LMFDB - Embedded newform 720.2.t.d.181.1

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			181.1
Root			$1.32147 - 0.503713i$ of defining polynomial
Character	$\chi$	$=$	720.181
Dual form			720.2.t.d.541.1

$q$-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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.32147	−	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	$0.170118\pi$
$7$			2.69529i			1.01872i	−0.860552	+	0.509362i	$0.829882\pi$
$8$	−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	0.164113	−	0.986442i	$-0.447524\pi$
$11$	−2.72735	−	2.72735i	−0.822328	−	0.822328i	−0.986442	+	0.164113i	$0.947524\pi$
$12$		0			0
$13$	1.82449	−	1.82449i	0.506023	−	0.506023i	−0.407281	−	0.913303i	$-0.633523\pi$
$13$	1.82449	−	1.82449i	0.506023	−	0.506023i	0.913303	+	0.407281i	$0.133523\pi$
$14$	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	−0.156029	−	0.987752i	$-0.549869\pi$
$19$	3.62540	−	3.62540i	0.831723	−	0.831723i	0.987752	+	0.156029i	$0.0498695\pi$
$20$	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	$0.383228\pi$
$23$			8.95345i			1.86692i	−0.358678	+	0.933461i	$0.616772\pi$
$24$		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	−0.919956	−	0.392021i	$-0.871776\pi$
$29$	−2.84302	+	2.84302i	−0.527935	+	0.527935i	0.392021	+	0.919956i	$0.371776\pi$
$30$		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	0.691286	−	0.722581i	$-0.257045\pi$
$37$	−0.190364	−	0.190364i	−0.0312956	−	0.0312956i	−0.722581	+	0.691286i	$0.757045\pi$
$38$	−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	$0.204650\pi$
$41$			7.67786i			1.19908i	−0.800345	+	0.599540i	$0.795350\pi$
$42$		0			0
$43$	7.98115	+	7.98115i	1.21711	+	1.21711i	0.968638	+	0.248477i	$0.0799299\pi$
$43$	7.98115	+	7.98115i	1.21711	+	1.21711i	0.248477	+	0.968638i	$0.420070\pi$
$44$	−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	0.997150	−	0.0754412i	$-0.0240365\pi$
$53$	6.71014	+	6.71014i	0.921709	+	0.921709i	−0.0754412	+	0.997150i	$0.524037\pi$
$54$		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	0.637968	−	0.770063i	$-0.279775\pi$
$59$	−1.01464	−	1.01464i	−0.132094	−	0.132094i	−0.770063	+	0.637968i	$0.779775\pi$
$60$		0			0
$61$	2.38996	−	2.38996i	0.306004	−	0.306004i	−0.537354	−	0.843357i	$-0.680576\pi$
$61$	2.38996	−	2.38996i	0.306004	−	0.306004i	0.843357	+	0.537354i	$0.180576\pi$
$62$	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	−0.993766	−	0.111490i	$-0.964438\pi$
$67$	−7.22173	+	7.22173i	−0.882275	+	0.882275i	0.111490	+	0.993766i	$0.464438\pi$
$68$	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	$0.0433614\pi$
$71$			2.28859i			0.271606i	−0.990736	+	0.135803i	$0.956639\pi$
$72$		0			0
$73$		−	1.31098i		−	0.153439i	−0.997053	−	0.0767196i	$-0.975555\pi$
$73$		−	1.31098i		−	0.153439i	0.997053	−	0.0767196i	$-0.0244446\pi$
$74$	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	−0.348377	−	0.937354i	$-0.613267\pi$
$83$	5.36584	−	5.36584i	0.588977	−	0.588977i	0.937354	+	0.348377i	$0.113267\pi$
$84$		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	$-0.710391\pi$
$89$		−	14.8944i		−	1.57880i	0.613877	−	0.789402i	$-0.289609\pi$
$90$		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	0.961242	−	0.275706i	$-0.0889115\pi$
$101$	6.88955	+	6.88955i	0.685536	+	0.685536i	−0.275706	+	0.961242i	$0.588912\pi$
$102$		0			0
$103$			4.39299i			0.432854i	0.976299	+	0.216427i	$0.0694403\pi$
$103$			4.39299i			0.432854i	−0.976299	+	0.216427i	$0.930560\pi$
$104$	−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	0.275590	−	0.961275i	$-0.411127\pi$
$107$	−7.09279	−	7.09279i	−0.685686	−	0.685686i	−0.961275	+	0.275590i	$0.911127\pi$
$108$		0			0
$109$	7.83035	−	7.83035i	0.750012	−	0.750012i	−0.224469	−	0.974481i	$-0.572065\pi$
$109$	7.83035	−	7.83035i	0.750012	−	0.750012i	0.974481	+	0.224469i	$0.0720649\pi$
$110$	−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	−0.434370	−	0.900735i	$-0.643029\pi$
$131$	5.33779	−	5.33779i	0.466365	−	0.466365i	0.900735	+	0.434370i	$0.143029\pi$
$132$		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	$-0.824393\pi$
$137$		−	12.2694i		−	1.04825i	0.851642	−	0.524124i	$-0.175607\pi$
$138$		0			0
$139$	−12.7593	−	12.7593i	−1.08223	−	1.08223i	−0.996301	−	0.0859285i	$-0.972614\pi$
$139$	−12.7593	−	12.7593i	−1.08223	−	1.08223i	−0.0859285	−	0.996301i	$-0.527386\pi$
$140$	−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	0.390405	−	0.920643i	$-0.372335\pi$
$149$	−6.47238	−	6.47238i	−0.530238	−	0.530238i	−0.920643	+	0.390405i	$0.872335\pi$
$150$		0			0
$151$			14.7782i			1.20263i	0.799012	+	0.601316i	$0.205357\pi$
$151$			14.7782i			1.20263i	−0.799012	+	0.601316i	$0.794643\pi$
$152$	−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	0.130592	−	0.991436i	$-0.458312\pi$
$157$	14.0590	−	14.0590i	1.12203	−	1.12203i	0.991436	−	0.130592i	$-0.0416878\pi$
$158$	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	−0.620145	−	0.784487i	$-0.712926\pi$
$163$	2.09819	−	2.09819i	0.164343	−	0.164343i	0.784487	+	0.620145i	$0.212926\pi$
$164$	−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	$-0.791148\pi$
$167$		−	15.7672i		−	1.22010i	0.792361	−	0.610052i	$-0.208852\pi$
$168$		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	−0.956359	−	0.292195i	$-0.905615\pi$
$173$	−8.73572	+	8.73572i	−0.664164	+	0.664164i	0.292195	+	0.956359i	$0.405615\pi$
$174$		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	−0.888027	−	0.459790i	$-0.847925\pi$
$179$	−5.72942	+	5.72942i	−0.428237	+	0.428237i	0.459790	+	0.888027i	$0.347925\pi$
$180$		0			0
$181$	−1.48317	−	1.48317i	−0.110243	−	0.110243i	0.649833	−	0.760077i	$-0.274839\pi$
$181$	−1.48317	−	1.48317i	−0.110243	−	0.110243i	−0.760077	+	0.649833i	$0.774839\pi$
$182$	−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	0.996209	−	0.0869919i	$-0.0277254\pi$
$197$	12.7615	+	12.7615i	0.909217	+	0.909217i	−0.0869919	+	0.996209i	$0.527725\pi$
$198$		0			0
$199$		−	11.6629i		−	0.826764i	−0.910558	−	0.413382i	$-0.864347\pi$
$199$		−	11.6629i		−	0.826764i	0.910558	−	0.413382i	$-0.135653\pi$
$200$	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	−0.721391	−	0.692528i	$-0.756497\pi$
$211$	−0.419270	+	0.419270i	−0.0288637	+	0.0288637i	0.692528	+	0.721391i	$0.256497\pi$
$212$	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	−0.796045	−	0.605238i	$-0.793078\pi$
$227$	−2.87480	+	2.87480i	−0.190807	+	0.190807i	0.605238	+	0.796045i	$0.293078\pi$
$228$		0			0
$229$	−6.78564	−	6.78564i	−0.448408	−	0.448408i	0.446417	−	0.894825i	$-0.352700\pi$
$229$	−6.78564	−	6.78564i	−0.448408	−	0.448408i	−0.894825	+	0.446417i	$0.852700\pi$
$230$	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	$0.366010\pi$
$233$			27.8637i			1.82541i	−0.408619	+	0.912705i	$0.633990\pi$
$234$		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	0.659434	−	0.751763i	$-0.270796\pi$
$251$	−1.46277	−	1.46277i	−0.0923293	−	0.0923293i	−0.751763	+	0.659434i	$0.770796\pi$
$252$		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	$0.301403\pi$
$263$			26.3239i			1.62320i	−0.584215	+	0.811599i	$0.698597\pi$
$264$		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	0.0901396	−	0.995929i	$-0.471269\pi$
$269$	17.8129	−	17.8129i	1.08607	−	1.08607i	0.995929	−	0.0901396i	$-0.0287313\pi$
$270$		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	0.947786	−	0.318907i	$-0.103316\pi$
$277$	10.4666	+	10.4666i	0.628879	+	0.628879i	−0.318907	+	0.947786i	$0.603316\pi$
$278$	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	$-0.830104\pi$
$281$		−	17.0567i		−	1.01752i	0.860909	−	0.508759i	$-0.169896\pi$
$282$		0			0
$283$	2.70727	+	2.70727i	0.160931	+	0.160931i	0.782979	−	0.622048i	$-0.213699\pi$
$283$	2.70727	+	2.70727i	0.160931	+	0.160931i	−0.622048	+	0.782979i	$0.713699\pi$
$284$	−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	0.0263968	−	0.999652i	$-0.491597\pi$
$293$	−16.6594	−	16.6594i	−0.973255	−	0.973255i	−0.999652	+	0.0263968i	$0.991597\pi$
$294$		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	0.0394558	−	0.999221i	$-0.487438\pi$
$307$	18.1991	−	18.1991i	1.03868	−	1.03868i	0.999221	−	0.0394558i	$-0.0125624\pi$
$308$	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	$-0.856240\pi$
$311$		−	15.3933i		−	0.872874i	0.899735	−	0.436437i	$-0.143760\pi$
$312$		0			0
$313$		−	23.7790i		−	1.34407i	−0.740520	−	0.672034i	$-0.765421\pi$
$313$		−	23.7790i		−	1.34407i	0.740520	−	0.672034i	$-0.234579\pi$
$314$	−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	−0.396070	−	0.918220i	$-0.629626\pi$
$317$	9.29662	−	9.29662i	0.522150	−	0.522150i	0.918220	+	0.396070i	$0.129626\pi$
$318$		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	0.159608	−	0.987180i	$-0.448977\pi$
$331$	−15.0564	−	15.0564i	−0.827572	−	0.827572i	−0.987180	+	0.159608i	$0.948977\pi$
$332$	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	0.284484	−	0.958681i	$-0.408178\pi$
$347$	−12.5589	−	12.5589i	−0.674197	−	0.674197i	−0.958681	+	0.284484i	$0.908178\pi$
$348$		0			0
$349$	−12.3114	+	12.3114i	−0.659014	+	0.659014i	−0.955147	−	0.296133i	$-0.904303\pi$
$349$	−12.3114	+	12.3114i	−0.659014	+	0.659014i	0.296133	+	0.955147i	$0.404303\pi$
$350$	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	$-0.958265\pi$
$359$		−	4.95429i		−	0.261477i	0.991417	−	0.130739i	$-0.0417349\pi$
$360$		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	0.449109	−	0.893477i	$-0.351742\pi$
$373$	−8.58218	−	8.58218i	−0.444368	−	0.444368i	−0.893477	+	0.449109i	$0.851742\pi$
$374$	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	0.803245	−	0.595649i	$-0.203105\pi$
$379$	4.04145	+	4.04145i	0.207595	+	0.207595i	−0.595649	+	0.803245i	$0.703105\pi$
$380$	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	−0.861606	−	0.507579i	$-0.830541\pi$
$389$	−27.0045	−	27.0045i	−1.36918	−	1.36918i	−0.507579	−	0.861606i	$-0.669459\pi$
$390$		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	−0.957078	−	0.289830i	$-0.906401\pi$
$397$	−13.2948	+	13.2948i	−0.667248	+	0.667248i	0.289830	+	0.957078i	$0.406401\pi$
$398$	−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	$0.198395\pi$
$409$			23.6091i			1.16740i	−0.811971	+	0.583698i	$0.801605\pi$
$410$	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	−0.292906	−	0.956141i	$-0.594622\pi$
$419$	13.5761	−	13.5761i	0.663235	−	0.663235i	0.956141	+	0.292906i	$0.0946225\pi$
$420$		0			0
$421$	9.30166	+	9.30166i	0.453335	+	0.453335i	0.896460	−	0.443125i	$-0.146130\pi$
$421$	9.30166	+	9.30166i	0.453335	+	0.453335i	−0.443125	+	0.896460i	$0.646130\pi$
$422$	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	$-0.969738\pi$
$439$		−	3.97789i		−	0.189855i	0.995484	−	0.0949273i	$-0.0302619\pi$
$440$	−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	0.270826	−	0.962628i	$-0.412703\pi$
$443$	−14.5607	−	14.5607i	−0.691802	−	0.691802i	−0.962628	+	0.270826i	$0.912703\pi$
$444$		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	$-0.632775\pi$
$457$		−	39.0892i		−	1.82851i	0.405135	−	0.914257i	$-0.367225\pi$
$458$	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	−0.551903	−	0.833908i	$-0.686098\pi$
$461$	6.05492	−	6.05492i	0.282006	−	0.282006i	0.833908	+	0.551903i	$0.186098\pi$
$462$		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	−0.336128	−	0.941816i	$-0.609117\pi$
$467$	13.0890	−	13.0890i	0.605689	−	0.605689i	0.941816	+	0.336128i	$0.109117\pi$
$468$		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	$0.0245353\pi$
$487$			3.39864i			0.154007i	−0.997031	+	0.0770036i	$0.975465\pi$
$488$	−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	0.875766	−	0.482735i	$-0.160357\pi$
$491$	8.70898	+	8.70898i	0.393031	+	0.393031i	−0.482735	+	0.875766i	$0.660357\pi$
$492$		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	−0.967413	−	0.253203i	$-0.918516\pi$
$499$	−15.9542	+	15.9542i	−0.714210	+	0.714210i	0.253203	+	0.967413i	$0.418516\pi$
$500$	−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	$-0.864986\pi$
$503$		−	18.4604i		−	0.823107i	0.911386	−	0.411553i	$-0.135014\pi$
$504$		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	−0.869552	−	0.493841i	$-0.835592\pi$
$509$	−8.47641	+	8.47641i	−0.375710	+	0.375710i	0.493841	+	0.869552i	$0.335592\pi$
$510$		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	$0.163006\pi$
$521$			22.3693i			0.980017i	−0.871718	+	0.490009i	$0.836994\pi$
$522$		0			0
$523$	−2.39235	−	2.39235i	−0.104610	−	0.104610i	0.652865	−	0.757475i	$-0.273567\pi$
$523$	−2.39235	−	2.39235i	−0.104610	−	0.104610i	−0.757475	+	0.652865i	$0.773567\pi$
$524$	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	−0.895211	−	0.445642i	$-0.852976\pi$
$541$	−10.4567	+	10.4567i	−0.449570	+	0.449570i	0.445642	+	0.895211i	$0.352976\pi$
$542$	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	0.176060	−	0.984379i	$-0.443665\pi$
$547$	27.1404	−	27.1404i	1.16044	−	1.16044i	0.984379	−	0.176060i	$-0.0563354\pi$
$548$	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	−0.679239	−	0.733918i	$-0.737690\pi$
$557$	1.29047	−	1.29047i	0.0546790	−	0.0546790i	0.733918	+	0.679239i	$0.237690\pi$
$558$		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	−0.631193	−	0.775626i	$-0.717434\pi$
$563$	3.42706	−	3.42706i	0.144433	−	0.144433i	0.775626	+	0.631193i	$0.217434\pi$
$564$		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	$0.187344\pi$
$569$			26.4853i			1.11032i	−0.831743	+	0.555161i	$0.812656\pi$
$570$		0			0
$571$	−1.42398	−	1.42398i	−0.0595918	−	0.0595918i	0.676683	−	0.736275i	$-0.263417\pi$
$571$	−1.42398	−	1.42398i	−0.0595918	−	0.0595918i	−0.736275	+	0.676683i	$0.763417\pi$
$572$	−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	0.664758	−	0.747059i	$-0.268535\pi$
$587$	−1.99399	−	1.99399i	−0.0823008	−	0.0823008i	−0.747059	+	0.664758i	$0.768535\pi$
$588$		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	$-0.750842\pi$
$599$		−	34.5205i		−	1.41047i	0.708974	−	0.705234i	$-0.249158\pi$
$600$		0			0
$601$			3.45113i			0.140775i	0.997520	+	0.0703873i	$0.0224235\pi$
$601$			3.45113i			0.140775i	−0.997520	+	0.0703873i	$0.977577\pi$
$602$	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	0.946673	+	0.322195i	$0.104421\pi$
$613$	31.4157	+	31.4157i	1.26887	+	1.26887i	0.322195	+	0.946673i	$0.395579\pi$
$614$	−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	$0.179035\pi$
$617$			26.4920i			1.06653i	−0.845949	+	0.533265i	$0.820965\pi$
$618$		0			0
$619$	23.9945	+	23.9945i	0.964422	+	0.964422i	0.999388	−	0.0349667i	$-0.0111325\pi$
$619$	23.9945	+	23.9945i	0.964422	+	0.964422i	−0.0349667	+	0.999388i	$0.511133\pi$
$620$	−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	$-0.757470\pi$
$631$		−	34.6813i		−	1.38064i	0.723504	−	0.690320i	$-0.242530\pi$
$632$	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	−0.428874	−	0.903364i	$-0.641090\pi$
$643$	12.0319	−	12.0319i	0.474490	−	0.474490i	0.903364	+	0.428874i	$0.141090\pi$
$644$	−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	$-0.868561\pi$
$647$		−	20.4148i		−	0.802587i	0.915950	−	0.401293i	$-0.131439\pi$
$648$		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	−0.940202	−	0.340616i	$-0.889364\pi$
$653$	−15.3217	+	15.3217i	−0.599586	+	0.599586i	0.340616	+	0.940202i	$0.389364\pi$
$654$		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	−0.772348	−	0.635200i	$-0.780918\pi$
$659$	−3.52074	+	3.52074i	−0.137148	+	0.137148i	0.635200	+	0.772348i	$0.280918\pi$
$660$		0			0
$661$	−23.8945	−	23.8945i	−0.929388	−	0.929388i	0.0682781	−	0.997666i	$-0.478249\pi$
$661$	−23.8945	−	23.8945i	−0.929388	−	0.929388i	−0.997666	+	0.0682781i	$0.978249\pi$
$662$	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	0.172796	−	0.984958i	$-0.444720\pi$
$677$	−21.1318	−	21.1318i	−0.812162	−	0.812162i	−0.984958	+	0.172796i	$0.944720\pi$
$678$		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	0.814767	−	0.579789i	$-0.196865\pi$
$683$	6.14096	+	6.14096i	0.234977	+	0.234977i	−0.579789	+	0.814767i	$0.696865\pi$
$684$		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	−0.680458	−	0.732787i	$-0.738219\pi$
$691$	1.37557	−	1.37557i	0.0523291	−	0.0523291i	0.732787	+	0.680458i	$0.238219\pi$
$692$	−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	−0.0223289	+	0.999751i	$0.507108\pi$
$701$	−27.0610	+	27.0610i	−1.02208	+	1.02208i	−0.999751	+	0.0223289i	$0.992892\pi$
$702$		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	−0.962560	−	0.271068i	$-0.912623\pi$
$709$	−32.8479	−	32.8479i	−1.23363	−	1.23363i	−0.271068	−	0.962560i	$-0.587377\pi$
$710$	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	$0.0447075\pi$
$727$			7.54917i			0.279983i	−0.990153	+	0.139992i	$0.955292\pi$
$728$	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	−0.908144	−	0.418657i	$-0.862501\pi$
$733$	−13.2524	+	13.2524i	−0.489487	+	0.489487i	0.418657	+	0.908144i	$0.362501\pi$
$734$	−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	−0.621083	−	0.783745i	$-0.713307\pi$
$739$	4.42190	−	4.42190i	0.162662	−	0.162662i	0.783745	+	0.621083i	$0.213307\pi$
$740$	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	$0.315057\pi$
$743$			45.5703i			1.67181i	−0.548873	+	0.835906i	$0.684943\pi$
$744$		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	0.386692	−	0.922209i	$-0.373618\pi$
$757$	−14.7340	−	14.7340i	−0.535517	−	0.535517i	−0.922209	+	0.386692i	$0.873618\pi$
$758$	−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	$-0.948475\pi$
$761$		−	8.89182i		−	0.322328i	0.986928	−	0.161164i	$-0.0515248\pi$
$762$		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	0.447525	−	0.894272i	$-0.352306\pi$
$773$	−12.4209	−	12.4209i	−0.446747	−	0.446747i	−0.894272	+	0.447525i	$0.852306\pi$
$774$		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	−0.984326	−	0.176361i	$-0.943567\pi$
$787$	−22.6663	+	22.6663i	−0.807965	+	0.807965i	0.176361	+	0.984326i	$0.443567\pi$
$788$	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	−0.827009	−	0.562189i	$-0.809959\pi$
$797$	−7.47619	+	7.47619i	−0.264820	+	0.264820i	0.562189	+	0.827009i	$0.309959\pi$
$798$		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	$-0.948274\pi$
$809$		−	9.20349i		−	0.323577i	0.986825	−	0.161789i	$-0.0517263\pi$
$810$		0			0
$811$	31.0252	+	31.0252i	1.08944	+	1.08944i	0.995586	+	0.0938555i	$0.0299192\pi$
$811$	31.0252	+	31.0252i	1.08944	+	1.08944i	0.0938555	+	0.995586i	$0.470081\pi$
$812$	−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	0.608157	−	0.793817i	$-0.291909\pi$
$821$	−5.31973	−	5.31973i	−0.185660	−	0.185660i	−0.793817	+	0.608157i	$0.791909\pi$
$822$		0			0
$823$		−	24.8425i		−	0.865956i	−0.901404	−	0.432978i	$-0.857463\pi$
$823$		−	24.8425i		−	0.865956i	0.901404	−	0.432978i	$-0.142537\pi$
$824$	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	0.469551	−	0.882905i	$-0.344416\pi$
$827$	−11.8871	−	11.8871i	−0.413354	−	0.413354i	−0.882905	+	0.469551i	$0.844416\pi$
$828$		0			0
$829$	6.17740	−	6.17740i	0.214550	−	0.214550i	−0.591647	−	0.806197i	$-0.701522\pi$
$829$	6.17740	−	6.17740i	0.214550	−	0.214550i	0.806197	+	0.591647i	$0.201522\pi$
$830$	−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	$0.0448848\pi$
$839$			8.14180i			0.281086i	−0.990075	+	0.140543i	$0.955115\pi$
$840$		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	0.999084	−	0.0427875i	$-0.0136239\pi$
$853$	27.9298	+	27.9298i	0.956297	+	0.956297i	−0.0427875	+	0.999084i	$0.513624\pi$
$854$	−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	$0.115069\pi$
$857$			20.7075i			0.707356i	−0.935367	+	0.353678i	$0.884931\pi$
$858$		0			0
$859$	−12.8547	−	12.8547i	−0.438597	−	0.438597i	0.452943	−	0.891539i	$-0.350374\pi$
$859$	−12.8547	−	12.8547i	−0.438597	−	0.438597i	−0.891539	+	0.452943i	$0.850374\pi$
$860$	−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	−0.595459	−	0.803386i	$-0.703030\pi$
$877$	6.15758	−	6.15758i	0.207927	−	0.207927i	0.803386	+	0.595459i	$0.203030\pi$
$878$	−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	−0.345554	−	0.938399i	$-0.612309\pi$
$883$	17.6166	−	17.6166i	0.592845	−	0.592845i	0.938399	+	0.345554i	$0.112309\pi$
$884$	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	$0.163431\pi$
$887$			29.2567i			0.982343i	−0.871063	+	0.491172i	$0.836569\pi$
$888$		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	0.995988	+	0.0894835i	$0.0285216\pi$
$907$	32.6905	+	32.6905i	1.08547	+	1.08547i	0.0894835	+	0.995988i	$0.471478\pi$
$908$	−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	$-0.884870\pi$
$919$		−	21.4544i		−	0.707716i	0.935299	−	0.353858i	$-0.115130\pi$
$920$	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	$0.0553596\pi$
$937$			10.5938i			0.346084i	−0.984914	+	0.173042i	$0.944640\pi$
$938$	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	−0.821731	−	0.569876i	$-0.806991\pi$
$941$	−7.72584	+	7.72584i	−0.251855	+	0.251855i	0.569876	+	0.821731i	$0.306991\pi$
$942$		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	−0.963945	−	0.266103i	$-0.914264\pi$
$947$	−21.4749	+	21.4749i	−0.697841	+	0.697841i	0.266103	+	0.963945i	$0.414264\pi$
$948$		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	$-0.844192\pi$
$953$		−	29.0291i		−	0.940344i	0.882575	−	0.470172i	$-0.155808\pi$
$954$		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	$-0.976942\pi$
$967$		−	4.50118i		−	0.144748i	0.997378	−	0.0723741i	$-0.0230576\pi$
$968$	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	0.0174280	−	0.999848i	$-0.494452\pi$
$971$	−30.6131	−	30.6131i	−0.982420	−	0.982420i	−0.999848	+	0.0174280i	$0.994452\pi$
$972$		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	$0.0840978\pi$
$983$			16.3748i			0.522276i	−0.965301	+	0.261138i	$0.915902\pi$
$984$		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	0.858968	−	0.512030i	$-0.171106\pi$
$997$	10.9547	+	10.9547i	0.346938	+	0.346938i	−0.512030	+	0.858968i	$0.671106\pi$
$998$	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.181.1		20
3.2	odd	2		240.2.s.c.181.10	yes	20
4.3	odd	2		2880.2.t.d.2161.6		20
12.11	even	2		960.2.s.c.241.6		20
16.3	odd	4		2880.2.t.d.721.10		20
16.13	even	4	inner	720.2.t.d.541.1		20
24.5	odd	2		1920.2.s.e.481.10		20
24.11	even	2		1920.2.s.f.481.1		20
48.5	odd	4		1920.2.s.e.1441.6		20
48.11	even	4		1920.2.s.f.1441.5		20
48.29	odd	4		240.2.s.c.61.10	✓	20
48.35	even	4		960.2.s.c.721.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.10	✓	20	48.29	odd	4
240.2.s.c.181.10	yes	20	3.2	odd	2
720.2.t.d.181.1		20	1.1	even	1	trivial
720.2.t.d.541.1		20	16.13	even	4	inner
960.2.s.c.241.6		20	12.11	even	2
960.2.s.c.721.10		20	48.35	even	4
1920.2.s.e.481.10		20	24.5	odd	2
1920.2.s.e.1441.6		20	48.5	odd	4
1920.2.s.f.481.1		20	24.11	even	2
1920.2.s.f.1441.5		20	48.11	even	4
2880.2.t.d.721.10		20	16.3	odd	4
2880.2.t.d.2161.6		20	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)

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