LMFDB - Embedded newform 726.2.e.d.493.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(487,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.487"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,-1,-1,1,-1,-4,-1,-1,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			493.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	726.493
Dual form			726.2.e.d.511.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-3.23607 - 2.35114i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} -1.00000 q^{10} +1.00000 q^{12} +(-1.54508 + 4.75528i) q^{13} +(-3.23607 + 2.35114i) q^{14} +(0.809017 + 0.587785i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.16312 + 6.65740i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-0.309017 + 0.951057i) q^{20} +4.00000 q^{21} +(0.309017 - 0.951057i) q^{24} +(3.23607 - 2.35114i) q^{25} +(4.04508 + 2.93893i) q^{26} +(0.309017 + 0.951057i) q^{27} +(1.23607 + 3.80423i) q^{28} +(-5.66312 - 4.11450i) q^{29} +(0.809017 - 0.587785i) q^{30} +(-2.47214 + 7.60845i) q^{31} +1.00000 q^{32} +7.00000 q^{34} +(-1.23607 + 3.80423i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(4.04508 + 2.93893i) q^{37} +(-1.54508 - 4.75528i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-8.89919 + 6.46564i) q^{41} +(1.23607 - 3.80423i) q^{42} -8.00000 q^{43} -1.00000 q^{45} +(-3.23607 + 2.35114i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(2.78115 + 8.55951i) q^{49} +(-1.23607 - 3.80423i) q^{50} +(-5.66312 - 4.11450i) q^{51} +(4.04508 - 2.93893i) q^{52} +(-1.54508 + 4.75528i) q^{53} +1.00000 q^{54} +4.00000 q^{56} +(-5.66312 + 4.11450i) q^{58} +(-0.309017 - 0.951057i) q^{60} +(-0.618034 - 1.90211i) q^{61} +(6.47214 + 4.70228i) q^{62} +(-3.23607 + 2.35114i) q^{63} +(0.309017 - 0.951057i) q^{64} +5.00000 q^{65} +12.0000 q^{67} +(2.16312 - 6.65740i) q^{68} +(3.23607 + 2.35114i) q^{70} +(-4.94427 - 15.2169i) q^{71} +(0.309017 + 0.951057i) q^{72} +(4.85410 + 3.52671i) q^{73} +(4.04508 - 2.93893i) q^{74} +(-1.23607 + 3.80423i) q^{75} -5.00000 q^{78} +(1.23607 - 3.80423i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.39919 + 10.4616i) q^{82} +(-2.47214 - 7.60845i) q^{83} +(-3.23607 - 2.35114i) q^{84} +(5.66312 - 4.11450i) q^{85} +(-2.47214 + 7.60845i) q^{86} +7.00000 q^{87} -17.0000 q^{89} +(-0.309017 + 0.951057i) q^{90} +(16.1803 - 11.7557i) q^{91} +(-2.47214 - 7.60845i) q^{93} +(1.23607 + 3.80423i) q^{94} +(-0.809017 + 0.587785i) q^{96} +(-1.54508 + 4.75528i) q^{97} +9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 4 q^{7} - q^{8} - q^{9} - 4 q^{10} + 4 q^{12} + 5 q^{13} - 4 q^{14} + q^{15} - q^{16} - 7 q^{17} - q^{18} + q^{20} + 16 q^{21} - q^{24} + 4 q^{25}+ \cdots + 36 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^3 - q^4 + q^5 - q^6 - 4 * q^7 - q^8 - q^9 - 4 * q^10 + 4 * q^12 + 5 * q^13 - 4 * q^14 + q^15 - q^16 - 7 * q^17 - q^18 + q^20 + 16 * q^21 - q^24 + 4 * q^25 + 5 * q^26 - q^27 - 4 * q^28 - 7 * q^29 + q^30 + 8 * q^31 + 4 * q^32 + 28 * q^34 + 4 * q^35 - q^36 + 5 * q^37 + 5 * q^39 + q^40 - 11 * q^41 - 4 * q^42 - 32 * q^43 - 4 * q^45 - 4 * q^47 - q^48 - 9 * q^49 + 4 * q^50 - 7 * q^51 + 5 * q^52 + 5 * q^53 + 4 * q^54 + 16 * q^56 - 7 * q^58 + q^60 + 2 * q^61 + 8 * q^62 - 4 * q^63 - q^64 + 20 * q^65 + 48 * q^67 - 7 * q^68 + 4 * q^70 + 16 * q^71 - q^72 + 6 * q^73 + 5 * q^74 + 4 * q^75 - 20 * q^78 - 4 * q^79 + q^80 - q^81 - 11 * q^82 + 8 * q^83 - 4 * q^84 + 7 * q^85 + 8 * q^86 + 28 * q^87 - 68 * q^89 + q^90 + 20 * q^91 + 8 * q^93 - 4 * q^94 - q^96 + 5 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i	0.857877	−	0.513855i	$-0.171783\pi$
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i	−0.996074	+	0.0885298i	$0.971783\pi$
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$	−3.23607	−	2.35114i	−1.22312	−	0.888648i	−0.226764	−	0.973950i	$-0.572814\pi$
$7$	−3.23607	−	2.35114i	−1.22312	−	0.888648i	−0.996355	+	0.0853021i	$0.972814\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−1.00000			−0.316228
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	−1.54508	+	4.75528i	−0.428529	+	1.31888i	0.471044	+	0.882109i	$0.343877\pi$
$13$	−1.54508	+	4.75528i	−0.428529	+	1.31888i	−0.899574	+	0.436769i	$0.856123\pi$
$14$	−3.23607	+	2.35114i	−0.864876	+	0.628369i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.16312	+	6.65740i	0.524633	+	1.61466i	0.765040	+	0.643983i	$0.222719\pi$
$17$	2.16312	+	6.65740i	0.524633	+	1.61466i	−0.240406	+	0.970672i	$0.577281\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$19$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	4.00000			0.872872
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	3.23607	−	2.35114i	0.647214	−	0.470228i
$26$	4.04508	+	2.93893i	0.793306	+	0.576371i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	1.23607	+	3.80423i	0.233595	+	0.718931i
$29$	−5.66312	−	4.11450i	−1.05161	−	0.764043i	−0.0790959	−	0.996867i	$-0.525203\pi$
$29$	−5.66312	−	4.11450i	−1.05161	−	0.764043i	−0.972519	+	0.232824i	$0.925203\pi$
$30$	0.809017	−	0.587785i	0.147706	−	0.107314i
$31$	−2.47214	+	7.60845i	−0.444009	+	1.36652i	0.439558	+	0.898214i	$0.355135\pi$
$31$	−2.47214	+	7.60845i	−0.444009	+	1.36652i	−0.883567	+	0.468304i	$0.844865\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	7.00000			1.20049
$35$	−1.23607	+	3.80423i	−0.208934	+	0.643032i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	4.04508	+	2.93893i	0.665008	+	0.483157i	0.868350	−	0.495951i	$-0.165181\pi$
$37$	4.04508	+	2.93893i	0.665008	+	0.483157i	−0.203343	+	0.979108i	$0.565181\pi$
$38$		0			0
$39$	−1.54508	−	4.75528i	−0.247412	−	0.761455i
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	−8.89919	+	6.46564i	−1.38982	+	1.00976i	−0.393934	+	0.919139i	$0.628886\pi$
$41$	−8.89919	+	6.46564i	−1.38982	+	1.00976i	−0.995885	+	0.0906244i	$0.971114\pi$
$42$	1.23607	−	3.80423i	0.190729	−	0.587005i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−3.23607	+	2.35114i	−0.472029	+	0.342949i	−0.798232	−	0.602351i	$-0.794231\pi$
$47$	−3.23607	+	2.35114i	−0.472029	+	0.342949i	0.326202	+	0.945300i	$0.394231\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	2.78115	+	8.55951i	0.397308	+	1.22279i
$50$	−1.23607	−	3.80423i	−0.174806	−	0.537999i
$51$	−5.66312	−	4.11450i	−0.792995	−	0.576145i
$52$	4.04508	−	2.93893i	0.560952	−	0.407556i
$53$	−1.54508	+	4.75528i	−0.212234	+	0.653188i	0.787105	+	0.616819i	$0.211579\pi$
$53$	−1.54508	+	4.75528i	−0.212234	+	0.653188i	−0.999338	+	0.0363689i	$0.988421\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	4.00000			0.534522
$57$		0			0
$58$	−5.66312	+	4.11450i	−0.743604	+	0.540260i
$59$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$59$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$60$	−0.309017	−	0.951057i	−0.0398939	−	0.122781i
$61$	−0.618034	−	1.90211i	−0.0791311	−	0.243541i	0.903663	−	0.428244i	$-0.140868\pi$
$61$	−0.618034	−	1.90211i	−0.0791311	−	0.243541i	−0.982794	+	0.184703i	$0.940868\pi$
$62$	6.47214	+	4.70228i	0.821962	+	0.597190i
$63$	−3.23607	+	2.35114i	−0.407706	+	0.296216i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	5.00000			0.620174
$66$		0			0
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$	2.16312	−	6.65740i	0.262317	−	0.807328i
$69$		0			0
$70$	3.23607	+	2.35114i	0.386784	+	0.281015i
$71$	−4.94427	−	15.2169i	−0.586777	−	1.80591i	−0.592014	−	0.805928i	$-0.701667\pi$
$71$	−4.94427	−	15.2169i	−0.586777	−	1.80591i	0.00523645	−	0.999986i	$-0.498333\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	4.85410	+	3.52671i	0.568130	+	0.412770i	0.834425	−	0.551121i	$-0.185800\pi$
$73$	4.85410	+	3.52671i	0.568130	+	0.412770i	−0.266296	+	0.963891i	$0.585800\pi$
$74$	4.04508	−	2.93893i	0.470232	−	0.341643i
$75$	−1.23607	+	3.80423i	−0.142729	+	0.439274i
$76$		0			0
$77$		0			0
$78$	−5.00000			−0.566139
$79$	1.23607	−	3.80423i	0.139069	−	0.428009i	−0.857132	−	0.515097i	$-0.827756\pi$
$79$	1.23607	−	3.80423i	0.139069	−	0.428009i	0.996201	+	0.0870877i	$0.0277560\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	3.39919	+	10.4616i	0.375377	+	1.15529i
$83$	−2.47214	−	7.60845i	−0.271352	−	0.835136i	−0.990162	−	0.139929i	$-0.955313\pi$
$83$	−2.47214	−	7.60845i	−0.271352	−	0.835136i	0.718809	−	0.695207i	$-0.244687\pi$
$84$	−3.23607	−	2.35114i	−0.353084	−	0.256531i
$85$	5.66312	−	4.11450i	0.614251	−	0.446280i
$86$	−2.47214	+	7.60845i	−0.266577	+	0.820440i
$87$	7.00000			0.750479
$88$		0			0
$89$	−17.0000			−1.80200			−0.900998	−	0.433823i	$-0.857164\pi$
$89$	−17.0000			−1.80200			−0.900998	+	0.433823i	$0.857164\pi$
$90$	−0.309017	+	0.951057i	−0.0325733	+	0.100250i
$91$	16.1803	−	11.7557i	1.69616	−	1.23233i
$92$		0			0
$93$	−2.47214	−	7.60845i	−0.256349	−	0.788960i
$94$	1.23607	+	3.80423i	0.127491	+	0.392376i
$95$		0			0
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	−1.54508	+	4.75528i	−0.156880	+	0.482826i	−0.998346	−	0.0574829i	$-0.981693\pi$
$97$	−1.54508	+	4.75528i	−0.156880	+	0.482826i	0.841467	+	0.540309i	$0.181693\pi$
$98$	9.00000			0.909137
$99$		0			0
$100$	−4.00000			−0.400000
$101$	−3.09017	+	9.51057i	−0.307483	+	0.946337i	0.671255	+	0.741226i	$0.265755\pi$
$101$	−3.09017	+	9.51057i	−0.307483	+	0.946337i	−0.978739	+	0.205110i	$0.934245\pi$
$102$	−5.66312	+	4.11450i	−0.560732	+	0.407396i
$103$	−3.23607	−	2.35114i	−0.318859	−	0.231665i	0.416829	−	0.908985i	$-0.363141\pi$
$103$	−3.23607	−	2.35114i	−0.318859	−	0.231665i	−0.735689	+	0.677320i	$0.763141\pi$
$104$	−1.54508	−	4.75528i	−0.151508	−	0.466294i
$105$	−1.23607	−	3.80423i	−0.120628	−	0.371254i
$106$	4.04508	+	2.93893i	0.392893	+	0.285454i
$107$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$107$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−1.00000			−0.0957826			−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000			−0.0957826			−0.0478913	+	0.998853i	$0.515250\pi$
$110$		0			0
$111$	−5.00000			−0.474579
$112$	1.23607	−	3.80423i	0.116797	−	0.359466i
$113$	−2.42705	+	1.76336i	−0.228318	+	0.165883i	−0.696063	−	0.717981i	$-0.745067\pi$
$113$	−2.42705	+	1.76336i	−0.228318	+	0.165883i	0.467745	+	0.883863i	$0.345067\pi$
$114$		0			0
$115$		0			0
$116$	2.16312	+	6.65740i	0.200841	+	0.618124i
$117$	4.04508	+	2.93893i	0.373968	+	0.271704i
$118$		0			0
$119$	8.65248	−	26.6296i	0.793171	−	2.44113i
$120$	−1.00000			−0.0912871
$121$		0			0
$122$	−2.00000			−0.181071
$123$	3.39919	−	10.4616i	0.306494	−	0.943293i
$124$	6.47214	−	4.70228i	0.581215	−	0.422277i
$125$	−7.28115	−	5.29007i	−0.651246	−	0.473158i
$126$	1.23607	+	3.80423i	0.110118	+	0.338907i
$127$	−1.23607	−	3.80423i	−0.109683	−	0.337570i	0.881118	−	0.472897i	$-0.156792\pi$
$127$	−1.23607	−	3.80423i	−0.109683	−	0.337570i	−0.990801	+	0.135326i	$0.956792\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	6.47214	−	4.70228i	0.569840	−	0.414013i
$130$	1.54508	−	4.75528i	0.135513	−	0.417066i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$		0			0
$134$	3.70820	−	11.4127i	0.320340	−	0.985905i
$135$	0.809017	−	0.587785i	0.0696291	−	0.0505885i
$136$	−5.66312	−	4.11450i	−0.485608	−	0.352815i
$137$	3.09017	+	9.51057i	0.264011	+	0.812542i	0.991920	+	0.126868i	$0.0404925\pi$
$137$	3.09017	+	9.51057i	0.264011	+	0.812542i	−0.727909	+	0.685674i	$0.759507\pi$
$138$		0			0
$139$	9.70820	+	7.05342i	0.823439	+	0.598264i	0.917696	−	0.397284i	$-0.130047\pi$
$139$	9.70820	+	7.05342i	0.823439	+	0.598264i	−0.0942564	+	0.995548i	$0.530047\pi$
$140$	3.23607	−	2.35114i	0.273498	−	0.198708i
$141$	1.23607	−	3.80423i	0.104096	−	0.320374i
$142$	−16.0000			−1.34269
$143$		0			0
$144$	1.00000			0.0833333
$145$	−2.16312	+	6.65740i	−0.179637	+	0.552867i
$146$	4.85410	−	3.52671i	0.401728	−	0.291873i
$147$	−7.28115	−	5.29007i	−0.600539	−	0.436317i
$148$	−1.54508	−	4.75528i	−0.127005	−	0.390882i
$149$	−0.309017	−	0.951057i	−0.0253157	−	0.0779136i	0.937600	−	0.347714i	$-0.113042\pi$
$149$	−0.309017	−	0.951057i	−0.0253157	−	0.0779136i	−0.962916	+	0.269801i	$0.913042\pi$
$150$	3.23607	+	2.35114i	0.264224	+	0.191970i
$151$	−16.1803	+	11.7557i	−1.31674	+	0.956666i	−0.316771	+	0.948502i	$0.602599\pi$
$151$	−16.1803	+	11.7557i	−1.31674	+	0.956666i	−0.999967	+	0.00816356i	$0.997401\pi$
$152$		0			0
$153$	7.00000			0.565916
$154$		0			0
$155$	8.00000			0.642575
$156$	−1.54508	+	4.75528i	−0.123706	+	0.380727i
$157$	14.5623	−	10.5801i	1.16220	−	0.844387i	0.172144	−	0.985072i	$-0.444931\pi$
$157$	14.5623	−	10.5801i	1.16220	−	0.844387i	0.990054	+	0.140685i	$0.0449305\pi$
$158$	−3.23607	−	2.35114i	−0.257448	−	0.187047i
$159$	−1.54508	−	4.75528i	−0.122533	−	0.377118i
$160$	−0.309017	−	0.951057i	−0.0244299	−	0.0751876i
$161$		0			0
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	1.23607	−	3.80423i	0.0968163	−	0.297970i	−0.890906	−	0.454187i	$-0.849930\pi$
$163$	1.23607	−	3.80423i	0.0968163	−	0.297970i	0.987723	+	0.156217i	$0.0499299\pi$
$164$	11.0000			0.858956
$165$		0			0
$166$	−8.00000			−0.620920
$167$	3.70820	−	11.4127i	0.286949	−	0.883140i	−0.698858	−	0.715260i	$-0.746308\pi$
$167$	3.70820	−	11.4127i	0.286949	−	0.883140i	0.985808	−	0.167879i	$-0.0536919\pi$
$168$	−3.23607	+	2.35114i	−0.249668	+	0.181394i
$169$	−9.70820	−	7.05342i	−0.746785	−	0.542571i
$170$	−2.16312	−	6.65740i	−0.165904	−	0.510599i
$171$		0			0
$172$	6.47214	+	4.70228i	0.493496	+	0.358546i
$173$	14.5623	−	10.5801i	1.10715	−	0.804393i	0.124939	−	0.992164i	$-0.460127\pi$
$173$	14.5623	−	10.5801i	1.10715	−	0.804393i	0.982213	+	0.187772i	$0.0601265\pi$
$174$	2.16312	−	6.65740i	0.163986	−	0.504696i
$175$	−16.0000			−1.20949
$176$		0			0
$177$		0			0
$178$	−5.25329	+	16.1680i	−0.393751	+	1.21184i
$179$	−9.70820	+	7.05342i	−0.725625	+	0.527198i	−0.888176	−	0.459503i	$-0.848028\pi$
$179$	−9.70820	+	7.05342i	−0.725625	+	0.527198i	0.162551	+	0.986700i	$0.448028\pi$
$180$	0.809017	+	0.587785i	0.0603006	+	0.0438109i
$181$	−0.309017	−	0.951057i	−0.0229691	−	0.0706915i	0.938915	−	0.344149i	$-0.111833\pi$
$181$	−0.309017	−	0.951057i	−0.0229691	−	0.0706915i	−0.961884	+	0.273458i	$0.911833\pi$
$182$	−6.18034	−	19.0211i	−0.458117	−	1.40994i
$183$	1.61803	+	1.17557i	0.119609	+	0.0869007i
$184$		0			0
$185$	1.54508	−	4.75528i	0.113597	−	0.349615i
$186$	−8.00000			−0.586588
$187$		0			0
$188$	4.00000			0.291730
$189$	1.23607	−	3.80423i	0.0899107	−	0.276717i
$190$		0			0
$191$	−3.23607	−	2.35114i	−0.234154	−	0.170123i	0.464521	−	0.885562i	$-0.346227\pi$
$191$	−3.23607	−	2.35114i	−0.234154	−	0.170123i	−0.698675	+	0.715439i	$0.746227\pi$
$192$	0.309017	+	0.951057i	0.0223014	+	0.0686366i
$193$	3.39919	+	10.4616i	0.244679	+	0.753044i	0.995689	+	0.0927535i	$0.0295669\pi$
$193$	3.39919	+	10.4616i	0.244679	+	0.753044i	−0.751010	+	0.660291i	$0.770433\pi$
$194$	4.04508	+	2.93893i	0.290420	+	0.211003i
$195$	−4.04508	+	2.93893i	−0.289675	+	0.210461i
$196$	2.78115	−	8.55951i	0.198654	−	0.611393i
$197$	−9.00000			−0.641223			−0.320612	−	0.947211i	$-0.603888\pi$
$197$	−9.00000			−0.641223			−0.320612	+	0.947211i	$0.603888\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−1.23607	+	3.80423i	−0.0874032	+	0.268999i
$201$	−9.70820	+	7.05342i	−0.684764	+	0.497510i
$202$	8.09017	+	5.87785i	0.569222	+	0.413564i
$203$	8.65248	+	26.6296i	0.607285	+	1.86903i
$204$	2.16312	+	6.65740i	0.151449	+	0.466111i
$205$	8.89919	+	6.46564i	0.621546	+	0.451580i
$206$	−3.23607	+	2.35114i	−0.225468	+	0.163812i
$207$		0			0
$208$	−5.00000			−0.346688
$209$		0			0
$210$	−4.00000			−0.276026
$211$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$211$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$212$	4.04508	−	2.93893i	0.277818	−	0.201846i
$213$	12.9443	+	9.40456i	0.886927	+	0.644390i
$214$		0			0
$215$	2.47214	+	7.60845i	0.168598	+	0.518892i
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	25.8885	−	18.8091i	1.75743	−	1.27685i
$218$	−0.309017	+	0.951057i	−0.0209293	+	0.0644137i
$219$	−6.00000			−0.405442
$220$		0			0
$221$	−35.0000			−2.35435
$222$	−1.54508	+	4.75528i	−0.103699	+	0.319154i
$223$	−16.1803	+	11.7557i	−1.08352	+	0.787220i	−0.978293	−	0.207228i	$-0.933556\pi$
$223$	−16.1803	+	11.7557i	−1.08352	+	0.787220i	−0.105223	+	0.994449i	$0.533556\pi$
$224$	−3.23607	−	2.35114i	−0.216219	−	0.157092i
$225$	−1.23607	−	3.80423i	−0.0824045	−	0.253615i
$226$	0.927051	+	2.85317i	0.0616665	+	0.189790i
$227$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$227$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$228$		0			0
$229$	−1.54508	+	4.75528i	−0.102102	+	0.314238i	−0.989039	−	0.147652i	$-0.952828\pi$
$229$	−1.54508	+	4.75528i	−0.102102	+	0.314238i	0.886937	+	0.461890i	$0.152828\pi$
$230$		0			0
$231$		0			0
$232$	7.00000			0.459573
$233$	−2.78115	+	8.55951i	−0.182199	+	0.560752i	−0.999889	−	0.0149075i	$-0.995255\pi$
$233$	−2.78115	+	8.55951i	−0.182199	+	0.560752i	0.817689	+	0.575660i	$0.195255\pi$
$234$	4.04508	−	2.93893i	0.264435	−	0.192124i
$235$	3.23607	+	2.35114i	0.211098	+	0.153372i
$236$		0			0
$237$	1.23607	+	3.80423i	0.0802912	+	0.247111i
$238$	−22.6525	−	16.4580i	−1.46834	−	1.06681i
$239$	−3.23607	+	2.35114i	−0.209324	+	0.152083i	−0.687508	−	0.726177i	$-0.741295\pi$
$239$	−3.23607	+	2.35114i	−0.209324	+	0.152083i	0.478184	+	0.878260i	$0.341295\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	−0.618034	+	1.90211i	−0.0395656	+	0.121770i
$245$	7.28115	−	5.29007i	0.465176	−	0.337970i
$246$	−8.89919	−	6.46564i	−0.567391	−	0.412234i
$247$		0			0
$248$	−2.47214	−	7.60845i	−0.156981	−	0.483137i
$249$	6.47214	+	4.70228i	0.410155	+	0.297995i
$250$	−7.28115	+	5.29007i	−0.460501	+	0.334573i
$251$	4.94427	−	15.2169i	0.312080	−	0.960482i	−0.664860	−	0.746968i	$-0.731509\pi$
$251$	4.94427	−	15.2169i	0.312080	−	0.960482i	0.976940	−	0.213515i	$-0.0684911\pi$
$252$	4.00000			0.251976
$253$		0			0
$254$	−4.00000			−0.250982
$255$	−2.16312	+	6.65740i	−0.135460	+	0.416902i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−2.42705	−	1.76336i	−0.151395	−	0.109995i	0.509509	−	0.860465i	$-0.329827\pi$
$257$	−2.42705	−	1.76336i	−0.151395	−	0.109995i	−0.660904	+	0.750470i	$0.729827\pi$
$258$	−2.47214	−	7.60845i	−0.153908	−	0.473682i
$259$	−6.18034	−	19.0211i	−0.384028	−	1.18192i
$260$	−4.04508	−	2.93893i	−0.250866	−	0.182264i
$261$	−5.66312	+	4.11450i	−0.350538	+	0.254681i
$262$	−3.70820	+	11.4127i	−0.229094	+	0.705078i
$263$	8.00000			0.493301			0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000			0.493301			0.246651	+	0.969104i	$0.420670\pi$
$264$		0			0
$265$	5.00000			0.307148
$266$		0			0
$267$	13.7533	−	9.99235i	0.841688	−	0.611522i
$268$	−9.70820	−	7.05342i	−0.593023	−	0.430856i
$269$	−1.54508	−	4.75528i	−0.0942055	−	0.289935i	0.892840	−	0.450373i	$-0.148709\pi$
$269$	−1.54508	−	4.75528i	−0.0942055	−	0.289935i	−0.987046	+	0.160439i	$0.948709\pi$
$270$	−0.309017	−	0.951057i	−0.0188062	−	0.0578795i
$271$	6.47214	+	4.70228i	0.393154	+	0.285643i	0.766747	−	0.641950i	$-0.221874\pi$
$271$	6.47214	+	4.70228i	0.393154	+	0.285643i	−0.373593	+	0.927593i	$0.621874\pi$
$272$	−5.66312	+	4.11450i	−0.343377	+	0.249478i
$273$	−6.18034	+	19.0211i	−0.374051	+	1.15121i
$274$	10.0000			0.604122
$275$		0			0
$276$		0			0
$277$	7.10739	−	21.8743i	0.427042	−	1.31430i	−0.473984	−	0.880533i	$-0.657185\pi$
$277$	7.10739	−	21.8743i	0.427042	−	1.31430i	0.901026	−	0.433766i	$-0.142815\pi$
$278$	9.70820	−	7.05342i	0.582259	−	0.423036i
$279$	6.47214	+	4.70228i	0.387477	+	0.281518i
$280$	−1.23607	−	3.80423i	−0.0738692	−	0.227346i
$281$	3.09017	+	9.51057i	0.184344	+	0.567353i	0.999936	−	0.0112742i	$-0.00358875\pi$
$281$	3.09017	+	9.51057i	0.184344	+	0.567353i	−0.815592	+	0.578627i	$0.803589\pi$
$282$	−3.23607	−	2.35114i	−0.192705	−	0.140008i
$283$	−3.23607	+	2.35114i	−0.192364	+	0.139761i	−0.679799	−	0.733399i	$-0.737933\pi$
$283$	−3.23607	+	2.35114i	−0.192364	+	0.139761i	0.487434	+	0.873160i	$0.337933\pi$
$284$	−4.94427	+	15.2169i	−0.293389	+	0.902957i
$285$		0			0
$286$		0			0
$287$	44.0000			2.59724
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−25.8885	+	18.8091i	−1.52286	+	1.10642i
$290$	5.66312	+	4.11450i	0.332550	+	0.241612i
$291$	−1.54508	−	4.75528i	−0.0905745	−	0.278760i
$292$	−1.85410	−	5.70634i	−0.108503	−	0.333938i
$293$	−18.6074	−	13.5191i	−1.08706	−	0.789792i	−0.108156	−	0.994134i	$-0.534495\pi$
$293$	−18.6074	−	13.5191i	−1.08706	−	0.789792i	−0.978900	+	0.204342i	$0.934495\pi$
$294$	−7.28115	+	5.29007i	−0.424645	+	0.308523i
$295$		0			0
$296$	−5.00000			−0.290619
$297$		0			0
$298$	−1.00000			−0.0579284
$299$		0			0
$300$	3.23607	−	2.35114i	0.186834	−	0.135743i
$301$	25.8885	+	18.8091i	1.49219	+	1.08414i
$302$	6.18034	+	19.0211i	0.355639	+	1.09454i
$303$	−3.09017	−	9.51057i	−0.177526	−	0.546368i
$304$		0			0
$305$	−1.61803	+	1.17557i	−0.0926484	+	0.0673130i
$306$	2.16312	−	6.65740i	0.123657	−	0.380578i
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$	2.47214	−	7.60845i	0.140408	−	0.432131i
$311$	−16.1803	+	11.7557i	−0.917503	+	0.666605i	−0.942901	−	0.333073i	$-0.891915\pi$
$311$	−16.1803	+	11.7557i	−0.917503	+	0.666605i	0.0253983	+	0.999677i	$0.491915\pi$
$312$	4.04508	+	2.93893i	0.229008	+	0.166384i
$313$	−2.78115	−	8.55951i	−0.157200	−	0.483812i	0.841177	−	0.540760i	$-0.181863\pi$
$313$	−2.78115	−	8.55951i	−0.157200	−	0.483812i	−0.998377	+	0.0569477i	$0.981863\pi$
$314$	−5.56231	−	17.1190i	−0.313899	−	0.966082i
$315$	3.23607	+	2.35114i	0.182332	+	0.132472i
$316$	−3.23607	+	2.35114i	−0.182043	+	0.132262i
$317$	−0.618034	+	1.90211i	−0.0347122	+	0.106833i	−0.966911	−	0.255113i	$-0.917887\pi$
$317$	−0.618034	+	1.90211i	−0.0347122	+	0.106833i	0.932199	+	0.361946i	$0.117887\pi$
$318$	−5.00000			−0.280386
$319$		0			0
$320$	−1.00000			−0.0559017
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	6.18034	+	19.0211i	0.342824	+	1.05510i
$326$	−3.23607	−	2.35114i	−0.179229	−	0.130218i
$327$	0.809017	−	0.587785i	0.0447387	−	0.0325046i
$328$	3.39919	−	10.4616i	0.187689	−	0.577646i
$329$	16.0000			0.882109
$330$		0			0
$331$	32.0000			1.75888			0.879440	−	0.476011i	$-0.157918\pi$
$331$	32.0000			1.75888			0.879440	+	0.476011i	$0.157918\pi$
$332$	−2.47214	+	7.60845i	−0.135676	+	0.417568i
$333$	4.04508	−	2.93893i	0.221669	−	0.161052i
$334$	−9.70820	−	7.05342i	−0.531209	−	0.385946i
$335$	−3.70820	−	11.4127i	−0.202601	−	0.623541i
$336$	1.23607	+	3.80423i	0.0674330	+	0.207538i
$337$	0.809017	+	0.587785i	0.0440700	+	0.0320187i	0.609602	−	0.792708i	$-0.291329\pi$
$337$	0.809017	+	0.587785i	0.0440700	+	0.0320187i	−0.565532	+	0.824726i	$0.691329\pi$
$338$	−9.70820	+	7.05342i	−0.528057	+	0.383656i
$339$	0.927051	−	2.85317i	0.0503505	−	0.154963i
$340$	−7.00000			−0.379628
$341$		0			0
$342$		0			0
$343$	2.47214	−	7.60845i	0.133483	−	0.410818i
$344$	6.47214	−	4.70228i	0.348954	−	0.253530i
$345$		0			0
$346$	−5.56231	−	17.1190i	−0.299031	−	0.920324i
$347$	7.41641	+	22.8254i	0.398134	+	1.22533i	0.926494	+	0.376309i	$0.122807\pi$
$347$	7.41641	+	22.8254i	0.398134	+	1.22533i	−0.528361	+	0.849020i	$0.677193\pi$
$348$	−5.66312	−	4.11450i	−0.303575	−	0.220560i
$349$	−5.66312	+	4.11450i	−0.303140	+	0.220244i	−0.728947	−	0.684570i	$-0.759990\pi$
$349$	−5.66312	+	4.11450i	−0.303140	+	0.220244i	0.425807	+	0.904814i	$0.359990\pi$
$350$	−4.94427	+	15.2169i	−0.264282	+	0.813378i
$351$	−5.00000			−0.266880
$352$		0			0
$353$	27.0000			1.43706			0.718532	−	0.695493i	$-0.244814\pi$
$353$	27.0000			1.43706			0.718532	+	0.695493i	$0.244814\pi$
$354$		0			0
$355$	−12.9443	+	9.40456i	−0.687011	+	0.499142i
$356$	13.7533	+	9.99235i	0.728923	+	0.529593i
$357$	8.65248	+	26.6296i	0.457938	+	1.40939i
$358$	3.70820	+	11.4127i	0.195985	+	0.603179i
$359$	−3.23607	−	2.35114i	−0.170793	−	0.124088i	0.499105	−	0.866542i	$-0.333662\pi$
$359$	−3.23607	−	2.35114i	−0.170793	−	0.124088i	−0.669898	+	0.742453i	$0.733662\pi$
$360$	0.809017	−	0.587785i	0.0426389	−	0.0309790i
$361$	−5.87132	+	18.0701i	−0.309017	+	0.951057i
$362$	−1.00000			−0.0525588
$363$		0			0
$364$	−20.0000			−1.04828
$365$	1.85410	−	5.70634i	0.0970481	−	0.298683i
$366$	1.61803	−	1.17557i	0.0845760	−	0.0614481i
$367$	−6.47214	−	4.70228i	−0.337843	−	0.245457i	0.405908	−	0.913914i	$-0.366955\pi$
$367$	−6.47214	−	4.70228i	−0.337843	−	0.245457i	−0.743751	+	0.668457i	$0.766955\pi$
$368$		0			0
$369$	3.39919	+	10.4616i	0.176955	+	0.544610i
$370$	−4.04508	−	2.93893i	−0.210294	−	0.152788i
$371$	16.1803	−	11.7557i	0.840041	−	0.610326i
$372$	−2.47214	+	7.60845i	−0.128174	+	0.394480i
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$		0			0
$375$	9.00000			0.464758
$376$	1.23607	−	3.80423i	0.0637453	−	0.196188i
$377$	28.3156	−	20.5725i	1.45833	−	1.05954i
$378$	−3.23607	−	2.35114i	−0.166445	−	0.120930i
$379$	−6.18034	−	19.0211i	−0.317463	−	0.977050i	−0.974729	−	0.223391i	$-0.928287\pi$
$379$	−6.18034	−	19.0211i	−0.317463	−	0.977050i	0.657266	−	0.753659i	$-0.271713\pi$
$380$		0			0
$381$	3.23607	+	2.35114i	0.165789	+	0.120453i
$382$	−3.23607	+	2.35114i	−0.165572	+	0.120295i
$383$	−11.1246	+	34.2380i	−0.568441	+	1.74948i	0.0890579	+	0.996026i	$0.471614\pi$
$383$	−11.1246	+	34.2380i	−0.568441	+	1.74948i	−0.657499	+	0.753455i	$0.728386\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	11.0000			0.559885
$387$	−2.47214	+	7.60845i	−0.125666	+	0.386759i
$388$	4.04508	−	2.93893i	0.205358	−	0.149201i
$389$	23.4615	+	17.0458i	1.18954	+	0.864255i	0.993216	−	0.116283i	$-0.0370980\pi$
$389$	23.4615	+	17.0458i	1.18954	+	0.864255i	0.196329	+	0.980538i	$0.437098\pi$
$390$	1.54508	+	4.75528i	0.0782384	+	0.240793i
$391$		0			0
$392$	−7.28115	−	5.29007i	−0.367754	−	0.267189i
$393$	9.70820	−	7.05342i	0.489714	−	0.355798i
$394$	−2.78115	+	8.55951i	−0.140112	+	0.431222i
$395$	−4.00000			−0.201262
$396$		0			0
$397$	−21.0000			−1.05396			−0.526980	−	0.849878i	$-0.676676\pi$
$397$	−21.0000			−1.05396			−0.526980	+	0.849878i	$0.676676\pi$
$398$	−4.94427	+	15.2169i	−0.247834	+	0.762754i
$399$		0			0
$400$	3.23607	+	2.35114i	0.161803	+	0.117557i
$401$	4.63525	+	14.2658i	0.231474	+	0.712402i	0.997570	+	0.0696764i	$0.0221967\pi$
$401$	4.63525	+	14.2658i	0.231474	+	0.712402i	−0.766096	+	0.642726i	$0.777803\pi$
$402$	3.70820	+	11.4127i	0.184948	+	0.569213i
$403$	−32.3607	−	23.5114i	−1.61200	−	1.17119i
$404$	8.09017	−	5.87785i	0.402501	−	0.292434i
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	28.0000			1.38962
$407$		0			0
$408$	7.00000			0.346552
$409$	−0.309017	+	0.951057i	−0.0152799	+	0.0470267i	−0.958406	−	0.285409i	$-0.907871\pi$
$409$	−0.309017	+	0.951057i	−0.0152799	+	0.0470267i	0.943126	+	0.332436i	$0.107871\pi$
$410$	8.89919	−	6.46564i	0.439500	−	0.319315i
$411$	−8.09017	−	5.87785i	−0.399059	−	0.289933i
$412$	1.23607	+	3.80423i	0.0608967	+	0.187421i
$413$		0			0
$414$		0			0
$415$	−6.47214	+	4.70228i	−0.317705	+	0.230826i
$416$	−1.54508	+	4.75528i	−0.0757540	+	0.233147i
$417$	−12.0000			−0.587643
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	−1.23607	+	3.80423i	−0.0603139	+	0.185627i
$421$	−12.1353	+	8.81678i	−0.591436	+	0.429704i	−0.842829	−	0.538182i	$-0.819111\pi$
$421$	−12.1353	+	8.81678i	−0.591436	+	0.429704i	0.251393	+	0.967885i	$0.419111\pi$
$422$		0			0
$423$	1.23607	+	3.80423i	0.0600997	+	0.184968i
$424$	−1.54508	−	4.75528i	−0.0750360	−	0.230937i
$425$	22.6525	+	16.4580i	1.09881	+	0.798330i
$426$	12.9443	−	9.40456i	0.627152	−	0.455653i
$427$	−2.47214	+	7.60845i	−0.119635	+	0.368199i
$428$		0			0
$429$		0			0
$430$	8.00000			0.385794
$431$	6.18034	−	19.0211i	0.297696	−	0.916216i	−0.684606	−	0.728913i	$-0.740026\pi$
$431$	6.18034	−	19.0211i	0.297696	−	0.916216i	0.982302	−	0.187302i	$-0.0599743\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	16.9894	+	12.3435i	0.816456	+	0.593190i	0.915695	−	0.401873i	$-0.131641\pi$
$433$	16.9894	+	12.3435i	0.816456	+	0.593190i	−0.0992389	+	0.995064i	$0.531641\pi$
$434$	−9.88854	−	30.4338i	−0.474665	−	1.46087i
$435$	−2.16312	−	6.65740i	−0.103714	−	0.319198i
$436$	0.809017	+	0.587785i	0.0387449	+	0.0281498i
$437$		0			0
$438$	−1.85410	+	5.70634i	−0.0885924	+	0.272659i
$439$	16.0000			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$	−10.8156	+	33.2870i	−0.514445	+	1.58330i
$443$	−29.1246	+	21.1603i	−1.38375	+	1.00535i	−0.387234	+	0.921982i	$0.626569\pi$
$443$	−29.1246	+	21.1603i	−1.38375	+	1.00535i	−0.996518	+	0.0833731i	$0.973431\pi$
$444$	4.04508	+	2.93893i	0.191971	+	0.139475i
$445$	5.25329	+	16.1680i	0.249030	+	0.766435i
$446$	6.18034	+	19.0211i	0.292648	+	0.900677i
$447$	0.809017	+	0.587785i	0.0382652	+	0.0278013i
$448$	−3.23607	+	2.35114i	−0.152890	+	0.111081i
$449$	4.63525	−	14.2658i	0.218751	−	0.673247i	−0.780115	−	0.625636i	$-0.784839\pi$
$449$	4.63525	−	14.2658i	0.218751	−	0.673247i	0.998866	−	0.0476105i	$-0.0151606\pi$
$450$	−4.00000			−0.188562
$451$		0			0
$452$	3.00000			0.141108
$453$	6.18034	−	19.0211i	0.290378	−	0.893691i
$454$		0			0
$455$	−16.1803	−	11.7557i	−0.758546	−	0.551116i
$456$		0			0
$457$	−5.25329	−	16.1680i	−0.245738	−	0.756305i	−0.995514	−	0.0946131i	$-0.969839\pi$
$457$	−5.25329	−	16.1680i	−0.245738	−	0.756305i	0.749776	−	0.661692i	$-0.230161\pi$
$458$	4.04508	+	2.93893i	0.189014	+	0.137327i
$459$	−5.66312	+	4.11450i	−0.264332	+	0.192048i
$460$		0			0
$461$	−33.0000			−1.53696			−0.768482	−	0.639872i	$-0.778987\pi$
$461$	−33.0000			−1.53696			−0.768482	+	0.639872i	$0.778987\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	2.16312	−	6.65740i	0.100420	−	0.309062i
$465$	−6.47214	+	4.70228i	−0.300138	+	0.218063i
$466$	7.28115	+	5.29007i	0.337293	+	0.245058i
$467$	8.65248	+	26.6296i	0.400389	+	1.23227i	0.924685	+	0.380734i	$0.124329\pi$
$467$	8.65248	+	26.6296i	0.400389	+	1.23227i	−0.524296	+	0.851536i	$0.675671\pi$
$468$	−1.54508	−	4.75528i	−0.0714216	−	0.219813i
$469$	−38.8328	−	28.2137i	−1.79313	−	1.30279i
$470$	3.23607	−	2.35114i	0.149269	−	0.108450i
$471$	−5.56231	+	17.1190i	−0.256298	+	0.788803i
$472$		0			0
$473$		0			0
$474$	4.00000			0.183726
$475$		0			0
$476$	−22.6525	+	16.4580i	−1.03827	+	0.754351i
$477$	4.04508	+	2.93893i	0.185212	+	0.134564i
$478$	1.23607	+	3.80423i	0.0565364	+	0.174001i
$479$	1.23607	+	3.80423i	0.0564774	+	0.173820i	0.975316	−	0.220814i	$-0.0708715\pi$
$479$	1.23607	+	3.80423i	0.0564774	+	0.173820i	−0.918838	+	0.394634i	$0.870871\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	−20.2254	+	14.6946i	−0.922200	+	0.670018i
$482$	5.56231	−	17.1190i	0.253356	−	0.779750i
$483$		0			0
$484$		0			0
$485$	5.00000			0.227038
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	16.1803	−	11.7557i	0.733201	−	0.532702i	−0.157373	−	0.987539i	$-0.550303\pi$
$487$	16.1803	−	11.7557i	0.733201	−	0.532702i	0.890575	+	0.454837i	$0.150303\pi$
$488$	1.61803	+	1.17557i	0.0732450	+	0.0532156i
$489$	1.23607	+	3.80423i	0.0558969	+	0.172033i
$490$	−2.78115	−	8.55951i	−0.125640	−	0.386679i
$491$	9.70820	+	7.05342i	0.438125	+	0.318317i	0.784890	−	0.619636i	$-0.212720\pi$
$491$	9.70820	+	7.05342i	0.438125	+	0.318317i	−0.346764	+	0.937952i	$0.612720\pi$
$492$	−8.89919	+	6.46564i	−0.401206	+	0.291493i
$493$	15.1418	−	46.6018i	0.681954	−	2.09884i
$494$		0			0
$495$		0			0
$496$	−8.00000			−0.359211
$497$	−19.7771	+	60.8676i	−0.887124	+	2.73029i
$498$	6.47214	−	4.70228i	0.290023	−	0.210714i
$499$	−32.3607	−	23.5114i	−1.44866	−	1.05252i	−0.986141	−	0.165907i	$-0.946945\pi$
$499$	−32.3607	−	23.5114i	−1.44866	−	1.05252i	−0.462522	−	0.886608i	$-0.653055\pi$
$500$	2.78115	+	8.55951i	0.124377	+	0.382793i
$501$	3.70820	+	11.4127i	0.165670	+	0.509881i
$502$	−12.9443	−	9.40456i	−0.577731	−	0.419746i
$503$	−12.9443	+	9.40456i	−0.577157	+	0.419329i	−0.837698	−	0.546134i	$-0.816099\pi$
$503$	−12.9443	+	9.40456i	−0.577157	+	0.419329i	0.260541	+	0.965463i	$0.416099\pi$
$504$	1.23607	−	3.80423i	0.0550588	−	0.169454i
$505$	10.0000			0.444994
$506$		0			0
$507$	12.0000			0.532939
$508$	−1.23607	+	3.80423i	−0.0548416	+	0.168785i
$509$	1.61803	−	1.17557i	0.0717181	−	0.0521062i	−0.551349	−	0.834275i	$-0.685887\pi$
$509$	1.61803	−	1.17557i	0.0717181	−	0.0521062i	0.623067	+	0.782169i	$0.285887\pi$
$510$	5.66312	+	4.11450i	0.250767	+	0.182193i
$511$	−7.41641	−	22.8254i	−0.328083	−	1.00973i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	−2.42705	+	1.76336i	−0.107053	+	0.0777783i
$515$	−1.23607	+	3.80423i	−0.0544677	+	0.167634i
$516$	−8.00000			−0.352180
$517$		0			0
$518$	−20.0000			−0.878750
$519$	−5.56231	+	17.1190i	−0.244158	+	0.751441i
$520$	−4.04508	+	2.93893i	−0.177389	+	0.128880i
$521$	4.85410	+	3.52671i	0.212662	+	0.154508i	0.689017	−	0.724745i	$-0.258042\pi$
$521$	4.85410	+	3.52671i	0.212662	+	0.154508i	−0.476355	+	0.879253i	$0.658042\pi$
$522$	2.16312	+	6.65740i	0.0946771	+	0.291386i
$523$	−4.94427	−	15.2169i	−0.216198	−	0.665389i	−0.999066	−	0.0432015i	$-0.986244\pi$
$523$	−4.94427	−	15.2169i	−0.216198	−	0.665389i	0.782868	−	0.622187i	$-0.213756\pi$
$524$	9.70820	+	7.05342i	0.424105	+	0.308130i
$525$	12.9443	−	9.40456i	0.564934	−	0.410449i
$526$	2.47214	−	7.60845i	0.107790	−	0.331744i
$527$	−56.0000			−2.43940
$528$		0			0
$529$	−23.0000			−1.00000
$530$	1.54508	−	4.75528i	0.0671142	−	0.206556i
$531$		0			0
$532$		0			0
$533$	−16.9959	−	52.3081i	−0.736176	−	2.26572i
$534$	−5.25329	−	16.1680i	−0.227332	−	0.699656i
$535$		0			0
$536$	−9.70820	+	7.05342i	−0.419331	+	0.304661i
$537$	3.70820	−	11.4127i	0.160021	−	0.492493i
$538$	−5.00000			−0.215565
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	9.27051	−	28.5317i	0.398570	−	1.22667i	−0.527576	−	0.849508i	$-0.676899\pi$
$541$	9.27051	−	28.5317i	0.398570	−	1.22667i	0.926146	−	0.377165i	$-0.123101\pi$
$542$	6.47214	−	4.70228i	0.278002	−	0.201980i
$543$	0.809017	+	0.587785i	0.0347182	+	0.0252243i
$544$	2.16312	+	6.65740i	0.0927430	+	0.285433i
$545$	0.309017	+	0.951057i	0.0132368	+	0.0407388i
$546$	16.1803	+	11.7557i	0.692455	+	0.503098i
$547$	−3.23607	+	2.35114i	−0.138364	+	0.100528i	−0.654814	−	0.755790i	$-0.727253\pi$
$547$	−3.23607	+	2.35114i	−0.138364	+	0.100528i	0.516450	+	0.856317i	$0.327253\pi$
$548$	3.09017	−	9.51057i	0.132006	−	0.406271i
$549$	−2.00000			−0.0853579
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−12.9443	+	9.40456i	−0.550446	+	0.399923i
$554$	−18.6074	−	13.5191i	−0.790552	−	0.574370i
$555$	1.54508	+	4.75528i	0.0655852	+	0.201851i
$556$	−3.70820	−	11.4127i	−0.157263	−	0.484005i
$557$	−11.3262	−	8.22899i	−0.479908	−	0.348674i	0.321382	−	0.946950i	$-0.395853\pi$
$557$	−11.3262	−	8.22899i	−0.479908	−	0.348674i	−0.801290	+	0.598276i	$0.795853\pi$
$558$	6.47214	−	4.70228i	0.273987	−	0.199063i
$559$	12.3607	−	38.0423i	0.522801	−	1.60902i
$560$	−4.00000			−0.169031
$561$		0			0
$562$	10.0000			0.421825
$563$	11.1246	−	34.2380i	0.468846	−	1.44296i	−0.385233	−	0.922819i	$-0.625879\pi$
$563$	11.1246	−	34.2380i	0.468846	−	1.44296i	0.854080	−	0.520142i	$-0.174121\pi$
$564$	−3.23607	+	2.35114i	−0.136263	+	0.0990009i
$565$	2.42705	+	1.76336i	0.102107	+	0.0741849i
$566$	1.23607	+	3.80423i	0.0519558	+	0.159904i
$567$	1.23607	+	3.80423i	0.0519100	+	0.159762i
$568$	12.9443	+	9.40456i	0.543130	+	0.394607i
$569$	−21.0344	+	15.2824i	−0.881810	+	0.640672i	−0.933730	−	0.357979i	$-0.883466\pi$
$569$	−21.0344	+	15.2824i	−0.881810	+	0.640672i	0.0519200	+	0.998651i	$0.483466\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$		0			0
$573$	4.00000			0.167102
$574$	13.5967	−	41.8465i	0.567517	−	1.74664i
$575$		0			0
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	2.16312	+	6.65740i	0.0900518	+	0.277151i	0.985933	−	0.167144i	$-0.0534544\pi$
$577$	2.16312	+	6.65740i	0.0900518	+	0.277151i	−0.895881	+	0.444295i	$0.853454\pi$
$578$	9.88854	+	30.4338i	0.411309	+	1.26588i
$579$	−8.89919	−	6.46564i	−0.369838	−	0.268703i
$580$	5.66312	−	4.11450i	0.235148	−	0.170845i
$581$	−9.88854	+	30.4338i	−0.410246	+	1.26261i
$582$	−5.00000			−0.207257
$583$		0			0
$584$	−6.00000			−0.248282
$585$	1.54508	−	4.75528i	0.0638814	−	0.196607i
$586$	−18.6074	+	13.5191i	−0.768664	+	0.558467i
$587$	22.6525	+	16.4580i	0.934968	+	0.679294i	0.947204	−	0.320631i	$-0.103895\pi$
$587$	22.6525	+	16.4580i	0.934968	+	0.679294i	−0.0122363	+	0.999925i	$0.503895\pi$
$588$	2.78115	+	8.55951i	0.114693	+	0.352988i
$589$		0			0
$590$		0			0
$591$	7.28115	−	5.29007i	0.299507	−	0.217604i
$592$	−1.54508	+	4.75528i	−0.0635026	+	0.195441i
$593$	35.0000			1.43728			0.718639	−	0.695383i	$-0.244765\pi$
$593$	35.0000			1.43728			0.718639	+	0.695383i	$0.244765\pi$
$594$		0			0
$595$	−28.0000			−1.14789
$596$	−0.309017	+	0.951057i	−0.0126578	+	0.0389568i
$597$	12.9443	−	9.40456i	0.529774	−	0.384903i
$598$		0			0
$599$	11.1246	+	34.2380i	0.454539	+	1.39893i	0.871675	+	0.490084i	$0.163034\pi$
$599$	11.1246	+	34.2380i	0.454539	+	1.39893i	−0.417136	+	0.908844i	$0.636966\pi$
$600$	−1.23607	−	3.80423i	−0.0504623	−	0.155307i
$601$	36.4058	+	26.4503i	1.48502	+	1.07893i	0.975895	+	0.218240i	$0.0700317\pi$
$601$	36.4058	+	26.4503i	1.48502	+	1.07893i	0.509127	+	0.860691i	$0.329968\pi$
$602$	25.8885	−	18.8091i	1.05514	−	0.766603i
$603$	3.70820	−	11.4127i	0.151010	−	0.464760i
$604$	20.0000			0.813788
$605$		0			0
$606$	−10.0000			−0.406222
$607$	−12.3607	+	38.0423i	−0.501705	+	1.54409i	0.304537	+	0.952501i	$0.401498\pi$
$607$	−12.3607	+	38.0423i	−0.501705	+	1.54409i	−0.806241	+	0.591587i	$0.798502\pi$
$608$		0			0
$609$	−22.6525	−	16.4580i	−0.917925	−	0.666911i
$610$	0.618034	+	1.90211i	0.0250235	+	0.0770143i
$611$	−6.18034	−	19.0211i	−0.250030	−	0.769513i
$612$	−5.66312	−	4.11450i	−0.228918	−	0.166319i
$613$	20.2254	−	14.6946i	0.816897	−	0.593511i	−0.0989248	−	0.995095i	$-0.531540\pi$
$613$	20.2254	−	14.6946i	0.816897	−	0.593511i	0.915822	+	0.401584i	$0.131540\pi$
$614$	2.47214	−	7.60845i	0.0997673	−	0.307052i
$615$	−11.0000			−0.443563
$616$		0			0
$617$	−25.0000			−1.00646			−0.503231	−	0.864152i	$-0.667856\pi$
$617$	−25.0000			−1.00646			−0.503231	+	0.864152i	$0.667856\pi$
$618$	1.23607	−	3.80423i	0.0497219	−	0.153028i
$619$	−3.23607	+	2.35114i	−0.130069	+	0.0945003i	−0.650917	−	0.759149i	$-0.725616\pi$
$619$	−3.23607	+	2.35114i	−0.130069	+	0.0945003i	0.520849	+	0.853649i	$0.325616\pi$
$620$	−6.47214	−	4.70228i	−0.259927	−	0.188848i
$621$		0			0
$622$	6.18034	+	19.0211i	0.247809	+	0.762678i
$623$	55.0132	+	39.9694i	2.20406	+	1.60134i
$624$	4.04508	−	2.93893i	0.161933	−	0.117651i
$625$	3.39919	−	10.4616i	0.135967	−	0.418465i
$626$	−9.00000			−0.359712
$627$		0			0
$628$	−18.0000			−0.718278
$629$	−10.8156	+	33.2870i	−0.431246	+	1.32724i
$630$	3.23607	−	2.35114i	0.128928	−	0.0936717i
$631$	19.4164	+	14.1068i	0.772955	+	0.561585i	0.902856	−	0.429942i	$-0.141466\pi$
$631$	19.4164	+	14.1068i	0.772955	+	0.561585i	−0.129901	+	0.991527i	$0.541466\pi$
$632$	1.23607	+	3.80423i	0.0491681	+	0.151324i
$633$		0			0
$634$	1.61803	+	1.17557i	0.0642603	+	0.0466879i
$635$	−3.23607	+	2.35114i	−0.128419	+	0.0933022i
$636$	−1.54508	+	4.75528i	−0.0612666	+	0.188559i
$637$	−45.0000			−1.78296
$638$		0			0
$639$	−16.0000			−0.632950
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	26.6976	−	19.3969i	1.05449	−	0.766132i	0.0814291	−	0.996679i	$-0.474052\pi$
$641$	26.6976	−	19.3969i	1.05449	−	0.766132i	0.973061	+	0.230547i	$0.0740516\pi$
$642$		0			0
$643$	−4.94427	−	15.2169i	−0.194983	−	0.600096i	−0.999977	−	0.00681282i	$-0.997831\pi$
$643$	−4.94427	−	15.2169i	−0.194983	−	0.600096i	0.804994	−	0.593283i	$-0.202169\pi$
$644$		0			0
$645$	−6.47214	−	4.70228i	−0.254840	−	0.185152i
$646$		0			0
$647$	−1.23607	+	3.80423i	−0.0485948	+	0.149560i	−0.972409	−	0.233281i	$-0.925054\pi$
$647$	−1.23607	+	3.80423i	−0.0485948	+	0.149560i	0.923815	+	0.382840i	$0.125054\pi$
$648$	1.00000			0.0392837
$649$		0			0
$650$	20.0000			0.784465
$651$	−9.88854	+	30.4338i	−0.387563	+	1.19279i
$652$	−3.23607	+	2.35114i	−0.126734	+	0.0920778i
$653$	−24.2705	−	17.6336i	−0.949778	−	0.690054i	0.000976014	−	1.00000i	$-0.499689\pi$
$653$	−24.2705	−	17.6336i	−0.949778	−	0.690054i	−0.950754	+	0.309945i	$0.899689\pi$
$654$	−0.309017	−	0.951057i	−0.0120835	−	0.0371893i
$655$	3.70820	+	11.4127i	0.144892	+	0.445930i
$656$	−8.89919	−	6.46564i	−0.347455	−	0.252441i
$657$	4.85410	−	3.52671i	0.189377	−	0.137590i
$658$	4.94427	−	15.2169i	0.192748	−	0.593217i
$659$	28.0000			1.09073			0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000			1.09073			0.545363	+	0.838200i	$0.316392\pi$
$660$		0			0
$661$	−9.00000			−0.350059			−0.175030	−	0.984563i	$-0.556002\pi$
$661$	−9.00000			−0.350059			−0.175030	+	0.984563i	$0.556002\pi$
$662$	9.88854	−	30.4338i	0.384329	−	1.18284i
$663$	28.3156	−	20.5725i	1.09969	−	0.798969i
$664$	6.47214	+	4.70228i	0.251168	+	0.182484i
$665$		0			0
$666$	−1.54508	−	4.75528i	−0.0598708	−	0.184263i
$667$		0			0
$668$	−9.70820	+	7.05342i	−0.375622	+	0.272905i
$669$	6.18034	−	19.0211i	0.238946	−	0.735399i
$670$	−12.0000			−0.463600
$671$		0			0
$672$	4.00000			0.154303
$673$	0.618034	−	1.90211i	0.0238235	−	0.0733211i	−0.938438	−	0.345448i	$-0.887727\pi$
$673$	0.618034	−	1.90211i	0.0238235	−	0.0733211i	0.962261	+	0.272127i	$0.0877270\pi$
$674$	0.809017	−	0.587785i	0.0311622	−	0.0226406i
$675$	3.23607	+	2.35114i	0.124556	+	0.0904955i
$676$	3.70820	+	11.4127i	0.142623	+	0.438949i
$677$	−7.72542	−	23.7764i	−0.296912	−	0.913802i	−0.982572	−	0.185880i	$-0.940486\pi$
$677$	−7.72542	−	23.7764i	−0.296912	−	0.913802i	0.685660	−	0.727922i	$-0.259514\pi$
$678$	−2.42705	−	1.76336i	−0.0932103	−	0.0677213i
$679$	16.1803	−	11.7557i	0.620944	−	0.451143i
$680$	−2.16312	+	6.65740i	−0.0829518	+	0.255299i
$681$		0			0
$682$		0			0
$683$	−52.0000			−1.98972			−0.994862	−	0.101237i	$-0.967720\pi$
$683$	−52.0000			−1.98972			−0.994862	+	0.101237i	$0.967720\pi$
$684$		0			0
$685$	8.09017	−	5.87785i	0.309110	−	0.224581i
$686$	−6.47214	−	4.70228i	−0.247107	−	0.179534i
$687$	−1.54508	−	4.75528i	−0.0589487	−	0.181425i
$688$	−2.47214	−	7.60845i	−0.0942493	−	0.290070i
$689$	−20.2254	−	14.6946i	−0.770527	−	0.559821i
$690$		0			0
$691$	1.23607	−	3.80423i	0.0470222	−	0.144720i	−0.924789	−	0.380481i	$-0.875758\pi$
$691$	1.23607	−	3.80423i	0.0470222	−	0.144720i	0.971811	+	0.235762i	$0.0757584\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	24.0000			0.911028
$695$	3.70820	−	11.4127i	0.140660	−	0.432908i
$696$	−5.66312	+	4.11450i	−0.214660	+	0.155960i
$697$	−62.2943	−	45.2595i	−2.35957	−	1.71432i
$698$	2.16312	+	6.65740i	0.0818753	+	0.251986i
$699$	−2.78115	−	8.55951i	−0.105193	−	0.323750i
$700$	12.9443	+	9.40456i	0.489247	+	0.355459i
$701$	26.6976	−	19.3969i	1.00835	−	0.732611i	0.0444900	−	0.999010i	$-0.485834\pi$
$701$	26.6976	−	19.3969i	1.00835	−	0.732611i	0.963863	+	0.266399i	$0.0858337\pi$
$702$	−1.54508	+	4.75528i	−0.0583155	+	0.179477i
$703$		0			0
$704$		0			0
$705$	−4.00000			−0.150649
$706$	8.34346	−	25.6785i	0.314010	−	0.966424i
$707$	32.3607	−	23.5114i	1.21705	−	0.884238i
$708$		0			0
$709$	−8.03444	−	24.7275i	−0.301740	−	0.928660i	−0.980874	−	0.194645i	$-0.937644\pi$
$709$	−8.03444	−	24.7275i	−0.301740	−	0.928660i	0.679134	−	0.734014i	$-0.262356\pi$
$710$	4.94427	+	15.2169i	0.185555	+	0.571080i
$711$	−3.23607	−	2.35114i	−0.121362	−	0.0881747i
$712$	13.7533	−	9.99235i	0.515426	−	0.374479i
$713$		0			0
$714$	28.0000			1.04787
$715$		0			0
$716$	12.0000			0.448461
$717$	1.23607	−	3.80423i	0.0461618	−	0.142071i
$718$	−3.23607	+	2.35114i	−0.120769	+	0.0877438i
$719$	−3.23607	−	2.35114i	−0.120685	−	0.0876828i	0.525805	−	0.850605i	$-0.323764\pi$
$719$	−3.23607	−	2.35114i	−0.120685	−	0.0876828i	−0.646490	+	0.762922i	$0.723764\pi$
$720$	−0.309017	−	0.951057i	−0.0115164	−	0.0354438i
$721$	4.94427	+	15.2169i	0.184134	+	0.566707i
$722$	15.3713	+	11.1679i	0.572061	+	0.415627i
$723$	−14.5623	+	10.5801i	−0.541578	+	0.393479i
$724$	−0.309017	+	0.951057i	−0.0114845	+	0.0353457i
$725$	−28.0000			−1.03989
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	−6.18034	+	19.0211i	−0.229059	+	0.704970i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−4.85410	−	3.52671i	−0.179658	−	0.130529i
$731$	−17.3050	−	53.2592i	−0.640047	−	1.96986i
$732$	−0.618034	−	1.90211i	−0.0228432	−	0.0703041i
$733$	13.7533	+	9.99235i	0.507989	+	0.369076i	0.812060	−	0.583574i	$-0.198346\pi$
$733$	13.7533	+	9.99235i	0.507989	+	0.369076i	−0.304071	+	0.952649i	$0.598346\pi$
$734$	−6.47214	+	4.70228i	−0.238891	+	0.173564i
$735$	−2.78115	+	8.55951i	−0.102584	+	0.315722i
$736$		0			0
$737$		0			0
$738$	11.0000			0.404916
$739$	6.18034	−	19.0211i	0.227347	−	0.699704i	−0.770697	−	0.637201i	$-0.780092\pi$
$739$	6.18034	−	19.0211i	0.227347	−	0.699704i	0.998045	−	0.0625022i	$-0.0199080\pi$
$740$	−4.04508	+	2.93893i	−0.148700	+	0.108037i
$741$		0			0
$742$	−6.18034	−	19.0211i	−0.226887	−	0.698288i
$743$	−4.94427	−	15.2169i	−0.181388	−	0.558254i	0.818480	−	0.574535i	$-0.194817\pi$
$743$	−4.94427	−	15.2169i	−0.181388	−	0.558254i	−0.999867	+	0.0162814i	$0.994817\pi$
$744$	6.47214	+	4.70228i	0.237280	+	0.172394i
$745$	−0.809017	+	0.587785i	−0.0296401	+	0.0215348i
$746$	6.79837	−	20.9232i	0.248906	−	0.766054i
$747$	−8.00000			−0.292705
$748$		0			0
$749$		0			0
$750$	2.78115	−	8.55951i	0.101553	−	0.312549i
$751$	25.8885	−	18.8091i	0.944686	−	0.686355i	−0.00485778	−	0.999988i	$-0.501546\pi$
$751$	25.8885	−	18.8091i	0.944686	−	0.686355i	0.949544	+	0.313633i	$0.101546\pi$
$752$	−3.23607	−	2.35114i	−0.118007	−	0.0857373i
$753$	4.94427	+	15.2169i	0.180179	+	0.554535i
$754$	−10.8156	−	33.2870i	−0.393881	−	1.21224i
$755$	16.1803	+	11.7557i	0.588863	+	0.427834i
$756$	−3.23607	+	2.35114i	−0.117695	+	0.0855102i
$757$	−10.1976	+	31.3849i	−0.370637	+	1.14070i	0.575739	+	0.817634i	$0.304714\pi$
$757$	−10.1976	+	31.3849i	−0.370637	+	1.14070i	−0.946376	+	0.323069i	$0.895286\pi$
$758$	−20.0000			−0.726433
$759$		0			0
$760$		0			0
$761$	13.2877	−	40.8954i	0.481680	−	1.48246i	−0.355053	−	0.934846i	$-0.615537\pi$
$761$	13.2877	−	40.8954i	0.481680	−	1.48246i	0.836732	−	0.547612i	$-0.184463\pi$
$762$	3.23607	−	2.35114i	0.117230	−	0.0851729i
$763$	3.23607	+	2.35114i	0.117154	+	0.0851170i
$764$	1.23607	+	3.80423i	0.0447194	+	0.137632i
$765$	−2.16312	−	6.65740i	−0.0782077	−	0.240699i
$766$	29.1246	+	21.1603i	1.05231	+	0.764552i
$767$		0			0
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	19.0000			0.685158			0.342579	−	0.939489i	$-0.388700\pi$
$769$	19.0000			0.685158			0.342579	+	0.939489i	$0.388700\pi$
$770$		0			0
$771$	3.00000			0.108042
$772$	3.39919	−	10.4616i	0.122339	−	0.376522i
$773$	21.0344	−	15.2824i	0.756556	−	0.549670i	−0.141296	−	0.989967i	$-0.545127\pi$
$773$	21.0344	−	15.2824i	0.756556	−	0.549670i	0.897852	+	0.440297i	$0.145127\pi$
$774$	6.47214	+	4.70228i	0.232636	+	0.169020i
$775$	9.88854	+	30.4338i	0.355207	+	1.09321i
$776$	−1.54508	−	4.75528i	−0.0554653	−	0.170705i
$777$	16.1803	+	11.7557i	0.580466	+	0.421734i
$778$	23.4615	−	17.0458i	0.841135	−	0.611121i
$779$		0			0
$780$	5.00000			0.179029
$781$		0			0
$782$		0			0
$783$	2.16312	−	6.65740i	0.0773036	−	0.237916i
$784$	−7.28115	+	5.29007i	−0.260041	+	0.188931i
$785$	−14.5623	−	10.5801i	−0.519751	−	0.377621i
$786$	−3.70820	−	11.4127i	−0.132267	−	0.407077i
$787$	−8.65248	−	26.6296i	−0.308427	−	0.949242i	−0.978376	−	0.206835i	$-0.933684\pi$
$787$	−8.65248	−	26.6296i	−0.308427	−	0.949242i	0.669948	−	0.742408i	$-0.266316\pi$
$788$	7.28115	+	5.29007i	0.259380	+	0.188451i
$789$	−6.47214	+	4.70228i	−0.230414	+	0.167406i
$790$	−1.23607	+	3.80423i	−0.0439773	+	0.135348i
$791$	12.0000			0.426671
$792$		0			0
$793$	10.0000			0.355110
$794$	−6.48936	+	19.9722i	−0.230299	+	0.708786i
$795$	−4.04508	+	2.93893i	−0.143464	+	0.104233i
$796$	12.9443	+	9.40456i	0.458798	+	0.333336i
$797$	−0.618034	−	1.90211i	−0.0218919	−	0.0673763i	0.939514	−	0.342511i	$-0.111277\pi$
$797$	−0.618034	−	1.90211i	−0.0218919	−	0.0673763i	−0.961406	+	0.275135i	$0.911277\pi$
$798$		0			0
$799$	−22.6525	−	16.4580i	−0.801387	−	0.582242i
$800$	3.23607	−	2.35114i	0.114412	−	0.0831254i
$801$	−5.25329	+	16.1680i	−0.185616	+	0.571267i
$802$	15.0000			0.529668
$803$		0			0
$804$	12.0000			0.423207
$805$		0			0
$806$	−32.3607	+	23.5114i	−1.13986	+	0.828154i
$807$	4.04508	+	2.93893i	0.142394	+	0.103455i
$808$	−3.09017	−	9.51057i	−0.108712	−	0.334581i
$809$	−11.7426	−	36.1401i	−0.412849	−	1.27062i	−0.914160	−	0.405353i	$-0.867149\pi$
$809$	−11.7426	−	36.1401i	−0.412849	−	1.27062i	0.501311	−	0.865267i	$-0.332851\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	−19.4164	+	14.1068i	−0.681802	+	0.495358i	−0.873955	−	0.486007i	$-0.838453\pi$
$811$	−19.4164	+	14.1068i	−0.681802	+	0.495358i	0.192153	+	0.981365i	$0.438453\pi$
$812$	8.65248	−	26.6296i	0.303642	−	0.934515i
$813$	−8.00000			−0.280572
$814$		0			0
$815$	−4.00000			−0.140114
$816$	2.16312	−	6.65740i	0.0757243	−	0.233055i
$817$		0			0
$818$	0.809017	+	0.587785i	0.0282866	+	0.0205514i
$819$	−6.18034	−	19.0211i	−0.215959	−	0.664652i
$820$	−3.39919	−	10.4616i	−0.118705	−	0.365336i
$821$	−17.7984	−	12.9313i	−0.621168	−	0.451305i	0.232162	−	0.972677i	$-0.425420\pi$
$821$	−17.7984	−	12.9313i	−0.621168	−	0.451305i	−0.853329	+	0.521373i	$0.825420\pi$
$822$	−8.09017	+	5.87785i	−0.282177	+	0.205014i
$823$	−7.41641	+	22.8254i	−0.258520	+	0.795642i	0.734596	+	0.678505i	$0.237372\pi$
$823$	−7.41641	+	22.8254i	−0.258520	+	0.795642i	−0.993116	+	0.117137i	$0.962628\pi$
$824$	4.00000			0.139347
$825$		0			0
$826$		0			0
$827$	3.70820	−	11.4127i	0.128947	−	0.396858i	−0.865653	−	0.500645i	$-0.833096\pi$
$827$	3.70820	−	11.4127i	0.128947	−	0.396858i	0.994600	+	0.103787i	$0.0330962\pi$
$828$		0			0
$829$	16.9894	+	12.3435i	0.590065	+	0.428707i	0.842339	−	0.538949i	$-0.181178\pi$
$829$	16.9894	+	12.3435i	0.590065	+	0.428707i	−0.252274	+	0.967656i	$0.581178\pi$
$830$	2.47214	+	7.60845i	0.0858091	+	0.264093i
$831$	7.10739	+	21.8743i	0.246553	+	0.758811i
$832$	4.04508	+	2.93893i	0.140238	+	0.101889i
$833$	−50.9681	+	37.0305i	−1.76594	+	1.28303i
$834$	−3.70820	+	11.4127i	−0.128405	+	0.395189i
$835$	−12.0000			−0.415277
$836$		0			0
$837$	−8.00000			−0.276520
$838$		0			0
$839$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$839$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$840$	3.23607	+	2.35114i	0.111655	+	0.0811221i
$841$	6.18034	+	19.0211i	0.213115	+	0.655901i
$842$	4.63525	+	14.2658i	0.159741	+	0.491634i
$843$	−8.09017	−	5.87785i	−0.278640	−	0.202444i
$844$		0			0
$845$	−3.70820	+	11.4127i	−0.127566	+	0.392608i
$846$	4.00000			0.137523
$847$		0			0
$848$	−5.00000			−0.171701
$849$	1.23607	−	3.80423i	0.0424217	−	0.130561i
$850$	22.6525	−	16.4580i	0.776974	−	0.564504i
$851$		0			0
$852$	−4.94427	−	15.2169i	−0.169388	−	0.521323i
$853$	−6.48936	−	19.9722i	−0.222191	−	0.683835i	−0.998565	−	0.0535612i	$-0.982943\pi$
$853$	−6.48936	−	19.9722i	−0.222191	−	0.683835i	0.776373	−	0.630273i	$-0.217057\pi$
$854$	6.47214	+	4.70228i	0.221472	+	0.160909i
$855$		0			0
$856$		0			0
$857$	26.0000			0.888143			0.444072	−	0.895991i	$-0.353534\pi$
$857$	26.0000			0.888143			0.444072	+	0.895991i	$0.353534\pi$
$858$		0			0
$859$	−56.0000			−1.91070			−0.955348	−	0.295484i	$-0.904519\pi$
$859$	−56.0000			−1.91070			−0.955348	+	0.295484i	$0.904519\pi$
$860$	2.47214	−	7.60845i	0.0842991	−	0.259446i
$861$	−35.5967	+	25.8626i	−1.21313	+	0.881393i
$862$	−16.1803	−	11.7557i	−0.551105	−	0.400401i
$863$	3.70820	+	11.4127i	0.126229	+	0.388492i	0.994123	−	0.108257i	$-0.0345269\pi$
$863$	3.70820	+	11.4127i	0.126229	+	0.388492i	−0.867894	+	0.496749i	$0.834527\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−14.5623	−	10.5801i	−0.495133	−	0.359735i
$866$	16.9894	−	12.3435i	0.577322	−	0.419449i
$867$	9.88854	−	30.4338i	0.335833	−	1.03359i
$868$	−32.0000			−1.08615
$869$		0			0
$870$	−7.00000			−0.237322
$871$	−18.5410	+	57.0634i	−0.628238	+	1.93352i
$872$	0.809017	−	0.587785i	0.0273968	−	0.0199049i
$873$	4.04508	+	2.93893i	0.136905	+	0.0994676i
$874$		0			0
$875$	11.1246	+	34.2380i	0.376081	+	1.15746i
$876$	4.85410	+	3.52671i	0.164005	+	0.119157i
$877$	4.04508	−	2.93893i	0.136593	−	0.0992405i	−0.517391	−	0.855749i	$-0.673097\pi$
$877$	4.04508	−	2.93893i	0.136593	−	0.0992405i	0.653983	+	0.756509i	$0.273097\pi$
$878$	4.94427	−	15.2169i	0.166861	−	0.513546i
$879$	23.0000			0.775771
$880$		0			0
$881$	19.0000			0.640126			0.320063	−	0.947396i	$-0.396296\pi$
$881$	19.0000			0.640126			0.320063	+	0.947396i	$0.396296\pi$
$882$	2.78115	−	8.55951i	0.0936463	−	0.288214i
$883$	22.6525	−	16.4580i	0.762317	−	0.553855i	−0.137303	−	0.990529i	$-0.543844\pi$
$883$	22.6525	−	16.4580i	0.762317	−	0.553855i	0.899620	+	0.436674i	$0.143844\pi$
$884$	28.3156	+	20.5725i	0.952357	+	0.691928i
$885$		0			0
$886$	11.1246	+	34.2380i	0.373739	+	1.15025i
$887$	−9.70820	−	7.05342i	−0.325970	−	0.236831i	0.412749	−	0.910845i	$-0.364569\pi$
$887$	−9.70820	−	7.05342i	−0.325970	−	0.236831i	−0.738718	+	0.674014i	$0.764569\pi$
$888$	4.04508	−	2.93893i	0.135744	−	0.0986239i
$889$	−4.94427	+	15.2169i	−0.165826	+	0.510359i
$890$	17.0000			0.569841
$891$		0			0
$892$	20.0000			0.669650
$893$		0			0
$894$	0.809017	−	0.587785i	0.0270576	−	0.0196585i
$895$	9.70820	+	7.05342i	0.324509	+	0.235770i
$896$	1.23607	+	3.80423i	0.0412941	+	0.127090i
$897$		0			0
$898$	−12.1353	−	8.81678i	−0.404959	−	0.294220i
$899$	45.3050	−	32.9160i	1.51100	−	1.09781i
$900$	−1.23607	+	3.80423i	−0.0412023	+	0.126808i
$901$	−35.0000			−1.16602
$902$		0			0
$903$	−32.0000			−1.06489
$904$	0.927051	−	2.85317i	0.0308333	−	0.0948950i
$905$	−0.809017	+	0.587785i	−0.0268926	+	0.0195386i
$906$	−16.1803	−	11.7557i	−0.537556	−	0.390557i
$907$	14.8328	+	45.6507i	0.492516	+	1.51581i	0.820793	+	0.571226i	$0.193532\pi$
$907$	14.8328	+	45.6507i	0.492516	+	1.51581i	−0.328277	+	0.944581i	$0.606468\pi$
$908$		0			0
$909$	8.09017	+	5.87785i	0.268334	+	0.194956i
$910$	−16.1803	+	11.7557i	−0.536373	+	0.389698i
$911$	6.18034	−	19.0211i	0.204764	−	0.630198i	−0.794959	−	0.606663i	$-0.792508\pi$
$911$	6.18034	−	19.0211i	0.204764	−	0.630198i	0.999723	−	0.0235353i	$-0.00749220\pi$
$912$		0			0
$913$		0			0
$914$	−17.0000			−0.562310
$915$	0.618034	−	1.90211i	0.0204316	−	0.0628819i
$916$	4.04508	−	2.93893i	0.133653	−	0.0971049i
$917$	38.8328	+	28.2137i	1.28237	+	0.931698i
$918$	2.16312	+	6.65740i	0.0713936	+	0.219727i
$919$	6.18034	+	19.0211i	0.203871	+	0.627449i	0.999758	+	0.0220044i	$0.00700477\pi$
$919$	6.18034	+	19.0211i	0.203871	+	0.627449i	−0.795887	+	0.605445i	$0.792995\pi$
$920$		0			0
$921$	−6.47214	+	4.70228i	−0.213264	+	0.154945i
$922$	−10.1976	+	31.3849i	−0.335839	+	1.03361i
$923$	80.0000			2.63323
$924$		0			0
$925$	20.0000			0.657596
$926$	−2.47214	+	7.60845i	−0.0812394	+	0.250029i
$927$	−3.23607	+	2.35114i	−0.106286	+	0.0772216i
$928$	−5.66312	−	4.11450i	−0.185901	−	0.135065i
$929$	−2.78115	−	8.55951i	−0.0912467	−	0.280828i	0.895011	−	0.446045i	$-0.147168\pi$
$929$	−2.78115	−	8.55951i	−0.0912467	−	0.280828i	−0.986257	+	0.165216i	$0.947168\pi$
$930$	2.47214	+	7.60845i	0.0810645	+	0.249491i
$931$		0			0
$932$	7.28115	−	5.29007i	0.238502	−	0.173282i
$933$	6.18034	−	19.0211i	0.202335	−	0.622724i
$934$	28.0000			0.916188
$935$		0			0
$936$	−5.00000			−0.163430
$937$	−16.3779	+	50.4060i	−0.535043	+	1.64669i	0.208514	+	0.978019i	$0.433137\pi$
$937$	−16.3779	+	50.4060i	−0.535043	+	1.64669i	−0.743557	+	0.668673i	$0.766863\pi$
$938$	−38.8328	+	28.2137i	−1.26794	+	0.921210i
$939$	7.28115	+	5.29007i	0.237611	+	0.172635i
$940$	−1.23607	−	3.80423i	−0.0403161	−	0.124080i
$941$	−10.1976	−	31.3849i	−0.332431	−	1.02312i	−0.967974	−	0.251052i	$-0.919224\pi$
$941$	−10.1976	−	31.3849i	−0.332431	−	1.02312i	0.635543	−	0.772066i	$-0.280776\pi$
$942$	14.5623	+	10.5801i	0.474466	+	0.344719i
$943$		0			0
$944$		0			0
$945$	−4.00000			−0.130120
$946$		0			0
$947$	52.0000			1.68977			0.844886	−	0.534946i	$-0.179668\pi$
$947$	52.0000			1.68977			0.844886	+	0.534946i	$0.179668\pi$
$948$	1.23607	−	3.80423i	0.0401456	−	0.123556i
$949$	−24.2705	+	17.6336i	−0.787854	+	0.572410i
$950$		0			0
$951$	−0.618034	−	1.90211i	−0.0200411	−	0.0616802i
$952$	8.65248	+	26.6296i	0.280428	+	0.863070i
$953$	−2.42705	−	1.76336i	−0.0786199	−	0.0571207i	0.547781	−	0.836622i	$-0.315473\pi$
$953$	−2.42705	−	1.76336i	−0.0786199	−	0.0571207i	−0.626401	+	0.779501i	$0.715473\pi$
$954$	4.04508	−	2.93893i	0.130964	−	0.0951513i
$955$	−1.23607	+	3.80423i	−0.0399982	+	0.123102i
$956$	4.00000			0.129369
$957$		0			0
$958$	4.00000			0.129234
$959$	12.3607	−	38.0423i	0.399147	−	1.22845i
$960$	0.809017	−	0.587785i	0.0261109	−	0.0189707i
$961$	−26.6976	−	19.3969i	−0.861212	−	0.625707i
$962$	7.72542	+	23.7764i	0.249078	+	0.766582i
$963$		0			0
$964$	−14.5623	−	10.5801i	−0.469020	−	0.340763i
$965$	8.89919	−	6.46564i	0.286475	−	0.208136i
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$		0			0
$969$		0			0
$970$	1.54508	−	4.75528i	0.0496097	−	0.152683i
$971$	−16.1803	+	11.7557i	−0.519252	+	0.377259i	−0.816322	−	0.577597i	$-0.803990\pi$
$971$	−16.1803	+	11.7557i	−0.519252	+	0.377259i	0.297070	+	0.954856i	$0.403990\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−14.8328	−	45.6507i	−0.475518	−	1.46349i
$974$	−6.18034	−	19.0211i	−0.198031	−	0.609476i
$975$	−16.1803	−	11.7557i	−0.518186	−	0.376484i
$976$	1.61803	−	1.17557i	0.0517920	−	0.0376291i
$977$	−15.1418	+	46.6018i	−0.484430	+	1.49092i	0.348374	+	0.937355i	$0.386734\pi$
$977$	−15.1418	+	46.6018i	−0.484430	+	1.49092i	−0.832805	+	0.553567i	$0.813266\pi$
$978$	4.00000			0.127906
$979$		0			0
$980$	−9.00000			−0.287494
$981$	−0.309017	+	0.951057i	−0.00986615	+	0.0303649i
$982$	9.70820	−	7.05342i	0.309801	−	0.225084i
$983$	22.6525	+	16.4580i	0.722502	+	0.524928i	0.887183	−	0.461419i	$-0.152659\pi$
$983$	22.6525	+	16.4580i	0.722502	+	0.524928i	−0.164681	+	0.986347i	$0.552659\pi$
$984$	3.39919	+	10.4616i	0.108362	+	0.333504i
$985$	2.78115	+	8.55951i	0.0886149	+	0.272729i
$986$	−39.6418	−	28.8015i	−1.26245	−	0.917226i
$987$	−12.9443	+	9.40456i	−0.412021	+	0.299351i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$	−2.47214	+	7.60845i	−0.0784904	+	0.241569i
$993$	−25.8885	+	18.8091i	−0.821548	+	0.596890i
$994$	51.7771	+	37.6183i	1.64227	+	1.19318i
$995$	4.94427	+	15.2169i	0.156744	+	0.482408i
$996$	−2.47214	−	7.60845i	−0.0783326	−	0.241083i
$997$	29.9336	+	21.7481i	0.948008	+	0.688768i	0.950335	−	0.311230i	$-0.100741\pi$
$997$	29.9336	+	21.7481i	0.948008	+	0.688768i	−0.00232725	+	0.999997i	$0.500741\pi$
$998$	−32.3607	+	23.5114i	−1.02436	+	0.744241i
$999$	−1.54508	+	4.75528i	−0.0488843	+	0.150450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.e.d.493.1		4
11.2	odd	10		726.2.e.l.487.1		4
11.3	even	5	inner	726.2.e.d.565.1		4
11.4	even	5		726.2.a.h.1.1	yes	1
11.5	even	5	inner	726.2.e.d.511.1		4
11.6	odd	10		726.2.e.l.511.1		4
11.7	odd	10		726.2.a.e.1.1	✓	1
11.8	odd	10		726.2.e.l.565.1		4
11.9	even	5	inner	726.2.e.d.487.1		4
11.10	odd	2		726.2.e.l.493.1		4
33.26	odd	10		2178.2.a.e.1.1		1
33.29	even	10		2178.2.a.j.1.1		1
44.7	even	10		5808.2.a.h.1.1		1
44.15	odd	10		5808.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
726.2.a.e.1.1	✓	1	11.7	odd	10
726.2.a.h.1.1	yes	1	11.4	even	5
726.2.e.d.487.1		4	11.9	even	5	inner
726.2.e.d.493.1		4	1.1	even	1	trivial
726.2.e.d.511.1		4	11.5	even	5	inner
726.2.e.d.565.1		4	11.3	even	5	inner
726.2.e.l.487.1		4	11.2	odd	10
726.2.e.l.493.1		4	11.10	odd	2
726.2.e.l.511.1		4	11.6	odd	10
726.2.e.l.565.1		4	11.8	odd	10
2178.2.a.e.1.1		1	33.26	odd	10
2178.2.a.j.1.1		1	33.29	even	10
5808.2.a.g.1.1		1	44.15	odd	10
5808.2.a.h.1.1		1	44.7	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-3.23607 - 2.35114i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} -1.00000 q^{10} +1.00000 q^{12} +(-1.54508 + 4.75528i) q^{13} +(-3.23607 + 2.35114i) q^{14} +(0.809017 + 0.587785i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.16312 + 6.65740i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-0.309017 + 0.951057i) q^{20} +4.00000 q^{21} +(0.309017 - 0.951057i) q^{24} +(3.23607 - 2.35114i) q^{25} +(4.04508 + 2.93893i) q^{26} +(0.309017 + 0.951057i) q^{27} +(1.23607 + 3.80423i) q^{28} +(-5.66312 - 4.11450i) q^{29} +(0.809017 - 0.587785i) q^{30} +(-2.47214 + 7.60845i) q^{31} +1.00000 q^{32} +7.00000 q^{34} +(-1.23607 + 3.80423i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(4.04508 + 2.93893i) q^{37} +(-1.54508 - 4.75528i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-8.89919 + 6.46564i) q^{41} +(1.23607 - 3.80423i) q^{42} -8.00000 q^{43} -1.00000 q^{45} +(-3.23607 + 2.35114i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(2.78115 + 8.55951i) q^{49} +(-1.23607 - 3.80423i) q^{50} +(-5.66312 - 4.11450i) q^{51} +(4.04508 - 2.93893i) q^{52} +(-1.54508 + 4.75528i) q^{53} +1.00000 q^{54} +4.00000 q^{56} +(-5.66312 + 4.11450i) q^{58} +(-0.309017 - 0.951057i) q^{60} +(-0.618034 - 1.90211i) q^{61} +(6.47214 + 4.70228i) q^{62} +(-3.23607 + 2.35114i) q^{63} +(0.309017 - 0.951057i) q^{64} +5.00000 q^{65} +12.0000 q^{67} +(2.16312 - 6.65740i) q^{68} +(3.23607 + 2.35114i) q^{70} +(-4.94427 - 15.2169i) q^{71} +(0.309017 + 0.951057i) q^{72} +(4.85410 + 3.52671i) q^{73} +(4.04508 - 2.93893i) q^{74} +(-1.23607 + 3.80423i) q^{75} -5.00000 q^{78} +(1.23607 - 3.80423i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.39919 + 10.4616i) q^{82} +(-2.47214 - 7.60845i) q^{83} +(-3.23607 - 2.35114i) q^{84} +(5.66312 - 4.11450i) q^{85} +(-2.47214 + 7.60845i) q^{86} +7.00000 q^{87} -17.0000 q^{89} +(-0.309017 + 0.951057i) q^{90} +(16.1803 - 11.7557i) q^{91} +(-2.47214 - 7.60845i) q^{93} +(1.23607 + 3.80423i) q^{94} +(-0.809017 + 0.587785i) q^{96} +(-1.54508 + 4.75528i) q^{97} +9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 4 q^{7} - q^{8} - q^{9} - 4 q^{10} + 4 q^{12} + 5 q^{13} - 4 q^{14} + q^{15} - q^{16} - 7 q^{17} - q^{18} + q^{20} + 16 q^{21} - q^{24} + 4 q^{25}+ \cdots + 36 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^3 - q^4 + q^5 - q^6 - 4 * q^7 - q^8 - q^9 - 4 * q^10 + 4 * q^12 + 5 * q^13 - 4 * q^14 + q^15 - q^16 - 7 * q^17 - q^18 + q^20 + 16 * q^21 - q^24 + 4 * q^25 + 5 * q^26 - q^27 - 4 * q^28 - 7 * q^29 + q^30 + 8 * q^31 + 4 * q^32 + 28 * q^34 + 4 * q^35 - q^36 + 5 * q^37 + 5 * q^39 + q^40 - 11 * q^41 - 4 * q^42 - 32 * q^43 - 4 * q^45 - 4 * q^47 - q^48 - 9 * q^49 + 4 * q^50 - 7 * q^51 + 5 * q^52 + 5 * q^53 + 4 * q^54 + 16 * q^56 - 7 * q^58 + q^60 + 2 * q^61 + 8 * q^62 - 4 * q^63 - q^64 + 20 * q^65 + 48 * q^67 - 7 * q^68 + 4 * q^70 + 16 * q^71 - q^72 + 6 * q^73 + 5 * q^74 + 4 * q^75 - 20 * q^78 - 4 * q^79 + q^80 - q^81 - 11 * q^82 + 8 * q^83 - 4 * q^84 + 7 * q^85 + 8 * q^86 + 28 * q^87 - 68 * q^89 + q^90 + 20 * q^91 + 8 * q^93 - 4 * q^94 - q^96 + 5 * q^97 + 36 * q^98

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