LMFDB - Embedded newform 1100.2.cb.a.49.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(49,1100)] 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("1100.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.cb (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0,0,16,0,-8,0,0,0,0,0,0,0,-14,0,36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.2
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	1100.49
Dual form			1100.2.cb.a.449.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.224514 - 0.309017i) q^{3} +(-1.67760 - 2.30902i) q^{7} +(0.881966 + 2.71441i) q^{9} +(-3.23607 - 0.726543i) q^{11} +(4.39201 - 1.42705i) q^{13} +(4.39201 + 1.42705i) q^{17} +(-2.30902 - 1.67760i) q^{19} -1.09017 q^{21} -6.47214i q^{23} +(2.12663 + 0.690983i) q^{27} +(5.16312 - 3.75123i) q^{29} +(-1.80902 - 5.56758i) q^{31} +(-0.951057 + 0.836881i) q^{33} +(-2.85317 - 3.92705i) q^{37} +(0.545085 - 1.67760i) q^{39} +(-5.16312 - 3.75123i) q^{41} +(2.12663 - 2.92705i) q^{47} +(-0.354102 + 1.08981i) q^{49} +(1.42705 - 1.03681i) q^{51} +(6.74315 - 2.19098i) q^{53} +(-1.03681 + 0.336881i) q^{57} +(-8.16312 + 5.93085i) q^{59} +(1.42705 - 4.39201i) q^{61} +(4.78804 - 6.59017i) q^{63} -4.94427i q^{67} +(-2.00000 - 1.45309i) q^{69} +(-2.66312 + 8.19624i) q^{71} +(-7.10642 - 9.78115i) q^{73} +(3.75123 + 8.69098i) q^{77} +(4.28115 + 13.1760i) q^{79} +(-6.23607 + 4.53077i) q^{81} +(15.2497 + 4.95492i) q^{83} -2.43769i q^{87} +8.47214 q^{89} +(-10.6631 - 7.74721i) q^{91} +(-2.12663 - 0.690983i) q^{93} +(-5.29007 + 1.71885i) q^{97} +(-0.881966 - 9.42481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{9} - 8 q^{11} - 14 q^{19} + 36 q^{21} + 10 q^{29} - 10 q^{31} - 18 q^{39} - 10 q^{41} + 24 q^{49} - 2 q^{51} - 34 q^{59} - 2 q^{61} - 16 q^{69} + 10 q^{71} - 6 q^{79} - 32 q^{81} + 32 q^{89}+ \cdots - 16 q^{99}+O(q^{100}) $ 8 * q + 16 * q^9 - 8 * q^11 - 14 * q^19 + 36 * q^21 + 10 * q^29 - 10 * q^31 - 18 * q^39 - 10 * q^41 + 24 * q^49 - 2 * q^51 - 34 * q^59 - 2 * q^61 - 16 * q^69 + 10 * q^71 - 6 * q^79 - 32 * q^81 + 32 * q^89 - 54 * q^91 - 16 * 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
$3$	0.224514	−	0.309017i	0.129623	−	0.178411i	−0.739272	−	0.673407i	$-0.764830\pi$
$3$	0.224514	−	0.309017i	0.129623	−	0.178411i	0.868895	+	0.494996i	$0.164830\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.67760	−	2.30902i	−0.634073	−	0.872726i	0.364209	−	0.931317i	$-0.381339\pi$
$7$	−1.67760	−	2.30902i	−0.634073	−	0.872726i	−0.998282	+	0.0585908i	$0.981339\pi$
$8$		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
$13$	4.39201	−	1.42705i	1.21812	−	0.395793i	0.371726	−	0.928342i	$-0.378766\pi$
$13$	4.39201	−	1.42705i	1.21812	−	0.395793i	0.846399	+	0.532550i	$0.178766\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.39201	+	1.42705i	1.06522	+	0.346111i	0.788624	−	0.614876i	$-0.210794\pi$
$17$	4.39201	+	1.42705i	1.06522	+	0.346111i	0.276595	+	0.960987i	$0.410794\pi$
$18$		0			0
$19$	−2.30902	−	1.67760i	−0.529725	−	0.384868i	0.290530	−	0.956866i	$-0.406168\pi$
$19$	−2.30902	−	1.67760i	−0.529725	−	0.384868i	−0.820255	+	0.571998i	$0.806168\pi$
$20$		0			0
$21$	−1.09017			−0.237895
$22$		0			0
$23$		−	6.47214i		−	1.34953i	−0.738031	−	0.674767i	$-0.764244\pi$
$23$		−	6.47214i		−	1.34953i	0.738031	−	0.674767i	$-0.235756\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.12663	+	0.690983i	0.409270	+	0.132980i
$28$		0			0
$29$	5.16312	−	3.75123i	0.958767	−	0.696585i	0.00590304	−	0.999983i	$-0.498121\pi$
$29$	5.16312	−	3.75123i	0.958767	−	0.696585i	0.952864	+	0.303397i	$0.0981210\pi$
$30$		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
$33$	−0.951057	+	0.836881i	−0.165558	+	0.145682i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.85317	−	3.92705i	−0.469058	−	0.645603i	0.507298	−	0.861771i	$-0.330644\pi$
$37$	−2.85317	−	3.92705i	−0.469058	−	0.645603i	−0.976356	+	0.216167i	$0.930644\pi$
$38$		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		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.12663	−	2.92705i	0.310200	−	0.426954i	−0.625243	−	0.780430i	$-0.715000\pi$
$47$	2.12663	−	2.92705i	0.310200	−	0.426954i	0.935444	+	0.353476i	$0.115000\pi$
$48$		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
$53$	6.74315	−	2.19098i	0.926243	−	0.300955i	0.193218	−	0.981156i	$-0.438108\pi$
$53$	6.74315	−	2.19098i	0.926243	−	0.300955i	0.733025	+	0.680201i	$0.238108\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.03681	+	0.336881i	−0.137329	+	0.0446210i
$58$		0			0
$59$	−8.16312	+	5.93085i	−1.06275	+	0.772131i	−0.974595	−	0.223976i	$-0.928096\pi$
$59$	−8.16312	+	5.93085i	−1.06275	+	0.772131i	−0.0881528	+	0.996107i	$0.528096\pi$
$60$		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
$63$	4.78804	−	6.59017i	0.603236	−	0.830283i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	4.94427i		−	0.604039i	−0.953302	−	0.302019i	$-0.902339\pi$
$67$		−	4.94427i		−	0.604039i	0.953302	−	0.302019i	$-0.0976608\pi$
$68$		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
$73$	−7.10642	−	9.78115i	−0.831744	−	1.14480i	−0.987596	−	0.157017i	$-0.949812\pi$
$73$	−7.10642	−	9.78115i	−0.831744	−	1.14480i	0.155852	−	0.987780i	$-0.450188\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.75123	+	8.69098i	0.427492	+	0.990429i
$78$		0			0
$79$	4.28115	+	13.1760i	0.481667	+	1.48242i	0.836750	+	0.547585i	$0.184453\pi$
$79$	4.28115	+	13.1760i	0.481667	+	1.48242i	−0.355083	+	0.934835i	$0.615547\pi$
$80$		0			0
$81$	−6.23607	+	4.53077i	−0.692896	+	0.503419i
$82$		0			0
$83$	15.2497	+	4.95492i	1.67387	+	0.543873i	0.983706	−	0.179783i	$-0.0575395\pi$
$83$	15.2497	+	4.95492i	1.67387	+	0.543873i	0.690161	+	0.723655i	$0.257540\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	2.43769i		−	0.261348i
$88$		0			0
$89$	8.47214			0.898045			0.449022	−	0.893521i	$-0.351772\pi$
$89$	8.47214			0.898045			0.449022	+	0.893521i	$0.351772\pi$
$90$		0			0
$91$	−10.6631	−	7.74721i	−1.11780	−	0.812128i
$92$		0			0
$93$	−2.12663	−	0.690983i	−0.220521	−	0.0716516i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.29007	+	1.71885i	−0.537125	+	0.174522i	−0.565003	−	0.825089i	$-0.691125\pi$
$97$	−5.29007	+	1.71885i	−0.537125	+	0.174522i	0.0278780	+	0.999611i	$0.491125\pi$
$98$		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
$103$	−0.673542	−	0.927051i	−0.0663661	−	0.0913450i	0.774544	−	0.632520i	$-0.217980\pi$
$103$	−0.673542	−	0.927051i	−0.0663661	−	0.0913450i	−0.840910	+	0.541175i	$0.817980\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.03280	−	6.92705i	0.486539	−	0.669663i	−0.493206	−	0.869912i	$-0.664175\pi$
$107$	5.03280	−	6.92705i	0.486539	−	0.669663i	0.979745	+	0.200249i	$0.0641752\pi$
$108$		0			0
$109$	3.52786			0.337908			0.168954	−	0.985624i	$-0.445961\pi$
$109$	3.52786			0.337908			0.168954	+	0.985624i	$0.445961\pi$
$110$		0			0
$111$	−1.85410			−0.175984
$112$		0			0
$113$	1.50609	−	2.07295i	0.141681	−	0.195007i	−0.732280	−	0.681004i	$-0.761544\pi$
$113$	1.50609	−	2.07295i	0.141681	−	0.195007i	0.873960	+	0.485997i	$0.161544\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	7.74721	+	10.6631i	0.716230	+	0.985806i
$118$		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
$123$	−2.31838	+	0.753289i	−0.209042	+	0.0679218i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−4.39201	−	1.42705i	−0.389728	−	0.126630i	0.107597	−	0.994195i	$-0.465684\pi$
$127$	−4.39201	−	1.42705i	−0.389728	−	0.126630i	−0.497325	+	0.867564i	$0.665684\pi$
$128$		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
$133$			8.14590i			0.706339i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.2699	−	3.33688i	−0.877414	−	0.285089i	−0.164531	−	0.986372i	$-0.552611\pi$
$137$	−10.2699	−	3.33688i	−0.877414	−	0.285089i	−0.712883	+	0.701283i	$0.752611\pi$
$138$		0			0
$139$	−6.92705	+	5.03280i	−0.587545	+	0.426876i	−0.841436	−	0.540356i	$-0.818289\pi$
$139$	−6.92705	+	5.03280i	−0.587545	+	0.426876i	0.253891	+	0.967233i	$0.418289\pi$
$140$		0			0
$141$	−0.427051	−	1.31433i	−0.0359642	−	0.110686i
$142$		0			0
$143$	−15.2497	+	1.42705i	−1.27524	+	0.119336i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.257270	+	0.354102i	0.0212193	+	0.0292058i
$148$		0			0
$149$	−1.42705	+	4.39201i	−0.116909	+	0.359808i	−0.992340	−	0.123534i	$-0.960577\pi$
$149$	−1.42705	+	4.39201i	−0.116909	+	0.359808i	0.875432	+	0.483342i	$0.160577\pi$
$150$		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
$153$			13.1803i			1.06557i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.50609	+	2.07295i	−0.120199	+	0.165439i	−0.864876	−	0.501985i	$-0.832603\pi$
$157$	−1.50609	+	2.07295i	−0.120199	+	0.165439i	0.744678	+	0.667424i	$0.232603\pi$
$158$		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
$163$	−4.11450	+	1.33688i	−0.322272	+	0.104713i	−0.465686	−	0.884950i	$-0.654192\pi$
$163$	−4.11450	+	1.33688i	−0.322272	+	0.104713i	0.143413	+	0.989663i	$0.454192\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.46564	−	2.10081i	0.500326	−	0.162566i	−0.0479722	−	0.998849i	$-0.515276\pi$
$167$	6.46564	−	2.10081i	0.500326	−	0.162566i	0.548298	+	0.836283i	$0.315276\pi$
$168$		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
$173$	−10.4616	+	14.3992i	−0.795382	+	1.09475i	0.198035	+	0.980195i	$0.436544\pi$
$173$	−10.4616	+	14.3992i	−0.795382	+	1.09475i	−0.993417	+	0.114555i	$0.963456\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			3.85410i			0.289692i
$178$		0			0
$179$	−0.309017	−	0.224514i	−0.0230970	−	0.0167810i	0.576177	−	0.817325i	$-0.304544\pi$
$179$	−0.309017	−	0.224514i	−0.0230970	−	0.0167810i	−0.599274	+	0.800544i	$0.704544\pi$
$180$		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
$183$	−1.03681	−	1.42705i	−0.0766434	−	0.105491i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−13.1760	−	7.80902i	−0.963527	−	0.571052i
$188$		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
$193$	2.31838	+	0.753289i	0.166881	+	0.0542229i	0.391266	−	0.920278i	$-0.372037\pi$
$193$	2.31838	+	0.753289i	0.166881	+	0.0542229i	−0.224385	+	0.974501i	$0.572037\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			14.9443i			1.06474i	0.846513	+	0.532368i	$0.178698\pi$
$197$			14.9443i			1.06474i	−0.846513	+	0.532368i	$0.821302\pi$
$198$		0			0
$199$	−16.9443			−1.20115			−0.600574	−	0.799569i	$-0.705061\pi$
$199$	−16.9443			−1.20115			−0.600574	+	0.799569i	$0.705061\pi$
$200$		0			0
$201$	−1.52786	−	1.11006i	−0.107767	−	0.0782975i
$202$		0			0
$203$	−17.3233	−	5.62868i	−1.21586	−	0.395056i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	17.5680	−	5.70820i	1.22106	−	0.396748i
$208$		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
$213$	1.93487	+	2.66312i	0.132575	+	0.182474i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−9.82084	+	13.5172i	−0.666682	+	0.917609i
$218$		0			0
$219$	−4.61803			−0.312058
$220$		0			0
$221$	21.3262			1.43456
$222$		0			0
$223$	11.0822	−	15.2533i	0.742117	−	1.02144i	−0.256378	−	0.966577i	$-0.582529\pi$
$223$	11.0822	−	15.2533i	0.742117	−	1.02144i	0.998494	−	0.0548591i	$-0.0174710\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.5352	−	17.2533i	−0.831994	−	1.14514i	−0.987549	−	0.157314i	$-0.949717\pi$
$227$	−12.5352	−	17.2533i	−0.831994	−	1.14514i	0.155555	−	0.987827i	$-0.450283\pi$
$228$		0			0
$229$	5.33688	+	16.4252i	0.352671	+	1.08541i	0.957348	+	0.288939i	$0.0933024\pi$
$229$	5.33688	+	16.4252i	0.352671	+	1.08541i	−0.604677	+	0.796471i	$0.706698\pi$
$230$		0			0
$231$	3.52786	+	0.792055i	0.232116	+	0.0521134i
$232$		0			0
$233$	4.39201	−	1.42705i	0.287730	−	0.0934892i	−0.161596	−	0.986857i	$-0.551664\pi$
$233$	4.39201	−	1.42705i	0.287730	−	0.0934892i	0.449326	+	0.893368i	$0.351664\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.03280	+	1.63525i	0.326915	+	0.106221i
$238$		0			0
$239$	6.92705	+	5.03280i	0.448074	+	0.325545i	0.788835	−	0.614605i	$-0.210685\pi$
$239$	6.92705	+	5.03280i	0.448074	+	0.325545i	−0.340761	+	0.940150i	$0.610685\pi$
$240$		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
$243$			9.65248i			0.619207i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−12.5352	−	4.07295i	−0.797599	−	0.259156i
$248$		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
$253$	−4.70228	+	20.9443i	−0.295630	+	1.31676i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.45756	+	13.0172i	0.589947	+	0.811992i	0.994742	−	0.102416i	$-0.0326571\pi$
$257$	9.45756	+	13.0172i	0.589947	+	0.811992i	−0.404795	+	0.914407i	$0.632657\pi$
$258$		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
$263$			29.8885i			1.84301i	0.388371	+	0.921503i	$0.373038\pi$
$263$			29.8885i			1.84301i	−0.388371	+	0.921503i	$0.626962\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.90211	−	2.61803i	0.116407	−	0.160221i
$268$		0			0
$269$	3.98936	−	12.2780i	0.243235	−	0.748602i	−0.752686	−	0.658379i	$-0.771242\pi$
$269$	3.98936	−	12.2780i	0.243235	−	0.748602i	0.995922	−	0.0902222i	$-0.0287577\pi$
$270$		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
$273$	−4.78804	+	1.55573i	−0.289785	+	0.0941569i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	2.31838	−	0.753289i	0.139298	−	0.0452607i	−0.238538	−	0.971133i	$-0.576668\pi$
$277$	2.31838	−	0.753289i	0.139298	−	0.0452607i	0.377836	+	0.925872i	$0.376668\pi$
$278$		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
$283$	−5.03280	+	6.92705i	−0.299169	+	0.411770i	−0.931965	−	0.362548i	$-0.881907\pi$
$283$	−5.03280	+	6.92705i	−0.299169	+	0.411770i	0.632796	+	0.774318i	$0.281907\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			18.2148i			1.07518i
$288$		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
$293$	3.75123	+	5.16312i	0.219149	+	0.301633i	0.904410	−	0.426665i	$-0.140312\pi$
$293$	3.75123	+	5.16312i	0.219149	+	0.301633i	−0.685261	+	0.728298i	$0.740312\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−6.37988	−	3.78115i	−0.370198	−	0.219405i
$298$		0			0
$299$	−9.23607	−	28.4257i	−0.534136	−	1.64390i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2.46965	−	0.802439i	−0.141878	−	0.0460989i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			18.4721i			1.05426i	0.849785	+	0.527130i	$0.176732\pi$
$307$			18.4721i			1.05426i	−0.849785	+	0.527130i	$0.823268\pi$
$308$		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
$313$	−29.0135	−	9.42705i	−1.63994	−	0.532848i	−0.663414	−	0.748253i	$-0.730893\pi$
$313$	−29.0135	−	9.42705i	−1.63994	−	0.532848i	−0.976525	+	0.215404i	$0.930893\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.29007	+	1.71885i	−0.297120	+	0.0965401i	−0.453784	−	0.891112i	$-0.649926\pi$
$317$	−5.29007	+	1.71885i	−0.297120	+	0.0965401i	0.156664	+	0.987652i	$0.449926\pi$
$318$		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
$323$	−7.74721	−	10.6631i	−0.431066	−	0.593312i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.792055	−	1.09017i	0.0438007	−	0.0602865i
$328$		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
$333$	8.14324	−	11.2082i	0.446247	−	0.614206i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.95917	+	4.07295i	0.161196	+	0.221868i	0.881973	−	0.471299i	$-0.156215\pi$
$337$	2.95917	+	4.07295i	0.161196	+	0.221868i	−0.720777	+	0.693167i	$0.756215\pi$
$338$		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
$343$	−15.8904	+	5.16312i	−0.858003	+	0.278782i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.46564	+	2.10081i	0.347094	+	0.112778i	0.477375	−	0.878699i	$-0.341588\pi$
$347$	6.46564	+	2.10081i	0.347094	+	0.112778i	−0.130282	+	0.991477i	$0.541588\pi$
$348$		0			0
$349$	−0.545085	−	0.396027i	−0.0291777	−	0.0211989i	0.573101	−	0.819485i	$-0.305740\pi$
$349$	−0.545085	−	0.396027i	−0.0291777	−	0.0211989i	−0.602279	+	0.798286i	$0.705740\pi$
$350$		0			0
$351$	10.3262			0.551174
$352$		0			0
$353$		−	2.94427i		−	0.156708i	−0.996926	−	0.0783539i	$-0.975034\pi$
$353$		−	2.94427i		−	0.156708i	0.996926	−	0.0783539i	$-0.0249664\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−4.78804	−	1.55573i	−0.253410	−	0.0823379i
$358$		0			0
$359$	−6.92705	+	5.03280i	−0.365596	+	0.265621i	−0.755382	−	0.655284i	$-0.772549\pi$
$359$	−6.92705	+	5.03280i	−0.365596	+	0.265621i	0.389787	+	0.920905i	$0.372549\pi$
$360$		0			0
$361$	−3.35410	−	10.3229i	−0.176532	−	0.543309i
$362$		0			0
$363$	3.68571	−	2.01722i	0.193450	−	0.105877i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−15.7844	−	21.7254i	−0.823941	−	1.13406i	−0.989021	−	0.147778i	$-0.952788\pi$
$367$	−15.7844	−	21.7254i	−0.823941	−	1.13406i	0.165079	−	0.986280i	$-0.447212\pi$
$368$		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
$373$			33.4164i			1.73024i	0.501568	+	0.865118i	$0.332757\pi$
$373$			33.4164i			1.73024i	−0.501568	+	0.865118i	$0.667243\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	17.3233	−	23.8435i	0.892195	−	1.22800i
$378$		0			0
$379$	−3.04508	+	9.37181i	−0.156416	+	0.481397i	−0.998302	−	0.0582579i	$-0.981445\pi$
$379$	−3.04508	+	9.37181i	−0.156416	+	0.481397i	0.841886	+	0.539655i	$0.181445\pi$
$380$		0			0
$381$	−1.42705	+	1.03681i	−0.0731100	+	0.0531176i
$382$		0			0
$383$	29.5685	−	9.60739i	1.51088	−	0.490915i	0.567711	−	0.823228i	$-0.307829\pi$
$383$	29.5685	−	9.60739i	1.51088	−	0.490915i	0.943169	+	0.332313i	$0.107829\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.78115	+	1.29408i	−0.0903080	+	0.0656126i	−0.632023	−	0.774950i	$-0.717775\pi$
$389$	−1.78115	+	1.29408i	−0.0903080	+	0.0656126i	0.541715	+	0.840562i	$0.317775\pi$
$390$		0			0
$391$	9.23607	−	28.4257i	0.467088	−	1.43755i
$392$		0			0
$393$	4.14725	−	5.70820i	0.209201	−	0.287941i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	20.8328i		−	1.04557i	−0.852465	−	0.522785i	$-0.824893\pi$
$397$		−	20.8328i		−	1.04557i	0.852465	−	0.522785i	$-0.175107\pi$
$398$		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
$403$	−15.8904	−	21.8713i	−0.791560	−	1.08949i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.37988	+	14.7812i	0.316239	+	0.732675i
$408$		0			0
$409$	4.28115	+	13.1760i	0.211689	+	0.651513i	0.999372	+	0.0354318i	$0.0112807\pi$
$409$	4.28115	+	13.1760i	0.211689	+	0.651513i	−0.787683	+	0.616081i	$0.788719\pi$
$410$		0			0
$411$	−3.33688	+	2.42439i	−0.164596	+	0.119586i
$412$		0			0
$413$	27.3889	+	8.89919i	1.34772	+	0.437900i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			3.27051i			0.160158i
$418$		0			0
$419$	31.4164			1.53479			0.767396	−	0.641173i	$-0.221552\pi$
$419$	31.4164			1.53479			0.767396	+	0.641173i	$0.221552\pi$
$420$		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
$423$	9.82084	+	3.19098i	0.477505	+	0.155151i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−12.5352	+	4.07295i	−0.606623	+	0.197104i
$428$		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
$433$	−21.4253	−	29.4894i	−1.02963	−	1.41717i	−0.905223	−	0.424937i	$-0.860296\pi$
$433$	−21.4253	−	29.4894i	−1.02963	−	1.41717i	−0.124410	−	0.992231i	$-0.539704\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.8576	+	14.9443i	−0.519392	+	0.714881i
$438$		0			0
$439$	−11.4164			−0.544875			−0.272438	−	0.962173i	$-0.587830\pi$
$439$	−11.4164			−0.544875			−0.272438	+	0.962173i	$0.587830\pi$
$440$		0			0
$441$	−3.27051			−0.155739
$442$		0			0
$443$	17.7926	−	24.4894i	0.845350	−	1.16352i	−0.139518	−	0.990220i	$-0.544555\pi$
$443$	17.7926	−	24.4894i	0.845350	−	1.16352i	0.984868	−	0.173305i	$-0.0554446\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.03681	+	1.42705i	0.0490396	+	0.0674972i
$448$		0			0
$449$	−1.71885	−	5.29007i	−0.0811174	−	0.249654i	0.902270	−	0.431171i	$-0.141899\pi$
$449$	−1.71885	−	5.29007i	−0.0811174	−	0.249654i	−0.983388	+	0.181517i	$0.941899\pi$
$450$		0			0
$451$	13.9828	+	15.8904i	0.658423	+	0.748252i
$452$		0			0
$453$	5.18407	−	1.68441i	0.243569	−	0.0791403i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−13.1760	−	4.28115i	−0.616349	−	0.200264i	−0.0158303	−	0.999875i	$-0.505039\pi$
$457$	−13.1760	−	4.28115i	−0.616349	−	0.200264i	−0.600519	+	0.799611i	$0.705039\pi$
$458$		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
$463$			12.0000i			0.557687i	0.960337	+	0.278844i	$0.0899511\pi$
$463$			12.0000i			0.557687i	−0.960337	+	0.278844i	$0.910049\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	26.9399	+	8.75329i	1.24663	+	0.405054i	0.856711	−	0.515796i	$-0.172504\pi$
$467$	26.9399	+	8.75329i	1.24663	+	0.405054i	0.389916	+	0.920850i	$0.372504\pi$
$468$		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
$477$	11.8945	+	16.3713i	0.544610	+	0.749591i
$478$		0			0
$479$	3.60739	−	11.1024i	0.164826	−	0.507282i	−0.834198	−	0.551466i	$-0.814069\pi$
$479$	3.60739	−	11.1024i	0.164826	−	0.507282i	0.999023	+	0.0441838i	$0.0140687\pi$
$480$		0			0
$481$	−18.1353	−	13.1760i	−0.826896	−	0.600775i
$482$		0			0
$483$			7.05573i			0.321047i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.48588	−	8.92705i	0.293903	−	0.404523i	−0.636374	−	0.771381i	$-0.719566\pi$
$487$	6.48588	−	8.92705i	0.293903	−	0.404523i	0.930277	+	0.366858i	$0.119566\pi$
$488$		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
$493$	28.0297	−	9.10739i	1.26239	−	0.410176i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	23.3929	−	7.60081i	1.04931	−	0.340943i
$498$		0			0
$499$	8.30902	−	6.03685i	0.371963	−	0.270247i	−0.386062	−	0.922473i	$-0.626165\pi$
$499$	8.30902	−	6.03685i	0.371963	−	0.270247i	0.758024	+	0.652226i	$0.226165\pi$
$500$		0			0
$501$	0.802439	−	2.46965i	0.0358503	−	0.110336i
$502$		0			0
$503$	−0.885544	+	1.21885i	−0.0394845	+	0.0543457i	−0.828303	−	0.560281i	$-0.810693\pi$
$503$	−0.885544	+	1.21885i	−0.0394845	+	0.0543457i	0.788818	+	0.614626i	$0.210693\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	3.18034i		−	0.141244i
$508$		0			0
$509$	25.6353	+	18.6251i	1.13626	+	0.825543i	0.986594	−	0.163193i	$-0.0521793\pi$
$509$	25.6353	+	18.6251i	1.13626	+	0.825543i	0.149669	+	0.988736i	$0.452179\pi$
$510$		0			0
$511$	−10.6631	+	32.8177i	−0.471709	+	1.45177i
$512$		0			0
$513$	−3.75123	−	5.16312i	−0.165621	−	0.227957i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−9.00854	+	7.92705i	−0.396195	+	0.348631i
$518$		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
$523$	26.1073	+	8.48278i	1.14159	+	0.370926i	0.817970	−	0.575260i	$-0.195099\pi$
$523$	26.1073	+	8.48278i	1.14159	+	0.370926i	0.323622	+	0.946186i	$0.395099\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	27.0344i		−	1.17764i
$528$		0			0
$529$	−18.8885			−0.821241
$530$		0			0
$531$	−23.2984	−	16.9273i	−1.01106	−	0.734580i
$532$		0			0
$533$	−28.0297	−	9.10739i	−1.21410	−	0.394485i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.138757	+	0.0450850i	−0.00598782	+	0.00194556i
$538$		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
$543$	−0.138757	−	0.190983i	−0.00595464	−	0.00819587i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.3273	−	18.3435i	0.569834	−	0.784310i	−0.422701	−	0.906269i	$-0.638918\pi$
$547$	13.3273	−	18.3435i	0.569834	−	0.784310i	0.992535	+	0.121960i	$0.0389179\pi$
$548$		0			0
$549$	13.1803			0.562523
$550$		0			0
$551$	−18.2148			−0.775976
$552$		0			0
$553$	23.2416	−	31.9894i	0.988335	−	1.36033i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.31437	−	8.69098i	−0.267548	−	0.368249i	0.654012	−	0.756484i	$-0.273085\pi$
$557$	−6.31437	−	8.69098i	−0.267548	−	0.368249i	−0.921560	+	0.388236i	$0.873085\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−5.37132	+	2.31838i	−0.226777	+	0.0978823i
$562$		0			0
$563$	15.2497	−	4.95492i	0.642697	−	0.208825i	0.0305054	−	0.999535i	$-0.490288\pi$
$563$	15.2497	−	4.95492i	0.642697	−	0.208825i	0.612191	+	0.790710i	$0.290288\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	20.9232	+	6.79837i	0.878694	+	0.285505i
$568$		0			0
$569$	−28.2533	−	20.5272i	−1.18444	−	0.860546i	−0.191774	−	0.981439i	$-0.561424\pi$
$569$	−28.2533	−	20.5272i	−1.18444	−	0.860546i	−0.992665	+	0.120893i	$0.961424\pi$
$570$		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
$573$		−	1.15905i		−	0.0484202i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−23.6907	−	7.69756i	−0.986255	−	0.320454i	−0.228895	−	0.973451i	$-0.573511\pi$
$577$	−23.6907	−	7.69756i	−0.986255	−	0.320454i	−0.757360	+	0.652998i	$0.773511\pi$
$578$		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
$583$	−23.4131	+	2.19098i	−0.969673	+	0.0907412i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.673542	+	0.927051i	0.0278001	+	0.0382635i	0.822691	−	0.568489i	$-0.192472\pi$
$587$	0.673542	+	0.927051i	0.0278001	+	0.0382635i	−0.794891	+	0.606753i	$0.792472\pi$
$588$		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
$593$		−	10.5836i		−	0.434616i	−0.976103	−	0.217308i	$-0.930272\pi$
$593$		−	10.5836i		−	0.434616i	0.976103	−	0.217308i	$-0.0697276\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.80423	+	5.23607i	−0.155697	+	0.214298i
$598$		0			0
$599$	0.302439	−	0.930812i	0.0123573	−	0.0380320i	−0.944688	−	0.327971i	$-0.893635\pi$
$599$	0.302439	−	0.930812i	0.0123573	−	0.0380320i	0.957045	+	0.289939i	$0.0936351\pi$
$600$		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
$603$	13.4208	−	4.36068i	0.546537	−	0.177581i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−39.5281	+	12.8435i	−1.60440	+	0.521300i	−0.968189	−	0.250219i	$-0.919497\pi$
$607$	−39.5281	+	12.8435i	−1.60440	+	0.521300i	−0.636207	+	0.771519i	$0.719497\pi$
$608$		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
$613$	17.9641	−	24.7254i	0.725562	−	0.998651i	−0.273759	−	0.961798i	$-0.588267\pi$
$613$	17.9641	−	24.7254i	0.725562	−	0.998651i	0.999321	−	0.0368521i	$-0.0117330\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	16.4721i		−	0.663143i	−0.943430	−	0.331572i	$-0.892421\pi$
$617$		−	16.4721i		−	0.663143i	0.943430	−	0.331572i	$-0.107579\pi$
$618$		0			0
$619$	5.39919	+	3.92274i	0.217012	+	0.157668i	0.690980	−	0.722873i	$-0.257179\pi$
$619$	5.39919	+	3.92274i	0.217012	+	0.157668i	−0.473969	+	0.880542i	$0.657179\pi$
$620$		0			0
$621$	4.47214	−	13.7638i	0.179461	−	0.552323i
$622$		0			0
$623$	−14.2128	−	19.5623i	−0.569426	−	0.783747i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.59996	−	0.336881i	0.143768	−	0.0134537i
$628$		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
$633$	8.38800	+	2.72542i	0.333393	+	0.108326i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			5.29180i			0.209669i
$638$		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
$643$	−20.2295	−	6.57295i	−0.797772	−	0.259212i	−0.118362	−	0.992971i	$-0.537764\pi$
$643$	−20.2295	−	6.57295i	−0.797772	−	0.259212i	−0.679410	+	0.733759i	$0.737764\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	33.9933	−	11.0451i	1.33641	−	0.434227i	0.448313	−	0.893877i	$-0.352025\pi$
$647$	33.9933	−	11.0451i	1.33641	−	0.434227i	0.888100	+	0.459649i	$0.152025\pi$
$648$		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
$653$	13.7108	+	18.8713i	0.536546	+	0.738492i	0.988110	−	0.153747i	$-0.0491339\pi$
$653$	13.7108	+	18.8713i	0.536546	+	0.738492i	−0.451565	+	0.892238i	$0.649134\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	20.2825	−	27.9164i	0.791294	−	1.08912i
$658$		0			0
$659$	4.36068			0.169868			0.0849340	−	0.996387i	$-0.472932\pi$
$659$	4.36068			0.169868			0.0849340	+	0.996387i	$0.472932\pi$
$660$		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
$663$	4.78804	−	6.59017i	0.185952	−	0.255941i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−24.2784	−	33.4164i	−0.940065	−	1.29389i
$668$		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
$673$	28.6705	−	9.31559i	1.10516	−	0.359090i	0.301077	−	0.953600i	$-0.402654\pi$
$673$	28.6705	−	9.31559i	1.10516	−	0.359090i	0.804088	+	0.594510i	$0.202654\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	32.8177	+	10.6631i	1.26129	+	0.409817i	0.861953	−	0.506989i	$-0.169241\pi$
$677$	32.8177	+	10.6631i	1.26129	+	0.409817i	0.399334	+	0.916805i	$0.369241\pi$
$678$		0			0
$679$	12.8435	+	9.33132i	0.492887	+	0.358103i
$680$		0			0
$681$	−8.14590			−0.312151
$682$		0			0
$683$		−	16.9443i		−	0.648355i	−0.945996	−	0.324177i	$-0.894913\pi$
$683$		−	16.9443i		−	0.648355i	0.945996	−	0.324177i	$-0.105087\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	6.27388	+	2.03851i	0.239363	+	0.0777739i
$688$		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
$693$	−20.2825	+	17.8475i	−0.770467	+	0.677971i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−17.3233	−	23.8435i	−0.656166	−	0.903135i
$698$		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
$703$			13.8541i			0.522517i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−11.4049	+	15.6976i	−0.428927	+	0.590368i
$708$		0			0
$709$	−2.37132	+	7.29818i	−0.0890569	+	0.274089i	−0.985659	−	0.168747i	$-0.946028\pi$
$709$	−2.37132	+	7.29818i	−0.0890569	+	0.274089i	0.896602	+	0.442836i	$0.146028\pi$
$710$		0			0
$711$	−31.9894	+	23.2416i	−1.19969	+	0.871629i
$712$		0			0
$713$	−36.0341	+	11.7082i	−1.34949	+	0.438476i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.11044	−	1.01064i	0.116161	−	0.0377432i
$718$		0			0
$719$	−4.63525	+	3.36771i	−0.172866	+	0.125594i	−0.670854	−	0.741589i	$-0.734072\pi$
$719$	−4.63525	+	3.36771i	−0.172866	+	0.125594i	0.497988	+	0.867184i	$0.334072\pi$
$720$		0			0
$721$	−1.01064	+	3.11044i	−0.0376383	+	0.115839i
$722$		0			0
$723$	0.792055	−	1.09017i	0.0294568	−	0.0405439i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			32.0000i			1.18681i	0.804902	+	0.593407i	$0.202218\pi$
$727$			32.0000i			1.18681i	−0.804902	+	0.593407i	$0.797782\pi$
$728$		0			0
$729$	−15.7254	−	11.4252i	−0.582423	−	0.423155i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	7.89848	+	10.8713i	0.291737	+	0.401541i	0.929577	−	0.368627i	$-0.120172\pi$
$733$	7.89848	+	10.8713i	0.291737	+	0.401541i	−0.637840	+	0.770169i	$0.720172\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.59222	+	16.0000i	−0.132321	+	0.589368i
$738$		0			0
$739$	11.3369	+	34.8913i	0.417034	+	1.28350i	0.910419	+	0.413687i	$0.135759\pi$
$739$	11.3369	+	34.8913i	0.417034	+	1.28350i	−0.493385	+	0.869811i	$0.664241\pi$
$740$		0			0
$741$	−4.07295	+	2.95917i	−0.149624	+	0.108708i
$742$		0			0
$743$	32.8177	+	10.6631i	1.20396	+	0.391192i	0.841218	−	0.540696i	$-0.181839\pi$
$743$	32.8177	+	10.6631i	1.20396	+	0.391192i	0.362747	+	0.931888i	$0.381839\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			45.7639i			1.67441i
$748$		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
$753$	0.436516	+	0.141833i	0.0159075	+	0.00516867i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	14.9721	−	4.86475i	0.544172	−	0.176812i	−0.0240152	−	0.999712i	$-0.507645\pi$
$757$	14.9721	−	4.86475i	0.544172	−	0.176812i	0.568187	+	0.822899i	$0.307645\pi$
$758$		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
$763$	−5.91834	−	8.14590i	−0.214258	−	0.294901i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−27.3889	+	37.6976i	−0.988955	+	1.36118i
$768$		0			0
$769$	−10.5836			−0.381654			−0.190827	−	0.981624i	$-0.561117\pi$
$769$	−10.5836			−0.381654			−0.190827	+	0.981624i	$0.561117\pi$
$770$		0			0
$771$	6.14590			0.221339
$772$		0			0
$773$	7.44945	−	10.2533i	0.267938	−	0.368785i	−0.653754	−	0.756707i	$-0.726807\pi$
$773$	7.44945	−	10.2533i	0.267938	−	0.368785i	0.921692	+	0.387922i	$0.126807\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	3.11044	+	4.28115i	0.111586	+	0.153586i
$778$		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
$783$	13.5721	−	4.40983i	0.485026	−	0.157594i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	30.7441	+	9.98936i	1.09591	+	0.356082i	0.800527	−	0.599297i	$-0.204553\pi$
$787$	30.7441	+	9.98936i	1.09591	+	0.356082i	0.295382	+	0.955379i	$0.404553\pi$
$788$		0			0
$789$	9.23607	+	6.71040i	0.328813	+	0.238896i
$790$		0			0
$791$	−7.31308			−0.260023
$792$		0			0
$793$		−	21.3262i		−	0.757317i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−10.2699	−	3.33688i	−0.363777	−	0.118198i	0.121424	−	0.992601i	$-0.461254\pi$
$797$	−10.2699	−	3.33688i	−0.363777	−	0.118198i	−0.485202	+	0.874402i	$0.661254\pi$
$798$		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
$803$	15.8904	+	36.8156i	0.560762	+	1.29919i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.89844	−	3.98936i	−0.102030	−	0.140432i
$808$		0			0
$809$	−14.1910	+	43.6754i	−0.498928	+	1.53554i	0.311815	+	0.950143i	$0.399063\pi$
$809$	−14.1910	+	43.6754i	−0.498928	+	1.53554i	−0.810744	+	0.585401i	$0.800937\pi$
$810$		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
$813$			5.45085i			0.191170i
$814$		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
$823$	−1.42033	+	0.461493i	−0.0495096	+	0.0160866i	−0.333667	−	0.942691i	$-0.608286\pi$
$823$	−1.42033	+	0.461493i	−0.0495096	+	0.0160866i	0.284158	+	0.958778i	$0.408286\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.2497	+	4.95492i	−0.530283	+	0.172299i	−0.561907	−	0.827201i	$-0.689932\pi$
$827$	−15.2497	+	4.95492i	−0.530283	+	0.172299i	0.0316241	+	0.999500i	$0.489932\pi$
$828$		0			0
$829$	−38.7254	+	28.1357i	−1.34499	+	0.977192i	−0.345745	+	0.938328i	$0.612374\pi$
$829$	−38.7254	+	28.1357i	−1.34499	+	0.977192i	−0.999245	+	0.0388637i	$0.987626\pi$
$830$		0			0
$831$	0.287731	−	0.885544i	0.00998127	−	0.0307192i
$832$		0			0
$833$	−3.11044	+	4.28115i	−0.107770	+	0.148333i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	13.0902i		−	0.452462i
$838$		0			0
$839$	−0.309017	−	0.224514i	−0.0106685	−	0.00775108i	0.582438	−	0.812875i	$-0.302099\pi$
$839$	−0.309017	−	0.224514i	−0.0106685	−	0.00775108i	−0.593107	+	0.805124i	$0.702099\pi$
$840$		0			0
$841$	3.62461	−	11.1554i	0.124987	−	0.384669i
$842$		0			0
$843$	−2.62092	−	3.60739i	−0.0902694	−	0.124245i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−5.82485	−	30.8500i	−0.200144	−	1.06002i
$848$		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
$853$	6.46564	+	2.10081i	0.221379	+	0.0719305i	0.417607	−	0.908628i	$-0.362869\pi$
$853$	6.46564	+	2.10081i	0.221379	+	0.0719305i	−0.196227	+	0.980558i	$0.562869\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	14.9443i		−	0.510487i	−0.966877	−	0.255243i	$-0.917844\pi$
$857$		−	14.9443i		−	0.510487i	0.966877	−	0.255243i	$-0.0821556\pi$
$858$		0			0
$859$	48.9443			1.66996			0.834979	−	0.550283i	$-0.185480\pi$
$859$	48.9443			1.66996			0.834979	+	0.550283i	$0.185480\pi$
$860$		0			0
$861$	5.62868	+	4.08947i	0.191825	+	0.139369i
$862$		0			0
$863$	−24.9317	−	8.10081i	−0.848686	−	0.275755i	−0.147791	−	0.989019i	$-0.547216\pi$
$863$	−24.9317	−	8.10081i	−0.848686	−	0.275755i	−0.700896	+	0.713264i	$0.747216\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	1.57160	−	0.510643i	0.0533743	−	0.0173423i
$868$		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
$873$	−9.33132	−	12.8435i	−0.315817	−	0.434685i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	25.4665	−	35.0517i	0.859943	−	1.18361i	−0.121640	−	0.992574i	$-0.538815\pi$
$877$	25.4665	−	35.0517i	0.859943	−	1.18361i	0.981583	−	0.191036i	$-0.0611848\pi$
$878$		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
$883$	−30.5523	+	42.0517i	−1.02817	+	1.41515i	−0.121853	+	0.992548i	$0.538883\pi$
$883$	−30.5523	+	42.0517i	−1.02817	+	1.41515i	−0.906315	+	0.422603i	$0.861117\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	15.8904	+	21.8713i	0.533549	+	0.734367i	0.987666	−	0.156575i	$-0.0500452\pi$
$887$	15.8904	+	21.8713i	0.533549	+	0.734367i	−0.454117	+	0.890942i	$0.650045\pi$
$888$		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
$893$	−9.82084	+	3.19098i	−0.328642	+	0.106782i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−10.8576	−	3.52786i	−0.362526	−	0.117792i
$898$		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
$907$	−42.7773	−	13.8992i	−1.42040	−	0.461515i	−0.504669	−	0.863313i	$-0.668385\pi$
$907$	−42.7773	−	13.8992i	−1.42040	−	0.461515i	−0.915728	+	0.401798i	$0.868385\pi$
$908$		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
$913$	−45.7490	−	27.1140i	−1.51407	−	0.897341i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−30.9888	−	42.6525i	−1.02334	−	1.40851i
$918$		0			0
$919$	12.8435	−	39.5281i	0.423667	−	1.30391i	−0.480599	−	0.876941i	$-0.659581\pi$
$919$	12.8435	−	39.5281i	0.423667	−	1.30391i	0.904265	−	0.426971i	$-0.140419\pi$
$920$		0			0
$921$	5.70820	+	4.14725i	0.188092	+	0.136657i
$922$		0			0
$923$			39.7984i			1.30998i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.92236	−	2.64590i	0.0631385	−	0.0869027i
$928$		0			0
$929$	−9.60739	+	29.5685i	−0.315208	+	0.970111i	0.660460	+	0.750861i	$0.270361\pi$
$929$	−9.60739	+	29.5685i	−0.315208	+	0.970111i	−0.975669	+	0.219250i	$0.929639\pi$
$930$		0			0
$931$	2.64590	−	1.92236i	0.0867158	−	0.0630027i
$932$		0			0
$933$	2.83293	−	0.920473i	0.0927458	−	0.0301349i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	13.1760	−	4.28115i	0.430442	−	0.139859i	−0.0857795	−	0.996314i	$-0.527338\pi$
$937$	13.1760	−	4.28115i	0.430442	−	0.139859i	0.516222	+	0.856455i	$0.327338\pi$
$938$		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
$943$	−24.2784	+	33.4164i	−0.790615	+	1.08819i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			47.7771i			1.55255i	0.630396	+	0.776273i	$0.282892\pi$
$947$			47.7771i			1.55255i	−0.630396	+	0.776273i	$0.717108\pi$
$948$		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
$953$	−27.2376	−	37.4894i	−0.882313	−	1.21440i	−0.975775	−	0.218777i	$-0.929793\pi$
$953$	−27.2376	−	37.4894i	−0.882313	−	1.21440i	0.0934622	−	0.995623i	$-0.470207\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.77109	+	7.88854i	−0.0572512	+	0.255000i
$958$		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
$963$	23.2416	+	7.55166i	0.748951	+	0.243349i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			44.0000i			1.41494i	0.706741	+	0.707472i	$0.250165\pi$
$967$			44.0000i			1.41494i	−0.706741	+	0.707472i	$0.749835\pi$
$968$		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
$973$	23.2416	+	7.55166i	0.745092	+	0.242095i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−33.7158	+	10.9549i	−1.07866	+	0.350479i	−0.793856	−	0.608106i	$-0.791930\pi$
$977$	−33.7158	+	10.9549i	−1.07866	+	0.350479i	−0.284807	+	0.958585i	$0.591930\pi$
$978$		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
$983$	−3.36771	−	4.63525i	−0.107413	−	0.147842i	0.751926	−	0.659247i	$-0.229125\pi$
$983$	−3.36771	−	4.63525i	−0.107413	−	0.147842i	−0.859339	+	0.511406i	$0.829125\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.31838	+	3.19098i	−0.0737950	+	0.101570i
$988$		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
$993$	−2.69417	+	3.70820i	−0.0854968	+	0.117676i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	20.5272	+	28.2533i	0.650103	+	0.894791i	0.999104	−	0.0423320i	$-0.0134787\pi$
$997$	20.5272	+	28.2533i	0.650103	+	0.894791i	−0.349000	+	0.937123i	$0.613479\pi$
$998$		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.cb.a.49.2		8
5.2	odd	4		1100.2.n.a.401.1		4
5.3	odd	4		44.2.e.a.5.1	✓	4
5.4	even	2	inner	1100.2.cb.a.49.1		8
11.9	even	5	inner	1100.2.cb.a.449.1		8
15.8	even	4		396.2.j.a.181.1		4
20.3	even	4		176.2.m.b.49.1		4
40.3	even	4		704.2.m.d.577.1		4
40.13	odd	4		704.2.m.e.577.1		4
55.3	odd	20		484.2.a.b.1.2		2
55.8	even	20		484.2.a.c.1.2		2
55.9	even	10	inner	1100.2.cb.a.449.2		8
55.13	even	20		484.2.e.c.9.1		4
55.18	even	20		484.2.e.d.245.1		4
55.28	even	20		484.2.e.d.81.1		4
55.38	odd	20		484.2.e.e.81.1		4
55.42	odd	20		1100.2.n.a.801.1		4
55.43	even	4		484.2.e.c.269.1		4
55.48	odd	20		484.2.e.e.245.1		4
55.53	odd	20		44.2.e.a.9.1	yes	4
165.8	odd	20		4356.2.a.u.1.1		2
165.53	even	20		396.2.j.a.361.1		4
165.113	even	20		4356.2.a.t.1.1		2
220.3	even	20		1936.2.a.ba.1.1		2
220.63	odd	20		1936.2.a.z.1.1		2
220.163	even	20		176.2.m.b.97.1		4
440.3	even	20		7744.2.a.bp.1.2		2
440.53	odd	20		704.2.m.e.449.1		4
440.163	even	20		704.2.m.d.449.1		4
440.173	even	20		7744.2.a.db.1.1		2
440.283	odd	20		7744.2.a.bo.1.2		2
440.333	odd	20		7744.2.a.da.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.e.a.5.1	✓	4	5.3	odd	4
44.2.e.a.9.1	yes	4	55.53	odd	20
176.2.m.b.49.1		4	20.3	even	4
176.2.m.b.97.1		4	220.163	even	20
396.2.j.a.181.1		4	15.8	even	4
396.2.j.a.361.1		4	165.53	even	20
484.2.a.b.1.2		2	55.3	odd	20
484.2.a.c.1.2		2	55.8	even	20
484.2.e.c.9.1		4	55.13	even	20
484.2.e.c.269.1		4	55.43	even	4
484.2.e.d.81.1		4	55.28	even	20
484.2.e.d.245.1		4	55.18	even	20
484.2.e.e.81.1		4	55.38	odd	20
484.2.e.e.245.1		4	55.48	odd	20
704.2.m.d.449.1		4	440.163	even	20
704.2.m.d.577.1		4	40.3	even	4
704.2.m.e.449.1		4	440.53	odd	20
704.2.m.e.577.1		4	40.13	odd	4
1100.2.n.a.401.1		4	5.2	odd	4
1100.2.n.a.801.1		4	55.42	odd	20
1100.2.cb.a.49.1		8	5.4	even	2	inner
1100.2.cb.a.49.2		8	1.1	even	1	trivial
1100.2.cb.a.449.1		8	11.9	even	5	inner
1100.2.cb.a.449.2		8	55.9	even	10	inner
1936.2.a.z.1.1		2	220.63	odd	20
1936.2.a.ba.1.1		2	220.3	even	20
4356.2.a.t.1.1		2	165.113	even	20
4356.2.a.u.1.1		2	165.8	odd	20
7744.2.a.bo.1.2		2	440.283	odd	20
7744.2.a.bp.1.2		2	440.3	even	20
7744.2.a.da.1.1		2	440.333	odd	20
7744.2.a.db.1.1		2	440.173	even	20

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.cb (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.224514 - 0.309017i) q^{3} +(-1.67760 - 2.30902i) q^{7} +(0.881966 + 2.71441i) q^{9} +(-3.23607 - 0.726543i) q^{11} +(4.39201 - 1.42705i) q^{13} +(4.39201 + 1.42705i) q^{17} +(-2.30902 - 1.67760i) q^{19} -1.09017 q^{21} -6.47214i q^{23} +(2.12663 + 0.690983i) q^{27} +(5.16312 - 3.75123i) q^{29} +(-1.80902 - 5.56758i) q^{31} +(-0.951057 + 0.836881i) q^{33} +(-2.85317 - 3.92705i) q^{37} +(0.545085 - 1.67760i) q^{39} +(-5.16312 - 3.75123i) q^{41} +(2.12663 - 2.92705i) q^{47} +(-0.354102 + 1.08981i) q^{49} +(1.42705 - 1.03681i) q^{51} +(6.74315 - 2.19098i) q^{53} +(-1.03681 + 0.336881i) q^{57} +(-8.16312 + 5.93085i) q^{59} +(1.42705 - 4.39201i) q^{61} +(4.78804 - 6.59017i) q^{63} -4.94427i q^{67} +(-2.00000 - 1.45309i) q^{69} +(-2.66312 + 8.19624i) q^{71} +(-7.10642 - 9.78115i) q^{73} +(3.75123 + 8.69098i) q^{77} +(4.28115 + 13.1760i) q^{79} +(-6.23607 + 4.53077i) q^{81} +(15.2497 + 4.95492i) q^{83} -2.43769i q^{87} +8.47214 q^{89} +(-10.6631 - 7.74721i) q^{91} +(-2.12663 - 0.690983i) q^{93} +(-5.29007 + 1.71885i) q^{97} +(-0.881966 - 9.42481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{9} - 8 q^{11} - 14 q^{19} + 36 q^{21} + 10 q^{29} - 10 q^{31} - 18 q^{39} - 10 q^{41} + 24 q^{49} - 2 q^{51} - 34 q^{59} - 2 q^{61} - 16 q^{69} + 10 q^{71} - 6 q^{79} - 32 q^{81} + 32 q^{89}+ \cdots - 16 q^{99}+O(q^{100}) \) 8 * q + 16 * q^9 - 8 * q^11 - 14 * q^19 + 36 * q^21 + 10 * q^29 - 10 * q^31 - 18 * q^39 - 10 * q^41 + 24 * q^49 - 2 * q^51 - 34 * q^59 - 2 * q^61 - 16 * q^69 + 10 * q^71 - 6 * q^79 - 32 * q^81 + 32 * q^89 - 54 * q^91 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more