LMFDB - Embedded newform 1323.2.h.h.802.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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([2, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (of order $3$, 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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.11
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.h.226.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.71513 q^{2} +5.37195 q^{4} +(0.793197 - 1.37386i) q^{5} +9.15528 q^{8} +O(q^{10})$	\(q+2.71513 q^{2} +5.37195 q^{4} +(0.793197 - 1.37386i) q^{5} +9.15528 q^{8} +(2.15363 - 3.73020i) q^{10} +(-0.674376 - 1.16805i) q^{11} +(-1.58916 - 2.75251i) q^{13} +14.1139 q^{16} +(-1.40027 + 2.42534i) q^{17} +(0.312846 + 0.541866i) q^{19} +(4.26101 - 7.38028i) q^{20} +(-1.83102 - 3.17142i) q^{22} +(-0.142434 + 0.246702i) q^{23} +(1.24168 + 2.15065i) q^{25} +(-4.31479 - 7.47343i) q^{26} +(-2.27396 + 3.93861i) q^{29} -7.43005 q^{31} +20.0106 q^{32} +(-3.80191 + 6.58511i) q^{34} +(-4.01126 - 6.94770i) q^{37} +(0.849420 + 1.47124i) q^{38} +(7.26194 - 12.5780i) q^{40} +(5.01329 + 8.68327i) q^{41} +(-3.12937 + 5.42022i) q^{43} +(-3.62271 - 6.27472i) q^{44} +(-0.386726 + 0.669829i) q^{46} +11.1477 q^{47} +(3.37132 + 5.83930i) q^{50} +(-8.53689 - 14.7863i) q^{52} +(1.39349 - 2.41359i) q^{53} -2.13965 q^{55} +(-6.17410 + 10.6939i) q^{58} +4.57469 q^{59} +0.385014 q^{61} -20.1736 q^{62} +26.1036 q^{64} -5.04207 q^{65} -2.53916 q^{67} +(-7.52217 + 13.0288i) q^{68} +1.45208 q^{71} +(-0.234067 + 0.405416i) q^{73} +(-10.8911 - 18.8639i) q^{74} +(1.68059 + 2.91087i) q^{76} -15.7124 q^{79} +(11.1951 - 19.3905i) q^{80} +(13.6117 + 23.5762i) q^{82} +(-6.99338 + 12.1129i) q^{83} +(2.22138 + 3.84754i) q^{85} +(-8.49665 + 14.7166i) q^{86} +(-6.17410 - 10.6939i) q^{88} +(1.29353 + 2.24046i) q^{89} +(-0.765146 + 1.32527i) q^{92} +30.2674 q^{94} +0.992595 q^{95} +(-7.22962 + 12.5221i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 20 q^{11} + 24 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} + 96 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} + 120 q^{65} + 24 q^{67} + 112 q^{71} - 68 q^{74} - 24 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} + 128 q^{95}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 20 * q^11 + 24 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 + 96 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 + 120 * q^65 + 24 * q^67 + 112 * q^71 - 68 * q^74 - 24 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 + 128 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.71513			1.91989			0.959944	−	0.280191i	$-0.0903976\pi$
$2$	2.71513			1.91989			0.959944	+	0.280191i	$0.0903976\pi$
$3$		0			0
$3$		0			0
$4$	5.37195			2.68597
$5$	0.793197	−	1.37386i	0.354728	−	0.614407i	−0.632343	−	0.774688i	$-0.717907\pi$
$5$	0.793197	−	1.37386i	0.354728	−	0.614407i	0.987071	+	0.160281i	$0.0512400\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	9.15528			3.23688
$9$		0			0
$10$	2.15363	−	3.73020i	0.681039	−	1.17959i
$11$	−0.674376	−	1.16805i	−0.203332	−	0.352181i	0.746268	−	0.665646i	$-0.231844\pi$
$11$	−0.674376	−	1.16805i	−0.203332	−	0.352181i	−0.949600	+	0.313464i	$0.898510\pi$
$12$		0			0
$13$	−1.58916	−	2.75251i	−0.440754	−	0.763409i	0.556991	−	0.830518i	$-0.311956\pi$
$13$	−1.58916	−	2.75251i	−0.440754	−	0.763409i	−0.997746	+	0.0671096i	$0.978622\pi$
$14$		0			0
$15$		0			0
$16$	14.1139			3.52848
$17$	−1.40027	+	2.42534i	−0.339615	+	0.588230i	−0.984360	−	0.176167i	$-0.943630\pi$
$17$	−1.40027	+	2.42534i	−0.339615	+	0.588230i	0.644745	+	0.764397i	$0.276963\pi$
$18$		0			0
$19$	0.312846	+	0.541866i	0.0717719	+	0.124313i	0.899678	−	0.436554i	$-0.143801\pi$
$19$	0.312846	+	0.541866i	0.0717719	+	0.124313i	−0.827906	+	0.560867i	$0.810468\pi$
$20$	4.26101	−	7.38028i	0.952791	−	1.65028i
$21$		0			0
$22$	−1.83102	−	3.17142i	−0.390375	−	0.676149i
$23$	−0.142434	+	0.246702i	−0.0296995	+	0.0514410i	−0.880493	−	0.474059i	$-0.842788\pi$
$23$	−0.142434	+	0.246702i	−0.0296995	+	0.0514410i	0.850794	+	0.525500i	$0.176122\pi$
$24$		0			0
$25$	1.24168	+	2.15065i	0.248336	+	0.430130i
$26$	−4.31479	−	7.47343i	−0.846199	−	1.46566i
$27$		0			0
$28$		0			0
$29$	−2.27396	+	3.93861i	−0.422264	+	0.731382i	−0.996161	−	0.0875454i	$-0.972098\pi$
$29$	−2.27396	+	3.93861i	−0.422264	+	0.731382i	0.573897	+	0.818928i	$0.305431\pi$
$30$		0			0
$31$	−7.43005			−1.33448			−0.667238	−	0.744845i	$-0.732524\pi$
$31$	−7.43005			−1.33448			−0.667238	+	0.744845i	$0.732524\pi$
$32$	20.0106			3.53741
$33$		0			0
$34$	−3.80191	+	6.58511i	−0.652023	+	1.12934i
$35$		0			0
$36$		0			0
$37$	−4.01126	−	6.94770i	−0.659447	−	1.14220i	−0.980759	−	0.195222i	$-0.937457\pi$
$37$	−4.01126	−	6.94770i	−0.659447	−	1.14220i	0.321312	−	0.946973i	$-0.395876\pi$
$38$	0.849420	+	1.47124i	0.137794	+	0.238666i
$39$		0			0
$40$	7.26194	−	12.5780i	1.14821	−	1.98876i
$41$	5.01329	+	8.68327i	0.782944	+	1.35610i	0.930219	+	0.367004i	$0.119616\pi$
$41$	5.01329	+	8.68327i	0.782944	+	1.35610i	−0.147275	+	0.989096i	$0.547050\pi$
$42$		0			0
$43$	−3.12937	+	5.42022i	−0.477224	+	0.826576i	−0.999659	−	0.0261027i	$-0.991690\pi$
$43$	−3.12937	+	5.42022i	−0.477224	+	0.826576i	0.522435	+	0.852679i	$0.325024\pi$
$44$	−3.62271	−	6.27472i	−0.546144	−	0.945950i
$45$		0			0
$46$	−0.386726	+	0.669829i	−0.0570197	+	0.0987609i
$47$	11.1477			1.62605			0.813026	−	0.582227i	$-0.197819\pi$
$47$	11.1477			1.62605			0.813026	+	0.582227i	$0.197819\pi$
$48$		0			0
$49$		0			0
$50$	3.37132	+	5.83930i	0.476777	+	0.825802i
$51$		0			0
$52$	−8.53689	−	14.7863i	−1.18385	−	2.05049i
$53$	1.39349	−	2.41359i	0.191410	−	0.331532i	−0.754308	−	0.656521i	$-0.772027\pi$
$53$	1.39349	−	2.41359i	0.191410	−	0.331532i	0.945718	+	0.324989i	$0.105361\pi$
$54$		0			0
$55$	−2.13965			−0.288510
$56$		0			0
$57$		0			0
$58$	−6.17410	+	10.6939i	−0.810699	+	1.40417i
$59$	4.57469			0.595574			0.297787	−	0.954632i	$-0.403752\pi$
$59$	4.57469			0.595574			0.297787	+	0.954632i	$0.403752\pi$
$60$		0			0
$61$	0.385014			0.0492960			0.0246480	−	0.999696i	$-0.492154\pi$
$61$	0.385014			0.0492960			0.0246480	+	0.999696i	$0.492154\pi$
$62$	−20.1736			−2.56205
$63$		0			0
$64$	26.1036			3.26295
$65$	−5.04207			−0.625392
$66$		0			0
$67$	−2.53916			−0.310208			−0.155104	−	0.987898i	$-0.549571\pi$
$67$	−2.53916			−0.310208			−0.155104	+	0.987898i	$0.549571\pi$
$68$	−7.52217	+	13.0288i	−0.912197	+	1.57997i
$69$		0			0
$70$		0			0
$71$	1.45208			0.172330			0.0861651	−	0.996281i	$-0.472539\pi$
$71$	1.45208			0.172330			0.0861651	+	0.996281i	$0.472539\pi$
$72$		0			0
$73$	−0.234067	+	0.405416i	−0.0273955	+	0.0474503i	−0.879398	−	0.476087i	$-0.842055\pi$
$73$	−0.234067	+	0.405416i	−0.0273955	+	0.0474503i	0.852003	+	0.523538i	$0.175388\pi$
$74$	−10.8911	−	18.8639i	−1.26606	−	2.19289i
$75$		0			0
$76$	1.68059	+	2.91087i	0.192777	+	0.333900i
$77$		0			0
$78$		0			0
$79$	−15.7124			−1.76778			−0.883892	−	0.467691i	$-0.845086\pi$
$79$	−15.7124			−1.76778			−0.883892	+	0.467691i	$0.845086\pi$
$80$	11.1951	−	19.3905i	1.25165	−	2.16792i
$81$		0			0
$82$	13.6117	+	23.5762i	1.50317	+	2.60356i
$83$	−6.99338	+	12.1129i	−0.767623	+	1.32956i	0.171225	+	0.985232i	$0.445228\pi$
$83$	−6.99338	+	12.1129i	−0.767623	+	1.32956i	−0.938848	+	0.344331i	$0.888106\pi$
$84$		0			0
$85$	2.22138	+	3.84754i	0.240942	+	0.417324i
$86$	−8.49665	+	14.7166i	−0.916217	+	1.58693i
$87$		0			0
$88$	−6.17410	−	10.6939i	−0.658162	−	1.13997i
$89$	1.29353	+	2.24046i	0.137114	+	0.237488i	0.926403	−	0.376534i	$-0.122884\pi$
$89$	1.29353	+	2.24046i	0.137114	+	0.237488i	−0.789289	+	0.614022i	$0.789551\pi$
$90$		0			0
$91$		0			0
$92$	−0.765146	+	1.32527i	−0.0797719	+	0.138169i
$93$		0			0
$94$	30.2674			3.12184
$95$	0.992595			0.101838
$96$		0			0
$97$	−7.22962	+	12.5221i	−0.734057	+	1.27142i	0.221079	+	0.975256i	$0.429042\pi$
$97$	−7.22962	+	12.5221i	−0.734057	+	1.27142i	−0.955136	+	0.296168i	$0.904291\pi$
$98$		0			0
$99$		0			0
$100$	6.67023	+	11.5532i	0.667023	+	1.15532i
$101$	−4.91888	−	8.51975i	−0.489447	−	0.847747i	0.510479	−	0.859890i	$-0.329468\pi$
$101$	−4.91888	−	8.51975i	−0.489447	−	0.847747i	−0.999926	+	0.0121430i	$0.996135\pi$
$102$		0			0
$103$	5.52897	−	9.57646i	0.544786	−	0.943597i	−0.453834	−	0.891086i	$-0.649944\pi$
$103$	5.52897	−	9.57646i	0.544786	−	0.943597i	0.998620	−	0.0525110i	$-0.0167225\pi$
$104$	−14.5492	−	25.2000i	−1.42667	−	2.47106i
$105$		0			0
$106$	3.78350	−	6.55322i	0.367486	−	0.636505i
$107$	−0.962153	−	1.66650i	−0.0930149	−	0.161106i	0.815764	−	0.578386i	$-0.196317\pi$
$107$	−0.962153	−	1.66650i	−0.0930149	−	0.161106i	−0.908778	+	0.417279i	$0.862984\pi$
$108$		0			0
$109$	9.30341	−	16.1140i	0.891105	−	1.54344i	0.0525523	−	0.998618i	$-0.483264\pi$
$109$	9.30341	−	16.1140i	0.891105	−	1.54344i	0.838553	−	0.544821i	$-0.183402\pi$
$110$	−5.80944			−0.553908
$111$		0			0
$112$		0			0
$113$	−1.59338	−	2.75982i	−0.149893	−	0.259622i	0.781295	−	0.624162i	$-0.214560\pi$
$113$	−1.59338	−	2.75982i	−0.149893	−	0.259622i	−0.931188	+	0.364540i	$0.881226\pi$
$114$		0			0
$115$	0.225956	+	0.391367i	0.0210705	+	0.0364951i
$116$	−12.2156	+	21.1580i	−1.13419	+	1.96447i
$117$		0			0
$118$	12.4209			1.14344
$119$		0			0
$120$		0			0
$121$	4.59043	−	7.95086i	0.417312	−	0.722806i
$122$	1.04536			0.0946428
$123$		0			0
$124$	−39.9138			−3.58437
$125$	11.8715			1.06182
$126$		0			0
$127$	−8.37387			−0.743061			−0.371530	−	0.928421i	$-0.621167\pi$
$127$	−8.37387			−0.743061			−0.371530	+	0.928421i	$0.621167\pi$
$128$	30.8535			2.72709
$129$		0			0
$130$	−13.6899			−1.20068
$131$	5.98629	−	10.3686i	0.523024	−	0.905905i	−0.476616	−	0.879111i	$-0.658137\pi$
$131$	5.98629	−	10.3686i	0.523024	−	0.905905i	0.999641	−	0.0267937i	$-0.00852971\pi$
$132$		0			0
$133$		0			0
$134$	−6.89415			−0.595564
$135$		0			0
$136$	−12.8199	+	22.2046i	−1.09929	+	1.90403i
$137$	8.27525	+	14.3332i	0.707003	+	1.22456i	0.965964	+	0.258677i	$0.0832865\pi$
$137$	8.27525	+	14.3332i	0.707003	+	1.22456i	−0.258961	+	0.965888i	$0.583380\pi$
$138$		0			0
$139$	−3.95119	−	6.84367i	−0.335136	−	0.580472i	0.648375	−	0.761321i	$-0.275449\pi$
$139$	−3.95119	−	6.84367i	−0.335136	−	0.580472i	−0.983511	+	0.180849i	$0.942116\pi$
$140$		0			0
$141$		0			0
$142$	3.94259			0.330855
$143$	−2.14339	+	3.71245i	−0.179239	+	0.310451i
$144$		0			0
$145$	3.60739	+	6.24819i	0.299578	+	0.518884i
$146$	−0.635523	+	1.10076i	−0.0525962	+	0.0910994i
$147$		0			0
$148$	−21.5483	−	37.3227i	−1.77126	−	3.06791i
$149$	−6.83427	+	11.8373i	−0.559885	+	0.969749i	0.437620	+	0.899160i	$0.355821\pi$
$149$	−6.83427	+	11.8373i	−0.559885	+	0.969749i	−0.997505	+	0.0705895i	$0.977512\pi$
$150$		0			0
$151$	−1.94982	−	3.37718i	−0.158674	−	0.274831i	0.775717	−	0.631081i	$-0.217389\pi$
$151$	−1.94982	−	3.37718i	−0.158674	−	0.274831i	−0.934391	+	0.356250i	$0.884055\pi$
$152$	2.86420	+	4.96093i	0.232317	+	0.402385i
$153$		0			0
$154$		0			0
$155$	−5.89349	+	10.2078i	−0.473376	+	0.819912i
$156$		0			0
$157$	0.294352			0.0234919			0.0117459	−	0.999931i	$-0.496261\pi$
$157$	0.294352			0.0234919			0.0117459	+	0.999931i	$0.496261\pi$
$158$	−42.6613			−3.39395
$159$		0			0
$160$	15.8723	−	27.4917i	1.25482	−	2.17341i
$161$		0			0
$162$		0			0
$163$	−5.35455	−	9.27436i	−0.419401	−	0.726424i	0.576478	−	0.817112i	$-0.304427\pi$
$163$	−5.35455	−	9.27436i	−0.419401	−	0.726424i	−0.995879	+	0.0906886i	$0.971093\pi$
$164$	26.9311	+	46.6461i	2.10297	+	3.64245i
$165$		0			0
$166$	−18.9880	+	32.8881i	−1.47375	+	2.55261i
$167$	1.59872	+	2.76907i	0.123713	+	0.214277i	0.921229	−	0.389020i	$-0.127186\pi$
$167$	1.59872	+	2.76907i	0.123713	+	0.214277i	−0.797516	+	0.603298i	$0.793853\pi$
$168$		0			0
$169$	1.44913	−	2.50997i	0.111472	−	0.193074i
$170$	6.03133	+	10.4466i	0.462582	+	0.801215i
$171$		0			0
$172$	−16.8108	+	29.1171i	−1.28181	+	2.22016i
$173$	−11.4375			−0.869577			−0.434789	−	0.900533i	$-0.643177\pi$
$173$	−11.4375			−0.869577			−0.434789	+	0.900533i	$0.643177\pi$
$174$		0			0
$175$		0			0
$176$	−9.51809	−	16.4858i	−0.717453	−	1.24266i
$177$		0			0
$178$	3.51210	+	6.08314i	0.263243	+	0.455951i
$179$	0.549275	−	0.951372i	0.0410547	−	0.0711089i	−0.844768	−	0.535133i	$-0.820262\pi$
$179$	0.549275	−	0.951372i	0.0410547	−	0.0711089i	0.885823	+	0.464024i	$0.153595\pi$
$180$		0			0
$181$	−3.19013			−0.237120			−0.118560	−	0.992947i	$-0.537828\pi$
$181$	−3.19013			−0.237120			−0.118560	+	0.992947i	$0.537828\pi$
$182$		0			0
$183$		0			0
$184$	−1.30402	+	2.25863i	−0.0961336	+	0.166508i
$185$	−12.7269			−0.935698
$186$		0			0
$187$	3.77723			0.276218
$188$	59.8846			4.36753
$189$		0			0
$190$	2.69503			0.195518
$191$	−3.86815			−0.279889			−0.139945	−	0.990159i	$-0.544692\pi$
$191$	−3.86815			−0.279889			−0.139945	+	0.990159i	$0.544692\pi$
$192$		0			0
$193$	−4.13585			−0.297705			−0.148853	−	0.988859i	$-0.547558\pi$
$193$	−4.13585			−0.297705			−0.148853	+	0.988859i	$0.547558\pi$
$194$	−19.6294	+	33.9991i	−1.40931	+	2.44099i
$195$		0			0
$196$		0			0
$197$	0.889267			0.0633576			0.0316788	−	0.999498i	$-0.489915\pi$
$197$	0.889267			0.0633576			0.0316788	+	0.999498i	$0.489915\pi$
$198$		0			0
$199$	3.16193	−	5.47663i	0.224143	−	0.388228i	−0.731919	−	0.681392i	$-0.761375\pi$
$199$	3.16193	−	5.47663i	0.224143	−	0.388228i	0.956062	+	0.293164i	$0.0947083\pi$
$200$	11.3679	+	19.6898i	0.803833	+	1.39228i
$201$		0			0
$202$	−13.3554	−	23.1323i	−0.939684	−	1.62758i
$203$		0			0
$204$		0			0
$205$	15.9061			1.11093
$206$	15.0119	−	26.0014i	1.04593	−	1.81160i
$207$		0			0
$208$	−22.4293	−	38.8487i	−1.55519	−	2.69367i
$209$	0.421952	−	0.730843i	0.0291870	−	0.0505535i
$210$		0			0
$211$	5.71291	+	9.89505i	0.393293	+	0.681204i	0.992882	−	0.119105i	$-0.0380025\pi$
$211$	5.71291	+	9.89505i	0.393293	+	0.681204i	−0.599589	+	0.800308i	$0.704669\pi$
$212$	7.48574	−	12.9657i	0.514123	−	0.890487i
$213$		0			0
$214$	−2.61237	−	4.52476i	−0.178578	−	0.309307i
$215$	4.96441	+	8.59860i	0.338570	+	0.586420i
$216$		0			0
$217$		0			0
$218$	25.2600	−	43.7516i	1.71082	−	2.96323i
$219$		0			0
$220$	−11.4941			−0.774931
$221$	8.90101			0.598747
$222$		0			0
$223$	−8.35953	+	14.4791i	−0.559796	+	0.969595i	0.437717	+	0.899113i	$0.355787\pi$
$223$	−8.35953	+	14.4791i	−0.559796	+	0.969595i	−0.997513	+	0.0704822i	$0.977546\pi$
$224$		0			0
$225$		0			0
$226$	−4.32625	−	7.49328i	−0.287778	−	0.498446i
$227$	−8.53501	−	14.7831i	−0.566489	−	0.981187i	−0.996909	−	0.0785588i	$-0.974968\pi$
$227$	−8.53501	−	14.7831i	−0.566489	−	0.981187i	0.430421	−	0.902628i	$-0.358365\pi$
$228$		0			0
$229$	9.89471	−	17.1381i	0.653861	−	1.13252i	−0.328317	−	0.944567i	$-0.606482\pi$
$229$	9.89471	−	17.1381i	0.653861	−	1.13252i	0.982178	−	0.187953i	$-0.0601851\pi$
$230$	0.613500	+	1.06261i	0.0404530	+	0.0700666i
$231$		0			0
$232$	−20.8187	+	36.0591i	−1.36682	+	2.36740i
$233$	2.96579	+	5.13691i	0.194296	+	0.336530i	0.946669	−	0.322207i	$-0.104425\pi$
$233$	2.96579	+	5.13691i	0.194296	+	0.336530i	−0.752374	+	0.658736i	$0.771091\pi$
$234$		0			0
$235$	8.84228	−	15.3153i	0.576807	−	0.999058i
$236$	24.5750			1.59969
$237$		0			0
$238$		0			0
$239$	10.0277	+	17.3685i	0.648637	+	1.12347i	0.983449	+	0.181187i	$0.0579939\pi$
$239$	10.0277	+	17.3685i	0.648637	+	1.12347i	−0.334812	+	0.942285i	$0.608673\pi$
$240$		0			0
$241$	14.6444	+	25.3648i	0.943326	+	1.63389i	0.759069	+	0.651010i	$0.225654\pi$
$241$	14.6444	+	25.3648i	0.943326	+	1.63389i	0.184256	+	0.982878i	$0.441012\pi$
$242$	12.4636	−	21.5877i	0.801193	−	1.38771i
$243$		0			0
$244$	2.06827			0.132408
$245$		0			0
$246$		0			0
$247$	0.994327	−	1.72223i	0.0632675	−	0.109583i
$248$	−68.0242			−4.31954
$249$		0			0
$250$	32.2328			2.03858
$251$	−22.7856			−1.43821			−0.719106	−	0.694901i	$-0.755448\pi$
$251$	−22.7856			−1.43821			−0.719106	+	0.694901i	$0.755448\pi$
$252$		0			0
$253$	0.384215			0.0241554
$254$	−22.7362			−1.42659
$255$		0			0
$256$	31.5642			1.97276
$257$	12.1444	−	21.0348i	0.757550	−	1.31211i	−0.186547	−	0.982446i	$-0.559730\pi$
$257$	12.1444	−	21.0348i	0.757550	−	1.31211i	0.944097	−	0.329668i	$-0.106937\pi$
$258$		0			0
$259$		0			0
$260$	−27.0857			−1.67979
$261$		0			0
$262$	16.2536	−	28.1520i	1.00415	−	1.73924i
$263$	−4.30578	−	7.45782i	−0.265506	−	0.459869i	0.702190	−	0.711989i	$-0.252206\pi$
$263$	−4.30578	−	7.45782i	−0.265506	−	0.459869i	−0.967696	+	0.252120i	$0.918872\pi$
$264$		0			0
$265$	−2.21062	−	3.82890i	−0.135797	−	0.235208i
$266$		0			0
$267$		0			0
$268$	−13.6402			−0.833209
$269$	7.61561	−	13.1906i	0.464332	−	0.804247i	−0.534839	−	0.844954i	$-0.679628\pi$
$269$	7.61561	−	13.1906i	0.464332	−	0.804247i	0.999171	+	0.0407073i	$0.0129611\pi$
$270$		0			0
$271$	−2.33910	−	4.05144i	−0.142090	−	0.246108i	0.786193	−	0.617981i	$-0.212049\pi$
$271$	−2.33910	−	4.05144i	−0.142090	−	0.246108i	−0.928284	+	0.371873i	$0.878716\pi$
$272$	−19.7633	+	34.2310i	−1.19832	+	2.07556i
$273$		0			0
$274$	22.4684	+	38.9164i	1.35737	+	2.35103i
$275$	1.67472	−	2.90069i	0.100989	−	0.174918i
$276$		0			0
$277$	8.19537	+	14.1948i	0.492412	+	0.852883i	0.999962	−	0.00873986i	$-0.00278202\pi$
$277$	8.19537	+	14.1948i	0.492412	+	0.852883i	−0.507550	+	0.861622i	$0.669449\pi$
$278$	−10.7280	−	18.5815i	−0.643423	−	1.11444i
$279$		0			0
$280$		0			0
$281$	−1.75702	+	3.04325i	−0.104815	+	0.181545i	−0.913663	−	0.406473i	$-0.866758\pi$
$281$	−1.75702	+	3.04325i	−0.104815	+	0.181545i	0.808848	+	0.588018i	$0.200092\pi$
$282$		0			0
$283$	−26.0708			−1.54975			−0.774874	−	0.632116i	$-0.782187\pi$
$283$	−26.0708			−1.54975			−0.774874	+	0.632116i	$0.782187\pi$
$284$	7.80050			0.462874
$285$		0			0
$286$	−5.81958	+	10.0798i	−0.344119	+	0.596031i
$287$		0			0
$288$		0			0
$289$	4.57850	+	7.93019i	0.269323	+	0.466482i
$290$	9.79455	+	16.9647i	0.575156	+	0.996199i
$291$		0			0
$292$	−1.25740	+	2.17787i	−0.0735835	+	0.127450i
$293$	−9.44192	−	16.3539i	−0.551603	−	0.955404i	−0.998159	−	0.0606487i	$-0.980683\pi$
$293$	−9.44192	−	16.3539i	−0.551603	−	0.955404i	0.446556	−	0.894756i	$-0.352650\pi$
$294$		0			0
$295$	3.62863	−	6.28497i	0.211267	−	0.365925i
$296$	−36.7242	−	63.6082i	−2.13455	−	3.69715i
$297$		0			0
$298$	−18.5559	+	32.1398i	−1.07492	+	1.86181i
$299$	0.905400			0.0523606
$300$		0			0
$301$		0			0
$302$	−5.29401	−	9.16950i	−0.304636	−	0.527645i
$303$		0			0
$304$	4.41549	+	7.64785i	0.253246	+	0.438634i
$305$	0.305392	−	0.528954i	0.0174867	−	0.0302878i
$306$		0			0
$307$	21.6407			1.23510			0.617551	−	0.786531i	$-0.288125\pi$
$307$	21.6407			1.23510			0.617551	+	0.786531i	$0.288125\pi$
$308$		0			0
$309$		0			0
$310$	−16.0016	+	27.7156i	−0.908830	+	1.57414i
$311$	4.49448			0.254859			0.127429	−	0.991848i	$-0.459327\pi$
$311$	4.49448			0.254859			0.127429	+	0.991848i	$0.459327\pi$
$312$		0			0
$313$	−8.60204			−0.486216			−0.243108	−	0.969999i	$-0.578167\pi$
$313$	−8.60204			−0.486216			−0.243108	+	0.969999i	$0.578167\pi$
$314$	0.799206			0.0451018
$315$		0			0
$316$	−84.4062			−4.74822
$317$	8.06255			0.452838			0.226419	−	0.974030i	$-0.427298\pi$
$317$	8.06255			0.452838			0.226419	+	0.974030i	$0.427298\pi$
$318$		0			0
$319$	6.13402			0.343439
$320$	20.7053	−	35.8626i	1.15746	−	2.00478i
$321$		0			0
$322$		0			0
$323$	−1.75228			−0.0974992
$324$		0			0
$325$	3.94646	−	6.83546i	0.218910	−	0.379163i
$326$	−14.5383	−	25.1811i	−0.805203	−	1.39465i
$327$		0			0
$328$	45.8981	+	79.4978i	2.53430	+	4.38953i
$329$		0			0
$330$		0			0
$331$	−22.9026			−1.25884			−0.629419	−	0.777066i	$-0.716707\pi$
$331$	−22.9026			−1.25884			−0.629419	+	0.777066i	$0.716707\pi$
$332$	−37.5681	+	65.0698i	−2.06182	+	3.57117i
$333$		0			0
$334$	4.34075	+	7.51840i	0.237515	+	0.411388i
$335$	−2.01405	+	3.48844i	−0.110039	+	0.190594i
$336$		0			0
$337$	−6.81891	−	11.8107i	−0.371450	−	0.643369i	0.618339	−	0.785911i	$-0.287806\pi$
$337$	−6.81891	−	11.8107i	−0.371450	−	0.643369i	−0.989789	+	0.142542i	$0.954472\pi$
$338$	3.93458	−	6.81489i	0.214013	−	0.370681i
$339$		0			0
$340$	11.9331	+	20.6688i	0.647164	+	1.12092i
$341$	5.01065	+	8.67869i	0.271342	+	0.469978i
$342$		0			0
$343$		0			0
$344$	−28.6502	+	49.6237i	−1.54472	+	2.67553i
$345$		0			0
$346$	−31.0543			−1.66949
$347$	2.82563			0.151688			0.0758440	−	0.997120i	$-0.475835\pi$
$347$	2.82563			0.151688			0.0758440	+	0.997120i	$0.475835\pi$
$348$		0			0
$349$	1.81202	−	3.13851i	0.0969951	−	0.168000i	−0.813444	−	0.581643i	$-0.802410\pi$
$349$	1.81202	−	3.13851i	0.0969951	−	0.168000i	0.910440	+	0.413642i	$0.135744\pi$
$350$		0			0
$351$		0			0
$352$	−13.4947	−	23.3734i	−0.719268	−	1.24581i
$353$	1.37701	+	2.38504i	0.0732907	+	0.126943i	0.900342	−	0.435184i	$-0.143317\pi$
$353$	1.37701	+	2.38504i	0.0732907	+	0.126943i	−0.827051	+	0.562127i	$0.809983\pi$
$354$		0			0
$355$	1.15179	−	1.99495i	0.0611304	−	0.105881i
$356$	6.94877	+	12.0356i	0.368284	+	0.637887i
$357$		0			0
$358$	1.49135	−	2.58310i	0.0788205	−	0.136521i
$359$	−8.40076	−	14.5505i	−0.443375	−	0.767948i	0.554562	−	0.832142i	$-0.312886\pi$
$359$	−8.40076	−	14.5505i	−0.443375	−	0.767948i	−0.997937	+	0.0641941i	$0.979552\pi$
$360$		0			0
$361$	9.30425	−	16.1154i	0.489698	−	0.848181i
$362$	−8.66163			−0.455245
$363$		0			0
$364$		0			0
$365$	0.371322	+	0.643149i	0.0194359	+	0.0336640i
$366$		0			0
$367$	−11.9670	−	20.7274i	−0.624670	−	1.08196i	−0.988605	−	0.150536i	$-0.951900\pi$
$367$	−11.9670	−	20.7274i	−0.624670	−	1.08196i	0.363934	−	0.931425i	$-0.381433\pi$
$368$	−2.01030	+	3.48193i	−0.104794	+	0.181508i
$369$		0			0
$370$	−34.5551			−1.79644
$371$		0			0
$372$		0			0
$373$	9.58030	−	16.5936i	0.496049	−	0.859182i	−0.503941	−	0.863738i	$-0.668117\pi$
$373$	9.58030	−	16.5936i	0.496049	−	0.859182i	0.999990	+	0.00455622i	$0.00145030\pi$
$374$	10.2557			0.530309
$375$		0			0
$376$	102.060			5.26334
$377$	14.4548			0.744458
$378$		0			0
$379$	10.0770			0.517622			0.258811	−	0.965928i	$-0.416669\pi$
$379$	10.0770			0.517622			0.258811	+	0.965928i	$0.416669\pi$
$380$	5.33217			0.273534
$381$		0			0
$382$	−10.5025			−0.537357
$383$	10.0718	−	17.4448i	0.514643	−	0.891388i	−0.485213	−	0.874396i	$-0.661258\pi$
$383$	10.0718	−	17.4448i	0.514643	−	0.891388i	0.999856	−	0.0169915i	$-0.00540883\pi$
$384$		0			0
$385$		0			0
$386$	−11.2294			−0.571561
$387$		0			0
$388$	−38.8372	+	67.2679i	−1.97166	+	3.41501i
$389$	6.69736	+	11.6002i	0.339570	+	0.588152i	0.984352	−	0.176215i	$-0.0563853\pi$
$389$	6.69736	+	11.6002i	0.339570	+	0.588152i	−0.644782	+	0.764366i	$0.723052\pi$
$390$		0			0
$391$	−0.398891	−	0.690899i	−0.0201728	−	0.0349402i
$392$		0			0
$393$		0			0
$394$	2.41448			0.121640
$395$	−12.4630	+	21.5866i	−0.627083	+	1.08614i
$396$		0			0
$397$	−9.00664	−	15.6000i	−0.452031	−	0.782940i	0.546482	−	0.837471i	$-0.315967\pi$
$397$	−9.00664	−	15.6000i	−0.452031	−	0.782940i	−0.998512	+	0.0545313i	$0.982634\pi$
$398$	8.58506	−	14.8698i	0.430330	−	0.745354i
$399$		0			0
$400$	17.5249	+	30.3541i	0.876247	+	1.51770i
$401$	14.4337	−	25.0000i	0.720787	−	1.24844i	−0.239898	−	0.970798i	$-0.577114\pi$
$401$	14.4337	−	25.0000i	0.720787	−	1.24844i	0.960685	−	0.277642i	$-0.0895528\pi$
$402$		0			0
$403$	11.8075	+	20.4513i	0.588176	+	1.01875i
$404$	−26.4240	−	45.7676i	−1.31464	−	2.27703i
$405$		0			0
$406$		0			0
$407$	−5.41019	+	9.37073i	−0.268173	+	0.464490i
$408$		0			0
$409$	10.8587			0.536931			0.268465	−	0.963289i	$-0.413484\pi$
$409$	10.8587			0.536931			0.268465	+	0.963289i	$0.413484\pi$
$410$	43.1872			2.13286
$411$		0			0
$412$	29.7014	−	51.4443i	1.46328	−	2.53448i
$413$		0			0
$414$		0			0
$415$	11.0943	+	19.2158i	0.544595	+	0.943267i
$416$	−31.8001	−	55.0793i	−1.55913	−	2.70049i
$417$		0			0
$418$	1.14566	−	1.98434i	0.0560359	−	0.0970570i
$419$	−0.247572	−	0.428807i	−0.0120947	−	0.0209486i	0.859915	−	0.510438i	$-0.170517\pi$
$419$	−0.247572	−	0.428807i	−0.0120947	−	0.0209486i	−0.872009	+	0.489489i	$0.837183\pi$
$420$		0			0
$421$	9.50320	−	16.4600i	0.463158	−	0.802212i	−0.535959	−	0.844244i	$-0.680050\pi$
$421$	9.50320	−	16.4600i	0.463158	−	0.802212i	0.999116	+	0.0420318i	$0.0133831\pi$
$422$	15.5113	+	26.8664i	0.755079	+	1.30784i
$423$		0			0
$424$	12.7578	−	22.0971i	0.619572	−	1.07313i
$425$	−6.95473			−0.337354
$426$		0			0
$427$		0			0
$428$	−5.16864	−	8.95234i	−0.249835	−	0.432728i
$429$		0			0
$430$	13.4790	+	23.3464i	0.650016	+	1.12586i
$431$	−8.46073	+	14.6544i	−0.407539	+	0.705878i	−0.994613	−	0.103655i	$-0.966946\pi$
$431$	−8.46073	+	14.6544i	−0.407539	+	0.705878i	0.587074	+	0.809533i	$0.300280\pi$
$432$		0			0
$433$	33.4740			1.60866			0.804330	−	0.594183i	$-0.202524\pi$
$433$	33.4740			1.60866			0.804330	+	0.594183i	$0.202524\pi$
$434$		0			0
$435$		0			0
$436$	49.9774	−	86.5634i	2.39348	−	4.14564i
$437$	−0.178239			−0.00852634
$438$		0			0
$439$	−20.9315			−0.999005			−0.499502	−	0.866313i	$-0.666484\pi$
$439$	−20.9315			−0.999005			−0.499502	+	0.866313i	$0.666484\pi$
$440$	−19.5891			−0.933874
$441$		0			0
$442$	24.1674			1.14953
$443$	30.8580			1.46611			0.733054	−	0.680170i	$-0.238094\pi$
$443$	30.8580			1.46611			0.733054	+	0.680170i	$0.238094\pi$
$444$		0			0
$445$	4.10409			0.194553
$446$	−22.6972	+	39.3128i	−1.07475	+	1.86151i
$447$		0			0
$448$		0			0
$449$	33.2789			1.57053			0.785263	−	0.619162i	$-0.212528\pi$
$449$	33.2789			1.57053			0.785263	+	0.619162i	$0.212528\pi$
$450$		0			0
$451$	6.76168	−	11.7116i	0.318395	−	0.551477i
$452$	−8.55957	−	14.8256i	−0.402608	−	0.697338i
$453$		0			0
$454$	−23.1737	−	40.1380i	−1.08760	−	1.88377i
$455$		0			0
$456$		0			0
$457$	23.7904			1.11287			0.556434	−	0.830892i	$-0.312169\pi$
$457$	23.7904			1.11287			0.556434	+	0.830892i	$0.312169\pi$
$458$	26.8654	−	46.5323i	1.25534	−	2.17431i
$459$		0			0
$460$	1.21382	+	2.10240i	0.0565947	+	0.0980249i
$461$	8.53122	−	14.7765i	0.397339	−	0.688211i	−0.596058	−	0.802941i	$-0.703267\pi$
$461$	8.53122	−	14.7765i	0.397339	−	0.688211i	0.993397	+	0.114731i	$0.0366005\pi$
$462$		0			0
$463$	18.1243	+	31.3922i	0.842306	+	1.45892i	0.887940	+	0.459959i	$0.152136\pi$
$463$	18.1243	+	31.3922i	0.842306	+	1.45892i	−0.0456338	+	0.998958i	$0.514531\pi$
$464$	−32.0945	+	55.5893i	−1.48995	+	2.58067i
$465$		0			0
$466$	8.05253	+	13.9474i	0.373026	+	0.646100i
$467$	4.09580	+	7.09413i	0.189531	+	0.328277i	0.945094	−	0.326799i	$-0.105970\pi$
$467$	4.09580	+	7.09413i	0.189531	+	0.328277i	−0.755563	+	0.655076i	$0.772637\pi$
$468$		0			0
$469$		0			0
$470$	24.0080	−	41.5830i	1.10740	−	1.91808i
$471$		0			0
$472$	41.8826			1.92780
$473$	8.44148			0.388140
$474$		0			0
$475$	−0.776909	+	1.34565i	−0.0356470	+	0.0617425i
$476$		0			0
$477$		0			0
$478$	27.2265	+	47.1577i	1.24531	+	2.15694i
$479$	12.7775	+	22.1312i	0.583817	+	1.01120i	0.995022	+	0.0996574i	$0.0317747\pi$
$479$	12.7775	+	22.1312i	0.583817	+	1.01120i	−0.411205	+	0.911543i	$0.634892\pi$
$480$		0			0
$481$	−12.7491	+	22.0820i	−0.581308	+	1.00685i
$482$	39.7614	+	68.8687i	1.81108	+	3.13688i
$483$		0			0
$484$	24.6596	−	42.7116i	1.12089	−	1.94144i
$485$	11.4690	+	19.8649i	0.520782	+	0.902020i
$486$		0			0
$487$	3.46140	−	5.99533i	0.156851	−	0.271674i	−0.776880	−	0.629648i	$-0.783199\pi$
$487$	3.46140	−	5.99533i	0.156851	−	0.271674i	0.933732	+	0.357974i	$0.116532\pi$
$488$	3.52491			0.159565
$489$		0			0
$490$		0			0
$491$	−18.7262	−	32.4348i	−0.845103	−	1.46376i	−0.885532	−	0.464578i	$-0.846206\pi$
$491$	−18.7262	−	32.4348i	−0.845103	−	1.46376i	0.0404294	−	0.999182i	$-0.487127\pi$
$492$		0			0
$493$	−6.36831	−	11.0302i	−0.286814	−	0.496777i
$494$	2.69973	−	4.67607i	0.121467	−	0.210386i
$495$		0			0
$496$	−104.867			−4.70867
$497$		0			0
$498$		0			0
$499$	−12.8125	+	22.1919i	−0.573566	+	0.993446i	0.422630	+	0.906302i	$0.361107\pi$
$499$	−12.8125	+	22.1919i	−0.573566	+	0.993446i	−0.996196	+	0.0871432i	$0.972226\pi$
$500$	63.7733			2.85203
$501$		0			0
$502$	−61.8658			−2.76121
$503$	−5.79692			−0.258472			−0.129236	−	0.991614i	$-0.541252\pi$
$503$	−5.79692			−0.258472			−0.129236	+	0.991614i	$0.541252\pi$
$504$		0			0
$505$	−15.6066			−0.694483
$506$	1.04320			0.0463757
$507$		0			0
$508$	−44.9840			−1.99584
$509$	−12.5697	+	21.7714i	−0.557144	+	0.965002i	0.440589	+	0.897709i	$0.354770\pi$
$509$	−12.5697	+	21.7714i	−0.557144	+	0.965002i	−0.997733	+	0.0672931i	$0.978564\pi$
$510$		0			0
$511$		0			0
$512$	23.9940			1.06039
$513$		0			0
$514$	32.9738	−	57.1123i	1.45441	−	2.51911i
$515$	−8.77113	−	15.1920i	−0.386502	−	0.669441i
$516$		0			0
$517$	−7.51771	−	13.0211i	−0.330629	−	0.572665i
$518$		0			0
$519$		0			0
$520$	−46.1616			−2.02432
$521$	−3.64828	+	6.31900i	−0.159834	+	0.276841i	−0.934809	−	0.355152i	$-0.884429\pi$
$521$	−3.64828	+	6.31900i	−0.159834	+	0.276841i	0.774975	+	0.631992i	$0.217763\pi$
$522$		0			0
$523$	8.38637	+	14.5256i	0.366710	+	0.635161i	0.989049	−	0.147587i	$-0.0471506\pi$
$523$	8.38637	+	14.5256i	0.366710	+	0.635161i	−0.622339	+	0.782748i	$0.713817\pi$
$524$	32.1580	−	55.6993i	1.40483	−	2.43324i
$525$		0			0
$526$	−11.6908	−	20.2490i	−0.509741	−	0.882898i
$527$	10.4041	−	18.0204i	0.453208	−	0.784979i
$528$		0			0
$529$	11.4594	+	19.8483i	0.498236	+	0.862970i
$530$	−6.00212	−	10.3960i	−0.260716	−	0.451573i
$531$		0			0
$532$		0			0
$533$	15.9339	−	27.5982i	0.690172	−	1.19541i
$534$		0			0
$535$	−3.05271			−0.131980
$536$	−23.2467			−1.00411
$537$		0			0
$538$	20.6774	−	35.8143i	0.891466	−	1.54406i
$539$		0			0
$540$		0			0
$541$	2.64908	+	4.58834i	0.113893	+	0.197268i	0.917337	−	0.398112i	$-0.130335\pi$
$541$	2.64908	+	4.58834i	0.113893	+	0.197268i	−0.803444	+	0.595381i	$0.797001\pi$
$542$	−6.35097	−	11.0002i	−0.272798	−	0.472499i
$543$		0			0
$544$	−28.0202	+	48.5324i	−1.20136	+	2.08081i
$545$	−14.7589	−	25.5631i	−0.632200	−	1.09500i
$546$		0			0
$547$	16.4325	−	28.4619i	0.702603	−	1.21694i	−0.264947	−	0.964263i	$-0.585354\pi$
$547$	16.4325	−	28.4619i	0.702603	−	1.21694i	0.967550	−	0.252681i	$-0.0813123\pi$
$548$	44.4542	+	76.9970i	1.89899	+	3.28915i
$549$		0			0
$550$	4.54708	−	7.87577i	0.193888	−	0.335824i
$551$	−2.84560			−0.121227
$552$		0			0
$553$		0			0
$554$	22.2515	+	38.5408i	0.945376	+	1.63744i
$555$		0			0
$556$	−21.2256	−	36.7638i	−0.900166	−	1.55913i
$557$	−9.40798	+	16.2951i	−0.398629	+	0.690446i	−0.993557	−	0.113333i	$-0.963847\pi$
$557$	−9.40798	+	16.2951i	−0.398629	+	0.690446i	0.594928	+	0.803779i	$0.297181\pi$
$558$		0			0
$559$	19.8923			0.841354
$560$		0			0
$561$		0			0
$562$	−4.77054	+	8.26282i	−0.201233	+	0.348546i
$563$	27.6650			1.16594			0.582970	−	0.812494i	$-0.301891\pi$
$563$	27.6650			1.16594			0.582970	+	0.812494i	$0.301891\pi$
$564$		0			0
$565$	−5.05547			−0.212685
$566$	−70.7856			−2.97534
$567$		0			0
$568$	13.2942			0.557812
$569$	40.1831			1.68456			0.842282	−	0.539037i	$-0.181212\pi$
$569$	40.1831			1.68456			0.842282	+	0.539037i	$0.181212\pi$
$570$		0			0
$571$	−6.81129			−0.285044			−0.142522	−	0.989792i	$-0.545521\pi$
$571$	−6.81129			−0.285044			−0.142522	+	0.989792i	$0.545521\pi$
$572$	−11.5142	+	19.9431i	−0.481431	+	0.833863i
$573$		0			0
$574$		0			0
$575$	−0.707427			−0.0295017
$576$		0			0
$577$	−18.2111	+	31.5425i	−0.758138	+	1.31313i	0.185661	+	0.982614i	$0.440557\pi$
$577$	−18.2111	+	31.5425i	−0.758138	+	1.31313i	−0.943799	+	0.330519i	$0.892776\pi$
$578$	12.4312	+	21.5315i	0.517071	+	0.895593i
$579$		0			0
$580$	19.3787	+	33.5649i	0.804658	+	1.39371i
$581$		0			0
$582$		0			0
$583$	−3.75894			−0.155679
$584$	−2.14295	+	3.71170i	−0.0886759	+	0.153591i
$585$		0			0
$586$	−25.6361	−	44.4030i	−1.05902	−	1.83427i
$587$	5.57943	−	9.66385i	0.230288	−	0.398870i	−0.727605	−	0.685996i	$-0.759367\pi$
$587$	5.57943	−	9.66385i	0.230288	−	0.398870i	0.957893	+	0.287126i	$0.0927000\pi$
$588$		0			0
$589$	−2.32446	−	4.02609i	−0.0957779	−	0.165892i
$590$	9.85220	−	17.0645i	0.405609	−	0.702535i
$591$		0			0
$592$	−56.6145	−	98.0593i	−2.32684	−	4.03021i
$593$	−9.90427	−	17.1547i	−0.406720	−	0.704459i	0.587800	−	0.809006i	$-0.299994\pi$
$593$	−9.90427	−	17.1547i	−0.406720	−	0.704459i	−0.994520	+	0.104547i	$0.966661\pi$
$594$		0			0
$595$		0			0
$596$	−36.7133	+	63.5893i	−1.50384	+	2.60472i
$597$		0			0
$598$	2.45828			0.100527
$599$	18.1320			0.740853			0.370427	−	0.928862i	$-0.379211\pi$
$599$	18.1320			0.740853			0.370427	+	0.928862i	$0.379211\pi$
$600$		0			0
$601$	12.3285	−	21.3536i	0.502889	−	0.871030i	−0.497105	−	0.867690i	$-0.665604\pi$
$601$	12.3285	−	21.3536i	0.502889	−	0.871030i	0.999994	−	0.00333942i	$-0.00106297\pi$
$602$		0			0
$603$		0			0
$604$	−10.4743	−	18.1420i	−0.426194	−	0.738189i
$605$	−7.28223	−	12.6132i	−0.296065	−	0.512799i
$606$		0			0
$607$	8.63876	−	14.9628i	0.350637	−	0.607320i	−0.635725	−	0.771916i	$-0.719299\pi$
$607$	8.63876	−	14.9628i	0.350637	−	0.607320i	0.986361	+	0.164596i	$0.0526319\pi$
$608$	6.26024	+	10.8431i	0.253886	+	0.439744i
$609$		0			0
$610$	0.829179	−	1.43618i	0.0335725	−	0.0581492i
$611$	−17.7154	−	30.6840i	−0.716689	−	1.24134i
$612$		0			0
$613$	−9.77828	+	16.9365i	−0.394941	+	0.684058i	−0.993094	−	0.117324i	$-0.962568\pi$
$613$	−9.77828	+	16.9365i	−0.394941	+	0.684058i	0.598153	+	0.801382i	$0.295902\pi$
$614$	58.7575			2.37126
$615$		0			0
$616$		0			0
$617$	−10.8723	−	18.8314i	−0.437702	−	0.758122i	0.559810	−	0.828621i	$-0.310874\pi$
$617$	−10.8723	−	18.8314i	−0.437702	−	0.758122i	−0.997512	+	0.0704988i	$0.977541\pi$
$618$		0			0
$619$	16.9024	+	29.2758i	0.679366	+	1.17670i	0.975172	+	0.221448i	$0.0710782\pi$
$619$	16.9024	+	29.2758i	0.679366	+	1.17670i	−0.295807	+	0.955248i	$0.595588\pi$
$620$	−31.6595	+	54.8359i	−1.27148	+	2.20226i
$621$		0			0
$622$	12.2031			0.489300
$623$		0			0
$624$		0			0
$625$	3.20808	−	5.55655i	0.128323	−	0.222262i
$626$	−23.3557			−0.933481
$627$		0			0
$628$	1.58125			0.0630986
$629$	22.4674			0.895832
$630$		0			0
$631$	−23.6410			−0.941134			−0.470567	−	0.882364i	$-0.655951\pi$
$631$	−23.6410			−0.941134			−0.470567	+	0.882364i	$0.655951\pi$
$632$	−143.852			−5.72211
$633$		0			0
$634$	21.8909			0.869399
$635$	−6.64213	+	11.5045i	−0.263585	+	0.456542i
$636$		0			0
$637$		0			0
$638$	16.6547			0.659365
$639$		0			0
$640$	24.4729	−	42.3883i	0.967375	−	1.67554i
$641$	7.95901	+	13.7854i	0.314362	+	0.544491i	0.979302	−	0.202406i	$-0.0648760\pi$
$641$	7.95901	+	13.7854i	0.314362	+	0.544491i	−0.664940	+	0.746897i	$0.731543\pi$
$642$		0			0
$643$	13.2527	+	22.9544i	0.522636	+	0.905231i	0.999653	+	0.0263376i	$0.00838450\pi$
$643$	13.2527	+	22.9544i	0.522636	+	0.905231i	−0.477017	+	0.878894i	$0.658282\pi$
$644$		0			0
$645$		0			0
$646$	−4.75766			−0.187188
$647$	−0.00801958	+	0.0138903i	−0.000315282	+	0.000546085i	−0.866183	−	0.499727i	$-0.833434\pi$
$647$	−0.00801958	+	0.0138903i	−0.000315282	+	0.000546085i	0.865868	+	0.500273i	$0.166767\pi$
$648$		0			0
$649$	−3.08506	−	5.34348i	−0.121099	−	0.209750i
$650$	10.7152	−	18.5592i	0.420283	−	0.727951i
$651$		0			0
$652$	−28.7644	−	49.8214i	−1.12650	−	1.95115i
$653$	−16.6440	+	28.8282i	−0.651328	+	1.12813i	0.331473	+	0.943465i	$0.392455\pi$
$653$	−16.6440	+	28.8282i	−0.651328	+	1.12813i	−0.982801	+	0.184669i	$0.940879\pi$
$654$		0			0
$655$	−9.49661	−	16.4486i	−0.371063	−	0.642700i
$656$	70.7571	+	122.555i	2.76260	+	4.78497i
$657$		0			0
$658$		0			0
$659$	−19.4156	+	33.6288i	−0.756324	+	1.30999i	0.188389	+	0.982094i	$0.439673\pi$
$659$	−19.4156	+	33.6288i	−0.756324	+	1.30999i	−0.944713	+	0.327897i	$0.893660\pi$
$660$		0			0
$661$	−5.30644			−0.206397			−0.103198	−	0.994661i	$-0.532908\pi$
$661$	−5.30644			−0.206397			−0.103198	+	0.994661i	$0.532908\pi$
$662$	−62.1835			−2.41683
$663$		0			0
$664$	−64.0264	+	110.897i	−2.48471	+	4.30364i
$665$		0			0
$666$		0			0
$667$	−0.647777	−	1.12198i	−0.0250820	−	0.0434433i
$668$	8.58826	+	14.8753i	0.332290	+	0.575543i
$669$		0			0
$670$	−5.46842	+	9.47158i	−0.211263	+	0.365919i
$671$	−0.259644	−	0.449717i	−0.0100235	−	0.0173611i
$672$		0			0
$673$	−3.03565	+	5.25789i	−0.117016	+	0.202677i	−0.918584	−	0.395227i	$-0.870666\pi$
$673$	−3.03565	+	5.25789i	−0.117016	+	0.202677i	0.801568	+	0.597903i	$0.203999\pi$
$674$	−18.5142	−	32.0676i	−0.713142	−	1.23520i
$675$		0			0
$676$	7.78465	−	13.4834i	0.299410	−	0.518593i
$677$	−34.7850			−1.33690			−0.668449	−	0.743758i	$-0.733041\pi$
$677$	−34.7850			−1.33690			−0.668449	+	0.743758i	$0.733041\pi$
$678$		0			0
$679$		0			0
$680$	20.3373	+	35.2253i	0.779901	+	1.35083i
$681$		0			0
$682$	13.6046	+	23.5638i	0.520946	+	0.902305i
$683$	9.71206	−	16.8218i	0.371622	−	0.643667i	−0.618194	−	0.786026i	$-0.712135\pi$
$683$	9.71206	−	16.8218i	0.371622	−	0.643667i	0.989815	+	0.142358i	$0.0454686\pi$
$684$		0			0
$685$	26.2556			1.00318
$686$		0			0
$687$		0			0
$688$	−44.1676	+	76.5006i	−1.68387	+	2.91656i
$689$	−8.85791			−0.337459
$690$		0			0
$691$	6.63675			0.252474			0.126237	−	0.992000i	$-0.459710\pi$
$691$	6.63675			0.252474			0.126237	+	0.992000i	$0.459710\pi$
$692$	−61.4416			−2.33566
$693$		0			0
$694$	7.67197			0.291224
$695$	−12.5363			−0.475529
$696$		0			0
$697$	−28.0798			−1.06360
$698$	4.91987	−	8.52147i	0.186220	−	0.322542i
$699$		0			0
$700$		0			0
$701$	13.9153			0.525574			0.262787	−	0.964854i	$-0.415358\pi$
$701$	13.9153			0.525574			0.262787	+	0.964854i	$0.415358\pi$
$702$		0			0
$703$	2.50982	−	4.34713i	0.0946595	−	0.163955i
$704$	−17.6036	−	30.4904i	−0.663462	−	1.14915i
$705$		0			0
$706$	3.73876	+	6.47571i	0.140710	+	0.243717i
$707$		0			0
$708$		0			0
$709$	34.1556			1.28274			0.641370	−	0.767231i	$-0.278366\pi$
$709$	34.1556			1.28274			0.641370	+	0.767231i	$0.278366\pi$
$710$	3.12725	−	5.41655i	0.117364	−	0.203280i
$711$		0			0
$712$	11.8426	+	20.5120i	0.443821	+	0.768721i
$713$	1.05829	−	1.83301i	0.0396332	−	0.0686467i
$714$		0			0
$715$	3.40025	+	5.88941i	0.127162	+	0.220251i
$716$	2.95068	−	5.11072i	0.110272	−	0.190997i
$717$		0			0
$718$	−22.8092	−	39.5066i	−0.851231	−	1.47437i
$719$	22.1450	+	38.3563i	0.825870	+	1.43045i	0.901253	+	0.433294i	$0.142649\pi$
$719$	22.1450	+	38.3563i	0.825870	+	1.43045i	−0.0753825	+	0.997155i	$0.524018\pi$
$720$		0			0
$721$		0			0
$722$	25.2623	−	43.7556i	0.940165	−	1.62841i
$723$		0			0
$724$	−17.1372			−0.636899
$725$	−11.2941			−0.419453
$726$		0			0
$727$	−14.1247	+	24.4647i	−0.523857	+	0.907346i	0.475758	+	0.879576i	$0.342174\pi$
$727$	−14.1247	+	24.4647i	−0.523857	+	0.907346i	−0.999614	+	0.0277700i	$0.991159\pi$
$728$		0			0
$729$		0			0
$730$	1.00819	+	1.74623i	0.0373147	+	0.0646310i
$731$	−8.76391	−	15.1795i	−0.324145	−	0.561435i
$732$		0			0
$733$	−12.5084	+	21.6653i	−0.462010	+	0.800225i	−0.999061	−	0.0433249i	$-0.986205\pi$
$733$	−12.5084	+	21.6653i	−0.462010	+	0.800225i	0.537051	+	0.843550i	$0.319538\pi$
$734$	−32.4919	−	56.2776i	−1.19930	−	2.07724i
$735$		0			0
$736$	−2.85018	+	4.93666i	−0.105059	+	0.181968i
$737$	1.71235	+	2.96587i	0.0630752	+	0.109249i
$738$		0			0
$739$	−16.0115	+	27.7327i	−0.588992	+	1.02016i	0.405373	+	0.914151i	$0.367142\pi$
$739$	−16.0115	+	27.7327i	−0.588992	+	1.02016i	−0.994365	+	0.106013i	$0.966192\pi$
$740$	−68.3680			−2.51326
$741$		0			0
$742$		0			0
$743$	−19.4031	−	33.6072i	−0.711833	−	1.23293i	−0.964169	−	0.265290i	$-0.914532\pi$
$743$	−19.4031	−	33.6072i	−0.711833	−	1.23293i	0.252336	−	0.967640i	$-0.418801\pi$
$744$		0			0
$745$	10.8418	+	18.7786i	0.397214	+	0.687995i
$746$	26.0118	−	45.0537i	0.952359	−	1.64953i
$747$		0			0
$748$	20.2911			0.741915
$749$		0			0
$750$		0			0
$751$	−10.8495	+	18.7920i	−0.395905	+	0.685728i	−0.993216	−	0.116282i	$-0.962903\pi$
$751$	−10.8495	+	18.7920i	−0.395905	+	0.685728i	0.597311	+	0.802010i	$0.296236\pi$
$752$	157.337			5.73749
$753$		0			0
$754$	39.2466			1.42928
$755$	−6.18635			−0.225144
$756$		0			0
$757$	33.5242			1.21846			0.609229	−	0.792995i	$-0.291479\pi$
$757$	33.5242			1.21846			0.609229	+	0.792995i	$0.291479\pi$
$758$	27.3605			0.993778
$759$		0			0
$760$	9.08748			0.329638
$761$	6.66048	−	11.5363i	0.241442	−	0.418190i	−0.719683	−	0.694303i	$-0.755713\pi$
$761$	6.66048	−	11.5363i	0.241442	−	0.418190i	0.961125	+	0.276113i	$0.0890462\pi$
$762$		0			0
$763$		0			0
$764$	−20.7795			−0.751775
$765$		0			0
$766$	27.3462	−	47.3649i	0.988057	−	1.71137i
$767$	−7.26992	−	12.5919i	−0.262502	−	0.454666i
$768$		0			0
$769$	−27.3568	−	47.3833i	−0.986510	−	1.70869i	−0.635022	−	0.772494i	$-0.719009\pi$
$769$	−27.3568	−	47.3833i	−0.986510	−	1.70869i	−0.351488	−	0.936192i	$-0.614324\pi$
$770$		0			0
$771$		0			0
$772$	−22.2176			−0.799628
$773$	−1.18021	+	2.04418i	−0.0424491	+	0.0735240i	−0.886469	−	0.462787i	$-0.846849\pi$
$773$	−1.18021	+	2.04418i	−0.0424491	+	0.0735240i	0.844020	+	0.536311i	$0.180183\pi$
$774$		0			0
$775$	−9.22573	−	15.9794i	−0.331398	−	0.573998i
$776$	−66.1892	+	114.643i	−2.37606	+	4.11545i
$777$		0			0
$778$	18.1842	+	31.4960i	0.651936	+	1.12919i
$779$	−3.13678	+	5.43306i	−0.112387	+	0.194660i
$780$		0			0
$781$	−0.979248	−	1.69611i	−0.0350403	−	0.0606915i
$782$	−1.08304	−	1.87588i	−0.0387295	−	0.0670814i
$783$		0			0
$784$		0			0
$785$	0.233479	−	0.404398i	0.00833323	−	0.0144336i
$786$		0			0
$787$	1.66794			0.0594557			0.0297278	−	0.999558i	$-0.490536\pi$
$787$	1.66794			0.0594557			0.0297278	+	0.999558i	$0.490536\pi$
$788$	4.77709			0.170177
$789$		0			0
$790$	−33.8388	+	58.6105i	−1.20393	+	2.08527i
$791$		0			0
$792$		0			0
$793$	−0.611849	−	1.05975i	−0.0217274	−	0.0376330i
$794$	−24.4542	−	42.3560i	−0.867848	−	1.50316i
$795$		0			0
$796$	16.9857	−	29.4201i	0.602043	−	1.04277i
$797$	−14.3148	−	24.7939i	−0.507055	−	0.878244i	−0.999967	−	0.00816511i	$-0.997401\pi$
$797$	−14.3148	−	24.7939i	−0.507055	−	0.878244i	0.492912	−	0.870079i	$-0.335932\pi$
$798$		0			0
$799$	−15.6097	+	27.0368i	−0.552232	+	0.956493i
$800$	24.8467	+	43.0358i	0.878464	+	1.52154i
$801$		0			0
$802$	39.1895	−	67.8783i	1.38383	−	2.39687i
$803$	0.631397			0.0222815
$804$		0			0
$805$		0			0
$806$	32.0591	+	55.5279i	1.12923	+	1.95589i
$807$		0			0
$808$	−45.0337	−	78.0007i	−1.58428	−	2.74406i
$809$	−1.42846	+	2.47416i	−0.0502219	+	0.0869868i	−0.890043	−	0.455876i	$-0.849326\pi$
$809$	−1.42846	+	2.47416i	−0.0502219	+	0.0869868i	0.839822	+	0.542862i	$0.182660\pi$
$810$		0			0
$811$	−26.2917			−0.923225			−0.461613	−	0.887082i	$-0.652729\pi$
$811$	−26.2917			−0.923225			−0.461613	+	0.887082i	$0.652729\pi$
$812$		0			0
$813$		0			0
$814$	−14.6894	+	25.4428i	−0.514863	+	0.891769i
$815$	−16.9889			−0.595094
$816$		0			0
$817$	−3.91605			−0.137005
$818$	29.4829			1.03085
$819$		0			0
$820$	85.4467			2.98393
$821$	2.65849			0.0927821			0.0463910	−	0.998923i	$-0.485228\pi$
$821$	2.65849			0.0927821			0.0463910	+	0.998923i	$0.485228\pi$
$822$		0			0
$823$	−12.2154			−0.425801			−0.212901	−	0.977074i	$-0.568291\pi$
$823$	−12.2154			−0.425801			−0.212901	+	0.977074i	$0.568291\pi$
$824$	50.6193	−	87.6752i	1.76341	−	3.05431i
$825$		0			0
$826$		0			0
$827$	−9.15812			−0.318459			−0.159230	−	0.987242i	$-0.550901\pi$
$827$	−9.15812			−0.318459			−0.159230	+	0.987242i	$0.550901\pi$
$828$		0			0
$829$	9.17156	−	15.8856i	0.318541	−	0.551730i	−0.661642	−	0.749819i	$-0.730140\pi$
$829$	9.17156	−	15.8856i	0.318541	−	0.551730i	0.980184	+	0.198089i	$0.0634737\pi$
$830$	30.1224	+	52.1735i	1.04556	+	1.81097i
$831$		0			0
$832$	−41.4828	−	71.8503i	−1.43816	−	2.49096i
$833$		0			0
$834$		0			0
$835$	5.07241			0.175538
$836$	2.26670	−	3.92605i	0.0783956	−	0.135785i
$837$		0			0
$838$	−0.672190	−	1.16427i	−0.0232204	−	0.0402190i
$839$	−9.47055	+	16.4035i	−0.326960	+	0.566311i	−0.981907	−	0.189364i	$-0.939357\pi$
$839$	−9.47055	+	16.4035i	−0.326960	+	0.566311i	0.654947	+	0.755675i	$0.272691\pi$
$840$		0			0
$841$	4.15821	+	7.20224i	0.143387	+	0.248353i
$842$	25.8024	−	44.6911i	0.889211	−	1.54016i
$843$		0			0
$844$	30.6895	+	53.1557i	1.05637	+	1.82969i
$845$	−2.29889	−	3.98179i	−0.0790842	−	0.136978i
$846$		0			0
$847$		0			0
$848$	19.6676	−	34.0652i	0.675387	−	1.16980i
$849$		0			0
$850$	−18.8830			−0.647682
$851$	2.28535			0.0783408
$852$		0			0
$853$	9.97922	−	17.2845i	0.341682	−	0.591811i	−0.643063	−	0.765813i	$-0.722337\pi$
$853$	9.97922	−	17.2845i	0.341682	−	0.591811i	0.984745	+	0.174002i	$0.0556701\pi$
$854$		0			0
$855$		0			0
$856$	−8.80878	−	15.2573i	−0.301078	−	0.521482i
$857$	8.20001	+	14.2028i	0.280107	+	0.485159i	0.971411	−	0.237405i	$-0.0762967\pi$
$857$	8.20001	+	14.2028i	0.280107	+	0.485159i	−0.691304	+	0.722564i	$0.742963\pi$
$858$		0			0
$859$	16.8575	−	29.1981i	0.575172	−	0.996226i	−0.420851	−	0.907130i	$-0.638269\pi$
$859$	16.8575	−	29.1981i	0.575172	−	0.996226i	0.996023	−	0.0890968i	$-0.0283980\pi$
$860$	26.6685	+	46.1912i	0.909389	+	1.57511i
$861$		0			0
$862$	−22.9720	+	39.7887i	−0.782429	+	1.35521i
$863$	−14.3415	−	24.8403i	−0.488191	−	0.845572i	0.511716	−	0.859154i	$-0.329010\pi$
$863$	−14.3415	−	24.8403i	−0.488191	−	0.845572i	−0.999908	+	0.0135822i	$0.995677\pi$
$864$		0			0
$865$	−9.07219	+	15.7135i	−0.308464	+	0.534275i
$866$	90.8865			3.08845
$867$		0			0
$868$		0			0
$869$	10.5961	+	18.3529i	0.359447	+	0.622581i
$870$		0			0
$871$	4.03513	+	6.98906i	0.136725	+	0.236815i
$872$	85.1753	−	147.528i	2.88440	−	4.99593i
$873$		0			0
$874$	−0.483944			−0.0163696
$875$		0			0
$876$		0			0
$877$	14.7621	−	25.5688i	0.498482	−	0.863396i	−0.501517	−	0.865148i	$-0.667224\pi$
$877$	14.7621	−	25.5688i	0.498482	−	0.863396i	0.999998	+	0.00175202i	$0.000557684\pi$
$878$	−56.8317			−1.91798
$879$		0			0
$880$	−30.1988			−1.01800
$881$	57.5032			1.93733			0.968666	−	0.248366i	$-0.0798934\pi$
$881$	57.5032			1.93733			0.968666	+	0.248366i	$0.0798934\pi$
$882$		0			0
$883$	19.8715			0.668730			0.334365	−	0.942444i	$-0.391478\pi$
$883$	19.8715			0.668730			0.334365	+	0.942444i	$0.391478\pi$
$884$	47.8158			1.60822
$885$		0			0
$886$	83.7836			2.81477
$887$	−18.5475	+	32.1253i	−0.622766	+	1.07866i	0.366203	+	0.930535i	$0.380658\pi$
$887$	−18.5475	+	32.1253i	−0.622766	+	1.07866i	−0.988968	+	0.148127i	$0.952676\pi$
$888$		0			0
$889$		0			0
$890$	11.1432			0.373519
$891$		0			0
$892$	−44.9070	+	77.7812i	−1.50360	+	2.60431i
$893$	3.48750	+	6.04053i	0.116705	+	0.202139i
$894$		0			0
$895$	−0.871366	−	1.50925i	−0.0291266	−	0.0504487i
$896$		0			0
$897$		0			0
$898$	90.3565			3.01524
$899$	16.8956	−	29.2641i	0.563501	−	0.976012i
$900$		0			0
$901$	3.90251	+	6.75935i	0.130012	+	0.225187i
$902$	18.3589	−	31.7985i	0.611284	−	1.05877i
$903$		0			0
$904$	−14.5879	−	25.2669i	−0.485185	−	0.840366i
$905$	−2.53040	+	4.38278i	−0.0841133	+	0.145689i
$906$		0			0
$907$	−12.2044	−	21.1386i	−0.405240	−	0.701896i	0.589110	−	0.808053i	$-0.299479\pi$
$907$	−12.2044	−	21.1386i	−0.405240	−	0.701896i	−0.994349	+	0.106157i	$0.966145\pi$
$908$	−45.8496	−	79.4139i	−1.52157	−	2.63544i
$909$		0			0
$910$		0			0
$911$	12.5493	−	21.7360i	0.415776	−	0.720146i	−0.579733	−	0.814806i	$-0.696843\pi$
$911$	12.5493	−	21.7360i	0.415776	−	0.720146i	0.995510	+	0.0946604i	$0.0301765\pi$
$912$		0			0
$913$	18.8647			0.624330
$914$	64.5941			2.13658
$915$		0			0
$916$	53.1538	−	92.0652i	1.75625	−	3.04192i
$917$		0			0
$918$		0			0
$919$	14.2988	+	24.7662i	0.471674	+	0.816963i	0.999475	−	0.0324050i	$-0.0103167\pi$
$919$	14.2988	+	24.7662i	0.471674	+	0.816963i	−0.527801	+	0.849368i	$0.676983\pi$
$920$	2.06869	+	3.58307i	0.0682026	+	0.118130i
$921$		0			0
$922$	23.1634	−	40.1202i	0.762846	−	1.32129i
$923$	−2.30759	−	3.99686i	−0.0759553	−	0.131558i
$924$		0			0
$925$	9.96139	−	17.2536i	0.327528	−	0.567296i
$926$	49.2098	+	85.2339i	1.61713	+	2.80096i
$927$		0			0
$928$	−45.5033	+	78.8140i	−1.49372	+	2.58720i
$929$	−45.4570			−1.49140			−0.745698	−	0.666284i	$-0.767884\pi$
$929$	−45.4570			−1.49140			−0.745698	+	0.666284i	$0.767884\pi$
$930$		0			0
$931$		0			0
$932$	15.9321	+	27.5952i	0.521873	+	0.903910i
$933$		0			0
$934$	11.1206	+	19.2615i	0.363878	+	0.630256i
$935$	2.99609	−	5.18937i	0.0979825	−	0.169711i
$936$		0			0
$937$	−27.0083			−0.882322			−0.441161	−	0.897428i	$-0.645433\pi$
$937$	−27.0083			−0.882322			−0.441161	+	0.897428i	$0.645433\pi$
$938$		0			0
$939$		0			0
$940$	47.5002	−	82.2728i	1.54929	−	2.68344i
$941$	12.7131			0.414436			0.207218	−	0.978295i	$-0.433559\pi$
$941$	12.7131			0.414436			0.207218	+	0.978295i	$0.433559\pi$
$942$		0			0
$943$	−2.85624			−0.0930121
$944$	64.5667			2.10147
$945$		0			0
$946$	22.9197			0.745185
$947$	−47.5447			−1.54500			−0.772498	−	0.635017i	$-0.780993\pi$
$947$	−47.5447			−1.54500			−0.772498	+	0.635017i	$0.780993\pi$
$948$		0			0
$949$	1.48788			0.0482987
$950$	−2.10941	+	3.65361i	−0.0684384	+	0.118539i
$951$		0			0
$952$		0			0
$953$	−38.2355			−1.23857			−0.619285	−	0.785166i	$-0.712577\pi$
$953$	−38.2355			−1.23857			−0.619285	+	0.785166i	$0.712577\pi$
$954$		0			0
$955$	−3.06820	+	5.31428i	−0.0992847	+	0.171966i
$956$	53.8682	+	93.3024i	1.74222	+	3.01762i
$957$		0			0
$958$	34.6925	+	60.0891i	1.12086	+	1.94139i
$959$		0			0
$960$		0			0
$961$	24.2056			0.780826
$962$	−34.6154	+	59.9557i	−1.11605	+	1.93305i
$963$		0			0
$964$	78.6687	+	136.258i	2.53375	+	4.38858i
$965$	−3.28054	+	5.68207i	−0.105604	+	0.182912i
$966$		0			0
$967$	−20.4093	−	35.3499i	−0.656317	−	1.13678i	−0.981562	−	0.191145i	$-0.938780\pi$
$967$	−20.4093	−	35.3499i	−0.656317	−	1.13678i	0.325244	−	0.945630i	$-0.394553\pi$
$968$	42.0267	−	72.7924i	1.35079	−	2.33964i
$969$		0			0
$970$	31.1399	+	53.9359i	0.999843	+	1.73178i
$971$	−22.4735	−	38.9253i	−0.721210	−	1.24917i	−0.960515	−	0.278228i	$-0.910253\pi$
$971$	−22.4735	−	38.9253i	−0.721210	−	1.24917i	0.239305	−	0.970944i	$-0.423080\pi$
$972$		0			0
$973$		0			0
$974$	9.39817	−	16.2781i	0.301137	−	0.521584i
$975$		0			0
$976$	5.43405			0.173940
$977$	−53.5104			−1.71195			−0.855974	−	0.517018i	$-0.827042\pi$
$977$	−53.5104			−1.71195			−0.855974	+	0.517018i	$0.827042\pi$
$978$		0			0
$979$	1.74465	−	3.02182i	0.0557593	−	0.0965779i
$980$		0			0
$981$		0			0
$982$	−50.8442	−	88.0647i	−1.62250	−	2.81026i
$983$	−5.80278	−	10.0507i	−0.185080	−	0.320568i	0.758524	−	0.651646i	$-0.225921\pi$
$983$	−5.80278	−	10.0507i	−0.185080	−	0.320568i	−0.943603	+	0.331078i	$0.892588\pi$
$984$		0			0
$985$	0.705363	−	1.22172i	0.0224747	−	0.0389274i
$986$	−17.2908	−	29.9485i	−0.550651	−	0.953756i
$987$		0			0
$988$	5.34147	−	9.25170i	0.169935	−	0.294336i
$989$	−0.891454	−	1.54404i	−0.0283466	−	0.0490977i
$990$		0			0
$991$	−13.0046	+	22.5246i	−0.413104	+	0.715517i	−0.995227	−	0.0975835i	$-0.968889\pi$
$991$	−13.0046	+	22.5246i	−0.413104	+	0.715517i	0.582123	+	0.813100i	$0.302222\pi$
$992$	−148.680			−4.72058
$993$		0			0
$994$		0			0
$995$	−5.01607	−	8.68808i	−0.159020	−	0.275431i
$996$		0			0
$997$	−23.4499	−	40.6164i	−0.742666	−	1.28633i	−0.951277	−	0.308336i	$-0.900228\pi$
$997$	−23.4499	−	40.6164i	−0.742666	−	1.28633i	0.208612	−	0.977999i	$-0.433105\pi$
$998$	−34.7876	+	60.2539i	−1.10118	+	1.90731i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.h.802.11		24
3.2	odd	2		441.2.h.h.214.1		24
7.2	even	3		1323.2.g.h.667.2		24
7.3	odd	6		1323.2.f.h.883.2		24
7.4	even	3		1323.2.f.h.883.1		24
7.5	odd	6		1323.2.g.h.667.1		24
7.6	odd	2	inner	1323.2.h.h.802.12		24
9.4	even	3		1323.2.g.h.361.2		24
9.5	odd	6		441.2.g.h.67.12		24
21.2	odd	6		441.2.g.h.79.12		24
21.5	even	6		441.2.g.h.79.11		24
21.11	odd	6		441.2.f.h.295.11	yes	24
21.17	even	6		441.2.f.h.295.12	yes	24
21.20	even	2		441.2.h.h.214.2		24
63.4	even	3		1323.2.f.h.442.1		24
63.5	even	6		441.2.h.h.373.2		24
63.11	odd	6		3969.2.a.bh.1.2		12
63.13	odd	6		1323.2.g.h.361.1		24
63.23	odd	6		441.2.h.h.373.1		24
63.25	even	3		3969.2.a.bi.1.11		12
63.31	odd	6		1323.2.f.h.442.2		24
63.32	odd	6		441.2.f.h.148.11	✓	24
63.38	even	6		3969.2.a.bh.1.1		12
63.40	odd	6	inner	1323.2.h.h.226.12		24
63.41	even	6		441.2.g.h.67.11		24
63.52	odd	6		3969.2.a.bi.1.12		12
63.58	even	3	inner	1323.2.h.h.226.11		24
63.59	even	6		441.2.f.h.148.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.11	✓	24	63.32	odd	6
441.2.f.h.148.12	yes	24	63.59	even	6
441.2.f.h.295.11	yes	24	21.11	odd	6
441.2.f.h.295.12	yes	24	21.17	even	6
441.2.g.h.67.11		24	63.41	even	6
441.2.g.h.67.12		24	9.5	odd	6
441.2.g.h.79.11		24	21.5	even	6
441.2.g.h.79.12		24	21.2	odd	6
441.2.h.h.214.1		24	3.2	odd	2
441.2.h.h.214.2		24	21.20	even	2
441.2.h.h.373.1		24	63.23	odd	6
441.2.h.h.373.2		24	63.5	even	6
1323.2.f.h.442.1		24	63.4	even	3
1323.2.f.h.442.2		24	63.31	odd	6
1323.2.f.h.883.1		24	7.4	even	3
1323.2.f.h.883.2		24	7.3	odd	6
1323.2.g.h.361.1		24	63.13	odd	6
1323.2.g.h.361.2		24	9.4	even	3
1323.2.g.h.667.1		24	7.5	odd	6
1323.2.g.h.667.2		24	7.2	even	3
1323.2.h.h.226.11		24	63.58	even	3	inner
1323.2.h.h.226.12		24	63.40	odd	6	inner
1323.2.h.h.802.11		24	1.1	even	1	trivial
1323.2.h.h.802.12		24	7.6	odd	2	inner
3969.2.a.bh.1.1		12	63.38	even	6
3969.2.a.bh.1.2		12	63.11	odd	6
3969.2.a.bi.1.11		12	63.25	even	3
3969.2.a.bi.1.12		12	63.52	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.71513 q^{2} +5.37195 q^{4} +(0.793197 - 1.37386i) q^{5} +9.15528 q^{8} +O(q^{10})\)	\(q+2.71513 q^{2} +5.37195 q^{4} +(0.793197 - 1.37386i) q^{5} +9.15528 q^{8} +(2.15363 - 3.73020i) q^{10} +(-0.674376 - 1.16805i) q^{11} +(-1.58916 - 2.75251i) q^{13} +14.1139 q^{16} +(-1.40027 + 2.42534i) q^{17} +(0.312846 + 0.541866i) q^{19} +(4.26101 - 7.38028i) q^{20} +(-1.83102 - 3.17142i) q^{22} +(-0.142434 + 0.246702i) q^{23} +(1.24168 + 2.15065i) q^{25} +(-4.31479 - 7.47343i) q^{26} +(-2.27396 + 3.93861i) q^{29} -7.43005 q^{31} +20.0106 q^{32} +(-3.80191 + 6.58511i) q^{34} +(-4.01126 - 6.94770i) q^{37} +(0.849420 + 1.47124i) q^{38} +(7.26194 - 12.5780i) q^{40} +(5.01329 + 8.68327i) q^{41} +(-3.12937 + 5.42022i) q^{43} +(-3.62271 - 6.27472i) q^{44} +(-0.386726 + 0.669829i) q^{46} +11.1477 q^{47} +(3.37132 + 5.83930i) q^{50} +(-8.53689 - 14.7863i) q^{52} +(1.39349 - 2.41359i) q^{53} -2.13965 q^{55} +(-6.17410 + 10.6939i) q^{58} +4.57469 q^{59} +0.385014 q^{61} -20.1736 q^{62} +26.1036 q^{64} -5.04207 q^{65} -2.53916 q^{67} +(-7.52217 + 13.0288i) q^{68} +1.45208 q^{71} +(-0.234067 + 0.405416i) q^{73} +(-10.8911 - 18.8639i) q^{74} +(1.68059 + 2.91087i) q^{76} -15.7124 q^{79} +(11.1951 - 19.3905i) q^{80} +(13.6117 + 23.5762i) q^{82} +(-6.99338 + 12.1129i) q^{83} +(2.22138 + 3.84754i) q^{85} +(-8.49665 + 14.7166i) q^{86} +(-6.17410 - 10.6939i) q^{88} +(1.29353 + 2.24046i) q^{89} +(-0.765146 + 1.32527i) q^{92} +30.2674 q^{94} +0.992595 q^{95} +(-7.22962 + 12.5221i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 20 q^{11} + 24 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} + 96 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} + 120 q^{65} + 24 q^{67} + 112 q^{71} - 68 q^{74} - 24 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} + 128 q^{95}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 20 * q^11 + 24 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 + 96 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 + 120 * q^65 + 24 * q^67 + 112 * q^71 - 68 * q^74 - 24 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 + 128 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more