LMFDB - Embedded newform 44.2.e.a.5.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [44,2,Mod(5,44)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("44.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 44 = 2^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	44.e (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.351341768894$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			5.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	44.5
Dual form			44.2.e.a.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.224514i) q^{3} +(0.190983 - 0.587785i) q^{5} +(-2.30902 + 1.67760i) q^{7} +(-0.881966 - 2.71441i) q^{9} +(-3.23607 - 0.726543i) q^{11} +(1.42705 + 4.39201i) q^{13} +(0.190983 - 0.138757i) q^{15} +(1.42705 - 4.39201i) q^{17} +(2.30902 + 1.67760i) q^{19} -1.09017 q^{21} +6.47214 q^{23} +(3.73607 + 2.71441i) q^{25} +(0.690983 - 2.12663i) q^{27} +(-5.16312 + 3.75123i) q^{29} +(-1.80902 - 5.56758i) q^{31} +(-0.836881 - 0.951057i) q^{33} +(0.545085 + 1.67760i) q^{35} +(-3.92705 + 2.85317i) q^{37} +(-0.545085 + 1.67760i) q^{39} +(-5.16312 - 3.75123i) q^{41} -1.76393 q^{45} +(-2.92705 - 2.12663i) q^{47} +(0.354102 - 1.08981i) q^{49} +(1.42705 - 1.03681i) q^{51} +(2.19098 + 6.74315i) q^{53} +(-1.04508 + 1.76336i) q^{55} +(0.336881 + 1.03681i) q^{57} +(8.16312 - 5.93085i) q^{59} +(1.42705 - 4.39201i) q^{61} +(6.59017 + 4.78804i) q^{63} +2.85410 q^{65} -4.94427 q^{67} +(2.00000 + 1.45309i) q^{69} +(-2.66312 + 8.19624i) q^{71} +(9.78115 - 7.10642i) q^{73} +(0.545085 + 1.67760i) q^{75} +(8.69098 - 3.75123i) q^{77} +(-4.28115 - 13.1760i) q^{79} +(-6.23607 + 4.53077i) q^{81} +(-4.95492 + 15.2497i) q^{83} +(-2.30902 - 1.67760i) q^{85} -2.43769 q^{87} -8.47214 q^{89} +(-10.6631 - 7.74721i) q^{91} +(0.690983 - 2.12663i) q^{93} +(1.42705 - 1.03681i) q^{95} +(1.71885 + 5.29007i) q^{97} +(0.881966 + 9.42481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 3 q^{5} - 7 q^{7} - 8 q^{9} - 4 q^{11} - q^{13} + 3 q^{15} - q^{17} + 7 q^{19} + 18 q^{21} + 8 q^{23} + 6 q^{25} + 5 q^{27} - 5 q^{29} - 5 q^{31} - 19 q^{33} - 9 q^{35} - 9 q^{37} + 9 q^{39}+ \cdots + 8 q^{99}+O(q^{100}) $ 4 * q - q^3 + 3 * q^5 - 7 * q^7 - 8 * q^9 - 4 * q^11 - q^13 + 3 * q^15 - q^17 + 7 * q^19 + 18 * q^21 + 8 * q^23 + 6 * q^25 + 5 * q^27 - 5 * q^29 - 5 * q^31 - 19 * q^33 - 9 * q^35 - 9 * q^37 + 9 * q^39 - 5 * q^41 - 16 * q^45 - 5 * q^47 - 12 * q^49 - q^51 + 11 * q^53 + 7 * q^55 + 17 * q^57 + 17 * q^59 - q^61 + 4 * q^63 - 2 * q^65 + 16 * q^67 + 8 * q^69 + 5 * q^71 + 19 * q^73 - 9 * q^75 + 37 * q^77 + 3 * q^79 - 16 * q^81 - 31 * q^83 - 7 * q^85 - 50 * q^87 - 16 * q^89 - 27 * q^91 + 5 * q^93 - q^95 + 27 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/44\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.309017	+	0.224514i	0.178411	+	0.129623i	0.673407	−	0.739272i	$-0.264830\pi$
$3$	0.309017	+	0.224514i	0.178411	+	0.129623i	−0.494996	+	0.868895i	$0.664830\pi$
$4$		0			0
$5$	0.190983	−	0.587785i	0.0854102	−	0.262866i	−0.899226	−	0.437485i	$-0.855869\pi$
$5$	0.190983	−	0.587785i	0.0854102	−	0.262866i	0.984636	+	0.174619i	$0.0558694\pi$
$6$		0			0
$7$	−2.30902	+	1.67760i	−0.872726	+	0.634073i	−0.931317	−	0.364209i	$-0.881339\pi$
$7$	−2.30902	+	1.67760i	−0.872726	+	0.634073i	0.0585908	+	0.998282i	$0.481339\pi$
$8$		0			0
$9$	−0.881966	−	2.71441i	−0.293989	−	0.904804i
$10$		0			0
$11$	−3.23607	−	0.726543i	−0.975711	−	0.219061i
$11$	−3.23607	−	0.726543i	−0.975711	−	0.219061i
$12$		0			0
$13$	1.42705	+	4.39201i	0.395793	+	1.21812i	0.928342	+	0.371726i	$0.121234\pi$
$13$	1.42705	+	4.39201i	0.395793	+	1.21812i	−0.532550	+	0.846399i	$0.678766\pi$
$14$		0			0
$15$	0.190983	−	0.138757i	0.0493116	−	0.0358270i
$16$		0			0
$17$	1.42705	−	4.39201i	0.346111	−	1.06522i	−0.614876	−	0.788624i	$-0.710794\pi$
$17$	1.42705	−	4.39201i	0.346111	−	1.06522i	0.960987	−	0.276595i	$-0.0892061\pi$
$18$		0			0
$19$	2.30902	+	1.67760i	0.529725	+	0.384868i	0.820255	−	0.571998i	$-0.193832\pi$
$19$	2.30902	+	1.67760i	0.529725	+	0.384868i	−0.290530	+	0.956866i	$0.593832\pi$
$20$		0			0
$21$	−1.09017			−0.237895
$22$		0			0
$23$	6.47214			1.34953			0.674767	−	0.738031i	$-0.264244\pi$
$23$	6.47214			1.34953			0.674767	+	0.738031i	$0.264244\pi$
$24$		0			0
$25$	3.73607	+	2.71441i	0.747214	+	0.542882i
$26$		0			0
$27$	0.690983	−	2.12663i	0.132980	−	0.409270i
$28$		0			0
$29$	−5.16312	+	3.75123i	−0.958767	+	0.696585i	−0.952864	−	0.303397i	$-0.901879\pi$
$29$	−5.16312	+	3.75123i	−0.958767	+	0.696585i	−0.00590304	+	0.999983i	$0.501879\pi$
$30$		0			0
$31$	−1.80902	−	5.56758i	−0.324909	−	0.999967i	−0.971482	−	0.237115i	$-0.923798\pi$
$31$	−1.80902	−	5.56758i	−0.324909	−	0.999967i	0.646573	−	0.762852i	$-0.276202\pi$
$32$		0			0
$33$	−0.836881	−	0.951057i	−0.145682	−	0.165558i
$34$		0			0
$35$	0.545085	+	1.67760i	0.0921362	+	0.283566i
$36$		0			0
$37$	−3.92705	+	2.85317i	−0.645603	+	0.469058i	−0.861771	−	0.507298i	$-0.830644\pi$
$37$	−3.92705	+	2.85317i	−0.645603	+	0.469058i	0.216167	+	0.976356i	$0.430644\pi$
$38$		0			0
$39$	−0.545085	+	1.67760i	−0.0872835	+	0.268631i
$40$		0			0
$41$	−5.16312	−	3.75123i	−0.806344	−	0.585843i	0.106425	−	0.994321i	$-0.466060\pi$
$41$	−5.16312	−	3.75123i	−0.806344	−	0.585843i	−0.912768	+	0.408478i	$0.866060\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−1.76393			−0.262951
$46$		0			0
$47$	−2.92705	−	2.12663i	−0.426954	−	0.310200i	0.353476	−	0.935444i	$-0.385000\pi$
$47$	−2.92705	−	2.12663i	−0.426954	−	0.310200i	−0.780430	+	0.625243i	$0.785000\pi$
$48$		0			0
$49$	0.354102	−	1.08981i	0.0505860	−	0.155688i
$50$		0			0
$51$	1.42705	−	1.03681i	0.199827	−	0.145183i
$52$		0			0
$53$	2.19098	+	6.74315i	0.300955	+	0.926243i	0.981156	+	0.193218i	$0.0618924\pi$
$53$	2.19098	+	6.74315i	0.300955	+	0.926243i	−0.680201	+	0.733025i	$0.738108\pi$
$54$		0			0
$55$	−1.04508	+	1.76336i	−0.140919	+	0.237771i
$56$		0			0
$57$	0.336881	+	1.03681i	0.0446210	+	0.137329i
$58$		0			0
$59$	8.16312	−	5.93085i	1.06275	−	0.772131i	0.0881528	−	0.996107i	$-0.471904\pi$
$59$	8.16312	−	5.93085i	1.06275	−	0.772131i	0.974595	+	0.223976i	$0.0719036\pi$
$60$		0			0
$61$	1.42705	−	4.39201i	0.182715	−	0.562339i	−0.817186	−	0.576374i	$-0.804467\pi$
$61$	1.42705	−	4.39201i	0.182715	−	0.562339i	0.999902	+	0.0140341i	$0.00446734\pi$
$62$		0			0
$63$	6.59017	+	4.78804i	0.830283	+	0.603236i
$64$		0			0
$65$	2.85410			0.354008
$66$		0			0
$67$	−4.94427			−0.604039			−0.302019	−	0.953302i	$-0.597661\pi$
$67$	−4.94427			−0.604039			−0.302019	+	0.953302i	$0.597661\pi$
$68$		0			0
$69$	2.00000	+	1.45309i	0.240772	+	0.174931i
$70$		0			0
$71$	−2.66312	+	8.19624i	−0.316054	+	0.972714i	0.659264	+	0.751911i	$0.270868\pi$
$71$	−2.66312	+	8.19624i	−0.316054	+	0.972714i	−0.975318	+	0.220803i	$0.929132\pi$
$72$		0			0
$73$	9.78115	−	7.10642i	1.14480	−	0.831744i	0.157017	−	0.987596i	$-0.449812\pi$
$73$	9.78115	−	7.10642i	1.14480	−	0.831744i	0.987780	+	0.155852i	$0.0498123\pi$
$74$		0			0
$75$	0.545085	+	1.67760i	0.0629410	+	0.193712i
$76$		0			0
$77$	8.69098	−	3.75123i	0.990429	−	0.427492i
$78$		0			0
$79$	−4.28115	−	13.1760i	−0.481667	−	1.48242i	−0.836750	−	0.547585i	$-0.815547\pi$
$79$	−4.28115	−	13.1760i	−0.481667	−	1.48242i	0.355083	−	0.934835i	$-0.384453\pi$
$80$		0			0
$81$	−6.23607	+	4.53077i	−0.692896	+	0.503419i
$82$		0			0
$83$	−4.95492	+	15.2497i	−0.543873	+	1.67387i	0.179783	+	0.983706i	$0.442460\pi$
$83$	−4.95492	+	15.2497i	−0.543873	+	1.67387i	−0.723655	+	0.690161i	$0.757540\pi$
$84$		0			0
$85$	−2.30902	−	1.67760i	−0.250448	−	0.181961i
$86$		0			0
$87$	−2.43769			−0.261348
$88$		0			0
$89$	−8.47214			−0.898045			−0.449022	−	0.893521i	$-0.648228\pi$
$89$	−8.47214			−0.898045			−0.449022	+	0.893521i	$0.648228\pi$
$90$		0			0
$91$	−10.6631	−	7.74721i	−1.11780	−	0.812128i
$92$		0			0
$93$	0.690983	−	2.12663i	0.0716516	−	0.220521i
$94$		0			0
$95$	1.42705	−	1.03681i	0.146412	−	0.106375i
$96$		0			0
$97$	1.71885	+	5.29007i	0.174522	+	0.537125i	0.999611	−	0.0278780i	$-0.00887501\pi$
$97$	1.71885	+	5.29007i	0.174522	+	0.537125i	−0.825089	+	0.565003i	$0.808875\pi$
$98$		0			0
$99$	0.881966	+	9.42481i	0.0886409	+	0.947229i
$100$		0			0
$101$	−2.10081	−	6.46564i	−0.209039	−	0.643355i	−0.999523	−	0.0308731i	$-0.990171\pi$
$101$	−2.10081	−	6.46564i	−0.209039	−	0.643355i	0.790485	−	0.612482i	$-0.209829\pi$
$102$		0			0
$103$	0.927051	−	0.673542i	0.0913450	−	0.0663661i	−0.541175	−	0.840910i	$-0.682020\pi$
$103$	0.927051	−	0.673542i	0.0913450	−	0.0663661i	0.632520	+	0.774544i	$0.282020\pi$
$104$		0			0
$105$	−0.208204	+	0.640786i	−0.0203186	+	0.0625343i
$106$		0			0
$107$	−6.92705	−	5.03280i	−0.669663	−	0.486539i	0.200249	−	0.979745i	$-0.435825\pi$
$107$	−6.92705	−	5.03280i	−0.669663	−	0.486539i	−0.869912	+	0.493206i	$0.835825\pi$
$108$		0			0
$109$	−3.52786			−0.337908			−0.168954	−	0.985624i	$-0.554039\pi$
$109$	−3.52786			−0.337908			−0.168954	+	0.985624i	$0.554039\pi$
$110$		0			0
$111$	−1.85410			−0.175984
$112$		0			0
$113$	2.07295	+	1.50609i	0.195007	+	0.141681i	0.681004	−	0.732280i	$-0.261544\pi$
$113$	2.07295	+	1.50609i	0.195007	+	0.141681i	−0.485997	+	0.873960i	$0.661544\pi$
$114$		0			0
$115$	1.23607	−	3.80423i	0.115264	−	0.354746i
$116$		0			0
$117$	10.6631	−	7.74721i	0.985806	−	0.716230i
$118$		0			0
$119$	4.07295	+	12.5352i	0.373367	+	1.14910i
$120$		0			0
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$		0			0
$123$	−0.753289	−	2.31838i	−0.0679218	−	0.209042i
$124$		0			0
$125$	4.80902	−	3.49396i	0.430132	−	0.312509i
$126$		0			0
$127$	−1.42705	+	4.39201i	−0.126630	+	0.389728i	−0.994195	−	0.107597i	$-0.965684\pi$
$127$	−1.42705	+	4.39201i	−0.126630	+	0.389728i	0.867564	+	0.497325i	$0.165684\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	18.4721			1.61392			0.806959	−	0.590607i	$-0.201112\pi$
$131$	18.4721			1.61392			0.806959	+	0.590607i	$0.201112\pi$
$132$		0			0
$133$	−8.14590			−0.706339
$134$		0			0
$135$	−1.11803	−	0.812299i	−0.0962250	−	0.0699116i
$136$		0			0
$137$	−3.33688	+	10.2699i	−0.285089	+	0.877414i	0.701283	+	0.712883i	$0.252611\pi$
$137$	−3.33688	+	10.2699i	−0.285089	+	0.877414i	−0.986372	+	0.164531i	$0.947389\pi$
$138$		0			0
$139$	6.92705	−	5.03280i	0.587545	−	0.426876i	−0.253891	−	0.967233i	$-0.581711\pi$
$139$	6.92705	−	5.03280i	0.587545	−	0.426876i	0.841436	+	0.540356i	$0.181711\pi$
$140$		0			0
$141$	−0.427051	−	1.31433i	−0.0359642	−	0.110686i
$142$		0			0
$143$	−1.42705	−	15.2497i	−0.119336	−	1.27524i
$144$		0			0
$145$	1.21885	+	3.75123i	0.101220	+	0.311522i
$146$		0			0
$147$	0.354102	−	0.257270i	0.0292058	−	0.0212193i
$148$		0			0
$149$	1.42705	−	4.39201i	0.116909	−	0.359808i	−0.875432	−	0.483342i	$-0.839423\pi$
$149$	1.42705	−	4.39201i	0.116909	−	0.359808i	0.992340	+	0.123534i	$0.0394229\pi$
$150$		0			0
$151$	11.5451	+	8.38800i	0.939526	+	0.682605i	0.948306	−	0.317356i	$-0.102795\pi$
$151$	11.5451	+	8.38800i	0.939526	+	0.682605i	−0.00878076	+	0.999961i	$0.502795\pi$
$152$		0			0
$153$	−13.1803			−1.06557
$154$		0			0
$155$	−3.61803			−0.290607
$156$		0			0
$157$	2.07295	+	1.50609i	0.165439	+	0.120199i	0.667424	−	0.744678i	$-0.267397\pi$
$157$	2.07295	+	1.50609i	0.165439	+	0.120199i	−0.501985	+	0.864876i	$0.667397\pi$
$158$		0			0
$159$	−0.836881	+	2.57565i	−0.0663690	+	0.204263i
$160$		0			0
$161$	−14.9443	+	10.8576i	−1.17777	+	0.855703i
$162$		0			0
$163$	−1.33688	−	4.11450i	−0.104713	−	0.322272i	0.884950	−	0.465686i	$-0.154192\pi$
$163$	−1.33688	−	4.11450i	−0.104713	−	0.322272i	−0.989663	+	0.143413i	$0.954192\pi$
$164$		0			0
$165$	−0.718847	+	0.310271i	−0.0559622	+	0.0241545i
$166$		0			0
$167$	−2.10081	−	6.46564i	−0.162566	−	0.500326i	0.836283	−	0.548298i	$-0.184724\pi$
$167$	−2.10081	−	6.46564i	−0.162566	−	0.500326i	−0.998849	+	0.0479722i	$0.984724\pi$
$168$		0			0
$169$	−6.73607	+	4.89404i	−0.518159	+	0.376465i
$170$		0			0
$171$	2.51722	−	7.74721i	0.192497	−	0.592444i
$172$		0			0
$173$	−14.3992	−	10.4616i	−1.09475	−	0.795382i	−0.114555	−	0.993417i	$-0.536544\pi$
$173$	−14.3992	−	10.4616i	−1.09475	−	0.795382i	−0.980195	+	0.198035i	$0.936544\pi$
$174$		0			0
$175$	−13.1803			−0.996340
$176$		0			0
$177$	3.85410			0.289692
$178$		0			0
$179$	0.309017	+	0.224514i	0.0230970	+	0.0167810i	0.599274	−	0.800544i	$-0.295456\pi$
$179$	0.309017	+	0.224514i	0.0230970	+	0.0167810i	−0.576177	+	0.817325i	$0.695456\pi$
$180$		0			0
$181$	0.190983	−	0.587785i	0.0141957	−	0.0436897i	−0.943708	−	0.330780i	$-0.892688\pi$
$181$	0.190983	−	0.587785i	0.0141957	−	0.0436897i	0.957903	+	0.287091i	$0.0926881\pi$
$182$		0			0
$183$	1.42705	−	1.03681i	0.105491	−	0.0766434i
$184$		0			0
$185$	0.927051	+	2.85317i	0.0681581	+	0.209769i
$186$		0			0
$187$	−7.80902	+	13.1760i	−0.571052	+	0.963527i
$188$		0			0
$189$	1.97214	+	6.06961i	0.143452	+	0.441499i
$190$		0			0
$191$	2.45492	−	1.78360i	0.177631	−	0.129057i	−0.495417	−	0.868655i	$-0.664985\pi$
$191$	2.45492	−	1.78360i	0.177631	−	0.129057i	0.673048	+	0.739599i	$0.264985\pi$
$192$		0			0
$193$	−0.753289	+	2.31838i	−0.0542229	+	0.166881i	−0.974501	−	0.224385i	$-0.927963\pi$
$193$	−0.753289	+	2.31838i	−0.0542229	+	0.166881i	0.920278	+	0.391266i	$0.127963\pi$
$194$		0			0
$195$	0.881966	+	0.640786i	0.0631589	+	0.0458876i
$196$		0			0
$197$	14.9443			1.06474			0.532368	−	0.846513i	$-0.321302\pi$
$197$	14.9443			1.06474			0.532368	+	0.846513i	$0.321302\pi$
$198$		0			0
$199$	16.9443			1.20115			0.600574	−	0.799569i	$-0.294939\pi$
$199$	16.9443			1.20115			0.600574	+	0.799569i	$0.294939\pi$
$200$		0			0
$201$	−1.52786	−	1.11006i	−0.107767	−	0.0782975i
$202$		0			0
$203$	5.62868	−	17.3233i	0.395056	−	1.21586i
$204$		0			0
$205$	−3.19098	+	2.31838i	−0.222868	+	0.161923i
$206$		0			0
$207$	−5.70820	−	17.5680i	−0.396748	−	1.22106i
$208$		0			0
$209$	−6.25329	−	7.10642i	−0.432549	−	0.491562i
$210$		0			0
$211$	7.13525	+	21.9601i	0.491211	+	1.51179i	0.822779	+	0.568361i	$0.192422\pi$
$211$	7.13525	+	21.9601i	0.491211	+	1.51179i	−0.331568	+	0.943431i	$0.607578\pi$
$212$		0			0
$213$	−2.66312	+	1.93487i	−0.182474	+	0.132575i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	13.5172	+	9.82084i	0.917609	+	0.666682i
$218$		0			0
$219$	4.61803			0.312058
$220$		0			0
$221$	21.3262			1.43456
$222$		0			0
$223$	15.2533	+	11.0822i	1.02144	+	0.742117i	0.966577	−	0.256378i	$-0.0825290\pi$
$223$	15.2533	+	11.0822i	1.02144	+	0.742117i	0.0548591	+	0.998494i	$0.482529\pi$
$224$		0			0
$225$	4.07295	−	12.5352i	0.271530	−	0.835683i
$226$		0			0
$227$	−17.2533	+	12.5352i	−1.14514	+	0.831994i	−0.987827	−	0.155555i	$-0.950283\pi$
$227$	−17.2533	+	12.5352i	−1.14514	+	0.831994i	−0.157314	+	0.987549i	$0.550283\pi$
$228$		0			0
$229$	−5.33688	−	16.4252i	−0.352671	−	1.08541i	−0.957348	−	0.288939i	$-0.906698\pi$
$229$	−5.33688	−	16.4252i	−0.352671	−	1.08541i	0.604677	−	0.796471i	$-0.293302\pi$
$230$		0			0
$231$	3.52786	+	0.792055i	0.232116	+	0.0521134i
$232$		0			0
$233$	1.42705	+	4.39201i	0.0934892	+	0.287730i	0.986857	−	0.161596i	$-0.0516641\pi$
$233$	1.42705	+	4.39201i	0.0934892	+	0.287730i	−0.893368	+	0.449326i	$0.851664\pi$
$234$		0			0
$235$	−1.80902	+	1.31433i	−0.118007	+	0.0857373i
$236$		0			0
$237$	1.63525	−	5.03280i	0.106221	−	0.326915i
$238$		0			0
$239$	−6.92705	−	5.03280i	−0.448074	−	0.325545i	0.340761	−	0.940150i	$-0.389315\pi$
$239$	−6.92705	−	5.03280i	−0.448074	−	0.325545i	−0.788835	+	0.614605i	$0.789315\pi$
$240$		0			0
$241$	3.52786			0.227250			0.113625	−	0.993524i	$-0.463754\pi$
$241$	3.52786			0.227250			0.113625	+	0.993524i	$0.463754\pi$
$242$		0			0
$243$	−9.65248			−0.619207
$244$		0			0
$245$	−0.572949	−	0.416272i	−0.0366044	−	0.0265946i
$246$		0			0
$247$	−4.07295	+	12.5352i	−0.259156	+	0.797599i
$248$		0			0
$249$	−4.95492	+	3.59996i	−0.314005	+	0.228138i
$250$		0			0
$251$	0.371323	+	1.14281i	0.0234377	+	0.0721338i	0.962091	−	0.272728i	$-0.0879258\pi$
$251$	0.371323	+	1.14281i	0.0234377	+	0.0721338i	−0.938654	+	0.344862i	$0.887926\pi$
$252$		0			0
$253$	−20.9443	−	4.70228i	−1.31676	−	0.295630i
$254$		0			0
$255$	−0.336881	−	1.03681i	−0.0210963	−	0.0649278i
$256$		0			0
$257$	13.0172	−	9.45756i	0.811992	−	0.589947i	−0.102416	−	0.994742i	$-0.532657\pi$
$257$	13.0172	−	9.45756i	0.811992	−	0.589947i	0.914407	+	0.404795i	$0.132657\pi$
$258$		0			0
$259$	4.28115	−	13.1760i	0.266018	−	0.818719i
$260$		0			0
$261$	14.7361	+	10.7064i	0.912140	+	0.662708i
$262$		0			0
$263$	−29.8885			−1.84301			−0.921503	−	0.388371i	$-0.873038\pi$
$263$	−29.8885			−1.84301			−0.921503	+	0.388371i	$0.873038\pi$
$264$		0			0
$265$	4.38197			0.269182
$266$		0			0
$267$	−2.61803	−	1.90211i	−0.160221	−	0.116407i
$268$		0			0
$269$	−3.98936	+	12.2780i	−0.243235	+	0.748602i	0.752686	+	0.658379i	$0.228758\pi$
$269$	−3.98936	+	12.2780i	−0.243235	+	0.748602i	−0.995922	+	0.0902222i	$0.971242\pi$
$270$		0			0
$271$	−11.5451	+	8.38800i	−0.701314	+	0.509534i	−0.880360	−	0.474306i	$-0.842699\pi$
$271$	−11.5451	+	8.38800i	−0.701314	+	0.509534i	0.179046	+	0.983841i	$0.442699\pi$
$272$		0			0
$273$	−1.55573	−	4.78804i	−0.0941569	−	0.289785i
$274$		0			0
$275$	−10.1180	−	11.4984i	−0.610140	−	0.693382i
$276$		0			0
$277$	−0.753289	−	2.31838i	−0.0452607	−	0.139298i	0.925872	−	0.377836i	$-0.123332\pi$
$277$	−0.753289	−	2.31838i	−0.0452607	−	0.139298i	−0.971133	+	0.238538i	$0.923332\pi$
$278$		0			0
$279$	−13.5172	+	9.82084i	−0.809255	+	0.587958i
$280$		0			0
$281$	3.60739	−	11.1024i	0.215199	−	0.662314i	−0.783941	−	0.620836i	$-0.786793\pi$
$281$	3.60739	−	11.1024i	0.215199	−	0.662314i	0.999139	−	0.0414782i	$-0.0132067\pi$
$282$		0			0
$283$	−6.92705	−	5.03280i	−0.411770	−	0.299169i	0.362548	−	0.931965i	$-0.381907\pi$
$283$	−6.92705	−	5.03280i	−0.411770	−	0.299169i	−0.774318	+	0.632796i	$0.781907\pi$
$284$		0			0
$285$	0.673762			0.0399102
$286$		0			0
$287$	18.2148			1.07518
$288$		0			0
$289$	−3.50000	−	2.54290i	−0.205882	−	0.149582i
$290$		0			0
$291$	−0.656541	+	2.02063i	−0.0384871	+	0.118451i
$292$		0			0
$293$	−5.16312	+	3.75123i	−0.301633	+	0.219149i	−0.728298	−	0.685261i	$-0.759688\pi$
$293$	−5.16312	+	3.75123i	−0.301633	+	0.219149i	0.426665	+	0.904410i	$0.359688\pi$
$294$		0			0
$295$	−1.92705	−	5.93085i	−0.112197	−	0.345308i
$296$		0			0
$297$	−3.78115	+	6.37988i	−0.219405	+	0.370198i
$298$		0			0
$299$	9.23607	+	28.4257i	0.534136	+	1.64390i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.802439	−	2.46965i	0.0460989	−	0.141878i
$304$		0			0
$305$	−2.30902	−	1.67760i	−0.132214	−	0.0960590i
$306$		0			0
$307$	18.4721			1.05426			0.527130	−	0.849785i	$-0.323268\pi$
$307$	18.4721			1.05426			0.527130	+	0.849785i	$0.323268\pi$
$308$		0			0
$309$	0.437694			0.0248995
$310$		0			0
$311$	6.30902	+	4.58377i	0.357752	+	0.259922i	0.752114	−	0.659033i	$-0.229034\pi$
$311$	6.30902	+	4.58377i	0.357752	+	0.259922i	−0.394362	+	0.918955i	$0.629034\pi$
$312$		0			0
$313$	9.42705	−	29.0135i	0.532848	−	1.63994i	−0.215404	−	0.976525i	$-0.569107\pi$
$313$	9.42705	−	29.0135i	0.532848	−	1.63994i	0.748253	−	0.663414i	$-0.230893\pi$
$314$		0			0
$315$	4.07295	−	2.95917i	0.229485	−	0.166730i
$316$		0			0
$317$	1.71885	+	5.29007i	0.0965401	+	0.297120i	0.987652	−	0.156664i	$-0.0500739\pi$
$317$	1.71885	+	5.29007i	0.0965401	+	0.297120i	−0.891112	+	0.453784i	$0.850074\pi$
$318$		0			0
$319$	19.4336	−	8.38800i	1.08807	−	0.469638i
$320$		0			0
$321$	−1.01064	−	3.11044i	−0.0564086	−	0.173608i
$322$		0			0
$323$	10.6631	−	7.74721i	0.593312	−	0.431066i
$324$		0			0
$325$	−6.59017	+	20.2825i	−0.365557	+	1.12507i
$326$		0			0
$327$	−1.09017	−	0.792055i	−0.0602865	−	0.0438007i
$328$		0			0
$329$	10.3262			0.569304
$330$		0			0
$331$	−12.0000			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$		0			0
$333$	11.2082	+	8.14324i	0.614206	+	0.446247i
$334$		0			0
$335$	−0.944272	+	2.90617i	−0.0515911	+	0.158781i
$336$		0			0
$337$	4.07295	−	2.95917i	0.221868	−	0.161196i	−0.471299	−	0.881973i	$-0.656215\pi$
$337$	4.07295	−	2.95917i	0.221868	−	0.161196i	0.693167	+	0.720777i	$0.256215\pi$
$338$		0			0
$339$	0.302439	+	0.930812i	0.0164262	+	0.0505548i
$340$		0			0
$341$	1.80902	+	19.3314i	0.0979638	+	1.04685i
$342$		0			0
$343$	−5.16312	−	15.8904i	−0.278782	−	0.858003i
$344$		0			0
$345$	1.23607	−	0.898056i	0.0665477	−	0.0483497i
$346$		0			0
$347$	2.10081	−	6.46564i	0.112778	−	0.347094i	−0.878699	−	0.477375i	$-0.841588\pi$
$347$	2.10081	−	6.46564i	0.112778	−	0.347094i	0.991477	+	0.130282i	$0.0415882\pi$
$348$		0			0
$349$	0.545085	+	0.396027i	0.0291777	+	0.0211989i	0.602279	−	0.798286i	$-0.294260\pi$
$349$	0.545085	+	0.396027i	0.0291777	+	0.0211989i	−0.573101	+	0.819485i	$0.694260\pi$
$350$		0			0
$351$	10.3262			0.551174
$352$		0			0
$353$	2.94427			0.156708			0.0783539	−	0.996926i	$-0.475034\pi$
$353$	2.94427			0.156708			0.0783539	+	0.996926i	$0.475034\pi$
$354$		0			0
$355$	4.30902	+	3.13068i	0.228699	+	0.166159i
$356$		0			0
$357$	−1.55573	+	4.78804i	−0.0823379	+	0.253410i
$358$		0			0
$359$	6.92705	−	5.03280i	0.365596	−	0.265621i	−0.389787	−	0.920905i	$-0.627451\pi$
$359$	6.92705	−	5.03280i	0.365596	−	0.265621i	0.755382	+	0.655284i	$0.227451\pi$
$360$		0			0
$361$	−3.35410	−	10.3229i	−0.176532	−	0.543309i
$362$		0			0
$363$	2.01722	+	3.68571i	0.105877	+	0.193450i
$364$		0			0
$365$	−2.30902	−	7.10642i	−0.120859	−	0.371967i
$366$		0			0
$367$	−21.7254	+	15.7844i	−1.13406	+	0.823941i	−0.986280	−	0.165079i	$-0.947212\pi$
$367$	−21.7254	+	15.7844i	−1.13406	+	0.823941i	−0.147778	+	0.989021i	$0.547212\pi$
$368$		0			0
$369$	−5.62868	+	17.3233i	−0.293017	+	0.901814i
$370$		0			0
$371$	−16.3713	−	11.8945i	−0.849957	−	0.617530i
$372$		0			0
$373$	−33.4164			−1.73024			−0.865118	−	0.501568i	$-0.832757\pi$
$373$	−33.4164			−1.73024			−0.865118	+	0.501568i	$0.832757\pi$
$374$		0			0
$375$	2.27051			0.117249
$376$		0			0
$377$	−23.8435	−	17.3233i	−1.22800	−	0.892195i
$378$		0			0
$379$	3.04508	−	9.37181i	0.156416	−	0.481397i	−0.841886	−	0.539655i	$-0.818555\pi$
$379$	3.04508	−	9.37181i	0.156416	−	0.481397i	0.998302	+	0.0582579i	$0.0185546\pi$
$380$		0			0
$381$	−1.42705	+	1.03681i	−0.0731100	+	0.0531176i
$382$		0			0
$383$	9.60739	+	29.5685i	0.490915	+	1.51088i	0.823228	+	0.567711i	$0.192171\pi$
$383$	9.60739	+	29.5685i	0.490915	+	1.51088i	−0.332313	+	0.943169i	$0.607829\pi$
$384$		0			0
$385$	−0.545085	−	5.82485i	−0.0277801	−	0.296862i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.78115	−	1.29408i	0.0903080	−	0.0656126i	−0.541715	−	0.840562i	$-0.682225\pi$
$389$	1.78115	−	1.29408i	0.0903080	−	0.0656126i	0.632023	+	0.774950i	$0.282225\pi$
$390$		0			0
$391$	9.23607	−	28.4257i	0.467088	−	1.43755i
$392$		0			0
$393$	5.70820	+	4.14725i	0.287941	+	0.209201i
$394$		0			0
$395$	−8.56231			−0.430816
$396$		0			0
$397$	−20.8328			−1.04557			−0.522785	−	0.852465i	$-0.675107\pi$
$397$	−20.8328			−1.04557			−0.522785	+	0.852465i	$0.675107\pi$
$398$		0			0
$399$	−2.51722	−	1.82887i	−0.126019	−	0.0915579i
$400$		0			0
$401$	−11.0451	+	33.9933i	−0.551565	+	1.69754i	0.153281	+	0.988183i	$0.451016\pi$
$401$	−11.0451	+	33.9933i	−0.551565	+	1.69754i	−0.704846	+	0.709361i	$0.748984\pi$
$402$		0			0
$403$	21.8713	−	15.8904i	1.08949	−	0.791560i
$404$		0			0
$405$	1.47214	+	4.53077i	0.0731510	+	0.225136i
$406$		0			0
$407$	14.7812	−	6.37988i	0.732675	−	0.316239i
$408$		0			0
$409$	−4.28115	−	13.1760i	−0.211689	−	0.651513i	−0.999372	−	0.0354318i	$-0.988719\pi$
$409$	−4.28115	−	13.1760i	−0.211689	−	0.651513i	0.787683	−	0.616081i	$-0.211281\pi$
$410$		0			0
$411$	−3.33688	+	2.42439i	−0.164596	+	0.119586i
$412$		0			0
$413$	−8.89919	+	27.3889i	−0.437900	+	1.34772i
$414$		0			0
$415$	8.01722	+	5.82485i	0.393550	+	0.285931i
$416$		0			0
$417$	3.27051			0.160158
$418$		0			0
$419$	−31.4164			−1.53479			−0.767396	−	0.641173i	$-0.778448\pi$
$419$	−31.4164			−1.53479			−0.767396	+	0.641173i	$0.778448\pi$
$420$		0			0
$421$	−19.6353	−	14.2658i	−0.956964	−	0.695275i	−0.00452016	−	0.999990i	$-0.501439\pi$
$421$	−19.6353	−	14.2658i	−0.956964	−	0.695275i	−0.952444	+	0.304715i	$0.901439\pi$
$422$		0			0
$423$	−3.19098	+	9.82084i	−0.155151	+	0.477505i
$424$		0			0
$425$	17.2533	−	12.5352i	0.836907	−	0.608049i
$426$		0			0
$427$	4.07295	+	12.5352i	0.197104	+	0.606623i
$428$		0			0
$429$	2.98278	−	5.03280i	0.144010	−	0.242986i
$430$		0			0
$431$	−9.98936	−	30.7441i	−0.481170	−	1.48089i	−0.837452	−	0.546511i	$-0.815956\pi$
$431$	−9.98936	−	30.7441i	−0.481170	−	1.48089i	0.356281	−	0.934379i	$-0.384044\pi$
$432$		0			0
$433$	29.4894	−	21.4253i	1.41717	−	1.02963i	0.424937	−	0.905223i	$-0.360296\pi$
$433$	29.4894	−	21.4253i	1.41717	−	1.02963i	0.992231	−	0.124410i	$-0.0397038\pi$
$434$		0			0
$435$	−0.465558	+	1.43284i	−0.0223218	+	0.0686995i
$436$		0			0
$437$	14.9443	+	10.8576i	0.714881	+	0.519392i
$438$		0			0
$439$	11.4164			0.544875			0.272438	−	0.962173i	$-0.412170\pi$
$439$	11.4164			0.544875			0.272438	+	0.962173i	$0.412170\pi$
$440$		0			0
$441$	−3.27051			−0.155739
$442$		0			0
$443$	24.4894	+	17.7926i	1.16352	+	0.845350i	0.990220	−	0.139518i	$-0.0445554\pi$
$443$	24.4894	+	17.7926i	1.16352	+	0.845350i	0.173305	+	0.984868i	$0.444555\pi$
$444$		0			0
$445$	−1.61803	+	4.97980i	−0.0767022	+	0.236065i
$446$		0			0
$447$	1.42705	−	1.03681i	0.0674972	−	0.0490396i
$448$		0			0
$449$	1.71885	+	5.29007i	0.0811174	+	0.249654i	0.983388	−	0.181517i	$-0.0581007\pi$
$449$	1.71885	+	5.29007i	0.0811174	+	0.249654i	−0.902270	+	0.431171i	$0.858101\pi$
$450$		0			0
$451$	13.9828	+	15.8904i	0.658423	+	0.748252i
$452$		0			0
$453$	1.68441	+	5.18407i	0.0791403	+	0.243569i
$454$		0			0
$455$	−6.59017	+	4.78804i	−0.308952	+	0.224467i
$456$		0			0
$457$	−4.28115	+	13.1760i	−0.200264	+	0.616349i	0.799611	+	0.600519i	$0.205039\pi$
$457$	−4.28115	+	13.1760i	−0.200264	+	0.616349i	−0.999875	+	0.0158303i	$0.994961\pi$
$458$		0			0
$459$	−8.35410	−	6.06961i	−0.389936	−	0.283305i
$460$		0			0
$461$	37.7771			1.75945			0.879727	−	0.475479i	$-0.157725\pi$
$461$	37.7771			1.75945			0.879727	+	0.475479i	$0.157725\pi$
$462$		0			0
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$		0			0
$465$	−1.11803	−	0.812299i	−0.0518476	−	0.0376695i
$466$		0			0
$467$	8.75329	−	26.9399i	0.405054	−	1.24663i	−0.515796	−	0.856711i	$-0.672504\pi$
$467$	8.75329	−	26.9399i	0.405054	−	1.24663i	0.920850	−	0.389916i	$-0.127496\pi$
$468$		0			0
$469$	11.4164	−	8.29451i	0.527161	−	0.383005i
$470$		0			0
$471$	0.302439	+	0.930812i	0.0139357	+	0.0428896i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	4.07295	+	12.5352i	0.186880	+	0.575157i
$476$		0			0
$477$	16.3713	−	11.8945i	0.749591	−	0.544610i
$478$		0			0
$479$	−3.60739	+	11.1024i	−0.164826	+	0.507282i	−0.999023	−	0.0441838i	$-0.985931\pi$
$479$	−3.60739	+	11.1024i	−0.164826	+	0.507282i	0.834198	+	0.551466i	$0.185931\pi$
$480$		0			0
$481$	−18.1353	−	13.1760i	−0.826896	−	0.600775i
$482$		0			0
$483$	−7.05573			−0.321047
$484$		0			0
$485$	3.43769			0.156098
$486$		0			0
$487$	−8.92705	−	6.48588i	−0.404523	−	0.293903i	0.366858	−	0.930277i	$-0.380434\pi$
$487$	−8.92705	−	6.48588i	−0.404523	−	0.293903i	−0.771381	+	0.636374i	$0.780434\pi$
$488$		0			0
$489$	0.510643	−	1.57160i	0.0230921	−	0.0710701i
$490$		0			0
$491$	6.92705	−	5.03280i	0.312613	−	0.227127i	−0.420404	−	0.907337i	$-0.638112\pi$
$491$	6.92705	−	5.03280i	0.312613	−	0.227127i	0.733017	+	0.680210i	$0.238112\pi$
$492$		0			0
$493$	9.10739	+	28.0297i	0.410176	+	1.26239i
$494$		0			0
$495$	5.70820	+	1.28157i	0.256565	+	0.0576024i
$496$		0			0
$497$	−7.60081	−	23.3929i	−0.340943	−	1.04931i
$498$		0			0
$499$	−8.30902	+	6.03685i	−0.371963	+	0.270247i	−0.758024	−	0.652226i	$-0.773835\pi$
$499$	−8.30902	+	6.03685i	−0.371963	+	0.270247i	0.386062	+	0.922473i	$0.373835\pi$
$500$		0			0
$501$	0.802439	−	2.46965i	0.0358503	−	0.110336i
$502$		0			0
$503$	−1.21885	−	0.885544i	−0.0543457	−	0.0394845i	0.560281	−	0.828303i	$-0.310693\pi$
$503$	−1.21885	−	0.885544i	−0.0543457	−	0.0394845i	−0.614626	+	0.788818i	$0.710693\pi$
$504$		0			0
$505$	−4.20163			−0.186970
$506$		0			0
$507$	−3.18034			−0.141244
$508$		0			0
$509$	−25.6353	−	18.6251i	−1.13626	−	0.825543i	−0.149669	−	0.988736i	$-0.547821\pi$
$509$	−25.6353	−	18.6251i	−1.13626	−	0.825543i	−0.986594	+	0.163193i	$0.947821\pi$
$510$		0			0
$511$	−10.6631	+	32.8177i	−0.471709	+	1.45177i
$512$		0			0
$513$	5.16312	−	3.75123i	0.227957	−	0.165621i
$514$		0			0
$515$	−0.218847	−	0.673542i	−0.00964355	−	0.0296798i
$516$		0			0
$517$	7.92705	+	9.00854i	0.348631	+	0.396195i
$518$		0			0
$519$	−2.10081	−	6.46564i	−0.0922155	−	0.283810i
$520$		0			0
$521$	−18.8713	+	13.7108i	−0.826768	+	0.600682i	−0.918643	−	0.395089i	$-0.870714\pi$
$521$	−18.8713	+	13.7108i	−0.826768	+	0.600682i	0.0918753	+	0.995771i	$0.470714\pi$
$522$		0			0
$523$	−8.48278	+	26.1073i	−0.370926	+	1.14159i	0.575260	+	0.817970i	$0.304901\pi$
$523$	−8.48278	+	26.1073i	−0.370926	+	1.14159i	−0.946186	+	0.323622i	$0.895099\pi$
$524$		0			0
$525$	−4.07295	−	2.95917i	−0.177758	−	0.129149i
$526$		0			0
$527$	−27.0344			−1.17764
$528$		0			0
$529$	18.8885			0.821241
$530$		0			0
$531$	−23.2984	−	16.9273i	−1.01106	−	0.734580i
$532$		0			0
$533$	9.10739	−	28.0297i	0.394485	−	1.21410i
$534$		0			0
$535$	−4.28115	+	3.11044i	−0.185090	+	0.134476i
$536$		0			0
$537$	0.0450850	+	0.138757i	0.00194556	+	0.00598782i
$538$		0			0
$539$	−1.93769	+	3.26944i	−0.0834624	+	0.140825i
$540$		0			0
$541$	−7.80902	−	24.0337i	−0.335736	−	1.03329i	−0.966358	−	0.257199i	$-0.917200\pi$
$541$	−7.80902	−	24.0337i	−0.335736	−	1.03329i	0.630623	−	0.776090i	$-0.282800\pi$
$542$		0			0
$543$	0.190983	−	0.138757i	0.00819587	−	0.00595464i
$544$		0			0
$545$	−0.673762	+	2.07363i	−0.0288608	+	0.0888244i
$546$		0			0
$547$	−18.3435	−	13.3273i	−0.784310	−	0.569834i	0.121960	−	0.992535i	$-0.461082\pi$
$547$	−18.3435	−	13.3273i	−0.784310	−	0.569834i	−0.906269	+	0.422701i	$0.861082\pi$
$548$		0			0
$549$	−13.1803			−0.562523
$550$		0			0
$551$	−18.2148			−0.775976
$552$		0			0
$553$	31.9894	+	23.2416i	1.36033	+	0.988335i
$554$		0			0
$555$	−0.354102	+	1.08981i	−0.0150308	+	0.0462600i
$556$		0			0
$557$	−8.69098	+	6.31437i	−0.368249	+	0.267548i	−0.756484	−	0.654012i	$-0.773085\pi$
$557$	−8.69098	+	6.31437i	−0.368249	+	0.267548i	0.388236	+	0.921560i	$0.373085\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−5.37132	+	2.31838i	−0.226777	+	0.0978823i
$562$		0			0
$563$	4.95492	+	15.2497i	0.208825	+	0.642697i	0.999535	+	0.0305054i	$0.00971169\pi$
$563$	4.95492	+	15.2497i	0.208825	+	0.642697i	−0.790710	+	0.612191i	$0.790288\pi$
$564$		0			0
$565$	1.28115	−	0.930812i	0.0538985	−	0.0391596i
$566$		0			0
$567$	6.79837	−	20.9232i	0.285505	−	0.878694i
$568$		0			0
$569$	28.2533	+	20.5272i	1.18444	+	0.860546i	0.992665	−	0.120893i	$-0.0385759\pi$
$569$	28.2533	+	20.5272i	1.18444	+	0.860546i	0.191774	+	0.981439i	$0.438576\pi$
$570$		0			0
$571$	18.4721			0.773035			0.386517	−	0.922282i	$-0.373678\pi$
$571$	18.4721			0.773035			0.386517	+	0.922282i	$0.373678\pi$
$572$		0			0
$573$	1.15905			0.0484202
$574$		0			0
$575$	24.1803	+	17.5680i	1.00839	+	0.732638i
$576$		0			0
$577$	−7.69756	+	23.6907i	−0.320454	+	0.986255i	0.652998	+	0.757360i	$0.273511\pi$
$577$	−7.69756	+	23.6907i	−0.320454	+	0.986255i	−0.973451	+	0.228895i	$0.926489\pi$
$578$		0			0
$579$	−0.753289	+	0.547296i	−0.0313056	+	0.0227449i
$580$		0			0
$581$	−14.1418	−	43.5241i	−0.586702	−	1.80568i
$582$		0			0
$583$	−2.19098	−	23.4131i	−0.0907412	−	0.969673i
$584$		0			0
$585$	−2.51722	−	7.74721i	−0.104074	−	0.320308i
$586$		0			0
$587$	0.927051	−	0.673542i	0.0382635	−	0.0278001i	−0.568489	−	0.822691i	$-0.692472\pi$
$587$	0.927051	−	0.673542i	0.0382635	−	0.0278001i	0.606753	+	0.794891i	$0.292472\pi$
$588$		0			0
$589$	5.16312	−	15.8904i	0.212743	−	0.654754i
$590$		0			0
$591$	4.61803	+	3.35520i	0.189961	+	0.138014i
$592$		0			0
$593$	10.5836			0.434616			0.217308	−	0.976103i	$-0.430272\pi$
$593$	10.5836			0.434616			0.217308	+	0.976103i	$0.430272\pi$
$594$		0			0
$595$	8.14590			0.333949
$596$		0			0
$597$	5.23607	+	3.80423i	0.214298	+	0.155697i
$598$		0			0
$599$	−0.302439	+	0.930812i	−0.0123573	+	0.0380320i	−0.957045	−	0.289939i	$-0.906365\pi$
$599$	−0.302439	+	0.930812i	−0.0123573	+	0.0380320i	0.944688	+	0.327971i	$0.106365\pi$
$600$		0			0
$601$	−10.8713	+	7.89848i	−0.443451	+	0.322186i	−0.787004	−	0.616947i	$-0.788369\pi$
$601$	−10.8713	+	7.89848i	−0.443451	+	0.322186i	0.343554	+	0.939133i	$0.388369\pi$
$602$		0			0
$603$	4.36068	+	13.4208i	0.177581	+	0.546537i
$604$		0			0
$605$	4.66312	−	4.94704i	0.189583	−	0.201126i
$606$		0			0
$607$	12.8435	+	39.5281i	0.521300	+	1.60440i	0.771519	+	0.636207i	$0.219497\pi$
$607$	12.8435	+	39.5281i	0.521300	+	1.60440i	−0.250219	+	0.968189i	$0.580503\pi$
$608$		0			0
$609$	5.62868	−	4.08947i	0.228086	−	0.165714i
$610$		0			0
$611$	5.16312	−	15.8904i	0.208877	−	0.642859i
$612$		0			0
$613$	24.7254	+	17.9641i	0.998651	+	0.725562i	0.961798	−	0.273759i	$-0.0882670\pi$
$613$	24.7254	+	17.9641i	0.998651	+	0.725562i	0.0368521	+	0.999321i	$0.488267\pi$
$614$		0			0
$615$	−1.50658			−0.0607511
$616$		0			0
$617$	−16.4721			−0.663143			−0.331572	−	0.943430i	$-0.607579\pi$
$617$	−16.4721			−0.663143			−0.331572	+	0.943430i	$0.607579\pi$
$618$		0			0
$619$	−5.39919	−	3.92274i	−0.217012	−	0.157668i	0.473969	−	0.880542i	$-0.342821\pi$
$619$	−5.39919	−	3.92274i	−0.217012	−	0.157668i	−0.690980	+	0.722873i	$0.742821\pi$
$620$		0			0
$621$	4.47214	−	13.7638i	0.179461	−	0.552323i
$622$		0			0
$623$	19.5623	−	14.2128i	0.783747	−	0.569426i
$624$		0			0
$625$	6.00000	+	18.4661i	0.240000	+	0.738644i
$626$		0			0
$627$	−0.336881	−	3.59996i	−0.0134537	−	0.143768i
$628$		0			0
$629$	6.92705	+	21.3193i	0.276200	+	0.850055i
$630$		0			0
$631$	13.8713	−	10.0781i	0.552209	−	0.401203i	−0.276390	−	0.961045i	$-0.589138\pi$
$631$	13.8713	−	10.0781i	0.552209	−	0.401203i	0.828599	+	0.559842i	$0.189138\pi$
$632$		0			0
$633$	−2.72542	+	8.38800i	−0.108326	+	0.333393i
$634$		0			0
$635$	2.30902	+	1.67760i	0.0916305	+	0.0665735i
$636$		0			0
$637$	5.29180			0.209669
$638$		0			0
$639$	24.5967			0.973032
$640$		0			0
$641$	−12.8713	−	9.35156i	−0.508387	−	0.369365i	0.303825	−	0.952728i	$-0.401736\pi$
$641$	−12.8713	−	9.35156i	−0.508387	−	0.369365i	−0.812211	+	0.583363i	$0.801736\pi$
$642$		0			0
$643$	6.57295	−	20.2295i	0.259212	−	0.797772i	−0.733759	−	0.679410i	$-0.762236\pi$
$643$	6.57295	−	20.2295i	0.259212	−	0.797772i	0.992971	−	0.118362i	$-0.0377643\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.0451	−	33.9933i	−0.434227	−	1.33641i	−0.893877	−	0.448313i	$-0.852025\pi$
$647$	−11.0451	−	33.9933i	−0.434227	−	1.33641i	0.459649	−	0.888100i	$-0.347975\pi$
$648$		0			0
$649$	−30.7254	+	13.2618i	−1.20608	+	0.520571i
$650$		0			0
$651$	1.97214	+	6.06961i	0.0772941	+	0.237887i
$652$		0			0
$653$	−18.8713	+	13.7108i	−0.738492	+	0.536546i	−0.892238	−	0.451565i	$-0.850866\pi$
$653$	−18.8713	+	13.7108i	−0.738492	+	0.536546i	0.153747	+	0.988110i	$0.450866\pi$
$654$		0			0
$655$	3.52786	−	10.8576i	0.137845	−	0.424243i
$656$		0			0
$657$	−27.9164	−	20.2825i	−1.08912	−	0.791294i
$658$		0			0
$659$	−4.36068			−0.169868			−0.0849340	−	0.996387i	$-0.527068\pi$
$659$	−4.36068			−0.169868			−0.0849340	+	0.996387i	$0.527068\pi$
$660$		0			0
$661$	14.3607			0.558566			0.279283	−	0.960209i	$-0.409903\pi$
$661$	14.3607			0.558566			0.279283	+	0.960209i	$0.409903\pi$
$662$		0			0
$663$	6.59017	+	4.78804i	0.255941	+	0.185952i
$664$		0			0
$665$	−1.55573	+	4.78804i	−0.0603285	+	0.185672i
$666$		0			0
$667$	−33.4164	+	24.2784i	−1.29389	+	0.940065i
$668$		0			0
$669$	2.22542	+	6.84915i	0.0860399	+	0.264804i
$670$		0			0
$671$	−7.80902	+	13.1760i	−0.301464	+	0.508655i
$672$		0			0
$673$	9.31559	+	28.6705i	0.359090	+	1.10516i	0.953600	+	0.301077i	$0.0973460\pi$
$673$	9.31559	+	28.6705i	0.359090	+	1.10516i	−0.594510	+	0.804088i	$0.702654\pi$
$674$		0			0
$675$	8.35410	−	6.06961i	0.321550	−	0.233619i
$676$		0			0
$677$	10.6631	−	32.8177i	0.409817	−	1.26129i	−0.506989	−	0.861953i	$-0.669241\pi$
$677$	10.6631	−	32.8177i	0.409817	−	1.26129i	0.916805	−	0.399334i	$-0.130759\pi$
$678$		0			0
$679$	−12.8435	−	9.33132i	−0.492887	−	0.358103i
$680$		0			0
$681$	−8.14590			−0.312151
$682$		0			0
$683$	16.9443			0.648355			0.324177	−	0.945996i	$-0.394913\pi$
$683$	16.9443			0.648355			0.324177	+	0.945996i	$0.394913\pi$
$684$		0			0
$685$	5.39919	+	3.92274i	0.206292	+	0.149880i
$686$		0			0
$687$	2.03851	−	6.27388i	0.0777739	−	0.239363i
$688$		0			0
$689$	−26.4894	+	19.2456i	−1.00916	+	0.733201i
$690$		0			0
$691$	−3.98936	−	12.2780i	−0.151762	−	0.467076i	0.846056	−	0.533094i	$-0.178971\pi$
$691$	−3.98936	−	12.2780i	−0.151762	−	0.467076i	−0.997818	+	0.0660174i	$0.978971\pi$
$692$		0			0
$693$	−17.8475	−	20.2825i	−0.677971	−	0.770467i
$694$		0			0
$695$	−1.63525	−	5.03280i	−0.0620288	−	0.190905i
$696$		0			0
$697$	−23.8435	+	17.3233i	−0.903135	+	0.656166i
$698$		0			0
$699$	−0.545085	+	1.67760i	−0.0206170	+	0.0634526i
$700$		0			0
$701$	−1.63525	−	1.18808i	−0.0617627	−	0.0448732i	0.556476	−	0.830864i	$-0.312153\pi$
$701$	−1.63525	−	1.18808i	−0.0617627	−	0.0448732i	−0.618238	+	0.785991i	$0.712153\pi$
$702$		0			0
$703$	−13.8541			−0.522517
$704$		0			0
$705$	−0.854102			−0.0321673
$706$		0			0
$707$	15.6976	+	11.4049i	0.590368	+	0.428927i
$708$		0			0
$709$	2.37132	−	7.29818i	0.0890569	−	0.274089i	−0.896602	−	0.442836i	$-0.853972\pi$
$709$	2.37132	−	7.29818i	0.0890569	−	0.274089i	0.985659	+	0.168747i	$0.0539722\pi$
$710$		0			0
$711$	−31.9894	+	23.2416i	−1.19969	+	0.871629i
$712$		0			0
$713$	−11.7082	−	36.0341i	−0.438476	−	1.34949i
$714$		0			0
$715$	−9.23607	−	2.07363i	−0.345409	−	0.0775492i
$716$		0			0
$717$	−1.01064	−	3.11044i	−0.0377432	−	0.116161i
$718$		0			0
$719$	4.63525	−	3.36771i	0.172866	−	0.125594i	−0.497988	−	0.867184i	$-0.665928\pi$
$719$	4.63525	−	3.36771i	0.172866	−	0.125594i	0.670854	+	0.741589i	$0.265928\pi$
$720$		0			0
$721$	−1.01064	+	3.11044i	−0.0376383	+	0.115839i
$722$		0			0
$723$	1.09017	+	0.792055i	0.0405439	+	0.0294568i
$724$		0			0
$725$	−29.4721			−1.09457
$726$		0			0
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	15.7254	+	11.4252i	0.582423	+	0.423155i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−10.8713	+	7.89848i	−0.401541	+	0.291737i	−0.770169	−	0.637840i	$-0.779828\pi$
$733$	−10.8713	+	7.89848i	−0.401541	+	0.291737i	0.368627	+	0.929577i	$0.379828\pi$
$734$		0			0
$735$	−0.0835921	−	0.257270i	−0.00308334	−	0.00948955i
$736$		0			0
$737$	16.0000	+	3.59222i	0.589368	+	0.132321i
$738$		0			0
$739$	−11.3369	−	34.8913i	−0.417034	−	1.28350i	−0.910419	−	0.413687i	$-0.864241\pi$
$739$	−11.3369	−	34.8913i	−0.417034	−	1.28350i	0.493385	−	0.869811i	$-0.335759\pi$
$740$		0			0
$741$	−4.07295	+	2.95917i	−0.149624	+	0.108708i
$742$		0			0
$743$	−10.6631	+	32.8177i	−0.391192	+	1.20396i	0.540696	+	0.841218i	$0.318161\pi$
$743$	−10.6631	+	32.8177i	−0.391192	+	1.20396i	−0.931888	+	0.362747i	$0.881839\pi$
$744$		0			0
$745$	−2.30902	−	1.67760i	−0.0845958	−	0.0614625i
$746$		0			0
$747$	45.7639			1.67441
$748$		0			0
$749$	24.4377			0.892934
$750$		0			0
$751$	−14.6353	−	10.6331i	−0.534048	−	0.388009i	0.287822	−	0.957684i	$-0.407069\pi$
$751$	−14.6353	−	10.6331i	−0.534048	−	0.388009i	−0.821870	+	0.569675i	$0.807069\pi$
$752$		0			0
$753$	−0.141833	+	0.436516i	−0.00516867	+	0.0159075i
$754$		0			0
$755$	7.13525	−	5.18407i	0.259679	−	0.188667i
$756$		0			0
$757$	−4.86475	−	14.9721i	−0.176812	−	0.544172i	0.822899	−	0.568187i	$-0.192355\pi$
$757$	−4.86475	−	14.9721i	−0.176812	−	0.544172i	−0.999712	+	0.0240152i	$0.992355\pi$
$758$		0			0
$759$	−5.41641	−	6.15537i	−0.196603	−	0.223426i
$760$		0			0
$761$	14.1910	+	43.6754i	0.514423	+	1.58323i	0.784330	+	0.620344i	$0.213007\pi$
$761$	14.1910	+	43.6754i	0.514423	+	1.58323i	−0.269907	+	0.962886i	$0.586993\pi$
$762$		0			0
$763$	8.14590	−	5.91834i	0.294901	−	0.214258i
$764$		0			0
$765$	−2.51722	+	7.74721i	−0.0910103	+	0.280101i
$766$		0			0
$767$	37.6976	+	27.3889i	1.36118	+	0.988955i
$768$		0			0
$769$	10.5836			0.381654			0.190827	−	0.981624i	$-0.438883\pi$
$769$	10.5836			0.381654			0.190827	+	0.981624i	$0.438883\pi$
$770$		0			0
$771$	6.14590			0.221339
$772$		0			0
$773$	10.2533	+	7.44945i	0.368785	+	0.267938i	0.756707	−	0.653754i	$-0.226807\pi$
$773$	10.2533	+	7.44945i	0.368785	+	0.267938i	−0.387922	+	0.921692i	$0.626807\pi$
$774$		0			0
$775$	8.35410	−	25.7113i	0.300088	−	0.923577i
$776$		0			0
$777$	4.28115	−	3.11044i	0.153586	−	0.111586i
$778$		0			0
$779$	−5.62868	−	17.3233i	−0.201668	−	0.620671i
$780$		0			0
$781$	14.5729	−	24.5887i	0.521461	−	0.879853i
$782$		0			0
$783$	4.40983	+	13.5721i	0.157594	+	0.485026i
$784$		0			0
$785$	1.28115	−	0.930812i	0.0457263	−	0.0332221i
$786$		0			0
$787$	9.98936	−	30.7441i	0.356082	−	1.09591i	−0.599297	−	0.800527i	$-0.704553\pi$
$787$	9.98936	−	30.7441i	0.356082	−	1.09591i	0.955379	−	0.295382i	$-0.0954468\pi$
$788$		0			0
$789$	−9.23607	−	6.71040i	−0.328813	−	0.238896i
$790$		0			0
$791$	−7.31308			−0.260023
$792$		0			0
$793$	21.3262			0.757317
$794$		0			0
$795$	1.35410	+	0.983813i	0.0480250	+	0.0348922i
$796$		0			0
$797$	−3.33688	+	10.2699i	−0.118198	+	0.363777i	−0.992601	−	0.121424i	$-0.961254\pi$
$797$	−3.33688	+	10.2699i	−0.118198	+	0.363777i	0.874402	+	0.485202i	$0.161254\pi$
$798$		0			0
$799$	−13.5172	+	9.82084i	−0.478205	+	0.347436i
$800$		0			0
$801$	7.47214	+	22.9969i	0.264015	+	0.812554i
$802$		0			0
$803$	−36.8156	+	15.8904i	−1.29919	+	0.560762i
$804$		0			0
$805$	3.52786	+	10.8576i	0.124341	+	0.382682i
$806$		0			0
$807$	−3.98936	+	2.89844i	−0.140432	+	0.102030i
$808$		0			0
$809$	14.1910	−	43.6754i	0.498928	−	1.53554i	−0.311815	−	0.950143i	$-0.600937\pi$
$809$	14.1910	−	43.6754i	0.498928	−	1.53554i	0.810744	−	0.585401i	$-0.199063\pi$
$810$		0			0
$811$	22.9615	+	16.6825i	0.806287	+	0.585802i	0.912752	−	0.408515i	$-0.133953\pi$
$811$	22.9615	+	16.6825i	0.806287	+	0.585802i	−0.106465	+	0.994316i	$0.533953\pi$
$812$		0			0
$813$	−5.45085			−0.191170
$814$		0			0
$815$	−2.67376			−0.0936578
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−11.6246	+	35.7769i	−0.406197	+	1.25015i
$820$		0			0
$821$	15.4894	−	11.2537i	0.540582	−	0.392756i	−0.283719	−	0.958907i	$-0.591568\pi$
$821$	15.4894	−	11.2537i	0.540582	−	0.392756i	0.824301	+	0.566151i	$0.191568\pi$
$822$		0			0
$823$	−0.461493	−	1.42033i	−0.0160866	−	0.0495096i	0.942691	−	0.333667i	$-0.108286\pi$
$823$	−0.461493	−	1.42033i	−0.0160866	−	0.0495096i	−0.958778	+	0.284158i	$0.908286\pi$
$824$		0			0
$825$	−0.545085	−	5.82485i	−0.0189774	−	0.202795i
$826$		0			0
$827$	4.95492	+	15.2497i	0.172299	+	0.530283i	0.999500	−	0.0316241i	$-0.0100680\pi$
$827$	4.95492	+	15.2497i	0.172299	+	0.530283i	−0.827201	+	0.561907i	$0.810068\pi$
$828$		0			0
$829$	38.7254	−	28.1357i	1.34499	−	0.977192i	0.345745	−	0.938328i	$-0.387626\pi$
$829$	38.7254	−	28.1357i	1.34499	−	0.977192i	0.999245	−	0.0388637i	$-0.0123738\pi$
$830$		0			0
$831$	0.287731	−	0.885544i	0.00998127	−	0.0307192i
$832$		0			0
$833$	−4.28115	−	3.11044i	−0.148333	−	0.107770i
$834$		0			0
$835$	−4.20163			−0.145403
$836$		0			0
$837$	−13.0902			−0.452462
$838$		0			0
$839$	0.309017	+	0.224514i	0.0106685	+	0.00775108i	0.593107	−	0.805124i	$-0.297901\pi$
$839$	0.309017	+	0.224514i	0.0106685	+	0.00775108i	−0.582438	+	0.812875i	$0.697901\pi$
$840$		0			0
$841$	3.62461	−	11.1554i	0.124987	−	0.384669i
$842$		0			0
$843$	3.60739	−	2.62092i	0.124245	−	0.0902694i
$844$		0			0
$845$	1.59017	+	4.89404i	0.0547035	+	0.168360i
$846$		0			0
$847$	−30.8500	+	5.82485i	−1.06002	+	0.200144i
$848$		0			0
$849$	−1.01064	−	3.11044i	−0.0346852	−	0.106750i
$850$		0			0
$851$	−25.4164	+	18.4661i	−0.871263	+	0.633010i
$852$		0			0
$853$	−2.10081	+	6.46564i	−0.0719305	+	0.221379i	−0.980558	−	0.196227i	$-0.937131\pi$
$853$	−2.10081	+	6.46564i	−0.0719305	+	0.221379i	0.908628	+	0.417607i	$0.137131\pi$
$854$		0			0
$855$	−4.07295	−	2.95917i	−0.139292	−	0.101202i
$856$		0			0
$857$	−14.9443			−0.510487			−0.255243	−	0.966877i	$-0.582156\pi$
$857$	−14.9443			−0.510487			−0.255243	+	0.966877i	$0.582156\pi$
$858$		0			0
$859$	−48.9443			−1.66996			−0.834979	−	0.550283i	$-0.814520\pi$
$859$	−48.9443			−1.66996			−0.834979	+	0.550283i	$0.814520\pi$
$860$		0			0
$861$	5.62868	+	4.08947i	0.191825	+	0.139369i
$862$		0			0
$863$	8.10081	−	24.9317i	0.275755	−	0.848686i	−0.713264	−	0.700896i	$-0.752784\pi$
$863$	8.10081	−	24.9317i	0.275755	−	0.848686i	0.989019	−	0.147791i	$-0.0472162\pi$
$864$		0			0
$865$	−8.89919	+	6.46564i	−0.302581	+	0.219838i
$866$		0			0
$867$	−0.510643	−	1.57160i	−0.0173423	−	0.0533743i
$868$		0			0
$869$	4.28115	+	45.7490i	0.145228	+	1.55193i
$870$		0			0
$871$	−7.05573	−	21.7153i	−0.239074	−	0.735795i
$872$		0			0
$873$	12.8435	−	9.33132i	0.434685	−	0.315817i
$874$		0			0
$875$	−5.24265	+	16.1352i	−0.177234	+	0.545469i
$876$		0			0
$877$	−35.0517	−	25.4665i	−1.18361	−	0.859943i	−0.191036	−	0.981583i	$-0.561185\pi$
$877$	−35.0517	−	25.4665i	−1.18361	−	0.859943i	−0.992574	+	0.121640i	$0.961185\pi$
$878$		0			0
$879$	−2.43769			−0.0822214
$880$		0			0
$881$	−19.8885			−0.670062			−0.335031	−	0.942207i	$-0.608747\pi$
$881$	−19.8885			−0.670062			−0.335031	+	0.942207i	$0.608747\pi$
$882$		0			0
$883$	−42.0517	−	30.5523i	−1.41515	−	1.02817i	−0.992548	−	0.121853i	$-0.961117\pi$
$883$	−42.0517	−	30.5523i	−1.41515	−	1.02817i	−0.422603	−	0.906315i	$-0.638883\pi$
$884$		0			0
$885$	0.736068	−	2.26538i	0.0247427	−	0.0761501i
$886$		0			0
$887$	21.8713	−	15.8904i	0.734367	−	0.533549i	−0.156575	−	0.987666i	$-0.550045\pi$
$887$	21.8713	−	15.8904i	0.734367	−	0.533549i	0.890942	+	0.454117i	$0.150045\pi$
$888$		0			0
$889$	−4.07295	−	12.5352i	−0.136602	−	0.420419i
$890$		0			0
$891$	23.4721	−	10.1311i	0.786346	−	0.339405i
$892$		0			0
$893$	−3.19098	−	9.82084i	−0.106782	−	0.328642i
$894$		0			0
$895$	0.190983	−	0.138757i	0.00638386	−	0.00463814i
$896$		0			0
$897$	−3.52786	+	10.8576i	−0.117792	+	0.362526i
$898$		0			0
$899$	30.2254	+	21.9601i	1.00807	+	0.732409i
$900$		0			0
$901$	32.7426			1.09082
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.309017	−	0.224514i	−0.0102721	−	0.00746310i
$906$		0			0
$907$	−13.8992	+	42.7773i	−0.461515	+	1.42040i	0.401798	+	0.915728i	$0.368385\pi$
$907$	−13.8992	+	42.7773i	−0.461515	+	1.42040i	−0.863313	+	0.504669i	$0.831615\pi$
$908$		0			0
$909$	−15.6976	+	11.4049i	−0.520655	+	0.378278i
$910$		0			0
$911$	5.71885	+	17.6008i	0.189474	+	0.583141i	0.999997	−	0.00256645i	$-0.000816927\pi$
$911$	5.71885	+	17.6008i	0.189474	+	0.583141i	−0.810523	+	0.585707i	$0.800817\pi$
$912$		0			0
$913$	27.1140	−	45.7490i	0.897341	−	1.51407i
$914$		0			0
$915$	−0.336881	−	1.03681i	−0.0111369	−	0.0342760i
$916$		0			0
$917$	−42.6525	+	30.9888i	−1.40851	+	1.02334i
$918$		0			0
$919$	−12.8435	+	39.5281i	−0.423667	+	1.30391i	0.480599	+	0.876941i	$0.340419\pi$
$919$	−12.8435	+	39.5281i	−0.423667	+	1.30391i	−0.904265	+	0.426971i	$0.859581\pi$
$920$		0			0
$921$	5.70820	+	4.14725i	0.188092	+	0.136657i
$922$		0			0
$923$	−39.7984			−1.30998
$924$		0			0
$925$	−22.4164			−0.737047
$926$		0			0
$927$	−2.64590	−	1.92236i	−0.0869027	−	0.0631385i
$928$		0			0
$929$	9.60739	−	29.5685i	0.315208	−	0.970111i	−0.660460	−	0.750861i	$-0.729639\pi$
$929$	9.60739	−	29.5685i	0.315208	−	0.970111i	0.975669	−	0.219250i	$-0.0703612\pi$
$930$		0			0
$931$	2.64590	−	1.92236i	0.0867158	−	0.0630027i
$932$		0			0
$933$	0.920473	+	2.83293i	0.0301349	+	0.0927458i
$934$		0			0
$935$	6.25329	+	7.10642i	0.204504	+	0.232405i
$936$		0			0
$937$	−4.28115	−	13.1760i	−0.139859	−	0.430442i	0.856455	−	0.516222i	$-0.172662\pi$
$937$	−4.28115	−	13.1760i	−0.139859	−	0.430442i	−0.996314	+	0.0857795i	$0.972662\pi$
$938$		0			0
$939$	9.42705	−	6.84915i	0.307640	−	0.223514i
$940$		0			0
$941$	7.13525	−	21.9601i	0.232603	−	0.715877i	−0.764828	−	0.644235i	$-0.777176\pi$
$941$	7.13525	−	21.9601i	0.232603	−	0.715877i	0.997430	−	0.0716425i	$-0.0228241\pi$
$942$		0			0
$943$	−33.4164	−	24.2784i	−1.08819	−	0.790615i
$944$		0			0
$945$	3.94427			0.128307
$946$		0			0
$947$	47.7771			1.55255			0.776273	−	0.630396i	$-0.217108\pi$
$947$	47.7771			1.55255			0.776273	+	0.630396i	$0.217108\pi$
$948$		0			0
$949$	45.1697	+	32.8177i	1.46627	+	1.06531i
$950$		0			0
$951$	−0.656541	+	2.02063i	−0.0212898	+	0.0655233i
$952$		0			0
$953$	37.4894	−	27.2376i	1.21440	−	0.882313i	0.218777	−	0.975775i	$-0.429793\pi$
$953$	37.4894	−	27.2376i	1.21440	−	0.882313i	0.995623	+	0.0934622i	$0.0297934\pi$
$954$		0			0
$955$	−0.579527	−	1.78360i	−0.0187530	−	0.0577159i
$956$		0			0
$957$	7.88854	+	1.77109i	0.255000	+	0.0572512i
$958$		0			0
$959$	−9.52380	−	29.3112i	−0.307540	−	0.946509i
$960$		0			0
$961$	−2.64590	+	1.92236i	−0.0853515	+	0.0620115i
$962$		0			0
$963$	−7.55166	+	23.2416i	−0.243349	+	0.748951i
$964$		0			0
$965$	1.21885	+	0.885544i	0.0392361	+	0.0285067i
$966$		0			0
$967$	44.0000			1.41494			0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000			1.41494			0.707472	+	0.706741i	$0.249835\pi$
$968$		0			0
$969$	5.03444			0.161730
$970$		0			0
$971$	−14.6353	−	10.6331i	−0.469668	−	0.341234i	0.327644	−	0.944801i	$-0.393745\pi$
$971$	−14.6353	−	10.6331i	−0.469668	−	0.341234i	−0.797312	+	0.603568i	$0.793745\pi$
$972$		0			0
$973$	−7.55166	+	23.2416i	−0.242095	+	0.745092i
$974$		0			0
$975$	−6.59017	+	4.78804i	−0.211054	+	0.153340i
$976$		0			0
$977$	10.9549	+	33.7158i	0.350479	+	1.07866i	0.958585	+	0.284807i	$0.0919295\pi$
$977$	10.9549	+	33.7158i	0.350479	+	1.07866i	−0.608106	+	0.793856i	$0.708070\pi$
$978$		0			0
$979$	27.4164	+	6.15537i	0.876232	+	0.196726i
$980$		0			0
$981$	3.11146	+	9.57608i	0.0993412	+	0.305741i
$982$		0			0
$983$	4.63525	−	3.36771i	0.147842	−	0.107413i	−0.511406	−	0.859339i	$-0.670875\pi$
$983$	4.63525	−	3.36771i	0.147842	−	0.107413i	0.659247	+	0.751926i	$0.270875\pi$
$984$		0			0
$985$	2.85410	−	8.78402i	0.0909393	−	0.279882i
$986$		0			0
$987$	3.19098	+	2.31838i	0.101570	+	0.0737950i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	24.0000			0.762385			0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000			0.762385			0.381193	+	0.924496i	$0.375513\pi$
$992$		0			0
$993$	−3.70820	−	2.69417i	−0.117676	−	0.0854968i
$994$		0			0
$995$	3.23607	−	9.95959i	0.102590	−	0.315740i
$996$		0			0
$997$	28.2533	−	20.5272i	0.894791	−	0.650103i	−0.0423320	−	0.999104i	$-0.513479\pi$
$997$	28.2533	−	20.5272i	0.894791	−	0.650103i	0.937123	+	0.349000i	$0.113479\pi$
$998$		0			0
$999$	3.35410	+	10.3229i	0.106119	+	0.326601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	44.2.e.a.5.1	✓	4
3.2	odd	2		396.2.j.a.181.1		4
4.3	odd	2		176.2.m.b.49.1		4
5.2	odd	4		1100.2.cb.a.49.2		8
5.3	odd	4		1100.2.cb.a.49.1		8
5.4	even	2		1100.2.n.a.401.1		4
8.3	odd	2		704.2.m.d.577.1		4
8.5	even	2		704.2.m.e.577.1		4
11.2	odd	10		484.2.e.c.9.1		4
11.3	even	5		484.2.a.b.1.2		2
11.4	even	5		484.2.e.e.245.1		4
11.5	even	5		484.2.e.e.81.1		4
11.6	odd	10		484.2.e.d.81.1		4
11.7	odd	10		484.2.e.d.245.1		4
11.8	odd	10		484.2.a.c.1.2		2
11.9	even	5	inner	44.2.e.a.9.1	yes	4
11.10	odd	2		484.2.e.c.269.1		4
33.8	even	10		4356.2.a.u.1.1		2
33.14	odd	10		4356.2.a.t.1.1		2
33.20	odd	10		396.2.j.a.361.1		4
44.3	odd	10		1936.2.a.ba.1.1		2
44.19	even	10		1936.2.a.z.1.1		2
44.31	odd	10		176.2.m.b.97.1		4
55.9	even	10		1100.2.n.a.801.1		4
55.42	odd	20		1100.2.cb.a.449.1		8
55.53	odd	20		1100.2.cb.a.449.2		8
88.3	odd	10		7744.2.a.bp.1.2		2
88.19	even	10		7744.2.a.bo.1.2		2
88.53	even	10		704.2.m.e.449.1		4
88.69	even	10		7744.2.a.da.1.1		2
88.75	odd	10		704.2.m.d.449.1		4
88.85	odd	10		7744.2.a.db.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.e.a.5.1	✓	4	1.1	even	1	trivial
44.2.e.a.9.1	yes	4	11.9	even	5	inner
176.2.m.b.49.1		4	4.3	odd	2
176.2.m.b.97.1		4	44.31	odd	10
396.2.j.a.181.1		4	3.2	odd	2
396.2.j.a.361.1		4	33.20	odd	10
484.2.a.b.1.2		2	11.3	even	5
484.2.a.c.1.2		2	11.8	odd	10
484.2.e.c.9.1		4	11.2	odd	10
484.2.e.c.269.1		4	11.10	odd	2
484.2.e.d.81.1		4	11.6	odd	10
484.2.e.d.245.1		4	11.7	odd	10
484.2.e.e.81.1		4	11.5	even	5
484.2.e.e.245.1		4	11.4	even	5
704.2.m.d.449.1		4	88.75	odd	10
704.2.m.d.577.1		4	8.3	odd	2
704.2.m.e.449.1		4	88.53	even	10
704.2.m.e.577.1		4	8.5	even	2
1100.2.n.a.401.1		4	5.4	even	2
1100.2.n.a.801.1		4	55.9	even	10
1100.2.cb.a.49.1		8	5.3	odd	4
1100.2.cb.a.49.2		8	5.2	odd	4
1100.2.cb.a.449.1		8	55.42	odd	20
1100.2.cb.a.449.2		8	55.53	odd	20
1936.2.a.z.1.1		2	44.19	even	10
1936.2.a.ba.1.1		2	44.3	odd	10
4356.2.a.t.1.1		2	33.14	odd	10
4356.2.a.u.1.1		2	33.8	even	10
7744.2.a.bo.1.2		2	88.19	even	10
7744.2.a.bp.1.2		2	88.3	odd	10
7744.2.a.da.1.1		2	88.69	even	10
7744.2.a.db.1.1		2	88.85	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	44.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.224514i) q^{3} +(0.190983 - 0.587785i) q^{5} +(-2.30902 + 1.67760i) q^{7} +(-0.881966 - 2.71441i) q^{9} +(-3.23607 - 0.726543i) q^{11} +(1.42705 + 4.39201i) q^{13} +(0.190983 - 0.138757i) q^{15} +(1.42705 - 4.39201i) q^{17} +(2.30902 + 1.67760i) q^{19} -1.09017 q^{21} +6.47214 q^{23} +(3.73607 + 2.71441i) q^{25} +(0.690983 - 2.12663i) q^{27} +(-5.16312 + 3.75123i) q^{29} +(-1.80902 - 5.56758i) q^{31} +(-0.836881 - 0.951057i) q^{33} +(0.545085 + 1.67760i) q^{35} +(-3.92705 + 2.85317i) q^{37} +(-0.545085 + 1.67760i) q^{39} +(-5.16312 - 3.75123i) q^{41} -1.76393 q^{45} +(-2.92705 - 2.12663i) q^{47} +(0.354102 - 1.08981i) q^{49} +(1.42705 - 1.03681i) q^{51} +(2.19098 + 6.74315i) q^{53} +(-1.04508 + 1.76336i) q^{55} +(0.336881 + 1.03681i) q^{57} +(8.16312 - 5.93085i) q^{59} +(1.42705 - 4.39201i) q^{61} +(6.59017 + 4.78804i) q^{63} +2.85410 q^{65} -4.94427 q^{67} +(2.00000 + 1.45309i) q^{69} +(-2.66312 + 8.19624i) q^{71} +(9.78115 - 7.10642i) q^{73} +(0.545085 + 1.67760i) q^{75} +(8.69098 - 3.75123i) q^{77} +(-4.28115 - 13.1760i) q^{79} +(-6.23607 + 4.53077i) q^{81} +(-4.95492 + 15.2497i) q^{83} +(-2.30902 - 1.67760i) q^{85} -2.43769 q^{87} -8.47214 q^{89} +(-10.6631 - 7.74721i) q^{91} +(0.690983 - 2.12663i) q^{93} +(1.42705 - 1.03681i) q^{95} +(1.71885 + 5.29007i) q^{97} +(0.881966 + 9.42481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 3 q^{5} - 7 q^{7} - 8 q^{9} - 4 q^{11} - q^{13} + 3 q^{15} - q^{17} + 7 q^{19} + 18 q^{21} + 8 q^{23} + 6 q^{25} + 5 q^{27} - 5 q^{29} - 5 q^{31} - 19 q^{33} - 9 q^{35} - 9 q^{37} + 9 q^{39}+ \cdots + 8 q^{99}+O(q^{100}) \) 4 * q - q^3 + 3 * q^5 - 7 * q^7 - 8 * q^9 - 4 * q^11 - q^13 + 3 * q^15 - q^17 + 7 * q^19 + 18 * q^21 + 8 * q^23 + 6 * q^25 + 5 * q^27 - 5 * q^29 - 5 * q^31 - 19 * q^33 - 9 * q^35 - 9 * q^37 + 9 * q^39 - 5 * q^41 - 16 * q^45 - 5 * q^47 - 12 * q^49 - q^51 + 11 * q^53 + 7 * q^55 + 17 * q^57 + 17 * q^59 - q^61 + 4 * q^63 - 2 * q^65 + 16 * q^67 + 8 * q^69 + 5 * q^71 + 19 * q^73 - 9 * q^75 + 37 * q^77 + 3 * q^79 - 16 * q^81 - 31 * q^83 - 7 * q^85 - 50 * q^87 - 16 * q^89 - 27 * q^91 + 5 * q^93 - q^95 + 27 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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