LMFDB - Embedded newform 720.2.t.c.541.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,2,Mod(181,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			541.4
Root			$-1.39563 - 0.228522i$ of defining polynomial
Character	$\chi$	$=$	720.541
Dual form			720.2.t.c.181.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.114638 + 1.40956i) q^{2} +(-1.97372 - 0.323179i) q^{4} +(-0.707107 + 0.707107i) q^{5} -0.690576i q^{7} +(0.681804 - 2.74502i) q^{8} +(-0.915648 - 1.07777i) q^{10} +(3.06057 - 3.06057i) q^{11} +(-2.33686 - 2.33686i) q^{13} +(0.973408 + 0.0791665i) q^{14} +(3.79111 + 1.27573i) q^{16} +5.28770 q^{17} +(5.38887 + 5.38887i) q^{19} +(1.62415 - 1.16711i) q^{20} +(3.96320 + 4.66492i) q^{22} +1.60841i q^{23} -1.00000i q^{25} +(3.56183 - 3.02605i) q^{26} +(-0.223180 + 1.36300i) q^{28} +(-1.70319 - 1.70319i) q^{29} -4.69807 q^{31} +(-2.23282 + 5.19755i) q^{32} +(-0.606174 + 7.45333i) q^{34} +(0.488311 + 0.488311i) q^{35} +(7.89871 - 7.89871i) q^{37} +(-8.21371 + 6.97817i) q^{38} +(1.45892 + 2.42313i) q^{40} +5.49891i q^{41} +(-0.256166 + 0.256166i) q^{43} +(-7.02981 + 5.05159i) q^{44} +(-2.26715 - 0.184385i) q^{46} +4.60743 q^{47} +6.52310 q^{49} +(1.40956 + 0.114638i) q^{50} +(3.85707 + 5.36752i) q^{52} +(4.99318 - 4.99318i) q^{53} +4.32830i q^{55} +(-1.89565 - 0.470837i) q^{56} +(2.59600 - 2.20549i) q^{58} +(-1.46478 + 1.46478i) q^{59} +(9.33004 + 9.33004i) q^{61} +(0.538579 - 6.62221i) q^{62} +(-7.07029 - 3.74313i) q^{64} +3.30482 q^{65} +(-1.94797 - 1.94797i) q^{67} +(-10.4364 - 1.70888i) q^{68} +(-0.744283 + 0.632324i) q^{70} +2.32246i q^{71} -1.29733i q^{73} +(10.2282 + 12.0392i) q^{74} +(-8.89454 - 12.3777i) q^{76} +(-2.11356 - 2.11356i) q^{77} -5.01968 q^{79} +(-3.58280 + 1.77864i) q^{80} +(-7.75103 - 0.630385i) q^{82} +(-7.30477 - 7.30477i) q^{83} +(-3.73897 + 3.73897i) q^{85} +(-0.331715 - 0.390448i) q^{86} +(-6.31463 - 10.4880i) q^{88} -1.81564i q^{89} +(-1.61378 + 1.61378i) q^{91} +(0.519803 - 3.17454i) q^{92} +(-0.528188 + 6.49445i) q^{94} -7.62102 q^{95} +5.27038 q^{97} +(-0.747798 + 9.19470i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47}+ \cdots - 60 q^{98}+O(q^{100}) $ 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

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 $

$2$	−0.114638	+	1.40956i	−0.0810615	+	0.996709i
$2$	−0.114638	+	1.40956i	−0.0810615	+	0.996709i
$3$		0			0
$3$		0			0
$4$	−1.97372	−	0.323179i	−0.986858	−	0.161590i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$		−	0.690576i		−	0.261013i	−0.991447	−	0.130507i	$-0.958340\pi$
$7$		−	0.690576i		−	0.261013i	0.991447	−	0.130507i	$-0.0416604\pi$
$8$	0.681804	−	2.74502i	0.241054	−	0.970512i
$9$		0			0
$10$	−0.915648	−	1.07777i	−0.289553	−	0.340821i
$11$	3.06057	−	3.06057i	0.922797	−	0.922797i	−0.0744292	−	0.997226i	$-0.523713\pi$
$11$	3.06057	−	3.06057i	0.922797	−	0.922797i	0.997226	+	0.0744292i	$0.0237135\pi$
$12$		0			0
$13$	−2.33686	−	2.33686i	−0.648128	−	0.648128i	0.304413	−	0.952540i	$-0.401540\pi$
$13$	−2.33686	−	2.33686i	−0.648128	−	0.648128i	−0.952540	+	0.304413i	$0.901540\pi$
$14$	0.973408	+	0.0791665i	0.260154	+	0.0211581i
$15$		0			0
$16$	3.79111	+	1.27573i	0.947778	+	0.318932i
$17$	5.28770			1.28246			0.641228	−	0.767350i	$-0.278425\pi$
$17$	5.28770			1.28246			0.641228	+	0.767350i	$0.278425\pi$
$18$		0			0
$19$	5.38887	+	5.38887i	1.23629	+	1.23629i	0.961505	+	0.274787i	$0.0886075\pi$
$19$	5.38887	+	5.38887i	1.23629	+	1.23629i	0.274787	+	0.961505i	$0.411393\pi$
$20$	1.62415	−	1.16711i	0.363171	−	0.260973i
$21$		0			0
$22$	3.96320	+	4.66492i	0.844957	+	0.994564i
$23$			1.60841i			0.335376i	0.985840	+	0.167688i	$0.0536301\pi$
$23$			1.60841i			0.335376i	−0.985840	+	0.167688i	$0.946370\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	3.56183	−	3.02605i	0.698533	−	0.593457i
$27$		0			0
$28$	−0.223180	+	1.36300i	−0.0421770	+	0.257583i
$29$	−1.70319	−	1.70319i	−0.316274	−	0.316274i	0.531060	−	0.847334i	$-0.321794\pi$
$29$	−1.70319	−	1.70319i	−0.316274	−	0.316274i	−0.847334	+	0.531060i	$0.821794\pi$
$30$		0			0
$31$	−4.69807			−0.843798			−0.421899	−	0.906643i	$-0.638636\pi$
$31$	−4.69807			−0.843798			−0.421899	+	0.906643i	$0.638636\pi$
$32$	−2.23282	+	5.19755i	−0.394711	+	0.918805i
$33$		0			0
$34$	−0.606174	+	7.45333i	−0.103958	+	1.27824i
$35$	0.488311	+	0.488311i	0.0825396	+	0.0825396i
$36$		0			0
$37$	7.89871	−	7.89871i	1.29854	−	1.29854i	0.369185	−	0.929356i	$-0.379637\pi$
$37$	7.89871	−	7.89871i	1.29854	−	1.29854i	0.929356	−	0.369185i	$-0.120363\pi$
$38$	−8.21371	+	6.97817i	−1.33244	+	1.13201i
$39$		0			0
$40$	1.45892	+	2.42313i	0.230675	+	0.383131i
$41$			5.49891i			0.858785i	0.903118	+	0.429392i	$0.141272\pi$
$41$			5.49891i			0.858785i	−0.903118	+	0.429392i	$0.858728\pi$
$42$		0			0
$43$	−0.256166	+	0.256166i	−0.0390650	+	0.0390650i	−0.726369	−	0.687304i	$-0.758794\pi$
$43$	−0.256166	+	0.256166i	−0.0390650	+	0.0390650i	0.687304	+	0.726369i	$0.258794\pi$
$44$	−7.02981	+	5.05159i	−1.05978	+	0.761555i
$45$		0			0
$46$	−2.26715	−	0.184385i	−0.334272	−	0.0271861i
$47$	4.60743			0.672063			0.336032	−	0.941851i	$-0.390915\pi$
$47$	4.60743			0.672063			0.336032	+	0.941851i	$0.390915\pi$
$48$		0			0
$49$	6.52310			0.931872
$50$	1.40956	+	0.114638i	0.199342	+	0.0162123i
$51$		0			0
$52$	3.85707	+	5.36752i	0.534879	+	0.744341i
$53$	4.99318	−	4.99318i	0.685866	−	0.685866i	−0.275449	−	0.961316i	$-0.588827\pi$
$53$	4.99318	−	4.99318i	0.685866	−	0.685866i	0.961316	+	0.275449i	$0.0888266\pi$
$54$		0			0
$55$			4.32830i			0.583628i
$56$	−1.89565	−	0.470837i	−0.253316	−	0.0629183i
$57$		0			0
$58$	2.59600	−	2.20549i	0.340871	−	0.289596i
$59$	−1.46478	+	1.46478i	−0.190698	+	0.190698i	−0.795998	−	0.605300i	$-0.793053\pi$
$59$	−1.46478	+	1.46478i	−0.190698	+	0.190698i	0.605300	+	0.795998i	$0.293053\pi$
$60$		0			0
$61$	9.33004	+	9.33004i	1.19459	+	1.19459i	0.975764	+	0.218825i	$0.0702224\pi$
$61$	9.33004	+	9.33004i	1.19459	+	1.19459i	0.218825	+	0.975764i	$0.429778\pi$
$62$	0.538579	−	6.62221i	0.0683996	−	0.841021i
$63$		0			0
$64$	−7.07029	−	3.74313i	−0.883786	−	0.467891i
$65$	3.30482			0.409912
$66$		0			0
$67$	−1.94797	−	1.94797i	−0.237982	−	0.237982i	0.578032	−	0.816014i	$-0.303821\pi$
$67$	−1.94797	−	1.94797i	−0.237982	−	0.237982i	−0.816014	+	0.578032i	$0.803821\pi$
$68$	−10.4364	−	1.70888i	−1.26560	−	0.207232i
$69$		0			0
$70$	−0.744283	+	0.632324i	−0.0889588	+	0.0755772i
$71$			2.32246i			0.275625i	0.990458	+	0.137813i	$0.0440072\pi$
$71$			2.32246i			0.275625i	−0.990458	+	0.137813i	$0.955993\pi$
$72$		0			0
$73$		−	1.29733i		−	0.151841i	−0.997114	−	0.0759206i	$-0.975810\pi$
$73$		−	1.29733i		−	0.151841i	0.997114	−	0.0759206i	$-0.0241896\pi$
$74$	10.2282	+	12.0392i	1.18901	+	1.39953i
$75$		0			0
$76$	−8.89454	−	12.3777i	−1.02027	−	1.41982i
$77$	−2.11356	−	2.11356i	−0.240862	−	0.240862i
$78$		0			0
$79$	−5.01968			−0.564758			−0.282379	−	0.959303i	$-0.591124\pi$
$79$	−5.01968			−0.564758			−0.282379	+	0.959303i	$0.591124\pi$
$80$	−3.58280	+	1.77864i	−0.400569	+	0.198858i
$81$		0			0
$82$	−7.75103	−	0.630385i	−0.855959	−	0.0696144i
$83$	−7.30477	−	7.30477i	−0.801802	−	0.801802i	0.181575	−	0.983377i	$-0.441881\pi$
$83$	−7.30477	−	7.30477i	−0.801802	−	0.801802i	−0.983377	+	0.181575i	$0.941881\pi$
$84$		0			0
$85$	−3.73897	+	3.73897i	−0.405548	+	0.405548i
$86$	−0.331715	−	0.390448i	−0.0357698	−	0.0421031i
$87$		0			0
$88$	−6.31463	−	10.4880i	−0.673141	−	1.11803i
$89$		−	1.81564i		−	0.192458i	−0.995359	−	0.0962290i	$-0.969322\pi$
$89$		−	1.81564i		−	0.192458i	0.995359	−	0.0962290i	$-0.0306781\pi$
$90$		0			0
$91$	−1.61378	+	1.61378i	−0.169170	+	0.169170i
$92$	0.519803	−	3.17454i	0.0541933	−	0.330969i
$93$		0			0
$94$	−0.528188	+	6.49445i	−0.0544785	+	0.669851i
$95$	−7.62102			−0.781900
$96$		0			0
$97$	5.27038			0.535126			0.267563	−	0.963540i	$-0.413782\pi$
$97$	5.27038			0.535126			0.267563	+	0.963540i	$0.413782\pi$
$98$	−0.747798	+	9.19470i	−0.0755390	+	0.928805i
$99$		0			0
$100$	−0.323179	+	1.97372i	−0.0323179	+	0.197372i
$101$	13.4502	−	13.4502i	1.33834	−	1.33834i	0.440675	−	0.897667i	$-0.354739\pi$
$101$	13.4502	−	13.4502i	1.33834	−	1.33834i	0.897667	−	0.440675i	$-0.145261\pi$
$102$		0			0
$103$		−	2.64310i		−	0.260432i	−0.991486	−	0.130216i	$-0.958433\pi$
$103$		−	2.64310i		−	0.260432i	0.991486	−	0.130216i	$-0.0415671\pi$
$104$	−8.00800	+	4.82145i	−0.785249	+	0.472782i
$105$		0			0
$106$	6.46578	+	7.61060i	0.628012	+	0.739207i
$107$	6.28120	−	6.28120i	0.607227	−	0.607227i	−0.334994	−	0.942220i	$-0.608734\pi$
$107$	6.28120	−	6.28120i	0.607227	−	0.607227i	0.942220	+	0.334994i	$0.108734\pi$
$108$		0			0
$109$	−6.89216	−	6.89216i	−0.660149	−	0.660149i	0.295266	−	0.955415i	$-0.404592\pi$
$109$	−6.89216	−	6.89216i	−0.660149	−	0.660149i	−0.955415	+	0.295266i	$0.904592\pi$
$110$	−6.10100	−	0.496189i	−0.581707	−	0.0473098i
$111$		0			0
$112$	0.880987	−	2.61805i	0.0832454	−	0.247382i
$113$	−6.46108			−0.607807			−0.303904	−	0.952703i	$-0.598290\pi$
$113$	−6.46108			−0.607807			−0.303904	+	0.952703i	$0.598290\pi$
$114$		0			0
$115$	−1.13732	−	1.13732i	−0.106055	−	0.106055i
$116$	2.81117	+	3.91204i	0.261011	+	0.363224i
$117$		0			0
$118$	−1.89677	−	2.23261i	−0.174612	−	0.205528i
$119$		−	3.65156i		−	0.334738i
$120$		0			0
$121$		−	7.73420i		−	0.703109i
$122$	−14.2208	+	12.0817i	−1.28749	+	1.09382i
$123$		0			0
$124$	9.27265	+	1.51832i	0.832709	+	0.136349i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$	−16.6123			−1.47411			−0.737054	−	0.675834i	$-0.763784\pi$
$127$	−16.6123			−1.47411			−0.737054	+	0.675834i	$0.763784\pi$
$128$	6.08669	−	9.53688i	0.537993	−	0.842949i
$129$		0			0
$130$	−0.378859	+	4.65834i	−0.0332281	+	0.408563i
$131$	11.7719	+	11.7719i	1.02851	+	1.02851i	0.999581	+	0.0289318i	$0.00921056\pi$
$131$	11.7719	+	11.7719i	1.02851	+	1.02851i	0.0289318	+	0.999581i	$0.490789\pi$
$132$		0			0
$133$	3.72143	−	3.72143i	0.322689	−	0.322689i
$134$	2.96909	−	2.52247i	0.256490	−	0.217908i
$135$		0			0
$136$	3.60518	−	14.5149i	0.309141	−	1.24464i
$137$			8.41495i			0.718937i	0.933157	+	0.359469i	$0.117042\pi$
$137$			8.41495i			0.718937i	−0.933157	+	0.359469i	$0.882958\pi$
$138$		0			0
$139$	−1.51845	+	1.51845i	−0.128793	+	0.128793i	−0.768565	−	0.639772i	$-0.779029\pi$
$139$	−1.51845	+	1.51845i	−0.128793	+	0.128793i	0.639772	+	0.768565i	$0.279029\pi$
$140$	−0.805975	−	1.12160i	−0.0681174	−	0.0947924i
$141$		0			0
$142$	−3.27364	−	0.266243i	−0.274718	−	0.0223426i
$143$	−14.3042			−1.19618
$144$		0			0
$145$	2.40867			0.200029
$146$	1.82867	+	0.148724i	0.151342	+	0.0123085i
$147$		0			0
$148$	−18.1425	+	13.0371i	−1.49131	+	1.07164i
$149$	2.61440	−	2.61440i	0.214180	−	0.214180i	−0.591860	−	0.806040i	$-0.701606\pi$
$149$	2.61440	−	2.61440i	0.214180	−	0.214180i	0.806040	+	0.591860i	$0.201606\pi$
$150$		0			0
$151$			12.7143i			1.03467i	0.855782	+	0.517337i	$0.173077\pi$
$151$			12.7143i			1.03467i	−0.855782	+	0.517337i	$0.826923\pi$
$152$	18.4667	−	11.1184i	1.49785	−	0.901823i
$153$		0			0
$154$	3.22148	−	2.73689i	0.259594	−	0.220545i
$155$	3.32204	−	3.32204i	0.266832	−	0.266832i
$156$		0			0
$157$	−7.17831	−	7.17831i	−0.572891	−	0.572891i	0.360044	−	0.932935i	$-0.382762\pi$
$157$	−7.17831	−	7.17831i	−0.572891	−	0.572891i	−0.932935	+	0.360044i	$0.882762\pi$
$158$	0.575448	−	7.07554i	0.0457802	−	0.562900i
$159$		0			0
$160$	−2.09638	−	5.25406i	−0.165733	−	0.415370i
$161$	1.11073			0.0875376
$162$		0			0
$163$	−7.05476	−	7.05476i	−0.552572	−	0.552572i	0.374611	−	0.927182i	$-0.377776\pi$
$163$	−7.05476	−	7.05476i	−0.552572	−	0.552572i	−0.927182	+	0.374611i	$0.877776\pi$
$164$	1.77713	−	10.8533i	0.138771	−	0.847499i
$165$		0			0
$166$	11.1339	−	9.45910i	0.864159	−	0.734168i
$167$			3.90586i			0.302244i	0.988515	+	0.151122i	$0.0482887\pi$
$167$			3.90586i			0.302244i	−0.988515	+	0.151122i	$0.951711\pi$
$168$		0			0
$169$		−	2.07819i		−	0.159861i
$170$	−4.84167	−	5.69893i	−0.371339	−	0.437088i
$171$		0			0
$172$	0.588387	−	0.422812i	0.0448641	−	0.0322391i
$173$	−8.20139	−	8.20139i	−0.623540	−	0.623540i	0.322895	−	0.946435i	$-0.395344\pi$
$173$	−8.20139	−	8.20139i	−0.623540	−	0.623540i	−0.946435	+	0.322895i	$0.895344\pi$
$174$		0			0
$175$	−0.690576			−0.0522026
$176$	15.5074	−	7.69851i	1.16892	−	0.580297i
$177$		0			0
$178$	2.55926	+	0.208142i	0.191825	+	0.0156009i
$179$	3.10363	+	3.10363i	0.231976	+	0.231976i	0.813517	−	0.581541i	$-0.197550\pi$
$179$	3.10363	+	3.10363i	0.231976	+	0.231976i	−0.581541	+	0.813517i	$0.697550\pi$
$180$		0			0
$181$	−1.91041	+	1.91041i	−0.141999	+	0.141999i	−0.774533	−	0.632534i	$-0.782015\pi$
$181$	−1.91041	+	1.91041i	−0.141999	+	0.141999i	0.632534	+	0.774533i	$0.282015\pi$
$182$	−2.08972	−	2.45972i	−0.154900	−	0.182326i
$183$		0			0
$184$	4.41511	+	1.09662i	0.325486	+	0.0808437i
$185$			11.1705i			0.821269i
$186$		0			0
$187$	16.1834	−	16.1834i	1.18345	−	1.18345i
$188$	−9.09376	−	1.48903i	−0.663231	−	0.108598i
$189$		0			0
$190$	0.873661	−	10.7423i	0.0633820	−	0.779327i
$191$	−5.61041			−0.405955			−0.202977	−	0.979183i	$-0.565062\pi$
$191$	−5.61041			−0.405955			−0.202977	+	0.979183i	$0.565062\pi$
$192$		0			0
$193$	3.90696			0.281229			0.140615	−	0.990064i	$-0.455092\pi$
$193$	3.90696			0.281229			0.140615	+	0.990064i	$0.455092\pi$
$194$	−0.604187	+	7.42891i	−0.0433781	+	0.533365i
$195$		0			0
$196$	−12.8748	−	2.10813i	−0.919625	−	0.150581i
$197$	−0.608436	+	0.608436i	−0.0433493	+	0.0433493i	−0.728449	−	0.685100i	$-0.759759\pi$
$197$	−0.608436	+	0.608436i	−0.0433493	+	0.0433493i	0.685100	+	0.728449i	$0.259759\pi$
$198$		0			0
$199$			15.5282i			1.10076i	0.834913	+	0.550382i	$0.185518\pi$
$199$			15.5282i			1.10076i	−0.834913	+	0.550382i	$0.814482\pi$
$200$	−2.74502	−	0.681804i	−0.194102	−	0.0482108i
$201$		0			0
$202$	17.4169	+	20.5007i	1.22545	+	1.44243i
$203$	−1.17618	+	1.17618i	−0.0825517	+	0.0825517i
$204$		0			0
$205$	−3.88831	−	3.88831i	−0.271572	−	0.271572i
$206$	3.72560	+	0.303000i	0.259575	+	0.0211110i
$207$		0			0
$208$	−5.87809	−	11.8405i	−0.407572	−	0.820990i
$209$	32.9861			2.28169
$210$		0			0
$211$	2.14501	+	2.14501i	0.147669	+	0.147669i	0.777076	−	0.629407i	$-0.216702\pi$
$211$	2.14501	+	2.14501i	0.147669	+	0.147669i	−0.629407	+	0.777076i	$0.716702\pi$
$212$	−11.4688	+	8.24143i	−0.787681	+	0.566024i
$213$		0			0
$214$	8.13366	+	9.57380i	0.556006	+	0.654451i
$215$		−	0.362274i		−	0.0247069i
$216$		0			0
$217$			3.24437i			0.220242i
$218$	10.5050	−	8.92480i	0.711489	−	0.604464i
$219$		0			0
$220$	1.39882	−	8.54284i	0.0943082	−	0.575958i
$221$	−12.3566	−	12.3566i	−0.831196	−	0.831196i
$222$		0			0
$223$	−2.34794			−0.157230			−0.0786148	−	0.996905i	$-0.525050\pi$
$223$	−2.34794			−0.157230			−0.0786148	+	0.996905i	$0.525050\pi$
$224$	3.58930	+	1.54193i	0.239820	+	0.103025i
$225$		0			0
$226$	0.740688	−	9.10728i	0.0492698	−	0.605807i
$227$	−13.1881	−	13.1881i	−0.875325	−	0.875325i	0.117722	−	0.993047i	$-0.462441\pi$
$227$	−13.1881	−	13.1881i	−0.875325	−	0.875325i	−0.993047	+	0.117722i	$0.962441\pi$
$228$		0			0
$229$	9.37860	−	9.37860i	0.619755	−	0.619755i	−0.325713	−	0.945469i	$-0.605604\pi$
$229$	9.37860	−	9.37860i	0.619755	−	0.619755i	0.945469	+	0.325713i	$0.105604\pi$
$230$	1.73349	−	1.47273i	0.114303	−	0.0971092i
$231$		0			0
$232$	−5.83653	+	3.51405i	−0.383187	+	0.230709i
$233$		−	16.3435i		−	1.07070i	−0.844630	−	0.535350i	$-0.820180\pi$
$233$		−	16.3435i		−	1.07070i	0.844630	−	0.535350i	$-0.179820\pi$
$234$		0			0
$235$	−3.25795	+	3.25795i	−0.212525	+	0.212525i
$236$	3.36444	−	2.41767i	0.219006	−	0.157377i
$237$		0			0
$238$	5.14709	+	0.418609i	0.333637	+	0.0271344i
$239$	−19.3818			−1.25371			−0.626854	−	0.779137i	$-0.715658\pi$
$239$	−19.3818			−1.25371			−0.626854	+	0.779137i	$0.715658\pi$
$240$		0			0
$241$	7.15965			0.461193			0.230597	−	0.973049i	$-0.425932\pi$
$241$	7.15965			0.461193			0.230597	+	0.973049i	$0.425932\pi$
$242$	10.9018	+	0.886636i	0.700795	+	0.0569951i
$243$		0			0
$244$	−15.3996	−	21.4301i	−0.985857	−	1.37192i
$245$	−4.61253	+	4.61253i	−0.294684	+	0.294684i
$246$		0			0
$247$		−	25.1861i		−	1.60255i
$248$	−3.20316	+	12.8963i	−0.203401	+	0.818916i
$249$		0			0
$250$	−1.07777	+	0.915648i	−0.0681642	+	0.0579106i
$251$	−10.4372	+	10.4372i	−0.658787	+	0.658787i	−0.955093	−	0.296306i	$-0.904245\pi$
$251$	−10.4372	+	10.4372i	−0.658787	+	0.658787i	0.296306	+	0.955093i	$0.404245\pi$
$252$		0			0
$253$	4.92264	+	4.92264i	0.309484	+	0.309484i
$254$	1.90441	−	23.4161i	0.119493	−	1.46926i
$255$		0			0
$256$	12.7450	+	9.67285i	0.796565	+	0.604553i
$257$	−5.72152			−0.356899			−0.178449	−	0.983949i	$-0.557108\pi$
$257$	−5.72152			−0.356899			−0.178449	+	0.983949i	$0.557108\pi$
$258$		0			0
$259$	−5.45466	−	5.45466i	−0.338936	−	0.338936i
$260$	−6.52277	−	1.06805i	−0.404525	−	0.0662375i
$261$		0			0
$262$	−17.9427	+	15.2436i	−1.10850	+	0.941756i
$263$			27.1378i			1.67339i	0.547669	+	0.836695i	$0.315515\pi$
$263$			27.1378i			1.67339i	−0.547669	+	0.836695i	$0.684485\pi$
$264$		0			0
$265$			7.06143i			0.433780i
$266$	4.81895	+	5.67219i	0.295469	+	0.347784i
$267$		0			0
$268$	3.21519	+	4.47428i	0.196399	+	0.273310i
$269$	−13.0770	−	13.0770i	−0.797320	−	0.797320i	0.185352	−	0.982672i	$-0.440657\pi$
$269$	−13.0770	−	13.0770i	−0.797320	−	0.797320i	−0.982672	+	0.185352i	$0.940657\pi$
$270$		0			0
$271$	6.55264			0.398044			0.199022	−	0.979995i	$-0.436223\pi$
$271$	6.55264			0.398044			0.199022	+	0.979995i	$0.436223\pi$
$272$	20.0463	+	6.74567i	1.21548	+	0.409016i
$273$		0			0
$274$	−11.8614	−	0.964675i	−0.716571	−	0.0582782i
$275$	−3.06057	−	3.06057i	−0.184559	−	0.184559i
$276$		0			0
$277$	−10.2851	+	10.2851i	−0.617973	+	0.617973i	−0.945011	−	0.327038i	$-0.893949\pi$
$277$	−10.2851	+	10.2851i	−0.617973	+	0.617973i	0.327038	+	0.945011i	$0.393949\pi$
$278$	−1.96627	−	2.31442i	−0.117929	−	0.138809i
$279$		0			0
$280$	1.67336	−	1.00749i	0.100002	−	0.0602092i
$281$			29.9714i			1.78794i	0.448124	+	0.893971i	$0.352092\pi$
$281$			29.9714i			1.78794i	−0.448124	+	0.893971i	$0.647908\pi$
$282$		0			0
$283$	−19.1176	+	19.1176i	−1.13642	+	1.13642i	−0.147334	+	0.989087i	$0.547069\pi$
$283$	−19.1176	+	19.1176i	−1.13642	+	1.13642i	−0.989087	+	0.147334i	$0.952931\pi$
$284$	0.750570	−	4.58387i	0.0445381	−	0.272003i
$285$		0			0
$286$	1.63981	−	20.1627i	0.0969643	−	1.19224i
$287$	3.79741			0.224154
$288$		0			0
$289$	10.9598			0.644695
$290$	−0.276126	+	3.39517i	−0.0162147	+	0.199371i
$291$		0			0
$292$	−0.419271	+	2.56056i	−0.0245360	+	0.149846i
$293$	−7.27952	+	7.27952i	−0.425274	+	0.425274i	−0.887015	−	0.461741i	$-0.847225\pi$
$293$	−7.27952	+	7.27952i	−0.425274	+	0.425274i	0.461741	+	0.887015i	$0.347225\pi$
$294$		0			0
$295$		−	2.07151i		−	0.120608i
$296$	−16.2968	−	27.0675i	−0.947230	−	1.57327i
$297$		0			0
$298$	3.38544	+	3.98486i	0.196113	+	0.230837i
$299$	3.75862	−	3.75862i	0.217366	−	0.217366i
$300$		0			0
$301$	0.176902	+	0.176902i	0.0101965	+	0.0101965i
$302$	−17.9216	−	1.45755i	−1.03127	−	0.0838723i
$303$		0			0
$304$	13.5551	+	27.3046i	0.777437	+	1.56602i
$305$	−13.1947			−0.755525
$306$		0			0
$307$	7.03304	+	7.03304i	0.401397	+	0.401397i	0.878725	−	0.477328i	$-0.158395\pi$
$307$	7.03304	+	7.03304i	0.401397	+	0.401397i	−0.477328	+	0.878725i	$0.658395\pi$
$308$	3.48850	+	4.85462i	0.198776	+	0.276618i
$309$		0			0
$310$	4.30177	+	5.06344i	0.244324	+	0.287584i
$311$			14.2833i			0.809929i	0.914332	+	0.404964i	$0.132716\pi$
$311$			14.2833i			0.809929i	−0.914332	+	0.404964i	$0.867284\pi$
$312$		0			0
$313$			18.4579i			1.04330i	0.853158	+	0.521652i	$0.174684\pi$
$313$			18.4579i			1.04330i	−0.853158	+	0.521652i	$0.825316\pi$
$314$	10.9412	−	9.29534i	0.617445	−	0.524567i
$315$		0			0
$316$	9.90743	+	1.62226i	0.557336	+	0.0912590i
$317$	7.21807	+	7.21807i	0.405407	+	0.405407i	0.880133	−	0.474726i	$-0.157453\pi$
$317$	7.21807	+	7.21807i	0.405407	+	0.405407i	−0.474726	+	0.880133i	$0.657453\pi$
$318$		0			0
$319$	−10.4255			−0.583714
$320$	7.64624	−	2.35265i	0.427438	−	0.131517i
$321$		0			0
$322$	−0.127332	+	1.56564i	−0.00709593	+	0.0872495i
$323$	28.4948	+	28.4948i	1.58549	+	1.58549i
$324$		0			0
$325$	−2.33686	+	2.33686i	−0.129626	+	0.129626i
$326$	10.7529	−	9.13536i	0.595545	−	0.505961i
$327$		0			0
$328$	15.0946	+	3.74917i	0.833461	+	0.207014i
$329$		−	3.18178i		−	0.175417i
$330$		0			0
$331$	−15.4847	+	15.4847i	−0.851116	+	0.851116i	−0.990271	−	0.139155i	$-0.955561\pi$
$331$	−15.4847	+	15.4847i	−0.851116	+	0.851116i	0.139155	+	0.990271i	$0.455561\pi$
$332$	12.0568	+	16.7783i	0.661702	+	0.920828i
$333$		0			0
$334$	−5.50554	−	0.447761i	−0.301250	−	0.0245004i
$335$	2.75484			0.150513
$336$		0			0
$337$	−26.0210			−1.41746			−0.708728	−	0.705482i	$-0.750731\pi$
$337$	−26.0210			−1.41746			−0.708728	+	0.705482i	$0.750731\pi$
$338$	2.92933	+	0.238240i	0.159335	+	0.0129586i
$339$		0			0
$340$	8.58803	−	6.17131i	0.465751	−	0.334686i
$341$	−14.3788	+	14.3788i	−0.778654	+	0.778654i
$342$		0			0
$343$		−	9.33873i		−	0.504244i
$344$	0.528527	+	0.877837i	0.0284963	+	0.0473298i
$345$		0			0
$346$	12.5005	−	10.6202i	0.672034	−	0.570943i
$347$	12.8554	−	12.8554i	0.690115	−	0.690115i	−0.272142	−	0.962257i	$-0.587732\pi$
$347$	12.8554	−	12.8554i	0.690115	−	0.690115i	0.962257	+	0.272142i	$0.0877321\pi$
$348$		0			0
$349$	−20.0227	−	20.0227i	−1.07179	−	1.07179i	−0.997216	−	0.0745736i	$-0.976240\pi$
$349$	−20.0227	−	20.0227i	−1.07179	−	1.07179i	−0.0745736	−	0.997216i	$-0.523760\pi$
$350$	0.0791665	−	0.973408i	0.00423163	−	0.0520308i
$351$		0			0
$352$	9.07376	+	22.7412i	0.483633	+	1.21211i
$353$	−13.7062			−0.729510			−0.364755	−	0.931104i	$-0.618847\pi$
$353$	−13.7062			−0.729510			−0.364755	+	0.931104i	$0.618847\pi$
$354$		0			0
$355$	−1.64223	−	1.64223i	−0.0871603	−	0.0871603i
$356$	−0.586778	+	3.58357i	−0.0310992	+	0.189929i
$357$		0			0
$358$	−4.73055	+	4.01896i	−0.250017	+	0.212409i
$359$			32.3506i			1.70740i	0.520764	+	0.853700i	$0.325647\pi$
$359$			32.3506i			1.70740i	−0.520764	+	0.853700i	$0.674353\pi$
$360$		0			0
$361$			39.0799i			2.05684i
$362$	−2.47383	−	2.91184i	−0.130021	−	0.153043i
$363$		0			0
$364$	3.70668	−	2.66360i	0.194283	−	0.139611i
$365$	0.917352	+	0.917352i	0.0480164	+	0.0480164i
$366$		0			0
$367$	16.3714			0.854582			0.427291	−	0.904114i	$-0.359468\pi$
$367$	16.3714			0.854582			0.427291	+	0.904114i	$0.359468\pi$
$368$	−2.05189	+	6.09765i	−0.106962	+	0.317862i
$369$		0			0
$370$	−15.7454	−	1.28056i	−0.818567	−	0.0665734i
$371$	−3.44817	−	3.44817i	−0.179020	−	0.179020i
$372$		0			0
$373$	15.5321	−	15.5321i	0.804222	−	0.804222i	−0.179530	−	0.983752i	$-0.557458\pi$
$373$	15.5321	−	15.5321i	0.804222	−	0.804222i	0.983752	+	0.179530i	$0.0574578\pi$
$374$	20.9562	+	24.6667i	1.08362	+	1.27548i
$375$		0			0
$376$	3.14136	−	12.6475i	0.162004	−	0.652245i
$377$			7.96022i			0.409972i
$378$		0			0
$379$	24.9538	−	24.9538i	1.28179	−	1.28179i	0.342145	−	0.939647i	$-0.388847\pi$
$379$	24.9538	−	24.9538i	1.28179	−	1.28179i	0.939647	−	0.342145i	$-0.111153\pi$
$380$	15.0417	+	2.46295i	0.771624	+	0.126347i
$381$		0			0
$382$	0.643168	−	7.90820i	0.0329073	−	0.404619i
$383$	−6.24887			−0.319302			−0.159651	−	0.987174i	$-0.551037\pi$
$383$	−6.24887			−0.319302			−0.159651	+	0.987174i	$0.551037\pi$
$384$		0			0
$385$	2.98902			0.152335
$386$	−0.447888	+	5.50710i	−0.0227969	+	0.280304i
$387$		0			0
$388$	−10.4022	−	1.70328i	−0.528093	−	0.0864707i
$389$	−2.10802	+	2.10802i	−0.106881	+	0.106881i	−0.758525	−	0.651644i	$-0.774080\pi$
$389$	−2.10802	+	2.10802i	−0.106881	+	0.106881i	0.651644	+	0.758525i	$0.274080\pi$
$390$		0			0
$391$			8.50478i			0.430105i
$392$	4.44748	−	17.9061i	0.224632	−	0.904393i
$393$		0			0
$394$	−0.787876	−	0.927377i	−0.0396926	−	0.0467206i
$395$	3.54945	−	3.54945i	0.178592	−	0.178592i
$396$		0			0
$397$	23.4977	+	23.4977i	1.17932	+	1.17932i	0.979919	+	0.199397i	$0.0638983\pi$
$397$	23.4977	+	23.4977i	1.17932	+	1.17932i	0.199397	+	0.979919i	$0.436102\pi$
$398$	−21.8879	−	1.78013i	−1.09714	−	0.0892296i
$399$		0			0
$400$	1.27573	−	3.79111i	0.0637864	−	0.189556i
$401$	20.9893			1.04816			0.524078	−	0.851670i	$-0.324410\pi$
$401$	20.9893			1.04816			0.524078	+	0.851670i	$0.324410\pi$
$402$		0			0
$403$	10.9787	+	10.9787i	0.546889	+	0.546889i
$404$	−30.8936	+	22.2000i	−1.53702	+	1.10449i
$405$		0			0
$406$	−1.52306	−	1.79273i	−0.0755883	−	0.0889718i
$407$		−	48.3492i		−	2.39658i
$408$		0			0
$409$		−	18.4025i		−	0.909944i	−0.890506	−	0.454972i	$-0.849649\pi$
$409$		−	18.4025i		−	0.909944i	0.890506	−	0.454972i	$-0.150351\pi$
$410$	5.92656	−	5.03506i	0.292692	−	0.248664i
$411$		0			0
$412$	−0.854193	+	5.21672i	−0.0420831	+	0.257009i
$413$	1.01154	+	1.01154i	0.0497746	+	0.0497746i
$414$		0			0
$415$	10.3305			0.507104
$416$	17.3637	−	6.92815i	0.851326	−	0.339680i
$417$		0			0
$418$	−3.78147	+	46.4958i	−0.184958	+	2.27419i
$419$	−14.9331	−	14.9331i	−0.729530	−	0.729530i	0.240996	−	0.970526i	$-0.422526\pi$
$419$	−14.9331	−	14.9331i	−0.729530	−	0.729530i	−0.970526	+	0.240996i	$0.922526\pi$
$420$		0			0
$421$	−16.2680	+	16.2680i	−0.792854	+	0.792854i	−0.981957	−	0.189103i	$-0.939442\pi$
$421$	−16.2680	+	16.2680i	−0.792854	+	0.792854i	0.189103	+	0.981957i	$0.439442\pi$
$422$	−3.26942	+	2.77762i	−0.159153	+	0.135212i
$423$		0			0
$424$	−10.3020	−	17.1108i	−0.500310	−	0.830972i
$425$		−	5.28770i		−	0.256491i
$426$		0			0
$427$	6.44310	−	6.44310i	0.311804	−	0.311804i
$428$	−14.4273	+	10.3674i	−0.697368	+	0.501125i
$429$		0			0
$430$	0.510647	+	0.0415305i	0.0246256	+	0.00200278i
$431$	−7.05425			−0.339791			−0.169896	−	0.985462i	$-0.554343\pi$
$431$	−7.05425			−0.339791			−0.169896	+	0.985462i	$0.554343\pi$
$432$		0			0
$433$	−14.3192			−0.688139			−0.344069	−	0.938944i	$-0.611806\pi$
$433$	−14.3192			−0.688139			−0.344069	+	0.938944i	$0.611806\pi$
$434$	−4.57314	−	0.371930i	−0.219518	−	0.0178532i
$435$		0			0
$436$	11.3758	+	15.8306i	0.544800	+	0.758146i
$437$	−8.66750	+	8.66750i	−0.414623	+	0.414623i
$438$		0			0
$439$			25.9047i			1.23637i	0.786034	+	0.618183i	$0.212131\pi$
$439$			25.9047i			1.23637i	−0.786034	+	0.618183i	$0.787869\pi$
$440$	11.8813	+	2.95105i	0.566418	+	0.140686i
$441$		0			0
$442$	18.8339	−	16.0008i	0.895838	−	0.761082i
$443$	11.1389	−	11.1389i	0.529224	−	0.529224i	−0.391117	−	0.920341i	$-0.627911\pi$
$443$	11.1389	−	11.1389i	0.529224	−	0.529224i	0.920341	+	0.391117i	$0.127911\pi$
$444$		0			0
$445$	1.28385	+	1.28385i	0.0608605	+	0.0608605i
$446$	0.269164	−	3.30956i	0.0127453	−	0.156712i
$447$		0			0
$448$	−2.58492	+	4.88257i	−0.122126	+	0.230680i
$449$	−12.6659			−0.597740			−0.298870	−	0.954294i	$-0.596610\pi$
$449$	−12.6659			−0.597740			−0.298870	+	0.954294i	$0.596610\pi$
$450$		0			0
$451$	16.8298	+	16.8298i	0.792484	+	0.792484i
$452$	12.7523	+	2.08809i	0.599820	+	0.0982153i
$453$		0			0
$454$	20.1013	−	17.0775i	0.943399	−	0.801489i
$455$		−	2.28223i		−	0.106992i
$456$		0			0
$457$		−	16.9442i		−	0.792617i	−0.918117	−	0.396308i	$-0.870291\pi$
$457$		−	16.9442i		−	0.792617i	0.918117	−	0.396308i	$-0.129709\pi$
$458$	12.1446	+	14.2948i	0.567478	+	0.667954i
$459$		0			0
$460$	1.87718	+	2.61229i	0.0875240	+	0.121799i
$461$	13.1888	+	13.1888i	0.614264	+	0.614264i	0.944054	−	0.329790i	$-0.106978\pi$
$461$	13.1888	+	13.1888i	0.614264	+	0.614264i	−0.329790	+	0.944054i	$0.606978\pi$
$462$		0			0
$463$	−14.0955			−0.655074			−0.327537	−	0.944838i	$-0.606219\pi$
$463$	−14.0955			−0.655074			−0.327537	+	0.944838i	$0.606219\pi$
$464$	−4.28417	−	8.62978i	−0.198888	−	0.400627i
$465$		0			0
$466$	23.0372	+	1.87360i	1.06718	+	0.0867927i
$467$	12.0918	+	12.0918i	0.559540	+	0.559540i	0.929177	−	0.369636i	$-0.120518\pi$
$467$	12.0918	+	12.0918i	0.559540	+	0.559540i	−0.369636	+	0.929177i	$0.620518\pi$
$468$		0			0
$469$	−1.34522	+	1.34522i	−0.0621165	+	0.0621165i
$470$	−4.21878	−	4.96576i	−0.194598	−	0.229053i
$471$		0			0
$472$	3.02215	+	5.01953i	0.139106	+	0.231043i
$473$			1.56803i			0.0720981i
$474$		0			0
$475$	5.38887	−	5.38887i	0.247258	−	0.247258i
$476$	−1.18011	+	7.20715i	−0.0540902	+	0.330339i
$477$		0			0
$478$	2.22190	−	27.3199i	0.101627	−	1.24958i
$479$	−14.2523			−0.651202			−0.325601	−	0.945507i	$-0.605567\pi$
$479$	−14.2523			−0.651202			−0.325601	+	0.945507i	$0.605567\pi$
$480$		0			0
$481$	−36.9163			−1.68324
$482$	−0.820770	+	10.0919i	−0.0373850	+	0.459676i
$483$		0			0
$484$	−2.49953	+	15.2651i	−0.113615	+	0.693869i
$485$	−3.72672	+	3.72672i	−0.169222	+	0.169222i
$486$		0			0
$487$			26.0424i			1.18010i	0.807368	+	0.590048i	$0.200891\pi$
$487$			26.0424i			1.18010i	−0.807368	+	0.590048i	$0.799109\pi$
$488$	31.9724	−	19.2499i	1.44732	−	0.871402i
$489$		0			0
$490$	−5.97286	−	7.03041i	−0.269827	−	0.317602i
$491$	−3.46798	+	3.46798i	−0.156508	+	0.156508i	−0.781017	−	0.624509i	$-0.785299\pi$
$491$	−3.46798	+	3.46798i	−0.156508	+	0.156508i	0.624509	+	0.781017i	$0.285299\pi$
$492$		0			0
$493$	−9.00595	−	9.00595i	−0.405608	−	0.405608i
$494$	35.5013	+	2.88729i	1.59728	+	0.129905i
$495$		0			0
$496$	−17.8109	−	5.99346i	−0.799733	−	0.269114i
$497$	1.60383			0.0719418
$498$		0			0
$499$	−5.30274	−	5.30274i	−0.237383	−	0.237383i	0.578383	−	0.815766i	$-0.303684\pi$
$499$	−5.30274	−	5.30274i	−0.237383	−	0.237383i	−0.815766	+	0.578383i	$0.803684\pi$
$500$	−1.16711	−	1.62415i	−0.0521946	−	0.0726342i
$501$		0			0
$502$	−13.5153	−	15.9083i	−0.603217	−	0.710021i
$503$		−	28.8492i		−	1.28632i	−0.765731	−	0.643161i	$-0.777622\pi$
$503$		−	28.8492i		−	1.28632i	0.765731	−	0.643161i	$-0.222378\pi$
$504$		0			0
$505$			19.0214i			0.846442i
$506$	−7.50308	+	6.37444i	−0.333553	+	0.283378i
$507$		0			0
$508$	32.7881	+	5.36876i	1.45473	+	0.238200i
$509$	−12.9968	−	12.9968i	−0.576072	−	0.576072i	0.357747	−	0.933819i	$-0.383545\pi$
$509$	−12.9968	−	12.9968i	−0.576072	−	0.576072i	−0.933819	+	0.357747i	$0.883545\pi$
$510$		0			0
$511$	−0.895906			−0.0396326
$512$	−15.0955	+	16.8560i	−0.667134	+	0.744937i
$513$		0			0
$514$	0.655906	−	8.06482i	0.0289308	−	0.355724i
$515$	1.86895	+	1.86895i	0.0823558	+	0.0823558i
$516$		0			0
$517$	14.1014	−	14.1014i	0.620178	−	0.620178i
$518$	8.31399	−	7.06336i	0.365296	−	0.310346i
$519$		0			0
$520$	2.25324	−	9.07179i	0.0988109	−	0.397824i
$521$		−	13.9833i		−	0.612618i	−0.951932	−	0.306309i	$-0.900906\pi$
$521$		−	13.9833i		−	0.612618i	0.951932	−	0.306309i	$-0.0990941\pi$
$522$		0			0
$523$	−6.30689	+	6.30689i	−0.275781	+	0.275781i	−0.831422	−	0.555641i	$-0.812473\pi$
$523$	−6.30689	+	6.30689i	−0.275781	+	0.275781i	0.555641	+	0.831422i	$0.312473\pi$
$524$	−19.4299	−	27.0388i	−0.848800	−	1.18119i
$525$		0			0
$526$	−38.2524	−	3.11104i	−1.66788	−	0.135648i
$527$	−24.8420			−1.08213
$528$		0			0
$529$	20.4130			0.887523
$530$	−9.95350	−	0.809510i	−0.432352	−	0.0351629i
$531$		0			0
$532$	−8.54773	+	6.14235i	−0.370591	+	0.266305i
$533$	12.8502	−	12.8502i	0.556602	−	0.556602i
$534$		0			0
$535$			8.88296i			0.384044i
$536$	−6.67535	+	4.01908i	−0.288331	+	0.173598i
$537$		0			0
$538$	19.9320	−	16.9337i	0.859328	−	0.730064i
$539$	19.9644	−	19.9644i	0.859929	−	0.859929i
$540$		0			0
$541$	3.89317	+	3.89317i	0.167381	+	0.167381i	0.785827	−	0.618446i	$-0.212238\pi$
$541$	3.89317	+	3.89317i	0.167381	+	0.167381i	−0.618446	+	0.785827i	$0.712238\pi$
$542$	−0.751184	+	9.23633i	−0.0322661	+	0.396735i
$543$		0			0
$544$	−11.8065	+	27.4831i	−0.506199	+	1.17833i
$545$	9.74698			0.417515
$546$		0			0
$547$	−27.8376	−	27.8376i	−1.19025	−	1.19025i	−0.976997	−	0.213251i	$-0.931595\pi$
$547$	−27.8376	−	27.8376i	−1.19025	−	1.19025i	−0.213251	−	0.976997i	$-0.568405\pi$
$548$	2.71953	−	16.6087i	0.116173	−	0.709489i
$549$		0			0
$550$	4.66492	−	3.96320i	0.198913	−	0.168991i
$551$		−	18.3565i		−	0.782014i
$552$		0			0
$553$			3.46647i			0.147409i
$554$	−13.3184	−	15.6766i	−0.565845	−	0.666033i
$555$		0			0
$556$	3.48772	−	2.50625i	0.147912	−	0.106289i
$557$	−1.50454	−	1.50454i	−0.0637492	−	0.0637492i	0.674513	−	0.738263i	$-0.264353\pi$
$557$	−1.50454	−	1.50454i	−0.0637492	−	0.0637492i	−0.738263	+	0.674513i	$0.764353\pi$
$558$		0			0
$559$	1.19725			0.0506382
$560$	1.22829	+	2.47419i	0.0519047	+	0.104554i
$561$		0			0
$562$	−42.2465	−	3.43587i	−1.78206	−	0.144933i
$563$	6.66663	+	6.66663i	0.280965	+	0.280965i	0.833494	−	0.552529i	$-0.186337\pi$
$563$	6.66663	+	6.66663i	0.280965	+	0.280965i	−0.552529	+	0.833494i	$0.686337\pi$
$564$		0			0
$565$	4.56867	−	4.56867i	0.192206	−	0.192206i
$566$	−24.7557	−	29.1389i	−1.04056	−	1.22480i
$567$		0			0
$568$	6.37520	+	1.58346i	0.267497	+	0.0664405i
$569$			8.38187i			0.351386i	0.984445	+	0.175693i	$0.0562167\pi$
$569$			8.38187i			0.351386i	−0.984445	+	0.175693i	$0.943783\pi$
$570$		0			0
$571$	28.4129	−	28.4129i	1.18904	−	1.18904i	0.211708	−	0.977333i	$-0.432097\pi$
$571$	28.4129	−	28.4129i	1.18904	−	1.18904i	0.977333	−	0.211708i	$-0.0679027\pi$
$572$	28.2325	+	4.62283i	1.18046	+	0.193290i
$573$		0			0
$574$	−0.435329	+	5.35268i	−0.0181703	+	0.223416i
$575$	1.60841			0.0670752
$576$		0			0
$577$	23.2045			0.966014			0.483007	−	0.875616i	$-0.339545\pi$
$577$	23.2045			0.966014			0.483007	+	0.875616i	$0.339545\pi$
$578$	−1.25642	+	15.4485i	−0.0522600	+	0.642574i
$579$		0			0
$580$	−4.75403	−	0.778432i	−0.197400	−	0.0323226i
$581$	−5.04450	+	5.04450i	−0.209281	+	0.209281i
$582$		0			0
$583$		−	30.5640i		−	1.26583i
$584$	−3.56120	−	0.884526i	−0.147364	−	0.0366019i
$585$		0			0
$586$	−9.42640	−	11.0954i	−0.389401	−	0.458348i
$587$	11.0197	−	11.0197i	0.454832	−	0.454832i	−0.442123	−	0.896955i	$-0.645774\pi$
$587$	11.0197	−	11.0197i	0.454832	−	0.454832i	0.896955	+	0.442123i	$0.145774\pi$
$588$		0			0
$589$	−25.3173	−	25.3173i	−1.04318	−	1.04318i
$590$	2.91991	+	0.237474i	0.120211	+	0.00977666i
$591$		0			0
$592$	40.0215	−	19.8683i	1.64487	−	0.816582i
$593$	6.98847			0.286982			0.143491	−	0.989652i	$-0.454167\pi$
$593$	6.98847			0.286982			0.143491	+	0.989652i	$0.454167\pi$
$594$		0			0
$595$	2.58204	+	2.58204i	0.105853	+	0.105853i
$596$	−6.00500	+	4.31516i	−0.245975	+	0.176756i
$597$		0			0
$598$	4.86711	+	5.72888i	0.199031	+	0.234271i
$599$			39.9642i			1.63289i	0.577420	+	0.816447i	$0.304059\pi$
$599$			39.9642i			1.63289i	−0.577420	+	0.816447i	$0.695941\pi$
$600$		0			0
$601$		−	21.0830i		−	0.859993i	−0.902831	−	0.429997i	$-0.858515\pi$
$601$		−	21.0830i		−	0.859993i	0.902831	−	0.429997i	$-0.141485\pi$
$602$	−0.269634	+	0.229075i	−0.0109895	+	0.00933638i
$603$		0			0
$604$	4.10899	−	25.0944i	0.167193	−	1.02108i
$605$	5.46890	+	5.46890i	0.222343	+	0.222343i
$606$		0			0
$607$	22.3189			0.905897			0.452949	−	0.891537i	$-0.350372\pi$
$607$	22.3189			0.905897			0.452949	+	0.891537i	$0.350372\pi$
$608$	−40.0413	+	15.9765i	−1.62389	+	0.647934i
$609$		0			0
$610$	1.51261	−	18.5987i	0.0612440	−	0.753038i
$611$	−10.7669	−	10.7669i	−0.435583	−	0.435583i
$612$		0			0
$613$	−10.6045	+	10.6045i	−0.428312	+	0.428312i	−0.888053	−	0.459741i	$-0.847942\pi$
$613$	−10.6045	+	10.6045i	−0.428312	+	0.428312i	0.459741	+	0.888053i	$0.347942\pi$
$614$	−10.7197	+	9.10724i	−0.432614	+	0.367538i
$615$		0			0
$616$	−7.24279	+	4.36073i	−0.291820	+	0.175699i
$617$			33.7636i			1.35927i	0.733550	+	0.679635i	$0.237862\pi$
$617$			33.7636i			1.35927i	−0.733550	+	0.679635i	$0.762138\pi$
$618$		0			0
$619$	4.86777	−	4.86777i	0.195652	−	0.195652i	−0.602481	−	0.798133i	$-0.705821\pi$
$619$	4.86777	−	4.86777i	0.195652	−	0.195652i	0.798133	+	0.602481i	$0.205821\pi$
$620$	−7.63037	+	5.48314i	−0.306443	+	0.220208i
$621$		0			0
$622$	−20.1331	−	1.63741i	−0.807263	−	0.0656541i
$623$	−1.25384			−0.0502341
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−26.0176	−	2.11599i	−1.03987	−	0.0845718i
$627$		0			0
$628$	11.8481	+	16.4878i	0.472789	+	0.657936i
$629$	41.7661	−	41.7661i	1.66532	−	1.66532i
$630$		0			0
$631$		−	16.1348i		−	0.642315i	−0.947026	−	0.321157i	$-0.895928\pi$
$631$		−	16.1348i		−	0.642315i	0.947026	−	0.321157i	$-0.104072\pi$
$632$	−3.42244	+	13.7791i	−0.136137	+	0.548105i
$633$		0			0
$634$	−11.0018	+	9.34683i	−0.436936	+	0.371210i
$635$	11.7467	−	11.7467i	0.466154	−	0.466154i
$636$		0			0
$637$	−15.2436	−	15.2436i	−0.603972	−	0.603972i
$638$	1.19516	−	14.6953i	0.0473167	−	0.581793i
$639$		0			0
$640$	2.43965	+	11.0475i	0.0964358	+	0.436692i
$641$	−20.3125			−0.802296			−0.401148	−	0.916013i	$-0.631389\pi$
$641$	−20.3125			−0.802296			−0.401148	+	0.916013i	$0.631389\pi$
$642$		0			0
$643$	7.78443	+	7.78443i	0.306988	+	0.306988i	0.843740	−	0.536752i	$-0.180349\pi$
$643$	7.78443	+	7.78443i	0.306988	+	0.306988i	−0.536752	+	0.843740i	$0.680349\pi$
$644$	−2.19226	−	0.358964i	−0.0863871	−	0.0141452i
$645$		0			0
$646$	−43.4317	+	36.8985i	−1.70880	+	1.45175i
$647$		−	21.7693i		−	0.855840i	−0.903817	−	0.427920i	$-0.859246\pi$
$647$		−	21.7693i		−	0.855840i	0.903817	−	0.427920i	$-0.140754\pi$
$648$		0			0
$649$			8.96611i			0.351951i
$650$	−3.02605	−	3.56183i	−0.118691	−	0.139707i
$651$		0			0
$652$	11.6441	+	16.2040i	0.456020	+	0.634600i
$653$	26.3118	+	26.3118i	1.02966	+	1.02966i	0.999546	+	0.0301152i	$0.00958743\pi$
$653$	26.3118	+	26.3118i	1.02966	+	1.02966i	0.0301152	+	0.999546i	$0.490413\pi$
$654$		0			0
$655$	−16.6479			−0.650489
$656$	−7.01511	+	20.8470i	−0.273894	+	0.813937i
$657$		0			0
$658$	4.48491	+	0.364754i	0.174840	+	0.0142196i
$659$	20.2389	+	20.2389i	0.788397	+	0.788397i	0.981231	−	0.192835i	$-0.0617681\pi$
$659$	20.2389	+	20.2389i	0.788397	+	0.788397i	−0.192835	+	0.981231i	$0.561768\pi$
$660$		0			0
$661$	6.81905	−	6.81905i	0.265230	−	0.265230i	−0.561945	−	0.827175i	$-0.689947\pi$
$661$	6.81905	−	6.81905i	0.265230	−	0.265230i	0.827175	+	0.561945i	$0.189947\pi$
$662$	−20.0515	−	23.6017i	−0.779322	−	0.917308i
$663$		0			0
$664$	−25.0322	+	15.0713i	−0.971436	+	0.584881i
$665$			5.26289i			0.204086i
$666$		0			0
$667$	2.73942	−	2.73942i	0.106071	−	0.106071i
$668$	1.26229	−	7.70905i	0.0488395	−	0.298272i
$669$		0			0
$670$	−0.315811	+	3.88311i	−0.0122008	+	0.150018i
$671$	57.1105			2.20473
$672$		0			0
$673$	−8.19512			−0.315899			−0.157949	−	0.987447i	$-0.550488\pi$
$673$	−8.19512			−0.315899			−0.157949	+	0.987447i	$0.550488\pi$
$674$	2.98301	−	36.6782i	0.114901	−	1.41279i
$675$		0			0
$676$	−0.671628	+	4.10176i	−0.0258318	+	0.157760i
$677$	−12.8834	+	12.8834i	−0.495151	+	0.495151i	−0.909925	−	0.414774i	$-0.863861\pi$
$677$	−12.8834	+	12.8834i	−0.495151	+	0.495151i	0.414774	+	0.909925i	$0.363861\pi$
$678$		0			0
$679$		−	3.63960i		−	0.139675i
$680$	7.71431	+	12.8128i	0.295830	+	0.491349i
$681$		0			0
$682$	−18.6194	−	21.9161i	−0.712973	−	0.839211i
$683$	−15.0673	+	15.0673i	−0.576535	+	0.576535i	−0.933947	−	0.357412i	$-0.883659\pi$
$683$	−15.0673	+	15.0673i	−0.576535	+	0.576535i	0.357412	+	0.933947i	$0.383659\pi$
$684$		0			0
$685$	−5.95027	−	5.95027i	−0.227348	−	0.227348i
$686$	13.1635	+	1.07058i	0.502585	+	0.0408748i
$687$		0			0
$688$	−1.29795	+	0.644356i	−0.0494840	+	0.0245659i
$689$	−23.3367			−0.889058
$690$		0			0
$691$	−5.23733	−	5.23733i	−0.199237	−	0.199237i	0.600436	−	0.799673i	$-0.294994\pi$
$691$	−5.23733	−	5.23733i	−0.199237	−	0.199237i	−0.799673	+	0.600436i	$0.794994\pi$
$692$	13.5367	+	18.8377i	0.514588	+	0.716104i
$693$		0			0
$694$	16.6467	+	19.5942i	0.631902	+	0.743786i
$695$		−	2.14741i		−	0.0814559i
$696$		0			0
$697$			29.0766i			1.10135i
$698$	30.5185	−	25.9278i	1.15514	−	0.981381i
$699$		0			0
$700$	1.36300	+	0.223180i	0.0515166	+	0.00843540i
$701$	−21.7664	−	21.7664i	−0.822106	−	0.822106i	0.164303	−	0.986410i	$-0.447462\pi$
$701$	−21.7664	−	21.7664i	−0.822106	−	0.822106i	−0.986410	+	0.164303i	$0.947462\pi$
$702$		0			0
$703$	85.1304			3.21075
$704$	−33.0952	+	10.1830i	−1.24732	+	0.383786i
$705$		0			0
$706$	1.57126	−	19.3198i	0.0591352	−	0.727109i
$707$	−9.28836	−	9.28836i	−0.349325	−	0.349325i
$708$		0			0
$709$	−23.9643	+	23.9643i	−0.899997	+	0.899997i	−0.995435	−	0.0954387i	$-0.969575\pi$
$709$	−23.9643	+	23.9643i	−0.899997	+	0.899997i	0.0954387	+	0.995435i	$0.469575\pi$
$710$	2.50308	−	2.12655i	0.0939388	−	0.0798081i
$711$		0			0
$712$	−4.98398	−	1.23791i	−0.186783	−	0.0463928i
$713$		−	7.55640i		−	0.282990i
$714$		0			0
$715$	10.1146	−	10.1146i	0.378266	−	0.378266i
$716$	−5.12266	−	7.12872i	−0.191443	−	0.266413i
$717$		0			0
$718$	−45.6001	−	3.70862i	−1.70178	−	0.138405i
$719$	44.4408			1.65736			0.828681	−	0.559721i	$-0.189092\pi$
$719$	44.4408			1.65736			0.828681	+	0.559721i	$0.189092\pi$
$720$		0			0
$721$	−1.82526			−0.0679762
$722$	−55.0855	−	4.48006i	−2.05007	−	0.166730i
$723$		0			0
$724$	4.38800	−	3.15320i	0.163079	−	0.117188i
$725$	−1.70319	+	1.70319i	−0.0632548	+	0.0632548i
$726$		0			0
$727$		−	46.6543i		−	1.73031i	−0.501504	−	0.865155i	$-0.667220\pi$
$727$		−	46.6543i		−	1.73031i	0.501504	−	0.865155i	$-0.332780\pi$
$728$	3.32958	+	5.53014i	0.123402	+	0.204960i
$729$		0			0
$730$	−1.39823	+	1.18790i	−0.0517507	+	0.0439661i
$731$	−1.35453	+	1.35453i	−0.0500992	+	0.0500992i
$732$		0			0
$733$	19.4202	+	19.4202i	0.717303	+	0.717303i	0.968052	−	0.250749i	$-0.0806770\pi$
$733$	19.4202	+	19.4202i	0.717303	+	0.717303i	−0.250749	+	0.968052i	$0.580677\pi$
$734$	−1.87679	+	23.0765i	−0.0692737	+	0.851769i
$735$		0			0
$736$	−8.35977	−	3.59128i	−0.308145	−	0.132376i
$737$	−11.9238			−0.439219
$738$		0			0
$739$	−20.5243	−	20.5243i	−0.754999	−	0.754999i	0.220409	−	0.975408i	$-0.429261\pi$
$739$	−20.5243	−	20.5243i	−0.754999	−	0.754999i	−0.975408	+	0.220409i	$0.929261\pi$
$740$	3.61006	−	22.0473i	0.132709	−	0.810476i
$741$		0			0
$742$	5.25570	−	4.46511i	0.192943	−	0.163919i
$743$		−	12.9245i		−	0.474154i	−0.971491	−	0.237077i	$-0.923811\pi$
$743$		−	12.9245i		−	0.474154i	0.971491	−	0.237077i	$-0.0761893\pi$
$744$		0			0
$745$			3.69732i			0.135459i
$746$	20.1129	+	23.6740i	0.736384	+	0.866767i
$747$		0			0
$748$	−37.1716	+	26.7113i	−1.35913	+	0.976662i
$749$	−4.33765	−	4.33765i	−0.158494	−	0.158494i
$750$		0			0
$751$	−52.2694			−1.90734			−0.953668	−	0.300861i	$-0.902726\pi$
$751$	−52.2694			−1.90734			−0.953668	+	0.300861i	$0.902726\pi$
$752$	17.4673	+	5.87783i	0.636966	+	0.214342i
$753$		0			0
$754$	−11.2204	−	0.912546i	−0.408623	−	0.0332330i
$755$	−8.99036	−	8.99036i	−0.327193	−	0.327193i
$756$		0			0
$757$	−34.4514	+	34.4514i	−1.25216	+	1.25216i	−0.297407	+	0.954751i	$0.596122\pi$
$757$	−34.4514	+	34.4514i	−1.25216	+	1.25216i	−0.954751	+	0.297407i	$0.903878\pi$
$758$	32.3132	+	38.0346i	1.17367	+	1.38148i
$759$		0			0
$760$	−5.19604	+	20.9199i	−0.188480	+	0.758843i
$761$		−	47.7467i		−	1.73082i	−0.501067	−	0.865408i	$-0.667059\pi$
$761$		−	47.7467i		−	1.73082i	0.501067	−	0.865408i	$-0.332941\pi$
$762$		0			0
$763$	−4.75956	+	4.75956i	−0.172308	+	0.172308i
$764$	11.0733	+	1.81317i	0.400620	+	0.0655980i
$765$		0			0
$766$	0.716360	−	8.80815i	0.0258831	−	0.318251i
$767$	6.84595			0.247193
$768$		0			0
$769$	−17.9108			−0.645882			−0.322941	−	0.946419i	$-0.604671\pi$
$769$	−17.9108			−0.645882			−0.322941	+	0.946419i	$0.604671\pi$
$770$	−0.342656	+	4.21320i	−0.0123485	+	0.151833i
$771$		0			0
$772$	−7.71124	−	1.26265i	−0.277534	−	0.0454437i
$773$	−3.73170	+	3.73170i	−0.134220	+	0.134220i	−0.771025	−	0.636805i	$-0.780256\pi$
$773$	−3.73170	+	3.73170i	−0.134220	+	0.134220i	0.636805	+	0.771025i	$0.280256\pi$
$774$		0			0
$775$			4.69807i			0.168760i
$776$	3.59336	−	14.4673i	0.128994	−	0.519346i
$777$		0			0
$778$	−2.72972	−	3.21304i	−0.0978652	−	0.115193i
$779$	−29.6329	+	29.6329i	−1.06171	+	1.06171i
$780$		0			0
$781$	7.10805	+	7.10805i	0.254346	+	0.254346i
$782$	−11.9880	−	0.974974i	−0.428690	−	0.0348650i
$783$		0			0
$784$	24.7298	+	8.32170i	0.883208	+	0.297204i
$785$	10.1517			0.362328
$786$		0			0
$787$	2.40160	+	2.40160i	0.0856076	+	0.0856076i	0.748614	−	0.663006i	$-0.230720\pi$
$787$	2.40160	+	2.40160i	0.0856076	+	0.0856076i	−0.663006	+	0.748614i	$0.730720\pi$
$788$	1.39751	−	1.00425i	0.0497843	−	0.0357748i
$789$		0			0
$790$	4.59626	+	5.41007i	0.163528	+	0.192481i
$791$			4.46187i			0.158646i
$792$		0			0
$793$		−	43.6060i		−	1.54849i
$794$	−35.8151	+	30.4277i	−1.27103	+	1.07984i
$795$		0			0
$796$	5.01839	−	30.6482i	0.177872	−	1.08630i
$797$	−35.4972	−	35.4972i	−1.25738	−	1.25738i	−0.952341	−	0.305035i	$-0.901332\pi$
$797$	−35.4972	−	35.4972i	−1.25738	−	1.25738i	−0.305035	−	0.952341i	$-0.598668\pi$
$798$		0			0
$799$	24.3627			0.861892
$800$	5.19755	+	2.23282i	0.183761	+	0.0789421i
$801$		0			0
$802$	−2.40618	+	29.5857i	−0.0849652	+	1.04471i
$803$	−3.97058	−	3.97058i	−0.140119	−	0.140119i
$804$		0			0
$805$	−0.785403	+	0.785403i	−0.0276818	+	0.0276818i
$806$	−16.7337	+	14.2166i	−0.589421	+	0.500757i
$807$		0			0
$808$	−27.7506	−	46.0914i	−0.976264	−	1.62149i
$809$		−	11.9182i		−	0.419021i	−0.977806	−	0.209510i	$-0.932813\pi$
$809$		−	11.9182i		−	0.419021i	0.977806	−	0.209510i	$-0.0671870\pi$
$810$		0			0
$811$	−22.1494	+	22.1494i	−0.777772	+	0.777772i	−0.979452	−	0.201680i	$-0.935360\pi$
$811$	−22.1494	+	22.1494i	−0.777772	+	0.777772i	0.201680	+	0.979452i	$0.435360\pi$
$812$	2.70156	−	1.94133i	0.0948063	−	0.0681273i
$813$		0			0
$814$	68.1510	+	5.54267i	2.38869	+	0.194270i
$815$	9.97694			0.349477
$816$		0			0
$817$	−2.76090			−0.0965915
$818$	25.9394	+	2.10963i	0.906949	+	0.0737615i
$819$		0			0
$820$	6.41780	+	8.93105i	0.224119	+	0.311886i
$821$	−13.3909	+	13.3909i	−0.467344	+	0.467344i	−0.901053	−	0.433709i	$-0.857205\pi$
$821$	−13.3909	+	13.3909i	−0.467344	+	0.467344i	0.433709	+	0.901053i	$0.357205\pi$
$822$		0			0
$823$		−	43.9496i		−	1.53199i	−0.642848	−	0.765994i	$-0.722247\pi$
$823$		−	43.9496i		−	1.53199i	0.642848	−	0.765994i	$-0.277753\pi$
$824$	−7.25536	−	1.80207i	−0.252752	−	0.0627782i
$825$		0			0
$826$	−1.54179	+	1.30986i	−0.0536456	+	0.0455760i
$827$	−1.79096	+	1.79096i	−0.0622777	+	0.0622777i	−0.737560	−	0.675282i	$-0.764022\pi$
$827$	−1.79096	+	1.79096i	−0.0622777	+	0.0622777i	0.675282	+	0.737560i	$0.264022\pi$
$828$		0			0
$829$	13.4979	+	13.4979i	0.468801	+	0.468801i	0.901526	−	0.432725i	$-0.142448\pi$
$829$	13.4979	+	13.4979i	0.468801	+	0.468801i	−0.432725	+	0.901526i	$0.642448\pi$
$830$	−1.18427	+	14.5615i	−0.0411067	+	0.505436i
$831$		0			0
$832$	7.77509	+	25.2694i	0.269553	+	0.876060i
$833$	34.4923			1.19509
$834$		0			0
$835$	−2.76186	−	2.76186i	−0.0955780	−	0.0955780i
$836$	−65.1051	−	10.6604i	−2.25171	−	0.368698i
$837$		0			0
$838$	22.7610	−	19.3372i	0.786266	−	0.667993i
$839$		−	14.5332i		−	0.501741i	−0.968021	−	0.250870i	$-0.919283\pi$
$839$		−	14.5332i		−	0.501741i	0.968021	−	0.250870i	$-0.0807168\pi$
$840$		0			0
$841$		−	23.1983i		−	0.799941i
$842$	−21.0658	−	24.7956i	−0.725975	−	0.854515i
$843$		0			0
$844$	−3.54042	−	4.92686i	−0.121866	−	0.169590i
$845$	1.46950	+	1.46950i	0.0505524	+	0.0505524i
$846$		0			0
$847$	−5.34105			−0.183521
$848$	25.2996	−	12.5598i	0.868793	−	0.431304i
$849$		0			0
$850$	7.45333	+	0.606174i	0.255647	+	0.0207916i
$851$	12.7043	+	12.7043i	0.435499	+	0.435499i
$852$		0			0
$853$	11.5836	−	11.5836i	0.396615	−	0.396615i	−0.480423	−	0.877037i	$-0.659517\pi$
$853$	11.5836	−	11.5836i	0.396615	−	0.396615i	0.877037	+	0.480423i	$0.159517\pi$
$854$	8.34331	+	9.82056i	0.285502	+	0.336053i
$855$		0			0
$856$	−12.9595	−	21.5246i	−0.442946	−	0.735695i
$857$			15.6443i			0.534399i	0.963641	+	0.267200i	$0.0860983\pi$
$857$			15.6443i			0.534399i	−0.963641	+	0.267200i	$0.913902\pi$
$858$		0			0
$859$	12.0947	−	12.0947i	0.412665	−	0.412665i	−0.470001	−	0.882666i	$-0.655746\pi$
$859$	12.0947	−	12.0947i	0.412665	−	0.412665i	0.882666	+	0.470001i	$0.155746\pi$
$860$	−0.117079	+	0.715026i	−0.00399237	+	0.0243822i
$861$		0			0
$862$	0.808687	−	9.94338i	0.0275440	−	0.338673i
$863$	9.28120			0.315936			0.157968	−	0.987444i	$-0.449506\pi$
$863$	9.28120			0.315936			0.157968	+	0.987444i	$0.449506\pi$
$864$		0			0
$865$	11.5985			0.394362
$866$	1.64153	−	20.1838i	0.0557816	−	0.685874i
$867$		0			0
$868$	1.04851	−	6.40347i	0.0355889	−	0.217348i
$869$	−15.3631	+	15.3631i	−0.521157	+	0.521157i
$870$		0			0
$871$			9.10425i			0.308486i
$872$	−23.6182	+	14.2200i	−0.799814	+	0.481551i
$873$		0			0
$874$	−11.2237	−	13.2110i	−0.379648	−	0.446868i
$875$	0.488311	−	0.488311i	0.0165079	−	0.0165079i
$876$		0			0
$877$	−2.97610	−	2.97610i	−0.100496	−	0.100496i	0.655071	−	0.755567i	$-0.272639\pi$
$877$	−2.97610	−	2.97610i	−0.100496	−	0.100496i	−0.755567	+	0.655071i	$0.772639\pi$
$878$	−36.5143	−	2.96968i	−1.23230	−	0.100222i
$879$		0			0
$880$	−5.52173	+	16.4091i	−0.186138	+	0.553150i
$881$	−29.3318			−0.988214			−0.494107	−	0.869401i	$-0.664505\pi$
$881$	−29.3318			−0.988214			−0.494107	+	0.869401i	$0.664505\pi$
$882$		0			0
$883$	35.5597	+	35.5597i	1.19668	+	1.19668i	0.975155	+	0.221525i	$0.0711033\pi$
$883$	35.5597	+	35.5597i	1.19668	+	1.19668i	0.221525	+	0.975155i	$0.428897\pi$
$884$	20.3950	+	28.3818i	0.685960	+	0.954585i
$885$		0			0
$886$	14.4240	+	16.9778i	0.484583	+	0.570382i
$887$			4.51671i			0.151656i	0.997121	+	0.0758282i	$0.0241601\pi$
$887$			4.51671i			0.151656i	−0.997121	+	0.0758282i	$0.975840\pi$
$888$		0			0
$889$			11.4721i			0.384762i
$890$	−1.95685	+	1.66249i	−0.0655937	+	0.0557268i
$891$		0			0
$892$	4.63416	+	0.758805i	0.155163	+	0.0254067i
$893$	24.8289	+	24.8289i	0.830867	+	0.830867i
$894$		0			0
$895$	−4.38920			−0.146715
$896$	−6.58594	−	4.20332i	−0.220021	−	0.140423i
$897$		0			0
$898$	1.45200	−	17.8533i	0.0484537	−	0.595773i
$899$	8.00169	+	8.00169i	0.266871	+	0.266871i
$900$		0			0
$901$	26.4025	−	26.4025i	0.879594	−	0.879594i
$902$	−25.6519	+	21.7933i	−0.854116	+	0.725636i
$903$		0			0
$904$	−4.40519	+	17.7358i	−0.146514	+	0.589884i
$905$		−	2.70172i		−	0.0898083i
$906$		0			0
$907$	−5.06769	+	5.06769i	−0.168270	+	0.168270i	−0.786218	−	0.617949i	$-0.787964\pi$
$907$	−5.06769	+	5.06769i	−0.168270	+	0.168270i	0.617949	+	0.786218i	$0.287964\pi$
$908$	21.7674	+	30.2917i	0.722378	+	1.00526i
$909$		0			0
$910$	3.21693	+	0.261631i	0.106640	+	0.00867297i
$911$	−36.7140			−1.21639			−0.608194	−	0.793788i	$-0.708106\pi$
$911$	−36.7140			−1.21639			−0.608194	+	0.793788i	$0.708106\pi$
$912$		0			0
$913$	−44.7135			−1.47980
$914$	23.8839	+	1.94246i	0.790008	+	0.0642507i
$915$		0			0
$916$	−21.5417	+	15.4797i	−0.711757	+	0.511465i
$917$	8.12937	−	8.12937i	0.268456	−	0.268456i
$918$		0			0
$919$			21.5651i			0.711365i	0.934607	+	0.355683i	$0.115752\pi$
$919$			21.5651i			0.711365i	−0.934607	+	0.355683i	$0.884248\pi$
$920$	−3.89738	+	2.34653i	−0.128493	+	0.0773628i
$921$		0			0
$922$	−20.1023	+	17.0785i	−0.662035	+	0.562449i
$923$	5.42725	−	5.42725i	0.178640	−	0.178640i
$924$		0			0
$925$	−7.89871	−	7.89871i	−0.259708	−	0.259708i
$926$	1.61589	−	19.8685i	0.0531013	−	0.652918i
$927$		0			0
$928$	12.6553	−	5.04949i	0.415431	−	0.165758i
$929$	45.6603			1.49807			0.749033	−	0.662532i	$-0.230518\pi$
$929$	45.6603			1.49807			0.749033	+	0.662532i	$0.230518\pi$
$930$		0			0
$931$	35.1522	+	35.1522i	1.15207	+	1.15207i
$932$	−5.28189	+	32.2575i	−0.173014	+	1.05663i
$933$		0			0
$934$	−18.4303	+	15.6579i	−0.603056	+	0.512342i
$935$			22.8868i			0.748478i
$936$		0			0
$937$		−	2.29807i		−	0.0750746i	−0.999295	−	0.0375373i	$-0.988049\pi$
$937$		−	2.29807i		−	0.0750746i	0.999295	−	0.0375373i	$-0.0119513\pi$
$938$	−1.74195	−	2.05038i	−0.0568768	−	0.0669473i
$939$		0			0
$940$	7.48316	−	5.37736i	0.244074	−	0.175390i
$941$	24.1999	+	24.1999i	0.788894	+	0.788894i	0.981313	−	0.192419i	$-0.0616333\pi$
$941$	24.1999	+	24.1999i	0.788894	+	0.788894i	−0.192419	+	0.981313i	$0.561633\pi$
$942$		0			0
$943$	−8.84448			−0.288016
$944$	−7.42179	+	3.68447i	−0.241559	+	0.119919i
$945$		0			0
$946$	−2.21023	−	0.179756i	−0.0718609	−	0.00584439i
$947$	−24.5182	−	24.5182i	−0.796733	−	0.796733i	0.185846	−	0.982579i	$-0.440498\pi$
$947$	−24.5182	−	24.5182i	−0.796733	−	0.796733i	−0.982579	+	0.185846i	$0.940498\pi$
$948$		0			0
$949$	−3.03168	+	3.03168i	−0.0984125	+	0.0984125i
$950$	6.97817	+	8.21371i	0.226402	+	0.266488i
$951$		0			0
$952$	−10.0236	−	2.48965i	−0.324867	−	0.0806900i
$953$		−	32.3462i		−	1.04780i	−0.851781	−	0.523898i	$-0.824477\pi$
$953$		−	32.3462i		−	1.04780i	0.851781	−	0.523898i	$-0.175523\pi$
$954$		0			0
$955$	3.96716	−	3.96716i	0.128374	−	0.128374i
$956$	38.2543	+	6.26381i	1.23723	+	0.202586i
$957$		0			0
$958$	1.63385	−	20.0894i	0.0527874	−	0.649059i
$959$	5.81116			0.187652
$960$		0			0
$961$	−8.92816			−0.288005
$962$	4.23203	−	52.0358i	0.136446	−	1.67770i
$963$		0			0
$964$	−14.1311	−	2.31385i	−0.455132	−	0.0745240i
$965$	−2.76264	+	2.76264i	−0.0889326	+	0.0889326i
$966$		0			0
$967$		−	14.6983i		−	0.472665i	−0.971672	−	0.236333i	$-0.924054\pi$
$967$		−	14.6983i		−	0.472665i	0.971672	−	0.236333i	$-0.0759455\pi$
$968$	−21.2305	−	5.27321i	−0.682376	−	0.169487i
$969$		0			0
$970$	−4.82581	−	5.68026i	−0.154947	−	0.182382i
$971$	−29.1065	+	29.1065i	−0.934073	+	0.934073i	−0.997957	−	0.0638845i	$-0.979651\pi$
$971$	−29.1065	+	29.1065i	−0.934073	+	0.934073i	0.0638845	+	0.997957i	$0.479651\pi$
$972$		0			0
$973$	1.04860	+	1.04860i	0.0336167	+	0.0336167i
$974$	−36.7084	−	2.98546i	−1.17621	−	0.0956604i
$975$		0			0
$976$	23.4686	+	47.2738i	0.751212	+	1.51320i
$977$	−17.3533			−0.555180			−0.277590	−	0.960700i	$-0.589536\pi$
$977$	−17.3533			−0.555180			−0.277590	+	0.960700i	$0.589536\pi$
$978$		0			0
$979$	−5.55691	−	5.55691i	−0.177600	−	0.177600i
$980$	10.5945	−	7.61315i	0.338429	−	0.243193i
$981$		0			0
$982$	−4.49076	−	5.28589i	−0.143306	−	0.168680i
$983$		−	27.5174i		−	0.877668i	−0.898568	−	0.438834i	$-0.855392\pi$
$983$		−	27.5174i		−	0.877668i	0.898568	−	0.438834i	$-0.144608\pi$
$984$		0			0
$985$		−	0.860458i		−	0.0274165i
$986$	13.7269	−	11.6620i	0.437152	−	0.371394i
$987$		0			0
$988$	−8.13961	+	49.7101i	−0.258955	+	1.58149i
$989$	−0.412020	−	0.412020i	−0.0131015	−	0.0131015i
$990$		0			0
$991$	6.96363			0.221207			0.110604	−	0.993865i	$-0.464722\pi$
$991$	6.96363			0.221207			0.110604	+	0.993865i	$0.464722\pi$
$992$	10.4899	−	24.4184i	0.333056	−	0.775286i
$993$		0			0
$994$	−0.183861	+	2.26070i	−0.00583171	+	0.0717050i
$995$	−10.9801	−	10.9801i	−0.348092	−	0.348092i
$996$		0			0
$997$	−15.7051	+	15.7051i	−0.497385	+	0.497385i	−0.910623	−	0.413238i	$-0.864398\pi$
$997$	−15.7051	+	15.7051i	−0.497385	+	0.497385i	0.413238	+	0.910623i	$0.364398\pi$
$998$	8.08242	−	6.86663i	0.255845	−	0.217359i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.c.541.4		16
3.2	odd	2		80.2.l.a.61.5	yes	16
4.3	odd	2		2880.2.t.c.721.3		16
12.11	even	2		320.2.l.a.81.2		16
15.2	even	4		400.2.q.h.349.8		16
15.8	even	4		400.2.q.g.349.1		16
15.14	odd	2		400.2.l.h.301.4		16
16.5	even	4	inner	720.2.t.c.181.4		16
16.11	odd	4		2880.2.t.c.2161.2		16
24.5	odd	2		640.2.l.b.161.2		16
24.11	even	2		640.2.l.a.161.7		16
48.5	odd	4		80.2.l.a.21.5	✓	16
48.11	even	4		320.2.l.a.241.2		16
48.29	odd	4		640.2.l.b.481.2		16
48.35	even	4		640.2.l.a.481.7		16
60.23	odd	4		1600.2.q.h.849.7		16
60.47	odd	4		1600.2.q.g.849.2		16
60.59	even	2		1600.2.l.i.401.7		16
96.5	odd	8		5120.2.a.v.1.2		8
96.11	even	8		5120.2.a.u.1.2		8
96.53	odd	8		5120.2.a.s.1.7		8
96.59	even	8		5120.2.a.t.1.7		8
240.53	even	4		400.2.q.h.149.8		16
240.59	even	4		1600.2.l.i.1201.7		16
240.107	odd	4		1600.2.q.h.49.7		16
240.149	odd	4		400.2.l.h.101.4		16
240.197	even	4		400.2.q.g.149.1		16
240.203	odd	4		1600.2.q.g.49.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.5	✓	16	48.5	odd	4
80.2.l.a.61.5	yes	16	3.2	odd	2
320.2.l.a.81.2		16	12.11	even	2
320.2.l.a.241.2		16	48.11	even	4
400.2.l.h.101.4		16	240.149	odd	4
400.2.l.h.301.4		16	15.14	odd	2
400.2.q.g.149.1		16	240.197	even	4
400.2.q.g.349.1		16	15.8	even	4
400.2.q.h.149.8		16	240.53	even	4
400.2.q.h.349.8		16	15.2	even	4
640.2.l.a.161.7		16	24.11	even	2
640.2.l.a.481.7		16	48.35	even	4
640.2.l.b.161.2		16	24.5	odd	2
640.2.l.b.481.2		16	48.29	odd	4
720.2.t.c.181.4		16	16.5	even	4	inner
720.2.t.c.541.4		16	1.1	even	1	trivial
1600.2.l.i.401.7		16	60.59	even	2
1600.2.l.i.1201.7		16	240.59	even	4
1600.2.q.g.49.2		16	240.203	odd	4
1600.2.q.g.849.2		16	60.47	odd	4
1600.2.q.h.49.7		16	240.107	odd	4
1600.2.q.h.849.7		16	60.23	odd	4
2880.2.t.c.721.3		16	4.3	odd	2
2880.2.t.c.2161.2		16	16.11	odd	4
5120.2.a.s.1.7		8	96.53	odd	8
5120.2.a.t.1.7		8	96.59	even	8
5120.2.a.u.1.2		8	96.11	even	8
5120.2.a.v.1.2		8	96.5	odd	8

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.114638 + 1.40956i) q^{2} +(-1.97372 - 0.323179i) q^{4} +(-0.707107 + 0.707107i) q^{5} -0.690576i q^{7} +(0.681804 - 2.74502i) q^{8} +(-0.915648 - 1.07777i) q^{10} +(3.06057 - 3.06057i) q^{11} +(-2.33686 - 2.33686i) q^{13} +(0.973408 + 0.0791665i) q^{14} +(3.79111 + 1.27573i) q^{16} +5.28770 q^{17} +(5.38887 + 5.38887i) q^{19} +(1.62415 - 1.16711i) q^{20} +(3.96320 + 4.66492i) q^{22} +1.60841i q^{23} -1.00000i q^{25} +(3.56183 - 3.02605i) q^{26} +(-0.223180 + 1.36300i) q^{28} +(-1.70319 - 1.70319i) q^{29} -4.69807 q^{31} +(-2.23282 + 5.19755i) q^{32} +(-0.606174 + 7.45333i) q^{34} +(0.488311 + 0.488311i) q^{35} +(7.89871 - 7.89871i) q^{37} +(-8.21371 + 6.97817i) q^{38} +(1.45892 + 2.42313i) q^{40} +5.49891i q^{41} +(-0.256166 + 0.256166i) q^{43} +(-7.02981 + 5.05159i) q^{44} +(-2.26715 - 0.184385i) q^{46} +4.60743 q^{47} +6.52310 q^{49} +(1.40956 + 0.114638i) q^{50} +(3.85707 + 5.36752i) q^{52} +(4.99318 - 4.99318i) q^{53} +4.32830i q^{55} +(-1.89565 - 0.470837i) q^{56} +(2.59600 - 2.20549i) q^{58} +(-1.46478 + 1.46478i) q^{59} +(9.33004 + 9.33004i) q^{61} +(0.538579 - 6.62221i) q^{62} +(-7.07029 - 3.74313i) q^{64} +3.30482 q^{65} +(-1.94797 - 1.94797i) q^{67} +(-10.4364 - 1.70888i) q^{68} +(-0.744283 + 0.632324i) q^{70} +2.32246i q^{71} -1.29733i q^{73} +(10.2282 + 12.0392i) q^{74} +(-8.89454 - 12.3777i) q^{76} +(-2.11356 - 2.11356i) q^{77} -5.01968 q^{79} +(-3.58280 + 1.77864i) q^{80} +(-7.75103 - 0.630385i) q^{82} +(-7.30477 - 7.30477i) q^{83} +(-3.73897 + 3.73897i) q^{85} +(-0.331715 - 0.390448i) q^{86} +(-6.31463 - 10.4880i) q^{88} -1.81564i q^{89} +(-1.61378 + 1.61378i) q^{91} +(0.519803 - 3.17454i) q^{92} +(-0.528188 + 6.49445i) q^{94} -7.62102 q^{95} +5.27038 q^{97} +(-0.747798 + 9.19470i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47}+ \cdots - 60 q^{98}+O(q^{100}) \) 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

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