LMFDB - Embedded newform 240.2.v.a.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(17,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))

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

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

chi := DirichletCharacter("240.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.v (of order $4$, degree $2$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	240.113
Dual form			240.2.v.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.41421i) q^{3} +(1.00000 - 2.00000i) q^{5} +(2.41421 - 2.41421i) q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.41421i) q^{3} +(1.00000 - 2.00000i) q^{5} +(2.41421 - 2.41421i) q^{7} +(-1.00000 - 2.82843i) q^{9} +0.828427i q^{11} +(3.82843 + 3.82843i) q^{13} +(1.82843 + 3.41421i) q^{15} +(1.82843 + 1.82843i) q^{17} -0.828427i q^{19} +(1.00000 + 5.82843i) q^{21} +(4.41421 - 4.41421i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(5.00000 + 1.41421i) q^{27} -3.65685 q^{29} -5.65685 q^{31} +(-1.17157 - 0.828427i) q^{33} +(-2.41421 - 7.24264i) q^{35} +(-5.82843 + 5.82843i) q^{37} +(-9.24264 + 1.58579i) q^{39} -5.65685i q^{41} +(0.414214 + 0.414214i) q^{43} +(-6.65685 - 0.828427i) q^{45} +(3.58579 + 3.58579i) q^{47} -4.65685i q^{49} +(-4.41421 + 0.757359i) q^{51} +(3.00000 - 3.00000i) q^{53} +(1.65685 + 0.828427i) q^{55} +(1.17157 + 0.828427i) q^{57} -4.00000 q^{59} +0.343146 q^{61} +(-9.24264 - 4.41421i) q^{63} +(11.4853 - 3.82843i) q^{65} +(-10.0711 + 10.0711i) q^{67} +(1.82843 + 10.6569i) q^{69} +10.4853i q^{71} +(-4.65685 - 4.65685i) q^{73} +(8.65685 - 0.242641i) q^{75} +(2.00000 + 2.00000i) q^{77} +0.828427i q^{79} +(-7.00000 + 5.65685i) q^{81} +(3.24264 - 3.24264i) q^{83} +(5.48528 - 1.82843i) q^{85} +(3.65685 - 5.17157i) q^{87} -15.6569 q^{89} +18.4853 q^{91} +(5.65685 - 8.00000i) q^{93} +(-1.65685 - 0.828427i) q^{95} +(1.00000 - 1.00000i) q^{97} +(2.34315 - 0.828427i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	$ 4 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{13} - 4 q^{15} - 4 q^{17} + 4 q^{21} + 12 q^{23} - 12 q^{25} + 20 q^{27} + 8 q^{29} - 16 q^{33} - 4 q^{35} - 12 q^{37} - 20 q^{39} - 4 q^{43} - 4 q^{45} + 20 q^{47} - 12 q^{51} + 12 q^{53} - 16 q^{55} + 16 q^{57} - 16 q^{59} + 24 q^{61} - 20 q^{63} + 12 q^{65} - 12 q^{67} - 4 q^{69} + 4 q^{73} + 12 q^{75} + 8 q^{77} - 28 q^{81} - 4 q^{83} - 12 q^{85} - 8 q^{87} - 40 q^{89} + 40 q^{91} + 16 q^{95} + 4 q^{97} + 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^13 - 4 * q^15 - 4 * q^17 + 4 * q^21 + 12 * q^23 - 12 * q^25 + 20 * q^27 + 8 * q^29 - 16 * q^33 - 4 * q^35 - 12 * q^37 - 20 * q^39 - 4 * q^43 - 4 * q^45 + 20 * q^47 - 12 * q^51 + 12 * q^53 - 16 * q^55 + 16 * q^57 - 16 * q^59 + 24 * q^61 - 20 * q^63 + 12 * q^65 - 12 * q^67 - 4 * q^69 + 4 * q^73 + 12 * q^75 + 8 * q^77 - 28 * q^81 - 4 * q^83 - 12 * q^85 - 8 * q^87 - 40 * q^89 + 40 * q^91 + 16 * q^95 + 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$3$	−1.00000	+	1.41421i	−0.577350	+	0.816497i
$4$		0			0
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$		0			0
$7$	2.41421	−	2.41421i	0.912487	−	0.912487i	−0.0839804	−	0.996467i	$-0.526763\pi$
$7$	2.41421	−	2.41421i	0.912487	−	0.912487i	0.996467	+	0.0839804i	$0.0267633\pi$
$8$		0			0
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$		0			0
$11$			0.828427i			0.249780i	0.992171	+	0.124890i	$0.0398578\pi$
$11$			0.828427i			0.249780i	−0.992171	+	0.124890i	$0.960142\pi$
$12$		0			0
$13$	3.82843	+	3.82843i	1.06181	+	1.06181i	0.997959	+	0.0638555i	$0.0203397\pi$
$13$	3.82843	+	3.82843i	1.06181	+	1.06181i	0.0638555	+	0.997959i	$0.479660\pi$
$14$		0			0
$15$	1.82843	+	3.41421i	0.472098	+	0.881546i
$16$		0			0
$17$	1.82843	+	1.82843i	0.443459	+	0.443459i	0.893173	−	0.449714i	$-0.148474\pi$
$17$	1.82843	+	1.82843i	0.443459	+	0.443459i	−0.449714	+	0.893173i	$0.648474\pi$
$18$		0			0
$19$		−	0.828427i		−	0.190054i	−0.995475	−	0.0950271i	$-0.969706\pi$
$19$		−	0.828427i		−	0.190054i	0.995475	−	0.0950271i	$-0.0302938\pi$
$20$		0			0
$21$	1.00000	+	5.82843i	0.218218	+	1.27187i
$22$		0			0
$23$	4.41421	−	4.41421i	0.920427	−	0.920427i	−0.0766323	−	0.997059i	$-0.524417\pi$
$23$	4.41421	−	4.41421i	0.920427	−	0.920427i	0.997059	+	0.0766323i	$0.0244167\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$		0			0
$29$	−3.65685			−0.679061			−0.339530	−	0.940595i	$-0.610268\pi$
$29$	−3.65685			−0.679061			−0.339530	+	0.940595i	$0.610268\pi$
$30$		0			0
$31$	−5.65685			−1.01600			−0.508001	−	0.861357i	$-0.669615\pi$
$31$	−5.65685			−1.01600			−0.508001	+	0.861357i	$0.669615\pi$
$32$		0			0
$33$	−1.17157	−	0.828427i	−0.203945	−	0.144211i
$34$		0			0
$35$	−2.41421	−	7.24264i	−0.408077	−	1.22423i
$36$		0			0
$37$	−5.82843	+	5.82843i	−0.958188	+	0.958188i	−0.999160	−	0.0409727i	$-0.986954\pi$
$37$	−5.82843	+	5.82843i	−0.958188	+	0.958188i	0.0409727	+	0.999160i	$0.486954\pi$
$38$		0			0
$39$	−9.24264	+	1.58579i	−1.48001	+	0.253929i
$40$		0			0
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$		0			0
$43$	0.414214	+	0.414214i	0.0631670	+	0.0631670i	0.737985	−	0.674818i	$-0.235778\pi$
$43$	0.414214	+	0.414214i	0.0631670	+	0.0631670i	−0.674818	+	0.737985i	$0.735778\pi$
$44$		0			0
$45$	−6.65685	−	0.828427i	−0.992345	−	0.123495i
$46$		0			0
$47$	3.58579	+	3.58579i	0.523041	+	0.523041i	0.918488	−	0.395448i	$-0.129411\pi$
$47$	3.58579	+	3.58579i	0.523041	+	0.523041i	−0.395448	+	0.918488i	$0.629411\pi$
$48$		0			0
$49$		−	4.65685i		−	0.665265i
$50$		0			0
$51$	−4.41421	+	0.757359i	−0.618114	+	0.106052i
$52$		0			0
$53$	3.00000	−	3.00000i	0.412082	−	0.412082i	−0.470381	−	0.882463i	$-0.655884\pi$
$53$	3.00000	−	3.00000i	0.412082	−	0.412082i	0.882463	+	0.470381i	$0.155884\pi$
$54$		0			0
$55$	1.65685	+	0.828427i	0.223410	+	0.111705i
$56$		0			0
$57$	1.17157	+	0.828427i	0.155179	+	0.109728i
$58$		0			0
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		0			0
$61$	0.343146			0.0439353			0.0219677	−	0.999759i	$-0.493007\pi$
$61$	0.343146			0.0439353			0.0219677	+	0.999759i	$0.493007\pi$
$62$		0			0
$63$	−9.24264	−	4.41421i	−1.16446	−	0.556139i
$64$		0			0
$65$	11.4853	−	3.82843i	1.42457	−	0.474858i
$66$		0			0
$67$	−10.0711	+	10.0711i	−1.23038	+	1.23038i	−0.266558	+	0.963819i	$0.585886\pi$
$67$	−10.0711	+	10.0711i	−1.23038	+	1.23038i	−0.963819	+	0.266558i	$0.914114\pi$
$68$		0			0
$69$	1.82843	+	10.6569i	0.220117	+	1.28293i
$70$		0			0
$71$			10.4853i			1.24437i	0.782869	+	0.622187i	$0.213756\pi$
$71$			10.4853i			1.24437i	−0.782869	+	0.622187i	$0.786244\pi$
$72$		0			0
$73$	−4.65685	−	4.65685i	−0.545044	−	0.545044i	0.379960	−	0.925003i	$-0.375938\pi$
$73$	−4.65685	−	4.65685i	−0.545044	−	0.545044i	−0.925003	+	0.379960i	$0.875938\pi$
$74$		0			0
$75$	8.65685	−	0.242641i	0.999607	−	0.0280177i
$76$		0			0
$77$	2.00000	+	2.00000i	0.227921	+	0.227921i
$78$		0			0
$79$			0.828427i			0.0932053i	0.998914	+	0.0466027i	$0.0148395\pi$
$79$			0.828427i			0.0932053i	−0.998914	+	0.0466027i	$0.985161\pi$
$80$		0			0
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$		0			0
$83$	3.24264	−	3.24264i	0.355926	−	0.355926i	−0.506383	−	0.862309i	$-0.669018\pi$
$83$	3.24264	−	3.24264i	0.355926	−	0.355926i	0.862309	+	0.506383i	$0.169018\pi$
$84$		0			0
$85$	5.48528	−	1.82843i	0.594962	−	0.198321i
$86$		0			0
$87$	3.65685	−	5.17157i	0.392056	−	0.554451i
$88$		0			0
$89$	−15.6569			−1.65962			−0.829812	−	0.558044i	$-0.811552\pi$
$89$	−15.6569			−1.65962			−0.829812	+	0.558044i	$0.811552\pi$
$90$		0			0
$91$	18.4853			1.93778
$92$		0			0
$93$	5.65685	−	8.00000i	0.586588	−	0.829561i
$94$		0			0
$95$	−1.65685	−	0.828427i	−0.169990	−	0.0849948i
$96$		0			0
$97$	1.00000	−	1.00000i	0.101535	−	0.101535i	−0.654515	−	0.756049i	$-0.727127\pi$
$97$	1.00000	−	1.00000i	0.101535	−	0.101535i	0.756049	+	0.654515i	$0.227127\pi$
$98$		0			0
$99$	2.34315	−	0.828427i	0.235495	−	0.0832601i
$100$		0			0
$101$			9.65685i			0.960893i	0.877024	+	0.480446i	$0.159525\pi$
$101$			9.65685i			0.960893i	−0.877024	+	0.480446i	$0.840475\pi$
$102$		0			0
$103$	5.58579	+	5.58579i	0.550384	+	0.550384i	0.926552	−	0.376168i	$-0.122758\pi$
$103$	5.58579	+	5.58579i	0.550384	+	0.550384i	−0.376168	+	0.926552i	$0.622758\pi$
$104$		0			0
$105$	12.6569	+	3.82843i	1.23518	+	0.373616i
$106$		0			0
$107$	−9.58579	−	9.58579i	−0.926693	−	0.926693i	0.0707977	−	0.997491i	$-0.477446\pi$
$107$	−9.58579	−	9.58579i	−0.926693	−	0.926693i	−0.997491	+	0.0707977i	$0.977446\pi$
$108$		0			0
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$	−2.41421	−	14.0711i	−0.229147	−	1.33557i
$112$		0			0
$113$	−9.48528	+	9.48528i	−0.892300	+	0.892300i	−0.994739	−	0.102439i	$-0.967335\pi$
$113$	−9.48528	+	9.48528i	−0.892300	+	0.892300i	0.102439	+	0.994739i	$0.467335\pi$
$114$		0			0
$115$	−4.41421	−	13.2426i	−0.411628	−	1.23488i
$116$		0			0
$117$	7.00000	−	14.6569i	0.647150	−	1.35503i
$118$		0			0
$119$	8.82843			0.809301
$120$		0			0
$121$	10.3137			0.937610
$122$		0			0
$123$	8.00000	+	5.65685i	0.721336	+	0.510061i
$124$		0			0
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$		0			0
$127$	−5.58579	+	5.58579i	−0.495658	+	0.495658i	−0.910083	−	0.414425i	$-0.863983\pi$
$127$	−5.58579	+	5.58579i	−0.495658	+	0.495658i	0.414425	+	0.910083i	$0.363983\pi$
$128$		0			0
$129$	−1.00000	+	0.171573i	−0.0880451	+	0.0151061i
$130$		0			0
$131$			8.82843i			0.771343i	0.922636	+	0.385672i	$0.126030\pi$
$131$			8.82843i			0.771343i	−0.922636	+	0.385672i	$0.873970\pi$
$132$		0			0
$133$	−2.00000	−	2.00000i	−0.173422	−	0.173422i
$134$		0			0
$135$	7.82843	−	8.58579i	0.673764	−	0.738947i
$136$		0			0
$137$	9.82843	+	9.82843i	0.839699	+	0.839699i	0.988819	−	0.149120i	$-0.0476440\pi$
$137$	9.82843	+	9.82843i	0.839699	+	0.839699i	−0.149120	+	0.988819i	$0.547644\pi$
$138$		0			0
$139$		−	8.82843i		−	0.748817i	−0.927264	−	0.374409i	$-0.877846\pi$
$139$		−	8.82843i		−	0.748817i	0.927264	−	0.374409i	$-0.122154\pi$
$140$		0			0
$141$	−8.65685	+	1.48528i	−0.729039	+	0.125083i
$142$		0			0
$143$	−3.17157	+	3.17157i	−0.265220	+	0.265220i
$144$		0			0
$145$	−3.65685	+	7.31371i	−0.303685	+	0.607370i
$146$		0			0
$147$	6.58579	+	4.65685i	0.543187	+	0.384091i
$148$		0			0
$149$	13.3137			1.09070			0.545351	−	0.838208i	$-0.316396\pi$
$149$	13.3137			1.09070			0.545351	+	0.838208i	$0.316396\pi$
$150$		0			0
$151$	13.6569			1.11138			0.555690	−	0.831390i	$-0.312454\pi$
$151$	13.6569			1.11138			0.555690	+	0.831390i	$0.312454\pi$
$152$		0			0
$153$	3.34315	−	7.00000i	0.270277	−	0.565916i
$154$		0			0
$155$	−5.65685	+	11.3137i	−0.454369	+	0.908739i
$156$		0			0
$157$	5.48528	−	5.48528i	0.437773	−	0.437773i	−0.453489	−	0.891262i	$-0.649821\pi$
$157$	5.48528	−	5.48528i	0.437773	−	0.437773i	0.891262	+	0.453489i	$0.149821\pi$
$158$		0			0
$159$	1.24264	+	7.24264i	0.0985478	+	0.574379i
$160$		0			0
$161$		−	21.3137i		−	1.67976i
$162$		0			0
$163$	0.414214	+	0.414214i	0.0324437	+	0.0324437i	0.723143	−	0.690699i	$-0.242697\pi$
$163$	0.414214	+	0.414214i	0.0324437	+	0.0324437i	−0.690699	+	0.723143i	$0.742697\pi$
$164$		0			0
$165$	−2.82843	+	1.51472i	−0.220193	+	0.117921i
$166$		0			0
$167$	9.24264	+	9.24264i	0.715217	+	0.715217i	0.967622	−	0.252405i	$-0.0812214\pi$
$167$	9.24264	+	9.24264i	0.715217	+	0.715217i	−0.252405	+	0.967622i	$0.581221\pi$
$168$		0			0
$169$			16.3137i			1.25490i
$170$		0			0
$171$	−2.34315	+	0.828427i	−0.179185	+	0.0633514i
$172$		0			0
$173$	0.656854	−	0.656854i	0.0499397	−	0.0499397i	−0.681696	−	0.731636i	$-0.738757\pi$
$173$	0.656854	−	0.656854i	0.0499397	−	0.0499397i	0.731636	+	0.681696i	$0.238757\pi$
$174$		0			0
$175$	−16.8995	−	2.41421i	−1.27748	−	0.182497i
$176$		0			0
$177$	4.00000	−	5.65685i	0.300658	−	0.425195i
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−5.31371			−0.394965			−0.197482	−	0.980306i	$-0.563277\pi$
$181$	−5.31371			−0.394965			−0.197482	+	0.980306i	$0.563277\pi$
$182$		0			0
$183$	−0.343146	+	0.485281i	−0.0253661	+	0.0358730i
$184$		0			0
$185$	5.82843	+	17.4853i	0.428514	+	1.28554i
$186$		0			0
$187$	−1.51472	+	1.51472i	−0.110767	+	0.110767i
$188$		0			0
$189$	15.4853	−	8.65685i	1.12639	−	0.629693i
$190$		0			0
$191$		−	4.14214i		−	0.299714i	−0.988708	−	0.149857i	$-0.952119\pi$
$191$		−	4.14214i		−	0.299714i	0.988708	−	0.149857i	$-0.0478814\pi$
$192$		0			0
$193$	14.6569	+	14.6569i	1.05502	+	1.05502i	0.998395	+	0.0566281i	$0.0180349\pi$
$193$	14.6569	+	14.6569i	1.05502	+	1.05502i	0.0566281	+	0.998395i	$0.481965\pi$
$194$		0			0
$195$	−6.07107	+	20.0711i	−0.434758	+	1.43732i
$196$		0			0
$197$	−14.6569	−	14.6569i	−1.04426	−	1.04426i	−0.998974	−	0.0452834i	$-0.985581\pi$
$197$	−14.6569	−	14.6569i	−1.04426	−	1.04426i	−0.0452834	−	0.998974i	$-0.514419\pi$
$198$		0			0
$199$		−	18.4853i		−	1.31039i	−0.755461	−	0.655193i	$-0.772587\pi$
$199$		−	18.4853i		−	1.31039i	0.755461	−	0.655193i	$-0.227413\pi$
$200$		0			0
$201$	−4.17157	−	24.3137i	−0.294240	−	1.71496i
$202$		0			0
$203$	−8.82843	+	8.82843i	−0.619634	+	0.619634i
$204$		0			0
$205$	−11.3137	−	5.65685i	−0.790184	−	0.395092i
$206$		0			0
$207$	−16.8995	−	8.07107i	−1.17460	−	0.560978i
$208$		0			0
$209$	0.686292			0.0474718
$210$		0			0
$211$	−20.9706			−1.44367			−0.721837	−	0.692064i	$-0.756702\pi$
$211$	−20.9706			−1.44367			−0.721837	+	0.692064i	$0.756702\pi$
$212$		0			0
$213$	−14.8284	−	10.4853i	−1.01603	−	0.718440i
$214$		0			0
$215$	1.24264	−	0.414214i	0.0847474	−	0.0282491i
$216$		0			0
$217$	−13.6569	+	13.6569i	−0.927088	+	0.927088i
$218$		0			0
$219$	11.2426	−	1.92893i	0.759707	−	0.130345i
$220$		0			0
$221$			14.0000i			0.941742i
$222$		0			0
$223$	5.58579	+	5.58579i	0.374052	+	0.374052i	0.868951	−	0.494899i	$-0.164795\pi$
$223$	5.58579	+	5.58579i	0.374052	+	0.374052i	−0.494899	+	0.868951i	$0.664795\pi$
$224$		0			0
$225$	−8.31371	+	12.4853i	−0.554247	+	0.832352i
$226$		0			0
$227$	−4.89949	−	4.89949i	−0.325191	−	0.325191i	0.525563	−	0.850754i	$-0.323855\pi$
$227$	−4.89949	−	4.89949i	−0.325191	−	0.325191i	−0.850754	+	0.525563i	$0.823855\pi$
$228$		0			0
$229$		−	14.3431i		−	0.947822i	−0.880573	−	0.473911i	$-0.842842\pi$
$229$		−	14.3431i		−	0.947822i	0.880573	−	0.473911i	$-0.157158\pi$
$230$		0			0
$231$	−4.82843	+	0.828427i	−0.317687	+	0.0545065i
$232$		0			0
$233$	−11.8284	+	11.8284i	−0.774906	+	0.774906i	−0.978960	−	0.204054i	$-0.934588\pi$
$233$	−11.8284	+	11.8284i	−0.774906	+	0.774906i	0.204054	+	0.978960i	$0.434588\pi$
$234$		0			0
$235$	10.7574	−	3.58579i	0.701733	−	0.233911i
$236$		0			0
$237$	−1.17157	−	0.828427i	−0.0761018	−	0.0538121i
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−0.343146			−0.0221040			−0.0110520	−	0.999939i	$-0.503518\pi$
$241$	−0.343146			−0.0221040			−0.0110520	+	0.999939i	$0.503518\pi$
$242$		0			0
$243$	−1.00000	−	15.5563i	−0.0641500	−	0.997940i
$244$		0			0
$245$	−9.31371	−	4.65685i	−0.595031	−	0.297516i
$246$		0			0
$247$	3.17157	−	3.17157i	0.201802	−	0.201802i
$248$		0			0
$249$	1.34315	+	7.82843i	0.0851184	+	0.496106i
$250$		0			0
$251$		−	26.4853i		−	1.67174i	−0.548930	−	0.835868i	$-0.684965\pi$
$251$		−	26.4853i		−	1.67174i	0.548930	−	0.835868i	$-0.315035\pi$
$252$		0			0
$253$	3.65685	+	3.65685i	0.229904	+	0.229904i
$254$		0			0
$255$	−2.89949	+	9.58579i	−0.181573	+	0.600285i
$256$		0			0
$257$	−9.48528	−	9.48528i	−0.591676	−	0.591676i	0.346408	−	0.938084i	$-0.387401\pi$
$257$	−9.48528	−	9.48528i	−0.591676	−	0.591676i	−0.938084	+	0.346408i	$0.887401\pi$
$258$		0			0
$259$			28.1421i			1.74867i
$260$		0			0
$261$	3.65685	+	10.3431i	0.226354	+	0.640225i
$262$		0			0
$263$	−6.89949	+	6.89949i	−0.425441	+	0.425441i	−0.887072	−	0.461631i	$-0.847264\pi$
$263$	−6.89949	+	6.89949i	−0.425441	+	0.425441i	0.461631	+	0.887072i	$0.347264\pi$
$264$		0			0
$265$	−3.00000	−	9.00000i	−0.184289	−	0.552866i
$266$		0			0
$267$	15.6569	−	22.1421i	0.958184	−	1.35508i
$268$		0			0
$269$	16.6274			1.01379			0.506896	−	0.862007i	$-0.330793\pi$
$269$	16.6274			1.01379			0.506896	+	0.862007i	$0.330793\pi$
$270$		0			0
$271$	−10.3431			−0.628301			−0.314151	−	0.949373i	$-0.601720\pi$
$271$	−10.3431			−0.628301			−0.314151	+	0.949373i	$0.601720\pi$
$272$		0			0
$273$	−18.4853	+	26.1421i	−1.11878	+	1.58219i
$274$		0			0
$275$	3.31371	−	2.48528i	0.199824	−	0.149868i
$276$		0			0
$277$	−8.17157	+	8.17157i	−0.490982	+	0.490982i	−0.908616	−	0.417633i	$-0.862860\pi$
$277$	−8.17157	+	8.17157i	−0.490982	+	0.490982i	0.417633	+	0.908616i	$0.362860\pi$
$278$		0			0
$279$	5.65685	+	16.0000i	0.338667	+	0.957895i
$280$		0			0
$281$			5.65685i			0.337460i	0.985662	+	0.168730i	$0.0539665\pi$
$281$			5.65685i			0.337460i	−0.985662	+	0.168730i	$0.946033\pi$
$282$		0			0
$283$	−5.24264	−	5.24264i	−0.311643	−	0.311643i	0.533903	−	0.845546i	$-0.320725\pi$
$283$	−5.24264	−	5.24264i	−0.311643	−	0.311643i	−0.845546	+	0.533903i	$0.820725\pi$
$284$		0			0
$285$	2.82843	−	1.51472i	0.167542	−	0.0897242i
$286$		0			0
$287$	−13.6569	−	13.6569i	−0.806139	−	0.806139i
$288$		0			0
$289$		−	10.3137i		−	0.606689i
$290$		0			0
$291$	0.414214	+	2.41421i	0.0242816	+	0.141524i
$292$		0			0
$293$	16.6569	−	16.6569i	0.973104	−	0.973104i	−0.0265438	−	0.999648i	$-0.508450\pi$
$293$	16.6569	−	16.6569i	0.973104	−	0.973104i	0.999648	+	0.0265438i	$0.00845016\pi$
$294$		0			0
$295$	−4.00000	+	8.00000i	−0.232889	+	0.465778i
$296$		0			0
$297$	−1.17157	+	4.14214i	−0.0679816	+	0.240351i
$298$		0			0
$299$	33.7990			1.95465
$300$		0			0
$301$	2.00000			0.115278
$302$		0			0
$303$	−13.6569	−	9.65685i	−0.784566	−	0.554772i
$304$		0			0
$305$	0.343146	−	0.686292i	0.0196485	−	0.0392969i
$306$		0			0
$307$	6.89949	−	6.89949i	0.393775	−	0.393775i	−0.482256	−	0.876031i	$-0.660182\pi$
$307$	6.89949	−	6.89949i	0.393775	−	0.393775i	0.876031	+	0.482256i	$0.160182\pi$
$308$		0			0
$309$	−13.4853	+	2.31371i	−0.767151	+	0.131622i
$310$		0			0
$311$		−	5.51472i		−	0.312711i	−0.987701	−	0.156356i	$-0.950025\pi$
$311$		−	5.51472i		−	0.312711i	0.987701	−	0.156356i	$-0.0499746\pi$
$312$		0			0
$313$	−2.31371	−	2.31371i	−0.130779	−	0.130779i	0.638688	−	0.769466i	$-0.279478\pi$
$313$	−2.31371	−	2.31371i	−0.130779	−	0.130779i	−0.769466	+	0.638688i	$0.779478\pi$
$314$		0			0
$315$	−18.0711	+	14.0711i	−1.01819	+	0.792815i
$316$		0			0
$317$	4.65685	+	4.65685i	0.261555	+	0.261555i	0.825686	−	0.564131i	$-0.190789\pi$
$317$	4.65685	+	4.65685i	0.261555	+	0.261555i	−0.564131	+	0.825686i	$0.690789\pi$
$318$		0			0
$319$		−	3.02944i		−	0.169616i
$320$		0			0
$321$	23.1421	−	3.97056i	1.29167	−	0.221615i
$322$		0			0
$323$	1.51472	−	1.51472i	0.0842812	−	0.0842812i
$324$		0			0
$325$	3.82843	−	26.7990i	0.212363	−	1.48654i
$326$		0			0
$327$	5.65685	+	4.00000i	0.312825	+	0.221201i
$328$		0			0
$329$	17.3137			0.954536
$330$		0			0
$331$	9.65685			0.530789			0.265394	−	0.964140i	$-0.414498\pi$
$331$	9.65685			0.530789			0.265394	+	0.964140i	$0.414498\pi$
$332$		0			0
$333$	22.3137	+	10.6569i	1.22278	+	0.583992i
$334$		0			0
$335$	10.0711	+	30.2132i	0.550241	+	1.65072i
$336$		0			0
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	−0.679345	−	0.733819i	$-0.737736\pi$
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	0.733819	+	0.679345i	$0.237736\pi$
$338$		0			0
$339$	−3.92893	−	22.8995i	−0.213390	−	1.24373i
$340$		0			0
$341$		−	4.68629i		−	0.253777i
$342$		0			0
$343$	5.65685	+	5.65685i	0.305441	+	0.305441i
$344$		0			0
$345$	23.1421	+	7.00000i	1.24593	+	0.376867i
$346$		0			0
$347$	12.0711	+	12.0711i	0.648009	+	0.648009i	0.952511	−	0.304503i	$-0.0984902\pi$
$347$	12.0711	+	12.0711i	0.648009	+	0.648009i	−0.304503	+	0.952511i	$0.598490\pi$
$348$		0			0
$349$			9.65685i			0.516920i	0.966022	+	0.258460i	$0.0832149\pi$
$349$			9.65685i			0.516920i	−0.966022	+	0.258460i	$0.916785\pi$
$350$		0			0
$351$	13.7279	+	24.5563i	0.732742	+	1.31072i
$352$		0			0
$353$	15.4853	−	15.4853i	0.824198	−	0.824198i	−0.162509	−	0.986707i	$-0.551959\pi$
$353$	15.4853	−	15.4853i	0.824198	−	0.824198i	0.986707	+	0.162509i	$0.0519586\pi$
$354$		0			0
$355$	20.9706	+	10.4853i	1.11300	+	0.556501i
$356$		0			0
$357$	−8.82843	+	12.4853i	−0.467250	+	0.660791i
$358$		0			0
$359$	−35.3137			−1.86379			−0.931893	−	0.362733i	$-0.881844\pi$
$359$	−35.3137			−1.86379			−0.931893	+	0.362733i	$0.881844\pi$
$360$		0			0
$361$	18.3137			0.963879
$362$		0			0
$363$	−10.3137	+	14.5858i	−0.541329	+	0.765555i
$364$		0			0
$365$	−13.9706	+	4.65685i	−0.731253	+	0.243751i
$366$		0			0
$367$	4.75736	−	4.75736i	0.248332	−	0.248332i	−0.571954	−	0.820286i	$-0.693814\pi$
$367$	4.75736	−	4.75736i	0.248332	−	0.248332i	0.820286	+	0.571954i	$0.193814\pi$
$368$		0			0
$369$	−16.0000	+	5.65685i	−0.832927	+	0.294484i
$370$		0			0
$371$		−	14.4853i		−	0.752038i
$372$		0			0
$373$	0.514719	+	0.514719i	0.0266511	+	0.0266511i	0.720307	−	0.693656i	$-0.244001\pi$
$373$	0.514719	+	0.514719i	0.0266511	+	0.0266511i	−0.693656	+	0.720307i	$0.744001\pi$
$374$		0			0
$375$	8.17157	−	17.5563i	0.421978	−	0.906606i
$376$		0			0
$377$	−14.0000	−	14.0000i	−0.721037	−	0.721037i
$378$		0			0
$379$			29.7990i			1.53067i	0.643631	+	0.765336i	$0.277427\pi$
$379$			29.7990i			1.53067i	−0.643631	+	0.765336i	$0.722573\pi$
$380$		0			0
$381$	−2.31371	−	13.4853i	−0.118535	−	0.690872i
$382$		0			0
$383$	12.4142	−	12.4142i	0.634337	−	0.634337i	−0.314816	−	0.949153i	$-0.601943\pi$
$383$	12.4142	−	12.4142i	0.634337	−	0.634337i	0.949153	+	0.314816i	$0.101943\pi$
$384$		0			0
$385$	6.00000	−	2.00000i	0.305788	−	0.101929i
$386$		0			0
$387$	0.757359	−	1.58579i	0.0384987	−	0.0806101i
$388$		0			0
$389$	6.68629			0.339008			0.169504	−	0.985529i	$-0.445783\pi$
$389$	6.68629			0.339008			0.169504	+	0.985529i	$0.445783\pi$
$390$		0			0
$391$	16.1421			0.816343
$392$		0			0
$393$	−12.4853	−	8.82843i	−0.629799	−	0.445335i
$394$		0			0
$395$	1.65685	+	0.828427i	0.0833654	+	0.0416827i
$396$		0			0
$397$	7.82843	−	7.82843i	0.392897	−	0.392897i	−0.482821	−	0.875719i	$-0.660388\pi$
$397$	7.82843	−	7.82843i	0.392897	−	0.392897i	0.875719	+	0.482821i	$0.160388\pi$
$398$		0			0
$399$	4.82843	−	0.828427i	0.241724	−	0.0414732i
$400$		0			0
$401$		−	16.0000i		−	0.799002i	−0.916733	−	0.399501i	$-0.869183\pi$
$401$		−	16.0000i		−	0.799002i	0.916733	−	0.399501i	$-0.130817\pi$
$402$		0			0
$403$	−21.6569	−	21.6569i	−1.07880	−	1.07880i
$404$		0			0
$405$	4.31371	+	19.6569i	0.214350	+	0.976757i
$406$		0			0
$407$	−4.82843	−	4.82843i	−0.239336	−	0.239336i
$408$		0			0
$409$		−	21.6569i		−	1.07086i	−0.844579	−	0.535431i	$-0.820149\pi$
$409$		−	21.6569i		−	1.07086i	0.844579	−	0.535431i	$-0.179851\pi$
$410$		0			0
$411$	−23.7279	+	4.07107i	−1.17041	+	0.200811i
$412$		0			0
$413$	−9.65685	+	9.65685i	−0.475183	+	0.475183i
$414$		0			0
$415$	−3.24264	−	9.72792i	−0.159175	−	0.477525i
$416$		0			0
$417$	12.4853	+	8.82843i	0.611407	+	0.432330i
$418$		0			0
$419$	−29.9411			−1.46272			−0.731360	−	0.681992i	$-0.761114\pi$
$419$	−29.9411			−1.46272			−0.731360	+	0.681992i	$0.761114\pi$
$420$		0			0
$421$	30.9706			1.50941			0.754706	−	0.656063i	$-0.227779\pi$
$421$	30.9706			1.50941			0.754706	+	0.656063i	$0.227779\pi$
$422$		0			0
$423$	6.55635	−	13.7279i	0.318781	−	0.667474i
$424$		0			0
$425$	1.82843	−	12.7990i	0.0886917	−	0.620842i
$426$		0			0
$427$	0.828427	−	0.828427i	0.0400904	−	0.0400904i
$428$		0			0
$429$	−1.31371	−	7.65685i	−0.0634264	−	0.369676i
$430$		0			0
$431$		−	20.1421i		−	0.970213i	−0.874455	−	0.485106i	$-0.838781\pi$
$431$		−	20.1421i		−	0.970213i	0.874455	−	0.485106i	$-0.161219\pi$
$432$		0			0
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	0.247925	−	0.968779i	$-0.420251\pi$
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	−0.968779	+	0.247925i	$0.920251\pi$
$434$		0			0
$435$	−6.68629	−	12.4853i	−0.320583	−	0.598623i
$436$		0			0
$437$	−3.65685	−	3.65685i	−0.174931	−	0.174931i
$438$		0			0
$439$		−	13.7990i		−	0.658590i	−0.944227	−	0.329295i	$-0.893189\pi$
$439$		−	13.7990i		−	0.658590i	0.944227	−	0.329295i	$-0.106811\pi$
$440$		0			0
$441$	−13.1716	+	4.65685i	−0.627218	+	0.221755i
$442$		0			0
$443$	−0.0710678	+	0.0710678i	−0.00337653	+	0.00337653i	−0.708793	−	0.705416i	$-0.750760\pi$
$443$	−0.0710678	+	0.0710678i	−0.00337653	+	0.00337653i	0.705416	+	0.708793i	$0.250760\pi$
$444$		0			0
$445$	−15.6569	+	31.3137i	−0.742206	+	1.48441i
$446$		0			0
$447$	−13.3137	+	18.8284i	−0.629717	+	0.890554i
$448$		0			0
$449$	1.31371			0.0619977			0.0309989	−	0.999519i	$-0.490131\pi$
$449$	1.31371			0.0619977			0.0309989	+	0.999519i	$0.490131\pi$
$450$		0			0
$451$	4.68629			0.220669
$452$		0			0
$453$	−13.6569	+	19.3137i	−0.641655	+	0.907437i
$454$		0			0
$455$	18.4853	−	36.9706i	0.866603	−	1.73321i
$456$		0			0
$457$	1.00000	−	1.00000i	0.0467780	−	0.0467780i	−0.683331	−	0.730109i	$-0.739469\pi$
$457$	1.00000	−	1.00000i	0.0467780	−	0.0467780i	0.730109	+	0.683331i	$0.239469\pi$
$458$		0			0
$459$	6.55635	+	11.7279i	0.306024	+	0.547413i
$460$		0			0
$461$			28.9706i			1.34929i	0.738141	+	0.674647i	$0.235704\pi$
$461$			28.9706i			1.34929i	−0.738141	+	0.674647i	$0.764296\pi$
$462$		0			0
$463$	21.5858	+	21.5858i	1.00318	+	1.00318i	0.999995	+	0.00318163i	$0.00101275\pi$
$463$	21.5858	+	21.5858i	1.00318	+	1.00318i	0.00318163	+	0.999995i	$0.498987\pi$
$464$		0			0
$465$	−10.3431	−	19.3137i	−0.479652	−	0.895652i
$466$		0			0
$467$	23.3848	+	23.3848i	1.08212	+	1.08212i	0.996312	+	0.0858066i	$0.0273467\pi$
$467$	23.3848	+	23.3848i	1.08212	+	1.08212i	0.0858066	+	0.996312i	$0.472653\pi$
$468$		0			0
$469$			48.6274i			2.24541i
$470$		0			0
$471$	2.27208	+	13.2426i	0.104692	+	0.610189i
$472$		0			0
$473$	−0.343146	+	0.343146i	−0.0157779	+	0.0157779i
$474$		0			0
$475$	−3.31371	+	2.48528i	−0.152043	+	0.114033i
$476$		0			0
$477$	−11.4853	−	5.48528i	−0.525875	−	0.251154i
$478$		0			0
$479$	22.6274			1.03387			0.516937	−	0.856024i	$-0.327072\pi$
$479$	22.6274			1.03387			0.516937	+	0.856024i	$0.327072\pi$
$480$		0			0
$481$	−44.6274			−2.03484
$482$		0			0
$483$	30.1421	+	21.3137i	1.37151	+	0.969807i
$484$		0			0
$485$	−1.00000	−	3.00000i	−0.0454077	−	0.136223i
$486$		0			0
$487$	−14.5563	+	14.5563i	−0.659611	+	0.659611i	−0.955288	−	0.295677i	$-0.904455\pi$
$487$	−14.5563	+	14.5563i	−0.659611	+	0.659611i	0.295677	+	0.955288i	$0.404455\pi$
$488$		0			0
$489$	−1.00000	+	0.171573i	−0.0452216	+	0.00775879i
$490$		0			0
$491$			21.5147i			0.970946i	0.874252	+	0.485473i	$0.161353\pi$
$491$			21.5147i			0.970946i	−0.874252	+	0.485473i	$0.838647\pi$
$492$		0			0
$493$	−6.68629	−	6.68629i	−0.301135	−	0.301135i
$494$		0			0
$495$	0.686292	−	5.51472i	0.0308465	−	0.247868i
$496$		0			0
$497$	25.3137	+	25.3137i	1.13548	+	1.13548i
$498$		0			0
$499$		−	34.7696i		−	1.55650i	−0.627955	−	0.778249i	$-0.716108\pi$
$499$		−	34.7696i		−	1.55650i	0.627955	−	0.778249i	$-0.283892\pi$
$500$		0			0
$501$	−22.3137	+	3.82843i	−0.996903	+	0.171042i
$502$		0			0
$503$	−5.92893	+	5.92893i	−0.264358	+	0.264358i	−0.826822	−	0.562464i	$-0.809854\pi$
$503$	−5.92893	+	5.92893i	−0.264358	+	0.264358i	0.562464	+	0.826822i	$0.309854\pi$
$504$		0			0
$505$	19.3137	+	9.65685i	0.859449	+	0.429724i
$506$		0			0
$507$	−23.0711	−	16.3137i	−1.02462	−	0.724517i
$508$		0			0
$509$	−3.65685			−0.162087			−0.0810436	−	0.996711i	$-0.525825\pi$
$509$	−3.65685			−0.162087			−0.0810436	+	0.996711i	$0.525825\pi$
$510$		0			0
$511$	−22.4853			−0.994690
$512$		0			0
$513$	1.17157	−	4.14214i	0.0517262	−	0.182880i
$514$		0			0
$515$	16.7574	−	5.58579i	0.738417	−	0.246139i
$516$		0			0
$517$	−2.97056	+	2.97056i	−0.130645	+	0.130645i
$518$		0			0
$519$	0.272078	+	1.58579i	0.0119429	+	0.0696083i
$520$		0			0
$521$			24.0000i			1.05146i	0.850652	+	0.525730i	$0.176208\pi$
$521$			24.0000i			1.05146i	−0.850652	+	0.525730i	$0.823792\pi$
$522$		0			0
$523$	−26.8995	−	26.8995i	−1.17623	−	1.17623i	−0.980696	−	0.195536i	$-0.937355\pi$
$523$	−26.8995	−	26.8995i	−1.17623	−	1.17623i	−0.195536	−	0.980696i	$-0.562645\pi$
$524$		0			0
$525$	20.3137	−	21.4853i	0.886563	−	0.937695i
$526$		0			0
$527$	−10.3431	−	10.3431i	−0.450555	−	0.450555i
$528$		0			0
$529$		−	15.9706i		−	0.694372i
$530$		0			0
$531$	4.00000	+	11.3137i	0.173585	+	0.490973i
$532$		0			0
$533$	21.6569	−	21.6569i	0.938062	−	0.938062i
$534$		0			0
$535$	−28.7574	+	9.58579i	−1.24329	+	0.414430i
$536$		0			0
$537$	12.0000	−	16.9706i	0.517838	−	0.732334i
$538$		0			0
$539$	3.85786			0.166170
$540$		0			0
$541$	−29.3137			−1.26029			−0.630147	−	0.776476i	$-0.717006\pi$
$541$	−29.3137			−1.26029			−0.630147	+	0.776476i	$0.717006\pi$
$542$		0			0
$543$	5.31371	−	7.51472i	0.228033	−	0.322487i
$544$		0			0
$545$	−8.00000	−	4.00000i	−0.342682	−	0.171341i
$546$		0			0
$547$	−15.7279	+	15.7279i	−0.672477	+	0.672477i	−0.958287	−	0.285809i	$-0.907738\pi$
$547$	−15.7279	+	15.7279i	−0.672477	+	0.672477i	0.285809	+	0.958287i	$0.407738\pi$
$548$		0			0
$549$	−0.343146	−	0.970563i	−0.0146451	−	0.0414226i
$550$		0			0
$551$			3.02944i			0.129058i
$552$		0			0
$553$	2.00000	+	2.00000i	0.0850487	+	0.0850487i
$554$		0			0
$555$	−30.5563	−	9.24264i	−1.29704	−	0.392328i
$556$		0			0
$557$	−15.6274	−	15.6274i	−0.662155	−	0.662155i	0.293733	−	0.955888i	$-0.405102\pi$
$557$	−15.6274	−	15.6274i	−0.662155	−	0.662155i	−0.955888	+	0.293733i	$0.905102\pi$
$558$		0			0
$559$			3.17157i			0.134143i
$560$		0			0
$561$	−0.627417	−	3.65685i	−0.0264896	−	0.154393i
$562$		0			0
$563$	−1.44365	+	1.44365i	−0.0608426	+	0.0608426i	−0.736873	−	0.676031i	$-0.763699\pi$
$563$	−1.44365	+	1.44365i	−0.0608426	+	0.0608426i	0.676031	+	0.736873i	$0.263699\pi$
$564$		0			0
$565$	9.48528	+	28.4558i	0.399049	+	1.19715i
$566$		0			0
$567$	−3.24264	+	30.5563i	−0.136178	+	1.28325i
$568$		0			0
$569$	−45.3137			−1.89965			−0.949825	−	0.312783i	$-0.898739\pi$
$569$	−45.3137			−1.89965			−0.949825	+	0.312783i	$0.898739\pi$
$570$		0			0
$571$	4.97056			0.208012			0.104006	−	0.994577i	$-0.466834\pi$
$571$	4.97056			0.208012			0.104006	+	0.994577i	$0.466834\pi$
$572$		0			0
$573$	5.85786	+	4.14214i	0.244716	+	0.173040i
$574$		0			0
$575$	−30.8995	−	4.41421i	−1.28860	−	0.184085i
$576$		0			0
$577$	14.6569	−	14.6569i	0.610173	−	0.610173i	−0.332818	−	0.942991i	$-0.608000\pi$
$577$	14.6569	−	14.6569i	0.610173	−	0.610173i	0.942991	+	0.332818i	$0.108000\pi$
$578$		0			0
$579$	−35.3848	+	6.07107i	−1.47054	+	0.252305i
$580$		0			0
$581$		−	15.6569i		−	0.649556i
$582$		0			0
$583$	2.48528	+	2.48528i	0.102930	+	0.102930i
$584$		0			0
$585$	−22.3137	−	28.6569i	−0.922558	−	1.18482i
$586$		0			0
$587$	−10.5563	−	10.5563i	−0.435707	−	0.435707i	0.454857	−	0.890564i	$-0.349690\pi$
$587$	−10.5563	−	10.5563i	−0.435707	−	0.435707i	−0.890564	+	0.454857i	$0.849690\pi$
$588$		0			0
$589$			4.68629i			0.193095i
$590$		0			0
$591$	35.3848	−	6.07107i	1.45554	−	0.249730i
$592$		0			0
$593$	15.4853	−	15.4853i	0.635904	−	0.635904i	−0.313638	−	0.949543i	$-0.601548\pi$
$593$	15.4853	−	15.4853i	0.635904	−	0.635904i	0.949543	+	0.313638i	$0.101548\pi$
$594$		0			0
$595$	8.82843	−	17.6569i	0.361930	−	0.723860i
$596$		0			0
$597$	26.1421	+	18.4853i	1.06993	+	0.756552i
$598$		0			0
$599$	−41.9411			−1.71367			−0.856834	−	0.515592i	$-0.827572\pi$
$599$	−41.9411			−1.71367			−0.856834	+	0.515592i	$0.827572\pi$
$600$		0			0
$601$	−14.9706			−0.610662			−0.305331	−	0.952246i	$-0.598767\pi$
$601$	−14.9706			−0.610662			−0.305331	+	0.952246i	$0.598767\pi$
$602$		0			0
$603$	38.5563	+	18.4142i	1.57014	+	0.749885i
$604$		0			0
$605$	10.3137	−	20.6274i	0.419312	−	0.838624i
$606$		0			0
$607$	33.0416	−	33.0416i	1.34112	−	1.34112i	0.446170	−	0.894948i	$-0.352788\pi$
$607$	33.0416	−	33.0416i	1.34112	−	1.34112i	0.894948	−	0.446170i	$-0.147212\pi$
$608$		0			0
$609$	−3.65685	−	21.3137i	−0.148183	−	0.863675i
$610$		0			0
$611$			27.4558i			1.11074i
$612$		0			0
$613$	9.48528	+	9.48528i	0.383107	+	0.383107i	0.872220	−	0.489113i	$-0.162680\pi$
$613$	9.48528	+	9.48528i	0.383107	+	0.383107i	−0.489113	+	0.872220i	$0.662680\pi$
$614$		0			0
$615$	19.3137	−	10.3431i	0.778804	−	0.417076i
$616$		0			0
$617$	12.1716	+	12.1716i	0.490009	+	0.490009i	0.908309	−	0.418300i	$-0.137374\pi$
$617$	12.1716	+	12.1716i	0.490009	+	0.490009i	−0.418300	+	0.908309i	$0.637374\pi$
$618$		0			0
$619$		−	20.1421i		−	0.809581i	−0.914410	−	0.404790i	$-0.867344\pi$
$619$		−	20.1421i		−	0.809581i	0.914410	−	0.404790i	$-0.132656\pi$
$620$		0			0
$621$	28.3137	−	15.8284i	1.13619	−	0.635173i
$622$		0			0
$623$	−37.7990	+	37.7990i	−1.51438	+	1.51438i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	−0.686292	+	0.970563i	−0.0274078	+	0.0387605i
$628$		0			0
$629$	−21.3137			−0.849833
$630$		0			0
$631$	−31.5980			−1.25790			−0.628948	−	0.777447i	$-0.716514\pi$
$631$	−31.5980			−1.25790			−0.628948	+	0.777447i	$0.716514\pi$
$632$		0			0
$633$	20.9706	−	29.6569i	0.833505	−	1.17875i
$634$		0			0
$635$	5.58579	+	16.7574i	0.221665	+	0.664996i
$636$		0			0
$637$	17.8284	−	17.8284i	0.706388	−	0.706388i
$638$		0			0
$639$	29.6569	−	10.4853i	1.17321	−	0.414791i
$640$		0			0
$641$			20.2843i			0.801181i	0.916257	+	0.400590i	$0.131195\pi$
$641$			20.2843i			0.801181i	−0.916257	+	0.400590i	$0.868805\pi$
$642$		0			0
$643$	28.6985	+	28.6985i	1.13176	+	1.13176i	0.989885	+	0.141873i	$0.0453124\pi$
$643$	28.6985	+	28.6985i	1.13176	+	1.13176i	0.141873	+	0.989885i	$0.454688\pi$
$644$		0			0
$645$	−0.656854	+	2.17157i	−0.0258636	+	0.0855056i
$646$		0			0
$647$	26.2132	+	26.2132i	1.03055	+	1.03055i	0.999518	+	0.0310289i	$0.00987838\pi$
$647$	26.2132	+	26.2132i	1.03055	+	1.03055i	0.0310289	+	0.999518i	$0.490122\pi$
$648$		0			0
$649$		−	3.31371i		−	0.130074i
$650$		0			0
$651$	−5.65685	−	32.9706i	−0.221710	−	1.29222i
$652$		0			0
$653$	−26.6569	+	26.6569i	−1.04316	+	1.04316i	−0.0441379	+	0.999025i	$0.514054\pi$
$653$	−26.6569	+	26.6569i	−1.04316	+	1.04316i	−0.999025	+	0.0441379i	$0.985946\pi$
$654$		0			0
$655$	17.6569	+	8.82843i	0.689910	+	0.344955i
$656$		0			0
$657$	−8.51472	+	17.8284i	−0.332191	+	0.695553i
$658$		0			0
$659$	10.6274			0.413985			0.206993	−	0.978342i	$-0.433632\pi$
$659$	10.6274			0.413985			0.206993	+	0.978342i	$0.433632\pi$
$660$		0			0
$661$	−7.65685			−0.297817			−0.148909	−	0.988851i	$-0.547576\pi$
$661$	−7.65685			−0.297817			−0.148909	+	0.988851i	$0.547576\pi$
$662$		0			0
$663$	−19.7990	−	14.0000i	−0.768929	−	0.543715i
$664$		0			0
$665$	−6.00000	+	2.00000i	−0.232670	+	0.0775567i
$666$		0			0
$667$	−16.1421	+	16.1421i	−0.625026	+	0.625026i
$668$		0			0
$669$	−13.4853	+	2.31371i	−0.521371	+	0.0894531i
$670$		0			0
$671$			0.284271i			0.0109742i
$672$		0			0
$673$	−3.68629	−	3.68629i	−0.142096	−	0.142096i	0.632480	−	0.774576i	$-0.282037\pi$
$673$	−3.68629	−	3.68629i	−0.142096	−	0.142096i	−0.774576	+	0.632480i	$0.782037\pi$
$674$		0			0
$675$	−9.34315	−	24.2426i	−0.359618	−	0.933100i
$676$		0			0
$677$	35.2843	+	35.2843i	1.35608	+	1.35608i	0.878688	+	0.477397i	$0.158420\pi$
$677$	35.2843	+	35.2843i	1.35608	+	1.35608i	0.477397	+	0.878688i	$0.341580\pi$
$678$		0			0
$679$		−	4.82843i		−	0.185298i
$680$		0			0
$681$	11.8284	−	2.02944i	0.453266	−	0.0777682i
$682$		0			0
$683$	22.5563	−	22.5563i	0.863095	−	0.863095i	−0.128602	−	0.991696i	$-0.541049\pi$
$683$	22.5563	−	22.5563i	0.863095	−	0.863095i	0.991696	+	0.128602i	$0.0410488\pi$
$684$		0			0
$685$	29.4853	−	9.82843i	1.12657	−	0.375525i
$686$		0			0
$687$	20.2843	+	14.3431i	0.773893	+	0.547225i
$688$		0			0
$689$	22.9706			0.875109
$690$		0			0
$691$	33.6569			1.28037			0.640184	−	0.768222i	$-0.278858\pi$
$691$	33.6569			1.28037			0.640184	+	0.768222i	$0.278858\pi$
$692$		0			0
$693$	3.65685	−	7.65685i	0.138912	−	0.290860i
$694$		0			0
$695$	−17.6569	−	8.82843i	−0.669763	−	0.334881i
$696$		0			0
$697$	10.3431	−	10.3431i	0.391775	−	0.391775i
$698$		0			0
$699$	−4.89949	−	28.5563i	−0.185316	−	1.08010i
$700$		0			0
$701$			4.00000i			0.151078i	0.997143	+	0.0755390i	$0.0240677\pi$
$701$			4.00000i			0.151078i	−0.997143	+	0.0755390i	$0.975932\pi$
$702$		0			0
$703$	4.82843	+	4.82843i	0.182108	+	0.182108i
$704$		0			0
$705$	−5.68629	+	18.7990i	−0.214158	+	0.708011i
$706$		0			0
$707$	23.3137	+	23.3137i	0.876802	+	0.876802i
$708$		0			0
$709$		−	32.2843i		−	1.21246i	−0.795289	−	0.606231i	$-0.792681\pi$
$709$		−	32.2843i		−	1.21246i	0.795289	−	0.606231i	$-0.207319\pi$
$710$		0			0
$711$	2.34315	−	0.828427i	0.0878748	−	0.0310684i
$712$		0			0
$713$	−24.9706	+	24.9706i	−0.935155	+	0.935155i
$714$		0			0
$715$	3.17157	+	9.51472i	0.118610	+	0.355830i
$716$		0			0
$717$	−16.0000	+	22.6274i	−0.597531	+	0.845036i
$718$		0			0
$719$	−16.0000			−0.596699			−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000			−0.596699			−0.298350	+	0.954457i	$0.596436\pi$
$720$		0			0
$721$	26.9706			1.00444
$722$		0			0
$723$	0.343146	−	0.485281i	0.0127617	−	0.0180478i
$724$		0			0
$725$	10.9706	+	14.6274i	0.407436	+	0.543249i
$726$		0			0
$727$	12.7574	−	12.7574i	0.473144	−	0.473144i	−0.429786	−	0.902931i	$-0.641411\pi$
$727$	12.7574	−	12.7574i	0.473144	−	0.473144i	0.902931	+	0.429786i	$0.141411\pi$
$728$		0			0
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$			1.51472i			0.0560239i
$732$		0			0
$733$	−5.14214	−	5.14214i	−0.189929	−	0.189929i	0.605736	−	0.795665i	$-0.292879\pi$
$733$	−5.14214	−	5.14214i	−0.189929	−	0.189929i	−0.795665	+	0.605736i	$0.792879\pi$
$734$		0			0
$735$	15.8995	−	8.51472i	0.586462	−	0.314070i
$736$		0			0
$737$	−8.34315	−	8.34315i	−0.307324	−	0.307324i
$738$		0			0
$739$			47.1716i			1.73523i	0.497233	+	0.867617i	$0.334350\pi$
$739$			47.1716i			1.73523i	−0.497233	+	0.867617i	$0.665650\pi$
$740$		0			0
$741$	1.31371	+	7.65685i	0.0482603	+	0.281282i
$742$		0			0
$743$	37.3848	−	37.3848i	1.37151	−	1.37151i	0.513313	−	0.858202i	$-0.328418\pi$
$743$	37.3848	−	37.3848i	1.37151	−	1.37151i	0.858202	−	0.513313i	$-0.171582\pi$
$744$		0			0
$745$	13.3137	−	26.6274i	0.487777	−	0.975553i
$746$		0			0
$747$	−12.4142	−	5.92893i	−0.454212	−	0.216928i
$748$		0			0
$749$	−46.2843			−1.69119
$750$		0			0
$751$	12.2843			0.448259			0.224130	−	0.974559i	$-0.428046\pi$
$751$	12.2843			0.448259			0.224130	+	0.974559i	$0.428046\pi$
$752$		0			0
$753$	37.4558	+	26.4853i	1.36497	+	0.965177i
$754$		0			0
$755$	13.6569	−	27.3137i	0.497024	−	0.994048i
$756$		0			0
$757$	14.4558	−	14.4558i	0.525407	−	0.525407i	−0.393793	−	0.919199i	$-0.628837\pi$
$757$	14.4558	−	14.4558i	0.525407	−	0.525407i	0.919199	+	0.393793i	$0.128837\pi$
$758$		0			0
$759$	−8.82843	+	1.51472i	−0.320452	+	0.0549808i
$760$		0			0
$761$			12.6863i			0.459878i	0.973205	+	0.229939i	$0.0738526\pi$
$761$			12.6863i			0.459878i	−0.973205	+	0.229939i	$0.926147\pi$
$762$		0			0
$763$	−9.65685	−	9.65685i	−0.349602	−	0.349602i
$764$		0			0
$765$	−10.6569	−	13.6863i	−0.385299	−	0.494829i
$766$		0			0
$767$	−15.3137	−	15.3137i	−0.552946	−	0.552946i
$768$		0			0
$769$			49.9411i			1.80092i	0.434936	+	0.900462i	$0.356771\pi$
$769$			49.9411i			1.80092i	−0.434936	+	0.900462i	$0.643229\pi$
$770$		0			0
$771$	22.8995	−	3.92893i	0.824705	−	0.141497i
$772$		0			0
$773$	−10.6569	+	10.6569i	−0.383300	+	0.383300i	−0.872290	−	0.488989i	$-0.837366\pi$
$773$	−10.6569	+	10.6569i	−0.383300	+	0.383300i	0.488989	+	0.872290i	$0.337366\pi$
$774$		0			0
$775$	16.9706	+	22.6274i	0.609601	+	0.812801i
$776$		0			0
$777$	−39.7990	−	28.1421i	−1.42778	−	1.00959i
$778$		0			0
$779$	−4.68629			−0.167904
$780$		0			0
$781$	−8.68629			−0.310820
$782$		0			0
$783$	−18.2843	−	5.17157i	−0.653427	−	0.184817i
$784$		0			0
$785$	−5.48528	−	16.4558i	−0.195778	−	0.587334i
$786$		0			0
$787$	27.5858	−	27.5858i	0.983327	−	0.983327i	−0.0165362	−	0.999863i	$-0.505264\pi$
$787$	27.5858	−	27.5858i	0.983327	−	0.983327i	0.999863	+	0.0165362i	$0.00526387\pi$
$788$		0			0
$789$	−2.85786	−	16.6569i	−0.101743	−	0.593000i
$790$		0			0
$791$			45.7990i			1.62842i
$792$		0			0
$793$	1.31371	+	1.31371i	0.0466512	+	0.0466512i
$794$		0			0
$795$	15.7279	+	4.75736i	0.557812	+	0.168726i
$796$		0			0
$797$	4.65685	+	4.65685i	0.164954	+	0.164954i	0.784757	−	0.619803i	$-0.212788\pi$
$797$	4.65685	+	4.65685i	0.164954	+	0.164954i	−0.619803	+	0.784757i	$0.712788\pi$
$798$		0			0
$799$			13.1127i			0.463894i
$800$		0			0
$801$	15.6569	+	44.2843i	0.553208	+	1.56471i
$802$		0			0
$803$	3.85786	−	3.85786i	0.136141	−	0.136141i
$804$		0			0
$805$	−42.6274	−	21.3137i	−1.50242	−	0.751210i
$806$		0			0
$807$	−16.6274	+	23.5147i	−0.585313	+	0.827757i
$808$		0			0
$809$	32.3431			1.13712			0.568562	−	0.822640i	$-0.307500\pi$
$809$	32.3431			1.13712			0.568562	+	0.822640i	$0.307500\pi$
$810$		0			0
$811$	−33.6569			−1.18185			−0.590926	−	0.806726i	$-0.701237\pi$
$811$	−33.6569			−1.18185			−0.590926	+	0.806726i	$0.701237\pi$
$812$		0			0
$813$	10.3431	−	14.6274i	0.362750	−	0.513006i
$814$		0			0
$815$	1.24264	−	0.414214i	0.0435278	−	0.0145093i
$816$		0			0
$817$	0.343146	−	0.343146i	0.0120052	−	0.0120052i
$818$		0			0
$819$	−18.4853	−	52.2843i	−0.645928	−	1.82696i
$820$		0			0
$821$		−	37.9411i		−	1.32415i	−0.749436	−	0.662077i	$-0.769675\pi$
$821$		−	37.9411i		−	1.32415i	0.749436	−	0.662077i	$-0.230325\pi$
$822$		0			0
$823$	−5.72792	−	5.72792i	−0.199663	−	0.199663i	0.600193	−	0.799855i	$-0.295091\pi$
$823$	−5.72792	−	5.72792i	−0.199663	−	0.199663i	−0.799855	+	0.600193i	$0.795091\pi$
$824$		0			0
$825$	0.201010	+	7.17157i	0.00699827	+	0.249682i
$826$		0			0
$827$	−27.5269	−	27.5269i	−0.957205	−	0.957205i	0.0419166	−	0.999121i	$-0.486654\pi$
$827$	−27.5269	−	27.5269i	−0.957205	−	0.957205i	−0.999121	+	0.0419166i	$0.986654\pi$
$828$		0			0
$829$		−	15.3137i		−	0.531867i	−0.963991	−	0.265934i	$-0.914320\pi$
$829$		−	15.3137i		−	0.531867i	0.963991	−	0.265934i	$-0.0856802\pi$
$830$		0			0
$831$	−3.38478	−	19.7279i	−0.117417	−	0.684354i
$832$		0			0
$833$	8.51472	−	8.51472i	0.295018	−	0.295018i
$834$		0			0
$835$	27.7279	−	9.24264i	0.959564	−	0.319855i
$836$		0			0
$837$	−28.2843	−	8.00000i	−0.977647	−	0.276520i
$838$		0			0
$839$	−12.6863			−0.437979			−0.218990	−	0.975727i	$-0.570276\pi$
$839$	−12.6863			−0.437979			−0.218990	+	0.975727i	$0.570276\pi$
$840$		0			0
$841$	−15.6274			−0.538876
$842$		0			0
$843$	−8.00000	−	5.65685i	−0.275535	−	0.194832i
$844$		0			0
$845$	32.6274	+	16.3137i	1.12242	+	0.561209i
$846$		0			0
$847$	24.8995	−	24.8995i	0.855557	−	0.855557i
$848$		0			0
$849$	12.6569	−	2.17157i	0.434382	−	0.0745282i
$850$		0			0
$851$			51.4558i			1.76388i
$852$		0			0
$853$	−24.4558	−	24.4558i	−0.837352	−	0.837352i	0.151158	−	0.988510i	$-0.451700\pi$
$853$	−24.4558	−	24.4558i	−0.837352	−	0.837352i	−0.988510	+	0.151158i	$0.951700\pi$
$854$		0			0
$855$	−0.686292	+	5.51472i	−0.0234707	+	0.188599i
$856$		0			0
$857$	−33.4853	−	33.4853i	−1.14384	−	1.14384i	−0.987742	−	0.156093i	$-0.950110\pi$
$857$	−33.4853	−	33.4853i	−1.14384	−	1.14384i	−0.156093	−	0.987742i	$-0.549890\pi$
$858$		0			0
$859$			52.4264i			1.78877i	0.447302	+	0.894383i	$0.352385\pi$
$859$			52.4264i			1.78877i	−0.447302	+	0.894383i	$0.647615\pi$
$860$		0			0
$861$	32.9706	−	5.65685i	1.12363	−	0.192785i
$862$		0			0
$863$	−3.58579	+	3.58579i	−0.122062	+	0.122062i	−0.765499	−	0.643437i	$-0.777508\pi$
$863$	−3.58579	+	3.58579i	−0.122062	+	0.122062i	0.643437	+	0.765499i	$0.277508\pi$
$864$		0			0
$865$	−0.656854	−	1.97056i	−0.0223337	−	0.0670011i
$866$		0			0
$867$	14.5858	+	10.3137i	0.495359	+	0.350272i
$868$		0			0
$869$	−0.686292			−0.0232808
$870$		0			0
$871$	−77.1127			−2.61286
$872$		0			0
$873$	−3.82843	−	1.82843i	−0.129573	−	0.0618829i
$874$		0			0
$875$	−21.7279	+	31.3848i	−0.734538	+	1.06100i
$876$		0			0
$877$	−12.4558	+	12.4558i	−0.420604	+	0.420604i	−0.885412	−	0.464808i	$-0.846123\pi$
$877$	−12.4558	+	12.4558i	−0.420604	+	0.420604i	0.464808	+	0.885412i	$0.346123\pi$
$878$		0			0
$879$	6.89949	+	40.2132i	0.232714	+	1.35636i
$880$		0			0
$881$		−	8.97056i		−	0.302226i	−0.988516	−	0.151113i	$-0.951714\pi$
$881$		−	8.97056i		−	0.302226i	0.988516	−	0.151113i	$-0.0482857\pi$
$882$		0			0
$883$	−31.5858	−	31.5858i	−1.06295	−	1.06295i	−0.997881	−	0.0650653i	$-0.979274\pi$
$883$	−31.5858	−	31.5858i	−1.06295	−	1.06295i	−0.0650653	−	0.997881i	$-0.520726\pi$
$884$		0			0
$885$	−7.31371	−	13.6569i	−0.245848	−	0.459070i
$886$		0			0
$887$	−7.72792	−	7.72792i	−0.259478	−	0.259478i	0.565364	−	0.824842i	$-0.308736\pi$
$887$	−7.72792	−	7.72792i	−0.259478	−	0.259478i	−0.824842	+	0.565364i	$0.808736\pi$
$888$		0			0
$889$			26.9706i			0.904564i
$890$		0			0
$891$	−4.68629	−	5.79899i	−0.156997	−	0.194273i
$892$		0			0
$893$	2.97056	−	2.97056i	0.0994061	−	0.0994061i
$894$		0			0
$895$	−12.0000	+	24.0000i	−0.401116	+	0.802232i
$896$		0			0
$897$	−33.7990	+	47.7990i	−1.12852	+	1.59596i
$898$		0			0
$899$	20.6863			0.689926
$900$		0			0
$901$	10.9706			0.365482
$902$		0			0
$903$	−2.00000	+	2.82843i	−0.0665558	+	0.0941242i
$904$		0			0
$905$	−5.31371	+	10.6274i	−0.176634	+	0.353267i
$906$		0			0
$907$	−28.4142	+	28.4142i	−0.943478	+	0.943478i	−0.998486	−	0.0550075i	$-0.982482\pi$
$907$	−28.4142	+	28.4142i	−0.943478	+	0.943478i	0.0550075	+	0.998486i	$0.482482\pi$
$908$		0			0
$909$	27.3137	−	9.65685i	0.905939	−	0.320298i
$910$		0			0
$911$		−	40.8284i		−	1.35271i	−0.736578	−	0.676353i	$-0.763559\pi$
$911$		−	40.8284i		−	1.35271i	0.736578	−	0.676353i	$-0.236441\pi$
$912$		0			0
$913$	2.68629	+	2.68629i	0.0889033	+	0.0889033i
$914$		0			0
$915$	0.627417	+	1.17157i	0.0207418	+	0.0387310i
$916$		0			0
$917$	21.3137	+	21.3137i	0.703841	+	0.703841i
$918$		0			0
$919$			8.82843i			0.291223i	0.989342	+	0.145611i	$0.0465149\pi$
$919$			8.82843i			0.291223i	−0.989342	+	0.145611i	$0.953485\pi$
$920$		0			0
$921$	2.85786	+	16.6569i	0.0941698	+	0.548862i
$922$		0			0
$923$	−40.1421	+	40.1421i	−1.32129	+	1.32129i
$924$		0			0
$925$	40.7990	+	5.82843i	1.34146	+	0.191638i
$926$		0			0
$927$	10.2132	−	21.3848i	0.335446	−	0.702368i
$928$		0			0
$929$	−11.9411			−0.391776			−0.195888	−	0.980626i	$-0.562759\pi$
$929$	−11.9411			−0.391776			−0.195888	+	0.980626i	$0.562759\pi$
$930$		0			0
$931$	−3.85786			−0.126436
$932$		0			0
$933$	7.79899	+	5.51472i	0.255327	+	0.180544i
$934$		0			0
$935$	1.51472	+	4.54416i	0.0495366	+	0.148610i
$936$		0			0
$937$	−31.0000	+	31.0000i	−1.01273	+	1.01273i	−0.0128079	+	0.999918i	$0.504077\pi$
$937$	−31.0000	+	31.0000i	−1.01273	+	1.01273i	−0.999918	+	0.0128079i	$0.995923\pi$
$938$		0			0
$939$	5.58579	−	0.958369i	0.182285	−	0.0312752i
$940$		0			0
$941$		−	43.5980i		−	1.42125i	−0.703569	−	0.710627i	$-0.748411\pi$
$941$		−	43.5980i		−	1.42125i	0.703569	−	0.710627i	$-0.251589\pi$
$942$		0			0
$943$	−24.9706	−	24.9706i	−0.813153	−	0.813153i
$944$		0			0
$945$	−1.82843	−	39.6274i	−0.0594787	−	1.28908i
$946$		0			0
$947$	1.72792	+	1.72792i	0.0561499	+	0.0561499i	0.734624	−	0.678474i	$-0.237359\pi$
$947$	1.72792	+	1.72792i	0.0561499	+	0.0561499i	−0.678474	+	0.734624i	$0.737359\pi$
$948$		0			0
$949$		−	35.6569i		−	1.15747i
$950$		0			0
$951$	−11.2426	+	1.92893i	−0.364568	+	0.0625499i
$952$		0			0
$953$	15.4853	−	15.4853i	0.501617	−	0.501617i	−0.410323	−	0.911940i	$-0.634584\pi$
$953$	15.4853	−	15.4853i	0.501617	−	0.501617i	0.911940	+	0.410323i	$0.134584\pi$
$954$		0			0
$955$	−8.28427	−	4.14214i	−0.268073	−	0.134036i
$956$		0			0
$957$	4.28427	+	3.02944i	0.138491	+	0.0979278i
$958$		0			0
$959$	47.4558			1.53243
$960$		0			0
$961$	1.00000			0.0322581
$962$		0			0
$963$	−17.5269	+	36.6985i	−0.564797	+	1.18259i
$964$		0			0
$965$	43.9706	−	14.6569i	1.41546	−	0.471821i
$966$		0			0
$967$	18.4142	−	18.4142i	0.592161	−	0.592161i	−0.346054	−	0.938215i	$-0.612478\pi$
$967$	18.4142	−	18.4142i	0.592161	−	0.592161i	0.938215	+	0.346054i	$0.112478\pi$
$968$		0			0
$969$	0.627417	+	3.65685i	0.0201555	+	0.117475i
$970$		0			0
$971$		−	42.4853i		−	1.36342i	−0.731624	−	0.681709i	$-0.761237\pi$
$971$		−	42.4853i		−	1.36342i	0.731624	−	0.681709i	$-0.238763\pi$
$972$		0			0
$973$	−21.3137	−	21.3137i	−0.683286	−	0.683286i
$974$		0			0
$975$	34.0711	+	32.2132i	1.09115	+	1.03165i
$976$		0			0
$977$	−23.1421	−	23.1421i	−0.740383	−	0.740383i	0.232269	−	0.972652i	$-0.425385\pi$
$977$	−23.1421	−	23.1421i	−0.740383	−	0.740383i	−0.972652	+	0.232269i	$0.925385\pi$
$978$		0			0
$979$		−	12.9706i		−	0.414541i
$980$		0			0
$981$	−11.3137	+	4.00000i	−0.361219	+	0.127710i
$982$		0			0
$983$	32.6985	−	32.6985i	1.04292	−	1.04292i	0.0438830	−	0.999037i	$-0.486027\pi$
$983$	32.6985	−	32.6985i	1.04292	−	1.04292i	0.999037	−	0.0438830i	$-0.0139729\pi$
$984$		0			0
$985$	−43.9706	+	14.6569i	−1.40102	+	0.467006i
$986$		0			0
$987$	−17.3137	+	24.4853i	−0.551101	+	0.779375i
$988$		0			0
$989$	3.65685			0.116281
$990$		0			0
$991$	48.9706			1.55560			0.777801	−	0.628511i	$-0.216335\pi$
$991$	48.9706			1.55560			0.777801	+	0.628511i	$0.216335\pi$
$992$		0			0
$993$	−9.65685	+	13.6569i	−0.306451	+	0.433387i
$994$		0			0
$995$	−36.9706	−	18.4853i	−1.17205	−	0.586023i
$996$		0			0
$997$	−30.7990	+	30.7990i	−0.975414	+	0.975414i	−0.999705	−	0.0242911i	$-0.992267\pi$
$997$	−30.7990	+	30.7990i	−0.975414	+	0.975414i	0.0242911	+	0.999705i	$0.492267\pi$
$998$		0			0
$999$	−37.3848	+	20.8995i	−1.18280	+	0.661231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.v.a.113.2		4
3.2	odd	2		240.2.v.c.113.2		4
4.3	odd	2		120.2.r.c.113.1	yes	4
5.2	odd	4		240.2.v.c.17.2		4
5.3	odd	4		1200.2.v.d.257.1		4
5.4	even	2		1200.2.v.j.593.1		4
8.3	odd	2		960.2.v.a.833.2		4
8.5	even	2		960.2.v.i.833.1		4
12.11	even	2		120.2.r.b.113.1	yes	4
15.2	even	4	inner	240.2.v.a.17.1		4
15.8	even	4		1200.2.v.j.257.2		4
15.14	odd	2		1200.2.v.d.593.1		4
20.3	even	4		600.2.r.c.257.2		4
20.7	even	4		120.2.r.b.17.1	✓	4
20.19	odd	2		600.2.r.b.593.2		4
24.5	odd	2		960.2.v.g.833.1		4
24.11	even	2		960.2.v.f.833.2		4
40.27	even	4		960.2.v.f.257.2		4
40.37	odd	4		960.2.v.g.257.1		4
60.23	odd	4		600.2.r.b.257.1		4
60.47	odd	4		120.2.r.c.17.2	yes	4
60.59	even	2		600.2.r.c.593.2		4
120.77	even	4		960.2.v.i.257.2		4
120.107	odd	4		960.2.v.a.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.r.b.17.1	✓	4	20.7	even	4
120.2.r.b.113.1	yes	4	12.11	even	2
120.2.r.c.17.2	yes	4	60.47	odd	4
120.2.r.c.113.1	yes	4	4.3	odd	2
240.2.v.a.17.1		4	15.2	even	4	inner
240.2.v.a.113.2		4	1.1	even	1	trivial
240.2.v.c.17.2		4	5.2	odd	4
240.2.v.c.113.2		4	3.2	odd	2
600.2.r.b.257.1		4	60.23	odd	4
600.2.r.b.593.2		4	20.19	odd	2
600.2.r.c.257.2		4	20.3	even	4
600.2.r.c.593.2		4	60.59	even	2
960.2.v.a.257.1		4	120.107	odd	4
960.2.v.a.833.2		4	8.3	odd	2
960.2.v.f.257.2		4	40.27	even	4
960.2.v.f.833.2		4	24.11	even	2
960.2.v.g.257.1		4	40.37	odd	4
960.2.v.g.833.1		4	24.5	odd	2
960.2.v.i.257.2		4	120.77	even	4
960.2.v.i.833.1		4	8.5	even	2
1200.2.v.d.257.1		4	5.3	odd	4
1200.2.v.d.593.1		4	15.14	odd	2
1200.2.v.j.257.2		4	15.8	even	4
1200.2.v.j.593.1		4	5.4	even	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.v (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.41421i) q^{3} +(1.00000 - 2.00000i) q^{5} +(2.41421 - 2.41421i) q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.41421i) q^{3} +(1.00000 - 2.00000i) q^{5} +(2.41421 - 2.41421i) q^{7} +(-1.00000 - 2.82843i) q^{9} +0.828427i q^{11} +(3.82843 + 3.82843i) q^{13} +(1.82843 + 3.41421i) q^{15} +(1.82843 + 1.82843i) q^{17} -0.828427i q^{19} +(1.00000 + 5.82843i) q^{21} +(4.41421 - 4.41421i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(5.00000 + 1.41421i) q^{27} -3.65685 q^{29} -5.65685 q^{31} +(-1.17157 - 0.828427i) q^{33} +(-2.41421 - 7.24264i) q^{35} +(-5.82843 + 5.82843i) q^{37} +(-9.24264 + 1.58579i) q^{39} -5.65685i q^{41} +(0.414214 + 0.414214i) q^{43} +(-6.65685 - 0.828427i) q^{45} +(3.58579 + 3.58579i) q^{47} -4.65685i q^{49} +(-4.41421 + 0.757359i) q^{51} +(3.00000 - 3.00000i) q^{53} +(1.65685 + 0.828427i) q^{55} +(1.17157 + 0.828427i) q^{57} -4.00000 q^{59} +0.343146 q^{61} +(-9.24264 - 4.41421i) q^{63} +(11.4853 - 3.82843i) q^{65} +(-10.0711 + 10.0711i) q^{67} +(1.82843 + 10.6569i) q^{69} +10.4853i q^{71} +(-4.65685 - 4.65685i) q^{73} +(8.65685 - 0.242641i) q^{75} +(2.00000 + 2.00000i) q^{77} +0.828427i q^{79} +(-7.00000 + 5.65685i) q^{81} +(3.24264 - 3.24264i) q^{83} +(5.48528 - 1.82843i) q^{85} +(3.65685 - 5.17157i) q^{87} -15.6569 q^{89} +18.4853 q^{91} +(5.65685 - 8.00000i) q^{93} +(-1.65685 - 0.828427i) q^{95} +(1.00000 - 1.00000i) q^{97} +(2.34315 - 0.828427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	\( 4 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{13} - 4 q^{15} - 4 q^{17} + 4 q^{21} + 12 q^{23} - 12 q^{25} + 20 q^{27} + 8 q^{29} - 16 q^{33} - 4 q^{35} - 12 q^{37} - 20 q^{39} - 4 q^{43} - 4 q^{45} + 20 q^{47} - 12 q^{51} + 12 q^{53} - 16 q^{55} + 16 q^{57} - 16 q^{59} + 24 q^{61} - 20 q^{63} + 12 q^{65} - 12 q^{67} - 4 q^{69} + 4 q^{73} + 12 q^{75} + 8 q^{77} - 28 q^{81} - 4 q^{83} - 12 q^{85} - 8 q^{87} - 40 q^{89} + 40 q^{91} + 16 q^{95} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^13 - 4 * q^15 - 4 * q^17 + 4 * q^21 + 12 * q^23 - 12 * q^25 + 20 * q^27 + 8 * q^29 - 16 * q^33 - 4 * q^35 - 12 * q^37 - 20 * q^39 - 4 * q^43 - 4 * q^45 + 20 * q^47 - 12 * q^51 + 12 * q^53 - 16 * q^55 + 16 * q^57 - 16 * q^59 + 24 * q^61 - 20 * q^63 + 12 * q^65 - 12 * q^67 - 4 * q^69 + 4 * q^73 + 12 * q^75 + 8 * q^77 - 28 * q^81 - 4 * q^83 - 12 * q^85 - 8 * q^87 - 40 * q^89 + 40 * q^91 + 16 * q^95 + 4 * q^97 + 32 * q^99

Introduction

L-functions

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