LMFDB - Embedded newform 361.2.c.a.68.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(68,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.68"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			68.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	361.68
Dual form			361.2.c.a.292.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +3.00000 q^{11} -4.00000 q^{12} +(-2.00000 - 3.46410i) q^{13} +(-3.00000 - 5.19615i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.50000 - 2.59808i) q^{17} -6.00000 q^{20} +(1.00000 - 1.73205i) q^{21} +(-2.00000 - 3.46410i) q^{25} -4.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(3.00000 + 5.19615i) q^{29} +4.00000 q^{31} +(-3.00000 + 5.19615i) q^{33} +(1.50000 - 2.59808i) q^{35} +(1.00000 - 1.73205i) q^{36} -2.00000 q^{37} +8.00000 q^{39} +(-3.00000 + 5.19615i) q^{41} +(0.500000 - 0.866025i) q^{43} +(3.00000 + 5.19615i) q^{44} +3.00000 q^{45} +(1.50000 + 2.59808i) q^{47} +(-4.00000 - 6.92820i) q^{48} -6.00000 q^{49} +(3.00000 + 5.19615i) q^{51} +(4.00000 - 6.92820i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-4.50000 + 7.79423i) q^{55} +(-3.00000 + 5.19615i) q^{59} +(6.00000 - 10.3923i) q^{60} +(0.500000 + 0.866025i) q^{61} +(0.500000 + 0.866025i) q^{63} -8.00000 q^{64} +12.0000 q^{65} +(-2.00000 - 3.46410i) q^{67} +6.00000 q^{68} +(3.00000 - 5.19615i) q^{71} +(3.50000 - 6.06218i) q^{73} +8.00000 q^{75} -3.00000 q^{77} +(4.00000 - 6.92820i) q^{79} +(-6.00000 - 10.3923i) q^{80} +(5.50000 - 9.52628i) q^{81} +12.0000 q^{83} +4.00000 q^{84} +(4.50000 + 7.79423i) q^{85} -12.0000 q^{87} +(6.00000 + 10.3923i) q^{89} +(2.00000 + 3.46410i) q^{91} +(-4.00000 + 6.92820i) q^{93} +(4.00000 - 6.92820i) q^{97} +(-1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{7} - q^{9} + 6 q^{11} - 8 q^{12} - 4 q^{13} - 6 q^{15} - 4 q^{16} + 3 q^{17} - 12 q^{20} + 2 q^{21} - 4 q^{25} - 8 q^{27} - 2 q^{28} + 6 q^{29} + 8 q^{31} - 6 q^{33}+ \cdots - 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^7 - q^9 + 6 * q^11 - 8 * q^12 - 4 * q^13 - 6 * q^15 - 4 * q^16 + 3 * q^17 - 12 * q^20 + 2 * q^21 - 4 * q^25 - 8 * q^27 - 2 * q^28 + 6 * q^29 + 8 * q^31 - 6 * q^33 + 3 * q^35 + 2 * q^36 - 4 * q^37 + 16 * q^39 - 6 * q^41 + q^43 + 6 * q^44 + 6 * q^45 + 3 * q^47 - 8 * q^48 - 12 * q^49 + 6 * q^51 + 8 * q^52 + 12 * q^53 - 9 * q^55 - 6 * q^59 + 12 * q^60 + q^61 + q^63 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 12 * q^68 + 6 * q^71 + 7 * q^73 + 16 * q^75 - 6 * q^77 + 8 * q^79 - 12 * q^80 + 11 * q^81 + 24 * q^83 + 8 * q^84 + 9 * q^85 - 24 * q^87 + 12 * q^89 + 4 * q^91 - 8 * q^93 + 8 * q^97 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$	−4.00000			−1.15470
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$		0			0
$15$	−3.00000	−	5.19615i	−0.774597	−	1.34164i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$		0			0
$19$		0			0
$20$	−6.00000			−1.34164
$21$	1.00000	−	1.73205i	0.218218	−	0.377964i
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$	−4.00000			−0.769800
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$		0			0
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		0			0
$39$	8.00000			1.28103
$40$		0			0
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	3.00000	+	5.19615i	0.452267	+	0.783349i
$45$	3.00000			0.447214
$46$		0			0
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$	−4.00000	−	6.92820i	−0.577350	−	1.00000i
$49$	−6.00000			−0.857143
$50$		0			0
$51$	3.00000	+	5.19615i	0.420084	+	0.727607i
$52$	4.00000	−	6.92820i	0.554700	−	0.960769i
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	0.902557	+	0.430570i	$0.141688\pi$
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	−0.0783936	+	0.996922i	$0.524979\pi$
$54$		0			0
$55$	−4.50000	+	7.79423i	−0.606780	+	1.05097i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$	6.00000	−	10.3923i	0.774597	−	1.34164i
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	−8.00000			−1.00000
$65$	12.0000			1.48842
$66$		0			0
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	6.00000			0.727607
$69$		0			0
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$		0			0
$75$	8.00000			0.923760
$76$		0			0
$77$	−3.00000			−0.341882
$78$		0			0
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	−6.00000	−	10.3923i	−0.670820	−	1.16190i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$	4.00000			0.436436
$85$	4.50000	+	7.79423i	0.488094	+	0.845403i
$86$		0			0
$87$	−12.0000			−1.28654
$88$		0			0
$89$	6.00000	+	10.3923i	0.635999	+	1.10158i	0.986303	+	0.164946i	$0.0527450\pi$
$89$	6.00000	+	10.3923i	0.635999	+	1.10158i	−0.350304	+	0.936636i	$0.613922\pi$
$90$		0			0
$91$	2.00000	+	3.46410i	0.209657	+	0.363137i
$92$		0			0
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.00000	−	6.92820i	0.406138	−	0.703452i	−0.588315	−	0.808632i	$-0.700208\pi$
$97$	4.00000	−	6.92820i	0.406138	−	0.703452i	0.994453	+	0.105180i	$0.0335417\pi$
$98$		0			0
$99$	−1.50000	−	2.59808i	−0.150756	−	0.261116i
$100$	4.00000	−	6.92820i	0.400000	−	0.692820i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$		0			0
$105$	3.00000	+	5.19615i	0.292770	+	0.507093i
$106$		0			0
$107$	18.0000			1.74013			0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000			1.74013			0.870063	+	0.492941i	$0.164078\pi$
$108$	−4.00000	−	6.92820i	−0.384900	−	0.666667i
$109$	−8.00000	+	13.8564i	−0.766261	+	1.32720i	0.173316	+	0.984866i	$0.444552\pi$
$109$	−8.00000	+	13.8564i	−0.766261	+	1.32720i	−0.939577	+	0.342337i	$0.888782\pi$
$110$		0			0
$111$	2.00000	−	3.46410i	0.189832	−	0.328798i
$112$	2.00000	−	3.46410i	0.188982	−	0.327327i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$		0			0
$116$	−6.00000	+	10.3923i	−0.557086	+	0.964901i
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$		0			0
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	0.906977	−	0.421180i	$-0.138384\pi$
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	−0.818241	+	0.574875i	$0.805051\pi$
$128$		0			0
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$		0			0
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	−0.326546	−	0.945181i	$-0.605885\pi$
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	0.981824	−	0.189794i	$-0.0607819\pi$
$132$	−12.0000			−1.04447
$133$		0			0
$134$		0			0
$135$	6.00000	−	10.3923i	0.516398	−	0.894427i
$136$		0			0
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	0.998179	+	0.0603135i	$0.0192101\pi$
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	−0.446857	+	0.894606i	$0.647457\pi$
$140$	6.00000			0.507093
$141$	−6.00000			−0.505291
$142$		0			0
$143$	−6.00000	−	10.3923i	−0.501745	−	0.869048i
$144$	4.00000			0.333333
$145$	−18.0000			−1.49482
$146$		0			0
$147$	6.00000	−	10.3923i	0.494872	−	0.857143i
$148$	−2.00000	−	3.46410i	−0.164399	−	0.284747i
$149$	−10.5000	+	18.1865i	−0.860194	+	1.48990i	0.0115483	+	0.999933i	$0.496324\pi$
$149$	−10.5000	+	18.1865i	−0.860194	+	1.48990i	−0.871742	+	0.489966i	$0.837009\pi$
$150$		0			0
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		0			0
$153$	−3.00000			−0.242536
$154$		0			0
$155$	−6.00000	+	10.3923i	−0.481932	+	0.834730i
$156$	8.00000	+	13.8564i	0.640513	+	1.10940i
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$	−24.0000			−1.90332
$160$		0			0
$161$		0			0
$162$		0			0
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$	−12.0000			−0.937043
$165$	−9.00000	−	15.5885i	−0.700649	−	1.21356i
$166$		0			0
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	−0.969693	−	0.244328i	$-0.921432\pi$
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	0.273252	−	0.961943i	$-0.411901\pi$
$168$		0			0
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$		0			0
$171$		0			0
$172$	2.00000			0.152499
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$		0			0
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	−6.00000	+	10.3923i	−0.452267	+	0.783349i
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$		0			0
$179$	18.0000			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$180$	3.00000	+	5.19615i	0.223607	+	0.387298i
$181$	1.00000	+	1.73205i	0.0743294	+	0.128742i	0.900794	−	0.434246i	$-0.142985\pi$
$181$	1.00000	+	1.73205i	0.0743294	+	0.128742i	−0.826465	+	0.562988i	$0.809652\pi$
$182$		0			0
$183$	−2.00000			−0.147844
$184$		0			0
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$		0			0
$187$	4.50000	−	7.79423i	0.329073	−	0.569970i
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$	4.00000			0.290957
$190$		0			0
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	8.00000	−	13.8564i	0.577350	−	1.00000i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$		0			0
$195$	−12.0000	+	20.7846i	−0.859338	+	1.48842i
$196$	−6.00000	−	10.3923i	−0.428571	−	0.742307i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	−0.992434	+	0.122782i	$0.960818\pi$
$200$		0			0
$201$	8.00000			0.564276
$202$		0			0
$203$	−3.00000	−	5.19615i	−0.210559	−	0.364698i
$204$	−6.00000	+	10.3923i	−0.420084	+	0.727607i
$205$	−9.00000	−	15.5885i	−0.628587	−	1.08875i
$206$		0			0
$207$		0			0
$208$	16.0000			1.10940
$209$		0			0
$210$		0			0
$211$	7.00000	−	12.1244i	0.481900	−	0.834675i	−0.517884	−	0.855451i	$-0.673280\pi$
$211$	7.00000	−	12.1244i	0.481900	−	0.834675i	0.999784	+	0.0207756i	$0.00661356\pi$
$212$	−12.0000	+	20.7846i	−0.824163	+	1.42749i
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$		0			0
$215$	1.50000	+	2.59808i	0.102299	+	0.177187i
$216$		0			0
$217$	−4.00000			−0.271538
$218$		0			0
$219$	7.00000	+	12.1244i	0.473016	+	0.819288i
$220$	−18.0000			−1.21356
$221$	−12.0000			−0.807207
$222$		0			0
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	−0.983451	−	0.181173i	$-0.942010\pi$
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	0.648626	+	0.761107i	$0.275344\pi$
$224$		0			0
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$		0			0
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$		0			0
$229$	5.00000			0.330409			0.165205	−	0.986259i	$-0.447172\pi$
$229$	5.00000			0.330409			0.165205	+	0.986259i	$0.447172\pi$
$230$		0			0
$231$	3.00000	−	5.19615i	0.197386	−	0.341882i
$232$		0			0
$233$	10.5000	−	18.1865i	0.687878	−	1.19144i	−0.284645	−	0.958633i	$-0.591876\pi$
$233$	10.5000	−	18.1865i	0.687878	−	1.19144i	0.972523	−	0.232806i	$-0.0747909\pi$
$234$		0			0
$235$	−9.00000			−0.587095
$236$	−12.0000			−0.781133
$237$	8.00000	+	13.8564i	0.519656	+	0.900070i
$238$		0			0
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$	24.0000			1.54919
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$		0			0
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$	9.00000	−	15.5885i	0.574989	−	0.995910i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−12.0000	+	20.7846i	−0.760469	+	1.31717i
$250$		0			0
$251$	−10.5000	−	18.1865i	−0.662754	−	1.14792i	−0.979889	−	0.199543i	$-0.936054\pi$
$251$	−10.5000	−	18.1865i	−0.662754	−	1.14792i	0.317135	−	0.948380i	$-0.397279\pi$
$252$	−1.00000	+	1.73205i	−0.0629941	+	0.109109i
$253$		0			0
$254$		0			0
$255$	−18.0000			−1.12720
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$	2.00000			0.124274
$260$	12.0000	+	20.7846i	0.744208	+	1.28901i
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	−0.970758	−	0.240059i	$-0.922833\pi$
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	0.693276	+	0.720672i	$0.256167\pi$
$264$		0			0
$265$	−36.0000			−2.21146
$266$		0			0
$267$	−24.0000			−1.46878
$268$	4.00000	−	6.92820i	0.244339	−	0.423207i
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	−0.224523	−	0.974469i	$-0.572083\pi$
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	6.00000	+	10.3923i	0.363803	+	0.630126i
$273$	−8.00000			−0.484182
$274$		0			0
$275$	−6.00000	−	10.3923i	−0.361814	−	0.626680i
$276$		0			0
$277$	−19.0000			−1.14160			−0.570800	−	0.821089i	$-0.693367\pi$
$277$	−19.0000			−1.14160			−0.570800	+	0.821089i	$0.693367\pi$
$278$		0			0
$279$	−2.00000	−	3.46410i	−0.119737	−	0.207390i
$280$		0			0
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	0.941526	−	0.336939i	$-0.109392\pi$
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	−0.762561	+	0.646916i	$0.776058\pi$
$282$		0			0
$283$	6.50000	−	11.2583i	0.386385	−	0.669238i	−0.605575	−	0.795788i	$-0.707057\pi$
$283$	6.50000	−	11.2583i	0.386385	−	0.669238i	0.991960	+	0.126550i	$0.0403903\pi$
$284$	12.0000			0.712069
$285$		0			0
$286$		0			0
$287$	3.00000	−	5.19615i	0.177084	−	0.306719i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	8.00000	+	13.8564i	0.468968	+	0.812277i
$292$	14.0000			0.819288
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$		0			0
$295$	−9.00000	−	15.5885i	−0.524000	−	0.907595i
$296$		0			0
$297$	−12.0000			−0.696311
$298$		0			0
$299$		0			0
$300$	8.00000	+	13.8564i	0.461880	+	0.800000i
$301$	−0.500000	+	0.866025i	−0.0288195	+	0.0499169i
$302$		0			0
$303$	12.0000			0.689382
$304$		0			0
$305$	−3.00000			−0.171780
$306$		0			0
$307$	10.0000	−	17.3205i	0.570730	−	0.988534i	−0.425761	−	0.904836i	$-0.639994\pi$
$307$	10.0000	−	17.3205i	0.570730	−	0.988534i	0.996491	−	0.0836980i	$-0.0266731\pi$
$308$	−3.00000	−	5.19615i	−0.170941	−	0.296078i
$309$	14.0000	−	24.2487i	0.796432	−	1.37946i
$310$		0			0
$311$	−3.00000			−0.170114			−0.0850572	−	0.996376i	$-0.527107\pi$
$311$	−3.00000			−0.170114			−0.0850572	+	0.996376i	$0.527107\pi$
$312$		0			0
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$		0			0
$315$	−3.00000			−0.169031
$316$	16.0000			0.900070
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$	12.0000	−	20.7846i	0.670820	−	1.16190i
$321$	−18.0000	+	31.1769i	−1.00466	+	1.74013i
$322$		0			0
$323$		0			0
$324$	22.0000			1.22222
$325$	−8.00000	+	13.8564i	−0.443760	+	0.768615i
$326$		0			0
$327$	−16.0000	−	27.7128i	−0.884802	−	1.53252i
$328$		0			0
$329$	−1.50000	−	2.59808i	−0.0826977	−	0.143237i
$330$		0			0
$331$	28.0000			1.53902			0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000			1.53902			0.769510	+	0.638635i	$0.220501\pi$
$332$	12.0000	+	20.7846i	0.658586	+	1.14070i
$333$	1.00000	+	1.73205i	0.0547997	+	0.0949158i
$334$		0			0
$335$	12.0000			0.655630
$336$	4.00000	+	6.92820i	0.218218	+	0.377964i
$337$	16.0000	−	27.7128i	0.871576	−	1.50961i	0.0112091	−	0.999937i	$-0.496432\pi$
$337$	16.0000	−	27.7128i	0.871576	−	1.50961i	0.860366	−	0.509676i	$-0.170235\pi$
$338$		0			0
$339$	6.00000	−	10.3923i	0.325875	−	0.564433i
$340$	−9.00000	+	15.5885i	−0.488094	+	0.845403i
$341$	12.0000			0.649836
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.5000	+	18.1865i	−0.563670	+	0.976304i	0.433503	+	0.901152i	$0.357278\pi$
$347$	−10.5000	+	18.1865i	−0.563670	+	0.976304i	−0.997172	+	0.0751519i	$0.976056\pi$
$348$	−12.0000	−	20.7846i	−0.643268	−	1.11417i
$349$	17.0000			0.909989			0.454995	−	0.890494i	$-0.349641\pi$
$349$	17.0000			0.909989			0.454995	+	0.890494i	$0.349641\pi$
$350$		0			0
$351$	8.00000	+	13.8564i	0.427008	+	0.739600i
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$	9.00000	+	15.5885i	0.477670	+	0.827349i
$356$	−12.0000	+	20.7846i	−0.635999	+	1.10158i
$357$	−3.00000	−	5.19615i	−0.158777	−	0.275010i
$358$		0			0
$359$	−7.50000	+	12.9904i	−0.395835	+	0.685606i	−0.993207	−	0.116358i	$-0.962878\pi$
$359$	−7.50000	+	12.9904i	−0.395835	+	0.685606i	0.597372	+	0.801964i	$0.296211\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	2.00000	−	3.46410i	0.104973	−	0.181818i
$364$	−4.00000	+	6.92820i	−0.209657	+	0.363137i
$365$	10.5000	+	18.1865i	0.549595	+	0.951927i
$366$		0			0
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$		0			0
$369$	6.00000			0.312348
$370$		0			0
$371$	−6.00000	−	10.3923i	−0.311504	−	0.539542i
$372$	−16.0000			−0.829561
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$		0			0
$375$	3.00000	−	5.19615i	0.154919	−	0.268328i
$376$		0			0
$377$	12.0000	−	20.7846i	0.618031	−	1.07046i
$378$		0			0
$379$	34.0000			1.74646			0.873231	−	0.487306i	$-0.162020\pi$
$379$	34.0000			1.74646			0.873231	+	0.487306i	$0.162020\pi$
$380$		0			0
$381$	−4.00000			−0.204926
$382$		0			0
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	−0.671027	−	0.741433i	$-0.734147\pi$
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	0.977613	+	0.210411i	$0.0674801\pi$
$384$		0			0
$385$	4.50000	−	7.79423i	0.229341	−	0.397231i
$386$		0			0
$387$	−1.00000			−0.0508329
$388$	16.0000			0.812277
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	0.610835	−	0.791758i	$-0.290834\pi$
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	−0.991100	+	0.133120i	$0.957501\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	15.0000	+	25.9808i	0.756650	+	1.31056i
$394$		0			0
$395$	12.0000	+	20.7846i	0.603786	+	1.04579i
$396$	3.00000	−	5.19615i	0.150756	−	0.261116i
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	0.940389	+	0.340099i	$0.110461\pi$
$398$		0			0
$399$		0			0
$400$	16.0000			0.800000
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$		0			0
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$	6.00000	−	10.3923i	0.298511	−	0.517036i
$405$	16.5000	+	28.5788i	0.819892	+	1.42009i
$406$		0			0
$407$	−6.00000			−0.297409
$408$		0			0
$409$	−2.00000	−	3.46410i	−0.0988936	−	0.171289i	0.812333	−	0.583193i	$-0.198197\pi$
$409$	−2.00000	−	3.46410i	−0.0988936	−	0.171289i	−0.911227	+	0.411905i	$0.864864\pi$
$410$		0			0
$411$	−6.00000			−0.295958
$412$	−14.0000	−	24.2487i	−0.689730	−	1.19465i
$413$	3.00000	−	5.19615i	0.147620	−	0.255686i
$414$		0			0
$415$	−18.0000	+	31.1769i	−0.883585	+	1.53041i
$416$		0			0
$417$	−26.0000			−1.27323
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$	−6.00000	+	10.3923i	−0.292770	+	0.507093i
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	−0.751935	−	0.659237i	$-0.770879\pi$
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	0.946883	+	0.321577i	$0.104213\pi$
$422$		0			0
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$		0			0
$425$	−12.0000			−0.582086
$426$		0			0
$427$	−0.500000	−	0.866025i	−0.0241967	−	0.0419099i
$428$	18.0000	+	31.1769i	0.870063	+	1.50699i
$429$	24.0000			1.15873
$430$		0			0
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	−0.995706	−	0.0925683i	$-0.970492\pi$
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	0.417687	−	0.908591i	$-0.362841\pi$
$432$	8.00000	−	13.8564i	0.384900	−	0.666667i
$433$	1.00000	+	1.73205i	0.0480569	+	0.0832370i	0.889053	−	0.457804i	$-0.151364\pi$
$433$	1.00000	+	1.73205i	0.0480569	+	0.0832370i	−0.840996	+	0.541041i	$0.818030\pi$
$434$		0			0
$435$	18.0000	−	31.1769i	0.863034	−	1.49482i
$436$	−32.0000			−1.53252
$437$		0			0
$438$		0			0
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$		0			0
$443$	1.50000	+	2.59808i	0.0712672	+	0.123438i	0.899457	−	0.437009i	$-0.143962\pi$
$443$	1.50000	+	2.59808i	0.0712672	+	0.123438i	−0.828190	+	0.560448i	$0.810629\pi$
$444$	8.00000			0.379663
$445$	−36.0000			−1.70656
$446$		0			0
$447$	−21.0000	−	36.3731i	−0.993266	−	1.72039i
$448$	8.00000			0.377964
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	−9.00000	+	15.5885i	−0.423793	+	0.734032i
$452$	−6.00000	−	10.3923i	−0.282216	−	0.488813i
$453$	−10.0000	+	17.3205i	−0.469841	+	0.813788i
$454$		0			0
$455$	−12.0000			−0.562569
$456$		0			0
$457$	−37.0000			−1.73079			−0.865393	−	0.501093i	$-0.832931\pi$
$457$	−37.0000			−1.73079			−0.865393	+	0.501093i	$0.832931\pi$
$458$		0			0
$459$	−6.00000	+	10.3923i	−0.280056	+	0.485071i
$460$		0			0
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	−0.951584	−	0.307388i	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$		0			0
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$	−24.0000			−1.11417
$465$	−12.0000	−	20.7846i	−0.556487	−	0.963863i
$466$		0			0
$467$	−27.0000			−1.24941			−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000			−1.24941			−0.624705	+	0.780860i	$0.714781\pi$
$468$	−8.00000			−0.369800
$469$	2.00000	+	3.46410i	0.0923514	+	0.159957i
$470$		0			0
$471$	−14.0000	−	24.2487i	−0.645086	−	1.11732i
$472$		0			0
$473$	1.50000	−	2.59808i	0.0689701	−	0.119460i
$474$		0			0
$475$		0			0
$476$	−6.00000			−0.275010
$477$	6.00000	−	10.3923i	0.274721	−	0.475831i
$478$		0			0
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	4.00000	+	6.92820i	0.182384	+	0.315899i
$482$		0			0
$483$		0			0
$484$	−2.00000	−	3.46410i	−0.0909091	−	0.157459i
$485$	12.0000	+	20.7846i	0.544892	+	0.943781i
$486$		0			0
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$		0			0
$489$	−20.0000	+	34.6410i	−0.904431	+	1.56652i
$490$		0			0
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	−0.969061	−	0.246822i	$-0.920614\pi$
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	0.698285	+	0.715820i	$0.253947\pi$
$492$	12.0000	−	20.7846i	0.541002	−	0.937043i
$493$	18.0000			0.810679
$494$		0			0
$495$	9.00000			0.404520
$496$	−8.00000	+	13.8564i	−0.359211	+	0.622171i
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$		0			0
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$	−3.00000	−	5.19615i	−0.134164	−	0.232379i
$501$	36.0000			1.60836
$502$		0			0
$503$	−6.00000	−	10.3923i	−0.267527	−	0.463370i	0.700696	−	0.713460i	$-0.252873\pi$
$503$	−6.00000	−	10.3923i	−0.267527	−	0.463370i	−0.968223	+	0.250090i	$0.919540\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$	−3.00000	−	5.19615i	−0.133235	−	0.230769i
$508$	−2.00000	+	3.46410i	−0.0887357	+	0.153695i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	−3.50000	+	6.06218i	−0.154831	+	0.268175i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	21.0000	−	36.3731i	0.925371	−	1.60279i
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$	4.50000	+	7.79423i	0.197910	+	0.342790i
$518$		0			0
$519$	−18.0000	−	31.1769i	−0.790112	−	1.36851i
$520$		0			0
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$	19.0000	+	32.9090i	0.830812	+	1.43901i	0.897395	+	0.441228i	$0.145457\pi$
$523$	19.0000	+	32.9090i	0.830812	+	1.43901i	−0.0665832	+	0.997781i	$0.521210\pi$
$524$	30.0000			1.31056
$525$	−8.00000			−0.349149
$526$		0			0
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$	−12.0000	−	20.7846i	−0.522233	−	0.904534i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	6.00000			0.260378
$532$		0			0
$533$	24.0000			1.03956
$534$		0			0
$535$	−27.0000	+	46.7654i	−1.16731	+	2.02184i
$536$		0			0
$537$	−18.0000	+	31.1769i	−0.776757	+	1.34538i
$538$		0			0
$539$	−18.0000			−0.775315
$540$	24.0000			1.03280
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$		0			0
$543$	−4.00000			−0.171656
$544$		0			0
$545$	−24.0000	−	41.5692i	−1.02805	−	1.78063i
$546$		0			0
$547$	−14.0000	−	24.2487i	−0.598597	−	1.03680i	−0.993028	−	0.117875i	$-0.962392\pi$
$547$	−14.0000	−	24.2487i	−0.598597	−	1.03680i	0.394432	−	0.918925i	$-0.370941\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$	0.500000	−	0.866025i	0.0213395	−	0.0369611i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$		0			0
$555$	6.00000	+	10.3923i	0.254686	+	0.441129i
$556$	−13.0000	+	22.5167i	−0.551323	+	0.954919i
$557$	−10.5000	−	18.1865i	−0.444899	−	0.770588i	0.553146	−	0.833084i	$-0.313427\pi$
$557$	−10.5000	−	18.1865i	−0.444899	−	0.770588i	−0.998045	+	0.0624962i	$0.980094\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	6.00000	+	10.3923i	0.253546	+	0.439155i
$561$	9.00000	+	15.5885i	0.379980	+	0.658145i
$562$		0			0
$563$	−6.00000			−0.252870			−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000			−0.252870			−0.126435	+	0.991975i	$0.540353\pi$
$564$	−6.00000	−	10.3923i	−0.252646	−	0.437595i
$565$	9.00000	−	15.5885i	0.378633	−	0.655811i
$566$		0			0
$567$	−5.50000	+	9.52628i	−0.230978	+	0.400066i
$568$		0			0
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	12.0000	−	20.7846i	0.501745	−	0.869048i
$573$	−3.00000	+	5.19615i	−0.125327	+	0.217072i
$574$		0			0
$575$		0			0
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$		0			0
$579$	−4.00000	−	6.92820i	−0.166234	−	0.287926i
$580$	−18.0000	−	31.1769i	−0.747409	−	1.29455i
$581$	−12.0000			−0.497844
$582$		0			0
$583$	18.0000	+	31.1769i	0.745484	+	1.29122i
$584$		0			0
$585$	−6.00000	−	10.3923i	−0.248069	−	0.429669i
$586$		0			0
$587$	−22.5000	+	38.9711i	−0.928674	+	1.60851i	−0.143132	+	0.989704i	$0.545717\pi$
$587$	−22.5000	+	38.9711i	−0.928674	+	1.60851i	−0.785543	+	0.618808i	$0.787616\pi$
$588$	24.0000			0.989743
$589$		0			0
$590$		0			0
$591$	−18.0000	+	31.1769i	−0.740421	+	1.28245i
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	21.0000	+	36.3731i	0.862367	+	1.49366i	0.869638	+	0.493689i	$0.164352\pi$
$593$	21.0000	+	36.3731i	0.862367	+	1.49366i	−0.00727173	+	0.999974i	$0.502315\pi$
$594$		0			0
$595$	−4.50000	−	7.79423i	−0.184482	−	0.319532i
$596$	−42.0000			−1.72039
$597$	22.0000			0.900400
$598$		0			0
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	−0.954521	−	0.298143i	$-0.903633\pi$
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	0.219061	−	0.975711i	$-0.429701\pi$
$600$		0			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	−2.00000	+	3.46410i	−0.0814463	+	0.141069i
$604$	10.0000	+	17.3205i	0.406894	+	0.704761i
$605$	3.00000	−	5.19615i	0.121967	−	0.211254i
$606$		0			0
$607$	−32.0000			−1.29884			−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000			−1.29884			−0.649420	+	0.760430i	$0.724988\pi$
$608$		0			0
$609$	12.0000			0.486265
$610$		0			0
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	−14.5000	+	25.1147i	−0.585649	+	1.01437i	0.409145	+	0.912470i	$0.365827\pi$
$613$	−14.5000	+	25.1147i	−0.585649	+	1.01437i	−0.994794	+	0.101905i	$0.967506\pi$
$614$		0			0
$615$	36.0000			1.45166
$616$		0			0
$617$	−4.50000	−	7.79423i	−0.181163	−	0.313784i	0.761114	−	0.648618i	$-0.224653\pi$
$617$	−4.50000	−	7.79423i	−0.181163	−	0.313784i	−0.942277	+	0.334835i	$0.891320\pi$
$618$		0			0
$619$	44.0000			1.76851			0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000			1.76851			0.884255	+	0.467005i	$0.154667\pi$
$620$	−24.0000			−0.963863
$621$		0			0
$622$		0			0
$623$	−6.00000	−	10.3923i	−0.240385	−	0.416359i
$624$	−16.0000	+	27.7128i	−0.640513	+	1.10940i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$	−28.0000			−1.11732
$629$	−3.00000	+	5.19615i	−0.119618	+	0.207184i
$630$		0			0
$631$	−5.50000	−	9.52628i	−0.218952	−	0.379235i	0.735536	−	0.677485i	$-0.236930\pi$
$631$	−5.50000	−	9.52628i	−0.218952	−	0.379235i	−0.954488	+	0.298250i	$0.903597\pi$
$632$		0			0
$633$	14.0000	+	24.2487i	0.556450	+	0.963800i
$634$		0			0
$635$	−6.00000			−0.238103
$636$	−24.0000	−	41.5692i	−0.951662	−	1.64833i
$637$	12.0000	+	20.7846i	0.475457	+	0.823516i
$638$		0			0
$639$	−6.00000			−0.237356
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$	6.50000	−	11.2583i	0.256335	−	0.443985i	−0.708922	−	0.705287i	$-0.750818\pi$
$643$	6.50000	−	11.2583i	0.256335	−	0.443985i	0.965257	+	0.261301i	$0.0841516\pi$
$644$		0			0
$645$	−6.00000			−0.236250
$646$		0			0
$647$	27.0000			1.06148			0.530740	−	0.847535i	$-0.321914\pi$
$647$	27.0000			1.06148			0.530740	+	0.847535i	$0.321914\pi$
$648$		0			0
$649$	−9.00000	+	15.5885i	−0.353281	+	0.611900i
$650$		0			0
$651$	4.00000	−	6.92820i	0.156772	−	0.271538i
$652$	20.0000	+	34.6410i	0.783260	+	1.35665i
$653$	−39.0000			−1.52619			−0.763094	−	0.646288i	$-0.776321\pi$
$653$	−39.0000			−1.52619			−0.763094	+	0.646288i	$0.776321\pi$
$654$		0			0
$655$	22.5000	+	38.9711i	0.879148	+	1.52273i
$656$	−12.0000	−	20.7846i	−0.468521	−	0.811503i
$657$	−7.00000			−0.273096
$658$		0			0
$659$	−15.0000	−	25.9808i	−0.584317	−	1.01207i	−0.994960	−	0.100271i	$-0.968029\pi$
$659$	−15.0000	−	25.9808i	−0.584317	−	1.01207i	0.410643	−	0.911796i	$-0.365304\pi$
$660$	18.0000	−	31.1769i	0.700649	−	1.21356i
$661$	16.0000	+	27.7128i	0.622328	+	1.07790i	0.989051	+	0.147573i	$0.0471463\pi$
$661$	16.0000	+	27.7128i	0.622328	+	1.07790i	−0.366723	+	0.930330i	$0.619520\pi$
$662$		0			0
$663$	12.0000	−	20.7846i	0.466041	−	0.807207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	18.0000	−	31.1769i	0.696441	−	1.20627i
$669$	−10.0000	−	17.3205i	−0.386622	−	0.669650i
$670$		0			0
$671$	1.50000	+	2.59808i	0.0579069	+	0.100298i
$672$		0			0
$673$	10.0000			0.385472			0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000			0.385472			0.192736	+	0.981251i	$0.438264\pi$
$674$		0			0
$675$	8.00000	+	13.8564i	0.307920	+	0.533333i
$676$	−6.00000			−0.230769
$677$	42.0000			1.61419			0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000			1.61419			0.807096	+	0.590421i	$0.201038\pi$
$678$		0			0
$679$	−4.00000	+	6.92820i	−0.153506	+	0.265880i
$680$		0			0
$681$	12.0000	−	20.7846i	0.459841	−	0.796468i
$682$		0			0
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$	−5.00000	+	8.66025i	−0.190762	+	0.330409i
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	24.0000	−	41.5692i	0.914327	−	1.58366i
$690$		0			0
$691$	17.0000			0.646710			0.323355	−	0.946278i	$-0.395189\pi$
$691$	17.0000			0.646710			0.323355	+	0.946278i	$0.395189\pi$
$692$	−36.0000			−1.36851
$693$	1.50000	+	2.59808i	0.0569803	+	0.0986928i
$694$		0			0
$695$	−39.0000			−1.47935
$696$		0			0
$697$	9.00000	+	15.5885i	0.340899	+	0.590455i
$698$		0			0
$699$	21.0000	+	36.3731i	0.794293	+	1.37576i
$700$	−4.00000	+	6.92820i	−0.151186	+	0.261861i
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	−0.917102	−	0.398652i	$-0.869478\pi$
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	0.803794	+	0.594908i	$0.202811\pi$
$702$		0			0
$703$		0			0
$704$	−24.0000			−0.904534
$705$	9.00000	−	15.5885i	0.338960	−	0.587095i
$706$		0			0
$707$	3.00000	+	5.19615i	0.112827	+	0.195421i
$708$	12.0000	−	20.7846i	0.450988	−	0.781133i
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	0.511683	−	0.859174i	$-0.329022\pi$
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	−0.999908	+	0.0135434i	$0.995689\pi$
$710$		0			0
$711$	−8.00000			−0.300023
$712$		0			0
$713$		0			0
$714$		0			0
$715$	36.0000			1.34632
$716$	18.0000	+	31.1769i	0.672692	+	1.16514i
$717$	−15.0000	+	25.9808i	−0.560185	+	0.970269i
$718$		0			0
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	−0.971311	−	0.237814i	$-0.923569\pi$
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	0.691608	+	0.722273i	$0.256903\pi$
$720$	−6.00000	+	10.3923i	−0.223607	+	0.387298i
$721$	14.0000			0.521387
$722$		0			0
$723$	20.0000			0.743808
$724$	−2.00000	+	3.46410i	−0.0743294	+	0.128742i
$725$	12.0000	−	20.7846i	0.445669	−	0.771921i
$726$		0			0
$727$	9.50000	−	16.4545i	0.352335	−	0.610263i	−0.634323	−	0.773068i	$-0.718721\pi$
$727$	9.50000	−	16.4545i	0.352335	−	0.610263i	0.986658	+	0.162805i	$0.0520543\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$	−2.00000	−	3.46410i	−0.0739221	−	0.128037i
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$		0			0
$735$	18.0000	+	31.1769i	0.663940	+	1.14998i
$736$		0			0
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$		0			0
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	−0.949276	−	0.314445i	$-0.898182\pi$
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	0.746955	+	0.664875i	$0.231515\pi$
$740$	12.0000			0.441129
$741$		0			0
$742$		0			0
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	−0.997707	−	0.0676840i	$-0.978439\pi$
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	0.557470	+	0.830197i	$0.311772\pi$
$744$		0			0
$745$	−31.5000	−	54.5596i	−1.15407	−	1.99891i
$746$		0			0
$747$	−6.00000	−	10.3923i	−0.219529	−	0.380235i
$748$	18.0000			0.658145
$749$	−18.0000			−0.657706
$750$		0			0
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	−12.0000			−0.437595
$753$	42.0000			1.53057
$754$		0			0
$755$	−15.0000	+	25.9808i	−0.545906	+	0.945537i
$756$	4.00000	+	6.92820i	0.145479	+	0.251976i
$757$	12.5000	−	21.6506i	0.454320	−	0.786906i	−0.544329	−	0.838872i	$-0.683216\pi$
$757$	12.5000	−	21.6506i	0.454320	−	0.786906i	0.998649	+	0.0519664i	$0.0165489\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	33.0000			1.19625			0.598125	−	0.801403i	$-0.295913\pi$
$761$	33.0000			1.19625			0.598125	+	0.801403i	$0.295913\pi$
$762$		0			0
$763$	8.00000	−	13.8564i	0.289619	−	0.501636i
$764$	3.00000	+	5.19615i	0.108536	+	0.187990i
$765$	4.50000	−	7.79423i	0.162698	−	0.281801i
$766$		0			0
$767$	24.0000			0.866590
$768$	32.0000			1.15470
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	0.580696	−	0.814120i	$-0.302780\pi$
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	−0.995397	+	0.0958377i	$0.969447\pi$
$770$		0			0
$771$		0			0
$772$	−8.00000			−0.287926
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	0.807018	−	0.590527i	$-0.201080\pi$
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	−0.914920	+	0.403634i	$0.867747\pi$
$774$		0			0
$775$	−8.00000	−	13.8564i	−0.287368	−	0.497737i
$776$		0			0
$777$	−2.00000	+	3.46410i	−0.0717496	+	0.124274i
$778$		0			0
$779$		0			0
$780$	−48.0000			−1.71868
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$	−12.0000	−	20.7846i	−0.428845	−	0.742781i
$784$	12.0000	−	20.7846i	0.428571	−	0.742307i
$785$	−21.0000	−	36.3731i	−0.749522	−	1.29821i
$786$		0			0
$787$	4.00000			0.142585			0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000			0.142585			0.0712923	+	0.997455i	$0.477288\pi$
$788$	18.0000	+	31.1769i	0.641223	+	1.11063i
$789$	−9.00000	−	15.5885i	−0.320408	−	0.554964i
$790$		0			0
$791$	6.00000			0.213335
$792$		0			0
$793$	2.00000	−	3.46410i	0.0710221	−	0.123014i
$794$		0			0
$795$	36.0000	−	62.3538i	1.27679	−	2.21146i
$796$	11.0000	−	19.0526i	0.389885	−	0.675300i
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$		0			0
$799$	9.00000			0.318397
$800$		0			0
$801$	6.00000	−	10.3923i	0.212000	−	0.367194i
$802$		0			0
$803$	10.5000	−	18.1865i	0.370537	−	0.641789i
$804$	8.00000	+	13.8564i	0.282138	+	0.488678i
$805$		0			0
$806$		0			0
$807$	24.0000	+	41.5692i	0.844840	+	1.46331i
$808$		0			0
$809$	−9.00000			−0.316423			−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000			−0.316423			−0.158212	+	0.987405i	$0.550573\pi$
$810$		0			0
$811$	−8.00000	−	13.8564i	−0.280918	−	0.486564i	0.690693	−	0.723148i	$-0.257306\pi$
$811$	−8.00000	−	13.8564i	−0.280918	−	0.486564i	−0.971611	+	0.236584i	$0.923972\pi$
$812$	6.00000	−	10.3923i	0.210559	−	0.364698i
$813$	16.0000	+	27.7128i	0.561144	+	0.971931i
$814$		0			0
$815$	−30.0000	+	51.9615i	−1.05085	+	1.82013i
$816$	−24.0000			−0.840168
$817$		0			0
$818$		0			0
$819$	2.00000	−	3.46410i	0.0698857	−	0.121046i
$820$	18.0000	−	31.1769i	0.628587	−	1.08875i
$821$	−16.5000	−	28.5788i	−0.575854	−	0.997408i	−0.995948	−	0.0899279i	$-0.971336\pi$
$821$	−16.5000	−	28.5788i	−0.575854	−	0.997408i	0.420094	−	0.907480i	$-0.361997\pi$
$822$		0			0
$823$	24.5000	+	42.4352i	0.854016	+	1.47920i	0.877555	+	0.479477i	$0.159174\pi$
$823$	24.5000	+	42.4352i	0.854016	+	1.47920i	−0.0235383	+	0.999723i	$0.507493\pi$
$824$		0			0
$825$	24.0000			0.835573
$826$		0			0
$827$	6.00000	+	10.3923i	0.208640	+	0.361376i	0.951286	−	0.308308i	$-0.0997628\pi$
$827$	6.00000	+	10.3923i	0.208640	+	0.361376i	−0.742646	+	0.669684i	$0.766429\pi$
$828$		0			0
$829$	16.0000			0.555703			0.277851	−	0.960624i	$-0.410378\pi$
$829$	16.0000			0.555703			0.277851	+	0.960624i	$0.410378\pi$
$830$		0			0
$831$	19.0000	−	32.9090i	0.659103	−	1.14160i
$832$	16.0000	+	27.7128i	0.554700	+	0.960769i
$833$	−9.00000	+	15.5885i	−0.311832	+	0.540108i
$834$		0			0
$835$	54.0000			1.86875
$836$		0			0
$837$	−16.0000			−0.553041
$838$		0			0
$839$	9.00000	−	15.5885i	0.310715	−	0.538173i	−0.667803	−	0.744338i	$-0.732765\pi$
$839$	9.00000	−	15.5885i	0.310715	−	0.538173i	0.978517	+	0.206165i	$0.0660984\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$	−12.0000			−0.413302
$844$	28.0000			0.963800
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$	2.00000			0.0687208
$848$	−48.0000			−1.64833
$849$	13.0000	+	22.5167i	0.446159	+	0.772770i
$850$		0			0
$851$		0			0
$852$	−12.0000	+	20.7846i	−0.411113	+	0.712069i
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	−0.998060	−	0.0622597i	$-0.980169\pi$
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	0.552948	+	0.833215i	$0.313503\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	24.5000	+	42.4352i	0.835929	+	1.44787i	0.893272	+	0.449517i	$0.148404\pi$
$859$	24.5000	+	42.4352i	0.835929	+	1.44787i	−0.0573424	+	0.998355i	$0.518263\pi$
$860$	−3.00000	+	5.19615i	−0.102299	+	0.177187i
$861$	6.00000	+	10.3923i	0.204479	+	0.354169i
$862$		0			0
$863$	−18.0000			−0.612727			−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000			−0.612727			−0.306364	+	0.951915i	$0.599112\pi$
$864$		0			0
$865$	−27.0000	−	46.7654i	−0.918028	−	1.59007i
$866$		0			0
$867$	−16.0000			−0.543388
$868$	−4.00000	−	6.92820i	−0.135769	−	0.235159i
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$		0			0
$871$	−8.00000	+	13.8564i	−0.271070	+	0.469506i
$872$		0			0
$873$	−8.00000			−0.270759
$874$		0			0
$875$	3.00000			0.101419
$876$	−14.0000	+	24.2487i	−0.473016	+	0.819288i
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	−0.989788	−	0.142548i	$-0.954470\pi$
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	0.618344	+	0.785907i	$0.287804\pi$
$878$		0			0
$879$	−12.0000	+	20.7846i	−0.404750	+	0.701047i
$880$	−18.0000	−	31.1769i	−0.606780	−	1.05097i
$881$	−27.0000			−0.909653			−0.454827	−	0.890580i	$-0.650299\pi$
$881$	−27.0000			−0.909653			−0.454827	+	0.890580i	$0.650299\pi$
$882$		0			0
$883$	−23.5000	−	40.7032i	−0.790838	−	1.36977i	−0.925449	−	0.378873i	$-0.876312\pi$
$883$	−23.5000	−	40.7032i	−0.790838	−	1.36977i	0.134611	−	0.990899i	$-0.457022\pi$
$884$	−12.0000	−	20.7846i	−0.403604	−	0.699062i
$885$	36.0000			1.21013
$886$		0			0
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	0.976632	−	0.214919i	$-0.0689488\pi$
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	−0.674441	+	0.738328i	$0.735615\pi$
$888$		0			0
$889$	−1.00000	−	1.73205i	−0.0335389	−	0.0580911i
$890$		0			0
$891$	16.5000	−	28.5788i	0.552771	−	0.957427i
$892$	−20.0000			−0.669650
$893$		0			0
$894$		0			0
$895$	−27.0000	+	46.7654i	−0.902510	+	1.56319i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	12.0000	+	20.7846i	0.400222	+	0.693206i
$900$	−8.00000			−0.266667
$901$	36.0000			1.19933
$902$		0			0
$903$	−1.00000	−	1.73205i	−0.0332779	−	0.0576390i
$904$		0			0
$905$	−6.00000			−0.199447
$906$		0			0
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	−0.791944	−	0.610594i	$-0.790931\pi$
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	0.924762	+	0.380547i	$0.124264\pi$
$908$	−12.0000	−	20.7846i	−0.398234	−	0.689761i
$909$	−3.00000	+	5.19615i	−0.0995037	+	0.172345i
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		0			0
$913$	36.0000			1.19143
$914$		0			0
$915$	3.00000	−	5.19615i	0.0991769	−	0.171780i
$916$	5.00000	+	8.66025i	0.165205	+	0.286143i
$917$	−7.50000	+	12.9904i	−0.247672	+	0.428980i
$918$		0			0
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$		0			0
$921$	20.0000	+	34.6410i	0.659022	+	1.14146i
$922$		0			0
$923$	−24.0000			−0.789970
$924$	12.0000			0.394771
$925$	4.00000	+	6.92820i	0.131519	+	0.227798i
$926$		0			0
$927$	7.00000	+	12.1244i	0.229910	+	0.398216i
$928$		0			0
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$		0			0
$931$		0			0
$932$	42.0000			1.37576
$933$	3.00000	−	5.19615i	0.0982156	−	0.170114i
$934$		0			0
$935$	13.5000	+	23.3827i	0.441497	+	0.764696i
$936$		0			0
$937$	3.50000	+	6.06218i	0.114340	+	0.198043i	0.917516	−	0.397699i	$-0.130191\pi$
$937$	3.50000	+	6.06218i	0.114340	+	0.198043i	−0.803176	+	0.595742i	$0.796858\pi$
$938$		0			0
$939$	−20.0000			−0.652675
$940$	−9.00000	−	15.5885i	−0.293548	−	0.508439i
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$		0			0
$943$		0			0
$944$	−12.0000	−	20.7846i	−0.390567	−	0.676481i
$945$	−6.00000	+	10.3923i	−0.195180	+	0.338062i
$946$		0			0
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	−0.409964	−	0.912102i	$-0.634459\pi$
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	0.994885	−	0.101012i	$-0.0322080\pi$
$948$	−16.0000	+	27.7128i	−0.519656	+	0.900070i
$949$	−28.0000			−0.908918
$950$		0			0
$951$	−12.0000			−0.389127
$952$		0			0
$953$	−24.0000	+	41.5692i	−0.777436	+	1.34656i	0.155979	+	0.987760i	$0.450147\pi$
$953$	−24.0000	+	41.5692i	−0.777436	+	1.34656i	−0.933415	+	0.358799i	$0.883186\pi$
$954$		0			0
$955$	−4.50000	+	7.79423i	−0.145617	+	0.252215i
$956$	15.0000	+	25.9808i	0.485135	+	0.840278i
$957$	−36.0000			−1.16371
$958$		0			0
$959$	−1.50000	−	2.59808i	−0.0484375	−	0.0838963i
$960$	24.0000	+	41.5692i	0.774597	+	1.34164i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−9.00000	−	15.5885i	−0.290021	−	0.502331i
$964$	10.0000	−	17.3205i	0.322078	−	0.557856i
$965$	−6.00000	−	10.3923i	−0.193147	−	0.334540i
$966$		0			0
$967$	20.0000	−	34.6410i	0.643157	−	1.11398i	−0.341567	−	0.939857i	$-0.610958\pi$
$967$	20.0000	−	34.6410i	0.643157	−	1.11398i	0.984724	−	0.174123i	$-0.0557089\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.247193	−	0.968966i	$-0.420492\pi$
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.715553	−	0.698558i	$-0.246175\pi$
$972$	−10.0000	+	17.3205i	−0.320750	+	0.555556i
$973$	−6.50000	−	11.2583i	−0.208380	−	0.360925i
$974$		0			0
$975$	−16.0000	−	27.7128i	−0.512410	−	0.887520i
$976$	−4.00000			−0.128037
$977$	−24.0000			−0.767828			−0.383914	−	0.923369i	$-0.625424\pi$
$977$	−24.0000			−0.767828			−0.383914	+	0.923369i	$0.625424\pi$
$978$		0			0
$979$	18.0000	+	31.1769i	0.575282	+	0.996419i
$980$	36.0000			1.14998
$981$	16.0000			0.510841
$982$		0			0
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	−27.0000	+	46.7654i	−0.860292	+	1.49007i
$986$		0			0
$987$	6.00000			0.190982
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−17.0000	+	29.4449i	−0.540023	+	0.935347i	0.458879	+	0.888499i	$0.348251\pi$
$991$	−17.0000	+	29.4449i	−0.540023	+	0.935347i	−0.998902	+	0.0468483i	$0.985082\pi$
$992$		0			0
$993$	−28.0000	+	48.4974i	−0.888553	+	1.53902i
$994$		0			0
$995$	33.0000			1.04617
$996$	−48.0000			−1.52094
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	0.699457	−	0.714675i	$-0.253425\pi$
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	−0.968655	+	0.248410i	$0.920092\pi$
$998$		0			0
$999$	8.00000			0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.c.a.68.1		2
19.2	odd	18		361.2.e.d.234.1		6
19.3	odd	18		361.2.e.d.99.1		6
19.4	even	9		361.2.e.e.62.1		6
19.5	even	9		361.2.e.e.28.1		6
19.6	even	9		361.2.e.e.54.1		6
19.7	even	3	inner	361.2.c.a.292.1		2
19.8	odd	6		19.2.a.a.1.1	✓	1
19.9	even	9		361.2.e.e.245.1		6
19.10	odd	18		361.2.e.d.245.1		6
19.11	even	3		361.2.a.b.1.1		1
19.12	odd	6		361.2.c.c.292.1		2
19.13	odd	18		361.2.e.d.54.1		6
19.14	odd	18		361.2.e.d.28.1		6
19.15	odd	18		361.2.e.d.62.1		6
19.16	even	9		361.2.e.e.99.1		6
19.17	even	9		361.2.e.e.234.1		6
19.18	odd	2		361.2.c.c.68.1		2
57.8	even	6		171.2.a.b.1.1		1
57.11	odd	6		3249.2.a.d.1.1		1
76.11	odd	6		5776.2.a.c.1.1		1
76.27	even	6		304.2.a.f.1.1		1
95.8	even	12		475.2.b.a.324.1		2
95.27	even	12		475.2.b.a.324.2		2
95.49	even	6		9025.2.a.d.1.1		1
95.84	odd	6		475.2.a.b.1.1		1
133.27	even	6		931.2.a.a.1.1		1
133.46	odd	6		931.2.f.c.324.1		2
133.65	odd	6		931.2.f.c.704.1		2
133.103	even	6		931.2.f.b.704.1		2
133.122	even	6		931.2.f.b.324.1		2
152.27	even	6		1216.2.a.b.1.1		1
152.141	odd	6		1216.2.a.o.1.1		1
209.65	even	6		2299.2.a.b.1.1		1
228.179	odd	6		2736.2.a.c.1.1		1
247.103	odd	6		3211.2.a.a.1.1		1
285.179	even	6		4275.2.a.i.1.1		1
323.84	odd	6		5491.2.a.b.1.1		1
380.179	even	6		7600.2.a.c.1.1		1
399.293	odd	6		8379.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.a.a.1.1	✓	1	19.8	odd	6
171.2.a.b.1.1		1	57.8	even	6
304.2.a.f.1.1		1	76.27	even	6
361.2.a.b.1.1		1	19.11	even	3
361.2.c.a.68.1		2	1.1	even	1	trivial
361.2.c.a.292.1		2	19.7	even	3	inner
361.2.c.c.68.1		2	19.18	odd	2
361.2.c.c.292.1		2	19.12	odd	6
361.2.e.d.28.1		6	19.14	odd	18
361.2.e.d.54.1		6	19.13	odd	18
361.2.e.d.62.1		6	19.15	odd	18
361.2.e.d.99.1		6	19.3	odd	18
361.2.e.d.234.1		6	19.2	odd	18
361.2.e.d.245.1		6	19.10	odd	18
361.2.e.e.28.1		6	19.5	even	9
361.2.e.e.54.1		6	19.6	even	9
361.2.e.e.62.1		6	19.4	even	9
361.2.e.e.99.1		6	19.16	even	9
361.2.e.e.234.1		6	19.17	even	9
361.2.e.e.245.1		6	19.9	even	9
475.2.a.b.1.1		1	95.84	odd	6
475.2.b.a.324.1		2	95.8	even	12
475.2.b.a.324.2		2	95.27	even	12
931.2.a.a.1.1		1	133.27	even	6
931.2.f.b.324.1		2	133.122	even	6
931.2.f.b.704.1		2	133.103	even	6
931.2.f.c.324.1		2	133.46	odd	6
931.2.f.c.704.1		2	133.65	odd	6
1216.2.a.b.1.1		1	152.27	even	6
1216.2.a.o.1.1		1	152.141	odd	6
2299.2.a.b.1.1		1	209.65	even	6
2736.2.a.c.1.1		1	228.179	odd	6
3211.2.a.a.1.1		1	247.103	odd	6
3249.2.a.d.1.1		1	57.11	odd	6
4275.2.a.i.1.1		1	285.179	even	6
5491.2.a.b.1.1		1	323.84	odd	6
5776.2.a.c.1.1		1	76.11	odd	6
7600.2.a.c.1.1		1	380.179	even	6
8379.2.a.j.1.1		1	399.293	odd	6
9025.2.a.d.1.1		1	95.49	even	6

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} -1.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +3.00000 q^{11} -4.00000 q^{12} +(-2.00000 - 3.46410i) q^{13} +(-3.00000 - 5.19615i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.50000 - 2.59808i) q^{17} -6.00000 q^{20} +(1.00000 - 1.73205i) q^{21} +(-2.00000 - 3.46410i) q^{25} -4.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(3.00000 + 5.19615i) q^{29} +4.00000 q^{31} +(-3.00000 + 5.19615i) q^{33} +(1.50000 - 2.59808i) q^{35} +(1.00000 - 1.73205i) q^{36} -2.00000 q^{37} +8.00000 q^{39} +(-3.00000 + 5.19615i) q^{41} +(0.500000 - 0.866025i) q^{43} +(3.00000 + 5.19615i) q^{44} +3.00000 q^{45} +(1.50000 + 2.59808i) q^{47} +(-4.00000 - 6.92820i) q^{48} -6.00000 q^{49} +(3.00000 + 5.19615i) q^{51} +(4.00000 - 6.92820i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-4.50000 + 7.79423i) q^{55} +(-3.00000 + 5.19615i) q^{59} +(6.00000 - 10.3923i) q^{60} +(0.500000 + 0.866025i) q^{61} +(0.500000 + 0.866025i) q^{63} -8.00000 q^{64} +12.0000 q^{65} +(-2.00000 - 3.46410i) q^{67} +6.00000 q^{68} +(3.00000 - 5.19615i) q^{71} +(3.50000 - 6.06218i) q^{73} +8.00000 q^{75} -3.00000 q^{77} +(4.00000 - 6.92820i) q^{79} +(-6.00000 - 10.3923i) q^{80} +(5.50000 - 9.52628i) q^{81} +12.0000 q^{83} +4.00000 q^{84} +(4.50000 + 7.79423i) q^{85} -12.0000 q^{87} +(6.00000 + 10.3923i) q^{89} +(2.00000 + 3.46410i) q^{91} +(-4.00000 + 6.92820i) q^{93} +(4.00000 - 6.92820i) q^{97} +(-1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{7} - q^{9} + 6 q^{11} - 8 q^{12} - 4 q^{13} - 6 q^{15} - 4 q^{16} + 3 q^{17} - 12 q^{20} + 2 q^{21} - 4 q^{25} - 8 q^{27} - 2 q^{28} + 6 q^{29} + 8 q^{31} - 6 q^{33}+ \cdots - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^7 - q^9 + 6 * q^11 - 8 * q^12 - 4 * q^13 - 6 * q^15 - 4 * q^16 + 3 * q^17 - 12 * q^20 + 2 * q^21 - 4 * q^25 - 8 * q^27 - 2 * q^28 + 6 * q^29 + 8 * q^31 - 6 * q^33 + 3 * q^35 + 2 * q^36 - 4 * q^37 + 16 * q^39 - 6 * q^41 + q^43 + 6 * q^44 + 6 * q^45 + 3 * q^47 - 8 * q^48 - 12 * q^49 + 6 * q^51 + 8 * q^52 + 12 * q^53 - 9 * q^55 - 6 * q^59 + 12 * q^60 + q^61 + q^63 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 12 * q^68 + 6 * q^71 + 7 * q^73 + 16 * q^75 - 6 * q^77 + 8 * q^79 - 12 * q^80 + 11 * q^81 + 24 * q^83 + 8 * q^84 + 9 * q^85 - 24 * q^87 + 12 * q^89 + 4 * q^91 - 8 * q^93 + 8 * q^97 - 3 * q^99

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