LMFDB - Embedded newform 720.2.t.d.541.1

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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			541.1
Root			$1.32147 + 0.503713i$ of defining polynomial
Character	$\chi$	$=$	720.541
Dual form			720.2.t.d.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32147 + 0.503713i) q^{2} +(1.49255 - 1.33128i) q^{4} +(0.707107 - 0.707107i) q^{5} -2.69529i q^{7} +(-1.30176 + 2.51106i) q^{8} +O(q^{10})$	\(q+(-1.32147 + 0.503713i) q^{2} +(1.49255 - 1.33128i) q^{4} +(0.707107 - 0.707107i) q^{5} -2.69529i q^{7} +(-1.30176 + 2.51106i) q^{8} +(-0.578239 + 1.29060i) q^{10} +(-2.72735 + 2.72735i) q^{11} +(1.82449 + 1.82449i) q^{13} +(1.35765 + 3.56173i) q^{14} +(0.455385 - 3.97399i) q^{16} +7.33517 q^{17} +(3.62540 + 3.62540i) q^{19} +(0.114032 - 1.99675i) q^{20} +(2.23030 - 4.97791i) q^{22} -8.95345i q^{23} -1.00000i q^{25} +(-3.33002 - 1.49198i) q^{26} +(-3.58819 - 4.02284i) q^{28} +(-2.84302 - 2.84302i) q^{29} -3.37977 q^{31} +(1.39998 + 5.48088i) q^{32} +(-9.69317 + 3.69482i) q^{34} +(-1.90586 - 1.90586i) q^{35} +(-0.190364 + 0.190364i) q^{37} +(-6.61700 - 2.96468i) q^{38} +(0.855099 + 2.69607i) q^{40} -7.67786i q^{41} +(7.98115 - 7.98115i) q^{43} +(-0.439827 + 7.70158i) q^{44} +(4.50997 + 11.8317i) q^{46} +1.31537 q^{47} -0.264584 q^{49} +(0.503713 + 1.32147i) q^{50} +(5.15204 + 0.294227i) q^{52} +(6.71014 - 6.71014i) q^{53} +3.85706i q^{55} +(6.76803 + 3.50863i) q^{56} +(5.18902 + 2.32488i) q^{58} +(-1.01464 + 1.01464i) q^{59} +(2.38996 + 2.38996i) q^{61} +(4.46625 - 1.70243i) q^{62} +(-4.61082 - 6.53761i) q^{64} +2.58022 q^{65} +(-7.22173 - 7.22173i) q^{67} +(10.9481 - 9.76516i) q^{68} +(3.47853 + 1.55852i) q^{70} -2.28859i q^{71} +1.31098i q^{73} +(0.155670 - 0.347448i) q^{74} +(10.2375 + 0.584650i) q^{76} +(7.35101 + 7.35101i) q^{77} -2.59319 q^{79} +(-2.48803 - 3.13204i) q^{80} +(3.86744 + 10.1460i) q^{82} +(5.36584 + 5.36584i) q^{83} +(5.18675 - 5.18675i) q^{85} +(-6.52661 + 14.5670i) q^{86} +(-3.29817 - 10.3989i) q^{88} +14.8944i q^{89} +(4.91753 - 4.91753i) q^{91} +(-11.9195 - 13.3634i) q^{92} +(-1.73822 + 0.662570i) q^{94} +5.12708 q^{95} +0.694695 q^{97} +(0.349639 - 0.133275i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} - 12 q^{8}+O(q^{10}) $ 20 * q + 4 * q^4 - 12 * q^8	$ 20 q + 4 q^{4} - 12 q^{8} - 8 q^{11} + 4 q^{14} - 20 q^{16} + 24 q^{17} - 4 q^{19} + 8 q^{20} + 8 q^{22} - 28 q^{26} - 8 q^{28} - 16 q^{29} + 40 q^{32} - 44 q^{34} + 16 q^{37} + 8 q^{38} + 12 q^{40} - 8 q^{43} - 24 q^{44} - 12 q^{46} - 52 q^{49} - 4 q^{50} - 56 q^{52} + 16 q^{53} - 64 q^{56} + 72 q^{58} + 16 q^{59} - 4 q^{61} + 44 q^{62} - 56 q^{64} - 8 q^{67} + 32 q^{68} + 20 q^{70} - 60 q^{74} + 28 q^{76} + 40 q^{77} + 56 q^{79} + 16 q^{80} - 24 q^{82} + 48 q^{83} + 4 q^{85} - 64 q^{86} + 40 q^{88} - 8 q^{91} - 88 q^{92} - 20 q^{94} + 56 q^{97} + 48 q^{98}+O(q^{100}) $ 20 * q + 4 * q^4 - 12 * q^8 - 8 * q^11 + 4 * q^14 - 20 * q^16 + 24 * q^17 - 4 * q^19 + 8 * q^20 + 8 * q^22 - 28 * q^26 - 8 * q^28 - 16 * q^29 + 40 * q^32 - 44 * q^34 + 16 * q^37 + 8 * q^38 + 12 * q^40 - 8 * q^43 - 24 * q^44 - 12 * q^46 - 52 * q^49 - 4 * q^50 - 56 * q^52 + 16 * q^53 - 64 * q^56 + 72 * q^58 + 16 * q^59 - 4 * q^61 + 44 * q^62 - 56 * q^64 - 8 * q^67 + 32 * q^68 + 20 * q^70 - 60 * q^74 + 28 * q^76 + 40 * q^77 + 56 * q^79 + 16 * q^80 - 24 * q^82 + 48 * q^83 + 4 * q^85 - 64 * q^86 + 40 * q^88 - 8 * q^91 - 88 * q^92 - 20 * q^94 + 56 * q^97 + 48 * 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 $

$2$	−1.32147	+	0.503713i	−0.934418	+	0.356179i
$2$	−1.32147	+	0.503713i	−0.934418	+	0.356179i
$3$		0			0
$3$		0			0
$4$	1.49255	−	1.33128i	0.746273	−	0.665640i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$		−	2.69529i		−	1.01872i	−0.860552	−	0.509362i	$-0.829882\pi$
$7$		−	2.69529i		−	1.01872i	0.860552	−	0.509362i	$-0.170118\pi$
$8$	−1.30176	+	2.51106i	−0.460243	+	0.887793i
$9$		0			0
$10$	−0.578239	+	1.29060i	−0.182855	+	0.408123i
$11$	−2.72735	+	2.72735i	−0.822328	+	0.822328i	−0.986442	−	0.164113i	$-0.947524\pi$
$11$	−2.72735	+	2.72735i	−0.822328	+	0.822328i	0.164113	+	0.986442i	$0.447524\pi$
$12$		0			0
$13$	1.82449	+	1.82449i	0.506023	+	0.506023i	0.913303	−	0.407281i	$-0.133523\pi$
$13$	1.82449	+	1.82449i	0.506023	+	0.506023i	−0.407281	+	0.913303i	$0.633523\pi$
$14$	1.35765	+	3.56173i	0.362848	+	0.951913i
$15$		0			0
$16$	0.455385	−	3.97399i	0.113846	−	0.993498i
$17$	7.33517			1.77904			0.889520	−	0.456897i	$-0.151039\pi$
$17$	7.33517			1.77904			0.889520	+	0.456897i	$0.151039\pi$
$18$		0			0
$19$	3.62540	+	3.62540i	0.831723	+	0.831723i	0.987752	−	0.156029i	$-0.0498695\pi$
$19$	3.62540	+	3.62540i	0.831723	+	0.831723i	−0.156029	+	0.987752i	$0.549869\pi$
$20$	0.114032	−	1.99675i	0.0254983	−	0.446486i
$21$		0			0
$22$	2.23030	−	4.97791i	0.475502	−	1.06129i
$23$		−	8.95345i		−	1.86692i	−0.358678	−	0.933461i	$-0.616772\pi$
$23$		−	8.95345i		−	1.86692i	0.358678	−	0.933461i	$-0.383228\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	−3.33002	−	1.49198i	−0.653071	−	0.292602i
$27$		0			0
$28$	−3.58819	−	4.02284i	−0.678103	−	0.760246i
$29$	−2.84302	−	2.84302i	−0.527935	−	0.527935i	0.392021	−	0.919956i	$-0.371776\pi$
$29$	−2.84302	−	2.84302i	−0.527935	−	0.527935i	−0.919956	+	0.392021i	$0.871776\pi$
$30$		0			0
$31$	−3.37977			−0.607024			−0.303512	−	0.952828i	$-0.598159\pi$
$31$	−3.37977			−0.607024			−0.303512	+	0.952828i	$0.598159\pi$
$32$	1.39998	+	5.48088i	0.247484	+	0.968892i
$33$		0			0
$34$	−9.69317	+	3.69482i	−1.66237	+	0.633657i
$35$	−1.90586	−	1.90586i	−0.322149	−	0.322149i
$36$		0			0
$37$	−0.190364	+	0.190364i	−0.0312956	+	0.0312956i	−0.722581	−	0.691286i	$-0.757045\pi$
$37$	−0.190364	+	0.190364i	−0.0312956	+	0.0312956i	0.691286	+	0.722581i	$0.257045\pi$
$38$	−6.61700	−	2.96468i	−1.07342	−	0.480934i
$39$		0			0
$40$	0.855099	+	2.69607i	0.135203	+	0.426286i
$41$		−	7.67786i		−	1.19908i	−0.800345	−	0.599540i	$-0.795350\pi$
$41$		−	7.67786i		−	1.19908i	0.800345	−	0.599540i	$-0.204650\pi$
$42$		0			0
$43$	7.98115	−	7.98115i	1.21711	−	1.21711i	0.248477	−	0.968638i	$-0.420070\pi$
$43$	7.98115	−	7.98115i	1.21711	−	1.21711i	0.968638	−	0.248477i	$-0.0799299\pi$
$44$	−0.439827	+	7.70158i	−0.0663065	+	1.16106i
$45$		0			0
$46$	4.50997	+	11.8317i	0.664959	+	1.74449i
$47$	1.31537			0.191866			0.0959332	−	0.995388i	$-0.469416\pi$
$47$	1.31537			0.191866			0.0959332	+	0.995388i	$0.469416\pi$
$48$		0			0
$49$	−0.264584			−0.0377977
$50$	0.503713	+	1.32147i	0.0712358	+	0.186884i
$51$		0			0
$52$	5.15204	+	0.294227i	0.714460	+	0.0408019i
$53$	6.71014	−	6.71014i	0.921709	−	0.921709i	−0.0754412	−	0.997150i	$-0.524037\pi$
$53$	6.71014	−	6.71014i	0.921709	−	0.921709i	0.997150	+	0.0754412i	$0.0240365\pi$
$54$		0			0
$55$			3.85706i			0.520086i
$56$	6.76803	+	3.50863i	0.904415	+	0.468861i
$57$		0			0
$58$	5.18902	+	2.32488i	0.681351	+	0.305272i
$59$	−1.01464	+	1.01464i	−0.132094	+	0.132094i	−0.770063	−	0.637968i	$-0.779775\pi$
$59$	−1.01464	+	1.01464i	−0.132094	+	0.132094i	0.637968	+	0.770063i	$0.279775\pi$
$60$		0			0
$61$	2.38996	+	2.38996i	0.306004	+	0.306004i	0.843357	−	0.537354i	$-0.180576\pi$
$61$	2.38996	+	2.38996i	0.306004	+	0.306004i	−0.537354	+	0.843357i	$0.680576\pi$
$62$	4.46625	−	1.70243i	0.567214	−	0.216209i
$63$		0			0
$64$	−4.61082	−	6.53761i	−0.576352	−	0.817201i
$65$	2.58022			0.320037
$66$		0			0
$67$	−7.22173	−	7.22173i	−0.882275	−	0.882275i	0.111490	−	0.993766i	$-0.464438\pi$
$67$	−7.22173	−	7.22173i	−0.882275	−	0.882275i	−0.993766	+	0.111490i	$0.964438\pi$
$68$	10.9481	−	9.76516i	1.32765	−	1.18420i
$69$		0			0
$70$	3.47853	+	1.55852i	0.415764	+	0.186279i
$71$		−	2.28859i		−	0.271606i	−0.990736	−	0.135803i	$-0.956639\pi$
$71$		−	2.28859i		−	0.271606i	0.990736	−	0.135803i	$-0.0433614\pi$
$72$		0			0
$73$			1.31098i			0.153439i	0.997053	+	0.0767196i	$0.0244446\pi$
$73$			1.31098i			0.153439i	−0.997053	+	0.0767196i	$0.975555\pi$
$74$	0.155670	−	0.347448i	0.0180963	−	0.0403900i
$75$		0			0
$76$	10.2375	+	0.584650i	1.17432	+	0.0670640i
$77$	7.35101	+	7.35101i	0.837725	+	0.837725i
$78$		0			0
$79$	−2.59319			−0.291757			−0.145879	−	0.989303i	$-0.546601\pi$
$79$	−2.59319			−0.291757			−0.145879	+	0.989303i	$0.546601\pi$
$80$	−2.48803	−	3.13204i	−0.278170	−	0.350173i
$81$		0			0
$82$	3.86744	+	10.1460i	0.427087	+	1.12044i
$83$	5.36584	+	5.36584i	0.588977	+	0.588977i	0.937354	−	0.348377i	$-0.113267\pi$
$83$	5.36584	+	5.36584i	0.588977	+	0.588977i	−0.348377	+	0.937354i	$0.613267\pi$
$84$		0			0
$85$	5.18675	−	5.18675i	0.562582	−	0.562582i
$86$	−6.52661	+	14.5670i	−0.703783	+	1.57080i
$87$		0			0
$88$	−3.29817	−	10.3989i	−0.351586	−	1.10853i
$89$			14.8944i			1.57880i	0.613877	+	0.789402i	$0.289609\pi$
$89$			14.8944i			1.57880i	−0.613877	+	0.789402i	$0.710391\pi$
$90$		0			0
$91$	4.91753	−	4.91753i	0.515497	−	0.515497i
$92$	−11.9195	−	13.3634i	−1.24270	−	1.39323i
$93$		0			0
$94$	−1.73822	+	0.662570i	−0.179283	+	0.0683388i
$95$	5.12708			0.526028
$96$		0			0
$97$	0.694695			0.0705356			0.0352678	−	0.999378i	$-0.488772\pi$
$97$	0.694695			0.0705356			0.0352678	+	0.999378i	$0.488772\pi$
$98$	0.349639	−	0.133275i	0.0353189	−	0.0134628i
$99$		0			0
$100$	−1.33128	−	1.49255i	−0.133128	−	0.149255i
$101$	6.88955	−	6.88955i	0.685536	−	0.685536i	−0.275706	−	0.961242i	$-0.588912\pi$
$101$	6.88955	−	6.88955i	0.685536	−	0.685536i	0.961242	+	0.275706i	$0.0889115\pi$
$102$		0			0
$103$		−	4.39299i		−	0.432854i	−0.976299	−	0.216427i	$-0.930560\pi$
$103$		−	4.39299i		−	0.432854i	0.976299	−	0.216427i	$-0.0694403\pi$
$104$	−6.95646	+	2.20634i	−0.682137	+	0.216350i
$105$		0			0
$106$	−5.48724	+	12.2472i	−0.532968	+	1.18955i
$107$	−7.09279	+	7.09279i	−0.685686	+	0.685686i	−0.961275	−	0.275590i	$-0.911127\pi$
$107$	−7.09279	+	7.09279i	−0.685686	+	0.685686i	0.275590	+	0.961275i	$0.411127\pi$
$108$		0			0
$109$	7.83035	+	7.83035i	0.750012	+	0.750012i	0.974481	−	0.224469i	$-0.0720649\pi$
$109$	7.83035	+	7.83035i	0.750012	+	0.750012i	−0.224469	+	0.974481i	$0.572065\pi$
$110$	−1.94285	−	5.09698i	−0.185244	−	0.485978i
$111$		0			0
$112$	−10.7111	−	1.22739i	−1.01210	−	0.115978i
$113$	4.63828			0.436332			0.218166	−	0.975912i	$-0.429993\pi$
$113$	4.63828			0.436332			0.218166	+	0.975912i	$0.429993\pi$
$114$		0			0
$115$	−6.33104	−	6.33104i	−0.590373	−	0.590373i
$116$	−8.02818	−	0.458479i	−0.745398	−	0.0425687i
$117$		0			0
$118$	0.829722	−	1.85189i	0.0763821	−	0.170481i
$119$		−	19.7704i		−	1.81235i
$120$		0			0
$121$		−	3.87693i		−	0.352448i
$122$	−4.36211	−	1.95440i	−0.394927	−	0.176943i
$123$		0			0
$124$	−5.04445	+	4.49942i	−0.453005	+	0.404059i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	−8.57901			−0.761264			−0.380632	−	0.924727i	$-0.624294\pi$
$127$	−8.57901			−0.761264			−0.380632	+	0.924727i	$0.624294\pi$
$128$	9.38612	+	6.31670i	0.829624	+	0.558323i
$129$		0			0
$130$	−3.40967	+	1.29969i	−0.299048	+	0.113990i
$131$	5.33779	+	5.33779i	0.466365	+	0.466365i	0.900735	−	0.434370i	$-0.143029\pi$
$131$	5.33779	+	5.33779i	0.466365	+	0.466365i	−0.434370	+	0.900735i	$0.643029\pi$
$132$		0			0
$133$	9.77149	−	9.77149i	0.847296	−	0.847296i
$134$	13.1810	+	5.90559i	1.13866	+	0.510165i
$135$		0			0
$136$	−9.54866	+	18.4190i	−0.818791	+	1.57942i
$137$			12.2694i			1.04825i	0.851642	+	0.524124i	$0.175607\pi$
$137$			12.2694i			1.04825i	−0.851642	+	0.524124i	$0.824393\pi$
$138$		0			0
$139$	−12.7593	+	12.7593i	−1.08223	+	1.08223i	−0.0859285	+	0.996301i	$0.527386\pi$
$139$	−12.7593	+	12.7593i	−1.08223	+	1.08223i	−0.996301	+	0.0859285i	$0.972614\pi$
$140$	−5.38181	−	0.307348i	−0.454846	−	0.0259757i
$141$		0			0
$142$	1.15279	+	3.02430i	0.0967404	+	0.253793i
$143$	−9.95206			−0.832233
$144$		0			0
$145$	−4.02063			−0.333895
$146$	−0.660361	−	1.73242i	−0.0546518	−	0.143376i
$147$		0			0
$148$	−0.0306990	+	0.537554i	−0.00252344	+	0.0441866i
$149$	−6.47238	+	6.47238i	−0.530238	+	0.530238i	−0.920643	−	0.390405i	$-0.872335\pi$
$149$	−6.47238	+	6.47238i	−0.530238	+	0.530238i	0.390405	+	0.920643i	$0.372335\pi$
$150$		0			0
$151$		−	14.7782i		−	1.20263i	−0.799012	−	0.601316i	$-0.794643\pi$
$151$		−	14.7782i		−	1.20263i	0.799012	−	0.601316i	$-0.205357\pi$
$152$	−13.8230	+	4.38417i	−1.12119	+	0.355603i
$153$		0			0
$154$	−13.4169	−	6.01131i	−1.08117	−	0.484405i
$155$	−2.38986	+	2.38986i	−0.191958	+	0.191958i
$156$		0			0
$157$	14.0590	+	14.0590i	1.12203	+	1.12203i	0.991436	+	0.130592i	$0.0416878\pi$
$157$	14.0590	+	14.0590i	1.12203	+	1.12203i	0.130592	+	0.991436i	$0.458312\pi$
$158$	3.42682	−	1.30623i	0.272623	−	0.103918i
$159$		0			0
$160$	4.86550	+	2.88563i	0.384652	+	0.228129i
$161$	−24.1321			−1.90188
$162$		0			0
$163$	2.09819	+	2.09819i	0.164343	+	0.164343i	0.784487	−	0.620145i	$-0.212926\pi$
$163$	2.09819	+	2.09819i	0.164343	+	0.164343i	−0.620145	+	0.784487i	$0.712926\pi$
$164$	−10.2214	−	11.4596i	−0.798156	−	0.894841i
$165$		0			0
$166$	−9.79362	−	4.38793i	−0.760132	−	0.340569i
$167$			15.7672i			1.22010i	0.792361	+	0.610052i	$0.208852\pi$
$167$			15.7672i			1.22010i	−0.792361	+	0.610052i	$0.791148\pi$
$168$		0			0
$169$		−	6.34247i		−	0.487882i
$170$	−4.24148	+	9.46674i	−0.325306	+	0.726066i
$171$		0			0
$172$	1.28708	−	22.5374i	0.0981391	−	1.71846i
$173$	−8.73572	−	8.73572i	−0.664164	−	0.664164i	0.292195	−	0.956359i	$-0.405615\pi$
$173$	−8.73572	−	8.73572i	−0.664164	−	0.664164i	−0.956359	+	0.292195i	$0.905615\pi$
$174$		0			0
$175$	−2.69529			−0.203745
$176$	9.59649	+	12.0805i	0.723363	+	0.910601i
$177$		0			0
$178$	−7.50251	−	19.6824i	−0.562337	−	1.47526i
$179$	−5.72942	−	5.72942i	−0.428237	−	0.428237i	0.459790	−	0.888027i	$-0.347925\pi$
$179$	−5.72942	−	5.72942i	−0.428237	−	0.428237i	−0.888027	+	0.459790i	$0.847925\pi$
$180$		0			0
$181$	−1.48317	+	1.48317i	−0.110243	+	0.110243i	−0.760077	−	0.649833i	$-0.774839\pi$
$181$	−1.48317	+	1.48317i	−0.110243	+	0.110243i	0.649833	+	0.760077i	$0.274839\pi$
$182$	−4.02132	+	8.97537i	−0.298080	+	0.665299i
$183$		0			0
$184$	22.4826	+	11.6553i	1.65744	+	0.859239i
$185$			0.269215i			0.0197931i
$186$		0			0
$187$	−20.0056	+	20.0056i	−1.46295	+	1.46295i
$188$	1.96325	−	1.75113i	0.143185	−	0.127714i
$189$		0			0
$190$	−6.77527	+	2.58258i	−0.491530	+	0.187360i
$191$	−1.00884			−0.0729970			−0.0364985	−	0.999334i	$-0.511620\pi$
$191$	−1.00884			−0.0729970			−0.0364985	+	0.999334i	$0.511620\pi$
$192$		0			0
$193$	−20.0273			−1.44160			−0.720798	−	0.693145i	$-0.756225\pi$
$193$	−20.0273			−1.44160			−0.720798	+	0.693145i	$0.756225\pi$
$194$	−0.918015	+	0.349927i	−0.0659097	+	0.0251233i
$195$		0			0
$196$	−0.394904	+	0.352236i	−0.0282074	+	0.0251597i
$197$	12.7615	−	12.7615i	0.909217	−	0.909217i	−0.0869919	−	0.996209i	$-0.527725\pi$
$197$	12.7615	−	12.7615i	0.909217	−	0.909217i	0.996209	+	0.0869919i	$0.0277254\pi$
$198$		0			0
$199$			11.6629i			0.826764i	0.910558	+	0.413382i	$0.135653\pi$
$199$			11.6629i			0.826764i	−0.910558	+	0.413382i	$0.864347\pi$
$200$	2.51106	+	1.30176i	0.177559	+	0.0920487i
$201$		0			0
$202$	−5.63395	+	12.5747i	−0.396404	+	0.884751i
$203$	−7.66275	+	7.66275i	−0.537820	+	0.537820i
$204$		0			0
$205$	−5.42907	−	5.42907i	−0.379183	−	0.379183i
$206$	2.21281	+	5.80518i	0.154174	+	0.404466i
$207$		0			0
$208$	8.08136	−	6.41967i	0.560341	−	0.445124i
$209$	−19.7755			−1.36790
$210$		0			0
$211$	−0.419270	−	0.419270i	−0.0288637	−	0.0288637i	0.692528	−	0.721391i	$-0.256497\pi$
$211$	−0.419270	−	0.419270i	−0.0288637	−	0.0288637i	−0.721391	+	0.692528i	$0.756497\pi$
$212$	1.08211	−	18.9483i	0.0743198	−	1.30137i
$213$		0			0
$214$	5.80015	−	12.9456i	0.396490	−	0.884944i
$215$		−	11.2871i		−	0.769771i
$216$		0			0
$217$			9.10945i			0.618389i
$218$	−14.2918	−	6.40329i	−0.967963	−	0.433686i
$219$		0			0
$220$	5.13483	+	5.75684i	0.346190	+	0.388126i
$221$	13.3829	+	13.3829i	0.900234	+	0.900234i
$222$		0			0
$223$	−20.3746			−1.36438			−0.682191	−	0.731174i	$-0.738973\pi$
$223$	−20.3746			−1.36438			−0.682191	+	0.731174i	$0.738973\pi$
$224$	14.7726	−	3.77335i	0.987033	−	0.252117i
$225$		0			0
$226$	−6.12933	+	2.33636i	−0.407717	+	0.155413i
$227$	−2.87480	−	2.87480i	−0.190807	−	0.190807i	0.605238	−	0.796045i	$-0.293078\pi$
$227$	−2.87480	−	2.87480i	−0.190807	−	0.190807i	−0.796045	+	0.605238i	$0.793078\pi$
$228$		0			0
$229$	−6.78564	+	6.78564i	−0.448408	+	0.448408i	−0.894825	−	0.446417i	$-0.852700\pi$
$229$	−6.78564	+	6.78564i	−0.448408	+	0.448408i	0.446417	+	0.894825i	$0.352700\pi$
$230$	11.5553	+	5.17723i	0.761933	+	0.341376i
$231$		0			0
$232$	10.8399	−	3.43804i	0.711675	−	0.225718i
$233$		−	27.8637i		−	1.82541i	−0.408619	−	0.912705i	$-0.633990\pi$
$233$		−	27.8637i		−	1.82541i	0.408619	−	0.912705i	$-0.366010\pi$
$234$		0			0
$235$	0.930107	−	0.930107i	0.0606735	−	0.0606735i
$236$	−0.163626	+	2.86516i	−0.0106511	+	0.186506i
$237$		0			0
$238$	9.95861	+	26.1259i	0.645521	+	1.69349i
$239$	19.7188			1.27550			0.637750	−	0.770243i	$-0.279865\pi$
$239$	19.7188			1.27550			0.637750	+	0.770243i	$0.279865\pi$
$240$		0			0
$241$	7.74263			0.498747			0.249373	−	0.968407i	$-0.419775\pi$
$241$	7.74263			0.498747			0.249373	+	0.968407i	$0.419775\pi$
$242$	1.95286	+	5.12323i	0.125535	+	0.329334i
$243$		0			0
$244$	6.74884	+	0.385418i	0.432050	+	0.0246738i
$245$	−0.187089	+	0.187089i	−0.0119527	+	0.0119527i
$246$		0			0
$247$			13.2290i			0.841741i
$248$	4.39966	−	8.48678i	0.279379	−	0.538911i
$249$		0			0
$250$	1.29060	+	0.578239i	0.0816245	+	0.0365710i
$251$	−1.46277	+	1.46277i	−0.0923293	+	0.0923293i	−0.751763	−	0.659434i	$-0.770796\pi$
$251$	−1.46277	+	1.46277i	−0.0923293	+	0.0923293i	0.659434	+	0.751763i	$0.270796\pi$
$252$		0			0
$253$	24.4192	+	24.4192i	1.53522	+	1.53522i
$254$	11.3369	−	4.32136i	0.711338	−	0.271146i
$255$		0			0
$256$	−15.5852	−	3.61939i	−0.974078	−	0.226212i
$257$	−20.6684			−1.28926			−0.644630	−	0.764495i	$-0.722988\pi$
$257$	−20.6684			−1.28926			−0.644630	+	0.764495i	$0.722988\pi$
$258$		0			0
$259$	0.513085	+	0.513085i	0.0318815	+	0.0318815i
$260$	3.85109	−	3.43499i	0.238835	−	0.213029i
$261$		0			0
$262$	−9.74242	−	4.36499i	−0.601889	−	0.269670i
$263$		−	26.3239i		−	1.62320i	−0.584215	−	0.811599i	$-0.698597\pi$
$263$		−	26.3239i		−	1.62320i	0.584215	−	0.811599i	$-0.301403\pi$
$264$		0			0
$265$		−	9.48958i		−	0.582940i
$266$	−7.99066	+	17.8347i	−0.489939	+	1.09352i
$267$		0			0
$268$	−20.3929	−	1.16461i	−1.24570	−	0.0711401i
$269$	17.8129	+	17.8129i	1.08607	+	1.08607i	0.995929	+	0.0901396i	$0.0287313\pi$
$269$	17.8129	+	17.8129i	1.08607	+	1.08607i	0.0901396	+	0.995929i	$0.471269\pi$
$270$		0			0
$271$	−7.19848			−0.437277			−0.218638	−	0.975806i	$-0.570162\pi$
$271$	−7.19848			−0.437277			−0.218638	+	0.975806i	$0.570162\pi$
$272$	3.34032	−	29.1499i	0.202537	−	1.76747i
$273$		0			0
$274$	−6.18027	−	16.2136i	−0.373364	−	0.979501i
$275$	2.72735	+	2.72735i	0.164466	+	0.164466i
$276$		0			0
$277$	10.4666	−	10.4666i	0.628879	−	0.628879i	−0.318907	−	0.947786i	$-0.603316\pi$
$277$	10.4666	−	10.4666i	0.628879	−	0.628879i	0.947786	+	0.318907i	$0.103316\pi$
$278$	10.4340	−	23.2880i	0.625787	−	1.39672i
$279$		0			0
$280$	7.26669	−	2.30474i	0.434268	−	0.137735i
$281$			17.0567i			1.01752i	0.860909	+	0.508759i	$0.169896\pi$
$281$			17.0567i			1.01752i	−0.860909	+	0.508759i	$0.830104\pi$
$282$		0			0
$283$	2.70727	−	2.70727i	0.160931	−	0.160931i	−0.622048	−	0.782979i	$-0.713699\pi$
$283$	2.70727	−	2.70727i	0.160931	−	0.160931i	0.782979	+	0.622048i	$0.213699\pi$
$284$	−3.04676	−	3.41583i	−0.180792	−	0.202692i
$285$		0			0
$286$	13.1513	−	5.01299i	0.777654	−	0.296424i
$287$	−20.6941			−1.22153
$288$		0			0
$289$	36.8047			2.16498
$290$	5.31313	−	2.02525i	0.311998	−	0.118927i
$291$		0			0
$292$	1.74529	+	1.95670i	0.102135	+	0.114507i
$293$	−16.6594	+	16.6594i	−0.973255	+	0.973255i	−0.999652	−	0.0263968i	$-0.991597\pi$
$293$	−16.6594	+	16.6594i	−0.973255	+	0.973255i	0.0263968	+	0.999652i	$0.491597\pi$
$294$		0			0
$295$			1.43491i			0.0835439i
$296$	−0.230205	−	0.725822i	−0.0133804	−	0.0421876i
$297$		0			0
$298$	5.29280	−	11.8133i	0.306604	−	0.684323i
$299$	16.3355	−	16.3355i	0.944705	−	0.944705i
$300$		0			0
$301$	−21.5115	−	21.5115i	−1.23990	−	1.23990i
$302$	7.44397	+	19.5289i	0.428352	+	1.12376i
$303$		0			0
$304$	16.0583	−	12.7564i	0.921004	−	0.731627i
$305$	3.37992			0.193534
$306$		0			0
$307$	18.1991	+	18.1991i	1.03868	+	1.03868i	0.999221	+	0.0394558i	$0.0125624\pi$
$307$	18.1991	+	18.1991i	1.03868	+	1.03868i	0.0394558	+	0.999221i	$0.487438\pi$
$308$	20.7580	+	1.18546i	1.18280	+	0.0675479i
$309$		0			0
$310$	1.95431	−	4.36191i	0.110997	−	0.247740i
$311$			15.3933i			0.872874i	0.899735	+	0.436437i	$0.143760\pi$
$311$			15.3933i			0.872874i	−0.899735	+	0.436437i	$0.856240\pi$
$312$		0			0
$313$			23.7790i			1.34407i	0.740520	+	0.672034i	$0.234579\pi$
$313$			23.7790i			1.34407i	−0.740520	+	0.672034i	$0.765421\pi$
$314$	−25.6602	−	11.4968i	−1.44809	−	0.648800i
$315$		0			0
$316$	−3.87046	+	3.45227i	−0.217730	+	0.194205i
$317$	9.29662	+	9.29662i	0.522150	+	0.522150i	0.918220	−	0.396070i	$-0.129626\pi$
$317$	9.29662	+	9.29662i	0.522150	+	0.522150i	−0.396070	+	0.918220i	$0.629626\pi$
$318$		0			0
$319$	15.5078			0.868272
$320$	−7.88313	−	1.36245i	−0.440680	−	0.0761632i
$321$		0			0
$322$	31.8898	−	12.1557i	1.77715	−	0.677409i
$323$	26.5929	+	26.5929i	1.47967	+	1.47967i
$324$		0			0
$325$	1.82449	−	1.82449i	0.101205	−	0.101205i
$326$	−3.82956	−	1.71580i	−0.212100	−	0.0950292i
$327$		0			0
$328$	19.2795	+	9.99477i	1.06453	+	0.551869i
$329$		−	3.54530i		−	0.195459i
$330$		0			0
$331$	−15.0564	+	15.0564i	−0.827572	+	0.827572i	−0.987180	−	0.159608i	$-0.948977\pi$
$331$	−15.0564	+	15.0564i	−0.827572	+	0.827572i	0.159608	+	0.987180i	$0.448977\pi$
$332$	15.1522	+	0.865323i	0.831585	+	0.0474908i
$333$		0			0
$334$	−7.94216	−	20.8359i	−0.434576	−	1.14009i
$335$	−10.2131			−0.558000
$336$		0			0
$337$	−11.7116			−0.637969			−0.318985	−	0.947760i	$-0.603342\pi$
$337$	−11.7116			−0.637969			−0.318985	+	0.947760i	$0.603342\pi$
$338$	3.19479	+	8.38136i	0.173774	+	0.455886i
$339$		0			0
$340$	0.836441	−	14.6465i	0.0453624	−	0.794316i
$341$	9.21782	−	9.21782i	0.499173	−	0.499173i
$342$		0			0
$343$		−	18.1539i		−	0.980218i
$344$	9.65155	+	30.4307i	0.520377	+	1.64071i
$345$		0			0
$346$	15.9443	+	7.14366i	0.857168	+	0.384045i
$347$	−12.5589	+	12.5589i	−0.674197	+	0.674197i	−0.958681	−	0.284484i	$-0.908178\pi$
$347$	−12.5589	+	12.5589i	−0.674197	+	0.674197i	0.284484	+	0.958681i	$0.408178\pi$
$348$		0			0
$349$	−12.3114	−	12.3114i	−0.659014	−	0.659014i	0.296133	−	0.955147i	$-0.404303\pi$
$349$	−12.3114	−	12.3114i	−0.659014	−	0.659014i	−0.955147	+	0.296133i	$0.904303\pi$
$350$	3.56173	−	1.35765i	0.190383	−	0.0725696i
$351$		0			0
$352$	−18.7665	−	11.1301i	−1.00026	−	0.593235i
$353$	5.99485			0.319073			0.159537	−	0.987192i	$-0.449000\pi$
$353$	5.99485			0.319073			0.159537	+	0.987192i	$0.449000\pi$
$354$		0			0
$355$	−1.61828	−	1.61828i	−0.0858894	−	0.0858894i
$356$	19.8286	+	22.2306i	1.05091	+	1.17822i
$357$		0			0
$358$	10.4572	+	4.68525i	0.552681	+	0.247623i
$359$			4.95429i			0.261477i	0.991417	+	0.130739i	$0.0417349\pi$
$359$			4.95429i			0.261477i	−0.991417	+	0.130739i	$0.958265\pi$
$360$		0			0
$361$			7.28700i			0.383526i
$362$	1.21287	−	2.70706i	0.0637469	−	0.142280i
$363$		0			0
$364$	0.793026	−	13.8862i	0.0415659	−	0.727837i
$365$	0.927006	+	0.927006i	0.0485217	+	0.0485217i
$366$		0			0
$367$	26.2297			1.36918			0.684591	−	0.728928i	$-0.259981\pi$
$367$	26.2297			1.36918			0.684591	+	0.728928i	$0.259981\pi$
$368$	−35.5809	−	4.07726i	−1.85478	−	0.212542i
$369$		0			0
$370$	−0.135607	−	0.355758i	−0.00704988	−	0.0184950i
$371$	−18.0858	−	18.0858i	−0.938967	−	0.938967i
$372$		0			0
$373$	−8.58218	+	8.58218i	−0.444368	+	0.444368i	−0.893477	−	0.449109i	$-0.851742\pi$
$373$	−8.58218	+	8.58218i	−0.444368	+	0.444368i	0.449109	+	0.893477i	$0.351742\pi$
$374$	16.3596	−	36.5138i	0.845937	−	1.88808i
$375$		0			0
$376$	−1.71230	+	3.30297i	−0.0883052	+	0.170338i
$377$		−	10.3741i		−	0.534294i
$378$		0			0
$379$	4.04145	−	4.04145i	0.207595	−	0.207595i	−0.595649	−	0.803245i	$-0.703105\pi$
$379$	4.04145	−	4.04145i	0.207595	−	0.207595i	0.803245	+	0.595649i	$0.203105\pi$
$380$	7.65241	−	6.82559i	0.392560	−	0.350145i
$381$		0			0
$382$	1.33315	−	0.508165i	0.0682097	−	0.0260000i
$383$	1.97475			0.100905			0.0504526	−	0.998726i	$-0.483934\pi$
$383$	1.97475			0.100905			0.0504526	+	0.998726i	$0.483934\pi$
$384$		0			0
$385$	10.3959			0.529824
$386$	26.4654	−	10.0880i	1.34705	−	0.513467i
$387$		0			0
$388$	1.03686	−	0.924833i	0.0526388	−	0.0469513i
$389$	−27.0045	+	27.0045i	−1.36918	+	1.36918i	−0.507579	+	0.861606i	$0.669459\pi$
$389$	−27.0045	+	27.0045i	−1.36918	+	1.36918i	−0.861606	+	0.507579i	$0.830541\pi$
$390$		0			0
$391$		−	65.6750i		−	3.32133i
$392$	0.344426	−	0.664386i	0.0173961	−	0.0335565i
$393$		0			0
$394$	−10.4357	+	23.2920i	−0.525744	+	1.17343i
$395$	−1.83367	+	1.83367i	−0.0922617	+	0.0922617i
$396$		0			0
$397$	−13.2948	−	13.2948i	−0.667248	−	0.667248i	0.289830	−	0.957078i	$-0.406401\pi$
$397$	−13.2948	−	13.2948i	−0.667248	−	0.667248i	−0.957078	+	0.289830i	$0.906401\pi$
$398$	−5.87478	−	15.4122i	−0.294476	−	0.772543i
$399$		0			0
$400$	−3.97399	−	0.455385i	−0.198700	−	0.0227692i
$401$	−3.97892			−0.198698			−0.0993490	−	0.995053i	$-0.531676\pi$
$401$	−3.97892			−0.198698			−0.0993490	+	0.995053i	$0.531676\pi$
$402$		0			0
$403$	−6.16635	−	6.16635i	−0.307168	−	0.307168i
$404$	1.11105	−	19.4549i	0.0552766	−	0.967918i
$405$		0			0
$406$	6.26624	−	13.9859i	0.310988	−	0.694108i
$407$		−	1.03838i		−	0.0514705i
$408$		0			0
$409$		−	23.6091i		−	1.16740i	−0.811971	−	0.583698i	$-0.801605\pi$
$409$		−	23.6091i		−	1.16740i	0.811971	−	0.583698i	$-0.198395\pi$
$410$	9.90902	+	4.43963i	0.489372	+	0.219258i
$411$		0			0
$412$	−5.84830	−	6.55673i	−0.288125	−	0.323027i
$413$	2.73474	+	2.73474i	0.134568	+	0.134568i
$414$		0			0
$415$	7.58844			0.372502
$416$	−7.44557	+	12.5541i	−0.365049	+	0.615513i
$417$		0			0
$418$	26.1326	−	9.96118i	1.27819	−	0.487217i
$419$	13.5761	+	13.5761i	0.663235	+	0.663235i	0.956141	−	0.292906i	$-0.0946225\pi$
$419$	13.5761	+	13.5761i	0.663235	+	0.663235i	−0.292906	+	0.956141i	$0.594622\pi$
$420$		0			0
$421$	9.30166	−	9.30166i	0.453335	−	0.453335i	−0.443125	−	0.896460i	$-0.646130\pi$
$421$	9.30166	−	9.30166i	0.453335	−	0.453335i	0.896460	+	0.443125i	$0.146130\pi$
$422$	0.765242	+	0.342859i	0.0372514	+	0.0166901i
$423$		0			0
$424$	8.11453	+	25.5846i	0.394076	+	1.24250i
$425$		−	7.33517i		−	0.355808i
$426$		0			0
$427$	6.44164	−	6.44164i	0.311733	−	0.311733i
$428$	−1.14382	+	20.0288i	−0.0552886	+	0.968129i
$429$		0			0
$430$	5.68544	+	14.9155i	0.274176	+	0.719287i
$431$	−6.40406			−0.308473			−0.154236	−	0.988034i	$-0.549292\pi$
$431$	−6.40406			−0.308473			−0.154236	+	0.988034i	$0.549292\pi$
$432$		0			0
$433$	−33.9234			−1.63025			−0.815127	−	0.579282i	$-0.803333\pi$
$433$	−33.9234			−1.63025			−0.815127	+	0.579282i	$0.803333\pi$
$434$	−4.58855	−	12.0378i	−0.220257	−	0.577834i
$435$		0			0
$436$	22.1116	+	1.26276i	1.05895	+	0.0604754i
$437$	32.4598	−	32.4598i	1.55276	−	1.55276i
$438$		0			0
$439$			3.97789i			0.189855i	0.995484	+	0.0949273i	$0.0302619\pi$
$439$			3.97789i			0.189855i	−0.995484	+	0.0949273i	$0.969738\pi$
$440$	−9.68530	−	5.02099i	−0.461729	−	0.239366i
$441$		0			0
$442$	−24.4263	−	10.9439i	−1.16184	−	0.520550i
$443$	−14.5607	+	14.5607i	−0.691802	+	0.691802i	−0.962628	−	0.270826i	$-0.912703\pi$
$443$	−14.5607	+	14.5607i	−0.691802	+	0.691802i	0.270826	+	0.962628i	$0.412703\pi$
$444$		0			0
$445$	10.5319	+	10.5319i	0.499261	+	0.499261i
$446$	26.9243	−	10.2629i	1.27490	−	0.485964i
$447$		0			0
$448$	−17.6208	+	12.4275i	−0.832502	+	0.587144i
$449$	−11.3678			−0.536481			−0.268240	−	0.963352i	$-0.586442\pi$
$449$	−11.3678			−0.536481			−0.268240	+	0.963352i	$0.586442\pi$
$450$		0			0
$451$	20.9402	+	20.9402i	0.986038	+	0.986038i
$452$	6.92284	−	6.17485i	0.325623	−	0.290440i
$453$		0			0
$454$	5.24702	+	2.35087i	0.246255	+	0.110332i
$455$		−	6.95444i		−	0.326029i
$456$		0			0
$457$			39.0892i			1.82851i	0.405135	+	0.914257i	$0.367225\pi$
$457$			39.0892i			1.82851i	−0.405135	+	0.914257i	$0.632775\pi$
$458$	5.54898	−	12.3850i	0.259287	−	0.578714i
$459$		0			0
$460$	−17.8778	−	1.02098i	−0.833555	−	0.0476033i
$461$	6.05492	+	6.05492i	0.282006	+	0.282006i	0.833908	−	0.551903i	$-0.186098\pi$
$461$	6.05492	+	6.05492i	0.282006	+	0.282006i	−0.551903	+	0.833908i	$0.686098\pi$
$462$		0			0
$463$	36.1375			1.67945			0.839725	−	0.543012i	$-0.182716\pi$
$463$	36.1375			1.67945			0.839725	+	0.543012i	$0.182716\pi$
$464$	−12.5928	+	10.0035i	−0.584606	+	0.464399i
$465$		0			0
$466$	14.0353	+	36.8209i	0.650173	+	1.70570i
$467$	13.0890	+	13.0890i	0.605689	+	0.605689i	0.941816	−	0.336128i	$-0.109117\pi$
$467$	13.0890	+	13.0890i	0.605689	+	0.605689i	−0.336128	+	0.941816i	$0.609117\pi$
$468$		0			0
$469$	−19.4647	+	19.4647i	−0.898795	+	0.898795i
$470$	−0.760598	+	1.69761i	−0.0350838	+	0.0783050i
$471$		0			0
$472$	−1.22699	−	3.86863i	−0.0564769	−	0.178068i
$473$			43.5349i			2.00174i
$474$		0			0
$475$	3.62540	−	3.62540i	0.166345	−	0.166345i
$476$	−26.3199	−	29.5082i	−1.20637	−	1.35251i
$477$		0			0
$478$	−26.0577	+	9.93261i	−1.19185	+	0.454307i
$479$	3.78947			0.173145			0.0865726	−	0.996246i	$-0.472409\pi$
$479$	3.78947			0.173145			0.0865726	+	0.996246i	$0.472409\pi$
$480$		0			0
$481$	−0.694633			−0.0316725
$482$	−10.2316	+	3.90007i	−0.466038	+	0.177643i
$483$		0			0
$484$	−5.16128	−	5.78649i	−0.234603	−	0.263022i
$485$	0.491223	−	0.491223i	0.0223053	−	0.0223053i
$486$		0			0
$487$		−	3.39864i		−	0.154007i	−0.997031	−	0.0770036i	$-0.975465\pi$
$487$		−	3.39864i		−	0.154007i	0.997031	−	0.0770036i	$-0.0245353\pi$
$488$	−9.11251	+	2.89017i	−0.412504	+	0.130832i
$489$		0			0
$490$	0.152993	−	0.341471i	0.00691150	−	0.0154261i
$491$	8.70898	−	8.70898i	0.393031	−	0.393031i	−0.482735	−	0.875766i	$-0.660357\pi$
$491$	8.70898	−	8.70898i	0.393031	−	0.393031i	0.875766	+	0.482735i	$0.160357\pi$
$492$		0			0
$493$	−20.8540	−	20.8540i	−0.939217	−	0.939217i
$494$	−6.66362	−	17.4817i	−0.299811	−	0.786538i
$495$		0			0
$496$	−1.53909	+	13.4312i	−0.0691073	+	0.603077i
$497$	−6.16842			−0.276691
$498$		0			0
$499$	−15.9542	−	15.9542i	−0.714210	−	0.714210i	0.253203	−	0.967413i	$-0.418516\pi$
$499$	−15.9542	−	15.9542i	−0.714210	−	0.714210i	−0.967413	+	0.253203i	$0.918516\pi$
$500$	−1.99675	−	0.114032i	−0.0892972	−	0.00509965i
$501$		0			0
$502$	1.19618	−	2.66982i	0.0533883	−	0.119160i
$503$			18.4604i			0.823107i	0.911386	+	0.411553i	$0.135014\pi$
$503$			18.4604i			0.823107i	−0.911386	+	0.411553i	$0.864986\pi$
$504$		0			0
$505$		−	9.74330i		−	0.433571i
$506$	−44.5695	−	19.9689i	−1.98135	−	0.887725i
$507$		0			0
$508$	−12.8046	+	11.4211i	−0.568111	+	0.506728i
$509$	−8.47641	−	8.47641i	−0.375710	−	0.375710i	0.493841	−	0.869552i	$-0.335592\pi$
$509$	−8.47641	−	8.47641i	−0.375710	−	0.375710i	−0.869552	+	0.493841i	$0.835592\pi$
$510$		0			0
$511$	3.53348			0.156312
$512$	22.4185	−	3.06760i	0.990768	−	0.135570i
$513$		0			0
$514$	27.3126	−	10.4110i	1.20471	−	0.459207i
$515$	−3.10631	−	3.10631i	−0.136880	−	0.136880i
$516$		0			0
$517$	−3.58748	+	3.58748i	−0.157777	+	0.157777i
$518$	−0.936472	−	0.419577i	−0.0411462	−	0.0184351i
$519$		0			0
$520$	−3.35884	+	6.47908i	−0.147295	+	0.284126i
$521$		−	22.3693i		−	0.980017i	−0.871718	−	0.490009i	$-0.836994\pi$
$521$		−	22.3693i		−	0.980017i	0.871718	−	0.490009i	$-0.163006\pi$
$522$		0			0
$523$	−2.39235	+	2.39235i	−0.104610	+	0.104610i	−0.757475	−	0.652865i	$-0.773567\pi$
$523$	−2.39235	+	2.39235i	−0.104610	+	0.104610i	0.652865	+	0.757475i	$0.273567\pi$
$524$	15.0730	+	0.860799i	0.658467	+	0.0376042i
$525$		0			0
$526$	13.2597	+	34.7861i	0.578149	+	1.51675i
$527$	−24.7911			−1.07992
$528$		0			0
$529$	−57.1642			−2.48540
$530$	4.78003	+	12.5402i	0.207631	+	0.544709i
$531$		0			0
$532$	1.57580	−	27.5930i	0.0683196	−	1.19631i
$533$	14.0082	−	14.0082i	0.606762	−	0.606762i
$534$		0			0
$535$			10.0307i			0.433666i
$536$	27.5352	−	8.73319i	1.18934	−	0.377216i
$537$		0			0
$538$	−32.5117	−	14.5665i	−1.40168	−	0.628007i
$539$	0.721614	−	0.721614i	0.0310821	−	0.0310821i
$540$		0			0
$541$	−10.4567	−	10.4567i	−0.449570	−	0.449570i	0.445642	−	0.895211i	$-0.352976\pi$
$541$	−10.4567	−	10.4567i	−0.449570	−	0.449570i	−0.895211	+	0.445642i	$0.852976\pi$
$542$	9.51255	−	3.62597i	0.408599	−	0.155749i
$543$		0			0
$544$	10.2691	+	40.2032i	0.440283	+	1.72370i
$545$	11.0738			0.474349
$546$		0			0
$547$	27.1404	+	27.1404i	1.16044	+	1.16044i	0.984379	+	0.176060i	$0.0563354\pi$
$547$	27.1404	+	27.1404i	1.16044	+	1.16044i	0.176060	+	0.984379i	$0.443665\pi$
$548$	16.3340	+	18.3127i	0.697756	+	0.782279i
$549$		0			0
$550$	−4.97791	−	2.23030i	−0.212259	−	0.0951004i
$551$		−	20.6141i		−	0.878191i
$552$		0			0
$553$			6.98941i			0.297220i
$554$	−8.55912	+	19.1035i	−0.363642	+	0.811630i
$555$		0			0
$556$	−2.05763	+	36.0300i	−0.0872630	+	1.52801i
$557$	1.29047	+	1.29047i	0.0546790	+	0.0546790i	0.733918	−	0.679239i	$-0.237690\pi$
$557$	1.29047	+	1.29047i	0.0546790	+	0.0546790i	−0.679239	+	0.733918i	$0.737690\pi$
$558$		0			0
$559$	29.1231			1.23177
$560$	−8.44176	+	6.70597i	−0.356730	+	0.283379i
$561$		0			0
$562$	−8.59169	−	22.5399i	−0.362419	−	0.950787i
$563$	3.42706	+	3.42706i	0.144433	+	0.144433i	0.775626	−	0.631193i	$-0.217434\pi$
$563$	3.42706	+	3.42706i	0.144433	+	0.144433i	−0.631193	+	0.775626i	$0.717434\pi$
$564$		0			0
$565$	3.27976	−	3.27976i	0.137980	−	0.137980i
$566$	−2.21388	+	4.94126i	−0.0930564	+	0.207697i
$567$		0			0
$568$	5.74679	+	2.97921i	0.241130	+	0.125005i
$569$		−	26.4853i		−	1.11032i	−0.831743	−	0.555161i	$-0.812656\pi$
$569$		−	26.4853i		−	1.11032i	0.831743	−	0.555161i	$-0.187344\pi$
$570$		0			0
$571$	−1.42398	+	1.42398i	−0.0595918	+	0.0595918i	−0.736275	−	0.676683i	$-0.763417\pi$
$571$	−1.42398	+	1.42398i	−0.0595918	+	0.0595918i	0.676683	+	0.736275i	$0.263417\pi$
$572$	−14.8539	+	13.2490i	−0.621073	+	0.553968i
$573$		0			0
$574$	27.3465	−	10.4239i	1.14142	−	0.435084i
$575$	−8.95345			−0.373385
$576$		0			0
$577$	37.6681			1.56814			0.784071	−	0.620671i	$-0.213140\pi$
$577$	37.6681			1.56814			0.784071	+	0.620671i	$0.213140\pi$
$578$	−48.6361	+	18.5390i	−2.02300	+	0.771121i
$579$		0			0
$580$	−6.00098	+	5.35259i	−0.249177	+	0.222254i
$581$	14.4625	−	14.4625i	0.600005	−	0.600005i
$582$		0			0
$583$			36.6019i			1.51589i
$584$	−3.29196	−	1.70659i	−0.136222	−	0.0706193i
$585$		0			0
$586$	13.6233	−	30.4065i	0.562773	−	1.25608i
$587$	−1.99399	+	1.99399i	−0.0823008	+	0.0823008i	−0.747059	−	0.664758i	$-0.768535\pi$
$587$	−1.99399	+	1.99399i	−0.0823008	+	0.0823008i	0.664758	+	0.747059i	$0.268535\pi$
$588$		0			0
$589$	−12.2530	−	12.2530i	−0.504876	−	0.504876i
$590$	−0.722785	−	1.89619i	−0.0297566	−	0.0780649i
$591$		0			0
$592$	0.669815	+	0.843192i	0.0275292	+	0.0346550i
$593$	−24.0023			−0.985657			−0.492828	−	0.870127i	$-0.664037\pi$
$593$	−24.0023			−0.985657			−0.492828	+	0.870127i	$0.664037\pi$
$594$		0			0
$595$	−13.9798	−	13.9798i	−0.573115	−	0.573115i
$596$	−1.04377	+	18.2769i	−0.0427544	+	0.748650i
$597$		0			0
$598$	−13.3584	+	29.8152i	−0.546265	+	1.21923i
$599$			34.5205i			1.41047i	0.708974	+	0.705234i	$0.249158\pi$
$599$			34.5205i			1.41047i	−0.708974	+	0.705234i	$0.750842\pi$
$600$		0			0
$601$		−	3.45113i		−	0.140775i	−0.997520	−	0.0703873i	$-0.977577\pi$
$601$		−	3.45113i		−	0.140775i	0.997520	−	0.0703873i	$-0.0224235\pi$
$602$	39.2624	+	17.5911i	1.60022	+	0.716960i
$603$		0			0
$604$	−19.6739	−	22.0571i	−0.800520	−	0.897491i
$605$	−2.74140	−	2.74140i	−0.111454	−	0.111454i
$606$		0			0
$607$	−43.2408			−1.75509			−0.877545	−	0.479494i	$-0.840820\pi$
$607$	−43.2408			−1.75509			−0.877545	+	0.479494i	$0.840820\pi$
$608$	−14.7949	+	24.9458i	−0.600012	+	1.01169i
$609$		0			0
$610$	−4.46645	+	1.70251i	−0.180841	+	0.0689326i
$611$	2.39988	+	2.39988i	0.0970887	+	0.0970887i
$612$		0			0
$613$	31.4157	−	31.4157i	1.26887	−	1.26887i	0.322195	−	0.946673i	$-0.395579\pi$
$613$	31.4157	−	31.4157i	1.26887	−	1.26887i	0.946673	−	0.322195i	$-0.104421\pi$
$614$	−33.2166	−	14.8824i	−1.34051	−	0.600603i
$615$		0			0
$616$	−28.0281	+	8.88952i	−1.12928	+	0.358169i
$617$		−	26.4920i		−	1.06653i	−0.845949	−	0.533265i	$-0.820965\pi$
$617$		−	26.4920i		−	1.06653i	0.845949	−	0.533265i	$-0.179035\pi$
$618$		0			0
$619$	23.9945	−	23.9945i	0.964422	−	0.964422i	−0.0349667	−	0.999388i	$-0.511133\pi$
$619$	23.9945	−	23.9945i	0.964422	−	0.964422i	0.999388	+	0.0349667i	$0.0111325\pi$
$620$	−0.385400	+	6.74853i	−0.0154780	+	0.271028i
$621$		0			0
$622$	−7.75381	−	20.3417i	−0.310899	−	0.815629i
$623$	40.1447			1.60836
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−11.9778	−	31.4231i	−0.478729	−	1.25592i
$627$		0			0
$628$	39.7001	+	2.26722i	1.58421	+	0.0904720i
$629$	−1.39635	+	1.39635i	−0.0556761	+	0.0556761i
$630$		0			0
$631$			34.6813i			1.38064i	0.723504	+	0.690320i	$0.242530\pi$
$631$			34.6813i			1.38064i	−0.723504	+	0.690320i	$0.757470\pi$
$632$	3.37573	−	6.51166i	0.134279	−	0.259020i
$633$		0			0
$634$	−16.9680	−	7.60234i	−0.673886	−	0.301927i
$635$	−6.06628	+	6.06628i	−0.240733	+	0.240733i
$636$		0			0
$637$	−0.482731	−	0.482731i	−0.0191265	−	0.0191265i
$638$	−20.4931	+	7.81150i	−0.811328	+	0.309260i
$639$		0			0
$640$	11.1036	−	2.17041i	0.438907	−	0.0857929i
$641$	−25.5477			−1.00908			−0.504538	−	0.863390i	$-0.668337\pi$
$641$	−25.5477			−1.00908			−0.504538	+	0.863390i	$0.668337\pi$
$642$		0			0
$643$	12.0319	+	12.0319i	0.474490	+	0.474490i	0.903364	−	0.428874i	$-0.141090\pi$
$643$	12.0319	+	12.0319i	0.474490	+	0.474490i	−0.428874	+	0.903364i	$0.641090\pi$
$644$	−36.0183	+	32.1266i	−1.41932	+	1.26597i
$645$		0			0
$646$	−48.5368	−	21.7464i	−1.90965	−	0.855601i
$647$			20.4148i			0.802587i	0.915950	+	0.401293i	$0.131439\pi$
$647$			20.4148i			0.802587i	−0.915950	+	0.401293i	$0.868561\pi$
$648$		0			0
$649$		−	5.53455i		−	0.217250i
$650$	−1.49198	+	3.33002i	−0.0585203	+	0.130614i
$651$		0			0
$652$	5.92491	+	0.338364i	0.232037	+	0.0132514i
$653$	−15.3217	−	15.3217i	−0.599586	−	0.599586i	0.340616	−	0.940202i	$-0.389364\pi$
$653$	−15.3217	−	15.3217i	−0.599586	−	0.599586i	−0.940202	+	0.340616i	$0.889364\pi$
$654$		0			0
$655$	7.54877			0.294955
$656$	−30.5118	−	3.49638i	−1.19128	−	0.136511i
$657$		0			0
$658$	1.78582	+	4.68500i	0.0696184	+	0.182640i
$659$	−3.52074	−	3.52074i	−0.137148	−	0.137148i	0.635200	−	0.772348i	$-0.280918\pi$
$659$	−3.52074	−	3.52074i	−0.137148	−	0.137148i	−0.772348	+	0.635200i	$0.780918\pi$
$660$		0			0
$661$	−23.8945	+	23.8945i	−0.929388	+	0.929388i	−0.997666	−	0.0682781i	$-0.978249\pi$
$661$	−23.8945	+	23.8945i	−0.929388	+	0.929388i	0.0682781	+	0.997666i	$0.478249\pi$
$662$	12.3124	−	27.4806i	0.478534	−	1.06806i
$663$		0			0
$664$	−20.4590	+	6.48887i	−0.793963	+	0.251817i
$665$		−	13.8190i		−	0.535877i
$666$		0			0
$667$	−25.4548	+	25.4548i	−0.985613	+	0.985613i
$668$	20.9906	+	23.5333i	0.812151	+	0.910531i
$669$		0			0
$670$	13.4962	−	5.14446i	0.521405	−	0.198748i
$671$	−13.0366			−0.503271
$672$		0			0
$673$	−25.4607			−0.981437			−0.490719	−	0.871318i	$-0.663266\pi$
$673$	−25.4607			−0.981437			−0.490719	+	0.871318i	$0.663266\pi$
$674$	15.4764	−	5.89927i	0.596130	−	0.227231i
$675$		0			0
$676$	−8.44361	−	9.46643i	−0.324754	−	0.364093i
$677$	−21.1318	+	21.1318i	−0.812162	+	0.812162i	−0.984958	−	0.172796i	$-0.944720\pi$
$677$	−21.1318	+	21.1318i	−0.812162	+	0.812162i	0.172796	+	0.984958i	$0.444720\pi$
$678$		0			0
$679$		−	1.87240i		−	0.0718562i
$680$	6.27229	+	19.7761i	0.240531	+	0.758380i
$681$		0			0
$682$	−7.53790	+	16.8242i	−0.288641	+	0.644231i
$683$	6.14096	−	6.14096i	0.234977	−	0.234977i	−0.579789	−	0.814767i	$-0.696865\pi$
$683$	6.14096	−	6.14096i	0.234977	−	0.234977i	0.814767	+	0.579789i	$0.196865\pi$
$684$		0			0
$685$	8.67579	+	8.67579i	0.331485	+	0.331485i
$686$	9.14436	+	23.9898i	0.349133	+	0.915933i
$687$		0			0
$688$	−28.0826	−	35.3515i	−1.07064	−	1.34777i
$689$	24.4852			0.932811
$690$		0			0
$691$	1.37557	+	1.37557i	0.0523291	+	0.0523291i	0.732787	−	0.680458i	$-0.238219\pi$
$691$	1.37557	+	1.37557i	0.0523291	+	0.0523291i	−0.680458	+	0.732787i	$0.738219\pi$
$692$	−24.6681	−	1.40877i	−0.937742	−	0.0535533i
$693$		0			0
$694$	10.2701	−	22.9222i	0.389846	−	0.870116i
$695$			18.0444i			0.684462i
$696$		0			0
$697$		−	56.3184i		−	2.13321i
$698$	22.4705	+	10.0677i	0.850521	+	0.381067i
$699$		0			0
$700$	−4.02284	+	3.58819i	−0.152049	+	0.135621i
$701$	−27.0610	−	27.0610i	−1.02208	−	1.02208i	−0.999751	−	0.0223289i	$-0.992892\pi$
$701$	−27.0610	−	27.0610i	−1.02208	−	1.02208i	−0.0223289	−	0.999751i	$-0.507108\pi$
$702$		0			0
$703$	−1.38029			−0.0520585
$704$	30.4057	+	5.25505i	1.14596	+	0.198057i
$705$		0			0
$706$	−7.92199	+	3.01968i	−0.298148	+	0.113647i
$707$	−18.5693	−	18.5693i	−0.698372	−	0.698372i
$708$		0			0
$709$	−32.8479	+	32.8479i	−1.23363	+	1.23363i	−0.271068	+	0.962560i	$0.587377\pi$
$709$	−32.8479	+	32.8479i	−1.23363	+	1.23363i	−0.962560	+	0.271068i	$0.912623\pi$
$710$	2.95365	+	1.32335i	0.110849	+	0.0496645i
$711$		0			0
$712$	−37.4007	−	19.3890i	−1.40165	−	0.726634i
$713$			30.2605i			1.13327i
$714$		0			0
$715$	−7.03717	+	7.03717i	−0.263175	+	0.263175i
$716$	−16.1789	−	0.923956i	−0.604633	−	0.0345298i
$717$		0			0
$718$	−2.49554	−	6.54692i	−0.0931327	−	0.244329i
$719$	33.7746			1.25958			0.629791	−	0.776765i	$-0.283141\pi$
$719$	33.7746			1.25958			0.629791	+	0.776765i	$0.283141\pi$
$720$		0			0
$721$	−11.8404			−0.440958
$722$	−3.67056	−	9.62952i	−0.136604	−	0.358374i
$723$		0			0
$724$	−0.239184	+	4.18822i	−0.00888920	+	0.155654i
$725$	−2.84302	+	2.84302i	−0.105587	+	0.105587i
$726$		0			0
$727$		−	7.54917i		−	0.279983i	−0.990153	−	0.139992i	$-0.955292\pi$
$727$		−	7.54917i		−	0.279983i	0.990153	−	0.139992i	$-0.0447075\pi$
$728$	5.94673	+	18.7497i	0.220401	+	0.694909i
$729$		0			0
$730$	−1.69195	−	0.758062i	−0.0626220	−	0.0280571i
$731$	58.5431	−	58.5431i	2.16529	−	2.16529i
$732$		0			0
$733$	−13.2524	−	13.2524i	−0.489487	−	0.489487i	0.418657	−	0.908144i	$-0.362501\pi$
$733$	−13.2524	−	13.2524i	−0.489487	−	0.489487i	−0.908144	+	0.418657i	$0.862501\pi$
$734$	−34.6617	+	13.2123i	−1.27939	+	0.487674i
$735$		0			0
$736$	49.0728	−	12.5346i	1.80885	−	0.462033i
$737$	39.3925			1.45104
$738$		0			0
$739$	4.42190	+	4.42190i	0.162662	+	0.162662i	0.783745	−	0.621083i	$-0.213307\pi$
$739$	4.42190	+	4.42190i	0.162662	+	0.162662i	−0.621083	+	0.783745i	$0.713307\pi$
$740$	0.358400	+	0.401815i	0.0131751	+	0.0147710i
$741$		0			0
$742$	33.0098	+	14.7897i	1.21183	+	0.542947i
$743$		−	45.5703i		−	1.67181i	−0.548873	−	0.835906i	$-0.684943\pi$
$743$		−	45.5703i		−	1.67181i	0.548873	−	0.835906i	$-0.315057\pi$
$744$		0			0
$745$			9.15332i			0.335352i
$746$	7.01810	−	15.6640i	0.256951	−	0.573501i
$747$		0			0
$748$	−3.22621	+	56.4923i	−0.117962	+	2.06556i
$749$	19.1171	+	19.1171i	0.698524	+	0.698524i
$750$		0			0
$751$	10.6007			0.386824			0.193412	−	0.981118i	$-0.438045\pi$
$751$	10.6007			0.386824			0.193412	+	0.981118i	$0.438045\pi$
$752$	0.598999	−	5.22727i	0.0218433	−	0.190619i
$753$		0			0
$754$	5.22558	+	13.7090i	0.190304	+	0.499254i
$755$	−10.4498	−	10.4498i	−0.380305	−	0.380305i
$756$		0			0
$757$	−14.7340	+	14.7340i	−0.535517	+	0.535517i	−0.922209	−	0.386692i	$-0.873618\pi$
$757$	−14.7340	+	14.7340i	−0.535517	+	0.535517i	0.386692	+	0.922209i	$0.373618\pi$
$758$	−3.30491	+	7.37637i	−0.120040	+	0.267922i
$759$		0			0
$760$	−6.67426	+	12.8744i	−0.242101	+	0.467004i
$761$			8.89182i			0.322328i	0.986928	+	0.161164i	$0.0515248\pi$
$761$			8.89182i			0.322328i	−0.986928	+	0.161164i	$0.948475\pi$
$762$		0			0
$763$	21.1051	−	21.1051i	0.764055	−	0.764055i
$764$	−1.50574	+	1.34305i	−0.0544757	+	0.0485897i
$765$		0			0
$766$	−2.60957	+	0.994710i	−0.0942876	+	0.0359403i
$767$	−3.70239			−0.133686
$768$		0			0
$769$	32.7022			1.17927			0.589636	−	0.807669i	$-0.299271\pi$
$769$	32.7022			1.17927			0.589636	+	0.807669i	$0.299271\pi$
$770$	−13.7378	+	5.23655i	−0.495077	+	0.188712i
$771$		0			0
$772$	−29.8916	+	26.6619i	−1.07582	+	0.959584i
$773$	−12.4209	+	12.4209i	−0.446747	+	0.446747i	−0.894272	−	0.447525i	$-0.852306\pi$
$773$	−12.4209	+	12.4209i	−0.446747	+	0.446747i	0.447525	+	0.894272i	$0.352306\pi$
$774$		0			0
$775$			3.37977i			0.121405i
$776$	−0.904329	+	1.74442i	−0.0324635	+	0.0626210i
$777$		0			0
$778$	22.0830	−	49.2881i	0.791715	−	1.76706i
$779$	27.8353	−	27.8353i	0.997303	−	0.997303i
$780$		0			0
$781$	6.24180	+	6.24180i	0.223349	+	0.223349i
$782$	33.0814	+	86.7873i	1.18299	+	3.10351i
$783$		0			0
$784$	−0.120488	+	1.05146i	−0.00430313	+	0.0375520i
$785$	19.8824			0.709633
$786$		0			0
$787$	−22.6663	−	22.6663i	−0.807965	−	0.807965i	0.176361	−	0.984326i	$-0.443567\pi$
$787$	−22.6663	−	22.6663i	−0.807965	−	0.807965i	−0.984326	+	0.176361i	$0.943567\pi$
$788$	2.05798	−	36.0362i	0.0733125	−	1.28374i
$789$		0			0
$790$	1.49948	−	3.34677i	0.0533493	−	0.119073i
$791$		−	12.5015i		−	0.444502i
$792$		0			0
$793$			8.72093i			0.309689i
$794$	24.2655	+	10.8719i	0.861149	+	0.385829i
$795$		0			0
$796$	15.5266	+	17.4075i	0.550327	+	0.616991i
$797$	−7.47619	−	7.47619i	−0.264820	−	0.264820i	0.562189	−	0.827009i	$-0.309959\pi$
$797$	−7.47619	−	7.47619i	−0.264820	−	0.264820i	−0.827009	+	0.562189i	$0.809959\pi$
$798$		0			0
$799$	9.64846			0.341338
$800$	5.48088	−	1.39998i	0.193778	−	0.0494967i
$801$		0			0
$802$	5.25801	−	2.00424i	0.185667	−	0.0707721i
$803$	−3.57552	−	3.57552i	−0.126177	−	0.126177i
$804$		0			0
$805$	−17.0640	+	17.0640i	−0.601427	+	0.601427i
$806$	11.2547	+	5.04255i	0.396430	+	0.177616i
$807$		0			0
$808$	8.33149	+	26.2686i	0.293101	+	0.924128i
$809$			9.20349i			0.323577i	0.986825	+	0.161789i	$0.0517263\pi$
$809$			9.20349i			0.323577i	−0.986825	+	0.161789i	$0.948274\pi$
$810$		0			0
$811$	31.0252	−	31.0252i	1.08944	−	1.08944i	0.0938555	−	0.995586i	$-0.470081\pi$
$811$	31.0252	−	31.0252i	1.08944	−	1.08944i	0.995586	−	0.0938555i	$-0.0299192\pi$
$812$	−1.23573	+	21.6383i	−0.0433658	+	0.759355i
$813$		0			0
$814$	0.523045	+	1.37218i	0.0183327	+	0.0480949i
$815$	2.96728			0.103939
$816$		0			0
$817$	57.8697			2.02460
$818$	11.8922	+	31.1987i	0.415802	+	1.09084i
$819$		0			0
$820$	−15.3307	−	0.875519i	−0.535373	−	0.0305745i
$821$	−5.31973	+	5.31973i	−0.185660	+	0.185660i	−0.793817	−	0.608157i	$-0.791909\pi$
$821$	−5.31973	+	5.31973i	−0.185660	+	0.185660i	0.608157	+	0.793817i	$0.291909\pi$
$822$		0			0
$823$			24.8425i			0.865956i	0.901404	+	0.432978i	$0.142537\pi$
$823$			24.8425i			0.865956i	−0.901404	+	0.432978i	$0.857463\pi$
$824$	11.0310	+	5.71863i	0.384285	+	0.199218i
$825$		0			0
$826$	−4.99139	−	2.23634i	−0.173673	−	0.0778122i
$827$	−11.8871	+	11.8871i	−0.413354	+	0.413354i	−0.882905	−	0.469551i	$-0.844416\pi$
$827$	−11.8871	+	11.8871i	−0.413354	+	0.413354i	0.469551	+	0.882905i	$0.344416\pi$
$828$		0			0
$829$	6.17740	+	6.17740i	0.214550	+	0.214550i	0.806197	−	0.591647i	$-0.201522\pi$
$829$	6.17740	+	6.17740i	0.214550	+	0.214550i	−0.591647	+	0.806197i	$0.701522\pi$
$830$	−10.0279	+	3.82240i	−0.348072	+	0.132677i
$831$		0			0
$832$	3.51542	−	20.3402i	0.121875	−	0.705169i
$833$	−1.94077			−0.0672436
$834$		0			0
$835$	11.1491	+	11.1491i	0.385831	+	0.385831i
$836$	−29.5158	+	26.3267i	−1.02083	+	0.910528i
$837$		0			0
$838$	−24.7788	−	11.1019i	−0.855969	−	0.383508i
$839$		−	8.14180i		−	0.281086i	−0.990075	−	0.140543i	$-0.955115\pi$
$839$		−	8.14180i		−	0.281086i	0.990075	−	0.140543i	$-0.0448848\pi$
$840$		0			0
$841$		−	12.8345i		−	0.442570i
$842$	−7.60646	+	16.9772i	−0.262136	+	0.585073i
$843$		0			0
$844$	−1.18394	−	0.0676136i	−0.0407531	−	0.00232736i
$845$	−4.48480	−	4.48480i	−0.154282	−	0.154282i
$846$		0			0
$847$	−10.4494			−0.359047
$848$	−23.6104	−	29.7218i	−0.810783	−	1.02065i
$849$		0			0
$850$	3.69482	+	9.69317i	0.126731	+	0.332473i
$851$	1.70441	+	1.70441i	0.0584264	+	0.0584264i
$852$		0			0
$853$	27.9298	−	27.9298i	0.956297	−	0.956297i	−0.0427875	−	0.999084i	$-0.513624\pi$
$853$	27.9298	−	27.9298i	0.956297	−	0.956297i	0.999084	+	0.0427875i	$0.0136239\pi$
$854$	−5.26767	+	11.7572i	−0.180256	+	0.402322i
$855$		0			0
$856$	−8.57726	−	27.0435i	−0.293165	−	0.924329i
$857$		−	20.7075i		−	0.707356i	−0.935367	−	0.353678i	$-0.884931\pi$
$857$		−	20.7075i		−	0.707356i	0.935367	−	0.353678i	$-0.115069\pi$
$858$		0			0
$859$	−12.8547	+	12.8547i	−0.438597	+	0.438597i	−0.891539	−	0.452943i	$-0.850374\pi$
$859$	−12.8547	+	12.8547i	−0.438597	+	0.438597i	0.452943	+	0.891539i	$0.350374\pi$
$860$	−15.0262	−	16.8464i	−0.512390	−	0.574459i
$861$		0			0
$862$	8.46274	−	3.22581i	0.288242	−	0.109872i
$863$	−11.9606			−0.407143			−0.203572	−	0.979060i	$-0.565255\pi$
$863$	−11.9606			−0.407143			−0.203572	+	0.979060i	$0.565255\pi$
$864$		0			0
$865$	−12.3542			−0.420054
$866$	44.8286	−	17.0877i	1.52334	−	0.580663i
$867$		0			0
$868$	12.1272	+	13.5963i	0.411625	+	0.461487i
$869$	7.07256	−	7.07256i	0.239920	−	0.239920i
$870$		0			0
$871$		−	26.3520i		−	0.892902i
$872$	−29.8557	+	9.46919i	−1.01104	+	0.320667i
$873$		0			0
$874$	−26.5441	+	59.2449i	−0.897867	+	2.00399i
$875$	−1.90586	+	1.90586i	−0.0644297	+	0.0644297i
$876$		0			0
$877$	6.15758	+	6.15758i	0.207927	+	0.207927i	0.803386	−	0.595459i	$-0.203030\pi$
$877$	6.15758	+	6.15758i	0.207927	+	0.207927i	−0.595459	+	0.803386i	$0.703030\pi$
$878$	−2.00372	−	5.25665i	−0.0676222	−	0.177403i
$879$		0			0
$880$	15.3279	+	1.75645i	0.516705	+	0.0592098i
$881$	19.5267			0.657871			0.328936	−	0.944352i	$-0.393310\pi$
$881$	19.5267			0.657871			0.328936	+	0.944352i	$0.393310\pi$
$882$		0			0
$883$	17.6166	+	17.6166i	0.592845	+	0.592845i	0.938399	−	0.345554i	$-0.112309\pi$
$883$	17.6166	+	17.6166i	0.592845	+	0.592845i	−0.345554	+	0.938399i	$0.612309\pi$
$884$	37.7911	+	2.15820i	1.27105	+	0.0725882i
$885$		0			0
$886$	11.9071	−	26.5760i	0.400027	−	0.892838i
$887$		−	29.2567i		−	0.982343i	−0.871063	−	0.491172i	$-0.836569\pi$
$887$		−	29.2567i		−	0.982343i	0.871063	−	0.491172i	$-0.163431\pi$
$888$		0			0
$889$			23.1229i			0.775518i
$890$	−19.2227	−	8.61251i	−0.644345	−	0.288692i
$891$		0			0
$892$	−30.4100	+	27.1242i	−1.01820	+	0.908187i
$893$	4.76874	+	4.76874i	0.159580	+	0.159580i
$894$		0			0
$895$	−8.10262			−0.270841
$896$	17.0253	−	25.2983i	0.568777	−	0.845157i
$897$		0			0
$898$	15.0222	−	5.72613i	0.501297	−	0.191083i
$899$	9.60873	+	9.60873i	0.320469	+	0.320469i
$900$		0			0
$901$	49.2200	−	49.2200i	1.63976	−	1.63976i
$902$	−38.2197	−	17.1239i	−1.27258	−	0.570165i
$903$		0			0
$904$	−6.03795	+	11.6470i	−0.200819	+	0.387373i
$905$			2.09752i			0.0697240i
$906$		0			0
$907$	32.6905	−	32.6905i	1.08547	−	1.08547i	0.0894835	−	0.995988i	$-0.471478\pi$
$907$	32.6905	−	32.6905i	1.08547	−	1.08547i	0.995988	−	0.0894835i	$-0.0285216\pi$
$908$	−8.11793	−	0.463605i	−0.269403	−	0.0153853i
$909$		0			0
$910$	3.50304	+	9.19005i	0.116125	+	0.304647i
$911$	44.0834			1.46055			0.730275	−	0.683153i	$-0.239392\pi$
$911$	44.0834			1.46055			0.730275	+	0.683153i	$0.239392\pi$
$912$		0			0
$913$	−29.2691			−0.968665
$914$	−19.6897	−	51.6550i	−0.651279	−	1.70860i
$915$		0			0
$916$	−1.09429	+	19.1615i	−0.0361563	+	0.633113i
$917$	14.3869	−	14.3869i	0.475097	−	0.475097i
$918$		0			0
$919$			21.4544i			0.707716i	0.935299	+	0.353858i	$0.115130\pi$
$919$			21.4544i			0.707716i	−0.935299	+	0.353858i	$0.884870\pi$
$920$	24.1391	−	7.65608i	0.795844	−	0.252414i
$921$		0			0
$922$	−11.0513	−	4.95142i	−0.363956	−	0.163066i
$923$	4.17551	−	4.17551i	0.137439	−	0.137439i
$924$		0			0
$925$	0.190364	+	0.190364i	0.00625912	+	0.00625912i
$926$	−47.7544	+	18.2029i	−1.56931	+	0.598185i
$927$		0			0
$928$	11.6021	−	19.5624i	0.380857	−	0.642167i
$929$	−33.6688			−1.10464			−0.552318	−	0.833634i	$-0.686257\pi$
$929$	−33.6688			−1.10464			−0.552318	+	0.833634i	$0.686257\pi$
$930$		0			0
$931$	−0.959222	−	0.959222i	−0.0314372	−	0.0314372i
$932$	−37.0944	−	41.5878i	−1.21507	−	1.36225i
$933$		0			0
$934$	−23.8899	−	10.7036i	−0.781700	−	0.350233i
$935$			28.2922i			0.925254i
$936$		0			0
$937$		−	10.5938i		−	0.346084i	−0.984914	−	0.173042i	$-0.944640\pi$
$937$		−	10.5938i		−	0.346084i	0.984914	−	0.173042i	$-0.0553596\pi$
$938$	15.9173	−	35.5265i	0.519718	−	1.15998i
$939$		0			0
$940$	0.149994	−	2.62646i	0.00489226	−	0.0856657i
$941$	−7.72584	−	7.72584i	−0.251855	−	0.251855i	0.569876	−	0.821731i	$-0.306991\pi$
$941$	−7.72584	−	7.72584i	−0.251855	−	0.251855i	−0.821731	+	0.569876i	$0.806991\pi$
$942$		0			0
$943$	−68.7433			−2.23859
$944$	3.57011	+	4.49421i	0.116197	+	0.146274i
$945$		0			0
$946$	−21.9291	−	57.5299i	−0.712977	−	1.87046i
$947$	−21.4749	−	21.4749i	−0.697841	−	0.697841i	0.266103	−	0.963945i	$-0.414264\pi$
$947$	−21.4749	−	21.4749i	−0.697841	−	0.697841i	−0.963945	+	0.266103i	$0.914264\pi$
$948$		0			0
$949$	−2.39188	+	2.39188i	−0.0776437	+	0.0776437i
$950$	−2.96468	+	6.61700i	−0.0961868	+	0.214684i
$951$		0			0
$952$	49.6446	+	25.7364i	1.60899	+	0.834122i
$953$			29.0291i			0.940344i	0.882575	+	0.470172i	$0.155808\pi$
$953$			29.0291i			0.940344i	−0.882575	+	0.470172i	$0.844192\pi$
$954$		0			0
$955$	−0.713357	+	0.713357i	−0.0230837	+	0.0230837i
$956$	29.4312	−	26.2512i	0.951872	−	0.849025i
$957$		0			0
$958$	−5.00765	+	1.90881i	−0.161790	+	0.0616707i
$959$	33.0696			1.06787
$960$		0			0
$961$	−19.5772			−0.631522
$962$	0.917934	−	0.349896i	0.0295954	−	0.0112811i
$963$		0			0
$964$	11.5562	−	10.3076i	0.372201	−	0.331986i
$965$	−14.1614	+	14.1614i	−0.455873	+	0.455873i
$966$		0			0
$967$			4.50118i			0.144748i	0.997378	+	0.0723741i	$0.0230576\pi$
$967$			4.50118i			0.144748i	−0.997378	+	0.0723741i	$0.976942\pi$
$968$	9.73519	+	5.04685i	0.312901	+	0.162212i
$969$		0			0
$970$	−0.401699	+	0.896571i	−0.0128978	+	0.0287872i
$971$	−30.6131	+	30.6131i	−0.982420	+	0.982420i	−0.999848	−	0.0174280i	$-0.994452\pi$
$971$	−30.6131	+	30.6131i	−0.982420	+	0.982420i	0.0174280	+	0.999848i	$0.494452\pi$
$972$		0			0
$973$	34.3900	+	34.3900i	1.10249	+	1.10249i
$974$	1.71194	+	4.49119i	0.0548542	+	0.143907i
$975$		0			0
$976$	10.5861	−	8.40935i	0.338851	−	0.269177i
$977$	36.6473			1.17245			0.586225	−	0.810148i	$-0.300613\pi$
$977$	36.6473			1.17245			0.586225	+	0.810148i	$0.300613\pi$
$978$		0			0
$979$	−40.6223	−	40.6223i	−1.29829	−	1.29829i
$980$	−0.0301710	+	0.528307i	−0.000963776	+	0.0168762i
$981$		0			0
$982$	−7.12180	+	15.8955i	−0.227266	+	0.507244i
$983$		−	16.3748i		−	0.522276i	−0.965301	−	0.261138i	$-0.915902\pi$
$983$		−	16.3748i		−	0.522276i	0.965301	−	0.261138i	$-0.0840978\pi$
$984$		0			0
$985$		−	18.0474i		−	0.575039i
$986$	38.0623	+	17.0534i	1.21215	+	0.543091i
$987$		0			0
$988$	17.6115	+	19.7449i	0.560297	+	0.628168i
$989$	−71.4588	−	71.4588i	−2.27226	−	2.27226i
$990$		0			0
$991$	13.8052			0.438537			0.219269	−	0.975665i	$-0.429633\pi$
$991$	13.8052			0.438537			0.219269	+	0.975665i	$0.429633\pi$
$992$	−4.73160	−	18.5241i	−0.150228	−	0.588141i
$993$		0			0
$994$	8.15136	−	3.10712i	0.258545	−	0.0985517i
$995$	8.24694	+	8.24694i	0.261446	+	0.261446i
$996$		0			0
$997$	10.9547	−	10.9547i	0.346938	−	0.346938i	−0.512030	−	0.858968i	$-0.671106\pi$
$997$	10.9547	−	10.9547i	0.346938	−	0.346938i	0.858968	+	0.512030i	$0.171106\pi$
$998$	29.1194	+	13.0466i	0.921757	+	0.412984i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.d.541.1		20
3.2	odd	2		240.2.s.c.61.10	✓	20
4.3	odd	2		2880.2.t.d.721.10		20
12.11	even	2		960.2.s.c.721.10		20
16.5	even	4	inner	720.2.t.d.181.1		20
16.11	odd	4		2880.2.t.d.2161.6		20
24.5	odd	2		1920.2.s.e.1441.6		20
24.11	even	2		1920.2.s.f.1441.5		20
48.5	odd	4		240.2.s.c.181.10	yes	20
48.11	even	4		960.2.s.c.241.6		20
48.29	odd	4		1920.2.s.e.481.10		20
48.35	even	4		1920.2.s.f.481.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.10	✓	20	3.2	odd	2
240.2.s.c.181.10	yes	20	48.5	odd	4
720.2.t.d.181.1		20	16.5	even	4	inner
720.2.t.d.541.1		20	1.1	even	1	trivial
960.2.s.c.241.6		20	48.11	even	4
960.2.s.c.721.10		20	12.11	even	2
1920.2.s.e.481.10		20	48.29	odd	4
1920.2.s.e.1441.6		20	24.5	odd	2
1920.2.s.f.481.1		20	48.35	even	4
1920.2.s.f.1441.5		20	24.11	even	2
2880.2.t.d.721.10		20	4.3	odd	2
2880.2.t.d.2161.6		20	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32147 + 0.503713i) q^{2} +(1.49255 - 1.33128i) q^{4} +(0.707107 - 0.707107i) q^{5} -2.69529i q^{7} +(-1.30176 + 2.51106i) q^{8} +O(q^{10})\)	\(q+(-1.32147 + 0.503713i) q^{2} +(1.49255 - 1.33128i) q^{4} +(0.707107 - 0.707107i) q^{5} -2.69529i q^{7} +(-1.30176 + 2.51106i) q^{8} +(-0.578239 + 1.29060i) q^{10} +(-2.72735 + 2.72735i) q^{11} +(1.82449 + 1.82449i) q^{13} +(1.35765 + 3.56173i) q^{14} +(0.455385 - 3.97399i) q^{16} +7.33517 q^{17} +(3.62540 + 3.62540i) q^{19} +(0.114032 - 1.99675i) q^{20} +(2.23030 - 4.97791i) q^{22} -8.95345i q^{23} -1.00000i q^{25} +(-3.33002 - 1.49198i) q^{26} +(-3.58819 - 4.02284i) q^{28} +(-2.84302 - 2.84302i) q^{29} -3.37977 q^{31} +(1.39998 + 5.48088i) q^{32} +(-9.69317 + 3.69482i) q^{34} +(-1.90586 - 1.90586i) q^{35} +(-0.190364 + 0.190364i) q^{37} +(-6.61700 - 2.96468i) q^{38} +(0.855099 + 2.69607i) q^{40} -7.67786i q^{41} +(7.98115 - 7.98115i) q^{43} +(-0.439827 + 7.70158i) q^{44} +(4.50997 + 11.8317i) q^{46} +1.31537 q^{47} -0.264584 q^{49} +(0.503713 + 1.32147i) q^{50} +(5.15204 + 0.294227i) q^{52} +(6.71014 - 6.71014i) q^{53} +3.85706i q^{55} +(6.76803 + 3.50863i) q^{56} +(5.18902 + 2.32488i) q^{58} +(-1.01464 + 1.01464i) q^{59} +(2.38996 + 2.38996i) q^{61} +(4.46625 - 1.70243i) q^{62} +(-4.61082 - 6.53761i) q^{64} +2.58022 q^{65} +(-7.22173 - 7.22173i) q^{67} +(10.9481 - 9.76516i) q^{68} +(3.47853 + 1.55852i) q^{70} -2.28859i q^{71} +1.31098i q^{73} +(0.155670 - 0.347448i) q^{74} +(10.2375 + 0.584650i) q^{76} +(7.35101 + 7.35101i) q^{77} -2.59319 q^{79} +(-2.48803 - 3.13204i) q^{80} +(3.86744 + 10.1460i) q^{82} +(5.36584 + 5.36584i) q^{83} +(5.18675 - 5.18675i) q^{85} +(-6.52661 + 14.5670i) q^{86} +(-3.29817 - 10.3989i) q^{88} +14.8944i q^{89} +(4.91753 - 4.91753i) q^{91} +(-11.9195 - 13.3634i) q^{92} +(-1.73822 + 0.662570i) q^{94} +5.12708 q^{95} +0.694695 q^{97} +(0.349639 - 0.133275i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} - 12 q^{8}+O(q^{10}) \) 20 * q + 4 * q^4 - 12 * q^8	\( 20 q + 4 q^{4} - 12 q^{8} - 8 q^{11} + 4 q^{14} - 20 q^{16} + 24 q^{17} - 4 q^{19} + 8 q^{20} + 8 q^{22} - 28 q^{26} - 8 q^{28} - 16 q^{29} + 40 q^{32} - 44 q^{34} + 16 q^{37} + 8 q^{38} + 12 q^{40} - 8 q^{43} - 24 q^{44} - 12 q^{46} - 52 q^{49} - 4 q^{50} - 56 q^{52} + 16 q^{53} - 64 q^{56} + 72 q^{58} + 16 q^{59} - 4 q^{61} + 44 q^{62} - 56 q^{64} - 8 q^{67} + 32 q^{68} + 20 q^{70} - 60 q^{74} + 28 q^{76} + 40 q^{77} + 56 q^{79} + 16 q^{80} - 24 q^{82} + 48 q^{83} + 4 q^{85} - 64 q^{86} + 40 q^{88} - 8 q^{91} - 88 q^{92} - 20 q^{94} + 56 q^{97} + 48 q^{98}+O(q^{100}) \) 20 * q + 4 * q^4 - 12 * q^8 - 8 * q^11 + 4 * q^14 - 20 * q^16 + 24 * q^17 - 4 * q^19 + 8 * q^20 + 8 * q^22 - 28 * q^26 - 8 * q^28 - 16 * q^29 + 40 * q^32 - 44 * q^34 + 16 * q^37 + 8 * q^38 + 12 * q^40 - 8 * q^43 - 24 * q^44 - 12 * q^46 - 52 * q^49 - 4 * q^50 - 56 * q^52 + 16 * q^53 - 64 * q^56 + 72 * q^58 + 16 * q^59 - 4 * q^61 + 44 * q^62 - 56 * q^64 - 8 * q^67 + 32 * q^68 + 20 * q^70 - 60 * q^74 + 28 * q^76 + 40 * q^77 + 56 * q^79 + 16 * q^80 - 24 * q^82 + 48 * q^83 + 4 * q^85 - 64 * q^86 + 40 * q^88 - 8 * q^91 - 88 * q^92 - 20 * q^94 + 56 * q^97 + 48 * q^98

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