LMFDB - Embedded newform 1323.2.o.e.440.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			440.6
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.e.881.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61855 - 0.934468i) q^{2} +(0.746462 + 1.29291i) q^{4} +(1.25287 + 2.17003i) q^{5} +0.947692i q^{8} +O(q^{10})$	\(q+(-1.61855 - 0.934468i) q^{2} +(0.746462 + 1.29291i) q^{4} +(1.25287 + 2.17003i) q^{5} +0.947692i q^{8} -4.68306i q^{10} +(4.85803 + 2.80479i) q^{11} +(-0.384312 + 0.221883i) q^{13} +(2.37851 - 4.11970i) q^{16} +3.07770 q^{17} +2.57419i q^{19} +(-1.87044 + 3.23969i) q^{20} +(-5.24197 - 9.07935i) q^{22} +(-6.83476 + 3.94605i) q^{23} +(-0.639351 + 1.10739i) q^{25} +0.829370 q^{26} +(-2.71041 - 1.56485i) q^{29} +(9.06457 - 5.23343i) q^{31} +(-6.05802 + 3.49760i) q^{32} +(-4.98140 - 2.87601i) q^{34} -1.41634 q^{37} +(2.40550 - 4.16645i) q^{38} +(-2.05652 + 1.18733i) q^{40} +(1.64665 + 2.85208i) q^{41} +(-4.75676 + 8.23894i) q^{43} +8.37467i q^{44} +14.7498 q^{46} +(-1.07190 + 1.85659i) q^{47} +(2.06964 - 1.19491i) q^{50} +(-0.573749 - 0.331254i) q^{52} +4.85412i q^{53} +14.0561i q^{55} +(2.92461 + 5.06558i) q^{58} +(-3.65496 - 6.33057i) q^{59} +(-7.40950 - 4.27788i) q^{61} -19.5619 q^{62} +3.55953 q^{64} +(-0.962984 - 0.555979i) q^{65} +(0.934442 + 1.61850i) q^{67} +(2.29739 + 3.97919i) q^{68} +2.95338i q^{71} +8.51943i q^{73} +(2.29241 + 1.32352i) q^{74} +(-3.32820 + 1.92154i) q^{76} +(0.287130 - 0.497324i) q^{79} +11.9198 q^{80} -6.15497i q^{82} +(4.23521 - 7.33560i) q^{83} +(3.85595 + 6.67870i) q^{85} +(15.3981 - 8.89008i) q^{86} +(-2.65807 + 4.60392i) q^{88} -7.57858 q^{89} +(-10.2038 - 5.89115i) q^{92} +(3.46984 - 2.00332i) q^{94} +(-5.58607 + 3.22512i) q^{95} +(3.22662 + 1.86289i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.61855	−	0.934468i	−1.14449	−	0.660769i	−0.196948	−	0.980414i	$-0.563103\pi$
$2$	−1.61855	−	0.934468i	−1.14449	−	0.660769i	−0.947537	+	0.319645i	$0.896436\pi$
$3$		0			0
$3$		0			0
$4$	0.746462	+	1.29291i	0.373231	+	0.646455i
$5$	1.25287	+	2.17003i	0.560299	+	0.970467i	0.997470	+	0.0710881i	$0.0226472\pi$
$5$	1.25287	+	2.17003i	0.560299	+	0.970467i	−0.437171	+	0.899378i	$0.644020\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			0.947692i			0.335060i
$9$		0			0
$10$		−	4.68306i		−	1.48091i
$11$	4.85803	+	2.80479i	1.46475	+	0.845675i	0.999225	−	0.0393590i	$-0.0125316\pi$
$11$	4.85803	+	2.80479i	1.46475	+	0.845675i	0.465527	+	0.885034i	$0.345865\pi$
$12$		0			0
$13$	−0.384312	+	0.221883i	−0.106589	+	0.0615392i	−0.552347	−	0.833614i	$-0.686268\pi$
$13$	−0.384312	+	0.221883i	−0.106589	+	0.0615392i	0.445758	+	0.895154i	$0.352934\pi$
$14$		0			0
$15$		0			0
$16$	2.37851	−	4.11970i	0.594628	−	1.02993i
$17$	3.07770			0.746451			0.373226	−	0.927741i	$-0.378252\pi$
$17$	3.07770			0.746451			0.373226	+	0.927741i	$0.378252\pi$
$18$		0			0
$19$			2.57419i			0.590560i	0.955411	+	0.295280i	$0.0954130\pi$
$19$			2.57419i			0.590560i	−0.955411	+	0.295280i	$0.904587\pi$
$20$	−1.87044	+	3.23969i	−0.418242	+	0.724417i
$21$		0			0
$22$	−5.24197	−	9.07935i	−1.11759	−	1.93572i
$23$	−6.83476	+	3.94605i	−1.42515	+	0.822808i	−0.996732	−	0.0807749i	$-0.974261\pi$
$23$	−6.83476	+	3.94605i	−1.42515	+	0.822808i	−0.428413	+	0.903583i	$0.640927\pi$
$24$		0			0
$25$	−0.639351	+	1.10739i	−0.127870	+	0.221478i
$26$	0.829370			0.162653
$27$		0			0
$28$		0			0
$29$	−2.71041	−	1.56485i	−0.503310	−	0.290586i	0.226770	−	0.973948i	$-0.427184\pi$
$29$	−2.71041	−	1.56485i	−0.503310	−	0.290586i	−0.730079	+	0.683362i	$0.760517\pi$
$30$		0			0
$31$	9.06457	−	5.23343i	1.62805	−	0.939952i	0.643370	−	0.765556i	$-0.277536\pi$
$31$	9.06457	−	5.23343i	1.62805	−	0.939952i	0.984675	−	0.174397i	$-0.0557975\pi$
$32$	−6.05802	+	3.49760i	−1.07092	+	0.618294i
$33$		0			0
$34$	−4.98140	−	2.87601i	−0.854303	−	0.493232i
$35$		0			0
$36$		0			0
$37$	−1.41634			−0.232844			−0.116422	−	0.993200i	$-0.537143\pi$
$37$	−1.41634			−0.232844			−0.116422	+	0.993200i	$0.537143\pi$
$38$	2.40550	−	4.16645i	0.390224	−	0.675887i
$39$		0			0
$40$	−2.05652	+	1.18733i	−0.325164	+	0.187734i
$41$	1.64665	+	2.85208i	0.257163	+	0.445420i	0.965481	−	0.260474i	$-0.0838788\pi$
$41$	1.64665	+	2.85208i	0.257163	+	0.445420i	−0.708318	+	0.705894i	$0.750545\pi$
$42$		0			0
$43$	−4.75676	+	8.23894i	−0.725398	+	1.25643i	0.233411	+	0.972378i	$0.425011\pi$
$43$	−4.75676	+	8.23894i	−0.725398	+	1.25643i	−0.958810	+	0.284049i	$0.908322\pi$
$44$			8.37467i			1.26253i
$45$		0			0
$46$	14.7498			2.17474
$47$	−1.07190	+	1.85659i	−0.156353	+	0.270811i	−0.933551	−	0.358445i	$-0.883307\pi$
$47$	−1.07190	+	1.85659i	−0.156353	+	0.270811i	0.777198	+	0.629256i	$0.216640\pi$
$48$		0			0
$49$		0			0
$50$	2.06964	−	1.19491i	0.292691	−	0.168985i
$51$		0			0
$52$	−0.573749	−	0.331254i	−0.0795647	−	0.0459367i
$53$			4.85412i			0.666764i	0.942792	+	0.333382i	$0.108190\pi$
$53$			4.85412i			0.666764i	−0.942792	+	0.333382i	$0.891810\pi$
$54$		0			0
$55$			14.0561i			1.89532i
$56$		0			0
$57$		0			0
$58$	2.92461	+	5.06558i	0.384020	+	0.665143i
$59$	−3.65496	−	6.33057i	−0.475835	−	0.824170i	0.523782	−	0.851852i	$-0.324521\pi$
$59$	−3.65496	−	6.33057i	−0.475835	−	0.824170i	−0.999617	+	0.0276824i	$0.991187\pi$
$60$		0			0
$61$	−7.40950	−	4.27788i	−0.948690	−	0.547726i	−0.0560160	−	0.998430i	$-0.517840\pi$
$61$	−7.40950	−	4.27788i	−0.948690	−	0.547726i	−0.892674	+	0.450704i	$0.851173\pi$
$62$	−19.5619			−2.48437
$63$		0			0
$64$	3.55953			0.444941
$65$	−0.962984	−	0.555979i	−0.119443	−	0.0689607i
$66$		0			0
$67$	0.934442	+	1.61850i	0.114160	+	0.197731i	0.917444	−	0.397865i	$-0.130249\pi$
$67$	0.934442	+	1.61850i	0.114160	+	0.197731i	−0.803284	+	0.595597i	$0.796916\pi$
$68$	2.29739	+	3.97919i	0.278599	+	0.482548i
$69$		0			0
$70$		0			0
$71$			2.95338i			0.350501i	0.984524	+	0.175251i	$0.0560736\pi$
$71$			2.95338i			0.350501i	−0.984524	+	0.175251i	$0.943926\pi$
$72$		0			0
$73$			8.51943i			0.997124i	0.866854	+	0.498562i	$0.166138\pi$
$73$			8.51943i			0.997124i	−0.866854	+	0.498562i	$0.833862\pi$
$74$	2.29241	+	1.32352i	0.266487	+	0.153856i
$75$		0			0
$76$	−3.32820	+	1.92154i	−0.381771	+	0.220415i
$77$		0			0
$78$		0			0
$79$	0.287130	−	0.497324i	0.0323047	−	0.0559533i	−0.849421	−	0.527716i	$-0.823049\pi$
$79$	0.287130	−	0.497324i	0.0323047	−	0.0559533i	0.881726	+	0.471762i	$0.156382\pi$
$80$	11.9198			1.33268
$81$		0			0
$82$		−	6.15497i		−	0.679702i
$83$	4.23521	−	7.33560i	0.464875	−	0.805186i	−0.534321	−	0.845281i	$-0.679433\pi$
$83$	4.23521	−	7.33560i	0.464875	−	0.805186i	0.999196	+	0.0400951i	$0.0127661\pi$
$84$		0			0
$85$	3.85595	+	6.67870i	0.418236	+	0.724406i
$86$	15.3981	−	8.89008i	1.66042	−	0.958642i
$87$		0			0
$88$	−2.65807	+	4.60392i	−0.283352	+	0.490779i
$89$	−7.57858			−0.803328			−0.401664	−	0.915787i	$-0.631568\pi$
$89$	−7.57858			−0.803328			−0.401664	+	0.915787i	$0.631568\pi$
$90$		0			0
$91$		0			0
$92$	−10.2038	−	5.89115i	−1.06382	−	0.614195i
$93$		0			0
$94$	3.46984	−	2.00332i	0.357887	−	0.206626i
$95$	−5.58607	+	3.22512i	−0.573119	+	0.330890i
$96$		0			0
$97$	3.22662	+	1.86289i	0.327614	+	0.189148i	0.654781	−	0.755818i	$-0.272761\pi$
$97$	3.22662	+	1.86289i	0.327614	+	0.189148i	−0.327167	+	0.944966i	$0.606094\pi$
$98$		0			0
$99$		0			0
$100$	−1.90901			−0.190901
$101$	−3.76725	+	6.52506i	−0.374855	+	0.649268i	−0.990305	−	0.138908i	$-0.955641\pi$
$101$	−3.76725	+	6.52506i	−0.374855	+	0.649268i	0.615450	+	0.788176i	$0.288974\pi$
$102$		0			0
$103$	12.4045	−	7.16173i	1.22225	−	0.705666i	0.256853	−	0.966451i	$-0.417315\pi$
$103$	12.4045	−	7.16173i	1.22225	−	0.705666i	0.965397	+	0.260784i	$0.0839812\pi$
$104$	−0.210276	−	0.364210i	−0.0206193	−	0.0357137i
$105$		0			0
$106$	4.53602	−	7.85662i	0.440577	−	0.763102i
$107$			13.4866i			1.30380i	0.758305	+	0.651900i	$0.226028\pi$
$107$			13.4866i			1.30380i	−0.758305	+	0.651900i	$0.773972\pi$
$108$		0			0
$109$	−0.918695			−0.0879950			−0.0439975	−	0.999032i	$-0.514009\pi$
$109$	−0.918695			−0.0879950			−0.0439975	+	0.999032i	$0.514009\pi$
$110$	13.1350	−	22.7504i	1.25237	−	2.16917i
$111$		0			0
$112$		0			0
$113$	−4.10412	+	2.36952i	−0.386083	+	0.222905i	−0.680462	−	0.732784i	$-0.738221\pi$
$113$	−4.10412	+	2.36952i	−0.386083	+	0.222905i	0.294378	+	0.955689i	$0.404887\pi$
$114$		0			0
$115$	−17.1261	−	9.88775i	−1.59702	−	0.922037i
$116$		−	4.67242i		−	0.433823i
$117$		0			0
$118$			13.6618i			1.25767i
$119$		0			0
$120$		0			0
$121$	10.2337	+	17.7252i	0.930332	+	1.61138i
$122$	7.99508	+	13.8479i	0.723841	+	1.25373i
$123$		0			0
$124$	13.5327	+	7.81312i	1.21527	+	0.701639i
$125$	9.32458			0.834016
$126$		0			0
$127$	7.37245			0.654200			0.327100	−	0.944990i	$-0.393929\pi$
$127$	7.37245			0.654200			0.327100	+	0.944990i	$0.393929\pi$
$128$	6.35477	+	3.66893i	0.561688	+	0.324291i
$129$		0			0
$130$	1.03909	+	1.79976i	0.0911342	+	0.157849i
$131$	3.93150	+	6.80955i	0.343497	+	0.594953i	0.985079	−	0.172100i	$-0.0550553\pi$
$131$	3.93150	+	6.80955i	0.343497	+	0.594953i	−0.641583	+	0.767054i	$0.721722\pi$
$132$		0			0
$133$		0			0
$134$		−	3.49283i		−	0.301734i
$135$		0			0
$136$			2.91671i			0.250106i
$137$	10.0198	+	5.78491i	0.856046	+	0.494238i	0.862686	−	0.505740i	$-0.168780\pi$
$137$	10.0198	+	5.78491i	0.856046	+	0.494238i	−0.00664016	+	0.999978i	$0.502114\pi$
$138$		0			0
$139$	16.9741	−	9.79999i	1.43972	−	0.831224i	0.441893	−	0.897068i	$-0.354307\pi$
$139$	16.9741	−	9.79999i	1.43972	−	0.831224i	0.997830	+	0.0658437i	$0.0209739\pi$
$140$		0			0
$141$		0			0
$142$	2.75984	−	4.78018i	0.231600	−	0.401144i
$143$	−2.48933			−0.208169
$144$		0			0
$145$		−	7.84221i		−	0.651260i
$146$	7.96114	−	13.7891i	0.658868	−	1.14119i
$147$		0			0
$148$	−1.05724	−	1.83120i	−0.0869047	−	0.150523i
$149$	13.6315	−	7.87012i	1.11673	−	0.644746i	0.176167	−	0.984360i	$-0.443630\pi$
$149$	13.6315	−	7.87012i	1.11673	−	0.644746i	0.940565	+	0.339615i	$0.110297\pi$
$150$		0			0
$151$	0.991353	−	1.71707i	0.0806752	−	0.139734i	−0.822865	−	0.568237i	$-0.807626\pi$
$151$	0.991353	−	1.71707i	0.0806752	−	0.139734i	0.903540	+	0.428503i	$0.140959\pi$
$152$	−2.43954			−0.197873
$153$		0			0
$154$		0			0
$155$	22.7134	+	13.1136i	1.82438	+	1.05331i
$156$		0			0
$157$	−7.26790	+	4.19612i	−0.580041	+	0.334887i	−0.761150	−	0.648576i	$-0.775365\pi$
$157$	−7.26790	+	4.19612i	−0.580041	+	0.334887i	0.181108	+	0.983463i	$0.442031\pi$
$158$	−0.929468	+	0.536628i	−0.0739445	+	0.0426919i
$159$		0			0
$160$	−15.1798	−	8.76405i	−1.20007	−	0.692859i
$161$		0			0
$162$		0			0
$163$	−1.07411			−0.0841306			−0.0420653	−	0.999115i	$-0.513394\pi$
$163$	−1.07411			−0.0841306			−0.0420653	+	0.999115i	$0.513394\pi$
$164$	−2.45832	+	4.25794i	−0.191963	+	0.332489i
$165$		0			0
$166$	−13.7098	+	7.91534i	−1.06408	+	0.614349i
$167$	−3.99731	−	6.92354i	−0.309321	−	0.535760i	0.668893	−	0.743359i	$-0.266768\pi$
$167$	−3.99731	−	6.92354i	−0.309321	−	0.535760i	−0.978214	+	0.207599i	$0.933435\pi$
$168$		0			0
$169$	−6.40154	+	11.0878i	−0.492426	+	0.852907i
$170$		−	14.4130i		−	1.10543i
$171$		0			0
$172$	−14.2030			−1.08297
$173$	−0.501744	+	0.869046i	−0.0381469	+	0.0660723i	−0.884468	−	0.466600i	$-0.845479\pi$
$173$	−0.501744	+	0.869046i	−0.0381469	+	0.0660723i	0.846322	+	0.532672i	$0.178812\pi$
$174$		0			0
$175$		0			0
$176$	23.1098	−	13.3424i	1.74197	−	1.00572i
$177$		0			0
$178$	12.2663	+	7.08195i	0.919398	+	0.530814i
$179$		−	1.47539i		−	0.110276i	−0.998479	−	0.0551379i	$-0.982440\pi$
$179$		−	1.47539i		−	0.110276i	0.998479	−	0.0551379i	$-0.0175599\pi$
$180$		0			0
$181$		−	15.0440i		−	1.11821i	−0.829096	−	0.559106i	$-0.811145\pi$
$181$		−	15.0440i		−	1.11821i	0.829096	−	0.559106i	$-0.188855\pi$
$182$		0			0
$183$		0			0
$184$	−3.73964	−	6.47724i	−0.275690	−	0.477509i
$185$	−1.77448	−	3.07349i	−0.130462	−	0.225967i
$186$		0			0
$187$	14.9516	+	8.63229i	1.09337	+	0.631255i
$188$	−3.20054			−0.233423
$189$		0			0
$190$	12.0551			0.874568
$191$	−11.4521	−	6.61187i	−0.828644	−	0.478418i	0.0247439	−	0.999694i	$-0.492123\pi$
$191$	−11.4521	−	6.61187i	−0.828644	−	0.478418i	−0.853388	+	0.521276i	$0.825456\pi$
$192$		0			0
$193$	0.777855	+	1.34728i	0.0559912	+	0.0969796i	0.892662	−	0.450726i	$-0.148835\pi$
$193$	0.777855	+	1.34728i	0.0559912	+	0.0969796i	−0.836671	+	0.547705i	$0.815501\pi$
$194$	−3.48163	−	6.03035i	−0.249966	−	0.432954i
$195$		0			0
$196$		0			0
$197$			4.96185i			0.353517i	0.984254	+	0.176759i	$0.0565612\pi$
$197$			4.96185i			0.353517i	−0.984254	+	0.176759i	$0.943439\pi$
$198$		0			0
$199$			11.1922i			0.793394i	0.917950	+	0.396697i	$0.129844\pi$
$199$			11.1922i			0.793394i	−0.917950	+	0.396697i	$0.870156\pi$
$200$	−1.04946	−	0.605908i	−0.0742083	−	0.0428442i
$201$		0			0
$202$	12.1949	−	7.04074i	0.858032	−	0.495385i
$203$		0			0
$204$		0			0
$205$	−4.12606	+	7.14655i	−0.288177	+	0.499137i
$206$	−26.7696			−1.86513
$207$		0			0
$208$			2.11100i			0.146372i
$209$	−7.22006	+	12.5055i	−0.499422	+	0.865024i
$210$		0			0
$211$	7.68026	+	13.3026i	0.528731	+	0.915789i	0.999439	+	0.0334999i	$0.0106654\pi$
$211$	7.68026	+	13.3026i	0.528731	+	0.915789i	−0.470708	+	0.882289i	$0.656001\pi$
$212$	−6.27594	+	3.62342i	−0.431033	+	0.248857i
$213$		0			0
$214$	12.6028	−	21.8287i	0.861511	−	1.49218i
$215$	−23.8383			−1.62576
$216$		0			0
$217$		0			0
$218$	1.48695	+	0.858492i	0.100709	+	0.0581444i
$219$		0			0
$220$	−18.1733	+	10.4923i	−1.22524	+	0.707394i
$221$	−1.18280	+	0.682888i	−0.0795635	+	0.0459360i
$222$		0			0
$223$	−2.76845	−	1.59837i	−0.185389	−	0.107034i	0.404433	−	0.914568i	$-0.367469\pi$
$223$	−2.76845	−	1.59837i	−0.185389	−	0.107034i	−0.589822	+	0.807533i	$0.700802\pi$
$224$		0			0
$225$		0			0
$226$	8.85695			0.589156
$227$	7.33494	−	12.7045i	0.486837	−	0.843227i	−0.513048	−	0.858360i	$-0.671484\pi$
$227$	7.33494	−	12.7045i	0.486837	−	0.843227i	0.999885	+	0.0151329i	$0.00481714\pi$
$228$		0			0
$229$	2.92550	−	1.68904i	0.193322	−	0.111615i	−0.400215	−	0.916421i	$-0.631064\pi$
$229$	2.92550	−	1.68904i	0.193322	−	0.111615i	0.593537	+	0.804807i	$0.297731\pi$
$230$	18.4796	+	32.0076i	1.21851	+	2.11052i
$231$		0			0
$232$	1.48300	−	2.56863i	0.0973637	−	0.168639i
$233$			4.88009i			0.319706i	0.987141	+	0.159853i	$0.0511020\pi$
$233$			4.88009i			0.319706i	−0.987141	+	0.159853i	$0.948898\pi$
$234$		0			0
$235$	−5.37180			−0.350418
$236$	5.45657	−	9.45106i	0.355193	−	0.615212i
$237$		0			0
$238$		0			0
$239$	−13.6253	+	7.86657i	−0.881347	+	0.508846i	−0.871102	−	0.491101i	$-0.836594\pi$
$239$	−13.6253	+	7.86657i	−0.881347	+	0.508846i	−0.0102448	+	0.999948i	$0.503261\pi$
$240$		0			0
$241$	−0.666305	−	0.384691i	−0.0429205	−	0.0247801i	0.478386	−	0.878150i	$-0.341222\pi$
$241$	−0.666305	−	0.384691i	−0.0429205	−	0.0247801i	−0.521307	+	0.853369i	$0.674555\pi$
$242$		−	38.2521i		−	2.45894i
$243$		0			0
$244$		−	12.7731i		−	0.817714i
$245$		0			0
$246$		0			0
$247$	−0.571169	−	0.989293i	−0.0363426	−	0.0629472i
$248$	4.95968	+	8.59042i	0.314940	+	0.545492i
$249$		0			0
$250$	−15.0923	−	8.71353i	−0.954519	−	0.551092i
$251$	−1.14544			−0.0722996			−0.0361498	−	0.999346i	$-0.511509\pi$
$251$	−1.14544			−0.0722996			−0.0361498	+	0.999346i	$0.511509\pi$
$252$		0			0
$253$	−44.2713			−2.78331
$254$	−11.9327	−	6.88933i	−0.748722	−	0.432275i
$255$		0			0
$256$	−10.4165	−	18.0420i	−0.651033	−	1.12762i
$257$	14.4917	+	25.1004i	0.903969	+	1.56572i	0.822295	+	0.569061i	$0.192693\pi$
$257$	14.4917	+	25.1004i	0.903969	+	1.56572i	0.0816738	+	0.996659i	$0.473973\pi$
$258$		0			0
$259$		0			0
$260$		−	1.66007i		−	0.102953i
$261$		0			0
$262$		−	14.6954i		−	0.907887i
$263$	−11.8643	−	6.84988i	−0.731586	−	0.422381i	0.0874160	−	0.996172i	$-0.472139\pi$
$263$	−11.8643	−	6.84988i	−0.731586	−	0.422381i	−0.819002	+	0.573790i	$0.805472\pi$
$264$		0			0
$265$	−10.5336	+	6.08156i	−0.647072	+	0.373587i
$266$		0			0
$267$		0			0
$268$	−1.39505	+	2.41630i	−0.0852163	+	0.147599i
$269$	−10.4795			−0.638944			−0.319472	−	0.947596i	$-0.603506\pi$
$269$	−10.4795			−0.638944			−0.319472	+	0.947596i	$0.603506\pi$
$270$		0			0
$271$			6.54607i			0.397646i	0.980035	+	0.198823i	$0.0637118\pi$
$271$			6.54607i			0.397646i	−0.980035	+	0.198823i	$0.936288\pi$
$272$	7.32034	−	12.6792i	0.443861	−	0.768790i
$273$		0			0
$274$	−10.8116	−	18.7263i	−0.653155	−	1.13130i
$275$	−6.21198	+	3.58649i	−0.374596	+	0.216273i
$276$		0			0
$277$	−11.2156	+	19.4261i	−0.673883	+	1.16720i	0.302911	+	0.953019i	$0.402041\pi$
$277$	−11.2156	+	19.4261i	−0.673883	+	1.16720i	−0.976794	+	0.214181i	$0.931292\pi$
$278$	−36.6311			−2.19699
$279$		0			0
$280$		0			0
$281$	−19.3552	−	11.1747i	−1.15463	−	0.666627i	−0.204621	−	0.978841i	$-0.565596\pi$
$281$	−19.3552	−	11.1747i	−1.15463	−	0.666627i	−0.950012	+	0.312214i	$0.898929\pi$
$282$		0			0
$283$	16.4296	−	9.48563i	0.976638	−	0.563862i	0.0753848	−	0.997155i	$-0.475981\pi$
$283$	16.4296	−	9.48563i	0.976638	−	0.563862i	0.901254	+	0.433292i	$0.142648\pi$
$284$	−3.81845	+	2.20459i	−0.226584	+	0.130818i
$285$		0			0
$286$	4.02910	+	2.32620i	0.238246	+	0.137551i
$287$		0			0
$288$		0			0
$289$	−7.52777			−0.442810
$290$	−7.32830	+	12.6930i	−0.430333	+	0.745358i
$291$		0			0
$292$	−11.0149	+	6.35943i	−0.644596	+	0.372158i
$293$	4.41136	+	7.64069i	0.257714	+	0.446374i	0.965629	−	0.259924i	$-0.0836974\pi$
$293$	4.41136	+	7.64069i	0.257714	+	0.446374i	−0.707915	+	0.706298i	$0.750364\pi$
$294$		0			0
$295$	9.15835	−	15.8627i	0.533220	−	0.923563i
$296$		−	1.34225i		−	0.0780167i
$297$		0			0
$298$	−29.4175			−1.70411
$299$	1.75112	−	3.03303i	0.101270	−	0.175405i
$300$		0			0
$301$		0			0
$302$	−3.20910	+	1.85278i	−0.184663	+	0.106615i
$303$		0			0
$304$	10.6049	+	6.12275i	0.608233	+	0.351164i
$305$		−	21.4385i		−	1.22756i
$306$		0			0
$307$		−	28.7533i		−	1.64104i	−0.571620	−	0.820519i	$-0.693685\pi$
$307$		−	28.7533i		−	1.64104i	0.571620	−	0.820519i	$-0.306315\pi$
$308$		0			0
$309$		0			0
$310$	−24.5085	−	42.4499i	−1.39199	−	2.41099i
$311$	−6.64294	−	11.5059i	−0.376687	−	0.652441i	0.613891	−	0.789391i	$-0.289603\pi$
$311$	−6.64294	−	11.5059i	−0.376687	−	0.652441i	−0.990578	+	0.136950i	$0.956270\pi$
$312$		0			0
$313$	−27.3227	−	15.7748i	−1.54437	−	0.891643i	−0.998555	−	0.0537372i	$-0.982887\pi$
$313$	−27.3227	−	15.7748i	−1.54437	−	0.891643i	−0.545815	−	0.837905i	$-0.683780\pi$
$314$	15.6846			0.885132
$315$		0			0
$316$	0.857328			0.0482285
$317$	−17.3819	−	10.0354i	−0.976264	−	0.563646i	−0.0751236	−	0.997174i	$-0.523935\pi$
$317$	−17.3819	−	10.0354i	−0.976264	−	0.563646i	−0.901140	+	0.433528i	$0.857268\pi$
$318$		0			0
$319$	−8.77816	−	15.2042i	−0.491483	−	0.851273i
$320$	4.45961	+	7.72428i	0.249300	+	0.431800i
$321$		0			0
$322$		0			0
$323$			7.92259i			0.440824i
$324$		0			0
$325$		−	0.567444i		−	0.0314761i
$326$	1.73849	+	1.00372i	0.0962862	+	0.0555909i
$327$		0			0
$328$	−2.70289	+	1.56052i	−0.149242	+	0.0861651i
$329$		0			0
$330$		0			0
$331$	−0.623957	+	1.08073i	−0.0342958	+	0.0594020i	−0.882664	−	0.470005i	$-0.844252\pi$
$331$	−0.623957	+	1.08073i	−0.0342958	+	0.0594020i	0.848368	+	0.529407i	$0.177585\pi$
$332$	12.6457			0.694023
$333$		0			0
$334$			14.9414i			0.817559i
$335$	−2.34146	+	4.05553i	−0.127928	+	0.221577i
$336$		0			0
$337$	6.58745	+	11.4098i	0.358842	+	0.621532i	0.987768	−	0.155933i	$-0.0498385\pi$
$337$	6.58745	+	11.4098i	0.358842	+	0.621532i	−0.628926	+	0.777465i	$0.716505\pi$
$338$	20.7224	−	11.9641i	1.12715	−	0.650759i
$339$		0			0
$340$	−5.75664	+	9.97079i	−0.312198	+	0.540742i
$341$	58.7146			3.17958
$342$		0			0
$343$		0			0
$344$	−7.80798	−	4.50794i	−0.420978	−	0.243052i
$345$		0			0
$346$	1.62419	−	0.937727i	0.0873171	−	0.0504125i
$347$	23.4411	−	13.5337i	1.25838	−	0.726529i	0.285624	−	0.958342i	$-0.407799\pi$
$347$	23.4411	−	13.5337i	1.25838	−	0.726529i	0.972760	+	0.231813i	$0.0744658\pi$
$348$		0			0
$349$	30.3413	+	17.5176i	1.62413	+	0.937694i	0.985798	+	0.167936i	$0.0537101\pi$
$349$	30.3413	+	17.5176i	1.62413	+	0.937694i	0.638336	+	0.769758i	$0.279623\pi$
$350$		0			0
$351$		0			0
$352$	−39.2401			−2.09150
$353$	−1.26256	+	2.18682i	−0.0671992	+	0.116392i	−0.897667	−	0.440674i	$-0.854740\pi$
$353$	−1.26256	+	2.18682i	−0.0671992	+	0.116392i	0.830468	+	0.557066i	$0.188073\pi$
$354$		0			0
$355$	−6.40892	+	3.70019i	−0.340150	+	0.196386i
$356$	−5.65713	−	9.79843i	−0.299827	−	0.519316i
$357$		0			0
$358$	−1.37871	+	2.38799i	−0.0728669	+	0.126209i
$359$			7.26762i			0.383570i	0.981437	+	0.191785i	$0.0614277\pi$
$359$			7.26762i			0.383570i	−0.981437	+	0.191785i	$0.938572\pi$
$360$		0			0
$361$	12.3735			0.651239
$362$	−14.0581	+	24.3494i	−0.738880	+	1.27978i
$363$		0			0
$364$		0			0
$365$	−18.4874	+	10.6737i	−0.967675	+	0.558688i
$366$		0			0
$367$	−11.6714	−	6.73848i	−0.609242	−	0.351746i	0.163427	−	0.986555i	$-0.447745\pi$
$367$	−11.6714	−	6.73848i	−0.609242	−	0.351746i	−0.772669	+	0.634809i	$0.781079\pi$
$368$			37.5429i			1.95706i
$369$		0			0
$370$			6.63278i			0.344822i
$371$		0			0
$372$		0			0
$373$	−11.8820	−	20.5801i	−0.615224	−	1.06560i	−0.990345	−	0.138624i	$-0.955732\pi$
$373$	−11.8820	−	20.5801i	−0.615224	−	1.06560i	0.375121	−	0.926976i	$-0.377601\pi$
$374$	−16.1332	−	27.9435i	−0.834228	−	1.44492i
$375$		0			0
$376$	−1.75947	−	1.01583i	−0.0907379	−	0.0523875i
$377$	1.38886			0.0715297
$378$		0			0
$379$	21.2283			1.09042			0.545211	−	0.838299i	$-0.316449\pi$
$379$	21.2283			1.09042			0.545211	+	0.838299i	$0.316449\pi$
$380$	−8.33958	−	4.81486i	−0.427812	−	0.246997i
$381$		0			0
$382$	12.3572	+	21.4032i	0.632248	+	1.09509i
$383$	−6.47930	−	11.2225i	−0.331077	−	0.573442i	0.651646	−	0.758523i	$-0.274079\pi$
$383$	−6.47930	−	11.2225i	−0.331077	−	0.573442i	−0.982723	+	0.185081i	$0.940745\pi$
$384$		0			0
$385$		0			0
$386$		−	2.90752i		−	0.147989i
$387$		0			0
$388$			5.56231i			0.282384i
$389$	−9.48037	−	5.47350i	−0.480674	−	0.277517i	0.240023	−	0.970767i	$-0.422845\pi$
$389$	−9.48037	−	5.47350i	−0.480674	−	0.277517i	−0.720697	+	0.693250i	$0.756178\pi$
$390$		0			0
$391$	−21.0353	+	12.1447i	−1.06380	+	0.614186i
$392$		0			0
$393$		0			0
$394$	4.63669	−	8.03098i	0.233593	−	0.404595i
$395$	1.43894			0.0724011
$396$		0			0
$397$			29.8901i			1.50014i	0.661358	+	0.750071i	$0.269981\pi$
$397$			29.8901i			1.50014i	−0.661358	+	0.750071i	$0.730019\pi$
$398$	10.4588	−	18.1151i	0.524250	−	0.908028i
$399$		0			0
$400$	3.04141	+	5.26788i	0.152071	+	0.263394i
$401$	−16.6233	+	9.59744i	−0.830126	+	0.479273i	−0.853896	−	0.520444i	$-0.825766\pi$
$401$	−16.6233	+	9.59744i	−0.830126	+	0.479273i	0.0237698	+	0.999717i	$0.492433\pi$
$402$		0			0
$403$	−2.32242	+	4.02254i	−0.115688	+	0.200377i
$404$	−11.2484			−0.559630
$405$		0			0
$406$		0			0
$407$	−6.88060	−	3.97252i	−0.341059	−	0.196910i
$408$		0			0
$409$	−24.9737	+	14.4186i	−1.23487	+	0.712953i	−0.968041	−	0.250790i	$-0.919309\pi$
$409$	−24.9737	+	14.4186i	−1.23487	+	0.712953i	−0.266830	+	0.963744i	$0.585976\pi$
$410$	13.3565	−	7.71135i	0.659628	−	0.380837i
$411$		0			0
$412$	18.5190	+	10.6919i	0.912363	+	0.526753i
$413$		0			0
$414$		0			0
$415$	21.2246			1.04188
$416$	1.55211	−	2.68834i	0.0760986	−	0.131807i
$417$		0			0
$418$	23.3720	−	13.4938i	1.14316	−	0.660005i
$419$	−5.06390	−	8.77094i	−0.247388	−	0.428488i	0.715412	−	0.698702i	$-0.246239\pi$
$419$	−5.06390	−	8.77094i	−0.247388	−	0.428488i	−0.962800	+	0.270214i	$0.912906\pi$
$420$		0			0
$421$	12.7094	−	22.0134i	0.619419	−	1.07287i	−0.370173	−	0.928963i	$-0.620702\pi$
$421$	12.7094	−	22.0134i	0.619419	−	1.07287i	0.989592	−	0.143902i	$-0.0459651\pi$
$422$		−	28.7079i		−	1.39748i
$423$		0			0
$424$	−4.60021			−0.223406
$425$	−1.96773	+	3.40821i	−0.0954490	+	0.165322i
$426$		0			0
$427$		0			0
$428$	−17.4370	+	10.0673i	−0.842849	+	0.486619i
$429$		0			0
$430$	38.5834	+	22.2762i	1.86066	+	1.07425i
$431$		−	10.8434i		−	0.522308i	−0.965297	−	0.261154i	$-0.915897\pi$
$431$		−	10.8434i		−	0.522308i	0.965297	−	0.261154i	$-0.0841031\pi$
$432$		0			0
$433$			13.0519i			0.627233i	0.949550	+	0.313616i	$0.101541\pi$
$433$			13.0519i			0.627233i	−0.949550	+	0.313616i	$0.898459\pi$
$434$		0			0
$435$		0			0
$436$	−0.685771	−	1.18779i	−0.0328425	−	0.0568849i
$437$	−10.1579	−	17.5940i	−0.485918	−	0.841634i
$438$		0			0
$439$	27.6736	+	15.9773i	1.32079	+	0.762557i	0.983854	−	0.178972i	$-0.0572772\pi$
$439$	27.6736	+	15.9773i	1.32079	+	0.762557i	0.336933	+	0.941529i	$0.390611\pi$
$440$	−13.3208			−0.635046
$441$		0			0
$442$	2.55255			0.121412
$443$	−21.4748	−	12.3985i	−1.02030	−	0.589068i	−0.106107	−	0.994355i	$-0.533838\pi$
$443$	−21.4748	−	12.3985i	−1.02030	−	0.589068i	−0.914190	+	0.405286i	$0.867172\pi$
$444$		0			0
$445$	−9.49496	−	16.4458i	−0.450104	−	0.779603i
$446$	2.98724	+	5.17406i	0.141450	+	0.244999i
$447$		0			0
$448$		0			0
$449$		−	13.7710i		−	0.649892i	−0.945733	−	0.324946i	$-0.894654\pi$
$449$		−	13.7710i		−	0.649892i	0.945733	−	0.324946i	$-0.105346\pi$
$450$		0			0
$451$			18.4740i			0.869906i
$452$	−6.12715	−	3.53751i	−0.288197	−	0.166390i
$453$		0			0
$454$	−23.7439	+	13.7085i	−1.11436	+	0.643374i
$455$		0			0
$456$		0			0
$457$	−13.6554	+	23.6518i	−0.638771	+	1.10638i	0.346931	+	0.937890i	$0.387224\pi$
$457$	−13.6554	+	23.6518i	−0.638771	+	1.10638i	−0.985703	+	0.168494i	$0.946110\pi$
$458$	−6.31340			−0.295006
$459$		0			0
$460$		−	29.5233i		−	1.37653i
$461$	5.51822	−	9.55784i	0.257009	−	0.445153i	−0.708430	−	0.705781i	$-0.750596\pi$
$461$	5.51822	−	9.55784i	0.257009	−	0.445153i	0.965439	+	0.260628i	$0.0839296\pi$
$462$		0			0
$463$	−12.2346	−	21.1910i	−0.568591	−	0.984829i	−0.996706	−	0.0811042i	$-0.974155\pi$
$463$	−12.2346	−	21.1910i	−0.568591	−	0.984829i	0.428115	−	0.903724i	$-0.359178\pi$
$464$	−12.8935	+	7.44405i	−0.598564	+	0.345581i
$465$		0			0
$466$	4.56029	−	7.89866i	0.211251	−	0.365898i
$467$	−15.9048			−0.735988			−0.367994	−	0.929828i	$-0.619955\pi$
$467$	−15.9048			−0.735988			−0.367994	+	0.929828i	$0.619955\pi$
$468$		0			0
$469$		0			0
$470$	8.69451	+	5.01978i	0.401048	+	0.231545i
$471$		0			0
$472$	5.99943	−	3.46377i	0.276146	−	0.159433i
$473$	−46.2169	+	26.6834i	−2.12506	+	1.22690i
$474$		0			0
$475$	−2.85063	−	1.64581i	−0.130796	−	0.0755151i
$476$		0			0
$477$		0			0
$478$	29.4042			1.34492
$479$	6.92685	−	11.9976i	0.316496	−	0.548187i	−0.663259	−	0.748390i	$-0.730827\pi$
$479$	6.92685	−	11.9976i	0.316496	−	0.548187i	0.979754	+	0.200204i	$0.0641604\pi$
$480$		0			0
$481$	0.544315	−	0.314261i	0.0248186	−	0.0143290i
$482$	0.718964	+	1.24528i	0.0327479	+	0.0567210i
$483$		0			0
$484$	−15.2781	+	26.4624i	−0.694458	+	1.20284i
$485$			9.33582i			0.423918i
$486$		0			0
$487$	28.7987			1.30499			0.652496	−	0.757792i	$-0.273722\pi$
$487$	28.7987			1.30499			0.652496	+	0.757792i	$0.273722\pi$
$488$	4.05411	−	7.02193i	0.183521	−	0.317868i
$489$		0			0
$490$		0			0
$491$	33.5627	−	19.3774i	1.51466	−	0.874492i	0.514812	−	0.857303i	$-0.327862\pi$
$491$	33.5627	−	19.3774i	1.51466	−	0.874492i	0.999852	−	0.0171884i	$-0.00547151\pi$
$492$		0			0
$493$	−8.34181	−	4.81615i	−0.375696	−	0.216908i
$494$			2.13496i			0.0960562i
$495$		0			0
$496$		−	49.7911i		−	2.23569i
$497$		0			0
$498$		0			0
$499$	1.73333	+	3.00222i	0.0775946	+	0.134398i	0.902212	−	0.431294i	$-0.141943\pi$
$499$	1.73333	+	3.00222i	0.0775946	+	0.134398i	−0.824617	+	0.565691i	$0.808609\pi$
$500$	6.96045	+	12.0558i	0.311281	+	0.539154i
$501$		0			0
$502$	1.85395	+	1.07038i	0.0827458	+	0.0477733i
$503$	28.2202			1.25828			0.629138	−	0.777293i	$-0.283408\pi$
$503$	28.2202			1.25828			0.629138	+	0.777293i	$0.283408\pi$
$504$		0			0
$505$	−18.8794			−0.840124
$506$	71.6552	+	41.3701i	3.18546	+	1.83913i
$507$		0			0
$508$	5.50326	+	9.53193i	0.244168	+	0.422911i
$509$	−17.9062	−	31.0144i	−0.793678	−	1.37469i	−0.923675	−	0.383176i	$-0.874830\pi$
$509$	−17.9062	−	31.0144i	−0.793678	−	1.37469i	0.129997	−	0.991514i	$-0.458503\pi$
$510$		0			0
$511$		0			0
$512$			24.2599i			1.07215i
$513$		0			0
$514$		−	54.1682i		−	2.38926i
$515$	31.0823	+	17.9454i	1.36965	+	0.790768i
$516$		0			0
$517$	−10.4147	+	6.01291i	−0.458036	+	0.264447i
$518$		0			0
$519$		0			0
$520$	0.526897	−	0.912612i	0.0231060	−	0.0400207i
$521$	26.9216			1.17946			0.589729	−	0.807601i	$-0.299234\pi$
$521$	26.9216			1.17946			0.589729	+	0.807601i	$0.299234\pi$
$522$		0			0
$523$			9.03185i			0.394935i	0.980309	+	0.197468i	$0.0632717\pi$
$523$			9.03185i			0.394935i	−0.980309	+	0.197468i	$0.936728\pi$
$524$	−5.86943	+	10.1662i	−0.256407	+	0.444110i
$525$		0			0
$526$	12.8020	+	22.1737i	0.558193	+	0.966819i
$527$	27.8980	−	16.1069i	1.21526	−	0.701629i
$528$		0			0
$529$	19.6426	−	34.0220i	0.854026	−	1.47922i
$530$	22.7321			0.987420
$531$		0			0
$532$		0			0
$533$	−1.26565	−	0.730726i	−0.0548216	−	0.0316513i
$534$		0			0
$535$	−29.2664	+	16.8969i	−1.26530	+	0.730518i
$536$	−1.53384	+	0.885563i	−0.0662518	+	0.0382505i
$537$		0			0
$538$	16.9615	+	9.79273i	0.731262	+	0.422195i
$539$		0			0
$540$		0			0
$541$	11.3358			0.487366			0.243683	−	0.969855i	$-0.421644\pi$
$541$	11.3358			0.487366			0.243683	+	0.969855i	$0.421644\pi$
$542$	6.11710	−	10.5951i	0.262752	−	0.455100i
$543$		0			0
$544$	−18.6447	+	10.7646i	−0.799387	+	0.461526i
$545$	−1.15100	−	1.99360i	−0.0493035	−	0.0853962i
$546$		0			0
$547$	19.4246	−	33.6444i	0.830537	−	1.43853i	−0.0670762	−	0.997748i	$-0.521367\pi$
$547$	19.4246	−	33.6444i	0.830537	−	1.43853i	0.897613	−	0.440784i	$-0.145300\pi$
$548$			17.2729i			0.737861i
$549$		0			0
$550$	13.4058			0.571627
$551$	4.02823	−	6.97711i	0.171609	−	0.297235i
$552$		0			0
$553$		0			0
$554$	36.3061	−	20.9613i	1.54250	−	0.890562i
$555$		0			0
$556$	25.3410	+	14.6306i	1.07470	+	0.620478i
$557$		−	7.26499i		−	0.307827i	−0.988084	−	0.153914i	$-0.950812\pi$
$557$		−	7.26499i		−	0.307827i	0.988084	−	0.153914i	$-0.0491878\pi$
$558$		0			0
$559$		−	4.22177i		−	0.178562i
$560$		0			0
$561$		0			0
$562$	20.8848	+	36.1736i	0.880973	+	1.52589i
$563$	11.5409	+	19.9894i	0.486390	+	0.842453i	0.999878	−	0.0156446i	$-0.00498004\pi$
$563$	11.5409	+	19.9894i	0.486390	+	0.842453i	−0.513487	+	0.858097i	$0.671647\pi$
$564$		0			0
$565$	−10.2838	−	5.93738i	−0.432644	−	0.249787i
$566$	−35.4561			−1.49033
$567$		0			0
$568$	−2.79889			−0.117439
$569$	15.5482	+	8.97677i	0.651815	+	0.376326i	0.789151	−	0.614199i	$-0.210521\pi$
$569$	15.5482	+	8.97677i	0.651815	+	0.376326i	−0.137336	+	0.990525i	$0.543854\pi$
$570$		0			0
$571$	7.04234	+	12.1977i	0.294713	+	0.510457i	0.974918	−	0.222564i	$-0.0714427\pi$
$571$	7.04234	+	12.1977i	0.294713	+	0.510457i	−0.680205	+	0.733022i	$0.738109\pi$
$572$	−1.85819	−	3.21849i	−0.0776950	−	0.134572i
$573$		0			0
$574$		0			0
$575$		−	10.0916i		−	0.420851i
$576$		0			0
$577$		−	30.0675i		−	1.25172i	−0.779934	−	0.625862i	$-0.784747\pi$
$577$		−	30.0675i		−	1.25172i	0.779934	−	0.625862i	$-0.215253\pi$
$578$	12.1841	+	7.03447i	0.506790	+	0.292595i
$579$		0			0
$580$	10.1393	−	5.85392i	0.421011	−	0.243071i
$581$		0			0
$582$		0			0
$583$	−13.6148	+	23.5815i	−0.563866	+	0.976644i
$584$	−8.07379			−0.334096
$585$		0			0
$586$		−	16.4891i		−	0.681158i
$587$	−18.0979	+	31.3465i	−0.746981	+	1.29381i	0.202283	+	0.979327i	$0.435164\pi$
$587$	−18.0979	+	31.3465i	−0.746981	+	1.29381i	−0.949264	+	0.314481i	$0.898169\pi$
$588$		0			0
$589$	13.4719	+	23.3339i	0.555098	+	0.961459i
$590$	−29.6464	+	17.1164i	−1.22052	+	0.704670i
$591$		0			0
$592$	−3.36877	+	5.83489i	−0.138456	+	0.239812i
$593$	2.04317			0.0839028			0.0419514	−	0.999120i	$-0.486643\pi$
$593$	2.04317			0.0839028			0.0419514	+	0.999120i	$0.486643\pi$
$594$		0			0
$595$		0			0
$596$	20.3507	+	11.7495i	0.833598	+	0.481278i
$597$		0			0
$598$	−5.66854	+	3.27273i	−0.231804	+	0.133832i
$599$	15.7873	−	9.11478i	0.645050	−	0.372420i	−0.141507	−	0.989937i	$-0.545195\pi$
$599$	15.7873	−	9.11478i	0.645050	−	0.372420i	0.786557	+	0.617517i	$0.211861\pi$
$600$		0			0
$601$	−32.1713	−	18.5741i	−1.31230	−	0.757654i	−0.329820	−	0.944044i	$-0.606988\pi$
$601$	−32.1713	−	18.5741i	−1.31230	−	0.757654i	−0.982476	+	0.186390i	$0.940321\pi$
$602$		0			0
$603$		0			0
$604$	2.96003			0.120442
$605$	−25.6428	+	44.4146i	−1.04253	+	1.80571i
$606$		0			0
$607$	17.1730	−	9.91482i	0.697030	−	0.402430i	−0.109211	−	0.994019i	$-0.534832\pi$
$607$	17.1730	−	9.91482i	0.697030	−	0.402430i	0.806240	+	0.591588i	$0.201499\pi$
$608$	−9.00349	−	15.5945i	−0.365140	−	0.632440i
$609$		0			0
$610$	−20.0336	+	34.6991i	−0.811135	+	1.40493i
$611$		−	0.951346i		−	0.0384873i
$612$		0			0
$613$	−12.6882			−0.512473			−0.256237	−	0.966614i	$-0.582483\pi$
$613$	−12.6882			−0.512473			−0.256237	+	0.966614i	$0.582483\pi$
$614$	−26.8690	+	46.5385i	−1.08435	+	1.87814i
$615$		0			0
$616$		0			0
$617$	−4.37247	+	2.52445i	−0.176029	+	0.101630i	−0.585426	−	0.810726i	$-0.699073\pi$
$617$	−4.37247	+	2.52445i	−0.176029	+	0.101630i	0.409397	+	0.912357i	$0.365739\pi$
$618$		0			0
$619$	0.231999	+	0.133945i	0.00932485	+	0.00538370i	0.504655	−	0.863321i	$-0.331620\pi$
$619$	0.231999	+	0.133945i	0.00932485	+	0.00538370i	−0.495330	+	0.868705i	$0.664953\pi$
$620$			39.1552i			1.57251i
$621$		0			0
$622$			24.8305i			0.995611i
$623$		0			0
$624$		0			0
$625$	14.8792	+	25.7716i	0.595169	+	1.03086i
$626$	29.4820	+	51.0644i	1.17834	+	2.04094i
$627$		0			0
$628$	−10.8504	−	6.26449i	−0.432979	−	0.249981i
$629$	−4.35905			−0.173807
$630$		0			0
$631$	37.7899			1.50439			0.752197	−	0.658938i	$-0.228994\pi$
$631$	37.7899			1.50439			0.752197	+	0.658938i	$0.228994\pi$
$632$	0.471310	+	0.272111i	0.0187477	+	0.0108240i
$633$		0			0
$634$	18.7556	+	32.4856i	0.744880	+	1.29017i
$635$	9.23671	+	15.9984i	0.366547	+	0.634879i
$636$		0			0
$637$		0			0
$638$			32.8117i			1.29903i
$639$		0			0
$640$			18.3867i			0.726799i
$641$	−29.7991	−	17.2045i	−1.17699	−	0.679537i	−0.221676	−	0.975120i	$-0.571153\pi$
$641$	−29.7991	−	17.2045i	−1.17699	−	0.679537i	−0.955317	+	0.295583i	$0.904486\pi$
$642$		0			0
$643$	0.676278	−	0.390449i	0.0266698	−	0.0153978i	−0.486606	−	0.873622i	$-0.661765\pi$
$643$	0.676278	−	0.390449i	0.0266698	−	0.0153978i	0.513276	+	0.858224i	$0.328432\pi$
$644$		0			0
$645$		0			0
$646$	7.40341	−	12.8231i	0.291283	−	0.504517i
$647$	19.6436			0.772271			0.386136	−	0.922442i	$-0.373810\pi$
$647$	19.6436			0.772271			0.386136	+	0.922442i	$0.373810\pi$
$648$		0			0
$649$		−	41.0055i		−	1.60961i
$650$	−0.530259	+	0.918435i	−0.0207985	+	0.0360240i
$651$		0			0
$652$	−0.801781	−	1.38872i	−0.0314001	−	0.0543867i
$653$	−2.77600	+	1.60272i	−0.108633	+	0.0627194i	−0.553332	−	0.832961i	$-0.686644\pi$
$653$	−2.77600	+	1.60272i	−0.108633	+	0.0627194i	0.444699	+	0.895680i	$0.353311\pi$
$654$		0			0
$655$	−9.85129	+	17.0629i	−0.384922	+	0.666704i
$656$	15.6663			0.611666
$657$		0			0
$658$		0			0
$659$	24.2959	+	14.0273i	0.946435	+	0.546425i	0.891972	−	0.452091i	$-0.149322\pi$
$659$	24.2959	+	14.0273i	0.946435	+	0.546425i	0.0544636	+	0.998516i	$0.482655\pi$
$660$		0			0
$661$	28.0490	−	16.1941i	1.09098	−	0.629878i	0.157143	−	0.987576i	$-0.449772\pi$
$661$	28.0490	−	16.1941i	1.09098	−	0.629878i	0.933837	+	0.357698i	$0.116438\pi$
$662$	2.01981	−	1.16614i	0.0785020	−	0.0453232i
$663$		0			0
$664$	6.95189	+	4.01367i	0.269785	+	0.155761i
$665$		0			0
$666$		0			0
$667$	24.7000			0.956386
$668$	5.96768	−	10.3363i	0.230897	−	0.399925i
$669$		0			0
$670$	7.57953	−	4.37605i	0.292823	−	0.169061i
$671$	−23.9971	−	41.5641i	−0.926397	−	1.60457i
$672$		0			0
$673$	−10.3088	+	17.8554i	−0.397375	+	0.688273i	−0.993401	−	0.114692i	$-0.963412\pi$
$673$	−10.3088	+	17.8554i	−0.397375	+	0.688273i	0.596026	+	0.802965i	$0.296745\pi$
$674$		−	24.6231i		−	0.948445i
$675$		0			0
$676$	−19.1140			−0.735155
$677$	25.1655	−	43.5880i	0.967190	−	1.67522i	0.263578	−	0.964638i	$-0.415097\pi$
$677$	25.1655	−	43.5880i	0.967190	−	1.67522i	0.703612	−	0.710585i	$-0.251569\pi$
$678$		0			0
$679$		0			0
$680$	−6.32935	+	3.65425i	−0.242719	+	0.140134i
$681$		0			0
$682$	−95.0324	−	54.8670i	−3.63898	−	2.10097i
$683$			13.7445i			0.525920i	0.964807	+	0.262960i	$0.0846987\pi$
$683$			13.7445i			0.525920i	−0.964807	+	0.262960i	$0.915301\pi$
$684$		0			0
$685$			28.9909i			1.10769i
$686$		0			0
$687$		0			0
$688$	22.6280	+	39.1929i	0.862685	+	1.49421i
$689$	−1.07705	−	1.86550i	−0.0410321	−	0.0710698i
$690$		0			0
$691$	25.4328	+	14.6837i	0.967511	+	0.558593i	0.898476	−	0.439022i	$-0.144675\pi$
$691$	25.4328	+	14.6837i	0.967511	+	0.558593i	0.0690343	+	0.997614i	$0.478008\pi$
$692$	−1.49813			−0.0569504
$693$		0			0
$694$	−50.5874			−1.92027
$695$	42.5325	+	24.5562i	1.61335	+	0.931468i
$696$		0			0
$697$	5.06789	+	8.77784i	0.191960	+	0.332484i
$698$	−32.7392	−	56.7060i	−1.23920	−	2.14635i
$699$		0			0
$700$		0			0
$701$		−	44.2011i		−	1.66945i	−0.550666	−	0.834726i	$-0.685626\pi$
$701$		−	44.2011i		−	1.66945i	0.550666	−	0.834726i	$-0.314374\pi$
$702$		0			0
$703$		−	3.64592i		−	0.137508i
$704$	17.2923	+	9.98371i	0.651728	+	0.376275i
$705$		0			0
$706$	4.08702	−	2.35964i	0.153817	−	0.0888063i
$707$		0			0
$708$		0			0
$709$	5.66629	−	9.81430i	0.212802	−	0.368584i	−0.739788	−	0.672840i	$-0.765074\pi$
$709$	5.66629	−	9.81430i	0.212802	−	0.368584i	0.952590	+	0.304256i	$0.0984077\pi$
$710$	13.8308			0.519062
$711$		0			0
$712$		−	7.18216i		−	0.269163i
$713$	−41.3028	+	71.5385i	−1.54680	+	2.67914i
$714$		0			0
$715$	−3.11881	−	5.40193i	−0.116637	−	0.202021i
$716$	1.90755	−	1.10132i	0.0712884	−	0.0411584i
$717$		0			0
$718$	6.79136	−	11.7630i	0.253451	−	0.438991i
$719$	36.1294			1.34740			0.673700	−	0.739005i	$-0.264704\pi$
$719$	36.1294			1.34740			0.673700	+	0.739005i	$0.264704\pi$
$720$		0			0
$721$		0			0
$722$	−20.0271	−	11.5627i	−0.745333	−	0.430318i
$723$		0			0
$724$	19.4505	−	11.2298i	0.722874	−	0.417351i
$725$	3.46580	−	2.00098i	0.128717	−	0.0743146i
$726$		0			0
$727$	−6.20547	−	3.58273i	−0.230148	−	0.132876i	0.380492	−	0.924784i	$-0.375755\pi$
$727$	−6.20547	−	3.58273i	−0.230148	−	0.132876i	−0.610640	+	0.791908i	$0.709088\pi$
$728$		0			0
$729$		0			0
$730$	39.8970			1.47665
$731$	−14.6399	+	25.3570i	−0.541475	+	0.937862i
$732$		0			0
$733$	41.4391	−	23.9249i	1.53059	−	0.883685i	0.531253	−	0.847213i	$-0.321721\pi$
$733$	41.4391	−	23.9249i	1.53059	−	0.883685i	0.999335	−	0.0364726i	$-0.0116122\pi$
$734$	12.5938	+	21.8131i	0.464846	+	0.805136i
$735$		0			0
$736$	27.6034	−	47.8105i	1.01747	−	1.76232i
$737$			10.4836i			0.386170i
$738$		0			0
$739$	15.3483			0.564597			0.282299	−	0.959327i	$-0.408903\pi$
$739$	15.3483			0.564597			0.282299	+	0.959327i	$0.408903\pi$
$740$	2.64917	−	4.58849i	0.0973853	−	0.168676i
$741$		0			0
$742$		0			0
$743$	−34.9422	+	20.1739i	−1.28191	+	0.740109i	−0.977197	−	0.212337i	$-0.931893\pi$
$743$	−34.9422	+	20.1739i	−1.28191	+	0.740109i	−0.304709	+	0.952445i	$0.598559\pi$
$744$		0			0
$745$	34.1568	+	19.7204i	1.25141	+	0.722501i
$746$			44.4132i			1.62608i
$747$		0			0
$748$			25.7747i			0.942417i
$749$		0			0
$750$		0			0
$751$	−16.9449	−	29.3494i	−0.618327	−	1.07097i	−0.989791	−	0.142527i	$-0.954477\pi$
$751$	−16.9449	−	29.3494i	−0.618327	−	1.07097i	0.371463	−	0.928448i	$-0.378856\pi$
$752$	5.09906	+	8.83183i	0.185944	+	0.322064i
$753$		0			0
$754$	−2.24793	−	1.29784i	−0.0818647	−	0.0472646i
$755$	4.96814			0.180809
$756$		0			0
$757$	−5.73237			−0.208346			−0.104173	−	0.994559i	$-0.533220\pi$
$757$	−5.73237			−0.208346			−0.104173	+	0.994559i	$0.533220\pi$
$758$	−34.3589	−	19.8371i	−1.24797	−	0.720517i
$759$		0			0
$760$	−3.05642	−	5.29387i	−0.110868	−	0.192029i
$761$	−13.2666	−	22.9784i	−0.480914	−	0.832968i	0.518846	−	0.854868i	$-0.326362\pi$
$761$	−13.2666	−	22.9784i	−0.480914	−	0.832968i	−0.999760	+	0.0218999i	$0.993028\pi$
$762$		0			0
$763$		0			0
$764$		−	19.7420i		−	0.714242i
$765$		0			0
$766$			24.2188i			0.875061i
$767$	2.80929	+	1.62194i	0.101438	+	0.0585650i
$768$		0			0
$769$	23.3944	−	13.5068i	0.843623	−	0.487066i	−0.0148711	−	0.999889i	$-0.504734\pi$
$769$	23.3944	−	13.5068i	0.843623	−	0.487066i	0.858494	+	0.512823i	$0.171400\pi$
$770$		0			0
$771$		0			0
$772$	−1.16128	+	2.01139i	−0.0417953	+	0.0723916i
$773$	22.6017			0.812927			0.406464	−	0.913667i	$-0.366762\pi$
$773$	22.6017			0.812927			0.406464	+	0.913667i	$0.366762\pi$
$774$		0			0
$775$			13.3840i			0.480768i
$776$	−1.76545	+	3.05784i	−0.0633758	+	0.109770i
$777$		0			0
$778$	10.2296	+	17.7182i	0.366750	+	0.635229i
$779$	−7.34180	+	4.23879i	−0.263047	+	0.151870i
$780$		0			0
$781$	−8.28359	+	14.3476i	−0.296410	+	0.513398i
$782$	45.3955			1.62334
$783$		0			0
$784$		0			0
$785$	−18.2114	−	10.5144i	−0.649993	−	0.375274i
$786$		0			0
$787$	22.6864	−	13.0980i	0.808683	−	0.466893i	−0.0378153	−	0.999285i	$-0.512040\pi$
$787$	22.6864	−	13.0980i	0.808683	−	0.466893i	0.846498	+	0.532391i	$0.178707\pi$
$788$	−6.41523	+	3.70383i	−0.228533	+	0.131944i
$789$		0			0
$790$	−2.32900	−	1.34465i	−0.0828620	−	0.0478404i
$791$		0			0
$792$		0			0
$793$	3.79675			0.134827
$794$	27.9314	−	48.3785i	0.991247	−	1.71689i
$795$		0			0
$796$	−14.4705	+	8.35456i	−0.512894	+	0.296120i
$797$	5.96560	+	10.3327i	0.211312	+	0.366004i	0.952126	−	0.305707i	$-0.0988929\pi$
$797$	5.96560	+	10.3327i	0.211312	+	0.366004i	−0.740813	+	0.671711i	$0.765560\pi$
$798$		0			0
$799$	−3.29899	+	5.71402i	−0.116710	+	0.202147i
$800$		−	8.94478i		−	0.316246i
$801$		0			0
$802$	35.8740			1.26676
$803$	−23.8952	+	41.3877i	−0.843242	+	1.46054i
$804$		0			0
$805$		0			0
$806$	7.51788	−	4.34045i	0.264806	−	0.152886i
$807$		0			0
$808$	−6.18375	−	3.57019i	−0.217543	−	0.125599i
$809$			26.4887i			0.931292i	0.884971	+	0.465646i	$0.154178\pi$
$809$			26.4887i			0.931292i	−0.884971	+	0.465646i	$0.845822\pi$
$810$		0			0
$811$		−	13.7419i		−	0.482544i	−0.970458	−	0.241272i	$-0.922435\pi$
$811$		−	13.7419i		−	0.482544i	0.970458	−	0.241272i	$-0.0775646\pi$
$812$		0			0
$813$		0			0
$814$	7.42439	+	12.8594i	0.260225	+	0.450722i
$815$	−1.34571	−	2.33084i	−0.0471383	−	0.0816459i
$816$		0			0
$817$	−21.2086	−	12.2448i	−0.741996	−	0.428391i
$818$	53.8949			1.88439
$819$		0			0
$820$	−12.3198			−0.430226
$821$	11.7493	+	6.78346i	0.410053	+	0.236744i	0.690813	−	0.723034i	$-0.257253\pi$
$821$	11.7493	+	6.78346i	0.410053	+	0.236744i	−0.280759	+	0.959778i	$0.590586\pi$
$822$		0			0
$823$	−7.34857	−	12.7281i	−0.256155	−	0.443674i	0.709053	−	0.705155i	$-0.249122\pi$
$823$	−7.34857	−	12.7281i	−0.256155	−	0.443674i	−0.965209	+	0.261481i	$0.915789\pi$
$824$	6.78711	+	11.7556i	0.236440	+	0.409527i
$825$		0			0
$826$		0			0
$827$		−	40.8787i		−	1.42149i	−0.703449	−	0.710746i	$-0.748358\pi$
$827$		−	40.8787i		−	1.42149i	0.703449	−	0.710746i	$-0.251642\pi$
$828$		0			0
$829$			20.4600i			0.710605i	0.934751	+	0.355302i	$0.115622\pi$
$829$			20.4600i			0.710605i	−0.934751	+	0.355302i	$0.884378\pi$
$830$	−34.3530	−	19.8337i	−1.19241	−	0.688439i
$831$		0			0
$832$	−1.36797	+	0.789798i	−0.0474258	+	0.0273813i
$833$		0			0
$834$		0			0
$835$	10.0162	−	17.3486i	0.346625	−	0.600372i
$836$	−21.5580			−0.745599
$837$		0			0
$838$			18.9282i			0.653865i
$839$	27.3475	−	47.3673i	0.944141	−	1.63530i	0.186680	−	0.982421i	$-0.440227\pi$
$839$	27.3475	−	47.3673i	0.944141	−	1.63530i	0.757462	−	0.652880i	$-0.226439\pi$
$840$		0			0
$841$	−9.60247	−	16.6320i	−0.331120	−	0.573516i
$842$	−41.1416	+	23.7531i	−1.41783	+	0.818586i
$843$		0			0
$844$	−11.4661	+	19.8598i	−0.394678	+	0.683602i
$845$	−32.0811			−1.10362
$846$		0			0
$847$		0			0
$848$	19.9975	+	11.5456i	0.686718	+	0.396477i
$849$		0			0
$850$	6.36973	−	3.67756i	0.218480	−	0.126139i
$851$	9.68031	−	5.58893i	0.331837	−	0.191586i
$852$		0			0
$853$	−11.0684	−	6.39037i	−0.378976	−	0.218802i	0.298396	−	0.954442i	$-0.403548\pi$
$853$	−11.0684	−	6.39037i	−0.378976	−	0.218802i	−0.677373	+	0.735640i	$0.736882\pi$
$854$		0			0
$855$		0			0
$856$	−12.7812			−0.436851
$857$	9.16200	−	15.8691i	0.312968	−	0.542077i	−0.666035	−	0.745920i	$-0.732010\pi$
$857$	9.16200	−	15.8691i	0.312968	−	0.542077i	0.979003	+	0.203844i	$0.0653434\pi$
$858$		0			0
$859$	−33.4579	+	19.3169i	−1.14157	+	0.659085i	−0.946819	−	0.321768i	$-0.895723\pi$
$859$	−33.4579	+	19.3169i	−1.14157	+	0.659085i	−0.194750	+	0.980853i	$0.562390\pi$
$860$	−17.7944	−	30.8208i	−0.606784	−	1.05098i
$861$		0			0
$862$	−10.1328	+	17.5505i	−0.345125	+	0.597774i
$863$			16.7000i			0.568475i	0.958754	+	0.284238i	$0.0917405\pi$
$863$			16.7000i			0.568475i	−0.958754	+	0.284238i	$0.908260\pi$
$864$		0			0
$865$	−2.51447			−0.0854947
$866$	12.1966	−	21.1251i	0.414456	−	0.717859i
$867$		0			0
$868$		0			0
$869$	2.78978	−	1.61068i	0.0946367	−	0.0546385i
$870$		0			0
$871$	−0.718235	−	0.414673i	−0.0243365	−	0.0140507i
$872$		−	0.870640i		−	0.0294836i
$873$		0			0
$874$			37.9689i			1.28432i
$875$		0			0
$876$		0			0
$877$	−16.7617	−	29.0321i	−0.566002	−	0.980345i	−0.996956	−	0.0779707i	$-0.975156\pi$
$877$	−16.7617	−	29.0321i	−0.566002	−	0.980345i	0.430953	−	0.902374i	$-0.358177\pi$
$878$	−29.8606	−	51.7201i	−1.00775	−	1.74547i
$879$		0			0
$880$	57.9070	+	33.4326i	1.95204	+	1.12701i
$881$	−28.6657			−0.965771			−0.482885	−	0.875684i	$-0.660411\pi$
$881$	−28.6657			−0.965771			−0.482885	+	0.875684i	$0.660411\pi$
$882$		0			0
$883$	−38.2091			−1.28584			−0.642919	−	0.765935i	$-0.722277\pi$
$883$	−38.2091			−1.28584			−0.642919	+	0.765935i	$0.722277\pi$
$884$	−1.76583	−	1.01950i	−0.0593912	−	0.0342895i
$885$		0			0
$886$	23.1719	+	40.1350i	0.778476	+	1.34836i
$887$	17.5914	+	30.4692i	0.590662	+	1.02306i	0.994143	+	0.108069i	$0.0344666\pi$
$887$	17.5914	+	30.4692i	0.590662	+	1.02306i	−0.403481	+	0.914988i	$0.632200\pi$
$888$		0			0
$889$		0			0
$890$			35.4910i			1.18966i
$891$		0			0
$892$		−	4.77248i		−	0.159794i
$893$	−4.77921	−	2.75928i	−0.159930	−	0.0923358i
$894$		0			0
$895$	3.20164	−	1.84847i	0.107019	−	0.0617875i
$896$		0			0
$897$		0			0
$898$	−12.8685	+	22.2890i	−0.429429	+	0.743792i
$899$	−32.7582			−1.09255
$900$		0			0
$901$			14.9395i			0.497707i
$902$	17.2634	−	29.9010i	0.574807	−	0.995595i
$903$		0			0
$904$	−2.24557	−	3.88944i	−0.0746866	−	0.129361i
$905$	32.6459	−	18.8481i	1.08519	−	0.626533i
$906$		0			0
$907$	21.2977	−	36.8887i	0.707179	−	1.22487i	−0.258720	−	0.965952i	$-0.583301\pi$
$907$	21.2977	−	36.8887i	0.707179	−	1.22487i	0.965899	−	0.258918i	$-0.0833660\pi$
$908$	21.9010			0.726811
$909$		0			0
$910$		0			0
$911$	43.5221	+	25.1275i	1.44195	+	0.832510i	0.997980	−	0.0635313i	$-0.0202363\pi$
$911$	43.5221	+	25.1275i	1.44195	+	0.832510i	0.443970	+	0.896042i	$0.353570\pi$
$912$		0			0
$913$	41.1496	−	23.7577i	1.36185	−	0.786265i
$914$	44.2037	−	25.5210i	1.46213	−	0.844160i
$915$		0			0
$916$	4.36754	+	2.52160i	0.144308	+	0.0833161i
$917$		0			0
$918$		0			0
$919$	−58.6972			−1.93624			−0.968121	−	0.250481i	$-0.919411\pi$
$919$	−58.6972			−1.93624			−0.968121	+	0.250481i	$0.919411\pi$
$920$	9.37054	−	16.2303i	0.308938	−	0.535096i
$921$		0			0
$922$	−17.8630	+	10.3132i	−0.588287	+	0.339647i
$923$	−0.655304	−	1.13502i	−0.0215696	−	0.0373596i
$924$		0			0
$925$	0.905536	−	1.56843i	0.0297738	−	0.0515698i
$926$			45.7315i			1.50283i
$927$		0			0
$928$	21.8929			0.718670
$929$	−7.19115	+	12.4554i	−0.235934	+	0.408650i	−0.959544	−	0.281560i	$-0.909148\pi$
$929$	−7.19115	+	12.4554i	−0.235934	+	0.408650i	0.723610	+	0.690209i	$0.242482\pi$
$930$		0			0
$931$		0			0
$932$	−6.30952	+	3.64281i	−0.206675	+	0.119324i
$933$		0			0
$934$	25.7427	+	14.8626i	0.842327	+	0.486318i
$935$			43.2604i			1.41477i
$936$		0			0
$937$			44.2981i			1.44716i	0.690243	+	0.723578i	$0.257504\pi$
$937$			44.2981i			1.44716i	−0.690243	+	0.723578i	$0.742496\pi$
$938$		0			0
$939$		0			0
$940$	−4.00985	−	6.94526i	−0.130787	−	0.226529i
$941$	−7.44400	−	12.8934i	−0.242667	−	0.420312i	0.718806	−	0.695211i	$-0.244689\pi$
$941$	−7.44400	−	12.8934i	−0.242667	−	0.420312i	−0.961473	+	0.274899i	$0.911356\pi$
$942$		0			0
$943$	−22.5089	−	12.9955i	−0.732990	−	0.423192i
$944$	−34.7734			−1.13178
$945$		0			0
$946$	99.7390			3.24280
$947$	−36.3343	−	20.9776i	−1.18071	−	0.681681i	−0.224528	−	0.974468i	$-0.572084\pi$
$947$	−36.3343	−	20.9776i	−1.18071	−	0.681681i	−0.956178	+	0.292787i	$0.905417\pi$
$948$		0			0
$949$	−1.89031	−	3.27412i	−0.0613622	−	0.106282i
$950$	3.07592	+	5.32765i	0.0997960	+	0.172852i
$951$		0			0
$952$		0			0
$953$			13.9821i			0.452926i	0.974020	+	0.226463i	$0.0727162\pi$
$953$			13.9821i			0.452926i	−0.974020	+	0.226463i	$0.927284\pi$
$954$		0			0
$955$		−	33.1352i		−	1.07223i
$956$	−20.3415	−	11.7442i	−0.657892	−	0.379834i
$957$		0			0
$958$	−22.4228	+	12.9458i	−0.724449	+	0.418261i
$959$		0			0
$960$		0			0
$961$	39.2776	−	68.0309i	1.26702	−	2.19454i
$962$	−1.17467			−0.0378728
$963$		0			0
$964$		−	1.14863i		−	0.0369949i
$965$	−1.94910	+	3.37593i	−0.0627436	+	0.108675i
$966$		0			0
$967$	−11.5757	−	20.0497i	−0.372249	−	0.644754i	0.617662	−	0.786443i	$-0.288080\pi$
$967$	−11.5757	−	20.0497i	−0.372249	−	0.644754i	−0.989911	+	0.141690i	$0.954746\pi$
$968$	−16.7980	+	9.69835i	−0.539909	+	0.311717i
$969$		0			0
$970$	8.72403	−	15.1105i	0.280112	−	0.485168i
$971$	−43.3737			−1.39193			−0.695965	−	0.718076i	$-0.745023\pi$
$971$	−43.3737			−1.39193			−0.695965	+	0.718076i	$0.745023\pi$
$972$		0			0
$973$		0			0
$974$	−46.6120	−	26.9114i	−1.49354	−	0.862298i
$975$		0			0
$976$	−35.2472	+	20.3500i	−1.12824	+	0.651387i
$977$	10.4210	−	6.01657i	0.333397	−	0.192487i	−0.323951	−	0.946074i	$-0.605011\pi$
$977$	10.4210	−	6.01657i	0.333397	−	0.192487i	0.657348	+	0.753587i	$0.271678\pi$
$978$		0			0
$979$	−36.8170	−	21.2563i	−1.17668	−	0.679355i
$980$		0			0
$981$		0			0
$982$	−72.4304			−2.31135
$983$	3.14829	−	5.45300i	0.100415	−	0.173924i	−0.811441	−	0.584435i	$-0.801316\pi$
$983$	3.14829	−	5.45300i	0.100415	−	0.173924i	0.911856	+	0.410511i	$0.134650\pi$
$984$		0			0
$985$	−10.7674	+	6.21654i	−0.343077	+	0.198075i
$986$	9.00108	+	15.5903i	0.286653	+	0.496497i
$987$		0			0
$988$	0.852712	−	1.47694i	0.0271284	−	0.0469877i
$989$		−	75.0816i		−	2.38745i
$990$		0			0
$991$	33.5627			1.06616			0.533078	−	0.846066i	$-0.321035\pi$
$991$	33.5627			1.06616			0.533078	+	0.846066i	$0.321035\pi$
$992$	−36.6089	+	63.4085i	−1.16233	+	2.01322i
$993$		0			0
$994$		0			0
$995$	−24.2874	+	14.0223i	−0.769963	+	0.444538i
$996$		0			0
$997$	9.74838	+	5.62823i	0.308734	+	0.178248i	0.646360	−	0.763033i	$-0.276290\pi$
$997$	9.74838	+	5.62823i	0.308734	+	0.178248i	−0.337626	+	0.941280i	$0.609624\pi$
$998$		−	6.47898i		−	0.205088i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.e.440.6		48
3.2	odd	2		441.2.o.e.146.19	✓	48
7.2	even	3		1323.2.i.d.521.7		48
7.3	odd	6		1323.2.s.d.656.20		48
7.4	even	3		1323.2.s.d.656.19		48
7.5	odd	6		1323.2.i.d.521.22		48
7.6	odd	2	inner	1323.2.o.e.440.5		48
9.4	even	3		441.2.o.e.293.20	yes	48
9.5	odd	6	inner	1323.2.o.e.881.5		48
21.2	odd	6		441.2.i.d.227.6		48
21.5	even	6		441.2.i.d.227.5		48
21.11	odd	6		441.2.s.d.362.5		48
21.17	even	6		441.2.s.d.362.6		48
21.20	even	2		441.2.o.e.146.20	yes	48
63.4	even	3		441.2.i.d.68.19		48
63.5	even	6		1323.2.s.d.962.19		48
63.13	odd	6		441.2.o.e.293.19	yes	48
63.23	odd	6		1323.2.s.d.962.20		48
63.31	odd	6		441.2.i.d.68.20		48
63.32	odd	6		1323.2.i.d.1097.22		48
63.40	odd	6		441.2.s.d.374.5		48
63.41	even	6	inner	1323.2.o.e.881.6		48
63.58	even	3		441.2.s.d.374.6		48
63.59	even	6		1323.2.i.d.1097.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.19		48	63.4	even	3
441.2.i.d.68.20		48	63.31	odd	6
441.2.i.d.227.5		48	21.5	even	6
441.2.i.d.227.6		48	21.2	odd	6
441.2.o.e.146.19	✓	48	3.2	odd	2
441.2.o.e.146.20	yes	48	21.20	even	2
441.2.o.e.293.19	yes	48	63.13	odd	6
441.2.o.e.293.20	yes	48	9.4	even	3
441.2.s.d.362.5		48	21.11	odd	6
441.2.s.d.362.6		48	21.17	even	6
441.2.s.d.374.5		48	63.40	odd	6
441.2.s.d.374.6		48	63.58	even	3
1323.2.i.d.521.7		48	7.2	even	3
1323.2.i.d.521.22		48	7.5	odd	6
1323.2.i.d.1097.7		48	63.59	even	6
1323.2.i.d.1097.22		48	63.32	odd	6
1323.2.o.e.440.5		48	7.6	odd	2	inner
1323.2.o.e.440.6		48	1.1	even	1	trivial
1323.2.o.e.881.5		48	9.5	odd	6	inner
1323.2.o.e.881.6		48	63.41	even	6	inner
1323.2.s.d.656.19		48	7.4	even	3
1323.2.s.d.656.20		48	7.3	odd	6
1323.2.s.d.962.19		48	63.5	even	6
1323.2.s.d.962.20		48	63.23	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61855 - 0.934468i) q^{2} +(0.746462 + 1.29291i) q^{4} +(1.25287 + 2.17003i) q^{5} +0.947692i q^{8} +O(q^{10})\)	\(q+(-1.61855 - 0.934468i) q^{2} +(0.746462 + 1.29291i) q^{4} +(1.25287 + 2.17003i) q^{5} +0.947692i q^{8} -4.68306i q^{10} +(4.85803 + 2.80479i) q^{11} +(-0.384312 + 0.221883i) q^{13} +(2.37851 - 4.11970i) q^{16} +3.07770 q^{17} +2.57419i q^{19} +(-1.87044 + 3.23969i) q^{20} +(-5.24197 - 9.07935i) q^{22} +(-6.83476 + 3.94605i) q^{23} +(-0.639351 + 1.10739i) q^{25} +0.829370 q^{26} +(-2.71041 - 1.56485i) q^{29} +(9.06457 - 5.23343i) q^{31} +(-6.05802 + 3.49760i) q^{32} +(-4.98140 - 2.87601i) q^{34} -1.41634 q^{37} +(2.40550 - 4.16645i) q^{38} +(-2.05652 + 1.18733i) q^{40} +(1.64665 + 2.85208i) q^{41} +(-4.75676 + 8.23894i) q^{43} +8.37467i q^{44} +14.7498 q^{46} +(-1.07190 + 1.85659i) q^{47} +(2.06964 - 1.19491i) q^{50} +(-0.573749 - 0.331254i) q^{52} +4.85412i q^{53} +14.0561i q^{55} +(2.92461 + 5.06558i) q^{58} +(-3.65496 - 6.33057i) q^{59} +(-7.40950 - 4.27788i) q^{61} -19.5619 q^{62} +3.55953 q^{64} +(-0.962984 - 0.555979i) q^{65} +(0.934442 + 1.61850i) q^{67} +(2.29739 + 3.97919i) q^{68} +2.95338i q^{71} +8.51943i q^{73} +(2.29241 + 1.32352i) q^{74} +(-3.32820 + 1.92154i) q^{76} +(0.287130 - 0.497324i) q^{79} +11.9198 q^{80} -6.15497i q^{82} +(4.23521 - 7.33560i) q^{83} +(3.85595 + 6.67870i) q^{85} +(15.3981 - 8.89008i) q^{86} +(-2.65807 + 4.60392i) q^{88} -7.57858 q^{89} +(-10.2038 - 5.89115i) q^{92} +(3.46984 - 2.00332i) q^{94} +(-5.58607 + 3.22512i) q^{95} +(3.22662 + 1.86289i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more