LMFDB - Embedded newform 650.2.e.j.451.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(451,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.451"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,0,-3,0,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.591408.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 $ x^6 - x^5 + 4x^4 + x^3 + 10x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.3
Root			$-0.740597 - 1.28275i$ of defining polynomial
Character	$\chi$	$=$	650.451
Dual form			650.2.e.j.601.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.837565 - 1.45071i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.837565 + 1.45071i) q^{6} +(0.903032 + 1.56410i) q^{7} +1.00000 q^{8} +(0.0969683 + 0.167954i) q^{9} +(-3.22179 + 5.58031i) q^{11} -1.67513 q^{12} +(-3.01270 + 1.98082i) q^{13} -1.80606 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.240597 + 0.416726i) q^{17} -0.193937 q^{18} +(3.14363 + 5.44492i) q^{19} +3.02539 q^{21} +(-3.22179 - 5.58031i) q^{22} +(3.55936 - 6.16499i) q^{23} +(0.837565 - 1.45071i) q^{24} +(-0.209095 - 3.59948i) q^{26} +5.35026 q^{27} +(0.903032 - 1.56410i) q^{28} +(-1.15633 + 2.00281i) q^{29} +3.25694 q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.39692 + 9.34774i) q^{33} -0.481194 q^{34} +(0.0969683 - 0.167954i) q^{36} +(1.53150 - 2.65264i) q^{37} -6.28726 q^{38} +(0.350262 + 6.02961i) q^{39} +(-3.75329 + 6.50089i) q^{41} +(-1.51270 + 2.62007i) q^{42} +(-1.00000 - 1.73205i) q^{43} +6.44358 q^{44} +(3.55936 + 6.16499i) q^{46} -2.19394 q^{47} +(0.837565 + 1.45071i) q^{48} +(1.86907 - 3.23732i) q^{49} +0.806063 q^{51} +(3.22179 + 1.61866i) q^{52} +0.906679 q^{53} +(-2.67513 + 4.63346i) q^{54} +(0.903032 + 1.56410i) q^{56} +10.5320 q^{57} +(-1.15633 - 2.00281i) q^{58} +(-3.28726 - 5.69370i) q^{59} +(5.47508 + 9.48313i) q^{61} +(-1.62847 + 2.82059i) q^{62} +(-0.175131 + 0.303336i) q^{63} +1.00000 q^{64} -10.7938 q^{66} +(0.324869 - 0.562690i) q^{67} +(0.240597 - 0.416726i) q^{68} +(-5.96239 - 10.3272i) q^{69} +(-1.83146 - 3.17217i) q^{71} +(0.0969683 + 0.167954i) q^{72} +2.60720 q^{73} +(1.53150 + 2.65264i) q^{74} +(3.14363 - 5.44492i) q^{76} -11.6375 q^{77} +(-5.39692 - 2.71147i) q^{78} -2.29455 q^{79} +(4.19029 - 7.25779i) q^{81} +(-3.75329 - 6.50089i) q^{82} -13.3380 q^{83} +(-1.51270 - 2.62007i) q^{84} +2.00000 q^{86} +(1.93700 + 3.35498i) q^{87} +(-3.22179 + 5.58031i) q^{88} +(0.578163 - 1.00141i) q^{89} +(-5.81876 - 2.92340i) q^{91} -7.11871 q^{92} +(2.72790 - 4.72486i) q^{93} +(1.09697 - 1.90000i) q^{94} -1.67513 q^{96} +(6.91573 + 11.9784i) q^{97} +(1.86907 + 3.23732i) q^{98} -1.24965 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + 5 q^{7} + 6 q^{8} + q^{9} - 3 q^{11} - 3 q^{13} - 10 q^{14} - 3 q^{16} - 4 q^{17} - 2 q^{18} + 13 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{27} + 5 q^{28} + 14 q^{29} + 12 q^{31}+ \cdots + 26 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 5 * q^7 + 6 * q^8 + q^9 - 3 * q^11 - 3 * q^13 - 10 * q^14 - 3 * q^16 - 4 * q^17 - 2 * q^18 + 13 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^27 + 5 * q^28 + 14 * q^29 + 12 * q^31 - 3 * q^32 + 6 * q^33 + 8 * q^34 + q^36 + 5 * q^37 - 26 * q^38 - 18 * q^39 - 2 * q^41 + 6 * q^42 - 6 * q^43 + 6 * q^44 - 14 * q^47 + 2 * q^49 + 4 * q^51 + 3 * q^52 + 18 * q^53 - 6 * q^54 + 5 * q^56 - 8 * q^57 + 14 * q^58 - 8 * q^59 - 4 * q^61 - 6 * q^62 + 9 * q^63 + 6 * q^64 - 12 * q^66 + 12 * q^67 - 4 * q^68 - 14 * q^69 + 20 * q^71 + q^72 - 12 * q^73 + 5 * q^74 + 13 * q^76 - 38 * q^77 - 6 * q^78 - 28 * q^79 + 13 * q^81 - 2 * q^82 - 8 * q^83 + 6 * q^84 + 12 * q^86 + 20 * q^87 - 3 * q^88 - 7 * q^89 - 19 * q^91 + 26 * q^93 + 7 * q^94 + 26 * q^97 + 2 * q^98 + 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.837565	−	1.45071i	0.483569	−	0.837565i	−0.516253	−	0.856436i	$-0.672674\pi$
$3$	0.837565	−	1.45071i	0.483569	−	0.837565i	0.999822	+	0.0188705i	$0.00600703\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.837565	+	1.45071i	0.341935	+	0.592248i
$7$	0.903032	+	1.56410i	0.341314	+	0.591173i	0.984677	−	0.174388i	$-0.0557948\pi$
$7$	0.903032	+	1.56410i	0.341314	+	0.591173i	−0.643363	+	0.765561i	$0.722461\pi$
$8$	1.00000			0.353553
$9$	0.0969683	+	0.167954i	0.0323228	+	0.0559847i
$10$		0			0
$11$	−3.22179	+	5.58031i	−0.971407	+	1.68253i	−0.280090	+	0.959974i	$0.590364\pi$
$11$	−3.22179	+	5.58031i	−0.971407	+	1.68253i	−0.691317	+	0.722552i	$0.742969\pi$
$12$	−1.67513			−0.483569
$13$	−3.01270	+	1.98082i	−0.835572	+	0.549382i
$13$	−3.01270	+	1.98082i	−0.835572	+	0.549382i
$14$	−1.80606			−0.482691
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.240597	+	0.416726i	0.0583534	+	0.101071i	0.893726	−	0.448612i	$-0.148082\pi$
$17$	0.240597	+	0.416726i	0.0583534	+	0.101071i	−0.835373	+	0.549684i	$0.814748\pi$
$18$	−0.193937			−0.0457113
$19$	3.14363	+	5.44492i	0.721198	+	1.24915i	0.960520	+	0.278211i	$0.0897415\pi$
$19$	3.14363	+	5.44492i	0.721198	+	1.24915i	−0.239322	+	0.970940i	$0.576925\pi$
$20$		0			0
$21$	3.02539			0.660195
$22$	−3.22179	−	5.58031i	−0.686888	−	1.18973i
$23$	3.55936	−	6.16499i	0.742177	−	1.28549i	−0.209325	−	0.977846i	$-0.567127\pi$
$23$	3.55936	−	6.16499i	0.742177	−	1.28549i	0.951502	−	0.307642i	$-0.0995401\pi$
$24$	0.837565	−	1.45071i	0.170967	−	0.296124i
$25$		0			0
$26$	−0.209095	−	3.59948i	−0.0410069	−	0.705917i
$27$	5.35026			1.02966
$28$	0.903032	−	1.56410i	0.170657	−	0.295587i
$29$	−1.15633	+	2.00281i	−0.214724	+	0.371913i	−0.953187	−	0.302381i	$-0.902219\pi$
$29$	−1.15633	+	2.00281i	−0.214724	+	0.371913i	0.738463	+	0.674294i	$0.235552\pi$
$30$		0			0
$31$	3.25694			0.584964			0.292482	−	0.956271i	$-0.405519\pi$
$31$	3.25694			0.584964			0.292482	+	0.956271i	$0.405519\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	5.39692	+	9.34774i	0.939484	+	1.62723i
$34$	−0.481194			−0.0825241
$35$		0			0
$36$	0.0969683	−	0.167954i	0.0161614	−	0.0279923i
$37$	1.53150	−	2.65264i	0.251777	−	0.436091i	−0.712238	−	0.701938i	$-0.752318\pi$
$37$	1.53150	−	2.65264i	0.251777	−	0.436091i	0.964015	+	0.265847i	$0.0856516\pi$
$38$	−6.28726			−1.01993
$39$	0.350262	+	6.02961i	0.0560868	+	0.965510i
$40$		0			0
$41$	−3.75329	+	6.50089i	−0.586166	+	1.01527i	0.408563	+	0.912730i	$0.366030\pi$
$41$	−3.75329	+	6.50089i	−0.586166	+	1.01527i	−0.994729	+	0.102539i	$0.967303\pi$
$42$	−1.51270	+	2.62007i	−0.233414	+	0.404285i
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	6.44358			0.971407
$45$		0			0
$46$	3.55936	+	6.16499i	0.524799	+	0.908978i
$47$	−2.19394			−0.320019			−0.160009	−	0.987116i	$-0.551152\pi$
$47$	−2.19394			−0.320019			−0.160009	+	0.987116i	$0.551152\pi$
$48$	0.837565	+	1.45071i	0.120892	+	0.209391i
$49$	1.86907	−	3.23732i	0.267010	−	0.462474i
$50$		0			0
$51$	0.806063			0.112871
$52$	3.22179	+	1.61866i	0.446782	+	0.224468i
$53$	0.906679			0.124542			0.0622710	−	0.998059i	$-0.480166\pi$
$53$	0.906679			0.124542			0.0622710	+	0.998059i	$0.480166\pi$
$54$	−2.67513	+	4.63346i	−0.364039	+	0.630534i
$55$		0			0
$56$	0.903032	+	1.56410i	0.120673	+	0.209011i
$57$	10.5320			1.39499
$58$	−1.15633	−	2.00281i	−0.151833	−	0.262982i
$59$	−3.28726	−	5.69370i	−0.427965	−	0.741256i	0.568728	−	0.822526i	$-0.307436\pi$
$59$	−3.28726	−	5.69370i	−0.427965	−	0.741256i	−0.996692	+	0.0812696i	$0.974103\pi$
$60$		0			0
$61$	5.47508	+	9.48313i	0.701013	+	1.21419i	0.968111	+	0.250521i	$0.0806018\pi$
$61$	5.47508	+	9.48313i	0.701013	+	1.21419i	−0.267098	+	0.963669i	$0.586065\pi$
$62$	−1.62847	+	2.82059i	−0.206816	+	0.358216i
$63$	−0.175131	+	0.303336i	−0.0220644	+	0.0382167i
$64$	1.00000			0.125000
$65$		0			0
$66$	−10.7938			−1.32863
$67$	0.324869	−	0.562690i	0.0396891	−	0.0687435i	−0.845499	−	0.533978i	$-0.820697\pi$
$67$	0.324869	−	0.562690i	0.0396891	−	0.0687435i	0.885188	+	0.465234i	$0.154030\pi$
$68$	0.240597	−	0.416726i	0.0291767	−	0.0505355i
$69$	−5.96239	−	10.3272i	−0.717787	−	1.24324i
$70$		0			0
$71$	−1.83146	−	3.17217i	−0.217354	−	0.376468i	0.736644	−	0.676280i	$-0.236409\pi$
$71$	−1.83146	−	3.17217i	−0.217354	−	0.376468i	−0.953998	+	0.299812i	$0.903076\pi$
$72$	0.0969683	+	0.167954i	0.0114278	+	0.0197936i
$73$	2.60720			0.305150			0.152575	−	0.988292i	$-0.451243\pi$
$73$	2.60720			0.305150			0.152575	+	0.988292i	$0.451243\pi$
$74$	1.53150	+	2.65264i	0.178033	+	0.308363i
$75$		0			0
$76$	3.14363	−	5.44492i	0.360599	−	0.624576i
$77$	−11.6375			−1.32622
$78$	−5.39692	−	2.71147i	−0.611081	−	0.307013i
$79$	−2.29455			−0.258157			−0.129079	−	0.991634i	$-0.541202\pi$
$79$	−2.29455			−0.258157			−0.129079	+	0.991634i	$0.541202\pi$
$80$		0			0
$81$	4.19029	−	7.25779i	0.465588	−	0.806422i
$82$	−3.75329	−	6.50089i	−0.414482	−	0.717904i
$83$	−13.3380			−1.46404			−0.732020	−	0.681283i	$-0.761422\pi$
$83$	−13.3380			−1.46404			−0.732020	+	0.681283i	$0.761422\pi$
$84$	−1.51270	−	2.62007i	−0.165049	−	0.285873i
$85$		0			0
$86$	2.00000			0.215666
$87$	1.93700	+	3.35498i	0.207668	+	0.359691i
$88$	−3.22179	+	5.58031i	−0.343444	+	0.594863i
$89$	0.578163	−	1.00141i	0.0612851	−	0.106149i	−0.833755	−	0.552135i	$-0.813813\pi$
$89$	0.578163	−	1.00141i	0.0612851	−	0.106149i	0.895040	+	0.445986i	$0.147147\pi$
$90$		0			0
$91$	−5.81876	−	2.92340i	−0.609972	−	0.306456i
$92$	−7.11871			−0.742177
$93$	2.72790	−	4.72486i	0.282870	−	0.489945i
$94$	1.09697	−	1.90000i	0.113144	−	0.195971i
$95$		0			0
$96$	−1.67513			−0.170967
$97$	6.91573	+	11.9784i	0.702186	+	1.21622i	0.967698	+	0.252114i	$0.0811257\pi$
$97$	6.91573	+	11.9784i	0.702186	+	1.21622i	−0.265512	+	0.964108i	$0.585541\pi$
$98$	1.86907	+	3.23732i	0.188804	+	0.327019i
$99$	−1.24965			−0.125594
$100$		0			0
$101$	4.79995	−	8.31376i	0.477613	−	0.827250i	−0.522057	−	0.852910i	$-0.674835\pi$
$101$	4.79995	−	8.31376i	0.477613	−	0.827250i	0.999671	+	0.0256599i	$0.00816868\pi$
$102$	−0.403032	+	0.698071i	−0.0399061	+	0.0691194i
$103$	−3.07522			−0.303011			−0.151505	−	0.988456i	$-0.548412\pi$
$103$	−3.07522			−0.303011			−0.151505	+	0.988456i	$0.548412\pi$
$104$	−3.01270	+	1.98082i	−0.295419	+	0.194236i
$105$		0			0
$106$	−0.453339	+	0.785207i	−0.0440322	+	0.0762660i
$107$	−0.837565	+	1.45071i	−0.0809705	+	0.140245i	−0.903667	−	0.428236i	$-0.859135\pi$
$107$	−0.837565	+	1.45071i	−0.0809705	+	0.140245i	0.822697	+	0.568481i	$0.192469\pi$
$108$	−2.67513	−	4.63346i	−0.257415	−	0.445855i
$109$	10.8872			1.04280			0.521401	−	0.853312i	$-0.325410\pi$
$109$	10.8872			1.04280			0.521401	+	0.853312i	$0.325410\pi$
$110$		0			0
$111$	−2.56547	−	4.44352i	−0.243503	−	0.421760i
$112$	−1.80606			−0.170657
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	0.981003	+	0.193993i	$0.0621440\pi$
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	−0.322498	+	0.946570i	$0.604523\pi$
$114$	−5.26599	+	9.12096i	−0.493205	+	0.854256i
$115$		0			0
$116$	2.31265			0.214724
$117$	−0.624823	−	0.313917i	−0.0577649	−	0.0290217i
$118$	6.57452			0.605233
$119$	−0.434534	+	0.752634i	−0.0398336	+	0.0689939i
$120$		0			0
$121$	−15.2599	−	26.4309i	−1.38726	−	2.40281i
$122$	−10.9502			−0.991382
$123$	6.28726	+	10.8898i	0.566903	+	0.981905i
$124$	−1.62847	−	2.82059i	−0.146241	−	0.253297i
$125$		0			0
$126$	−0.175131	−	0.303336i	−0.0156019	−	0.0270233i
$127$	−2.59332	+	4.49176i	−0.230120	+	0.398580i	−0.957843	−	0.287291i	$-0.907245\pi$
$127$	−2.59332	+	4.49176i	−0.230120	+	0.398580i	0.727723	+	0.685871i	$0.240579\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.35026			−0.294974
$130$		0			0
$131$	−10.8011			−0.943700			−0.471850	−	0.881679i	$-0.656414\pi$
$131$	−10.8011			−0.943700			−0.471850	+	0.881679i	$0.656414\pi$
$132$	5.39692	−	9.34774i	0.469742	−	0.813617i
$133$	−5.67759	+	9.83388i	−0.492310	+	0.852706i
$134$	0.324869	+	0.562690i	0.0280644	+	0.0486090i
$135$		0			0
$136$	0.240597	+	0.416726i	0.0206310	+	0.0357340i
$137$	−3.07205	−	5.32095i	−0.262463	−	0.454600i	0.704433	−	0.709771i	$-0.251202\pi$
$137$	−3.07205	−	5.32095i	−0.262463	−	0.454600i	−0.966896	+	0.255171i	$0.917868\pi$
$138$	11.9248			1.01510
$139$	−5.16902	−	8.95301i	−0.438431	−	0.759384i	0.559138	−	0.829075i	$-0.311132\pi$
$139$	−5.16902	−	8.95301i	−0.438431	−	0.759384i	−0.997569	+	0.0696904i	$0.977799\pi$
$140$		0			0
$141$	−1.83757	+	3.18276i	−0.154751	+	0.268036i
$142$	3.66291			0.307385
$143$	−1.34732	−	23.1936i	−0.112669	−	1.93954i
$144$	−0.193937			−0.0161614
$145$		0			0
$146$	−1.30360	+	2.25790i	−0.107887	+	0.186865i
$147$	−3.13093	−	5.42293i	−0.258235	−	0.447276i
$148$	−3.06300			−0.251777
$149$	8.02539	+	13.9004i	0.657466	+	1.13876i	0.981270	+	0.192640i	$0.0617049\pi$
$149$	8.02539	+	13.9004i	0.657466	+	1.13876i	−0.323804	+	0.946124i	$0.604962\pi$
$150$		0			0
$151$	9.31757			0.758253			0.379127	−	0.925345i	$-0.376224\pi$
$151$	9.31757			0.758253			0.379127	+	0.925345i	$0.376224\pi$
$152$	3.14363	+	5.44492i	0.254982	+	0.441642i
$153$	−0.0466606	+	0.0808185i	−0.00377228	+	0.00653379i
$154$	5.81876	−	10.0784i	0.468889	−	0.812140i
$155$		0			0
$156$	5.04666	−	3.31814i	0.404056	−	0.265664i
$157$	14.7562			1.17768			0.588838	−	0.808251i	$-0.299586\pi$
$157$	14.7562			1.17768			0.588838	+	0.808251i	$0.299586\pi$
$158$	1.14728	−	1.98714i	0.0912724	−	0.158088i
$159$	0.759403	−	1.31532i	0.0602246	−	0.104312i
$160$		0			0
$161$	12.8568			1.01326
$162$	4.19029	+	7.25779i	0.329220	+	0.570226i
$163$	−6.76234	−	11.7127i	−0.529668	−	0.917411i	−0.999401	−	0.0346029i	$-0.988983\pi$
$163$	−6.76234	−	11.7127i	−0.529668	−	0.917411i	0.469734	−	0.882808i	$-0.344350\pi$
$164$	7.50659			0.586166
$165$		0			0
$166$	6.66902	−	11.5511i	0.517616	−	0.896538i
$167$	11.7120	−	20.2858i	0.906304	−	1.56977i	0.0871479	−	0.996195i	$-0.472225\pi$
$167$	11.7120	−	20.2858i	0.906304	−	1.56977i	0.819157	−	0.573570i	$-0.194442\pi$
$168$	3.02539			0.233414
$169$	5.15268	−	11.9352i	0.396360	−	0.918095i
$170$		0			0
$171$	−0.609665	+	1.05597i	−0.0466222	+	0.0807520i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−2.31217	−	4.00480i	−0.175791	−	0.304479i	0.764644	−	0.644453i	$-0.222915\pi$
$173$	−2.31217	−	4.00480i	−0.175791	−	0.304479i	−0.940435	+	0.339974i	$0.889582\pi$
$174$	−3.87399			−0.293687
$175$		0			0
$176$	−3.22179	−	5.58031i	−0.242852	−	0.420631i
$177$	−11.0132			−0.827801
$178$	0.578163	+	1.00141i	0.0433351	+	0.0750586i
$179$	4.15633	−	7.19897i	0.310658	−	0.538076i	−0.667847	−	0.744299i	$-0.732784\pi$
$179$	4.15633	−	7.19897i	0.310658	−	0.538076i	0.978505	+	0.206223i	$0.0661172\pi$
$180$		0			0
$181$	−1.02539			−0.0762168			−0.0381084	−	0.999274i	$-0.512133\pi$
$181$	−1.02539			−0.0762168			−0.0381084	+	0.999274i	$0.512133\pi$
$182$	5.44112	−	3.57749i	0.403323	−	0.265181i
$183$	18.3430			1.35595
$184$	3.55936	−	6.16499i	0.262399	−	0.454489i
$185$		0			0
$186$	2.72790	+	4.72486i	0.200019	+	0.346444i
$187$	−3.10062			−0.226739
$188$	1.09697	+	1.90000i	0.0800046	+	0.138572i
$189$	4.83146	+	8.36833i	0.351437	+	0.608706i
$190$		0			0
$191$	−0.177593	−	0.307600i	−0.0128502	−	0.0222572i	0.859529	−	0.511087i	$-0.170757\pi$
$191$	−0.177593	−	0.307600i	−0.0128502	−	0.0222572i	−0.872379	+	0.488830i	$0.837424\pi$
$192$	0.837565	−	1.45071i	0.0604461	−	0.104696i
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	−13.8315			−0.993041
$195$		0			0
$196$	−3.73813			−0.267010
$197$	−7.05325	+	12.2166i	−0.502523	+	0.870396i	0.497473	+	0.867480i	$0.334261\pi$
$197$	−7.05325	+	12.2166i	−0.502523	+	0.870396i	−0.999996	+	0.00291585i	$0.999072\pi$
$198$	0.624823	−	1.08223i	0.0444042	−	0.0769104i
$199$	1.57452	+	2.72714i	0.111614	+	0.193322i	0.916421	−	0.400215i	$-0.131065\pi$
$199$	1.57452	+	2.72714i	0.111614	+	0.193322i	−0.804807	+	0.593537i	$0.797731\pi$
$200$		0			0
$201$	−0.544198	−	0.942579i	−0.0383848	−	0.0664844i
$202$	4.79995	+	8.31376i	0.337724	+	0.584954i
$203$	−4.17679			−0.293153
$204$	−0.403032	−	0.698071i	−0.0282179	−	0.0488748i
$205$		0			0
$206$	1.53761	−	2.66322i	0.107130	−	0.185555i
$207$	1.38058			0.0959569
$208$	−0.209095	−	3.59948i	−0.0144981	−	0.249579i
$209$	−40.5125			−2.80231
$210$		0			0
$211$	−1.54666	+	2.67889i	−0.106477	+	0.184423i	−0.914340	−	0.404946i	$-0.867290\pi$
$211$	−1.54666	+	2.67889i	−0.106477	+	0.184423i	0.807864	+	0.589369i	$0.200624\pi$
$212$	−0.453339	−	0.785207i	−0.0311355	−	0.0539282i
$213$	−6.13586			−0.420422
$214$	−0.837565	−	1.45071i	−0.0572548	−	0.0991682i
$215$		0			0
$216$	5.35026			0.364039
$217$	2.94112	+	5.09417i	0.199656	+	0.345815i
$218$	−5.44358	+	9.42856i	−0.368686	+	0.638583i
$219$	2.18370	−	3.78228i	0.147561	−	0.255583i
$220$		0			0
$221$	−1.55031	−	0.778890i	−0.104285	−	0.0523938i
$222$	5.13093			0.344366
$223$	11.0970	−	19.2205i	0.743108	−	1.28710i	−0.207966	−	0.978136i	$-0.566684\pi$
$223$	11.0970	−	19.2205i	0.743108	−	1.28710i	0.951074	−	0.308965i	$-0.0999825\pi$
$224$	0.903032	−	1.56410i	0.0603363	−	0.104506i
$225$		0			0
$226$	−14.0000			−0.931266
$227$	−6.66784	−	11.5490i	−0.442560	−	0.766536i	0.555319	−	0.831638i	$-0.312596\pi$
$227$	−6.66784	−	11.5490i	−0.442560	−	0.766536i	−0.997879	+	0.0651014i	$0.979263\pi$
$228$	−5.26599	−	9.12096i	−0.348749	−	0.604050i
$229$	26.1744			1.72965			0.864827	−	0.502069i	$-0.167428\pi$
$229$	26.1744			1.72965			0.864827	+	0.502069i	$0.167428\pi$
$230$		0			0
$231$	−9.74718	+	16.8826i	−0.641318	+	1.11079i
$232$	−1.15633	+	2.00281i	−0.0759165	+	0.131491i
$233$	−20.8691			−1.36718			−0.683589	−	0.729867i	$-0.739582\pi$
$233$	−20.8691			−1.36718			−0.683589	+	0.729867i	$0.739582\pi$
$234$	0.584272	−	0.384154i	0.0381951	−	0.0251129i
$235$		0			0
$236$	−3.28726	+	5.69370i	−0.213982	+	0.370628i
$237$	−1.92184	+	3.32872i	−0.124837	+	0.216224i
$238$	−0.434534	−	0.752634i	−0.0281666	−	0.0487860i
$239$	−15.2931			−0.989231			−0.494615	−	0.869112i	$-0.664691\pi$
$239$	−15.2931			−0.989231			−0.494615	+	0.869112i	$0.664691\pi$
$240$		0			0
$241$	6.38423	+	11.0578i	0.411244	+	0.712296i	0.995026	−	0.0996147i	$-0.0317610\pi$
$241$	6.38423	+	11.0578i	0.411244	+	0.712296i	−0.583782	+	0.811910i	$0.698428\pi$
$242$	30.5198			1.96188
$243$	1.00611	+	1.74263i	0.0645419	+	0.111790i
$244$	5.47508	−	9.48313i	0.350506	−	0.607095i
$245$		0			0
$246$	−12.5745			−0.801722
$247$	−20.2562	−	10.1769i	−1.28887	−	0.647543i
$248$	3.25694			0.206816
$249$	−11.1715	+	19.3496i	−0.707964	+	1.22623i
$250$		0			0
$251$	2.10602	+	3.64773i	0.132931	+	0.230243i	0.924805	−	0.380441i	$-0.124228\pi$
$251$	2.10602	+	3.64773i	0.132931	+	0.230243i	−0.791874	+	0.610684i	$0.790895\pi$
$252$	0.350262			0.0220644
$253$	22.9350	+	39.7246i	1.44191	+	2.49746i
$254$	−2.59332	−	4.49176i	−0.162719	−	0.281838i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.31265	−	16.1300i	0.580907	−	1.00616i	−0.414465	−	0.910065i	$-0.636031\pi$
$257$	9.31265	−	16.1300i	0.580907	−	1.00616i	0.995372	−	0.0960955i	$-0.0306354\pi$
$258$	1.67513	−	2.90141i	0.104289	−	0.180634i
$259$	5.53198			0.343740
$260$		0			0
$261$	−0.448507			−0.0277619
$262$	5.40057	−	9.35406i	0.333648	−	0.577896i
$263$	−11.5102	+	19.9363i	−0.709751	+	1.22933i	0.255198	+	0.966889i	$0.417859\pi$
$263$	−11.5102	+	19.9363i	−0.709751	+	1.22933i	−0.964949	+	0.262437i	$0.915474\pi$
$264$	5.39692	+	9.34774i	0.332158	+	0.575314i
$265$		0			0
$266$	−5.67759	−	9.83388i	−0.348116	−	0.602954i
$267$	−0.968498	−	1.67749i	−0.0592711	−	0.102661i
$268$	−0.649738			−0.0396891
$269$	6.73695	+	11.6687i	0.410759	+	0.711456i	0.994973	−	0.100144i	$-0.0319304\pi$
$269$	6.73695	+	11.6687i	0.410759	+	0.711456i	−0.584214	+	0.811600i	$0.698597\pi$
$270$		0			0
$271$	8.95017	−	15.5021i	0.543684	−	0.941688i	−0.455004	−	0.890489i	$-0.650362\pi$
$271$	8.95017	−	15.5021i	0.543684	−	0.941688i	0.998688	−	0.0511993i	$-0.0163044\pi$
$272$	−0.481194			−0.0291767
$273$	−9.11459	+	5.99277i	−0.551640	+	0.362699i
$274$	6.14411			0.371179
$275$		0			0
$276$	−5.96239	+	10.3272i	−0.358894	+	0.621622i
$277$	4.24424	+	7.35125i	0.255012	+	0.441694i	0.964899	−	0.262622i	$-0.0845873\pi$
$277$	4.24424	+	7.35125i	0.255012	+	0.441694i	−0.709887	+	0.704316i	$0.751254\pi$
$278$	10.3380			0.620035
$279$	0.315820	+	0.547016i	0.0189076	+	0.0327490i
$280$		0			0
$281$	−16.5296			−0.986074			−0.493037	−	0.870008i	$-0.664113\pi$
$281$	−16.5296			−0.986074			−0.493037	+	0.870008i	$0.664113\pi$
$282$	−1.83757	−	3.18276i	−0.109425	−	0.189530i
$283$	0.768452	−	1.33100i	0.0456797	−	0.0791196i	−0.842282	−	0.539038i	$-0.818788\pi$
$283$	0.768452	−	1.33100i	0.0456797	−	0.0791196i	0.887961	+	0.459918i	$0.152121\pi$
$284$	−1.83146	+	3.17217i	−0.108677	+	0.188234i
$285$		0			0
$286$	20.7599	+	10.4300i	1.22756	+	0.616737i
$287$	−13.5574			−0.800266
$288$	0.0969683	−	0.167954i	0.00571391	−	0.00989678i
$289$	8.38423	−	14.5219i	0.493190	−	0.854230i
$290$		0			0
$291$	23.1695			1.35822
$292$	−1.30360	−	2.25790i	−0.0762875	−	0.132134i
$293$	2.96485	+	5.13527i	0.173208	+	0.300006i	0.939540	−	0.342440i	$-0.111253\pi$
$293$	2.96485	+	5.13527i	0.173208	+	0.300006i	−0.766331	+	0.642446i	$0.777920\pi$
$294$	6.26187			0.365199
$295$		0			0
$296$	1.53150	−	2.65264i	0.0890167	−	0.154182i
$297$	−17.2374	+	29.8561i	−1.00022	+	1.73243i
$298$	−16.0508			−0.929797
$299$	1.48849	+	25.6237i	0.0860815	+	1.48186i
$300$		0			0
$301$	1.80606	−	3.12819i	0.104100	−	0.180306i
$302$	−4.65879	+	8.06926i	−0.268083	+	0.464334i
$303$	−8.04055	−	13.9266i	−0.461918	−	0.800065i
$304$	−6.28726			−0.360599
$305$		0			0
$306$	−0.0466606	−	0.0808185i	−0.00266741	−	0.00462009i
$307$	−17.9756			−1.02592			−0.512960	−	0.858413i	$-0.671451\pi$
$307$	−17.9756			−1.02592			−0.512960	+	0.858413i	$0.671451\pi$
$308$	5.81876	+	10.0784i	0.331555	+	0.574269i
$309$	−2.57570	+	4.46124i	−0.146526	+	0.253791i
$310$		0			0
$311$	15.9575			0.904865			0.452432	−	0.891799i	$-0.350556\pi$
$311$	15.9575			0.904865			0.452432	+	0.891799i	$0.350556\pi$
$312$	0.350262	+	6.02961i	0.0198297	+	0.341359i
$313$	−23.4372			−1.32475			−0.662376	−	0.749172i	$-0.730452\pi$
$313$	−23.4372			−1.32475			−0.662376	+	0.749172i	$0.730452\pi$
$314$	−7.37812	+	12.7793i	−0.416371	+	0.721176i
$315$		0			0
$316$	1.14728	+	1.98714i	0.0645393	+	0.111785i
$317$	−20.6507			−1.15986			−0.579929	−	0.814667i	$-0.696920\pi$
$317$	−20.6507			−1.15986			−0.579929	+	0.814667i	$0.696920\pi$
$318$	0.759403	+	1.31532i	0.0425852	+	0.0737597i
$319$	−7.45088	−	12.9053i	−0.417169	−	0.722558i
$320$		0			0
$321$	1.40303	+	2.43012i	0.0783096	+	0.135636i
$322$	−6.42842	+	11.1344i	−0.358242	+	0.620493i
$323$	−1.51270	+	2.62007i	−0.0841687	+	0.145784i
$324$	−8.38058			−0.465588
$325$		0			0
$326$	13.5247			0.749063
$327$	9.11871	−	15.7941i	0.504266	−	0.873414i
$328$	−3.75329	+	6.50089i	−0.207241	+	0.358952i
$329$	−1.98119	−	3.43153i	−0.109227	−	0.189186i
$330$		0			0
$331$	13.3380	+	23.1022i	0.733125	+	1.26981i	0.955541	+	0.294858i	$0.0952724\pi$
$331$	13.3380	+	23.1022i	0.733125	+	1.26981i	−0.222416	+	0.974952i	$0.571394\pi$
$332$	6.66902	+	11.5511i	0.366010	+	0.633948i
$333$	0.594028			0.0325526
$334$	11.7120	+	20.2858i	0.640854	+	1.10999i
$335$		0			0
$336$	−1.51270	+	2.62007i	−0.0825243	+	0.142936i
$337$	−8.40597			−0.457902			−0.228951	−	0.973438i	$-0.573530\pi$
$337$	−8.40597			−0.457902			−0.228951	+	0.973438i	$0.573530\pi$
$338$	7.75988	+	10.4300i	0.422082	+	0.567316i
$339$	23.4518			1.27373
$340$		0			0
$341$	−10.4932	+	18.1747i	−0.568238	+	0.984217i
$342$	−0.609665	−	1.05597i	−0.0329669	−	0.0571003i
$343$	19.3938			1.04716
$344$	−1.00000	−	1.73205i	−0.0539164	−	0.0933859i
$345$		0			0
$346$	4.62435			0.248606
$347$	10.5757	+	18.3177i	0.567733	+	0.983343i	0.996790	+	0.0800652i	$0.0255129\pi$
$347$	10.5757	+	18.3177i	0.567733	+	0.983343i	−0.429056	+	0.903278i	$0.641154\pi$
$348$	1.93700	−	3.35498i	0.103834	−	0.179846i
$349$	−2.73695	+	4.74054i	−0.146506	+	0.253755i	−0.929934	−	0.367727i	$-0.880136\pi$
$349$	−2.73695	+	4.74054i	−0.146506	+	0.253755i	0.783428	+	0.621482i	$0.213469\pi$
$350$		0			0
$351$	−16.1187	+	10.5979i	−0.860353	+	0.565675i
$352$	6.44358			0.343444
$353$	15.0721	−	26.1056i	0.802204	−	1.38946i	−0.115958	−	0.993254i	$-0.536994\pi$
$353$	15.0721	−	26.1056i	0.802204	−	1.38946i	0.918162	−	0.396205i	$-0.129673\pi$
$354$	5.50659	−	9.53769i	0.292672	−	0.506922i
$355$		0			0
$356$	−1.15633			−0.0612851
$357$	0.727901	+	1.26076i	0.0385246	+	0.0667266i
$358$	4.15633	+	7.19897i	0.219669	+	0.380477i
$359$	−8.38787			−0.442695			−0.221348	−	0.975195i	$-0.571046\pi$
$359$	−8.38787			−0.442695			−0.221348	+	0.975195i	$0.571046\pi$
$360$		0			0
$361$	−10.2648	+	17.7792i	−0.540253	+	0.935745i
$362$	0.512696	−	0.888016i	0.0269467	−	0.0466731i
$363$	−51.1246			−2.68335
$364$	0.377639	+	6.50089i	0.0197937	+	0.340739i
$365$		0			0
$366$	−9.17148	+	15.8855i	−0.479401	+	0.830347i
$367$	9.75623	−	16.8983i	0.509271	−	0.882084i	−0.490671	−	0.871345i	$-0.663248\pi$
$367$	9.75623	−	16.8983i	0.509271	−	0.882084i	0.999942	−	0.0107388i	$-0.00341833\pi$
$368$	3.55936	+	6.16499i	0.185544	+	0.321372i
$369$	−1.45580			−0.0757860
$370$		0			0
$371$	0.818760	+	1.41813i	0.0425079	+	0.0736258i
$372$	−5.45580			−0.282870
$373$	4.25694	+	7.37324i	0.220416	+	0.381772i	0.954934	−	0.296817i	$-0.0959252\pi$
$373$	4.25694	+	7.37324i	0.220416	+	0.381772i	−0.734518	+	0.678589i	$0.762592\pi$
$374$	1.55031	−	2.68521i	0.0801645	−	0.138849i
$375$		0			0
$376$	−2.19394			−0.113144
$377$	−0.483564	−	8.32435i	−0.0249048	−	0.428726i
$378$	−9.66291			−0.497007
$379$	9.85931	−	17.0768i	0.506439	−	0.877178i	−0.493533	−	0.869727i	$-0.664295\pi$
$379$	9.85931	−	17.0768i	0.506439	−	0.877178i	0.999972	−	0.00745089i	$-0.00237172\pi$
$380$		0			0
$381$	4.34415	+	7.52429i	0.222558	+	0.385481i
$382$	0.355186			0.0181729
$383$	−13.8598	−	24.0059i	−0.708202	−	1.22664i	−0.965523	−	0.260316i	$-0.916173\pi$
$383$	−13.8598	−	24.0059i	−0.708202	−	1.22664i	0.257321	−	0.966326i	$-0.417160\pi$
$384$	0.837565	+	1.45071i	0.0427418	+	0.0740310i
$385$		0			0
$386$	7.00000	+	12.1244i	0.356291	+	0.617113i
$387$	0.193937	−	0.335908i	0.00985835	−	0.0170752i
$388$	6.91573	−	11.9784i	0.351093	−	0.608111i
$389$	9.15140			0.463994			0.231997	−	0.972716i	$-0.425474\pi$
$389$	9.15140			0.463994			0.231997	+	0.972716i	$0.425474\pi$
$390$		0			0
$391$	3.42548			0.173234
$392$	1.86907	−	3.23732i	0.0944022	−	0.163509i
$393$	−9.04666	+	15.6693i	−0.456344	+	0.790410i
$394$	−7.05325	−	12.2166i	−0.355337	−	0.615463i
$395$		0			0
$396$	0.624823	+	1.08223i	0.0313985	+	0.0543839i
$397$	−0.715205	−	1.23877i	−0.0358951	−	0.0621721i	0.847520	−	0.530764i	$-0.178095\pi$
$397$	−0.715205	−	1.23877i	−0.0358951	−	0.0621721i	−0.883415	+	0.468592i	$0.844762\pi$
$398$	−3.14903			−0.157847
$399$	9.51071	+	16.4730i	0.476131	+	0.824683i
$400$		0			0
$401$	−10.8351	+	18.7669i	−0.541079	+	0.937177i	0.457763	+	0.889074i	$0.348651\pi$
$401$	−10.8351	+	18.7669i	−0.541079	+	0.937177i	−0.998842	+	0.0481025i	$0.984683\pi$
$402$	1.08840			0.0542843
$403$	−9.81217	+	6.45142i	−0.488779	+	0.321368i
$404$	−9.59991			−0.477613
$405$		0			0
$406$	2.08840	−	3.61721i	0.103645	−	0.179519i
$407$	9.86836	+	17.0925i	0.489156	+	0.847244i
$408$	0.806063			0.0399061
$409$	−4.54055	−	7.86447i	−0.224516	−	0.388873i	0.731658	−	0.681672i	$-0.238747\pi$
$409$	−4.54055	−	7.86447i	−0.224516	−	0.388873i	−0.956174	+	0.292799i	$0.905413\pi$
$410$		0			0
$411$	−10.2922			−0.507676
$412$	1.53761	+	2.66322i	0.0757527	+	0.131207i
$413$	5.93700	−	10.2832i	0.292140	−	0.506002i
$414$	−0.690289	+	1.19562i	−0.0339259	+	0.0587613i
$415$		0			0
$416$	3.22179	+	1.61866i	0.157961	+	0.0793613i
$417$	−17.3176			−0.848045
$418$	20.2562	−	35.0848i	0.990765	−	1.71605i
$419$	7.77139	−	13.4604i	0.379657	−	0.657586i	−0.611355	−	0.791356i	$-0.709375\pi$
$419$	7.77139	−	13.4604i	0.379657	−	0.657586i	0.991012	+	0.133771i	$0.0427086\pi$
$420$		0			0
$421$	−4.96476			−0.241968			−0.120984	−	0.992654i	$-0.538605\pi$
$421$	−4.96476			−0.241968			−0.120984	+	0.992654i	$0.538605\pi$
$422$	−1.54666	−	2.67889i	−0.0752903	−	0.130407i
$423$	−0.212742	−	0.368480i	−0.0103439	−	0.0179161i
$424$	0.906679			0.0440322
$425$		0			0
$426$	3.06793	−	5.31381i	0.148642	−	0.257455i
$427$	−9.88835	+	17.1271i	−0.478531	+	0.828840i
$428$	1.67513			0.0809705
$429$	−34.7755	−	17.4716i	−1.67898	−	0.843535i
$430$		0			0
$431$	16.4853	−	28.5534i	0.794070	−	1.37537i	−0.129358	−	0.991598i	$-0.541292\pi$
$431$	16.4853	−	28.5534i	0.794070	−	1.37537i	0.923428	−	0.383771i	$-0.125375\pi$
$432$	−2.67513	+	4.63346i	−0.128707	+	0.222928i
$433$	8.05571	+	13.9529i	0.387133	+	0.670534i	0.992063	−	0.125745i	$-0.0401322\pi$
$433$	8.05571	+	13.9529i	0.387133	+	0.670534i	−0.604930	+	0.796279i	$0.706799\pi$
$434$	−5.88224			−0.282357
$435$		0			0
$436$	−5.44358	−	9.42856i	−0.260700	−	0.451546i
$437$	44.7572			2.14103
$438$	2.18370	+	3.78228i	0.104341	+	0.180725i
$439$	0.0417360	−	0.0722889i	0.00199195	−	0.00345016i	−0.865028	−	0.501724i	$-0.832699\pi$
$439$	0.0417360	−	0.0722889i	0.00199195	−	0.00345016i	0.867020	+	0.498274i	$0.166033\pi$
$440$		0			0
$441$	0.724961			0.0345220
$442$	1.44969	−	0.953161i	0.0689548	−	0.0453372i
$443$	40.9135			1.94386			0.971930	−	0.235271i	$-0.0755977\pi$
$443$	40.9135			1.94386			0.971930	+	0.235271i	$0.0755977\pi$
$444$	−2.56547	+	4.44352i	−0.121752	+	0.210880i
$445$		0			0
$446$	11.0970	+	19.2205i	0.525457	+	0.910118i
$447$	26.8872			1.27172
$448$	0.903032	+	1.56410i	0.0426642	+	0.0738966i
$449$	14.5659	+	25.2290i	0.687409	+	1.19063i	0.972673	+	0.232179i	$0.0745855\pi$
$449$	14.5659	+	25.2290i	0.687409	+	1.19063i	−0.285264	+	0.958449i	$0.592081\pi$
$450$		0			0
$451$	−24.1847	−	41.8891i	−1.13881	−	1.97248i
$452$	7.00000	−	12.1244i	0.329252	−	0.570282i
$453$	7.80408	−	13.5171i	0.366668	−	0.635087i
$454$	13.3357			0.625874
$455$		0			0
$456$	10.5320			0.493205
$457$	16.3339	−	28.2912i	0.764068	−	1.32341i	−0.176669	−	0.984270i	$-0.556532\pi$
$457$	16.3339	−	28.2912i	0.764068	−	1.32341i	0.940738	−	0.339135i	$-0.110134\pi$
$458$	−13.0872	+	22.6677i	−0.611525	+	1.05919i
$459$	1.28726	+	2.22960i	0.0600840	+	0.104069i
$460$		0			0
$461$	9.55031	+	16.5416i	0.444802	+	0.770420i	0.998038	−	0.0626044i	$-0.0199407\pi$
$461$	9.55031	+	16.5416i	0.444802	+	0.770420i	−0.553236	+	0.833024i	$0.686607\pi$
$462$	−9.74718	−	16.8826i	−0.453480	−	0.785450i
$463$	8.29218			0.385370			0.192685	−	0.981261i	$-0.438280\pi$
$463$	8.29218			0.385370			0.192685	+	0.981261i	$0.438280\pi$
$464$	−1.15633	−	2.00281i	−0.0536810	−	0.0929783i
$465$		0			0
$466$	10.4345	−	18.0731i	0.483370	−	0.837222i
$467$	−23.5369			−1.08916			−0.544579	−	0.838710i	$-0.683311\pi$
$467$	−23.5369			−1.08916			−0.544579	+	0.838710i	$0.683311\pi$
$468$	0.0405512	+	0.698071i	0.00187448	+	0.0322684i
$469$	1.17347			0.0541857
$470$		0			0
$471$	12.3593	−	21.4070i	0.569487	−	0.986380i
$472$	−3.28726	−	5.69370i	−0.151308	−	0.262074i
$473$	12.8872			0.592553
$474$	−1.92184	−	3.32872i	−0.0882729	−	0.152893i
$475$		0			0
$476$	0.869067			0.0398336
$477$	0.0879191	+	0.152280i	0.00402554	+	0.00697244i
$478$	7.64657	−	13.2442i	0.349746	−	0.605778i
$479$	−3.27821	+	5.67802i	−0.149785	+	0.259436i	−0.931148	−	0.364642i	$-0.881192\pi$
$479$	−3.27821	+	5.67802i	−0.149785	+	0.259436i	0.781363	+	0.624077i	$0.214525\pi$
$480$		0			0
$481$	0.640459	+	11.0252i	0.0292024	+	0.502707i
$482$	−12.7685			−0.581587
$483$	10.7685	−	18.6515i	0.489982	−	0.848673i
$484$	−15.2599	+	26.4309i	−0.693631	+	1.20140i
$485$		0			0
$486$	−2.01222			−0.0912761
$487$	6.77996	+	11.7432i	0.307229	+	0.532137i	0.977755	−	0.209749i	$-0.0672648\pi$
$487$	6.77996	+	11.7432i	0.307229	+	0.532137i	−0.670526	+	0.741886i	$0.733931\pi$
$488$	5.47508	+	9.48313i	0.247845	+	0.429281i
$489$	−22.6556			−1.02452
$490$		0			0
$491$	−2.47873	+	4.29329i	−0.111864	+	0.193753i	−0.916522	−	0.399985i	$-0.869015\pi$
$491$	−2.47873	+	4.29329i	−0.111864	+	0.193753i	0.804658	+	0.593739i	$0.202349\pi$
$492$	6.28726	−	10.8898i	0.283451	−	0.490952i
$493$	−1.11283			−0.0501195
$494$	18.9416	−	12.4539i	0.852223	−	0.560330i
$495$		0			0
$496$	−1.62847	+	2.82059i	−0.0731205	+	0.126648i
$497$	3.30773	−	5.72915i	0.148372	−	0.256987i
$498$	−11.1715	−	19.3496i	−0.500606	−	0.867075i
$499$	−13.8700			−0.620907			−0.310454	−	0.950588i	$-0.600481\pi$
$499$	−13.8700			−0.620907			−0.310454	+	0.950588i	$0.600481\pi$
$500$		0			0
$501$	−19.6192	−	33.9814i	−0.876521	−	1.51818i
$502$	−4.21203			−0.187992
$503$	1.72425	+	2.98650i	0.0768807	+	0.133161i	0.901903	−	0.431940i	$-0.142171\pi$
$503$	1.72425	+	2.98650i	0.0768807	+	0.133161i	−0.825022	+	0.565101i	$0.808837\pi$
$504$	−0.175131	+	0.303336i	−0.00780095	+	0.0135116i
$505$		0			0
$506$	−45.8700			−2.03917
$507$	−12.9988	−	17.4716i	−0.577298	−	0.775939i
$508$	5.18664			0.230120
$509$	15.4812	−	26.8142i	0.686192	−	1.18852i	−0.286869	−	0.957970i	$-0.592614\pi$
$509$	15.4812	−	26.8142i	0.686192	−	1.18852i	0.973061	−	0.230549i	$-0.0740523\pi$
$510$		0			0
$511$	2.35439	+	4.07792i	0.104152	+	0.180396i
$512$	1.00000			0.0441942
$513$	16.8192	+	29.1318i	0.742587	+	1.28620i
$514$	9.31265	+	16.1300i	0.410763	+	0.711463i
$515$		0			0
$516$	1.67513	+	2.90141i	0.0737435	+	0.127728i
$517$	7.06841	−	12.2428i	0.310868	−	0.538439i
$518$	−2.76599	+	4.79083i	−0.121531	+	0.210497i
$519$	−7.74638			−0.340029
$520$		0			0
$521$	14.2506			0.624330			0.312165	−	0.950028i	$-0.398946\pi$
$521$	14.2506			0.624330			0.312165	+	0.950028i	$0.398946\pi$
$522$	0.224254	−	0.388419i	0.00981532	−	0.0170006i
$523$	−5.25694	+	9.10529i	−0.229870	+	0.398146i	−0.957769	−	0.287537i	$-0.907163\pi$
$523$	−5.25694	+	9.10529i	−0.229870	+	0.398146i	0.727899	+	0.685684i	$0.240497\pi$
$524$	5.40057	+	9.35406i	0.235925	+	0.408634i
$525$		0			0
$526$	−11.5102	−	19.9363i	−0.501870	−	0.869264i
$527$	0.783611	+	1.35725i	0.0341346	+	0.0591229i
$528$	−10.7938			−0.469742
$529$	−13.8380	−	23.9682i	−0.601654	−	1.04210i
$530$		0			0
$531$	0.637519	−	1.10422i	0.0276660	−	0.0479189i
$532$	11.3552			0.492310
$533$	−1.56959	−	27.0198i	−0.0679865	−	1.17036i
$534$	1.93700			0.0838220
$535$		0			0
$536$	0.324869	−	0.562690i	0.0140322	−	0.0243045i
$537$	−6.96239	−	12.0592i	−0.300449	−	0.520393i
$538$	−13.4739			−0.580901
$539$	12.0435	+	20.8599i	0.518750	+	0.898501i
$540$		0			0
$541$	15.5345			0.667882			0.333941	−	0.942594i	$-0.391621\pi$
$541$	15.5345			0.667882			0.333941	+	0.942594i	$0.391621\pi$
$542$	8.95017	+	15.5021i	0.384443	+	0.665874i
$543$	−0.858833	+	1.48754i	−0.0368561	+	0.0638366i
$544$	0.240597	−	0.416726i	0.0103155	−	0.0178670i
$545$		0			0
$546$	−0.632595	−	10.8898i	−0.0270726	−	0.466043i
$547$	23.5515			1.00699			0.503495	−	0.863998i	$-0.332047\pi$
$547$	23.5515			1.00699			0.503495	+	0.863998i	$0.332047\pi$
$548$	−3.07205	+	5.32095i	−0.131232	+	0.227300i
$549$	−1.06182	+	1.83912i	−0.0453173	+	0.0784919i
$550$		0			0
$551$	−14.5402			−0.619435
$552$	−5.96239	−	10.3272i	−0.253776	−	0.439553i
$553$	−2.07205	−	3.58890i	−0.0881127	−	0.152616i
$554$	−8.48849			−0.360641
$555$		0			0
$556$	−5.16902	+	8.95301i	−0.219215	+	0.379692i
$557$	10.0229	−	17.3602i	0.424685	−	0.735576i	−0.571706	−	0.820459i	$-0.693718\pi$
$557$	10.0229	−	17.3602i	0.424685	−	0.735576i	0.996391	+	0.0848824i	$0.0270515\pi$
$558$	−0.631640			−0.0267394
$559$	6.44358	+	3.23732i	0.272535	+	0.136924i
$560$		0			0
$561$	−2.59697	+	4.49808i	−0.109644	+	0.189909i
$562$	8.26480	−	14.3151i	0.348630	−	0.603844i
$563$	−6.28726	−	10.8898i	−0.264976	−	0.458952i	0.702581	−	0.711604i	$-0.252031\pi$
$563$	−6.28726	−	10.8898i	−0.264976	−	0.458952i	−0.967557	+	0.252651i	$0.918697\pi$
$564$	3.67513			0.154751
$565$		0			0
$566$	0.768452	+	1.33100i	0.0323004	+	0.0559460i
$567$	15.1359			0.635646
$568$	−1.83146	−	3.17217i	−0.0768462	−	0.133102i
$569$	−2.14481	+	3.71493i	−0.0899153	+	0.155738i	−0.907475	−	0.420106i	$-0.861993\pi$
$569$	−2.14481	+	3.71493i	−0.0899153	+	0.155738i	0.817560	+	0.575844i	$0.195326\pi$
$570$		0			0
$571$	6.39280			0.267530			0.133765	−	0.991013i	$-0.457293\pi$
$571$	6.39280			0.267530			0.133765	+	0.991013i	$0.457293\pi$
$572$	−19.4126	+	12.7636i	−0.811680	+	0.533673i
$573$	−0.594984			−0.0248558
$574$	6.77869	−	11.7410i	0.282937	−	0.490061i
$575$		0			0
$576$	0.0969683	+	0.167954i	0.00404035	+	0.00699808i
$577$	−37.8169			−1.57434			−0.787168	−	0.616738i	$-0.788454\pi$
$577$	−37.8169			−1.57434			−0.787168	+	0.616738i	$0.788454\pi$
$578$	8.38423	+	14.5219i	0.348738	+	0.604032i
$579$	−11.7259	−	20.3099i	−0.487312	−	0.844050i
$580$		0			0
$581$	−12.0447	−	20.8620i	−0.499697	−	0.865501i
$582$	−11.5847	+	20.0654i	−0.480203	+	0.831737i
$583$	−2.92113	+	5.05955i	−0.120981	+	0.209545i
$584$	2.60720			0.107887
$585$		0			0
$586$	−5.92970			−0.244954
$587$	−11.2750	+	19.5289i	−0.465371	+	0.806046i	−0.999218	−	0.0395351i	$-0.987412\pi$
$587$	−11.2750	+	19.5289i	−0.465371	+	0.806046i	0.533848	+	0.845581i	$0.320746\pi$
$588$	−3.13093	+	5.42293i	−0.129117	+	0.223638i
$589$	10.2386	+	17.7338i	0.421875	+	0.730708i
$590$		0			0
$591$	11.8151	+	20.4644i	0.486009	+	0.841792i
$592$	1.53150	+	2.65264i	0.0629443	+	0.109023i
$593$	8.38787			0.344449			0.172224	−	0.985058i	$-0.444905\pi$
$593$	8.38787			0.344449			0.172224	+	0.985058i	$0.444905\pi$
$594$	−17.2374	−	29.8561i	−0.707260	−	1.22501i
$595$		0			0
$596$	8.02539	−	13.9004i	0.328733	−	0.569382i
$597$	5.27504			0.215893
$598$	−22.9350	−	11.5228i	−0.937882	−	0.471201i
$599$	29.0884			1.18852			0.594260	−	0.804273i	$-0.297445\pi$
$599$	29.0884			1.18852			0.594260	+	0.804273i	$0.297445\pi$
$600$		0			0
$601$	21.5059	−	37.2493i	0.877243	−	1.51943i	0.0228892	−	0.999738i	$-0.492713\pi$
$601$	21.5059	−	37.2493i	0.877243	−	1.51943i	0.854354	−	0.519692i	$-0.173953\pi$
$602$	1.80606	+	3.12819i	0.0736097	+	0.127496i
$603$	0.126008			0.00513144
$604$	−4.65879	−	8.06926i	−0.189563	−	0.328333i
$605$		0			0
$606$	16.0811			0.653250
$607$	−10.8757	−	18.8372i	−0.441429	−	0.764578i	0.556367	−	0.830937i	$-0.312195\pi$
$607$	−10.8757	−	18.8372i	−0.441429	−	0.764578i	−0.997796	+	0.0663591i	$0.978862\pi$
$608$	3.14363	−	5.44492i	0.127491	−	0.220821i
$609$	−3.49834	+	6.05930i	−0.141760	+	0.245535i
$610$		0			0
$611$	6.60966	−	4.34580i	0.267398	−	0.175812i
$612$	0.0933212			0.00377228
$613$	−15.4064	+	26.6848i	−0.622261	+	1.07779i	0.366803	+	0.930299i	$0.380452\pi$
$613$	−15.4064	+	26.6848i	−0.622261	+	1.07779i	−0.989064	+	0.147488i	$0.952881\pi$
$614$	8.98778	−	15.5673i	0.362717	−	0.628245i
$615$		0			0
$616$	−11.6375			−0.468889
$617$	23.0435	+	39.9125i	0.927696	+	1.60682i	0.787167	+	0.616740i	$0.211547\pi$
$617$	23.0435	+	39.9125i	0.927696	+	1.60682i	0.140529	+	0.990077i	$0.455120\pi$
$618$	−2.57570	−	4.46124i	−0.103610	−	0.179458i
$619$	−13.5564			−0.544878			−0.272439	−	0.962173i	$-0.587830\pi$
$619$	−13.5564			−0.544878			−0.272439	+	0.962173i	$0.587830\pi$
$620$		0			0
$621$	19.0435	−	32.9843i	0.764189	−	1.32361i
$622$	−7.97873	+	13.8196i	−0.319918	+	0.554114i
$623$	2.08840			0.0836698
$624$	−5.39692	−	2.71147i	−0.216050	−	0.108546i
$625$		0			0
$626$	11.7186	−	20.2972i	0.468370	−	0.811241i
$627$	−33.9318	+	58.7717i	−1.35511	+	2.34711i
$628$	−7.37812	−	12.7793i	−0.294419	−	0.509949i
$629$	1.47390			0.0587682
$630$		0			0
$631$	2.67513	+	4.63346i	0.106495	+	0.184455i	0.914348	−	0.404929i	$-0.132704\pi$
$631$	2.67513	+	4.63346i	0.106495	+	0.184455i	−0.807853	+	0.589384i	$0.799370\pi$
$632$	−2.29455			−0.0912724
$633$	2.59086	+	4.48750i	0.102977	+	0.178362i
$634$	10.3253	−	17.8840i	0.410072	−	0.710265i
$635$		0			0
$636$	−1.51881			−0.0602246
$637$	0.781626	+	13.4554i	0.0309691	+	0.533121i
$638$	14.9018			0.589966
$639$	0.355186	−	0.615201i	0.0140510	−	0.0243370i
$640$		0			0
$641$	−6.19029	−	10.7219i	−0.244502	−	0.423489i	0.717490	−	0.696569i	$-0.245291\pi$
$641$	−6.19029	−	10.7219i	−0.244502	−	0.423489i	−0.961991	+	0.273080i	$0.911958\pi$
$642$	−2.80606			−0.110746
$643$	−5.76234	−	9.98067i	−0.227245	−	0.393599i	0.729746	−	0.683718i	$-0.239638\pi$
$643$	−5.76234	−	9.98067i	−0.227245	−	0.393599i	−0.956991	+	0.290119i	$0.906305\pi$
$644$	−6.42842	−	11.1344i	−0.253315	−	0.438755i
$645$		0			0
$646$	−1.51270	−	2.62007i	−0.0595162	−	0.103085i
$647$	1.83510	−	3.17849i	0.0721453	−	0.124959i	−0.827696	−	0.561177i	$-0.810349\pi$
$647$	1.83510	−	3.17849i	0.0721453	−	0.124959i	0.899841	+	0.436217i	$0.143682\pi$
$648$	4.19029	−	7.25779i	0.164610	−	0.285113i
$649$	42.3634			1.66291
$650$		0			0
$651$	9.85352			0.386190
$652$	−6.76234	+	11.7127i	−0.264834	+	0.458706i
$653$	4.05325	−	7.02043i	0.158616	−	0.274731i	−0.775754	−	0.631036i	$-0.782630\pi$
$653$	4.05325	−	7.02043i	0.158616	−	0.274731i	0.934370	+	0.356305i	$0.115964\pi$
$654$	9.11871	+	15.7941i	0.356570	+	0.617597i
$655$		0			0
$656$	−3.75329	−	6.50089i	−0.146541	−	0.253817i
$657$	0.252816	+	0.437890i	0.00986329	+	0.0170837i
$658$	3.96239			0.154470
$659$	−9.27210	−	16.0597i	−0.361190	−	0.625599i	0.626967	−	0.779046i	$-0.284296\pi$
$659$	−9.27210	−	16.0597i	−0.361190	−	0.625599i	−0.988157	+	0.153447i	$0.950963\pi$
$660$		0			0
$661$	−23.2059	+	40.1938i	−0.902606	+	1.56336i	−0.0785068	+	0.996914i	$0.525015\pi$
$661$	−23.2059	+	40.1938i	−0.902606	+	1.56336i	−0.824099	+	0.566446i	$0.808318\pi$
$662$	−26.6761			−1.03680
$663$	−2.42842	+	1.59667i	−0.0943122	+	0.0620095i
$664$	−13.3380			−0.517616
$665$		0			0
$666$	−0.297014	+	0.514444i	−0.0115091	+	0.0199343i
$667$	8.23155	+	14.2575i	0.318727	+	0.552051i
$668$	−23.4241			−0.906304
$669$	−18.5889	−	32.1969i	−0.718687	−	1.24480i
$670$		0			0
$671$	−70.5583			−2.72387
$672$	−1.51270	−	2.62007i	−0.0583535	−	0.101071i
$673$	−20.2047	+	34.9956i	−0.778836	+	1.34898i	0.153778	+	0.988105i	$0.450856\pi$
$673$	−20.2047	+	34.9956i	−0.778836	+	1.34898i	−0.932613	+	0.360877i	$0.882477\pi$
$674$	4.20299	−	7.27978i	0.161893	−	0.280407i
$675$		0			0
$676$	−12.9126	+	1.50527i	−0.496637	+	0.0578950i
$677$	14.2473			0.547567			0.273784	−	0.961791i	$-0.411725\pi$
$677$	14.2473			0.547567			0.273784	+	0.961791i	$0.411725\pi$
$678$	−11.7259	+	20.3099i	−0.450331	+	0.779996i
$679$	−12.4902	+	21.6337i	−0.479332	+	0.830227i
$680$		0			0
$681$	−22.3390			−0.856032
$682$	−10.4932	−	18.1747i	−0.401805	−	0.695946i
$683$	2.90175	+	5.02599i	0.111033	+	0.192314i	0.916187	−	0.400751i	$-0.131251\pi$
$683$	2.90175	+	5.02599i	0.111033	+	0.192314i	−0.805154	+	0.593065i	$0.797918\pi$
$684$	1.21933			0.0466222
$685$		0			0
$686$	−9.69688	+	16.7955i	−0.370228	+	0.641255i
$687$	21.9228	−	37.9714i	0.836407	−	1.44870i
$688$	2.00000			0.0762493
$689$	−2.73155	+	1.79597i	−0.104064	+	0.0684210i
$690$		0			0
$691$	9.61990	−	16.6622i	0.365958	−	0.633858i	−0.622971	−	0.782245i	$-0.714075\pi$
$691$	9.61990	−	16.6622i	0.365958	−	0.633858i	0.988929	+	0.148387i	$0.0474080\pi$
$692$	−2.31217	+	4.00480i	−0.0878956	+	0.152240i
$693$	−1.12847	−	1.95457i	−0.0428670	−	0.0742479i
$694$	−21.1514			−0.802896
$695$		0			0
$696$	1.93700	+	3.35498i	0.0734216	+	0.127170i
$697$	−3.61213			−0.136819
$698$	−2.73695	−	4.74054i	−0.103595	−	0.179432i
$699$	−17.4792	+	30.2749i	−0.661124	+	1.14510i
$700$		0			0
$701$	45.3742			1.71376			0.856881	−	0.515515i	$-0.172399\pi$
$701$	45.3742			1.71376			0.856881	+	0.515515i	$0.172399\pi$
$702$	−1.11871	−	19.2582i	−0.0422231	−	0.726853i
$703$	19.2579			0.726325
$704$	−3.22179	+	5.58031i	−0.121426	+	0.210316i
$705$		0			0
$706$	15.0721	+	26.1056i	0.567244	+	0.982496i
$707$	17.3380			0.652064
$708$	5.50659	+	9.53769i	0.206950	+	0.358448i
$709$	−1.98660	−	3.44089i	−0.0746082	−	0.129225i	0.826308	−	0.563219i	$-0.190437\pi$
$709$	−1.98660	−	3.44089i	−0.0746082	−	0.129225i	−0.900916	+	0.433994i	$0.857104\pi$
$710$		0			0
$711$	−0.222499	−	0.385379i	−0.00834436	−	0.0144528i
$712$	0.578163	−	1.00141i	0.0216676	−	0.0375293i
$713$	11.5926	−	20.0790i	0.434147	−	0.751964i
$714$	−1.45580			−0.0544820
$715$		0			0
$716$	−8.31265			−0.310658
$717$	−12.8090	+	22.1858i	−0.478361	+	0.828546i
$718$	4.19394	−	7.26411i	0.156516	−	0.271094i
$719$	−22.8496	−	39.5766i	−0.852145	−	1.47596i	−0.879269	−	0.476326i	$-0.841968\pi$
$719$	−22.8496	−	39.5766i	−0.852145	−	1.47596i	0.0271244	−	0.999632i	$-0.491365\pi$
$720$		0			0
$721$	−2.77702	−	4.80995i	−0.103422	−	0.179132i
$722$	−10.2648	−	17.7792i	−0.382016	−	0.661672i
$723$	21.3888			0.795459
$724$	0.512696	+	0.888016i	0.0190542	+	0.0330029i
$725$		0			0
$726$	25.5623	−	44.2752i	0.948706	−	1.64321i
$727$	24.7948			0.919588			0.459794	−	0.888026i	$-0.347923\pi$
$727$	24.7948			0.919588			0.459794	+	0.888026i	$0.347923\pi$
$728$	−5.81876	−	2.92340i	−0.215658	−	0.108349i
$729$	28.5125			1.05602
$730$		0			0
$731$	0.481194	−	0.833453i	0.0177976	−	0.0308264i
$732$	−9.17148	−	15.8855i	−0.338988	−	0.587144i
$733$	−45.8651			−1.69407			−0.847033	−	0.531540i	$-0.821613\pi$
$733$	−45.8651			−1.69407			−0.847033	+	0.531540i	$0.821613\pi$
$734$	9.75623	+	16.8983i	0.360109	+	0.623727i
$735$		0			0
$736$	−7.11871			−0.262399
$737$	2.09332	+	3.62574i	0.0771085	+	0.133556i
$738$	0.727901	−	1.26076i	0.0267944	−	0.0464093i
$739$	−17.4817	+	30.2791i	−0.643074	+	1.11384i	0.341669	+	0.939820i	$0.389008\pi$
$739$	−17.4817	+	30.2791i	−0.643074	+	1.11384i	−0.984743	+	0.174016i	$0.944326\pi$
$740$		0			0
$741$	−31.7297	+	20.8620i	−1.16562	+	0.766384i
$742$	−1.63752			−0.0601152
$743$	−3.43335	+	5.94673i	−0.125957	+	0.218165i	−0.922107	−	0.386936i	$-0.873534\pi$
$743$	−3.43335	+	5.94673i	−0.125957	+	0.218165i	0.796149	+	0.605100i	$0.206867\pi$
$744$	2.72790	−	4.72486i	0.100010	−	0.173222i
$745$		0			0
$746$	−8.51388			−0.311715
$747$	−1.29337	−	2.24018i	−0.0473218	−	0.0819638i
$748$	1.55031	+	2.68521i	0.0566849	+	0.0981811i
$749$	−3.02539			−0.110545
$750$		0			0
$751$	−2.40009	+	4.15708i	−0.0875806	+	0.151694i	−0.906488	−	0.422232i	$-0.861247\pi$
$751$	−2.40009	+	4.15708i	−0.0875806	+	0.151694i	0.818907	+	0.573926i	$0.194580\pi$
$752$	1.09697	−	1.90000i	0.0400023	−	0.0692860i
$753$	7.05571			0.257124
$754$	7.45088	+	3.74339i	0.271345	+	0.136326i
$755$		0			0
$756$	4.83146	−	8.36833i	0.175718	−	0.304353i
$757$	−13.8876	+	24.0541i	−0.504755	+	0.874261i	0.495230	+	0.868762i	$0.335084\pi$
$757$	−13.8876	+	24.0541i	−0.504755	+	0.874261i	−0.999985	+	0.00549931i	$0.998250\pi$
$758$	9.85931	+	17.0768i	0.358106	+	0.620258i
$759$	76.8383			2.78905
$760$		0			0
$761$	1.58110	+	2.73855i	0.0573149	+	0.0992723i	0.893259	−	0.449542i	$-0.148413\pi$
$761$	1.58110	+	2.73855i	0.0573149	+	0.0992723i	−0.835944	+	0.548814i	$0.815079\pi$
$762$	−8.68830			−0.314744
$763$	9.83146	+	17.0286i	0.355923	+	0.616476i
$764$	−0.177593	+	0.307600i	−0.00642509	+	0.0111286i
$765$		0			0
$766$	27.7196			1.00155
$767$	21.1817	+	10.6419i	0.764828	+	0.384257i
$768$	−1.67513			−0.0604461
$769$	−4.07816	+	7.06358i	−0.147062	+	0.254719i	−0.930140	−	0.367204i	$-0.880315\pi$
$769$	−4.07816	+	7.06358i	−0.147062	+	0.254719i	0.783078	+	0.621923i	$0.213648\pi$
$770$		0			0
$771$	−15.5999	−	27.0198i	−0.561817	−	0.973096i
$772$	−14.0000			−0.503871
$773$	2.93946	+	5.09129i	0.105725	+	0.183121i	0.914034	−	0.405637i	$-0.132950\pi$
$773$	2.93946	+	5.09129i	0.105725	+	0.183121i	−0.808309	+	0.588758i	$0.799617\pi$
$774$	0.193937	+	0.335908i	0.00697091	+	0.0120740i
$775$		0			0
$776$	6.91573	+	11.9784i	0.248260	+	0.429999i
$777$	4.63339	−	8.02528i	0.166222	−	0.287905i
$778$	−4.57570	+	7.92535i	−0.164047	+	0.284137i
$779$	−47.1958			−1.69097
$780$		0			0
$781$	23.6023			0.844556
$782$	−1.71274	+	2.96656i	−0.0612475	+	0.106084i
$783$	−6.18664	+	10.7156i	−0.221093	+	0.382944i
$784$	1.86907	+	3.23732i	0.0667524	+	0.115619i
$785$		0			0
$786$	−9.04666	−	15.6693i	−0.322684	−	0.558905i
$787$	11.8507	+	20.5261i	0.422433	+	0.731676i	0.996177	−	0.0873591i	$-0.0278428\pi$
$787$	11.8507	+	20.5261i	0.422433	+	0.731676i	−0.573744	+	0.819035i	$0.694509\pi$
$788$	14.1065			0.502523
$789$	19.2811	+	33.3959i	0.686427	+	1.18893i
$790$		0			0
$791$	−12.6424	+	21.8974i	−0.449514	+	0.778580i
$792$	−1.24965			−0.0444042
$793$	−35.2792	−	17.7246i	−1.25280	−	0.629419i
$794$	1.43041			0.0507633
$795$		0			0
$796$	1.57452	−	2.72714i	0.0558072	−	0.0966609i
$797$	−24.2599	−	42.0193i	−0.859329	−	1.48840i	−0.872570	−	0.488489i	$-0.837548\pi$
$797$	−24.2599	−	42.0193i	−0.859329	−	1.48840i	0.0132409	−	0.999912i	$-0.495785\pi$
$798$	−19.0214			−0.673351
$799$	−0.527855	−	0.914271i	−0.0186742	−	0.0323446i
$800$		0			0
$801$	0.224254			0.00792362
$802$	−10.8351	−	18.7669i	−0.382601	−	0.662684i
$803$	−8.39986	+	14.5490i	−0.296425	+	0.513423i
$804$	−0.544198	+	0.942579i	−0.0191924	+	0.0332422i
$805$		0			0
$806$	−0.681010	−	11.7233i	−0.0239876	−	0.412936i
$807$	22.5705			0.794521
$808$	4.79995	−	8.31376i	0.168862	−	0.292477i
$809$	8.55936	−	14.8252i	0.300931	−	0.521228i	−0.675416	−	0.737437i	$-0.736036\pi$
$809$	8.55936	−	14.8252i	0.300931	−	0.521228i	0.976347	+	0.216209i	$0.0693693\pi$
$810$		0			0
$811$	−7.67372			−0.269461			−0.134730	−	0.990882i	$-0.543017\pi$
$811$	−7.67372			−0.269461			−0.134730	+	0.990882i	$0.543017\pi$
$812$	2.08840	+	3.61721i	0.0732884	+	0.126939i
$813$	−14.9927	−	25.9681i	−0.525817	−	0.910742i
$814$	−19.7367			−0.691772
$815$		0			0
$816$	−0.403032	+	0.698071i	−0.0141089	+	0.0244374i
$817$	6.28726	−	10.8898i	0.219963	−	0.380988i
$818$	9.08110			0.317513
$819$	−0.0732380	−	1.26076i	−0.00255914	−	0.0440546i
$820$		0			0
$821$	26.8933	−	46.5805i	0.938582	−	1.62567i	0.170463	−	0.985364i	$-0.445474\pi$
$821$	26.8933	−	46.5805i	0.938582	−	1.62567i	0.768119	−	0.640307i	$-0.221193\pi$
$822$	5.14609	−	8.91329i	0.179491	−	0.310887i
$823$	4.88787	+	8.46604i	0.170381	+	0.295108i	0.938553	−	0.345135i	$-0.112167\pi$
$823$	4.88787	+	8.46604i	0.170381	+	0.295108i	−0.768172	+	0.640243i	$0.778834\pi$
$824$	−3.07522			−0.107130
$825$		0			0
$826$	5.93700	+	10.2832i	0.206575	+	0.357798i
$827$	−28.1598			−0.979213			−0.489607	−	0.871943i	$-0.662860\pi$
$827$	−28.1598			−0.979213			−0.489607	+	0.871943i	$0.662860\pi$
$828$	−0.690289	−	1.19562i	−0.0239892	−	0.0415505i
$829$	−10.1065	+	17.5050i	−0.351013	+	0.607972i	−0.986427	−	0.164199i	$-0.947496\pi$
$829$	−10.1065	+	17.5050i	−0.351013	+	0.607972i	0.635414	+	0.772172i	$0.280829\pi$
$830$		0			0
$831$	14.2193			0.493263
$832$	−3.01270	+	1.98082i	−0.104446	+	0.0686727i
$833$	1.79877			0.0623237
$834$	8.65879	−	14.9975i	0.299829	−	0.519320i
$835$		0			0
$836$	20.2562	+	35.0848i	0.700576	+	1.21343i
$837$	17.4255			0.602313
$838$	7.77139	+	13.4604i	0.268458	+	0.464983i
$839$	−6.29631	−	10.9055i	−0.217373	−	0.376500i	0.736631	−	0.676295i	$-0.236415\pi$
$839$	−6.29631	−	10.9055i	−0.217373	−	0.376500i	−0.954004	+	0.299794i	$0.903082\pi$
$840$		0			0
$841$	11.8258	+	20.4829i	0.407787	+	0.706308i
$842$	2.48238	−	4.29961i	0.0855484	−	0.148174i
$843$	−13.8446	+	23.9796i	−0.476834	+	0.825901i
$844$	3.09332			0.106477
$845$		0			0
$846$	0.425485			0.0146285
$847$	27.5603	−	47.7359i	0.946984	−	1.64022i
$848$	−0.453339	+	0.785207i	−0.0155677	+	0.0269641i
$849$	−1.28726	−	2.22960i	−0.0441786	−	0.0765195i
$850$		0			0
$851$	−10.9023	−	18.8834i	−0.373727	−	0.647314i
$852$	3.06793	+	5.31381i	0.105106	+	0.182048i
$853$	45.7704			1.56715			0.783574	−	0.621299i	$-0.213395\pi$
$853$	45.7704			1.56715			0.783574	+	0.621299i	$0.213395\pi$
$854$	−9.88835	−	17.1271i	−0.338372	−	0.586078i
$855$		0			0
$856$	−0.837565	+	1.45071i	−0.0286274	+	0.0495841i
$857$	27.8169			0.950206			0.475103	−	0.879930i	$-0.342411\pi$
$857$	27.8169			0.950206			0.475103	+	0.879930i	$0.342411\pi$
$858$	32.5186	−	21.3807i	1.11017	−	0.729925i
$859$	25.9706			0.886107			0.443053	−	0.896495i	$-0.353895\pi$
$859$	25.9706			0.886107			0.443053	+	0.896495i	$0.353895\pi$
$860$		0			0
$861$	−11.3552	+	19.6678i	−0.386984	+	0.670275i
$862$	16.4853	+	28.5534i	0.561492	+	0.972533i
$863$	−18.7210			−0.637270			−0.318635	−	0.947877i	$-0.603224\pi$
$863$	−18.7210			−0.637270			−0.318635	+	0.947877i	$0.603224\pi$
$864$	−2.67513	−	4.63346i	−0.0910098	−	0.157634i
$865$		0			0
$866$	−16.1114			−0.547488
$867$	−14.0447	−	24.3261i	−0.476982	−	0.826157i
$868$	2.94112	−	5.09417i	0.0998281	−	0.172907i
$869$	7.39257	−	12.8043i	0.250776	−	0.434356i
$870$		0			0
$871$	0.135857	+	2.33872i	0.00460334	+	0.0792446i
$872$	10.8872			0.368686
$873$	−1.34121	+	2.32305i	−0.0453932	+	0.0786233i
$874$	−22.3786	+	38.7609i	−0.756967	+	1.31111i
$875$		0			0
$876$	−4.36741			−0.147561
$877$	−11.3430	−	19.6466i	−0.383025	−	0.663418i	0.608468	−	0.793578i	$-0.291784\pi$
$877$	−11.3430	−	19.6466i	−0.383025	−	0.663418i	−0.991493	+	0.130160i	$0.958451\pi$
$878$	0.0417360	+	0.0722889i	0.00140852	+	0.00243963i
$879$	9.93303			0.335033
$880$		0			0
$881$	1.23813	−	2.14451i	0.0417138	−	0.0722505i	−0.844415	−	0.535690i	$-0.820052\pi$
$881$	1.23813	−	2.14451i	0.0417138	−	0.0722505i	0.886129	+	0.463440i	$0.153385\pi$
$882$	−0.362481	+	0.627835i	−0.0122054	+	0.0211403i
$883$	31.4641			1.05885			0.529425	−	0.848357i	$-0.322408\pi$
$883$	31.4641			1.05885			0.529425	+	0.848357i	$0.322408\pi$
$884$	0.100615	+	1.73205i	0.00338406	+	0.0582552i
$885$		0			0
$886$	−20.4568	+	35.4321i	−0.687258	+	1.19037i
$887$	19.8581	−	34.3953i	0.666771	−	1.15488i	−0.312031	−	0.950072i	$-0.601009\pi$
$887$	19.8581	−	34.3953i	0.666771	−	1.15488i	0.978802	−	0.204809i	$-0.0656573\pi$
$888$	−2.56547	−	4.44352i	−0.0860914	−	0.149115i
$889$	−9.36741			−0.314173
$890$		0			0
$891$	27.0005	+	46.7662i	0.904550	+	1.56673i
$892$	−22.1939			−0.743108
$893$	−6.89692	−	11.9458i	−0.230797	−	0.399752i
$894$	−13.4436	+	23.2850i	−0.449621	+	0.778766i
$895$		0			0
$896$	−1.80606			−0.0603363
$897$	38.4191	+	19.3022i	1.28278	+	0.644480i
$898$	−29.1319			−0.972144
$899$	−3.76608	+	6.52305i	−0.125606	+	0.217556i
$900$		0			0
$901$	0.218144	+	0.377837i	0.00726744	+	0.0125876i
$902$	48.3693			1.61052
$903$	−3.02539	−	5.24013i	−0.100679	−	0.174381i
$904$	7.00000	+	12.1244i	0.232817	+	0.403250i
$905$		0			0
$906$	7.80408	+	13.5171i	0.259273	+	0.449074i
$907$	−26.7877	+	46.3977i	−0.889472	+	1.54061i	−0.0489717	+	0.998800i	$0.515594\pi$
$907$	−26.7877	+	46.3977i	−0.889472	+	1.54061i	−0.840500	+	0.541811i	$0.817739\pi$
$908$	−6.66784	+	11.5490i	−0.221280	+	0.383268i
$909$	1.86177			0.0617511
$910$		0			0
$911$	14.6253			0.484558			0.242279	−	0.970207i	$-0.422105\pi$
$911$	14.6253			0.484558			0.242279	+	0.970207i	$0.422105\pi$
$912$	−5.26599	+	9.12096i	−0.174374	+	0.302025i
$913$	42.9724	−	74.4304i	1.42218	−	2.46329i
$914$	16.3339	+	28.2912i	0.540278	+	0.935789i
$915$		0			0
$916$	−13.0872	−	22.6677i	−0.432414	−	0.748962i
$917$	−9.75377	−	16.8940i	−0.322098	−	0.557890i
$918$	−2.57452			−0.0849717
$919$	−26.5247	−	45.9421i	−0.874969	−	1.51549i	−0.856796	−	0.515655i	$-0.827549\pi$
$919$	−26.5247	−	45.9421i	−0.874969	−	1.51549i	−0.0181725	−	0.999835i	$-0.505785\pi$
$920$		0			0
$921$	−15.0557	+	26.0773i	−0.496103	+	0.859275i
$922$	−19.1006			−0.629045
$923$	11.8011	+	5.92901i	0.388439	+	0.195156i
$924$	19.4944			0.641318
$925$		0			0
$926$	−4.14609	+	7.18124i	−0.136249	+	0.235990i
$927$	−0.298199	−	0.516496i	−0.00979414	−	0.0169640i
$928$	2.31265			0.0759165
$929$	5.22521	+	9.05033i	0.171434	+	0.296932i	0.938921	−	0.344132i	$-0.111827\pi$
$929$	5.22521	+	9.05033i	0.171434	+	0.296932i	−0.767488	+	0.641064i	$0.778493\pi$
$930$		0			0
$931$	23.5026			0.770267
$932$	10.4345	+	18.0731i	0.341795	+	0.592005i
$933$	13.3654	−	23.1496i	0.437564	−	0.757883i
$934$	11.7685	−	20.3836i	0.385076	−	0.666970i
$935$		0			0
$936$	−0.624823	−	0.313917i	−0.0204230	−	0.0102607i
$937$	−10.5745			−0.345454			−0.172727	−	0.984970i	$-0.555258\pi$
$937$	−10.5745			−0.345454			−0.172727	+	0.984970i	$0.555258\pi$
$938$	−0.586734	+	1.01625i	−0.0191576	+	0.0331819i
$939$	−19.6302	+	34.0005i	−0.640608	+	1.10957i
$940$		0			0
$941$	−16.6107			−0.541494			−0.270747	−	0.962651i	$-0.587271\pi$
$941$	−16.6107			−0.541494			−0.270747	+	0.962651i	$0.587271\pi$
$942$	12.3593	+	21.4070i	0.402688	+	0.697476i
$943$	26.7186	+	46.2780i	0.870078	+	1.50702i
$944$	6.57452			0.213982
$945$		0			0
$946$	−6.44358	+	11.1606i	−0.209499	+	0.362863i
$947$	−21.2435	+	36.7949i	−0.690322	+	1.19567i	0.281410	+	0.959588i	$0.409198\pi$
$947$	−21.2435	+	36.7949i	−0.690322	+	1.19567i	−0.971732	+	0.236086i	$0.924135\pi$
$948$	3.84367			0.124837
$949$	−7.85471	+	5.16441i	−0.254975	+	0.167644i
$950$		0			0
$951$	−17.2963	+	29.9581i	−0.560871	+	0.971457i
$952$	−0.434534	+	0.752634i	−0.0140833	+	0.0243930i
$953$	−22.5107	−	38.9897i	−0.729193	−	1.26300i	−0.957224	−	0.289346i	$-0.906562\pi$
$953$	−22.5107	−	38.9897i	−0.729193	−	1.26300i	0.228031	−	0.973654i	$-0.426771\pi$
$954$	−0.175838			−0.00569297
$955$		0			0
$956$	7.64657	+	13.2442i	0.247308	+	0.428350i
$957$	−24.9624			−0.806919
$958$	−3.27821	−	5.67802i	−0.105914	−	0.183449i
$959$	5.54832	−	9.60998i	0.179165	−	0.310322i
$960$		0			0
$961$	−20.3923			−0.657817
$962$	−9.86836	−	4.95796i	−0.318169	−	0.159851i
$963$	−0.324869			−0.0104688
$964$	6.38423	−	11.0578i	0.205622	−	0.356148i
$965$		0			0
$966$	10.7685	+	18.6515i	0.346469	+	0.600102i
$967$	−24.4763			−0.787104			−0.393552	−	0.919302i	$-0.628754\pi$
$967$	−24.4763			−0.787104			−0.393552	+	0.919302i	$0.628754\pi$
$968$	−15.2599	−	26.4309i	−0.490471	−	0.849521i
$969$	2.53396	+	4.38895i	0.0814027	+	0.140994i
$970$		0			0
$971$	28.2023	+	48.8478i	0.905054	+	1.56760i	0.820844	+	0.571152i	$0.193503\pi$
$971$	28.2023	+	48.8478i	0.905054	+	1.56760i	0.0842097	+	0.996448i	$0.473163\pi$
$972$	1.00611	−	1.74263i	0.0322710	−	0.0558950i
$973$	9.33558	−	16.1697i	0.299285	−	0.518377i
$974$	−13.5599			−0.434488
$975$		0			0
$976$	−10.9502			−0.350506
$977$	6.75623	−	11.7021i	0.216151	−	0.374385i	−0.737477	−	0.675372i	$-0.763983\pi$
$977$	6.75623	−	11.7021i	0.216151	−	0.374385i	0.953628	+	0.300988i	$0.0973163\pi$
$978$	11.3278	−	19.6203i	0.362223	−	0.627389i
$979$	3.72544	+	6.45265i	0.119066	+	0.206228i
$980$		0			0
$981$	1.05571	+	1.82854i	0.0337062	+	0.0583809i
$982$	−2.47873	−	4.29329i	−0.0790995	−	0.137004i
$983$	−30.1187			−0.960638			−0.480319	−	0.877094i	$-0.659479\pi$
$983$	−30.1187			−0.960638			−0.480319	+	0.877094i	$0.659479\pi$
$984$	6.28726	+	10.8898i	0.200430	+	0.347156i
$985$		0			0
$986$	0.556417	−	0.963743i	0.0177199	−	0.0306918i
$987$	−6.63752			−0.211275
$988$	1.31464	+	22.6309i	0.0418241	+	0.719984i
$989$	−14.2374			−0.452724
$990$		0			0
$991$	−17.6629	+	30.5931i	−0.561081	+	0.971821i	0.436322	+	0.899791i	$0.356281\pi$
$991$	−17.6629	+	30.5931i	−0.561081	+	0.971821i	−0.997402	+	0.0720298i	$0.977052\pi$
$992$	−1.62847	−	2.82059i	−0.0517040	−	0.0895539i
$993$	44.6859			1.41807
$994$	3.30773	+	5.72915i	0.104915	+	0.181718i
$995$		0			0
$996$	22.3430			0.707964
$997$	8.40843	+	14.5638i	0.266298	+	0.461241i	0.967903	−	0.251325i	$-0.0808662\pi$
$997$	8.40843	+	14.5638i	0.266298	+	0.461241i	−0.701605	+	0.712566i	$0.747533\pi$
$998$	6.93501	−	12.0118i	0.219524	−	0.380227i
$999$	8.19394	−	14.1923i	0.259245	−	0.449025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.e.j.451.3		6
5.2	odd	4		130.2.n.a.9.1	✓	12
5.3	odd	4		130.2.n.a.9.6	yes	12
5.4	even	2		650.2.e.k.451.1		6
13.3	even	3	inner	650.2.e.j.601.3		6
13.4	even	6		8450.2.a.bt.1.1		3
13.9	even	3		8450.2.a.cb.1.1		3
15.2	even	4		1170.2.bp.h.919.6		12
15.8	even	4		1170.2.bp.h.919.3		12
20.3	even	4		1040.2.dh.b.529.2		12
20.7	even	4		1040.2.dh.b.529.5		12
65.3	odd	12		130.2.n.a.29.1	yes	12
65.4	even	6		8450.2.a.ca.1.3		3
65.7	even	12		1690.2.c.b.1689.5		6
65.9	even	6		8450.2.a.bu.1.3		3
65.17	odd	12		1690.2.b.b.339.3		6
65.22	odd	12		1690.2.b.c.339.6		6
65.29	even	6		650.2.e.k.601.1		6
65.32	even	12		1690.2.c.c.1689.5		6
65.33	even	12		1690.2.c.c.1689.2		6
65.42	odd	12		130.2.n.a.29.6	yes	12
65.43	odd	12		1690.2.b.b.339.4		6
65.48	odd	12		1690.2.b.c.339.1		6
65.58	even	12		1690.2.c.b.1689.2		6
195.68	even	12		1170.2.bp.h.289.6		12
195.107	even	12		1170.2.bp.h.289.3		12
260.3	even	12		1040.2.dh.b.289.5		12
260.107	even	12		1040.2.dh.b.289.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.1	✓	12	5.2	odd	4
130.2.n.a.9.6	yes	12	5.3	odd	4
130.2.n.a.29.1	yes	12	65.3	odd	12
130.2.n.a.29.6	yes	12	65.42	odd	12
650.2.e.j.451.3		6	1.1	even	1	trivial
650.2.e.j.601.3		6	13.3	even	3	inner
650.2.e.k.451.1		6	5.4	even	2
650.2.e.k.601.1		6	65.29	even	6
1040.2.dh.b.289.2		12	260.107	even	12
1040.2.dh.b.289.5		12	260.3	even	12
1040.2.dh.b.529.2		12	20.3	even	4
1040.2.dh.b.529.5		12	20.7	even	4
1170.2.bp.h.289.3		12	195.107	even	12
1170.2.bp.h.289.6		12	195.68	even	12
1170.2.bp.h.919.3		12	15.8	even	4
1170.2.bp.h.919.6		12	15.2	even	4
1690.2.b.b.339.3		6	65.17	odd	12
1690.2.b.b.339.4		6	65.43	odd	12
1690.2.b.c.339.1		6	65.48	odd	12
1690.2.b.c.339.6		6	65.22	odd	12
1690.2.c.b.1689.2		6	65.58	even	12
1690.2.c.b.1689.5		6	65.7	even	12
1690.2.c.c.1689.2		6	65.33	even	12
1690.2.c.c.1689.5		6	65.32	even	12
8450.2.a.bt.1.1		3	13.4	even	6
8450.2.a.bu.1.3		3	65.9	even	6
8450.2.a.ca.1.3		3	65.4	even	6
8450.2.a.cb.1.1		3	13.9	even	3

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.837565 - 1.45071i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.837565 + 1.45071i) q^{6} +(0.903032 + 1.56410i) q^{7} +1.00000 q^{8} +(0.0969683 + 0.167954i) q^{9} +(-3.22179 + 5.58031i) q^{11} -1.67513 q^{12} +(-3.01270 + 1.98082i) q^{13} -1.80606 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.240597 + 0.416726i) q^{17} -0.193937 q^{18} +(3.14363 + 5.44492i) q^{19} +3.02539 q^{21} +(-3.22179 - 5.58031i) q^{22} +(3.55936 - 6.16499i) q^{23} +(0.837565 - 1.45071i) q^{24} +(-0.209095 - 3.59948i) q^{26} +5.35026 q^{27} +(0.903032 - 1.56410i) q^{28} +(-1.15633 + 2.00281i) q^{29} +3.25694 q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.39692 + 9.34774i) q^{33} -0.481194 q^{34} +(0.0969683 - 0.167954i) q^{36} +(1.53150 - 2.65264i) q^{37} -6.28726 q^{38} +(0.350262 + 6.02961i) q^{39} +(-3.75329 + 6.50089i) q^{41} +(-1.51270 + 2.62007i) q^{42} +(-1.00000 - 1.73205i) q^{43} +6.44358 q^{44} +(3.55936 + 6.16499i) q^{46} -2.19394 q^{47} +(0.837565 + 1.45071i) q^{48} +(1.86907 - 3.23732i) q^{49} +0.806063 q^{51} +(3.22179 + 1.61866i) q^{52} +0.906679 q^{53} +(-2.67513 + 4.63346i) q^{54} +(0.903032 + 1.56410i) q^{56} +10.5320 q^{57} +(-1.15633 - 2.00281i) q^{58} +(-3.28726 - 5.69370i) q^{59} +(5.47508 + 9.48313i) q^{61} +(-1.62847 + 2.82059i) q^{62} +(-0.175131 + 0.303336i) q^{63} +1.00000 q^{64} -10.7938 q^{66} +(0.324869 - 0.562690i) q^{67} +(0.240597 - 0.416726i) q^{68} +(-5.96239 - 10.3272i) q^{69} +(-1.83146 - 3.17217i) q^{71} +(0.0969683 + 0.167954i) q^{72} +2.60720 q^{73} +(1.53150 + 2.65264i) q^{74} +(3.14363 - 5.44492i) q^{76} -11.6375 q^{77} +(-5.39692 - 2.71147i) q^{78} -2.29455 q^{79} +(4.19029 - 7.25779i) q^{81} +(-3.75329 - 6.50089i) q^{82} -13.3380 q^{83} +(-1.51270 - 2.62007i) q^{84} +2.00000 q^{86} +(1.93700 + 3.35498i) q^{87} +(-3.22179 + 5.58031i) q^{88} +(0.578163 - 1.00141i) q^{89} +(-5.81876 - 2.92340i) q^{91} -7.11871 q^{92} +(2.72790 - 4.72486i) q^{93} +(1.09697 - 1.90000i) q^{94} -1.67513 q^{96} +(6.91573 + 11.9784i) q^{97} +(1.86907 + 3.23732i) q^{98} -1.24965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 5 q^{7} + 6 q^{8} + q^{9} - 3 q^{11} - 3 q^{13} - 10 q^{14} - 3 q^{16} - 4 q^{17} - 2 q^{18} + 13 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{27} + 5 q^{28} + 14 q^{29} + 12 q^{31}+ \cdots + 26 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 5 * q^7 + 6 * q^8 + q^9 - 3 * q^11 - 3 * q^13 - 10 * q^14 - 3 * q^16 - 4 * q^17 - 2 * q^18 + 13 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^27 + 5 * q^28 + 14 * q^29 + 12 * q^31 - 3 * q^32 + 6 * q^33 + 8 * q^34 + q^36 + 5 * q^37 - 26 * q^38 - 18 * q^39 - 2 * q^41 + 6 * q^42 - 6 * q^43 + 6 * q^44 - 14 * q^47 + 2 * q^49 + 4 * q^51 + 3 * q^52 + 18 * q^53 - 6 * q^54 + 5 * q^56 - 8 * q^57 + 14 * q^58 - 8 * q^59 - 4 * q^61 - 6 * q^62 + 9 * q^63 + 6 * q^64 - 12 * q^66 + 12 * q^67 - 4 * q^68 - 14 * q^69 + 20 * q^71 + q^72 - 12 * q^73 + 5 * q^74 + 13 * q^76 - 38 * q^77 - 6 * q^78 - 28 * q^79 + 13 * q^81 - 2 * q^82 - 8 * q^83 + 6 * q^84 + 12 * q^86 + 20 * q^87 - 3 * q^88 - 7 * q^89 - 19 * q^91 + 26 * q^93 + 7 * q^94 + 26 * q^97 + 2 * q^98 + 26 * q^99

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