LMFDB - Embedded newform 1161.2.f.c.775.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1161,2,Mod(388,1161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1161, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1161.388");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1161 = 3^{3} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1161.f (of order $3$, degree $2$, not 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:	$9.27063167467$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 387)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			775.4
Character	$\chi$	$=$	1161.775
Dual form			1161.2.f.c.388.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.887526 + 1.53724i) q^{2} +(-0.575406 - 0.996632i) q^{4} +(1.84963 + 3.20365i) q^{5} +(0.0448503 - 0.0776831i) q^{7} -1.50735 q^{8} +O(q^{10})$	\(q+(-0.887526 + 1.53724i) q^{2} +(-0.575406 - 0.996632i) q^{4} +(1.84963 + 3.20365i) q^{5} +(0.0448503 - 0.0776831i) q^{7} -1.50735 q^{8} -6.56638 q^{10} +(-2.40540 + 4.16628i) q^{11} +(-2.20207 - 3.81410i) q^{13} +(0.0796117 + 0.137892i) q^{14} +(2.48863 - 4.31043i) q^{16} -4.51570 q^{17} +0.457142 q^{19} +(2.12858 - 3.68680i) q^{20} +(-4.26972 - 7.39537i) q^{22} +(-3.13921 - 5.43728i) q^{23} +(-4.34227 + 7.52103i) q^{25} +7.81759 q^{26} -0.103229 q^{28} +(2.41056 - 4.17521i) q^{29} +(1.62230 + 2.80991i) q^{31} +(2.91009 + 5.04043i) q^{32} +(4.00780 - 6.94171i) q^{34} +0.331826 q^{35} -9.48421 q^{37} +(-0.405726 + 0.702738i) q^{38} +(-2.78805 - 4.82904i) q^{40} +(3.54390 + 6.13822i) q^{41} +(-0.500000 + 0.866025i) q^{43} +5.53633 q^{44} +11.1445 q^{46} +(1.98801 - 3.44334i) q^{47} +(3.49598 + 6.05521i) q^{49} +(-7.70775 - 13.3502i) q^{50} +(-2.53417 + 4.38932i) q^{52} -8.18271 q^{53} -17.7964 q^{55} +(-0.0676053 + 0.117096i) q^{56} +(4.27886 + 7.41121i) q^{58} +(4.89338 + 8.47559i) q^{59} +(-5.86886 + 10.1652i) q^{61} -5.75934 q^{62} -0.376622 q^{64} +(8.14605 - 14.1094i) q^{65} +(3.11026 + 5.38713i) q^{67} +(2.59836 + 4.50049i) q^{68} +(-0.294505 + 0.510097i) q^{70} -13.8969 q^{71} +11.2453 q^{73} +(8.41748 - 14.5795i) q^{74} +(-0.263042 - 0.455603i) q^{76} +(0.215766 + 0.373718i) q^{77} +(4.64684 - 8.04856i) q^{79} +18.4122 q^{80} -12.5812 q^{82} +(2.01802 - 3.49531i) q^{83} +(-8.35237 - 14.4667i) q^{85} +(-0.887526 - 1.53724i) q^{86} +(3.62579 - 6.28006i) q^{88} -8.46429 q^{89} -0.395055 q^{91} +(-3.61264 + 6.25728i) q^{92} +(3.52883 + 6.11211i) q^{94} +(0.845545 + 1.46453i) q^{95} +(0.339574 - 0.588160i) q^{97} -12.4111 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 4 q^{2} - 22 q^{4} + 9 q^{5} - 7 q^{7} - 24 q^{8}+O(q^{10}) $ 38 * q + 4 * q^2 - 22 * q^4 + 9 * q^5 - 7 * q^7 - 24 * q^8	$ 38 q + 4 q^{2} - 22 q^{4} + 9 q^{5} - 7 q^{7} - 24 q^{8} - 14 q^{10} + 5 q^{11} + 5 q^{13} + 17 q^{14} - 24 q^{16} - 42 q^{17} - 8 q^{19} + 21 q^{20} + 20 q^{22} + 22 q^{23} - 10 q^{25} - 34 q^{26} - 2 q^{28} + 30 q^{29} + 5 q^{31} + 48 q^{32} + 6 q^{34} - 106 q^{35} - 2 q^{37} + 21 q^{38} - 16 q^{40} + 29 q^{41} - 19 q^{43} - 58 q^{44} + 32 q^{47} + 10 q^{49} - 11 q^{50} - q^{52} - 76 q^{53} + 4 q^{55} + 46 q^{56} - 30 q^{58} + 30 q^{59} + 10 q^{61} - 50 q^{62} + 28 q^{64} + 8 q^{65} - 3 q^{67} + 47 q^{68} - 56 q^{70} - 42 q^{71} + 16 q^{73} + 28 q^{74} + 36 q^{76} + 49 q^{77} - 4 q^{79} - 140 q^{80} - 8 q^{82} + 29 q^{83} + 4 q^{85} + 4 q^{86} + 47 q^{88} - 108 q^{89} + 8 q^{91} + 12 q^{92} + 23 q^{94} + 33 q^{95} + 4 q^{97} - 98 q^{98}+O(q^{100}) $ 38 * q + 4 * q^2 - 22 * q^4 + 9 * q^5 - 7 * q^7 - 24 * q^8 - 14 * q^10 + 5 * q^11 + 5 * q^13 + 17 * q^14 - 24 * q^16 - 42 * q^17 - 8 * q^19 + 21 * q^20 + 20 * q^22 + 22 * q^23 - 10 * q^25 - 34 * q^26 - 2 * q^28 + 30 * q^29 + 5 * q^31 + 48 * q^32 + 6 * q^34 - 106 * q^35 - 2 * q^37 + 21 * q^38 - 16 * q^40 + 29 * q^41 - 19 * q^43 - 58 * q^44 + 32 * q^47 + 10 * q^49 - 11 * q^50 - q^52 - 76 * q^53 + 4 * q^55 + 46 * q^56 - 30 * q^58 + 30 * q^59 + 10 * q^61 - 50 * q^62 + 28 * q^64 + 8 * q^65 - 3 * q^67 + 47 * q^68 - 56 * q^70 - 42 * q^71 + 16 * q^73 + 28 * q^74 + 36 * q^76 + 49 * q^77 - 4 * q^79 - 140 * q^80 - 8 * q^82 + 29 * q^83 + 4 * q^85 + 4 * q^86 + 47 * q^88 - 108 * q^89 + 8 * q^91 + 12 * q^92 + 23 * q^94 + 33 * q^95 + 4 * q^97 - 98 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1161\mathbb{Z}\right)^\times$.

$n$	$433$	$947$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.887526	+	1.53724i	−0.627576	+	1.08699i	0.360461	+	0.932774i	$0.382619\pi$
$2$	−0.887526	+	1.53724i	−0.627576	+	1.08699i	−0.988037	+	0.154219i	$0.950714\pi$
$3$		0			0
$3$		0			0
$4$	−0.575406	−	0.996632i	−0.287703	−	0.498316i
$5$	1.84963	+	3.20365i	0.827180	+	1.43272i	0.900242	+	0.435390i	$0.143390\pi$
$5$	1.84963	+	3.20365i	0.827180	+	1.43272i	−0.0730618	+	0.997327i	$0.523277\pi$
$6$		0			0
$7$	0.0448503	−	0.0776831i	0.0169518	−	0.0293614i	−0.857425	−	0.514609i	$-0.827937\pi$
$7$	0.0448503	−	0.0776831i	0.0169518	−	0.0293614i	0.874377	+	0.485247i	$0.161270\pi$
$8$	−1.50735			−0.532930
$9$		0			0
$10$	−6.56638			−2.07647
$11$	−2.40540	+	4.16628i	−0.725256	+	1.25618i	0.233612	+	0.972330i	$0.424945\pi$
$11$	−2.40540	+	4.16628i	−0.725256	+	1.25618i	−0.958868	+	0.283851i	$0.908388\pi$
$12$		0			0
$13$	−2.20207	−	3.81410i	−0.610745	−	1.05784i	−0.991115	−	0.133007i	$-0.957537\pi$
$13$	−2.20207	−	3.81410i	−0.610745	−	1.05784i	0.380370	−	0.924835i	$-0.375797\pi$
$14$	0.0796117	+	0.137892i	0.0212771	+	0.0368531i
$15$		0			0
$16$	2.48863	−	4.31043i	0.622157	−	1.07761i
$17$	−4.51570			−1.09522			−0.547609	−	0.836735i	$-0.684462\pi$
$17$	−4.51570			−1.09522			−0.547609	+	0.836735i	$0.684462\pi$
$18$		0			0
$19$	0.457142			0.104876			0.0524378	−	0.998624i	$-0.483301\pi$
$19$	0.457142			0.104876			0.0524378	+	0.998624i	$0.483301\pi$
$20$	2.12858	−	3.68680i	0.475964	−	0.824394i
$21$		0			0
$22$	−4.26972	−	7.39537i	−0.910307	−	1.57670i
$23$	−3.13921	−	5.43728i	−0.654571	−	1.13375i	−0.982001	−	0.188875i	$-0.939516\pi$
$23$	−3.13921	−	5.43728i	−0.654571	−	1.13375i	0.327430	−	0.944875i	$-0.393817\pi$
$24$		0			0
$25$	−4.34227	+	7.52103i	−0.868453	+	1.50421i
$26$	7.81759			1.53316
$27$		0			0
$28$	−0.103229			−0.0195084
$29$	2.41056	−	4.17521i	0.447629	−	0.775316i	−0.550602	−	0.834768i	$-0.685602\pi$
$29$	2.41056	−	4.17521i	0.447629	−	0.775316i	0.998231	+	0.0594516i	$0.0189352\pi$
$30$		0			0
$31$	1.62230	+	2.80991i	0.291374	+	0.504674i	0.974135	−	0.225967i	$-0.0725543\pi$
$31$	1.62230	+	2.80991i	0.291374	+	0.504674i	−0.682761	+	0.730642i	$0.739221\pi$
$32$	2.91009	+	5.04043i	0.514436	+	0.891030i
$33$		0			0
$34$	4.00780	−	6.94171i	0.687332	−	1.19049i
$35$	0.331826			0.0560889
$36$		0			0
$37$	−9.48421			−1.55919			−0.779597	−	0.626282i	$-0.784576\pi$
$37$	−9.48421			−1.55919			−0.779597	+	0.626282i	$0.784576\pi$
$38$	−0.405726	+	0.702738i	−0.0658174	+	0.113999i
$39$		0			0
$40$	−2.78805	−	4.82904i	−0.440829	−	0.763538i
$41$	3.54390	+	6.13822i	0.553465	+	0.958629i	0.998021	+	0.0628784i	$0.0200280\pi$
$41$	3.54390	+	6.13822i	0.553465	+	0.958629i	−0.444556	+	0.895751i	$0.646639\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i
$44$	5.53633			0.834634
$45$		0			0
$46$	11.1445			1.64317
$47$	1.98801	−	3.44334i	0.289982	−	0.502263i	−0.683823	−	0.729648i	$-0.739684\pi$
$47$	1.98801	−	3.44334i	0.289982	−	0.502263i	0.973805	+	0.227385i	$0.0730174\pi$
$48$		0			0
$49$	3.49598	+	6.05521i	0.499425	+	0.865030i
$50$	−7.70775	−	13.3502i	−1.09004	−	1.88801i
$51$		0			0
$52$	−2.53417	+	4.38932i	−0.351427	+	0.608689i
$53$	−8.18271			−1.12398			−0.561991	−	0.827143i	$-0.689964\pi$
$53$	−8.18271			−1.12398			−0.561991	+	0.827143i	$0.689964\pi$
$54$		0			0
$55$	−17.7964			−2.39967
$56$	−0.0676053	+	0.117096i	−0.00903414	+	0.0156476i
$57$		0			0
$58$	4.27886	+	7.41121i	0.561842	+	0.973140i
$59$	4.89338	+	8.47559i	0.637064	+	1.10343i	0.986074	+	0.166308i	$0.0531847\pi$
$59$	4.89338	+	8.47559i	0.637064	+	1.10343i	−0.349010	+	0.937119i	$0.613482\pi$
$60$		0			0
$61$	−5.86886	+	10.1652i	−0.751431	+	1.30152i	0.195698	+	0.980664i	$0.437303\pi$
$61$	−5.86886	+	10.1652i	−0.751431	+	1.30152i	−0.947129	+	0.320853i	$0.896031\pi$
$62$	−5.75934			−0.731437
$63$		0			0
$64$	−0.376622			−0.0470778
$65$	8.14605	−	14.1094i	1.01039	−	1.75005i
$66$		0			0
$67$	3.11026	+	5.38713i	0.379979	+	0.658143i	0.991059	−	0.133426i	$-0.0425979\pi$
$67$	3.11026	+	5.38713i	0.379979	+	0.658143i	−0.611080	+	0.791569i	$0.709265\pi$
$68$	2.59836	+	4.50049i	0.315097	+	0.545765i
$69$		0			0
$70$	−0.294505	+	0.510097i	−0.0352000	+	0.0609682i
$71$	−13.8969			−1.64925			−0.824627	−	0.565676i	$-0.808615\pi$
$71$	−13.8969			−1.64925			−0.824627	+	0.565676i	$0.808615\pi$
$72$		0			0
$73$	11.2453			1.31616			0.658078	−	0.752949i	$-0.271369\pi$
$73$	11.2453			1.31616			0.658078	+	0.752949i	$0.271369\pi$
$74$	8.41748	−	14.5795i	0.978513	−	1.69483i
$75$		0			0
$76$	−0.263042	−	0.455603i	−0.0301730	−	0.0522612i
$77$	0.215766	+	0.373718i	0.0245889	+	0.0425892i
$78$		0			0
$79$	4.64684	−	8.04856i	0.522810	−	0.905534i	−0.476838	−	0.878991i	$-0.658217\pi$
$79$	4.64684	−	8.04856i	0.522810	−	0.905534i	0.999648	−	0.0265422i	$-0.00844963\pi$
$80$	18.4122			2.05854
$81$		0			0
$82$	−12.5812			−1.38936
$83$	2.01802	−	3.49531i	0.221506	−	0.383660i	−0.733759	−	0.679409i	$-0.762236\pi$
$83$	2.01802	−	3.49531i	0.221506	−	0.383660i	0.955266	+	0.295750i	$0.0955694\pi$
$84$		0			0
$85$	−8.35237	−	14.4667i	−0.905942	−	1.56914i
$86$	−0.887526	−	1.53724i	−0.0957044	−	0.165765i
$87$		0			0
$88$	3.62579	−	6.28006i	0.386511	−	0.669456i
$89$	−8.46429			−0.897213			−0.448607	−	0.893729i	$-0.648080\pi$
$89$	−8.46429			−0.897213			−0.448607	+	0.893729i	$0.648080\pi$
$90$		0			0
$91$	−0.395055			−0.0414130
$92$	−3.61264	+	6.25728i	−0.376644	+	0.652367i
$93$		0			0
$94$	3.52883	+	6.11211i	0.363971	+	0.630416i
$95$	0.845545	+	1.46453i	0.0867510	+	0.150257i
$96$		0			0
$97$	0.339574	−	0.588160i	0.0344785	−	0.0597186i	−0.848271	−	0.529562i	$-0.822356\pi$
$97$	0.339574	−	0.588160i	0.0344785	−	0.0597186i	0.882750	+	0.469843i	$0.155690\pi$
$98$	−12.4111			−1.25371
$99$		0			0
$100$	9.99427			0.999427
$101$	1.81569	−	3.14487i	0.180668	−	0.312926i	−0.761440	−	0.648235i	$-0.775507\pi$
$101$	1.81569	−	3.14487i	0.180668	−	0.312926i	0.942108	+	0.335309i	$0.108841\pi$
$102$		0			0
$103$	2.72973	+	4.72803i	0.268968	+	0.465867i	0.968596	−	0.248641i	$-0.0799839\pi$
$103$	2.72973	+	4.72803i	0.268968	+	0.465867i	−0.699627	+	0.714508i	$0.746651\pi$
$104$	3.31930	+	5.74920i	0.325484	+	0.563756i
$105$		0			0
$106$	7.26237	−	12.5788i	0.705384	−	1.22176i
$107$	2.04706			0.197896			0.0989482	−	0.995093i	$-0.468452\pi$
$107$	2.04706			0.197896			0.0989482	+	0.995093i	$0.468452\pi$
$108$		0			0
$109$	−1.75892			−0.168474			−0.0842371	−	0.996446i	$-0.526845\pi$
$109$	−1.75892			−0.168474			−0.0842371	+	0.996446i	$0.526845\pi$
$110$	15.7948	−	27.3574i	1.50598	−	2.60843i
$111$		0			0
$112$	−0.223232	−	0.386649i	−0.0210934	−	0.0365349i
$113$	−6.71065	−	11.6232i	−0.631285	−	1.09342i	−0.987289	−	0.158933i	$-0.949195\pi$
$113$	−6.71065	−	11.6232i	−0.631285	−	1.09342i	0.356005	−	0.934484i	$-0.384139\pi$
$114$		0			0
$115$	11.6128	−	20.1139i	1.08290	−	1.87563i
$116$	−5.54819			−0.515137
$117$		0			0
$118$	−17.3720			−1.59922
$119$	−0.202531	+	0.350793i	−0.0185659	+	0.0321572i
$120$		0			0
$121$	−6.07193	−	10.5169i	−0.551994	−	0.956081i
$122$	−10.4175	−	18.0437i	−0.943160	−	1.63360i
$123$		0			0
$124$	1.86696	−	3.23368i	0.167658	−	0.290393i
$125$	−13.6301			−1.21911
$126$		0			0
$127$	5.69493			0.505344			0.252672	−	0.967552i	$-0.418691\pi$
$127$	5.69493			0.505344			0.252672	+	0.967552i	$0.418691\pi$
$128$	−5.48592	+	9.50190i	−0.484892	+	0.839857i
$129$		0			0
$130$	14.4597	+	25.0449i	1.26820	+	2.19658i
$131$	−0.210408	−	0.364437i	−0.0183834	−	0.0318410i	0.856687	−	0.515836i	$-0.172519\pi$
$131$	−0.210408	−	0.364437i	−0.0183834	−	0.0318410i	−0.875071	+	0.483995i	$0.839185\pi$
$132$		0			0
$133$	0.0205030	−	0.0355122i	0.00177784	−	0.00307930i
$134$	−11.0418			−0.953862
$135$		0			0
$136$	6.80675			0.583674
$137$	−6.53263	+	11.3149i	−0.558120	+	0.966693i	0.439533	+	0.898226i	$0.355144\pi$
$137$	−6.53263	+	11.3149i	−0.558120	+	0.966693i	−0.997653	+	0.0684665i	$0.978189\pi$
$138$		0			0
$139$	−3.71118	−	6.42796i	−0.314778	−	0.545212i	0.664612	−	0.747189i	$-0.268597\pi$
$139$	−3.71118	−	6.42796i	−0.314778	−	0.545212i	−0.979390	+	0.201977i	$0.935264\pi$
$140$	−0.190935	−	0.330709i	−0.0161369	−	0.0279500i
$141$		0			0
$142$	12.3338	−	21.3628i	1.03503	−	1.79273i
$143$	21.1875			1.77179
$144$		0			0
$145$	17.8346			1.48108
$146$	−9.98046	+	17.2867i	−0.825988	+	1.43065i
$147$		0			0
$148$	5.45727	+	9.45227i	0.448585	+	0.776972i
$149$	−1.28740	−	2.22984i	−0.105468	−	0.182676i	0.808461	−	0.588549i	$-0.200301\pi$
$149$	−1.28740	−	2.22984i	−0.105468	−	0.182676i	−0.913929	+	0.405874i	$0.866967\pi$
$150$		0			0
$151$	−9.06181	+	15.6955i	−0.737440	+	1.27728i	0.216205	+	0.976348i	$0.430632\pi$
$151$	−9.06181	+	15.6955i	−0.737440	+	1.27728i	−0.953645	+	0.300935i	$0.902701\pi$
$152$	−0.689075			−0.0558914
$153$		0			0
$154$	−0.765993			−0.0617255
$155$	−6.00131	+	10.3946i	−0.482037	+	0.834913i
$156$		0			0
$157$	−3.35336	−	5.80818i	−0.267627	−	0.463543i	0.700622	−	0.713533i	$-0.252906\pi$
$157$	−3.35336	−	5.80818i	−0.267627	−	0.463543i	−0.968249	+	0.249990i	$0.919573\pi$
$158$	8.24838	+	14.2866i	0.656206	+	1.13658i
$159$		0			0
$160$	−10.7652	+	18.6459i	−0.851063	+	1.47408i
$161$	−0.563179			−0.0443847
$162$		0			0
$163$	1.31744			0.103190			0.0515949	−	0.998668i	$-0.483570\pi$
$163$	1.31744			0.103190			0.0515949	+	0.998668i	$0.483570\pi$
$164$	4.07837	−	7.06394i	0.318467	−	0.551601i
$165$		0			0
$166$	3.58209	+	6.20436i	0.278024	+	0.481551i
$167$	11.8993	+	20.6102i	0.920795	+	1.59486i	0.798188	+	0.602408i	$0.205792\pi$
$167$	11.8993	+	20.6102i	0.920795	+	1.59486i	0.122607	+	0.992455i	$0.460875\pi$
$168$		0			0
$169$	−3.19826	+	5.53954i	−0.246020	+	0.426119i
$170$	29.6518			2.27419
$171$		0			0
$172$	1.15081			0.0877486
$173$	−2.23015	+	3.86273i	−0.169555	+	0.293678i	−0.938263	−	0.345921i	$-0.887566\pi$
$173$	−2.23015	+	3.86273i	−0.169555	+	0.293678i	0.768709	+	0.639599i	$0.220900\pi$
$174$		0			0
$175$	0.389504	+	0.674641i	0.0294438	+	0.0509981i
$176$	11.9723	+	20.7366i	0.902447	+	1.56308i
$177$		0			0
$178$	7.51228	−	13.0117i	0.563069	−	0.975265i
$179$	14.0146			1.04750			0.523749	−	0.851873i	$-0.324533\pi$
$179$	14.0146			1.04750			0.523749	+	0.851873i	$0.324533\pi$
$180$		0			0
$181$	−22.6669			−1.68481			−0.842407	−	0.538842i	$-0.818862\pi$
$181$	−22.6669			−1.68481			−0.842407	+	0.538842i	$0.818862\pi$
$182$	0.350622	−	0.607295i	0.0259898	−	0.0450157i
$183$		0			0
$184$	4.73190	+	8.19590i	0.348841	+	0.604210i
$185$	−17.5423	−	30.3841i	−1.28973	−	2.23388i
$186$		0			0
$187$	10.8621	−	18.8137i	0.794313	−	1.37579i
$188$	−4.57566			−0.333714
$189$		0			0
$190$	−3.00177			−0.217771
$191$	1.92889	−	3.34094i	0.139570	−	0.241742i	−0.787764	−	0.615977i	$-0.788761\pi$
$191$	1.92889	−	3.34094i	0.139570	−	0.241742i	0.927334	+	0.374235i	$0.122095\pi$
$192$		0			0
$193$	7.02503	+	12.1677i	0.505673	+	0.875851i	0.999978	+	0.00656281i	$0.00208902\pi$
$193$	7.02503	+	12.1677i	0.505673	+	0.875851i	−0.494306	+	0.869288i	$0.664578\pi$
$194$	0.602762	+	1.04401i	0.0432758	+	0.0749559i
$195$		0			0
$196$	4.02321	−	6.96841i	0.287372	−	0.497743i
$197$	−1.78785			−0.127379			−0.0636897	−	0.997970i	$-0.520287\pi$
$197$	−1.78785			−0.127379			−0.0636897	+	0.997970i	$0.520287\pi$
$198$		0			0
$199$	−17.5450			−1.24373			−0.621865	−	0.783125i	$-0.713625\pi$
$199$	−17.5450			−1.24373			−0.621865	+	0.783125i	$0.713625\pi$
$200$	6.54533	−	11.3368i	0.462825	−	0.801636i
$201$		0			0
$202$	3.22295	+	5.58231i	0.226766	+	0.392770i
$203$	−0.216229	−	0.374519i	−0.0151763	−	0.0262861i
$204$		0			0
$205$	−13.1098	+	22.7069i	−0.915630	+	1.58592i
$206$	−9.69083			−0.675192
$207$		0			0
$208$	−21.9206			−1.51992
$209$	−1.09961	+	1.90458i	−0.0760618	+	0.131743i
$210$		0			0
$211$	5.52699	+	9.57302i	0.380493	+	0.659034i	0.991133	−	0.132875i	$-0.0424208\pi$
$211$	5.52699	+	9.57302i	0.380493	+	0.659034i	−0.610639	+	0.791909i	$0.709087\pi$
$212$	4.70838	+	8.15515i	0.323373	+	0.560098i
$213$		0			0
$214$	−1.81682	+	3.14682i	−0.124195	+	0.215112i
$215$	−3.69926			−0.252288
$216$		0			0
$217$	0.291043			0.0197573
$218$	1.56109	−	2.70389i	0.105730	−	0.183130i
$219$		0			0
$220$	10.2402	+	17.7365i	0.690392	+	1.19579i
$221$	9.94390	+	17.2233i	0.668899	+	1.15857i
$222$		0			0
$223$	1.38127	−	2.39243i	0.0924968	−	0.160209i	−0.816064	−	0.577961i	$-0.803849\pi$
$223$	1.38127	−	2.39243i	0.0924968	−	0.160209i	0.908561	+	0.417752i	$0.137182\pi$
$224$	0.522075			0.0348826
$225$		0			0
$226$	23.8235			1.58472
$227$	4.95711	−	8.58597i	0.329015	−	0.569871i	−0.653302	−	0.757098i	$-0.726617\pi$
$227$	4.95711	−	8.58597i	0.329015	−	0.569871i	0.982317	+	0.187227i	$0.0599499\pi$
$228$		0			0
$229$	−2.55779	−	4.43023i	−0.169024	−	0.292758i	0.769053	−	0.639185i	$-0.220728\pi$
$229$	−2.55779	−	4.43023i	−0.169024	−	0.292758i	−0.938077	+	0.346427i	$0.887395\pi$
$230$	20.6133	+	35.7032i	1.35920	+	2.35420i
$231$		0			0
$232$	−3.63356	+	6.29351i	−0.238555	+	0.413189i
$233$	−14.9600			−0.980063			−0.490032	−	0.871705i	$-0.663015\pi$
$233$	−14.9600			−0.980063			−0.490032	+	0.871705i	$0.663015\pi$
$234$		0			0
$235$	14.7084			0.959468
$236$	5.63136	−	9.75381i	0.366570	−	0.634919i
$237$		0			0
$238$	−0.359502	−	0.622676i	−0.0233031	−	0.0403621i
$239$	−5.95980	−	10.3227i	−0.385507	−	0.667718i	0.606332	−	0.795212i	$-0.292640\pi$
$239$	−5.95980	−	10.3227i	−0.385507	−	0.667718i	−0.991839	+	0.127493i	$0.959307\pi$
$240$		0			0
$241$	−8.84983	+	15.3284i	−0.570068	+	0.987387i	0.426490	+	0.904492i	$0.359750\pi$
$241$	−8.84983	+	15.3284i	−0.570068	+	0.987387i	−0.996558	+	0.0828945i	$0.973584\pi$
$242$	21.5560			1.38567
$243$		0			0
$244$	13.5079			0.864756
$245$	−12.9325	+	22.3998i	−0.826229	+	1.43107i
$246$		0			0
$247$	−1.00666	−	1.74359i	−0.0640523	−	0.110942i
$248$	−2.44538	−	4.23552i	−0.155282	−	0.268956i
$249$		0			0
$250$	12.0970	−	20.9527i	0.765084	−	1.32516i
$251$	−20.2883			−1.28058			−0.640292	−	0.768131i	$-0.721187\pi$
$251$	−20.2883			−1.28058			−0.640292	+	0.768131i	$0.721187\pi$
$252$		0			0
$253$	30.2043			1.89893
$254$	−5.05440	+	8.75448i	−0.317141	+	0.549305i
$255$		0			0
$256$	−10.1144	−	17.5187i	−0.632151	−	1.09492i
$257$	13.4531	+	23.3015i	0.839182	+	1.45351i	0.890580	+	0.454827i	$0.150299\pi$
$257$	13.4531	+	23.3015i	0.839182	+	1.45351i	−0.0513980	+	0.998678i	$0.516368\pi$
$258$		0			0
$259$	−0.425370	+	0.736762i	−0.0264312	+	0.0457802i
$260$	−18.7491			−1.16277
$261$		0			0
$262$	0.746970			0.0461480
$263$	9.87604	−	17.1058i	0.608983	−	1.05479i	−0.382426	−	0.923986i	$-0.624911\pi$
$263$	9.87604	−	17.1058i	0.608983	−	1.05479i	0.991408	−	0.130803i	$-0.0417554\pi$
$264$		0			0
$265$	−15.1350	−	26.2146i	−0.929735	−	1.61035i
$266$	0.0363939	+	0.0630361i	0.00223145	+	0.00386499i
$267$		0			0
$268$	3.57933	−	6.19957i	0.218642	−	0.378699i
$269$	−12.3187			−0.751085			−0.375542	−	0.926805i	$-0.622544\pi$
$269$	−12.3187			−0.751085			−0.375542	+	0.926805i	$0.622544\pi$
$270$		0			0
$271$	10.3245			0.627168			0.313584	−	0.949560i	$-0.398470\pi$
$271$	10.3245			0.627168			0.313584	+	0.949560i	$0.398470\pi$
$272$	−11.2379	+	19.4646i	−0.681397	+	1.18021i
$273$		0			0
$274$	−11.5958	−	20.0845i	−0.700526	−	1.21335i
$275$	−20.8898	−	36.1822i	−1.25970	−	2.18187i
$276$		0			0
$277$	−10.6063	+	18.3706i	−0.637269	+	1.10378i	0.348760	+	0.937212i	$0.386603\pi$
$277$	−10.6063	+	18.3706i	−0.637269	+	1.10378i	−0.986029	+	0.166571i	$0.946731\pi$
$278$	13.1751			0.790189
$279$		0			0
$280$	−0.500180			−0.0298914
$281$	2.75338	−	4.76900i	0.164253	−	0.284495i	−0.772137	−	0.635456i	$-0.780812\pi$
$281$	2.75338	−	4.76900i	0.164253	−	0.284495i	0.936390	+	0.350962i	$0.114145\pi$
$282$		0			0
$283$	4.75839	+	8.24177i	0.282857	+	0.489922i	0.972087	−	0.234620i	$-0.0753845\pi$
$283$	4.75839	+	8.24177i	0.282857	+	0.489922i	−0.689230	+	0.724542i	$0.742051\pi$
$284$	7.99634	+	13.8501i	0.474495	+	0.821850i
$285$		0			0
$286$	−18.8045	+	32.5703i	−1.11193	+	1.92592i
$287$	0.635781			0.0375290
$288$		0			0
$289$	3.39152			0.199501
$290$	−15.8286	+	27.4160i	−0.929490	+	1.60992i
$291$		0			0
$292$	−6.47058	−	11.2074i	−0.378662	−	0.655862i
$293$	3.30265	+	5.72035i	0.192943	+	0.334187i	0.946224	−	0.323512i	$-0.104864\pi$
$293$	3.30265	+	5.72035i	0.192943	+	0.334187i	−0.753281	+	0.657698i	$0.771530\pi$
$294$		0			0
$295$	−18.1019	+	31.3534i	−1.05393	+	1.82547i
$296$	14.2961			0.830941
$297$		0			0
$298$	4.57040			0.264756
$299$	−13.8256	+	23.9466i	−0.799553	+	1.38487i
$300$		0			0
$301$	0.0448503	+	0.0776831i	0.00258513	+	0.00447758i
$302$	−16.0852	−	27.8604i	−0.925599	−	1.60318i
$303$		0			0
$304$	1.13766	−	1.97048i	0.0652491	−	0.113015i
$305$	−43.4209			−2.48627
$306$		0			0
$307$	9.30227			0.530908			0.265454	−	0.964123i	$-0.414478\pi$
$307$	9.30227			0.530908			0.265454	+	0.964123i	$0.414478\pi$
$308$	0.248307	−	0.430080i	0.0141486	−	0.0245061i
$309$		0			0
$310$	−10.6527	−	18.4509i	−0.605030	−	1.04794i
$311$	11.3860	+	19.7211i	0.645641	+	1.11828i	0.984153	+	0.177321i	$0.0567430\pi$
$311$	11.3860	+	19.7211i	0.645641	+	1.11828i	−0.338512	+	0.940962i	$0.609924\pi$
$312$		0			0
$313$	−4.81844	+	8.34578i	−0.272354	+	0.471731i	−0.969464	−	0.245233i	$-0.921136\pi$
$313$	−4.81844	+	8.34578i	−0.272354	+	0.471731i	0.697110	+	0.716964i	$0.254469\pi$
$314$	11.9048			0.671825
$315$		0			0
$316$	−10.6953			−0.601656
$317$	−16.5490	+	28.6637i	−0.929485	+	1.60992i	−0.145302	+	0.989387i	$0.546415\pi$
$317$	−16.5490	+	28.6637i	−0.929485	+	1.60992i	−0.784184	+	0.620529i	$0.786918\pi$
$318$		0			0
$319$	11.5967	+	20.0861i	0.649292	+	1.12461i
$320$	−0.696612	−	1.20657i	−0.0389418	−	0.0674491i
$321$		0			0
$322$	0.499836	−	0.865742i	0.0278548	−	0.0482459i
$323$	−2.06432			−0.114862
$324$		0			0
$325$	38.2480			2.12162
$326$	−1.16926	+	2.02522i	−0.0647594	+	0.112167i
$327$		0			0
$328$	−5.34192	−	9.25247i	−0.294958	−	0.510882i
$329$	−0.178326	−	0.308870i	−0.00983145	−	0.0170286i
$330$		0			0
$331$	−6.08451	+	10.5387i	−0.334435	+	0.579258i	−0.983376	−	0.181580i	$-0.941879\pi$
$331$	−6.08451	+	10.5387i	−0.334435	+	0.579258i	0.648941	+	0.760839i	$0.275212\pi$
$332$	−4.64472			−0.254912
$333$		0			0
$334$	−42.2437			−2.31147
$335$	−11.5057	+	19.9284i	−0.628622	+	1.08880i
$336$		0			0
$337$	1.84427	+	3.19438i	0.100464	+	0.174009i	0.911876	−	0.410466i	$-0.134634\pi$
$337$	1.84427	+	3.19438i	0.100464	+	0.174009i	−0.811412	+	0.584475i	$0.801301\pi$
$338$	−5.67707	−	9.83298i	−0.308792	−	0.534844i
$339$		0			0
$340$	−9.61201	+	16.6485i	−0.521284	+	0.902891i
$341$	−15.6092			−0.845283
$342$		0			0
$343$	1.25509			0.0677684
$344$	0.753677	−	1.30541i	0.0406355	−	0.0703828i
$345$		0			0
$346$	−3.95863	−	6.85655i	−0.212817	−	0.368610i
$347$	−10.9502	−	18.9663i	−0.587837	−	1.01816i	−0.994515	−	0.104593i	$-0.966646\pi$
$347$	−10.9502	−	18.9663i	−0.587837	−	1.01816i	0.406678	−	0.913572i	$-0.366687\pi$
$348$		0			0
$349$	3.95348	−	6.84762i	0.211625	−	0.366545i	−0.740598	−	0.671948i	$-0.765458\pi$
$349$	3.95348	−	6.84762i	0.211625	−	0.366545i	0.952223	+	0.305403i	$0.0987912\pi$
$350$	−1.38278			−0.0739128
$351$		0			0
$352$	−27.9998			−1.49239
$353$	−4.71820	+	8.17216i	−0.251124	+	0.434960i	−0.963836	−	0.266497i	$-0.914134\pi$
$353$	−4.71820	+	8.17216i	−0.251124	+	0.434960i	0.712711	+	0.701458i	$0.247467\pi$
$354$		0			0
$355$	−25.7041	−	44.5208i	−1.36423	−	2.36292i
$356$	4.87040	+	8.43579i	0.258131	+	0.447096i
$357$		0			0
$358$	−12.4383	+	21.5438i	−0.657384	+	1.13862i
$359$	20.4163			1.07753			0.538765	−	0.842456i	$-0.318891\pi$
$359$	20.4163			1.07753			0.538765	+	0.842456i	$0.318891\pi$
$360$		0			0
$361$	−18.7910			−0.989001
$362$	20.1174	−	34.8444i	1.05735	−	1.83138i
$363$		0			0
$364$	0.227317	+	0.393725i	0.0119147	+	0.0206368i
$365$	20.7996	+	36.0259i	1.08870	+	1.88568i
$366$		0			0
$367$	−2.01465	+	3.48947i	−0.105164	+	0.182149i	−0.913805	−	0.406153i	$-0.866870\pi$
$367$	−2.01465	+	3.48947i	−0.105164	+	0.182149i	0.808641	+	0.588302i	$0.200203\pi$
$368$	−31.2493			−1.62898
$369$		0			0
$370$	62.2769			3.23762
$371$	−0.366997	+	0.635658i	−0.0190536	+	0.0330017i
$372$		0			0
$373$	−4.64427	−	8.04412i	−0.240471	−	0.416509i	0.720377	−	0.693582i	$-0.243969\pi$
$373$	−4.64427	−	8.04412i	−0.240471	−	0.416509i	−0.960849	+	0.277074i	$0.910635\pi$
$374$	19.2808	+	33.3952i	0.996984	+	1.72683i
$375$		0			0
$376$	−2.99664	+	5.19033i	−0.154540	+	0.267671i
$377$	−21.2329			−1.09355
$378$		0			0
$379$	29.2337			1.50164			0.750818	−	0.660509i	$-0.229660\pi$
$379$	29.2337			1.50164			0.750818	+	0.660509i	$0.229660\pi$
$380$	0.973063	−	1.68539i	0.0499171	−	0.0864589i
$381$		0			0
$382$	3.42388	+	5.93034i	0.175181	+	0.303422i
$383$	6.92866	+	12.0008i	0.354038	+	0.613212i	0.986953	−	0.161010i	$-0.0514750\pi$
$383$	6.92866	+	12.0008i	0.354038	+	0.613212i	−0.632915	+	0.774221i	$0.718142\pi$
$384$		0			0
$385$	−0.798176	+	1.38248i	−0.0406788	+	0.0704578i
$386$	−24.9396			−1.26939
$387$		0			0
$388$	−0.781572			−0.0396783
$389$	5.47168	−	9.47723i	0.277425	−	0.480514i	−0.693319	−	0.720631i	$-0.743852\pi$
$389$	5.47168	−	9.47723i	0.277425	−	0.480514i	0.970744	+	0.240116i	$0.0771856\pi$
$390$		0			0
$391$	14.1757	+	24.5531i	0.716898	+	1.24170i
$392$	−5.26967	−	9.12734i	−0.266159	−	0.461000i
$393$		0			0
$394$	1.58677	−	2.74836i	0.0799402	−	0.138460i
$395$	34.3797			1.72983
$396$		0			0
$397$	−32.9079			−1.65160			−0.825799	−	0.563964i	$-0.809276\pi$
$397$	−32.9079			−1.65160			−0.825799	+	0.563964i	$0.809276\pi$
$398$	15.5716	−	26.9708i	0.780535	−	1.35193i
$399$		0			0
$400$	21.6126	+	37.4341i	1.08063	+	1.87170i
$401$	−6.40291	−	11.0902i	−0.319746	−	0.553817i	0.660689	−	0.750660i	$-0.270264\pi$
$401$	−6.40291	−	11.0902i	−0.319746	−	0.553817i	−0.980435	+	0.196843i	$0.936931\pi$
$402$		0			0
$403$	7.14485	−	12.3752i	0.355910	−	0.616455i
$404$	−4.17904			−0.207915
$405$		0			0
$406$	0.767634			0.0380970
$407$	22.8133	−	39.5139i	1.13082	−	1.95863i
$408$		0			0
$409$	10.4185	+	18.0453i	0.515160	+	0.892283i	0.999845	+	0.0175947i	$0.00560085\pi$
$409$	10.4185	+	18.0453i	0.515160	+	0.892283i	−0.484685	+	0.874689i	$0.661066\pi$
$410$	−23.2706	−	40.3059i	−1.14925	−	1.99057i
$411$		0			0
$412$	3.14141	−	5.44108i	0.154766	−	0.268063i
$413$	0.877879			0.0431976
$414$		0			0
$415$	14.9303			0.732902
$416$	12.8165	−	22.1988i	0.628379	−	1.08838i
$417$		0			0
$418$	−1.95187	−	3.38074i	−0.0954690	−	0.165357i
$419$	9.12325	+	15.8019i	0.445700	+	0.771975i	0.998101	−	0.0616036i	$-0.0196214\pi$
$419$	9.12325	+	15.8019i	0.445700	+	0.771975i	−0.552401	+	0.833579i	$0.686288\pi$
$420$		0			0
$421$	−10.3176	+	17.8706i	−0.502849	+	0.870960i	0.497146	+	0.867667i	$0.334381\pi$
$421$	−10.3176	+	17.8706i	−0.502849	+	0.870960i	−0.999995	+	0.00329287i	$0.998952\pi$
$422$	−19.6214			−0.955154
$423$		0			0
$424$	12.3342			0.599003
$425$	19.6084	−	33.9627i	0.951145	−	1.64743i
$426$		0			0
$427$	0.526441	+	0.911823i	0.0254763	+	0.0441262i
$428$	−1.17789	−	2.04016i	−0.0569354	−	0.0986150i
$429$		0			0
$430$	3.28319	−	5.68666i	0.158330	−	0.274235i
$431$	21.7596			1.04812			0.524062	−	0.851680i	$-0.324416\pi$
$431$	21.7596			1.04812			0.524062	+	0.851680i	$0.324416\pi$
$432$		0			0
$433$	28.7635			1.38229			0.691144	−	0.722717i	$-0.257107\pi$
$433$	28.7635			1.38229			0.691144	+	0.722717i	$0.257107\pi$
$434$	−0.258308	+	0.447403i	−0.0123992	+	0.0214760i
$435$		0			0
$436$	1.01209	+	1.75300i	0.0484705	+	0.0839534i
$437$	−1.43507	−	2.48561i	−0.0686486	−	0.118903i
$438$		0			0
$439$	13.1793	−	22.8273i	0.629015	−	1.08949i	−0.358735	−	0.933439i	$-0.616792\pi$
$439$	13.1793	−	22.8273i	0.629015	−	1.08949i	0.987750	−	0.156046i	$-0.0498749\pi$
$440$	26.8255			1.27886
$441$		0			0
$442$	−35.3019			−1.67914
$443$	−7.54201	+	13.0632i	−0.358332	+	0.620649i	−0.987682	−	0.156473i	$-0.949988\pi$
$443$	−7.54201	+	13.0632i	−0.358332	+	0.620649i	0.629350	+	0.777122i	$0.283321\pi$
$444$		0			0
$445$	−15.6558	−	27.1167i	−0.742157	−	1.28545i
$446$	2.45183	+	4.24669i	0.116097	+	0.201087i
$447$		0			0
$448$	−0.0168916	+	0.0292572i	−0.000798055	+	0.00138227i
$449$	29.9757			1.41464			0.707320	−	0.706893i	$-0.249904\pi$
$449$	29.9757			1.41464			0.707320	+	0.706893i	$0.249904\pi$
$450$		0			0
$451$	−34.0981			−1.60562
$452$	−7.72269	+	13.3761i	−0.363245	+	0.629159i
$453$		0			0
$454$	8.79914	+	15.2406i	0.412964	+	0.715275i
$455$	−0.730706	−	1.26562i	−0.0342560	−	0.0593332i
$456$		0			0
$457$	10.6554	−	18.4557i	0.498439	−	0.863322i	−0.501559	−	0.865123i	$-0.667240\pi$
$457$	10.6554	−	18.4557i	0.498439	−	0.863322i	0.999998	+	0.00180135i	$0.000573387\pi$
$458$	9.08043			0.424301
$459$		0			0
$460$	−26.7282			−1.24621
$461$	4.38481	−	7.59472i	0.204221	−	0.353721i	−0.745663	−	0.666323i	$-0.767867\pi$
$461$	4.38481	−	7.59472i	0.204221	−	0.353721i	0.949884	+	0.312602i	$0.101200\pi$
$462$		0			0
$463$	−15.7534	−	27.2856i	−0.732121	−	1.26807i	−0.955975	−	0.293448i	$-0.905197\pi$
$463$	−15.7534	−	27.2856i	−0.732121	−	1.26807i	0.223854	−	0.974623i	$-0.428136\pi$
$464$	−11.9980	−	20.7811i	−0.556991	−	0.964737i
$465$		0			0
$466$	13.2774	−	22.9971i	0.615064	−	1.06532i
$467$	−19.0342			−0.880796			−0.440398	−	0.897803i	$-0.645163\pi$
$467$	−19.0342			−0.880796			−0.440398	+	0.897803i	$0.645163\pi$
$468$		0			0
$469$	0.557985			0.0257654
$470$	−13.0541	+	22.6103i	−0.602139	+	1.04294i
$471$		0			0
$472$	−7.37606	−	12.7757i	−0.339510	−	0.588049i
$473$	−2.40540	−	4.16628i	−0.110601	−	0.191566i
$474$		0			0
$475$	−1.98503	+	3.43818i	−0.0910796	+	0.157755i
$476$	0.466149			0.0213659
$477$		0			0
$478$	21.1579			0.967741
$479$	18.1095	−	31.3665i	0.827443	−	1.43317i	−0.0725947	−	0.997362i	$-0.523128\pi$
$479$	18.1095	−	31.3665i	0.827443	−	1.43317i	0.900038	−	0.435812i	$-0.143539\pi$
$480$		0			0
$481$	20.8849	+	36.1737i	0.952270	+	1.64938i
$482$	−15.7089	−	27.2086i	−0.715522	−	1.23932i
$483$		0			0
$484$	−6.98765	+	12.1030i	−0.317621	+	0.550135i
$485$	2.51235			0.114080
$486$		0			0
$487$	17.1775			0.778386			0.389193	−	0.921156i	$-0.372754\pi$
$487$	17.1775			0.778386			0.389193	+	0.921156i	$0.372754\pi$
$488$	8.84645	−	15.3225i	0.400460	−	0.693617i
$489$		0			0
$490$	−22.9559	−	39.7608i	−1.03704	−	1.79621i
$491$	21.2708	+	36.8422i	0.959940	+	1.66266i	0.722636	+	0.691228i	$0.242930\pi$
$491$	21.2708	+	36.8422i	0.959940	+	1.66266i	0.237303	+	0.971436i	$0.423737\pi$
$492$		0			0
$493$	−10.8853	+	18.8540i	−0.490251	+	0.849140i
$494$	3.57375			0.160791
$495$		0			0
$496$	16.1492			0.725121
$497$	−0.623279	+	1.07955i	−0.0279579	+	0.0484245i
$498$		0			0
$499$	−4.14753	−	7.18374i	−0.185669	−	0.321588i	0.758133	−	0.652100i	$-0.226112\pi$
$499$	−4.14753	−	7.18374i	−0.185669	−	0.321588i	−0.943802	+	0.330512i	$0.892779\pi$
$500$	7.84282	+	13.5842i	0.350741	+	0.607502i
$501$		0			0
$502$	18.0064	−	31.1880i	0.803664	−	1.39199i
$503$	25.8405			1.15217			0.576085	−	0.817390i	$-0.304580\pi$
$503$	25.8405			1.15217			0.576085	+	0.817390i	$0.304580\pi$
$504$		0			0
$505$	13.4334			0.597780
$506$	−26.8071	+	46.4313i	−1.19172	+	2.06412i
$507$		0			0
$508$	−3.27690	−	5.67576i	−0.145389	−	0.251821i
$509$	−12.3424	−	21.3777i	−0.547069	−	0.947551i	−0.998474	−	0.0552315i	$-0.982410\pi$
$509$	−12.3424	−	21.3777i	−0.547069	−	0.947551i	0.451405	−	0.892319i	$-0.350923\pi$
$510$		0			0
$511$	0.504353	−	0.873566i	0.0223113	−	0.0386443i
$512$	13.9636			0.617109
$513$		0			0
$514$	−47.7599			−2.10660
$515$	−10.0980	+	17.4902i	−0.444971	+	0.770712i
$516$		0			0
$517$	9.56395	+	16.5653i	0.420622	+	0.728539i
$518$	−0.755054	−	1.30779i	−0.0331752	−	0.0574611i
$519$		0			0
$520$	−12.2790	+	21.2678i	−0.538468	+	0.932655i
$521$	39.1146			1.71364			0.856822	−	0.515613i	$-0.172436\pi$
$521$	39.1146			1.71364			0.856822	+	0.515613i	$0.172436\pi$
$522$		0			0
$523$	2.94374			0.128721			0.0643603	−	0.997927i	$-0.479499\pi$
$523$	2.94374			0.128721			0.0643603	+	0.997927i	$0.479499\pi$
$524$	−0.242140	+	0.419399i	−0.0105779	+	0.0183215i
$525$		0			0
$526$	17.5305	+	30.3637i	0.764366	+	1.32392i
$527$	−7.32582	−	12.6887i	−0.319118	−	0.552728i
$528$		0			0
$529$	−8.20932	+	14.2190i	−0.356927	+	0.618215i
$530$	53.7308			2.33392
$531$		0			0
$532$	−0.0471902			−0.00204595
$533$	15.6079	−	27.0336i	0.676052	−	1.17096i
$534$		0			0
$535$	3.78630	+	6.55806i	0.163696	+	0.283530i
$536$	−4.68826	−	8.12031i	−0.202502	−	0.350744i
$537$		0			0
$538$	10.9332	−	18.9368i	0.471363	−	0.816424i
$539$	−33.6369			−1.44885
$540$		0			0
$541$	−9.17458			−0.394446			−0.197223	−	0.980359i	$-0.563192\pi$
$541$	−9.17458			−0.394446			−0.197223	+	0.980359i	$0.563192\pi$
$542$	−9.16325	+	15.8712i	−0.393595	+	0.681727i
$543$		0			0
$544$	−13.1411	−	22.7610i	−0.563420	−	0.975872i
$545$	−3.25336	−	5.63498i	−0.139358	−	0.241376i
$546$		0			0
$547$	8.91666	−	15.4441i	0.381249	−	0.660343i	−0.609992	−	0.792407i	$-0.708827\pi$
$547$	8.91666	−	15.4441i	0.381249	−	0.660343i	0.991241	+	0.132065i	$0.0421607\pi$
$548$	15.0357			0.642292
$549$		0			0
$550$	74.1610			3.16224
$551$	1.10197	−	1.90866i	0.0469454	−	0.0813118i
$552$		0			0
$553$	−0.416825	−	0.721961i	−0.0177252	−	0.0307009i
$554$	−18.8267	−	32.6088i	−0.799870	−	1.38542i
$555$		0			0
$556$	−4.27087	+	7.39737i	−0.181125	+	0.313718i
$557$	−46.8931			−1.98693			−0.993463	−	0.114154i	$-0.963584\pi$
$557$	−46.8931			−1.98693			−0.993463	+	0.114154i	$0.963584\pi$
$558$		0			0
$559$	4.40415			0.186276
$560$	0.825792	−	1.43031i	0.0348961	−	0.0604418i
$561$		0			0
$562$	4.88740	+	8.46523i	0.206163	+	0.357084i
$563$	14.2646	+	24.7071i	0.601183	+	1.04128i	0.992642	+	0.121084i	$0.0386370\pi$
$563$	14.2646	+	24.7071i	0.601183	+	1.04128i	−0.391459	+	0.920195i	$0.628030\pi$
$564$		0			0
$565$	24.8244	−	42.9972i	1.04437	−	1.80891i
$566$	−16.8928			−0.710056
$567$		0			0
$568$	20.9475			0.878937
$569$	−7.20081	+	12.4722i	−0.301874	+	0.522860i	−0.976560	−	0.215244i	$-0.930945\pi$
$569$	−7.20081	+	12.4722i	−0.301874	+	0.522860i	0.674687	+	0.738104i	$0.264279\pi$
$570$		0			0
$571$	−4.92154	−	8.52435i	−0.205960	−	0.356733i	0.744478	−	0.667647i	$-0.232698\pi$
$571$	−4.92154	−	8.52435i	−0.205960	−	0.356733i	−0.950438	+	0.310914i	$0.899365\pi$
$572$	−12.1914	−	21.1162i	−0.509749	−	0.882911i
$573$		0			0
$574$	−0.564273	+	0.977349i	−0.0235523	+	0.0407938i
$575$	54.5252			2.27386
$576$		0			0
$577$	37.4871			1.56061			0.780304	−	0.625400i	$-0.215064\pi$
$577$	37.4871			1.56061			0.780304	+	0.625400i	$0.215064\pi$
$578$	−3.01006	+	5.21358i	−0.125202	+	0.216856i
$579$		0			0
$580$	−10.2621	−	17.7745i	−0.426111	−	0.738046i
$581$	−0.181018	−	0.313532i	−0.00750987	−	0.0130075i
$582$		0			0
$583$	19.6827	−	34.0915i	0.815175	−	1.41192i
$584$	−16.9506			−0.701419
$585$		0			0
$586$	−11.7247			−0.484345
$587$	−5.83335	+	10.1037i	−0.240768	+	0.417023i	−0.960933	−	0.276780i	$-0.910733\pi$
$587$	−5.83335	+	10.1037i	−0.240768	+	0.417023i	0.720165	+	0.693803i	$0.244066\pi$
$588$		0			0
$589$	0.741623	+	1.28453i	0.0305580	+	0.0529281i
$590$	−32.1318	−	55.6539i	−1.32285	−	2.29124i
$591$		0			0
$592$	−23.6027	+	40.8810i	−0.970063	+	1.68020i
$593$	15.7994			0.648805			0.324402	−	0.945919i	$-0.394837\pi$
$593$	15.7994			0.648805			0.324402	+	0.945919i	$0.394837\pi$
$594$		0			0
$595$	−1.49843			−0.0614295
$596$	−1.48155	+	2.56613i	−0.0606868	+	0.105113i
$597$		0			0
$598$	−24.5411	−	42.5064i	−1.00356	−	1.73822i
$599$	9.26903	+	16.0544i	0.378722	+	0.655967i	0.990877	−	0.134772i	$-0.0430302\pi$
$599$	9.26903	+	16.0544i	0.378722	+	0.655967i	−0.612154	+	0.790738i	$0.709697\pi$
$600$		0			0
$601$	−20.3049	+	35.1692i	−0.828256	+	1.43458i	0.0711491	+	0.997466i	$0.477333\pi$
$601$	−20.3049	+	35.1692i	−0.828256	+	1.43458i	−0.899405	+	0.437116i	$0.856000\pi$
$602$	−0.159223			−0.00648946
$603$		0			0
$604$	20.8569			0.848654
$605$	22.4617	−	38.9047i	0.913197	−	1.58170i
$606$		0			0
$607$	4.38698	+	7.59846i	0.178062	+	0.308412i	0.941217	−	0.337804i	$-0.109684\pi$
$607$	4.38698	+	7.59846i	0.178062	+	0.308412i	−0.763155	+	0.646216i	$0.776351\pi$
$608$	1.33033	+	2.30419i	0.0539519	+	0.0934474i
$609$		0			0
$610$	38.5372	−	66.7484i	1.56033	−	2.70256i
$611$	−17.5110			−0.708420
$612$		0			0
$613$	−13.3507			−0.539230			−0.269615	−	0.962968i	$-0.586897\pi$
$613$	−13.3507			−0.539230			−0.269615	+	0.962968i	$0.586897\pi$
$614$	−8.25601	+	14.2998i	−0.333185	+	0.577094i
$615$		0			0
$616$	−0.325236	−	0.563326i	−0.0131041	−	0.0226970i
$617$	−14.2483	−	24.6788i	−0.573615	−	0.993530i	−0.996191	−	0.0872027i	$-0.972207\pi$
$617$	−14.2483	−	24.6788i	−0.573615	−	0.993530i	0.422575	−	0.906328i	$-0.361126\pi$
$618$		0			0
$619$	−3.15880	+	5.47120i	−0.126963	+	0.219906i	−0.922498	−	0.386001i	$-0.873856\pi$
$619$	−3.15880	+	5.47120i	−0.126963	+	0.219906i	0.795536	+	0.605907i	$0.207190\pi$
$620$	13.8128			0.554734
$621$		0			0
$622$	−40.4215			−1.62075
$623$	−0.379626	+	0.657532i	−0.0152094	+	0.0263435i
$624$		0			0
$625$	−3.49923	−	6.06085i	−0.139969	−	0.242434i
$626$	−8.55298	−	14.8142i	−0.341846	−	0.592095i
$627$		0			0
$628$	−3.85908	+	6.68413i	−0.153994	+	0.266726i
$629$	42.8278			1.70766
$630$		0			0
$631$	−8.72945			−0.347514			−0.173757	−	0.984789i	$-0.555591\pi$
$631$	−8.72945			−0.347514			−0.173757	+	0.984789i	$0.555591\pi$
$632$	−7.00443	+	12.1320i	−0.278621	+	0.482586i
$633$		0			0
$634$	−29.3754	−	50.8796i	−1.16665	−	2.02069i
$635$	10.5335	+	18.2446i	0.418010	+	0.724015i
$636$		0			0
$637$	15.3968	−	26.6680i	0.610043	−	1.05663i
$638$	−41.1696			−1.62992
$639$		0			0
$640$	−40.5877			−1.60437
$641$	12.9501	−	22.4303i	0.511499	−	0.885943i	−0.488412	−	0.872613i	$-0.662424\pi$
$641$	12.9501	−	22.4303i	0.511499	−	0.885943i	0.999911	−	0.0133295i	$-0.00424305\pi$
$642$		0			0
$643$	12.5461	+	21.7305i	0.494771	+	0.856969i	0.999982	−	0.00602722i	$-0.00191854\pi$
$643$	12.5461	+	21.7305i	0.494771	+	0.856969i	−0.505211	+	0.862996i	$0.668585\pi$
$644$	0.324057	+	0.561283i	0.0127696	+	0.0221176i
$645$		0			0
$646$	1.83214	−	3.17335i	0.0720844	−	0.124854i
$647$	−39.8334			−1.56601			−0.783006	−	0.622014i	$-0.786315\pi$
$647$	−39.8334			−1.56601			−0.783006	+	0.622014i	$0.786315\pi$
$648$		0			0
$649$	−47.0822			−1.84814
$650$	−33.9461	+	58.7963i	−1.33147	+	2.30618i
$651$		0			0
$652$	−0.758062	−	1.31300i	−0.0296880	−	0.0514211i
$653$	−14.1805	−	24.5614i	−0.554926	−	0.961160i	−0.997909	−	0.0646301i	$-0.979413\pi$
$653$	−14.1805	−	24.5614i	−0.554926	−	0.961160i	0.442983	−	0.896530i	$-0.353920\pi$
$654$		0			0
$655$	0.778354	−	1.34815i	0.0304128	−	0.0526765i
$656$	35.2778			1.37737
$657$		0			0
$658$	0.633077			0.0246799
$659$	−7.37678	+	12.7769i	−0.287358	+	0.497719i	−0.973178	−	0.230052i	$-0.926110\pi$
$659$	−7.37678	+	12.7769i	−0.287358	+	0.497719i	0.685820	+	0.727771i	$0.259444\pi$
$660$		0			0
$661$	17.2080	+	29.8051i	0.669312	+	1.15928i	0.978097	+	0.208150i	$0.0667443\pi$
$661$	17.2080	+	29.8051i	0.669312	+	1.15928i	−0.308785	+	0.951132i	$0.599922\pi$
$662$	−10.8003	−	18.7067i	−0.419767	−	0.727057i
$663$		0			0
$664$	−3.04186	+	5.26866i	−0.118047	+	0.204464i
$665$	0.151692			0.00588236
$666$		0			0
$667$	−30.2690			−1.17202
$668$	13.6938	−	23.7184i	0.529831	−	0.917694i
$669$		0			0
$670$	−20.4232	−	35.3740i	−0.789016	−	1.36662i
$671$	−28.2340	−	48.9027i	−1.08996	−	1.88787i
$672$		0			0
$673$	−0.242517	+	0.420052i	−0.00934835	+	0.0161918i	−0.870662	−	0.491882i	$-0.836309\pi$
$673$	−0.242517	+	0.420052i	−0.00934835	+	0.0161918i	0.861313	+	0.508074i	$0.169642\pi$
$674$	−6.54737			−0.252195
$675$		0			0
$676$	7.36118			0.283122
$677$	7.60798	−	13.1774i	0.292398	−	0.506449i	−0.681978	−	0.731373i	$-0.738880\pi$
$677$	7.60798	−	13.1774i	0.292398	−	0.506449i	0.974376	+	0.224924i	$0.0722133\pi$
$678$		0			0
$679$	−0.0304600	−	0.0527583i	−0.00116895	−	0.00202468i
$680$	12.5900	+	21.8065i	0.482804	+	0.836240i
$681$		0			0
$682$	13.8535	−	23.9950i	0.530479	−	0.918817i
$683$	−15.8107			−0.604978			−0.302489	−	0.953153i	$-0.597818\pi$
$683$	−15.8107			−0.604978			−0.302489	+	0.953153i	$0.597818\pi$
$684$		0			0
$685$	−48.3318			−1.84666
$686$	−1.11392	+	1.92937i	−0.0425298	+	0.0736638i
$687$		0			0
$688$	2.48863	+	4.31043i	0.0948780	+	0.164334i
$689$	18.0189	+	31.2097i	0.686467	+	1.18899i
$690$		0			0
$691$	−10.5608	+	18.2918i	−0.401750	+	0.695852i	−0.993937	−	0.109949i	$-0.964931\pi$
$691$	−10.5608	+	18.2918i	−0.401750	+	0.695852i	0.592187	+	0.805801i	$0.298265\pi$
$692$	5.13296			0.195126
$693$		0			0
$694$	38.8744			1.47565
$695$	13.7286	−	23.7787i	0.520757	−	0.901977i
$696$		0			0
$697$	−16.0032	−	27.7184i	−0.606164	−	1.04991i
$698$	7.01763	+	12.1549i	0.265621	+	0.460069i
$699$		0			0
$700$	0.448246	−	0.776385i	0.0169421	−	0.0293446i
$701$	40.9055			1.54498			0.772491	−	0.635026i	$-0.219011\pi$
$701$	40.9055			1.54498			0.772491	+	0.635026i	$0.219011\pi$
$702$		0			0
$703$	−4.33563			−0.163522
$704$	0.905928	−	1.56911i	0.0341435	−	0.0591382i
$705$		0			0
$706$	−8.37505	−	14.5060i	−0.315199	−	0.545941i
$707$	−0.162869	−	0.282097i	−0.00612532	−	0.0106094i
$708$		0			0
$709$	−16.0136	+	27.7364i	−0.601404	+	1.04166i	0.391205	+	0.920303i	$0.372058\pi$
$709$	−16.0136	+	27.7364i	−0.601404	+	1.04166i	−0.992609	+	0.121358i	$0.961275\pi$
$710$	91.2522			3.42463
$711$		0			0
$712$	12.7587			0.478152
$713$	10.1855	−	17.6418i	0.381450	−	0.660691i
$714$		0			0
$715$	39.1891	+	67.8774i	1.46559	+	2.53847i
$716$	−8.06406	−	13.9674i	−0.301368	−	0.521985i
$717$		0			0
$718$	−18.1200	+	31.3847i	−0.676232	+	1.17127i
$719$	9.63404			0.359289			0.179644	−	0.983732i	$-0.442505\pi$
$719$	9.63404			0.359289			0.179644	+	0.983732i	$0.442505\pi$
$720$		0			0
$721$	0.489718			0.0182380
$722$	16.6775	−	28.8863i	0.620673	−	1.07504i
$723$		0			0
$724$	13.0426	+	22.5905i	0.484726	+	0.839570i
$725$	20.9346	+	36.2597i	0.777490	+	1.34665i
$726$		0			0
$727$	5.99536	−	10.3843i	0.222356	−	0.385131i	−0.733167	−	0.680048i	$-0.761959\pi$
$727$	5.99536	−	10.3843i	0.222356	−	0.385131i	0.955523	+	0.294917i	$0.0952920\pi$
$728$	0.595488			0.0220702
$729$		0			0
$730$	−73.8406			−2.73296
$731$	2.25785	−	3.91071i	0.0835095	−	0.144643i
$732$		0			0
$733$	−0.0282171	−	0.0488735i	−0.00104222	−	0.00180518i	0.865504	−	0.500902i	$-0.166998\pi$
$733$	−0.0282171	−	0.0488735i	−0.00104222	−	0.00180518i	−0.866546	+	0.499097i	$0.833665\pi$
$734$	−3.57610	−	6.19399i	−0.131996	−	0.228624i
$735$		0			0
$736$	18.2708	−	31.6460i	0.673471	−	1.16649i
$737$	−29.9257			−1.10233
$738$		0			0
$739$	−6.30302			−0.231860			−0.115930	−	0.993257i	$-0.536985\pi$
$739$	−6.30302			−0.231860			−0.115930	+	0.993257i	$0.536985\pi$
$740$	−20.1879	+	34.9664i	−0.742121	+	1.28539i
$741$		0			0
$742$	−0.651440	−	1.12833i	−0.0239151	−	0.0414222i
$743$	26.3068	+	45.5647i	0.965103	+	1.67161i	0.709339	+	0.704868i	$0.248994\pi$
$743$	26.3068	+	45.5647i	0.965103	+	1.67161i	0.255764	+	0.966739i	$0.417673\pi$
$744$		0			0
$745$	4.76243	−	8.24876i	0.174482	−	0.302211i
$746$	16.4877			0.603656
$747$		0			0
$748$	−25.0004			−0.914105
$749$	0.0918112	−	0.159022i	0.00335471	−	0.00581053i
$750$		0			0
$751$	1.10626	+	1.91609i	0.0403679	+	0.0699193i	0.885503	−	0.464633i	$-0.153814\pi$
$751$	1.10626	+	1.91609i	0.0403679	+	0.0699193i	−0.845136	+	0.534552i	$0.820480\pi$
$752$	−9.89486	−	17.1384i	−0.360828	−	0.624973i
$753$		0			0
$754$	18.8447	−	32.6401i	0.686285	−	1.18868i
$755$	−67.0440			−2.43998
$756$		0			0
$757$	−43.0907			−1.56616			−0.783079	−	0.621923i	$-0.786352\pi$
$757$	−43.0907			−1.56616			−0.783079	+	0.621923i	$0.786352\pi$
$758$	−25.9457	+	44.9393i	−0.942391	+	1.63227i
$759$		0			0
$760$	−1.27453	−	2.20756i	−0.0462322	−	0.0800766i
$761$	−20.8486	−	36.1109i	−0.755763	−	1.30902i	−0.944994	−	0.327087i	$-0.893933\pi$
$761$	−20.8486	−	36.1109i	−0.755763	−	1.30902i	0.189231	−	0.981933i	$-0.439400\pi$
$762$		0			0
$763$	−0.0788883	+	0.136638i	−0.00285595	+	0.00494665i
$764$	−4.43958			−0.160618
$765$		0			0
$766$	−24.5975			−0.888743
$767$	21.5512	−	37.3277i	0.778168	−	1.34783i
$768$		0			0
$769$	−18.3752	−	31.8268i	−0.662627	−	1.14770i	−0.979923	−	0.199377i	$-0.936108\pi$
$769$	−18.3752	−	31.8268i	−0.662627	−	1.14770i	0.317296	−	0.948326i	$-0.397225\pi$
$770$	−1.41680	−	2.45398i	−0.0510581	−	0.0884352i
$771$		0			0
$772$	8.08449	−	14.0027i	0.290967	−	0.503970i
$773$	−10.3042			−0.370617			−0.185309	−	0.982680i	$-0.559329\pi$
$773$	−10.3042			−0.370617			−0.185309	+	0.982680i	$0.559329\pi$
$774$		0			0
$775$	−28.1779			−1.01218
$776$	−0.511858	+	0.886564i	−0.0183746	+	0.0318258i
$777$		0			0
$778$	9.71252	+	16.8226i	0.348211	+	0.603119i
$779$	1.62007	+	2.80604i	0.0580450	+	0.100537i
$780$		0			0
$781$	33.4276	−	57.8982i	1.19613	−	2.07176i
$782$	−50.3254			−1.79963
$783$		0			0
$784$	34.8007			1.24288
$785$	12.4049	−	21.4860i	0.442751	−	0.766868i
$786$		0			0
$787$	3.37035	+	5.83762i	0.120140	+	0.208089i	0.919823	−	0.392334i	$-0.128332\pi$
$787$	3.37035	+	5.83762i	0.120140	+	0.208089i	−0.799683	+	0.600423i	$0.794999\pi$
$788$	1.02874	+	1.78183i	0.0366474	+	0.0634752i
$789$		0			0
$790$	−30.5129	+	52.8499i	−1.08560	+	1.88032i
$791$	−1.20390			−0.0428057
$792$		0			0
$793$	51.6947			1.83573
$794$	29.2066	−	50.5873i	1.03650	−	1.79528i
$795$		0			0
$796$	10.0955	+	17.4859i	0.357825	+	0.619771i
$797$	−18.9731	−	32.8624i	−0.672063	−	1.16405i	−0.977318	−	0.211776i	$-0.932075\pi$
$797$	−18.9731	−	32.8624i	−0.672063	−	1.16405i	0.305255	−	0.952271i	$-0.401258\pi$
$798$		0			0
$799$	−8.97727	+	15.5491i	−0.317593	+	0.550087i
$800$	−50.5456			−1.78706
$801$		0			0
$802$	22.7310			0.802660
$803$	−27.0494	+	46.8509i	−0.954551	+	1.65333i
$804$		0			0
$805$	−1.04167	−	1.80423i	−0.0367142	−	0.0635908i
$806$	12.6825	+	21.9667i	0.446722	+	0.773745i
$807$		0			0
$808$	−2.73689	+	4.74043i	−0.0962835	+	0.166768i
$809$	13.5355			0.475884			0.237942	−	0.971279i	$-0.423527\pi$
$809$	13.5355			0.475884			0.237942	+	0.971279i	$0.423527\pi$
$810$		0			0
$811$	−21.9654			−0.771309			−0.385654	−	0.922643i	$-0.626024\pi$
$811$	−21.9654			−0.771309			−0.385654	+	0.922643i	$0.626024\pi$
$812$	−0.248838	+	0.431001i	−0.00873252	+	0.0151252i
$813$		0			0
$814$	40.4949	+	70.1392i	1.41935	+	2.45838i
$815$	2.43677	+	4.22062i	0.0853565	+	0.147842i
$816$		0			0
$817$	−0.228571	+	0.395897i	−0.00799669	+	0.0138507i
$818$	−36.9867			−1.29321
$819$		0			0
$820$	30.1739			1.05372
$821$	4.48947	−	7.77600i	0.156684	−	0.271384i	−0.776987	−	0.629516i	$-0.783253\pi$
$821$	4.48947	−	7.77600i	0.156684	−	0.271384i	0.933671	+	0.358132i	$0.116586\pi$
$822$		0			0
$823$	−17.8366	−	30.8940i	−0.621746	−	1.07690i	−0.989161	−	0.146838i	$-0.953090\pi$
$823$	−17.8366	−	30.8940i	−0.621746	−	1.07690i	0.367414	−	0.930057i	$-0.380243\pi$
$824$	−4.11467	−	7.12682i	−0.143341	−	0.248274i
$825$		0			0
$826$	−0.779141	+	1.34951i	−0.0271098	+	0.0469555i
$827$	14.9924			0.521337			0.260668	−	0.965428i	$-0.416057\pi$
$827$	14.9924			0.521337			0.260668	+	0.965428i	$0.416057\pi$
$828$		0			0
$829$	3.42729			0.119035			0.0595174	−	0.998227i	$-0.481044\pi$
$829$	3.42729			0.119035			0.0595174	+	0.998227i	$0.481044\pi$
$830$	−13.2511	+	22.9515i	−0.459951	+	0.796659i
$831$		0			0
$832$	0.829350	+	1.43648i	0.0287525	+	0.0498008i
$833$	−15.7868	−	27.3435i	−0.546979	−	0.947396i
$834$		0			0
$835$	−44.0186	+	76.2424i	−1.52333	+	2.63848i
$836$	2.53089			0.0875328
$837$		0			0
$838$	−32.3885			−1.11884
$839$	−28.0222	+	48.5358i	−0.967433	+	1.67564i	−0.264502	+	0.964385i	$0.585208\pi$
$839$	−28.0222	+	48.5358i	−0.967433	+	1.67564i	−0.702931	+	0.711258i	$0.748126\pi$
$840$		0			0
$841$	2.87844	+	4.98560i	0.0992565	+	0.171917i
$842$	−18.3143	−	31.7213i	−0.631152	−	1.09319i
$843$		0			0
$844$	6.36052	−	11.0167i	0.218938	−	0.379212i
$845$	−23.6624			−0.814010
$846$		0			0
$847$	−1.08931			−0.0374292
$848$	−20.3637	+	35.2710i	−0.699293	+	1.21121i
$849$		0			0
$850$	34.8059	+	60.2855i	1.19383	+	2.06778i
$851$	29.7729	+	51.5683i	1.02060	+	1.76774i
$852$		0			0
$853$	10.4191	−	18.0464i	0.356744	−	0.617899i	−0.630671	−	0.776050i	$-0.717220\pi$
$853$	10.4191	−	18.0464i	0.356744	−	0.617899i	0.987415	+	0.158152i	$0.0505535\pi$
$854$	−1.86892			−0.0639532
$855$		0			0
$856$	−3.08564			−0.105465
$857$	11.1473	−	19.3077i	0.380785	−	0.659539i	−0.610389	−	0.792101i	$-0.708987\pi$
$857$	11.1473	−	19.3077i	0.380785	−	0.659539i	0.991175	+	0.132562i	$0.0423204\pi$
$858$		0			0
$859$	−15.1810	−	26.2943i	−0.517970	−	0.897151i	−0.999782	−	0.0208763i	$-0.993354\pi$
$859$	−15.1810	−	26.2943i	−0.517970	−	0.897151i	0.481812	−	0.876275i	$-0.339979\pi$
$860$	2.12858	+	3.68680i	0.0725839	+	0.125719i
$861$		0			0
$862$	−19.3122	+	33.4498i	−0.657777	+	1.13930i
$863$	11.2552			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$863$	11.2552			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$864$		0			0
$865$	−16.4998			−0.561010
$866$	−25.5284	+	44.2165i	−0.867490	+	1.50254i
$867$		0			0
$868$	−0.167468	−	0.290063i	−0.00568423	−	0.00984538i
$869$	22.3550	+	38.7201i	0.758343	+	1.31349i
$870$		0			0
$871$	13.6980	−	23.7257i	0.464141	−	0.803915i
$872$	2.65132			0.0897849
$873$		0			0
$874$	5.09464			0.172329
$875$	−0.611313	+	1.05882i	−0.0206661	+	0.0357948i
$876$		0			0
$877$	−1.81204	−	3.13854i	−0.0611881	−	0.105981i	0.833809	−	0.552054i	$-0.186156\pi$
$877$	−1.81204	−	3.13854i	−0.0611881	−	0.105981i	−0.894997	+	0.446073i	$0.852822\pi$
$878$	23.3940	+	40.5196i	0.789509	+	1.36747i
$879$		0			0
$880$	−44.2887	+	76.7103i	−1.49297	+	2.58590i
$881$	44.6822			1.50538			0.752692	−	0.658373i	$-0.228755\pi$
$881$	44.6822			1.50538			0.752692	+	0.658373i	$0.228755\pi$
$882$		0			0
$883$	54.4600			1.83273			0.916363	−	0.400348i	$-0.131111\pi$
$883$	54.4600			1.83273			0.916363	+	0.400348i	$0.131111\pi$
$884$	11.4436	−	19.8208i	0.384888	−	0.666646i
$885$		0			0
$886$	−13.3875	−	23.1878i	−0.449761	−	0.779009i
$887$	3.53223	+	6.11800i	0.118601	+	0.205422i	0.919213	−	0.393760i	$-0.128826\pi$
$887$	3.53223	+	6.11800i	0.118601	+	0.205422i	−0.800613	+	0.599182i	$0.795493\pi$
$888$		0			0
$889$	0.255420	−	0.442400i	0.00856650	−	0.0148376i
$890$	55.5798			1.86304
$891$		0			0
$892$	−3.17917			−0.106446
$893$	0.908806	−	1.57410i	0.0304120	−	0.0526752i
$894$		0			0
$895$	25.9218	+	44.8978i	0.866469	+	1.50077i
$896$	0.492091	+	0.852327i	0.0164396	+	0.0284742i
$897$		0			0
$898$	−26.6042	+	46.0799i	−0.887795	+	1.53771i
$899$	15.6426			0.521710
$900$		0			0
$901$	36.9506			1.23100
$902$	30.2629	−	52.4170i	1.00765	−	1.74529i
$903$		0			0
$904$	10.1153	+	17.5202i	0.336430	+	0.582715i
$905$	−41.9253	−	72.6168i	−1.39364	−	2.41386i
$906$		0			0
$907$	14.0197	−	24.2828i	0.465516	−	0.806297i	−0.533709	−	0.845668i	$-0.679202\pi$
$907$	14.0197	−	24.2828i	0.465516	−	0.806297i	0.999225	+	0.0393716i	$0.0125356\pi$
$908$	−11.4094			−0.378635
$909$		0			0
$910$	2.59408			0.0859930
$911$	−21.5130	+	37.2616i	−0.712758	+	1.23453i	0.251061	+	0.967971i	$0.419221\pi$
$911$	−21.5130	+	37.2616i	−0.712758	+	1.23453i	−0.963818	+	0.266561i	$0.914113\pi$
$912$		0			0
$913$	9.70829	+	16.8153i	0.321297	+	0.556504i
$914$	18.9139	+	32.7599i	0.625617	+	1.08360i
$915$		0			0
$916$	−2.94354	+	5.09836i	−0.0972572	+	0.168454i
$917$	−0.0377475			−0.00124653
$918$		0			0
$919$	9.18522			0.302993			0.151496	−	0.988458i	$-0.451591\pi$
$919$	9.18522			0.302993			0.151496	+	0.988458i	$0.451591\pi$
$920$	−17.5045	+	30.3188i	−0.577108	+	0.999580i
$921$		0			0
$922$	7.78328	+	13.4810i	0.256329	+	0.443974i
$923$	30.6019	+	53.0041i	1.00727	+	1.74465i
$924$		0			0
$925$	41.1830	−	71.3310i	1.35409	−	2.34535i
$926$	55.9261			1.83785
$927$		0			0
$928$	28.0598			0.921107
$929$	0.265051	−	0.459082i	0.00869604	−	0.0150620i	−0.861645	−	0.507512i	$-0.830565\pi$
$929$	0.265051	−	0.459082i	0.00869604	−	0.0150620i	0.870341	+	0.492450i	$0.163899\pi$
$930$		0			0
$931$	1.59816	+	2.76809i	0.0523776	+	0.0907206i
$932$	8.60808	+	14.9096i	0.281967	+	0.488381i
$933$		0			0
$934$	16.8933	−	29.2601i	0.552766	−	0.957419i
$935$	80.3633			2.62816
$936$		0			0
$937$	−36.8282			−1.20313			−0.601563	−	0.798825i	$-0.705455\pi$
$937$	−36.8282			−1.20313			−0.601563	+	0.798825i	$0.705455\pi$
$938$	−0.495227	+	0.857758i	−0.0161697	+	0.0280068i
$939$		0			0
$940$	−8.46328	−	14.6588i	−0.276042	−	0.478119i
$941$	−13.6057	−	23.5658i	−0.443535	−	0.768224i	0.554414	−	0.832241i	$-0.312942\pi$
$941$	−13.6057	−	23.5658i	−0.443535	−	0.768224i	−0.997949	+	0.0640165i	$0.979609\pi$
$942$		0			0
$943$	22.2501	−	38.5384i	0.724564	−	1.25498i
$944$	48.7112			1.58542
$945$		0			0
$946$	8.53944			0.277641
$947$	−1.71551	+	2.97135i	−0.0557466	+	0.0965559i	−0.892552	−	0.450945i	$-0.851087\pi$
$947$	−1.71551	+	2.97135i	−0.0557466	+	0.0965559i	0.836805	+	0.547500i	$0.184421\pi$
$948$		0			0
$949$	−24.7629	−	42.8905i	−0.803837	−	1.39229i
$950$	−3.52354	−	6.10295i	−0.114319	−	0.198006i
$951$		0			0
$952$	0.305285	−	0.528769i	0.00989435	−	0.0171375i
$953$	−27.0518			−0.876293			−0.438146	−	0.898904i	$-0.644365\pi$
$953$	−27.0518			−0.876293			−0.438146	+	0.898904i	$0.644365\pi$
$954$		0			0
$955$	14.2709			0.461797
$956$	−6.85861	+	11.8795i	−0.221823	+	0.384209i
$957$		0			0
$958$	32.1453	+	55.6772i	1.03857	+	1.79885i
$959$	0.585982	+	1.01495i	0.0189223	+	0.0327744i
$960$		0			0
$961$	10.2363	−	17.7298i	0.330203	−	0.571928i
$962$	−74.1437			−2.39049
$963$		0			0
$964$	20.3690			0.656041
$965$	−25.9874	+	45.0115i	−0.836565	+	1.44897i
$966$		0			0
$967$	10.7214	+	18.5700i	0.344777	+	0.597171i	0.985313	−	0.170757i	$-0.0546212\pi$
$967$	10.7214	+	18.5700i	0.344777	+	0.597171i	−0.640536	+	0.767928i	$0.721288\pi$
$968$	9.15255	+	15.8527i	0.294174	+	0.509524i
$969$		0			0
$970$	−2.22977	+	3.86208i	−0.0715937	+	0.124004i
$971$	27.1957			0.872751			0.436376	−	0.899765i	$-0.356262\pi$
$971$	27.1957			0.872751			0.436376	+	0.899765i	$0.356262\pi$
$972$		0			0
$973$	−0.665791			−0.0213443
$974$	−15.2455	+	26.4059i	−0.488496	+	0.846100i
$975$		0			0
$976$	29.2108	+	50.5947i	0.935016	+	1.61950i
$977$	9.95284	+	17.2388i	0.318420	+	0.551519i	0.980158	−	0.198216i	$-0.0635146\pi$
$977$	9.95284	+	17.2388i	0.318420	+	0.551519i	−0.661739	+	0.749734i	$0.730181\pi$
$978$		0			0
$979$	20.3600	−	35.2646i	0.650710	−	1.12706i
$980$	29.7658			0.950834
$981$		0			0
$982$	−75.5137			−2.40974
$983$	4.05129	−	7.01704i	0.129216	−	0.223809i	−0.794157	−	0.607713i	$-0.792087\pi$
$983$	4.05129	−	7.01704i	0.129216	−	0.223809i	0.923373	+	0.383904i	$0.125421\pi$
$984$		0			0
$985$	−3.30687	−	5.72767i	−0.105366	−	0.182499i
$986$	−19.3221	−	33.4668i	−0.615340	−	1.06580i
$987$		0			0
$988$	−1.15848	+	2.00654i	−0.0368561	+	0.0638366i
$989$	6.27843			0.199642
$990$		0			0
$991$	−33.1910			−1.05435			−0.527174	−	0.849757i	$-0.676748\pi$
$991$	−33.1910			−1.05435			−0.527174	+	0.849757i	$0.676748\pi$
$992$	−9.44209	+	16.3542i	−0.299787	+	0.519246i
$993$		0			0
$994$	−1.10635	−	1.91626i	−0.0350914	−	0.0607801i
$995$	−32.4517	−	56.2080i	−1.02879	−	1.78191i
$996$		0			0
$997$	−1.17342	+	2.03242i	−0.0371626	+	0.0643674i	−0.884008	−	0.467471i	$-0.845165\pi$
$997$	−1.17342	+	2.03242i	−0.0371626	+	0.0643674i	0.846846	+	0.531838i	$0.178499\pi$
$998$	14.7242			0.466086
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1161.2.f.c.775.4		38
3.2	odd	2		387.2.f.c.259.16	yes	38
9.2	odd	6		3483.2.a.s.1.4		19
9.4	even	3	inner	1161.2.f.c.388.4		38
9.5	odd	6		387.2.f.c.130.16	✓	38
9.7	even	3		3483.2.a.r.1.16		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.c.130.16	✓	38	9.5	odd	6
387.2.f.c.259.16	yes	38	3.2	odd	2
1161.2.f.c.388.4		38	9.4	even	3	inner
1161.2.f.c.775.4		38	1.1	even	1	trivial
3483.2.a.r.1.16		19	9.7	even	3
3483.2.a.s.1.4		19	9.2	odd	6

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:	\( N \)	\(=\)	\( 1161 = 3^{3} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1161.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.887526 + 1.53724i) q^{2} +(-0.575406 - 0.996632i) q^{4} +(1.84963 + 3.20365i) q^{5} +(0.0448503 - 0.0776831i) q^{7} -1.50735 q^{8} +O(q^{10})\)	\(q+(-0.887526 + 1.53724i) q^{2} +(-0.575406 - 0.996632i) q^{4} +(1.84963 + 3.20365i) q^{5} +(0.0448503 - 0.0776831i) q^{7} -1.50735 q^{8} -6.56638 q^{10} +(-2.40540 + 4.16628i) q^{11} +(-2.20207 - 3.81410i) q^{13} +(0.0796117 + 0.137892i) q^{14} +(2.48863 - 4.31043i) q^{16} -4.51570 q^{17} +0.457142 q^{19} +(2.12858 - 3.68680i) q^{20} +(-4.26972 - 7.39537i) q^{22} +(-3.13921 - 5.43728i) q^{23} +(-4.34227 + 7.52103i) q^{25} +7.81759 q^{26} -0.103229 q^{28} +(2.41056 - 4.17521i) q^{29} +(1.62230 + 2.80991i) q^{31} +(2.91009 + 5.04043i) q^{32} +(4.00780 - 6.94171i) q^{34} +0.331826 q^{35} -9.48421 q^{37} +(-0.405726 + 0.702738i) q^{38} +(-2.78805 - 4.82904i) q^{40} +(3.54390 + 6.13822i) q^{41} +(-0.500000 + 0.866025i) q^{43} +5.53633 q^{44} +11.1445 q^{46} +(1.98801 - 3.44334i) q^{47} +(3.49598 + 6.05521i) q^{49} +(-7.70775 - 13.3502i) q^{50} +(-2.53417 + 4.38932i) q^{52} -8.18271 q^{53} -17.7964 q^{55} +(-0.0676053 + 0.117096i) q^{56} +(4.27886 + 7.41121i) q^{58} +(4.89338 + 8.47559i) q^{59} +(-5.86886 + 10.1652i) q^{61} -5.75934 q^{62} -0.376622 q^{64} +(8.14605 - 14.1094i) q^{65} +(3.11026 + 5.38713i) q^{67} +(2.59836 + 4.50049i) q^{68} +(-0.294505 + 0.510097i) q^{70} -13.8969 q^{71} +11.2453 q^{73} +(8.41748 - 14.5795i) q^{74} +(-0.263042 - 0.455603i) q^{76} +(0.215766 + 0.373718i) q^{77} +(4.64684 - 8.04856i) q^{79} +18.4122 q^{80} -12.5812 q^{82} +(2.01802 - 3.49531i) q^{83} +(-8.35237 - 14.4667i) q^{85} +(-0.887526 - 1.53724i) q^{86} +(3.62579 - 6.28006i) q^{88} -8.46429 q^{89} -0.395055 q^{91} +(-3.61264 + 6.25728i) q^{92} +(3.52883 + 6.11211i) q^{94} +(0.845545 + 1.46453i) q^{95} +(0.339574 - 0.588160i) q^{97} -12.4111 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 4 q^{2} - 22 q^{4} + 9 q^{5} - 7 q^{7} - 24 q^{8}+O(q^{10}) \) 38 * q + 4 * q^2 - 22 * q^4 + 9 * q^5 - 7 * q^7 - 24 * q^8	\( 38 q + 4 q^{2} - 22 q^{4} + 9 q^{5} - 7 q^{7} - 24 q^{8} - 14 q^{10} + 5 q^{11} + 5 q^{13} + 17 q^{14} - 24 q^{16} - 42 q^{17} - 8 q^{19} + 21 q^{20} + 20 q^{22} + 22 q^{23} - 10 q^{25} - 34 q^{26} - 2 q^{28} + 30 q^{29} + 5 q^{31} + 48 q^{32} + 6 q^{34} - 106 q^{35} - 2 q^{37} + 21 q^{38} - 16 q^{40} + 29 q^{41} - 19 q^{43} - 58 q^{44} + 32 q^{47} + 10 q^{49} - 11 q^{50} - q^{52} - 76 q^{53} + 4 q^{55} + 46 q^{56} - 30 q^{58} + 30 q^{59} + 10 q^{61} - 50 q^{62} + 28 q^{64} + 8 q^{65} - 3 q^{67} + 47 q^{68} - 56 q^{70} - 42 q^{71} + 16 q^{73} + 28 q^{74} + 36 q^{76} + 49 q^{77} - 4 q^{79} - 140 q^{80} - 8 q^{82} + 29 q^{83} + 4 q^{85} + 4 q^{86} + 47 q^{88} - 108 q^{89} + 8 q^{91} + 12 q^{92} + 23 q^{94} + 33 q^{95} + 4 q^{97} - 98 q^{98}+O(q^{100}) \) 38 * q + 4 * q^2 - 22 * q^4 + 9 * q^5 - 7 * q^7 - 24 * q^8 - 14 * q^10 + 5 * q^11 + 5 * q^13 + 17 * q^14 - 24 * q^16 - 42 * q^17 - 8 * q^19 + 21 * q^20 + 20 * q^22 + 22 * q^23 - 10 * q^25 - 34 * q^26 - 2 * q^28 + 30 * q^29 + 5 * q^31 + 48 * q^32 + 6 * q^34 - 106 * q^35 - 2 * q^37 + 21 * q^38 - 16 * q^40 + 29 * q^41 - 19 * q^43 - 58 * q^44 + 32 * q^47 + 10 * q^49 - 11 * q^50 - q^52 - 76 * q^53 + 4 * q^55 + 46 * q^56 - 30 * q^58 + 30 * q^59 + 10 * q^61 - 50 * q^62 + 28 * q^64 + 8 * q^65 - 3 * q^67 + 47 * q^68 - 56 * q^70 - 42 * q^71 + 16 * q^73 + 28 * q^74 + 36 * q^76 + 49 * q^77 - 4 * q^79 - 140 * q^80 - 8 * q^82 + 29 * q^83 + 4 * q^85 + 4 * q^86 + 47 * q^88 - 108 * q^89 + 8 * q^91 + 12 * q^92 + 23 * q^94 + 33 * q^95 + 4 * q^97 - 98 * q^98

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