LMFDB - Embedded newform 252.2.w.a.101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, degree $2$, 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:	$2.01223013094$
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} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.5
Root			$-0.213160 + 1.71888i$ of defining polynomial
Character	$\chi$	$=$	252.101
Dual form			252.2.w.a.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.106783 - 1.72876i) q^{3} +(1.43402 - 2.48379i) q^{5} +(2.56899 + 0.632668i) q^{7} +(-2.97719 - 0.369204i) q^{9} +O(q^{10})$	\(q+(0.106783 - 1.72876i) q^{3} +(1.43402 - 2.48379i) q^{5} +(2.56899 + 0.632668i) q^{7} +(-2.97719 - 0.369204i) q^{9} +(-2.34941 + 1.35643i) q^{11} +(-3.18987 + 1.84167i) q^{13} +(-4.14074 - 2.74429i) q^{15} +(3.22192 - 5.58052i) q^{17} +(2.73867 - 1.58117i) q^{19} +(1.36805 - 4.37361i) q^{21} +(2.59068 + 1.49573i) q^{23} +(-1.61282 - 2.79348i) q^{25} +(-0.956179 + 5.10742i) q^{27} +(-2.48332 - 1.43375i) q^{29} +9.54636i q^{31} +(2.09406 + 4.20639i) q^{33} +(5.25540 - 5.47359i) q^{35} +(-1.70640 - 2.95556i) q^{37} +(2.84318 + 5.71117i) q^{39} +(-0.794538 - 1.37618i) q^{41} +(-4.67828 + 8.10302i) q^{43} +(-5.18638 + 6.86529i) q^{45} +11.3074 q^{47} +(6.19946 + 3.25064i) q^{49} +(-9.30332 - 6.16581i) q^{51} +(2.16419 + 1.24950i) q^{53} +7.78058i q^{55} +(-2.44102 - 4.90333i) q^{57} -8.67361 q^{59} +0.654617i q^{61} +(-7.41481 - 2.83206i) q^{63} +10.5640i q^{65} +7.72292 q^{67} +(2.86240 - 4.31894i) q^{69} -7.86582i q^{71} +(11.0769 + 6.39527i) q^{73} +(-5.00146 + 2.48987i) q^{75} +(-6.89378 + 1.99827i) q^{77} +5.19132 q^{79} +(8.72738 + 2.19839i) q^{81} +(-7.92948 + 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(-2.74378 + 4.13996i) q^{87} +(3.14826 + 5.45295i) q^{89} +(-9.35993 + 2.71312i) q^{91} +(16.5033 + 1.01939i) q^{93} -9.06971i q^{95} +(-13.2065 - 7.62477i) q^{97} +(7.49544 - 3.17095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7} + 6 q^{9}+O(q^{10}) $ 16 * q - q^7 + 6 * q^9	$ 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.106783	−	1.72876i	0.0616513	−	0.998098i
$3$	0.106783	−	1.72876i	0.0616513	−	0.998098i
$4$		0			0
$5$	1.43402	−	2.48379i	0.641312	−	1.11079i	−0.343828	−	0.939033i	$-0.611724\pi$
$5$	1.43402	−	2.48379i	0.641312	−	1.11079i	0.985140	−	0.171753i	$-0.0549431\pi$
$6$		0			0
$7$	2.56899	+	0.632668i	0.970989	+	0.239126i
$7$	2.56899	+	0.632668i	0.970989	+	0.239126i
$8$		0			0
$9$	−2.97719	−	0.369204i	−0.992398	−	0.123068i
$10$		0			0
$11$	−2.34941	+	1.35643i	−0.708373	+	0.408979i	−0.810458	−	0.585797i	$-0.800782\pi$
$11$	−2.34941	+	1.35643i	−0.708373	+	0.408979i	0.102086	+	0.994776i	$0.467448\pi$
$12$		0			0
$13$	−3.18987	+	1.84167i	−0.884712	+	0.510789i	−0.872209	−	0.489133i	$-0.837313\pi$
$13$	−3.18987	+	1.84167i	−0.884712	+	0.510789i	−0.0125026	+	0.999922i	$0.503980\pi$
$14$		0			0
$15$	−4.14074	−	2.74429i	−1.06913	−	0.708574i
$16$		0			0
$17$	3.22192	−	5.58052i	0.781429	−	1.35348i	−0.149680	−	0.988735i	$-0.547824\pi$
$17$	3.22192	−	5.58052i	0.781429	−	1.35348i	0.931109	−	0.364741i	$-0.118842\pi$
$18$		0			0
$19$	2.73867	−	1.58117i	0.628294	−	0.362746i	−0.151797	−	0.988412i	$-0.548506\pi$
$19$	2.73867	−	1.58117i	0.628294	−	0.362746i	0.780091	+	0.625666i	$0.215173\pi$
$20$		0			0
$21$	1.36805	−	4.37361i	0.298534	−	0.954399i
$22$		0			0
$23$	2.59068	+	1.49573i	0.540195	+	0.311882i	0.745158	−	0.666888i	$-0.232374\pi$
$23$	2.59068	+	1.49573i	0.540195	+	0.311882i	−0.204963	+	0.978770i	$0.565707\pi$
$24$		0			0
$25$	−1.61282	−	2.79348i	−0.322563	−	0.558696i
$26$		0			0
$27$	−0.956179	+	5.10742i	−0.184017	+	0.982923i
$28$		0			0
$29$	−2.48332	−	1.43375i	−0.461142	−	0.266240i	0.251383	−	0.967888i	$-0.419115\pi$
$29$	−2.48332	−	1.43375i	−0.461142	−	0.266240i	−0.712524	+	0.701648i	$0.752448\pi$
$30$		0			0
$31$			9.54636i			1.71458i	0.514836	+	0.857289i	$0.327853\pi$
$31$			9.54636i			1.71458i	−0.514836	+	0.857289i	$0.672147\pi$
$32$		0			0
$33$	2.09406	+	4.20639i	0.364529	+	0.732239i
$34$		0			0
$35$	5.25540	−	5.47359i	0.888325	−	0.925205i
$36$		0			0
$37$	−1.70640	−	2.95556i	−0.280530	−	0.485892i	0.690986	−	0.722868i	$-0.257177\pi$
$37$	−1.70640	−	2.95556i	−0.280530	−	0.485892i	−0.971515	+	0.236977i	$0.923843\pi$
$38$		0			0
$39$	2.84318	+	5.71117i	0.455273	+	0.914520i
$40$		0			0
$41$	−0.794538	−	1.37618i	−0.124086	−	0.214923i	0.797289	−	0.603597i	$-0.206267\pi$
$41$	−0.794538	−	1.37618i	−0.124086	−	0.214923i	−0.921375	+	0.388674i	$0.872933\pi$
$42$		0			0
$43$	−4.67828	+	8.10302i	−0.713431	+	1.23570i	0.250131	+	0.968212i	$0.419526\pi$
$43$	−4.67828	+	8.10302i	−0.713431	+	1.23570i	−0.963562	+	0.267487i	$0.913807\pi$
$44$		0			0
$45$	−5.18638	+	6.86529i	−0.773140	+	1.02342i
$46$		0			0
$47$	11.3074			1.64936			0.824680	−	0.565599i	$-0.191355\pi$
$47$	11.3074			1.64936			0.824680	+	0.565599i	$0.191355\pi$
$48$		0			0
$49$	6.19946	+	3.25064i	0.885637	+	0.464378i
$50$		0			0
$51$	−9.30332	−	6.16581i	−1.30272	−	0.863387i
$52$		0			0
$53$	2.16419	+	1.24950i	0.297275	+	0.171632i	0.641218	−	0.767359i	$-0.278429\pi$
$53$	2.16419	+	1.24950i	0.297275	+	0.171632i	−0.343943	+	0.938990i	$0.611763\pi$
$54$		0			0
$55$			7.78058i			1.04913i
$56$		0			0
$57$	−2.44102	−	4.90333i	−0.323320	−	0.649462i
$58$		0			0
$59$	−8.67361			−1.12921			−0.564604	−	0.825362i	$-0.690971\pi$
$59$	−8.67361			−1.12921			−0.564604	+	0.825362i	$0.690971\pi$
$60$		0			0
$61$			0.654617i			0.0838151i	0.999121	+	0.0419075i	$0.0133435\pi$
$61$			0.654617i			0.0838151i	−0.999121	+	0.0419075i	$0.986657\pi$
$62$		0			0
$63$	−7.41481	−	2.83206i	−0.934178	−	0.356806i
$64$		0			0
$65$			10.5640i			1.31030i
$66$		0			0
$67$	7.72292			0.943505			0.471752	−	0.881731i	$-0.343622\pi$
$67$	7.72292			0.943505			0.471752	+	0.881731i	$0.343622\pi$
$68$		0			0
$69$	2.86240	−	4.31894i	0.344592	−	0.519939i
$70$		0			0
$71$		−	7.86582i		−	0.933501i	−0.884389	−	0.466750i	$-0.845425\pi$
$71$		−	7.86582i		−	0.933501i	0.884389	−	0.466750i	$-0.154575\pi$
$72$		0			0
$73$	11.0769	+	6.39527i	1.29646	+	0.748510i	0.979790	−	0.200027i	$-0.0641028\pi$
$73$	11.0769	+	6.39527i	1.29646	+	0.748510i	0.316667	+	0.948537i	$0.397436\pi$
$74$		0			0
$75$	−5.00146	+	2.48987i	−0.577519	+	0.287505i
$76$		0			0
$77$	−6.89378	+	1.99827i	−0.785619	+	0.227724i
$78$		0			0
$79$	5.19132			0.584069			0.292034	−	0.956408i	$-0.405668\pi$
$79$	5.19132			0.584069			0.292034	+	0.956408i	$0.405668\pi$
$80$		0			0
$81$	8.72738	+	2.19839i	0.969708	+	0.244265i
$82$		0			0
$83$	−7.92948	+	13.7343i	−0.870373	+	1.50753i	−0.00876173	+	0.999962i	$0.502789\pi$
$83$	−7.92948	+	13.7343i	−0.870373	+	1.50753i	−0.861611	+	0.507569i	$0.830544\pi$
$84$		0			0
$85$	−9.24057	−	16.0051i	−1.00228	−	1.73600i
$86$		0			0
$87$	−2.74378	+	4.13996i	−0.294164	+	0.443850i
$88$		0			0
$89$	3.14826	+	5.45295i	0.333715	+	0.578012i	0.983237	−	0.182331i	$-0.0583643\pi$
$89$	3.14826	+	5.45295i	0.333715	+	0.578012i	−0.649522	+	0.760343i	$0.725031\pi$
$90$		0			0
$91$	−9.35993	+	2.71312i	−0.981188	+	0.284412i
$92$		0			0
$93$	16.5033	+	1.01939i	1.71132	+	0.105706i
$94$		0			0
$95$		−	9.06971i		−	0.930533i
$96$		0			0
$97$	−13.2065	−	7.62477i	−1.34092	−	0.774178i	−0.353974	−	0.935255i	$-0.615170\pi$
$97$	−13.2065	−	7.62477i	−1.34092	−	0.774178i	−0.986942	+	0.161077i	$0.948503\pi$
$98$		0			0
$99$	7.49544	−	3.17095i	0.753320	−	0.318692i
$100$		0			0
$101$	−1.74451	−	3.02158i	−0.173585	−	0.300658i	0.766086	−	0.642739i	$-0.222202\pi$
$101$	−1.74451	−	3.02158i	−0.173585	−	0.300658i	−0.939671	+	0.342080i	$0.888869\pi$
$102$		0			0
$103$	−2.89161	−	1.66947i	−0.284919	−	0.164498i	0.350729	−	0.936477i	$-0.385934\pi$
$103$	−2.89161	−	1.66947i	−0.284919	−	0.164498i	−0.635648	+	0.771979i	$0.719267\pi$
$104$		0			0
$105$	−8.90131	−	9.66979i	−0.868679	−	0.943675i
$106$		0			0
$107$	−3.10776	+	1.79427i	−0.300439	+	0.173458i	−0.642640	−	0.766168i	$-0.722161\pi$
$107$	−3.10776	+	1.79427i	−0.300439	+	0.173458i	0.342201	+	0.939627i	$0.388828\pi$
$108$		0			0
$109$	6.89673	−	11.9455i	0.660587	−	1.14417i	−0.319875	−	0.947460i	$-0.603641\pi$
$109$	6.89673	−	11.9455i	0.660587	−	1.14417i	0.980462	−	0.196710i	$-0.0630258\pi$
$110$		0			0
$111$	−5.29166	+	2.63434i	−0.502262	+	0.250040i
$112$		0			0
$113$	−5.28607	+	3.05191i	−0.497271	+	0.287100i	−0.727586	−	0.686016i	$-0.759358\pi$
$113$	−5.28607	+	3.05191i	−0.497271	+	0.287100i	0.230315	+	0.973116i	$0.426024\pi$
$114$		0			0
$115$	7.43018	−	4.28981i	0.692867	−	0.400027i
$116$		0			0
$117$	10.1768	−	4.30531i	0.940848	−	0.398026i
$118$		0			0
$119$	11.8077	−	12.2979i	1.08241	−	1.12735i
$120$		0			0
$121$	−1.82019	+	3.15267i	−0.165472	+	0.286606i
$122$		0			0
$123$	−2.46392	+	1.22661i	−0.222164	+	0.110600i
$124$		0			0
$125$	5.08895			0.455170
$126$		0			0
$127$	−13.3819			−1.18745			−0.593727	−	0.804666i	$-0.702344\pi$
$127$	−13.3819			−1.18745			−0.593727	+	0.804666i	$0.702344\pi$
$128$		0			0
$129$	13.5086	+	8.95287i	1.18936	+	0.788256i
$130$		0			0
$131$	−0.388964	+	0.673705i	−0.0339839	+	0.0588619i	−0.882517	−	0.470280i	$-0.844153\pi$
$131$	−0.388964	+	0.673705i	−0.0339839	+	0.0588619i	0.848533	+	0.529142i	$0.177486\pi$
$132$		0			0
$133$	8.03598	−	2.32935i	0.696808	−	0.201980i
$134$		0			0
$135$	11.3146	+	9.69908i	0.973805	+	0.834764i
$136$		0			0
$137$	−14.3082	+	8.26083i	−1.22243	+	0.705771i	−0.965435	−	0.260642i	$-0.916066\pi$
$137$	−14.3082	+	8.26083i	−1.22243	+	0.705771i	−0.256995	+	0.966413i	$0.582732\pi$
$138$		0			0
$139$	9.91826	−	5.72631i	0.841256	−	0.485699i	−0.0164348	−	0.999865i	$-0.505232\pi$
$139$	9.91826	−	5.72631i	0.841256	−	0.485699i	0.857691	+	0.514165i	$0.171898\pi$
$140$		0			0
$141$	1.20745	−	19.5478i	0.101685	−	1.64622i
$142$		0			0
$143$	4.99620	−	8.65368i	0.417804	−	0.723657i
$144$		0			0
$145$	−7.12226	+	4.11204i	−0.591472	+	0.341486i
$146$		0			0
$147$	6.28157	−	10.3702i	0.518095	−	0.855323i
$148$		0			0
$149$	−4.24781	−	2.45247i	−0.347994	−	0.200914i	0.315807	−	0.948823i	$-0.397725\pi$
$149$	−4.24781	−	2.45247i	−0.347994	−	0.200914i	−0.663801	+	0.747909i	$0.731058\pi$
$150$		0			0
$151$	−4.92814	−	8.53579i	−0.401047	−	0.694633i	0.592806	−	0.805345i	$-0.298020\pi$
$151$	−4.92814	−	8.53579i	−0.401047	−	0.694633i	−0.993852	+	0.110712i	$0.964687\pi$
$152$		0			0
$153$	−11.6526	+	15.4248i	−0.942059	+	1.24702i
$154$		0			0
$155$	23.7112	+	13.6897i	1.90453	+	1.09958i
$156$		0			0
$157$		−	15.4169i		−	1.23040i	−0.788371	−	0.615200i	$-0.789075\pi$
$157$		−	15.4169i		−	1.23040i	0.788371	−	0.615200i	$-0.210925\pi$
$158$		0			0
$159$	2.39118	−	3.60794i	0.189633	−	0.286128i
$160$		0			0
$161$	5.70915	+	5.48157i	0.449944	+	0.432008i
$162$		0			0
$163$	−5.72053	−	9.90825i	−0.448066	−	0.776074i	0.550194	−	0.835037i	$-0.314554\pi$
$163$	−5.72053	−	9.90825i	−0.448066	−	0.776074i	−0.998260	+	0.0589632i	$0.981221\pi$
$164$		0			0
$165$	13.4507	+	0.830835i	1.04714	+	0.0646805i
$166$		0			0
$167$	−6.49103	−	11.2428i	−0.502291	−	0.869993i	−0.999996	−	0.00264735i	$-0.999157\pi$
$167$	−6.49103	−	11.2428i	−0.502291	−	0.869993i	0.497706	−	0.867346i	$-0.334176\pi$
$168$		0			0
$169$	0.283528	−	0.491084i	0.0218098	−	0.0377757i
$170$		0			0
$171$	−8.73733	+	3.69633i	−0.668160	+	0.282665i
$172$		0			0
$173$	−19.5997			−1.49014			−0.745068	−	0.666988i	$-0.767583\pi$
$173$	−19.5997			−1.49014			−0.745068	+	0.666988i	$0.767583\pi$
$174$		0			0
$175$	−2.37597	−	8.19681i	−0.179606	−	0.619620i
$176$		0			0
$177$	−0.926196	+	14.9945i	−0.0696171	+	1.12706i
$178$		0			0
$179$	−16.2630	−	9.38942i	−1.21555	−	0.701799i	−0.251588	−	0.967835i	$-0.580953\pi$
$179$	−16.2630	−	9.38942i	−1.21555	−	0.701799i	−0.963963	+	0.266036i	$0.914286\pi$
$180$		0			0
$181$		−	4.47775i		−	0.332829i	−0.986056	−	0.166414i	$-0.946781\pi$
$181$		−	4.47775i		−	0.332829i	0.986056	−	0.166414i	$-0.0532190\pi$
$182$		0			0
$183$	1.13167	+	0.0699021i	0.0836556	+	0.00516731i
$184$		0			0
$185$	−9.78801			−0.719629
$186$		0			0
$187$			17.4812i			1.27835i
$188$		0			0
$189$	−5.68772	+	12.5160i	−0.413721	+	0.910404i
$190$		0			0
$191$		−	6.81331i		−	0.492994i	−0.969144	−	0.246497i	$-0.920720\pi$
$191$		−	6.81331i		−	0.492994i	0.969144	−	0.246497i	$-0.0792795\pi$
$192$		0			0
$193$	−15.9539			−1.14839			−0.574193	−	0.818720i	$-0.694684\pi$
$193$	−15.9539			−1.14839			−0.574193	+	0.818720i	$0.694684\pi$
$194$		0			0
$195$	18.2625	+	1.12806i	1.30781	+	0.0807817i
$196$		0			0
$197$			25.9511i			1.84894i	0.381254	+	0.924470i	$0.375492\pi$
$197$			25.9511i			1.84894i	−0.381254	+	0.924470i	$0.624508\pi$
$198$		0			0
$199$	2.75706	+	1.59179i	0.195443	+	0.112839i	0.594528	−	0.804075i	$-0.297339\pi$
$199$	2.75706	+	1.59179i	0.195443	+	0.112839i	−0.399085	+	0.916914i	$0.630672\pi$
$200$		0			0
$201$	0.824678	−	13.3510i	0.0581683	−	0.941710i
$202$		0			0
$203$	−5.47256	−	5.25441i	−0.384098	−	0.368787i
$204$		0			0
$205$	−4.55752			−0.318311
$206$		0			0
$207$	−7.16074	−	5.40958i	−0.497706	−	0.375992i
$208$		0			0
$209$	−4.28950	+	7.42963i	−0.296711	+	0.513918i
$210$		0			0
$211$	−0.0552411	−	0.0956804i	−0.00380295	−	0.00658691i	0.864118	−	0.503290i	$-0.167877\pi$
$211$	−0.0552411	−	0.0956804i	−0.00380295	−	0.00658691i	−0.867921	+	0.496703i	$0.834544\pi$
$212$		0			0
$213$	−13.5981	−	0.839937i	−0.931725	−	0.0575516i
$214$		0			0
$215$	13.4175	+	23.2397i	0.915064	+	1.58494i
$216$		0			0
$217$	−6.03968	+	24.5245i	−0.410000	+	1.66483i
$218$		0			0
$219$	12.2387	−	18.4664i	0.827015	−	1.24784i
$220$		0			0
$221$			23.7349i			1.59658i
$222$		0			0
$223$	11.3064	+	6.52775i	0.757132	+	0.437130i	0.828265	−	0.560336i	$-0.189328\pi$
$223$	11.3064	+	6.52775i	0.757132	+	0.437130i	−0.0711331	+	0.997467i	$0.522661\pi$
$224$		0			0
$225$	3.77030	+	8.91219i	0.251353	+	0.594146i
$226$		0			0
$227$	4.63392	+	8.02618i	0.307564	+	0.532716i	0.977829	−	0.209406i	$-0.0671529\pi$
$227$	4.63392	+	8.02618i	0.307564	+	0.532716i	−0.670265	+	0.742122i	$0.733820\pi$
$228$		0			0
$229$	11.6204	+	6.70902i	0.767895	+	0.443344i	0.832123	−	0.554591i	$-0.187125\pi$
$229$	11.6204	+	6.70902i	0.767895	+	0.443344i	−0.0642281	+	0.997935i	$0.520459\pi$
$230$		0			0
$231$	2.71837	+	12.1310i	0.178856	+	0.798164i
$232$		0			0
$233$	−18.3415	+	10.5895i	−1.20159	+	0.693738i	−0.960909	−	0.276866i	$-0.910704\pi$
$233$	−18.3415	+	10.5895i	−1.20159	+	0.693738i	−0.240681	+	0.970604i	$0.577371\pi$
$234$		0			0
$235$	16.2151	−	28.0853i	1.05776	−	1.83209i
$236$		0			0
$237$	0.554346	−	8.97452i	0.0360086	−	0.582958i
$238$		0			0
$239$	−7.73342	+	4.46489i	−0.500233	+	0.288810i	−0.728810	−	0.684716i	$-0.759926\pi$
$239$	−7.73342	+	4.46489i	−0.500233	+	0.288810i	0.228577	+	0.973526i	$0.426593\pi$
$240$		0			0
$241$	15.9430	−	9.20469i	1.02698	−	0.592926i	0.110860	−	0.993836i	$-0.464639\pi$
$241$	15.9430	−	9.20469i	1.02698	−	0.592926i	0.916117	+	0.400910i	$0.131306\pi$
$242$		0			0
$243$	4.73241	−	14.8528i	0.303584	−	0.952805i
$244$		0			0
$245$	16.9641	−	10.7367i	1.08379	−	0.685942i
$246$		0			0
$247$	−5.82401	+	10.0875i	−0.370573	+	0.641851i
$248$		0			0
$249$	22.8964	+	15.1747i	1.45100	+	0.961659i
$250$		0			0
$251$	−6.33194			−0.399669			−0.199834	−	0.979830i	$-0.564040\pi$
$251$	−6.33194			−0.399669			−0.199834	+	0.979830i	$0.564040\pi$
$252$		0			0
$253$	−8.11542			−0.510212
$254$		0			0
$255$	−28.6557	+	14.2656i	−1.79449	+	0.893347i
$256$		0			0
$257$	8.19283	−	14.1904i	0.511054	−	0.885172i	−0.488863	−	0.872360i	$-0.662588\pi$
$257$	8.19283	−	14.1904i	0.511054	−	0.885172i	0.999918	−	0.0128120i	$-0.00407829\pi$
$258$		0			0
$259$	−2.51383	−	8.67241i	−0.156202	−	0.538877i
$260$		0			0
$261$	6.86399	+	5.18540i	0.424870	+	0.320968i
$262$		0			0
$263$	−10.4663	+	6.04270i	−0.645377	+	0.372609i	−0.786683	−	0.617357i	$-0.788203\pi$
$263$	−10.4663	+	6.04270i	−0.645377	+	0.372609i	0.141306	+	0.989966i	$0.454870\pi$
$264$		0			0
$265$	6.20698	−	3.58360i	0.381292	−	0.220139i
$266$		0			0
$267$	9.76300	−	4.86029i	0.597486	−	0.297445i
$268$		0			0
$269$	12.6652	−	21.9368i	0.772212	−	1.33751i	−0.164136	−	0.986438i	$-0.552484\pi$
$269$	12.6652	−	21.9368i	0.772212	−	1.33751i	0.936348	−	0.351072i	$-0.114183\pi$
$270$		0			0
$271$	−0.195591	+	0.112924i	−0.0118813	+	0.00685967i	−0.505929	−	0.862575i	$-0.668850\pi$
$271$	−0.195591	+	0.112924i	−0.0118813	+	0.00685967i	0.494048	+	0.869435i	$0.335517\pi$
$272$		0			0
$273$	3.69084	+	16.4708i	0.223380	+	0.996856i
$274$		0			0
$275$	7.57832	+	4.37534i	0.456990	+	0.263843i
$276$		0			0
$277$	10.2170	+	17.6963i	0.613878	+	1.06327i	0.990580	+	0.136934i	$0.0437248\pi$
$277$	10.2170	+	17.6963i	0.613878	+	1.06327i	−0.376702	+	0.926335i	$0.622942\pi$
$278$		0			0
$279$	3.52456	−	28.4214i	0.211010	−	1.70154i
$280$		0			0
$281$	8.96635	+	5.17672i	0.534887	+	0.308817i	0.743004	−	0.669287i	$-0.233400\pi$
$281$	8.96635	+	5.17672i	0.534887	+	0.308817i	−0.208117	+	0.978104i	$0.566733\pi$
$282$		0			0
$283$			13.7157i			0.815311i	0.913136	+	0.407656i	$0.133654\pi$
$283$			13.7157i			0.815311i	−0.913136	+	0.407656i	$0.866346\pi$
$284$		0			0
$285$	−15.6793	−	0.968493i	−0.928763	−	0.0573686i
$286$		0			0
$287$	−1.17050	−	4.03808i	−0.0690923	−	0.238360i
$288$		0			0
$289$	−12.2615	−	21.2375i	−0.721264	−	1.24927i
$290$		0			0
$291$	−14.5916	+	22.0166i	−0.855375	+	1.29064i
$292$		0			0
$293$	4.21527	+	7.30105i	0.246258	+	0.426532i	0.962485	−	0.271336i	$-0.0874655\pi$
$293$	4.21527	+	7.30105i	0.246258	+	0.426532i	−0.716226	+	0.697868i	$0.754132\pi$
$294$		0			0
$295$	−12.4381	+	21.5434i	−0.724175	+	1.25431i
$296$		0			0
$297$	−4.68140	−	13.2964i	−0.271643	−	0.771535i
$298$		0			0
$299$	−11.0186			−0.637222
$300$		0			0
$301$	−17.1450	+	17.8568i	−0.988221	+	1.02925i
$302$		0			0
$303$	−5.40986	+	2.69318i	−0.310788	+	0.154719i
$304$		0			0
$305$	1.62593	+	0.938732i	0.0931006	+	0.0537516i
$306$		0			0
$307$			5.34345i			0.304967i	0.988306	+	0.152484i	$0.0487271\pi$
$307$			5.34345i			0.304967i	−0.988306	+	0.152484i	$0.951273\pi$
$308$		0			0
$309$	−3.19488	+	4.82061i	−0.181751	+	0.274235i
$310$		0			0
$311$	−9.41734			−0.534008			−0.267004	−	0.963695i	$-0.586034\pi$
$311$	−9.41734			−0.534008			−0.267004	+	0.963695i	$0.586034\pi$
$312$		0			0
$313$		−	16.5523i		−	0.935590i	−0.883837	−	0.467795i	$-0.845049\pi$
$313$		−	16.5523i		−	0.935590i	0.883837	−	0.467795i	$-0.154951\pi$
$314$		0			0
$315$	−17.6672	+	14.3556i	−0.995435	+	0.808848i
$316$		0			0
$317$		−	26.5264i		−	1.48987i	−0.667138	−	0.744934i	$-0.732481\pi$
$317$		−	26.5264i		−	1.48987i	0.667138	−	0.744934i	$-0.267519\pi$
$318$		0			0
$319$	7.77911			0.435547
$320$		0			0
$321$	2.76999	+	5.56416i	0.154606	+	0.310561i
$322$		0			0
$323$		−	20.3776i		−	1.13384i
$324$		0			0
$325$	10.2894	+	5.94056i	0.570751	+	0.329523i
$326$		0			0
$327$	−19.9144	−	13.1983i	−1.10127	−	0.729870i
$328$		0			0
$329$	29.0488	+	7.15386i	1.60151	+	0.394405i
$330$		0			0
$331$	−17.6400			−0.969582			−0.484791	−	0.874630i	$-0.661104\pi$
$331$	−17.6400			−0.969582			−0.484791	+	0.874630i	$0.661104\pi$
$332$		0			0
$333$	3.98906	+	9.42930i	0.218599	+	0.516722i
$334$		0			0
$335$	11.0748	−	19.1821i	0.605081	−	1.04803i
$336$		0			0
$337$	7.31169	+	12.6642i	0.398293	+	0.689864i	0.993515	−	0.113697i	$-0.0362694\pi$
$337$	7.31169	+	12.6642i	0.398293	+	0.689864i	−0.595222	+	0.803561i	$0.702936\pi$
$338$		0			0
$339$	4.71155	+	9.46421i	0.255896	+	0.514026i
$340$		0			0
$341$	−12.9490	−	22.4283i	−0.701226	−	1.21456i
$342$		0			0
$343$	13.8698	+	12.2731i	0.748899	+	0.662684i
$344$		0			0
$345$	−6.62262	−	13.3030i	−0.356550	−	0.716212i
$346$		0			0
$347$		−	1.21893i		−	0.0654358i	−0.999465	−	0.0327179i	$-0.989584\pi$
$347$		−	1.21893i		−	0.0654358i	0.999465	−	0.0327179i	$-0.0104163\pi$
$348$		0			0
$349$	−10.6857	−	6.16942i	−0.571995	−	0.330241i	0.185951	−	0.982559i	$-0.440463\pi$
$349$	−10.6857	−	6.16942i	−0.571995	−	0.330241i	−0.757946	+	0.652318i	$0.773797\pi$
$350$		0			0
$351$	−6.35611	−	18.0530i	−0.339264	−	0.963597i
$352$		0			0
$353$	−11.1484	−	19.3097i	−0.593372	−	1.02775i	−0.993774	−	0.111411i	$-0.964463\pi$
$353$	−11.1484	−	19.3097i	−0.593372	−	1.02775i	0.400402	−	0.916339i	$-0.368870\pi$
$354$		0			0
$355$	−19.5371	−	11.2797i	−1.03692	−	0.598666i
$356$		0			0
$357$	−19.9992	−	21.7259i	−1.05847	−	1.14985i
$358$		0			0
$359$	10.4819	−	6.05173i	0.553214	−	0.319398i	−0.197204	−	0.980363i	$-0.563186\pi$
$359$	10.4819	−	6.05173i	0.553214	−	0.319398i	0.750417	+	0.660965i	$0.229853\pi$
$360$		0			0
$361$	−4.49979	+	7.79387i	−0.236831	+	0.410204i
$362$		0			0
$363$	5.25583	+	3.48333i	0.275860	+	0.182827i
$364$		0			0
$365$	31.7691	−	18.3419i	1.66287	−	0.960058i
$366$		0			0
$367$	12.7544	−	7.36375i	0.665774	−	0.384385i	−0.128700	−	0.991684i	$-0.541080\pi$
$367$	12.7544	−	7.36375i	0.665774	−	0.384385i	0.794473	+	0.607299i	$0.207747\pi$
$368$		0			0
$369$	1.85740	+	4.39050i	0.0966925	+	0.228560i
$370$		0			0
$371$	4.76928	+	4.57917i	0.247609	+	0.237739i
$372$		0			0
$373$	4.54279	−	7.86834i	0.235217	−	0.407407i	−0.724119	−	0.689675i	$-0.757753\pi$
$373$	4.54279	−	7.86834i	0.235217	−	0.407407i	0.959336	+	0.282268i	$0.0910867\pi$
$374$		0			0
$375$	0.543415	−	8.79756i	0.0280618	−	0.454304i
$376$		0			0
$377$	10.5620			0.543970
$378$		0			0
$379$	21.2298			1.09050			0.545250	−	0.838273i	$-0.316435\pi$
$379$	21.2298			1.09050			0.545250	+	0.838273i	$0.316435\pi$
$380$		0			0
$381$	−1.42897	+	23.1341i	−0.0732082	+	1.18520i
$382$		0			0
$383$	3.35227	−	5.80630i	0.171293	−	0.296688i	−0.767579	−	0.640954i	$-0.778539\pi$
$383$	3.35227	−	5.80630i	0.171293	−	0.296688i	0.938872	+	0.344266i	$0.111872\pi$
$384$		0			0
$385$	−4.92253	+	19.9883i	−0.250875	+	1.01870i
$386$		0			0
$387$	16.9198	−	22.3970i	0.860083	−	1.13850i
$388$		0			0
$389$	−6.66661	+	3.84897i	−0.338011	+	0.195151i	−0.659392	−	0.751799i	$-0.729186\pi$
$389$	−6.66661	+	3.84897i	−0.338011	+	0.195151i	0.321381	+	0.946950i	$0.395853\pi$
$390$		0			0
$391$	16.6939	−	9.63825i	0.844249	−	0.487427i
$392$		0			0
$393$	1.12314	+	0.744364i	0.0566548	+	0.0375482i
$394$		0			0
$395$	7.44444	−	12.8942i	0.374571	−	0.648775i
$396$		0			0
$397$	−0.0428112	+	0.0247170i	−0.00214863	+	0.00124051i	−0.501074	−	0.865404i	$-0.667062\pi$
$397$	−0.0428112	+	0.0247170i	−0.00214863	+	0.00124051i	0.498925	+	0.866645i	$0.333728\pi$
$398$		0			0
$399$	−3.16877	−	14.1410i	−0.158637	−	0.707935i
$400$		0			0
$401$	17.6039	+	10.1636i	0.879096	+	0.507546i	0.870360	−	0.492416i	$-0.163886\pi$
$401$	17.6039	+	10.1636i	0.879096	+	0.507546i	0.00873572	+	0.999962i	$0.497219\pi$
$402$		0			0
$403$	−17.5813	−	30.4517i	−0.875786	−	1.51691i
$404$		0			0
$405$	17.9755	−	18.5245i	0.893212	−	0.920488i
$406$		0			0
$407$	8.01803	+	4.62921i	0.397439	+	0.229461i
$408$		0			0
$409$			13.9886i			0.691689i	0.938292	+	0.345845i	$0.112408\pi$
$409$			13.9886i			0.691689i	−0.938292	+	0.345845i	$0.887592\pi$
$410$		0			0
$411$	12.7531	+	25.6175i	0.629064	+	1.26362i
$412$		0			0
$413$	−22.2824	−	5.48752i	−1.09645	−	0.270023i
$414$		0			0
$415$	22.7420	+	39.3903i	1.11636	+	1.93360i
$416$		0			0
$417$	−8.84029	−	17.7577i	−0.432911	−	0.869600i
$418$		0			0
$419$	10.6718	+	18.4842i	0.521353	+	0.903010i	0.999692	+	0.0248344i	$0.00790585\pi$
$419$	10.6718	+	18.4842i	0.521353	+	0.903010i	−0.478339	+	0.878176i	$0.658761\pi$
$420$		0			0
$421$	3.97287	−	6.88121i	0.193626	−	0.335370i	−0.752823	−	0.658223i	$-0.771309\pi$
$421$	3.97287	−	6.88121i	0.193626	−	0.335370i	0.946449	+	0.322853i	$0.104642\pi$
$422$		0			0
$423$	−33.6645	−	4.17476i	−1.63682	−	0.202984i
$424$		0			0
$425$	−20.7854			−1.00824
$426$		0			0
$427$	−0.414155	+	1.68171i	−0.0200424	+	0.0813835i
$428$		0			0
$429$	−14.4266	−	9.56129i	−0.696522	−	0.461623i
$430$		0			0
$431$	−27.6515	−	15.9646i	−1.33193	−	0.768989i	−0.346333	−	0.938112i	$-0.612573\pi$
$431$	−27.6515	−	15.9646i	−1.33193	−	0.768989i	−0.985595	+	0.169123i	$0.945907\pi$
$432$		0			0
$433$		−	18.5300i		−	0.890493i	−0.895408	−	0.445247i	$-0.853116\pi$
$433$		−	18.5300i		−	0.890493i	0.895408	−	0.445247i	$-0.146884\pi$
$434$		0			0
$435$	6.34817	+	12.7517i	0.304372	+	0.611400i
$436$		0			0
$437$	9.46004			0.452535
$438$		0			0
$439$		−	2.08211i		−	0.0993739i	−0.998765	−	0.0496869i	$-0.984178\pi$
$439$		−	2.08211i		−	0.0993739i	0.998765	−	0.0496869i	$-0.0158224\pi$
$440$		0			0
$441$	−17.2569	−	11.9667i	−0.821755	−	0.569841i
$442$		0			0
$443$			2.46985i			0.117346i	0.998277	+	0.0586731i	$0.0186870\pi$
$443$			2.46985i			0.117346i	−0.998277	+	0.0586731i	$0.981313\pi$
$444$		0			0
$445$	18.0587			0.856063
$446$		0			0
$447$	−4.69332	+	7.08154i	−0.221986	+	0.334945i
$448$		0			0
$449$			37.5094i			1.77018i	0.465424	+	0.885088i	$0.345902\pi$
$449$			37.5094i			1.77018i	−0.465424	+	0.885088i	$0.654098\pi$
$450$		0			0
$451$	3.73338	+	2.15547i	0.175798	+	0.101497i
$452$		0			0
$453$	−15.2825	+	7.60808i	−0.718037	+	0.357459i
$454$		0			0
$455$	−6.68349	+	27.1388i	−0.313327	+	1.27229i
$456$		0			0
$457$	5.84690			0.273506			0.136753	−	0.990605i	$-0.456333\pi$
$457$	5.84690			0.273506			0.136753	+	0.990605i	$0.456333\pi$
$458$		0			0
$459$	25.4213	+	21.7916i	1.18657	+	1.01715i
$460$		0			0
$461$	3.82830	−	6.63081i	0.178302	−	0.308827i	−0.762997	−	0.646402i	$-0.776273\pi$
$461$	3.82830	−	6.63081i	0.178302	−	0.308827i	0.941299	+	0.337574i	$0.109606\pi$
$462$		0			0
$463$	4.89449	+	8.47751i	0.227466	+	0.393983i	0.957057	−	0.289901i	$-0.0936225\pi$
$463$	4.89449	+	8.47751i	0.227466	+	0.393983i	−0.729590	+	0.683885i	$0.760289\pi$
$464$		0			0
$465$	26.1980	−	39.5290i	1.21490	−	1.83311i
$466$		0			0
$467$	14.0806	+	24.3883i	0.651572	+	1.12856i	0.982741	+	0.184985i	$0.0592235\pi$
$467$	14.0806	+	24.3883i	0.651572	+	1.12856i	−0.331169	+	0.943571i	$0.607443\pi$
$468$		0			0
$469$	19.8401	+	4.88605i	0.916132	+	0.225617i
$470$		0			0
$471$	−26.6520	−	1.64626i	−1.22806	−	0.0758558i
$472$		0			0
$473$		−	25.3830i		−	1.16711i
$474$		0			0
$475$	−8.83394	−	5.10028i	−0.405329	−	0.234017i
$476$		0			0
$477$	−5.98190	−	4.51903i	−0.273893	−	0.206912i
$478$		0			0
$479$	−14.8053	−	25.6435i	−0.676470	−	1.17168i	−0.976037	−	0.217605i	$-0.930175\pi$
$479$	−14.8053	−	25.6435i	−0.676470	−	1.17168i	0.299567	−	0.954075i	$-0.403158\pi$
$480$		0			0
$481$	10.8864	+	6.28525i	0.496376	+	0.286583i
$482$		0			0
$483$	10.0859	−	9.28439i	0.458926	−	0.422454i
$484$		0			0
$485$	−37.8767	+	21.8681i	−1.71989	+	0.992980i
$486$		0			0
$487$	−14.6701	+	25.4094i	−0.664767	+	1.15141i	0.314582	+	0.949230i	$0.398136\pi$
$487$	−14.6701	+	25.4094i	−0.664767	+	1.15141i	−0.979348	+	0.202180i	$0.935198\pi$
$488$		0			0
$489$	−17.7398	+	8.83136i	−0.802221	+	0.399368i
$490$		0			0
$491$	−8.63745	+	4.98683i	−0.389803	+	0.225053i	−0.682075	−	0.731283i	$-0.738922\pi$
$491$	−8.63745	+	4.98683i	−0.389803	+	0.225053i	0.292272	+	0.956335i	$0.405589\pi$
$492$		0			0
$493$	−16.0021	+	9.23883i	−0.720699	+	0.416096i
$494$		0			0
$495$	2.87262	−	23.1643i	0.129115	−	1.04116i
$496$		0			0
$497$	4.97645	−	20.2072i	0.223224	−	0.906419i
$498$		0			0
$499$	9.79784	−	16.9704i	0.438611	−	0.759697i	−0.558971	−	0.829187i	$-0.688804\pi$
$499$	9.79784	−	16.9704i	0.438611	−	0.759697i	0.997583	+	0.0694898i	$0.0221371\pi$
$500$		0			0
$501$	−20.1292	+	10.0209i	−0.899305	+	0.447699i
$502$		0			0
$503$	21.2907			0.949304			0.474652	−	0.880174i	$-0.342574\pi$
$503$	21.2907			0.949304			0.474652	+	0.880174i	$0.342574\pi$
$504$		0			0
$505$	−10.0066			−0.445289
$506$		0			0
$507$	−0.818689	−	0.542590i	−0.0363593	−	0.0240973i
$508$		0			0
$509$	21.8307	−	37.8119i	0.967630	−	1.67598i	0.265252	−	0.964179i	$-0.414545\pi$
$509$	21.8307	−	37.8119i	0.967630	−	1.67598i	0.702378	−	0.711804i	$-0.252122\pi$
$510$		0			0
$511$	24.4105	+	23.4374i	1.07986	+	1.03681i
$512$		0			0
$513$	5.45705	+	15.4994i	0.240935	+	0.684316i
$514$		0			0
$515$	−8.29324	+	4.78810i	−0.365444	+	0.210989i
$516$		0			0
$517$	−26.5658	+	15.3378i	−1.16836	+	0.674554i
$518$		0			0
$519$	−2.09292	+	33.8831i	−0.0918689	+	1.48730i
$520$		0			0
$521$	2.60043	−	4.50408i	0.113927	−	0.197327i	−0.803423	−	0.595408i	$-0.796990\pi$
$521$	2.60043	−	4.50408i	0.113927	−	0.197327i	0.917350	+	0.398081i	$0.130324\pi$
$522$		0			0
$523$	−34.7043	+	20.0365i	−1.51751	+	0.876137i	−0.517726	+	0.855547i	$0.673221\pi$
$523$	−34.7043	+	20.0365i	−1.51751	+	0.876137i	−0.999788	+	0.0205902i	$0.993445\pi$
$524$		0			0
$525$	−14.4240	+	3.23219i	−0.629515	+	0.141064i
$526$		0			0
$527$	53.2737	+	30.7576i	2.32064	+	1.33982i
$528$		0			0
$529$	−7.02557	−	12.1686i	−0.305460	−	0.529072i
$530$		0			0
$531$	25.8230	+	3.20233i	1.12062	+	0.138969i
$532$		0			0
$533$	5.06895	+	2.92656i	0.219561	+	0.126763i
$534$		0			0
$535$			10.2920i			0.444964i
$536$		0			0
$537$	−17.9686	+	27.1121i	−0.775404	+	1.16997i
$538$		0			0
$539$	−18.9743	+	0.772057i	−0.817282	+	0.0332549i
$540$		0			0
$541$	−4.12096	−	7.13771i	−0.177174	−	0.306874i	0.763738	−	0.645527i	$-0.223362\pi$
$541$	−4.12096	−	7.13771i	−0.177174	−	0.306874i	−0.940911	+	0.338653i	$0.890029\pi$
$542$		0			0
$543$	−7.74094	−	0.478149i	−0.332196	−	0.0205193i
$544$		0			0
$545$	−19.7801	−	34.2601i	−0.847285	−	1.46754i
$546$		0			0
$547$	−2.53756	+	4.39518i	−0.108498	+	0.187925i	−0.915162	−	0.403086i	$-0.867938\pi$
$547$	−2.53756	+	4.39518i	−0.108498	+	0.187925i	0.806664	+	0.591011i	$0.201271\pi$
$548$		0			0
$549$	0.241687	−	1.94892i	0.0103150	−	0.0831779i
$550$		0			0
$551$	−9.06800			−0.386310
$552$		0			0
$553$	13.3365	+	3.28438i	0.567124	+	0.139666i
$554$		0			0
$555$	−1.04519	+	16.9211i	−0.0443660	+	0.718260i
$556$		0			0
$557$	37.6102	+	21.7142i	1.59359	+	0.920062i	0.992684	+	0.120745i	$0.0385285\pi$
$557$	37.6102	+	21.7142i	1.59359	+	0.920062i	0.600910	+	0.799316i	$0.294805\pi$
$558$		0			0
$559$		−	34.4635i		−	1.45765i
$560$		0			0
$561$	30.2208	+	1.86670i	1.27592	+	0.0788122i
$562$		0			0
$563$	−9.98237			−0.420707			−0.210353	−	0.977625i	$-0.567461\pi$
$563$	−9.98237			−0.420707			−0.210353	+	0.977625i	$0.567461\pi$
$564$		0			0
$565$			17.5060i			0.736483i
$566$		0			0
$567$	21.0297	+	11.1692i	0.883166	+	0.469061i
$568$		0			0
$569$		−	16.2348i		−	0.680598i	−0.940317	−	0.340299i	$-0.889472\pi$
$569$		−	16.2348i		−	0.680598i	0.940317	−	0.340299i	$-0.110528\pi$
$570$		0			0
$571$	−12.6206			−0.528154			−0.264077	−	0.964502i	$-0.585067\pi$
$571$	−12.6206			−0.528154			−0.264077	+	0.964502i	$0.585067\pi$
$572$		0			0
$573$	−11.7785	−	0.727547i	−0.492056	−	0.0303937i
$574$		0			0
$575$		−	9.64936i		−	0.402406i
$576$		0			0
$577$	−4.18012	−	2.41339i	−0.174020	−	0.100471i	0.410460	−	0.911879i	$-0.365368\pi$
$577$	−4.18012	−	2.41339i	−0.174020	−	0.100471i	−0.584480	+	0.811408i	$0.698702\pi$
$578$		0			0
$579$	−1.70361	+	27.5804i	−0.0707995	+	1.14620i
$580$		0			0
$581$	−29.0600	+	30.2665i	−1.20561	+	1.25567i
$582$		0			0
$583$	−6.77942			−0.280775
$584$		0			0
$585$	3.90026	−	31.4510i	0.161256	−	1.30034i
$586$		0			0
$587$	5.26032	−	9.11114i	0.217117	−	0.376057i	−0.736809	−	0.676101i	$-0.763668\pi$
$587$	5.26032	−	9.11114i	0.217117	−	0.376057i	0.953925	+	0.300044i	$0.0970015\pi$
$588$		0			0
$589$	15.0944	+	26.1443i	0.621955	+	1.07726i
$590$		0			0
$591$	44.8632	+	2.77114i	1.84542	+	0.113990i
$592$		0			0
$593$	14.7342	+	25.5205i	0.605063	+	1.04800i	0.992042	+	0.125911i	$0.0401853\pi$
$593$	14.7342	+	25.5205i	0.605063	+	1.04800i	−0.386979	+	0.922089i	$0.626481\pi$
$594$		0			0
$595$	−13.6130	−	46.9633i	−0.558080	−	1.92531i
$596$		0			0
$597$	3.04622	−	4.59630i	0.124673	−	0.188114i
$598$		0			0
$599$			8.21752i			0.335759i	0.985808	+	0.167879i	$0.0536919\pi$
$599$			8.21752i			0.335759i	−0.985808	+	0.167879i	$0.946308\pi$
$600$		0			0
$601$	32.7131	+	18.8869i	1.33439	+	0.770413i	0.985970	−	0.166924i	$-0.0533833\pi$
$601$	32.7131	+	18.8869i	1.33439	+	0.770413i	0.348425	+	0.937337i	$0.386717\pi$
$602$		0			0
$603$	−22.9926	−	2.85133i	−0.936333	−	0.116115i
$604$		0			0
$605$	5.22038	+	9.04197i	0.212239	+	0.367608i
$606$		0			0
$607$	−30.8497	−	17.8111i	−1.25215	−	0.722929i	−0.280613	−	0.959821i	$-0.590538\pi$
$607$	−30.8497	−	17.8111i	−1.25215	−	0.722929i	−0.971536	+	0.236892i	$0.923871\pi$
$608$		0			0
$609$	−9.66797	+	8.89963i	−0.391766	+	0.360631i
$610$		0			0
$611$	−36.0693	+	20.8246i	−1.45921	+	0.842474i
$612$		0			0
$613$	11.9660	−	20.7256i	0.483301	−	0.837101i	−0.516516	−	0.856278i	$-0.672771\pi$
$613$	11.9660	−	20.7256i	0.483301	−	0.837101i	0.999816	+	0.0191767i	$0.00610451\pi$
$614$		0			0
$615$	−0.486667	+	7.87885i	−0.0196243	+	0.317706i
$616$		0			0
$617$	−1.98622	+	1.14675i	−0.0799623	+	0.0461663i	−0.539448	−	0.842019i	$-0.681367\pi$
$617$	−1.98622	+	1.14675i	−0.0799623	+	0.0461663i	0.459486	+	0.888185i	$0.348034\pi$
$618$		0			0
$619$	−9.10806	+	5.25854i	−0.366084	+	0.211359i	−0.671746	−	0.740781i	$-0.734455\pi$
$619$	−9.10806	+	5.25854i	−0.366084	+	0.211359i	0.305662	+	0.952140i	$0.401122\pi$
$620$		0			0
$621$	−10.1165	+	11.8015i	−0.405961	+	0.473579i
$622$		0			0
$623$	4.63796	+	16.0004i	0.185816	+	0.641043i
$624$		0			0
$625$	15.3617	−	26.6073i	0.614469	−	1.06429i
$626$		0			0
$627$	12.3860	+	8.20885i	0.494648	+	0.327830i
$628$		0			0
$629$	−21.9914			−0.876856
$630$		0			0
$631$	−2.02836			−0.0807477			−0.0403739	−	0.999185i	$-0.512855\pi$
$631$	−2.02836			−0.0807477			−0.0403739	+	0.999185i	$0.512855\pi$
$632$		0			0
$633$	−0.171307	+	0.0852813i	−0.00680884	+	0.00338963i
$634$		0			0
$635$	−19.1899	+	33.2380i	−0.761530	+	1.31901i
$636$		0			0
$637$	−25.7621	+	1.04825i	−1.02073	+	0.0415332i
$638$		0			0
$639$	−2.90409	+	23.4181i	−0.114884	+	0.926405i
$640$		0			0
$641$	10.7778	−	6.22257i	0.425698	−	0.245777i	−0.271814	−	0.962350i	$-0.587624\pi$
$641$	10.7778	−	6.22257i	0.425698	−	0.245777i	0.697512	+	0.716573i	$0.254290\pi$
$642$		0			0
$643$	−12.3358	+	7.12209i	−0.486477	+	0.280868i	−0.723112	−	0.690731i	$-0.757289\pi$
$643$	−12.3358	+	7.12209i	−0.486477	+	0.280868i	0.236635	+	0.971599i	$0.423956\pi$
$644$		0			0
$645$	41.6086	−	20.7139i	1.63834	−	0.815610i
$646$		0			0
$647$	−10.1910	+	17.6513i	−0.400649	+	0.693945i	−0.993804	−	0.111143i	$-0.964549\pi$
$647$	−10.1910	+	17.6513i	−0.400649	+	0.693945i	0.593155	+	0.805088i	$0.297882\pi$
$648$		0			0
$649$	20.3778	−	11.7651i	0.799899	−	0.461822i
$650$		0			0
$651$	41.7520	+	13.0599i	1.63639	+	0.511860i
$652$		0			0
$653$	7.55335	+	4.36093i	0.295585	+	0.170656i	0.640458	−	0.767993i	$-0.278745\pi$
$653$	7.55335	+	4.36093i	0.295585	+	0.170656i	−0.344873	+	0.938650i	$0.612078\pi$
$654$		0			0
$655$	1.11556	+	1.93221i	0.0435887	+	0.0754978i
$656$		0			0
$657$	−30.6170	−	23.1296i	−1.19448	−	0.902373i
$658$		0			0
$659$	−16.7524	−	9.67200i	−0.652581	−	0.376768i	0.136864	−	0.990590i	$-0.456298\pi$
$659$	−16.7524	−	9.67200i	−0.652581	−	0.376768i	−0.789444	+	0.613822i	$0.789631\pi$
$660$		0			0
$661$		−	36.8289i		−	1.43248i	−0.697854	−	0.716240i	$-0.745862\pi$
$661$		−	36.8289i		−	1.43248i	0.697854	−	0.716240i	$-0.254138\pi$
$662$		0			0
$663$	41.0318	+	2.53449i	1.59354	+	0.0984313i
$664$		0			0
$665$	5.73812	−	23.3000i	0.222515	−	0.903537i
$666$		0			0
$667$	−4.28900	−	7.42877i	−0.166071	−	0.287643i
$668$		0			0
$669$	12.4922	−	18.8489i	0.482977	−	0.728742i
$670$		0			0
$671$	−0.887942	−	1.53796i	−0.0342786	−	0.0593723i
$672$		0			0
$673$	8.79204	−	15.2283i	0.338908	−	0.587006i	−0.645319	−	0.763913i	$-0.723276\pi$
$673$	8.79204	−	15.2283i	0.338908	−	0.587006i	0.984228	+	0.176907i	$0.0566091\pi$
$674$		0			0
$675$	15.8096	−	5.56626i	0.608512	−	0.214245i
$676$		0			0
$677$	40.8291			1.56919			0.784595	−	0.620009i	$-0.212871\pi$
$677$	40.8291			1.56919			0.784595	+	0.620009i	$0.212871\pi$
$678$		0			0
$679$	−29.1035	−	27.9433i	−1.11689	−	1.07237i
$680$		0			0
$681$	14.3701	−	7.15385i	0.550665	−	0.274136i
$682$		0			0
$683$	−8.56287	−	4.94377i	−0.327649	−	0.189168i	0.327148	−	0.944973i	$-0.393912\pi$
$683$	−8.56287	−	4.94377i	−0.327649	−	0.189168i	−0.654797	+	0.755805i	$0.727246\pi$
$684$		0			0
$685$			47.3847i			1.81048i
$686$		0			0
$687$	12.8391	−	19.3724i	0.489843	−	0.739102i
$688$		0			0
$689$	−9.20467			−0.350670
$690$		0			0
$691$		−	43.7882i		−	1.66578i	−0.553436	−	0.832891i	$-0.686684\pi$
$691$		−	43.7882i		−	1.66578i	0.553436	−	0.832891i	$-0.313316\pi$
$692$		0			0
$693$	21.2619	−	3.40401i	0.807673	−	0.129308i
$694$		0			0
$695$		−	32.8465i		−	1.24594i
$696$		0			0
$697$	−10.2397			−0.387858
$698$		0			0
$699$	16.3480	+	32.8387i	0.618339	+	1.24207i
$700$		0			0
$701$		−	29.6742i		−	1.12078i	−0.828229	−	0.560389i	$-0.810651\pi$
$701$		−	29.6742i		−	1.12078i	0.828229	−	0.560389i	$-0.189349\pi$
$702$		0			0
$703$	−9.34651	−	5.39621i	−0.352510	−	0.203522i
$704$		0			0
$705$	−46.8212	−	31.0310i	−1.76339	−	1.16869i
$706$		0			0
$707$	−2.56998	−	8.86612i	−0.0966540	−	0.333445i
$708$		0			0
$709$	47.0538			1.76714			0.883572	−	0.468296i	$-0.155132\pi$
$709$	47.0538			1.76714			0.883572	+	0.468296i	$0.155132\pi$
$710$		0			0
$711$	−15.4556	−	1.91666i	−0.579629	−	0.0718802i
$712$		0			0
$713$	−14.2788	+	24.7316i	−0.534745	+	0.926206i
$714$		0			0
$715$	−14.3293	−	24.8191i	−0.535885	−	0.928180i
$716$		0			0
$717$	6.89291	+	13.8460i	0.257420	+	0.517087i
$718$		0			0
$719$	0.909148	+	1.57469i	0.0339055	+	0.0587261i	0.882480	−	0.470349i	$-0.155872\pi$
$719$	0.909148	+	1.57469i	0.0339055	+	0.0587261i	−0.848575	+	0.529076i	$0.822539\pi$
$720$		0			0
$721$	−6.37230	−	6.11829i	−0.237317	−	0.227857i
$722$		0			0
$723$	−14.2102	−	28.5444i	−0.528483	−	1.06158i
$724$		0			0
$725$			9.24948i			0.343517i
$726$		0			0
$727$	21.7854	+	12.5778i	0.807976	+	0.466485i	0.846252	−	0.532782i	$-0.178853\pi$
$727$	21.7854	+	12.5778i	0.807976	+	0.466485i	−0.0382766	+	0.999267i	$0.512187\pi$
$728$		0			0
$729$	−25.1714	−	9.76721i	−0.932276	−	0.361748i
$730$		0			0
$731$	30.1460	+	52.2145i	1.11499	+	1.93122i
$732$		0			0
$733$	−3.84543	−	2.22016i	−0.142034	−	0.0820034i	0.427299	−	0.904110i	$-0.359465\pi$
$733$	−3.84543	−	2.22016i	−0.142034	−	0.0820034i	−0.569333	+	0.822107i	$0.692799\pi$
$734$		0			0
$735$	−16.7496	−	30.4732i	−0.617820	−	1.12402i
$736$		0			0
$737$	−18.1443	+	10.4756i	−0.668353	+	0.385874i
$738$		0			0
$739$	−8.97608	+	15.5470i	−0.330191	+	0.571907i	−0.982549	−	0.186004i	$-0.940446\pi$
$739$	−8.97608	+	15.5470i	−0.330191	+	0.571907i	0.652358	+	0.757911i	$0.273780\pi$
$740$		0			0
$741$	16.8169	+	11.1455i	0.617783	+	0.409439i
$742$		0			0
$743$	−31.3712	+	18.1122i	−1.15090	+	0.664472i	−0.949106	−	0.314956i	$-0.898010\pi$
$743$	−31.3712	+	18.1122i	−1.15090	+	0.664472i	−0.201793	+	0.979428i	$0.564677\pi$
$744$		0			0
$745$	−12.1829	+	7.03378i	−0.446345	+	0.257698i
$746$		0			0
$747$	28.6783	−	37.9620i	1.04929	−	1.38896i
$748$		0			0
$749$	−9.11899	+	2.64328i	−0.333201	+	0.0965833i
$750$		0			0
$751$	−5.98210	+	10.3613i	−0.218290	+	0.378089i	−0.954285	−	0.298897i	$-0.903381\pi$
$751$	−5.98210	+	10.3613i	−0.218290	+	0.378089i	0.735995	+	0.676986i	$0.236714\pi$
$752$		0			0
$753$	−0.676145	+	10.9464i	−0.0246401	+	0.398908i
$754$		0			0
$755$	−28.2682			−1.02878
$756$		0			0
$757$	−49.4440			−1.79707			−0.898537	−	0.438898i	$-0.855369\pi$
$757$	−49.4440			−1.79707			−0.898537	+	0.438898i	$0.855369\pi$
$758$		0			0
$759$	−0.866591	+	14.0296i	−0.0314553	+	0.509242i
$760$		0			0
$761$	14.6192	−	25.3212i	0.529945	−	0.917892i	−0.469445	−	0.882962i	$-0.655546\pi$
$761$	14.6192	−	25.3212i	0.529945	−	0.917892i	0.999390	−	0.0349300i	$-0.0111208\pi$
$762$		0			0
$763$	25.2752	−	26.3245i	0.915023	−	0.953012i
$764$		0			0
$765$	21.6018	+	51.0621i	0.781015	+	1.84615i
$766$		0			0
$767$	27.6677	−	15.9740i	0.999023	−	0.576786i
$768$		0			0
$769$	−4.54689	+	2.62515i	−0.163965	+	0.0946653i	−0.579737	−	0.814804i	$-0.696845\pi$
$769$	−4.54689	+	2.62515i	−0.163965	+	0.0946653i	0.415772	+	0.909469i	$0.363511\pi$
$770$		0			0
$771$	−23.6569	−	15.6787i	−0.851981	−	0.564654i
$772$		0			0
$773$	−15.6829	+	27.1635i	−0.564073	+	0.977003i	0.433062	+	0.901364i	$0.357433\pi$
$773$	−15.6829	+	27.1635i	−0.564073	+	0.977003i	−0.997135	+	0.0756393i	$0.975900\pi$
$774$		0			0
$775$	26.6676	−	15.3965i	0.957927	−	0.553059i
$776$		0			0
$777$	−15.2609	+	3.41973i	−0.547482	+	0.122682i
$778$		0			0
$779$	−4.35195	−	2.51260i	−0.155925	−	0.0900233i
$780$		0			0
$781$	10.6694	+	18.4800i	0.381782	+	0.661266i
$782$		0			0
$783$	9.69725	−	11.3125i	0.346551	−	0.404274i
$784$		0			0
$785$	−38.2923	−	22.1081i	−1.36671	−	0.789071i
$786$		0			0
$787$		−	1.83971i		−	0.0655786i	−0.999462	−	0.0327893i	$-0.989561\pi$
$787$		−	1.83971i		−	0.0655786i	0.999462	−	0.0327893i	$-0.0104390\pi$
$788$		0			0
$789$	9.32873	+	18.7389i	0.332112	+	0.667121i
$790$		0			0
$791$	−15.5107	+	4.49602i	−0.551498	+	0.159860i
$792$		0			0
$793$	−1.20559	−	2.08814i	−0.0428118	−	0.0741522i
$794$		0			0
$795$	−5.53237	−	11.1130i	−0.196213	−	0.394138i
$796$		0			0
$797$	−6.39659	−	11.0792i	−0.226579	−	0.392446i	0.730213	−	0.683219i	$-0.239421\pi$
$797$	−6.39659	−	11.0792i	−0.226579	−	0.392446i	−0.956792	+	0.290773i	$0.906087\pi$
$798$		0			0
$799$	36.4316	−	63.1015i	1.28886	−	2.23237i
$800$		0			0
$801$	−7.35974	−	17.3968i	−0.260044	−	0.614687i
$802$		0			0
$803$	−34.6990			−1.22450
$804$		0			0
$805$	21.8021	−	6.31967i	0.768423	−	0.222739i
$806$		0			0
$807$	−36.5709	−	24.2375i	−1.28736	−	0.853202i
$808$		0			0
$809$	12.9217	+	7.46032i	0.454301	+	0.262291i	0.709645	−	0.704559i	$-0.248855\pi$
$809$	12.9217	+	7.46032i	0.454301	+	0.262291i	−0.255344	+	0.966850i	$0.582189\pi$
$810$		0			0
$811$		−	37.5478i		−	1.31848i	−0.751933	−	0.659240i	$-0.770878\pi$
$811$		−	37.5478i		−	1.31848i	0.751933	−	0.659240i	$-0.229122\pi$
$812$		0			0
$813$	0.174333	+	0.350187i	0.00611413	+	0.0122816i
$814$		0			0
$815$	−32.8134			−1.14940
$816$		0			0
$817$			29.5887i			1.03518i
$818$		0			0
$819$	28.8680	−	4.62175i	1.00873	−	0.161497i
$820$		0			0
$821$		−	3.32743i		−	0.116128i	−0.998313	−	0.0580640i	$-0.981507\pi$
$821$		−	3.32743i		−	0.116128i	0.998313	−	0.0580640i	$-0.0184927\pi$
$822$		0			0
$823$	50.9307			1.77533			0.887667	−	0.460486i	$-0.152325\pi$
$823$	50.9307			1.77533			0.887667	+	0.460486i	$0.152325\pi$
$824$		0			0
$825$	8.37314	−	12.6338i	0.291515	−	0.439854i
$826$		0			0
$827$			16.9198i			0.588360i	0.955750	+	0.294180i	$0.0950465\pi$
$827$			16.9198i			0.588360i	−0.955750	+	0.294180i	$0.904954\pi$
$828$		0			0
$829$	−4.65467	−	2.68737i	−0.161663	−	0.0933364i	0.416986	−	0.908913i	$-0.363087\pi$
$829$	−4.65467	−	2.68737i	−0.161663	−	0.0933364i	−0.578649	+	0.815577i	$0.696420\pi$
$830$		0			0
$831$	31.6836	−	15.7730i	1.09909	−	0.547159i
$832$		0			0
$833$	38.1144	−	24.1229i	1.32059	−	0.835810i
$834$		0			0
$835$	−37.2330			−1.28850
$836$		0			0
$837$	−48.7573	−	9.12803i	−1.68530	−	0.315511i
$838$		0			0
$839$	−11.8714	+	20.5618i	−0.409846	+	0.709874i	−0.994872	−	0.101140i	$-0.967751\pi$
$839$	−11.8714	+	20.5618i	−0.409846	+	0.709874i	0.585026	+	0.811014i	$0.301084\pi$
$840$		0			0
$841$	−10.3887	−	17.9938i	−0.358232	−	0.620477i
$842$		0			0
$843$	9.90674	−	14.9478i	0.341206	−	0.514831i
$844$		0			0
$845$	−0.813168	−	1.40845i	−0.0279738	−	0.0484521i
$846$		0			0
$847$	−6.67066	+	6.94761i	−0.229207	+	0.238723i
$848$		0			0
$849$	23.7110	+	1.46460i	0.813760	+	0.0502650i
$850$		0			0
$851$		−	10.2092i		−	0.349968i
$852$		0			0
$853$	−10.3810	−	5.99345i	−0.355437	−	0.205212i	0.311640	−	0.950200i	$-0.399122\pi$
$853$	−10.3810	−	5.99345i	−0.355437	−	0.205212i	−0.667077	+	0.744988i	$0.732455\pi$
$854$		0			0
$855$	−3.34858	+	27.0023i	−0.114519	+	0.923459i
$856$		0			0
$857$	27.5318	+	47.6864i	0.940467	+	1.62894i	0.764583	+	0.644526i	$0.222945\pi$
$857$	27.5318	+	47.6864i	0.940467	+	1.62894i	0.175884	+	0.984411i	$0.443722\pi$
$858$		0			0
$859$	33.8798	+	19.5605i	1.15596	+	0.667395i	0.950333	−	0.311235i	$-0.100742\pi$
$859$	33.8798	+	19.5605i	1.15596	+	0.667395i	0.205630	+	0.978630i	$0.434076\pi$
$860$		0			0
$861$	−7.10584	+	1.59231i	−0.242166	+	0.0542656i
$862$		0			0
$863$	39.2319	−	22.6506i	1.33547	−	0.771034i	0.349338	−	0.936997i	$-0.386407\pi$
$863$	39.2319	−	22.6506i	1.33547	−	0.771034i	0.986132	+	0.165963i	$0.0530733\pi$
$864$		0			0
$865$	−28.1063	+	48.6815i	−0.955643	+	1.65522i
$866$		0			0
$867$	−38.0238	+	18.9293i	−1.29136	+	0.642873i
$868$		0			0
$869$	−12.1965	+	7.04166i	−0.413738	+	0.238872i
$870$		0			0
$871$	−24.6351	+	14.2231i	−0.834730	+	0.481931i
$872$		0			0
$873$	36.5032	+	27.5763i	1.23545	+	0.933317i
$874$		0			0
$875$	13.0735	+	3.21962i	0.441965	+	0.108843i
$876$		0			0
$877$	2.02825	−	3.51304i	0.0684893	−	0.118627i	−0.829747	−	0.558139i	$-0.811515\pi$
$877$	2.02825	−	3.51304i	0.0684893	−	0.118627i	0.898236	+	0.439512i	$0.144849\pi$
$878$		0			0
$879$	13.0719	−	6.50754i	0.440903	−	0.219494i
$880$		0			0
$881$	54.3727			1.83186			0.915931	−	0.401336i	$-0.131454\pi$
$881$	54.3727			1.83186			0.915931	+	0.401336i	$0.131454\pi$
$882$		0			0
$883$	23.1175			0.777965			0.388982	−	0.921245i	$-0.372827\pi$
$883$	23.1175			0.777965			0.388982	+	0.921245i	$0.372827\pi$
$884$		0			0
$885$	35.9152	+	23.8029i	1.20728	+	0.800127i
$886$		0			0
$887$	12.7818	−	22.1387i	0.429171	−	0.743346i	−0.567629	−	0.823285i	$-0.692139\pi$
$887$	12.7818	−	22.1387i	0.429171	−	0.743346i	0.996800	+	0.0799384i	$0.0254724\pi$
$888$		0			0
$889$	−34.3781	−	8.46633i	−1.15301	−	0.283952i
$890$		0			0
$891$	−23.4861	+	6.67318i	−0.786814	+	0.223560i
$892$		0			0
$893$	30.9674	−	17.8790i	1.03628	−	0.598298i
$894$		0			0
$895$	−46.6428	+	26.9292i	−1.55910	+	0.900144i
$896$		0			0
$897$	−1.17660	+	19.0485i	−0.0392856	+	0.636010i
$898$		0			0
$899$	13.6871	−	23.7067i	0.456489	−	0.790663i
$900$		0			0
$901$	13.9457	−	8.05155i	0.464598	−	0.268236i
$902$		0			0
$903$	29.0393	+	31.5463i	0.966366	+	1.04980i
$904$		0			0
$905$	−11.1218	−	6.42118i	−0.369702	−	0.213447i
$906$		0			0
$907$	18.5065	+	32.0542i	0.614498	+	1.06434i	0.990472	+	0.137712i	$0.0439748\pi$
$907$	18.5065	+	32.0542i	0.614498	+	1.06434i	−0.375974	+	0.926630i	$0.622692\pi$
$908$		0			0
$909$	4.07817	+	9.63991i	0.135264	+	0.319736i
$910$		0			0
$911$	3.16266	+	1.82596i	0.104784	+	0.0604969i	0.551476	−	0.834191i	$-0.314065\pi$
$911$	3.16266	+	1.82596i	0.104784	+	0.0604969i	−0.446692	+	0.894688i	$0.647398\pi$
$912$		0			0
$913$		−	43.0231i		−	1.42386i
$914$		0			0
$915$	1.79646	−	2.71060i	0.0593892	−	0.0896096i
$916$		0			0
$917$	−1.42548	+	1.48466i	−0.0470734	+	0.0490278i
$918$		0			0
$919$	17.3994	+	30.1367i	0.573954	+	0.994117i	0.996154	+	0.0876145i	$0.0279244\pi$
$919$	17.3994	+	30.1367i	0.573954	+	0.994117i	−0.422201	+	0.906502i	$0.638742\pi$
$920$		0			0
$921$	9.23753	+	0.570591i	0.304387	+	0.0188016i
$922$		0			0
$923$	14.4863	+	25.0910i	0.476822	+	0.825879i
$924$		0			0
$925$	−5.50420	+	9.53356i	−0.180977	+	0.313461i
$926$		0			0
$927$	7.99251	+	6.03793i	0.262508	+	0.198312i
$928$		0			0
$929$	−50.3471			−1.65183			−0.825917	−	0.563791i	$-0.809342\pi$
$929$	−50.3471			−1.65183			−0.825917	+	0.563791i	$0.809342\pi$
$930$		0			0
$931$	22.1181	−	0.899977i	0.724891	−	0.0294955i
$932$		0			0
$933$	−1.00561	+	16.2803i	−0.0329223	+	0.532992i
$934$		0			0
$935$	43.4197	+	25.0684i	1.41998	+	0.819824i
$936$		0			0
$937$		−	6.48087i		−	0.211721i	−0.994381	−	0.105860i	$-0.966240\pi$
$937$		−	6.48087i		−	0.211721i	0.994381	−	0.105860i	$-0.0337596\pi$
$938$		0			0
$939$	−28.6148	−	1.76751i	−0.933810	−	0.0576804i
$940$		0			0
$941$	0.668048			0.0217777			0.0108889	−	0.999941i	$-0.496534\pi$
$941$	0.668048			0.0217777			0.0108889	+	0.999941i	$0.496534\pi$
$942$		0			0
$943$		−	4.75366i		−	0.154801i
$944$		0			0
$945$	22.9308	+	32.0753i	0.745939	+	1.04341i
$946$		0			0
$947$		−	58.5966i		−	1.90413i	−0.305890	−	0.952067i	$-0.598954\pi$
$947$		−	58.5966i		−	1.90413i	0.305890	−	0.952067i	$-0.401046\pi$
$948$		0			0
$949$	−47.1120			−1.52932
$950$		0			0
$951$	−45.8576	−	2.83257i	−1.48703	−	0.0918524i
$952$		0			0
$953$		−	48.3707i		−	1.56688i	−0.621467	−	0.783441i	$-0.713463\pi$
$953$		−	48.3707i		−	1.56688i	0.621467	−	0.783441i	$-0.286537\pi$
$954$		0			0
$955$	−16.9228	−	9.77041i	−0.547610	−	0.316163i
$956$		0			0
$957$	0.830679	−	13.4482i	0.0268520	−	0.434718i
$958$		0			0
$959$	−41.9840	+	12.1697i	−1.35573	+	0.392980i
$960$		0			0
$961$	−60.1330			−1.93977
$962$		0			0
$963$	9.91486	−	4.19448i	0.319502	−	0.135165i
$964$		0			0
$965$	−22.8781	+	39.6261i	−0.736474	+	1.27561i
$966$		0			0
$967$	8.51390	+	14.7465i	0.273788	+	0.474216i	0.969829	−	0.243787i	$-0.0783898\pi$
$967$	8.51390	+	14.7465i	0.273788	+	0.474216i	−0.696040	+	0.718003i	$0.745057\pi$
$968$		0			0
$969$	−35.2279	−	2.17599i	−1.13168	−	0.0699028i
$970$		0			0
$971$	13.5651	+	23.4955i	0.435325	+	0.754006i	0.997322	−	0.0731339i	$-0.0233000\pi$
$971$	13.5651	+	23.4955i	0.435325	+	0.754006i	−0.561997	+	0.827139i	$0.689967\pi$
$972$		0			0
$973$	29.1028	−	8.43589i	0.932994	−	0.270442i
$974$		0			0
$975$	11.3685	−	17.1534i	0.364084	−	0.549349i
$976$		0			0
$977$		−	6.34898i		−	0.203122i	−0.994829	−	0.101561i	$-0.967616\pi$
$977$		−	6.34898i		−	0.203122i	0.994829	−	0.101561i	$-0.0323837\pi$
$978$		0			0
$979$	−14.7931	−	8.54080i	−0.472789	−	0.272965i
$980$		0			0
$981$	−24.9432	+	33.0177i	−0.796376	+	1.05418i
$982$		0			0
$983$	9.98300	+	17.2911i	0.318408	+	0.551499i	0.980156	−	0.198227i	$-0.0635184\pi$
$983$	9.98300	+	17.2911i	0.318408	+	0.551499i	−0.661748	+	0.749727i	$0.730185\pi$
$984$		0			0
$985$	64.4572	+	37.2144i	2.05378	+	1.18575i
$986$		0			0
$987$	15.4692	−	49.4543i	0.492390	−	1.57415i
$988$		0			0
$989$	−24.2399	+	13.9949i	−0.770784	+	0.445012i
$990$		0			0
$991$	6.38803	−	11.0644i	0.202922	−	0.351472i	−0.746546	−	0.665333i	$-0.768289\pi$
$991$	6.38803	−	11.0644i	0.202922	−	0.351472i	0.949469	+	0.313861i	$0.101623\pi$
$992$		0			0
$993$	−1.88366	+	30.4952i	−0.0597760	+	0.967737i
$994$		0			0
$995$	7.90734	−	4.56530i	0.250679	−	0.144730i
$996$		0			0
$997$	−17.9846	+	10.3834i	−0.569579	+	0.328847i	−0.756981	−	0.653436i	$-0.773327\pi$
$997$	−17.9846	+	10.3834i	−0.569579	+	0.328847i	0.187402	+	0.982283i	$0.439993\pi$
$998$		0			0
$999$	16.7269	−	5.88923i	0.529216	−	0.186327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.w.a.101.5	yes	16
3.2	odd	2		756.2.w.a.521.1		16
4.3	odd	2		1008.2.ca.d.353.4		16
7.2	even	3		1764.2.bm.a.1685.7		16
7.3	odd	6		1764.2.x.b.1469.8		16
7.4	even	3		1764.2.x.a.1469.1		16
7.5	odd	6		252.2.bm.a.173.2	yes	16
7.6	odd	2		1764.2.w.b.1109.4		16
9.2	odd	6		2268.2.t.a.1781.1		16
9.4	even	3		756.2.bm.a.17.1		16
9.5	odd	6		252.2.bm.a.185.2	yes	16
9.7	even	3		2268.2.t.b.1781.8		16
12.11	even	2		3024.2.ca.d.2033.1		16
21.2	odd	6		5292.2.bm.a.4625.8		16
21.5	even	6		756.2.bm.a.89.1		16
21.11	odd	6		5292.2.x.a.4409.1		16
21.17	even	6		5292.2.x.b.4409.8		16
21.20	even	2		5292.2.w.b.521.8		16
28.19	even	6		1008.2.df.d.929.7		16
36.23	even	6		1008.2.df.d.689.7		16
36.31	odd	6		3024.2.df.d.17.1		16
63.4	even	3		5292.2.x.b.881.8		16
63.5	even	6	inner	252.2.w.a.5.5	✓	16
63.13	odd	6		5292.2.bm.a.2285.8		16
63.23	odd	6		1764.2.w.b.509.4		16
63.31	odd	6		5292.2.x.a.881.1		16
63.32	odd	6		1764.2.x.b.293.8		16
63.40	odd	6		756.2.w.a.341.1		16
63.41	even	6		1764.2.bm.a.1697.7		16
63.47	even	6		2268.2.t.b.2105.8		16
63.58	even	3		5292.2.w.b.1097.8		16
63.59	even	6		1764.2.x.a.293.1		16
63.61	odd	6		2268.2.t.a.2105.1		16
84.47	odd	6		3024.2.df.d.1601.1		16
252.103	even	6		3024.2.ca.d.2609.1		16
252.131	odd	6		1008.2.ca.d.257.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.5	✓	16	63.5	even	6	inner
252.2.w.a.101.5	yes	16	1.1	even	1	trivial
252.2.bm.a.173.2	yes	16	7.5	odd	6
252.2.bm.a.185.2	yes	16	9.5	odd	6
756.2.w.a.341.1		16	63.40	odd	6
756.2.w.a.521.1		16	3.2	odd	2
756.2.bm.a.17.1		16	9.4	even	3
756.2.bm.a.89.1		16	21.5	even	6
1008.2.ca.d.257.4		16	252.131	odd	6
1008.2.ca.d.353.4		16	4.3	odd	2
1008.2.df.d.689.7		16	36.23	even	6
1008.2.df.d.929.7		16	28.19	even	6
1764.2.w.b.509.4		16	63.23	odd	6
1764.2.w.b.1109.4		16	7.6	odd	2
1764.2.x.a.293.1		16	63.59	even	6
1764.2.x.a.1469.1		16	7.4	even	3
1764.2.x.b.293.8		16	63.32	odd	6
1764.2.x.b.1469.8		16	7.3	odd	6
1764.2.bm.a.1685.7		16	7.2	even	3
1764.2.bm.a.1697.7		16	63.41	even	6
2268.2.t.a.1781.1		16	9.2	odd	6
2268.2.t.a.2105.1		16	63.61	odd	6
2268.2.t.b.1781.8		16	9.7	even	3
2268.2.t.b.2105.8		16	63.47	even	6
3024.2.ca.d.2033.1		16	12.11	even	2
3024.2.ca.d.2609.1		16	252.103	even	6
3024.2.df.d.17.1		16	36.31	odd	6
3024.2.df.d.1601.1		16	84.47	odd	6
5292.2.w.b.521.8		16	21.20	even	2
5292.2.w.b.1097.8		16	63.58	even	3
5292.2.x.a.881.1		16	63.31	odd	6
5292.2.x.a.4409.1		16	21.11	odd	6
5292.2.x.b.881.8		16	63.4	even	3
5292.2.x.b.4409.8		16	21.17	even	6
5292.2.bm.a.2285.8		16	63.13	odd	6
5292.2.bm.a.4625.8		16	21.2	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.106783 - 1.72876i) q^{3} +(1.43402 - 2.48379i) q^{5} +(2.56899 + 0.632668i) q^{7} +(-2.97719 - 0.369204i) q^{9} +O(q^{10})\)	\(q+(0.106783 - 1.72876i) q^{3} +(1.43402 - 2.48379i) q^{5} +(2.56899 + 0.632668i) q^{7} +(-2.97719 - 0.369204i) q^{9} +(-2.34941 + 1.35643i) q^{11} +(-3.18987 + 1.84167i) q^{13} +(-4.14074 - 2.74429i) q^{15} +(3.22192 - 5.58052i) q^{17} +(2.73867 - 1.58117i) q^{19} +(1.36805 - 4.37361i) q^{21} +(2.59068 + 1.49573i) q^{23} +(-1.61282 - 2.79348i) q^{25} +(-0.956179 + 5.10742i) q^{27} +(-2.48332 - 1.43375i) q^{29} +9.54636i q^{31} +(2.09406 + 4.20639i) q^{33} +(5.25540 - 5.47359i) q^{35} +(-1.70640 - 2.95556i) q^{37} +(2.84318 + 5.71117i) q^{39} +(-0.794538 - 1.37618i) q^{41} +(-4.67828 + 8.10302i) q^{43} +(-5.18638 + 6.86529i) q^{45} +11.3074 q^{47} +(6.19946 + 3.25064i) q^{49} +(-9.30332 - 6.16581i) q^{51} +(2.16419 + 1.24950i) q^{53} +7.78058i q^{55} +(-2.44102 - 4.90333i) q^{57} -8.67361 q^{59} +0.654617i q^{61} +(-7.41481 - 2.83206i) q^{63} +10.5640i q^{65} +7.72292 q^{67} +(2.86240 - 4.31894i) q^{69} -7.86582i q^{71} +(11.0769 + 6.39527i) q^{73} +(-5.00146 + 2.48987i) q^{75} +(-6.89378 + 1.99827i) q^{77} +5.19132 q^{79} +(8.72738 + 2.19839i) q^{81} +(-7.92948 + 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(-2.74378 + 4.13996i) q^{87} +(3.14826 + 5.45295i) q^{89} +(-9.35993 + 2.71312i) q^{91} +(16.5033 + 1.01939i) q^{93} -9.06971i q^{95} +(-13.2065 - 7.62477i) q^{97} +(7.49544 - 3.17095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7} + 6 q^{9}+O(q^{10}) \) 16 * q - q^7 + 6 * q^9	\( 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Introduction

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