LMFDB - Embedded newform 729.2.g.c.55.2

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			55.2
Character	$\chi$	$=$	729.55
Dual form			729.2.g.c.676.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.880274 + 2.04070i) q^{2} +(-2.01711 - 2.13801i) q^{4} +(0.171269 + 2.94057i) q^{5} +(2.87602 + 0.681629i) q^{7} +(1.96178 - 0.714030i) q^{8} +O(q^{10})$	\(q+(-0.880274 + 2.04070i) q^{2} +(-2.01711 - 2.13801i) q^{4} +(0.171269 + 2.94057i) q^{5} +(2.87602 + 0.681629i) q^{7} +(1.96178 - 0.714030i) q^{8} +(-6.15160 - 2.23900i) q^{10} +(4.43417 + 2.91640i) q^{11} +(0.730282 + 0.0853577i) q^{13} +(-3.92268 + 5.26908i) q^{14} +(0.0720359 - 1.23681i) q^{16} +(1.11298 - 0.933897i) q^{17} +(4.21153 + 3.53390i) q^{19} +(5.94150 - 6.29762i) q^{20} +(-9.85479 + 6.48160i) q^{22} +(-0.438705 + 0.103975i) q^{23} +(-3.65143 + 0.426791i) q^{25} +(-0.817038 + 1.41515i) q^{26} +(-4.34391 - 7.52387i) q^{28} +(2.12271 + 2.85130i) q^{29} +(0.319104 - 1.06588i) q^{31} +(6.19179 + 3.10963i) q^{32} +(0.926085 + 3.09334i) q^{34} +(-1.51181 + 8.57387i) q^{35} +(-0.643205 - 3.64780i) q^{37} +(-10.9189 + 5.48370i) q^{38} +(2.43565 + 5.64646i) q^{40} +(-4.05045 - 9.39000i) q^{41} +(-7.08750 + 3.55948i) q^{43} +(-2.70891 - 15.3630i) q^{44} +(0.173998 - 0.986793i) q^{46} +(-1.58391 - 5.29061i) q^{47} +(1.55143 + 0.779157i) q^{49} +(2.34330 - 7.82718i) q^{50} +(-1.29056 - 1.73353i) q^{52} +(-1.83020 - 3.17001i) q^{53} +(-7.81644 + 13.5385i) q^{55} +(6.12882 - 0.716356i) q^{56} +(-7.68722 + 1.82190i) q^{58} +(-5.98693 + 3.93766i) q^{59} +(-2.98858 + 3.16771i) q^{61} +(1.89425 + 1.58947i) q^{62} +(-9.89820 + 8.30558i) q^{64} +(-0.125926 + 2.16206i) q^{65} +(6.75776 - 9.07724i) q^{67} +(-4.24167 - 0.495780i) q^{68} +(-16.1659 - 10.6325i) q^{70} +(-12.6408 - 4.60088i) q^{71} +(3.72979 - 1.35753i) q^{73} +(8.01028 + 1.89847i) q^{74} +(-0.939614 - 16.1325i) q^{76} +(10.7649 + 11.4101i) q^{77} +(1.12592 - 2.61017i) q^{79} +3.64926 q^{80} +22.7277 q^{82} +(0.139359 - 0.323070i) q^{83} +(2.93681 + 3.11283i) q^{85} +(-1.02490 - 17.5968i) q^{86} +(10.7813 + 2.55521i) q^{88} +(5.34347 - 1.94487i) q^{89} +(2.04212 + 0.743272i) q^{91} +(1.10721 + 0.728226i) q^{92} +(12.1908 + 1.42491i) q^{94} +(-9.67036 + 12.9896i) q^{95} +(0.409894 - 7.03762i) q^{97} +(-2.95571 + 2.48014i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 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 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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 $

$2$	−0.880274	+	2.04070i	−0.622448	+	1.44300i	0.256721	+	0.966485i	$0.417358\pi$
$2$	−0.880274	+	2.04070i	−0.622448	+	1.44300i	−0.879169	+	0.476510i	$0.841902\pi$
$3$		0			0
$3$		0			0
$4$	−2.01711	−	2.13801i	−1.00855	−	1.06900i
$5$	0.171269	+	2.94057i	0.0765937	+	1.31506i	0.789477	+	0.613780i	$0.210352\pi$
$5$	0.171269	+	2.94057i	0.0765937	+	1.31506i	−0.712883	+	0.701283i	$0.752611\pi$
$6$		0			0
$7$	2.87602	+	0.681629i	1.08703	+	0.257631i	0.734802	−	0.678282i	$-0.237275\pi$
$7$	2.87602	+	0.681629i	1.08703	+	0.257631i	0.352231	+	0.935913i	$0.385423\pi$
$8$	1.96178	−	0.714030i	0.693594	−	0.252448i
$9$		0			0
$10$	−6.15160	−	2.23900i	−1.94531	−	0.708033i
$11$	4.43417	+	2.91640i	1.33695	+	0.879328i	0.998106	−	0.0615139i	$-0.0195929\pi$
$11$	4.43417	+	2.91640i	1.33695	+	0.879328i	0.338847	+	0.940842i	$0.389963\pi$
$12$		0			0
$13$	0.730282	+	0.0853577i	0.202544	+	0.0236740i	0.216760	−	0.976225i	$-0.430451\pi$
$13$	0.730282	+	0.0853577i	0.202544	+	0.0236740i	−0.0142160	+	0.999899i	$0.504525\pi$
$14$	−3.92268	+	5.26908i	−1.04838	+	1.40822i
$15$		0			0
$16$	0.0720359	−	1.23681i	0.0180090	−	0.309202i
$17$	1.11298	−	0.933897i	0.269936	−	0.226503i	−0.497764	−	0.867312i	$-0.665845\pi$
$17$	1.11298	−	0.933897i	0.269936	−	0.226503i	0.767700	+	0.640809i	$0.221401\pi$
$18$		0			0
$19$	4.21153	+	3.53390i	0.966192	+	0.810731i	0.981949	−	0.189145i	$-0.0605715\pi$
$19$	4.21153	+	3.53390i	0.966192	+	0.810731i	−0.0157573	+	0.999876i	$0.505016\pi$
$20$	5.94150	−	6.29762i	1.32856	−	1.40819i
$21$		0			0
$22$	−9.85479	+	6.48160i	−2.10105	+	1.38188i
$23$	−0.438705	+	0.103975i	−0.0914763	+	0.0216803i	−0.276099	−	0.961129i	$-0.589042\pi$
$23$	−0.438705	+	0.103975i	−0.0914763	+	0.0216803i	0.184623	+	0.982809i	$0.440894\pi$
$24$		0			0
$25$	−3.65143	+	0.426791i	−0.730286	+	0.0853581i
$26$	−0.817038	+	1.41515i	−0.160234	+	0.277534i
$27$		0			0
$28$	−4.34391	−	7.52387i	−0.820921	−	1.42188i
$29$	2.12271	+	2.85130i	0.394178	+	0.529472i	0.954265	−	0.298961i	$-0.0966400\pi$
$29$	2.12271	+	2.85130i	0.394178	+	0.529472i	−0.560088	+	0.828433i	$0.689233\pi$
$30$		0			0
$31$	0.319104	−	1.06588i	0.0573128	−	0.191438i	−0.924539	−	0.381087i	$-0.875550\pi$
$31$	0.319104	−	1.06588i	0.0573128	−	0.191438i	0.981852	+	0.189649i	$0.0607350\pi$
$32$	6.19179	+	3.10963i	1.09456	+	0.549711i
$33$		0			0
$34$	0.926085	+	3.09334i	0.158822	+	0.530503i
$35$	−1.51181	+	8.57387i	−0.255542	+	1.44925i
$36$		0			0
$37$	−0.643205	−	3.64780i	−0.105742	−	0.599695i	−0.990921	−	0.134444i	$-0.957075\pi$
$37$	−0.643205	−	3.64780i	−0.105742	−	0.599695i	0.885179	−	0.465251i	$-0.154036\pi$
$38$	−10.9189	+	5.48370i	−1.77129	+	0.889573i
$39$		0			0
$40$	2.43565	+	5.64646i	0.385109	+	0.892784i
$41$	−4.05045	−	9.39000i	−0.632574	−	1.46647i	−0.868995	−	0.494820i	$-0.835234\pi$
$41$	−4.05045	−	9.39000i	−0.632574	−	1.46647i	0.236421	−	0.971651i	$-0.424025\pi$
$42$		0			0
$43$	−7.08750	+	3.55948i	−1.08083	+	0.542815i	−0.897850	−	0.440301i	$-0.854872\pi$
$43$	−7.08750	+	3.55948i	−1.08083	+	0.542815i	−0.182984	+	0.983116i	$0.558576\pi$
$44$	−2.70891	−	15.3630i	−0.408383	−	2.31606i
$45$		0			0
$46$	0.173998	−	0.986793i	0.0256546	−	0.145495i
$47$	−1.58391	−	5.29061i	−0.231036	−	0.771715i	−0.992364	−	0.123347i	$-0.960637\pi$
$47$	−1.58391	−	5.29061i	−0.231036	−	0.771715i	0.761327	−	0.648368i	$-0.224548\pi$
$48$		0			0
$49$	1.55143	+	0.779157i	0.221633	+	0.111308i
$50$	2.34330	−	7.82718i	0.331393	−	1.10693i
$51$		0			0
$52$	−1.29056	−	1.73353i	−0.178969	−	0.240397i
$53$	−1.83020	−	3.17001i	−0.251398	−	0.435434i	0.712513	−	0.701659i	$-0.247557\pi$
$53$	−1.83020	−	3.17001i	−0.251398	−	0.435434i	−0.963911	+	0.266225i	$0.914224\pi$
$54$		0			0
$55$	−7.81644	+	13.5385i	−1.05397	+	1.82553i
$56$	6.12882	−	0.716356i	0.818998	−	0.0957271i
$57$		0			0
$58$	−7.68722	+	1.82190i	−1.00938	+	0.239228i
$59$	−5.98693	+	3.93766i	−0.779431	+	0.512640i	−0.875782	−	0.482707i	$-0.839653\pi$
$59$	−5.98693	+	3.93766i	−0.779431	+	0.512640i	0.0963503	+	0.995347i	$0.469283\pi$
$60$		0			0
$61$	−2.98858	+	3.16771i	−0.382649	+	0.405584i	−0.889857	−	0.456240i	$-0.849196\pi$
$61$	−2.98858	+	3.16771i	−0.382649	+	0.405584i	0.507208	+	0.861823i	$0.330677\pi$
$62$	1.89425	+	1.58947i	0.240570	+	0.201862i
$63$		0			0
$64$	−9.89820	+	8.30558i	−1.23728	+	1.03820i
$65$	−0.125926	+	2.16206i	−0.0156192	+	0.268171i
$66$		0			0
$67$	6.75776	−	9.07724i	0.825591	−	1.10896i	−0.166818	−	0.985988i	$-0.553349\pi$
$67$	6.75776	−	9.07724i	0.825591	−	1.10896i	0.992410	−	0.122974i	$-0.0392432\pi$
$68$	−4.24167	−	0.495780i	−0.514378	−	0.0601222i
$69$		0			0
$70$	−16.1659	−	10.6325i	−1.93220	−	1.27083i
$71$	−12.6408	−	4.60088i	−1.50019	−	0.546024i	−0.544079	−	0.839034i	$-0.683121\pi$
$71$	−12.6408	−	4.60088i	−1.50019	−	0.546024i	−0.956109	+	0.293010i	$0.905343\pi$
$72$		0			0
$73$	3.72979	−	1.35753i	0.436538	−	0.158887i	−0.114397	−	0.993435i	$-0.536493\pi$
$73$	3.72979	−	1.35753i	0.436538	−	0.158887i	0.550935	+	0.834548i	$0.314271\pi$
$74$	8.01028	+	1.89847i	0.931176	+	0.220693i
$75$		0			0
$76$	−0.939614	−	16.1325i	−0.107781	−	1.85053i
$77$	10.7649	+	11.4101i	1.22677	+	1.30030i
$78$		0			0
$79$	1.12592	−	2.61017i	0.126675	−	0.293667i	−0.843062	−	0.537816i	$-0.819250\pi$
$79$	1.12592	−	2.61017i	0.126675	−	0.293667i	0.969738	+	0.244149i	$0.0785088\pi$
$80$	3.64926			0.408000
$81$		0			0
$82$	22.7277			2.50986
$83$	0.139359	−	0.323070i	0.0152966	−	0.0354615i	−0.910397	−	0.413737i	$-0.864223\pi$
$83$	0.139359	−	0.323070i	0.0152966	−	0.0354615i	0.925693	+	0.378275i	$0.123483\pi$
$84$		0			0
$85$	2.93681	+	3.11283i	0.318542	+	0.337634i
$86$	−1.02490	−	17.5968i	−0.110518	−	1.89751i
$87$		0			0
$88$	10.7813	+	2.55521i	1.14929	+	0.272386i
$89$	5.34347	−	1.94487i	0.566407	−	0.206155i	−0.0429141	−	0.999079i	$-0.513664\pi$
$89$	5.34347	−	1.94487i	0.566407	−	0.206155i	0.609321	+	0.792923i	$0.291442\pi$
$90$		0			0
$91$	2.04212	+	0.743272i	0.214073	+	0.0779160i
$92$	1.10721	+	0.728226i	0.115435	+	0.0759228i
$93$		0			0
$94$	12.1908	+	1.42491i	1.25739	+	0.146968i
$95$	−9.67036	+	12.9896i	−0.992158	+	1.33270i
$96$		0			0
$97$	0.409894	−	7.03762i	0.0416185	−	0.714562i	−0.911376	−	0.411574i	$-0.864979\pi$
$97$	0.409894	−	7.03762i	0.0416185	−	0.714562i	0.952995	−	0.302987i	$-0.0979839\pi$
$98$	−2.95571	+	2.48014i	−0.298572	+	0.250532i
$99$		0			0
$100$	8.27780	+	6.94590i	0.827780	+	0.694590i
$101$	−7.28225	+	7.71874i	−0.724611	+	0.768043i	−0.980043	−	0.198784i	$-0.936301\pi$
$101$	−7.28225	+	7.71874i	−0.724611	+	0.768043i	0.255432	+	0.966827i	$0.417782\pi$
$102$		0			0
$103$	14.8895	−	9.79298i	1.46711	−	0.964931i	0.470519	−	0.882390i	$-0.344067\pi$
$103$	14.8895	−	9.79298i	1.46711	−	0.964931i	0.996588	−	0.0825411i	$-0.0263036\pi$
$104$	1.49360	−	0.353990i	0.146460	−	0.0347116i
$105$		0			0
$106$	8.08012	−	0.944431i	0.784811	−	0.0917313i
$107$	0.0249146	−	0.0431534i	0.00240859	−	0.00417180i	−0.864819	−	0.502084i	$-0.832567\pi$
$107$	0.0249146	−	0.0431534i	0.00240859	−	0.00417180i	0.867227	+	0.497913i	$0.165900\pi$
$108$		0			0
$109$	0.202520	+	0.350775i	0.0193979	+	0.0335981i	0.875561	−	0.483107i	$-0.160492\pi$
$109$	0.202520	+	0.350775i	0.0193979	+	0.0335981i	−0.856164	+	0.516705i	$0.827158\pi$
$110$	−20.7474	−	27.8686i	−1.97819	−	2.65717i
$111$		0			0
$112$	1.05022	−	3.50798i	0.0992365	−	0.331473i
$113$	−10.1658	−	5.10543i	−0.956313	−	0.480279i	−0.0990079	−	0.995087i	$-0.531567\pi$
$113$	−10.1658	−	5.10543i	−0.956313	−	0.480279i	−0.857305	+	0.514808i	$0.827863\pi$
$114$		0			0
$115$	−0.380882	−	1.27223i	−0.0355174	−	0.118636i
$116$	1.81436	−	10.2897i	0.168459	−	0.955379i
$117$		0			0
$118$	−2.76547	−	15.6838i	−0.254582	−	1.44381i
$119$	3.83751	−	1.92727i	0.351784	−	0.176672i
$120$		0			0
$121$	6.79960	+	15.7633i	0.618146	+	1.43302i
$122$	−3.83359	−	8.88726i	−0.347077	−	0.804615i
$123$		0			0
$124$	−2.92253	+	1.46775i	−0.262451	+	0.131808i
$125$	0.677067	+	3.83984i	0.0605587	+	0.343445i
$126$		0			0
$127$	2.26532	−	12.8473i	0.201015	−	1.14001i	−0.702574	−	0.711611i	$-0.747966\pi$
$127$	2.26532	−	12.8473i	0.201015	−	1.14001i	0.903589	−	0.428401i	$-0.140923\pi$
$128$	−4.26170	−	14.2351i	−0.376685	−	1.25821i
$129$		0			0
$130$	−4.30128	−	2.16019i	−0.377248	−	0.189461i
$131$	−2.29663	+	7.67128i	−0.200658	+	0.670243i	0.797133	+	0.603804i	$0.206349\pi$
$131$	−2.29663	+	7.67128i	−0.200658	+	0.670243i	−0.997790	+	0.0664391i	$0.978836\pi$
$132$		0			0
$133$	9.70364	+	13.0342i	0.841412	+	1.13021i
$134$	12.5753	+	21.7810i	1.08634	+	1.88160i
$135$		0			0
$136$	1.51658	−	2.62680i	0.130046	−	0.225246i
$137$	10.2507	−	1.19814i	0.875777	−	0.102364i	0.333687	−	0.942684i	$-0.391707\pi$
$137$	10.2507	−	1.19814i	0.875777	−	0.102364i	0.542090	+	0.840320i	$0.317633\pi$
$138$		0			0
$139$	−16.9835	+	4.02516i	−1.44052	+	0.341410i	−0.875320	−	0.483544i	$-0.839349\pi$
$139$	−16.9835	+	4.02516i	−1.44052	+	0.341410i	−0.565200	+	0.824954i	$0.691201\pi$
$140$	21.3805	−	14.0622i	1.80698	−	1.18847i
$141$		0			0
$142$	20.5164	−	21.7461i	1.72170	−	1.82489i
$143$	2.98926	+	2.50829i	0.249974	+	0.209753i
$144$		0			0
$145$	−8.02088	+	6.73032i	−0.666098	+	0.558923i
$146$	−0.512914	+	8.80639i	−0.0424490	+	0.728822i
$147$		0			0
$148$	−6.50161	+	8.73318i	−0.534429	+	0.717863i
$149$	8.25798	+	0.965219i	0.676520	+	0.0790739i	0.447413	−	0.894327i	$-0.352345\pi$
$149$	8.25798	+	0.965219i	0.676520	+	0.0790739i	0.229107	+	0.973401i	$0.426419\pi$
$150$		0			0
$151$	14.7051	+	9.67168i	1.19668	+	0.787071i	0.981865	−	0.189584i	$-0.0607138\pi$
$151$	14.7051	+	9.67168i	1.19668	+	0.787071i	0.214818	+	0.976654i	$0.431084\pi$
$152$	10.7854	+	3.92557i	0.874812	+	0.318406i
$153$		0			0
$154$	−32.7606	+	11.9239i	−2.63992	+	0.960854i
$155$	3.18895	+	0.755796i	0.256143	+	0.0607070i
$156$		0			0
$157$	0.125292	+	2.15117i	0.00999936	+	0.171682i	0.999610	+	0.0279117i	$0.00888574\pi$
$157$	0.125292	+	2.15117i	0.00999936	+	0.171682i	−0.989611	+	0.143771i	$0.954077\pi$
$158$	4.33546	+	4.59532i	0.344911	+	0.365584i
$159$		0			0
$160$	−8.08364	+	18.7400i	−0.639068	+	1.48153i
$161$	−1.33260			−0.105023
$162$		0			0
$163$	9.47594			0.742213			0.371106	−	0.928590i	$-0.378979\pi$
$163$	9.47594			0.742213			0.371106	+	0.928590i	$0.378979\pi$
$164$	−11.9057	+	27.6005i	−0.929679	+	2.15524i
$165$		0			0
$166$	0.536616	+	0.568780i	0.0416495	+	0.0441459i
$167$	0.222204	+	3.81509i	0.0171946	+	0.295221i	0.995932	+	0.0901046i	$0.0287201\pi$
$167$	0.222204	+	3.81509i	0.0171946	+	0.295221i	−0.978738	+	0.205116i	$0.934243\pi$
$168$		0			0
$169$	−12.1236	−	2.87334i	−0.932581	−	0.221026i
$170$	−8.93757	+	3.25301i	−0.685480	+	0.249494i
$171$		0			0
$172$	21.9064	+	7.97329i	1.67035	+	0.607958i
$173$	−6.99032	−	4.59760i	−0.531464	−	0.349549i	0.255242	−	0.966877i	$-0.417845\pi$
$173$	−6.99032	−	4.59760i	−0.531464	−	0.349549i	−0.786706	+	0.617328i	$0.788215\pi$
$174$		0			0
$175$	−10.7925	−	1.26146i	−0.815835	−	0.0953574i
$176$	3.92645	−	5.27413i	0.295967	−	0.397553i
$177$		0			0
$178$	−0.734825	+	12.6165i	−0.0550775	+	0.945644i
$179$	4.19854	−	3.52299i	0.313814	−	0.263321i	−0.472252	−	0.881463i	$-0.656559\pi$
$179$	4.19854	−	3.52299i	0.313814	−	0.263321i	0.786066	+	0.618142i	$0.212114\pi$
$180$		0			0
$181$	16.7963	+	14.0938i	1.24846	+	1.04758i	0.996814	+	0.0797621i	$0.0254161\pi$
$181$	16.7963	+	14.0938i	1.24846	+	1.04758i	0.251645	+	0.967820i	$0.419028\pi$
$182$	−3.31442	+	3.51308i	−0.245681	+	0.260407i
$183$		0			0
$184$	−0.786401	+	0.517224i	−0.0579743	+	0.0381303i
$185$	10.6164	−	2.51614i	0.780537	−	0.184991i
$186$		0			0
$187$	7.65874	−	0.895178i	0.560063	−	0.0654619i
$188$	−8.11647	+	14.0581i	−0.591955	+	1.02530i
$189$		0			0
$190$	−17.9953	−	31.1687i	−1.30551	−	2.26122i
$191$	−7.60922	−	10.2210i	−0.550584	−	0.739562i	0.436511	−	0.899699i	$-0.356214\pi$
$191$	−7.60922	−	10.2210i	−0.550584	−	0.739562i	−0.987095	+	0.160136i	$0.948807\pi$
$192$		0			0
$193$	−5.83150	+	19.4786i	−0.419761	+	1.40210i	0.443016	+	0.896514i	$0.353908\pi$
$193$	−5.83150	+	19.4786i	−0.419761	+	1.40210i	−0.862777	+	0.505585i	$0.831277\pi$
$194$	14.0009	+	7.03150i	1.00520	+	0.504832i
$195$		0			0
$196$	−1.46356	−	4.88862i	−0.104540	−	0.349187i
$197$	−0.696981	+	3.95277i	−0.0496578	+	0.281623i	−0.999518	−	0.0310522i	$-0.990114\pi$
$197$	−0.696981	+	3.95277i	−0.0496578	+	0.281623i	0.949860	+	0.312676i	$0.101225\pi$
$198$		0			0
$199$	0.667809	+	3.78734i	0.0473398	+	0.268477i	0.999286	−	0.0377889i	$-0.0120314\pi$
$199$	0.667809	+	3.78734i	0.0473398	+	0.268477i	−0.951946	+	0.306266i	$0.900920\pi$
$200$	−6.85856	+	3.44450i	−0.484973	+	0.243563i
$201$		0			0
$202$	−9.34128	−	21.6555i	−0.657250	−	1.52368i
$203$	4.16143	+	9.64728i	0.292075	+	0.677106i
$204$		0			0
$205$	26.9182	−	13.5188i	1.88005	−	0.944197i
$206$	6.87773	+	39.0056i	0.479195	+	2.71765i
$207$		0			0
$208$	0.158178	−	0.897070i	0.0109676	−	0.0622006i
$209$	8.36840	+	27.9524i	0.578855	+	1.93351i
$210$		0			0
$211$	6.36991	+	3.19909i	0.438522	+	0.220234i	0.654342	−	0.756199i	$-0.272946\pi$
$211$	6.36991	+	3.19909i	0.438522	+	0.220234i	−0.215819	+	0.976433i	$0.569242\pi$
$212$	−3.08578	+	10.3072i	−0.211932	+	0.707904i
$213$		0			0
$214$	0.0661317	+	0.0888303i	0.00452067	+	0.00607231i
$215$	−11.6808	−	20.2317i	−0.796621	−	1.37979i
$216$		0			0
$217$	1.64429	−	2.84799i	0.111621	−	0.193334i
$218$	−0.894100	+	0.104505i	−0.0605561	+	0.00707799i
$219$		0			0
$220$	44.7120	−	10.5969i	3.01448	−	0.714445i
$221$	0.892501	−	0.587007i	0.0600361	−	0.0394864i
$222$		0			0
$223$	−10.1902	+	10.8009i	−0.682384	+	0.723285i	−0.972292	−	0.233770i	$-0.924894\pi$
$223$	−10.1902	+	10.8009i	−0.682384	+	0.723285i	0.289908	+	0.957055i	$0.406375\pi$
$224$	15.6881	+	13.1639i	1.04820	+	0.879548i
$225$		0			0
$226$	19.3673	−	16.2511i	1.28829	−	1.08101i
$227$	0.782420	−	13.4336i	0.0519310	−	0.891621i	−0.867271	−	0.497836i	$-0.834128\pi$
$227$	0.782420	−	13.4336i	0.0519310	−	0.891621i	0.919202	−	0.393786i	$-0.128835\pi$
$228$		0			0
$229$	−1.94638	+	2.61445i	−0.128621	+	0.172768i	−0.861768	−	0.507302i	$-0.830643\pi$
$229$	−1.94638	+	2.61445i	−0.128621	+	0.172768i	0.733148	+	0.680069i	$0.238050\pi$
$230$	2.93153	+	0.342647i	0.193300	+	0.0225935i
$231$		0			0
$232$	6.20020	+	4.07794i	0.407063	+	0.267730i
$233$	7.77413	+	2.82955i	0.509300	+	0.185370i	0.583872	−	0.811846i	$-0.301537\pi$
$233$	7.77413	+	2.82955i	0.509300	+	0.185370i	−0.0745722	+	0.997216i	$0.523759\pi$
$234$		0			0
$235$	15.2861	−	5.56370i	0.997158	−	0.362936i
$236$	20.4950	+	4.85741i	1.33411	+	0.316191i
$237$		0			0
$238$	0.554928	+	9.52774i	0.0359706	+	0.617592i
$239$	−8.96426	−	9.50156i	−0.579850	−	0.614605i	0.369346	−	0.929292i	$-0.379582\pi$
$239$	−8.96426	−	9.50156i	−0.579850	−	0.614605i	−0.949195	+	0.314687i	$0.898100\pi$
$240$		0			0
$241$	−0.250623	+	0.581008i	−0.0161440	+	0.0374260i	−0.926097	−	0.377284i	$-0.876858\pi$
$241$	−0.250623	+	0.581008i	−0.0161440	+	0.0374260i	0.909953	+	0.414711i	$0.136117\pi$
$242$	−38.1537			−2.45261
$243$		0			0
$244$	12.8009			0.819493
$245$	−2.02546	+	4.69553i	−0.129402	+	0.299987i
$246$		0			0
$247$	2.77396	+	2.94023i	0.176503	+	0.187082i
$248$	−0.135059	−	2.31888i	−0.00857627	−	0.147249i
$249$		0			0
$250$	−8.43197	−	1.99841i	−0.533285	−	0.126391i
$251$	12.9984	−	4.73104i	0.820454	−	0.298621i	0.102519	−	0.994731i	$-0.467310\pi$
$251$	12.9984	−	4.73104i	0.820454	−	0.298621i	0.717935	+	0.696110i	$0.245088\pi$
$252$		0			0
$253$	−2.24852	−	0.818396i	−0.141364	−	0.0514521i
$254$	24.2234	+	15.9320i	1.51991	+	0.999662i
$255$		0			0
$256$	7.13340	+	0.833775i	0.445837	+	0.0521109i
$257$	15.6489	−	21.0202i	0.976153	−	1.31120i	0.0259190	−	0.999664i	$-0.491749\pi$
$257$	15.6489	−	21.0202i	0.976153	−	1.31120i	0.950234	−	0.311537i	$-0.100844\pi$
$258$		0			0
$259$	0.636574	−	10.9296i	0.0395548	−	0.679130i
$260$	4.87652	−	4.09189i	0.302429	−	0.253768i
$261$		0			0
$262$	−13.6332	−	11.4396i	−0.842259	−	0.706739i
$263$	−0.976219	+	1.03473i	−0.0601963	+	0.0638043i	−0.756772	−	0.653679i	$-0.773225\pi$
$263$	−0.976219	+	1.03473i	−0.0601963	+	0.0638043i	0.696576	+	0.717483i	$0.254706\pi$
$264$		0			0
$265$	9.00817	−	5.92477i	0.553367	−	0.363955i
$266$	−35.1409	+	8.32855i	−2.15463	+	0.510656i
$267$		0			0
$268$	−33.0383	+	3.86163i	−2.01814	+	0.235887i
$269$	−2.73320	+	4.73405i	−0.166646	+	0.288640i	−0.937239	−	0.348688i	$-0.886627\pi$
$269$	−2.73320	+	4.73405i	−0.166646	+	0.288640i	0.770592	+	0.637328i	$0.219961\pi$
$270$		0			0
$271$	−15.3667	−	26.6158i	−0.933458	−	1.61680i	−0.777360	−	0.629056i	$-0.783442\pi$
$271$	−15.3667	−	26.6158i	−0.933458	−	1.61680i	−0.156099	−	0.987741i	$-0.549892\pi$
$272$	−1.07488	−	1.44381i	−0.0651740	−	0.0875439i
$273$		0			0
$274$	−6.57839	+	21.9733i	−0.397415	+	1.32746i
$275$	−17.4357	−	8.75656i	−1.05142	−	0.528041i
$276$		0			0
$277$	−1.30655	−	4.36417i	−0.0785029	−	0.262218i	0.909724	−	0.415213i	$-0.136293\pi$
$277$	−1.30655	−	4.36417i	−0.0785029	−	0.262218i	−0.988227	+	0.152996i	$0.951108\pi$
$278$	6.73596	−	38.2015i	0.403996	−	2.29117i
$279$		0			0
$280$	3.15617	+	17.8995i	0.188617	+	1.06970i
$281$	16.3300	−	8.20123i	0.974166	−	0.489244i	0.110811	−	0.993842i	$-0.464655\pi$
$281$	16.3300	−	8.20123i	0.974166	−	0.489244i	0.863355	+	0.504597i	$0.168359\pi$
$282$		0			0
$283$	−9.38158	−	21.7489i	−0.557677	−	1.29284i	−0.930959	−	0.365123i	$-0.881027\pi$
$283$	−9.38158	−	21.7489i	−0.557677	−	1.29284i	0.373282	−	0.927718i	$-0.378232\pi$
$284$	15.6612	+	36.3066i	0.929319	+	2.15440i
$285$		0			0
$286$	−7.75003	+	3.89221i	−0.458269	+	0.230151i
$287$	−5.24867	−	29.7667i	−0.309819	−	1.75707i
$288$		0			0
$289$	−2.58547	+	14.6629i	−0.152086	+	0.862525i
$290$	−6.67402	−	22.2928i	−0.391912	−	1.30908i
$291$		0			0
$292$	−10.4258	−	5.23603i	−0.610123	−	0.306415i
$293$	1.36749	−	4.56773i	0.0798895	−	0.266849i	−0.908708	−	0.417433i	$-0.862930\pi$
$293$	1.36749	−	4.56773i	0.0798895	−	0.266849i	0.988597	+	0.150583i	$0.0481152\pi$
$294$		0			0
$295$	−12.6043	−	16.9306i	−0.733854	−	0.985736i
$296$	−3.86647	−	6.69691i	−0.224734	−	0.389250i
$297$		0			0
$298$	−9.23901	+	16.0024i	−0.535202	+	0.926996i
$299$	−0.329253	+	0.0384842i	−0.0190412	+	0.00222560i
$300$		0			0
$301$	−22.8100	+	5.40607i	−1.31475	+	0.311601i
$302$	−32.6815	+	21.4950i	−1.88061	+	1.23690i
$303$		0			0
$304$	4.67413	−	4.95429i	0.268080	−	0.284148i
$305$	−9.82673	−	8.24560i	−0.562677	−	0.472142i
$306$		0			0
$307$	−8.26674	+	6.93662i	−0.471808	+	0.395894i	−0.847453	−	0.530870i	$-0.821865\pi$
$307$	−8.26674	+	6.93662i	−0.471808	+	0.395894i	0.375646	+	0.926763i	$0.377421\pi$
$308$	2.68098	−	46.0307i	0.152763	−	2.62284i
$309$		0			0
$310$	−4.34951	+	5.84241i	−0.247036	+	0.331826i
$311$	−9.61593	−	1.12394i	−0.545269	−	0.0637328i	−0.161001	−	0.986954i	$-0.551472\pi$
$311$	−9.61593	−	1.12394i	−0.545269	−	0.0637328i	−0.384268	+	0.923221i	$0.625546\pi$
$312$		0			0
$313$	5.33634	+	3.50977i	0.301628	+	0.198384i	0.691296	−	0.722571i	$-0.257040\pi$
$313$	5.33634	+	3.50977i	0.301628	+	0.198384i	−0.389668	+	0.920955i	$0.627410\pi$
$314$	−4.50020	−	1.63794i	−0.253961	−	0.0924343i
$315$		0			0
$316$	−7.85165	+	2.85777i	−0.441690	+	0.160762i
$317$	−20.0555	−	4.75324i	−1.12643	−	0.266969i	−0.375157	−	0.926961i	$-0.622411\pi$
$317$	−20.0555	−	4.75324i	−1.12643	−	0.266969i	−0.751272	+	0.659993i	$0.770559\pi$
$318$		0			0
$319$	1.09694	+	18.8338i	0.0614171	+	1.05449i
$320$	−26.1184	−	27.6839i	−1.46006	−	1.54758i
$321$		0			0
$322$	1.17305	−	2.71943i	0.0653714	−	0.151548i
$323$	7.98763			0.444444
$324$		0			0
$325$	−2.70300			−0.149936
$326$	−8.34142	+	19.3376i	−0.461989	+	1.07101i
$327$		0			0
$328$	−14.6508	−	15.5290i	−0.808957	−	0.857444i
$329$	−0.949107	−	16.2955i	−0.0523259	−	0.898402i
$330$		0			0
$331$	19.7505	+	4.68095i	1.08558	+	0.257288i	0.734193	−	0.678941i	$-0.237561\pi$
$331$	19.7505	+	4.68095i	1.08558	+	0.257288i	0.351391	+	0.936229i	$0.385709\pi$
$332$	−0.971828	+	0.353716i	−0.0533360	+	0.0194127i
$333$		0			0
$334$	−7.98107	−	2.90487i	−0.436705	−	0.158948i
$335$	27.8497	+	18.3170i	1.52159	+	1.00077i
$336$		0			0
$337$	3.63159	+	0.424472i	0.197825	+	0.0231225i	0.214428	−	0.976740i	$-0.431211\pi$
$337$	3.63159	+	0.424472i	0.197825	+	0.0231225i	−0.0166032	+	0.999862i	$0.505285\pi$
$338$	16.5357	−	22.2113i	0.899422	−	1.20813i
$339$		0			0
$340$	0.731411	−	12.5578i	0.0396663	−	0.681045i
$341$	4.52350	−	3.79567i	0.244961	−	0.205547i
$342$		0			0
$343$	−11.9185	−	10.0008i	−0.643537	−	0.539992i
$344$	−11.3626	+	12.0436i	−0.612628	+	0.649347i
$345$		0			0
$346$	15.5357	−	10.2180i	0.835207	−	0.549324i
$347$	28.3703	−	6.72388i	1.52300	−	0.360957i	0.617932	−	0.786232i	$-0.287971\pi$
$347$	28.3703	−	6.72388i	1.52300	−	0.360957i	0.905064	+	0.425275i	$0.139823\pi$
$348$		0			0
$349$	−16.8175	+	1.96569i	−0.900222	+	0.105221i	−0.553599	−	0.832784i	$-0.686746\pi$
$349$	−16.8175	+	1.96569i	−0.900222	+	0.105221i	−0.346623	+	0.938004i	$0.612672\pi$
$350$	12.0746	−	20.9138i	0.645415	−	1.11789i
$351$		0			0
$352$	18.3865	+	31.8464i	0.980005	+	1.69742i
$353$	−13.5844	−	18.2471i	−0.723027	−	0.971194i	−0.999947	−	0.0103008i	$-0.996721\pi$
$353$	−13.5844	−	18.2471i	−0.723027	−	0.971194i	0.276920	−	0.960893i	$-0.410686\pi$
$354$		0			0
$355$	11.3642	−	37.9592i	0.603151	−	2.01466i
$356$	−14.9365	−	7.50139i	−0.791633	−	0.397573i
$357$		0			0
$358$	3.49352	+	11.6692i	0.184638	+	0.616735i
$359$	−2.65948	+	15.0826i	−0.140362	+	0.796032i	0.830613	+	0.556850i	$0.187990\pi$
$359$	−2.65948	+	15.0826i	−0.140362	+	0.796032i	−0.970975	+	0.239182i	$0.923121\pi$
$360$		0			0
$361$	1.94928	+	11.0549i	0.102593	+	0.581836i
$362$	−43.5466	+	21.8699i	−2.28876	+	1.14946i
$363$		0			0
$364$	−2.53006	−	5.86533i	−0.132611	−	0.307427i
$365$	4.63071	+	10.7352i	0.242382	+	0.561906i
$366$		0			0
$367$	12.5438	−	6.29975i	0.654782	−	0.328844i	−0.0902045	−	0.995923i	$-0.528752\pi$
$367$	12.5438	−	6.29975i	0.654782	−	0.328844i	0.744987	+	0.667079i	$0.232456\pi$
$368$	0.0969946	+	0.550084i	0.00505619	+	0.0286751i
$369$		0			0
$370$	−4.21068	+	23.8799i	−0.218903	+	1.24146i
$371$	−3.10293	−	10.3645i	−0.161096	−	0.538099i
$372$		0			0
$373$	−24.3484	−	12.2282i	−1.26071	−	0.633153i	−0.312236	−	0.950005i	$-0.601078\pi$
$373$	−24.3484	−	12.2282i	−1.26071	−	0.633153i	−0.948475	+	0.316852i	$0.897374\pi$
$374$	−4.91499	+	16.4172i	−0.254148	+	0.848914i
$375$		0			0
$376$	−6.88493	−	9.24807i	−0.355063	−	0.476933i
$377$	1.30680	+	2.26344i	0.0673035	+	0.116573i
$378$		0			0
$379$	−4.29852	+	7.44526i	−0.220800	+	0.382437i	−0.955051	−	0.296441i	$-0.904200\pi$
$379$	−4.29852	+	7.44526i	−0.220800	+	0.382437i	0.734251	+	0.678878i	$0.237534\pi$
$380$	47.2779	−	5.52600i	2.42531	−	0.283478i
$381$		0			0
$382$	27.5561	−	6.53093i	1.40989	−	0.334151i
$383$	16.1154	−	10.5992i	0.823456	−	0.541596i	−0.0664232	−	0.997792i	$-0.521159\pi$
$383$	16.1154	−	10.5992i	0.823456	−	0.541596i	0.889879	+	0.456196i	$0.150788\pi$
$384$		0			0
$385$	−31.7084	+	33.6090i	−1.61601	+	1.71287i
$386$	−34.6167	−	29.0469i	−1.76194	−	1.47845i
$387$		0			0
$388$	−15.8733	+	13.3193i	−0.805844	+	0.676183i
$389$	1.81076	−	31.0895i	0.0918091	−	1.57630i	−0.566826	−	0.823838i	$-0.691829\pi$
$389$	1.81076	−	31.0895i	0.0918091	−	1.57630i	0.658635	−	0.752463i	$-0.271134\pi$
$390$		0			0
$391$	−0.391166	+	0.525427i	−0.0197821	+	0.0265720i
$392$	3.59991	+	0.420769i	0.181823	+	0.0212520i
$393$		0			0
$394$	−7.45291	−	4.90185i	−0.375472	−	0.246952i
$395$	7.86821	+	2.86379i	0.395893	+	0.144093i
$396$		0			0
$397$	−10.0204	+	3.64712i	−0.502908	+	0.183044i	−0.581002	−	0.813902i	$-0.697339\pi$
$397$	−10.0204	+	3.64712i	−0.502908	+	0.183044i	0.0780935	+	0.996946i	$0.475117\pi$
$398$	−8.31668	−	1.97109i	−0.416878	−	0.0988018i
$399$		0			0
$400$	0.264824	+	4.54686i	0.0132412	+	0.227343i
$401$	5.55906	+	5.89226i	0.277606	+	0.294246i	0.851142	−	0.524935i	$-0.175910\pi$
$401$	5.55906	+	5.89226i	0.277606	+	0.294246i	−0.573536	+	0.819180i	$0.694429\pi$
$402$		0			0
$403$	0.324017	−	0.751157i	0.0161405	−	0.0374178i
$404$	31.1918			1.55185
$405$		0			0
$406$	−23.3504			−1.15886
$407$	7.78636	−	18.0508i	0.385956	−	0.894745i
$408$		0			0
$409$	25.7216	+	27.2633i	1.27185	+	1.34808i	0.909312	+	0.416115i	$0.136609\pi$
$409$	25.7216	+	27.2633i	1.27185	+	1.34808i	0.362539	+	0.931968i	$0.381910\pi$
$410$	3.89254	+	66.8324i	0.192239	+	3.30062i
$411$		0			0
$412$	−50.9712	−	12.0804i	−2.51117	−	0.595159i
$413$	−19.9025	+	7.24393i	−0.979339	+	0.356450i
$414$		0			0
$415$	0.973877	+	0.354462i	0.0478058	+	0.0173999i
$416$	4.25632	+	2.79943i	0.208683	+	0.137253i
$417$		0			0
$418$	−64.4091	−	7.52834i	−3.15035	−	0.368223i
$419$	−7.70081	+	10.3440i	−0.376209	+	0.505337i	−0.949393	−	0.314090i	$-0.898301\pi$
$419$	−7.70081	+	10.3440i	−0.376209	+	0.505337i	0.573184	+	0.819427i	$0.305708\pi$
$420$		0			0
$421$	−1.34506	+	23.0938i	−0.0655543	+	1.12552i	0.791794	+	0.610788i	$0.209147\pi$
$421$	−1.34506	+	23.0938i	−0.0655543	+	1.12552i	−0.857349	+	0.514736i	$0.827890\pi$
$422$	−12.1357	+	10.1830i	−0.590754	+	0.495702i
$423$		0			0
$424$	−5.85394	−	4.91204i	−0.284292	−	0.238550i
$425$	−3.66537	+	3.88507i	−0.177797	+	0.188453i
$426$		0			0
$427$	−10.7544	+	7.07329i	−0.520443	+	0.342300i
$428$	−0.142518	+	0.0337774i	−0.00688887	+	0.00163269i
$429$		0			0
$430$	51.5691	−	6.02757i	2.48688	−	0.290675i
$431$	11.3499	−	19.6586i	0.546706	−	0.946923i	−0.451791	−	0.892124i	$-0.649215\pi$
$431$	11.3499	−	19.6586i	0.546706	−	0.946923i	0.998497	−	0.0547992i	$-0.0174519\pi$
$432$		0			0
$433$	9.10550	+	15.7712i	0.437583	+	0.757915i	0.997502	−	0.0706315i	$-0.0225015\pi$
$433$	9.10550	+	15.7712i	0.437583	+	0.757915i	−0.559920	+	0.828547i	$0.689168\pi$
$434$	4.36448	+	5.86251i	0.209502	+	0.281409i
$435$		0			0
$436$	0.341455	−	1.14054i	0.0163527	−	0.0546219i
$437$	−2.21506	−	1.11244i	−0.105961	−	0.0532154i
$438$		0			0
$439$	−7.88601	−	26.3411i	−0.376379	−	1.25719i	−0.911107	−	0.412169i	$-0.864771\pi$
$439$	−7.88601	−	26.3411i	−0.376379	−	1.25719i	0.534728	−	0.845024i	$-0.320414\pi$
$440$	−5.66727	+	32.1407i	−0.270177	+	1.53225i
$441$		0			0
$442$	0.412263	+	2.33806i	0.0196093	+	0.111210i
$443$	10.9576	−	5.50312i	0.520612	−	0.261461i	−0.169031	−	0.985611i	$-0.554064\pi$
$443$	10.9576	−	5.50312i	0.520612	−	0.261461i	0.689643	+	0.724150i	$0.257768\pi$
$444$		0			0
$445$	6.63418	+	15.3798i	0.314491	+	0.729071i
$446$	−13.0714	−	30.3029i	−0.618949	−	1.43488i
$447$		0			0
$448$	−34.1287	+	17.1401i	−1.61243	+	0.809793i
$449$	−1.20505	−	6.83416i	−0.0568697	−	0.322524i	0.943080	−	0.332566i	$-0.107915\pi$
$449$	−1.20505	−	6.83416i	−0.0568697	−	0.322524i	−0.999950	+	0.0100422i	$0.996803\pi$
$450$		0			0
$451$	9.42460	−	53.4496i	0.443787	−	2.51684i
$452$	9.58995	+	32.0327i	0.451073	+	1.50669i
$453$		0			0
$454$	26.7253	+	13.4220i	1.25428	+	0.629924i
$455$	−1.83589	+	6.13230i	−0.0860679	+	0.287487i
$456$		0			0
$457$	17.8340	+	23.9553i	0.834241	+	1.12058i	0.991121	+	0.132962i	$0.0424490\pi$
$457$	17.8340	+	23.9553i	0.834241	+	1.12058i	−0.156880	+	0.987618i	$0.550144\pi$
$458$	−3.62196	−	6.27342i	−0.169243	−	0.293138i
$459$		0			0
$460$	−1.95177	+	3.38056i	−0.0910017	+	0.157620i
$461$	−0.814896	+	0.0952477i	−0.0379535	+	0.00443613i	−0.135048	−	0.990839i	$-0.543119\pi$
$461$	−0.814896	+	0.0952477i	−0.0379535	+	0.00443613i	0.0970950	+	0.995275i	$0.469045\pi$
$462$		0			0
$463$	−27.8479	+	6.60007i	−1.29420	+	0.306731i	−0.819329	−	0.573324i	$-0.805654\pi$
$463$	−27.8479	+	6.60007i	−1.29420	+	0.306731i	−0.474872	+	0.880055i	$0.657506\pi$
$464$	3.67942	−	2.41999i	0.170813	−	0.112345i
$465$		0			0
$466$	−12.6176	+	13.3739i	−0.584501	+	0.619535i
$467$	9.57011	+	8.03027i	0.442852	+	0.371597i	0.836775	−	0.547546i	$-0.184438\pi$
$467$	9.57011	+	8.03027i	0.442852	+	0.371597i	−0.393924	+	0.919143i	$0.628883\pi$
$468$		0			0
$469$	25.6227	−	21.5000i	1.18315	−	0.992779i
$470$	−2.10212	+	36.0921i	−0.0969638	+	1.66480i
$471$		0			0
$472$	−8.93343	+	11.9997i	−0.411194	+	0.552330i
$473$	−41.8081	−	4.88666i	−1.92234	−	0.224689i
$474$		0			0
$475$	−16.8863	−	11.1063i	−0.774799	−	0.509593i
$476$	−11.8612	−	4.31712i	−0.543656	−	0.197875i
$477$		0			0
$478$	27.2809	−	9.92943i	1.24780	−	0.454161i
$479$	4.41364	+	1.04605i	0.201664	+	0.0477953i	0.330206	−	0.943909i	$-0.392882\pi$
$479$	4.41364	+	1.04605i	0.201664	+	0.0477953i	−0.128542	+	0.991704i	$0.541030\pi$
$480$		0			0
$481$	−0.158354	−	2.71883i	−0.00722030	−	0.123968i
$482$	−0.965049	−	1.02289i	−0.0439568	−	0.0465915i
$483$		0			0
$484$	19.9864	−	46.3338i	0.908475	−	2.10608i
$485$	20.7648			0.942881
$486$		0			0
$487$	−28.2887			−1.28188			−0.640941	−	0.767590i	$-0.721456\pi$
$487$	−28.2887			−1.28188			−0.640941	+	0.767590i	$0.721456\pi$
$488$	−3.60110	+	8.34829i	−0.163014	+	0.377909i
$489$		0			0
$490$	−7.79924	−	8.26671i	−0.352334	−	0.373452i
$491$	1.13872	+	19.5510i	0.0513896	+	0.882325i	0.921236	+	0.389003i	$0.127180\pi$
$491$	1.13872	+	19.5510i	0.0513896	+	0.882325i	−0.869847	+	0.493322i	$0.835782\pi$
$492$		0			0
$493$	5.02534	+	1.19103i	0.226330	+	0.0536412i
$494$	−8.44198	+	3.07263i	−0.379823	+	0.138244i
$495$		0			0
$496$	−1.29531	−	0.471453i	−0.0581609	−	0.0211688i
$497$	−33.2191	−	21.8486i	−1.49008	−	0.980042i
$498$		0			0
$499$	29.3991	+	3.43626i	1.31608	+	0.153828i	0.745000	−	0.667064i	$-0.232449\pi$
$499$	29.3991	+	3.43626i	1.31608	+	0.153828i	0.571083	+	0.820892i	$0.306523\pi$
$500$	6.84389	−	9.19294i	0.306068	−	0.411121i
$501$		0			0
$502$	−1.78752	+	30.6906i	−0.0797810	+	1.36979i
$503$	−18.2284	+	15.2955i	−0.812765	+	0.681991i	−0.951266	−	0.308371i	$-0.900216\pi$
$503$	−18.2284	+	15.2955i	−0.812765	+	0.681991i	0.138501	+	0.990362i	$0.455772\pi$
$504$		0			0
$505$	−23.9447	−	20.0920i	−1.06553	−	0.894082i
$506$	3.64942	−	3.86816i	0.162237	−	0.171961i
$507$		0			0
$508$	−32.0370	+	21.0711i	−1.42141	+	0.934878i
$509$	−12.1044	+	2.86880i	−0.536519	+	0.127157i	−0.489938	−	0.871757i	$-0.662981\pi$
$509$	−12.1044	+	2.86880i	−0.536519	+	0.127157i	−0.0465808	+	0.998915i	$0.514833\pi$
$510$		0			0
$511$	11.6523	−	1.36195i	0.515466	−	0.0602493i
$512$	6.87849	−	11.9139i	0.303989	−	0.526525i
$513$		0			0
$514$	29.1206	+	50.4383i	1.28445	+	2.22474i
$515$	31.3471	+	42.1064i	1.38132	+	1.85543i
$516$		0			0
$517$	8.40624	−	28.0788i	0.369706	−	1.23490i
$518$	21.7436	+	10.9201i	0.955361	+	0.479800i
$519$		0			0
$520$	1.29674	+	4.33141i	0.0568658	+	0.189945i
$521$	−6.26330	+	35.5209i	−0.274400	+	1.55620i	0.466461	+	0.884542i	$0.345529\pi$
$521$	−6.26330	+	35.5209i	−0.274400	+	1.55620i	−0.740861	+	0.671659i	$0.765582\pi$
$522$		0			0
$523$	−3.40284	−	19.2985i	−0.148796	−	0.843864i	−0.964241	−	0.265029i	$-0.914619\pi$
$523$	−3.40284	−	19.2985i	−0.148796	−	0.843864i	0.815445	−	0.578835i	$-0.196493\pi$
$524$	21.0338	−	10.5636i	0.918867	−	0.461472i
$525$		0			0
$526$	−1.25224	−	2.90302i	−0.0546003	−	0.126578i
$527$	−0.640270	−	1.48431i	−0.0278906	−	0.0646576i
$528$		0			0
$529$	−20.3719	+	10.2312i	−0.885735	+	0.444833i
$530$	4.16104	+	23.5984i	0.180744	+	1.02505i
$531$		0			0
$532$	8.29406	−	47.0379i	0.359593	−	2.03935i
$533$	−2.15646	−	7.20308i	−0.0934067	−	0.312000i
$534$		0			0
$535$	0.131163	+	0.0658724i	0.00567066	+	0.00284791i
$536$	6.77582	−	22.6328i	0.292671	−	0.977588i
$537$		0			0
$538$	−7.25483	−	9.74492i	−0.312778	−	0.420133i
$539$	4.60697	+	7.97951i	0.198436	+	0.343702i
$540$		0			0
$541$	9.81665	−	17.0029i	0.422051	−	0.731013i	−0.574089	−	0.818793i	$-0.694644\pi$
$541$	9.81665	−	17.0029i	0.422051	−	0.731013i	0.996140	+	0.0877794i	$0.0279771\pi$
$542$	67.8419	−	7.92959i	2.91406	−	0.340605i
$543$		0			0
$544$	9.79539	−	2.32155i	0.419974	−	0.0995356i
$545$	−0.996792	+	0.655600i	−0.0426979	+	0.0280828i
$546$		0			0
$547$	20.9915	−	22.2497i	0.897533	−	0.951329i	−0.101520	−	0.994833i	$-0.532371\pi$
$547$	20.9915	−	22.2497i	0.897533	−	0.951329i	0.999053	+	0.0435043i	$0.0138522\pi$
$548$	−23.2384	−	19.4993i	−0.992695	−	0.832970i
$549$		0			0
$550$	33.2178	−	27.8730i	1.41641	−	1.18851i
$551$	−1.13631	+	19.5098i	−0.0484086	+	0.831144i
$552$		0			0
$553$	5.01732	−	6.73942i	0.213358	−	0.286589i
$554$	10.0561	+	1.17539i	0.427243	+	0.0499375i
$555$		0			0
$556$	42.8633	+	28.1917i	1.81781	+	1.19559i
$557$	31.4323	+	11.4404i	1.33183	+	0.484746i	0.907230	−	0.420636i	$-0.138193\pi$
$557$	31.4323	+	11.4404i	1.33183	+	0.484746i	0.424599	+	0.905382i	$0.360415\pi$
$558$		0			0
$559$	−5.47970	+	1.99445i	−0.231767	+	0.0843562i
$560$	10.4953	+	2.48744i	0.443509	+	0.105113i
$561$		0			0
$562$	2.36142	+	40.5440i	0.0996105	+	1.71025i
$563$	−0.144057	−	0.152692i	−0.00607128	−	0.00643518i	0.724331	−	0.689453i	$-0.242149\pi$
$563$	−0.144057	−	0.152692i	−0.00607128	−	0.00643518i	−0.730402	+	0.683017i	$0.760667\pi$
$564$		0			0
$565$	13.2718	−	30.7675i	0.558349	−	1.29440i
$566$	52.6415			2.21269
$567$		0			0
$568$	−28.0837			−1.17836
$569$	−16.2102	+	37.5794i	−0.679566	+	1.57541i	0.132066	+	0.991241i	$0.457839\pi$
$569$	−16.2102	+	37.5794i	−0.679566	+	1.57541i	−0.811632	+	0.584169i	$0.801420\pi$
$570$		0			0
$571$	−19.2901	−	20.4463i	−0.807267	−	0.855653i	0.184616	−	0.982811i	$-0.440896\pi$
$571$	−19.2901	−	20.4463i	−0.807267	−	0.855653i	−0.991882	+	0.127158i	$0.959414\pi$
$572$	−0.666918	−	11.4505i	−0.0278852	−	0.478771i
$573$		0			0
$574$	65.3653	+	15.4919i	2.72829	+	0.646618i
$575$	1.55752	−	0.566892i	0.0649532	−	0.0236410i
$576$		0			0
$577$	−12.8095	−	4.66227i	−0.533266	−	0.194093i	0.0613301	−	0.998118i	$-0.480466\pi$
$577$	−12.8095	−	4.66227i	−0.533266	−	0.194093i	−0.594596	+	0.804025i	$0.702688\pi$
$578$	−27.6468	−	18.1836i	−1.14995	−	0.756336i
$579$		0			0
$580$	30.5685	+	3.57294i	1.26929	+	0.148358i
$581$	0.621012	−	0.834164i	0.0257639	−	0.0346069i
$582$		0			0
$583$	1.12957	−	19.3940i	0.0467820	−	0.803216i
$584$	6.34770	−	5.32636i	0.262670	−	0.220406i
$585$		0			0
$586$	8.11761	+	6.81149i	0.335336	+	0.281380i
$587$	−19.2852	+	20.4412i	−0.795987	+	0.843697i	−0.990544	−	0.137194i	$-0.956192\pi$
$587$	−19.2852	+	20.4412i	−0.795987	+	0.843697i	0.194557	+	0.980891i	$0.437673\pi$
$588$		0			0
$589$	5.11064	−	3.36132i	0.210580	−	0.138501i
$590$	45.6456	−	10.8182i	1.87920	−	0.445378i
$591$		0			0
$592$	−4.55796	+	0.532749i	−0.187331	+	0.0218959i
$593$	−2.12487	+	3.68039i	−0.0872581	+	0.151135i	−0.906351	−	0.422525i	$-0.861144\pi$
$593$	−2.12487	+	3.68039i	−0.0872581	+	0.151135i	0.819093	+	0.573661i	$0.194477\pi$
$594$		0			0
$595$	6.32451	+	10.9544i	0.259280	+	0.449086i
$596$	−14.5936	−	19.6026i	−0.597777	−	0.802953i
$597$		0			0
$598$	0.211298	−	0.705785i	0.00864063	−	0.0288617i
$599$	18.9670	+	9.52557i	0.774970	+	0.389204i	0.791899	−	0.610652i	$-0.209093\pi$
$599$	18.9670	+	9.52557i	0.774970	+	0.389204i	−0.0169292	+	0.999857i	$0.505389\pi$
$600$		0			0
$601$	11.1975	+	37.4023i	0.456757	+	1.52567i	0.807882	+	0.589345i	$0.200614\pi$
$601$	11.1975	+	37.4023i	0.456757	+	1.52567i	−0.351125	+	0.936329i	$0.614201\pi$
$602$	9.04687	−	51.3073i	0.368723	−	2.09113i
$603$		0			0
$604$	−8.98358	−	50.9484i	−0.365537	−	2.07306i
$605$	−45.1884	+	22.6945i	−1.83717	+	0.922661i
$606$		0			0
$607$	17.7038	+	41.0420i	0.718574	+	1.66584i	0.745762	+	0.666212i	$0.232086\pi$
$607$	17.7038	+	41.0420i	0.718574	+	1.66584i	−0.0271878	+	0.999630i	$0.508655\pi$
$608$	15.0878	+	34.9775i	0.611892	+	1.41852i
$609$		0			0
$610$	25.4770	−	12.7951i	1.03154	−	0.518057i
$611$	−0.705103	−	3.99884i	−0.0285254	−	0.161776i
$612$		0			0
$613$	−7.96425	+	45.1675i	−0.321673	+	1.82430i	0.210418	+	0.977611i	$0.432517\pi$
$613$	−7.96425	+	45.1675i	−0.321673	+	1.82430i	−0.532091	+	0.846687i	$0.678594\pi$
$614$	−6.87859	−	22.9761i	−0.277597	−	0.927239i
$615$		0			0
$616$	29.2654	+	14.6976i	1.17914	+	0.592185i
$617$	6.22717	−	20.8002i	0.250696	−	0.837384i	−0.736302	−	0.676653i	$-0.763430\pi$
$617$	6.22717	−	20.8002i	0.250696	−	0.837384i	0.986998	−	0.160731i	$-0.0513851\pi$
$618$		0			0
$619$	−17.5933	−	23.6319i	−0.707135	−	0.949848i	0.292845	−	0.956160i	$-0.405398\pi$
$619$	−17.5933	−	23.6319i	−0.707135	−	0.949848i	−0.999980	+	0.00631239i	$0.997991\pi$
$620$	−4.81657	−	8.34254i	−0.193438	−	0.335044i
$621$		0			0
$622$	10.7583	−	18.6339i	0.431368	−	0.747151i
$623$	16.6936	−	1.95120i	0.668815	−	0.0781733i
$624$		0			0
$625$	−29.0613	+	6.88765i	−1.16245	+	0.275506i
$626$	−11.8598	+	7.80034i	−0.474015	+	0.311764i
$627$		0			0
$628$	4.34650	−	4.60703i	0.173444	−	0.183840i
$629$	−4.12254	−	3.45922i	−0.164376	−	0.137928i
$630$		0			0
$631$	−23.1628	+	19.4359i	−0.922098	+	0.773732i	−0.974382	−	0.224900i	$-0.927794\pi$
$631$	−23.1628	+	19.4359i	−0.922098	+	0.773732i	0.0522840	+	0.998632i	$0.483350\pi$
$632$	0.345063	−	5.92451i	0.0137259	−	0.235664i
$633$		0			0
$634$	27.3543	−	36.7432i	1.08638	−	1.45926i
$635$	38.1663	+	4.46100i	1.51458	+	0.177030i
$636$		0			0
$637$	1.06647	+	0.701431i	0.0422553	+	0.0277917i
$638$	−39.3998	−	14.3404i	−1.55985	−	0.567741i
$639$		0			0
$640$	41.1293	−	14.9699i	1.62578	−	0.591735i
$641$	−0.595982	−	0.141250i	−0.0235399	−	0.00557905i	0.218829	−	0.975763i	$-0.429776\pi$
$641$	−0.595982	−	0.141250i	−0.0235399	−	0.00557905i	−0.242369	+	0.970184i	$0.577924\pi$
$642$		0			0
$643$	−1.08540	−	18.6357i	−0.0428042	−	0.734919i	−0.949622	−	0.313397i	$-0.898533\pi$
$643$	−1.08540	−	18.6357i	−0.0428042	−	0.734919i	0.906818	−	0.421522i	$-0.138504\pi$
$644$	2.68799	+	2.84910i	0.105922	+	0.112270i
$645$		0			0
$646$	−7.03130	+	16.3004i	−0.276643	+	0.641330i
$647$	−44.8197			−1.76204			−0.881022	−	0.473075i	$-0.843144\pi$
$647$	−44.8197			−1.76204			−0.881022	+	0.473075i	$0.843144\pi$
$648$		0			0
$649$	−38.0309			−1.49284
$650$	2.37938	−	5.51603i	0.0933270	−	0.216356i
$651$		0			0
$652$	−19.1140	−	20.2596i	−0.748561	−	0.793429i
$653$	−2.87763	−	49.4069i	−0.112610	−	1.93344i	−0.305443	−	0.952210i	$-0.598805\pi$
$653$	−2.87763	−	49.4069i	−0.112610	−	1.93344i	0.192833	−	0.981232i	$-0.438233\pi$
$654$		0			0
$655$	−22.9513	−	5.43955i	−0.896781	−	0.212541i
$656$	−11.9054	+	4.33321i	−0.464828	+	0.169183i
$657$		0			0
$658$	34.0898	+	12.4077i	1.32896	+	0.483702i
$659$	−9.50779	−	6.25337i	−0.370371	−	0.243597i	0.350655	−	0.936505i	$-0.385959\pi$
$659$	−9.50779	−	6.25337i	−0.370371	−	0.243597i	−0.721026	+	0.692908i	$0.756329\pi$
$660$		0			0
$661$	−2.62498	−	0.306816i	−0.102100	−	0.0119337i	0.0648896	−	0.997892i	$-0.479330\pi$
$661$	−2.62498	−	0.306816i	−0.102100	−	0.0119337i	−0.166989	+	0.985959i	$0.553405\pi$
$662$	−26.9382	+	36.1843i	−1.04698	+	1.40634i
$663$		0			0
$664$	0.0427098	−	0.733298i	0.00165746	−	0.0284575i
$665$	−36.6662	+	30.7666i	−1.42185	+	1.19308i
$666$		0			0
$667$	−1.22771	−	1.03017i	−0.0475370	−	0.0398883i
$668$	7.70849	−	8.17052i	0.298250	−	0.316127i
$669$		0			0
$670$	−61.8949	+	40.7089i	−2.39121	+	1.57272i
$671$	−22.4902	+	5.33027i	−0.868224	+	0.205773i
$672$		0			0
$673$	2.32816	−	0.272123i	0.0897442	−	0.0104896i	−0.0711023	−	0.997469i	$-0.522652\pi$
$673$	2.32816	−	0.272123i	0.0897442	−	0.0104896i	0.160846	+	0.986979i	$0.448578\pi$
$674$	−4.06301	+	7.03734i	−0.156501	+	0.271068i
$675$		0			0
$676$	18.3113	+	31.7161i	0.704281	+	1.21985i
$677$	5.57808	+	7.49266i	0.214383	+	0.287966i	0.896286	−	0.443476i	$-0.146255\pi$
$677$	5.57808	+	7.49266i	0.214383	+	0.287966i	−0.681903	+	0.731442i	$0.738847\pi$
$678$		0			0
$679$	5.97590	−	19.9609i	0.229334	−	0.766029i
$680$	7.98403	+	4.00973i	0.306174	+	0.153766i
$681$		0			0
$682$	3.76392	+	12.5724i	0.144128	+	0.481420i
$683$	−5.08900	+	28.8612i	−0.194725	+	1.10434i	0.718084	+	0.695956i	$0.245019\pi$
$683$	−5.08900	+	28.8612i	−0.194725	+	1.10434i	−0.912809	+	0.408386i	$0.866092\pi$
$684$		0			0
$685$	5.27883	+	29.9377i	0.201694	+	1.14386i
$686$	30.9002	−	15.5187i	1.17977	−	0.592505i
$687$		0			0
$688$	3.89184	+	9.02229i	0.148375	+	0.343972i
$689$	−1.06598	−	2.47122i	−0.0406106	−	0.0941460i
$690$		0			0
$691$	−12.1669	+	6.11043i	−0.462849	+	0.232452i	−0.664913	−	0.746921i	$-0.731531\pi$
$691$	−12.1669	+	6.11043i	−0.462849	+	0.232452i	0.202064	+	0.979372i	$0.435235\pi$
$692$	4.27050	+	24.2192i	0.162340	+	0.920677i
$693$		0			0
$694$	−11.2522	+	63.8142i	−0.427126	+	2.42235i
$695$	−14.7450	−	49.2518i	−0.559310	−	1.86823i
$696$		0			0
$697$	−13.2773	−	6.66813i	−0.502915	−	0.252573i
$698$	10.7926	−	36.0500i	0.408508	−	1.36451i
$699$		0			0
$700$	19.0726	+	25.6189i	0.720876	+	0.968304i
$701$	20.8102	+	36.0443i	0.785989	+	1.36137i	0.928407	+	0.371566i	$0.121179\pi$
$701$	20.8102	+	36.0443i	0.785989	+	1.36137i	−0.142418	+	0.989807i	$0.545488\pi$
$702$		0			0
$703$	10.1821	−	17.6358i	0.384024	−	0.665149i
$704$	−68.1127	+	7.96124i	−2.56709	+	0.300050i
$705$		0			0
$706$	49.1949	−	11.6594i	1.85147	−	0.438808i
$707$	−26.2052	+	17.2354i	−0.985548	+	0.648205i
$708$		0			0
$709$	7.92161	−	8.39642i	0.297502	−	0.315334i	−0.561329	−	0.827593i	$-0.689710\pi$
$709$	7.92161	−	8.39642i	0.297502	−	0.315334i	0.858831	+	0.512259i	$0.171191\pi$
$710$	67.4598	+	56.6055i	2.53172	+	2.12437i
$711$		0			0
$712$	9.09403	−	7.63080i	0.340813	−	0.285976i
$713$	−0.0291675	+	0.500787i	−0.00109233	+	0.0187546i
$714$		0			0
$715$	−6.86382	+	9.21971i	−0.256692	+	0.344798i
$716$	−16.0011	−	1.87026i	−0.597989	−	0.0698949i
$717$		0			0
$718$	−28.4382	−	18.7041i	−1.06130	−	0.698030i
$719$	29.9388	+	10.8968i	1.11653	+	0.406383i	0.833384	−	0.552695i	$-0.186401\pi$
$719$	29.9388	+	10.8968i	1.11653	+	0.406383i	0.283143	+	0.959078i	$0.408623\pi$
$720$		0			0
$721$	49.4976	−	18.0157i	1.84339	−	0.670939i
$722$	−24.2757	−	5.75344i	−0.903446	−	0.214121i
$723$		0			0
$724$	−3.74734	−	64.3393i	−0.139269	−	2.39115i
$725$	−8.96783	−	9.50535i	−0.333057	−	0.353020i
$726$		0			0
$727$	−11.9587	+	27.7234i	−0.443524	+	1.02821i	0.539040	+	0.842280i	$0.318787\pi$
$727$	−11.9587	+	27.7234i	−0.443524	+	1.02821i	−0.982564	+	0.185925i	$0.940472\pi$
$728$	4.53691			0.168149
$729$		0			0
$730$	−25.9836			−0.961698
$731$	−4.56403	+	10.5806i	−0.168807	+	0.391338i
$732$		0			0
$733$	10.9774	+	11.6353i	0.405458	+	0.429760i	0.897638	−	0.440733i	$-0.145281\pi$
$733$	10.9774	+	11.6353i	0.405458	+	0.429760i	−0.492180	+	0.870493i	$0.663800\pi$
$734$	1.81392	+	31.1437i	0.0669529	+	1.14954i
$735$		0			0
$736$	−3.03969	−	0.720421i	−0.112045	−	0.0265551i
$737$	56.4379	−	20.5417i	2.07892	−	0.756664i
$738$		0			0
$739$	13.9238	+	5.06784i	0.512194	+	0.186423i	0.585171	−	0.810910i	$-0.301028\pi$
$739$	13.9238	+	5.06784i	0.512194	+	0.186423i	−0.0729763	+	0.997334i	$0.523250\pi$
$740$	−26.7941	−	17.6227i	−0.984969	−	0.647824i
$741$		0			0
$742$	23.8823	+	2.79144i	0.876748	+	0.102477i
$743$	−0.620612	+	0.833627i	−0.0227681	+	0.0305828i	−0.813361	−	0.581759i	$-0.802365\pi$
$743$	−0.620612	+	0.833627i	−0.0227681	+	0.0305828i	0.790593	+	0.612341i	$0.209772\pi$
$744$		0			0
$745$	−1.42396	+	24.4485i	−0.0521699	+	0.895723i
$746$	46.3874	−	38.9236i	1.69836	−	1.42510i
$747$		0			0
$748$	−17.3624	−	14.5688i	−0.634832	−	0.532688i
$749$	0.101070	−	0.107127i	0.00369300	−	0.00391435i
$750$		0			0
$751$	27.5815	−	18.1407i	1.00647	−	0.661962i	0.0645851	−	0.997912i	$-0.479428\pi$
$751$	27.5815	−	18.1407i	1.00647	−	0.661962i	0.941880	+	0.335950i	$0.109057\pi$
$752$	−6.65757	+	1.57787i	−0.242777	+	0.0575391i
$753$		0			0
$754$	−5.76935	+	0.674340i	−0.210107	+	0.0245580i
$755$	−25.9217	+	44.8978i	−0.943389	+	1.63400i
$756$		0			0
$757$	16.5939	+	28.7414i	0.603114	+	1.04462i	0.992346	+	0.123485i	$0.0394070\pi$
$757$	16.5939	+	28.7414i	0.603114	+	1.04462i	−0.389232	+	0.921140i	$0.627260\pi$
$758$	−11.4097	−	15.3259i	−0.414419	−	0.556661i
$759$		0			0
$760$	−9.69621	+	32.3876i	−0.351718	+	1.17482i
$761$	33.3883	+	16.7682i	1.21032	+	0.607847i	0.935391	−	0.353616i	$-0.115048\pi$
$761$	33.3883	+	16.7682i	1.21032	+	0.607847i	0.274933	+	0.961463i	$0.411344\pi$
$762$		0			0
$763$	0.343352	+	1.14688i	0.0124302	+	0.0415197i
$764$	−6.50388	+	36.8853i	−0.235302	+	1.33446i
$765$		0			0
$766$	7.44398	+	42.2169i	0.268962	+	1.52536i
$767$	−4.70826	+	2.36457i	−0.170005	+	0.0853798i
$768$		0			0
$769$	−16.9380	−	39.2666i	−0.610798	−	1.41599i	−0.890091	−	0.455784i	$-0.849359\pi$
$769$	−16.9380	−	39.2666i	−0.610798	−	1.41599i	0.279292	−	0.960206i	$-0.409900\pi$
$770$	−40.6739	−	94.2927i	−1.46578	−	3.39807i
$771$		0			0
$772$	53.4081	−	26.8226i	1.92220	−	0.965366i
$773$	−4.28338	−	24.2923i	−0.154062	−	0.873732i	−0.959638	−	0.281239i	$-0.909255\pi$
$773$	−4.28338	−	24.2923i	−0.154062	−	0.873732i	0.805575	−	0.592493i	$-0.201856\pi$
$774$		0			0
$775$	−0.710278	+	4.02818i	−0.0255139	+	0.144697i
$776$	−4.22094	−	14.0989i	−0.151523	−	0.506122i
$777$		0			0
$778$	61.8505	+	31.0625i	2.21745	+	1.11364i
$779$	16.1247	−	53.8601i	0.577726	−	1.92974i
$780$		0			0
$781$	−42.6335	−	57.2668i	−1.52555	−	2.04917i
$782$	−0.727908	−	1.26077i	−0.0260299	−	0.0450851i
$783$		0			0
$784$	1.07543	−	1.86269i	0.0384081	−	0.0665248i
$785$	−6.30422	+	0.736858i	−0.225007	+	0.0262996i
$786$		0			0
$787$	33.2228	−	7.87395i	1.18426	−	0.280676i	0.409132	−	0.912475i	$-0.365831\pi$
$787$	33.2228	−	7.87395i	1.18426	−	0.280676i	0.775132	+	0.631799i	$0.217683\pi$
$788$	9.85695	−	6.48302i	0.351139	−	0.230948i
$789$		0			0
$790$	−12.7703	+	13.5358i	−0.454348	+	0.481581i
$791$	−25.7569	−	21.6126i	−0.915809	−	0.768455i
$792$		0			0
$793$	−2.45290	+	2.05822i	−0.0871049	+	0.0730897i
$794$	1.37798	−	23.6591i	0.0489028	−	0.839629i
$795$		0			0
$796$	6.75031	−	9.06724i	0.239259	−	0.321380i
$797$	16.8253	+	1.96660i	0.595983	+	0.0696604i	0.408736	−	0.912652i	$-0.365970\pi$
$797$	16.8253	+	1.96660i	0.595983	+	0.0696604i	0.187247	+	0.982313i	$0.440044\pi$
$798$		0			0
$799$	−6.70374	−	4.40912i	−0.237161	−	0.155983i
$800$	−23.9360	−	8.71201i	−0.846267	−	0.308016i
$801$		0			0
$802$	−16.9179	+	6.15760i	−0.597390	+	0.217432i
$803$	20.4976	+	4.85802i	0.723345	+	0.171436i
$804$		0			0
$805$	−0.228232	−	3.91859i	−0.00804412	−	0.138112i
$806$	1.24766	+	1.32245i	0.0439471	+	0.0465812i
$807$		0			0
$808$	−8.77478	+	20.3422i	−0.308696	+	0.715637i
$809$	−18.5465			−0.652062			−0.326031	−	0.945359i	$-0.605711\pi$
$809$	−18.5465			−0.652062			−0.326031	+	0.945359i	$0.605711\pi$
$810$		0			0
$811$	24.9560			0.876325			0.438163	−	0.898896i	$-0.355629\pi$
$811$	24.9560			0.876325			0.438163	+	0.898896i	$0.355629\pi$
$812$	12.2319	−	28.3568i	0.429256	−	0.995127i
$813$		0			0
$814$	29.9822	+	31.7793i	1.05088	+	1.11386i
$815$	1.62293	+	27.8647i	0.0568488	+	0.976057i
$816$		0			0
$817$	−42.4281	−	10.0556i	−1.48437	−	0.351802i
$818$	−78.2784	+	28.4910i	−2.73694	+	0.996164i
$819$		0			0
$820$	−83.2004	−	30.2825i	−2.90548	−	1.05751i
$821$	−1.12880	−	0.742425i	−0.0393955	−	0.0259108i	0.529658	−	0.848211i	$-0.322320\pi$
$821$	−1.12880	−	0.742425i	−0.0393955	−	0.0259108i	−0.569054	+	0.822300i	$0.692690\pi$
$822$		0			0
$823$	−43.5920	−	5.09517i	−1.51952	−	0.177606i	−0.684983	−	0.728559i	$-0.740190\pi$
$823$	−43.5920	−	5.09517i	−1.51952	−	0.177606i	−0.834537	+	0.550952i	$0.814265\pi$
$824$	22.2175	−	29.8432i	0.773982	−	1.03964i
$825$		0			0
$826$	2.73696	−	46.9918i	0.0952311	−	1.63505i
$827$	43.1798	−	36.2322i	1.50151	−	1.25992i	0.622970	−	0.782246i	$-0.285926\pi$
$827$	43.1798	−	36.2322i	1.50151	−	1.25992i	0.878539	−	0.477670i	$-0.158519\pi$
$828$		0			0
$829$	11.2414	+	9.43268i	0.390431	+	0.327610i	0.816781	−	0.576948i	$-0.195756\pi$
$829$	11.2414	+	9.43268i	0.390431	+	0.327610i	−0.426350	+	0.904558i	$0.640201\pi$
$830$	−1.58063	+	1.67537i	−0.0548645	+	0.0581530i
$831$		0			0
$832$	−7.93743	+	5.22053i	−0.275181	+	0.180989i
$833$	2.45436	−	0.581693i	0.0850384	−	0.0201545i
$834$		0			0
$835$	−11.1805	+	1.30681i	−0.386917	+	0.0452241i
$836$	42.8825	−	74.2747i	1.48312	−	2.56885i
$837$		0			0
$838$	−14.3302	−	24.8206i	−0.495028	−	0.857414i
$839$	0.566230	+	0.760578i	0.0195484	+	0.0262581i	0.811790	−	0.583950i	$-0.198493\pi$
$839$	0.566230	+	0.760578i	0.0195484	+	0.0262581i	−0.792242	+	0.610208i	$0.791086\pi$
$840$		0			0
$841$	4.69331	−	15.6767i	0.161838	−	0.540577i
$842$	−45.9436	−	23.0737i	−1.58332	−	0.795174i
$843$		0			0
$844$	−6.00911	−	20.0718i	−0.206842	−	0.690901i
$845$	6.37286	−	36.1423i	0.219233	−	1.24333i
$846$		0			0
$847$	8.81110	+	49.9702i	0.302753	+	1.71700i
$848$	−4.05253	+	2.03526i	−0.139164	+	0.0698910i
$849$		0			0
$850$	−4.70174	−	10.8999i	−0.161268	−	0.373862i
$851$	0.661457	+	1.53343i	0.0226745	+	0.0525653i
$852$		0			0
$853$	2.85592	−	1.43430i	0.0977849	−	0.0491094i	−0.399234	−	0.916849i	$-0.630724\pi$
$853$	2.85592	−	1.43430i	0.0977849	−	0.0491094i	0.497019	+	0.867739i	$0.334428\pi$
$854$	−4.96766	−	28.1730i	−0.169990	−	0.964060i
$855$		0			0
$856$	0.0180642	−	0.102447i	0.000617423	−	0.00350158i
$857$	8.51405	+	28.4389i	0.290835	+	0.971455i	0.971137	+	0.238523i	$0.0766633\pi$
$857$	8.51405	+	28.4389i	0.290835	+	0.971455i	−0.680302	+	0.732932i	$0.738151\pi$
$858$		0			0
$859$	−12.3635	−	6.20916i	−0.421836	−	0.211854i	0.225202	−	0.974312i	$-0.427696\pi$
$859$	−12.3635	−	6.20916i	−0.421836	−	0.211854i	−0.647037	+	0.762458i	$0.723992\pi$
$860$	−19.6941	+	65.7830i	−0.671565	+	2.24318i
$861$		0			0
$862$	30.1264	+	40.4668i	1.02611	+	1.37830i
$863$	−28.9772	−	50.1899i	−0.986394	−	1.70849i	−0.635568	−	0.772045i	$-0.719234\pi$
$863$	−28.9772	−	50.1899i	−0.986394	−	1.70849i	−0.350826	−	0.936440i	$-0.614099\pi$
$864$		0			0
$865$	12.3224	−	21.3429i	0.418973	−	0.725682i
$866$	−40.1997	+	4.69867i	−1.36604	+	0.159667i
$867$		0			0
$868$	−9.40572	+	2.22920i	−0.319251	+	0.0756639i
$869$	12.6048	−	8.29030i	0.427588	−	0.281229i
$870$		0			0
$871$	5.70988	−	6.05212i	0.193472	−	0.205068i
$872$	0.647763	+	0.543538i	0.0219360	+	0.0184065i
$873$		0			0
$874$	4.22002	−	3.54102i	0.142744	−	0.119777i
$875$	−0.670087	+	11.5049i	−0.0226531	+	0.388938i
$876$		0			0
$877$	8.10205	−	10.8829i	0.273587	−	0.367491i	−0.644001	−	0.765025i	$-0.722727\pi$
$877$	8.10205	−	10.8829i	0.273587	−	0.367491i	0.917587	+	0.397534i	$0.130134\pi$
$878$	60.6963	+	7.09438i	2.04840	+	0.239424i
$879$		0			0
$880$	16.1814	+	10.6427i	0.545476	+	0.358765i
$881$	−2.92937	−	1.06621i	−0.0986931	−	0.0359214i	0.292202	−	0.956357i	$-0.405612\pi$
$881$	−2.92937	−	1.06621i	−0.0986931	−	0.0359214i	−0.390895	+	0.920435i	$0.627834\pi$
$882$		0			0
$883$	5.52287	−	2.01016i	0.185859	−	0.0676472i	−0.247414	−	0.968910i	$-0.579581\pi$
$883$	5.52287	−	2.01016i	0.185859	−	0.0676472i	0.433273	+	0.901263i	$0.357359\pi$
$884$	−3.05530	−	0.724119i	−0.102761	−	0.0243548i
$885$		0			0
$886$	1.58454	+	27.2055i	0.0532336	+	0.913986i
$887$	3.21262	+	3.40517i	0.107869	+	0.114335i	0.779058	−	0.626952i	$-0.215698\pi$
$887$	3.21262	+	3.40517i	0.107869	+	0.114335i	−0.671189	+	0.741286i	$0.734216\pi$
$888$		0			0
$889$	15.2722	−	35.4049i	0.512213	−	1.18744i
$890$	−37.2255			−1.24780
$891$		0			0
$892$	43.6472			1.46142
$893$	12.0258	−	27.8790i	0.402428	−	0.932934i
$894$		0			0
$895$	11.0787	+	11.7427i	0.370320	+	0.392516i
$896$	−2.55369	−	43.8452i	−0.0853129	−	1.46477i
$897$		0			0
$898$	15.0073	+	3.55679i	0.500799	+	0.118692i
$899$	3.71651	−	1.35270i	0.123953	−	0.0451151i
$900$		0			0
$901$	−4.99743	−	1.81892i	−0.166489	−	0.0605969i
$902$	100.779	+	66.2831i	3.35556	+	2.20699i
$903$		0			0
$904$	−23.5884	−	2.75709i	−0.784539	−	0.0916994i
$905$	−38.5670	+	51.8045i	−1.28201	+	1.72204i
$906$		0			0
$907$	−0.0542661	+	0.931713i	−0.00180188	+	0.0309370i	−0.999089	−	0.0426693i	$-0.986414\pi$
$907$	−0.0542661	+	0.931713i	−0.00180188	+	0.0309370i	0.997287	+	0.0736064i	$0.0234508\pi$
$908$	−30.2994	+	25.4243i	−1.00552	+	0.843734i
$909$		0			0
$910$	−10.8981	−	9.14461i	−0.361269	−	0.303141i
$911$	31.1840	−	33.0531i	1.03317	−	1.09510i	0.0377732	−	0.999286i	$-0.487974\pi$
$911$	31.1840	−	33.0531i	1.03317	−	1.09510i	0.995399	−	0.0958126i	$-0.0305450\pi$
$912$		0			0
$913$	1.56014	−	1.02612i	0.0516331	−	0.0339597i
$914$	−64.5844	+	15.3068i	−2.13626	+	0.506304i
$915$		0			0
$916$	9.51578	−	1.11223i	0.314410	−	0.0367493i
$917$	−11.8341	+	20.4973i	−0.390797	+	0.676880i
$918$		0			0
$919$	−20.1320	−	34.8697i	−0.664095	−	1.15025i	−0.979530	−	0.201299i	$-0.935484\pi$
$919$	−20.1320	−	34.8697i	−0.664095	−	1.15025i	0.315435	−	0.948947i	$-0.397849\pi$
$920$	−1.65562	−	2.22388i	−0.0545842	−	0.0733193i
$921$		0			0
$922$	0.522959	−	1.74681i	0.0172228	−	0.0575280i
$923$	−8.83864	−	4.43893i	−0.290927	−	0.146109i
$924$		0			0
$925$	3.90547	+	13.0452i	0.128411	+	0.428922i
$926$	11.0450	−	62.6392i	0.362960	−	2.05845i
$927$		0			0
$928$	4.27690	+	24.2555i	0.140396	+	0.796225i
$929$	11.7038	−	5.87788i	0.383990	−	0.192847i	−0.246323	−	0.969188i	$-0.579223\pi$
$929$	11.7038	−	5.87788i	0.383990	−	0.192847i	0.630314	+	0.776341i	$0.282926\pi$
$930$		0			0
$931$	3.78044	+	8.76404i	0.123899	+	0.287230i
$932$	−9.63164	−	22.3287i	−0.315495	−	0.731400i
$933$		0			0
$934$	−24.8117	+	12.4609i	−0.811864	+	0.407734i
$935$	3.94404	+	22.3677i	0.128984	+	0.731504i
$936$		0			0
$937$	−5.42867	+	30.7875i	−0.177347	+	1.00578i	0.758053	+	0.652193i	$0.226151\pi$
$937$	−5.42867	+	30.7875i	−0.177347	+	1.00578i	−0.935400	+	0.353591i	$0.884960\pi$
$938$	21.3202	+	71.2143i	0.696128	+	2.32523i
$939$		0			0
$940$	−42.7290	−	21.4593i	−1.39367	−	0.699926i
$941$	−13.4797	+	45.0255i	−0.439427	+	1.46779i	0.396033	+	0.918236i	$0.370387\pi$
$941$	−13.4797	+	45.0255i	−0.439427	+	1.46779i	−0.835460	+	0.549552i	$0.814798\pi$
$942$		0			0
$943$	2.75328	+	3.69829i	0.0896590	+	0.120433i
$944$	4.43886	+	7.68833i	0.144473	+	0.250234i
$945$		0			0
$946$	46.7748	−	81.0163i	1.52078	−	2.63407i
$947$	−30.4706	+	3.56151i	−0.990163	+	0.115733i	−0.595724	−	0.803189i	$-0.703135\pi$
$947$	−30.4706	+	3.56151i	−0.990163	+	0.115733i	−0.394438	+	0.918922i	$0.629061\pi$
$948$		0			0
$949$	2.83967	−	0.673015i	0.0921796	−	0.0218470i
$950$	37.5293	−	24.6834i	1.21761	−	0.800836i
$951$		0			0
$952$	6.15222	−	6.52097i	0.199395	−	0.211346i
$953$	5.18464	+	4.35043i	0.167947	+	0.140924i	0.722887	−	0.690966i	$-0.242815\pi$
$953$	5.18464	+	4.35043i	0.167947	+	0.140924i	−0.554940	+	0.831890i	$0.687259\pi$
$954$		0			0
$955$	28.7522	−	24.1260i	0.930400	−	0.780698i
$956$	−2.23255	+	38.3313i	−0.0722057	+	1.23972i
$957$		0			0
$958$	−6.01989	+	8.08611i	−0.194494	+	0.261250i
$959$	30.2979	+	3.54132i	0.978370	+	0.114355i
$960$		0			0
$961$	24.8658	+	16.3545i	0.802124	+	0.527565i
$962$	5.68771	+	2.07016i	0.183379	+	0.0667446i
$963$		0			0
$964$	1.74773	−	0.636123i	0.0562907	−	0.0204881i
$965$	−58.2769	−	13.8119i	−1.87600	−	0.444620i
$966$		0			0
$967$	−1.12337	−	19.2875i	−0.0361251	−	0.620244i	−0.966980	−	0.254854i	$-0.917973\pi$
$967$	−1.12337	−	19.2875i	−0.0361251	−	0.620244i	0.930854	−	0.365390i	$-0.119064\pi$
$968$	24.5948	+	26.0689i	0.790506	+	0.837887i
$969$		0			0
$970$	−18.2787	+	42.3748i	−0.586894	+	1.36057i
$971$	−42.4827			−1.36333			−0.681667	−	0.731662i	$-0.738745\pi$
$971$	−42.4827			−1.36333			−0.681667	+	0.731662i	$0.738745\pi$
$972$		0			0
$973$	−51.5885			−1.65385
$974$	24.9018	−	57.7288i	0.797904	−	1.84975i
$975$		0			0
$976$	3.70257	+	3.92449i	0.118516	+	0.125620i
$977$	−2.20981	−	37.9410i	−0.0706982	−	1.21384i	−0.827982	−	0.560755i	$-0.810511\pi$
$977$	−2.20981	−	37.9410i	−0.0706982	−	1.21384i	0.757284	−	0.653086i	$-0.226526\pi$
$978$		0			0
$979$	29.3659	+	6.95984i	0.938538	+	0.222438i
$980$	14.1247	−	5.14095i	0.451196	−	0.164222i
$981$		0			0
$982$	−40.9002	−	14.8865i	−1.30518	−	0.475046i
$983$	4.62569	+	3.04237i	0.147537	+	0.0970365i	0.621131	−	0.783707i	$-0.286673\pi$
$983$	4.62569	+	3.04237i	0.147537	+	0.0970365i	−0.473594	+	0.880743i	$0.657044\pi$
$984$		0			0
$985$	−11.7428	−	1.37253i	−0.374156	−	0.0437326i
$986$	−6.85421	+	9.20681i	−0.218283	+	0.293204i
$987$		0			0
$988$	0.690854	−	11.8615i	0.0219790	−	0.377365i
$989$	2.73922	−	2.29848i	0.0871023	−	0.0730875i
$990$		0			0
$991$	16.9547	+	14.2267i	0.538583	+	0.451925i	0.871053	−	0.491189i	$-0.163438\pi$
$991$	16.9547	+	14.2267i	0.538583	+	0.451925i	−0.332470	+	0.943114i	$0.607882\pi$
$992$	5.29033	−	5.60743i	0.167968	−	0.178036i
$993$		0			0
$994$	73.8283	−	48.5577i	2.34169	−	1.54016i
$995$	−11.0225	+	2.61239i	−0.349438	+	0.0828184i
$996$		0			0
$997$	−20.3532	+	2.37894i	−0.644591	+	0.0753419i	−0.432107	−	0.901823i	$-0.642230\pi$
$997$	−20.3532	+	2.37894i	−0.644591	+	0.0753419i	−0.212484	+	0.977164i	$0.568155\pi$
$998$	−32.8916	+	56.9700i	−1.04117	+	1.80335i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.55.2		144
3.2	odd	2		729.2.g.b.55.7		144
9.2	odd	6		729.2.g.a.298.2		144
9.4	even	3		81.2.g.a.7.2	✓	144
9.5	odd	6		243.2.g.a.100.7		144
9.7	even	3		729.2.g.d.298.7		144
81.4	even	27		81.2.g.a.58.2	yes	144
81.23	odd	54		729.2.g.a.433.2		144
81.29	odd	54		6561.2.a.d.1.62		72
81.31	even	27	inner	729.2.g.c.676.2		144
81.50	odd	54		729.2.g.b.676.7		144
81.52	even	27		6561.2.a.c.1.11		72
81.58	even	27		729.2.g.d.433.7		144
81.77	odd	54		243.2.g.a.226.7		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.2	✓	144	9.4	even	3
81.2.g.a.58.2	yes	144	81.4	even	27
243.2.g.a.100.7		144	9.5	odd	6
243.2.g.a.226.7		144	81.77	odd	54
729.2.g.a.298.2		144	9.2	odd	6
729.2.g.a.433.2		144	81.23	odd	54
729.2.g.b.55.7		144	3.2	odd	2
729.2.g.b.676.7		144	81.50	odd	54
729.2.g.c.55.2		144	1.1	even	1	trivial
729.2.g.c.676.2		144	81.31	even	27	inner
729.2.g.d.298.7		144	9.7	even	3
729.2.g.d.433.7		144	81.58	even	27
6561.2.a.c.1.11		72	81.52	even	27
6561.2.a.d.1.62		72	81.29	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)

\(f(q)\)	\(=\)	\(q+(-0.880274 + 2.04070i) q^{2} +(-2.01711 - 2.13801i) q^{4} +(0.171269 + 2.94057i) q^{5} +(2.87602 + 0.681629i) q^{7} +(1.96178 - 0.714030i) q^{8} +O(q^{10})\)	\(q+(-0.880274 + 2.04070i) q^{2} +(-2.01711 - 2.13801i) q^{4} +(0.171269 + 2.94057i) q^{5} +(2.87602 + 0.681629i) q^{7} +(1.96178 - 0.714030i) q^{8} +(-6.15160 - 2.23900i) q^{10} +(4.43417 + 2.91640i) q^{11} +(0.730282 + 0.0853577i) q^{13} +(-3.92268 + 5.26908i) q^{14} +(0.0720359 - 1.23681i) q^{16} +(1.11298 - 0.933897i) q^{17} +(4.21153 + 3.53390i) q^{19} +(5.94150 - 6.29762i) q^{20} +(-9.85479 + 6.48160i) q^{22} +(-0.438705 + 0.103975i) q^{23} +(-3.65143 + 0.426791i) q^{25} +(-0.817038 + 1.41515i) q^{26} +(-4.34391 - 7.52387i) q^{28} +(2.12271 + 2.85130i) q^{29} +(0.319104 - 1.06588i) q^{31} +(6.19179 + 3.10963i) q^{32} +(0.926085 + 3.09334i) q^{34} +(-1.51181 + 8.57387i) q^{35} +(-0.643205 - 3.64780i) q^{37} +(-10.9189 + 5.48370i) q^{38} +(2.43565 + 5.64646i) q^{40} +(-4.05045 - 9.39000i) q^{41} +(-7.08750 + 3.55948i) q^{43} +(-2.70891 - 15.3630i) q^{44} +(0.173998 - 0.986793i) q^{46} +(-1.58391 - 5.29061i) q^{47} +(1.55143 + 0.779157i) q^{49} +(2.34330 - 7.82718i) q^{50} +(-1.29056 - 1.73353i) q^{52} +(-1.83020 - 3.17001i) q^{53} +(-7.81644 + 13.5385i) q^{55} +(6.12882 - 0.716356i) q^{56} +(-7.68722 + 1.82190i) q^{58} +(-5.98693 + 3.93766i) q^{59} +(-2.98858 + 3.16771i) q^{61} +(1.89425 + 1.58947i) q^{62} +(-9.89820 + 8.30558i) q^{64} +(-0.125926 + 2.16206i) q^{65} +(6.75776 - 9.07724i) q^{67} +(-4.24167 - 0.495780i) q^{68} +(-16.1659 - 10.6325i) q^{70} +(-12.6408 - 4.60088i) q^{71} +(3.72979 - 1.35753i) q^{73} +(8.01028 + 1.89847i) q^{74} +(-0.939614 - 16.1325i) q^{76} +(10.7649 + 11.4101i) q^{77} +(1.12592 - 2.61017i) q^{79} +3.64926 q^{80} +22.7277 q^{82} +(0.139359 - 0.323070i) q^{83} +(2.93681 + 3.11283i) q^{85} +(-1.02490 - 17.5968i) q^{86} +(10.7813 + 2.55521i) q^{88} +(5.34347 - 1.94487i) q^{89} +(2.04212 + 0.743272i) q^{91} +(1.10721 + 0.728226i) q^{92} +(12.1908 + 1.42491i) q^{94} +(-9.67036 + 12.9896i) q^{95} +(0.409894 - 7.03762i) q^{97} +(-2.95571 + 2.48014i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) 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 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

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