LMFDB - Embedded newform 720.2.cu.b.257.2

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			257.2
Root			$0.500000 + 0.589118i$ of defining polynomial
Character	$\chi$	$=$	720.257
Dual form			720.2.cu.b.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933998 + 1.45865i) q^{3} +(-2.22612 - 0.210717i) q^{5} +(0.521929 - 1.94786i) q^{7} +(-1.25529 - 2.72474i) q^{9} +O(q^{10})$	\(q+(-0.933998 + 1.45865i) q^{3} +(-2.22612 - 0.210717i) q^{5} +(0.521929 - 1.94786i) q^{7} +(-1.25529 - 2.72474i) q^{9} +(1.70563 - 0.984748i) q^{11} +(1.05248 + 3.92790i) q^{13} +(2.38655 - 3.05031i) q^{15} +(2.35877 - 2.35877i) q^{17} +3.70753i q^{19} +(2.35376 + 2.58061i) q^{21} +(6.05338 - 1.62200i) q^{23} +(4.91120 + 0.938160i) q^{25} +(5.14688 + 0.713876i) q^{27} +(-3.74863 - 6.49281i) q^{29} +(-3.48837 + 6.04204i) q^{31} +(-0.156660 + 3.40767i) q^{33} +(-1.57232 + 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(-6.71243 - 2.13346i) q^{39} +(6.13601 + 3.54263i) q^{41} +(9.09714 + 2.43757i) q^{43} +(2.22028 + 6.33011i) q^{45} +(-7.49533 - 2.00837i) q^{47} +(2.54041 + 1.46671i) q^{49} +(1.23752 + 5.64369i) q^{51} +(7.03027 + 7.03027i) q^{53} +(-4.00444 + 1.83276i) q^{55} +(-5.40797 - 3.46282i) q^{57} +(-1.34967 + 2.33769i) q^{59} +(-4.37353 - 7.57518i) q^{61} +(-5.96261 + 1.02302i) q^{63} +(-1.51527 - 8.96575i) q^{65} +(8.18285 - 2.19259i) q^{67} +(-3.28793 + 10.3447i) q^{69} -5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} +(-5.95549 + 6.28746i) q^{75} +(-1.02794 - 3.83631i) q^{77} +(10.0535 - 5.80440i) q^{79} +(-5.84847 + 6.84072i) q^{81} +(0.440961 - 1.64569i) q^{83} +(-5.74792 + 4.75386i) q^{85} +(12.9719 + 0.596356i) q^{87} -2.04989 q^{89} +8.20034 q^{91} +(-5.55506 - 10.7315i) q^{93} +(0.781237 - 8.25339i) q^{95} +(2.60421 - 9.71905i) q^{97} +(-4.82426 - 3.41127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.933998	+	1.45865i	−0.539244	+	0.842150i
$3$	−0.933998	+	1.45865i	−0.539244	+	0.842150i
$4$		0			0
$5$	−2.22612	−	0.210717i	−0.995550	−	0.0942354i
$5$	−2.22612	−	0.210717i	−0.995550	−	0.0942354i
$6$		0			0
$7$	0.521929	−	1.94786i	0.197270	−	0.736223i	−0.794397	−	0.607399i	$-0.792213\pi$
$7$	0.521929	−	1.94786i	0.197270	−	0.736223i	0.991667	−	0.128824i	$-0.0411204\pi$
$8$		0			0
$9$	−1.25529	−	2.72474i	−0.418432	−	0.908248i
$10$		0			0
$11$	1.70563	−	0.984748i	0.514268	−	0.296913i	−0.220318	−	0.975428i	$-0.570710\pi$
$11$	1.70563	−	0.984748i	0.514268	−	0.296913i	0.734586	+	0.678515i	$0.237376\pi$
$12$		0			0
$13$	1.05248	+	3.92790i	0.291905	+	1.08940i	0.943644	+	0.330961i	$0.107373\pi$
$13$	1.05248	+	3.92790i	0.291905	+	1.08940i	−0.651739	+	0.758443i	$0.725960\pi$
$14$		0			0
$15$	2.38655	−	3.05031i	0.616205	−	0.787586i
$16$		0			0
$17$	2.35877	−	2.35877i	0.572085	−	0.572085i	−0.360626	−	0.932711i	$-0.617437\pi$
$17$	2.35877	−	2.35877i	0.572085	−	0.572085i	0.932711	+	0.360626i	$0.117437\pi$
$18$		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
$23$	6.05338	−	1.62200i	1.26222	−	0.338210i	0.435173	−	0.900347i	$-0.356687\pi$
$23$	6.05338	−	1.62200i	1.26222	−	0.338210i	0.827044	+	0.562137i	$0.190021\pi$
$24$		0			0
$25$	4.91120	+	0.938160i	0.982239	+	0.187632i
$26$		0			0
$27$	5.14688	+	0.713876i	0.990518	+	0.137386i
$28$		0			0
$29$	−3.74863	−	6.49281i	−0.696103	−	1.20569i	−0.969808	−	0.243872i	$-0.921582\pi$
$29$	−3.74863	−	6.49281i	−0.696103	−	1.20569i	0.273705	−	0.961814i	$-0.411751\pi$
$30$		0			0
$31$	−3.48837	+	6.04204i	−0.626530	+	1.08518i	0.361713	+	0.932289i	$0.382192\pi$
$31$	−3.48837	+	6.04204i	−0.626530	+	1.08518i	−0.988243	+	0.152892i	$0.951141\pi$
$32$		0			0
$33$	−0.156660	+	3.40767i	−0.0272710	+	0.593199i
$34$		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	0.895644	−	0.444771i	$-0.146715\pi$
$41$	6.13601	+	3.54263i	0.958284	+	0.553266i	0.0626396	+	0.998036i	$0.480048\pi$
$42$		0			0
$43$	9.09714	+	2.43757i	1.38730	+	0.371726i	0.873767	−	0.486344i	$-0.161670\pi$
$43$	9.09714	+	2.43757i	1.38730	+	0.371726i	0.513533	+	0.858070i	$0.328336\pi$
$44$		0			0
$45$	2.22028	+	6.33011i	0.330981	+	0.943638i
$46$		0			0
$47$	−7.49533	−	2.00837i	−1.09331	−	0.292951i	−0.333270	−	0.942831i	$-0.608152\pi$
$47$	−7.49533	−	2.00837i	−1.09331	−	0.292951i	−0.760036	+	0.649881i	$0.774819\pi$
$48$		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	0.999430	−	0.0337485i	$-0.0107445\pi$
$53$	7.03027	+	7.03027i	0.965682	+	0.965682i	−0.0337485	+	0.999430i	$0.510745\pi$
$54$		0			0
$55$	−4.00444	+	1.83276i	−0.539959	+	0.247129i
$56$		0			0
$57$	−5.40797	−	3.46282i	−0.716303	−	0.458662i
$58$		0			0
$59$	−1.34967	+	2.33769i	−0.175712	+	0.304341i	−0.940407	−	0.340050i	$-0.889556\pi$
$59$	−1.34967	+	2.33769i	−0.175712	+	0.304341i	0.764696	+	0.644392i	$0.222889\pi$
$60$		0			0
$61$	−4.37353	−	7.57518i	−0.559973	−	0.969902i	−0.997498	−	0.0706960i	$-0.977478\pi$
$61$	−4.37353	−	7.57518i	−0.559973	−	0.969902i	0.437524	−	0.899207i	$-0.355855\pi$
$62$		0			0
$63$	−5.96261	+	1.02302i	−0.751218	+	0.128889i
$64$		0			0
$65$	−1.51527	−	8.96575i	−0.187946	−	1.11206i
$66$		0			0
$67$	8.18285	−	2.19259i	0.999694	−	0.267867i	0.278377	−	0.960472i	$-0.410204\pi$
$67$	8.18285	−	2.19259i	0.999694	−	0.267867i	0.721317	+	0.692605i	$0.243537\pi$
$68$		0			0
$69$	−3.28793	+	10.3447i	−0.395820	+	1.24535i
$70$		0			0
$71$		−	5.68481i		−	0.674663i	−0.941386	−	0.337332i	$-0.890476\pi$
$71$		−	5.68481i		−	0.674663i	0.941386	−	0.337332i	$-0.109524\pi$
$72$		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
$75$	−5.95549	+	6.28746i	−0.687681	+	0.726013i
$76$		0			0
$77$	−1.02794	−	3.83631i	−0.117144	−	0.437188i
$78$		0			0
$79$	10.0535	−	5.80440i	1.13111	−	0.653046i	0.186895	−	0.982380i	$-0.440158\pi$
$79$	10.0535	−	5.80440i	1.13111	−	0.653046i	0.944214	+	0.329334i	$0.106824\pi$
$80$		0			0
$81$	−5.84847	+	6.84072i	−0.649830	+	0.760080i
$82$		0			0
$83$	0.440961	−	1.64569i	0.0484017	−	0.180638i	−0.937493	−	0.348004i	$-0.886860\pi$
$83$	0.440961	−	1.64569i	0.0484017	−	0.180638i	0.985895	+	0.167366i	$0.0535262\pi$
$84$		0			0
$85$	−5.74792	+	4.75386i	−0.623449	+	0.515628i
$86$		0			0
$87$	12.9719	+	0.596356i	1.39074	+	0.0639361i
$88$		0			0
$89$	−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
$92$		0			0
$93$	−5.55506	−	10.7315i	−0.576033	−	1.11281i
$94$		0			0
$95$	0.781237	−	8.25339i	0.0801533	−	0.846780i
$96$		0			0
$97$	2.60421	−	9.71905i	0.264418	−	0.986820i	−0.698188	−	0.715914i	$-0.746010\pi$
$97$	2.60421	−	9.71905i	0.264418	−	0.986820i	0.962606	−	0.270906i	$-0.0873232\pi$
$98$		0			0
$99$	−4.82426	−	3.41127i	−0.484856	−	0.342845i
$100$		0			0
$101$	−4.09014	+	2.36144i	−0.406984	+	0.234972i	−0.689493	−	0.724292i	$-0.742167\pi$
$101$	−4.09014	+	2.36144i	−0.406984	+	0.234972i	0.282509	+	0.959265i	$0.408833\pi$
$102$		0			0
$103$	−1.03662	−	3.86872i	−0.102141	−	0.381196i	0.895864	−	0.444329i	$-0.146558\pi$
$103$	−1.03662	−	3.86872i	−0.102141	−	0.381196i	−0.998005	+	0.0631321i	$0.979891\pi$
$104$		0			0
$105$	−4.69598	−	6.24072i	−0.458280	−	0.609032i
$106$		0			0
$107$	5.40296	−	5.40296i	0.522324	−	0.522324i	−0.395949	−	0.918273i	$-0.629584\pi$
$107$	5.40296	−	5.40296i	0.522324	−	0.522324i	0.918273	+	0.395949i	$0.129584\pi$
$108$		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
$113$	2.86451	−	0.767544i	0.269471	−	0.0722045i	−0.121553	−	0.992585i	$-0.538788\pi$
$113$	2.86451	−	0.767544i	0.269471	−	0.0722045i	0.391024	+	0.920380i	$0.372121\pi$
$114$		0			0
$115$	−13.8173	+	2.33521i	−1.28847	+	0.217760i
$116$		0			0
$117$	9.38136	−	7.79841i	0.867307	−	0.720964i
$118$		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
$123$	−10.8985	+	5.64146i	−0.982681	+	0.508673i
$124$		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	0.517859	−	0.855466i	$-0.326729\pi$
$131$	0.411267	+	0.237445i	0.0359326	+	0.0207457i	−0.481926	+	0.876212i	$0.660063\pi$
$132$		0			0
$133$	7.22176	+	1.93506i	0.626206	+	0.167791i
$134$		0			0
$135$	−11.3071	−	2.67371i	−0.973163	−	0.230116i
$136$		0			0
$137$	9.51618	+	2.54985i	0.813022	+	0.217849i	0.641293	−	0.767296i	$-0.278398\pi$
$137$	9.51618	+	2.54985i	0.813022	+	0.217849i	0.171728	+	0.985144i	$0.445065\pi$
$138$		0			0
$139$	−0.608318	−	0.351212i	−0.0515968	−	0.0297894i	0.473980	−	0.880536i	$-0.342817\pi$
$139$	−0.608318	−	0.351212i	−0.0515968	−	0.0297894i	−0.525577	+	0.850746i	$0.676150\pi$
$140$		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
$147$	−4.51215	+	2.33566i	−0.372156	+	0.192642i
$148$		0			0
$149$	4.05609	−	7.02536i	0.332288	−	0.575540i	−0.650672	−	0.759359i	$-0.725513\pi$
$149$	4.05609	−	7.02536i	0.332288	−	0.575540i	0.982960	+	0.183819i	$0.0588460\pi$
$150$		0			0
$151$	−4.61739	−	7.99755i	−0.375758	−	0.650832i	0.614682	−	0.788775i	$-0.289284\pi$
$151$	−4.61739	−	7.99755i	−0.375758	−	0.650832i	−0.990440	+	0.137943i	$0.955951\pi$
$152$		0			0
$153$	−9.38798	−	3.46609i	−0.758973	−	0.280217i
$154$		0			0
$155$	9.03868	−	12.7152i	0.726004	−	1.02131i
$156$		0			0
$157$	10.4848	−	2.80938i	0.836775	−	0.224213i	0.185108	−	0.982718i	$-0.440736\pi$
$157$	10.4848	−	2.80938i	0.836775	−	0.224213i	0.651667	+	0.758505i	$0.274070\pi$
$158$		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
$165$	1.06680	−	7.55286i	0.0830500	−	0.587989i
$166$		0			0
$167$	−1.32254	−	4.93579i	−0.102341	−	0.381943i	0.895689	−	0.444682i	$-0.146683\pi$
$167$	−1.32254	−	4.93579i	−0.102341	−	0.381943i	−0.998030	+	0.0627387i	$0.980017\pi$
$168$		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
$173$	−1.91916	+	7.16239i	−0.145911	+	0.544546i	0.853802	+	0.520597i	$0.174291\pi$
$173$	−1.91916	+	7.16239i	−0.145911	+	0.544546i	−0.999713	+	0.0239492i	$0.992376\pi$
$174$		0			0
$175$	4.39070	−	9.07669i	0.331906	−	0.686133i
$176$		0			0
$177$	−2.14928	−	4.15208i	−0.161550	−	0.312090i
$178$		0			0
$179$	−2.73426			−0.204369			−0.102184	−	0.994765i	$-0.532583\pi$
$179$	−2.73426			−0.204369			−0.102184	+	0.994765i	$0.532583\pi$
$180$		0			0
$181$	−22.7081			−1.68788			−0.843941	−	0.536437i	$-0.819770\pi$
$181$	−22.7081			−1.68788			−0.843941	+	0.536437i	$0.819770\pi$
$182$		0			0
$183$	15.1344	+	0.695770i	1.11877	+	0.0514328i
$184$		0			0
$185$	−8.59956	−	10.3978i	−0.632252	−	0.764460i
$186$		0			0
$187$	1.70040	−	6.34598i	0.124346	−	0.464064i
$188$		0			0
$189$	4.07684	−	9.65283i	0.296546	−	0.702140i
$190$		0			0
$191$	1.11154	−	0.641749i	0.0804283	−	0.0464353i	−0.459246	−	0.888309i	$-0.651881\pi$
$191$	1.11154	−	0.641749i	0.0804283	−	0.0464353i	0.539675	+	0.841874i	$0.318547\pi$
$192$		0			0
$193$	1.41494	+	5.28063i	0.101850	+	0.380108i	0.997969	−	0.0637057i	$-0.0202919\pi$
$193$	1.41494	+	5.28063i	0.101850	+	0.380108i	−0.896119	+	0.443814i	$0.853625\pi$
$194$		0			0
$195$	14.4931	+	6.16376i	1.03787	+	0.441396i
$196$		0			0
$197$	−12.0386	+	12.0386i	−0.857716	+	0.857716i	−0.991069	−	0.133353i	$-0.957426\pi$
$197$	−12.0386	+	12.0386i	−0.857716	+	0.857716i	0.133353	+	0.991069i	$0.457426\pi$
$198$		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
$203$	−14.6036	+	3.91303i	−1.02497	+	0.274641i
$204$		0			0
$205$	−12.9130	−	9.17927i	−0.901882	−	0.641108i
$206$		0			0
$207$	−12.0183	−	14.4578i	−0.835331	−	1.00489i
$208$		0			0
$209$	3.65098	+	6.32368i	0.252543	+	0.437418i
$210$		0			0
$211$	−12.0425	+	20.8582i	−0.829038	+	1.43594i	0.0697556	+	0.997564i	$0.477778\pi$
$211$	−12.0425	+	20.8582i	−0.829038	+	1.43594i	−0.898794	+	0.438372i	$0.855555\pi$
$212$		0			0
$213$	8.29213	+	5.30960i	0.568167	+	0.363808i
$214$		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
$223$	16.2073	+	4.34272i	1.08532	+	0.290810i	0.756773	−	0.653678i	$-0.226775\pi$
$223$	16.2073	+	4.34272i	1.08532	+	0.290810i	0.328546	+	0.944488i	$0.393441\pi$
$224$		0			0
$225$	−3.60875	−	14.5594i	−0.240584	−	0.970628i
$226$		0			0
$227$	−7.18543	−	1.92533i	−0.476914	−	0.127789i	0.0123515	−	0.999924i	$-0.496068\pi$
$227$	−7.18543	−	1.92533i	−0.476914	−	0.127789i	−0.489265	+	0.872135i	$0.662735\pi$
$228$		0			0
$229$	−7.74183	−	4.46975i	−0.511595	−	0.295369i	0.221894	−	0.975071i	$-0.428776\pi$
$229$	−7.74183	−	4.46975i	−0.511595	−	0.295369i	−0.733489	+	0.679701i	$0.762109\pi$
$230$		0			0
$231$	6.55591	+	2.08371i	0.431347	+	0.137098i
$232$		0			0
$233$	−15.0591	−	15.0591i	−0.986558	−	0.986558i	0.0133533	−	0.999911i	$-0.495749\pi$
$233$	−15.0591	−	15.0591i	−0.986558	−	0.986558i	−0.999911	+	0.0133533i	$0.995749\pi$
$234$		0			0
$235$	16.2623	+	6.05025i	1.06083	+	0.394675i
$236$		0			0
$237$	−0.923401	+	20.0858i	−0.0599814	+	1.30471i
$238$		0			0
$239$	−5.42731	+	9.40038i	−0.351064	+	0.608060i	−0.986436	−	0.164146i	$-0.947513\pi$
$239$	−5.42731	+	9.40038i	−0.351064	+	0.608060i	0.635372	+	0.772206i	$0.280847\pi$
$240$		0			0
$241$	11.6659	+	20.2059i	0.751467	+	1.30158i	0.947112	+	0.320904i	$0.103987\pi$
$241$	11.6659	+	20.2059i	0.751467	+	1.30158i	−0.195645	+	0.980675i	$0.562680\pi$
$242$		0			0
$243$	−4.51572	−	14.9201i	−0.289684	−	0.957122i
$244$		0			0
$245$	−5.34620	−	3.80037i	−0.341556	−	0.242797i
$246$		0			0
$247$	−14.5628	+	3.90209i	−0.926609	+	0.248284i
$248$		0			0
$249$	1.98862	+	2.18027i	0.126024	+	0.138169i
$250$		0			0
$251$			13.3860i			0.844914i	0.906383	+	0.422457i	$0.138832\pi$
$251$			13.3860i			0.844914i	−0.906383	+	0.422457i	$0.861168\pi$
$252$		0			0
$253$	8.72759	−	8.72759i	0.548699	−	0.548699i
$254$		0			0
$255$	−1.56565	−	12.8243i	−0.0980447	−	0.803087i
$256$		0			0
$257$	−1.95494	−	7.29595i	−0.121946	−	0.455109i	0.877766	−	0.479089i	$-0.159033\pi$
$257$	−1.95494	−	7.29595i	−0.121946	−	0.455109i	−0.999712	+	0.0239802i	$0.992366\pi$
$258$		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
$263$	−2.88569	+	10.7695i	−0.177939	+	0.664078i	0.818093	+	0.575086i	$0.195031\pi$
$263$	−2.88569	+	10.7695i	−0.177939	+	0.664078i	−0.996032	+	0.0889923i	$0.971635\pi$
$264$		0			0
$265$	−14.1688	−	17.1316i	−0.870383	−	1.05239i
$266$		0			0
$267$	1.91459	−	2.99006i	0.117171	−	0.182989i
$268$		0			0
$269$	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	$-0.713203\pi$
$271$	−20.4402			−1.24165			−0.620827	+	0.783947i	$0.713203\pi$
$272$		0			0
$273$	−7.65910	+	11.9614i	−0.463550	+	0.723936i
$274$		0			0
$275$	9.30055	−	3.23613i	0.560844	−	0.195146i
$276$		0			0
$277$	6.27326	−	23.4121i	0.376924	−	1.40670i	−0.473590	−	0.880745i	$-0.657042\pi$
$277$	6.27326	−	23.4121i	0.376924	−	1.40670i	0.850514	−	0.525953i	$-0.176291\pi$
$278$		0			0
$279$	20.8419	+	1.92038i	1.24777	+	0.114970i
$280$		0			0
$281$	19.5424	−	11.2828i	1.16580	−	0.673076i	0.213114	−	0.977027i	$-0.431640\pi$
$281$	19.5424	−	11.2828i	1.16580	−	0.673076i	0.952687	+	0.303952i	$0.0983062\pi$
$282$		0			0
$283$	−0.549660	−	2.05136i	−0.0326739	−	0.121941i	0.947663	−	0.319273i	$-0.103439\pi$
$283$	−0.549660	−	2.05136i	−0.0326739	−	0.121941i	−0.980337	+	0.197333i	$0.936772\pi$
$284$		0			0
$285$	11.3091	+	8.84820i	0.669893	+	0.524122i
$286$		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
$293$	−3.53204	+	0.946406i	−0.206344	+	0.0552896i	−0.360510	−	0.932755i	$-0.617397\pi$
$293$	−3.53204	+	0.946406i	−0.206344	+	0.0552896i	0.154167	+	0.988045i	$0.450731\pi$
$294$		0			0
$295$	3.49711	−	4.91958i	0.203609	−	0.286429i
$296$		0			0
$297$	9.48168	−	3.85077i	0.550183	−	0.223444i
$298$		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
$303$	0.375673	−	8.17164i	0.0215819	−	0.469449i
$304$		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	0.734938	−	0.678134i	$-0.237211\pi$
$311$	9.08436	+	5.24485i	0.515127	+	0.297408i	−0.219812	+	0.975542i	$0.570544\pi$
$312$		0			0
$313$	17.0518	+	4.56901i	0.963824	+	0.258256i	0.706218	−	0.707994i	$-0.250400\pi$
$313$	17.0518	+	4.56901i	0.963824	+	0.258256i	0.257606	+	0.966250i	$0.417066\pi$
$314$		0			0
$315$	13.4890	−	1.02095i	0.760021	−	0.0575238i
$316$		0			0
$317$	−22.3972	−	6.00131i	−1.25795	−	0.337067i	−0.432549	−	0.901611i	$-0.642386\pi$
$317$	−22.3972	−	6.00131i	−1.25795	−	0.337067i	−0.825403	+	0.564543i	$0.809052\pi$
$318$		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
$327$	6.35032	+	4.06623i	0.351173	+	0.224863i
$328$		0			0
$329$	−7.82405	+	13.5517i	−0.431354	+	0.747127i
$330$		0			0
$331$	−12.9130	−	22.3659i	−0.709761	−	1.22934i	−0.964946	−	0.262450i	$-0.915470\pi$
$331$	−12.9130	−	22.3659i	−0.709761	−	1.22934i	0.255185	−	0.966892i	$-0.417864\pi$
$332$		0			0
$333$	6.27003	−	16.9825i	0.343595	−	0.930636i
$334$		0			0
$335$	−18.6780	+	3.15670i	−1.02049	+	0.172469i
$336$		0			0
$337$	−30.9889	+	8.30344i	−1.68807	+	0.452317i	−0.969891	−	0.243541i	$-0.921691\pi$
$337$	−30.9889	+	8.30344i	−1.68807	+	0.452317i	−0.718180	+	0.695858i	$0.755024\pi$
$338$		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
$345$	9.49911	−	22.3357i	0.511415	−	1.20251i
$346$		0			0
$347$	3.83170	+	14.3001i	0.205696	+	0.767670i	0.989236	+	0.146328i	$0.0467454\pi$
$347$	3.83170	+	14.3001i	0.205696	+	0.767670i	−0.783540	+	0.621342i	$0.786588\pi$
$348$		0			0
$349$	13.3741	−	7.72151i	0.715897	−	0.413323i	−0.0973439	−	0.995251i	$-0.531035\pi$
$349$	13.3741	−	7.72151i	0.715897	−	0.413323i	0.813241	+	0.581928i	$0.197701\pi$
$350$		0			0
$351$	2.61295	+	20.9678i	0.139469	+	1.11918i
$352$		0			0
$353$	−5.39774	+	20.1446i	−0.287293	+	1.07219i	0.659855	+	0.751393i	$0.270618\pi$
$353$	−5.39774	+	20.1446i	−0.287293	+	1.07219i	−0.947148	+	0.320798i	$0.896049\pi$
$354$		0			0
$355$	−1.19788	+	12.6551i	−0.0635771	+	0.671661i
$356$		0			0
$357$	11.6390	+	0.535079i	0.616003	+	0.0283194i
$358$		0			0
$359$	3.39466			0.179163			0.0895815	−	0.995979i	$-0.471447\pi$
$359$	3.39466			0.179163			0.0895815	+	0.995979i	$0.471447\pi$
$360$		0			0
$361$	5.25425			0.276540
$362$		0			0
$363$	−5.66999	−	10.9536i	−0.297597	−	0.574914i
$364$		0			0
$365$	−2.80059	+	2.31625i	−0.146590	+	0.121238i
$366$		0			0
$367$	−5.68801	+	21.2279i	−0.296912	+	1.10809i	0.642776	+	0.766054i	$0.277783\pi$
$367$	−5.68801	+	21.2279i	−0.296912	+	1.10809i	−0.939687	+	0.342035i	$0.888884\pi$
$368$		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
$373$	−0.381044	−	1.42207i	−0.0197297	−	0.0736322i	0.955359	−	0.295447i	$-0.0954686\pi$
$373$	−0.381044	−	1.42207i	−0.0197297	−	0.0736322i	−0.975089	+	0.221815i	$0.928802\pi$
$374$		0			0
$375$	14.5825	−	12.7417i	0.753037	−	0.657978i
$376$		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
$383$	16.5638	−	4.43826i	0.846372	−	0.226785i	0.190528	−	0.981682i	$-0.438980\pi$
$383$	16.5638	−	4.43826i	0.846372	−	0.226785i	0.655843	+	0.754897i	$0.272313\pi$
$384$		0			0
$385$	1.47993	+	8.75668i	0.0754243	+	0.446282i
$386$		0			0
$387$	−4.77783	−	27.8472i	−0.242871	−	1.41556i
$388$		0			0
$389$	15.1070	+	26.1660i	0.765953	+	1.32667i	0.939741	+	0.341886i	$0.111066\pi$
$389$	15.1070	+	26.1660i	0.765953	+	1.32667i	−0.173789	+	0.984783i	$0.555601\pi$
$390$		0			0
$391$	10.4526	−	18.1044i	0.528610	−	0.915580i
$392$		0			0
$393$	−0.730471	+	0.378120i	−0.0368474	+	0.0190736i
$394$		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	0.159752	−	0.987157i	$-0.448931\pi$
$401$	−12.3209	−	7.11346i	−0.615275	−	0.355229i	−0.775027	+	0.631928i	$0.782264\pi$
$402$		0			0
$403$	−27.4040	−	7.34287i	−1.36509	−	0.365774i
$404$		0			0
$405$	14.4608	−	13.9959i	0.718565	−	0.695460i
$406$		0			0
$407$	11.4796	+	3.07596i	0.569025	+	0.152470i
$408$		0			0
$409$	−10.2963	−	5.94456i	−0.509118	−	0.293939i	0.223353	−	0.974738i	$-0.428300\pi$
$409$	−10.2963	−	5.94456i	−0.509118	−	0.293939i	−0.732471	+	0.680798i	$0.761633\pi$
$410$		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
$417$	1.08046	−	0.559288i	0.0529104	−	0.0273885i
$418$		0			0
$419$	19.6354	−	34.0095i	0.959251	−	1.66147i	0.234926	−	0.972013i	$-0.424515\pi$
$419$	19.6354	−	34.0095i	0.959251	−	1.66147i	0.724325	−	0.689458i	$-0.242151\pi$
$420$		0			0
$421$	−12.2493	−	21.2163i	−0.596992	−	1.03402i	−0.993262	−	0.115887i	$-0.963029\pi$
$421$	−12.2493	−	21.2163i	−0.596992	−	1.03402i	0.396270	−	0.918134i	$-0.370304\pi$
$422$		0			0
$423$	3.93656	+	22.9440i	0.191402	+	1.11557i
$424$		0			0
$425$	13.7973	−	9.37146i	0.669265	−	0.454583i
$426$		0			0
$427$	−17.0381	+	4.56534i	−0.824531	+	0.220932i
$428$		0			0
$429$	−13.5499	+	2.97115i	−0.654194	+	0.143449i
$430$		0			0
$431$			6.10703i			0.294165i	0.989124	+	0.147083i	$0.0469883\pi$
$431$			6.10703i			0.294165i	−0.989124	+	0.147083i	$0.953012\pi$
$432$		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
$435$	−28.7514	−	4.06096i	−1.37852	−	0.194708i
$436$		0			0
$437$	6.01360	+	22.4431i	0.287670	+	1.07360i
$438$		0			0
$439$	−1.96604	+	1.13510i	−0.0938342	+	0.0541752i	−0.546183	−	0.837666i	$-0.683920\pi$
$439$	−1.96604	+	1.13510i	−0.0938342	+	0.0541752i	0.452349	+	0.891841i	$0.350586\pi$
$440$		0			0
$441$	0.807438	−	8.76313i	0.0384494	−	0.417292i
$442$		0			0
$443$	−7.20031	+	26.8719i	−0.342097	+	1.27672i	0.553870	+	0.832603i	$0.313150\pi$
$443$	−7.20031	+	26.8719i	−0.342097	+	1.27672i	−0.895967	+	0.444120i	$0.853516\pi$
$444$		0			0
$445$	4.56329	+	0.431946i	0.216321	+	0.0204762i
$446$		0			0
$447$	6.45913	+	12.4781i	0.305506	+	0.590193i
$448$		0			0
$449$	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
$452$		0			0
$453$	15.9782	+	0.734564i	0.750723	+	0.0345128i
$454$		0			0
$455$	−18.2549	−	1.72795i	−0.855804	−	0.0810075i
$456$		0			0
$457$	−10.0741	+	37.5970i	−0.471246	+	1.75871i	0.164058	+	0.986451i	$0.447542\pi$
$457$	−10.0741	+	37.5970i	−0.471246	+	1.75871i	−0.635303	+	0.772263i	$0.719125\pi$
$458$		0			0
$459$	13.8242	−	10.4564i	0.645256	−	0.488064i
$460$		0			0
$461$	−2.62200	+	1.51381i	−0.122119	+	0.0705053i	−0.559815	−	0.828618i	$-0.689128\pi$
$461$	−2.62200	+	1.51381i	−0.122119	+	0.0705053i	0.437696	+	0.899123i	$0.355795\pi$
$462$		0			0
$463$	−1.76940	−	6.60350i	−0.0822311	−	0.306891i	0.912544	−	0.408978i	$-0.134115\pi$
$463$	−1.76940	−	6.60350i	−0.0822311	−	0.306891i	−0.994775	+	0.102087i	$0.967448\pi$
$464$		0			0
$465$	10.1049	+	25.0602i	0.468603	+	1.16214i
$466$		0			0
$467$	8.05359	−	8.05359i	0.372676	−	0.372676i	−0.495775	−	0.868451i	$-0.665116\pi$
$467$	8.05359	−	8.05359i	0.372676	−	0.372676i	0.868451	+	0.495775i	$0.165116\pi$
$468$		0			0
$469$		−	17.0835i		−	0.788841i
$470$		0			0
$471$	−5.69485	+	17.9175i	−0.262405	+	0.825596i
$472$		0			0
$473$	17.9168	−	4.80079i	0.823814	−	0.220740i
$474$		0			0
$475$	−3.47825	+	18.2084i	−0.159593	+	0.835458i
$476$		0			0
$477$	10.3306	−	27.9808i	0.473007	−	1.28115i
$478$		0			0
$479$	16.5711	+	28.7020i	0.757154	+	1.31143i	0.944296	+	0.329097i	$0.106744\pi$
$479$	16.5711	+	28.7020i	0.757154	+	1.31143i	−0.187142	+	0.982333i	$0.559922\pi$
$480$		0			0
$481$	−12.2692	+	21.2509i	−0.559428	+	0.968958i
$482$		0			0
$483$	18.4340	+	11.8036i	0.838775	+	0.537083i
$484$		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	0.0891441	−	0.996019i	$-0.471587\pi$
$491$	−16.1505	−	9.32449i	−0.728861	−	0.420808i	−0.818005	+	0.575210i	$0.804920\pi$
$492$		0			0
$493$	−24.1572	−	6.47289i	−1.08798	−	0.291524i
$494$		0			0
$495$	10.0206	+	8.61043i	0.450391	+	0.387010i
$496$		0			0
$497$	−11.0732	−	2.96707i	−0.496703	−	0.133091i
$498$		0			0
$499$	−19.6189	−	11.3270i	−0.878263	−	0.507065i	−0.00817742	−	0.999967i	$-0.502603\pi$
$499$	−19.6189	−	11.3270i	−0.878263	−	0.507065i	−0.870085	+	0.492901i	$0.835936\pi$
$500$		0			0
$501$	8.43482	+	2.68090i	0.376840	+	0.119774i
$502$		0			0
$503$	−9.64801	−	9.64801i	−0.430183	−	0.430183i	0.458507	−	0.888691i	$-0.348384\pi$
$503$	−9.64801	−	9.64801i	−0.430183	−	0.430183i	−0.888691	+	0.458507i	$0.848384\pi$
$504$		0			0
$505$	9.60272	−	4.39499i	0.427315	−	0.195574i
$506$		0			0
$507$	0.281276	−	6.11831i	0.0124919	−	0.271724i
$508$		0			0
$509$	−13.5882	+	23.5355i	−0.602286	+	1.04319i	0.390188	+	0.920735i	$0.372410\pi$
$509$	−13.5882	+	23.5355i	−0.602286	+	1.04319i	−0.992474	+	0.122455i	$0.960923\pi$
$510$		0			0
$511$	−1.63879	−	2.83847i	−0.0724959	−	0.125567i
$512$		0			0
$513$	−2.64671	+	19.0822i	−0.116855	+	0.842499i
$514$		0			0
$515$	1.49244	+	8.83066i	0.0657646	+	0.389125i
$516$		0			0
$517$	−14.7620	+	3.95547i	−0.649233	+	0.173961i
$518$		0			0
$519$	−8.65490	−	9.48903i	−0.379908	−	0.416522i
$520$		0			0
$521$		−	18.3542i		−	0.804114i	−0.915615	−	0.402057i	$-0.868295\pi$
$521$		−	18.3542i		−	0.804114i	0.915615	−	0.402057i	$-0.131705\pi$
$522$		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
$525$	9.13877	+	14.8821i	0.398849	+	0.649508i
$526$		0			0
$527$	6.02350	+	22.4800i	0.262388	+	0.979244i
$528$		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
$533$	−7.45708	+	27.8302i	−0.323002	+	1.20546i
$534$		0			0
$535$	−13.1661	+	10.8891i	−0.569221	+	0.470778i
$536$		0			0
$537$	2.55380	−	3.98832i	0.110205	−	0.172109i
$538$		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
$543$	21.2093	−	33.1231i	0.910180	−	1.42145i
$544$		0			0
$545$	−0.917370	+	9.69156i	−0.0392958	+	0.415141i
$546$		0			0
$547$	5.79252	−	21.6180i	0.247670	−	0.924319i	−0.724352	−	0.689430i	$-0.757861\pi$
$547$	5.79252	−	21.6180i	0.247670	−	0.924319i	0.972022	−	0.234888i	$-0.0754724\pi$
$548$		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
$553$	−6.05896	−	22.6124i	−0.257653	−	0.961575i
$554$		0			0
$555$	23.1987	−	2.83220i	0.984728	−	0.120220i
$556$		0			0
$557$	−20.5740	+	20.5740i	−0.871749	+	0.871749i	−0.992663	−	0.120914i	$-0.961417\pi$
$557$	−20.5740	+	20.5740i	−0.871749	+	0.871749i	0.120914	+	0.992663i	$0.461417\pi$
$558$		0			0
$559$			38.2982i			1.61984i
$560$		0			0
$561$	7.66836	+	8.40741i	0.323759	+	0.354961i
$562$		0			0
$563$	−34.2529	+	9.17805i	−1.44359	+	0.386809i	−0.893789	−	0.448487i	$-0.851963\pi$
$563$	−34.2529	+	9.17805i	−1.44359	+	0.386809i	−0.549800	+	0.835296i	$0.685296\pi$
$564$		0			0
$565$	−6.53848	+	1.10504i	−0.275076	+	0.0464895i
$566$		0			0
$567$	10.2723	+	14.9624i	0.431396	+	0.628361i
$568$		0			0
$569$	−12.0592	−	20.8872i	−0.505549	−	0.875637i	−0.999979	−	0.00641982i	$-0.997956\pi$
$569$	−12.0592	−	20.8872i	−0.505549	−	0.875637i	0.494430	−	0.869217i	$-0.335377\pi$
$570$		0			0
$571$	−2.24726	+	3.89236i	−0.0940448	+	0.162890i	−0.909210	−	0.416339i	$-0.863313\pi$
$571$	−2.24726	+	3.89236i	−0.0940448	+	0.162890i	0.815165	+	0.579229i	$0.196646\pi$
$572$		0			0
$573$	−0.102094	+	2.22074i	−0.00426502	+	0.0927726i
$574$		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
$583$	18.9141	+	5.06802i	0.783342	+	0.209896i
$584$		0			0
$585$	−22.5273	+	15.3834i	−0.931388	+	0.636024i
$586$		0			0
$587$	−43.6620	−	11.6992i	−1.80212	−	0.482878i	−0.807818	−	0.589433i	$-0.799351\pi$
$587$	−43.6620	−	11.6992i	−1.80212	−	0.482878i	−0.994307	+	0.106555i	$0.966018\pi$
$588$		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	0.777209	−	0.629242i	$-0.216635\pi$
$593$	3.60323	+	3.60323i	0.147967	+	0.147967i	−0.629242	+	0.777209i	$0.716635\pi$
$594$		0			0
$595$	6.25986	+	13.6773i	0.256629	+	0.560716i
$596$		0			0
$597$	−6.47392	−	4.14537i	−0.264960	−	0.169659i
$598$		0			0
$599$	−23.4581	+	40.6307i	−0.958473	+	1.66012i	−0.232260	+	0.972654i	$0.574612\pi$
$599$	−23.4581	+	40.6307i	−0.958473	+	1.66012i	−0.726213	+	0.687470i	$0.758721\pi$
$600$		0			0
$601$	−20.5688	−	35.6263i	−0.839020	−	1.45323i	−0.890715	−	0.454563i	$-0.849795\pi$
$601$	−20.5688	−	35.6263i	−0.839020	−	1.45323i	0.0516943	−	0.998663i	$-0.483538\pi$
$602$		0			0
$603$	−16.2461	−	19.5438i	−0.661594	−	0.795887i
$604$		0			0
$605$	9.22568	−	12.9783i	0.375077	−	0.527643i
$606$		0			0
$607$	15.9755	−	4.28061i	0.648424	−	0.173745i	0.0804079	−	0.996762i	$-0.474378\pi$
$607$	15.9755	−	4.28061i	0.648424	−	0.173745i	0.568016	+	0.823017i	$0.307711\pi$
$608$		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
$615$	25.4500	−	10.2621i	1.02624	−	0.413806i
$616$		0			0
$617$	−2.72427	−	10.1671i	−0.109675	−	0.409312i	0.889159	−	0.457599i	$-0.151290\pi$
$617$	−2.72427	−	10.1671i	−0.109675	−	0.409312i	−0.998834	+	0.0482869i	$0.984624\pi$
$618$		0			0
$619$	2.77044	−	1.59951i	0.111353	−	0.0642898i	−0.443289	−	0.896379i	$-0.646188\pi$
$619$	2.77044	−	1.59951i	0.111353	−	0.0642898i	0.554642	+	0.832089i	$0.312855\pi$
$620$		0			0
$621$	32.3139	−	4.02687i	1.29671	−	0.161593i
$622$		0			0
$623$	−1.06990	+	3.99290i	−0.0428644	+	0.159972i
$624$		0			0
$625$	23.2397	+	9.21498i	0.929588	+	0.368599i
$626$		0			0
$627$	−12.6340	−	0.580821i	−0.504554	−	0.0231958i
$628$		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
$633$	−19.1770	−	37.0472i	−0.762219	−	1.47249i
$634$		0			0
$635$	−6.88732	−	8.32750i	−0.273315	−	0.330467i
$636$		0			0
$637$	−3.08736	+	11.5222i	−0.122326	+	0.456525i
$638$		0			0
$639$	−15.4897	+	7.13612i	−0.612762	+	0.282300i
$640$		0			0
$641$	42.6583	−	24.6288i	1.68490	−	0.972778i	0.726582	−	0.687080i	$-0.241108\pi$
$641$	42.6583	−	24.6288i	1.68490	−	0.972778i	0.958320	−	0.285698i	$-0.0922254\pi$
$642$		0			0
$643$	5.25595	+	19.6155i	0.207274	+	0.773559i	0.988744	+	0.149616i	$0.0478036\pi$
$643$	5.25595	+	19.6155i	0.207274	+	0.773559i	−0.781470	+	0.623943i	$0.785530\pi$
$644$		0			0
$645$	29.1461	−	21.9317i	1.14763	−	0.863559i
$646$		0			0
$647$	−29.0632	+	29.0632i	−1.14259	+	1.14259i	−0.154619	+	0.987974i	$0.549415\pi$
$647$	−29.0632	+	29.0632i	−1.14259	+	1.14259i	−0.987974	+	0.154619i	$0.950585\pi$
$648$		0			0
$649$			5.31632i			0.208684i
$650$		0			0
$651$	−23.8029	+	5.21939i	−0.932911	+	0.204564i
$652$		0			0
$653$	2.75027	−	0.736931i	0.107626	−	0.0288384i	−0.204604	−	0.978845i	$-0.565591\pi$
$653$	2.75027	−	0.736931i	0.107626	−	0.0288384i	0.312230	+	0.950006i	$0.398924\pi$
$654$		0			0
$655$	−0.865495	−	0.615241i	−0.0338177	−	0.0240395i
$656$		0			0
$657$	−4.57416	−	1.68880i	−0.178455	−	0.0658865i
$658$		0			0
$659$	−18.8486	−	32.6467i	−0.734236	−	1.27173i	−0.955058	−	0.296420i	$-0.904207\pi$
$659$	−18.8486	−	32.6467i	−0.734236	−	1.27173i	0.220822	−	0.975314i	$-0.429126\pi$
$660$		0			0
$661$	3.68907	−	6.38966i	0.143488	−	0.248529i	−0.785320	−	0.619091i	$-0.787501\pi$
$661$	3.68907	−	6.38966i	0.143488	−	0.248529i	0.928808	+	0.370561i	$0.120835\pi$
$662$		0			0
$663$	−20.8654	+	10.8007i	−0.810345	+	0.419465i
$664$		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
$673$	−6.88414	−	1.84460i	−0.265364	−	0.0711041i	0.123684	−	0.992322i	$-0.460529\pi$
$673$	−6.88414	−	1.84460i	−0.265364	−	0.0711041i	−0.389048	+	0.921218i	$0.627196\pi$
$674$		0			0
$675$	24.6076	+	8.33458i	0.947148	+	0.320798i
$676$		0			0
$677$	8.09727	+	2.16966i	0.311203	+	0.0833867i	0.411040	−	0.911617i	$-0.365166\pi$
$677$	8.09727	+	2.16966i	0.311203	+	0.0833867i	−0.0998372	+	0.995004i	$0.531832\pi$
$678$		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	0.334488	−	0.942400i	$-0.391436\pi$
$683$	−15.8873	−	15.8873i	−0.607911	−	0.607911i	−0.942400	+	0.334488i	$0.891436\pi$
$684$		0			0
$685$	−20.6468	−	7.68149i	−0.788875	−	0.293494i
$686$		0			0
$687$	13.7506	−	7.11785i	0.524619	−	0.271563i
$688$		0			0
$689$	−20.2150	+	35.0134i	−0.770131	+	1.33391i
$690$		0			0
$691$	−9.16297	−	15.8707i	−0.348576	−	0.603751i	0.637421	−	0.770516i	$-0.280001\pi$
$691$	−9.16297	−	15.8707i	−0.348576	−	0.603751i	−0.985997	+	0.166765i	$0.946668\pi$
$692$		0			0
$693$	−9.16260	+	7.61656i	−0.348058	+	0.289329i
$694$		0			0
$695$	1.28018	+	0.910023i	0.0485600	+	0.0345191i
$696$		0			0
$697$	22.8296	−	6.11718i	0.864734	−	0.231705i
$698$		0			0
$699$	36.0312	−	7.90075i	1.36282	−	0.298834i
$700$		0			0
$701$		−	21.1738i		−	0.799724i	−0.916575	−	0.399862i	$-0.869058\pi$
$701$		−	21.1738i		−	0.799724i	0.916575	−	0.399862i	$-0.130942\pi$
$702$		0			0
$703$	−15.8197	+	15.8197i	−0.596652	+	0.596652i
$704$		0			0
$705$	−24.0141	+	18.0700i	−0.904424	+	0.680555i
$706$		0			0
$707$	2.46501	+	9.19953i	0.0927062	+	0.345984i
$708$		0			0
$709$	20.4846	−	11.8268i	0.769316	−	0.444165i	−0.0633143	−	0.997994i	$-0.520167\pi$
$709$	20.4846	−	11.8268i	0.769316	−	0.444165i	0.832631	+	0.553829i	$0.186834\pi$
$710$		0			0
$711$	−28.4356	−	20.1070i	−1.06642	−	0.754072i
$712$		0			0
$713$	−11.3163	+	42.2329i	−0.423798	+	1.58163i
$714$		0			0
$715$	−11.4135	−	13.8001i	−0.426840	−	0.516095i
$716$		0			0
$717$	−8.64273	−	16.6965i	−0.322769	−	0.623541i
$718$		0			0
$719$	21.3695			0.796947			0.398473	−	0.917180i	$-0.369540\pi$
$719$	21.3695			0.796947			0.398473	+	0.917180i	$0.369540\pi$
$720$		0			0
$721$	−8.07679			−0.300795
$722$		0			0
$723$	−40.3692	−	1.85589i	−1.50135	−	0.0690212i
$724$		0			0
$725$	−12.3190	−	35.4043i	−0.457514	−	1.31488i
$726$		0			0
$727$	0.796213	−	2.97151i	0.0295299	−	0.110207i	−0.949588	−	0.313501i	$-0.898498\pi$
$727$	0.796213	−	2.97151i	0.0295299	−	0.110207i	0.979118	+	0.203294i	$0.0651647\pi$
$728$		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
$733$	−6.30661	−	23.5366i	−0.232940	−	0.869343i	−0.979067	−	0.203540i	$-0.934755\pi$
$733$	−6.30661	−	23.5366i	−0.232940	−	0.869343i	0.746127	−	0.665804i	$-0.231911\pi$
$734$		0			0
$735$	10.5367	−	4.24867i	0.388653	−	0.156715i
$736$		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
$743$	15.1100	−	4.04871i	0.554332	−	0.148533i	0.0292311	−	0.999573i	$-0.490694\pi$
$743$	15.1100	−	4.04871i	0.554332	−	0.148533i	0.525101	+	0.851040i	$0.324027\pi$
$744$		0			0
$745$	−10.5097	+	14.7846i	−0.385046	+	0.541665i
$746$		0			0
$747$	−5.03761	+	0.864318i	−0.184317	+	0.0316237i
$748$		0			0
$749$	−7.70428	−	13.3442i	−0.281508	−	0.487586i
$750$		0			0
$751$	21.6240	−	37.4538i	0.789070	−	1.36671i	−0.137467	−	0.990506i	$-0.543896\pi$
$751$	21.6240	−	37.4538i	0.789070	−	1.36671i	0.926537	−	0.376203i	$-0.122771\pi$
$752$		0			0
$753$	−19.5254	−	12.5025i	−0.711544	−	0.455615i
$754$		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	−0.0239461	−	0.999713i	$-0.507623\pi$
$761$	−24.8744	−	14.3612i	−0.901696	−	0.520595i	−0.877750	+	0.479119i	$0.840956\pi$
$762$		0			0
$763$	−8.48016	−	2.27225i	−0.307002	−	0.0822611i
$764$		0			0
$765$	20.1684	+	9.69412i	0.729189	+	0.350492i
$766$		0			0
$767$	−10.6027	−	2.84099i	−0.382842	−	0.102582i
$768$		0			0
$769$	29.3558	+	16.9486i	1.05860	+	0.611180i	0.925043	−	0.379861i	$-0.124028\pi$
$769$	29.3558	+	16.9486i	1.05860	+	0.611180i	0.133552	+	0.991042i	$0.457362\pi$
$770$		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	$-0.972360\pi$
$773$	−30.1093	−	30.1093i	−1.08296	−	1.08296i	−0.0867231	−	0.996232i	$-0.527640\pi$
$774$		0			0
$775$	−22.8005	+	26.4010i	−0.819017	+	0.948351i
$776$		0			0
$777$	−0.967939	+	21.0546i	−0.0347246	+	0.755329i
$778$		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
$783$	−14.6587	−	36.0938i	−0.523858	−	1.28989i
$784$		0			0
$785$	−23.9323	+	4.04470i	−0.854181	+	0.144362i
$786$		0			0
$787$	10.2212	−	2.73876i	0.364346	−	0.0976263i	−0.0720011	−	0.997405i	$-0.522939\pi$
$787$	10.2212	−	2.73876i	0.364346	−	0.0976263i	0.436347	+	0.899778i	$0.356272\pi$
$788$		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
$795$	38.2226	−	4.66639i	1.35562	−	0.165500i
$796$		0			0
$797$	−3.52110	−	13.1409i	−0.124724	−	0.465476i	0.875106	−	0.483932i	$-0.160792\pi$
$797$	−3.52110	−	13.1409i	−0.124724	−	0.465476i	−0.999830	+	0.0184558i	$0.994125\pi$
$798$		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
$803$	0.828496	−	3.09199i	0.0292370	−	0.109114i
$804$		0			0
$805$	−2.66298	+	28.1331i	−0.0938577	+	0.991561i
$806$		0			0
$807$	−12.5816	+	19.6490i	−0.442895	+	0.691679i
$808$		0			0
$809$	−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	$-0.621378\pi$
$811$	−21.1960			−0.744294			−0.372147	+	0.928174i	$0.621378\pi$
$812$		0			0
$813$	19.0911	−	29.8150i	0.669555	−	1.04566i
$814$		0			0
$815$	23.5934	−	19.5131i	0.826440	−	0.683513i
$816$		0			0
$817$	−9.03736	+	33.7279i	−0.316177	+	1.17999i
$818$		0			0
$819$	−10.2938	−	22.3438i	−0.359696	−	0.780757i
$820$		0			0
$821$	−38.4941	+	22.2246i	−1.34345	+	0.775643i	−0.987313	−	0.158789i	$-0.949241\pi$
$821$	−38.4941	+	22.2246i	−1.34345	+	0.775643i	−0.356141	+	0.934432i	$0.615908\pi$
$822$		0			0
$823$	−6.59989	−	24.6311i	−0.230058	−	0.858588i	−0.980315	−	0.197441i	$-0.936737\pi$
$823$	−6.59989	−	24.6311i	−0.230058	−	0.858588i	0.750257	−	0.661146i	$-0.229930\pi$
$824$		0			0
$825$	−3.96633	+	16.5888i	−0.138090	+	0.577546i
$826$		0			0
$827$	10.7808	−	10.7808i	0.374885	−	0.374885i	−0.494368	−	0.869253i	$-0.664600\pi$
$827$	10.7808	−	10.7808i	0.374885	−	0.374885i	0.869253	+	0.494368i	$0.164600\pi$
$828$		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
$833$	9.45186	−	2.53262i	0.327488	−	0.0877500i
$834$		0			0
$835$	1.90408	+	11.2663i	0.0658934	+	0.389887i
$836$		0			0
$837$	−22.2675	+	28.6074i	−0.769677	+	0.988815i
$838$		0			0
$839$	−16.7880	−	29.0777i	−0.579588	−	1.00388i	−0.995527	−	0.0944825i	$-0.969880\pi$
$839$	−16.7880	−	29.0777i	−0.579588	−	1.00388i	0.415939	−	0.909393i	$-0.363453\pi$
$840$		0			0
$841$	−13.6044	+	23.5635i	−0.469118	+	0.812536i
$842$		0			0
$843$	−1.79494	+	39.0435i	−0.0618211	+	1.34473i
$844$		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
$853$	22.9734	+	6.15572i	0.786596	+	0.210768i	0.629691	−	0.776846i	$-0.283182\pi$
$853$	22.9734	+	6.15572i	0.786596	+	0.210768i	0.156905	+	0.987614i	$0.449848\pi$
$854$		0			0
$855$	−23.4691	+	8.23176i	−0.802625	+	0.281520i
$856$		0			0
$857$	11.4475	+	3.06736i	0.391040	+	0.104779i	0.448981	−	0.893541i	$-0.351787\pi$
$857$	11.4475	+	3.06736i	0.391040	+	0.104779i	−0.0579412	+	0.998320i	$0.518454\pi$
$858$		0			0
$859$	34.6670	+	20.0150i	1.18282	+	0.682904i	0.956666	−	0.291187i	$-0.0940501\pi$
$859$	34.6670	+	20.0150i	1.18282	+	0.682904i	0.226158	+	0.974091i	$0.427383\pi$
$860$		0			0
$861$	5.30058	+	24.1732i	0.180643	+	0.823819i
$862$		0			0
$863$	−1.78680	−	1.78680i	−0.0608233	−	0.0608233i	0.676041	−	0.736864i	$-0.263694\pi$
$863$	−1.78680	−	1.78680i	−0.0608233	−	0.0608233i	−0.736864	+	0.676041i	$0.763694\pi$
$864$		0			0
$865$	5.78150	−	15.5399i	0.196577	−	0.528373i
$866$		0			0
$867$	−8.56583	−	5.48486i	−0.290911	−	0.186276i
$868$		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
$873$	−29.7510	+	5.10446i	−1.00692	+	0.172760i
$874$		0			0
$875$	−11.6868	+	19.2806i	−0.395087	+	0.651803i
$876$		0			0
$877$	6.66309	−	1.78537i	0.224996	−	0.0602876i	−0.144559	−	0.989496i	$-0.546176\pi$
$877$	6.66309	−	1.78537i	0.224996	−	0.0602876i	0.369556	+	0.929208i	$0.379510\pi$
$878$		0			0
$879$	1.91844	−	6.03593i	0.0647075	−	0.203587i
$880$		0			0
$881$		−	3.01999i		−	0.101746i	−0.998705	−	0.0508731i	$-0.983800\pi$
$881$		−	3.01999i		−	0.101746i	0.998705	−	0.0508731i	$-0.0162004\pi$
$882$		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
$885$	3.90963	+	9.69591i	0.131421	+	0.325925i
$886$		0			0
$887$	4.61020	+	17.2055i	0.154796	+	0.577705i	0.999123	+	0.0418769i	$0.0133337\pi$
$887$	4.61020	+	17.2055i	0.154796	+	0.577705i	−0.844327	+	0.535828i	$0.820000\pi$
$888$		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
$893$	7.44607	−	27.7891i	0.249173	−	0.929928i
$894$		0			0
$895$	6.08679	+	0.576155i	0.203459	+	0.0192587i
$896$		0			0
$897$	−44.0934	−	2.02710i	−1.47224	−	0.0676828i
$898$		0			0
$899$	52.3064			1.74452
$900$		0			0
$901$	33.1655			1.10490
$902$		0			0
$903$	15.1221	+	29.2136i	0.503231	+	0.972169i
$904$		0			0
$905$	50.5509	+	4.78498i	1.68037	+	0.159058i
$906$		0			0
$907$	−0.324723	+	1.21188i	−0.0107822	+	0.0402399i	−0.971107	−	0.238643i	$-0.923297\pi$
$907$	−0.324723	+	1.21188i	−0.0107822	+	0.0402399i	0.960325	+	0.278883i	$0.0899641\pi$
$908$		0			0
$909$	11.5687	+	8.18027i	0.383708	+	0.271323i
$910$		0			0
$911$	23.3987	−	13.5092i	0.775232	−	0.447581i	−0.0595057	−	0.998228i	$-0.518952\pi$
$911$	23.3987	−	13.5092i	0.775232	−	0.447581i	0.834738	+	0.550647i	$0.185619\pi$
$912$		0			0
$913$	−0.868470	−	3.24117i	−0.0287422	−	0.107267i
$914$		0			0
$915$	−33.5443	−	4.73793i	−1.10894	−	0.156631i
$916$		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
$923$	22.3294	−	5.98314i	0.734981	−	0.196938i
$924$		0			0
$925$	16.9526	+	24.9588i	0.557399	+	0.820639i
$926$		0			0
$927$	−9.24002	+	7.68091i	−0.303482	+	0.252274i
$928$		0			0
$929$	13.9274	+	24.1230i	0.456944	+	0.791450i	0.998798	−	0.0490228i	$-0.0156107\pi$
$929$	13.9274	+	24.1230i	0.456944	+	0.791450i	−0.541854	+	0.840473i	$0.682277\pi$
$930$		0			0
$931$	−5.43786	+	9.41865i	−0.178219	+	0.308684i
$932$		0			0
$933$	−16.1352	+	8.35217i	−0.528241	+	0.273438i
$934$		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	0.886559	−	0.462616i	$-0.153089\pi$
$941$	28.5039	+	16.4567i	0.929201	+	0.536474i	0.0426420	+	0.999090i	$0.486423\pi$
$942$		0			0
$943$	42.8898	+	11.4923i	1.39668	+	0.374240i
$944$		0			0
$945$	−11.1095	+	20.6293i	−0.361393	+	0.671070i
$946$		0			0
$947$	−11.5072	−	3.08335i	−0.373934	−	0.100195i	0.0669572	−	0.997756i	$-0.478671\pi$
$947$	−11.5072	−	3.08335i	−0.373934	−	0.100195i	−0.440891	+	0.897560i	$0.645338\pi$
$948$		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	0.890802	−	0.454391i	$-0.150143\pi$
$953$	13.4723	+	13.4723i	0.436411	+	0.436411i	−0.454391	+	0.890802i	$0.650143\pi$
$954$		0			0
$955$	−2.60965	+	1.19439i	−0.0844463	+	0.0386495i
$956$		0			0
$957$	22.7126	−	11.7569i	0.734195	−	0.380047i
$958$		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
$963$	−21.5040	−	7.93938i	−0.692957	−	0.255843i
$964$		0			0
$965$	−2.03711	−	12.0534i	−0.0655768	−	0.388014i
$966$		0			0
$967$	−8.95826	+	2.40036i	−0.288078	+	0.0771904i	−0.399964	−	0.916531i	$-0.630978\pi$
$967$	−8.95826	+	2.40036i	−0.288078	+	0.0771904i	0.111886	+	0.993721i	$0.464311\pi$
$968$		0			0
$969$	−20.9241	+	4.58814i	−0.672179	+	0.147392i
$970$		0			0
$971$			24.7290i			0.793590i	0.917907	+	0.396795i	$0.129878\pi$
$971$			24.7290i			0.793590i	−0.917907	+	0.396795i	$0.870122\pi$
$972$		0			0
$973$	−1.00161	+	1.00161i	−0.0321102	+	0.0321102i
$974$		0			0
$975$	−30.9646	−	16.7752i	−0.991659	−	0.537236i
$976$		0			0
$977$	6.35548	+	23.7190i	0.203330	+	0.758837i	0.989952	+	0.141403i	$0.0451612\pi$
$977$	6.35548	+	23.7190i	0.203330	+	0.758837i	−0.786622	+	0.617434i	$0.788172\pi$
$978$		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
$983$	−10.7435	+	40.0954i	−0.342666	+	1.27885i	0.552650	+	0.833414i	$0.313617\pi$
$983$	−10.7435	+	40.0954i	−0.342666	+	1.27885i	−0.895316	+	0.445433i	$0.853050\pi$
$984$		0			0
$985$	29.3361	−	24.2626i	0.934726	−	0.773072i
$986$		0			0
$987$	−12.4594	−	24.0697i	−0.396588	−	0.766148i
$988$		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
$993$	44.6846	+	2.05428i	1.41802	+	0.0651906i
$994$		0			0
$995$	0.935226	−	9.88020i	0.0296487	−	0.313223i
$996$		0			0
$997$	3.09617	−	11.5550i	0.0980565	−	0.365952i	−0.899409	−	0.437109i	$-0.856002\pi$
$997$	3.09617	−	11.5550i	0.0980565	−	0.365952i	0.997465	+	0.0711569i	$0.0226691\pi$
$998$		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.257.2		16
4.3	odd	2		90.2.l.b.77.4	yes	16
5.3	odd	4	inner	720.2.cu.b.113.1		16
9.2	odd	6	inner	720.2.cu.b.497.1		16
12.11	even	2		270.2.m.b.17.2		16
20.3	even	4		90.2.l.b.23.4	✓	16
20.7	even	4		450.2.p.h.293.1		16
20.19	odd	2		450.2.p.h.257.1		16
36.7	odd	6		270.2.m.b.197.2		16
36.11	even	6		90.2.l.b.47.4	yes	16
36.23	even	6		810.2.f.c.647.7		16
36.31	odd	6		810.2.f.c.647.2		16
45.38	even	12	inner	720.2.cu.b.353.2		16
60.23	odd	4		270.2.m.b.233.2		16
60.47	odd	4		1350.2.q.h.1043.3		16
60.59	even	2		1350.2.q.h.557.4		16
180.7	even	12		1350.2.q.h.143.4		16
180.23	odd	12		810.2.f.c.323.2		16
180.43	even	12		270.2.m.b.143.2		16
180.47	odd	12		450.2.p.h.443.1		16
180.79	odd	6		1350.2.q.h.1007.3		16
180.83	odd	12		90.2.l.b.83.4	yes	16
180.103	even	12		810.2.f.c.323.7		16
180.119	even	6		450.2.p.h.407.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	20.3	even	4
90.2.l.b.47.4	yes	16	36.11	even	6
90.2.l.b.77.4	yes	16	4.3	odd	2
90.2.l.b.83.4	yes	16	180.83	odd	12
270.2.m.b.17.2		16	12.11	even	2
270.2.m.b.143.2		16	180.43	even	12
270.2.m.b.197.2		16	36.7	odd	6
270.2.m.b.233.2		16	60.23	odd	4
450.2.p.h.257.1		16	20.19	odd	2
450.2.p.h.293.1		16	20.7	even	4
450.2.p.h.407.1		16	180.119	even	6
450.2.p.h.443.1		16	180.47	odd	12
720.2.cu.b.113.1		16	5.3	odd	4	inner
720.2.cu.b.257.2		16	1.1	even	1	trivial
720.2.cu.b.353.2		16	45.38	even	12	inner
720.2.cu.b.497.1		16	9.2	odd	6	inner
810.2.f.c.323.2		16	180.23	odd	12
810.2.f.c.323.7		16	180.103	even	12
810.2.f.c.647.2		16	36.31	odd	6
810.2.f.c.647.7		16	36.23	even	6
1350.2.q.h.143.4		16	180.7	even	12
1350.2.q.h.557.4		16	60.59	even	2
1350.2.q.h.1007.3		16	180.79	odd	6
1350.2.q.h.1043.3		16	60.47	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.933998 + 1.45865i) q^{3} +(-2.22612 - 0.210717i) q^{5} +(0.521929 - 1.94786i) q^{7} +(-1.25529 - 2.72474i) q^{9} +O(q^{10})\)	\(q+(-0.933998 + 1.45865i) q^{3} +(-2.22612 - 0.210717i) q^{5} +(0.521929 - 1.94786i) q^{7} +(-1.25529 - 2.72474i) q^{9} +(1.70563 - 0.984748i) q^{11} +(1.05248 + 3.92790i) q^{13} +(2.38655 - 3.05031i) q^{15} +(2.35877 - 2.35877i) q^{17} +3.70753i q^{19} +(2.35376 + 2.58061i) q^{21} +(6.05338 - 1.62200i) q^{23} +(4.91120 + 0.938160i) q^{25} +(5.14688 + 0.713876i) q^{27} +(-3.74863 - 6.49281i) q^{29} +(-3.48837 + 6.04204i) q^{31} +(-0.156660 + 3.40767i) q^{33} +(-1.57232 + 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(-6.71243 - 2.13346i) q^{39} +(6.13601 + 3.54263i) q^{41} +(9.09714 + 2.43757i) q^{43} +(2.22028 + 6.33011i) q^{45} +(-7.49533 - 2.00837i) q^{47} +(2.54041 + 1.46671i) q^{49} +(1.23752 + 5.64369i) q^{51} +(7.03027 + 7.03027i) q^{53} +(-4.00444 + 1.83276i) q^{55} +(-5.40797 - 3.46282i) q^{57} +(-1.34967 + 2.33769i) q^{59} +(-4.37353 - 7.57518i) q^{61} +(-5.96261 + 1.02302i) q^{63} +(-1.51527 - 8.96575i) q^{65} +(8.18285 - 2.19259i) q^{67} +(-3.28793 + 10.3447i) q^{69} -5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} +(-5.95549 + 6.28746i) q^{75} +(-1.02794 - 3.83631i) q^{77} +(10.0535 - 5.80440i) q^{79} +(-5.84847 + 6.84072i) q^{81} +(0.440961 - 1.64569i) q^{83} +(-5.74792 + 4.75386i) q^{85} +(12.9719 + 0.596356i) q^{87} -2.04989 q^{89} +8.20034 q^{91} +(-5.55506 - 10.7315i) q^{93} +(0.781237 - 8.25339i) q^{95} +(2.60421 - 9.71905i) q^{97} +(-4.82426 - 3.41127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) 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

Groups

Database

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