LMFDB - Embedded newform 1386.2.bu.b.827.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			827.2
Character	$\chi$	$=$	1386.827
Dual form			1386.2.bu.b.1205.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-3.30760 + 1.07471i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-3.30760 + 1.07471i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} -3.47782i q^{10} +(0.456033 + 3.28512i) q^{11} +(-4.44321 - 1.44369i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.244124 - 0.751336i) q^{17} +(-2.58258 - 3.55461i) q^{19} +(3.30760 + 1.07471i) q^{20} +(-3.26526 - 0.581446i) q^{22} +1.98632i q^{23} +(5.74016 - 4.17047i) q^{25} +(2.74606 - 3.77962i) q^{26} +(0.951057 - 0.309017i) q^{28} +(4.94178 + 3.59041i) q^{29} +(1.57506 - 4.84753i) q^{31} -1.00000 q^{32} +0.790002 q^{34} +(1.07471 - 3.30760i) q^{35} +(1.78842 + 1.29936i) q^{37} +(4.17869 - 1.35774i) q^{38} +(-2.04421 + 2.81361i) q^{40} +(-6.36613 + 4.62526i) q^{41} -3.15321i q^{43} +(1.56201 - 2.92577i) q^{44} +(-1.88910 - 0.613807i) q^{46} +(-2.53157 - 3.48440i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(2.19255 + 6.74796i) q^{50} +(2.74606 + 3.77962i) q^{52} +(-3.63873 - 1.18229i) q^{53} +(-5.03891 - 10.3758i) q^{55} +1.00000i q^{56} +(-4.94178 + 3.59041i) q^{58} +(7.54262 - 10.3815i) q^{59} +(13.9369 - 4.52837i) q^{61} +(4.12356 + 2.99594i) q^{62} +(0.309017 - 0.951057i) q^{64} +16.2479 q^{65} +15.2649 q^{67} +(-0.244124 + 0.751336i) q^{68} +(2.81361 + 2.04421i) q^{70} +(2.32533 - 0.755545i) q^{71} +(5.79892 - 7.98153i) q^{73} +(-1.78842 + 1.29936i) q^{74} +4.39374i q^{76} +(-2.92577 - 1.56201i) q^{77} +(-11.5847 - 3.76411i) q^{79} +(-2.04421 - 2.81361i) q^{80} +(-2.43165 - 7.48383i) q^{82} +(1.07209 + 3.29956i) q^{83} +(1.61493 + 2.22276i) q^{85} +(2.99888 + 0.974395i) q^{86} +(2.29989 + 2.38967i) q^{88} +0.827686i q^{89} +(3.77962 - 2.74606i) q^{91} +(1.16753 - 1.60697i) q^{92} +(4.09616 - 1.33092i) q^{94} +(12.3623 + 8.98173i) q^{95} +(-3.84201 + 11.8245i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−3.30760	+	1.07471i	−1.47920	+	0.480623i	−0.933875	−	0.357599i	$-0.883595\pi$
$5$	−3.30760	+	1.07471i	−1.47920	+	0.480623i	−0.545330	+	0.838222i	$0.683595\pi$
$6$		0			0
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$		0			0
$10$		−	3.47782i		−	1.09978i
$11$	0.456033	+	3.28512i	0.137499	+	0.990502i
$11$	0.456033	+	3.28512i	0.137499	+	0.990502i
$12$		0			0
$13$	−4.44321	−	1.44369i	−1.23233	−	0.400407i	−0.380769	−	0.924670i	$-0.624341\pi$
$13$	−4.44321	−	1.44369i	−1.23233	−	0.400407i	−0.851556	+	0.524263i	$0.824341\pi$
$14$	−0.587785	−	0.809017i	−0.157092	−	0.216219i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.244124	−	0.751336i	−0.0592088	−	0.182226i	0.917078	−	0.398709i	$-0.130541\pi$
$17$	−0.244124	−	0.751336i	−0.0592088	−	0.182226i	−0.976286	+	0.216483i	$0.930541\pi$
$18$		0			0
$19$	−2.58258	−	3.55461i	−0.592483	−	0.815483i	0.402511	−	0.915415i	$-0.368138\pi$
$19$	−2.58258	−	3.55461i	−0.592483	−	0.815483i	−0.994994	+	0.0999318i	$0.968138\pi$
$20$	3.30760	+	1.07471i	0.739602	+	0.240311i
$21$		0			0
$22$	−3.26526	−	0.581446i	−0.696156	−	0.123965i
$23$			1.98632i			0.414177i	0.978322	+	0.207088i	$0.0663988\pi$
$23$			1.98632i			0.414177i	−0.978322	+	0.207088i	$0.933601\pi$
$24$		0			0
$25$	5.74016	−	4.17047i	1.14803	−	0.834094i
$26$	2.74606	−	3.77962i	0.538546	−	0.741245i
$27$		0			0
$28$	0.951057	−	0.309017i	0.179733	−	0.0583987i
$29$	4.94178	+	3.59041i	0.917665	+	0.666723i	0.942942	−	0.332958i	$-0.108047\pi$
$29$	4.94178	+	3.59041i	0.917665	+	0.666723i	−0.0252766	+	0.999680i	$0.508047\pi$
$30$		0			0
$31$	1.57506	−	4.84753i	0.282889	−	0.870643i	−0.704134	−	0.710067i	$-0.748665\pi$
$31$	1.57506	−	4.84753i	0.282889	−	0.870643i	0.987023	−	0.160576i	$-0.0513352\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	0.790002			0.135484
$35$	1.07471	−	3.30760i	0.181658	−	0.559087i
$36$		0			0
$37$	1.78842	+	1.29936i	0.294015	+	0.213614i	0.725007	−	0.688741i	$-0.241836\pi$
$37$	1.78842	+	1.29936i	0.294015	+	0.213614i	−0.430992	+	0.902356i	$0.641836\pi$
$38$	4.17869	−	1.35774i	0.677874	−	0.220255i
$39$		0			0
$40$	−2.04421	+	2.81361i	−0.323218	+	0.444872i
$41$	−6.36613	+	4.62526i	−0.994222	+	0.722345i	−0.960842	−	0.277098i	$-0.910627\pi$
$41$	−6.36613	+	4.62526i	−0.994222	+	0.722345i	−0.0333808	+	0.999443i	$0.510627\pi$
$42$		0			0
$43$		−	3.15321i		−	0.480860i	−0.970667	−	0.240430i	$-0.922712\pi$
$43$		−	3.15321i		−	0.480860i	0.970667	−	0.240430i	$-0.0772884\pi$
$44$	1.56201	−	2.92577i	0.235482	−	0.441076i
$45$		0			0
$46$	−1.88910	−	0.613807i	−0.278533	−	0.0905009i
$47$	−2.53157	−	3.48440i	−0.369267	−	0.508252i	0.583434	−	0.812160i	$-0.301709\pi$
$47$	−2.53157	−	3.48440i	−0.369267	−	0.508252i	−0.952701	+	0.303908i	$0.901709\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$	2.19255	+	6.74796i	0.310073	+	0.954306i
$51$		0			0
$52$	2.74606	+	3.77962i	0.380809	+	0.524139i
$53$	−3.63873	−	1.18229i	−0.499818	−	0.162401i	0.0482490	−	0.998835i	$-0.484636\pi$
$53$	−3.63873	−	1.18229i	−0.499818	−	0.162401i	−0.548066	+	0.836435i	$0.684636\pi$
$54$		0			0
$55$	−5.03891	−	10.3758i	−0.679447	−	1.39907i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−4.94178	+	3.59041i	−0.648887	+	0.471444i
$59$	7.54262	−	10.3815i	0.981965	−	1.35156i	0.0462016	−	0.998932i	$-0.485288\pi$
$59$	7.54262	−	10.3815i	0.981965	−	1.35156i	0.935764	−	0.352627i	$-0.114712\pi$
$60$		0			0
$61$	13.9369	−	4.52837i	1.78444	−	0.579798i	0.785213	−	0.619226i	$-0.212553\pi$
$61$	13.9369	−	4.52837i	1.78444	−	0.579798i	0.999222	+	0.0394275i	$0.0125534\pi$
$62$	4.12356	+	2.99594i	0.523693	+	0.380485i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	16.2479			2.01531
$66$		0			0
$67$	15.2649			1.86490			0.932450	−	0.361299i	$-0.117667\pi$
$67$	15.2649			1.86490			0.932450	+	0.361299i	$0.117667\pi$
$68$	−0.244124	+	0.751336i	−0.0296044	+	0.0911129i
$69$		0			0
$70$	2.81361	+	2.04421i	0.336291	+	0.244330i
$71$	2.32533	−	0.755545i	0.275966	−	0.0896667i	−0.167765	−	0.985827i	$-0.553655\pi$
$71$	2.32533	−	0.755545i	0.275966	−	0.0896667i	0.443730	+	0.896160i	$0.353655\pi$
$72$		0			0
$73$	5.79892	−	7.98153i	0.678712	−	0.934167i	−0.321206	−	0.947009i	$-0.604088\pi$
$73$	5.79892	−	7.98153i	0.678712	−	0.934167i	0.999918	+	0.0128426i	$0.00408805\pi$
$74$	−1.78842	+	1.29936i	−0.207900	+	0.151048i
$75$		0			0
$76$			4.39374i			0.503996i
$77$	−2.92577	−	1.56201i	−0.333422	−	0.178007i
$78$		0			0
$79$	−11.5847	−	3.76411i	−1.30338	−	0.423495i	−0.426626	−	0.904428i	$-0.640298\pi$
$79$	−11.5847	−	3.76411i	−1.30338	−	0.423495i	−0.876757	+	0.480933i	$0.840298\pi$
$80$	−2.04421	−	2.81361i	−0.228550	−	0.314572i
$81$		0			0
$82$	−2.43165	−	7.48383i	−0.268530	−	0.826451i
$83$	1.07209	+	3.29956i	0.117678	+	0.362174i	0.992496	−	0.122277i	$-0.0390195\pi$
$83$	1.07209	+	3.29956i	0.117678	+	0.362174i	−0.874819	+	0.484451i	$0.839019\pi$
$84$		0			0
$85$	1.61493	+	2.22276i	0.175164	+	0.241092i
$86$	2.99888	+	0.974395i	0.323377	+	0.105072i
$87$		0			0
$88$	2.29989	+	2.38967i	0.245169	+	0.254740i
$89$			0.827686i			0.0877345i	0.999037	+	0.0438673i	$0.0139679\pi$
$89$			0.827686i			0.0877345i	−0.999037	+	0.0438673i	$0.986032\pi$
$90$		0			0
$91$	3.77962	−	2.74606i	0.396212	−	0.287865i
$92$	1.16753	−	1.60697i	0.121723	−	0.167538i
$93$		0			0
$94$	4.09616	−	1.33092i	0.422487	−	0.137274i
$95$	12.3623	+	8.98173i	1.26834	+	0.921506i
$96$		0			0
$97$	−3.84201	+	11.8245i	−0.390097	+	1.20059i	0.542618	+	0.839979i	$0.317433\pi$
$97$	−3.84201	+	11.8245i	−0.390097	+	1.20059i	−0.932715	+	0.360615i	$0.882567\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	−7.09523			−0.709523
$101$	3.31684	−	10.2082i	0.330038	−	1.01575i	−0.639077	−	0.769143i	$-0.720684\pi$
$101$	3.31684	−	10.2082i	0.330038	−	1.01575i	0.969115	−	0.246609i	$-0.0793164\pi$
$102$		0			0
$103$	−3.63119	−	2.63821i	−0.357792	−	0.259951i	0.394339	−	0.918965i	$-0.370974\pi$
$103$	−3.63119	−	2.63821i	−0.357792	−	0.259951i	−0.752131	+	0.659014i	$0.770974\pi$
$104$	−4.44321	+	1.44369i	−0.435693	+	0.141565i
$105$		0			0
$106$	2.24886	−	3.09529i	0.218428	−	0.300641i
$107$	7.06789	−	5.13513i	0.683279	−	0.496431i	−0.191165	−	0.981558i	$-0.561226\pi$
$107$	7.06789	−	5.13513i	0.683279	−	0.496431i	0.874444	+	0.485127i	$0.161226\pi$
$108$		0			0
$109$		−	2.70911i		−	0.259486i	−0.991548	−	0.129743i	$-0.958585\pi$
$109$		−	2.70911i		−	0.259486i	0.991548	−	0.129743i	$-0.0414152\pi$
$110$	11.4251	−	1.58600i	1.08934	−	0.151219i
$111$		0			0
$112$	−0.951057	−	0.309017i	−0.0898664	−	0.0291994i
$113$	−8.60850	−	11.8486i	−0.809819	−	1.11462i	−0.991351	−	0.131235i	$-0.958106\pi$
$113$	−8.60850	−	11.8486i	−0.809819	−	1.11462i	0.181532	−	0.983385i	$-0.441894\pi$
$114$		0			0
$115$	−2.13471	−	6.56996i	−0.199063	−	0.612652i
$116$	−1.88759	−	5.80941i	−0.175258	−	0.539390i
$117$		0			0
$118$	7.54262	+	10.3815i	0.694354	+	0.955697i
$119$	0.751336	+	0.244124i	0.0688749	+	0.0223788i
$120$		0			0
$121$	−10.5841	+	2.99625i	−0.962188	+	0.272386i
$122$			14.6541i			1.32672i
$123$		0			0
$124$	−4.12356	+	2.99594i	−0.370307	+	0.269043i
$125$	−4.28308	+	5.89516i	−0.383091	+	0.527279i
$126$		0			0
$127$	−15.8460	+	5.14868i	−1.40611	+	0.456872i	−0.911160	−	0.412052i	$-0.864812\pi$
$127$	−15.8460	+	5.14868i	−1.40611	+	0.456872i	−0.494946	+	0.868924i	$0.664812\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	−5.02088	+	15.4527i	−0.440361	+	1.35529i
$131$	11.9396			1.04317			0.521584	−	0.853200i	$-0.325341\pi$
$131$	11.9396			1.04317			0.521584	+	0.853200i	$0.325341\pi$
$132$		0			0
$133$	4.39374			0.380986
$134$	−4.71710	+	14.5177i	−0.407496	+	1.25414i
$135$		0			0
$136$	−0.639125	−	0.464351i	−0.0548045	−	0.0398178i
$137$	−8.83368	+	2.87024i	−0.754712	+	0.245221i	−0.661008	−	0.750379i	$-0.729871\pi$
$137$	−8.83368	+	2.87024i	−0.754712	+	0.245221i	−0.0937046	+	0.995600i	$0.529871\pi$
$138$		0			0
$139$	5.42635	−	7.46874i	0.460257	−	0.633490i	−0.514305	−	0.857608i	$-0.671950\pi$
$139$	5.42635	−	7.46874i	0.460257	−	0.633490i	0.974562	+	0.224118i	$0.0719500\pi$
$140$	−2.81361	+	2.04421i	−0.237794	+	0.172767i
$141$		0			0
$142$			2.44499i			0.205179i
$143$	2.71644	−	15.2549i	0.227160	−	1.27568i
$144$		0			0
$145$	−20.2041	−	6.56470i	−1.67786	−	0.545169i
$146$	5.79892	+	7.98153i	0.479922	+	0.660556i
$147$		0			0
$148$	−0.683116	−	2.10242i	−0.0561518	−	0.172818i
$149$	−4.37528	−	13.4657i	−0.358437	−	1.10316i	−0.953990	−	0.299840i	$-0.903067\pi$
$149$	−4.37528	−	13.4657i	−0.358437	−	1.10316i	0.595552	−	0.803317i	$-0.296933\pi$
$150$		0			0
$151$	−1.00167	−	1.37868i	−0.0815147	−	0.112195i	0.766312	−	0.642468i	$-0.222090\pi$
$151$	−1.00167	−	1.37868i	−0.0815147	−	0.112195i	−0.847827	+	0.530273i	$0.822090\pi$
$152$	−4.17869	−	1.35774i	−0.338937	−	0.110127i
$153$		0			0
$154$	2.38967	−	2.29989i	0.192565	−	0.185330i
$155$			17.7264i			1.42382i
$156$		0			0
$157$	9.33047	−	6.77898i	0.744653	−	0.541022i	−0.149512	−	0.988760i	$-0.547770\pi$
$157$	9.33047	−	6.77898i	0.744653	−	0.541022i	0.894165	+	0.447738i	$0.147770\pi$
$158$	7.15976	−	9.85456i	0.569600	−	0.783987i
$159$		0			0
$160$	3.30760	−	1.07471i	0.261489	−	0.0849629i
$161$	−1.60697	−	1.16753i	−0.126647	−	0.0920143i
$162$		0			0
$163$	−3.47934	+	10.7083i	−0.272523	+	0.838739i	0.717342	+	0.696722i	$0.245359\pi$
$163$	−3.47934	+	10.7083i	−0.272523	+	0.838739i	−0.989864	+	0.142017i	$0.954641\pi$
$164$	7.86897			0.614463
$165$		0			0
$166$	−3.46937			−0.269275
$167$	−3.91731	+	12.0562i	−0.303131	+	0.932940i	0.677238	+	0.735764i	$0.263177\pi$
$167$	−3.91731	+	12.0562i	−0.303131	+	0.932940i	−0.980368	+	0.197176i	$0.936823\pi$
$168$		0			0
$169$	7.14068	+	5.18801i	0.549283	+	0.399078i
$170$	−2.61301	+	0.849019i	−0.200409	+	0.0651168i
$171$		0			0
$172$	−1.85341	+	2.55100i	−0.141321	+	0.194512i
$173$	−14.3700	+	10.4404i	−1.09253	+	0.793772i	−0.979825	−	0.199856i	$-0.935953\pi$
$173$	−14.3700	+	10.4404i	−1.09253	+	0.793772i	−0.112709	+	0.993628i	$0.535953\pi$
$174$		0			0
$175$			7.09523i			0.536349i
$176$	−2.98342	+	1.44887i	−0.224883	+	0.109213i
$177$		0			0
$178$	−0.787176	−	0.255769i	−0.0590014	−	0.0191707i
$179$	−4.46415	−	6.14438i	−0.333666	−	0.459252i	0.608912	−	0.793238i	$-0.291606\pi$
$179$	−4.46415	−	6.14438i	−0.333666	−	0.459252i	−0.942578	+	0.333986i	$0.891606\pi$
$180$		0			0
$181$	2.71132	+	8.34458i	0.201531	+	0.620248i	0.999838	+	0.0179975i	$0.00572910\pi$
$181$	2.71132	+	8.34458i	0.201531	+	0.620248i	−0.798307	+	0.602250i	$0.794271\pi$
$182$	1.44369	+	4.44321i	0.107013	+	0.329353i
$183$		0			0
$184$	1.16753	+	1.60697i	0.0860715	+	0.118467i
$185$	−7.31182	−	2.37575i	−0.537576	−	0.174669i
$186$		0			0
$187$	2.35690	−	1.14461i	0.172354	−	0.0837023i
$188$			4.30696i			0.314117i
$189$		0			0
$190$	−12.3623	+	8.98173i	−0.896855	+	0.651603i
$191$	−9.04235	+	12.4457i	−0.654281	+	0.900541i	−0.999275	−	0.0380639i	$-0.987881\pi$
$191$	−9.04235	+	12.4457i	−0.654281	+	0.900541i	0.344994	+	0.938605i	$0.387881\pi$
$192$		0			0
$193$	13.8113	−	4.48757i	0.994161	−	0.323022i	0.233631	−	0.972325i	$-0.424939\pi$
$193$	13.8113	−	4.48757i	0.994161	−	0.323022i	0.760530	+	0.649303i	$0.224939\pi$
$194$	−10.0585	−	7.30793i	−0.722159	−	0.524679i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	−18.7009			−1.33238			−0.666192	−	0.745780i	$-0.732077\pi$
$197$	−18.7009			−1.33238			−0.666192	+	0.745780i	$0.732077\pi$
$198$		0			0
$199$	−17.8239			−1.26350			−0.631752	−	0.775170i	$-0.717664\pi$
$199$	−17.8239			−1.26350			−0.631752	+	0.775170i	$0.717664\pi$
$200$	2.19255	−	6.74796i	0.155036	−	0.477153i
$201$		0			0
$202$	8.68360	+	6.30900i	0.610976	+	0.443900i
$203$	−5.80941	+	1.88759i	−0.407741	+	0.132483i
$204$		0			0
$205$	16.0858	−	22.1402i	1.12348	−	1.54634i
$206$	3.63119	−	2.63821i	0.252997	−	0.183813i
$207$		0			0
$208$		−	4.67187i		−	0.323936i
$209$	10.4996	−	10.1051i	0.726272	−	0.698984i
$210$		0			0
$211$	12.5069	+	4.06375i	0.861012	+	0.279760i	0.706051	−	0.708161i	$-0.250475\pi$
$211$	12.5069	+	4.06375i	0.861012	+	0.279760i	0.154961	+	0.987921i	$0.450475\pi$
$212$	2.24886	+	3.09529i	0.154452	+	0.212585i
$213$		0			0
$214$	2.69970	+	8.30881i	0.184547	+	0.567978i
$215$	3.38877	+	10.4296i	0.231112	+	0.711290i
$216$		0			0
$217$	2.99594	+	4.12356i	0.203378	+	0.279925i
$218$	2.57652	+	0.837162i	0.174504	+	0.0566997i
$219$		0			0
$220$	−2.02216	+	11.3560i	−0.136334	+	0.765620i
$221$			3.69079i			0.248269i
$222$		0			0
$223$	2.47425	−	1.79765i	0.165688	−	0.120379i	−0.501851	−	0.864954i	$-0.667348\pi$
$223$	2.47425	−	1.79765i	0.165688	−	0.120379i	0.667539	+	0.744575i	$0.267348\pi$
$224$	0.587785	−	0.809017i	0.0392731	−	0.0540547i
$225$		0			0
$226$	13.9288	−	4.52575i	0.926533	−	0.301049i
$227$	−1.12156	−	0.814863i	−0.0744408	−	0.0540844i	0.549942	−	0.835203i	$-0.314650\pi$
$227$	−1.12156	−	0.814863i	−0.0744408	−	0.0540844i	−0.624383	+	0.781118i	$0.714650\pi$
$228$		0			0
$229$	2.83979	−	8.73996i	0.187658	−	0.577553i	−0.812326	−	0.583204i	$-0.801799\pi$
$229$	2.83979	−	8.73996i	0.187658	−	0.577553i	0.999984	+	0.00565101i	$0.00179878\pi$
$230$	6.90807			0.455505
$231$		0			0
$232$	6.10837			0.401034
$233$	6.98068	−	21.4843i	0.457319	−	1.40748i	−0.411071	−	0.911603i	$-0.634845\pi$
$233$	6.98068	−	21.4843i	0.457319	−	1.40748i	0.868391	−	0.495881i	$-0.165155\pi$
$234$		0			0
$235$	12.1181	+	8.80433i	0.790499	+	0.574331i
$236$	−12.2042	+	3.96539i	−0.794427	+	0.258125i
$237$		0			0
$238$	−0.464351	+	0.639125i	−0.0300994	+	0.0414283i
$239$	−14.7306	+	10.7024i	−0.952846	+	0.692283i	−0.951478	−	0.307716i	$-0.900435\pi$
$239$	−14.7306	+	10.7024i	−0.952846	+	0.692283i	−0.00136744	+	0.999999i	$0.500435\pi$
$240$		0			0
$241$			25.8385i			1.66441i	0.554471	+	0.832203i	$0.312921\pi$
$241$			25.8385i			1.66441i	−0.554471	+	0.832203i	$0.687079\pi$
$242$	0.421054	−	10.9919i	0.0270664	−	0.706589i
$243$		0			0
$244$	−13.9369	−	4.52837i	−0.892218	−	0.289899i
$245$	2.04421	+	2.81361i	0.130600	+	0.179755i
$246$		0			0
$247$	6.34319	+	19.5223i	0.403607	+	1.24218i
$248$	−1.57506	−	4.84753i	−0.100016	−	0.307819i
$249$		0			0
$250$	−4.28308	−	5.89516i	−0.270886	−	0.372843i
$251$	4.55106	+	1.47873i	0.287260	+	0.0933364i	0.449103	−	0.893480i	$-0.351744\pi$
$251$	4.55106	+	1.47873i	0.287260	+	0.0933364i	−0.161843	+	0.986817i	$0.551744\pi$
$252$		0			0
$253$	−6.52531	+	0.905828i	−0.410243	+	0.0569489i
$254$		−	16.6615i		−	1.04543i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.22971	−	1.69255i	0.0767072	−	0.105578i	−0.768939	−	0.639322i	$-0.779215\pi$
$257$	1.22971	−	1.69255i	0.0767072	−	0.105578i	0.845646	+	0.533743i	$0.179215\pi$
$258$		0			0
$259$	−2.10242	+	0.683116i	−0.130638	+	0.0424468i
$260$	−13.1448	−	9.55029i	−0.815209	−	0.592284i
$261$		0			0
$262$	−3.68954	+	11.3552i	−0.227941	+	0.701529i
$263$	−0.400405			−0.0246901			−0.0123450	−	0.999924i	$-0.503930\pi$
$263$	−0.400405			−0.0246901			−0.0123450	+	0.999924i	$0.503930\pi$
$264$		0			0
$265$	13.3061			0.817386
$266$	−1.35774	+	4.17869i	−0.0832484	+	0.256212i
$267$		0			0
$268$	−12.3495	−	8.97246i	−0.754368	−	0.548080i
$269$	20.8356	−	6.76991i	1.27037	−	0.412769i	0.405192	−	0.914231i	$-0.367205\pi$
$269$	20.8356	−	6.76991i	1.27037	−	0.412769i	0.865179	+	0.501463i	$0.167205\pi$
$270$		0			0
$271$	−12.6144	+	17.3622i	−0.766270	+	1.05468i	0.230396	+	0.973097i	$0.425998\pi$
$271$	−12.6144	+	17.3622i	−0.766270	+	1.05468i	−0.996667	+	0.0815835i	$0.974002\pi$
$272$	0.639125	−	0.464351i	0.0387526	−	0.0281554i
$273$		0			0
$274$		−	9.28828i		−	0.561126i
$275$	16.3182	+	16.9553i	0.984025	+	1.02244i
$276$		0			0
$277$	9.63016	+	3.12903i	0.578620	+	0.188005i	0.583682	−	0.811982i	$-0.301611\pi$
$277$	9.63016	+	3.12903i	0.578620	+	0.188005i	−0.00506223	+	0.999987i	$0.501611\pi$
$278$	5.42635	+	7.46874i	0.325451	+	0.447945i
$279$		0			0
$280$	−1.07471	−	3.30760i	−0.0642259	−	0.197667i
$281$	−8.85066	−	27.2395i	−0.527986	−	1.62497i	−0.758334	−	0.651866i	$-0.773986\pi$
$281$	−8.85066	−	27.2395i	−0.527986	−	1.62497i	0.230348	−	0.973108i	$-0.426014\pi$
$282$		0			0
$283$	−18.7099	−	25.7520i	−1.11219	−	1.53080i	−0.818152	−	0.575002i	$-0.805001\pi$
$283$	−18.7099	−	25.7520i	−1.11219	−	1.53080i	−0.294037	−	0.955794i	$-0.594999\pi$
$284$	−2.32533	−	0.755545i	−0.137983	−	0.0448333i
$285$		0			0
$286$	13.6688	+	7.29750i	0.808254	+	0.431510i
$287$		−	7.86897i		−	0.464491i
$288$		0			0
$289$	13.2484	−	9.62551i	0.779316	−	0.566207i
$290$	12.4868	−	17.1866i	0.733250	−	1.00923i
$291$		0			0
$292$	−9.38285	+	3.04867i	−0.549089	+	0.178410i
$293$	−20.9906	−	15.2505i	−1.22628	−	0.890946i	−0.229676	−	0.973267i	$-0.573767\pi$
$293$	−20.9906	−	15.2505i	−1.22628	−	0.890946i	−0.996606	+	0.0823212i	$0.973767\pi$
$294$		0			0
$295$	−13.7909	+	42.4441i	−0.802938	+	2.47119i
$296$	2.21061			0.128489
$297$		0			0
$298$	14.1587			0.820192
$299$	2.86763	−	8.82565i	0.165839	−	0.510400i
$300$		0			0
$301$	2.55100	+	1.85341i	0.147037	+	0.106829i
$302$	1.62073	−	0.526609i	0.0932628	−	0.0303029i
$303$		0			0
$304$	2.58258	−	3.55461i	0.148121	−	0.203871i
$305$	−41.2310	+	29.9561i	−2.36088	+	1.71528i
$306$		0			0
$307$		−	1.08986i		−	0.0622015i	−0.999516	−	0.0311008i	$-0.990099\pi$
$307$		−	1.08986i		−	0.0622015i	0.999516	−	0.0311008i	$-0.00990128\pi$
$308$	1.44887	+	2.98342i	0.0825571	+	0.169996i
$309$		0			0
$310$	−16.8588	−	5.47777i	−0.957518	−	0.311117i
$311$	−17.1278	−	23.5744i	−0.971227	−	1.33678i	−0.941425	−	0.337224i	$-0.890512\pi$
$311$	−17.1278	−	23.5744i	−0.971227	−	1.33678i	−0.0298027	−	0.999556i	$-0.509488\pi$
$312$		0			0
$313$	−1.92611	−	5.92797i	−0.108870	−	0.335069i	0.881749	−	0.471719i	$-0.156366\pi$
$313$	−1.92611	−	5.92797i	−0.108870	−	0.335069i	−0.990619	+	0.136650i	$0.956366\pi$
$314$	3.56392	+	10.9686i	0.201124	+	0.618995i
$315$		0			0
$316$	7.15976	+	9.85456i	0.402768	+	0.554362i
$317$	−10.4518	−	3.39601i	−0.587033	−	0.190739i	0.000415655	−	1.00000i	$-0.499868\pi$
$317$	−10.4518	−	3.39601i	−0.587033	−	0.190739i	−0.587449	+	0.809261i	$0.699868\pi$
$318$		0			0
$319$	−9.54133	+	17.8717i	−0.534212	+	1.00062i
$320$			3.47782i			0.194416i
$321$		0			0
$322$	1.60697	−	1.16753i	0.0895528	−	0.0650639i
$323$	−2.04024	+	2.80815i	−0.113522	+	0.156250i
$324$		0			0
$325$	−31.5256	+	10.2433i	−1.74873	+	0.568195i
$326$	−9.10902	−	6.61809i	−0.504502	−	0.366542i
$327$		0			0
$328$	−2.43165	+	7.48383i	−0.134265	+	0.413226i
$329$	4.30696			0.237450
$330$		0			0
$331$	30.2721			1.66390			0.831951	−	0.554849i	$-0.187224\pi$
$331$	30.2721			1.66390			0.831951	+	0.554849i	$0.187224\pi$
$332$	1.07209	−	3.29956i	0.0588388	−	0.181087i
$333$		0			0
$334$	−10.2556	−	7.45117i	−0.561164	−	0.407710i
$335$	−50.4901	+	16.4052i	−2.75857	+	0.896313i
$336$		0			0
$337$	17.2826	−	23.7874i	0.941443	−	1.29578i	−0.0137824	−	0.999905i	$-0.504387\pi$
$337$	17.2826	−	23.7874i	0.941443	−	1.29578i	0.955225	−	0.295880i	$-0.0956128\pi$
$338$	−7.14068	+	5.18801i	−0.388402	+	0.282191i
$339$		0			0
$340$		−	2.74748i		−	0.149003i
$341$	16.6430	+	2.96363i	0.901270	+	0.160489i
$342$		0			0
$343$	0.951057	+	0.309017i	0.0513522	+	0.0166853i
$344$	−1.85341	−	2.55100i	−0.0999291	−	0.137541i
$345$		0			0
$346$	−5.48887	−	16.8930i	−0.295083	−	0.908173i
$347$	0.0723834	+	0.222773i	0.00388575	+	0.0119591i	0.952981	−	0.303031i	$-0.0979987\pi$
$347$	0.0723834	+	0.222773i	0.00388575	+	0.0119591i	−0.949095	+	0.314990i	$0.897999\pi$
$348$		0			0
$349$	−7.82456	−	10.7696i	−0.418839	−	0.576483i	0.546507	−	0.837454i	$-0.315957\pi$
$349$	−7.82456	−	10.7696i	−0.418839	−	0.576483i	−0.965346	+	0.260972i	$0.915957\pi$
$350$	−6.74796	−	2.19255i	−0.360694	−	0.117196i
$351$		0			0
$352$	−0.456033	−	3.28512i	−0.0243066	−	0.175098i
$353$			9.69068i			0.515783i	0.966174	+	0.257891i	$0.0830276\pi$
$353$			9.69068i			0.515783i	−0.966174	+	0.257891i	$0.916972\pi$
$354$		0			0
$355$	−6.87927	+	4.99808i	−0.365114	+	0.265271i
$356$	0.486502	−	0.669612i	0.0257845	−	0.0354894i
$357$		0			0
$358$	7.22315	−	2.34694i	0.381755	−	0.124040i
$359$	−21.8191	−	15.8525i	−1.15157	−	0.836664i	−0.162881	−	0.986646i	$-0.552079\pi$
$359$	−21.8191	−	15.8525i	−1.15157	−	0.836664i	−0.988689	+	0.149982i	$0.952079\pi$
$360$		0			0
$361$	−0.0942337	+	0.290022i	−0.00495967	+	0.0152643i
$362$	−8.77401			−0.461152
$363$		0			0
$364$	−4.67187			−0.244873
$365$	−10.6027	+	32.6318i	−0.554972	+	1.70803i
$366$		0			0
$367$	−3.28812	−	2.38896i	−0.171638	−	0.124703i	0.498650	−	0.866804i	$-0.333829\pi$
$367$	−3.28812	−	2.38896i	−0.171638	−	0.124703i	−0.670288	+	0.742101i	$0.733829\pi$
$368$	−1.88910	+	0.613807i	−0.0984764	+	0.0319969i
$369$		0			0
$370$	4.51895	−	6.21981i	0.234929	−	0.323352i
$371$	3.09529	−	2.24886i	0.160699	−	0.116755i
$372$		0			0
$373$			9.87452i			0.511283i	0.966772	+	0.255642i	$0.0822867\pi$
$373$			9.87452i			0.511283i	−0.966772	+	0.255642i	$0.917713\pi$
$374$	0.360267	+	2.59525i	0.0186290	+	0.134197i
$375$		0			0
$376$	−4.09616	−	1.33092i	−0.211243	−	0.0686371i
$377$	−16.7739	−	23.0873i	−0.863902	−	1.18906i
$378$		0			0
$379$	−10.5753	−	32.5474i	−0.543217	−	1.67185i	−0.725193	−	0.688546i	$-0.758249\pi$
$379$	−10.5753	−	32.5474i	−0.543217	−	1.67185i	0.181976	−	0.983303i	$-0.441751\pi$
$380$	−4.72197	−	14.5327i	−0.242232	−	0.745514i
$381$		0			0
$382$	−9.04235	−	12.4457i	−0.462647	−	0.636779i
$383$	8.65561	+	2.81238i	0.442281	+	0.143706i	0.521688	−	0.853137i	$-0.325303\pi$
$383$	8.65561	+	2.81238i	0.442281	+	0.143706i	−0.0794069	+	0.996842i	$0.525303\pi$
$384$		0			0
$385$	11.3560	+	2.02216i	0.578754	+	0.103059i
$386$			14.5221i			0.739155i
$387$		0			0
$388$	10.0585	−	7.30793i	0.510643	−	0.371004i
$389$	−15.7371	+	21.6602i	−0.797901	+	1.09822i	0.195178	+	0.980768i	$0.437472\pi$
$389$	−15.7371	+	21.6602i	−0.797901	+	1.09822i	−0.993079	+	0.117449i	$0.962528\pi$
$390$		0			0
$391$	1.49240	−	0.484909i	0.0754737	−	0.0245229i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$		0			0
$394$	5.77890	−	17.7856i	0.291137	−	0.896026i
$395$	42.3630			2.13151
$396$		0			0
$397$	−8.34394			−0.418770			−0.209385	−	0.977833i	$-0.567146\pi$
$397$	−8.34394			−0.418770			−0.209385	+	0.977833i	$0.567146\pi$
$398$	5.50790	−	16.9516i	0.276086	−	0.849705i
$399$		0			0
$400$	5.74016	+	4.17047i	0.287008	+	0.208523i
$401$	30.8305	−	10.0174i	1.53960	−	0.500246i	0.588334	−	0.808618i	$-0.299784\pi$
$401$	30.8305	−	10.0174i	1.53960	−	0.500246i	0.951266	+	0.308372i	$0.0997840\pi$
$402$		0			0
$403$	−13.9966	+	19.2647i	−0.697223	+	0.959645i
$404$	−8.68360	+	6.30900i	−0.432025	+	0.313885i
$405$		0			0
$406$		−	6.10837i		−	0.303153i
$407$	−3.45299	+	6.46774i	−0.171158	+	0.320594i
$408$		0			0
$409$	−8.80452	−	2.86076i	−0.435356	−	0.141456i	0.0831363	−	0.996538i	$-0.473506\pi$
$409$	−8.80452	−	2.86076i	−0.435356	−	0.141456i	−0.518492	+	0.855083i	$0.673506\pi$
$410$	16.0858	+	22.1402i	0.794423	+	1.09343i
$411$		0			0
$412$	1.38699	+	4.26872i	0.0683322	+	0.210305i
$413$	3.96539	+	12.2042i	0.195124	+	0.600530i
$414$		0			0
$415$	−7.09212	−	9.76146i	−0.348138	−	0.479171i
$416$	4.44321	+	1.44369i	0.217846	+	0.0707826i
$417$		0			0
$418$	6.36597	+	13.1084i	0.311370	+	0.641150i
$419$			17.8231i			0.870717i	0.900257	+	0.435359i	$0.143378\pi$
$419$			17.8231i			0.870717i	−0.900257	+	0.435359i	$0.856622\pi$
$420$		0			0
$421$	12.3385	−	8.96445i	0.601342	−	0.436900i	−0.245013	−	0.969520i	$-0.578792\pi$
$421$	12.3385	−	8.96445i	0.601342	−	0.436900i	0.846355	+	0.532619i	$0.178792\pi$
$422$	−7.72970	+	10.6390i	−0.376276	+	0.517900i
$423$		0			0
$424$	−3.63873	+	1.18229i	−0.176712	+	0.0574173i
$425$	−4.53473	−	3.29468i	−0.219967	−	0.159815i
$426$		0			0
$427$	−4.52837	+	13.9369i	−0.219143	+	0.674453i
$428$	−8.73640			−0.422290
$429$		0			0
$430$	−10.9663			−0.528841
$431$	−6.63542	+	20.4217i	−0.319617	+	0.983679i	0.654195	+	0.756326i	$0.273007\pi$
$431$	−6.63542	+	20.4217i	−0.319617	+	0.983679i	−0.973812	+	0.227354i	$0.926993\pi$
$432$		0			0
$433$	−27.8020	−	20.1994i	−1.33608	−	0.970719i	−0.999578	−	0.0290363i	$-0.990756\pi$
$433$	−27.8020	−	20.1994i	−1.33608	−	0.970719i	−0.336502	−	0.941683i	$-0.609244\pi$
$434$	−4.84753	+	1.57506i	−0.232689	+	0.0756053i
$435$		0			0
$436$	−1.59238	+	2.19172i	−0.0762610	+	0.104964i
$437$	7.06060	−	5.12983i	0.337754	−	0.245393i
$438$		0			0
$439$			10.6319i			0.507431i	0.967279	+	0.253716i	$0.0816527\pi$
$439$			10.6319i			0.507431i	−0.967279	+	0.253716i	$0.918347\pi$
$440$	−10.1753	−	5.43238i	−0.485088	−	0.258979i
$441$		0			0
$442$	−3.51015	−	1.14052i	−0.166961	−	0.0542488i
$443$	−9.92579	−	13.6617i	−0.471589	−	0.649086i	0.505273	−	0.862960i	$-0.331392\pi$
$443$	−9.92579	−	13.6617i	−0.471589	−	0.649086i	−0.976861	+	0.213874i	$0.931392\pi$
$444$		0			0
$445$	−0.889519	−	2.73766i	−0.0421672	−	0.129777i
$446$	0.945078	+	2.90865i	0.0447508	+	0.137729i
$447$		0			0
$448$	0.587785	+	0.809017i	0.0277702	+	0.0382225i
$449$	33.6588	+	10.9364i	1.58846	+	0.516120i	0.964217	−	0.265114i	$-0.0854095\pi$
$449$	33.6588	+	10.9364i	1.58846	+	0.516120i	0.624238	+	0.781234i	$0.285410\pi$
$450$		0			0
$451$	−18.0977	−	18.8042i	−0.852189	−	0.885457i
$452$			14.6456i			0.688873i
$453$		0			0
$454$	1.12156	−	0.814863i	0.0526376	−	0.0382434i
$455$	−9.55029	+	13.1448i	−0.447724	+	0.616240i
$456$		0			0
$457$	−7.25747	+	2.35809i	−0.339490	+	0.110307i	−0.473800	−	0.880632i	$-0.657118\pi$
$457$	−7.25747	+	2.35809i	−0.339490	+	0.110307i	0.134310	+	0.990939i	$0.457118\pi$
$458$	7.43466	+	5.40159i	0.347399	+	0.252400i
$459$		0			0
$460$	−2.13471	+	6.56996i	−0.0995314	+	0.306326i
$461$	−2.76299			−0.128685			−0.0643427	−	0.997928i	$-0.520495\pi$
$461$	−2.76299			−0.128685			−0.0643427	+	0.997928i	$0.520495\pi$
$462$		0			0
$463$	34.8507			1.61965			0.809825	−	0.586672i	$-0.199562\pi$
$463$	34.8507			1.61965			0.809825	+	0.586672i	$0.199562\pi$
$464$	−1.88759	+	5.80941i	−0.0876292	+	0.269695i
$465$		0			0
$466$	18.2756	+	13.2780i	0.846603	+	0.615093i
$467$	−23.7328	+	7.71126i	−1.09822	+	0.356834i	−0.801419	−	0.598104i	$-0.795921\pi$
$467$	−23.7328	+	7.71126i	−1.09822	+	0.356834i	−0.296805	+	0.954938i	$0.595921\pi$
$468$		0			0
$469$	−8.97246	+	12.3495i	−0.414310	+	0.570248i
$470$	−12.1181	+	8.80433i	−0.558967	+	0.406114i
$471$		0			0
$472$		−	12.8323i		−	0.590653i
$473$	10.3587	−	1.43797i	0.476293	−	0.0661178i
$474$		0			0
$475$	−29.6488	−	9.63347i	−1.36038	−	0.442014i
$476$	−0.464351	−	0.639125i	−0.0212835	−	0.0292942i
$477$		0			0
$478$	−5.62660	−	17.3169i	−0.257355	−	0.792057i
$479$	−3.76191	−	11.5780i	−0.171886	−	0.529011i	0.827591	−	0.561331i	$-0.189710\pi$
$479$	−3.76191	−	11.5780i	−0.171886	−	0.529011i	−0.999478	+	0.0323198i	$0.989710\pi$
$480$		0			0
$481$	−6.07046	−	8.35527i	−0.276789	−	0.380968i
$482$	−24.5739	−	7.98455i	−1.11931	−	0.363686i
$483$		0			0
$484$	10.3238	+	3.79714i	0.469266	+	0.172597i
$485$		−	43.2397i		−	1.96341i
$486$		0			0
$487$	−1.57029	+	1.14089i	−0.0711569	+	0.0516985i	−0.622795	−	0.782385i	$-0.714003\pi$
$487$	−1.57029	+	1.14089i	−0.0711569	+	0.0516985i	0.551638	+	0.834084i	$0.314003\pi$
$488$	8.61347	−	11.8554i	0.389913	−	0.536670i
$489$		0			0
$490$	−3.30760	+	1.07471i	−0.149422	+	0.0485502i
$491$	−13.2192	−	9.60431i	−0.596574	−	0.433437i	0.248087	−	0.968738i	$-0.420198\pi$
$491$	−13.2192	−	9.60431i	−0.596574	−	0.433437i	−0.844661	+	0.535301i	$0.820198\pi$
$492$		0			0
$493$	1.49120	−	4.58944i	0.0671603	−	0.206698i
$494$	−20.5270			−0.923552
$495$		0			0
$496$	5.09700			0.228862
$497$	−0.755545	+	2.32533i	−0.0338908	+	0.104305i
$498$		0			0
$499$	31.9720	+	23.2290i	1.43126	+	1.03987i	0.989780	+	0.142602i	$0.0455468\pi$
$499$	31.9720	+	23.2290i	1.43126	+	1.03987i	0.441481	+	0.897271i	$0.354453\pi$
$500$	6.93017	−	2.25175i	0.309927	−	0.100701i
$501$		0			0
$502$	−2.81271	+	3.87136i	−0.125537	+	0.172787i
$503$	21.0487	−	15.2928i	0.938517	−	0.681872i	−0.00954637	−	0.999954i	$-0.503039\pi$
$503$	21.0487	−	15.2928i	0.938517	−	0.681872i	0.948063	+	0.318082i	$0.103039\pi$
$504$		0			0
$505$			37.3292i			1.66113i
$506$	1.15494	−	6.48586i	0.0513433	−	0.288331i
$507$		0			0
$508$	15.8460	+	5.14868i	0.703053	+	0.228436i
$509$	17.6718	+	24.3231i	0.783287	+	1.07810i	0.994912	+	0.100751i	$0.0321245\pi$
$509$	17.6718	+	24.3231i	0.783287	+	1.07810i	−0.211625	+	0.977351i	$0.567876\pi$
$510$		0			0
$511$	3.04867	+	9.38285i	0.134865	+	0.415073i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	1.22971	+	1.69255i	0.0542402	+	0.0746552i
$515$	14.8458	+	4.82371i	0.654186	+	0.212558i
$516$		0			0
$517$	10.2922	−	9.90551i	0.452651	−	0.435644i
$518$		−	2.21061i		−	0.0971287i
$519$		0			0
$520$	13.1448	−	9.55029i	0.576439	−	0.418808i
$521$	3.84159	−	5.28749i	0.168303	−	0.231649i	−0.716531	−	0.697555i	$-0.754271\pi$
$521$	3.84159	−	5.28749i	0.168303	−	0.231649i	0.884834	+	0.465906i	$0.154271\pi$
$522$		0			0
$523$	−14.0859	+	4.57678i	−0.615933	+	0.200129i	−0.600334	−	0.799750i	$-0.704966\pi$
$523$	−14.0859	+	4.57678i	−0.615933	+	0.200129i	−0.0155993	+	0.999878i	$0.504966\pi$
$524$	−9.65935	−	7.01793i	−0.421971	−	0.306580i
$525$		0			0
$526$	0.123732	−	0.380808i	0.00539498	−	0.0166040i
$527$	−4.02664			−0.175403
$528$		0			0
$529$	19.0545			0.828458
$530$	−4.11180	+	12.6548i	−0.178605	+	0.549691i
$531$		0			0
$532$	−3.55461	−	2.58258i	−0.154112	−	0.111969i
$533$	34.9635	−	11.3603i	1.51444	−	0.492071i
$534$		0			0
$535$	−17.8590	+	24.5809i	−0.772114	+	1.06272i
$536$	12.3495	−	8.97246i	0.533419	−	0.387551i
$537$		0			0
$538$			21.9079i			0.944516i
$539$	2.98342	−	1.44887i	0.128505	−	0.0624073i
$540$		0			0
$541$	−4.51932	−	1.46842i	−0.194301	−	0.0631321i	0.210250	−	0.977648i	$-0.432572\pi$
$541$	−4.51932	−	1.46842i	−0.194301	−	0.0631321i	−0.404551	+	0.914515i	$0.632572\pi$
$542$	−12.6144	−	17.3622i	−0.541835	−	0.745772i
$543$		0			0
$544$	0.244124	+	0.751336i	0.0104667	+	0.0322133i
$545$	2.91150	+	8.96066i	0.124715	+	0.383833i
$546$		0			0
$547$	14.0364	+	19.3195i	0.600154	+	0.826041i	0.995722	−	0.0923952i	$-0.0294523\pi$
$547$	14.0364	+	19.3195i	0.600154	+	0.826041i	−0.395568	+	0.918437i	$0.629452\pi$
$548$	8.83368	+	2.87024i	0.377356	+	0.122610i
$549$		0			0
$550$	−21.1680	+	10.2801i	−0.902607	+	0.438344i
$551$		−	26.8386i		−	1.14336i
$552$		0			0
$553$	9.85456	−	7.15976i	0.419058	−	0.304464i
$554$	−5.95176	+	8.19190i	−0.252866	+	0.348041i
$555$		0			0
$556$	−8.78003	+	2.85280i	−0.372356	+	0.120986i
$557$	−6.17184	−	4.48410i	−0.261509	−	0.189998i	0.449303	−	0.893379i	$-0.351672\pi$
$557$	−6.17184	−	4.48410i	−0.261509	−	0.189998i	−0.710812	+	0.703382i	$0.751672\pi$
$558$		0			0
$559$	−4.55225	+	14.0104i	−0.192540	+	0.592576i
$560$	3.47782			0.146965
$561$		0			0
$562$	28.6413			1.20816
$563$	−10.2524	+	31.5535i	−0.432085	+	1.32982i	0.463959	+	0.885857i	$0.346428\pi$
$563$	−10.2524	+	31.5535i	−0.432085	+	1.32982i	−0.896044	+	0.443965i	$0.853572\pi$
$564$		0			0
$565$	41.2072	+	29.9388i	1.73360	+	1.25953i
$566$	30.2733	−	9.83638i	1.27248	−	0.413454i
$567$		0			0
$568$	1.43713	−	1.97804i	0.0603007	−	0.0829968i
$569$	31.6526	−	22.9969i	1.32694	−	0.964082i	0.327127	−	0.944980i	$-0.393919\pi$
$569$	31.6526	−	22.9969i	1.32694	−	0.964082i	0.999818	−	0.0191016i	$-0.00608060\pi$
$570$		0			0
$571$		−	0.790998i		−	0.0331022i	−0.999863	−	0.0165511i	$-0.994731\pi$
$571$		−	0.790998i		−	0.0331022i	0.999863	−	0.0165511i	$-0.00526862\pi$
$572$	−11.1642	+	10.7448i	−0.466800	+	0.449261i
$573$		0			0
$574$	7.48383	+	2.43165i	0.312369	+	0.101495i
$575$	8.28389	+	11.4018i	0.345462	+	0.475488i
$576$		0			0
$577$	−14.0546	−	43.2555i	−0.585099	−	1.80075i	−0.598872	−	0.800845i	$-0.704384\pi$
$577$	−14.0546	−	43.2555i	−0.585099	−	1.80075i	0.0137730	−	0.999905i	$-0.495616\pi$
$578$	5.06043	+	15.5744i	0.210486	+	0.647810i
$579$		0			0
$580$	12.4868	+	17.1866i	0.518486	+	0.713635i
$581$	−3.29956	−	1.07209i	−0.136889	−	0.0444779i
$582$		0			0
$583$	2.22460	−	12.4928i	0.0921336	−	0.517400i
$584$		−	9.86571i		−	0.408246i
$585$		0			0
$586$	20.9906	−	15.2505i	0.867112	−	0.629994i
$587$	−5.65114	+	7.77812i	−0.233247	+	0.321037i	−0.909556	−	0.415581i	$-0.863578\pi$
$587$	−5.65114	+	7.77812i	−0.233247	+	0.321037i	0.676309	+	0.736618i	$0.263578\pi$
$588$		0			0
$589$	−21.2988	+	6.92040i	−0.877602	+	0.285150i
$590$	−36.1051	−	26.2319i	−1.48642	−	1.07995i
$591$		0			0
$592$	−0.683116	+	2.10242i	−0.0280759	+	0.0864088i
$593$	18.7548			0.770169			0.385084	−	0.922881i	$-0.374172\pi$
$593$	18.7548			0.770169			0.385084	+	0.922881i	$0.374172\pi$
$594$		0			0
$595$	−2.74748			−0.112636
$596$	−4.37528	+	13.4657i	−0.179219	+	0.551578i
$597$		0			0
$598$	7.50755	+	5.45455i	0.307006	+	0.223053i
$599$	35.1021	−	11.4054i	1.43423	−	0.466010i	0.514138	−	0.857708i	$-0.328112\pi$
$599$	35.1021	−	11.4054i	1.43423	−	0.466010i	0.920094	+	0.391698i	$0.128112\pi$
$600$		0			0
$601$	13.9106	−	19.1463i	0.567426	−	0.780994i	−0.424821	−	0.905277i	$-0.639663\pi$
$601$	13.9106	−	19.1463i	0.567426	−	0.780994i	0.992247	+	0.124283i	$0.0396631\pi$
$602$	−2.55100	+	1.85341i	−0.103971	+	0.0755393i
$603$		0			0
$604$			1.70414i			0.0693405i
$605$	31.7878	−	21.2852i	1.29236	−	0.865365i
$606$		0			0
$607$	−43.5197	−	14.1404i	−1.76641	−	0.573941i	−0.768577	−	0.639757i	$-0.779035\pi$
$607$	−43.5197	−	14.1404i	−1.76641	−	0.573941i	−0.997832	+	0.0658162i	$0.979035\pi$
$608$	2.58258	+	3.55461i	0.104737	+	0.144158i
$609$		0			0
$610$	−15.7488	−	48.4700i	−0.637652	−	1.96249i
$611$	6.21790	+	19.1367i	0.251549	+	0.774189i
$612$		0			0
$613$	−21.2662	−	29.2704i	−0.858935	−	1.18222i	−0.981822	−	0.189802i	$-0.939215\pi$
$613$	−21.2662	−	29.2704i	−0.858935	−	1.18222i	0.122888	−	0.992421i	$-0.460785\pi$
$614$	1.03652	+	0.336785i	0.0418304	+	0.0135915i
$615$		0			0
$616$	−3.28512	+	0.456033i	−0.132361	+	0.0183741i
$617$			42.1076i			1.69519i	0.530645	+	0.847594i	$0.321950\pi$
$617$			42.1076i			1.69519i	−0.530645	+	0.847594i	$0.678050\pi$
$618$		0			0
$619$	19.6787	−	14.2974i	0.790956	−	0.574663i	−0.117291	−	0.993098i	$-0.537421\pi$
$619$	19.6787	−	14.2974i	0.790956	−	0.574663i	0.908247	+	0.418435i	$0.137421\pi$
$620$	10.4193	−	14.3410i	0.418451	−	0.575948i
$621$		0			0
$622$	27.7133	−	9.00461i	1.11120	−	0.361052i
$623$	−0.669612	−	0.486502i	−0.0268274	−	0.0194913i
$624$		0			0
$625$	−3.13155	+	9.63791i	−0.125262	+	0.385517i
$626$	6.23304			0.249122
$627$		0			0
$628$	−11.5331			−0.460221
$629$	0.539663	−	1.66091i	0.0215178	−	0.0662249i
$630$		0			0
$631$	22.4901	+	16.3400i	0.895319	+	0.650487i	0.937259	−	0.348633i	$-0.113354\pi$
$631$	22.4901	+	16.3400i	0.895319	+	0.650487i	−0.0419407	+	0.999120i	$0.513354\pi$
$632$	−11.5847	+	3.76411i	−0.460816	+	0.149728i
$633$		0			0
$634$	6.45959	−	8.89086i	0.256543	−	0.353101i
$635$	46.8790	−	34.0596i	1.86034	−	1.35161i
$636$		0			0
$637$			4.67187i			0.185106i
$638$	−14.0486	−	14.5970i	−0.556188	−	0.577901i
$639$		0			0
$640$	−3.30760	−	1.07471i	−0.130744	−	0.0424815i
$641$	−24.7910	−	34.1218i	−0.979184	−	1.34773i	−0.937268	−	0.348610i	$-0.886654\pi$
$641$	−24.7910	−	34.1218i	−0.979184	−	1.34773i	−0.0419160	−	0.999121i	$-0.513346\pi$
$642$		0			0
$643$	6.00962	+	18.4957i	0.236996	+	0.729400i	0.996850	+	0.0793062i	$0.0252705\pi$
$643$	6.00962	+	18.4957i	0.236996	+	0.729400i	−0.759854	+	0.650094i	$0.774730\pi$
$644$	0.613807	+	1.88910i	0.0241874	+	0.0744411i
$645$		0			0
$646$	−2.04024	−	2.80815i	−0.0802721	−	0.110485i
$647$	32.7731	+	10.6486i	1.28844	+	0.418640i	0.871546	−	0.490314i	$-0.163118\pi$
$647$	32.7731	+	10.6486i	1.28844	+	0.418640i	0.416896	+	0.908954i	$0.363118\pi$
$648$		0			0
$649$	37.5443	+	20.0441i	1.47374	+	0.786800i
$650$		−	33.1480i		−	1.30017i
$651$		0			0
$652$	9.10902	−	6.61809i	0.356737	−	0.259184i
$653$	19.7230	−	27.1464i	0.771822	−	1.06232i	−0.224316	−	0.974516i	$-0.572015\pi$
$653$	19.7230	−	27.1464i	0.771822	−	1.06232i	0.996138	−	0.0878048i	$-0.0279852\pi$
$654$		0			0
$655$	−39.4915	+	12.8316i	−1.54306	+	0.501371i
$656$	−6.36613	−	4.62526i	−0.248556	−	0.180586i
$657$		0			0
$658$	−1.33092	+	4.09616i	−0.0518848	+	0.159685i
$659$	−13.4149			−0.522570			−0.261285	−	0.965262i	$-0.584146\pi$
$659$	−13.4149			−0.522570			−0.261285	+	0.965262i	$0.584146\pi$
$660$		0			0
$661$	13.5695			0.527792			0.263896	−	0.964551i	$-0.414992\pi$
$661$	13.5695			0.527792			0.263896	+	0.964551i	$0.414992\pi$
$662$	−9.35458	+	28.7904i	−0.363576	+	1.11897i
$663$		0			0
$664$	2.80678	+	2.03924i	0.108924	+	0.0791380i
$665$	−14.5327	+	4.72197i	−0.563556	+	0.183110i
$666$		0			0
$667$	−7.13171	+	9.81596i	−0.276141	+	0.380076i
$668$	10.2556	−	7.45117i	0.396803	−	0.288294i
$669$		0			0
$670$		−	53.0884i		−	2.05098i
$671$	21.2319	+	43.7193i	0.819650	+	1.68776i
$672$		0			0
$673$	17.6877	+	5.74708i	0.681810	+	0.221534i	0.629388	−	0.777091i	$-0.283306\pi$
$673$	17.6877	+	5.74708i	0.681810	+	0.221534i	0.0524225	+	0.998625i	$0.483306\pi$
$674$	17.2826	+	23.7874i	0.665701	+	0.916258i
$675$		0			0
$676$	−2.72750	−	8.39438i	−0.104904	−	0.322861i
$677$	−4.90385	−	15.0925i	−0.188470	−	0.580052i	0.811520	−	0.584324i	$-0.198640\pi$
$677$	−4.90385	−	15.0925i	−0.188470	−	0.580052i	−0.999991	+	0.00427176i	$0.998640\pi$
$678$		0			0
$679$	−7.30793	−	10.0585i	−0.280453	−	0.386010i
$680$	2.61301	+	0.849019i	0.100204	+	0.0325584i
$681$		0			0
$682$	−7.96156	+	14.9126i	−0.304864	+	0.571035i
$683$		−	33.6735i		−	1.28848i	−0.764823	−	0.644240i	$-0.777174\pi$
$683$		−	33.6735i		−	1.28848i	0.764823	−	0.644240i	$-0.222826\pi$
$684$		0			0
$685$	26.1336	−	18.9872i	0.998515	−	0.725464i
$686$	−0.587785	+	0.809017i	−0.0224417	+	0.0308884i
$687$		0			0
$688$	2.99888	−	0.974395i	0.114331	−	0.0371485i
$689$	14.4608	+	10.5064i	0.550912	+	0.400261i
$690$		0			0
$691$	−3.58416	+	11.0309i	−0.136348	+	0.419636i	−0.995797	−	0.0915850i	$-0.970807\pi$
$691$	−3.58416	+	11.0309i	−0.136348	+	0.419636i	0.859449	+	0.511221i	$0.170807\pi$
$692$	17.7623			0.675223
$693$		0			0
$694$	−0.234238			−0.00889154
$695$	−9.92153	+	30.5353i	−0.376345	+	1.15827i
$696$		0			0
$697$	5.02925	+	3.65397i	0.190497	+	0.138404i
$698$	12.6604	−	4.11362i	0.479204	−	0.155703i
$699$		0			0
$700$	4.17047	−	5.74016i	0.157629	−	0.216958i
$701$	20.3493	−	14.7846i	0.768583	−	0.558408i	−0.132948	−	0.991123i	$-0.542444\pi$
$701$	20.3493	−	14.7846i	0.768583	−	0.558408i	0.901531	+	0.432715i	$0.142444\pi$
$702$		0			0
$703$		−	9.71285i		−	0.366327i
$704$	3.26526	+	0.581446i	0.123064	+	0.0219141i
$705$		0			0
$706$	−9.21638	−	2.99458i	−0.346863	−	0.112703i
$707$	6.30900	+	8.68360i	0.237274	+	0.326580i
$708$		0			0
$709$	4.01451	+	12.3554i	0.150768	+	0.464016i	0.997708	−	0.0676731i	$-0.0215575\pi$
$709$	4.01451	+	12.3554i	0.150768	+	0.464016i	−0.846940	+	0.531689i	$0.821557\pi$
$710$	−2.62765	−	8.08707i	−0.0986139	−	0.303502i
$711$		0			0
$712$	0.486502	+	0.669612i	0.0182324	+	0.0250948i
$713$	9.62876	+	3.12857i	0.360600	+	0.117166i
$714$		0			0
$715$	7.40959	+	53.3764i	0.277103	+	1.99616i
$716$			7.59487i			0.283834i
$717$		0			0
$718$	21.8191	−	15.8525i	0.814283	−	0.591611i
$719$	−1.50647	+	2.07348i	−0.0561819	+	0.0773278i	−0.836184	−	0.548450i	$-0.815218\pi$
$719$	−1.50647	+	2.07348i	−0.0561819	+	0.0773278i	0.780002	+	0.625778i	$0.215218\pi$
$720$		0			0
$721$	4.26872	−	1.38699i	0.158975	−	0.0516543i
$722$	−0.246707	−	0.179243i	−0.00918149	−	0.00667074i
$723$		0			0
$724$	2.71132	−	8.34458i	0.100765	−	0.310124i
$725$	43.3403			1.60962
$726$		0			0
$727$	−31.7532			−1.17766			−0.588831	−	0.808256i	$-0.700412\pi$
$727$	−31.7532			−1.17766			−0.588831	+	0.808256i	$0.700412\pi$
$728$	1.44369	−	4.44321i	0.0535066	−	0.164676i
$729$		0			0
$730$	−27.7583	−	20.1676i	−1.02738	−	0.746436i
$731$	−2.36912	+	0.769774i	−0.0876251	+	0.0284711i
$732$		0			0
$733$	−5.90752	+	8.13101i	−0.218199	+	0.300326i	−0.904059	−	0.427409i	$-0.859427\pi$
$733$	−5.90752	+	8.13101i	−0.218199	+	0.300326i	0.685859	+	0.727734i	$0.259427\pi$
$734$	3.28812	−	2.38896i	0.121367	−	0.0881780i
$735$		0			0
$736$		−	1.98632i		−	0.0732168i
$737$	6.96128	+	50.1470i	0.256422	+	1.84719i
$738$		0			0
$739$	−46.8601	−	15.2258i	−1.72378	−	0.560089i	−0.731249	−	0.682110i	$-0.761062\pi$
$739$	−46.8601	−	15.2258i	−1.72378	−	0.560089i	−0.992527	+	0.122022i	$0.961062\pi$
$740$	4.51895	+	6.21981i	0.166120	+	0.228645i
$741$		0			0
$742$	1.18229	+	3.63873i	0.0434034	+	0.133582i
$743$	0.623527	+	1.91902i	0.0228750	+	0.0704019i	0.961842	−	0.273604i	$-0.0882159\pi$
$743$	0.623527	+	1.91902i	0.0228750	+	0.0704019i	−0.938967	+	0.344006i	$0.888216\pi$
$744$		0			0
$745$	28.9434	+	39.8372i	1.06040	+	1.45952i
$746$	−9.39122	−	3.05139i	−0.343837	−	0.111719i
$747$		0			0
$748$	−2.57956	−	0.459343i	−0.0943181	−	0.0167952i
$749$			8.73640i			0.319221i
$750$		0			0
$751$	−0.706655	+	0.513415i	−0.0257862	+	0.0187348i	−0.600604	−	0.799547i	$-0.705073\pi$
$751$	−0.706655	+	0.513415i	−0.0257862	+	0.0187348i	0.574818	+	0.818282i	$0.305073\pi$
$752$	2.53157	−	3.48440i	0.0923168	−	0.127063i
$753$		0			0
$754$	27.1408	−	8.81858i	0.988410	−	0.321154i
$755$	4.79480	+	3.48362i	0.174501	+	0.126782i
$756$		0			0
$757$	13.7094	−	42.1930i	0.498275	−	1.53353i	−0.313515	−	0.949583i	$-0.601507\pi$
$757$	13.7094	−	42.1930i	0.498275	−	1.53353i	0.811790	−	0.583949i	$-0.198493\pi$
$758$	34.2224			1.24301
$759$		0			0
$760$	15.2806			0.554287
$761$	8.47118	−	26.0716i	0.307080	−	0.945095i	−0.671813	−	0.740721i	$-0.734484\pi$
$761$	8.47118	−	26.0716i	0.307080	−	0.945095i	0.978893	−	0.204374i	$-0.0655159\pi$
$762$		0			0
$763$	2.19172	+	1.59238i	0.0793455	+	0.0576479i
$764$	14.6308	−	4.75384i	0.529325	−	0.171988i
$765$		0			0
$766$	−5.34946	+	7.36290i	−0.193284	+	0.266032i
$767$	−48.5011	+	35.2381i	−1.75127	+	1.27238i
$768$		0			0
$769$		−	29.2956i		−	1.05642i	−0.849112	−	0.528212i	$-0.822863\pi$
$769$		−	29.2956i		−	1.05642i	0.849112	−	0.528212i	$-0.177137\pi$
$770$	−5.43238	+	10.1753i	−0.195769	+	0.366692i
$771$		0			0
$772$	−13.8113	−	4.48757i	−0.497080	−	0.161511i
$773$	4.60764	+	6.34187i	0.165725	+	0.228101i	0.883800	−	0.467864i	$-0.154976\pi$
$773$	4.60764	+	6.34187i	0.165725	+	0.228101i	−0.718075	+	0.695966i	$0.754976\pi$
$774$		0			0
$775$	−11.1754	−	34.3943i	−0.401432	−	1.23548i
$776$	3.84201	+	11.8245i	0.137920	+	0.424474i
$777$		0			0
$778$	−15.7371	−	21.6602i	−0.564201	−	0.776556i
$779$	32.8820	+	10.6840i	1.17812	+	0.382795i
$780$		0			0
$781$	3.54248	+	7.29444i	0.126760	+	0.261015i
$782$			1.56920i			0.0561144i
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	−23.5761	+	32.4497i	−0.841466	+	1.15818i
$786$		0			0
$787$	8.00324	−	2.60041i	0.285285	−	0.0926946i	−0.162879	−	0.986646i	$-0.552078\pi$
$787$	8.00324	−	2.60041i	0.285285	−	0.0926946i	0.448164	+	0.893951i	$0.352078\pi$
$788$	15.1293	+	10.9921i	0.538961	+	0.391578i
$789$		0			0
$790$	−13.0909	+	40.2896i	−0.465753	+	1.43344i
$791$	14.6456			0.520739
$792$		0			0
$793$	−68.4621			−2.43116
$794$	2.57842	−	7.93555i	0.0915046	−	0.281622i
$795$		0			0
$796$	14.4199	+	10.4766i	0.511098	+	0.371335i
$797$	−44.5139	+	14.4634i	−1.57676	+	0.512321i	−0.961220	−	0.275783i	$-0.911063\pi$
$797$	−44.5139	+	14.4634i	−1.57676	+	0.512321i	−0.615542	+	0.788104i	$0.711063\pi$
$798$		0			0
$799$	−1.99994	+	2.75268i	−0.0707529	+	0.0973830i
$800$	−5.74016	+	4.17047i	−0.202945	+	0.147448i
$801$		0			0
$802$			32.4171i			1.14469i
$803$	28.8648	+	15.4103i	1.01862	+	0.543818i
$804$		0			0
$805$	6.56996	+	2.13471i	0.231561	+	0.0752387i
$806$	−13.9966	−	19.2647i	−0.493011	−	0.678571i
$807$		0			0
$808$	−3.31684	−	10.2082i	−0.116686	−	0.359122i
$809$	−12.6720	−	39.0004i	−0.445523	−	1.37118i	−0.881909	−	0.471420i	$-0.843742\pi$
$809$	−12.6720	−	39.0004i	−0.445523	−	1.37118i	0.436386	−	0.899760i	$-0.356258\pi$
$810$		0			0
$811$	19.8977	+	27.3869i	0.698704	+	0.961684i	0.999967	+	0.00814269i	$0.00259193\pi$
$811$	19.8977	+	27.3869i	0.698704	+	0.961684i	−0.301263	+	0.953541i	$0.597408\pi$
$812$	5.80941	+	1.88759i	0.203870	+	0.0662415i
$813$		0			0
$814$	−5.08415	−	5.28263i	−0.178199	−	0.185156i
$815$		−	39.1581i		−	1.37165i
$816$		0			0
$817$	−11.2084	+	8.14340i	−0.392133	+	0.284901i
$818$	5.44149	−	7.48957i	0.190257	−	0.261867i
$819$		0			0
$820$	−26.0274	+	8.45682i	−0.908917	+	0.295325i
$821$	15.6276	+	11.3541i	0.545406	+	0.396261i	0.826089	−	0.563540i	$-0.190561\pi$
$821$	15.6276	+	11.3541i	0.545406	+	0.396261i	−0.280683	+	0.959801i	$0.590561\pi$
$822$		0			0
$823$	6.42849	−	19.7849i	0.224083	−	0.689657i	−0.774300	−	0.632818i	$-0.781898\pi$
$823$	6.42849	−	19.7849i	0.224083	−	0.689657i	0.998383	−	0.0568386i	$-0.0181020\pi$
$824$	−4.48840			−0.156361
$825$		0			0
$826$	−12.8323			−0.446492
$827$	−5.61499	+	17.2812i	−0.195252	+	0.600925i	0.804721	+	0.593653i	$0.202315\pi$
$827$	−5.61499	+	17.2812i	−0.195252	+	0.600925i	−0.999974	+	0.00727225i	$0.997685\pi$
$828$		0			0
$829$	18.9640	+	13.7781i	0.658646	+	0.478534i	0.866205	−	0.499688i	$-0.166552\pi$
$829$	18.9640	+	13.7781i	0.658646	+	0.478534i	−0.207560	+	0.978222i	$0.566552\pi$
$830$	11.4753	−	3.72855i	0.398313	−	0.129420i
$831$		0			0
$832$	−2.74606	+	3.77962i	−0.0952024	+	0.131035i
$833$	−0.639125	+	0.464351i	−0.0221444	+	0.0160888i
$834$		0			0
$835$		−	44.0872i		−	1.52570i
$836$	−14.4340	+	2.00369i	−0.499209	+	0.0692991i
$837$		0			0
$838$	−16.9508	−	5.50765i	−0.585556	−	0.190259i
$839$	22.8608	+	31.4651i	0.789241	+	1.08630i	0.994202	+	0.107527i	$0.0342933\pi$
$839$	22.8608	+	31.4651i	0.789241	+	1.08630i	−0.204961	+	0.978770i	$0.565707\pi$
$840$		0			0
$841$	2.56862	+	7.90540i	0.0885731	+	0.272600i
$842$	4.71289	+	14.5048i	0.162417	+	0.499868i
$843$		0			0
$844$	−7.72970	−	10.6390i	−0.266067	−	0.366210i
$845$	−29.1941	−	9.48574i	−1.00431	−	0.326320i
$846$		0			0
$847$	3.79714	−	10.3238i	0.130471	−	0.354731i
$848$		−	3.82598i		−	0.131385i
$849$		0			0
$850$	4.53473	−	3.29468i	0.155540	−	0.113007i
$851$	−2.58096	+	3.55238i	−0.0884740	+	0.121774i
$852$		0			0
$853$	−14.6735	+	4.76770i	−0.502410	+	0.163243i	−0.549248	−	0.835660i	$-0.685086\pi$
$853$	−14.6735	+	4.76770i	−0.502410	+	0.163243i	0.0468376	+	0.998903i	$0.485086\pi$
$854$	−11.8554	−	8.61347i	−0.405684	−	0.294747i
$855$		0			0
$856$	2.69970	−	8.30881i	0.0922737	−	0.283989i
$857$	−32.5804			−1.11292			−0.556462	−	0.830873i	$-0.687842\pi$
$857$	−32.5804			−1.11292			−0.556462	+	0.830873i	$0.687842\pi$
$858$		0			0
$859$	33.3321			1.13728			0.568639	−	0.822587i	$-0.307470\pi$
$859$	33.3321			1.13728			0.568639	+	0.822587i	$0.307470\pi$
$860$	3.38877	−	10.4296i	0.115556	−	0.355645i
$861$		0			0
$862$	−17.3717	−	12.6213i	−0.591684	−	0.429884i
$863$	5.57200	−	1.81045i	0.189673	−	0.0616285i	−0.212640	−	0.977131i	$-0.568206\pi$
$863$	5.57200	−	1.81045i	0.189673	−	0.0616285i	0.402313	+	0.915502i	$0.368206\pi$
$864$		0			0
$865$	36.3100	−	49.9764i	1.23458	−	1.69925i
$866$	27.8020	−	20.1994i	0.944751	−	0.686402i
$867$		0			0
$868$		−	5.09700i		−	0.173003i
$869$	7.08254	−	39.7738i	0.240259	−	1.34923i
$870$		0			0
$871$	−67.8250	−	22.0377i	−2.29816	−	0.746719i
$872$	−1.59238	−	2.19172i	−0.0539247	−	0.0742209i
$873$		0			0
$874$	2.69691	+	8.30023i	0.0912243	+	0.280760i
$875$	−2.25175	−	6.93017i	−0.0761230	−	0.234283i
$876$		0			0
$877$	−28.1815	−	38.7885i	−0.951623	−	1.30980i	−0.950803	−	0.309796i	$-0.899739\pi$
$877$	−28.1815	−	38.7885i	−0.951623	−	1.30980i	−0.000819620	−	1.00000i	$-0.500261\pi$
$878$	−10.1115	−	3.28543i	−0.341247	−	0.110878i
$879$		0			0
$880$	8.31084	−	7.99859i	0.280158	−	0.269632i
$881$			19.7367i			0.664946i	0.943113	+	0.332473i	$0.107883\pi$
$881$			19.7367i			0.664946i	−0.943113	+	0.332473i	$0.892117\pi$
$882$		0			0
$883$	−10.2479	+	7.44556i	−0.344870	+	0.250563i	−0.746714	−	0.665145i	$-0.768370\pi$
$883$	−10.2479	+	7.44556i	−0.344870	+	0.250563i	0.401844	+	0.915708i	$0.368370\pi$
$884$	2.16939	−	2.98591i	0.0729645	−	0.100427i
$885$		0			0
$886$	16.0603	−	5.21830i	0.539555	−	0.175312i
$887$	−22.5303	−	16.3692i	−0.756493	−	0.549624i	0.141340	−	0.989961i	$-0.454859\pi$
$887$	−22.5303	−	16.3692i	−0.756493	−	0.549624i	−0.897833	+	0.440337i	$0.854859\pi$
$888$		0			0
$889$	5.14868	−	15.8460i	0.172681	−	0.531458i
$890$	2.87854			0.0964890
$891$		0			0
$892$	−3.05834			−0.102401
$893$	−5.84773	+	17.9975i	−0.195687	+	0.602262i
$894$		0			0
$895$	21.3690	+	15.5255i	0.714288	+	0.518961i
$896$	−0.951057	+	0.309017i	−0.0317726	+	0.0103235i
$897$		0			0
$898$	−20.8023	+	28.6319i	−0.694180	+	0.955457i
$899$	25.1882	−	18.3003i	0.840075	−	0.610350i
$900$		0			0
$901$			3.02253i			0.100695i
$902$	23.4764	−	11.4011i	0.781679	−	0.379616i
$903$		0			0
$904$	−13.9288	−	4.52575i	−0.463266	−	0.150524i
$905$	−17.9359	−	24.6867i	−0.596211	−	0.820613i
$906$		0			0
$907$	6.70593	+	20.6387i	0.222667	+	0.685298i	0.998520	+	0.0543846i	$0.0173197\pi$
$907$	6.70593	+	20.6387i	0.222667	+	0.685298i	−0.775853	+	0.630913i	$0.782680\pi$
$908$	0.428399	+	1.31848i	0.0142169	+	0.0437552i
$909$		0			0
$910$	−9.55029	−	13.1448i	−0.316589	−	0.435747i
$911$	37.8733	+	12.3058i	1.25480	+	0.407709i	0.859638	−	0.510903i	$-0.170689\pi$
$911$	37.8733	+	12.3058i	1.25480	+	0.407709i	0.395161	+	0.918612i	$0.370689\pi$
$912$		0			0
$913$	−10.3506	+	5.02667i	−0.342554	+	0.166358i
$914$		−	7.63095i		−	0.252409i
$915$		0			0
$916$	−7.43466	+	5.40159i	−0.245648	+	0.178474i
$917$	−7.01793	+	9.65935i	−0.231752	+	0.318980i
$918$		0			0
$919$	−9.67603	+	3.14393i	−0.319183	+	0.103709i	−0.464227	−	0.885716i	$-0.653668\pi$
$919$	−9.67603	+	3.14393i	−0.319183	+	0.103709i	0.145044	+	0.989425i	$0.453668\pi$
$920$	−5.58874	−	4.06046i	−0.184255	−	0.133869i
$921$		0			0
$922$	0.853812	−	2.62776i	0.0281188	−	0.0865407i
$923$	−11.4227			−0.375983
$924$		0			0
$925$	15.6848			0.515712
$926$	−10.7695	+	33.1450i	−0.353906	+	1.08921i
$927$		0			0
$928$	−4.94178	−	3.59041i	−0.162222	−	0.117861i
$929$	−4.82549	+	1.56790i	−0.158319	+	0.0514411i	−0.387104	−	0.922036i	$-0.626525\pi$
$929$	−4.82549	+	1.56790i	−0.158319	+	0.0514411i	0.228785	+	0.973477i	$0.426525\pi$
$930$		0			0
$931$	−2.58258	+	3.55461i	−0.0846405	+	0.116498i
$932$	−18.2756	+	13.2780i	−0.598639	+	0.434936i
$933$		0			0
$934$		−	24.9542i		−	0.816525i
$935$	−6.56558	+	6.31890i	−0.214717	+	0.206650i
$936$		0			0
$937$	−5.36691	−	1.74382i	−0.175329	−	0.0569680i	0.220037	−	0.975492i	$-0.429382\pi$
$937$	−5.36691	−	1.74382i	−0.175329	−	0.0569680i	−0.395366	+	0.918524i	$0.629382\pi$
$938$	−8.97246	−	12.3495i	−0.292961	−	0.403227i
$939$		0			0
$940$	−4.62871	−	14.2457i	−0.150972	−	0.464644i
$941$	−9.85925	−	30.3437i	−0.321402	−	0.989175i	−0.973038	−	0.230643i	$-0.925917\pi$
$941$	−9.85925	−	30.3437i	−0.321402	−	0.989175i	0.651636	−	0.758532i	$-0.274083\pi$
$942$		0			0
$943$	−9.18726	−	12.6452i	−0.299178	−	0.411784i
$944$	12.2042	+	3.96539i	0.397213	+	0.129062i
$945$		0			0
$946$	−1.83342	+	10.2960i	−0.0596096	+	0.334753i
$947$			22.3346i			0.725778i	0.931832	+	0.362889i	$0.118210\pi$
$947$			22.3346i			0.725778i	−0.931832	+	0.362889i	$0.881790\pi$
$948$		0			0
$949$	−37.2886	+	27.0918i	−1.21044	+	0.879437i
$950$	18.3240	−	25.2208i	0.594508	−	0.818269i
$951$		0			0
$952$	0.751336	−	0.244124i	0.0243509	−	0.00791210i
$953$	−34.8764	−	25.3392i	−1.12976	−	0.820817i	−0.144098	−	0.989563i	$-0.546028\pi$
$953$	−34.8764	−	25.3392i	−1.12976	−	0.820817i	−0.985659	+	0.168747i	$0.946028\pi$
$954$		0			0
$955$	16.5330	−	50.8834i	0.534996	−	1.64655i
$956$	18.2081			0.588891
$957$		0			0
$958$	12.1738			0.393318
$959$	2.87024	−	8.83368i	0.0926848	−	0.285254i
$960$		0			0
$961$	4.06175	+	2.95103i	0.131024	+	0.0951947i
$962$	9.82221	−	3.19143i	0.316681	−	0.102896i
$963$		0			0
$964$	15.1875	−	20.9038i	0.489157	−	0.673267i
$965$	−40.8595	+	29.6862i	−1.31532	+	0.955633i
$966$		0			0
$967$			36.7712i			1.18248i	0.806495	+	0.591240i	$0.201362\pi$
$967$			36.7712i			1.18248i	−0.806495	+	0.591240i	$0.798638\pi$
$968$	−6.80154	+	8.64518i	−0.218610	+	0.277866i
$969$		0			0
$970$	41.1234	+	13.3618i	1.32039	+	0.429022i
$971$	4.70413	+	6.47467i	0.150963	+	0.207782i	0.877800	−	0.479028i	$-0.159011\pi$
$971$	4.70413	+	6.47467i	0.150963	+	0.207782i	−0.726837	+	0.686810i	$0.759011\pi$
$972$		0			0
$973$	2.85280	+	8.78003i	0.0914567	+	0.281475i
$974$	−0.599799	−	1.84599i	−0.0192188	−	0.0591494i
$975$		0			0
$976$	8.61347	+	11.8554i	0.275710	+	0.379483i
$977$	−6.03302	−	1.96025i	−0.193013	−	0.0627138i	0.210915	−	0.977504i	$-0.432356\pi$
$977$	−6.03302	−	1.96025i	−0.193013	−	0.0627138i	−0.403929	+	0.914791i	$0.632356\pi$
$978$		0			0
$979$	−2.71905	+	0.377452i	−0.0869012	+	0.0120634i
$980$		−	3.47782i		−	0.111095i
$981$		0			0
$982$	13.2192	−	9.60431i	0.421842	−	0.306486i
$983$	−15.2039	+	20.9263i	−0.484928	+	0.667446i	−0.979443	−	0.201723i	$-0.935346\pi$
$983$	−15.2039	+	20.9263i	−0.484928	+	0.667446i	0.494515	+	0.869169i	$0.335346\pi$
$984$		0			0
$985$	61.8552	−	20.0980i	1.97087	−	0.640374i
$986$	3.90401	+	2.83643i	0.124329	+	0.0903304i
$987$		0			0
$988$	6.34319	−	19.5223i	0.201804	−	0.621088i
$989$	6.26329			0.199161
$990$		0			0
$991$	7.03781			0.223564			0.111782	−	0.993733i	$-0.464344\pi$
$991$	7.03781			0.223564			0.111782	+	0.993733i	$0.464344\pi$
$992$	−1.57506	+	4.84753i	−0.0500082	+	0.153909i
$993$		0			0
$994$	−1.97804	−	1.43713i	−0.0627397	−	0.0455830i
$995$	58.9545	−	19.1555i	1.86898	−	0.607269i
$996$		0			0
$997$	24.9296	−	34.3126i	0.789527	−	1.08669i	−0.204639	−	0.978837i	$-0.565602\pi$
$997$	24.9296	−	34.3126i	0.789527	−	1.08669i	0.994167	−	0.107854i	$-0.0343978\pi$
$998$	−31.9720	+	23.2290i	−1.01205	+	0.735301i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.b.827.2	yes	48
3.2	odd	2		1386.2.bu.a.827.11	✓	48
11.6	odd	10		1386.2.bu.a.1205.11	yes	48
33.17	even	10	inner	1386.2.bu.b.1205.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.827.11	✓	48	3.2	odd	2
1386.2.bu.a.1205.11	yes	48	11.6	odd	10
1386.2.bu.b.827.2	yes	48	1.1	even	1	trivial
1386.2.bu.b.1205.2	yes	48	33.17	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-3.30760 + 1.07471i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-3.30760 + 1.07471i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} -3.47782i q^{10} +(0.456033 + 3.28512i) q^{11} +(-4.44321 - 1.44369i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.244124 - 0.751336i) q^{17} +(-2.58258 - 3.55461i) q^{19} +(3.30760 + 1.07471i) q^{20} +(-3.26526 - 0.581446i) q^{22} +1.98632i q^{23} +(5.74016 - 4.17047i) q^{25} +(2.74606 - 3.77962i) q^{26} +(0.951057 - 0.309017i) q^{28} +(4.94178 + 3.59041i) q^{29} +(1.57506 - 4.84753i) q^{31} -1.00000 q^{32} +0.790002 q^{34} +(1.07471 - 3.30760i) q^{35} +(1.78842 + 1.29936i) q^{37} +(4.17869 - 1.35774i) q^{38} +(-2.04421 + 2.81361i) q^{40} +(-6.36613 + 4.62526i) q^{41} -3.15321i q^{43} +(1.56201 - 2.92577i) q^{44} +(-1.88910 - 0.613807i) q^{46} +(-2.53157 - 3.48440i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(2.19255 + 6.74796i) q^{50} +(2.74606 + 3.77962i) q^{52} +(-3.63873 - 1.18229i) q^{53} +(-5.03891 - 10.3758i) q^{55} +1.00000i q^{56} +(-4.94178 + 3.59041i) q^{58} +(7.54262 - 10.3815i) q^{59} +(13.9369 - 4.52837i) q^{61} +(4.12356 + 2.99594i) q^{62} +(0.309017 - 0.951057i) q^{64} +16.2479 q^{65} +15.2649 q^{67} +(-0.244124 + 0.751336i) q^{68} +(2.81361 + 2.04421i) q^{70} +(2.32533 - 0.755545i) q^{71} +(5.79892 - 7.98153i) q^{73} +(-1.78842 + 1.29936i) q^{74} +4.39374i q^{76} +(-2.92577 - 1.56201i) q^{77} +(-11.5847 - 3.76411i) q^{79} +(-2.04421 - 2.81361i) q^{80} +(-2.43165 - 7.48383i) q^{82} +(1.07209 + 3.29956i) q^{83} +(1.61493 + 2.22276i) q^{85} +(2.99888 + 0.974395i) q^{86} +(2.29989 + 2.38967i) q^{88} +0.827686i q^{89} +(3.77962 - 2.74606i) q^{91} +(1.16753 - 1.60697i) q^{92} +(4.09616 - 1.33092i) q^{94} +(12.3623 + 8.98173i) q^{95} +(-3.84201 + 11.8245i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more