LMFDB - Embedded newform 720.2.t.d.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("720.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$20$
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			541.2
Root			$1.19834 - 0.750988i$ of defining polynomial
Character	$\chi$	$=$	720.541
Dual form			720.2.t.d.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19834 - 0.750988i) q^{2} +(0.872033 + 1.79988i) q^{4} +(0.707107 - 0.707107i) q^{5} +3.79862i q^{7} +(0.306697 - 2.81175i) q^{8} +O(q^{10})$	\(q+(-1.19834 - 0.750988i) q^{2} +(0.872033 + 1.79988i) q^{4} +(0.707107 - 0.707107i) q^{5} +3.79862i q^{7} +(0.306697 - 2.81175i) q^{8} +(-1.37838 + 0.316325i) q^{10} +(-3.08662 + 3.08662i) q^{11} +(1.54638 + 1.54638i) q^{13} +(2.85272 - 4.55203i) q^{14} +(-2.47912 + 3.13910i) q^{16} -4.32428 q^{17} +(-5.37165 - 5.37165i) q^{19} +(1.88933 + 0.656085i) q^{20} +(6.01683 - 1.38080i) q^{22} +3.91059i q^{23} -1.00000i q^{25} +(-0.691773 - 3.01440i) q^{26} +(-6.83704 + 3.31252i) q^{28} +(-1.84243 - 1.84243i) q^{29} -9.52790 q^{31} +(5.32825 - 1.89992i) q^{32} +(5.18195 + 3.24748i) q^{34} +(2.68603 + 2.68603i) q^{35} +(4.55033 - 4.55033i) q^{37} +(2.40301 + 10.4711i) q^{38} +(-1.77134 - 2.20507i) q^{40} -0.580195i q^{41} +(0.994741 - 0.994741i) q^{43} +(-8.24716 - 2.86390i) q^{44} +(2.93681 - 4.68621i) q^{46} -2.22461 q^{47} -7.42948 q^{49} +(-0.750988 + 1.19834i) q^{50} +(-1.43480 + 4.13178i) q^{52} +(-4.80257 + 4.80257i) q^{53} +4.36514i q^{55} +(10.6808 + 1.16502i) q^{56} +(0.824214 + 3.59151i) q^{58} +(-7.26404 + 7.26404i) q^{59} +(0.301222 + 0.301222i) q^{61} +(11.4176 + 7.15534i) q^{62} +(-7.81187 - 1.72471i) q^{64} +2.18691 q^{65} +(6.97711 + 6.97711i) q^{67} +(-3.77091 - 7.78318i) q^{68} +(-1.20160 - 5.23595i) q^{70} -0.585051i q^{71} +11.9999i q^{73} +(-8.87009 + 2.03559i) q^{74} +(4.98406 - 14.3526i) q^{76} +(-11.7249 - 11.7249i) q^{77} +12.6436 q^{79} +(0.466680 + 3.97268i) q^{80} +(-0.435720 + 0.695270i) q^{82} +(11.1632 + 11.1632i) q^{83} +(-3.05773 + 3.05773i) q^{85} +(-1.93908 + 0.444998i) q^{86} +(7.73214 + 9.62545i) q^{88} +12.9706i q^{89} +(-5.87409 + 5.87409i) q^{91} +(-7.03858 + 3.41016i) q^{92} +(2.66583 + 1.67065i) q^{94} -7.59666 q^{95} -6.78553 q^{97} +(8.90303 + 5.57945i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.19834	−	0.750988i	−0.847354	−	0.531029i
$2$	−1.19834	−	0.750988i	−0.847354	−	0.531029i
$3$		0			0
$3$		0			0
$4$	0.872033	+	1.79988i	0.436016	+	0.899939i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$			3.79862i			1.43574i	0.696176	+	0.717871i	$0.254883\pi$
$7$			3.79862i			1.43574i	−0.696176	+	0.717871i	$0.745117\pi$
$8$	0.306697	−	2.81175i	0.108434	−	0.994104i
$9$		0			0
$10$	−1.37838	+	0.316325i	−0.435883	+	0.100031i
$11$	−3.08662	+	3.08662i	−0.930650	+	0.930650i	−0.997746	−	0.0670964i	$-0.978626\pi$
$11$	−3.08662	+	3.08662i	−0.930650	+	0.930650i	0.0670964	+	0.997746i	$0.478626\pi$
$12$		0			0
$13$	1.54638	+	1.54638i	0.428888	+	0.428888i	0.888249	−	0.459361i	$-0.151922\pi$
$13$	1.54638	+	1.54638i	0.428888	+	0.428888i	−0.459361	+	0.888249i	$0.651922\pi$
$14$	2.85272	−	4.55203i	0.762420	−	1.21658i
$15$		0			0
$16$	−2.47912	+	3.13910i	−0.619780	+	0.784776i
$17$	−4.32428			−1.04879			−0.524396	−	0.851474i	$-0.675709\pi$
$17$	−4.32428			−1.04879			−0.524396	+	0.851474i	$0.675709\pi$
$18$		0			0
$19$	−5.37165	−	5.37165i	−1.23234	−	1.23234i	−0.963062	−	0.269279i	$-0.913215\pi$
$19$	−5.37165	−	5.37165i	−1.23234	−	1.23234i	−0.269279	−	0.963062i	$-0.586785\pi$
$20$	1.88933	+	0.656085i	0.422466	+	0.146705i
$21$		0			0
$22$	6.01683	−	1.38080i	1.28279	−	0.294387i
$23$			3.91059i			0.815414i	0.913113	+	0.407707i	$0.133671\pi$
$23$			3.91059i			0.815414i	−0.913113	+	0.407707i	$0.866329\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	−0.691773	−	3.01440i	−0.135668	−	0.591172i
$27$		0			0
$28$	−6.83704	+	3.31252i	−1.29208	+	0.626007i
$29$	−1.84243	−	1.84243i	−0.342131	−	0.342131i	0.515037	−	0.857168i	$-0.327778\pi$
$29$	−1.84243	−	1.84243i	−0.342131	−	0.342131i	−0.857168	+	0.515037i	$0.827778\pi$
$30$		0			0
$31$	−9.52790			−1.71126			−0.855630	−	0.517587i	$-0.826830\pi$
$31$	−9.52790			−1.71126			−0.855630	+	0.517587i	$0.826830\pi$
$32$	5.32825	−	1.89992i	0.941911	−	0.335862i
$33$		0			0
$34$	5.18195	+	3.24748i	0.888698	+	0.556939i
$35$	2.68603	+	2.68603i	0.454021	+	0.454021i
$36$		0			0
$37$	4.55033	−	4.55033i	0.748070	−	0.748070i	−0.226047	−	0.974116i	$-0.572580\pi$
$37$	4.55033	−	4.55033i	0.748070	−	0.748070i	0.974116	+	0.226047i	$0.0725802\pi$
$38$	2.40301	+	10.4711i	0.389820	+	1.69864i
$39$		0			0
$40$	−1.77134	−	2.20507i	−0.280073	−	0.348653i
$41$		−	0.580195i		−	0.0906112i	−0.998973	−	0.0453056i	$-0.985574\pi$
$41$		−	0.580195i		−	0.0906112i	0.998973	−	0.0453056i	$-0.0144262\pi$
$42$		0			0
$43$	0.994741	−	0.994741i	0.151697	−	0.151697i	−0.627179	−	0.778875i	$-0.715790\pi$
$43$	0.994741	−	0.994741i	0.151697	−	0.151697i	0.778875	+	0.627179i	$0.215790\pi$
$44$	−8.24716	−	2.86390i	−1.24331	−	0.431749i
$45$		0			0
$46$	2.93681	−	4.68621i	0.433008	−	0.690944i
$47$	−2.22461			−0.324492			−0.162246	−	0.986750i	$-0.551874\pi$
$47$	−2.22461			−0.324492			−0.162246	+	0.986750i	$0.551874\pi$
$48$		0			0
$49$	−7.42948			−1.06135
$50$	−0.750988	+	1.19834i	−0.106206	+	0.169471i
$51$		0			0
$52$	−1.43480	+	4.13178i	−0.198971	+	0.572975i
$53$	−4.80257	+	4.80257i	−0.659684	+	0.659684i	−0.955305	−	0.295622i	$-0.904473\pi$
$53$	−4.80257	+	4.80257i	−0.659684	+	0.659684i	0.295622	+	0.955305i	$0.404473\pi$
$54$		0			0
$55$			4.36514i			0.588595i
$56$	10.6808	+	1.16502i	1.42728	+	0.155683i
$57$		0			0
$58$	0.824214	+	3.59151i	0.108225	+	0.471588i
$59$	−7.26404	+	7.26404i	−0.945698	+	0.945698i	−0.998600	−	0.0529020i	$-0.983153\pi$
$59$	−7.26404	+	7.26404i	−0.945698	+	0.945698i	0.0529020	+	0.998600i	$0.483153\pi$
$60$		0			0
$61$	0.301222	+	0.301222i	0.0385676	+	0.0385676i	0.726128	−	0.687560i	$-0.241318\pi$
$61$	0.301222	+	0.301222i	0.0385676	+	0.0385676i	−0.687560	+	0.726128i	$0.741318\pi$
$62$	11.4176	+	7.15534i	1.45004	+	0.908729i
$63$		0			0
$64$	−7.81187	−	1.72471i	−0.976484	−	0.215588i
$65$	2.18691			0.271253
$66$		0			0
$67$	6.97711	+	6.97711i	0.852389	+	0.852389i	0.990427	−	0.138038i	$-0.0440795\pi$
$67$	6.97711	+	6.97711i	0.852389	+	0.852389i	−0.138038	+	0.990427i	$0.544079\pi$
$68$	−3.77091	−	7.78318i	−0.457290	−	0.943849i
$69$		0			0
$70$	−1.20160	−	5.23595i	−0.143618	−	0.625815i
$71$		−	0.585051i		−	0.0694327i	−0.999397	−	0.0347164i	$-0.988947\pi$
$71$		−	0.585051i		−	0.0694327i	0.999397	−	0.0347164i	$-0.0110528\pi$
$72$		0			0
$73$			11.9999i			1.40448i	0.711939	+	0.702241i	$0.247817\pi$
$73$			11.9999i			1.40448i	−0.711939	+	0.702241i	$0.752183\pi$
$74$	−8.87009	+	2.03559i	−1.03113	+	0.236633i
$75$		0			0
$76$	4.98406	−	14.3526i	0.571711	−	1.64635i
$77$	−11.7249	−	11.7249i	−1.33617	−	1.33617i
$78$		0			0
$79$	12.6436			1.42252			0.711260	−	0.702929i	$-0.248125\pi$
$79$	12.6436			1.42252			0.711260	+	0.702929i	$0.248125\pi$
$80$	0.466680	+	3.97268i	0.0521765	+	0.444159i
$81$		0			0
$82$	−0.435720	+	0.695270i	−0.0481172	+	0.0767797i
$83$	11.1632	+	11.1632i	1.22532	+	1.22532i	0.965713	+	0.259610i	$0.0835941\pi$
$83$	11.1632	+	11.1632i	1.22532	+	1.22532i	0.259610	+	0.965713i	$0.416406\pi$
$84$		0			0
$85$	−3.05773	+	3.05773i	−0.331657	+	0.331657i
$86$	−1.93908	+	0.444998i	−0.209096	+	0.0479854i
$87$		0			0
$88$	7.73214	+	9.62545i	0.824249	+	1.02608i
$89$			12.9706i			1.37488i	0.726241	+	0.687440i	$0.241266\pi$
$89$			12.9706i			1.37488i	−0.726241	+	0.687440i	$0.758734\pi$
$90$		0			0
$91$	−5.87409	+	5.87409i	−0.615772	+	0.615772i
$92$	−7.03858	+	3.41016i	−0.733822	+	0.355534i
$93$		0			0
$94$	2.66583	+	1.67065i	0.274960	+	0.172315i
$95$	−7.59666			−0.779401
$96$		0			0
$97$	−6.78553			−0.688966			−0.344483	−	0.938793i	$-0.611946\pi$
$97$	−6.78553			−0.688966			−0.344483	+	0.938793i	$0.611946\pi$
$98$	8.90303	+	5.57945i	0.899342	+	0.563610i
$99$		0			0
$100$	1.79988	−	0.872033i	0.179988	−	0.0872033i
$101$	6.19304	−	6.19304i	0.616231	−	0.616231i	−0.328332	−	0.944562i	$-0.606486\pi$
$101$	6.19304	−	6.19304i	0.616231	−	0.616231i	0.944562	+	0.328332i	$0.106486\pi$
$102$		0			0
$103$			11.3519i			1.11854i	0.828987	+	0.559269i	$0.188918\pi$
$103$			11.3519i			1.11854i	−0.828987	+	0.559269i	$0.811082\pi$
$104$	4.82230	−	3.87376i	0.472865	−	0.379853i
$105$		0			0
$106$	9.36178	−	2.14843i	0.909296	−	0.208674i
$107$	8.58488	−	8.58488i	0.829932	−	0.829932i	−0.157575	−	0.987507i	$-0.550368\pi$
$107$	8.58488	−	8.58488i	0.829932	−	0.829932i	0.987507	+	0.157575i	$0.0503677\pi$
$108$		0			0
$109$	−10.6624	−	10.6624i	−1.02127	−	1.02127i	−0.999769	−	0.0215039i	$-0.993155\pi$
$109$	−10.6624	−	10.6624i	−1.02127	−	1.02127i	−0.0215039	−	0.999769i	$-0.506845\pi$
$110$	3.27817	−	5.23091i	0.312561	−	0.498748i
$111$		0			0
$112$	−11.9242	−	9.41722i	−1.12674	−	0.889843i
$113$	3.11152			0.292707			0.146354	−	0.989232i	$-0.453246\pi$
$113$	3.11152			0.292707			0.146354	+	0.989232i	$0.453246\pi$
$114$		0			0
$115$	2.76520	+	2.76520i	0.257856	+	0.257856i
$116$	1.70949	−	4.92282i	0.158722	−	0.457072i
$117$		0			0
$118$	14.1600	−	3.24957i	1.30353	−	0.299147i
$119$		−	16.4263i		−	1.50579i
$120$		0			0
$121$		−	8.05441i		−	0.732219i
$122$	−0.134752	−	0.587181i	−0.0121999	−	0.0531609i
$123$		0			0
$124$	−8.30864	−	17.1490i	−0.746138	−	1.54003i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	−7.16390			−0.635693			−0.317846	−	0.948142i	$-0.602960\pi$
$127$	−7.16390			−0.635693			−0.317846	+	0.948142i	$0.602960\pi$
$128$	8.06604	+	7.93341i	0.712944	+	0.701221i
$129$		0			0
$130$	−2.62066	−	1.64234i	−0.229847	−	0.144043i
$131$	6.55090	+	6.55090i	0.572355	+	0.572355i	0.932786	−	0.360431i	$-0.117370\pi$
$131$	6.55090	+	6.55090i	0.572355	+	0.572355i	−0.360431	+	0.932786i	$0.617370\pi$
$132$		0			0
$133$	20.4048	−	20.4048i	1.76932	−	1.76932i
$134$	−3.12121	−	13.6007i	−0.269632	−	1.17492i
$135$		0			0
$136$	−1.32624	+	12.1588i	−0.113724	+	1.04261i
$137$		−	11.0502i		−	0.944082i	−0.881577	−	0.472041i	$-0.843518\pi$
$137$		−	11.0502i		−	0.944082i	0.881577	−	0.472041i	$-0.156482\pi$
$138$		0			0
$139$	−5.17171	+	5.17171i	−0.438659	+	0.438659i	−0.891561	−	0.452902i	$-0.850389\pi$
$139$	−5.17171	+	5.17171i	−0.438659	+	0.438659i	0.452902	+	0.891561i	$0.350389\pi$
$140$	−2.49222	+	7.17682i	−0.210631	+	0.606552i
$141$		0			0
$142$	−0.439366	+	0.701089i	−0.0368708	+	0.0588341i
$143$	−9.54615			−0.798289
$144$		0			0
$145$	−2.60559			−0.216383
$146$	9.01178	−	14.3799i	0.745821	−	1.19009i
$147$		0			0
$148$	12.1581	+	4.22200i	0.999388	+	0.347046i
$149$	5.80335	−	5.80335i	0.475429	−	0.475429i	−0.428237	−	0.903666i	$-0.640865\pi$
$149$	5.80335	−	5.80335i	0.475429	−	0.475429i	0.903666	+	0.428237i	$0.140865\pi$
$150$		0			0
$151$			13.2591i			1.07901i	0.841982	+	0.539505i	$0.181389\pi$
$151$			13.2591i			1.07901i	−0.841982	+	0.539505i	$0.818611\pi$
$152$	−16.7512	+	13.4563i	−1.35870	+	1.09145i
$153$		0			0
$154$	5.24513	+	22.8556i	0.422664	+	1.84176i
$155$	−6.73724	+	6.73724i	−0.541148	+	0.541148i
$156$		0			0
$157$	6.83329	+	6.83329i	0.545356	+	0.545356i	0.925094	−	0.379738i	$-0.123986\pi$
$157$	6.83329	+	6.83329i	0.545356	+	0.545356i	−0.379738	+	0.925094i	$0.623986\pi$
$158$	−15.1514	−	9.49522i	−1.20538	−	0.755399i
$159$		0			0
$160$	2.42420	−	5.11109i	0.191650	−	0.404067i
$161$	−14.8548			−1.17072
$162$		0			0
$163$	−7.11541	−	7.11541i	−0.557322	−	0.557322i	0.371222	−	0.928544i	$-0.378939\pi$
$163$	−7.11541	−	7.11541i	−0.557322	−	0.557322i	−0.928544	+	0.371222i	$0.878939\pi$
$164$	1.04428	−	0.505949i	0.0815445	−	0.0395080i
$165$		0			0
$166$	−4.99388	−	21.7608i	−0.387600	−	1.68896i
$167$		−	6.14029i		−	0.475150i	−0.971369	−	0.237575i	$-0.923648\pi$
$167$		−	6.14029i		−	0.475150i	0.971369	−	0.237575i	$-0.0763525\pi$
$168$		0			0
$169$		−	8.21743i		−	0.632110i
$170$	5.96051	−	1.36788i	0.457150	−	0.104911i
$171$		0			0
$172$	2.65786	+	0.922965i	0.202660	+	0.0703754i
$173$	7.29269	+	7.29269i	0.554453	+	0.554453i	0.927723	−	0.373270i	$-0.121763\pi$
$173$	7.29269	+	7.29269i	0.554453	+	0.554453i	−0.373270	+	0.927723i	$0.621763\pi$
$174$		0			0
$175$	3.79862			0.287148
$176$	−2.03712	−	17.3413i	−0.153554	−	1.30715i
$177$		0			0
$178$	9.74077	−	15.5432i	0.730101	−	1.16501i
$179$	−6.22897	−	6.22897i	−0.465575	−	0.465575i	0.434902	−	0.900478i	$-0.356783\pi$
$179$	−6.22897	−	6.22897i	−0.465575	−	0.465575i	−0.900478	+	0.434902i	$0.856783\pi$
$180$		0			0
$181$	−1.27302	+	1.27302i	−0.0946227	+	0.0946227i	−0.752834	−	0.658211i	$-0.771314\pi$
$181$	−1.27302	+	1.27302i	−0.0946227	+	0.0946227i	0.658211	+	0.752834i	$0.271314\pi$
$182$	11.4505	−	2.62778i	0.848770	−	0.194784i
$183$		0			0
$184$	10.9956	+	1.19936i	0.810606	+	0.0884182i
$185$		−	6.43514i		−	0.473121i
$186$		0			0
$187$	13.3474	−	13.3474i	0.976058	−	0.976058i
$188$	−1.93993	−	4.00402i	−0.141484	−	0.292023i
$189$		0			0
$190$	9.10337	+	5.70500i	0.660428	+	0.413885i
$191$	−9.63638			−0.697264			−0.348632	−	0.937260i	$-0.613354\pi$
$191$	−9.63638			−0.697264			−0.348632	+	0.937260i	$0.613354\pi$
$192$		0			0
$193$	−3.64530			−0.262394			−0.131197	−	0.991356i	$-0.541882\pi$
$193$	−3.64530			−0.262394			−0.131197	+	0.991356i	$0.541882\pi$
$194$	8.13137	+	5.09586i	0.583798	+	0.365861i
$195$		0			0
$196$	−6.47875	−	13.3721i	−0.462768	−	0.955153i
$197$	7.55422	−	7.55422i	0.538216	−	0.538216i	−0.384789	−	0.923005i	$-0.625726\pi$
$197$	7.55422	−	7.55422i	0.538216	−	0.538216i	0.923005	+	0.384789i	$0.125726\pi$
$198$		0			0
$199$		−	23.7442i		−	1.68318i	−0.540116	−	0.841591i	$-0.681620\pi$
$199$		−	23.7442i		−	1.68318i	0.540116	−	0.841591i	$-0.318380\pi$
$200$	−2.81175	−	0.306697i	−0.198821	−	0.0216867i
$201$		0			0
$202$	−12.0723	+	2.77046i	−0.849402	+	0.194929i
$203$	6.99870	−	6.99870i	0.491212	−	0.491212i
$204$		0			0
$205$	−0.410260	−	0.410260i	−0.0286538	−	0.0286538i
$206$	8.52516	−	13.6034i	0.593976	−	0.947797i
$207$		0			0
$208$	−8.68789	+	1.02059i	−0.602397	+	0.0707650i
$209$	33.1605			2.29376
$210$		0			0
$211$	14.5856	+	14.5856i	1.00412	+	1.00412i	0.999991	+	0.00412399i	$0.00131271\pi$
$211$	14.5856	+	14.5856i	1.00412	+	1.00412i	0.00412399	+	0.999991i	$0.498687\pi$
$212$	−12.8320	−	4.45604i	−0.881308	−	0.306042i
$213$		0			0
$214$	−16.7347	+	3.84045i	−1.14396	+	0.262528i
$215$		−	1.40678i		−	0.0959413i
$216$		0			0
$217$		−	36.1928i		−	2.45693i
$218$	4.76983	+	20.7845i	0.323054	+	1.40770i
$219$		0			0
$220$	−7.85671	+	3.80654i	−0.529699	+	0.256637i
$221$	−6.68697	−	6.68697i	−0.449814	−	0.449814i
$222$		0			0
$223$	−13.6893			−0.916702			−0.458351	−	0.888771i	$-0.651560\pi$
$223$	−13.6893			−0.916702			−0.458351	+	0.888771i	$0.651560\pi$
$224$	7.21707	+	20.2400i	0.482211	+	1.35234i
$225$		0			0
$226$	−3.72865	−	2.33671i	−0.248026	−	0.155436i
$227$	11.9490	+	11.9490i	0.793085	+	0.793085i	0.981994	−	0.188910i	$-0.0604953\pi$
$227$	11.9490	+	11.9490i	0.793085	+	0.793085i	−0.188910	+	0.981994i	$0.560495\pi$
$228$		0			0
$229$	9.40821	−	9.40821i	0.621712	−	0.621712i	−0.324257	−	0.945969i	$-0.605114\pi$
$229$	9.40821	−	9.40821i	0.621712	−	0.621712i	0.945969	+	0.324257i	$0.105114\pi$
$230$	−1.23701	−	5.39029i	−0.0815663	−	0.355425i
$231$		0			0
$232$	−5.74553	+	4.61539i	−0.377213	+	0.303016i
$233$			11.8223i			0.774505i	0.921974	+	0.387253i	$0.126576\pi$
$233$			11.8223i			0.774505i	−0.921974	+	0.387253i	$0.873424\pi$
$234$		0			0
$235$	−1.57304	+	1.57304i	−0.102614	+	0.102614i
$236$	−19.4089	−	6.73990i	−1.26341	−	0.438730i
$237$		0			0
$238$	−12.3359	+	19.6842i	−0.799621	+	1.27594i
$239$	−11.2115			−0.725213			−0.362607	−	0.931942i	$-0.618113\pi$
$239$	−11.2115			−0.725213			−0.362607	+	0.931942i	$0.618113\pi$
$240$		0			0
$241$	7.89997			0.508881			0.254441	−	0.967088i	$-0.418109\pi$
$241$	7.89997			0.508881			0.254441	+	0.967088i	$0.418109\pi$
$242$	−6.04877	+	9.65191i	−0.388830	+	0.620448i
$243$		0			0
$244$	−0.279488	+	0.804839i	−0.0178924	+	0.0515245i
$245$	−5.25343	+	5.25343i	−0.335630	+	0.335630i
$246$		0			0
$247$		−	16.6132i		−	1.05707i
$248$	−2.92217	+	26.7901i	−0.185558	+	1.70117i
$249$		0			0
$250$	0.316325	+	1.37838i	0.0200061	+	0.0871766i
$251$	5.34286	−	5.34286i	0.337238	−	0.337238i	−0.518089	−	0.855327i	$-0.673356\pi$
$251$	5.34286	−	5.34286i	0.337238	−	0.337238i	0.855327	+	0.518089i	$0.173356\pi$
$252$		0			0
$253$	−12.0705	−	12.0705i	−0.758865	−	0.758865i
$254$	8.58477	+	5.38000i	0.538657	+	0.337571i
$255$		0			0
$256$	−3.70795	−	15.5644i	−0.231747	−	0.972776i
$257$	−15.5250			−0.968420			−0.484210	−	0.874952i	$-0.660893\pi$
$257$	−15.5250			−0.968420			−0.484210	+	0.874952i	$0.660893\pi$
$258$		0			0
$259$	17.2850	+	17.2850i	1.07404	+	1.07404i
$260$	1.90706	+	3.93617i	0.118271	+	0.244111i
$261$		0			0
$262$	−2.93055	−	12.7698i	−0.181050	−	0.788924i
$263$		−	14.3705i		−	0.886126i	−0.896491	−	0.443063i	$-0.853892\pi$
$263$		−	14.3705i		−	0.886126i	0.896491	−	0.443063i	$-0.146108\pi$
$264$		0			0
$265$			6.79186i			0.417221i
$266$	−39.7757	+	9.12811i	−2.43880	+	0.559680i
$267$		0			0
$268$	−6.47367	+	18.6422i	−0.395443	+	1.13875i
$269$	19.0607	+	19.0607i	1.16215	+	1.16215i	0.984004	+	0.178145i	$0.0570098\pi$
$269$	19.0607	+	19.0607i	1.16215	+	1.16215i	0.178145	+	0.984004i	$0.442990\pi$
$270$		0			0
$271$	−4.66889			−0.283615			−0.141808	−	0.989894i	$-0.545291\pi$
$271$	−4.66889			−0.283615			−0.141808	+	0.989894i	$0.545291\pi$
$272$	10.7204	−	13.5744i	0.650020	−	0.823067i
$273$		0			0
$274$	−8.29857	+	13.2419i	−0.501335	+	0.799971i
$275$	3.08662	+	3.08662i	0.186130	+	0.186130i
$276$		0			0
$277$	−6.24572	+	6.24572i	−0.375269	+	0.375269i	−0.869392	−	0.494123i	$-0.835489\pi$
$277$	−6.24572	+	6.24572i	−0.375269	+	0.375269i	0.494123	+	0.869392i	$0.335489\pi$
$278$	10.0814	−	2.31357i	0.604640	−	0.138759i
$279$		0			0
$280$	8.37623	−	6.72864i	0.500575	−	0.402113i
$281$			29.7389i			1.77407i	0.461699	+	0.887037i	$0.347240\pi$
$281$			29.7389i			1.77407i	−0.461699	+	0.887037i	$0.652760\pi$
$282$		0			0
$283$	−9.49040	+	9.49040i	−0.564146	+	0.564146i	−0.930482	−	0.366337i	$-0.880612\pi$
$283$	−9.49040	+	9.49040i	−0.564146	+	0.564146i	0.366337	+	0.930482i	$0.380612\pi$
$284$	1.05302	−	0.510183i	0.0624852	−	0.0302738i
$285$		0			0
$286$	11.4395	+	7.16905i	0.676433	+	0.423915i
$287$	2.20394			0.130094
$288$		0			0
$289$	1.69940			0.0999648
$290$	3.12239	+	1.95677i	0.183353	+	0.114906i
$291$		0			0
$292$	−21.5983	+	10.4643i	−1.26395	+	0.612377i
$293$	1.72797	−	1.72797i	0.100949	−	0.100949i	−0.654829	−	0.755777i	$-0.727259\pi$
$293$	1.72797	−	1.72797i	0.100949	−	0.100949i	0.755777	+	0.654829i	$0.227259\pi$
$294$		0			0
$295$			10.2729i			0.598112i
$296$	−11.3988	−	14.1900i	−0.662543	−	0.824775i
$297$		0			0
$298$	−11.3126	+	2.59613i	−0.655323	+	0.150390i
$299$	−6.04724	+	6.04724i	−0.349721	+	0.349721i
$300$		0			0
$301$	3.77864	+	3.77864i	0.217797	+	0.217797i
$302$	9.95743	−	15.8889i	0.572986	−	0.914304i
$303$		0			0
$304$	30.1791	−	3.54521i	1.73089	−	0.203332i
$305$	0.425993			0.0243923
$306$		0			0
$307$	17.5875	+	17.5875i	1.00377	+	1.00377i	0.999993	+	0.00377977i	$0.00120314\pi$
$307$	17.5875	+	17.5875i	1.00377	+	1.00377i	0.00377977	+	0.999993i	$0.498797\pi$
$308$	10.8789	−	31.3278i	0.619881	−	1.78507i
$309$		0			0
$310$	13.1331	−	3.01391i	0.745909	−	0.171178i
$311$			1.71809i			0.0974241i	0.998813	+	0.0487120i	$0.0155117\pi$
$311$			1.71809i			0.0974241i	−0.998813	+	0.0487120i	$0.984488\pi$
$312$		0			0
$313$			16.4421i			0.929363i	0.885478	+	0.464682i	$0.153831\pi$
$313$			16.4421i			0.929363i	−0.885478	+	0.464682i	$0.846169\pi$
$314$	−3.05687	−	13.3203i	−0.172509	−	0.751709i
$315$		0			0
$316$	11.0257	+	22.7570i	0.620242	+	1.28018i
$317$	7.96065	+	7.96065i	0.447114	+	0.447114i	0.894394	−	0.447280i	$-0.147607\pi$
$317$	7.96065	+	7.96065i	0.447114	+	0.447114i	−0.447280	+	0.894394i	$0.647607\pi$
$318$		0			0
$319$	11.3738			0.636809
$320$	−6.74338	+	4.30428i	−0.376967	+	0.240616i
$321$		0			0
$322$	17.8011	+	11.1558i	0.992017	+	0.621688i
$323$	23.2285	+	23.2285i	1.29247	+	1.29247i
$324$		0			0
$325$	1.54638	−	1.54638i	0.0857776	−	0.0857776i
$326$	3.18308	+	13.8703i	0.176295	+	0.768203i
$327$		0			0
$328$	−1.63136	−	0.177944i	−0.0900769	−	0.00982530i
$329$		−	8.45043i		−	0.465887i
$330$		0			0
$331$	9.02535	−	9.02535i	0.496078	−	0.496078i	−0.414137	−	0.910215i	$-0.635916\pi$
$331$	9.02535	−	9.02535i	0.496078	−	0.496078i	0.910215	+	0.414137i	$0.135916\pi$
$332$	−10.3577	+	29.8271i	−0.568455	+	1.63698i
$333$		0			0
$334$	−4.61128	+	7.35814i	−0.252318	+	0.402620i
$335$	9.86712			0.539098
$336$		0			0
$337$	7.44173			0.405377			0.202688	−	0.979243i	$-0.435032\pi$
$337$	7.44173			0.405377			0.202688	+	0.979243i	$0.435032\pi$
$338$	−6.17120	+	9.84727i	−0.335669	+	0.535621i
$339$		0			0
$340$	−8.16997	−	2.83710i	−0.443079	−	0.153863i
$341$	29.4090	−	29.4090i	1.59258	−	1.59258i
$342$		0			0
$343$		−	1.63142i		−	0.0880882i
$344$	−2.49188	−	3.10205i	−0.134353	−	0.167251i
$345$		0			0
$346$	−3.26239	−	14.2158i	−0.175387	−	0.764249i
$347$	0.659315	−	0.659315i	0.0353939	−	0.0353939i	−0.689188	−	0.724582i	$-0.742033\pi$
$347$	0.659315	−	0.659315i	0.0353939	−	0.0353939i	0.724582	+	0.689188i	$0.242033\pi$
$348$		0			0
$349$	8.04705	+	8.04705i	0.430749	+	0.430749i	0.888883	−	0.458134i	$-0.151482\pi$
$349$	8.04705	+	8.04705i	0.430749	+	0.430749i	−0.458134	+	0.888883i	$0.651482\pi$
$350$	−4.55203	−	2.85272i	−0.243316	−	0.152484i
$351$		0			0
$352$	−10.5820	+	22.3106i	−0.564020	+	1.18916i
$353$	−18.3339			−0.975815			−0.487907	−	0.872895i	$-0.662240\pi$
$353$	−18.3339			−0.975815			−0.487907	+	0.872895i	$0.662240\pi$
$354$		0			0
$355$	−0.413693	−	0.413693i	−0.0219566	−	0.0219566i
$356$	−23.3455	+	11.3108i	−1.23731	+	0.599470i
$357$		0			0
$358$	2.78653	+	12.1423i	0.147273	+	0.641741i
$359$			11.8783i			0.626912i	0.949603	+	0.313456i	$0.101487\pi$
$359$			11.8783i			0.626912i	−0.949603	+	0.313456i	$0.898513\pi$
$360$		0			0
$361$			38.7093i			2.03733i
$362$	2.48153	−	0.569485i	0.130426	−	0.0299315i
$363$		0			0
$364$	−15.6951	−	5.45025i	−0.822644	−	0.285671i
$365$	8.48521	+	8.48521i	0.444136	+	0.444136i
$366$		0			0
$367$	−24.0792			−1.25692			−0.628462	−	0.777841i	$-0.716315\pi$
$367$	−24.0792			−1.25692			−0.628462	+	0.777841i	$0.716315\pi$
$368$	−12.2757	−	9.69481i	−0.639917	−	0.505377i
$369$		0			0
$370$	−4.83272	+	7.71148i	−0.251241	+	0.400901i
$371$	−18.2431	−	18.2431i	−0.947135	−	0.947135i
$372$		0			0
$373$	5.50986	−	5.50986i	0.285290	−	0.285290i	−0.549925	−	0.835214i	$-0.685344\pi$
$373$	5.50986	−	5.50986i	0.285290	−	0.285290i	0.835214	+	0.549925i	$0.185344\pi$
$374$	−26.0184	+	5.97097i	−1.34538	+	0.308751i
$375$		0			0
$376$	−0.682279	+	6.25504i	−0.0351859	+	0.322579i
$377$		−	5.69820i		−	0.293472i
$378$		0			0
$379$	−4.41212	+	4.41212i	−0.226635	+	0.226635i	−0.811285	−	0.584650i	$-0.801232\pi$
$379$	−4.41212	+	4.41212i	−0.226635	+	0.226635i	0.584650	+	0.811285i	$0.301232\pi$
$380$	−6.62454	−	13.6731i	−0.339832	−	0.701413i
$381$		0			0
$382$	11.5477	+	7.23681i	0.590829	+	0.370267i
$383$	−12.4394			−0.635625			−0.317812	−	0.948154i	$-0.602948\pi$
$383$	−12.4394			−0.635625			−0.317812	+	0.948154i	$0.602948\pi$
$384$		0			0
$385$	−16.5815			−0.845070
$386$	4.36830	+	2.73757i	0.222341	+	0.139339i
$387$		0			0
$388$	−5.91720	−	12.2131i	−0.300401	−	0.620027i
$389$	22.7006	−	22.7006i	1.15097	−	1.15097i	0.164609	−	0.986359i	$-0.447364\pi$
$389$	22.7006	−	22.7006i	1.15097	−	1.15097i	0.986359	−	0.164609i	$-0.0526363\pi$
$390$		0			0
$391$		−	16.9105i		−	0.855199i
$392$	−2.27859	+	20.8898i	−0.115086	+	1.05510i
$393$		0			0
$394$	−14.7257	+	3.37939i	−0.741868	+	0.170251i
$395$	8.94040	−	8.94040i	0.449840	−	0.449840i
$396$		0			0
$397$	−23.2641	−	23.2641i	−1.16759	−	1.16759i	−0.982773	−	0.184819i	$-0.940830\pi$
$397$	−23.2641	−	23.2641i	−1.16759	−	1.16759i	−0.184819	−	0.982773i	$-0.559170\pi$
$398$	−17.8316	+	28.4536i	−0.893818	+	1.42625i
$399$		0			0
$400$	3.13910	+	2.47912i	0.156955	+	0.123956i
$401$	−31.5965			−1.57786			−0.788928	−	0.614486i	$-0.789364\pi$
$401$	−31.5965			−1.57786			−0.788928	+	0.614486i	$0.789364\pi$
$402$		0			0
$403$	−14.7337	−	14.7337i	−0.733939	−	0.733939i
$404$	16.5473	+	5.74618i	0.823257	+	0.285883i
$405$		0			0
$406$	−13.6428	+	3.13087i	−0.677078	+	0.155383i
$407$			28.0903i			1.39238i
$408$		0			0
$409$			14.4988i			0.716917i	0.933546	+	0.358459i	$0.116698\pi$
$409$			14.4988i			0.716917i	−0.933546	+	0.358459i	$0.883302\pi$
$410$	0.183530	+	0.799730i	0.00906390	+	0.0394959i
$411$		0			0
$412$	−20.4321	+	9.89924i	−1.00661	+	0.487700i
$413$	−27.5933	−	27.5933i	−1.35778	−	1.35778i
$414$		0			0
$415$	15.7872			0.774963
$416$	11.1775	+	5.30150i	0.548022	+	0.259927i
$417$		0			0
$418$	−39.7375	−	24.9031i	−1.94362	−	1.21805i
$419$	−24.0709	−	24.0709i	−1.17594	−	1.17594i	−0.980770	−	0.195169i	$-0.937475\pi$
$419$	−24.0709	−	24.0709i	−1.17594	−	1.17594i	−0.195169	−	0.980770i	$-0.562525\pi$
$420$		0			0
$421$	−20.1095	+	20.1095i	−0.980079	+	0.980079i	−0.999805	−	0.0197268i	$-0.993720\pi$
$421$	−20.1095	+	20.1095i	−0.980079	+	0.980079i	0.0197268	+	0.999805i	$0.493720\pi$
$422$	−6.52488	−	28.4321i	−0.317626	−	1.38406i
$423$		0			0
$424$	12.0307	+	14.9766i	0.584262	+	0.727326i
$425$			4.32428i			0.209758i
$426$		0			0
$427$	−1.14423	+	1.14423i	−0.0553730	+	0.0553730i
$428$	22.9380	+	7.96544i	1.10875	+	0.385024i
$429$		0			0
$430$	−1.05647	+	1.68579i	−0.0509476	+	0.0812962i
$431$	29.9026			1.44036			0.720180	−	0.693787i	$-0.244059\pi$
$431$	29.9026			1.44036			0.720180	+	0.693787i	$0.244059\pi$
$432$		0			0
$433$	17.7487			0.852950			0.426475	−	0.904499i	$-0.359755\pi$
$433$	17.7487			0.852950			0.426475	+	0.904499i	$0.359755\pi$
$434$	−27.1804	+	43.3713i	−1.30470	+	2.08189i
$435$		0			0
$436$	9.89305	−	28.4890i	0.473791	−	1.36437i
$437$	21.0063	−	21.0063i	1.00487	−	1.00487i
$438$		0			0
$439$			15.1376i			0.722478i	0.932473	+	0.361239i	$0.117646\pi$
$439$			15.1376i			0.722478i	−0.932473	+	0.361239i	$0.882354\pi$
$440$	12.2737	+	1.33877i	0.585124	+	0.0638234i
$441$		0			0
$442$	2.99142	+	13.0351i	0.142287	+	0.620016i
$443$	16.4687	−	16.4687i	0.782451	−	0.782451i	−0.197793	−	0.980244i	$-0.563377\pi$
$443$	16.4687	−	16.4687i	0.782451	−	0.782451i	0.980244	+	0.197793i	$0.0633773\pi$
$444$		0			0
$445$	9.17160	+	9.17160i	0.434775	+	0.434775i
$446$	16.4044	+	10.2805i	0.776771	+	0.486795i
$447$		0			0
$448$	6.55150	−	29.6743i	0.309529	−	1.40198i
$449$	−35.6078			−1.68044			−0.840218	−	0.542249i	$-0.817573\pi$
$449$	−35.6078			−1.68044			−0.840218	+	0.542249i	$0.817573\pi$
$450$		0			0
$451$	1.79084	+	1.79084i	0.0843273	+	0.0843273i
$452$	2.71335	+	5.60035i	0.127625	+	0.263418i
$453$		0			0
$454$	−5.34540	−	23.2926i	−0.250872	−	1.09317i
$455$			8.30722i			0.389449i
$456$		0			0
$457$			1.98064i			0.0926502i	0.998926	+	0.0463251i	$0.0147510\pi$
$457$			1.98064i			0.0926502i	−0.998926	+	0.0463251i	$0.985249\pi$
$458$	−18.3397	+	4.20877i	−0.856957	+	0.196663i
$459$		0			0
$460$	−2.56568	+	7.38837i	−0.119625	+	0.344485i
$461$	4.13532	+	4.13532i	0.192601	+	0.192601i	0.796819	−	0.604218i	$-0.206514\pi$
$461$	4.13532	+	4.13532i	0.192601	+	0.192601i	−0.604218	+	0.796819i	$0.706514\pi$
$462$		0			0
$463$	23.4228			1.08855			0.544274	−	0.838907i	$-0.316805\pi$
$463$	23.4228			1.08855			0.544274	+	0.838907i	$0.316805\pi$
$464$	10.3512	−	1.21598i	0.480542	−	0.0564505i
$465$		0			0
$466$	8.87842	−	14.1671i	0.411285	−	0.656280i
$467$	4.20786	+	4.20786i	0.194717	+	0.194717i	0.797731	−	0.603014i	$-0.206034\pi$
$467$	4.20786	+	4.20786i	0.194717	+	0.194717i	−0.603014	+	0.797731i	$0.706034\pi$
$468$		0			0
$469$	−26.5033	+	26.5033i	−1.22381	+	1.22381i
$470$	3.06636	−	0.703698i	0.141441	−	0.0324592i
$471$		0			0
$472$	18.1968	+	22.6525i	0.837576	+	1.04267i
$473$			6.14077i			0.282353i
$474$		0			0
$475$	−5.37165	+	5.37165i	−0.246468	+	0.246468i
$476$	29.5653	−	14.3242i	1.35512	−	0.656551i
$477$		0			0
$478$	13.4352	+	8.41973i	0.614512	+	0.385109i
$479$	−5.52216			−0.252314			−0.126157	−	0.992010i	$-0.540264\pi$
$479$	−5.52216			−0.252314			−0.126157	+	0.992010i	$0.540264\pi$
$480$		0			0
$481$	14.0731			0.641676
$482$	−9.46684	−	5.93278i	−0.431203	−	0.270231i
$483$		0			0
$484$	14.4970	−	7.02371i	0.658952	−	0.319259i
$485$	−4.79809	+	4.79809i	−0.217870	+	0.217870i
$486$		0			0
$487$		−	28.0612i		−	1.27158i	−0.771864	−	0.635788i	$-0.780675\pi$
$487$		−	28.0612i		−	1.27158i	0.771864	−	0.635788i	$-0.219325\pi$
$488$	0.939345	−	0.754578i	0.0425222	−	0.0341581i
$489$		0			0
$490$	10.2407	−	2.35013i	0.462626	−	0.106168i
$491$	1.27407	−	1.27407i	0.0574979	−	0.0574979i	−0.677773	−	0.735271i	$-0.737055\pi$
$491$	1.27407	−	1.27407i	0.0574979	−	0.0574979i	0.735271	+	0.677773i	$0.237055\pi$
$492$		0			0
$493$	7.96720	+	7.96720i	0.358825	+	0.358825i
$494$	−12.4763	+	19.9082i	−0.561336	+	0.895714i
$495$		0			0
$496$	23.6208	−	29.9091i	1.06060	−	1.34296i
$497$	2.22238			0.0996875
$498$		0			0
$499$	−26.3351	−	26.3351i	−1.17892	−	1.17892i	−0.980020	−	0.198901i	$-0.936263\pi$
$499$	−26.3351	−	26.3351i	−1.17892	−	1.17892i	−0.198901	−	0.980020i	$-0.563737\pi$
$500$	0.656085	−	1.88933i	0.0293410	−	0.0844932i
$501$		0			0
$502$	−10.4150	+	2.39013i	−0.464843	+	0.106677i
$503$		−	33.2293i		−	1.48162i	−0.671715	−	0.740810i	$-0.734442\pi$
$503$		−	33.2293i		−	1.48162i	0.671715	−	0.740810i	$-0.265558\pi$
$504$		0			0
$505$		−	8.75828i		−	0.389739i
$506$	5.39974	+	23.5293i	0.240048	+	1.04601i
$507$		0			0
$508$	−6.24715	−	12.8941i	−0.277172	−	0.572085i
$509$	5.03424	+	5.03424i	0.223139	+	0.223139i	0.809819	−	0.586680i	$-0.199565\pi$
$509$	5.03424	+	5.03424i	0.223139	+	0.223139i	−0.586680	+	0.809819i	$0.699565\pi$
$510$		0			0
$511$	−45.5830			−2.01647
$512$	−7.24532	+	21.4361i	−0.320201	+	0.947350i
$513$		0			0
$514$	18.6042	+	11.6591i	0.820594	+	0.514259i
$515$	8.02701	+	8.02701i	0.353713	+	0.353713i
$516$		0			0
$517$	6.86651	−	6.86651i	0.301989	−	0.301989i
$518$	−7.73244	−	33.6940i	−0.339744	−	1.48043i
$519$		0			0
$520$	0.670717	−	6.14904i	0.0294129	−	0.269653i
$521$			29.6023i			1.29690i	0.761257	+	0.648450i	$0.224582\pi$
$521$			29.6023i			1.29690i	−0.761257	+	0.648450i	$0.775418\pi$
$522$		0			0
$523$	6.90122	−	6.90122i	0.301769	−	0.301769i	−0.539937	−	0.841706i	$-0.681552\pi$
$523$	6.90122	−	6.90122i	0.301769	−	0.301769i	0.841706	+	0.539937i	$0.181552\pi$
$524$	−6.07822	+	17.5034i	−0.265528	+	0.764640i
$525$		0			0
$526$	−10.7921	+	17.2208i	−0.470559	+	0.750862i
$527$	41.2013			1.79476
$528$		0			0
$529$	7.70731			0.335100
$530$	5.10061	−	8.13895i	0.221556	−	0.353533i
$531$		0			0
$532$	54.5199	+	18.9325i	2.36374	+	0.820829i
$533$	0.897200	−	0.897200i	0.0388621	−	0.0388621i
$534$		0			0
$535$		−	12.1409i		−	0.524895i
$536$	21.7577	−	17.4780i	0.939791	−	0.754936i
$537$		0			0
$538$	−8.52680	−	37.1555i	−0.367617	−	1.60189i
$539$	22.9319	−	22.9319i	0.987749	−	0.987749i
$540$		0			0
$541$	−7.18248	−	7.18248i	−0.308799	−	0.308799i	0.535645	−	0.844443i	$-0.320069\pi$
$541$	−7.18248	−	7.18248i	−0.308799	−	0.308799i	−0.844443	+	0.535645i	$0.820069\pi$
$542$	5.59492	+	3.50628i	0.240322	+	0.150608i
$543$		0			0
$544$	−23.0409	+	8.21579i	−0.987869	+	0.352249i
$545$	−15.0789			−0.645910
$546$		0			0
$547$	−14.9525	−	14.9525i	−0.639323	−	0.639323i	0.311066	−	0.950388i	$-0.399314\pi$
$547$	−14.9525	−	14.9525i	−0.639323	−	0.639323i	−0.950388	+	0.311066i	$0.899314\pi$
$548$	19.8890	−	9.63613i	0.849616	−	0.411635i
$549$		0			0
$550$	−1.38080	−	6.01683i	−0.0588775	−	0.256558i
$551$			19.7938i			0.843245i
$552$		0			0
$553$			48.0283i			2.04237i
$554$	12.1749	−	2.79402i	0.517264	−	0.118707i
$555$		0			0
$556$	−13.8184	−	4.79855i	−0.586029	−	0.203504i
$557$	−24.8706	−	24.8706i	−1.05380	−	1.05380i	−0.998468	−	0.0553344i	$-0.982378\pi$
$557$	−24.8706	−	24.8706i	−1.05380	−	1.05380i	−0.0553344	−	0.998468i	$-0.517622\pi$
$558$		0			0
$559$	3.07649			0.130122
$560$	−15.0907	+	1.77274i	−0.637698	+	0.0749119i
$561$		0			0
$562$	22.3336	−	35.6373i	0.942085	−	1.50327i
$563$	−11.1111	−	11.1111i	−0.468277	−	0.468277i	0.433079	−	0.901356i	$-0.357427\pi$
$563$	−11.1111	−	11.1111i	−0.468277	−	0.468277i	−0.901356	+	0.433079i	$0.857427\pi$
$564$		0			0
$565$	2.20018	−	2.20018i	0.0925621	−	0.0925621i
$566$	18.4999	−	4.24554i	0.777609	−	0.178453i
$567$		0			0
$568$	−1.64502	−	0.179433i	−0.0690233	−	0.00752884i
$569$			12.9347i			0.542250i	0.962544	+	0.271125i	$0.0873956\pi$
$569$			12.9347i			0.542250i	−0.962544	+	0.271125i	$0.912604\pi$
$570$		0			0
$571$	−14.5979	+	14.5979i	−0.610903	+	0.610903i	−0.943181	−	0.332278i	$-0.892183\pi$
$571$	−14.5979	+	14.5979i	−0.610903	+	0.610903i	0.332278	+	0.943181i	$0.392183\pi$
$572$	−8.32456	−	17.1819i	−0.348067	−	0.718411i
$573$		0			0
$574$	−2.64106	−	1.65513i	−0.110236	−	0.0690838i
$575$	3.91059			0.163083
$576$		0			0
$577$	15.7906			0.657373			0.328687	−	0.944439i	$-0.393394\pi$
$577$	15.7906			0.657373			0.328687	+	0.944439i	$0.393394\pi$
$578$	−2.03646	−	1.27623i	−0.0847055	−	0.0530842i
$579$		0			0
$580$	−2.27216	−	4.68975i	−0.0943465	−	0.194731i
$581$	−42.4048	+	42.4048i	−1.75925	+	1.75925i
$582$		0			0
$583$		−	29.6474i		−	1.22787i
$584$	33.7407	+	3.68033i	1.39620	+	0.152293i
$585$		0			0
$586$	−3.36837	+	0.773006i	−0.139146	+	0.0319326i
$587$	−13.9365	+	13.9365i	−0.575221	+	0.575221i	−0.933583	−	0.358362i	$-0.883335\pi$
$587$	−13.9365	+	13.9365i	−0.575221	+	0.575221i	0.358362	+	0.933583i	$0.383335\pi$
$588$		0			0
$589$	51.1805	+	51.1805i	2.10886	+	2.10886i
$590$	7.71483	−	12.3104i	0.317615	−	0.506812i
$591$		0			0
$592$	3.00315	+	25.5648i	0.123429	+	1.05071i
$593$	47.4176			1.94721			0.973604	−	0.228242i	$-0.0732979\pi$
$593$	47.4176			1.94721			0.973604	+	0.228242i	$0.0732979\pi$
$594$		0			0
$595$	−11.6151	−	11.6151i	−0.476174	−	0.476174i
$596$	15.5060	+	5.38461i	0.635152	+	0.220562i
$597$		0			0
$598$	11.7881	−	2.70524i	0.482050	−	0.110625i
$599$		−	23.5791i		−	0.963415i	−0.876332	−	0.481707i	$-0.840017\pi$
$599$		−	23.5791i		−	0.963415i	0.876332	−	0.481707i	$-0.159983\pi$
$600$		0			0
$601$			3.86582i			0.157690i	0.996887	+	0.0788450i	$0.0251232\pi$
$601$			3.86582i			0.157690i	−0.996887	+	0.0788450i	$0.974877\pi$
$602$	−1.69038	−	7.36580i	−0.0688946	−	0.300208i
$603$		0			0
$604$	−23.8648	+	11.5624i	−0.971043	+	0.470466i
$605$	−5.69533	−	5.69533i	−0.231548	−	0.231548i
$606$		0			0
$607$	32.4306			1.31632			0.658159	−	0.752879i	$-0.271335\pi$
$607$	32.4306			1.31632			0.658159	+	0.752879i	$0.271335\pi$
$608$	−38.8272	−	18.4158i	−1.57465	−	0.746860i
$609$		0			0
$610$	−0.510484	−	0.319916i	−0.0206689	−	0.0129530i
$611$	−3.44008	−	3.44008i	−0.139171	−	0.139171i
$612$		0			0
$613$	21.7952	−	21.7952i	0.880298	−	0.880298i	−0.113267	−	0.993565i	$-0.536131\pi$
$613$	21.7952	−	21.7952i	0.880298	−	0.880298i	0.993565	+	0.113267i	$0.0361314\pi$
$614$	−7.86779	−	34.2838i	−0.317518	−	1.38358i
$615$		0			0
$616$	−36.5634	+	29.3714i	−1.47318	+	1.18341i
$617$			1.49837i			0.0603219i	0.999545	+	0.0301610i	$0.00960199\pi$
$617$			1.49837i			0.0603219i	−0.999545	+	0.0301610i	$0.990398\pi$
$618$		0			0
$619$	16.7004	−	16.7004i	0.671246	−	0.671246i	−0.286757	−	0.958003i	$-0.592577\pi$
$619$	16.7004	−	16.7004i	0.671246	−	0.671246i	0.958003	+	0.286757i	$0.0925772\pi$
$620$	−18.0013	−	6.25111i	−0.722950	−	0.251051i
$621$		0			0
$622$	1.29027	−	2.05886i	0.0517350	−	0.0825526i
$623$	−49.2703			−1.97397
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	12.3478	−	19.7032i	0.493519	−	0.787499i
$627$		0			0
$628$	−6.34023	+	18.2579i	−0.253003	+	0.728571i
$629$	−19.6769	+	19.6769i	−0.784570	+	0.784570i
$630$		0			0
$631$		−	28.6304i		−	1.13976i	−0.821729	−	0.569878i	$-0.806990\pi$
$631$		−	28.6304i		−	1.13976i	0.821729	−	0.569878i	$-0.193010\pi$
$632$	3.87776	−	35.5507i	0.154249	−	1.41413i
$633$		0			0
$634$	−3.56120	−	15.5179i	−0.141433	−	0.616295i
$635$	−5.06564	+	5.06564i	−0.201024	+	0.201024i
$636$		0			0
$637$	−11.4888	−	11.4888i	−0.455202	−	0.455202i
$638$	−13.6296	−	8.54157i	−0.539603	−	0.338164i
$639$		0			0
$640$	11.3133	−	0.0937806i	0.447198	−	0.00370700i
$641$	47.4097			1.87257			0.936286	−	0.351239i	$-0.114240\pi$
$641$	47.4097			1.87257			0.936286	+	0.351239i	$0.114240\pi$
$642$		0			0
$643$	22.0744	+	22.0744i	0.870528	+	0.870528i	0.992530	−	0.122002i	$-0.0389314\pi$
$643$	22.0744	+	22.0744i	0.870528	+	0.870528i	−0.122002	+	0.992530i	$0.538931\pi$
$644$	−12.9539	−	26.7368i	−0.510455	−	1.05358i
$645$		0			0
$646$	−10.3913	−	45.2800i	−0.408840	−	1.78152i
$647$			28.8171i			1.13292i	0.824090	+	0.566459i	$0.191687\pi$
$647$			28.8171i			1.13292i	−0.824090	+	0.566459i	$0.808313\pi$
$648$		0			0
$649$		−	44.8426i		−	1.76023i
$650$	−3.01440	+	0.691773i	−0.118234	+	0.0271336i
$651$		0			0
$652$	6.60200	−	19.0117i	0.258554	−	0.744557i
$653$	25.1198	+	25.1198i	0.983015	+	0.983015i	0.999858	−	0.0168430i	$-0.00536155\pi$
$653$	25.1198	+	25.1198i	0.983015	+	0.983015i	−0.0168430	+	0.999858i	$0.505362\pi$
$654$		0			0
$655$	9.26437			0.361989
$656$	1.82129	+	1.43837i	0.0711095	+	0.0561590i
$657$		0			0
$658$	−6.34617	+	10.1265i	−0.247400	+	0.394771i
$659$	−11.3103	−	11.3103i	−0.440585	−	0.440585i	0.451623	−	0.892209i	$-0.350845\pi$
$659$	−11.3103	−	11.3103i	−0.440585	−	0.440585i	−0.892209	+	0.451623i	$0.850845\pi$
$660$		0			0
$661$	−19.4036	+	19.4036i	−0.754713	+	0.754713i	−0.975355	−	0.220642i	$-0.929185\pi$
$661$	−19.4036	+	19.4036i	−0.754713	+	0.754713i	0.220642	+	0.975355i	$0.429185\pi$
$662$	−17.5934	+	4.03749i	−0.683785	+	0.156922i
$663$		0			0
$664$	34.8119	−	27.9645i	1.35097	−	1.08523i
$665$		−	28.8568i		−	1.11902i
$666$		0			0
$667$	7.20500	−	7.20500i	0.278979	−	0.278979i
$668$	11.0518	−	5.35453i	0.427606	−	0.207173i
$669$		0			0
$670$	−11.8242	−	7.41009i	−0.456807	−	0.286277i
$671$	−1.85952			−0.0717858
$672$		0			0
$673$	−6.76645			−0.260827			−0.130414	−	0.991460i	$-0.541631\pi$
$673$	−6.76645			−0.260827			−0.130414	+	0.991460i	$0.541631\pi$
$674$	−8.91772	−	5.58865i	−0.343498	−	0.215267i
$675$		0			0
$676$	14.7904	−	7.16587i	0.568860	−	0.275610i
$677$	2.12216	−	2.12216i	0.0815613	−	0.0815613i	−0.665149	−	0.746710i	$-0.731632\pi$
$677$	2.12216	−	2.12216i	0.0815613	−	0.0815613i	0.746710	+	0.665149i	$0.231632\pi$
$678$		0			0
$679$		−	25.7756i		−	0.989177i
$680$	7.65977	+	9.53536i	0.293739	+	0.365664i
$681$		0			0
$682$	−57.3277	+	13.1561i	−2.19519	+	0.503774i
$683$	−16.9525	+	16.9525i	−0.648669	+	0.648669i	−0.952671	−	0.304002i	$-0.901677\pi$
$683$	−16.9525	+	16.9525i	−0.648669	+	0.648669i	0.304002	+	0.952671i	$0.401677\pi$
$684$		0			0
$685$	−7.81367	−	7.81367i	−0.298545	−	0.298545i
$686$	−1.22517	+	1.95499i	−0.0467774	+	0.0746419i
$687$		0			0
$688$	0.656515	+	5.58867i	0.0250294	+	0.213066i
$689$	−14.8532			−0.565861
$690$		0			0
$691$	18.4439	+	18.4439i	0.701640	+	0.701640i	0.964763	−	0.263122i	$-0.0847523\pi$
$691$	18.4439	+	18.4439i	0.701640	+	0.701640i	−0.263122	+	0.964763i	$0.584752\pi$
$692$	−6.76649	+	19.4854i	−0.257223	+	0.740725i
$693$		0			0
$694$	−1.28522	+	0.294945i	−0.0487863	+	0.0111960i
$695$			7.31391i			0.277432i
$696$		0			0
$697$			2.50893i			0.0950323i
$698$	−3.59985	−	15.6863i	−0.136256	−	0.593737i
$699$		0			0
$700$	3.31252	+	6.83704i	0.125201	+	0.258416i
$701$	−6.59102	−	6.59102i	−0.248940	−	0.248940i	0.571596	−	0.820535i	$-0.306325\pi$
$701$	−6.59102	−	6.59102i	−0.248940	−	0.248940i	−0.820535	+	0.571596i	$0.806325\pi$
$702$		0			0
$703$	−48.8856			−1.84375
$704$	29.4358	−	18.7888i	1.10940	−	0.708128i
$705$		0			0
$706$	21.9702	+	13.7685i	0.826860	+	0.518186i
$707$	23.5250	+	23.5250i	0.884748	+	0.884748i
$708$		0			0
$709$	−12.7715	+	12.7715i	−0.479642	+	0.479642i	−0.905017	−	0.425375i	$-0.860142\pi$
$709$	−12.7715	+	12.7715i	−0.479642	+	0.479642i	0.425375	+	0.905017i	$0.360142\pi$
$710$	0.185066	+	0.806424i	0.00694540	+	0.0302645i
$711$		0			0
$712$	36.4701	+	3.97804i	1.36677	+	0.149083i
$713$		−	37.2597i		−	1.39539i
$714$		0			0
$715$	−6.75015	+	6.75015i	−0.252441	+	0.252441i
$716$	5.77952	−	16.6432i	0.215991	−	0.621987i
$717$		0			0
$718$	8.92046	−	14.2342i	0.332908	−	0.531216i
$719$	−17.1105			−0.638115			−0.319057	−	0.947735i	$-0.603366\pi$
$719$	−17.1105			−0.638115			−0.319057	+	0.947735i	$0.603366\pi$
$720$		0			0
$721$	−43.1215			−1.60593
$722$	29.0702	−	46.3868i	1.08188	−	1.72634i
$723$		0			0
$724$	−3.40139	−	1.18116i	−0.126412	−	0.0438976i
$725$	−1.84243	+	1.84243i	−0.0684263	+	0.0684263i
$726$		0			0
$727$			43.9133i			1.62865i	0.580407	+	0.814327i	$0.302893\pi$
$727$			43.9133i			1.62865i	−0.580407	+	0.814327i	$0.697107\pi$
$728$	14.7149	+	18.3180i	0.545371	+	0.678912i
$729$		0			0
$730$	−3.79586	−	16.5405i	−0.140491	−	0.612190i
$731$	−4.30154	+	4.30154i	−0.159098	+	0.159098i
$732$		0			0
$733$	−16.5301	−	16.5301i	−0.610553	−	0.610553i	0.332537	−	0.943090i	$-0.392095\pi$
$733$	−16.5301	−	16.5301i	−0.610553	−	0.610553i	−0.943090	+	0.332537i	$0.892095\pi$
$734$	28.8550	+	18.0832i	1.06506	+	0.667463i
$735$		0			0
$736$	7.42981	+	20.8366i	0.273866	+	0.768047i
$737$	−43.0713			−1.58655
$738$		0			0
$739$	−17.2689	−	17.2689i	−0.635246	−	0.635246i	0.314133	−	0.949379i	$-0.398286\pi$
$739$	−17.2689	−	17.2689i	−0.635246	−	0.635246i	−0.949379	+	0.314133i	$0.898286\pi$
$740$	11.5825	−	5.61165i	0.425780	−	0.206288i
$741$		0			0
$742$	8.16107	+	35.5618i	0.299602	+	1.30551i
$743$		−	20.9862i		−	0.769909i	−0.922936	−	0.384955i	$-0.874217\pi$
$743$		−	20.9862i		−	0.769909i	0.922936	−	0.384955i	$-0.125783\pi$
$744$		0			0
$745$		−	8.20718i		−	0.300688i
$746$	−10.7405	+	2.46484i	−0.393239	+	0.0902442i
$747$		0			0
$748$	35.6630	+	12.3843i	1.30397	+	0.452815i
$749$	32.6107	+	32.6107i	1.19157	+	1.19157i
$750$		0			0
$751$	−1.64813			−0.0601413			−0.0300706	−	0.999548i	$-0.509573\pi$
$751$	−1.64813			−0.0601413			−0.0300706	+	0.999548i	$0.509573\pi$
$752$	5.51507	−	6.98327i	0.201114	−	0.254654i
$753$		0			0
$754$	−4.27928	+	6.82837i	−0.155842	+	0.248675i
$755$	9.37560	+	9.37560i	0.341213	+	0.341213i
$756$		0			0
$757$	2.50864	−	2.50864i	0.0911779	−	0.0911779i	−0.660047	−	0.751225i	$-0.729464\pi$
$757$	2.50864	−	2.50864i	0.0911779	−	0.0911779i	0.751225	+	0.660047i	$0.229464\pi$
$758$	8.60066	−	1.97376i	0.312390	−	0.0716903i
$759$		0			0
$760$	−2.32987	+	21.3599i	−0.0845132	+	0.774805i
$761$			19.9555i			0.723387i	0.932297	+	0.361693i	$0.117801\pi$
$761$			19.9555i			0.723387i	−0.932297	+	0.361693i	$0.882199\pi$
$762$		0			0
$763$	40.5024	−	40.5024i	1.46628	−	1.46628i
$764$	−8.40324	−	17.3443i	−0.304019	−	0.627495i
$765$		0			0
$766$	14.9066	+	9.34187i	0.538599	+	0.337535i
$767$	−22.4659			−0.811197
$768$		0			0
$769$	28.8082			1.03885			0.519426	−	0.854516i	$-0.326146\pi$
$769$	28.8082			1.03885			0.519426	+	0.854516i	$0.326146\pi$
$770$	19.8702	+	12.4525i	0.716073	+	0.448757i
$771$		0			0
$772$	−3.17882	−	6.56109i	−0.114408	−	0.236139i
$773$	−33.6461	+	33.6461i	−1.21017	+	1.21017i	−0.239195	+	0.970972i	$0.576884\pi$
$773$	−33.6461	+	33.6461i	−1.21017	+	1.21017i	−0.970972	+	0.239195i	$0.923116\pi$
$774$		0			0
$775$			9.52790i			0.342252i
$776$	−2.08110	+	19.0792i	−0.0747071	+	0.684904i
$777$		0			0
$778$	−44.2510	+	10.1551i	−1.58647	+	0.364080i
$779$	−3.11660	+	3.11660i	−0.111664	+	0.111664i
$780$		0			0
$781$	1.80583	+	1.80583i	0.0646176	+	0.0646176i
$782$	−12.6996	+	20.2645i	−0.454136	+	0.724656i
$783$		0			0
$784$	18.4185	−	23.3219i	0.657805	−	0.832925i
$785$	9.66373			0.344913
$786$		0			0
$787$	−11.0029	−	11.0029i	−0.392211	−	0.392211i	0.483264	−	0.875475i	$-0.339451\pi$
$787$	−11.0029	−	11.0029i	−0.392211	−	0.392211i	−0.875475	+	0.483264i	$0.839451\pi$
$788$	20.1842	+	7.00915i	0.719033	+	0.249691i
$789$		0			0
$790$	−17.4278	+	3.99949i	−0.620052	+	0.142296i
$791$			11.8195i			0.420252i
$792$		0			0
$793$			0.931607i			0.0330823i
$794$	10.4072	+	45.3493i	0.369338	+	1.60939i
$795$		0			0
$796$	42.7366	−	20.7057i	1.51476	−	0.733894i
$797$	−13.3729	−	13.3729i	−0.473692	−	0.473692i	0.429415	−	0.903107i	$-0.358720\pi$
$797$	−13.3729	−	13.3729i	−0.473692	−	0.473692i	−0.903107	+	0.429415i	$0.858720\pi$
$798$		0			0
$799$	9.61983			0.340325
$800$	−1.89992	−	5.32825i	−0.0671724	−	0.188382i
$801$		0			0
$802$	37.8634	+	23.7286i	1.33700	+	0.837887i
$803$	−37.0391	−	37.0391i	−1.30708	−	1.30708i
$804$		0			0
$805$	−10.5039	+	10.5039i	−0.370215	+	0.370215i
$806$	6.59114	+	28.7209i	0.232163	+	1.01165i
$807$		0			0
$808$	−15.5139	−	19.3127i	−0.545777	−	0.679417i
$809$		−	20.9970i		−	0.738214i	−0.929387	−	0.369107i	$-0.879664\pi$
$809$		−	20.9970i		−	0.738214i	0.929387	−	0.369107i	$-0.120336\pi$
$810$		0			0
$811$	26.7257	−	26.7257i	0.938468	−	0.938468i	−0.0597459	−	0.998214i	$-0.519029\pi$
$811$	26.7257	−	26.7257i	0.938468	−	0.938468i	0.998214	+	0.0597459i	$0.0190290\pi$
$812$	18.6999	+	6.49370i	0.656237	+	0.227884i
$813$		0			0
$814$	21.0955	−	33.6617i	0.739396	−	1.17984i
$815$	−10.0627			−0.352481
$816$		0			0
$817$	−10.6868			−0.373884
$818$	10.8884	−	17.3744i	0.380704	−	0.607482i
$819$		0			0
$820$	0.380657	−	1.09618i	0.0132931	−	0.0382802i
$821$	9.81609	−	9.81609i	0.342584	−	0.342584i	−0.514754	−	0.857338i	$-0.672117\pi$
$821$	9.81609	−	9.81609i	0.342584	−	0.342584i	0.857338	+	0.514754i	$0.172117\pi$
$822$		0			0
$823$			23.7241i			0.826969i	0.910511	+	0.413484i	$0.135688\pi$
$823$			23.7241i			0.826969i	−0.910511	+	0.413484i	$0.864312\pi$
$824$	31.9187	+	3.48159i	1.11194	+	0.121287i
$825$		0			0
$826$	12.3439	+	53.7884i	0.429498	+	1.87154i
$827$	−13.8903	+	13.8903i	−0.483014	+	0.483014i	−0.906093	−	0.423079i	$-0.860949\pi$
$827$	−13.8903	+	13.8903i	−0.483014	+	0.483014i	0.423079	+	0.906093i	$0.360949\pi$
$828$		0			0
$829$	34.7927	+	34.7927i	1.20840	+	1.20840i	0.971545	+	0.236856i	$0.0761169\pi$
$829$	34.7927	+	34.7927i	1.20840	+	1.20840i	0.236856	+	0.971545i	$0.423883\pi$
$830$	−18.9184	−	11.8560i	−0.656668	−	0.411528i
$831$		0			0
$832$	−9.41306	−	14.7472i	−0.326339	−	0.511266i
$833$	32.1271			1.11314
$834$		0			0
$835$	−4.34184	−	4.34184i	−0.150256	−	0.150256i
$836$	28.9170	+	59.6848i	1.00012	+	2.06424i
$837$		0			0
$838$	10.7681	+	46.9220i	0.371978	+	1.62089i
$839$		−	41.9136i		−	1.44702i	−0.690314	−	0.723510i	$-0.742528\pi$
$839$		−	41.9136i		−	1.44702i	0.690314	−	0.723510i	$-0.257472\pi$
$840$		0			0
$841$		−	22.2109i		−	0.765892i
$842$	39.2001	−	8.99601i	1.35092	−	0.310023i
$843$		0			0
$844$	−13.5332	+	38.9715i	−0.465832	+	1.34145i
$845$	−5.81060	−	5.81060i	−0.199891	−	0.199891i
$846$		0			0
$847$	30.5956			1.05128
$848$	−3.16963	−	26.9819i	−0.108845	−	0.926562i
$849$		0			0
$850$	3.24748	−	5.18195i	0.111388	−	0.177740i
$851$	17.7945	+	17.7945i	0.609987	+	0.609987i
$852$		0			0
$853$	−17.8552	+	17.8552i	−0.611349	+	0.611349i	−0.943297	−	0.331949i	$-0.892294\pi$
$853$	−17.8552	+	17.8552i	−0.611349	+	0.611349i	0.331949	+	0.943297i	$0.392294\pi$
$854$	2.23047	−	0.511871i	0.0763252	−	0.0175159i
$855$		0			0
$856$	−21.5056	−	26.7715i	−0.735046	−	0.915031i
$857$			37.8604i			1.29328i	0.762793	+	0.646642i	$0.223827\pi$
$857$			37.8604i			1.29328i	−0.762793	+	0.646642i	$0.776173\pi$
$858$		0			0
$859$	−33.0486	+	33.0486i	−1.12760	+	1.12760i	−0.137036	+	0.990566i	$0.543758\pi$
$859$	−33.0486	+	33.0486i	−1.12760	+	1.12760i	−0.990566	+	0.137036i	$0.956242\pi$
$860$	2.53202	−	1.22675i	0.0863413	−	0.0418320i
$861$		0			0
$862$	−35.8335	−	22.4565i	−1.22049	−	0.764873i
$863$	−7.90340			−0.269035			−0.134518	−	0.990911i	$-0.542948\pi$
$863$	−7.90340			−0.269035			−0.134518	+	0.990911i	$0.542948\pi$
$864$		0			0
$865$	10.3134			0.350667
$866$	−21.2690	−	13.3291i	−0.722750	−	0.452941i
$867$		0			0
$868$	65.1426	−	31.5613i	2.21108	−	1.07126i
$869$	−39.0260	+	39.0260i	−1.32387	+	1.32387i
$870$		0			0
$871$			21.5785i			0.731159i
$872$	−33.2501	+	26.7099i	−1.12599	+	0.904511i
$873$		0			0
$874$	−40.9482	+	9.39718i	−1.38509	+	0.317864i
$875$	2.68603	−	2.68603i	0.0908043	−	0.0908043i
$876$		0			0
$877$	−23.4020	−	23.4020i	−0.790229	−	0.790229i	0.191302	−	0.981531i	$-0.438729\pi$
$877$	−23.4020	−	23.4020i	−0.790229	−	0.790229i	−0.981531	+	0.191302i	$0.938729\pi$
$878$	11.3682	−	18.1400i	0.383657	−	0.612194i
$879$		0			0
$880$	−13.7026	−	10.8217i	−0.461915	−	0.364799i
$881$	−4.99400			−0.168252			−0.0841261	−	0.996455i	$-0.526810\pi$
$881$	−4.99400			−0.168252			−0.0841261	+	0.996455i	$0.526810\pi$
$882$		0			0
$883$	−22.8573	−	22.8573i	−0.769209	−	0.769209i	0.208758	−	0.977967i	$-0.433058\pi$
$883$	−22.8573	−	22.8573i	−0.769209	−	0.769209i	−0.977967	+	0.208758i	$0.933058\pi$
$884$	6.20447	−	17.8670i	0.208679	−	0.600932i
$885$		0			0
$886$	−32.1029	+	7.36728i	−1.07852	+	0.247509i
$887$		−	20.5245i		−	0.689146i	−0.938760	−	0.344573i	$-0.888024\pi$
$887$		−	20.5245i		−	0.689146i	0.938760	−	0.344573i	$-0.111976\pi$
$888$		0			0
$889$		−	27.2129i		−	0.912691i
$890$	−4.10292	−	17.8784i	−0.137530	−	0.599287i
$891$		0			0
$892$	−11.9375	−	24.6390i	−0.399697	−	0.824975i
$893$	11.9498	+	11.9498i	0.399885	+	0.399885i
$894$		0			0
$895$	−8.80909			−0.294456
$896$	−30.1360	+	30.6398i	−1.00677	+	1.02360i
$897$		0			0
$898$	42.6702	+	26.7410i	1.42392	+	0.892360i
$899$	17.5545	+	17.5545i	0.585476	+	0.585476i
$900$		0			0
$901$	20.7677	−	20.7677i	0.691871	−	0.691871i
$902$	−0.801133	−	3.49093i	−0.0266748	−	0.116235i
$903$		0			0
$904$	0.954292	−	8.74881i	0.0317393	−	0.290981i
$905$			1.80032i			0.0598446i
$906$		0			0
$907$	−12.1526	+	12.1526i	−0.403521	+	0.403521i	−0.879472	−	0.475951i	$-0.842104\pi$
$907$	−12.1526	+	12.1526i	−0.403521	+	0.403521i	0.475951	+	0.879472i	$0.342104\pi$
$908$	−11.0868	+	31.9267i	−0.367930	+	1.05953i
$909$		0			0
$910$	6.23863	−	9.95487i	0.206809	−	0.330001i
$911$	−26.1222			−0.865468			−0.432734	−	0.901522i	$-0.642451\pi$
$911$	−26.1222			−0.865468			−0.432734	+	0.901522i	$0.642451\pi$
$912$		0			0
$913$	−68.9132			−2.28070
$914$	1.48743	−	2.37347i	0.0492000	−	0.0785075i
$915$		0			0
$916$	25.1379	+	8.72936i	0.830580	+	0.288426i
$917$	−24.8843	+	24.8843i	−0.821753	+	0.821753i
$918$		0			0
$919$			12.3754i			0.408228i	0.978947	+	0.204114i	$0.0654313\pi$
$919$			12.3754i			0.408228i	−0.978947	+	0.204114i	$0.934569\pi$
$920$	8.62314	−	6.92698i	0.284296	−	0.228376i
$921$		0			0
$922$	−1.84994	−	8.06109i	−0.0609244	−	0.265478i
$923$	0.904709	−	0.904709i	0.0297789	−	0.0297789i
$924$		0			0
$925$	−4.55033	−	4.55033i	−0.149614	−	0.149614i
$926$	−28.0684	−	17.5902i	−0.922385	−	0.578051i
$927$		0			0
$928$	−13.3174	−	6.31648i	−0.437166	−	0.207349i
$929$	14.1300			0.463591			0.231795	−	0.972765i	$-0.425540\pi$
$929$	14.1300			0.463591			0.231795	+	0.972765i	$0.425540\pi$
$930$		0			0
$931$	39.9085	+	39.9085i	1.30795	+	1.30795i
$932$	−21.2787	+	10.3094i	−0.697007	+	0.337697i
$933$		0			0
$934$	−1.88239	−	8.20250i	−0.0615937	−	0.268394i
$935$		−	18.8761i		−	0.617314i
$936$		0			0
$937$			39.1538i			1.27910i	0.768750	+	0.639549i	$0.220879\pi$
$937$			39.1538i			1.27910i	−0.768750	+	0.639549i	$0.779121\pi$
$938$	51.6637	−	11.8563i	1.68688	−	0.387121i
$939$		0			0
$940$	−4.20301	−	1.45953i	−0.137087	−	0.0476047i
$941$	17.1373	+	17.1373i	0.558661	+	0.558661i	0.928926	−	0.370265i	$-0.120733\pi$
$941$	17.1373	+	17.1373i	0.558661	+	0.558661i	−0.370265	+	0.928926i	$0.620733\pi$
$942$		0			0
$943$	2.26890			0.0738856
$944$	−4.79416	−	40.8110i	−0.156037	−	1.32828i
$945$		0			0
$946$	4.61165	−	7.35872i	0.149938	−	0.239253i
$947$	−21.7252	−	21.7252i	−0.705973	−	0.705973i	0.259713	−	0.965686i	$-0.416372\pi$
$947$	−21.7252	−	21.7252i	−0.705973	−	0.705973i	−0.965686	+	0.259713i	$0.916372\pi$
$948$		0			0
$949$	−18.5564	+	18.5564i	−0.602365	+	0.602365i
$950$	10.4711	−	2.40301i	0.339728	−	0.0779640i
$951$		0			0
$952$	−46.1866	−	5.03788i	−1.49692	−	0.163279i
$953$			6.05956i			0.196288i	0.995172	+	0.0981442i	$0.0312906\pi$
$953$			6.05956i			0.196288i	−0.995172	+	0.0981442i	$0.968709\pi$
$954$		0			0
$955$	−6.81395	+	6.81395i	−0.220494	+	0.220494i
$956$	−9.77682	−	20.1794i	−0.316205	−	0.652648i
$957$		0			0
$958$	6.61742	+	4.14708i	0.213799	+	0.133986i
$959$	41.9754			1.35546
$960$		0			0
$961$	59.7808			1.92841
$962$	−16.8643	−	10.5687i	−0.543727	−	0.340749i
$963$		0			0
$964$	6.88903	+	14.2190i	0.221881	+	0.457962i
$965$	−2.57761	+	2.57761i	−0.0829763	+	0.0829763i
$966$		0			0
$967$			32.6389i			1.04959i	0.851227	+	0.524797i	$0.175859\pi$
$967$			32.6389i			1.04959i	−0.851227	+	0.524797i	$0.824141\pi$
$968$	−22.6470	−	2.47026i	−0.727902	−	0.0793971i
$969$		0			0
$970$	9.35306	−	2.14643i	0.300309	−	0.0689177i
$971$	4.73662	−	4.73662i	0.152005	−	0.152005i	−0.627008	−	0.779013i	$-0.715721\pi$
$971$	4.73662	−	4.73662i	0.152005	−	0.152005i	0.779013	+	0.627008i	$0.215721\pi$
$972$		0			0
$973$	−19.6453	−	19.6453i	−0.629801	−	0.629801i
$974$	−21.0737	+	33.6269i	−0.675244	+	1.07747i
$975$		0			0
$976$	−1.69233	+	0.198802i	−0.0541703	+	0.00636351i
$977$	31.9605			1.02251			0.511254	−	0.859430i	$-0.329181\pi$
$977$	31.9605			1.02251			0.511254	+	0.859430i	$0.329181\pi$
$978$		0			0
$979$	−40.0353	−	40.0353i	−1.27953	−	1.27953i
$980$	−14.0367	−	4.87437i	−0.448386	−	0.155706i
$981$		0			0
$982$	−2.48358	+	0.569955i	−0.0792541	+	0.0181880i
$983$			36.1044i			1.15155i	0.817607	+	0.575776i	$0.195300\pi$
$983$			36.1044i			1.15155i	−0.817607	+	0.575776i	$0.804700\pi$
$984$		0			0
$985$		−	10.6833i		−	0.340398i
$986$	−3.56413	−	15.5307i	−0.113505	−	0.494598i
$987$		0			0
$988$	29.9017	−	14.4873i	0.951301	−	0.460901i
$989$	3.89002	+	3.89002i	0.123695	+	0.123695i
$990$		0			0
$991$	19.3054			0.613255			0.306628	−	0.951830i	$-0.400799\pi$
$991$	19.3054			0.613255			0.306628	+	0.951830i	$0.400799\pi$
$992$	−50.7671	+	18.1023i	−1.61186	+	0.574747i
$993$		0			0
$994$	−2.66317	−	1.66898i	−0.0844705	−	0.0529369i
$995$	−16.7897	−	16.7897i	−0.532269	−	0.532269i
$996$		0			0
$997$	−6.99944	+	6.99944i	−0.221674	+	0.221674i	−0.809203	−	0.587529i	$-0.800101\pi$
$997$	−6.99944	+	6.99944i	−0.221674	+	0.221674i	0.587529	+	0.809203i	$0.300101\pi$
$998$	11.7810	+	51.3357i	0.372922	+	1.62500i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.d.541.2		20
3.2	odd	2		240.2.s.c.61.9	✓	20
4.3	odd	2		2880.2.t.d.721.6		20
12.11	even	2		960.2.s.c.721.6		20
16.5	even	4	inner	720.2.t.d.181.2		20
16.11	odd	4		2880.2.t.d.2161.10		20
24.5	odd	2		1920.2.s.e.1441.10		20
24.11	even	2		1920.2.s.f.1441.1		20
48.5	odd	4		240.2.s.c.181.9	yes	20
48.11	even	4		960.2.s.c.241.10		20
48.29	odd	4		1920.2.s.e.481.6		20
48.35	even	4		1920.2.s.f.481.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.9	✓	20	3.2	odd	2
240.2.s.c.181.9	yes	20	48.5	odd	4
720.2.t.d.181.2		20	16.5	even	4	inner
720.2.t.d.541.2		20	1.1	even	1	trivial
960.2.s.c.241.10		20	48.11	even	4
960.2.s.c.721.6		20	12.11	even	2
1920.2.s.e.481.6		20	48.29	odd	4
1920.2.s.e.1441.10		20	24.5	odd	2
1920.2.s.f.481.5		20	48.35	even	4
1920.2.s.f.1441.1		20	24.11	even	2
2880.2.t.d.721.6		20	4.3	odd	2
2880.2.t.d.2161.10		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)

\(f(q)\)	\(=\)	\(q+(-1.19834 - 0.750988i) q^{2} +(0.872033 + 1.79988i) q^{4} +(0.707107 - 0.707107i) q^{5} +3.79862i q^{7} +(0.306697 - 2.81175i) q^{8} +O(q^{10})\)	\(q+(-1.19834 - 0.750988i) q^{2} +(0.872033 + 1.79988i) q^{4} +(0.707107 - 0.707107i) q^{5} +3.79862i q^{7} +(0.306697 - 2.81175i) q^{8} +(-1.37838 + 0.316325i) q^{10} +(-3.08662 + 3.08662i) q^{11} +(1.54638 + 1.54638i) q^{13} +(2.85272 - 4.55203i) q^{14} +(-2.47912 + 3.13910i) q^{16} -4.32428 q^{17} +(-5.37165 - 5.37165i) q^{19} +(1.88933 + 0.656085i) q^{20} +(6.01683 - 1.38080i) q^{22} +3.91059i q^{23} -1.00000i q^{25} +(-0.691773 - 3.01440i) q^{26} +(-6.83704 + 3.31252i) q^{28} +(-1.84243 - 1.84243i) q^{29} -9.52790 q^{31} +(5.32825 - 1.89992i) q^{32} +(5.18195 + 3.24748i) q^{34} +(2.68603 + 2.68603i) q^{35} +(4.55033 - 4.55033i) q^{37} +(2.40301 + 10.4711i) q^{38} +(-1.77134 - 2.20507i) q^{40} -0.580195i q^{41} +(0.994741 - 0.994741i) q^{43} +(-8.24716 - 2.86390i) q^{44} +(2.93681 - 4.68621i) q^{46} -2.22461 q^{47} -7.42948 q^{49} +(-0.750988 + 1.19834i) q^{50} +(-1.43480 + 4.13178i) q^{52} +(-4.80257 + 4.80257i) q^{53} +4.36514i q^{55} +(10.6808 + 1.16502i) q^{56} +(0.824214 + 3.59151i) q^{58} +(-7.26404 + 7.26404i) q^{59} +(0.301222 + 0.301222i) q^{61} +(11.4176 + 7.15534i) q^{62} +(-7.81187 - 1.72471i) q^{64} +2.18691 q^{65} +(6.97711 + 6.97711i) q^{67} +(-3.77091 - 7.78318i) q^{68} +(-1.20160 - 5.23595i) q^{70} -0.585051i q^{71} +11.9999i q^{73} +(-8.87009 + 2.03559i) q^{74} +(4.98406 - 14.3526i) q^{76} +(-11.7249 - 11.7249i) q^{77} +12.6436 q^{79} +(0.466680 + 3.97268i) q^{80} +(-0.435720 + 0.695270i) q^{82} +(11.1632 + 11.1632i) q^{83} +(-3.05773 + 3.05773i) q^{85} +(-1.93908 + 0.444998i) q^{86} +(7.73214 + 9.62545i) q^{88} +12.9706i q^{89} +(-5.87409 + 5.87409i) q^{91} +(-7.03858 + 3.41016i) q^{92} +(2.66583 + 1.67065i) q^{94} -7.59666 q^{95} -6.78553 q^{97} +(8.90303 + 5.57945i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} - 12 q^{8}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more