LMFDB - Embedded newform 1323.2.h.h.802.2

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			802.2
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.h.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17631 q^{2} +2.73633 q^{4} +(0.634145 - 1.09837i) q^{5} -1.60248 q^{8} +O(q^{10})$	\(q-2.17631 q^{2} +2.73633 q^{4} +(0.634145 - 1.09837i) q^{5} -1.60248 q^{8} +(-1.38010 + 2.39040i) q^{10} +(-2.73867 - 4.74351i) q^{11} +(2.37268 + 4.10960i) q^{13} -1.98516 q^{16} +(-2.40822 + 4.17116i) q^{17} +(-2.69059 - 4.66025i) q^{19} +(1.73523 - 3.00550i) q^{20} +(5.96019 + 10.3233i) q^{22} +(-2.58816 + 4.48282i) q^{23} +(1.69572 + 2.93707i) q^{25} +(-5.16368 - 8.94376i) q^{26} +(-2.01656 + 3.49278i) q^{29} -1.46419 q^{31} +7.52529 q^{32} +(5.24103 - 9.07773i) q^{34} +(-0.959170 - 1.66133i) q^{37} +(5.85557 + 10.1421i) q^{38} +(-1.01621 + 1.76012i) q^{40} +(1.94808 + 3.37418i) q^{41} +(-1.66016 + 2.87549i) q^{43} +(-7.49389 - 12.9798i) q^{44} +(5.63263 - 9.75600i) q^{46} -3.15546 q^{47} +(-3.69042 - 6.39199i) q^{50} +(6.49243 + 11.2452i) q^{52} +(-3.57149 + 6.18601i) q^{53} -6.94684 q^{55} +(4.38866 - 7.60138i) q^{58} -0.308683 q^{59} +10.3429 q^{61} +3.18652 q^{62} -12.4070 q^{64} +6.01848 q^{65} +4.47310 q^{67} +(-6.58968 + 11.4137i) q^{68} +1.96688 q^{71} +(5.27515 - 9.13683i) q^{73} +(2.08745 + 3.61557i) q^{74} +(-7.36235 - 12.7520i) q^{76} -9.01643 q^{79} +(-1.25888 + 2.18044i) q^{80} +(-4.23963 - 7.34326i) q^{82} +(5.08023 - 8.79921i) q^{83} +(3.05432 + 5.29023i) q^{85} +(3.61303 - 6.25796i) q^{86} +(4.38866 + 7.60138i) q^{88} +(2.59776 + 4.49945i) q^{89} +(-7.08205 + 12.2665i) q^{92} +6.86726 q^{94} -6.82490 q^{95} +(-2.48521 + 4.30451i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.17631			−1.53888			−0.769442	−	0.638717i	$-0.779466\pi$
$2$	−2.17631			−1.53888			−0.769442	+	0.638717i	$0.779466\pi$
$3$		0			0
$3$		0			0
$4$	2.73633			1.36816
$5$	0.634145	−	1.09837i	0.283598	−	0.491206i	−0.688670	−	0.725075i	$-0.741805\pi$
$5$	0.634145	−	1.09837i	0.283598	−	0.491206i	0.972268	+	0.233868i	$0.0751385\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.60248			−0.566563
$9$		0			0
$10$	−1.38010	+	2.39040i	−0.436425	+	0.755910i
$11$	−2.73867	−	4.74351i	−0.825739	−	1.43022i	−0.901353	−	0.433084i	$-0.857425\pi$
$11$	−2.73867	−	4.74351i	−0.825739	−	1.43022i	0.0756148	−	0.997137i	$-0.475908\pi$
$12$		0			0
$13$	2.37268	+	4.10960i	0.658062	+	1.13980i	0.981117	+	0.193417i	$0.0619570\pi$
$13$	2.37268	+	4.10960i	0.658062	+	1.13980i	−0.323054	+	0.946380i	$0.604710\pi$
$14$		0			0
$15$		0			0
$16$	−1.98516			−0.496290
$17$	−2.40822	+	4.17116i	−0.584079	+	1.01165i	0.410911	+	0.911676i	$0.365211\pi$
$17$	−2.40822	+	4.17116i	−0.584079	+	1.01165i	−0.994990	+	0.0999785i	$0.968123\pi$
$18$		0			0
$19$	−2.69059	−	4.66025i	−0.617265	−	1.06913i	−0.989983	−	0.141189i	$-0.954907\pi$
$19$	−2.69059	−	4.66025i	−0.617265	−	1.06913i	0.372718	−	0.927945i	$-0.378426\pi$
$20$	1.73523	−	3.00550i	0.388009	−	0.672051i
$21$		0			0
$22$	5.96019	+	10.3233i	1.27072	+	2.20095i
$23$	−2.58816	+	4.48282i	−0.539668	+	0.934732i	0.459254	+	0.888305i	$0.348117\pi$
$23$	−2.58816	+	4.48282i	−0.539668	+	0.934732i	−0.998922	+	0.0464269i	$0.985217\pi$
$24$		0			0
$25$	1.69572	+	2.93707i	0.339144	+	0.587415i
$26$	−5.16368	−	8.94376i	−1.01268	−	1.75402i
$27$		0			0
$28$		0			0
$29$	−2.01656	+	3.49278i	−0.374466	+	0.648594i	−0.990247	−	0.139324i	$-0.955507\pi$
$29$	−2.01656	+	3.49278i	−0.374466	+	0.648594i	0.615781	+	0.787917i	$0.288841\pi$
$30$		0			0
$31$	−1.46419			−0.262976			−0.131488	−	0.991318i	$-0.541975\pi$
$31$	−1.46419			−0.262976			−0.131488	+	0.991318i	$0.541975\pi$
$32$	7.52529			1.33030
$33$		0			0
$34$	5.24103	−	9.07773i	0.898830	−	1.55682i
$35$		0			0
$36$		0			0
$37$	−0.959170	−	1.66133i	−0.157687	−	0.273121i	0.776347	−	0.630305i	$-0.217070\pi$
$37$	−0.959170	−	1.66133i	−0.157687	−	0.273121i	−0.934034	+	0.357184i	$0.883737\pi$
$38$	5.85557	+	10.1421i	0.949899	+	1.64527i
$39$		0			0
$40$	−1.01621	+	1.76012i	−0.160676	+	0.278299i
$41$	1.94808	+	3.37418i	0.304239	+	0.526958i	0.977092	−	0.212819i	$-0.0682644\pi$
$41$	1.94808	+	3.37418i	0.304239	+	0.526958i	−0.672852	+	0.739777i	$0.734931\pi$
$42$		0			0
$43$	−1.66016	+	2.87549i	−0.253173	+	0.438508i	−0.964398	−	0.264457i	$-0.914807\pi$
$43$	−1.66016	+	2.87549i	−0.253173	+	0.438508i	0.711225	+	0.702964i	$0.248141\pi$
$44$	−7.49389	−	12.9798i	−1.12975	−	1.95678i
$45$		0			0
$46$	5.63263	−	9.75600i	0.830486	−	1.43844i
$47$	−3.15546			−0.460271			−0.230135	−	0.973159i	$-0.573917\pi$
$47$	−3.15546			−0.460271			−0.230135	+	0.973159i	$0.573917\pi$
$48$		0			0
$49$		0			0
$50$	−3.69042	−	6.39199i	−0.521904	−	0.903964i
$51$		0			0
$52$	6.49243	+	11.2452i	0.900338	+	1.55943i
$53$	−3.57149	+	6.18601i	−0.490582	+	0.849714i	−0.999941	−	0.0108405i	$-0.996549\pi$
$53$	−3.57149	+	6.18601i	−0.490582	+	0.849714i	0.509359	+	0.860554i	$0.329883\pi$
$54$		0			0
$55$	−6.94684			−0.936712
$56$		0			0
$57$		0			0
$58$	4.38866	−	7.60138i	0.576259	−	0.998111i
$59$	−0.308683			−0.0401871			−0.0200935	−	0.999798i	$-0.506396\pi$
$59$	−0.308683			−0.0401871			−0.0200935	+	0.999798i	$0.506396\pi$
$60$		0			0
$61$	10.3429			1.32427			0.662134	−	0.749385i	$-0.269651\pi$
$61$	10.3429			1.32427			0.662134	+	0.749385i	$0.269651\pi$
$62$	3.18652			0.404689
$63$		0			0
$64$	−12.4070			−1.55088
$65$	6.01848			0.746501
$66$		0			0
$67$	4.47310			0.546476			0.273238	−	0.961946i	$-0.411905\pi$
$67$	4.47310			0.546476			0.273238	+	0.961946i	$0.411905\pi$
$68$	−6.58968	+	11.4137i	−0.799116	+	1.38411i
$69$		0			0
$70$		0			0
$71$	1.96688			0.233426			0.116713	−	0.993166i	$-0.462764\pi$
$71$	1.96688			0.233426			0.116713	+	0.993166i	$0.462764\pi$
$72$		0			0
$73$	5.27515	−	9.13683i	0.617409	−	1.06938i	−0.372547	−	0.928013i	$-0.621516\pi$
$73$	5.27515	−	9.13683i	0.617409	−	1.06938i	0.989957	−	0.141371i	$-0.0451512\pi$
$74$	2.08745	+	3.61557i	0.242662	+	0.420302i
$75$		0			0
$76$	−7.36235	−	12.7520i	−0.844520	−	1.46275i
$77$		0			0
$78$		0			0
$79$	−9.01643			−1.01443			−0.507214	−	0.861820i	$-0.669325\pi$
$79$	−9.01643			−1.01443			−0.507214	+	0.861820i	$0.669325\pi$
$80$	−1.25888	+	2.18044i	−0.140747	+	0.243781i
$81$		0			0
$82$	−4.23963	−	7.34326i	−0.468189	−	0.810927i
$83$	5.08023	−	8.79921i	0.557627	−	0.965839i	−0.440066	−	0.897965i	$-0.645045\pi$
$83$	5.08023	−	8.79921i	0.557627	−	0.965839i	0.997694	−	0.0678739i	$-0.0216216\pi$
$84$		0			0
$85$	3.05432	+	5.29023i	0.331287	+	0.573806i
$86$	3.61303	−	6.25796i	0.389603	−	0.674813i
$87$		0			0
$88$	4.38866	+	7.60138i	0.467833	+	0.810310i
$89$	2.59776	+	4.49945i	0.275362	+	0.476941i	0.970226	−	0.242200i	$-0.0778690\pi$
$89$	2.59776	+	4.49945i	0.275362	+	0.476941i	−0.694864	+	0.719141i	$0.744536\pi$
$90$		0			0
$91$		0			0
$92$	−7.08205	+	12.2665i	−0.738354	+	1.27887i
$93$		0			0
$94$	6.86726			0.708303
$95$	−6.82490			−0.700220
$96$		0			0
$97$	−2.48521	+	4.30451i	−0.252335	+	0.437057i	−0.964168	−	0.265291i	$-0.914532\pi$
$97$	−2.48521	+	4.30451i	−0.252335	+	0.437057i	0.711833	+	0.702348i	$0.247865\pi$
$98$		0			0
$99$		0			0
$100$	4.64005	+	8.03680i	0.464005	+	0.803680i
$101$	0.00266904	+	0.00462292i	0.000265580	+	0.000459997i	0.866158	−	0.499770i	$-0.166582\pi$
$101$	0.00266904	+	0.00462292i	0.000265580	+	0.000459997i	−0.865893	+	0.500230i	$0.833249\pi$
$102$		0			0
$103$	−6.51741	+	11.2885i	−0.642180	+	1.11229i	0.342765	+	0.939421i	$0.388636\pi$
$103$	−6.51741	+	11.2885i	−0.642180	+	1.11229i	−0.984945	+	0.172867i	$0.944697\pi$
$104$	−3.80217	−	6.58555i	−0.372834	−	0.645767i
$105$		0			0
$106$	7.77268	−	13.4627i	0.754950	−	1.30761i
$107$	4.71081	+	8.15936i	0.455411	+	0.788795i	0.998712	−	0.0507430i	$-0.0161589\pi$
$107$	4.71081	+	8.15936i	0.455411	+	0.788795i	−0.543301	+	0.839538i	$0.682826\pi$
$108$		0			0
$109$	−8.44513	+	14.6274i	−0.808896	+	1.40105i	0.104732	+	0.994500i	$0.466601\pi$
$109$	−8.44513	+	14.6274i	−0.808896	+	1.40105i	−0.913629	+	0.406549i	$0.866732\pi$
$110$	15.1185			1.44149
$111$		0			0
$112$		0			0
$113$	3.07313	+	5.32281i	0.289095	+	0.500728i	0.973594	−	0.228286i	$-0.0733122\pi$
$113$	3.07313	+	5.32281i	0.289095	+	0.500728i	−0.684499	+	0.729014i	$0.739979\pi$
$114$		0			0
$115$	3.28253	+	5.68551i	0.306098	+	0.530176i
$116$	−5.51797	+	9.55741i	−0.512331	+	0.887383i
$117$		0			0
$118$	0.671790			0.0618432
$119$		0			0
$120$		0			0
$121$	−9.50058	+	16.4555i	−0.863689	+	1.49595i
$122$	−22.5093			−2.03790
$123$		0			0
$124$	−4.00649			−0.359794
$125$	10.6428			0.951919
$126$		0			0
$127$	−13.9305			−1.23613			−0.618065	−	0.786127i	$-0.712083\pi$
$127$	−13.9305			−1.23613			−0.618065	+	0.786127i	$0.712083\pi$
$128$	11.9510			1.05633
$129$		0			0
$130$	−13.0981			−1.14878
$131$	−0.0895778	+	0.155153i	−0.00782645	+	0.0135558i	−0.869912	−	0.493207i	$-0.835825\pi$
$131$	−0.0895778	+	0.155153i	−0.00782645	+	0.0135558i	0.862086	+	0.506763i	$0.169158\pi$
$132$		0			0
$133$		0			0
$134$	−9.73486			−0.840964
$135$		0			0
$136$	3.85913	−	6.68420i	0.330917	−	0.573166i
$137$	1.57603	+	2.72977i	0.134649	+	0.233220i	0.925463	−	0.378837i	$-0.123676\pi$
$137$	1.57603	+	2.72977i	0.134649	+	0.233220i	−0.790814	+	0.612056i	$0.790343\pi$
$138$		0			0
$139$	9.42857	+	16.3308i	0.799721	+	1.38516i	0.919798	+	0.392392i	$0.128352\pi$
$139$	9.42857	+	16.3308i	0.799721	+	1.38516i	−0.120077	+	0.992765i	$0.538314\pi$
$140$		0			0
$141$		0			0
$142$	−4.28054			−0.359215
$143$	12.9959	−	22.5096i	1.08677	−	1.88235i
$144$		0			0
$145$	2.55758	+	4.42986i	0.212396	+	0.367880i
$146$	−11.4804	+	19.8846i	−0.950122	+	1.64566i
$147$		0			0
$148$	−2.62461	−	4.54595i	−0.215741	−	0.373675i
$149$	−10.6370	+	18.4238i	−0.871418	+	1.50934i	−0.0108879	+	0.999941i	$0.503466\pi$
$149$	−10.6370	+	18.4238i	−0.871418	+	1.50934i	−0.860530	+	0.509400i	$0.829868\pi$
$150$		0			0
$151$	−3.18281	−	5.51278i	−0.259013	−	0.448624i	0.706965	−	0.707249i	$-0.250064\pi$
$151$	−3.18281	−	5.51278i	−0.259013	−	0.448624i	−0.965978	+	0.258625i	$0.916731\pi$
$152$	4.31163	+	7.46796i	0.349719	+	0.605731i
$153$		0			0
$154$		0			0
$155$	−0.928506	+	1.60822i	−0.0745794	+	0.129175i
$156$		0			0
$157$	1.39595			0.111409			0.0557045	−	0.998447i	$-0.482260\pi$
$157$	1.39595			0.111409			0.0557045	+	0.998447i	$0.482260\pi$
$158$	19.6226			1.56109
$159$		0			0
$160$	4.77212	−	8.26556i	0.377269	−	0.653450i
$161$		0			0
$162$		0			0
$163$	9.53086	+	16.5079i	0.746515	+	1.29300i	0.949484	+	0.313816i	$0.101608\pi$
$163$	9.53086	+	16.5079i	0.746515	+	1.29300i	−0.202969	+	0.979185i	$0.565059\pi$
$164$	5.33059	+	9.23286i	0.416249	+	0.720965i
$165$		0			0
$166$	−11.0562	+	19.1498i	−0.858124	+	1.48631i
$167$	−0.872003	−	1.51035i	−0.0674776	−	0.116875i	0.830313	−	0.557298i	$-0.188162\pi$
$167$	−0.872003	−	1.51035i	−0.0674776	−	0.116875i	−0.897790	+	0.440423i	$0.854828\pi$
$168$		0			0
$169$	−4.75919	+	8.24317i	−0.366092	+	0.634090i
$170$	−6.64715	−	11.5132i	−0.509813	−	0.883022i
$171$		0			0
$172$	−4.54276	+	7.86828i	−0.346382	+	0.599951i
$173$	10.0759			0.766056			0.383028	−	0.923737i	$-0.374881\pi$
$173$	10.0759			0.766056			0.383028	+	0.923737i	$0.374881\pi$
$174$		0			0
$175$		0			0
$176$	5.43669	+	9.41662i	0.409806	+	0.709805i
$177$		0			0
$178$	−5.65353	−	9.79221i	−0.423750	−	0.733957i
$179$	−9.27118	+	16.0582i	−0.692961	+	1.20024i	0.277902	+	0.960609i	$0.410361\pi$
$179$	−9.27118	+	16.0582i	−0.692961	+	1.20024i	−0.970863	+	0.239634i	$0.922973\pi$
$180$		0			0
$181$	−8.80982			−0.654829			−0.327414	−	0.944881i	$-0.606177\pi$
$181$	−8.80982			−0.654829			−0.327414	+	0.944881i	$0.606177\pi$
$182$		0			0
$183$		0			0
$184$	4.14747	−	7.18363i	0.305756	−	0.529584i
$185$	−2.43301			−0.178879
$186$		0			0
$187$	26.3812			1.92919
$188$	−8.63437			−0.629726
$189$		0			0
$190$	14.8531			1.07756
$191$	−4.90939			−0.355231			−0.177615	−	0.984100i	$-0.556838\pi$
$191$	−4.90939			−0.355231			−0.177615	+	0.984100i	$0.556838\pi$
$192$		0			0
$193$	−9.76760			−0.703087			−0.351544	−	0.936171i	$-0.614343\pi$
$193$	−9.76760			−0.703087			−0.351544	+	0.936171i	$0.614343\pi$
$194$	5.40859	−	9.36796i	0.388314	−	0.672580i
$195$		0			0
$196$		0			0
$197$	−3.31445			−0.236145			−0.118073	−	0.993005i	$-0.537672\pi$
$197$	−3.31445			−0.236145			−0.118073	+	0.993005i	$0.537672\pi$
$198$		0			0
$199$	−5.54432	+	9.60304i	−0.393026	+	0.680742i	−0.992847	−	0.119393i	$-0.961905\pi$
$199$	−5.54432	+	9.60304i	−0.393026	+	0.680742i	0.599821	+	0.800134i	$0.295239\pi$
$200$	−2.71736	−	4.70661i	−0.192146	−	0.332807i
$201$		0			0
$202$	−0.00580866	−	0.0100609i	−0.000408696	−	0.000707883i
$203$		0			0
$204$		0			0
$205$	4.94146			0.345127
$206$	14.1839	−	24.5673i	0.988240	−	1.71168i
$207$		0			0
$208$	−4.71014	−	8.15821i	−0.326590	−	0.565670i
$209$	−14.7373	+	25.5257i	−1.01940	+	1.76565i
$210$		0			0
$211$	−3.66118	−	6.34135i	−0.252046	−	0.436557i	0.712043	−	0.702136i	$-0.247770\pi$
$211$	−3.66118	−	6.34135i	−0.252046	−	0.436557i	−0.964089	+	0.265579i	$0.914437\pi$
$212$	−9.77278	+	16.9270i	−0.671198	+	1.16255i
$213$		0			0
$214$	−10.2522	−	17.7573i	−0.700825	−	1.21386i
$215$	2.10557	+	3.64695i	0.143599	+	0.248720i
$216$		0			0
$217$		0			0
$218$	18.3792	−	31.8337i	1.24480	−	2.15605i
$219$		0			0
$220$	−19.0088			−1.28158
$221$	−22.8557			−1.53744
$222$		0			0
$223$	2.02765	−	3.51199i	0.135782	−	0.235181i	−0.790114	−	0.612960i	$-0.789979\pi$
$223$	2.02765	−	3.51199i	0.135782	−	0.235181i	0.925896	+	0.377779i	$0.123312\pi$
$224$		0			0
$225$		0			0
$226$	−6.68808	−	11.5841i	−0.444884	−	0.770562i
$227$	0.667087	+	1.15543i	0.0442761	+	0.0766884i	0.887314	−	0.461165i	$-0.152569\pi$
$227$	0.667087	+	1.15543i	0.0442761	+	0.0766884i	−0.843038	+	0.537854i	$0.819235\pi$
$228$		0			0
$229$	7.99832	−	13.8535i	0.528544	−	0.915465i	−0.470902	−	0.882185i	$-0.656072\pi$
$229$	7.99832	−	13.8535i	0.528544	−	0.915465i	0.999446	−	0.0332795i	$-0.0105952\pi$
$230$	−7.14381	−	12.3734i	−0.471049	−	0.815880i
$231$		0			0
$232$	3.23150	−	5.59712i	0.212158	−	0.367469i
$233$	4.06542	+	7.04151i	0.266334	+	0.461305i	0.967912	−	0.251288i	$-0.0808542\pi$
$233$	4.06542	+	7.04151i	0.266334	+	0.461305i	−0.701578	+	0.712593i	$0.747521\pi$
$234$		0			0
$235$	−2.00102	+	3.46586i	−0.130532	+	0.226088i
$236$	−0.844658			−0.0549825
$237$		0			0
$238$		0			0
$239$	−11.0509	−	19.1407i	−0.714823	−	1.23811i	−0.963028	−	0.269403i	$-0.913174\pi$
$239$	−11.0509	−	19.1407i	−0.714823	−	1.23811i	0.248204	−	0.968708i	$-0.420160\pi$
$240$		0			0
$241$	−13.7973	−	23.8977i	−0.888765	−	1.53939i	−0.841336	−	0.540512i	$-0.818230\pi$
$241$	−13.7973	−	23.8977i	−0.888765	−	1.53939i	−0.0474292	−	0.998875i	$-0.515103\pi$
$242$	20.6762	−	35.8122i	1.32912	−	2.30210i
$243$		0			0
$244$	28.3015			1.81182
$245$		0			0
$246$		0			0
$247$	12.7678	−	22.1145i	0.812397	−	1.40711i
$248$	2.34633			0.148992
$249$		0			0
$250$	−23.1620			−1.46489
$251$	16.5610			1.04532			0.522661	−	0.852541i	$-0.324939\pi$
$251$	16.5610			1.04532			0.522661	+	0.852541i	$0.324939\pi$
$252$		0			0
$253$	28.3524			1.78250
$254$	30.3171			1.90226
$255$		0			0
$256$	−1.19503			−0.0746896
$257$	1.03287	−	1.78898i	0.0644285	−	0.111593i	−0.832012	−	0.554758i	$-0.812811\pi$
$257$	1.03287	−	1.78898i	0.0644285	−	0.111593i	0.896440	+	0.443164i	$0.146144\pi$
$258$		0			0
$259$		0			0
$260$	16.4686			1.02134
$261$		0			0
$262$	0.194949	−	0.337662i	0.0120440	−	0.0208608i
$263$	5.06482	+	8.77252i	0.312310	+	0.540937i	0.978862	−	0.204522i	$-0.0655639\pi$
$263$	5.06482	+	8.77252i	0.312310	+	0.540937i	−0.666552	+	0.745458i	$0.732231\pi$
$264$		0			0
$265$	4.52969	+	7.84565i	0.278257	+	0.481954i
$266$		0			0
$267$		0			0
$268$	12.2399			0.747670
$269$	−7.54972	+	13.0765i	−0.460315	+	0.797289i	−0.998976	−	0.0452336i	$-0.985597\pi$
$269$	−7.54972	+	13.0765i	−0.460315	+	0.797289i	0.538662	+	0.842522i	$0.318930\pi$
$270$		0			0
$271$	14.4026	+	24.9459i	0.874893	+	1.51536i	0.856877	+	0.515521i	$0.172402\pi$
$271$	14.4026	+	24.9459i	0.874893	+	1.51536i	0.0180156	+	0.999838i	$0.494265\pi$
$272$	4.78070	−	8.28041i	0.289872	−	0.502074i
$273$		0			0
$274$	−3.42993	−	5.94082i	−0.207210	−	0.358898i
$275$	9.28802	−	16.0873i	0.560089	−	0.970102i
$276$		0			0
$277$	1.34982	+	2.33795i	0.0811026	+	0.140474i	0.903724	−	0.428116i	$-0.140823\pi$
$277$	1.34982	+	2.33795i	0.0811026	+	0.140474i	−0.822621	+	0.568590i	$0.807489\pi$
$278$	−20.5195	−	35.5408i	−1.23068	−	2.13160i
$279$		0			0
$280$		0			0
$281$	2.46312	−	4.26626i	0.146938	−	0.254503i	−0.783157	−	0.621825i	$-0.786392\pi$
$281$	2.46312	−	4.26626i	0.146938	−	0.254503i	0.930094	+	0.367321i	$0.119725\pi$
$282$		0			0
$283$	3.58157			0.212903			0.106451	−	0.994318i	$-0.466051\pi$
$283$	3.58157			0.212903			0.106451	+	0.994318i	$0.466051\pi$
$284$	5.38203			0.319365
$285$		0			0
$286$	−28.2832	+	48.9879i	−1.67242	+	2.89672i
$287$		0			0
$288$		0			0
$289$	−3.09903	−	5.36768i	−0.182296	−	0.315746i
$290$	−5.56609	−	9.64075i	−0.326852	−	0.566125i
$291$		0			0
$292$	14.4345	−	25.0014i	0.844718	−	1.46309i
$293$	−12.1955	−	21.1232i	−0.712469	−	1.23403i	−0.963928	−	0.266164i	$-0.914244\pi$
$293$	−12.1955	−	21.1232i	−0.712469	−	1.23403i	0.251459	−	0.967868i	$-0.419090\pi$
$294$		0			0
$295$	−0.195750	+	0.339048i	−0.0113970	+	0.0197401i
$296$	1.53705	+	2.66225i	0.0893394	+	0.154740i
$297$		0			0
$298$	23.1494	−	40.0960i	1.34101	−	2.32270i
$299$	−24.5634			−1.42054
$300$		0			0
$301$		0			0
$302$	6.92678	+	11.9975i	0.398591	+	0.690380i
$303$		0			0
$304$	5.34126	+	9.25134i	0.306342	+	0.530600i
$305$	6.55887	−	11.3603i	0.375560	−	0.650489i
$306$		0			0
$307$	−23.9025			−1.36419			−0.682094	−	0.731265i	$-0.738930\pi$
$307$	−23.9025			−1.36419			−0.682094	+	0.731265i	$0.738930\pi$
$308$		0			0
$309$		0			0
$310$	2.02072	−	3.49998i	0.114769	−	0.198786i
$311$	12.9416			0.733853			0.366926	−	0.930250i	$-0.380410\pi$
$311$	12.9416			0.733853			0.366926	+	0.930250i	$0.380410\pi$
$312$		0			0
$313$	−26.8681			−1.51867			−0.759336	−	0.650698i	$-0.774476\pi$
$313$	−26.8681			−1.51867			−0.759336	+	0.650698i	$0.774476\pi$
$314$	−3.03802			−0.171446
$315$		0			0
$316$	−24.6719			−1.38790
$317$	−8.31169			−0.466831			−0.233415	−	0.972377i	$-0.574990\pi$
$317$	−8.31169			−0.466831			−0.233415	+	0.972377i	$0.574990\pi$
$318$		0			0
$319$	22.0907			1.23684
$320$	−7.86786	+	13.6275i	−0.439827	+	0.761803i
$321$		0			0
$322$		0			0
$323$	25.9182			1.44212
$324$		0			0
$325$	−8.04680	+	13.9375i	−0.446356	+	0.773111i
$326$	−20.7421	−	35.9264i	−1.14880	−	1.98978i
$327$		0			0
$328$	−3.12177	−	5.40706i	−0.172371	−	0.298555i
$329$		0			0
$330$		0			0
$331$	12.3978			0.681443			0.340722	−	0.940164i	$-0.389329\pi$
$331$	12.3978			0.681443			0.340722	+	0.940164i	$0.389329\pi$
$332$	13.9012	−	24.0775i	0.762926	−	1.32143i
$333$		0			0
$334$	1.89775	+	3.28700i	0.103840	+	0.179857i
$335$	2.83659	−	4.91312i	0.154980	−	0.268433i
$336$		0			0
$337$	−12.9588	−	22.4454i	−0.705913	−	1.22268i	−0.966361	−	0.257189i	$-0.917204\pi$
$337$	−12.9588	−	22.4454i	−0.705913	−	1.22268i	0.260448	−	0.965488i	$-0.416130\pi$
$338$	10.3575	−	17.9397i	0.563373	−	0.975791i
$339$		0			0
$340$	8.35762	+	14.4758i	0.453256	+	0.785062i
$341$	4.00992	+	6.94538i	0.217149	+	0.376113i
$342$		0			0
$343$		0			0
$344$	2.66038	−	4.60792i	0.143438	−	0.248442i
$345$		0			0
$346$	−21.9283			−1.17887
$347$	16.8483			0.904464			0.452232	−	0.891900i	$-0.350628\pi$
$347$	16.8483			0.904464			0.452232	+	0.891900i	$0.350628\pi$
$348$		0			0
$349$	15.5503	−	26.9340i	0.832390	−	1.44174i	−0.0637477	−	0.997966i	$-0.520305\pi$
$349$	15.5503	−	26.9340i	0.832390	−	1.44174i	0.896138	−	0.443776i	$-0.146361\pi$
$350$		0			0
$351$		0			0
$352$	−20.6092	−	35.6963i	−1.09848	−	1.90262i
$353$	1.32969	+	2.30309i	0.0707722	+	0.122581i	0.899240	−	0.437456i	$-0.144120\pi$
$353$	1.32969	+	2.30309i	0.0707722	+	0.122581i	−0.828468	+	0.560037i	$0.810787\pi$
$354$		0			0
$355$	1.24729	−	2.16036i	0.0661991	−	0.114660i
$356$	7.10833	+	12.3120i	0.376741	+	0.652534i
$357$		0			0
$358$	20.1770	−	34.9476i	1.06639	−	1.84704i
$359$	−16.2715	−	28.1830i	−0.858775	−	1.48744i	−0.873098	−	0.487545i	$-0.837893\pi$
$359$	−16.2715	−	28.1830i	−0.858775	−	1.48744i	0.0143230	−	0.999897i	$-0.495441\pi$
$360$		0			0
$361$	−4.97859	+	8.62318i	−0.262031	+	0.453852i
$362$	19.1729			1.00771
$363$		0			0
$364$		0			0
$365$	−6.69042	−	11.5881i	−0.350192	−	0.606551i
$366$		0			0
$367$	−7.07678	−	12.2573i	−0.369405	−	0.639828i	0.620068	−	0.784548i	$-0.287105\pi$
$367$	−7.07678	−	12.2573i	−0.369405	−	0.639828i	−0.989473	+	0.144720i	$0.953772\pi$
$368$	5.13790	−	8.89911i	0.267832	−	0.463898i
$369$		0			0
$370$	5.29499			0.275273
$371$		0			0
$372$		0			0
$373$	−1.33814	+	2.31773i	−0.0692863	+	0.120007i	−0.898587	−	0.438795i	$-0.855406\pi$
$373$	−1.33814	+	2.31773i	−0.0692863	+	0.120007i	0.829301	+	0.558802i	$0.188739\pi$
$374$	−57.4137			−2.96879
$375$		0			0
$376$	5.05656			0.260772
$377$	−19.1386			−0.985687
$378$		0			0
$379$	−0.312929			−0.0160741			−0.00803705	−	0.999968i	$-0.502558\pi$
$379$	−0.312929			−0.0160741			−0.00803705	+	0.999968i	$0.502558\pi$
$380$	−18.6752			−0.958017
$381$		0			0
$382$	10.6844			0.546659
$383$	−4.49440	+	7.78453i	−0.229653	+	0.397771i	−0.957705	−	0.287751i	$-0.907093\pi$
$383$	−4.49440	+	7.78453i	−0.229653	+	0.397771i	0.728052	+	0.685522i	$0.240426\pi$
$384$		0			0
$385$		0			0
$386$	21.2573			1.08197
$387$		0			0
$388$	−6.80036	+	11.7786i	−0.345236	+	0.597966i
$389$	−13.4934	−	23.3713i	−0.684144	−	1.18497i	−0.973705	−	0.227813i	$-0.926842\pi$
$389$	−13.4934	−	23.3713i	−0.684144	−	1.18497i	0.289560	−	0.957160i	$-0.406491\pi$
$390$		0			0
$391$	−12.4657	−	21.5912i	−0.630417	−	1.09191i
$392$		0			0
$393$		0			0
$394$	7.21328			0.363400
$395$	−5.71772	+	9.90339i	−0.287690	+	0.498293i
$396$		0			0
$397$	−14.7503	−	25.5482i	−0.740295	−	1.28223i	−0.952361	−	0.304973i	$-0.901352\pi$
$397$	−14.7503	−	25.5482i	−0.740295	−	1.28223i	0.212066	−	0.977255i	$-0.431981\pi$
$398$	12.0662	−	20.8992i	0.604822	−	1.04758i
$399$		0			0
$400$	−3.36628	−	5.83056i	−0.168314	−	0.291528i
$401$	−17.1392	+	29.6860i	−0.855891	+	1.48245i	0.0199251	+	0.999801i	$0.493657\pi$
$401$	−17.1392	+	29.6860i	−0.855891	+	1.48245i	−0.875816	+	0.482645i	$0.839676\pi$
$402$		0			0
$403$	−3.47404	−	6.01721i	−0.173054	−	0.299739i
$404$	0.00730338	+	0.0126498i	0.000363357	+	0.000629352i
$405$		0			0
$406$		0			0
$407$	−5.25369	+	9.09966i	−0.260416	+	0.451054i
$408$		0			0
$409$	10.9845			0.543149			0.271574	−	0.962417i	$-0.412456\pi$
$409$	10.9845			0.543149			0.271574	+	0.962417i	$0.412456\pi$
$410$	−10.7542			−0.531110
$411$		0			0
$412$	−17.8338	+	30.8890i	−0.878608	+	1.52179i
$413$		0			0
$414$		0			0
$415$	−6.44320	−	11.1599i	−0.316284	−	0.547820i
$416$	17.8551	+	30.9259i	0.875417	+	1.51627i
$417$		0			0
$418$	32.0729	−	55.5519i	1.56874	−	2.71713i
$419$	3.33207	+	5.77132i	0.162782	+	0.281947i	0.935866	−	0.352357i	$-0.114620\pi$
$419$	3.33207	+	5.77132i	0.162782	+	0.281947i	−0.773083	+	0.634305i	$0.781286\pi$
$420$		0			0
$421$	−17.0430	+	29.5193i	−0.830625	+	1.43868i	0.0669186	+	0.997758i	$0.478683\pi$
$421$	−17.0430	+	29.5193i	−0.830625	+	1.43868i	−0.897543	+	0.440926i	$0.854650\pi$
$422$	7.96787	+	13.8008i	0.387870	+	0.671810i
$423$		0			0
$424$	5.72325	−	9.91297i	0.277946	−	0.481416i
$425$	−16.3347			−0.792348
$426$		0			0
$427$		0			0
$428$	12.8903	+	22.3267i	0.623077	+	1.07920i
$429$		0			0
$430$	−4.58237	−	7.93690i	−0.220982	−	0.382751i
$431$	1.12969	−	1.95669i	0.0544155	−	0.0942504i	−0.837535	−	0.546384i	$-0.816004\pi$
$431$	1.12969	−	1.95669i	0.0544155	−	0.0942504i	0.891950	+	0.452134i	$0.149337\pi$
$432$		0			0
$433$	34.3904			1.65270			0.826348	−	0.563160i	$-0.190415\pi$
$433$	34.3904			1.65270			0.826348	+	0.563160i	$0.190415\pi$
$434$		0			0
$435$		0			0
$436$	−23.1086	+	40.0254i	−1.10670	+	1.91687i
$437$	27.8547			1.33247
$438$		0			0
$439$	5.99139			0.285953			0.142977	−	0.989726i	$-0.454333\pi$
$439$	5.99139			0.285953			0.142977	+	0.989726i	$0.454333\pi$
$440$	11.1322			0.530706
$441$		0			0
$442$	49.7411			2.36594
$443$	39.4380			1.87376			0.936879	−	0.349654i	$-0.113701\pi$
$443$	39.4380			1.87376			0.936879	+	0.349654i	$0.113701\pi$
$444$		0			0
$445$	6.58942			0.312369
$446$	−4.41280	+	7.64319i	−0.208952	+	0.361916i
$447$		0			0
$448$		0			0
$449$	−2.45092			−0.115666			−0.0578330	−	0.998326i	$-0.518419\pi$
$449$	−2.45092			−0.115666			−0.0578330	+	0.998326i	$0.518419\pi$
$450$		0			0
$451$	10.6703	−	18.4815i	0.502444	−	0.870259i
$452$	8.40909	+	14.5650i	0.395530	+	0.685078i
$453$		0			0
$454$	−1.45179	−	2.51457i	−0.0681358	−	0.118015i
$455$		0			0
$456$		0			0
$457$	11.0212			0.515548			0.257774	−	0.966205i	$-0.417011\pi$
$457$	11.0212			0.515548			0.257774	+	0.966205i	$0.417011\pi$
$458$	−17.4068	+	30.1495i	−0.813368	+	1.40879i
$459$		0			0
$460$	8.98208	+	15.5574i	0.418792	+	0.725369i
$461$	−14.6540	+	25.3814i	−0.682503	+	1.18213i	0.291711	+	0.956506i	$0.405775\pi$
$461$	−14.6540	+	25.3814i	−0.682503	+	1.18213i	−0.974215	+	0.225624i	$0.927558\pi$
$462$		0			0
$463$	0.593566	+	1.02809i	0.0275853	+	0.0477792i	0.879489	−	0.475920i	$-0.157885\pi$
$463$	0.593566	+	1.02809i	0.0275853	+	0.0477792i	−0.851903	+	0.523699i	$0.824552\pi$
$464$	4.00319	−	6.93374i	0.185844	−	0.321891i
$465$		0			0
$466$	−8.84761	−	15.3245i	−0.409858	−	0.709894i
$467$	11.0573	+	19.1519i	0.511673	+	0.886243i	0.999908	+	0.0135313i	$0.00430729\pi$
$467$	11.0573	+	19.1519i	0.511673	+	0.886243i	−0.488236	+	0.872712i	$0.662359\pi$
$468$		0			0
$469$		0			0
$470$	4.35483	−	7.54280i	0.200874	−	0.347923i
$471$		0			0
$472$	0.494658			0.0227685
$473$	18.1865			0.836218
$474$		0			0
$475$	9.12499	−	15.8050i	0.418683	−	0.725181i
$476$		0			0
$477$		0			0
$478$	24.0502	+	41.6562i	1.10003	+	1.90531i
$479$	−12.5714	−	21.7743i	−0.574402	−	0.994894i	−0.996106	−	0.0881606i	$-0.971901\pi$
$479$	−12.5714	−	21.7743i	−0.574402	−	0.994894i	0.421704	−	0.906734i	$-0.361432\pi$
$480$		0			0
$481$	4.55160	−	7.88361i	0.207535	−	0.359462i
$482$	30.0273	+	52.0088i	1.36771	+	2.36894i
$483$		0			0
$484$	−25.9967	+	45.0276i	−1.18167	+	2.04671i
$485$	3.15197	+	5.45937i	0.143123	+	0.247897i
$486$		0			0
$487$	−6.78904	+	11.7590i	−0.307641	+	0.532849i	−0.977846	−	0.209327i	$-0.932873\pi$
$487$	−6.78904	+	11.7590i	−0.307641	+	0.532849i	0.670205	+	0.742176i	$0.266206\pi$
$488$	−16.5743			−0.750281
$489$		0			0
$490$		0			0
$491$	−7.25177	−	12.5604i	−0.327268	−	0.566844i	0.654701	−	0.755888i	$-0.272795\pi$
$491$	−7.25177	−	12.5604i	−0.327268	−	0.566844i	−0.981969	+	0.189044i	$0.939461\pi$
$492$		0			0
$493$	−9.71263	−	16.8228i	−0.437435	−	0.757659i
$494$	−27.7868	+	48.1281i	−1.25019	+	2.16538i
$495$		0			0
$496$	2.90664			0.130512
$497$		0			0
$498$		0			0
$499$	−6.99574	+	12.1170i	−0.313172	+	0.542431i	−0.979047	−	0.203633i	$-0.934725\pi$
$499$	−6.99574	+	12.1170i	−0.313172	+	0.542431i	0.665875	+	0.746063i	$0.268058\pi$
$500$	29.1221			1.30238
$501$		0			0
$502$	−36.0419			−1.60863
$503$	−28.4011			−1.26634			−0.633171	−	0.774012i	$-0.718247\pi$
$503$	−28.4011			−1.26634			−0.633171	+	0.774012i	$0.718247\pi$
$504$		0			0
$505$	0.00677023			0.000301271
$506$	−61.7036			−2.74306
$507$		0			0
$508$	−38.1184			−1.69123
$509$	−1.72997	+	2.99639i	−0.0766794	+	0.132813i	−0.901815	−	0.432122i	$-0.857765\pi$
$509$	−1.72997	+	2.99639i	−0.0766794	+	0.132813i	0.825136	+	0.564934i	$0.191098\pi$
$510$		0			0
$511$		0			0
$512$	−21.3013			−0.941392
$513$		0			0
$514$	−2.24784	+	3.89337i	−0.0991480	+	0.171729i
$515$	8.26597	+	14.3171i	0.364242	+	0.630886i
$516$		0			0
$517$	8.64174	+	14.9679i	0.380063	+	0.658289i
$518$		0			0
$519$		0			0
$520$	−9.64451			−0.422940
$521$	3.56797	−	6.17991i	0.156316	−	0.270747i	−0.777222	−	0.629227i	$-0.783372\pi$
$521$	3.56797	−	6.17991i	0.156316	−	0.270747i	0.933537	+	0.358480i	$0.116705\pi$
$522$		0			0
$523$	6.53235	+	11.3144i	0.285640	+	0.494743i	0.972764	−	0.231797i	$-0.0744606\pi$
$523$	6.53235	+	11.3144i	0.285640	+	0.494743i	−0.687124	+	0.726540i	$0.741127\pi$
$524$	−0.245114	+	0.424551i	−0.0107079	+	0.0185466i
$525$		0			0
$526$	−11.0226	−	19.0917i	−0.480609	−	0.832439i
$527$	3.52608	−	6.10735i	0.153598	−	0.266040i
$528$		0			0
$529$	−1.89710	−	3.28587i	−0.0824825	−	0.142864i
$530$	−9.85801	−	17.0746i	−0.428205	−	0.741672i
$531$		0			0
$532$		0			0
$533$	−9.24434	+	16.0117i	−0.400417	+	0.693542i
$534$		0			0
$535$	11.9493			0.516615
$536$	−7.16806			−0.309613
$537$		0			0
$538$	16.4305	−	28.4585i	0.708371	−	1.22693i
$539$		0			0
$540$		0			0
$541$	−2.46788	−	4.27450i	−0.106103	−	0.183775i	0.808086	−	0.589065i	$-0.200504\pi$
$541$	−2.46788	−	4.27450i	−0.106103	−	0.183775i	−0.914188	+	0.405290i	$0.867171\pi$
$542$	−31.3444	−	54.2901i	−1.34636	−	2.33196i
$543$		0			0
$544$	−18.1225	+	31.3892i	−0.776997	+	1.34580i
$545$	10.7109	+	18.5518i	0.458803	+	0.794670i
$546$		0			0
$547$	0.559964	−	0.969887i	0.0239423	−	0.0414694i	−0.853806	−	0.520591i	$-0.825712\pi$
$547$	0.559964	−	0.969887i	0.0239423	−	0.0414694i	0.877748	+	0.479122i	$0.159045\pi$
$548$	4.31254	+	7.46954i	0.184223	+	0.319083i
$549$		0			0
$550$	−20.2136	+	35.0110i	−0.861912	+	1.49288i
$551$	21.7030			0.924578
$552$		0			0
$553$		0			0
$554$	−2.93762	−	5.08811i	−0.124808	−	0.216173i
$555$		0			0
$556$	25.7997	+	44.6863i	1.09415	+	1.89512i
$557$	−5.47832	+	9.48873i	−0.232124	+	0.402050i	−0.958433	−	0.285318i	$-0.907901\pi$
$557$	−5.47832	+	9.48873i	−0.232124	+	0.402050i	0.726309	+	0.687368i	$0.241234\pi$
$558$		0			0
$559$	−15.7561			−0.666413
$560$		0			0
$561$		0			0
$562$	−5.36052	+	9.28470i	−0.226120	+	0.391651i
$563$	4.76096			0.200650			0.100325	−	0.994955i	$-0.468012\pi$
$563$	4.76096			0.200650			0.100325	+	0.994955i	$0.468012\pi$
$564$		0			0
$565$	7.79523			0.327948
$566$	−7.79462			−0.327632
$567$		0			0
$568$	−3.15189			−0.132250
$569$	−3.49976			−0.146718			−0.0733588	−	0.997306i	$-0.523372\pi$
$569$	−3.49976			−0.146718			−0.0733588	+	0.997306i	$0.523372\pi$
$570$		0			0
$571$	7.06101			0.295494			0.147747	−	0.989025i	$-0.452798\pi$
$571$	7.06101			0.295494			0.147747	+	0.989025i	$0.452798\pi$
$572$	35.5612	−	61.5937i	1.48689	−	2.57536i
$573$		0			0
$574$		0			0
$575$	−17.5552			−0.732101
$576$		0			0
$577$	−6.44149	+	11.1570i	−0.268163	+	0.464472i	−0.968387	−	0.249451i	$-0.919750\pi$
$577$	−6.44149	+	11.1570i	−0.268163	+	0.464472i	0.700225	+	0.713923i	$0.253083\pi$
$578$	6.74445	+	11.6817i	0.280532	+	0.485896i
$579$		0			0
$580$	6.99838	+	12.1216i	0.290592	+	0.503320i
$581$		0			0
$582$		0			0
$583$	39.1245			1.62037
$584$	−8.45333	+	14.6416i	−0.349801	+	0.605874i
$585$		0			0
$586$	26.5412	+	45.9707i	1.09641	+	1.89903i
$587$	19.5044	−	33.7826i	0.805034	−	1.39436i	−0.111235	−	0.993794i	$-0.535481\pi$
$587$	19.5044	−	33.7826i	0.805034	−	1.39436i	0.916268	−	0.400565i	$-0.131186\pi$
$588$		0			0
$589$	3.93953	+	6.82347i	0.162326	+	0.281156i
$590$	0.426012	−	0.737874i	0.0175386	−	0.0303778i
$591$		0			0
$592$	1.90411	+	3.29801i	0.0782583	+	0.135547i
$593$	20.1513	+	34.9031i	0.827515	+	1.43330i	0.899982	+	0.435927i	$0.143579\pi$
$593$	20.1513	+	34.9031i	0.827515	+	1.43330i	−0.0724676	+	0.997371i	$0.523087\pi$
$594$		0			0
$595$		0			0
$596$	−29.1064	+	50.4137i	−1.19224	+	2.06503i
$597$		0			0
$598$	53.4577			2.18605
$599$	12.7821			0.522261			0.261130	−	0.965304i	$-0.415905\pi$
$599$	12.7821			0.522261			0.261130	+	0.965304i	$0.415905\pi$
$600$		0			0
$601$	−4.86311	+	8.42316i	−0.198371	+	0.343588i	−0.948000	−	0.318270i	$-0.896898\pi$
$601$	−4.86311	+	8.42316i	−0.198371	+	0.343588i	0.749630	+	0.661858i	$0.230232\pi$
$602$		0			0
$603$		0			0
$604$	−8.70921	−	15.0848i	−0.354373	−	0.613792i
$605$	12.0495	+	20.8703i	0.489881	+	0.848499i
$606$		0			0
$607$	−20.7437	+	35.9291i	−0.841959	+	1.45832i	0.0462763	+	0.998929i	$0.485265\pi$
$607$	−20.7437	+	35.9291i	−0.841959	+	1.45832i	−0.888236	+	0.459388i	$0.848069\pi$
$608$	−20.2475	−	35.0697i	−0.821145	−	1.42226i
$609$		0			0
$610$	−14.2742	+	24.7236i	−0.577943	+	1.00103i
$611$	−7.48688	−	12.9677i	−0.302887	−	0.524615i
$612$		0			0
$613$	−7.64783	+	13.2464i	−0.308893	+	0.535018i	−0.978120	−	0.208039i	$-0.933292\pi$
$613$	−7.64783	+	13.2464i	−0.308893	+	0.535018i	0.669228	+	0.743057i	$0.266625\pi$
$614$	52.0193			2.09933
$615$		0			0
$616$		0			0
$617$	2.66563	+	4.61700i	0.107314	+	0.185873i	0.914681	−	0.404176i	$-0.132442\pi$
$617$	2.66563	+	4.61700i	0.107314	+	0.185873i	−0.807367	+	0.590049i	$0.799108\pi$
$618$		0			0
$619$	6.34205	+	10.9847i	0.254908	+	0.441514i	0.964871	−	0.262726i	$-0.0846214\pi$
$619$	6.34205	+	10.9847i	0.254908	+	0.441514i	−0.709962	+	0.704240i	$0.751288\pi$
$620$	−2.54070	+	4.40062i	−0.102037	+	0.176733i
$621$		0			0
$622$	−28.1650			−1.12931
$623$		0			0
$624$		0			0
$625$	−1.72954	+	2.99566i	−0.0691817	+	0.119826i
$626$	58.4733			2.33706
$627$		0			0
$628$	3.81978			0.152426
$629$	9.23957			0.368406
$630$		0			0
$631$	0.123764			0.00492698			0.00246349	−	0.999997i	$-0.499216\pi$
$631$	0.123764			0.00492698			0.00246349	+	0.999997i	$0.499216\pi$
$632$	14.4487			0.574737
$633$		0			0
$634$	18.0888			0.718399
$635$	−8.83394	+	15.3008i	−0.350564	+	0.607195i
$636$		0			0
$637$		0			0
$638$	−48.0763			−1.90336
$639$		0			0
$640$	7.57868	−	13.1267i	0.299573	−	0.518876i
$641$	2.96588	+	5.13706i	0.117145	+	0.202902i	0.918635	−	0.395107i	$-0.129292\pi$
$641$	2.96588	+	5.13706i	0.117145	+	0.202902i	−0.801490	+	0.598008i	$0.795959\pi$
$642$		0			0
$643$	−23.4140	−	40.5542i	−0.923358	−	1.59930i	−0.794180	−	0.607682i	$-0.792100\pi$
$643$	−23.4140	−	40.5542i	−0.923358	−	1.59930i	−0.129178	−	0.991621i	$-0.541234\pi$
$644$		0			0
$645$		0			0
$646$	−56.4060			−2.21926
$647$	−19.5701	+	33.8964i	−0.769379	+	1.33260i	0.168521	+	0.985698i	$0.446101\pi$
$647$	−19.5701	+	33.8964i	−0.769379	+	1.33260i	−0.937900	+	0.346905i	$0.887233\pi$
$648$		0			0
$649$	0.845379	+	1.46424i	0.0331840	+	0.0574764i
$650$	17.5123	−	30.3322i	0.686890	−	1.18973i
$651$		0			0
$652$	26.0796	+	45.1711i	1.02135	+	1.76904i
$653$	21.6640	−	37.5232i	0.847779	−	1.46840i	−0.0354068	−	0.999373i	$-0.511273\pi$
$653$	21.6640	−	37.5232i	0.847779	−	1.46840i	0.883186	−	0.469023i	$-0.155394\pi$
$654$		0			0
$655$	0.113611	+	0.196779i	0.00443913	+	0.00768881i
$656$	−3.86726	−	6.69828i	−0.150991	−	0.261524i
$657$		0			0
$658$		0			0
$659$	−3.43895	+	5.95643i	−0.133962	+	0.232030i	−0.925201	−	0.379478i	$-0.876103\pi$
$659$	−3.43895	+	5.95643i	−0.133962	+	0.232030i	0.791238	+	0.611508i	$0.209437\pi$
$660$		0			0
$661$	38.7671			1.50786			0.753932	−	0.656952i	$-0.228155\pi$
$661$	38.7671			1.50786			0.753932	+	0.656952i	$0.228155\pi$
$662$	−26.9814			−1.04866
$663$		0			0
$664$	−8.14097	+	14.1006i	−0.315931	+	0.547209i
$665$		0			0
$666$		0			0
$667$	−10.4383	−	18.0797i	−0.404174	−	0.700050i
$668$	−2.38609	−	4.13282i	−0.0923205	−	0.159904i
$669$		0			0
$670$	−6.17331	+	10.6925i	−0.238496	+	0.413087i
$671$	−28.3257	−	49.0615i	−1.09350	−	1.89400i
$672$		0			0
$673$	17.9897	−	31.1591i	0.693452	−	1.20109i	−0.277248	−	0.960798i	$-0.589422\pi$
$673$	17.9897	−	31.1591i	0.693452	−	1.20109i	0.970700	−	0.240295i	$-0.0772443\pi$
$674$	28.2025	+	48.8481i	1.08632	+	1.88156i
$675$		0			0
$676$	−13.0227	+	22.5560i	−0.500874	+	0.867539i
$677$	−4.46658			−0.171664			−0.0858322	−	0.996310i	$-0.527355\pi$
$677$	−4.46658			−0.171664			−0.0858322	+	0.996310i	$0.527355\pi$
$678$		0			0
$679$		0			0
$680$	−4.89449	−	8.47750i	−0.187695	−	0.325097i
$681$		0			0
$682$	−8.72682	−	15.1153i	−0.334167	−	0.578795i
$683$	−13.3356	+	23.0980i	−0.510274	+	0.883821i	0.489655	+	0.871916i	$0.337123\pi$
$683$	−13.3356	+	23.0980i	−0.510274	+	0.883821i	−0.999929	+	0.0119046i	$0.996211\pi$
$684$		0			0
$685$	3.99773			0.152745
$686$		0			0
$687$		0			0
$688$	3.29569	−	5.70831i	0.125647	−	0.217627i
$689$	−33.8960			−1.29134
$690$		0			0
$691$	−41.0440			−1.56139			−0.780694	−	0.624913i	$-0.785134\pi$
$691$	−41.0440			−1.56139			−0.780694	+	0.624913i	$0.785134\pi$
$692$	27.5709			1.04809
$693$		0			0
$694$	−36.6671			−1.39187
$695$	23.9163			0.907197
$696$		0			0
$697$	−18.7656			−0.710799
$698$	−33.8424	+	58.6167i	−1.28095	+	2.21867i
$699$		0			0
$700$		0			0
$701$	−9.63355			−0.363854			−0.181927	−	0.983312i	$-0.558233\pi$
$701$	−9.63355			−0.363854			−0.181927	+	0.983312i	$0.558233\pi$
$702$		0			0
$703$	−5.16148	+	8.93994i	−0.194669	+	0.337176i
$704$	33.9788	+	58.8529i	1.28062	+	2.21810i
$705$		0			0
$706$	−2.89382	−	5.01224i	−0.108910	−	0.188638i
$707$		0			0
$708$		0			0
$709$	−10.1426			−0.380914			−0.190457	−	0.981696i	$-0.560997\pi$
$709$	−10.1426			−0.380914			−0.190457	+	0.981696i	$0.560997\pi$
$710$	−2.71448	+	4.70162i	−0.101873	+	0.176449i
$711$		0			0
$712$	−4.16286	−	7.21029i	−0.156010	−	0.270217i
$713$	3.78954	−	6.56368i	0.141919	−	0.245812i
$714$		0			0
$715$	−16.4826	−	28.5487i	−0.616415	−	1.06766i
$716$	−25.3690	+	43.9404i	−0.948085	+	1.64213i
$717$		0			0
$718$	35.4118	+	61.3350i	1.32156	+	2.28900i
$719$	−20.6844	−	35.8264i	−0.771397	−	1.33610i	−0.936797	−	0.349873i	$-0.886225\pi$
$719$	−20.6844	−	35.8264i	−0.771397	−	1.33610i	0.165400	−	0.986227i	$-0.447109\pi$
$720$		0			0
$721$		0			0
$722$	10.8350	−	18.7667i	0.403236	−	0.698425i
$723$		0			0
$724$	−24.1066			−0.895914
$725$	−13.6781			−0.507991
$726$		0			0
$727$	−4.86372	+	8.42422i	−0.180386	+	0.312437i	−0.942012	−	0.335580i	$-0.891068\pi$
$727$	−4.86372	+	8.42422i	−0.180386	+	0.312437i	0.761626	+	0.648016i	$0.224401\pi$
$728$		0			0
$729$		0			0
$730$	14.5604	+	25.2194i	0.538906	+	0.933412i
$731$	−7.99607	−	13.8496i	−0.295745	−	0.512246i
$732$		0			0
$733$	−14.4554	+	25.0375i	−0.533922	+	0.924780i	0.465292	+	0.885157i	$0.345949\pi$
$733$	−14.4554	+	25.0375i	−0.533922	+	0.924780i	−0.999215	+	0.0396234i	$0.987384\pi$
$734$	15.4013	+	26.6758i	0.568471	+	0.984621i
$735$		0			0
$736$	−19.4766	+	33.7345i	−0.717918	+	1.24347i
$737$	−12.2503	−	21.2182i	−0.451247	−	0.781582i
$738$		0			0
$739$	6.67467	−	11.5609i	0.245532	−	0.425273i	−0.716749	−	0.697331i	$-0.754371\pi$
$739$	6.67467	−	11.5609i	0.245532	−	0.425273i	0.962281	+	0.272058i	$0.0877041\pi$
$740$	−6.65752			−0.244735
$741$		0			0
$742$		0			0
$743$	−19.9100	−	34.4851i	−0.730425	−	1.26513i	−0.956702	−	0.291071i	$-0.905988\pi$
$743$	−19.9100	−	34.4851i	−0.730425	−	1.26513i	0.226276	−	0.974063i	$-0.427345\pi$
$744$		0			0
$745$	13.4908	+	23.3668i	0.494265	+	0.856092i
$746$	2.91221	−	5.04410i	0.106624	−	0.184678i
$747$		0			0
$748$	72.1877			2.63944
$749$		0			0
$750$		0			0
$751$	19.2173	−	33.2853i	0.701248	−	1.21460i	−0.266780	−	0.963757i	$-0.585960\pi$
$751$	19.2173	−	33.2853i	0.701248	−	1.21460i	0.968029	−	0.250840i	$-0.0807069\pi$
$752$	6.26409			0.228428
$753$		0			0
$754$	41.6515			1.51686
$755$	−8.07344			−0.293823
$756$		0			0
$757$	−5.66698			−0.205970			−0.102985	−	0.994683i	$-0.532839\pi$
$757$	−5.66698			−0.205970			−0.102985	+	0.994683i	$0.532839\pi$
$758$	0.681032			0.0247362
$759$		0			0
$760$	10.9368			0.396719
$761$	26.1661	−	45.3210i	0.948519	−	1.64288i	0.199973	−	0.979801i	$-0.435915\pi$
$761$	26.1661	−	45.3210i	0.948519	−	1.64288i	0.748546	−	0.663082i	$-0.230752\pi$
$762$		0			0
$763$		0			0
$764$	−13.4337			−0.486014
$765$		0			0
$766$	9.78121	−	16.9416i	0.353410	−	0.612123i
$767$	−0.732404	−	1.26856i	−0.0264456	−	0.0458051i
$768$		0			0
$769$	1.17360	+	2.03274i	0.0423212	+	0.0733025i	0.886410	−	0.462901i	$-0.153191\pi$
$769$	1.17360	+	2.03274i	0.0423212	+	0.0733025i	−0.844089	+	0.536203i	$0.819858\pi$
$770$		0			0
$771$		0			0
$772$	−26.7274			−0.961939
$773$	18.1814	−	31.4912i	0.653941	−	1.13266i	−0.328217	−	0.944602i	$-0.606448\pi$
$773$	18.1814	−	31.4912i	0.653941	−	1.13266i	0.982158	−	0.188057i	$-0.0602189\pi$
$774$		0			0
$775$	−2.48285	−	4.30042i	−0.0891866	−	0.154476i
$776$	3.98251	−	6.89790i	0.142964	−	0.247620i
$777$		0			0
$778$	29.3659	+	50.8633i	1.05282	+	1.82354i
$779$	10.4830	−	18.1571i	0.375592	−	0.650545i
$780$		0			0
$781$	−5.38663	−	9.32991i	−0.192749	−	0.333851i
$782$	27.1292	+	46.9892i	0.970139	+	1.68033i
$783$		0			0
$784$		0			0
$785$	0.885235	−	1.53327i	0.0315954	−	0.0547248i
$786$		0			0
$787$	−31.7692			−1.13245			−0.566224	−	0.824251i	$-0.691596\pi$
$787$	−31.7692			−1.13245			−0.566224	+	0.824251i	$0.691596\pi$
$788$	−9.06944			−0.323085
$789$		0			0
$790$	12.4435	−	21.5528i	0.442721	−	0.766816i
$791$		0			0
$792$		0			0
$793$	24.5403	+	42.5050i	0.871451	+	1.50940i
$794$	32.1012	+	55.6009i	1.13923	+	1.97320i
$795$		0			0
$796$	−15.1711	+	26.2771i	−0.537725	+	0.931367i
$797$	7.45306	+	12.9091i	0.264001	+	0.457263i	0.967301	−	0.253630i	$-0.0816245\pi$
$797$	7.45306	+	12.9091i	0.264001	+	0.457263i	−0.703301	+	0.710893i	$0.748291\pi$
$798$		0			0
$799$	7.59903	−	13.1619i	0.268834	−	0.465635i
$800$	12.7608	+	22.1023i	0.451162	+	0.781436i
$801$		0			0
$802$	37.3002	−	64.6059i	1.31712	−	2.28131i
$803$	−57.7875			−2.03928
$804$		0			0
$805$		0			0
$806$	7.56059	+	13.0953i	0.266311	+	0.461263i
$807$		0			0
$808$	−0.00427709	−	0.00740814i	−0.000150467	−	0.000260617i
$809$	23.9018	−	41.3992i	0.840344	−	1.45552i	−0.0492597	−	0.998786i	$-0.515686\pi$
$809$	23.9018	−	41.3992i	0.840344	−	1.45552i	0.889604	−	0.456733i	$-0.150980\pi$
$810$		0			0
$811$	−32.1131			−1.12764			−0.563821	−	0.825897i	$-0.690669\pi$
$811$	−32.1131			−1.12764			−0.563821	+	0.825897i	$0.690669\pi$
$812$		0			0
$813$		0			0
$814$	11.4337	−	19.8037i	0.400750	−	0.694119i
$815$	24.1758			0.846841
$816$		0			0
$817$	17.8673			0.625098
$818$	−23.9057			−0.835843
$819$		0			0
$820$	13.5215			0.472190
$821$	−47.1070			−1.64405			−0.822023	−	0.569455i	$-0.807154\pi$
$821$	−47.1070			−1.64405			−0.822023	+	0.569455i	$0.807154\pi$
$822$		0			0
$823$	33.7910			1.17788			0.588941	−	0.808176i	$-0.299545\pi$
$823$	33.7910			1.17788			0.588941	+	0.808176i	$0.299545\pi$
$824$	10.4440	−	18.0896i	0.363835	−	0.630181i
$825$		0			0
$826$		0			0
$827$	−2.98023			−0.103633			−0.0518164	−	0.998657i	$-0.516501\pi$
$827$	−2.98023			−0.103633			−0.0518164	+	0.998657i	$0.516501\pi$
$828$		0			0
$829$	−3.03978	+	5.26506i	−0.105576	+	0.182863i	−0.913973	−	0.405774i	$-0.867002\pi$
$829$	−3.03978	+	5.26506i	−0.105576	+	0.182863i	0.808397	+	0.588637i	$0.200335\pi$
$830$	14.0224	+	24.2875i	0.486725	+	0.843032i
$831$		0			0
$832$	−29.4379	−	50.9880i	−1.02058	−	1.76769i
$833$		0			0
$834$		0			0
$835$	−2.21190			−0.0765461
$836$	−40.3260	+	69.8467i	−1.39471	+	2.41570i
$837$		0			0
$838$	−7.25163	−	12.5602i	−0.250503	−	0.433885i
$839$	−1.85858	+	3.21915i	−0.0641653	+	0.111138i	−0.896323	−	0.443401i	$-0.853772\pi$
$839$	−1.85858	+	3.21915i	−0.0641653	+	0.111138i	0.832158	+	0.554538i	$0.187105\pi$
$840$		0			0
$841$	6.36697	+	11.0279i	0.219551	+	0.380273i
$842$	37.0909	−	64.2433i	1.27824	−	2.21397i
$843$		0			0
$844$	−10.0182	−	17.3520i	−0.344841	−	0.597281i
$845$	6.03604	+	10.4547i	0.207646	+	0.359653i
$846$		0			0
$847$		0			0
$848$	7.08999	−	12.2802i	0.243471	−	0.421705i
$849$		0			0
$850$	35.5493			1.21933
$851$	9.92993			0.340394
$852$		0			0
$853$	−0.553861	+	0.959315i	−0.0189638	+	0.0328463i	−0.875352	−	0.483487i	$-0.839370\pi$
$853$	−0.553861	+	0.959315i	−0.0189638	+	0.0328463i	0.856388	+	0.516333i	$0.172703\pi$
$854$		0			0
$855$		0			0
$856$	−7.54899	−	13.0752i	−0.258019	−	0.446902i
$857$	−19.2597	−	33.3589i	−0.657900	−	1.13952i	−0.981158	−	0.193206i	$-0.938111\pi$
$857$	−19.2597	−	33.3589i	−0.657900	−	1.13952i	0.323258	−	0.946311i	$-0.395222\pi$
$858$		0			0
$859$	17.4437	−	30.2134i	0.595171	−	1.03087i	−0.398352	−	0.917233i	$-0.630418\pi$
$859$	17.4437	−	30.2134i	0.595171	−	1.03087i	0.993523	−	0.113634i	$-0.0362491\pi$
$860$	5.76153	+	9.97926i	0.196467	+	0.340290i
$861$		0			0
$862$	−2.45857	+	4.25836i	−0.0837391	+	0.145040i
$863$	1.07924	+	1.86931i	0.0367379	+	0.0636319i	0.883810	−	0.467847i	$-0.154970\pi$
$863$	1.07924	+	1.86931i	0.0367379	+	0.0636319i	−0.847072	+	0.531478i	$0.821637\pi$
$864$		0			0
$865$	6.38957	−	11.0671i	0.217252	−	0.376291i
$866$	−74.8441			−2.54331
$867$		0			0
$868$		0			0
$869$	24.6930	+	42.7695i	0.837652	+	1.45086i
$870$		0			0
$871$	10.6132	+	18.3826i	0.359615	+	0.622872i
$872$	13.5332	−	23.4401i	0.458291	−	0.793783i
$873$		0			0
$874$	−60.6205			−2.05052
$875$		0			0
$876$		0			0
$877$	−9.43950	+	16.3497i	−0.318749	+	0.552090i	−0.980227	−	0.197875i	$-0.936596\pi$
$877$	−9.43950	+	16.3497i	−0.318749	+	0.552090i	0.661478	+	0.749965i	$0.269929\pi$
$878$	−13.0391			−0.440049
$879$		0			0
$880$	13.7906			0.464881
$881$	18.7203			0.630704			0.315352	−	0.948975i	$-0.397877\pi$
$881$	18.7203			0.630704			0.315352	+	0.948975i	$0.397877\pi$
$882$		0			0
$883$	−13.3717			−0.449993			−0.224996	−	0.974360i	$-0.572237\pi$
$883$	−13.3717			−0.449993			−0.224996	+	0.974360i	$0.572237\pi$
$884$	−62.5407			−2.10347
$885$		0			0
$886$	−85.8294			−2.88350
$887$	20.6284	−	35.7294i	0.692633	−	1.19968i	−0.278339	−	0.960483i	$-0.589784\pi$
$887$	20.6284	−	35.7294i	0.692633	−	1.19968i	0.970972	−	0.239193i	$-0.0768829\pi$
$888$		0			0
$889$		0			0
$890$	−14.3406			−0.480699
$891$		0			0
$892$	5.54832	−	9.60997i	0.185772	−	0.321766i
$893$	8.49006	+	14.7052i	0.284109	+	0.492091i
$894$		0			0
$895$	11.7585	+	20.3664i	0.393045	+	0.680774i
$896$		0			0
$897$		0			0
$898$	5.33396			0.177996
$899$	2.95262	−	5.11408i	0.0984753	−	0.170564i
$900$		0			0
$901$	−17.2019	−	29.7945i	−0.573078	−	0.992599i
$902$	−23.2219	+	40.2215i	−0.773204	+	1.33923i
$903$		0			0
$904$	−4.92463	−	8.52971i	−0.163791	−	0.283694i
$905$	−5.58670	+	9.67645i	−0.185708	+	0.321656i
$906$		0			0
$907$	−1.84519	−	3.19595i	−0.0612684	−	0.106120i	0.833764	−	0.552121i	$-0.186181\pi$
$907$	−1.84519	−	3.19595i	−0.0612684	−	0.106120i	−0.895033	+	0.446001i	$0.852848\pi$
$908$	1.82537	+	3.16163i	0.0605770	+	0.104922i
$909$		0			0
$910$		0			0
$911$	3.43831	−	5.95533i	0.113916	−	0.197309i	−0.803430	−	0.595400i	$-0.796994\pi$
$911$	3.43831	−	5.95533i	0.113916	−	0.197309i	0.917346	+	0.398091i	$0.130327\pi$
$912$		0			0
$913$	−55.6522			−1.84182
$914$	−23.9855			−0.793369
$915$		0			0
$916$	21.8860	−	37.9077i	0.723135	−	1.25251i
$917$		0			0
$918$		0			0
$919$	−18.6473	−	32.2981i	−0.615119	−	1.06542i	−0.990364	−	0.138491i	$-0.955775\pi$
$919$	−18.6473	−	32.2981i	−0.615119	−	1.06542i	0.375245	−	0.926926i	$-0.377559\pi$
$920$	−5.26019	−	9.11092i	−0.173423	−	0.300378i
$921$		0			0
$922$	31.8916	−	55.2378i	1.05029	−	1.81916i
$923$	4.66677	+	8.08309i	0.153609	+	0.266058i
$924$		0			0
$925$	3.25297	−	5.63431i	0.106957	−	0.185255i
$926$	−1.29178	−	2.23743i	−0.0424506	−	0.0735267i
$927$		0			0
$928$	−15.1752	+	26.2842i	−0.498150	+	0.862821i
$929$	17.9787			0.589861			0.294930	−	0.955519i	$-0.404704\pi$
$929$	17.9787			0.589861			0.294930	+	0.955519i	$0.404704\pi$
$930$		0			0
$931$		0			0
$932$	11.1243	+	19.2679i	0.364389	+	0.631141i
$933$		0			0
$934$	−24.0642	−	41.6804i	−0.787405	−	1.36383i
$935$	16.7295	−	28.9764i	0.547113	−	0.947628i
$936$		0			0
$937$	34.7312			1.13462			0.567310	−	0.823504i	$-0.307984\pi$
$937$	34.7312			1.13462			0.567310	+	0.823504i	$0.307984\pi$
$938$		0			0
$939$		0			0
$940$	−5.47544	+	9.48374i	−0.178589	+	0.309326i
$941$	−43.3025			−1.41162			−0.705810	−	0.708401i	$-0.749417\pi$
$941$	−43.3025			−1.41162			−0.705810	+	0.708401i	$0.749417\pi$
$942$		0			0
$943$	−20.1678			−0.656752
$944$	0.612785			0.0199444
$945$		0			0
$946$	−39.5796			−1.28684
$947$	−38.2591			−1.24325			−0.621626	−	0.783314i	$-0.713528\pi$
$947$	−38.2591			−1.24325			−0.621626	+	0.783314i	$0.713528\pi$
$948$		0			0
$949$	50.0649			1.62518
$950$	−19.8588	+	34.3965i	−0.644305	+	1.11597i
$951$		0			0
$952$		0			0
$953$	47.8757			1.55085			0.775423	−	0.631442i	$-0.217537\pi$
$953$	47.8757			1.55085			0.775423	+	0.631442i	$0.217537\pi$
$954$		0			0
$955$	−3.11326	+	5.39233i	−0.100743	+	0.174492i
$956$	−30.2389	−	52.3753i	−0.977996	−	1.69394i
$957$		0			0
$958$	27.3593	+	47.3877i	0.883939	+	1.53103i
$959$		0			0
$960$		0			0
$961$	−28.8562			−0.930844
$962$	−9.90570	+	17.1572i	−0.319373	+	0.553170i
$963$		0			0
$964$	−37.7541	−	65.3920i	−1.21598	−	2.10613i
$965$	−6.19407	+	10.7284i	−0.199394	+	0.345361i
$966$		0			0
$967$	15.5575	+	26.9463i	0.500294	+	0.866535i	1.00000		0.000339469i	$0.000108056\pi$
$967$	15.5575	+	26.9463i	0.500294	+	0.866535i	−0.499706	+	0.866195i	$0.666559\pi$
$968$	15.2245	−	26.3696i	0.489334	−	0.847551i
$969$		0			0
$970$	−6.85966	−	11.8813i	−0.220250	−	0.381485i
$971$	15.1312	+	26.2080i	0.485583	+	0.841055i	0.999863	−	0.0165676i	$-0.00527387\pi$
$971$	15.1312	+	26.2080i	0.485583	+	0.841055i	−0.514279	+	0.857623i	$0.671941\pi$
$972$		0			0
$973$		0			0
$974$	14.7751	−	25.5911i	0.473423	−	0.819993i
$975$		0			0
$976$	−20.5323			−0.657221
$977$	−38.2201			−1.22277			−0.611385	−	0.791333i	$-0.709387\pi$
$977$	−38.2201			−1.22277			−0.611385	+	0.791333i	$0.709387\pi$
$978$		0			0
$979$	14.2288	−	24.6450i	0.454754	−	0.787657i
$980$		0			0
$981$		0			0
$982$	15.7821	+	27.3354i	0.503627	+	0.872308i
$983$	18.6964	+	32.3832i	0.596324	+	1.03286i	0.993359	+	0.115059i	$0.0367058\pi$
$983$	18.6964	+	32.3832i	0.596324	+	1.03286i	−0.397035	+	0.917803i	$0.629961\pi$
$984$		0			0
$985$	−2.10184	+	3.64050i	−0.0669703	+	0.115996i
$986$	21.1377	+	36.6116i	0.673162	+	1.16595i
$987$		0			0
$988$	34.9370	−	60.5126i	1.11149	−	1.92516i
$989$	−8.59353	−	14.8844i	−0.273258	−	0.473297i
$990$		0			0
$991$	11.9299	−	20.6631i	0.378965	−	0.656386i	−0.611947	−	0.790899i	$-0.709613\pi$
$991$	11.9299	−	20.6631i	0.378965	−	0.656386i	0.990912	+	0.134512i	$0.0429468\pi$
$992$	−11.0184			−0.349835
$993$		0			0
$994$		0			0
$995$	7.03180	+	12.1794i	0.222923	+	0.386114i
$996$		0			0
$997$	25.8413	+	44.7585i	0.818403	+	1.41751i	0.906859	+	0.421435i	$0.138473\pi$
$997$	25.8413	+	44.7585i	0.818403	+	1.41751i	−0.0884560	+	0.996080i	$0.528193\pi$
$998$	15.2249	−	26.3703i	0.481936	−	0.834738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.h.802.2		24
3.2	odd	2		441.2.h.h.214.11		24
7.2	even	3		1323.2.g.h.667.11		24
7.3	odd	6		1323.2.f.h.883.11		24
7.4	even	3		1323.2.f.h.883.12		24
7.5	odd	6		1323.2.g.h.667.12		24
7.6	odd	2	inner	1323.2.h.h.802.1		24
9.4	even	3		1323.2.g.h.361.11		24
9.5	odd	6		441.2.g.h.67.1		24
21.2	odd	6		441.2.g.h.79.1		24
21.5	even	6		441.2.g.h.79.2		24
21.11	odd	6		441.2.f.h.295.2	yes	24
21.17	even	6		441.2.f.h.295.1	yes	24
21.20	even	2		441.2.h.h.214.12		24
63.4	even	3		1323.2.f.h.442.12		24
63.5	even	6		441.2.h.h.373.12		24
63.11	odd	6		3969.2.a.bh.1.12		12
63.13	odd	6		1323.2.g.h.361.12		24
63.23	odd	6		441.2.h.h.373.11		24
63.25	even	3		3969.2.a.bi.1.1		12
63.31	odd	6		1323.2.f.h.442.11		24
63.32	odd	6		441.2.f.h.148.2	yes	24
63.38	even	6		3969.2.a.bh.1.11		12
63.40	odd	6	inner	1323.2.h.h.226.1		24
63.41	even	6		441.2.g.h.67.2		24
63.52	odd	6		3969.2.a.bi.1.2		12
63.58	even	3	inner	1323.2.h.h.226.2		24
63.59	even	6		441.2.f.h.148.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.1	✓	24	63.59	even	6
441.2.f.h.148.2	yes	24	63.32	odd	6
441.2.f.h.295.1	yes	24	21.17	even	6
441.2.f.h.295.2	yes	24	21.11	odd	6
441.2.g.h.67.1		24	9.5	odd	6
441.2.g.h.67.2		24	63.41	even	6
441.2.g.h.79.1		24	21.2	odd	6
441.2.g.h.79.2		24	21.5	even	6
441.2.h.h.214.11		24	3.2	odd	2
441.2.h.h.214.12		24	21.20	even	2
441.2.h.h.373.11		24	63.23	odd	6
441.2.h.h.373.12		24	63.5	even	6
1323.2.f.h.442.11		24	63.31	odd	6
1323.2.f.h.442.12		24	63.4	even	3
1323.2.f.h.883.11		24	7.3	odd	6
1323.2.f.h.883.12		24	7.4	even	3
1323.2.g.h.361.11		24	9.4	even	3
1323.2.g.h.361.12		24	63.13	odd	6
1323.2.g.h.667.11		24	7.2	even	3
1323.2.g.h.667.12		24	7.5	odd	6
1323.2.h.h.226.1		24	63.40	odd	6	inner
1323.2.h.h.226.2		24	63.58	even	3	inner
1323.2.h.h.802.1		24	7.6	odd	2	inner
1323.2.h.h.802.2		24	1.1	even	1	trivial
3969.2.a.bh.1.11		12	63.38	even	6
3969.2.a.bh.1.12		12	63.11	odd	6
3969.2.a.bi.1.1		12	63.25	even	3
3969.2.a.bi.1.2		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)

\(f(q)\)	\(=\)	\(q-2.17631 q^{2} +2.73633 q^{4} +(0.634145 - 1.09837i) q^{5} -1.60248 q^{8} +O(q^{10})\)	\(q-2.17631 q^{2} +2.73633 q^{4} +(0.634145 - 1.09837i) q^{5} -1.60248 q^{8} +(-1.38010 + 2.39040i) q^{10} +(-2.73867 - 4.74351i) q^{11} +(2.37268 + 4.10960i) q^{13} -1.98516 q^{16} +(-2.40822 + 4.17116i) q^{17} +(-2.69059 - 4.66025i) q^{19} +(1.73523 - 3.00550i) q^{20} +(5.96019 + 10.3233i) q^{22} +(-2.58816 + 4.48282i) q^{23} +(1.69572 + 2.93707i) q^{25} +(-5.16368 - 8.94376i) q^{26} +(-2.01656 + 3.49278i) q^{29} -1.46419 q^{31} +7.52529 q^{32} +(5.24103 - 9.07773i) q^{34} +(-0.959170 - 1.66133i) q^{37} +(5.85557 + 10.1421i) q^{38} +(-1.01621 + 1.76012i) q^{40} +(1.94808 + 3.37418i) q^{41} +(-1.66016 + 2.87549i) q^{43} +(-7.49389 - 12.9798i) q^{44} +(5.63263 - 9.75600i) q^{46} -3.15546 q^{47} +(-3.69042 - 6.39199i) q^{50} +(6.49243 + 11.2452i) q^{52} +(-3.57149 + 6.18601i) q^{53} -6.94684 q^{55} +(4.38866 - 7.60138i) q^{58} -0.308683 q^{59} +10.3429 q^{61} +3.18652 q^{62} -12.4070 q^{64} +6.01848 q^{65} +4.47310 q^{67} +(-6.58968 + 11.4137i) q^{68} +1.96688 q^{71} +(5.27515 - 9.13683i) q^{73} +(2.08745 + 3.61557i) q^{74} +(-7.36235 - 12.7520i) q^{76} -9.01643 q^{79} +(-1.25888 + 2.18044i) q^{80} +(-4.23963 - 7.34326i) q^{82} +(5.08023 - 8.79921i) q^{83} +(3.05432 + 5.29023i) q^{85} +(3.61303 - 6.25796i) q^{86} +(4.38866 + 7.60138i) q^{88} +(2.59776 + 4.49945i) q^{89} +(-7.08205 + 12.2665i) q^{92} +6.86726 q^{94} -6.82490 q^{95} +(-2.48521 + 4.30451i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) \) 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

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