LMFDB - Embedded newform 1008.2.df.c.689.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(689,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("1008.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			689.3
Root			$1.27866 + 1.16834i$ of defining polynomial
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.c.929.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.626615 + 1.61473i) q^{3} +3.55225 q^{5} +(1.49384 - 2.18368i) q^{7} +(-2.21471 - 2.02363i) q^{9} +O(q^{10})$	\(q+(-0.626615 + 1.61473i) q^{3} +3.55225 q^{5} +(1.49384 - 2.18368i) q^{7} +(-2.21471 - 2.02363i) q^{9} +3.02237i q^{11} +(0.888944 + 0.513232i) q^{13} +(-2.22589 + 5.73592i) q^{15} +(0.809204 - 1.40158i) q^{17} +(7.12643 - 4.11444i) q^{19} +(2.58998 + 3.78047i) q^{21} -3.35830i q^{23} +7.61848 q^{25} +(4.65538 - 2.30812i) q^{27} +(-3.70319 + 2.13804i) q^{29} +(-5.18382 + 2.99288i) q^{31} +(-4.88031 - 1.89386i) q^{33} +(5.30650 - 7.75696i) q^{35} +(2.92323 + 5.06319i) q^{37} +(-1.38576 + 1.11381i) q^{39} +(-0.0472226 + 0.0817920i) q^{41} +(-3.05899 - 5.29833i) q^{43} +(-7.86719 - 7.18843i) q^{45} +(2.57023 - 4.45176i) q^{47} +(-2.53687 - 6.52413i) q^{49} +(1.75612 + 2.18490i) q^{51} +(2.76235 + 1.59484i) q^{53} +10.7362i q^{55} +(2.17819 + 14.0854i) q^{57} +(4.42036 + 7.65628i) q^{59} +(-4.06195 - 2.34517i) q^{61} +(-7.72737 + 1.81322i) q^{63} +(3.15775 + 1.82313i) q^{65} +(-0.187838 - 0.325345i) q^{67} +(5.42275 + 2.10436i) q^{69} +13.9868i q^{71} +(1.13546 + 0.655556i) q^{73} +(-4.77385 + 12.3018i) q^{75} +(6.59987 + 4.51494i) q^{77} +(0.462067 - 0.800324i) q^{79} +(0.809858 + 8.96349i) q^{81} +(5.43209 + 9.40866i) q^{83} +(2.87450 - 4.97877i) q^{85} +(-1.13188 - 7.31938i) q^{87} +(2.35495 + 4.07888i) q^{89} +(2.44867 - 1.17448i) q^{91} +(-1.58443 - 10.2459i) q^{93} +(25.3148 - 14.6155i) q^{95} +(-13.3330 + 7.69782i) q^{97} +(6.11615 - 6.69367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q - 2 * q^7 - 6 * q^9	$ 16 q - 2 q^{7} - 6 q^{9} - 6 q^{13} + 18 q^{15} + 18 q^{17} - 18 q^{21} + 16 q^{25} + 36 q^{27} + 6 q^{29} - 6 q^{31} + 18 q^{33} + 30 q^{35} - 2 q^{37} + 30 q^{39} + 6 q^{41} + 2 q^{43} + 12 q^{45} + 18 q^{47} + 10 q^{49} + 36 q^{53} + 6 q^{57} - 30 q^{59} - 60 q^{61} - 42 q^{63} + 42 q^{65} - 14 q^{67} + 42 q^{69} - 30 q^{75} - 18 q^{77} + 16 q^{79} + 54 q^{81} - 12 q^{85} + 48 q^{87} + 24 q^{89} + 12 q^{91} + 30 q^{93} + 66 q^{95} - 6 q^{97} - 18 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 - 6 * q^9 - 6 * q^13 + 18 * q^15 + 18 * q^17 - 18 * q^21 + 16 * q^25 + 36 * q^27 + 6 * q^29 - 6 * q^31 + 18 * q^33 + 30 * q^35 - 2 * q^37 + 30 * q^39 + 6 * q^41 + 2 * q^43 + 12 * q^45 + 18 * q^47 + 10 * q^49 + 36 * q^53 + 6 * q^57 - 30 * q^59 - 60 * q^61 - 42 * q^63 + 42 * q^65 - 14 * q^67 + 42 * q^69 - 30 * q^75 - 18 * q^77 + 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 + 24 * q^89 + 12 * q^91 + 30 * q^93 + 66 * q^95 - 6 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$2$		0			0
$3$	−0.626615	+	1.61473i	−0.361776	+	0.932265i
$3$	−0.626615	+	1.61473i	−0.361776	+	0.932265i
$4$		0			0
$5$	3.55225			1.58861			0.794307	−	0.607516i	$-0.207834\pi$
$5$	3.55225			1.58861			0.794307	+	0.607516i	$0.207834\pi$
$6$		0			0
$7$	1.49384	−	2.18368i	0.564619	−	0.825352i
$7$	1.49384	−	2.18368i	0.564619	−	0.825352i
$8$		0			0
$9$	−2.21471	−	2.02363i	−0.738236	−	0.674543i
$10$		0			0
$11$			3.02237i			0.911279i	0.890164	+	0.455639i	$0.150589\pi$
$11$			3.02237i			0.911279i	−0.890164	+	0.455639i	$0.849411\pi$
$12$		0			0
$13$	0.888944	+	0.513232i	0.246549	+	0.142345i	0.618183	−	0.786034i	$-0.287869\pi$
$13$	0.888944	+	0.513232i	0.246549	+	0.142345i	−0.371634	+	0.928379i	$0.621202\pi$
$14$		0			0
$15$	−2.22589	+	5.73592i	−0.574723	+	1.48101i
$16$		0			0
$17$	0.809204	−	1.40158i	0.196261	−	0.339934i	−0.751052	−	0.660243i	$-0.770453\pi$
$17$	0.809204	−	1.40158i	0.196261	−	0.339934i	0.947313	+	0.320309i	$0.103787\pi$
$18$		0			0
$19$	7.12643	−	4.11444i	1.63491	−	0.943918i	0.652368	−	0.757903i	$-0.273776\pi$
$19$	7.12643	−	4.11444i	1.63491	−	0.943918i	0.982547	−	0.186016i	$-0.0595575\pi$
$20$		0			0
$21$	2.58998	+	3.78047i	0.565181	+	0.824967i
$22$		0			0
$23$		−	3.35830i		−	0.700254i	−0.936702	−	0.350127i	$-0.886138\pi$
$23$		−	3.35830i		−	0.700254i	0.936702	−	0.350127i	$-0.113862\pi$
$24$		0			0
$25$	7.61848			1.52370
$26$		0			0
$27$	4.65538	−	2.30812i	0.895929	−	0.444198i
$28$		0			0
$29$	−3.70319	+	2.13804i	−0.687666	+	0.397024i	−0.802737	−	0.596333i	$-0.796624\pi$
$29$	−3.70319	+	2.13804i	−0.687666	+	0.397024i	0.115071	+	0.993357i	$0.463290\pi$
$30$		0			0
$31$	−5.18382	+	2.99288i	−0.931041	+	0.537537i	−0.887141	−	0.461499i	$-0.847312\pi$
$31$	−5.18382	+	2.99288i	−0.931041	+	0.537537i	−0.0439006	+	0.999036i	$0.513978\pi$
$32$		0			0
$33$	−4.88031	−	1.89386i	−0.849553	−	0.329679i
$34$		0			0
$35$	5.30650	−	7.75696i	0.896962	−	1.31117i
$36$		0			0
$37$	2.92323	+	5.06319i	0.480577	+	0.832384i	0.999752	−	0.0222846i	$-0.00709398\pi$
$37$	2.92323	+	5.06319i	0.480577	+	0.832384i	−0.519175	+	0.854668i	$0.673761\pi$
$38$		0			0
$39$	−1.38576	+	1.11381i	−0.221899	+	0.178352i
$40$		0			0
$41$	−0.0472226	+	0.0817920i	−0.00737493	+	0.0127738i	−0.869689	−	0.493600i	$-0.835681\pi$
$41$	−0.0472226	+	0.0817920i	−0.00737493	+	0.0127738i	0.862314	+	0.506373i	$0.169014\pi$
$42$		0			0
$43$	−3.05899	−	5.29833i	−0.466492	−	0.807988i	0.532775	−	0.846257i	$-0.321149\pi$
$43$	−3.05899	−	5.29833i	−0.466492	−	0.807988i	−0.999267	+	0.0382684i	$0.987816\pi$
$44$		0			0
$45$	−7.86719	−	7.18843i	−1.17277	−	1.07159i
$46$		0			0
$47$	2.57023	−	4.45176i	0.374906	−	0.649356i	−0.615407	−	0.788210i	$-0.711008\pi$
$47$	2.57023	−	4.45176i	0.374906	−	0.649356i	0.990313	+	0.138853i	$0.0443416\pi$
$48$		0			0
$49$	−2.53687	−	6.52413i	−0.362411	−	0.932019i
$50$		0			0
$51$	1.75612	+	2.18490i	0.245906	+	0.305947i
$52$		0			0
$53$	2.76235	+	1.59484i	0.379438	+	0.219068i	0.677574	−	0.735455i	$-0.263032\pi$
$53$	2.76235	+	1.59484i	0.379438	+	0.219068i	−0.298136	+	0.954523i	$0.596365\pi$
$54$		0			0
$55$			10.7362i			1.44767i
$56$		0			0
$57$	2.17819	+	14.0854i	0.288509	+	1.86566i
$58$		0			0
$59$	4.42036	+	7.65628i	0.575481	+	0.996763i	0.995989	+	0.0894739i	$0.0285186\pi$
$59$	4.42036	+	7.65628i	0.575481	+	0.996763i	−0.420508	+	0.907289i	$0.638148\pi$
$60$		0			0
$61$	−4.06195	−	2.34517i	−0.520080	−	0.300268i	0.216887	−	0.976197i	$-0.430410\pi$
$61$	−4.06195	−	2.34517i	−0.520080	−	0.300268i	−0.736967	+	0.675928i	$0.763743\pi$
$62$		0			0
$63$	−7.72737	+	1.81322i	−0.973557	+	0.228444i
$64$		0			0
$65$	3.15775	+	1.82313i	0.391671	+	0.226131i
$66$		0			0
$67$	−0.187838	−	0.325345i	−0.0229480	−	0.0397472i	0.854323	−	0.519742i	$-0.173972\pi$
$67$	−0.187838	−	0.325345i	−0.0229480	−	0.0397472i	−0.877271	+	0.479995i	$0.840639\pi$
$68$		0			0
$69$	5.42275	+	2.10436i	0.652822	+	0.253335i
$70$		0			0
$71$			13.9868i			1.65993i	0.557815	+	0.829966i	$0.311640\pi$
$71$			13.9868i			1.65993i	−0.557815	+	0.829966i	$0.688360\pi$
$72$		0			0
$73$	1.13546	+	0.655556i	0.132895	+	0.0767270i	0.564974	−	0.825109i	$-0.308886\pi$
$73$	1.13546	+	0.655556i	0.132895	+	0.0767270i	−0.432079	+	0.901836i	$0.642220\pi$
$74$		0			0
$75$	−4.77385	+	12.3018i	−0.551237	+	1.42049i
$76$		0			0
$77$	6.59987	+	4.51494i	0.752125	+	0.514525i
$78$		0			0
$79$	0.462067	−	0.800324i	0.0519866	−	0.0900434i	−0.838861	−	0.544346i	$-0.816778\pi$
$79$	0.462067	−	0.800324i	0.0519866	−	0.0900434i	0.890848	+	0.454302i	$0.150111\pi$
$80$		0			0
$81$	0.809858	+	8.96349i	0.0899842	+	0.995943i
$82$		0			0
$83$	5.43209	+	9.40866i	0.596250	+	1.03273i	0.993369	+	0.114968i	$0.0366765\pi$
$83$	5.43209	+	9.40866i	0.596250	+	1.03273i	−0.397119	+	0.917767i	$0.629990\pi$
$84$		0			0
$85$	2.87450	−	4.97877i	0.311783	−	0.540024i
$86$		0			0
$87$	−1.13188	−	7.31938i	−0.121350	−	0.784720i
$88$		0			0
$89$	2.35495	+	4.07888i	0.249624	+	0.432361i	0.963421	−	0.267991i	$-0.0863598\pi$
$89$	2.35495	+	4.07888i	0.249624	+	0.432361i	−0.713798	+	0.700352i	$0.753026\pi$
$90$		0			0
$91$	2.44867	−	1.17448i	0.256691	−	0.123119i
$92$		0			0
$93$	−1.58443	−	10.2459i	−0.164298	−	1.06245i
$94$		0			0
$95$	25.3148	−	14.6155i	2.59725	−	1.49952i
$96$		0			0
$97$	−13.3330	+	7.69782i	−1.35376	+	0.781595i	−0.988774	−	0.149417i	$-0.952260\pi$
$97$	−13.3330	+	7.69782i	−1.35376	+	0.781595i	−0.364988	+	0.931012i	$0.618927\pi$
$98$		0			0
$99$	6.11615	−	6.69367i	0.614697	−	0.672739i
$100$		0			0
$101$	−13.7047			−1.36367			−0.681833	−	0.731508i	$-0.738817\pi$
$101$	−13.7047			−1.36367			−0.681833	+	0.731508i	$0.738817\pi$
$102$		0			0
$103$			3.04857i			0.300385i	0.988657	+	0.150192i	$0.0479893\pi$
$103$			3.04857i			0.300385i	−0.988657	+	0.150192i	$0.952011\pi$
$104$		0			0
$105$	9.20026	+	13.4292i	0.897854	+	1.31055i
$106$		0			0
$107$	−11.3681	+	6.56336i	−1.09899	+	0.634504i	−0.935956	−	0.352116i	$-0.885462\pi$
$107$	−11.3681	+	6.56336i	−1.09899	+	0.634504i	−0.163037	+	0.986620i	$0.552129\pi$
$108$		0			0
$109$	5.28574	−	9.15516i	0.506282	−	0.876906i	−0.493692	−	0.869637i	$-0.664353\pi$
$109$	5.28574	−	9.15516i	0.506282	−	0.876906i	0.999974	−	0.00726875i	$-0.00231373\pi$
$110$		0			0
$111$	−10.0074	+	1.54756i	−0.949863	+	0.146888i
$112$		0			0
$113$	10.6520	+	6.14993i	1.00205	+	0.578537i	0.908856	−	0.417111i	$-0.136957\pi$
$113$	10.6520	+	6.14993i	1.00205	+	0.578537i	0.0931992	+	0.995647i	$0.470291\pi$
$114$		0			0
$115$		−	11.9295i		−	1.11243i
$116$		0			0
$117$	−0.930160	−	2.93555i	−0.0859934	−	0.271392i
$118$		0			0
$119$	−1.85178	−	3.86078i	−0.169752	−	0.353917i
$120$		0			0
$121$	1.86528			0.169571
$122$		0			0
$123$	−0.102482	−	0.127504i	−0.00924045	−	0.0114966i
$124$		0			0
$125$	9.30148			0.831950
$126$		0			0
$127$	−0.287164			−0.0254817			−0.0127408	−	0.999919i	$-0.504056\pi$
$127$	−0.287164			−0.0254817			−0.0127408	+	0.999919i	$0.504056\pi$
$128$		0			0
$129$	10.4722	−	1.61944i	0.922025	−	0.142583i
$130$		0			0
$131$	−0.372949			−0.0325847			−0.0162923	−	0.999867i	$-0.505186\pi$
$131$	−0.372949			−0.0325847			−0.0162923	+	0.999867i	$0.505186\pi$
$132$		0			0
$133$	1.66114	−	21.7081i	0.144039	−	1.88233i
$134$		0			0
$135$	16.5371	−	8.19902i	1.42329	−	0.705659i
$136$		0			0
$137$		−	7.06222i		−	0.603366i	−0.953408	−	0.301683i	$-0.902451\pi$
$137$		−	7.06222i		−	0.603366i	0.953408	−	0.301683i	$-0.0975485\pi$
$138$		0			0
$139$	−12.6320	−	7.29308i	−1.07143	−	0.618591i	−0.142858	−	0.989743i	$-0.545629\pi$
$139$	−12.6320	−	7.29308i	−1.07143	−	0.618591i	−0.928572	+	0.371152i	$0.878963\pi$
$140$		0			0
$141$	5.57785	+	6.93976i	0.469740	+	0.584434i
$142$		0			0
$143$	−1.55118	+	2.68672i	−0.129716	+	0.224675i
$144$		0			0
$145$	−13.1547	+	7.59485i	−1.09244	+	0.630718i
$146$		0			0
$147$	12.1244	−	0.00824974i	1.00000	−	0.000680427i
$148$		0			0
$149$		−	10.7021i		−	0.876753i	−0.898791	−	0.438376i	$-0.855554\pi$
$149$		−	10.7021i		−	0.876753i	0.898791	−	0.438376i	$-0.144446\pi$
$150$		0			0
$151$	−16.0013			−1.30217			−0.651084	−	0.759006i	$-0.725685\pi$
$151$	−16.0013			−1.30217			−0.651084	+	0.759006i	$0.725685\pi$
$152$		0			0
$153$	−4.62843	+	1.46657i	−0.374187	+	0.118565i
$154$		0			0
$155$	−18.4142	+	10.6315i	−1.47907	+	0.853939i
$156$		0			0
$157$	−9.98239	+	5.76334i	−0.796681	+	0.459964i	−0.842309	−	0.538994i	$-0.818804\pi$
$157$	−9.98239	+	5.76334i	−0.796681	+	0.459964i	0.0456280	+	0.998958i	$0.485471\pi$
$158$		0			0
$159$	−4.30617	+	3.46109i	−0.341501	+	0.274483i
$160$		0			0
$161$	−7.33344	−	5.01677i	−0.577956	−	0.395377i
$162$		0			0
$163$	−1.37386	−	2.37960i	−0.107609	−	0.186385i	0.807192	−	0.590289i	$-0.200986\pi$
$163$	−1.37386	−	2.37960i	−0.107609	−	0.186385i	−0.914801	+	0.403904i	$0.867653\pi$
$164$		0			0
$165$	−17.3361	−	6.72747i	−1.34961	−	0.523733i
$166$		0			0
$167$	−2.76946	+	4.79685i	−0.214307	+	0.371191i	−0.953058	−	0.302788i	$-0.902083\pi$
$167$	−2.76946	+	4.79685i	−0.214307	+	0.371191i	0.738751	+	0.673979i	$0.235416\pi$
$168$		0			0
$169$	−5.97319	−	10.3459i	−0.459476	−	0.795835i
$170$		0			0
$171$	−24.1091	−	5.30895i	−1.84367	−	0.405985i
$172$		0			0
$173$	5.60253	−	9.70387i	0.425953	−	0.737772i	−0.570556	−	0.821259i	$-0.693272\pi$
$173$	5.60253	−	9.70387i	0.425953	−	0.737772i	0.996509	+	0.0834869i	$0.0266057\pi$
$174$		0			0
$175$	11.3808	−	16.6363i	0.860307	−	1.25758i
$176$		0			0
$177$	−15.1327	+	2.34014i	−1.13744	+	0.175896i
$178$		0			0
$179$	−2.37445	−	1.37089i	−0.177475	−	0.102465i	0.408631	−	0.912700i	$-0.366006\pi$
$179$	−2.37445	−	1.37089i	−0.177475	−	0.102465i	−0.586106	+	0.810235i	$0.699340\pi$
$180$		0			0
$181$		−	22.2899i		−	1.65679i	−0.560142	−	0.828397i	$-0.689253\pi$
$181$		−	22.2899i		−	1.65679i	0.560142	−	0.828397i	$-0.310747\pi$
$182$		0			0
$183$	6.33210	−	5.08944i	0.468082	−	0.376222i
$184$		0			0
$185$	10.3841	+	17.9857i	0.763451	+	1.32234i
$186$		0			0
$187$	4.23610	+	2.44571i	0.309774	+	0.178848i
$188$		0			0
$189$	1.91422	−	13.6138i	0.139239	−	0.990259i
$190$		0			0
$191$	−4.44499	−	2.56632i	−0.321628	−	0.185692i	0.330490	−	0.943810i	$-0.392786\pi$
$191$	−4.44499	−	2.56632i	−0.321628	−	0.185692i	−0.652118	+	0.758117i	$0.726119\pi$
$192$		0			0
$193$	−7.99235	−	13.8432i	−0.575302	−	0.996452i	−0.996009	−	0.0892557i	$-0.971551\pi$
$193$	−7.99235	−	13.8432i	−0.575302	−	0.996452i	0.420707	−	0.907197i	$-0.361782\pi$
$194$		0			0
$195$	−4.92256	+	3.95652i	−0.352512	+	0.283332i
$196$		0			0
$197$			4.72572i			0.336694i	0.985728	+	0.168347i	$0.0538428\pi$
$197$			4.72572i			0.336694i	−0.985728	+	0.168347i	$0.946157\pi$
$198$		0			0
$199$	−1.83679	−	1.06047i	−0.130207	−	0.0751749i	0.433482	−	0.901162i	$-0.357285\pi$
$199$	−1.83679	−	1.06047i	−0.130207	−	0.0751749i	−0.563689	+	0.825987i	$0.690618\pi$
$200$		0			0
$201$	0.643046	−	0.0994416i	0.0453569	−	0.00701407i
$202$		0			0
$203$	−0.863200	+	11.2805i	−0.0605848	+	0.791733i
$204$		0			0
$205$	−0.167747	+	0.290545i	−0.0117159	+	0.0202926i
$206$		0			0
$207$	−6.79595	+	7.43765i	−0.472351	+	0.516953i
$208$		0			0
$209$	12.4354	+	21.5387i	0.860173	+	1.48986i
$210$		0			0
$211$	13.8079	−	23.9160i	0.950578	−	1.64645i	0.206399	−	0.978468i	$-0.433826\pi$
$211$	13.8079	−	23.9160i	0.950578	−	1.64645i	0.744179	−	0.667981i	$-0.232841\pi$
$212$		0			0
$213$	−22.5850	−	8.76436i	−1.54750	−	0.600524i
$214$		0			0
$215$	−10.8663	−	18.8210i	−0.741076	−	1.28358i
$216$		0			0
$217$	−1.20833	+	15.7907i	−0.0820267	+	1.07194i
$218$		0			0
$219$	−1.77004	+	1.42267i	−0.119608	+	0.0961354i
$220$		0			0
$221$	1.43867	−	0.830619i	0.0967757	−	0.0558735i
$222$		0			0
$223$	−17.6209	+	10.1734i	−1.17998	+	0.681264i	−0.956011	−	0.293331i	$-0.905236\pi$
$223$	−17.6209	+	10.1734i	−1.17998	+	0.681264i	−0.223973	+	0.974595i	$0.571903\pi$
$224$		0			0
$225$	−16.8727	−	15.4170i	−1.12485	−	1.02780i
$226$		0			0
$227$	4.16000			0.276109			0.138054	−	0.990425i	$-0.455915\pi$
$227$	4.16000			0.276109			0.138054	+	0.990425i	$0.455915\pi$
$228$		0			0
$229$			5.96964i			0.394485i	0.980355	+	0.197242i	$0.0631986\pi$
$229$			5.96964i			0.394485i	−0.980355	+	0.197242i	$0.936801\pi$
$230$		0			0
$231$	−11.4260	+	7.82789i	−0.751775	+	0.515037i
$232$		0			0
$233$	3.88603	−	2.24360i	0.254582	−	0.146983i	−0.367278	−	0.930111i	$-0.619710\pi$
$233$	3.88603	−	2.24360i	0.254582	−	0.146983i	0.621861	+	0.783128i	$0.286377\pi$
$234$		0			0
$235$	9.13009	−	15.8138i	0.595581	−	1.03158i
$236$		0			0
$237$	1.00277	+	1.24761i	0.0651368	+	0.0810409i
$238$		0			0
$239$	3.02944	+	1.74905i	0.195958	+	0.113136i	0.594769	−	0.803897i	$-0.297244\pi$
$239$	3.02944	+	1.74905i	0.195958	+	0.113136i	−0.398811	+	0.917033i	$0.630577\pi$
$240$		0			0
$241$			11.5666i			0.745073i	0.928018	+	0.372537i	$0.121512\pi$
$241$			11.5666i			0.745073i	−0.928018	+	0.372537i	$0.878488\pi$
$242$		0			0
$243$	−14.9811	−	4.30895i	−0.961037	−	0.276419i
$244$		0			0
$245$	−9.01161	−	23.1753i	−0.575731	−	1.48062i
$246$		0			0
$247$	8.44666			0.537448
$248$		0			0
$249$	−18.5963	+	2.87576i	−1.17849	+	0.182244i
$250$		0			0
$251$	26.7426			1.68798			0.843988	−	0.536361i	$-0.180202\pi$
$251$	26.7426			1.68798			0.843988	+	0.536361i	$0.180202\pi$
$252$		0			0
$253$	10.1500			0.638127
$254$		0			0
$255$	6.23817	+	7.76131i	0.390649	+	0.486032i
$256$		0			0
$257$	5.21227			0.325133			0.162566	−	0.986698i	$-0.448023\pi$
$257$	5.21227			0.325133			0.162566	+	0.986698i	$0.448023\pi$
$258$		0			0
$259$	15.4232	+	1.18021i	0.958352	+	0.0733348i
$260$		0			0
$261$	12.5281	+	2.75875i	0.775469	+	0.170763i
$262$		0			0
$263$		−	15.0374i		−	0.927245i	−0.886033	−	0.463622i	$-0.846549\pi$
$263$		−	15.0374i		−	0.927245i	0.886033	−	0.463622i	$-0.153451\pi$
$264$		0			0
$265$	9.81255	+	5.66528i	0.602780	+	0.348015i
$266$		0			0
$267$	−8.06194	+	1.24671i	−0.493383	+	0.0762975i
$268$		0			0
$269$	11.5657	−	20.0323i	0.705170	−	1.22139i	−0.261460	−	0.965214i	$-0.584204\pi$
$269$	11.5657	−	20.0323i	0.705170	−	1.22139i	0.966630	−	0.256177i	$-0.0824628\pi$
$270$		0			0
$271$	−8.58661	+	4.95748i	−0.521599	+	0.301146i	−0.737589	−	0.675250i	$-0.764036\pi$
$271$	−8.58661	+	4.95748i	−0.521599	+	0.301146i	0.215989	+	0.976396i	$0.430702\pi$
$272$		0			0
$273$	0.362089	+	4.68989i	0.0219146	+	0.283845i
$274$		0			0
$275$			23.0259i			1.38851i
$276$		0			0
$277$	−8.59443			−0.516389			−0.258195	−	0.966093i	$-0.583128\pi$
$277$	−8.59443			−0.516389			−0.258195	+	0.966093i	$0.583128\pi$
$278$		0			0
$279$	17.5371	+	3.86177i	1.04992	+	0.231198i
$280$		0			0
$281$	−17.9508	+	10.3639i	−1.07085	+	0.618258i	−0.928415	−	0.371545i	$-0.878828\pi$
$281$	−17.9508	+	10.3639i	−1.07085	+	0.618258i	−0.142440	+	0.989803i	$0.545495\pi$
$282$		0			0
$283$	2.04997	−	1.18355i	0.121858	−	0.0703547i	−0.437832	−	0.899057i	$-0.644254\pi$
$283$	2.04997	−	1.18355i	0.121858	−	0.0703547i	0.559690	+	0.828702i	$0.310920\pi$
$284$		0			0
$285$	7.73748	+	50.0350i	0.458329	+	2.96382i
$286$		0			0
$287$	0.108064	+	0.225303i	0.00637882	+	0.0132992i
$288$		0			0
$289$	7.19038	+	12.4541i	0.422963	+	0.732594i
$290$		0			0
$291$	−4.07524	−	26.3528i	−0.238895	−	1.54483i
$292$		0			0
$293$	−8.83774	+	15.3074i	−0.516306	+	0.894268i	0.483515	+	0.875336i	$0.339360\pi$
$293$	−8.83774	+	15.3074i	−0.516306	+	0.894268i	−0.999821	+	0.0189321i	$0.993973\pi$
$294$		0			0
$295$	15.7022	+	27.1970i	0.914218	+	1.58347i
$296$		0			0
$297$	6.97599	+	14.0703i	0.404788	+	0.816441i
$298$		0			0
$299$	1.72359	−	2.98534i	0.0996777	−	0.172647i
$300$		0			0
$301$	−16.1395	−	1.23502i	−0.930265	−	0.0711855i
$302$		0			0
$303$	8.58755	−	22.1294i	0.493342	−	1.27130i
$304$		0			0
$305$	−14.4291	−	8.33063i	−0.826206	−	0.477011i
$306$		0			0
$307$		−	1.28155i		−	0.0731422i	−0.999331	−	0.0365711i	$-0.988356\pi$
$307$		−	1.28155i		−	0.0731422i	0.999331	−	0.0365711i	$-0.0116435\pi$
$308$		0			0
$309$	−4.92262	−	1.91028i	−0.280038	−	0.108672i
$310$		0			0
$311$	−6.26643	−	10.8538i	−0.355336	−	0.615461i	0.631839	−	0.775100i	$-0.282300\pi$
$311$	−6.26643	−	10.8538i	−0.355336	−	0.615461i	−0.987175	+	0.159639i	$0.948967\pi$
$312$		0			0
$313$	7.58105	+	4.37692i	0.428507	+	0.247398i	0.698710	−	0.715405i	$-0.253758\pi$
$313$	7.58105	+	4.37692i	0.428507	+	0.247398i	−0.270204	+	0.962803i	$0.587091\pi$
$314$		0			0
$315$	−27.4495	+	6.44101i	−1.54661	+	0.362910i
$316$		0			0
$317$	11.8458	+	6.83920i	0.665329	+	0.384128i	0.794304	−	0.607520i	$-0.207836\pi$
$317$	11.8458	+	6.83920i	0.665329	+	0.384128i	−0.128976	+	0.991648i	$0.541169\pi$
$318$		0			0
$319$	−6.46195	−	11.1924i	−0.361799	−	0.626655i
$320$		0			0
$321$	−3.47465	−	22.4691i	−0.193936	−	1.25410i
$322$		0			0
$323$		−	13.3177i		−	0.741017i
$324$		0			0
$325$	6.77240	+	3.91005i	0.375665	+	0.216890i
$326$		0			0
$327$	11.4710	+	14.2718i	0.634348	+	0.789232i
$328$		0			0
$329$	−5.88169	−	12.2628i	−0.324268	−	0.676068i
$330$		0			0
$331$	−5.44858	+	9.43721i	−0.299481	+	0.518716i	−0.976017	−	0.217693i	$-0.930147\pi$
$331$	−5.44858	+	9.43721i	−0.299481	+	0.518716i	0.676536	+	0.736409i	$0.263480\pi$
$332$		0			0
$333$	3.77191	−	17.1290i	0.206699	−	0.938665i
$334$		0			0
$335$	−0.667247	−	1.15570i	−0.0364556	−	0.0631429i
$336$		0			0
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	−0.271496	−	0.962440i	$-0.587518\pi$
$337$	12.8090	−	22.1858i	0.697749	−	1.20854i	0.969245	−	0.246098i	$-0.0791484\pi$
$338$		0			0
$339$	−16.6052	+	13.3465i	−0.901869	+	0.724880i
$340$		0			0
$341$	−9.04559	−	15.6674i	−0.489846	−	0.848438i
$342$		0			0
$343$	−18.0363	−	4.20631i	−0.973867	−	0.227119i
$344$		0			0
$345$	19.2630	+	7.47522i	1.03708	+	0.402452i
$346$		0			0
$347$	−14.5166	+	8.38116i	−0.779291	+	0.449924i	−0.836179	−	0.548457i	$-0.815216\pi$
$347$	−14.5166	+	8.38116i	−0.779291	+	0.449924i	0.0568878	+	0.998381i	$0.481882\pi$
$348$		0			0
$349$	−14.4455	+	8.34010i	−0.773249	+	0.446435i	−0.834032	−	0.551716i	$-0.813973\pi$
$349$	−14.4455	+	8.34010i	−0.773249	+	0.446435i	0.0607835	+	0.998151i	$0.480640\pi$
$350$		0			0
$351$	5.32298	+	0.337503i	0.284119	+	0.0180146i
$352$		0			0
$353$	−35.9137			−1.91149			−0.955746	−	0.294195i	$-0.904949\pi$
$353$	−35.9137			−1.91149			−0.955746	+	0.294195i	$0.904949\pi$
$354$		0			0
$355$			49.6847i			2.63699i
$356$		0			0
$357$	7.39447	−	0.570899i	0.391357	−	0.0302152i
$358$		0			0
$359$	24.7248	−	14.2749i	1.30493	−	0.753399i	0.323681	−	0.946166i	$-0.395079\pi$
$359$	24.7248	−	14.2749i	1.30493	−	0.753399i	0.981245	+	0.192767i	$0.0617461\pi$
$360$		0			0
$361$	24.3573	−	42.1881i	1.28196	−	2.22043i
$362$		0			0
$363$	−1.16881	+	3.01192i	−0.0613467	+	0.158085i
$364$		0			0
$365$	4.03342	+	2.32870i	0.211119	+	0.121890i
$366$		0			0
$367$		−	0.358725i		−	0.0187253i	−0.999956	−	0.00936264i	$-0.997020\pi$
$367$		−	0.358725i		−	0.0187253i	0.999956	−	0.00936264i	$-0.00298026\pi$
$368$		0			0
$369$	0.270101	−	0.0855843i	0.0140609	−	0.00445534i
$370$		0			0
$371$	7.60913	−	3.64963i	0.395046	−	0.189479i
$372$		0			0
$373$	25.3708			1.31365			0.656826	−	0.754042i	$-0.271898\pi$
$373$	25.3708			1.31365			0.656826	+	0.754042i	$0.271898\pi$
$374$		0			0
$375$	−5.82845	+	15.0194i	−0.300980	+	0.775597i
$376$		0			0
$377$	−4.38924			−0.226057
$378$		0			0
$379$	−26.9063			−1.38209			−0.691043	−	0.722814i	$-0.742848\pi$
$379$	−26.9063			−1.38209			−0.691043	+	0.722814i	$0.742848\pi$
$380$		0			0
$381$	0.179941	−	0.463692i	0.00921867	−	0.0237557i
$382$		0			0
$383$	12.5717			0.642385			0.321192	−	0.947014i	$-0.395916\pi$
$383$	12.5717			0.642385			0.321192	+	0.947014i	$0.395916\pi$
$384$		0			0
$385$	23.4444	+	16.0382i	1.19484	+	0.817382i
$386$		0			0
$387$	−3.94708	+	17.9245i	−0.200641	+	0.911155i
$388$		0			0
$389$			16.2587i			0.824351i	0.911105	+	0.412175i	$0.135231\pi$
$389$			16.2587i			0.824351i	−0.911105	+	0.412175i	$0.864769\pi$
$390$		0			0
$391$	−4.70694	−	2.71755i	−0.238040	−	0.137432i
$392$		0			0
$393$	0.233695	−	0.602212i	0.0117884	−	0.0303776i
$394$		0			0
$395$	1.64138	−	2.84295i	0.0825866	−	0.143044i
$396$		0			0
$397$	−12.7252	+	7.34692i	−0.638662	+	0.368732i	−0.784099	−	0.620636i	$-0.786875\pi$
$397$	−12.7252	+	7.34692i	−0.638662	+	0.368732i	0.145437	+	0.989368i	$0.453541\pi$
$398$		0			0
$399$	34.0119	+	16.2849i	1.70272	+	0.815267i
$400$		0			0
$401$			16.6464i			0.831280i	0.909529	+	0.415640i	$0.136442\pi$
$401$			16.6464i			0.831280i	−0.909529	+	0.415640i	$0.863558\pi$
$402$		0			0
$403$	−6.14417			−0.306063
$404$		0			0
$405$	2.87682	+	31.8405i	0.142950	+	1.58217i
$406$		0			0
$407$	−15.3028	+	8.83510i	−0.758534	+	0.437940i
$408$		0			0
$409$	−2.43254	+	1.40443i	−0.120282	+	0.0694446i	−0.558934	−	0.829212i	$-0.688789\pi$
$409$	−2.43254	+	1.40443i	−0.120282	+	0.0694446i	0.438652	+	0.898657i	$0.355456\pi$
$410$		0			0
$411$	11.4036	+	4.42529i	0.562497	+	0.218284i
$412$		0			0
$413$	23.3221	+	1.78465i	1.14761	+	0.0878169i
$414$		0			0
$415$	19.2962	+	33.4219i	0.947211	+	1.64062i
$416$		0			0
$417$	19.6917	−	15.8273i	0.964308	−	0.775066i
$418$		0			0
$419$	7.47362	−	12.9447i	0.365110	−	0.632390i	−0.623684	−	0.781677i	$-0.714365\pi$
$419$	7.47362	−	12.9447i	0.365110	−	0.632390i	0.988794	+	0.149287i	$0.0476980\pi$
$420$		0			0
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	0.610794	−	0.791789i	$-0.290850\pi$
$421$	−7.80336	−	13.5158i	−0.380312	−	0.658720i	−0.991107	+	0.133069i	$0.957517\pi$
$422$		0			0
$423$	−14.7010	+	4.65817i	−0.714788	+	0.226488i
$424$		0			0
$425$	6.16490	−	10.6779i	0.299042	−	0.517955i
$426$		0			0
$427$	−11.1890	+	5.36668i	−0.541474	+	0.259712i
$428$		0			0
$429$	−3.36633	−	4.18827i	−0.162528	−	0.202212i
$430$		0			0
$431$	−14.0087	−	8.08792i	−0.674775	−	0.389581i	0.123109	−	0.992393i	$-0.460714\pi$
$431$	−14.0087	−	8.08792i	−0.674775	−	0.389581i	−0.797883	+	0.602812i	$0.794047\pi$
$432$		0			0
$433$			27.2499i			1.30955i	0.755824	+	0.654774i	$0.227236\pi$
$433$			27.2499i			1.30955i	−0.755824	+	0.654774i	$0.772764\pi$
$434$		0			0
$435$	−4.02072	−	26.0003i	−0.192779	−	1.24662i
$436$		0			0
$437$	−13.8175	−	23.9327i	−0.660983	−	1.14486i
$438$		0			0
$439$	−28.6955	−	16.5674i	−1.36956	−	0.790717i	−0.378690	−	0.925523i	$-0.623625\pi$
$439$	−28.6955	−	16.5674i	−1.36956	−	0.790717i	−0.990872	+	0.134806i	$0.956959\pi$
$440$		0			0
$441$	−7.58398	+	19.5827i	−0.361142	+	0.932511i
$442$		0			0
$443$	−19.2808	−	11.1318i	−0.916060	−	0.528887i	−0.0336837	−	0.999433i	$-0.510724\pi$
$443$	−19.2808	−	11.1318i	−0.916060	−	0.528887i	−0.882376	+	0.470545i	$0.844057\pi$
$444$		0			0
$445$	8.36535	+	14.4892i	0.396556	+	0.686855i
$446$		0			0
$447$	17.2811	+	6.70612i	0.817366	+	0.317188i
$448$		0			0
$449$		−	6.80819i		−	0.321298i	−0.987012	−	0.160649i	$-0.948641\pi$
$449$		−	6.80819i		−	0.321298i	0.987012	−	0.160649i	$-0.0513588\pi$
$450$		0			0
$451$	−0.247206	−	0.142724i	−0.0116405	−	0.00672062i
$452$		0			0
$453$	10.0267	−	25.8378i	0.471093	−	1.21396i
$454$		0			0
$455$	8.69830	−	4.17204i	0.407783	−	0.195588i
$456$		0			0
$457$	−7.61298	+	13.1861i	−0.356120	+	0.616818i	−0.987309	−	0.158811i	$-0.949234\pi$
$457$	−7.61298	+	13.1861i	−0.356120	+	0.616818i	0.631189	+	0.775629i	$0.282567\pi$
$458$		0			0
$459$	0.532134	−	8.39264i	0.0248379	−	0.391735i
$460$		0			0
$461$	−0.103381	−	0.179060i	−0.00481492	−	0.00833968i	0.863608	−	0.504164i	$-0.168199\pi$
$461$	−0.103381	−	0.179060i	−0.00481492	−	0.00833968i	−0.868423	+	0.495824i	$0.834866\pi$
$462$		0			0
$463$	7.60217	−	13.1673i	0.353303	−	0.611938i	−0.633523	−	0.773724i	$-0.718392\pi$
$463$	7.60217	−	13.1673i	0.353303	−	0.611938i	0.986826	+	0.161785i	$0.0517253\pi$
$464$		0			0
$465$	−5.62831	−	36.3958i	−0.261006	−	1.68782i
$466$		0			0
$467$	1.15424	+	1.99921i	0.0534120	+	0.0925123i	0.891495	−	0.453030i	$-0.149657\pi$
$467$	1.15424	+	1.99921i	0.0534120	+	0.0925123i	−0.838083	+	0.545542i	$0.816324\pi$
$468$		0			0
$469$	−0.991047	−	0.0758366i	−0.0457623	−	0.00350181i
$470$		0			0
$471$	−3.05112	−	19.7303i	−0.140588	−	0.909122i
$472$		0			0
$473$	16.0135	−	9.24541i	0.736303	−	0.425105i
$474$		0			0
$475$	54.2925	−	31.3458i	2.49111	−	1.43824i
$476$		0			0
$477$	−2.89042	−	9.12207i	−0.132343	−	0.417671i
$478$		0			0
$479$	−12.4332			−0.568086			−0.284043	−	0.958812i	$-0.591676\pi$
$479$	−12.4332			−0.568086			−0.284043	+	0.958812i	$0.591676\pi$
$480$		0			0
$481$			6.00119i			0.273631i
$482$		0			0
$483$	12.6960	−	8.69794i	0.577687	−	0.395770i
$484$		0			0
$485$	−47.3622	+	27.3446i	−2.15061	+	1.24165i
$486$		0			0
$487$	18.6503	−	32.3033i	0.845128	−	1.46380i	−0.0403829	−	0.999184i	$-0.512858\pi$
$487$	18.6503	−	32.3033i	0.845128	−	1.46380i	0.885510	−	0.464620i	$-0.153809\pi$
$488$		0			0
$489$	4.70330	−	0.727325i	0.212690	−	0.0328908i
$490$		0			0
$491$	11.8191	+	6.82377i	0.533389	+	0.307952i	0.742396	−	0.669962i	$-0.233690\pi$
$491$	11.8191	+	6.82377i	0.533389	+	0.307952i	−0.209006	+	0.977914i	$0.567023\pi$
$492$		0			0
$493$			6.92044i			0.311681i
$494$		0			0
$495$	21.7261	−	23.7776i	0.976516	−	1.06872i
$496$		0			0
$497$	30.5427	+	20.8941i	1.37003	+	0.937229i
$498$		0			0
$499$	21.0019			0.940175			0.470088	−	0.882620i	$-0.344222\pi$
$499$	21.0019			0.940175			0.470088	+	0.882620i	$0.344222\pi$
$500$		0			0
$501$	−6.01023	−	7.47771i	−0.268517	−	0.334079i
$502$		0			0
$503$	−22.3018			−0.994388			−0.497194	−	0.867639i	$-0.665636\pi$
$503$	−22.3018			−0.994388			−0.497194	+	0.867639i	$0.665636\pi$
$504$		0			0
$505$	−48.6824			−2.16634
$506$		0			0
$507$	20.4487	−	3.16221i	0.908157	−	0.140439i
$508$		0			0
$509$	−21.9179			−0.971493			−0.485746	−	0.874100i	$-0.661452\pi$
$509$	−21.9179			−0.971493			−0.485746	+	0.874100i	$0.661452\pi$
$510$		0			0
$511$	3.12771	−	1.50017i	0.138362	−	0.0663636i
$512$		0			0
$513$	23.6796	−	35.6030i	1.04548	−	1.57191i
$514$		0			0
$515$			10.8293i			0.477196i
$516$		0			0
$517$	13.4549	+	7.76818i	0.591745	+	0.341644i
$518$		0			0
$519$	12.1585	+	15.1272i	0.533699	+	0.664009i
$520$		0			0
$521$	−13.3839	+	23.1816i	−0.586358	+	1.01560i	0.408346	+	0.912827i	$0.366106\pi$
$521$	−13.3839	+	23.1816i	−0.586358	+	1.01560i	−0.994705	+	0.102775i	$0.967228\pi$
$522$		0			0
$523$	−14.8576	+	8.57805i	−0.649678	+	0.375092i	−0.788333	−	0.615249i	$-0.789055\pi$
$523$	−14.8576	+	8.57805i	−0.649678	+	0.375092i	0.138655	+	0.990341i	$0.455722\pi$
$524$		0			0
$525$	19.7317	+	28.8015i	0.861163	+	1.25700i
$526$		0			0
$527$			9.68740i			0.421990i
$528$		0			0
$529$	11.7218			0.509644
$530$		0			0
$531$	5.70367	−	25.9016i	0.247518	−	1.12403i
$532$		0			0
$533$	−0.0839566	+	0.0484723i	−0.00363656	+	0.00209957i
$534$		0			0
$535$	−40.3822	+	23.3147i	−1.74588	+	1.00798i
$536$		0			0
$537$	3.70149	−	2.97508i	0.159731	−	0.128384i
$538$		0			0
$539$	19.7183	−	7.66737i	0.849329	−	0.330257i
$540$		0			0
$541$	−14.4091	−	24.9573i	−0.619496	−	1.07300i	−0.989578	−	0.144000i	$-0.954004\pi$
$541$	−14.4091	−	24.9573i	−0.619496	−	1.07300i	0.370081	−	0.928999i	$-0.379330\pi$
$542$		0			0
$543$	35.9921	+	13.9672i	1.54457	+	0.599389i
$544$		0			0
$545$	18.7763	−	32.5214i	0.804286	−	1.39306i
$546$		0			0
$547$	16.4045	+	28.4135i	0.701407	+	1.21487i	0.967972	+	0.251056i	$0.0807779\pi$
$547$	16.4045	+	28.4135i	0.701407	+	1.21487i	−0.266565	+	0.963817i	$0.585889\pi$
$548$		0			0
$549$	4.25029	+	13.4138i	0.181398	+	0.572485i
$550$		0			0
$551$	−17.5937	+	30.4732i	−0.749516	+	1.29820i
$552$		0			0
$553$	−1.05739	−	2.20456i	−0.0449649	−	0.0937475i
$554$		0			0
$555$	−35.5489	+	5.49733i	−1.50897	+	0.233349i
$556$		0			0
$557$	40.0544	+	23.1254i	1.69716	+	0.979855i	0.948434	+	0.316975i	$0.102667\pi$
$557$	40.0544	+	23.1254i	1.69716	+	0.979855i	0.748725	+	0.662880i	$0.230666\pi$
$558$		0			0
$559$		−	6.27990i		−	0.265611i
$560$		0			0
$561$	−6.60357	+	5.30764i	−0.278803	+	0.224089i
$562$		0			0
$563$	−0.988637	−	1.71237i	−0.0416661	−	0.0721678i	0.844440	−	0.535650i	$-0.179933\pi$
$563$	−0.988637	−	1.71237i	−0.0416661	−	0.0721678i	−0.886106	+	0.463482i	$0.846600\pi$
$564$		0			0
$565$	37.8385	+	21.8461i	1.59188	+	0.919071i
$566$		0			0
$567$	20.7831	+	11.6216i	0.872810	+	0.488060i
$568$		0			0
$569$	−28.5702	−	16.4950i	−1.19773	−	0.691508i	−0.237679	−	0.971344i	$-0.576387\pi$
$569$	−28.5702	−	16.4950i	−1.19773	−	0.691508i	−0.960048	+	0.279836i	$0.909720\pi$
$570$		0			0
$571$	7.40326	+	12.8228i	0.309817	+	0.536618i	0.978322	−	0.207089i	$-0.0663989\pi$
$571$	7.40326	+	12.8228i	0.309817	+	0.536618i	−0.668505	+	0.743707i	$0.733066\pi$
$572$		0			0
$573$	6.92921	−	5.56937i	0.289472	−	0.232664i
$574$		0			0
$575$		−	25.5851i		−	1.06697i
$576$		0			0
$577$	−15.9505	−	9.20901i	−0.664027	−	0.383376i	0.129783	−	0.991542i	$-0.458572\pi$
$577$	−15.9505	−	9.20901i	−0.664027	−	0.383376i	−0.793810	+	0.608166i	$0.791905\pi$
$578$		0			0
$579$	27.3611	−	4.23116i	1.13709	−	0.175841i
$580$		0			0
$581$	28.6602	+	2.19312i	1.18902	+	0.0909861i
$582$		0			0
$583$	−4.82020	+	8.34884i	−0.199632	+	0.345774i
$584$		0			0
$585$	−3.30416	−	10.4278i	−0.136610	−	0.431137i
$586$		0			0
$587$	23.1065	+	40.0216i	0.953707	+	1.65187i	0.737301	+	0.675565i	$0.236100\pi$
$587$	23.1065	+	40.0216i	0.953707	+	1.65187i	0.216406	+	0.976304i	$0.430567\pi$
$588$		0			0
$589$	−24.6281	+	42.6571i	−1.01478	+	1.75765i
$590$		0			0
$591$	−7.63076	−	2.96121i	−0.313888	−	0.121808i
$592$		0			0
$593$	−6.80465	−	11.7860i	−0.279434	−	0.483993i	0.691810	−	0.722079i	$-0.256813\pi$
$593$	−6.80465	−	11.7860i	−0.279434	−	0.483993i	−0.971244	+	0.238086i	$0.923480\pi$
$594$		0			0
$595$	−6.57798	−	13.7145i	−0.269671	−	0.562238i
$596$		0			0
$597$	2.86334	−	2.30142i	0.117189	−	0.0941907i
$598$		0			0
$599$	−20.4214	+	11.7903i	−0.834396	+	0.481739i	−0.855355	−	0.518042i	$-0.826661\pi$
$599$	−20.4214	+	11.7903i	−0.834396	+	0.481739i	0.0209595	+	0.999780i	$0.493328\pi$
$600$		0			0
$601$	31.0765	−	17.9420i	1.26764	−	0.731871i	0.293097	−	0.956083i	$-0.405314\pi$
$601$	31.0765	−	17.9420i	1.26764	−	0.731871i	0.974540	+	0.224212i	$0.0719808\pi$
$602$		0			0
$603$	−0.242371	+	1.10066i	−0.00987010	+	0.0448222i
$604$		0			0
$605$	6.62594			0.269383
$606$		0			0
$607$		−	19.4569i		−	0.789732i	−0.918739	−	0.394866i	$-0.870791\pi$
$607$		−	19.4569i		−	0.789732i	0.918739	−	0.394866i	$-0.129209\pi$
$608$		0			0
$609$	−17.6740	−	8.46234i	−0.716187	−	0.342911i
$610$		0			0
$611$	4.56958	−	2.63825i	0.184865	−	0.106732i
$612$		0			0
$613$	−21.1210	+	36.5827i	−0.853071	+	1.47756i	0.0253526	+	0.999679i	$0.491929\pi$
$613$	−21.1210	+	36.5827i	−0.853071	+	1.47756i	−0.878423	+	0.477883i	$0.841404\pi$
$614$		0			0
$615$	−0.364040	−	0.452926i	−0.0146795	−	0.0182637i
$616$		0			0
$617$	9.63660	+	5.56369i	0.387955	+	0.223986i	0.681274	−	0.732029i	$-0.261426\pi$
$617$	9.63660	+	5.56369i	0.387955	+	0.223986i	−0.293319	+	0.956015i	$0.594760\pi$
$618$		0			0
$619$		−	10.0619i		−	0.404422i	−0.979342	−	0.202211i	$-0.935187\pi$
$619$		−	10.0619i		−	0.404422i	0.979342	−	0.202211i	$-0.0648127\pi$
$620$		0			0
$621$	−7.75136	−	15.6342i	−0.311051	−	0.627378i
$622$		0			0
$623$	12.4249	+	0.950773i	0.497792	+	0.0380919i
$624$		0			0
$625$	−5.05121			−0.202048
$626$		0			0
$627$	−42.5714	+	6.58330i	−1.70014	+	0.262912i
$628$		0			0
$629$	9.46198			0.377274
$630$		0			0
$631$	−10.3528			−0.412139			−0.206070	−	0.978537i	$-0.566067\pi$
$631$	−10.3528			−0.412139			−0.206070	+	0.978537i	$0.566067\pi$
$632$		0			0
$633$	29.9657	+	37.2822i	1.19103	+	1.48184i
$634$		0			0
$635$	−1.02008			−0.0404806
$636$		0			0
$637$	1.09325	−	7.10159i	0.0433163	−	0.281375i
$638$		0			0
$639$	28.3041	−	30.9767i	1.11969	−	1.22542i
$640$		0			0
$641$			26.6364i			1.05207i	0.850461	+	0.526037i	$0.176323\pi$
$641$			26.6364i			1.05207i	−0.850461	+	0.526037i	$0.823677\pi$
$642$		0			0
$643$	40.0493	+	23.1225i	1.57939	+	0.911861i	0.994944	+	0.100429i	$0.0320214\pi$
$643$	40.0493	+	23.1225i	1.57939	+	0.911861i	0.584446	+	0.811433i	$0.301312\pi$
$644$		0			0
$645$	37.1998	−	5.75264i	1.46474	−	0.226510i
$646$		0			0
$647$	−15.7032	+	27.1987i	−0.617355	+	1.06929i	0.372611	+	0.927988i	$0.378463\pi$
$647$	−15.7032	+	27.1987i	−0.617355	+	1.06929i	−0.989966	+	0.141303i	$0.954871\pi$
$648$		0			0
$649$	−23.1401	+	13.3600i	−0.908329	+	0.524424i
$650$		0			0
$651$	−24.7405	−	11.8458i	−0.969657	−	0.464273i
$652$		0			0
$653$			46.1464i			1.80585i	0.429801	+	0.902924i	$0.358584\pi$
$653$			46.1464i			1.80585i	−0.429801	+	0.902924i	$0.641416\pi$
$654$		0			0
$655$	−1.32481			−0.0517645
$656$		0			0
$657$	−1.18810	−	3.74960i	−0.0463522	−	0.146286i
$658$		0			0
$659$	−1.18052	+	0.681575i	−0.0459867	+	0.0265504i	−0.522817	−	0.852445i	$-0.675119\pi$
$659$	−1.18052	+	0.681575i	−0.0459867	+	0.0265504i	0.476830	+	0.878995i	$0.341786\pi$
$660$		0			0
$661$	6.23888	−	3.60202i	0.242664	−	0.140102i	−0.373736	−	0.927535i	$-0.621924\pi$
$661$	6.23888	−	3.60202i	0.242664	−	0.140102i	0.616401	+	0.787433i	$0.288590\pi$
$662$		0			0
$663$	0.439731	+	2.84355i	0.0170777	+	0.110434i
$664$		0			0
$665$	5.90080	−	77.1127i	0.228823	−	2.99030i
$666$		0			0
$667$	7.18018	+	12.4364i	0.278018	+	0.481541i
$668$		0			0
$669$	−5.38584	−	34.8279i	−0.208228	−	1.34652i
$670$		0			0
$671$	7.08797	−	12.2767i	0.273628	−	0.473938i
$672$		0			0
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	0.947558	+	0.319585i	$0.103544\pi$
$673$	19.4709	+	33.7246i	0.750548	+	1.29999i	−0.197010	+	0.980402i	$0.563123\pi$
$674$		0			0
$675$	35.4669	−	17.5844i	1.36512	−	0.676822i
$676$		0			0
$677$	1.20505	−	2.08722i	0.0463140	−	0.0802182i	−0.841939	−	0.539573i	$-0.818586\pi$
$677$	1.20505	−	2.08722i	0.0463140	−	0.0802182i	0.888253	+	0.459354i	$0.151919\pi$
$678$		0			0
$679$	−3.10788	+	40.6143i	−0.119269	+	1.55863i
$680$		0			0
$681$	−2.60672	+	6.71727i	−0.0998896	+	0.257407i
$682$		0			0
$683$	24.5302	+	14.1625i	0.938624	+	0.541915i	0.889529	−	0.456879i	$-0.151033\pi$
$683$	24.5302	+	14.1625i	0.938624	+	0.541915i	0.0490952	+	0.998794i	$0.484366\pi$
$684$		0			0
$685$		−	25.0868i		−	0.958517i
$686$		0			0
$687$	−9.63935	−	3.74066i	−0.367764	−	0.142715i
$688$		0			0
$689$	1.63705	+	2.83545i	0.0623666	+	0.108022i
$690$		0			0
$691$	2.95334	+	1.70511i	0.112350	+	0.0648655i	0.555122	−	0.831769i	$-0.312672\pi$
$691$	2.95334	+	1.70511i	0.112350	+	0.0648655i	−0.442772	+	0.896634i	$0.646005\pi$
$692$		0			0
$693$	−5.48023	−	23.3550i	−0.208177	−	0.887182i
$694$		0			0
$695$	−44.8719	−	25.9068i	−1.70209	−	0.982702i
$696$		0			0
$697$	0.0764255	+	0.132373i	0.00289482	+	0.00501398i
$698$		0			0
$699$	1.18776	+	7.68076i	0.0449254	+	0.290513i
$700$		0			0
$701$		−	51.4943i		−	1.94491i	−0.233087	−	0.972456i	$-0.574883\pi$
$701$		−	51.4943i		−	1.94491i	0.233087	−	0.972456i	$-0.425117\pi$
$702$		0			0
$703$	41.6644	+	24.0550i	1.57140	+	0.907251i
$704$		0			0
$705$	19.8139	+	24.6518i	0.746236	+	0.928439i
$706$		0			0
$707$	−20.4726	+	29.9266i	−0.769952	+	1.12550i
$708$		0			0
$709$	−5.04218	+	8.73331i	−0.189363	+	0.327986i	−0.945038	−	0.326960i	$-0.893976\pi$
$709$	−5.04218	+	8.73331i	−0.189363	+	0.327986i	0.755675	+	0.654947i	$0.227309\pi$
$710$		0			0
$711$	−2.64290	+	0.837431i	−0.0991165	+	0.0314061i
$712$		0			0
$713$	10.0510	+	17.4088i	0.376412	+	0.651965i
$714$		0			0
$715$	−5.51017	+	9.54389i	−0.206069	+	0.356921i
$716$		0			0
$717$	−4.72253	+	3.79575i	−0.176366	+	0.141755i
$718$		0			0
$719$	−15.9584	−	27.6408i	−0.595148	−	1.03083i	−0.993526	−	0.113605i	$-0.963760\pi$
$719$	−15.9584	−	27.6408i	−0.595148	−	1.03083i	0.398378	−	0.917221i	$-0.369573\pi$
$720$		0			0
$721$	6.65709	+	4.55409i	0.247923	+	0.169603i
$722$		0			0
$723$	−18.6770	−	7.24783i	−0.694605	−	0.269550i
$724$		0			0
$725$	−28.2127	+	16.2886i	−1.04779	+	0.604943i
$726$		0			0
$727$	−17.9336	+	10.3540i	−0.665120	+	0.384007i	−0.794225	−	0.607624i	$-0.792123\pi$
$727$	−17.9336	+	10.3540i	−0.665120	+	0.384007i	0.129105	+	0.991631i	$0.458790\pi$
$728$		0			0
$729$	16.3452	−	21.4904i	0.605377	−	0.795939i
$730$		0			0
$731$	−9.90141			−0.366217
$732$		0			0
$733$		−	8.89115i		−	0.328402i	−0.986427	−	0.164201i	$-0.947495\pi$
$733$		−	8.89115i		−	0.328402i	0.986427	−	0.164201i	$-0.0525046\pi$
$734$		0			0
$735$	43.0687	−	0.0293051i	1.58861	−	0.00108094i
$736$		0			0
$737$	0.983312	−	0.567715i	0.0362207	−	0.0209121i
$738$		0			0
$739$	16.3882	−	28.3851i	0.602848	−	1.04416i	−0.389539	−	0.921010i	$-0.627366\pi$
$739$	16.3882	−	28.3851i	0.602848	−	1.04416i	0.992388	−	0.123154i	$-0.0393010\pi$
$740$		0			0
$741$	−5.29280	+	13.6391i	−0.194436	+	0.501044i
$742$		0			0
$743$	6.68055	+	3.85702i	0.245086	+	0.141500i	0.617512	−	0.786562i	$-0.288141\pi$
$743$	6.68055	+	3.85702i	0.245086	+	0.141500i	−0.372426	+	0.928062i	$0.621474\pi$
$744$		0			0
$745$		−	38.0166i		−	1.39282i
$746$		0			0
$747$	7.00914	−	31.8300i	0.256451	−	1.16460i
$748$		0			0
$749$	−2.64986	+	34.6288i	−0.0968236	+	1.26531i
$750$		0			0
$751$	−30.7608			−1.12248			−0.561239	−	0.827654i	$-0.689675\pi$
$751$	−30.7608			−1.12248			−0.561239	+	0.827654i	$0.689675\pi$
$752$		0			0
$753$	−16.7573	+	43.1821i	−0.610670	+	1.57364i
$754$		0			0
$755$	−56.8406			−2.06864
$756$		0			0
$757$	46.4611			1.68866			0.844328	−	0.535827i	$-0.180000\pi$
$757$	46.4611			1.68866			0.844328	+	0.535827i	$0.180000\pi$
$758$		0			0
$759$	−6.36016	+	16.3896i	−0.230859	+	0.594903i
$760$		0			0
$761$	−37.1917			−1.34820			−0.674099	−	0.738641i	$-0.735468\pi$
$761$	−37.1917			−1.34820			−0.674099	+	0.738641i	$0.735468\pi$
$762$		0			0
$763$	−12.0958	−	25.2187i	−0.437899	−	0.912978i
$764$		0			0
$765$	−16.4413	+	5.20961i	−0.594438	+	0.188354i
$766$		0			0
$767$			9.07468i			0.327668i
$768$		0			0
$769$	12.2312	+	7.06166i	0.441067	+	0.254650i	0.704050	−	0.710150i	$-0.251373\pi$
$769$	12.2312	+	7.06166i	0.441067	+	0.254650i	−0.262983	+	0.964800i	$0.584706\pi$
$770$		0			0
$771$	−3.26609	+	8.41642i	−0.117625	+	0.303110i
$772$		0			0
$773$	−15.4728	+	26.7996i	−0.556517	+	0.963915i	0.441267	+	0.897376i	$0.354529\pi$
$773$	−15.4728	+	26.7996i	−0.556517	+	0.963915i	−0.997784	+	0.0665393i	$0.978804\pi$
$774$		0			0
$775$	−39.4928	+	22.8012i	−1.41862	+	0.819043i
$776$		0			0
$777$	−11.5701	+	24.1648i	−0.415076	+	0.866907i
$778$		0			0
$779$			0.777179i			0.0278453i
$780$		0			0
$781$	−42.2734			−1.51266
$782$		0			0
$783$	−12.3049	+	18.5008i	−0.439742	+	0.661165i
$784$		0			0
$785$	−35.4599	+	20.4728i	−1.26562	+	0.730706i
$786$		0			0
$787$	15.8704	−	9.16280i	0.565720	−	0.326619i	−0.189718	−	0.981839i	$-0.560757\pi$
$787$	15.8704	−	9.16280i	0.565720	−	0.326619i	0.755438	+	0.655220i	$0.227424\pi$
$788$		0			0
$789$	24.2813	+	9.42265i	0.864438	+	0.335455i
$790$		0			0
$791$	29.3418	−	14.0735i	1.04328	−	0.500395i
$792$		0			0
$793$	−2.40723	−	4.16945i	−0.0854834	−	0.148062i
$794$		0			0
$795$	−15.2966	+	12.2947i	−0.542514	+	0.436047i
$796$		0			0
$797$	1.07681	−	1.86508i	0.0381424	−	0.0660646i	−0.846324	−	0.532668i	$-0.821189\pi$
$797$	1.07681	−	1.86508i	0.0381424	−	0.0660646i	0.884466	+	0.466604i	$0.154523\pi$
$798$		0			0
$799$	−4.15968	−	7.20477i	−0.147159	−	0.254886i
$800$		0			0
$801$	3.03863	−	13.7991i	0.107365	−	0.487566i
$802$		0			0
$803$	−1.98133	+	3.43177i	−0.0699197	+	0.121104i
$804$		0			0
$805$	−26.0502	−	17.8208i	−0.918149	−	0.628101i
$806$		0			0
$807$	25.0996	+	31.2280i	0.883546	+	1.09928i
$808$		0			0
$809$	−17.0147	−	9.82342i	−0.598204	−	0.345373i	0.170131	−	0.985421i	$-0.445581\pi$
$809$	−17.0147	−	9.82342i	−0.598204	−	0.345373i	−0.768335	+	0.640048i	$0.778914\pi$
$810$		0			0
$811$			12.3340i			0.433105i	0.976271	+	0.216552i	$0.0694812\pi$
$811$			12.3340i			0.433105i	−0.976271	+	0.216552i	$0.930519\pi$
$812$		0			0
$813$	−2.62450	−	16.9715i	−0.0920452	−	0.595216i
$814$		0			0
$815$	−4.88030	−	8.45293i	−0.170950	−	0.296093i
$816$		0			0
$817$	−43.5994	−	25.1721i	−1.52535	−	0.880661i
$818$		0			0
$819$	−7.79980	−	2.35408i	−0.272547	−	0.0822583i
$820$		0			0
$821$	−19.3763	−	11.1869i	−0.676238	−	0.390426i	0.122198	−	0.992506i	$-0.461006\pi$
$821$	−19.3763	−	11.1869i	−0.676238	−	0.390426i	−0.798436	+	0.602079i	$0.794339\pi$
$822$		0			0
$823$	13.5033	+	23.3883i	0.470694	+	0.815266i	0.999438	−	0.0335154i	$-0.0106703\pi$
$823$	13.5033	+	23.3883i	0.470694	+	0.815266i	−0.528744	+	0.848781i	$0.677337\pi$
$824$		0			0
$825$	−37.1805	−	14.4283i	−1.29446	−	0.502330i
$826$		0			0
$827$		−	26.3189i		−	0.915196i	−0.889159	−	0.457598i	$-0.848710\pi$
$827$		−	26.3189i		−	0.915196i	0.889159	−	0.457598i	$-0.151290\pi$
$828$		0			0
$829$	28.8691	+	16.6676i	1.00266	+	0.578888i	0.909035	−	0.416719i	$-0.136820\pi$
$829$	28.8691	+	16.6676i	1.00266	+	0.578888i	0.0936287	+	0.995607i	$0.470153\pi$
$830$		0			0
$831$	5.38540	−	13.8777i	0.186817	−	0.481412i
$832$		0			0
$833$	−11.1970	−	1.72371i	−0.387952	−	0.0597232i
$834$		0			0
$835$	−9.83781	+	17.0396i	−0.340452	+	0.589679i
$836$		0			0
$837$	−17.2247	+	25.8979i	−0.595374	+	0.895161i
$838$		0			0
$839$	−18.6896	−	32.3713i	−0.645236	−	1.11758i	−0.984247	−	0.176799i	$-0.943426\pi$
$839$	−18.6896	−	32.3713i	−0.645236	−	1.11758i	0.339011	−	0.940782i	$-0.389908\pi$
$840$		0			0
$841$	−5.35758	+	9.27960i	−0.184744	+	0.319986i
$842$		0			0
$843$	−5.48666	−	35.4799i	−0.188971	−	1.22199i
$844$		0			0
$845$	−21.2182	−	36.7511i	−0.729930	−	1.26428i
$846$		0			0
$847$	2.78643	−	4.07316i	0.0957429	−	0.139956i
$848$		0			0
$849$	0.626573	+	4.05177i	0.0215039	+	0.139057i
$850$		0			0
$851$	17.0037	−	9.81710i	0.582880	−	0.336526i
$852$		0			0
$853$	4.65798	−	2.68929i	0.159486	−	0.0920795i	−0.418133	−	0.908386i	$-0.637315\pi$
$853$	4.65798	−	2.68929i	0.159486	−	0.0920795i	0.577619	+	0.816306i	$0.303982\pi$
$854$		0			0
$855$	−85.6414	−	18.8587i	−2.92887	−	0.644954i
$856$		0			0
$857$	45.4000			1.55084			0.775418	−	0.631448i	$-0.217539\pi$
$857$	45.4000			1.55084			0.775418	+	0.631448i	$0.217539\pi$
$858$		0			0
$859$			3.88281i			0.132480i	0.997804	+	0.0662399i	$0.0211003\pi$
$859$			3.88281i			0.132480i	−0.997804	+	0.0662399i	$0.978900\pi$
$860$		0			0
$861$	−0.431518	+	0.0333159i	−0.0147061	+	0.00113540i
$862$		0			0
$863$	−20.3332	+	11.7394i	−0.692152	+	0.399614i	−0.804418	−	0.594064i	$-0.797522\pi$
$863$	−20.3332	+	11.7394i	−0.692152	+	0.399614i	0.112266	+	0.993678i	$0.464189\pi$
$864$		0			0
$865$	19.9016	−	34.4706i	0.676674	−	1.17203i
$866$		0			0
$867$	−24.6156	+	3.80660i	−0.835990	+	0.129279i
$868$		0			0
$869$	2.41887	+	1.39654i	0.0820547	+	0.0473743i
$870$		0			0
$871$		−	0.385618i		−	0.0130662i
$872$		0			0
$873$	45.1062	+	9.93264i	1.52662	+	0.336169i
$874$		0			0
$875$	13.8949	−	20.3114i	0.469735	−	0.686651i
$876$		0			0
$877$	32.9591			1.11295			0.556475	−	0.830864i	$-0.312153\pi$
$877$	32.9591			1.11295			0.556475	+	0.830864i	$0.312153\pi$
$878$		0			0
$879$	−19.1795	−	23.8624i	−0.646908	−	0.804859i
$880$		0			0
$881$	−7.44403			−0.250796			−0.125398	−	0.992107i	$-0.540021\pi$
$881$	−7.44403			−0.250796			−0.125398	+	0.992107i	$0.540021\pi$
$882$		0			0
$883$	28.2839			0.951828			0.475914	−	0.879492i	$-0.342117\pi$
$883$	28.2839			0.951828			0.475914	+	0.879492i	$0.342117\pi$
$884$		0			0
$885$	−53.7551	+	8.31277i	−1.80696	+	0.279431i
$886$		0			0
$887$	−12.1275			−0.407203			−0.203602	−	0.979054i	$-0.565265\pi$
$887$	−12.1275			−0.407203			−0.203602	+	0.979054i	$0.565265\pi$
$888$		0			0
$889$	−0.428977	+	0.627073i	−0.0143874	+	0.0210313i
$890$		0			0
$891$	−27.0910	+	2.44769i	−0.907582	+	0.0820007i
$892$		0			0
$893$		−	42.3002i		−	1.41552i
$894$		0			0
$895$	−8.43465	−	4.86975i	−0.281939	−	0.162778i
$896$		0			0
$897$	3.74050	+	4.65379i	0.124892	+	0.155385i
$898$		0			0
$899$	12.7978	−	22.1664i	0.426830	−	0.739291i
$900$		0			0
$901$	4.47061	−	2.58111i	0.148938	−	0.0859891i
$902$		0			0
$903$	12.1075	−	25.2870i	0.402912	−	0.841500i
$904$		0			0
$905$		−	79.1792i		−	2.63201i
$906$		0			0
$907$	46.1780			1.53331			0.766657	−	0.642057i	$-0.221919\pi$
$907$	46.1780			1.53331			0.766657	+	0.642057i	$0.221919\pi$
$908$		0			0
$909$	30.3518	+	27.7332i	1.00671	+	0.919851i
$910$		0			0
$911$	12.7284	−	7.34874i	0.421710	−	0.243475i	−0.274098	−	0.961702i	$-0.588379\pi$
$911$	12.7284	−	7.34874i	0.421710	−	0.243475i	0.695809	+	0.718227i	$0.255046\pi$
$912$		0			0
$913$	−28.4365	+	16.4178i	−0.941110	+	0.543350i
$914$		0			0
$915$	22.4932	−	18.0790i	0.743602	−	0.597672i
$916$		0			0
$917$	−0.557126	+	0.814399i	−0.0183979	+	0.0268938i
$918$		0			0
$919$	12.9345	+	22.4033i	0.426671	+	0.739015i	0.996575	−	0.0826958i	$-0.0263530\pi$
$919$	12.9345	+	22.4033i	0.426671	+	0.739015i	−0.569904	+	0.821711i	$0.693020\pi$
$920$		0			0
$921$	2.06936	+	0.803041i	0.0681879	+	0.0264611i
$922$		0			0
$923$	−7.17849	+	12.4335i	−0.236283	+	0.409254i
$924$		0			0
$925$	22.2706	+	38.5738i	0.732253	+	1.26830i
$926$		0			0
$927$	6.16918	−	6.75170i	0.202622	−	0.221755i
$928$		0			0
$929$	6.59673	−	11.4259i	0.216432	−	0.374870i	−0.737283	−	0.675584i	$-0.763892\pi$
$929$	6.59673	−	11.4259i	0.216432	−	0.374870i	0.953714	+	0.300714i	$0.0972248\pi$
$930$		0			0
$931$	−44.9220	−	36.0559i	−1.47226	−	1.18168i
$932$		0			0
$933$	21.4525	−	3.31745i	0.702325	−	0.108609i
$934$		0			0
$935$	15.0477	+	8.68779i	0.492112	+	0.284121i
$936$		0			0
$937$		−	8.86021i		−	0.289451i	−0.989472	−	0.144725i	$-0.953770\pi$
$937$		−	8.86021i		−	0.289451i	0.989472	−	0.144725i	$-0.0462298\pi$
$938$		0			0
$939$	−11.8180	+	9.49871i	−0.385664	+	0.309979i
$940$		0			0
$941$	−2.05919	−	3.56663i	−0.0671278	−	0.116269i	0.830508	−	0.557007i	$-0.188050\pi$
$941$	−2.05919	−	3.56663i	−0.0671278	−	0.116269i	−0.897636	+	0.440738i	$0.854717\pi$
$942$		0			0
$943$	0.274682	+	0.158588i	0.00894488	+	0.00516433i
$944$		0			0
$945$	6.79979	−	48.3596i	0.221197	−	1.57314i
$946$		0			0
$947$	21.4498	+	12.3840i	0.697024	+	0.402427i	0.806238	−	0.591591i	$-0.201500\pi$
$947$	21.4498	+	12.3840i	0.697024	+	0.402427i	−0.109214	+	0.994018i	$0.534833\pi$
$948$		0			0
$949$	0.672905	+	1.16550i	0.0218434	+	0.0378339i
$950$		0			0
$951$	−18.4662	+	14.8423i	−0.598809	+	0.481294i
$952$		0			0
$953$		−	9.62625i		−	0.311825i	−0.987771	−	0.155912i	$-0.950168\pi$
$953$		−	9.62625i		−	0.311825i	0.987771	−	0.155912i	$-0.0498317\pi$
$954$		0			0
$955$	−15.7897	−	9.11620i	−0.510944	−	0.294993i
$956$		0			0
$957$	22.1219	−	3.42096i	0.715099	−	0.110584i
$958$		0			0
$959$	−15.4216	−	10.5498i	−0.497989	−	0.340672i
$960$		0			0
$961$	2.41465	−	4.18230i	0.0778920	−	0.134913i
$962$		0			0
$963$	38.4588	+	8.46883i	1.23932	+	0.272904i
$964$		0			0
$965$	−28.3908	−	49.1744i	−0.913933	−	1.58298i
$966$		0			0
$967$	−5.05558	+	8.75652i	−0.162576	+	0.281591i	−0.935792	−	0.352553i	$-0.885314\pi$
$967$	−5.05558	+	8.75652i	−0.162576	+	0.281591i	0.773216	+	0.634143i	$0.218647\pi$
$968$		0			0
$969$	21.5045	+	8.34507i	0.690824	+	0.268082i
$970$		0			0
$971$	−12.6574	−	21.9233i	−0.406196	−	0.703552i	0.588264	−	0.808669i	$-0.299812\pi$
$971$	−12.6574	−	21.9233i	−0.406196	−	0.703552i	−0.994460	+	0.105117i	$0.966478\pi$
$972$		0			0
$973$	−34.7959	+	16.6894i	−1.11550	+	0.535039i
$974$		0			0
$975$	−10.5574	+	8.48551i	−0.338106	+	0.271754i
$976$		0			0
$977$	7.84008	−	4.52647i	0.250826	−	0.144815i	−0.369316	−	0.929304i	$-0.620408\pi$
$977$	7.84008	−	4.52647i	0.250826	−	0.144815i	0.620143	+	0.784489i	$0.287075\pi$
$978$		0			0
$979$	−12.3279	+	7.11752i	−0.394001	+	0.227477i
$980$		0			0
$981$	−30.2330	+	9.57964i	−0.965266	+	0.305855i
$982$		0			0
$983$	6.39303			0.203906			0.101953	−	0.994789i	$-0.467491\pi$
$983$	6.39303			0.203906			0.101953	+	0.994789i	$0.467491\pi$
$984$		0			0
$985$			16.7869i			0.534876i
$986$		0			0
$987$	23.4866	−	1.81331i	0.747587	−	0.0577184i
$988$		0			0
$989$	−17.7934	+	10.2730i	−0.565797	+	0.326663i
$990$		0			0
$991$	−6.92230	+	11.9898i	−0.219894	+	0.380868i	−0.954775	−	0.297328i	$-0.903905\pi$
$991$	−6.92230	+	11.9898i	−0.219894	+	0.380868i	0.734881	+	0.678196i	$0.237238\pi$
$992$		0			0
$993$	−11.8244	−	14.7115i	−0.375236	−	0.466855i
$994$		0			0
$995$	−6.52475	−	3.76706i	−0.206848	−	0.119424i
$996$		0			0
$997$		−	6.92118i		−	0.219196i	−0.993976	−	0.109598i	$-0.965044\pi$
$997$		−	6.92118i		−	0.219196i	0.993976	−	0.109598i	$-0.0349563\pi$
$998$		0			0
$999$	25.2952	+	16.8239i	0.800306	+	0.532285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.c.689.3		16
3.2	odd	2		3024.2.df.c.17.1		16
4.3	odd	2		126.2.t.a.59.4	yes	16
7.5	odd	6		1008.2.ca.c.257.7		16
9.2	odd	6		1008.2.ca.c.353.7		16
9.7	even	3		3024.2.ca.c.2033.1		16
12.11	even	2		378.2.t.a.17.5		16
21.5	even	6		3024.2.ca.c.2609.1		16
28.3	even	6		882.2.m.b.293.8		16
28.11	odd	6		882.2.m.a.293.5		16
28.19	even	6		126.2.l.a.5.6	✓	16
28.23	odd	6		882.2.l.b.509.7		16
28.27	even	2		882.2.t.a.815.1		16
36.7	odd	6		378.2.l.a.143.5		16
36.11	even	6		126.2.l.a.101.2	yes	16
36.23	even	6		1134.2.k.a.647.4		16
36.31	odd	6		1134.2.k.b.647.5		16
63.47	even	6	inner	1008.2.df.c.929.3		16
63.61	odd	6		3024.2.df.c.1601.1		16
84.11	even	6		2646.2.m.a.881.4		16
84.23	even	6		2646.2.l.a.1097.4		16
84.47	odd	6		378.2.l.a.341.1		16
84.59	odd	6		2646.2.m.b.881.1		16
84.83	odd	2		2646.2.t.b.2285.8		16
252.11	even	6		882.2.m.b.587.8		16
252.47	odd	6		126.2.t.a.47.4	yes	16
252.79	odd	6		2646.2.t.b.1979.8		16
252.83	odd	6		882.2.l.b.227.3		16
252.103	even	6		1134.2.k.a.971.4		16
252.115	even	6		2646.2.m.a.1763.4		16
252.131	odd	6		1134.2.k.b.971.5		16
252.151	odd	6		2646.2.m.b.1763.1		16
252.187	even	6		378.2.t.a.89.5		16
252.191	even	6		882.2.t.a.803.1		16
252.223	even	6		2646.2.l.a.521.8		16
252.227	odd	6		882.2.m.a.587.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.6	✓	16	28.19	even	6
126.2.l.a.101.2	yes	16	36.11	even	6
126.2.t.a.47.4	yes	16	252.47	odd	6
126.2.t.a.59.4	yes	16	4.3	odd	2
378.2.l.a.143.5		16	36.7	odd	6
378.2.l.a.341.1		16	84.47	odd	6
378.2.t.a.17.5		16	12.11	even	2
378.2.t.a.89.5		16	252.187	even	6
882.2.l.b.227.3		16	252.83	odd	6
882.2.l.b.509.7		16	28.23	odd	6
882.2.m.a.293.5		16	28.11	odd	6
882.2.m.a.587.5		16	252.227	odd	6
882.2.m.b.293.8		16	28.3	even	6
882.2.m.b.587.8		16	252.11	even	6
882.2.t.a.803.1		16	252.191	even	6
882.2.t.a.815.1		16	28.27	even	2
1008.2.ca.c.257.7		16	7.5	odd	6
1008.2.ca.c.353.7		16	9.2	odd	6
1008.2.df.c.689.3		16	1.1	even	1	trivial
1008.2.df.c.929.3		16	63.47	even	6	inner
1134.2.k.a.647.4		16	36.23	even	6
1134.2.k.a.971.4		16	252.103	even	6
1134.2.k.b.647.5		16	36.31	odd	6
1134.2.k.b.971.5		16	252.131	odd	6
2646.2.l.a.521.8		16	252.223	even	6
2646.2.l.a.1097.4		16	84.23	even	6
2646.2.m.a.881.4		16	84.11	even	6
2646.2.m.a.1763.4		16	252.115	even	6
2646.2.m.b.881.1		16	84.59	odd	6
2646.2.m.b.1763.1		16	252.151	odd	6
2646.2.t.b.1979.8		16	252.79	odd	6
2646.2.t.b.2285.8		16	84.83	odd	2
3024.2.ca.c.2033.1		16	9.7	even	3
3024.2.ca.c.2609.1		16	21.5	even	6
3024.2.df.c.17.1		16	3.2	odd	2
3024.2.df.c.1601.1		16	63.61	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.626615 + 1.61473i) q^{3} +3.55225 q^{5} +(1.49384 - 2.18368i) q^{7} +(-2.21471 - 2.02363i) q^{9} +O(q^{10})\)	\(q+(-0.626615 + 1.61473i) q^{3} +3.55225 q^{5} +(1.49384 - 2.18368i) q^{7} +(-2.21471 - 2.02363i) q^{9} +3.02237i q^{11} +(0.888944 + 0.513232i) q^{13} +(-2.22589 + 5.73592i) q^{15} +(0.809204 - 1.40158i) q^{17} +(7.12643 - 4.11444i) q^{19} +(2.58998 + 3.78047i) q^{21} -3.35830i q^{23} +7.61848 q^{25} +(4.65538 - 2.30812i) q^{27} +(-3.70319 + 2.13804i) q^{29} +(-5.18382 + 2.99288i) q^{31} +(-4.88031 - 1.89386i) q^{33} +(5.30650 - 7.75696i) q^{35} +(2.92323 + 5.06319i) q^{37} +(-1.38576 + 1.11381i) q^{39} +(-0.0472226 + 0.0817920i) q^{41} +(-3.05899 - 5.29833i) q^{43} +(-7.86719 - 7.18843i) q^{45} +(2.57023 - 4.45176i) q^{47} +(-2.53687 - 6.52413i) q^{49} +(1.75612 + 2.18490i) q^{51} +(2.76235 + 1.59484i) q^{53} +10.7362i q^{55} +(2.17819 + 14.0854i) q^{57} +(4.42036 + 7.65628i) q^{59} +(-4.06195 - 2.34517i) q^{61} +(-7.72737 + 1.81322i) q^{63} +(3.15775 + 1.82313i) q^{65} +(-0.187838 - 0.325345i) q^{67} +(5.42275 + 2.10436i) q^{69} +13.9868i q^{71} +(1.13546 + 0.655556i) q^{73} +(-4.77385 + 12.3018i) q^{75} +(6.59987 + 4.51494i) q^{77} +(0.462067 - 0.800324i) q^{79} +(0.809858 + 8.96349i) q^{81} +(5.43209 + 9.40866i) q^{83} +(2.87450 - 4.97877i) q^{85} +(-1.13188 - 7.31938i) q^{87} +(2.35495 + 4.07888i) q^{89} +(2.44867 - 1.17448i) q^{91} +(-1.58443 - 10.2459i) q^{93} +(25.3148 - 14.6155i) q^{95} +(-13.3330 + 7.69782i) q^{97} +(6.11615 - 6.69367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q - 2 * q^7 - 6 * q^9	\( 16 q - 2 q^{7} - 6 q^{9} - 6 q^{13} + 18 q^{15} + 18 q^{17} - 18 q^{21} + 16 q^{25} + 36 q^{27} + 6 q^{29} - 6 q^{31} + 18 q^{33} + 30 q^{35} - 2 q^{37} + 30 q^{39} + 6 q^{41} + 2 q^{43} + 12 q^{45} + 18 q^{47} + 10 q^{49} + 36 q^{53} + 6 q^{57} - 30 q^{59} - 60 q^{61} - 42 q^{63} + 42 q^{65} - 14 q^{67} + 42 q^{69} - 30 q^{75} - 18 q^{77} + 16 q^{79} + 54 q^{81} - 12 q^{85} + 48 q^{87} + 24 q^{89} + 12 q^{91} + 30 q^{93} + 66 q^{95} - 6 q^{97} - 18 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 - 6 * q^9 - 6 * q^13 + 18 * q^15 + 18 * q^17 - 18 * q^21 + 16 * q^25 + 36 * q^27 + 6 * q^29 - 6 * q^31 + 18 * q^33 + 30 * q^35 - 2 * q^37 + 30 * q^39 + 6 * q^41 + 2 * q^43 + 12 * q^45 + 18 * q^47 + 10 * q^49 + 36 * q^53 + 6 * q^57 - 30 * q^59 - 60 * q^61 - 42 * q^63 + 42 * q^65 - 14 * q^67 + 42 * q^69 - 30 * q^75 - 18 * q^77 + 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 + 24 * q^89 + 12 * q^91 + 30 * q^93 + 66 * q^95 - 6 * q^97 - 18 * q^99

Introduction

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