LMFDB - Embedded newform 2646.2.l.b.1097.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(521,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2646.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.l (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:	$21.1284163748$
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} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1097.5
Root			$-1.62181 + 0.608059i$ of defining polynomial
Character	$\chi$	$=$	2646.1097
Dual form			2646.2.l.b.521.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-1.94556 - 3.36980i) q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.94556 - 3.36980i) q^{5} -1.00000i q^{8} +(3.36980 - 1.94556i) q^{10} +(3.41614 + 1.97231i) q^{11} +(2.46687 + 1.42425i) q^{13} +1.00000 q^{16} +(0.371058 + 0.642692i) q^{17} +(1.54563 + 0.892369i) q^{19} +(1.94556 + 3.36980i) q^{20} +(-1.97231 + 3.41614i) q^{22} +(-5.41535 + 3.12656i) q^{23} +(-5.07039 + 8.78217i) q^{25} +(-1.42425 + 2.46687i) q^{26} +(2.50079 - 1.44383i) q^{29} -3.51174i q^{31} +1.00000i q^{32} +(-0.642692 + 0.371058i) q^{34} +(-1.50079 + 2.59944i) q^{37} +(-0.892369 + 1.54563i) q^{38} +(-3.36980 + 1.94556i) q^{40} +(5.24705 - 9.08816i) q^{41} +(0.471521 + 0.816699i) q^{43} +(-3.41614 - 1.97231i) q^{44} +(-3.12656 - 5.41535i) q^{46} +2.18525 q^{47} +(-8.78217 - 5.07039i) q^{50} +(-2.46687 - 1.42425i) q^{52} -15.3490i q^{55} +(1.44383 + 2.50079i) q^{58} +0.0211346 q^{59} -2.46911i q^{61} +3.51174 q^{62} -1.00000 q^{64} -11.0838i q^{65} +13.4493 q^{67} +(-0.371058 - 0.642692i) q^{68} +1.94304i q^{71} +(4.20443 - 2.42743i) q^{73} +(-2.59944 - 1.50079i) q^{74} +(-1.54563 - 0.892369i) q^{76} +3.63613 q^{79} +(-1.94556 - 3.36980i) q^{80} +(9.08816 + 5.24705i) q^{82} +(4.02998 + 6.98012i) q^{83} +(1.44383 - 2.50079i) q^{85} +(-0.816699 + 0.471521i) q^{86} +(1.97231 - 3.41614i) q^{88} +(-4.63323 + 8.02499i) q^{89} +(5.41535 - 3.12656i) q^{92} +2.18525i q^{94} -6.94462i q^{95} +(16.2983 - 9.40980i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} - 12 q^{11} + 16 q^{16} - 48 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} + 12 q^{44} - 12 q^{46} - 60 q^{50} - 12 q^{58} - 16 q^{64} + 56 q^{67} + 36 q^{74} + 8 q^{79} - 12 q^{85} - 24 q^{86} + 48 q^{92}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^11 + 16 * q^16 - 48 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 + 12 * q^44 - 12 * q^46 - 60 * q^50 - 12 * q^58 - 16 * q^64 + 56 * q^67 + 36 * q^74 + 8 * q^79 - 12 * q^85 - 24 * q^86 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.94556	−	3.36980i	−0.870080	−	1.50702i	−0.861913	−	0.507056i	$-0.830734\pi$
$5$	−1.94556	−	3.36980i	−0.870080	−	1.50702i	−0.00816625	−	0.999967i	$-0.502599\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	3.36980	−	1.94556i	1.06563	−	0.615239i
$11$	3.41614	+	1.97231i	1.03001	+	0.594674i	0.916986	−	0.398919i	$-0.130615\pi$
$11$	3.41614	+	1.97231i	1.03001	+	0.594674i	0.113019	+	0.993593i	$0.463948\pi$
$12$		0			0
$13$	2.46687	+	1.42425i	0.684186	+	0.395015i	0.801430	−	0.598088i	$-0.204073\pi$
$13$	2.46687	+	1.42425i	0.684186	+	0.395015i	−0.117244	+	0.993103i	$0.537406\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	0.371058	+	0.642692i	0.0899949	+	0.155876i	0.907509	−	0.420033i	$-0.137982\pi$
$17$	0.371058	+	0.642692i	0.0899949	+	0.155876i	−0.817514	+	0.575909i	$0.804648\pi$
$18$		0			0
$19$	1.54563	+	0.892369i	0.354591	+	0.204723i	0.666706	−	0.745321i	$-0.267704\pi$
$19$	1.54563	+	0.892369i	0.354591	+	0.204723i	−0.312114	+	0.950045i	$0.601037\pi$
$20$	1.94556	+	3.36980i	0.435040	+	0.753511i
$21$		0			0
$22$	−1.97231	+	3.41614i	−0.420498	+	0.728324i
$23$	−5.41535	+	3.12656i	−1.12918	+	0.651932i	−0.943728	−	0.330722i	$-0.892708\pi$
$23$	−5.41535	+	3.12656i	−1.12918	+	0.651932i	−0.185451	+	0.982654i	$0.559374\pi$
$24$		0			0
$25$	−5.07039	+	8.78217i	−1.01408	+	1.75643i
$26$	−1.42425	+	2.46687i	−0.279318	+	0.483793i
$27$		0			0
$28$		0			0
$29$	2.50079	−	1.44383i	0.464385	−	0.268113i	−0.249501	−	0.968374i	$-0.580267\pi$
$29$	2.50079	−	1.44383i	0.464385	−	0.268113i	0.713886	+	0.700262i	$0.246933\pi$
$30$		0			0
$31$		−	3.51174i		−	0.630726i	−0.948971	−	0.315363i	$-0.897874\pi$
$31$		−	3.51174i		−	0.630726i	0.948971	−	0.315363i	$-0.102126\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−0.642692	+	0.371058i	−0.110221	+	0.0636360i
$35$		0			0
$36$		0			0
$37$	−1.50079	+	2.59944i	−0.246728	+	0.427346i	−0.962616	−	0.270870i	$-0.912689\pi$
$37$	−1.50079	+	2.59944i	−0.246728	+	0.427346i	0.715888	+	0.698215i	$0.246022\pi$
$38$	−0.892369	+	1.54563i	−0.144761	+	0.250734i
$39$		0			0
$40$	−3.36980	+	1.94556i	−0.532813	+	0.307620i
$41$	5.24705	−	9.08816i	0.819452	−	1.41933i	−0.0866345	−	0.996240i	$-0.527611\pi$
$41$	5.24705	−	9.08816i	0.819452	−	1.41933i	0.906087	−	0.423092i	$-0.139055\pi$
$42$		0			0
$43$	0.471521	+	0.816699i	0.0719063	+	0.124545i	0.899737	−	0.436433i	$-0.143758\pi$
$43$	0.471521	+	0.816699i	0.0719063	+	0.124545i	−0.827830	+	0.560978i	$0.810425\pi$
$44$	−3.41614	−	1.97231i	−0.515003	−	0.297337i
$45$		0			0
$46$	−3.12656	−	5.41535i	−0.460985	−	0.798450i
$47$	2.18525			0.318752			0.159376	−	0.987218i	$-0.449052\pi$
$47$	2.18525			0.318752			0.159376	+	0.987218i	$0.449052\pi$
$48$		0			0
$49$		0			0
$50$	−8.78217	−	5.07039i	−1.24199	−	0.717061i
$51$		0			0
$52$	−2.46687	−	1.42425i	−0.342093	−	0.197507i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$		0			0
$55$		−	15.3490i		−	2.06965i
$56$		0			0
$57$		0			0
$58$	1.44383	+	2.50079i	0.189584	+	0.328370i
$59$	0.0211346			0.00275149			0.00137575	−	0.999999i	$-0.499562\pi$
$59$	0.0211346			0.00275149			0.00137575	+	0.999999i	$0.499562\pi$
$60$		0			0
$61$		−	2.46911i		−	0.316138i	−0.987428	−	0.158069i	$-0.949473\pi$
$61$		−	2.46911i		−	0.316138i	0.987428	−	0.158069i	$-0.0505268\pi$
$62$	3.51174			0.445991
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	11.0838i		−	1.37478i
$66$		0			0
$67$	13.4493			1.64309			0.821544	−	0.570144i	$-0.193113\pi$
$67$	13.4493			1.64309			0.821544	+	0.570144i	$0.193113\pi$
$68$	−0.371058	−	0.642692i	−0.0449974	−	0.0779379i
$69$		0			0
$70$		0			0
$71$			1.94304i			0.230597i	0.993331	+	0.115298i	$0.0367824\pi$
$71$			1.94304i			0.230597i	−0.993331	+	0.115298i	$0.963218\pi$
$72$		0			0
$73$	4.20443	−	2.42743i	0.492092	−	0.284109i	−0.233350	−	0.972393i	$-0.574969\pi$
$73$	4.20443	−	2.42743i	0.492092	−	0.284109i	0.725442	+	0.688284i	$0.241636\pi$
$74$	−2.59944	−	1.50079i	−0.302179	−	0.174463i
$75$		0			0
$76$	−1.54563	−	0.892369i	−0.177296	−	0.102362i
$77$		0			0
$78$		0			0
$79$	3.63613			0.409096			0.204548	−	0.978856i	$-0.434427\pi$
$79$	3.63613			0.409096			0.204548	+	0.978856i	$0.434427\pi$
$80$	−1.94556	−	3.36980i	−0.217520	−	0.376756i
$81$		0			0
$82$	9.08816	+	5.24705i	1.00362	+	0.579440i
$83$	4.02998	+	6.98012i	0.442347	+	0.766168i	0.997863	−	0.0653378i	$-0.0208125\pi$
$83$	4.02998	+	6.98012i	0.442347	+	0.766168i	−0.555516	+	0.831506i	$0.687479\pi$
$84$		0			0
$85$	1.44383	−	2.50079i	0.156605	−	0.271249i
$86$	−0.816699	+	0.471521i	−0.0880669	+	0.0508454i
$87$		0			0
$88$	1.97231	−	3.41614i	0.210249	−	0.364162i
$89$	−4.63323	+	8.02499i	−0.491122	+	0.850647i	−0.999948	−	0.0102218i	$-0.996746\pi$
$89$	−4.63323	+	8.02499i	−0.491122	+	0.850647i	0.508826	+	0.860869i	$0.330080\pi$
$90$		0			0
$91$		0			0
$92$	5.41535	−	3.12656i	0.564589	−	0.325966i
$93$		0			0
$94$			2.18525i			0.225392i
$95$		−	6.94462i		−	0.712503i
$96$		0			0
$97$	16.2983	−	9.40980i	1.65484	−	0.955421i	0.679794	−	0.733403i	$-0.262069\pi$
$97$	16.2983	−	9.40980i	1.65484	−	0.955421i	0.975043	−	0.222018i	$-0.0712643\pi$
$98$		0			0
$99$		0			0
$100$	5.07039	−	8.78217i	0.507039	−	0.878217i
$101$	−4.14079	+	7.17206i	−0.412024	+	0.713647i	−0.995111	−	0.0987631i	$-0.968511\pi$
$101$	−4.14079	+	7.17206i	−0.412024	+	0.713647i	0.583087	+	0.812410i	$0.301845\pi$
$102$		0			0
$103$	14.7646	−	8.52435i	1.45480	−	0.839929i	0.456051	−	0.889953i	$-0.349263\pi$
$103$	14.7646	−	8.52435i	1.45480	−	0.839929i	0.998748	+	0.0500247i	$0.0159300\pi$
$104$	1.42425	−	2.46687i	0.139659	−	0.241896i
$105$		0			0
$106$		0			0
$107$	12.4161	+	7.16846i	1.20031	+	0.693001i	0.960625	−	0.277848i	$-0.0896213\pi$
$107$	12.4161	+	7.16846i	1.20031	+	0.693001i	0.239689	+	0.970850i	$0.422955\pi$
$108$		0			0
$109$	−5.63998	−	9.76874i	−0.540212	−	0.935675i	−0.998891	−	0.0470733i	$-0.985011\pi$
$109$	−5.63998	−	9.76874i	−0.540212	−	0.935675i	0.458679	−	0.888602i	$-0.348323\pi$
$110$	15.3490			1.46347
$111$		0			0
$112$		0			0
$113$	8.51501	+	4.91614i	0.801024	+	0.462472i	0.843829	−	0.536612i	$-0.180296\pi$
$113$	8.51501	+	4.91614i	0.801024	+	0.462472i	−0.0428049	+	0.999083i	$0.513629\pi$
$114$		0			0
$115$	21.0718	+	12.1658i	1.96495	+	1.13447i
$116$	−2.50079	+	1.44383i	−0.232192	+	0.134056i
$117$		0			0
$118$			0.0211346i			0.00194560i
$119$		0			0
$120$		0			0
$121$	2.28001	+	3.94910i	0.207274	+	0.359009i
$122$	2.46911			0.223543
$123$		0			0
$124$			3.51174i			0.315363i
$125$	20.0033			1.78915
$126$		0			0
$127$	2.94462			0.261293			0.130646	−	0.991429i	$-0.458295\pi$
$127$	2.94462			0.261293			0.130646	+	0.991429i	$0.458295\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	11.0838			0.972115
$131$	−7.53255	−	13.0468i	−0.658122	−	1.13990i	−0.981101	−	0.193495i	$-0.938018\pi$
$131$	−7.53255	−	13.0468i	−0.658122	−	1.13990i	0.322979	−	0.946406i	$-0.395316\pi$
$132$		0			0
$133$		0			0
$134$			13.4493i			1.16184i
$135$		0			0
$136$	0.642692	−	0.371058i	0.0551104	−	0.0318180i
$137$	−13.6139	−	7.85997i	−1.16311	−	0.671523i	−0.211064	−	0.977472i	$-0.567693\pi$
$137$	−13.6139	−	7.85997i	−1.16311	−	0.671523i	−0.952048	+	0.305950i	$0.901026\pi$
$138$		0			0
$139$	2.86373	+	1.65337i	0.242898	+	0.140237i	0.616508	−	0.787349i	$-0.288547\pi$
$139$	2.86373	+	1.65337i	0.242898	+	0.140237i	−0.373610	+	0.927586i	$0.621880\pi$
$140$		0			0
$141$		0			0
$142$	−1.94304			−0.163056
$143$	5.61811	+	9.73085i	0.469810	+	0.813735i
$144$		0			0
$145$	−9.73085	−	5.61811i	−0.808103	−	0.466559i
$146$	2.42743	+	4.20443i	0.200896	+	0.347961i
$147$		0			0
$148$	1.50079	−	2.59944i	0.123364	−	0.213673i
$149$	9.52765	−	5.50079i	0.780535	−	0.450642i	−0.0560848	−	0.998426i	$-0.517862\pi$
$149$	9.52765	−	5.50079i	0.780535	−	0.450642i	0.836620	+	0.547784i	$0.184528\pi$
$150$		0			0
$151$	0.719988	−	1.24706i	0.0585918	−	0.101484i	−0.835242	−	0.549883i	$-0.814672\pi$
$151$	0.719988	−	1.24706i	0.0585918	−	0.101484i	0.893834	+	0.448399i	$0.148006\pi$
$152$	0.892369	−	1.54563i	0.0723807	−	0.125367i
$153$		0			0
$154$		0			0
$155$	−11.8339	+	6.83228i	−0.950518	+	0.548782i
$156$		0			0
$157$		−	16.6071i		−	1.32539i	−0.748890	−	0.662695i	$-0.769413\pi$
$157$		−	16.6071i		−	1.32539i	0.748890	−	0.662695i	$-0.230587\pi$
$158$			3.63613i			0.289275i
$159$		0			0
$160$	3.36980	−	1.94556i	0.266406	−	0.153810i
$161$		0			0
$162$		0			0
$163$	6.19773	−	10.7348i	0.485444	−	0.840813i	−0.514416	−	0.857541i	$-0.671991\pi$
$163$	6.19773	−	10.7348i	0.485444	−	0.840813i	0.999860	+	0.0167274i	$0.00532476\pi$
$164$	−5.24705	+	9.08816i	−0.409726	+	0.709666i
$165$		0			0
$166$	−6.98012	+	4.02998i	−0.541763	+	0.312787i
$167$	5.86087	−	10.1513i	0.453528	−	0.785534i	−0.545074	−	0.838388i	$-0.683498\pi$
$167$	5.86087	−	10.1513i	0.453528	−	0.785534i	0.998602	+	0.0528541i	$0.0168318\pi$
$168$		0			0
$169$	−2.44304	−	4.23147i	−0.187926	−	0.325498i
$170$	2.50079	+	1.44383i	0.191802	+	0.110737i
$171$		0			0
$172$	−0.471521	−	0.816699i	−0.0359532	−	0.0622727i
$173$	−16.7710			−1.27507			−0.637536	−	0.770420i	$-0.720046\pi$
$173$	−16.7710			−1.27507			−0.637536	+	0.770420i	$0.720046\pi$
$174$		0			0
$175$		0			0
$176$	3.41614	+	1.97231i	0.257501	+	0.148668i
$177$		0			0
$178$	−8.02499	−	4.63323i	−0.601499	−	0.347275i
$179$	5.00158	−	2.88766i	0.373835	−	0.215834i	−0.301297	−	0.953530i	$-0.597420\pi$
$179$	5.00158	−	2.88766i	0.373835	−	0.215834i	0.675133	+	0.737696i	$0.264086\pi$
$180$		0			0
$181$			5.53310i			0.411272i	0.978629	+	0.205636i	$0.0659263\pi$
$181$			5.53310i			0.411272i	−0.978629	+	0.205636i	$0.934074\pi$
$182$		0			0
$183$		0			0
$184$	3.12656	+	5.41535i	0.230493	+	0.399225i
$185$	11.6795			0.858692
$186$		0			0
$187$			2.92737i			0.214070i
$188$	−2.18525			−0.159376
$189$		0			0
$190$	6.94462			0.503816
$191$			6.21372i			0.449609i	0.974404	+	0.224805i	$0.0721744\pi$
$191$			6.21372i			0.449609i	−0.974404	+	0.224805i	$0.927826\pi$
$192$		0			0
$193$	−7.80542			−0.561847			−0.280923	−	0.959730i	$-0.590641\pi$
$193$	−7.80542			−0.561847			−0.280923	+	0.959730i	$0.590641\pi$
$194$	9.40980	+	16.2983i	0.675584	+	1.17015i
$195$		0			0
$196$		0			0
$197$		−	12.7737i		−	0.910092i	−0.890468	−	0.455046i	$-0.849623\pi$
$197$		−	12.7737i		−	0.910092i	0.890468	−	0.455046i	$-0.150377\pi$
$198$		0			0
$199$	1.56925	−	0.906005i	0.111241	−	0.0642250i	−0.443347	−	0.896350i	$-0.646209\pi$
$199$	1.56925	−	0.906005i	0.111241	−	0.0642250i	0.554588	+	0.832125i	$0.312876\pi$
$200$	8.78217	+	5.07039i	0.620993	+	0.358530i
$201$		0			0
$202$	−7.17206	−	4.14079i	−0.504624	−	0.291345i
$203$		0			0
$204$		0			0
$205$	−40.8338			−2.85195
$206$	8.52435	+	14.7646i	0.593919	+	1.02870i
$207$		0			0
$208$	2.46687	+	1.42425i	0.171047	+	0.0987537i
$209$	3.52006	+	6.09692i	0.243487	+	0.421732i
$210$		0			0
$211$	−1.88766	+	3.26953i	−0.129952	+	0.225083i	−0.923658	−	0.383218i	$-0.874816\pi$
$211$	−1.88766	+	3.26953i	−0.129952	+	0.225083i	0.793706	+	0.608302i	$0.208149\pi$
$212$		0			0
$213$		0			0
$214$	−7.16846	+	12.4161i	−0.490026	+	0.848750i
$215$	1.83474	−	3.17787i	0.125128	−	0.216729i
$216$		0			0
$217$		0			0
$218$	9.76874	−	5.63998i	0.661622	−	0.381988i
$219$		0			0
$220$			15.3490i			1.03483i
$221$			2.11392i			0.142197i
$222$		0			0
$223$	11.0662	−	6.38910i	0.741051	−	0.427846i	−0.0814006	−	0.996681i	$-0.525939\pi$
$223$	11.0662	−	6.38910i	0.741051	−	0.427846i	0.822451	+	0.568836i	$0.192606\pi$
$224$		0			0
$225$		0			0
$226$	−4.91614	+	8.51501i	−0.327017	+	0.566410i
$227$	9.99110	−	17.3051i	0.663133	−	1.14858i	−0.316655	−	0.948541i	$-0.602560\pi$
$227$	9.99110	−	17.3051i	0.663133	−	1.14858i	0.979788	−	0.200039i	$-0.0641068\pi$
$228$		0			0
$229$	−8.77402	+	5.06568i	−0.579804	+	0.334750i	−0.761055	−	0.648687i	$-0.775318\pi$
$229$	−8.77402	+	5.06568i	−0.579804	+	0.334750i	0.181252	+	0.983437i	$0.441985\pi$
$230$	−12.1658	+	21.0718i	−0.802188	+	1.38943i
$231$		0			0
$232$	−1.44383	−	2.50079i	−0.0947921	−	0.164185i
$233$	6.33070	+	3.65503i	0.414738	+	0.239449i	0.692824	−	0.721107i	$-0.256366\pi$
$233$	6.33070	+	3.65503i	0.414738	+	0.239449i	−0.278085	+	0.960556i	$0.589700\pi$
$234$		0			0
$235$	−4.25153	−	7.36387i	−0.277339	−	0.480366i
$236$	−0.0211346			−0.00137575
$237$		0			0
$238$		0			0
$239$	−7.28317	−	4.20494i	−0.471109	−	0.271995i	0.245595	−	0.969373i	$-0.421017\pi$
$239$	−7.28317	−	4.20494i	−0.471109	−	0.271995i	−0.716704	+	0.697378i	$0.754350\pi$
$240$		0			0
$241$	7.75277	+	4.47607i	0.499400	+	0.288329i	0.728466	−	0.685082i	$-0.240234\pi$
$241$	7.75277	+	4.47607i	0.499400	+	0.288329i	−0.229066	+	0.973411i	$0.573567\pi$
$242$	−3.94910	+	2.28001i	−0.253858	+	0.146565i
$243$		0			0
$244$			2.46911i			0.158069i
$245$		0			0
$246$		0			0
$247$	2.54191	+	4.40271i	0.161738	+	0.280138i
$248$	−3.51174			−0.222995
$249$		0			0
$250$			20.0033i			1.26512i
$251$	−12.6432			−0.798033			−0.399017	−	0.916944i	$-0.630648\pi$
$251$	−12.6432			−0.798033			−0.399017	+	0.916944i	$0.630648\pi$
$252$		0			0
$253$	−24.6661			−1.55075
$254$			2.94462i			0.184762i
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.15329	+	14.1219i	0.508588	+	0.880900i	0.999951	+	0.00994523i	$0.00316572\pi$
$257$	8.15329	+	14.1219i	0.508588	+	0.880900i	−0.491362	+	0.870955i	$0.663501\pi$
$258$		0			0
$259$		0			0
$260$			11.0838i			0.687389i
$261$		0			0
$262$	13.0468	−	7.53255i	0.806032	−	0.465363i
$263$	20.5434	+	11.8608i	1.26676	+	0.731366i	0.974374	−	0.224934i	$-0.0722166\pi$
$263$	20.5434	+	11.8608i	1.26676	+	0.731366i	0.292389	+	0.956300i	$0.405550\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−13.4493			−0.821544
$269$	3.64144	+	6.30716i	0.222022	+	0.384554i	0.955422	−	0.295244i	$-0.0954009\pi$
$269$	3.64144	+	6.30716i	0.222022	+	0.384554i	−0.733400	+	0.679798i	$0.762068\pi$
$270$		0			0
$271$	−19.6483	−	11.3440i	−1.19355	−	0.689097i	−0.234441	−	0.972130i	$-0.575326\pi$
$271$	−19.6483	−	11.3440i	−1.19355	−	0.689097i	−0.959110	+	0.283033i	$0.908659\pi$
$272$	0.371058	+	0.642692i	0.0224987	+	0.0389689i
$273$		0			0
$274$	7.85997	−	13.6139i	0.474838	−	0.822444i
$275$	−34.6423	+	20.0007i	−2.08901	+	1.20609i
$276$		0			0
$277$	−12.0838	+	20.9298i	−0.726046	+	1.25755i	0.232496	+	0.972597i	$0.425311\pi$
$277$	−12.0838	+	20.9298i	−0.726046	+	1.25755i	−0.958542	+	0.284951i	$0.908023\pi$
$278$	−1.65337	+	2.86373i	−0.0991628	+	0.171755i
$279$		0			0
$280$		0			0
$281$	4.11229	−	2.37423i	0.245319	−	0.141635i	−0.372300	−	0.928112i	$-0.621431\pi$
$281$	4.11229	−	2.37423i	0.245319	−	0.141635i	0.617619	+	0.786478i	$0.288097\pi$
$282$		0			0
$283$			29.3853i			1.74677i	0.487027	+	0.873387i	$0.338081\pi$
$283$			29.3853i			1.74677i	−0.487027	+	0.873387i	$0.661919\pi$
$284$		−	1.94304i		−	0.115298i
$285$		0			0
$286$	−9.73085	+	5.61811i	−0.575398	+	0.332206i
$287$		0			0
$288$		0			0
$289$	8.22463	−	14.2455i	0.483802	−	0.837969i
$290$	5.61811	−	9.73085i	0.329907	−	0.571415i
$291$		0			0
$292$	−4.20443	+	2.42743i	−0.246046	+	0.142055i
$293$	−3.31206	+	5.73666i	−0.193493	+	0.335139i	−0.946405	−	0.322981i	$-0.895315\pi$
$293$	−3.31206	+	5.73666i	−0.193493	+	0.335139i	0.752913	+	0.658121i	$0.228648\pi$
$294$		0			0
$295$	−0.0411186	−	0.0712195i	−0.00239402	−	0.00414656i
$296$	2.59944	+	1.50079i	0.151090	+	0.0872316i
$297$		0			0
$298$	5.50079	+	9.52765i	0.318652	+	0.551922i
$299$	−17.8119			−1.03009
$300$		0			0
$301$		0			0
$302$	1.24706	+	0.719988i	0.0717600	+	0.0414307i
$303$		0			0
$304$	1.54563	+	0.892369i	0.0886479	+	0.0511809i
$305$	−8.32043	+	4.80380i	−0.476426	+	0.275065i
$306$		0			0
$307$		−	21.7242i		−	1.23987i	−0.784655	−	0.619933i	$-0.787160\pi$
$307$		−	21.7242i		−	1.23987i	0.784655	−	0.619933i	$-0.212840\pi$
$308$		0			0
$309$		0			0
$310$	−6.83228	−	11.8339i	−0.388048	−	0.672118i
$311$	6.29800			0.357127			0.178563	−	0.983928i	$-0.442855\pi$
$311$	6.29800			0.357127			0.178563	+	0.983928i	$0.442855\pi$
$312$		0			0
$313$		−	22.2191i		−	1.25590i	−0.778256	−	0.627948i	$-0.783895\pi$
$313$		−	22.2191i		−	1.25590i	0.778256	−	0.627948i	$-0.216105\pi$
$314$	16.6071			0.937192
$315$		0			0
$316$	−3.63613			−0.204548
$317$		−	15.6614i		−	0.879632i	−0.898088	−	0.439816i	$-0.855044\pi$
$317$		−	15.6614i		−	0.879632i	0.898088	−	0.439816i	$-0.144956\pi$
$318$		0			0
$319$	11.3907			0.637758
$320$	1.94556	+	3.36980i	0.108760	+	0.188378i
$321$		0			0
$322$		0			0
$323$			1.32448i			0.0736963i
$324$		0			0
$325$	−25.0159	+	14.4430i	−1.38763	+	0.801151i
$326$	10.7348	+	6.19773i	0.594545	+	0.343260i
$327$		0			0
$328$	−9.08816	−	5.24705i	−0.501810	−	0.289720i
$329$		0			0
$330$		0			0
$331$	1.27226			0.0699296			0.0349648	−	0.999389i	$-0.488868\pi$
$331$	1.27226			0.0699296			0.0349648	+	0.999389i	$0.488868\pi$
$332$	−4.02998	−	6.98012i	−0.221174	−	0.383084i
$333$		0			0
$334$	10.1513	+	5.86087i	0.555456	+	0.320693i
$335$	−26.1663	−	45.3214i	−1.42962	−	2.47617i
$336$		0			0
$337$	−3.78001	+	6.54717i	−0.205910	+	0.356647i	−0.950422	−	0.310962i	$-0.899349\pi$
$337$	−3.78001	+	6.54717i	−0.205910	+	0.356647i	0.744512	+	0.667609i	$0.232682\pi$
$338$	4.23147	−	2.44304i	0.230162	−	0.132884i
$339$		0			0
$340$	−1.44383	+	2.50079i	−0.0783027	+	0.135624i
$341$	6.92623	−	11.9966i	0.375076	−	0.649651i
$342$		0			0
$343$		0			0
$344$	0.816699	−	0.471521i	0.0440334	−	0.0254227i
$345$		0			0
$346$		−	16.7710i		−	0.901613i
$347$			22.1091i			1.18688i	0.804879	+	0.593439i	$0.202230\pi$
$347$			22.1091i			1.18688i	−0.804879	+	0.593439i	$0.797770\pi$
$348$		0			0
$349$	−12.7682	+	7.37173i	−0.683467	+	0.394600i	−0.801160	−	0.598450i	$-0.795783\pi$
$349$	−12.7682	+	7.37173i	−0.683467	+	0.394600i	0.117693	+	0.993050i	$0.462450\pi$
$350$		0			0
$351$		0			0
$352$	−1.97231	+	3.41614i	−0.105124	+	0.182081i
$353$	−8.63881	+	14.9629i	−0.459798	+	0.796393i	−0.998950	−	0.0458154i	$-0.985411\pi$
$353$	−8.63881	+	14.9629i	−0.459798	+	0.796393i	0.539152	+	0.842208i	$0.318745\pi$
$354$		0			0
$355$	6.54767	−	3.78030i	0.347514	−	0.200638i
$356$	4.63323	−	8.02499i	0.245561	−	0.425324i
$357$		0			0
$358$	2.88766	+	5.00158i	0.152618	+	0.264342i
$359$	9.45088	+	5.45647i	0.498799	+	0.287982i	0.728217	−	0.685346i	$-0.240349\pi$
$359$	9.45088	+	5.45647i	0.498799	+	0.287982i	−0.229419	+	0.973328i	$0.573682\pi$
$360$		0			0
$361$	−7.90736	−	13.6959i	−0.416177	−	0.720839i
$362$	−5.53310			−0.290813
$363$		0			0
$364$		0			0
$365$	−16.3599	−	9.44541i	−0.856318	−	0.494395i
$366$		0			0
$367$	−30.9407	−	17.8636i	−1.61509	−	0.932472i	−0.988166	−	0.153391i	$-0.950981\pi$
$367$	−30.9407	−	17.8636i	−1.61509	−	0.932472i	−0.626923	−	0.779081i	$-0.715686\pi$
$368$	−5.41535	+	3.12656i	−0.282295	+	0.162983i
$369$		0			0
$370$			11.6795i			0.607187i
$371$		0			0
$372$		0			0
$373$	16.0300	+	27.7648i	0.830003	+	1.43761i	0.898035	+	0.439923i	$0.144994\pi$
$373$	16.0300	+	27.7648i	0.830003	+	1.43761i	−0.0680328	+	0.997683i	$0.521672\pi$
$374$	−2.92737			−0.151371
$375$		0			0
$376$		−	2.18525i		−	0.112696i
$377$	8.22549			0.423634
$378$		0			0
$379$	34.8891			1.79214			0.896068	−	0.443918i	$-0.146412\pi$
$379$	34.8891			1.79214			0.896068	+	0.443918i	$0.146412\pi$
$380$			6.94462i			0.356251i
$381$		0			0
$382$	−6.21372			−0.317922
$383$	8.76711	+	15.1851i	0.447978	+	0.775921i	0.998254	−	0.0590616i	$-0.0188108\pi$
$383$	8.76711	+	15.1851i	0.447978	+	0.775921i	−0.550276	+	0.834983i	$0.685477\pi$
$384$		0			0
$385$		0			0
$386$		−	7.80542i		−	0.397286i
$387$		0			0
$388$	−16.2983	+	9.40980i	−0.827418	+	0.477710i
$389$	−6.60060	−	3.81086i	−0.334664	−	0.193218i	0.323246	−	0.946315i	$-0.395226\pi$
$389$	−6.60060	−	3.81086i	−0.334664	−	0.193218i	−0.657910	+	0.753097i	$0.728559\pi$
$390$		0			0
$391$	−4.01882	−	2.32027i	−0.203241	−	0.117341i
$392$		0			0
$393$		0			0
$394$	12.7737			0.643532
$395$	−7.07430	−	12.2530i	−0.355947	−	0.616517i
$396$		0			0
$397$	32.6032	+	18.8234i	1.63631	+	0.944722i	0.982090	+	0.188414i	$0.0603348\pi$
$397$	32.6032	+	18.8234i	1.63631	+	0.944722i	0.654216	+	0.756307i	$0.272999\pi$
$398$	0.906005	+	1.56925i	0.0454139	+	0.0786592i
$399$		0			0
$400$	−5.07039	+	8.78217i	−0.253519	+	0.439108i
$401$	18.5689	−	10.7207i	0.927284	−	0.535368i	0.0413326	−	0.999145i	$-0.486840\pi$
$401$	18.5689	−	10.7207i	0.927284	−	0.535368i	0.885952	+	0.463778i	$0.153506\pi$
$402$		0			0
$403$	5.00158	−	8.66299i	0.249146	−	0.431534i
$404$	4.14079	−	7.17206i	0.206012	−	0.356823i
$405$		0			0
$406$		0			0
$407$	−10.2538	+	5.92004i	−0.508262	+	0.293445i
$408$		0			0
$409$			29.5703i			1.46216i	0.682293	+	0.731079i	$0.260983\pi$
$409$			29.5703i			1.46216i	−0.682293	+	0.731079i	$0.739017\pi$
$410$		−	40.8338i		−	2.01664i
$411$		0			0
$412$	−14.7646	+	8.52435i	−0.727400	+	0.419964i
$413$		0			0
$414$		0			0
$415$	15.6811	−	27.1605i	0.769755	−	1.33325i
$416$	−1.42425	+	2.46687i	−0.0698294	+	0.120948i
$417$		0			0
$418$	−6.09692	+	3.52006i	−0.298210	+	0.172172i
$419$	−3.56481	+	6.17443i	−0.174152	+	0.301641i	−0.939868	−	0.341539i	$-0.889052\pi$
$419$	−3.56481	+	6.17443i	−0.174152	+	0.301641i	0.765715	+	0.643180i	$0.222385\pi$
$420$		0			0
$421$	−2.31007	−	4.00115i	−0.112586	−	0.195004i	0.804226	−	0.594323i	$-0.202580\pi$
$421$	−2.31007	−	4.00115i	−0.112586	−	0.195004i	−0.916812	+	0.399319i	$0.869247\pi$
$422$	−3.26953	−	1.88766i	−0.159158	−	0.0918899i
$423$		0			0
$424$		0			0
$425$	−7.52564			−0.365047
$426$		0			0
$427$		0			0
$428$	−12.4161	−	7.16846i	−0.600157	−	0.346501i
$429$		0			0
$430$	3.17787	+	1.83474i	0.153250	+	0.0884792i
$431$	3.47078	−	2.00385i	0.167181	−	0.0965223i	−0.414075	−	0.910243i	$-0.635895\pi$
$431$	3.47078	−	2.00385i	0.167181	−	0.0965223i	0.581256	+	0.813721i	$0.302561\pi$
$432$		0			0
$433$			29.4125i			1.41348i	0.707475	+	0.706738i	$0.249834\pi$
$433$			29.4125i			1.41348i	−0.707475	+	0.706738i	$0.750166\pi$
$434$		0			0
$435$		0			0
$436$	5.63998	+	9.76874i	0.270106	+	0.467838i
$437$	−11.1602			−0.533863
$438$		0			0
$439$			21.3769i			1.02027i	0.860096	+	0.510133i	$0.170404\pi$
$439$			21.3769i			1.02027i	−0.860096	+	0.510133i	$0.829596\pi$
$440$	−15.3490			−0.731733
$441$		0			0
$442$	−2.11392			−0.100549
$443$		−	5.83386i		−	0.277175i	−0.990350	−	0.138587i	$-0.955744\pi$
$443$		−	5.83386i		−	0.277175i	0.990350	−	0.138587i	$-0.0442562\pi$
$444$		0			0
$445$	36.0569			1.70926
$446$	6.38910	+	11.0662i	0.302533	+	0.524002i
$447$		0			0
$448$		0			0
$449$			22.5823i			1.06573i	0.846202	+	0.532863i	$0.178884\pi$
$449$			22.5823i			1.06573i	−0.846202	+	0.532863i	$0.821116\pi$
$450$		0			0
$451$	35.8493	−	20.6976i	1.68808	−	0.974613i
$452$	−8.51501	−	4.91614i	−0.400512	−	0.231236i
$453$		0			0
$454$	17.3051	+	9.99110i	0.812168	+	0.468906i
$455$		0			0
$456$		0			0
$457$	39.8623			1.86468			0.932340	−	0.361584i	$-0.117764\pi$
$457$	39.8623			1.86468			0.932340	+	0.361584i	$0.117764\pi$
$458$	−5.06568	−	8.77402i	−0.236704	−	0.409983i
$459$		0			0
$460$	−21.0718	−	12.1658i	−0.982476	−	0.567233i
$461$	−3.68254	−	6.37834i	−0.171513	−	0.297069i	0.767436	−	0.641125i	$-0.221532\pi$
$461$	−3.68254	−	6.37834i	−0.171513	−	0.297069i	−0.938949	+	0.344056i	$0.888199\pi$
$462$		0			0
$463$	−14.3457	+	24.8475i	−0.666702	+	1.15476i	0.312119	+	0.950043i	$0.398961\pi$
$463$	−14.3457	+	24.8475i	−0.666702	+	1.15476i	−0.978821	+	0.204718i	$0.934372\pi$
$464$	2.50079	−	1.44383i	0.116096	−	0.0670282i
$465$		0			0
$466$	−3.65503	+	6.33070i	−0.169316	+	0.293264i
$467$	6.83519	−	11.8389i	0.316295	−	0.547839i	−0.663417	−	0.748250i	$-0.730894\pi$
$467$	6.83519	−	11.8389i	0.316295	−	0.547839i	0.979712	+	0.200411i	$0.0642278\pi$
$468$		0			0
$469$		0			0
$470$	7.36387	−	4.25153i	0.339670	−	0.196109i
$471$		0			0
$472$		−	0.0211346i		−	0.000972799i
$473$			3.71994i			0.171043i
$474$		0			0
$475$	−15.6739	+	9.04931i	−0.719166	+	0.415211i
$476$		0			0
$477$		0			0
$478$	4.20494	−	7.28317i	0.192329	−	0.333124i
$479$	5.20537	−	9.01596i	0.237839	−	0.411950i	−0.722255	−	0.691627i	$-0.756894\pi$
$479$	5.20537	−	9.01596i	0.237839	−	0.411950i	0.960094	+	0.279677i	$0.0902275\pi$
$480$		0			0
$481$	−7.40449	+	4.27499i	−0.337616	+	0.194923i
$482$	−4.47607	+	7.75277i	−0.203879	+	0.353129i
$483$		0			0
$484$	−2.28001	−	3.94910i	−0.103637	−	0.179504i
$485$	−63.4184	−	36.6146i	−2.87968	−	1.66258i
$486$		0			0
$487$	−1.16925	−	2.02520i	−0.0529838	−	0.0917707i	0.838317	−	0.545183i	$-0.183540\pi$
$487$	−1.16925	−	2.02520i	−0.0529838	−	0.0917707i	−0.891301	+	0.453412i	$0.850207\pi$
$488$	−2.46911			−0.111772
$489$		0			0
$490$		0			0
$491$	29.3448	+	16.9422i	1.32431	+	0.764591i	0.984413	−	0.175871i	$-0.0562742\pi$
$491$	29.3448	+	16.9422i	1.32431	+	0.764591i	0.339898	+	0.940462i	$0.389608\pi$
$492$		0			0
$493$	1.85588	+	1.07149i	0.0835845	+	0.0482575i
$494$	−4.40271	+	2.54191i	−0.198087	+	0.114366i
$495$		0			0
$496$		−	3.51174i		−	0.157682i
$497$		0			0
$498$		0			0
$499$	8.30223	+	14.3799i	0.371659	+	0.643732i	0.989821	−	0.142319i	$-0.0454558\pi$
$499$	8.30223	+	14.3799i	0.371659	+	0.643732i	−0.618162	+	0.786051i	$0.712123\pi$
$500$	−20.0033			−0.894576
$501$		0			0
$502$		−	12.6432i		−	0.564295i
$503$	−35.3661			−1.57690			−0.788449	−	0.615100i	$-0.789115\pi$
$503$	−35.3661			−1.57690			−0.788449	+	0.615100i	$0.789115\pi$
$504$		0			0
$505$	32.2246			1.43398
$506$		−	24.6661i		−	1.09654i
$507$		0			0
$508$	−2.94462			−0.130646
$509$	−18.5291	−	32.0933i	−0.821287	−	1.42251i	−0.904724	−	0.425998i	$-0.859923\pi$
$509$	−18.5291	−	32.0933i	−0.821287	−	1.42251i	0.0834371	−	0.996513i	$-0.473410\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−14.1219	+	8.15329i	−0.622891	+	0.359626i
$515$	−57.4507	−	33.1692i	−2.53158	−	1.46161i
$516$		0			0
$517$	7.46513	+	4.30999i	0.328316	+	0.189553i
$518$		0			0
$519$		0			0
$520$	−11.0838			−0.486057
$521$	−0.891547	−	1.54420i	−0.0390594	−	0.0676528i	0.845835	−	0.533445i	$-0.179103\pi$
$521$	−0.891547	−	1.54420i	−0.0390594	−	0.0676528i	−0.884894	+	0.465792i	$0.845769\pi$
$522$		0			0
$523$	−20.8312	−	12.0269i	−0.910886	−	0.525901i	−0.0301702	−	0.999545i	$-0.509605\pi$
$523$	−20.8312	−	12.0269i	−0.910886	−	0.525901i	−0.880716	+	0.473644i	$0.842938\pi$
$524$	7.53255	+	13.0468i	0.329061	+	0.569950i
$525$		0			0
$526$	−11.8608	+	20.5434i	−0.517154	+	0.895737i
$527$	2.25696	−	1.30306i	0.0983149	−	0.0567621i
$528$		0			0
$529$	8.05069	−	13.9442i	0.350030	−	0.606270i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	25.8876	−	14.9462i	1.12132	−	0.647392i
$534$		0			0
$535$		−	55.7866i		−	2.41187i
$536$		−	13.4493i		−	0.580920i
$537$		0			0
$538$	−6.30716	+	3.64144i	−0.271921	+	0.156994i
$539$		0			0
$540$		0			0
$541$	−15.0016	+	25.9835i	−0.644968	+	1.11712i	0.339341	+	0.940664i	$0.389796\pi$
$541$	−15.0016	+	25.9835i	−0.644968	+	1.11712i	−0.984309	+	0.176454i	$0.943537\pi$
$542$	11.3440	−	19.6483i	0.487265	−	0.843968i
$543$		0			0
$544$	−0.642692	+	0.371058i	−0.0275552	+	0.0159090i
$545$	−21.9458	+	38.0113i	−0.940056	+	1.62822i
$546$		0			0
$547$	−10.7816	−	18.6743i	−0.460987	−	0.798454i	0.538023	−	0.842930i	$-0.319171\pi$
$547$	−10.7816	−	18.6743i	−0.460987	−	0.798454i	−0.999010	+	0.0444765i	$0.985838\pi$
$548$	13.6139	+	7.85997i	0.581556	+	0.335761i
$549$		0			0
$550$	−20.0007	−	34.6423i	−0.852835	−	1.47715i
$551$	5.15372			0.219556
$552$		0			0
$553$		0			0
$554$	−20.9298	−	12.0838i	−0.889221	−	0.513392i
$555$		0			0
$556$	−2.86373	−	1.65337i	−0.121449	−	0.0701187i
$557$	31.9976	−	18.4738i	1.35578	−	0.782762i	0.366731	−	0.930327i	$-0.380477\pi$
$557$	31.9976	−	18.4738i	1.35578	−	0.782762i	0.989052	+	0.147565i	$0.0471436\pi$
$558$		0			0
$559$			2.68625i			0.113616i
$560$		0			0
$561$		0			0
$562$	2.37423	+	4.11229i	0.100151	+	0.173467i
$563$	−15.1684			−0.639273			−0.319637	−	0.947540i	$-0.603561\pi$
$563$	−15.1684			−0.639273			−0.319637	+	0.947540i	$0.603561\pi$
$564$		0			0
$565$		−	38.2585i		−	1.60955i
$566$	−29.3853			−1.23516
$567$		0			0
$568$	1.94304			0.0815282
$569$			36.7292i			1.53977i	0.638183	+	0.769885i	$0.279686\pi$
$569$			36.7292i			1.53977i	−0.638183	+	0.769885i	$0.720314\pi$
$570$		0			0
$571$	11.2277			0.469866			0.234933	−	0.972012i	$-0.424513\pi$
$571$	11.2277			0.469866			0.234933	+	0.972012i	$0.424513\pi$
$572$	−5.61811	−	9.73085i	−0.234905	−	0.406867i
$573$		0			0
$574$		0			0
$575$		−	63.4114i		−	2.64444i
$576$		0			0
$577$	−31.6545	+	18.2757i	−1.31780	+	0.760829i	−0.983374	−	0.181594i	$-0.941874\pi$
$577$	−31.6545	+	18.2757i	−1.31780	+	0.760829i	−0.334422	+	0.942424i	$0.608541\pi$
$578$	14.2455	+	8.22463i	0.592534	+	0.342100i
$579$		0			0
$580$	9.73085	+	5.61811i	0.404052	+	0.233279i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−2.42743	−	4.20443i	−0.100448	−	0.173981i
$585$		0			0
$586$	−5.73666	−	3.31206i	−0.236979	−	0.136820i
$587$	4.99738	+	8.65571i	0.206264	+	0.357259i	0.950535	−	0.310619i	$-0.100536\pi$
$587$	4.99738	+	8.65571i	0.206264	+	0.357259i	−0.744271	+	0.667878i	$0.767203\pi$
$588$		0			0
$589$	3.13376	−	5.42784i	0.129124	−	0.223650i
$590$	0.0712195	−	0.0411186i	0.00293206	−	0.00169283i
$591$		0			0
$592$	−1.50079	+	2.59944i	−0.0616820	+	0.106836i
$593$	−3.89111	+	6.73961i	−0.159789	+	0.276763i	−0.934792	−	0.355194i	$-0.884415\pi$
$593$	−3.89111	+	6.73961i	−0.159789	+	0.276763i	0.775004	+	0.631957i	$0.217748\pi$
$594$		0			0
$595$		0			0
$596$	−9.52765	+	5.50079i	−0.390268	+	0.225321i
$597$		0			0
$598$		−	17.8119i		−	0.728385i
$599$			25.0124i			1.02198i	0.859586	+	0.510990i	$0.170721\pi$
$599$			25.0124i			1.02198i	−0.859586	+	0.510990i	$0.829279\pi$
$600$		0			0
$601$	−25.9925	+	15.0068i	−1.06026	+	0.612139i	−0.925503	−	0.378740i	$-0.876357\pi$
$601$	−25.9925	+	15.0068i	−1.06026	+	0.612139i	−0.134753	+	0.990879i	$0.543024\pi$
$602$		0			0
$603$		0			0
$604$	−0.719988	+	1.24706i	−0.0292959	+	0.0507420i
$605$	8.87179	−	15.3664i	0.360689	−	0.624732i
$606$		0			0
$607$	3.96882	−	2.29140i	0.161089	−	0.0930050i	−0.417288	−	0.908774i	$-0.637019\pi$
$607$	3.96882	−	2.29140i	0.161089	−	0.0930050i	0.578378	+	0.815769i	$0.303686\pi$
$608$	−0.892369	+	1.54563i	−0.0361903	+	0.0626835i
$609$		0			0
$610$	−4.80380	−	8.32043i	−0.194500	−	0.336884i
$611$	5.39073	+	3.11234i	0.218085	+	0.125912i
$612$		0			0
$613$	−15.2761	−	26.4590i	−0.616996	−	1.06867i	−0.990031	−	0.140852i	$-0.955016\pi$
$613$	−15.2761	−	26.4590i	−0.616996	−	1.06867i	0.373034	−	0.927818i	$-0.378317\pi$
$614$	21.7242			0.876717
$615$		0			0
$616$		0			0
$617$	28.2484	+	16.3092i	1.13724	+	0.656585i	0.945745	−	0.324909i	$-0.105334\pi$
$617$	28.2484	+	16.3092i	1.13724	+	0.656585i	0.191493	+	0.981494i	$0.438667\pi$
$618$		0			0
$619$	−17.3244	−	10.0023i	−0.696327	−	0.402024i	0.109651	−	0.993970i	$-0.465027\pi$
$619$	−17.3244	−	10.0023i	−0.696327	−	0.402024i	−0.805978	+	0.591946i	$0.798360\pi$
$620$	11.8339	−	6.83228i	0.475259	−	0.274391i
$621$		0			0
$622$			6.29800i			0.252527i
$623$		0			0
$624$		0			0
$625$	−13.5657	−	23.4965i	−0.542628	−	0.939859i
$626$	22.2191			0.888052
$627$		0			0
$628$			16.6071i			0.662695i
$629$	−2.22752			−0.0888171
$630$		0			0
$631$	6.09634			0.242692			0.121346	−	0.992610i	$-0.461279\pi$
$631$	6.09634			0.242692			0.121346	+	0.992610i	$0.461279\pi$
$632$		−	3.63613i		−	0.144637i
$633$		0			0
$634$	15.6614			0.621994
$635$	−5.72893	−	9.92279i	−0.227345	−	0.393774i
$636$		0			0
$637$		0			0
$638$			11.3907i			0.450963i
$639$		0			0
$640$	−3.36980	+	1.94556i	−0.133203	+	0.0769049i
$641$	28.9612	+	16.7207i	1.14390	+	0.660429i	0.947393	−	0.320074i	$-0.103708\pi$
$641$	28.9612	+	16.7207i	1.14390	+	0.660429i	0.196504	+	0.980503i	$0.437041\pi$
$642$		0			0
$643$	16.6022	+	9.58527i	0.654726	+	0.378006i	0.790264	−	0.612766i	$-0.209943\pi$
$643$	16.6022	+	9.58527i	0.654726	+	0.378006i	−0.135539	+	0.990772i	$0.543276\pi$
$644$		0			0
$645$		0			0
$646$	−1.32448			−0.0521111
$647$	−22.3025	−	38.6290i	−0.876800	−	1.51866i	−0.854832	−	0.518904i	$-0.826340\pi$
$647$	−22.3025	−	38.6290i	−0.876800	−	1.51866i	−0.0219681	−	0.999759i	$-0.506993\pi$
$648$		0			0
$649$	0.0721988	+	0.0416840i	0.00283405	+	0.00163624i
$650$	−14.4430	−	25.0159i	−0.566500	−	0.981206i
$651$		0			0
$652$	−6.19773	+	10.7348i	−0.242722	+	0.420407i
$653$	−0.564755	+	0.326061i	−0.0221006	+	0.0127598i	−0.511010	−	0.859575i	$-0.670728\pi$
$653$	−0.564755	+	0.326061i	−0.0221006	+	0.0127598i	0.488909	+	0.872335i	$0.337395\pi$
$654$		0			0
$655$	−29.3100	+	50.7664i	−1.14524	+	1.98361i
$656$	5.24705	−	9.08816i	0.204863	−	0.354833i
$657$		0			0
$658$		0			0
$659$	−26.2738	+	15.1692i	−1.02348	+	0.590908i	−0.915111	−	0.403202i	$-0.867897\pi$
$659$	−26.2738	+	15.1692i	−1.02348	+	0.590908i	−0.108372	+	0.994110i	$0.534564\pi$
$660$		0			0
$661$			12.8176i			0.498548i	0.968433	+	0.249274i	$0.0801919\pi$
$661$			12.8176i			0.498548i	−0.968433	+	0.249274i	$0.919808\pi$
$662$			1.27226i			0.0494477i
$663$		0			0
$664$	6.98012	−	4.02998i	0.270881	−	0.156393i
$665$		0			0
$666$		0			0
$667$	−9.02843	+	15.6377i	−0.349582	+	0.605494i
$668$	−5.86087	+	10.1513i	−0.226764	+	0.392767i
$669$		0			0
$670$	45.3214	−	26.1663i	1.75092	−	1.01089i
$671$	4.86986	−	8.43484i	0.187999	−	0.325623i
$672$		0			0
$673$	11.2246	+	19.4416i	0.432678	+	0.749420i	0.997103	−	0.0760644i	$-0.0242355\pi$
$673$	11.2246	+	19.4416i	0.432678	+	0.749420i	−0.564425	+	0.825484i	$0.690902\pi$
$674$	−6.54717	−	3.78001i	−0.252188	−	0.145601i
$675$		0			0
$676$	2.44304	+	4.23147i	0.0939632	+	0.162749i
$677$	51.1807			1.96703			0.983516	−	0.180820i	$-0.0578752\pi$
$677$	51.1807			1.96703			0.983516	+	0.180820i	$0.0578752\pi$
$678$		0			0
$679$		0			0
$680$	−2.50079	−	1.44383i	−0.0959009	−	0.0553684i
$681$		0			0
$682$	11.9966	+	6.92623i	0.459373	+	0.265219i
$683$	12.6107	−	7.28080i	0.482536	−	0.278592i	−0.238937	−	0.971035i	$-0.576799\pi$
$683$	12.6107	−	7.28080i	0.482536	−	0.278592i	0.721473	+	0.692443i	$0.243466\pi$
$684$		0			0
$685$			61.1681i			2.33711i
$686$		0			0
$687$		0			0
$688$	0.471521	+	0.816699i	0.0179766	+	0.0311363i
$689$		0			0
$690$		0			0
$691$		−	24.4515i		−	0.930180i	−0.885263	−	0.465090i	$-0.846022\pi$
$691$		−	24.4515i		−	0.930180i	0.885263	−	0.465090i	$-0.153978\pi$
$692$	16.7710			0.637536
$693$		0			0
$694$	−22.1091			−0.839250
$695$		−	12.8669i		−	0.488071i
$696$		0			0
$697$	7.78785			0.294986
$698$	−7.37173	−	12.7682i	−0.279024	−	0.483284i
$699$		0			0
$700$		0			0
$701$			2.21697i			0.0837337i	0.999123	+	0.0418669i	$0.0133305\pi$
$701$			2.21697i			0.0837337i	−0.999123	+	0.0418669i	$0.986669\pi$
$702$		0			0
$703$	−4.63932	+	2.67851i	−0.174975	+	0.101022i
$704$	−3.41614	−	1.97231i	−0.128751	−	0.0743342i
$705$		0			0
$706$	−14.9629	−	8.63881i	−0.563135	−	0.325126i
$707$		0			0
$708$		0			0
$709$	−24.3923			−0.916072			−0.458036	−	0.888934i	$-0.651447\pi$
$709$	−24.3923			−0.916072			−0.458036	+	0.888934i	$0.651447\pi$
$710$	3.78030	+	6.54767i	0.141872	+	0.245730i
$711$		0			0
$712$	8.02499	+	4.63323i	0.300749	+	0.173638i
$713$	10.9796	+	19.0173i	0.411190	+	0.712203i
$714$		0			0
$715$	21.8607	−	37.8639i	0.817544	−	1.41603i
$716$	−5.00158	+	2.88766i	−0.186918	+	0.107917i
$717$		0			0
$718$	−5.45647	+	9.45088i	−0.203634	+	0.352704i
$719$	−1.11376	+	1.92909i	−0.0415363	+	0.0719429i	−0.886046	−	0.463597i	$-0.846559\pi$
$719$	−1.11376	+	1.92909i	−0.0415363	+	0.0719429i	0.844510	+	0.535540i	$0.179892\pi$
$720$		0			0
$721$		0			0
$722$	13.6959	−	7.90736i	0.509710	−	0.294281i
$723$		0			0
$724$		−	5.53310i		−	0.205636i
$725$			29.2831i			1.08755i
$726$		0			0
$727$	10.4880	−	6.05523i	0.388977	−	0.224576i	−0.292740	−	0.956192i	$-0.594567\pi$
$727$	10.4880	−	6.05523i	0.388977	−	0.224576i	0.681717	+	0.731616i	$0.261234\pi$
$728$		0			0
$729$		0			0
$730$	9.44541	−	16.3599i	0.349590	−	0.605508i
$731$	−0.349924	+	0.606086i	−0.0129424	+	0.0224169i
$732$		0			0
$733$	−13.5673	+	7.83306i	−0.501118	+	0.289321i	−0.729175	−	0.684327i	$-0.760096\pi$
$733$	−13.5673	+	7.83306i	−0.501118	+	0.289321i	0.228057	+	0.973648i	$0.426763\pi$
$734$	17.8636	−	30.9407i	0.659357	−	1.14204i
$735$		0			0
$736$	−3.12656	−	5.41535i	−0.115246	−	0.199613i
$737$	45.9446	+	26.5261i	1.69239	+	0.977102i
$738$		0			0
$739$	4.05227	+	7.01874i	0.149065	+	0.258188i	0.930882	−	0.365319i	$-0.119040\pi$
$739$	4.05227	+	7.01874i	0.149065	+	0.258188i	−0.781817	+	0.623508i	$0.785707\pi$
$740$	−11.6795			−0.429346
$741$		0			0
$742$		0			0
$743$	10.5429	+	6.08697i	0.386783	+	0.223309i	0.680765	−	0.732502i	$-0.261647\pi$
$743$	10.5429	+	6.08697i	0.386783	+	0.223309i	−0.293982	+	0.955811i	$0.594981\pi$
$744$		0			0
$745$	−37.0732	−	21.4042i	−1.35826	−	0.784189i
$746$	−27.7648	+	16.0300i	−1.01654	+	0.586900i
$747$		0			0
$748$		−	2.92737i		−	0.107035i
$749$		0			0
$750$		0			0
$751$	−17.3062	−	29.9752i	−0.631511	−	1.09381i	−0.987243	−	0.159221i	$-0.949102\pi$
$751$	−17.3062	−	29.9752i	−0.631511	−	1.09381i	0.355732	−	0.934588i	$-0.384232\pi$
$752$	2.18525			0.0796879
$753$		0			0
$754$			8.22549i			0.299555i
$755$	−5.60311			−0.203918
$756$		0			0
$757$	−39.0553			−1.41949			−0.709744	−	0.704459i	$-0.751190\pi$
$757$	−39.0553			−1.41949			−0.709744	+	0.704459i	$0.751190\pi$
$758$			34.8891i			1.26723i
$759$		0			0
$760$	−6.94462			−0.251908
$761$	−5.11262	−	8.85532i	−0.185332	−	0.321005i	0.758356	−	0.651840i	$-0.226003\pi$
$761$	−5.11262	−	8.85532i	−0.185332	−	0.321005i	−0.943688	+	0.330835i	$0.892670\pi$
$762$		0			0
$763$		0			0
$764$		−	6.21372i		−	0.224805i
$765$		0			0
$766$	−15.1851	+	8.76711i	−0.548659	+	0.316769i
$767$	0.0521363	+	0.0301009i	0.00188253	+	0.00108688i
$768$		0			0
$769$	−26.6746	−	15.4006i	−0.961910	−	0.555359i	−0.0651494	−	0.997876i	$-0.520752\pi$
$769$	−26.6746	−	15.4006i	−0.961910	−	0.555359i	−0.896760	+	0.442517i	$0.854086\pi$
$770$		0			0
$771$		0			0
$772$	7.80542			0.280923
$773$	−17.8916	−	30.9892i	−0.643518	−	1.11461i	−0.984642	−	0.174587i	$-0.944141\pi$
$773$	−17.8916	−	30.9892i	−0.643518	−	1.11461i	0.341124	−	0.940018i	$-0.389192\pi$
$774$		0			0
$775$	30.8406	+	17.8059i	1.10783	+	0.639605i
$776$	−9.40980	−	16.2983i	−0.337792	−	0.585073i
$777$		0			0
$778$	3.81086	−	6.60060i	0.136626	−	0.236643i
$779$	16.2200	−	9.36461i	0.581141	−	0.335522i
$780$		0			0
$781$	−3.83228	+	6.63771i	−0.137130	+	0.237516i
$782$	2.32027	−	4.01882i	0.0829727	−	0.143713i
$783$		0			0
$784$		0			0
$785$	−55.9626	+	32.3100i	−1.99739	+	1.15319i
$786$		0			0
$787$		−	15.3413i		−	0.546857i	−0.961892	−	0.273429i	$-0.911842\pi$
$787$		−	15.3413i		−	0.546857i	0.961892	−	0.273429i	$-0.0881578\pi$
$788$			12.7737i			0.455046i
$789$		0			0
$790$	12.2530	−	7.07430i	0.435944	−	0.251692i
$791$		0			0
$792$		0			0
$793$	3.51663	−	6.09098i	0.124879	−	0.216297i
$794$	−18.8234	+	32.6032i	−0.668019	+	1.15704i
$795$		0			0
$796$	−1.56925	+	0.906005i	−0.0556205	+	0.0321125i
$797$	17.5200	−	30.3455i	0.620590	−	1.07489i	−0.368786	−	0.929514i	$-0.620226\pi$
$797$	17.5200	−	30.3455i	0.620590	−	1.07489i	0.989376	−	0.145379i	$-0.0464402\pi$
$798$		0			0
$799$	0.810856	+	1.40444i	0.0286860	+	0.0496857i
$800$	−8.78217	−	5.07039i	−0.310496	−	0.179265i
$801$		0			0
$802$	10.7207	+	18.5689i	0.378562	+	0.655689i
$803$	19.1506			0.675809
$804$		0			0
$805$		0			0
$806$	8.66299	+	5.00158i	0.305141	+	0.176173i
$807$		0			0
$808$	7.17206	+	4.14079i	0.252312	+	0.145673i
$809$	−23.6360	+	13.6462i	−0.830997	+	0.479777i	−0.854194	−	0.519954i	$-0.825949\pi$
$809$	−23.6360	+	13.6462i	−0.830997	+	0.479777i	0.0231967	+	0.999731i	$0.492616\pi$
$810$		0			0
$811$		−	27.7628i		−	0.974883i	−0.873156	−	0.487442i	$-0.837930\pi$
$811$		−	27.7628i		−	0.974883i	0.873156	−	0.487442i	$-0.162070\pi$
$812$		0			0
$813$		0			0
$814$	−5.92004	−	10.2538i	−0.207497	−	0.359396i
$815$	−48.2322			−1.68950
$816$		0			0
$817$			1.68308i			0.0588836i
$818$	−29.5703			−1.03390
$819$		0			0
$820$	40.8338			1.42598
$821$			44.4523i			1.55140i	0.631104	+	0.775698i	$0.282602\pi$
$821$			44.4523i			1.55140i	−0.631104	+	0.775698i	$0.717398\pi$
$822$		0			0
$823$	−51.1153			−1.78177			−0.890884	−	0.454231i	$-0.849914\pi$
$823$	−51.1153			−1.78177			−0.890884	+	0.454231i	$0.849914\pi$
$824$	−8.52435	−	14.7646i	−0.296960	−	0.514349i
$825$		0			0
$826$		0			0
$827$			14.5414i			0.505653i	0.967512	+	0.252826i	$0.0813601\pi$
$827$			14.5414i			0.505653i	−0.967512	+	0.252826i	$0.918640\pi$
$828$		0			0
$829$	24.2211	−	13.9841i	0.841234	−	0.485686i	−0.0164497	−	0.999865i	$-0.505236\pi$
$829$	24.2211	−	13.9841i	0.841234	−	0.485686i	0.857683	+	0.514178i	$0.171903\pi$
$830$	27.1605	+	15.6811i	0.942754	+	0.544299i
$831$		0			0
$832$	−2.46687	−	1.42425i	−0.0855233	−	0.0493769i
$833$		0			0
$834$		0			0
$835$	−45.6107			−1.57842
$836$	−3.52006	−	6.09692i	−0.121744	−	0.210866i
$837$		0			0
$838$	−6.17443	−	3.56481i	−0.213292	−	0.123144i
$839$	0.499354	+	0.864906i	0.0172396	+	0.0298599i	0.874517	−	0.484996i	$-0.161179\pi$
$839$	0.499354	+	0.864906i	0.0172396	+	0.0298599i	−0.857277	+	0.514856i	$0.827846\pi$
$840$		0			0
$841$	−10.3307	+	17.8933i	−0.356231	+	0.617011i
$842$	4.00115	−	2.31007i	0.137889	−	0.0796102i
$843$		0			0
$844$	1.88766	−	3.26953i	0.0649760	−	0.112542i
$845$	−9.50616	+	16.4651i	−0.327022	+	0.566418i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		−	7.52564i		−	0.258127i
$851$		−	18.7692i		−	0.643400i
$852$		0			0
$853$	8.48739	−	4.90020i	0.290603	−	0.167780i	−0.347611	−	0.937639i	$-0.613007\pi$
$853$	8.48739	−	4.90020i	0.290603	−	0.167780i	0.638214	+	0.769859i	$0.279674\pi$
$854$		0			0
$855$		0			0
$856$	7.16846	−	12.4161i	0.245013	−	0.424375i
$857$	−3.85002	+	6.66842i	−0.131514	+	0.227789i	−0.924260	−	0.381763i	$-0.875317\pi$
$857$	−3.85002	+	6.66842i	−0.131514	+	0.227789i	0.792746	+	0.609552i	$0.208651\pi$
$858$		0			0
$859$	16.4022	−	9.46979i	0.559634	−	0.323105i	−0.193364	−	0.981127i	$-0.561940\pi$
$859$	16.4022	−	9.46979i	0.559634	−	0.323105i	0.752999	+	0.658022i	$0.228607\pi$
$860$	−1.83474	+	3.17787i	−0.0625642	+	0.108364i
$861$		0			0
$862$	2.00385	+	3.47078i	0.0682515	+	0.118215i
$863$	15.1156	+	8.72700i	0.514541	+	0.297070i	0.734698	−	0.678394i	$-0.237324\pi$
$863$	15.1156	+	8.72700i	0.514541	+	0.297070i	−0.220157	+	0.975464i	$0.570657\pi$
$864$		0			0
$865$	32.6289	+	56.5149i	1.10942	+	1.92156i
$866$	−29.4125			−0.999479
$867$		0			0
$868$		0			0
$869$	12.4215	+	7.17157i	0.421371	+	0.243279i
$870$		0			0
$871$	33.1776	+	19.1551i	1.12418	+	0.649045i
$872$	−9.76874	+	5.63998i	−0.330811	+	0.190994i
$873$		0			0
$874$		−	11.1602i		−	0.377498i
$875$		0			0
$876$		0			0
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	0.862695	−	0.505725i	$-0.168775\pi$
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	−0.869318	+	0.494253i	$0.835442\pi$
$878$	−21.3769			−0.721436
$879$		0			0
$880$		−	15.3490i		−	0.517414i
$881$	−37.0259			−1.24744			−0.623718	−	0.781650i	$-0.714378\pi$
$881$	−37.0259			−1.24744			−0.623718	+	0.781650i	$0.714378\pi$
$882$		0			0
$883$	−29.9586			−1.00819			−0.504094	−	0.863649i	$-0.668174\pi$
$883$	−29.9586			−1.00819			−0.504094	+	0.863649i	$0.668174\pi$
$884$		−	2.11392i		−	0.0710987i
$885$		0			0
$886$	5.83386			0.195992
$887$	14.4930	+	25.1026i	0.486626	+	0.842861i	0.999882	−	0.0153745i	$-0.00489405\pi$
$887$	14.4930	+	25.1026i	0.486626	+	0.842861i	−0.513256	+	0.858236i	$0.671561\pi$
$888$		0			0
$889$		0			0
$890$			36.0569i			1.20863i
$891$		0			0
$892$	−11.0662	+	6.38910i	−0.370525	+	0.213923i
$893$	3.37759	+	1.95005i	0.113027	+	0.0652560i
$894$		0			0
$895$	−19.4617	−	11.2362i	−0.650533	−	0.375586i
$896$		0			0
$897$		0			0
$898$	−22.5823			−0.753582
$899$	−5.07035	−	8.78211i	−0.169106	−	0.292900i
$900$		0			0
$901$		0			0
$902$	20.6976	+	35.8493i	0.689156	+	1.19365i
$903$		0			0
$904$	4.91614	−	8.51501i	0.163508	−	0.283205i
$905$	18.6455	−	10.7650i	0.619796	−	0.357839i
$906$		0			0
$907$	1.94773	−	3.37357i	0.0646733	−	0.112017i	−0.831876	−	0.554962i	$-0.812733\pi$
$907$	1.94773	−	3.37357i	0.0646733	−	0.112017i	0.896549	+	0.442945i	$0.146066\pi$
$908$	−9.99110	+	17.3051i	−0.331566	+	0.574290i
$909$		0			0
$910$		0			0
$911$	−1.32768	+	0.766538i	−0.0439881	+	0.0253966i	−0.521833	−	0.853048i	$-0.674752\pi$
$911$	−1.32768	+	0.766538i	−0.0439881	+	0.0253966i	0.477845	+	0.878444i	$0.341418\pi$
$912$		0			0
$913$			31.7935i			1.05221i
$914$			39.8623i			1.31853i
$915$		0			0
$916$	8.77402	−	5.06568i	0.289902	−	0.167375i
$917$		0			0
$918$		0			0
$919$	−14.1266	+	24.4679i	−0.465992	+	0.807122i	−0.999246	−	0.0388335i	$-0.987636\pi$
$919$	−14.1266	+	24.4679i	−0.465992	+	0.807122i	0.533254	+	0.845955i	$0.320969\pi$
$920$	12.1658	−	21.0718i	0.401094	−	0.694715i
$921$		0			0
$922$	6.37834	−	3.68254i	0.210059	−	0.121278i
$923$	−2.76737	+	4.79323i	−0.0910892	+	0.157771i
$924$		0			0
$925$	−15.2192	−	26.3603i	−0.500403	−	0.866723i
$926$	−24.8475	−	14.3457i	−0.816539	−	0.471429i
$927$		0			0
$928$	1.44383	+	2.50079i	0.0473961	+	0.0820924i
$929$	3.28726			0.107851			0.0539257	−	0.998545i	$-0.482827\pi$
$929$	3.28726			0.107851			0.0539257	+	0.998545i	$0.482827\pi$
$930$		0			0
$931$		0			0
$932$	−6.33070	−	3.65503i	−0.207369	−	0.119725i
$933$		0			0
$934$	11.8389	+	6.83519i	0.387380	+	0.223654i
$935$	9.86466	−	5.69536i	0.322609	−	0.186258i
$936$		0			0
$937$			35.5084i			1.16001i	0.814613	+	0.580005i	$0.196949\pi$
$937$			35.5084i			1.16001i	−0.814613	+	0.580005i	$0.803051\pi$
$938$		0			0
$939$		0			0
$940$	4.25153	+	7.36387i	0.138670	+	0.240183i
$941$	12.4988			0.407450			0.203725	−	0.979028i	$-0.434695\pi$
$941$	12.4988			0.407450			0.203725	+	0.979028i	$0.434695\pi$
$942$		0			0
$943$			65.6208i			2.13691i
$944$	0.0211346			0.000687873
$945$		0			0
$946$	−3.71994			−0.120946
$947$		−	36.1154i		−	1.17359i	−0.809734	−	0.586796i	$-0.800389\pi$
$947$		−	36.1154i		−	1.17359i	0.809734	−	0.586796i	$-0.199611\pi$
$948$		0			0
$949$	13.8290			0.448910
$950$	−9.04931	−	15.6739i	−0.293598	−	0.508527i
$951$		0			0
$952$		0			0
$953$		−	45.2925i		−	1.46717i	−0.679599	−	0.733584i	$-0.737846\pi$
$953$		−	45.2925i		−	1.46717i	0.679599	−	0.733584i	$-0.262154\pi$
$954$		0			0
$955$	20.9390	−	12.0892i	0.677571	−	0.391196i
$956$	7.28317	+	4.20494i	0.235554	+	0.135997i
$957$		0			0
$958$	9.01596	+	5.20537i	0.291293	+	0.168178i
$959$		0			0
$960$		0			0
$961$	18.6677			0.602184
$962$	−4.27499	−	7.40449i	−0.137831	−	0.238730i
$963$		0			0
$964$	−7.75277	−	4.47607i	−0.249700	−	0.144164i
$965$	15.1859	+	26.3028i	0.488851	+	0.846716i
$966$		0			0
$967$	12.0000	−	20.7845i	0.385893	−	0.668385i	−0.606000	−	0.795465i	$-0.707227\pi$
$967$	12.0000	−	20.7845i	0.385893	−	0.668385i	0.991893	+	0.127079i	$0.0405602\pi$
$968$	3.94910	−	2.28001i	0.126929	−	0.0732824i
$969$		0			0
$970$	36.6146	−	63.4184i	1.17562	−	2.03624i
$971$	−16.6813	+	28.8928i	−0.535328	+	0.927215i	0.463819	+	0.885930i	$0.346479\pi$
$971$	−16.6813	+	28.8928i	−0.535328	+	0.927215i	−0.999147	+	0.0412855i	$0.986855\pi$
$972$		0			0
$973$		0			0
$974$	2.02520	−	1.16925i	0.0648917	−	0.0374652i
$975$		0			0
$976$		−	2.46911i		−	0.0790344i
$977$		−	34.5077i		−	1.10400i	−0.833844	−	0.552000i	$-0.813865\pi$
$977$		−	34.5077i		−	1.10400i	0.833844	−	0.552000i	$-0.186135\pi$
$978$		0			0
$979$	−31.6555	+	18.2763i	−1.01172	+	0.584114i
$980$		0			0
$981$		0			0
$982$	−16.9422	+	29.3448i	−0.540648	+	0.936429i
$983$	1.20651	−	2.08973i	0.0384817	−	0.0666522i	−0.846143	−	0.532956i	$-0.821081\pi$
$983$	1.20651	−	2.08973i	0.0384817	−	0.0666522i	0.884625	+	0.466304i	$0.154415\pi$
$984$		0			0
$985$	−43.0450	+	24.8521i	−1.37153	+	0.791852i
$986$	−1.07149	+	1.85588i	−0.0341232	+	0.0591032i
$987$		0			0
$988$	−2.54191	−	4.40271i	−0.0808688	−	0.140069i
$989$	−5.10691	−	2.94847i	−0.162390	−	0.0937560i
$990$		0			0
$991$	−24.2991	−	42.0873i	−0.771887	−	1.33695i	−0.936528	−	0.350594i	$-0.885980\pi$
$991$	−24.2991	−	42.0873i	−0.771887	−	1.33695i	0.164641	−	0.986354i	$-0.447353\pi$
$992$	3.51174			0.111498
$993$		0			0
$994$		0			0
$995$	−6.10612	−	3.52537i	−0.193577	−	0.111762i
$996$		0			0
$997$	−38.8449	−	22.4271i	−1.23023	−	0.710274i	−0.263152	−	0.964754i	$-0.584762\pi$
$997$	−38.8449	−	22.4271i	−1.23023	−	0.710274i	−0.967078	+	0.254481i	$0.918095\pi$
$998$	−14.3799	+	8.30223i	−0.455187	+	0.262802i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.l.b.1097.5		16
3.2	odd	2		882.2.l.a.509.4		16
7.2	even	3		378.2.m.a.125.5		16
7.3	odd	6		2646.2.t.a.2285.1		16
7.4	even	3		2646.2.t.a.2285.4		16
7.5	odd	6		378.2.m.a.125.8		16
7.6	odd	2	inner	2646.2.l.b.1097.8		16
9.2	odd	6		2646.2.t.a.1979.1		16
9.7	even	3		882.2.t.b.803.6		16
21.2	odd	6		126.2.m.a.41.1	✓	16
21.5	even	6		126.2.m.a.41.4	yes	16
21.11	odd	6		882.2.t.b.815.7		16
21.17	even	6		882.2.t.b.815.6		16
21.20	even	2		882.2.l.a.509.1		16
28.19	even	6		3024.2.cc.b.881.8		16
28.23	odd	6		3024.2.cc.b.881.1		16
63.2	odd	6		378.2.m.a.251.8		16
63.5	even	6		1134.2.d.a.1133.8		16
63.11	odd	6	inner	2646.2.l.b.521.4		16
63.16	even	3		126.2.m.a.83.4	yes	16
63.20	even	6		2646.2.t.a.1979.4		16
63.23	odd	6		1134.2.d.a.1133.1		16
63.25	even	3		882.2.l.a.227.5		16
63.34	odd	6		882.2.t.b.803.7		16
63.38	even	6	inner	2646.2.l.b.521.1		16
63.40	odd	6		1134.2.d.a.1133.9		16
63.47	even	6		378.2.m.a.251.5		16
63.52	odd	6		882.2.l.a.227.8		16
63.58	even	3		1134.2.d.a.1133.16		16
63.61	odd	6		126.2.m.a.83.1	yes	16
84.23	even	6		1008.2.cc.b.545.7		16
84.47	odd	6		1008.2.cc.b.545.2		16
252.47	odd	6		3024.2.cc.b.2897.1		16
252.79	odd	6		1008.2.cc.b.209.2		16
252.187	even	6		1008.2.cc.b.209.7		16
252.191	even	6		3024.2.cc.b.2897.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.1	✓	16	21.2	odd	6
126.2.m.a.41.4	yes	16	21.5	even	6
126.2.m.a.83.1	yes	16	63.61	odd	6
126.2.m.a.83.4	yes	16	63.16	even	3
378.2.m.a.125.5		16	7.2	even	3
378.2.m.a.125.8		16	7.5	odd	6
378.2.m.a.251.5		16	63.47	even	6
378.2.m.a.251.8		16	63.2	odd	6
882.2.l.a.227.5		16	63.25	even	3
882.2.l.a.227.8		16	63.52	odd	6
882.2.l.a.509.1		16	21.20	even	2
882.2.l.a.509.4		16	3.2	odd	2
882.2.t.b.803.6		16	9.7	even	3
882.2.t.b.803.7		16	63.34	odd	6
882.2.t.b.815.6		16	21.17	even	6
882.2.t.b.815.7		16	21.11	odd	6
1008.2.cc.b.209.2		16	252.79	odd	6
1008.2.cc.b.209.7		16	252.187	even	6
1008.2.cc.b.545.2		16	84.47	odd	6
1008.2.cc.b.545.7		16	84.23	even	6
1134.2.d.a.1133.1		16	63.23	odd	6
1134.2.d.a.1133.8		16	63.5	even	6
1134.2.d.a.1133.9		16	63.40	odd	6
1134.2.d.a.1133.16		16	63.58	even	3
2646.2.l.b.521.1		16	63.38	even	6	inner
2646.2.l.b.521.4		16	63.11	odd	6	inner
2646.2.l.b.1097.5		16	1.1	even	1	trivial
2646.2.l.b.1097.8		16	7.6	odd	2	inner
2646.2.t.a.1979.1		16	9.2	odd	6
2646.2.t.a.1979.4		16	63.20	even	6
2646.2.t.a.2285.1		16	7.3	odd	6
2646.2.t.a.2285.4		16	7.4	even	3
3024.2.cc.b.881.1		16	28.23	odd	6
3024.2.cc.b.881.8		16	28.19	even	6
3024.2.cc.b.2897.1		16	252.47	odd	6
3024.2.cc.b.2897.8		16	252.191	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.94556 - 3.36980i) q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.94556 - 3.36980i) q^{5} -1.00000i q^{8} +(3.36980 - 1.94556i) q^{10} +(3.41614 + 1.97231i) q^{11} +(2.46687 + 1.42425i) q^{13} +1.00000 q^{16} +(0.371058 + 0.642692i) q^{17} +(1.54563 + 0.892369i) q^{19} +(1.94556 + 3.36980i) q^{20} +(-1.97231 + 3.41614i) q^{22} +(-5.41535 + 3.12656i) q^{23} +(-5.07039 + 8.78217i) q^{25} +(-1.42425 + 2.46687i) q^{26} +(2.50079 - 1.44383i) q^{29} -3.51174i q^{31} +1.00000i q^{32} +(-0.642692 + 0.371058i) q^{34} +(-1.50079 + 2.59944i) q^{37} +(-0.892369 + 1.54563i) q^{38} +(-3.36980 + 1.94556i) q^{40} +(5.24705 - 9.08816i) q^{41} +(0.471521 + 0.816699i) q^{43} +(-3.41614 - 1.97231i) q^{44} +(-3.12656 - 5.41535i) q^{46} +2.18525 q^{47} +(-8.78217 - 5.07039i) q^{50} +(-2.46687 - 1.42425i) q^{52} -15.3490i q^{55} +(1.44383 + 2.50079i) q^{58} +0.0211346 q^{59} -2.46911i q^{61} +3.51174 q^{62} -1.00000 q^{64} -11.0838i q^{65} +13.4493 q^{67} +(-0.371058 - 0.642692i) q^{68} +1.94304i q^{71} +(4.20443 - 2.42743i) q^{73} +(-2.59944 - 1.50079i) q^{74} +(-1.54563 - 0.892369i) q^{76} +3.63613 q^{79} +(-1.94556 - 3.36980i) q^{80} +(9.08816 + 5.24705i) q^{82} +(4.02998 + 6.98012i) q^{83} +(1.44383 - 2.50079i) q^{85} +(-0.816699 + 0.471521i) q^{86} +(1.97231 - 3.41614i) q^{88} +(-4.63323 + 8.02499i) q^{89} +(5.41535 - 3.12656i) q^{92} +2.18525i q^{94} -6.94462i q^{95} +(16.2983 - 9.40980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} - 12 q^{11} + 16 q^{16} - 48 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} + 12 q^{44} - 12 q^{46} - 60 q^{50} - 12 q^{58} - 16 q^{64} + 56 q^{67} + 36 q^{74} + 8 q^{79} - 12 q^{85} - 24 q^{86} + 48 q^{92}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^11 + 16 * q^16 - 48 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 + 12 * q^44 - 12 * q^46 - 60 * q^50 - 12 * q^58 - 16 * q^64 + 56 * q^67 + 36 * q^74 + 8 * q^79 - 12 * q^85 - 24 * q^86 + 48 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more