LMFDB - Embedded newform 720.2.t.d.181.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("720.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$20$
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			181.4
Root			$1.15787 + 0.811989i$ of defining polynomial
Character	$\chi$	$=$	720.181
Dual form			720.2.t.d.541.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15787 + 0.811989i) q^{2} +(0.681349 - 1.88036i) q^{4} +(-0.707107 - 0.707107i) q^{5} +2.18060i q^{7} +(0.737916 + 2.73047i) q^{8} +O(q^{10})$	\(q+(-1.15787 + 0.811989i) q^{2} +(0.681349 - 1.88036i) q^{4} +(-0.707107 - 0.707107i) q^{5} +2.18060i q^{7} +(0.737916 + 2.73047i) q^{8} +(1.39290 + 0.244579i) q^{10} +(0.00889637 + 0.00889637i) q^{11} +(1.72965 - 1.72965i) q^{13} +(-1.77062 - 2.52486i) q^{14} +(-3.07153 - 2.56237i) q^{16} +5.54943 q^{17} +(-4.94702 + 4.94702i) q^{19} +(-1.81140 + 0.847831i) q^{20} +(-0.0175246 - 0.00307713i) q^{22} -3.01309i q^{23} +1.00000i q^{25} +(-0.598263 + 3.40718i) q^{26} +(4.10031 + 1.48575i) q^{28} +(-3.20471 + 3.20471i) q^{29} +3.58009 q^{31} +(5.63706 + 0.472855i) q^{32} +(-6.42554 + 4.50607i) q^{34} +(1.54192 - 1.54192i) q^{35} +(4.97761 + 4.97761i) q^{37} +(1.71111 - 9.74496i) q^{38} +(1.40895 - 2.45252i) q^{40} +3.76487i q^{41} +(6.81210 + 6.81210i) q^{43} +(0.0227899 - 0.0106669i) q^{44} +(2.44659 + 3.48878i) q^{46} +10.0800 q^{47} +2.24499 q^{49} +(-0.811989 - 1.15787i) q^{50} +(-2.07388 - 4.43087i) q^{52} +(0.932644 + 0.932644i) q^{53} -0.0125814i q^{55} +(-5.95406 + 1.60910i) q^{56} +(1.10846 - 6.31283i) q^{58} +(4.60522 + 4.60522i) q^{59} +(4.17149 - 4.17149i) q^{61} +(-4.14530 + 2.90700i) q^{62} +(-6.91096 + 4.02972i) q^{64} -2.44610 q^{65} +(-11.0105 + 11.0105i) q^{67} +(3.78110 - 10.4349i) q^{68} +(-0.533328 + 3.03736i) q^{70} +12.1092i q^{71} -7.12981i q^{73} +(-9.80521 - 1.72169i) q^{74} +(5.93155 + 12.6729i) q^{76} +(-0.0193994 + 0.0193994i) q^{77} -3.41789 q^{79} +(0.360031 + 3.98376i) q^{80} +(-3.05704 - 4.35925i) q^{82} +(-5.31631 + 5.31631i) q^{83} +(-3.92404 - 3.92404i) q^{85} +(-13.4189 - 2.35621i) q^{86} +(-0.0177265 + 0.0308561i) q^{88} +5.06405i q^{89} +(3.77168 + 3.77168i) q^{91} +(-5.66569 - 2.05296i) q^{92} +(-11.6714 + 8.18483i) q^{94} +6.99615 q^{95} -10.3646 q^{97} +(-2.59942 + 1.82291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.15787	+	0.811989i	−0.818741	+	0.574163i
$2$	−1.15787	+	0.811989i	−0.818741	+	0.574163i
$3$		0			0
$3$		0			0
$4$	0.681349	−	1.88036i	0.340674	−	0.940181i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$			2.18060i			0.824189i	0.911141	+	0.412094i	$0.135203\pi$
$7$			2.18060i			0.824189i	−0.911141	+	0.412094i	$0.864797\pi$
$8$	0.737916	+	2.73047i	0.260893	+	0.965368i
$9$		0			0
$10$	1.39290	+	0.244579i	0.440475	+	0.0773425i
$11$	0.00889637	+	0.00889637i	0.00268236	+	0.00268236i	0.708447	−	0.705764i	$-0.249396\pi$
$11$	0.00889637	+	0.00889637i	0.00268236	+	0.00268236i	−0.705764	+	0.708447i	$0.749396\pi$
$12$		0			0
$13$	1.72965	−	1.72965i	0.479719	−	0.479719i	−0.425323	−	0.905042i	$-0.639839\pi$
$13$	1.72965	−	1.72965i	0.479719	−	0.479719i	0.905042	+	0.425323i	$0.139839\pi$
$14$	−1.77062	−	2.52486i	−0.473218	−	0.674797i
$15$		0			0
$16$	−3.07153	−	2.56237i	−0.767882	−	0.640592i
$17$	5.54943			1.34593			0.672967	−	0.739673i	$-0.265020\pi$
$17$	5.54943			1.34593			0.672967	+	0.739673i	$0.265020\pi$
$18$		0			0
$19$	−4.94702	+	4.94702i	−1.13493	+	1.13493i	−0.145579	+	0.989347i	$0.546504\pi$
$19$	−4.94702	+	4.94702i	−1.13493	+	1.13493i	−0.989347	+	0.145579i	$0.953496\pi$
$20$	−1.81140	+	0.847831i	−0.405042	+	0.189581i
$21$		0			0
$22$	−0.0175246	−	0.00307713i	−0.00373626	−	0.000656047i
$23$		−	3.01309i		−	0.628272i	−0.949378	−	0.314136i	$-0.898285\pi$
$23$		−	3.01309i		−	0.628272i	0.949378	−	0.314136i	$-0.101715\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$	−0.598263	+	3.40718i	−0.117329	+	0.668203i
$27$		0			0
$28$	4.10031	+	1.48575i	0.774887	+	0.280780i
$29$	−3.20471	+	3.20471i	−0.595099	+	0.595099i	−0.939004	−	0.343905i	$-0.888250\pi$
$29$	−3.20471	+	3.20471i	−0.595099	+	0.595099i	0.343905	+	0.939004i	$0.388250\pi$
$30$		0			0
$31$	3.58009			0.643004			0.321502	−	0.946909i	$-0.395812\pi$
$31$	3.58009			0.643004			0.321502	+	0.946909i	$0.395812\pi$
$32$	5.63706	+	0.472855i	0.996500	+	0.0835897i
$33$		0			0
$34$	−6.42554	+	4.50607i	−1.10197	+	0.772785i
$35$	1.54192	−	1.54192i	0.260631	−	0.260631i
$36$		0			0
$37$	4.97761	+	4.97761i	0.818314	+	0.818314i	0.985864	−	0.167550i	$-0.0535856\pi$
$37$	4.97761	+	4.97761i	0.818314	+	0.818314i	−0.167550	+	0.985864i	$0.553586\pi$
$38$	1.71111	−	9.74496i	0.277578	−	1.58084i
$39$		0			0
$40$	1.40895	−	2.45252i	0.222775	−	0.387778i
$41$			3.76487i			0.587975i	0.955809	+	0.293987i	$0.0949823\pi$
$41$			3.76487i			0.587975i	−0.955809	+	0.293987i	$0.905018\pi$
$42$		0			0
$43$	6.81210	+	6.81210i	1.03884	+	1.03884i	0.999215	+	0.0396204i	$0.0126149\pi$
$43$	6.81210	+	6.81210i	1.03884	+	1.03884i	0.0396204	+	0.999215i	$0.487385\pi$
$44$	0.0227899	−	0.0106669i	0.00343571	−	0.00160809i
$45$		0			0
$46$	2.44659	+	3.48878i	0.360730	+	0.514392i
$47$	10.0800			1.47032			0.735158	−	0.677896i	$-0.237108\pi$
$47$	10.0800			1.47032			0.735158	+	0.677896i	$0.237108\pi$
$48$		0			0
$49$	2.24499			0.320713
$50$	−0.811989	−	1.15787i	−0.114833	−	0.163748i
$51$		0			0
$52$	−2.07388	−	4.43087i	−0.287595	−	0.614451i
$53$	0.932644	+	0.932644i	0.128108	+	0.128108i	0.768254	−	0.640145i	$-0.221126\pi$
$53$	0.932644	+	0.932644i	0.128108	+	0.128108i	−0.640145	+	0.768254i	$0.721126\pi$
$54$		0			0
$55$		−	0.0125814i		−	0.00169647i
$56$	−5.95406	+	1.60910i	−0.795645	+	0.215025i
$57$		0			0
$58$	1.10846	−	6.31283i	0.145548	−	0.828915i
$59$	4.60522	+	4.60522i	0.599548	+	0.599548i	0.940192	−	0.340644i	$-0.110645\pi$
$59$	4.60522	+	4.60522i	0.599548	+	0.599548i	−0.340644	+	0.940192i	$0.610645\pi$
$60$		0			0
$61$	4.17149	−	4.17149i	0.534105	−	0.534105i	−0.387686	−	0.921791i	$-0.626726\pi$
$61$	4.17149	−	4.17149i	0.534105	−	0.534105i	0.921791	+	0.387686i	$0.126726\pi$
$62$	−4.14530	+	2.90700i	−0.526454	+	0.369189i
$63$		0			0
$64$	−6.91096	+	4.02972i	−0.863870	+	0.503715i
$65$	−2.44610			−0.303401
$66$		0			0
$67$	−11.0105	+	11.0105i	−1.34515	+	1.34515i	−0.454293	+	0.890852i	$0.650108\pi$
$67$	−11.0105	+	11.0105i	−1.34515	+	1.34515i	−0.890852	+	0.454293i	$0.849892\pi$
$68$	3.78110	−	10.4349i	0.458525	−	1.26542i
$69$		0			0
$70$	−0.533328	+	3.03736i	−0.0637448	+	0.363034i
$71$			12.1092i			1.43710i	0.695475	+	0.718550i	$0.255194\pi$
$71$			12.1092i			1.43710i	−0.695475	+	0.718550i	$0.744806\pi$
$72$		0			0
$73$		−	7.12981i		−	0.834481i	−0.908796	−	0.417240i	$-0.862997\pi$
$73$		−	7.12981i		−	0.834481i	0.908796	−	0.417240i	$-0.137003\pi$
$74$	−9.80521	−	1.72169i	−1.13983	−	0.200142i
$75$		0			0
$76$	5.93155	+	12.6729i	0.680396	+	1.45368i
$77$	−0.0193994	+	0.0193994i	−0.00221077	+	0.00221077i
$78$		0			0
$79$	−3.41789			−0.384543			−0.192272	−	0.981342i	$-0.561585\pi$
$79$	−3.41789			−0.384543			−0.192272	+	0.981342i	$0.561585\pi$
$80$	0.360031	+	3.98376i	0.0402527	+	0.445398i
$81$		0			0
$82$	−3.05704	−	4.35925i	−0.337593	−	0.481399i
$83$	−5.31631	+	5.31631i	−0.583541	+	0.583541i	−0.935875	−	0.352333i	$-0.885388\pi$
$83$	−5.31631	+	5.31631i	−0.583541	+	0.583541i	0.352333	+	0.935875i	$0.385388\pi$
$84$		0			0
$85$	−3.92404	−	3.92404i	−0.425622	−	0.425622i
$86$	−13.4189	−	2.35621i	−1.44700	−	0.254077i
$87$		0			0
$88$	−0.0177265	+	0.0308561i	−0.00188965	+	0.00328927i
$89$			5.06405i			0.536788i	0.963309	+	0.268394i	$0.0864929\pi$
$89$			5.06405i			0.536788i	−0.963309	+	0.268394i	$0.913507\pi$
$90$		0			0
$91$	3.77168	+	3.77168i	0.395379	+	0.395379i
$92$	−5.66569	−	2.05296i	−0.590689	−	0.214036i
$93$		0			0
$94$	−11.6714	+	8.18483i	−1.20381	+	0.844201i
$95$	6.99615			0.717790
$96$		0			0
$97$	−10.3646			−1.05237			−0.526184	−	0.850371i	$-0.676378\pi$
$97$	−10.3646			−1.05237			−0.526184	+	0.850371i	$0.676378\pi$
$98$	−2.59942	+	1.82291i	−0.262581	+	0.184142i
$99$		0			0
$100$	1.88036	+	0.681349i	0.188036	+	0.0681349i
$101$	−9.96414	−	9.96414i	−0.991469	−	0.991469i	0.00849458	−	0.999964i	$-0.497296\pi$
$101$	−9.96414	−	9.96414i	−0.991469	−	0.991469i	−0.999964	+	0.00849458i	$0.997296\pi$
$102$		0			0
$103$		−	2.25154i		−	0.221851i	−0.993829	−	0.110926i	$-0.964618\pi$
$103$		−	2.25154i		−	0.221851i	0.993829	−	0.110926i	$-0.0353815\pi$
$104$	5.99911	+	3.44643i	0.588261	+	0.337950i
$105$		0			0
$106$	−1.83718	−	0.322589i	−0.178443	−	0.0313326i
$107$	−2.51098	−	2.51098i	−0.242746	−	0.242746i	0.575239	−	0.817985i	$-0.304909\pi$
$107$	−2.51098	−	2.51098i	−0.242746	−	0.242746i	−0.817985	+	0.575239i	$0.804909\pi$
$108$		0			0
$109$	12.0668	−	12.0668i	1.15579	−	1.15579i	0.170420	−	0.985372i	$-0.445488\pi$
$109$	12.0668	−	12.0668i	1.15579	−	1.15579i	0.985372	−	0.170420i	$-0.0545124\pi$
$110$	0.0102159	+	0.0145676i	0.000974050	+	0.00138897i
$111$		0			0
$112$	5.58749	−	6.69777i	0.527968	−	0.632879i
$113$	19.7954			1.86219			0.931097	−	0.364772i	$-0.118853\pi$
$113$	19.7954			1.86219			0.931097	+	0.364772i	$0.118853\pi$
$114$		0			0
$115$	−2.13057	+	2.13057i	−0.198677	+	0.198677i
$116$	3.84249	+	8.20953i	0.356766	+	0.762236i
$117$		0			0
$118$	−9.07165	−	1.59288i	−0.835113	−	0.146637i
$119$			12.1011i			1.10930i
$120$		0			0
$121$		−	10.9998i		−	0.999986i
$122$	−1.44286	+	8.21727i	−0.130631	+	0.743957i
$123$		0			0
$124$	2.43929	−	6.73188i	0.219055	−	0.604540i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	14.3984			1.27765			0.638825	−	0.769352i	$-0.279421\pi$
$127$	14.3984			1.27765			0.638825	+	0.769352i	$0.279421\pi$
$128$	4.72994	−	10.2775i	0.418072	−	0.908414i
$129$		0			0
$130$	2.83228	−	1.98620i	0.248407	−	0.174202i
$131$	0.574754	−	0.574754i	0.0502165	−	0.0502165i	−0.681553	−	0.731769i	$-0.738695\pi$
$131$	0.574754	−	0.574754i	0.0502165	−	0.0502165i	0.731769	+	0.681553i	$0.238695\pi$
$132$		0			0
$133$	−10.7875	−	10.7875i	−0.935393	−	0.935393i
$134$	3.80838	−	21.6892i	0.328994	−	1.87366i
$135$		0			0
$136$	4.09501	+	15.1526i	0.351144	+	1.29932i
$137$			16.0077i			1.36763i	0.729654	+	0.683817i	$0.239681\pi$
$137$			16.0077i			1.36763i	−0.729654	+	0.683817i	$0.760319\pi$
$138$		0			0
$139$	−1.52424	−	1.52424i	−0.129284	−	0.129284i	0.639504	−	0.768788i	$-0.279140\pi$
$139$	−1.52424	−	1.52424i	−0.129284	−	0.129284i	−0.768788	+	0.639504i	$0.779140\pi$
$140$	−1.84878	−	3.94994i	−0.156250	−	0.333831i
$141$		0			0
$142$	−9.83255	−	14.0210i	−0.825129	−	1.17661i
$143$	0.0307753			0.00257356
$144$		0			0
$145$	4.53214			0.376374
$146$	5.78932	+	8.25543i	0.479128	+	0.683224i
$147$		0			0
$148$	12.7512	−	5.96822i	1.04814	−	0.490585i
$149$	−12.1410	−	12.1410i	−0.994629	−	0.994629i	0.00535669	−	0.999986i	$-0.498295\pi$
$149$	−12.1410	−	12.1410i	−0.994629	−	0.994629i	−0.999986	+	0.00535669i	$0.998295\pi$
$150$		0			0
$151$		−	12.7940i		−	1.04116i	−0.853813	−	0.520580i	$-0.825716\pi$
$151$		−	12.7940i		−	1.04116i	0.853813	−	0.520580i	$-0.174284\pi$
$152$	−17.1582	−	9.85723i	−1.39171	−	0.799527i
$153$		0			0
$154$	0.00670999	−	0.0382142i	0.000540706	−	0.00307939i
$155$	−2.53151	−	2.53151i	−0.203336	−	0.203336i
$156$		0			0
$157$	−10.3333	+	10.3333i	−0.824686	+	0.824686i	−0.986776	−	0.162090i	$-0.948177\pi$
$157$	−10.3333	+	10.3333i	−0.824686	+	0.824686i	0.162090	+	0.986776i	$0.448177\pi$
$158$	3.95749	−	2.77529i	0.314841	−	0.220790i
$159$		0			0
$160$	−3.65164	−	4.32036i	−0.288688	−	0.341554i
$161$	6.57033			0.517814
$162$		0			0
$163$	13.4362	−	13.4362i	1.05241	−	1.05241i	0.0538580	−	0.998549i	$-0.482848\pi$
$163$	13.4362	−	13.4362i	1.05241	−	1.05241i	0.998549	−	0.0538580i	$-0.0171518\pi$
$164$	7.07933	+	2.56519i	0.552803	+	0.200308i
$165$		0			0
$166$	1.83884	−	10.4724i	0.142722	−	0.812817i
$167$		−	5.08389i		−	0.393403i	−0.980463	−	0.196702i	$-0.936977\pi$
$167$		−	5.08389i		−	0.393403i	0.980463	−	0.196702i	$-0.0630230\pi$
$168$		0			0
$169$			7.01660i			0.539739i
$170$	7.72982	+	1.35727i	0.592850	+	0.104098i
$171$		0			0
$172$	17.4506	−	8.16780i	1.33060	−	0.622789i
$173$	10.8821	−	10.8821i	0.827350	−	0.827350i	−0.159799	−	0.987150i	$-0.551085\pi$
$173$	10.8821	−	10.8821i	0.827350	−	0.827350i	0.987150	+	0.159799i	$0.0510847\pi$
$174$		0			0
$175$	−2.18060			−0.164838
$176$	−0.00452968	−	0.0501212i	−0.000341438	−	0.00377803i
$177$		0			0
$178$	−4.11195	−	5.86353i	−0.308204	−	0.439490i
$179$	−11.1719	+	11.1719i	−0.835028	+	0.835028i	−0.988200	−	0.153172i	$-0.951051\pi$
$179$	−11.1719	+	11.1719i	−0.835028	+	0.835028i	0.153172	+	0.988200i	$0.451051\pi$
$180$		0			0
$181$	−10.1479	−	10.1479i	−0.754290	−	0.754290i	0.220987	−	0.975277i	$-0.429072\pi$
$181$	−10.1479	−	10.1479i	−0.754290	−	0.754290i	−0.975277	+	0.220987i	$0.929072\pi$
$182$	−7.42969	−	1.30457i	−0.550725	−	0.0967013i
$183$		0			0
$184$	8.22715	−	2.22340i	0.606513	−	0.163912i
$185$		−	7.03940i		−	0.517547i
$186$		0			0
$187$	0.0493697	+	0.0493697i	0.00361027	+	0.00361027i
$188$	6.86798	−	18.9540i	0.500899	−	1.38236i
$189$		0			0
$190$	−8.10067	+	5.68079i	−0.587684	+	0.412128i
$191$	−13.3716			−0.967532			−0.483766	−	0.875197i	$-0.660731\pi$
$191$	−13.3716			−0.967532			−0.483766	+	0.875197i	$0.660731\pi$
$192$		0			0
$193$	8.32925			0.599553			0.299776	−	0.954009i	$-0.403088\pi$
$193$	8.32925			0.599553			0.299776	+	0.954009i	$0.403088\pi$
$194$	12.0009	−	8.41596i	0.861617	−	0.604230i
$195$		0			0
$196$	1.52962	−	4.22140i	0.109259	−	0.301529i
$197$	−13.1995	−	13.1995i	−0.940427	−	0.940427i	0.0578960	−	0.998323i	$-0.481561\pi$
$197$	−13.1995	−	13.1995i	−0.940427	−	0.940427i	−0.998323	+	0.0578960i	$0.981561\pi$
$198$		0			0
$199$			3.66713i			0.259956i	0.991517	+	0.129978i	$0.0414906\pi$
$199$			3.66713i			0.259956i	−0.991517	+	0.129978i	$0.958509\pi$
$200$	−2.73047	+	0.737916i	−0.193074	+	0.0521786i
$201$		0			0
$202$	19.6280	+	3.44646i	1.38102	+	0.242492i
$203$	−6.98817	−	6.98817i	−0.490474	−	0.490474i
$204$		0			0
$205$	2.66217	−	2.66217i	0.185934	−	0.185934i
$206$	1.82823	+	2.60700i	0.127379	+	0.181639i
$207$		0			0
$208$	−9.74468	+	0.880672i	−0.675672	+	0.0610636i
$209$	−0.0880211			−0.00608855
$210$		0			0
$211$	−12.6423	+	12.6423i	−0.870332	+	0.870332i	−0.992508	−	0.122176i	$-0.961013\pi$
$211$	−12.6423	+	12.6423i	−0.870332	+	0.870332i	0.122176	+	0.992508i	$0.461013\pi$
$212$	2.38916	−	1.11825i	0.164088	−	0.0768019i
$213$		0			0
$214$	4.94629	+	0.868514i	0.338121	+	0.0593704i
$215$		−	9.63376i		−	0.657017i
$216$		0			0
$217$			7.80675i			0.529956i
$218$	−4.17375	+	23.7700i	−0.282682	+	1.60991i
$219$		0			0
$220$	−0.0236575	−	0.00857230i	−0.00159499	−	0.000577944i
$221$	9.59858	−	9.59858i	0.645670	−	0.645670i
$222$		0			0
$223$	−5.37431			−0.359891			−0.179945	−	0.983677i	$-0.557592\pi$
$223$	−5.37431			−0.359891			−0.179945	+	0.983677i	$0.557592\pi$
$224$	−1.03111	+	12.2922i	−0.0688936	+	0.821304i
$225$		0			0
$226$	−22.9206	+	16.0736i	−1.52465	+	1.06920i
$227$	−1.92306	+	1.92306i	−0.127638	+	0.127638i	−0.768040	−	0.640402i	$-0.778768\pi$
$227$	−1.92306	+	1.92306i	−0.127638	+	0.127638i	0.640402	+	0.768040i	$0.278768\pi$
$228$		0			0
$229$	5.08104	+	5.08104i	0.335765	+	0.335765i	0.854771	−	0.519006i	$-0.173698\pi$
$229$	5.08104	+	5.08104i	0.335765	+	0.335765i	−0.519006	+	0.854771i	$0.673698\pi$
$230$	0.736936	−	4.19694i	0.0485921	−	0.276738i
$231$		0			0
$232$	−11.1152	−	6.38556i	−0.729746	−	0.419232i
$233$		−	26.2417i		−	1.71915i	−0.511011	−	0.859574i	$-0.670729\pi$
$233$		−	26.2417i		−	1.71915i	0.511011	−	0.859574i	$-0.329271\pi$
$234$		0			0
$235$	−7.12762	−	7.12762i	−0.464955	−	0.464955i
$236$	11.7972	−	5.52172i	0.767935	−	0.359433i
$237$		0			0
$238$	−9.82593	−	14.0115i	−0.636920	−	0.908232i
$239$	7.40931			0.479268			0.239634	−	0.970863i	$-0.422973\pi$
$239$	7.40931			0.479268			0.239634	+	0.970863i	$0.422973\pi$
$240$		0			0
$241$	−19.6231			−1.26404			−0.632019	−	0.774953i	$-0.717773\pi$
$241$	−19.6231			−1.26404			−0.632019	+	0.774953i	$0.717773\pi$
$242$	8.93175	+	12.7364i	0.574154	+	0.818729i
$243$		0			0
$244$	−5.00168	−	10.6862i	−0.320200	−	0.684112i
$245$	−1.58745	−	1.58745i	−0.101418	−	0.101418i
$246$		0			0
$247$			17.1133i			1.08889i
$248$	2.64181	+	9.77535i	0.167755	+	0.620735i
$249$		0			0
$250$	−0.244579	+	1.39290i	−0.0154685	+	0.0880950i
$251$	−1.23610	−	1.23610i	−0.0780217	−	0.0780217i	0.667019	−	0.745041i	$-0.267570\pi$
$251$	−1.23610	−	1.23610i	−0.0780217	−	0.0780217i	−0.745041	+	0.667019i	$0.767570\pi$
$252$		0			0
$253$	0.0268055	−	0.0268055i	0.00168525	−	0.00168525i
$254$	−16.6715	+	11.6913i	−1.04606	+	0.733579i
$255$		0			0
$256$	2.86856	+	15.7408i	0.179285	+	0.983797i
$257$	−3.01050			−0.187790			−0.0938948	−	0.995582i	$-0.529932\pi$
$257$	−3.01050			−0.187790			−0.0938948	+	0.995582i	$0.529932\pi$
$258$		0			0
$259$	−10.8542	+	10.8542i	−0.674445	+	0.674445i
$260$	−1.66665	+	4.59955i	−0.103361	+	0.285252i
$261$		0			0
$262$	−0.198800	+	1.13219i	−0.0122819	+	0.0699468i
$263$		−	11.9000i		−	0.733788i	−0.930263	−	0.366894i	$-0.880421\pi$
$263$		−	11.9000i		−	0.733788i	0.930263	−	0.366894i	$-0.119579\pi$
$264$		0			0
$265$		−	1.31896i		−	0.0810229i
$266$	21.2498	+	3.73124i	1.30291	+	0.228777i
$267$		0			0
$268$	13.2017	+	28.2057i	0.806424	+	1.72294i
$269$	15.4949	−	15.4949i	0.944742	−	0.944742i	−0.0538091	−	0.998551i	$-0.517136\pi$
$269$	15.4949	−	15.4949i	0.944742	−	0.944742i	0.998551	+	0.0538091i	$0.0171363\pi$
$270$		0			0
$271$	7.30492			0.443742			0.221871	−	0.975076i	$-0.428784\pi$
$271$	7.30492			0.443742			0.221871	+	0.975076i	$0.428784\pi$
$272$	−17.0452	−	14.2197i	−1.03352	−	0.862194i
$273$		0			0
$274$	−12.9981	−	18.5350i	−0.785244	−	1.11974i
$275$	−0.00889637	+	0.00889637i	−0.000536471	+	0.000536471i
$276$		0			0
$277$	2.23718	+	2.23718i	0.134419	+	0.134419i	0.771115	−	0.636696i	$-0.219699\pi$
$277$	2.23718	+	2.23718i	0.134419	+	0.134419i	−0.636696	+	0.771115i	$0.719699\pi$
$278$	3.00254	+	0.527212i	0.180080	+	0.0316201i
$279$		0			0
$280$	5.34796	+	3.07235i	0.319602	+	0.183608i
$281$			4.85036i			0.289348i	0.989479	+	0.144674i	$0.0462134\pi$
$281$			4.85036i			0.289348i	−0.989479	+	0.144674i	$0.953787\pi$
$282$		0			0
$283$	11.4295	+	11.4295i	0.679414	+	0.679414i	0.959867	−	0.280454i	$-0.0904850\pi$
$283$	11.4295	+	11.4295i	0.679414	+	0.679414i	−0.280454	+	0.959867i	$0.590485\pi$
$284$	22.7697	+	8.25060i	1.35113	+	0.489583i
$285$		0			0
$286$	−0.0356339	+	0.0249892i	−0.00210708	+	0.00147764i
$287$	−8.20968			−0.484602
$288$		0			0
$289$	13.7961			0.811537
$290$	−5.24765	+	3.68004i	−0.308153	+	0.216100i
$291$		0			0
$292$	−13.4066	−	4.85789i	−0.784563	−	0.284286i
$293$	11.1686	+	11.1686i	0.652475	+	0.652475i	0.953588	−	0.301113i	$-0.0973582\pi$
$293$	11.1686	+	11.1686i	0.652475	+	0.652475i	−0.301113	+	0.953588i	$0.597358\pi$
$294$		0			0
$295$		−	6.51276i		−	0.379188i
$296$	−9.91816	+	17.2643i	−0.576481	+	1.00347i
$297$		0			0
$298$	23.9161	+	4.19940i	1.38542	+	0.243265i
$299$	−5.21159	−	5.21159i	−0.301394	−	0.301394i
$300$		0			0
$301$	−14.8544	+	14.8544i	−0.856196	+	0.856196i
$302$	10.3886	+	14.8138i	0.597795	+	0.852440i
$303$		0			0
$304$	27.8710	−	2.51883i	1.59851	−	0.144465i
$305$	−5.89938			−0.337798
$306$		0			0
$307$	13.5366	−	13.5366i	0.772575	−	0.772575i	−0.205981	−	0.978556i	$-0.566038\pi$
$307$	13.5366	−	13.5366i	0.772575	−	0.772575i	0.978556	+	0.205981i	$0.0660384\pi$
$308$	0.0232602	+	0.0496957i	0.00132537	+	0.00283167i
$309$		0			0
$310$	4.98673	+	0.875614i	0.283227	+	0.0497316i
$311$		−	16.4956i		−	0.935378i	−0.883893	−	0.467689i	$-0.845087\pi$
$311$		−	16.4956i		−	0.935378i	0.883893	−	0.467689i	$-0.154913\pi$
$312$		0			0
$313$			27.2549i			1.54054i	0.637719	+	0.770269i	$0.279878\pi$
$313$			27.2549i			1.54054i	−0.637719	+	0.770269i	$0.720122\pi$
$314$	3.57414	−	20.3552i	0.201701	−	1.14871i
$315$		0			0
$316$	−2.32878	+	6.42688i	−0.131004	+	0.361540i
$317$	−23.2962	+	23.2962i	−1.30845	+	1.30845i	−0.385911	+	0.922536i	$0.626113\pi$
$317$	−23.2962	+	23.2962i	−1.30845	+	1.30845i	−0.922536	+	0.385911i	$0.873887\pi$
$318$		0			0
$319$	−0.0570205			−0.00319253
$320$	7.73623	+	2.03734i	0.432468	+	0.113891i
$321$		0			0
$322$	−7.60762	+	5.33503i	−0.423956	+	0.297310i
$323$	−27.4531	+	27.4531i	−1.52753	+	1.52753i
$324$		0			0
$325$	1.72965	+	1.72965i	0.0959439	+	0.0959439i
$326$	−4.64741	+	26.4675i	−0.257396	+	1.46590i
$327$		0			0
$328$	−10.2799	+	2.77816i	−0.567612	+	0.153398i
$329$			21.9804i			1.21182i
$330$		0			0
$331$	−15.9057	−	15.9057i	−0.874257	−	0.874257i	0.118676	−	0.992933i	$-0.462135\pi$
$331$	−15.9057	−	15.9057i	−0.874257	−	0.874257i	−0.992933	+	0.118676i	$0.962135\pi$
$332$	6.37433	+	13.6189i	0.349837	+	0.747432i
$333$		0			0
$334$	4.12806	+	5.88651i	0.225877	+	0.322096i
$335$	15.5712			0.850745
$336$		0			0
$337$	7.15503			0.389759			0.194880	−	0.980827i	$-0.437568\pi$
$337$	7.15503			0.389759			0.194880	+	0.980827i	$0.437568\pi$
$338$	−5.69740	−	8.12435i	−0.309898	−	0.441906i
$339$		0			0
$340$	−10.0523	+	4.70497i	−0.545160	+	0.255163i
$341$	0.0318498	+	0.0318498i	0.00172477	+	0.00172477i
$342$		0			0
$343$			20.1596i			1.08852i
$344$	−13.5735	+	23.6270i	−0.731833	+	1.27388i
$345$		0			0
$346$	−3.76397	+	21.4362i	−0.202352	+	1.15242i
$347$	9.64716	+	9.64716i	0.517887	+	0.517887i	0.916931	−	0.399045i	$-0.130658\pi$
$347$	9.64716	+	9.64716i	0.517887	+	0.517887i	−0.399045	+	0.916931i	$0.630658\pi$
$348$		0			0
$349$	20.3332	−	20.3332i	1.08841	−	1.08841i	0.0927209	−	0.995692i	$-0.470444\pi$
$349$	20.3332	−	20.3332i	1.08841	−	1.08841i	0.995692	−	0.0927209i	$-0.0295564\pi$
$350$	2.52486	−	1.77062i	0.134959	−	0.0946437i
$351$		0			0
$352$	0.0459426	+	0.0543560i	0.00244875	+	0.00289719i
$353$	−32.1660			−1.71202			−0.856010	−	0.516958i	$-0.827064\pi$
$353$	−32.1660			−1.71202			−0.856010	+	0.516958i	$0.827064\pi$
$354$		0			0
$355$	8.56251	−	8.56251i	0.454451	−	0.454451i
$356$	9.52225	+	3.45038i	0.504678	+	0.182870i
$357$		0			0
$358$	3.86421	−	22.0071i	0.204230	−	1.16311i
$359$		−	15.8239i		−	0.835155i	−0.908641	−	0.417578i	$-0.862879\pi$
$359$		−	15.8239i		−	0.835155i	0.908641	−	0.417578i	$-0.137121\pi$
$360$		0			0
$361$		−	29.9461i		−	1.57611i
$362$	19.9901	+	3.51003i	1.05065	+	0.184483i
$363$		0			0
$364$	9.66195	−	4.52229i	0.506424	−	0.237033i
$365$	−5.04154	+	5.04154i	−0.263886	+	0.263886i
$366$		0			0
$367$	4.34838			0.226984			0.113492	−	0.993539i	$-0.463796\pi$
$367$	4.34838			0.226984			0.113492	+	0.993539i	$0.463796\pi$
$368$	−7.72063	+	9.25477i	−0.402466	+	0.482438i
$369$		0			0
$370$	5.71591	+	8.15074i	0.297156	+	0.423737i
$371$	−2.03372	+	2.03372i	−0.105586	+	0.105586i
$372$		0			0
$373$	−17.3659	−	17.3659i	−0.899171	−	0.899171i	0.0961919	−	0.995363i	$-0.469334\pi$
$373$	−17.3659	−	17.3659i	−0.899171	−	0.899171i	−0.995363	+	0.0961919i	$0.969334\pi$
$374$	−0.0972517	−	0.0170763i	−0.00502876	−	0.000882996i
$375$		0			0
$376$	7.43818	+	27.5231i	0.383595	+	1.41940i
$377$			11.0861i			0.570961i
$378$		0			0
$379$	−15.3936	−	15.3936i	−0.790717	−	0.790717i	0.190893	−	0.981611i	$-0.438862\pi$
$379$	−15.3936	−	15.3936i	−0.790717	−	0.790717i	−0.981611	+	0.190893i	$0.938862\pi$
$380$	4.76682	−	13.1553i	0.244533	−	0.674853i
$381$		0			0
$382$	15.4826	−	10.8576i	0.792159	−	0.555521i
$383$	15.6393			0.799129			0.399564	−	0.916705i	$-0.369161\pi$
$383$	15.6393			0.799129			0.399564	+	0.916705i	$0.369161\pi$
$384$		0			0
$385$	0.0274349			0.00139821
$386$	−9.64423	+	6.76326i	−0.490879	+	0.344241i
$387$		0			0
$388$	−7.06193	+	19.4893i	−0.358515	+	0.989417i
$389$	−17.0067	−	17.0067i	−0.862276	−	0.862276i	0.129326	−	0.991602i	$-0.458719\pi$
$389$	−17.0067	−	17.0067i	−0.862276	−	0.862276i	−0.991602	+	0.129326i	$0.958719\pi$
$390$		0			0
$391$		−	16.7209i		−	0.845612i
$392$	1.65662	+	6.12989i	0.0836717	+	0.309606i
$393$		0			0
$394$	26.0012	+	4.56553i	1.30992	+	0.230008i
$395$	2.41682	+	2.41682i	0.121603	+	0.121603i
$396$		0			0
$397$	−12.5043	+	12.5043i	−0.627572	+	0.627572i	−0.947457	−	0.319884i	$-0.896356\pi$
$397$	−12.5043	+	12.5043i	−0.627572	+	0.627572i	0.319884	+	0.947457i	$0.396356\pi$
$398$	−2.97767	−	4.24608i	−0.149257	−	0.212837i
$399$		0			0
$400$	2.56237	−	3.07153i	0.128118	−	0.153576i
$401$	14.6398			0.731079			0.365539	−	0.930796i	$-0.380885\pi$
$401$	14.6398			0.731079			0.365539	+	0.930796i	$0.380885\pi$
$402$		0			0
$403$	6.19232	−	6.19232i	0.308461	−	0.308461i
$404$	−25.5253	+	11.9471i	−1.26993	+	0.594393i
$405$		0			0
$406$	13.7657	+	2.41711i	0.683183	+	0.119959i
$407$			0.0885653i			0.00439002i
$408$		0			0
$409$			33.5504i			1.65896i	0.558537	+	0.829479i	$0.311363\pi$
$409$			33.5504i			1.65896i	−0.558537	+	0.829479i	$0.688637\pi$
$410$	−0.920808	+	5.24411i	−0.0454754	+	0.258988i
$411$		0			0
$412$	−4.23372	−	1.53409i	−0.208580	−	0.0755790i
$413$	−10.0421	+	10.0421i	−0.494141	+	0.494141i
$414$		0			0
$415$	7.51840			0.369064
$416$	10.5680	−	8.93227i	0.518140	−	0.437941i
$417$		0			0
$418$	0.101917	−	0.0714721i	0.00498495	−	0.00349582i
$419$	−16.5641	+	16.5641i	−0.809211	+	0.809211i	−0.984514	−	0.175303i	$-0.943909\pi$
$419$	−16.5641	+	16.5641i	−0.809211	+	0.809211i	0.175303	+	0.984514i	$0.443909\pi$
$420$		0			0
$421$	14.1472	+	14.1472i	0.689492	+	0.689492i	0.962120	−	0.272628i	$-0.0878928\pi$
$421$	14.1472	+	14.1472i	0.689492	+	0.689492i	−0.272628	+	0.962120i	$0.587893\pi$
$422$	4.37280	−	24.9036i	0.212865	−	1.21229i
$423$		0			0
$424$	−1.85834	+	3.23477i	−0.0902492	+	0.157094i
$425$			5.54943i			0.269187i
$426$		0			0
$427$	9.09635	+	9.09635i	0.440203	+	0.440203i
$428$	−6.43241	+	3.01070i	−0.310922	+	0.145528i
$429$		0			0
$430$	7.82250	+	11.1547i	0.377235	+	0.537927i
$431$	−13.1169			−0.631819			−0.315909	−	0.948789i	$-0.602310\pi$
$431$	−13.1169			−0.631819			−0.315909	+	0.948789i	$0.602310\pi$
$432$		0			0
$433$	0.300976			0.0144640			0.00723199	−	0.999974i	$-0.497698\pi$
$433$	0.300976			0.0144640			0.00723199	+	0.999974i	$0.497698\pi$
$434$	−6.33899	−	9.03924i	−0.304281	−	0.433897i
$435$		0			0
$436$	−14.4683	−	30.9117i	−0.692905	−	1.48040i
$437$	14.9058	+	14.9058i	0.713041	+	0.713041i
$438$		0			0
$439$			30.3358i			1.44785i	0.689879	+	0.723925i	$0.257664\pi$
$439$			30.3358i			1.44785i	−0.689879	+	0.723925i	$0.742336\pi$
$440$	0.0343531	−	0.00928399i	0.00163772	−	0.000442597i
$441$		0			0
$442$	−3.32002	+	18.9079i	−0.157917	+	0.899357i
$443$	3.99367	+	3.99367i	0.189745	+	0.189745i	0.795586	−	0.605841i	$-0.207163\pi$
$443$	3.99367	+	3.99367i	0.189745	+	0.189745i	−0.605841	+	0.795586i	$0.707163\pi$
$444$		0			0
$445$	3.58082	−	3.58082i	0.169747	−	0.169747i
$446$	6.22278	−	4.36388i	0.294657	−	0.206636i
$447$		0			0
$448$	−8.78720	−	15.0700i	−0.415156	−	0.711992i
$449$	10.4806			0.494610			0.247305	−	0.968938i	$-0.420455\pi$
$449$	10.4806			0.494610			0.247305	+	0.968938i	$0.420455\pi$
$450$		0			0
$451$	−0.0334937	+	0.0334937i	−0.00157716	+	0.00157716i
$452$	13.4876	−	37.2225i	0.634402	−	1.75080i
$453$		0			0
$454$	0.665160	−	3.78816i	0.0312175	−	0.177787i
$455$		−	5.33396i		−	0.250060i
$456$		0			0
$457$		−	5.70188i		−	0.266723i	−0.991067	−	0.133361i	$-0.957423\pi$
$457$		−	5.70188i		−	0.266723i	0.991067	−	0.133361i	$-0.0425771\pi$
$458$	−10.0090	−	1.75746i	−0.467688	−	0.0821208i
$459$		0			0
$460$	2.55459	+	5.45791i	0.119108	+	0.254477i
$461$	−1.78282	+	1.78282i	−0.0830341	+	0.0830341i	−0.747404	−	0.664370i	$-0.768700\pi$
$461$	−1.78282	+	1.78282i	−0.0830341	+	0.0830341i	0.664370	+	0.747404i	$0.268700\pi$
$462$		0			0
$463$	−37.2015			−1.72890			−0.864451	−	0.502717i	$-0.832334\pi$
$463$	−37.2015			−1.72890			−0.864451	+	0.502717i	$0.832334\pi$
$464$	18.0550	−	1.63171i	0.838181	−	0.0757503i
$465$		0			0
$466$	21.3079	+	30.3846i	0.987071	+	1.40754i
$467$	14.3669	−	14.3669i	0.664822	−	0.664822i	−0.291691	−	0.956513i	$-0.594218\pi$
$467$	14.3669	−	14.3669i	0.664822	−	0.664822i	0.956513	+	0.291691i	$0.0942179\pi$
$468$		0			0
$469$	−24.0094	−	24.0094i	−1.10865	−	1.10865i
$470$	14.0404	+	2.46535i	0.647637	+	0.113718i
$471$		0			0
$472$	−9.17616	+	15.9727i	−0.422367	+	0.735202i
$473$			0.121206i			0.00557305i
$474$		0			0
$475$	−4.94702	−	4.94702i	−0.226985	−	0.226985i
$476$	22.7544	+	8.24505i	1.04295	+	0.377911i
$477$		0			0
$478$	−8.57905	+	6.01627i	−0.392397	+	0.275178i
$479$	36.6561			1.67486			0.837431	−	0.546544i	$-0.184057\pi$
$479$	36.6561			1.67486			0.837431	+	0.546544i	$0.184057\pi$
$480$		0			0
$481$	17.2191			0.785122
$482$	22.7211	−	15.9338i	1.03492	−	0.725763i
$483$		0			0
$484$	−20.6837	−	7.49473i	−0.940168	−	0.340670i
$485$	7.32890	+	7.32890i	0.332788	+	0.332788i
$486$		0			0
$487$		−	34.3322i		−	1.55574i	−0.628425	−	0.777870i	$-0.716300\pi$
$487$		−	34.3322i		−	1.55574i	0.628425	−	0.777870i	$-0.283700\pi$
$488$	14.4684	+	8.31194i	0.654952	+	0.376264i
$489$		0			0
$490$	3.12706	+	0.549077i	0.141266	+	0.0248048i
$491$	−17.6224	−	17.6224i	−0.795287	−	0.795287i	0.187061	−	0.982348i	$-0.440104\pi$
$491$	−17.6224	−	17.6224i	−0.795287	−	0.795287i	−0.982348	+	0.187061i	$0.940104\pi$
$492$		0			0
$493$	−17.7843	+	17.7843i	−0.800963	+	0.800963i
$494$	−13.8958	−	19.8150i	−0.625201	−	0.891520i
$495$		0			0
$496$	−10.9964	−	9.17351i	−0.493751	−	0.411903i
$497$	−26.4053			−1.18444
$498$		0			0
$499$	−14.6801	+	14.6801i	−0.657173	+	0.657173i	−0.954710	−	0.297537i	$-0.903835\pi$
$499$	−14.6801	+	14.6801i	−0.657173	+	0.657173i	0.297537	+	0.954710i	$0.403835\pi$
$500$	−0.847831	−	1.81140i	−0.0379161	−	0.0810084i
$501$		0			0
$502$	2.43494	+	0.427549i	0.108677	+	0.0190824i
$503$		−	13.0618i		−	0.582398i	−0.956663	−	0.291199i	$-0.905946\pi$
$503$		−	13.0618i		−	0.582398i	0.956663	−	0.291199i	$-0.0940541\pi$
$504$		0			0
$505$			14.0914i			0.627060i
$506$	−0.00927166	+	0.0528032i	−0.000412176	+	0.00234739i
$507$		0			0
$508$	9.81032	−	27.0742i	0.435263	−	1.20122i
$509$	22.0202	−	22.0202i	0.976027	−	0.976027i	−0.0236921	−	0.999719i	$-0.507542\pi$
$509$	22.0202	−	22.0202i	0.976027	−	0.976027i	0.999719	+	0.0236921i	$0.00754213\pi$
$510$		0			0
$511$	15.5472			0.687770
$512$	−16.1027	−	15.8966i	−0.711648	−	0.702537i
$513$		0			0
$514$	3.48578	−	2.44449i	0.153751	−	0.107822i
$515$	−1.59208	+	1.59208i	−0.0701555	+	0.0701555i
$516$		0			0
$517$	0.0896752	+	0.0896752i	0.00394391	+	0.00394391i
$518$	3.75431	−	21.3812i	0.164955	−	0.939437i
$519$		0			0
$520$	−1.80502	−	6.67900i	−0.0791552	−	0.292894i
$521$			22.0123i			0.964375i	0.876068	+	0.482188i	$0.160158\pi$
$521$			22.0123i			0.964375i	−0.876068	+	0.482188i	$0.839842\pi$
$522$		0			0
$523$	−14.7575	−	14.7575i	−0.645299	−	0.645299i	0.306554	−	0.951853i	$-0.400824\pi$
$523$	−14.7575	−	14.7575i	−0.645299	−	0.645299i	−0.951853	+	0.306554i	$0.900824\pi$
$524$	−0.689138	−	1.47235i	−0.0301051	−	0.0643201i
$525$		0			0
$526$	9.66269	+	13.7788i	0.421313	+	0.600782i
$527$	19.8675			0.865441
$528$		0			0
$529$	13.9213			0.605275
$530$	1.07098	+	1.52719i	0.0465203	+	0.0663368i
$531$		0			0
$532$	−27.6344	+	12.9343i	−1.19810	+	0.560774i
$533$	6.51192	+	6.51192i	0.282063	+	0.282063i
$534$		0			0
$535$			3.55106i			0.153526i
$536$	−38.1887	−	21.9390i	−1.64950	−	0.947621i
$537$		0			0
$538$	−5.35948	+	30.5229i	−0.231064	+	1.31593i
$539$	0.0199723	+	0.0199723i	0.000860267	+	0.000860267i
$540$		0			0
$541$	8.39925	−	8.39925i	0.361112	−	0.361112i	−0.503110	−	0.864222i	$-0.667811\pi$
$541$	8.39925	−	8.39925i	0.361112	−	0.361112i	0.864222	+	0.503110i	$0.167811\pi$
$542$	−8.45818	+	5.93151i	−0.363310	+	0.254780i
$543$		0			0
$544$	31.2824	+	2.62407i	1.34122	+	0.112506i
$545$	−17.0651			−0.730987
$546$		0			0
$547$	−8.81903	+	8.81903i	−0.377074	+	0.377074i	−0.870046	−	0.492971i	$-0.835911\pi$
$547$	−8.81903	+	8.81903i	−0.377074	+	0.377074i	0.492971	+	0.870046i	$0.335911\pi$
$548$	30.1003	+	10.9069i	1.28582	+	0.465918i
$549$		0			0
$550$	0.00307713	−	0.0175246i	0.000131209	−	0.000747253i
$551$		−	31.7075i		−	1.35079i
$552$		0			0
$553$		−	7.45305i		−	0.316936i
$554$	−4.40694	−	0.773810i	−0.187233	−	0.0328760i
$555$		0			0
$556$	−3.90465	+	1.82758i	−0.165594	+	0.0775066i
$557$	−6.98592	+	6.98592i	−0.296003	+	0.296003i	−0.839446	−	0.543443i	$-0.817120\pi$
$557$	−6.98592	+	6.98592i	−0.296003	+	0.296003i	0.543443	+	0.839446i	$0.317120\pi$
$558$		0			0
$559$	23.5651			0.996699
$560$	−8.68699	+	0.785083i	−0.367092	+	0.0331758i
$561$		0			0
$562$	−3.93844	−	5.61612i	−0.166133	−	0.236902i
$563$	−3.94396	+	3.94396i	−0.166218	+	0.166218i	−0.785315	−	0.619097i	$-0.787499\pi$
$563$	−3.94396	+	3.94396i	−0.166218	+	0.166218i	0.619097	+	0.785315i	$0.287499\pi$
$564$		0			0
$565$	−13.9975	−	13.9975i	−0.588877	−	0.588877i
$566$	−22.5146	−	3.95331i	−0.946358	−	0.166170i
$567$		0			0
$568$	−33.0639	+	8.93559i	−1.38733	+	0.374929i
$569$		−	31.6307i		−	1.32603i	−0.748607	−	0.663014i	$-0.769277\pi$
$569$		−	31.6307i		−	1.32603i	0.748607	−	0.663014i	$-0.230723\pi$
$570$		0			0
$571$	5.70590	+	5.70590i	0.238785	+	0.238785i	0.816347	−	0.577562i	$-0.195996\pi$
$571$	5.70590	+	5.70590i	0.238785	+	0.238785i	−0.577562	+	0.816347i	$0.695996\pi$
$572$	0.0209687	−	0.0578686i	0.000876745	−	0.00241961i
$573$		0			0
$574$	9.50578	−	6.66616i	0.396764	−	0.278240i
$575$	3.01309			0.125654
$576$		0			0
$577$	21.9772			0.914921			0.457461	−	0.889230i	$-0.348759\pi$
$577$	21.9772			0.914921			0.457461	+	0.889230i	$0.348759\pi$
$578$	−15.9742	+	11.2023i	−0.664439	+	0.465954i
$579$		0			0
$580$	3.08797	−	8.52206i	0.128221	−	0.353859i
$581$	−11.5927	−	11.5927i	−0.480948	−	0.480948i
$582$		0			0
$583$			0.0165943i			0.000687265i
$584$	19.4677	−	5.26120i	0.805581	−	0.217710i
$585$		0			0
$586$	−22.0006	−	3.86306i	−0.908835	−	0.159581i
$587$	15.3747	+	15.3747i	0.634583	+	0.634583i	0.949214	−	0.314631i	$-0.101881\pi$
$587$	15.3747	+	15.3747i	0.634583	+	0.634583i	−0.314631	+	0.949214i	$0.601881\pi$
$588$		0			0
$589$	−17.7108	+	17.7108i	−0.729761	+	0.729761i
$590$	5.28829	+	7.54096i	0.217715	+	0.310457i
$591$		0			0
$592$	−2.53440	−	28.0433i	−0.104163	−	1.15257i
$593$	16.9206			0.694846			0.347423	−	0.937708i	$-0.387057\pi$
$593$	16.9206			0.694846			0.347423	+	0.937708i	$0.387057\pi$
$594$		0			0
$595$	8.55675	−	8.55675i	0.350792	−	0.350792i
$596$	−31.1017	+	14.5572i	−1.27398	+	0.596287i
$597$		0			0
$598$	10.2661	+	1.80262i	0.419813	+	0.0737145i
$599$			19.1715i			0.783327i	0.920109	+	0.391663i	$0.128100\pi$
$599$			19.1715i			0.783327i	−0.920109	+	0.391663i	$0.871900\pi$
$600$		0			0
$601$		−	10.1428i		−	0.413735i	−0.978369	−	0.206867i	$-0.933673\pi$
$601$		−	10.1428i		−	0.413735i	0.978369	−	0.206867i	$-0.0663269\pi$
$602$	5.13795	−	29.2612i	0.209407	−	1.19260i
$603$		0			0
$604$	−24.0573	−	8.71717i	−0.978879	−	0.354696i
$605$	−7.77806	+	7.77806i	−0.316223	+	0.316223i
$606$		0			0
$607$	6.80048			0.276023			0.138011	−	0.990431i	$-0.455929\pi$
$607$	6.80048			0.276023			0.138011	+	0.990431i	$0.455929\pi$
$608$	−30.2259	+	25.5474i	−1.22582	+	1.03609i
$609$		0			0
$610$	6.83075	−	4.79023i	0.276569	−	0.193951i
$611$	17.4349	−	17.4349i	0.705339	−	0.705339i
$612$		0			0
$613$	18.1431	+	18.1431i	0.732793	+	0.732793i	0.971172	−	0.238379i	$-0.0766161\pi$
$613$	18.1431	+	18.1431i	0.732793	+	0.732793i	−0.238379	+	0.971172i	$0.576616\pi$
$614$	−4.68213	+	26.6653i	−0.188955	+	1.07612i
$615$		0			0
$616$	−0.0672847	−	0.0386544i	−0.00271098	−	0.00155743i
$617$			30.4488i			1.22582i	0.790151	+	0.612912i	$0.210002\pi$
$617$			30.4488i			1.22582i	−0.790151	+	0.612912i	$0.789998\pi$
$618$		0			0
$619$	−12.1946	−	12.1946i	−0.490143	−	0.490143i	0.418208	−	0.908351i	$-0.362658\pi$
$619$	−12.1946	−	12.1946i	−0.490143	−	0.490143i	−0.908351	+	0.418208i	$0.862658\pi$
$620$	−6.48500	+	3.03531i	−0.260444	+	0.121901i
$621$		0			0
$622$	13.3942	+	19.0998i	0.537059	+	0.765833i
$623$	−11.0427			−0.442415
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−22.1307	−	31.5578i	−0.884519	−	1.26130i
$627$		0			0
$628$	12.3898	+	26.4709i	0.494405	+	1.05630i
$629$	27.6229	+	27.6229i	1.10140	+	1.10140i
$630$		0			0
$631$		−	27.9943i		−	1.11444i	−0.830366	−	0.557218i	$-0.811869\pi$
$631$		−	27.9943i		−	1.11444i	0.830366	−	0.557218i	$-0.188131\pi$
$632$	−2.52212	−	9.33246i	−0.100324	−	0.371225i
$633$		0			0
$634$	8.05785	−	45.8904i	0.320018	−	1.82254i
$635$	−10.1812	−	10.1812i	−0.404028	−	0.404028i
$636$		0			0
$637$	3.88306	−	3.88306i	0.153852	−	0.153852i
$638$	0.0660226	−	0.0463000i	0.00261386	−	0.00183303i
$639$		0			0
$640$	−10.6119	+	3.92274i	−0.419472	+	0.155060i
$641$	−5.01913			−0.198244			−0.0991219	−	0.995075i	$-0.531603\pi$
$641$	−5.01913			−0.198244			−0.0991219	+	0.995075i	$0.531603\pi$
$642$		0			0
$643$	1.55218	−	1.55218i	0.0612118	−	0.0612118i	−0.675838	−	0.737050i	$-0.736218\pi$
$643$	1.55218	−	1.55218i	0.0612118	−	0.0612118i	0.737050	+	0.675838i	$0.236218\pi$
$644$	4.47669	−	12.3546i	0.176406	−	0.486839i
$645$		0			0
$646$	9.49567	−	54.0790i	0.373602	−	2.12771i
$647$		−	24.6915i		−	0.970722i	−0.874314	−	0.485361i	$-0.838688\pi$
$647$		−	24.6915i		−	0.970722i	0.874314	−	0.485361i	$-0.161312\pi$
$648$		0			0
$649$			0.0819394i			0.00321640i
$650$	−3.40718	−	0.598263i	−0.133641	−	0.0234658i
$651$		0			0
$652$	−16.1102	−	34.4197i	−0.630925	−	1.34798i
$653$	10.4301	−	10.4301i	0.408161	−	0.408161i	−0.472936	−	0.881097i	$-0.656806\pi$
$653$	10.4301	−	10.4301i	0.408161	−	0.408161i	0.881097	+	0.472936i	$0.156806\pi$
$654$		0			0
$655$	−0.812825			−0.0317597
$656$	9.64699	−	11.5639i	0.376652	−	0.451495i
$657$		0			0
$658$	−17.8478	−	25.4505i	−0.695781	−	0.992165i
$659$	15.4151	−	15.4151i	0.600487	−	0.600487i	−0.339955	−	0.940442i	$-0.610412\pi$
$659$	15.4151	−	15.4151i	0.600487	−	0.600487i	0.940442	+	0.339955i	$0.110412\pi$
$660$		0			0
$661$	17.9150	+	17.9150i	0.696813	+	0.696813i	0.963722	−	0.266909i	$-0.0860022\pi$
$661$	17.9150	+	17.9150i	0.696813	+	0.696813i	−0.266909	+	0.963722i	$0.586002\pi$
$662$	31.3321	+	5.50157i	1.21776	+	0.213825i
$663$		0			0
$664$	−18.4390	−	10.5931i	−0.715574	−	0.411090i
$665$			15.2558i			0.591594i
$666$		0			0
$667$	9.65605	+	9.65605i	0.373884	+	0.373884i
$668$	−9.55956	−	3.46390i	−0.369870	−	0.134022i
$669$		0			0
$670$	−18.0295	+	12.6436i	−0.696540	+	0.488466i
$671$	0.0742223			0.00286532
$672$		0			0
$673$	28.8891			1.11359			0.556796	−	0.830649i	$-0.312030\pi$
$673$	28.8891			1.11359			0.556796	+	0.830649i	$0.312030\pi$
$674$	−8.28463	+	5.80981i	−0.319112	+	0.223785i
$675$		0			0
$676$	13.1938	+	4.78076i	0.507452	+	0.183875i
$677$	−10.8421	−	10.8421i	−0.416695	−	0.416695i	0.467368	−	0.884063i	$-0.345202\pi$
$677$	−10.8421	−	10.8421i	−0.416695	−	0.416695i	−0.884063	+	0.467368i	$0.845202\pi$
$678$		0			0
$679$		−	22.6011i		−	0.867350i
$680$	7.81886	−	13.6101i	0.299840	−	0.521923i
$681$		0			0
$682$	−0.0627398	−	0.0110164i	−0.00240243	−	0.000421841i
$683$	2.04256	+	2.04256i	0.0781564	+	0.0781564i	0.745104	−	0.666948i	$-0.232400\pi$
$683$	2.04256	+	2.04256i	0.0781564	+	0.0781564i	−0.666948	+	0.745104i	$0.732400\pi$
$684$		0			0
$685$	11.3192	−	11.3192i	0.432484	−	0.432484i
$686$	−16.3694	−	23.3423i	−0.624986	−	0.891214i
$687$		0			0
$688$	−3.46845	−	38.3786i	−0.132234	−	1.46317i
$689$	3.22630			0.122912
$690$		0			0
$691$	33.4347	−	33.4347i	1.27192	−	1.27192i	0.326837	−	0.945081i	$-0.394017\pi$
$691$	33.4347	−	33.4347i	1.27192	−	1.27192i	0.945081	−	0.326837i	$-0.105983\pi$
$692$	−13.0478	−	27.8768i	−0.496002	−	1.05972i
$693$		0			0
$694$	−19.0036	−	3.33682i	−0.721366	−	0.126664i
$695$			2.15559i			0.0817664i
$696$		0			0
$697$			20.8929i			0.791375i
$698$	−7.03299	+	40.0537i	−0.266203	+	1.51605i
$699$		0			0
$700$	−1.48575	+	4.10031i	−0.0561560	+	0.154977i
$701$	−4.02037	+	4.02037i	−0.151847	+	0.151847i	−0.778943	−	0.627095i	$-0.784244\pi$
$701$	−4.02037	+	4.02037i	−0.151847	+	0.151847i	0.627095	+	0.778943i	$0.284244\pi$
$702$		0			0
$703$	−49.2487			−1.85745
$704$	−0.0973323	−	0.0256326i	−0.00366835	−	0.000966064i
$705$		0			0
$706$	37.2442	−	26.1184i	1.40170	−	0.982978i
$707$	21.7278	−	21.7278i	0.817158	−	0.817158i
$708$		0			0
$709$	18.0101	+	18.0101i	0.676385	+	0.676385i	0.959180	−	0.282795i	$-0.0912617\pi$
$709$	18.0101	+	18.0101i	0.676385	+	0.676385i	−0.282795	+	0.959180i	$0.591262\pi$
$710$	−2.96166	+	16.8670i	−0.111149	+	0.633006i
$711$		0			0
$712$	−13.8272	+	3.73684i	−0.518198	+	0.140044i
$713$		−	10.7871i		−	0.403981i
$714$		0			0
$715$	−0.0217614	−	0.0217614i	−0.000813830	−	0.000813830i
$716$	13.3953	+	28.6192i	0.500605	+	1.06955i
$717$		0			0
$718$	12.8489	+	18.3221i	0.479515	+	0.683776i
$719$	−50.2917			−1.87556			−0.937782	−	0.347224i	$-0.887124\pi$
$719$	−50.2917			−1.87556			−0.937782	+	0.347224i	$0.887124\pi$
$720$		0			0
$721$	4.90971			0.182847
$722$	24.3159	+	34.6739i	0.904944	+	1.29043i
$723$		0			0
$724$	−25.9961	+	12.1675i	−0.966137	+	0.452202i
$725$	−3.20471	−	3.20471i	−0.119020	−	0.119020i
$726$		0			0
$727$		−	15.1799i		−	0.562991i	−0.959562	−	0.281496i	$-0.909169\pi$
$727$		−	15.1799i		−	0.562991i	0.959562	−	0.281496i	$-0.0908305\pi$
$728$	−7.51528	+	13.0816i	−0.278535	+	0.484838i
$729$		0			0
$730$	1.74380	−	9.93114i	0.0645409	−	0.367568i
$731$	37.8032	+	37.8032i	1.39820	+	1.39820i
$732$		0			0
$733$	−12.1524	+	12.1524i	−0.448859	+	0.448859i	−0.894975	−	0.446116i	$-0.852807\pi$
$733$	−12.1524	+	12.1524i	−0.448859	+	0.448859i	0.446116	+	0.894975i	$0.352807\pi$
$734$	−5.03488	+	3.53084i	−0.185841	+	0.130326i
$735$		0			0
$736$	1.42475	−	16.9849i	0.0525170	−	0.626073i
$737$	−0.195907			−0.00721632
$738$		0			0
$739$	−17.9947	+	17.9947i	−0.661947	+	0.661947i	−0.955839	−	0.293892i	$-0.905050\pi$
$739$	−17.9947	+	17.9947i	−0.661947	+	0.661947i	0.293892	+	0.955839i	$0.405050\pi$
$740$	−13.2366	−	4.79629i	−0.486588	−	0.176315i
$741$		0			0
$742$	0.703436	−	4.00615i	0.0258240	−	0.147070i
$743$			19.2456i			0.706051i	0.935614	+	0.353026i	$0.114847\pi$
$743$			19.2456i			0.706051i	−0.935614	+	0.353026i	$0.885153\pi$
$744$		0			0
$745$			17.1700i			0.629059i
$746$	34.2084	+	6.00662i	1.25246	+	0.219918i
$747$		0			0
$748$	0.126471	−	0.0591950i	0.00462424	−	0.00216438i
$749$	5.47544	−	5.47544i	0.200068	−	0.200068i
$750$		0			0
$751$	−53.5813			−1.95521			−0.977604	−	0.210451i	$-0.932507\pi$
$751$	−53.5813			−1.95521			−0.977604	+	0.210451i	$0.932507\pi$
$752$	−30.9609	−	25.8286i	−1.12903	−	0.941872i
$753$		0			0
$754$	−9.00175	−	12.8363i	−0.327824	−	0.467469i
$755$	−9.04671	+	9.04671i	−0.329244	+	0.329244i
$756$		0			0
$757$	10.4133	+	10.4133i	0.378477	+	0.378477i	0.870552	−	0.492076i	$-0.163762\pi$
$757$	10.4133	+	10.4133i	0.378477	+	0.378477i	−0.492076	+	0.870552i	$0.663762\pi$
$758$	30.3233	+	5.32445i	1.10139	+	0.193393i
$759$		0			0
$760$	5.16257	+	19.1028i	0.187266	+	0.692931i
$761$		−	38.1651i		−	1.38348i	−0.722145	−	0.691742i	$-0.756844\pi$
$761$		−	38.1651i		−	1.38348i	0.722145	−	0.691742i	$-0.243156\pi$
$762$		0			0
$763$	26.3129	+	26.3129i	0.952590	+	0.952590i
$764$	−9.11070	+	25.1434i	−0.329614	+	0.909656i
$765$		0			0
$766$	−18.1083	+	12.6989i	−0.654279	+	0.458830i
$767$	15.9309			0.575230
$768$		0			0
$769$	−38.1071			−1.37418			−0.687089	−	0.726573i	$-0.741112\pi$
$769$	−38.1071			−1.37418			−0.687089	+	0.726573i	$0.741112\pi$
$770$	−0.0317662	+	0.0222768i	−0.00114477	+	0.000802801i
$771$		0			0
$772$	5.67513	−	15.6620i	0.204252	−	0.563688i
$773$	32.9401	+	32.9401i	1.18477	+	1.18477i	0.978493	+	0.206280i	$0.0661358\pi$
$773$	32.9401	+	32.9401i	1.18477	+	1.18477i	0.206280	+	0.978493i	$0.433864\pi$
$774$		0			0
$775$			3.58009i			0.128601i
$776$	−7.64822	−	28.3003i	−0.274555	−	1.01592i
$777$		0			0
$778$	33.5010	+	5.88240i	1.20107	+	0.210894i
$779$	−18.6249	−	18.6249i	−0.667307	−	0.667307i
$780$		0			0
$781$	−0.107728	+	0.107728i	−0.00385481	+	0.00385481i
$782$	13.5772	+	19.3607i	0.485519	+	0.692337i
$783$		0			0
$784$	−6.89556	−	5.75249i	−0.246270	−	0.205446i
$785$	14.6135			0.521577
$786$		0			0
$787$	21.5631	−	21.5631i	0.768642	−	0.768642i	−0.209225	−	0.977867i	$-0.567094\pi$
$787$	21.5631	−	21.5631i	0.768642	−	0.768642i	0.977867	+	0.209225i	$0.0670942\pi$
$788$	−33.8134	+	15.8264i	−1.20455	+	0.563792i
$789$		0			0
$790$	−4.76080	−	0.835944i	−0.169382	−	0.0297415i
$791$			43.1658i			1.53480i
$792$		0			0
$793$		−	14.4305i		−	0.512441i
$794$	4.32506	−	24.6317i	0.153491	−	0.874148i
$795$		0			0
$796$	6.89553	+	2.49859i	0.244406	+	0.0885603i
$797$	−7.81695	+	7.81695i	−0.276891	+	0.276891i	−0.831866	−	0.554976i	$-0.812727\pi$
$797$	−7.81695	+	7.81695i	−0.276891	+	0.276891i	0.554976	+	0.831866i	$0.312727\pi$
$798$		0			0
$799$	55.9381			1.97895
$800$	−0.472855	+	5.63706i	−0.0167179	+	0.199300i
$801$		0			0
$802$	−16.9511	+	11.8874i	−0.598564	+	0.419758i
$803$	0.0634294	−	0.0634294i	0.00223837	−	0.00223837i
$804$		0			0
$805$	−4.64592	−	4.64592i	−0.163747	−	0.163747i
$806$	−2.14184	+	12.1980i	−0.0754430	+	0.429657i
$807$		0			0
$808$	19.8541	−	34.5595i	0.698465	−	1.21580i
$809$			8.21009i			0.288651i	0.989530	+	0.144326i	$0.0461013\pi$
$809$			8.21009i			0.288651i	−0.989530	+	0.144326i	$0.953899\pi$
$810$		0			0
$811$	−0.466318	−	0.466318i	−0.0163746	−	0.0163746i	0.698872	−	0.715247i	$-0.253686\pi$
$811$	−0.466318	−	0.466318i	−0.0163746	−	0.0163746i	−0.715247	+	0.698872i	$0.753686\pi$
$812$	−17.9017	+	8.37892i	−0.628226	+	0.294042i
$813$		0			0
$814$	−0.0719140	−	0.102547i	−0.00252058	−	0.00359429i
$815$	−19.0017			−0.665600
$816$		0			0
$817$	−67.3992			−2.35800
$818$	−27.2425	−	38.8471i	−0.952512	−	1.35826i
$819$		0			0
$820$	−3.19198	−	6.81971i	−0.111469	−	0.238154i
$821$	−22.1688	−	22.1688i	−0.773696	−	0.773696i	0.205054	−	0.978751i	$-0.434263\pi$
$821$	−22.1688	−	22.1688i	−0.773696	−	0.773696i	−0.978751	+	0.205054i	$0.934263\pi$
$822$		0			0
$823$			14.7926i			0.515636i	0.966193	+	0.257818i	$0.0830035\pi$
$823$			14.7926i			0.515636i	−0.966193	+	0.257818i	$0.916996\pi$
$824$	6.14777	−	1.66145i	0.214168	−	0.0578793i
$825$		0			0
$826$	3.47344	−	19.7816i	0.120856	−	0.688291i
$827$	−27.9227	−	27.9227i	−0.970967	−	0.970967i	0.0286237	−	0.999590i	$-0.490888\pi$
$827$	−27.9227	−	27.9227i	−0.970967	−	0.970967i	−0.999590	+	0.0286237i	$0.990888\pi$
$828$		0			0
$829$	−0.798074	+	0.798074i	−0.0277182	+	0.0277182i	−0.720830	−	0.693112i	$-0.756239\pi$
$829$	−0.798074	+	0.798074i	−0.0277182	+	0.0277182i	0.693112	+	0.720830i	$0.256239\pi$
$830$	−8.70537	+	6.10486i	−0.302168	+	0.211903i
$831$		0			0
$832$	−4.98354	+	18.9236i	−0.172773	+	0.656057i
$833$	12.4584			0.431659
$834$		0			0
$835$	−3.59485	+	3.59485i	−0.124405	+	0.124405i
$836$	−0.0599731	+	0.165512i	−0.00207421	+	0.00572434i
$837$		0			0
$838$	5.72931	−	32.6291i	0.197916	−	1.12715i
$839$			29.3983i			1.01494i	0.861669	+	0.507470i	$0.169419\pi$
$839$			29.3983i			1.01494i	−0.861669	+	0.507470i	$0.830581\pi$
$840$		0			0
$841$			8.45973i			0.291715i
$842$	−27.8680	−	4.89332i	−0.960396	−	0.168635i
$843$		0			0
$844$	15.1583	+	32.3859i	0.521770	+	1.11477i
$845$	4.96149	−	4.96149i	0.170680	−	0.170680i
$846$		0			0
$847$	23.9862			0.824177
$848$	−0.474866	−	5.25441i	−0.0163070	−	0.180437i
$849$		0			0
$850$	−4.50607	−	6.42554i	−0.154557	−	0.220394i
$851$	14.9980	−	14.9980i	0.514123	−	0.514123i
$852$		0			0
$853$	24.2137	+	24.2137i	0.829060	+	0.829060i	0.987387	−	0.158326i	$-0.0506098\pi$
$853$	24.2137	+	24.2137i	0.829060	+	0.829060i	−0.158326	+	0.987387i	$0.550610\pi$
$854$	−17.9186	−	3.14630i	−0.613161	−	0.107664i
$855$		0			0
$856$	5.00327	−	8.70906i	0.171008	−	0.297669i
$857$			16.2011i			0.553419i	0.960954	+	0.276709i	$0.0892440\pi$
$857$			16.2011i			0.553419i	−0.960954	+	0.276709i	$0.910756\pi$
$858$		0			0
$859$	0.266646	+	0.266646i	0.00909783	+	0.00909783i	0.711641	−	0.702543i	$-0.247952\pi$
$859$	0.266646	+	0.266646i	0.00909783	+	0.00909783i	−0.702543	+	0.711641i	$0.747952\pi$
$860$	−18.1150	−	6.56395i	−0.617715	−	0.223829i
$861$		0			0
$862$	15.1877	−	10.6508i	0.517296	−	0.362767i
$863$	−10.2561			−0.349121			−0.174560	−	0.984646i	$-0.555850\pi$
$863$	−10.2561			−0.349121			−0.174560	+	0.984646i	$0.555850\pi$
$864$		0			0
$865$	−15.3896			−0.523262
$866$	−0.348492	+	0.244389i	−0.0118422	+	0.00830467i
$867$		0			0
$868$	14.6795	+	5.31912i	0.498255	+	0.180543i
$869$	−0.0304068	−	0.0304068i	−0.00103148	−	0.00103148i
$870$		0			0
$871$			38.0886i			1.29058i
$872$	41.8524	+	24.0438i	1.41730	+	0.814226i
$873$		0			0
$874$	−29.3624	−	5.15572i	−0.993198	−	0.174395i
$875$	1.54192	+	1.54192i	0.0521263	+	0.0521263i
$876$		0			0
$877$	−20.4974	+	20.4974i	−0.692149	+	0.692149i	−0.962704	−	0.270555i	$-0.912793\pi$
$877$	−20.4974	+	20.4974i	−0.692149	+	0.692149i	0.270555	+	0.962704i	$0.412793\pi$
$878$	−24.6323	−	35.1251i	−0.831301	−	1.18541i
$879$		0			0
$880$	−0.0322381	+	0.0386440i	−0.00108675	+	0.00130269i
$881$	56.8144			1.91413			0.957063	−	0.289881i	$-0.0936159\pi$
$881$	56.8144			1.91413			0.957063	+	0.289881i	$0.0936159\pi$
$882$		0			0
$883$	26.2082	−	26.2082i	0.881978	−	0.881978i	−0.111758	−	0.993735i	$-0.535648\pi$
$883$	26.2082	−	26.2082i	0.881978	−	0.881978i	0.993735	+	0.111758i	$0.0356481\pi$
$884$	−11.5088	−	24.5888i	−0.387084	−	0.827011i
$885$		0			0
$886$	−7.86698	−	1.38136i	−0.264296	−	0.0464075i
$887$			26.0161i			0.873537i	0.899574	+	0.436768i	$0.143877\pi$
$887$			26.0161i			0.873537i	−0.899574	+	0.436768i	$0.856123\pi$
$888$		0			0
$889$			31.3971i			1.05302i
$890$	−1.23856	+	7.05373i	−0.0415165	+	0.236442i
$891$		0			0
$892$	−3.66178	+	10.1057i	−0.122606	+	0.338362i
$893$	−49.8659	+	49.8659i	−1.66870	+	1.66870i
$894$		0			0
$895$	15.7995			0.528118
$896$	22.4112	+	10.3141i	0.748704	+	0.344570i
$897$		0			0
$898$	−12.1352	+	8.51013i	−0.404958	+	0.283987i
$899$	−11.4731	+	11.4731i	−0.382651	+	0.382651i
$900$		0			0
$901$	5.17564	+	5.17564i	0.172425	+	0.172425i
$902$	0.0115850	−	0.0659780i	0.000385739	−	0.00219683i
$903$		0			0
$904$	14.6073	+	54.0508i	0.485833	+	1.79770i
$905$			14.3513i			0.477055i
$906$		0			0
$907$	−27.6233	−	27.6233i	−0.917218	−	0.917218i	0.0796085	−	0.996826i	$-0.474633\pi$
$907$	−27.6233	−	27.6233i	−0.917218	−	0.917218i	−0.996826	+	0.0796085i	$0.974633\pi$
$908$	2.30577	+	4.92632i	0.0765198	+	0.163486i
$909$		0			0
$910$	4.33111	+	6.17605i	0.143575	+	0.204734i
$911$	5.83194			0.193221			0.0966104	−	0.995322i	$-0.469200\pi$
$911$	5.83194			0.193221			0.0966104	+	0.995322i	$0.469200\pi$
$912$		0			0
$913$	−0.0945918			−0.00313053
$914$	4.62986	+	6.60207i	0.153142	+	0.218377i
$915$		0			0
$916$	13.0162	−	6.09224i	0.430066	−	0.201293i
$917$	1.25331	+	1.25331i	0.0413879	+	0.0413879i
$918$		0			0
$919$		−	11.8292i		−	0.390208i	−0.980783	−	0.195104i	$-0.937496\pi$
$919$		−	11.8292i		−	0.390208i	0.980783	−	0.195104i	$-0.0625045\pi$
$920$	−7.38965	−	4.24529i	−0.243630	−	0.139963i
$921$		0			0
$922$	0.616653	−	3.51191i	0.0203084	−	0.115659i
$923$	20.9447	+	20.9447i	0.689405	+	0.689405i
$924$		0			0
$925$	−4.97761	+	4.97761i	−0.163663	+	0.163663i
$926$	43.0747	−	30.2072i	1.41552	−	0.992671i
$927$		0			0
$928$	−19.5805	+	16.5497i	−0.642760	+	0.543272i
$929$	45.8141			1.50311			0.751556	−	0.659669i	$-0.229304\pi$
$929$	45.8141			1.50311			0.751556	+	0.659669i	$0.229304\pi$
$930$		0			0
$931$	−11.1060	+	11.1060i	−0.363986	+	0.363986i
$932$	−49.3438	−	17.8797i	−1.61631	−	0.585670i
$933$		0			0
$934$	−4.96932	+	28.3009i	−0.162601	+	0.926033i
$935$		−	0.0698194i		−	0.00228334i
$936$		0			0
$937$			6.21014i			0.202876i	0.994842	+	0.101438i	$0.0323444\pi$
$937$			6.21014i			0.202876i	−0.994842	+	0.101438i	$0.967656\pi$
$938$	47.2953	+	8.30454i	1.54425	+	0.271153i
$939$		0			0
$940$	−18.2589	+	8.54612i	−0.595540	+	0.278744i
$941$	2.43886	−	2.43886i	0.0795045	−	0.0795045i	−0.666236	−	0.745741i	$-0.732096\pi$
$941$	2.43886	−	2.43886i	0.0795045	−	0.0795045i	0.745741	+	0.666236i	$0.232096\pi$
$942$		0			0
$943$	11.3439			0.369408
$944$	−2.34480	−	25.9453i	−0.0763167	−	0.844448i
$945$		0			0
$946$	−0.0984178	−	0.140341i	−0.00319984	−	0.00456289i
$947$	33.4856	−	33.4856i	1.08814	−	1.08814i	0.0924159	−	0.995720i	$-0.470541\pi$
$947$	33.4856	−	33.4856i	1.08814	−	1.08814i	0.995720	−	0.0924159i	$-0.0294589\pi$
$948$		0			0
$949$	−12.3321	−	12.3321i	−0.400317	−	0.400317i
$950$	9.74496	+	1.71111i	0.316168	+	0.0555157i
$951$		0			0
$952$	−33.0416	+	8.92957i	−1.07089	+	0.289409i
$953$		−	14.3013i		−	0.463266i	−0.972803	−	0.231633i	$-0.925593\pi$
$953$		−	14.3013i		−	0.463266i	0.972803	−	0.231633i	$-0.0744068\pi$
$954$		0			0
$955$	9.45512	+	9.45512i	0.305961	+	0.305961i
$956$	5.04832	−	13.9322i	0.163274	−	0.450599i
$957$		0			0
$958$	−42.4432	+	29.7644i	−1.37128	+	0.961643i
$959$	−34.9064			−1.12719
$960$		0			0
$961$	−18.1829			−0.586546
$962$	−19.9375	+	13.9817i	−0.642811	+	0.450787i
$963$		0			0
$964$	−13.3702	+	36.8986i	−0.430625	+	1.18842i
$965$	−5.88967	−	5.88967i	−0.189595	−	0.189595i
$966$		0			0
$967$		−	53.0546i		−	1.70612i	−0.521812	−	0.853060i	$-0.674744\pi$
$967$		−	53.0546i		−	1.70612i	0.521812	−	0.853060i	$-0.325256\pi$
$968$	30.0348	−	8.11696i	0.965354	−	0.260889i
$969$		0			0
$970$	−14.4369	−	2.53497i	−0.463542	−	0.0813928i
$971$	−4.58090	−	4.58090i	−0.147008	−	0.147008i	0.629772	−	0.776780i	$-0.283148\pi$
$971$	−4.58090	−	4.58090i	−0.147008	−	0.147008i	−0.776780	+	0.629772i	$0.783148\pi$
$972$		0			0
$973$	3.32375	−	3.32375i	0.106554	−	0.106554i
$974$	27.8774	+	39.7524i	0.893248	+	1.27375i
$975$		0			0
$976$	−23.5018	+	2.12396i	−0.752273	+	0.0679864i
$977$	−11.2092			−0.358614			−0.179307	−	0.983793i	$-0.557385\pi$
$977$	−11.2092			−0.358614			−0.179307	+	0.983793i	$0.557385\pi$
$978$		0			0
$979$	−0.0450516	+	0.0450516i	−0.00143986	+	0.00143986i
$980$	−4.06659	+	1.90337i	−0.129902	+	0.0608010i
$981$		0			0
$982$	34.7137	+	6.09534i	1.10776	+	0.194510i
$983$			20.1018i			0.641147i	0.947224	+	0.320573i	$0.103876\pi$
$983$			20.1018i			0.641147i	−0.947224	+	0.320573i	$0.896124\pi$
$984$		0			0
$985$			18.6669i			0.594778i
$986$	6.15134	−	35.0326i	0.195899	−	1.11567i
$987$		0			0
$988$	32.1791	+	11.6601i	1.02376	+	0.370957i
$989$	20.5254	−	20.5254i	0.652671	−	0.652671i
$990$		0			0
$991$	20.7088			0.657835			0.328918	−	0.944359i	$-0.393316\pi$
$991$	20.7088			0.657835			0.328918	+	0.944359i	$0.393316\pi$
$992$	20.1812	+	1.69286i	0.640754	+	0.0537485i
$993$		0			0
$994$	30.5741	−	21.4408i	0.969751	−	0.680062i
$995$	2.59305	−	2.59305i	0.0822052	−	0.0822052i
$996$		0			0
$997$	0.704128	+	0.704128i	0.0223000	+	0.0223000i	0.718169	−	0.695869i	$-0.244981\pi$
$997$	0.704128	+	0.704128i	0.0223000	+	0.0223000i	−0.695869	+	0.718169i	$0.744981\pi$
$998$	5.07766	−	28.9179i	0.160730	−	0.915379i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.d.181.4		20
3.2	odd	2		240.2.s.c.181.7	yes	20
4.3	odd	2		2880.2.t.d.2161.2		20
12.11	even	2		960.2.s.c.241.2		20
16.3	odd	4		2880.2.t.d.721.4		20
16.13	even	4	inner	720.2.t.d.541.4		20
24.5	odd	2		1920.2.s.e.481.4		20
24.11	even	2		1920.2.s.f.481.7		20
48.5	odd	4		1920.2.s.e.1441.2		20
48.11	even	4		1920.2.s.f.1441.9		20
48.29	odd	4		240.2.s.c.61.7	✓	20
48.35	even	4		960.2.s.c.721.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.7	✓	20	48.29	odd	4
240.2.s.c.181.7	yes	20	3.2	odd	2
720.2.t.d.181.4		20	1.1	even	1	trivial
720.2.t.d.541.4		20	16.13	even	4	inner
960.2.s.c.241.2		20	12.11	even	2
960.2.s.c.721.4		20	48.35	even	4
1920.2.s.e.481.4		20	24.5	odd	2
1920.2.s.e.1441.2		20	48.5	odd	4
1920.2.s.f.481.7		20	24.11	even	2
1920.2.s.f.1441.9		20	48.11	even	4
2880.2.t.d.721.4		20	16.3	odd	4
2880.2.t.d.2161.2		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)

\(f(q)\)	\(=\)	\(q+(-1.15787 + 0.811989i) q^{2} +(0.681349 - 1.88036i) q^{4} +(-0.707107 - 0.707107i) q^{5} +2.18060i q^{7} +(0.737916 + 2.73047i) q^{8} +O(q^{10})\)	\(q+(-1.15787 + 0.811989i) q^{2} +(0.681349 - 1.88036i) q^{4} +(-0.707107 - 0.707107i) q^{5} +2.18060i q^{7} +(0.737916 + 2.73047i) q^{8} +(1.39290 + 0.244579i) q^{10} +(0.00889637 + 0.00889637i) q^{11} +(1.72965 - 1.72965i) q^{13} +(-1.77062 - 2.52486i) q^{14} +(-3.07153 - 2.56237i) q^{16} +5.54943 q^{17} +(-4.94702 + 4.94702i) q^{19} +(-1.81140 + 0.847831i) q^{20} +(-0.0175246 - 0.00307713i) q^{22} -3.01309i q^{23} +1.00000i q^{25} +(-0.598263 + 3.40718i) q^{26} +(4.10031 + 1.48575i) q^{28} +(-3.20471 + 3.20471i) q^{29} +3.58009 q^{31} +(5.63706 + 0.472855i) q^{32} +(-6.42554 + 4.50607i) q^{34} +(1.54192 - 1.54192i) q^{35} +(4.97761 + 4.97761i) q^{37} +(1.71111 - 9.74496i) q^{38} +(1.40895 - 2.45252i) q^{40} +3.76487i q^{41} +(6.81210 + 6.81210i) q^{43} +(0.0227899 - 0.0106669i) q^{44} +(2.44659 + 3.48878i) q^{46} +10.0800 q^{47} +2.24499 q^{49} +(-0.811989 - 1.15787i) q^{50} +(-2.07388 - 4.43087i) q^{52} +(0.932644 + 0.932644i) q^{53} -0.0125814i q^{55} +(-5.95406 + 1.60910i) q^{56} +(1.10846 - 6.31283i) q^{58} +(4.60522 + 4.60522i) q^{59} +(4.17149 - 4.17149i) q^{61} +(-4.14530 + 2.90700i) q^{62} +(-6.91096 + 4.02972i) q^{64} -2.44610 q^{65} +(-11.0105 + 11.0105i) q^{67} +(3.78110 - 10.4349i) q^{68} +(-0.533328 + 3.03736i) q^{70} +12.1092i q^{71} -7.12981i q^{73} +(-9.80521 - 1.72169i) q^{74} +(5.93155 + 12.6729i) q^{76} +(-0.0193994 + 0.0193994i) q^{77} -3.41789 q^{79} +(0.360031 + 3.98376i) q^{80} +(-3.05704 - 4.35925i) q^{82} +(-5.31631 + 5.31631i) q^{83} +(-3.92404 - 3.92404i) q^{85} +(-13.4189 - 2.35621i) q^{86} +(-0.0177265 + 0.0308561i) q^{88} +5.06405i q^{89} +(3.77168 + 3.77168i) q^{91} +(-5.66569 - 2.05296i) q^{92} +(-11.6714 + 8.18483i) q^{94} +6.99615 q^{95} -10.3646 q^{97} +(-2.59942 + 1.82291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} - 12 q^{8}+O(q^{10}) \) 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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