LMFDB - Embedded newform 648.2.d.k.325.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(325,648)] 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("648.325"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,1,0,1,0,0,-6,1,0,-8,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.31435290000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{4} - 8x + 16 $ x^8 - x^7 - 2x^4 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			325.8
Root			$1.40782 - 0.134277i$ of defining polynomial
Character	$\chi$	$=$	648.325
Dual form			648.2.d.k.325.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40782 + 0.134277i) q^{2} +(1.96394 + 0.378078i) q^{4} -2.28102i q^{5} +1.81565 q^{7} +(2.71411 + 0.795980i) q^{8} +(0.306290 - 3.21128i) q^{10} +4.89769i q^{11} -4.62914i q^{13} +(2.55611 + 0.243801i) q^{14} +(3.71411 + 1.48504i) q^{16} -1.92788 q^{17} -2.12907i q^{19} +(0.862405 - 4.47979i) q^{20} +(-0.657649 + 6.89509i) q^{22} -2.31530 q^{23} -0.203069 q^{25} +(0.621589 - 6.51702i) q^{26} +(3.56582 + 0.686457i) q^{28} -3.65394i q^{29} +5.31600 q^{31} +(5.02941 + 2.58940i) q^{32} +(-2.71411 - 0.258870i) q^{34} -4.14154i q^{35} +7.98438i q^{37} +(0.285886 - 2.99736i) q^{38} +(1.81565 - 6.19096i) q^{40} -4.72481 q^{41} -2.54958i q^{43} +(-1.85171 + 9.61877i) q^{44} +(-3.25953 - 0.310892i) q^{46} -4.04011 q^{47} -3.70342 q^{49} +(-0.285886 - 0.0272676i) q^{50} +(1.75018 - 9.09135i) q^{52} +8.95958i q^{53} +11.1718 q^{55} +(4.92788 + 1.44522i) q^{56} +(0.490641 - 5.14410i) q^{58} +3.52478i q^{59} +1.98233i q^{61} +(7.48399 + 0.713818i) q^{62} +(6.73283 + 4.32076i) q^{64} -10.5592 q^{65} +8.92263i q^{67} +(-3.78624 - 0.728888i) q^{68} +(0.556115 - 5.83056i) q^{70} -13.3561 q^{71} -11.5592 q^{73} +(-1.07212 + 11.2406i) q^{74} +(0.804954 - 4.18136i) q^{76} +8.89249i q^{77} +9.94660 q^{79} +(3.38742 - 8.47198i) q^{80} +(-6.65170 - 0.634435i) q^{82} -3.60443i q^{83} +4.39754i q^{85} +(0.342351 - 3.58936i) q^{86} +(-3.89847 + 13.2929i) q^{88} -2.49965 q^{89} -8.40489i q^{91} +(-4.54711 - 0.875363i) q^{92} +(-5.68776 - 0.542495i) q^{94} -4.85646 q^{95} -13.9874 q^{97} +(-5.21376 - 0.497285i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{4} - 6 q^{7} + q^{8} - 8 q^{10} + 16 q^{14} + 9 q^{16} + 14 q^{17} - 8 q^{20} - q^{22} - 10 q^{23} - 2 q^{25} - 14 q^{26} + 2 q^{28} + 10 q^{31} + 11 q^{32} - q^{34} + 23 q^{38} - 6 q^{40}+ \cdots - 33 q^{98}+O(q^{100}) $ 8 * q + q^2 + q^4 - 6 * q^7 + q^8 - 8 * q^10 + 16 * q^14 + 9 * q^16 + 14 * q^17 - 8 * q^20 - q^22 - 10 * q^23 - 2 * q^25 - 14 * q^26 + 2 * q^28 + 10 * q^31 + 11 * q^32 - q^34 + 23 * q^38 - 6 * q^40 - 8 * q^41 - 9 * q^44 - 10 * q^46 + 6 * q^47 - 18 * q^49 - 23 * q^50 + 8 * q^52 - 2 * q^55 + 10 * q^56 + 14 * q^58 + 26 * q^62 + 13 * q^64 - 14 * q^65 - 39 * q^68 - 36 * q^71 - 22 * q^73 - 38 * q^74 - 5 * q^76 + 30 * q^79 + 48 * q^80 + 19 * q^82 + 7 * q^86 - 31 * q^88 - 32 * q^89 - 30 * q^92 + 12 * q^94 + 44 * q^95 - 33 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.40782	+	0.134277i	0.995482	+	0.0949484i
$2$	1.40782	+	0.134277i	0.995482	+	0.0949484i
$3$		0			0
$3$		0			0
$4$	1.96394	+	0.378078i	0.981970	+	0.189039i
$5$		−	2.28102i		−	1.02010i	−0.860143	−	0.510052i	$-0.829626\pi$
$5$		−	2.28102i		−	1.02010i	0.860143	−	0.510052i	$-0.170374\pi$
$6$		0			0
$7$	1.81565			0.686251			0.343125	−	0.939290i	$-0.388514\pi$
$7$	1.81565			0.686251			0.343125	+	0.939290i	$0.388514\pi$
$8$	2.71411	+	0.795980i	0.959584	+	0.281421i
$9$		0			0
$10$	0.306290	−	3.21128i	0.0968573	−	1.01550i
$11$			4.89769i			1.47671i	0.674412	+	0.738355i	$0.264397\pi$
$11$			4.89769i			1.47671i	−0.674412	+	0.738355i	$0.735603\pi$
$12$		0			0
$13$		−	4.62914i		−	1.28389i	−0.766750	−	0.641946i	$-0.778127\pi$
$13$		−	4.62914i		−	1.28389i	0.766750	−	0.641946i	$-0.221873\pi$
$14$	2.55611	+	0.243801i	0.683150	+	0.0651584i
$15$		0			0
$16$	3.71411	+	1.48504i	0.928529	+	0.371261i
$17$	−1.92788			−0.467579			−0.233790	−	0.972287i	$-0.575113\pi$
$17$	−1.92788			−0.467579			−0.233790	+	0.972287i	$0.575113\pi$
$18$		0			0
$19$		−	2.12907i		−	0.488442i	−0.969720	−	0.244221i	$-0.921468\pi$
$19$		−	2.12907i		−	0.488442i	0.969720	−	0.244221i	$-0.0785322\pi$
$20$	0.862405	−	4.47979i	0.192840	−	1.00171i
$21$		0			0
$22$	−0.657649	+	6.89509i	−0.140211	+	1.47004i
$23$	−2.31530			−0.482773			−0.241387	−	0.970429i	$-0.577602\pi$
$23$	−2.31530			−0.482773			−0.241387	+	0.970429i	$0.577602\pi$
$24$		0			0
$25$	−0.203069			−0.0406138
$26$	0.621589	−	6.51702i	0.121904	−	1.27809i
$27$		0			0
$28$	3.56582	+	0.686457i	0.673877	+	0.129728i
$29$		−	3.65394i		−	0.678519i	−0.940693	−	0.339260i	$-0.889824\pi$
$29$		−	3.65394i		−	0.678519i	0.940693	−	0.339260i	$-0.110176\pi$
$30$		0			0
$31$	5.31600			0.954782			0.477391	−	0.878691i	$-0.341583\pi$
$31$	5.31600			0.954782			0.477391	+	0.878691i	$0.341583\pi$
$32$	5.02941	+	2.58940i	0.889083	+	0.457746i
$33$		0			0
$34$	−2.71411	−	0.258870i	−0.465467	−	0.0443959i
$35$		−	4.14154i		−	0.700048i
$36$		0			0
$37$			7.98438i			1.31262i	0.754489	+	0.656312i	$0.227885\pi$
$37$			7.98438i			1.31262i	−0.754489	+	0.656312i	$0.772115\pi$
$38$	0.285886	−	2.99736i	0.0463768	−	0.486235i
$39$		0			0
$40$	1.81565	−	6.19096i	0.287079	−	0.978877i
$41$	−4.72481			−0.737891			−0.368946	−	0.929451i	$-0.620281\pi$
$41$	−4.72481			−0.737891			−0.368946	+	0.929451i	$0.620281\pi$
$42$		0			0
$43$		−	2.54958i		−	0.388807i	−0.980922	−	0.194404i	$-0.937723\pi$
$43$		−	2.54958i		−	0.388807i	0.980922	−	0.194404i	$-0.0622771\pi$
$44$	−1.85171	+	9.61877i	−0.279156	+	1.45008i
$45$		0			0
$46$	−3.25953	−	0.310892i	−0.480592	−	0.0458386i
$47$	−4.04011			−0.589310			−0.294655	−	0.955604i	$-0.595205\pi$
$47$	−4.04011			−0.589310			−0.294655	+	0.955604i	$0.595205\pi$
$48$		0			0
$49$	−3.70342			−0.529060
$50$	−0.285886	−	0.0272676i	−0.0404304	−	0.00385622i
$51$		0			0
$52$	1.75018	−	9.09135i	0.242706	−	1.26074i
$53$			8.95958i			1.23069i	0.788257	+	0.615347i	$0.210984\pi$
$53$			8.95958i			1.23069i	−0.788257	+	0.615347i	$0.789016\pi$
$54$		0			0
$55$	11.1718			1.50640
$56$	4.92788	+	1.44522i	0.658515	+	0.193126i
$57$		0			0
$58$	0.490641	−	5.14410i	0.0644243	−	0.675454i
$59$			3.52478i			0.458887i	0.973322	+	0.229444i	$0.0736907\pi$
$59$			3.52478i			0.458887i	−0.973322	+	0.229444i	$0.926309\pi$
$60$		0			0
$61$			1.98233i			0.253811i	0.991915	+	0.126906i	$0.0405045\pi$
$61$			1.98233i			0.253811i	−0.991915	+	0.126906i	$0.959495\pi$
$62$	7.48399	+	0.713818i	0.950468	+	0.0906550i
$63$		0			0
$64$	6.73283	+	4.32076i	0.841604	+	0.540095i
$65$	−10.5592			−1.30970
$66$		0			0
$67$			8.92263i			1.09007i	0.838412	+	0.545036i	$0.183484\pi$
$67$			8.92263i			1.09007i	−0.838412	+	0.545036i	$0.816516\pi$
$68$	−3.78624	−	0.728888i	−0.459149	−	0.0883907i
$69$		0			0
$70$	0.556115	−	5.83056i	0.0664684	−	0.696885i
$71$	−13.3561			−1.58508			−0.792539	−	0.609821i	$-0.791241\pi$
$71$	−13.3561			−1.58508			−0.792539	+	0.609821i	$0.791241\pi$
$72$		0			0
$73$	−11.5592			−1.35290			−0.676450	−	0.736489i	$-0.736482\pi$
$73$	−11.5592			−1.35290			−0.676450	+	0.736489i	$0.736482\pi$
$74$	−1.07212	+	11.2406i	−0.124632	+	1.30669i
$75$		0			0
$76$	0.804954	−	4.18136i	0.0923345	−	0.479635i
$77$			8.89249i			1.01339i
$78$		0			0
$79$	9.94660			1.11908			0.559540	−	0.828804i	$-0.310978\pi$
$79$	9.94660			1.11908			0.559540	+	0.828804i	$0.310978\pi$
$80$	3.38742	−	8.47198i	0.378725	−	0.947196i
$81$		0			0
$82$	−6.65170	−	0.634435i	−0.734558	−	0.0700616i
$83$		−	3.60443i		−	0.395637i	−0.980239	−	0.197819i	$-0.936614\pi$
$83$		−	3.60443i		−	0.395637i	0.980239	−	0.197819i	$-0.0633857\pi$
$84$		0			0
$85$			4.39754i			0.476980i
$86$	0.342351	−	3.58936i	0.0369166	−	0.387051i
$87$		0			0
$88$	−3.89847	+	13.2929i	−0.415578	+	1.41703i
$89$	−2.49965			−0.264962			−0.132481	−	0.991186i	$-0.542294\pi$
$89$	−2.49965			−0.264962			−0.132481	+	0.991186i	$0.542294\pi$
$90$		0			0
$91$		−	8.40489i		−	0.881072i
$92$	−4.54711	−	0.875363i	−0.474069	−	0.0912629i
$93$		0			0
$94$	−5.68776	−	0.542495i	−0.586648	−	0.0559541i
$95$	−4.85646			−0.498262
$96$		0			0
$97$	−13.9874			−1.42021			−0.710103	−	0.704098i	$-0.751352\pi$
$97$	−13.9874			−1.42021			−0.710103	+	0.704098i	$0.751352\pi$
$98$	−5.21376	−	0.497285i	−0.526670	−	0.0502334i
$99$		0			0
$100$	−0.398816	−	0.0767760i	−0.0398816	−	0.00767760i
$101$			1.30582i			0.129934i	0.997887	+	0.0649671i	$0.0206942\pi$
$101$			1.30582i			0.129934i	−0.997887	+	0.0649671i	$0.979306\pi$
$102$		0			0
$103$	6.44625			0.635168			0.317584	−	0.948230i	$-0.397129\pi$
$103$	6.44625			0.635168			0.317584	+	0.948230i	$0.397129\pi$
$104$	3.68470	−	12.5640i	0.361315	−	1.23200i
$105$		0			0
$106$	−1.20307	+	12.6135i	−0.116852	+	1.22513i
$107$			3.10427i			0.300101i	0.988678	+	0.150051i	$0.0479437\pi$
$107$			3.10427i			0.300101i	−0.988678	+	0.150051i	$0.952056\pi$
$108$		0			0
$109$		−	18.0837i		−	1.73210i	−0.499955	−	0.866051i	$-0.666650\pi$
$109$		−	18.0837i		−	1.73210i	0.499955	−	0.866051i	$-0.333350\pi$
$110$	15.7279	+	1.50011i	1.49959	+	0.143030i
$111$		0			0
$112$	6.74353	+	2.69632i	0.637203	+	0.254778i
$113$	−2.83437			−0.266635			−0.133317	−	0.991073i	$-0.542563\pi$
$113$	−2.83437			−0.266635			−0.133317	+	0.991073i	$0.542563\pi$
$114$		0			0
$115$			5.28125i			0.492479i
$116$	1.38147	−	7.17611i	0.128267	−	0.666285i
$117$		0			0
$118$	−0.473298	+	4.96227i	−0.0435706	+	0.456814i
$119$	−3.50035			−0.320877
$120$		0			0
$121$	−12.9874			−1.18067
$122$	−0.266182	+	2.79077i	−0.0240990	+	0.252665i
$123$		0			0
$124$	10.4403	+	2.00986i	0.937566	+	0.180491i
$125$		−	10.9419i		−	0.978674i
$126$		0			0
$127$	−7.44962			−0.661047			−0.330523	−	0.943798i	$-0.607225\pi$
$127$	−7.44962			−0.661047			−0.330523	+	0.943798i	$0.607225\pi$
$128$	8.89847	+	6.98694i	0.786521	+	0.617564i
$129$		0			0
$130$	−14.8655	−	1.41786i	−1.30379	−	0.124354i
$131$		−	3.60443i		−	0.314920i	−0.987525	−	0.157460i	$-0.949669\pi$
$131$		−	3.60443i		−	0.314920i	0.987525	−	0.157460i	$-0.0503306\pi$
$132$		0			0
$133$		−	3.86564i		−	0.335194i
$134$	−1.19811	+	12.5615i	−0.103501	+	1.08515i
$135$		0			0
$136$	−5.23248	−	1.53455i	−0.448682	−	0.131587i
$137$	11.7629			1.00498			0.502488	−	0.864584i	$-0.332418\pi$
$137$	11.7629			1.00498			0.502488	+	0.864584i	$0.332418\pi$
$138$		0			0
$139$		−	12.7479i		−	1.08126i	−0.841260	−	0.540631i	$-0.818186\pi$
$139$		−	12.7479i		−	1.08126i	0.841260	−	0.540631i	$-0.181814\pi$
$140$	1.56582	−	8.13373i	0.132336	−	0.687426i
$141$		0			0
$142$	−18.8031	−	1.79342i	−1.57792	−	0.150501i
$143$	22.6721			1.89594
$144$		0			0
$145$	−8.33472			−0.692161
$146$	−16.2733	−	1.55214i	−1.34679	−	0.128456i
$147$		0			0
$148$	−3.01872	+	15.6808i	−0.248137	+	1.28896i
$149$		−	7.61860i		−	0.624140i	−0.950059	−	0.312070i	$-0.898978\pi$
$149$		−	7.61860i		−	0.624140i	0.950059	−	0.312070i	$-0.101022\pi$
$150$		0			0
$151$	−4.53976			−0.369440			−0.184720	−	0.982791i	$-0.559138\pi$
$151$	−4.53976			−0.369440			−0.184720	+	0.982791i	$0.559138\pi$
$152$	1.69470	−	5.77854i	0.137458	−	0.468701i
$153$		0			0
$154$	−1.19406	+	12.5191i	−0.0962201	+	1.00882i
$155$		−	12.1259i		−	0.973977i
$156$		0			0
$157$			13.1757i			1.05154i	0.850627	+	0.525769i	$0.176223\pi$
$157$			13.1757i			1.05154i	−0.850627	+	0.525769i	$0.823777\pi$
$158$	14.0031	+	1.33560i	1.11402	+	0.106255i
$159$		0			0
$160$	5.90649	−	11.4722i	0.466949	−	0.906958i
$161$	−4.20377			−0.331303
$162$		0			0
$163$			20.5911i			1.61282i	0.591358	+	0.806409i	$0.298592\pi$
$163$			20.5911i			1.61282i	−0.591358	+	0.806409i	$0.701408\pi$
$164$	−9.27924	−	1.78635i	−0.724587	−	0.139490i
$165$		0			0
$166$	0.483993	−	5.07440i	0.0375652	−	0.393850i
$167$	5.07824			0.392966			0.196483	−	0.980507i	$-0.437048\pi$
$167$	5.07824			0.392966			0.196483	+	0.980507i	$0.437048\pi$
$168$		0			0
$169$	−8.42893			−0.648379
$170$	−0.590490	+	6.19096i	−0.0452885	+	0.474825i
$171$		0			0
$172$	0.963939	−	5.00722i	0.0734997	−	0.381797i
$173$			12.7477i			0.969190i	0.874739	+	0.484595i	$0.161033\pi$
$173$			12.7477i			0.969190i	−0.874739	+	0.484595i	$0.838967\pi$
$174$		0			0
$175$	−0.368702			−0.0278713
$176$	−7.27329	+	18.1906i	−0.548245	+	1.37117i
$177$		0			0
$178$	−3.51907	−	0.335646i	−0.263765	−	0.0251578i
$179$			8.82019i			0.659252i	0.944112	+	0.329626i	$0.106923\pi$
$179$			8.82019i			0.659252i	−0.944112	+	0.329626i	$0.893077\pi$
$180$		0			0
$181$			15.4369i			1.14741i	0.819061	+	0.573707i	$0.194495\pi$
$181$			15.4369i			1.14741i	−0.819061	+	0.573707i	$0.805505\pi$
$182$	1.12859	−	11.8326i	0.0836564	−	0.877091i
$183$		0			0
$184$	−6.28399	−	1.84293i	−0.463262	−	0.135863i
$185$	18.2126			1.33901
$186$		0			0
$187$		−	9.44216i		−	0.690479i
$188$	−7.93453	−	1.52748i	−0.578685	−	0.111403i
$189$		0			0
$190$	−6.83704	−	0.652112i	−0.496011	−	0.0473092i
$191$	9.63397			0.697090			0.348545	−	0.937292i	$-0.386676\pi$
$191$	9.63397			0.697090			0.348545	+	0.937292i	$0.386676\pi$
$192$		0			0
$193$	−6.98670			−0.502914			−0.251457	−	0.967868i	$-0.580910\pi$
$193$	−6.98670			−0.502914			−0.251457	+	0.967868i	$0.580910\pi$
$194$	−19.6918	−	1.87819i	−1.41379	−	0.134846i
$195$		0			0
$196$	−7.27329	−	1.40018i	−0.519521	−	0.100013i
$197$		−	4.31842i		−	0.307675i	−0.988096	−	0.153837i	$-0.950837\pi$
$197$		−	4.31842i		−	0.307675i	0.988096	−	0.153837i	$-0.0491632\pi$
$198$		0			0
$199$	5.90649			0.418700			0.209350	−	0.977841i	$-0.432865\pi$
$199$	5.90649			0.418700			0.209350	+	0.977841i	$0.432865\pi$
$200$	−0.551153	−	0.161639i	−0.0389724	−	0.0114296i
$201$		0			0
$202$	−0.175342	+	1.83837i	−0.0123370	+	0.129347i
$203$		−	6.63427i		−	0.465634i
$204$		0			0
$205$			10.7774i			0.752726i
$206$	9.07518	+	0.865585i	0.632298	+	0.0603082i
$207$		0			0
$208$	6.87447	−	17.1932i	0.476659	−	1.19213i
$209$	10.4275			0.721287
$210$		0			0
$211$		−	18.3345i		−	1.26220i	−0.775703	−	0.631098i	$-0.782604\pi$
$211$		−	18.3345i		−	1.26220i	0.775703	−	0.631098i	$-0.217396\pi$
$212$	−3.38742	+	17.5961i	−0.232649	+	1.20850i
$213$		0			0
$214$	−0.416833	+	4.37027i	−0.0284941	+	0.298745i
$215$	−5.81565			−0.396624
$216$		0			0
$217$	9.65199			0.655220
$218$	2.42823	−	25.4586i	0.164460	−	1.72428i
$219$		0			0
$220$	21.9406	+	4.22379i	1.47924	+	0.284768i
$221$			8.92442i			0.600321i
$222$		0			0
$223$	5.26527			0.352588			0.176294	−	0.984338i	$-0.443589\pi$
$223$	5.26527			0.352588			0.176294	+	0.984338i	$0.443589\pi$
$224$	9.13165	+	4.70145i	0.610134	+	0.314129i
$225$		0			0
$226$	−3.99029	−	0.380591i	−0.265430	−	0.0253166i
$227$			1.77405i			0.117748i	0.998265	+	0.0588741i	$0.0187510\pi$
$227$			1.77405i			0.117748i	−0.998265	+	0.0588741i	$0.981249\pi$
$228$		0			0
$229$		−	3.81845i		−	0.252330i	−0.992009	−	0.126165i	$-0.959733\pi$
$229$		−	3.81845i		−	0.252330i	0.992009	−	0.126165i	$-0.0402669\pi$
$230$	−0.709152	+	7.43507i	−0.0467601	+	0.490254i
$231$		0			0
$232$	2.90846	−	9.91720i	0.190950	−	0.651096i
$233$	20.3207			1.33125			0.665627	−	0.746284i	$-0.268164\pi$
$233$	20.3207			1.33125			0.665627	+	0.746284i	$0.268164\pi$
$234$		0			0
$235$			9.21558i			0.601158i
$236$	−1.33264	+	6.92245i	−0.0867476	+	0.450613i
$237$		0			0
$238$	−4.92788	−	0.470018i	−0.319427	−	0.0304667i
$239$	17.3962			1.12527			0.562634	−	0.826706i	$-0.309788\pi$
$239$	17.3962			1.12527			0.562634	+	0.826706i	$0.309788\pi$
$240$		0			0
$241$	13.7122			0.883281			0.441641	−	0.897192i	$-0.354397\pi$
$241$	13.7122			0.883281			0.441641	+	0.897192i	$0.354397\pi$
$242$	−18.2840	−	1.74391i	−1.17534	−	0.112103i
$243$		0			0
$244$	−0.749475	+	3.89317i	−0.0479802	+	0.249235i
$245$			8.44759i			0.539697i
$246$		0			0
$247$	−9.85576			−0.627107
$248$	14.4282	+	4.23143i	0.916193	+	0.268696i
$249$		0			0
$250$	1.46925	−	15.4043i	0.0929236	−	0.974253i
$251$			4.50751i			0.284512i	0.989830	+	0.142256i	$0.0454356\pi$
$251$			4.50751i			0.284512i	−0.989830	+	0.142256i	$0.954564\pi$
$252$		0			0
$253$		−	11.3396i		−	0.712916i
$254$	−10.4878	−	1.00032i	−0.658060	−	0.0627653i
$255$		0			0
$256$	11.5893	+	11.0312i	0.724331	+	0.689453i
$257$	−8.22516			−0.513071			−0.256536	−	0.966535i	$-0.582581\pi$
$257$	−8.22516			−0.513071			−0.256536	+	0.966535i	$0.582581\pi$
$258$		0			0
$259$			14.4968i			0.900789i
$260$	−20.7376	−	3.99219i	−1.28609	−	0.247585i
$261$		0			0
$262$	0.483993	−	5.07440i	0.0299012	−	0.313498i
$263$	5.02751			0.310010			0.155005	−	0.987914i	$-0.450461\pi$
$263$	5.02751			0.310010			0.155005	+	0.987914i	$0.450461\pi$
$264$		0			0
$265$	20.4370			1.25544
$266$	0.519068	−	5.44214i	0.0318261	−	0.333679i
$267$		0			0
$268$	−3.37345	+	17.5235i	−0.206066	+	1.07042i
$269$		−	23.1577i		−	1.41195i	−0.708236	−	0.705976i	$-0.750509\pi$
$269$		−	23.1577i		−	1.41195i	0.708236	−	0.705976i	$-0.249491\pi$
$270$		0			0
$271$	20.9367			1.27181			0.635906	−	0.771766i	$-0.280627\pi$
$271$	20.9367			1.27181			0.635906	+	0.771766i	$0.280627\pi$
$272$	−7.16036	−	2.86298i	−0.434161	−	0.173594i
$273$		0			0
$274$	16.5602	+	1.57950i	1.00044	+	0.0954209i
$275$		−	0.994571i		−	0.0599749i
$276$		0			0
$277$		−	22.2496i		−	1.33685i	−0.743780	−	0.668425i	$-0.766969\pi$
$277$		−	22.2496i		−	1.33685i	0.743780	−	0.668425i	$-0.233031\pi$
$278$	1.71175	−	17.9468i	0.102664	−	1.07638i
$279$		0			0
$280$	3.29658	−	11.2406i	0.197008	−	0.671755i
$281$	−18.5606			−1.10723			−0.553616	−	0.832772i	$-0.686752\pi$
$281$	−18.5606			−1.10723			−0.553616	+	0.832772i	$0.686752\pi$
$282$		0			0
$283$			2.03184i			0.120780i	0.998175	+	0.0603901i	$0.0192345\pi$
$283$			2.03184i			0.120780i	−0.998175	+	0.0603901i	$0.980766\pi$
$284$	−26.2306	−	5.04965i	−1.55650	−	0.299642i
$285$		0			0
$286$	31.9183	+	3.04435i	1.88737	+	0.180016i
$287$	−8.57859			−0.506378
$288$		0			0
$289$	−13.2833			−0.781370
$290$	−11.7338	−	1.11916i	−0.689034	−	0.0657196i
$291$		0			0
$292$	−22.7015	−	4.37027i	−1.32851	−	0.255751i
$293$		−	34.1195i		−	1.99328i	−0.0818798	−	0.996642i	$-0.526092\pi$
$293$		−	34.1195i		−	1.99328i	0.0818798	−	0.996642i	$-0.473908\pi$
$294$		0			0
$295$	8.04011			0.468113
$296$	−6.35541	+	21.6705i	−0.369401	+	1.25957i
$297$		0			0
$298$	1.02300	−	10.7256i	0.0592611	−	0.621320i
$299$			10.7178i			0.619829i
$300$		0			0
$301$		−	4.62914i		−	0.266819i
$302$	−6.39118	−	0.609587i	−0.367771	−	0.0350778i
$303$		0			0
$304$	3.16176	−	7.90761i	0.181339	−	0.453532i
$305$	4.52174			0.258914
$306$		0			0
$307$		−	4.77588i		−	0.272574i	−0.990669	−	0.136287i	$-0.956483\pi$
$307$		−	4.77588i		−	0.272574i	0.990669	−	0.136287i	$-0.0435169\pi$
$308$	−3.36205	+	17.4643i	−0.191571	+	0.995122i
$309$		0			0
$310$	1.62824	−	17.0712i	0.0924776	−	0.969577i
$311$	−22.3541			−1.26759			−0.633793	−	0.773502i	$-0.718503\pi$
$311$	−22.3541			−1.26759			−0.633793	+	0.773502i	$0.718503\pi$
$312$		0			0
$313$	−2.44822			−0.138381			−0.0691907	−	0.997603i	$-0.522042\pi$
$313$	−2.44822			−0.138381			−0.0691907	+	0.997603i	$0.522042\pi$
$314$	−1.76920	+	18.5491i	−0.0998420	+	1.04679i
$315$		0			0
$316$	19.5345	+	3.76059i	1.09890	+	0.211550i
$317$		−	16.4991i		−	0.926680i	−0.886181	−	0.463340i	$-0.846651\pi$
$317$		−	16.4991i		−	0.926680i	0.886181	−	0.463340i	$-0.153349\pi$
$318$		0			0
$319$	17.8959			1.00198
$320$	9.85576	−	15.3578i	0.550954	−	0.858524i
$321$		0			0
$322$	−5.91817	−	0.564471i	−0.329807	−	0.0314567i
$323$			4.10459i			0.228385i
$324$		0			0
$325$			0.940035i			0.0521438i
$326$	−2.76492	+	28.9886i	−0.153135	+	1.60553i
$327$		0			0
$328$	−12.8237	−	3.76085i	−0.708069	−	0.207658i
$329$	−7.33542			−0.404415
$330$		0			0
$331$			0.380128i			0.0208937i	0.999945	+	0.0104469i	$0.00332540\pi$
$331$			0.380128i			0.0208937i	−0.999945	+	0.0104469i	$0.996675\pi$
$332$	1.36275	−	7.07888i	0.0747909	−	0.388504i
$333$		0			0
$334$	7.14928	+	0.681893i	0.391191	+	0.0373115i
$335$	20.3527			1.11199
$336$		0			0
$337$	5.03744			0.274407			0.137203	−	0.990543i	$-0.456189\pi$
$337$	5.03744			0.274407			0.137203	+	0.990543i	$0.456189\pi$
$338$	−11.8665	−	1.13181i	−0.645450	−	0.0615626i
$339$		0			0
$340$	−1.66261	+	8.63649i	−0.0901678	+	0.468380i
$341$			26.0361i			1.40994i
$342$		0			0
$343$	−19.4337			−1.04932
$344$	2.02941	−	6.91985i	0.109419	−	0.373093i
$345$		0			0
$346$	−1.71173	+	17.9465i	−0.0920231	+	0.964811i
$347$			9.70337i			0.520904i	0.965487	+	0.260452i	$0.0838716\pi$
$347$			9.70337i			0.520904i	−0.965487	+	0.260452i	$0.916128\pi$
$348$		0			0
$349$			30.1653i			1.61471i	0.590065	+	0.807356i	$0.299102\pi$
$349$			30.1653i			1.61471i	−0.590065	+	0.807356i	$0.700898\pi$
$350$	−0.519068	−	0.0495084i	−0.0277454	−	0.00264633i
$351$		0			0
$352$	−12.6821	+	24.6325i	−0.675958	+	1.31292i
$353$	26.4752			1.40913			0.704565	−	0.709639i	$-0.251142\pi$
$353$	26.4752			1.40913			0.704565	+	0.709639i	$0.251142\pi$
$354$		0			0
$355$			30.4656i			1.61695i
$356$	−4.90916	−	0.945062i	−0.260185	−	0.0500882i
$357$		0			0
$358$	−1.18435	+	12.4173i	−0.0625949	+	0.656273i
$359$	23.4619			1.23827			0.619135	−	0.785285i	$-0.287483\pi$
$359$	23.4619			1.23827			0.619135	+	0.785285i	$0.287483\pi$
$360$		0			0
$361$	14.4671			0.761424
$362$	−2.07282	+	21.7324i	−0.108945	+	1.14223i
$363$		0			0
$364$	3.17770	−	16.5067i	0.166557	−	0.865186i
$365$			26.3668i			1.38010i
$366$		0			0
$367$	−19.2520			−1.00494			−0.502472	−	0.864593i	$-0.667576\pi$
$367$	−19.2520			−1.00494			−0.502472	+	0.864593i	$0.667576\pi$
$368$	−8.59928	−	3.43832i	−0.448269	−	0.179235i
$369$		0			0
$370$	25.6401	+	2.44553i	1.33296	+	0.127137i
$371$			16.2675i			0.844564i
$372$		0			0
$373$		−	10.4986i		−	0.543597i	−0.962354	−	0.271799i	$-0.912382\pi$
$373$		−	10.4986i		−	0.543597i	0.962354	−	0.271799i	$-0.0876185\pi$
$374$	1.26787	−	13.2929i	0.0655599	−	0.687360i
$375$		0			0
$376$	−10.9653	−	3.21584i	−0.565493	−	0.165845i
$377$	−16.9146			−0.871145
$378$		0			0
$379$		−	35.5203i		−	1.82455i	−0.409574	−	0.912277i	$-0.634323\pi$
$379$		−	35.5203i		−	1.82455i	0.409574	−	0.912277i	$-0.365677\pi$
$380$	−9.53779	−	1.83612i	−0.489278	−	0.0941909i
$381$		0			0
$382$	13.5629	+	1.29362i	0.693940	+	0.0661876i
$383$	36.0789			1.84355			0.921774	−	0.387728i	$-0.126740\pi$
$383$	36.0789			1.84355			0.921774	+	0.387728i	$0.126740\pi$
$384$		0			0
$385$	20.2840			1.03377
$386$	−9.83605	−	0.938156i	−0.500642	−	0.0477509i
$387$		0			0
$388$	−27.4704	−	5.28833i	−1.39460	−	0.268474i
$389$		−	20.2354i		−	1.02597i	−0.858397	−	0.512987i	$-0.828539\pi$
$389$		−	20.2354i		−	1.02597i	0.858397	−	0.512987i	$-0.171461\pi$
$390$		0			0
$391$	4.46361			0.225735
$392$	−10.0515	−	2.94785i	−0.507678	−	0.148889i
$393$		0			0
$394$	0.579866	−	6.07957i	0.0292132	−	0.306285i
$395$		−	22.6884i		−	1.14158i
$396$		0			0
$397$		−	3.99499i		−	0.200503i	−0.994962	−	0.100251i	$-0.968035\pi$
$397$		−	3.99499i		−	0.200503i	0.994962	−	0.100251i	$-0.0319647\pi$
$398$	8.31530	+	0.793108i	0.416808	+	0.0397549i
$399$		0			0
$400$	−0.754222	−	0.301567i	−0.0377111	−	0.0150783i
$401$	28.0248			1.39949			0.699747	−	0.714391i	$-0.253296\pi$
$401$	28.0248			1.39949			0.699747	+	0.714391i	$0.253296\pi$
$402$		0			0
$403$		−	24.6085i		−	1.22584i
$404$	−0.493702	+	2.56455i	−0.0245626	+	0.127591i
$405$		0			0
$406$	0.890832	−	9.33988i	0.0442112	−	0.463531i
$407$	−39.1051			−1.93837
$408$		0			0
$409$	−16.4496			−0.813381			−0.406691	−	0.913566i	$-0.633317\pi$
$409$	−16.4496			−0.813381			−0.406691	+	0.913566i	$0.633317\pi$
$410$	−1.44716	+	15.1727i	−0.0714702	+	0.749326i
$411$		0			0
$412$	12.6600	+	2.43718i	0.623715	+	0.120071i
$413$			6.39976i			0.314912i
$414$		0			0
$415$	−8.22179			−0.403592
$416$	11.9867	−	23.2819i	0.587697	−	1.14149i
$417$		0			0
$418$	14.6801	+	1.40018i	0.718029	+	0.0684851i
$419$			23.7375i			1.15965i	0.814740	+	0.579827i	$0.196880\pi$
$419$			23.7375i			1.15965i	−0.814740	+	0.579827i	$0.803120\pi$
$420$		0			0
$421$		−	29.9552i		−	1.45993i	−0.683486	−	0.729963i	$-0.739537\pi$
$421$		−	29.9552i		−	1.45993i	0.683486	−	0.729963i	$-0.260463\pi$
$422$	2.46190	−	25.8117i	0.119844	−	1.25649i
$423$		0			0
$424$	−7.13165	+	24.3173i	−0.346343	+	1.18095i
$425$	0.391493			0.0189902
$426$		0			0
$427$			3.59921i			0.174178i
$428$	−1.17366	+	6.09660i	−0.0567308	+	0.294690i
$429$		0			0
$430$	−8.18741	−	0.780910i	−0.394832	−	0.0376588i
$431$	11.0367			0.531621			0.265810	−	0.964025i	$-0.414360\pi$
$431$	11.0367			0.531621			0.265810	+	0.964025i	$0.414360\pi$
$432$		0			0
$433$	34.9394			1.67908			0.839541	−	0.543297i	$-0.182824\pi$
$433$	34.9394			1.67908			0.839541	+	0.543297i	$0.182824\pi$
$434$	13.5883	+	1.29604i	0.652259	+	0.0622121i
$435$		0			0
$436$	6.83704	−	35.5152i	0.327435	−	1.70087i
$437$			4.92943i			0.235807i
$438$		0			0
$439$	13.1704			0.628587			0.314293	−	0.949326i	$-0.398232\pi$
$439$	13.1704			0.628587			0.314293	+	0.949326i	$0.398232\pi$
$440$	30.3214	+	8.89249i	1.44552	+	0.423933i
$441$		0			0
$442$	−1.19835	+	12.5640i	−0.0569996	+	0.597609i
$443$		−	27.3490i		−	1.29939i	−0.760196	−	0.649694i	$-0.774897\pi$
$443$		−	27.3490i		−	1.29939i	0.760196	−	0.649694i	$-0.225103\pi$
$444$		0			0
$445$			5.70176i			0.270289i
$446$	7.41257	+	0.707006i	0.350995	+	0.0334777i
$447$		0			0
$448$	12.2245	+	7.84498i	0.577551	+	0.370641i
$449$	13.8225			0.652323			0.326161	−	0.945314i	$-0.394245\pi$
$449$	13.8225			0.652323			0.326161	+	0.945314i	$0.394245\pi$
$450$		0			0
$451$		−	23.1407i		−	1.08965i
$452$	−5.56652	−	1.07161i	−0.261827	−	0.0504044i
$453$		0			0
$454$	−0.238215	+	2.49756i	−0.0111800	+	0.117216i
$455$	−19.1718			−0.898786
$456$		0			0
$457$	5.72411			0.267763			0.133881	−	0.990997i	$-0.457256\pi$
$457$	5.72411			0.267763			0.133881	+	0.990997i	$0.457256\pi$
$458$	0.512731	−	5.37570i	0.0239584	−	0.251190i
$459$		0			0
$460$	−1.99672	+	10.3721i	−0.0930977	+	0.483600i
$461$		−	22.3685i		−	1.04181i	−0.853616	−	0.520903i	$-0.825595\pi$
$461$		−	22.3685i		−	1.04181i	0.853616	−	0.520903i	$-0.174405\pi$
$462$		0			0
$463$	−37.1466			−1.72635			−0.863174	−	0.504907i	$-0.831527\pi$
$463$	−37.1466			−1.72635			−0.863174	+	0.504907i	$0.831527\pi$
$464$	5.42626	−	13.5711i	0.251908	−	0.630024i
$465$		0			0
$466$	28.6080	+	2.72861i	1.32524	+	0.126401i
$467$		−	22.6850i		−	1.04974i	−0.851184	−	0.524868i	$-0.824115\pi$
$467$		−	22.6850i		−	1.04974i	0.851184	−	0.524868i	$-0.175885\pi$
$468$		0			0
$469$			16.2004i			0.748063i
$470$	−1.23744	+	12.9739i	−0.0570790	+	0.598442i
$471$		0			0
$472$	−2.80565	+	9.56666i	−0.129141	+	0.440341i
$473$	12.4871			0.574155
$474$		0			0
$475$			0.432348i			0.0198375i
$476$	−6.87447	−	1.32340i	−0.315091	−	0.0606582i
$477$		0			0
$478$	24.4908	+	2.33592i	1.12018	+	0.106842i
$479$	26.3153			1.20238			0.601188	−	0.799107i	$-0.294694\pi$
$479$	26.3153			1.20238			0.601188	+	0.799107i	$0.294694\pi$
$480$		0			0
$481$	36.9608			1.68527
$482$	19.3044	+	1.84124i	0.879291	+	0.0838662i
$483$		0			0
$484$	−25.5065	−	4.91025i	−1.15939	−	0.223193i
$485$			31.9056i			1.44876i
$486$		0			0
$487$	−24.0388			−1.08930			−0.544652	−	0.838662i	$-0.683338\pi$
$487$	−24.0388			−1.08930			−0.544652	+	0.838662i	$0.683338\pi$
$488$	−1.57789	+	5.38027i	−0.0714279	+	0.243553i
$489$		0			0
$490$	−1.13432	+	11.8927i	−0.0512433	+	0.537258i
$491$		−	31.4374i		−	1.41875i	−0.704832	−	0.709374i	$-0.748978\pi$
$491$		−	31.4374i		−	1.41875i	0.704832	−	0.709374i	$-0.251022\pi$
$492$		0			0
$493$			7.04435i			0.317261i
$494$	−13.8752	−	1.32340i	−0.624274	−	0.0595428i
$495$		0			0
$496$	19.7442	+	7.89449i	0.886542	+	0.354473i
$497$	−24.2500			−1.08776
$498$		0			0
$499$			5.86768i			0.262673i	0.991338	+	0.131337i	$0.0419269\pi$
$499$			5.86768i			0.262673i	−0.991338	+	0.131337i	$0.958073\pi$
$500$	4.13690	−	21.4893i	0.185008	−	0.961029i
$501$		0			0
$502$	−0.605257	+	6.34579i	−0.0270139	+	0.283226i
$503$	−32.4317			−1.44606			−0.723029	−	0.690818i	$-0.757251\pi$
$503$	−32.4317			−1.44606			−0.723029	+	0.690818i	$0.757251\pi$
$504$		0			0
$505$	2.97861			0.132546
$506$	1.52265	−	15.9642i	0.0676903	−	0.709695i
$507$		0			0
$508$	−14.6306	−	2.81654i	−0.649128	−	0.124964i
$509$			15.8027i			0.700440i	0.936667	+	0.350220i	$0.113893\pi$
$509$			15.8027i			0.700440i	−0.936667	+	0.350220i	$0.886107\pi$
$510$		0			0
$511$	−20.9874			−0.928428
$512$	14.8344	+	17.0862i	0.655596	+	0.755112i
$513$		0			0
$514$	−11.5796	−	1.10445i	−0.510753	−	0.0487153i
$515$		−	14.7040i		−	0.647937i
$516$		0			0
$517$		−	19.7872i		−	0.870241i
$518$	−1.94660	+	20.4090i	−0.0855285	+	0.896720i
$519$		0			0
$520$	−28.6588	−	8.40489i	−1.25677	−	0.368579i
$521$	−5.50310			−0.241095			−0.120548	−	0.992708i	$-0.538465\pi$
$521$	−5.50310			−0.241095			−0.120548	+	0.992708i	$0.538465\pi$
$522$		0			0
$523$			38.5894i			1.68740i	0.536818	+	0.843698i	$0.319626\pi$
$523$			38.5894i			1.68740i	−0.536818	+	0.843698i	$0.680374\pi$
$524$	1.36275	−	7.07888i	0.0595322	−	0.309242i
$525$		0			0
$526$	7.07785	+	0.675081i	0.308609	+	0.0294349i
$527$	−10.2486			−0.446436
$528$		0			0
$529$	−17.6394			−0.766930
$530$	28.7717	+	2.74423i	1.24976	+	0.119202i
$531$		0			0
$532$	1.46151	−	7.59189i	0.0633647	−	0.329150i
$533$			21.8718i			0.947373i
$534$		0			0
$535$	7.08092			0.306135
$536$	−7.10223	+	24.2170i	−0.306770	+	1.04602i
$537$		0			0
$538$	3.10956	−	32.6020i	0.134063	−	1.40557i
$539$		−	18.1382i		−	0.781268i
$540$		0			0
$541$			22.5666i			0.970214i	0.874455	+	0.485107i	$0.161219\pi$
$541$			22.5666i			0.970214i	−0.874455	+	0.485107i	$0.838781\pi$
$542$	29.4752	+	2.81132i	1.26607	+	0.120757i
$543$		0			0
$544$	−9.69610	−	4.99205i	−0.415717	−	0.214033i
$545$	−41.2493			−1.76693
$546$		0			0
$547$			13.0110i			0.556312i	0.960536	+	0.278156i	$0.0897232\pi$
$547$			13.0110i			0.556312i	−0.960536	+	0.278156i	$0.910277\pi$
$548$	23.1017	+	4.44731i	0.986856	+	0.189980i
$549$		0			0
$550$	0.133548	−	1.40018i	0.00569452	−	0.0597039i
$551$	−7.77948			−0.331417
$552$		0			0
$553$	18.0595			0.767969
$554$	2.98762	−	31.3235i	0.126932	−	1.33081i
$555$		0			0
$556$	4.81970	−	25.0361i	0.204401	−	1.06177i
$557$			5.73693i			0.243081i	0.992586	+	0.121541i	$0.0387835\pi$
$557$			5.73693i			0.243081i	−0.992586	+	0.121541i	$0.961217\pi$
$558$		0			0
$559$	−11.8024			−0.499186
$560$	6.15037	−	15.3821i	0.259900	−	0.650014i
$561$		0			0
$562$	−26.1300	−	2.49227i	−1.10223	−	0.105130i
$563$		−	15.3009i		−	0.644856i	−0.946594	−	0.322428i	$-0.895501\pi$
$563$		−	15.3009i		−	0.644856i	0.946594	−	0.322428i	$-0.104499\pi$
$564$		0			0
$565$			6.46526i			0.271995i
$566$	−0.272830	+	2.86047i	−0.0114679	+	0.120235i
$567$		0			0
$568$	−36.2500	−	10.6312i	−1.52102	−	0.446075i
$569$	13.2619			0.555968			0.277984	−	0.960586i	$-0.410334\pi$
$569$	13.2619			0.555968			0.277984	+	0.960586i	$0.410334\pi$
$570$		0			0
$571$			27.0503i			1.13202i	0.824399	+	0.566009i	$0.191513\pi$
$571$			27.0503i			1.13202i	−0.824399	+	0.566009i	$0.808487\pi$
$572$	44.5266	+	8.57182i	1.86175	+	0.358406i
$573$		0			0
$574$	−12.0772	−	1.15191i	−0.504091	−	0.0480798i
$575$	0.470166			0.0196073
$576$		0			0
$577$	−4.78434			−0.199174			−0.0995872	−	0.995029i	$-0.531752\pi$
$577$	−4.78434			−0.199174			−0.0995872	+	0.995029i	$0.531752\pi$
$578$	−18.7005	−	1.78364i	−0.777840	−	0.0741898i
$579$		0			0
$580$	−16.3689	−	3.15117i	−0.679681	−	0.130845i
$581$		−	6.54438i		−	0.271506i
$582$		0			0
$583$	−43.8813			−1.81738
$584$	−31.3729	−	9.20087i	−1.29822	−	0.380735i
$585$		0			0
$586$	4.58148	−	48.0343i	0.189259	−	1.98428i
$587$			42.8158i			1.76720i	0.468246	+	0.883598i	$0.344886\pi$
$587$			42.8158i			1.76720i	−0.468246	+	0.883598i	$0.655114\pi$
$588$		0			0
$589$		−	11.3181i		−	0.466355i
$590$	11.3191	+	1.07960i	0.465998	+	0.0444466i
$591$		0			0
$592$	−11.8572	+	29.6549i	−0.487326	+	1.21881i
$593$	0.825572			0.0339022			0.0169511	−	0.999856i	$-0.494604\pi$
$593$	0.825572			0.0339022			0.0169511	+	0.999856i	$0.494604\pi$
$594$		0			0
$595$			7.98438i			0.327328i
$596$	2.88042	−	14.9625i	0.117987	−	0.612886i
$597$		0			0
$598$	−1.43916	+	15.0888i	−0.0588518	+	0.617028i
$599$	−1.92246			−0.0785494			−0.0392747	−	0.999228i	$-0.512505\pi$
$599$	−1.92246			−0.0785494			−0.0392747	+	0.999228i	$0.512505\pi$
$600$		0			0
$601$	43.1874			1.76165			0.880825	−	0.473442i	$-0.156989\pi$
$601$	43.1874			1.76165			0.880825	+	0.473442i	$0.156989\pi$
$602$	0.621589	−	6.51702i	0.0253341	−	0.265614i
$603$		0			0
$604$	−8.91581	−	1.71638i	−0.362779	−	0.0698386i
$605$			29.6246i			1.20441i
$606$		0			0
$607$	−41.0156			−1.66477			−0.832386	−	0.554196i	$-0.813026\pi$
$607$	−41.0156			−1.66477			−0.832386	+	0.554196i	$0.813026\pi$
$608$	5.51302	−	10.7080i	0.223582	−	0.434265i
$609$		0			0
$610$	6.36582	+	0.607167i	0.257744	+	0.0245835i
$611$			18.7022i			0.756611i
$612$		0			0
$613$		−	5.05878i		−	0.204322i	−0.994768	−	0.102161i	$-0.967424\pi$
$613$		−	5.05878i		−	0.204322i	0.994768	−	0.102161i	$-0.0325757\pi$
$614$	0.641292	−	6.72360i	0.0258805	−	0.271342i
$615$		0			0
$616$	−7.07824	+	24.1352i	−0.285191	+	0.972437i
$617$	−32.1478			−1.29422			−0.647112	−	0.762395i	$-0.724023\pi$
$617$	−32.1478			−1.29422			−0.647112	+	0.762395i	$0.724023\pi$
$618$		0			0
$619$			31.5883i			1.26964i	0.772660	+	0.634820i	$0.218926\pi$
$619$			31.5883i			1.26964i	−0.772660	+	0.634820i	$0.781074\pi$
$620$	4.58454	−	23.8146i	0.184120	−	0.956416i
$621$		0			0
$622$	−31.4707	−	3.00165i	−1.26186	−	0.120355i
$623$	−4.53849			−0.181831
$624$		0			0
$625$	−25.9741			−1.03896
$626$	−3.44666	−	0.328740i	−0.137756	−	0.0131391i
$627$		0			0
$628$	−4.98146	+	25.8764i	−0.198782	+	1.03258i
$629$		−	15.3929i		−	0.613756i
$630$		0			0
$631$	−15.4885			−0.616586			−0.308293	−	0.951292i	$-0.599758\pi$
$631$	−15.4885			−0.616586			−0.308293	+	0.951292i	$0.599758\pi$
$632$	26.9962	+	7.91729i	1.07385	+	0.314933i
$633$		0			0
$634$	2.21545	−	23.2278i	0.0879868	−	0.922493i
$635$			16.9928i			0.674337i
$636$		0			0
$637$			17.1436i			0.679256i
$638$	25.1942	+	2.40301i	0.997449	+	0.0951361i
$639$		0			0
$640$	15.9374	−	20.2976i	0.629980	−	0.802334i
$641$	−30.4496			−1.20269			−0.601344	−	0.798990i	$-0.705368\pi$
$641$	−30.4496			−1.20269			−0.601344	+	0.798990i	$0.705368\pi$
$642$		0			0
$643$		−	16.8484i		−	0.664435i	−0.943203	−	0.332218i	$-0.892203\pi$
$643$		−	16.8484i		−	0.664435i	0.943203	−	0.332218i	$-0.107797\pi$
$644$	−8.25595	−	1.58935i	−0.325330	−	0.0626293i
$645$		0			0
$646$	−0.551153	+	5.77854i	−0.0216848	+	0.227353i
$647$	−18.6734			−0.734126			−0.367063	−	0.930196i	$-0.619637\pi$
$647$	−18.6734			−0.734126			−0.367063	+	0.930196i	$0.619637\pi$
$648$		0			0
$649$	−17.2633			−0.677644
$650$	−0.126225	+	1.32340i	−0.00495097	+	0.0519082i
$651$		0			0
$652$	−7.78504	+	40.4396i	−0.304886	+	1.58374i
$653$		−	36.2895i		−	1.42012i	−0.704142	−	0.710059i	$-0.748668\pi$
$653$		−	36.2895i		−	1.42012i	0.704142	−	0.710059i	$-0.251332\pi$
$654$		0			0
$655$	−8.22179			−0.321252
$656$	−17.5485	−	7.01655i	−0.685153	−	0.273950i
$657$		0			0
$658$	−10.3270	−	0.984980i	−0.402588	−	0.0383985i
$659$			22.2959i			0.868526i	0.900786	+	0.434263i	$0.142991\pi$
$659$			22.2959i			0.868526i	−0.900786	+	0.434263i	$0.857009\pi$
$660$		0			0
$661$			6.00205i			0.233453i	0.993164	+	0.116726i	$0.0372401\pi$
$661$			6.00205i			0.233453i	−0.993164	+	0.116726i	$0.962760\pi$
$662$	−0.0510426	+	0.535153i	−0.00198383	+	0.0207993i
$663$		0			0
$664$	2.86905	−	9.78283i	0.111341	−	0.379647i
$665$	−8.81762			−0.341933
$666$		0			0
$667$			8.45996i			0.327571i
$668$	9.97336	+	1.91997i	0.385881	+	0.0742859i
$669$		0			0
$670$	28.6531	+	2.73291i	1.10696	+	0.105582i
$671$	−9.70884			−0.374806
$672$		0			0
$673$	7.40889			0.285592			0.142796	−	0.989752i	$-0.454391\pi$
$673$	7.40889			0.285592			0.142796	+	0.989752i	$0.454391\pi$
$674$	7.09183	+	0.676414i	0.273167	+	0.0260545i
$675$		0			0
$676$	−16.5539	−	3.18679i	−0.636689	−	0.122569i
$677$			9.90286i			0.380598i	0.981726	+	0.190299i	$0.0609457\pi$
$677$			9.90286i			0.380598i	−0.981726	+	0.190299i	$0.939054\pi$
$678$		0			0
$679$	−25.3962			−0.974617
$680$	−3.50035	+	11.9354i	−0.134232	+	0.457702i
$681$		0			0
$682$	−3.49606	+	36.6543i	−0.133871	+	1.40357i
$683$			39.0736i			1.49511i	0.664200	+	0.747555i	$0.268772\pi$
$683$			39.0736i			1.49511i	−0.664200	+	0.747555i	$0.731228\pi$
$684$		0			0
$685$		−	26.8316i		−	1.02518i
$686$	−27.3592	−	2.60950i	−1.04458	−	0.0996311i
$687$		0			0
$688$	3.78624	−	9.46943i	0.144349	−	0.361018i
$689$	41.4752			1.58008
$690$		0			0
$691$		−	2.39603i		−	0.0911491i	−0.998961	−	0.0455746i	$-0.985488\pi$
$691$		−	2.39603i		−	0.0911491i	0.998961	−	0.0455746i	$-0.0145119\pi$
$692$	−4.81962	+	25.0357i	−0.183215	+	0.951715i
$693$		0			0
$694$	−1.30294	+	13.6606i	−0.0494590	+	0.518551i
$695$	−29.0782			−1.10300
$696$		0			0
$697$	9.10886			0.345023
$698$	−4.05052	+	42.4675i	−0.153314	+	1.60742i
$699$		0			0
$700$	−0.724109	−	0.139398i	−0.0273687	−	0.00526876i
$701$		−	30.9184i		−	1.16777i	−0.811836	−	0.583885i	$-0.801532\pi$
$701$		−	30.9184i		−	1.16777i	0.811836	−	0.583885i	$-0.198468\pi$
$702$		0			0
$703$	16.9993			0.641141
$704$	−21.1618	+	32.9754i	−0.797564	+	1.24281i
$705$		0			0
$706$	37.2724	+	3.55501i	1.40276	+	0.133795i
$707$			2.37091i			0.0891674i
$708$		0			0
$709$			5.16103i			0.193827i	0.995293	+	0.0969133i	$0.0308970\pi$
$709$			5.16103i			0.193827i	−0.995293	+	0.0969133i	$0.969103\pi$
$710$	−4.09084	+	42.8902i	−0.153526	+	1.60964i
$711$		0			0
$712$	−6.78434	−	1.98967i	−0.254254	−	0.0745661i
$713$	−12.3081			−0.460943
$714$		0			0
$715$		−	51.7156i		−	1.93405i
$716$	−3.33472	+	17.3223i	−0.124624	+	0.647365i
$717$		0			0
$718$	33.0302	+	3.15040i	1.23268	+	0.117572i
$719$	−14.7871			−0.551465			−0.275733	−	0.961234i	$-0.588920\pi$
$719$	−14.7871			−0.551465			−0.275733	+	0.961234i	$0.588920\pi$
$720$		0			0
$721$	11.7041			0.435884
$722$	20.3671	+	1.94260i	0.757985	+	0.0722961i
$723$		0			0
$724$	−5.83634	+	30.3171i	−0.216906	+	1.12673i
$725$			0.742002i			0.0275573i
$726$		0			0
$727$	2.13362			0.0791316			0.0395658	−	0.999217i	$-0.487403\pi$
$727$	2.13362			0.0791316			0.0395658	+	0.999217i	$0.487403\pi$
$728$	6.69012	−	22.8118i	0.247952	−	0.845463i
$729$		0			0
$730$	−3.54046	+	37.1198i	−0.131038	+	1.37386i
$731$			4.91528i			0.181798i
$732$		0			0
$733$			25.6688i			0.948097i	0.880499	+	0.474048i	$0.157208\pi$
$733$			25.6688i			0.948097i	−0.880499	+	0.474048i	$0.842792\pi$
$734$	−27.1034	−	2.58510i	−1.00040	−	0.0954179i
$735$		0			0
$736$	−11.6446	−	5.99524i	−0.429225	−	0.220987i
$737$	−43.7003			−1.60972
$738$		0			0
$739$		−	5.46282i		−	0.200953i	−0.994939	−	0.100476i	$-0.967963\pi$
$739$		−	5.46282i		−	0.200953i	0.994939	−	0.100476i	$-0.0320367\pi$
$740$	35.7684	+	6.88577i	1.31487	+	0.253126i
$741$		0			0
$742$	−2.18435	+	22.9017i	−0.0801901	+	0.840749i
$743$	−33.6340			−1.23391			−0.616955	−	0.786998i	$-0.711634\pi$
$743$	−33.6340			−1.23391			−0.616955	+	0.786998i	$0.711634\pi$
$744$		0			0
$745$	−17.3782			−0.636688
$746$	1.40972	−	14.7802i	0.0516137	−	0.541141i
$747$		0			0
$748$	3.56987	−	18.5438i	0.130527	−	0.678029i
$749$			5.63627i			0.205945i
$750$		0			0
$751$	25.3455			0.924870			0.462435	−	0.886653i	$-0.346976\pi$
$751$	25.3455			0.924870			0.462435	+	0.886653i	$0.346976\pi$
$752$	−15.0054	−	5.99974i	−0.547191	−	0.218788i
$753$		0			0
$754$	−23.8128	−	2.27125i	−0.867210	−	0.0827139i
$755$			10.3553i			0.376868i
$756$		0			0
$757$			3.95103i			0.143603i	0.997419	+	0.0718014i	$0.0228748\pi$
$757$			3.95103i			0.143603i	−0.997419	+	0.0718014i	$0.977125\pi$
$758$	4.76957	−	50.0063i	0.173239	−	1.81631i
$759$		0			0
$760$	−13.1810	−	3.86564i	−0.478124	−	0.140222i
$761$	−46.7959			−1.69635			−0.848175	−	0.529717i	$-0.822298\pi$
$761$	−46.7959			−1.69635			−0.848175	+	0.529717i	$0.822298\pi$
$762$		0			0
$763$		−	32.8336i		−	1.18866i
$764$	18.9205	+	3.64239i	0.684521	+	0.131777i
$765$		0			0
$766$	50.7928	+	4.84459i	1.83522	+	0.175042i
$767$	16.3167			0.589162
$768$		0			0
$769$	−5.20167			−0.187577			−0.0937885	−	0.995592i	$-0.529898\pi$
$769$	−5.20167			−0.187577			−0.0937885	+	0.995592i	$0.529898\pi$
$770$	28.5563	+	2.72368i	1.02910	+	0.0981546i
$771$		0			0
$772$	−13.7215	−	2.64152i	−0.493846	−	0.0950703i
$773$		−	38.8477i		−	1.39725i	−0.715486	−	0.698627i	$-0.753795\pi$
$773$		−	38.8477i		−	1.39725i	0.715486	−	0.698627i	$-0.246205\pi$
$774$		0			0
$775$	−1.07952			−0.0387773
$776$	−37.9634	−	11.1337i	−1.36281	−	0.399676i
$777$		0			0
$778$	2.71715	−	28.4878i	0.0974146	−	1.02134i
$779$			10.0594i			0.360417i
$780$		0			0
$781$		−	65.4141i		−	2.34070i
$782$	6.28399	+	0.599362i	0.224715	+	0.0214332i
$783$		0			0
$784$	−13.7549	−	5.49974i	−0.491247	−	0.196419i
$785$	30.0542			1.07268
$786$		0			0
$787$		−	47.1787i		−	1.68174i	−0.541239	−	0.840869i	$-0.682044\pi$
$787$		−	47.1787i		−	1.68174i	0.541239	−	0.840869i	$-0.317956\pi$
$788$	1.63270	−	8.48111i	0.0581625	−	0.302127i
$789$		0			0
$790$	3.04654	−	31.9413i	0.108391	−	1.13642i
$791$	−5.14621			−0.182978
$792$		0			0
$793$	9.17648			0.325866
$794$	0.536436	−	5.62424i	0.0190374	−	0.199597i
$795$		0			0
$796$	11.6000	+	2.23311i	0.411151	+	0.0791506i
$797$		−	7.33980i		−	0.259989i	−0.991515	−	0.129995i	$-0.958504\pi$
$797$		−	7.33980i		−	0.259989i	0.991515	−	0.129995i	$-0.0414960\pi$
$798$		0			0
$799$	7.78884			0.275549
$800$	−1.02132	−	0.525828i	−0.0361091	−	0.0185908i
$801$		0			0
$802$	39.4541	+	3.76310i	1.39317	+	0.132880i
$803$		−	56.6133i		−	1.99784i
$804$		0			0
$805$			9.58890i			0.337964i
$806$	3.30436	−	34.6444i	0.116391	−	1.22030i
$807$		0			0
$808$	−1.03941	+	3.54415i	−0.0365662	+	0.124683i
$809$	−2.25520			−0.0792887			−0.0396443	−	0.999214i	$-0.512622\pi$
$809$	−2.25520			−0.0792887			−0.0396443	+	0.999214i	$0.512622\pi$
$810$		0			0
$811$			15.9986i			0.561785i	0.959739	+	0.280893i	$0.0906305\pi$
$811$			15.9986i			0.561785i	−0.959739	+	0.280893i	$0.909369\pi$
$812$	2.50827	−	13.0293i	0.0880230	−	0.457239i
$813$		0			0
$814$	−55.0531	−	5.25092i	−1.92961	−	0.184045i
$815$	46.9688			1.64524
$816$		0			0
$817$	−5.42823			−0.189910
$818$	−23.1582	−	2.20881i	−0.809707	−	0.0772293i
$819$		0			0
$820$	−4.07470	+	21.1662i	−0.142295	+	0.739154i
$821$		−	29.1462i		−	1.01721i	−0.861001	−	0.508604i	$-0.830162\pi$
$821$		−	29.1462i		−	1.01721i	0.861001	−	0.508604i	$-0.169838\pi$
$822$		0			0
$823$	8.31390			0.289804			0.144902	−	0.989446i	$-0.453713\pi$
$823$	8.31390			0.289804			0.144902	+	0.989446i	$0.453713\pi$
$824$	17.4958	+	5.13108i	0.609497	+	0.178750i
$825$		0			0
$826$	−0.859343	+	9.00974i	−0.0299004	+	0.313489i
$827$			43.5035i			1.51277i	0.654129	+	0.756383i	$0.273035\pi$
$827$			43.5035i			1.51277i	−0.654129	+	0.756383i	$0.726965\pi$
$828$		0			0
$829$		−	15.9248i		−	0.553092i	−0.961001	−	0.276546i	$-0.910810\pi$
$829$		−	15.9248i		−	0.553092i	0.961001	−	0.276546i	$-0.0891897\pi$
$830$	−11.5748	−	1.10400i	−0.401768	−	0.0383204i
$831$		0			0
$832$	20.0014	−	31.1672i	0.693424	−	1.08053i
$833$	7.13974			0.247377
$834$		0			0
$835$		−	11.5836i		−	0.400867i
$836$	20.4790	+	3.94242i	0.708282	+	0.136351i
$837$		0			0
$838$	−3.18741	+	33.4183i	−0.110107	+	1.15442i
$839$	−42.1164			−1.45402			−0.727009	−	0.686627i	$-0.759090\pi$
$839$	−42.1164			−1.45402			−0.727009	+	0.686627i	$0.759090\pi$
$840$		0			0
$841$	15.6487			0.539612
$842$	4.02230	−	42.1717i	0.138618	−	1.45333i
$843$		0			0
$844$	6.93185	−	36.0078i	0.238604	−	1.23944i
$845$			19.2266i			0.661415i
$846$		0			0
$847$	−23.5806			−0.810238
$848$	−13.3054	+	33.2769i	−0.456908	+	1.14273i
$849$		0			0
$850$	0.551153	+	0.0525686i	0.0189044	+	0.00180309i
$851$		−	18.4862i		−	0.633700i
$852$		0			0
$853$			39.4923i			1.35219i	0.736815	+	0.676095i	$0.236329\pi$
$853$			39.4923i			1.35219i	−0.736815	+	0.676095i	$0.763671\pi$
$854$	−0.483293	+	5.06706i	−0.0165379	+	0.173391i
$855$		0			0
$856$	−2.47094	+	8.42535i	−0.0844549	+	0.287972i
$857$	−25.2340			−0.861975			−0.430988	−	0.902358i	$-0.641835\pi$
$857$	−25.2340			−0.861975			−0.430988	+	0.902358i	$0.641835\pi$
$858$		0			0
$859$			54.9105i			1.87352i	0.349970	+	0.936761i	$0.386192\pi$
$859$			54.9105i			1.87352i	−0.349970	+	0.936761i	$0.613808\pi$
$860$	−11.4216	−	2.19877i	−0.389473	−	0.0749774i
$861$		0			0
$862$	15.5378	+	1.48198i	0.529219	+	0.0504766i
$863$	54.3877			1.85138			0.925689	−	0.378285i	$-0.123486\pi$
$863$	54.3877			1.85138			0.925689	+	0.378285i	$0.123486\pi$
$864$		0			0
$865$	29.0778			0.988675
$866$	49.1886	+	4.69157i	1.67150	+	0.159426i
$867$		0			0
$868$	18.9559	+	3.64920i	0.643406	+	0.123862i
$869$			48.7154i			1.65256i
$870$		0			0
$871$	41.3041			1.39954
$872$	14.3942	−	49.0812i	0.487451	−	1.66210i
$873$		0			0
$874$	−0.661911	+	6.93977i	−0.0223895	+	0.234741i
$875$		−	19.8667i		−	0.671616i
$876$		0			0
$877$			6.81274i			0.230050i	0.993363	+	0.115025i	$0.0366948\pi$
$877$			6.81274i			0.230050i	−0.993363	+	0.115025i	$0.963305\pi$
$878$	18.5415	+	1.76848i	0.625747	+	0.0596833i
$879$		0			0
$880$	41.4932	+	16.5905i	1.39873	+	0.559267i
$881$	43.2881			1.45841			0.729207	−	0.684293i	$-0.239889\pi$
$881$	43.2881			1.45841			0.729207	+	0.684293i	$0.239889\pi$
$882$		0			0
$883$			31.1510i			1.04832i	0.851621	+	0.524158i	$0.175620\pi$
$883$			31.1510i			1.04832i	−0.851621	+	0.524158i	$0.824380\pi$
$884$	−3.37412	+	17.5270i	−0.113484	+	0.589497i
$885$		0			0
$886$	3.67235	−	38.5025i	0.123375	−	1.29352i
$887$	−49.7772			−1.67135			−0.835677	−	0.549222i	$-0.814924\pi$
$887$	−49.7772			−1.67135			−0.835677	+	0.549222i	$0.814924\pi$
$888$		0			0
$889$	−13.5259			−0.453644
$890$	−0.765617	+	8.02708i	−0.0256636	+	0.269068i
$891$		0			0
$892$	10.3407	+	1.99068i	0.346231	+	0.0666529i
$893$			8.60167i			0.287844i
$894$		0			0
$895$	20.1191			0.672506
$896$	16.1565	+	12.6858i	0.539750	+	0.423804i
$897$		0			0
$898$	19.4596	+	1.85604i	0.649376	+	0.0619370i
$899$		−	19.4243i		−	0.647838i
$900$		0			0
$901$		−	17.2730i		−	0.575447i
$902$	3.10727	−	32.5780i	0.103461	−	1.08473i
$903$		0			0
$904$	−7.69280	−	2.25610i	−0.255859	−	0.0750367i
$905$	35.2119			1.17048
$906$		0			0
$907$			19.2503i			0.639195i	0.947553	+	0.319598i	$0.103548\pi$
$907$			19.2503i			0.639195i	−0.947553	+	0.319598i	$0.896452\pi$
$908$	−0.670731	+	3.48413i	−0.0222590	+	0.115625i
$909$		0			0
$910$	−26.9905	−	2.57433i	−0.894725	−	0.0853383i
$911$	22.2793			0.738145			0.369072	−	0.929401i	$-0.379675\pi$
$911$	22.2793			0.738145			0.369072	+	0.929401i	$0.379675\pi$
$912$		0			0
$913$	17.6534			0.584242
$914$	8.05854	+	0.768618i	0.266553	+	0.0254236i
$915$		0			0
$916$	1.44367	−	7.49920i	0.0477002	−	0.247781i
$917$		−	6.54438i		−	0.216114i
$918$		0			0
$919$	28.0122			0.924039			0.462019	−	0.886870i	$-0.347125\pi$
$919$	28.0122			0.924039			0.462019	+	0.886870i	$0.347125\pi$
$920$	−4.20377	+	14.3339i	−0.138594	+	0.472575i
$921$		0			0
$922$	3.00359	−	31.4910i	0.0989179	−	1.03710i
$923$			61.8273i			2.03507i
$924$		0			0
$925$		−	1.62138i		−	0.0533107i
$926$	−52.2958	−	4.98794i	−1.71855	−	0.163914i
$927$		0			0
$928$	9.46151	−	18.3772i	0.310589	−	0.603260i
$929$	−7.88440			−0.258679			−0.129339	−	0.991600i	$-0.541286\pi$
$929$	−7.88440			−0.258679			−0.129339	+	0.991600i	$0.541286\pi$
$930$		0			0
$931$			7.88484i			0.258415i
$932$	39.9087	+	7.68281i	1.30725	+	0.251659i
$933$		0			0
$934$	3.04608	−	31.9365i	0.0996708	−	1.04499i
$935$	−21.5378			−0.704361
$936$		0			0
$937$	−8.98600			−0.293560			−0.146780	−	0.989169i	$-0.546891\pi$
$937$	−8.98600			−0.293560			−0.146780	+	0.989169i	$0.546891\pi$
$938$	−2.17534	+	22.8073i	−0.0710274	+	0.744684i
$939$		0			0
$940$	−3.48421	+	18.0988i	−0.113642	+	0.590319i
$941$			24.2750i			0.791342i	0.918392	+	0.395671i	$0.129488\pi$
$941$			24.2750i			0.791342i	−0.918392	+	0.395671i	$0.870512\pi$
$942$		0			0
$943$	10.9393			0.356234
$944$	−5.23445	+	13.0914i	−0.170367	+	0.426090i
$945$		0			0
$946$	17.5796	+	1.67673i	0.571561	+	0.0545151i
$947$		−	1.97895i		−	0.0643071i	−0.999483	−	0.0321536i	$-0.989763\pi$
$947$		−	1.97895i		−	0.0643071i	0.999483	−	0.0321536i	$-0.0102366\pi$
$948$		0			0
$949$			53.5090i			1.73698i
$950$	−0.0580546	+	0.608671i	−0.00188354	+	0.0197479i
$951$		0			0
$952$	−9.50035	−	2.78621i	−0.307908	−	0.0903015i
$953$	−28.9674			−0.938347			−0.469173	−	0.883106i	$-0.655448\pi$
$953$	−28.9674			−0.938347			−0.469173	+	0.883106i	$0.655448\pi$
$954$		0			0
$955$		−	21.9753i		−	0.711104i
$956$	34.1651	+	6.57712i	1.10498	+	0.212719i
$957$		0			0
$958$	37.0473	+	3.53355i	1.19694	+	0.114164i
$959$	21.3574			0.689666
$960$		0			0
$961$	−2.74016			−0.0883921
$962$	52.0343	+	4.96300i	1.67765	+	0.160014i
$963$		0			0
$964$	26.9300	+	5.18428i	0.867355	+	0.166975i
$965$			15.9368i			0.513025i
$966$		0			0
$967$	−0.0106238			−0.000341640			−0.000170820	−	1.00000i	$-0.500054\pi$
$967$	−0.0106238			−0.000341640			−0.000170820		1.00000i	$0.500054\pi$
$968$	−35.2493	−	10.3377i	−1.13296	−	0.332267i
$969$		0			0
$970$	−4.28420	+	44.9175i	−0.137557	+	1.44221i
$971$		−	17.0984i		−	0.548715i	−0.961628	−	0.274357i	$-0.911535\pi$
$971$		−	17.0984i		−	0.548715i	0.961628	−	0.274357i	$-0.0884651\pi$
$972$		0			0
$973$		−	23.1457i		−	0.742017i
$974$	−33.8425	−	3.22787i	−1.08438	−	0.103428i
$975$		0			0
$976$	−2.94385	+	7.36260i	−0.0942302	+	0.235671i
$977$	−11.0122			−0.352313			−0.176156	−	0.984362i	$-0.556366\pi$
$977$	−11.0122			−0.352313			−0.176156	+	0.984362i	$0.556366\pi$
$978$		0			0
$979$		−	12.2425i		−	0.391273i
$980$	−3.19385	+	16.5905i	−0.102024	+	0.529966i
$981$		0			0
$982$	4.22133	−	44.2583i	0.134708	−	1.41234i
$983$	45.4887			1.45086			0.725432	−	0.688294i	$-0.241640\pi$
$983$	45.4887			1.45086			0.725432	+	0.688294i	$0.241640\pi$
$984$		0			0
$985$	−9.85041			−0.313860
$986$	−0.945896	+	9.91720i	−0.0301235	+	0.315828i
$987$		0			0
$988$	−19.3561	−	3.72624i	−0.615800	−	0.118548i
$989$			5.90304i			0.187706i
$990$		0			0
$991$	3.93737			0.125075			0.0625374	−	0.998043i	$-0.480081\pi$
$991$	3.93737			0.125075			0.0625374	+	0.998043i	$0.480081\pi$
$992$	26.7364	+	13.7653i	0.848880	+	0.437047i
$993$		0			0
$994$	−34.1397	−	3.25623i	−1.08285	−	0.103281i
$995$		−	13.4728i		−	0.427118i
$996$		0			0
$997$		−	2.50060i		−	0.0791948i	−0.999216	−	0.0395974i	$-0.987392\pi$
$997$		−	2.50060i		−	0.0791948i	0.999216	−	0.0395974i	$-0.0126075\pi$
$998$	−0.787897	+	8.26066i	−0.0249404	+	0.261487i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.d.k.325.8		8
3.2	odd	2		648.2.d.j.325.1		8
4.3	odd	2		2592.2.d.k.1297.2		8
8.3	odd	2		2592.2.d.k.1297.7		8
8.5	even	2	inner	648.2.d.k.325.7		8
9.2	odd	6		72.2.n.b.13.5	✓	16
9.4	even	3		216.2.n.b.181.3		16
9.5	odd	6		72.2.n.b.61.6	yes	16
9.7	even	3		216.2.n.b.37.4		16
12.11	even	2		2592.2.d.j.1297.7		8
24.5	odd	2		648.2.d.j.325.2		8
24.11	even	2		2592.2.d.j.1297.2		8
36.7	odd	6		864.2.r.b.145.7		16
36.11	even	6		288.2.r.b.49.1		16
36.23	even	6		288.2.r.b.241.8		16
36.31	odd	6		864.2.r.b.721.2		16
72.5	odd	6		72.2.n.b.61.5	yes	16
72.11	even	6		288.2.r.b.49.8		16
72.13	even	6		216.2.n.b.181.4		16
72.29	odd	6		72.2.n.b.13.6	yes	16
72.43	odd	6		864.2.r.b.145.2		16
72.59	even	6		288.2.r.b.241.1		16
72.61	even	6		216.2.n.b.37.3		16
72.67	odd	6		864.2.r.b.721.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.5	✓	16	9.2	odd	6
72.2.n.b.13.6	yes	16	72.29	odd	6
72.2.n.b.61.5	yes	16	72.5	odd	6
72.2.n.b.61.6	yes	16	9.5	odd	6
216.2.n.b.37.3		16	72.61	even	6
216.2.n.b.37.4		16	9.7	even	3
216.2.n.b.181.3		16	9.4	even	3
216.2.n.b.181.4		16	72.13	even	6
288.2.r.b.49.1		16	36.11	even	6
288.2.r.b.49.8		16	72.11	even	6
288.2.r.b.241.1		16	72.59	even	6
288.2.r.b.241.8		16	36.23	even	6
648.2.d.j.325.1		8	3.2	odd	2
648.2.d.j.325.2		8	24.5	odd	2
648.2.d.k.325.7		8	8.5	even	2	inner
648.2.d.k.325.8		8	1.1	even	1	trivial
864.2.r.b.145.2		16	72.43	odd	6
864.2.r.b.145.7		16	36.7	odd	6
864.2.r.b.721.2		16	36.31	odd	6
864.2.r.b.721.7		16	72.67	odd	6
2592.2.d.j.1297.2		8	24.11	even	2
2592.2.d.j.1297.7		8	12.11	even	2
2592.2.d.k.1297.2		8	4.3	odd	2
2592.2.d.k.1297.7		8	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40782 + 0.134277i) q^{2} +(1.96394 + 0.378078i) q^{4} -2.28102i q^{5} +1.81565 q^{7} +(2.71411 + 0.795980i) q^{8} +(0.306290 - 3.21128i) q^{10} +4.89769i q^{11} -4.62914i q^{13} +(2.55611 + 0.243801i) q^{14} +(3.71411 + 1.48504i) q^{16} -1.92788 q^{17} -2.12907i q^{19} +(0.862405 - 4.47979i) q^{20} +(-0.657649 + 6.89509i) q^{22} -2.31530 q^{23} -0.203069 q^{25} +(0.621589 - 6.51702i) q^{26} +(3.56582 + 0.686457i) q^{28} -3.65394i q^{29} +5.31600 q^{31} +(5.02941 + 2.58940i) q^{32} +(-2.71411 - 0.258870i) q^{34} -4.14154i q^{35} +7.98438i q^{37} +(0.285886 - 2.99736i) q^{38} +(1.81565 - 6.19096i) q^{40} -4.72481 q^{41} -2.54958i q^{43} +(-1.85171 + 9.61877i) q^{44} +(-3.25953 - 0.310892i) q^{46} -4.04011 q^{47} -3.70342 q^{49} +(-0.285886 - 0.0272676i) q^{50} +(1.75018 - 9.09135i) q^{52} +8.95958i q^{53} +11.1718 q^{55} +(4.92788 + 1.44522i) q^{56} +(0.490641 - 5.14410i) q^{58} +3.52478i q^{59} +1.98233i q^{61} +(7.48399 + 0.713818i) q^{62} +(6.73283 + 4.32076i) q^{64} -10.5592 q^{65} +8.92263i q^{67} +(-3.78624 - 0.728888i) q^{68} +(0.556115 - 5.83056i) q^{70} -13.3561 q^{71} -11.5592 q^{73} +(-1.07212 + 11.2406i) q^{74} +(0.804954 - 4.18136i) q^{76} +8.89249i q^{77} +9.94660 q^{79} +(3.38742 - 8.47198i) q^{80} +(-6.65170 - 0.634435i) q^{82} -3.60443i q^{83} +4.39754i q^{85} +(0.342351 - 3.58936i) q^{86} +(-3.89847 + 13.2929i) q^{88} -2.49965 q^{89} -8.40489i q^{91} +(-4.54711 - 0.875363i) q^{92} +(-5.68776 - 0.542495i) q^{94} -4.85646 q^{95} -13.9874 q^{97} +(-5.21376 - 0.497285i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{4} - 6 q^{7} + q^{8} - 8 q^{10} + 16 q^{14} + 9 q^{16} + 14 q^{17} - 8 q^{20} - q^{22} - 10 q^{23} - 2 q^{25} - 14 q^{26} + 2 q^{28} + 10 q^{31} + 11 q^{32} - q^{34} + 23 q^{38} - 6 q^{40}+ \cdots - 33 q^{98}+O(q^{100}) \) 8 * q + q^2 + q^4 - 6 * q^7 + q^8 - 8 * q^10 + 16 * q^14 + 9 * q^16 + 14 * q^17 - 8 * q^20 - q^22 - 10 * q^23 - 2 * q^25 - 14 * q^26 + 2 * q^28 + 10 * q^31 + 11 * q^32 - q^34 + 23 * q^38 - 6 * q^40 - 8 * q^41 - 9 * q^44 - 10 * q^46 + 6 * q^47 - 18 * q^49 - 23 * q^50 + 8 * q^52 - 2 * q^55 + 10 * q^56 + 14 * q^58 + 26 * q^62 + 13 * q^64 - 14 * q^65 - 39 * q^68 - 36 * q^71 - 22 * q^73 - 38 * q^74 - 5 * q^76 + 30 * q^79 + 48 * q^80 + 19 * q^82 + 7 * q^86 - 31 * q^88 - 32 * q^89 - 30 * q^92 + 12 * q^94 + 44 * q^95 - 33 * q^98

Introduction

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