LMFDB - Embedded newform 243.2.g.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(10,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.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:	$1.94036476912$
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			19.1
Character	$\chi$	$=$	243.19
Dual form			243.2.g.a.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43604 + 0.284732i) q^{2} +(3.90713 - 0.926007i) q^{4} +(3.57352 + 1.79469i) q^{5} +(0.377600 + 1.26127i) q^{7} +(-4.64483 + 1.69058i) q^{8} +O(q^{10})$	\(q+(-2.43604 + 0.284732i) q^{2} +(3.90713 - 0.926007i) q^{4} +(3.57352 + 1.79469i) q^{5} +(0.377600 + 1.26127i) q^{7} +(-4.64483 + 1.69058i) q^{8} +(-9.21624 - 3.35444i) q^{10} +(0.142583 - 2.44806i) q^{11} +(0.783462 - 1.05237i) q^{13} +(-1.27897 - 2.96500i) q^{14} +(3.65712 - 1.83667i) q^{16} +(-0.206593 + 0.173352i) q^{17} +(1.02778 + 0.862409i) q^{19} +(15.6241 + 3.70298i) q^{20} +(0.349704 + 6.00418i) q^{22} +(-1.71576 + 5.73105i) q^{23} +(6.56334 + 8.81609i) q^{25} +(-1.60890 + 2.78670i) q^{26} +(2.64328 + 4.57830i) q^{28} +(2.19520 - 5.08906i) q^{29} +(0.884536 + 0.937554i) q^{31} +(-0.126410 + 0.0831411i) q^{32} +(0.453909 - 0.481116i) q^{34} +(-0.914230 + 5.18486i) q^{35} +(-0.00841562 - 0.0477273i) q^{37} +(-2.74927 - 1.80822i) q^{38} +(-19.6325 - 2.29471i) q^{40} +(4.11791 + 0.481314i) q^{41} +(-5.22957 - 3.43954i) q^{43} +(-1.70983 - 9.69693i) q^{44} +(2.54785 - 14.4496i) q^{46} +(-5.69554 + 6.03692i) q^{47} +(4.40019 - 2.89405i) q^{49} +(-18.4988 - 19.6076i) q^{50} +(2.08658 - 4.83724i) q^{52} +(5.79529 + 10.0377i) q^{53} +(4.90304 - 8.49231i) q^{55} +(-3.88617 - 5.22004i) q^{56} +(-3.89859 + 13.0222i) q^{58} +(-0.567212 - 9.73865i) q^{59} +(-4.15895 - 0.985689i) q^{61} +(-2.42172 - 2.03206i) q^{62} +(-5.98568 + 5.02258i) q^{64} +(4.68839 - 2.35460i) q^{65} +(-0.525148 - 1.21743i) q^{67} +(-0.646660 + 0.868614i) q^{68} +(0.750805 - 12.8908i) q^{70} +(-7.40721 - 2.69600i) q^{71} +(-8.12155 + 2.95600i) q^{73} +(0.0340903 + 0.113869i) q^{74} +(4.81426 + 2.41781i) q^{76} +(3.14152 - 0.744553i) q^{77} +(-5.19362 + 0.607048i) q^{79} +16.3650 q^{80} -10.1684 q^{82} +(-5.64086 + 0.659323i) q^{83} +(-1.04938 + 0.248707i) q^{85} +(13.7188 + 6.88984i) q^{86} +(3.47637 + 11.6119i) q^{88} +(8.61170 - 3.13440i) q^{89} +(1.62316 + 0.590783i) q^{91} +(-1.39672 + 23.9807i) q^{92} +(12.1557 - 16.3279i) q^{94} +(2.12503 + 4.92638i) q^{95} +(11.0880 - 5.56859i) q^{97} +(-9.89500 + 8.30289i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{26}{27}\right)$

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 $

$2$	−2.43604	+	0.284732i	−1.72254	+	0.201336i	−0.919093	−	0.394040i	$-0.871077\pi$
$2$	−2.43604	+	0.284732i	−1.72254	+	0.201336i	−0.803447	+	0.595376i	$0.797003\pi$
$3$		0			0
$3$		0			0
$4$	3.90713	−	0.926007i	1.95356	−	0.463003i
$5$	3.57352	+	1.79469i	1.59813	+	0.802609i	0.999999	+	0.00120769i	$0.000384420\pi$
$5$	3.57352	+	1.79469i	1.59813	+	0.802609i	0.598127	+	0.801401i	$0.295912\pi$
$6$		0			0
$7$	0.377600	+	1.26127i	0.142720	+	0.476716i	0.999223	−	0.0394257i	$-0.0125528\pi$
$7$	0.377600	+	1.26127i	0.142720	+	0.476716i	−0.856503	+	0.516142i	$0.827368\pi$
$8$	−4.64483	+	1.69058i	−1.64220	+	0.597711i
$9$		0			0
$10$	−9.21624	−	3.35444i	−2.91443	−	1.06077i
$11$	0.142583	−	2.44806i	0.0429905	−	0.738119i	−0.906090	−	0.423085i	$-0.860947\pi$
$11$	0.142583	−	2.44806i	0.0429905	−	0.738119i	0.949080	−	0.315034i	$-0.102016\pi$
$12$		0			0
$13$	0.783462	−	1.05237i	0.217293	−	0.291875i	−0.680089	−	0.733130i	$-0.738059\pi$
$13$	0.783462	−	1.05237i	0.217293	−	0.291875i	0.897382	+	0.441254i	$0.145466\pi$
$14$	−1.27897	−	2.96500i	−0.341820	−	0.792429i
$15$		0			0
$16$	3.65712	−	1.83667i	0.914279	−	0.459168i
$17$	−0.206593	+	0.173352i	−0.0501061	+	0.0420440i	−0.667497	−	0.744613i	$-0.732634\pi$
$17$	−0.206593	+	0.173352i	−0.0501061	+	0.0420440i	0.617391	+	0.786657i	$0.288190\pi$
$18$		0			0
$19$	1.02778	+	0.862409i	0.235789	+	0.197850i	0.753024	−	0.657993i	$-0.228594\pi$
$19$	1.02778	+	0.862409i	0.235789	+	0.197850i	−0.517235	+	0.855843i	$0.673039\pi$
$20$	15.6241	+	3.70298i	3.49365	+	0.828011i
$21$		0			0
$22$	0.349704	+	6.00418i	0.0745570	+	1.28010i
$23$	−1.71576	+	5.73105i	−0.357761	+	1.19501i	0.569941	+	0.821685i	$0.306966\pi$
$23$	−1.71576	+	5.73105i	−0.357761	+	1.19501i	−0.927702	+	0.373320i	$0.878219\pi$
$24$		0			0
$25$	6.56334	+	8.81609i	1.31267	+	1.76322i
$26$	−1.60890	+	2.78670i	−0.315531	+	0.546516i
$27$		0			0
$28$	2.64328	+	4.57830i	0.499533	+	0.865216i
$29$	2.19520	−	5.08906i	0.407639	−	0.945014i	−0.583491	−	0.812120i	$-0.698314\pi$
$29$	2.19520	−	5.08906i	0.407639	−	0.945014i	0.991130	−	0.132894i	$-0.0424271\pi$
$30$		0			0
$31$	0.884536	+	0.937554i	0.158867	+	0.168390i	0.801918	−	0.597434i	$-0.203813\pi$
$31$	0.884536	+	0.937554i	0.158867	+	0.168390i	−0.643051	+	0.765824i	$0.722332\pi$
$32$	−0.126410	+	0.0831411i	−0.0223463	+	0.0146974i
$33$		0			0
$34$	0.453909	−	0.481116i	0.0778448	−	0.0825107i
$35$	−0.914230	+	5.18486i	−0.154533	+	0.876401i
$36$		0			0
$37$	−0.00841562	−	0.0477273i	−0.00138352	−	0.00784632i	0.984108	−	0.177570i	$-0.0568236\pi$
$37$	−0.00841562	−	0.0477273i	−0.00138352	−	0.00784632i	−0.985492	+	0.169724i	$0.945712\pi$
$38$	−2.74927	−	1.80822i	−0.445990	−	0.293332i
$39$		0			0
$40$	−19.6325	−	2.29471i	−3.10417	−	0.362825i
$41$	4.11791	+	0.481314i	0.643109	+	0.0751686i	0.431395	−	0.902163i	$-0.358022\pi$
$41$	4.11791	+	0.481314i	0.643109	+	0.0751686i	0.211714	+	0.977332i	$0.432096\pi$
$42$		0			0
$43$	−5.22957	−	3.43954i	−0.797502	−	0.524525i	0.0841345	−	0.996454i	$-0.473187\pi$
$43$	−5.22957	−	3.43954i	−0.797502	−	0.524525i	−0.881637	+	0.471929i	$0.843558\pi$
$44$	−1.70983	−	9.69693i	−0.257767	−	1.46187i
$45$		0			0
$46$	2.54785	−	14.4496i	0.375660	−	2.13048i
$47$	−5.69554	+	6.03692i	−0.830780	+	0.880575i	−0.994371	−	0.105953i	$-0.966211\pi$
$47$	−5.69554	+	6.03692i	−0.830780	+	0.880575i	0.163592	+	0.986528i	$0.447692\pi$
$48$		0			0
$49$	4.40019	−	2.89405i	0.628598	−	0.413436i
$50$	−18.4988	−	19.6076i	−2.61612	−	2.77293i
$51$		0			0
$52$	2.08658	−	4.83724i	0.289357	−	0.670805i
$53$	5.79529	+	10.0377i	0.796044	+	1.37879i	0.922174	+	0.386775i	$0.126411\pi$
$53$	5.79529	+	10.0377i	0.796044	+	1.37879i	−0.126130	+	0.992014i	$0.540256\pi$
$54$		0			0
$55$	4.90304	−	8.49231i	0.661125	−	1.14510i
$56$	−3.88617	−	5.22004i	−0.519312	−	0.697557i
$57$		0			0
$58$	−3.89859	+	13.0222i	−0.511910	+	1.70990i
$59$	−0.567212	−	9.73865i	−0.0738447	−	1.26786i	−0.808122	−	0.589015i	$-0.799516\pi$
$59$	−0.567212	−	9.73865i	−0.0738447	−	1.26786i	0.734277	−	0.678850i	$-0.237521\pi$
$60$		0			0
$61$	−4.15895	−	0.985689i	−0.532499	−	0.126205i	−0.0444347	−	0.999012i	$-0.514149\pi$
$61$	−4.15895	−	0.985689i	−0.532499	−	0.126205i	−0.488064	+	0.872808i	$0.662297\pi$
$62$	−2.42172	−	2.03206i	−0.307558	−	0.258072i
$63$		0			0
$64$	−5.98568	+	5.02258i	−0.748210	+	0.627823i
$65$	4.68839	−	2.35460i	0.581524	−	0.292052i
$66$		0			0
$67$	−0.525148	−	1.21743i	−0.0641571	−	0.148733i	0.883121	−	0.469145i	$-0.155438\pi$
$67$	−0.525148	−	1.21743i	−0.0641571	−	0.148733i	−0.947278	+	0.320412i	$0.896179\pi$
$68$	−0.646660	+	0.868614i	−0.0784190	+	0.105335i
$69$		0			0
$70$	0.750805	−	12.8908i	0.0897384	−	1.54075i
$71$	−7.40721	−	2.69600i	−0.879074	−	0.319957i	−0.137238	−	0.990538i	$-0.543823\pi$
$71$	−7.40721	−	2.69600i	−0.879074	−	0.319957i	−0.741836	+	0.670581i	$0.766045\pi$
$72$		0			0
$73$	−8.12155	+	2.95600i	−0.950556	+	0.345974i	−0.770326	−	0.637650i	$-0.779906\pi$
$73$	−8.12155	+	2.95600i	−0.950556	+	0.345974i	−0.180230	+	0.983624i	$0.557684\pi$
$74$	0.0340903	+	0.113869i	0.00396292	+	0.0132371i
$75$		0			0
$76$	4.81426	+	2.41781i	0.552234	+	0.277342i
$77$	3.14152	−	0.744553i	0.358009	−	0.0848497i
$78$		0			0
$79$	−5.19362	+	0.607048i	−0.584328	+	0.0682982i	−0.403121	−	0.915147i	$-0.632075\pi$
$79$	−5.19362	+	0.607048i	−0.584328	+	0.0682982i	−0.181207	+	0.983445i	$0.558001\pi$
$80$	16.3650			1.82967
$81$		0			0
$82$	−10.1684			−1.12291
$83$	−5.64086	+	0.659323i	−0.619165	+	0.0723700i	−0.419892	−	0.907574i	$-0.637932\pi$
$83$	−5.64086	+	0.659323i	−0.619165	+	0.0723700i	−0.199273	+	0.979944i	$0.563858\pi$
$84$		0			0
$85$	−1.04938	+	0.248707i	−0.113821	+	0.0269760i
$86$	13.7188	+	6.88984i	1.47934	+	0.742950i
$87$		0			0
$88$	3.47637	+	11.6119i	0.370583	+	1.23783i
$89$	8.61170	−	3.13440i	0.912838	−	0.332246i	0.157453	−	0.987527i	$-0.449672\pi$
$89$	8.61170	−	3.13440i	0.912838	−	0.332246i	0.755385	+	0.655281i	$0.227450\pi$
$90$		0			0
$91$	1.62316	+	0.590783i	0.170154	+	0.0619309i
$92$	−1.39672	+	23.9807i	−0.145618	+	2.50017i
$93$		0			0
$94$	12.1557	−	16.3279i	1.25376	−	1.68409i
$95$	2.12503	+	4.92638i	0.218024	+	0.505436i
$96$		0			0
$97$	11.0880	−	5.56859i	1.12581	−	0.565405i	0.214338	−	0.976759i	$-0.431241\pi$
$97$	11.0880	−	5.56859i	1.12581	−	0.565405i	0.911475	+	0.411355i	$0.134944\pi$
$98$	−9.89500	+	8.30289i	−0.999546	+	0.838719i
$99$		0			0
$100$	33.8076	+	28.3679i	3.38076	+	2.83679i
$101$	−12.1161	−	2.87156i	−1.20560	−	0.285731i	−0.421764	−	0.906705i	$-0.638589\pi$
$101$	−12.1161	−	2.87156i	−1.20560	−	0.285731i	−0.783831	+	0.620974i	$0.786737\pi$
$102$		0			0
$103$	0.363442	+	6.24005i	0.0358110	+	0.614851i	0.967700	+	0.252106i	$0.0811232\pi$
$103$	0.363442	+	6.24005i	0.0358110	+	0.614851i	−0.931889	+	0.362745i	$0.881840\pi$
$104$	−1.85993	+	6.21260i	−0.182381	+	0.609195i
$105$		0			0
$106$	−16.9756	−	22.8022i	−1.64882	−	2.21475i
$107$	9.92075	−	17.1832i	0.959075	−	1.66117i	0.234320	−	0.972159i	$-0.424714\pi$
$107$	9.92075	−	17.1832i	0.959075	−	1.66117i	0.724755	−	0.689007i	$-0.241953\pi$
$108$		0			0
$109$	−1.91684	−	3.32007i	−0.183600	−	0.318005i	0.759504	−	0.650503i	$-0.225442\pi$
$109$	−1.91684	−	3.32007i	−0.183600	−	0.318005i	−0.943104	+	0.332498i	$0.892109\pi$
$110$	−9.52596	+	22.0837i	−0.908264	+	2.10559i
$111$		0			0
$112$	3.69747	+	3.91909i	0.349378	+	0.370320i
$113$	−2.91572	+	1.91770i	−0.274288	+	0.180402i	−0.679199	−	0.733954i	$-0.737673\pi$
$113$	−2.91572	+	1.91770i	−0.274288	+	0.180402i	0.404911	+	0.914356i	$0.367302\pi$
$114$		0			0
$115$	−16.4168	+	17.4007i	−1.53087	+	1.62263i
$116$	3.86445	−	21.9164i	0.358805	−	2.03488i
$117$		0			0
$118$	4.15466	+	23.5622i	0.382467	+	2.16908i
$119$	−0.296654	−	0.195112i	−0.0271942	−	0.0178859i
$120$		0			0
$121$	4.95294	+	0.578916i	0.450267	+	0.0526287i
$122$	10.4120	+	1.21699i	0.942660	+	0.110181i
$123$		0			0
$124$	4.32418	+	2.84406i	0.388323	+	0.255404i
$125$	4.16009	+	23.5930i	0.372090	+	2.11022i
$126$		0			0
$127$	2.28154	−	12.9392i	0.202454	−	1.14817i	−0.698943	−	0.715177i	$-0.746346\pi$
$127$	2.28154	−	12.9392i	0.202454	−	1.14817i	0.901397	−	0.432994i	$-0.142543\pi$
$128$	13.3589	−	14.1596i	1.18077	−	1.25155i
$129$		0			0
$130$	−10.7507	+	7.07084i	−0.942897	+	0.620153i
$131$	−2.97214	−	3.15028i	−0.259677	−	0.275241i	0.584398	−	0.811467i	$-0.301331\pi$
$131$	−2.97214	−	3.15028i	−0.259677	−	0.275241i	−0.844074	+	0.536226i	$0.819849\pi$
$132$		0			0
$133$	−0.699643	+	1.62196i	−0.0606668	+	0.140641i
$134$	1.62592	+	2.81618i	0.140458	+	0.243281i
$135$		0			0
$136$	0.666523	−	1.15445i	0.0571539	−	0.0989935i
$137$	−13.3885	−	17.9839i	−1.14386	−	1.53647i	−0.802618	−	0.596493i	$-0.796560\pi$
$137$	−13.3885	−	17.9839i	−1.14386	−	1.53647i	−0.341241	−	0.939976i	$-0.610847\pi$
$138$		0			0
$139$	2.75308	−	9.19593i	0.233513	−	0.779989i	−0.758257	−	0.651956i	$-0.773949\pi$
$139$	2.75308	−	9.19593i	0.233513	−	0.779989i	0.991770	−	0.128033i	$-0.0408663\pi$
$140$	1.22920	+	21.1045i	0.103886	+	1.78365i
$141$		0			0
$142$	18.8119	+	4.45850i	1.57866	+	0.374149i
$143$	−2.46456	−	2.06801i	−0.206097	−	0.172936i
$144$		0			0
$145$	16.9779	−	14.2461i	1.40994	−	1.18308i
$146$	18.9428	−	9.51341i	1.56771	−	0.787336i
$147$		0			0
$148$	−0.0770767	−	0.178684i	−0.00633567	−	0.0146877i
$149$	−9.93888	+	13.3502i	−0.814225	+	1.09369i	0.179710	+	0.983720i	$0.442484\pi$
$149$	−9.93888	+	13.3502i	−0.814225	+	1.09369i	−0.993934	+	0.109974i	$0.964923\pi$
$150$		0			0
$151$	0.106543	−	1.82928i	0.00867039	−	0.148865i	−0.991194	−	0.132415i	$-0.957727\pi$
$151$	0.106543	−	1.82928i	0.00867039	−	0.148865i	0.999865	−	0.0164494i	$-0.00523624\pi$
$152$	−6.23183	−	2.26820i	−0.505468	−	0.183975i
$153$		0			0
$154$	−7.44086	+	2.70825i	−0.599601	+	0.218237i
$155$	1.47829	+	4.93783i	0.118739	+	0.396616i
$156$		0			0
$157$	−9.65812	−	4.85049i	−0.770802	−	0.387111i	0.0195149	−	0.999810i	$-0.493788\pi$
$157$	−9.65812	−	4.85049i	−0.770802	−	0.387111i	−0.790317	+	0.612698i	$0.790084\pi$
$158$	12.4790	−	2.95758i	0.992778	−	0.235293i
$159$		0			0
$160$	−0.600940	+	0.0702398i	−0.0475085	+	0.00555295i
$161$	−7.87629			−0.620738
$162$		0			0
$163$	3.76716			0.295067			0.147533	−	0.989057i	$-0.452867\pi$
$163$	3.76716			0.295067			0.147533	+	0.989057i	$0.452867\pi$
$164$	16.5349	−	1.93265i	1.29116	−	0.150915i
$165$		0			0
$166$	13.5536	−	3.21227i	1.05197	−	0.249321i
$167$	−10.5761	−	5.31150i	−0.818400	−	0.411016i	−0.0102172	−	0.999948i	$-0.503252\pi$
$167$	−10.5761	−	5.31150i	−0.818400	−	0.411016i	−0.808183	+	0.588932i	$0.799549\pi$
$168$		0			0
$169$	3.23477	+	10.8049i	0.248828	+	0.831144i
$170$	2.48551	−	0.904650i	0.190630	−	0.0693835i
$171$		0			0
$172$	−23.6176	−	8.59612i	−1.80083	−	0.655448i
$173$	−0.556322	+	9.55169i	−0.0422964	+	0.726201i	0.908786	+	0.417263i	$0.137011\pi$
$173$	−0.556322	+	9.55169i	−0.0422964	+	0.726201i	−0.951082	+	0.308938i	$0.900026\pi$
$174$		0			0
$175$	−8.64118	+	11.6071i	−0.653212	+	0.877416i
$176$	−3.97485	−	9.21473i	−0.299615	−	0.694586i
$177$		0			0
$178$	−20.0860	+	10.0876i	−1.50551	+	0.756094i
$179$	1.08723	−	0.912294i	0.0812633	−	0.0681880i	−0.601251	−	0.799060i	$-0.705331\pi$
$179$	1.08723	−	0.912294i	0.0812633	−	0.0681880i	0.682514	+	0.730872i	$0.260886\pi$
$180$		0			0
$181$	−7.58350	−	6.36331i	−0.563677	−	0.472981i	0.315864	−	0.948804i	$-0.397706\pi$
$181$	−7.58350	−	6.36331i	−0.563677	−	0.472981i	−0.879541	+	0.475823i	$0.842150\pi$
$182$	−4.12231	−	0.977004i	−0.305566	−	0.0724204i
$183$		0			0
$184$	−1.71937	−	29.5204i	−0.126753	−	2.17627i
$185$	0.0555823	−	0.185658i	0.00408649	−	0.0136498i
$186$		0			0
$187$	0.394920	+	0.530469i	0.0288794	+	0.0387918i
$188$	−16.6630	+	28.8611i	−1.21527	+	2.10491i
$189$		0			0
$190$	−6.57936	−	11.3958i	−0.477317	−	0.826737i
$191$	7.05983	−	16.3665i	0.510831	−	1.18424i	−0.446378	−	0.894844i	$-0.647286\pi$
$191$	7.05983	−	16.3665i	0.510831	−	1.18424i	0.957210	−	0.289396i	$-0.0934544\pi$
$192$		0			0
$193$	−18.9616	−	20.0981i	−1.36488	−	1.44669i	−0.758886	−	0.651223i	$-0.774256\pi$
$193$	−18.9616	−	20.0981i	−1.36488	−	1.44669i	−0.605996	−	0.795468i	$-0.707225\pi$
$194$	−25.4252	+	16.7224i	−1.82542	+	1.20060i
$195$		0			0
$196$	14.5122	−	15.3820i	1.03659	−	1.09872i
$197$	1.04040	−	5.90042i	0.0741256	−	0.420387i	−0.925052	−	0.379840i	$-0.875979\pi$
$197$	1.04040	−	5.90042i	0.0741256	−	0.420387i	0.999178	−	0.0405468i	$-0.0129100\pi$
$198$		0			0
$199$	2.78863	+	15.8151i	0.197681	+	1.12110i	0.908549	+	0.417779i	$0.137191\pi$
$199$	2.78863	+	15.8151i	0.197681	+	1.12110i	−0.710868	+	0.703326i	$0.751698\pi$
$200$	−45.3899	−	29.8534i	−3.20955	−	2.11096i
$201$		0			0
$202$	30.3329	+	3.54541i	2.13421	+	0.249454i
$203$	7.24760	+	0.847123i	0.508682	+	0.0594564i
$204$		0			0
$205$	13.8516	+	9.11034i	0.967438	+	0.636294i
$206$	−2.66210	−	15.0975i	−0.185478	−	1.05190i
$207$		0			0
$208$	0.932348	−	5.28761i	0.0646467	−	0.366630i
$209$	2.25778	−	2.39310i	0.156174	−	0.165534i
$210$		0			0
$211$	8.41443	−	5.53426i	0.579273	−	0.380994i	−0.225796	−	0.974175i	$-0.572498\pi$
$211$	8.41443	−	5.53426i	0.579273	−	0.380994i	0.805069	+	0.593181i	$0.202128\pi$
$212$	31.9380	+	33.8523i	2.19351	+	2.32498i
$213$		0			0
$214$	−19.2747	+	44.6838i	−1.31759	+	3.05452i
$215$	−12.5151	−	21.6767i	−0.853520	−	1.47834i
$216$		0			0
$217$	−0.848510	+	1.46966i	−0.0576006	+	0.0997672i
$218$	5.61484	+	7.54203i	0.380285	+	0.510811i
$219$		0			0
$220$	11.2929	−	37.7208i	0.761364	−	2.54313i
$221$	0.0205731	+	0.353227i	0.00138390	+	0.0237606i
$222$		0			0
$223$	−12.6909	−	3.00779i	−0.849844	−	0.201417i	−0.217457	−	0.976070i	$-0.569776\pi$
$223$	−12.6909	−	3.00779i	−0.849844	−	0.201417i	−0.632386	+	0.774653i	$0.717924\pi$
$224$	−0.152596	−	0.128043i	−0.0101957	−	0.00855525i
$225$		0			0
$226$	6.55678	−	5.50179i	0.436151	−	0.365974i
$227$	−14.5592	+	7.31190i	−0.966328	+	0.485308i	−0.860708	−	0.509098i	$-0.829979\pi$
$227$	−14.5592	+	7.31190i	−0.966328	+	0.485308i	−0.105620	+	0.994407i	$0.533683\pi$
$228$		0			0
$229$	−2.66861	−	6.18653i	−0.176347	−	0.408817i	0.807002	−	0.590549i	$-0.201089\pi$
$229$	−2.66861	−	6.18653i	−0.176347	−	0.408817i	−0.983348	+	0.181732i	$0.941830\pi$
$230$	35.0373	−	47.0633i	2.31029	−	3.10326i
$231$		0			0
$232$	−1.59290	+	27.3490i	−0.104579	+	1.79555i
$233$	12.9692	+	4.72040i	0.849641	+	0.309244i	0.729894	−	0.683560i	$-0.239569\pi$
$233$	12.9692	+	4.72040i	0.849641	+	0.309244i	0.119747	+	0.992804i	$0.461792\pi$
$234$		0			0
$235$	−31.1875	+	11.3513i	−2.03445	+	0.740479i
$236$	−11.2342	−	37.5249i	−0.731286	−	2.44266i
$237$		0			0
$238$	0.778215	+	0.390834i	0.0504442	+	0.0253340i
$239$	−12.2001	+	2.89148i	−0.789159	+	0.187034i	−0.605383	−	0.795934i	$-0.706980\pi$
$239$	−12.2001	+	2.89148i	−0.789159	+	0.187034i	−0.183776	+	0.982968i	$0.558832\pi$
$240$		0			0
$241$	−13.5982	+	1.58941i	−0.875940	+	0.102383i	−0.542167	−	0.840271i	$-0.682396\pi$
$241$	−13.5982	+	1.58941i	−0.875940	+	0.102383i	−0.333773	+	0.942653i	$0.608322\pi$
$242$	−12.2304			−0.786199
$243$		0			0
$244$	−17.1623			−1.09870
$245$	20.9181	−	2.44497i	1.33641	−	0.156203i
$246$		0			0
$247$	1.71280	−	0.405941i	0.108983	−	0.0258294i
$248$	−5.69353	−	2.85940i	−0.361540	−	0.181572i
$249$		0			0
$250$	−16.8518	−	56.2890i	−1.06580	−	3.56003i
$251$	12.4879	−	4.54521i	0.788226	−	0.286891i	0.0836277	−	0.996497i	$-0.473349\pi$
$251$	12.4879	−	4.54521i	0.788226	−	0.286891i	0.704599	+	0.709606i	$0.251127\pi$
$252$		0			0
$253$	13.7853	+	5.01745i	0.866676	+	0.315444i
$254$	−1.87370	+	32.1701i	−0.117566	+	2.01853i
$255$		0			0
$256$	−19.1791	+	25.7620i	−1.19869	+	1.61012i
$257$	1.33177	+	3.08739i	0.0830736	+	0.192586i	0.954690	−	0.297603i	$-0.0961870\pi$
$257$	1.33177	+	3.08739i	0.0830736	+	0.192586i	−0.871616	+	0.490189i	$0.836928\pi$
$258$		0			0
$259$	0.0570194	−	0.0286362i	0.00354302	−	0.00177937i
$260$	16.1378	−	13.5412i	1.00082	−	0.839790i
$261$		0			0
$262$	8.13723	+	6.82794i	0.502720	+	0.421832i
$263$	23.7653	+	5.63248i	1.46543	+	0.347313i	0.884462	−	0.466612i	$-0.154526\pi$
$263$	23.7653	+	5.63248i	1.46543	+	0.347313i	0.580969	+	0.813926i	$0.302674\pi$
$264$		0			0
$265$	2.69497	+	46.2708i	0.165550	+	2.84239i
$266$	1.24254	−	4.15036i	0.0761848	−	0.254475i
$267$		0			0
$268$	−3.17917	−	4.27037i	−0.194199	−	0.260854i
$269$	−0.417322	+	0.722824i	−0.0254446	+	0.0440713i	−0.878467	−	0.477802i	$-0.841433\pi$
$269$	−0.417322	+	0.722824i	−0.0254446	+	0.0440713i	0.853023	+	0.521874i	$0.174767\pi$
$270$		0			0
$271$	14.1085	+	24.4366i	0.857029	+	1.48442i	0.874750	+	0.484575i	$0.161026\pi$
$271$	14.1085	+	24.4366i	0.857029	+	1.48442i	−0.0177208	+	0.999843i	$0.505641\pi$
$272$	−0.437143	+	1.01341i	−0.0265057	+	0.0614471i
$273$		0			0
$274$	37.7356	+	39.9974i	2.27969	+	2.41633i
$275$	22.5182	−	14.8104i	1.35790	−	0.893103i
$276$		0			0
$277$	18.4055	−	19.5087i	1.10588	−	1.17217i	0.122151	−	0.992512i	$-0.461021\pi$
$277$	18.4055	−	19.5087i	1.10588	−	1.17217i	0.983730	−	0.179654i	$-0.0574978\pi$
$278$	−4.08824	+	23.1856i	−0.245196	+	1.39058i
$279$		0			0
$280$	−4.51897	−	25.6284i	−0.270060	−	1.53159i
$281$	12.2272	+	8.04196i	0.729414	+	0.479743i	0.859097	−	0.511812i	$-0.171026\pi$
$281$	12.2272	+	8.04196i	0.729414	+	0.479743i	−0.129683	+	0.991555i	$0.541396\pi$
$282$		0			0
$283$	−1.15958	−	0.135536i	−0.0689299	−	0.00805675i	0.0815580	−	0.996669i	$-0.474010\pi$
$283$	−1.15958	−	0.135536i	−0.0689299	−	0.00805675i	−0.150488	+	0.988612i	$0.548084\pi$
$284$	−31.4374	−	3.67451i	−1.86547	−	0.218042i
$285$		0			0
$286$	6.59261	+	4.33603i	0.389829	+	0.256395i
$287$	0.947854	+	5.37555i	0.0559500	+	0.317308i
$288$		0			0
$289$	−2.93939	+	16.6701i	−0.172905	+	0.980594i
$290$	−37.3025	+	39.5383i	−2.19048	+	2.32177i
$291$		0			0
$292$	−28.9947	+	19.0701i	−1.69679	+	1.11599i
$293$	11.4840	+	12.1723i	0.670902	+	0.711114i	0.969999	−	0.243108i	$-0.0781670\pi$
$293$	11.4840	+	12.1723i	0.670902	+	0.711114i	−0.299097	+	0.954223i	$0.596686\pi$
$294$		0			0
$295$	15.4509	−	35.8192i	0.899586	−	2.08548i
$296$	0.119776	+	0.207458i	0.00696184	+	0.0120583i
$297$		0			0
$298$	20.4103	−	35.3516i	1.18234	−	2.04786i
$299$	4.68696	+	6.29568i	0.271054	+	0.364088i
$300$		0			0
$301$	2.36351	−	7.89469i	0.136231	−	0.455042i
$302$	0.261311	+	4.48654i	0.0150368	+	0.258171i
$303$		0			0
$304$	5.34267	+	1.26624i	0.306423	+	0.0726236i
$305$	−13.0931	−	10.9864i	−0.749707	−	0.629079i
$306$		0			0
$307$	−15.6362	+	13.1204i	−0.892407	+	0.748818i	−0.968691	−	0.248268i	$-0.920139\pi$
$307$	−15.6362	+	13.1204i	−0.892407	+	0.748818i	0.0762844	+	0.997086i	$0.475694\pi$
$308$	11.5848	−	5.81813i	0.660108	−	0.331519i
$309$		0			0
$310$	−5.00713	−	11.6078i	−0.284386	−	0.659281i
$311$	−3.96265	+	5.32276i	−0.224701	+	0.301826i	−0.900149	−	0.435581i	$-0.856543\pi$
$311$	−3.96265	+	5.32276i	−0.224701	+	0.301826i	0.675448	+	0.737407i	$0.263950\pi$
$312$		0			0
$313$	0.533740	−	9.16397i	0.0301688	−	0.517978i	−0.949044	−	0.315143i	$-0.897947\pi$
$313$	0.533740	−	9.16397i	0.0301688	−	0.517978i	0.979213	−	0.202835i	$-0.0650155\pi$
$314$	24.9087	+	9.06601i	1.40568	+	0.511625i
$315$		0			0
$316$	−19.7300	+	7.18114i	−1.10990	+	0.403971i
$317$	0.0143668	+	0.0479884i	0.000806919	+	0.00269530i	0.958392	−	0.285455i	$-0.0921448\pi$
$317$	0.0143668	+	0.0479884i	0.000806919	+	0.00269530i	−0.957585	+	0.288151i	$0.906960\pi$
$318$		0			0
$319$	−12.1453	−	6.09962i	−0.680008	−	0.341513i
$320$	−30.4039	+	7.20586i	−1.69963	+	0.402820i
$321$		0			0
$322$	19.1869	−	2.24263i	1.06925	−	0.124977i
$323$	−0.361832			−0.0201329
$324$		0			0
$325$	14.4199			0.799874
$326$	−9.17695	+	1.07263i	−0.508264	+	0.0594076i
$327$		0			0
$328$	−19.9407	+	4.72603i	−1.10104	+	0.260951i
$329$	−9.76484	−	4.90409i	−0.538353	−	0.270371i
$330$		0			0
$331$	5.30612	+	17.7237i	0.291651	+	0.974181i	0.970742	+	0.240127i	$0.0771890\pi$
$331$	5.30612	+	17.7237i	0.291651	+	0.974181i	−0.679091	+	0.734054i	$0.737626\pi$
$332$	−21.4290	+	7.79954i	−1.17607	+	0.428055i
$333$		0			0
$334$	27.2761	+	9.92767i	1.49248	+	0.543218i
$335$	0.308281	−	5.29299i	0.0168432	−	0.289187i
$336$		0			0
$337$	−2.17944	+	2.92750i	−0.118722	+	0.159471i	−0.857511	−	0.514465i	$-0.827990\pi$
$337$	−2.17944	+	2.92750i	−0.118722	+	0.159471i	0.738789	+	0.673936i	$0.235398\pi$
$338$	−10.9565	−	25.4001i	−0.595956	−	1.38158i
$339$		0			0
$340$	−3.86974	+	1.94346i	−0.209866	+	0.105399i
$341$	2.42131	−	2.03172i	0.131121	−	0.110024i
$342$		0			0
$343$	12.3716	+	10.3810i	0.668005	+	0.560523i
$344$	30.1053	+	7.13509i	1.62317	+	0.384698i
$345$		0			0
$346$	−1.36445	−	23.4267i	−0.0733533	−	1.25943i
$347$	1.17599	−	3.92808i	0.0631305	−	0.210870i	−0.920605	−	0.390496i	$-0.872303\pi$
$347$	1.17599	−	3.92808i	0.0631305	−	0.210870i	0.983735	+	0.179626i	$0.0574887\pi$
$348$		0			0
$349$	4.51755	+	6.06813i	0.241819	+	0.324819i	0.906419	−	0.422380i	$-0.138805\pi$
$349$	4.51755	+	6.06813i	0.241819	+	0.324819i	−0.664600	+	0.747200i	$0.731398\pi$
$350$	17.7453	−	30.7358i	0.948528	−	1.64290i
$351$		0			0
$352$	0.185511	+	0.321314i	0.00988775	+	0.0171261i
$353$	−0.812133	+	1.88274i	−0.0432255	+	0.100208i	−0.938461	−	0.345386i	$-0.887748\pi$
$353$	−0.812133	+	1.88274i	−0.0432255	+	0.100208i	0.895235	+	0.445594i	$0.147007\pi$
$354$		0			0
$355$	−21.6313	−	22.9279i	−1.14807	−	1.21688i
$356$	30.7445	−	20.2210i	1.62946	−	1.07171i
$357$		0			0
$358$	−2.38878	+	2.53195i	−0.126251	+	0.133818i
$359$	1.74531	−	9.89817i	0.0921141	−	0.522405i	−0.903479	−	0.428631i	$-0.858996\pi$
$359$	1.74531	−	9.89817i	0.0921141	−	0.522405i	0.995594	−	0.0937737i	$-0.0298930\pi$
$360$		0			0
$361$	−2.98674	−	16.9386i	−0.157197	−	0.891506i
$362$	20.2855	+	13.3420i	1.06618	+	0.701240i
$363$		0			0
$364$	6.88898	+	0.805206i	0.361080	+	0.0422043i
$365$	−34.3276	−	4.01232i	−1.79679	−	0.210015i
$366$		0			0
$367$	−27.1341	−	17.8464i	−1.41639	−	0.931574i	−0.999747	−	0.0225041i	$-0.992836\pi$
$367$	−27.1341	−	17.8464i	−1.41639	−	0.931574i	−0.416643	−	0.909070i	$-0.636794\pi$
$368$	4.25131	+	24.1104i	0.221615	+	1.25684i
$369$		0			0
$370$	−0.0825380	+	0.468096i	−0.00429095	+	0.0243352i
$371$	−10.4720	+	11.0997i	−0.543680	+	0.576267i
$372$		0			0
$373$	−12.6178	+	8.29884i	−0.653324	+	0.429698i	−0.832429	−	0.554132i	$-0.813050\pi$
$373$	−12.6178	+	8.29884i	−0.653324	+	0.429698i	0.179105	+	0.983830i	$0.442680\pi$
$374$	−1.11308	−	1.17980i	−0.0575561	−	0.0610059i
$375$		0			0
$376$	16.2489	−	37.6692i	0.837974	−	1.94264i
$377$	−3.63572	−	6.29725i	−0.187249	−	0.324325i
$378$		0			0
$379$	1.32973	−	2.30316i	0.0683037	−	0.118305i	−0.829851	−	0.557985i	$-0.811575\pi$
$379$	1.32973	−	2.30316i	0.0683037	−	0.118305i	0.898155	+	0.439680i	$0.144908\pi$
$380$	12.8646	+	17.2802i	0.659942	+	0.886455i
$381$		0			0
$382$	−12.5380	+	41.8797i	−0.641497	+	2.14275i
$383$	−0.0903647	−	1.55150i	−0.00461742	−	0.0792780i	0.995212	−	0.0977380i	$-0.0311607\pi$
$383$	−0.0903647	−	1.55150i	−0.00461742	−	0.0792780i	−0.999830	+	0.0184600i	$0.994124\pi$
$384$		0			0
$385$	12.5625	+	2.97737i	0.640244	+	0.151741i
$386$	51.9137	+	43.5607i	2.64234	+	2.21718i
$387$		0			0
$388$	38.1656	−	32.0247i	1.93757	−	1.62581i
$389$	3.28564	−	1.65011i	0.166588	−	0.0836638i	−0.363551	−	0.931574i	$-0.618436\pi$
$389$	3.28564	−	1.65011i	0.166588	−	0.0836638i	0.530140	+	0.847910i	$0.322140\pi$
$390$		0			0
$391$	−0.639024	−	1.48142i	−0.0323168	−	0.0749188i
$392$	−15.5455	+	20.8812i	−0.785167	+	1.05466i
$393$		0			0
$394$	−0.854424	+	14.6699i	−0.0430452	+	0.739058i
$395$	−19.6490	−	7.15164i	−0.988647	−	0.359838i
$396$		0			0
$397$	36.1674	−	13.1638i	1.81519	−	0.660674i	0.818965	−	0.573844i	$-0.194548\pi$
$397$	36.1674	−	13.1638i	1.81519	−	0.660674i	0.996223	−	0.0868301i	$-0.0276737\pi$
$398$	−11.2963	−	37.7323i	−0.566232	−	1.89135i
$399$		0			0
$400$	40.1952	+	20.1868i	2.00976	+	1.00934i
$401$	−17.3252	+	4.10616i	−0.865182	+	0.205052i	−0.639163	−	0.769071i	$-0.720719\pi$
$401$	−17.3252	+	4.10616i	−0.865182	+	0.205052i	−0.226018	+	0.974123i	$0.572571\pi$
$402$		0			0
$403$	1.67965	−	0.196324i	0.0836696	−	0.00977957i
$404$	−49.9982			−2.48750
$405$		0			0
$406$	−17.8966			−0.888196
$407$	−0.118039	+	0.0137968i	−0.00585100	+	0.000683884i
$408$		0			0
$409$	−17.8371	+	4.22746i	−0.881986	+	0.209035i	−0.646565	−	0.762859i	$-0.723795\pi$
$409$	−17.8371	+	4.22746i	−0.881986	+	0.209035i	−0.235421	+	0.971893i	$0.575647\pi$
$410$	−36.3371	−	18.2492i	−1.79456	−	0.901262i
$411$		0			0
$412$	7.19834	+	24.0441i	0.354637	+	1.18457i
$413$	12.0689	−	4.39273i	0.593873	−	0.216152i
$414$		0			0
$415$	−21.3410	−	7.76749i	−1.04759	−	0.381291i
$416$	−0.0115420	+	0.198168i	−0.000565892	+	0.00971598i
$417$		0			0
$418$	−4.81864	+	6.47255i	−0.235687	+	0.316583i
$419$	4.94733	+	11.4692i	0.241693	+	0.560308i	0.995280	−	0.0970402i	$-0.0309375\pi$
$419$	4.94733	+	11.4692i	0.241693	+	0.560308i	−0.753587	+	0.657348i	$0.771678\pi$
$420$		0			0
$421$	19.3203	−	9.70302i	0.941614	−	0.472896i	0.0893456	−	0.996001i	$-0.471522\pi$
$421$	19.3203	−	9.70302i	0.941614	−	0.472896i	0.852269	+	0.523104i	$0.175226\pi$
$422$	−18.9221	+	15.8775i	−0.921114	+	0.772906i
$423$		0			0
$424$	−43.8878	−	36.8262i	−2.13138	−	1.78844i
$425$	−2.88422	−	0.683574i	−0.139905	−	0.0331582i
$426$		0			0
$427$	−0.327198	−	5.61777i	−0.0158342	−	0.271863i
$428$	22.8498	−	76.3238i	1.10449	−	3.68925i
$429$		0			0
$430$	36.6592	+	49.2419i	1.76787	+	2.37466i
$431$	−15.5400	+	26.9162i	−0.748538	+	1.29651i	0.199986	+	0.979799i	$0.435910\pi$
$431$	−15.5400	+	26.9162i	−0.748538	+	1.29651i	−0.948524	+	0.316707i	$0.897423\pi$
$432$		0			0
$433$	−6.64480	−	11.5091i	−0.319329	−	0.553093i	0.661019	−	0.750369i	$-0.270124\pi$
$433$	−6.64480	−	11.5091i	−0.319329	−	0.553093i	−0.980348	+	0.197275i	$0.936791\pi$
$434$	1.64854	−	3.82175i	0.0791326	−	0.183450i
$435$		0			0
$436$	−10.5638	−	11.1969i	−0.505912	−	0.536236i
$437$	−6.70593	+	4.41056i	−0.320788	+	0.210986i
$438$		0			0
$439$	0.880146	−	0.932901i	0.0420071	−	0.0445249i	−0.706029	−	0.708183i	$-0.749515\pi$
$439$	0.880146	−	0.932901i	0.0420071	−	0.0445249i	0.748036	+	0.663658i	$0.230997\pi$
$440$	−8.41685	+	47.7343i	−0.401258	+	2.27564i
$441$		0			0
$442$	−0.150692	−	0.854617i	−0.00716769	−	0.0406500i
$443$	−32.6702	−	21.4875i	−1.55221	−	1.02090i	−0.979572	−	0.201094i	$-0.935550\pi$
$443$	−32.6702	−	21.4875i	−1.55221	−	1.02090i	−0.572637	−	0.819809i	$-0.694079\pi$
$444$		0			0
$445$	36.3993	+	4.25447i	1.72549	+	0.201681i
$446$	31.7719	+	3.71360i	1.50444	+	0.175844i
$447$		0			0
$448$	−8.59504	−	5.65305i	−0.406077	−	0.267081i
$449$	2.78437	+	15.7909i	0.131403	+	0.745221i	0.977298	+	0.211871i	$0.0679558\pi$
$449$	2.78437	+	15.7909i	0.131403	+	0.745221i	−0.845895	+	0.533349i	$0.820933\pi$
$450$		0			0
$451$	1.76543	−	10.0123i	0.0831310	−	0.471459i
$452$	−9.61630	+	10.1927i	−0.452313	+	0.479423i
$453$		0			0
$454$	33.3849	−	21.9576i	1.56683	−	1.03052i
$455$	4.74013	+	5.02425i	0.222221	+	0.235540i
$456$		0			0
$457$	−1.53118	+	3.54968i	−0.0716256	+	0.166047i	−0.950268	−	0.311434i	$-0.899191\pi$
$457$	−1.53118	+	3.54968i	−0.0716256	+	0.166047i	0.878642	+	0.477481i	$0.158450\pi$
$458$	8.26234	+	14.3108i	0.386074	+	0.668699i
$459$		0			0
$460$	−48.0292	+	83.1890i	−2.23937	+	3.87871i
$461$	12.6783	+	17.0299i	0.590486	+	0.793160i	0.992470	−	0.122486i	$-0.0390868\pi$
$461$	12.6783	+	17.0299i	0.590486	+	0.793160i	−0.401984	+	0.915647i	$0.631679\pi$
$462$		0			0
$463$	−5.53918	+	18.5021i	−0.257427	+	0.859867i	0.727383	+	0.686232i	$0.240737\pi$
$463$	−5.53918	+	18.5021i	−0.257427	+	0.859867i	−0.984810	+	0.173635i	$0.944449\pi$
$464$	−1.31881	−	22.6431i	−0.0612244	−	1.05118i
$465$		0			0
$466$	−32.9376	−	7.80634i	−1.52580	−	0.361622i
$467$	3.15564	+	2.64790i	0.146026	+	0.122530i	0.712874	−	0.701292i	$-0.247393\pi$
$467$	3.15564	+	2.64790i	0.146026	+	0.122530i	−0.566848	+	0.823822i	$0.691838\pi$
$468$		0			0
$469$	1.33722	−	1.12206i	0.0617469	−	0.0518118i
$470$	72.7419	−	36.5324i	3.35533	−	1.68511i
$471$		0			0
$472$	19.0986	+	44.2755i	0.879084	+	2.03794i
$473$	−9.16587	+	12.3119i	−0.421447	+	0.566102i
$474$		0			0
$475$	−0.857416	+	14.7213i	−0.0393410	+	0.675458i
$476$	−1.33974	−	0.487625i	−0.0614068	−	0.0223503i
$477$		0			0
$478$	28.8966	−	10.5175i	1.32170	−	0.481060i
$479$	8.24624	+	27.5443i	0.376780	+	1.25853i	0.910725	+	0.413014i	$0.135524\pi$
$479$	8.24624	+	27.5443i	0.376780	+	1.25853i	−0.533945	+	0.845520i	$0.679291\pi$
$480$		0			0
$481$	−0.0568202	−	0.0285362i	−0.00259078	−	0.00130114i
$482$	32.6733	−	7.74372i	1.48823	−	0.352717i
$483$		0			0
$484$	19.8878	−	2.32456i	0.903993	−	0.105662i
$485$	49.6170			2.25299
$486$		0			0
$487$	8.88765			0.402738			0.201369	−	0.979515i	$-0.435461\pi$
$487$	8.88765			0.402738			0.201369	+	0.979515i	$0.435461\pi$
$488$	20.9840	−	2.45268i	0.949901	−	0.111028i
$489$		0			0
$490$	−50.2611	+	11.9121i	−2.27056	+	0.538134i
$491$	25.2009	+	12.6563i	1.13730	+	0.571173i	0.914859	−	0.403773i	$-0.132302\pi$
$491$	25.2009	+	12.6563i	1.13730	+	0.571173i	0.222440	+	0.974946i	$0.428598\pi$
$492$		0			0
$493$	0.428684	+	1.43191i	0.0193070	+	0.0644898i
$494$	−4.05686	+	1.47658i	−0.182527	+	0.0664344i
$495$		0			0
$496$	4.95683	+	1.80414i	0.222568	+	0.0810082i
$497$	0.603432	−	10.3605i	0.0270676	−	0.464733i
$498$		0			0
$499$	0.710634	−	0.954547i	0.0318123	−	0.0427314i	−0.785932	−	0.618312i	$-0.787817\pi$
$499$	0.710634	−	0.954547i	0.0318123	−	0.0427314i	0.817745	+	0.575581i	$0.195224\pi$
$500$	38.1013	+	88.3287i	1.70394	+	3.95018i
$501$		0			0
$502$	−29.1267	+	14.6280i	−1.29999	+	0.652880i
$503$	−4.59276	+	3.85379i	−0.204781	+	0.171832i	−0.739411	−	0.673255i	$-0.764896\pi$
$503$	−4.59276	+	3.85379i	−0.204781	+	0.171832i	0.534629	+	0.845087i	$0.320451\pi$
$504$		0			0
$505$	−38.1435	−	32.0062i	−1.69736	−	1.42426i
$506$	−35.0102	−	8.29758i	−1.55639	−	0.368872i
$507$		0			0
$508$	−3.06756	−	52.6680i	−0.136101	−	2.33676i
$509$	7.20888	−	24.0793i	0.319528	−	1.06730i	−0.635826	−	0.771833i	$-0.719340\pi$
$509$	7.20888	−	24.0793i	0.319528	−	1.06730i	0.955354	−	0.295465i	$-0.0954745\pi$
$510$		0			0
$511$	−6.79503	−	9.12731i	−0.300594	−	0.403768i
$512$	19.9189	−	34.5006i	0.880300	−	1.52473i
$513$		0			0
$514$	−4.12333	−	7.14181i	−0.181872	−	0.315012i
$515$	−9.90019	+	22.9512i	−0.436254	+	1.01135i
$516$		0			0
$517$	13.9667	+	14.8038i	0.614253	+	0.651070i
$518$	−0.130748	+	0.0859943i	−0.00574474	+	0.00377837i
$519$		0			0
$520$	−17.7962	+	18.8628i	−0.780414	+	0.827190i
$521$	5.84968	−	33.1752i	0.256279	−	1.45343i	−0.536488	−	0.843908i	$-0.680250\pi$
$521$	5.84968	−	33.1752i	0.256279	−	1.45343i	0.792768	−	0.609524i	$-0.208639\pi$
$522$		0			0
$523$	4.18478	+	23.7331i	0.182988	+	1.03778i	0.928513	+	0.371299i	$0.121087\pi$
$523$	4.18478	+	23.7331i	0.182988	+	1.03778i	−0.745526	+	0.666477i	$0.767801\pi$
$524$	−14.5297	−	9.55633i	−0.634733	−	0.417470i
$525$		0			0
$526$	−59.4970	−	6.95420i	−2.59419	−	0.303217i
$527$	−0.345265	−	0.0403557i	−0.0150400	−	0.00175792i
$528$		0			0
$529$	−10.6848	−	7.02753i	−0.464558	−	0.305545i
$530$	−19.7398	−	111.950i	−0.857443	−	4.86280i
$531$		0			0
$532$	−1.23166	+	6.98506i	−0.0533990	+	0.302841i
$533$	3.73274	−	3.95648i	0.161683	−	0.171374i
$534$		0			0
$535$	66.2905	−	43.6000i	2.86599	−	1.88499i
$536$	4.49739	+	4.76696i	0.194258	+	0.205901i
$537$		0			0
$538$	0.810803	−	1.87965i	0.0349562	−	0.0810376i
$539$	−6.45742	−	11.1846i	−0.278141	−	0.481754i
$540$		0			0
$541$	−11.3703	+	19.6940i	−0.488849	+	0.846712i	−0.999918	−	0.0128282i	$-0.995917\pi$
$541$	−11.3703	+	19.6940i	−0.488849	+	0.846712i	0.511068	+	0.859540i	$0.329250\pi$
$542$	−41.3267	−	55.5114i	−1.77513	−	2.38442i
$543$		0			0
$544$	0.0117027	−	0.0390897i	0.000501749	−	0.00167596i
$545$	−0.891384	−	15.3045i	−0.0381827	−	0.655571i
$546$		0			0
$547$	0.378936	+	0.0898095i	0.0162021	+	0.00383998i	0.238709	−	0.971091i	$-0.423276\pi$
$547$	0.378936	+	0.0898095i	0.0162021	+	0.00383998i	−0.222507	+	0.974931i	$0.571424\pi$
$548$	−68.9639	−	57.8676i	−2.94599	−	2.47198i
$549$		0			0
$550$	−50.6382	+	42.4905i	−2.15922	+	1.81180i
$551$	6.64503	−	3.33726i	0.283088	−	0.142172i
$552$		0			0
$553$	−2.72677	−	6.32136i	−0.115954	−	0.268811i
$554$	−39.2818	+	52.7647i	−1.66893	+	2.24176i
$555$		0			0
$556$	2.24115	−	38.4791i	0.0950460	−	1.63188i
$557$	−19.6611	−	7.15607i	−0.833069	−	0.303212i	−0.109951	−	0.993937i	$-0.535069\pi$
$557$	−19.6611	−	7.15607i	−0.833069	−	0.303212i	−0.723118	+	0.690725i	$0.757292\pi$
$558$		0			0
$559$	−7.71685	+	2.80870i	−0.326388	+	0.118795i
$560$	6.17944	+	20.6408i	0.261129	+	0.872232i
$561$		0			0
$562$	−32.0758	−	16.1091i	−1.35303	−	0.679520i
$563$	13.4939	−	3.19812i	0.568701	−	0.134785i	0.0638013	−	0.997963i	$-0.479678\pi$
$563$	13.4939	−	3.19812i	0.568701	−	0.134785i	0.504900	+	0.863178i	$0.331529\pi$
$564$		0			0
$565$	−13.8611	+	1.62013i	−0.583139	+	0.0681592i
$566$	2.86338			0.120357
$567$		0			0
$568$	38.9631			1.63485
$569$	−9.23784	+	1.07975i	−0.387270	+	0.0452654i	−0.307501	−	0.951548i	$-0.599493\pi$
$569$	−9.23784	+	1.07975i	−0.387270	+	0.0452654i	−0.0797697	+	0.996813i	$0.525419\pi$
$570$		0			0
$571$	35.0608	−	8.30957i	1.46725	−	0.347745i	0.582126	−	0.813099i	$-0.302221\pi$
$571$	35.0608	−	8.30957i	1.46725	−	0.347745i	0.885125	+	0.465354i	$0.154073\pi$
$572$	−11.5444	−	5.79780i	−0.482694	−	0.242418i
$573$		0			0
$574$	−3.83960	−	12.8252i	−0.160262	−	0.535312i
$575$	−61.7866	+	22.4885i	−2.57668	+	0.937834i
$576$		0			0
$577$	8.15363	+	2.96768i	0.339440	+	0.123546i	0.506115	−	0.862466i	$-0.331081\pi$
$577$	8.15363	+	2.96768i	0.339440	+	0.123546i	−0.166675	+	0.986012i	$0.553303\pi$
$578$	2.41395	−	41.4460i	0.100407	−	1.72393i
$579$		0			0
$580$	53.1427	−	71.3831i	2.20663	−	2.96402i
$581$	−2.96158	−	6.86571i	−0.122867	−	0.284838i
$582$		0			0
$583$	25.3993	−	12.7560i	1.05193	−	0.528300i
$584$	32.7259	−	27.4603i	1.35421	−	1.13631i
$585$		0			0
$586$	−31.4413	−	26.3824i	−1.29883	−	1.08985i
$587$	−9.00828	−	2.13500i	−0.371812	−	0.0881210i	0.0404620	−	0.999181i	$-0.487117\pi$
$587$	−9.00828	−	2.13500i	−0.371812	−	0.0881210i	−0.412274	+	0.911060i	$0.635265\pi$
$588$		0			0
$589$	0.100553	+	1.72643i	0.00414322	+	0.0711363i
$590$	−27.4401	+	91.6564i	−1.12969	+	3.77344i
$591$		0			0
$592$	−0.118436	−	0.159088i	−0.00486771	−	0.00653846i
$593$	−18.3119	+	31.7171i	−0.751979	+	1.30247i	0.194884	+	0.980826i	$0.437567\pi$
$593$	−18.3119	+	31.7171i	−0.751979	+	1.30247i	−0.946862	+	0.321639i	$0.895766\pi$
$594$		0			0
$595$	−0.709932	−	1.22964i	−0.0291044	−	0.0504102i
$596$	−26.4701	+	61.3645i	−1.08426	+	2.51359i
$597$		0			0
$598$	−13.2102	−	14.0020i	−0.540205	−	0.572584i
$599$	20.6854	−	13.6050i	0.845182	−	0.555885i	−0.0514430	−	0.998676i	$-0.516382\pi$
$599$	20.6854	−	13.6050i	0.845182	−	0.555885i	0.896625	+	0.442791i	$0.146012\pi$
$600$		0			0
$601$	−15.1593	+	16.0679i	−0.618359	+	0.655423i	−0.958547	−	0.284935i	$-0.908028\pi$
$601$	−15.1593	+	16.0679i	−0.618359	+	0.655423i	0.340188	+	0.940358i	$0.389509\pi$
$602$	−3.50974	+	19.9047i	−0.143046	+	0.811257i
$603$		0			0
$604$	−1.27765	−	7.24590i	−0.0519867	−	0.294831i
$605$	16.6604	+	10.9577i	0.677343	+	0.445496i
$606$		0			0
$607$	9.50492	+	1.11097i	0.385793	+	0.0450927i	0.306779	−	0.951781i	$-0.400749\pi$
$607$	9.50492	+	1.11097i	0.385793	+	0.0450927i	0.0790138	+	0.996874i	$0.474823\pi$
$608$	−0.201623	−	0.0235663i	−0.00817689	−	0.000955741i
$609$		0			0
$610$	35.0234	+	23.0353i	1.41806	+	0.932671i
$611$	1.89085	+	10.7235i	0.0764954	+	0.433827i
$612$		0			0
$613$	−2.38544	+	13.5285i	−0.0963469	+	0.546410i	0.897979	+	0.440037i	$0.145035\pi$
$613$	−2.38544	+	13.5285i	−0.0963469	+	0.546410i	−0.994326	+	0.106373i	$0.966076\pi$
$614$	34.3547	−	36.4139i	1.38644	−	1.46954i
$615$		0			0
$616$	−13.3331	+	8.76931i	−0.537205	+	0.353326i
$617$	−9.33576	−	9.89532i	−0.375843	−	0.398371i	0.511648	−	0.859195i	$-0.329035\pi$
$617$	−9.33576	−	9.89532i	−0.375843	−	0.398371i	−0.887491	+	0.460825i	$0.847554\pi$
$618$		0			0
$619$	−5.64861	+	13.0949i	−0.227037	+	0.526330i	−0.993214	−	0.116299i	$-0.962897\pi$
$619$	−5.64861	+	13.0949i	−0.227037	+	0.526330i	0.766178	+	0.642629i	$0.222156\pi$
$620$	10.3483	+	17.9238i	0.415599	+	0.719839i
$621$		0			0
$622$	8.13761	−	14.0947i	0.326288	−	0.565148i
$623$	7.20511	+	9.67815i	0.288667	+	0.387747i
$624$		0			0
$625$	−11.7148	+	39.1301i	−0.468592	+	1.56521i
$626$	1.30906	+	22.4758i	0.0523207	+	0.898312i
$627$		0			0
$628$	−42.2271	−	10.0080i	−1.68505	−	0.399363i
$629$	0.0100122	+	0.00840126i	0.000399214	+	0.000334980i
$630$		0			0
$631$	−6.09157	+	5.11144i	−0.242502	+	0.203483i	−0.755935	−	0.654646i	$-0.772818\pi$
$631$	−6.09157	+	5.11144i	−0.242502	+	0.203483i	0.513434	+	0.858129i	$0.328373\pi$
$632$	23.0973	−	11.5999i	0.918759	−	0.461418i
$633$		0			0
$634$	−0.0486619	−	0.112811i	−0.00193261	−	0.00448030i
$635$	31.3750	−	42.1440i	1.24508	−	1.67243i
$636$		0			0
$637$	0.401763	−	6.89801i	0.0159184	−	0.273309i
$638$	31.3233	+	11.4007i	1.24010	+	0.451360i
$639$		0			0
$640$	73.1505	−	26.6246i	2.89153	−	1.05243i
$641$	1.20559	+	4.02695i	0.0476179	+	0.159055i	0.978492	−	0.206286i	$-0.0661377\pi$
$641$	1.20559	+	4.02695i	0.0476179	+	0.159055i	−0.930874	+	0.365341i	$0.880952\pi$
$642$		0			0
$643$	17.1475	+	8.61180i	0.676232	+	0.339616i	0.753551	−	0.657390i	$-0.228340\pi$
$643$	17.1475	+	8.61180i	0.676232	+	0.339616i	−0.0773186	+	0.997006i	$0.524636\pi$
$644$	−30.7737	+	7.29349i	−1.21265	+	0.287404i
$645$		0			0
$646$	0.881437	−	0.103025i	0.0346797	−	0.00405347i
$647$	33.3755			1.31213			0.656063	−	0.754706i	$-0.272221\pi$
$647$	33.3755			1.31213			0.656063	+	0.754706i	$0.272221\pi$
$648$		0			0
$649$	−23.9217			−0.939009
$650$	−35.1275	+	4.10582i	−1.37781	+	0.161043i
$651$		0			0
$652$	14.7188	−	3.48841i	0.576432	−	0.136617i
$653$	−10.8992	−	5.47380i	−0.426520	−	0.214206i	0.222572	−	0.974916i	$-0.428555\pi$
$653$	−10.8992	−	5.47380i	−0.426520	−	0.214206i	−0.649092	+	0.760710i	$0.724851\pi$
$654$		0			0
$655$	−4.96721	−	16.5916i	−0.194085	−	0.648289i
$656$	15.9437	−	5.80302i	0.622496	−	0.226570i
$657$		0			0
$658$	25.1839	+	9.16619i	0.981770	+	0.357335i
$659$	−1.36161	+	23.3779i	−0.0530408	+	0.910675i	0.861898	+	0.507082i	$0.169276\pi$
$659$	−1.36161	+	23.3779i	−0.0530408	+	0.910675i	−0.914939	+	0.403593i	$0.867761\pi$
$660$		0			0
$661$	−20.1047	+	27.0053i	−0.781982	+	1.05038i	0.215289	+	0.976550i	$0.430931\pi$
$661$	−20.1047	+	27.0053i	−0.781982	+	1.05038i	−0.997271	+	0.0738336i	$0.976477\pi$
$662$	−17.9724	−	41.6647i	−0.698518	−	1.61935i
$663$		0			0
$664$	25.0862	−	12.5988i	0.973535	−	0.488928i
$665$	−5.41109	+	4.54045i	−0.209833	+	0.176071i
$666$		0			0
$667$	25.3992	+	21.3124i	0.983460	+	0.825221i
$668$	−46.2405	−	10.9592i	−1.78910	−	0.424024i
$669$		0			0
$670$	0.756098	+	12.9817i	0.0292106	+	0.501527i
$671$	−3.00603	+	10.0408i	−0.116046	+	0.387622i
$672$		0			0
$673$	−7.41080	−	9.95443i	−0.285665	−	0.383715i	0.636008	−	0.771683i	$-0.280585\pi$
$673$	−7.41080	−	9.95443i	−0.285665	−	0.383715i	−0.921673	+	0.387968i	$0.873177\pi$
$674$	4.47565	−	7.75205i	0.172396	−	0.298598i
$675$		0			0
$676$	22.6440	+	39.2206i	0.870925	+	1.50849i
$677$	5.86348	−	13.5931i	0.225352	−	0.522425i	−0.767602	−	0.640927i	$-0.778550\pi$
$677$	5.86348	−	13.5931i	0.225352	−	0.522425i	0.992954	+	0.118502i	$0.0378093\pi$
$678$		0			0
$679$	11.2103	+	11.8823i	0.430213	+	0.455999i
$680$	4.45372	−	2.92926i	0.170792	−	0.112332i
$681$		0			0
$682$	−5.31991	+	5.63878i	−0.203710	+	0.215920i
$683$	−6.94875	+	39.4083i	−0.265887	+	1.50792i	0.500612	+	0.865672i	$0.333108\pi$
$683$	−6.94875	+	39.4083i	−0.265887	+	1.50792i	−0.766499	+	0.642246i	$0.778003\pi$
$684$		0			0
$685$	−15.5686	−	88.2941i	−0.594847	−	3.37354i
$686$	−33.0936	−	21.7660i	−1.26352	−	0.831030i
$687$		0			0
$688$	−25.4425	−	2.97380i	−0.969985	−	0.113375i
$689$	15.1038	+	1.76538i	0.575410	+	0.0672557i
$690$		0			0
$691$	32.8873	+	21.6303i	1.25109	+	0.822857i	0.989809	−	0.142405i	$-0.0454834\pi$
$691$	32.8873	+	21.6303i	1.25109	+	0.822857i	0.261285	+	0.965262i	$0.415854\pi$
$692$	6.67130	+	37.8348i	0.253605	+	1.43826i
$693$		0			0
$694$	−1.74631	+	9.90380i	−0.0662889	+	0.375943i
$695$	26.3420	−	27.9209i	0.999210	−	1.05910i
$696$		0			0
$697$	−0.934166	+	0.614411i	−0.0353841	+	0.0232725i
$698$	−12.7327	−	13.4959i	−0.481941	−	0.510828i
$699$		0			0
$700$	−23.0139	+	53.3523i	−0.869845	+	2.01653i
$701$	2.37301	+	4.11018i	0.0896274	+	0.155239i	0.907354	−	0.420368i	$-0.138099\pi$
$701$	2.37301	+	4.11018i	0.0896274	+	0.155239i	−0.817726	+	0.575607i	$0.804766\pi$
$702$		0			0
$703$	0.0325111	−	0.0563108i	0.00122618	−	0.00212380i
$704$	11.4421	+	15.3695i	0.431242	+	0.579258i
$705$		0			0
$706$	1.44231	−	4.81766i	0.0542822	−	0.181315i
$707$	−0.953210	−	16.3660i	−0.0358492	−	0.615506i
$708$		0			0
$709$	0.354156	+	0.0839366i	0.0133006	+	0.00315231i	0.237261	−	0.971446i	$-0.423750\pi$
$709$	0.354156	+	0.0839366i	0.0133006	+	0.00315231i	−0.223960	+	0.974598i	$0.571899\pi$
$710$	59.2231	+	49.6940i	2.22260	+	1.86498i
$711$		0			0
$712$	−34.7009	+	29.1175i	−1.30047	+	1.09123i
$713$	−6.89082	+	3.46070i	−0.258063	+	0.129604i
$714$		0			0
$715$	−5.09572	−	11.8132i	−0.190569	−	0.441789i
$716$	3.40316	−	4.57123i	0.127182	−	0.170835i
$717$		0			0
$718$	−1.43333	+	24.6093i	−0.0534913	+	0.918410i
$719$	15.2471	+	5.54950i	0.568622	+	0.206961i	0.610301	−	0.792170i	$-0.291049\pi$
$719$	15.2471	+	5.54950i	0.568622	+	0.206961i	−0.0416792	+	0.999131i	$0.513271\pi$
$720$		0			0
$721$	−7.73318	+	2.81465i	−0.287998	+	0.104823i
$722$	12.0988	+	40.4127i	0.450270	+	1.50401i
$723$		0			0
$724$	−35.5222	−	17.8399i	−1.32017	−	0.663015i
$725$	59.2735	−	14.0481i	2.20136	−	0.521732i
$726$		0			0
$727$	15.7245	−	1.83793i	0.583188	−	0.0681649i	0.180617	−	0.983554i	$-0.442191\pi$
$727$	15.7245	−	1.83793i	0.583188	−	0.0681649i	0.402571	+	0.915389i	$0.368117\pi$
$728$	−8.53809			−0.316443
$729$		0			0
$730$	84.7659			3.13733
$731$	1.67664	−	0.195971i	0.0620129	−	0.00724827i
$732$		0			0
$733$	44.4587	−	10.5369i	1.64212	−	0.389190i	0.697301	−	0.716779i	$-0.254384\pi$
$733$	44.4587	−	10.5369i	1.64212	−	0.389190i	0.944820	+	0.327589i	$0.106236\pi$
$734$	71.1813	+	35.7486i	2.62735	+	1.31950i
$735$		0			0
$736$	−0.259596	−	0.867111i	−0.00956884	−	0.0319621i
$737$	−3.05522	+	1.11201i	−0.112541	+	0.0409614i
$738$		0			0
$739$	−2.12852	−	0.774717i	−0.0782987	−	0.0284984i	0.302574	−	0.953126i	$-0.402154\pi$
$739$	−2.12852	−	0.774717i	−0.0782987	−	0.0284984i	−0.380873	+	0.924628i	$0.624376\pi$
$740$	0.0452469	−	0.776859i	0.00166331	−	0.0285579i
$741$		0			0
$742$	22.3498	−	30.0210i	0.820488	−	1.10211i
$743$	1.08128	+	2.50670i	0.0396685	+	0.0919619i	0.936898	−	0.349602i	$-0.113683\pi$
$743$	1.08128	+	2.50670i	0.0396685	+	0.0919619i	−0.897230	+	0.441564i	$0.854424\pi$
$744$		0			0
$745$	−59.4763	+	29.8701i	−2.17904	+	1.09436i
$746$	28.3745	−	23.8090i	1.03886	−	0.871709i
$747$		0			0
$748$	2.03422	+	1.70691i	0.0743785	+	0.0624109i
$749$	25.4188	+	6.02437i	0.928784	+	0.220126i
$750$		0			0
$751$	2.50704	+	43.0442i	0.0914831	+	1.57070i	0.662054	+	0.749456i	$0.269685\pi$
$751$	2.50704	+	43.0442i	0.0914831	+	1.57070i	−0.570571	+	0.821248i	$0.693278\pi$
$752$	−9.74140	+	32.5386i	−0.355232	+	1.18656i
$753$		0			0
$754$	10.6498	+	14.3052i	0.387843	+	0.520963i
$755$	3.66372	−	6.34576i	0.133337	−	0.230946i
$756$		0			0
$757$	19.3916	+	33.5873i	0.704800	+	1.22075i	0.966764	+	0.255672i	$0.0822968\pi$
$757$	19.3916	+	33.5873i	0.704800	+	1.22075i	−0.261963	+	0.965078i	$0.584370\pi$
$758$	−2.58349	+	5.98921i	−0.0938367	+	0.217538i
$759$		0			0
$760$	−18.1989	−	19.2897i	−0.660142	−	0.699710i
$761$	−36.1896	+	23.8023i	−1.31187	+	0.862831i	−0.996289	−	0.0860672i	$-0.972570\pi$
$761$	−36.1896	+	23.8023i	−1.31187	+	0.862831i	−0.315582	+	0.948898i	$0.602200\pi$
$762$		0			0
$763$	3.46371	−	3.67132i	0.125395	−	0.132911i
$764$	12.4282	−	70.4836i	0.449635	−	2.55001i
$765$		0			0
$766$	0.661895	+	3.75379i	0.0239152	+	0.135630i
$767$	−10.6931	−	7.03294i	−0.386104	−	0.253945i
$768$		0			0
$769$	−49.5707	−	5.79399i	−1.78757	−	0.208936i	−0.843147	−	0.537682i	$-0.819300\pi$
$769$	−49.5707	−	5.79399i	−1.78757	−	0.208936i	−0.944418	+	0.328746i	$0.893374\pi$
$770$	−31.4505	−	3.67604i	−1.13340	−	0.132475i
$771$		0			0
$772$	−92.6962	−	60.9672i	−3.33621	−	2.19426i
$773$	−1.64610	−	9.33547i	−0.0592059	−	0.335774i	0.940789	−	0.338993i	$-0.110086\pi$
$773$	−1.64610	−	9.33547i	−0.0592059	−	0.335774i	−0.999995	+	0.00321947i	$0.998975\pi$
$774$		0			0
$775$	−2.46005	+	13.9516i	−0.0883676	+	0.501157i
$776$	−42.0877	+	44.6103i	−1.51086	+	1.60142i
$777$		0			0
$778$	−7.53410	+	4.95526i	−0.270111	+	0.177655i
$779$	3.81721	+	4.04600i	0.136766	+	0.144963i
$780$		0			0
$781$	−7.65613	+	17.7489i	−0.273958	+	0.635106i
$782$	1.97850	+	3.42686i	0.0707509	+	0.122544i
$783$		0			0
$784$	10.7766	−	18.6656i	0.384878	−	0.666628i
$785$	−25.8084	−	34.6666i	−0.921140	−	1.23731i
$786$		0			0
$787$	13.4634	−	44.9710i	0.479920	−	1.60304i	−0.284736	−	0.958606i	$-0.591906\pi$
$787$	13.4634	−	44.9710i	0.479920	−	1.60304i	0.764656	−	0.644438i	$-0.222909\pi$
$788$	−1.39884	−	24.0171i	−0.0498315	−	0.855574i
$789$		0			0
$790$	49.9020	+	11.8270i	1.77543	+	0.420785i
$791$	−3.51972	−	2.95340i	−0.125147	−	0.105011i
$792$		0			0
$793$	−4.29569	+	3.60451i	−0.152544	+	0.128000i
$794$	−84.3570	+	42.3657i	−2.99372	+	1.50350i
$795$		0			0
$796$	25.5405	+	59.2094i	0.905257	+	2.09862i
$797$	−17.6009	+	23.6421i	−0.623456	+	0.837447i	−0.995886	−	0.0906135i	$-0.971117\pi$
$797$	−17.6009	+	23.6421i	−0.623456	+	0.837447i	0.372430	+	0.928060i	$0.378525\pi$
$798$		0			0
$799$	0.130146	−	2.23452i	0.00460423	−	0.0790515i
$800$	−1.56265	−	0.568758i	−0.0552480	−	0.0201086i
$801$		0			0
$802$	41.0358	−	14.9358i	1.44903	−	0.527402i
$803$	6.07849	+	20.3036i	0.214505	+	0.716497i
$804$		0			0
$805$	−28.1461	−	14.1355i	−0.992018	−	0.498210i
$806$	−4.03581	+	0.956504i	−0.142155	+	0.0336914i
$807$		0			0
$808$	61.1318	−	7.14528i	2.15061	−	0.251370i
$809$	10.6073			0.372933			0.186467	−	0.982461i	$-0.440296\pi$
$809$	10.6073			0.372933			0.186467	+	0.982461i	$0.440296\pi$
$810$		0			0
$811$	−6.86583			−0.241092			−0.120546	−	0.992708i	$-0.538465\pi$
$811$	−6.86583			−0.241092			−0.120546	+	0.992708i	$0.538465\pi$
$812$	29.1017	−	3.40151i	1.02127	−	0.119369i
$813$		0			0
$814$	0.283620	−	0.0672193i	0.00994089	−	0.00235603i
$815$	13.4620	+	6.76088i	0.471554	+	0.236823i
$816$		0			0
$817$	−2.40855	−	8.04512i	−0.0842645	−	0.281463i
$818$	42.2481	−	15.3771i	1.47717	−	0.537646i
$819$		0			0
$820$	62.5562	+	22.7686i	2.18456	+	0.795114i
$821$	1.16962	−	20.0816i	0.0408200	−	0.700852i	−0.914374	−	0.404871i	$-0.867316\pi$
$821$	1.16962	−	20.0816i	0.0408200	−	0.700852i	0.955194	−	0.295981i	$-0.0956465\pi$
$822$		0			0
$823$	−32.3008	+	43.3874i	−1.12593	+	1.51239i	−0.295441	+	0.955361i	$0.595467\pi$
$823$	−32.3008	+	43.3874i	−1.12593	+	1.51239i	−0.830492	+	0.557030i	$0.811941\pi$
$824$	−12.2374	−	28.3696i	−0.426312	−	0.988301i
$825$		0			0
$826$	−28.1496	+	14.1373i	−0.979450	+	0.491899i
$827$	28.7038	−	24.0854i	0.998129	−	0.837530i	0.0114051	−	0.999935i	$-0.496370\pi$
$827$	28.7038	−	24.0854i	0.998129	−	0.837530i	0.986724	+	0.162405i	$0.0519251\pi$
$828$		0			0
$829$	−35.2264	−	29.5585i	−1.22346	−	1.02661i	−0.998636	−	0.0522095i	$-0.983374\pi$
$829$	−35.2264	−	29.5585i	−1.22346	−	1.02661i	−0.224828	−	0.974399i	$-0.572182\pi$
$830$	54.1992	+	12.8455i	1.88128	+	0.445872i
$831$		0			0
$832$	0.596072	+	10.2342i	0.0206651	+	0.354806i
$833$	−0.407358	+	1.36067i	−0.0141141	+	0.0471444i
$834$		0			0
$835$	−28.2613	−	37.9615i	−0.978021	−	1.31371i
$836$	6.60539	−	11.4409i	0.228452	−	0.395691i
$837$		0			0
$838$	−15.3176	−	26.5308i	−0.529136	−	0.916491i
$839$	6.99599	−	16.2185i	0.241529	−	0.559926i	−0.753731	−	0.657183i	$-0.771748\pi$
$839$	6.99599	−	16.2185i	0.241529	−	0.559926i	0.995259	+	0.0972573i	$0.0310070\pi$
$840$		0			0
$841$	−1.17857	−	1.24921i	−0.0406403	−	0.0430762i
$842$	−44.3023	+	29.1381i	−1.52676	+	1.00416i
$843$		0			0
$844$	27.7515	−	29.4149i	0.955246	−	1.01250i
$845$	−7.83189	+	44.4168i	−0.269425	+	1.52799i
$846$		0			0
$847$	1.14006	+	6.46561i	0.0391730	+	0.222161i
$848$	39.6301	+	26.0651i	1.36090	+	0.895080i
$849$		0			0
$850$	7.22072	+	0.843981i	0.247669	+	0.0289483i
$851$	0.287967	+	0.0336585i	0.00987137	+	0.00115380i
$852$		0			0
$853$	30.7365	+	20.2157i	1.05240	+	0.692173i	0.953030	−	0.302877i	$-0.0979473\pi$
$853$	30.7365	+	20.2157i	1.05240	+	0.692173i	0.0993688	+	0.995051i	$0.468318\pi$
$854$	2.39663	+	13.5919i	0.0820108	+	0.465107i
$855$		0			0
$856$	−17.0306	+	96.5851i	−0.582093	+	3.30121i
$857$	−17.6257	+	18.6822i	−0.602083	+	0.638171i	−0.954690	−	0.297601i	$-0.903814\pi$
$857$	−17.6257	+	18.6822i	−0.602083	+	0.638171i	0.352607	+	0.935771i	$0.385295\pi$
$858$		0			0
$859$	25.1974	−	16.5726i	0.859724	−	0.565449i	−0.0413353	−	0.999145i	$-0.513161\pi$
$859$	25.1974	−	16.5726i	0.859724	−	0.565449i	0.901059	+	0.433696i	$0.142791\pi$
$860$	−68.9707	−	73.1047i	−2.35188	−	2.49285i
$861$		0			0
$862$	30.1923	−	69.9936i	1.02835	−	2.38399i
$863$	−23.2433	−	40.2586i	−0.791212	−	1.37042i	−0.925217	−	0.379438i	$-0.876117\pi$
$863$	−23.2433	−	40.2586i	−0.791212	−	1.37042i	0.134006	−	0.990981i	$-0.457216\pi$
$864$		0			0
$865$	−19.1303	+	33.1347i	−0.650451	+	1.12661i
$866$	19.4640	+	26.1447i	0.661414	+	0.888433i
$867$		0			0
$868$	−1.95432	+	6.52788i	−0.0663339	+	0.221571i
$869$	0.745566	+	12.8009i	0.0252916	+	0.434240i
$870$		0			0
$871$	−1.69262	−	0.401159i	−0.0573523	−	0.0135928i
$872$	14.5163	+	12.1806i	0.491583	+	0.412487i
$873$		0			0
$874$	15.0801	−	12.6537i	0.510091	−	0.428018i
$875$	−28.1864	+	14.1557i	−0.952874	+	0.478551i
$876$		0			0
$877$	−3.68783	−	8.54936i	−0.124529	−	0.288691i	0.844535	−	0.535501i	$-0.179877\pi$
$877$	−3.68783	−	8.54936i	−0.124529	−	0.288691i	−0.969064	+	0.246809i	$0.920618\pi$
$878$	−1.87844	+	2.52319i	−0.0633944	+	0.0851535i
$879$		0			0
$880$	2.33338	−	40.0626i	0.0786583	−	1.35051i
$881$	−36.4164	−	13.2545i	−1.22690	−	0.446555i	−0.354366	−	0.935107i	$-0.615303\pi$
$881$	−36.4164	−	13.2545i	−1.22690	−	0.446555i	−0.872535	+	0.488551i	$0.837526\pi$
$882$		0			0
$883$	16.7575	−	6.09921i	0.563933	−	0.205255i	−0.0442931	−	0.999019i	$-0.514104\pi$
$883$	16.7575	−	6.09921i	0.563933	−	0.205255i	0.608226	+	0.793764i	$0.291881\pi$
$884$	0.407472	+	1.36105i	0.0137048	+	0.0457771i
$885$		0			0
$886$	85.7041	+	43.0422i	2.87929	+	1.44603i
$887$	43.1987	−	10.2383i	1.45047	−	0.343768i	0.571484	−	0.820613i	$-0.306368\pi$
$887$	43.1987	−	10.2383i	1.45047	−	0.343768i	0.878987	+	0.476845i	$0.158220\pi$
$888$		0			0
$889$	17.1814	−	2.00822i	0.576246	−	0.0673535i
$890$	−89.8816			−3.01284
$891$		0			0
$892$	−52.3701			−1.75348
$893$	−11.0600	+	1.29273i	−0.370110	+	0.0432597i
$894$		0			0
$895$	5.52252	−	1.30886i	0.184597	−	0.0437504i
$896$	22.9035	+	11.5026i	0.765152	+	0.384274i
$897$		0			0
$898$	−11.2790	−	37.6746i	−0.376386	−	1.25722i
$899$	6.71300	−	2.44333i	0.223891	−	0.0814897i
$900$		0			0
$901$	−2.93733	−	1.06910i	−0.0978565	−	0.0356169i
$902$	−1.44985	+	24.8930i	−0.0482747	+	0.828845i
$903$		0			0
$904$	10.3010	−	13.8367i	0.342607	−	0.460201i
$905$	−15.6796	−	36.3494i	−0.521208	−	1.20830i
$906$		0			0
$907$	−8.14778	+	4.09197i	−0.270543	+	0.135872i	−0.578899	−	0.815399i	$-0.696517\pi$
$907$	−8.14778	+	4.09197i	−0.270543	+	0.135872i	0.308356	+	0.951271i	$0.400221\pi$
$908$	−50.1138	+	42.0505i	−1.66308	+	1.39549i
$909$		0			0
$910$	−12.9777	−	10.8896i	−0.430207	−	0.360987i
$911$	−1.64805	−	0.390596i	−0.0546024	−	0.0129410i	0.203224	−	0.979132i	$-0.434858\pi$
$911$	−1.64805	−	0.390596i	−0.0546024	−	0.0129410i	−0.257826	+	0.966191i	$0.583006\pi$
$912$		0			0
$913$	0.809769	+	13.9032i	0.0267995	+	0.460129i
$914$	2.71931	−	9.08313i	0.0899468	−	0.300443i
$915$		0			0
$916$	−16.1554	−	21.7004i	−0.533788	−	0.717002i
$917$	2.85108	−	4.93822i	0.0941511	−	0.163074i
$918$		0			0
$919$	−20.4302	−	35.3862i	−0.673931	−	1.16728i	−0.976780	−	0.214245i	$-0.931271\pi$
$919$	−20.4302	−	35.3862i	−0.673931	−	1.16728i	0.302849	−	0.953039i	$-0.402062\pi$
$920$	46.8357	−	108.577i	1.54413	−	3.57969i
$921$		0			0
$922$	−35.7337	−	37.8755i	−1.17683	−	1.24736i
$923$	−8.64046	+	5.68292i	−0.284404	+	0.187056i
$924$		0			0
$925$	0.365534	−	0.387443i	0.0120187	−	0.0127391i
$926$	8.22550	−	46.6491i	0.270307	−	1.53299i
$927$		0			0
$928$	0.145614	+	0.825819i	0.00478002	+	0.0271088i
$929$	−21.7758	−	14.3222i	−0.714442	−	0.469896i	0.139528	−	0.990218i	$-0.455441\pi$
$929$	−21.7758	−	14.3222i	−0.714442	−	0.469896i	−0.853970	+	0.520322i	$0.825812\pi$
$930$		0			0
$931$	7.01827	+	0.820318i	0.230015	+	0.0268849i
$932$	55.0435	+	6.43366i	1.80301	+	0.210742i
$933$		0			0
$934$	−8.44121	−	5.55187i	−0.276205	−	0.181663i
$935$	0.459226	+	2.60440i	0.0150183	+	0.0851730i
$936$		0			0
$937$	−6.10524	+	34.6246i	−0.199450	+	1.13114i	0.706488	+	0.707725i	$0.250278\pi$
$937$	−6.10524	+	34.6246i	−0.199450	+	1.13114i	−0.905938	+	0.423410i	$0.860833\pi$
$938$	−2.93803	+	3.11412i	−0.0959299	+	0.101680i
$939$		0			0
$940$	−111.342	+	73.2309i	−3.63158	+	2.38853i
$941$	6.54114	+	6.93320i	0.213235	+	0.226016i	0.825159	−	0.564901i	$-0.191086\pi$
$941$	6.54114	+	6.93320i	0.213235	+	0.226016i	−0.611924	+	0.790917i	$0.709604\pi$
$942$		0			0
$943$	−9.82378	+	22.7741i	−0.319906	+	0.741626i
$944$	−19.9611	−	34.5736i	−0.649678	−	1.12527i
$945$		0			0
$946$	18.8228	−	32.6021i	0.611983	−	1.05999i
$947$	3.18430	+	4.27726i	0.103476	+	0.138992i	0.850845	−	0.525417i	$-0.176091\pi$
$947$	3.18430	+	4.27726i	0.103476	+	0.138992i	−0.747369	+	0.664409i	$0.768683\pi$
$948$		0			0
$949$	−3.25211	+	10.8628i	−0.105568	+	0.352622i
$950$	−2.10292	−	36.1057i	−0.0682277	−	1.17142i
$951$		0			0
$952$	1.70776	+	0.404746i	0.0553488	+	0.0131179i
$953$	−18.6871	−	15.6804i	−0.605335	−	0.507937i	0.287820	−	0.957684i	$-0.407069\pi$
$953$	−18.6871	−	15.6804i	−0.605335	−	0.507937i	−0.893156	+	0.449748i	$0.851514\pi$
$954$		0			0
$955$	54.6013	−	45.8159i	1.76686	−	1.48257i
$956$	−44.9899	+	22.5948i	−1.45508	+	0.730767i
$957$		0			0
$958$	−27.9309	−	64.7512i	−0.902407	−	2.09202i
$959$	17.6271	−	23.6773i	0.569209	−	0.764580i
$960$		0			0
$961$	1.70589	−	29.2890i	0.0550286	−	0.944805i
$962$	0.146541	+	0.0533367i	0.00472469	+	0.00171965i
$963$		0			0
$964$	−51.6583	+	18.8021i	−1.66380	+	0.605574i
$965$	−31.6897	−	105.851i	−1.02013	−	3.40746i
$966$		0			0
$967$	−19.4354	−	9.76085i	−0.625002	−	0.313888i	0.107962	−	0.994155i	$-0.465567\pi$
$967$	−19.4354	−	9.76085i	−0.625002	−	0.313888i	−0.732964	+	0.680267i	$0.761864\pi$
$968$	−23.9843	+	5.68438i	−0.770884	+	0.182703i
$969$		0			0
$970$	−120.869	+	14.1276i	−3.88087	+	0.453608i
$971$	−29.3878			−0.943100			−0.471550	−	0.881839i	$-0.656305\pi$
$971$	−29.3878			−0.943100			−0.471550	+	0.881839i	$0.656305\pi$
$972$		0			0
$973$	12.6381			0.405160
$974$	−21.6507	+	2.53060i	−0.693732	+	0.0810857i
$975$		0			0
$976$	−17.0201	+	4.03385i	−0.544802	+	0.129120i
$977$	−53.6095	−	26.9237i	−1.71512	−	0.861365i	−0.983787	−	0.179344i	$-0.942603\pi$
$977$	−53.6095	−	26.9237i	−1.71512	−	0.861365i	−0.731332	−	0.682021i	$-0.761101\pi$
$978$		0			0
$979$	−6.44533	−	21.5289i	−0.205994	−	0.688066i
$980$	79.4655	−	28.9231i	2.53843	−	0.923914i
$981$		0			0
$982$	−64.9940	−	23.6559i	−2.07404	−	0.754889i
$983$	−1.62069	+	27.8262i	−0.0516920	+	0.887517i	0.868412	+	0.495843i	$0.165141\pi$
$983$	−1.62069	+	27.8262i	−0.0516920	+	0.887517i	−0.920104	+	0.391674i	$0.871896\pi$
$984$		0			0
$985$	14.3073	−	19.2180i	0.455869	−	0.612338i
$986$	−1.45200	−	3.36612i	−0.0462412	−	0.107199i
$987$		0			0
$988$	6.31623	−	3.17213i	0.200946	−	0.100919i
$989$	28.6849	−	24.0695i	0.912126	−	0.765365i
$990$		0			0
$991$	12.6278	+	10.5959i	0.401134	+	0.336591i	0.820932	−	0.571026i	$-0.193455\pi$
$991$	12.6278	+	10.5959i	0.401134	+	0.336591i	−0.419798	+	0.907618i	$0.637899\pi$
$992$	−0.189763	−	0.0449747i	−0.00602499	−	0.00142795i
$993$		0			0
$994$	1.47999	+	25.4105i	0.0469425	+	0.805971i
$995$	−18.4180	+	61.5204i	−0.583889	+	1.95033i
$996$		0			0
$997$	−13.5708	−	18.2288i	−0.429793	−	0.577312i	0.533488	−	0.845808i	$-0.320881\pi$
$997$	−13.5708	−	18.2288i	−0.429793	−	0.577312i	−0.963281	+	0.268495i	$0.913474\pi$
$998$	−1.45934	+	2.52765i	−0.0461947	+	0.0800115i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.19.1		144
3.2	odd	2		81.2.g.a.61.8	yes	144
9.2	odd	6		729.2.g.c.541.1		144
9.4	even	3		729.2.g.a.55.8		144
9.5	odd	6		729.2.g.d.55.1		144
9.7	even	3		729.2.g.b.541.8		144
81.2	odd	54		6561.2.a.c.1.7		72
81.4	even	27	inner	243.2.g.a.64.1		144
81.23	odd	54		729.2.g.d.676.1		144
81.31	even	27		729.2.g.b.190.8		144
81.50	odd	54		729.2.g.c.190.1		144
81.58	even	27		729.2.g.a.676.8		144
81.77	odd	54		81.2.g.a.4.8	✓	144
81.79	even	27		6561.2.a.d.1.66		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.8	✓	144	81.77	odd	54
81.2.g.a.61.8	yes	144	3.2	odd	2
243.2.g.a.19.1		144	1.1	even	1	trivial
243.2.g.a.64.1		144	81.4	even	27	inner
729.2.g.a.55.8		144	9.4	even	3
729.2.g.a.676.8		144	81.58	even	27
729.2.g.b.190.8		144	81.31	even	27
729.2.g.b.541.8		144	9.7	even	3
729.2.g.c.190.1		144	81.50	odd	54
729.2.g.c.541.1		144	9.2	odd	6
729.2.g.d.55.1		144	9.5	odd	6
729.2.g.d.676.1		144	81.23	odd	54
6561.2.a.c.1.7		72	81.2	odd	54
6561.2.a.d.1.66		72	81.79	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.43604 + 0.284732i) q^{2} +(3.90713 - 0.926007i) q^{4} +(3.57352 + 1.79469i) q^{5} +(0.377600 + 1.26127i) q^{7} +(-4.64483 + 1.69058i) q^{8} +O(q^{10})\)	\(q+(-2.43604 + 0.284732i) q^{2} +(3.90713 - 0.926007i) q^{4} +(3.57352 + 1.79469i) q^{5} +(0.377600 + 1.26127i) q^{7} +(-4.64483 + 1.69058i) q^{8} +(-9.21624 - 3.35444i) q^{10} +(0.142583 - 2.44806i) q^{11} +(0.783462 - 1.05237i) q^{13} +(-1.27897 - 2.96500i) q^{14} +(3.65712 - 1.83667i) q^{16} +(-0.206593 + 0.173352i) q^{17} +(1.02778 + 0.862409i) q^{19} +(15.6241 + 3.70298i) q^{20} +(0.349704 + 6.00418i) q^{22} +(-1.71576 + 5.73105i) q^{23} +(6.56334 + 8.81609i) q^{25} +(-1.60890 + 2.78670i) q^{26} +(2.64328 + 4.57830i) q^{28} +(2.19520 - 5.08906i) q^{29} +(0.884536 + 0.937554i) q^{31} +(-0.126410 + 0.0831411i) q^{32} +(0.453909 - 0.481116i) q^{34} +(-0.914230 + 5.18486i) q^{35} +(-0.00841562 - 0.0477273i) q^{37} +(-2.74927 - 1.80822i) q^{38} +(-19.6325 - 2.29471i) q^{40} +(4.11791 + 0.481314i) q^{41} +(-5.22957 - 3.43954i) q^{43} +(-1.70983 - 9.69693i) q^{44} +(2.54785 - 14.4496i) q^{46} +(-5.69554 + 6.03692i) q^{47} +(4.40019 - 2.89405i) q^{49} +(-18.4988 - 19.6076i) q^{50} +(2.08658 - 4.83724i) q^{52} +(5.79529 + 10.0377i) q^{53} +(4.90304 - 8.49231i) q^{55} +(-3.88617 - 5.22004i) q^{56} +(-3.89859 + 13.0222i) q^{58} +(-0.567212 - 9.73865i) q^{59} +(-4.15895 - 0.985689i) q^{61} +(-2.42172 - 2.03206i) q^{62} +(-5.98568 + 5.02258i) q^{64} +(4.68839 - 2.35460i) q^{65} +(-0.525148 - 1.21743i) q^{67} +(-0.646660 + 0.868614i) q^{68} +(0.750805 - 12.8908i) q^{70} +(-7.40721 - 2.69600i) q^{71} +(-8.12155 + 2.95600i) q^{73} +(0.0340903 + 0.113869i) q^{74} +(4.81426 + 2.41781i) q^{76} +(3.14152 - 0.744553i) q^{77} +(-5.19362 + 0.607048i) q^{79} +16.3650 q^{80} -10.1684 q^{82} +(-5.64086 + 0.659323i) q^{83} +(-1.04938 + 0.248707i) q^{85} +(13.7188 + 6.88984i) q^{86} +(3.47637 + 11.6119i) q^{88} +(8.61170 - 3.13440i) q^{89} +(1.62316 + 0.590783i) q^{91} +(-1.39672 + 23.9807i) q^{92} +(12.1557 - 16.3279i) q^{94} +(2.12503 + 4.92638i) q^{95} +(11.0880 - 5.56859i) q^{97} +(-9.89500 + 8.30289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

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