LMFDB - Embedded newform 1386.2.bu.a.827.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			827.3
Character	$\chi$	$=$	1386.827
Dual form			1386.2.bu.a.1205.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.17923 + 0.708075i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.17923 + 0.708075i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +2.29138i q^{10} +(-0.675973 - 3.24701i) q^{11} +(3.85486 + 1.25252i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.654006 - 2.01282i) q^{17} +(-2.04736 - 2.81796i) q^{19} +(2.17923 + 0.708075i) q^{20} +(-3.29698 - 0.360492i) q^{22} +4.13903i q^{23} +(0.202590 - 0.147190i) q^{25} +(2.38244 - 3.27914i) q^{26} +(-0.951057 + 0.309017i) q^{28} +(-5.33058 - 3.87289i) q^{29} +(-0.408754 + 1.25802i) q^{31} +1.00000 q^{32} -2.11641 q^{34} +(-0.708075 + 2.17923i) q^{35} +(-6.69252 - 4.86240i) q^{37} +(-3.31271 + 1.07636i) q^{38} +(1.34684 - 1.85376i) q^{40} +(-8.63531 + 6.27392i) q^{41} +6.09215i q^{43} +(-1.36167 + 3.02421i) q^{44} +(3.93645 + 1.27903i) q^{46} +(-4.08598 - 5.62387i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-0.0773823 - 0.238158i) q^{50} +(-2.38244 - 3.27914i) q^{52} +(-8.58958 - 2.79092i) q^{53} +(3.77223 + 6.59734i) q^{55} +1.00000i q^{56} +(-5.33058 + 3.87289i) q^{58} +(-1.63244 + 2.24686i) q^{59} +(4.23807 - 1.37703i) q^{61} +(1.07013 + 0.777497i) q^{62} +(0.309017 - 0.951057i) q^{64} -9.28751 q^{65} -1.32097 q^{67} +(-0.654006 + 2.01282i) q^{68} +(1.85376 + 1.34684i) q^{70} +(-9.93582 + 3.22834i) q^{71} +(5.47303 - 7.53298i) q^{73} +(-6.69252 + 4.86240i) q^{74} +3.48318i q^{76} +(-3.02421 - 1.36167i) q^{77} +(-14.1766 - 4.60625i) q^{79} +(-1.34684 - 1.85376i) q^{80} +(3.29839 + 10.1514i) q^{82} +(2.27937 + 7.01519i) q^{83} +(2.85046 + 3.92332i) q^{85} +(5.79398 + 1.88258i) q^{86} +(2.45542 + 2.22956i) q^{88} -11.2426i q^{89} +(3.27914 - 2.38244i) q^{91} +(2.43286 - 3.34855i) q^{92} +(-6.61126 + 2.14813i) q^{94} +(6.45700 + 4.69129i) q^{95} +(-3.69989 + 11.3871i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−2.17923	+	0.708075i	−0.974581	+	0.316661i	−0.752664	−	0.658405i	$-0.771232\pi$
$5$	−2.17923	+	0.708075i	−0.974581	+	0.316661i	−0.221917	+	0.975065i	$0.571232\pi$
$6$		0			0
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$			2.29138i			0.724597i
$11$	−0.675973	−	3.24701i	−0.203814	−	0.979010i
$11$	−0.675973	−	3.24701i	−0.203814	−	0.979010i
$12$		0			0
$13$	3.85486	+	1.25252i	1.06915	+	0.347387i	0.790155	−	0.612907i	$-0.210000\pi$
$13$	3.85486	+	1.25252i	1.06915	+	0.347387i	0.278991	+	0.960294i	$0.410000\pi$
$14$	−0.587785	−	0.809017i	−0.157092	−	0.216219i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.654006	−	2.01282i	−0.158620	−	0.488182i	0.839890	−	0.542757i	$-0.182619\pi$
$17$	−0.654006	−	2.01282i	−0.158620	−	0.488182i	−0.998510	+	0.0545753i	$0.982619\pi$
$18$		0			0
$19$	−2.04736	−	2.81796i	−0.469698	−	0.646483i	0.506787	−	0.862071i	$-0.330833\pi$
$19$	−2.04736	−	2.81796i	−0.469698	−	0.646483i	−0.976484	+	0.215588i	$0.930833\pi$
$20$	2.17923	+	0.708075i	0.487291	+	0.158330i
$21$		0			0
$22$	−3.29698	−	0.360492i	−0.702917	−	0.0768571i
$23$			4.13903i			0.863047i	0.902102	+	0.431524i	$0.142024\pi$
$23$			4.13903i			0.863047i	−0.902102	+	0.431524i	$0.857976\pi$
$24$		0			0
$25$	0.202590	−	0.147190i	0.0405179	−	0.0294380i
$26$	2.38244	−	3.27914i	0.467234	−	0.643093i
$27$		0			0
$28$	−0.951057	+	0.309017i	−0.179733	+	0.0583987i
$29$	−5.33058	−	3.87289i	−0.989863	−	0.719178i	−0.0299723	−	0.999551i	$-0.509542\pi$
$29$	−5.33058	−	3.87289i	−0.989863	−	0.719178i	−0.959891	+	0.280373i	$0.909542\pi$
$30$		0			0
$31$	−0.408754	+	1.25802i	−0.0734145	+	0.225946i	−0.981030	−	0.193856i	$-0.937901\pi$
$31$	−0.408754	+	1.25802i	−0.0734145	+	0.225946i	0.907616	+	0.419802i	$0.137901\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.11641			−0.362961
$35$	−0.708075	+	2.17923i	−0.119686	+	0.368357i
$36$		0			0
$37$	−6.69252	−	4.86240i	−1.10024	−	0.799374i	−0.119145	−	0.992877i	$-0.538015\pi$
$37$	−6.69252	−	4.86240i	−1.10024	−	0.799374i	−0.981100	+	0.193503i	$0.938015\pi$
$38$	−3.31271	+	1.07636i	−0.537392	+	0.174609i
$39$		0			0
$40$	1.34684	−	1.85376i	0.212954	−	0.293106i
$41$	−8.63531	+	6.27392i	−1.34861	+	0.979821i	−0.349529	+	0.936926i	$0.613658\pi$
$41$	−8.63531	+	6.27392i	−1.34861	+	0.979821i	−0.999080	+	0.0428955i	$0.986342\pi$
$42$		0			0
$43$			6.09215i			0.929044i	0.885562	+	0.464522i	$0.153774\pi$
$43$			6.09215i			0.929044i	−0.885562	+	0.464522i	$0.846226\pi$
$44$	−1.36167	+	3.02421i	−0.205279	+	0.455917i
$45$		0			0
$46$	3.93645	+	1.27903i	0.580398	+	0.188583i
$47$	−4.08598	−	5.62387i	−0.596002	−	0.820326i	0.399333	−	0.916806i	$-0.369242\pi$
$47$	−4.08598	−	5.62387i	−0.596002	−	0.820326i	−0.995335	+	0.0964797i	$0.969242\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$	−0.0773823	−	0.238158i	−0.0109435	−	0.0336807i
$51$		0			0
$52$	−2.38244	−	3.27914i	−0.330384	−	0.454735i
$53$	−8.58958	−	2.79092i	−1.17987	−	0.383363i	−0.347551	−	0.937661i	$-0.612987\pi$
$53$	−8.58958	−	2.79092i	−1.17987	−	0.383363i	−0.832318	+	0.554298i	$0.812987\pi$
$54$		0			0
$55$	3.77223	+	6.59734i	0.508647	+	0.889585i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−5.33058	+	3.87289i	−0.699939	+	0.508536i
$59$	−1.63244	+	2.24686i	−0.212526	+	0.292516i	−0.901949	−	0.431842i	$-0.857864\pi$
$59$	−1.63244	+	2.24686i	−0.212526	+	0.292516i	0.689424	+	0.724358i	$0.257864\pi$
$60$		0			0
$61$	4.23807	−	1.37703i	0.542629	−	0.176311i	−0.0248615	−	0.999691i	$-0.507914\pi$
$61$	4.23807	−	1.37703i	0.542629	−	0.176311i	0.567490	+	0.823380i	$0.307914\pi$
$62$	1.07013	+	0.777497i	0.135907	+	0.0987422i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−9.28751			−1.15197
$66$		0			0
$67$	−1.32097			−0.161382			−0.0806911	−	0.996739i	$-0.525713\pi$
$67$	−1.32097			−0.161382			−0.0806911	+	0.996739i	$0.525713\pi$
$68$	−0.654006	+	2.01282i	−0.0793099	+	0.244091i
$69$		0			0
$70$	1.85376	+	1.34684i	0.221567	+	0.160978i
$71$	−9.93582	+	3.22834i	−1.17916	+	0.383134i	−0.832056	−	0.554691i	$-0.812836\pi$
$71$	−9.93582	+	3.22834i	−1.17916	+	0.383134i	−0.347108	+	0.937825i	$0.612836\pi$
$72$		0			0
$73$	5.47303	−	7.53298i	0.640569	−	0.881668i	−0.358076	−	0.933692i	$-0.616567\pi$
$73$	5.47303	−	7.53298i	0.640569	−	0.881668i	0.998646	+	0.0520241i	$0.0165673\pi$
$74$	−6.69252	+	4.86240i	−0.777990	+	0.565243i
$75$		0			0
$76$			3.48318i			0.399549i
$77$	−3.02421	−	1.36167i	−0.344641	−	0.155177i
$78$		0			0
$79$	−14.1766	−	4.60625i	−1.59499	−	0.518243i	−0.629128	−	0.777302i	$-0.716588\pi$
$79$	−14.1766	−	4.60625i	−1.59499	−	0.518243i	−0.965862	+	0.259059i	$0.916588\pi$
$80$	−1.34684	−	1.85376i	−0.150581	−	0.207257i
$81$		0			0
$82$	3.29839	+	10.1514i	0.364247	+	1.12104i
$83$	2.27937	+	7.01519i	0.250194	+	0.770017i	0.994739	+	0.102445i	$0.0326665\pi$
$83$	2.27937	+	7.01519i	0.250194	+	0.770017i	−0.744545	+	0.667572i	$0.767334\pi$
$84$		0			0
$85$	2.85046	+	3.92332i	0.309176	+	0.425544i
$86$	5.79398	+	1.88258i	0.624781	+	0.203004i
$87$		0			0
$88$	2.45542	+	2.22956i	0.261748	+	0.237672i
$89$		−	11.2426i		−	1.19172i	−0.803089	−	0.595859i	$-0.796812\pi$
$89$		−	11.2426i		−	1.19172i	0.803089	−	0.595859i	$-0.203188\pi$
$90$		0			0
$91$	3.27914	−	2.38244i	0.343747	−	0.249747i
$92$	2.43286	−	3.34855i	0.253643	−	0.349110i
$93$		0			0
$94$	−6.61126	+	2.14813i	−0.681899	+	0.221563i
$95$	6.45700	+	4.69129i	0.662474	+	0.481316i
$96$		0			0
$97$	−3.69989	+	11.3871i	−0.375667	+	1.15618i	0.567361	+	0.823469i	$0.307964\pi$
$97$	−3.69989	+	11.3871i	−0.375667	+	1.15618i	−0.943028	+	0.332714i	$0.892036\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	−0.250415			−0.0250415
$101$	3.33191	−	10.2546i	0.331537	−	1.02037i	−0.636865	−	0.770975i	$-0.719769\pi$
$101$	3.33191	−	10.2546i	0.331537	−	1.02037i	0.968403	−	0.249392i	$-0.0802307\pi$
$102$		0			0
$103$	5.36015	+	3.89438i	0.528151	+	0.383724i	0.819666	−	0.572842i	$-0.194159\pi$
$103$	5.36015	+	3.89438i	0.528151	+	0.383724i	−0.291514	+	0.956566i	$0.594159\pi$
$104$	−3.85486	+	1.25252i	−0.378000	+	0.122820i
$105$		0			0
$106$	−5.30865	+	7.30673i	−0.515622	+	0.709693i
$107$	9.92430	−	7.21042i	0.959418	−	0.697058i	0.00640247	−	0.999980i	$-0.497962\pi$
$107$	9.92430	−	7.21042i	0.959418	−	0.697058i	0.953015	+	0.302922i	$0.0979620\pi$
$108$		0			0
$109$			4.32675i			0.414428i	0.978296	+	0.207214i	$0.0664396\pi$
$109$			4.32675i			0.414428i	−0.978296	+	0.207214i	$0.933560\pi$
$110$	7.44012	−	1.54891i	0.709388	−	0.147683i
$111$		0			0
$112$	0.951057	+	0.309017i	0.0898664	+	0.0291994i
$113$	3.08740	+	4.24944i	0.290438	+	0.399754i	0.929156	−	0.369687i	$-0.120535\pi$
$113$	3.08740	+	4.24944i	0.290438	+	0.399754i	−0.638718	+	0.769441i	$0.720535\pi$
$114$		0			0
$115$	−2.93074	−	9.01990i	−0.273293	−	0.841110i
$116$	2.03610	+	6.26647i	0.189047	+	0.581827i
$117$		0			0
$118$	1.63244	+	2.24686i	0.150278	+	0.206840i
$119$	−2.01282	−	0.654006i	−0.184515	−	0.0599526i
$120$		0			0
$121$	−10.0861	+	4.38978i	−0.916920	+	0.399071i
$122$		−	4.45617i		−	0.403442i
$123$		0			0
$124$	1.07013	−	0.777497i	0.0961008	−	0.0698213i
$125$	6.39692	−	8.80461i	0.572158	−	0.787508i
$126$		0			0
$127$	11.9435	−	3.88067i	1.05981	−	0.344354i	0.273300	−	0.961929i	$-0.411885\pi$
$127$	11.9435	−	3.88067i	1.05981	−	0.344354i	0.786512	+	0.617575i	$0.211885\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	−2.87000	+	8.83295i	−0.251716	+	0.774701i
$131$	0.118253			0.0103318			0.00516590	−	0.999987i	$-0.498356\pi$
$131$	0.118253			0.0103318			0.00516590	+	0.999987i	$0.498356\pi$
$132$		0			0
$133$	−3.48318			−0.302030
$134$	−0.408202	+	1.25632i	−0.0352633	+	0.108529i
$135$		0			0
$136$	1.71221	+	1.24399i	0.146821	+	0.106672i
$137$	−17.0948	+	5.55445i	−1.46051	+	0.474548i	−0.928226	−	0.372018i	$-0.878666\pi$
$137$	−17.0948	+	5.55445i	−1.46051	+	0.474548i	−0.532284	+	0.846566i	$0.678666\pi$
$138$		0			0
$139$	12.8865	−	17.7367i	1.09302	−	1.50441i	0.248688	−	0.968584i	$-0.420001\pi$
$139$	12.8865	−	17.7367i	1.09302	−	1.50441i	0.844329	−	0.535825i	$-0.179999\pi$
$140$	1.85376	−	1.34684i	0.156672	−	0.113829i
$141$		0			0
$142$			10.4471i			0.876704i
$143$	1.46116	−	13.3634i	0.122188	−	1.11751i
$144$		0			0
$145$	14.3589	+	4.66547i	1.19244	+	0.387447i
$146$	−5.47303	−	7.53298i	−0.452951	−	0.623434i
$147$		0			0
$148$	2.55632	+	7.86753i	0.210128	+	0.646707i
$149$	−0.391092	−	1.20366i	−0.0320395	−	0.0986075i	0.933758	−	0.357905i	$-0.116509\pi$
$149$	−0.391092	−	1.20366i	−0.0320395	−	0.0986075i	−0.965797	+	0.259298i	$0.916509\pi$
$150$		0			0
$151$	−3.29887	−	4.54050i	−0.268458	−	0.369501i	0.653410	−	0.757004i	$-0.273338\pi$
$151$	−3.29887	−	4.54050i	−0.268458	−	0.369501i	−0.921868	+	0.387503i	$0.873338\pi$
$152$	3.31271	+	1.07636i	0.268696	+	0.0873046i
$153$		0			0
$154$	−2.22956	+	2.45542i	−0.179663	+	0.197863i
$155$		−	3.03094i		−	0.243451i
$156$		0			0
$157$	1.00081	−	0.727129i	0.0798731	−	0.0580312i	−0.547132	−	0.837046i	$-0.684280\pi$
$157$	1.00081	−	0.727129i	0.0798731	−	0.0580312i	0.627005	+	0.779015i	$0.284280\pi$
$158$	−8.76160	+	12.0593i	−0.697036	+	0.959387i
$159$		0			0
$160$	−2.17923	+	0.708075i	−0.172283	+	0.0559782i
$161$	3.34855	+	2.43286i	0.263902	+	0.191736i
$162$		0			0
$163$	−3.73087	+	11.4824i	−0.292224	+	0.899373i	0.691916	+	0.721978i	$0.256767\pi$
$163$	−3.73087	+	11.4824i	−0.292224	+	0.899373i	−0.984140	+	0.177395i	$0.943233\pi$
$164$	10.6738			0.833486
$165$		0			0
$166$	7.37621			0.572505
$167$	−1.85154	+	5.69845i	−0.143276	+	0.440959i	−0.996785	−	0.0801191i	$-0.974470\pi$
$167$	−1.85154	+	5.69845i	−0.143276	+	0.440959i	0.853509	+	0.521078i	$0.174470\pi$
$168$		0			0
$169$	2.77393	+	2.01538i	0.213380	+	0.155029i
$170$	4.61214	−	1.49858i	0.353735	−	0.114936i
$171$		0			0
$172$	3.58088	−	4.92865i	0.273039	−	0.375806i
$173$	3.00527	−	2.18346i	0.228487	−	0.166005i	−0.467652	−	0.883913i	$-0.654900\pi$
$173$	3.00527	−	2.18346i	0.228487	−	0.166005i	0.696139	+	0.717907i	$0.254900\pi$
$174$		0			0
$175$		−	0.250415i		−	0.0189296i
$176$	2.87920	−	1.64627i	0.217028	−	0.124092i
$177$		0			0
$178$	−10.6924	−	3.47417i	−0.801428	−	0.260400i
$179$	5.75870	+	7.92617i	0.430426	+	0.592430i	0.968051	−	0.250754i	$-0.0806785\pi$
$179$	5.75870	+	7.92617i	0.430426	+	0.592430i	−0.537625	+	0.843184i	$0.680679\pi$
$180$		0			0
$181$	0.590608	+	1.81770i	0.0438995	+	0.135109i	0.970604	−	0.240682i	$-0.0773711\pi$
$181$	0.590608	+	1.81770i	0.0438995	+	0.135109i	−0.926704	+	0.375791i	$0.877371\pi$
$182$	−1.25252	−	3.85486i	−0.0928430	−	0.285741i
$183$		0			0
$184$	−2.43286	−	3.34855i	−0.179353	−	0.246858i
$185$	18.0275	+	5.85749i	1.32541	+	0.430651i
$186$		0			0
$187$	−6.09356	+	3.48418i	−0.445606	+	0.254788i
$188$			6.95149i			0.506989i
$189$		0			0
$190$	6.45700	−	4.69129i	0.468440	−	0.340342i
$191$	12.5924	−	17.3320i	0.911155	−	1.25410i	−0.0556160	−	0.998452i	$-0.517712\pi$
$191$	12.5924	−	17.3320i	0.911155	−	1.25410i	0.966771	−	0.255645i	$-0.0822877\pi$
$192$		0			0
$193$	14.5186	−	4.71738i	1.04507	−	0.339564i	0.264339	−	0.964430i	$-0.414846\pi$
$193$	14.5186	−	4.71738i	1.04507	−	0.339564i	0.780732	+	0.624865i	$0.214846\pi$
$194$	9.68643	+	7.03760i	0.695445	+	0.505271i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	8.13140			0.579338			0.289669	−	0.957127i	$-0.406455\pi$
$197$	8.13140			0.579338			0.289669	+	0.957127i	$0.406455\pi$
$198$		0			0
$199$	−11.5978			−0.822145			−0.411073	−	0.911603i	$-0.634846\pi$
$199$	−11.5978			−0.822145			−0.411073	+	0.911603i	$0.634846\pi$
$200$	−0.0773823	+	0.238158i	−0.00547176	+	0.0168403i
$201$		0			0
$202$	−8.72305	−	6.33767i	−0.613752	−	0.445917i
$203$	−6.26647	+	2.03610i	−0.439820	+	0.142906i
$204$		0			0
$205$	14.3759	−	19.7868i	1.00406	−	1.38197i
$206$	5.36015	−	3.89438i	0.373459	−	0.271334i
$207$		0			0
$208$			4.05324i			0.281042i
$209$	−7.76596	+	8.55267i	−0.537183	+	0.591601i
$210$		0			0
$211$	−13.0877	−	4.25244i	−0.900992	−	0.292750i	−0.178346	−	0.983968i	$-0.557075\pi$
$211$	−13.0877	−	4.25244i	−0.900992	−	0.292750i	−0.722646	+	0.691218i	$0.757075\pi$
$212$	5.30865	+	7.30673i	0.364600	+	0.501829i
$213$		0			0
$214$	−3.79074	−	11.6667i	−0.259130	−	0.797520i
$215$	−4.31370	−	13.2762i	−0.294192	−	0.905429i
$216$		0			0
$217$	0.777497	+	1.07013i	0.0527799	+	0.0726454i
$218$	4.11499	+	1.33704i	0.278702	+	0.0905558i
$219$		0			0
$220$	0.826023	−	7.55462i	0.0556905	−	0.509332i
$221$		−	8.57832i		−	0.577040i
$222$		0			0
$223$	−9.67766	+	7.03123i	−0.648064	+	0.470846i	−0.862611	−	0.505868i	$-0.831172\pi$
$223$	−9.67766	+	7.03123i	−0.648064	+	0.470846i	0.214547	+	0.976714i	$0.431172\pi$
$224$	0.587785	−	0.809017i	0.0392731	−	0.0540547i
$225$		0			0
$226$	4.99551	−	1.62314i	0.332297	−	0.107970i
$227$	15.6477	+	11.3687i	1.03858	+	0.754570i	0.970007	−	0.243076i	$-0.0781566\pi$
$227$	15.6477	+	11.3687i	1.03858	+	0.754570i	0.0685693	+	0.997646i	$0.478157\pi$
$228$		0			0
$229$	1.54410	−	4.75224i	0.102037	−	0.314037i	−0.886987	−	0.461795i	$-0.847206\pi$
$229$	1.54410	−	4.75224i	0.102037	−	0.314037i	0.989024	+	0.147758i	$0.0472056\pi$
$230$	−9.48408			−0.625362
$231$		0			0
$232$	6.58896			0.432586
$233$	−6.71688	+	20.6724i	−0.440037	+	1.35430i	0.447799	+	0.894134i	$0.352208\pi$
$233$	−6.71688	+	20.6724i	−0.440037	+	1.35430i	−0.887836	+	0.460161i	$0.847792\pi$
$234$		0			0
$235$	12.8864	+	9.36253i	0.840617	+	0.610744i
$236$	2.64134	−	0.858224i	0.171937	−	0.0558656i
$237$		0			0
$238$	−1.24399	+	1.71221i	−0.0806361	+	0.110986i
$239$	−7.16484	+	5.20556i	−0.463455	+	0.336720i	−0.794885	−	0.606760i	$-0.792469\pi$
$239$	−7.16484	+	5.20556i	−0.463455	+	0.336720i	0.331430	+	0.943480i	$0.392469\pi$
$240$		0			0
$241$		−	12.3936i		−	0.798344i	−0.916876	−	0.399172i	$-0.869298\pi$
$241$		−	12.3936i		−	0.798344i	0.916876	−	0.399172i	$-0.130702\pi$
$242$	1.05815	+	10.9490i	0.0680203	+	0.703828i
$243$		0			0
$244$	−4.23807	−	1.37703i	−0.271314	−	0.0881554i
$245$	1.34684	+	1.85376i	0.0860463	+	0.118433i
$246$		0			0
$247$	−4.36276	−	13.4272i	−0.277596	−	0.854352i
$248$	−0.408754	−	1.25802i	−0.0259559	−	0.0798841i
$249$		0			0
$250$	−6.39692	−	8.80461i	−0.404577	−	0.556852i
$251$	15.2291	+	4.94824i	0.961253	+	0.312330i	0.747280	−	0.664509i	$-0.231359\pi$
$251$	15.2291	+	4.94824i	0.961253	+	0.312330i	0.213973	+	0.976840i	$0.431359\pi$
$252$		0			0
$253$	13.4395	−	2.79787i	0.844932	−	0.175901i
$254$		−	12.5581i		−	0.787966i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	17.5671	−	24.1791i	1.09581	−	1.50825i	0.254982	−	0.966946i	$-0.417930\pi$
$257$	17.5671	−	24.1791i	1.09581	−	1.50825i	0.840826	−	0.541305i	$-0.182070\pi$
$258$		0			0
$259$	−7.86753	+	2.55632i	−0.488865	+	0.158842i
$260$	7.51375	+	5.45906i	0.465983	+	0.338557i
$261$		0			0
$262$	0.0365421	−	0.112465i	0.00225758	−	0.00694812i
$263$	−8.44885			−0.520979			−0.260489	−	0.965477i	$-0.583884\pi$
$263$	−8.44885			−0.520979			−0.260489	+	0.965477i	$0.583884\pi$
$264$		0			0
$265$	20.6949			1.27128
$266$	−1.07636	+	3.31271i	−0.0659961	+	0.203115i
$267$		0			0
$268$	1.06869	+	0.776447i	0.0652804	+	0.0474290i
$269$	−7.12504	+	2.31507i	−0.434421	+	0.141152i	−0.518060	−	0.855344i	$-0.673346\pi$
$269$	−7.12504	+	2.31507i	−0.434421	+	0.141152i	0.0836391	+	0.996496i	$0.473346\pi$
$270$		0			0
$271$	−6.61450	+	9.10408i	−0.401802	+	0.553034i	−0.961195	−	0.275869i	$-0.911034\pi$
$271$	−6.61450	+	9.10408i	−0.401802	+	0.553034i	0.559393	+	0.828903i	$0.311034\pi$
$272$	1.71221	−	1.24399i	0.103818	−	0.0754282i
$273$		0			0
$274$			17.9746i			1.08588i
$275$	−0.614872	−	0.558314i	−0.0370782	−	0.0336676i
$276$		0			0
$277$	−28.8344	−	9.36886i	−1.73249	−	0.562920i	−0.738685	−	0.674051i	$-0.764553\pi$
$277$	−28.8344	−	9.36886i	−1.73249	−	0.562920i	−0.993806	+	0.111131i	$0.964553\pi$
$278$	−12.8865	−	17.7367i	−0.772880	−	1.06378i
$279$		0			0
$280$	−0.708075	−	2.17923i	−0.0423156	−	0.130234i
$281$	3.78772	+	11.6574i	0.225957	+	0.695423i	0.998193	+	0.0600877i	$0.0191380\pi$
$281$	3.78772	+	11.6574i	0.225957	+	0.695423i	−0.772237	+	0.635335i	$0.780862\pi$
$282$		0			0
$283$	−8.70573	−	11.9824i	−0.517502	−	0.712280i	0.467660	−	0.883908i	$-0.345097\pi$
$283$	−8.70573	−	11.9824i	−0.517502	−	0.712280i	−0.985162	+	0.171628i	$0.945097\pi$
$284$	9.93582	+	3.22834i	0.589582	+	0.191567i
$285$		0			0
$286$	−12.2579	−	5.51918i	−0.724823	−	0.326356i
$287$			10.6738i			0.630056i
$288$		0			0
$289$	10.1296	−	7.35955i	0.595856	−	0.432915i
$290$	8.87426	−	12.2144i	0.521114	−	0.717253i
$291$		0			0
$292$	−8.85554	+	2.87734i	−0.518232	+	0.168384i
$293$	2.12470	+	1.54368i	0.124126	+	0.0901829i	0.648116	−	0.761541i	$-0.275557\pi$
$293$	2.12470	+	1.54368i	0.124126	+	0.0901829i	−0.523990	+	0.851724i	$0.675557\pi$
$294$		0			0
$295$	1.96652	−	6.05231i	0.114495	−	0.352379i
$296$	8.27242			0.480824
$297$		0			0
$298$	−1.26560			−0.0733143
$299$	−5.18422	+	15.9554i	−0.299811	+	0.922724i
$300$		0			0
$301$	4.92865	+	3.58088i	0.284083	+	0.206398i
$302$	−5.33768	+	1.73432i	−0.307149	+	0.0997988i
$303$		0			0
$304$	2.04736	−	2.81796i	0.117424	−	0.161621i
$305$	−8.26068	+	6.00173i	−0.473005	+	0.343658i
$306$		0			0
$307$			4.30360i			0.245619i	0.992430	+	0.122810i	$0.0391905\pi$
$307$			4.30360i			0.245619i	−0.992430	+	0.122810i	$0.960810\pi$
$308$	1.64627	+	2.87920i	0.0938049	+	0.164058i
$309$		0			0
$310$	−2.88259	−	0.936611i	−0.163720	−	0.0531959i
$311$	−2.43258	−	3.34816i	−0.137939	−	0.189857i	0.734459	−	0.678653i	$-0.237436\pi$
$311$	−2.43258	−	3.34816i	−0.137939	−	0.189857i	−0.872398	+	0.488796i	$0.837436\pi$
$312$		0			0
$313$	−9.17282	−	28.2310i	−0.518478	−	1.59571i	−0.776863	−	0.629670i	$-0.783190\pi$
$313$	−9.17282	−	28.2310i	−0.518478	−	1.59571i	0.258384	−	0.966042i	$-0.416810\pi$
$314$	−0.382274	−	1.17652i	−0.0215730	−	0.0663948i
$315$		0			0
$316$	8.76160	+	12.0593i	0.492879	+	0.678389i
$317$	0.751836	+	0.244286i	0.0422273	+	0.0137205i	0.330054	−	0.943962i	$-0.392933\pi$
$317$	0.751836	+	0.244286i	0.0422273	+	0.0137205i	−0.287827	+	0.957682i	$0.592933\pi$
$318$		0			0
$319$	−8.97198	+	19.9264i	−0.502334	+	1.11566i
$320$			2.29138i			0.128092i
$321$		0			0
$322$	3.34855	−	2.43286i	0.186607	−	0.135578i
$323$	−4.33306	+	5.96394i	−0.241098	+	0.331843i
$324$		0			0
$325$	0.965313	−	0.313649i	0.0535460	−	0.0173981i
$326$	9.76754	+	7.09653i	0.540974	+	0.393041i
$327$		0			0
$328$	3.29839	−	10.1514i	0.182123	−	0.560518i
$329$	−6.95149			−0.383248
$330$		0			0
$331$	−11.2556			−0.618666			−0.309333	−	0.950954i	$-0.600106\pi$
$331$	−11.2556			−0.618666			−0.309333	+	0.950954i	$0.600106\pi$
$332$	2.27937	−	7.01519i	0.125097	−	0.385009i
$333$		0			0
$334$	4.84739	+	3.52183i	0.265237	+	0.192706i
$335$	2.87870	−	0.935345i	0.157280	−	0.0511034i
$336$		0			0
$337$	5.31496	−	7.31541i	0.289524	−	0.398496i	−0.639335	−	0.768928i	$-0.720790\pi$
$337$	5.31496	−	7.31541i	0.289524	−	0.398496i	0.928859	+	0.370432i	$0.120790\pi$
$338$	2.77393	−	2.01538i	0.150882	−	0.109622i
$339$		0			0
$340$		−	4.84949i		−	0.263001i
$341$	4.36110	+	0.476843i	0.236167	+	0.0258225i
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.0513522	−	0.0166853i
$344$	−3.58088	−	4.92865i	−0.193068	−	0.265735i
$345$		0			0
$346$	−1.14791	−	3.53291i	−0.0617121	−	0.189930i
$347$	4.02401	+	12.3846i	0.216020	+	0.664842i	0.999080	+	0.0428948i	$0.0136580\pi$
$347$	4.02401	+	12.3846i	0.216020	+	0.664842i	−0.783059	+	0.621947i	$0.786342\pi$
$348$		0			0
$349$	19.9058	+	27.3980i	1.06554	+	1.46658i	0.874516	+	0.484998i	$0.161180\pi$
$349$	19.9058	+	27.3980i	1.06554	+	1.46658i	0.191020	+	0.981586i	$0.438820\pi$
$350$	−0.238158	−	0.0773823i	−0.0127301	−	0.00413626i
$351$		0			0
$352$	−0.675973	−	3.24701i	−0.0360295	−	0.173066i
$353$		−	31.0661i		−	1.65348i	−0.562583	−	0.826741i	$-0.690192\pi$
$353$		−	31.0661i		−	1.65348i	0.562583	−	0.826741i	$-0.309808\pi$
$354$		0			0
$355$	19.3665	−	14.0706i	1.02787	−	0.746790i
$356$	−6.60826	+	9.09549i	−0.350237	+	0.482060i
$357$		0			0
$358$	9.31777	−	3.02753i	0.492460	−	0.160010i
$359$	−17.4385	−	12.6698i	−0.920370	−	0.668688i	0.0232459	−	0.999730i	$-0.492600\pi$
$359$	−17.4385	−	12.6698i	−0.920370	−	0.668688i	−0.943616	+	0.331042i	$0.892600\pi$
$360$		0			0
$361$	2.12215	−	6.53131i	0.111692	−	0.343753i
$362$	1.91125			0.100453
$363$		0			0
$364$	−4.05324			−0.212448
$365$	−6.59308	+	20.2914i	−0.345097	+	1.06210i
$366$		0			0
$367$	−23.9393	−	17.3929i	−1.24962	−	0.907904i	−0.251422	−	0.967877i	$-0.580898\pi$
$367$	−23.9393	−	17.3929i	−1.24962	−	0.907904i	−0.998200	+	0.0599738i	$0.980898\pi$
$368$	−3.93645	+	1.27903i	−0.205202	+	0.0666741i
$369$		0			0
$370$	11.1416	−	15.3351i	0.579225	−	0.797234i
$371$	−7.30673	+	5.30865i	−0.379347	+	0.275612i
$372$		0			0
$373$		−	36.6174i		−	1.89598i	−0.318304	−	0.947989i	$-0.603113\pi$
$373$		−	36.6174i		−	1.89598i	0.318304	−	0.947989i	$-0.396887\pi$
$374$	1.43064	+	6.87199i	0.0739764	+	0.355342i
$375$		0			0
$376$	6.61126	+	2.14813i	0.340950	+	0.110781i
$377$	−15.6978	−	21.6061i	−0.808476	−	1.11277i
$378$		0			0
$379$	5.85236	+	18.0117i	0.300615	+	0.925199i	0.981277	+	0.192601i	$0.0616924\pi$
$379$	5.85236	+	18.0117i	0.300615	+	0.925199i	−0.680662	+	0.732598i	$0.738308\pi$
$380$	−2.46636	−	7.59066i	−0.126521	−	0.389393i
$381$		0			0
$382$	−12.5924	−	17.3320i	−0.644284	−	0.886780i
$383$	29.6825	+	9.64444i	1.51671	+	0.492808i	0.944838	−	0.327537i	$-0.106219\pi$
$383$	29.6825	+	9.64444i	1.51671	+	0.492808i	0.571869	+	0.820345i	$0.306219\pi$
$384$		0			0
$385$	7.55462	+	0.826023i	0.385019	+	0.0420980i
$386$		−	15.2658i		−	0.777007i
$387$		0			0
$388$	9.68643	−	7.03760i	0.491754	−	0.357280i
$389$	10.8090	−	14.8774i	0.548041	−	0.754313i	−0.441704	−	0.897161i	$-0.645626\pi$
$389$	10.8090	−	14.8774i	0.548041	−	0.754313i	0.989745	+	0.142848i	$0.0456259\pi$
$390$		0			0
$391$	8.33114	−	2.70695i	0.421324	−	0.136896i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$		0			0
$394$	2.51274	−	7.73342i	0.126590	−	0.389604i
$395$	34.1556			1.71855
$396$		0			0
$397$	−0.606598			−0.0304443			−0.0152221	−	0.999884i	$-0.504846\pi$
$397$	−0.606598			−0.0304443			−0.0152221	+	0.999884i	$0.504846\pi$
$398$	−3.58391	+	11.0301i	−0.179645	+	0.552891i
$399$		0			0
$400$	0.202590	+	0.147190i	0.0101295	+	0.00735950i
$401$	20.5614	−	6.68080i	1.02679	−	0.333623i	0.253268	−	0.967396i	$-0.418495\pi$
$401$	20.5614	−	6.68080i	1.02679	−	0.333623i	0.773519	+	0.633773i	$0.218495\pi$
$402$		0			0
$403$	−3.15138	+	4.33751i	−0.156982	+	0.216067i
$404$	−8.72305	+	6.33767i	−0.433988	+	0.315311i
$405$		0			0
$406$			6.58896i			0.327004i
$407$	−11.2643	+	25.0175i	−0.558350	+	1.24007i
$408$		0			0
$409$	−29.5006	−	9.58533i	−1.45871	−	0.473964i	−0.531035	−	0.847350i	$-0.678197\pi$
$409$	−29.5006	−	9.58533i	−1.45871	−	0.473964i	−0.927676	+	0.373386i	$0.878197\pi$
$410$	−14.3759	−	19.7868i	−0.709976	−	0.977198i
$411$		0			0
$412$	−2.04740	−	6.30124i	−0.100868	−	0.310440i
$413$	0.858224	+	2.64134i	0.0422305	+	0.129972i
$414$		0			0
$415$	−9.93456	−	13.6737i	−0.487668	−	0.671218i
$416$	3.85486	+	1.25252i	0.189000	+	0.0614099i
$417$		0			0
$418$	5.73426	+	10.0288i	0.280472	+	0.490524i
$419$			0.0710859i			0.00347277i	0.999998	+	0.00173639i	$0.000552709\pi$
$419$			0.0710859i			0.00347277i	−0.999998	+	0.00173639i	$0.999447\pi$
$420$		0			0
$421$	26.3841	−	19.1692i	1.28588	−	0.934249i	0.286169	−	0.958179i	$-0.407618\pi$
$421$	26.3841	−	19.1692i	1.28588	−	0.934249i	0.999714	+	0.0239305i	$0.00761804\pi$
$422$	−8.08862	+	11.1330i	−0.393748	+	0.541948i
$423$		0			0
$424$	8.58958	−	2.79092i	0.417147	−	0.135539i
$425$	−0.428762	−	0.311514i	−0.0207980	−	0.0151107i
$426$		0			0
$427$	1.37703	−	4.23807i	0.0666392	−	0.205094i
$428$	−12.2671			−0.592953
$429$		0			0
$430$	−13.9594			−0.673183
$431$	−10.7979	+	33.2325i	−0.520117	+	1.60075i	0.253659	+	0.967294i	$0.418366\pi$
$431$	−10.7979	+	33.2325i	−0.520117	+	1.60075i	−0.773775	+	0.633460i	$0.781634\pi$
$432$		0			0
$433$	19.8861	+	14.4481i	0.955665	+	0.694331i	0.952140	−	0.305662i	$-0.0988779\pi$
$433$	19.8861	+	14.4481i	0.955665	+	0.694331i	0.00352523	+	0.999994i	$0.498878\pi$
$434$	1.25802	−	0.408754i	0.0603867	−	0.0196208i
$435$		0			0
$436$	2.54320	−	3.50042i	0.121797	−	0.167640i
$437$	11.6636	−	8.47410i	0.557946	−	0.405371i
$438$		0			0
$439$			37.1786i			1.77444i	0.461347	+	0.887220i	$0.347366\pi$
$439$			37.1786i			1.77444i	−0.461347	+	0.887220i	$0.652634\pi$
$440$	−6.92961	−	3.12010i	−0.330356	−	0.148745i
$441$		0			0
$442$	−8.15846	−	2.65085i	−0.388059	−	0.126088i
$443$	6.84944	+	9.42744i	0.325427	+	0.447911i	0.940114	−	0.340859i	$-0.110718\pi$
$443$	6.84944	+	9.42744i	0.325427	+	0.447911i	−0.614688	+	0.788771i	$0.710718\pi$
$444$		0			0
$445$	7.96063	+	24.5003i	0.377370	+	1.16143i
$446$	3.69654	+	11.3768i	0.175036	+	0.538706i
$447$		0			0
$448$	−0.587785	−	0.809017i	−0.0277702	−	0.0382225i
$449$	1.11905	+	0.363601i	0.0528112	+	0.0171594i	0.335303	−	0.942110i	$-0.391161\pi$
$449$	1.11905	+	0.363601i	0.0528112	+	0.0171594i	−0.282492	+	0.959270i	$0.591161\pi$
$450$		0			0
$451$	26.2087	+	23.7979i	1.23412	+	1.12060i
$452$		−	5.25259i		−	0.247061i
$453$		0			0
$454$	15.6477	−	11.3687i	0.734384	−	0.533562i
$455$	−5.45906	+	7.51375i	−0.255925	+	0.352250i
$456$		0			0
$457$	7.67437	−	2.49356i	0.358992	−	0.116644i	−0.123967	−	0.992286i	$-0.539562\pi$
$457$	7.67437	−	2.49356i	0.358992	−	0.116644i	0.482960	+	0.875643i	$0.339562\pi$
$458$	−4.04250	−	2.93705i	−0.188894	−	0.137239i
$459$		0			0
$460$	−2.93074	+	9.01990i	−0.136647	+	0.420555i
$461$	28.1646			1.31176			0.655879	−	0.754866i	$-0.272298\pi$
$461$	28.1646			1.31176			0.655879	+	0.754866i	$0.272298\pi$
$462$		0			0
$463$	−23.3453			−1.08495			−0.542475	−	0.840072i	$-0.682512\pi$
$463$	−23.3453			−1.08495			−0.542475	+	0.840072i	$0.682512\pi$
$464$	2.03610	−	6.26647i	0.0945236	−	0.290914i
$465$		0			0
$466$	17.5850	+	12.7763i	0.814610	+	0.591849i
$467$	36.5614	−	11.8795i	1.69186	−	0.549719i	0.704708	−	0.709498i	$-0.251078\pi$
$467$	36.5614	−	11.8795i	1.69186	−	0.549719i	0.987153	+	0.159779i	$0.0510781\pi$
$468$		0			0
$469$	−0.776447	+	1.06869i	−0.0358530	+	0.0493474i
$470$	12.8864	−	9.36253i	0.594406	−	0.431861i
$471$		0			0
$472$		−	2.77727i		−	0.127834i
$473$	19.7813	−	4.11813i	0.909543	−	0.189352i
$474$		0			0
$475$	−0.829549	−	0.269537i	−0.0380623	−	0.0123672i
$476$	1.24399	+	1.71221i	0.0570184	+	0.0784790i
$477$		0			0
$478$	2.73673	+	8.42278i	0.125175	+	0.385249i
$479$	9.15255	+	28.1687i	0.418191	+	1.28706i	0.909365	+	0.415998i	$0.136568\pi$
$479$	9.15255	+	28.1687i	0.418191	+	1.28706i	−0.491175	+	0.871061i	$0.663432\pi$
$480$		0			0
$481$	−19.7085	−	27.1264i	−0.898630	−	1.23686i
$482$	−11.7870	−	3.82984i	−0.536885	−	0.174445i
$483$		0			0
$484$	10.7401	+	2.37706i	0.488186	+	0.108048i
$485$		−	27.4349i		−	1.24575i
$486$		0			0
$487$	−8.01182	+	5.82093i	−0.363050	+	0.263772i	−0.754323	−	0.656503i	$-0.772035\pi$
$487$	−8.01182	+	5.82093i	−0.363050	+	0.263772i	0.391273	+	0.920275i	$0.372035\pi$
$488$	−2.61927	+	3.60511i	−0.118569	+	0.163196i
$489$		0			0
$490$	2.17923	−	0.708075i	0.0984476	−	0.0319876i
$491$	−34.7436	−	25.2427i	−1.56796	−	1.13919i	−0.929079	−	0.369881i	$-0.879398\pi$
$491$	−34.7436	−	25.2427i	−1.56796	−	1.13919i	−0.638879	−	0.769307i	$-0.720602\pi$
$492$		0			0
$493$	−4.30922	+	13.2624i	−0.194077	+	0.597309i
$494$	−14.1182			−0.635207
$495$		0			0
$496$	−1.32276			−0.0593935
$497$	−3.22834	+	9.93582i	−0.144811	+	0.445682i
$498$		0			0
$499$	−10.3606	−	7.52742i	−0.463804	−	0.336973i	0.331218	−	0.943554i	$-0.392541\pi$
$499$	−10.3606	−	7.52742i	−0.463804	−	0.336973i	−0.795022	+	0.606581i	$0.792541\pi$
$500$	−10.3504	+	3.36306i	−0.462886	+	0.150401i
$501$		0			0
$502$	9.41211	−	12.9547i	0.420083	−	0.578195i
$503$	13.5587	−	9.85097i	0.604552	−	0.439233i	−0.242940	−	0.970041i	$-0.578112\pi$
$503$	13.5587	−	9.85097i	0.604552	−	0.439233i	0.847492	+	0.530808i	$0.178112\pi$
$504$		0			0
$505$			24.7063i			1.09942i
$506$	1.49209	−	13.6463i	0.0663313	−	0.606651i
$507$		0			0
$508$	−11.9435	−	3.88067i	−0.529906	−	0.172177i
$509$	−2.65574	−	3.65531i	−0.117714	−	0.162019i	0.746094	−	0.665840i	$-0.231927\pi$
$509$	−2.65574	−	3.65531i	−0.117714	−	0.162019i	−0.863808	+	0.503822i	$0.831927\pi$
$510$		0			0
$511$	−2.87734	−	8.85554i	−0.127286	−	0.391746i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	−17.5671	−	24.1791i	−0.774854	−	1.06649i
$515$	−14.4385	−	4.69136i	−0.636237	−	0.206726i
$516$		0			0
$517$	−15.4987	+	17.0688i	−0.681634	+	0.750685i
$518$			8.27242i			0.363469i
$519$		0			0
$520$	7.51375	−	5.45906i	0.329500	−	0.239396i
$521$	23.2961	−	32.0644i	1.02062	−	1.40477i	0.108855	−	0.994058i	$-0.465282\pi$
$521$	23.2961	−	32.0644i	1.02062	−	1.40477i	0.911767	−	0.410708i	$-0.134718\pi$
$522$		0			0
$523$	−8.96804	+	2.91389i	−0.392145	+	0.127416i	−0.498451	−	0.866918i	$-0.666098\pi$
$523$	−8.96804	+	2.91389i	−0.392145	+	0.127416i	0.106306	+	0.994333i	$0.466098\pi$
$524$	−0.0956685	−	0.0695072i	−0.00417930	−	0.00303644i
$525$		0			0
$526$	−2.61084	+	8.03534i	−0.113838	+	0.350357i
$527$	2.79949			0.121948
$528$		0			0
$529$	5.86844			0.255149
$530$	6.39506	−	19.6820i	0.277784	−	0.854931i
$531$		0			0
$532$	2.81796	+	2.04736i	0.122174	+	0.0887645i
$533$	−41.1461	+	13.3692i	−1.78224	+	0.579084i
$534$		0			0
$535$	−16.5218	+	22.7403i	−0.714300	+	0.983150i
$536$	1.06869	−	0.776447i	0.0461602	−	0.0335374i
$537$		0			0
$538$			7.49171i			0.322990i
$539$	−2.87920	+	1.64627i	−0.124016	+	0.0709098i
$540$		0			0
$541$	14.1796	+	4.60724i	0.609630	+	0.198081i	0.597531	−	0.801846i	$-0.296149\pi$
$541$	14.1796	+	4.60724i	0.609630	+	0.198081i	0.0120990	+	0.999927i	$0.496149\pi$
$542$	6.61450	+	9.10408i	0.284117	+	0.391054i
$543$		0			0
$544$	−0.654006	−	2.01282i	−0.0280403	−	0.0862991i
$545$	−3.06366	−	9.42899i	−0.131233	−	0.403893i
$546$		0			0
$547$	−12.7018	−	17.4826i	−0.543091	−	0.747500i	0.445964	−	0.895051i	$-0.352861\pi$
$547$	−12.7018	−	17.4826i	−0.543091	−	0.747500i	−0.989054	+	0.147551i	$0.952861\pi$
$548$	17.0948	+	5.55445i	0.730255	+	0.237274i
$549$		0			0
$550$	−0.720994	+	0.412250i	−0.0307433	+	0.0175784i
$551$			22.9506i			0.977726i
$552$		0			0
$553$	−12.0593	+	8.76160i	−0.512814	+	0.372581i
$554$	−17.8206	+	24.5280i	−0.757126	+	1.04209i
$555$		0			0
$556$	−20.8508	+	6.77482i	−0.884269	+	0.287316i
$557$	−1.57567	−	1.14479i	−0.0667633	−	0.0485064i	0.553903	−	0.832581i	$-0.313138\pi$
$557$	−1.57567	−	1.14479i	−0.0667633	−	0.0485064i	−0.620666	+	0.784075i	$0.713138\pi$
$558$		0			0
$559$	−7.63054	+	23.4844i	−0.322738	+	0.993284i
$560$	−2.29138			−0.0968284
$561$		0			0
$562$	12.2573			0.517044
$563$	3.29047	−	10.1270i	0.138677	−	0.426804i	−0.857467	−	0.514539i	$-0.827963\pi$
$563$	3.29047	−	10.1270i	0.138677	−	0.426804i	0.996144	+	0.0877355i	$0.0279630\pi$
$564$		0			0
$565$	−9.73707	−	7.07440i	−0.409642	−	0.297622i
$566$	−14.0862	+	4.57687i	−0.592086	+	0.192380i
$567$		0			0
$568$	6.14067	−	8.45191i	0.257657	−	0.354634i
$569$	−9.91287	+	7.20212i	−0.415569	+	0.301929i	−0.775853	−	0.630914i	$-0.782680\pi$
$569$	−9.91287	+	7.20212i	−0.415569	+	0.301929i	0.360284	+	0.932843i	$0.382680\pi$
$570$		0			0
$571$			15.9842i			0.668917i	0.942411	+	0.334458i	$0.108553\pi$
$571$			15.9842i			0.668917i	−0.942411	+	0.334458i	$0.891447\pi$
$572$	−9.03694	+	9.95240i	−0.377853	+	0.416131i
$573$		0			0
$574$	10.1514	+	3.29839i	0.423712	+	0.137672i
$575$	0.609224	+	0.838524i	0.0254064	+	0.0349689i
$576$		0			0
$577$	−11.6414	−	35.8286i	−0.484638	−	1.49156i	−0.832504	−	0.554019i	$-0.813093\pi$
$577$	−11.6414	−	35.8286i	−0.484638	−	1.49156i	0.347866	−	0.937544i	$-0.386907\pi$
$578$	−3.86914	−	11.9080i	−0.160935	−	0.495308i
$579$		0			0
$580$	−8.87426	−	12.2144i	−0.368484	−	0.507174i
$581$	7.01519	+	2.27937i	0.291039	+	0.0945643i
$582$		0			0
$583$	−3.25582	+	29.7770i	−0.134842	+	1.23324i
$584$			9.31127i			0.385303i
$585$		0			0
$586$	2.12470	−	1.54368i	0.0877705	−	0.0637690i
$587$	13.7669	−	18.9486i	0.568222	−	0.782091i	−0.424120	−	0.905606i	$-0.639417\pi$
$587$	13.7669	−	18.9486i	0.568222	−	0.782091i	0.992343	+	0.123515i	$0.0394167\pi$
$588$		0			0
$589$	4.38190	−	1.42377i	0.180553	−	0.0586653i
$590$	−5.14841	−	3.74054i	−0.211957	−	0.153995i
$591$		0			0
$592$	2.55632	−	7.86753i	0.105064	−	0.323354i
$593$	−30.2860			−1.24370			−0.621848	−	0.783138i	$-0.713618\pi$
$593$	−30.2860			−1.24370			−0.621848	+	0.783138i	$0.713618\pi$
$594$		0			0
$595$	4.84949			0.198810
$596$	−0.391092	+	1.20366i	−0.0160198	+	0.0493038i
$597$		0			0
$598$	13.5725	+	9.86097i	0.555019	+	0.403245i
$599$	−13.1204	+	4.26307i	−0.536085	+	0.174184i	−0.564533	−	0.825411i	$-0.690944\pi$
$599$	−13.1204	+	4.26307i	−0.536085	+	0.174184i	0.0284479	+	0.999595i	$0.490944\pi$
$600$		0			0
$601$	−3.85040	+	5.29963i	−0.157061	+	0.216176i	−0.880295	−	0.474428i	$-0.842655\pi$
$601$	−3.85040	+	5.29963i	−0.157061	+	0.216176i	0.723233	+	0.690604i	$0.242655\pi$
$602$	4.92865	−	3.58088i	0.200877	−	0.145946i
$603$		0			0
$604$			5.61237i			0.228364i
$605$	18.8717	−	16.7081i	0.767243	−	0.679280i
$606$		0			0
$607$	−29.3755	−	9.54467i	−1.19231	−	0.387406i	−0.355386	−	0.934720i	$-0.615650\pi$
$607$	−29.3755	−	9.54467i	−1.19231	−	0.387406i	−0.836928	+	0.547314i	$0.815650\pi$
$608$	−2.04736	−	2.81796i	−0.0830316	−	0.114283i
$609$		0			0
$610$	3.15530	+	9.71101i	0.127754	+	0.393187i
$611$	−8.70688	−	26.7970i	−0.352243	−	1.08409i
$612$		0			0
$613$	12.7021	+	17.4829i	0.513032	+	0.706129i	0.984427	−	0.175794i	$-0.0562492\pi$
$613$	12.7021	+	17.4829i	0.513032	+	0.706129i	−0.471395	+	0.881922i	$0.656249\pi$
$614$	4.09296	+	1.32988i	0.165179	+	0.0536698i
$615$		0			0
$616$	3.24701	−	0.675973i	0.130826	−	0.0272357i
$617$		−	21.1217i		−	0.850329i	−0.905116	−	0.425164i	$-0.860216\pi$
$617$		−	21.1217i		−	0.850329i	0.905116	−	0.425164i	$-0.139784\pi$
$618$		0			0
$619$	−5.97110	+	4.33826i	−0.239999	+	0.174369i	−0.701283	−	0.712883i	$-0.747389\pi$
$619$	−5.97110	+	4.33826i	−0.239999	+	0.174369i	0.461284	+	0.887253i	$0.347389\pi$
$620$	−1.78154	+	2.45208i	−0.0715484	+	0.0984779i
$621$		0			0
$622$	−3.93600	+	1.27888i	−0.157819	+	0.0512786i
$623$	−9.09549	−	6.60826i	−0.364403	−	0.264754i
$624$		0			0
$625$	−8.09296	+	24.9076i	−0.323718	+	0.996303i
$626$	−29.6839			−1.18641
$627$		0			0
$628$	−1.23707			−0.0493643
$629$	−5.41021	+	16.6509i	−0.215719	+	0.663916i
$630$		0			0
$631$	3.50452	+	2.54618i	0.139513	+	0.101362i	0.655353	−	0.755323i	$-0.272520\pi$
$631$	3.50452	+	2.54618i	0.139513	+	0.101362i	−0.515840	+	0.856685i	$0.672520\pi$
$632$	14.1766	−	4.60625i	0.563914	−	0.183227i
$633$		0			0
$634$	0.464660	−	0.639550i	0.0184540	−	0.0253998i
$635$	−23.2798	+	16.9138i	−0.923830	+	0.671202i
$636$		0			0
$637$		−	4.05324i		−	0.160595i
$638$	16.1786	+	14.6905i	0.640518	+	0.581601i
$639$		0			0
$640$	2.17923	+	0.708075i	0.0861416	+	0.0279891i
$641$	13.5098	+	18.5946i	0.533603	+	0.734442i	0.987674	−	0.156524i	$-0.0500287\pi$
$641$	13.5098	+	18.5946i	0.533603	+	0.734442i	−0.454071	+	0.890966i	$0.650029\pi$
$642$		0			0
$643$	3.65764	+	11.2570i	0.144243	+	0.443935i	0.996913	−	0.0785156i	$-0.0250180\pi$
$643$	3.65764	+	11.2570i	0.144243	+	0.443935i	−0.852670	+	0.522450i	$0.825018\pi$
$644$	−1.27903	−	3.93645i	−0.0504009	−	0.155118i
$645$		0			0
$646$	4.33306	+	5.96394i	0.170482	+	0.234648i
$647$	4.16772	+	1.35417i	0.163850	+	0.0532381i	0.389793	−	0.920902i	$-0.372546\pi$
$647$	4.16772	+	1.35417i	0.163850	+	0.0532381i	−0.225943	+	0.974140i	$0.572546\pi$
$648$		0			0
$649$	8.39906	+	3.78173i	0.329692	+	0.148446i
$650$		−	1.01499i		−	0.0398112i
$651$		0			0
$652$	9.76754	−	7.09653i	0.382526	−	0.277922i
$653$	−17.0460	+	23.4619i	−0.667063	+	0.918134i	−0.999689	−	0.0249250i	$-0.992065\pi$
$653$	−17.0460	+	23.4619i	−0.667063	+	0.918134i	0.332626	+	0.943059i	$0.392065\pi$
$654$		0			0
$655$	−0.257700	+	0.0837318i	−0.0100692	+	0.00327167i
$656$	−8.63531	−	6.27392i	−0.337152	−	0.244955i
$657$		0			0
$658$	−2.14813	+	6.61126i	−0.0837428	+	0.257734i
$659$	15.9222			0.620239			0.310119	−	0.950698i	$-0.399631\pi$
$659$	15.9222			0.620239			0.310119	+	0.950698i	$0.399631\pi$
$660$		0			0
$661$	−19.2008			−0.746823			−0.373412	−	0.927666i	$-0.621812\pi$
$661$	−19.2008			−0.746823			−0.373412	+	0.927666i	$0.621812\pi$
$662$	−3.47818	+	10.7048i	−0.135183	+	0.416052i
$663$		0			0
$664$	−5.96748	−	4.33563i	−0.231583	−	0.168255i
$665$	7.59066	−	2.46636i	0.294353	−	0.0956412i
$666$		0			0
$667$	16.0300	−	22.0634i	0.620685	−	0.854299i
$668$	4.84739	−	3.52183i	0.187551	−	0.136264i
$669$		0			0
$670$		−	3.02684i		−	0.116937i
$671$	−7.33605	−	12.8302i	−0.283205	−	0.495304i
$672$		0			0
$673$	−11.9377	−	3.87878i	−0.460163	−	0.149516i	0.0697565	−	0.997564i	$-0.477778\pi$
$673$	−11.9377	−	3.87878i	−0.460163	−	0.149516i	−0.529919	+	0.848048i	$0.677778\pi$
$674$	−5.31496	−	7.31541i	−0.204724	−	0.281779i
$675$		0			0
$676$	−1.05955	−	3.26096i	−0.0407519	−	0.125421i
$677$	6.88039	+	21.1757i	0.264435	+	0.813846i	0.991823	+	0.127620i	$0.0407339\pi$
$677$	6.88039	+	21.1757i	0.264435	+	0.813846i	−0.727388	+	0.686226i	$0.759266\pi$
$678$		0			0
$679$	7.03760	+	9.68643i	0.270078	+	0.371731i
$680$	−4.61214	−	1.49858i	−0.176868	−	0.0574678i
$681$		0			0
$682$	1.80116	−	4.00030i	0.0689699	−	0.153179i
$683$			7.44591i			0.284910i	0.989801	+	0.142455i	$0.0454996\pi$
$683$			7.44591i			0.284910i	−0.989801	+	0.142455i	$0.954500\pi$
$684$		0			0
$685$	33.3206	−	24.2088i	1.27311	−	0.924972i
$686$	−0.587785	+	0.809017i	−0.0224417	+	0.0308884i
$687$		0			0
$688$	−5.79398	+	1.88258i	−0.220893	+	0.0717726i
$689$	−29.6160	−	21.5173i	−1.12828	−	0.819742i
$690$		0			0
$691$	−3.11918	+	9.59986i	−0.118659	+	0.365196i	−0.992693	−	0.120670i	$-0.961496\pi$
$691$	−3.11918	+	9.59986i	−0.118659	+	0.365196i	0.874033	+	0.485866i	$0.161496\pi$
$692$	−3.71472			−0.141213
$693$		0			0
$694$	13.0220			0.494307
$695$	−15.5237	+	47.7770i	−0.588847	+	1.81228i
$696$		0			0
$697$	18.2758	+	13.2782i	0.692247	+	0.502947i
$698$	32.2083	−	10.4651i	1.21910	−	0.396111i
$699$		0			0
$700$	−0.147190	+	0.202590i	−0.00556326	+	0.00765717i
$701$	12.6117	−	9.16295i	0.476338	−	0.346080i	−0.323568	−	0.946205i	$-0.604882\pi$
$701$	12.6117	−	9.16295i	0.476338	−	0.346080i	0.799906	+	0.600125i	$0.204882\pi$
$702$		0			0
$703$			28.8143i			1.08675i
$704$	−3.29698	−	0.360492i	−0.124259	−	0.0135865i
$705$		0			0
$706$	−29.5456	−	9.59995i	−1.11196	−	0.361299i
$707$	−6.33767	−	8.72305i	−0.238352	−	0.328064i
$708$		0			0
$709$	−1.36248	−	4.19329i	−0.0511691	−	0.157482i	0.922207	−	0.386697i	$-0.126384\pi$
$709$	−1.36248	−	4.19329i	−0.0511691	−	0.157482i	−0.973376	+	0.229215i	$0.926384\pi$
$710$	−7.39736	−	22.7667i	−0.277618	−	0.854420i
$711$		0			0
$712$	6.60826	+	9.09549i	0.247655	+	0.340868i
$713$	−5.20697	−	1.69185i	−0.195002	−	0.0633601i
$714$		0			0
$715$	6.27811	+	30.1566i	0.234788	+	1.12779i
$716$		−	9.79729i		−	0.366142i
$717$		0			0
$718$	−17.4385	+	12.6698i	−0.650800	+	0.472834i
$719$	−23.8291	+	32.7979i	−0.888674	+	1.22315i	0.0852686	+	0.996358i	$0.472825\pi$
$719$	−23.8291	+	32.7979i	−0.888674	+	1.22315i	−0.973942	+	0.226796i	$0.927175\pi$
$720$		0			0
$721$	6.30124	−	2.04740i	0.234670	−	0.0762490i
$722$	−5.55586	−	4.03657i	−0.206768	−	0.150226i
$723$		0			0
$724$	0.590608	−	1.81770i	0.0219498	−	0.0675544i
$725$	−1.64997			−0.0612784
$726$		0			0
$727$	−35.6308			−1.32147			−0.660737	−	0.750618i	$-0.729756\pi$
$727$	−35.6308			−1.32147			−0.660737	+	0.750618i	$0.729756\pi$
$728$	−1.25252	+	3.85486i	−0.0464215	+	0.142871i
$729$		0			0
$730$	17.2609	+	12.5408i	0.638854	+	0.464155i
$731$	12.2624	−	3.98430i	0.453542	−	0.147365i
$732$		0			0
$733$	−9.58876	+	13.1978i	−0.354169	+	0.487472i	−0.948513	−	0.316739i	$-0.897412\pi$
$733$	−9.58876	+	13.1978i	−0.354169	+	0.487472i	0.594344	+	0.804211i	$0.297412\pi$
$734$	−23.9393	+	17.3929i	−0.883616	+	0.641985i
$735$		0			0
$736$			4.13903i			0.152567i
$737$	0.892940	+	4.28920i	0.0328919	+	0.157995i
$738$		0			0
$739$	39.4659	+	12.8233i	1.45178	+	0.471711i	0.925548	−	0.378632i	$-0.123605\pi$
$739$	39.4659	+	12.8233i	1.45178	+	0.471711i	0.526230	+	0.850342i	$0.323605\pi$
$740$	−11.1416	−	15.3351i	−0.409574	−	0.563730i
$741$		0			0
$742$	2.79092	+	8.58958i	0.102458	+	0.315333i
$743$	9.30211	+	28.6290i	0.341261	+	1.05029i	0.963555	+	0.267511i	$0.0862011\pi$
$743$	9.30211	+	28.6290i	0.341261	+	1.05029i	−0.622293	+	0.782784i	$0.713799\pi$
$744$		0			0
$745$	1.70456	+	2.34613i	0.0624503	+	0.0859554i
$746$	−34.8252	−	11.3154i	−1.27504	−	0.414286i
$747$		0			0
$748$	6.97775	+	0.762948i	0.255132	+	0.0278961i
$749$		−	12.2671i		−	0.448230i
$750$		0			0
$751$	−31.4104	+	22.8210i	−1.14618	+	0.832749i	−0.987968	−	0.154656i	$-0.950573\pi$
$751$	−31.4104	+	22.8210i	−1.14618	+	0.832749i	−0.158213	+	0.987405i	$0.550573\pi$
$752$	4.08598	−	5.62387i	0.149000	−	0.205082i
$753$		0			0
$754$	−25.3995	+	8.25280i	−0.924996	+	0.300549i
$755$	10.4040	+	7.55896i	0.378641	+	0.275099i
$756$		0			0
$757$	−14.9803	+	46.1047i	−0.544470	+	1.67571i	0.177778	+	0.984071i	$0.443109\pi$
$757$	−14.9803	+	46.1047i	−0.544470	+	1.67571i	−0.722247	+	0.691635i	$0.756891\pi$
$758$	18.9386			0.687882
$759$		0			0
$760$	−7.98129			−0.289512
$761$	−0.0199492	+	0.0613974i	−0.000723158	+	0.00222565i	−0.951417	−	0.307904i	$-0.900372\pi$
$761$	−0.0199492	+	0.0613974i	−0.000723158	+	0.00222565i	0.950694	+	0.310130i	$0.100372\pi$
$762$		0			0
$763$	3.50042	+	2.54320i	0.126724	+	0.0920701i
$764$	−20.3749	+	6.62022i	−0.737140	+	0.239511i
$765$		0			0
$766$	18.3448	−	25.2495i	0.662825	−	0.912301i
$767$	−9.10707	+	6.61667i	−0.328837	+	0.238914i
$768$		0			0
$769$			36.0450i			1.29982i	0.760012	+	0.649909i	$0.225193\pi$
$769$			36.0450i			1.29982i	−0.760012	+	0.649909i	$0.774807\pi$
$770$	3.12010	−	6.92961i	0.112441	−	0.249726i
$771$		0			0
$772$	−14.5186	−	4.71738i	−0.522536	−	0.169782i
$773$	−7.36725	−	10.1402i	−0.264982	−	0.364716i	0.655706	−	0.755016i	$-0.272371\pi$
$773$	−7.36725	−	10.1402i	−0.264982	−	0.364716i	−0.920688	+	0.390300i	$0.872371\pi$
$774$		0			0
$775$	0.102358	+	0.315026i	0.00367681	+	0.0113161i
$776$	−3.69989	−	11.3871i	−0.132818	−	0.408772i
$777$		0			0
$778$	−10.8090	−	14.8774i	−0.387523	−	0.533380i
$779$	35.3592	+	11.4889i	1.26688	+	0.411633i
$780$		0			0
$781$	17.1988	+	30.0794i	0.615422	+	1.07633i
$782$		−	8.75988i		−	0.313253i
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	−1.66613	+	2.29323i	−0.0594666	+	0.0818488i
$786$		0			0
$787$	13.1278	−	4.26549i	0.467957	−	0.152048i	−0.0655408	−	0.997850i	$-0.520877\pi$
$787$	13.1278	−	4.26549i	0.467957	−	0.152048i	0.533498	+	0.845801i	$0.320877\pi$
$788$	−6.57844	−	4.77952i	−0.234347	−	0.170263i
$789$		0			0
$790$	10.5547	−	32.4839i	0.375518	−	1.15573i
$791$	5.25259			0.186761
$792$		0			0
$793$	18.0619			0.641397
$794$	−0.187449	+	0.576909i	−0.00665232	+	0.0204737i
$795$		0			0
$796$	9.38281	+	6.81701i	0.332565	+	0.241622i
$797$	3.67627	−	1.19449i	0.130220	−	0.0423111i	−0.243182	−	0.969981i	$-0.578191\pi$
$797$	3.67627	−	1.19449i	0.130220	−	0.0423111i	0.373402	+	0.927670i	$0.378191\pi$
$798$		0			0
$799$	−8.64761	+	11.9024i	−0.305930	+	0.421077i
$800$	0.202590	−	0.147190i	0.00716262	−	0.00520395i
$801$		0			0
$802$		−	21.6195i		−	0.763412i
$803$	−28.1593	−	12.6789i	−0.993718	−	0.447428i
$804$		0			0
$805$	−9.01990	−	2.93074i	−0.317910	−	0.103295i
$806$	3.15138	+	4.33751i	0.111003	+	0.152782i
$807$		0			0
$808$	3.33191	+	10.2546i	0.117216	+	0.360754i
$809$	−3.88161	−	11.9464i	−0.136470	−	0.420011i	0.859346	−	0.511395i	$-0.170871\pi$
$809$	−3.88161	−	11.9464i	−0.136470	−	0.420011i	−0.995816	+	0.0913836i	$0.970871\pi$
$810$		0			0
$811$	22.1879	+	30.5390i	0.779123	+	1.07237i	0.995378	+	0.0960339i	$0.0306157\pi$
$811$	22.1879	+	30.5390i	0.779123	+	1.07237i	−0.216255	+	0.976337i	$0.569384\pi$
$812$	6.26647	+	2.03610i	0.219910	+	0.0714531i
$813$		0			0
$814$	20.3122	+	18.4438i	0.711943	+	0.646456i
$815$		−	27.6646i		−	0.969048i
$816$		0			0
$817$	17.1674	−	12.4729i	0.600612	−	0.436370i
$818$	−18.2324	+	25.0947i	−0.637480	+	0.877416i
$819$		0			0
$820$	−23.2607	+	7.55787i	−0.812300	+	0.263932i
$821$	−18.0978	−	13.1488i	−0.631618	−	0.458897i	0.225343	−	0.974280i	$-0.427650\pi$
$821$	−18.0978	−	13.1488i	−0.631618	−	0.458897i	−0.856960	+	0.515382i	$0.827650\pi$
$822$		0			0
$823$	2.58630	−	7.95981i	0.0901528	−	0.277462i	−0.895807	−	0.444442i	$-0.853402\pi$
$823$	2.58630	−	7.95981i	0.0901528	−	0.277462i	0.985960	+	0.166981i	$0.0534018\pi$
$824$	−6.62551			−0.230811
$825$		0			0
$826$	2.77727			0.0966336
$827$	2.24411	−	6.90666i	0.0780354	−	0.240168i	−0.904427	−	0.426628i	$-0.859701\pi$
$827$	2.24411	−	6.90666i	0.0780354	−	0.240168i	0.982463	+	0.186460i	$0.0597014\pi$
$828$		0			0
$829$	−3.19943	−	2.32452i	−0.111121	−	0.0807341i	0.530837	−	0.847474i	$-0.321878\pi$
$829$	−3.19943	−	2.32452i	−0.111121	−	0.0807341i	−0.641958	+	0.766740i	$0.721878\pi$
$830$	−16.0745	+	5.22291i	−0.557952	+	0.181290i
$831$		0			0
$832$	2.38244	−	3.27914i	0.0825961	−	0.113684i
$833$	−1.71221	+	1.24399i	−0.0593246	+	0.0431018i
$834$		0			0
$835$		−	13.7293i		−	0.475120i
$836$	11.3099	−	2.35454i	0.391162	−	0.0814335i
$837$		0			0
$838$	0.0676067	+	0.0219667i	0.00233543	+	0.000758829i
$839$	−12.0136	−	16.5353i	−0.414757	−	0.570864i	0.549614	−	0.835419i	$-0.314775\pi$
$839$	−12.0136	−	16.5353i	−0.414757	−	0.570864i	−0.964371	+	0.264555i	$0.914775\pi$
$840$		0			0
$841$	4.45428	+	13.7089i	0.153596	+	0.472719i
$842$	−10.0778	−	31.0164i	−0.347305	−	1.06890i
$843$		0			0
$844$	8.08862	+	11.1330i	0.278422	+	0.383215i
$845$	−7.47208	−	2.42783i	−0.257047	−	0.0835198i
$846$		0			0
$847$	−2.37706	+	10.7401i	−0.0816769	+	0.369034i
$848$		−	9.03162i		−	0.310147i
$849$		0			0
$850$	−0.428762	+	0.311514i	−0.0147064	+	0.0106848i
$851$	20.1256	−	27.7006i	0.689898	−	0.949563i
$852$		0			0
$853$	−32.5908	+	10.5894i	−1.11589	+	0.362574i	−0.808197	−	0.588913i	$-0.799556\pi$
$853$	−32.5908	+	10.5894i	−1.11589	+	0.362574i	−0.307691	+	0.951486i	$0.599556\pi$
$854$	−3.60511	−	2.61927i	−0.123364	−	0.0896295i
$855$		0			0
$856$	−3.79074	+	11.6667i	−0.129565	+	0.398760i
$857$	−0.0797385			−0.00272381			−0.00136191	−	0.999999i	$-0.500434\pi$
$857$	−0.0797385			−0.00272381			−0.00136191	+	0.999999i	$0.500434\pi$
$858$		0			0
$859$	47.5370			1.62194			0.810970	−	0.585087i	$-0.198940\pi$
$859$	47.5370			1.62194			0.810970	+	0.585087i	$0.198940\pi$
$860$	−4.31370	+	13.2762i	−0.147096	+	0.452715i
$861$		0			0
$862$	28.2693	+	20.5388i	0.962855	+	0.699555i
$863$	18.2785	−	5.93905i	0.622208	−	0.202168i	0.0190875	−	0.999818i	$-0.493924\pi$
$863$	18.2785	−	5.93905i	0.622208	−	0.202168i	0.603120	+	0.797650i	$0.293924\pi$
$864$		0			0
$865$	−5.00313	+	6.88622i	−0.170111	+	0.234138i
$866$	19.8861	−	14.4481i	0.675757	−	0.490966i
$867$		0			0
$868$		−	1.32276i		−	0.0448973i
$869$	−5.37354	+	49.1451i	−0.182285	+	1.66713i
$870$		0			0
$871$	−5.09216	−	1.65454i	−0.172541	−	0.0560620i
$872$	−2.54320	−	3.50042i	−0.0861236	−	0.118539i
$873$		0			0
$874$	−4.45510	−	13.7114i	−0.150696	−	0.463794i
$875$	−3.36306	−	10.3504i	−0.113692	−	0.349909i
$876$		0			0
$877$	−15.6125	−	21.4888i	−0.527197	−	0.725624i	0.459503	−	0.888176i	$-0.348028\pi$
$877$	−15.6125	−	21.4888i	−0.527197	−	0.725624i	−0.986700	+	0.162552i	$0.948028\pi$
$878$	35.3590	+	11.4888i	1.19331	+	0.387729i
$879$		0			0
$880$	−5.10876	+	5.62629i	−0.172216	+	0.189662i
$881$			27.6186i			0.930493i	0.885181	+	0.465246i	$0.154034\pi$
$881$			27.6186i			0.930493i	−0.885181	+	0.465246i	$0.845966\pi$
$882$		0			0
$883$	32.4782	−	23.5968i	1.09298	−	0.794096i	0.113080	−	0.993586i	$-0.463928\pi$
$883$	32.4782	−	23.5968i	1.09298	−	0.794096i	0.979900	+	0.199489i	$0.0639284\pi$
$884$	−5.04221	+	6.94000i	−0.169588	+	0.233418i
$885$		0			0
$886$	11.0826	−	3.60096i	0.372328	−	0.120977i
$887$	−18.9550	−	13.7716i	−0.636445	−	0.462405i	0.222182	−	0.975005i	$-0.428682\pi$
$887$	−18.9550	−	13.7716i	−0.636445	−	0.462405i	−0.858627	+	0.512601i	$0.828682\pi$
$888$		0			0
$889$	3.88067	−	11.9435i	0.130154	−	0.400571i
$890$	25.7611			0.863516
$891$		0			0
$892$	11.9622			0.400526
$893$	−7.48233	+	23.0282i	−0.250387	+	0.770611i
$894$		0			0
$895$	−18.1619	−	13.1954i	−0.607084	−	0.441072i
$896$	−0.951057	+	0.309017i	−0.0317726	+	0.0103235i
$897$		0			0
$898$	0.691610	−	0.951920i	0.0230793	−	0.0317660i
$899$	7.05106	−	5.12289i	0.235166	−	0.170858i
$900$		0			0
$901$			19.1146i			0.636800i
$902$	30.7321	−	17.5720i	1.02327	−	0.585083i
$903$		0			0
$904$	−4.99551	−	1.62314i	−0.166148	−	0.0539849i
$905$	−2.57414	−	3.54300i	−0.0855673	−	0.117773i
$906$		0			0
$907$	−4.97620	−	15.3152i	−0.165232	−	0.508532i	0.833821	−	0.552034i	$-0.186148\pi$
$907$	−4.97620	−	15.3152i	−0.165232	−	0.508532i	−0.999053	+	0.0435026i	$0.986148\pi$
$908$	−5.97690	−	18.3950i	−0.198350	−	0.610460i
$909$		0			0
$910$	5.45906	+	7.51375i	0.180966	+	0.249079i
$911$	−33.7174	−	10.9554i	−1.11711	−	0.362970i	−0.308444	−	0.951242i	$-0.599808\pi$
$911$	−33.7174	−	10.9554i	−1.11711	−	0.362970i	−0.808663	+	0.588272i	$0.799808\pi$
$912$		0			0
$913$	21.2376	−	12.1432i	0.702861	−	0.401882i
$914$		−	8.06931i		−	0.266909i
$915$		0			0
$916$	−4.04250	+	2.93705i	−0.133568	+	0.0970428i
$917$	0.0695072	−	0.0956685i	0.00229533	−	0.00315925i
$918$		0			0
$919$	−52.6835	+	17.1179i	−1.73787	+	0.564668i	−0.994549	−	0.104269i	$-0.966750\pi$
$919$	−52.6835	+	17.1179i	−1.73787	+	0.564668i	−0.743319	+	0.668937i	$0.766750\pi$
$920$	7.67278	+	5.57460i	0.252964	+	0.183789i
$921$		0			0
$922$	8.70336	−	26.7862i	0.286630	−	0.882156i
$923$	−42.3448			−1.39380
$924$		0			0
$925$	−2.07153			−0.0681116
$926$	−7.21410	+	22.2027i	−0.237070	+	0.729627i
$927$		0			0
$928$	−5.33058	−	3.87289i	−0.174985	−	0.127134i
$929$	−1.93532	+	0.628822i	−0.0634957	+	0.0206310i	−0.340593	−	0.940211i	$-0.610628\pi$
$929$	−1.93532	+	0.628822i	−0.0634957	+	0.0206310i	0.277097	+	0.960842i	$0.410628\pi$
$930$		0			0
$931$	−2.04736	+	2.81796i	−0.0670997	+	0.0923548i
$932$	17.5850	−	12.7763i	0.576016	−	0.418500i
$933$		0			0
$934$		−	38.4430i		−	1.25789i
$935$	10.8122	−	11.9075i	0.353597	−	0.389418i
$936$		0			0
$937$	−28.2962	−	9.19398i	−0.924395	−	0.300354i	−0.192127	−	0.981370i	$-0.561538\pi$
$937$	−28.2962	−	9.19398i	−0.924395	−	0.300354i	−0.732269	+	0.681016i	$0.761538\pi$
$938$	0.776447	+	1.06869i	0.0253519	+	0.0348939i
$939$		0			0
$940$	−4.92217	−	15.1489i	−0.160544	−	0.494103i
$941$	4.26764	+	13.1344i	0.139121	+	0.428171i	0.996208	−	0.0870007i	$-0.0277282\pi$
$941$	4.26764	+	13.1344i	0.139121	+	0.428171i	−0.857087	+	0.515171i	$0.827728\pi$
$942$		0			0
$943$	−25.9679	−	35.7418i	−0.845632	−	1.16391i
$944$	−2.64134	−	0.858224i	−0.0859684	−	0.0279328i
$945$		0			0
$946$	2.19617	−	20.0857i	0.0714036	−	0.653041i
$947$		−	8.36727i		−	0.271900i	−0.990716	−	0.135950i	$-0.956591\pi$
$947$		−	8.36727i		−	0.271900i	0.990716	−	0.135950i	$-0.0434086\pi$
$948$		0			0
$949$	30.5330	−	22.1835i	0.991142	−	0.720107i
$950$	−0.512690	+	0.705657i	−0.0166339	+	0.0228945i
$951$		0			0
$952$	2.01282	−	0.654006i	0.0652360	−	0.0211965i
$953$	−18.1461	−	13.1839i	−0.587809	−	0.427068i	0.253722	−	0.967277i	$-0.418345\pi$
$953$	−18.1461	−	13.1839i	−0.587809	−	0.427068i	−0.841531	+	0.540209i	$0.818345\pi$
$954$		0			0
$955$	−15.1694	+	46.6867i	−0.490871	+	1.51075i
$956$	8.85623			0.286431
$957$		0			0
$958$	29.6183			0.956924
$959$	−5.55445	+	17.0948i	−0.179362	+	0.552021i
$960$		0			0
$961$	23.6640	+	17.1929i	0.763355	+	0.554610i
$962$	−31.8890	+	10.3614i	−1.02814	+	0.334064i
$963$		0			0
$964$	−7.28479	+	10.0267i	−0.234627	+	0.322937i
$965$	−28.2991	+	20.5605i	−0.910981	+	0.661866i
$966$		0			0
$967$		−	61.8603i		−	1.98929i	−0.103338	−	0.994646i	$-0.532952\pi$
$967$		−	61.8603i		−	1.98929i	0.103338	−	0.994646i	$-0.467048\pi$
$968$	5.57959	−	9.47988i	0.179335	−	0.304695i
$969$		0			0
$970$	−26.0921	−	8.47784i	−0.837767	−	0.272207i
$971$	2.68482	+	3.69534i	0.0861600	+	0.118589i	0.849921	−	0.526910i	$-0.176649\pi$
$971$	2.68482	+	3.69534i	0.0861600	+	0.118589i	−0.763761	+	0.645499i	$0.776649\pi$
$972$		0			0
$973$	−6.77482	−	20.8508i	−0.217191	−	0.668445i
$974$	3.06024	+	9.41846i	0.0980565	+	0.301787i
$975$		0			0
$976$	2.61927	+	3.60511i	0.0838407	+	0.115397i
$977$	37.3209	+	12.1263i	1.19400	+	0.387955i	0.837551	−	0.546359i	$-0.183987\pi$
$977$	37.3209	+	12.1263i	1.19400	+	0.387955i	0.356451	+	0.934314i	$0.383987\pi$
$978$		0			0
$979$	−36.5049	+	7.59973i	−1.16670	+	0.242888i
$980$		−	2.29138i		−	0.0731954i
$981$		0			0
$982$	−34.7436	+	25.2427i	−1.10871	+	0.805528i
$983$	−5.02841	+	6.92101i	−0.160381	+	0.220746i	−0.881643	−	0.471917i	$-0.843562\pi$
$983$	−5.02841	+	6.92101i	−0.160381	+	0.220746i	0.721262	+	0.692662i	$0.243562\pi$
$984$		0			0
$985$	−17.7202	+	5.75764i	−0.564612	+	0.183454i
$986$	11.2817	+	8.19662i	0.359282	+	0.261034i
$987$		0			0
$988$	−4.36276	+	13.4272i	−0.138798	+	0.427176i
$989$	−25.2156			−0.801809
$990$		0			0
$991$	36.1365			1.14792			0.573958	−	0.818885i	$-0.305407\pi$
$991$	36.1365			1.14792			0.573958	+	0.818885i	$0.305407\pi$
$992$	−0.408754	+	1.25802i	−0.0129780	+	0.0399421i
$993$		0			0
$994$	8.45191	+	6.14067i	0.268078	+	0.194770i
$995$	25.2742	−	8.21210i	0.801247	−	0.260341i
$996$		0			0
$997$	29.9135	−	41.1725i	0.947372	−	1.30395i	−0.00531341	−	0.999986i	$-0.501691\pi$
$997$	29.9135	−	41.1725i	0.947372	−	1.30395i	0.952685	−	0.303959i	$-0.0983087\pi$
$998$	−10.3606	+	7.52742i	−0.327959	+	0.238276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.a.827.3	✓	48
3.2	odd	2		1386.2.bu.b.827.10	yes	48
11.6	odd	10		1386.2.bu.b.1205.10	yes	48
33.17	even	10	inner	1386.2.bu.a.1205.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.827.3	✓	48	1.1	even	1	trivial
1386.2.bu.a.1205.3	yes	48	33.17	even	10	inner
1386.2.bu.b.827.10	yes	48	3.2	odd	2
1386.2.bu.b.1205.10	yes	48	11.6	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.17923 + 0.708075i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.17923 + 0.708075i) q^{5} +(0.587785 - 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +2.29138i q^{10} +(-0.675973 - 3.24701i) q^{11} +(3.85486 + 1.25252i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.654006 - 2.01282i) q^{17} +(-2.04736 - 2.81796i) q^{19} +(2.17923 + 0.708075i) q^{20} +(-3.29698 - 0.360492i) q^{22} +4.13903i q^{23} +(0.202590 - 0.147190i) q^{25} +(2.38244 - 3.27914i) q^{26} +(-0.951057 + 0.309017i) q^{28} +(-5.33058 - 3.87289i) q^{29} +(-0.408754 + 1.25802i) q^{31} +1.00000 q^{32} -2.11641 q^{34} +(-0.708075 + 2.17923i) q^{35} +(-6.69252 - 4.86240i) q^{37} +(-3.31271 + 1.07636i) q^{38} +(1.34684 - 1.85376i) q^{40} +(-8.63531 + 6.27392i) q^{41} +6.09215i q^{43} +(-1.36167 + 3.02421i) q^{44} +(3.93645 + 1.27903i) q^{46} +(-4.08598 - 5.62387i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-0.0773823 - 0.238158i) q^{50} +(-2.38244 - 3.27914i) q^{52} +(-8.58958 - 2.79092i) q^{53} +(3.77223 + 6.59734i) q^{55} +1.00000i q^{56} +(-5.33058 + 3.87289i) q^{58} +(-1.63244 + 2.24686i) q^{59} +(4.23807 - 1.37703i) q^{61} +(1.07013 + 0.777497i) q^{62} +(0.309017 - 0.951057i) q^{64} -9.28751 q^{65} -1.32097 q^{67} +(-0.654006 + 2.01282i) q^{68} +(1.85376 + 1.34684i) q^{70} +(-9.93582 + 3.22834i) q^{71} +(5.47303 - 7.53298i) q^{73} +(-6.69252 + 4.86240i) q^{74} +3.48318i q^{76} +(-3.02421 - 1.36167i) q^{77} +(-14.1766 - 4.60625i) q^{79} +(-1.34684 - 1.85376i) q^{80} +(3.29839 + 10.1514i) q^{82} +(2.27937 + 7.01519i) q^{83} +(2.85046 + 3.92332i) q^{85} +(5.79398 + 1.88258i) q^{86} +(2.45542 + 2.22956i) q^{88} -11.2426i q^{89} +(3.27914 - 2.38244i) q^{91} +(2.43286 - 3.34855i) q^{92} +(-6.61126 + 2.14813i) q^{94} +(6.45700 + 4.69129i) q^{95} +(-3.69989 + 11.3871i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

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