LMFDB - Embedded newform 729.2.g.d.676.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			676.4
Character	$\chi$	$=$	729.676
Dual form			729.2.g.d.55.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0742143 + 0.172048i) q^{2} +(1.34839 - 1.42921i) q^{4} +(-0.0921050 + 1.58138i) q^{5} +(-3.93765 + 0.933240i) q^{7} +(0.698107 + 0.254090i) q^{8} +O(q^{10})$	\(q+(0.0742143 + 0.172048i) q^{2} +(1.34839 - 1.42921i) q^{4} +(-0.0921050 + 1.58138i) q^{5} +(-3.93765 + 0.933240i) q^{7} +(0.698107 + 0.254090i) q^{8} +(-0.278909 + 0.101515i) q^{10} +(3.21202 - 2.11258i) q^{11} +(1.58861 - 0.185682i) q^{13} +(-0.452792 - 0.608205i) q^{14} +(-0.220403 - 3.78417i) q^{16} +(5.79317 + 4.86105i) q^{17} +(1.26984 - 1.06552i) q^{19} +(2.13593 + 2.26396i) q^{20} +(0.601842 + 0.395838i) q^{22} +(6.23886 + 1.47864i) q^{23} +(2.47391 + 0.289158i) q^{25} +(0.149844 + 0.259538i) q^{26} +(-3.97569 + 6.88610i) q^{28} +(-0.163549 + 0.219684i) q^{29} +(0.530826 + 1.77308i) q^{31} +(1.96248 - 0.985594i) q^{32} +(-0.406398 + 1.35746i) q^{34} +(-1.11313 - 6.31289i) q^{35} +(-0.295248 + 1.67443i) q^{37} +(0.277561 + 0.139396i) q^{38} +(-0.466113 + 1.08057i) q^{40} +(1.18553 - 2.74838i) q^{41} +(-4.35056 - 2.18493i) q^{43} +(1.31174 - 7.43922i) q^{44} +(0.208616 + 1.18312i) q^{46} +(-0.0382623 + 0.127805i) q^{47} +(8.37873 - 4.20796i) q^{49} +(0.133850 + 0.447090i) q^{50} +(1.87669 - 2.52084i) q^{52} +(-4.93888 + 8.55438i) q^{53} +(3.04495 + 5.27400i) q^{55} +(-2.98603 - 0.349017i) q^{56} +(-0.0499339 - 0.0118346i) q^{58} +(-6.47138 - 4.25629i) q^{59} +(-2.83624 - 3.00624i) q^{61} +(-0.265660 + 0.222915i) q^{62} +(-5.49230 - 4.60858i) q^{64} +(0.147315 + 2.52931i) q^{65} +(-8.03004 - 10.7862i) q^{67} +(14.7589 - 1.72507i) q^{68} +(1.00351 - 0.660018i) q^{70} +(2.39924 - 0.873251i) q^{71} +(5.29149 + 1.92595i) q^{73} +(-0.309995 + 0.0734701i) q^{74} +(0.189384 - 3.25160i) q^{76} +(-10.6763 + 11.3162i) q^{77} +(3.20983 + 7.44121i) q^{79} +6.00452 q^{80} +0.560836 q^{82} +(2.17210 + 5.03548i) q^{83} +(-8.22075 + 8.71349i) q^{85} +(0.0530398 - 0.910658i) q^{86} +(2.77911 - 0.658662i) q^{88} +(-6.33932 - 2.30732i) q^{89} +(-6.08212 + 2.21371i) q^{91} +(10.5257 - 6.92286i) q^{92} +(-0.0248282 + 0.00290200i) q^{94} +(1.56804 + 2.10624i) q^{95} +(-0.108820 - 1.86837i) q^{97} +(1.34579 + 1.12925i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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 $

$2$	0.0742143	+	0.172048i	0.0524774	+	0.121656i	0.942438	−	0.334382i	$-0.108527\pi$
$2$	0.0742143	+	0.172048i	0.0524774	+	0.121656i	−0.889960	+	0.456038i	$0.849268\pi$
$3$		0			0
$3$		0			0
$4$	1.34839	−	1.42921i	0.674195	−	0.714605i
$5$	−0.0921050	+	1.58138i	−0.0411906	+	0.707215i	0.912990	+	0.407983i	$0.133768\pi$
$5$	−0.0921050	+	1.58138i	−0.0411906	+	0.707215i	−0.954180	+	0.299233i	$0.903269\pi$
$6$		0			0
$7$	−3.93765	+	0.933240i	−1.48829	+	0.352732i	−0.892735	−	0.450582i	$-0.851217\pi$
$7$	−3.93765	+	0.933240i	−1.48829	+	0.352732i	−0.595557	+	0.803313i	$0.703069\pi$
$8$	0.698107	+	0.254090i	0.246818	+	0.0898344i
$9$		0			0
$10$	−0.278909	+	0.101515i	−0.0881988	+	0.0321017i
$11$	3.21202	−	2.11258i	0.968459	−	0.636966i	0.0364251	−	0.999336i	$-0.488403\pi$
$11$	3.21202	−	2.11258i	0.968459	−	0.636966i	0.932034	+	0.362371i	$0.118033\pi$
$12$		0			0
$13$	1.58861	−	0.185682i	0.440602	−	0.0514990i	0.107100	−	0.994248i	$-0.465844\pi$
$13$	1.58861	−	0.185682i	0.440602	−	0.0514990i	0.333502	+	0.942749i	$0.391769\pi$
$14$	−0.452792	−	0.608205i	−0.121014	−	0.162550i
$15$		0			0
$16$	−0.220403	−	3.78417i	−0.0551007	−	0.946042i
$17$	5.79317	+	4.86105i	1.40505	+	1.17898i	0.958804	+	0.284067i	$0.0916838\pi$
$17$	5.79317	+	4.86105i	1.40505	+	1.17898i	0.446246	+	0.894910i	$0.352761\pi$
$18$		0			0
$19$	1.26984	−	1.06552i	0.291321	−	0.244447i	−0.485400	−	0.874292i	$-0.661326\pi$
$19$	1.26984	−	1.06552i	0.291321	−	0.244447i	0.776721	+	0.629845i	$0.216882\pi$
$20$	2.13593	+	2.26396i	0.477609	+	0.506236i
$21$		0			0
$22$	0.601842	+	0.395838i	0.128313	+	0.0843929i
$23$	6.23886	+	1.47864i	1.30089	+	0.308317i	0.821965	−	0.569538i	$-0.192878\pi$
$23$	6.23886	+	1.47864i	1.30089	+	0.308317i	0.478926	+	0.877855i	$0.341026\pi$
$24$		0			0
$25$	2.47391	+	0.289158i	0.494781	+	0.0578316i
$26$	0.149844	+	0.259538i	0.0293868	+	0.0508995i
$27$		0			0
$28$	−3.97569	+	6.88610i	−0.751336	+	1.30135i
$29$	−0.163549	+	0.219684i	−0.0303703	+	0.0407944i	−0.817049	−	0.576568i	$-0.804391\pi$
$29$	−0.163549	+	0.219684i	−0.0303703	+	0.0407944i	0.786679	+	0.617363i	$0.211799\pi$
$30$		0			0
$31$	0.530826	+	1.77308i	0.0953391	+	0.318455i	0.992334	−	0.123586i	$-0.0394396\pi$
$31$	0.530826	+	1.77308i	0.0953391	+	0.318455i	−0.896995	+	0.442041i	$0.854254\pi$
$32$	1.96248	−	0.985594i	0.346920	−	0.174230i
$33$		0			0
$34$	−0.406398	+	1.35746i	−0.0696966	+	0.232803i
$35$	−1.11313	−	6.31289i	−0.188154	−	1.06707i
$36$		0			0
$37$	−0.295248	+	1.67443i	−0.0485385	+	0.275275i	−0.999411	−	0.0343062i	$-0.989078\pi$
$37$	−0.295248	+	1.67443i	−0.0485385	+	0.275275i	0.950873	+	0.309582i	$0.100189\pi$
$38$	0.277561	+	0.139396i	0.0450263	+	0.0226131i
$39$		0			0
$40$	−0.466113	+	1.08057i	−0.0736989	+	0.170853i
$41$	1.18553	−	2.74838i	0.185149	−	0.429224i	−0.800209	−	0.599721i	$-0.795278\pi$
$41$	1.18553	−	2.74838i	0.185149	−	0.429224i	0.985358	+	0.170497i	$0.0545374\pi$
$42$		0			0
$43$	−4.35056	−	2.18493i	−0.663454	−	0.333199i	0.0850049	−	0.996381i	$-0.472909\pi$
$43$	−4.35056	−	2.18493i	−0.663454	−	0.333199i	−0.748459	+	0.663182i	$0.769206\pi$
$44$	1.31174	−	7.43922i	0.197752	−	1.12151i
$45$		0			0
$46$	0.208616	+	1.18312i	0.0307587	+	0.174441i
$47$	−0.0382623	+	0.127805i	−0.00558113	+	0.0186423i	−0.960735	−	0.277469i	$-0.910505\pi$
$47$	−0.0382623	+	0.127805i	−0.00558113	+	0.0186423i	0.955154	+	0.296111i	$0.0956898\pi$
$48$		0			0
$49$	8.37873	−	4.20796i	1.19696	−	0.601136i
$50$	0.133850	+	0.447090i	0.0189293	+	0.0632281i
$51$		0			0
$52$	1.87669	−	2.52084i	0.260250	−	0.349577i
$53$	−4.93888	+	8.55438i	−0.678407	+	1.17504i	0.297054	+	0.954861i	$0.403996\pi$
$53$	−4.93888	+	8.55438i	−0.678407	+	1.17504i	−0.975461	+	0.220174i	$0.929337\pi$
$54$		0			0
$55$	3.04495	+	5.27400i	0.410580	+	0.711146i
$56$	−2.98603	−	0.349017i	−0.399025	−	0.0466393i
$57$		0			0
$58$	−0.0499339	−	0.0118346i	−0.00655665	−	0.00155395i
$59$	−6.47138	−	4.25629i	−0.842501	−	0.554122i	0.0532989	−	0.998579i	$-0.483026\pi$
$59$	−6.47138	−	4.25629i	−0.842501	−	0.554122i	−0.895800	+	0.444457i	$0.853397\pi$
$60$		0			0
$61$	−2.83624	−	3.00624i	−0.363143	−	0.384909i	0.519879	−	0.854240i	$-0.325977\pi$
$61$	−2.83624	−	3.00624i	−0.363143	−	0.384909i	−0.883023	+	0.469330i	$0.844495\pi$
$62$	−0.265660	+	0.222915i	−0.0337389	+	0.0283103i
$63$		0			0
$64$	−5.49230	−	4.60858i	−0.686537	−	0.576073i
$65$	0.147315	+	2.52931i	0.0182722	+	0.313722i
$66$		0			0
$67$	−8.03004	−	10.7862i	−0.981026	−	1.31775i	−0.947993	−	0.318292i	$-0.896891\pi$
$67$	−8.03004	−	10.7862i	−0.981026	−	1.31775i	−0.0330332	−	0.999454i	$-0.510517\pi$
$68$	14.7589	−	1.72507i	1.78978	−	0.209195i
$69$		0			0
$70$	1.00351	−	0.660018i	0.119942	−	0.0788873i
$71$	2.39924	−	0.873251i	0.284737	−	0.103636i	−0.195703	−	0.980663i	$-0.562699\pi$
$71$	2.39924	−	0.873251i	0.284737	−	0.103636i	0.480441	+	0.877027i	$0.340477\pi$
$72$		0			0
$73$	5.29149	+	1.92595i	0.619322	+	0.225415i	0.632577	−	0.774497i	$-0.281997\pi$
$73$	5.29149	+	1.92595i	0.619322	+	0.225415i	−0.0132549	+	0.999912i	$0.504219\pi$
$74$	−0.309995	+	0.0734701i	−0.0360362	+	0.00854073i
$75$		0			0
$76$	0.189384	−	3.25160i	0.0217239	−	0.372985i
$77$	−10.6763	+	11.3162i	−1.21667	+	1.28960i
$78$		0			0
$79$	3.20983	+	7.44121i	0.361134	+	0.837202i	0.997815	+	0.0660746i	$0.0210475\pi$
$79$	3.20983	+	7.44121i	0.361134	+	0.837202i	−0.636681	+	0.771127i	$0.719693\pi$
$80$	6.00452			0.671325
$81$		0			0
$82$	0.560836			0.0619340
$83$	2.17210	+	5.03548i	0.238418	+	0.552716i	0.994850	−	0.101357i	$-0.0323183\pi$
$83$	2.17210	+	5.03548i	0.238418	+	0.552716i	−0.756432	+	0.654073i	$0.773059\pi$
$84$		0			0
$85$	−8.22075	+	8.71349i	−0.891666	+	0.945111i
$86$	0.0530398	−	0.910658i	0.00571942	−	0.0981987i
$87$		0			0
$88$	2.77911	−	0.658662i	0.296255	−	0.0702136i
$89$	−6.33932	−	2.30732i	−0.671966	−	0.244576i	−0.0165720	−	0.999863i	$-0.505275\pi$
$89$	−6.33932	−	2.30732i	−0.671966	−	0.244576i	−0.655394	+	0.755287i	$0.727497\pi$
$90$		0			0
$91$	−6.08212	+	2.21371i	−0.637580	+	0.232060i
$92$	10.5257	−	6.92286i	1.09738	−	0.721758i
$93$		0			0
$94$	−0.0248282	+	0.00290200i	−0.00256083	+	0.000299319i
$95$	1.56804	+	2.10624i	0.160877	+	0.216096i
$96$		0			0
$97$	−0.108820	−	1.86837i	−0.0110490	−	0.189704i	−0.999316	−	0.0369704i	$-0.988229\pi$
$97$	−0.108820	−	1.86837i	−0.0110490	−	0.189704i	0.988267	−	0.152734i	$-0.0488078\pi$
$98$	1.34579	+	1.12925i	0.135945	+	0.114072i
$99$		0			0
$100$	3.74906	−	3.14584i	0.374906	−	0.314584i
$101$	11.4483	+	12.1345i	1.13915	+	1.20743i	0.975286	+	0.220944i	$0.0709139\pi$
$101$	11.4483	+	12.1345i	1.13915	+	1.20743i	0.163863	+	0.986483i	$0.447605\pi$
$102$		0			0
$103$	4.80896	+	3.16291i	0.473841	+	0.311650i	0.763873	−	0.645367i	$-0.223295\pi$
$103$	4.80896	+	3.16291i	0.473841	+	0.311650i	−0.290032	+	0.957017i	$0.593666\pi$
$104$	1.15620	+	0.274025i	0.113375	+	0.0268704i
$105$		0			0
$106$	−1.83830	−	0.214866i	−0.178551	−	0.0208697i
$107$	0.810593	+	1.40399i	0.0783630	+	0.135729i	0.902544	−	0.430598i	$-0.141697\pi$
$107$	0.810593	+	1.40399i	0.0783630	+	0.135729i	−0.824181	+	0.566327i	$0.808364\pi$
$108$		0			0
$109$	5.75519	−	9.96829i	0.551248	−	0.954789i	−0.446937	−	0.894565i	$-0.647485\pi$
$109$	5.75519	−	9.96829i	0.551248	−	0.954789i	0.998185	−	0.0602237i	$-0.0191814\pi$
$110$	−0.681403	+	0.915283i	−0.0649692	+	0.0872688i
$111$		0			0
$112$	4.39941	+	14.6951i	0.415705	+	1.38855i
$113$	−7.80192	+	3.91827i	−0.733943	+	0.368600i	−0.776183	−	0.630508i	$-0.782847\pi$
$113$	−7.80192	+	3.91827i	−0.733943	+	0.368600i	0.0422404	+	0.999107i	$0.486550\pi$
$114$		0			0
$115$	−2.91292	+	9.72982i	−0.271631	+	0.907311i
$116$	0.0934474	+	0.529966i	0.00867637	+	0.0492061i
$117$		0			0
$118$	0.252018	−	1.42926i	0.0232001	−	0.131575i
$119$	−27.3480	−	13.7347i	−2.50699	−	1.25906i
$120$		0			0
$121$	1.49719	−	3.47088i	0.136108	−	0.315534i
$122$	0.306728	−	0.711075i	0.0277698	−	0.0643777i
$123$		0			0
$124$	3.24987	+	1.63214i	0.291847	+	0.146571i
$125$	−2.06048	+	11.6855i	−0.184295	+	1.04519i
$126$		0			0
$127$	−3.29466	−	18.6850i	−0.292354	−	1.65802i	−0.677766	−	0.735278i	$-0.737052\pi$
$127$	−3.29466	−	18.6850i	−0.292354	−	1.65802i	0.385411	−	0.922745i	$-0.374060\pi$
$128$	1.64497	−	5.49458i	0.145396	−	0.485657i
$129$		0			0
$130$	−0.424229	+	0.213056i	−0.0372074	+	0.0186863i
$131$	−1.73595	−	5.79846i	−0.151670	−	0.506614i	0.848058	−	0.529903i	$-0.177772\pi$
$131$	−1.73595	−	5.79846i	−0.151670	−	0.506614i	−0.999729	+	0.0232885i	$0.992586\pi$
$132$		0			0
$133$	−4.00579	+	5.38071i	−0.347346	+	0.466567i
$134$	1.25980	−	2.18204i	0.108830	−	0.188500i
$135$		0			0
$136$	2.80911	+	4.86552i	0.240879	+	0.417215i
$137$	−22.0876	−	2.58167i	−1.88707	−	0.220567i	−0.907271	−	0.420547i	$-0.861838\pi$
$137$	−22.0876	−	2.58167i	−1.88707	−	0.220567i	−0.979800	+	0.199980i	$0.935912\pi$
$138$		0			0
$139$	−12.3791	−	2.93391i	−1.04998	−	0.248851i	−0.330822	−	0.943693i	$-0.607326\pi$
$139$	−12.3791	−	2.93391i	−1.04998	−	0.248851i	−0.719162	+	0.694843i	$0.755474\pi$
$140$	−10.5234	−	6.92133i	−0.889388	−	0.584960i
$141$		0			0
$142$	0.328299	+	0.347977i	0.0275502	+	0.0292015i
$143$	4.71039	−	3.95248i	0.393902	−	0.330523i
$144$		0			0
$145$	−0.332341	−	0.278867i	−0.0275994	−	0.0231587i
$146$	0.0613491	+	1.05332i	0.00507729	+	0.0871737i
$147$		0			0
$148$	1.99501	+	2.67976i	0.163989	+	0.220275i
$149$	−9.73145	+	1.13744i	−0.797231	+	0.0931830i	−0.504949	−	0.863149i	$-0.668489\pi$
$149$	−9.73145	+	1.13744i	−0.797231	+	0.0931830i	−0.292282	+	0.956332i	$0.594415\pi$
$150$		0			0
$151$	7.95586	−	5.23265i	0.647439	−	0.425827i	−0.182865	−	0.983138i	$-0.558537\pi$
$151$	7.95586	−	5.23265i	0.647439	−	0.425827i	0.830304	+	0.557311i	$0.188167\pi$
$152$	1.15722	−	0.421194i	0.0938630	−	0.0341633i
$153$		0			0
$154$	−2.73925	−	0.997007i	−0.220735	−	0.0803411i
$155$	−2.85281	+	0.676128i	−0.229143	+	0.0543079i
$156$		0			0
$157$	−0.431930	+	7.41595i	−0.0344718	+	0.591857i	0.936203	+	0.351460i	$0.114315\pi$
$157$	−0.431930	+	7.41595i	−0.0344718	+	0.591857i	−0.970675	+	0.240397i	$0.922722\pi$
$158$	−1.04203	+	1.10449i	−0.0828995	+	0.0878684i
$159$		0			0
$160$	1.37785	+	3.19421i	0.108928	+	0.252524i
$161$	−25.9464			−2.04486
$162$		0			0
$163$	4.98806			0.390695			0.195347	−	0.980734i	$-0.437417\pi$
$163$	4.98806			0.390695			0.195347	+	0.980734i	$0.437417\pi$
$164$	−2.32945	−	5.40026i	−0.181899	−	0.421690i
$165$		0			0
$166$	−0.705144	+	0.747409i	−0.0547298	+	0.0580102i
$167$	0.253555	−	4.35337i	0.0196207	−	0.336874i	−0.974186	−	0.225748i	$-0.927517\pi$
$167$	0.253555	−	4.35337i	0.0196207	−	0.336874i	0.993806	−	0.111126i	$-0.0354457\pi$
$168$		0			0
$169$	−10.1604	+	2.40805i	−0.781567	+	0.185235i
$170$	−2.10924	−	0.767699i	−0.161771	−	0.0588798i
$171$		0			0
$172$	−8.98898	+	3.27172i	−0.685403	+	0.249466i
$173$	13.4039	−	8.81588i	1.01908	−	0.670259i	0.0740530	−	0.997254i	$-0.476407\pi$
$173$	13.4039	−	8.81588i	1.01908	−	0.670259i	0.945026	+	0.326996i	$0.106036\pi$
$174$		0			0
$175$	−10.0112	+	1.17015i	−0.756778	+	0.0884547i
$176$	−8.70228	−	11.6892i	−0.655959	−	0.881106i
$177$		0			0
$178$	−0.0734975	−	1.26190i	−0.00550887	−	0.0945836i
$179$	−14.7729	−	12.3960i	−1.10418	−	0.926518i	−0.106483	−	0.994315i	$-0.533959\pi$
$179$	−14.7729	−	12.3960i	−1.10418	−	0.926518i	−0.997699	+	0.0677961i	$0.978403\pi$
$180$		0			0
$181$	0.116035	−	0.0973645i	0.00862478	−	0.00723705i	−0.638465	−	0.769651i	$-0.720430\pi$
$181$	0.116035	−	0.0973645i	0.00862478	−	0.00723705i	0.647090	+	0.762414i	$0.275986\pi$
$182$	−0.832245	−	0.882128i	−0.0616901	−	0.0653877i
$183$		0			0
$184$	3.97968	+	2.61748i	0.293386	+	0.192963i
$185$	−2.62073	−	0.621124i	−0.192680	−	0.0456659i
$186$		0			0
$187$	28.8771	+	3.37525i	2.11170	+	0.246823i
$188$	0.131068	+	0.227016i	0.00955910	+	0.0165568i
$189$		0			0
$190$	−0.246003	+	0.426090i	−0.0178470	+	0.0309119i
$191$	−6.39393	+	8.58854i	−0.462649	+	0.621445i	−0.970820	−	0.239811i	$-0.922914\pi$
$191$	−6.39393	+	8.58854i	−0.462649	+	0.621445i	0.508171	+	0.861256i	$0.330322\pi$
$192$		0			0
$193$	−4.55179	−	15.2040i	−0.327645	−	1.09441i	−0.950150	−	0.311794i	$-0.899070\pi$
$193$	−4.55179	−	15.2040i	−0.327645	−	1.09441i	0.622505	−	0.782616i	$-0.286115\pi$
$194$	0.313374	−	0.157382i	0.0224989	−	0.0112994i
$195$		0			0
$196$	5.28374	−	17.6489i	0.377410	−	1.26064i
$197$	−0.213838	−	1.21273i	−0.0152353	−	0.0864037i	0.976242	−	0.216683i	$-0.0695238\pi$
$197$	−0.213838	−	1.21273i	−0.0152353	−	0.0864037i	−0.991477	+	0.130279i	$0.958413\pi$
$198$		0			0
$199$	0.406772	−	2.30692i	0.0288353	−	0.163533i	−0.966990	−	0.254815i	$-0.917985\pi$
$199$	0.406772	−	2.30692i	0.0288353	−	0.163533i	0.995825	+	0.0912821i	$0.0290965\pi$
$200$	1.65358	+	0.830459i	0.116926	+	0.0587223i
$201$		0			0
$202$	−1.23809	+	2.87021i	−0.0871116	+	0.201947i
$203$	0.438980	−	1.01767i	0.0308104	−	0.0714265i
$204$		0			0
$205$	4.23704	+	2.12792i	0.295928	+	0.148620i
$206$	−0.187278	+	1.06211i	−0.0130483	+	0.0740004i
$207$		0			0
$208$	−1.05279	−	5.97066i	−0.0729978	−	0.413991i
$209$	1.82775	−	6.10510i	0.126428	−	0.422298i
$210$		0			0
$211$	−10.1780	+	5.11157i	−0.700681	+	0.351895i	−0.763212	−	0.646148i	$-0.776379\pi$
$211$	−10.1780	+	5.11157i	−0.700681	+	0.351895i	0.0625316	+	0.998043i	$0.480083\pi$
$212$	5.56648	+	18.5933i	0.382308	+	1.27700i
$213$		0			0
$214$	−0.181396	+	0.243657i	−0.0124000	+	0.0166560i
$215$	3.85592	−	6.67865i	0.262971	−	0.455480i
$216$		0			0
$217$	−3.74492	−	6.48639i	−0.254222	−	0.440325i
$218$	2.14214	+	0.250380i	0.145084	+	0.0169579i
$219$		0			0
$220$	11.6434	+	2.75954i	0.785000	+	0.186048i
$221$	10.1057	+	6.64664i	0.679785	+	0.447101i
$222$		0			0
$223$	10.3801	+	11.0023i	0.695106	+	0.736770i	0.974741	−	0.223337i	$-0.0716950\pi$
$223$	10.3801	+	11.0023i	0.695106	+	0.736770i	−0.279635	+	0.960106i	$0.590213\pi$
$224$	−6.80776	+	5.71239i	−0.454863	+	0.381675i
$225$		0			0
$226$	−1.25314	−	1.05151i	−0.0833579	−	0.0699456i
$227$	1.23726	+	21.2429i	0.0821198	+	1.40994i	0.747908	+	0.663802i	$0.231058\pi$
$227$	1.23726	+	21.2429i	0.0821198	+	1.40994i	−0.665789	+	0.746140i	$0.731905\pi$
$228$		0			0
$229$	2.33003	+	3.12978i	0.153973	+	0.206822i	0.872416	−	0.488764i	$-0.162552\pi$
$229$	2.33003	+	3.12978i	0.153973	+	0.206822i	−0.718443	+	0.695586i	$0.755145\pi$
$230$	−1.89018	+	0.220930i	−0.124635	+	0.0145677i
$231$		0			0
$232$	−0.169994	+	0.111807i	−0.0111607	+	0.00734049i
$233$	18.1958	−	6.62273i	1.19205	−	0.433869i	0.331604	−	0.943419i	$-0.392410\pi$
$233$	18.1958	−	6.62273i	1.19205	−	0.433869i	0.860441	+	0.509549i	$0.170188\pi$
$234$		0			0
$235$	−0.198584	−	0.0722788i	−0.0129542	−	0.00471495i
$236$	−14.8091	+	3.50982i	−0.963989	+	0.228470i
$237$		0			0
$238$	0.333413	−	5.72448i	0.0216120	−	0.371063i
$239$	9.74423	−	10.3283i	0.630302	−	0.668081i	−0.330983	−	0.943637i	$-0.607380\pi$
$239$	9.74423	−	10.3283i	0.630302	−	0.668081i	0.961285	+	0.275556i	$0.0888619\pi$
$240$		0			0
$241$	−4.42332	−	10.2544i	−0.284931	−	0.660544i	0.714297	−	0.699843i	$-0.246747\pi$
$241$	−4.42332	−	10.2544i	−0.284931	−	0.660544i	−0.999227	+	0.0392991i	$0.987487\pi$
$242$	0.708270			0.0455293
$243$		0			0
$244$	−8.12090			−0.519888
$245$	5.88266	+	13.6375i	0.375829	+	0.871271i
$246$		0			0
$247$	1.81943	−	1.92849i	0.115768	−	0.122707i
$248$	−0.0799494	+	1.37268i	−0.00507679	+	0.0871651i
$249$		0			0
$250$	−2.16339	+	0.512733i	−0.136825	+	0.0324281i
$251$	−8.61554	−	3.13580i	−0.543808	−	0.197930i	0.0554853	−	0.998460i	$-0.482329\pi$
$251$	−8.61554	−	3.13580i	−0.543808	−	0.197930i	−0.599293	+	0.800530i	$0.704552\pi$
$252$		0			0
$253$	23.1630	−	8.43066i	1.45625	−	0.530031i
$254$	2.97020	−	1.95353i	0.186367	−	0.122575i
$255$		0			0
$256$	−13.1750	+	1.53994i	−0.823437	+	0.0962460i
$257$	10.3133	+	13.8532i	0.643328	+	0.864139i	0.997473	−	0.0710513i	$-0.0226354\pi$
$257$	10.3133	+	13.8532i	0.643328	+	0.864139i	−0.354145	+	0.935191i	$0.615228\pi$
$258$		0			0
$259$	−0.400066	−	6.86888i	−0.0248589	−	0.426811i
$260$	3.81355	+	3.19995i	0.236506	+	0.198452i
$261$		0			0
$262$	0.868782	−	0.728995i	0.0536735	−	0.0450375i
$263$	3.22173	+	3.41483i	0.198660	+	0.210568i	0.819044	−	0.573731i	$-0.194505\pi$
$263$	3.22173	+	3.41483i	0.198660	+	0.210568i	−0.620384	+	0.784299i	$0.713023\pi$
$264$		0			0
$265$	−13.0729	−	8.59815i	−0.803059	−	0.528180i
$266$	−1.22303	−	0.289863i	−0.0749886	−	0.0177726i
$267$		0			0
$268$	−26.2434	−	3.06741i	−1.60307	−	0.187372i
$269$	6.52546	+	11.3024i	0.397864	+	0.689121i	0.993462	−	0.114162i	$-0.0364182\pi$
$269$	6.52546	+	11.3024i	0.397864	+	0.689121i	−0.595598	+	0.803283i	$0.703085\pi$
$270$		0			0
$271$	−11.8170	+	20.4676i	−0.717832	+	1.24332i	0.244026	+	0.969769i	$0.421532\pi$
$271$	−11.8170	+	20.4676i	−0.717832	+	1.24332i	−0.961857	+	0.273552i	$0.911801\pi$
$272$	17.1182	−	22.9937i	1.03794	−	1.39420i
$273$		0			0
$274$	−1.19504	−	3.99172i	−0.0721952	−	0.241149i
$275$	8.55710	−	4.29753i	0.516012	−	0.259151i
$276$		0			0
$277$	−6.82482	+	22.7965i	−0.410064	+	1.36971i	0.464833	+	0.885398i	$0.346114\pi$
$277$	−6.82482	+	22.7965i	−0.410064	+	1.36971i	−0.874897	+	0.484310i	$0.839071\pi$
$278$	−0.413935	−	2.34754i	−0.0248262	−	0.140796i
$279$		0			0
$280$	0.826957	−	4.68990i	0.0494201	−	0.280275i
$281$	−12.3376	−	6.19616i	−0.735997	−	0.369632i	0.0409803	−	0.999160i	$-0.486952\pi$
$281$	−12.3376	−	6.19616i	−0.735997	−	0.369632i	−0.776978	+	0.629528i	$0.783248\pi$
$282$		0			0
$283$	5.81388	−	13.4781i	0.345599	−	0.801189i	−0.653424	−	0.756992i	$-0.726668\pi$
$283$	5.81388	−	13.4781i	0.345599	−	0.801189i	0.999023	−	0.0441964i	$-0.0140727\pi$
$284$	1.98705	−	4.60650i	0.117910	−	0.273346i
$285$		0			0
$286$	1.02959	+	0.517082i	0.0608812	+	0.0305757i
$287$	−2.10332	+	11.9285i	−0.124155	+	0.704119i
$288$		0			0
$289$	6.97903	+	39.5800i	0.410531	+	2.32824i
$290$	0.0233141	−	0.0778746i	0.00136905	−	0.00457295i
$291$		0			0
$292$	9.88758	−	4.96573i	0.578627	−	0.290597i
$293$	−1.11671	−	3.73009i	−0.0652392	−	0.217914i	0.919154	−	0.393899i	$-0.128874\pi$
$293$	−1.11671	−	3.73009i	−0.0652392	−	0.217914i	−0.984393	+	0.175985i	$0.943689\pi$
$294$		0			0
$295$	7.32687	−	9.84169i	0.426587	−	0.573005i
$296$	−0.631572	+	1.09391i	−0.0367094	+	0.0635825i
$297$		0			0
$298$	−0.917907	−	1.58986i	−0.0531729	−	0.0920982i
$299$	10.1857	+	1.19054i	0.589054	+	0.0688505i
$300$		0			0
$301$	19.1700	+	4.54338i	1.10494	+	0.261876i
$302$	1.49071	+	0.980453i	0.0857805	+	0.0564187i
$303$		0			0
$304$	−4.31199	−	4.57044i	−0.247309	−	0.262133i
$305$	5.01524	−	4.20829i	0.287172	−	0.240966i
$306$		0			0
$307$	−0.636621	−	0.534188i	−0.0363339	−	0.0304877i	0.624440	−	0.781073i	$-0.285327\pi$
$307$	−0.636621	−	0.534188i	−0.0363339	−	0.0304877i	−0.660774	+	0.750585i	$0.729772\pi$
$308$	1.77743	+	30.5172i	0.101278	+	1.73888i
$309$		0			0
$310$	−0.328046	−	0.440642i	−0.0186317	−	0.0250268i
$311$	−10.9127	+	1.27552i	−0.618805	+	0.0723279i	−0.419719	−	0.907654i	$-0.637871\pi$
$311$	−10.9127	+	1.27552i	−0.618805	+	0.0723279i	−0.199086	+	0.979982i	$0.563797\pi$
$312$		0			0
$313$	−14.4466	+	9.50167i	−0.816570	+	0.537066i	−0.887712	−	0.460400i	$-0.847706\pi$
$313$	−14.4466	+	9.50167i	−0.816570	+	0.537066i	0.0711419	+	0.997466i	$0.477336\pi$
$314$	−1.30795	+	0.476057i	−0.0738121	+	0.0268654i
$315$		0			0
$316$	14.9632	+	5.44614i	0.841743	+	0.306370i
$317$	−17.7179	+	4.19923i	−0.995138	+	0.235852i	−0.695754	−	0.718281i	$-0.744929\pi$
$317$	−17.7179	+	4.19923i	−0.995138	+	0.235852i	−0.299384	+	0.954133i	$0.596781\pi$
$318$		0			0
$319$	−0.0612219	+	1.05114i	−0.00342777	+	0.0588525i
$320$	7.79380	−	8.26094i	0.435687	−	0.461801i
$321$		0			0
$322$	−1.92559	−	4.46402i	−0.107309	−	0.248770i
$323$	12.5359			0.697518
$324$		0			0
$325$	3.98377			0.220980
$326$	0.370185	+	0.858185i	0.0205026	+	0.0475305i
$327$		0			0
$328$	1.52596	−	1.61743i	0.0842573	−	0.0893075i
$329$	0.0313908	−	0.538959i	0.00173063	−	0.0297138i
$330$		0			0
$331$	17.5916	−	4.16929i	0.966923	−	0.229165i	0.283325	−	0.959024i	$-0.408562\pi$
$331$	17.5916	−	4.16929i	0.966923	−	0.229165i	0.683598	+	0.729859i	$0.260414\pi$
$332$	10.1256	+	3.68542i	0.555714	+	0.202263i
$333$		0			0
$334$	0.767807	−	0.279459i	0.0420125	−	0.0152913i
$335$	17.7967	−	11.7051i	0.972340	−	0.639518i
$336$		0			0
$337$	20.8508	−	2.43711i	1.13582	−	0.132758i	0.472664	−	0.881243i	$-0.343292\pi$
$337$	20.8508	−	2.43711i	1.13582	−	0.132758i	0.663152	+	0.748485i	$0.269218\pi$
$338$	−1.16834	−	1.56936i	−0.0635496	−	0.0853619i
$339$		0			0
$340$	1.36862	+	23.4984i	0.0742241	+	1.27438i
$341$	5.45079	+	4.57376i	0.295177	+	0.247683i
$342$		0			0
$343$	−7.36564	+	6.18050i	−0.397707	+	0.333716i
$344$	−2.48198	−	2.63075i	−0.133820	−	0.141840i
$345$		0			0
$346$	2.51151	+	1.65185i	0.135020	+	0.0888039i
$347$	−19.8413	−	4.70248i	−1.06514	−	0.252443i	−0.339562	−	0.940584i	$-0.610279\pi$
$347$	−19.8413	−	4.70248i	−1.06514	−	0.252443i	−0.725577	+	0.688141i	$0.758427\pi$
$348$		0			0
$349$	−17.5899	−	2.05597i	−0.941567	−	0.110053i	−0.368560	−	0.929604i	$-0.620149\pi$
$349$	−17.5899	−	2.05597i	−0.941567	−	0.110053i	−0.573007	+	0.819550i	$0.694223\pi$
$350$	−0.944298	−	1.63557i	−0.0504748	−	0.0874250i
$351$		0			0
$352$	4.22137	−	7.31163i	0.225000	−	0.389711i
$353$	12.4103	−	16.6700i	0.660535	−	0.887252i	−0.338012	−	0.941142i	$-0.609755\pi$
$353$	12.4103	−	16.6700i	0.660535	−	0.887252i	0.998547	+	0.0538897i	$0.0171620\pi$
$354$		0			0
$355$	1.15996	+	3.87454i	0.0615644	+	0.205639i
$356$	−11.8455	+	5.94905i	−0.627811	+	0.315299i
$357$		0			0
$358$	1.03634	−	3.46161i	0.0547722	−	0.182952i
$359$	3.40920	+	19.3346i	0.179931	+	1.02044i	0.932297	+	0.361693i	$0.117801\pi$
$359$	3.40920	+	19.3346i	0.179931	+	1.02044i	−0.752366	+	0.658745i	$0.771088\pi$
$360$		0			0
$361$	−2.82216	+	16.0053i	−0.148535	+	0.842383i
$362$	0.0253628	+	0.0127377i	0.00133304	+	0.000669477i
$363$		0			0
$364$	−5.03722	+	11.6776i	−0.264022	+	0.612071i
$365$	−3.53303	+	8.19048i	−0.184927	+	0.428709i
$366$		0			0
$367$	−29.1383	−	14.6338i	−1.52101	−	0.763878i	−0.524828	−	0.851209i	$-0.675870\pi$
$367$	−29.1383	−	14.6338i	−1.52101	−	0.763878i	−0.996179	+	0.0873300i	$0.972167\pi$
$368$	4.22035	−	23.9348i	0.220001	−	1.24769i
$369$		0			0
$370$	−0.0876322	−	0.496987i	−0.00455578	−	0.0258371i
$371$	11.4643	−	38.2933i	0.595195	−	1.98809i
$372$		0			0
$373$	−15.8648	+	7.96762i	−0.821450	+	0.412548i	−0.809312	−	0.587379i	$-0.800160\pi$
$373$	−15.8648	+	7.96762i	−0.821450	+	0.412548i	−0.0121379	+	0.999926i	$0.503864\pi$
$374$	1.56239	+	5.21874i	0.0807891	+	0.269854i
$375$		0			0
$376$	−0.0591852	+	0.0794995i	−0.00305224	+	0.00409987i
$377$	−0.219025	+	0.379362i	−0.0112803	+	0.0195381i
$378$		0			0
$379$	−13.5735	−	23.5099i	−0.697222	−	1.20762i	−0.969426	−	0.245384i	$-0.921086\pi$
$379$	−13.5735	−	23.5099i	−0.697222	−	1.20762i	0.272204	−	0.962240i	$-0.412247\pi$
$380$	5.12458	+	0.598978i	0.262886	+	0.0307269i
$381$		0			0
$382$	−1.95216	−	0.462671i	−0.0998814	−	0.0236723i
$383$	29.7103	+	19.5408i	1.51813	+	0.998488i	0.988662	+	0.150156i	$0.0479775\pi$
$383$	29.7103	+	19.5408i	1.51813	+	0.998488i	0.529465	+	0.848332i	$0.322393\pi$
$384$		0			0
$385$	−16.9118	−	17.9255i	−0.861908	−	0.913569i
$386$	2.27802	−	1.91148i	0.115948	−	0.0972919i
$387$		0			0
$388$	−2.81703	−	2.36377i	−0.143013	−	0.120002i
$389$	1.18310	+	20.3130i	0.0599855	+	1.02991i	0.885236	+	0.465143i	$0.153997\pi$
$389$	1.18310	+	20.3130i	0.0599855	+	1.02991i	−0.825250	+	0.564768i	$0.808966\pi$
$390$		0			0
$391$	28.9550	+	38.8934i	1.46432	+	1.96692i
$392$	6.91845	−	0.808650i	0.349434	−	0.0408430i
$393$		0			0
$394$	0.192779	−	0.126793i	0.00971205	−	0.00638771i
$395$	−12.0630	+	4.39059i	−0.606957	+	0.220914i
$396$		0			0
$397$	−24.9491	−	9.08072i	−1.25216	−	0.455748i	−0.371028	−	0.928622i	$-0.620995\pi$
$397$	−24.9491	−	9.08072i	−1.25216	−	0.455748i	−0.881130	+	0.472874i	$0.843217\pi$
$398$	0.427089	−	0.101222i	0.0214080	−	0.00507380i
$399$		0			0
$400$	0.548968	−	9.42541i	0.0274484	−	0.471271i
$401$	17.6522	−	18.7102i	0.881508	−	0.934344i	−0.116761	−	0.993160i	$-0.537251\pi$
$401$	17.6522	−	18.7102i	0.881508	−	0.934344i	0.998269	+	0.0588160i	$0.0187325\pi$
$402$		0			0
$403$	1.17251	+	2.71818i	0.0584067	+	0.135402i
$404$	32.7795			1.63084
$405$		0			0
$406$	0.207667			0.0103063
$407$	2.58903	+	6.00204i	0.128333	+	0.297510i
$408$		0			0
$409$	19.1127	−	20.2582i	0.945060	−	1.00170i	−0.0549349	−	0.998490i	$-0.517495\pi$
$409$	19.1127	−	20.2582i	0.945060	−	1.00170i	0.999995	−	0.00321505i	$-0.00102338\pi$
$410$	−0.0516558	+	0.886896i	−0.00255110	+	0.0438007i
$411$		0			0
$412$	11.0048	−	2.60819i	0.542169	−	0.128496i
$413$	29.4542	+	10.7204i	1.44934	+	0.527518i
$414$		0			0
$415$	−8.16308	+	2.97112i	−0.400710	+	0.145846i
$416$	2.93461	−	1.93013i	0.143881	−	0.0946322i
$417$		0			0
$418$	1.18601	−	0.138625i	0.0580099	−	0.00678038i
$419$	0.643757	+	0.864716i	0.0314496	+	0.0422441i	0.817570	−	0.575829i	$-0.195321\pi$
$419$	0.643757	+	0.864716i	0.0314496	+	0.0422441i	−0.786120	+	0.618074i	$0.787913\pi$
$420$		0			0
$421$	−0.456887	−	7.84445i	−0.0222673	−	0.382315i	−0.990969	−	0.134089i	$-0.957189\pi$
$421$	−0.456887	−	7.84445i	−0.0222673	−	0.382315i	0.968702	−	0.248226i	$-0.0798477\pi$
$422$	−1.63479	−	1.37175i	−0.0795801	−	0.0667757i
$423$		0			0
$424$	−5.62145	+	4.71695i	−0.273002	+	0.229076i
$425$	12.9262	+	13.7009i	0.627011	+	0.664592i
$426$		0			0
$427$	13.9737	+	9.19062i	0.676233	+	0.444765i
$428$	3.09959	+	0.734617i	0.149824	+	0.0355090i
$429$		0			0
$430$	1.43521	+	0.167752i	0.0692121	+	0.00808973i
$431$	−13.8447	−	23.9798i	−0.666877	−	1.15507i	−0.978773	−	0.204949i	$-0.934297\pi$
$431$	−13.8447	−	23.9798i	−0.666877	−	1.15507i	0.311895	−	0.950116i	$-0.399036\pi$
$432$		0			0
$433$	9.89513	−	17.1389i	0.475530	−	0.823642i	−0.524077	−	0.851671i	$-0.675590\pi$
$433$	9.89513	−	17.1389i	0.475530	−	0.823642i	0.999607	+	0.0280289i	$0.00892305\pi$
$434$	0.838044	−	1.12569i	0.0402274	−	0.0540348i
$435$		0			0
$436$	−6.48653	−	21.6665i	−0.310649	−	1.03764i
$437$	9.49785	−	4.77000i	0.454344	−	0.228180i
$438$		0			0
$439$	9.64837	−	32.2278i	0.460492	−	1.53815i	−0.340953	−	0.940080i	$-0.610750\pi$
$439$	9.64837	−	32.2278i	0.460492	−	1.53815i	0.801445	−	0.598069i	$-0.204065\pi$
$440$	0.785626	+	4.45551i	0.0374533	+	0.212408i
$441$		0			0
$442$	−0.393552	+	2.23195i	−0.0187194	+	0.106163i
$443$	−14.1788	−	7.12086i	−0.673655	−	0.338322i	0.0788709	−	0.996885i	$-0.474868\pi$
$443$	−14.1788	−	7.12086i	−0.673655	−	0.338322i	−0.752526	+	0.658563i	$0.771165\pi$
$444$		0			0
$445$	4.23264	−	9.81236i	0.200646	−	0.465151i
$446$	−1.12257	+	2.60241i	−0.0531553	+	0.123228i
$447$		0			0
$448$	25.9277	+	13.0214i	1.22497	+	0.615202i
$449$	0.153072	−	0.868114i	0.00722391	−	0.0409688i	−0.980983	−	0.194095i	$-0.937823\pi$
$449$	0.153072	−	0.868114i	0.00722391	−	0.0409688i	0.988207	+	0.153126i	$0.0489341\pi$
$450$		0			0
$451$	−1.99820	−	11.3324i	−0.0940916	−	0.533620i
$452$	−4.92000	+	16.4339i	−0.231417	+	0.772988i
$453$		0			0
$454$	−3.56298	+	1.78940i	−0.167219	+	0.0839805i
$455$	−2.94053	−	9.82205i	−0.137854	−	0.460465i
$456$		0			0
$457$	−11.0899	+	14.8963i	−0.518763	+	0.696820i	−0.981886	−	0.189474i	$-0.939322\pi$
$457$	−11.0899	+	14.8963i	−0.518763	+	0.696820i	0.463122	+	0.886294i	$0.346729\pi$
$458$	−0.365551	+	0.633152i	−0.0170811	+	0.0295853i
$459$		0			0
$460$	9.97822	+	17.2828i	0.465237	+	0.805814i
$461$	3.04933	+	0.356416i	0.142022	+	0.0165999i	0.186807	−	0.982397i	$-0.440186\pi$
$461$	3.04933	+	0.356416i	0.142022	+	0.0165999i	−0.0447850	+	0.998997i	$0.514260\pi$
$462$		0			0
$463$	−27.8853	−	6.60895i	−1.29594	−	0.307144i	−0.475926	−	0.879485i	$-0.657887\pi$
$463$	−27.8853	−	6.60895i	−1.29594	−	0.307144i	−0.820016	+	0.572341i	$0.806035\pi$
$464$	0.867370	+	0.570478i	0.0402666	+	0.0264838i
$465$		0			0
$466$	2.48981	+	2.63905i	0.115338	+	0.122252i
$467$	10.6188	−	8.91027i	0.491382	−	0.412318i	−0.363139	−	0.931735i	$-0.618295\pi$
$467$	10.6188	−	8.91027i	0.491382	−	0.412318i	0.854521	+	0.519417i	$0.173851\pi$
$468$		0			0
$469$	41.6856	+	34.9784i	1.92486	+	1.61515i
$470$	−0.00230237	−	0.0395302i	−0.000106200	−	0.00182339i
$471$		0			0
$472$	−3.43623	−	4.61566i	−0.158165	−	0.212453i
$473$	−18.5899	+	2.17285i	−0.854764	+	0.0999076i
$474$		0			0
$475$	3.44956	−	2.26881i	0.158277	−	0.104100i
$476$	−56.5056	+	20.5663i	−2.58993	+	0.942657i
$477$		0			0
$478$	2.50012	+	0.909969i	0.114353	+	0.0416210i
$479$	24.7530	−	5.86656i	1.13099	−	0.268050i	0.377824	−	0.925878i	$-0.376673\pi$
$479$	24.7530	−	5.86656i	1.13099	−	0.268050i	0.753169	+	0.657827i	$0.228524\pi$
$480$		0			0
$481$	−0.158122	+	2.71485i	−0.00720975	+	0.123787i
$482$	1.43598	−	1.52205i	0.0654069	−	0.0693273i
$483$		0			0
$484$	−2.94182	−	6.81990i	−0.133719	−	0.309995i
$485$	2.96463			0.134617
$486$		0			0
$487$	−1.98229			−0.0898263			−0.0449132	−	0.998991i	$-0.514301\pi$
$487$	−1.98229			−0.0898263			−0.0449132	+	0.998991i	$0.514301\pi$
$488$	−1.21614	−	2.81934i	−0.0550522	−	0.127625i
$489$		0			0
$490$	−1.90973	+	2.02420i	−0.0862730	+	0.0914440i
$491$	0.0272326	−	0.467566i	0.00122899	−	0.0211010i	−0.997638	−	0.0686921i	$-0.978117\pi$
$491$	0.0272326	−	0.467566i	0.00122899	−	0.0211010i	0.998867	+	0.0475911i	$0.0151544\pi$
$492$		0			0
$493$	−2.01536	+	0.477650i	−0.0907674	+	0.0215123i
$494$	0.466820	+	0.169909i	0.0210032	+	0.00764456i
$495$		0			0
$496$	6.59265	−	2.39953i	0.296019	−	0.107742i
$497$	−8.63241	+	5.67763i	−0.387217	+	0.254676i
$498$		0			0
$499$	23.5292	−	2.75017i	1.05331	−	0.123115i	0.428227	−	0.903671i	$-0.359138\pi$
$499$	23.5292	−	2.75017i	1.05331	−	0.123115i	0.625085	+	0.780557i	$0.285064\pi$
$500$	13.9228	+	18.7015i	0.622645	+	0.836358i
$501$		0			0
$502$	−0.0998878	−	1.71501i	−0.00445821	−	0.0765445i
$503$	−0.513245	−	0.430663i	−0.0228844	−	0.0192023i	0.631274	−	0.775560i	$-0.282532\pi$
$503$	−0.513245	−	0.430663i	−0.0228844	−	0.0192023i	−0.654158	+	0.756358i	$0.726977\pi$
$504$		0			0
$505$	−20.2437	+	16.9865i	−0.900834	+	0.755889i
$506$	3.16951	+	3.35948i	0.140902	+	0.149347i
$507$		0			0
$508$	−31.1472	−	20.4859i	−1.38194	−	0.908913i
$509$	−7.12235	−	1.68803i	−0.315693	−	0.0748206i	0.0697149	−	0.997567i	$-0.477791\pi$
$509$	−7.12235	−	1.68803i	−0.315693	−	0.0748206i	−0.385408	+	0.922746i	$0.625939\pi$
$510$		0			0
$511$	−22.6334	−	2.64547i	−1.00124	−	0.117029i
$512$	−6.97825	−	12.0867i	−0.308398	−	0.534161i
$513$		0			0
$514$	−1.61802	+	2.80249i	−0.0713678	+	0.123613i
$515$	−5.44469	+	7.31349i	−0.239922	+	0.322271i
$516$		0			0
$517$	0.147099	+	0.491344i	0.00646939	+	0.0216093i
$518$	1.15209	−	0.578599i	0.0506197	−	0.0254222i
$519$		0			0
$520$	−0.539830	+	1.80316i	−0.0236731	+	0.0790737i
$521$	0.747254	+	4.23789i	0.0327378	+	0.185665i	0.996791	−	0.0800423i	$-0.0255056\pi$
$521$	0.747254	+	4.23789i	0.0327378	+	0.185665i	−0.964054	+	0.265708i	$0.914394\pi$
$522$		0			0
$523$	−1.42678	+	8.09165i	−0.0623885	+	0.353823i	0.937593	+	0.347735i	$0.113049\pi$
$523$	−1.42678	+	8.09165i	−0.0623885	+	0.353823i	−0.999981	+	0.00608816i	$0.998062\pi$
$524$	−10.6280	−	5.33756i	−0.464285	−	0.233172i
$525$		0			0
$526$	−0.348417	+	0.807721i	−0.0151917	+	0.0352183i
$527$	−5.54387	+	12.8521i	−0.241495	+	0.559848i
$528$		0			0
$529$	16.1834	+	8.12761i	0.703627	+	0.353375i
$530$	0.509102	−	2.88726i	0.0221140	−	0.125415i
$531$		0			0
$532$	2.28880	+	12.9804i	0.0992320	+	0.562773i
$533$	1.37303	−	4.58624i	0.0594726	−	0.198652i
$534$		0			0
$535$	−2.29490	+	1.15254i	−0.0992173	+	0.0498288i
$536$	−2.86516	−	9.57029i	−0.123756	−	0.413373i
$537$		0			0
$538$	−1.46028	+	1.96149i	−0.0629570	+	0.0845660i
$539$	18.0230	−	31.2167i	0.776305	−	1.34460i
$540$		0			0
$541$	−1.90293	−	3.29597i	−0.0818132	−	0.141705i	0.822216	−	0.569176i	$-0.192738\pi$
$541$	−1.90293	−	3.29597i	−0.0818132	−	0.141705i	−0.904029	+	0.427472i	$0.859404\pi$
$542$	−4.39841	−	0.514100i	−0.188928	−	0.0220825i
$543$		0			0
$544$	16.1600	+	3.82999i	0.692854	+	0.164209i
$545$	15.2336	+	10.0193i	0.652535	+	0.429179i
$546$		0			0
$547$	19.7705	+	20.9555i	0.845325	+	0.895992i	0.995700	−	0.0926369i	$-0.0295296\pi$
$547$	19.7705	+	20.9555i	0.845325	+	0.895992i	−0.150375	+	0.988629i	$0.548048\pi$
$548$	−33.4725	+	28.0867i	−1.42987	+	1.19981i
$549$		0			0
$550$	1.37444	+	1.15329i	0.0586064	+	0.0491766i
$551$	0.0263976	+	0.453228i	0.00112457	+	0.0193082i
$552$		0			0
$553$	−19.5836	−	26.3054i	−0.832780	−	1.11862i
$554$	−4.42859	+	0.517628i	−0.188153	+	0.0219919i
$555$		0			0
$556$	−20.8851	+	13.7363i	−0.885724	+	0.582550i
$557$	−0.617137	+	0.224620i	−0.0261489	+	0.00951744i	−0.355062	−	0.934843i	$-0.615540\pi$
$557$	−0.617137	+	0.224620i	−0.0261489	+	0.00951744i	0.328913	+	0.944360i	$0.393318\pi$
$558$		0			0
$559$	−7.31706	−	2.66319i	−0.309479	−	0.112641i
$560$	−23.6437	+	5.60366i	−0.999128	+	0.236798i
$561$		0			0
$562$	0.150413	−	2.58250i	0.00634480	−	0.108936i
$563$	6.57618	−	6.97035i	0.277153	−	0.293765i	−0.573812	−	0.818987i	$-0.694536\pi$
$563$	6.57618	−	6.97035i	0.277153	−	0.293765i	0.850965	+	0.525222i	$0.176018\pi$
$564$		0			0
$565$	−5.47769	−	12.6987i	−0.230448	−	0.534238i
$566$	2.75035			0.115606
$567$		0			0
$568$	1.89681			0.0795884
$569$	10.0440	+	23.2846i	0.421066	+	0.976142i	0.988291	+	0.152579i	$0.0487578\pi$
$569$	10.0440	+	23.2846i	0.421066	+	0.976142i	−0.567225	+	0.823563i	$0.691983\pi$
$570$		0			0
$571$	−5.55709	+	5.89017i	−0.232557	+	0.246496i	−0.833134	−	0.553071i	$-0.813456\pi$
$571$	−5.55709	+	5.89017i	−0.232557	+	0.246496i	0.600577	+	0.799567i	$0.294937\pi$
$572$	0.702509	−	12.0616i	0.0293734	−	0.504322i
$573$		0			0
$574$	−2.20838	+	0.523395i	−0.0921759	+	0.0218461i
$575$	15.0068	+	5.46202i	0.625826	+	0.227782i
$576$		0			0
$577$	2.58521	−	0.940940i	0.107624	−	0.0391718i	−0.287647	−	0.957736i	$-0.592873\pi$
$577$	2.58521	−	0.940940i	0.107624	−	0.0391718i	0.395271	+	0.918565i	$0.370651\pi$
$578$	−6.29172	+	4.13813i	−0.261701	+	0.172124i
$579$		0			0
$580$	−0.846686	+	0.0989634i	−0.0351567	+	0.00410923i
$581$	−13.2523	−	17.8009i	−0.549797	−	0.738505i
$582$		0			0
$583$	2.20804	+	37.9106i	0.0914476	+	1.57010i
$584$	3.20466	+	2.68903i	0.132610	+	0.111273i
$585$		0			0
$586$	0.558878	−	0.468954i	0.0230870	−	0.0193723i
$587$	−28.8821	−	30.6133i	−1.19209	−	1.26354i	−0.956513	−	0.291689i	$-0.905783\pi$
$587$	−28.8821	−	30.6133i	−1.19209	−	1.26354i	−0.235580	−	0.971855i	$-0.575699\pi$
$588$		0			0
$589$	2.56332	+	1.68592i	0.105620	+	0.0694671i
$590$	2.23700	+	0.530179i	0.0920959	+	0.0218271i
$591$		0			0
$592$	6.40142	+	0.748219i	0.263097	+	0.0307516i
$593$	3.28564	+	5.69090i	0.134925	+	0.233697i	0.925569	−	0.378579i	$-0.123587\pi$
$593$	3.28564	+	5.69090i	0.134925	+	0.233697i	−0.790644	+	0.612277i	$0.790254\pi$
$594$		0			0
$595$	24.2387	−	41.9826i	0.993689	−	1.72112i
$596$	−11.4961	+	15.4420i	−0.470901	+	0.632529i
$597$		0			0
$598$	0.551094	+	1.84078i	0.0225359	+	0.0752752i
$599$	13.3200	−	6.68956i	0.544241	−	0.273328i	−0.155365	−	0.987857i	$-0.549655\pi$
$599$	13.3200	−	6.68956i	0.544241	−	0.273328i	0.699606	+	0.714529i	$0.253359\pi$
$600$		0			0
$601$	7.32196	−	24.4570i	0.298669	−	0.997624i	−0.668547	−	0.743670i	$-0.733084\pi$
$601$	7.32196	−	24.4570i	0.298669	−	0.997624i	0.967216	−	0.253954i	$-0.0817312\pi$
$602$	0.641010	+	3.63535i	0.0261256	+	0.148166i
$603$		0			0
$604$	3.24905	−	18.4263i	0.132202	−	0.749754i
$605$	5.35088	+	2.68731i	0.217544	+	0.109255i
$606$		0			0
$607$	−11.8994	+	27.5859i	−0.482982	+	1.11968i	0.486315	+	0.873784i	$0.338341\pi$
$607$	−11.8994	+	27.5859i	−0.482982	+	1.11968i	−0.969297	+	0.245894i	$0.920918\pi$
$608$	1.44186	−	3.34261i	0.0584751	−	0.135561i
$609$		0			0
$610$	1.09623	+	0.550547i	0.0443851	+	0.0222910i
$611$	−0.0370529	+	0.210137i	−0.00149900	+	0.00850125i
$612$		0			0
$613$	−2.50656	−	14.2154i	−0.101239	−	0.574154i	−0.992656	−	0.120970i	$-0.961399\pi$
$613$	−2.50656	−	14.2154i	−0.101239	−	0.574154i	0.891417	−	0.453183i	$-0.149712\pi$
$614$	0.0446597	−	0.149174i	0.00180232	−	0.00602016i
$615$		0			0
$616$	−10.3285	+	5.18716i	−0.416147	+	0.208997i
$617$	−3.90332	−	13.0380i	−0.157142	−	0.524890i	0.842769	−	0.538276i	$-0.180924\pi$
$617$	−3.90332	−	13.0380i	−0.157142	−	0.524890i	−0.999910	+	0.0133857i	$0.995739\pi$
$618$		0			0
$619$	13.0490	−	17.5278i	0.524482	−	0.704502i	−0.458398	−	0.888747i	$-0.651577\pi$
$619$	13.0490	−	17.5278i	0.524482	−	0.704502i	0.982880	+	0.184245i	$0.0589840\pi$
$620$	−2.88037	+	4.98895i	−0.115679	+	0.200361i
$621$		0			0
$622$	−1.02933	−	1.78285i	−0.0412724	−	0.0714859i
$623$	27.1153	+	3.16932i	1.08635	+	0.126976i
$624$		0			0
$625$	−6.17147	−	1.46267i	−0.246859	−	0.0585066i
$626$	−2.70689	−	1.78035i	−0.108189	−	0.0711570i
$627$		0			0
$628$	10.0165	+	10.6169i	0.399704	+	0.423661i
$629$	−9.84993	+	8.26507i	−0.392742	+	0.329550i
$630$		0			0
$631$	−18.5327	−	15.5508i	−0.737775	−	0.619066i	0.194464	−	0.980910i	$-0.437703\pi$
$631$	−18.5327	−	15.5508i	−0.737775	−	0.619066i	−0.932239	+	0.361843i	$0.882148\pi$
$632$	0.350063	+	6.01035i	0.0139248	+	0.239079i
$633$		0			0
$634$	−2.03739	−	2.73669i	−0.0809151	−	0.108688i
$635$	29.8515	−	3.48914i	1.18462	−	0.138462i
$636$		0			0
$637$	12.5292	−	8.24060i	0.496426	−	0.326504i
$638$	−0.185390	+	0.0674764i	−0.00733966	+	0.00267142i
$639$		0			0
$640$	8.53752	+	3.10740i	0.337475	+	0.122831i
$641$	−34.7871	+	8.24470i	−1.37401	+	0.325646i	−0.850321	−	0.526264i	$-0.823592\pi$
$641$	−34.7871	+	8.24470i	−1.37401	+	0.325646i	−0.523688	+	0.851910i	$0.675444\pi$
$642$		0			0
$643$	−2.63836	+	45.2988i	−0.104047	+	1.78641i	0.393850	+	0.919175i	$0.371143\pi$
$643$	−2.63836	+	45.2988i	−0.104047	+	1.78641i	−0.497896	+	0.867237i	$0.665894\pi$
$644$	−34.9858	+	37.0828i	−1.37863	+	1.46127i
$645$		0			0
$646$	0.930345	+	2.15678i	0.0366039	+	0.0848575i
$647$	−18.8974			−0.742935			−0.371468	−	0.928446i	$-0.621145\pi$
$647$	−18.8974			−0.742935			−0.371468	+	0.928446i	$0.621145\pi$
$648$		0			0
$649$	−29.7779			−1.16888
$650$	0.295653	+	0.685400i	0.0115965	+	0.0268836i
$651$		0			0
$652$	6.72585	−	7.12898i	0.263405	−	0.279192i
$653$	−1.26424	+	21.7062i	−0.0494737	+	0.849430i	0.878721	+	0.477336i	$0.158397\pi$
$653$	−1.26424	+	21.7062i	−0.0494737	+	0.849430i	−0.928195	+	0.372095i	$0.878640\pi$
$654$		0			0
$655$	9.32948	−	2.21113i	0.364533	−	0.0863959i
$656$	−10.6616	−	3.88051i	−0.416266	−	0.151509i
$657$		0			0
$658$	0.0950565	−	0.0345978i	0.00370569	−	0.00134876i
$659$	13.6785	−	8.99649i	0.532839	−	0.350453i	−0.254403	−	0.967098i	$-0.581879\pi$
$659$	13.6785	−	8.99649i	0.532839	−	0.350453i	0.787241	+	0.616645i	$0.211509\pi$
$660$		0			0
$661$	−20.5523	+	2.40222i	−0.799392	+	0.0934355i	−0.505974	−	0.862549i	$-0.668867\pi$
$661$	−20.5523	+	2.40222i	−0.799392	+	0.0934355i	−0.293418	+	0.955984i	$0.594793\pi$
$662$	2.02287	+	2.71718i	0.0786210	+	0.105606i
$663$		0			0
$664$	0.236888	+	4.06721i	0.00919304	+	0.157838i
$665$	−8.14001	−	6.83028i	−0.315656	−	0.264867i
$666$		0			0
$667$	−1.34519	+	1.12875i	−0.0520860	+	0.0437054i
$668$	−5.87999	−	6.23243i	−0.227504	−	0.241140i
$669$		0			0
$670$	3.33461	+	2.19321i	0.128827	+	0.0847310i
$671$	−15.4610	−	3.66431i	−0.596863	−	0.141459i
$672$		0			0
$673$	23.8569	+	2.78847i	0.919615	+	0.107488i	0.562711	−	0.826654i	$-0.309758\pi$
$673$	23.8569	+	2.78847i	0.919615	+	0.107488i	0.356904	+	0.934141i	$0.383832\pi$
$674$	1.96673	+	3.40647i	0.0757555	+	0.131212i
$675$		0			0
$676$	−10.2585	+	17.7683i	−0.394559	+	0.683396i
$677$	27.0852	−	36.3818i	1.04097	−	1.39827i	0.127275	−	0.991867i	$-0.459377\pi$
$677$	27.0852	−	36.3818i	1.04097	−	1.39827i	0.913696	−	0.406399i	$-0.133216\pi$
$678$		0			0
$679$	2.17214	+	7.25544i	0.0833589	+	0.278438i
$680$	−7.95298	+	3.99413i	−0.304983	+	0.153168i
$681$		0			0
$682$	−0.382379	+	1.27724i	−0.0146421	+	0.0489079i
$683$	−3.38555	−	19.2004i	−0.129544	−	0.734683i	−0.978504	−	0.206226i	$-0.933882\pi$
$683$	−3.38555	−	19.2004i	−0.129544	−	0.734683i	0.848960	−	0.528457i	$-0.177229\pi$
$684$		0			0
$685$	6.11698	−	34.6911i	0.233718	−	1.32548i
$686$	−1.60998	−	0.808562i	−0.0614693	−	0.0308710i
$687$		0			0
$688$	−7.30928	+	16.9448i	−0.278664	+	0.646015i
$689$	−6.25757	+	14.5067i	−0.238394	+	0.552660i
$690$		0			0
$691$	18.3456	+	9.21350i	0.697899	+	0.350498i	0.762118	−	0.647438i	$-0.224159\pi$
$691$	18.3456	+	9.21350i	0.697899	+	0.350498i	−0.0642194	+	0.997936i	$0.520456\pi$
$692$	5.47393	−	31.0442i	0.208088	−	1.18012i
$693$		0			0
$694$	−0.663458	−	3.76266i	−0.0251845	−	0.142828i
$695$	5.77980	−	19.3059i	0.219240	−	0.732314i
$696$		0			0
$697$	20.2280	−	10.1589i	0.766190	−	0.384795i
$698$	−0.951699	−	3.17889i	−0.0360223	−	0.120323i
$699$		0			0
$700$	−11.8267	+	15.8860i	−0.447006	+	0.600433i
$701$	−3.27119	+	5.66587i	−0.123551	+	0.213997i	−0.921166	−	0.389171i	$-0.872762\pi$
$701$	−3.27119	+	5.66587i	−0.123551	+	0.213997i	0.797615	+	0.603168i	$0.206095\pi$
$702$		0			0
$703$	1.40923	+	2.44085i	0.0531500	+	0.0920585i
$704$	−27.3773	−	3.19995i	−1.03182	−	0.120603i
$705$		0			0
$706$	3.78905	+	0.898022i	0.142603	+	0.0337975i
$707$	−56.4038	−	37.0974i	−2.12128	−	1.39519i
$708$		0			0
$709$	−6.58581	−	6.98055i	−0.247335	−	0.262160i	0.591798	−	0.806087i	$-0.298418\pi$
$709$	−6.58581	−	6.98055i	−0.247335	−	0.262160i	−0.839133	+	0.543927i	$0.816937\pi$
$710$	−0.580522	+	0.487116i	−0.0217866	+	0.0182811i
$711$		0			0
$712$	−3.83925	−	3.22152i	−0.143882	−	0.120731i
$713$	0.690003	+	11.8469i	0.0258408	+	0.443670i
$714$		0			0
$715$	5.81653	+	7.81296i	0.217526	+	0.292188i
$716$	−37.6362	+	4.39904i	−1.40653	+	0.164400i
$717$		0			0
$718$	−3.07346	+	2.02145i	−0.114700	+	0.0754397i
$719$	24.3548	−	8.86441i	0.908280	−	0.330587i	0.154714	−	0.987959i	$-0.450554\pi$
$719$	24.3548	−	8.86441i	0.908280	−	0.330587i	0.753566	+	0.657372i	$0.228332\pi$
$720$		0			0
$721$	−21.8878	−	7.96650i	−0.815143	−	0.296688i
$722$	−2.96312	+	0.702272i	−0.110276	+	0.0261359i
$723$		0			0
$724$	0.0173055	−	0.297123i	0.000643152	−	0.0110425i
$725$	−0.468129	+	0.496187i	−0.0173859	+	0.0184279i
$726$		0			0
$727$	−8.25148	−	19.1291i	−0.306030	−	0.709458i	0.693913	−	0.720058i	$-0.255885\pi$
$727$	−8.25148	−	19.1291i	−0.306030	−	0.709458i	−0.999944	+	0.0106003i	$0.996626\pi$
$728$	−4.80845			−0.178213
$729$		0			0
$730$	−1.67136			−0.0618597
$731$	−14.5825	−	33.8059i	−0.539352	−	1.25036i
$732$		0			0
$733$	−5.85032	+	6.20098i	−0.216086	+	0.229038i	−0.826345	−	0.563164i	$-0.809584\pi$
$733$	−5.85032	+	6.20098i	−0.216086	+	0.229038i	0.610259	+	0.792202i	$0.291065\pi$
$734$	0.355239	−	6.09922i	0.0131121	−	0.225126i
$735$		0			0
$736$	13.7010	−	3.24719i	0.505024	−	0.119693i
$737$	−48.5793	−	17.6814i	−1.78944	−	0.651304i
$738$		0			0
$739$	34.6163	−	12.5993i	1.27338	−	0.463473i	0.385143	−	0.922857i	$-0.374152\pi$
$739$	34.6163	−	12.5993i	1.27338	−	0.463473i	0.888238	+	0.459384i	$0.151930\pi$
$740$	−4.42148	+	2.90805i	−0.162537	+	0.106902i
$741$		0			0
$742$	7.43910	−	0.869507i	0.273098	−	0.0319206i
$743$	−17.8874	−	24.0269i	−0.656223	−	0.881461i	0.342081	−	0.939670i	$-0.388868\pi$
$743$	−17.8874	−	24.0269i	−0.656223	−	0.881461i	−0.998304	+	0.0582096i	$0.981461\pi$
$744$		0			0
$745$	−0.902417	−	15.4939i	−0.0330620	−	0.567653i
$746$	−2.54821	−	2.13820i	−0.0932966	−	0.0782852i
$747$		0			0
$748$	43.7615	−	36.7203i	1.60008	−	1.34263i
$749$	−4.50209	−	4.77194i	−0.164503	−	0.174363i
$750$		0			0
$751$	−5.85565	−	3.85132i	−0.213676	−	0.140537i	0.438160	−	0.898897i	$-0.355630\pi$
$751$	−5.85565	−	3.85132i	−0.213676	−	0.140537i	−0.651835	+	0.758360i	$0.726001\pi$
$752$	0.492069	+	0.116622i	0.0179439	+	0.00425278i
$753$		0			0
$754$	−0.0815232	−	0.00952870i	−0.00296890	−	0.000347015i
$755$	7.54205	+	13.0632i	0.274483	+	0.475419i
$756$		0			0
$757$	−11.1739	+	19.3538i	−0.406123	+	0.703426i	−0.994452	−	0.105196i	$-0.966453\pi$
$757$	−11.1739	+	19.3538i	−0.406123	+	0.703426i	0.588328	+	0.808622i	$0.299786\pi$
$758$	3.03749	−	4.08006i	0.110327	−	0.148194i
$759$		0			0
$760$	0.559483	+	1.86880i	0.0202946	+	0.0677886i
$761$	2.87464	−	1.44370i	0.104206	−	0.0523340i	−0.395933	−	0.918279i	$-0.629579\pi$
$761$	2.87464	−	1.44370i	0.104206	−	0.0523340i	0.500139	+	0.865945i	$0.333282\pi$
$762$		0			0
$763$	−13.3591	+	44.6226i	−0.483633	+	1.61545i
$764$	3.65332	+	20.7190i	0.132172	+	0.749587i
$765$		0			0
$766$	−1.15702	+	6.56181i	−0.0418050	+	0.237088i
$767$	−11.0708	−	5.55998i	−0.399745	−	0.200759i
$768$		0			0
$769$	−2.22533	+	5.15891i	−0.0802476	+	0.186035i	−0.953616	−	0.301025i	$-0.902671\pi$
$769$	−2.22533	+	5.15891i	−0.0802476	+	0.186035i	0.873369	+	0.487060i	$0.161931\pi$
$770$	1.82895	−	4.23998i	0.0659107	−	0.152798i
$771$		0			0
$772$	−27.8673	−	13.9955i	−1.00297	−	0.503709i
$773$	−9.17966	+	52.0604i	−0.330169	+	1.87248i	0.140362	+	0.990100i	$0.455173\pi$
$773$	−9.17966	+	52.0604i	−0.330169	+	1.87248i	−0.470531	+	0.882383i	$0.655938\pi$
$774$		0			0
$775$	0.800512	+	4.53993i	0.0287552	+	0.163079i
$776$	0.398767	−	1.33197i	0.0143149	−	0.0478150i
$777$		0			0
$778$	−3.40701	+	1.71106i	−0.122147	+	0.0613447i
$779$	−1.42302	−	4.75320i	−0.0509848	−	0.170301i
$780$		0			0
$781$	5.86158	−	7.87347i	0.209744	−	0.281735i
$782$	−4.54265	+	7.86810i	−0.162445	+	0.281363i
$783$		0			0
$784$	−17.7703	−	30.7791i	−0.634654	−	1.09925i
$785$	−11.6877	−	1.36609i	−0.417151	−	0.0487579i
$786$		0			0
$787$	−14.9797	−	3.55026i	−0.533969	−	0.126553i	−0.0452195	−	0.998977i	$-0.514399\pi$
$787$	−14.9797	−	3.55026i	−0.533969	−	0.126553i	−0.488750	+	0.872424i	$0.662547\pi$
$788$	−2.02159	−	1.32962i	−0.0720161	−	0.0473657i
$789$		0			0
$790$	−1.65064	−	1.74958i	−0.0587272	−	0.0622472i
$791$	27.0645	−	22.7098i	0.962304	−	0.807469i
$792$		0			0
$793$	−5.06389	−	4.24911i	−0.179824	−	0.150890i
$794$	−0.289257	−	4.96636i	−0.0102654	−	0.176249i
$795$		0			0
$796$	−2.74858	−	3.69199i	−0.0974210	−	0.130859i
$797$	−21.4001	+	2.50131i	−0.758030	+	0.0886010i	−0.486323	−	0.873779i	$-0.661662\pi$
$797$	−21.4001	+	2.50131i	−0.758030	+	0.0886010i	−0.271707	+	0.962380i	$0.587588\pi$
$798$		0			0
$799$	−0.842926	+	0.554401i	−0.0298206	+	0.0196133i
$800$	5.13998	−	1.87080i	0.181726	−	0.0661428i
$801$		0			0
$802$	4.52910	+	1.64846i	0.159928	+	0.0582091i
$803$	21.0651	−	4.99251i	0.743370	−	0.176182i
$804$		0			0
$805$	2.38979	−	41.0311i	0.0842290	−	1.44616i
$806$	−0.380640	+	0.403455i	−0.0134075	+	0.0142111i
$807$		0			0
$808$	4.90889	+	11.3801i	0.172694	+	0.400350i
$809$	−19.2040			−0.675177			−0.337588	−	0.941294i	$-0.609611\pi$
$809$	−19.2040			−0.675177			−0.337588	+	0.941294i	$0.609611\pi$
$810$		0			0
$811$	−4.66474			−0.163801			−0.0819006	−	0.996641i	$-0.526099\pi$
$811$	−4.66474			−0.163801			−0.0819006	+	0.996641i	$0.526099\pi$
$812$	−0.862549	−	1.99961i	−0.0302695	−	0.0701727i
$813$		0			0
$814$	−0.840497	+	0.890875i	−0.0294594	+	0.0312251i
$815$	−0.459425	+	7.88802i	−0.0160930	+	0.276305i
$816$		0			0
$817$	−7.85259	+	1.86110i	−0.274727	+	0.0651116i
$818$	4.90382	+	1.78484i	0.171458	+	0.0624056i
$819$		0			0
$820$	8.75443	−	3.18635i	0.305718	−	0.111272i
$821$	−35.2261	+	23.1686i	−1.22940	+	0.808589i	−0.986864	−	0.161553i	$-0.948350\pi$
$821$	−35.2261	+	23.1686i	−1.22940	+	0.808589i	−0.242537	+	0.970142i	$0.577979\pi$
$822$		0			0
$823$	8.45091	−	0.987770i	0.294580	−	0.0344315i	0.0324808	−	0.999472i	$-0.489659\pi$
$823$	8.45091	−	0.987770i	0.294580	−	0.0344315i	0.262099	+	0.965041i	$0.415585\pi$
$824$	2.55351	+	3.42996i	0.0889557	+	0.119488i
$825$		0			0
$826$	0.341489	+	5.86314i	0.0118819	+	0.204005i
$827$	−28.1921	−	23.6560i	−0.980336	−	0.822600i	0.00380365	−	0.999993i	$-0.498789\pi$
$827$	−28.1921	−	23.6560i	−0.980336	−	0.822600i	−0.984140	+	0.177393i	$0.943234\pi$
$828$		0			0
$829$	−16.2832	+	13.6632i	−0.565537	+	0.474542i	−0.880162	−	0.474674i	$-0.842566\pi$
$829$	−16.2832	+	13.6632i	−0.565537	+	0.474542i	0.314624	+	0.949216i	$0.398121\pi$
$830$	−1.11699	−	1.18394i	−0.0387714	−	0.0410952i
$831$		0			0
$832$	−9.58087	−	6.30144i	−0.332157	−	0.218463i
$833$	68.9945	+	16.3520i	2.39052	+	0.566563i
$834$		0			0
$835$	6.86099	+	0.801935i	0.237434	+	0.0277521i
$836$	−6.26095	−	10.8443i	−0.216540	−	0.375058i
$837$		0			0
$838$	−0.100997	+	0.174931i	−0.00348887	+	0.00604290i
$839$	−24.7813	+	33.2871i	−0.855545	+	1.14920i	0.131904	+	0.991262i	$0.457891\pi$
$839$	−24.7813	+	33.2871i	−0.855545	+	1.14920i	−0.987450	+	0.157934i	$0.949517\pi$
$840$		0			0
$841$	8.29578	+	27.7098i	0.286061	+	0.955512i
$842$	1.31571	−	0.660776i	0.0453425	−	0.0227719i
$843$		0			0
$844$	−6.41837	+	21.4389i	−0.220929	+	0.737956i
$845$	−2.87223	−	16.2892i	−0.0988076	−	0.560366i
$846$		0			0
$847$	−2.65625	+	15.0643i	−0.0912698	+	0.517617i
$848$	33.4598	+	16.8041i	1.14901	+	0.577056i
$849$		0			0
$850$	−1.39791	+	3.24072i	−0.0479480	+	0.111156i
$851$	−4.31789	+	10.0100i	−0.148015	+	0.343138i
$852$		0			0
$853$	−20.4252	−	10.2579i	−0.699346	−	0.351225i	0.0633417	−	0.997992i	$-0.479824\pi$
$853$	−20.4252	−	10.2579i	−0.699346	−	0.351225i	−0.762687	+	0.646767i	$0.776120\pi$
$854$	−0.544183	+	3.08622i	−0.0186216	+	0.105608i
$855$		0			0
$856$	0.209141	+	1.18610i	0.00714829	+	0.0405400i
$857$	−14.7869	+	49.3915i	−0.505109	+	1.68718i	0.201425	+	0.979504i	$0.435443\pi$
$857$	−14.7869	+	49.3915i	−0.505109	+	1.68718i	−0.706534	+	0.707679i	$0.749742\pi$
$858$		0			0
$859$	−23.7183	+	11.9118i	−0.809257	+	0.406424i	−0.804785	−	0.593566i	$-0.797720\pi$
$859$	−23.7183	+	11.9118i	−0.809257	+	0.406424i	−0.00447138	+	0.999990i	$0.501423\pi$
$860$	−4.34591	−	14.5163i	−0.148194	−	0.495003i
$861$		0			0
$862$	3.09820	−	4.16160i	0.105525	−	0.141745i
$863$	1.22953	−	2.12962i	0.0418538	−	0.0724930i	−0.844340	−	0.535808i	$-0.820007\pi$
$863$	1.22953	−	2.12962i	0.0418538	−	0.0724930i	0.886193	+	0.463315i	$0.153340\pi$
$864$		0			0
$865$	12.7067	+	22.0087i	0.432041	+	0.748317i
$866$	3.68307	+	0.430489i	0.125156	+	0.0146286i
$867$		0			0
$868$	−14.3200	−	3.39391i	−0.486053	−	0.115197i
$869$	26.0301	+	17.1203i	0.883012	+	0.580766i
$870$		0			0
$871$	−14.7594	−	15.6441i	−0.500105	−	0.530080i
$872$	6.55058	−	5.49659i	0.221831	−	0.186138i
$873$		0			0
$874$	1.52555	+	1.28008i	0.0516023	+	0.0432995i
$875$	−2.79198	−	47.9365i	−0.0943862	−	1.62055i
$876$		0			0
$877$	1.51036	+	2.02876i	0.0510011	+	0.0685064i	0.826892	−	0.562361i	$-0.190107\pi$
$877$	1.51036	+	2.02876i	0.0510011	+	0.0685064i	−0.775891	+	0.630867i	$0.782699\pi$
$878$	6.26078	−	0.731780i	0.211291	−	0.0246964i
$879$		0			0
$880$	19.2866	−	12.6850i	0.650151	−	0.427611i
$881$	46.6808	−	16.9904i	1.57272	−	0.572421i	0.599111	−	0.800666i	$-0.295521\pi$
$881$	46.6808	−	16.9904i	1.57272	−	0.572421i	0.973604	+	0.228244i	$0.0732985\pi$
$882$		0			0
$883$	29.8038	+	10.8477i	1.00298	+	0.365054i	0.790732	−	0.612162i	$-0.209700\pi$
$883$	29.8038	+	10.8477i	1.00298	+	0.365054i	0.212245	+	0.977216i	$0.431922\pi$
$884$	23.1259	−	5.48094i	0.777809	−	0.184344i
$885$		0			0
$886$	0.172861	−	2.96790i	0.00580737	−	0.0997087i
$887$	−1.98208	+	2.10088i	−0.0665516	+	0.0705406i	−0.759794	−	0.650164i	$-0.774700\pi$
$887$	−1.98208	+	2.10088i	−0.0665516	+	0.0705406i	0.693242	+	0.720705i	$0.256182\pi$
$888$		0			0
$889$	30.4108	+	70.5002i	1.01995	+	2.36450i
$890$	2.00232			0.0671179
$891$		0			0
$892$	29.7211			0.995137
$893$	0.0875919	+	0.203061i	0.00293115	+	0.00679518i
$894$		0			0
$895$	20.9634	−	22.2199i	0.700730	−	0.742731i
$896$	−1.34955	+	23.1709i	−0.0450853	+	0.774085i
$897$		0			0
$898$	0.160717	−	0.0380907i	0.00536321	−	0.00127110i
$899$	−0.476334	−	0.173372i	−0.0158866	−	0.00578227i
$900$		0			0
$901$	−70.1950	+	25.5489i	−2.33854	+	0.851157i
$902$	1.80141	−	1.18481i	0.0599805	−	0.0394498i
$903$		0			0
$904$	−6.44217	+	0.752981i	−0.214263	+	0.0250438i
$905$	0.143283	+	0.192463i	0.00476289	+	0.00639768i
$906$		0			0
$907$	−1.79688	−	30.8512i	−0.0596644	−	1.02440i	−0.886729	−	0.462290i	$-0.847028\pi$
$907$	−1.79688	−	30.8512i	−0.0596644	−	1.02440i	0.827064	−	0.562107i	$-0.190009\pi$
$908$	32.0289	+	26.8755i	1.06292	+	0.891893i
$909$		0			0
$910$	1.47163	−	1.23485i	0.0487842	−	0.0409348i
$911$	29.3161	+	31.0733i	0.971287	+	1.02950i	0.999553	+	0.0299037i	$0.00952006\pi$
$911$	29.3161	+	31.0733i	0.971287	+	1.02950i	−0.0282657	+	0.999600i	$0.508998\pi$
$912$		0			0
$913$	17.6146	+	11.5853i	0.582960	+	0.383419i
$914$	−3.38591	−	0.802475i	−0.111996	−	0.0265435i
$915$		0			0
$916$	7.61491	+	0.890055i	0.251604	+	0.0294083i
$917$	12.2469	+	21.2123i	0.404429	+	0.700491i
$918$		0			0
$919$	−10.3318	+	17.8951i	−0.340813	+	0.590306i	−0.984584	−	0.174913i	$-0.944036\pi$
$919$	−10.3318	+	17.8951i	−0.340813	+	0.590306i	0.643771	+	0.765218i	$0.277369\pi$
$920$	−4.50578	+	6.05231i	−0.148551	+	0.199539i
$921$		0			0
$922$	0.164983	+	0.551083i	0.00543344	+	0.0181489i
$923$	3.64932	−	1.83276i	0.120119	−	0.0603259i
$924$		0			0
$925$	−1.21459	+	4.05702i	−0.0399356	+	0.133394i
$926$	−0.932434	−	5.28810i	−0.0306417	−	0.173778i
$927$		0			0
$928$	−0.104442	+	0.592319i	−0.00342847	+	0.0194438i
$929$	37.6341	+	18.9005i	1.23473	+	0.620106i	0.941847	−	0.336041i	$-0.109088\pi$
$929$	37.6341	+	18.9005i	1.23473	+	0.620106i	0.292886	+	0.956147i	$0.405384\pi$
$930$		0			0
$931$	6.15596	−	14.2711i	0.201754	−	0.467717i
$932$	15.0698	−	34.9356i	0.493626	−	1.14435i
$933$		0			0
$934$	2.32106	+	1.16568i	0.0759476	+	0.0381423i
$935$	−7.99728	+	45.3548i	−0.261539	+	1.48326i
$936$		0			0
$937$	5.62432	+	31.8971i	0.183738	+	1.04203i	0.927566	+	0.373660i	$0.121897\pi$
$937$	5.62432	+	31.8971i	0.183738	+	1.04203i	−0.743827	+	0.668372i	$0.766991\pi$
$938$	−2.92430	+	9.76783i	−0.0954816	+	0.318931i
$939$		0			0
$940$	−0.371071	+	0.186359i	−0.0121030	+	0.00607835i
$941$	−1.43114	−	4.78033i	−0.0466538	−	0.155834i	0.931489	−	0.363770i	$-0.118511\pi$
$941$	−1.43114	−	4.78033i	−0.0466538	−	0.155834i	−0.978142	+	0.207936i	$0.933325\pi$
$942$		0			0
$943$	11.4602	−	15.3938i	0.373196	−	0.501289i
$944$	−14.6802	+	25.4269i	−0.477800	+	0.827575i
$945$		0			0
$946$	−1.75347	−	3.03710i	−0.0570102	−	0.0987445i
$947$	−1.36483	−	0.159526i	−0.0443512	−	0.00518391i	0.0938884	−	0.995583i	$-0.470070\pi$
$947$	−1.36483	−	0.159526i	−0.0443512	−	0.00518391i	−0.138240	+	0.990399i	$0.544144\pi$
$948$		0			0
$949$	8.76375	+	2.07705i	0.284483	+	0.0674238i
$950$	0.646352	+	0.425112i	0.0209704	+	0.0137925i
$951$		0			0
$952$	−15.6020	−	16.5371i	−0.505663	−	0.535972i
$953$	23.8952	−	20.0504i	0.774041	−	0.649497i	−0.167699	−	0.985838i	$-0.553634\pi$
$953$	23.8952	−	20.0504i	0.774041	−	0.649497i	0.941740	+	0.336341i	$0.109189\pi$
$954$		0			0
$955$	−12.9929	−	10.9023i	−0.420439	−	0.352790i
$956$	−1.62226	−	27.8531i	−0.0524676	−	0.900834i
$957$		0			0
$958$	2.84635	+	3.82332i	0.0919616	+	0.123526i
$959$	89.3826	−	10.4473i	2.88631	−	0.337362i
$960$		0			0
$961$	23.0381	−	15.1524i	0.743164	−	0.488787i
$962$	−0.478820	+	0.174276i	−0.0154378	+	0.00561889i
$963$		0			0
$964$	−20.6201	−	7.50509i	−0.664127	−	0.241723i
$965$	24.4626	−	5.79775i	0.787480	−	0.186636i
$966$		0			0
$967$	−1.30389	+	22.3869i	−0.0419303	+	0.719915i	0.910190	+	0.414191i	$0.135935\pi$
$967$	−1.30389	+	22.3869i	−0.0419303	+	0.719915i	−0.952120	+	0.305724i	$0.901102\pi$
$968$	1.92711	−	2.04262i	0.0619398	−	0.0656523i
$969$		0			0
$970$	0.220018	+	0.510059i	0.00706435	+	0.0163770i
$971$	−25.8564			−0.829773			−0.414886	−	0.909873i	$-0.636179\pi$
$971$	−25.8564			−0.829773			−0.414886	+	0.909873i	$0.636179\pi$
$972$		0			0
$973$	51.4827			1.65046
$974$	−0.147114	−	0.341050i	−0.00471385	−	0.0109279i
$975$		0			0
$976$	−10.7510	+	11.3954i	−0.344131	+	0.364758i
$977$	−1.54843	+	26.5856i	−0.0495388	+	0.850548i	0.878426	+	0.477879i	$0.158594\pi$
$977$	−1.54843	+	26.5856i	−0.0495388	+	0.850548i	−0.927964	+	0.372669i	$0.878443\pi$
$978$		0			0
$979$	−25.2364	+	5.98113i	−0.806558	+	0.191158i
$980$	27.4230	+	9.98117i	0.875997	+	0.318837i
$981$		0			0
$982$	0.0824649	−	0.0300148i	0.00263156	−	0.000957810i
$983$	5.96401	−	3.92259i	0.190222	−	0.125111i	−0.450826	−	0.892612i	$-0.648870\pi$
$983$	5.96401	−	3.92259i	0.190222	−	0.125111i	0.641048	+	0.767501i	$0.278500\pi$
$984$		0			0
$985$	1.93749	−	0.226460i	0.0617336	−	0.00721562i
$986$	−0.231748	−	0.311291i	−0.00738034	−	0.00991352i
$987$		0			0
$988$	−0.302907	−	5.20071i	−0.00963675	−	0.165457i
$989$	−23.9118	−	20.0644i	−0.760350	−	0.638010i
$990$		0			0
$991$	33.2529	−	27.9025i	1.05631	−	0.886353i	0.0625710	−	0.998041i	$-0.480070\pi$
$991$	33.2529	−	27.9025i	1.05631	−	0.886353i	0.993743	+	0.111688i	$0.0356256\pi$
$992$	2.78927	+	2.95646i	0.0885595	+	0.0938676i
$993$		0			0
$994$	−1.61747	−	1.06383i	−0.0513031	−	0.0337426i
$995$	3.61065	+	0.855741i	0.114465	+	0.0271288i
$996$		0			0
$997$	2.80791	+	0.328198i	0.0889276	+	0.0103941i	0.160440	−	0.987046i	$-0.448709\pi$
$997$	2.80791	+	0.328198i	0.0889276	+	0.0103941i	−0.0715128	+	0.997440i	$0.522783\pi$
$998$	2.21936	+	3.84405i	0.0702528	+	0.121681i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.676.4		144
3.2	odd	2		729.2.g.a.676.5		144
9.2	odd	6		729.2.g.b.190.5		144
9.4	even	3		81.2.g.a.4.5	✓	144
9.5	odd	6		243.2.g.a.64.4		144
9.7	even	3		729.2.g.c.190.4		144
81.7	even	27		81.2.g.a.61.5	yes	144
81.14	odd	54		6561.2.a.d.1.33		72
81.20	odd	54		729.2.g.b.541.5		144
81.34	even	27	inner	729.2.g.d.55.4		144
81.47	odd	54		729.2.g.a.55.5		144
81.61	even	27		729.2.g.c.541.4		144
81.67	even	27		6561.2.a.c.1.40		72
81.74	odd	54		243.2.g.a.19.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.5	✓	144	9.4	even	3
81.2.g.a.61.5	yes	144	81.7	even	27
243.2.g.a.19.4		144	81.74	odd	54
243.2.g.a.64.4		144	9.5	odd	6
729.2.g.a.55.5		144	81.47	odd	54
729.2.g.a.676.5		144	3.2	odd	2
729.2.g.b.190.5		144	9.2	odd	6
729.2.g.b.541.5		144	81.20	odd	54
729.2.g.c.190.4		144	9.7	even	3
729.2.g.c.541.4		144	81.61	even	27
729.2.g.d.55.4		144	81.34	even	27	inner
729.2.g.d.676.4		144	1.1	even	1	trivial
6561.2.a.c.1.40		72	81.67	even	27
6561.2.a.d.1.33		72	81.14	odd	54

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0742143 + 0.172048i) q^{2} +(1.34839 - 1.42921i) q^{4} +(-0.0921050 + 1.58138i) q^{5} +(-3.93765 + 0.933240i) q^{7} +(0.698107 + 0.254090i) q^{8} +O(q^{10})\)	\(q+(0.0742143 + 0.172048i) q^{2} +(1.34839 - 1.42921i) q^{4} +(-0.0921050 + 1.58138i) q^{5} +(-3.93765 + 0.933240i) q^{7} +(0.698107 + 0.254090i) q^{8} +(-0.278909 + 0.101515i) q^{10} +(3.21202 - 2.11258i) q^{11} +(1.58861 - 0.185682i) q^{13} +(-0.452792 - 0.608205i) q^{14} +(-0.220403 - 3.78417i) q^{16} +(5.79317 + 4.86105i) q^{17} +(1.26984 - 1.06552i) q^{19} +(2.13593 + 2.26396i) q^{20} +(0.601842 + 0.395838i) q^{22} +(6.23886 + 1.47864i) q^{23} +(2.47391 + 0.289158i) q^{25} +(0.149844 + 0.259538i) q^{26} +(-3.97569 + 6.88610i) q^{28} +(-0.163549 + 0.219684i) q^{29} +(0.530826 + 1.77308i) q^{31} +(1.96248 - 0.985594i) q^{32} +(-0.406398 + 1.35746i) q^{34} +(-1.11313 - 6.31289i) q^{35} +(-0.295248 + 1.67443i) q^{37} +(0.277561 + 0.139396i) q^{38} +(-0.466113 + 1.08057i) q^{40} +(1.18553 - 2.74838i) q^{41} +(-4.35056 - 2.18493i) q^{43} +(1.31174 - 7.43922i) q^{44} +(0.208616 + 1.18312i) q^{46} +(-0.0382623 + 0.127805i) q^{47} +(8.37873 - 4.20796i) q^{49} +(0.133850 + 0.447090i) q^{50} +(1.87669 - 2.52084i) q^{52} +(-4.93888 + 8.55438i) q^{53} +(3.04495 + 5.27400i) q^{55} +(-2.98603 - 0.349017i) q^{56} +(-0.0499339 - 0.0118346i) q^{58} +(-6.47138 - 4.25629i) q^{59} +(-2.83624 - 3.00624i) q^{61} +(-0.265660 + 0.222915i) q^{62} +(-5.49230 - 4.60858i) q^{64} +(0.147315 + 2.52931i) q^{65} +(-8.03004 - 10.7862i) q^{67} +(14.7589 - 1.72507i) q^{68} +(1.00351 - 0.660018i) q^{70} +(2.39924 - 0.873251i) q^{71} +(5.29149 + 1.92595i) q^{73} +(-0.309995 + 0.0734701i) q^{74} +(0.189384 - 3.25160i) q^{76} +(-10.6763 + 11.3162i) q^{77} +(3.20983 + 7.44121i) q^{79} +6.00452 q^{80} +0.560836 q^{82} +(2.17210 + 5.03548i) q^{83} +(-8.22075 + 8.71349i) q^{85} +(0.0530398 - 0.910658i) q^{86} +(2.77911 - 0.658662i) q^{88} +(-6.33932 - 2.30732i) q^{89} +(-6.08212 + 2.21371i) q^{91} +(10.5257 - 6.92286i) q^{92} +(-0.0248282 + 0.00290200i) q^{94} +(1.56804 + 2.10624i) q^{95} +(-0.108820 - 1.86837i) q^{97} +(1.34579 + 1.12925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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