LMFDB - Embedded newform 1323.2.o.e.881.6

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			881.6
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.e.440.6

$q$-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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	−0.947537	−	0.319645i	$-0.896436\pi$
$2$	−1.61855	+	0.934468i	−1.14449	+	0.660769i	−0.196948	+	0.980414i	$0.563103\pi$
$3$		0			0
$3$		0			0
$4$	0.746462	−	1.29291i	0.373231	−	0.646455i
$5$	1.25287	−	2.17003i	0.560299	−	0.970467i	−0.437171	−	0.899378i	$-0.644020\pi$
$5$	1.25287	−	2.17003i	0.560299	−	0.970467i	0.997470	−	0.0710881i	$-0.0226472\pi$
$6$		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	0.465527	−	0.885034i	$-0.345865\pi$
$11$	4.85803	−	2.80479i	1.46475	−	0.845675i	0.999225	+	0.0393590i	$0.0125316\pi$
$12$		0			0
$13$	−0.384312	−	0.221883i	−0.106589	−	0.0615392i	0.445758	−	0.895154i	$-0.352934\pi$
$13$	−0.384312	−	0.221883i	−0.106589	−	0.0615392i	−0.552347	+	0.833614i	$0.686268\pi$
$14$		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	$-0.904587\pi$
$19$		−	2.57419i		−	0.590560i	0.955411	−	0.295280i	$-0.0954130\pi$
$20$	−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	−0.428413	−	0.903583i	$-0.640927\pi$
$23$	−6.83476	−	3.94605i	−1.42515	−	0.822808i	−0.996732	+	0.0807749i	$0.974261\pi$
$24$		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	−0.730079	−	0.683362i	$-0.760517\pi$
$29$	−2.71041	+	1.56485i	−0.503310	+	0.290586i	0.226770	+	0.973948i	$0.427184\pi$
$30$		0			0
$31$	9.06457	+	5.23343i	1.62805	+	0.939952i	0.984675	+	0.174397i	$0.0557975\pi$
$31$	9.06457	+	5.23343i	1.62805	+	0.939952i	0.643370	+	0.765556i	$0.277536\pi$
$32$	−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	−0.708318	−	0.705894i	$-0.750545\pi$
$41$	1.64665	−	2.85208i	0.257163	−	0.445420i	0.965481	+	0.260474i	$0.0838788\pi$
$42$		0			0
$43$	−4.75676	−	8.23894i	−0.725398	−	1.25643i	−0.958810	−	0.284049i	$-0.908322\pi$
$43$	−4.75676	−	8.23894i	−0.725398	−	1.25643i	0.233411	−	0.972378i	$-0.425011\pi$
$44$		−	8.37467i		−	1.26253i
$45$		0			0
$46$	14.7498			2.17474
$47$	−1.07190	−	1.85659i	−0.156353	−	0.270811i	0.777198	−	0.629256i	$-0.216640\pi$
$47$	−1.07190	−	1.85659i	−0.156353	−	0.270811i	−0.933551	+	0.358445i	$0.883307\pi$
$48$		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	$-0.891810\pi$
$53$		−	4.85412i		−	0.666764i	0.942792	−	0.333382i	$-0.108190\pi$
$54$		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	−0.999617	−	0.0276824i	$-0.991187\pi$
$59$	−3.65496	+	6.33057i	−0.475835	+	0.824170i	0.523782	+	0.851852i	$0.324521\pi$
$60$		0			0
$61$	−7.40950	+	4.27788i	−0.948690	+	0.547726i	−0.892674	−	0.450704i	$-0.851173\pi$
$61$	−7.40950	+	4.27788i	−0.948690	+	0.547726i	−0.0560160	+	0.998430i	$0.517840\pi$
$62$	−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	−0.803284	−	0.595597i	$-0.796916\pi$
$67$	0.934442	−	1.61850i	0.114160	−	0.197731i	0.917444	+	0.397865i	$0.130249\pi$
$68$	2.29739	−	3.97919i	0.278599	−	0.482548i
$69$		0			0
$70$		0			0
$71$		−	2.95338i		−	0.350501i	−0.984524	−	0.175251i	$-0.943926\pi$
$71$		−	2.95338i		−	0.350501i	0.984524	−	0.175251i	$-0.0560736\pi$
$72$		0			0
$73$		−	8.51943i		−	0.997124i	−0.866854	−	0.498562i	$-0.833862\pi$
$73$		−	8.51943i		−	0.997124i	0.866854	−	0.498562i	$-0.166138\pi$
$74$	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	0.881726	−	0.471762i	$-0.156382\pi$
$79$	0.287130	+	0.497324i	0.0323047	+	0.0559533i	−0.849421	+	0.527716i	$0.823049\pi$
$80$	11.9198			1.33268
$81$		0			0
$82$			6.15497i			0.679702i
$83$	4.23521	+	7.33560i	0.464875	+	0.805186i	0.999196	−	0.0400951i	$-0.0127661\pi$
$83$	4.23521	+	7.33560i	0.464875	+	0.805186i	−0.534321	+	0.845281i	$0.679433\pi$
$84$		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	−0.327167	−	0.944966i	$-0.606094\pi$
$97$	3.22662	−	1.86289i	0.327614	−	0.189148i	0.654781	+	0.755818i	$0.272761\pi$
$98$		0			0
$99$		0			0
$100$	−1.90901			−0.190901
$101$	−3.76725	−	6.52506i	−0.374855	−	0.649268i	0.615450	−	0.788176i	$-0.288974\pi$
$101$	−3.76725	−	6.52506i	−0.374855	−	0.649268i	−0.990305	+	0.138908i	$0.955641\pi$
$102$		0			0
$103$	12.4045	+	7.16173i	1.22225	+	0.705666i	0.965397	−	0.260784i	$-0.0839812\pi$
$103$	12.4045	+	7.16173i	1.22225	+	0.705666i	0.256853	+	0.966451i	$0.417315\pi$
$104$	−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	$-0.773972\pi$
$107$		−	13.4866i		−	1.30380i	0.758305	−	0.651900i	$-0.226028\pi$
$108$		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	0.294378	−	0.955689i	$-0.404887\pi$
$113$	−4.10412	−	2.36952i	−0.386083	−	0.222905i	−0.680462	+	0.732784i	$0.738221\pi$
$114$		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	−0.641583	−	0.767054i	$-0.721722\pi$
$131$	3.93150	−	6.80955i	0.343497	−	0.594953i	0.985079	+	0.172100i	$0.0550553\pi$
$132$		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	−0.00664016	−	0.999978i	$-0.502114\pi$
$137$	10.0198	−	5.78491i	0.856046	−	0.494238i	0.862686	+	0.505740i	$0.168780\pi$
$138$		0			0
$139$	16.9741	+	9.79999i	1.43972	+	0.831224i	0.997830	−	0.0658437i	$-0.0209739\pi$
$139$	16.9741	+	9.79999i	1.43972	+	0.831224i	0.441893	+	0.897068i	$0.354307\pi$
$140$		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	0.940565	−	0.339615i	$-0.110297\pi$
$149$	13.6315	+	7.87012i	1.11673	+	0.644746i	0.176167	+	0.984360i	$0.443630\pi$
$150$		0			0
$151$	0.991353	+	1.71707i	0.0806752	+	0.139734i	0.903540	−	0.428503i	$-0.140959\pi$
$151$	0.991353	+	1.71707i	0.0806752	+	0.139734i	−0.822865	+	0.568237i	$0.807626\pi$
$152$	−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	0.181108	−	0.983463i	$-0.442031\pi$
$157$	−7.26790	−	4.19612i	−0.580041	−	0.334887i	−0.761150	+	0.648576i	$0.775365\pi$
$158$	−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	−0.978214	−	0.207599i	$-0.933435\pi$
$167$	−3.99731	+	6.92354i	−0.309321	+	0.535760i	0.668893	+	0.743359i	$0.266768\pi$
$168$		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	0.846322	−	0.532672i	$-0.178812\pi$
$173$	−0.501744	−	0.869046i	−0.0381469	−	0.0660723i	−0.884468	+	0.466600i	$0.845479\pi$
$174$		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	$0.0175599\pi$
$179$			1.47539i			0.110276i	−0.998479	+	0.0551379i	$0.982440\pi$
$180$		0			0
$181$			15.0440i			1.11821i	0.829096	+	0.559106i	$0.188855\pi$
$181$			15.0440i			1.11821i	−0.829096	+	0.559106i	$0.811145\pi$
$182$		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	−0.853388	−	0.521276i	$-0.825456\pi$
$191$	−11.4521	+	6.61187i	−0.828644	+	0.478418i	0.0247439	+	0.999694i	$0.492123\pi$
$192$		0			0
$193$	0.777855	−	1.34728i	0.0559912	−	0.0969796i	−0.836671	−	0.547705i	$-0.815501\pi$
$193$	0.777855	−	1.34728i	0.0559912	−	0.0969796i	0.892662	+	0.450726i	$0.148835\pi$
$194$	−3.48163	+	6.03035i	−0.249966	+	0.432954i
$195$		0			0
$196$		0			0
$197$		−	4.96185i		−	0.353517i	−0.984254	−	0.176759i	$-0.943439\pi$
$197$		−	4.96185i		−	0.353517i	0.984254	−	0.176759i	$-0.0565612\pi$
$198$		0			0
$199$		−	11.1922i		−	0.793394i	−0.917950	−	0.396697i	$-0.870156\pi$
$199$		−	11.1922i		−	0.793394i	0.917950	−	0.396697i	$-0.129844\pi$
$200$	−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	−0.470708	−	0.882289i	$-0.656001\pi$
$211$	7.68026	−	13.3026i	0.528731	−	0.915789i	0.999439	−	0.0334999i	$-0.0106654\pi$
$212$	−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	−0.589822	−	0.807533i	$-0.700802\pi$
$223$	−2.76845	+	1.59837i	−0.185389	+	0.107034i	0.404433	+	0.914568i	$0.367469\pi$
$224$		0			0
$225$		0			0
$226$	8.85695			0.589156
$227$	7.33494	+	12.7045i	0.486837	+	0.843227i	0.999885	−	0.0151329i	$-0.00481714\pi$
$227$	7.33494	+	12.7045i	0.486837	+	0.843227i	−0.513048	+	0.858360i	$0.671484\pi$
$228$		0			0
$229$	2.92550	+	1.68904i	0.193322	+	0.111615i	0.593537	−	0.804807i	$-0.297731\pi$
$229$	2.92550	+	1.68904i	0.193322	+	0.111615i	−0.400215	+	0.916421i	$0.631064\pi$
$230$	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	$-0.948898\pi$
$233$		−	4.88009i		−	0.319706i	0.987141	−	0.159853i	$-0.0511020\pi$
$234$		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	−0.0102448	−	0.999948i	$-0.503261\pi$
$239$	−13.6253	−	7.86657i	−0.881347	−	0.508846i	−0.871102	+	0.491101i	$0.836594\pi$
$240$		0			0
$241$	−0.666305	+	0.384691i	−0.0429205	+	0.0247801i	−0.521307	−	0.853369i	$-0.674555\pi$
$241$	−0.666305	+	0.384691i	−0.0429205	+	0.0247801i	0.478386	+	0.878150i	$0.341222\pi$
$242$			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	0.0816738	−	0.996659i	$-0.473973\pi$
$257$	14.4917	−	25.1004i	0.903969	−	1.56572i	0.822295	−	0.569061i	$-0.192693\pi$
$258$		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	−0.819002	−	0.573790i	$-0.805472\pi$
$263$	−11.8643	+	6.84988i	−0.731586	+	0.422381i	0.0874160	+	0.996172i	$0.472139\pi$
$264$		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	$-0.936288\pi$
$271$		−	6.54607i		−	0.397646i	0.980035	−	0.198823i	$-0.0637118\pi$
$272$	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	−0.976794	−	0.214181i	$-0.931292\pi$
$277$	−11.2156	−	19.4261i	−0.673883	−	1.16720i	0.302911	−	0.953019i	$-0.402041\pi$
$278$	−36.6311			−2.19699
$279$		0			0
$280$		0			0
$281$	−19.3552	+	11.1747i	−1.15463	+	0.666627i	−0.950012	−	0.312214i	$-0.898929\pi$
$281$	−19.3552	+	11.1747i	−1.15463	+	0.666627i	−0.204621	+	0.978841i	$0.565596\pi$
$282$		0			0
$283$	16.4296	+	9.48563i	0.976638	+	0.563862i	0.901254	−	0.433292i	$-0.142648\pi$
$283$	16.4296	+	9.48563i	0.976638	+	0.563862i	0.0753848	+	0.997155i	$0.475981\pi$
$284$	−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	−0.707915	−	0.706298i	$-0.750364\pi$
$293$	4.41136	−	7.64069i	0.257714	−	0.446374i	0.965629	+	0.259924i	$0.0836974\pi$
$294$		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	$0.306315\pi$
$307$			28.7533i			1.64104i	−0.571620	+	0.820519i	$0.693685\pi$
$308$		0			0
$309$		0			0
$310$	−24.5085	+	42.4499i	−1.39199	+	2.41099i
$311$	−6.64294	+	11.5059i	−0.376687	+	0.652441i	−0.990578	−	0.136950i	$-0.956270\pi$
$311$	−6.64294	+	11.5059i	−0.376687	+	0.652441i	0.613891	+	0.789391i	$0.289603\pi$
$312$		0			0
$313$	−27.3227	+	15.7748i	−1.54437	+	0.891643i	−0.545815	+	0.837905i	$0.683780\pi$
$313$	−27.3227	+	15.7748i	−1.54437	+	0.891643i	−0.998555	+	0.0537372i	$0.982887\pi$
$314$	15.6846			0.885132
$315$		0			0
$316$	0.857328			0.0482285
$317$	−17.3819	+	10.0354i	−0.976264	+	0.563646i	−0.901140	−	0.433528i	$-0.857268\pi$
$317$	−17.3819	+	10.0354i	−0.976264	+	0.563646i	−0.0751236	+	0.997174i	$0.523935\pi$
$318$		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	0.848368	−	0.529407i	$-0.177585\pi$
$331$	−0.623957	−	1.08073i	−0.0342958	−	0.0594020i	−0.882664	+	0.470005i	$0.844252\pi$
$332$	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	−0.628926	−	0.777465i	$-0.716505\pi$
$337$	6.58745	−	11.4098i	0.358842	−	0.621532i	0.987768	+	0.155933i	$0.0498385\pi$
$338$	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	0.972760	−	0.231813i	$-0.0744658\pi$
$347$	23.4411	+	13.5337i	1.25838	+	0.726529i	0.285624	+	0.958342i	$0.407799\pi$
$348$		0			0
$349$	30.3413	−	17.5176i	1.62413	−	0.937694i	0.638336	−	0.769758i	$-0.279623\pi$
$349$	30.3413	−	17.5176i	1.62413	−	0.937694i	0.985798	−	0.167936i	$-0.0537101\pi$
$350$		0			0
$351$		0			0
$352$	−39.2401			−2.09150
$353$	−1.26256	−	2.18682i	−0.0671992	−	0.116392i	0.830468	−	0.557066i	$-0.188073\pi$
$353$	−1.26256	−	2.18682i	−0.0671992	−	0.116392i	−0.897667	+	0.440674i	$0.854740\pi$
$354$		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	$-0.938572\pi$
$359$		−	7.26762i		−	0.383570i	0.981437	−	0.191785i	$-0.0614277\pi$
$360$		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	−0.772669	−	0.634809i	$-0.781079\pi$
$367$	−11.6714	+	6.73848i	−0.609242	+	0.351746i	0.163427	+	0.986555i	$0.447745\pi$
$368$		−	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	0.375121	+	0.926976i	$0.377601\pi$
$373$	−11.8820	+	20.5801i	−0.615224	+	1.06560i	−0.990345	+	0.138624i	$0.955732\pi$
$374$	−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	−0.982723	−	0.185081i	$-0.940745\pi$
$383$	−6.47930	+	11.2225i	−0.331077	+	0.573442i	0.651646	+	0.758523i	$0.274079\pi$
$384$		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	−0.720697	−	0.693250i	$-0.756178\pi$
$389$	−9.48037	+	5.47350i	−0.480674	+	0.277517i	0.240023	+	0.970767i	$0.422845\pi$
$390$		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	$-0.730019\pi$
$397$		−	29.8901i		−	1.50014i	0.661358	−	0.750071i	$-0.269981\pi$
$398$	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	0.0237698	−	0.999717i	$-0.492433\pi$
$401$	−16.6233	−	9.59744i	−0.830126	−	0.479273i	−0.853896	+	0.520444i	$0.825766\pi$
$402$		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	−0.266830	−	0.963744i	$-0.585976\pi$
$409$	−24.9737	−	14.4186i	−1.23487	−	0.712953i	−0.968041	+	0.250790i	$0.919309\pi$
$410$	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	−0.962800	−	0.270214i	$-0.912906\pi$
$419$	−5.06390	+	8.77094i	−0.247388	+	0.428488i	0.715412	+	0.698702i	$0.246239\pi$
$420$		0			0
$421$	12.7094	+	22.0134i	0.619419	+	1.07287i	0.989592	+	0.143902i	$0.0459651\pi$
$421$	12.7094	+	22.0134i	0.619419	+	1.07287i	−0.370173	+	0.928963i	$0.620702\pi$
$422$			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	$0.0841031\pi$
$431$			10.8434i			0.522308i	−0.965297	+	0.261154i	$0.915897\pi$
$432$		0			0
$433$		−	13.0519i		−	0.627233i	−0.949550	−	0.313616i	$-0.898459\pi$
$433$		−	13.0519i		−	0.627233i	0.949550	−	0.313616i	$-0.101541\pi$
$434$		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	0.336933	−	0.941529i	$-0.390611\pi$
$439$	27.6736	−	15.9773i	1.32079	−	0.762557i	0.983854	+	0.178972i	$0.0572772\pi$
$440$	−13.3208			−0.635046
$441$		0			0
$442$	2.55255			0.121412
$443$	−21.4748	+	12.3985i	−1.02030	+	0.589068i	−0.914190	−	0.405286i	$-0.867172\pi$
$443$	−21.4748	+	12.3985i	−1.02030	+	0.589068i	−0.106107	+	0.994355i	$0.533838\pi$
$444$		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	$0.105346\pi$
$449$			13.7710i			0.649892i	−0.945733	+	0.324946i	$0.894654\pi$
$450$		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	−0.985703	−	0.168494i	$-0.946110\pi$
$457$	−13.6554	−	23.6518i	−0.638771	−	1.10638i	0.346931	−	0.937890i	$-0.387224\pi$
$458$	−6.31340			−0.295006
$459$		0			0
$460$			29.5233i			1.37653i
$461$	5.51822	+	9.55784i	0.257009	+	0.445153i	0.965439	−	0.260628i	$-0.0839296\pi$
$461$	5.51822	+	9.55784i	0.257009	+	0.445153i	−0.708430	+	0.705781i	$0.750596\pi$
$462$		0			0
$463$	−12.2346	+	21.1910i	−0.568591	+	0.984829i	0.428115	+	0.903724i	$0.359178\pi$
$463$	−12.2346	+	21.1910i	−0.568591	+	0.984829i	−0.996706	+	0.0811042i	$0.974155\pi$
$464$	−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	0.979754	−	0.200204i	$-0.0641604\pi$
$479$	6.92685	+	11.9976i	0.316496	+	0.548187i	−0.663259	+	0.748390i	$0.730827\pi$
$480$		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	0.999852	+	0.0171884i	$0.00547151\pi$
$491$	33.5627	+	19.3774i	1.51466	+	0.874492i	0.514812	+	0.857303i	$0.327862\pi$
$492$		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	−0.824617	−	0.565691i	$-0.808609\pi$
$499$	1.73333	−	3.00222i	0.0775946	−	0.134398i	0.902212	+	0.431294i	$0.141943\pi$
$500$	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	0.129997	+	0.991514i	$0.458503\pi$
$509$	−17.9062	+	31.0144i	−0.793678	+	1.37469i	−0.923675	+	0.383176i	$0.874830\pi$
$510$		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	$-0.936728\pi$
$523$		−	9.03185i		−	0.394935i	0.980309	−	0.197468i	$-0.0632717\pi$
$524$	−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	0.897613	+	0.440784i	$0.145300\pi$
$547$	19.4246	+	33.6444i	0.830537	+	1.43853i	−0.0670762	+	0.997748i	$0.521367\pi$
$548$		−	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	$0.0491878\pi$
$557$			7.26499i			0.307827i	−0.988084	+	0.153914i	$0.950812\pi$
$558$		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	−0.513487	−	0.858097i	$-0.671647\pi$
$563$	11.5409	−	19.9894i	0.486390	−	0.842453i	0.999878	+	0.0156446i	$0.00498004\pi$
$564$		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	−0.137336	−	0.990525i	$-0.543854\pi$
$569$	15.5482	−	8.97677i	0.651815	−	0.376326i	0.789151	+	0.614199i	$0.210521\pi$
$570$		0			0
$571$	7.04234	−	12.1977i	0.294713	−	0.510457i	−0.680205	−	0.733022i	$-0.738109\pi$
$571$	7.04234	−	12.1977i	0.294713	−	0.510457i	0.974918	+	0.222564i	$0.0714427\pi$
$572$	−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	$0.215253\pi$
$577$			30.0675i			1.25172i	−0.779934	+	0.625862i	$0.784747\pi$
$578$	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	−0.949264	−	0.314481i	$-0.898169\pi$
$587$	−18.0979	−	31.3465i	−0.746981	−	1.29381i	0.202283	−	0.979327i	$-0.435164\pi$
$588$		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	0.786557	−	0.617517i	$-0.211861\pi$
$599$	15.7873	+	9.11478i	0.645050	+	0.372420i	−0.141507	+	0.989937i	$0.545195\pi$
$600$		0			0
$601$	−32.1713	+	18.5741i	−1.31230	+	0.757654i	−0.982476	−	0.186390i	$-0.940321\pi$
$601$	−32.1713	+	18.5741i	−1.31230	+	0.757654i	−0.329820	+	0.944044i	$0.606988\pi$
$602$		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	0.806240	−	0.591588i	$-0.201499\pi$
$607$	17.1730	+	9.91482i	0.697030	+	0.402430i	−0.109211	+	0.994019i	$0.534832\pi$
$608$	−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	0.409397	−	0.912357i	$-0.365739\pi$
$617$	−4.37247	−	2.52445i	−0.176029	−	0.101630i	−0.585426	+	0.810726i	$0.699073\pi$
$618$		0			0
$619$	0.231999	−	0.133945i	0.00932485	−	0.00538370i	−0.495330	−	0.868705i	$-0.664953\pi$
$619$	0.231999	−	0.133945i	0.00932485	−	0.00538370i	0.504655	+	0.863321i	$0.331620\pi$
$620$		−	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	−0.955317	−	0.295583i	$-0.904486\pi$
$641$	−29.7991	+	17.2045i	−1.17699	+	0.679537i	−0.221676	+	0.975120i	$0.571153\pi$
$642$		0			0
$643$	0.676278	+	0.390449i	0.0266698	+	0.0153978i	0.513276	−	0.858224i	$-0.328432\pi$
$643$	0.676278	+	0.390449i	0.0266698	+	0.0153978i	−0.486606	+	0.873622i	$0.661765\pi$
$644$		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	0.444699	−	0.895680i	$-0.353311\pi$
$653$	−2.77600	−	1.60272i	−0.108633	−	0.0627194i	−0.553332	+	0.832961i	$0.686644\pi$
$654$		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	0.0544636	−	0.998516i	$-0.482655\pi$
$659$	24.2959	−	14.0273i	0.946435	−	0.546425i	0.891972	+	0.452091i	$0.149322\pi$
$660$		0			0
$661$	28.0490	+	16.1941i	1.09098	+	0.629878i	0.933837	−	0.357698i	$-0.116438\pi$
$661$	28.0490	+	16.1941i	1.09098	+	0.629878i	0.157143	+	0.987576i	$0.449772\pi$
$662$	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	0.596026	−	0.802965i	$-0.296745\pi$
$673$	−10.3088	−	17.8554i	−0.397375	−	0.688273i	−0.993401	+	0.114692i	$0.963412\pi$
$674$			24.6231i			0.948445i
$675$		0			0
$676$	−19.1140			−0.735155
$677$	25.1655	+	43.5880i	0.967190	+	1.67522i	0.703612	+	0.710585i	$0.251569\pi$
$677$	25.1655	+	43.5880i	0.967190	+	1.67522i	0.263578	+	0.964638i	$0.415097\pi$
$678$		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	$-0.915301\pi$
$683$		−	13.7445i		−	0.525920i	0.964807	−	0.262960i	$-0.0846987\pi$
$684$		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	0.0690343	−	0.997614i	$-0.478008\pi$
$691$	25.4328	−	14.6837i	0.967511	−	0.558593i	0.898476	+	0.439022i	$0.144675\pi$
$692$	−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	$0.314374\pi$
$701$			44.2011i			1.66945i	−0.550666	+	0.834726i	$0.685626\pi$
$702$		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	0.952590	−	0.304256i	$-0.0984077\pi$
$709$	5.66629	+	9.81430i	0.212802	+	0.368584i	−0.739788	+	0.672840i	$0.765074\pi$
$710$	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	−0.610640	−	0.791908i	$-0.709088\pi$
$727$	−6.20547	+	3.58273i	−0.230148	+	0.132876i	0.380492	+	0.924784i	$0.375755\pi$
$728$		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	0.999335	+	0.0364726i	$0.0116122\pi$
$733$	41.4391	+	23.9249i	1.53059	+	0.883685i	0.531253	+	0.847213i	$0.321721\pi$
$734$	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	−0.304709	−	0.952445i	$-0.598559\pi$
$743$	−34.9422	−	20.1739i	−1.28191	−	0.740109i	−0.977197	+	0.212337i	$0.931893\pi$
$744$		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	0.371463	+	0.928448i	$0.378856\pi$
$751$	−16.9449	+	29.3494i	−0.618327	+	1.07097i	−0.989791	+	0.142527i	$0.954477\pi$
$752$	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	−0.999760	−	0.0218999i	$-0.993028\pi$
$761$	−13.2666	+	22.9784i	−0.480914	+	0.832968i	0.518846	+	0.854868i	$0.326362\pi$
$762$		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	0.858494	−	0.512823i	$-0.171400\pi$
$769$	23.3944	+	13.5068i	0.843623	+	0.487066i	−0.0148711	+	0.999889i	$0.504734\pi$
$770$		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	0.846498	−	0.532391i	$-0.178707\pi$
$787$	22.6864	+	13.0980i	0.808683	+	0.466893i	−0.0378153	+	0.999285i	$0.512040\pi$
$788$	−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	−0.740813	−	0.671711i	$-0.765560\pi$
$797$	5.96560	−	10.3327i	0.211312	−	0.366004i	0.952126	+	0.305707i	$0.0988929\pi$
$798$		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	$-0.845822\pi$
$809$		−	26.4887i		−	0.931292i	0.884971	−	0.465646i	$-0.154178\pi$
$810$		0			0
$811$			13.7419i			0.482544i	0.970458	+	0.241272i	$0.0775646\pi$
$811$			13.7419i			0.482544i	−0.970458	+	0.241272i	$0.922435\pi$
$812$		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	−0.280759	−	0.959778i	$-0.590586\pi$
$821$	11.7493	−	6.78346i	0.410053	−	0.236744i	0.690813	+	0.723034i	$0.257253\pi$
$822$		0			0
$823$	−7.34857	+	12.7281i	−0.256155	+	0.443674i	−0.965209	−	0.261481i	$-0.915789\pi$
$823$	−7.34857	+	12.7281i	−0.256155	+	0.443674i	0.709053	+	0.705155i	$0.249122\pi$
$824$	6.78711	−	11.7556i	0.236440	−	0.409527i
$825$		0			0
$826$		0			0
$827$			40.8787i			1.42149i	0.703449	+	0.710746i	$0.251642\pi$
$827$			40.8787i			1.42149i	−0.703449	+	0.710746i	$0.748358\pi$
$828$		0			0
$829$		−	20.4600i		−	0.710605i	−0.934751	−	0.355302i	$-0.884378\pi$
$829$		−	20.4600i		−	0.710605i	0.934751	−	0.355302i	$-0.115622\pi$
$830$	−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	0.757462	+	0.652880i	$0.226439\pi$
$839$	27.3475	+	47.3673i	0.944141	+	1.63530i	0.186680	+	0.982421i	$0.440227\pi$
$840$		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	−0.677373	−	0.735640i	$-0.736882\pi$
$853$	−11.0684	+	6.39037i	−0.378976	+	0.218802i	0.298396	+	0.954442i	$0.403548\pi$
$854$		0			0
$855$		0			0
$856$	−12.7812			−0.436851
$857$	9.16200	+	15.8691i	0.312968	+	0.542077i	0.979003	−	0.203844i	$-0.0653434\pi$
$857$	9.16200	+	15.8691i	0.312968	+	0.542077i	−0.666035	+	0.745920i	$0.732010\pi$
$858$		0			0
$859$	−33.4579	−	19.3169i	−1.14157	−	0.659085i	−0.194750	−	0.980853i	$-0.562390\pi$
$859$	−33.4579	−	19.3169i	−1.14157	−	0.659085i	−0.946819	+	0.321768i	$0.895723\pi$
$860$	−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	$-0.908260\pi$
$863$		−	16.7000i		−	0.568475i	0.958754	−	0.284238i	$-0.0917405\pi$
$864$		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	0.430953	+	0.902374i	$0.358177\pi$
$877$	−16.7617	+	29.0321i	−0.566002	+	0.980345i	−0.996956	+	0.0779707i	$0.975156\pi$
$878$	−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	−0.403481	−	0.914988i	$-0.632200\pi$
$887$	17.5914	−	30.4692i	0.590662	−	1.02306i	0.994143	−	0.108069i	$-0.0344666\pi$
$888$		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	0.965899	+	0.258918i	$0.0833660\pi$
$907$	21.2977	+	36.8887i	0.707179	+	1.22487i	−0.258720	+	0.965952i	$0.583301\pi$
$908$	21.9010			0.726811
$909$		0			0
$910$		0			0
$911$	43.5221	−	25.1275i	1.44195	−	0.832510i	0.443970	−	0.896042i	$-0.353570\pi$
$911$	43.5221	−	25.1275i	1.44195	−	0.832510i	0.997980	+	0.0635313i	$0.0202363\pi$
$912$		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	0.723610	−	0.690209i	$-0.242482\pi$
$929$	−7.19115	−	12.4554i	−0.235934	−	0.408650i	−0.959544	+	0.281560i	$0.909148\pi$
$930$		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	$-0.742496\pi$
$937$		−	44.2981i		−	1.44716i	0.690243	−	0.723578i	$-0.257504\pi$
$938$		0			0
$939$		0			0
$940$	−4.00985	+	6.94526i	−0.130787	+	0.226529i
$941$	−7.44400	+	12.8934i	−0.242667	+	0.420312i	−0.961473	−	0.274899i	$-0.911356\pi$
$941$	−7.44400	+	12.8934i	−0.242667	+	0.420312i	0.718806	+	0.695211i	$0.244689\pi$
$942$		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	−0.956178	−	0.292787i	$-0.905417\pi$
$947$	−36.3343	+	20.9776i	−1.18071	+	0.681681i	−0.224528	+	0.974468i	$0.572084\pi$
$948$		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	$-0.927284\pi$
$953$		−	13.9821i		−	0.452926i	0.974020	−	0.226463i	$-0.0727162\pi$
$954$		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	−0.989911	−	0.141690i	$-0.954746\pi$
$967$	−11.5757	+	20.0497i	−0.372249	+	0.644754i	0.617662	+	0.786443i	$0.288080\pi$
$968$	−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	0.657348	−	0.753587i	$-0.271678\pi$
$977$	10.4210	+	6.01657i	0.333397	+	0.192487i	−0.323951	+	0.946074i	$0.605011\pi$
$978$		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	0.911856	−	0.410511i	$-0.134650\pi$
$983$	3.14829	+	5.45300i	0.100415	+	0.173924i	−0.811441	+	0.584435i	$0.801316\pi$
$984$		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	−0.337626	−	0.941280i	$-0.609624\pi$
$997$	9.74838	−	5.62823i	0.308734	−	0.178248i	0.646360	+	0.763033i	$0.276290\pi$
$998$			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.881.6		48
3.2	odd	2		441.2.o.e.293.19	yes	48
7.2	even	3		1323.2.s.d.962.19		48
7.3	odd	6		1323.2.i.d.1097.22		48
7.4	even	3		1323.2.i.d.1097.7		48
7.5	odd	6		1323.2.s.d.962.20		48
7.6	odd	2	inner	1323.2.o.e.881.5		48
9.2	odd	6	inner	1323.2.o.e.440.5		48
9.7	even	3		441.2.o.e.146.20	yes	48
21.2	odd	6		441.2.s.d.374.5		48
21.5	even	6		441.2.s.d.374.6		48
21.11	odd	6		441.2.i.d.68.20		48
21.17	even	6		441.2.i.d.68.19		48
21.20	even	2		441.2.o.e.293.20	yes	48
63.2	odd	6		1323.2.i.d.521.22		48
63.11	odd	6		1323.2.s.d.656.20		48
63.16	even	3		441.2.i.d.227.5		48
63.20	even	6	inner	1323.2.o.e.440.6		48
63.25	even	3		441.2.s.d.362.6		48
63.34	odd	6		441.2.o.e.146.19	✓	48
63.38	even	6		1323.2.s.d.656.19		48
63.47	even	6		1323.2.i.d.521.7		48
63.52	odd	6		441.2.s.d.362.5		48
63.61	odd	6		441.2.i.d.227.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.19		48	21.17	even	6
441.2.i.d.68.20		48	21.11	odd	6
441.2.i.d.227.5		48	63.16	even	3
441.2.i.d.227.6		48	63.61	odd	6
441.2.o.e.146.19	✓	48	63.34	odd	6
441.2.o.e.146.20	yes	48	9.7	even	3
441.2.o.e.293.19	yes	48	3.2	odd	2
441.2.o.e.293.20	yes	48	21.20	even	2
441.2.s.d.362.5		48	63.52	odd	6
441.2.s.d.362.6		48	63.25	even	3
441.2.s.d.374.5		48	21.2	odd	6
441.2.s.d.374.6		48	21.5	even	6
1323.2.i.d.521.7		48	63.47	even	6
1323.2.i.d.521.22		48	63.2	odd	6
1323.2.i.d.1097.7		48	7.4	even	3
1323.2.i.d.1097.22		48	7.3	odd	6
1323.2.o.e.440.5		48	9.2	odd	6	inner
1323.2.o.e.440.6		48	63.20	even	6	inner
1323.2.o.e.881.5		48	7.6	odd	2	inner
1323.2.o.e.881.6		48	1.1	even	1	trivial
1323.2.s.d.656.19		48	63.38	even	6
1323.2.s.d.656.20		48	63.11	odd	6
1323.2.s.d.962.19		48	7.2	even	3
1323.2.s.d.962.20		48	7.5	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

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