LMFDB - Embedded newform 720.2.t.c.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(181,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("720.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.t (of order $4$, degree $2$, 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:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			541.2
Root			$-0.296075 + 1.38287i$ of defining polynomial
Character	$\chi$	$=$	720.541
Dual form			720.2.t.c.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09971 + 0.889181i) q^{2} +(0.418713 - 1.95568i) q^{4} +(0.707107 - 0.707107i) q^{5} +2.66881i q^{7} +(1.27849 + 2.52299i) q^{8} +O(q^{10})$	\(q+(-1.09971 + 0.889181i) q^{2} +(0.418713 - 1.95568i) q^{4} +(0.707107 - 0.707107i) q^{5} +2.66881i q^{7} +(1.27849 + 2.52299i) q^{8} +(-0.148864 + 1.40636i) q^{10} +(3.49714 - 3.49714i) q^{11} +(2.94072 + 2.94072i) q^{13} +(-2.37306 - 2.93491i) q^{14} +(-3.64936 - 1.63774i) q^{16} -1.85116 q^{17} +(-3.44856 - 3.44856i) q^{19} +(-1.08680 - 1.67895i) q^{20} +(-0.736240 + 6.95543i) q^{22} +0.707288i q^{23} -1.00000i q^{25} +(-5.84877 - 0.619099i) q^{26} +(5.21934 + 1.11747i) q^{28} +(3.49909 + 3.49909i) q^{29} +6.84272 q^{31} +(5.46947 - 1.44391i) q^{32} +(2.03573 - 1.64601i) q^{34} +(1.88714 + 1.88714i) q^{35} +(-0.0975060 + 0.0975060i) q^{37} +(6.85881 + 0.726013i) q^{38} +(2.68805 + 0.879991i) q^{40} +10.2052i q^{41} +(4.43844 - 4.43844i) q^{43} +(-5.37499 - 8.30359i) q^{44} +(-0.628908 - 0.777810i) q^{46} +1.89428 q^{47} -0.122561 q^{49} +(0.889181 + 1.09971i) q^{50} +(6.98243 - 4.51979i) q^{52} +(7.43897 - 7.43897i) q^{53} -4.94571i q^{55} +(-6.73338 + 3.41205i) q^{56} +(-6.95931 - 0.736651i) q^{58} +(-0.959574 + 0.959574i) q^{59} +(6.49825 + 6.49825i) q^{61} +(-7.52499 + 6.08442i) q^{62} +(-4.73092 + 6.45123i) q^{64} +4.15881 q^{65} +(3.49691 + 3.49691i) q^{67} +(-0.775103 + 3.62027i) q^{68} +(-3.75330 - 0.397291i) q^{70} -7.86777i q^{71} +15.6564i q^{73} +(0.0205276 - 0.193929i) q^{74} +(-8.18824 + 5.30033i) q^{76} +(9.33322 + 9.33322i) q^{77} -6.70212 q^{79} +(-3.73854 + 1.42243i) q^{80} +(-9.07431 - 11.2228i) q^{82} +(3.87327 + 3.87327i) q^{83} +(-1.30896 + 1.30896i) q^{85} +(-0.934407 + 8.82755i) q^{86} +(13.2943 + 4.35218i) q^{88} -10.5055i q^{89} +(-7.84824 + 7.84824i) q^{91} +(1.38323 + 0.296151i) q^{92} +(-2.08316 + 1.68436i) q^{94} -4.87701 q^{95} +4.79937 q^{97} +(0.134781 - 0.108979i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4}+O(q^{10}) $ 16 * q - 4 * q^4	$ 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47} - 16 q^{49} + 4 q^{50} + 56 q^{52} - 16 q^{53} - 16 q^{56} - 12 q^{58} + 8 q^{59} + 16 q^{61} + 8 q^{62} - 16 q^{64} + 40 q^{67} + 48 q^{68} - 8 q^{70} + 72 q^{74} - 16 q^{77} + 16 q^{79} - 16 q^{80} - 76 q^{82} - 40 q^{83} - 16 q^{85} - 28 q^{86} + 32 q^{91} + 52 q^{92} - 36 q^{94} - 32 q^{95} - 60 q^{98}+O(q^{100}) $ 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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 $

$2$	−1.09971	+	0.889181i	−0.777611	+	0.628746i
$2$	−1.09971	+	0.889181i	−0.777611	+	0.628746i
$3$		0			0
$3$		0			0
$4$	0.418713	−	1.95568i	0.209357	−	0.977839i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$			2.66881i			1.00872i	0.863495	+	0.504358i	$0.168271\pi$
$7$			2.66881i			1.00872i	−0.863495	+	0.504358i	$0.831729\pi$
$8$	1.27849	+	2.52299i	0.452015	+	0.892010i
$9$		0			0
$10$	−0.148864	+	1.40636i	−0.0470751	+	0.444729i
$11$	3.49714	−	3.49714i	1.05443	−	1.05443i	0.0559977	−	0.998431i	$-0.482166\pi$
$11$	3.49714	−	3.49714i	1.05443	−	1.05443i	0.998431	−	0.0559977i	$-0.0178339\pi$
$12$		0			0
$13$	2.94072	+	2.94072i	0.815610	+	0.815610i	0.985468	−	0.169858i	$-0.0543310\pi$
$13$	2.94072	+	2.94072i	0.815610	+	0.815610i	−0.169858	+	0.985468i	$0.554331\pi$
$14$	−2.37306	−	2.93491i	−0.634227	−	0.784389i
$15$		0			0
$16$	−3.64936	−	1.63774i	−0.912340	−	0.409434i
$17$	−1.85116			−0.448971			−0.224486	−	0.974477i	$-0.572070\pi$
$17$	−1.85116			−0.448971			−0.224486	+	0.974477i	$0.572070\pi$
$18$		0			0
$19$	−3.44856	−	3.44856i	−0.791155	−	0.791155i	0.190527	−	0.981682i	$-0.438980\pi$
$19$	−3.44856	−	3.44856i	−0.791155	−	0.791155i	−0.981682	+	0.190527i	$0.938980\pi$
$20$	−1.08680	−	1.67895i	−0.243016	−	0.375424i
$21$		0			0
$22$	−0.736240	+	6.95543i	−0.156967	+	1.48290i
$23$			0.707288i			0.147480i	0.997278	+	0.0737399i	$0.0234935\pi$
$23$			0.707288i			0.147480i	−0.997278	+	0.0737399i	$0.976507\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	−5.84877	−	0.619099i	−1.14704	−	0.121415i
$27$		0			0
$28$	5.21934	+	1.11747i	0.986363	+	0.211181i
$29$	3.49909	+	3.49909i	0.649766	+	0.649766i	0.952936	−	0.303171i	$-0.0980452\pi$
$29$	3.49909	+	3.49909i	0.649766	+	0.649766i	−0.303171	+	0.952936i	$0.598045\pi$
$30$		0			0
$31$	6.84272			1.22899			0.614494	−	0.788921i	$-0.289360\pi$
$31$	6.84272			1.22899			0.614494	+	0.788921i	$0.289360\pi$
$32$	5.46947	−	1.44391i	0.966875	−	0.255250i
$33$		0			0
$34$	2.03573	−	1.64601i	0.349125	−	0.282289i
$35$	1.88714	+	1.88714i	0.318984	+	0.318984i
$36$		0			0
$37$	−0.0975060	+	0.0975060i	−0.0160299	+	0.0160299i	−0.715076	−	0.699046i	$-0.753608\pi$
$37$	−0.0975060	+	0.0975060i	−0.0160299	+	0.0160299i	0.699046	+	0.715076i	$0.253608\pi$
$38$	6.85881	+	0.726013i	1.11265	+	0.117775i
$39$		0			0
$40$	2.68805	+	0.879991i	0.425018	+	0.139139i
$41$			10.2052i			1.59379i	0.604117	+	0.796896i	$0.293526\pi$
$41$			10.2052i			1.59379i	−0.604117	+	0.796896i	$0.706474\pi$
$42$		0			0
$43$	4.43844	−	4.43844i	0.676855	−	0.676855i	−0.282432	−	0.959287i	$-0.591141\pi$
$43$	4.43844	−	4.43844i	0.676855	−	0.676855i	0.959287	+	0.282432i	$0.0911412\pi$
$44$	−5.37499	−	8.30359i	−0.810310	−	1.25181i
$45$		0			0
$46$	−0.628908	−	0.777810i	−0.0927274	−	0.114682i
$47$	1.89428			0.276310			0.138155	−	0.990411i	$-0.455883\pi$
$47$	1.89428			0.276310			0.138155	+	0.990411i	$0.455883\pi$
$48$		0			0
$49$	−0.122561			−0.0175087
$50$	0.889181	+	1.09971i	0.125749	+	0.155522i
$51$		0			0
$52$	6.98243	−	4.51979i	0.968289	−	0.626782i
$53$	7.43897	−	7.43897i	1.02182	−	1.02182i	0.0220650	−	0.999757i	$-0.492976\pi$
$53$	7.43897	−	7.43897i	1.02182	−	1.02182i	0.999757	−	0.0220650i	$-0.00702407\pi$
$54$		0			0
$55$		−	4.94571i		−	0.666879i
$56$	−6.73338	+	3.41205i	−0.899786	+	0.455955i
$57$		0			0
$58$	−6.95931	−	0.736651i	−0.913802	−	0.0967270i
$59$	−0.959574	+	0.959574i	−0.124926	+	0.124926i	−0.766805	−	0.641880i	$-0.778155\pi$
$59$	−0.959574	+	0.959574i	−0.124926	+	0.124926i	0.641880	+	0.766805i	$0.278155\pi$
$60$		0			0
$61$	6.49825	+	6.49825i	0.832015	+	0.832015i	0.987792	−	0.155777i	$-0.0497881\pi$
$61$	6.49825	+	6.49825i	0.832015	+	0.832015i	−0.155777	+	0.987792i	$0.549788\pi$
$62$	−7.52499	+	6.08442i	−0.955674	+	0.772722i
$63$		0			0
$64$	−4.73092	+	6.45123i	−0.591365	+	0.806404i
$65$	4.15881			0.515837
$66$		0			0
$67$	3.49691	+	3.49691i	0.427216	+	0.427216i	0.887679	−	0.460463i	$-0.152317\pi$
$67$	3.49691	+	3.49691i	0.427216	+	0.427216i	−0.460463	+	0.887679i	$0.652317\pi$
$68$	−0.775103	+	3.62027i	−0.0939951	+	0.439022i
$69$		0			0
$70$	−3.75330	−	0.397291i	−0.448605	−	0.0474854i
$71$		−	7.86777i		−	0.933733i	−0.884328	−	0.466866i	$-0.845383\pi$
$71$		−	7.86777i		−	0.933733i	0.884328	−	0.466866i	$-0.154617\pi$
$72$		0			0
$73$			15.6564i			1.83244i	0.400675	+	0.916220i	$0.368776\pi$
$73$			15.6564i			1.83244i	−0.400675	+	0.916220i	$0.631224\pi$
$74$	0.0205276	−	0.193929i	0.00238628	−	0.0225437i
$75$		0			0
$76$	−8.18824	+	5.30033i	−0.939256	+	0.607989i
$77$	9.33322	+	9.33322i	1.06362	+	1.06362i
$78$		0			0
$79$	−6.70212			−0.754047			−0.377024	−	0.926204i	$-0.623052\pi$
$79$	−6.70212			−0.754047			−0.377024	+	0.926204i	$0.623052\pi$
$80$	−3.73854	+	1.42243i	−0.417982	+	0.159033i
$81$		0			0
$82$	−9.07431	−	11.2228i	−1.00209	−	1.23935i
$83$	3.87327	+	3.87327i	0.425147	+	0.425147i	0.886971	−	0.461825i	$-0.152805\pi$
$83$	3.87327	+	3.87327i	0.425147	+	0.425147i	−0.461825	+	0.886971i	$0.652805\pi$
$84$		0			0
$85$	−1.30896	+	1.30896i	−0.141977	+	0.141977i
$86$	−0.934407	+	8.82755i	−0.100760	+	0.951900i
$87$		0			0
$88$	13.2943	+	4.35218i	1.41718	+	0.463944i
$89$		−	10.5055i		−	1.11358i	−0.830653	−	0.556790i	$-0.812033\pi$
$89$		−	10.5055i		−	1.11358i	0.830653	−	0.556790i	$-0.187967\pi$
$90$		0			0
$91$	−7.84824	+	7.84824i	−0.822719	+	0.822719i
$92$	1.38323	+	0.296151i	0.144212	+	0.0308759i
$93$		0			0
$94$	−2.08316	+	1.68436i	−0.214861	+	0.173729i
$95$	−4.87701			−0.500370
$96$		0			0
$97$	4.79937			0.487303			0.243651	−	0.969863i	$-0.421655\pi$
$97$	4.79937			0.487303			0.243651	+	0.969863i	$0.421655\pi$
$98$	0.134781	−	0.108979i	0.0136150	−	0.0110085i
$99$		0			0
$100$	−1.95568	−	0.418713i	−0.195568	−	0.0418713i
$101$	−0.372979	+	0.372979i	−0.0371128	+	0.0371128i	−0.725420	−	0.688307i	$-0.758354\pi$
$101$	−0.372979	+	0.372979i	−0.0371128	+	0.0371128i	0.688307	+	0.725420i	$0.258354\pi$
$102$		0			0
$103$		−	10.3013i		−	1.01502i	−0.861647	−	0.507508i	$-0.830567\pi$
$103$		−	10.3013i		−	1.01502i	0.861647	−	0.507508i	$-0.169433\pi$
$104$	−3.65972	+	11.1791i	−0.358865	+	1.09620i
$105$		0			0
$106$	−1.56610	+	14.7953i	−0.152113	+	1.43705i
$107$	−14.5069	+	14.5069i	−1.40244	+	1.40244i	−0.610165	+	0.792274i	$0.708897\pi$
$107$	−14.5069	+	14.5069i	−1.40244	+	1.40244i	−0.792274	+	0.610165i	$0.791103\pi$
$108$		0			0
$109$	0.796284	+	0.796284i	0.0762701	+	0.0762701i	0.744213	−	0.667943i	$-0.232825\pi$
$109$	0.796284	+	0.796284i	0.0762701	+	0.0762701i	−0.667943	+	0.744213i	$0.732825\pi$
$110$	4.39763	+	5.43883i	0.419298	+	0.518572i
$111$		0			0
$112$	4.37081	−	9.73945i	0.413003	−	0.920292i
$113$	−0.842524			−0.0792580			−0.0396290	−	0.999214i	$-0.512618\pi$
$113$	−0.842524			−0.0792580			−0.0396290	+	0.999214i	$0.512618\pi$
$114$		0			0
$115$	0.500128	+	0.500128i	0.0466372	+	0.0466372i
$116$	8.30822	−	5.37799i	0.771399	−	0.499334i
$117$		0			0
$118$	0.202015	−	1.90849i	0.0185970	−	0.175690i
$119$		−	4.94039i		−	0.452885i
$120$		0			0
$121$		−	13.4600i		−	1.22364i
$122$	−12.9243	−	1.36805i	−1.17011	−	0.123858i
$123$		0			0
$124$	2.86513	−	13.3822i	0.257297	−	1.20175i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	−21.1693			−1.87847			−0.939234	−	0.343277i	$-0.888463\pi$
$127$	−21.1693			−1.87847			−0.939234	+	0.343277i	$0.888463\pi$
$128$	−0.533685	−	11.3011i	−0.0471715	−	0.998887i
$129$		0			0
$130$	−4.57348	+	3.69794i	−0.401120	+	0.324331i
$131$	−4.67248	−	4.67248i	−0.408237	−	0.408237i	0.472887	−	0.881123i	$-0.343212\pi$
$131$	−4.67248	−	4.67248i	−0.408237	−	0.408237i	−0.881123	+	0.472887i	$0.843212\pi$
$132$		0			0
$133$	9.20357	−	9.20357i	0.798051	−	0.798051i
$134$	−6.95497	−	0.736191i	−0.600818	−	0.0635973i
$135$		0			0
$136$	−2.36669	−	4.67044i	−0.202942	−	0.400487i
$137$		−	10.2840i		−	0.878623i	−0.898335	−	0.439312i	$-0.855222\pi$
$137$		−	10.2840i		−	0.878623i	0.898335	−	0.439312i	$-0.144778\pi$
$138$		0			0
$139$	4.98588	−	4.98588i	0.422897	−	0.422897i	−0.463303	−	0.886200i	$-0.653336\pi$
$139$	4.98588	−	4.98588i	0.422897	−	0.422897i	0.886200	+	0.463303i	$0.153336\pi$
$140$	4.48080	−	2.90046i	0.378697	−	0.245134i
$141$		0			0
$142$	6.99588	+	8.65225i	0.587081	+	0.726080i
$143$	20.5683			1.72001
$144$		0			0
$145$	4.94847			0.410948
$146$	−13.9214	−	17.2174i	−1.15214	−	1.42493i
$147$		0			0
$148$	0.149863	+	0.231518i	0.0123187	+	0.0190306i
$149$	−8.79493	+	8.79493i	−0.720509	+	0.720509i	−0.968709	−	0.248200i	$-0.920161\pi$
$149$	−8.79493	+	8.79493i	−0.720509	+	0.720509i	0.248200	+	0.968709i	$0.420161\pi$
$150$		0			0
$151$		−	22.1838i		−	1.80529i	−0.430385	−	0.902645i	$-0.641622\pi$
$151$		−	22.1838i		−	1.80529i	0.430385	−	0.902645i	$-0.358378\pi$
$152$	4.29172	−	13.1096i	0.348105	−	1.06333i
$153$		0			0
$154$	−18.5627	−	1.96489i	−1.49583	−	0.158335i
$155$	4.83853	−	4.83853i	0.388640	−	0.388640i
$156$		0			0
$157$	−3.72187	−	3.72187i	−0.297038	−	0.297038i	0.542815	−	0.839852i	$-0.317359\pi$
$157$	−3.72187	−	3.72187i	−0.297038	−	0.297038i	−0.839852	+	0.542815i	$0.817359\pi$
$158$	7.37037	−	5.95940i	0.586355	−	0.474104i
$159$		0			0
$160$	2.84650	−	4.88850i	0.225036	−	0.386470i
$161$	−1.88762			−0.148765
$162$		0			0
$163$	2.11630	+	2.11630i	0.165761	+	0.165761i	0.785113	−	0.619352i	$-0.212605\pi$
$163$	2.11630	+	2.11630i	0.165761	+	0.165761i	−0.619352	+	0.785113i	$0.712605\pi$
$164$	19.9582	+	4.27307i	1.55847	+	0.333671i
$165$		0			0
$166$	−7.70350	−	0.815425i	−0.597908	−	0.0632892i
$167$		−	18.1604i		−	1.40530i	−0.711538	−	0.702648i	$-0.752001\pi$
$167$		−	18.1604i		−	1.40530i	0.711538	−	0.702648i	$-0.247999\pi$
$168$		0			0
$169$			4.29572i			0.330440i
$170$	0.275571	−	2.60339i	0.0211354	−	0.199671i
$171$		0			0
$172$	−6.82172	−	10.5386i	−0.520151	−	0.803560i
$173$	8.53542	+	8.53542i	0.648936	+	0.648936i	0.952736	−	0.303800i	$-0.0982555\pi$
$173$	8.53542	+	8.53542i	0.648936	+	0.648936i	−0.303800	+	0.952736i	$0.598255\pi$
$174$		0			0
$175$	2.66881			0.201743
$176$	−18.4897	+	7.03493i	−1.39372	+	0.530278i
$177$		0			0
$178$	9.34128	+	11.5530i	0.700159	+	0.865931i
$179$	2.42499	+	2.42499i	0.181252	+	0.181252i	0.791901	−	0.610649i	$-0.209091\pi$
$179$	2.42499	+	2.42499i	0.181252	+	0.181252i	−0.610649	+	0.791901i	$0.709091\pi$
$180$		0			0
$181$	4.46593	−	4.46593i	0.331950	−	0.331950i	−0.521377	−	0.853327i	$-0.674581\pi$
$181$	4.46593	−	4.46593i	0.331950	−	0.331950i	0.853327	+	0.521377i	$0.174581\pi$
$182$	1.65226	−	15.6093i	0.122474	−	1.15704i
$183$		0			0
$184$	−1.78448	+	0.904262i	−0.131554	+	0.0666631i
$185$			0.137894i			0.0101382i
$186$		0			0
$187$	−6.47376	+	6.47376i	−0.473408	+	0.473408i
$188$	0.793162	−	3.70461i	0.0578473	−	0.270187i
$189$		0			0
$190$	5.36328	−	4.33654i	0.389093	−	0.314606i
$191$	−7.75030			−0.560792			−0.280396	−	0.959884i	$-0.590466\pi$
$191$	−7.75030			−0.560792			−0.280396	+	0.959884i	$0.590466\pi$
$192$		0			0
$193$	−11.3388			−0.816181			−0.408091	−	0.912941i	$-0.633805\pi$
$193$	−11.3388			−0.816181			−0.408091	+	0.912941i	$0.633805\pi$
$194$	−5.27791	+	4.26751i	−0.378932	+	0.306390i
$195$		0			0
$196$	−0.0513179	+	0.239690i	−0.00366557	+	0.0171207i
$197$	−1.10001	+	1.10001i	−0.0783725	+	0.0783725i	−0.745206	−	0.666834i	$-0.767649\pi$
$197$	−1.10001	+	1.10001i	−0.0783725	+	0.0783725i	0.666834	+	0.745206i	$0.267649\pi$
$198$		0			0
$199$			14.2722i			1.01173i	0.862614	+	0.505864i	$0.168826\pi$
$199$			14.2722i			1.01173i	−0.862614	+	0.505864i	$0.831174\pi$
$200$	2.52299	−	1.27849i	0.178402	−	0.0904030i
$201$		0			0
$202$	0.0785219	−	0.741814i	0.00552478	−	0.0521939i
$203$	−9.33843	+	9.33843i	−0.655429	+	0.655429i
$204$		0			0
$205$	7.21620	+	7.21620i	0.504001	+	0.504001i
$206$	9.15971	+	11.3284i	0.638187	+	0.789287i
$207$		0			0
$208$	−5.91563	−	15.5479i	−0.410175	−	1.07805i
$209$	−24.1203			−1.66843
$210$		0			0
$211$	−12.4716	−	12.4716i	−0.858577	−	0.858577i	0.132593	−	0.991171i	$-0.457670\pi$
$211$	−12.4716	−	12.4716i	−0.858577	−	0.858577i	−0.991171	+	0.132593i	$0.957670\pi$
$212$	−11.4334	−	17.6630i	−0.785252	−	1.21310i
$213$		0			0
$214$	3.05409	−	28.8527i	0.208773	−	1.97233i
$215$		−	6.27690i		−	0.428081i
$216$		0			0
$217$			18.2619i			1.23970i
$218$	−1.58372	−	0.167639i	−0.107263	−	0.0113539i
$219$		0			0
$220$	−9.67222	−	2.07083i	−0.652101	−	0.139616i
$221$	−5.44374	−	5.44374i	−0.366186	−	0.366186i
$222$		0			0
$223$	3.08673			0.206703			0.103351	−	0.994645i	$-0.467043\pi$
$223$	3.08673			0.206703			0.103351	+	0.994645i	$0.467043\pi$
$224$	3.85353	+	14.5970i	0.257475	+	0.975303i
$225$		0			0
$226$	0.926530	−	0.749157i	0.0616319	−	0.0498332i
$227$	−8.31678	−	8.31678i	−0.552004	−	0.552004i	0.375015	−	0.927019i	$-0.377638\pi$
$227$	−8.31678	−	8.31678i	−0.552004	−	0.552004i	−0.927019	+	0.375015i	$0.877638\pi$
$228$		0			0
$229$	−9.98910	+	9.98910i	−0.660098	+	0.660098i	−0.955403	−	0.295305i	$-0.904579\pi$
$229$	−9.98910	+	9.98910i	−0.660098	+	0.660098i	0.295305	+	0.955403i	$0.404579\pi$
$230$	−0.994700	−	0.105290i	−0.0655886	−	0.00694262i
$231$		0			0
$232$	−4.35461	+	13.3017i	−0.285894	+	0.873301i
$233$			13.9015i			0.910718i	0.890308	+	0.455359i	$0.150489\pi$
$233$			13.9015i			0.910718i	−0.890308	+	0.455359i	$0.849511\pi$
$234$		0			0
$235$	1.33946	−	1.33946i	0.0873768	−	0.0873768i
$236$	1.47483	+	2.27840i	0.0960034	+	0.148311i
$237$		0			0
$238$	4.39290	+	5.43298i	0.284750	+	0.352168i
$239$	10.7687			0.696569			0.348284	−	0.937389i	$-0.386764\pi$
$239$	10.7687			0.696569			0.348284	+	0.937389i	$0.386764\pi$
$240$		0			0
$241$	−12.4707			−0.803305			−0.401653	−	0.915792i	$-0.631564\pi$
$241$	−12.4707			−0.803305			−0.401653	+	0.915792i	$0.631564\pi$
$242$	11.9684	+	14.8021i	0.769358	+	0.951515i
$243$		0			0
$244$	15.4294	−	9.98758i	0.987765	−	0.639390i
$245$	−0.0866638	+	0.0866638i	−0.00553675	+	0.00553675i
$246$		0			0
$247$		−	20.2826i		−	1.29055i
$248$	8.74835	+	17.2641i	0.555521	+	1.09627i
$249$		0			0
$250$	1.40636	+	0.148864i	0.0889458	+	0.00941502i
$251$	−3.69093	+	3.69093i	−0.232969	+	0.232969i	−0.813931	−	0.580962i	$-0.802677\pi$
$251$	−3.69093	+	3.69093i	−0.232969	+	0.232969i	0.580962	+	0.813931i	$0.302677\pi$
$252$		0			0
$253$	2.47349	+	2.47349i	0.155507	+	0.155507i
$254$	23.2800	−	18.8233i	1.46072	−	1.18108i
$255$		0			0
$256$	10.6356	+	11.9534i	0.664727	+	0.747086i
$257$	−3.11011			−0.194003			−0.0970016	−	0.995284i	$-0.530925\pi$
$257$	−3.11011			−0.194003			−0.0970016	+	0.995284i	$0.530925\pi$
$258$		0			0
$259$	−0.260225	−	0.260225i	−0.0161696	−	0.0161696i
$260$	1.74135	−	8.13330i	0.107994	−	0.504406i
$261$		0			0
$262$	9.29305	+	0.983680i	0.574126	+	0.0607719i
$263$		−	17.9512i		−	1.10692i	−0.832877	−	0.553458i	$-0.813308\pi$
$263$		−	17.9512i		−	1.10692i	0.832877	−	0.553458i	$-0.186692\pi$
$264$		0			0
$265$		−	10.5203i		−	0.646257i
$266$	−1.93759	+	18.3049i	−0.118801	+	1.12234i
$267$		0			0
$268$	8.30304	−	5.37463i	0.507189	−	0.328308i
$269$	−1.62436	−	1.62436i	−0.0990392	−	0.0990392i	0.655851	−	0.754890i	$-0.272310\pi$
$269$	−1.62436	−	1.62436i	−0.0990392	−	0.0990392i	−0.754890	+	0.655851i	$0.772310\pi$
$270$		0			0
$271$	18.1808			1.10440			0.552201	−	0.833711i	$-0.313788\pi$
$271$	18.1808			1.10440			0.552201	+	0.833711i	$0.313788\pi$
$272$	6.75553	+	3.03171i	0.409614	+	0.183824i
$273$		0			0
$274$	9.14436	+	11.3094i	0.552431	+	0.683227i
$275$	−3.49714	−	3.49714i	−0.210886	−	0.210886i
$276$		0			0
$277$	−13.8675	+	13.8675i	−0.833218	+	0.833218i	−0.987956	−	0.154737i	$-0.950547\pi$
$277$	−13.8675	+	13.8675i	−0.833218	+	0.833218i	0.154737	+	0.987956i	$0.450547\pi$
$278$	−1.04966	+	9.91636i	−0.0629543	+	0.594744i
$279$		0			0
$280$	−2.34853	+	7.17390i	−0.140352	+	0.428723i
$281$		−	10.7377i		−	0.640556i	−0.947324	−	0.320278i	$-0.896224\pi$
$281$		−	10.7377i		−	0.640556i	0.947324	−	0.320278i	$-0.103776\pi$
$282$		0			0
$283$	−16.3679	+	16.3679i	−0.972971	+	0.972971i	−0.999644	−	0.0266735i	$-0.991509\pi$
$283$	−16.3679	+	16.3679i	−0.972971	+	0.972971i	0.0266735	+	0.999644i	$0.491509\pi$
$284$	−15.3868	−	3.29434i	−0.913041	−	0.195483i
$285$		0			0
$286$	−22.6191	+	18.2889i	−1.33749	+	1.08145i
$287$	−27.2359			−1.60768
$288$		0			0
$289$	−13.5732			−0.798425
$290$	−5.44187	+	4.40008i	−0.319557	+	0.258382i
$291$		0			0
$292$	30.6188	+	6.55553i	1.79183	+	0.383633i
$293$	4.22052	−	4.22052i	0.246566	−	0.246566i	−0.572994	−	0.819560i	$-0.694218\pi$
$293$	4.22052	−	4.22052i	0.246566	−	0.246566i	0.819560	+	0.572994i	$0.194218\pi$
$294$		0			0
$295$			1.35704i			0.0790101i
$296$	−0.370667	−	0.121346i	−0.0215446	−	0.00705308i
$297$		0			0
$298$	1.85156	−	17.4921i	0.107258	−	1.01329i
$299$	−2.07994	+	2.07994i	−0.120286	+	0.120286i
$300$		0			0
$301$	11.8454	+	11.8454i	0.682755	+	0.682755i
$302$	19.7254	+	24.3957i	1.13507	+	1.40381i
$303$		0			0
$304$	6.93721	+	18.2329i	0.397876	+	1.04573i
$305$	9.18991			0.526213
$306$		0			0
$307$	−12.6363	−	12.6363i	−0.721190	−	0.721190i	0.247658	−	0.968848i	$-0.420339\pi$
$307$	−12.6363	−	12.6363i	−0.721190	−	0.721190i	−0.968848	+	0.247658i	$0.920339\pi$
$308$	22.1607	−	14.3448i	1.26272	−	0.817373i
$309$		0			0
$310$	−1.01864	+	9.62330i	−0.0578547	+	0.546567i
$311$			8.56815i			0.485855i	0.970044	+	0.242928i	$0.0781078\pi$
$311$			8.56815i			0.485855i	−0.970044	+	0.242928i	$0.921892\pi$
$312$		0			0
$313$		−	19.1825i		−	1.08426i	−0.840295	−	0.542129i	$-0.817618\pi$
$313$		−	19.1825i		−	1.08426i	0.840295	−	0.542129i	$-0.182382\pi$
$314$	7.40239	+	0.783551i	0.417741	+	0.0442183i
$315$		0			0
$316$	−2.80626	+	13.1072i	−0.157865	+	0.737337i
$317$	9.41764	+	9.41764i	0.528947	+	0.528947i	0.920258	−	0.391311i	$-0.127978\pi$
$317$	9.41764	+	9.41764i	0.528947	+	0.528947i	−0.391311	+	0.920258i	$0.627978\pi$
$318$		0			0
$319$	24.4737			1.37026
$320$	1.21644	+	7.90698i	0.0680012	+	0.442013i
$321$		0			0
$322$	2.07583	−	1.67844i	0.115681	−	0.0935356i
$323$	6.38383	+	6.38383i	0.355206	+	0.355206i
$324$		0			0
$325$	2.94072	−	2.94072i	0.163122	−	0.163122i
$326$	−4.20908	−	0.445536i	−0.233120	−	0.0246760i
$327$		0			0
$328$	−25.7477	+	13.0473i	−1.42168	+	0.720417i
$329$			5.05549i			0.278718i
$330$		0			0
$331$	12.8579	−	12.8579i	0.706733	−	0.706733i	−0.259114	−	0.965847i	$-0.583431\pi$
$331$	12.8579	−	12.8579i	0.706733	−	0.706733i	0.965847	+	0.259114i	$0.0834305\pi$
$332$	9.19666	−	5.95308i	0.504732	−	0.326718i
$333$		0			0
$334$	16.1479	+	19.9711i	0.883574	+	1.09277i
$335$	4.94538			0.270195
$336$		0			0
$337$	3.31961			0.180831			0.0904153	−	0.995904i	$-0.471181\pi$
$337$	3.31961			0.180831			0.0904153	+	0.995904i	$0.471181\pi$
$338$	−3.81967	−	4.72403i	−0.207763	−	0.256954i
$339$		0			0
$340$	2.01183	+	3.10800i	0.109107	+	0.168555i
$341$	23.9300	−	23.9300i	1.29588	−	1.29588i
$342$		0			0
$343$			18.3546i			0.991055i
$344$	16.8726	+	5.52361i	0.909710	+	0.297813i
$345$		0			0
$346$	−16.9760	−	1.79693i	−0.912635	−	0.0966035i
$347$	−17.8860	+	17.8860i	−0.960171	+	0.960171i	−0.999237	−	0.0390656i	$-0.987562\pi$
$347$	−17.8860	+	17.8860i	−0.960171	+	0.960171i	0.0390656	+	0.999237i	$0.487562\pi$
$348$		0			0
$349$	−3.68796	−	3.68796i	−0.197412	−	0.197412i	0.601478	−	0.798890i	$-0.294579\pi$
$349$	−3.68796	−	3.68796i	−0.197412	−	0.197412i	−0.798890	+	0.601478i	$0.794579\pi$
$350$	−2.93491	+	2.37306i	−0.156878	+	0.126845i
$351$		0			0
$352$	14.0780	−	24.1771i	0.750358	−	1.28864i
$353$	−33.0951			−1.76148			−0.880738	−	0.473604i	$-0.842953\pi$
$353$	−33.0951			−1.76148			−0.880738	+	0.473604i	$0.842953\pi$
$354$		0			0
$355$	−5.56335	−	5.56335i	−0.295272	−	0.295272i
$356$	−20.5454	−	4.39879i	−1.08890	−	0.233135i
$357$		0			0
$358$	−4.82303	−	0.510524i	−0.254905	−	0.0269820i
$359$			6.52522i			0.344388i	0.985063	+	0.172194i	$0.0550856\pi$
$359$			6.52522i			0.344388i	−0.985063	+	0.172194i	$0.944914\pi$
$360$		0			0
$361$			4.78519i			0.251852i
$362$	−0.940195	+	8.88224i	−0.0494156	+	0.466840i
$363$		0			0
$364$	12.0625	+	18.6348i	0.632246	+	0.976729i
$365$	11.0707	+	11.0707i	0.579469	+	0.579469i
$366$		0			0
$367$	−11.0338			−0.575959			−0.287980	−	0.957636i	$-0.592984\pi$
$367$	−11.0338			−0.575959			−0.287980	+	0.957636i	$0.592984\pi$
$368$	1.15835	−	2.58115i	0.0603833	−	0.134552i
$369$		0			0
$370$	−0.122613	−	0.151643i	−0.00637435	−	0.00788357i
$371$	19.8532	+	19.8532i	1.03073	+	1.03073i
$372$		0			0
$373$	6.84468	−	6.84468i	0.354404	−	0.354404i	−0.507341	−	0.861745i	$-0.669372\pi$
$373$	6.84468	−	6.84468i	0.354404	−	0.354404i	0.861745	+	0.507341i	$0.169372\pi$
$374$	1.36290	−	12.8756i	0.0704737	−	0.665781i
$375$		0			0
$376$	2.42183	+	4.77925i	0.124896	+	0.246471i
$377$			20.5797i			1.05991i
$378$		0			0
$379$	−10.1072	+	10.1072i	−0.519171	+	0.519171i	−0.917321	−	0.398150i	$-0.869653\pi$
$379$	−10.1072	+	10.1072i	−0.519171	+	0.519171i	0.398150	+	0.917321i	$0.369653\pi$
$380$	−2.04207	+	9.53786i	−0.104756	+	0.489282i
$381$		0			0
$382$	8.52307	−	6.89143i	0.436078	−	0.352596i
$383$	−29.5283			−1.50883			−0.754413	−	0.656400i	$-0.772078\pi$
$383$	−29.5283			−1.50883			−0.754413	+	0.656400i	$0.772078\pi$
$384$		0			0
$385$	13.1992			0.672692
$386$	12.4693	−	10.0822i	0.634671	−	0.513171i
$387$		0			0
$388$	2.00956	−	9.38604i	0.102020	−	0.476504i
$389$	−0.990949	+	0.990949i	−0.0502431	+	0.0502431i	−0.731782	−	0.681539i	$-0.761311\pi$
$389$	−0.990949	+	0.990949i	−0.0502431	+	0.0502431i	0.681539	+	0.731782i	$0.261311\pi$
$390$		0			0
$391$		−	1.30930i		−	0.0662142i
$392$	−0.156693	−	0.309220i	−0.00791420	−	0.0156180i
$393$		0			0
$394$	0.231581	−	2.18780i	0.0116669	−	0.110220i
$395$	−4.73911	+	4.73911i	−0.238451	+	0.238451i
$396$		0			0
$397$	17.0024	+	17.0024i	0.853326	+	0.853326i	0.990541	−	0.137216i	$-0.0438153\pi$
$397$	17.0024	+	17.0024i	0.853326	+	0.853326i	−0.137216	+	0.990541i	$0.543815\pi$
$398$	−12.6905	−	15.6952i	−0.636119	−	0.786730i
$399$		0			0
$400$	−1.63774	+	3.64936i	−0.0818868	+	0.182468i
$401$	−26.7791			−1.33728			−0.668642	−	0.743585i	$-0.733124\pi$
$401$	−26.7791			−1.33728			−0.668642	+	0.743585i	$0.733124\pi$
$402$		0			0
$403$	20.1225	+	20.1225i	1.00238	+	1.00238i
$404$	0.573256	+	0.885599i	0.0285206	+	0.0440602i
$405$		0			0
$406$	1.96598	−	18.5731i	0.0975701	−	0.921767i
$407$			0.681985i			0.0338048i
$408$		0			0
$409$		−	13.1970i		−	0.652550i	−0.945275	−	0.326275i	$-0.894206\pi$
$409$		−	13.1970i		−	0.652550i	0.945275	−	0.326275i	$-0.105794\pi$
$410$	−14.3522	−	1.51920i	−0.708805	−	0.0750279i
$411$		0			0
$412$	−20.1460	−	4.31328i	−0.992523	−	0.212500i
$413$	−2.56092	−	2.56092i	−0.126015	−	0.126015i
$414$		0			0
$415$	5.47763			0.268886
$416$	20.3304	+	11.8381i	0.996777	+	0.580409i
$417$		0			0
$418$	26.5252	−	21.4473i	1.29739	−	1.04902i
$419$	9.92468	+	9.92468i	0.484852	+	0.484852i	0.906677	−	0.421825i	$-0.138610\pi$
$419$	9.92468	+	9.92468i	0.484852	+	0.484852i	−0.421825	+	0.906677i	$0.638610\pi$
$420$		0			0
$421$	15.7930	−	15.7930i	0.769702	−	0.769702i	−0.208352	−	0.978054i	$-0.566810\pi$
$421$	15.7930	−	15.7930i	0.769702	−	0.769702i	0.978054	+	0.208352i	$0.0668100\pi$
$422$	24.8045	+	2.62559i	1.20747	+	0.127812i
$423$		0			0
$424$	28.2791	+	9.25777i	1.37335	+	0.449597i
$425$			1.85116i			0.0897943i
$426$		0			0
$427$	−17.3426	+	17.3426i	−0.839268	+	0.839268i
$428$	22.2967	+	34.4452i	1.07775	+	1.66497i
$429$		0			0
$430$	5.58130	+	6.90275i	0.269154	+	0.332880i
$431$	0.285215			0.0137383			0.00686917	−	0.999976i	$-0.497813\pi$
$431$	0.285215			0.0137383			0.00686917	+	0.999976i	$0.497813\pi$
$432$		0			0
$433$	−18.1101			−0.870318			−0.435159	−	0.900354i	$-0.643308\pi$
$433$	−18.1101			−0.870318			−0.435159	+	0.900354i	$0.643308\pi$
$434$	−16.2382	−	20.0828i	−0.779457	−	0.964004i
$435$		0			0
$436$	1.89069	−	1.22386i	0.0905476	−	0.0586123i
$437$	2.43913	−	2.43913i	0.116679	−	0.116679i
$438$		0			0
$439$			11.5931i			0.553308i	0.960970	+	0.276654i	$0.0892256\pi$
$439$			11.5931i			0.553308i	−0.960970	+	0.276654i	$0.910774\pi$
$440$	12.4780	−	6.32304i	0.594863	−	0.301439i
$441$		0			0
$442$	10.8270	+	1.14605i	0.514988	+	0.0545120i
$443$	22.6855	−	22.6855i	1.07782	−	1.07782i	0.0811145	−	0.996705i	$-0.474152\pi$
$443$	22.6855	−	22.6855i	1.07782	−	1.07782i	0.996705	−	0.0811145i	$-0.0258479\pi$
$444$		0			0
$445$	−7.42850	−	7.42850i	−0.352145	−	0.352145i
$446$	−3.39450	+	2.74466i	−0.160734	+	0.129963i
$447$		0			0
$448$	−17.2171	−	12.6259i	−0.813433	−	0.596520i
$449$	−12.1999			−0.575747			−0.287873	−	0.957669i	$-0.592948\pi$
$449$	−12.1999			−0.575747			−0.287873	+	0.957669i	$0.592948\pi$
$450$		0			0
$451$	35.6892	+	35.6892i	1.68054	+	1.68054i
$452$	−0.352776	+	1.64771i	−0.0165932	+	0.0775016i
$453$		0			0
$454$	16.5411	+	1.75090i	0.776315	+	0.0821738i
$455$			11.0991i			0.520333i
$456$		0			0
$457$		−	1.70660i		−	0.0798314i	−0.999203	−	0.0399157i	$-0.987291\pi$
$457$		−	1.70660i		−	0.0798314i	0.999203	−	0.0399157i	$-0.0127089\pi$
$458$	2.10297	−	19.8672i	0.0982652	−	0.928334i
$459$		0			0
$460$	1.18750	−	0.768680i	0.0553675	−	0.0358399i
$461$	4.74710	+	4.74710i	0.221094	+	0.221094i	0.808959	−	0.587865i	$-0.200031\pi$
$461$	4.74710	+	4.74710i	0.221094	+	0.221094i	−0.587865	+	0.808959i	$0.700031\pi$
$462$		0			0
$463$	−11.1761			−0.519398			−0.259699	−	0.965690i	$-0.583623\pi$
$463$	−11.1761			−0.519398			−0.259699	+	0.965690i	$0.583623\pi$
$464$	−7.03886	−	18.5000i	−0.326771	−	0.858843i
$465$		0			0
$466$	−12.3610	−	15.2876i	−0.572610	−	0.708184i
$467$	−2.06471	−	2.06471i	−0.0955435	−	0.0955435i	0.657719	−	0.753263i	$-0.271521\pi$
$467$	−2.06471	−	2.06471i	−0.0955435	−	0.0955435i	−0.753263	+	0.657719i	$0.771521\pi$
$468$		0			0
$469$	−9.33260	+	9.33260i	−0.430940	+	0.430940i
$470$	−0.281992	+	2.66404i	−0.0130073	+	0.122883i
$471$		0			0
$472$	−3.64780	−	1.19419i	−0.167904	−	0.0549668i
$473$		−	31.0437i		−	1.42739i
$474$		0			0
$475$	−3.44856	+	3.44856i	−0.158231	+	0.158231i
$476$	−9.66181	−	2.06861i	−0.442848	−	0.0948144i
$477$		0			0
$478$	−11.8424	+	9.57532i	−0.541659	+	0.437965i
$479$	41.6214			1.90173			0.950864	−	0.309608i	$-0.100198\pi$
$479$	41.6214			1.90173			0.950864	+	0.309608i	$0.100198\pi$
$480$		0			0
$481$	−0.573477			−0.0261483
$482$	13.7141	−	11.0887i	0.624659	−	0.505075i
$483$		0			0
$484$	−26.3235	−	5.63589i	−1.19652	−	0.256177i
$485$	3.39367	−	3.39367i	0.154099	−	0.154099i
$486$		0			0
$487$			8.25627i			0.374127i	0.982348	+	0.187064i	$0.0598970\pi$
$487$			8.25627i			0.374127i	−0.982348	+	0.187064i	$0.940103\pi$
$488$	−8.08704	+	24.7029i	−0.366083	+	1.11825i
$489$		0			0
$490$	0.0182450	−	0.172365i	0.000824225	−	0.00778664i
$491$	−4.28512	+	4.28512i	−0.193385	+	0.193385i	−0.797157	−	0.603772i	$-0.793664\pi$
$491$	−4.28512	+	4.28512i	−0.193385	+	0.193385i	0.603772	+	0.797157i	$0.293664\pi$
$492$		0			0
$493$	−6.47737	−	6.47737i	−0.291726	−	0.291726i
$494$	18.0349	+	22.3049i	0.811427	+	1.00354i
$495$		0			0
$496$	−24.9715	−	11.2066i	−1.12125	−	0.503190i
$497$	20.9976			0.941871
$498$		0			0
$499$	−15.1287	−	15.1287i	−0.677253	−	0.677253i	0.282125	−	0.959378i	$-0.408961\pi$
$499$	−15.1287	−	15.1287i	−0.677253	−	0.677253i	−0.959378	+	0.282125i	$0.908961\pi$
$500$	−1.67895	+	1.08680i	−0.0750849	+	0.0486031i
$501$		0			0
$502$	0.777037	−	7.34084i	0.0346808	−	0.327638i
$503$		−	18.6439i		−	0.831291i	−0.909527	−	0.415646i	$-0.863556\pi$
$503$		−	18.6439i		−	0.831291i	0.909527	−	0.415646i	$-0.136444\pi$
$504$		0			0
$505$			0.527472i			0.0234722i
$506$	−4.91950	−	0.520734i	−0.218698	−	0.0231495i
$507$		0			0
$508$	−8.86385	+	41.4003i	−0.393270	+	1.83684i
$509$	−11.6243	−	11.6243i	−0.515239	−	0.515239i	0.400888	−	0.916127i	$-0.368702\pi$
$509$	−11.6243	−	11.6243i	−0.515239	−	0.515239i	−0.916127	+	0.400888i	$0.868702\pi$
$510$		0			0
$511$	−41.7839			−1.84841
$512$	−22.3248	−	3.68821i	−0.986627	−	0.162997i
$513$		0			0
$514$	3.42021	−	2.76545i	0.150859	−	0.121979i
$515$	−7.28411	−	7.28411i	−0.320976	−	0.320976i
$516$		0			0
$517$	6.62459	−	6.62459i	0.291349	−	0.291349i
$518$	0.517559	+	0.0547842i	0.0227402	+	0.00240708i
$519$		0			0
$520$	5.31700	+	10.4926i	0.233166	+	0.460132i
$521$		−	36.9052i		−	1.61684i	−0.588603	−	0.808422i	$-0.700322\pi$
$521$		−	36.9052i		−	1.61684i	0.588603	−	0.808422i	$-0.299678\pi$
$522$		0			0
$523$	6.04158	−	6.04158i	0.264180	−	0.264180i	−0.562570	−	0.826750i	$-0.690187\pi$
$523$	6.04158	−	6.04158i	0.264180	−	0.264180i	0.826750	+	0.562570i	$0.190187\pi$
$524$	−11.0943	+	7.18144i	−0.484657	+	0.313723i
$525$		0			0
$526$	15.9618	+	19.7410i	0.695969	+	0.860750i
$527$	−12.6669			−0.551780
$528$		0			0
$529$	22.4997			0.978250
$530$	9.35445	+	11.5692i	0.406331	+	0.502536i
$531$		0			0
$532$	−14.1456	−	21.8529i	−0.613288	−	0.947443i
$533$	−30.0108	+	30.0108i	−1.29991	+	1.29991i
$534$		0			0
$535$			20.5159i			0.886981i
$536$	−4.35189	+	13.2934i	−0.187973	+	0.574189i
$537$		0			0
$538$	3.23068	+	0.341971i	0.139284	+	0.0147434i
$539$	−0.428614	+	0.428614i	−0.0184617	+	0.0184617i
$540$		0			0
$541$	−28.4222	−	28.4222i	−1.22197	−	1.22197i	−0.966932	−	0.255035i	$-0.917913\pi$
$541$	−28.4222	−	28.4222i	−1.22197	−	1.22197i	−0.255035	−	0.966932i	$-0.582087\pi$
$542$	−19.9935	+	16.1660i	−0.858795	+	0.694389i
$543$		0			0
$544$	−10.1248	+	2.67290i	−0.434099	+	0.114600i
$545$	1.12612			0.0482375
$546$		0			0
$547$	23.3562	+	23.3562i	0.998640	+	0.998640i	0.999999	−	0.00135902i	$-0.000432589\pi$
$547$	23.3562	+	23.3562i	0.998640	+	0.998640i	−0.00135902	+	0.999999i	$0.500433\pi$
$548$	−20.1122	−	4.30605i	−0.859152	−	0.183945i
$549$		0			0
$550$	6.95543	+	0.736240i	0.296581	+	0.0313934i
$551$		−	24.1337i		−	1.02813i
$552$		0			0
$553$		−	17.8867i		−	0.760620i
$554$	2.91948	−	27.5810i	0.124037	−	1.17180i
$555$		0			0
$556$	−7.66312	−	11.8384i	−0.324989	−	0.502061i
$557$	4.89520	+	4.89520i	0.207416	+	0.207416i	0.803168	−	0.595752i	$-0.203146\pi$
$557$	4.89520	+	4.89520i	0.207416	+	0.207416i	−0.595752	+	0.803168i	$0.703146\pi$
$558$		0			0
$559$	26.1044			1.10410
$560$	−3.79620	−	9.97747i	−0.160419	−	0.421625i
$561$		0			0
$562$	9.54774	+	11.8083i	0.402747	+	0.498103i
$563$	−1.28613	−	1.28613i	−0.0542040	−	0.0542040i	0.679485	−	0.733689i	$-0.262203\pi$
$563$	−1.28613	−	1.28613i	−0.0542040	−	0.0542040i	−0.733689	+	0.679485i	$0.762203\pi$
$564$		0			0
$565$	−0.595755	+	0.595755i	−0.0250636	+	0.0250636i
$566$	3.44587	−	32.5539i	0.144841	−	1.36834i
$567$		0			0
$568$	19.8503	−	10.0589i	0.832899	−	0.422061i
$569$			11.4799i			0.481261i	0.970617	+	0.240631i	$0.0773543\pi$
$569$			11.4799i			0.481261i	−0.970617	+	0.240631i	$0.922646\pi$
$570$		0			0
$571$	28.7069	−	28.7069i	1.20134	−	1.20134i	0.227587	−	0.973758i	$-0.426917\pi$
$571$	28.7069	−	28.7069i	1.20134	−	1.20134i	0.973758	−	0.227587i	$-0.0730835\pi$
$572$	8.61221	−	40.2249i	0.360094	−	1.68189i
$573$		0			0
$574$	29.9515	−	24.2176i	1.25015	−	1.01082i
$575$	0.707288			0.0294960
$576$		0			0
$577$	−20.3419			−0.846842			−0.423421	−	0.905933i	$-0.639171\pi$
$577$	−20.3419			−0.846842			−0.423421	+	0.905933i	$0.639171\pi$
$578$	14.9266	−	12.0691i	0.620864	−	0.502007i
$579$		0			0
$580$	2.07199	−	9.67761i	0.0860346	−	0.401841i
$581$	−10.3370	+	10.3370i	−0.428852	+	0.428852i
$582$		0			0
$583$		−	52.0303i		−	2.15488i
$584$	−39.5008	+	20.0165i	−1.63456	+	0.828290i
$585$		0			0
$586$	−0.888530	+	8.39415i	−0.0367048	+	0.346759i
$587$	25.8136	−	25.8136i	1.06544	−	1.06544i	0.0677360	−	0.997703i	$-0.478422\pi$
$587$	25.8136	−	25.8136i	1.06544	−	1.06544i	0.997703	−	0.0677360i	$-0.0215775\pi$
$588$		0			0
$589$	−23.5975	−	23.5975i	−0.972320	−	0.972320i
$590$	−1.20666	−	1.49235i	−0.0496773	−	0.0614391i
$591$		0			0
$592$	0.515524	−	0.196145i	0.0211879	−	0.00806152i
$593$	−4.02945			−0.165470			−0.0827349	−	0.996572i	$-0.526365\pi$
$593$	−4.02945			−0.165470			−0.0827349	+	0.996572i	$0.526365\pi$
$594$		0			0
$595$	−3.49338	−	3.49338i	−0.143215	−	0.143215i
$596$	13.5175	+	20.8826i	0.553699	+	0.855385i
$597$		0			0
$598$	0.437882	−	4.13677i	0.0179063	−	0.169165i
$599$			31.6701i			1.29400i	0.762489	+	0.647002i	$0.223977\pi$
$599$			31.6701i			1.29400i	−0.762489	+	0.647002i	$0.776023\pi$
$600$		0			0
$601$			19.4667i			0.794065i	0.917805	+	0.397032i	$0.129960\pi$
$601$			19.4667i			0.794065i	−0.917805	+	0.397032i	$0.870040\pi$
$602$	−23.5591	−	2.49376i	−0.960197	−	0.101638i
$603$		0			0
$604$	−43.3843	−	9.28864i	−1.76528	−	0.377949i
$605$	−9.51768	−	9.51768i	−0.386949	−	0.386949i
$606$		0			0
$607$	13.6128			0.552528			0.276264	−	0.961082i	$-0.410904\pi$
$607$	13.6128			0.552528			0.276264	+	0.961082i	$0.410904\pi$
$608$	−23.8412	−	13.8824i	−0.966890	−	0.563006i
$609$		0			0
$610$	−10.1062	+	8.17150i	−0.409189	+	0.330854i
$611$	5.57057	+	5.57057i	0.225361	+	0.225361i
$612$		0			0
$613$	−11.1480	+	11.1480i	−0.450265	+	0.450265i	−0.895442	−	0.445177i	$-0.853141\pi$
$613$	−11.1480	+	11.1480i	−0.450265	+	0.450265i	0.445177	+	0.895442i	$0.353141\pi$
$614$	25.1321	+	2.66026i	1.01425	+	0.107360i
$615$		0			0
$616$	−11.6152	+	35.4800i	−0.467988	+	1.42953i
$617$		−	1.96695i		−	0.0791863i	−0.999216	−	0.0395932i	$-0.987394\pi$
$617$		−	1.96695i		−	0.0791863i	0.999216	−	0.0395932i	$-0.0126062\pi$
$618$		0			0
$619$	7.84144	−	7.84144i	0.315174	−	0.315174i	−0.531736	−	0.846910i	$-0.678460\pi$
$619$	7.84144	−	7.84144i	0.315174	−	0.315174i	0.846910	+	0.531736i	$0.178460\pi$
$620$	−7.43666	−	11.4886i	−0.298663	−	0.461392i
$621$		0			0
$622$	−7.61864	−	9.42246i	−0.305480	−	0.377806i
$623$	28.0372			1.12329
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	17.0567	+	21.0951i	0.681723	+	0.843131i
$627$		0			0
$628$	−8.83718	+	5.72039i	−0.352642	+	0.228268i
$629$	0.180499	−	0.180499i	0.00719696	−	0.00719696i
$630$		0			0
$631$			0.220729i			0.00878708i	0.999990	+	0.00439354i	$0.00139851\pi$
$631$			0.220729i			0.00878708i	−0.999990	+	0.00439354i	$0.998601\pi$
$632$	−8.56860	−	16.9093i	−0.340840	−	0.672618i
$633$		0			0
$634$	−18.7306	−	1.98266i	−0.743888	−	0.0787414i
$635$	−14.9689	+	14.9689i	−0.594024	+	0.594024i
$636$		0			0
$637$	−0.360418	−	0.360418i	−0.0142803	−	0.0142803i
$638$	−26.9139	+	21.7615i	−1.06553	+	0.861547i
$639$		0			0
$640$	−8.36847	−	7.61372i	−0.330793	−	0.300959i
$641$	19.2037			0.758502			0.379251	−	0.925294i	$-0.376182\pi$
$641$	19.2037			0.758502			0.379251	+	0.925294i	$0.376182\pi$
$642$		0			0
$643$	−7.17110	−	7.17110i	−0.282801	−	0.282801i	0.551424	−	0.834225i	$-0.314085\pi$
$643$	−7.17110	−	7.17110i	−0.282801	−	0.282801i	−0.834225	+	0.551424i	$0.814085\pi$
$644$	−0.790371	+	3.69158i	−0.0311450	+	0.145469i
$645$		0			0
$646$	−12.6967	−	1.34396i	−0.499546	−	0.0528775i
$647$			26.4735i			1.04078i	0.853928	+	0.520391i	$0.174214\pi$
$647$			26.4735i			1.04078i	−0.853928	+	0.520391i	$0.825786\pi$
$648$		0			0
$649$			6.71153i			0.263451i
$650$	−0.619099	+	5.84877i	−0.0242831	+	0.229408i
$651$		0			0
$652$	5.02492	−	3.25268i	0.196791	−	0.127385i
$653$	−10.5746	−	10.5746i	−0.413815	−	0.413815i	0.469250	−	0.883065i	$-0.344524\pi$
$653$	−10.5746	−	10.5746i	−0.413815	−	0.413815i	−0.883065	+	0.469250i	$0.844524\pi$
$654$		0			0
$655$	−6.60789			−0.258192
$656$	16.7135	−	37.2426i	0.652553	−	1.45408i
$657$		0			0
$658$	−4.49525	−	5.55956i	−0.175243	−	0.216734i
$659$	−24.1291	−	24.1291i	−0.939937	−	0.939937i	0.0583584	−	0.998296i	$-0.481413\pi$
$659$	−24.1291	−	24.1291i	−0.939937	−	0.939937i	−0.998296	+	0.0583584i	$0.981413\pi$
$660$		0			0
$661$	23.4294	−	23.4294i	0.911299	−	0.911299i	−0.0850756	−	0.996374i	$-0.527113\pi$
$661$	23.4294	−	23.4294i	0.911299	−	0.911299i	0.996374	+	0.0850756i	$0.0271132\pi$
$662$	−2.70692	+	25.5729i	−0.105207	+	0.993919i
$663$		0			0
$664$	−4.82027	+	14.7241i	−0.187063	+	0.571408i
$665$		−	13.0158i		−	0.504732i
$666$		0			0
$667$	−2.47487	+	2.47487i	−0.0958273	+	0.0958273i
$668$	−35.5159	−	7.60401i	−1.37415	−	0.294208i
$669$		0			0
$670$	−5.43847	+	4.39734i	−0.210107	+	0.169884i
$671$	45.4506			1.75460
$672$		0			0
$673$	−41.8069			−1.61154			−0.805769	−	0.592230i	$-0.798248\pi$
$673$	−41.8069			−1.61154			−0.805769	+	0.592230i	$0.798248\pi$
$674$	−3.65060	+	2.95173i	−0.140616	+	0.113697i
$675$		0			0
$676$	8.40105	+	1.79867i	0.323117	+	0.0691798i
$677$	22.7350	−	22.7350i	0.873776	−	0.873776i	−0.119106	−	0.992882i	$-0.538003\pi$
$677$	22.7350	−	22.7350i	0.873776	−	0.873776i	0.992882	+	0.119106i	$0.0380027\pi$
$678$		0			0
$679$			12.8086i			0.491550i
$680$	−4.97600	−	1.62900i	−0.190821	−	0.0624693i
$681$		0			0
$682$	−5.03788	+	47.5940i	−0.192911	+	1.82247i
$683$	−34.4402	+	34.4402i	−1.31782	+	1.31782i	−0.402315	+	0.915501i	$0.631794\pi$
$683$	−34.4402	+	34.4402i	−1.31782	+	1.31782i	−0.915501	+	0.402315i	$0.868206\pi$
$684$		0			0
$685$	−7.27190	−	7.27190i	−0.277845	−	0.277845i
$686$	−16.3206	−	20.1847i	−0.623122	−	0.770655i
$687$		0			0
$688$	−23.4664	+	8.92845i	−0.894649	+	0.340394i
$689$	43.7519			1.66682
$690$		0			0
$691$	16.0991	+	16.0991i	0.612438	+	0.612438i	0.943581	−	0.331143i	$-0.107434\pi$
$691$	16.0991	+	16.0991i	0.612438	+	0.612438i	−0.331143	+	0.943581i	$0.607434\pi$
$692$	20.2664	−	13.1186i	0.770414	−	0.498696i
$693$		0			0
$694$	3.76547	−	35.5733i	0.142935	−	1.35034i
$695$		−	7.05110i		−	0.267463i
$696$		0			0
$697$		−	18.8915i		−	0.715567i
$698$	7.33495	+	0.776413i	0.277632	+	0.0293877i
$699$		0			0
$700$	1.11747	−	5.21934i	0.0422363	−	0.197273i
$701$	30.0507	+	30.0507i	1.13500	+	1.13500i	0.989334	+	0.145666i	$0.0465325\pi$
$701$	30.0507	+	30.0507i	1.13500	+	1.13500i	0.145666	+	0.989334i	$0.453467\pi$
$702$		0			0
$703$	0.672512			0.0253643
$704$	6.01617	+	39.1056i	0.226743	+	1.47385i
$705$		0			0
$706$	36.3950	−	29.4276i	1.36974	−	1.10752i
$707$	−0.995412	−	0.995412i	−0.0374363	−	0.0374363i
$708$		0			0
$709$	−12.9188	+	12.9188i	−0.485176	+	0.485176i	−0.906780	−	0.421604i	$-0.861467\pi$
$709$	−12.9188	+	12.9188i	−0.485176	+	0.485176i	0.421604	+	0.906780i	$0.361467\pi$
$710$	11.0649	+	1.17123i	0.415258	+	0.0439555i
$711$		0			0
$712$	26.5052	−	13.4312i	0.993325	−	0.503355i
$713$			4.83977i			0.181251i
$714$		0			0
$715$	14.5440	−	14.5440i	0.543913	−	0.543913i
$716$	5.75788	−	3.72713i	0.215182	−	0.139289i
$717$		0			0
$718$	−5.80211	−	7.17584i	−0.216533	−	0.267800i
$719$	−17.0356			−0.635319			−0.317659	−	0.948205i	$-0.602897\pi$
$719$	−17.0356			−0.635319			−0.317659	+	0.948205i	$0.602897\pi$
$720$		0			0
$721$	27.4922			1.02386
$722$	−4.25490	−	5.26231i	−0.158351	−	0.195843i
$723$		0			0
$724$	−6.86398	−	10.6039i	−0.255098	−	0.394090i
$725$	3.49909	−	3.49909i	0.129953	−	0.129953i
$726$		0			0
$727$			31.7051i			1.17588i	0.808905	+	0.587939i	$0.200061\pi$
$727$			31.7051i			1.17588i	−0.808905	+	0.587939i	$0.799939\pi$
$728$	−29.8349	−	9.76710i	−1.10576	−	0.361993i
$729$		0			0
$730$	−22.0185	−	2.33068i	−0.814940	−	0.0862623i
$731$	−8.21624	+	8.21624i	−0.303888	+	0.303888i
$732$		0			0
$733$	3.87657	+	3.87657i	0.143184	+	0.143184i	0.775065	−	0.631881i	$-0.217717\pi$
$733$	3.87657	+	3.87657i	0.143184	+	0.143184i	−0.631881	+	0.775065i	$0.717717\pi$
$734$	12.1339	−	9.81105i	0.447872	−	0.362132i
$735$		0			0
$736$	1.02126	+	3.86849i	0.0376442	+	0.142595i
$737$	24.4584			0.900937
$738$		0			0
$739$	11.3024	+	11.3024i	0.415766	+	0.415766i	0.883742	−	0.467975i	$-0.155016\pi$
$739$	11.3024	+	11.3024i	0.415766	+	0.415766i	−0.467975	+	0.883742i	$0.655016\pi$
$740$	0.269677	+	0.0577382i	0.00991352	+	0.00212250i
$741$		0			0
$742$	−39.4859	−	4.17962i	−1.44957	−	0.153439i
$743$			30.7210i			1.12704i	0.826102	+	0.563521i	$0.190554\pi$
$743$			30.7210i			1.12704i	−0.826102	+	0.563521i	$0.809446\pi$
$744$		0			0
$745$			12.4379i			0.455690i
$746$	−1.44098	+	13.6133i	−0.0527582	+	0.498419i
$747$		0			0
$748$	9.94995	+	15.3712i	0.363806	+	0.562028i
$749$	−38.7163	−	38.7163i	−1.41466	−	1.41466i
$750$		0			0
$751$	16.4695			0.600981			0.300491	−	0.953785i	$-0.402850\pi$
$751$	16.4695			0.600981			0.300491	+	0.953785i	$0.402850\pi$
$752$	−6.91292	−	3.10234i	−0.252088	−	0.113131i
$753$		0			0
$754$	−18.2991	−	22.6317i	−0.666415	−	0.824198i
$755$	−15.6863	−	15.6863i	−0.570883	−	0.570883i
$756$		0			0
$757$	21.9737	−	21.9737i	0.798649	−	0.798649i	−0.184233	−	0.982883i	$-0.558980\pi$
$757$	21.9737	−	21.9737i	0.798649	−	0.798649i	0.982883	+	0.184233i	$0.0589802\pi$
$758$	2.12783	−	20.1021i	0.0772861	−	0.730140i
$759$		0			0
$760$	−6.23521	−	12.3046i	−0.226175	−	0.446336i
$761$			5.91749i			0.214509i	0.994232	+	0.107254i	$0.0342060\pi$
$761$			5.91749i			0.214509i	−0.994232	+	0.107254i	$0.965794\pi$
$762$		0			0
$763$	−2.12513	+	2.12513i	−0.0769349	+	0.0769349i
$764$	−3.24515	+	15.1571i	−0.117406	+	0.548365i
$765$		0			0
$766$	32.4725	−	26.2560i	1.17328	−	0.948668i
$767$	−5.64368			−0.203782
$768$		0			0
$769$	10.7206			0.386596			0.193298	−	0.981140i	$-0.438082\pi$
$769$	10.7206			0.386596			0.193298	+	0.981140i	$0.438082\pi$
$770$	−14.5152	+	11.7365i	−0.523092	+	0.422952i
$771$		0			0
$772$	−4.74769	+	22.1750i	−0.170873	+	0.798094i
$773$	16.8329	−	16.8329i	0.605438	−	0.605438i	−0.336312	−	0.941750i	$-0.609180\pi$
$773$	16.8329	−	16.8329i	0.605438	−	0.605438i	0.941750	+	0.336312i	$0.109180\pi$
$774$		0			0
$775$		−	6.84272i		−	0.245798i
$776$	6.13596	+	12.1088i	0.220268	+	0.434679i
$777$		0			0
$778$	0.208621	−	1.97089i	0.00747941	−	0.0706597i
$779$	35.1934	−	35.1934i	1.26094	−	1.26094i
$780$		0			0
$781$	−27.5147	−	27.5147i	−0.984554	−	0.984554i
$782$	1.16421	+	1.43985i	0.0416319	+	0.0514889i
$783$		0			0
$784$	0.447269	+	0.200723i	0.0159739	+	0.00716867i
$785$	−5.26352			−0.187863
$786$		0			0
$787$	−25.4619	−	25.4619i	−0.907619	−	0.907619i	0.0884603	−	0.996080i	$-0.471805\pi$
$787$	−25.4619	−	25.4619i	−0.907619	−	0.907619i	−0.996080	+	0.0884603i	$0.971805\pi$
$788$	1.69068	+	2.61186i	0.0602280	+	0.0930436i
$789$		0			0
$790$	0.997707	−	9.42557i	0.0354968	−	0.335347i
$791$		−	2.24854i		−	0.0799489i
$792$		0			0
$793$			38.2191i			1.35720i
$794$	−33.8159	−	3.57945i	−1.20008	−	0.127030i
$795$		0			0
$796$	27.9118	+	5.97594i	0.989307	+	0.211812i
$797$	−7.14518	−	7.14518i	−0.253095	−	0.253095i	0.569143	−	0.822238i	$-0.307275\pi$
$797$	−7.14518	−	7.14518i	−0.253095	−	0.253095i	−0.822238	+	0.569143i	$0.807275\pi$
$798$		0			0
$799$	−3.50662			−0.124055
$800$	−1.44391	−	5.46947i	−0.0510499	−	0.193375i
$801$		0			0
$802$	29.4492	−	23.8115i	1.03989	−	0.840812i
$803$	54.7526	+	54.7526i	1.93218	+	1.93218i
$804$		0			0
$805$	−1.33475	+	1.33475i	−0.0470437	+	0.0470437i
$806$	−40.0215	−	4.23632i	−1.40970	−	0.149218i
$807$		0			0
$808$	−1.41787	−	0.464171i	−0.0498806	−	0.0163295i
$809$		−	12.4413i		−	0.437412i	−0.975791	−	0.218706i	$-0.929817\pi$
$809$		−	12.4413i		−	0.437412i	0.975791	−	0.218706i	$-0.0701835\pi$
$810$		0			0
$811$	−30.6494	+	30.6494i	−1.07624	+	1.07624i	−0.0794022	+	0.996843i	$0.525301\pi$
$811$	−30.6494	+	30.6494i	−1.07624	+	1.07624i	−0.996843	+	0.0794022i	$0.974699\pi$
$812$	14.3528	+	22.1731i	0.503686	+	0.778123i
$813$		0			0
$814$	−0.606409	−	0.749984i	−0.0212546	−	0.0262869i
$815$	2.99290			0.104837
$816$		0			0
$817$	−30.6125			−1.07099
$818$	11.7345	+	14.5129i	0.410288	+	0.507430i
$819$		0			0
$820$	17.1341	−	11.0910i	0.598348	−	0.387316i
$821$	−8.84907	+	8.84907i	−0.308835	+	0.308835i	−0.844457	−	0.535623i	$-0.820077\pi$
$821$	−8.84907	+	8.84907i	−0.308835	+	0.308835i	0.535623	+	0.844457i	$0.320077\pi$
$822$		0			0
$823$			11.7501i			0.409583i	0.978806	+	0.204792i	$0.0656516\pi$
$823$			11.7501i			0.409583i	−0.978806	+	0.204792i	$0.934348\pi$
$824$	25.9900	−	13.1701i	0.905405	−	0.458802i
$825$		0			0
$826$	5.09339	+	0.539141i	0.177222	+	0.0187591i
$827$	3.40407	−	3.40407i	0.118371	−	0.118371i	−0.645440	−	0.763811i	$-0.723326\pi$
$827$	3.40407	−	3.40407i	0.118371	−	0.118371i	0.763811	+	0.645440i	$0.223326\pi$
$828$		0			0
$829$	24.8718	+	24.8718i	0.863834	+	0.863834i	0.991781	−	0.127947i	$-0.0408389\pi$
$829$	24.8718	+	24.8718i	0.863834	+	0.863834i	−0.127947	+	0.991781i	$0.540839\pi$
$830$	−6.02379	+	4.87061i	−0.209089	+	0.169061i
$831$		0			0
$832$	−32.8836	+	5.05896i	−1.14003	+	0.175388i
$833$	0.226880			0.00786092
$834$		0			0
$835$	−12.8414	−	12.8414i	−0.444393	−	0.444393i
$836$	−10.0995	+	47.1715i	−0.349297	+	1.63146i
$837$		0			0
$838$	−19.7391	−	2.08940i	−0.681875	−	0.0721773i
$839$		−	3.26196i		−	0.112615i	−0.998413	−	0.0563076i	$-0.982067\pi$
$839$		−	3.26196i		−	0.112615i	0.998413	−	0.0563076i	$-0.0179328\pi$
$840$		0			0
$841$		−	4.51268i		−	0.155610i
$842$	−3.32483	+	31.4104i	−0.114581	+	1.08248i
$843$		0			0
$844$	−29.6124	+	19.1683i	−1.01930	+	0.659802i
$845$	3.03753	+	3.03753i	0.104494	+	0.104494i
$846$		0			0
$847$	35.9223			1.23430
$848$	−39.3306	+	14.9644i	−1.35062	+	0.513880i
$849$		0			0
$850$	−1.64601	−	2.03573i	−0.0564578	−	0.0698250i
$851$	−0.0689649	−	0.0689649i	−0.00236409	−	0.00236409i
$852$		0			0
$853$	4.02276	−	4.02276i	0.137737	−	0.137737i	−0.634877	−	0.772613i	$-0.718949\pi$
$853$	4.02276	−	4.02276i	0.137737	−	0.137737i	0.772613	+	0.634877i	$0.218949\pi$
$854$	3.65107	−	34.4925i	0.124937	−	1.18031i
$855$		0			0
$856$	−55.1478	−	18.0538i	−1.88491	−	0.617067i
$857$			44.6563i			1.52543i	0.646736	+	0.762714i	$0.276134\pi$
$857$			44.6563i			1.52543i	−0.646736	+	0.762714i	$0.723866\pi$
$858$		0			0
$859$	5.22864	−	5.22864i	0.178399	−	0.178399i	−0.612259	−	0.790658i	$-0.709739\pi$
$859$	5.22864	−	5.22864i	0.178399	−	0.178399i	0.790658	+	0.612259i	$0.209739\pi$
$860$	−12.2756	−	2.62822i	−0.418594	−	0.0896215i
$861$		0			0
$862$	−0.313653	+	0.253608i	−0.0106831	+	0.00863793i
$863$	−36.9653			−1.25831			−0.629157	−	0.777278i	$-0.716600\pi$
$863$	−36.9653			−1.25831			−0.629157	+	0.777278i	$0.716600\pi$
$864$		0			0
$865$	12.0709			0.410423
$866$	19.9159	−	16.1032i	0.676769	−	0.547209i
$867$		0			0
$868$	35.7145	+	7.64651i	1.21223	+	0.259539i
$869$	−23.4383	+	23.4383i	−0.795089	+	0.795089i
$870$		0			0
$871$			20.5669i			0.696883i
$872$	−0.990971	+	3.02705i	−0.0335585	+	0.102509i
$873$		0			0
$874$	−0.513501	+	4.85116i	−0.0173694	+	0.164093i
$875$	1.88714	−	1.88714i	0.0637968	−	0.0637968i
$876$		0			0
$877$	9.40192	+	9.40192i	0.317480	+	0.317480i	0.847799	−	0.530318i	$-0.177928\pi$
$877$	9.40192	+	9.40192i	0.317480	+	0.317480i	−0.530318	+	0.847799i	$0.677928\pi$
$878$	−10.3084	−	12.7490i	−0.347890	−	0.430258i
$879$		0			0
$880$	−8.09977	+	18.0487i	−0.273043	+	0.608420i
$881$	10.3069			0.347248			0.173624	−	0.984812i	$-0.444452\pi$
$881$	10.3069			0.347248			0.173624	+	0.984812i	$0.444452\pi$
$882$		0			0
$883$	34.3375	+	34.3375i	1.15555	+	1.15555i	0.985422	+	0.170128i	$0.0544182\pi$
$883$	34.3375	+	34.3375i	1.15555	+	1.15555i	0.170128	+	0.985422i	$0.445582\pi$
$884$	−12.9256	+	8.36684i	−0.434734	+	0.281407i
$885$		0			0
$886$	−4.77589	+	45.1189i	−0.160449	+	1.51580i
$887$		−	6.79523i		−	0.228161i	−0.993471	−	0.114081i	$-0.963608\pi$
$887$		−	6.79523i		−	0.228161i	0.993471	−	0.114081i	$-0.0363922\pi$
$888$		0			0
$889$		−	56.4968i		−	1.89484i
$890$	14.7745	+	1.56389i	0.495241	+	0.0524218i
$891$		0			0
$892$	1.29245	−	6.03665i	0.0432745	−	0.202122i
$893$	−6.53256	−	6.53256i	−0.218604	−	0.218604i
$894$		0			0
$895$	3.42945			0.114634
$896$	30.1606	−	1.42431i	1.00759	−	0.0475827i
$897$		0			0
$898$	13.4163	−	10.8479i	0.447707	−	0.361998i
$899$	23.9433	+	23.9433i	0.798554	+	0.798554i
$900$		0			0
$901$	−13.7707	+	13.7707i	−0.458769	+	0.458769i
$902$	−70.9819	−	7.51351i	−2.36344	−	0.250173i
$903$		0			0
$904$	−1.07716	−	2.12568i	−0.0358258	−	0.0706990i
$905$		−	6.31578i		−	0.209944i
$906$		0			0
$907$	−3.82391	+	3.82391i	−0.126971	+	0.126971i	−0.767737	−	0.640766i	$-0.778617\pi$
$907$	−3.82391	+	3.82391i	−0.126971	+	0.126971i	0.640766	+	0.767737i	$0.278617\pi$
$908$	−19.7473	+	12.7826i	−0.655337	+	0.424206i
$909$		0			0
$910$	−9.86910	−	12.2058i	−0.327158	−	0.404617i
$911$	18.9169			0.626743			0.313372	−	0.949631i	$-0.398541\pi$
$911$	18.9169			0.626743			0.313372	+	0.949631i	$0.398541\pi$
$912$		0			0
$913$	27.0908			0.896574
$914$	1.51748	+	1.87676i	0.0501937	+	0.0620777i
$915$		0			0
$916$	15.3529	+	23.7180i	0.507274	+	0.783666i
$917$	12.4700	−	12.4700i	0.411795	−	0.411795i
$918$		0			0
$919$			48.9075i			1.61331i	0.591022	+	0.806655i	$0.298724\pi$
$919$			48.9075i			1.61331i	−0.591022	+	0.806655i	$0.701276\pi$
$920$	−0.622407	+	1.90123i	−0.0205202	+	0.0626816i
$921$		0			0
$922$	−9.44144	−	0.999388i	−0.310937	−	0.0329131i
$923$	23.1369	−	23.1369i	0.761562	−	0.761562i
$924$		0			0
$925$	0.0975060	+	0.0975060i	0.00320598	+	0.00320598i
$926$	12.2905	−	9.93759i	0.403890	−	0.326570i
$927$		0			0
$928$	24.1906	+	14.0858i	0.794095	+	0.462390i
$929$	−35.4660			−1.16360			−0.581801	−	0.813331i	$-0.697652\pi$
$929$	−35.4660			−1.16360			−0.581801	+	0.813331i	$0.697652\pi$
$930$		0			0
$931$	0.422660	+	0.422660i	0.0138521	+	0.0138521i
$932$	27.1869	+	5.82074i	0.890536	+	0.190665i
$933$		0			0
$934$	4.10649	+	0.434676i	0.134368	+	0.0142230i
$935$			9.15528i			0.299410i
$936$		0			0
$937$		−	56.4991i		−	1.84575i	−0.385105	−	0.922873i	$-0.625835\pi$
$937$		−	56.4991i		−	1.84575i	0.385105	−	0.922873i	$-0.374165\pi$
$938$	1.96476	−	18.5615i	0.0641516	−	0.606055i
$939$		0			0
$940$	−2.05871	−	3.18041i	−0.0671476	−	0.103733i
$941$	2.86034	+	2.86034i	0.0932445	+	0.0932445i	0.752190	−	0.658946i	$-0.228997\pi$
$941$	2.86034	+	2.86034i	0.0932445	+	0.0932445i	−0.658946	+	0.752190i	$0.728997\pi$
$942$		0			0
$943$	−7.21805			−0.235052
$944$	5.07336	−	1.93030i	0.165124	−	0.0628259i
$945$		0			0
$946$	27.6035	+	34.1390i	0.897466	+	1.10995i
$947$	−5.86681	−	5.86681i	−0.190646	−	0.190646i	0.605329	−	0.795975i	$-0.293041\pi$
$947$	−5.86681	−	5.86681i	−0.190646	−	0.190646i	−0.795975	+	0.605329i	$0.793041\pi$
$948$		0			0
$949$	−46.0411	+	46.0411i	−1.49456	+	1.49456i
$950$	0.726013	−	6.85881i	0.0235550	−	0.222529i
$951$		0			0
$952$	12.4645	−	6.31624i	0.403978	−	0.204711i
$953$			25.0238i			0.810599i	0.914184	+	0.405299i	$0.132833\pi$
$953$			25.0238i			0.810599i	−0.914184	+	0.405299i	$0.867167\pi$
$954$		0			0
$955$	−5.48029	+	5.48029i	−0.177338	+	0.177338i
$956$	4.50899	−	21.0601i	0.145831	−	0.681132i
$957$		0			0
$958$	−45.7713	+	37.0089i	−1.47880	+	1.19570i
$959$	27.4461			0.886281
$960$		0			0
$961$	15.8228			0.510412
$962$	0.630657	−	0.509925i	0.0203332	−	0.0164406i
$963$		0			0
$964$	−5.22163	+	24.3886i	−0.168177	+	0.785504i
$965$	−8.01771	+	8.01771i	−0.258099	+	0.258099i
$966$		0			0
$967$		−	16.6523i		−	0.535502i	−0.963488	−	0.267751i	$-0.913720\pi$
$967$		−	16.6523i		−	0.535502i	0.963488	−	0.267751i	$-0.0862804\pi$
$968$	33.9595	−	17.2085i	1.09150	−	0.553103i
$969$		0			0
$970$	−0.714456	+	6.74963i	−0.0229398	+	0.216718i
$971$	30.6552	−	30.6552i	0.983771	−	0.983771i	−0.0160991	−	0.999870i	$-0.505125\pi$
$971$	30.6552	−	30.6552i	0.983771	−	0.983771i	0.999870	+	0.0160991i	$0.00512472\pi$
$972$		0			0
$973$	13.3064	+	13.3064i	0.426583	+	0.426583i
$974$	−7.34132	−	9.07948i	−0.235231	−	0.290925i
$975$		0			0
$976$	−13.0720	−	34.3569i	−0.418425	−	1.09974i
$977$	13.4307			0.429687			0.214844	−	0.976648i	$-0.431076\pi$
$977$	13.4307			0.429687			0.214844	+	0.976648i	$0.431076\pi$
$978$		0			0
$979$	−36.7392	−	36.7392i	−1.17419	−	1.17419i
$980$	0.133199	+	0.205774i	0.00425489	+	0.00657320i
$981$		0			0
$982$	0.902130	−	8.52263i	0.0287881	−	0.271968i
$983$			7.94549i			0.253422i	0.991940	+	0.126711i	$0.0404420\pi$
$983$			7.94549i			0.253422i	−0.991940	+	0.126711i	$0.959558\pi$
$984$		0			0
$985$			1.55565i			0.0495672i
$986$	12.8828	+	1.36366i	0.410271	+	0.0434276i
$987$		0			0
$988$	−39.6662	−	8.49257i	−1.26195	−	0.270185i
$989$	3.13925	+	3.13925i	0.0998225	+	0.0998225i
$990$		0			0
$991$	−25.0787			−0.796652			−0.398326	−	0.917244i	$-0.630409\pi$
$991$	−25.0787			−0.796652			−0.398326	+	0.917244i	$0.630409\pi$
$992$	37.4260	−	9.88027i	1.18828	−	0.313699i
$993$		0			0
$994$	−23.0912	+	18.6707i	−0.732409	+	0.592198i
$995$	10.0919	+	10.0919i	0.319936	+	0.319936i
$996$		0			0
$997$	36.1819	−	36.1819i	1.14589	−	1.14589i	0.158539	−	0.987353i	$-0.449322\pi$
$997$	36.1819	−	36.1819i	1.14589	−	1.14589i	0.987353	−	0.158539i	$-0.0506783\pi$
$998$	30.0893	+	3.18498i	0.952459	+	0.100819i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.c.541.2		16
3.2	odd	2		80.2.l.a.61.7	yes	16
4.3	odd	2		2880.2.t.c.721.6		16
12.11	even	2		320.2.l.a.81.5		16
15.2	even	4		400.2.q.h.349.6		16
15.8	even	4		400.2.q.g.349.3		16
15.14	odd	2		400.2.l.h.301.2		16
16.5	even	4	inner	720.2.t.c.181.2		16
16.11	odd	4		2880.2.t.c.2161.7		16
24.5	odd	2		640.2.l.b.161.5		16
24.11	even	2		640.2.l.a.161.4		16
48.5	odd	4		80.2.l.a.21.7	✓	16
48.11	even	4		320.2.l.a.241.5		16
48.29	odd	4		640.2.l.b.481.5		16
48.35	even	4		640.2.l.a.481.4		16
60.23	odd	4		1600.2.q.h.849.4		16
60.47	odd	4		1600.2.q.g.849.5		16
60.59	even	2		1600.2.l.i.401.4		16
96.5	odd	8		5120.2.a.s.1.5		8
96.11	even	8		5120.2.a.t.1.5		8
96.53	odd	8		5120.2.a.v.1.4		8
96.59	even	8		5120.2.a.u.1.4		8
240.53	even	4		400.2.q.h.149.6		16
240.59	even	4		1600.2.l.i.1201.4		16
240.107	odd	4		1600.2.q.h.49.4		16
240.149	odd	4		400.2.l.h.101.2		16
240.197	even	4		400.2.q.g.149.3		16
240.203	odd	4		1600.2.q.g.49.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.7	✓	16	48.5	odd	4
80.2.l.a.61.7	yes	16	3.2	odd	2
320.2.l.a.81.5		16	12.11	even	2
320.2.l.a.241.5		16	48.11	even	4
400.2.l.h.101.2		16	240.149	odd	4
400.2.l.h.301.2		16	15.14	odd	2
400.2.q.g.149.3		16	240.197	even	4
400.2.q.g.349.3		16	15.8	even	4
400.2.q.h.149.6		16	240.53	even	4
400.2.q.h.349.6		16	15.2	even	4
640.2.l.a.161.4		16	24.11	even	2
640.2.l.a.481.4		16	48.35	even	4
640.2.l.b.161.5		16	24.5	odd	2
640.2.l.b.481.5		16	48.29	odd	4
720.2.t.c.181.2		16	16.5	even	4	inner
720.2.t.c.541.2		16	1.1	even	1	trivial
1600.2.l.i.401.4		16	60.59	even	2
1600.2.l.i.1201.4		16	240.59	even	4
1600.2.q.g.49.5		16	240.203	odd	4
1600.2.q.g.849.5		16	60.47	odd	4
1600.2.q.h.49.4		16	240.107	odd	4
1600.2.q.h.849.4		16	60.23	odd	4
2880.2.t.c.721.6		16	4.3	odd	2
2880.2.t.c.2161.7		16	16.11	odd	4
5120.2.a.s.1.5		8	96.5	odd	8
5120.2.a.t.1.5		8	96.11	even	8
5120.2.a.u.1.4		8	96.59	even	8
5120.2.a.v.1.4		8	96.53	odd	8

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.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09971 + 0.889181i) q^{2} +(0.418713 - 1.95568i) q^{4} +(0.707107 - 0.707107i) q^{5} +2.66881i q^{7} +(1.27849 + 2.52299i) q^{8} +O(q^{10})\)	\(q+(-1.09971 + 0.889181i) q^{2} +(0.418713 - 1.95568i) q^{4} +(0.707107 - 0.707107i) q^{5} +2.66881i q^{7} +(1.27849 + 2.52299i) q^{8} +(-0.148864 + 1.40636i) q^{10} +(3.49714 - 3.49714i) q^{11} +(2.94072 + 2.94072i) q^{13} +(-2.37306 - 2.93491i) q^{14} +(-3.64936 - 1.63774i) q^{16} -1.85116 q^{17} +(-3.44856 - 3.44856i) q^{19} +(-1.08680 - 1.67895i) q^{20} +(-0.736240 + 6.95543i) q^{22} +0.707288i q^{23} -1.00000i q^{25} +(-5.84877 - 0.619099i) q^{26} +(5.21934 + 1.11747i) q^{28} +(3.49909 + 3.49909i) q^{29} +6.84272 q^{31} +(5.46947 - 1.44391i) q^{32} +(2.03573 - 1.64601i) q^{34} +(1.88714 + 1.88714i) q^{35} +(-0.0975060 + 0.0975060i) q^{37} +(6.85881 + 0.726013i) q^{38} +(2.68805 + 0.879991i) q^{40} +10.2052i q^{41} +(4.43844 - 4.43844i) q^{43} +(-5.37499 - 8.30359i) q^{44} +(-0.628908 - 0.777810i) q^{46} +1.89428 q^{47} -0.122561 q^{49} +(0.889181 + 1.09971i) q^{50} +(6.98243 - 4.51979i) q^{52} +(7.43897 - 7.43897i) q^{53} -4.94571i q^{55} +(-6.73338 + 3.41205i) q^{56} +(-6.95931 - 0.736651i) q^{58} +(-0.959574 + 0.959574i) q^{59} +(6.49825 + 6.49825i) q^{61} +(-7.52499 + 6.08442i) q^{62} +(-4.73092 + 6.45123i) q^{64} +4.15881 q^{65} +(3.49691 + 3.49691i) q^{67} +(-0.775103 + 3.62027i) q^{68} +(-3.75330 - 0.397291i) q^{70} -7.86777i q^{71} +15.6564i q^{73} +(0.0205276 - 0.193929i) q^{74} +(-8.18824 + 5.30033i) q^{76} +(9.33322 + 9.33322i) q^{77} -6.70212 q^{79} +(-3.73854 + 1.42243i) q^{80} +(-9.07431 - 11.2228i) q^{82} +(3.87327 + 3.87327i) q^{83} +(-1.30896 + 1.30896i) q^{85} +(-0.934407 + 8.82755i) q^{86} +(13.2943 + 4.35218i) q^{88} -10.5055i q^{89} +(-7.84824 + 7.84824i) q^{91} +(1.38323 + 0.296151i) q^{92} +(-2.08316 + 1.68436i) q^{94} -4.87701 q^{95} +4.79937 q^{97} +(0.134781 - 0.108979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4}+O(q^{10}) \) 16 * q - 4 * q^4	\( 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47} - 16 q^{49} + 4 q^{50} + 56 q^{52} - 16 q^{53} - 16 q^{56} - 12 q^{58} + 8 q^{59} + 16 q^{61} + 8 q^{62} - 16 q^{64} + 40 q^{67} + 48 q^{68} - 8 q^{70} + 72 q^{74} - 16 q^{77} + 16 q^{79} - 16 q^{80} - 76 q^{82} - 40 q^{83} - 16 q^{85} - 28 q^{86} + 32 q^{91} + 52 q^{92} - 36 q^{94} - 32 q^{95} - 60 q^{98}+O(q^{100}) \) 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

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