LMFDB - Embedded newform 729.2.g.b.55.7

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			55.7
Character	$\chi$	$=$	729.55
Dual form			729.2.g.b.676.7

$q$-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	$-0.582642\pi$
$2$	0.880274	−	2.04070i	0.622448	−	1.44300i	0.879169	−	0.476510i	$-0.158098\pi$
$3$		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	$-0.789648\pi$
$5$	−0.171269	−	2.94057i	−0.0765937	−	1.31506i	0.712883	−	0.701283i	$-0.247389\pi$
$6$		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	−0.338847	−	0.940842i	$-0.610037\pi$
$11$	−4.43417	−	2.91640i	−1.33695	−	0.879328i	−0.998106	+	0.0615139i	$0.980407\pi$
$12$		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	−0.767700	−	0.640809i	$-0.778599\pi$
$17$	−1.11298	+	0.933897i	−0.269936	+	0.226503i	0.497764	+	0.867312i	$0.334155\pi$
$18$		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	−0.184623	−	0.982809i	$-0.559106\pi$
$23$	0.438705	−	0.103975i	0.0914763	−	0.0216803i	0.276099	+	0.961129i	$0.410958\pi$
$24$		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	0.560088	−	0.828433i	$-0.310767\pi$
$29$	−2.12271	−	2.85130i	−0.394178	−	0.529472i	−0.954265	+	0.298961i	$0.903360\pi$
$30$		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	$0.164766\pi$
$41$	4.05045	+	9.39000i	0.632574	+	1.46647i	−0.236421	+	0.971651i	$0.575975\pi$
$42$		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	$0.0393630\pi$
$47$	1.58391	+	5.29061i	0.231036	+	0.771715i	−0.761327	+	0.648368i	$0.775452\pi$
$48$		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	0.963911	−	0.266225i	$-0.0857764\pi$
$53$	1.83020	+	3.17001i	0.251398	+	0.435434i	−0.712513	+	0.701659i	$0.752443\pi$
$54$		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	−0.0963503	−	0.995347i	$-0.530717\pi$
$59$	5.98693	−	3.93766i	0.779431	−	0.512640i	0.875782	+	0.482707i	$0.160347\pi$
$60$		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	0.956109	−	0.293010i	$-0.0946568\pi$
$71$	12.6408	+	4.60088i	1.50019	+	0.546024i	0.544079	+	0.839034i	$0.316879\pi$
$72$		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	−0.925693	−	0.378275i	$-0.876517\pi$
$83$	−0.139359	+	0.323070i	−0.0152966	+	0.0354615i	0.910397	+	0.413737i	$0.135777\pi$
$84$		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	−0.609321	−	0.792923i	$-0.708558\pi$
$89$	−5.34347	+	1.94487i	−0.566407	+	0.206155i	0.0429141	+	0.999079i	$0.486336\pi$
$90$		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	−0.255432	−	0.966827i	$-0.582218\pi$
$101$	7.28225	−	7.71874i	0.724611	−	0.768043i	0.980043	+	0.198784i	$0.0636992\pi$
$102$		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	−0.867227	−	0.497913i	$-0.834100\pi$
$107$	−0.0249146	+	0.0431534i	−0.00240859	+	0.00417180i	0.864819	+	0.502084i	$0.167433\pi$
$108$		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	0.857305	−	0.514808i	$-0.172137\pi$
$113$	10.1658	+	5.10543i	0.956313	+	0.480279i	0.0990079	+	0.995087i	$0.468433\pi$
$114$		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	$-0.793651\pi$
$131$	2.29663	−	7.67128i	0.200658	−	0.670243i	0.997790	−	0.0664391i	$-0.0211638\pi$
$132$		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	−0.542090	−	0.840320i	$-0.682367\pi$
$137$	−10.2507	+	1.19814i	−0.875777	+	0.102364i	−0.333687	+	0.942684i	$0.608293\pi$
$138$		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	−0.229107	−	0.973401i	$-0.573581\pi$
$149$	−8.25798	−	0.965219i	−0.676520	−	0.0790739i	−0.447413	+	0.894327i	$0.647655\pi$
$150$		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	$-0.971280\pi$
$167$	−0.222204	−	3.81509i	−0.0171946	−	0.295221i	0.978738	−	0.205116i	$-0.0657572\pi$
$168$		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	0.786706	−	0.617328i	$-0.211785\pi$
$173$	6.99032	+	4.59760i	0.531464	+	0.349549i	−0.255242	+	0.966877i	$0.582155\pi$
$174$		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	−0.786066	−	0.618142i	$-0.787886\pi$
$179$	−4.19854	+	3.52299i	−0.313814	+	0.263321i	0.472252	+	0.881463i	$0.343441\pi$
$180$		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	0.987095	−	0.160136i	$-0.0511934\pi$
$191$	7.60922	+	10.2210i	0.550584	+	0.739562i	−0.436511	+	0.899699i	$0.643786\pi$
$192$		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	−0.949860	−	0.312676i	$-0.898775\pi$
$197$	0.696981	−	3.95277i	0.0496578	−	0.281623i	0.999518	+	0.0310522i	$0.00988582\pi$
$198$		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	$0.165872\pi$
$227$	−0.782420	+	13.4336i	−0.0519310	+	0.891621i	−0.919202	+	0.393786i	$0.871165\pi$
$228$		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	0.0745722	−	0.997216i	$-0.476241\pi$
$233$	−7.77413	−	2.82955i	−0.509300	−	0.185370i	−0.583872	+	0.811846i	$0.698463\pi$
$234$		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	0.949195	−	0.314687i	$-0.101900\pi$
$239$	8.96426	+	9.50156i	0.579850	+	0.614605i	−0.369346	+	0.929292i	$0.620418\pi$
$240$		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	−0.717935	−	0.696110i	$-0.754912\pi$
$251$	−12.9984	+	4.73104i	−0.820454	+	0.298621i	−0.102519	+	0.994731i	$0.532690\pi$
$252$		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	$0.508251\pi$
$257$	−15.6489	+	21.0202i	−0.976153	+	1.31120i	−0.950234	+	0.311537i	$0.899156\pi$
$258$		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	−0.696576	−	0.717483i	$-0.745294\pi$
$263$	0.976219	−	1.03473i	0.0601963	−	0.0638043i	0.756772	+	0.653679i	$0.226775\pi$
$264$		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	−0.770592	−	0.637328i	$-0.780039\pi$
$269$	2.73320	−	4.73405i	0.166646	−	0.288640i	0.937239	+	0.348688i	$0.113373\pi$
$270$		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	−0.863355	−	0.504597i	$-0.831641\pi$
$281$	−16.3300	+	8.20123i	−0.974166	+	0.489244i	−0.110811	+	0.993842i	$0.535345\pi$
$282$		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	−0.988597	−	0.150583i	$-0.951885\pi$
$293$	−1.36749	+	4.56773i	−0.0798895	+	0.266849i	0.908708	+	0.417433i	$0.137070\pi$
$294$		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	0.384268	−	0.923221i	$-0.374454\pi$
$311$	9.61593	+	1.12394i	0.545269	+	0.0637328i	0.161001	+	0.986954i	$0.448528\pi$
$312$		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	0.751272	−	0.659993i	$-0.229441\pi$
$317$	20.0555	+	4.75324i	1.12643	+	0.266969i	0.375157	+	0.926961i	$0.377589\pi$
$318$		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	−0.905064	−	0.425275i	$-0.860177\pi$
$347$	−28.3703	+	6.72388i	−1.52300	+	0.360957i	−0.617932	+	0.786232i	$0.712029\pi$
$348$		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	$0.00327892\pi$
$353$	13.5844	+	18.2471i	0.723027	+	0.971194i	−0.276920	+	0.960893i	$0.589314\pi$
$354$		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	$-0.812010\pi$
$359$	2.65948	−	15.0826i	0.140362	−	0.796032i	0.970975	−	0.239182i	$-0.0768791\pi$
$360$		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	−0.889879	−	0.456196i	$-0.849212\pi$
$383$	−16.1154	+	10.5992i	−0.823456	+	0.541596i	0.0664232	+	0.997792i	$0.478841\pi$
$384$		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	$0.308171\pi$
$389$	−1.81076	+	31.0895i	−0.0918091	+	1.57630i	−0.658635	+	0.752463i	$0.728866\pi$
$390$		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	0.573536	−	0.819180i	$-0.305571\pi$
$401$	−5.55906	−	5.89226i	−0.277606	−	0.294246i	−0.851142	+	0.524935i	$0.824090\pi$
$402$		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	−0.573184	−	0.819427i	$-0.694292\pi$
$419$	7.70081	−	10.3440i	0.376209	−	0.505337i	0.949393	+	0.314090i	$0.101699\pi$
$420$		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	$0.350785\pi$
$431$	−11.3499	+	19.6586i	−0.546706	+	0.946923i	−0.998497	+	0.0547992i	$0.982548\pi$
$432$		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	−0.689643	−	0.724150i	$-0.742232\pi$
$443$	−10.9576	+	5.50312i	−0.520612	+	0.261461i	0.169031	+	0.985611i	$0.445936\pi$
$444$		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	0.999950	−	0.0100422i	$-0.00319658\pi$
$449$	1.20505	+	6.83416i	0.0568697	+	0.322524i	−0.943080	+	0.332566i	$0.892085\pi$
$450$		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	−0.0970950	−	0.995275i	$-0.530955\pi$
$461$	0.814896	−	0.0952477i	0.0379535	−	0.00443613i	0.135048	+	0.990839i	$0.456881\pi$
$462$		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	0.393924	−	0.919143i	$-0.371117\pi$
$467$	−9.57011	−	8.03027i	−0.442852	−	0.371597i	−0.836775	+	0.547546i	$0.815562\pi$
$468$		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	0.128542	−	0.991704i	$-0.458970\pi$
$479$	−4.41364	−	1.04605i	−0.201664	−	0.0477953i	−0.330206	+	0.943909i	$0.607118\pi$
$480$		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	$-0.872820\pi$
$491$	−1.13872	−	19.5510i	−0.0513896	−	0.882325i	0.869847	−	0.493322i	$-0.164218\pi$
$492$		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	−0.138501	−	0.990362i	$-0.544228\pi$
$503$	18.2284	−	15.2955i	0.812765	−	0.681991i	0.951266	+	0.308371i	$0.0997839\pi$
$504$		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	0.0465808	−	0.998915i	$-0.485167\pi$
$509$	12.1044	−	2.86880i	0.536519	−	0.127157i	0.489938	+	0.871757i	$0.337019\pi$
$510$		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	$-0.654471\pi$
$521$	6.26330	−	35.5209i	0.274400	−	1.55620i	0.740861	−	0.671659i	$-0.234418\pi$
$522$		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	−0.424599	−	0.905382i	$-0.639585\pi$
$557$	−31.4323	−	11.4404i	−1.33183	−	0.484746i	−0.907230	+	0.420636i	$0.861807\pi$
$558$		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	0.730402	−	0.683017i	$-0.239333\pi$
$563$	0.144057	+	0.152692i	0.00607128	+	0.00643518i	−0.724331	+	0.689453i	$0.757851\pi$
$564$		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	$-0.542161\pi$
$569$	16.2102	−	37.5794i	0.679566	−	1.57541i	0.811632	−	0.584169i	$-0.198580\pi$
$570$		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	−0.194557	−	0.980891i	$-0.562327\pi$
$587$	19.2852	−	20.4412i	0.795987	−	0.843697i	0.990544	+	0.137194i	$0.0438084\pi$
$588$		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	−0.819093	−	0.573661i	$-0.805523\pi$
$593$	2.12487	−	3.68039i	0.0872581	−	0.151135i	0.906351	+	0.422525i	$0.138856\pi$
$594$		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	0.0169292	−	0.999857i	$-0.494611\pi$
$599$	−18.9670	−	9.52557i	−0.774970	−	0.389204i	−0.791899	+	0.610652i	$0.790907\pi$
$600$		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	$0.236570\pi$
$617$	−6.22717	+	20.8002i	−0.250696	+	0.837384i	−0.986998	+	0.160731i	$0.948615\pi$
$618$		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	0.242369	−	0.970184i	$-0.422076\pi$
$641$	0.595982	+	0.141250i	0.0235399	+	0.00557905i	−0.218829	+	0.975763i	$0.570224\pi$
$642$		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	$-0.156856\pi$
$647$	44.8197			1.76204			0.881022	+	0.473075i	$0.156856\pi$
$648$		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	$0.401195\pi$
$653$	2.87763	+	49.4069i	0.112610	+	1.93344i	−0.192833	+	0.981232i	$0.561767\pi$
$654$		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	0.721026	−	0.692908i	$-0.243671\pi$
$659$	9.50779	+	6.25337i	0.370371	+	0.243597i	−0.350655	+	0.936505i	$0.614041\pi$
$660$		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	0.681903	−	0.731442i	$-0.261153\pi$
$677$	−5.57808	−	7.49266i	−0.214383	−	0.287966i	−0.896286	+	0.443476i	$0.853745\pi$
$678$		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	$-0.754981\pi$
$683$	5.08900	−	28.8612i	0.194725	−	1.10434i	0.912809	−	0.408386i	$-0.133908\pi$
$684$		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	$-0.878821\pi$
$701$	−20.8102	−	36.0443i	−0.785989	−	1.36137i	0.142418	−	0.989807i	$-0.454512\pi$
$702$		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	−0.283143	−	0.959078i	$-0.591377\pi$
$719$	−29.9388	−	10.8968i	−1.11653	−	0.406383i	−0.833384	+	0.552695i	$0.813599\pi$
$720$		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	−0.790593	−	0.612341i	$-0.790228\pi$
$743$	0.620612	−	0.833627i	0.0227681	−	0.0305828i	0.813361	+	0.581759i	$0.197635\pi$
$744$		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	−0.274933	−	0.961463i	$-0.588656\pi$
$761$	−33.3883	−	16.7682i	−1.21032	−	0.607847i	−0.935391	+	0.353616i	$0.884952\pi$
$762$		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	$0.0907452\pi$
$773$	4.28338	+	24.2923i	0.154062	+	0.873732i	−0.805575	+	0.592493i	$0.798144\pi$
$774$		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	−0.187247	−	0.982313i	$-0.559956\pi$
$797$	−16.8253	−	1.96660i	−0.595983	−	0.0696604i	−0.408736	+	0.912652i	$0.634030\pi$
$798$		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	$-0.394289\pi$
$809$	18.5465			0.652062			0.326031	+	0.945359i	$0.394289\pi$
$810$		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	0.569054	−	0.822300i	$-0.307310\pi$
$821$	1.12880	+	0.742425i	0.0393955	+	0.0259108i	−0.529658	+	0.848211i	$0.677680\pi$
$822$		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	$0.714074\pi$
$827$	−43.1798	+	36.2322i	−1.50151	+	1.25992i	−0.878539	+	0.477670i	$0.841481\pi$
$828$		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	0.792242	−	0.610208i	$-0.208914\pi$
$839$	−0.566230	−	0.760578i	−0.0195484	−	0.0262581i	−0.811790	+	0.583950i	$0.801507\pi$
$840$		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	$-0.923337\pi$
$857$	−8.51405	−	28.4389i	−0.290835	−	0.971455i	0.680302	−	0.732932i	$-0.261849\pi$
$858$		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	$0.280766\pi$
$863$	28.9772	+	50.1899i	0.986394	+	1.70849i	0.350826	+	0.936440i	$0.385901\pi$
$864$		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	0.390895	−	0.920435i	$-0.372166\pi$
$881$	2.92937	+	1.06621i	0.0986931	+	0.0359214i	−0.292202	+	0.956357i	$0.594388\pi$
$882$		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	0.671189	−	0.741286i	$-0.265784\pi$
$887$	−3.21262	−	3.40517i	−0.107869	−	0.114335i	−0.779058	+	0.626952i	$0.784302\pi$
$888$		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	$0.512026\pi$
$911$	−31.1840	+	33.0531i	−1.03317	+	1.09510i	−0.995399	+	0.0958126i	$0.969455\pi$
$912$		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	−0.630314	−	0.776341i	$-0.717074\pi$
$929$	−11.7038	+	5.87788i	−0.383990	+	0.192847i	0.246323	+	0.969188i	$0.420777\pi$
$930$		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	$-0.629613\pi$
$941$	13.4797	−	45.0255i	0.439427	−	1.46779i	0.835460	−	0.549552i	$-0.185202\pi$
$942$		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	0.394438	−	0.918922i	$-0.370939\pi$
$947$	30.4706	−	3.56151i	0.990163	−	0.115733i	0.595724	+	0.803189i	$0.296865\pi$
$948$		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	0.554940	−	0.831890i	$-0.312741\pi$
$953$	−5.18464	−	4.35043i	−0.167947	−	0.140924i	−0.722887	+	0.690966i	$0.757185\pi$
$954$		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	$-0.261255\pi$
$971$	42.4827			1.36333			0.681667	+	0.731662i	$0.261255\pi$
$972$		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	$0.189489\pi$
$977$	2.20981	+	37.9410i	0.0706982	+	1.21384i	−0.757284	+	0.653086i	$0.773474\pi$
$978$		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	0.473594	−	0.880743i	$-0.342956\pi$
$983$	−4.62569	−	3.04237i	−0.147537	−	0.0970365i	−0.621131	+	0.783707i	$0.713327\pi$
$984$		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.b.55.7		144
3.2	odd	2		729.2.g.c.55.2		144
9.2	odd	6		729.2.g.d.298.7		144
9.4	even	3		243.2.g.a.100.7		144
9.5	odd	6		81.2.g.a.7.2	✓	144
9.7	even	3		729.2.g.a.298.2		144
81.4	even	27		243.2.g.a.226.7		144
81.23	odd	54		729.2.g.d.433.7		144
81.29	odd	54		6561.2.a.c.1.11		72
81.31	even	27	inner	729.2.g.b.676.7		144
81.50	odd	54		729.2.g.c.676.2		144
81.52	even	27		6561.2.a.d.1.62		72
81.58	even	27		729.2.g.a.433.2		144
81.77	odd	54		81.2.g.a.58.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.2	✓	144	9.5	odd	6
81.2.g.a.58.2	yes	144	81.77	odd	54
243.2.g.a.100.7		144	9.4	even	3
243.2.g.a.226.7		144	81.4	even	27
729.2.g.a.298.2		144	9.7	even	3
729.2.g.a.433.2		144	81.58	even	27
729.2.g.b.55.7		144	1.1	even	1	trivial
729.2.g.b.676.7		144	81.31	even	27	inner
729.2.g.c.55.2		144	3.2	odd	2
729.2.g.c.676.2		144	81.50	odd	54
729.2.g.d.298.7		144	9.2	odd	6
729.2.g.d.433.7		144	81.23	odd	54
6561.2.a.c.1.11		72	81.29	odd	54
6561.2.a.d.1.62		72	81.52	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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
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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