LMFDB - Embedded newform 2040.2.cf.d.1441.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2040,2,Mod(361,2040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2040, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2040.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2040.cf (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$16.2894820123$
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} + 56 x^{18} + 1252 x^{16} + 14246 x^{14} + 87676 x^{12} + 294068 x^{10} + 556337 x^{8} + \cdots + 16384 $ x^20 + 56x^18 + 1252x^16 + 14246x^14 + 87676x^12 + 294068x^10 + 556337x^8 + 606400x^6 + 376064x^4 + 122880*x^2 + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1441.3
Root			$0.936527i$ of defining polynomial
Character	$\chi$	$=$	2040.1441
Dual form			2040.2.cf.d.361.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(-0.707107 - 0.707107i) q^{5} +(-0.495578 + 0.495578i) q^{7} +1.00000i q^{9} +(-0.726655 + 0.726655i) q^{11} -3.72133 q^{13} +1.00000i q^{15} +(3.25135 + 2.53549i) q^{17} -3.95026i q^{19} +0.700853 q^{21} +(0.802136 - 0.802136i) q^{23} +1.00000i q^{25} +(0.707107 - 0.707107i) q^{27} +(-1.19043 - 1.19043i) q^{29} +(1.19355 + 1.19355i) q^{31} +1.02765 q^{33} +0.700853 q^{35} +(5.01679 + 5.01679i) q^{37} +(2.63138 + 2.63138i) q^{39} +(-4.36916 + 4.36916i) q^{41} +6.64394i q^{43} +(0.707107 - 0.707107i) q^{45} +7.90627 q^{47} +6.50880i q^{49} +(-0.506189 - 4.09192i) q^{51} -0.694352i q^{53} +1.02765 q^{55} +(-2.79326 + 2.79326i) q^{57} +0.237027i q^{59} +(7.68550 - 7.68550i) q^{61} +(-0.495578 - 0.495578i) q^{63} +(2.63138 + 2.63138i) q^{65} +5.30814 q^{67} -1.13439 q^{69} +(-3.87865 - 3.87865i) q^{71} +(9.04109 + 9.04109i) q^{73} +(0.707107 - 0.707107i) q^{75} -0.720228i q^{77} +(8.99382 - 8.99382i) q^{79} -1.00000 q^{81} -9.89941i q^{83} +(-0.506189 - 4.09192i) q^{85} +1.68352i q^{87} -7.51797 q^{89} +(1.84421 - 1.84421i) q^{91} -1.68793i q^{93} +(-2.79326 + 2.79326i) q^{95} +(11.9197 + 11.9197i) q^{97} +(-0.726655 - 0.726655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{7} - 4 q^{11} + 8 q^{13} + 4 q^{17} - 4 q^{23} + 12 q^{29} + 8 q^{31} - 8 q^{33} - 12 q^{37} + 4 q^{39} - 12 q^{41} - 48 q^{47} + 16 q^{51} - 8 q^{55} + 8 q^{57} + 24 q^{61} - 4 q^{63} + 4 q^{65}+ \cdots - 4 q^{99}+O(q^{100}) $ 20 * q - 4 * q^7 - 4 * q^11 + 8 * q^13 + 4 * q^17 - 4 * q^23 + 12 * q^29 + 8 * q^31 - 8 * q^33 - 12 * q^37 + 4 * q^39 - 12 * q^41 - 48 * q^47 + 16 * q^51 - 8 * q^55 + 8 * q^57 + 24 * q^61 - 4 * q^63 + 4 * q^65 + 56 * q^67 - 24 * q^69 + 16 * q^71 + 4 * q^73 + 12 * q^79 - 20 * q^81 + 16 * q^85 - 44 * q^91 + 8 * q^95 - 40 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2040\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$817$	$1021$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$	−0.495578	+	0.495578i	−0.187311	+	0.187311i	−0.794533	−	0.607222i	$-0.792284\pi$
$7$	−0.495578	+	0.495578i	−0.187311	+	0.187311i	0.607222	+	0.794533i	$0.292284\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−0.726655	+	0.726655i	−0.219095	+	0.219095i	−0.808117	−	0.589022i	$-0.799513\pi$
$11$	−0.726655	+	0.726655i	−0.219095	+	0.219095i	0.589022	+	0.808117i	$0.299513\pi$
$12$		0			0
$13$	−3.72133			−1.03211			−0.516056	−	0.856555i	$-0.672600\pi$
$13$	−3.72133			−1.03211			−0.516056	+	0.856555i	$0.672600\pi$
$14$		0			0
$15$			1.00000i			0.258199i
$16$		0			0
$17$	3.25135	+	2.53549i	0.788568	+	0.614947i
$17$	3.25135	+	2.53549i	0.788568	+	0.614947i
$18$		0			0
$19$		−	3.95026i		−	0.906252i	−0.891447	−	0.453126i	$-0.850309\pi$
$19$		−	3.95026i		−	0.906252i	0.891447	−	0.453126i	$-0.149691\pi$
$20$		0			0
$21$	0.700853			0.152939
$22$		0			0
$23$	0.802136	−	0.802136i	0.167257	−	0.167257i	−0.618516	−	0.785772i	$-0.712266\pi$
$23$	0.802136	−	0.802136i	0.167257	−	0.167257i	0.785772	+	0.618516i	$0.212266\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$	−1.19043	−	1.19043i	−0.221057	−	0.221057i	0.587886	−	0.808943i	$-0.299960\pi$
$29$	−1.19043	−	1.19043i	−0.221057	−	0.221057i	−0.808943	+	0.587886i	$0.799960\pi$
$30$		0			0
$31$	1.19355	+	1.19355i	0.214367	+	0.214367i	0.806120	−	0.591752i	$-0.201564\pi$
$31$	1.19355	+	1.19355i	0.214367	+	0.214367i	−0.591752	+	0.806120i	$0.701564\pi$
$32$		0			0
$33$	1.02765			0.178890
$34$		0			0
$35$	0.700853			0.118466
$36$		0			0
$37$	5.01679	+	5.01679i	0.824755	+	0.824755i	0.986786	−	0.162031i	$-0.0518043\pi$
$37$	5.01679	+	5.01679i	0.824755	+	0.824755i	−0.162031	+	0.986786i	$0.551804\pi$
$38$		0			0
$39$	2.63138	+	2.63138i	0.421358	+	0.421358i
$40$		0			0
$41$	−4.36916	+	4.36916i	−0.682348	+	0.682348i	−0.960529	−	0.278181i	$-0.910268\pi$
$41$	−4.36916	+	4.36916i	−0.682348	+	0.682348i	0.278181	+	0.960529i	$0.410268\pi$
$42$		0			0
$43$			6.64394i			1.01319i	0.862184	+	0.506596i	$0.169096\pi$
$43$			6.64394i			1.01319i	−0.862184	+	0.506596i	$0.830904\pi$
$44$		0			0
$45$	0.707107	−	0.707107i	0.105409	−	0.105409i
$46$		0			0
$47$	7.90627			1.15325			0.576624	−	0.817010i	$-0.304370\pi$
$47$	7.90627			1.15325			0.576624	+	0.817010i	$0.304370\pi$
$48$		0			0
$49$			6.50880i			0.929829i
$50$		0			0
$51$	−0.506189	−	4.09192i	−0.0708807	−	0.572983i
$52$		0			0
$53$		−	0.694352i		−	0.0953766i	−0.998862	−	0.0476883i	$-0.984815\pi$
$53$		−	0.694352i		−	0.0953766i	0.998862	−	0.0476883i	$-0.0151854\pi$
$54$		0			0
$55$	1.02765			0.138568
$56$		0			0
$57$	−2.79326	+	2.79326i	−0.369976	+	0.369976i
$58$		0			0
$59$			0.237027i			0.0308583i	0.999881	+	0.0154292i	$0.00491145\pi$
$59$			0.237027i			0.0308583i	−0.999881	+	0.0154292i	$0.995089\pi$
$60$		0			0
$61$	7.68550	−	7.68550i	0.984028	−	0.984028i	−0.0158468	−	0.999874i	$-0.505044\pi$
$61$	7.68550	−	7.68550i	0.984028	−	0.984028i	0.999874	+	0.0158468i	$0.00504439\pi$
$62$		0			0
$63$	−0.495578	−	0.495578i	−0.0624370	−	0.0624370i
$64$		0			0
$65$	2.63138	+	2.63138i	0.326382	+	0.326382i
$66$		0			0
$67$	5.30814			0.648492			0.324246	−	0.945973i	$-0.394889\pi$
$67$	5.30814			0.648492			0.324246	+	0.945973i	$0.394889\pi$
$68$		0			0
$69$	−1.13439			−0.136565
$70$		0			0
$71$	−3.87865	−	3.87865i	−0.460311	−	0.460311i	0.438446	−	0.898757i	$-0.355529\pi$
$71$	−3.87865	−	3.87865i	−0.460311	−	0.460311i	−0.898757	+	0.438446i	$0.855529\pi$
$72$		0			0
$73$	9.04109	+	9.04109i	1.05818	+	1.05818i	0.998200	+	0.0599803i	$0.0191038\pi$
$73$	9.04109	+	9.04109i	1.05818	+	1.05818i	0.0599803	+	0.998200i	$0.480896\pi$
$74$		0			0
$75$	0.707107	−	0.707107i	0.0816497	−	0.0816497i
$76$		0			0
$77$		−	0.720228i		−	0.0820776i
$78$		0			0
$79$	8.99382	−	8.99382i	1.01188	−	1.01188i	0.0119554	−	0.999929i	$-0.496194\pi$
$79$	8.99382	−	8.99382i	1.01188	−	1.01188i	0.999929	−	0.0119554i	$-0.00380561\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$		−	9.89941i		−	1.08660i	−0.839538	−	0.543301i	$-0.817174\pi$
$83$		−	9.89941i		−	1.08660i	0.839538	−	0.543301i	$-0.182826\pi$
$84$		0			0
$85$	−0.506189	−	4.09192i	−0.0549039	−	0.443831i
$86$		0			0
$87$			1.68352i			0.180492i
$88$		0			0
$89$	−7.51797			−0.796903			−0.398452	−	0.917189i	$-0.630452\pi$
$89$	−7.51797			−0.796903			−0.398452	+	0.917189i	$0.630452\pi$
$90$		0			0
$91$	1.84421	−	1.84421i	0.193326	−	0.193326i
$92$		0			0
$93$		−	1.68793i		−	0.175030i
$94$		0			0
$95$	−2.79326	+	2.79326i	−0.286582	+	0.286582i
$96$		0			0
$97$	11.9197	+	11.9197i	1.21026	+	1.21026i	0.970941	+	0.239319i	$0.0769241\pi$
$97$	11.9197	+	11.9197i	1.21026	+	1.21026i	0.239319	+	0.970941i	$0.423076\pi$
$98$		0			0
$99$	−0.726655	−	0.726655i	−0.0730316	−	0.0730316i
$100$		0			0
$101$	13.2007			1.31352			0.656761	−	0.754099i	$-0.271926\pi$
$101$	13.2007			1.31352			0.656761	+	0.754099i	$0.271926\pi$
$102$		0			0
$103$	10.8849			1.07252			0.536261	−	0.844052i	$-0.319836\pi$
$103$	10.8849			1.07252			0.536261	+	0.844052i	$0.319836\pi$
$104$		0			0
$105$	−0.495578	−	0.495578i	−0.0483635	−	0.0483635i
$106$		0			0
$107$	−6.81283	−	6.81283i	−0.658621	−	0.658621i	0.296433	−	0.955054i	$-0.404203\pi$
$107$	−6.81283	−	6.81283i	−0.658621	−	0.658621i	−0.955054	+	0.296433i	$0.904203\pi$
$108$		0			0
$109$	−10.3733	+	10.3733i	−0.993582	+	0.993582i	−0.999980	−	0.00639799i	$-0.997963\pi$
$109$	−10.3733	+	10.3733i	−0.993582	+	0.993582i	0.00639799	+	0.999980i	$0.497963\pi$
$110$		0			0
$111$		−	7.09481i		−	0.673410i
$112$		0			0
$113$	1.47390	−	1.47390i	0.138653	−	0.138653i	−0.634373	−	0.773027i	$-0.718742\pi$
$113$	1.47390	−	1.47390i	0.138653	−	0.138653i	0.773027	+	0.634373i	$0.218742\pi$
$114$		0			0
$115$	−1.13439			−0.105783
$116$		0			0
$117$		−	3.72133i		−	0.344037i
$118$		0			0
$119$	−2.86783	+	0.354764i	−0.262894	+	0.0325212i
$120$		0			0
$121$			9.94395i			0.903995i
$122$		0			0
$123$	6.17892			0.557134
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$			4.26828i			0.378749i	0.981905	+	0.189374i	$0.0606460\pi$
$127$			4.26828i			0.378749i	−0.981905	+	0.189374i	$0.939354\pi$
$128$		0			0
$129$	4.69798	−	4.69798i	0.413634	−	0.413634i
$130$		0			0
$131$	−4.49787	−	4.49787i	−0.392981	−	0.392981i	0.482768	−	0.875748i	$-0.339632\pi$
$131$	−4.49787	−	4.49787i	−0.392981	−	0.392981i	−0.875748	+	0.482768i	$0.839632\pi$
$132$		0			0
$133$	1.95766	+	1.95766i	0.169751	+	0.169751i
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	16.0631			1.37236			0.686182	−	0.727430i	$-0.259285\pi$
$137$	16.0631			1.37236			0.686182	+	0.727430i	$0.259285\pi$
$138$		0			0
$139$	13.1291	+	13.1291i	1.11360	+	1.11360i	0.992660	+	0.120937i	$0.0385900\pi$
$139$	13.1291	+	13.1291i	1.11360	+	1.11360i	0.120937	+	0.992660i	$0.461410\pi$
$140$		0			0
$141$	−5.59058	−	5.59058i	−0.470812	−	0.470812i
$142$		0			0
$143$	2.70412	−	2.70412i	0.226130	−	0.226130i
$144$		0			0
$145$			1.68352i			0.139809i
$146$		0			0
$147$	4.60242	−	4.60242i	0.379601	−	0.379601i
$148$		0			0
$149$	9.52366			0.780209			0.390104	−	0.920771i	$-0.372439\pi$
$149$	9.52366			0.780209			0.390104	+	0.920771i	$0.372439\pi$
$150$		0			0
$151$		−	15.7089i		−	1.27837i	−0.769052	−	0.639186i	$-0.779271\pi$
$151$		−	15.7089i		−	1.27837i	0.769052	−	0.639186i	$-0.220729\pi$
$152$		0			0
$153$	−2.53549	+	3.25135i	−0.204982	+	0.262856i
$154$		0			0
$155$		−	1.68793i		−	0.135578i
$156$		0			0
$157$	3.85592			0.307736			0.153868	−	0.988091i	$-0.450827\pi$
$157$	3.85592			0.307736			0.153868	+	0.988091i	$0.450827\pi$
$158$		0			0
$159$	−0.490981	+	0.490981i	−0.0389374	+	0.0389374i
$160$		0			0
$161$			0.795042i			0.0626581i
$162$		0			0
$163$	6.25717	−	6.25717i	0.490099	−	0.490099i	−0.418238	−	0.908337i	$-0.637352\pi$
$163$	6.25717	−	6.25717i	0.490099	−	0.490099i	0.908337	+	0.418238i	$0.137352\pi$
$164$		0			0
$165$	−0.726655	−	0.726655i	−0.0565700	−	0.0565700i
$166$		0			0
$167$	10.4033	+	10.4033i	0.805033	+	0.805033i	0.983877	−	0.178844i	$-0.0572358\pi$
$167$	10.4033	+	10.4033i	0.805033	+	0.805033i	−0.178844	+	0.983877i	$0.557236\pi$
$168$		0			0
$169$	0.848296			0.0652535
$170$		0			0
$171$	3.95026			0.302084
$172$		0			0
$173$	6.17671	+	6.17671i	0.469607	+	0.469607i	0.901787	−	0.432180i	$-0.142256\pi$
$173$	6.17671	+	6.17671i	0.469607	+	0.469607i	−0.432180	+	0.901787i	$0.642256\pi$
$174$		0			0
$175$	−0.495578	−	0.495578i	−0.0374622	−	0.0374622i
$176$		0			0
$177$	0.167603	−	0.167603i	0.0125979	−	0.0125979i
$178$		0			0
$179$			3.66563i			0.273982i	0.990572	+	0.136991i	$0.0437432\pi$
$179$			3.66563i			0.273982i	−0.990572	+	0.136991i	$0.956257\pi$
$180$		0			0
$181$	−16.0294	+	16.0294i	−1.19146	+	1.19146i	−0.214797	+	0.976659i	$0.568909\pi$
$181$	−16.0294	+	16.0294i	−1.19146	+	1.19146i	−0.976659	+	0.214797i	$0.931091\pi$
$182$		0			0
$183$	−10.8689			−0.803455
$184$		0			0
$185$		−	7.09481i		−	0.521621i
$186$		0			0
$187$	−4.20504	+	0.520183i	−0.307503	+	0.0380396i
$188$		0			0
$189$			0.700853i			0.0509796i
$190$		0			0
$191$	0.170859			0.0123629			0.00618145	−	0.999981i	$-0.498032\pi$
$191$	0.170859			0.0123629			0.00618145	+	0.999981i	$0.498032\pi$
$192$		0			0
$193$	−13.2995	+	13.2995i	−0.957322	+	0.957322i	−0.999126	−	0.0418037i	$-0.986690\pi$
$193$	−13.2995	+	13.2995i	−0.957322	+	0.957322i	0.0418037	+	0.999126i	$0.486690\pi$
$194$		0			0
$195$		−	3.72133i		−	0.266490i
$196$		0			0
$197$	4.50191	−	4.50191i	0.320748	−	0.320748i	−0.528306	−	0.849054i	$-0.677173\pi$
$197$	4.50191	−	4.50191i	0.320748	−	0.320748i	0.849054	+	0.528306i	$0.177173\pi$
$198$		0			0
$199$	3.99517	+	3.99517i	0.283210	+	0.283210i	0.834388	−	0.551178i	$-0.185821\pi$
$199$	3.99517	+	3.99517i	0.283210	+	0.283210i	−0.551178	+	0.834388i	$0.685821\pi$
$200$		0			0
$201$	−3.75342	−	3.75342i	−0.264746	−	0.264746i
$202$		0			0
$203$	1.17990			0.0828128
$204$		0			0
$205$	6.17892			0.431555
$206$		0			0
$207$	0.802136	+	0.802136i	0.0557523	+	0.0557523i
$208$		0			0
$209$	2.87047	+	2.87047i	0.198555	+	0.198555i
$210$		0			0
$211$	14.9522	−	14.9522i	1.02935	−	1.02935i	0.0297954	−	0.999556i	$-0.490514\pi$
$211$	14.9522	−	14.9522i	1.02935	−	1.02935i	0.999556	−	0.0297954i	$-0.00948558\pi$
$212$		0			0
$213$			5.48524i			0.375842i
$214$		0			0
$215$	4.69798	−	4.69798i	0.320399	−	0.320399i
$216$		0			0
$217$	−1.18299			−0.0803067
$218$		0			0
$219$		−	12.7860i		−	0.864000i
$220$		0			0
$221$	−12.0994	−	9.43540i	−0.813890	−	0.634694i
$222$		0			0
$223$			9.83074i			0.658315i	0.944275	+	0.329157i	$0.106765\pi$
$223$			9.83074i			0.658315i	−0.944275	+	0.329157i	$0.893235\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	−9.35083	+	9.35083i	−0.620636	+	0.620636i	−0.945694	−	0.325058i	$-0.894616\pi$
$227$	−9.35083	+	9.35083i	−0.620636	+	0.620636i	0.325058	+	0.945694i	$0.394616\pi$
$228$		0			0
$229$			0.00923168i			0.000610047i	1.00000		0.000305023i	$9.70920e-5\pi$
$229$			0.00923168i			0.000610047i	−1.00000		0.000305023i	$0.999903\pi$
$230$		0			0
$231$	−0.509278	+	0.509278i	−0.0335081	+	0.0335081i
$232$		0			0
$233$	−7.36277	−	7.36277i	−0.482351	−	0.482351i	0.423531	−	0.905882i	$-0.360791\pi$
$233$	−7.36277	−	7.36277i	−0.482351	−	0.482351i	−0.905882	+	0.423531i	$0.860791\pi$
$234$		0			0
$235$	−5.59058	−	5.59058i	−0.364689	−	0.364689i
$236$		0			0
$237$	−12.7192			−0.826200
$238$		0			0
$239$	−4.77552			−0.308903			−0.154451	−	0.988000i	$-0.549361\pi$
$239$	−4.77552			−0.308903			−0.154451	+	0.988000i	$0.549361\pi$
$240$		0			0
$241$	−10.3957	−	10.3957i	−0.669646	−	0.669646i	0.287988	−	0.957634i	$-0.407014\pi$
$241$	−10.3957	−	10.3957i	−0.669646	−	0.669646i	−0.957634	+	0.287988i	$0.907014\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	4.60242	−	4.60242i	0.294038	−	0.294038i
$246$		0			0
$247$			14.7002i			0.935352i
$248$		0			0
$249$	−6.99994	+	6.99994i	−0.443603	+	0.443603i
$250$		0			0
$251$	−25.7247			−1.62373			−0.811863	−	0.583848i	$-0.801546\pi$
$251$	−25.7247			−1.62373			−0.811863	+	0.583848i	$0.801546\pi$
$252$		0			0
$253$			1.16575i			0.0732902i
$254$		0			0
$255$	−2.53549	+	3.25135i	−0.158779	+	0.203608i
$256$		0			0
$257$			6.48757i			0.404683i	0.979315	+	0.202342i	$0.0648551\pi$
$257$			6.48757i			0.404683i	−0.979315	+	0.202342i	$0.935145\pi$
$258$		0			0
$259$	−4.97242			−0.308971
$260$		0			0
$261$	1.19043	−	1.19043i	0.0736857	−	0.0736857i
$262$		0			0
$263$		−	17.0164i		−	1.04927i	−0.851326	−	0.524637i	$-0.824201\pi$
$263$		−	17.0164i		−	1.04927i	0.851326	−	0.524637i	$-0.175799\pi$
$264$		0			0
$265$	−0.490981	+	0.490981i	−0.0301607	+	0.0301607i
$266$		0			0
$267$	5.31601	+	5.31601i	0.325334	+	0.325334i
$268$		0			0
$269$	9.05468	+	9.05468i	0.552074	+	0.552074i	0.927039	−	0.374965i	$-0.122345\pi$
$269$	9.05468	+	9.05468i	0.552074	+	0.552074i	−0.374965	+	0.927039i	$0.622345\pi$
$270$		0			0
$271$	−3.25162			−0.197522			−0.0987609	−	0.995111i	$-0.531488\pi$
$271$	−3.25162			−0.197522			−0.0987609	+	0.995111i	$0.531488\pi$
$272$		0			0
$273$	−2.60811			−0.157850
$274$		0			0
$275$	−0.726655	−	0.726655i	−0.0438189	−	0.0438189i
$276$		0			0
$277$	11.6118	+	11.6118i	0.697684	+	0.697684i	0.963910	−	0.266227i	$-0.0857770\pi$
$277$	11.6118	+	11.6118i	0.697684	+	0.697684i	−0.266227	+	0.963910i	$0.585777\pi$
$278$		0			0
$279$	−1.19355	+	1.19355i	−0.0714558	+	0.0714558i
$280$		0			0
$281$		−	13.6008i		−	0.811357i	−0.914016	−	0.405678i	$-0.867035\pi$
$281$		−	13.6008i		−	0.811357i	0.914016	−	0.405678i	$-0.132965\pi$
$282$		0			0
$283$	−5.97736	+	5.97736i	−0.355317	+	0.355317i	−0.862084	−	0.506766i	$-0.830841\pi$
$283$	−5.97736	+	5.97736i	−0.355317	+	0.355317i	0.506766	+	0.862084i	$0.330841\pi$
$284$		0			0
$285$	3.95026			0.233993
$286$		0			0
$287$		−	4.33052i		−	0.255622i
$288$		0			0
$289$	4.14257	+	16.4875i	0.243680	+	0.969856i
$290$		0			0
$291$		−	16.8570i		−	0.988173i
$292$		0			0
$293$	−7.21246			−0.421356			−0.210678	−	0.977555i	$-0.567567\pi$
$293$	−7.21246			−0.421356			−0.210678	+	0.977555i	$0.567567\pi$
$294$		0			0
$295$	0.167603	−	0.167603i	0.00975825	−	0.00975825i
$296$		0			0
$297$			1.02765i			0.0596300i
$298$		0			0
$299$	−2.98501	+	2.98501i	−0.172628	+	0.172628i
$300$		0			0
$301$	−3.29259	−	3.29259i	−0.189782	−	0.189782i
$302$		0			0
$303$	−9.33433	−	9.33433i	−0.536243	−	0.536243i
$304$		0			0
$305$	−10.8689			−0.622354
$306$		0			0
$307$	12.8014			0.730612			0.365306	−	0.930887i	$-0.380964\pi$
$307$	12.8014			0.730612			0.365306	+	0.930887i	$0.380964\pi$
$308$		0			0
$309$	−7.69679	−	7.69679i	−0.437855	−	0.437855i
$310$		0			0
$311$	5.30160	+	5.30160i	0.300626	+	0.300626i	0.841259	−	0.540633i	$-0.181815\pi$
$311$	5.30160	+	5.30160i	0.300626	+	0.300626i	−0.540633	+	0.841259i	$0.681815\pi$
$312$		0			0
$313$	−16.3795	+	16.3795i	−0.925825	+	0.925825i	−0.997433	−	0.0716077i	$-0.977187\pi$
$313$	−16.3795	+	16.3795i	−0.925825	+	0.925825i	0.0716077	+	0.997433i	$0.477187\pi$
$314$		0			0
$315$			0.700853i			0.0394886i
$316$		0			0
$317$	−8.56631	+	8.56631i	−0.481132	+	0.481132i	−0.905493	−	0.424361i	$-0.860499\pi$
$317$	−8.56631	+	8.56631i	−0.481132	+	0.481132i	0.424361	+	0.905493i	$0.360499\pi$
$318$		0			0
$319$	1.73006			0.0968649
$320$		0			0
$321$			9.63479i			0.537762i
$322$		0			0
$323$	10.0158	−	12.8437i	0.557297	−	0.714641i
$324$		0			0
$325$		−	3.72133i		−	0.206422i
$326$		0			0
$327$	14.6701			0.811256
$328$		0			0
$329$	−3.91817	+	3.91817i	−0.216016	+	0.216016i
$330$		0			0
$331$			1.16846i			0.0642245i	0.999484	+	0.0321122i	$0.0102234\pi$
$331$			1.16846i			0.0642245i	−0.999484	+	0.0321122i	$0.989777\pi$
$332$		0			0
$333$	−5.01679	+	5.01679i	−0.274918	+	0.274918i
$334$		0			0
$335$	−3.75342	−	3.75342i	−0.205071	−	0.205071i
$336$		0			0
$337$	9.44915	+	9.44915i	0.514728	+	0.514728i	0.915971	−	0.401244i	$-0.131422\pi$
$337$	9.44915	+	9.44915i	0.514728	+	0.514728i	−0.401244	+	0.915971i	$0.631422\pi$
$338$		0			0
$339$	−2.08442			−0.113210
$340$		0			0
$341$	−1.73459			−0.0939335
$342$		0			0
$343$	−6.69467	−	6.69467i	−0.361478	−	0.361478i
$344$		0			0
$345$	0.802136	+	0.802136i	0.0431855	+	0.0431855i
$346$		0			0
$347$	−22.7469	+	22.7469i	−1.22112	+	1.22112i	−0.253886	+	0.967234i	$0.581709\pi$
$347$	−22.7469	+	22.7469i	−1.22112	+	1.22112i	−0.967234	+	0.253886i	$0.918291\pi$
$348$		0			0
$349$		−	20.2106i		−	1.08185i	−0.841071	−	0.540924i	$-0.818075\pi$
$349$		−	20.2106i		−	1.08185i	0.841071	−	0.540924i	$-0.181925\pi$
$350$		0			0
$351$	−2.63138	+	2.63138i	−0.140453	+	0.140453i
$352$		0			0
$353$	−0.898226			−0.0478077			−0.0239039	−	0.999714i	$-0.507610\pi$
$353$	−0.898226			−0.0478077			−0.0239039	+	0.999714i	$0.507610\pi$
$354$		0			0
$355$			5.48524i			0.291126i
$356$		0			0
$357$	2.27872	+	1.77701i	0.120603	+	0.0940492i
$358$		0			0
$359$		−	3.36863i		−	0.177789i	−0.996041	−	0.0888947i	$-0.971667\pi$
$359$		−	3.36863i		−	0.177789i	0.996041	−	0.0888947i	$-0.0283335\pi$
$360$		0			0
$361$	3.39545			0.178708
$362$		0			0
$363$	7.03143	−	7.03143i	0.369054	−	0.369054i
$364$		0			0
$365$		−	12.7860i		−	0.669252i
$366$		0			0
$367$	4.29082	−	4.29082i	0.223979	−	0.223979i	−0.586193	−	0.810172i	$-0.699374\pi$
$367$	4.29082	−	4.29082i	0.223979	−	0.223979i	0.810172	+	0.586193i	$0.199374\pi$
$368$		0			0
$369$	−4.36916	−	4.36916i	−0.227449	−	0.227449i
$370$		0			0
$371$	0.344106	+	0.344106i	0.0178651	+	0.0178651i
$372$		0			0
$373$	−6.86133			−0.355266			−0.177633	−	0.984097i	$-0.556844\pi$
$373$	−6.86133			−0.355266			−0.177633	+	0.984097i	$0.556844\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	4.42998	+	4.42998i	0.228156	+	0.228156i
$378$		0			0
$379$	−1.00471	−	1.00471i	−0.0516083	−	0.0516083i	0.680832	−	0.732440i	$-0.261619\pi$
$379$	−1.00471	−	1.00471i	−0.0516083	−	0.0516083i	−0.732440	+	0.680832i	$0.761619\pi$
$380$		0			0
$381$	3.01813	−	3.01813i	0.154623	−	0.154623i
$382$		0			0
$383$		−	15.9561i		−	0.815319i	−0.913134	−	0.407660i	$-0.866345\pi$
$383$		−	15.9561i		−	0.815319i	0.913134	−	0.407660i	$-0.133655\pi$
$384$		0			0
$385$	−0.509278	+	0.509278i	−0.0259552	+	0.0259552i
$386$		0			0
$387$	−6.64394			−0.337731
$388$		0			0
$389$		−	38.4164i		−	1.94779i	−0.227005	−	0.973894i	$-0.572893\pi$
$389$		−	38.4164i		−	1.94779i	0.227005	−	0.973894i	$-0.427107\pi$
$390$		0			0
$391$	4.64183	−	0.574217i	0.234748	−	0.0290394i
$392$		0			0
$393$			6.36095i			0.320867i
$394$		0			0
$395$	−12.7192			−0.639972
$396$		0			0
$397$	9.00384	−	9.00384i	0.451890	−	0.451890i	−0.444092	−	0.895981i	$-0.646474\pi$
$397$	9.00384	−	9.00384i	0.451890	−	0.451890i	0.895981	+	0.444092i	$0.146474\pi$
$398$		0			0
$399$		−	2.76855i		−	0.138601i
$400$		0			0
$401$	−12.4962	+	12.4962i	−0.624030	+	0.624030i	−0.946559	−	0.322530i	$-0.895467\pi$
$401$	−12.4962	+	12.4962i	−0.624030	+	0.624030i	0.322530	+	0.946559i	$0.395467\pi$
$402$		0			0
$403$	−4.44158	−	4.44158i	−0.221251	−	0.221251i
$404$		0			0
$405$	0.707107	+	0.707107i	0.0351364	+	0.0351364i
$406$		0			0
$407$	−7.29095			−0.361399
$408$		0			0
$409$	−7.67066			−0.379290			−0.189645	−	0.981853i	$-0.560734\pi$
$409$	−7.67066			−0.379290			−0.189645	+	0.981853i	$0.560734\pi$
$410$		0			0
$411$	−11.3583	−	11.3583i	−0.560265	−	0.560265i
$412$		0			0
$413$	−0.117465	−	0.117465i	−0.00578010	−	0.00578010i
$414$		0			0
$415$	−6.99994	+	6.99994i	−0.343614	+	0.343614i
$416$		0			0
$417$		−	18.5674i		−	0.909248i
$418$		0			0
$419$	−3.87395	+	3.87395i	−0.189255	+	0.189255i	−0.795374	−	0.606119i	$-0.792725\pi$
$419$	−3.87395	+	3.87395i	−0.189255	+	0.189255i	0.606119	+	0.795374i	$0.292725\pi$
$420$		0			0
$421$	−24.3203			−1.18530			−0.592650	−	0.805460i	$-0.701918\pi$
$421$	−24.3203			−1.18530			−0.592650	+	0.805460i	$0.701918\pi$
$422$		0			0
$423$			7.90627i			0.384416i
$424$		0			0
$425$	−2.53549	+	3.25135i	−0.122989	+	0.157714i
$426$		0			0
$427$			7.61753i			0.368638i
$428$		0			0
$429$	−3.82421			−0.184634
$430$		0			0
$431$	−9.81064	+	9.81064i	−0.472562	+	0.472562i	−0.902743	−	0.430181i	$-0.858450\pi$
$431$	−9.81064	+	9.81064i	−0.472562	+	0.472562i	0.430181	+	0.902743i	$0.358450\pi$
$432$		0			0
$433$		−	9.28570i		−	0.446242i	−0.974791	−	0.223121i	$-0.928375\pi$
$433$		−	9.28570i		−	0.446242i	0.974791	−	0.223121i	$-0.0716246\pi$
$434$		0			0
$435$	1.19043	−	1.19043i	0.0570767	−	0.0570767i
$436$		0			0
$437$	−3.16864	−	3.16864i	−0.151577	−	0.151577i
$438$		0			0
$439$	26.6533	+	26.6533i	1.27209	+	1.27209i	0.944988	+	0.327105i	$0.106073\pi$
$439$	26.6533	+	26.6533i	1.27209	+	1.27209i	0.327105	+	0.944988i	$0.393927\pi$
$440$		0			0
$441$	−6.50880			−0.309943
$442$		0			0
$443$	6.83183			0.324590			0.162295	−	0.986742i	$-0.448110\pi$
$443$	6.83183			0.324590			0.162295	+	0.986742i	$0.448110\pi$
$444$		0			0
$445$	5.31601	+	5.31601i	0.252003	+	0.252003i
$446$		0			0
$447$	−6.73425	−	6.73425i	−0.318519	−	0.318519i
$448$		0			0
$449$	−7.37109	+	7.37109i	−0.347863	+	0.347863i	−0.859313	−	0.511450i	$-0.829109\pi$
$449$	−7.37109	+	7.37109i	−0.347863	+	0.347863i	0.511450	+	0.859313i	$0.329109\pi$
$450$		0			0
$451$		−	6.34974i		−	0.298997i
$452$		0			0
$453$	−11.1079	+	11.1079i	−0.521893	+	0.521893i
$454$		0			0
$455$	−2.60811			−0.122270
$456$		0			0
$457$			8.73831i			0.408761i	0.978892	+	0.204380i	$0.0655180\pi$
$457$			8.73831i			0.408761i	−0.978892	+	0.204380i	$0.934482\pi$
$458$		0			0
$459$	4.09192	−	0.506189i	0.190994	−	0.0236269i
$460$		0			0
$461$		−	27.6010i		−	1.28551i	−0.766074	−	0.642753i	$-0.777792\pi$
$461$		−	27.6010i		−	1.28551i	0.766074	−	0.642753i	$-0.222208\pi$
$462$		0			0
$463$	14.9583			0.695173			0.347586	−	0.937648i	$-0.387001\pi$
$463$	14.9583			0.695173			0.347586	+	0.937648i	$0.387001\pi$
$464$		0			0
$465$	−1.19355	+	1.19355i	−0.0553494	+	0.0553494i
$466$		0			0
$467$			24.1589i			1.11794i	0.829188	+	0.558970i	$0.188803\pi$
$467$			24.1589i			1.11794i	−0.829188	+	0.558970i	$0.811197\pi$
$468$		0			0
$469$	−2.63060	+	2.63060i	−0.121470	+	0.121470i
$470$		0			0
$471$	−2.72655	−	2.72655i	−0.125633	−	0.125633i
$472$		0			0
$473$	−4.82785	−	4.82785i	−0.221985	−	0.221985i
$474$		0			0
$475$	3.95026			0.181250
$476$		0			0
$477$	0.694352			0.0317922
$478$		0			0
$479$	5.22619	+	5.22619i	0.238791	+	0.238791i	0.816349	−	0.577558i	$-0.195994\pi$
$479$	5.22619	+	5.22619i	0.238791	+	0.238791i	−0.577558	+	0.816349i	$0.695994\pi$
$480$		0			0
$481$	−18.6691	−	18.6691i	−0.851239	−	0.851239i
$482$		0			0
$483$	0.562179	−	0.562179i	0.0255800	−	0.0255800i
$484$		0			0
$485$		−	16.8570i		−	0.765435i
$486$		0			0
$487$	−27.8970	+	27.8970i	−1.26413	+	1.26413i	−0.315062	+	0.949071i	$0.602025\pi$
$487$	−27.8970	+	27.8970i	−1.26413	+	1.26413i	−0.949071	+	0.315062i	$0.897975\pi$
$488$		0			0
$489$	−8.84897			−0.400164
$490$		0			0
$491$		−	42.8025i		−	1.93165i	−0.259197	−	0.965825i	$-0.583458\pi$
$491$		−	42.8025i		−	1.93165i	0.259197	−	0.965825i	$-0.416542\pi$
$492$		0			0
$493$	−0.852180	−	6.88882i	−0.0383803	−	0.310257i
$494$		0			0
$495$			1.02765i			0.0461892i
$496$		0			0
$497$	3.84435			0.172443
$498$		0			0
$499$	−27.6934	+	27.6934i	−1.23973	+	1.23973i	−0.279617	+	0.960112i	$0.590207\pi$
$499$	−27.6934	+	27.6934i	−1.23973	+	1.23973i	−0.960112	+	0.279617i	$0.909793\pi$
$500$		0			0
$501$		−	14.7125i		−	0.657307i
$502$		0			0
$503$	−19.3788	+	19.3788i	−0.864060	+	0.864060i	−0.991807	−	0.127747i	$-0.959226\pi$
$503$	−19.3788	+	19.3788i	−0.864060	+	0.864060i	0.127747	+	0.991807i	$0.459226\pi$
$504$		0			0
$505$	−9.33433	−	9.33433i	−0.415372	−	0.415372i
$506$		0			0
$507$	−0.599836	−	0.599836i	−0.0266396	−	0.0266396i
$508$		0			0
$509$	−30.1174			−1.33493			−0.667466	−	0.744640i	$-0.732621\pi$
$509$	−30.1174			−1.33493			−0.667466	+	0.744640i	$0.732621\pi$
$510$		0			0
$511$	−8.96113			−0.396417
$512$		0			0
$513$	−2.79326	−	2.79326i	−0.123325	−	0.123325i
$514$		0			0
$515$	−7.69679	−	7.69679i	−0.339161	−	0.339161i
$516$		0			0
$517$	−5.74513	+	5.74513i	−0.252671	+	0.252671i
$518$		0			0
$519$		−	8.73519i		−	0.383432i
$520$		0			0
$521$	−6.48823	+	6.48823i	−0.284255	+	0.284255i	−0.834803	−	0.550549i	$-0.814419\pi$
$521$	−6.48823	+	6.48823i	−0.284255	+	0.284255i	0.550549	+	0.834803i	$0.314419\pi$
$522$		0			0
$523$	−5.35644			−0.234221			−0.117110	−	0.993119i	$-0.537363\pi$
$523$	−5.35644			−0.234221			−0.117110	+	0.993119i	$0.537363\pi$
$524$		0			0
$525$			0.700853i			0.0305877i
$526$		0			0
$527$	0.854412	+	6.90687i	0.0372188	+	0.300868i
$528$		0			0
$529$			21.7132i			0.944050i
$530$		0			0
$531$	−0.237027			−0.0102861
$532$		0			0
$533$	16.2591	−	16.2591i	0.704259	−	0.704259i
$534$		0			0
$535$			9.63479i			0.416548i
$536$		0			0
$537$	2.59199	−	2.59199i	0.111853	−	0.111853i
$538$		0			0
$539$	−4.72965	−	4.72965i	−0.203721	−	0.203721i
$540$		0			0
$541$	−8.26481	−	8.26481i	−0.355332	−	0.355332i	0.506757	−	0.862089i	$-0.330844\pi$
$541$	−8.26481	−	8.26481i	−0.355332	−	0.355332i	−0.862089	+	0.506757i	$0.830844\pi$
$542$		0			0
$543$	22.6690			0.972820
$544$		0			0
$545$	14.6701			0.628396
$546$		0			0
$547$	−8.56770	−	8.56770i	−0.366328	−	0.366328i	0.499808	−	0.866136i	$-0.333404\pi$
$547$	−8.56770	−	8.56770i	−0.366328	−	0.366328i	−0.866136	+	0.499808i	$0.833404\pi$
$548$		0			0
$549$	7.68550	+	7.68550i	0.328009	+	0.328009i
$550$		0			0
$551$	−4.70250	+	4.70250i	−0.200333	+	0.200333i
$552$		0			0
$553$			8.91428i			0.379074i
$554$		0			0
$555$	−5.01679	+	5.01679i	−0.212951	+	0.212951i
$556$		0			0
$557$	20.7902			0.880911			0.440456	−	0.897774i	$-0.354817\pi$
$557$	20.7902			0.880911			0.440456	+	0.897774i	$0.354817\pi$
$558$		0			0
$559$		−	24.7243i		−	1.04573i
$560$		0			0
$561$	3.34124	+	2.60559i	0.141067	+	0.110008i
$562$		0			0
$563$			3.03112i			0.127747i	0.997958	+	0.0638733i	$0.0203453\pi$
$563$			3.03112i			0.127747i	−0.997958	+	0.0638733i	$0.979655\pi$
$564$		0			0
$565$	−2.08442			−0.0876921
$566$		0			0
$567$	0.495578	−	0.495578i	0.0208123	−	0.0208123i
$568$		0			0
$569$			23.7348i			0.995013i	0.867460	+	0.497507i	$0.165751\pi$
$569$			23.7348i			0.995013i	−0.867460	+	0.497507i	$0.834249\pi$
$570$		0			0
$571$	11.7353	−	11.7353i	0.491106	−	0.491106i	−0.417549	−	0.908655i	$-0.637111\pi$
$571$	11.7353	−	11.7353i	0.491106	−	0.491106i	0.908655	+	0.417549i	$0.137111\pi$
$572$		0			0
$573$	−0.120815	−	0.120815i	−0.00504713	−	0.00504713i
$574$		0			0
$575$	0.802136	+	0.802136i	0.0334514	+	0.0334514i
$576$		0			0
$577$	41.0437			1.70867			0.854335	−	0.519723i	$-0.173965\pi$
$577$	41.0437			1.70867			0.854335	+	0.519723i	$0.173965\pi$
$578$		0			0
$579$	18.8084			0.781650
$580$		0			0
$581$	4.90593	+	4.90593i	0.203532	+	0.203532i
$582$		0			0
$583$	0.504555	+	0.504555i	0.0208965	+	0.0208965i
$584$		0			0
$585$	−2.63138	+	2.63138i	−0.108794	+	0.108794i
$586$		0			0
$587$			14.7480i			0.608717i	0.952558	+	0.304358i	$0.0984421\pi$
$587$			14.7480i			0.608717i	−0.952558	+	0.304358i	$0.901558\pi$
$588$		0			0
$589$	4.71482	−	4.71482i	0.194271	−	0.194271i
$590$		0			0
$591$	−6.36667			−0.261890
$592$		0			0
$593$			8.22591i			0.337798i	0.985633	+	0.168899i	$0.0540211\pi$
$593$			8.22591i			0.337798i	−0.985633	+	0.168899i	$0.945979\pi$
$594$		0			0
$595$	2.27872	+	1.77701i	0.0934184	+	0.0728502i
$596$		0			0
$597$		−	5.65003i		−	0.231240i
$598$		0			0
$599$	3.14063			0.128323			0.0641614	−	0.997940i	$-0.479563\pi$
$599$	3.14063			0.128323			0.0641614	+	0.997940i	$0.479563\pi$
$600$		0			0
$601$	0.991175	−	0.991175i	0.0404309	−	0.0404309i	−0.686602	−	0.727033i	$-0.740899\pi$
$601$	0.991175	−	0.991175i	0.0404309	−	0.0404309i	0.727033	+	0.686602i	$0.240899\pi$
$602$		0			0
$603$			5.30814i			0.216164i
$604$		0			0
$605$	7.03143	−	7.03143i	0.285868	−	0.285868i
$606$		0			0
$607$	−27.3065	−	27.3065i	−1.10834	−	1.10834i	−0.993369	−	0.114967i	$-0.963324\pi$
$607$	−27.3065	−	27.3065i	−1.10834	−	1.10834i	−0.114967	−	0.993369i	$-0.536676\pi$
$608$		0			0
$609$	−0.834316	−	0.834316i	−0.0338082	−	0.0338082i
$610$		0			0
$611$	−29.4218			−1.19028
$612$		0			0
$613$	36.9494			1.49237			0.746185	−	0.665738i	$-0.231883\pi$
$613$	36.9494			1.49237			0.746185	+	0.665738i	$0.231883\pi$
$614$		0			0
$615$	−4.36916	−	4.36916i	−0.176181	−	0.176181i
$616$		0			0
$617$	0.612821	+	0.612821i	0.0246713	+	0.0246713i	0.719335	−	0.694664i	$-0.244447\pi$
$617$	0.612821	+	0.612821i	0.0246713	+	0.0246713i	−0.694664	+	0.719335i	$0.744447\pi$
$618$		0			0
$619$	17.6664	−	17.6664i	0.710073	−	0.710073i	−0.256477	−	0.966550i	$-0.582562\pi$
$619$	17.6664	−	17.6664i	0.710073	−	0.710073i	0.966550	+	0.256477i	$0.0825618\pi$
$620$		0			0
$621$		−	1.13439i		−	0.0455215i
$622$		0			0
$623$	3.72574	−	3.72574i	0.149269	−	0.149269i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		−	4.05946i		−	0.162119i
$628$		0			0
$629$	3.59132	+	29.0314i	0.143195	+	1.15756i
$630$		0			0
$631$		−	5.63808i		−	0.224448i	−0.993683	−	0.112224i	$-0.964203\pi$
$631$		−	5.63808i		−	0.224448i	0.993683	−	0.112224i	$-0.0357975\pi$
$632$		0			0
$633$	−21.1456			−0.840462
$634$		0			0
$635$	3.01813	−	3.01813i	0.119771	−	0.119771i
$636$		0			0
$637$		−	24.2214i		−	0.959687i
$638$		0			0
$639$	3.87865	−	3.87865i	0.153437	−	0.153437i
$640$		0			0
$641$	−1.52609	−	1.52609i	−0.0602770	−	0.0602770i	0.676326	−	0.736603i	$-0.263571\pi$
$641$	−1.52609	−	1.52609i	−0.0602770	−	0.0602770i	−0.736603	+	0.676326i	$0.763571\pi$
$642$		0			0
$643$	26.2062	+	26.2062i	1.03347	+	1.03347i	0.999420	+	0.0340535i	$0.0108417\pi$
$643$	26.2062	+	26.2062i	1.03347	+	1.03347i	0.0340535	+	0.999420i	$0.489158\pi$
$644$		0			0
$645$	−6.64394			−0.261605
$646$		0			0
$647$	−17.7695			−0.698589			−0.349295	−	0.937013i	$-0.613579\pi$
$647$	−17.7695			−0.698589			−0.349295	+	0.937013i	$0.613579\pi$
$648$		0			0
$649$	−0.172237	−	0.172237i	−0.00676089	−	0.00676089i
$650$		0			0
$651$	0.836501	+	0.836501i	0.0327851	+	0.0327851i
$652$		0			0
$653$	32.2881	−	32.2881i	1.26353	−	1.26353i	0.314164	−	0.949369i	$-0.398276\pi$
$653$	32.2881	−	32.2881i	1.26353	−	1.26353i	0.949369	−	0.314164i	$-0.101724\pi$
$654$		0			0
$655$			6.36095i			0.248543i
$656$		0			0
$657$	−9.04109	+	9.04109i	−0.352727	+	0.352727i
$658$		0			0
$659$	16.2874			0.634466			0.317233	−	0.948348i	$-0.397246\pi$
$659$	16.2874			0.634466			0.317233	+	0.948348i	$0.397246\pi$
$660$		0			0
$661$		−	24.6193i		−	0.957581i	−0.877929	−	0.478790i	$-0.841075\pi$
$661$		−	24.6193i		−	0.957581i	0.877929	−	0.478790i	$-0.158925\pi$
$662$		0			0
$663$	1.88370	+	15.2274i	0.0731568	+	0.591382i
$664$		0			0
$665$		−	2.76855i		−	0.107360i
$666$		0			0
$667$	−1.90977			−0.0739466
$668$		0			0
$669$	6.95138	−	6.95138i	0.268756	−	0.268756i
$670$		0			0
$671$			11.1694i			0.431190i
$672$		0			0
$673$	−9.42174	+	9.42174i	−0.363181	+	0.363181i	−0.864983	−	0.501801i	$-0.832671\pi$
$673$	−9.42174	+	9.42174i	−0.363181	+	0.363181i	0.501801	+	0.864983i	$0.332671\pi$
$674$		0			0
$675$	0.707107	+	0.707107i	0.0272166	+	0.0272166i
$676$		0			0
$677$	−3.54825	−	3.54825i	−0.136370	−	0.136370i	0.635627	−	0.771997i	$-0.280742\pi$
$677$	−3.54825	−	3.54825i	−0.136370	−	0.136370i	−0.771997	+	0.635627i	$0.780742\pi$
$678$		0			0
$679$	−11.8143			−0.453390
$680$		0			0
$681$	13.2241			0.506747
$682$		0			0
$683$	−19.5488	−	19.5488i	−0.748015	−	0.748015i	0.226091	−	0.974106i	$-0.427405\pi$
$683$	−19.5488	−	19.5488i	−0.748015	−	0.748015i	−0.974106	+	0.226091i	$0.927405\pi$
$684$		0			0
$685$	−11.3583	−	11.3583i	−0.433980	−	0.433980i
$686$		0			0
$687$	0.00652779	−	0.00652779i	0.000249051	−	0.000249051i
$688$		0			0
$689$			2.58391i			0.0984393i
$690$		0			0
$691$	7.29522	−	7.29522i	0.277523	−	0.277523i	−0.554596	−	0.832120i	$-0.687127\pi$
$691$	7.29522	−	7.29522i	0.277523	−	0.277523i	0.832120	+	0.554596i	$0.187127\pi$
$692$		0			0
$693$	0.720228			0.0273592
$694$		0			0
$695$		−	18.5674i		−	0.704301i
$696$		0			0
$697$	−25.2836	+	3.12770i	−0.957685	+	0.118470i
$698$		0			0
$699$			10.4125i			0.393838i
$700$		0			0
$701$	−8.47019			−0.319915			−0.159957	−	0.987124i	$-0.551136\pi$
$701$	−8.47019			−0.319915			−0.159957	+	0.987124i	$0.551136\pi$
$702$		0			0
$703$	19.8176	−	19.8176i	0.747436	−	0.747436i
$704$		0			0
$705$			7.90627i			0.297767i
$706$		0			0
$707$	−6.54199	+	6.54199i	−0.246037	+	0.246037i
$708$		0			0
$709$	25.9418	+	25.9418i	0.974265	+	0.974265i	0.999677	−	0.0254117i	$-0.00808967\pi$
$709$	25.9418	+	25.9418i	0.974265	+	0.974265i	−0.0254117	+	0.999677i	$0.508090\pi$
$710$		0			0
$711$	8.99382	+	8.99382i	0.337295	+	0.337295i
$712$		0			0
$713$	1.91477			0.0717088
$714$		0			0
$715$	−3.82421			−0.143017
$716$		0			0
$717$	3.37680	+	3.37680i	0.126109	+	0.126109i
$718$		0			0
$719$	7.53238	+	7.53238i	0.280910	+	0.280910i	0.833472	−	0.552562i	$-0.186350\pi$
$719$	7.53238	+	7.53238i	0.280910	+	0.280910i	−0.552562	+	0.833472i	$0.686350\pi$
$720$		0			0
$721$	−5.39432	+	5.39432i	−0.200895	+	0.200895i
$722$		0			0
$723$			14.7017i			0.546764i
$724$		0			0
$725$	1.19043	−	1.19043i	0.0442114	−	0.0442114i
$726$		0			0
$727$	−18.9985			−0.704616			−0.352308	−	0.935884i	$-0.614603\pi$
$727$	−18.9985			−0.704616			−0.352308	+	0.935884i	$0.614603\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−16.8457	+	21.6018i	−0.623059	+	0.798971i
$732$		0			0
$733$			17.7453i			0.655436i	0.944776	+	0.327718i	$0.106280\pi$
$733$			17.7453i			0.655436i	−0.944776	+	0.327718i	$0.893720\pi$
$734$		0			0
$735$	−6.50880			−0.240081
$736$		0			0
$737$	−3.85718	+	3.85718i	−0.142081	+	0.142081i
$738$		0			0
$739$		−	36.5429i		−	1.34425i	−0.740436	−	0.672127i	$-0.765381\pi$
$739$		−	36.5429i		−	1.34425i	0.740436	−	0.672127i	$-0.234619\pi$
$740$		0			0
$741$	10.3946	−	10.3946i	0.381856	−	0.381856i
$742$		0			0
$743$	−6.84312	−	6.84312i	−0.251050	−	0.251050i	0.570351	−	0.821401i	$-0.306807\pi$
$743$	−6.84312	−	6.84312i	−0.251050	−	0.251050i	−0.821401	+	0.570351i	$0.806807\pi$
$744$		0			0
$745$	−6.73425	−	6.73425i	−0.246724	−	0.246724i
$746$		0			0
$747$	9.89941			0.362200
$748$		0			0
$749$	6.75258			0.246734
$750$		0			0
$751$	−9.06554	−	9.06554i	−0.330806	−	0.330806i	0.522086	−	0.852893i	$-0.325154\pi$
$751$	−9.06554	−	9.06554i	−0.330806	−	0.330806i	−0.852893	+	0.522086i	$0.825154\pi$
$752$		0			0
$753$	18.1901	+	18.1901i	0.662883	+	0.662883i
$754$		0			0
$755$	−11.1079	+	11.1079i	−0.404257	+	0.404257i
$756$		0			0
$757$		−	6.13521i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$757$		−	6.13521i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$758$		0			0
$759$	0.824311	−	0.824311i	0.0299206	−	0.0299206i
$760$		0			0
$761$	37.5051			1.35956			0.679779	−	0.733417i	$-0.262076\pi$
$761$	37.5051			1.35956			0.679779	+	0.733417i	$0.262076\pi$
$762$		0			0
$763$		−	10.2816i		−	0.372217i
$764$		0			0
$765$	4.09192	−	0.506189i	0.147944	−	0.0183013i
$766$		0			0
$767$		−	0.882056i		−	0.0318492i
$768$		0			0
$769$	−11.8273			−0.426504			−0.213252	−	0.976997i	$-0.568406\pi$
$769$	−11.8273			−0.426504			−0.213252	+	0.976997i	$0.568406\pi$
$770$		0			0
$771$	4.58740	−	4.58740i	0.165211	−	0.165211i
$772$		0			0
$773$		−	27.7733i		−	0.998937i	−0.866332	−	0.499469i	$-0.833529\pi$
$773$		−	27.7733i		−	0.998937i	0.866332	−	0.499469i	$-0.166471\pi$
$774$		0			0
$775$	−1.19355	+	1.19355i	−0.0428735	+	0.0428735i
$776$		0			0
$777$	3.51603	+	3.51603i	0.126137	+	0.126137i
$778$		0			0
$779$	17.2593	+	17.2593i	0.618379	+	0.618379i
$780$		0			0
$781$	5.63688			0.201703
$782$		0			0
$783$	−1.68352			−0.0601641
$784$		0			0
$785$	−2.72655	−	2.72655i	−0.0973147	−	0.0973147i
$786$		0			0
$787$	21.8950	+	21.8950i	0.780473	+	0.780473i	0.979910	−	0.199438i	$-0.0639116\pi$
$787$	21.8950	+	21.8950i	0.780473	+	0.780473i	−0.199438	+	0.979910i	$0.563912\pi$
$788$		0			0
$789$	−12.0324	+	12.0324i	−0.428364	+	0.428364i
$790$		0			0
$791$			1.46087i			0.0519426i
$792$		0			0
$793$	−28.6003	+	28.6003i	−1.01563	+	1.01563i
$794$		0			0
$795$	0.694352			0.0246261
$796$		0			0
$797$		−	2.48271i		−	0.0879420i	−0.999033	−	0.0439710i	$-0.985999\pi$
$797$		−	2.48271i		−	0.0879420i	0.999033	−	0.0439710i	$-0.0140009\pi$
$798$		0			0
$799$	25.7061	+	20.0463i	0.909415	+	0.709186i
$800$		0			0
$801$		−	7.51797i		−	0.265634i
$802$		0			0
$803$	−13.1395			−0.463683
$804$		0			0
$805$	0.562179	−	0.562179i	0.0198142	−	0.0198142i
$806$		0			0
$807$		−	12.8053i		−	0.450766i
$808$		0			0
$809$	24.0086	−	24.0086i	0.844097	−	0.844097i	−0.145292	−	0.989389i	$-0.546412\pi$
$809$	24.0086	−	24.0086i	0.844097	−	0.844097i	0.989389	+	0.145292i	$0.0464121\pi$
$810$		0			0
$811$	11.0734	+	11.0734i	0.388840	+	0.388840i	0.874273	−	0.485434i	$-0.161338\pi$
$811$	11.0734	+	11.0734i	0.388840	+	0.388840i	−0.485434	+	0.874273i	$0.661338\pi$
$812$		0			0
$813$	2.29924	+	2.29924i	0.0806380	+	0.0806380i
$814$		0			0
$815$	−8.84897			−0.309966
$816$		0			0
$817$	26.2453			0.918207
$818$		0			0
$819$	1.84421	+	1.84421i	0.0644419	+	0.0644419i
$820$		0			0
$821$	2.02082	+	2.02082i	0.0705273	+	0.0705273i	0.741491	−	0.670963i	$-0.234119\pi$
$821$	2.02082	+	2.02082i	0.0705273	+	0.0705273i	−0.670963	+	0.741491i	$0.734119\pi$
$822$		0			0
$823$	−23.1991	+	23.1991i	−0.808669	+	0.808669i	−0.984432	−	0.175764i	$-0.943761\pi$
$823$	−23.1991	+	23.1991i	−0.808669	+	0.808669i	0.175764	+	0.984432i	$0.443761\pi$
$824$		0			0
$825$			1.02765i			0.0357780i
$826$		0			0
$827$	−29.5467	+	29.5467i	−1.02744	+	1.02744i	−0.0278261	+	0.999613i	$0.508858\pi$
$827$	−29.5467	+	29.5467i	−1.02744	+	1.02744i	−0.999613	+	0.0278261i	$0.991142\pi$
$828$		0			0
$829$	4.77641			0.165892			0.0829459	−	0.996554i	$-0.473567\pi$
$829$	4.77641			0.165892			0.0829459	+	0.996554i	$0.473567\pi$
$830$		0			0
$831$		−	16.4215i		−	0.569656i
$832$		0			0
$833$	−16.5030	+	21.1624i	−0.571796	+	0.733234i
$834$		0			0
$835$		−	14.7125i		−	0.509148i
$836$		0			0
$837$	1.68793			0.0583434
$838$		0			0
$839$	8.72408	−	8.72408i	0.301189	−	0.301189i	−0.540290	−	0.841479i	$-0.681685\pi$
$839$	8.72408	−	8.72408i	0.301189	−	0.301189i	0.841479	+	0.540290i	$0.181685\pi$
$840$		0			0
$841$		−	26.1658i		−	0.902268i
$842$		0			0
$843$	−9.61723	+	9.61723i	−0.331235	+	0.331235i
$844$		0			0
$845$	−0.599836	−	0.599836i	−0.0206350	−	0.0206350i
$846$		0			0
$847$	−4.92800	−	4.92800i	−0.169328	−	0.169328i
$848$		0			0
$849$	8.45327			0.290115
$850$		0			0
$851$	8.04829			0.275892
$852$		0			0
$853$	−3.24497	−	3.24497i	−0.111106	−	0.111106i	0.649368	−	0.760474i	$-0.275033\pi$
$853$	−3.24497	−	3.24497i	−0.111106	−	0.111106i	−0.760474	+	0.649368i	$0.775033\pi$
$854$		0			0
$855$	−2.79326	−	2.79326i	−0.0955273	−	0.0955273i
$856$		0			0
$857$	19.0232	−	19.0232i	0.649821	−	0.649821i	−0.303129	−	0.952950i	$-0.598031\pi$
$857$	19.0232	−	19.0232i	0.649821	−	0.649821i	0.952950	+	0.303129i	$0.0980312\pi$
$858$		0			0
$859$			4.39230i			0.149863i	0.997189	+	0.0749316i	$0.0238738\pi$
$859$			4.39230i			0.149863i	−0.997189	+	0.0749316i	$0.976126\pi$
$860$		0			0
$861$	−3.06214	+	3.06214i	−0.104357	+	0.104357i
$862$		0			0
$863$	−15.1478			−0.515636			−0.257818	−	0.966194i	$-0.583003\pi$
$863$	−15.1478			−0.515636			−0.257818	+	0.966194i	$0.583003\pi$
$864$		0			0
$865$		−	8.73519i		−	0.297005i
$866$		0			0
$867$	8.72922	−	14.5877i	0.296460	−	0.495424i
$868$		0			0
$869$			13.0708i			0.443397i
$870$		0			0
$871$	−19.7533			−0.669316
$872$		0			0
$873$	−11.9197	+	11.9197i	−0.403420	+	0.403420i
$874$		0			0
$875$			0.700853i			0.0236932i
$876$		0			0
$877$	34.3907	−	34.3907i	1.16129	−	1.16129i	0.177099	−	0.984193i	$-0.443329\pi$
$877$	34.3907	−	34.3907i	1.16129	−	1.16129i	0.984193	−	0.177099i	$-0.0566713\pi$
$878$		0			0
$879$	5.09998	+	5.09998i	0.172018	+	0.172018i
$880$		0			0
$881$	−4.53591	−	4.53591i	−0.152819	−	0.152819i	0.626557	−	0.779376i	$-0.284464\pi$
$881$	−4.53591	−	4.53591i	−0.152819	−	0.152819i	−0.779376	+	0.626557i	$0.784464\pi$
$882$		0			0
$883$	28.0472			0.943863			0.471931	−	0.881635i	$-0.343557\pi$
$883$	28.0472			0.943863			0.471931	+	0.881635i	$0.343557\pi$
$884$		0			0
$885$	−0.237027			−0.00796758
$886$		0			0
$887$	33.6130	+	33.6130i	1.12861	+	1.12861i	0.990403	+	0.138211i	$0.0441353\pi$
$887$	33.6130	+	33.6130i	1.12861	+	1.12861i	0.138211	+	0.990403i	$0.455865\pi$
$888$		0			0
$889$	−2.11527	−	2.11527i	−0.0709438	−	0.0709438i
$890$		0			0
$891$	0.726655	−	0.726655i	0.0243439	−	0.0243439i
$892$		0			0
$893$		−	31.2318i		−	1.04513i
$894$		0			0
$895$	2.59199	−	2.59199i	0.0866408	−	0.0866408i
$896$		0			0
$897$	4.22144			0.140950
$898$		0			0
$899$		−	2.84166i		−	0.0947748i
$900$		0			0
$901$	1.76052	−	2.25758i	0.0586516	−	0.0752110i
$902$		0			0
$903$			4.65643i			0.154956i
$904$		0			0
$905$	22.6690			0.753543
$906$		0			0
$907$	−23.7069	+	23.7069i	−0.787174	+	0.787174i	−0.981030	−	0.193856i	$-0.937901\pi$
$907$	−23.7069	+	23.7069i	−0.787174	+	0.787174i	0.193856	+	0.981030i	$0.437901\pi$
$908$		0			0
$909$			13.2007i			0.437841i
$910$		0			0
$911$	16.7890	−	16.7890i	0.556246	−	0.556246i	−0.371991	−	0.928236i	$-0.621325\pi$
$911$	16.7890	−	16.7890i	0.556246	−	0.556246i	0.928236	+	0.371991i	$0.121325\pi$
$912$		0			0
$913$	7.19345	+	7.19345i	0.238069	+	0.238069i
$914$		0			0
$915$	7.68550	+	7.68550i	0.254075	+	0.254075i
$916$		0			0
$917$	4.45809			0.147219
$918$		0			0
$919$	28.3419			0.934914			0.467457	−	0.884016i	$-0.345170\pi$
$919$	28.3419			0.934914			0.467457	+	0.884016i	$0.345170\pi$
$920$		0			0
$921$	−9.05193	−	9.05193i	−0.298271	−	0.298271i
$922$		0			0
$923$	14.4337	+	14.4337i	0.475092	+	0.475092i
$924$		0			0
$925$	−5.01679	+	5.01679i	−0.164951	+	0.164951i
$926$		0			0
$927$			10.8849i			0.357507i
$928$		0			0
$929$	−0.0454483	+	0.0454483i	−0.00149111	+	0.00149111i	−0.707852	−	0.706361i	$-0.750336\pi$
$929$	−0.0454483	+	0.0454483i	−0.00149111	+	0.00149111i	0.706361	+	0.707852i	$0.250336\pi$
$930$		0			0
$931$	25.7115			0.842659
$932$		0			0
$933$		−	7.49760i		−	0.245460i
$934$		0			0
$935$	3.34124	+	2.60559i	0.109270	+	0.0852117i
$936$		0			0
$937$			4.27502i			0.139659i	0.997559	+	0.0698295i	$0.0222455\pi$
$937$			4.27502i			0.139659i	−0.997559	+	0.0698295i	$0.977754\pi$
$938$		0			0
$939$	23.1641			0.755933
$940$		0			0
$941$	5.47147	−	5.47147i	0.178365	−	0.178365i	−0.612278	−	0.790643i	$-0.709747\pi$
$941$	5.47147	−	5.47147i	0.178365	−	0.178365i	0.790643	+	0.612278i	$0.209747\pi$
$942$		0			0
$943$			7.00931i			0.228255i
$944$		0			0
$945$	0.495578	−	0.495578i	0.0161212	−	0.0161212i
$946$		0			0
$947$	−12.4524	−	12.4524i	−0.404648	−	0.404648i	0.475219	−	0.879867i	$-0.342369\pi$
$947$	−12.4524	−	12.4524i	−0.404648	−	0.404648i	−0.879867	+	0.475219i	$0.842369\pi$
$948$		0			0
$949$	−33.6449	−	33.6449i	−1.09216	−	1.09216i
$950$		0			0
$951$	12.1146			0.392843
$952$		0			0
$953$	44.8118			1.45160			0.725798	−	0.687907i	$-0.241471\pi$
$953$	44.8118			1.45160			0.725798	+	0.687907i	$0.241471\pi$
$954$		0			0
$955$	−0.120815	−	0.120815i	−0.00390949	−	0.00390949i
$956$		0			0
$957$	−1.22334	−	1.22334i	−0.0395449	−	0.0395449i
$958$		0			0
$959$	−7.96053	+	7.96053i	−0.257059	+	0.257059i
$960$		0			0
$961$		−	28.1509i		−	0.908093i
$962$		0			0
$963$	6.81283	−	6.81283i	0.219540	−	0.219540i
$964$		0			0
$965$	18.8084			0.605464
$966$		0			0
$967$		−	13.8845i		−	0.446497i	−0.974762	−	0.223248i	$-0.928334\pi$
$967$		−	13.8845i		−	0.446497i	0.974762	−	0.223248i	$-0.0716661\pi$
$968$		0			0
$969$	−16.1641	+	1.99958i	−0.519267	+	0.0642357i
$970$		0			0
$971$			53.5344i			1.71800i	0.511975	+	0.859000i	$0.328914\pi$
$971$			53.5344i			1.71800i	−0.511975	+	0.859000i	$0.671086\pi$
$972$		0			0
$973$	−13.0130			−0.417178
$974$		0			0
$975$	−2.63138	+	2.63138i	−0.0842715	+	0.0842715i
$976$		0			0
$977$			11.6340i			0.372206i	0.982530	+	0.186103i	$0.0595857\pi$
$977$			11.6340i			0.372206i	−0.982530	+	0.186103i	$0.940414\pi$
$978$		0			0
$979$	5.46297	−	5.46297i	0.174597	−	0.174597i
$980$		0			0
$981$	−10.3733	−	10.3733i	−0.331194	−	0.331194i
$982$		0			0
$983$	23.0219	+	23.0219i	0.734284	+	0.734284i	0.971465	−	0.237181i	$-0.0762235\pi$
$983$	23.0219	+	23.0219i	0.734284	+	0.734284i	−0.237181	+	0.971465i	$0.576224\pi$
$984$		0			0
$985$	−6.36667			−0.202859
$986$		0			0
$987$	5.54114			0.176376
$988$		0			0
$989$	5.32934	+	5.32934i	0.169463	+	0.169463i
$990$		0			0
$991$	19.2935	+	19.2935i	0.612877	+	0.612877i	0.943695	−	0.330817i	$-0.107324\pi$
$991$	19.2935	+	19.2935i	0.612877	+	0.612877i	−0.330817	+	0.943695i	$0.607324\pi$
$992$		0			0
$993$	0.826227	−	0.826227i	0.0262195	−	0.0262195i
$994$		0			0
$995$		−	5.65003i		−	0.179118i
$996$		0			0
$997$	0.558779	−	0.558779i	0.0176967	−	0.0176967i	−0.698203	−	0.715900i	$-0.746017\pi$
$997$	0.558779	−	0.558779i	0.0176967	−	0.0176967i	0.715900	+	0.698203i	$0.246017\pi$
$998$		0			0
$999$	7.09481			0.224470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2040.2.cf.d.1441.3	yes	20
17.4	even	4	inner	2040.2.cf.d.361.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2040.2.cf.d.361.3	✓	20	17.4	even	4	inner
2040.2.cf.d.1441.3	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2040.cf (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-0.707107 - 0.707107i) q^{5} +(-0.495578 + 0.495578i) q^{7} +1.00000i q^{9} +(-0.726655 + 0.726655i) q^{11} -3.72133 q^{13} +1.00000i q^{15} +(3.25135 + 2.53549i) q^{17} -3.95026i q^{19} +0.700853 q^{21} +(0.802136 - 0.802136i) q^{23} +1.00000i q^{25} +(0.707107 - 0.707107i) q^{27} +(-1.19043 - 1.19043i) q^{29} +(1.19355 + 1.19355i) q^{31} +1.02765 q^{33} +0.700853 q^{35} +(5.01679 + 5.01679i) q^{37} +(2.63138 + 2.63138i) q^{39} +(-4.36916 + 4.36916i) q^{41} +6.64394i q^{43} +(0.707107 - 0.707107i) q^{45} +7.90627 q^{47} +6.50880i q^{49} +(-0.506189 - 4.09192i) q^{51} -0.694352i q^{53} +1.02765 q^{55} +(-2.79326 + 2.79326i) q^{57} +0.237027i q^{59} +(7.68550 - 7.68550i) q^{61} +(-0.495578 - 0.495578i) q^{63} +(2.63138 + 2.63138i) q^{65} +5.30814 q^{67} -1.13439 q^{69} +(-3.87865 - 3.87865i) q^{71} +(9.04109 + 9.04109i) q^{73} +(0.707107 - 0.707107i) q^{75} -0.720228i q^{77} +(8.99382 - 8.99382i) q^{79} -1.00000 q^{81} -9.89941i q^{83} +(-0.506189 - 4.09192i) q^{85} +1.68352i q^{87} -7.51797 q^{89} +(1.84421 - 1.84421i) q^{91} -1.68793i q^{93} +(-2.79326 + 2.79326i) q^{95} +(11.9197 + 11.9197i) q^{97} +(-0.726655 - 0.726655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{7} - 4 q^{11} + 8 q^{13} + 4 q^{17} - 4 q^{23} + 12 q^{29} + 8 q^{31} - 8 q^{33} - 12 q^{37} + 4 q^{39} - 12 q^{41} - 48 q^{47} + 16 q^{51} - 8 q^{55} + 8 q^{57} + 24 q^{61} - 4 q^{63} + 4 q^{65}+ \cdots - 4 q^{99}+O(q^{100}) \) 20 * q - 4 * q^7 - 4 * q^11 + 8 * q^13 + 4 * q^17 - 4 * q^23 + 12 * q^29 + 8 * q^31 - 8 * q^33 - 12 * q^37 + 4 * q^39 - 12 * q^41 - 48 * q^47 + 16 * q^51 - 8 * q^55 + 8 * q^57 + 24 * q^61 - 4 * q^63 + 4 * q^65 + 56 * q^67 - 24 * q^69 + 16 * q^71 + 4 * q^73 + 12 * q^79 - 20 * q^81 + 16 * q^85 - 44 * q^91 + 8 * q^95 - 40 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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