804114i	0.915615	+	0.402057i	$0.131705\pi$
$521$			18.3542i			0.804114i	−0.915615	+	0.402057i	$0.868295\pi$
$522$	−14.3778	+	17.2962i	−0.629298	+	0.757035i
$523$	25.8576	−	25.8576i	1.13067	−	1.13067i	0.140607	−	0.990066i	$-0.455095\pi$
$523$	25.8576	−	25.8576i	1.13067	−	1.13067i	0.990066	−	0.140607i	$-0.0449053\pi$
$524$	0.237445	−	0.411267i	0.0103728	−	0.0179663i
$525$		0			0
$526$	5.57472	+	9.65570i	0.243069	+	0.421009i
$527$	22.4800	+	6.02350i	0.979244	+	0.262388i
$528$	1.56816	−	3.02946i	0.0682455	−	0.131840i
$529$	−14.0940	−	8.13716i	−0.612781	−	0.353789i
$530$		0			0
$531$	−8.06384	+	0.743005i	−0.349941	+	0.0322437i
$532$	−5.28669	−	5.28669i	−0.229207	−	0.229207i
$533$	27.8302	−	7.45708i	1.20546	−	0.323002i
$534$	2.62324	+	2.39264i	0.113519	+	0.103540i
$535$		0			0
$536$	−7.33654	+	4.23576i	−0.316890	+	0.182957i
$537$	3.98832	−	2.55380i	0.172109	−	0.110205i
$538$	3.48649	+	13.0117i	0.150313	+	0.560976i
$539$	5.77735			0.248848
$540$		0			0
$541$	−4.54804			−0.195536			−0.0977678	−	0.995209i	$-0.531170\pi$
$541$	−4.54804			−0.195536			−0.0977678	+	0.995209i	$0.531170\pi$
$542$	−5.29032	−	19.7437i	−0.227239	−	0.848066i
$543$	33.1231	−	21.2093i	1.42145	−	0.910180i
$544$	−2.88889	+	1.66790i	−0.123860	+	0.0715106i
$545$		0			0
$546$	−10.4940	−	9.57149i	−0.449100	−	0.409622i
$547$	−21.6180	+	5.79252i	−0.924319	+	0.247670i	−0.689430	−	0.724352i	$-0.742139\pi$
$547$	−21.6180	+	5.79252i	−0.924319	+	0.247670i	−0.234888	+	0.972022i	$0.575472\pi$
$548$	6.96632	+	6.96632i	0.297587	+	0.297587i
$549$	15.1504	+	21.4258i	0.646602	+	0.914433i
$550$		0			0
$551$	−24.0723	−	13.8981i	−1.02551	−	0.592080i
$552$	−4.98988	+	9.63971i	−0.212383	+	0.410293i
$553$	−22.6124	−	6.05896i	−0.961575	−	0.257653i
$554$	−12.1190	−	20.9907i	−0.514887	−	0.891811i
$555$		0			0
$556$	0.351212	−	0.608318i	0.0148947	−	0.0257984i
$557$	−20.5740	+	20.5740i	−0.871749	+	0.871749i	−0.992663	−	0.120914i	$-0.961417\pi$
$557$	−20.5740	+	20.5740i	−0.871749	+	0.871749i	0.120914	+	0.992663i	$0.461417\pi$
$558$	−7.24924	−	19.6347i	−0.306885	−	0.831205i
$559$		−	38.2982i		−	1.61984i
$560$		0			0
$561$	7.66836	−	8.40741i	0.323759	−	0.354961i
$562$	5.84041	−	21.7967i	0.246363	−	0.919438i
$563$	−9.17805	+	34.2529i	−0.386809	+	1.44359i	0.448487	+	0.893789i	$0.351963\pi$
$563$	−9.17805	+	34.2529i	−0.386809	+	1.44359i	−0.835296	+	0.549800i	$0.814704\pi$
$564$	−13.1283	−	2.87872i	−0.552803	−	0.121216i
$565$		0			0
$566$		−	2.12372i		−	0.0892668i
$567$	14.9624	+	10.2723i	0.628361	+	0.431396i
$568$	4.01977	−	4.01977i	0.168666	−	0.168666i
$569$	12.0592	−	20.8872i	0.505549	−	0.875637i	−0.494430	−	0.869217i	$-0.664623\pi$
$569$	12.0592	−	20.8872i	0.505549	−	0.875637i	0.999979	−	0.00641982i	$-0.00204351\pi$
$570$		0			0
$571$	2.24726	+	3.89236i	0.0940448	+	0.162890i	0.909210	−	0.416339i	$-0.136687\pi$
$571$	2.24726	+	3.89236i	0.0940448	+	0.162890i	−0.815165	+	0.579229i	$0.803354\pi$
$572$	7.73599	+	2.07285i	0.323458	+	0.0866703i
$573$	2.22074	−	0.102094i	0.0927726	−	0.00426502i
$574$	12.3737	+	7.14398i	0.516470	+	0.298184i
$575$		0			0
$576$	2.72474	+	1.25529i	0.113531	+	0.0523040i
$577$	−0.186522	−	0.186522i	−0.00776502	−	0.00776502i	0.703214	−	0.710979i	$-0.251748\pi$
$577$	−0.186522	−	0.186522i	−0.00776502	−	0.00776502i	−0.710979	+	0.703214i	$0.751748\pi$
$578$	5.67235	−	1.51990i	0.235939	−	0.0632196i
$579$	−9.02412	+	2.86820i	−0.375030	+	0.119198i
$580$		0			0
$581$	−2.97543	+	1.71786i	−0.123441	+	0.0712689i
$582$	15.4771	+	8.01154i	0.641547	+	0.332089i
$583$	−5.06802	−	18.9141i	−0.209896	−	0.783342i
$584$	−1.62532			−0.0672563
$585$		0			0
$586$	−3.65663			−0.151054
$587$	−11.6992	−	43.6620i	−0.482878	−	1.80212i	−0.589433	−	0.807818i	$-0.700649\pi$
$587$	−11.6992	−	43.6620i	−0.482878	−	1.80212i	0.106555	−	0.994307i	$-0.466018\pi$
$588$	0.233334	+	5.07547i	0.00962251	+	0.209309i
$589$	22.4010	−	12.9332i	0.923017	−	0.532904i
$590$		0			0
$591$	6.31603	−	28.8041i	0.259807	−	1.18484i
$592$	−5.82872	+	1.56180i	−0.239559	+	0.0641897i
$593$	3.60323	+	3.60323i	0.147967	+	0.147967i	0.777209	−	0.629242i	$-0.216635\pi$
$593$	3.60323	+	3.60323i	0.147967	+	0.147967i	−0.629242	+	0.777209i	$0.716635\pi$
$594$	−10.1553	−	1.26552i	−0.416675	−	0.0519248i
$595$		0			0
$596$	7.02536	+	4.05609i	0.287770	+	0.166144i
$597$	4.14537	+	6.47392i	0.169659	+	0.264960i
$598$	−24.6159	−	6.59580i	−1.00662	−	0.269722i
$599$	−23.4581	−	40.6307i	−0.958473	−	1.66012i	−0.726213	−	0.687470i	$-0.758721\pi$
$599$	−23.4581	−	40.6307i	−0.958473	−	1.66012i	−0.232260	−	0.972654i	$-0.574612\pi$
$600$		0			0
$601$	−20.5688	+	35.6263i	−0.839020	+	1.45323i	0.0516943	+	0.998663i	$0.483538\pi$
$601$	−20.5688	+	35.6263i	−0.839020	+	1.45323i	−0.890715	+	0.454563i	$0.849795\pi$
$602$	13.4295	−	13.4295i	0.547347	−	0.547347i
$603$	19.5438	+	16.2461i	0.795887	+	0.661594i
$604$			9.23478i			0.375758i
$605$		0			0
$606$	−2.47785	−	7.79597i	−0.100656	−	0.316690i
$607$	−4.28061	+	15.9755i	−0.173745	+	0.648424i	0.823017	+	0.568016i	$0.192289\pi$
$607$	−4.28061	+	15.9755i	−0.173745	+	0.648424i	−0.996762	+	0.0804079i	$0.974378\pi$
$608$	−0.959578	+	3.58120i	−0.0389160	+	0.145237i
$609$	−7.93204	−	24.9563i	−0.321422	−	1.01128i
$610$		0			0
$611$		−	31.5547i		−	1.27657i
$612$	7.69571	+	6.39719i	0.311081	+	0.258591i
$613$	21.1512	−	21.1512i	0.854290	−	0.854290i	−0.136368	−	0.990658i	$-0.543543\pi$
$613$	21.1512	−	21.1512i	0.854290	−	0.854290i	0.990658	+	0.136368i	$0.0435429\pi$
$614$	7.45544	−	12.9132i	0.300877	−	0.521134i
$615$		0			0
$616$	1.98582	+	3.43954i	0.0800110	+	0.138583i
$617$	10.1671	+	2.72427i	0.409312	+	0.109675i	0.457599	−	0.889159i	$-0.348710\pi$
$617$	10.1671	+	2.72427i	0.409312	+	0.109675i	−0.0482869	+	0.998834i	$0.515376\pi$
$618$	3.74085	+	5.84216i	0.150479	+	0.235006i
$619$	2.77044	+	1.59951i	0.111353	+	0.0642898i	0.554642	−	0.832089i	$-0.312855\pi$
$619$	2.77044	+	1.59951i	0.111353	+	0.0642898i	−0.443289	+	0.896379i	$0.646188\pi$
$620$		0			0
$621$	32.3139	+	4.02687i	1.29671	+	0.161593i
$622$	7.41734	+	7.41734i	0.297408	+	0.297408i
$623$	−3.99290	+	1.06990i	−0.159972	+	0.0428644i
$624$	−1.50858	+	6.87987i	−0.0603917	+	0.275415i
$625$		0			0
$626$	15.2882	−	8.82666i	0.611040	−	0.352784i
$627$	−0.580821	−	12.6340i	−0.0231958	−	0.504554i
$628$	2.80938	+	10.4848i	0.112107	+	0.418388i
$629$	−20.1293			−0.802609
$630$		0			0
$631$	21.2335			0.845291			0.422645	−	0.906295i	$-0.361102\pi$
$631$	21.2335			0.845291			0.422645	+	0.906295i	$0.361102\pi$
$632$	3.00458	+	11.2132i	0.119516	+	0.446039i
$633$	−37.0472	−	19.1770i	−1.47249	−	0.762219i
$634$	20.0808	−	11.5936i	0.797510	−	0.460442i
$635$		0			0
$636$	16.4116	−	5.21621i	0.650761	−	0.206836i
$637$	−11.5222	+	3.08736i	−0.456525	+	0.122326i
$638$	10.4410	+	10.4410i	0.413363	+	0.413363i
$639$	−15.4897	−	7.13612i	−0.612762	−	0.282300i
$640$		0			0
$641$	42.6583	+	24.6288i	1.68490	+	0.972778i	0.958320	+	0.285698i	$0.0922254\pi$
$641$	42.6583	+	24.6288i	1.68490	+	0.972778i	0.726582	+	0.687080i	$0.241108\pi$
$642$	−13.2205	+	0.607785i	−0.521773	+	0.0239874i
$643$	−19.6155	−	5.25595i	−0.773559	−	0.207274i	−0.149616	−	0.988744i	$-0.547804\pi$
$643$	−19.6155	−	5.25595i	−0.773559	−	0.207274i	−0.623943	+	0.781470i	$0.714470\pi$
$644$	−6.31887	−	10.9446i	−0.248998	−	0.431278i
$645$		0			0
$646$	−6.18378	+	10.7106i	−0.243298	+	0.421404i
$647$	29.0632	−	29.0632i	1.14259	−	1.14259i	0.154619	−	0.987974i	$-0.450585\pi$
$647$	29.0632	−	29.0632i	1.14259	−	1.14259i	0.987974	−	0.154619i	$-0.0494151\pi$
$648$	0.701625	−	8.97261i	0.0275624	−	0.352477i
$649$			5.31632i			0.208684i
$650$		0			0
$651$	23.8029	+	5.21939i	0.932911	+	0.204564i
$652$	3.54385	−	13.2258i	0.138788	−	0.517963i
$653$	−0.736931	+	2.75027i	−0.0288384	+	0.107626i	−0.978845	−	0.204604i	$-0.934409\pi$
$653$	−0.736931	+	2.75027i	−0.0288384	+	0.107626i	0.950006	+	0.312230i	$0.101076\pi$
$654$	5.08152	−	5.57126i	0.198703	−	0.217853i
$655$		0			0
$656$		−	7.08526i		−	0.276633i
$657$	1.68880	+	4.57416i	0.0658865	+	0.178455i
$658$	11.0649	−	11.0649i	0.431354	−	0.431354i
$659$	−18.8486	+	32.6467i	−0.734236	+	1.27173i	0.220822	+	0.975314i	$0.429126\pi$
$659$	−18.8486	+	32.6467i	−0.734236	+	1.27173i	−0.955058	+	0.296420i	$0.904207\pi$
$660$		0			0
$661$	3.68907	+	6.38966i	0.143488	+	0.248529i	0.928808	−	0.370561i	$-0.120835\pi$
$661$	3.68907	+	6.38966i	0.143488	+	0.248529i	−0.785320	+	0.619091i	$0.787501\pi$
$662$	−24.9459	−	6.68424i	−0.969551	−	0.259791i
$663$	−10.8007	+	20.8654i	−0.419465	+	0.810345i
$664$	1.47548	+	0.851871i	0.0572598	+	0.0330590i
$665$		0			0
$666$	10.4518	+	14.7811i	0.404998	+	0.572754i
$667$	−33.2232	−	33.2232i	−1.28641	−	1.28641i
$668$	4.93579	−	1.32254i	0.190971	−	0.0511707i
$669$	21.4721	+	19.5846i	0.830157	+	0.757183i
$670$		0			0
$671$	14.9193	−	8.61365i	0.575953	−	0.332526i
$672$	−2.94147	+	1.88348i	−0.113470	+	0.0726568i
$673$	−1.84460	−	6.88414i	−0.0711041	−	0.265364i	0.921218	−	0.389048i	$-0.127196\pi$
$673$	−1.84460	−	6.88414i	−0.0711041	−	0.265364i	−0.992322	+	0.123684i	$0.960529\pi$
$674$	32.0820			1.23575
$675$		0			0
$676$	−3.53614			−0.136005
$677$	−2.16966	−	8.09727i	−0.0833867	−	0.311203i	0.911617	−	0.411040i	$-0.134834\pi$
$677$	−2.16966	−	8.09727i	−0.0833867	−	0.311203i	−0.995004	+	0.0998372i	$0.968168\pi$
$678$	−4.32570	+	2.76983i	−0.166128	+	0.106375i
$679$	−17.5722	+	10.1453i	−0.674358	+	0.389341i
$680$		0			0
$681$	9.51955	+	8.68274i	0.364790	+	0.332723i
$682$	−13.2725	+	3.55635i	−0.508229	+	0.136180i
$683$	15.8873	+	15.8873i	0.607911	+	0.607911i	0.942400	−	0.334488i	$-0.108564\pi$
$683$	15.8873	+	15.8873i	0.607911	+	0.607911i	−0.334488	+	0.942400i	$0.608564\pi$
$684$	11.0757	−	1.02052i	0.423489	−	0.0390204i
$685$		0			0
$686$	−17.3478	−	10.0158i	−0.662342	−	0.382403i
$687$	−7.11785	+	13.7506i	−0.271563	+	0.524619i
$688$	−9.09714	−	2.43757i	−0.346825	−	0.0929315i
$689$	20.2150	+	35.0134i	0.770131	+	1.33391i
$690$		0			0
$691$	9.16297	−	15.8707i	0.348576	−	0.603751i	−0.637421	−	0.770516i	$-0.719999\pi$
$691$	9.16297	−	15.8707i	0.348576	−	0.603751i	0.985997	+	0.166765i	$0.0533321\pi$
$692$	−5.24323	+	5.24323i	−0.199318	+	0.199318i
$693$	7.61656	−	9.16260i	0.289329	−	0.348058i
$694$		−	14.8046i		−	0.561973i
$695$		0			0
$696$	−8.75085	+	9.59422i	−0.331700	+	0.363668i
$697$	6.11718	−	22.8296i	0.231705	−	0.864734i
$698$	−3.99695	+	14.9168i	−0.151287	+	0.564610i
$699$	36.0312	+	7.90075i	1.36282	+	0.298834i
$700$		0			0
$701$			21.1738i			0.799724i	0.916575	+	0.399862i	$0.130942\pi$
$701$			21.1738i			0.799724i	−0.916575	+	0.399862i	$0.869058\pi$
$702$	20.9296	−	2.90295i	0.789937	−	0.109565i
$703$	−15.8197	+	15.8197i	−0.596652	+	0.596652i
$704$	0.984748	−	1.70563i	0.0371141	−	0.0642835i
$705$		0			0
$706$	−10.4276	−	18.0612i	−0.392449	−	0.679742i
$707$	9.19953	+	2.46501i	0.345984	+	0.0927062i
$708$	−4.67045	+	0.214714i	−0.175526	+	0.00806943i
$709$	−20.4846	−	11.8268i	−0.769316	−	0.444165i	0.0633143	−	0.997994i	$-0.479833\pi$
$709$	−20.4846	−	11.8268i	−0.769316	−	0.444165i	−0.832631	+	0.553829i	$0.813166\pi$
$710$		0			0
$711$	28.4356	−	20.1070i	1.06642	−	0.754072i
$712$	1.44949	+	1.44949i	0.0543219	+	0.0543219i
$713$	42.2329	−	11.3163i	1.58163	−	0.423798i
$714$	−11.1039	+	3.52925i	−0.415555	+	0.132079i
$715$		0			0
$716$	2.36794	−	1.36713i	0.0884942	−	0.0510921i
$717$	16.6965	+	8.64273i	0.623541	+	0.322769i
$718$	−0.878601	−	3.27899i	−0.0327891	−	0.122371i
$719$	21.3695			0.796947			0.398473	−	0.917180i	$-0.369540\pi$
$719$	21.3695			0.796947			0.398473	+	0.917180i	$0.369540\pi$
$720$		0			0
$721$	−8.07679			−0.300795
$722$	−1.35990	−	5.07522i	−0.0506102	−	0.188880i
$723$	1.85589	+	40.3692i	0.0690212	+	1.50135i
$724$	19.6658	−	11.3541i	0.730874	−	0.421970i
$725$		0			0
$726$	2.64179	−	12.0478i	0.0980462	−	0.447137i
$727$	−2.97151	+	0.796213i	−0.110207	+	0.0295299i	−0.313501	−	0.949588i	$-0.601502\pi$
$727$	−2.97151	+	0.796213i	−0.110207	+	0.0295299i	0.203294	+	0.979118i	$0.434835\pi$
$728$	−5.79852	−	5.79852i	−0.214907	−	0.214907i
$729$	−25.9808	+	7.34847i	−0.962250	+	0.272166i
$730$		0			0
$731$	−27.2077	−	15.7084i	−1.00631	−	0.580994i
$732$	8.16974	+	12.7589i	0.301962	+	0.471581i
$733$	−23.5366	−	6.30661i	−0.869343	−	0.232940i	−0.203540	−	0.979067i	$-0.565245\pi$
$733$	−23.5366	−	6.30661i	−0.869343	−	0.232940i	−0.665804	+	0.746127i	$0.731911\pi$
$734$	−10.9884	−	19.0324i	−0.405589	−	0.702500i
$735$		0			0
$736$	−3.13346	+	5.42731i	−0.115501	+	0.200053i
$737$	11.7978	−	11.7978i	0.434578	−	0.434578i
$738$	−19.9401	+	7.36199i	−0.734006	+	0.270999i
$739$			5.68805i			0.209238i	0.994512	+	0.104619i	$0.0333624\pi$
$739$			5.68805i			0.209238i	−0.994512	+	0.104619i	$0.966638\pi$
$740$		0			0
$741$	7.90986	+	24.8865i	0.290576	+	0.914229i
$742$	−5.18917	+	19.3663i	−0.190500	+	0.710958i
$743$	4.04871	−	15.1100i	0.148533	−	0.554332i	−0.851040	−	0.525101i	$-0.824027\pi$
$743$	4.04871	−	15.1100i	0.148533	−	0.554332i	0.999573	−	0.0292311i	$-0.00930587\pi$
$744$	−3.66033	−	11.5164i	−0.134194	−	0.422211i
$745$		0			0
$746$			1.47224i			0.0539025i
$747$	0.864318	−	5.03761i	0.0316237	−	0.184317i
$748$	4.64558	−	4.64558i	0.169859	−	0.169859i
$749$	7.70428	−	13.3442i	0.281508	−	0.487586i
$750$		0			0
$751$	−21.6240	−	37.4538i	−0.789070	−	1.36671i	−0.926537	−	0.376203i	$-0.877229\pi$
$751$	−21.6240	−	37.4538i	−0.789070	−	1.36671i	0.137467	−	0.990506i	$-0.456104\pi$
$752$	−7.49533	−	2.00837i	−0.273327	−	0.0732376i
$753$	−12.5025	−	19.5254i	−0.455615	−	0.711544i
$754$	−26.4028	−	15.2437i	−0.961533	−	0.555141i
$755$		0			0
$756$	8.35706	+	6.32118i	0.303943	+	0.229899i
$757$	−22.7266	−	22.7266i	−0.826013	−	0.826013i	0.160950	−	0.986963i	$-0.448544\pi$
$757$	−22.7266	−	22.7266i	−0.826013	−	0.826013i	−0.986963	+	0.160950i	$0.948544\pi$
$758$	29.1055	−	7.79880i	1.05716	−	0.283265i
$759$	4.57891	−	20.8820i	0.166204	−	0.757969i
$760$		0			0
$761$	−24.8744	+	14.3612i	−0.901696	+	0.520595i	−0.877750	−	0.479119i	$-0.840956\pi$
$761$	−24.8744	+	14.3612i	−0.901696	+	0.520595i	−0.0239461	+	0.999713i	$0.507623\pi$
$762$	0.384421	+	8.36192i	0.0139261	+	0.302920i
$763$	2.27225	+	8.48016i	0.0822611	+	0.307002i
$764$	1.28350			0.0464353
$765$		0			0
$766$	−17.1481			−0.619587
$767$	−2.84099	−	10.6027i	−0.102582	−	0.382842i
$768$	1.53819	+	0.796225i	0.0555046	+	0.0287313i
$769$	−29.3558	+	16.9486i	−1.05860	+	0.611180i	−0.925043	−	0.379861i	$-0.875972\pi$
$769$	−29.3558	+	16.9486i	−1.05860	+	0.611180i	−0.133552	+	0.991042i	$0.542638\pi$
$770$		0			0
$771$	−12.4681	+	3.96283i	−0.449028	+	0.142718i
$772$	−5.28063	+	1.41494i	−0.190054	+	0.0509248i
$773$	−30.1093	−	30.1093i	−1.08296	−	1.08296i	−0.996232	−	0.0867231i	$-0.972360\pi$
$773$	−30.1093	−	30.1093i	−1.08296	−	1.08296i	−0.0867231	−	0.996232i	$-0.527640\pi$
$774$	2.59237	+	28.1350i	0.0931807	+	1.01129i
$775$		0			0
$776$	8.71386	+	5.03095i	0.312809	+	0.180601i
$777$	−21.0546	+	0.967939i	−0.755329	+	0.0347246i
$778$	29.1844	+	7.81993i	1.04631	+	0.280358i
$779$	−13.1344	−	22.7494i	−0.470588	−	0.815083i
$780$		0			0
$781$	−5.59811	+	9.69621i	−0.200316	+	0.346958i
$782$	−14.7822	+	14.7822i	−0.528610	+	0.528610i
$783$	36.0938	+	14.6587i	1.28989	+	0.523858i
$784$			2.93342i			0.104765i
$785$		0			0
$786$	−0.803445	−	0.176176i	−0.0286579	−	0.00628398i
$787$	−2.73876	+	10.2212i	−0.0976263	+	0.364346i	−0.997405	−	0.0720011i	$-0.977061\pi$
$787$	−2.73876	+	10.2212i	−0.0976263	+	0.364346i	0.899778	+	0.436347i	$0.143728\pi$
$788$	4.40644	−	16.4450i	0.156973	−	0.585831i
$789$	13.0137	−	14.2679i	0.463300	−	0.507952i
$790$		0			0
$791$		−	5.98028i		−	0.212634i
$792$	−5.82340	−	0.999137i	−0.206925	−	0.0355028i
$793$	−25.1515	+	25.1515i	−0.893157	+	0.893157i
$794$	1.53420	−	2.65731i	0.0544467	−	0.0943045i
$795$		0			0
$796$	2.21916	+	3.84369i	0.0786559	+	0.136236i
$797$	13.1409	+	3.52110i	0.465476	+	0.124724i	0.483932	−	0.875106i	$-0.339208\pi$
$797$	13.1409	+	3.52110i	0.465476	+	0.124724i	−0.0184558	+	0.999830i	$0.505875\pi$
$798$	−5.95299	+	11.5003i	−0.210733	+	0.407106i
$799$	−22.4170	−	12.9425i	−0.793056	−	0.457871i
$800$		0			0
$801$	2.57321	−	5.58542i	0.0909200	−	0.197351i
$802$	10.0599	+	10.0599i	0.355229	+	0.355229i
$803$	3.09199	−	0.828496i	0.109114	−	0.0292370i
$804$	10.8410	+	9.88801i	0.382332	+	0.348723i
$805$		0			0
$806$	24.5697	−	14.1853i	0.865432	−	0.499657i
$807$	19.6490	−	12.5816i	0.691679	−	0.442895i
$808$	−1.22237	−	4.56196i	−0.0430029	−	0.160489i
$809$	33.4429			1.17579			0.587895	−	0.808937i	$-0.299957\pi$
$809$	33.4429			1.17579			0.587895	+	0.808937i	$0.299957\pi$
$810$		0			0
$811$	21.1960			0.744294			0.372147	−	0.928174i	$-0.378622\pi$
$811$	21.1960			0.744294			0.372147	+	0.928174i	$0.378622\pi$
$812$	−3.91303	−	14.6036i	−0.137320	−	0.512487i
$813$	−29.8150	+	19.0911i	−1.04566	+	0.669555i
$814$	10.2924	−	5.94230i	0.360747	−	0.208278i
$815$		0			0
$816$	4.26881	+	3.89357i	0.149438	+	0.136302i
$817$	−33.7279	+	9.03736i	−1.17999	+	0.316177i
$818$	−8.40687	−	8.40687i	−0.293939	−	0.293939i
$819$	−10.2938	+	22.3438i	−0.359696	+	0.780757i
$820$		0			0
$821$	−38.4941	−	22.2246i	−1.34345	−	0.775643i	−0.356141	−	0.934432i	$-0.615908\pi$
$821$	−38.4941	−	22.2246i	−1.34345	−	0.775643i	−0.987313	+	0.158789i	$0.949241\pi$
$822$	7.84431	−	15.1540i	0.273602	−	0.528558i
$823$	24.6311	+	6.59989i	0.858588	+	0.230058i	0.661146	−	0.750257i	$-0.270070\pi$
$823$	24.6311	+	6.59989i	0.858588	+	0.230058i	0.197441	+	0.980315i	$0.436737\pi$
$824$	2.00260	+	3.46860i	0.0697638	+	0.120834i
$825$		0			0
$826$	2.72171	−	4.71413i	0.0947003	−	0.164026i
$827$	−10.7808	+	10.7808i	−0.374885	+	0.374885i	−0.869253	−	0.494368i	$-0.835400\pi$
$827$	−10.7808	+	10.7808i	−0.374885	+	0.374885i	0.494368	+	0.869253i	$0.335400\pi$
$828$	18.5300	+	3.17925i	0.643962	+	0.110486i
$829$		−	4.02079i		−	0.139648i	−0.997559	−	0.0698239i	$-0.977756\pi$
$829$		−	4.02079i		−	0.139648i	0.997559	−	0.0698239i	$-0.0222437\pi$
$830$		0			0
$831$	−28.2908	+	31.0173i	−0.981396	+	1.07598i
$832$	−1.05248	+	3.92790i	−0.0364881	+	0.136176i
$833$	−2.53262	+	9.45186i	−0.0877500	+	0.327488i
$834$	−1.18840	−	0.260587i	−0.0411509	−	0.00902338i
$835$		0			0
$836$		−	7.30196i		−	0.252543i
$837$	−28.6074	+	22.2675i	−0.988815	+	0.769677i
$838$	27.7686	−	27.7686i	0.959251	−	0.959251i
$839$	−16.7880	+	29.0777i	−0.579588	+	1.00388i	0.415939	+	0.909393i	$0.363453\pi$
$839$	−16.7880	+	29.0777i	−0.579588	+	1.00388i	−0.995527	+	0.0944825i	$0.969880\pi$
$840$		0			0
$841$	−13.6044	−	23.5635i	−0.469118	−	0.812536i
$842$	23.6637	+	6.34068i	0.815506	+	0.218514i
$843$	−39.0435	+	1.79494i	−1.34473	+	0.0618211i
$844$	−20.8582	−	12.0425i	−0.717968	−	0.414519i
$845$		0			0
$846$	2.13591	+	23.1810i	0.0734340	+	0.796980i
$847$	10.1542	+	10.1542i	0.348903	+	0.348903i
$848$	9.60353	−	2.57326i	0.329786	−	0.0883660i
$849$	−3.50559	+	1.11421i	−0.120312	+	0.0382395i
$850$		0			0
$851$	−32.7503	+	18.9084i	−1.12266	+	0.648171i
$852$	−8.74432	−	4.52639i	−0.299575	−	0.155072i
$853$	6.15572	+	22.9734i	0.210768	+	0.786596i	0.987614	+	0.156905i	$0.0501517\pi$
$853$	6.15572	+	22.9734i	0.210768	+	0.786596i	−0.776846	+	0.629691i	$0.783182\pi$
$854$	−17.6391			−0.603599
$855$		0			0
$856$	−7.64094			−0.261162
$857$	−3.06736	−	11.4475i	−0.104779	−	0.391040i	0.893541	−	0.448981i	$-0.148213\pi$
$857$	−3.06736	−	11.4475i	−0.104779	−	0.391040i	−0.998320	+	0.0579412i	$0.981546\pi$
$858$	−0.637053	−	13.8572i	−0.0217486	−	0.473076i
$859$	34.6670	−	20.0150i	1.18282	−	0.682904i	0.226158	−	0.974091i	$-0.427383\pi$
$859$	34.6670	−	20.0150i	1.18282	−	0.682904i	0.956666	+	0.291187i	$0.0940501\pi$
$860$		0			0
$861$	5.30058	−	24.1732i	0.180643	−	0.823819i
$862$	5.89894	−	1.58062i	0.200919	−	0.0538360i
$863$	1.78680	+	1.78680i	0.0608233	+	0.0608233i	0.736864	−	0.676041i	$-0.236306\pi$
$863$	1.78680	+	1.78680i	0.0608233	+	0.0608233i	−0.676041	+	0.736864i	$0.736306\pi$
$864$	0.642559	−	5.15627i	0.0218603	−	0.175420i
$865$		0			0
$866$	12.5665	+	7.25527i	0.427027	+	0.246544i
$867$	−5.48486	−	8.56583i	−0.186276	−	0.290911i
$868$	13.5897	+	3.64136i	0.461266	+	0.123596i
$869$	−11.4317	−	19.8004i	−0.387795	−	0.671681i
$870$		0			0
$871$	−17.2246	+	29.8338i	−0.583632	+	1.01088i
$872$	3.07844	−	3.07844i	0.104249	−	0.104249i
$873$	5.10446	−	29.7510i	0.172760	−	1.00692i
$874$			23.2348i			0.785928i
$875$		0			0
$876$	0.852721	+	2.68289i	0.0288108	+	0.0906463i
$877$	1.78537	−	6.66309i	0.0602876	−	0.224996i	−0.929208	−	0.369556i	$-0.879510\pi$
$877$	1.78537	−	6.66309i	0.0602876	−	0.224996i	0.989496	+	0.144559i	$0.0461765\pi$
$878$	−0.587569	+	2.19284i	−0.0198295	+	0.0740047i
$879$	1.91844	+	6.03593i	0.0647075	+	0.203587i
$880$		0			0
$881$			3.01999i			0.101746i	0.998705	+	0.0508731i	$0.0162004\pi$
$881$			3.01999i			0.101746i	−0.998705	+	0.0508731i	$0.983800\pi$
$882$	8.25555	−	3.04799i	0.277979	−	0.102631i
$883$	8.50404	−	8.50404i	0.286184	−	0.286184i	−0.549385	−	0.835569i	$-0.685138\pi$
$883$	8.50404	−	8.50404i	0.286184	−	0.286184i	0.835569	+	0.549385i	$0.185138\pi$
$884$	−6.78245	+	11.7476i	−0.228119	+	0.395113i
$885$		0			0
$886$	13.9099	+	24.0927i	0.467313	+	0.809410i
$887$	17.2055	+	4.61020i	0.577705	+	0.154796i	0.535828	−	0.844327i	$-0.320000\pi$
$887$	17.2055	+	4.61020i	0.577705	+	0.154796i	0.0418769	+	0.999123i	$0.486666\pi$
$888$	5.63606	+	8.80196i	0.189134	+	0.295375i
$889$	−8.44013	−	4.87291i	−0.283073	−	0.163432i
$890$		0			0
$891$	3.23896	+	17.4270i	0.108509	+	0.583827i
$892$	11.8645	+	11.8645i	0.397254	+	0.397254i
$893$	−27.7891	+	7.44607i	−0.929928	+	0.249173i
$894$	3.00947	−	13.7246i	0.100652	−	0.459021i
$895$		0			0
$896$	−1.74641	+	1.00829i	−0.0583434	+	0.0336846i
$897$	2.02710	+	44.0934i	0.0676828	+	1.47224i
$898$	3.04660	+	11.3701i	0.101666	+	0.379424i
$899$	52.3064			1.74452
$900$		0			0
$901$	33.1655			1.10490
$902$	3.61166	+	13.4789i	0.120255	+	0.448798i
$903$	−29.2136	−	15.1221i	−0.972169	−	0.503231i
$904$	−2.56825	+	1.48278i	−0.0854188	+	0.0493166i
$905$		0			0
$906$	15.2437	−	4.84500i	0.506437	−	0.160964i
$907$	1.21188	−	0.324723i	0.0402399	−	0.0107822i	−0.238643	−	0.971107i	$-0.576703\pi$
$907$	1.21188	−	0.324723i	0.0402399	−	0.0107822i	0.278883	+	0.960325i	$0.410036\pi$
$908$	5.26010	+	5.26010i	0.174562	+	0.174562i
$909$	−11.5687	+	8.18027i	−0.383708	+	0.271323i
$910$		0			0
$911$	−23.3987	−	13.5092i	−0.775232	−	0.447581i	0.0595057	−	0.998228i	$-0.481048\pi$
$911$	−23.3987	−	13.5092i	−0.775232	−	0.447581i	−0.834738	+	0.550647i	$0.814381\pi$
$912$	6.41485	−	0.294909i	0.212417	−	0.00976540i
$913$	−3.24117	−	0.868470i	−0.107267	−	0.0287422i
$914$	19.4616	+	33.7085i	0.643734	+	1.11498i
$915$		0			0
$916$	−4.46975	+	7.74183i	−0.147685	+	0.255797i
$917$	0.677163	−	0.677163i	0.0223619	−	0.0223619i
$918$	6.52217	−	16.0594i	0.215264	−	0.530040i
$919$			54.3202i			1.79186i	0.444196	+	0.895930i	$0.353489\pi$
$919$			54.3202i			1.79186i	−0.444196	+	0.895930i	$0.646511\pi$
$920$		0			0
$921$	−25.2270	−	5.53167i	−0.831259	−	0.182275i
$922$	−0.783607	+	2.92446i	−0.0258067	+	0.0963121i
$923$	5.98314	−	22.3294i	0.196938	−	0.734981i
$924$	4.63573	−	5.08250i	0.152504	−	0.167202i
$925$		0			0
$926$		−	6.83645i		−	0.224660i
$927$	7.68091	−	9.24002i	0.252274	−	0.303482i
$928$	−5.30136	+	5.30136i	−0.174026	+	0.174026i
$929$	−13.9274	+	24.1230i	−0.456944	+	0.791450i	−0.998798	−	0.0490228i	$-0.984389\pi$
$929$	−13.9274	+	24.1230i	−0.456944	+	0.791450i	0.541854	+	0.840473i	$0.317723\pi$
$930$		0			0
$931$	5.43786	+	9.41865i	0.178219	+	0.308684i
$932$	20.5712	+	5.51203i	0.673831	+	0.180553i
$933$	8.35217	−	16.1352i	0.273438	−	0.528241i
$934$	9.86360	+	5.69475i	0.322747	+	0.186338i
$935$		0			0
$936$	12.1479	−	1.11932i	0.397068	−	0.0365860i
$937$	16.8770	+	16.8770i	0.551349	+	0.551349i	0.926830	−	0.375481i	$-0.122523\pi$
$937$	16.8770	+	16.8770i	0.551349	+	0.551349i	−0.375481	+	0.926830i	$0.622523\pi$
$938$	−16.5014	+	4.42152i	−0.538788	+	0.144368i
$939$	−22.5909	−	20.6051i	−0.737227	−	0.672421i
$940$		0			0
$941$	28.5039	−	16.4567i	0.929201	−	0.536474i	0.0426420	−	0.999090i	$-0.486423\pi$
$941$	28.5039	−	16.4567i	0.929201	−	0.536474i	0.886559	+	0.462616i	$0.153089\pi$
$942$	15.8331	−	10.1382i	0.515869	−	0.330320i
$943$	−11.4923	−	42.8898i	−0.374240	−	1.39668i
$944$	−2.69933			−0.0878558
$945$		0			0
$946$	18.5488			0.603074
$947$	−3.08335	−	11.5072i	−0.100195	−	0.373934i	0.897560	−	0.440891i	$-0.145338\pi$
$947$	−3.08335	−	11.5072i	−0.100195	−	0.373934i	−0.997756	+	0.0669572i	$0.978671\pi$
$948$	16.9331	−	10.8426i	0.549962	−	0.352151i
$949$	−5.72383	+	3.30466i	−0.185804	+	0.107274i
$950$		0			0
$951$	−29.6727	−	27.0644i	−0.962204	−	0.877622i
$952$	−6.49768	+	1.74105i	−0.210591	+	0.0564277i
$953$	13.4723	+	13.4723i	0.436411	+	0.436411i	0.890802	−	0.454391i	$-0.150143\pi$
$953$	13.4723	+	13.4723i	0.436411	+	0.436411i	−0.454391	+	0.890802i	$0.650143\pi$
$954$	−17.2206	−	24.3536i	−0.557537	−	0.788476i
$955$		0			0
$956$	9.40038	+	5.42731i	0.304030	+	0.175532i
$957$	11.7569	−	22.7126i	0.380047	−	0.734195i
$958$	−32.0130	−	8.57785i	−1.03429	−	0.277138i
$959$	9.93353	+	17.2054i	0.320770	+	0.555591i
$960$		0			0
$961$	−8.83746	+	15.3069i	−0.285079	+	0.493772i
$962$	−17.3513	+	17.3513i	−0.559428	+	0.559428i
$963$	7.93938	+	21.5040i	0.255843	+	0.692957i
$964$			23.3318i			0.751467i
$965$		0			0
$966$	−14.7508	+	16.1725i	−0.474601	+	0.520341i
$967$	2.40036	−	8.95826i	0.0771904	−	0.288078i	−0.916531	−	0.399964i	$-0.869022\pi$
$967$	2.40036	−	8.95826i	0.0771904	−	0.288078i	0.993721	+	0.111886i	$0.0356892\pi$
$968$	1.84307	−	6.87844i	0.0592386	−	0.221081i
$969$	20.9241	+	4.58814i	0.672179	+	0.147392i
$970$		0			0
$971$			24.7290i			0.793590i	0.917907	+	0.396795i	$0.129878\pi$
$971$			24.7290i			0.793590i	−0.917907	+	0.396795i	$0.870122\pi$
$972$	−15.1790	+	3.54930i	−0.486867	+	0.113844i
$973$	1.00161	−	1.00161i	0.0321102	−	0.0321102i
$974$	10.4827	−	18.1566i	0.335889	−	0.581776i
$975$		0			0
$976$	4.37353	+	7.57518i	0.139993	+	0.242476i
$977$	−23.7190	−	6.35548i	−0.758837	−	0.203330i	−0.141403	−	0.989952i	$-0.545161\pi$
$977$	−23.7190	−	6.35548i	−0.758837	−	0.203330i	−0.617434	+	0.786622i	$0.711828\pi$
$978$	−23.6909	+	1.08914i	−0.757551	+	0.0348267i
$979$	−3.49636	−	2.01862i	−0.111744	−	0.0645155i
$980$		0			0
$981$	−11.8624	−	5.46502i	−0.378736	−	0.174485i
$982$	−13.1868	−	13.1868i	−0.420808	−	0.420808i
$983$	−40.0954	+	10.7435i	−1.27885	+	0.342666i	−0.833414	−	0.552650i	$-0.813617\pi$
$983$	−40.0954	+	10.7435i	−1.27885	+	0.342666i	−0.445433	+	0.895316i	$0.646950\pi$
$984$	−11.6955	+	3.71726i	−0.372839	+	0.118502i
$985$		0			0
$986$	−21.6587	+	12.5047i	−0.689754	+	0.398230i
$987$	−24.0697	−	12.4594i	−0.766148	−	0.396588i
$988$	3.90209	+	14.5628i	0.124142	+	0.463305i
$989$	−59.0222			−1.87680
$990$		0			0
$991$	36.6089			1.16292			0.581460	−	0.813575i	$-0.302481\pi$
$991$	36.6089			1.16292			0.581460	+	0.813575i	$0.302481\pi$
$992$	−1.80571	−	6.73901i	−0.0573315	−	0.213964i
$993$	2.05428	+	44.6846i	0.0651906	+	1.41802i
$994$	9.92800	−	5.73193i	0.314897	−	0.181806i
$995$		0			0
$996$	0.632057	−	2.88248i	0.0200275	−	0.0913349i
$997$	11.5550	−	3.09617i	0.365952	−	0.0980565i	−0.0711569	−	0.997465i	$-0.522669\pi$
$997$	11.5550	−	3.09617i	0.365952	−	0.0980565i	0.437109	+	0.899409i	$0.356002\pi$
$998$	16.0188	+	16.0188i	0.507065	+	0.507065i
$999$	18.9153	−	25.0074i	0.598453	−	0.791199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.p.h.407.1		16
3.2	odd	2		1350.2.q.h.1007.3		16
5.2	odd	4		90.2.l.b.83.4	yes	16
5.3	odd	4	inner	450.2.p.h.443.1		16
5.4	even	2		90.2.l.b.47.4	yes	16
9.4	even	3		1350.2.q.h.557.4		16
9.5	odd	6	inner	450.2.p.h.257.1		16
15.2	even	4		270.2.m.b.143.2		16
15.8	even	4		1350.2.q.h.143.4		16
15.14	odd	2		270.2.m.b.197.2		16
20.7	even	4		720.2.cu.b.353.2		16
20.19	odd	2		720.2.cu.b.497.1		16
45.2	even	12		810.2.f.c.323.7		16
45.4	even	6		270.2.m.b.17.2		16
45.7	odd	12		810.2.f.c.323.2		16
45.13	odd	12		1350.2.q.h.1043.3		16
45.14	odd	6		90.2.l.b.77.4	yes	16
45.22	odd	12		270.2.m.b.233.2		16
45.23	even	12	inner	450.2.p.h.293.1		16
45.29	odd	6		810.2.f.c.647.2		16
45.32	even	12		90.2.l.b.23.4	✓	16
45.34	even	6		810.2.f.c.647.7		16
180.59	even	6		720.2.cu.b.257.2		16
180.167	odd	12		720.2.cu.b.113.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	45.32	even	12
90.2.l.b.47.4	yes	16	5.4	even	2
90.2.l.b.77.4	yes	16	45.14	odd	6
90.2.l.b.83.4	yes	16	5.2	odd	4
270.2.m.b.17.2		16	45.4	even	6
270.2.m.b.143.2		16	15.2	even	4
270.2.m.b.197.2		16	15.14	odd	2
270.2.m.b.233.2		16	45.22	odd	12
450.2.p.h.257.1		16	9.5	odd	6	inner
450.2.p.h.293.1		16	45.23	even	12	inner
450.2.p.h.407.1		16	1.1	even	1	trivial
450.2.p.h.443.1		16	5.3	odd	4	inner
720.2.cu.b.113.1		16	180.167	odd	12
720.2.cu.b.257.2		16	180.59	even	6
720.2.cu.b.353.2		16	20.7	even	4
720.2.cu.b.497.1		16	20.19	odd	2
810.2.f.c.323.2		16	45.7	odd	12
810.2.f.c.323.7		16	45.2	even	12
810.2.f.c.647.2		16	45.29	odd	6
810.2.f.c.647.7		16	45.34	even	6
1350.2.q.h.143.4		16	15.8	even	4
1350.2.q.h.557.4		16	9.4	even	3
1350.2.q.h.1007.3		16	3.2	odd	2
1350.2.q.h.1043.3		16	45.13	odd	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.45865 + 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.27970 + 1.16721i) q^{6} +(-1.94786 + 0.521929i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.45865 + 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.27970 + 1.16721i) q^{6} +(-1.94786 + 0.521929i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +(-1.70563 - 0.984748i) q^{11} +(0.796225 - 1.53819i) q^{12} +(3.92790 + 1.05248i) q^{13} +(1.00829 + 1.74641i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.35877 - 2.35877i) q^{17} +(-2.95680 - 0.507306i) q^{18} -3.70753i q^{19} +(2.35376 - 2.58061i) q^{21} +(-0.509743 + 1.90239i) q^{22} +(1.62200 - 6.05338i) q^{23} +(-1.69185 - 0.370982i) q^{24} -4.06647i q^{26} +(0.713876 + 5.14688i) q^{27} +(1.42594 - 1.42594i) q^{28} +(3.74863 - 6.49281i) q^{29} +(3.48837 + 6.04204i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.40767 - 0.156660i) q^{33} +(-2.88889 - 1.66790i) q^{34} +(0.275255 + 2.98735i) q^{36} +(-4.26692 - 4.26692i) q^{37} +(-3.58120 + 0.959578i) q^{38} +(-6.71243 + 2.13346i) q^{39} +(6.13601 - 3.54263i) q^{41} +(-3.10188 - 1.60565i) q^{42} +(-2.43757 - 9.09714i) q^{43} +1.96950 q^{44} -6.26692 q^{46} +(-2.00837 - 7.49533i) q^{47} +(0.0795432 + 1.73022i) q^{48} +(-2.54041 + 1.46671i) q^{49} +(-1.23752 + 5.64369i) q^{51} +(-3.92790 + 1.05248i) q^{52} +(7.03027 + 7.03027i) q^{53} +(4.78674 - 2.02166i) q^{54} +(-1.74641 - 1.00829i) q^{56} +(3.46282 + 5.40797i) q^{57} +(-7.24179 - 1.94043i) q^{58} +(-1.34967 - 2.33769i) q^{59} +(-4.37353 + 7.57518i) q^{61} +(4.93330 - 4.93330i) q^{62} +(-1.02302 + 5.96261i) q^{63} +1.00000i q^{64} +(-1.03329 - 3.25101i) q^{66} +(-2.19259 + 8.18285i) q^{67} +(-0.863368 + 3.22213i) q^{68} +(3.28793 + 10.3447i) q^{69} -5.68481i q^{71} +(2.81431 - 1.03906i) q^{72} +(-1.14928 + 1.14928i) q^{73} +(-3.01717 + 5.22589i) q^{74} +(1.85376 + 3.21081i) q^{76} +(3.83631 + 1.02794i) q^{77} +(3.79807 + 5.93153i) q^{78} +(10.0535 + 5.80440i) q^{79} +(-5.84847 - 6.84072i) q^{81} +(-5.01003 - 5.01003i) q^{82} +(1.64569 - 0.440961i) q^{83} +(-0.748114 + 3.41176i) q^{84} +(-8.15627 + 4.70902i) q^{86} +(0.596356 + 12.9719i) q^{87} +(-0.509743 - 1.90239i) q^{88} +2.04989 q^{89} -8.20034 q^{91} +(1.62200 + 6.05338i) q^{92} +(-10.7315 - 5.55506i) q^{93} +(-6.72013 + 3.87987i) q^{94} +(1.65068 - 0.524648i) q^{96} +(9.71905 - 2.60421i) q^{97} +(2.07424 + 2.07424i) q^{98} +(-4.82426 + 3.41127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 8 q^{16} + 24 q^{21} - 8 q^{22} + 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{36} - 24 q^{38} + 24 q^{41} - 24 q^{42} - 32 q^{46} - 48 q^{47} - 48 q^{51} + 24 q^{56} - 24 q^{57} - 16 q^{58} - 24 q^{61} + 48 q^{63} - 48 q^{66} + 16 q^{67} + 24 q^{68} + 24 q^{72} - 16 q^{73} + 16 q^{76} + 72 q^{77} + 24 q^{81} + 16 q^{82} - 48 q^{83} - 48 q^{86} + 48 q^{87} - 8 q^{88} + 24 q^{92} - 72 q^{93} + 48 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 8 * q^16 + 24 * q^21 - 8 * q^22 + 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^36 - 24 * q^38 + 24 * q^41 - 24 * q^42 - 32 * q^46 - 48 * q^47 - 48 * q^51 + 24 * q^56 - 24 * q^57 - 16 * q^58 - 24 * q^61 + 48 * q^63 - 48 * q^66 + 16 * q^67 + 24 * q^68 + 24 * q^72 - 16 * q^73 + 16 * q^76 + 72 * q^77 + 24 * q^81 + 16 * q^82 - 48 * q^83 - 48 * q^86 + 48 * q^87 - 8 * q^88 + 24 * q^92 - 72 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

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