LMFDB - Embedded newform 1323.2.f.h.883.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (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			883.2
Character	$\chi$	$=$	1323.883
Dual form			1323.2.f.h.442.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35757 + 2.35137i) q^{2} +(-2.68597 - 4.65224i) q^{4} +(-0.793197 - 1.37386i) q^{5} +9.15528 q^{8} +O(q^{10})$	\(q+(-1.35757 + 2.35137i) q^{2} +(-2.68597 - 4.65224i) q^{4} +(-0.793197 - 1.37386i) q^{5} +9.15528 q^{8} +4.30727 q^{10} +(-0.674376 + 1.16805i) q^{11} +(1.58916 + 2.75251i) q^{13} +(-7.05696 + 12.2230i) q^{16} -2.80054 q^{17} +0.625693 q^{19} +(-4.26101 + 7.38028i) q^{20} +(-1.83102 - 3.17142i) q^{22} +(-0.142434 - 0.246702i) q^{23} +(1.24168 - 2.15065i) q^{25} -8.62957 q^{26} +(-2.27396 + 3.93861i) q^{29} +(-3.71502 - 6.43461i) q^{31} +(-10.0053 - 17.3297i) q^{32} +(3.80191 - 6.58511i) q^{34} +8.02252 q^{37} +(-0.849420 + 1.47124i) q^{38} +(-7.26194 - 12.5780i) q^{40} +(-5.01329 - 8.68327i) q^{41} +(-3.12937 + 5.42022i) q^{43} +7.24542 q^{44} +0.773452 q^{46} +(5.57383 - 9.65415i) q^{47} +(3.37132 + 5.83930i) q^{50} +(8.53689 - 14.7863i) q^{52} -2.78698 q^{53} +2.13965 q^{55} +(-6.17410 - 10.6939i) q^{58} +(2.28734 + 3.96180i) q^{59} +(0.192507 - 0.333432i) q^{61} +20.1736 q^{62} +26.1036 q^{64} +(2.52104 - 4.36656i) q^{65} +(1.26958 + 2.19898i) q^{67} +(7.52217 + 13.0288i) q^{68} +1.45208 q^{71} -0.468134 q^{73} +(-10.8911 + 18.8639i) q^{74} +(-1.68059 - 2.91087i) q^{76} +(7.85620 - 13.6073i) q^{79} +22.3902 q^{80} +27.2235 q^{82} +(6.99338 - 12.1129i) q^{83} +(2.22138 + 3.84754i) q^{85} +(-8.49665 - 14.7166i) q^{86} +(-6.17410 + 10.6939i) q^{88} +2.58706 q^{89} +(-0.765146 + 1.32527i) q^{92} +(15.1337 + 26.2123i) q^{94} +(-0.496297 - 0.859612i) q^{95} +(7.22962 - 12.5221i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	$ 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 - 20 * q^11 - 12 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 - 48 * q^32 + 24 * q^37 + 112 * q^44 - 48 * q^46 + 4 * q^50 + 64 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 - 68 * q^74 + 12 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 - 64 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.35757	+	2.35137i	−0.959944	+	1.66267i	−0.237320	+	0.971432i	$0.576269\pi$
$2$	−1.35757	+	2.35137i	−0.959944	+	1.66267i	−0.722624	+	0.691241i	$0.757064\pi$
$3$		0			0
$3$		0			0
$4$	−2.68597	−	4.65224i	−1.34299	−	2.32612i
$5$	−0.793197	−	1.37386i	−0.354728	−	0.614407i	0.632343	−	0.774688i	$-0.282093\pi$
$5$	−0.793197	−	1.37386i	−0.354728	−	0.614407i	−0.987071	+	0.160281i	$0.948760\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	9.15528			3.23688
$9$		0			0
$10$	4.30727			1.36208
$11$	−0.674376	+	1.16805i	−0.203332	+	0.352181i	−0.949600	−	0.313464i	$-0.898510\pi$
$11$	−0.674376	+	1.16805i	−0.203332	+	0.352181i	0.746268	+	0.665646i	$0.231844\pi$
$12$		0			0
$13$	1.58916	+	2.75251i	0.440754	+	0.763409i	0.997746	−	0.0671096i	$-0.0213777\pi$
$13$	1.58916	+	2.75251i	0.440754	+	0.763409i	−0.556991	+	0.830518i	$0.688044\pi$
$14$		0			0
$15$		0			0
$16$	−7.05696	+	12.2230i	−1.76424	+	3.05575i
$17$	−2.80054			−0.679230			−0.339615	−	0.940565i	$-0.610297\pi$
$17$	−2.80054			−0.679230			−0.339615	+	0.940565i	$0.610297\pi$
$18$		0			0
$19$	0.625693			0.143544			0.0717719	−	0.997421i	$-0.477135\pi$
$19$	0.625693			0.143544			0.0717719	+	0.997421i	$0.477135\pi$
$20$	−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	0.850794	−	0.525500i	$-0.176122\pi$
$23$	−0.142434	−	0.246702i	−0.0296995	−	0.0514410i	−0.880493	+	0.474059i	$0.842788\pi$
$24$		0			0
$25$	1.24168	−	2.15065i	0.248336	−	0.430130i
$26$	−8.62957			−1.69240
$27$		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
$31$	−3.71502	−	6.43461i	−0.667238	−	1.15569i	−0.978673	−	0.205423i	$-0.934143\pi$
$31$	−3.71502	−	6.43461i	−0.667238	−	1.15569i	0.311435	−	0.950267i	$-0.399190\pi$
$32$	−10.0053	−	17.3297i	−1.76870	−	3.06348i
$33$		0			0
$34$	3.80191	−	6.58511i	0.652023	−	1.12934i
$35$		0			0
$36$		0			0
$37$	8.02252			1.31889			0.659447	−	0.751751i	$-0.270791\pi$
$37$	8.02252			1.31889			0.659447	+	0.751751i	$0.270791\pi$
$38$	−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	$-0.880384\pi$
$41$	−5.01329	−	8.68327i	−0.782944	−	1.35610i	0.147275	−	0.989096i	$-0.452950\pi$
$42$		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	$0.325024\pi$
$44$	7.24542			1.09229
$45$		0			0
$46$	0.773452			0.114039
$47$	5.57383	−	9.65415i	0.813026	−	1.40820i	−0.0977106	−	0.995215i	$-0.531152\pi$
$47$	5.57383	−	9.65415i	0.813026	−	1.40820i	0.910737	−	0.412988i	$-0.135515\pi$
$48$		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
$53$	−2.78698			−0.382821			−0.191410	−	0.981510i	$-0.561306\pi$
$53$	−2.78698			−0.382821			−0.191410	+	0.981510i	$0.561306\pi$
$54$		0			0
$55$	2.13965			0.288510
$56$		0			0
$57$		0			0
$58$	−6.17410	−	10.6939i	−0.810699	−	1.40417i
$59$	2.28734	+	3.96180i	0.297787	+	0.515782i	0.975629	−	0.219425i	$-0.0704182\pi$
$59$	2.28734	+	3.96180i	0.297787	+	0.515782i	−0.677842	+	0.735207i	$0.737085\pi$
$60$		0			0
$61$	0.192507	−	0.333432i	0.0246480	−	0.0426916i	−0.853438	−	0.521194i	$-0.825487\pi$
$61$	0.192507	−	0.333432i	0.0246480	−	0.0426916i	0.878086	+	0.478502i	$0.158820\pi$
$62$	20.1736			2.56205
$63$		0			0
$64$	26.1036			3.26295
$65$	2.52104	−	4.36656i	0.312696	−	0.541605i
$66$		0			0
$67$	1.26958	+	2.19898i	0.155104	+	0.268648i	0.933097	−	0.359625i	$-0.117095\pi$
$67$	1.26958	+	2.19898i	0.155104	+	0.268648i	−0.777993	+	0.628273i	$0.783762\pi$
$68$	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
$73$	−0.468134			−0.0547909			−0.0273955	−	0.999625i	$-0.508721\pi$
$73$	−0.468134			−0.0547909			−0.0273955	+	0.999625i	$0.508721\pi$
$74$	−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
$79$	7.85620	−	13.6073i	0.883892	−	1.53095i	0.0369135	−	0.999318i	$-0.488247\pi$
$79$	7.85620	−	13.6073i	0.883892	−	1.53095i	0.846978	−	0.531627i	$-0.178419\pi$
$80$	22.3902			2.50330
$81$		0			0
$82$	27.2235			3.00633
$83$	6.99338	−	12.1129i	0.767623	−	1.32956i	−0.171225	−	0.985232i	$-0.554772\pi$
$83$	6.99338	−	12.1129i	0.767623	−	1.32956i	0.938848	−	0.344331i	$-0.111894\pi$
$84$		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
$89$	2.58706			0.274228			0.137114	−	0.990555i	$-0.456217\pi$
$89$	2.58706			0.274228			0.137114	+	0.990555i	$0.456217\pi$
$90$		0			0
$91$		0			0
$92$	−0.765146	+	1.32527i	−0.0797719	+	0.138169i
$93$		0			0
$94$	15.1337	+	26.2123i	1.56092	+	2.70359i
$95$	−0.496297	−	0.859612i	−0.0509190	−	0.0881944i
$96$		0			0
$97$	7.22962	−	12.5221i	0.734057	−	1.27142i	−0.221079	−	0.975256i	$-0.570958\pi$
$97$	7.22962	−	12.5221i	0.734057	−	1.27142i	0.955136	−	0.296168i	$-0.0957089\pi$
$98$		0			0
$99$		0			0
$100$	−13.3405			−1.33405
$101$	4.91888	−	8.51975i	0.489447	−	0.847747i	−0.510479	−	0.859890i	$-0.670532\pi$
$101$	4.91888	−	8.51975i	0.489447	−	0.847747i	0.999926	+	0.0121430i	$0.00386534\pi$
$102$		0			0
$103$	−5.52897	−	9.57646i	−0.544786	−	0.943597i	−0.998620	−	0.0525110i	$-0.983278\pi$
$103$	−5.52897	−	9.57646i	−0.544786	−	0.943597i	0.453834	−	0.891086i	$-0.350056\pi$
$104$	14.5492	+	25.2000i	1.42667	+	2.47106i
$105$		0			0
$106$	3.78350	−	6.55322i	0.367486	−	0.636505i
$107$	1.92431			0.186030			0.0930149	−	0.995665i	$-0.470350\pi$
$107$	1.92431			0.186030			0.0930149	+	0.995665i	$0.470350\pi$
$108$		0			0
$109$	−18.6068			−1.78221			−0.891105	−	0.453797i	$-0.850069\pi$
$109$	−18.6068			−1.78221			−0.891105	+	0.453797i	$0.850069\pi$
$110$	−2.90472	+	5.03112i	−0.276954	+	0.479698i
$111$		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
$116$	24.4312			2.26838
$117$		0			0
$118$	−12.4209			−1.14344
$119$		0			0
$120$		0			0
$121$	4.59043	+	7.95086i	0.417312	+	0.722806i
$122$	0.522682	+	0.905312i	0.0473214	+	0.0819631i
$123$		0			0
$124$	−19.9569	+	34.5664i	−1.79218	+	3.10415i
$125$	−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	$0.621167\pi$
$128$	−15.4267	+	26.7199i	−1.36354	+	2.36173i
$129$		0			0
$130$	6.84495	+	11.8558i	0.600341	+	1.03982i
$131$	−5.98629	−	10.3686i	−0.523024	−	0.905905i	−0.999641	−	0.0267937i	$-0.991470\pi$
$131$	−5.98629	−	10.3686i	−0.523024	−	0.905905i	0.476616	−	0.879111i	$-0.341863\pi$
$132$		0			0
$133$		0			0
$134$	−6.89415			−0.595564
$135$		0			0
$136$	−25.6397			−2.19859
$137$	8.27525	−	14.3332i	0.707003	−	1.22456i	−0.258961	−	0.965888i	$-0.583380\pi$
$137$	8.27525	−	14.3332i	0.707003	−	1.22456i	0.965964	−	0.258677i	$-0.0832865\pi$
$138$		0			0
$139$	3.95119	+	6.84367i	0.335136	+	0.580472i	0.983511	−	0.180849i	$-0.0578845\pi$
$139$	3.95119	+	6.84367i	0.335136	+	0.580472i	−0.648375	+	0.761321i	$0.724551\pi$
$140$		0			0
$141$		0			0
$142$	−1.97130	+	3.41438i	−0.165427	+	0.286529i
$143$	−4.28677			−0.358478
$144$		0			0
$145$	7.21479			0.599156
$146$	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	−0.997505	−	0.0705895i	$-0.977512\pi$
$149$	−6.83427	−	11.8373i	−0.559885	−	0.969749i	0.437620	−	0.899160i	$-0.355821\pi$
$150$		0			0
$151$	−1.94982	+	3.37718i	−0.158674	+	0.274831i	−0.934391	−	0.356250i	$-0.884055\pi$
$151$	−1.94982	+	3.37718i	−0.158674	+	0.274831i	0.775717	+	0.631081i	$0.217389\pi$
$152$	5.72839			0.464634
$153$		0			0
$154$		0			0
$155$	−5.89349	+	10.2078i	−0.473376	+	0.819912i
$156$		0			0
$157$	0.147176	+	0.254917i	0.0117459	+	0.0203446i	0.871839	−	0.489793i	$-0.162928\pi$
$157$	0.147176	+	0.254917i	0.0117459	+	0.0203446i	−0.860093	+	0.510138i	$0.829594\pi$
$158$	21.3306	+	36.9457i	1.69697	+	2.93925i
$159$		0			0
$160$	−15.8723	+	27.4917i	−1.25482	+	2.17341i
$161$		0			0
$162$		0			0
$163$	10.7091			0.838802			0.419401	−	0.907801i	$-0.362240\pi$
$163$	10.7091			0.838802			0.419401	+	0.907801i	$0.362240\pi$
$164$	−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	0.797516	−	0.603298i	$-0.206147\pi$
$167$	−1.59872	−	2.76907i	−0.123713	−	0.214277i	−0.921229	+	0.389020i	$0.872814\pi$
$168$		0			0
$169$	1.44913	−	2.50997i	0.111472	−	0.193074i
$170$	−12.0627			−0.925164
$171$		0			0
$172$	33.6216			2.56362
$173$	−5.71875	+	9.90517i	−0.434789	+	0.753076i	−0.997278	−	0.0737284i	$-0.976510\pi$
$173$	−5.71875	+	9.90517i	−0.434789	+	0.753076i	0.562490	+	0.826804i	$0.309844\pi$
$174$		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
$179$	−1.09855			−0.0821095			−0.0410547	−	0.999157i	$-0.513072\pi$
$179$	−1.09855			−0.0821095			−0.0410547	+	0.999157i	$0.513072\pi$
$180$		0			0
$181$	3.19013			0.237120			0.118560	−	0.992947i	$-0.462172\pi$
$181$	3.19013			0.237120			0.118560	+	0.992947i	$0.462172\pi$
$182$		0			0
$183$		0			0
$184$	−1.30402	−	2.25863i	−0.0961336	−	0.166508i
$185$	−6.36343	−	11.0218i	−0.467849	−	0.810338i
$186$		0			0
$187$	1.88861	−	3.27118i	0.138109	−	0.239212i
$188$	−59.8846			−4.36753
$189$		0			0
$190$	2.69503			0.195518
$191$	1.93407	−	3.34992i	0.139945	−	0.242391i	−0.787531	−	0.616275i	$-0.788641\pi$
$191$	1.93407	−	3.34992i	0.139945	−	0.242391i	0.927475	+	0.373884i	$0.121974\pi$
$192$		0			0
$193$	2.06793	+	3.58175i	0.148853	+	0.257820i	0.930804	−	0.365520i	$-0.119109\pi$
$193$	2.06793	+	3.58175i	0.148853	+	0.257820i	−0.781951	+	0.623340i	$0.785775\pi$
$194$	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
$199$	6.32386			0.448287			0.224143	−	0.974556i	$-0.428042\pi$
$199$	6.32386			0.448287			0.224143	+	0.974556i	$0.428042\pi$
$200$	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
$205$	−7.95305	+	13.7751i	−0.555465	+	0.962093i
$206$	30.0238			2.09186
$207$		0			0
$208$	−44.8586			−3.11038
$209$	−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
$215$	9.92881			0.677139
$216$		0			0
$217$		0			0
$218$	25.2600	−	43.7516i	1.71082	−	2.96323i
$219$		0			0
$220$	−5.74705	−	9.95417i	−0.387466	−	0.671110i
$221$	−4.45051	−	7.70850i	−0.299373	−	0.518530i
$222$		0			0
$223$	8.35953	−	14.4791i	0.559796	−	0.969595i	−0.437717	−	0.899113i	$-0.644213\pi$
$223$	8.35953	−	14.4791i	0.559796	−	0.969595i	0.997513	−	0.0704822i	$-0.0224538\pi$
$224$		0			0
$225$		0			0
$226$	8.65250			0.575555
$227$	8.53501	−	14.7831i	0.566489	−	0.981187i	−0.430421	−	0.902628i	$-0.641635\pi$
$227$	8.53501	−	14.7831i	0.566489	−	0.981187i	0.996909	−	0.0785588i	$-0.0250318\pi$
$228$		0			0
$229$	−9.89471	−	17.1381i	−0.653861	−	1.13252i	−0.982178	−	0.187953i	$-0.939815\pi$
$229$	−9.89471	−	17.1381i	−0.653861	−	1.13252i	0.328317	−	0.944567i	$-0.393518\pi$
$230$	−0.613500	−	1.06261i	−0.0404530	−	0.0700666i
$231$		0			0
$232$	−20.8187	+	36.0591i	−1.36682	+	2.36740i
$233$	−5.93159			−0.388591			−0.194296	−	0.980943i	$-0.562242\pi$
$233$	−5.93159			−0.388591			−0.194296	+	0.980943i	$0.562242\pi$
$234$		0			0
$235$	−17.6846			−1.15361
$236$	12.2875	−	21.2826i	0.799847	−	1.38538i
$237$		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	−0.184256	+	0.982878i	$0.558988\pi$
$241$	−14.6444	+	25.3648i	−0.943326	+	1.63389i	−0.759069	+	0.651010i	$0.774346\pi$
$242$	−24.9273			−1.60239
$243$		0			0
$244$	−2.06827			−0.132408
$245$		0			0
$246$		0			0
$247$	0.994327	+	1.72223i	0.0632675	+	0.109583i
$248$	−34.0121	−	58.9107i	−2.15977	−	3.74083i
$249$		0			0
$250$	16.1164	−	27.9144i	1.01929	−	1.76546i
$251$	22.7856			1.43821			0.719106	−	0.694901i	$-0.244552\pi$
$251$	22.7856			1.43821			0.719106	+	0.694901i	$0.244552\pi$
$252$		0			0
$253$	0.384215			0.0241554
$254$	11.3681	−	19.6901i	0.713297	−	1.23547i
$255$		0			0
$256$	−15.7821	−	27.3354i	−0.986381	−	1.70846i
$257$	−12.1444	−	21.0348i	−0.757550	−	1.31211i	−0.944097	−	0.329668i	$-0.893063\pi$
$257$	−12.1444	−	21.0348i	−0.757550	−	1.31211i	0.186547	−	0.982446i	$-0.440270\pi$
$258$		0			0
$259$		0			0
$260$	−27.0857			−1.67979
$261$		0			0
$262$	32.5071			2.00830
$263$	−4.30578	+	7.45782i	−0.265506	+	0.459869i	−0.967696	−	0.252120i	$-0.918872\pi$
$263$	−4.30578	+	7.45782i	−0.265506	+	0.459869i	0.702190	+	0.711989i	$0.252206\pi$
$264$		0			0
$265$	2.21062	+	3.82890i	0.135797	+	0.235208i
$266$		0			0
$267$		0			0
$268$	6.82011	−	11.8128i	0.416605	−	0.721581i
$269$	15.2312			0.928664			0.464332	−	0.885661i	$-0.346294\pi$
$269$	15.2312			0.928664			0.464332	+	0.885661i	$0.346294\pi$
$270$		0			0
$271$	−4.67820			−0.284181			−0.142090	−	0.989854i	$-0.545382\pi$
$271$	−4.67820			−0.284181			−0.142090	+	0.989854i	$0.545382\pi$
$272$	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	−0.507550	−	0.861622i	$-0.669449\pi$
$277$	8.19537	−	14.1948i	0.492412	−	0.852883i	0.999962	+	0.00873986i	$0.00278202\pi$
$278$	−21.4560			−1.28685
$279$		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
$283$	−13.0354	−	22.5780i	−0.774874	−	1.34212i	−0.934865	−	0.355002i	$-0.884480\pi$
$283$	−13.0354	−	22.5780i	−0.774874	−	1.34212i	0.159992	−	0.987118i	$-0.448853\pi$
$284$	−3.90025	−	6.75543i	−0.231437	−	0.400861i
$285$		0			0
$286$	5.81958	−	10.0798i	0.344119	−	0.596031i
$287$		0			0
$288$		0			0
$289$	−9.15699			−0.538647
$290$	−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	$0.0193169\pi$
$293$	9.44192	+	16.3539i	0.551603	+	0.955404i	−0.446556	+	0.894756i	$0.647350\pi$
$294$		0			0
$295$	3.62863	−	6.28497i	0.211267	−	0.365925i
$296$	73.4484			4.26910
$297$		0			0
$298$	37.1119			2.14983
$299$	0.452700	−	0.784099i	0.0261803	−	0.0453456i
$300$		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
$305$	−0.610783			−0.0349734
$306$		0			0
$307$	−21.6407			−1.23510			−0.617551	−	0.786531i	$-0.711875\pi$
$307$	−21.6407			−1.23510			−0.617551	+	0.786531i	$0.711875\pi$
$308$		0			0
$309$		0			0
$310$	−16.0016	−	27.7156i	−0.908830	−	1.57414i
$311$	2.24724	+	3.89234i	0.127429	+	0.220714i	0.922680	−	0.385567i	$-0.125994\pi$
$311$	2.24724	+	3.89234i	0.127429	+	0.220714i	−0.795251	+	0.606281i	$0.792661\pi$
$312$		0			0
$313$	−4.30102	+	7.44958i	−0.243108	+	0.421075i	−0.961598	−	0.274462i	$-0.911500\pi$
$313$	−4.30102	+	7.44958i	−0.243108	+	0.421075i	0.718490	+	0.695537i	$0.244834\pi$
$314$	−0.799206			−0.0451018
$315$		0			0
$316$	−84.4062			−4.74822
$317$	−4.03128	+	6.98237i	−0.226419	+	0.392169i	−0.956744	−	0.290930i	$-0.906035\pi$
$317$	−4.03128	+	6.98237i	−0.226419	+	0.392169i	0.730325	+	0.683100i	$0.239369\pi$
$318$		0			0
$319$	−3.06701	−	5.31221i	−0.171719	−	0.297427i
$320$	−20.7053	−	35.8626i	−1.15746	−	2.00478i
$321$		0			0
$322$		0			0
$323$	−1.75228			−0.0974992
$324$		0			0
$325$	7.89291			0.437820
$326$	−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
$331$	11.4513	−	19.8342i	0.629419	−	1.09019i	−0.358249	−	0.933626i	$-0.616626\pi$
$331$	11.4513	−	19.8342i	0.629419	−	1.09019i	0.987668	−	0.156560i	$-0.0500405\pi$
$332$	−75.1361			−4.12363
$333$		0			0
$334$	8.68150			0.475030
$335$	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
$341$	10.0213			0.542683
$342$		0			0
$343$		0			0
$344$	−28.6502	+	49.6237i	−1.54472	+	2.67553i
$345$		0			0
$346$	−15.5272	−	26.8938i	−0.834746	−	1.44582i
$347$	−1.41282	−	2.44707i	−0.0758440	−	0.131366i	0.825609	−	0.564243i	$-0.190832\pi$
$347$	−1.41282	−	2.44707i	−0.0758440	−	0.131366i	−0.901453	+	0.432877i	$0.857498\pi$
$348$		0			0
$349$	−1.81202	+	3.13851i	−0.0969951	+	0.168000i	−0.910440	−	0.413642i	$-0.864256\pi$
$349$	−1.81202	+	3.13851i	−0.0969951	+	0.168000i	0.813444	+	0.581643i	$0.197590\pi$
$350$		0			0
$351$		0			0
$352$	26.9893			1.43854
$353$	−1.37701	+	2.38504i	−0.0732907	+	0.126943i	−0.900342	−	0.435184i	$-0.856683\pi$
$353$	−1.37701	+	2.38504i	−0.0732907	+	0.126943i	0.827051	+	0.562127i	$0.190017\pi$
$354$		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
$359$	16.8015			0.886750			0.443375	−	0.896336i	$-0.353781\pi$
$359$	16.8015			0.886750			0.443375	+	0.896336i	$0.353781\pi$
$360$		0			0
$361$	−18.6085			−0.979395
$362$	−4.33081	+	7.50119i	−0.227622	+	0.394254i
$363$		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	−0.363934	−	0.931425i	$-0.618567\pi$
$367$	11.9670	−	20.7274i	0.624670	−	1.08196i	0.988605	−	0.150536i	$-0.0480999\pi$
$368$	4.02059			0.209588
$369$		0			0
$370$	34.5551			1.79644
$371$		0			0
$372$		0			0
$373$	9.58030	+	16.5936i	0.496049	+	0.859182i	0.999990	−	0.00455622i	$-0.00145030\pi$
$373$	9.58030	+	16.5936i	0.496049	+	0.859182i	−0.503941	+	0.863738i	$0.668117\pi$
$374$	5.12784	+	8.88168i	0.265154	+	0.459261i
$375$		0			0
$376$	51.0299	−	88.3865i	2.63167	−	4.55818i
$377$	−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	$0.416669\pi$
$380$	−2.66608	+	4.61779i	−0.136767	+	0.236888i
$381$		0			0
$382$	5.25127	+	9.09546i	0.268678	+	0.465364i
$383$	−10.0718	−	17.4448i	−0.514643	−	0.891388i	−0.999856	−	0.0169915i	$-0.994591\pi$
$383$	−10.0718	−	17.4448i	−0.514643	−	0.891388i	0.485213	−	0.874396i	$-0.338742\pi$
$384$		0			0
$385$		0			0
$386$	−11.2294			−0.571561
$387$		0			0
$388$	−77.6743			−3.94332
$389$	6.69736	−	11.6002i	0.339570	−	0.588152i	−0.644782	−	0.764366i	$-0.723052\pi$
$389$	6.69736	−	11.6002i	0.339570	−	0.588152i	0.984352	+	0.176215i	$0.0563853\pi$
$390$		0			0
$391$	0.398891	+	0.690899i	0.0201728	+	0.0349402i
$392$		0			0
$393$		0			0
$394$	−1.20724	+	2.09100i	−0.0608198	+	0.105343i
$395$	−24.9261			−1.25417
$396$		0			0
$397$	−18.0133			−0.904061			−0.452031	−	0.892002i	$-0.649300\pi$
$397$	−18.0133			−0.904061			−0.452031	+	0.892002i	$0.649300\pi$
$398$	−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	0.960685	+	0.277642i	$0.0895528\pi$
$401$	14.4337	+	25.0000i	0.720787	+	1.24844i	−0.239898	+	0.970798i	$0.577114\pi$
$402$		0			0
$403$	11.8075	−	20.4513i	0.588176	−	1.01875i
$404$	−52.8479			−2.62928
$405$		0			0
$406$		0			0
$407$	−5.41019	+	9.37073i	−0.268173	+	0.464490i
$408$		0			0
$409$	5.42937	+	9.40395i	0.268465	+	0.464995i	0.968466	−	0.249147i	$-0.0801502\pi$
$409$	5.42937	+	9.40395i	0.268465	+	0.464995i	−0.700000	+	0.714142i	$0.746817\pi$
$410$	−21.5936	−	37.4012i	−1.06643	−	1.84711i
$411$		0			0
$412$	−29.7014	+	51.4443i	−1.46328	+	2.53448i
$413$		0			0
$414$		0			0
$415$	−22.1885			−1.08919
$416$	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	0.872009	−	0.489489i	$-0.162817\pi$
$419$	0.247572	+	0.428807i	0.0120947	+	0.0209486i	−0.859915	+	0.510438i	$0.829483\pi$
$420$		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	$0.0133831\pi$
$422$	−31.0226			−1.51016
$423$		0			0
$424$	−25.5155			−1.23914
$425$	−3.47737	+	6.02298i	−0.168677	+	0.292157i
$426$		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
$431$	16.9215			0.815078			0.407539	−	0.913188i	$-0.366387\pi$
$431$	16.9215			0.815078			0.407539	+	0.913188i	$0.366387\pi$
$432$		0			0
$433$	−33.4740			−1.60866			−0.804330	−	0.594183i	$-0.797476\pi$
$433$	−33.4740			−1.60866			−0.804330	+	0.594183i	$0.797476\pi$
$434$		0			0
$435$		0			0
$436$	49.9774	+	86.5634i	2.39348	+	4.14564i
$437$	−0.0891197	−	0.154360i	−0.00426317	−	0.00738403i
$438$		0			0
$439$	−10.4657	+	18.1272i	−0.499502	+	0.865163i	−1.00000		0.000574559i	$-0.999817\pi$
$439$	−10.4657	+	18.1272i	−0.499502	+	0.865163i	0.500498	+	0.865738i	$0.333150\pi$
$440$	19.5891			0.933874
$441$		0			0
$442$	24.1674			1.14953
$443$	−15.4290	+	26.7238i	−0.733054	+	1.26969i	0.222517	+	0.974929i	$0.428573\pi$
$443$	−15.4290	+	26.7238i	−0.733054	+	1.26969i	−0.955572	+	0.294759i	$0.904761\pi$
$444$		0			0
$445$	−2.05205	−	3.55425i	−0.0972763	−	0.168487i
$446$	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
$451$	13.5234			0.636791
$452$	−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
$457$	−11.8952	+	20.6031i	−0.556434	+	0.963772i	0.441356	+	0.897332i	$0.354498\pi$
$457$	−11.8952	+	20.6031i	−0.556434	+	0.963772i	−0.997790	+	0.0664402i	$0.978836\pi$
$458$	53.7309			2.51068
$459$		0			0
$460$	2.42764			0.113189
$461$	−8.53122	+	14.7765i	−0.397339	+	0.688211i	−0.993397	−	0.114731i	$-0.963400\pi$
$461$	−8.53122	+	14.7765i	−0.397339	+	0.688211i	0.596058	+	0.802941i	$0.296733\pi$
$462$		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
$467$	8.19160			0.379062			0.189531	−	0.981875i	$-0.439303\pi$
$467$	8.19160			0.379062			0.189531	+	0.981875i	$0.439303\pi$
$468$		0			0
$469$		0			0
$470$	24.0080	−	41.5830i	1.10740	−	1.91808i
$471$		0			0
$472$	20.9413	+	36.2714i	0.963900	+	1.66952i
$473$	−4.22074	−	7.31054i	−0.194070	−	0.336139i
$474$		0			0
$475$	0.776909	−	1.34565i	0.0356470	−	0.0617425i
$476$		0			0
$477$		0			0
$478$	−54.4530			−2.49062
$479$	−12.7775	+	22.1312i	−0.583817	+	1.01120i	0.411205	+	0.911543i	$0.365108\pi$
$479$	−12.7775	+	22.1312i	−0.583817	+	1.01120i	−0.995022	+	0.0996574i	$0.968225\pi$
$480$		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
$485$	−22.9381			−1.04156
$486$		0			0
$487$	−6.92281			−0.313702			−0.156851	−	0.987622i	$-0.550134\pi$
$487$	−6.92281			−0.313702			−0.156851	+	0.987622i	$0.550134\pi$
$488$	1.76246	−	3.05266i	0.0797826	−	0.138188i
$489$		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
$494$	−5.39946			−0.242933
$495$		0			0
$496$	104.867			4.70867
$497$		0			0
$498$		0			0
$499$	−12.8125	−	22.1919i	−0.573566	−	0.993446i	−0.996196	−	0.0871432i	$-0.972226\pi$
$499$	−12.8125	−	22.1919i	−0.573566	−	0.993446i	0.422630	−	0.906302i	$-0.361107\pi$
$500$	31.8867	+	55.2293i	1.42601	+	2.46993i
$501$		0			0
$502$	−30.9329	+	53.5774i	−1.38060	+	2.39127i
$503$	5.79692			0.258472			0.129236	−	0.991614i	$-0.458748\pi$
$503$	5.79692			0.258472			0.129236	+	0.991614i	$0.458748\pi$
$504$		0			0
$505$	−15.6066			−0.694483
$506$	−0.521598	+	0.903434i	−0.0231878	+	0.0401625i
$507$		0			0
$508$	22.4920	+	38.9573i	0.997921	+	1.72845i
$509$	12.5697	+	21.7714i	0.557144	+	0.965002i	0.997733	+	0.0672931i	$0.0214363\pi$
$509$	12.5697	+	21.7714i	0.557144	+	0.965002i	−0.440589	+	0.897709i	$0.645230\pi$
$510$		0			0
$511$		0			0
$512$	23.9940			1.06039
$513$		0			0
$514$	65.9475			2.90882
$515$	−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
$520$	23.0808	−	39.9771i	1.01216	−	1.75311i
$521$	−7.29656			−0.319668			−0.159834	−	0.987144i	$-0.551096\pi$
$521$	−7.29656			−0.319668			−0.159834	+	0.987144i	$0.551096\pi$
$522$		0			0
$523$	16.7727			0.733421			0.366710	−	0.930335i	$-0.380484\pi$
$523$	16.7727			0.733421			0.366710	+	0.930335i	$0.380484\pi$
$524$	−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
$530$	−12.0042			−0.521431
$531$		0			0
$532$		0			0
$533$	15.9339	−	27.5982i	0.690172	−	1.19541i
$534$		0			0
$535$	−1.52635	−	2.64372i	−0.0659900	−	0.114298i
$536$	11.6234	+	20.1322i	0.502053	+	0.869581i
$537$		0			0
$538$	−20.6774	+	35.8143i	−0.891466	+	1.54406i
$539$		0			0
$540$		0			0
$541$	−5.29816			−0.227786			−0.113893	−	0.993493i	$-0.536332\pi$
$541$	−5.29816			−0.227786			−0.113893	+	0.993493i	$0.536332\pi$
$542$	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	$-0.0813123\pi$
$548$	−88.9084			−3.79798
$549$		0			0
$550$	−9.09416			−0.387776
$551$	−1.42280	+	2.46436i	−0.0606133	+	0.104985i
$552$		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
$557$	18.8160			0.797258			0.398629	−	0.917112i	$-0.369486\pi$
$557$	18.8160			0.797258			0.398629	+	0.917112i	$0.369486\pi$
$558$		0			0
$559$	−19.8923			−0.841354
$560$		0			0
$561$		0			0
$562$	−4.77054	−	8.26282i	−0.201233	−	0.348546i
$563$	13.8325	+	23.9586i	0.582970	+	1.00973i	0.995125	+	0.0986197i	$0.0314427\pi$
$563$	13.8325	+	23.9586i	0.582970	+	1.00973i	−0.412155	+	0.911114i	$0.635224\pi$
$564$		0			0
$565$	−2.52773	+	4.37816i	−0.106343	+	0.184191i
$566$	70.7856			2.97534
$567$		0			0
$568$	13.2942			0.557812
$569$	−20.0916	+	34.7996i	−0.842282	+	1.45888i	0.0456782	+	0.998956i	$0.485455\pi$
$569$	−20.0916	+	34.7996i	−0.842282	+	1.45888i	−0.887961	+	0.459920i	$0.847878\pi$
$570$		0			0
$571$	3.40565	+	5.89875i	0.142522	+	0.246855i	0.928446	−	0.371468i	$-0.121146\pi$
$571$	3.40565	+	5.89875i	0.142522	+	0.246855i	−0.785924	+	0.618323i	$0.787812\pi$
$572$	11.5142	+	19.9431i	0.481431	+	0.833863i
$573$		0			0
$574$		0			0
$575$	−0.707427			−0.0295017
$576$		0			0
$577$	−36.4222			−1.51628			−0.758138	−	0.652094i	$-0.773891\pi$
$577$	−36.4222			−1.51628			−0.758138	+	0.652094i	$0.773891\pi$
$578$	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
$583$	1.87947	−	3.25534i	0.0778397	−	0.134822i
$584$	−4.28590			−0.177352
$585$		0			0
$586$	−51.2721			−2.11803
$587$	−5.57943	+	9.66385i	−0.230288	+	0.398870i	−0.957893	−	0.287126i	$-0.907300\pi$
$587$	−5.57943	+	9.66385i	−0.230288	+	0.398870i	0.727605	+	0.685996i	$0.240633\pi$
$588$		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
$593$	−19.8085			−0.813439			−0.406720	−	0.913553i	$-0.633327\pi$
$593$	−19.8085			−0.813439			−0.406720	+	0.913553i	$0.633327\pi$
$594$		0			0
$595$		0			0
$596$	−36.7133	+	63.5893i	−1.50384	+	2.60472i
$597$		0			0
$598$	1.22914	+	2.12893i	0.0502633	+	0.0870586i
$599$	−9.06600	−	15.7028i	−0.370427	−	0.641598i	0.619204	−	0.785230i	$-0.287455\pi$
$599$	−9.06600	−	15.7028i	−0.370427	−	0.641598i	−0.989631	+	0.143632i	$0.954122\pi$
$600$		0			0
$601$	−12.3285	+	21.3536i	−0.502889	+	0.871030i	0.497105	+	0.867690i	$0.334396\pi$
$601$	−12.3285	+	21.3536i	−0.502889	+	0.871030i	−0.999994	+	0.00333942i	$0.998937\pi$
$602$		0			0
$603$		0			0
$604$	20.9486			0.852387
$605$	7.28223	−	12.6132i	0.296065	−	0.512799i
$606$		0			0
$607$	−8.63876	−	14.9628i	−0.350637	−	0.607320i	0.635725	−	0.771916i	$-0.280701\pi$
$607$	−8.63876	−	14.9628i	−0.350637	−	0.607320i	−0.986361	+	0.164596i	$0.947368\pi$
$608$	−6.26024	−	10.8431i	−0.253886	−	0.439744i
$609$		0			0
$610$	0.829179	−	1.43618i	0.0335725	−	0.0581492i
$611$	35.4308			1.43338
$612$		0			0
$613$	19.5566			0.789882			0.394941	−	0.918707i	$-0.370765\pi$
$613$	19.5566			0.789882			0.394941	+	0.918707i	$0.370765\pi$
$614$	29.3787	−	50.8855i	1.18563	−	2.05357i
$615$		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	0.295807	+	0.955248i	$0.404412\pi$
$619$	−16.9024	+	29.2758i	−0.679366	+	1.17670i	−0.975172	+	0.221448i	$0.928922\pi$
$620$	63.3190			2.54295
$621$		0			0
$622$	−12.2031			−0.489300
$623$		0			0
$624$		0			0
$625$	3.20808	+	5.55655i	0.128323	+	0.222262i
$626$	−11.6778	−	20.2266i	−0.466740	−	0.808418i
$627$		0			0
$628$	0.790623	−	1.36940i	0.0315493	−	0.0546450i
$629$	−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	$0.655951\pi$
$632$	71.9258	−	124.579i	2.86105	−	4.95549i
$633$		0			0
$634$	−10.9454	−	18.9581i	−0.434699	−	0.752921i
$635$	6.64213	+	11.5045i	0.263585	+	0.456542i
$636$		0			0
$637$		0			0
$638$	16.6547			0.659365
$639$		0			0
$640$	48.9458			1.93475
$641$	7.95901	−	13.7854i	0.314362	−	0.544491i	−0.664940	−	0.746897i	$-0.731543\pi$
$641$	7.95901	−	13.7854i	0.314362	−	0.544491i	0.979302	+	0.202406i	$0.0648760\pi$
$642$		0			0
$643$	−13.2527	−	22.9544i	−0.522636	−	0.905231i	−0.999653	−	0.0263376i	$-0.991616\pi$
$643$	−13.2527	−	22.9544i	−0.522636	−	0.905231i	0.477017	−	0.878894i	$-0.341718\pi$
$644$		0			0
$645$		0			0
$646$	2.37883	−	4.12026i	0.0935938	−	0.162109i
$647$	−0.0160392			−0.000630565			−0.000315282	−	1.00000i	$-0.500100\pi$
$647$	−0.0160392			−0.000630565			−0.000315282		1.00000i	$0.500100\pi$
$648$		0			0
$649$	−6.17012			−0.242198
$650$	−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	−0.982801	−	0.184669i	$-0.940879\pi$
$653$	−16.6440	−	28.8282i	−0.651328	−	1.12813i	0.331473	−	0.943465i	$-0.392455\pi$
$654$		0			0
$655$	−9.49661	+	16.4486i	−0.371063	+	0.642700i
$656$	141.514			5.52520
$657$		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
$661$	−2.65322	−	4.59551i	−0.103198	−	0.178745i	0.809802	−	0.586703i	$-0.199574\pi$
$661$	−2.65322	−	4.59551i	−0.103198	−	0.178745i	−0.913001	+	0.407958i	$0.866241\pi$
$662$	31.0917	+	53.8525i	1.20842	+	2.09304i
$663$		0			0
$664$	64.0264	−	110.897i	2.48471	−	4.30364i
$665$		0			0
$666$		0			0
$667$	1.29555			0.0501640
$668$	−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	$0.203999\pi$
$674$	37.0285			1.42628
$675$		0			0
$676$	−15.5693			−0.598819
$677$	−17.3925	+	30.1247i	−0.668449	+	1.15779i	0.309889	+	0.950773i	$0.399708\pi$
$677$	−17.3925	+	30.1247i	−0.668449	+	1.15779i	−0.978338	+	0.207014i	$0.933625\pi$
$678$		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
$683$	−19.4241			−0.743243			−0.371622	−	0.928384i	$-0.621198\pi$
$683$	−19.4241			−0.743243			−0.371622	+	0.928384i	$0.621198\pi$
$684$		0			0
$685$	−26.2556			−1.00318
$686$		0			0
$687$		0			0
$688$	−44.1676	−	76.5006i	−1.68387	−	2.91656i
$689$	−4.42895	−	7.67117i	−0.168730	−	0.292248i
$690$		0			0
$691$	3.31837	−	5.74759i	0.126237	−	0.218649i	−0.795979	−	0.605324i	$-0.793043\pi$
$691$	3.31837	−	5.74759i	0.126237	−	0.218649i	0.922216	+	0.386676i	$0.126377\pi$
$692$	61.4416			2.33566
$693$		0			0
$694$	7.67197			0.291224
$695$	6.26814	−	10.8567i	0.237764	−	0.411820i
$696$		0			0
$697$	14.0399	+	24.3178i	0.531799	+	0.921103i
$698$	−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
$703$	5.01963			0.189319
$704$	−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
$709$	−17.0778	+	29.5796i	−0.641370	+	1.11089i	0.343757	+	0.939059i	$0.388300\pi$
$709$	−17.0778	+	29.5796i	−0.641370	+	1.11089i	−0.985127	+	0.171827i	$0.945033\pi$
$710$	6.25450			0.234727
$711$		0			0
$712$	23.6852			0.887642
$713$	−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
$719$	44.2900			1.65174			0.825870	−	0.563861i	$-0.190684\pi$
$719$	44.2900			1.65174			0.825870	+	0.563861i	$0.190684\pi$
$720$		0			0
$721$		0			0
$722$	25.2623	−	43.7556i	0.940165	−	1.62841i
$723$		0			0
$724$	−8.56860	−	14.8413i	−0.318450	−	0.551571i
$725$	5.64705	+	9.78099i	0.209726	+	0.363257i
$726$		0			0
$727$	14.1247	−	24.4647i	0.523857	−	0.907346i	−0.475758	−	0.879576i	$-0.657826\pi$
$727$	14.1247	−	24.4647i	0.523857	−	0.907346i	0.999614	−	0.0277700i	$-0.00884060\pi$
$728$		0			0
$729$		0			0
$730$	−2.01638			−0.0746295
$731$	8.76391	−	15.1795i	0.324145	−	0.561435i
$732$		0			0
$733$	12.5084	+	21.6653i	0.462010	+	0.800225i	0.999061	−	0.0433249i	$-0.0137951\pi$
$733$	12.5084	+	21.6653i	0.462010	+	0.800225i	−0.537051	+	0.843550i	$0.680462\pi$
$734$	32.4919	+	56.2776i	1.19930	+	2.07724i
$735$		0			0
$736$	−2.85018	+	4.93666i	−0.105059	+	0.181968i
$737$	−3.42470			−0.126150
$738$		0			0
$739$	32.0230			1.17798			0.588992	−	0.808139i	$-0.299525\pi$
$739$	32.0230			1.17798			0.588992	+	0.808139i	$0.299525\pi$
$740$	−34.1840	+	59.2084i	−1.25663	+	2.17655i
$741$		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
$746$	−52.0236			−1.90472
$747$		0			0
$748$	−20.2911			−0.741915
$749$		0			0
$750$		0			0
$751$	−10.8495	−	18.7920i	−0.395905	−	0.685728i	0.597311	−	0.802010i	$-0.296236\pi$
$751$	−10.8495	−	18.7920i	−0.395905	−	0.685728i	−0.993216	+	0.116282i	$0.962903\pi$
$752$	78.6685	+	136.258i	2.86874	+	4.96881i
$753$		0			0
$754$	19.6233	−	33.9885i	0.714638	−	1.23779i
$755$	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	$0.291479\pi$
$758$	−13.6802	+	23.6949i	−0.496889	+	0.860637i
$759$		0			0
$760$	−4.54374	−	7.86999i	−0.164819	−	0.285475i
$761$	−6.66048	−	11.5363i	−0.241442	−	0.418190i	0.719683	−	0.694303i	$-0.244287\pi$
$761$	−6.66048	−	11.5363i	−0.241442	−	0.418190i	−0.961125	+	0.276113i	$0.910954\pi$
$762$		0			0
$763$		0			0
$764$	−20.7795			−0.751775
$765$		0			0
$766$	54.6923			1.97611
$767$	−7.26992	+	12.5919i	−0.262502	+	0.454666i
$768$		0			0
$769$	27.3568	+	47.3833i	0.986510	+	1.70869i	0.635022	+	0.772494i	$0.280991\pi$
$769$	27.3568	+	47.3833i	0.986510	+	1.70869i	0.351488	+	0.936192i	$0.385676\pi$
$770$		0			0
$771$		0			0
$772$	11.1088	−	19.2410i	0.399814	−	0.692498i
$773$	−2.36042			−0.0848983			−0.0424491	−	0.999099i	$-0.513516\pi$
$773$	−2.36042			−0.0848983			−0.0424491	+	0.999099i	$0.513516\pi$
$774$		0			0
$775$	−18.4515			−0.662796
$776$	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
$782$	−2.16608			−0.0774589
$783$		0			0
$784$		0			0
$785$	0.233479	−	0.404398i	0.00833323	−	0.0144336i
$786$		0			0
$787$	0.833971	+	1.44448i	0.0297278	+	0.0514901i	0.880507	−	0.474034i	$-0.157203\pi$
$787$	0.833971	+	1.44448i	0.0297278	+	0.0514901i	−0.850779	+	0.525524i	$0.823869\pi$
$788$	−2.38855	−	4.13708i	−0.0850884	−	0.147377i
$789$		0			0
$790$	33.8388	−	58.6105i	1.20393	−	2.08527i
$791$		0			0
$792$		0			0
$793$	1.22370			0.0434548
$794$	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	$0.00259906\pi$
$797$	14.3148	+	24.7939i	0.507055	+	0.878244i	−0.492912	+	0.870079i	$0.664068\pi$
$798$		0			0
$799$	−15.6097	+	27.0368i	−0.552232	+	0.956493i
$800$	−49.6934			−1.75693
$801$		0			0
$802$	−78.3791			−2.76766
$803$	0.315698	−	0.546805i	0.0111408	−	0.0192963i
$804$		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
$809$	2.85691			0.100444			0.0502219	−	0.998738i	$-0.484007\pi$
$809$	2.85691			0.100444			0.0502219	+	0.998738i	$0.484007\pi$
$810$		0			0
$811$	26.2917			0.923225			0.461613	−	0.887082i	$-0.347271\pi$
$811$	26.2917			0.923225			0.461613	+	0.887082i	$0.347271\pi$
$812$		0			0
$813$		0			0
$814$	−14.6894	−	25.4428i	−0.514863	−	0.891769i
$815$	−8.49443	−	14.7128i	−0.297547	−	0.515366i
$816$		0			0
$817$	−1.95802	+	3.39139i	−0.0685025	+	0.118650i
$818$	−29.4829			−1.03085
$819$		0			0
$820$	85.4467			2.98393
$821$	−1.32925	+	2.30232i	−0.0463910	+	0.0803517i	−0.888289	−	0.459286i	$-0.848105\pi$
$821$	−1.32925	+	2.30232i	−0.0463910	+	0.0803517i	0.841897	+	0.539638i	$0.181439\pi$
$822$		0			0
$823$	6.10769	+	10.5788i	0.212901	+	0.368755i	0.952621	−	0.304160i	$-0.0983756\pi$
$823$	6.10769	+	10.5788i	0.212901	+	0.368755i	−0.739721	+	0.672914i	$0.765042\pi$
$824$	−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
$829$	18.3431			0.637083			0.318541	−	0.947909i	$-0.396807\pi$
$829$	18.3431			0.637083			0.318541	+	0.947909i	$0.396807\pi$
$830$	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
$835$	−2.53620	+	4.39284i	−0.0877690	+	0.152020i
$836$	4.53341			0.156791
$837$		0			0
$838$	−1.34438			−0.0464409
$839$	9.47055	−	16.4035i	0.326960	−	0.566311i	−0.654947	−	0.755675i	$-0.727309\pi$
$839$	9.47055	−	16.4035i	0.326960	−	0.566311i	0.981907	+	0.189364i	$0.0606425\pi$
$840$		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
$845$	−4.59778			−0.158168
$846$		0			0
$847$		0			0
$848$	19.6676	−	34.0652i	0.675387	−	1.16980i
$849$		0			0
$850$	−9.44151	−	16.3532i	−0.323841	−	0.560909i
$851$	−1.14268	−	1.97917i	−0.0391704	−	0.0678452i
$852$		0			0
$853$	−9.97922	+	17.2845i	−0.341682	+	0.591811i	−0.984745	−	0.174002i	$-0.944330\pi$
$853$	−9.97922	+	17.2845i	−0.341682	+	0.591811i	0.643063	+	0.765813i	$0.277663\pi$
$854$		0			0
$855$		0			0
$856$	17.6176			0.602156
$857$	−8.20001	+	14.2028i	−0.280107	+	0.485159i	−0.971411	−	0.237405i	$-0.923703\pi$
$857$	−8.20001	+	14.2028i	−0.280107	+	0.485159i	0.691304	+	0.722564i	$0.257037\pi$
$858$		0			0
$859$	−16.8575	−	29.1981i	−0.575172	−	0.996226i	−0.996023	−	0.0890968i	$-0.971602\pi$
$859$	−16.8575	−	29.1981i	−0.575172	−	0.996226i	0.420851	−	0.907130i	$-0.361731\pi$
$860$	−26.6685	−	46.1912i	−0.909389	−	1.57511i
$861$		0			0
$862$	−22.9720	+	39.7887i	−0.782429	+	1.35521i
$863$	28.6831			0.976383			0.488191	−	0.872737i	$-0.337657\pi$
$863$	28.6831			0.976383			0.488191	+	0.872737i	$0.337657\pi$
$864$		0			0
$865$	18.1444			0.616927
$866$	45.4432	−	78.7100i	1.54422	−	2.67467i
$867$		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
$872$	−170.351			−5.76880
$873$		0			0
$874$	0.483944			0.0163696
$875$		0			0
$876$		0			0
$877$	14.7621	+	25.5688i	0.498482	+	0.863396i	0.999998	−	0.00175202i	$-0.000557684\pi$
$877$	14.7621	+	25.5688i	0.498482	+	0.863396i	−0.501517	+	0.865148i	$0.667224\pi$
$878$	−28.4159	−	49.2177i	−0.958989	−	1.66102i
$879$		0			0
$880$	−15.0994	+	26.1530i	−0.509001	+	0.881616i
$881$	−57.5032			−1.93733			−0.968666	−	0.248366i	$-0.920107\pi$
$881$	−57.5032			−1.93733			−0.968666	+	0.248366i	$0.920107\pi$
$882$		0			0
$883$	19.8715			0.668730			0.334365	−	0.942444i	$-0.391478\pi$
$883$	19.8715			0.668730			0.334365	+	0.942444i	$0.391478\pi$
$884$	−23.9079	+	41.4097i	−0.804109	+	1.39276i
$885$		0			0
$886$	−41.8918	−	72.5587i	−1.40738	−	2.43766i
$887$	18.5475	+	32.1253i	0.622766	+	1.07866i	0.988968	+	0.148127i	$0.0473243\pi$
$887$	18.5475	+	32.1253i	0.622766	+	1.07866i	−0.366203	+	0.930535i	$0.619342\pi$
$888$		0			0
$889$		0			0
$890$	11.1432			0.373519
$891$		0			0
$892$	−89.8139			−3.00719
$893$	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
$898$	−45.1783	+	78.2511i	−1.50762	+	2.61127i
$899$	33.7913			1.12700
$900$		0			0
$901$	7.80503			0.260023
$902$	−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	−0.994349	−	0.106157i	$-0.966145\pi$
$907$	−12.2044	+	21.1386i	−0.405240	+	0.701896i	0.589110	+	0.808053i	$0.299479\pi$
$908$	−91.6993			−3.04315
$909$		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
$913$	9.43234	+	16.3373i	0.312165	+	0.540685i
$914$	−32.2971	−	55.9401i	−1.06829	−	1.85034i
$915$		0			0
$916$	−53.1538	+	92.0652i	−1.75625	+	3.04192i
$917$		0			0
$918$		0			0
$919$	−28.5976			−0.943348			−0.471674	−	0.881773i	$-0.656350\pi$
$919$	−28.5976			−0.943348			−0.471674	+	0.881773i	$0.656350\pi$
$920$	−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
$926$	−98.4196			−3.23427
$927$		0			0
$928$	91.0065			2.98744
$929$	−22.7285	+	39.3669i	−0.745698	+	1.29159i	0.204170	+	0.978935i	$0.434550\pi$
$929$	−22.7285	+	39.3669i	−0.745698	+	1.29159i	−0.949868	+	0.312651i	$0.898783\pi$
$930$		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
$935$	−5.99217			−0.195965
$936$		0			0
$937$	27.0083			0.882322			0.441161	−	0.897428i	$-0.354567\pi$
$937$	27.0083			0.882322			0.441161	+	0.897428i	$0.354567\pi$
$938$		0			0
$939$		0			0
$940$	47.5002	+	82.2728i	1.54929	+	2.68344i
$941$	6.35657	+	11.0099i	0.207218	+	0.358912i	0.950837	−	0.309691i	$-0.100226\pi$
$941$	6.35657	+	11.0099i	0.207218	+	0.358912i	−0.743619	+	0.668604i	$0.766892\pi$
$942$		0			0
$943$	−1.42812	+	2.47358i	−0.0465060	+	0.0805508i
$944$	−64.5667			−2.10147
$945$		0			0
$946$	22.9197			0.745185
$947$	23.7724	−	41.1749i	0.772498	−	1.33801i	−0.163692	−	0.986511i	$-0.552340\pi$
$947$	23.7724	−	41.1749i	0.772498	−	1.33801i	0.936190	−	0.351494i	$-0.114326\pi$
$948$		0			0
$949$	−0.743940	−	1.28854i	−0.0241493	−	0.0418279i
$950$	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
$955$	−6.13640			−0.198569
$956$	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
$961$	−12.1028	+	20.9627i	−0.390413	+	0.676215i
$962$	−69.2309			−2.23209
$963$		0			0
$964$	157.337			5.06749
$965$	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
$971$	−44.9471			−1.44242			−0.721210	−	0.692717i	$-0.756414\pi$
$971$	−44.9471			−1.44242			−0.721210	+	0.692717i	$0.756414\pi$
$972$		0			0
$973$		0			0
$974$	9.39817	−	16.2781i	0.301137	−	0.521584i
$975$		0			0
$976$	2.71703	+	4.70603i	0.0869699	+	0.150636i
$977$	26.7552	+	46.3414i	0.855974	+	1.48259i	0.875738	+	0.482787i	$0.160375\pi$
$977$	26.7552	+	46.3414i	0.855974	+	1.48259i	−0.0197635	+	0.999805i	$0.506291\pi$
$978$		0			0
$979$	−1.74465	+	3.02182i	−0.0557593	+	0.0965779i
$980$		0			0
$981$		0			0
$982$	101.688			3.24501
$983$	5.80278	−	10.0507i	0.185080	−	0.320568i	−0.758524	−	0.651646i	$-0.774079\pi$
$983$	5.80278	−	10.0507i	0.185080	−	0.320568i	0.943603	+	0.331078i	$0.107412\pi$
$984$		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
$989$	1.78291			0.0566932
$990$		0			0
$991$	26.0091			0.826208			0.413104	−	0.910684i	$-0.364445\pi$
$991$	26.0091			0.826208			0.413104	+	0.910684i	$0.364445\pi$
$992$	−74.3398	+	128.760i	−2.36029	+	4.08814i
$993$		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	−0.208612	−	0.977999i	$-0.566895\pi$
$997$	23.4499	−	40.6164i	0.742666	−	1.28633i	0.951277	−	0.308336i	$-0.0997721\pi$
$998$	69.5753			2.20237
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.11	✓	24	63.41	even	6
441.2.f.h.148.12	yes	24	9.5	odd	6
441.2.f.h.295.11	yes	24	21.20	even	2
441.2.f.h.295.12	yes	24	3.2	odd	2
441.2.g.h.67.11		24	63.23	odd	6
441.2.g.h.67.12		24	63.5	even	6
441.2.g.h.79.11		24	21.11	odd	6
441.2.g.h.79.12		24	21.17	even	6
441.2.h.h.214.1		24	21.5	even	6
441.2.h.h.214.2		24	21.2	odd	6
441.2.h.h.373.1		24	63.59	even	6
441.2.h.h.373.2		24	63.32	odd	6
1323.2.f.h.442.1		24	63.13	odd	6	inner
1323.2.f.h.442.2		24	9.4	even	3	inner
1323.2.f.h.883.1		24	7.6	odd	2	inner
1323.2.f.h.883.2		24	1.1	even	1	trivial
1323.2.g.h.361.1		24	63.58	even	3
1323.2.g.h.361.2		24	63.40	odd	6
1323.2.g.h.667.1		24	7.4	even	3
1323.2.g.h.667.2		24	7.3	odd	6
1323.2.h.h.226.11		24	63.31	odd	6
1323.2.h.h.226.12		24	63.4	even	3
1323.2.h.h.802.11		24	7.5	odd	6
1323.2.h.h.802.12		24	7.2	even	3
3969.2.a.bh.1.1		12	9.2	odd	6
3969.2.a.bh.1.2		12	63.20	even	6
3969.2.a.bi.1.11		12	63.34	odd	6
3969.2.a.bi.1.12		12	9.7	even	3

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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.35757 + 2.35137i) q^{2} +(-2.68597 - 4.65224i) q^{4} +(-0.793197 - 1.37386i) q^{5} +9.15528 q^{8} +O(q^{10})\)	\(q+(-1.35757 + 2.35137i) q^{2} +(-2.68597 - 4.65224i) q^{4} +(-0.793197 - 1.37386i) q^{5} +9.15528 q^{8} +4.30727 q^{10} +(-0.674376 + 1.16805i) q^{11} +(1.58916 + 2.75251i) q^{13} +(-7.05696 + 12.2230i) q^{16} -2.80054 q^{17} +0.625693 q^{19} +(-4.26101 + 7.38028i) q^{20} +(-1.83102 - 3.17142i) q^{22} +(-0.142434 - 0.246702i) q^{23} +(1.24168 - 2.15065i) q^{25} -8.62957 q^{26} +(-2.27396 + 3.93861i) q^{29} +(-3.71502 - 6.43461i) q^{31} +(-10.0053 - 17.3297i) q^{32} +(3.80191 - 6.58511i) q^{34} +8.02252 q^{37} +(-0.849420 + 1.47124i) q^{38} +(-7.26194 - 12.5780i) q^{40} +(-5.01329 - 8.68327i) q^{41} +(-3.12937 + 5.42022i) q^{43} +7.24542 q^{44} +0.773452 q^{46} +(5.57383 - 9.65415i) q^{47} +(3.37132 + 5.83930i) q^{50} +(8.53689 - 14.7863i) q^{52} -2.78698 q^{53} +2.13965 q^{55} +(-6.17410 - 10.6939i) q^{58} +(2.28734 + 3.96180i) q^{59} +(0.192507 - 0.333432i) q^{61} +20.1736 q^{62} +26.1036 q^{64} +(2.52104 - 4.36656i) q^{65} +(1.26958 + 2.19898i) q^{67} +(7.52217 + 13.0288i) q^{68} +1.45208 q^{71} -0.468134 q^{73} +(-10.8911 + 18.8639i) q^{74} +(-1.68059 - 2.91087i) q^{76} +(7.85620 - 13.6073i) q^{79} +22.3902 q^{80} +27.2235 q^{82} +(6.99338 - 12.1129i) q^{83} +(2.22138 + 3.84754i) q^{85} +(-8.49665 - 14.7166i) q^{86} +(-6.17410 + 10.6939i) q^{88} +2.58706 q^{89} +(-0.765146 + 1.32527i) q^{92} +(15.1337 + 26.2123i) q^{94} +(-0.496297 - 0.859612i) q^{95} +(7.22962 - 12.5221i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 - 20 * q^11 - 12 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 - 48 * q^32 + 24 * q^37 + 112 * q^44 - 48 * q^46 + 4 * q^50 + 64 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 - 68 * q^74 + 12 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 - 64 * q^95

Introduction

L-functions

Modular forms

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Database

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