LMFDB - Embedded newform 1161.2.f.c.775.1

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			775.1
Character	$\chi$	$=$	1161.775
Dual form			1161.2.f.c.388.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27673 + 2.21136i) q^{2} +(-2.26008 - 3.91458i) q^{4} +(1.39974 + 2.42442i) q^{5} +(0.0769910 - 0.133352i) q^{7} +6.43513 q^{8} +O(q^{10})$	\(q+(-1.27673 + 2.21136i) q^{2} +(-2.26008 - 3.91458i) q^{4} +(1.39974 + 2.42442i) q^{5} +(0.0769910 - 0.133352i) q^{7} +6.43513 q^{8} -7.14837 q^{10} +(1.85795 - 3.21806i) q^{11} +(0.642256 + 1.11242i) q^{13} +(0.196594 + 0.340510i) q^{14} +(-3.69577 + 6.40126i) q^{16} -0.563748 q^{17} -6.62305 q^{19} +(6.32706 - 10.9588i) q^{20} +(4.74420 + 8.21719i) q^{22} +(3.02258 + 5.23526i) q^{23} +(-1.41855 + 2.45700i) q^{25} -3.27995 q^{26} -0.696024 q^{28} +(-4.34197 + 7.52050i) q^{29} +(0.846788 + 1.46668i) q^{31} +(-3.00187 - 5.19939i) q^{32} +(0.719755 - 1.24665i) q^{34} +0.431070 q^{35} +4.07664 q^{37} +(8.45585 - 14.6460i) q^{38} +(9.00752 + 15.6015i) q^{40} +(5.55726 + 9.62547i) q^{41} +(-0.500000 + 0.866025i) q^{43} -16.7964 q^{44} -15.4361 q^{46} +(-3.69248 + 6.39556i) q^{47} +(3.48814 + 6.04164i) q^{49} +(-3.62222 - 6.27386i) q^{50} +(2.90310 - 5.02832i) q^{52} -2.30102 q^{53} +10.4026 q^{55} +(0.495447 - 0.858140i) q^{56} +(-11.0870 - 19.2033i) q^{58} +(2.94982 + 5.10923i) q^{59} +(2.07507 - 3.59412i) q^{61} -4.32448 q^{62} +0.547229 q^{64} +(-1.79798 + 3.11420i) q^{65} +(-5.34393 - 9.25596i) q^{67} +(1.27412 + 2.20683i) q^{68} +(-0.550360 + 0.953252i) q^{70} -12.6183 q^{71} +1.47133 q^{73} +(-5.20476 + 9.01492i) q^{74} +(14.9686 + 25.9264i) q^{76} +(-0.286090 - 0.495523i) q^{77} +(-4.16420 + 7.21261i) q^{79} -20.6925 q^{80} -28.3805 q^{82} +(3.48869 - 6.04259i) q^{83} +(-0.789102 - 1.36676i) q^{85} +(-1.27673 - 2.21136i) q^{86} +(11.9561 - 20.7086i) q^{88} -15.8842 q^{89} +0.197792 q^{91} +(13.6625 - 23.6642i) q^{92} +(-9.42859 - 16.3308i) q^{94} +(-9.27056 - 16.0571i) q^{95} +(-8.27317 + 14.3296i) q^{97} -17.8137 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.27673	+	2.21136i	−0.902785	+	1.56367i	−0.0789211	+	0.996881i	$0.525148\pi$
$2$	−1.27673	+	2.21136i	−0.902785	+	1.56367i	−0.823864	+	0.566788i	$0.808186\pi$
$3$		0			0
$3$		0			0
$4$	−2.26008	−	3.91458i	−1.13004	−	1.95729i
$5$	1.39974	+	2.42442i	0.625983	+	1.08423i	0.988350	+	0.152199i	$0.0486355\pi$
$5$	1.39974	+	2.42442i	0.625983	+	1.08423i	−0.362366	+	0.932036i	$0.618031\pi$
$6$		0			0
$7$	0.0769910	−	0.133352i	0.0290999	−	0.0504024i	−0.851109	−	0.524989i	$-0.824069\pi$
$7$	0.0769910	−	0.133352i	0.0290999	−	0.0504024i	0.880209	+	0.474587i	$0.157403\pi$
$8$	6.43513			2.27516
$9$		0			0
$10$	−7.14837			−2.26051
$11$	1.85795	−	3.21806i	0.560192	−	0.970281i	−0.437287	−	0.899322i	$-0.644061\pi$
$11$	1.85795	−	3.21806i	0.560192	−	0.970281i	0.997479	−	0.0709593i	$-0.0226060\pi$
$12$		0			0
$13$	0.642256	+	1.11242i	0.178130	+	0.308530i	0.941240	−	0.337739i	$-0.109662\pi$
$13$	0.642256	+	1.11242i	0.178130	+	0.308530i	−0.763110	+	0.646268i	$0.776329\pi$
$14$	0.196594	+	0.340510i	0.0525418	+	0.0910051i
$15$		0			0
$16$	−3.69577	+	6.40126i	−0.923942	+	1.60032i
$17$	−0.563748			−0.136729			−0.0683645	−	0.997660i	$-0.521778\pi$
$17$	−0.563748			−0.136729			−0.0683645	+	0.997660i	$0.521778\pi$
$18$		0			0
$19$	−6.62305			−1.51943			−0.759716	−	0.650255i	$-0.774662\pi$
$19$	−6.62305			−1.51943			−0.759716	+	0.650255i	$0.774662\pi$
$20$	6.32706	−	10.9588i	1.41477	−	2.45046i
$21$		0			0
$22$	4.74420	+	8.21719i	1.01147	+	1.75191i
$23$	3.02258	+	5.23526i	0.630251	+	1.09163i	0.987500	+	0.157617i	$0.0503812\pi$
$23$	3.02258	+	5.23526i	0.630251	+	1.09163i	−0.357250	+	0.934009i	$0.616285\pi$
$24$		0			0
$25$	−1.41855	+	2.45700i	−0.283710	+	0.491401i
$26$	−3.27995			−0.643251
$27$		0			0
$28$	−0.696024			−0.131536
$29$	−4.34197	+	7.52050i	−0.806283	+	1.39652i	0.109139	+	0.994027i	$0.465191\pi$
$29$	−4.34197	+	7.52050i	−0.806283	+	1.39652i	−0.915422	+	0.402496i	$0.868143\pi$
$30$		0			0
$31$	0.846788	+	1.46668i	0.152088	+	0.263424i	0.931995	−	0.362472i	$-0.118067\pi$
$31$	0.846788	+	1.46668i	0.152088	+	0.263424i	−0.779907	+	0.625895i	$0.784734\pi$
$32$	−3.00187	−	5.19939i	−0.530660	−	0.919131i
$33$		0			0
$34$	0.719755	−	1.24665i	0.123437	−	0.213799i
$35$	0.431070			0.0728641
$36$		0			0
$37$	4.07664			0.670195			0.335097	−	0.942183i	$-0.391231\pi$
$37$	4.07664			0.670195			0.335097	+	0.942183i	$0.391231\pi$
$38$	8.45585	−	14.6460i	1.37172	−	2.37589i
$39$		0			0
$40$	9.00752	+	15.6015i	1.42421	+	2.46681i
$41$	5.55726	+	9.62547i	0.867899	+	1.50325i	0.864140	+	0.503252i	$0.167863\pi$
$41$	5.55726	+	9.62547i	0.867899	+	1.50325i	0.00375938	+	0.999993i	$0.498803\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i
$44$	−16.7964			−2.53216
$45$		0			0
$46$	−15.4361			−2.27592
$47$	−3.69248	+	6.39556i	−0.538603	+	0.932888i	0.460377	+	0.887724i	$0.347714\pi$
$47$	−3.69248	+	6.39556i	−0.538603	+	0.932888i	−0.998980	+	0.0451639i	$0.985619\pi$
$48$		0			0
$49$	3.48814	+	6.04164i	0.498306	+	0.863092i
$50$	−3.62222	−	6.27386i	−0.512259	−	0.887258i
$51$		0			0
$52$	2.90310	−	5.02832i	0.402588	−	0.697302i
$53$	−2.30102			−0.316069			−0.158034	−	0.987434i	$-0.550516\pi$
$53$	−2.30102			−0.316069			−0.158034	+	0.987434i	$0.550516\pi$
$54$		0			0
$55$	10.4026			1.40268
$56$	0.495447	−	0.858140i	0.0662070	−	0.114674i
$57$		0			0
$58$	−11.0870	−	19.2033i	−1.45580	−	2.52152i
$59$	2.94982	+	5.10923i	0.384033	+	0.665165i	0.991635	−	0.129077i	$-0.0412014\pi$
$59$	2.94982	+	5.10923i	0.384033	+	0.665165i	−0.607601	+	0.794242i	$0.707868\pi$
$60$		0			0
$61$	2.07507	−	3.59412i	0.265685	−	0.460180i	−0.702058	−	0.712120i	$-0.747735\pi$
$61$	2.07507	−	3.59412i	0.265685	−	0.460180i	0.967743	+	0.251940i	$0.0810686\pi$
$62$	−4.32448			−0.549210
$63$		0			0
$64$	0.547229			0.0684037
$65$	−1.79798	+	3.11420i	−0.223013	+	0.386269i
$66$		0			0
$67$	−5.34393	−	9.25596i	−0.652865	−	1.13080i	−0.982424	−	0.186661i	$-0.940233\pi$
$67$	−5.34393	−	9.25596i	−0.652865	−	1.13080i	0.329559	−	0.944135i	$-0.393100\pi$
$68$	1.27412	+	2.20683i	0.154509	+	0.267618i
$69$		0			0
$70$	−0.550360	+	0.953252i	−0.0657806	+	0.113935i
$71$	−12.6183			−1.49752			−0.748758	−	0.662843i	$-0.769350\pi$
$71$	−12.6183			−1.49752			−0.748758	+	0.662843i	$0.769350\pi$
$72$		0			0
$73$	1.47133			0.172206			0.0861030	−	0.996286i	$-0.472559\pi$
$73$	1.47133			0.172206			0.0861030	+	0.996286i	$0.472559\pi$
$74$	−5.20476	+	9.01492i	−0.605042	+	1.04796i
$75$		0			0
$76$	14.9686	+	25.9264i	1.71702	+	2.97397i
$77$	−0.286090	−	0.495523i	−0.0326030	−	0.0564701i
$78$		0			0
$79$	−4.16420	+	7.21261i	−0.468509	+	0.811482i	−0.999352	−	0.0359886i	$-0.988542\pi$
$79$	−4.16420	+	7.21261i	−0.468509	+	0.811482i	0.530843	+	0.847470i	$0.321875\pi$
$80$	−20.6925			−2.31349
$81$		0			0
$82$	−28.3805			−3.13410
$83$	3.48869	−	6.04259i	0.382933	−	0.663260i	−0.608547	−	0.793518i	$-0.708247\pi$
$83$	3.48869	−	6.04259i	0.382933	−	0.663260i	0.991480	+	0.130258i	$0.0415805\pi$
$84$		0			0
$85$	−0.789102	−	1.36676i	−0.0855901	−	0.148246i
$86$	−1.27673	−	2.21136i	−0.137673	−	0.238457i
$87$		0			0
$88$	11.9561	−	20.7086i	1.27453	−	2.20755i
$89$	−15.8842			−1.68373			−0.841864	−	0.539690i	$-0.818541\pi$
$89$	−15.8842			−1.68373			−0.841864	+	0.539690i	$0.818541\pi$
$90$		0			0
$91$	0.197792			0.0207342
$92$	13.6625	−	23.6642i	1.42442	−	2.46716i
$93$		0			0
$94$	−9.42859	−	16.3308i	−0.972485	−	1.68439i
$95$	−9.27056	−	16.0571i	−0.951139	−	1.64742i
$96$		0			0
$97$	−8.27317	+	14.3296i	−0.840013	+	1.45495i	0.0498688	+	0.998756i	$0.484120\pi$
$97$	−8.27317	+	14.3296i	−0.840013	+	1.45495i	−0.889882	+	0.456190i	$0.849214\pi$
$98$	−17.8137			−1.79945
$99$		0			0
$100$	12.8242			1.28242
$101$	5.59941	−	9.69846i	0.557162	−	0.965033i	−0.440570	−	0.897718i	$-0.645224\pi$
$101$	5.59941	−	9.69846i	0.557162	−	0.965033i	0.997732	−	0.0673145i	$-0.0214431\pi$
$102$		0			0
$103$	−7.19198	−	12.4569i	−0.708647	−	1.22741i	−0.965359	−	0.260924i	$-0.915973\pi$
$103$	−7.19198	−	12.4569i	−0.708647	−	1.22741i	0.256713	−	0.966488i	$-0.417361\pi$
$104$	4.13300	+	7.15857i	0.405274	+	0.701956i
$105$		0			0
$106$	2.93778	−	5.08838i	0.285342	−	0.494227i
$107$	10.3317			0.998801			0.499400	−	0.866371i	$-0.333554\pi$
$107$	10.3317			0.998801			0.499400	+	0.866371i	$0.333554\pi$
$108$		0			0
$109$	8.69073			0.832421			0.416211	−	0.909268i	$-0.363358\pi$
$109$	8.69073			0.832421			0.416211	+	0.909268i	$0.363358\pi$
$110$	−13.2813	+	23.0039i	−1.26632	+	2.19333i
$111$		0			0
$112$	0.569082	+	0.985679i	0.0537732	+	0.0931379i
$113$	2.69829	+	4.67357i	0.253834	+	0.439653i	0.964578	−	0.263798i	$-0.0849751\pi$
$113$	2.69829	+	4.67357i	0.253834	+	0.439653i	−0.710744	+	0.703450i	$0.751642\pi$
$114$		0			0
$115$	−8.46165	+	14.6560i	−0.789053	+	1.36668i
$116$	39.2528			3.64453
$117$		0			0
$118$	−15.0645			−1.38680
$119$	−0.0434035	+	0.0751771i	−0.00397880	+	0.00689148i
$120$		0			0
$121$	−1.40394	−	2.43169i	−0.127631	−	0.221063i
$122$	5.29860	+	9.17744i	0.479712	+	0.830886i
$123$		0			0
$124$	3.82762	−	6.62963i	0.343730	−	0.595359i
$125$	6.05499			0.541575
$126$		0			0
$127$	8.93444			0.792803			0.396402	−	0.918077i	$-0.370259\pi$
$127$	8.93444			0.792803			0.396402	+	0.918077i	$0.370259\pi$
$128$	5.30507	−	9.18866i	0.468907	−	0.812170i
$129$		0			0
$130$	−4.59108	−	7.95199i	−0.402665	−	0.697435i
$131$	−4.50361	−	7.80048i	−0.393482	−	0.681531i	0.599424	−	0.800432i	$-0.295396\pi$
$131$	−4.50361	−	7.80048i	−0.393482	−	0.681531i	−0.992906	+	0.118901i	$0.962063\pi$
$132$		0			0
$133$	−0.509915	+	0.883199i	−0.0442153	+	0.0765831i
$134$	27.2910			2.35759
$135$		0			0
$136$	−3.62780			−0.311081
$137$	−7.30352	+	12.6501i	−0.623982	+	1.08077i	0.364755	+	0.931104i	$0.381153\pi$
$137$	−7.30352	+	12.6501i	−0.623982	+	1.08077i	−0.988737	+	0.149665i	$0.952180\pi$
$138$		0			0
$139$	6.22405	+	10.7804i	0.527917	+	0.914379i	0.999470	+	0.0325417i	$0.0103602\pi$
$139$	6.22405	+	10.7804i	0.527917	+	0.914379i	−0.471553	+	0.881838i	$0.656307\pi$
$140$	−0.974253	−	1.68746i	−0.0823394	−	0.142616i
$141$		0			0
$142$	16.1102	−	27.9036i	1.35194	−	2.34162i
$143$	4.77311			0.399148
$144$		0			0
$145$	−24.3105			−2.01888
$146$	−1.87849	+	3.25364i	−0.155465	+	0.269273i
$147$		0			0
$148$	−9.21353	−	15.9583i	−0.757347	−	1.31176i
$149$	8.17481	+	14.1592i	0.669706	+	1.15997i	0.977986	+	0.208670i	$0.0669134\pi$
$149$	8.17481	+	14.1592i	0.669706	+	1.15997i	−0.308280	+	0.951296i	$0.599753\pi$
$150$		0			0
$151$	8.02286	−	13.8960i	0.652891	−	1.13084i	−0.329527	−	0.944146i	$-0.606889\pi$
$151$	8.02286	−	13.8960i	0.652891	−	1.13084i	0.982418	−	0.186694i	$-0.0597772\pi$
$152$	−42.6202			−3.45696
$153$		0			0
$154$	1.46104			0.117734
$155$	−2.37057	+	4.10595i	−0.190409	+	0.329798i
$156$		0			0
$157$	−0.757906	−	1.31273i	−0.0604875	−	0.104767i	0.834196	−	0.551468i	$-0.185932\pi$
$157$	−0.757906	−	1.31273i	−0.0604875	−	0.104767i	−0.894683	+	0.446701i	$0.852599\pi$
$158$	−10.6331	−	18.4171i	−0.845926	−	1.46519i
$159$		0			0
$160$	8.40368	−	14.5556i	0.664369	−	1.15072i
$161$	0.930845			0.0733608
$162$		0			0
$163$	18.1419			1.42098			0.710490	−	0.703707i	$-0.248473\pi$
$163$	18.1419			1.42098			0.710490	+	0.703707i	$0.248473\pi$
$164$	25.1197	−	43.5087i	1.96152	−	3.39746i
$165$		0			0
$166$	8.90823	+	15.4295i	0.691413	+	1.19756i
$167$	−10.5220	−	18.2247i	−0.814218	−	1.41027i	−0.909888	−	0.414855i	$-0.863832\pi$
$167$	−10.5220	−	18.2247i	−0.814218	−	1.41027i	0.0956693	−	0.995413i	$-0.469501\pi$
$168$		0			0
$169$	5.67501	−	9.82941i	0.436540	−	0.756109i
$170$	4.02988			0.309078
$171$		0			0
$172$	4.52016			0.344659
$173$	7.85288	−	13.6016i	0.597043	−	1.03411i	−0.396212	−	0.918159i	$-0.629675\pi$
$173$	7.85288	−	13.6016i	0.597043	−	1.03411i	0.993255	−	0.115950i	$-0.0369913\pi$
$174$		0			0
$175$	0.218431	+	0.378334i	0.0165119	+	0.0285994i
$176$	13.7331	+	23.7864i	1.03517	+	1.79297i
$177$		0			0
$178$	20.2799	−	35.1258i	1.52004	−	2.63279i
$179$	−15.3843			−1.14988			−0.574939	−	0.818196i	$-0.694974\pi$
$179$	−15.3843			−1.14988			−0.574939	+	0.818196i	$0.694974\pi$
$180$		0			0
$181$	−4.19026			−0.311460			−0.155730	−	0.987800i	$-0.549773\pi$
$181$	−4.19026			−0.311460			−0.155730	+	0.987800i	$0.549773\pi$
$182$	−0.252527	+	0.437389i	−0.0187185	+	0.0324214i
$183$		0			0
$184$	19.4507	+	33.6896i	1.43392	+	2.48363i
$185$	5.70624	+	9.88349i	0.419531	+	0.726649i
$186$		0			0
$187$	−1.04741	+	1.81418i	−0.0765945	+	0.132666i
$188$	33.3812			2.43457
$189$		0			0
$190$	47.3440			3.43470
$191$	−8.26169	+	14.3097i	−0.597795	+	1.03541i	0.395351	+	0.918530i	$0.370623\pi$
$191$	−8.26169	+	14.3097i	−0.597795	+	1.03541i	−0.993146	+	0.116881i	$0.962710\pi$
$192$		0			0
$193$	0.222898	+	0.386070i	0.0160445	+	0.0277899i	0.873936	−	0.486041i	$-0.161559\pi$
$193$	0.222898	+	0.386070i	0.0160445	+	0.0277899i	−0.857892	+	0.513831i	$0.828226\pi$
$194$	−21.1252	−	36.5900i	−1.51670	−	2.62701i
$195$		0			0
$196$	15.7670	−	27.3092i	1.12621	−	1.95066i
$197$	−2.28962			−0.163128			−0.0815642	−	0.996668i	$-0.525992\pi$
$197$	−2.28962			−0.163128			−0.0815642	+	0.996668i	$0.525992\pi$
$198$		0			0
$199$	−3.92413			−0.278174			−0.139087	−	0.990280i	$-0.544417\pi$
$199$	−3.92413			−0.278174			−0.139087	+	0.990280i	$0.544417\pi$
$200$	−9.12857	+	15.8111i	−0.645487	+	1.11802i
$201$		0			0
$202$	14.2979	+	24.7646i	1.00599	+	1.74243i
$203$	0.668585	+	1.15802i	0.0469254	+	0.0812772i
$204$		0			0
$205$	−15.5575	+	26.9463i	−1.08658	+	1.88201i
$206$	36.7289			2.55902
$207$		0			0
$208$	−9.49452			−0.658327
$209$	−12.3053	+	21.3134i	−0.851174	+	1.47428i
$210$		0			0
$211$	9.02888	+	15.6385i	0.621574	+	1.07660i	0.989193	+	0.146621i	$0.0468397\pi$
$211$	9.02888	+	15.6385i	0.621574	+	1.07660i	−0.367619	+	0.929977i	$0.619827\pi$
$212$	5.20048	+	9.00750i	0.357171	+	0.618638i
$213$		0			0
$214$	−13.1908	+	22.8471i	−0.901702	+	1.56179i
$215$	−2.79948			−0.190923
$216$		0			0
$217$	0.260780			0.0177029
$218$	−11.0957	+	19.2184i	−0.751497	+	1.30163i
$219$		0			0
$220$	−23.5107	−	40.7217i	−1.58509	−	2.74546i
$221$	−0.362071	−	0.627125i	−0.0243555	−	0.0421850i
$222$		0			0
$223$	4.15911	−	7.20379i	0.278515	−	0.482402i	−0.692501	−	0.721417i	$-0.743491\pi$
$223$	4.15911	−	7.20379i	0.278515	−	0.482402i	0.971016	+	0.239015i	$0.0768246\pi$
$224$	−0.924468			−0.0617686
$225$		0			0
$226$	−13.7799			−0.916628
$227$	−6.96766	+	12.0683i	−0.462460	+	0.801004i	−0.999083	−	0.0428182i	$-0.986366\pi$
$227$	−6.96766	+	12.0683i	−0.462460	+	0.801004i	0.536623	+	0.843822i	$0.319700\pi$
$228$		0			0
$229$	0.834130	+	1.44476i	0.0551209	+	0.0954722i	0.892269	−	0.451504i	$-0.149112\pi$
$229$	0.834130	+	1.44476i	0.0551209	+	0.0954722i	−0.837148	+	0.546976i	$0.815779\pi$
$230$	−21.6065	−	37.4235i	−1.42469	−	2.46764i
$231$		0			0
$232$	−27.9411	+	48.3955i	−1.83443	+	3.17732i
$233$	−0.0999337			−0.00654687			−0.00327344	−	0.999995i	$-0.501042\pi$
$233$	−0.0999337			−0.00654687			−0.00327344	+	0.999995i	$0.501042\pi$
$234$		0			0
$235$	−20.6740			−1.34863
$236$	13.3336	−	23.0946i	0.867946	−	1.50333i
$237$		0			0
$238$	−0.110829	−	0.191962i	−0.00718399	−	0.0124430i
$239$	5.84080	+	10.1166i	0.377810	+	0.654386i	0.990743	−	0.135749i	$-0.0433440\pi$
$239$	5.84080	+	10.1166i	0.377810	+	0.654386i	−0.612934	+	0.790134i	$0.710011\pi$
$240$		0			0
$241$	2.50504	−	4.33885i	0.161364	−	0.279490i	−0.773994	−	0.633193i	$-0.781744\pi$
$241$	2.50504	−	4.33885i	0.161364	−	0.279490i	0.935358	+	0.353702i	$0.115077\pi$
$242$	7.16979			0.460892
$243$		0			0
$244$	−18.7593			−1.20094
$245$	−9.76500	+	16.9135i	−0.623863	+	1.08056i
$246$		0			0
$247$	−4.25369	−	7.36761i	−0.270656	−	0.468790i
$248$	5.44920	+	9.43829i	0.346024	+	0.599332i
$249$		0			0
$250$	−7.73059	+	13.3898i	−0.488926	+	0.846844i
$251$	4.73634			0.298955			0.149478	−	0.988765i	$-0.452241\pi$
$251$	4.73634			0.298955			0.149478	+	0.988765i	$0.452241\pi$
$252$		0			0
$253$	22.4631			1.41225
$254$	−11.4069	+	19.7573i	−0.715731	+	1.23968i
$255$		0			0
$256$	14.0935	+	24.4107i	0.880845	+	1.52567i
$257$	8.19567	+	14.1953i	0.511232	+	0.885480i	0.999915	+	0.0130184i	$0.00414400\pi$
$257$	8.19567	+	14.1953i	0.511232	+	0.885480i	−0.488683	+	0.872461i	$0.662523\pi$
$258$		0			0
$259$	0.313864	−	0.543629i	0.0195026	−	0.0337795i
$260$	16.2544			1.00805
$261$		0			0
$262$	22.9996			1.42092
$263$	8.02200	−	13.8945i	0.494658	−	0.856772i	−0.505323	−	0.862930i	$-0.668627\pi$
$263$	8.02200	−	13.8945i	0.494658	−	0.856772i	0.999981	+	0.00615770i	$0.00196007\pi$
$264$		0			0
$265$	−3.22083	−	5.57864i	−0.197854	−	0.342693i
$266$	−1.30205	−	2.25521i	−0.0798337	−	0.138276i
$267$		0			0
$268$	−24.1554	+	41.8384i	−1.47553	+	2.55569i
$269$	−15.7847			−0.962412			−0.481206	−	0.876607i	$-0.659801\pi$
$269$	−15.7847			−0.962412			−0.481206	+	0.876607i	$0.659801\pi$
$270$		0			0
$271$	30.4843			1.85179			0.925894	−	0.377784i	$-0.123314\pi$
$271$	30.4843			1.85179			0.925894	+	0.377784i	$0.123314\pi$
$272$	2.08348	−	3.60870i	0.126330	−	0.218810i
$273$		0			0
$274$	−18.6493	−	32.3015i	−1.12664	−	1.95140i
$275$	5.27119	+	9.12996i	0.317865	+	0.550558i
$276$		0			0
$277$	−9.67683	+	16.7608i	−0.581424	+	1.00706i	0.413887	+	0.910328i	$0.364171\pi$
$277$	−9.67683	+	16.7608i	−0.581424	+	1.00706i	−0.995311	+	0.0967280i	$0.969162\pi$
$278$	−31.7857			−1.90638
$279$		0			0
$280$	2.77399			0.165778
$281$	−9.15517	+	15.8572i	−0.546152	+	0.945962i	0.452382	+	0.891824i	$0.350574\pi$
$281$	−9.15517	+	15.8572i	−0.546152	+	0.945962i	−0.998533	+	0.0541381i	$0.982759\pi$
$282$		0			0
$283$	−6.00971	−	10.4091i	−0.357240	−	0.618758i	0.630259	−	0.776385i	$-0.282949\pi$
$283$	−6.00971	−	10.4091i	−0.357240	−	0.618758i	−0.987499	+	0.157627i	$0.949616\pi$
$284$	28.5184	+	49.3953i	1.69225	+	2.93107i
$285$		0			0
$286$	−6.09398	+	10.5551i	−0.360344	+	0.624135i
$287$	1.71144			0.101023
$288$		0			0
$289$	−16.6822			−0.981305
$290$	31.0380	−	53.7593i	1.82261	−	3.15686i
$291$		0			0
$292$	−3.32532	−	5.75963i	−0.194600	−	0.337057i
$293$	8.79180	+	15.2278i	0.513623	+	0.889620i	0.999875	+	0.0158021i	$0.00503018\pi$
$293$	8.79180	+	15.2278i	0.513623	+	0.889620i	−0.486253	+	0.873818i	$0.661636\pi$
$294$		0			0
$295$	−8.25796	+	14.3032i	−0.480797	+	0.832765i
$296$	26.2337			1.52480
$297$		0			0
$298$	−41.7481			−2.41840
$299$	−3.88253	+	6.72475i	−0.224533	+	0.388902i
$300$		0			0
$301$	0.0769910	+	0.133352i	0.00443769	+	0.00768630i
$302$	20.4860	+	35.4829i	1.17884	+	2.04181i
$303$		0			0
$304$	24.4773	−	42.3959i	1.40387	−	2.43157i
$305$	11.6182			0.665257
$306$		0			0
$307$	−9.91335			−0.565785			−0.282892	−	0.959152i	$-0.591294\pi$
$307$	−9.91335			−0.565785			−0.282892	+	0.959152i	$0.591294\pi$
$308$	−1.29318	+	2.23985i	−0.0736855	+	0.127627i
$309$		0			0
$310$	−6.05316	−	10.4844i	−0.343796	−	0.595472i
$311$	−13.0471	−	22.5982i	−0.739831	−	1.28143i	−0.952571	−	0.304316i	$-0.901572\pi$
$311$	−13.0471	−	22.5982i	−0.739831	−	1.28143i	0.212740	−	0.977109i	$-0.431761\pi$
$312$		0			0
$313$	−2.38738	+	4.13507i	−0.134943	+	0.233728i	−0.925576	−	0.378563i	$-0.876418\pi$
$313$	−2.38738	+	4.13507i	−0.134943	+	0.233728i	0.790633	+	0.612291i	$0.209752\pi$
$314$	3.87057			0.218429
$315$		0			0
$316$	37.6457			2.11774
$317$	10.6534	−	18.4523i	0.598357	−	1.03639i	−0.394706	−	0.918807i	$-0.629154\pi$
$317$	10.6534	−	18.4523i	0.598357	−	1.03639i	0.993064	−	0.117578i	$-0.0375130\pi$
$318$		0			0
$319$	16.1343	+	27.9454i	0.903347	+	1.56464i
$320$	0.765979	+	1.32672i	0.0428195	+	0.0741656i
$321$		0			0
$322$	−1.18844	+	2.05843i	−0.0662290	+	0.114712i
$323$	3.73373			0.207750
$324$		0			0
$325$	−3.64429			−0.202149
$326$	−23.1623	+	40.1182i	−1.28284	+	2.22194i
$327$		0			0
$328$	35.7617	+	61.9412i	1.97461	+	3.42013i
$329$	0.568575	+	0.984800i	0.0313465	+	0.0542938i
$330$		0			0
$331$	−2.03831	+	3.53046i	−0.112036	+	0.194052i	−0.916591	−	0.399826i	$-0.869070\pi$
$331$	−2.03831	+	3.53046i	−0.112036	+	0.194052i	0.804555	+	0.593878i	$0.202404\pi$
$332$	−31.5389			−1.73092
$333$		0			0
$334$	53.7351			2.94026
$335$	14.9602	−	25.9119i	0.817365	−	1.41572i
$336$		0			0
$337$	−2.30238	−	3.98784i	−0.125419	−	0.217231i	0.796478	−	0.604668i	$-0.206694\pi$
$337$	−2.30238	−	3.98784i	−0.125419	−	0.217231i	−0.921896	+	0.387436i	$0.873361\pi$
$338$	14.4909	+	25.0990i	0.788203	+	1.36521i
$339$		0			0
$340$	−3.56687	+	6.17800i	−0.193441	+	0.335049i
$341$	6.29315			0.340793
$342$		0			0
$343$	2.15210			0.116202
$344$	−3.21757	+	5.57299i	−0.173480	+	0.300475i
$345$		0			0
$346$	20.0520	+	34.7311i	1.07800	+	1.86716i
$347$	6.62588	+	11.4764i	0.355696	+	0.616084i	0.987237	−	0.159259i	$-0.0509105\pi$
$347$	6.62588	+	11.4764i	0.355696	+	0.616084i	−0.631541	+	0.775343i	$0.717577\pi$
$348$		0			0
$349$	−1.46592	+	2.53905i	−0.0784690	+	0.135912i	−0.902590	−	0.430502i	$-0.858336\pi$
$349$	−1.46592	+	2.53905i	−0.0784690	+	0.135912i	0.824121	+	0.566414i	$0.191670\pi$
$350$	−1.11551			−0.0596266
$351$		0			0
$352$	−22.3093			−1.18909
$353$	14.7204	−	25.4964i	0.783487	−	1.35704i	−0.146412	−	0.989224i	$-0.546773\pi$
$353$	14.7204	−	25.4964i	0.783487	−	1.35704i	0.929899	−	0.367815i	$-0.119894\pi$
$354$		0			0
$355$	−17.6624	−	30.5921i	−0.937420	−	1.62366i
$356$	35.8997	+	62.1801i	1.90268	+	3.29554i
$357$		0			0
$358$	19.6416	−	34.0203i	1.03809	−	1.79803i
$359$	35.4312			1.86999			0.934994	−	0.354664i	$-0.115405\pi$
$359$	35.4312			1.86999			0.934994	+	0.354664i	$0.115405\pi$
$360$		0			0
$361$	24.8648			1.30867
$362$	5.34983	−	9.26618i	0.281181	−	0.487020i
$363$		0			0
$364$	−0.447025	−	0.774270i	−0.0234305	−	0.0405828i
$365$	2.05948	+	3.56712i	0.107798	+	0.186712i
$366$		0			0
$367$	3.95549	−	6.85111i	0.206475	−	0.357625i	−0.744127	−	0.668039i	$-0.767134\pi$
$367$	3.95549	−	6.85111i	0.206475	−	0.357625i	0.950602	+	0.310413i	$0.100467\pi$
$368$	−44.6830			−2.32926
$369$		0			0
$370$	−29.1413			−1.51498
$371$	−0.177158	+	0.306846i	−0.00919756	+	0.0159306i
$372$		0			0
$373$	−0.971984	−	1.68353i	−0.0503274	−	0.0871697i	0.839764	−	0.542951i	$-0.182693\pi$
$373$	−0.971984	−	1.68353i	−0.0503274	−	0.0871697i	−0.890092	+	0.455782i	$0.849360\pi$
$374$	−2.67453	−	4.63243i	−0.138297	−	0.239537i
$375$		0			0
$376$	−23.7616	+	41.1563i	−1.22541	+	2.12247i
$377$	−11.1546			−0.574492
$378$		0			0
$379$	8.52784			0.438046			0.219023	−	0.975720i	$-0.429713\pi$
$379$	8.52784			0.438046			0.219023	+	0.975720i	$0.429713\pi$
$380$	−41.9044	+	72.5806i	−2.14965	+	3.72331i
$381$		0			0
$382$	−21.0959	−	36.5392i	−1.07936	−	1.86951i
$383$	5.04469	+	8.73766i	0.257772	+	0.446474i	0.965645	−	0.259866i	$-0.0836784\pi$
$383$	5.04469	+	8.73766i	0.257772	+	0.446474i	−0.707873	+	0.706340i	$0.750345\pi$
$384$		0			0
$385$	0.800905	−	1.38721i	0.0408179	−	0.0706987i
$386$	−1.13832			−0.0579390
$387$		0			0
$388$	74.7922			3.79700
$389$	0.792197	−	1.37213i	0.0401660	−	0.0695695i	−0.845244	−	0.534381i	$-0.820545\pi$
$389$	0.792197	−	1.37213i	0.0401660	−	0.0695695i	0.885410	+	0.464812i	$0.153878\pi$
$390$		0			0
$391$	−1.70397	−	2.95137i	−0.0861736	−	0.149257i
$392$	22.4467	+	38.8788i	1.13373	+	1.96368i
$393$		0			0
$394$	2.92322	−	5.06317i	0.147270	−	0.255079i
$395$	−23.3152			−1.17312
$396$		0			0
$397$	−5.37215			−0.269620			−0.134810	−	0.990871i	$-0.543042\pi$
$397$	−5.37215			−0.269620			−0.134810	+	0.990871i	$0.543042\pi$
$398$	5.01005	−	8.67767i	0.251131	−	0.434972i
$399$		0			0
$400$	−10.4853	−	18.1610i	−0.524264	−	0.908052i
$401$	−6.75094	−	11.6930i	−0.337126	−	0.583919i	0.646765	−	0.762689i	$-0.276121\pi$
$401$	−6.75094	−	11.6930i	−0.337126	−	0.583919i	−0.983891	+	0.178770i	$0.942788\pi$
$402$		0			0
$403$	−1.08771	+	1.88397i	−0.0541827	+	0.0938471i
$404$	−50.6205			−2.51846
$405$		0			0
$406$	−3.41441			−0.169454
$407$	7.57417	−	13.1189i	0.375438	−	0.650277i
$408$		0			0
$409$	−9.36718	−	16.2244i	−0.463177	−	0.802247i	0.535940	−	0.844256i	$-0.319957\pi$
$409$	−9.36718	−	16.2244i	−0.463177	−	0.802247i	−0.999117	+	0.0420093i	$0.986624\pi$
$410$	−39.7254	−	68.8064i	−1.96190	−	3.39810i
$411$		0			0
$412$	−32.5089	+	56.3071i	−1.60160	+	2.77405i
$413$	0.908437			0.0447013
$414$		0			0
$415$	19.5331			0.958840
$416$	3.85594	−	6.67868i	0.189053	−	0.327449i
$417$		0			0
$418$	−31.4210	−	54.4228i	−1.53685	−	2.66191i
$419$	4.59794	+	7.96387i	0.224624	+	0.389060i	0.956207	−	0.292693i	$-0.0945513\pi$
$419$	4.59794	+	7.96387i	0.224624	+	0.389060i	−0.731583	+	0.681753i	$0.761218\pi$
$420$		0			0
$421$	2.48856	−	4.31031i	0.121285	−	0.210072i	−0.798990	−	0.601345i	$-0.794632\pi$
$421$	2.48856	−	4.31031i	0.121285	−	0.210072i	0.920275	+	0.391273i	$0.127965\pi$
$422$	−46.1098			−2.24459
$423$		0			0
$424$	−14.8074			−0.719109
$425$	0.799706	−	1.38513i	0.0387914	−	0.0671887i
$426$		0			0
$427$	−0.319523	−	0.553430i	−0.0154628	−	0.0267823i
$428$	−23.3504	−	40.4441i	−1.12869	−	1.95494i
$429$		0			0
$430$	3.57418	−	6.19067i	0.172362	−	0.298541i
$431$	2.97671			0.143383			0.0716916	−	0.997427i	$-0.477160\pi$
$431$	2.97671			0.143383			0.0716916	+	0.997427i	$0.477160\pi$
$432$		0			0
$433$	−2.07208			−0.0995780			−0.0497890	−	0.998760i	$-0.515855\pi$
$433$	−2.07208			−0.0995780			−0.0497890	+	0.998760i	$0.515855\pi$
$434$	−0.332946	+	0.576680i	−0.0159819	+	0.0276815i
$435$		0			0
$436$	−19.6418	−	34.0205i	−0.940670	−	1.62929i
$437$	−20.0187	−	34.6734i	−0.957623	−	1.65865i
$438$		0			0
$439$	10.8388	−	18.7734i	0.517310	−	0.896007i	−0.482488	−	0.875903i	$-0.660267\pi$
$439$	10.8388	−	18.7734i	0.517310	−	0.896007i	0.999798	−	0.0201044i	$-0.00639985\pi$
$440$	66.9420			3.19134
$441$		0			0
$442$	1.84907			0.0879511
$443$	8.90773	−	15.4286i	0.423219	−	0.733037i	−0.573033	−	0.819532i	$-0.694233\pi$
$443$	8.90773	−	15.4286i	0.423219	−	0.733037i	0.996252	+	0.0864954i	$0.0275668\pi$
$444$		0			0
$445$	−22.2338	−	38.5101i	−1.05399	−	1.82556i
$446$	10.6201	+	18.3946i	0.502878	+	0.871010i
$447$		0			0
$448$	0.0421317	−	0.0729743i	0.00199054	−	0.00344771i
$449$	39.1785			1.84895			0.924475	−	0.381243i	$-0.124504\pi$
$449$	39.1785			1.84895			0.924475	+	0.381243i	$0.124504\pi$
$450$		0			0
$451$	41.3004			1.94476
$452$	12.1967	−	21.1253i	0.573684	−	0.993650i
$453$		0			0
$454$	−17.7916	−	30.8160i	−0.835003	−	1.44627i
$455$	0.276857	+	0.479531i	0.0129793	+	0.0224807i
$456$		0			0
$457$	−1.53806	+	2.66400i	−0.0719474	+	0.124617i	−0.899755	−	0.436396i	$-0.856255\pi$
$457$	−1.53806	+	2.66400i	−0.0719474	+	0.124617i	0.827807	+	0.561012i	$0.189588\pi$
$458$	−4.25984			−0.199049
$459$		0			0
$460$	76.4960			3.56665
$461$	−2.07652	+	3.59664i	−0.0967131	+	0.167512i	−0.910322	−	0.413900i	$-0.864166\pi$
$461$	−2.07652	+	3.59664i	−0.0967131	+	0.167512i	0.813609	+	0.581412i	$0.197500\pi$
$462$		0			0
$463$	−3.54662	−	6.14292i	−0.164825	−	0.285486i	0.771768	−	0.635904i	$-0.219373\pi$
$463$	−3.54662	−	6.14292i	−0.164825	−	0.285486i	−0.936593	+	0.350418i	$0.886039\pi$
$464$	−32.0938	−	55.5881i	−1.48992	−	2.58061i
$465$		0			0
$466$	0.127588	−	0.220990i	0.00591042	−	0.0102371i
$467$	10.7211			0.496112			0.248056	−	0.968746i	$-0.420208\pi$
$467$	10.7211			0.496112			0.248056	+	0.968746i	$0.420208\pi$
$468$		0			0
$469$	−1.64574			−0.0759932
$470$	26.3952	−	45.7178i	1.21752	−	2.10880i
$471$		0			0
$472$	18.9825	+	32.8786i	0.873739	+	1.51336i
$473$	1.85795	+	3.21806i	0.0854285	+	0.147967i
$474$		0			0
$475$	9.39514	−	16.2729i	0.431078	−	0.746650i
$476$	0.392382			0.0179848
$477$		0			0
$478$	−29.8285			−1.36432
$479$	−3.40786	+	5.90259i	−0.155709	+	0.269696i	−0.933317	−	0.359053i	$-0.883100\pi$
$479$	−3.40786	+	5.90259i	−0.155709	+	0.269696i	0.777608	+	0.628750i	$0.216433\pi$
$480$		0			0
$481$	2.61824	+	4.53493i	0.119382	+	0.206775i
$482$	6.39652	+	11.0791i	0.291353	+	0.504639i
$483$		0			0
$484$	−6.34602	+	10.9916i	−0.288455	+	0.499619i
$485$	−46.3212			−2.10334
$486$		0			0
$487$	−17.3377			−0.785645			−0.392823	−	0.919614i	$-0.628501\pi$
$487$	−17.3377			−0.785645			−0.392823	+	0.919614i	$0.628501\pi$
$488$	13.3533	−	23.1286i	0.604477	−	1.04698i
$489$		0			0
$490$	−24.9345	−	43.1879i	−1.12643	−	1.95103i
$491$	7.95116	+	13.7718i	0.358831	+	0.621514i	0.987766	−	0.155944i	$-0.0498421\pi$
$491$	7.95116	+	13.7718i	0.358831	+	0.621514i	−0.628935	+	0.777458i	$0.716509\pi$
$492$		0			0
$493$	2.44778	−	4.23967i	0.110242	−	0.190945i
$494$	21.7233			0.977376
$495$		0			0
$496$	−12.5181			−0.562081
$497$	−0.971496	+	1.68268i	−0.0435775	+	0.0754785i
$498$		0			0
$499$	2.26248	+	3.91873i	0.101282	+	0.175426i	0.912213	−	0.409716i	$-0.134372\pi$
$499$	2.26248	+	3.91873i	0.101282	+	0.175426i	−0.810931	+	0.585142i	$0.801039\pi$
$500$	−13.6848	−	23.7027i	−0.612002	−	1.06002i
$501$		0			0
$502$	−6.04703	+	10.4738i	−0.269892	+	0.467467i
$503$	19.5945			0.873674			0.436837	−	0.899541i	$-0.356099\pi$
$503$	19.5945			0.873674			0.436837	+	0.899541i	$0.356099\pi$
$504$		0			0
$505$	31.3509			1.39510
$506$	−28.6794	+	49.6742i	−1.27495	+	2.20829i
$507$		0			0
$508$	−20.1926	−	34.9745i	−0.895900	−	1.55174i
$509$	−14.4162	−	24.9696i	−0.638988	−	1.10676i	−0.985655	−	0.168772i	$-0.946020\pi$
$509$	−14.4162	−	24.9696i	−0.638988	−	1.10676i	0.346667	−	0.937988i	$-0.387313\pi$
$510$		0			0
$511$	0.113279	−	0.196205i	0.00501117	−	0.00867960i
$512$	−50.7542			−2.24304
$513$		0			0
$514$	−41.8546			−1.84613
$515$	20.1338	−	34.8728i	0.887202	−	1.53668i
$516$		0			0
$517$	13.7208	+	23.7652i	0.603442	+	1.04519i
$518$	0.801440	+	1.38814i	0.0352133	+	0.0609912i
$519$		0			0
$520$	−11.5703	+	20.0403i	−0.507390	+	0.878825i
$521$	−39.0982			−1.71292			−0.856461	−	0.516211i	$-0.827342\pi$
$521$	−39.0982			−1.71292			−0.856461	+	0.516211i	$0.827342\pi$
$522$		0			0
$523$	−20.7298			−0.906453			−0.453226	−	0.891395i	$-0.649727\pi$
$523$	−20.7298			−0.906453			−0.453226	+	0.891395i	$0.649727\pi$
$524$	−20.3570	+	35.2594i	−0.889301	+	1.54032i
$525$		0			0
$526$	20.4839	+	35.4791i	0.893139	+	1.54696i
$527$	−0.477375	−	0.826839i	−0.0207948	−	0.0360177i
$528$		0			0
$529$	−6.77193	+	11.7293i	−0.294432	+	0.509971i
$530$	16.4485			0.714478
$531$		0			0
$532$	4.60980			0.199860
$533$	−7.13837	+	12.3640i	−0.309197	+	0.535545i
$534$		0			0
$535$	14.4617	+	25.0484i	0.625233	+	1.08293i
$536$	−34.3889	−	59.5634i	−1.48538	−	2.57275i
$537$		0			0
$538$	20.1529	−	34.9058i	0.868851	−	1.50489i
$539$	25.9232			1.11659
$540$		0			0
$541$	42.2499			1.81647			0.908233	−	0.418466i	$-0.137432\pi$
$541$	42.2499			1.81647			0.908233	+	0.418466i	$0.137432\pi$
$542$	−38.9202	+	67.4117i	−1.67177	+	2.89558i
$543$		0			0
$544$	1.69230	+	2.93115i	0.0725567	+	0.125672i
$545$	12.1648	+	21.0700i	0.521082	+	0.902540i
$546$		0			0
$547$	6.84352	−	11.8533i	0.292608	−	0.506811i	−0.681818	−	0.731522i	$-0.738810\pi$
$547$	6.84352	−	11.8533i	0.292608	−	0.506811i	0.974426	+	0.224711i	$0.0721437\pi$
$548$	66.0262			2.82050
$549$		0			0
$550$	−26.9195			−1.14785
$551$	28.7571	−	49.8087i	1.22509	−	2.12192i
$552$		0			0
$553$	0.641212	+	1.11061i	0.0272671	+	0.0472280i
$554$	−24.7094	−	42.7979i	−1.04980	−	1.81831i
$555$		0			0
$556$	28.1337	−	48.7290i	1.19314	−	2.06657i
$557$	19.8203			0.839813			0.419907	−	0.907567i	$-0.362063\pi$
$557$	19.8203			0.839813			0.419907	+	0.907567i	$0.362063\pi$
$558$		0			0
$559$	−1.28451			−0.0543291
$560$	−1.59314	+	2.75939i	−0.0673223	+	0.116606i
$561$		0			0
$562$	−23.3774	−	40.4908i	−0.986115	−	1.70800i
$563$	20.6593	+	35.7830i	0.870686	+	1.50807i	0.861288	+	0.508117i	$0.169658\pi$
$563$	20.6593	+	35.7830i	0.870686	+	1.50807i	0.00939822	+	0.999956i	$0.497008\pi$
$564$		0			0
$565$	−7.55381	+	13.0836i	−0.317791	+	0.550430i
$566$	30.6911			1.29004
$567$		0			0
$568$	−81.2005			−3.40710
$569$	2.77982	−	4.81479i	0.116536	−	0.201846i	−0.801857	−	0.597516i	$-0.796154\pi$
$569$	2.77982	−	4.81479i	0.116536	−	0.201846i	0.918393	+	0.395670i	$0.129488\pi$
$570$		0			0
$571$	21.1657	+	36.6600i	0.885756	+	1.53417i	0.844845	+	0.535011i	$0.179693\pi$
$571$	21.1657	+	36.6600i	0.885756	+	1.53417i	0.0409107	+	0.999163i	$0.486974\pi$
$572$	−10.7876	−	18.6847i	−0.451053	−	0.781247i
$573$		0			0
$574$	−2.18504	+	3.78461i	−0.0912020	+	0.157966i
$575$	−17.1507			−0.715234
$576$		0			0
$577$	18.7514			0.780631			0.390316	−	0.920681i	$-0.372366\pi$
$577$	18.7514			0.780631			0.390316	+	0.920681i	$0.372366\pi$
$578$	21.2987	−	36.8904i	0.885907	−	1.53444i
$579$		0			0
$580$	54.9437	+	95.1653i	2.28141	+	3.95153i
$581$	−0.537195	−	0.930450i	−0.0222866	−	0.0386016i
$582$		0			0
$583$	−4.27517	+	7.40481i	−0.177059	+	0.306676i
$584$	9.46820			0.391797
$585$		0			0
$586$	−44.8990			−1.85476
$587$	−6.01774	+	10.4230i	−0.248379	+	0.430204i	−0.963076	−	0.269229i	$-0.913231\pi$
$587$	−6.01774	+	10.4230i	−0.248379	+	0.430204i	0.714698	+	0.699434i	$0.246564\pi$
$588$		0			0
$589$	−5.60832	−	9.71390i	−0.231087	−	0.400254i
$590$	−21.0864	−	36.5227i	−0.868112	−	1.50361i
$591$		0			0
$592$	−15.0663	+	26.0956i	−0.619221	+	1.07252i
$593$	−15.9739			−0.655970			−0.327985	−	0.944683i	$-0.606370\pi$
$593$	−15.9739			−0.655970			−0.327985	+	0.944683i	$0.606370\pi$
$594$		0			0
$595$	−0.243015			−0.00996264
$596$	36.9515	−	64.0018i	1.51359	−	2.62162i
$597$		0			0
$598$	−9.91390	−	17.1714i	−0.405410	−	0.702190i
$599$	1.12275	+	1.94466i	0.0458743	+	0.0794565i	0.888051	−	0.459745i	$-0.152059\pi$
$599$	1.12275	+	1.94466i	0.0458743	+	0.0794565i	−0.842177	+	0.539202i	$0.818726\pi$
$600$		0			0
$601$	−2.39385	+	4.14626i	−0.0976470	+	0.169130i	−0.910710	−	0.413046i	$-0.864465\pi$
$601$	−2.39385	+	4.14626i	−0.0976470	+	0.169130i	0.813063	+	0.582175i	$0.197798\pi$
$602$	−0.393187			−0.0160251
$603$		0			0
$604$	−72.5292			−2.95117
$605$	3.93029	−	6.80747i	0.159789	−	0.276763i
$606$		0			0
$607$	−14.5002	−	25.1152i	−0.588547	−	1.01939i	−0.994423	−	0.105465i	$-0.966367\pi$
$607$	−14.5002	−	25.1152i	−0.588547	−	1.01939i	0.405876	−	0.913928i	$-0.366966\pi$
$608$	19.8815	+	34.4358i	0.806302	+	1.39656i
$609$		0			0
$610$	−14.8333	+	25.6921i	−0.600584	+	1.04024i
$611$	−9.48606			−0.383765
$612$		0			0
$613$	−36.6015			−1.47832			−0.739160	−	0.673530i	$-0.764777\pi$
$613$	−36.6015			−1.47832			−0.739160	+	0.673530i	$0.764777\pi$
$614$	12.6567	−	21.9220i	0.510782	−	0.884700i
$615$		0			0
$616$	−1.84103	−	3.18876i	−0.0741772	−	0.128479i
$617$	−17.9241	−	31.0455i	−0.721599	−	1.24985i	−0.960359	−	0.278767i	$-0.910074\pi$
$617$	−17.9241	−	31.0455i	−0.721599	−	1.24985i	0.238760	−	0.971079i	$-0.423259\pi$
$618$		0			0
$619$	16.4769	−	28.5388i	0.662261	−	1.14707i	−0.317759	−	0.948171i	$-0.602930\pi$
$619$	16.4769	−	28.5388i	0.662261	−	1.14707i	0.980020	−	0.198898i	$-0.0637363\pi$
$620$	21.4307			0.860678
$621$		0			0
$622$	66.6303			2.67163
$623$	−1.22294	+	2.11820i	−0.0489962	+	0.0848640i
$624$		0			0
$625$	15.5682	+	26.9649i	0.622727	+	1.07860i
$626$	−6.09608	−	10.5587i	−0.243649	−	0.422012i
$627$		0			0
$628$	−3.42586	+	5.93376i	−0.136707	+	0.236783i
$629$	−2.29820			−0.0916351
$630$		0			0
$631$	10.8066			0.430203			0.215101	−	0.976592i	$-0.430992\pi$
$631$	10.8066			0.430203			0.215101	+	0.976592i	$0.430992\pi$
$632$	−26.7972	+	46.4141i	−1.06593	+	1.84625i
$633$		0			0
$634$	27.2032	+	47.1173i	1.08038	+	1.87127i
$635$	12.5059	+	21.6609i	0.496282	+	0.859585i
$636$		0			0
$637$	−4.48056	+	7.76056i	−0.177526	+	0.307485i
$638$	−82.3965			−3.26211
$639$		0			0
$640$	29.7029			1.17411
$641$	−7.98234	+	13.8258i	−0.315284	+	0.546087i	−0.979498	−	0.201455i	$-0.935433\pi$
$641$	−7.98234	+	13.8258i	−0.315284	+	0.546087i	0.664214	+	0.747542i	$0.268766\pi$
$642$		0			0
$643$	−17.8131	−	30.8532i	−0.702481	−	1.21673i	−0.967593	−	0.252515i	$-0.918742\pi$
$643$	−17.8131	−	30.8532i	−0.702481	−	1.21673i	0.265113	−	0.964217i	$-0.414591\pi$
$644$	−2.10378	−	3.64386i	−0.0829007	−	0.143588i
$645$		0			0
$646$	−4.76697	+	8.25664i	−0.187554	+	0.324853i
$647$	−16.4474			−0.646612			−0.323306	−	0.946294i	$-0.604794\pi$
$647$	−16.4474			−0.646612			−0.323306	+	0.946294i	$0.604794\pi$
$648$		0			0
$649$	21.9224			0.860530
$650$	4.65278	−	8.05885i	0.182497	−	0.316094i
$651$		0			0
$652$	−41.0021	−	71.0177i	−1.60577	−	2.78127i
$653$	−2.91944	−	5.05662i	−0.114246	−	0.197881i	0.803232	−	0.595667i	$-0.203112\pi$
$653$	−2.91944	−	5.05662i	−0.114246	−	0.197881i	−0.917478	+	0.397786i	$0.869779\pi$
$654$		0			0
$655$	12.6078	−	21.8373i	0.492626	−	0.853254i
$656$	−82.1535			−3.20755
$657$		0			0
$658$	−2.90367			−0.113197
$659$	0.379323	−	0.657008i	0.0147763	−	0.0255934i	−0.858543	−	0.512742i	$-0.828630\pi$
$659$	0.379323	−	0.657008i	0.0147763	−	0.0255934i	0.873319	+	0.487149i	$0.161963\pi$
$660$		0			0
$661$	22.5030	+	38.9764i	0.875266	+	1.51601i	0.856479	+	0.516182i	$0.172647\pi$
$661$	22.5030	+	38.9764i	0.875266	+	1.51601i	0.0187875	+	0.999823i	$0.494019\pi$
$662$	−5.20475	−	9.01489i	−0.202288	−	0.350374i
$663$		0			0
$664$	22.4502	−	38.8849i	0.871236	−	1.50903i
$665$	−2.85500			−0.110712
$666$		0			0
$667$	−52.4957			−2.03264
$668$	−47.5612	+	82.3785i	−1.84020	+	3.18732i
$669$		0			0
$670$	38.2004	+	66.1650i	1.47581	+	2.55618i
$671$	−7.71072	−	13.3554i	−0.297669	−	0.515578i
$672$		0			0
$673$	8.44242	−	14.6227i	0.325431	−	0.563664i	−0.656168	−	0.754615i	$-0.727824\pi$
$673$	8.44242	−	14.6227i	0.325431	−	0.563664i	0.981600	+	0.190951i	$0.0611572\pi$
$674$	11.7581			0.452904
$675$		0			0
$676$	−51.3040			−1.97323
$677$	17.8495	−	30.9163i	0.686014	−	1.18821i	−0.287103	−	0.957900i	$-0.592692\pi$
$677$	17.8495	−	30.9163i	0.686014	−	1.18821i	0.973117	−	0.230311i	$-0.0739743\pi$
$678$		0			0
$679$	1.27392	+	2.20649i	0.0488886	+	0.0846775i
$680$	−5.07798	−	8.79531i	−0.194731	−	0.337285i
$681$		0			0
$682$	−8.03466	+	13.9164i	−0.307663	+	0.532888i
$683$	−13.0146			−0.497989			−0.248995	−	0.968505i	$-0.580100\pi$
$683$	−13.0146			−0.497989			−0.248995	+	0.968505i	$0.580100\pi$
$684$		0			0
$685$	−40.8922			−1.56241
$686$	−2.74765	+	4.75907i	−0.104906	+	0.181702i
$687$		0			0
$688$	−3.69577	−	6.40126i	−0.140900	−	0.244046i
$689$	−1.47784	−	2.55970i	−0.0563013	−	0.0975167i
$690$		0			0
$691$	0.417863	−	0.723760i	0.0158963	−	0.0275331i	−0.857968	−	0.513703i	$-0.828273\pi$
$691$	0.417863	−	0.723760i	0.0158963	−	0.0275331i	0.873864	+	0.486170i	$0.161607\pi$
$692$	−70.9926			−2.69873
$693$		0			0
$694$	−33.8379			−1.28447
$695$	−17.4241	+	30.1795i	−0.660935	+	1.14477i
$696$		0			0
$697$	−3.13290	−	5.42634i	−0.118667	−	0.205537i
$698$	−3.74317	−	6.48337i	−0.141681	−	0.245399i
$699$		0			0
$700$	0.987345	−	1.71013i	0.0373181	−	0.0646369i
$701$	−45.3676			−1.71351			−0.856755	−	0.515723i	$-0.827523\pi$
$701$	−45.3676			−1.71351			−0.856755	+	0.515723i	$0.827523\pi$
$702$		0			0
$703$	−26.9998			−1.01832
$704$	1.01672	−	1.76102i	0.0383192	−	0.0663708i
$705$		0			0
$706$	37.5879	+	65.1042i	1.41464	+	2.45023i
$707$	−0.862208	−	1.49339i	−0.0324267	−	0.0561647i
$708$		0			0
$709$	−0.101566	+	0.175917i	−0.00381438	+	0.00660669i	−0.867926	−	0.496693i	$-0.834547\pi$
$709$	−0.101566	+	0.175917i	−0.00381438	+	0.00660669i	0.864112	+	0.503300i	$0.167881\pi$
$710$	90.2003			3.38516
$711$		0			0
$712$	−102.217			−3.83075
$713$	−5.11896	+	8.86631i	−0.191707	+	0.332046i
$714$		0			0
$715$	6.68112	+	11.5720i	0.249860	+	0.432770i
$716$	34.7698	+	60.2230i	1.29941	+	2.25064i
$717$		0			0
$718$	−45.2361	+	78.3512i	−1.68820	+	2.92404i
$719$	15.9357			0.594302			0.297151	−	0.954830i	$-0.403963\pi$
$719$	15.9357			0.594302			0.297151	+	0.954830i	$0.403963\pi$
$720$		0			0
$721$	−2.21487			−0.0824861
$722$	−31.7456	+	54.9851i	−1.18145	+	2.04633i
$723$		0			0
$724$	9.47033	+	16.4031i	0.351962	+	0.609616i
$725$	−12.3186	−	21.3364i	−0.457501	−	0.792416i
$726$		0			0
$727$	22.9224	−	39.7028i	0.850146	−	1.47250i	−0.0309292	−	0.999522i	$-0.509847\pi$
$727$	22.9224	−	39.7028i	0.850146	−	1.47250i	0.881076	−	0.472975i	$-0.156820\pi$
$728$	1.27282			0.0471737
$729$		0			0
$730$	−10.5176			−0.389274
$731$	0.281874	−	0.488220i	0.0104255	−	0.0180575i
$732$		0			0
$733$	−3.17170	−	5.49354i	−0.117149	−	0.202908i	0.801488	−	0.598011i	$-0.204042\pi$
$733$	−3.17170	−	5.49354i	−0.117149	−	0.202908i	−0.918637	+	0.395103i	$0.870709\pi$
$734$	10.1002	+	17.4940i	0.372805	+	0.645717i
$735$		0			0
$736$	18.1468	−	31.4311i	0.668898	−	1.15857i
$737$	−39.7150			−1.46292
$738$		0			0
$739$	32.6732			1.20190			0.600951	−	0.799286i	$-0.294789\pi$
$739$	32.6732			1.20190			0.600951	+	0.799286i	$0.294789\pi$
$740$	25.7931	−	44.6750i	0.948174	−	1.64228i
$741$		0			0
$742$	−0.452365	−	0.783519i	−0.0166068	−	0.0287639i
$743$	−10.1642	−	17.6049i	−0.372888	−	0.645861i	0.617120	−	0.786869i	$-0.288299\pi$
$743$	−10.1642	−	17.6049i	−0.372888	−	0.645861i	−0.990009	+	0.141008i	$0.954966\pi$
$744$		0			0
$745$	−22.8852	+	39.6384i	−0.838450	+	1.45224i
$746$	4.96385			0.181739
$747$		0			0
$748$	9.46897			0.346220
$749$	0.795446	−	1.37775i	0.0290650	−	0.0503420i
$750$		0			0
$751$	6.69532	+	11.5966i	0.244316	+	0.423167i	0.961939	−	0.273264i	$-0.0881034\pi$
$751$	6.69532	+	11.5966i	0.244316	+	0.423167i	−0.717623	+	0.696431i	$0.754770\pi$
$752$	−27.2931	−	47.2730i	−0.995276	−	1.72387i
$753$		0			0
$754$	14.2414	−	24.6669i	0.518642	−	0.898315i
$755$	44.9197			1.63479
$756$		0			0
$757$	33.6454			1.22286			0.611432	−	0.791297i	$-0.290594\pi$
$757$	33.6454			1.22286			0.611432	+	0.791297i	$0.290594\pi$
$758$	−10.8878	+	18.8581i	−0.395461	+	0.684959i
$759$		0			0
$760$	−59.6573	−	103.329i	−2.16400	−	3.74815i
$761$	7.03148	+	12.1789i	0.254891	+	0.441484i	0.964866	−	0.262743i	$-0.0846271\pi$
$761$	7.03148	+	12.1789i	0.254891	+	0.441484i	−0.709975	+	0.704227i	$0.751294\pi$
$762$		0			0
$763$	0.669108	−	1.15893i	0.0242233	−	0.0419561i
$764$	74.6883			2.70213
$765$		0			0
$766$	−25.7628			−0.930849
$767$	−3.78907	+	6.56287i	−0.136816	+	0.236971i
$768$		0			0
$769$	1.83464	+	3.17768i	0.0661587	+	0.114590i	0.897207	−	0.441609i	$-0.145592\pi$
$769$	1.83464	+	3.17768i	0.0661587	+	0.114590i	−0.831049	+	0.556200i	$0.812259\pi$
$770$	2.04508	+	3.54218i	0.0736996	+	0.127651i
$771$		0			0
$772$	1.00753	−	1.74510i	0.0362619	−	0.0628075i
$773$	−27.7108			−0.996686			−0.498343	−	0.866980i	$-0.666058\pi$
$773$	−27.7108			−0.996686			−0.498343	+	0.866980i	$0.666058\pi$
$774$		0			0
$775$	−4.80485			−0.172595
$776$	−53.2390	+	92.2126i	−1.91117	+	3.31024i
$777$		0			0
$778$	2.02284	+	3.50367i	0.0725225	+	0.125613i
$779$	−36.8060	−	63.7499i	−1.31871	−	2.28408i
$780$		0			0
$781$	−23.4441	+	40.6064i	−0.838897	+	1.45301i
$782$	8.70205			0.311185
$783$		0			0
$784$	−51.5655			−1.84163
$785$	2.12175	−	3.67497i	0.0757283	−	0.131165i
$786$		0			0
$787$	13.6833	+	23.7002i	0.487757	+	0.844820i	0.999901	−	0.0140795i	$-0.00448178\pi$
$787$	13.6833	+	23.7002i	0.487757	+	0.844820i	−0.512144	+	0.858900i	$0.671148\pi$
$788$	5.17472	+	8.96287i	0.184342	+	0.319289i
$789$		0			0
$790$	29.7672	−	51.5584i	1.05907	−	1.83436i
$791$	0.830975			0.0295461
$792$		0			0
$793$	5.33089			0.189306
$794$	6.85879	−	11.8798i	0.243409	−	0.421597i
$795$		0			0
$796$	8.86885	+	15.3613i	0.314348	+	0.544467i
$797$	19.2017	+	33.2583i	0.680159	+	1.17807i	0.974932	+	0.222503i	$0.0714226\pi$
$797$	19.2017	+	33.2583i	0.680159	+	1.17807i	−0.294773	+	0.955567i	$0.595244\pi$
$798$		0			0
$799$	2.08163	−	3.60548i	0.0736427	−	0.127553i
$800$	17.0332			0.602215
$801$		0			0
$802$	34.4765			1.21741
$803$	2.73365	−	4.73482i	0.0964684	−	0.167088i
$804$		0			0
$805$	1.30294	+	2.25676i	0.0459227	+	0.0795404i
$806$	−2.77742	−	4.81064i	−0.0978306	−	0.169448i
$807$		0			0
$808$	36.0329	−	62.4109i	1.26763	−	2.19561i
$809$	−38.1968			−1.34293			−0.671464	−	0.741037i	$-0.734334\pi$
$809$	−38.1968			−1.34293			−0.671464	+	0.741037i	$0.734334\pi$
$810$		0			0
$811$	−7.50867			−0.263665			−0.131833	−	0.991272i	$-0.542086\pi$
$811$	−7.50867			−0.263665			−0.131833	+	0.991272i	$0.542086\pi$
$812$	3.02211	−	5.23445i	0.106055	−	0.183693i
$813$		0			0
$814$	19.3404	+	33.4985i	0.677879	+	1.17412i
$815$	25.3939	+	43.9835i	0.889510	+	1.54068i
$816$		0			0
$817$	3.31153	−	5.73573i	0.115856	−	0.200668i
$818$	47.8375			1.67260
$819$		0			0
$820$	140.645			4.91152
$821$	3.60607	−	6.24590i	0.125853	−	0.217984i	−0.796213	−	0.605016i	$-0.793167\pi$
$821$	3.60607	−	6.24590i	0.125853	−	0.217984i	0.922066	+	0.387033i	$0.126500\pi$
$822$		0			0
$823$	−1.95071	−	3.37873i	−0.0679975	−	0.117775i	0.830022	−	0.557730i	$-0.188328\pi$
$823$	−1.95071	−	3.37873i	−0.0679975	−	0.117775i	−0.898020	+	0.439955i	$0.854994\pi$
$824$	−46.2814	−	80.1616i	−1.61229	−	2.79256i
$825$		0			0
$826$	−1.15983	+	2.00888i	−0.0403556	+	0.0698980i
$827$	56.2324			1.95539			0.977696	−	0.210023i	$-0.0673540\pi$
$827$	56.2324			1.95539			0.977696	+	0.210023i	$0.0673540\pi$
$828$		0			0
$829$	−21.3784			−0.742502			−0.371251	−	0.928533i	$-0.621071\pi$
$829$	−21.3784			−0.742502			−0.371251	+	0.928533i	$0.621071\pi$
$830$	−24.9384	+	43.1946i	−0.865626	+	1.49931i
$831$		0			0
$832$	0.351461	+	0.608749i	0.0121847	+	0.0211046i
$833$	−1.96644	−	3.40597i	−0.0681330	−	0.118010i
$834$		0			0
$835$	29.4562	−	51.0197i	1.01937	−	1.76561i
$836$	111.244			3.84744
$837$		0			0
$838$	−23.4813			−0.811149
$839$	16.2334	−	28.1171i	0.560439	−	0.970709i	−0.437019	−	0.899452i	$-0.643966\pi$
$839$	16.2334	−	28.1171i	0.560439	−	0.970709i	0.997458	−	0.0712567i	$-0.0227009\pi$
$840$		0			0
$841$	−23.2053	−	40.1928i	−0.800184	−	1.38596i
$842$	6.35444	+	11.0062i	0.218989	+	0.379299i
$843$		0			0
$844$	40.8120	−	70.6885i	1.40481	−	2.43320i
$845$	31.7742			1.09307
$846$		0			0
$847$	−0.432362			−0.0148561
$848$	8.50403	−	14.7294i	0.292030	−	0.505810i
$849$		0			0
$850$	2.04202	+	3.53688i	0.0700406	+	0.121314i
$851$	12.3219	+	21.3422i	0.422391	+	0.731602i
$852$		0			0
$853$	4.38253	−	7.59076i	0.150055	−	0.259903i	−0.781193	−	0.624290i	$-0.785388\pi$
$853$	4.38253	−	7.59076i	0.150055	−	0.259903i	0.931247	+	0.364387i	$0.118722\pi$
$854$	1.63178			0.0558383
$855$		0			0
$856$	66.4857			2.27244
$857$	19.6447	−	34.0256i	0.671049	−	1.16229i	−0.306557	−	0.951852i	$-0.599177\pi$
$857$	19.6447	−	34.0256i	0.671049	−	1.16229i	0.977607	−	0.210440i	$-0.0674895\pi$
$858$		0			0
$859$	18.7541	+	32.4830i	0.639880	+	1.10831i	0.985459	+	0.169915i	$0.0543494\pi$
$859$	18.7541	+	32.4830i	0.639880	+	1.10831i	−0.345578	+	0.938390i	$0.612317\pi$
$860$	6.32706	+	10.9588i	0.215751	+	0.373691i
$861$		0			0
$862$	−3.80046	+	6.58259i	−0.129444	+	0.224204i
$863$	−35.2574			−1.20018			−0.600088	−	0.799934i	$-0.704868\pi$
$863$	−35.2574			−1.20018			−0.600088	+	0.799934i	$0.704868\pi$
$864$		0			0
$865$	43.9680			1.49496
$866$	2.64549	−	4.58213i	0.0898975	−	0.155707i
$867$		0			0
$868$	−0.589385	−	1.02084i	−0.0200050	−	0.0346497i
$869$	15.4737	+	26.8013i	0.524910	+	0.909171i
$870$		0			0
$871$	6.86434	−	11.8894i	0.232589	−	0.402857i
$872$	55.9260			1.89389
$873$		0			0
$874$	102.234			3.45811
$875$	0.466180	−	0.807447i	0.0157598	−	0.0272967i
$876$		0			0
$877$	4.40354	+	7.62715i	0.148697	+	0.257551i	0.930746	−	0.365666i	$-0.119159\pi$
$877$	4.40354	+	7.62715i	0.148697	+	0.257551i	−0.782049	+	0.623217i	$0.785825\pi$
$878$	27.6766	+	47.9372i	0.934039	+	1.61780i
$879$		0			0
$880$	−38.4455	+	66.5896i	−1.29600	+	2.24474i
$881$	22.3061			0.751512			0.375756	−	0.926719i	$-0.377383\pi$
$881$	22.3061			0.751512			0.375756	+	0.926719i	$0.377383\pi$
$882$		0			0
$883$	−12.9751			−0.436648			−0.218324	−	0.975876i	$-0.570059\pi$
$883$	−12.9751			−0.436648			−0.218324	+	0.975876i	$0.570059\pi$
$884$	−1.63662	+	2.83471i	−0.0550454	+	0.0953415i
$885$		0			0
$886$	22.7455	+	39.3964i	0.764151	+	1.32355i
$887$	−18.4547	−	31.9645i	−0.619648	−	1.07326i	−0.989550	−	0.144191i	$-0.953942\pi$
$887$	−18.4547	−	31.9645i	−0.619648	−	1.07326i	0.369902	−	0.929071i	$-0.379391\pi$
$888$		0			0
$889$	0.687871	−	1.19143i	0.0230705	−	0.0399592i
$890$	113.546			3.80609
$891$		0			0
$892$	−37.5997			−1.25893
$893$	24.4555	−	42.3581i	0.818370	−	1.41746i
$894$		0			0
$895$	−21.5341	−	37.2981i	−0.719804	−	1.24674i
$896$	−0.816886	−	1.41489i	−0.0272902	−	0.0472681i
$897$		0			0
$898$	−50.0204	+	86.6379i	−1.66920	+	2.89115i
$899$	−14.7069			−0.490503
$900$		0			0
$901$	1.29719			0.0432158
$902$	−52.7295	+	91.3302i	−1.75570	+	3.04096i
$903$		0			0
$904$	17.3638	+	30.0751i	0.577513	+	1.00028i
$905$	−5.86528	−	10.1590i	−0.194969	−	0.337695i
$906$		0			0
$907$	−23.9021	+	41.3996i	−0.793656	+	1.37465i	0.130033	+	0.991510i	$0.458492\pi$
$907$	−23.9021	+	41.3996i	−0.793656	+	1.37465i	−0.923689	+	0.383143i	$0.874842\pi$
$908$	62.9899			2.09039
$909$		0			0
$910$	−1.41389			−0.0468699
$911$	8.12177	−	14.0673i	0.269086	−	0.466071i	−0.699540	−	0.714594i	$-0.746612\pi$
$911$	8.12177	−	14.0673i	0.269086	−	0.466071i	0.968626	+	0.248523i	$0.0799450\pi$
$912$		0			0
$913$	−12.9636	−	22.4536i	−0.429033	−	0.743106i
$914$	−3.92737	−	6.80241i	−0.129906	−	0.225004i
$915$		0			0
$916$	3.77040	−	6.53053i	0.124578	−	0.215775i
$917$	−1.38695			−0.0458011
$918$		0			0
$919$	−16.1366			−0.532297			−0.266149	−	0.963932i	$-0.585751\pi$
$919$	−16.1366			−0.532297			−0.266149	+	0.963932i	$0.585751\pi$
$920$	−54.4519	+	94.3134i	−1.79522	+	3.10942i
$921$		0			0
$922$	−5.30231	−	9.18387i	−0.174622	−	0.302455i
$923$	−8.10418	−	14.0368i	−0.266752	−	0.462028i
$924$		0			0
$925$	−5.78292	+	10.0163i	−0.190141	+	0.329334i
$926$	18.1123			0.595207
$927$		0			0
$928$	52.1360			1.71145
$929$	7.13260	−	12.3540i	0.234013	−	0.405322i	−0.724972	−	0.688778i	$-0.758148\pi$
$929$	7.13260	−	12.3540i	0.234013	−	0.405322i	0.958985	+	0.283456i	$0.0914808\pi$
$930$		0			0
$931$	−23.1022	−	40.0141i	−0.757143	−	1.31141i
$932$	0.225858	+	0.391198i	0.00739823	+	0.0128141i
$933$		0			0
$934$	−13.6879	+	23.7082i	−0.447882	+	0.775755i
$935$	−5.86444			−0.191788
$936$		0			0
$937$	28.3390			0.925795			0.462897	−	0.886412i	$-0.346810\pi$
$937$	28.3390			0.925795			0.462897	+	0.886412i	$0.346810\pi$
$938$	2.10116	−	3.63932i	0.0686055	−	0.118828i
$939$		0			0
$940$	46.7250	+	80.9301i	1.52400	+	2.63965i
$941$	24.2002	+	41.9160i	0.788904	+	1.36642i	0.926639	+	0.375952i	$0.122684\pi$
$941$	24.2002	+	41.9160i	0.788904	+	1.36642i	−0.137735	+	0.990469i	$0.543982\pi$
$942$		0			0
$943$	−33.5945	+	58.1874i	−1.09399	+	1.89484i
$944$	−43.6074			−1.41930
$945$		0			0
$946$	−9.48839			−0.308494
$947$	−17.3778	+	30.0992i	−0.564703	+	0.978094i	0.432374	+	0.901694i	$0.357676\pi$
$947$	−17.3778	+	30.0992i	−0.564703	+	0.978094i	−0.997077	+	0.0763999i	$0.975657\pi$
$948$		0			0
$949$	0.944969	+	1.63673i	0.0306750	+	0.0531307i
$950$	23.9901	+	41.5521i	0.778342	+	1.34813i
$951$		0			0
$952$	−0.279308	+	0.483775i	−0.00905241	+	0.0156792i
$953$	39.1055			1.26675			0.633375	−	0.773845i	$-0.281669\pi$
$953$	39.1055			1.26675			0.633375	+	0.773845i	$0.281669\pi$
$954$		0			0
$955$	−46.2569			−1.49684
$956$	26.4013	−	45.7285i	0.853880	−	1.47896i
$957$		0			0
$958$	−8.70185	−	15.0720i	−0.281144	−	0.486955i
$959$	1.12461	+	1.94788i	0.0363156	+	0.0629004i
$960$		0			0
$961$	14.0659	−	24.3629i	0.453739	−	0.785898i
$962$	−13.3712			−0.431104
$963$		0			0
$964$	−22.6464			−0.729390
$965$	−0.623998	+	1.08080i	−0.0200872	+	0.0347921i
$966$		0			0
$967$	2.84849	+	4.93373i	0.0916014	+	0.158658i	0.908185	−	0.418569i	$-0.137468\pi$
$967$	2.84849	+	4.93373i	0.0916014	+	0.158658i	−0.816584	+	0.577227i	$0.804135\pi$
$968$	−9.03452	−	15.6482i	−0.290380	−	0.502954i
$969$		0			0
$970$	59.1397	−	102.433i	1.89886	−	3.28892i
$971$	−24.9838			−0.801768			−0.400884	−	0.916129i	$-0.631297\pi$
$971$	−24.9838			−0.801768			−0.400884	+	0.916129i	$0.631297\pi$
$972$		0			0
$973$	1.91678			0.0614493
$974$	22.1355	−	38.3399i	0.709268	−	1.22849i
$975$		0			0
$976$	15.3379	+	26.5661i	0.490955	+	0.850359i
$977$	−6.73626	−	11.6675i	−0.215512	−	0.373278i	0.737919	−	0.674890i	$-0.235809\pi$
$977$	−6.73626	−	11.6675i	−0.215512	−	0.373278i	−0.953431	+	0.301612i	$0.902475\pi$
$978$		0			0
$979$	−29.5121	+	51.1165i	−0.943211	+	1.63369i
$980$	88.2788			2.81996
$981$		0			0
$982$	−40.6060			−1.29579
$983$	−5.61344	+	9.72276i	−0.179041	+	0.310108i	−0.941552	−	0.336867i	$-0.890633\pi$
$983$	−5.61344	+	9.72276i	−0.179041	+	0.310108i	0.762511	+	0.646975i	$0.223966\pi$
$984$		0			0
$985$	−3.20487	−	5.55100i	−0.102116	−	0.176870i
$986$	6.25030	+	10.8258i	0.199050	+	0.344765i
$987$		0			0
$988$	−19.2274	+	33.3028i	−0.611705	+	1.05950i
$989$	−6.04515			−0.192225
$990$		0			0
$991$	−55.8592			−1.77443			−0.887213	−	0.461360i	$-0.847362\pi$
$991$	−55.8592			−1.77443			−0.887213	+	0.461360i	$0.847362\pi$
$992$	5.08390	−	8.80556i	0.161414	−	0.279577i
$993$		0			0
$994$	−2.48068	−	4.29666i	−0.0786823	−	0.136282i
$995$	−5.49276	−	9.51374i	−0.174132	−	0.301606i
$996$		0			0
$997$	26.8633	−	46.5286i	0.850769	−	1.47358i	−0.0297456	−	0.999558i	$-0.509470\pi$
$997$	26.8633	−	46.5286i	0.850769	−	1.47358i	0.880515	−	0.474018i	$-0.157197\pi$
$998$	−11.5543			−0.365745
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1161.2.f.c.775.1		38
3.2	odd	2		387.2.f.c.259.19	yes	38
9.2	odd	6		3483.2.a.s.1.1		19
9.4	even	3	inner	1161.2.f.c.388.1		38
9.5	odd	6		387.2.f.c.130.19	✓	38
9.7	even	3		3483.2.a.r.1.19		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.c.130.19	✓	38	9.5	odd	6
387.2.f.c.259.19	yes	38	3.2	odd	2
1161.2.f.c.388.1		38	9.4	even	3	inner
1161.2.f.c.775.1		38	1.1	even	1	trivial
3483.2.a.r.1.19		19	9.7	even	3
3483.2.a.s.1.1		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)

\(f(q)\)	\(=\)	\(q+(-1.27673 + 2.21136i) q^{2} +(-2.26008 - 3.91458i) q^{4} +(1.39974 + 2.42442i) q^{5} +(0.0769910 - 0.133352i) q^{7} +6.43513 q^{8} +O(q^{10})\)	\(q+(-1.27673 + 2.21136i) q^{2} +(-2.26008 - 3.91458i) q^{4} +(1.39974 + 2.42442i) q^{5} +(0.0769910 - 0.133352i) q^{7} +6.43513 q^{8} -7.14837 q^{10} +(1.85795 - 3.21806i) q^{11} +(0.642256 + 1.11242i) q^{13} +(0.196594 + 0.340510i) q^{14} +(-3.69577 + 6.40126i) q^{16} -0.563748 q^{17} -6.62305 q^{19} +(6.32706 - 10.9588i) q^{20} +(4.74420 + 8.21719i) q^{22} +(3.02258 + 5.23526i) q^{23} +(-1.41855 + 2.45700i) q^{25} -3.27995 q^{26} -0.696024 q^{28} +(-4.34197 + 7.52050i) q^{29} +(0.846788 + 1.46668i) q^{31} +(-3.00187 - 5.19939i) q^{32} +(0.719755 - 1.24665i) q^{34} +0.431070 q^{35} +4.07664 q^{37} +(8.45585 - 14.6460i) q^{38} +(9.00752 + 15.6015i) q^{40} +(5.55726 + 9.62547i) q^{41} +(-0.500000 + 0.866025i) q^{43} -16.7964 q^{44} -15.4361 q^{46} +(-3.69248 + 6.39556i) q^{47} +(3.48814 + 6.04164i) q^{49} +(-3.62222 - 6.27386i) q^{50} +(2.90310 - 5.02832i) q^{52} -2.30102 q^{53} +10.4026 q^{55} +(0.495447 - 0.858140i) q^{56} +(-11.0870 - 19.2033i) q^{58} +(2.94982 + 5.10923i) q^{59} +(2.07507 - 3.59412i) q^{61} -4.32448 q^{62} +0.547229 q^{64} +(-1.79798 + 3.11420i) q^{65} +(-5.34393 - 9.25596i) q^{67} +(1.27412 + 2.20683i) q^{68} +(-0.550360 + 0.953252i) q^{70} -12.6183 q^{71} +1.47133 q^{73} +(-5.20476 + 9.01492i) q^{74} +(14.9686 + 25.9264i) q^{76} +(-0.286090 - 0.495523i) q^{77} +(-4.16420 + 7.21261i) q^{79} -20.6925 q^{80} -28.3805 q^{82} +(3.48869 - 6.04259i) q^{83} +(-0.789102 - 1.36676i) q^{85} +(-1.27673 - 2.21136i) q^{86} +(11.9561 - 20.7086i) q^{88} -15.8842 q^{89} +0.197792 q^{91} +(13.6625 - 23.6642i) q^{92} +(-9.42859 - 16.3308i) q^{94} +(-9.27056 - 16.0571i) q^{95} +(-8.27317 + 14.3296i) q^{97} -17.8137 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 4 q^{2} - 22 q^{4} + 9 q^{5} - 7 q^{7} - 24 q^{8}+O(q^{10}) \) 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

Introduction

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Modular forms

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