LMFDB - Embedded newform 1100.2.n.a.401.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(201,1100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1100.201"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$8.78354422234$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			401.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	1100.401
Dual form			1100.2.n.a.801.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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	0.494996	−	0.868895i	$-0.335170\pi$
$3$	−0.309017	−	0.224514i	−0.178411	−	0.129623i	−0.673407	+	0.739272i	$0.735170\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.30902	−	1.67760i	0.872726	−	0.634073i	−0.0585908	−	0.998282i	$-0.518661\pi$
$7$	2.30902	−	1.67760i	0.872726	−	0.634073i	0.931317	+	0.364209i	$0.118661\pi$
$8$		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	$-0.878766\pi$
$13$	−1.42705	−	4.39201i	−0.395793	−	1.21812i	0.532550	−	0.846399i	$-0.321234\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.42705	+	4.39201i	−0.346111	+	1.06522i	0.614876	+	0.788624i	$0.289206\pi$
$17$	−1.42705	+	4.39201i	−0.346111	+	1.06522i	−0.960987	+	0.276595i	$0.910794\pi$
$18$		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	$-0.735756\pi$
$23$	−6.47214			−1.34953			−0.674767	+	0.738031i	$0.735756\pi$
$24$		0			0
$25$		0			0
$26$		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			0
$36$		0			0
$37$	3.92705	−	2.85317i	0.645603	−	0.469058i	−0.216167	−	0.976356i	$-0.569356\pi$
$37$	3.92705	−	2.85317i	0.645603	−	0.469058i	0.861771	+	0.507298i	$0.169356\pi$
$38$		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
$45$		0			0
$46$		0			0
$47$	2.92705	+	2.12663i	0.426954	+	0.310200i	0.780430	−	0.625243i	$-0.215000\pi$
$47$	2.92705	+	2.12663i	0.426954	+	0.310200i	−0.353476	+	0.935444i	$0.615000\pi$
$48$		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	$-0.938108\pi$
$53$	−2.19098	−	6.74315i	−0.300955	−	0.926243i	0.680201	−	0.733025i	$-0.261892\pi$
$54$		0			0
$55$		0			0
$56$		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
$65$		0			0
$66$		0			0
$67$	4.94427			0.604039			0.302019	−	0.953302i	$-0.402339\pi$
$67$	4.94427			0.604039			0.302019	+	0.953302i	$0.402339\pi$
$68$		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	−0.987780	−	0.155852i	$-0.950188\pi$
$73$	−9.78115	+	7.10642i	−1.14480	+	0.831744i	−0.157017	+	0.987596i	$0.550188\pi$
$74$		0			0
$75$		0			0
$76$		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	$-0.557540\pi$
$83$	4.95492	−	15.2497i	0.543873	−	1.67387i	0.723655	−	0.690161i	$-0.242460\pi$
$84$		0			0
$85$		0			0
$86$		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
$95$		0			0
$96$		0			0
$97$	−1.71885	−	5.29007i	−0.174522	−	0.537125i	0.825089	−	0.565003i	$-0.191125\pi$
$97$	−1.71885	−	5.29007i	−0.174522	−	0.537125i	−0.999611	+	0.0278780i	$0.991125\pi$
$98$		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	−0.632520	−	0.774544i	$-0.717980\pi$
$103$	−0.927051	+	0.673542i	−0.0913450	+	0.0663661i	0.541175	+	0.840910i	$0.317980\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.92705	+	5.03280i	0.669663	+	0.486539i	0.869912	−	0.493206i	$-0.164175\pi$
$107$	6.92705	+	5.03280i	0.669663	+	0.486539i	−0.200249	+	0.979745i	$0.564175\pi$
$108$		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	0.485997	−	0.873960i	$-0.338456\pi$
$113$	−2.07295	−	1.50609i	−0.195007	−	0.141681i	−0.681004	+	0.732280i	$0.738456\pi$
$114$		0			0
$115$		0			0
$116$		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
$125$		0			0
$126$		0			0
$127$	1.42705	−	4.39201i	0.126630	−	0.389728i	−0.867564	−	0.497325i	$-0.834316\pi$
$127$	1.42705	−	4.39201i	0.126630	−	0.389728i	0.994195	+	0.107597i	$0.0343156\pi$
$128$		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
$135$		0			0
$136$		0			0
$137$	3.33688	−	10.2699i	0.285089	−	0.877414i	−0.701283	−	0.712883i	$-0.747389\pi$
$137$	3.33688	−	10.2699i	0.285089	−	0.877414i	0.986372	−	0.164531i	$-0.0526110\pi$
$138$		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
$145$		0			0
$146$		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
$155$		0			0
$156$		0			0
$157$	−2.07295	−	1.50609i	−0.165439	−	0.120199i	0.501985	−	0.864876i	$-0.332603\pi$
$157$	−2.07295	−	1.50609i	−0.165439	−	0.120199i	−0.667424	+	0.744678i	$0.732603\pi$
$158$		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	0.989663	−	0.143413i	$-0.0458078\pi$
$163$	1.33688	+	4.11450i	0.104713	+	0.322272i	−0.884950	+	0.465686i	$0.845808\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.10081	+	6.46564i	0.162566	+	0.500326i	0.998849	−	0.0479722i	$-0.0152759\pi$
$167$	2.10081	+	6.46564i	0.162566	+	0.500326i	−0.836283	+	0.548298i	$0.815276\pi$
$168$		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	0.980195	−	0.198035i	$-0.0634558\pi$
$173$	14.3992	+	10.4616i	1.09475	+	0.795382i	0.114555	+	0.993417i	$0.463456\pi$
$174$		0			0
$175$		0			0
$176$		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			0
$186$		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	−0.920278	−	0.391266i	$-0.872037\pi$
$193$	0.753289	−	2.31838i	0.0542229	−	0.166881i	0.974501	+	0.224385i	$0.0720373\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.9443			−1.06474			−0.532368	−	0.846513i	$-0.678698\pi$
$197$	−14.9443			−1.06474			−0.532368	+	0.846513i	$0.678698\pi$
$198$		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
$205$		0			0
$206$		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	−0.0548591	−	0.998494i	$-0.517471\pi$
$223$	−15.2533	−	11.0822i	−1.02144	−	0.742117i	−0.966577	+	0.256378i	$0.917471\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.2533	−	12.5352i	1.14514	−	0.831994i	0.157314	−	0.987549i	$-0.449717\pi$
$227$	17.2533	−	12.5352i	1.14514	−	0.831994i	0.987827	+	0.155555i	$0.0497166\pi$
$228$		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	0.893368	−	0.449326i	$-0.148336\pi$
$233$	−1.42705	−	4.39201i	−0.0934892	−	0.287730i	−0.986857	+	0.161596i	$0.948336\pi$
$234$		0			0
$235$		0			0
$236$		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			0
$246$		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			0
$256$		0			0
$257$	−13.0172	+	9.45756i	−0.811992	+	0.589947i	−0.914407	−	0.404795i	$-0.867343\pi$
$257$	−13.0172	+	9.45756i	−0.811992	+	0.589947i	0.102416	+	0.994742i	$0.467343\pi$
$258$		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	$-0.126962\pi$
$263$	29.8885			1.84301			0.921503	+	0.388371i	$0.126962\pi$
$264$		0			0
$265$		0			0
$266$		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
$275$		0			0
$276$		0			0
$277$	0.753289	+	2.31838i	0.0452607	+	0.139298i	0.971133	−	0.238538i	$-0.0766682\pi$
$277$	0.753289	+	2.31838i	0.0452607	+	0.139298i	−0.925872	+	0.377836i	$0.876668\pi$
$278$		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	0.774318	−	0.632796i	$-0.218093\pi$
$283$	6.92705	+	5.03280i	0.411770	+	0.299169i	−0.362548	+	0.931965i	$0.618093\pi$
$284$		0			0
$285$		0			0
$286$		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	−0.426665	−	0.904410i	$-0.640312\pi$
$293$	5.16312	−	3.75123i	0.301633	−	0.219149i	0.728298	+	0.685261i	$0.240312\pi$
$294$		0			0
$295$		0			0
$296$		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
$305$		0			0
$306$		0			0
$307$	−18.4721			−1.05426			−0.527130	−	0.849785i	$-0.676732\pi$
$307$	−18.4721			−1.05426			−0.527130	+	0.849785i	$0.676732\pi$
$308$		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	$0.430893\pi$
$313$	−9.42705	+	29.0135i	−0.532848	+	1.63994i	−0.748253	+	0.663414i	$0.769107\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.71885	−	5.29007i	−0.0965401	−	0.297120i	0.891112	−	0.453784i	$-0.149926\pi$
$317$	−1.71885	−	5.29007i	−0.0965401	−	0.297120i	−0.987652	+	0.156664i	$0.949926\pi$
$318$		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
$325$		0			0
$326$		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			0
$336$		0			0
$337$	−4.07295	+	2.95917i	−0.221868	+	0.161196i	−0.693167	−	0.720777i	$-0.743785\pi$
$337$	−4.07295	+	2.95917i	−0.221868	+	0.161196i	0.471299	+	0.881973i	$0.343785\pi$
$338$		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
$345$		0			0
$346$		0			0
$347$	−2.10081	+	6.46564i	−0.112778	+	0.347094i	−0.991477	−	0.130282i	$-0.958412\pi$
$347$	−2.10081	+	6.46564i	−0.112778	+	0.347094i	0.878699	+	0.477375i	$0.158412\pi$
$348$		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	$-0.524966\pi$
$353$	−2.94427			−0.156708			−0.0783539	+	0.996926i	$0.524966\pi$
$354$		0			0
$355$		0			0
$356$		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
$365$		0			0
$366$		0			0
$367$	21.7254	−	15.7844i	1.13406	−	0.823941i	0.147778	−	0.989021i	$-0.452788\pi$
$367$	21.7254	−	15.7844i	1.13406	−	0.823941i	0.986280	+	0.165079i	$0.0527880\pi$
$368$		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	$-0.167243\pi$
$373$	33.4164			1.73024			0.865118	+	0.501568i	$0.167243\pi$
$374$		0			0
$375$		0			0
$376$		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	$-0.807829\pi$
$383$	−9.60739	−	29.5685i	−0.490915	−	1.51088i	0.332313	−	0.943169i	$-0.392171\pi$
$384$		0			0
$385$		0			0
$386$		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
$395$		0			0
$396$		0			0
$397$	20.8328			1.04557			0.522785	−	0.852465i	$-0.324893\pi$
$397$	20.8328			1.04557			0.522785	+	0.852465i	$0.324893\pi$
$398$		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
$405$		0			0
$406$		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
$415$		0			0
$416$		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
$425$		0			0
$426$		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	$0.639704\pi$
$433$	−29.4894	+	21.4253i	−1.41717	+	1.02963i	−0.992231	+	0.124410i	$0.960296\pi$
$434$		0			0
$435$		0			0
$436$		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	−0.173305	−	0.984868i	$-0.555445\pi$
$443$	−24.4894	−	17.7926i	−1.16352	−	0.845350i	−0.990220	+	0.139518i	$0.955445\pi$
$444$		0			0
$445$		0			0
$446$		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
$455$		0			0
$456$		0			0
$457$	4.28115	−	13.1760i	0.200264	−	0.616349i	−0.799611	−	0.600519i	$-0.794961\pi$
$457$	4.28115	−	13.1760i	0.200264	−	0.616349i	0.999875	−	0.0158303i	$-0.00503915\pi$
$458$		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	$-0.410049\pi$
$463$	12.0000			0.557687			0.278844	+	0.960337i	$0.410049\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.75329	+	26.9399i	−0.405054	+	1.24663i	0.515796	+	0.856711i	$0.327496\pi$
$467$	−8.75329	+	26.9399i	−0.405054	+	1.24663i	−0.920850	+	0.389916i	$0.872504\pi$
$468$		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
$475$		0			0
$476$		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
$485$		0			0
$486$		0			0
$487$	8.92705	+	6.48588i	0.404523	+	0.293903i	0.771381	−	0.636374i	$-0.219566\pi$
$487$	8.92705	+	6.48588i	0.404523	+	0.293903i	−0.366858	+	0.930277i	$0.619566\pi$
$488$		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
$495$		0			0
$496$		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	0.614626	−	0.788818i	$-0.289307\pi$
$503$	1.21885	+	0.885544i	0.0543457	+	0.0394845i	−0.560281	+	0.828303i	$0.689307\pi$
$504$		0			0
$505$		0			0
$506$		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			0
$516$		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	$-0.695099\pi$
$523$	8.48278	−	26.1073i	0.370926	−	1.14159i	0.946186	−	0.323622i	$-0.104901\pi$
$524$		0			0
$525$		0			0
$526$		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
$535$		0			0
$536$		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			0
$546$		0			0
$547$	18.3435	+	13.3273i	0.784310	+	0.569834i	0.906269	−	0.422701i	$-0.138918\pi$
$547$	18.3435	+	13.3273i	0.784310	+	0.569834i	−0.121960	+	0.992535i	$0.538918\pi$
$548$		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			0
$556$		0			0
$557$	8.69098	−	6.31437i	0.368249	−	0.267548i	−0.388236	−	0.921560i	$-0.626915\pi$
$557$	8.69098	−	6.31437i	0.368249	−	0.267548i	0.756484	+	0.654012i	$0.226915\pi$
$558$		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	$-0.990288\pi$
$563$	−4.95492	−	15.2497i	−0.208825	−	0.642697i	0.790710	−	0.612191i	$-0.209712\pi$
$564$		0			0
$565$		0			0
$566$		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
$575$		0			0
$576$		0			0
$577$	7.69756	−	23.6907i	0.320454	−	0.986255i	−0.652998	−	0.757360i	$-0.726489\pi$
$577$	7.69756	−	23.6907i	0.320454	−	0.986255i	0.973451	−	0.228895i	$-0.0735112\pi$
$578$		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
$585$		0			0
$586$		0			0
$587$	−0.927051	+	0.673542i	−0.0382635	+	0.0278001i	−0.606753	−	0.794891i	$-0.707528\pi$
$587$	−0.927051	+	0.673542i	−0.0382635	+	0.0278001i	0.568489	+	0.822691i	$0.307528\pi$
$588$		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	$-0.569728\pi$
$593$	−10.5836			−0.434616			−0.217308	+	0.976103i	$0.569728\pi$
$594$		0			0
$595$		0			0
$596$		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
$605$		0			0
$606$		0			0
$607$	−12.8435	−	39.5281i	−0.521300	−	1.60440i	−0.771519	−	0.636207i	$-0.780503\pi$
$607$	−12.8435	−	39.5281i	−0.521300	−	1.60440i	0.250219	−	0.968189i	$-0.419497\pi$
$608$		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	−0.0368521	−	0.999321i	$-0.511733\pi$
$613$	−24.7254	−	17.9641i	−0.998651	−	0.725562i	−0.961798	+	0.273759i	$0.911733\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.4721			0.663143			0.331572	−	0.943430i	$-0.392421\pi$
$617$	16.4721			0.663143			0.331572	+	0.943430i	$0.392421\pi$
$618$		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
$625$		0			0
$626$		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
$635$		0			0
$636$		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	$0.237764\pi$
$643$	−6.57295	+	20.2295i	−0.259212	+	0.797772i	−0.992971	+	0.118362i	$0.962236\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.0451	+	33.9933i	0.434227	+	1.33641i	0.893877	+	0.448313i	$0.147975\pi$
$647$	11.0451	+	33.9933i	0.434227	+	1.33641i	−0.459649	+	0.888100i	$0.652025\pi$
$648$		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	−0.153747	−	0.988110i	$-0.549134\pi$
$653$	18.8713	−	13.7108i	0.738492	−	0.536546i	0.892238	+	0.451565i	$0.149134\pi$
$654$		0			0
$655$		0			0
$656$		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
$665$		0			0
$666$		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	$-0.902654\pi$
$673$	−9.31559	−	28.6705i	−0.359090	−	1.10516i	0.594510	−	0.804088i	$-0.297346\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.6631	+	32.8177i	−0.409817	+	1.26129i	0.506989	+	0.861953i	$0.330759\pi$
$677$	−10.6631	+	32.8177i	−0.409817	+	1.26129i	−0.916805	+	0.399334i	$0.869241\pi$
$678$		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	$-0.605087\pi$
$683$	−16.9443			−0.648355			−0.324177	+	0.945996i	$0.605087\pi$
$684$		0			0
$685$		0			0
$686$		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
$695$		0			0
$696$		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			0
$706$		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
$715$		0			0
$716$		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
$725$		0			0
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		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	−0.368627	−	0.929577i	$-0.620172\pi$
$733$	10.8713	−	7.89848i	0.401541	−	0.291737i	0.770169	+	0.637840i	$0.220172\pi$
$734$		0			0
$735$		0			0
$736$		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	$-0.681839\pi$
$743$	10.6631	−	32.8177i	0.391192	−	1.20396i	0.931888	−	0.362747i	$-0.118161\pi$
$744$		0			0
$745$		0			0
$746$		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
$755$		0			0
$756$		0			0
$757$	4.86475	+	14.9721i	0.176812	+	0.544172i	0.999712	−	0.0240152i	$-0.00764500\pi$
$757$	4.86475	+	14.9721i	0.176812	+	0.544172i	−0.822899	+	0.568187i	$0.807645\pi$
$758$		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
$765$		0			0
$766$		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	0.387922	−	0.921692i	$-0.373193\pi$
$773$	−10.2533	−	7.44945i	−0.368785	−	0.267938i	−0.756707	+	0.653754i	$0.773193\pi$
$774$		0			0
$775$		0			0
$776$		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
$785$		0			0
$786$		0			0
$787$	−9.98936	+	30.7441i	−0.356082	+	1.09591i	0.599297	+	0.800527i	$0.295447\pi$
$787$	−9.98936	+	30.7441i	−0.356082	+	1.09591i	−0.955379	+	0.295382i	$0.904553\pi$
$788$		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
$795$		0			0
$796$		0			0
$797$	3.33688	−	10.2699i	0.118198	−	0.363777i	−0.874402	−	0.485202i	$-0.838746\pi$
$797$	3.33688	−	10.2699i	0.118198	−	0.363777i	0.992601	+	0.121424i	$0.0387462\pi$
$798$		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
$805$		0			0
$806$		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
$815$		0			0
$816$		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	0.958778	−	0.284158i	$-0.0917139\pi$
$823$	0.461493	+	1.42033i	0.0160866	+	0.0495096i	−0.942691	+	0.333667i	$0.891714\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.95492	−	15.2497i	−0.172299	−	0.530283i	0.827201	−	0.561907i	$-0.189932\pi$
$827$	−4.95492	−	15.2497i	−0.172299	−	0.530283i	−0.999500	+	0.0316241i	$0.989932\pi$
$828$		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
$835$		0			0
$836$		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
$845$		0			0
$846$		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	−0.908628	−	0.417607i	$-0.862869\pi$
$853$	2.10081	−	6.46564i	0.0719305	−	0.221379i	0.980558	+	0.196227i	$0.0628691\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.9443			0.510487			0.255243	−	0.966877i	$-0.417844\pi$
$857$	14.9443			0.510487			0.255243	+	0.966877i	$0.417844\pi$
$858$		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	$0.247216\pi$
$863$	−8.10081	+	24.9317i	−0.275755	+	0.848686i	−0.989019	+	0.147791i	$0.952784\pi$
$864$		0			0
$865$		0			0
$866$		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
$875$		0			0
$876$		0			0
$877$	35.0517	+	25.4665i	1.18361	+	0.859943i	0.992574	−	0.121640i	$-0.0388152\pi$
$877$	35.0517	+	25.4665i	1.18361	+	0.859943i	0.191036	+	0.981583i	$0.438815\pi$
$878$		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	$0.0388835\pi$
$883$	42.0517	+	30.5523i	1.41515	+	1.02817i	0.422603	+	0.906315i	$0.361117\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.8713	+	15.8904i	−0.734367	+	0.533549i	−0.890942	−	0.454117i	$-0.849955\pi$
$887$	−21.8713	+	15.8904i	−0.734367	+	0.533549i	0.156575	+	0.987666i	$0.449955\pi$
$888$		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			0
$896$		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			0
$906$		0			0
$907$	13.8992	−	42.7773i	0.461515	−	1.42040i	−0.401798	−	0.915728i	$-0.631615\pi$
$907$	13.8992	−	42.7773i	0.461515	−	1.42040i	0.863313	−	0.504669i	$-0.168385\pi$
$908$		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			0
$916$		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
$925$		0			0
$926$		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
$935$		0			0
$936$		0			0
$937$	4.28115	+	13.1760i	0.139859	+	0.430442i	0.996314	−	0.0857795i	$-0.0273380\pi$
$937$	4.28115	+	13.1760i	0.139859	+	0.430442i	−0.856455	+	0.516222i	$0.827338\pi$
$938$		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
$945$		0			0
$946$		0			0
$947$	−47.7771			−1.55255			−0.776273	−	0.630396i	$-0.782892\pi$
$947$	−47.7771			−1.55255			−0.776273	+	0.630396i	$0.782892\pi$
$948$		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	−0.995623	−	0.0934622i	$-0.970207\pi$
$953$	−37.4894	+	27.2376i	−1.21440	+	0.882313i	−0.218777	+	0.975775i	$0.570207\pi$
$954$		0			0
$955$		0			0
$956$		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
$965$		0			0
$966$		0			0
$967$	−44.0000			−1.41494			−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000			−1.41494			−0.707472	+	0.706741i	$0.750165\pi$
$968$		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
$975$		0			0
$976$		0			0
$977$	−10.9549	−	33.7158i	−0.350479	−	1.07866i	−0.958585	−	0.284807i	$-0.908070\pi$
$977$	−10.9549	−	33.7158i	−0.350479	−	1.07866i	0.608106	−	0.793856i	$-0.291930\pi$
$978$		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	−0.659247	−	0.751926i	$-0.729125\pi$
$983$	−4.63525	+	3.36771i	−0.147842	+	0.107413i	0.511406	+	0.859339i	$0.329125\pi$
$984$		0			0
$985$		0			0
$986$		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
$995$		0			0
$996$		0			0
$997$	−28.2533	+	20.5272i	−0.894791	+	0.650103i	−0.937123	−	0.349000i	$-0.886521\pi$
$997$	−28.2533	+	20.5272i	−0.894791	+	0.650103i	0.0423320	+	0.999104i	$0.486521\pi$
$998$		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	1100.2.n.a.401.1		4
5.2	odd	4		1100.2.cb.a.49.1		8
5.3	odd	4		1100.2.cb.a.49.2		8
5.4	even	2		44.2.e.a.5.1	✓	4
11.9	even	5	inner	1100.2.n.a.801.1		4
15.14	odd	2		396.2.j.a.181.1		4
20.19	odd	2		176.2.m.b.49.1		4
40.19	odd	2		704.2.m.d.577.1		4
40.29	even	2		704.2.m.e.577.1		4
55.4	even	10		484.2.e.e.245.1		4
55.9	even	10		44.2.e.a.9.1	yes	4
55.14	even	10		484.2.a.b.1.2		2
55.19	odd	10		484.2.a.c.1.2		2
55.24	odd	10		484.2.e.c.9.1		4
55.29	odd	10		484.2.e.d.245.1		4
55.39	odd	10		484.2.e.d.81.1		4
55.42	odd	20		1100.2.cb.a.449.2		8
55.49	even	10		484.2.e.e.81.1		4
55.53	odd	20		1100.2.cb.a.449.1		8
55.54	odd	2		484.2.e.c.269.1		4
165.14	odd	10		4356.2.a.t.1.1		2
165.74	even	10		4356.2.a.u.1.1		2
165.119	odd	10		396.2.j.a.361.1		4
220.19	even	10		1936.2.a.z.1.1		2
220.119	odd	10		176.2.m.b.97.1		4
220.179	odd	10		1936.2.a.ba.1.1		2
440.19	even	10		7744.2.a.bo.1.2		2
440.69	even	10		7744.2.a.da.1.1		2
440.179	odd	10		7744.2.a.bp.1.2		2
440.229	even	10		704.2.m.e.449.1		4
440.339	odd	10		704.2.m.d.449.1		4
440.349	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	5.4	even	2
44.2.e.a.9.1	yes	4	55.9	even	10
176.2.m.b.49.1		4	20.19	odd	2
176.2.m.b.97.1		4	220.119	odd	10
396.2.j.a.181.1		4	15.14	odd	2
396.2.j.a.361.1		4	165.119	odd	10
484.2.a.b.1.2		2	55.14	even	10
484.2.a.c.1.2		2	55.19	odd	10
484.2.e.c.9.1		4	55.24	odd	10
484.2.e.c.269.1		4	55.54	odd	2
484.2.e.d.81.1		4	55.39	odd	10
484.2.e.d.245.1		4	55.29	odd	10
484.2.e.e.81.1		4	55.49	even	10
484.2.e.e.245.1		4	55.4	even	10
704.2.m.d.449.1		4	440.339	odd	10
704.2.m.d.577.1		4	40.19	odd	2
704.2.m.e.449.1		4	440.229	even	10
704.2.m.e.577.1		4	40.29	even	2
1100.2.n.a.401.1		4	1.1	even	1	trivial
1100.2.n.a.801.1		4	11.9	even	5	inner
1100.2.cb.a.49.1		8	5.2	odd	4
1100.2.cb.a.49.2		8	5.3	odd	4
1100.2.cb.a.449.1		8	55.53	odd	20
1100.2.cb.a.449.2		8	55.42	odd	20
1936.2.a.z.1.1		2	220.19	even	10
1936.2.a.ba.1.1		2	220.179	odd	10
4356.2.a.t.1.1		2	165.14	odd	10
4356.2.a.u.1.1		2	165.74	even	10
7744.2.a.bo.1.2		2	440.19	even	10
7744.2.a.bp.1.2		2	440.179	odd	10
7744.2.a.da.1.1		2	440.69	even	10
7744.2.a.db.1.1		2	440.349	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:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.n (of order \(5\), degree \(4\), minimal)

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

Introduction

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