LMFDB - Embedded newform 450.2.p.h.443.1

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			443.1
Root			$0.500000 - 2.74530i$ of defining polynomial
Character	$\chi$	$=$	450.443
Dual form			450.2.p.h.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.933998 - 1.45865i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.27970 + 1.16721i) q^{6} +(0.521929 + 1.94786i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.25529 + 2.72474i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.933998 - 1.45865i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.27970 + 1.16721i) q^{6} +(0.521929 + 1.94786i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.25529 + 2.72474i) q^{9} +(-1.70563 - 0.984748i) q^{11} +(-1.53819 - 0.796225i) q^{12} +(-1.05248 + 3.92790i) q^{13} +(-1.00829 - 1.74641i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.35877 - 2.35877i) q^{17} +(0.507306 - 2.95680i) q^{18} +3.70753i q^{19} +(2.35376 - 2.58061i) q^{21} +(1.90239 + 0.509743i) q^{22} +(6.05338 + 1.62200i) q^{23} +(1.69185 + 0.370982i) q^{24} -4.06647i q^{26} +(5.14688 - 0.713876i) q^{27} +(1.42594 + 1.42594i) q^{28} +(-3.74863 + 6.49281i) q^{29} +(3.48837 + 6.04204i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.156660 + 3.40767i) q^{33} +(2.88889 + 1.66790i) q^{34} +(0.275255 + 2.98735i) q^{36} +(-4.26692 + 4.26692i) q^{37} +(-0.959578 - 3.58120i) q^{38} +(6.71243 - 2.13346i) q^{39} +(6.13601 - 3.54263i) q^{41} +(-1.60565 + 3.10188i) q^{42} +(9.09714 - 2.43757i) q^{43} -1.96950 q^{44} -6.26692 q^{46} +(-7.49533 + 2.00837i) q^{47} +(-1.73022 + 0.0795432i) q^{48} +(2.54041 - 1.46671i) q^{49} +(-1.23752 + 5.64369i) q^{51} +(1.05248 + 3.92790i) q^{52} +(-7.03027 + 7.03027i) q^{53} +(-4.78674 + 2.02166i) q^{54} +(-1.74641 - 1.00829i) q^{56} +(5.40797 - 3.46282i) q^{57} +(1.94043 - 7.24179i) q^{58} +(1.34967 + 2.33769i) q^{59} +(-4.37353 + 7.57518i) q^{61} +(-4.93330 - 4.93330i) q^{62} +(-5.96261 - 1.02302i) q^{63} -1.00000i q^{64} +(-1.03329 - 3.25101i) q^{66} +(8.18285 + 2.19259i) q^{67} +(-3.22213 - 0.863368i) q^{68} +(-3.28793 - 10.3447i) q^{69} -5.68481i q^{71} +(-1.03906 - 2.81431i) q^{72} +(-1.14928 - 1.14928i) q^{73} +(3.01717 - 5.22589i) q^{74} +(1.85376 + 3.21081i) q^{76} +(1.02794 - 3.83631i) q^{77} +(-5.93153 + 3.79807i) q^{78} +(-10.0535 - 5.80440i) q^{79} +(-5.84847 - 6.84072i) q^{81} +(-5.01003 + 5.01003i) q^{82} +(0.440961 + 1.64569i) q^{83} +(0.748114 - 3.41176i) q^{84} +(-8.15627 + 4.70902i) q^{86} +(12.9719 - 0.596356i) q^{87} +(1.90239 - 0.509743i) q^{88} -2.04989 q^{89} -8.20034 q^{91} +(6.05338 - 1.62200i) q^{92} +(5.55506 - 10.7315i) q^{93} +(6.72013 - 3.87987i) q^{94} +(1.65068 - 0.524648i) q^{96} +(-2.60421 - 9.71905i) 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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.933998	−	1.45865i	−0.539244	−	0.842150i
$3$	−0.933998	−	1.45865i	−0.539244	−	0.842150i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	1.27970	+	1.16721i	0.522435	+	0.476510i
$7$	0.521929	+	1.94786i	0.197270	+	0.736223i	0.991667	+	0.128824i	$0.0411204\pi$
$7$	0.521929	+	1.94786i	0.197270	+	0.736223i	−0.794397	+	0.607399i	$0.792213\pi$
$8$	−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	$0.762624\pi$
$12$	−1.53819	−	0.796225i	−0.444037	−	0.229850i
$13$	−1.05248	+	3.92790i	−0.291905	+	1.08940i	0.651739	+	0.758443i	$0.274040\pi$
$13$	−1.05248	+	3.92790i	−0.291905	+	1.08940i	−0.943644	+	0.330961i	$0.892627\pi$
$14$	−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	$-0.382563\pi$
$17$	−2.35877	−	2.35877i	−0.572085	−	0.572085i	−0.932711	+	0.360626i	$0.882563\pi$
$18$	0.507306	−	2.95680i	0.119573	−	0.696923i
$19$			3.70753i			0.850565i	0.905061	+	0.425282i	$0.139825\pi$
$19$			3.70753i			0.850565i	−0.905061	+	0.425282i	$0.860175\pi$
$20$		0			0
$21$	2.35376	−	2.58061i	0.513633	−	0.563135i
$22$	1.90239	+	0.509743i	0.405590	+	0.108678i
$23$	6.05338	+	1.62200i	1.26222	+	0.338210i	0.827044	−	0.562137i	$-0.190021\pi$
$23$	6.05338	+	1.62200i	1.26222	+	0.338210i	0.435173	+	0.900347i	$0.356687\pi$
$24$	1.69185	+	0.370982i	0.345348	+	0.0757264i
$25$		0			0
$26$		−	4.06647i		−	0.797499i
$27$	5.14688	−	0.713876i	0.990518	−	0.137386i
$28$	1.42594	+	1.42594i	0.269476	+	0.269476i
$29$	−3.74863	+	6.49281i	−0.696103	+	1.20569i	0.273705	+	0.961814i	$0.411751\pi$
$29$	−3.74863	+	6.49281i	−0.696103	+	1.20569i	−0.969808	+	0.243872i	$0.921582\pi$
$30$		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	$0.617808\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	0.156660	+	3.40767i	0.0272710	+	0.593199i
$34$	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	−0.964728	−	0.263250i	$-0.915206\pi$
$37$	−4.26692	+	4.26692i	−0.701478	+	0.701478i	0.263250	+	0.964728i	$0.415206\pi$
$38$	−0.959578	−	3.58120i	−0.155664	−	0.580947i
$39$	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	$0.146715\pi$
$42$	−1.60565	+	3.10188i	−0.247757	+	0.478630i
$43$	9.09714	−	2.43757i	1.38730	−	0.371726i	0.513533	−	0.858070i	$-0.328336\pi$
$43$	9.09714	−	2.43757i	1.38730	−	0.371726i	0.873767	+	0.486344i	$0.161670\pi$
$44$	−1.96950			−0.296913
$45$		0			0
$46$	−6.26692			−0.924007
$47$	−7.49533	+	2.00837i	−1.09331	+	0.292951i	−0.760036	−	0.649881i	$-0.774819\pi$
$47$	−7.49533	+	2.00837i	−1.09331	+	0.292951i	−0.333270	+	0.942831i	$0.608152\pi$
$48$	−1.73022	+	0.0795432i	−0.249736	+	0.0114811i
$49$	2.54041	−	1.46671i	0.362916	−	0.209530i
$50$		0			0
$51$	−1.23752	+	5.64369i	−0.173288	+	0.790274i
$52$	1.05248	+	3.92790i	0.145953	+	0.544702i
$53$	−7.03027	+	7.03027i	−0.965682	+	0.965682i	−0.999430	−	0.0337485i	$-0.989255\pi$
$53$	−7.03027	+	7.03027i	−0.965682	+	0.965682i	0.0337485	+	0.999430i	$0.489255\pi$
$54$	−4.78674	+	2.02166i	−0.651393	+	0.275113i
$55$		0			0
$56$	−1.74641	−	1.00829i	−0.233373	−	0.134738i
$57$	5.40797	−	3.46282i	0.716303	−	0.458662i
$58$	1.94043	−	7.24179i	0.254791	−	0.950894i
$59$	1.34967	+	2.33769i	0.175712	+	0.304341i	0.940407	−	0.340050i	$-0.110444\pi$
$59$	1.34967	+	2.33769i	0.175712	+	0.304341i	−0.764696	+	0.644392i	$0.777111\pi$
$60$		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
$63$	−5.96261	−	1.02302i	−0.751218	−	0.128889i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−1.03329	−	3.25101i	−0.127189	−	0.400171i
$67$	8.18285	+	2.19259i	0.999694	+	0.267867i	0.721317	−	0.692605i	$-0.243537\pi$
$67$	8.18285	+	2.19259i	0.999694	+	0.267867i	0.278377	+	0.960472i	$0.410204\pi$
$68$	−3.22213	−	0.863368i	−0.390741	−	0.104699i
$69$	−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	$-0.109524\pi$
$72$	−1.03906	−	2.81431i	−0.122454	−	0.331670i
$73$	−1.14928	−	1.14928i	−0.134513	−	0.134513i	0.636645	−	0.771157i	$-0.280322\pi$
$73$	−1.14928	−	1.14928i	−0.134513	−	0.134513i	−0.771157	+	0.636645i	$0.780322\pi$
$74$	3.01717	−	5.22589i	0.350739	−	0.607498i
$75$		0			0
$76$	1.85376	+	3.21081i	0.212641	+	0.368305i
$77$	1.02794	−	3.83631i	0.117144	−	0.437188i
$78$	−5.93153	+	3.79807i	−0.671614	+	0.430047i
$79$	−10.0535	−	5.80440i	−1.13111	−	0.653046i	−0.186895	−	0.982380i	$-0.559842\pi$
$79$	−10.0535	−	5.80440i	−1.13111	−	0.653046i	−0.944214	+	0.329334i	$0.893176\pi$
$80$		0			0
$81$	−5.84847	−	6.84072i	−0.649830	−	0.760080i
$82$	−5.01003	+	5.01003i	−0.553266	+	0.553266i
$83$	0.440961	+	1.64569i	0.0484017	+	0.180638i	0.985895	−	0.167366i	$-0.0535262\pi$
$83$	0.440961	+	1.64569i	0.0484017	+	0.180638i	−0.937493	+	0.348004i	$0.886860\pi$
$84$	0.748114	−	3.41176i	0.0816259	−	0.372253i
$85$		0			0
$86$	−8.15627	+	4.70902i	−0.879513	+	0.507787i
$87$	12.9719	−	0.596356i	1.39074	−	0.0639361i
$88$	1.90239	−	0.509743i	0.202795	−	0.0543388i
$89$	−2.04989			−0.217288			−0.108644	−	0.994081i	$-0.534651\pi$
$89$	−2.04989			−0.217288			−0.108644	+	0.994081i	$0.534651\pi$
$90$		0			0
$91$	−8.20034			−0.859629
$92$	6.05338	−	1.62200i	0.631109	−	0.169105i
$93$	5.55506	−	10.7315i	0.576033	−	1.11281i
$94$	6.72013	−	3.87987i	0.693128	−	0.400178i
$95$		0			0
$96$	1.65068	−	0.524648i	0.168472	−	0.0535466i
$97$	−2.60421	−	9.71905i	−0.264418	−	0.986820i	−0.962606	−	0.270906i	$-0.912677\pi$
$97$	−2.60421	−	9.71905i	−0.264418	−	0.986820i	0.698188	−	0.715914i	$-0.253990\pi$
$98$	−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	$0.742167\pi$
$102$	−0.265340	−	5.77168i	−0.0262726	−	0.571481i
$103$	−1.03662	+	3.86872i	−0.102141	+	0.381196i	−0.998005	−	0.0631321i	$-0.979891\pi$
$103$	−1.03662	+	3.86872i	−0.102141	+	0.381196i	0.895864	+	0.444329i	$0.146558\pi$
$104$	−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	$-0.129584\pi$
$107$	5.40296	+	5.40296i	0.522324	+	0.522324i	−0.395949	+	0.918273i	$0.629584\pi$
$108$	4.10039	−	3.19168i	0.394560	−	0.307119i
$109$			4.35357i			0.416996i	0.978023	+	0.208498i	$0.0668575\pi$
$109$			4.35357i			0.416996i	−0.978023	+	0.208498i	$0.933142\pi$
$110$		0			0
$111$	10.2092	+	2.23863i	0.969017	+	0.212481i
$112$	1.94786	+	0.521929i	0.184056	+	0.0493176i
$113$	−2.86451	−	0.767544i	−0.269471	−	0.0722045i	0.121553	−	0.992585i	$-0.461212\pi$
$113$	−2.86451	−	0.767544i	−0.269471	−	0.0722045i	−0.391024	+	0.920380i	$0.627879\pi$
$114$	−4.32745	+	4.74451i	−0.405303	+	0.444364i
$115$		0			0
$116$			7.49726i			0.696103i
$117$	−9.38136	−	7.79841i	−0.867307	−	0.720964i
$118$	−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
$122$	2.26391	−	8.44902i	0.204965	−	0.764938i
$123$	−10.8985	−	5.64146i	−0.982681	−	0.508673i
$124$	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	−0.539040	−	0.842280i	$-0.681213\pi$
$127$	3.41734	−	3.41734i	0.303240	−	0.303240i	0.842280	+	0.539040i	$0.181213\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−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	$0.339937\pi$
$132$	1.83951	+	2.87280i	0.160108	+	0.250045i
$133$	−7.22176	+	1.93506i	−0.626206	+	0.167791i
$134$	−8.47151			−0.731827
$135$		0			0
$136$	3.33580			0.286042
$137$	−9.51618	+	2.54985i	−0.813022	+	0.217849i	−0.641293	−	0.767296i	$-0.721602\pi$
$137$	−9.51618	+	2.54985i	−0.813022	+	0.217849i	−0.171728	+	0.985144i	$0.554935\pi$
$138$	5.85329	+	9.14122i	0.498265	+	0.778152i
$139$	0.608318	−	0.351212i	0.0515968	−	0.0297894i	−0.473980	−	0.880536i	$-0.657183\pi$
$139$	0.608318	−	0.351212i	0.0515968	−	0.0297894i	0.525577	+	0.850746i	$0.323850\pi$
$140$		0			0
$141$	9.93012	+	9.05722i	0.836267	+	0.762755i
$142$	1.47134	+	5.49111i	0.123472	+	0.460803i
$143$	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
$147$	−4.51215	−	2.33566i	−0.372156	−	0.192642i
$148$	−1.56180	+	5.82872i	−0.128379	+	0.479118i
$149$	4.05609	+	7.02536i	0.332288	+	0.575540i	0.982960	−	0.183819i	$-0.0588460\pi$
$149$	4.05609	+	7.02536i	0.332288	+	0.575540i	−0.650672	+	0.759359i	$0.725513\pi$
$150$		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
$153$	9.38798	−	3.46609i	0.758973	−	0.280217i
$154$			3.97164i			0.320044i
$155$		0			0
$156$	4.74641	−	5.20385i	0.380017	−	0.416641i
$157$	−10.4848	−	2.80938i	−0.836775	−	0.224213i	−0.185108	−	0.982718i	$-0.559264\pi$
$157$	−10.4848	−	2.80938i	−0.836775	−	0.224213i	−0.651667	+	0.758505i	$0.725930\pi$
$158$	11.2132	+	3.00458i	0.892077	+	0.239031i
$159$	16.8209	+	3.68841i	1.33399	+	0.292510i
$160$		0			0
$161$			12.6377i			0.995993i
$162$	7.41970	+	5.09393i	0.582946	+	0.400217i
$163$	−9.68197	−	9.68197i	−0.758351	−	0.758351i	0.217671	−	0.976022i	$-0.430154\pi$
$163$	−9.68197	−	9.68197i	−0.758351	−	0.758351i	−0.976022	+	0.217671i	$0.930154\pi$
$164$	3.54263	−	6.13601i	0.276633	−	0.479142i
$165$		0			0
$166$	−0.851871	−	1.47548i	−0.0661180	−	0.114520i
$167$	−1.32254	+	4.93579i	−0.102341	+	0.381943i	−0.998030	−	0.0627387i	$-0.980017\pi$
$167$	−1.32254	+	4.93579i	−0.102341	+	0.381943i	0.895689	+	0.444682i	$0.146683\pi$
$168$	0.160405	+	3.48913i	0.0123755	+	0.269192i
$169$	−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
$173$	1.91916	+	7.16239i	0.145911	+	0.544546i	0.999713	+	0.0239492i	$0.00762400\pi$
$173$	1.91916	+	7.16239i	0.145911	+	0.544546i	−0.853802	+	0.520597i	$0.825709\pi$
$174$	−12.3756	+	3.93342i	−0.938190	+	0.298192i
$175$		0			0
$176$	−1.70563	+	0.984748i	−0.128567	+	0.0742282i
$177$	2.14928	−	4.15208i	0.161550	−	0.312090i
$178$	1.98004	−	0.530550i	0.148410	−	0.0397664i
$179$	2.73426			0.204369			0.102184	−	0.994765i	$-0.467417\pi$
$179$	2.73426			0.204369			0.102184	+	0.994765i	$0.467417\pi$
$180$		0			0
$181$	−22.7081			−1.68788			−0.843941	−	0.536437i	$-0.819770\pi$
$181$	−22.7081			−1.68788			−0.843941	+	0.536437i	$0.819770\pi$
$182$	7.92092	−	2.12240i	0.587138	−	0.157323i
$183$	15.1344	−	0.695770i	1.11877	−	0.0514328i
$184$	−5.42731	+	3.13346i	−0.400107	+	0.231002i
$185$		0			0
$186$	−2.58824	+	11.8036i	−0.189779	+	0.865484i
$187$	1.70040	+	6.34598i	0.124346	+	0.464064i
$188$	−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	$0.681453\pi$
$192$	−1.45865	+	0.933998i	−0.105269	+	0.0674055i
$193$	−1.41494	+	5.28063i	−0.101850	+	0.380108i	−0.997969	−	0.0637057i	$-0.979708\pi$
$193$	−1.41494	+	5.28063i	−0.101850	+	0.380108i	0.896119	+	0.443814i	$0.146375\pi$
$194$	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	$-0.0425744\pi$
$197$	12.0386	+	12.0386i	0.857716	+	0.857716i	−0.133353	+	0.991069i	$0.542574\pi$
$198$	−3.77698	+	4.54364i	−0.268418	+	0.322903i
$199$			4.43831i			0.314623i	0.987549	+	0.157312i	$0.0502827\pi$
$199$			4.43831i			0.314623i	−0.987549	+	0.157312i	$0.949717\pi$
$200$		0			0
$201$	−4.44456	−	13.9838i	−0.313495	−	0.986338i
$202$	4.56196	+	1.22237i	0.320978	+	0.0860058i
$203$	−14.6036	−	3.91303i	−1.02497	−	0.274641i
$204$	1.75012	+	5.50634i	0.122533	+	0.385521i
$205$		0			0
$206$		−	4.00520i		−	0.279055i
$207$	−12.0183	+	14.4578i	−0.835331	+	1.00489i
$208$	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	$0.522222\pi$
$212$	−2.57326	+	9.60353i	−0.176732	+	0.659573i
$213$	−8.29213	+	5.30960i	−0.568167	+	0.363808i
$214$	−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
$218$	−1.12679	−	4.20523i	−0.0763156	−	0.284814i
$219$	−0.602965	+	2.74981i	−0.0407446	+	0.185815i
$220$		0			0
$221$	11.7476	−	6.78245i	0.790226	−	0.456237i
$222$	−10.4408	+	0.479991i	−0.700738	+	0.0322149i
$223$	16.2073	−	4.34272i	1.08532	−	0.290810i	0.328546	−	0.944488i	$-0.393441\pi$
$223$	16.2073	−	4.34272i	1.08532	−	0.290810i	0.756773	+	0.653678i	$0.226775\pi$
$224$	−2.01658			−0.134738
$225$		0			0
$226$	2.96556			0.197266
$227$	−7.18543	+	1.92533i	−0.476914	+	0.127789i	−0.489265	−	0.872135i	$-0.662735\pi$
$227$	−7.18543	+	1.92533i	−0.476914	+	0.127789i	0.0123515	+	0.999924i	$0.496068\pi$
$228$	2.95203	−	5.70288i	0.195503	−	0.377682i
$229$	−7.74183	+	4.46975i	−0.511595	+	0.295369i	−0.733489	−	0.679701i	$-0.762109\pi$
$229$	−7.74183	+	4.46975i	−0.511595	+	0.295369i	0.221894	+	0.975071i	$0.428776\pi$
$230$		0			0
$231$	−6.55591	+	2.08371i	−0.431347	+	0.137098i
$232$	−1.94043	−	7.24179i	−0.127396	−	0.475447i
$233$	15.0591	−	15.0591i	0.986558	−	0.986558i	−0.0133533	−	0.999911i	$-0.504251\pi$
$233$	15.0591	−	15.0591i	0.986558	−	0.986558i	0.999911	+	0.0133533i	$0.00425061\pi$
$234$	11.0801	+	5.10461i	0.724327	+	0.333699i
$235$		0			0
$236$	2.33769	+	1.34967i	0.152171	+	0.0878558i
$237$	0.923401	+	20.0858i	0.0599814	+	1.30471i
$238$	−1.74105	+	6.49768i	−0.112855	+	0.421182i
$239$	5.42731	+	9.40038i	0.351064	+	0.608060i	0.986436	−	0.164146i	$-0.0524867\pi$
$239$	5.42731	+	9.40038i	0.351064	+	0.608060i	−0.635372	+	0.772206i	$0.719153\pi$
$240$		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
$243$	−4.51572	+	14.9201i	−0.289684	+	0.957122i
$244$			8.74707i			0.559973i
$245$		0			0
$246$	11.9872	+	2.62850i	0.764277	+	0.167587i
$247$	−14.5628	−	3.90209i	−0.926609	−	0.248284i
$248$	−6.73901	−	1.80571i	−0.427928	−	0.114663i
$249$	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	$0.861168\pi$
$252$	−5.67528	+	2.09534i	−0.357509	+	0.131994i
$253$	−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
$257$	1.95494	−	7.29595i	0.121946	−	0.455109i	−0.877766	−	0.479089i	$-0.840967\pi$
$257$	1.95494	−	7.29595i	0.121946	−	0.455109i	0.999712	+	0.0239802i	$0.00763386\pi$
$258$	14.4867	+	7.49889i	0.901905	+	0.466860i
$259$	−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
$263$	−2.88569	−	10.7695i	−0.177939	−	0.664078i	−0.996032	−	0.0889923i	$-0.971635\pi$
$263$	−2.88569	−	10.7695i	−0.177939	−	0.664078i	0.818093	−	0.575086i	$-0.195031\pi$
$264$	−2.52036	−	2.29881i	−0.155117	−	0.141482i
$265$		0			0
$266$	6.47485	−	3.73826i	0.396998	−	0.229207i
$267$	1.91459	+	2.99006i	0.117171	+	0.182989i
$268$	8.18285	−	2.19259i	0.499847	−	0.133934i
$269$	13.4707			0.821326			0.410663	−	0.911787i	$-0.365297\pi$
$269$	13.4707			0.821326			0.410663	+	0.911787i	$0.365297\pi$
$270$		0			0
$271$	20.4402			1.24165			0.620827	−	0.783947i	$-0.286797\pi$
$271$	20.4402			1.24165			0.620827	+	0.783947i	$0.286797\pi$
$272$	−3.22213	+	0.863368i	−0.195371	+	0.0523494i
$273$	7.65910	+	11.9614i	0.463550	+	0.723936i
$274$	8.53197	−	4.92594i	0.515435	−	0.297587i
$275$		0			0
$276$	−8.01977	−	7.31480i	−0.482733	−	0.440299i
$277$	−6.27326	−	23.4121i	−0.376924	−	1.40670i	−0.850514	−	0.525953i	$-0.823709\pi$
$277$	−6.27326	−	23.4121i	−0.376924	−	1.40670i	0.473590	−	0.880745i	$-0.342958\pi$
$278$	−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	$0.431640\pi$
$282$	−11.9359	−	6.17850i	−0.710775	−	0.367924i
$283$	−0.549660	+	2.05136i	−0.0326739	+	0.121941i	−0.980337	−	0.197333i	$-0.936772\pi$
$283$	−0.549660	+	2.05136i	−0.0326739	+	0.121941i	0.947663	+	0.319273i	$0.103439\pi$
$284$	−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
$288$	−2.30701	−	1.91774i	−0.135942	−	0.113004i
$289$		−	5.87245i		−	0.345438i
$290$		0			0
$291$	−11.7443	+	12.8762i	−0.688464	+	0.754816i
$292$	−1.56994	−	0.420664i	−0.0918738	−	0.0246175i
$293$	3.53204	+	0.946406i	0.206344	+	0.0552896i	0.360510	−	0.932755i	$-0.382603\pi$
$293$	3.53204	+	0.946406i	0.206344	+	0.0552896i	−0.154167	+	0.988045i	$0.549269\pi$
$294$	4.96292	+	1.08824i	0.289443	+	0.0634677i
$295$		0			0
$296$		−	6.03434i		−	0.350739i
$297$	−9.48168	−	3.85077i	−0.550183	−	0.223444i
$298$	−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
$302$	−2.39014	+	8.92011i	−0.137537	+	0.513295i
$303$	0.375673	+	8.17164i	0.0215819	+	0.469449i
$304$	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	−0.339024	−	0.940778i	$-0.610097\pi$
$307$	10.5436	−	10.5436i	0.601754	−	0.601754i	0.940778	+	0.339024i	$0.110097\pi$
$308$	−1.02794	−	3.83631i	−0.0585721	−	0.218594i
$309$	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	$0.429456\pi$
$312$	−3.23782	+	6.25499i	−0.183306	+	0.354119i
$313$	−17.0518	+	4.56901i	−0.963824	+	0.258256i	−0.706218	−	0.707994i	$-0.749600\pi$
$313$	−17.0518	+	4.56901i	−0.963824	+	0.258256i	−0.257606	+	0.966250i	$0.582934\pi$
$314$	10.8546			0.612562
$315$		0			0
$316$	−11.6088			−0.653046
$317$	22.3972	−	6.00131i	1.25795	−	0.337067i	0.432549	−	0.901611i	$-0.357614\pi$
$317$	22.3972	−	6.00131i	1.25795	−	0.337067i	0.825403	+	0.564543i	$0.190948\pi$
$318$	−17.2024	+	0.790843i	−0.964663	+	0.0443483i
$319$	12.7876	−	7.38291i	0.715966	−	0.413363i
$320$		0			0
$321$	2.83465	−	12.9274i	0.158215	−	0.721535i
$322$	−3.27089	−	12.2071i	−0.182279	−	0.680276i
$323$	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
$327$	6.35032	−	4.06623i	0.351173	−	0.224863i
$328$	−1.83380	+	6.84383i	−0.101255	+	0.377887i
$329$	−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
$333$	−6.27003	−	16.9825i	−0.343595	−	0.930636i
$334$		−	5.10991i		−	0.279602i
$335$		0			0
$336$	−1.05799	−	3.32872i	−0.0577182	−	0.181597i
$337$	30.9889	+	8.30344i	1.68807	+	0.452317i	0.969891	−	0.243541i	$-0.0783089\pi$
$337$	30.9889	+	8.30344i	1.68807	+	0.452317i	0.718180	+	0.695858i	$0.244976\pi$
$338$	3.41565	+	0.915220i	0.185787	+	0.0497814i
$339$	1.55588	+	4.89519i	0.0845035	+	0.265870i
$340$		0			0
$341$		−	13.7407i		−	0.744099i
$342$	10.9624	+	1.88085i	0.592779	+	0.101705i
$343$	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
$347$	3.83170	−	14.3001i	0.205696	−	0.767670i	−0.783540	−	0.621342i	$-0.786588\pi$
$347$	3.83170	−	14.3001i	0.205696	−	0.767670i	0.989236	−	0.146328i	$-0.0467454\pi$
$348$	10.9358	−	7.00242i	0.586223	−	0.375369i
$349$	13.3741	+	7.72151i	0.715897	+	0.413323i	0.813241	−	0.581928i	$-0.197701\pi$
$349$	13.3741	+	7.72151i	0.715897	+	0.413323i	−0.0973439	+	0.995251i	$0.531035\pi$
$350$		0			0
$351$	−2.61295	+	20.9678i	−0.139469	+	1.11918i
$352$	1.39264	−	1.39264i	0.0742282	−	0.0742282i
$353$	5.39774	+	20.1446i	0.287293	+	1.07219i	0.947148	+	0.320798i	$0.103951\pi$
$353$	5.39774	+	20.1446i	0.287293	+	1.07219i	−0.659855	+	0.751393i	$0.729382\pi$
$354$	−1.00140	+	4.56688i	−0.0532240	+	0.242727i
$355$		0			0
$356$	−1.77526	+	1.02494i	−0.0940883	+	0.0543219i
$357$	−11.6390	+	0.535079i	−0.616003	+	0.0283194i
$358$	−2.64110	+	0.707680i	−0.139586	+	0.0374020i
$359$	−3.39466			−0.179163			−0.0895815	−	0.995979i	$-0.528553\pi$
$359$	−3.39466			−0.179163			−0.0895815	+	0.995979i	$0.528553\pi$
$360$		0			0
$361$	5.25425			0.276540
$362$	21.9344	−	5.87729i	1.15284	−	0.308904i
$363$	−5.66999	+	10.9536i	−0.297597	+	0.574914i
$364$	−7.10170	+	4.10017i	−0.372230	+	0.214907i
$365$		0			0
$366$	−14.4386	+	4.58913i	−0.754718	+	0.239878i
$367$	−5.68801	−	21.2279i	−0.296912	−	1.10809i	−0.939687	−	0.342035i	$-0.888884\pi$
$367$	−5.68801	−	21.2279i	−0.296912	−	1.10809i	0.642776	−	0.766054i	$-0.277783\pi$
$368$	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
$372$	−0.554953	−	12.0713i	−0.0287730	−	0.625869i
$373$	0.381044	−	1.42207i	0.0197297	−	0.0736322i	−0.955359	−	0.295447i	$-0.904531\pi$
$373$	0.381044	−	1.42207i	0.0197297	−	0.0736322i	0.975089	+	0.221815i	$0.0711981\pi$
$374$	−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
$378$	−6.43626	−	8.26875i	−0.331045	−	0.425299i
$379$		−	30.1323i		−	1.54779i	−0.633314	−	0.773895i	$-0.718306\pi$
$379$		−	30.1323i		−	1.54779i	0.633314	−	0.773895i	$-0.281694\pi$
$380$		0			0
$381$	−8.17649	−	1.79290i	−0.418894	−	0.0918531i
$382$	1.23976	+	0.332194i	0.0634318	+	0.0169965i
$383$	16.5638	+	4.43826i	0.846372	+	0.226785i	0.655843	−	0.754897i	$-0.272313\pi$
$383$	16.5638	+	4.43826i	0.846372	+	0.226785i	0.190528	+	0.981682i	$0.438980\pi$
$384$	1.16721	−	1.27970i	0.0595638	−	0.0653043i
$385$		0			0
$386$		−	5.46691i		−	0.278258i
$387$	−4.77783	+	27.8472i	−0.242871	+	1.41556i
$388$	−7.11484	−	7.11484i	−0.361201	−	0.361201i
$389$	15.1070	−	26.1660i	0.765953	−	1.32667i	−0.173789	−	0.984783i	$-0.555601\pi$
$389$	15.1070	−	26.1660i	0.765953	−	1.32667i	0.939741	−	0.341886i	$-0.111066\pi$
$390$		0			0
$391$	−10.4526	−	18.1044i	−0.528610	−	0.915580i
$392$	−0.759224	+	2.83346i	−0.0383466	+	0.143112i
$393$	0.730471	+	0.378120i	0.0368474	+	0.0190736i
$394$	−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	−0.650561	−	0.759454i	$-0.725466\pi$
$397$	2.16969	−	2.16969i	0.108893	−	0.108893i	0.759454	+	0.650561i	$0.225466\pi$
$398$	−1.14872	−	4.28708i	−0.0575801	−	0.214892i
$399$	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	$0.448931\pi$
$402$	7.91238	+	12.3569i	0.394633	+	0.616308i
$403$	−27.4040	+	7.34287i	−1.36509	+	0.365774i
$404$	−4.72288			−0.234972
$405$		0			0
$406$	15.1188			0.750333
$407$	11.4796	−	3.07596i	0.569025	−	0.152470i
$408$	−3.11563	−	4.86575i	−0.154247	−	0.240890i
$409$	−10.2963	+	5.94456i	−0.509118	+	0.293939i	−0.732471	−	0.680798i	$-0.761633\pi$
$409$	−10.2963	+	5.94456i	−0.509118	+	0.293939i	0.223353	+	0.974738i	$0.428300\pi$
$410$		0			0
$411$	12.6074	+	11.4992i	0.621878	+	0.567212i
$412$	1.03662	+	3.86872i	0.0510706	+	0.190598i
$413$	−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
$417$	−1.08046	−	0.559288i	−0.0529104	−	0.0273885i
$418$	−1.88989	+	7.05315i	−0.0924373	+	0.344981i
$419$	−19.6354	−	34.0095i	−0.959251	−	1.66147i	−0.724325	−	0.689458i	$-0.757849\pi$
$419$	−19.6354	−	34.0095i	−0.959251	−	1.66147i	−0.234926	−	0.972013i	$-0.575485\pi$
$420$		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
$423$	3.93656	−	22.9440i	0.191402	−	1.11557i
$424$		−	9.94230i		−	0.482841i
$425$		0			0
$426$	6.63535	−	7.27484i	0.321484	−	0.352467i
$427$	−17.0381	−	4.56534i	−0.824531	−	0.220932i
$428$	7.38058	+	1.97762i	0.356754	+	0.0955920i
$429$	−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	$0.953012\pi$
$432$	1.95521	−	4.81427i	0.0940699	−	0.231627i
$433$	−10.2605	−	10.2605i	−0.493088	−	0.493088i	0.416190	−	0.909278i	$-0.363365\pi$
$433$	−10.2605	−	10.2605i	−0.493088	−	0.493088i	−0.909278	+	0.416190i	$0.863365\pi$
$434$	7.03457	−	12.1842i	0.337670	−	0.584862i
$435$		0			0
$436$	2.17679	+	3.77030i	0.104249	+	0.180565i
$437$	−6.01360	+	22.4431i	−0.287670	+	1.07360i
$438$	−0.129283	−	2.81217i	−0.00617740	−	0.134371i
$439$	1.96604	+	1.13510i	0.0938342	+	0.0541752i	0.546183	−	0.837666i	$-0.316080\pi$
$439$	1.96604	+	1.13510i	0.0938342	+	0.0541752i	−0.452349	+	0.891841i	$0.649414\pi$
$440$		0			0
$441$	0.807438	+	8.76313i	0.0384494	+	0.417292i
$442$	−9.59184	+	9.59184i	−0.456237	+	0.456237i
$443$	−7.20031	−	26.8719i	−0.342097	−	1.27672i	−0.895967	−	0.444120i	$-0.853516\pi$
$443$	−7.20031	−	26.8719i	−0.342097	−	1.27672i	0.553870	−	0.832603i	$-0.313150\pi$
$444$	9.96076	−	3.16590i	0.472717	−	0.150247i
$445$		0			0
$446$	−14.5310	+	8.38950i	−0.688065	+	0.397254i
$447$	6.45913	−	12.4781i	0.305506	−	0.590193i
$448$	1.94786	−	0.521929i	0.0920279	−	0.0246588i
$449$	11.7712			0.555516			0.277758	−	0.960651i	$-0.410409\pi$
$449$	11.7712			0.555516			0.277758	+	0.960651i	$0.410409\pi$
$450$		0			0
$451$	−13.9544			−0.657086
$452$	−2.86451	+	0.767544i	−0.134735	+	0.0361022i
$453$	−15.9782	+	0.734564i	−0.750723	+	0.0345128i
$454$	6.44228	−	3.71945i	0.302351	−	0.174562i
$455$		0			0
$456$	−1.37542	+	6.27260i	−0.0644102	+	0.293741i
$457$	10.0741	+	37.5970i	0.471246	+	1.75871i	0.635303	+	0.772263i	$0.280875\pi$
$457$	10.0741	+	37.5970i	0.471246	+	1.75871i	−0.164058	+	0.986451i	$0.552458\pi$
$458$	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	$0.689128\pi$
$462$	5.79322	−	3.70950i	0.269525	−	0.172582i
$463$	−1.76940	+	6.60350i	−0.0822311	+	0.306891i	−0.994775	−	0.102087i	$-0.967448\pi$
$463$	−1.76940	+	6.60350i	−0.0822311	+	0.306891i	0.912544	+	0.408978i	$0.134115\pi$
$464$	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	$-0.165116\pi$
$467$	8.05359	+	8.05359i	0.372676	+	0.372676i	−0.495775	+	0.868451i	$0.665116\pi$
$468$	−12.0237	−	2.06294i	−0.555796	−	0.0953595i
$469$			17.0835i			0.788841i
$470$		0			0
$471$	5.69485	+	17.9175i	0.262405	+	0.825596i
$472$	−2.60736	−	0.698639i	−0.120013	−	0.0321575i
$473$	−17.9168	−	4.80079i	−0.823814	−	0.220740i
$474$	−6.09053	−	19.1624i	−0.279747	−	0.880159i
$475$		0			0
$476$		−	6.72689i		−	0.308327i
$477$	−10.3306	−	27.9808i	−0.473007	−	1.28115i
$478$	−7.67538	−	7.67538i	−0.351064	−	0.351064i
$479$	−16.5711	+	28.7020i	−0.757154	+	1.31143i	0.187142	+	0.982333i	$0.440078\pi$
$479$	−16.5711	+	28.7020i	−0.757154	+	1.31143i	−0.944296	+	0.329097i	$0.893256\pi$
$480$		0			0
$481$	−12.2692	−	21.2509i	−0.559428	−	0.968958i
$482$	−6.03872	+	22.5368i	−0.275056	+	1.02652i
$483$	18.4340	−	11.8036i	0.838775	−	0.537083i
$484$	−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	−0.286349	−	0.958126i	$-0.592442\pi$
$487$	14.8248	−	14.8248i	0.671777	−	0.671777i	0.958126	+	0.286349i	$0.0924415\pi$
$488$	−2.26391	−	8.44902i	−0.102482	−	0.382469i
$489$	−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	$0.195080\pi$
$492$	−12.2591	+	0.563584i	−0.552682	+	0.0254083i
$493$	24.1572	−	6.47289i	1.08798	−	0.291524i
$494$	15.0765			0.678325
$495$		0			0
$496$	6.97674			0.313265
$497$	11.0732	−	2.96707i	0.496703	−	0.133091i
$498$	−1.35656	+	2.62068i	−0.0607890	+	0.117435i
$499$	19.6189	−	11.3270i	0.878263	−	0.507065i	0.00817742	−	0.999967i	$-0.497397\pi$
$499$	19.6189	−	11.3270i	0.878263	−	0.507065i	0.870085	+	0.492901i	$0.164064\pi$
$500$		0			0
$501$	8.43482	−	2.68090i	0.376840	−	0.119774i
$502$	−3.46454	−	12.9298i	−0.154630	−	0.577087i
$503$	−9.64801	+	9.64801i	−0.430183	+	0.430183i	−0.888691	−	0.458507i	$-0.848384\pi$
$503$	−9.64801	+	9.64801i	−0.430183	+	0.430183i	0.458507	+	0.888691i	$0.348384\pi$
$504$	4.93958	−	3.49281i	0.220027	−	0.155582i
$505$		0			0
$506$	10.6891	+	6.17134i	0.475187	+	0.274349i
$507$	0.281276	+	6.11831i	0.0124919	+	0.271724i
$508$	1.25084	−	4.66818i	0.0554968	−	0.207117i
$509$	−13.5882	−	23.5355i	−0.602286	−	1.04319i	−0.992474	−	0.122455i	$-0.960923\pi$
$509$	−13.5882	−	23.5355i	−0.602286	−	1.04319i	0.390188	−	0.920735i	$-0.372410\pi$
$510$		0			0
$511$	1.63879	−	2.83847i	0.0724959	−	0.125567i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.64671	+	19.0822i	0.116855	+	0.842499i
$514$			7.55332i			0.333163i
$515$		0			0
$516$	−15.9340	−	3.49393i	−0.701454	−	0.153812i
$517$	14.7620	+	3.95547i	0.649233	+	0.173961i
$518$	11.7541	+	3.14949i	0.516444	+	0.138381i
$519$	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	$0.868295\pi$
$522$	17.2962	+	14.3778i	0.757035	+	0.629298i
$523$	25.8576	+	25.8576i	1.13067	+	1.13067i	0.990066	+	0.140607i	$0.0449053\pi$
$523$	25.8576	+	25.8576i	1.13067	+	1.13067i	0.140607	+	0.990066i	$0.455095\pi$
$524$	−0.237445	+	0.411267i	−0.0103728	+	0.0179663i
$525$		0			0
$526$	5.57472	+	9.65570i	0.243069	+	0.421009i
$527$	6.02350	−	22.4800i	0.262388	−	0.979244i
$528$	3.02946	+	1.56816i	0.131840	+	0.0682455i
$529$	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
$533$	7.45708	+	27.8302i	0.323002	+	1.20546i
$534$	−2.62324	−	2.39264i	−0.113519	−	0.103540i
$535$		0			0
$536$	−7.33654	+	4.23576i	−0.316890	+	0.182957i
$537$	−2.55380	−	3.98832i	−0.110205	−	0.172109i
$538$	−13.0117	+	3.48649i	−0.560976	+	0.150313i
$539$	−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	$0.531170\pi$
$542$	−19.7437	+	5.29032i	−0.848066	+	0.227239i
$543$	21.2093	+	33.1231i	0.910180	+	1.42145i
$544$	2.88889	−	1.66790i	0.123860	−	0.0715106i
$545$		0			0
$546$	−10.4940	−	9.57149i	−0.449100	−	0.409622i
$547$	5.79252	+	21.6180i	0.247670	+	0.924319i	0.972022	+	0.234888i	$0.0754724\pi$
$547$	5.79252	+	21.6180i	0.247670	+	0.924319i	−0.724352	+	0.689430i	$0.757861\pi$
$548$	−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
$552$	9.63971	+	4.98988i	0.410293	+	0.212383i
$553$	6.05896	−	22.6124i	0.257653	−	0.961575i
$554$	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	$-0.0385825\pi$
$557$	20.5740	+	20.5740i	0.871749	+	0.871749i	−0.120914	+	0.992663i	$0.538583\pi$
$558$	19.6347	−	7.24924i	0.831205	−	0.306885i
$559$			38.2982i			1.61984i
$560$		0			0
$561$	7.66836	−	8.40741i	0.323759	−	0.354961i
$562$	−21.7967	−	5.84041i	−0.919438	−	0.246363i
$563$	−34.2529	−	9.17805i	−1.44359	−	0.386809i	−0.549800	−	0.835296i	$-0.685296\pi$
$563$	−34.2529	−	9.17805i	−1.44359	−	0.386809i	−0.893789	+	0.448487i	$0.851963\pi$
$564$	13.1283	+	2.87872i	0.552803	+	0.121216i
$565$		0			0
$566$		−	2.12372i		−	0.0892668i
$567$	10.2723	−	14.9624i	0.431396	−	0.628361i
$568$	4.01977	+	4.01977i	0.168666	+	0.168666i
$569$	−12.0592	+	20.8872i	−0.505549	+	0.875637i	0.494430	+	0.869217i	$0.335377\pi$
$569$	−12.0592	+	20.8872i	−0.505549	+	0.875637i	−0.999979	+	0.00641982i	$0.997956\pi$
$570$		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	$0.803354\pi$
$572$	2.07285	−	7.73599i	0.0866703	−	0.323458i
$573$	0.102094	+	2.22074i	0.00426502	+	0.0927726i
$574$	−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	−0.710979	−	0.703214i	$-0.751748\pi$
$577$	−0.186522	+	0.186522i	−0.00776502	+	0.00776502i	0.703214	+	0.710979i	$0.251748\pi$
$578$	1.51990	+	5.67235i	0.0632196	+	0.235939i
$579$	9.02412	−	2.86820i	0.375030	−	0.119198i
$580$		0			0
$581$	−2.97543	+	1.71786i	−0.123441	+	0.0712689i
$582$	8.01154	−	15.4771i	0.332089	−	0.641547i
$583$	18.9141	−	5.06802i	0.783342	−	0.209896i
$584$	1.62532			0.0672563
$585$		0			0
$586$	−3.65663			−0.151054
$587$	−43.6620	+	11.6992i	−1.80212	+	0.482878i	−0.994307	−	0.106555i	$-0.966018\pi$
$587$	−43.6620	+	11.6992i	−1.80212	+	0.482878i	−0.807818	+	0.589433i	$0.799351\pi$
$588$	−5.07547	+	0.233334i	−0.209309	+	0.00962251i
$589$	−22.4010	+	12.9332i	−0.923017	+	0.532904i
$590$		0			0
$591$	6.31603	−	28.8041i	0.259807	−	1.18484i
$592$	1.56180	+	5.82872i	0.0641897	+	0.239559i
$593$	−3.60323	+	3.60323i	−0.147967	+	0.147967i	−0.777209	−	0.629242i	$-0.783365\pi$
$593$	−3.60323	+	3.60323i	−0.147967	+	0.147967i	0.629242	+	0.777209i	$0.283365\pi$
$594$	10.1553	+	1.26552i	0.416675	+	0.0519248i
$595$		0			0
$596$	7.02536	+	4.05609i	0.287770	+	0.166144i
$597$	6.47392	−	4.14537i	0.264960	−	0.169659i
$598$	6.59580	−	24.6159i	0.269722	−	1.00662i
$599$	23.4581	+	40.6307i	0.958473	+	1.66012i	0.726213	+	0.687470i	$0.241279\pi$
$599$	23.4581	+	40.6307i	0.958473	+	1.66012i	0.232260	+	0.972654i	$0.425388\pi$
$600$		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
$603$	−16.2461	+	19.5438i	−0.661594	+	0.795887i
$604$		−	9.23478i		−	0.375758i
$605$		0			0
$606$	−2.47785	−	7.79597i	−0.100656	−	0.316690i
$607$	15.9755	+	4.28061i	0.648424	+	0.173745i	0.568016	−	0.823017i	$-0.307711\pi$
$607$	15.9755	+	4.28061i	0.648424	+	0.173745i	0.0804079	+	0.996762i	$0.474378\pi$
$608$	−3.58120	−	0.959578i	−0.145237	−	0.0389160i
$609$	7.93204	+	24.9563i	0.321422	+	1.01128i
$610$		0			0
$611$		−	31.5547i		−	1.27657i
$612$	6.39719	−	7.69571i	0.258591	−	0.311081i
$613$	21.1512	+	21.1512i	0.854290	+	0.854290i	0.990658	−	0.136368i	$-0.0435429\pi$
$613$	21.1512	+	21.1512i	0.854290	+	0.854290i	−0.136368	+	0.990658i	$0.543543\pi$
$614$	−7.45544	+	12.9132i	−0.300877	+	0.521134i
$615$		0			0
$616$	1.98582	+	3.43954i	0.0800110	+	0.138583i
$617$	2.72427	−	10.1671i	0.109675	−	0.409312i	−0.889159	−	0.457599i	$-0.848710\pi$
$617$	2.72427	−	10.1671i	0.109675	−	0.409312i	0.998834	+	0.0482869i	$0.0153762\pi$
$618$	−5.84216	+	3.74085i	−0.235006	+	0.150479i
$619$	−2.77044	−	1.59951i	−0.111353	−	0.0642898i	0.443289	−	0.896379i	$-0.353812\pi$
$619$	−2.77044	−	1.59951i	−0.111353	−	0.0642898i	−0.554642	+	0.832089i	$0.687145\pi$
$620$		0			0
$621$	32.3139	+	4.02687i	1.29671	+	0.161593i
$622$	7.41734	−	7.41734i	0.297408	−	0.297408i
$623$	−1.06990	−	3.99290i	−0.0428644	−	0.159972i
$624$	1.50858	−	6.87987i	0.0603917	−	0.275415i
$625$		0			0
$626$	15.2882	−	8.82666i	0.611040	−	0.352784i
$627$	−12.6340	+	0.580821i	−0.504554	+	0.0231958i
$628$	−10.4848	+	2.80938i	−0.418388	+	0.112107i
$629$	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	$0.361102\pi$
$632$	11.2132	−	3.00458i	0.446039	−	0.119516i
$633$	19.1770	−	37.0472i	0.762219	−	1.47249i
$634$	−20.0808	+	11.5936i	−0.797510	+	0.460442i
$635$		0			0
$636$	16.4116	−	5.21621i	0.650761	−	0.206836i
$637$	3.08736	+	11.5222i	0.122326	+	0.456525i
$638$	−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	$0.241108\pi$
$642$	0.607785	+	13.2205i	0.0239874	+	0.521773i
$643$	5.25595	−	19.6155i	0.207274	−	0.773559i	−0.781470	−	0.623943i	$-0.785530\pi$
$643$	5.25595	−	19.6155i	0.207274	−	0.773559i	0.988744	−	0.149616i	$-0.0478036\pi$
$644$	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	−0.987974	−	0.154619i	$-0.950585\pi$
$647$	−29.0632	−	29.0632i	−1.14259	−	1.14259i	−0.154619	−	0.987974i	$-0.549415\pi$
$648$	8.97261	+	0.701625i	0.352477	+	0.0275624i
$649$		−	5.31632i		−	0.208684i
$650$		0			0
$651$	23.8029	+	5.21939i	0.932911	+	0.204564i
$652$	−13.2258	−	3.54385i	−0.517963	−	0.138788i
$653$	−2.75027	−	0.736931i	−0.107626	−	0.0288384i	0.204604	−	0.978845i	$-0.434409\pi$
$653$	−2.75027	−	0.736931i	−0.107626	−	0.0288384i	−0.312230	+	0.950006i	$0.601076\pi$
$654$	−5.08152	+	5.57126i	−0.198703	+	0.217853i
$655$		0			0
$656$		−	7.08526i		−	0.276633i
$657$	4.57416	−	1.68880i	0.178455	−	0.0658865i
$658$	11.0649	+	11.0649i	0.431354	+	0.431354i
$659$	18.8486	−	32.6467i	0.734236	−	1.27173i	−0.220822	−	0.975314i	$-0.570874\pi$
$659$	18.8486	−	32.6467i	0.734236	−	1.27173i	0.955058	−	0.296420i	$-0.0957928\pi$
$660$		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	$0.787501\pi$
$662$	−6.68424	+	24.9459i	−0.259791	+	0.969551i
$663$	−20.8654	−	10.8007i	−0.810345	−	0.419465i
$664$	−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
$668$	1.32254	+	4.93579i	0.0511707	+	0.190971i
$669$	−21.4721	−	19.5846i	−0.830157	−	0.757183i
$670$		0			0
$671$	14.9193	−	8.61365i	0.575953	−	0.332526i
$672$	1.88348	+	2.94147i	0.0726568	+	0.113470i
$673$	6.88414	−	1.84460i	0.265364	−	0.0711041i	−0.123684	−	0.992322i	$-0.539471\pi$
$673$	6.88414	−	1.84460i	0.265364	−	0.0711041i	0.389048	+	0.921218i	$0.372804\pi$
$674$	−32.0820			−1.23575
$675$		0			0
$676$	−3.53614			−0.136005
$677$	−8.09727	+	2.16966i	−0.311203	+	0.0833867i	−0.411040	−	0.911617i	$-0.634834\pi$
$677$	−8.09727	+	2.16966i	−0.311203	+	0.0833867i	0.0998372	+	0.995004i	$0.468168\pi$
$678$	−2.76983	−	4.32570i	−0.106375	−	0.166128i
$679$	17.5722	−	10.1453i	0.674358	−	0.389341i
$680$		0			0
$681$	9.51955	+	8.68274i	0.364790	+	0.332723i
$682$	3.55635	+	13.2725i	0.136180	+	0.508229i
$683$	−15.8873	+	15.8873i	−0.607911	+	0.607911i	−0.942400	−	0.334488i	$-0.891436\pi$
$683$	−15.8873	+	15.8873i	−0.607911	+	0.607911i	0.334488	+	0.942400i	$0.391436\pi$
$684$	−11.0757	+	1.02052i	−0.423489	+	0.0390204i
$685$		0			0
$686$	−17.3478	−	10.0158i	−0.662342	−	0.382403i
$687$	13.7506	+	7.11785i	0.524619	+	0.271563i
$688$	2.43757	−	9.09714i	0.0929315	−	0.346825i
$689$	−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
$693$	9.16260	+	7.61656i	0.348058	+	0.289329i
$694$			14.8046i			0.561973i
$695$		0			0
$696$	−8.75085	+	9.59422i	−0.331700	+	0.363668i
$697$	−22.8296	−	6.11718i	−0.864734	−	0.231705i
$698$	−14.9168	−	3.99695i	−0.564610	−	0.151287i
$699$	−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	$0.869058\pi$
$702$	−2.90295	−	20.9296i	−0.109565	−	0.789937i
$703$	−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
$707$	2.46501	−	9.19953i	0.0927062	−	0.345984i
$708$	−0.214714	−	4.67045i	−0.00806943	−	0.175526i
$709$	20.4846	+	11.8268i	0.769316	+	0.444165i	0.832631	−	0.553829i	$-0.186834\pi$
$709$	20.4846	+	11.8268i	0.769316	+	0.444165i	−0.0633143	+	0.997994i	$0.520167\pi$
$710$		0			0
$711$	28.4356	−	20.1070i	1.06642	−	0.754072i
$712$	1.44949	−	1.44949i	0.0543219	−	0.0543219i
$713$	11.3163	+	42.2329i	0.423798	+	1.58163i
$714$	11.1039	−	3.52925i	0.415555	−	0.132079i
$715$		0			0
$716$	2.36794	−	1.36713i	0.0884942	−	0.0510921i
$717$	8.64273	−	16.6965i	0.322769	−	0.623541i
$718$	3.27899	−	0.878601i	0.122371	−	0.0327891i
$719$	−21.3695			−0.796947			−0.398473	−	0.917180i	$-0.630460\pi$
$719$	−21.3695			−0.796947			−0.398473	+	0.917180i	$0.630460\pi$
$720$		0			0
$721$	−8.07679			−0.300795
$722$	−5.07522	+	1.35990i	−0.188880	+	0.0506102i
$723$	−40.3692	+	1.85589i	−1.50135	+	0.0690212i
$724$	−19.6658	+	11.3541i	−0.730874	+	0.421970i
$725$		0			0
$726$	2.64179	−	12.0478i	0.0980462	−	0.447137i
$727$	0.796213	+	2.97151i	0.0295299	+	0.110207i	0.979118	−	0.203294i	$-0.0651647\pi$
$727$	0.796213	+	2.97151i	0.0295299	+	0.110207i	−0.949588	+	0.313501i	$0.898498\pi$
$728$	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
$732$	12.7589	−	8.16974i	0.471581	−	0.301962i
$733$	6.30661	−	23.5366i	0.232940	−	0.869343i	−0.746127	−	0.665804i	$-0.768089\pi$
$733$	6.30661	−	23.5366i	0.232940	−	0.869343i	0.979067	−	0.203540i	$-0.0652446\pi$
$734$	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
$738$	−7.36199	−	19.9401i	−0.270999	−	0.734006i
$739$		−	5.68805i		−	0.209238i	−0.994512	−	0.104619i	$-0.966638\pi$
$739$		−	5.68805i		−	0.209238i	0.994512	−	0.104619i	$-0.0333624\pi$
$740$		0			0
$741$	7.90986	+	24.8865i	0.290576	+	0.914229i
$742$	19.3663	+	5.18917i	0.710958	+	0.190500i
$743$	15.1100	+	4.04871i	0.554332	+	0.148533i	0.525101	−	0.851040i	$-0.324027\pi$
$743$	15.1100	+	4.04871i	0.554332	+	0.148533i	0.0292311	+	0.999573i	$0.490694\pi$
$744$	3.66033	+	11.5164i	0.134194	+	0.422211i
$745$		0			0
$746$			1.47224i			0.0539025i
$747$	−5.03761	−	0.864318i	−0.184317	−	0.0316237i
$748$	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	$-0.456104\pi$
$752$	−2.00837	+	7.49533i	−0.0732376	+	0.273327i
$753$	19.5254	−	12.5025i	0.711544	−	0.455615i
$754$	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	−0.986963	−	0.160950i	$-0.948544\pi$
$757$	−22.7266	+	22.7266i	−0.826013	+	0.826013i	0.160950	+	0.986963i	$0.448544\pi$
$758$	7.79880	+	29.1055i	0.283265	+	1.05716i
$759$	−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	$0.507623\pi$
$762$	8.36192	−	0.384421i	0.302920	−	0.0139261i
$763$	−8.48016	+	2.27225i	−0.307002	+	0.0822611i
$764$	−1.28350			−0.0464353
$765$		0			0
$766$	−17.1481			−0.619587
$767$	−10.6027	+	2.84099i	−0.382842	+	0.102582i
$768$	−0.796225	+	1.53819i	−0.0287313	+	0.0555046i
$769$	29.3558	−	16.9486i	1.05860	−	0.611180i	0.133552	−	0.991042i	$-0.457362\pi$
$769$	29.3558	−	16.9486i	1.05860	−	0.611180i	0.925043	+	0.379861i	$0.124028\pi$
$770$		0			0
$771$	−12.4681	+	3.96283i	−0.449028	+	0.142718i
$772$	1.41494	+	5.28063i	0.0509248	+	0.190054i
$773$	30.1093	−	30.1093i	1.08296	−	1.08296i	0.0867231	−	0.996232i	$-0.472360\pi$
$773$	30.1093	−	30.1093i	1.08296	−	1.08296i	0.996232	−	0.0867231i	$-0.0276395\pi$
$774$	−2.59237	−	28.1350i	−0.0931807	−	1.01129i
$775$		0			0
$776$	8.71386	+	5.03095i	0.312809	+	0.180601i
$777$	0.967939	+	21.0546i	0.0347246	+	0.755329i
$778$	−7.81993	+	29.1844i	−0.280358	+	1.04631i
$779$	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
$783$	−14.6587	+	36.0938i	−0.523858	+	1.28989i
$784$		−	2.93342i		−	0.104765i
$785$		0			0
$786$	−0.803445	−	0.176176i	−0.0286579	−	0.00628398i
$787$	10.2212	+	2.73876i	0.364346	+	0.0976263i	0.436347	−	0.899778i	$-0.356272\pi$
$787$	10.2212	+	2.73876i	0.364346	+	0.0976263i	−0.0720011	+	0.997405i	$0.522939\pi$
$788$	16.4450	+	4.40644i	0.585831	+	0.156973i
$789$	−13.0137	+	14.2679i	−0.463300	+	0.507952i
$790$		0			0
$791$		−	5.98028i		−	0.212634i
$792$	−0.999137	+	5.82340i	−0.0355028	+	0.206925i
$793$	−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
$797$	3.52110	−	13.1409i	0.124724	−	0.465476i	−0.875106	−	0.483932i	$-0.839208\pi$
$797$	3.52110	−	13.1409i	0.124724	−	0.465476i	0.999830	+	0.0184558i	$0.00587500\pi$
$798$	−11.5003	−	5.95299i	−0.407106	−	0.210733i
$799$	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
$803$	0.828496	+	3.09199i	0.0292370	+	0.109114i
$804$	−10.8410	−	9.88801i	−0.382332	−	0.348723i
$805$		0			0
$806$	24.5697	−	14.1853i	0.865432	−	0.499657i
$807$	−12.5816	−	19.6490i	−0.442895	−	0.691679i
$808$	4.56196	−	1.22237i	0.160489	−	0.0430029i
$809$	−33.4429			−1.17579			−0.587895	−	0.808937i	$-0.700043\pi$
$809$	−33.4429			−1.17579			−0.587895	+	0.808937i	$0.700043\pi$
$810$		0			0
$811$	21.1960			0.744294			0.372147	−	0.928174i	$-0.378622\pi$
$811$	21.1960			0.744294			0.372147	+	0.928174i	$0.378622\pi$
$812$	−14.6036	+	3.91303i	−0.512487	+	0.137320i
$813$	−19.0911	−	29.8150i	−0.669555	−	1.04566i
$814$	−10.2924	+	5.94230i	−0.360747	+	0.208278i
$815$		0			0
$816$	4.26881	+	3.89357i	0.149438	+	0.136302i
$817$	9.03736	+	33.7279i	0.316177	+	1.17999i
$818$	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	$0.949241\pi$
$822$	−15.1540	−	7.84431i	−0.528558	−	0.273602i
$823$	−6.59989	+	24.6311i	−0.230058	+	0.858588i	0.750257	+	0.661146i	$0.229930\pi$
$823$	−6.59989	+	24.6311i	−0.230058	+	0.858588i	−0.980315	+	0.197441i	$0.936737\pi$
$824$	−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	$-0.164600\pi$
$827$	10.7808	+	10.7808i	0.374885	+	0.374885i	−0.494368	+	0.869253i	$0.664600\pi$
$828$	−3.17925	+	18.5300i	−0.110486	+	0.643962i
$829$			4.02079i			0.139648i	0.997559	+	0.0698239i	$0.0222437\pi$
$829$			4.02079i			0.139648i	−0.997559	+	0.0698239i	$0.977756\pi$
$830$		0			0
$831$	−28.2908	+	31.0173i	−0.981396	+	1.07598i
$832$	3.92790	+	1.05248i	0.136176	+	0.0364881i
$833$	−9.45186	−	2.53262i	−0.327488	−	0.0877500i
$834$	1.18840	+	0.260587i	0.0411509	+	0.00902338i
$835$		0			0
$836$		−	7.30196i		−	0.252543i
$837$	22.2675	+	28.6074i	0.769677	+	0.988815i
$838$	27.7686	+	27.7686i	0.959251	+	0.959251i
$839$	16.7880	−	29.0777i	0.579588	−	1.00388i	−0.415939	−	0.909393i	$-0.636547\pi$
$839$	16.7880	−	29.0777i	0.579588	−	1.00388i	0.995527	−	0.0944825i	$-0.0301196\pi$
$840$		0			0
$841$	−13.6044	−	23.5635i	−0.469118	−	0.812536i
$842$	6.34068	−	23.6637i	0.218514	−	0.815506i
$843$	−1.79494	−	39.0435i	−0.0618211	−	1.34473i
$844$	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
$848$	2.57326	+	9.60353i	0.0883660	+	0.329786i
$849$	3.50559	−	1.11421i	0.120312	−	0.0382395i
$850$		0			0
$851$	−32.7503	+	18.9084i	−1.12266	+	0.648171i
$852$	−4.52639	+	8.74432i	−0.155072	+	0.299575i
$853$	−22.9734	+	6.15572i	−0.786596	+	0.210768i	−0.629691	−	0.776846i	$-0.716818\pi$
$853$	−22.9734	+	6.15572i	−0.786596	+	0.210768i	−0.156905	+	0.987614i	$0.550152\pi$
$854$	17.6391			0.603599
$855$		0			0
$856$	−7.64094			−0.261162
$857$	−11.4475	+	3.06736i	−0.391040	+	0.104779i	−0.448981	−	0.893541i	$-0.648213\pi$
$857$	−11.4475	+	3.06736i	−0.391040	+	0.104779i	0.0579412	+	0.998320i	$0.481546\pi$
$858$	13.8572	−	0.637053i	0.473076	−	0.0217486i
$859$	−34.6670	+	20.0150i	−1.18282	+	0.682904i	−0.956666	−	0.291187i	$-0.905950\pi$
$859$	−34.6670	+	20.0150i	−1.18282	+	0.682904i	−0.226158	+	0.974091i	$0.572617\pi$
$860$		0			0
$861$	5.30058	−	24.1732i	0.180643	−	0.823819i
$862$	−1.58062	−	5.89894i	−0.0538360	−	0.200919i
$863$	−1.78680	+	1.78680i	−0.0608233	+	0.0608233i	−0.736864	−	0.676041i	$-0.763694\pi$
$863$	−1.78680	+	1.78680i	−0.0608233	+	0.0608233i	0.676041	+	0.736864i	$0.263694\pi$
$864$	−0.642559	+	5.15627i	−0.0218603	+	0.175420i
$865$		0			0
$866$	12.5665	+	7.25527i	0.427027	+	0.246544i
$867$	−8.56583	+	5.48486i	−0.290911	+	0.186276i
$868$	−3.64136	+	13.5897i	−0.123596	+	0.461266i
$869$	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
$873$	29.7510	+	5.10446i	1.00692	+	0.172760i
$874$		−	23.2348i		−	0.785928i
$875$		0			0
$876$	0.852721	+	2.68289i	0.0288108	+	0.0906463i
$877$	−6.66309	−	1.78537i	−0.224996	−	0.0602876i	0.144559	−	0.989496i	$-0.453824\pi$
$877$	−6.66309	−	1.78537i	−0.224996	−	0.0602876i	−0.369556	+	0.929208i	$0.620490\pi$
$878$	−2.19284	−	0.587569i	−0.0740047	−	0.0198295i
$879$	−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	$0.983800\pi$
$882$	−3.04799	−	8.25555i	−0.102631	−	0.277979i
$883$	8.50404	+	8.50404i	0.286184	+	0.286184i	0.835569	−	0.549385i	$-0.185138\pi$
$883$	8.50404	+	8.50404i	0.286184	+	0.286184i	−0.549385	+	0.835569i	$0.685138\pi$
$884$	6.78245	−	11.7476i	0.228119	−	0.395113i
$885$		0			0
$886$	13.9099	+	24.0927i	0.467313	+	0.809410i
$887$	4.61020	−	17.2055i	0.154796	−	0.577705i	−0.844327	−	0.535828i	$-0.820000\pi$
$887$	4.61020	−	17.2055i	0.154796	−	0.577705i	0.999123	−	0.0418769i	$-0.0133337\pi$
$888$	−8.80196	+	5.63606i	−0.295375	+	0.189134i
$889$	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
$893$	−7.44607	−	27.7891i	−0.249173	−	0.929928i
$894$	−3.00947	+	13.7246i	−0.100652	+	0.459021i
$895$		0			0
$896$	−1.74641	+	1.00829i	−0.0583434	+	0.0336846i
$897$	44.0934	−	2.02710i	1.47224	−	0.0676828i
$898$	−11.3701	+	3.04660i	−0.379424	+	0.101666i
$899$	−52.3064			−1.74452
$900$		0			0
$901$	33.1655			1.10490
$902$	13.4789	−	3.61166i	0.448798	−	0.120255i
$903$	15.1221	−	29.2136i	0.503231	−	0.972169i
$904$	2.56825	−	1.48278i	0.0854188	−	0.0493166i
$905$		0			0
$906$	15.2437	−	4.84500i	0.506437	−	0.160964i
$907$	−0.324723	−	1.21188i	−0.0107822	−	0.0402399i	0.960325	−	0.278883i	$-0.0899641\pi$
$907$	−0.324723	−	1.21188i	−0.0107822	−	0.0402399i	−0.971107	+	0.238643i	$0.923297\pi$
$908$	−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	$0.814381\pi$
$912$	−0.294909	−	6.41485i	−0.00976540	−	0.212417i
$913$	0.868470	−	3.24117i	0.0287422	−	0.107267i
$914$	−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
$918$	16.0594	+	6.52217i	0.530040	+	0.215264i
$919$		−	54.3202i		−	1.79186i	−0.444196	−	0.895930i	$-0.646511\pi$
$919$		−	54.3202i		−	1.79186i	0.444196	−	0.895930i	$-0.353489\pi$
$920$		0			0
$921$	−25.2270	−	5.53167i	−0.831259	−	0.182275i
$922$	2.92446	+	0.783607i	0.0963121	+	0.0258067i
$923$	22.3294	+	5.98314i	0.734981	+	0.196938i
$924$	−4.63573	+	5.08250i	−0.152504	+	0.167202i
$925$		0			0
$926$		−	6.83645i		−	0.224660i
$927$	−9.24002	−	7.68091i	−0.303482	−	0.252274i
$928$	−5.30136	−	5.30136i	−0.174026	−	0.174026i
$929$	13.9274	−	24.1230i	0.456944	−	0.791450i	−0.541854	−	0.840473i	$-0.682277\pi$
$929$	13.9274	−	24.1230i	0.456944	−	0.791450i	0.998798	+	0.0490228i	$0.0156107\pi$
$930$		0			0
$931$	5.43786	+	9.41865i	0.178219	+	0.308684i
$932$	5.51203	−	20.5712i	0.180553	−	0.673831i
$933$	16.1352	+	8.35217i	0.528241	+	0.273438i
$934$	−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	−0.375481	−	0.926830i	$-0.622523\pi$
$937$	16.8770	−	16.8770i	0.551349	−	0.551349i	0.926830	+	0.375481i	$0.122523\pi$
$938$	−4.42152	−	16.5014i	−0.144368	−	0.538788i
$939$	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	$0.153089\pi$
$942$	−10.1382	−	15.8331i	−0.330320	−	0.515869i
$943$	42.8898	−	11.4923i	1.39668	−	0.374240i
$944$	2.69933			0.0878558
$945$		0			0
$946$	18.5488			0.603074
$947$	−11.5072	+	3.08335i	−0.373934	+	0.100195i	−0.440891	−	0.897560i	$-0.645338\pi$
$947$	−11.5072	+	3.08335i	−0.373934	+	0.100195i	0.0669572	+	0.997756i	$0.478671\pi$
$948$	10.8426	+	16.9331i	0.352151	+	0.549962i
$949$	5.72383	−	3.30466i	0.185804	−	0.107274i
$950$		0			0
$951$	−29.6727	−	27.0644i	−0.962204	−	0.877622i
$952$	1.74105	+	6.49768i	0.0564277	+	0.210591i
$953$	−13.4723	+	13.4723i	−0.436411	+	0.436411i	−0.890802	−	0.454391i	$-0.849857\pi$
$953$	−13.4723	+	13.4723i	−0.436411	+	0.436411i	0.454391	+	0.890802i	$0.349857\pi$
$954$	17.2206	+	24.3536i	0.557537	+	0.788476i
$955$		0			0
$956$	9.40038	+	5.42731i	0.304030	+	0.175532i
$957$	−22.7126	−	11.7569i	−0.734195	−	0.380047i
$958$	8.57785	−	32.0130i	0.277138	−	1.03429i
$959$	−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
$963$	−21.5040	+	7.93938i	−0.692957	+	0.255843i
$964$		−	23.3318i		−	0.751467i
$965$		0			0
$966$	−14.7508	+	16.1725i	−0.474601	+	0.520341i
$967$	−8.95826	−	2.40036i	−0.288078	−	0.0771904i	0.111886	−	0.993721i	$-0.464311\pi$
$967$	−8.95826	−	2.40036i	−0.288078	−	0.0771904i	−0.399964	+	0.916531i	$0.630978\pi$
$968$	6.87844	+	1.84307i	0.221081	+	0.0592386i
$969$	−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	$0.870122\pi$
$972$	3.54930	+	15.1790i	0.113844	+	0.486867i
$973$	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
$977$	−6.35548	+	23.7190i	−0.203330	+	0.758837i	0.786622	+	0.617434i	$0.211828\pi$
$977$	−6.35548	+	23.7190i	−0.203330	+	0.758837i	−0.989952	+	0.141403i	$0.954839\pi$
$978$	−1.08914	−	23.6909i	−0.0348267	−	0.757551i
$979$	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
$983$	−10.7435	−	40.0954i	−0.342666	−	1.27885i	−0.895316	−	0.445433i	$-0.853050\pi$
$983$	−10.7435	−	40.0954i	−0.342666	−	1.27885i	0.552650	−	0.833414i	$-0.313617\pi$
$984$	11.6955	−	3.71726i	0.372839	−	0.118502i
$985$		0			0
$986$	−21.6587	+	12.5047i	−0.689754	+	0.398230i
$987$	−12.4594	+	24.0697i	−0.396588	+	0.766148i
$988$	−14.5628	+	3.90209i	−0.463305	+	0.124142i
$989$	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	$0.302481\pi$
$992$	−6.73901	+	1.80571i	−0.213964	+	0.0573315i
$993$	−44.6846	+	2.05428i	−1.41802	+	0.0651906i
$994$	−9.92800	+	5.73193i	−0.314897	+	0.181806i
$995$		0			0
$996$	0.632057	−	2.88248i	0.0200275	−	0.0913349i
$997$	−3.09617	−	11.5550i	−0.0980565	−	0.365952i	0.899409	−	0.437109i	$-0.143998\pi$
$997$	−3.09617	−	11.5550i	−0.0980565	−	0.365952i	−0.997465	+	0.0711569i	$0.977331\pi$
$998$	−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.443.1		16
3.2	odd	2		1350.2.q.h.143.4		16
5.2	odd	4	inner	450.2.p.h.407.1		16
5.3	odd	4		90.2.l.b.47.4	yes	16
5.4	even	2		90.2.l.b.83.4	yes	16
9.4	even	3		1350.2.q.h.1043.3		16
9.5	odd	6	inner	450.2.p.h.293.1		16
15.2	even	4		1350.2.q.h.1007.3		16
15.8	even	4		270.2.m.b.197.2		16
15.14	odd	2		270.2.m.b.143.2		16
20.3	even	4		720.2.cu.b.497.1		16
20.19	odd	2		720.2.cu.b.353.2		16
45.4	even	6		270.2.m.b.233.2		16
45.13	odd	12		270.2.m.b.17.2		16
45.14	odd	6		90.2.l.b.23.4	✓	16
45.22	odd	12		1350.2.q.h.557.4		16
45.23	even	12		90.2.l.b.77.4	yes	16
45.29	odd	6		810.2.f.c.323.7		16
45.32	even	12	inner	450.2.p.h.257.1		16
45.34	even	6		810.2.f.c.323.2		16
45.38	even	12		810.2.f.c.647.2		16
45.43	odd	12		810.2.f.c.647.7		16
180.23	odd	12		720.2.cu.b.257.2		16
180.59	even	6		720.2.cu.b.113.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	45.14	odd	6
90.2.l.b.47.4	yes	16	5.3	odd	4
90.2.l.b.77.4	yes	16	45.23	even	12
90.2.l.b.83.4	yes	16	5.4	even	2
270.2.m.b.17.2		16	45.13	odd	12
270.2.m.b.143.2		16	15.14	odd	2
270.2.m.b.197.2		16	15.8	even	4
270.2.m.b.233.2		16	45.4	even	6
450.2.p.h.257.1		16	45.32	even	12	inner
450.2.p.h.293.1		16	9.5	odd	6	inner
450.2.p.h.407.1		16	5.2	odd	4	inner
450.2.p.h.443.1		16	1.1	even	1	trivial
720.2.cu.b.113.1		16	180.59	even	6
720.2.cu.b.257.2		16	180.23	odd	12
720.2.cu.b.353.2		16	20.19	odd	2
720.2.cu.b.497.1		16	20.3	even	4
810.2.f.c.323.2		16	45.34	even	6
810.2.f.c.323.7		16	45.29	odd	6
810.2.f.c.647.2		16	45.38	even	12
810.2.f.c.647.7		16	45.43	odd	12
1350.2.q.h.143.4		16	3.2	odd	2
1350.2.q.h.557.4		16	45.22	odd	12
1350.2.q.h.1007.3		16	15.2	even	4
1350.2.q.h.1043.3		16	9.4	even	3

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)

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

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