LMFDB - Embedded newform 1440.2.q.q.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(481,1440)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1440.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + x^{10} + 4x^{8} - 21x^{6} + 36x^{4} + 81x^{2} + 729 $ x^12 + x^10 + 4x^8 - 21x^6 + 36x^4 + 81x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$1.66309 + 0.483872i$ of defining polynomial
Character	$\chi$	$=$	1440.961
Dual form			1440.2.q.q.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66309 + 0.483872i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.56078 + 2.70334i) q^{7} +(2.53174 - 1.60944i) q^{9} +O(q^{10})$	\(q+(-1.66309 + 0.483872i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.56078 + 2.70334i) q^{7} +(2.53174 - 1.60944i) q^{9} +(-0.412500 + 0.714470i) q^{11} +(-3.03174 - 5.25112i) q^{13} +(-1.25059 - 1.19834i) q^{15} -2.74410 q^{17} -0.824999 q^{19} +(1.28764 - 5.25112i) q^{21} +(-1.76540 - 3.05777i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-3.43174 + 3.90169i) q^{27} +(3.15969 - 5.47274i) q^{29} +(3.63637 + 6.29837i) q^{31} +(0.340312 - 1.38783i) q^{33} -3.12155 q^{35} -2.06347 q^{37} +(7.58292 + 7.26611i) q^{39} +(2.78764 + 4.82833i) q^{41} +(3.73868 - 6.47558i) q^{43} +(2.65969 + 1.38783i) q^{45} +(3.75177 - 6.49826i) q^{47} +(-1.37205 - 2.37646i) q^{49} +(4.56368 - 1.32779i) q^{51} -1.48819 q^{53} -0.824999 q^{55} +(1.37205 - 0.399194i) q^{57} +(0.722686 + 1.25173i) q^{59} +(4.19142 - 7.25976i) q^{61} +(0.399409 + 9.35614i) q^{63} +(3.03174 - 5.25112i) q^{65} +(-5.91983 - 10.2534i) q^{67} +(4.41559 + 4.23111i) q^{69} -15.5751 q^{71} +13.4463 q^{73} +(0.412500 - 1.68221i) q^{75} +(-1.28764 - 2.23026i) q^{77} +(7.06811 - 12.2423i) q^{79} +(3.81938 - 8.14938i) q^{81} +(2.18115 - 3.77786i) q^{83} +(-1.37205 - 2.37646i) q^{85} +(-2.60674 + 10.6305i) q^{87} -2.83118 q^{89} +18.9275 q^{91} +(-9.09521 - 8.71522i) q^{93} +(-0.412500 - 0.714470i) q^{95} +(2.65969 - 4.60671i) q^{97} +(0.105560 + 2.47275i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} - 2 q^{9}+O(q^{10}) $ 12 * q + 6 * q^5 - 2 * q^9	$ 12 q + 6 q^{5} - 2 q^{9} - 4 q^{13} - 28 q^{17} - 12 q^{21} - 6 q^{25} + 8 q^{29} + 34 q^{33} + 40 q^{37} + 6 q^{41} + 2 q^{45} - 14 q^{49} - 8 q^{53} + 14 q^{57} - 12 q^{61} + 4 q^{65} + 28 q^{69} - 28 q^{73} + 12 q^{77} - 14 q^{81} - 14 q^{85} + 16 q^{89} - 12 q^{93} + 2 q^{97}+O(q^{100}) $ 12 * q + 6 * q^5 - 2 * q^9 - 4 * q^13 - 28 * q^17 - 12 * q^21 - 6 * q^25 + 8 * q^29 + 34 * q^33 + 40 * q^37 + 6 * q^41 + 2 * q^45 - 14 * q^49 - 8 * q^53 + 14 * q^57 - 12 * q^61 + 4 * q^65 + 28 * q^69 - 28 * q^73 + 12 * q^77 - 14 * q^81 - 14 * q^85 + 16 * q^89 - 12 * q^93 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−1.66309	+	0.483872i	−0.960185	+	0.279364i
$3$	−1.66309	+	0.483872i	−0.960185	+	0.279364i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−1.56078	+	2.70334i	−0.589918	+	1.02177i	0.404324	+	0.914616i	$0.367507\pi$
$7$	−1.56078	+	2.70334i	−0.589918	+	1.02177i	−0.994243	+	0.107153i	$0.965827\pi$
$8$		0			0
$9$	2.53174	−	1.60944i	0.843912	−	0.536482i
$10$		0			0
$11$	−0.412500	+	0.714470i	−0.124373	+	0.215421i	−0.921488	−	0.388407i	$-0.873025\pi$
$11$	−0.412500	+	0.714470i	−0.124373	+	0.215421i	0.797114	+	0.603828i	$0.206359\pi$
$12$		0			0
$13$	−3.03174	−	5.25112i	−0.840852	−	1.45640i	−0.889175	−	0.457567i	$-0.848721\pi$
$13$	−3.03174	−	5.25112i	−0.840852	−	1.45640i	0.0483227	−	0.998832i	$-0.484612\pi$
$14$		0			0
$15$	−1.25059	−	1.19834i	−0.322901	−	0.309411i
$16$		0			0
$17$	−2.74410			−0.665541			−0.332771	−	0.943008i	$-0.607983\pi$
$17$	−2.74410			−0.665541			−0.332771	+	0.943008i	$0.607983\pi$
$18$		0			0
$19$	−0.824999			−0.189268			−0.0946339	−	0.995512i	$-0.530168\pi$
$19$	−0.824999			−0.189268			−0.0946339	+	0.995512i	$0.530168\pi$
$20$		0			0
$21$	1.28764	−	5.25112i	0.280986	−	1.14589i
$22$		0			0
$23$	−1.76540	−	3.05777i	−0.368112	−	0.637589i	0.621158	−	0.783685i	$-0.286662\pi$
$23$	−1.76540	−	3.05777i	−0.368112	−	0.637589i	−0.989270	+	0.146096i	$0.953329\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−3.43174	+	3.90169i	−0.660439	+	0.750880i
$28$		0			0
$29$	3.15969	−	5.47274i	0.586739	−	1.01626i	−0.407917	−	0.913019i	$-0.633745\pi$
$29$	3.15969	−	5.47274i	0.586739	−	1.01626i	0.994656	−	0.103243i	$-0.0329220\pi$
$30$		0			0
$31$	3.63637	+	6.29837i	0.653111	+	1.13122i	0.982364	+	0.186979i	$0.0598697\pi$
$31$	3.63637	+	6.29837i	0.653111	+	1.13122i	−0.329253	+	0.944242i	$0.606797\pi$
$32$		0			0
$33$	0.340312	−	1.38783i	0.0592407	−	0.241589i
$34$		0			0
$35$	−3.12155			−0.527639
$36$		0			0
$37$	−2.06347			−0.339233			−0.169616	−	0.985510i	$-0.554253\pi$
$37$	−2.06347			−0.339233			−0.169616	+	0.985510i	$0.554253\pi$
$38$		0			0
$39$	7.58292	+	7.26611i	1.21424	+	1.16351i
$40$		0			0
$41$	2.78764	+	4.82833i	0.435356	+	0.754059i	0.997325	−	0.0730996i	$-0.0232891\pi$
$41$	2.78764	+	4.82833i	0.435356	+	0.754059i	−0.561968	+	0.827159i	$0.689956\pi$
$42$		0			0
$43$	3.73868	−	6.47558i	0.570143	−	0.987517i	−0.426407	−	0.904531i	$-0.640221\pi$
$43$	3.73868	−	6.47558i	0.570143	−	0.987517i	0.996551	−	0.0829859i	$-0.0264457\pi$
$44$		0			0
$45$	2.65969	+	1.38783i	0.396483	+	0.206885i
$46$		0			0
$47$	3.75177	−	6.49826i	0.547252	−	0.947868i	−0.451209	−	0.892418i	$-0.649007\pi$
$47$	3.75177	−	6.49826i	0.547252	−	0.947868i	0.998461	−	0.0554502i	$-0.0176594\pi$
$48$		0			0
$49$	−1.37205	−	2.37646i	−0.196007	−	0.339494i
$50$		0			0
$51$	4.56368	−	1.32779i	0.639043	−	0.185928i
$52$		0			0
$53$	−1.48819			−0.204419			−0.102209	−	0.994763i	$-0.532591\pi$
$53$	−1.48819			−0.204419			−0.102209	+	0.994763i	$0.532591\pi$
$54$		0			0
$55$	−0.824999			−0.111243
$56$		0			0
$57$	1.37205	−	0.399194i	0.181732	−	0.0528745i
$58$		0			0
$59$	0.722686	+	1.25173i	0.0940857	+	0.162961i	0.909227	−	0.416301i	$-0.136674\pi$
$59$	0.722686	+	1.25173i	0.0940857	+	0.162961i	−0.815141	+	0.579263i	$0.803341\pi$
$60$		0			0
$61$	4.19142	−	7.25976i	0.536657	−	0.929517i	−0.462424	−	0.886659i	$-0.653020\pi$
$61$	4.19142	−	7.25976i	0.536657	−	0.929517i	0.999081	−	0.0428582i	$-0.0136464\pi$
$62$		0			0
$63$	0.399409	+	9.35614i	0.0503207	+	1.17876i
$64$		0			0
$65$	3.03174	−	5.25112i	0.376041	−	0.651321i
$66$		0			0
$67$	−5.91983	−	10.2534i	−0.723222	−	1.25266i	−0.959702	−	0.281021i	$-0.909327\pi$
$67$	−5.91983	−	10.2534i	−0.723222	−	1.25266i	0.236479	−	0.971637i	$-0.424006\pi$
$68$		0			0
$69$	4.41559	+	4.23111i	0.531575	+	0.509366i
$70$		0			0
$71$	−15.5751			−1.84842			−0.924212	−	0.381881i	$-0.875277\pi$
$71$	−15.5751			−1.84842			−0.924212	+	0.381881i	$0.875277\pi$
$72$		0			0
$73$	13.4463			1.57377			0.786886	−	0.617098i	$-0.211692\pi$
$73$	13.4463			1.57377			0.786886	+	0.617098i	$0.211692\pi$
$74$		0			0
$75$	0.412500	−	1.68221i	0.0476314	−	0.194245i
$76$		0			0
$77$	−1.28764	−	2.23026i	−0.146740	−	0.254161i
$78$		0			0
$79$	7.06811	−	12.2423i	0.795224	−	1.37737i	−0.127473	−	0.991842i	$-0.540687\pi$
$79$	7.06811	−	12.2423i	0.795224	−	1.37737i	0.922697	−	0.385526i	$-0.125980\pi$
$80$		0			0
$81$	3.81938	−	8.14938i	0.424375	−	0.905486i
$82$		0			0
$83$	2.18115	−	3.77786i	0.239412	−	0.414674i	−0.721134	−	0.692796i	$-0.756379\pi$
$83$	2.18115	−	3.77786i	0.239412	−	0.414674i	0.960546	+	0.278122i	$0.0897119\pi$
$84$		0			0
$85$	−1.37205	−	2.37646i	−0.148820	−	0.257763i
$86$		0			0
$87$	−2.60674	+	10.6305i	−0.279472	+	1.13971i
$88$		0			0
$89$	−2.83118			−0.300105			−0.150052	−	0.988678i	$-0.547944\pi$
$89$	−2.83118			−0.300105			−0.150052	+	0.988678i	$0.547944\pi$
$90$		0			0
$91$	18.9275			1.98414
$92$		0			0
$93$	−9.09521	−	8.71522i	−0.943129	−	0.903726i
$94$		0			0
$95$	−0.412500	−	0.714470i	−0.0423216	−	0.0733031i
$96$		0			0
$97$	2.65969	−	4.60671i	0.270050	−	0.467741i	−0.698824	−	0.715294i	$-0.746293\pi$
$97$	2.65969	−	4.60671i	0.270050	−	0.467741i	0.968874	+	0.247553i	$0.0796263\pi$
$98$		0			0
$99$	0.105560	+	2.47275i	0.0106092	+	0.248520i
$100$		0			0
$101$	8.06347	−	13.9663i	0.802345	−	1.38970i	−0.115723	−	0.993282i	$-0.536919\pi$
$101$	8.06347	−	13.9663i	0.802345	−	1.38970i	0.918069	−	0.396422i	$-0.129748\pi$
$102$		0			0
$103$	−1.33981	−	2.32062i	−0.132016	−	0.228658i	0.792438	−	0.609953i	$-0.208812\pi$
$103$	−1.33981	−	2.32062i	−0.132016	−	0.228658i	−0.924453	+	0.381295i	$0.875478\pi$
$104$		0			0
$105$	5.19142	−	1.51043i	0.506631	−	0.147403i
$106$		0			0
$107$	−16.2216			−1.56821			−0.784103	−	0.620631i	$-0.786877\pi$
$107$	−16.2216			−1.56821			−0.784103	+	0.620631i	$0.786877\pi$
$108$		0			0
$109$	−9.87104			−0.945474			−0.472737	−	0.881204i	$-0.656734\pi$
$109$	−9.87104			−0.945474			−0.472737	+	0.881204i	$0.656734\pi$
$110$		0			0
$111$	3.43174	−	0.998456i	0.325726	−	0.0947693i
$112$		0			0
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$		0			0
$115$	1.76540	−	3.05777i	0.164625	−	0.285138i
$116$		0			0
$117$	−16.1269	−	8.41504i	−1.49094	−	0.777971i
$118$		0			0
$119$	4.28292	−	7.41824i	0.392615	−	0.680029i
$120$		0			0
$121$	5.15969	+	8.93684i	0.469063	+	0.812440i
$122$		0			0
$123$	−6.97239	−	6.68109i	−0.628679	−	0.602414i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.91043			0.258259			0.129130	−	0.991628i	$-0.458782\pi$
$127$	2.91043			0.258259			0.129130	+	0.991628i	$0.458782\pi$
$128$		0			0
$129$	−3.08441	+	12.5785i	−0.271567	+	1.10748i
$130$		0			0
$131$	−5.00236	−	8.66434i	−0.437058	−	0.757007i	0.560403	−	0.828220i	$-0.310646\pi$
$131$	−5.00236	−	8.66434i	−0.437058	−	0.757007i	−0.997461	+	0.0712130i	$0.977313\pi$
$132$		0			0
$133$	1.28764	−	2.23026i	0.111653	−	0.193388i
$134$		0			0
$135$	−5.09483	−	1.02113i	−0.438493	−	0.0878849i
$136$		0			0
$137$	2.34031	−	4.05354i	0.199946	−	0.346317i	−0.748564	−	0.663062i	$-0.769257\pi$
$137$	2.34031	−	4.05354i	0.199946	−	0.346317i	0.948511	+	0.316745i	$0.102590\pi$
$138$		0			0
$139$	8.02160	+	13.8938i	0.680383	+	1.17846i	0.974864	+	0.222801i	$0.0715200\pi$
$139$	8.02160	+	13.8938i	0.680383	+	1.17846i	−0.294481	+	0.955657i	$0.595147\pi$
$140$		0			0
$141$	−3.09521	+	12.6226i	−0.260664	+	1.06301i
$142$		0			0
$143$	5.00236			0.418318
$144$		0			0
$145$	6.31938			0.524796
$146$		0			0
$147$	3.43174	+	3.28837i	0.283045	+	0.271220i
$148$		0			0
$149$	−9.25490	−	16.0300i	−0.758191	−	1.31322i	−0.943772	−	0.330596i	$-0.892750\pi$
$149$	−9.25490	−	16.0300i	−0.758191	−	1.31322i	0.185582	−	0.982629i	$-0.440583\pi$
$150$		0			0
$151$	−1.98637	+	3.44049i	−0.161648	+	0.279983i	−0.935460	−	0.353433i	$-0.885014\pi$
$151$	−1.98637	+	3.44049i	−0.161648	+	0.279983i	0.773812	+	0.633416i	$0.218348\pi$
$152$		0			0
$153$	−6.94733	+	4.41647i	−0.561658	+	0.357051i
$154$		0			0
$155$	−3.63637	+	6.29837i	−0.292080	+	0.505897i
$156$		0			0
$157$	−0.511807	−	0.886476i	−0.0408467	−	0.0707485i	0.844879	−	0.534957i	$-0.179672\pi$
$157$	−0.511807	−	0.886476i	−0.0408467	−	0.0707485i	−0.885726	+	0.464208i	$0.846339\pi$
$158$		0			0
$159$	2.47500	−	0.720094i	0.196280	−	0.0571072i
$160$		0			0
$161$	11.0216			0.868624
$162$		0			0
$163$	20.6298			1.61585			0.807926	−	0.589284i	$-0.200590\pi$
$163$	20.6298			1.61585			0.807926	+	0.589284i	$0.200590\pi$
$164$		0			0
$165$	1.37205	−	0.399194i	0.106814	−	0.0310772i
$166$		0			0
$167$	−9.57913	−	16.5915i	−0.741255	−	1.28389i	−0.951924	−	0.306334i	$-0.900897\pi$
$167$	−9.57913	−	16.5915i	−0.741255	−	1.28389i	0.210669	−	0.977558i	$-0.432436\pi$
$168$		0			0
$169$	−11.8828	+	20.5817i	−0.914065	+	1.58321i
$170$		0			0
$171$	−2.08868	+	1.32779i	−0.159725	+	0.101539i
$172$		0			0
$173$	−6.80757	+	11.7911i	−0.517570	+	0.896457i	0.482222	+	0.876049i	$0.339830\pi$
$173$	−6.80757	+	11.7911i	−0.517570	+	0.896457i	−0.999792	+	0.0204082i	$0.993503\pi$
$174$		0			0
$175$	−1.56078	−	2.70334i	−0.117984	−	0.204354i
$176$		0			0
$177$	−1.80757	−	1.73205i	−0.135865	−	0.130189i
$178$		0			0
$179$	1.86112			0.139107			0.0695533	−	0.997578i	$-0.477843\pi$
$179$	1.86112			0.139107			0.0695533	+	0.997578i	$0.477843\pi$
$180$		0			0
$181$	16.9581			1.26049			0.630244	−	0.776397i	$-0.282955\pi$
$181$	16.9581			1.26049			0.630244	+	0.776397i	$0.282955\pi$
$182$		0			0
$183$	−3.45792	+	14.1017i	−0.255617	+	1.04243i
$184$		0			0
$185$	−1.03174	−	1.78702i	−0.0758548	−	0.131384i
$186$		0			0
$187$	1.13194	−	1.96058i	0.0827756	−	0.143371i
$188$		0			0
$189$	−5.19142	−	15.3668i	−0.377621	−	1.11777i
$190$		0			0
$191$	4.69217	−	8.12708i	0.339514	−	0.588055i	−0.644828	−	0.764328i	$-0.723071\pi$
$191$	4.69217	−	8.12708i	0.339514	−	0.588055i	0.984341	+	0.176273i	$0.0564041\pi$
$192$		0			0
$193$	3.11614	+	5.39732i	0.224305	+	0.388508i	0.956111	−	0.293006i	$-0.0946555\pi$
$193$	3.11614	+	5.39732i	0.224305	+	0.388508i	−0.731806	+	0.681513i	$0.761322\pi$
$194$		0			0
$195$	−2.50118	+	10.2001i	−0.179113	+	0.730441i
$196$		0			0
$197$	−16.6388			−1.18546			−0.592731	−	0.805400i	$-0.701950\pi$
$197$	−16.6388			−1.18546			−0.592731	+	0.805400i	$0.701950\pi$
$198$		0			0
$199$	7.68199			0.544562			0.272281	−	0.962218i	$-0.412222\pi$
$199$	7.68199			0.544562			0.272281	+	0.962218i	$0.412222\pi$
$200$		0			0
$201$	14.8066	+	14.1880i	1.04437	+	1.00074i
$202$		0			0
$203$	9.86314	+	17.0835i	0.692256	+	1.19902i
$204$		0			0
$205$	−2.78764	+	4.82833i	−0.194697	+	0.337225i
$206$		0			0
$207$	−9.39084	−	4.90014i	−0.652709	−	0.340583i
$208$		0			0
$209$	0.340312	−	0.589438i	0.0235399	−	0.0407723i
$210$		0			0
$211$	0.540995	+	0.937031i	0.0372436	+	0.0645079i	0.884046	−	0.467399i	$-0.154809\pi$
$211$	0.540995	+	0.937031i	0.0372436	+	0.0645079i	−0.846803	+	0.531907i	$0.821476\pi$
$212$		0			0
$213$	25.9028	−	7.53635i	1.77483	−	0.516382i
$214$		0			0
$215$	7.47736			0.509952
$216$		0			0
$217$	−22.7022			−1.54113
$218$		0			0
$219$	−22.3624	+	6.50630i	−1.51111	+	0.439655i
$220$		0			0
$221$	8.31938	+	14.4096i	0.559622	+	0.969293i
$222$		0			0
$223$	8.54951	−	14.8082i	0.572517	−	0.991629i	−0.423789	−	0.905761i	$-0.639300\pi$
$223$	8.54951	−	14.8082i	0.572517	−	0.991629i	0.996307	−	0.0858681i	$-0.0273664\pi$
$224$		0			0
$225$	0.127952	+	2.99727i	0.00853012	+	0.199818i
$226$		0			0
$227$	−6.86023	+	11.8823i	−0.455330	+	0.788654i	−0.998707	−	0.0508344i	$-0.983812\pi$
$227$	−6.86023	+	11.8823i	−0.455330	+	0.788654i	0.543377	+	0.839489i	$0.317145\pi$
$228$		0			0
$229$	−6.15969	−	10.6689i	−0.407044	−	0.705020i	0.587513	−	0.809214i	$-0.300107\pi$
$229$	−6.15969	−	10.6689i	−0.407044	−	0.705020i	−0.994557	+	0.104194i	$0.966774\pi$
$230$		0			0
$231$	3.22062	+	3.08607i	0.211901	+	0.203048i
$232$		0			0
$233$	−9.76771			−0.639904			−0.319952	−	0.947434i	$-0.603667\pi$
$233$	−9.76771			−0.639904			−0.319952	+	0.947434i	$0.603667\pi$
$234$		0			0
$235$	7.50354			0.489477
$236$		0			0
$237$	−5.83118	+	23.7801i	−0.378776	+	1.54469i
$238$		0			0
$239$	−11.6285	−	20.1412i	−0.752188	−	1.30283i	−0.946760	−	0.321939i	$-0.895665\pi$
$239$	−11.6285	−	20.1412i	−0.752188	−	1.30283i	0.194573	−	0.980888i	$-0.437668\pi$
$240$		0			0
$241$	14.0834	−	24.3932i	0.907192	−	1.57130i	0.0892436	−	0.996010i	$-0.471555\pi$
$241$	14.0834	−	24.3932i	0.907192	−	1.57130i	0.817948	−	0.575292i	$-0.195112\pi$
$242$		0			0
$243$	−2.40871	+	15.4012i	−0.154519	+	0.987990i
$244$		0			0
$245$	1.37205	−	2.37646i	0.0876569	−	0.151826i
$246$		0			0
$247$	2.50118	+	4.33217i	0.159146	+	0.275649i
$248$		0			0
$249$	−1.79945	+	7.33832i	−0.114035	+	0.465047i
$250$		0			0
$251$	−19.5413			−1.23344			−0.616719	−	0.787183i	$-0.711539\pi$
$251$	−19.5413			−1.23344			−0.616719	+	0.787183i	$0.711539\pi$
$252$		0			0
$253$	2.91291			0.183133
$254$		0			0
$255$	3.43174	+	3.28837i	0.214904	+	0.205925i
$256$		0			0
$257$	9.14788	+	15.8446i	0.570629	+	0.988359i	0.996501	+	0.0835754i	$0.0266339\pi$
$257$	9.14788	+	15.8446i	0.570629	+	0.988359i	−0.425872	+	0.904783i	$0.640033\pi$
$258$		0			0
$259$	3.22062	−	5.57828i	0.200120	−	0.346617i
$260$		0			0
$261$	−0.808576	−	18.9409i	−0.0500496	−	1.17241i
$262$		0			0
$263$	−6.55329	+	11.3506i	−0.404093	+	0.699910i	−0.994215	−	0.107404i	$-0.965746\pi$
$263$	−6.55329	+	11.3506i	−0.404093	+	0.699910i	0.590122	+	0.807314i	$0.299080\pi$
$264$		0			0
$265$	−0.744096	−	1.28881i	−0.0457095	−	0.0791711i
$266$		0			0
$267$	4.70851	−	1.36993i	0.288156	−	0.0838383i
$268$		0			0
$269$	−4.25590			−0.259487			−0.129744	−	0.991548i	$-0.541415\pi$
$269$	−4.25590			−0.259487			−0.129744	+	0.991548i	$0.541415\pi$
$270$		0			0
$271$	−28.9322			−1.75750			−0.878752	−	0.477278i	$-0.841623\pi$
$271$	−28.9322			−1.75750			−0.878752	+	0.477278i	$0.841623\pi$
$272$		0			0
$273$	−31.4781	+	9.15846i	−1.90514	+	0.554295i
$274$		0			0
$275$	−0.412500	−	0.714470i	−0.0248747	−	0.0430842i
$276$		0			0
$277$	−16.1587	+	27.9877i	−0.970881	+	1.68162i	−0.277974	+	0.960589i	$0.589663\pi$
$277$	−16.1587	+	27.9877i	−0.970881	+	1.68162i	−0.692907	+	0.721027i	$0.743671\pi$
$278$		0			0
$279$	19.3432	+	10.0933i	1.15805	+	0.604269i
$280$		0			0
$281$	−6.19142	+	10.7239i	−0.369349	+	0.639732i	−0.989464	−	0.144779i	$-0.953753\pi$
$281$	−6.19142	+	10.7239i	−0.369349	+	0.639732i	0.620115	+	0.784511i	$0.287086\pi$
$282$		0			0
$283$	−4.86077	−	8.41911i	−0.288943	−	0.500464i	0.684615	−	0.728905i	$-0.259970\pi$
$283$	−4.86077	−	8.41911i	−0.288943	−	0.500464i	−0.973558	+	0.228441i	$0.926637\pi$
$284$		0			0
$285$	1.03174	+	0.988632i	0.0611148	+	0.0585615i
$286$		0			0
$287$	−17.4035			−1.02730
$288$		0			0
$289$	−9.46994			−0.557055
$290$		0			0
$291$	−2.19424	+	8.94833i	−0.128629	+	0.524560i
$292$		0			0
$293$	6.60702	+	11.4437i	0.385986	+	0.668547i	0.991905	−	0.126979i	$-0.0405280\pi$
$293$	6.60702	+	11.4437i	0.385986	+	0.668547i	−0.605919	+	0.795526i	$0.707195\pi$
$294$		0			0
$295$	−0.722686	+	1.25173i	−0.0420764	+	0.0728785i
$296$		0			0
$297$	−1.37205	−	4.06132i	−0.0796143	−	0.235662i
$298$		0			0
$299$	−10.7045	+	18.5407i	−0.619056	+	1.07224i
$300$		0			0
$301$	11.6705	+	20.2139i	0.672676	+	1.16511i
$302$		0			0
$303$	−6.65236	+	27.1290i	−0.382168	+	1.55852i
$304$		0			0
$305$	8.38285			0.480001
$306$		0			0
$307$	29.9486			1.70926			0.854629	−	0.519240i	$-0.173785\pi$
$307$	29.9486			1.70926			0.854629	+	0.519240i	$0.173785\pi$
$308$		0			0
$309$	3.35111	+	3.21111i	0.190638	+	0.182674i
$310$		0			0
$311$	−11.1399	−	19.2949i	−0.631686	−	1.09411i	−0.987207	−	0.159444i	$-0.949030\pi$
$311$	−11.1399	−	19.2949i	−0.631686	−	1.09411i	0.355521	−	0.934668i	$-0.384304\pi$
$312$		0			0
$313$	−6.75490	+	11.6998i	−0.381809	+	0.661313i	−0.991321	−	0.131464i	$-0.958032\pi$
$313$	−6.75490	+	11.6998i	−0.381809	+	0.661313i	0.609512	+	0.792777i	$0.291366\pi$
$314$		0			0
$315$	−7.90295	+	5.02397i	−0.445281	+	0.283069i
$316$		0			0
$317$	−13.4781	+	23.3447i	−0.757003	+	1.31117i	0.187369	+	0.982290i	$0.440004\pi$
$317$	−13.4781	+	23.3447i	−0.757003	+	1.31117i	−0.944372	+	0.328878i	$0.893329\pi$
$318$		0			0
$319$	2.60674	+	4.51501i	0.145949	+	0.252792i
$320$		0			0
$321$	26.9781	−	7.84920i	1.50577	−	0.438099i
$322$		0			0
$323$	2.26388			0.125966
$324$		0			0
$325$	6.06347			0.336341
$326$		0			0
$327$	16.4164	−	4.77632i	0.907831	−	0.264131i
$328$		0			0
$329$	11.7114	+	20.2847i	0.645668	+	1.11833i
$330$		0			0
$331$	7.04192	−	12.1970i	0.387059	−	0.670406i	−0.604993	−	0.796231i	$-0.706824\pi$
$331$	7.04192	−	12.1970i	0.387059	−	0.670406i	0.992053	+	0.125824i	$0.0401576\pi$
$332$		0			0
$333$	−5.22417	+	3.32104i	−0.286283	+	0.181992i
$334$		0			0
$335$	5.91983	−	10.2534i	0.323435	−	0.560206i
$336$		0			0
$337$	−0.403784	−	0.699375i	−0.0219955	−	0.0380974i	0.854818	−	0.518928i	$-0.173669\pi$
$337$	−0.403784	−	0.699375i	−0.0219955	−	0.0380974i	−0.876814	+	0.480830i	$0.840335\pi$
$338$		0			0
$339$	−7.50354	−	7.19005i	−0.407536	−	0.390510i
$340$		0			0
$341$	−6.00000			−0.324918
$342$		0			0
$343$	−13.2850			−0.717324
$344$		0			0
$345$	−1.45646	+	5.93957i	−0.0784130	+	0.319776i
$346$		0			0
$347$	−2.70905	−	4.69222i	−0.145430	−	0.251892i	0.784104	−	0.620630i	$-0.213123\pi$
$347$	−2.70905	−	4.69222i	−0.145430	−	0.251892i	−0.929533	+	0.368739i	$0.879790\pi$
$348$		0			0
$349$	−1.84031	+	3.18751i	−0.0985096	+	0.170624i	−0.911068	−	0.412256i	$-0.864741\pi$
$349$	−1.84031	+	3.18751i	−0.0985096	+	0.170624i	0.812558	+	0.582880i	$0.198074\pi$
$350$		0			0
$351$	30.8924	+	6.19160i	1.64891	+	0.330483i
$352$		0			0
$353$	9.34031	−	16.1779i	0.497135	−	0.861062i	−0.502860	−	0.864368i	$-0.667719\pi$
$353$	9.34031	−	16.1779i	0.497135	−	0.861062i	0.999995	+	0.00330547i	$0.00105217\pi$
$354$		0			0
$355$	−7.78755	−	13.4884i	−0.413320	−	0.715891i
$356$		0			0
$357$	−3.53341	+	14.4096i	−0.187008	+	0.762636i
$358$		0			0
$359$	−28.4706			−1.50262			−0.751309	−	0.659950i	$-0.770577\pi$
$359$	−28.4706			−1.50262			−0.751309	+	0.659950i	$0.770577\pi$
$360$		0			0
$361$	−18.3194			−0.964178
$362$		0			0
$363$	−12.9053	−	12.3661i	−0.677353	−	0.649054i
$364$		0			0
$365$	6.72316	+	11.6449i	0.351906	+	0.609520i
$366$		0			0
$367$	−12.5853	+	21.7983i	−0.656946	+	1.13786i	0.324456	+	0.945901i	$0.394819\pi$
$367$	−12.5853	+	21.7983i	−0.656946	+	1.13786i	−0.981402	+	0.191963i	$0.938514\pi$
$368$		0			0
$369$	14.8285	+	7.73752i	0.771941	+	0.402799i
$370$		0			0
$371$	2.32274	−	4.02310i	0.120590	−	0.208869i
$372$		0			0
$373$	−12.8710	−	22.2933i	−0.666437	−	1.15430i	−0.978894	−	0.204371i	$-0.934485\pi$
$373$	−12.8710	−	22.2933i	−0.666437	−	1.15430i	0.312456	−	0.949932i	$-0.398848\pi$
$374$		0			0
$375$	1.66309	−	0.483872i	0.0858816	−	0.0249870i
$376$		0			0
$377$	−38.3174			−1.97344
$378$		0			0
$379$	7.67549			0.394264			0.197132	−	0.980377i	$-0.436837\pi$
$379$	7.67549			0.394264			0.197132	+	0.980377i	$0.436837\pi$
$380$		0			0
$381$	−4.84031	+	1.40828i	−0.247977	+	0.0721482i
$382$		0			0
$383$	−1.55093	−	2.68629i	−0.0792490	−	0.137263i	0.823677	−	0.567059i	$-0.191919\pi$
$383$	−1.55093	−	2.68629i	−0.0792490	−	0.137263i	−0.902926	+	0.429796i	$0.858586\pi$
$384$		0			0
$385$	1.28764	−	2.23026i	0.0656242	−	0.113664i
$386$		0			0
$387$	−0.956742	−	22.4117i	−0.0486339	−	1.13925i
$388$		0			0
$389$	−2.93552	+	5.08447i	−0.148837	+	0.257793i	−0.930798	−	0.365534i	$-0.880886\pi$
$389$	−2.93552	+	5.08447i	−0.148837	+	0.257793i	0.781961	+	0.623327i	$0.214220\pi$
$390$		0			0
$391$	4.84444	+	8.39081i	0.244994	+	0.424341i
$392$		0			0
$393$	12.5118	+	11.9891i	0.631137	+	0.604769i
$394$		0			0
$395$	14.1362			0.711270
$396$		0			0
$397$	−9.66237			−0.484940			−0.242470	−	0.970159i	$-0.577958\pi$
$397$	−9.66237			−0.484940			−0.242470	+	0.970159i	$0.577958\pi$
$398$		0			0
$399$	−1.06230	+	4.33217i	−0.0531816	+	0.216880i
$400$		0			0
$401$	3.85212	+	6.67207i	0.192366	+	0.333187i	0.946034	−	0.324068i	$-0.105051\pi$
$401$	3.85212	+	6.67207i	0.192366	+	0.333187i	−0.753668	+	0.657255i	$0.771717\pi$
$402$		0			0
$403$	22.0490	−	38.1900i	1.09834	−	1.90238i
$404$		0			0
$405$	8.96726	−	0.767012i	0.445587	−	0.0381132i
$406$		0			0
$407$	0.851182	−	1.47429i	0.0421915	−	0.0730778i
$408$		0			0
$409$	3.21135	+	5.56223i	0.158791	+	0.275034i	0.934433	−	0.356139i	$-0.115907\pi$
$409$	3.21135	+	5.56223i	0.158791	+	0.275034i	−0.775642	+	0.631173i	$0.782574\pi$
$410$		0			0
$411$	−1.93076	+	7.87381i	−0.0952372	+	0.388386i
$412$		0			0
$413$	−4.51181			−0.222012
$414$		0			0
$415$	4.36230			0.214137
$416$		0			0
$417$	−20.0635	−	19.2252i	−0.982512	−	0.941464i
$418$		0			0
$419$	−4.05211	−	7.01847i	−0.197959	−	0.342874i	0.749908	−	0.661542i	$-0.230098\pi$
$419$	−4.05211	−	7.01847i	−0.197959	−	0.342874i	−0.947866	+	0.318668i	$0.896765\pi$
$420$		0			0
$421$	−0.936528	+	1.62211i	−0.0456436	+	0.0790570i	−0.887945	−	0.459950i	$-0.847867\pi$
$421$	−0.936528	+	1.62211i	−0.0456436	+	0.0790570i	0.842301	+	0.539007i	$0.181201\pi$
$422$		0			0
$423$	−0.960092	−	22.4901i	−0.0466813	−	1.09351i
$424$		0			0
$425$	1.37205	−	2.37646i	0.0665541	−	0.115275i
$426$		0			0
$427$	13.0838	+	22.6617i	0.633167	+	1.09668i
$428$		0			0
$429$	−8.31938	+	2.42050i	−0.401663	+	0.116863i
$430$		0			0
$431$	37.0364			1.78398			0.891990	−	0.452054i	$-0.149309\pi$
$431$	37.0364			1.78398			0.891990	+	0.452054i	$0.149309\pi$
$432$		0			0
$433$	−30.8710			−1.48357			−0.741784	−	0.670639i	$-0.766020\pi$
$433$	−30.8710			−1.48357			−0.741784	+	0.670639i	$0.766020\pi$
$434$		0			0
$435$	−10.5097	+	3.05777i	−0.503901	+	0.146609i
$436$		0			0
$437$	1.45646	+	2.52266i	0.0696718	+	0.120675i
$438$		0			0
$439$	−4.35581	+	7.54448i	−0.207891	+	0.360078i	−0.951050	−	0.309037i	$-0.899993\pi$
$439$	−4.35581	+	7.54448i	−0.207891	+	0.360078i	0.743159	+	0.669115i	$0.233327\pi$
$440$		0			0
$441$	−7.29844	−	3.80833i	−0.347545	−	0.181349i
$442$		0			0
$443$	1.09591	−	1.89818i	0.0520684	−	0.0901851i	−0.838816	−	0.544414i	$-0.816752\pi$
$443$	1.09591	−	1.89818i	0.0520684	−	0.0901851i	0.890885	+	0.454229i	$0.150085\pi$
$444$		0			0
$445$	−1.41559	−	2.45188i	−0.0671055	−	0.116230i
$446$		0			0
$447$	23.1482	+	22.1811i	1.09487	+	1.04913i
$448$		0			0
$449$	−38.9345			−1.83743			−0.918717	−	0.394917i	$-0.870773\pi$
$449$	−38.9345			−1.83743			−0.918717	+	0.394917i	$0.870773\pi$
$450$		0			0
$451$	−4.59960			−0.216587
$452$		0			0
$453$	1.63875	−	6.68299i	0.0769953	−	0.313994i
$454$		0			0
$455$	9.46373	+	16.3917i	0.443666	+	0.768453i
$456$		0			0
$457$	17.6914	−	30.6424i	0.827570	−	1.43339i	−0.0723694	−	0.997378i	$-0.523056\pi$
$457$	17.6914	−	30.6424i	0.827570	−	1.43339i	0.899939	−	0.436015i	$-0.143611\pi$
$458$		0			0
$459$	9.41703	−	10.7066i	0.439549	−	0.499742i
$460$		0			0
$461$	19.7748	−	34.2510i	0.921005	−	1.59523i	0.123143	−	0.992389i	$-0.460703\pi$
$461$	19.7748	−	34.2510i	0.921005	−	1.59523i	0.797863	−	0.602839i	$-0.205964\pi$
$462$		0			0
$463$	−9.25261	−	16.0260i	−0.430005	−	0.744791i	0.566868	−	0.823809i	$-0.308155\pi$
$463$	−9.25261	−	16.0260i	−0.430005	−	0.744791i	−0.996873	+	0.0790179i	$0.974822\pi$
$464$		0			0
$465$	3.00000	−	12.2343i	0.139122	−	0.567352i
$466$		0			0
$467$	37.8090			1.74959			0.874797	−	0.484490i	$-0.160995\pi$
$467$	37.8090			1.74959			0.874797	+	0.484490i	$0.160995\pi$
$468$		0			0
$469$	36.9581			1.70657
$470$		0			0
$471$	1.28012	+	1.22664i	0.0589849	+	0.0565206i
$472$		0			0
$473$	3.08441	+	5.34235i	0.141821	+	0.245642i
$474$		0			0
$475$	0.412500	−	0.714470i	0.0189268	−	0.0327822i
$476$		0			0
$477$	−3.76771	+	2.39516i	−0.172512	+	0.109667i
$478$		0			0
$479$	10.8297	−	18.7576i	0.494823	−	0.857058i	−0.505160	−	0.863026i	$-0.668566\pi$
$479$	10.8297	−	18.7576i	0.494823	−	0.857058i	0.999982	+	0.00596807i	$0.00189971\pi$
$480$		0			0
$481$	6.25590	+	10.8355i	0.285245	+	0.494058i
$482$		0			0
$483$	−18.3299	+	5.33304i	−0.834040	+	0.242662i
$484$		0			0
$485$	5.31938			0.241540
$486$		0			0
$487$	34.7267			1.57361			0.786807	−	0.617199i	$-0.211732\pi$
$487$	34.7267			1.57361			0.786807	+	0.617199i	$0.211732\pi$
$488$		0			0
$489$	−34.3092	+	9.98219i	−1.55152	+	0.451410i
$490$		0			0
$491$	−15.7298	−	27.2448i	−0.709875	−	1.22954i	−0.964903	−	0.262605i	$-0.915418\pi$
$491$	−15.7298	−	27.2448i	−0.709875	−	1.22954i	0.255029	−	0.966933i	$-0.417915\pi$
$492$		0			0
$493$	−8.67049	+	15.0177i	−0.390499	+	0.676364i
$494$		0			0
$495$	−2.08868	+	1.32779i	−0.0938792	+	0.0596798i
$496$		0			0
$497$	24.3092	−	42.1048i	1.09042	−	1.88866i
$498$		0			0
$499$	−4.90005	−	8.48713i	−0.219356	−	0.379936i	0.735255	−	0.677791i	$-0.237062\pi$
$499$	−4.90005	−	8.48713i	−0.219356	−	0.379936i	−0.954611	+	0.297854i	$0.903729\pi$
$500$		0			0
$501$	23.9591	+	22.9582i	1.07042	+	1.02569i
$502$		0			0
$503$	27.8829			1.24324			0.621618	−	0.783321i	$-0.286476\pi$
$503$	27.8829			1.24324			0.621618	+	0.783321i	$0.286476\pi$
$504$		0			0
$505$	16.1269			0.717640
$506$		0			0
$507$	9.80334	−	39.9790i	0.435382	−	1.77553i
$508$		0			0
$509$	14.2232	+	24.6352i	0.630430	+	1.09194i	0.987464	+	0.157846i	$0.0504550\pi$
$509$	14.2232	+	24.6352i	0.630430	+	1.09194i	−0.357033	+	0.934092i	$0.616212\pi$
$510$		0			0
$511$	−20.9867	+	36.3500i	−0.928397	+	1.60803i
$512$		0			0
$513$	2.83118	−	3.21889i	0.125000	−	0.142117i
$514$		0			0
$515$	1.33981	−	2.32062i	0.0590392	−	0.102259i
$516$		0			0
$517$	3.09521	+	5.36106i	0.136127	+	0.235779i
$518$		0			0
$519$	5.61624	−	22.9036i	0.246526	−	1.00536i
$520$		0			0
$521$	17.1269			0.750345			0.375173	−	0.926955i	$-0.377583\pi$
$521$	17.1269			0.750345			0.375173	+	0.926955i	$0.377583\pi$
$522$		0			0
$523$	−24.8874			−1.08825			−0.544125	−	0.839004i	$-0.683138\pi$
$523$	−24.8874			−1.08825			−0.544125	+	0.839004i	$0.683138\pi$
$524$		0			0
$525$	3.90378	+	3.74069i	0.170375	+	0.163257i
$526$		0			0
$527$	−9.97854	−	17.2833i	−0.434672	−	0.752874i
$528$		0			0
$529$	5.26670	−	9.12220i	0.228987	−	0.396617i
$530$		0			0
$531$	3.84424	+	2.00592i	0.166826	+	0.0870497i
$532$		0			0
$533$	16.9028	−	29.2765i	0.732141	−	1.26810i
$534$		0			0
$535$	−8.11082	−	14.0484i	−0.350661	−	0.607363i
$536$		0			0
$537$	−3.09521	+	0.900543i	−0.133568	+	0.0388613i
$538$		0			0
$539$	2.26388			0.0975121
$540$		0			0
$541$	8.44632			0.363136			0.181568	−	0.983378i	$-0.441883\pi$
$541$	8.44632			0.363136			0.181568	+	0.983378i	$0.441883\pi$
$542$		0			0
$543$	−28.2029	+	8.20556i	−1.21030	+	0.352134i
$544$		0			0
$545$	−4.93552	−	8.54857i	−0.211414	−	0.366181i
$546$		0			0
$547$	−15.5882	+	26.9995i	−0.666503	+	1.15442i	0.312373	+	0.949960i	$0.398876\pi$
$547$	−15.5882	+	26.9995i	−0.666503	+	1.15442i	−0.978876	+	0.204457i	$0.934457\pi$
$548$		0			0
$549$	−1.07260	−	25.1257i	−0.0457775	−	1.07234i
$550$		0			0
$551$	−2.60674	+	4.51501i	−0.111051	+	0.192346i
$552$		0			0
$553$	22.0635	+	38.2151i	0.938234	+	1.62507i
$554$		0			0
$555$	2.58056	+	2.47275i	0.109539	+	0.104962i
$556$		0			0
$557$	−13.5354			−0.573514			−0.286757	−	0.958003i	$-0.592577\pi$
$557$	−13.5354			−0.573514			−0.286757	+	0.958003i	$0.592577\pi$
$558$		0			0
$559$	−45.3388			−1.91763
$560$		0			0
$561$	−0.933849	+	3.80833i	−0.0394271	+	0.160788i
$562$		0			0
$563$	15.3304	+	26.5530i	0.646098	+	1.11907i	0.984047	+	0.177910i	$0.0569335\pi$
$563$	15.3304	+	26.5530i	0.646098	+	1.11907i	−0.337949	+	0.941164i	$0.609733\pi$
$564$		0			0
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$		0			0
$567$	16.0694	+	23.0444i	0.674851	+	0.967776i
$568$		0			0
$569$	−2.46726	+	4.27341i	−0.103433	+	0.179151i	−0.913097	−	0.407743i	$-0.866316\pi$
$569$	−2.46726	+	4.27341i	−0.103433	+	0.179151i	0.809664	+	0.586894i	$0.199649\pi$
$570$		0			0
$571$	19.4717	+	33.7260i	0.814865	+	1.41139i	0.909425	+	0.415869i	$0.136522\pi$
$571$	19.4717	+	33.7260i	0.814865	+	1.41139i	−0.0945596	+	0.995519i	$0.530144\pi$
$572$		0			0
$573$	−3.87104	+	15.7865i	−0.161715	+	0.659490i
$574$		0			0
$575$	3.53081			0.147245
$576$		0			0
$577$	−0.633394			−0.0263686			−0.0131843	−	0.999913i	$-0.504197\pi$
$577$	−0.633394			−0.0263686			−0.0131843	+	0.999913i	$0.504197\pi$
$578$		0			0
$579$	−7.79404	−	7.46841i	−0.323909	−	0.310377i
$580$		0			0
$581$	6.80858	+	11.7928i	0.282467	+	0.489248i
$582$		0			0
$583$	0.613879	−	1.06327i	0.0254243	−	0.0440361i
$584$		0			0
$585$	−0.775832	−	18.1739i	−0.0320767	−	0.751397i
$586$		0			0
$587$	−1.45197	+	2.51489i	−0.0599292	+	0.103800i	−0.894433	−	0.447201i	$-0.852421\pi$
$587$	−1.45197	+	2.51489i	−0.0599292	+	0.103800i	0.834504	+	0.551002i	$0.185754\pi$
$588$		0			0
$589$	−3.00000	−	5.19615i	−0.123613	−	0.214104i
$590$		0			0
$591$	27.6717	−	8.05102i	1.13826	−	0.331175i
$592$		0			0
$593$	−36.8292			−1.51239			−0.756196	−	0.654345i	$-0.772945\pi$
$593$	−36.8292			−1.51239			−0.756196	+	0.654345i	$0.772945\pi$
$594$		0			0
$595$	8.56584			0.351165
$596$		0			0
$597$	−12.7758	+	3.71710i	−0.522880	+	0.152131i
$598$		0			0
$599$	9.54310	+	16.5291i	0.389921	+	0.675362i	0.992438	−	0.122743i	$-0.0391691\pi$
$599$	9.54310	+	16.5291i	0.389921	+	0.675362i	−0.602518	+	0.798105i	$0.705836\pi$
$600$		0			0
$601$	0.852119	−	1.47591i	0.0347587	−	0.0602038i	−0.848123	−	0.529800i	$-0.822267\pi$
$601$	0.852119	−	1.47591i	0.0347587	−	0.0602038i	0.882881	+	0.469596i	$0.155600\pi$
$602$		0			0
$603$	−31.4898	−	16.4314i	−1.28236	−	0.669138i
$604$		0			0
$605$	−5.15969	+	8.93684i	−0.209771	+	0.363334i
$606$		0			0
$607$	−11.4664	−	19.8604i	−0.465408	−	0.806111i	0.533812	−	0.845603i	$-0.320759\pi$
$607$	−11.4664	−	19.8604i	−0.465408	−	0.806111i	−0.999220	+	0.0394928i	$0.987426\pi$
$608$		0			0
$609$	−24.6695	−	23.6388i	−0.999658	−	0.957893i
$610$		0			0
$611$	−45.4975			−1.84063
$612$		0			0
$613$	5.08709			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$613$	5.08709			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$614$		0			0
$615$	2.29980	−	9.37881i	0.0927369	−	0.378190i
$616$		0			0
$617$	−7.95545	−	13.7792i	−0.320274	−	0.554731i	0.660270	−	0.751028i	$-0.270442\pi$
$617$	−7.95545	−	13.7792i	−0.320274	−	0.554731i	−0.980545	+	0.196297i	$0.937108\pi$
$618$		0			0
$619$	1.24399	−	2.15466i	0.0500003	−	0.0866031i	−0.839942	−	0.542676i	$-0.817411\pi$
$619$	1.24399	−	2.15466i	0.0500003	−	0.0866031i	0.889942	+	0.456073i	$0.150744\pi$
$620$		0			0
$621$	17.9889	+	3.60541i	0.721868	+	0.144680i
$622$		0			0
$623$	4.41885	−	7.65366i	0.177037	−	0.306638i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−0.280757	+	1.14496i	−0.0112124	+	0.0457251i
$628$		0			0
$629$	5.66237			0.225773
$630$		0			0
$631$	−8.81634			−0.350973			−0.175486	−	0.984482i	$-0.556150\pi$
$631$	−8.81634			−0.350973			−0.175486	+	0.984482i	$0.556150\pi$
$632$		0			0
$633$	−1.35313	−	1.29659i	−0.0537820	−	0.0515350i
$634$		0			0
$635$	1.45522	+	2.52051i	0.0577485	+	0.100023i
$636$		0			0
$637$	−8.31938	+	14.4096i	−0.329626	+	0.570928i
$638$		0			0
$639$	−39.4320	+	25.0672i	−1.55991	+	0.991645i
$640$		0			0
$641$	8.53174	−	14.7774i	0.336983	−	0.583672i	−0.646880	−	0.762591i	$-0.723927\pi$
$641$	8.53174	−	14.7774i	0.336983	−	0.583672i	0.983864	+	0.178919i	$0.0572601\pi$
$642$		0			0
$643$	−9.88607	−	17.1232i	−0.389869	−	0.675272i	0.602563	−	0.798071i	$-0.294146\pi$
$643$	−9.88607	−	17.1232i	−0.389869	−	0.675272i	−0.992432	+	0.122799i	$0.960813\pi$
$644$		0			0
$645$	−12.4355	+	3.61808i	−0.489648	+	0.142462i
$646$		0			0
$647$	−18.2744			−0.718441			−0.359220	−	0.933253i	$-0.616957\pi$
$647$	−18.2744			−0.718441			−0.359220	+	0.933253i	$0.616957\pi$
$648$		0			0
$649$	−1.19243			−0.0468070
$650$		0			0
$651$	37.7558	−	10.9850i	1.47977	−	0.430535i
$652$		0			0
$653$	−6.92639	−	11.9969i	−0.271051	−	0.469474i	0.698080	−	0.716019i	$-0.254038\pi$
$653$	−6.92639	−	11.9969i	−0.271051	−	0.469474i	−0.969131	+	0.246546i	$0.920704\pi$
$654$		0			0
$655$	5.00236	−	8.66434i	0.195458	−	0.338544i
$656$		0			0
$657$	34.0425	−	21.6411i	1.32813	−	0.844300i
$658$		0			0
$659$	−19.3694	+	33.5488i	−0.754524	+	1.30687i	0.191087	+	0.981573i	$0.438799\pi$
$659$	−19.3694	+	33.5488i	−0.754524	+	1.30687i	−0.945611	+	0.325301i	$0.894534\pi$
$660$		0			0
$661$	−13.8710	−	24.0253i	−0.539521	−	0.934478i	−0.998930	−	0.0462528i	$-0.985272\pi$
$661$	−13.8710	−	24.0253i	−0.539521	−	0.934478i	0.459409	−	0.888225i	$-0.348061\pi$
$662$		0			0
$663$	−20.8083	−	19.9389i	−0.808126	−	0.774363i
$664$		0			0
$665$	2.57528			0.0998651
$666$		0			0
$667$	−22.3125			−0.863943
$668$		0			0
$669$	−7.05334	+	28.7642i	−0.272698	+	1.11209i
$670$		0			0
$671$	3.45792	+	5.98930i	0.133492	+	0.231214i
$672$		0			0
$673$	22.6070	−	39.1565i	0.871436	−	1.50937i	0.0109254	−	0.999940i	$-0.496522\pi$
$673$	22.6070	−	39.1565i	0.871436	−	1.50937i	0.860511	−	0.509432i	$-0.170144\pi$
$674$		0			0
$675$	−1.66309	−	4.92282i	−0.0640124	−	0.189479i
$676$		0			0
$677$	7.28764	−	12.6226i	0.280087	−	0.485124i	−0.691319	−	0.722550i	$-0.742970\pi$
$677$	7.28764	−	12.6226i	0.280087	−	0.485124i	0.971406	+	0.237425i	$0.0763034\pi$
$678$		0			0
$679$	8.30236	+	14.3801i	0.318615	+	0.551858i
$680$		0			0
$681$	5.65969	−	23.0808i	0.216880	−	0.884457i
$682$		0			0
$683$	15.7274			0.601790			0.300895	−	0.953657i	$-0.402715\pi$
$683$	15.7274			0.601790			0.300895	+	0.953657i	$0.402715\pi$
$684$		0			0
$685$	4.68062			0.178837
$686$		0			0
$687$	15.4065	+	14.7628i	0.587794	+	0.563237i
$688$		0			0
$689$	4.51181	+	7.81468i	0.171886	+	0.297716i
$690$		0			0
$691$	−14.1362	+	24.4846i	−0.537767	+	0.931440i	0.461257	+	0.887267i	$0.347399\pi$
$691$	−14.1362	+	24.4846i	−0.537767	+	0.931440i	−0.999024	+	0.0441730i	$0.985935\pi$
$692$		0			0
$693$	−6.84944	−	3.57404i	−0.260189	−	0.135767i
$694$		0			0
$695$	−8.02160	+	13.8938i	−0.304277	+	0.527023i
$696$		0			0
$697$	−7.64955	−	13.2494i	−0.289747	−	0.501857i
$698$		0			0
$699$	16.2446	−	4.72632i	0.614427	−	0.178766i
$700$		0			0
$701$	−2.97840			−0.112493			−0.0562463	−	0.998417i	$-0.517913\pi$
$701$	−2.97840			−0.112493			−0.0562463	+	0.998417i	$0.517913\pi$
$702$		0			0
$703$	1.70236			0.0642059
$704$		0			0
$705$	−12.4791	+	3.63075i	−0.469989	+	0.136742i
$706$		0			0
$707$	25.1706	+	43.5967i	0.946636	+	1.63962i
$708$		0			0
$709$	7.35011	−	12.7308i	0.276039	−	0.478114i	−0.694358	−	0.719630i	$-0.744311\pi$
$709$	7.35011	−	12.7308i	0.276039	−	0.478114i	0.970397	+	0.241516i	$0.0776448\pi$
$710$		0			0
$711$	−1.80875	−	42.3700i	−0.0678336	−	1.58900i
$712$		0			0
$713$	12.8393	−	22.2383i	0.480836	−	0.832832i
$714$		0			0
$715$	2.50118	+	4.33217i	0.0935388	+	0.162014i
$716$		0			0
$717$	29.0851	+	27.8699i	1.08620	+	1.04082i
$718$		0			0
$719$	17.8848			0.666992			0.333496	−	0.942752i	$-0.391772\pi$
$719$	17.8848			0.666992			0.333496	+	0.942752i	$0.391772\pi$
$720$		0			0
$721$	8.36459			0.311514
$722$		0			0
$723$	−11.6188	+	47.3826i	−0.432108	+	1.76218i
$724$		0			0
$725$	3.15969	+	5.47274i	0.117348	+	0.203252i
$726$		0			0
$727$	9.94251	−	17.2209i	0.368747	−	0.638689i	−0.620623	−	0.784109i	$-0.713120\pi$
$727$	9.94251	−	17.2209i	0.368747	−	0.638689i	0.989370	+	0.145420i	$0.0464534\pi$
$728$		0			0
$729$	−3.44632	−	26.7791i	−0.127642	−	0.991820i
$730$		0			0
$731$	−10.2593	+	17.7696i	−0.379454	+	0.657233i
$732$		0			0
$733$	8.38285	+	14.5195i	0.309628	+	0.536291i	0.978281	−	0.207284i	$-0.0664623\pi$
$733$	8.38285	+	14.5195i	0.309628	+	0.536291i	−0.668653	+	0.743574i	$0.733129\pi$
$734$		0			0
$735$	−1.13194	+	4.61616i	−0.0417522	+	0.170270i
$736$		0			0
$737$	9.76771			0.359798
$738$		0			0
$739$	−40.1188			−1.47579			−0.737897	−	0.674914i	$-0.764181\pi$
$739$	−40.1188			−1.47579			−0.737897	+	0.674914i	$0.764181\pi$
$740$		0			0
$741$	−6.25590	−	5.99454i	−0.229816	−	0.220215i
$742$		0			0
$743$	13.8294	+	23.9532i	0.507351	+	0.878757i	0.999964	+	0.00850866i	$0.00270842\pi$
$743$	13.8294	+	23.9532i	0.507351	+	0.878757i	−0.492613	+	0.870248i	$0.663958\pi$
$744$		0			0
$745$	9.25490	−	16.0300i	0.339073	−	0.587292i
$746$		0			0
$747$	−0.558164	−	13.0750i	−0.0204222	−	0.478389i
$748$		0			0
$749$	25.3184	−	43.8527i	0.925113	−	1.60234i
$750$		0			0
$751$	7.53055	+	13.0433i	0.274794	+	0.475957i	0.970083	−	0.242773i	$-0.0780571\pi$
$751$	7.53055	+	13.0433i	0.274794	+	0.475957i	−0.695289	+	0.718730i	$0.744724\pi$
$752$		0			0
$753$	32.4990	−	9.45550i	1.18433	−	0.344578i
$754$		0			0
$755$	−3.97274			−0.144583
$756$		0			0
$757$	−4.57528			−0.166291			−0.0831457	−	0.996537i	$-0.526497\pi$
$757$	−4.57528			−0.166291			−0.0831457	+	0.996537i	$0.526497\pi$
$758$		0			0
$759$	−4.84444	+	1.40948i	−0.175842	+	0.0511608i
$760$		0			0
$761$	−17.7350	−	30.7179i	−0.642892	−	1.11352i	−0.984784	−	0.173782i	$-0.944401\pi$
$761$	−17.7350	−	30.7179i	−0.642892	−	1.11352i	0.341892	−	0.939739i	$-0.388932\pi$
$762$		0			0
$763$	15.4065	−	26.6848i	0.557752	−	0.966056i
$764$		0			0
$765$	−7.29844	−	3.80833i	−0.263876	−	0.137690i
$766$		0			0
$767$	4.38199	−	7.58983i	0.158224	−	0.274053i
$768$		0			0
$769$	−9.54254	−	16.5282i	−0.344113	−	0.596021i	0.641079	−	0.767474i	$-0.278487\pi$
$769$	−9.54254	−	16.5282i	−0.344113	−	0.596021i	−0.985192	+	0.171454i	$0.945154\pi$
$770$		0			0
$771$	−22.8805	−	21.9246i	−0.824021	−	0.789595i
$772$		0			0
$773$	15.7893			0.567902			0.283951	−	0.958839i	$-0.408355\pi$
$773$	15.7893			0.567902			0.283951	+	0.958839i	$0.408355\pi$
$774$		0			0
$775$	−7.27273			−0.261244
$776$		0			0
$777$	−2.65701	+	10.8355i	−0.0953197	+	0.388723i
$778$		0			0
$779$	−2.29980	−	3.98337i	−0.0823989	−	0.142719i
$780$		0			0
$781$	6.42472	−	11.1279i	0.229895	−	0.398189i
$782$		0			0
$783$	10.5097	+	31.1091i	0.375586	+	1.11175i
$784$		0			0
$785$	0.511807	−	0.886476i	0.0182672	−	0.0316397i
$786$		0			0
$787$	−1.80143	−	3.12017i	−0.0642140	−	0.111222i	0.832131	−	0.554579i	$-0.187121\pi$
$787$	−1.80143	−	3.12017i	−0.0642140	−	0.111222i	−0.896345	+	0.443357i	$0.853787\pi$
$788$		0			0
$789$	5.40646	−	22.0481i	0.192475	−	0.784933i
$790$		0			0
$791$	−18.7293			−0.665938
$792$		0			0
$793$	−50.8292			−1.80500
$794$		0			0
$795$	1.86112	+	1.78336i	0.0660071	+	0.0632494i
$796$		0			0
$797$	17.9264	+	31.0494i	0.634985	+	1.09983i	0.986518	+	0.163651i	$0.0523272\pi$
$797$	17.9264	+	31.0494i	0.634985	+	1.09983i	−0.351533	+	0.936176i	$0.614339\pi$
$798$		0			0
$799$	−10.2952	+	17.8318i	−0.364219	+	0.630845i
$800$		0			0
$801$	−7.16781	+	4.55663i	−0.253262	+	0.161001i
$802$		0			0
$803$	−5.54660	+	9.60700i	−0.195735	+	0.339024i
$804$		0			0
$805$	5.51080	+	9.54499i	0.194230	+	0.336417i
$806$		0			0
$807$	7.07795	−	2.05931i	0.249156	−	0.0724912i
$808$		0			0
$809$	−14.8076			−0.520606			−0.260303	−	0.965527i	$-0.583823\pi$
$809$	−14.8076			−0.520606			−0.260303	+	0.965527i	$0.583823\pi$
$810$		0			0
$811$	46.6794			1.63914			0.819568	−	0.572982i	$-0.194214\pi$
$811$	46.6794			1.63914			0.819568	+	0.572982i	$0.194214\pi$
$812$		0			0
$813$	48.1168	−	13.9995i	1.68753	−	0.490983i
$814$		0			0
$815$	10.3149	+	17.8659i	0.361315	+	0.625817i
$816$		0			0
$817$	−3.08441	+	5.34235i	−0.107910	+	0.186905i
$818$		0			0
$819$	47.9193	−	30.4627i	1.67444	−	1.06445i
$820$		0			0
$821$	3.38386	−	5.86101i	0.118097	−	0.204551i	−0.800916	−	0.598776i	$-0.795654\pi$
$821$	3.38386	−	5.86101i	0.118097	−	0.204551i	0.919014	+	0.394226i	$0.128987\pi$
$822$		0			0
$823$	−6.23326	−	10.7963i	−0.217278	−	0.376336i	0.736697	−	0.676223i	$-0.236384\pi$
$823$	−6.23326	−	10.7963i	−0.217278	−	0.376336i	−0.953975	+	0.299887i	$0.903051\pi$
$824$		0			0
$825$	1.03174	+	0.988632i	0.0359204	+	0.0344197i
$826$		0			0
$827$	4.91732			0.170992			0.0854960	−	0.996339i	$-0.472753\pi$
$827$	4.91732			0.170992			0.0854960	+	0.996339i	$0.472753\pi$
$828$		0			0
$829$	35.0216			1.21635			0.608175	−	0.793803i	$-0.291902\pi$
$829$	35.0216			1.21635			0.608175	+	0.793803i	$0.291902\pi$
$830$		0			0
$831$	13.3309	−	54.3647i	0.462444	−	1.88589i
$832$		0			0
$833$	3.76503	+	6.52123i	0.130451	+	0.225947i
$834$		0			0
$835$	9.57913	−	16.5915i	0.331499	−	0.574174i
$836$		0			0
$837$	−37.0533	−	7.42641i	−1.28075	−	0.256694i
$838$		0			0
$839$	5.49749	−	9.52192i	0.189794	−	0.328733i	−0.755387	−	0.655279i	$-0.772551\pi$
$839$	5.49749	−	9.52192i	0.189794	−	0.328733i	0.945182	+	0.326545i	$0.105885\pi$
$840$		0			0
$841$	−5.46726	−	9.46957i	−0.188526	−	0.326537i
$842$		0			0
$843$	5.10792	−	20.8306i	0.175926	−	0.717444i
$844$		0			0
$845$	−23.7657			−0.817565
$846$		0			0
$847$	−32.2125			−1.10683
$848$		0			0
$849$	12.1577	+	11.6497i	0.417250	+	0.399818i
$850$		0			0
$851$	3.64286	+	6.30962i	0.124876	+	0.216291i
$852$		0			0
$853$	14.9662	−	25.9223i	0.512435	−	0.887563i	−0.487461	−	0.873145i	$-0.662077\pi$
$853$	14.9662	−	25.9223i	0.512435	−	0.887563i	0.999896	−	0.0144183i	$-0.00458964\pi$
$854$		0			0
$855$	−2.19424	−	1.14496i	−0.0750415	−	0.0391566i
$856$		0			0
$857$	−13.8393	+	23.9704i	−0.472742	+	0.818813i	−0.999513	−	0.0311943i	$-0.990069\pi$
$857$	−13.8393	+	23.9704i	−0.472742	+	0.818813i	0.526772	+	0.850007i	$0.323402\pi$
$858$		0			0
$859$	−3.11831	−	5.40107i	−0.106395	−	0.184282i	0.807912	−	0.589303i	$-0.200598\pi$
$859$	−3.11831	−	5.40107i	−0.106395	−	0.184282i	−0.914307	+	0.405021i	$0.867264\pi$
$860$		0			0
$861$	28.9436	−	8.42108i	0.986397	−	0.286990i
$862$		0			0
$863$	32.8199			1.11720			0.558601	−	0.829437i	$-0.311338\pi$
$863$	32.8199			1.11720			0.558601	+	0.829437i	$0.311338\pi$
$864$		0			0
$865$	−13.6151			−0.462929
$866$		0			0
$867$	15.7494	−	4.58223i	0.534876	−	0.155621i
$868$		0			0
$869$	5.83118	+	10.0999i	0.197809	+	0.342616i
$870$		0			0
$871$	−35.8947	+	62.1715i	−1.21625	+	2.10660i
$872$		0			0
$873$	−0.680624	−	15.9436i	−0.0230356	−	0.539609i
$874$		0			0
$875$	1.56078	−	2.70334i	0.0527639	−	0.0913897i
$876$		0			0
$877$	4.86292	+	8.42282i	0.164209	+	0.284419i	0.936374	−	0.351003i	$-0.114159\pi$
$877$	4.86292	+	8.42282i	0.164209	+	0.284419i	−0.772165	+	0.635422i	$0.780826\pi$
$878$		0			0
$879$	−16.5253	−	15.8349i	−0.557386	−	0.534099i
$880$		0			0
$881$	−4.38285			−0.147662			−0.0738310	−	0.997271i	$-0.523523\pi$
$881$	−4.38285			−0.147662			−0.0738310	+	0.997271i	$0.523523\pi$
$882$		0			0
$883$	−20.5513			−0.691605			−0.345803	−	0.938307i	$-0.612393\pi$
$883$	−20.5513			−0.691605			−0.345803	+	0.938307i	$0.612393\pi$
$884$		0			0
$885$	0.596216	−	2.43143i	0.0200416	−	0.0817315i
$886$		0			0
$887$	−5.51717	−	9.55603i	−0.185249	−	0.320860i	0.758412	−	0.651776i	$-0.225976\pi$
$887$	−5.51717	−	9.55603i	−0.185249	−	0.320860i	−0.943660	+	0.330916i	$0.892642\pi$
$888$		0			0
$889$	−4.54254	+	7.86790i	−0.152352	+	0.263881i
$890$		0			0
$891$	4.24700	+	6.09045i	0.142280	+	0.204038i
$892$		0			0
$893$	−3.09521	+	5.36106i	−0.103577	+	0.179401i
$894$		0			0
$895$	0.930560	+	1.61178i	0.0311052	+	0.0538757i
$896$		0			0
$897$	8.83118	−	36.0144i	0.294865	−	1.20249i
$898$		0			0
$899$	45.9591			1.53282
$900$		0			0
$901$	4.08374			0.136049
$902$		0			0
$903$	−29.1900	−	27.9705i	−0.971382	−	0.930799i
$904$		0			0
$905$	8.47906	+	14.6862i	0.281854	+	0.488185i
$906$		0			0
$907$	−27.1373	+	47.0033i	−0.901081	+	1.56072i	−0.0749871	+	0.997185i	$0.523892\pi$
$907$	−27.1373	+	47.0033i	−0.901081	+	1.56072i	−0.826094	+	0.563533i	$0.809442\pi$
$908$		0			0
$909$	−2.06347	−	48.3368i	−0.0684411	−	1.60323i
$910$		0			0
$911$	−1.46506	+	2.53756i	−0.0485396	+	0.0840731i	−0.889274	−	0.457374i	$-0.848790\pi$
$911$	−1.46506	+	2.53756i	−0.0485396	+	0.0840731i	0.840735	+	0.541447i	$0.182123\pi$
$912$		0			0
$913$	1.79945	+	3.11673i	0.0595530	+	0.103149i
$914$		0			0
$915$	−13.9414	+	4.05622i	−0.460889	+	0.134095i
$916$		0			0
$917$	31.2303			1.03131
$918$		0			0
$919$	12.8955			0.425382			0.212691	−	0.977119i	$-0.431777\pi$
$919$	12.8955			0.425382			0.212691	+	0.977119i	$0.431777\pi$
$920$		0			0
$921$	−49.8072	+	14.4913i	−1.64120	+	0.477504i
$922$		0			0
$923$	47.2196	+	81.7867i	1.55425	+	2.69204i
$924$		0			0
$925$	1.03174	−	1.78702i	0.0339233	−	0.0587568i
$926$		0			0
$927$	−7.12697	−	3.71885i	−0.234080	−	0.122143i
$928$		0			0
$929$	−13.7022	+	23.7329i	−0.449555	+	0.778653i	−0.998357	−	0.0572998i	$-0.981751\pi$
$929$	−13.7022	+	23.7329i	−0.449555	+	0.778653i	0.548802	+	0.835953i	$0.315084\pi$
$930$		0			0
$931$	1.13194	+	1.96058i	0.0370978	+	0.0642553i
$932$		0			0
$933$	27.8629	+	26.6988i	0.912191	+	0.874081i
$934$		0			0
$935$	2.26388			0.0740367
$936$		0			0
$937$	2.12694			0.0694843			0.0347421	−	0.999396i	$-0.488939\pi$
$937$	2.12694			0.0694843			0.0347421	+	0.999396i	$0.488939\pi$
$938$		0			0
$939$	5.57279	−	22.7264i	0.181861	−	0.741647i
$940$		0			0
$941$	10.1597	+	17.5971i	0.331196	+	0.573649i	0.982747	−	0.184956i	$-0.0592144\pi$
$941$	10.1597	+	17.5971i	0.331196	+	0.573649i	−0.651550	+	0.758605i	$0.725881\pi$
$942$		0			0
$943$	9.84262	−	17.0479i	0.320520	−	0.555156i
$944$		0			0
$945$	10.7124	−	12.1793i	0.348473	−	0.396193i
$946$		0			0
$947$	27.2961	−	47.2782i	0.887004	−	1.53634i	0.0436046	−	0.999049i	$-0.486116\pi$
$947$	27.2961	−	47.2782i	0.887004	−	1.53634i	0.843399	−	0.537287i	$-0.180551\pi$
$948$		0			0
$949$	−40.7657	−	70.6083i	−1.32331	−	2.29204i
$950$		0			0
$951$	11.1194	−	45.3460i	0.360571	−	1.47044i
$952$		0			0
$953$	34.7873			1.12687			0.563436	−	0.826160i	$-0.309479\pi$
$953$	34.7873			1.12687			0.563436	+	0.826160i	$0.309479\pi$
$954$		0			0
$955$	9.38435			0.303670
$956$		0			0
$957$	−6.51993	−	6.24753i	−0.210759	−	0.201954i
$958$		0			0
$959$	7.30541	+	12.6533i	0.235904	+	0.408598i
$960$		0			0
$961$	−10.9463	+	18.9596i	−0.353107	+	0.611599i
$962$		0			0
$963$	−41.0689	+	26.1078i	−1.32343	+	0.841313i
$964$		0			0
$965$	−3.11614	+	5.39732i	−0.100312	+	0.173746i
$966$		0			0
$967$	4.90664	+	8.49856i	0.157787	+	0.273295i	0.934070	−	0.357089i	$-0.116231\pi$
$967$	4.90664	+	8.49856i	0.157787	+	0.273295i	−0.776283	+	0.630384i	$0.782897\pi$
$968$		0			0
$969$	−3.76503	+	1.09543i	−0.120950	+	0.0351902i
$970$		0			0
$971$	−43.0554			−1.38171			−0.690857	−	0.722992i	$-0.742766\pi$
$971$	−43.0554			−1.38171			−0.690857	+	0.722992i	$0.742766\pi$
$972$		0			0
$973$	−50.0797			−1.60548
$974$		0			0
$975$	−10.0841	+	2.93394i	−0.322950	+	0.0939614i
$976$		0			0
$977$	−22.3066	−	38.6361i	−0.713650	−	1.23608i	−0.963478	−	0.267788i	$-0.913707\pi$
$977$	−22.3066	−	38.6361i	−0.713650	−	1.23608i	0.249828	−	0.968290i	$-0.419626\pi$
$978$		0			0
$979$	1.16786	−	2.02280i	0.0373250	−	0.0646489i
$980$		0			0
$981$	−24.9909	+	15.8869i	−0.797897	+	0.507229i
$982$		0			0
$983$	14.4366	−	25.0048i	0.460455	−	0.797531i	−0.538529	−	0.842607i	$-0.681020\pi$
$983$	14.4366	−	25.0048i	0.460455	−	0.797531i	0.998984	+	0.0450762i	$0.0143531\pi$
$984$		0			0
$985$	−8.31938	−	14.4096i	−0.265077	−	0.459127i
$986$		0			0
$987$	−29.2922	−	28.0684i	−0.932381	−	0.893428i
$988$		0			0
$989$	−26.4011			−0.839506
$990$		0			0
$991$	−37.0758			−1.17775			−0.588875	−	0.808224i	$-0.700429\pi$
$991$	−37.0758			−1.17775			−0.588875	+	0.808224i	$0.700429\pi$
$992$		0			0
$993$	−5.80958	+	23.6920i	−0.184362	+	0.751844i
$994$		0			0
$995$	3.84099	+	6.65279i	0.121768	+	0.210908i
$996$		0			0
$997$	4.80757	−	8.32695i	0.152257	−	0.263717i	−0.779800	−	0.626029i	$-0.784679\pi$
$997$	4.80757	−	8.32695i	0.152257	−	0.263717i	0.932057	+	0.362312i	$0.118012\pi$
$998$		0			0
$999$	7.08130	−	8.05102i	0.224042	−	0.254723i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.q.q.961.1	yes	12
3.2	odd	2		4320.2.q.q.2881.2		12
4.3	odd	2	inner	1440.2.q.q.961.6	yes	12
9.4	even	3	inner	1440.2.q.q.481.1	✓	12
9.5	odd	6		4320.2.q.q.1441.2		12
12.11	even	2		4320.2.q.q.2881.5		12
36.23	even	6		4320.2.q.q.1441.5		12
36.31	odd	6	inner	1440.2.q.q.481.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.q.q.481.1	✓	12	9.4	even	3	inner
1440.2.q.q.481.6	yes	12	36.31	odd	6	inner
1440.2.q.q.961.1	yes	12	1.1	even	1	trivial
1440.2.q.q.961.6	yes	12	4.3	odd	2	inner
4320.2.q.q.1441.2		12	9.5	odd	6
4320.2.q.q.1441.5		12	36.23	even	6
4320.2.q.q.2881.2		12	3.2	odd	2
4320.2.q.q.2881.5		12	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66309 + 0.483872i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.56078 + 2.70334i) q^{7} +(2.53174 - 1.60944i) q^{9} +O(q^{10})\)	\(q+(-1.66309 + 0.483872i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.56078 + 2.70334i) q^{7} +(2.53174 - 1.60944i) q^{9} +(-0.412500 + 0.714470i) q^{11} +(-3.03174 - 5.25112i) q^{13} +(-1.25059 - 1.19834i) q^{15} -2.74410 q^{17} -0.824999 q^{19} +(1.28764 - 5.25112i) q^{21} +(-1.76540 - 3.05777i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-3.43174 + 3.90169i) q^{27} +(3.15969 - 5.47274i) q^{29} +(3.63637 + 6.29837i) q^{31} +(0.340312 - 1.38783i) q^{33} -3.12155 q^{35} -2.06347 q^{37} +(7.58292 + 7.26611i) q^{39} +(2.78764 + 4.82833i) q^{41} +(3.73868 - 6.47558i) q^{43} +(2.65969 + 1.38783i) q^{45} +(3.75177 - 6.49826i) q^{47} +(-1.37205 - 2.37646i) q^{49} +(4.56368 - 1.32779i) q^{51} -1.48819 q^{53} -0.824999 q^{55} +(1.37205 - 0.399194i) q^{57} +(0.722686 + 1.25173i) q^{59} +(4.19142 - 7.25976i) q^{61} +(0.399409 + 9.35614i) q^{63} +(3.03174 - 5.25112i) q^{65} +(-5.91983 - 10.2534i) q^{67} +(4.41559 + 4.23111i) q^{69} -15.5751 q^{71} +13.4463 q^{73} +(0.412500 - 1.68221i) q^{75} +(-1.28764 - 2.23026i) q^{77} +(7.06811 - 12.2423i) q^{79} +(3.81938 - 8.14938i) q^{81} +(2.18115 - 3.77786i) q^{83} +(-1.37205 - 2.37646i) q^{85} +(-2.60674 + 10.6305i) q^{87} -2.83118 q^{89} +18.9275 q^{91} +(-9.09521 - 8.71522i) q^{93} +(-0.412500 - 0.714470i) q^{95} +(2.65969 - 4.60671i) q^{97} +(0.105560 + 2.47275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} - 2 q^{9}+O(q^{10}) \) 12 * q + 6 * q^5 - 2 * q^9	\( 12 q + 6 q^{5} - 2 q^{9} - 4 q^{13} - 28 q^{17} - 12 q^{21} - 6 q^{25} + 8 q^{29} + 34 q^{33} + 40 q^{37} + 6 q^{41} + 2 q^{45} - 14 q^{49} - 8 q^{53} + 14 q^{57} - 12 q^{61} + 4 q^{65} + 28 q^{69} - 28 q^{73} + 12 q^{77} - 14 q^{81} - 14 q^{85} + 16 q^{89} - 12 q^{93} + 2 q^{97}+O(q^{100}) \) 12 * q + 6 * q^5 - 2 * q^9 - 4 * q^13 - 28 * q^17 - 12 * q^21 - 6 * q^25 + 8 * q^29 + 34 * q^33 + 40 * q^37 + 6 * q^41 + 2 * q^45 - 14 * q^49 - 8 * q^53 + 14 * q^57 - 12 * q^61 + 4 * q^65 + 28 * q^69 - 28 * q^73 + 12 * q^77 - 14 * q^81 - 14 * q^85 + 16 * q^89 - 12 * q^93 + 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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