LMFDB - Embedded newform 720.2.cu.b.497.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(113,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("720.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cu (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
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:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			497.1
Root			$0.500000 - 0.331082i$ of defining polynomial
Character	$\chi$	$=$	720.497
Dual form			720.2.cu.b.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45865 + 0.933998i) q^{3} +(-1.29554 + 1.82252i) q^{5} +(-1.94786 + 0.521929i) q^{7} +(1.25529 - 2.72474i) q^{9} +O(q^{10})$	\(q+(-1.45865 + 0.933998i) q^{3} +(-1.29554 + 1.82252i) q^{5} +(-1.94786 + 0.521929i) q^{7} +(1.25529 - 2.72474i) q^{9} +(1.70563 + 0.984748i) q^{11} +(-3.92790 - 1.05248i) q^{13} +(0.187514 - 3.86844i) q^{15} +(-2.35877 + 2.35877i) q^{17} +3.70753i q^{19} +(2.35376 - 2.58061i) q^{21} +(1.62200 - 6.05338i) q^{23} +(-1.64313 - 4.72230i) q^{25} +(0.713876 + 5.14688i) q^{27} +(3.74863 - 6.49281i) q^{29} +(-3.48837 - 6.04204i) q^{31} +(-3.40767 + 0.156660i) q^{33} +(1.57232 - 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(6.71243 - 2.13346i) q^{39} +(6.13601 - 3.54263i) q^{41} +(-2.43757 - 9.09714i) q^{43} +(3.33960 + 5.81782i) q^{45} +(-2.00837 - 7.49533i) q^{47} +(-2.54041 + 1.46671i) q^{49} +(1.23752 - 5.64369i) q^{51} +(-7.03027 - 7.03027i) q^{53} +(-4.00444 + 1.83276i) q^{55} +(-3.46282 - 5.40797i) q^{57} +(1.34967 + 2.33769i) q^{59} +(-4.37353 + 7.57518i) q^{61} +(-1.02302 + 5.96261i) q^{63} +(7.00693 - 5.79513i) q^{65} +(-2.19259 + 8.18285i) q^{67} +(3.28793 + 10.3447i) q^{69} +5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} +(6.80736 + 5.35349i) q^{75} +(-3.83631 - 1.02794i) q^{77} +(-10.0535 - 5.80440i) q^{79} +(-5.84847 - 6.84072i) q^{81} +(1.64569 - 0.440961i) q^{83} +(-1.24300 - 7.35477i) q^{85} +(0.596356 + 12.9719i) q^{87} +2.04989 q^{89} +8.20034 q^{91} +(10.7315 + 5.55506i) q^{93} +(-6.75702 - 4.80327i) q^{95} +(-9.71905 + 2.60421i) q^{97} +(4.82426 - 3.41127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 - 8 * q^7	$ 16 q - 12 q^{5} - 8 q^{7} + 24 q^{15} + 24 q^{21} + 24 q^{23} - 16 q^{25} + 8 q^{31} + 24 q^{41} + 36 q^{45} - 48 q^{47} + 48 q^{51} - 24 q^{55} + 24 q^{57} - 24 q^{61} + 48 q^{63} + 16 q^{67} + 16 q^{73} - 72 q^{77} + 24 q^{81} - 48 q^{83} - 4 q^{85} + 48 q^{87} + 72 q^{93} - 84 q^{95} - 48 q^{97}+O(q^{100}) $ 16 * q - 12 * q^5 - 8 * q^7 + 24 * q^15 + 24 * q^21 + 24 * q^23 - 16 * q^25 + 8 * q^31 + 24 * q^41 + 36 * q^45 - 48 * q^47 + 48 * q^51 - 24 * q^55 + 24 * q^57 - 24 * q^61 + 48 * q^63 + 16 * q^67 + 16 * q^73 - 72 * q^77 + 24 * q^81 - 48 * q^83 - 4 * q^85 + 48 * q^87 + 72 * q^93 - 84 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	−1.45865	+	0.933998i	−0.842150	+	0.539244i
$3$	−1.45865	+	0.933998i	−0.842150	+	0.539244i
$4$		0			0
$5$	−1.29554	+	1.82252i	−0.579385	+	0.815054i
$5$	−1.29554	+	1.82252i	−0.579385	+	0.815054i
$6$		0			0
$7$	−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			0
$9$	1.25529	−	2.72474i	0.418432	−	0.908248i
$10$		0			0
$11$	1.70563	+	0.984748i	0.514268	+	0.296913i	0.734586	−	0.678515i	$-0.237376\pi$
$11$	1.70563	+	0.984748i	0.514268	+	0.296913i	−0.220318	+	0.975428i	$0.570710\pi$
$12$		0			0
$13$	−3.92790	−	1.05248i	−1.08940	−	0.291905i	−0.330961	−	0.943644i	$-0.607373\pi$
$13$	−3.92790	−	1.05248i	−1.08940	−	0.291905i	−0.758443	+	0.651739i	$0.774040\pi$
$14$		0			0
$15$	0.187514	−	3.86844i	0.0484160	−	0.998827i
$16$		0			0
$17$	−2.35877	+	2.35877i	−0.572085	+	0.572085i	−0.932711	−	0.360626i	$-0.882563\pi$
$17$	−2.35877	+	2.35877i	−0.572085	+	0.572085i	0.360626	+	0.932711i	$0.382563\pi$
$18$		0			0
$19$			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
$22$		0			0
$23$	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	$-0.143313\pi$
$24$		0			0
$25$	−1.64313	−	4.72230i	−0.328626	−	0.944460i
$26$		0			0
$27$	0.713876	+	5.14688i	0.137386	+	0.990518i
$28$		0			0
$29$	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	$-0.951141\pi$
$31$	−3.48837	−	6.04204i	−0.626530	−	1.08518i	0.361713	−	0.932289i	$-0.382192\pi$
$32$		0			0
$33$	−3.40767	+	0.156660i	−0.593199	+	0.0272710i
$34$		0			0
$35$	1.57232	−	4.22619i	0.265771	−	0.714357i
$36$		0			0
$37$	4.26692	+	4.26692i	0.701478	+	0.701478i	0.964728	−	0.263250i	$-0.0847944\pi$
$37$	4.26692	+	4.26692i	0.701478	+	0.701478i	−0.263250	+	0.964728i	$0.584794\pi$
$38$		0			0
$39$	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	$0.146715\pi$
$42$		0			0
$43$	−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	$-0.338330\pi$
$44$		0			0
$45$	3.33960	+	5.81782i	0.497838	+	0.867270i
$46$		0			0
$47$	−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			0
$49$	−2.54041	+	1.46671i	−0.362916	+	0.209530i
$50$		0			0
$51$	1.23752	−	5.64369i	0.173288	−	0.790274i
$52$		0			0
$53$	−7.03027	−	7.03027i	−0.965682	−	0.965682i	0.0337485	−	0.999430i	$-0.489255\pi$
$53$	−7.03027	−	7.03027i	−0.965682	−	0.965682i	−0.999430	+	0.0337485i	$0.989255\pi$
$54$		0			0
$55$	−4.00444	+	1.83276i	−0.539959	+	0.247129i
$56$		0			0
$57$	−3.46282	−	5.40797i	−0.458662	−	0.716303i
$58$		0			0
$59$	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	$0.977478\pi$
$62$		0			0
$63$	−1.02302	+	5.96261i	−0.128889	+	0.751218i
$64$		0			0
$65$	7.00693	−	5.79513i	0.869103	−	0.718798i
$66$		0			0
$67$	−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			0
$69$	3.28793	+	10.3447i	0.395820	+	1.24535i
$70$		0			0
$71$			5.68481i			0.674663i	0.941386	+	0.337332i	$0.109524\pi$
$71$			5.68481i			0.674663i	−0.941386	+	0.337332i	$0.890476\pi$
$72$		0			0
$73$	1.14928	−	1.14928i	0.134513	−	0.134513i	−0.636645	−	0.771157i	$-0.719678\pi$
$73$	1.14928	−	1.14928i	0.134513	−	0.134513i	0.771157	+	0.636645i	$0.219678\pi$
$74$		0			0
$75$	6.80736	+	5.35349i	0.786047	+	0.618167i
$76$		0			0
$77$	−3.83631	−	1.02794i	−0.437188	−	0.117144i
$78$		0			0
$79$	−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
$82$		0			0
$83$	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			0
$85$	−1.24300	−	7.35477i	−0.134822	−	0.797737i
$86$		0			0
$87$	0.596356	+	12.9719i	0.0639361	+	1.39074i
$88$		0			0
$89$	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
$92$		0			0
$93$	10.7315	+	5.55506i	1.11281	+	0.576033i
$94$		0			0
$95$	−6.75702	−	4.80327i	−0.693256	−	0.492805i
$96$		0			0
$97$	−9.71905	+	2.60421i	−0.986820	+	0.264418i	−0.715914	−	0.698188i	$-0.753990\pi$
$97$	−9.71905	+	2.60421i	−0.986820	+	0.264418i	−0.270906	+	0.962606i	$0.587323\pi$
$98$		0			0
$99$	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			0
$103$	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	$0.520109\pi$
$104$		0			0
$105$	1.65380	+	7.63307i	0.161394	+	0.744911i
$106$		0			0
$107$	−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	$0.370416\pi$
$108$		0			0
$109$		−	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			0
$113$	0.767544	−	2.86451i	0.0722045	−	0.269471i	−0.920380	−	0.391024i	$-0.872121\pi$
$113$	0.767544	−	2.86451i	0.0722045	−	0.269471i	0.992585	+	0.121553i	$0.0387876\pi$
$114$		0			0
$115$	8.93101	+	10.7985i	0.832821	+	1.00697i
$116$		0			0
$117$	−7.79841	+	9.38136i	−0.720964	+	0.867307i
$118$		0			0
$119$	3.36345	−	5.82566i	0.308327	−	0.534037i
$120$		0			0
$121$	−3.56054	−	6.16704i	−0.323686	−	0.560640i
$122$		0			0
$123$	−5.64146	+	10.8985i	−0.508673	+	0.982681i
$124$		0			0
$125$	10.7352	+	3.12333i	0.960187	+	0.279359i
$126$		0			0
$127$	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			0
$129$	12.0523	+	10.9928i	1.06114	+	0.967863i
$130$		0			0
$131$	0.411267	−	0.237445i	0.0359326	−	0.0207457i	−0.481926	−	0.876212i	$-0.660063\pi$
$131$	0.411267	−	0.237445i	0.0359326	−	0.0207457i	0.517859	+	0.855466i	$0.326729\pi$
$132$		0			0
$133$	−1.93506	−	7.22176i	−0.167791	−	0.626206i
$134$		0			0
$135$	−10.3051	−	5.36696i	−0.886924	−	0.461915i
$136$		0			0
$137$	2.54985	+	9.51618i	0.217849	+	0.813022i	0.985144	+	0.171728i	$0.0549352\pi$
$137$	2.54985	+	9.51618i	0.217849	+	0.813022i	−0.767296	+	0.641293i	$0.778398\pi$
$138$		0			0
$139$	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
$142$		0			0
$143$	−5.66314	−	5.66314i	−0.473575	−	0.473575i
$144$		0			0
$145$	6.97674	+	15.2437i	0.579387	+	1.26592i
$146$		0			0
$147$	2.33566	−	4.51215i	0.192642	−	0.372156i
$148$		0			0
$149$	−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	−0.990440	−	0.137943i	$-0.955951\pi$
$151$	−4.61739	+	7.99755i	−0.375758	+	0.650832i	0.614682	+	0.788775i	$0.289284\pi$
$152$		0			0
$153$	3.46609	+	9.38798i	0.280217	+	0.758973i
$154$		0			0
$155$	15.5310	+	1.47012i	1.24748	+	0.118083i
$156$		0			0
$157$	−2.80938	+	10.4848i	−0.224213	+	0.836775i	0.758505	+	0.651667i	$0.225930\pi$
$157$	−2.80938	+	10.4848i	−0.224213	+	0.836775i	−0.982718	+	0.185108i	$0.940736\pi$
$158$		0			0
$159$	16.8209	+	3.68841i	1.33399	+	0.292510i
$160$		0			0
$161$			12.6377i			0.995993i
$162$		0			0
$163$	−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	$0.430154\pi$
$164$		0			0
$165$	4.12927	−	6.41349i	0.321463	−	0.499289i
$166$		0			0
$167$	−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	$0.646683\pi$
$168$		0			0
$169$	3.06239	+	1.76807i	0.235568	+	0.136005i
$170$		0			0
$171$	10.1021	+	4.65404i	0.772524	+	0.355903i
$172$		0			0
$173$	−7.16239	+	1.91916i	−0.544546	+	0.145911i	−0.520597	−	0.853802i	$-0.674291\pi$
$173$	−7.16239	+	1.91916i	−0.544546	+	0.145911i	−0.0239492	+	0.999713i	$0.507624\pi$
$174$		0			0
$175$	5.66529	+	8.34080i	0.428256	+	0.630506i
$176$		0			0
$177$	−4.15208	−	2.14928i	−0.312090	−	0.161550i
$178$		0			0
$179$	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	$0.819770\pi$
$182$		0			0
$183$	−0.695770	−	15.1344i	−0.0514328	−	1.11877i
$184$		0			0
$185$	−13.3045	+	2.24855i	−0.978168	+	0.165316i
$186$		0			0
$187$	−6.34598	+	1.70040i	−0.464064	+	0.124346i
$188$		0			0
$189$	−4.07684	−	9.65283i	−0.296546	−	0.702140i
$190$		0			0
$191$	1.11154	+	0.641749i	0.0804283	+	0.0464353i	0.539675	−	0.841874i	$-0.318547\pi$
$191$	1.11154	+	0.641749i	0.0804283	+	0.0464353i	−0.459246	+	0.888309i	$0.651881\pi$
$192$		0			0
$193$	−5.28063	−	1.41494i	−0.380108	−	0.101850i	0.0637057	−	0.997969i	$-0.479708\pi$
$193$	−5.28063	−	1.41494i	−0.380108	−	0.101850i	−0.443814	+	0.896119i	$0.646375\pi$
$194$		0			0
$195$	−4.80799	+	14.9975i	−0.344307	+	1.07399i
$196$		0			0
$197$	12.0386	−	12.0386i	0.857716	−	0.857716i	−0.133353	−	0.991069i	$-0.542574\pi$
$197$	12.0386	−	12.0386i	0.857716	−	0.857716i	0.991069	+	0.133353i	$0.0425744\pi$
$198$		0			0
$199$			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
$202$		0			0
$203$	−3.91303	+	14.6036i	−0.274641	+	1.02497i
$204$		0			0
$205$	−1.49298	+	15.7726i	−0.104274	+	1.10161i
$206$		0			0
$207$	−14.4578	−	12.0183i	−1.00489	−	0.835331i
$208$		0			0
$209$	−3.65098	+	6.32368i	−0.252543	+	0.437418i
$210$		0			0
$211$	−12.0425	−	20.8582i	−0.829038	−	1.43594i	−0.898794	−	0.438372i	$-0.855555\pi$
$211$	−12.0425	−	20.8582i	−0.829038	−	1.43594i	0.0697556	−	0.997564i	$-0.477778\pi$
$212$		0			0
$213$	−5.30960	−	8.29213i	−0.363808	−	0.568167i
$214$		0			0
$215$	19.7377	+	7.34324i	1.34610	+	0.500805i
$216$		0			0
$217$	9.94838	+	9.94838i	0.675340	+	0.675340i
$218$		0			0
$219$	−0.602965	+	2.74981i	−0.0407446	+	0.185815i
$220$		0			0
$221$	11.7476	−	6.78245i	0.790226	−	0.456237i
$222$		0			0
$223$	−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	$-0.273225\pi$
$224$		0			0
$225$	−14.9297	−	1.45078i	−0.995312	−	0.0967184i
$226$		0			0
$227$	−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	$0.996068\pi$
$228$		0			0
$229$	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
$232$		0			0
$233$	15.0591	+	15.0591i	0.986558	+	0.986558i	0.999911	−	0.0133533i	$-0.00425061\pi$
$233$	15.0591	+	15.0591i	0.986558	+	0.986558i	−0.0133533	+	0.999911i	$0.504251\pi$
$234$		0			0
$235$	16.2623	+	6.05025i	1.06083	+	0.394675i
$236$		0			0
$237$	20.0858	−	0.923401i	1.30471	−	0.0599814i
$238$		0			0
$239$	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	$-0.103987\pi$
$242$		0			0
$243$	14.9201	+	4.51572i	0.957122	+	0.289684i
$244$		0			0
$245$	0.618120	−	6.53013i	0.0394902	−	0.417195i
$246$		0			0
$247$	3.90209	−	14.5628i	0.248284	−	0.926609i
$248$		0			0
$249$	−1.98862	+	2.18027i	−0.126024	+	0.138169i
$250$		0			0
$251$		−	13.3860i		−	0.844914i	−0.906383	−	0.422457i	$-0.861168\pi$
$251$		−	13.3860i		−	0.844914i	0.906383	−	0.422457i	$-0.138832\pi$
$252$		0			0
$253$	8.72759	−	8.72759i	0.548699	−	0.548699i
$254$		0			0
$255$	8.68244	+	9.56705i	0.543716	+	0.599112i
$256$		0			0
$257$	−7.29595	−	1.95494i	−0.455109	−	0.121946i	0.0239802	−	0.999712i	$-0.492366\pi$
$257$	−7.29595	−	1.95494i	−0.455109	−	0.121946i	−0.479089	+	0.877766i	$0.659033\pi$
$258$		0			0
$259$	−10.5384	−	6.08436i	−0.654825	−	0.378063i
$260$		0			0
$261$	−12.9856	−	18.3645i	−0.803790	−	1.13673i
$262$		0			0
$263$	−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	$0.528365\pi$
$264$		0			0
$265$	21.9208	−	3.70475i	1.34658	−	0.227581i
$266$		0			0
$267$	−2.99006	+	1.91459i	−0.182989	+	0.117171i
$268$		0			0
$269$	−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	$-0.713203\pi$
$271$	−20.4402			−1.24165			−0.620827	+	0.783947i	$0.713203\pi$
$272$		0			0
$273$	−11.9614	+	7.65910i	−0.723936	+	0.463550i
$274$		0			0
$275$	1.84770	−	9.67258i	0.111421	−	0.583279i
$276$		0			0
$277$	−23.4121	+	6.27326i	−1.40670	+	0.376924i	−0.880745	−	0.473590i	$-0.842958\pi$
$277$	−23.4121	+	6.27326i	−1.40670	+	0.376924i	−0.525953	+	0.850514i	$0.676291\pi$
$278$		0			0
$279$	−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	$0.431640\pi$
$282$		0			0
$283$	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	$0.563228\pi$
$284$		0			0
$285$	14.3423	+	0.695214i	0.849567	+	0.0411809i
$286$		0			0
$287$	−10.1031	+	10.1031i	−0.596368	+	0.596368i
$288$		0			0
$289$			5.87245i			0.345438i
$290$		0			0
$291$	11.7443	−	12.8762i	0.688464	−	0.754816i
$292$		0			0
$293$	−0.946406	+	3.53204i	−0.0552896	+	0.206344i	−0.988045	−	0.154167i	$-0.950731\pi$
$293$	−0.946406	+	3.53204i	−0.0552896	+	0.206344i	0.932755	+	0.360510i	$0.117397\pi$
$294$		0			0
$295$	−6.00903	−	0.568794i	−0.349859	−	0.0331165i
$296$		0			0
$297$	−3.85077	+	9.48168i	−0.223444	+	0.550183i
$298$		0			0
$299$	−12.7421	+	22.0700i	−0.736895	+	1.27634i
$300$		0			0
$301$	9.49611	+	16.4477i	0.547347	+	0.948032i
$302$		0			0
$303$	8.17164	−	0.375673i	0.469449	−	0.0215819i
$304$		0			0
$305$	−8.13978	−	17.7848i	−0.466082	−	1.01836i
$306$		0			0
$307$	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	$0.610097\pi$
$308$		0			0
$309$	−6.61130	+	2.10132i	−0.376104	+	0.119540i
$310$		0			0
$311$	9.08436	−	5.24485i	0.515127	−	0.297408i	−0.219812	−	0.975542i	$-0.570544\pi$
$311$	9.08436	−	5.24485i	0.515127	−	0.297408i	0.734938	+	0.678134i	$0.237211\pi$
$312$		0			0
$313$	−4.56901	−	17.0518i	−0.258256	−	0.963824i	−0.966250	−	0.257606i	$-0.917066\pi$
$313$	−4.56901	−	17.0518i	−0.258256	−	0.963824i	0.707994	−	0.706218i	$-0.249600\pi$
$314$		0			0
$315$	−9.54157	−	9.58930i	−0.537607	−	0.540296i
$316$		0			0
$317$	−6.00131	−	22.3972i	−0.337067	−	1.25795i	−0.901611	−	0.432549i	$-0.857614\pi$
$317$	−6.00131	−	22.3972i	−0.337067	−	1.25795i	0.564543	−	0.825403i	$-0.309052\pi$
$318$		0			0
$319$	12.7876	−	7.38291i	0.715966	−	0.413363i
$320$		0			0
$321$	2.83465	−	12.9274i	0.158215	−	0.721535i
$322$		0			0
$323$	−8.74518	−	8.74518i	−0.486595	−	0.486595i
$324$		0			0
$325$	1.48393	+	20.2781i	0.0823135	+	1.12483i
$326$		0			0
$327$	4.06623	+	6.35032i	0.224863	+	0.351173i
$328$		0			0
$329$	7.82405	+	13.5517i	0.431354	+	0.747127i
$330$		0			0
$331$	−12.9130	+	22.3659i	−0.709761	+	1.22934i	0.255185	+	0.966892i	$0.417864\pi$
$331$	−12.9130	+	22.3659i	−0.709761	+	1.22934i	−0.964946	+	0.262450i	$0.915470\pi$
$332$		0			0
$333$	16.9825	−	6.27003i	0.930636	−	0.343595i
$334$		0			0
$335$	−12.0728	−	14.5973i	−0.659606	−	0.797534i
$336$		0			0
$337$	8.30344	−	30.9889i	0.452317	−	1.68807i	−0.243541	−	0.969891i	$-0.578309\pi$
$337$	8.30344	−	30.9889i	0.452317	−	1.68807i	0.695858	−	0.718180i	$-0.255024\pi$
$338$		0			0
$339$	1.55588	+	4.89519i	0.0845035	+	0.265870i
$340$		0			0
$341$		−	13.7407i		−	0.744099i
$342$		0			0
$343$	14.1644	−	14.1644i	0.764806	−	0.764806i
$344$		0			0
$345$	−23.1130	−	7.40970i	−1.24436	−	0.398925i
$346$		0			0
$347$	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	$0.453255\pi$
$348$		0			0
$349$	−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
$352$		0			0
$353$	−20.1446	+	5.39774i	−1.07219	+	0.287293i	−0.751393	−	0.659855i	$-0.770618\pi$
$353$	−20.1446	+	5.39774i	−1.07219	+	0.287293i	−0.320798	+	0.947148i	$0.603951\pi$
$354$		0			0
$355$	−10.3607	−	7.36493i	−0.549887	−	0.390890i
$356$		0			0
$357$	0.535079	+	11.6390i	0.0283194	+	0.616003i
$358$		0			0
$359$	−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
$362$		0			0
$363$	10.9536	+	5.66999i	0.574914	+	0.297597i
$364$		0			0
$365$	0.605635	+	3.58351i	0.0317004	+	0.187570i
$366$		0			0
$367$	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	$0.222217\pi$
$368$		0			0
$369$	−1.95025	−	21.1661i	−0.101526	−	1.10186i
$370$		0			0
$371$	17.3633	+	10.0247i	0.901458	+	0.520457i
$372$		0			0
$373$	1.42207	+	0.381044i	0.0736322	+	0.0197297i	0.295447	−	0.955359i	$-0.404531\pi$
$373$	1.42207	+	0.381044i	0.0736322	+	0.0197297i	−0.221815	+	0.975089i	$0.571198\pi$
$374$		0			0
$375$	−18.5761	+	5.47085i	−0.959263	+	0.282513i
$376$		0			0
$377$	−21.5578	+	21.5578i	−1.11028	+	1.11028i
$378$		0			0
$379$		−	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
$382$		0			0
$383$	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	$-0.0610201\pi$
$384$		0			0
$385$	6.84354	−	5.66000i	0.348779	−	0.288460i
$386$		0			0
$387$	−27.8472	−	4.77783i	−1.41556	−	0.242871i
$388$		0			0
$389$	−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
$392$		0			0
$393$	−0.378120	+	0.730471i	−0.0190736	+	0.0368474i
$394$		0			0
$395$	23.6034	−	10.8028i	1.18762	−	0.543549i
$396$		0			0
$397$	−2.16969	−	2.16969i	−0.108893	−	0.108893i	0.650561	−	0.759454i	$-0.274534\pi$
$397$	−2.16969	−	2.16969i	−0.108893	−	0.108893i	−0.759454	+	0.650561i	$0.774534\pi$
$398$		0			0
$399$	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	$0.448931\pi$
$402$		0			0
$403$	7.34287	+	27.4040i	0.365774	+	1.36509i
$404$		0			0
$405$	20.0443	−	1.79647i	0.996008	−	0.0892675i
$406$		0			0
$407$	3.07596	+	11.4796i	0.152470	+	0.569025i
$408$		0			0
$409$	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
$412$		0			0
$413$	−3.84907	−	3.84907i	−0.189401	−	0.189401i
$414$		0			0
$415$	−1.32840	+	3.57058i	−0.0652088	+	0.175273i
$416$		0			0
$417$	−0.559288	+	1.08046i	−0.0273885	+	0.0529104i
$418$		0			0
$419$	−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	$0.963029\pi$
$422$		0			0
$423$	−22.9440	−	3.93656i	−1.11557	−	0.191402i
$424$		0			0
$425$	15.0146	+	7.26305i	0.728313	+	0.352310i
$426$		0			0
$427$	4.56534	−	17.0381i	0.220932	−	0.824531i
$428$		0			0
$429$	13.5499	+	2.97115i	0.654194	+	0.143449i
$430$		0			0
$431$		−	6.10703i		−	0.294165i	−0.989124	−	0.147083i	$-0.953012\pi$
$431$		−	6.10703i		−	0.294165i	0.989124	−	0.147083i	$-0.0469883\pi$
$432$		0			0
$433$	10.2605	−	10.2605i	0.493088	−	0.493088i	−0.416190	−	0.909278i	$-0.636635\pi$
$433$	10.2605	−	10.2605i	0.493088	−	0.493088i	0.909278	+	0.416190i	$0.136635\pi$
$434$		0			0
$435$	−24.4141	−	15.7188i	−1.17057	−	0.753661i
$436$		0			0
$437$	22.4431	+	6.01360i	1.07360	+	0.287670i
$438$		0			0
$439$	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
$442$		0			0
$443$	−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	$0.646484\pi$
$444$		0			0
$445$	−2.65572	+	3.73595i	−0.125893	+	0.177101i
$446$		0			0
$447$	12.4781	+	6.45913i	0.590193	+	0.305506i
$448$		0			0
$449$	−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			0
$453$	−0.734564	−	15.9782i	−0.0345128	−	0.750723i
$454$		0			0
$455$	−10.6239	+	14.9452i	−0.498056	+	0.700644i
$456$		0			0
$457$	37.5970	−	10.0741i	1.75871	−	0.471246i	0.772263	−	0.635303i	$-0.219125\pi$
$457$	37.5970	−	10.0741i	1.75871	−	0.471246i	0.986451	+	0.164058i	$0.0524583\pi$
$458$		0			0
$459$	−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	$0.689128\pi$
$462$		0			0
$463$	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	$0.532552\pi$
$464$		0			0
$465$	−24.0274	+	12.3616i	−1.11424	+	0.573255i
$466$		0			0
$467$	−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	$0.334884\pi$
$468$		0			0
$469$		−	17.0835i		−	0.788841i
$470$		0			0
$471$	−5.69485	−	17.9175i	−0.262405	−	0.825596i
$472$		0			0
$473$	4.80079	−	17.9168i	0.220740	−	0.823814i
$474$		0			0
$475$	17.5081	−	6.09194i	0.803325	−	0.279517i
$476$		0			0
$477$	−27.9808	+	10.3306i	−1.28115	+	0.473007i
$478$		0			0
$479$	−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
$482$		0			0
$483$	−11.8036	−	18.4340i	−0.537083	−	0.838775i
$484$		0			0
$485$	7.84525	−	21.0870i	0.356234	−	0.957511i
$486$		0			0
$487$	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	$0.592442\pi$
$488$		0			0
$489$	5.07962	−	23.1655i	0.229709	−	1.04758i
$490$		0			0
$491$	−16.1505	+	9.32449i	−0.728861	+	0.420808i	−0.818005	−	0.575210i	$-0.804920\pi$
$491$	−16.1505	+	9.32449i	−0.728861	+	0.420808i	0.0891441	+	0.996019i	$0.471587\pi$
$492$		0			0
$493$	6.47289	+	24.1572i	0.291524	+	1.08798i
$494$		0			0
$495$	−0.0329562	+	13.2117i	−0.00148127	+	0.593824i
$496$		0			0
$497$	−2.96707	−	11.0732i	−0.133091	−	0.496703i
$498$		0			0
$499$	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
$502$		0			0
$503$	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	$0.651616\pi$
$504$		0			0
$505$	9.60272	−	4.39499i	0.427315	−	0.195574i
$506$		0			0
$507$	−6.11831	+	0.281276i	−0.271724	+	0.0124919i
$508$		0			0
$509$	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			0
$513$	−19.0822	+	2.64671i	−0.842499	+	0.116855i
$514$		0			0
$515$	−6.90136	+	5.70782i	−0.304110	+	0.251517i
$516$		0			0
$517$	3.95547	−	14.7620i	0.173961	−	0.649233i
$518$		0			0
$519$	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	$0.868295\pi$
$522$		0			0
$523$	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			0
$525$	−16.0540	−	6.87491i	−0.700652	−	0.300045i
$526$		0			0
$527$	22.4800	+	6.02350i	0.979244	+	0.262388i
$528$		0			0
$529$	−14.0940	−	8.13716i	−0.612781	−	0.353789i
$530$		0			0
$531$	8.06384	−	0.743005i	0.349941	−	0.0322437i
$532$		0			0
$533$	−27.8302	+	7.45708i	−1.20546	+	0.323002i
$534$		0			0
$535$	−2.84721	−	16.8468i	−0.123095	−	0.728349i
$536$		0			0
$537$	−3.98832	+	2.55380i	−0.172109	+	0.110205i
$538$		0			0
$539$	−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	$0.531170\pi$
$542$		0			0
$543$	33.1231	−	21.2093i	1.42145	−	0.910180i
$544$		0			0
$545$	7.93445	+	5.64024i	0.339875	+	0.241602i
$546$		0			0
$547$	−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	$0.575472\pi$
$548$		0			0
$549$	15.1504	+	21.4258i	0.646602	+	0.914433i
$550$		0			0
$551$	24.0723	+	13.8981i	1.02551	+	0.592080i
$552$		0			0
$553$	22.6124	+	6.05896i	0.961575	+	0.257653i
$554$		0			0
$555$	17.3064	−	15.7062i	0.734618	−	0.666692i
$556$		0			0
$557$	20.5740	−	20.5740i	0.871749	−	0.871749i	−0.120914	−	0.992663i	$-0.538583\pi$
$557$	20.5740	−	20.5740i	0.871749	−	0.871749i	0.992663	+	0.120914i	$0.0385825\pi$
$558$		0			0
$559$			38.2982i			1.61984i
$560$		0			0
$561$	7.66836	−	8.40741i	0.323759	−	0.354961i
$562$		0			0
$563$	−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	$0.814704\pi$
$564$		0			0
$565$	4.22623	+	5.10997i	0.177799	+	0.214978i
$566$		0			0
$567$	14.9624	+	10.2723i	0.628361	+	0.431396i
$568$		0			0
$569$	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	0.815165	−	0.579229i	$-0.196646\pi$
$571$	−2.24726	−	3.89236i	−0.0940448	−	0.162890i	−0.909210	+	0.416339i	$0.863313\pi$
$572$		0			0
$573$	−2.22074	+	0.102094i	−0.0927726	+	0.00426502i
$574$		0			0
$575$	−31.2510	+	2.28691i	−1.30326	+	0.0953709i
$576$		0			0
$577$	0.186522	+	0.186522i	0.00776502	+	0.00776502i	0.710979	−	0.703214i	$-0.248252\pi$
$577$	0.186522	+	0.186522i	0.00776502	+	0.00776502i	−0.703214	+	0.710979i	$0.748252\pi$
$578$		0			0
$579$	9.02412	−	2.86820i	0.375030	−	0.119198i
$580$		0			0
$581$	−2.97543	+	1.71786i	−0.123441	+	0.0712689i
$582$		0			0
$583$	−5.06802	−	18.9141i	−0.209896	−	0.783342i
$584$		0			0
$585$	−6.99449	−	26.3667i	−0.289187	−	1.09013i
$586$		0			0
$587$	−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			0
$589$	22.4010	−	12.9332i	0.923017	−	0.532904i
$590$		0			0
$591$	−6.31603	+	28.8041i	−0.259807	+	1.18484i
$592$		0			0
$593$	−3.60323	−	3.60323i	−0.147967	−	0.147967i	0.629242	−	0.777209i	$-0.283365\pi$
$593$	−3.60323	−	3.60323i	−0.147967	−	0.147967i	−0.777209	+	0.629242i	$0.783365\pi$
$594$		0			0
$595$	6.25986	+	13.6773i	0.256629	+	0.560716i
$596$		0			0
$597$	−4.14537	−	6.47392i	−0.169659	−	0.264960i
$598$		0			0
$599$	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	$0.849795\pi$
$602$		0			0
$603$	19.5438	+	16.2461i	0.795887	+	0.661594i
$604$		0			0
$605$	15.8524	+	1.50053i	0.644491	+	0.0610053i
$606$		0			0
$607$	−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			0
$609$	−7.93204	−	24.9563i	−0.321422	−	1.01128i
$610$		0			0
$611$			31.5547i			1.27657i
$612$		0			0
$613$	−21.1512	+	21.1512i	−0.854290	+	0.854290i	−0.990658	−	0.136368i	$-0.956457\pi$
$613$	−21.1512	+	21.1512i	−0.854290	+	0.854290i	0.136368	+	0.990658i	$0.456457\pi$
$614$		0			0
$615$	−12.5539	−	24.4011i	−0.506220	−	0.983947i
$616$		0			0
$617$	−10.1671	−	2.72427i	−0.409312	−	0.109675i	0.0482869	−	0.998834i	$-0.484624\pi$
$617$	−10.1671	−	2.72427i	−0.409312	−	0.109675i	−0.457599	+	0.889159i	$0.651290\pi$
$618$		0			0
$619$	−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
$622$		0			0
$623$	−3.99290	+	1.06990i	−0.159972	+	0.0428644i
$624$		0			0
$625$	−19.6003	+	15.5187i	−0.784010	+	0.620748i
$626$		0			0
$627$	−0.580821	−	12.6340i	−0.0231958	−	0.504554i
$628$		0			0
$629$	−20.1293			−0.802609
$630$		0			0
$631$	−21.2335			−0.845291			−0.422645	−	0.906295i	$-0.638898\pi$
$631$	−21.2335			−0.845291			−0.422645	+	0.906295i	$0.638898\pi$
$632$		0			0
$633$	37.0472	+	19.1770i	1.47249	+	0.762219i
$634$		0			0
$635$	−10.6555	+	1.80084i	−0.422850	+	0.0714642i
$636$		0			0
$637$	11.5222	−	3.08736i	0.456525	−	0.122326i
$638$		0			0
$639$	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			0
$643$	−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	$0.714470\pi$
$644$		0			0
$645$	−35.6488	+	7.72376i	−1.40367	+	0.304123i
$646$		0			0
$647$	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			0
$649$			5.31632i			0.208684i
$650$		0			0
$651$	−23.8029	−	5.21939i	−0.932911	−	0.204564i
$652$		0			0
$653$	0.736931	−	2.75027i	0.0288384	−	0.107626i	−0.950006	−	0.312230i	$-0.898924\pi$
$653$	0.736931	−	2.75027i	0.0288384	−	0.107626i	0.978845	+	0.204604i	$0.0655906\pi$
$654$		0			0
$655$	−0.100067	+	1.05716i	−0.00390995	+	0.0413067i
$656$		0			0
$657$	−1.68880	−	4.57416i	−0.0658865	−	0.178455i
$658$		0			0
$659$	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	$0.787501\pi$
$662$		0			0
$663$	−10.8007	+	20.8654i	−0.419465	+	0.810345i
$664$		0			0
$665$	15.6687	+	5.82942i	0.607607	+	0.226055i
$666$		0			0
$667$	−33.2232	−	33.2232i	−1.28641	−	1.28641i
$668$		0			0
$669$	21.4721	+	19.5846i	0.830157	+	0.757183i
$670$		0			0
$671$	−14.9193	+	8.61365i	−0.575953	+	0.332526i
$672$		0			0
$673$	1.84460	+	6.88414i	0.0711041	+	0.265364i	0.992322	−	0.123684i	$-0.0394708\pi$
$673$	1.84460	+	6.88414i	0.0711041	+	0.265364i	−0.921218	+	0.389048i	$0.872804\pi$
$674$		0			0
$675$	23.1321	−	11.8281i	0.890356	−	0.455265i
$676$		0			0
$677$	2.16966	+	8.09727i	0.0833867	+	0.311203i	0.995004	−	0.0998372i	$-0.0318322\pi$
$677$	2.16966	+	8.09727i	0.0833867	+	0.311203i	−0.911617	+	0.411040i	$0.865166\pi$
$678$		0			0
$679$	17.5722	−	10.1453i	0.674358	−	0.389341i
$680$		0			0
$681$	9.51955	+	8.68274i	0.364790	+	0.332723i
$682$		0			0
$683$	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	$0.608564\pi$
$684$		0			0
$685$	−20.6468	−	7.68149i	−0.788875	−	0.293494i
$686$		0			0
$687$	−7.11785	+	13.7506i	−0.271563	+	0.524619i
$688$		0			0
$689$	20.2150	+	35.0134i	0.770131	+	1.33391i
$690$		0			0
$691$	−9.16297	+	15.8707i	−0.348576	+	0.603751i	−0.985997	−	0.166765i	$-0.946668\pi$
$691$	−9.16297	+	15.8707i	−0.348576	+	0.603751i	0.637421	+	0.770516i	$0.280001\pi$
$692$		0			0
$693$	−7.61656	+	9.16260i	−0.289329	+	0.348058i
$694$		0			0
$695$	−0.148013	+	1.56368i	−0.00561444	+	0.0593138i
$696$		0			0
$697$	−6.11718	+	22.8296i	−0.231705	+	0.864734i
$698$		0			0
$699$	−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	$0.869058\pi$
$702$		0			0
$703$	−15.8197	+	15.8197i	−0.596652	+	0.596652i
$704$		0			0
$705$	−29.3718	+	6.36377i	−1.10621	+	0.239673i
$706$		0			0
$707$	9.19953	+	2.46501i	0.345984	+	0.0927062i
$708$		0			0
$709$	−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
$712$		0			0
$713$	−42.2329	+	11.3163i	−1.58163	+	0.423798i
$714$		0			0
$715$	17.6580	−	2.98431i	0.660372	−	0.111607i
$716$		0			0
$717$	−16.6965	−	8.64273i	−0.623541	−	0.322769i
$718$		0			0
$719$	−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
$722$		0			0
$723$	1.85589	+	40.3692i	0.0690212	+	1.50135i
$724$		0			0
$725$	−36.8205	−	7.03363i	−1.36748	−	0.261222i
$726$		0			0
$727$	−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	$0.434835\pi$
$728$		0			0
$729$	−25.9808	+	7.34847i	−0.962250	+	0.272166i
$730$		0			0
$731$	27.2077	+	15.7084i	1.00631	+	0.580994i
$732$		0			0
$733$	23.5366	+	6.30661i	0.869343	+	0.232940i	0.665804	−	0.746127i	$-0.268089\pi$
$733$	23.5366	+	6.30661i	0.869343	+	0.232940i	0.203540	+	0.979067i	$0.434755\pi$
$734$		0			0
$735$	5.19751	+	10.1025i	0.191713	+	0.372635i
$736$		0			0
$737$	−11.7978	+	11.7978i	−0.434578	+	0.434578i
$738$		0			0
$739$		−	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
$742$		0			0
$743$	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	$-0.00930587\pi$
$744$		0			0
$745$	18.0587	+	1.70937i	0.661619	+	0.0626266i
$746$		0			0
$747$	0.864318	−	5.03761i	0.0316237	−	0.184317i
$748$		0			0
$749$	7.70428	−	13.3442i	0.281508	−	0.487586i
$750$		0			0
$751$	21.6240	+	37.4538i	0.789070	+	1.36671i	0.926537	+	0.376203i	$0.122771\pi$
$751$	21.6240	+	37.4538i	0.789070	+	1.36671i	−0.137467	+	0.990506i	$0.543896\pi$
$752$		0			0
$753$	12.5025	+	19.5254i	0.455615	+	0.711544i
$754$		0			0
$755$	−8.59363	−	18.7764i	−0.312754	−	0.683345i
$756$		0			0
$757$	22.7266	+	22.7266i	0.826013	+	0.826013i	0.986963	−	0.160950i	$-0.0514557\pi$
$757$	22.7266	+	22.7266i	0.826013	+	0.826013i	−0.160950	+	0.986963i	$0.551456\pi$
$758$		0			0
$759$	−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			0
$763$	2.27225	+	8.48016i	0.0822611	+	0.307002i
$764$		0			0
$765$	−21.6002	−	5.84555i	−0.780957	−	0.211346i
$766$		0			0
$767$	−2.84099	−	10.6027i	−0.102582	−	0.382842i
$768$		0			0
$769$	−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
$772$		0			0
$773$	30.1093	+	30.1093i	1.08296	+	1.08296i	0.996232	+	0.0867231i	$0.0276395\pi$
$773$	30.1093	+	30.1093i	1.08296	+	1.08296i	0.0867231	+	0.996232i	$0.472360\pi$
$774$		0			0
$775$	−22.8005	+	26.4010i	−0.819017	+	0.948351i
$776$		0			0
$777$	21.0546	−	0.967939i	0.755329	−	0.0347246i
$778$		0			0
$779$	13.1344	+	22.7494i	0.470588	+	0.815083i
$780$		0			0
$781$	−5.59811	+	9.69621i	−0.200316	+	0.346958i
$782$		0			0
$783$	36.0938	+	14.6587i	1.28989	+	0.523858i
$784$		0			0
$785$	−15.4690	−	18.7036i	−0.552111	−	0.667561i
$786$		0			0
$787$	−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	$0.143728\pi$
$788$		0			0
$789$	13.0137	−	14.2679i	0.463300	−	0.507952i
$790$		0			0
$791$			5.98028i			0.212634i
$792$		0			0
$793$	25.1515	−	25.1515i	0.893157	−	0.893157i
$794$		0			0
$795$	−28.5145	+	25.8779i	−1.01130	+	0.917795i
$796$		0			0
$797$	−13.1409	−	3.52110i	−0.465476	−	0.124724i	0.0184558	−	0.999830i	$-0.494125\pi$
$797$	−13.1409	−	3.52110i	−0.465476	−	0.124724i	−0.483932	+	0.875106i	$0.660792\pi$
$798$		0			0
$799$	22.4170	+	12.9425i	0.793056	+	0.457871i
$800$		0			0
$801$	2.57321	−	5.58542i	0.0909200	−	0.197351i
$802$		0			0
$803$	3.09199	−	0.828496i	0.109114	−	0.0292370i
$804$		0			0
$805$	−23.0325	−	16.3727i	−0.811788	−	0.577063i
$806$		0			0
$807$	19.6490	−	12.5816i	0.691679	−	0.442895i
$808$		0			0
$809$	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	$-0.621378\pi$
$811$	−21.1960			−0.744294			−0.372147	+	0.928174i	$0.621378\pi$
$812$		0			0
$813$	29.8150	−	19.0911i	1.04566	−	0.669555i
$814$		0			0
$815$	−5.10212	−	30.1890i	−0.178720	−	1.05747i
$816$		0			0
$817$	33.7279	−	9.03736i	1.17999	−	0.316177i
$818$		0			0
$819$	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	$0.949241\pi$
$822$		0			0
$823$	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	$0.436737\pi$
$824$		0			0
$825$	6.33903	+	15.8346i	0.220697	+	0.551291i
$826$		0			0
$827$	−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	$0.335400\pi$
$828$		0			0
$829$		−	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
$832$		0			0
$833$	2.53262	−	9.45186i	0.0877500	−	0.327488i
$834$		0			0
$835$	8.80489	−	7.28215i	0.304706	−	0.252009i
$836$		0			0
$837$	28.6074	−	22.2675i	0.988815	−	0.769677i
$838$		0			0
$839$	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
$842$		0			0
$843$	−39.0435	+	1.79494i	−1.34473	+	0.0618211i
$844$		0			0
$845$	−7.18979	+	3.29063i	−0.247336	+	0.113201i
$846$		0			0
$847$	10.1542	+	10.1542i	0.348903	+	0.348903i
$848$		0			0
$849$	−3.50559	+	1.11421i	−0.120312	+	0.0382395i
$850$		0			0
$851$	32.7503	−	18.9084i	1.12266	−	0.648171i
$852$		0			0
$853$	−6.15572	−	22.9734i	−0.210768	−	0.786596i	−0.987614	−	0.156905i	$-0.949848\pi$
$853$	−6.15572	−	22.9734i	−0.210768	−	0.786596i	0.776846	−	0.629691i	$-0.216818\pi$
$854$		0			0
$855$	−21.5697	+	12.3817i	−0.737669	+	0.423444i
$856$		0			0
$857$	3.06736	+	11.4475i	0.104779	+	0.391040i	0.998320	−	0.0579412i	$-0.0184536\pi$
$857$	3.06736	+	11.4475i	0.104779	+	0.391040i	−0.893541	+	0.448981i	$0.851787\pi$
$858$		0			0
$859$	−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
$862$		0			0
$863$	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			0
$865$	5.78150	−	15.5399i	0.196577	−	0.528373i
$866$		0			0
$867$	−5.48486	−	8.56583i	−0.186276	−	0.290911i
$868$		0			0
$869$	−11.4317	−	19.8004i	−0.387795	−	0.671681i
$870$		0			0
$871$	17.2246	−	29.8338i	0.583632	−	1.01088i
$872$		0			0
$873$	−5.10446	+	29.7510i	−0.172760	+	1.00692i
$874$		0			0
$875$	−22.5409	−	0.480797i	−0.762021	−	0.0162539i
$876$		0			0
$877$	−1.78537	+	6.66309i	−0.0602876	+	0.224996i	−0.989496	−	0.144559i	$-0.953824\pi$
$877$	−1.78537	+	6.66309i	−0.0602876	+	0.224996i	0.929208	+	0.369556i	$0.120490\pi$
$878$		0			0
$879$	−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	$0.983800\pi$
$882$		0			0
$883$	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	$0.185138\pi$
$884$		0			0
$885$	9.29630	−	4.78275i	0.312492	−	0.160771i
$886$		0			0
$887$	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	$0.486666\pi$
$888$		0			0
$889$	−8.44013	−	4.87291i	−0.283073	−	0.163432i
$890$		0			0
$891$	−3.23896	−	17.4270i	−0.108509	−	0.583827i
$892$		0			0
$893$	27.7891	−	7.44607i	0.929928	−	0.249173i
$894$		0			0
$895$	−3.54236	+	4.98324i	−0.118408	+	0.166571i
$896$		0			0
$897$	−2.02710	−	44.0934i	−0.0676828	−	1.47224i
$898$		0			0
$899$	−52.3064			−1.74452
$900$		0			0
$901$	33.1655			1.10490
$902$		0			0
$903$	−29.2136	−	15.1221i	−0.972169	−	0.503231i
$904$		0			0
$905$	29.4194	−	41.3859i	0.977933	−	1.37571i
$906$		0			0
$907$	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	$0.410036\pi$
$908$		0			0
$909$	−11.5687	+	8.18027i	−0.383708	+	0.271323i
$910$		0			0
$911$	23.3987	+	13.5092i	0.775232	+	0.447581i	0.834738	−	0.550647i	$-0.185619\pi$
$911$	23.3987	+	13.5092i	0.775232	+	0.447581i	−0.0595057	+	0.998228i	$0.518952\pi$
$912$		0			0
$913$	3.24117	+	0.868470i	0.107267	+	0.0287422i
$914$		0			0
$915$	28.4840	+	18.3392i	0.941653	+	0.606276i
$916$		0			0
$917$	−0.677163	+	0.677163i	−0.0223619	+	0.0223619i
$918$		0			0
$919$		−	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
$922$		0			0
$923$	5.98314	−	22.3294i	0.196938	−	0.734981i
$924$		0			0
$925$	13.1386	−	27.1608i	0.431994	−	0.893041i
$926$		0			0
$927$	7.68091	−	9.24002i	0.252274	−	0.303482i
$928$		0			0
$929$	−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
$932$		0			0
$933$	−8.35217	+	16.1352i	−0.273438	+	0.528241i
$934$		0			0
$935$	5.12249	−	13.7686i	0.167523	−	0.450281i
$936$		0			0
$937$	−16.8770	−	16.8770i	−0.551349	−	0.551349i	0.375481	−	0.926830i	$-0.377477\pi$
$937$	−16.8770	−	16.8770i	−0.551349	−	0.551349i	−0.926830	+	0.375481i	$0.877477\pi$
$938$		0			0
$939$	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	$0.153089\pi$
$942$		0			0
$943$	−11.4923	−	42.8898i	−0.374240	−	1.39668i
$944$		0			0
$945$	22.8742	+	5.07557i	0.744097	+	0.165108i
$946$		0			0
$947$	−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	$0.978671\pi$
$948$		0			0
$949$	−5.72383	+	3.30466i	−0.185804	+	0.107274i
$950$		0			0
$951$	29.6727	+	27.0644i	0.962204	+	0.877622i
$952$		0			0
$953$	−13.4723	−	13.4723i	−0.436411	−	0.436411i	0.454391	−	0.890802i	$-0.349857\pi$
$953$	−13.4723	−	13.4723i	−0.436411	−	0.436411i	−0.890802	+	0.454391i	$0.849857\pi$
$954$		0			0
$955$	−2.60965	+	1.19439i	−0.0844463	+	0.0386495i
$956$		0			0
$957$	−11.7569	+	22.7126i	−0.380047	+	0.734195i
$958$		0			0
$959$	−9.93353	−	17.2054i	−0.320770	−	0.555591i
$960$		0			0
$961$	−8.83746	+	15.3069i	−0.285079	+	0.493772i
$962$		0			0
$963$	7.93938	+	21.5040i	0.255843	+	0.692957i
$964$		0			0
$965$	9.42004	−	7.79091i	0.303242	−	0.250798i
$966$		0			0
$967$	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	$0.0356892\pi$
$968$		0			0
$969$	20.9241	+	4.58814i	0.672179	+	0.147392i
$970$		0			0
$971$		−	24.7290i		−	0.793590i	−0.917907	−	0.396795i	$-0.870122\pi$
$971$		−	24.7290i		−	0.793590i	0.917907	−	0.396795i	$-0.129878\pi$
$972$		0			0
$973$	−1.00161	+	1.00161i	−0.0321102	+	0.0321102i
$974$		0			0
$975$	−21.1042	−	28.1926i	−0.675876	−	0.902885i
$976$		0			0
$977$	23.7190	+	6.35548i	0.758837	+	0.203330i	0.617434	−	0.786622i	$-0.288172\pi$
$977$	23.7190	+	6.35548i	0.758837	+	0.203330i	0.141403	+	0.989952i	$0.454839\pi$
$978$		0			0
$979$	3.49636	+	2.01862i	0.111744	+	0.0645155i
$980$		0			0
$981$	−11.8624	−	5.46502i	−0.378736	−	0.174485i
$982$		0			0
$983$	−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	$0.646950\pi$
$984$		0			0
$985$	6.34400	+	37.5371i	0.202137	+	1.19603i
$986$		0			0
$987$	−24.0697	−	12.4594i	−0.766148	−	0.396588i
$988$		0			0
$989$	−59.0222			−1.87680
$990$		0			0
$991$	−36.6089			−1.16292			−0.581460	−	0.813575i	$-0.697519\pi$
$991$	−36.6089			−1.16292			−0.581460	+	0.813575i	$0.697519\pi$
$992$		0			0
$993$	−2.05428	−	44.6846i	−0.0651906	−	1.41802i
$994$		0			0
$995$	−8.08889	−	5.75003i	−0.256435	−	0.182288i
$996$		0			0
$997$	−11.5550	+	3.09617i	−0.365952	+	0.0980565i	−0.437109	−	0.899409i	$-0.643998\pi$
$997$	−11.5550	+	3.09617i	−0.365952	+	0.0980565i	0.0711569	+	0.997465i	$0.477331\pi$
$998$		0			0
$999$	−18.9153	+	25.0074i	−0.598453	+	0.791199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cu.b.497.1		16
4.3	odd	2		90.2.l.b.47.4	yes	16
5.3	odd	4	inner	720.2.cu.b.353.2		16
9.5	odd	6	inner	720.2.cu.b.257.2		16
12.11	even	2		270.2.m.b.197.2		16
20.3	even	4		90.2.l.b.83.4	yes	16
20.7	even	4		450.2.p.h.443.1		16
20.19	odd	2		450.2.p.h.407.1		16
36.7	odd	6		810.2.f.c.647.7		16
36.11	even	6		810.2.f.c.647.2		16
36.23	even	6		90.2.l.b.77.4	yes	16
36.31	odd	6		270.2.m.b.17.2		16
45.23	even	12	inner	720.2.cu.b.113.1		16
60.23	odd	4		270.2.m.b.143.2		16
60.47	odd	4		1350.2.q.h.143.4		16
60.59	even	2		1350.2.q.h.1007.3		16
180.23	odd	12		90.2.l.b.23.4	✓	16
180.43	even	12		810.2.f.c.323.2		16
180.59	even	6		450.2.p.h.257.1		16
180.67	even	12		1350.2.q.h.1043.3		16
180.83	odd	12		810.2.f.c.323.7		16
180.103	even	12		270.2.m.b.233.2		16
180.139	odd	6		1350.2.q.h.557.4		16
180.167	odd	12		450.2.p.h.293.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	180.23	odd	12
90.2.l.b.47.4	yes	16	4.3	odd	2
90.2.l.b.77.4	yes	16	36.23	even	6
90.2.l.b.83.4	yes	16	20.3	even	4
270.2.m.b.17.2		16	36.31	odd	6
270.2.m.b.143.2		16	60.23	odd	4
270.2.m.b.197.2		16	12.11	even	2
270.2.m.b.233.2		16	180.103	even	12
450.2.p.h.257.1		16	180.59	even	6
450.2.p.h.293.1		16	180.167	odd	12
450.2.p.h.407.1		16	20.19	odd	2
450.2.p.h.443.1		16	20.7	even	4
720.2.cu.b.113.1		16	45.23	even	12	inner
720.2.cu.b.257.2		16	9.5	odd	6	inner
720.2.cu.b.353.2		16	5.3	odd	4	inner
720.2.cu.b.497.1		16	1.1	even	1	trivial
810.2.f.c.323.2		16	180.43	even	12
810.2.f.c.323.7		16	180.83	odd	12
810.2.f.c.647.2		16	36.11	even	6
810.2.f.c.647.7		16	36.7	odd	6
1350.2.q.h.143.4		16	60.47	odd	4
1350.2.q.h.557.4		16	180.139	odd	6
1350.2.q.h.1007.3		16	60.59	even	2
1350.2.q.h.1043.3		16	180.67	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cu (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.45865 + 0.933998i) q^{3} +(-1.29554 + 1.82252i) q^{5} +(-1.94786 + 0.521929i) q^{7} +(1.25529 - 2.72474i) q^{9} +O(q^{10})\)	\(q+(-1.45865 + 0.933998i) q^{3} +(-1.29554 + 1.82252i) q^{5} +(-1.94786 + 0.521929i) q^{7} +(1.25529 - 2.72474i) q^{9} +(1.70563 + 0.984748i) q^{11} +(-3.92790 - 1.05248i) q^{13} +(0.187514 - 3.86844i) q^{15} +(-2.35877 + 2.35877i) q^{17} +3.70753i q^{19} +(2.35376 - 2.58061i) q^{21} +(1.62200 - 6.05338i) q^{23} +(-1.64313 - 4.72230i) q^{25} +(0.713876 + 5.14688i) q^{27} +(3.74863 - 6.49281i) q^{29} +(-3.48837 - 6.04204i) q^{31} +(-3.40767 + 0.156660i) q^{33} +(1.57232 - 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(6.71243 - 2.13346i) q^{39} +(6.13601 - 3.54263i) q^{41} +(-2.43757 - 9.09714i) q^{43} +(3.33960 + 5.81782i) q^{45} +(-2.00837 - 7.49533i) q^{47} +(-2.54041 + 1.46671i) q^{49} +(1.23752 - 5.64369i) q^{51} +(-7.03027 - 7.03027i) q^{53} +(-4.00444 + 1.83276i) q^{55} +(-3.46282 - 5.40797i) q^{57} +(1.34967 + 2.33769i) q^{59} +(-4.37353 + 7.57518i) q^{61} +(-1.02302 + 5.96261i) q^{63} +(7.00693 - 5.79513i) q^{65} +(-2.19259 + 8.18285i) q^{67} +(3.28793 + 10.3447i) q^{69} +5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} +(6.80736 + 5.35349i) q^{75} +(-3.83631 - 1.02794i) q^{77} +(-10.0535 - 5.80440i) q^{79} +(-5.84847 - 6.84072i) q^{81} +(1.64569 - 0.440961i) q^{83} +(-1.24300 - 7.35477i) q^{85} +(0.596356 + 12.9719i) q^{87} +2.04989 q^{89} +8.20034 q^{91} +(10.7315 + 5.55506i) q^{93} +(-6.75702 - 4.80327i) q^{95} +(-9.71905 + 2.60421i) q^{97} +(4.82426 - 3.41127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 - 8 * q^7	\( 16 q - 12 q^{5} - 8 q^{7} + 24 q^{15} + 24 q^{21} + 24 q^{23} - 16 q^{25} + 8 q^{31} + 24 q^{41} + 36 q^{45} - 48 q^{47} + 48 q^{51} - 24 q^{55} + 24 q^{57} - 24 q^{61} + 48 q^{63} + 16 q^{67} + 16 q^{73} - 72 q^{77} + 24 q^{81} - 48 q^{83} - 4 q^{85} + 48 q^{87} + 72 q^{93} - 84 q^{95} - 48 q^{97}+O(q^{100}) \) 16 * q - 12 * q^5 - 8 * q^7 + 24 * q^15 + 24 * q^21 + 24 * q^23 - 16 * q^25 + 8 * q^31 + 24 * q^41 + 36 * q^45 - 48 * q^47 + 48 * q^51 - 24 * q^55 + 24 * q^57 - 24 * q^61 + 48 * q^63 + 16 * q^67 + 16 * q^73 - 72 * q^77 + 24 * q^81 - 48 * q^83 - 4 * q^85 + 48 * q^87 + 72 * q^93 - 84 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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