LMFDB - Embedded newform 552.2.f.d.277.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 2x^17 + x^16 - 4x^15 + 16x^14 - 24x^13 + 32x^12 - 16x^11 - 16x^10 - 32x^9 + 128x^8 - 192x^7 + 256x^6 - 128x^5 + 64x^4 - 256x^3 + 512x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.19
Root			$-1.34141 + 0.447910i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.d.277.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34141 - 0.447910i) q^{2} +1.00000i q^{3} +(1.59875 - 1.20166i) q^{4} -1.69969i q^{5} +(0.447910 + 1.34141i) q^{6} +2.41449 q^{7} +(1.60635 - 2.32801i) q^{8} -1.00000 q^{9} +(-0.761306 - 2.27997i) q^{10} +0.133083i q^{11} +(1.20166 + 1.59875i) q^{12} -0.529878i q^{13} +(3.23881 - 1.08147i) q^{14} +1.69969 q^{15} +(1.11203 - 3.84232i) q^{16} -3.72410 q^{17} +(-1.34141 + 0.447910i) q^{18} +1.26626i q^{19} +(-2.04245 - 2.71738i) q^{20} +2.41449i q^{21} +(0.0596093 + 0.178519i) q^{22} +1.00000 q^{23} +(2.32801 + 1.60635i) q^{24} +2.11106 q^{25} +(-0.237337 - 0.710782i) q^{26} -1.00000i q^{27} +(3.86017 - 2.90139i) q^{28} +2.58119i q^{29} +(2.27997 - 0.761306i) q^{30} +4.37283 q^{31} +(-0.229326 - 5.65220i) q^{32} -0.133083 q^{33} +(-4.99554 + 1.66806i) q^{34} -4.10387i q^{35} +(-1.59875 + 1.20166i) q^{36} +3.36341i q^{37} +(0.567169 + 1.69857i) q^{38} +0.529878 q^{39} +(-3.95689 - 2.73029i) q^{40} -5.68297 q^{41} +(1.08147 + 3.23881i) q^{42} +2.62040i q^{43} +(0.159921 + 0.212767i) q^{44} +1.69969i q^{45} +(1.34141 - 0.447910i) q^{46} -0.552068 q^{47} +(3.84232 + 1.11203i) q^{48} -1.17025 q^{49} +(2.83180 - 0.945566i) q^{50} -3.72410i q^{51} +(-0.636732 - 0.847144i) q^{52} +10.6278i q^{53} +(-0.447910 - 1.34141i) q^{54} +0.226200 q^{55} +(3.87851 - 5.62096i) q^{56} -1.26626 q^{57} +(1.15614 + 3.46243i) q^{58} -3.59762i q^{59} +(2.71738 - 2.04245i) q^{60} +6.75147i q^{61} +(5.86575 - 1.95863i) q^{62} -2.41449 q^{63} +(-2.83930 - 7.47920i) q^{64} -0.900626 q^{65} +(-0.178519 + 0.0596093i) q^{66} +0.405445i q^{67} +(-5.95392 + 4.47510i) q^{68} +1.00000i q^{69} +(-1.83816 - 5.50497i) q^{70} -5.62993 q^{71} +(-1.60635 + 2.32801i) q^{72} -8.66291 q^{73} +(1.50651 + 4.51171i) q^{74} +2.11106i q^{75} +(1.52161 + 2.02444i) q^{76} +0.321328i q^{77} +(0.710782 - 0.237337i) q^{78} -2.77706 q^{79} +(-6.53073 - 1.89010i) q^{80} +1.00000 q^{81} +(-7.62318 + 2.54546i) q^{82} +1.80097i q^{83} +(2.90139 + 3.86017i) q^{84} +6.32980i q^{85} +(1.17370 + 3.51502i) q^{86} -2.58119 q^{87} +(0.309820 + 0.213778i) q^{88} -14.1306 q^{89} +(0.761306 + 2.27997i) q^{90} -1.27938i q^{91} +(1.59875 - 1.20166i) q^{92} +4.37283i q^{93} +(-0.740549 + 0.247277i) q^{94} +2.15224 q^{95} +(5.65220 - 0.229326i) q^{96} +5.11325 q^{97} +(-1.56978 + 0.524166i) q^{98} -0.133083i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32}+ \cdots - 26 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	1.34141	−	0.447910i	0.948519	−	0.316720i
$2$	1.34141	−	0.447910i	0.948519	−	0.316720i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.59875	−	1.20166i	0.799377	−	0.600830i
$5$		−	1.69969i		−	0.760123i	−0.924961	−	0.380062i	$-0.875903\pi$
$5$		−	1.69969i		−	0.760123i	0.924961	−	0.380062i	$-0.124097\pi$
$6$	0.447910	+	1.34141i	0.182858	+	0.547628i
$7$	2.41449			0.912591			0.456295	−	0.889828i	$-0.349176\pi$
$7$	2.41449			0.912591			0.456295	+	0.889828i	$0.349176\pi$
$8$	1.60635	−	2.32801i	0.567930	−	0.823077i
$9$	−1.00000			−0.333333
$10$	−0.761306	−	2.27997i	−0.240746	−	0.720991i
$11$			0.133083i			0.0401261i	0.999799	+	0.0200631i	$0.00638670\pi$
$11$			0.133083i			0.0401261i	−0.999799	+	0.0200631i	$0.993613\pi$
$12$	1.20166	+	1.59875i	0.346889	+	0.461521i
$13$		−	0.529878i		−	0.146962i	−0.997297	−	0.0734808i	$-0.976589\pi$
$13$		−	0.529878i		−	0.146962i	0.997297	−	0.0734808i	$-0.0234108\pi$
$14$	3.23881	−	1.08147i	0.865610	−	0.289036i
$15$	1.69969			0.438857
$16$	1.11203	−	3.84232i	0.278007	−	0.960579i
$17$	−3.72410			−0.903226			−0.451613	−	0.892214i	$-0.649151\pi$
$17$	−3.72410			−0.903226			−0.451613	+	0.892214i	$0.649151\pi$
$18$	−1.34141	+	0.447910i	−0.316173	+	0.105573i
$19$			1.26626i			0.290500i	0.989395	+	0.145250i	$0.0463986\pi$
$19$			1.26626i			0.290500i	−0.989395	+	0.145250i	$0.953601\pi$
$20$	−2.04245	−	2.71738i	−0.456705	−	0.607625i
$21$			2.41449i			0.526884i
$22$	0.0596093	+	0.178519i	0.0127087	+	0.0380604i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	2.32801	+	1.60635i	0.475204	+	0.327894i
$25$	2.11106			0.422213
$26$	−0.237337	−	0.710782i	−0.0465457	−	0.139396i
$27$		−	1.00000i		−	0.192450i
$28$	3.86017	−	2.90139i	0.729504	−	0.548312i
$29$			2.58119i			0.479314i	0.970858	+	0.239657i	$0.0770350\pi$
$29$			2.58119i			0.479314i	−0.970858	+	0.239657i	$0.922965\pi$
$30$	2.27997	−	0.761306i	0.416265	−	0.138995i
$31$	4.37283			0.785383			0.392691	−	0.919670i	$-0.371544\pi$
$31$	4.37283			0.785383			0.392691	+	0.919670i	$0.371544\pi$
$32$	−0.229326	−	5.65220i	−0.0405395	−	0.999178i
$33$	−0.133083			−0.0231668
$34$	−4.99554	+	1.66806i	−0.856728	+	0.286070i
$35$		−	4.10387i		−	0.693681i
$36$	−1.59875	+	1.20166i	−0.266459	+	0.200277i
$37$			3.36341i			0.552942i	0.961022	+	0.276471i	$0.0891650\pi$
$37$			3.36341i			0.552942i	−0.961022	+	0.276471i	$0.910835\pi$
$38$	0.567169	+	1.69857i	0.0920070	+	0.275544i
$39$	0.529878			0.0848483
$40$	−3.95689	−	2.73029i	−0.625640	−	0.431696i
$41$	−5.68297			−0.887530			−0.443765	−	0.896143i	$-0.646358\pi$
$41$	−5.68297			−0.887530			−0.443765	+	0.896143i	$0.646358\pi$
$42$	1.08147	+	3.23881i	0.166875	+	0.499760i
$43$			2.62040i			0.399607i	0.979836	+	0.199803i	$0.0640303\pi$
$43$			2.62040i			0.399607i	−0.979836	+	0.199803i	$0.935970\pi$
$44$	0.159921	+	0.212767i	0.0241090	+	0.0320759i
$45$			1.69969i			0.253374i
$46$	1.34141	−	0.447910i	0.197780	−	0.0660407i
$47$	−0.552068			−0.0805274			−0.0402637	−	0.999189i	$-0.512820\pi$
$47$	−0.552068			−0.0805274			−0.0402637	+	0.999189i	$0.512820\pi$
$48$	3.84232	+	1.11203i	0.554591	+	0.160507i
$49$	−1.17025			−0.167178
$50$	2.83180	−	0.945566i	0.400477	−	0.133723i
$51$		−	3.72410i		−	0.521478i
$52$	−0.636732	−	0.847144i	−0.0882989	−	0.117478i
$53$			10.6278i			1.45984i	0.683531	+	0.729922i	$0.260444\pi$
$53$			10.6278i			1.45984i	−0.683531	+	0.729922i	$0.739556\pi$
$54$	−0.447910	−	1.34141i	−0.0609528	−	0.182543i
$55$	0.226200			0.0305008
$56$	3.87851	−	5.62096i	0.518287	−	0.751132i
$57$	−1.26626			−0.167720
$58$	1.15614	+	3.46243i	0.151808	+	0.454639i
$59$		−	3.59762i		−	0.468370i	−0.972192	−	0.234185i	$-0.924758\pi$
$59$		−	3.59762i		−	0.468370i	0.972192	−	0.234185i	$-0.0752422\pi$
$60$	2.71738	−	2.04245i	0.350812	−	0.263679i
$61$			6.75147i			0.864437i	0.901769	+	0.432218i	$0.142269\pi$
$61$			6.75147i			0.864437i	−0.901769	+	0.432218i	$0.857731\pi$
$62$	5.86575	−	1.95863i	0.744950	−	0.248746i
$63$	−2.41449			−0.304197
$64$	−2.83930	−	7.47920i	−0.354912	−	0.934900i
$65$	−0.900626			−0.111709
$66$	−0.178519	+	0.0596093i	−0.0219742	+	0.00733740i
$67$			0.405445i			0.0495329i	0.999693	+	0.0247665i	$0.00788422\pi$
$67$			0.405445i			0.0495329i	−0.999693	+	0.0247665i	$0.992116\pi$
$68$	−5.95392	+	4.47510i	−0.722018	+	0.542685i
$69$			1.00000i			0.120386i
$70$	−1.83816	−	5.50497i	−0.219703	−	0.657970i
$71$	−5.62993			−0.668149			−0.334075	−	0.942547i	$-0.608424\pi$
$71$	−5.62993			−0.668149			−0.334075	+	0.942547i	$0.608424\pi$
$72$	−1.60635	+	2.32801i	−0.189310	+	0.274359i
$73$	−8.66291			−1.01392			−0.506959	−	0.861970i	$-0.669230\pi$
$73$	−8.66291			−1.01392			−0.506959	+	0.861970i	$0.669230\pi$
$74$	1.50651	+	4.51171i	0.175128	+	0.524476i
$75$			2.11106i			0.243765i
$76$	1.52161	+	2.02444i	0.174541	+	0.232219i
$77$			0.321328i			0.0366187i
$78$	0.710782	−	0.237337i	0.0804803	−	0.0268732i
$79$	−2.77706			−0.312444			−0.156222	−	0.987722i	$-0.549931\pi$
$79$	−2.77706			−0.312444			−0.156222	+	0.987722i	$0.549931\pi$
$80$	−6.53073	−	1.89010i	−0.730158	−	0.211320i
$81$	1.00000			0.111111
$82$	−7.62318	+	2.54546i	−0.841839	+	0.281099i
$83$			1.80097i			0.197682i	0.995103	+	0.0988412i	$0.0315136\pi$
$83$			1.80097i			0.197682i	−0.995103	+	0.0988412i	$0.968486\pi$
$84$	2.90139	+	3.86017i	0.316568	+	0.421179i
$85$			6.32980i			0.686563i
$86$	1.17370	+	3.51502i	0.126563	+	0.379035i
$87$	−2.58119			−0.276732
$88$	0.309820	+	0.213778i	0.0330269	+	0.0227888i
$89$	−14.1306			−1.49784			−0.748921	−	0.662659i	$-0.769428\pi$
$89$	−14.1306			−1.49784			−0.748921	+	0.662659i	$0.769428\pi$
$90$	0.761306	+	2.27997i	0.0802487	+	0.240330i
$91$		−	1.27938i		−	0.134116i
$92$	1.59875	−	1.20166i	0.166682	−	0.125282i
$93$			4.37283i			0.453441i
$94$	−0.740549	+	0.247277i	−0.0763818	+	0.0255046i
$95$	2.15224			0.220815
$96$	5.65220	−	0.229326i	0.576876	−	0.0234055i
$97$	5.11325			0.519172			0.259586	−	0.965720i	$-0.416414\pi$
$97$	5.11325			0.519172			0.259586	+	0.965720i	$0.416414\pi$
$98$	−1.56978	+	0.524166i	−0.158572	+	0.0529487i
$99$		−	0.133083i		−	0.0133754i
$100$	3.37507	−	2.53678i	0.337507	−	0.253678i
$101$			3.26595i			0.324974i	0.986711	+	0.162487i	$0.0519515\pi$
$101$			3.26595i			0.324974i	−0.986711	+	0.162487i	$0.948048\pi$
$102$	−1.66806	−	4.99554i	−0.165162	−	0.494632i
$103$	−12.0290			−1.18525			−0.592624	−	0.805479i	$-0.701908\pi$
$103$	−12.0290			−1.18525			−0.592624	+	0.805479i	$0.701908\pi$
$104$	−1.23356	−	0.851167i	−0.120961	−	0.0834638i
$105$	4.10387			0.400497
$106$	4.76030	+	14.2563i	0.462362	+	1.38469i
$107$		−	18.5502i		−	1.79332i	−0.442724	−	0.896658i	$-0.645988\pi$
$107$		−	18.5502i		−	1.79332i	0.442724	−	0.896658i	$-0.354012\pi$
$108$	−1.20166	−	1.59875i	−0.115630	−	0.153840i
$109$			6.35506i			0.608704i	0.952560	+	0.304352i	$0.0984400\pi$
$109$			6.35506i			0.608704i	−0.952560	+	0.304352i	$0.901560\pi$
$110$	0.303427	−	0.101317i	0.0289306	−	0.00966021i
$111$	−3.36341			−0.319241
$112$	2.68498	−	9.27723i	0.253707	−	0.876615i
$113$	−3.48804			−0.328127			−0.164063	−	0.986450i	$-0.552460\pi$
$113$	−3.48804			−0.328127			−0.164063	+	0.986450i	$0.552460\pi$
$114$	−1.69857	+	0.567169i	−0.159086	+	0.0531203i
$115$		−	1.69969i		−	0.158497i
$116$	3.10171	+	4.12668i	0.287986	+	0.383153i
$117$			0.529878i			0.0489872i
$118$	−1.61141	−	4.82588i	−0.148342	−	0.444258i
$119$	−8.99179			−0.824276
$120$	2.73029	−	3.95689i	0.249240	−	0.361213i
$121$	10.9823			0.998390
$122$	3.02405	+	9.05647i	0.273784	+	0.819935i
$123$		−	5.68297i		−	0.512416i
$124$	6.99107	−	5.25465i	0.627817	−	0.471881i
$125$		−	12.0866i		−	1.08106i
$126$	−3.23881	+	1.08147i	−0.288537	+	0.0963452i
$127$	9.10511			0.807948			0.403974	−	0.914770i	$-0.367629\pi$
$127$	9.10511			0.807948			0.403974	+	0.914770i	$0.367629\pi$
$128$	−7.15866	−	8.76091i	−0.632742	−	0.774363i
$129$	−2.62040			−0.230713
$130$	−1.20811	+	0.403399i	−0.105958	+	0.0353804i
$131$			0.553501i			0.0483596i	0.999708	+	0.0241798i	$0.00769742\pi$
$131$			0.553501i			0.0483596i	−0.999708	+	0.0241798i	$0.992303\pi$
$132$	−0.212767	+	0.159921i	−0.0185190	+	0.0139193i
$133$			3.05736i			0.265107i
$134$	0.181603	+	0.543867i	0.0156881	+	0.0469829i
$135$	−1.69969			−0.146286
$136$	−5.98220	+	8.66975i	−0.512969	+	0.743425i
$137$	−12.3118			−1.05187			−0.525933	−	0.850526i	$-0.676284\pi$
$137$	−12.3118			−1.05187			−0.525933	+	0.850526i	$0.676284\pi$
$138$	0.447910	+	1.34141i	0.0381286	+	0.114188i
$139$		−	6.84557i		−	0.580633i	−0.956931	−	0.290317i	$-0.906239\pi$
$139$		−	6.84557i		−	0.580633i	0.956931	−	0.290317i	$-0.0937607\pi$
$140$	−4.93146	−	6.56108i	−0.416784	−	0.554513i
$141$		−	0.552068i		−	0.0464925i
$142$	−7.55203	+	2.52170i	−0.633752	+	0.211616i
$143$	0.0705179			0.00589700
$144$	−1.11203	+	3.84232i	−0.0926690	+	0.320193i
$145$	4.38721			0.364338
$146$	−11.6205	+	3.88020i	−0.961720	+	0.321128i
$147$		−	1.17025i		−	0.0965205i
$148$	4.04168	+	5.37727i	0.332224	+	0.442009i
$149$			8.52131i			0.698093i	0.937105	+	0.349046i	$0.113494\pi$
$149$			8.52131i			0.698093i	−0.937105	+	0.349046i	$0.886506\pi$
$150$	0.945566	+	2.83180i	0.0772051	+	0.231215i
$151$	3.58823			0.292006			0.146003	−	0.989284i	$-0.453359\pi$
$151$	3.58823			0.292006			0.146003	+	0.989284i	$0.453359\pi$
$152$	2.94787	+	2.03405i	0.239104	+	0.164983i
$153$	3.72410			0.301075
$154$	0.143926	+	0.431032i	0.0115979	+	0.0347336i
$155$		−	7.43243i		−	0.596987i
$156$	0.847144	−	0.636732i	0.0678258	−	0.0509794i
$157$			5.46190i			0.435907i	0.975959	+	0.217953i	$0.0699381\pi$
$157$			5.46190i			0.435907i	−0.975959	+	0.217953i	$0.930062\pi$
$158$	−3.72517	+	1.24387i	−0.296359	+	0.0989572i
$159$	−10.6278			−0.842841
$160$	−9.60698	+	0.389782i	−0.759498	+	0.0308150i
$161$	2.41449			0.190288
$162$	1.34141	−	0.447910i	0.105391	−	0.0351911i
$163$			20.4988i			1.60559i	0.596253	+	0.802797i	$0.296656\pi$
$163$			20.4988i			1.60559i	−0.596253	+	0.802797i	$0.703344\pi$
$164$	−9.08566	+	6.82899i	−0.709471	+	0.533255i
$165$			0.226200i			0.0176096i
$166$	0.806673	+	2.41584i	0.0626100	+	0.187506i
$167$	22.8294			1.76659			0.883295	−	0.468817i	$-0.155320\pi$
$167$	22.8294			1.76659			0.883295	+	0.468817i	$0.155320\pi$
$168$	5.62096	+	3.87851i	0.433667	+	0.299233i
$169$	12.7192			0.978402
$170$	2.83518	+	8.49085i	0.217448	+	0.651218i
$171$		−	1.26626i		−	0.0968332i
$172$	3.14882	+	4.18937i	0.240096	+	0.319436i
$173$		−	23.7819i		−	1.80810i	−0.427423	−	0.904052i	$-0.640578\pi$
$173$		−	23.7819i		−	1.80810i	0.427423	−	0.904052i	$-0.359422\pi$
$174$	−3.46243	+	1.15614i	−0.262486	+	0.0876466i
$175$	5.09714			0.385307
$176$	0.511348	+	0.147992i	0.0385443	+	0.0111553i
$177$	3.59762			0.270414
$178$	−18.9549	+	6.32924i	−1.42073	+	0.474396i
$179$			5.89695i			0.440758i	0.975414	+	0.220379i	$0.0707295\pi$
$179$			5.89695i			0.440758i	−0.975414	+	0.220379i	$0.929271\pi$
$180$	2.04245	+	2.71738i	0.152235	+	0.202542i
$181$			20.1013i			1.49412i	0.664757	+	0.747060i	$0.268535\pi$
$181$			20.1013i			1.49412i	−0.664757	+	0.747060i	$0.731465\pi$
$182$	−0.573048	−	1.71618i	−0.0424771	−	0.127211i
$183$	−6.75147			−0.499083
$184$	1.60635	−	2.32801i	0.118421	−	0.171623i
$185$	5.71675			0.420304
$186$	1.95863	+	5.86575i	0.143614	+	0.430097i
$187$		−	0.495615i		−	0.0362430i
$188$	−0.882621	+	0.663398i	−0.0643718	+	0.0483833i
$189$		−	2.41449i		−	0.175628i
$190$	2.88704	−	0.964010i	0.209448	−	0.0699366i
$191$	24.9549			1.80568			0.902838	−	0.429981i	$-0.141480\pi$
$191$	24.9549			1.80568			0.902838	+	0.429981i	$0.141480\pi$
$192$	7.47920	−	2.83930i	0.539765	−	0.204909i
$193$	25.4125			1.82923			0.914617	−	0.404322i	$-0.132493\pi$
$193$	25.4125			1.82923			0.914617	+	0.404322i	$0.132493\pi$
$194$	6.85896	−	2.29028i	0.492445	−	0.164432i
$195$		−	0.900626i		−	0.0644952i
$196$	−1.87094	+	1.40624i	−0.133639	+	0.100446i
$197$		−	16.1816i		−	1.15289i	−0.817137	−	0.576444i	$-0.804440\pi$
$197$		−	16.1816i		−	1.15289i	0.817137	−	0.576444i	$-0.195560\pi$
$198$	−0.0596093	−	0.178519i	−0.00423625	−	0.0126868i
$199$	−3.13607			−0.222310			−0.111155	−	0.993803i	$-0.535455\pi$
$199$	−3.13607			−0.222310			−0.111155	+	0.993803i	$0.535455\pi$
$200$	3.39110	−	4.91459i	0.239787	−	0.347514i
$201$	−0.405445			−0.0285979
$202$	1.46285	+	4.38097i	0.102926	+	0.308244i
$203$			6.23224i			0.437418i
$204$	−4.47510	−	5.95392i	−0.313320	−	0.416858i
$205$			9.65926i			0.674632i
$206$	−16.1358	+	5.38789i	−1.12423	+	0.375392i
$207$	−1.00000			−0.0695048
$208$	−2.03596	−	0.589239i	−0.141168	−	0.0408564i
$209$	−0.168518			−0.0116566
$210$	5.50497	−	1.83816i	0.379879	−	0.126845i
$211$		−	15.2931i		−	1.05282i	−0.850231	−	0.526410i	$-0.823538\pi$
$211$		−	15.2931i		−	1.05282i	0.850231	−	0.526410i	$-0.176462\pi$
$212$	12.7710	+	16.9913i	0.877117	+	1.16697i
$213$		−	5.62993i		−	0.385756i
$214$	−8.30882	−	24.8834i	−0.567979	−	1.70099i
$215$	4.45385			0.303750
$216$	−2.32801	−	1.60635i	−0.158401	−	0.109298i
$217$	10.5581			0.716733
$218$	2.84649	+	8.52473i	0.192789	+	0.577368i
$219$		−	8.66291i		−	0.585385i
$220$	0.361638	−	0.271815i	0.0243816	−	0.0183258i
$221$			1.97332i			0.132740i
$222$	−4.51171	+	1.50651i	−0.302806	+	0.101110i
$223$	0.888570			0.0595030			0.0297515	−	0.999557i	$-0.490528\pi$
$223$	0.888570			0.0595030			0.0297515	+	0.999557i	$0.490528\pi$
$224$	−0.553705	−	13.6472i	−0.0369959	−	0.911840i
$225$	−2.11106			−0.140738
$226$	−4.67888	+	1.56232i	−0.311234	+	0.103924i
$227$			11.0383i			0.732636i	0.930490	+	0.366318i	$0.119382\pi$
$227$			11.0383i			0.732636i	−0.930490	+	0.366318i	$0.880618\pi$
$228$	−2.02444	+	1.52161i	−0.134071	+	0.100771i
$229$		−	13.7109i		−	0.906040i	−0.891500	−	0.453020i	$-0.850347\pi$
$229$		−	13.7109i		−	0.906040i	0.891500	−	0.453020i	$-0.149653\pi$
$230$	−0.761306	−	2.27997i	−0.0501990	−	0.150337i
$231$	−0.321328			−0.0211418
$232$	6.00904	+	4.14628i	0.394513	+	0.272217i
$233$	−22.0260			−1.44297			−0.721487	−	0.692428i	$-0.756541\pi$
$233$	−22.0260			−1.44297			−0.721487	+	0.692428i	$0.756541\pi$
$234$	0.237337	+	0.710782i	0.0155152	+	0.0464653i
$235$			0.938343i			0.0612108i
$236$	−4.32311	−	5.75171i	−0.281411	−	0.374404i
$237$		−	2.77706i		−	0.180390i
$238$	−12.0617	+	4.02751i	−0.781841	+	0.261065i
$239$	14.9020			0.963931			0.481966	−	0.876190i	$-0.339923\pi$
$239$	14.9020			0.963931			0.481966	+	0.876190i	$0.339923\pi$
$240$	1.89010	−	6.53073i	0.122005	−	0.421557i
$241$	−14.6875			−0.946104			−0.473052	−	0.881035i	$-0.656848\pi$
$241$	−14.6875			−0.946104			−0.473052	+	0.881035i	$0.656848\pi$
$242$	14.7317	−	4.91907i	0.946992	−	0.316210i
$243$			1.00000i			0.0641500i
$244$	8.11296	+	10.7939i	0.519379	+	0.691011i
$245$			1.98906i			0.127076i
$246$	−2.54546	−	7.62318i	−0.162292	−	0.486036i
$247$	0.670962			0.0426923
$248$	7.02428	−	10.1800i	0.446042	−	0.646430i
$249$	−1.80097			−0.114132
$250$	−5.41370	−	16.2130i	−0.342392	−	1.02540i
$251$		−	16.1350i		−	1.01843i	−0.860638	−	0.509217i	$-0.829935\pi$
$251$		−	16.1350i		−	1.01843i	0.860638	−	0.509217i	$-0.170065\pi$
$252$	−3.86017	+	2.90139i	−0.243168	+	0.182771i
$253$			0.133083i			0.00836687i
$254$	12.2137	−	4.07827i	0.766354	−	0.255893i
$255$	−6.32980			−0.396388
$256$	−13.5268	−	8.54553i	−0.845424	−	0.534096i
$257$	−10.1862			−0.635399			−0.317700	−	0.948191i	$-0.602910\pi$
$257$	−10.1862			−0.635399			−0.317700	+	0.948191i	$0.602910\pi$
$258$	−3.51502	+	1.17370i	−0.218836	+	0.0730714i
$259$			8.12092i			0.504610i
$260$	−1.43988	+	1.08225i	−0.0892975	+	0.0671180i
$261$		−	2.58119i		−	0.159771i
$262$	0.247919	+	0.742471i	0.0153165	+	0.0458700i
$263$	−3.10560			−0.191499			−0.0957496	−	0.995405i	$-0.530525\pi$
$263$	−3.10560			−0.191499			−0.0957496	+	0.995405i	$0.530525\pi$
$264$	−0.213778	+	0.309820i	−0.0131571	+	0.0190681i
$265$	18.0640			1.10966
$266$	1.36942	+	4.10118i	0.0839647	+	0.251459i
$267$		−	14.1306i		−	0.864779i
$268$	0.487206	+	0.648206i	0.0297609	+	0.0395955i
$269$		−	3.56163i		−	0.217156i	−0.994088	−	0.108578i	$-0.965370\pi$
$269$		−	3.56163i		−	0.217156i	0.994088	−	0.108578i	$-0.0346297\pi$
$270$	−2.27997	+	0.761306i	−0.138755	+	0.0463316i
$271$	19.2112			1.16700			0.583498	−	0.812115i	$-0.301684\pi$
$271$	19.2112			1.16700			0.583498	+	0.812115i	$0.301684\pi$
$272$	−4.14130	+	14.3092i	−0.251103	+	0.867620i
$273$	1.27938			0.0774318
$274$	−16.5151	+	5.51456i	−0.997715	+	0.333147i
$275$			0.280947i			0.0169418i
$276$	1.20166	+	1.59875i	0.0723314	+	0.0962337i
$277$		−	4.58461i		−	0.275463i	−0.990470	−	0.137731i	$-0.956019\pi$
$277$		−	4.58461i		−	0.275463i	0.990470	−	0.137731i	$-0.0439811\pi$
$278$	−3.06620	−	9.18270i	−0.183898	−	0.550742i
$279$	−4.37283			−0.261794
$280$	−9.55387	−	6.59225i	−0.570953	−	0.393962i
$281$	−8.02427			−0.478688			−0.239344	−	0.970935i	$-0.576932\pi$
$281$	−8.02427			−0.478688			−0.239344	+	0.970935i	$0.576932\pi$
$282$	−0.247277	−	0.740549i	−0.0147251	−	0.0440991i
$283$		−	24.9437i		−	1.48275i	−0.671090	−	0.741375i	$-0.734174\pi$
$283$		−	24.9437i		−	1.48275i	0.671090	−	0.741375i	$-0.265826\pi$
$284$	−9.00087	+	6.76525i	−0.534103	+	0.401444i
$285$			2.15224i			0.127488i
$286$	0.0945933	−	0.0315856i	0.00559342	−	0.00186770i
$287$	−13.7215			−0.809952
$288$	0.229326	+	5.65220i	0.0135132	+	0.333059i
$289$	−3.13109			−0.184182
$290$	5.88504	−	1.96507i	0.345581	−	0.115393i
$291$			5.11325i			0.299744i
$292$	−13.8499	+	10.4099i	−0.810502	+	0.609192i
$293$			0.0719030i			0.00420062i	0.999998	+	0.00210031i	$0.000668550\pi$
$293$			0.0719030i			0.00420062i	−0.999998	+	0.00210031i	$0.999331\pi$
$294$	−0.524166	−	1.56978i	−0.0305700	−	0.0915515i
$295$	−6.11483			−0.356019
$296$	7.83007	+	5.40281i	0.455114	+	0.314032i
$297$	0.133083			0.00772228
$298$	3.81678	+	11.4306i	0.221100	+	0.662154i
$299$		−	0.529878i		−	0.0306436i
$300$	2.53678	+	3.37507i	0.146461	+	0.194860i
$301$			6.32691i			0.364677i
$302$	4.81328	−	1.60720i	0.276973	−	0.0924841i
$303$	−3.26595			−0.187624
$304$	4.86536	+	1.40811i	0.279048	+	0.0807609i
$305$	11.4754			0.657078
$306$	4.99554	−	1.66806i	0.285576	−	0.0953566i
$307$		−	1.58805i		−	0.0906350i	−0.998973	−	0.0453175i	$-0.985570\pi$
$307$		−	1.58805i		−	0.0906350i	0.998973	−	0.0453175i	$-0.0144299\pi$
$308$	0.386127	+	0.513724i	0.0220016	+	0.0292722i
$309$		−	12.0290i		−	0.684304i
$310$	−3.32906	−	9.96993i	−0.189078	−	0.566254i
$311$	19.9240			1.12979			0.564893	−	0.825164i	$-0.308917\pi$
$311$	19.9240			1.12979			0.564893	+	0.825164i	$0.308917\pi$
$312$	0.851167	−	1.23356i	0.0481879	−	0.0698367i
$313$	−27.8661			−1.57509			−0.787543	−	0.616260i	$-0.788647\pi$
$313$	−27.8661			−1.57509			−0.787543	+	0.616260i	$0.788647\pi$
$314$	2.44644	+	7.32664i	0.138060	+	0.413466i
$315$			4.10387i			0.231227i
$316$	−4.43984	+	3.33708i	−0.249760	+	0.187726i
$317$		−	20.1696i		−	1.13284i	−0.824118	−	0.566418i	$-0.808329\pi$
$317$		−	20.1696i		−	1.13284i	0.824118	−	0.566418i	$-0.191671\pi$
$318$	−14.2563	+	4.76030i	−0.799451	+	0.266945i
$319$	−0.343513			−0.0192330
$320$	−12.7123	+	4.82591i	−0.710639	+	0.269777i
$321$	18.5502			1.03537
$322$	3.23881	−	1.08147i	0.180492	−	0.0602681i
$323$		−	4.71567i		−	0.262387i
$324$	1.59875	−	1.20166i	0.0888197	−	0.0667589i
$325$		−	1.11861i		−	0.0620491i
$326$	9.18163	+	27.4973i	0.508524	+	1.52294i
$327$	−6.35506			−0.351436
$328$	−9.12882	+	13.2300i	−0.504055	+	0.730506i
$329$	−1.33296			−0.0734886
$330$	0.101317	+	0.303427i	0.00557732	+	0.0167031i
$331$		−	31.0193i		−	1.70498i	−0.522747	−	0.852488i	$-0.675093\pi$
$331$		−	31.0193i		−	1.70498i	0.522747	−	0.852488i	$-0.324907\pi$
$332$	2.16416	+	2.87931i	0.118774	+	0.158023i
$333$		−	3.36341i		−	0.184314i
$334$	30.6235	−	10.2255i	1.67565	−	0.559514i
$335$	0.689129			0.0376511
$336$	9.27723	+	2.68498i	0.506114	+	0.146478i
$337$	2.10280			0.114547			0.0572734	−	0.998359i	$-0.481759\pi$
$337$	2.10280			0.114547			0.0572734	+	0.998359i	$0.481759\pi$
$338$	17.0617	−	5.69707i	0.928033	−	0.309880i
$339$		−	3.48804i		−	0.189444i
$340$	7.60627	+	10.1198i	0.412508	+	0.548823i
$341$			0.581950i			0.0315144i
$342$	−0.567169	−	1.69857i	−0.0306690	−	0.0918481i
$343$	−19.7270			−1.06516
$344$	6.10032	+	4.20927i	0.328907	+	0.226948i
$345$	1.69969			0.0915081
$346$	−10.6521	−	31.9012i	−0.572663	−	1.71502i
$347$			27.5984i			1.48156i	0.671748	+	0.740780i	$0.265544\pi$
$347$			27.5984i			1.48156i	−0.671748	+	0.740780i	$0.734456\pi$
$348$	−4.12668	+	3.10171i	−0.221213	+	0.166269i
$349$		−	31.2355i		−	1.67200i	−0.548729	−	0.836000i	$-0.684888\pi$
$349$		−	31.2355i		−	1.67200i	0.548729	−	0.836000i	$-0.315112\pi$
$350$	6.83735	−	2.28306i	0.365471	−	0.122035i
$351$	−0.529878			−0.0282828
$352$	0.752214	−	0.0305194i	0.0400931	−	0.00162669i
$353$	−0.185500			−0.00987319			−0.00493660	−	0.999988i	$-0.501571\pi$
$353$	−0.185500			−0.00987319			−0.00493660	+	0.999988i	$0.501571\pi$
$354$	4.82588	−	1.61141i	0.256493	−	0.0856454i
$355$			9.56911i			0.507876i
$356$	−22.5914	+	16.9802i	−1.19734	+	0.899948i
$357$		−	8.99179i		−	0.475896i
$358$	2.64130	+	7.91021i	0.139597	+	0.418068i
$359$	15.2061			0.802547			0.401274	−	0.915958i	$-0.368568\pi$
$359$	15.2061			0.802547			0.401274	+	0.915958i	$0.368568\pi$
$360$	3.95689	+	2.73029i	0.208547	+	0.143899i
$361$	17.3966			0.915610
$362$	9.00358	+	26.9641i	0.473218	+	1.41720i
$363$			10.9823i			0.576421i
$364$	−1.53738	−	2.04542i	−0.0805808	−	0.107209i
$365$			14.7242i			0.770702i
$366$	−9.05647	+	3.02405i	−0.473390	+	0.158069i
$367$	17.8962			0.934175			0.467088	−	0.884211i	$-0.345303\pi$
$367$	17.8962			0.934175			0.467088	+	0.884211i	$0.345303\pi$
$368$	1.11203	−	3.84232i	0.0579685	−	0.200295i
$369$	5.68297			0.295843
$370$	7.66850	−	2.56059i	0.398666	−	0.133119i
$371$			25.6607i			1.33224i
$372$	5.25465	+	6.99107i	0.272441	+	0.362470i
$373$		−	13.1514i		−	0.680953i	−0.940253	−	0.340476i	$-0.889412\pi$
$373$		−	13.1514i		−	0.680953i	0.940253	−	0.340476i	$-0.110588\pi$
$374$	−0.221991	−	0.664822i	−0.0114789	−	0.0343772i
$375$	12.0866			0.624148
$376$	−0.886813	+	1.28522i	−0.0457339	+	0.0662803i
$377$	1.36771			0.0704408
$378$	−1.08147	−	3.23881i	−0.0556249	−	0.166587i
$379$			3.51471i			0.180539i	0.995917	+	0.0902693i	$0.0287728\pi$
$379$			3.51471i			0.180539i	−0.995917	+	0.0902693i	$0.971227\pi$
$380$	3.44091	−	2.58626i	0.176515	−	0.132672i
$381$			9.10511i			0.466469i
$382$	33.4748	−	11.1776i	1.71272	−	0.571894i
$383$	−4.19234			−0.214218			−0.107109	−	0.994247i	$-0.534159\pi$
$383$	−4.19234			−0.214218			−0.107109	+	0.994247i	$0.534159\pi$
$384$	8.76091	−	7.15866i	0.447078	−	0.365314i
$385$	0.546157			0.0278347
$386$	34.0886	−	11.3825i	1.73506	−	0.579355i
$387$		−	2.62040i		−	0.133202i
$388$	8.17483	−	6.14439i	0.415014	−	0.311934i
$389$			3.05078i			0.154681i	0.997005	+	0.0773404i	$0.0246428\pi$
$389$			3.05078i			0.154681i	−0.997005	+	0.0773404i	$0.975357\pi$
$390$	−0.403399	−	1.20811i	−0.0204269	−	0.0611749i
$391$	−3.72410			−0.188336
$392$	−1.87983	+	2.72436i	−0.0949456	+	0.137601i
$393$	−0.553501			−0.0279204
$394$	−7.24788	−	21.7061i	−0.365143	−	1.09354i
$395$			4.72014i			0.237496i
$396$	−0.159921	−	0.212767i	−0.00803632	−	0.0106920i
$397$		−	12.9942i		−	0.652162i	−0.945342	−	0.326081i	$-0.894272\pi$
$397$		−	12.9942i		−	0.652162i	0.945342	−	0.326081i	$-0.105728\pi$
$398$	−4.20675	+	1.40468i	−0.210866	+	0.0704101i
$399$	−3.05736			−0.153060
$400$	2.34756	−	8.11138i	0.117378	−	0.405569i
$401$	17.5289			0.875350			0.437675	−	0.899133i	$-0.355802\pi$
$401$	17.5289			0.875350			0.437675	+	0.899133i	$0.355802\pi$
$402$	−0.543867	+	0.181603i	−0.0271256	+	0.00905751i
$403$		−	2.31706i		−	0.115421i
$404$	3.92455	+	5.22144i	0.195254	+	0.259776i
$405$		−	1.69969i		−	0.0844581i
$406$	2.79148	+	8.35998i	0.138539	+	0.414899i
$407$	−0.447614			−0.0221874
$408$	−8.66975	−	5.98220i	−0.429217	−	0.296163i
$409$	12.5394			0.620033			0.310016	−	0.950731i	$-0.399665\pi$
$409$	12.5394			0.620033			0.310016	+	0.950731i	$0.399665\pi$
$410$	4.32648	+	12.9570i	0.213669	+	0.639902i
$411$		−	12.3118i		−	0.607295i
$412$	−19.2314	+	14.4547i	−0.947461	+	0.712133i
$413$		−	8.68641i		−	0.427430i
$414$	−1.34141	+	0.447910i	−0.0659266	+	0.0220136i
$415$	3.06109			0.150263
$416$	−2.99498	+	0.121515i	−0.146841	+	0.00595775i
$417$	6.84557			0.335229
$418$	−0.226051	+	0.0754807i	−0.0110565	+	0.00369188i
$419$			29.9688i			1.46407i	0.681265	+	0.732037i	$0.261430\pi$
$419$			29.9688i			1.46407i	−0.681265	+	0.732037i	$0.738570\pi$
$420$	6.56108	−	4.93146i	0.320148	−	0.240631i
$421$		−	36.3642i		−	1.77228i	−0.463415	−	0.886141i	$-0.653376\pi$
$421$		−	36.3642i		−	1.77228i	0.463415	−	0.886141i	$-0.346624\pi$
$422$	−6.84993	−	20.5143i	−0.333449	−	0.998620i
$423$	0.552068			0.0268425
$424$	24.7417	+	17.0720i	1.20156	+	0.829088i
$425$	−7.86181			−0.381354
$426$	−2.52170	−	7.55203i	−0.122177	−	0.365897i
$427$			16.3013i			0.788877i
$428$	−22.2910	−	29.6572i	−1.07748	−	1.43354i
$429$			0.0705179i			0.00340463i
$430$	5.97444	−	1.99492i	0.288113	−	0.0962038i
$431$	−1.24232			−0.0598405			−0.0299203	−	0.999552i	$-0.509525\pi$
$431$	−1.24232			−0.0598405			−0.0299203	+	0.999552i	$0.509525\pi$
$432$	−3.84232	−	1.11203i	−0.184864	−	0.0535025i
$433$	−29.4685			−1.41616			−0.708082	−	0.706130i	$-0.750439\pi$
$433$	−29.4685			−1.41616			−0.708082	+	0.706130i	$0.750439\pi$
$434$	14.1628	−	4.72909i	0.679835	−	0.227004i
$435$			4.38721i			0.210351i
$436$	7.63662	+	10.1602i	0.365728	+	0.486584i
$437$			1.26626i			0.0605733i
$438$	−3.88020	−	11.6205i	−0.185403	−	0.555249i
$439$	−32.0586			−1.53007			−0.765037	−	0.643987i	$-0.777279\pi$
$439$	−32.0586			−1.53007			−0.765037	+	0.643987i	$0.777279\pi$
$440$	0.363356	−	0.526597i	0.0173223	−	0.0251045i
$441$	1.17025			0.0557261
$442$	0.883867	+	2.64702i	0.0420413	+	0.125906i
$443$			31.8663i			1.51401i	0.653407	+	0.757007i	$0.273339\pi$
$443$			31.8663i			1.51401i	−0.653407	+	0.757007i	$0.726661\pi$
$444$	−5.37727	+	4.04168i	−0.255194	+	0.191810i
$445$			24.0176i			1.13854i
$446$	1.19194	−	0.397999i	0.0564398	−	0.0188458i
$447$	−8.52131			−0.403044
$448$	−6.85545	−	18.0584i	−0.323889	−	0.853181i
$449$	27.1974			1.28352			0.641762	−	0.766904i	$-0.278204\pi$
$449$	27.1974			1.28352			0.641762	+	0.766904i	$0.278204\pi$
$450$	−2.83180	+	0.945566i	−0.133492	+	0.0445744i
$451$		−	0.756308i		−	0.0356131i
$452$	−5.57651	+	4.19143i	−0.262297	+	0.197148i
$453$			3.58823i			0.168590i
$454$	4.94415	+	14.8068i	0.232040	+	0.694919i
$455$	−2.17455			−0.101945
$456$	−2.03405	+	2.94787i	−0.0952531	+	0.138046i
$457$	−12.7673			−0.597231			−0.298616	−	0.954373i	$-0.596525\pi$
$457$	−12.7673			−0.597231			−0.298616	+	0.954373i	$0.596525\pi$
$458$	−6.14123	−	18.3919i	−0.286961	−	0.859396i
$459$			3.72410i			0.173826i
$460$	−2.04245	−	2.71738i	−0.0952295	−	0.126699i
$461$			26.7601i			1.24634i	0.782086	+	0.623171i	$0.214156\pi$
$461$			26.7601i			1.24634i	−0.782086	+	0.623171i	$0.785844\pi$
$462$	−0.431032	+	0.143926i	−0.0200534	+	0.00669604i
$463$	−37.9494			−1.76366			−0.881828	−	0.471570i	$-0.843687\pi$
$463$	−37.9494			−1.76366			−0.881828	+	0.471570i	$0.843687\pi$
$464$	9.91773	+	2.87035i	0.460419	+	0.133253i
$465$	7.43243			0.344671
$466$	−29.5459	+	9.86567i	−1.36869	+	0.457019i
$467$			1.64359i			0.0760564i	0.999277	+	0.0380282i	$0.0121077\pi$
$467$			1.64359i			0.0760564i	−0.999277	+	0.0380282i	$0.987892\pi$
$468$	0.636732	+	0.847144i	0.0294330	+	0.0391592i
$469$			0.978941i			0.0452033i
$470$	0.420293	+	1.25870i	0.0193867	+	0.0580596i
$471$	−5.46190			−0.251671
$472$	−8.37531	−	5.77903i	−0.385505	−	0.266001i
$473$	−0.348731			−0.0160347
$474$	−1.24387	−	3.72517i	−0.0571330	−	0.171103i
$475$			2.67315i			0.122653i
$476$	−14.3757	+	10.8051i	−0.658907	+	0.495250i
$477$		−	10.6278i		−	0.486614i
$478$	19.9897	−	6.67476i	0.914307	−	0.305296i
$479$	4.62787			0.211453			0.105726	−	0.994395i	$-0.466283\pi$
$479$	4.62787			0.211453			0.105726	+	0.994395i	$0.466283\pi$
$480$	−0.389782	−	9.60698i	−0.0177910	−	0.438497i
$481$	1.78220			0.0812612
$482$	−19.7019	+	6.57866i	−0.897397	+	0.299650i
$483$			2.41449i			0.109863i
$484$	17.5580	−	13.1970i	0.798090	−	0.599862i
$485$		−	8.69093i		−	0.394635i
$486$	0.447910	+	1.34141i	0.0203176	+	0.0608475i
$487$	14.7409			0.667972			0.333986	−	0.942578i	$-0.391606\pi$
$487$	14.7409			0.667972			0.333986	+	0.942578i	$0.391606\pi$
$488$	15.7175	+	10.8452i	0.711498	+	0.490939i
$489$	−20.4988			−0.926990
$490$	0.890918	+	2.66814i	0.0402476	+	0.120534i
$491$			1.66845i			0.0752961i	0.999291	+	0.0376480i	$0.0119866\pi$
$491$			1.66845i			0.0752961i	−0.999291	+	0.0376480i	$0.988013\pi$
$492$	−6.82899	−	9.08566i	−0.307875	−	0.409613i
$493$		−	9.61259i		−	0.432929i
$494$	0.900034	−	0.300530i	0.0404944	−	0.0135215i
$495$	−0.226200			−0.0101669
$496$	4.86271	−	16.8018i	0.218342	−	0.754422i
$497$	−13.5934			−0.609747
$498$	−2.41584	+	0.806673i	−0.108256	+	0.0361479i
$499$			0.891210i			0.0398960i	0.999801	+	0.0199480i	$0.00635007\pi$
$499$			0.891210i			0.0398960i	−0.999801	+	0.0199480i	$0.993650\pi$
$500$	−14.5240	−	19.3235i	−0.649531	−	0.864172i
$501$			22.8294i			1.01994i
$502$	−7.22703	−	21.6437i	−0.322558	−	0.966004i
$503$	15.8912			0.708555			0.354277	−	0.935140i	$-0.384727\pi$
$503$	15.8912			0.708555			0.354277	+	0.935140i	$0.384727\pi$
$504$	−3.87851	+	5.62096i	−0.172762	+	0.250377i
$505$	5.55108			0.247020
$506$	0.0596093	+	0.178519i	0.00264996	+	0.00793614i
$507$			12.7192i			0.564881i
$508$	14.5568	−	10.9412i	0.645855	−	0.485439i
$509$			14.3527i			0.636172i	0.948062	+	0.318086i	$0.103040\pi$
$509$			14.3527i			0.636172i	−0.948062	+	0.318086i	$0.896960\pi$
$510$	−8.49085	+	2.83518i	−0.375981	+	0.125544i
$511$	−20.9165			−0.925291
$512$	−21.9726	−	5.40427i	−0.971060	−	0.238837i
$513$	1.26626			0.0559067
$514$	−13.6639	+	4.56251i	−0.602689	+	0.201244i
$515$			20.4455i			0.900935i
$516$	−4.18937	+	3.14882i	−0.184427	+	0.138619i
$517$		−	0.0734711i		−	0.00323125i
$518$	3.63744	+	10.8935i	0.159820	+	0.478632i
$519$	23.7819			1.04391
$520$	−1.44672	+	2.09667i	−0.0634428	+	0.0919451i
$521$	−23.8534			−1.04503			−0.522517	−	0.852629i	$-0.675007\pi$
$521$	−23.8534			−1.04503			−0.522517	+	0.852629i	$0.675007\pi$
$522$	−1.15614	−	3.46243i	−0.0506028	−	0.151546i
$523$			38.6389i			1.68956i	0.535114	+	0.844780i	$0.320269\pi$
$523$			38.6389i			1.68956i	−0.535114	+	0.844780i	$0.679731\pi$
$524$	0.665120	+	0.884912i	0.0290559	+	0.0386576i
$525$			5.09714i			0.222457i
$526$	−4.16587	+	1.39103i	−0.181641	+	0.0606516i
$527$	−16.2848			−0.709378
$528$	−0.147992	+	0.511348i	−0.00644054	+	0.0222536i
$529$	1.00000			0.0434783
$530$	24.2312	−	8.09103i	1.05253	−	0.351452i
$531$			3.59762i			0.156123i
$532$	3.67391	+	4.88797i	0.159284	+	0.211921i
$533$			3.01128i			0.130433i
$534$	−6.32924	−	18.9549i	−0.273893	−	0.820260i
$535$	−31.5295			−1.36314
$536$	0.943881	+	0.651285i	0.0407694	+	0.0281312i
$537$	−5.89695			−0.254472
$538$	−1.59529	−	4.77759i	−0.0687777	−	0.205977i
$539$		−	0.155741i		−	0.00670822i
$540$	−2.71738	+	2.04245i	−0.116937	+	0.0878928i
$541$		−	22.2151i		−	0.955101i	−0.878604	−	0.477551i	$-0.841525\pi$
$541$		−	22.2151i		−	0.955101i	0.878604	−	0.477551i	$-0.158475\pi$
$542$	25.7700	−	8.60487i	1.10692	−	0.369611i
$543$	−20.1013			−0.862631
$544$	0.854032	+	21.0494i	0.0366163	+	0.902484i
$545$	10.8016			0.462690
$546$	1.71618	−	0.573048i	0.0734455	−	0.0245242i
$547$			20.8590i			0.891867i	0.895066	+	0.445934i	$0.147128\pi$
$547$			20.8590i			0.891867i	−0.895066	+	0.445934i	$0.852872\pi$
$548$	−19.6835	+	14.7946i	−0.840838	+	0.631993i
$549$		−	6.75147i		−	0.288146i
$550$	0.125839	+	0.376865i	0.00536579	+	0.0160696i
$551$	−3.26845			−0.139241
$552$	2.32801	+	1.60635i	0.0990868	+	0.0683707i
$553$	−6.70518			−0.285133
$554$	−2.05349	−	6.14984i	−0.0872445	−	0.261282i
$555$			5.71675i			0.242663i
$556$	−8.22604	−	10.9444i	−0.348862	−	0.464145i
$557$			7.01465i			0.297220i	0.988896	+	0.148610i	$0.0474799\pi$
$557$			7.01465i			0.297220i	−0.988896	+	0.148610i	$0.952520\pi$
$558$	−5.86575	+	1.95863i	−0.248317	+	0.0829154i
$559$	1.38849			0.0587268
$560$	−15.7684	−	4.56362i	−0.666336	−	0.192848i
$561$	0.495615			0.0209249
$562$	−10.7638	+	3.59415i	−0.454045	+	0.151610i
$563$			24.0352i			1.01296i	0.862251	+	0.506481i	$0.169054\pi$
$563$			24.0352i			1.01296i	−0.862251	+	0.506481i	$0.830946\pi$
$564$	−0.663398	−	0.882621i	−0.0279341	−	0.0371651i
$565$			5.92857i			0.249417i
$566$	−11.1725	−	33.4597i	−0.469617	−	1.40642i
$567$	2.41449			0.101399
$568$	−9.04362	+	13.1065i	−0.379462	+	0.549938i
$569$	22.4691			0.941955			0.470977	−	0.882145i	$-0.343901\pi$
$569$	22.4691			0.941955			0.470977	+	0.882145i	$0.343901\pi$
$570$	0.964010	+	2.88704i	0.0403779	+	0.120925i
$571$		−	21.3224i		−	0.892313i	−0.894955	−	0.446156i	$-0.852793\pi$
$571$		−	21.3224i		−	0.892313i	0.894955	−	0.446156i	$-0.147207\pi$
$572$	0.112741	−	0.0847385i	0.00471393	−	0.00354309i
$573$			24.9549i			1.04251i
$574$	−18.4061	+	6.14597i	−0.768255	+	0.256528i
$575$	2.11106			0.0880375
$576$	2.83930	+	7.47920i	0.118304	+	0.311633i
$577$	−5.43764			−0.226372			−0.113186	−	0.993574i	$-0.536106\pi$
$577$	−5.43764			−0.226372			−0.113186	+	0.993574i	$0.536106\pi$
$578$	−4.20008	+	1.40245i	−0.174700	+	0.0583341i
$579$			25.4125i			1.05611i
$580$	7.01407	−	5.27193i	0.291243	−	0.218905i
$581$			4.34843i			0.180403i
$582$	2.29028	+	6.85896i	0.0949350	+	0.284313i
$583$	−1.41439			−0.0585779
$584$	−13.9156	+	20.1674i	−0.575833	+	0.834532i
$585$	0.900626			0.0372363
$586$	0.0322061	+	0.0964513i	0.00133042	+	0.00398437i
$587$		−	28.5498i		−	1.17838i	−0.807995	−	0.589189i	$-0.799447\pi$
$587$		−	28.5498i		−	1.17838i	0.807995	−	0.589189i	$-0.200553\pi$
$588$	−1.40624	−	1.87094i	−0.0579924	−	0.0771563i
$589$			5.53713i			0.228153i
$590$	−8.20248	+	2.73889i	−0.337691	+	0.112758i
$591$	16.1816			0.665620
$592$	12.9233	+	3.74021i	0.531144	+	0.153722i
$593$	−45.1524			−1.85419			−0.927094	−	0.374829i	$-0.877702\pi$
$593$	−45.1524			−1.85419			−0.927094	+	0.374829i	$0.877702\pi$
$594$	0.178519	−	0.0596093i	0.00732473	−	0.00244580i
$595$			15.2832i			0.626551i
$596$	10.2397	+	13.6235i	0.419435	+	0.558039i
$597$		−	3.13607i		−	0.128351i
$598$	−0.237337	−	0.710782i	−0.00970544	−	0.0290661i
$599$	−14.8561			−0.607006			−0.303503	−	0.952831i	$-0.598156\pi$
$599$	−14.8561			−0.607006			−0.303503	+	0.952831i	$0.598156\pi$
$600$	4.91459	+	3.39110i	0.200637	+	0.138441i
$601$	−26.7822			−1.09247			−0.546234	−	0.837633i	$-0.683939\pi$
$601$	−26.7822			−1.09247			−0.546234	+	0.837633i	$0.683939\pi$
$602$	2.83389	+	8.48698i	0.115501	+	0.345903i
$603$		−	0.405445i		−	0.0165110i
$604$	5.73670	−	4.31183i	0.233423	−	0.175446i
$605$		−	18.6665i		−	0.758899i
$606$	−4.38097	+	1.46285i	−0.177965	+	0.0594241i
$607$	−18.6146			−0.755545			−0.377772	−	0.925898i	$-0.623310\pi$
$607$	−18.6146			−0.755545			−0.377772	+	0.925898i	$0.623310\pi$
$608$	7.15715	−	0.290386i	0.290261	−	0.0117767i
$609$	−6.23224			−0.252543
$610$	15.3932	−	5.13993i	0.623251	−	0.208110i
$611$			0.292529i			0.0118344i
$612$	5.95392	−	4.47510i	0.240673	−	0.180895i
$613$			24.6603i			0.996022i	0.867171	+	0.498011i	$0.165936\pi$
$613$			24.6603i			0.996022i	−0.867171	+	0.498011i	$0.834064\pi$
$614$	−0.711304	−	2.13023i	−0.0287059	−	0.0859690i
$615$	−9.65926			−0.389499
$616$	0.748056	+	0.516164i	0.0301400	+	0.0207969i
$617$	18.9235			0.761831			0.380916	−	0.924610i	$-0.375609\pi$
$617$	18.9235			0.761831			0.380916	+	0.924610i	$0.375609\pi$
$618$	−5.38789	−	16.1358i	−0.216733	−	0.649075i
$619$		−	42.8755i		−	1.72331i	−0.507494	−	0.861655i	$-0.669428\pi$
$619$		−	42.8755i		−	1.72331i	0.507494	−	0.861655i	$-0.330572\pi$
$620$	−8.93126	−	11.8826i	−0.358688	−	0.477218i
$621$		−	1.00000i		−	0.0401286i
$622$	26.7262	−	8.92415i	1.07162	−	0.357826i
$623$	−34.1182			−1.36692
$624$	0.589239	−	2.03596i	0.0235884	−	0.0815035i
$625$	−9.98809			−0.399523
$626$	−37.3798	+	12.4815i	−1.49400	+	0.498861i
$627$		−	0.168518i		−	0.00672995i
$628$	6.56334	+	8.73223i	0.261906	+	0.348454i
$629$		−	12.5257i		−	0.499432i
$630$	1.83816	+	5.50497i	0.0732342	+	0.219323i
$631$	14.1106			0.561734			0.280867	−	0.959747i	$-0.409378\pi$
$631$	14.1106			0.561734			0.280867	+	0.959747i	$0.409378\pi$
$632$	−4.46093	+	6.46504i	−0.177446	+	0.257165i
$633$	15.2931			0.607846
$634$	−9.03414	−	27.0556i	−0.358791	−	1.07452i
$635$		−	15.4758i		−	0.614140i
$636$	−16.9913	+	12.7710i	−0.673748	+	0.506404i
$637$			0.620089i			0.0245688i
$638$	−0.460791	+	0.153863i	−0.0182429	+	0.00609148i
$639$	5.62993			0.222716
$640$	−14.8908	+	12.1675i	−0.588611	+	0.480962i
$641$	−13.1583			−0.519722			−0.259861	−	0.965646i	$-0.583677\pi$
$641$	−13.1583			−0.519722			−0.259861	+	0.965646i	$0.583677\pi$
$642$	24.8834	−	8.30882i	0.982070	−	0.327923i
$643$			34.9534i			1.37843i	0.724559	+	0.689213i	$0.242043\pi$
$643$			34.9534i			1.37843i	−0.724559	+	0.689213i	$0.757957\pi$
$644$	3.86017	−	2.90139i	0.152112	−	0.114331i
$645$			4.45385i			0.175370i
$646$	−2.11219	−	6.32564i	−0.0831031	−	0.248879i
$647$	10.8981			0.428448			0.214224	−	0.976785i	$-0.431278\pi$
$647$	10.8981			0.428448			0.214224	+	0.976785i	$0.431278\pi$
$648$	1.60635	−	2.32801i	0.0631033	−	0.0914530i
$649$	0.478783			0.0187939
$650$	−0.501034	−	1.50051i	−0.0196522	−	0.0588547i
$651$			10.5581i			0.413806i
$652$	24.6326	+	32.7726i	0.964689	+	1.28347i
$653$			1.77561i			0.0694851i	0.999396	+	0.0347425i	$0.0110611\pi$
$653$			1.77561i			0.0694851i	−0.999396	+	0.0347425i	$0.988939\pi$
$654$	−8.52473	+	2.84649i	−0.333343	+	0.111307i
$655$	0.940779			0.0367593
$656$	−6.31962	+	21.8358i	−0.246740	+	0.852543i
$657$	8.66291			0.337972
$658$	−1.78805	+	0.597047i	−0.0697053	+	0.0232753i
$659$		−	26.4553i		−	1.03055i	−0.857024	−	0.515277i	$-0.827689\pi$
$659$		−	26.4553i		−	1.03055i	0.857024	−	0.515277i	$-0.172311\pi$
$660$	0.271815	+	0.361638i	0.0105804	+	0.0140767i
$661$		−	23.9878i		−	0.933019i	−0.884516	−	0.466509i	$-0.845511\pi$
$661$		−	23.9878i		−	0.933019i	0.884516	−	0.466509i	$-0.154489\pi$
$662$	−13.8939	−	41.6096i	−0.540000	−	1.61720i
$663$	−1.97332			−0.0766372
$664$	4.19269	+	2.89299i	0.162708	+	0.112270i
$665$	5.19656			0.201514
$666$	−1.50651	−	4.51171i	−0.0583759	−	0.174825i
$667$			2.58119i			0.0999439i
$668$	36.4986	−	27.4331i	1.41217	−	1.06142i
$669$			0.888570i			0.0343541i
$670$	0.924404	−	0.308668i	0.0357128	−	0.0119249i
$671$	−0.898507			−0.0346865
$672$	13.6472	−	0.553705i	0.526451	−	0.0213596i
$673$	−1.72805			−0.0666113			−0.0333057	−	0.999445i	$-0.510603\pi$
$673$	−1.72805			−0.0666113			−0.0333057	+	0.999445i	$0.510603\pi$
$674$	2.82071	−	0.941864i	0.108650	−	0.0362792i
$675$		−	2.11106i		−	0.0812549i
$676$	20.3349	−	15.2842i	0.782112	−	0.587853i
$677$		−	40.3052i		−	1.54905i	−0.632541	−	0.774526i	$-0.717988\pi$
$677$		−	40.3052i		−	1.54905i	0.632541	−	0.774526i	$-0.282012\pi$
$678$	−1.56232	−	4.67888i	−0.0600007	−	0.179691i
$679$	12.3459			0.473792
$680$	14.7359	+	10.1679i	0.565095	+	0.389920i
$681$	−11.0383			−0.422988
$682$	0.260661	+	0.780633i	0.00998122	+	0.0298920i
$683$			0.553046i			0.0211617i	0.999944	+	0.0105809i	$0.00336806\pi$
$683$			0.553046i			0.0211617i	−0.999944	+	0.0105809i	$0.996632\pi$
$684$	−1.52161	−	2.02444i	−0.0581803	−	0.0774062i
$685$			20.9262i			0.799548i
$686$	−26.4619	+	8.83590i	−1.01032	+	0.337356i
$687$	13.7109			0.523103
$688$	10.0684	+	2.91395i	0.383854	+	0.111093i
$689$	5.63144			0.214541
$690$	2.27997	−	0.761306i	0.0867972	−	0.0289824i
$691$			12.5766i			0.478435i	0.970966	+	0.239218i	$0.0768910\pi$
$691$			12.5766i			0.478435i	−0.970966	+	0.239218i	$0.923109\pi$
$692$	−28.5777	−	38.0214i	−1.08636	−	1.44536i
$693$		−	0.321328i		−	0.0122062i
$694$	12.3616	+	37.0207i	0.469240	+	1.40529i
$695$	−11.6353			−0.441353
$696$	−4.14628	+	6.00904i	−0.157164	+	0.227772i
$697$	21.1639			0.801641
$698$	−13.9907	−	41.8996i	−0.529556	−	1.58592i
$699$		−	22.0260i		−	0.833101i
$700$	8.14907	−	6.12503i	0.308006	−	0.231504i
$701$			19.5742i			0.739306i	0.929170	+	0.369653i	$0.120523\pi$
$701$			19.5742i			0.739306i	−0.929170	+	0.369653i	$0.879477\pi$
$702$	−0.710782	+	0.237337i	−0.0268268	+	0.00895772i
$703$	−4.25895			−0.160629
$704$	0.995356	−	0.377863i	0.0375139	−	0.0142412i
$705$	−0.938343			−0.0353401
$706$	−0.248832	+	0.0830874i	−0.00936491	+	0.00312704i
$707$			7.88558i			0.296568i
$708$	5.75171	−	4.32311i	0.216162	−	0.162473i
$709$		−	34.9383i		−	1.31213i	−0.754703	−	0.656067i	$-0.772219\pi$
$709$		−	34.9383i		−	1.31213i	0.754703	−	0.656067i	$-0.227781\pi$
$710$	4.28610	+	12.8361i	0.160854	+	0.481730i
$711$	2.77706			0.104148
$712$	−22.6987	+	32.8963i	−0.850669	+	1.23284i
$713$	4.37283			0.163764
$714$	−4.02751	−	12.0617i	−0.150726	−	0.451396i
$715$		−	0.119858i		−	0.00448245i
$716$	7.08612	+	9.42776i	0.264821	+	0.352332i
$717$			14.9020i			0.556526i
$718$	20.3976	−	6.81096i	0.761231	−	0.254183i
$719$	4.63883			0.172999			0.0864995	−	0.996252i	$-0.472432\pi$
$719$	4.63883			0.172999			0.0864995	+	0.996252i	$0.472432\pi$
$720$	6.53073	+	1.89010i	0.243386	+	0.0704399i
$721$	−29.0438			−1.08165
$722$	23.3359	−	7.79210i	0.868474	−	0.289992i
$723$		−	14.6875i		−	0.546233i
$724$	24.1550	+	32.1371i	0.897712	+	1.19437i
$725$			5.44905i			0.202373i
$726$	4.91907	+	14.7317i	0.182564	+	0.546746i
$727$	3.32762			0.123415			0.0617074	−	0.998094i	$-0.480345\pi$
$727$	3.32762			0.123415			0.0617074	+	0.998094i	$0.480345\pi$
$728$	−2.97842	−	2.05513i	−0.110388	−	0.0761683i
$729$	−1.00000			−0.0370370
$730$	6.59513	+	19.7512i	0.244097	+	0.731025i
$731$		−	9.75861i		−	0.360935i
$732$	−10.7939	+	8.11296i	−0.398955	+	0.299864i
$733$			34.6735i			1.28069i	0.768086	+	0.640347i	$0.221209\pi$
$733$			34.6735i			1.28069i	−0.768086	+	0.640347i	$0.778791\pi$
$734$	24.0061	−	8.01589i	0.886083	−	0.295872i
$735$	−1.98906			−0.0733675
$736$	−0.229326	−	5.65220i	−0.00845307	−	0.208343i
$737$	−0.0539579			−0.00198757
$738$	7.62318	−	2.54546i	0.280613	−	0.0936995i
$739$			33.5915i			1.23568i	0.786303	+	0.617841i	$0.211992\pi$
$739$			33.5915i			1.23568i	−0.786303	+	0.617841i	$0.788008\pi$
$740$	9.13968	−	6.86959i	0.335981	−	0.252531i
$741$			0.670962i			0.0246484i
$742$	11.4937	+	34.4215i	0.421947	+	1.26365i
$743$	40.8340			1.49806			0.749028	−	0.662539i	$-0.230521\pi$
$743$	40.8340			1.49806			0.749028	+	0.662539i	$0.230521\pi$
$744$	10.1800	+	7.02428i	0.373217	+	0.257522i
$745$	14.4836			0.530636
$746$	−5.89063	−	17.6414i	−0.215671	−	0.645896i
$747$		−	1.80097i		−	0.0658942i
$748$	−0.595561	−	0.792367i	−0.0217759	−	0.0289718i
$749$		−	44.7893i		−	1.63656i
$750$	16.2130	−	5.41370i	0.592017	−	0.197680i
$751$	−34.4766			−1.25807			−0.629034	−	0.777378i	$-0.716549\pi$
$751$	−34.4766			−1.25807			−0.629034	+	0.777378i	$0.716549\pi$
$752$	−0.613916	+	2.12122i	−0.0223872	+	0.0773530i
$753$	16.1350			0.587993
$754$	1.83466	−	0.612612i	0.0668144	−	0.0223100i
$755$		−	6.09887i		−	0.221961i
$756$	−2.90139	−	3.86017i	−0.105523	−	0.140393i
$757$			13.3236i			0.484256i	0.970244	+	0.242128i	$0.0778454\pi$
$757$			13.3236i			0.484256i	−0.970244	+	0.242128i	$0.922155\pi$
$758$	1.57427	+	4.71466i	0.0571802	+	0.171244i
$759$	−0.133083			−0.00483062
$760$	3.45725	−	5.01045i	0.125408	−	0.181748i
$761$	0.677685			0.0245661			0.0122830	−	0.999925i	$-0.496090\pi$
$761$	0.677685			0.0245661			0.0122830	+	0.999925i	$0.496090\pi$
$762$	4.07827	+	12.2137i	0.147740	+	0.442455i
$763$			15.3442i			0.555498i
$764$	39.8968	−	29.9873i	1.44342	−	1.08490i
$765$		−	6.32980i		−	0.228854i
$766$	−5.62363	+	1.87779i	−0.203190	+	0.0678472i
$767$	−1.90630			−0.0688324
$768$	8.54553	−	13.5268i	0.308360	−	0.488106i
$769$	30.7832			1.11007			0.555036	−	0.831827i	$-0.312705\pi$
$769$	30.7832			1.11007			0.555036	+	0.831827i	$0.312705\pi$
$770$	0.732620	−	0.244629i	0.0264018	−	0.00881582i
$771$		−	10.1862i		−	0.366848i
$772$	40.6284	−	30.5372i	1.46225	−	1.09906i
$773$			43.3139i			1.55789i	0.627090	+	0.778947i	$0.284246\pi$
$773$			43.3139i			1.55789i	−0.627090	+	0.778947i	$0.715754\pi$
$774$	−1.17370	−	3.51502i	−0.0421878	−	0.126345i
$775$	9.23131			0.331599
$776$	8.21366	−	11.9037i	0.294853	−	0.427319i
$777$	−8.12092			−0.291336
$778$	1.36647	+	4.09235i	0.0489905	+	0.146718i
$779$		−	7.19610i		−	0.257827i
$780$	−1.08225	−	1.43988i	−0.0387506	−	0.0515560i
$781$		−	0.749249i		−	0.0268102i
$782$	−4.99554	+	1.66806i	−0.178640	+	0.0596497i
$783$	2.58119			0.0922441
$784$	−1.30135	+	4.49647i	−0.0464768	+	0.160588i
$785$	9.28352			0.331343
$786$	−0.742471	+	0.247919i	−0.0264831	+	0.00884296i
$787$			27.0873i			0.965558i	0.875742	+	0.482779i	$0.160373\pi$
$787$			27.0873i			0.965558i	−0.875742	+	0.482779i	$0.839627\pi$
$788$	−19.4447	−	25.8703i	−0.692690	−	0.921592i
$789$		−	3.10560i		−	0.110562i
$790$	2.11419	+	6.33163i	0.0752196	+	0.225269i
$791$	−8.42182			−0.299445
$792$	−0.309820	−	0.213778i	−0.0110090	−	0.00759627i
$793$	3.57745			0.127039
$794$	−5.82024	−	17.4306i	−0.206553	−	0.618588i
$795$			18.0640i			0.640663i
$796$	−5.01381	+	3.76849i	−0.177710	+	0.133571i
$797$		−	5.59625i		−	0.198229i	−0.995076	−	0.0991146i	$-0.968399\pi$
$797$		−	5.59625i		−	0.198229i	0.995076	−	0.0991146i	$-0.0316010\pi$
$798$	−4.10118	+	1.36942i	−0.145180	+	0.0484771i
$799$	2.05596			0.0727345
$800$	−0.484122	−	11.9322i	−0.0171163	−	0.421866i
$801$	14.1306			0.499281
$802$	23.5134	−	7.85135i	0.830286	−	0.277241i
$803$		−	1.15289i		−	0.0406846i
$804$	−0.648206	+	0.487206i	−0.0228605	+	0.0171824i
$805$		−	4.10387i		−	0.144643i
$806$	−1.03783	−	3.10813i	−0.0365562	−	0.109479i
$807$	3.56163			0.125375
$808$	7.60317	+	5.24624i	0.267478	+	0.184562i
$809$	10.0599			0.353687			0.176843	−	0.984239i	$-0.443411\pi$
$809$	10.0599			0.353687			0.176843	+	0.984239i	$0.443411\pi$
$810$	−0.761306	−	2.27997i	−0.0267496	−	0.0801101i
$811$		−	7.70304i		−	0.270490i	−0.990812	−	0.135245i	$-0.956818\pi$
$811$		−	7.70304i		−	0.270490i	0.990812	−	0.135245i	$-0.0431822\pi$
$812$	7.48904	+	9.96382i	0.262814	+	0.349662i
$813$			19.2112i			0.673765i
$814$	−0.600434	+	0.200491i	−0.0210452	+	0.00702720i
$815$	34.8416			1.22045
$816$	−14.3092	−	4.14130i	−0.500921	−	0.144975i
$817$	−3.31810			−0.116086
$818$	16.8204	−	5.61651i	0.588113	−	0.196377i
$819$			1.27938i			0.0447053i
$820$	11.6071	+	15.4428i	0.405339	+	0.539285i
$821$			17.0007i			0.593329i	0.954982	+	0.296665i	$0.0958744\pi$
$821$			17.0007i			0.593329i	−0.954982	+	0.296665i	$0.904126\pi$
$822$	−5.51456	−	16.5151i	−0.192343	−	0.576031i
$823$	−29.4307			−1.02589			−0.512944	−	0.858422i	$-0.671445\pi$
$823$	−29.4307			−1.02589			−0.512944	+	0.858422i	$0.671445\pi$
$824$	−19.3227	+	28.0036i	−0.673138	+	0.975551i
$825$	−0.280947			−0.00978133
$826$	−3.89073	−	11.6520i	−0.135376	−	0.405426i
$827$		−	56.1603i		−	1.95289i	−0.215775	−	0.976443i	$-0.569228\pi$
$827$		−	56.1603i		−	1.95289i	0.215775	−	0.976443i	$-0.430772\pi$
$828$	−1.59875	+	1.20166i	−0.0555605	+	0.0417606i
$829$			14.1827i			0.492587i	0.969195	+	0.246293i	$0.0792127\pi$
$829$			14.1827i			0.492587i	−0.969195	+	0.246293i	$0.920787\pi$
$830$	4.10617	−	1.37109i	0.142527	−	0.0475913i
$831$	4.58461			0.159038
$832$	−3.96306	+	1.50448i	−0.137394	+	0.0521584i
$833$	4.35812			0.151000
$834$	9.18270	−	3.06620i	0.317971	−	0.106174i
$835$		−	38.8028i		−	1.34283i
$836$	−0.269418	+	0.202501i	−0.00931803	+	0.00700364i
$837$		−	4.37283i		−	0.151147i
$838$	13.4233	+	40.2005i	0.463701	+	1.38870i
$839$	−15.3497			−0.529929			−0.264965	−	0.964258i	$-0.585360\pi$
$839$	−15.3497			−0.529929			−0.264965	+	0.964258i	$0.585360\pi$
$840$	6.59225	−	9.55387i	0.227454	−	0.329640i
$841$	22.3375			0.770258
$842$	−16.2879	−	48.7792i	−0.561317	−	1.68104i
$843$		−	8.02427i		−	0.276371i
$844$	−18.3771	−	24.4499i	−0.632566	−	0.841600i
$845$		−	21.6187i		−	0.743706i
$846$	0.740549	−	0.247277i	0.0254606	−	0.00850155i
$847$	26.5166			0.911121
$848$	40.8354	+	11.8184i	1.40230	+	0.405847i
$849$	24.9437			0.856067
$850$	−10.5459	+	3.52138i	−0.361721	+	0.120782i
$851$			3.36341i			0.115296i
$852$	−6.76525	−	9.00087i	−0.231774	−	0.308365i
$853$		−	3.59227i		−	0.122997i	−0.998107	−	0.0614986i	$-0.980412\pi$
$853$		−	3.59227i		−	0.122997i	0.998107	−	0.0614986i	$-0.0195880\pi$
$854$	7.30152	+	21.8667i	0.249853	+	0.748265i
$855$	−2.15224			−0.0736051
$856$	−43.1851	−	29.7981i	−1.47604	−	1.01848i
$857$	−34.1843			−1.16771			−0.583856	−	0.811857i	$-0.698457\pi$
$857$	−34.1843			−1.16771			−0.583856	+	0.811857i	$0.698457\pi$
$858$	0.0315856	+	0.0945933i	0.00107832	+	0.00322936i
$859$		−	33.6746i		−	1.14896i	−0.818518	−	0.574481i	$-0.805204\pi$
$859$		−	33.6746i		−	1.14896i	0.818518	−	0.574481i	$-0.194796\pi$
$860$	7.12062	−	5.35202i	0.242811	−	0.182502i
$861$		−	13.7215i		−	0.467626i
$862$	−1.66646	+	0.556448i	−0.0567599	+	0.0189527i
$863$	23.0372			0.784195			0.392098	−	0.919924i	$-0.371750\pi$
$863$	23.0372			0.784195			0.392098	+	0.919924i	$0.371750\pi$
$864$	−5.65220	+	0.229326i	−0.192292	+	0.00780183i
$865$	−40.4218			−1.37438
$866$	−39.5293	+	13.1992i	−1.34326	+	0.448527i
$867$		−	3.13109i		−	0.106338i
$868$	16.8799	−	12.6873i	0.572940	−	0.430634i
$869$		−	0.369580i		−	0.0125372i
$870$	1.96507	+	5.88504i	0.0666222	+	0.199522i
$871$	0.214836			0.00727944
$872$	14.7947	+	10.2084i	0.501011	+	0.345701i
$873$	−5.11325			−0.173057
$874$	0.567169	+	1.69857i	0.0191848	+	0.0574550i
$875$		−	29.1829i		−	0.986562i
$876$	−10.4099	−	13.8499i	−0.351717	−	0.467944i
$877$		−	20.7873i		−	0.701937i	−0.936387	−	0.350968i	$-0.885852\pi$
$877$		−	20.7873i		−	0.701937i	0.936387	−	0.350968i	$-0.114148\pi$
$878$	−43.0037	+	14.3594i	−1.45130	+	0.484605i
$879$	−0.0719030			−0.00242523
$880$	0.251541	−	0.869132i	0.00847944	−	0.0292984i
$881$	1.38162			0.0465481			0.0232741	−	0.999729i	$-0.492591\pi$
$881$	1.38162			0.0465481			0.0232741	+	0.999729i	$0.492591\pi$
$882$	1.56978	−	0.524166i	0.0528573	−	0.0176496i
$883$		−	31.7819i		−	1.06955i	−0.844996	−	0.534773i	$-0.820397\pi$
$883$		−	31.7819i		−	1.06955i	0.844996	−	0.534773i	$-0.179603\pi$
$884$	2.37125	+	3.15485i	0.0797539	+	0.106109i
$885$		−	6.11483i		−	0.205548i
$886$	14.2732	+	42.7457i	0.479518	+	1.43607i
$887$	0.644205			0.0216303			0.0108151	−	0.999942i	$-0.496557\pi$
$887$	0.644205			0.0216303			0.0108151	+	0.999942i	$0.496557\pi$
$888$	−5.40281	+	7.83007i	−0.181306	+	0.262760i
$889$	21.9842			0.737326
$890$	10.7577	+	32.2174i	0.360600	+	1.07993i
$891$			0.133083i			0.00445846i
$892$	1.42060	−	1.06776i	0.0475654	−	0.0357512i
$893$		−	0.699061i		−	0.0233932i
$894$	−11.4306	+	3.81678i	−0.382295	+	0.127652i
$895$	10.0230			0.335031
$896$	−17.2845	−	21.1531i	−0.577435	−	0.706676i
$897$	0.529878			0.0176921
$898$	36.4828	−	12.1820i	1.21745	−	0.406517i
$899$			11.2871i			0.376445i
$900$	−3.37507	+	2.53678i	−0.112502	+	0.0845594i
$901$		−	39.5790i		−	1.31857i
$902$	−0.338758	−	1.01452i	−0.0112794	−	0.0337797i
$903$	−6.32691			−0.210547
$904$	−5.60300	+	8.12019i	−0.186353	+	0.270074i
$905$	34.1660			1.13572
$906$	1.60720	+	4.81328i	0.0533957	+	0.159911i
$907$		−	14.6256i		−	0.485634i	−0.970072	−	0.242817i	$-0.921928\pi$
$907$		−	14.6256i		−	0.485634i	0.970072	−	0.242817i	$-0.0780715\pi$
$908$	13.2642	+	17.6475i	0.440190	+	0.585652i
$909$		−	3.26595i		−	0.108325i
$910$	−2.91696	+	0.974002i	−0.0966963	+	0.0322879i
$911$	1.85594			0.0614901			0.0307451	−	0.999527i	$-0.490212\pi$
$911$	1.85594			0.0614901			0.0307451	+	0.999527i	$0.490212\pi$
$912$	−1.40811	+	4.86536i	−0.0466273	+	0.161108i
$913$	−0.239679			−0.00793223
$914$	−17.1262	+	5.71862i	−0.566485	+	0.189155i
$915$			11.4754i			0.379364i
$916$	−16.4758	−	21.9203i	−0.544376	−	0.724268i
$917$			1.33642i			0.0441325i
$918$	1.66806	+	4.99554i	0.0550542	+	0.164877i
$919$	52.6826			1.73784			0.868920	−	0.494953i	$-0.164815\pi$
$919$	52.6826			1.73784			0.868920	+	0.494953i	$0.164815\pi$
$920$	−3.95689	−	2.73029i	−0.130455	−	0.0900149i
$921$	1.58805			0.0523281
$922$	11.9861	+	35.8962i	0.394741	+	1.18218i
$923$			2.98317i			0.0981923i
$924$	−0.513724	+	0.386127i	−0.0169003	+	0.0127026i
$925$			7.10038i			0.233459i
$926$	−50.9056	+	16.9979i	−1.67286	+	0.558585i
$927$	12.0290			0.395083
$928$	14.5894	−	0.591933i	0.478920	−	0.0194312i
$929$	16.8664			0.553367			0.276684	−	0.960961i	$-0.410765\pi$
$929$	16.8664			0.553367			0.276684	+	0.960961i	$0.410765\pi$
$930$	9.96993	−	3.32906i	0.326927	−	0.109164i
$931$		−	1.48184i		−	0.0485652i
$932$	−35.2142	+	26.4678i	−1.15348	+	0.866982i
$933$			19.9240i			0.652282i
$934$	0.736181	+	2.20473i	0.0240886	+	0.0721409i
$935$	−0.842391			−0.0275491
$936$	1.23356	+	0.851167i	0.0403202	+	0.0278213i
$937$	23.7329			0.775319			0.387659	−	0.921803i	$-0.373284\pi$
$937$	23.7329			0.775319			0.387659	+	0.921803i	$0.373284\pi$
$938$	0.438477	+	1.31316i	0.0143168	+	0.0428762i
$939$		−	27.8661i		−	0.909376i
$940$	1.12757	+	1.50018i	0.0367773	+	0.0489305i
$941$			25.9620i			0.846336i	0.906051	+	0.423168i	$0.139082\pi$
$941$			25.9620i			0.846336i	−0.906051	+	0.423168i	$0.860918\pi$
$942$	−7.32664	+	2.44644i	−0.238715	+	0.0797092i
$943$	−5.68297			−0.185063
$944$	−13.8232	−	4.00065i	−0.449907	−	0.130210i
$945$	−4.10387			−0.133499
$946$	−0.467791	+	0.156200i	−0.0152092	+	0.00507850i
$947$			24.7835i			0.805355i	0.915342	+	0.402678i	$0.131920\pi$
$947$			24.7835i			0.805355i	−0.915342	+	0.402678i	$0.868080\pi$
$948$	−3.33708	−	4.43984i	−0.108383	−	0.144199i
$949$			4.59028i			0.149007i
$950$	1.19733	+	3.58579i	0.0388465	+	0.116338i
$951$	20.1696			0.654043
$952$	−14.4439	+	20.9330i	−0.468131	+	0.678443i
$953$	−2.03249			−0.0658388			−0.0329194	−	0.999458i	$-0.510480\pi$
$953$	−2.03249			−0.0658388			−0.0329194	+	0.999458i	$0.510480\pi$
$954$	−4.76030	−	14.2563i	−0.154121	−	0.461563i
$955$		−	42.4156i		−	1.37254i
$956$	23.8247	−	17.9071i	0.770544	−	0.579159i
$957$		−	0.343513i		−	0.0111042i
$958$	6.20786	−	2.07287i	0.200567	−	0.0669713i
$959$	−29.7266			−0.959923
$960$	−4.82591	−	12.7123i	−0.155756	−	0.410288i
$961$	−11.8784			−0.383174
$962$	2.39066	−	0.798263i	0.0770778	−	0.0257370i
$963$			18.5502i			0.597772i
$964$	−23.4817	+	17.6493i	−0.756293	+	0.568447i
$965$		−	43.1933i		−	1.39044i
$966$	1.08147	+	3.23881i	0.0347958	+	0.104207i
$967$	32.6911			1.05127			0.525637	−	0.850709i	$-0.323827\pi$
$967$	32.6911			1.05127			0.525637	+	0.850709i	$0.323827\pi$
$968$	17.6414	−	25.5669i	0.567015	−	0.821752i
$969$	4.71567			0.151489
$970$	−3.89275	−	11.6581i	−0.124989	−	0.374319i
$971$			16.0877i			0.516280i	0.966107	+	0.258140i	$0.0831096\pi$
$971$			16.0877i			0.516280i	−0.966107	+	0.258140i	$0.916890\pi$
$972$	1.20166	+	1.59875i	0.0385432	+	0.0512801i
$973$		−	16.5285i		−	0.529881i
$974$	19.7735	−	6.60258i	0.633585	−	0.211560i
$975$	1.11861			0.0358240
$976$	25.9413	+	7.50782i	0.830360	+	0.240320i
$977$	−0.00261102			−8.35340e−5			−4.17670e−5	−	1.00000i	$-0.500013\pi$
$977$	−0.00261102			−8.35340e−5			−4.17670e−5		1.00000i	$0.500013\pi$
$978$	−27.4973	+	9.18163i	−0.879268	+	0.293596i
$979$		−	1.88055i		−	0.0601026i
$980$	2.39017	+	3.18001i	0.0763511	+	0.101582i
$981$		−	6.35506i		−	0.202901i
$982$	0.747314	+	2.23807i	0.0238478	+	0.0714197i
$983$	−34.4657			−1.09929			−0.549643	−	0.835400i	$-0.685236\pi$
$983$	−34.4657			−1.09929			−0.549643	+	0.835400i	$0.685236\pi$
$984$	−13.2300	−	9.12882i	−0.421758	−	0.291016i
$985$	−27.5036			−0.876337
$986$	−4.30557	−	12.8944i	−0.137117	−	0.410642i
$987$		−	1.33296i		−	0.0424287i
$988$	1.07270	−	0.806268i	0.0341272	−	0.0256508i
$989$			2.62040i			0.0833238i
$990$	−0.303427	+	0.101317i	−0.00964353	+	0.00322007i
$991$	−12.9440			−0.411178			−0.205589	−	0.978638i	$-0.565911\pi$
$991$	−12.9440			−0.411178			−0.205589	+	0.978638i	$0.565911\pi$
$992$	−1.00280	−	24.7161i	−0.0318390	−	0.784737i
$993$	31.0193			0.984368
$994$	−18.2343	+	6.08861i	−0.578356	+	0.193119i
$995$			5.33034i			0.168983i
$996$	−2.87931	+	2.16416i	−0.0912345	+	0.0685739i
$997$		−	20.4976i		−	0.649167i	−0.945857	−	0.324583i	$-0.894776\pi$
$997$		−	20.4976i		−	0.649167i	0.945857	−	0.324583i	$-0.105224\pi$
$998$	0.399181	+	1.19548i	0.0126359	+	0.0378421i
$999$	3.36341			0.106414

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.d.277.19	✓	20
4.3	odd	2		2208.2.f.d.1105.4		20
8.3	odd	2		2208.2.f.d.1105.17		20
8.5	even	2	inner	552.2.f.d.277.20	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.d.277.19	✓	20	1.1	even	1	trivial
552.2.f.d.277.20	yes	20	8.5	even	2	inner
2208.2.f.d.1105.4		20	4.3	odd	2
2208.2.f.d.1105.17		20	8.3	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34141 - 0.447910i) q^{2} +1.00000i q^{3} +(1.59875 - 1.20166i) q^{4} -1.69969i q^{5} +(0.447910 + 1.34141i) q^{6} +2.41449 q^{7} +(1.60635 - 2.32801i) q^{8} -1.00000 q^{9} +(-0.761306 - 2.27997i) q^{10} +0.133083i q^{11} +(1.20166 + 1.59875i) q^{12} -0.529878i q^{13} +(3.23881 - 1.08147i) q^{14} +1.69969 q^{15} +(1.11203 - 3.84232i) q^{16} -3.72410 q^{17} +(-1.34141 + 0.447910i) q^{18} +1.26626i q^{19} +(-2.04245 - 2.71738i) q^{20} +2.41449i q^{21} +(0.0596093 + 0.178519i) q^{22} +1.00000 q^{23} +(2.32801 + 1.60635i) q^{24} +2.11106 q^{25} +(-0.237337 - 0.710782i) q^{26} -1.00000i q^{27} +(3.86017 - 2.90139i) q^{28} +2.58119i q^{29} +(2.27997 - 0.761306i) q^{30} +4.37283 q^{31} +(-0.229326 - 5.65220i) q^{32} -0.133083 q^{33} +(-4.99554 + 1.66806i) q^{34} -4.10387i q^{35} +(-1.59875 + 1.20166i) q^{36} +3.36341i q^{37} +(0.567169 + 1.69857i) q^{38} +0.529878 q^{39} +(-3.95689 - 2.73029i) q^{40} -5.68297 q^{41} +(1.08147 + 3.23881i) q^{42} +2.62040i q^{43} +(0.159921 + 0.212767i) q^{44} +1.69969i q^{45} +(1.34141 - 0.447910i) q^{46} -0.552068 q^{47} +(3.84232 + 1.11203i) q^{48} -1.17025 q^{49} +(2.83180 - 0.945566i) q^{50} -3.72410i q^{51} +(-0.636732 - 0.847144i) q^{52} +10.6278i q^{53} +(-0.447910 - 1.34141i) q^{54} +0.226200 q^{55} +(3.87851 - 5.62096i) q^{56} -1.26626 q^{57} +(1.15614 + 3.46243i) q^{58} -3.59762i q^{59} +(2.71738 - 2.04245i) q^{60} +6.75147i q^{61} +(5.86575 - 1.95863i) q^{62} -2.41449 q^{63} +(-2.83930 - 7.47920i) q^{64} -0.900626 q^{65} +(-0.178519 + 0.0596093i) q^{66} +0.405445i q^{67} +(-5.95392 + 4.47510i) q^{68} +1.00000i q^{69} +(-1.83816 - 5.50497i) q^{70} -5.62993 q^{71} +(-1.60635 + 2.32801i) q^{72} -8.66291 q^{73} +(1.50651 + 4.51171i) q^{74} +2.11106i q^{75} +(1.52161 + 2.02444i) q^{76} +0.321328i q^{77} +(0.710782 - 0.237337i) q^{78} -2.77706 q^{79} +(-6.53073 - 1.89010i) q^{80} +1.00000 q^{81} +(-7.62318 + 2.54546i) q^{82} +1.80097i q^{83} +(2.90139 + 3.86017i) q^{84} +6.32980i q^{85} +(1.17370 + 3.51502i) q^{86} -2.58119 q^{87} +(0.309820 + 0.213778i) q^{88} -14.1306 q^{89} +(0.761306 + 2.27997i) q^{90} -1.27938i q^{91} +(1.59875 - 1.20166i) q^{92} +4.37283i q^{93} +(-0.740549 + 0.247277i) q^{94} +2.15224 q^{95} +(5.65220 - 0.229326i) q^{96} +5.11325 q^{97} +(-1.56978 + 0.524166i) q^{98} -0.133083i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32}+ \cdots - 26 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

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