LMFDB - Embedded newform 720.2.t.b.181.4

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			181.4
Root			$0.500000 + 2.10607i$ of defining polynomial
Character	$\chi$	$=$	720.181
Dual form			720.2.t.b.541.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34277 + 0.443806i) q^{2} +(1.60607 + 1.19186i) q^{4} +(0.707107 + 0.707107i) q^{5} -1.41421i q^{7} +(1.62764 + 2.31318i) q^{8} +O(q^{10})$	\(q+(1.34277 + 0.443806i) q^{2} +(1.60607 + 1.19186i) q^{4} +(0.707107 + 0.707107i) q^{5} -1.41421i q^{7} +(1.62764 + 2.31318i) q^{8} +(0.635665 + 1.26330i) q^{10} +(0.526602 + 0.526602i) q^{11} +(3.68554 - 3.68554i) q^{13} +(0.627636 - 1.89897i) q^{14} +(1.15894 + 3.82843i) q^{16} +1.57316 q^{17} +(-0.383719 + 0.383719i) q^{19} +(0.292893 + 1.97844i) q^{20} +(0.473398 + 0.940816i) q^{22} +6.42429i q^{23} +1.00000i q^{25} +(6.58451 - 3.31318i) q^{26} +(1.68554 - 2.27133i) q^{28} +(-4.38372 + 4.38372i) q^{29} -5.75481 q^{31} +(-0.142883 + 5.65505i) q^{32} +(2.11239 + 0.698175i) q^{34} +(1.00000 - 1.00000i) q^{35} +(1.91032 + 1.91032i) q^{37} +(-0.685544 + 0.344951i) q^{38} +(-0.484753 + 2.78658i) q^{40} -11.9747i q^{41} +(-1.12845 - 1.12845i) q^{43} +(0.218126 + 1.47340i) q^{44} +(-2.85114 + 8.62636i) q^{46} +2.09311 q^{47} +5.00000 q^{49} +(-0.443806 + 1.34277i) q^{50} +(10.3119 - 1.52660i) q^{52} +(-9.55274 - 9.55274i) q^{53} +0.744728i q^{55} +(3.27133 - 2.30182i) q^{56} +(-7.83185 + 3.94082i) q^{58} +(-4.61971 - 4.61971i) q^{59} +(4.53003 - 4.53003i) q^{61} +(-7.72739 - 2.55402i) q^{62} +(-2.70160 + 7.53003i) q^{64} +5.21215 q^{65} +(-5.59587 + 5.59587i) q^{67} +(2.52660 + 1.87498i) q^{68} +(1.78658 - 0.898966i) q^{70} -11.8816i q^{71} +12.1995i q^{73} +(1.71731 + 3.41294i) q^{74} +(-1.07362 + 0.158942i) q^{76} +(0.744728 - 0.744728i) q^{77} -3.33051 q^{79} +(-1.88761 + 3.52660i) q^{80} +(5.31446 - 16.0793i) q^{82} +(-6.31788 + 6.31788i) q^{83} +(1.11239 + 1.11239i) q^{85} +(-1.01444 - 2.01606i) q^{86} +(-0.361009 + 2.07524i) q^{88} +5.42847i q^{89} +(-5.21215 - 5.21215i) q^{91} +(-7.65685 + 10.3179i) q^{92} +(2.81056 + 0.928932i) q^{94} -0.542661 q^{95} +2.13853 q^{97} +(6.71386 + 2.21903i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 12 q^{8}+O(q^{10}) $ 8 * q - 4 * q^4 + 12 * q^8	$ 8 q - 4 q^{4} + 12 q^{8} - 8 q^{11} + 8 q^{13} + 4 q^{14} - 8 q^{17} + 8 q^{19} + 8 q^{20} + 16 q^{22} + 20 q^{26} - 8 q^{28} - 24 q^{29} + 8 q^{31} + 16 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{40} + 16 q^{44} + 24 q^{46} + 40 q^{49} - 4 q^{50} + 16 q^{52} + 16 q^{56} - 8 q^{59} - 16 q^{61} - 28 q^{62} + 8 q^{64} + 8 q^{65} + 8 q^{68} + 4 q^{70} + 36 q^{74} - 40 q^{76} + 8 q^{77} - 40 q^{79} - 16 q^{80} + 64 q^{82} - 32 q^{83} + 8 q^{85} - 16 q^{86} - 16 q^{88} - 8 q^{91} - 16 q^{92} + 32 q^{94} + 16 q^{95} - 48 q^{97}+O(q^{100}) $ 8 * q - 4 * q^4 + 12 * q^8 - 8 * q^11 + 8 * q^13 + 4 * q^14 - 8 * q^17 + 8 * q^19 + 8 * q^20 + 16 * q^22 + 20 * q^26 - 8 * q^28 - 24 * q^29 + 8 * q^31 + 16 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^40 + 16 * q^44 + 24 * q^46 + 40 * q^49 - 4 * q^50 + 16 * q^52 + 16 * q^56 - 8 * q^59 - 16 * q^61 - 28 * q^62 + 8 * q^64 + 8 * q^65 + 8 * q^68 + 4 * q^70 + 36 * q^74 - 40 * q^76 + 8 * q^77 - 40 * q^79 - 16 * q^80 + 64 * q^82 - 32 * q^83 + 8 * q^85 - 16 * q^86 - 16 * q^88 - 8 * q^91 - 16 * q^92 + 32 * q^94 + 16 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.34277	+	0.443806i	0.949483	+	0.313818i
$2$	1.34277	+	0.443806i	0.949483	+	0.313818i
$3$		0			0
$3$		0			0
$4$	1.60607	+	1.19186i	0.803037	+	0.595930i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$		−	1.41421i		−	0.534522i	−0.963624	−	0.267261i	$-0.913881\pi$
$7$		−	1.41421i		−	0.534522i	0.963624	−	0.267261i	$-0.0861187\pi$
$8$	1.62764	+	2.31318i	0.575456	+	0.817833i
$9$		0			0
$10$	0.635665	+	1.26330i	0.201015	+	0.399491i
$11$	0.526602	+	0.526602i	0.158777	+	0.158777i	0.782024	−	0.623248i	$-0.214187\pi$
$11$	0.526602	+	0.526602i	0.158777	+	0.158777i	−0.623248	+	0.782024i	$0.714187\pi$
$12$		0			0
$13$	3.68554	−	3.68554i	1.02219	−	1.02219i	0.0224377	−	0.999748i	$-0.492857\pi$
$13$	3.68554	−	3.68554i	1.02219	−	1.02219i	0.999748	−	0.0224377i	$-0.00714275\pi$
$14$	0.627636	−	1.89897i	0.167743	−	0.507520i
$15$		0			0
$16$	1.15894	+	3.82843i	0.289735	+	0.957107i
$17$	1.57316			0.381546			0.190773	−	0.981634i	$-0.438901\pi$
$17$	1.57316			0.381546			0.190773	+	0.981634i	$0.438901\pi$
$18$		0			0
$19$	−0.383719	+	0.383719i	−0.0880312	+	0.0880312i	−0.749751	−	0.661720i	$-0.769827\pi$
$19$	−0.383719	+	0.383719i	−0.0880312	+	0.0880312i	0.661720	+	0.749751i	$0.269827\pi$
$20$	0.292893	+	1.97844i	0.0654929	+	0.442392i
$21$		0			0
$22$	0.473398	+	0.940816i	0.100929	+	0.200583i
$23$			6.42429i			1.33956i	0.742561	+	0.669779i	$0.233611\pi$
$23$			6.42429i			1.33956i	−0.742561	+	0.669779i	$0.766389\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$	6.58451	−	3.31318i	1.29133	−	0.649768i
$27$		0			0
$28$	1.68554	−	2.27133i	0.318538	−	0.429241i
$29$	−4.38372	+	4.38372i	−0.814036	+	0.814036i	−0.985236	−	0.171200i	$-0.945236\pi$
$29$	−4.38372	+	4.38372i	−0.814036	+	0.814036i	0.171200	+	0.985236i	$0.445236\pi$
$30$		0			0
$31$	−5.75481			−1.03359			−0.516797	−	0.856108i	$-0.672876\pi$
$31$	−5.75481			−1.03359			−0.516797	+	0.856108i	$0.672876\pi$
$32$	−0.142883	+	5.65505i	−0.0252584	+	0.999681i
$33$		0			0
$34$	2.11239	+	0.698175i	0.362272	+	0.119736i
$35$	1.00000	−	1.00000i	0.169031	−	0.169031i
$36$		0			0
$37$	1.91032	+	1.91032i	0.314055	+	0.314055i	0.846478	−	0.532423i	$-0.178719\pi$
$37$	1.91032	+	1.91032i	0.314055	+	0.314055i	−0.532423	+	0.846478i	$0.678719\pi$
$38$	−0.685544	+	0.344951i	−0.111210	+	0.0559584i
$39$		0			0
$40$	−0.484753	+	2.78658i	−0.0766461	+	0.440597i
$41$		−	11.9747i		−	1.87014i	−0.354463	−	0.935070i	$-0.615336\pi$
$41$		−	11.9747i		−	1.87014i	0.354463	−	0.935070i	$-0.384664\pi$
$42$		0			0
$43$	−1.12845	−	1.12845i	−0.172087	−	0.172087i	0.615809	−	0.787896i	$-0.288829\pi$
$43$	−1.12845	−	1.12845i	−0.172087	−	0.172087i	−0.787896	+	0.615809i	$0.788829\pi$
$44$	0.218126	+	1.47340i	0.0328837	+	0.222123i
$45$		0			0
$46$	−2.85114	+	8.62636i	−0.420377	+	1.27189i
$47$	2.09311			0.305311			0.152655	−	0.988279i	$-0.451218\pi$
$47$	2.09311			0.305311			0.152655	+	0.988279i	$0.451218\pi$
$48$		0			0
$49$	5.00000			0.714286
$50$	−0.443806	+	1.34277i	−0.0627636	+	0.189897i
$51$		0			0
$52$	10.3119	−	1.52660i	1.43000	−	0.211702i
$53$	−9.55274	−	9.55274i	−1.31217	−	1.31217i	−0.919813	−	0.392356i	$-0.871660\pi$
$53$	−9.55274	−	9.55274i	−1.31217	−	1.31217i	−0.392356	−	0.919813i	$-0.628340\pi$
$54$		0			0
$55$			0.744728i			0.100419i
$56$	3.27133	−	2.30182i	0.437150	−	0.307594i
$57$		0			0
$58$	−7.83185	+	3.94082i	−1.02837	+	0.517454i
$59$	−4.61971	−	4.61971i	−0.601435	−	0.601435i	0.339258	−	0.940693i	$-0.389824\pi$
$59$	−4.61971	−	4.61971i	−0.601435	−	0.601435i	−0.940693	+	0.339258i	$0.889824\pi$
$60$		0			0
$61$	4.53003	−	4.53003i	0.580011	−	0.580011i	−0.354895	−	0.934906i	$-0.615483\pi$
$61$	4.53003	−	4.53003i	0.580011	−	0.580011i	0.934906	+	0.354895i	$0.115483\pi$
$62$	−7.72739	−	2.55402i	−0.981380	−	0.324360i
$63$		0			0
$64$	−2.70160	+	7.53003i	−0.337700	+	0.941254i
$65$	5.21215			0.646487
$66$		0			0
$67$	−5.59587	+	5.59587i	−0.683644	+	0.683644i	−0.960819	−	0.277176i	$-0.910602\pi$
$67$	−5.59587	+	5.59587i	−0.683644	+	0.683644i	0.277176	+	0.960819i	$0.410602\pi$
$68$	2.52660	+	1.87498i	0.306396	+	0.227375i
$69$		0			0
$70$	1.78658	−	0.898966i	0.213537	−	0.107447i
$71$		−	11.8816i		−	1.41009i	−0.709162	−	0.705045i	$-0.750927\pi$
$71$		−	11.8816i		−	1.41009i	0.709162	−	0.705045i	$-0.249073\pi$
$72$		0			0
$73$			12.1995i			1.42785i	0.700225	+	0.713923i	$0.253083\pi$
$73$			12.1995i			1.42785i	−0.700225	+	0.713923i	$0.746917\pi$
$74$	1.71731	+	3.41294i	0.199634	+	0.396746i
$75$		0			0
$76$	−1.07362	+	0.158942i	−0.123153	+	0.0182319i
$77$	0.744728	−	0.744728i	0.0848696	−	0.0848696i
$78$		0			0
$79$	−3.33051			−0.374712			−0.187356	−	0.982292i	$-0.559992\pi$
$79$	−3.33051			−0.374712			−0.187356	+	0.982292i	$0.559992\pi$
$80$	−1.88761	+	3.52660i	−0.211041	+	0.394286i
$81$		0			0
$82$	5.31446	−	16.0793i	0.586883	−	1.77567i
$83$	−6.31788	+	6.31788i	−0.693478	+	0.693478i	−0.962995	−	0.269518i	$-0.913136\pi$
$83$	−6.31788	+	6.31788i	−0.693478	+	0.693478i	0.269518	+	0.962995i	$0.413136\pi$
$84$		0			0
$85$	1.11239	+	1.11239i	0.120655	+	0.120655i
$86$	−1.01444	−	2.01606i	−0.109389	−	0.217397i
$87$		0			0
$88$	−0.361009	+	2.07524i	−0.0384837	+	0.221222i
$89$			5.42847i			0.575416i	0.957718	+	0.287708i	$0.0928933\pi$
$89$			5.42847i			0.575416i	−0.957718	+	0.287708i	$0.907107\pi$
$90$		0			0
$91$	−5.21215	−	5.21215i	−0.546381	−	0.546381i
$92$	−7.65685	+	10.3179i	−0.798282	+	1.07571i
$93$		0			0
$94$	2.81056	+	0.928932i	0.289888	+	0.0958120i
$95$	−0.542661			−0.0556758
$96$		0			0
$97$	2.13853			0.217134			0.108567	−	0.994089i	$-0.465374\pi$
$97$	2.13853			0.217134			0.108567	+	0.994089i	$0.465374\pi$
$98$	6.71386	+	2.21903i	0.678202	+	0.224156i
$99$		0			0
$100$	−1.19186	+	1.60607i	−0.119186	+	0.160607i
$101$	−5.83851	−	5.83851i	−0.580953	−	0.580953i	0.354212	−	0.935165i	$-0.384749\pi$
$101$	−5.83851	−	5.83851i	−0.580953	−	0.580953i	−0.935165	+	0.354212i	$0.884749\pi$
$102$		0			0
$103$		−	16.4385i		−	1.61974i	−0.586611	−	0.809869i	$-0.699538\pi$
$103$		−	16.4385i		−	1.61974i	0.586611	−	0.809869i	$-0.300462\pi$
$104$	14.5240	+	2.52660i	1.42420	+	0.247754i
$105$		0			0
$106$	−8.58759	−	17.0667i	−0.834101	−	1.65767i
$107$	−5.08532	−	5.08532i	−0.491617	−	0.491617i	0.417199	−	0.908815i	$-0.363012\pi$
$107$	−5.08532	−	5.08532i	−0.491617	−	0.491617i	−0.908815	+	0.417199i	$0.863012\pi$
$108$		0			0
$109$	5.47682	−	5.47682i	0.524585	−	0.524585i	−0.394368	−	0.918953i	$-0.629036\pi$
$109$	5.47682	−	5.47682i	0.524585	−	0.524585i	0.918953	+	0.394368i	$0.129036\pi$
$110$	−0.330515	+	1.00000i	−0.0315133	+	0.0953463i
$111$		0			0
$112$	5.41421	−	1.63899i	0.511595	−	0.154870i
$113$	14.9575			1.40709			0.703544	−	0.710652i	$-0.251600\pi$
$113$	14.9575			1.40709			0.703544	+	0.710652i	$0.251600\pi$
$114$		0			0
$115$	−4.54266	+	4.54266i	−0.423605	+	0.423605i
$116$	−12.2654	+	1.81580i	−1.13881	+	0.168592i
$117$		0			0
$118$	−4.15296	−	8.25347i	−0.382311	−	0.759793i
$119$		−	2.22478i		−	0.203945i
$120$		0			0
$121$		−	10.4454i		−	0.949580i
$122$	8.09325	−	4.07234i	0.732728	−	0.368693i
$123$		0			0
$124$	−9.24264	−	6.85892i	−0.830014	−	0.615949i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−19.3890			−1.72049			−0.860246	−	0.509880i	$-0.829690\pi$
$127$	−19.3890			−1.72049			−0.860246	+	0.509880i	$0.829690\pi$
$128$	−6.96951	+	8.91213i	−0.616023	+	0.787728i
$129$		0			0
$130$	6.99872	+	2.31318i	0.613829	+	0.202879i
$131$	−4.78350	+	4.78350i	−0.417936	+	0.417936i	−0.884492	−	0.466556i	$-0.845495\pi$
$131$	−4.78350	+	4.78350i	−0.417936	+	0.417936i	0.466556	+	0.884492i	$0.345495\pi$
$132$		0			0
$133$	0.542661	+	0.542661i	0.0470547	+	0.0470547i
$134$	−9.99745	+	5.03049i	−0.863648	+	0.434569i
$135$		0			0
$136$	2.56052	+	3.63899i	0.219563	+	0.312041i
$137$		−	3.91630i		−	0.334592i	−0.985907	−	0.167296i	$-0.946496\pi$
$137$		−	3.91630i		−	0.334592i	0.985907	−	0.167296i	$-0.0535036\pi$
$138$		0			0
$139$	15.1665	+	15.1665i	1.28640	+	1.28640i	0.936956	+	0.349447i	$0.113630\pi$
$139$	15.1665	+	15.1665i	1.28640	+	1.28640i	0.349447	+	0.936956i	$0.386370\pi$
$140$	2.79793	−	0.414214i	0.236468	−	0.0350074i
$141$		0			0
$142$	5.27314	−	15.9543i	0.442512	−	1.33886i
$143$	3.88163			0.324598
$144$		0			0
$145$	−6.19951			−0.514842
$146$	−5.41421	+	16.3812i	−0.448084	+	1.35572i
$147$		0			0
$148$	0.791281	+	5.34495i	0.0650429	+	0.439352i
$149$	1.53003	+	1.53003i	0.125345	+	0.125345i	0.766996	−	0.641651i	$-0.221750\pi$
$149$	1.53003	+	1.53003i	0.125345	+	0.125345i	−0.641651	+	0.766996i	$0.721750\pi$
$150$		0			0
$151$		−	11.8158i		−	0.961556i	−0.876842	−	0.480778i	$-0.840354\pi$
$151$		−	11.8158i		−	0.961556i	0.876842	−	0.480778i	$-0.159646\pi$
$152$	−1.51217	−	0.263056i	−0.122653	−	0.0213367i
$153$		0			0
$154$	1.33051	−	0.669485i	0.107216	−	0.0539487i
$155$	−4.06926	−	4.06926i	−0.326851	−	0.326851i
$156$		0			0
$157$	−10.1961	+	10.1961i	−0.813736	+	0.813736i	−0.985192	−	0.171455i	$-0.945153\pi$
$157$	−10.1961	+	10.1961i	−0.813736	+	0.813736i	0.171455	+	0.985192i	$0.445153\pi$
$158$	−4.47212	−	1.47810i	−0.355783	−	0.117591i
$159$		0			0
$160$	−4.09976	+	3.89769i	−0.324114	+	0.308139i
$161$	9.08532			0.716024
$162$		0			0
$163$	−12.6991	+	12.6991i	−0.994666	+	0.994666i	−0.999986	−	0.00531949i	$-0.998307\pi$
$163$	−12.6991	+	12.6991i	−0.994666	+	0.994666i	0.00531949	+	0.999986i	$0.498307\pi$
$164$	14.2722	−	19.2323i	1.11447	−	1.50179i
$165$		0			0
$166$	−11.2874	+	5.67956i	−0.876071	+	0.440820i
$167$		−	19.4775i		−	1.50721i	−0.657325	−	0.753607i	$-0.728312\pi$
$167$		−	19.4775i		−	1.50721i	0.657325	−	0.753607i	$-0.271688\pi$
$168$		0			0
$169$		−	14.1665i		−	1.08973i
$170$	1.00000	+	1.98737i	0.0766965	+	0.152424i
$171$		0			0
$172$	−0.467418	−	3.15732i	−0.0356403	−	0.240743i
$173$	−10.0085	+	10.0085i	−0.760929	+	0.760929i	−0.976490	−	0.215561i	$-0.930842\pi$
$173$	−10.0085	+	10.0085i	−0.760929	+	0.760929i	0.215561	+	0.976490i	$0.430842\pi$
$174$		0			0
$175$	1.41421			0.106904
$176$	−1.40576	+	2.62636i	−0.105963	+	0.197969i
$177$		0			0
$178$	−2.40918	+	7.28919i	−0.180576	+	0.546348i
$179$	−4.18346	+	4.18346i	−0.312686	+	0.312686i	−0.845949	−	0.533263i	$-0.820966\pi$
$179$	−4.18346	+	4.18346i	−0.312686	+	0.312686i	0.533263	+	0.845949i	$0.320966\pi$
$180$		0			0
$181$	−10.4117	−	10.4117i	−0.773893	−	0.773893i	0.204892	−	0.978785i	$-0.434316\pi$
$181$	−10.4117	−	10.4117i	−0.773893	−	0.773893i	−0.978785	+	0.204892i	$0.934316\pi$
$182$	−4.68554	−	9.31190i	−0.347316	−	0.690244i
$183$		0			0
$184$	−14.8605	+	10.4564i	−1.09553	+	0.770857i
$185$			2.70160i			0.198626i
$186$		0			0
$187$	0.828427	+	0.828427i	0.0605806	+	0.0605806i
$188$	3.36168	+	2.49469i	0.245176	+	0.181944i
$189$		0			0
$190$	−0.728670	−	0.240836i	−0.0528633	−	0.0174721i
$191$	−6.47843			−0.468763			−0.234381	−	0.972145i	$-0.575306\pi$
$191$	−6.47843			−0.468763			−0.234381	+	0.972145i	$0.575306\pi$
$192$		0			0
$193$	0.696756			0.0501536			0.0250768	−	0.999686i	$-0.492017\pi$
$193$	0.696756			0.0501536			0.0250768	+	0.999686i	$0.492017\pi$
$194$	2.87155	+	0.949090i	0.206165	+	0.0681407i
$195$		0			0
$196$	8.03037	+	5.95930i	0.573598	+	0.425664i
$197$	11.6364	+	11.6364i	0.829062	+	0.829062i	0.987387	−	0.158325i	$-0.0506094\pi$
$197$	11.6364	+	11.6364i	0.829062	+	0.829062i	−0.158325	+	0.987387i	$0.550609\pi$
$198$		0			0
$199$			22.8759i			1.62163i	0.585305	+	0.810813i	$0.300975\pi$
$199$			22.8759i			1.62163i	−0.585305	+	0.810813i	$0.699025\pi$
$200$	−2.31318	+	1.62764i	−0.163567	+	0.115091i
$201$		0			0
$202$	−5.24862	−	10.4309i	−0.369292	−	0.733919i
$203$	6.19951	+	6.19951i	0.435121	+	0.435121i
$204$		0			0
$205$	8.46742	−	8.46742i	0.591390	−	0.591390i
$206$	7.29552	−	22.0732i	0.508303	−	1.53791i
$207$		0			0
$208$	18.3812	+	9.83851i	1.27450	+	0.682178i
$209$	−0.404135			−0.0279546
$210$		0			0
$211$	13.2780	−	13.2780i	0.914094	−	0.914094i	−0.0824973	−	0.996591i	$-0.526290\pi$
$211$	13.2780	−	13.2780i	0.914094	−	0.914094i	0.996591	+	0.0824973i	$0.0262896\pi$
$212$	−3.95687	−	26.7279i	−0.271759	−	1.83568i
$213$		0			0
$214$	−4.57153	−	9.08532i	−0.312504	−	0.621060i
$215$		−	1.59587i		−	0.108837i
$216$		0			0
$217$			8.13853i			0.552479i
$218$	9.78477	−	4.92348i	0.662708	−	0.333460i
$219$		0			0
$220$	−0.887611	+	1.19609i	−0.0598427	+	0.0806402i
$221$	5.79793	−	5.79793i	0.390011	−	0.390011i
$222$		0			0
$223$	5.61012			0.375681			0.187841	−	0.982200i	$-0.439851\pi$
$223$	5.61012			0.375681			0.187841	+	0.982200i	$0.439851\pi$
$224$	7.99745	+	0.202067i	0.534352	+	0.0135012i
$225$		0			0
$226$	20.0846	+	6.63824i	1.33601	+	0.441569i
$227$	−11.5349	+	11.5349i	−0.765597	+	0.765597i	−0.977328	−	0.211731i	$-0.932090\pi$
$227$	−11.5349	+	11.5349i	−0.765597	+	0.765597i	0.211731	+	0.977328i	$0.432090\pi$
$228$		0			0
$229$	−7.74702	−	7.74702i	−0.511938	−	0.511938i	0.403182	−	0.915120i	$-0.367904\pi$
$229$	−7.74702	−	7.74702i	−0.511938	−	0.511938i	−0.915120	+	0.403182i	$0.867904\pi$
$230$	−8.11582	+	4.08370i	−0.535141	+	0.269271i
$231$		0			0
$232$	−17.2754	−	3.00523i	−1.13419	−	0.197303i
$233$			6.97636i			0.457037i	0.973540	+	0.228518i	$0.0733881\pi$
$233$			6.97636i			0.457037i	−0.973540	+	0.228518i	$0.926612\pi$
$234$		0			0
$235$	1.48005	+	1.48005i	0.0965478	+	0.0965478i
$236$	−1.91355	−	12.9256i	−0.124561	−	0.841387i
$237$		0			0
$238$	0.987369	−	2.98737i	0.0640016	−	0.193642i
$239$	−4.77105			−0.308613			−0.154307	−	0.988023i	$-0.549314\pi$
$239$	−4.77105			−0.308613			−0.154307	+	0.988023i	$0.549314\pi$
$240$		0			0
$241$	30.5307			1.96666			0.983328	−	0.181842i	$-0.0582061\pi$
$241$	30.5307			1.96666			0.983328	+	0.181842i	$0.0582061\pi$
$242$	4.63572	−	14.0258i	0.297995	−	0.901610i
$243$		0			0
$244$	12.6747	−	1.87640i	0.811416	−	0.120124i
$245$	3.53553	+	3.53553i	0.225877	+	0.225877i
$246$		0			0
$247$			2.82843i			0.179969i
$248$	−9.36673	−	13.3119i	−0.594788	−	0.845307i
$249$		0			0
$250$	−1.26330	+	0.635665i	−0.0798982	+	0.0402030i
$251$	12.5266	+	12.5266i	0.790672	+	0.790672i	0.981603	−	0.190931i	$-0.0611508\pi$
$251$	12.5266	+	12.5266i	0.790672	+	0.790672i	−0.190931	+	0.981603i	$0.561151\pi$
$252$		0			0
$253$	−3.38305	+	3.38305i	−0.212690	+	0.212690i
$254$	−26.0349	−	8.60493i	−1.63358	−	0.539921i
$255$		0			0
$256$	−13.3137	+	8.87385i	−0.832107	+	0.554615i
$257$	23.4713			1.46410			0.732051	−	0.681250i	$-0.238563\pi$
$257$	23.4713			1.46410			0.732051	+	0.681250i	$0.238563\pi$
$258$		0			0
$259$	2.70160	−	2.70160i	0.167869	−	0.167869i
$260$	8.37109	+	6.21215i	0.519153	+	0.385261i
$261$		0			0
$262$	−8.54609	+	4.30020i	−0.527979	+	0.265667i
$263$			24.1133i			1.48689i	0.668798	+	0.743444i	$0.266809\pi$
$263$			24.1133i			1.48689i	−0.668798	+	0.743444i	$0.733191\pi$
$264$		0			0
$265$		−	13.5096i		−	0.829889i
$266$	0.487834	+	0.969506i	0.0299110	+	0.0594442i
$267$		0			0
$268$	−15.6569	+	2.31788i	−0.956395	+	0.141587i
$269$	−8.06584	+	8.06584i	−0.491783	+	0.491783i	−0.908868	−	0.417085i	$-0.863052\pi$
$269$	−8.06584	+	8.06584i	−0.491783	+	0.491783i	0.417085	+	0.908868i	$0.363052\pi$
$270$		0			0
$271$	15.9475			0.968740			0.484370	−	0.874863i	$-0.339049\pi$
$271$	15.9475			0.968740			0.484370	+	0.874863i	$0.339049\pi$
$272$	1.82320	+	6.02271i	0.110547	+	0.365180i
$273$		0			0
$274$	1.73808	−	5.25870i	0.105001	−	0.317690i
$275$	−0.526602	+	0.526602i	−0.0317553	+	0.0317553i
$276$		0			0
$277$	5.23599	+	5.23599i	0.314600	+	0.314600i	0.846689	−	0.532089i	$-0.178593\pi$
$277$	5.23599	+	5.23599i	0.314600	+	0.314600i	−0.532089	+	0.846689i	$0.678593\pi$
$278$	13.6341	+	27.0961i	0.817722	+	1.62511i
$279$		0			0
$280$	3.94082	+	0.685544i	0.235509	+	0.0409691i
$281$			4.46512i			0.266367i	0.991091	+	0.133183i	$0.0425200\pi$
$281$			4.46512i			0.266367i	−0.991091	+	0.133183i	$0.957480\pi$
$282$		0			0
$283$	11.0211	+	11.0211i	0.655136	+	0.655136i	0.954225	−	0.299089i	$-0.0966829\pi$
$283$	11.0211	+	11.0211i	0.655136	+	0.655136i	−0.299089	+	0.954225i	$0.596683\pi$
$284$	14.1612	−	19.0828i	0.840315	−	1.13235i
$285$		0			0
$286$	5.21215	+	1.72269i	0.308201	+	0.101865i
$287$	−16.9348			−0.999632
$288$		0			0
$289$	−14.5252			−0.854423
$290$	−8.32453	−	2.75138i	−0.488834	−	0.161567i
$291$		0			0
$292$	−14.5401	+	19.5933i	−0.850895	+	1.14661i
$293$	−3.78692	−	3.78692i	−0.221234	−	0.221234i	0.587784	−	0.809018i	$-0.300001\pi$
$293$	−3.78692	−	3.78692i	−0.221234	−	0.221234i	−0.809018	+	0.587784i	$0.800001\pi$
$294$		0			0
$295$		−	6.53325i		−	0.380381i
$296$	−1.30961	+	7.52822i	−0.0761195	+	0.437569i
$297$		0			0
$298$	1.37545	+	2.73352i	0.0796774	+	0.158348i
$299$	23.6770	+	23.6770i	1.36928	+	1.36928i
$300$		0			0
$301$	−1.59587	+	1.59587i	−0.0919841	+	0.0919841i
$302$	5.24392	−	15.8659i	0.301754	−	0.912981i
$303$		0			0
$304$	−1.91375	−	1.02433i	−0.109761	−	0.0587495i
$305$	6.40643			0.366831
$306$		0			0
$307$	−13.3390	+	13.3390i	−0.761295	+	0.761295i	−0.976557	−	0.215261i	$-0.930940\pi$
$307$	−13.3390	+	13.3390i	−0.761295	+	0.761295i	0.215261	+	0.976557i	$0.430940\pi$
$308$	2.08370	−	0.308476i	0.118730	−	0.0175771i
$309$		0			0
$310$	−3.65813	−	7.27005i	−0.207768	−	0.412911i
$311$		−	25.4977i		−	1.44584i	−0.690932	−	0.722920i	$-0.742800\pi$
$311$		−	25.4977i		−	1.44584i	0.690932	−	0.722920i	$-0.257200\pi$
$312$		0			0
$313$			6.04542i			0.341707i	0.985296	+	0.170854i	$0.0546525\pi$
$313$			6.04542i			0.341707i	−0.985296	+	0.170854i	$0.945347\pi$
$314$	−18.2161	+	9.16594i	−1.02799	+	0.517264i
$315$		0			0
$316$	−5.34905	−	3.96951i	−0.300908	−	0.223302i
$317$	8.64061	−	8.64061i	0.485305	−	0.485305i	−0.421516	−	0.906821i	$-0.638502\pi$
$317$	8.64061	−	8.64061i	0.485305	−	0.485305i	0.906821	+	0.421516i	$0.138502\pi$
$318$		0			0
$319$	−4.61695			−0.258500
$320$	−7.23486	+	3.41421i	−0.404441	+	0.190860i
$321$		0			0
$322$	12.1995	+	4.03212i	0.679852	+	0.224701i
$323$	−0.603650	+	0.603650i	−0.0335880	+	0.0335880i
$324$		0			0
$325$	3.68554	+	3.68554i	0.204437	+	0.204437i
$326$	−22.6878	+	11.4160i	−1.25656	+	0.632275i
$327$		0			0
$328$	27.6997	−	19.4905i	1.52946	−	1.07618i
$329$		−	2.96010i		−	0.163196i
$330$		0			0
$331$	−16.2197	−	16.2197i	−0.891514	−	0.891514i	0.103152	−	0.994666i	$-0.467107\pi$
$331$	−16.2197	−	16.2197i	−0.891514	−	0.891514i	−0.994666	+	0.103152i	$0.967107\pi$
$332$	−17.6770	+	2.61695i	−0.970152	+	0.143624i
$333$		0			0
$334$	8.64422	−	26.1538i	0.472991	−	1.43107i
$335$	−7.91375			−0.432374
$336$		0			0
$337$	30.3702			1.65437			0.827184	−	0.561931i	$-0.189941\pi$
$337$	30.3702			1.65437			0.827184	+	0.561931i	$0.189941\pi$
$338$	6.28716	−	19.0223i	0.341976	−	1.03468i
$339$		0			0
$340$	0.460766	+	3.11239i	0.0249886	+	0.168793i
$341$	−3.03049	−	3.03049i	−0.164110	−	0.164110i
$342$		0			0
$343$		−	16.9706i		−	0.916324i
$344$	0.773600	−	4.44700i	0.0417097	−	0.239766i
$345$		0			0
$346$	−17.8809	+	8.99727i	−0.961282	+	0.483696i
$347$	8.22478	+	8.22478i	0.441529	+	0.441529i	0.892526	−	0.450997i	$-0.148931\pi$
$347$	8.22478	+	8.22478i	0.441529	+	0.441529i	−0.450997	+	0.892526i	$0.648931\pi$
$348$		0			0
$349$	−19.9754	+	19.9754i	−1.06926	+	1.06926i	−0.0718432	+	0.997416i	$0.522888\pi$
$349$	−19.9754	+	19.9754i	−1.06926	+	1.06926i	−0.997416	+	0.0718432i	$0.977112\pi$
$350$	1.89897	+	0.627636i	0.101504	+	0.0335486i
$351$		0			0
$352$	−3.05320	+	2.90272i	−0.162736	+	0.154715i
$353$	8.40669			0.447443			0.223721	−	0.974653i	$-0.428179\pi$
$353$	8.40669			0.447443			0.223721	+	0.974653i	$0.428179\pi$
$354$		0			0
$355$	8.40158	−	8.40158i	0.445910	−	0.445910i
$356$	−6.46997	+	8.71852i	−0.342908	+	0.462080i
$357$		0			0
$358$	−7.47407	+	3.76079i	−0.395017	+	0.198764i
$359$		−	13.2812i		−	0.700956i	−0.936571	−	0.350478i	$-0.886019\pi$
$359$		−	13.2812i		−	0.700956i	0.936571	−	0.350478i	$-0.113981\pi$
$360$		0			0
$361$			18.7055i			0.984501i
$362$	−9.35973	−	18.6012i	−0.491937	−	0.977660i
$363$		0			0
$364$	−2.15894	−	14.5832i	−0.113159	−	0.764369i
$365$	−8.62636	+	8.62636i	−0.451524	+	0.451524i
$366$		0			0
$367$	27.7426			1.44815			0.724075	−	0.689721i	$-0.242267\pi$
$367$	27.7426			1.44815			0.724075	+	0.689721i	$0.242267\pi$
$368$	−24.5949	+	7.44538i	−1.28210	+	0.388117i
$369$		0			0
$370$	−1.19899	+	3.62764i	−0.0623323	+	0.188592i
$371$	−13.5096	+	13.5096i	−0.701384	+	0.701384i
$372$		0			0
$373$	14.7387	+	14.7387i	0.763143	+	0.763143i	0.976889	−	0.213746i	$-0.0685664\pi$
$373$	14.7387	+	14.7387i	0.763143	+	0.763143i	−0.213746	+	0.976889i	$0.568566\pi$
$374$	0.744728	+	1.48005i	0.0385090	+	0.0765315i
$375$		0			0
$376$	3.40681	+	4.84173i	0.175693	+	0.249693i
$377$			32.3128i			1.66419i
$378$		0			0
$379$	−3.45249	−	3.45249i	−0.177343	−	0.177343i	0.612854	−	0.790196i	$-0.290021\pi$
$379$	−3.45249	−	3.45249i	−0.177343	−	0.177343i	−0.790196	+	0.612854i	$0.790021\pi$
$380$	−0.871553	−	0.646775i	−0.0447097	−	0.0331789i
$381$		0			0
$382$	−8.69905	−	2.87516i	−0.445082	−	0.147106i
$383$	13.7023			0.700154			0.350077	−	0.936721i	$-0.386155\pi$
$383$	13.7023			0.700154			0.350077	+	0.936721i	$0.386155\pi$
$384$		0			0
$385$	1.05320			0.0536763
$386$	0.935584	+	0.309224i	0.0476200	+	0.0157391i
$387$		0			0
$388$	3.43463	+	2.54882i	0.174367	+	0.129397i
$389$	−8.20181	−	8.20181i	−0.415848	−	0.415848i	0.467922	−	0.883770i	$-0.345003\pi$
$389$	−8.20181	−	8.20181i	−0.415848	−	0.415848i	−0.883770	+	0.467922i	$0.845003\pi$
$390$		0			0
$391$			10.1064i			0.511103i
$392$	8.13818	+	11.5659i	0.411040	+	0.584166i
$393$		0			0
$394$	10.4608	+	20.7894i	0.527006	+	1.04735i
$395$	−2.35503	−	2.35503i	−0.118494	−	0.118494i
$396$		0			0
$397$	−8.68137	+	8.68137i	−0.435705	+	0.435705i	−0.890564	−	0.454858i	$-0.849690\pi$
$397$	−8.68137	+	8.68137i	−0.435705	+	0.435705i	0.454858	+	0.890564i	$0.349690\pi$
$398$	−10.1524	+	30.7171i	−0.508896	+	1.53971i
$399$		0			0
$400$	−3.82843	+	1.15894i	−0.191421	+	0.0579471i
$401$	−23.0445			−1.15079			−0.575393	−	0.817877i	$-0.695151\pi$
$401$	−23.0445			−1.15079			−0.575393	+	0.817877i	$0.695151\pi$
$402$		0			0
$403$	−21.2096	+	21.2096i	−1.05653	+	1.05653i
$404$	−2.41839	−	16.3357i	−0.120319	−	0.812734i
$405$		0			0
$406$	5.57316	+	11.0759i	0.276591	+	0.549688i
$407$			2.01196i			0.0997291i
$408$		0			0
$409$		−	15.7464i		−	0.778607i	−0.921110	−	0.389303i	$-0.872716\pi$
$409$		−	15.7464i		−	0.778607i	0.921110	−	0.389303i	$-0.127284\pi$
$410$	15.1277	−	7.61192i	0.747104	−	0.375926i
$411$		0			0
$412$	19.5924	−	26.4015i	0.965250	−	1.30071i
$413$	−6.53325	+	6.53325i	−0.321480	+	0.321480i
$414$		0			0
$415$	−8.93484			−0.438594
$416$	20.3153	+	21.3685i	0.996041	+	1.04768i
$417$		0			0
$418$	−0.542661	−	0.179357i	−0.0265424	−	0.00877265i
$419$	24.4404	−	24.4404i	1.19399	−	1.19399i	0.218052	−	0.975937i	$-0.430030\pi$
$419$	24.4404	−	24.4404i	1.19399	−	1.19399i	0.975937	−	0.218052i	$-0.0699703\pi$
$420$		0			0
$421$	−21.7218	−	21.7218i	−1.05865	−	1.05865i	−0.998169	−	0.0604847i	$-0.980735\pi$
$421$	−21.7218	−	21.7218i	−1.05865	−	1.05865i	−0.0604847	−	0.998169i	$-0.519265\pi$
$422$	23.7221	−	11.9365i	1.15478	−	0.581058i
$423$		0			0
$424$	6.54882	−	37.6456i	0.318039	−	1.82823i
$425$			1.57316i			0.0763092i
$426$		0			0
$427$	−6.40643	−	6.40643i	−0.310029	−	0.310029i
$428$	−2.10641	−	14.2284i	−0.101817	−	0.687755i
$429$		0			0
$430$	0.708254	−	2.14288i	0.0341550	−	0.103339i
$431$	27.3876			1.31922			0.659608	−	0.751610i	$-0.270722\pi$
$431$	27.3876			1.31922			0.659608	+	0.751610i	$0.270722\pi$
$432$		0			0
$433$	3.74996			0.180212			0.0901058	−	0.995932i	$-0.471279\pi$
$433$	3.74996			0.180212			0.0901058	+	0.995932i	$0.471279\pi$
$434$	−3.61192	+	10.9282i	−0.173378	+	0.524570i
$435$		0			0
$436$	15.3238	−	2.26858i	0.733876	−	0.108645i
$437$	−2.46512	−	2.46512i	−0.117923	−	0.117923i
$438$		0			0
$439$			22.5580i			1.07663i	0.842743	+	0.538317i	$0.180940\pi$
$439$			22.5580i			1.07663i	−0.842743	+	0.538317i	$0.819060\pi$
$440$	−1.72269	+	1.21215i	−0.0821260	+	0.0577868i
$441$		0			0
$442$	10.3585	−	5.21215i	0.492702	−	0.247917i
$443$	13.0922	+	13.0922i	0.622028	+	0.622028i	0.946050	−	0.324022i	$-0.105035\pi$
$443$	13.0922	+	13.0922i	0.622028	+	0.622028i	−0.324022	+	0.946050i	$0.605035\pi$
$444$		0			0
$445$	−3.83851	+	3.83851i	−0.181963	+	0.181963i
$446$	7.53311	+	2.48980i	0.356703	+	0.117896i
$447$		0			0
$448$	10.6491	+	3.82064i	0.503121	+	0.180508i
$449$	−4.13492			−0.195139			−0.0975694	−	0.995229i	$-0.531107\pi$
$449$	−4.13492			−0.195139			−0.0975694	+	0.995229i	$0.531107\pi$
$450$		0			0
$451$	6.30592	−	6.30592i	0.296934	−	0.296934i
$452$	24.0229	+	17.8273i	1.12994	+	0.838525i
$453$		0			0
$454$	−20.6080	+	10.3695i	−0.967179	+	0.486663i
$455$		−	7.37109i		−	0.345562i
$456$		0			0
$457$			26.3008i			1.23030i	0.788410	+	0.615150i	$0.210905\pi$
$457$			26.3008i			1.23030i	−0.788410	+	0.615150i	$0.789095\pi$
$458$	−6.96431	−	13.8407i	−0.325421	−	0.646731i
$459$		0			0
$460$	−12.7101	+	1.88163i	−0.592610	+	0.0877315i
$461$	13.3795	−	13.3795i	0.623148	−	0.623148i	−0.323187	−	0.946335i	$-0.604754\pi$
$461$	13.3795	−	13.3795i	0.623148	−	0.623148i	0.946335	+	0.323187i	$0.104754\pi$
$462$		0			0
$463$	14.5995			0.678496			0.339248	−	0.940697i	$-0.389827\pi$
$463$	14.5995			0.678496			0.339248	+	0.940697i	$0.389827\pi$
$464$	−21.8632	−	11.7023i	−1.01497	−	0.543264i
$465$		0			0
$466$	−3.09615	+	9.36766i	−0.143426	+	0.433948i
$467$	−23.7344	+	23.7344i	−1.09830	+	1.09830i	−0.103687	+	0.994610i	$0.533064\pi$
$467$	−23.7344	+	23.7344i	−1.09830	+	1.09830i	−0.994610	+	0.103687i	$0.966936\pi$
$468$		0			0
$469$	7.91375	+	7.91375i	0.365423	+	0.365423i
$470$	1.33051	+	2.64422i	0.0613721	+	0.121969i
$471$		0			0
$472$	3.16701	−	18.2054i	0.145774	−	0.837972i
$473$		−	1.18849i		−	0.0546466i
$474$		0			0
$475$	−0.383719	−	0.383719i	−0.0176062	−	0.0176062i
$476$	2.65162	−	3.57316i	0.121537	−	0.163775i
$477$		0			0
$478$	−6.40643	−	2.11742i	−0.293023	−	0.0968484i
$479$	18.5018			0.845370			0.422685	−	0.906277i	$-0.361088\pi$
$479$	18.5018			0.845370			0.422685	+	0.906277i	$0.361088\pi$
$480$		0			0
$481$	14.0811			0.642045
$482$	40.9958	+	13.5497i	1.86731	+	0.617172i
$483$		0			0
$484$	12.4494	−	16.7760i	0.565883	−	0.762547i
$485$	1.51217	+	1.51217i	0.0686639	+	0.0686639i
$486$		0			0
$487$			14.0312i			0.635813i	0.948122	+	0.317906i	$0.102980\pi$
$487$			14.0312i			0.635813i	−0.948122	+	0.317906i	$0.897020\pi$
$488$	17.8520	+	3.10553i	0.808123	+	0.140581i
$489$		0			0
$490$	3.17833	+	6.31651i	0.143582	+	0.285351i
$491$	8.60089	+	8.60089i	0.388153	+	0.388153i	0.874028	−	0.485875i	$-0.161499\pi$
$491$	8.60089	+	8.60089i	0.388153	+	0.388153i	−0.485875	+	0.874028i	$0.661499\pi$
$492$		0			0
$493$	−6.89627	+	6.89627i	−0.310592	+	0.310592i
$494$	−1.25527	+	3.79793i	−0.0564774	+	0.170877i
$495$		0			0
$496$	−6.66949	−	22.0319i	−0.299469	−	0.989260i
$497$	−16.8032			−0.753725
$498$		0			0
$499$	10.5628	−	10.5628i	0.472857	−	0.472857i	−0.429981	−	0.902838i	$-0.641480\pi$
$499$	10.5628	−	10.5628i	0.472857	−	0.472857i	0.902838	+	0.429981i	$0.141480\pi$
$500$	−1.97844	+	0.292893i	−0.0884784	+	0.0130986i
$501$		0			0
$502$	11.2610	+	22.3797i	0.502603	+	0.998857i
$503$		−	20.3857i		−	0.908955i	−0.890758	−	0.454477i	$-0.849826\pi$
$503$		−	20.3857i		−	0.908955i	0.890758	−	0.454477i	$-0.150174\pi$
$504$		0			0
$505$		−	8.25689i		−	0.367427i
$506$	−6.04408	+	3.04125i	−0.268692	+	0.135200i
$507$		0			0
$508$	−31.1401	−	23.1089i	−1.38162	−	1.02529i
$509$	10.1972	−	10.1972i	0.451984	−	0.451984i	−0.444029	−	0.896013i	$-0.646451\pi$
$509$	10.1972	−	10.1972i	0.451984	−	0.451984i	0.896013	+	0.444029i	$0.146451\pi$
$510$		0			0
$511$	17.2527			0.763215
$512$	−21.8155	+	6.00685i	−0.964120	+	0.265468i
$513$		0			0
$514$	31.5167	+	10.4167i	1.39014	+	0.459461i
$515$	11.6238	−	11.6238i	0.512206	−	0.512206i
$516$		0			0
$517$	1.10223	+	1.10223i	0.0484762	+	0.0484762i
$518$	4.82662	−	2.42865i	0.212070	−	0.106709i
$519$		0			0
$520$	8.48348	+	12.0566i	0.372025	+	0.528718i
$521$		−	6.25365i		−	0.273977i	−0.990573	−	0.136989i	$-0.956258\pi$
$521$		−	6.25365i		−	0.273977i	0.990573	−	0.136989i	$-0.0437424\pi$
$522$		0			0
$523$	17.2349	+	17.2349i	0.753628	+	0.753628i	0.975154	−	0.221527i	$-0.0711040\pi$
$523$	17.2349	+	17.2349i	0.753628	+	0.753628i	−0.221527	+	0.975154i	$0.571104\pi$
$524$	−13.3839	+	1.98139i	−0.584678	+	0.0865574i
$525$		0			0
$526$	−10.7016	+	32.3786i	−0.466612	+	1.41177i
$527$	−9.05320			−0.394364
$528$		0			0
$529$	−18.2715			−0.794414
$530$	5.99564	−	18.1403i	0.260434	−	0.787966i
$531$		0			0
$532$	0.224777	+	1.51833i	0.00974534	+	0.0658279i
$533$	−44.1334	−	44.1334i	−1.91163	−	1.91163i
$534$		0			0
$535$		−	7.19173i		−	0.310926i
$536$	−22.0523	−	3.83621i	−0.952513	−	0.165699i
$537$		0			0
$538$	−14.4102	+	7.25091i	−0.621270	+	0.312609i
$539$	2.63301	+	2.63301i	0.113412	+	0.113412i
$540$		0			0
$541$	−22.6231	+	22.6231i	−0.972645	+	0.972645i	−0.999636	−	0.0269911i	$-0.991407\pi$
$541$	−22.6231	+	22.6231i	−0.972645	+	0.972645i	0.0269911	+	0.999636i	$0.491407\pi$
$542$	21.4138	+	7.07758i	0.919802	+	0.304008i
$543$		0			0
$544$	−0.224777	+	8.89627i	−0.00963725	+	0.381424i
$545$	7.74540			0.331776
$546$		0			0
$547$	16.0380	−	16.0380i	0.685736	−	0.685736i	−0.275550	−	0.961287i	$-0.588860\pi$
$547$	16.0380	−	16.0380i	0.685736	−	0.685736i	0.961287	+	0.275550i	$0.0888601\pi$
$548$	4.66768	−	6.28987i	0.199393	−	0.268690i
$549$		0			0
$550$	−0.940816	+	0.473398i	−0.0401165	+	0.0201857i
$551$		−	3.36423i		−	0.143321i
$552$		0			0
$553$			4.71006i			0.200292i
$554$	4.70698	+	9.35450i	0.199980	+	0.397435i
$555$		0			0
$556$	6.28216	+	42.4348i	0.266423	+	1.79963i
$557$	−17.3053	+	17.3053i	−0.733247	+	0.733247i	−0.971262	−	0.238015i	$-0.923503\pi$
$557$	−17.3053	+	17.3053i	−0.733247	+	0.733247i	0.238015	+	0.971262i	$0.423503\pi$
$558$		0			0
$559$	−8.31788			−0.351809
$560$	4.98737	+	2.66949i	0.210755	+	0.112806i
$561$		0			0
$562$	−1.98165	+	5.99564i	−0.0835907	+	0.252911i
$563$	24.4885	−	24.4885i	1.03207	−	1.03207i	0.0325998	−	0.999468i	$-0.489621\pi$
$563$	24.4885	−	24.4885i	1.03207	−	1.03207i	0.999468	−	0.0325998i	$-0.0103787\pi$
$564$		0			0
$565$	10.5766	+	10.5766i	0.444960	+	0.444960i
$566$	9.90759	+	19.6900i	0.416447	+	0.827634i
$567$		0			0
$568$	27.4844	−	19.3390i	1.15322	−	0.811445i
$569$		−	21.3371i		−	0.894498i	−0.894409	−	0.447249i	$-0.852404\pi$
$569$		−	21.3371i		−	0.894498i	0.894409	−	0.447249i	$-0.147596\pi$
$570$		0			0
$571$	−2.90272	−	2.90272i	−0.121475	−	0.121475i	0.643756	−	0.765231i	$-0.277375\pi$
$571$	−2.90272	−	2.90272i	−0.121475	−	0.121475i	−0.765231	+	0.643756i	$0.777375\pi$
$572$	6.23418	+	4.62636i	0.260664	+	0.193438i
$573$		0			0
$574$	−22.7396	−	7.51578i	−0.949134	−	0.313702i
$575$	−6.42429			−0.267912
$576$		0			0
$577$	−0.390831			−0.0162705			−0.00813526	−	0.999967i	$-0.502590\pi$
$577$	−0.390831			−0.0162705			−0.00813526	+	0.999967i	$0.502590\pi$
$578$	−19.5040	−	6.44636i	−0.811260	−	0.268133i
$579$		0			0
$580$	−9.95687	−	7.38895i	−0.413437	−	0.306809i
$581$	8.93484	+	8.93484i	0.370679	+	0.370679i
$582$		0			0
$583$		−	10.0610i		−	0.416684i
$584$	−28.2197	+	19.8564i	−1.16774	+	0.821662i
$585$		0			0
$586$	−3.40432	−	6.76563i	−0.140631	−	0.279486i
$587$	−1.90689	−	1.90689i	−0.0787059	−	0.0787059i	0.666658	−	0.745364i	$-0.267724\pi$
$587$	−1.90689	−	1.90689i	−0.0787059	−	0.0787059i	−0.745364	+	0.666658i	$0.767724\pi$
$588$		0			0
$589$	2.20823	−	2.20823i	0.0909885	−	0.0909885i
$590$	2.89949	−	8.77267i	0.119370	−	0.361165i
$591$		0			0
$592$	−5.09958	+	9.52748i	−0.209591	+	0.391577i
$593$	15.9469			0.654862			0.327431	−	0.944875i	$-0.393817\pi$
$593$	15.9469			0.654862			0.327431	+	0.944875i	$0.393817\pi$
$594$		0			0
$595$	1.57316	−	1.57316i	0.0644931	−	0.0644931i
$596$	0.633759	+	4.28092i	0.0259598	+	0.175353i
$597$		0			0
$598$	21.2848	+	42.3008i	0.870402	+	1.72981i
$599$			19.4591i			0.795077i	0.917586	+	0.397538i	$0.130135\pi$
$599$			19.4591i			0.795077i	−0.917586	+	0.397538i	$0.869865\pi$
$600$		0			0
$601$		−	6.91468i		−	0.282056i	−0.990006	−	0.141028i	$-0.954959\pi$
$601$		−	6.91468i		−	0.282056i	0.990006	−	0.141028i	$-0.0450407\pi$
$602$	−2.85114	+	1.43463i	−0.116204	+	0.0584711i
$603$		0			0
$604$	14.0828	−	18.9770i	0.573020	−	0.772164i
$605$	7.38600	−	7.38600i	0.300284	−	0.300284i
$606$		0			0
$607$	−1.14175			−0.0463422			−0.0231711	−	0.999732i	$-0.507376\pi$
$607$	−1.14175			−0.0463422			−0.0231711	+	0.999732i	$0.507376\pi$
$608$	−2.11512	−	2.22478i	−0.0857796	−	0.0902266i
$609$		0			0
$610$	8.60237	+	2.84321i	0.348300	+	0.115118i
$611$	7.71423	−	7.71423i	0.312084	−	0.312084i
$612$		0			0
$613$	−24.5497	−	24.5497i	−0.991553	−	0.991553i	0.00841168	−	0.999965i	$-0.497322\pi$
$613$	−24.5497	−	24.5497i	−0.991553	−	0.991553i	−0.999965	+	0.00841168i	$0.997322\pi$
$614$	−23.8311	+	11.9913i	−0.961745	+	0.483929i
$615$		0			0
$616$	2.93484	+	0.510544i	0.118248	+	0.0205704i
$617$			17.8671i			0.719303i	0.933087	+	0.359652i	$0.117104\pi$
$617$			17.8671i			0.719303i	−0.933087	+	0.359652i	$0.882896\pi$
$618$		0			0
$619$	−11.3578	−	11.3578i	−0.456508	−	0.456508i	0.440999	−	0.897507i	$-0.354624\pi$
$619$	−11.3578	−	11.3578i	−0.456508	−	0.456508i	−0.897507	+	0.440999i	$0.854624\pi$
$620$	−1.68554	−	11.3855i	−0.0676931	−	0.457254i
$621$		0			0
$622$	11.3160	−	34.2375i	0.453730	−	1.37280i
$623$	7.67701			0.307573
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−2.68299	+	8.11762i	−0.107234	+	0.324445i
$627$		0			0
$628$	−28.5280	+	4.22336i	−1.13839	+	0.168530i
$629$	3.00523	+	3.00523i	0.119826	+	0.119826i
$630$		0			0
$631$		−	20.7001i		−	0.824058i	−0.911171	−	0.412029i	$-0.864820\pi$
$631$		−	20.7001i		−	0.824058i	0.911171	−	0.412029i	$-0.135180\pi$
$632$	−5.42087	−	7.70408i	−0.215630	−	0.306452i
$633$		0			0
$634$	15.4371	−	7.76762i	0.613087	−	0.308492i
$635$	−13.7101	−	13.7101i	−0.544067	−	0.544067i
$636$		0			0
$637$	18.4277	−	18.4277i	0.730133	−	0.730133i
$638$	−6.19951	−	2.04903i	−0.245441	−	0.0811219i
$639$		0			0
$640$	−11.2300	+	1.37364i	−0.443905	+	0.0542979i
$641$	−23.4435			−0.925963			−0.462982	−	0.886368i	$-0.653220\pi$
$641$	−23.4435			−0.925963			−0.462982	+	0.886368i	$0.653220\pi$
$642$		0			0
$643$	14.5738	−	14.5738i	0.574736	−	0.574736i	−0.358712	−	0.933448i	$-0.616784\pi$
$643$	14.5738	−	14.5738i	0.574736	−	0.574736i	0.933448	+	0.358712i	$0.116784\pi$
$644$	14.5917	+	10.8284i	0.574993	+	0.426700i
$645$		0			0
$646$	−1.07847	+	0.542661i	−0.0424317	+	0.0213507i
$647$		−	14.9417i		−	0.587418i	−0.955895	−	0.293709i	$-0.905110\pi$
$647$		−	14.9417i		−	0.587418i	0.955895	−	0.293709i	$-0.0948897\pi$
$648$		0			0
$649$		−	4.86550i		−	0.190987i
$650$	3.31318	+	6.58451i	0.129954	+	0.258266i
$651$		0			0
$652$	−35.5311	+	5.26012i	−1.39150	+	0.206002i
$653$	−1.78262	+	1.78262i	−0.0697594	+	0.0697594i	−0.741126	−	0.671366i	$-0.765708\pi$
$653$	−1.78262	+	1.78262i	−0.0697594	+	0.0697594i	0.671366	+	0.741126i	$0.265708\pi$
$654$		0			0
$655$	−6.76489			−0.264326
$656$	45.8444	−	13.8780i	1.78992	−	0.541846i
$657$		0			0
$658$	1.31371	−	3.97474i	0.0512137	−	0.154951i
$659$	−11.7844	+	11.7844i	−0.459056	+	0.459056i	−0.898346	−	0.439289i	$-0.855230\pi$
$659$	−11.7844	+	11.7844i	−0.459056	+	0.459056i	0.439289	+	0.898346i	$0.355230\pi$
$660$		0			0
$661$	−3.89751	−	3.89751i	−0.151595	−	0.151595i	0.627235	−	0.778830i	$-0.284187\pi$
$661$	−3.89751	−	3.89751i	−0.151595	−	0.151595i	−0.778830	+	0.627235i	$0.784187\pi$
$662$	−14.5809	−	28.9777i	−0.566704	−	1.12625i
$663$		0			0
$664$	−24.8976	−	4.33119i	−0.966215	−	0.168083i
$665$			0.767438i			0.0297600i
$666$		0			0
$667$	−28.1623	−	28.1623i	−1.09045	−	1.09045i
$668$	23.2144	−	31.2823i	0.898194	−	1.21035i
$669$		0			0
$670$	−10.6264	−	3.51217i	−0.410532	−	0.135687i
$671$	4.77105			0.184184
$672$		0			0
$673$	−42.2243			−1.62763			−0.813813	−	0.581127i	$-0.802612\pi$
$673$	−42.2243			−1.62763			−0.813813	+	0.581127i	$0.802612\pi$
$674$	40.7802	+	13.4784i	1.57079	+	0.519170i
$675$		0			0
$676$	16.8844	−	22.7524i	0.649402	−	0.875092i
$677$	24.7733	+	24.7733i	0.952117	+	0.952117i	0.998905	−	0.0467880i	$-0.0148985\pi$
$677$	24.7733	+	24.7733i	0.952117	+	0.952117i	−0.0467880	+	0.998905i	$0.514899\pi$
$678$		0			0
$679$		−	3.02433i		−	0.116063i
$680$	−0.762591	+	4.38372i	−0.0292440	+	0.168108i
$681$		0			0
$682$	−2.72431	−	5.41421i	−0.104319	−	0.207321i
$683$	−13.3912	−	13.3912i	−0.512402	−	0.512402i	0.402860	−	0.915262i	$-0.368016\pi$
$683$	−13.3912	−	13.3912i	−0.512402	−	0.512402i	−0.915262	+	0.402860i	$0.868016\pi$
$684$		0			0
$685$	2.76924	−	2.76924i	0.105807	−	0.105807i
$686$	7.53163	−	22.7876i	0.287559	−	0.870034i
$687$		0			0
$688$	3.01237	−	5.62798i	0.114846	−	0.214565i
$689$	−70.4141			−2.68256
$690$		0			0
$691$	−19.8648	+	19.8648i	−0.755694	+	0.755694i	−0.975536	−	0.219842i	$-0.929446\pi$
$691$	−19.8648	+	19.8648i	−0.755694	+	0.755694i	0.219842	+	0.975536i	$0.429446\pi$
$692$	−28.0030	+	4.14564i	−1.06451	+	0.157594i
$693$		0			0
$694$	7.39380	+	14.6942i	0.280665	+	0.557784i
$695$			21.4486i			0.813593i
$696$		0			0
$697$		−	18.8381i		−	0.713545i
$698$	−35.6876	+	17.9572i	−1.35080	+	0.679691i
$699$		0			0
$700$	2.27133	+	1.68554i	0.0858482	+	0.0637076i
$701$	−0.771998	+	0.771998i	−0.0291580	+	0.0291580i	−0.721535	−	0.692377i	$-0.756563\pi$
$701$	−0.771998	+	0.771998i	−0.0291580	+	0.0291580i	0.692377	+	0.721535i	$0.256563\pi$
$702$		0			0
$703$	−1.46605			−0.0552933
$704$	−5.38800	+	2.54266i	−0.203068	+	0.0958301i
$705$		0			0
$706$	11.2883	+	3.73094i	0.424839	+	0.140416i
$707$	−8.25689	+	8.25689i	−0.310532	+	0.310532i
$708$		0			0
$709$	7.16580	+	7.16580i	0.269117	+	0.269117i	0.828744	−	0.559627i	$-0.189056\pi$
$709$	7.16580	+	7.16580i	0.269117	+	0.269117i	−0.559627	+	0.828744i	$0.689056\pi$
$710$	15.0101	−	7.55274i	0.563318	−	0.283449i
$711$		0			0
$712$	−12.5570	+	8.83557i	−0.470594	+	0.331127i
$713$		−	36.9706i		−	1.38456i
$714$		0			0
$715$	2.74473	+	2.74473i	0.102647	+	0.102647i
$716$	−11.7050	+	1.73284i	−0.437437	+	0.0647594i
$717$		0			0
$718$	5.89428	−	17.8337i	0.219973	−	0.665546i
$719$	4.88942			0.182344			0.0911722	−	0.995835i	$-0.470939\pi$
$719$	4.88942			0.182344			0.0911722	+	0.995835i	$0.470939\pi$
$720$		0			0
$721$	−23.2476			−0.865786
$722$	−8.30161	+	25.1172i	−0.308954	+	0.934767i
$723$		0			0
$724$	−4.31265	−	29.1311i	−0.160278	−	1.08265i
$725$	−4.38372	−	4.38372i	−0.162807	−	0.162807i
$726$		0			0
$727$		−	14.1531i		−	0.524911i	−0.964944	−	0.262456i	$-0.915468\pi$
$727$		−	14.1531i		−	0.524911i	0.964944	−	0.262456i	$-0.0845323\pi$
$728$	3.57316	−	20.5401i	0.132430	−	0.761267i
$729$		0			0
$730$	−15.4117	+	7.75481i	−0.570411	+	0.287018i
$731$	−1.77522	−	1.77522i	−0.0656590	−	0.0656590i
$732$		0			0
$733$	11.2850	−	11.2850i	0.416822	−	0.416822i	−0.467285	−	0.884107i	$-0.654768\pi$
$733$	11.2850	−	11.2850i	0.416822	−	0.416822i	0.884107	+	0.467285i	$0.154768\pi$
$734$	37.2519	+	12.3123i	1.37499	+	0.454455i
$735$		0			0
$736$	−36.3297	−	0.917923i	−1.33913	−	0.0338351i
$737$	−5.89359			−0.217093
$738$		0			0
$739$	30.9164	−	30.9164i	1.13728	−	1.13728i	0.148343	−	0.988936i	$-0.452606\pi$
$739$	30.9164	−	30.9164i	1.13728	−	1.13728i	0.988936	−	0.148343i	$-0.0473940\pi$
$740$	−3.21993	+	4.33897i	−0.118367	+	0.159504i
$741$		0			0
$742$	−24.1360	+	12.1447i	−0.886059	+	0.445846i
$743$			17.5161i			0.642602i	0.946977	+	0.321301i	$0.104120\pi$
$743$			17.5161i			0.642602i	−0.946977	+	0.321301i	$0.895880\pi$
$744$		0			0
$745$			2.16379i			0.0792751i
$746$	13.2496	+	26.3319i	0.485104	+	0.964080i
$747$		0			0
$748$	0.343146	+	2.31788i	0.0125467	+	0.0847502i
$749$	−7.19173	+	7.19173i	−0.262780	+	0.262780i
$750$		0			0
$751$	−1.99154			−0.0726725			−0.0363362	−	0.999340i	$-0.511569\pi$
$751$	−1.99154			−0.0726725			−0.0363362	+	0.999340i	$0.511569\pi$
$752$	2.42579	+	8.01330i	0.0884594	+	0.292215i
$753$		0			0
$754$	−14.3406	+	43.3887i	−0.522254	+	1.58012i
$755$	8.35503	−	8.35503i	0.304071	−	0.304071i
$756$		0			0
$757$	−12.3823	−	12.3823i	−0.450042	−	0.450042i	0.445326	−	0.895368i	$-0.353088\pi$
$757$	−12.3823	−	12.3823i	−0.450042	−	0.450042i	−0.895368	+	0.445326i	$0.853088\pi$
$758$	−3.10367	−	6.16815i	−0.112731	−	0.224037i
$759$		0			0
$760$	−0.883254	−	1.25527i	−0.0320390	−	0.0455335i
$761$			34.4159i			1.24758i	0.781593	+	0.623788i	$0.214407\pi$
$761$			34.4159i			1.24758i	−0.781593	+	0.623788i	$0.785593\pi$
$762$		0			0
$763$	−7.74540	−	7.74540i	−0.280402	−	0.280402i
$764$	−10.4048	−	7.72137i	−0.376433	−	0.279350i
$765$		0			0
$766$	18.3990	+	6.08115i	0.664784	+	0.219721i
$767$	−34.0523			−1.22956
$768$		0			0
$769$	−48.5054			−1.74915			−0.874575	−	0.484889i	$-0.838860\pi$
$769$	−48.5054			−1.74915			−0.874575	+	0.484889i	$0.838860\pi$
$770$	1.41421	+	0.467418i	0.0509647	+	0.0168446i
$771$		0			0
$772$	1.11904	+	0.830435i	0.0402751	+	0.0298880i
$773$	−0.980514	−	0.980514i	−0.0352666	−	0.0352666i	0.689254	−	0.724520i	$-0.257939\pi$
$773$	−0.980514	−	0.980514i	−0.0352666	−	0.0352666i	−0.724520	+	0.689254i	$0.757939\pi$
$774$		0			0
$775$		−	5.75481i		−	0.206719i
$776$	3.48074	+	4.94680i	0.124951	+	0.177580i
$777$		0			0
$778$	−7.37315	−	14.6532i	−0.264340	−	0.525342i
$779$	4.59494	+	4.59494i	0.164631	+	0.164631i
$780$		0			0
$781$	6.25689	−	6.25689i	0.223889	−	0.223889i
$782$	−4.48528	+	13.5706i	−0.160393	+	0.485284i
$783$		0			0
$784$	5.79471	+	19.1421i	0.206954	+	0.683648i
$785$	−14.4194			−0.514652
$786$		0			0
$787$	17.6390	−	17.6390i	0.628762	−	0.628762i	−0.318994	−	0.947757i	$-0.603345\pi$
$787$	17.6390	−	17.6390i	0.628762	−	0.628762i	0.947757	+	0.318994i	$0.103345\pi$
$788$	4.81997	+	32.5580i	0.171704	+	1.15983i
$789$		0			0
$790$	−2.11709	−	4.20744i	−0.0753228	−	0.149694i
$791$		−	21.1532i		−	0.752120i
$792$		0			0
$793$		−	33.3912i		−	1.18576i
$794$	−15.5099	+	7.80426i	−0.550427	+	0.276963i
$795$		0			0
$796$	−27.2648	+	36.7403i	−0.966375	+	1.30223i
$797$	−0.451563	+	0.451563i	−0.0159952	+	0.0159952i	−0.715059	−	0.699064i	$-0.753600\pi$
$797$	−0.451563	+	0.451563i	−0.0159952	+	0.0159952i	0.699064	+	0.715059i	$0.253600\pi$
$798$		0			0
$799$	3.29278			0.116490
$800$	−5.65505	−	0.142883i	−0.199936	−	0.00505168i
$801$		0			0
$802$	−30.9435	−	10.2273i	−1.09265	−	0.361138i
$803$	−6.42429	+	6.42429i	−0.226708	+	0.226708i
$804$		0			0
$805$	6.42429	+	6.42429i	0.226427	+	0.226427i
$806$	−37.8926	+	19.0667i	−1.33471	+	0.671596i
$807$		0			0
$808$	4.00255	−	23.0085i	0.140809	−	0.809435i
$809$		−	20.0844i		−	0.706130i	−0.935599	−	0.353065i	$-0.885140\pi$
$809$		−	20.0844i		−	0.706130i	0.935599	−	0.353065i	$-0.114860\pi$
$810$		0			0
$811$	21.4675	+	21.4675i	0.753827	+	0.753827i	0.975191	−	0.221364i	$-0.0710508\pi$
$811$	21.4675	+	21.4675i	0.753827	+	0.753827i	−0.221364	+	0.975191i	$0.571051\pi$
$812$	2.56792	+	17.3458i	0.0901164	+	0.608719i
$813$		0			0
$814$	−0.892919	+	2.70160i	−0.0312968	+	0.0946911i
$815$	−17.9592			−0.629082
$816$		0			0
$817$	0.866013			0.0302980
$818$	6.98832	−	21.1438i	0.244341	−	0.739274i
$819$		0			0
$820$	23.6913	−	3.50732i	0.827335	−	0.122481i
$821$	−5.82776	−	5.82776i	−0.203390	−	0.203390i	0.598061	−	0.801451i	$-0.295938\pi$
$821$	−5.82776	−	5.82776i	−0.203390	−	0.203390i	−0.801451	+	0.598061i	$0.795938\pi$
$822$		0			0
$823$		−	39.1302i		−	1.36399i	−0.731355	−	0.681996i	$-0.761112\pi$
$823$		−	39.1302i		−	1.36399i	0.731355	−	0.681996i	$-0.238888\pi$
$824$	38.0253	−	26.7560i	1.32467	−	0.932088i
$825$		0			0
$826$	−11.6722	+	5.87318i	−0.406127	+	0.204354i
$827$	−37.3252	−	37.3252i	−1.29792	−	1.29792i	−0.929762	−	0.368160i	$-0.879988\pi$
$827$	−37.3252	−	37.3252i	−1.29792	−	1.29792i	−0.368160	−	0.929762i	$-0.620012\pi$
$828$		0			0
$829$	−17.7182	+	17.7182i	−0.615377	+	0.615377i	−0.944342	−	0.328965i	$-0.893300\pi$
$829$	−17.7182	+	17.7182i	−0.615377	+	0.615377i	0.328965	+	0.944342i	$0.393300\pi$
$830$	−11.9974	−	3.96533i	−0.416437	−	0.137639i
$831$		0			0
$832$	17.7954	+	37.7091i	0.616944	+	1.30733i
$833$	7.86578			0.272533
$834$		0			0
$835$	13.7727	−	13.7727i	0.476623	−	0.476623i
$836$	−0.649070	−	0.481672i	−0.0224486	−	0.0166590i
$837$		0			0
$838$	43.6646	−	21.9711i	1.50837	−	0.758977i
$839$			35.3371i			1.21997i	0.792412	+	0.609986i	$0.208825\pi$
$839$			35.3371i			1.21997i	−0.792412	+	0.609986i	$0.791175\pi$
$840$		0			0
$841$		−	9.43399i		−	0.325310i
$842$	−19.5271	−	38.8076i	−0.672949	−	1.33740i
$843$		0			0
$844$	37.1509	−	5.49992i	1.27879	−	0.189315i
$845$	10.0172	−	10.0172i	0.344602	−	0.344602i
$846$		0			0
$847$	−14.7720			−0.507572
$848$	25.5009	−	47.6430i	0.875704	−	1.63607i
$849$		0			0
$850$	−0.698175	+	2.11239i	−0.0239472	+	0.0724543i
$851$	−12.2725	+	12.2725i	−0.420695	+	0.420695i
$852$		0			0
$853$	−35.7126	−	35.7126i	−1.22277	−	1.22277i	−0.966642	−	0.256133i	$-0.917551\pi$
$853$	−35.7126	−	35.7126i	−1.22277	−	1.22277i	−0.256133	−	0.966642i	$-0.582449\pi$
$854$	−5.75916	−	11.4456i	−0.197075	−	0.391660i
$855$		0			0
$856$	3.48621	−	20.0403i	0.119156	−	0.684964i
$857$		−	28.0974i		−	0.959789i	−0.877326	−	0.479895i	$-0.840675\pi$
$857$		−	28.0974i		−	0.959789i	0.877326	−	0.479895i	$-0.159325\pi$
$858$		0			0
$859$	26.5677	+	26.5677i	0.906477	+	0.906477i	0.995986	−	0.0895090i	$-0.0285298\pi$
$859$	26.5677	+	26.5677i	0.906477	+	0.906477i	−0.0895090	+	0.995986i	$0.528530\pi$
$860$	1.90205	−	2.56308i	0.0648593	−	0.0874002i
$861$		0			0
$862$	36.7753	+	12.1548i	1.25257	+	0.413994i
$863$	−12.4481			−0.423737			−0.211868	−	0.977298i	$-0.567955\pi$
$863$	−12.4481			−0.423737			−0.211868	+	0.977298i	$0.567955\pi$
$864$		0			0
$865$	−14.1541			−0.481254
$866$	5.03534	+	1.66425i	0.171108	+	0.0565536i
$867$		0			0
$868$	−9.69998	+	13.0711i	−0.329239	+	0.443661i
$869$	−1.75386	−	1.75386i	−0.0594955	−	0.0594955i
$870$		0			0
$871$			41.2476i			1.39762i
$872$	21.5832	+	3.75460i	0.730898	+	0.127147i
$873$		0			0
$874$	−2.21606	−	4.40413i	−0.0749595	−	0.148972i
$875$	1.00000	+	1.00000i	0.0338062	+	0.0338062i
$876$		0			0
$877$	6.42087	−	6.42087i	0.216817	−	0.216817i	−0.590339	−	0.807156i	$-0.701006\pi$
$877$	6.42087	−	6.42087i	0.216817	−	0.216817i	0.807156	+	0.590339i	$0.201006\pi$
$878$	−10.0114	+	30.2902i	−0.337867	+	1.02225i
$879$		0			0
$880$	−2.85114	+	0.863096i	−0.0961118	+	0.0290950i
$881$	14.0591			0.473664			0.236832	−	0.971551i	$-0.423891\pi$
$881$	14.0591			0.473664			0.236832	+	0.971551i	$0.423891\pi$
$882$		0			0
$883$	−37.6339	+	37.6339i	−1.26648	+	1.26648i	−0.318588	+	0.947893i	$0.603209\pi$
$883$	−37.6339	+	37.6339i	−1.26648	+	1.26648i	−0.947893	+	0.318588i	$0.896791\pi$
$884$	16.2222	−	2.40158i	0.545612	−	0.0807740i
$885$		0			0
$886$	11.7694	+	23.3902i	0.395402	+	0.785809i
$887$		−	22.1691i		−	0.744367i	−0.928159	−	0.372184i	$-0.878609\pi$
$887$		−	22.1691i		−	0.744367i	0.928159	−	0.372184i	$-0.121391\pi$
$888$		0			0
$889$			27.4201i			0.919641i
$890$	−6.85779	+	3.45069i	−0.229874	+	0.115667i
$891$		0			0
$892$	9.01026	+	6.68647i	0.301686	+	0.223880i
$893$	−0.803165	+	0.803165i	−0.0268769	+	0.0268769i
$894$		0			0
$895$	−5.91630			−0.197760
$896$	12.6036	+	9.85637i	0.421058	+	0.329278i
$897$		0			0
$898$	−5.55225	−	1.83510i	−0.185281	−	0.0612381i
$899$	25.2275	−	25.2275i	0.841383	−	0.841383i
$900$		0			0
$901$	−15.0279	−	15.0279i	−0.500653	−	0.500653i
$902$	11.2660	−	5.66881i	0.375118	−	0.188751i
$903$		0			0
$904$	24.3454	+	34.5995i	0.809717	+	1.15076i
$905$		−	14.7243i		−	0.489453i
$906$		0			0
$907$	31.1389	+	31.1389i	1.03395	+	1.03395i	0.999403	+	0.0345475i	$0.0109990\pi$
$907$	31.1389	+	31.1389i	1.03395	+	1.03395i	0.0345475	+	0.999403i	$0.489001\pi$
$908$	−32.2738	+	4.77790i	−1.07104	+	0.158560i
$909$		0			0
$910$	3.27133	−	9.89769i	0.108444	−	0.328105i
$911$	25.7283			0.852417			0.426208	−	0.904625i	$-0.359849\pi$
$911$	25.7283			0.852417			0.426208	+	0.904625i	$0.359849\pi$
$912$		0			0
$913$	−6.65402			−0.220216
$914$	−11.6725	+	35.3160i	−0.386090	+	1.16815i
$915$		0			0
$916$	−3.20892	−	21.6756i	−0.106026	−	0.716184i
$917$	6.76489	+	6.76489i	0.223396	+	0.223396i
$918$		0			0
$919$			2.17776i			0.0718375i	0.999355	+	0.0359188i	$0.0114358\pi$
$919$			2.17776i			0.0718375i	−0.999355	+	0.0359188i	$0.988564\pi$
$920$	−17.9018	−	3.11419i	−0.590205	−	0.102672i
$921$		0			0
$922$	23.9036	−	12.0278i	0.787223	−	0.396113i
$923$	−43.7903	−	43.7903i	−1.44137	−	1.44137i
$924$		0			0
$925$	−1.91032	+	1.91032i	−0.0628110	+	0.0628110i
$926$	19.6038	+	6.47934i	0.644221	+	0.212924i
$927$		0			0
$928$	−24.1638	−	25.4165i	−0.793215	−	0.834338i
$929$	25.3234			0.830834			0.415417	−	0.909631i	$-0.363636\pi$
$929$	25.3234			0.830834			0.415417	+	0.909631i	$0.363636\pi$
$930$		0			0
$931$	−1.91860	+	1.91860i	−0.0628794	+	0.0628794i
$932$	−8.31484	+	11.2045i	−0.272362	+	0.367017i
$933$		0			0
$934$	−42.4033	+	21.3364i	−1.38748	+	0.698149i
$935$			1.17157i			0.0383145i
$936$		0			0
$937$			36.5560i			1.19423i	0.802155	+	0.597116i	$0.203687\pi$
$937$			36.5560i			1.19423i	−0.802155	+	0.597116i	$0.796313\pi$
$938$	7.11419	+	14.1385i	0.232287	+	0.461639i
$939$		0			0
$940$	0.613057	+	4.14108i	0.0199957	+	0.135067i
$941$	−10.0143	+	10.0143i	−0.326455	+	0.326455i	−0.851237	−	0.524782i	$-0.824147\pi$
$941$	−10.0143	+	10.0143i	−0.326455	+	0.326455i	0.524782	+	0.851237i	$0.324147\pi$
$942$		0			0
$943$	76.9292			2.50516
$944$	12.3322	−	23.0402i	0.401380	−	0.749894i
$945$		0			0
$946$	0.527457	−	1.59587i	0.0171491	−	0.0518861i
$947$	39.9949	−	39.9949i	1.29966	−	1.29966i	0.371044	−	0.928615i	$-0.379000\pi$
$947$	39.9949	−	39.9949i	1.29966	−	1.29966i	0.928615	−	0.371044i	$-0.121000\pi$
$948$		0			0
$949$	44.9618	+	44.9618i	1.45952	+	1.45952i
$950$	−0.344951	−	0.685544i	−0.0111917	−	0.0222420i
$951$		0			0
$952$	5.14631	−	3.62113i	0.166793	−	0.117361i
$953$			49.8263i			1.61403i	0.590530	+	0.807016i	$0.298919\pi$
$953$			49.8263i			1.61403i	−0.590530	+	0.807016i	$0.701081\pi$
$954$		0			0
$955$	−4.58094	−	4.58094i	−0.148236	−	0.148236i
$956$	−7.66265	−	5.68642i	−0.247828	−	0.183912i
$957$		0			0
$958$	24.8437	+	8.21122i	0.802665	+	0.265292i
$959$	−5.53849			−0.178847
$960$		0			0
$961$	2.11780			0.0683162
$962$	18.9078	+	6.24929i	0.609611	+	0.201485i
$963$		0			0
$964$	49.0345	+	36.3883i	1.57930	+	1.17199i
$965$	0.492681	+	0.492681i	0.0158599	+	0.0158599i
$966$		0			0
$967$			21.0321i			0.676347i	0.941084	+	0.338173i	$0.109809\pi$
$967$			21.0321i			0.676347i	−0.941084	+	0.338173i	$0.890191\pi$
$968$	24.1620	−	17.0013i	0.776597	−	0.546442i
$969$		0			0
$970$	1.35939	+	2.70160i	0.0436473	+	0.0867432i
$971$	−37.7385	−	37.7385i	−1.21109	−	1.21109i	−0.970670	−	0.240416i	$-0.922716\pi$
$971$	−37.7385	−	37.7385i	−1.21109	−	1.21109i	−0.240416	−	0.970670i	$-0.577284\pi$
$972$		0			0
$973$	21.4486	−	21.4486i	0.687611	−	0.687611i
$974$	−6.22711	+	18.8407i	−0.199530	+	0.603694i
$975$		0			0
$976$	22.5929	+	12.0928i	0.723182	+	0.387083i
$977$	53.5629			1.71363			0.856815	−	0.515624i	$-0.172440\pi$
$977$	53.5629			1.71363			0.856815	+	0.515624i	$0.172440\pi$
$978$		0			0
$979$	−2.85864	+	2.85864i	−0.0913626	+	0.0913626i
$980$	1.46447	+	9.89219i	0.0467807	+	0.315994i
$981$		0			0
$982$	7.73191	+	15.3662i	0.246735	+	0.490354i
$983$		−	44.1169i		−	1.40711i	−0.710641	−	0.703555i	$-0.751595\pi$
$983$		−	44.1169i		−	1.40711i	0.710641	−	0.703555i	$-0.248405\pi$
$984$		0			0
$985$			16.4564i			0.524345i
$986$	−12.3207	+	6.19951i	−0.392372	+	0.197433i
$987$		0			0
$988$	−3.37109	+	4.54266i	−0.107249	+	0.144521i
$989$	7.24947	−	7.24947i	0.230520	−	0.230520i
$990$		0			0
$991$	−1.51348			−0.0480773			−0.0240387	−	0.999711i	$-0.507652\pi$
$991$	−1.51348			−0.0480773			−0.0240387	+	0.999711i	$0.507652\pi$
$992$	0.822265	−	32.5437i	0.0261069	−	1.03326i
$993$		0			0
$994$	−22.5628	−	7.45734i	−0.715649	−	0.236532i
$995$	−16.1757	+	16.1757i	−0.512803	+	0.512803i
$996$		0			0
$997$	−3.84609	−	3.84609i	−0.121807	−	0.121807i	0.643576	−	0.765382i	$-0.277450\pi$
$997$	−3.84609	−	3.84609i	−0.121807	−	0.121807i	−0.765382	+	0.643576i	$0.777450\pi$
$998$	18.8713	−	9.49562i	0.597360	−	0.300579i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.b.181.4		8
3.2	odd	2		240.2.s.b.181.1	yes	8
4.3	odd	2		2880.2.t.b.2161.3		8
12.11	even	2		960.2.s.b.241.2		8
16.3	odd	4		2880.2.t.b.721.3		8
16.13	even	4	inner	720.2.t.b.541.4		8
24.5	odd	2		1920.2.s.c.481.2		8
24.11	even	2		1920.2.s.d.481.3		8
48.5	odd	4		1920.2.s.c.1441.2		8
48.11	even	4		1920.2.s.d.1441.3		8
48.29	odd	4		240.2.s.b.61.1	✓	8
48.35	even	4		960.2.s.b.721.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.b.61.1	✓	8	48.29	odd	4
240.2.s.b.181.1	yes	8	3.2	odd	2
720.2.t.b.181.4		8	1.1	even	1	trivial
720.2.t.b.541.4		8	16.13	even	4	inner
960.2.s.b.241.2		8	12.11	even	2
960.2.s.b.721.2		8	48.35	even	4
1920.2.s.c.481.2		8	24.5	odd	2
1920.2.s.c.1441.2		8	48.5	odd	4
1920.2.s.d.481.3		8	24.11	even	2
1920.2.s.d.1441.3		8	48.11	even	4
2880.2.t.b.721.3		8	16.3	odd	4
2880.2.t.b.2161.3		8	4.3	odd	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34277 + 0.443806i) q^{2} +(1.60607 + 1.19186i) q^{4} +(0.707107 + 0.707107i) q^{5} -1.41421i q^{7} +(1.62764 + 2.31318i) q^{8} +O(q^{10})\)	\(q+(1.34277 + 0.443806i) q^{2} +(1.60607 + 1.19186i) q^{4} +(0.707107 + 0.707107i) q^{5} -1.41421i q^{7} +(1.62764 + 2.31318i) q^{8} +(0.635665 + 1.26330i) q^{10} +(0.526602 + 0.526602i) q^{11} +(3.68554 - 3.68554i) q^{13} +(0.627636 - 1.89897i) q^{14} +(1.15894 + 3.82843i) q^{16} +1.57316 q^{17} +(-0.383719 + 0.383719i) q^{19} +(0.292893 + 1.97844i) q^{20} +(0.473398 + 0.940816i) q^{22} +6.42429i q^{23} +1.00000i q^{25} +(6.58451 - 3.31318i) q^{26} +(1.68554 - 2.27133i) q^{28} +(-4.38372 + 4.38372i) q^{29} -5.75481 q^{31} +(-0.142883 + 5.65505i) q^{32} +(2.11239 + 0.698175i) q^{34} +(1.00000 - 1.00000i) q^{35} +(1.91032 + 1.91032i) q^{37} +(-0.685544 + 0.344951i) q^{38} +(-0.484753 + 2.78658i) q^{40} -11.9747i q^{41} +(-1.12845 - 1.12845i) q^{43} +(0.218126 + 1.47340i) q^{44} +(-2.85114 + 8.62636i) q^{46} +2.09311 q^{47} +5.00000 q^{49} +(-0.443806 + 1.34277i) q^{50} +(10.3119 - 1.52660i) q^{52} +(-9.55274 - 9.55274i) q^{53} +0.744728i q^{55} +(3.27133 - 2.30182i) q^{56} +(-7.83185 + 3.94082i) q^{58} +(-4.61971 - 4.61971i) q^{59} +(4.53003 - 4.53003i) q^{61} +(-7.72739 - 2.55402i) q^{62} +(-2.70160 + 7.53003i) q^{64} +5.21215 q^{65} +(-5.59587 + 5.59587i) q^{67} +(2.52660 + 1.87498i) q^{68} +(1.78658 - 0.898966i) q^{70} -11.8816i q^{71} +12.1995i q^{73} +(1.71731 + 3.41294i) q^{74} +(-1.07362 + 0.158942i) q^{76} +(0.744728 - 0.744728i) q^{77} -3.33051 q^{79} +(-1.88761 + 3.52660i) q^{80} +(5.31446 - 16.0793i) q^{82} +(-6.31788 + 6.31788i) q^{83} +(1.11239 + 1.11239i) q^{85} +(-1.01444 - 2.01606i) q^{86} +(-0.361009 + 2.07524i) q^{88} +5.42847i q^{89} +(-5.21215 - 5.21215i) q^{91} +(-7.65685 + 10.3179i) q^{92} +(2.81056 + 0.928932i) q^{94} -0.542661 q^{95} +2.13853 q^{97} +(6.71386 + 2.21903i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 12 q^{8}+O(q^{10}) \) 8 * q - 4 * q^4 + 12 * q^8	\( 8 q - 4 q^{4} + 12 q^{8} - 8 q^{11} + 8 q^{13} + 4 q^{14} - 8 q^{17} + 8 q^{19} + 8 q^{20} + 16 q^{22} + 20 q^{26} - 8 q^{28} - 24 q^{29} + 8 q^{31} + 16 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{40} + 16 q^{44} + 24 q^{46} + 40 q^{49} - 4 q^{50} + 16 q^{52} + 16 q^{56} - 8 q^{59} - 16 q^{61} - 28 q^{62} + 8 q^{64} + 8 q^{65} + 8 q^{68} + 4 q^{70} + 36 q^{74} - 40 q^{76} + 8 q^{77} - 40 q^{79} - 16 q^{80} + 64 q^{82} - 32 q^{83} + 8 q^{85} - 16 q^{86} - 16 q^{88} - 8 q^{91} - 16 q^{92} + 32 q^{94} + 16 q^{95} - 48 q^{97}+O(q^{100}) \) 8 * q - 4 * q^4 + 12 * q^8 - 8 * q^11 + 8 * q^13 + 4 * q^14 - 8 * q^17 + 8 * q^19 + 8 * q^20 + 16 * q^22 + 20 * q^26 - 8 * q^28 - 24 * q^29 + 8 * q^31 + 16 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^40 + 16 * q^44 + 24 * q^46 + 40 * q^49 - 4 * q^50 + 16 * q^52 + 16 * q^56 - 8 * q^59 - 16 * q^61 - 28 * q^62 + 8 * q^64 + 8 * q^65 + 8 * q^68 + 4 * q^70 + 36 * q^74 - 40 * q^76 + 8 * q^77 - 40 * q^79 - 16 * q^80 + 64 * q^82 - 32 * q^83 + 8 * q^85 - 16 * q^86 - 16 * q^88 - 8 * q^91 - 16 * q^92 + 32 * q^94 + 16 * q^95 - 48 * q^97

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