LMFDB - Embedded newform 650.2.c.f.649.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(649,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.649"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,6,0,6,0,0,-6] 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:	$6$
Coefficient field:	6.0.126157824.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 4 $ x^6 + 18x^4 + 81x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.5
Root			$2.88202i$ of defining polynomial
Character	$\chi$	$=$	650.649
Dual form			650.2.c.f.649.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +2.88202i q^{3} +1.00000 q^{4} +2.88202i q^{6} +1.88202 q^{7} +1.00000 q^{8} -5.30604 q^{9} +6.18806i q^{11} +2.88202i q^{12} +(0.287989 - 3.59403i) q^{13} +1.88202 q^{14} +1.00000 q^{16} -3.00000i q^{17} -5.30604 q^{18} +4.88202i q^{19} +5.42402i q^{21} +6.18806i q^{22} +0.575978i q^{23} +2.88202i q^{24} +(0.287989 - 3.59403i) q^{26} -6.64606i q^{27} +1.88202 q^{28} -5.07008 q^{29} -7.30604i q^{31} +1.00000 q^{32} -17.8341 q^{33} -3.00000i q^{34} -5.30604 q^{36} +9.18806 q^{37} +4.88202i q^{38} +(10.3581 + 0.829990i) q^{39} -5.45800i q^{41} +5.42402i q^{42} +4.00000i q^{43} +6.18806i q^{44} +0.575978i q^{46} -2.45800 q^{47} +2.88202i q^{48} -3.45800 q^{49} +8.64606 q^{51} +(0.287989 - 3.59403i) q^{52} -11.0701i q^{53} -6.64606i q^{54} +1.88202 q^{56} -14.0701 q^{57} -5.07008 q^{58} +8.83412i q^{59} +3.64606 q^{61} -7.30604i q^{62} -9.98608 q^{63} +1.00000 q^{64} -17.8341 q^{66} -3.57598 q^{67} -3.00000i q^{68} -1.65998 q^{69} -5.30604 q^{72} +11.8341 q^{73} +9.18806 q^{74} +4.88202i q^{76} +11.6461i q^{77} +(10.3581 + 0.829990i) q^{78} +11.1881 q^{79} +3.23596 q^{81} -5.45800i q^{82} +0.188063 q^{83} +5.42402i q^{84} +4.00000i q^{86} -14.6121i q^{87} +6.18806i q^{88} +11.4580i q^{89} +(0.542001 - 6.76404i) q^{91} +0.575978i q^{92} +21.0562 q^{93} -2.45800 q^{94} +2.88202i q^{96} +15.7640 q^{97} -3.45800 q^{98} -32.8341i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{7} + 6 q^{8} - 18 q^{9} - 6 q^{14} + 6 q^{16} - 18 q^{18} - 6 q^{28} + 18 q^{29} + 6 q^{32} - 24 q^{33} - 18 q^{36} + 24 q^{37} + 12 q^{39} + 6 q^{47} - 6 q^{56} - 36 q^{57}+ \cdots + 60 q^{97}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^7 + 6 * q^8 - 18 * q^9 - 6 * q^14 + 6 * q^16 - 18 * q^18 - 6 * q^28 + 18 * q^29 + 6 * q^32 - 24 * q^33 - 18 * q^36 + 24 * q^37 + 12 * q^39 + 6 * q^47 - 6 * q^56 - 36 * q^57 + 18 * q^58 - 30 * q^61 + 30 * q^63 + 6 * q^64 - 24 * q^66 - 18 * q^67 - 48 * q^69 - 18 * q^72 - 12 * q^73 + 24 * q^74 + 12 * q^78 + 36 * q^79 + 54 * q^81 - 30 * q^83 + 24 * q^91 - 12 * q^93 + 6 * q^94 + 60 * q^97

Character values

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

$n$	$27$	$301$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$			2.88202i			1.66394i	0.554824	+	0.831968i	$0.312786\pi$
$3$			2.88202i			1.66394i	−0.554824	+	0.831968i	$0.687214\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$			2.88202i			1.17658i
$7$	1.88202			0.711337			0.355668	−	0.934612i	$-0.384253\pi$
$7$	1.88202			0.711337			0.355668	+	0.934612i	$0.384253\pi$
$8$	1.00000			0.353553
$9$	−5.30604			−1.76868
$10$		0			0
$11$			6.18806i			1.86577i	0.360173	+	0.932886i	$0.382718\pi$
$11$			6.18806i			1.86577i	−0.360173	+	0.932886i	$0.617282\pi$
$12$			2.88202i			0.831968i
$13$	0.287989	−	3.59403i	0.0798738	−	0.996805i
$13$	0.287989	−	3.59403i	0.0798738	−	0.996805i
$14$	1.88202			0.502991
$15$		0			0
$16$	1.00000			0.250000
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$	−5.30604			−1.25065
$19$			4.88202i			1.12001i	0.828488	+	0.560006i	$0.189201\pi$
$19$			4.88202i			1.12001i	−0.828488	+	0.560006i	$0.810799\pi$
$20$		0			0
$21$			5.42402i			1.18362i
$22$			6.18806i			1.31930i
$23$			0.575978i			0.120100i	0.998195	+	0.0600499i	$0.0191260\pi$
$23$			0.575978i			0.120100i	−0.998195	+	0.0600499i	$0.980874\pi$
$24$			2.88202i			0.588290i
$25$		0			0
$26$	0.287989	−	3.59403i	0.0564793	−	0.704848i
$27$		−	6.64606i		−	1.27904i
$28$	1.88202			0.355668
$29$	−5.07008			−0.941491			−0.470745	−	0.882269i	$-0.656015\pi$
$29$	−5.07008			−0.941491			−0.470745	+	0.882269i	$0.656015\pi$
$30$		0			0
$31$		−	7.30604i		−	1.31220i	−0.754672	−	0.656102i	$-0.772204\pi$
$31$		−	7.30604i		−	1.31220i	0.754672	−	0.656102i	$-0.227796\pi$
$32$	1.00000			0.176777
$33$	−17.8341			−3.10452
$34$		−	3.00000i		−	0.514496i
$35$		0			0
$36$	−5.30604			−0.884340
$37$	9.18806			1.51051			0.755254	−	0.655432i	$-0.227513\pi$
$37$	9.18806			1.51051			0.755254	+	0.655432i	$0.227513\pi$
$38$			4.88202i			0.791968i
$39$	10.3581	+	0.829990i	1.65862	+	0.132905i
$40$		0			0
$41$		−	5.45800i		−	0.852396i	−0.904630	−	0.426198i	$-0.859853\pi$
$41$		−	5.45800i		−	0.852396i	0.904630	−	0.426198i	$-0.140147\pi$
$42$			5.42402i			0.836945i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$			6.18806i			0.932886i
$45$		0			0
$46$			0.575978i			0.0849233i
$47$	−2.45800			−0.358536			−0.179268	−	0.983800i	$-0.557373\pi$
$47$	−2.45800			−0.358536			−0.179268	+	0.983800i	$0.557373\pi$
$48$			2.88202i			0.415984i
$49$	−3.45800			−0.494000
$50$		0			0
$51$	8.64606			1.21069
$52$	0.287989	−	3.59403i	0.0399369	−	0.498402i
$53$		−	11.0701i		−	1.52059i	−0.649576	−	0.760296i	$-0.725054\pi$
$53$		−	11.0701i		−	1.52059i	0.649576	−	0.760296i	$-0.274946\pi$
$54$		−	6.64606i		−	0.904414i
$55$		0			0
$56$	1.88202			0.251496
$57$	−14.0701			−1.86363
$58$	−5.07008			−0.665735
$59$			8.83412i			1.15011i	0.818116	+	0.575053i	$0.195018\pi$
$59$			8.83412i			1.15011i	−0.818116	+	0.575053i	$0.804982\pi$
$60$		0			0
$61$	3.64606			0.466830			0.233415	−	0.972377i	$-0.425010\pi$
$61$	3.64606			0.466830			0.233415	+	0.972377i	$0.425010\pi$
$62$		−	7.30604i		−	0.927868i
$63$	−9.98608			−1.25813
$64$	1.00000			0.125000
$65$		0			0
$66$	−17.8341			−2.19523
$67$	−3.57598			−0.436875			−0.218438	−	0.975851i	$-0.570096\pi$
$67$	−3.57598			−0.436875			−0.218438	+	0.975851i	$0.570096\pi$
$68$		−	3.00000i		−	0.363803i
$69$	−1.65998			−0.199838
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−5.30604			−0.625323
$73$	11.8341			1.38508			0.692540	−	0.721380i	$-0.256492\pi$
$73$	11.8341			1.38508			0.692540	+	0.721380i	$0.256492\pi$
$74$	9.18806			1.06809
$75$		0			0
$76$			4.88202i			0.560006i
$77$			11.6461i			1.32719i
$78$	10.3581	+	0.829990i	1.17282	+	0.0939779i
$79$	11.1881			1.25876			0.629378	−	0.777100i	$-0.283310\pi$
$79$	11.1881			1.25876			0.629378	+	0.777100i	$0.283310\pi$
$80$		0			0
$81$	3.23596			0.359551
$82$		−	5.45800i		−	0.602735i
$83$	0.188063			0.0206426			0.0103213	−	0.999947i	$-0.496715\pi$
$83$	0.188063			0.0206426			0.0103213	+	0.999947i	$0.496715\pi$
$84$			5.42402i			0.591809i
$85$		0			0
$86$			4.00000i			0.431331i
$87$		−	14.6121i		−	1.56658i
$88$			6.18806i			0.659650i
$89$			11.4580i			1.21455i	0.794493	+	0.607273i	$0.207736\pi$
$89$			11.4580i			1.21455i	−0.794493	+	0.607273i	$0.792264\pi$
$90$		0			0
$91$	0.542001	−	6.76404i	0.0568172	−	0.709064i
$92$			0.575978i			0.0600499i
$93$	21.0562			2.18342
$94$	−2.45800			−0.253523
$95$		0			0
$96$			2.88202i			0.294145i
$97$	15.7640			1.60060			0.800298	−	0.599603i	$-0.204675\pi$
$97$	15.7640			1.60060			0.800298	+	0.599603i	$0.204675\pi$
$98$	−3.45800			−0.349311
$99$		−	32.8341i		−	3.29995i
$100$		0			0
$101$	10.4941			1.04420			0.522101	−	0.852884i	$-0.325148\pi$
$101$	10.4941			1.04420			0.522101	+	0.852884i	$0.325148\pi$
$102$	8.64606			0.856088
$103$		−	17.1881i		−	1.69359i	−0.531919	−	0.846795i	$-0.678529\pi$
$103$		−	17.1881i		−	1.69359i	0.531919	−	0.846795i	$-0.321471\pi$
$104$	0.287989	−	3.59403i	0.0282397	−	0.352424i
$105$		0			0
$106$		−	11.0701i		−	1.07522i
$107$		−	1.49411i		−	0.144441i	−0.997389	−	0.0722203i	$-0.976992\pi$
$107$		−	1.49411i		−	0.144441i	0.997389	−	0.0722203i	$-0.0230085\pi$
$108$		−	6.64606i		−	0.639518i
$109$		−	12.9521i		−	1.24059i	−0.784370	−	0.620293i	$-0.787014\pi$
$109$		−	12.9521i		−	1.24059i	0.784370	−	0.620293i	$-0.212986\pi$
$110$		0			0
$111$			26.4802i			2.51339i
$112$	1.88202			0.177834
$113$		−	9.22204i		−	0.867537i	−0.901024	−	0.433768i	$-0.857184\pi$
$113$		−	9.22204i		−	0.867537i	0.901024	−	0.433768i	$-0.142816\pi$
$114$	−14.0701			−1.31778
$115$		0			0
$116$	−5.07008			−0.470745
$117$	−1.52808	+	19.0701i	−0.141271	+	1.76303i
$118$			8.83412i			0.813247i
$119$		−	5.64606i		−	0.517574i
$120$		0			0
$121$	−27.2921			−2.48110
$122$	3.64606			0.330099
$123$	15.7301			1.41833
$124$		−	7.30604i		−	0.656102i
$125$		0			0
$126$	−9.98608			−0.889631
$127$			4.37613i			0.388318i	0.980970	+	0.194159i	$0.0621978\pi$
$127$			4.37613i			0.388318i	−0.980970	+	0.194159i	$0.937802\pi$
$128$	1.00000			0.0883883
$129$	−11.5281			−1.01499
$130$		0			0
$131$	22.1402			1.93440			0.967198	−	0.254025i	$-0.0817545\pi$
$131$	22.1402			1.93440			0.967198	+	0.254025i	$0.0817545\pi$
$132$	−17.8341			−1.55226
$133$			9.18806i			0.796706i
$134$	−3.57598			−0.308917
$135$		0			0
$136$		−	3.00000i		−	0.257248i
$137$	5.83412			0.498443			0.249221	−	0.968447i	$-0.419825\pi$
$137$	5.83412			0.498443			0.249221	+	0.968447i	$0.419825\pi$
$138$	−1.65998			−0.141307
$139$	−4.26994			−0.362171			−0.181086	−	0.983467i	$-0.557961\pi$
$139$	−4.26994			−0.362171			−0.181086	+	0.983467i	$0.557961\pi$
$140$		0			0
$141$		−	7.08400i		−	0.596581i
$142$		0			0
$143$	22.2401	+	1.78209i	1.85981	+	0.149026i
$144$	−5.30604			−0.442170
$145$		0			0
$146$	11.8341			0.979399
$147$		−	9.96602i		−	0.821984i
$148$	9.18806			0.755254
$149$			16.9160i			1.38581i	0.721028	+	0.692906i	$0.243670\pi$
$149$			16.9160i			1.38581i	−0.721028	+	0.692906i	$0.756330\pi$
$150$		0			0
$151$		−	17.4462i		−	1.41975i	−0.704326	−	0.709876i	$-0.748751\pi$
$151$		−	17.4462i		−	1.41975i	0.704326	−	0.709876i	$-0.251249\pi$
$152$			4.88202i			0.395984i
$153$			15.9181i			1.28690i
$154$			11.6461i			0.938466i
$155$		0			0
$156$	10.3581	+	0.829990i	0.829310	+	0.0664524i
$157$			2.73006i			0.217883i	0.994048	+	0.108941i	$0.0347461\pi$
$157$			2.73006i			0.217883i	−0.994048	+	0.108941i	$0.965254\pi$
$158$	11.1881			0.890074
$159$	31.9042			2.53017
$160$		0			0
$161$			1.08400i			0.0854314i
$162$	3.23596			0.254241
$163$	−15.7980			−1.23740			−0.618698	−	0.785629i	$-0.712340\pi$
$163$	−15.7980			−1.23740			−0.618698	+	0.785629i	$0.712340\pi$
$164$		−	5.45800i		−	0.426198i
$165$		0			0
$166$	0.188063			0.0145965
$167$	−15.5642			−1.20439			−0.602197	−	0.798348i	$-0.705708\pi$
$167$	−15.5642			−1.20439			−0.602197	+	0.798348i	$0.705708\pi$
$168$			5.42402i			0.418472i
$169$	−12.8341	−	2.07008i	−0.987240	−	0.159237i
$170$		0			0
$171$		−	25.9042i		−	1.98094i
$172$			4.00000i			0.304997i
$173$			5.64606i			0.429262i	0.976695	+	0.214631i	$0.0688549\pi$
$173$			5.64606i			0.429262i	−0.976695	+	0.214631i	$0.931145\pi$
$174$		−	14.6121i		−	1.10774i
$175$		0			0
$176$			6.18806i			0.466443i
$177$	−25.4601			−1.91370
$178$			11.4580i			0.858813i
$179$	−13.4941			−1.00860			−0.504298	−	0.863529i	$-0.668249\pi$
$179$	−13.4941			−1.00860			−0.504298	+	0.863529i	$0.668249\pi$
$180$		0			0
$181$	2.73006			0.202924			0.101462	−	0.994839i	$-0.467648\pi$
$181$	2.73006			0.202924			0.101462	+	0.994839i	$0.467648\pi$
$182$	0.542001	−	6.76404i	0.0401758	−	0.501384i
$183$			10.5080i			0.776776i
$184$			0.575978i			0.0424617i
$185$		0			0
$186$	21.0562			1.54391
$187$	18.5642			1.35755
$188$	−2.45800			−0.179268
$189$		−	12.5080i		−	0.909825i
$190$		0			0
$191$	−4.84804			−0.350792			−0.175396	−	0.984498i	$-0.556121\pi$
$191$	−4.84804			−0.350792			−0.175396	+	0.984498i	$0.556121\pi$
$192$			2.88202i			0.207992i
$193$	−10.6822			−0.768919			−0.384460	−	0.923142i	$-0.625612\pi$
$193$	−10.6822			−0.768919			−0.384460	+	0.923142i	$0.625612\pi$
$194$	15.7640			1.13179
$195$		0			0
$196$	−3.45800			−0.247000
$197$	−15.5642			−1.10890			−0.554451	−	0.832216i	$-0.687072\pi$
$197$	−15.5642			−1.10890			−0.554451	+	0.832216i	$0.687072\pi$
$198$		−	32.8341i		−	2.33342i
$199$	0.272066			0.0192862			0.00964311	−	0.999954i	$-0.496930\pi$
$199$	0.272066			0.0192862			0.00964311	+	0.999954i	$0.496930\pi$
$200$		0			0
$201$		−	10.3060i		−	0.726932i
$202$	10.4941			0.738363
$203$	−9.54200			−0.669717
$204$	8.64606			0.605345
$205$		0			0
$206$		−	17.1881i		−	1.19755i
$207$		−	3.05616i		−	0.212418i
$208$	0.287989	−	3.59403i	0.0199684	−	0.249201i
$209$	−30.2103			−2.08969
$210$		0			0
$211$	−17.0222			−1.17186			−0.585928	−	0.810363i	$-0.699270\pi$
$211$	−17.0222			−1.17186			−0.585928	+	0.810363i	$0.699270\pi$
$212$		−	11.0701i		−	0.760296i
$213$		0			0
$214$		−	1.49411i		−	0.102135i
$215$		0			0
$216$		−	6.64606i		−	0.452207i
$217$		−	13.7501i		−	0.933419i
$218$		−	12.9521i		−	0.877227i
$219$			34.1062i			2.30468i
$220$		0			0
$221$	−10.7821	−	0.863967i	−0.725282	−	0.0581167i
$222$			26.4802i			1.77723i
$223$	−1.65998			−0.111161			−0.0555803	−	0.998454i	$-0.517701\pi$
$223$	−1.65998			−0.111161			−0.0555803	+	0.998454i	$0.517701\pi$
$224$	1.88202			0.125748
$225$		0			0
$226$		−	9.22204i		−	0.613441i
$227$	8.45800			0.561377			0.280689	−	0.959799i	$-0.409437\pi$
$227$	8.45800			0.561377			0.280689	+	0.959799i	$0.409437\pi$
$228$	−14.0701			−0.931814
$229$		−	9.38792i		−	0.620371i	−0.950676	−	0.310185i	$-0.899609\pi$
$229$		−	9.38792i		−	0.620371i	0.950676	−	0.310185i	$-0.100391\pi$
$230$		0			0
$231$	−33.5642			−2.20836
$232$	−5.07008			−0.332867
$233$			20.9882i			1.37498i	0.726192	+	0.687492i	$0.241288\pi$
$233$			20.9882i			1.37498i	−0.726192	+	0.687492i	$0.758712\pi$
$234$	−1.52808	+	19.0701i	−0.0998939	+	1.24665i
$235$		0			0
$236$			8.83412i			0.575053i
$237$			32.2442i			2.09449i
$238$		−	5.64606i		−	0.365980i
$239$		−	14.4580i		−	0.935210i	−0.883937	−	0.467605i	$-0.845117\pi$
$239$		−	14.4580i		−	0.935210i	0.883937	−	0.467605i	$-0.154883\pi$
$240$		0			0
$241$			9.92992i			0.639642i	0.947478	+	0.319821i	$0.103623\pi$
$241$			9.92992i			0.639642i	−0.947478	+	0.319821i	$0.896377\pi$
$242$	−27.2921			−1.75440
$243$		−	10.6121i		−	0.680766i
$244$	3.64606			0.233415
$245$		0			0
$246$	15.7301			1.00291
$247$	17.5461	+	1.40597i	1.11643	+	0.0894596i
$248$		−	7.30604i		−	0.463934i
$249$			0.542001i			0.0343479i
$250$		0			0
$251$	−14.6461			−0.924451			−0.462226	−	0.886762i	$-0.652949\pi$
$251$	−14.6461			−0.924451			−0.462226	+	0.886762i	$0.652949\pi$
$252$	−9.98608			−0.629064
$253$	−3.56419			−0.224079
$254$			4.37613i			0.274583i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	23.0701i		−	1.43907i	−0.694455	−	0.719536i	$-0.744354\pi$
$257$		−	23.0701i		−	1.43907i	0.694455	−	0.719536i	$-0.255646\pi$
$258$	−11.5281			−0.717707
$259$	17.2921			1.07448
$260$		0			0
$261$	26.9021			1.66520
$262$	22.1402			1.36782
$263$		−	9.56419i		−	0.589753i	−0.955535	−	0.294877i	$-0.904721\pi$
$263$		−	9.56419i		−	0.589753i	0.955535	−	0.294877i	$-0.0952785\pi$
$264$	−17.8341			−1.09761
$265$		0			0
$266$			9.18806i			0.563356i
$267$	−33.0222			−2.02093
$268$	−3.57598			−0.218438
$269$	−5.07008			−0.309128			−0.154564	−	0.987983i	$-0.549397\pi$
$269$	−5.07008			−0.309128			−0.154564	+	0.987983i	$0.549397\pi$
$270$		0			0
$271$		−	0.730064i		−	0.0443482i	−0.999754	−	0.0221741i	$-0.992941\pi$
$271$		−	0.730064i		−	0.0443482i	0.999754	−	0.0221741i	$-0.00705882\pi$
$272$		−	3.00000i		−	0.181902i
$273$	19.4941	+	1.56206i	1.17984	+	0.0945401i
$274$	5.83412			0.352452
$275$		0			0
$276$	−1.65998			−0.0999191
$277$			5.56419i			0.334320i	0.985930	+	0.167160i	$0.0534596\pi$
$277$			5.56419i			0.334320i	−0.985930	+	0.167160i	$0.946540\pi$
$278$	−4.26994			−0.256094
$279$			38.7662i			2.32087i
$280$		0			0
$281$			23.2921i			1.38949i	0.719255	+	0.694746i	$0.244483\pi$
$281$			23.2921i			1.38949i	−0.719255	+	0.694746i	$0.755517\pi$
$282$		−	7.08400i		−	0.421846i
$283$		−	14.1062i		−	0.838526i	−0.907865	−	0.419263i	$-0.862289\pi$
$283$		−	14.1062i		−	0.838526i	0.907865	−	0.419263i	$-0.137711\pi$
$284$		0			0
$285$		0			0
$286$	22.2401	+	1.78209i	1.31508	+	0.105377i
$287$		−	10.2721i		−	0.606341i
$288$	−5.30604			−0.312662
$289$	8.00000			0.470588
$290$		0			0
$291$			45.4323i			2.66329i
$292$	11.8341			0.692540
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		−	9.96602i		−	0.581230i
$295$		0			0
$296$	9.18806			0.534045
$297$	41.1262			2.38639
$298$			16.9160i			0.979917i
$299$	2.07008	+	0.165875i	0.119716	+	0.00959282i
$300$		0			0
$301$			7.52808i			0.433911i
$302$		−	17.4462i		−	1.00392i
$303$			30.2442i			1.73749i
$304$			4.88202i			0.280003i
$305$		0			0
$306$			15.9181i			0.909979i
$307$	−9.42189			−0.537736			−0.268868	−	0.963177i	$-0.586650\pi$
$307$	−9.42189			−0.537736			−0.268868	+	0.963177i	$0.586650\pi$
$308$			11.6461i			0.663596i
$309$	49.5364			2.81802
$310$		0			0
$311$	−31.7044			−1.79779			−0.898895	−	0.438165i	$-0.855629\pi$
$311$	−31.7044			−1.79779			−0.898895	+	0.438165i	$0.855629\pi$
$312$	10.3581	+	0.829990i	0.586410	+	0.0469890i
$313$			15.3740i			0.868990i	0.900674	+	0.434495i	$0.143073\pi$
$313$			15.3740i			0.868990i	−0.900674	+	0.434495i	$0.856927\pi$
$314$			2.73006i			0.154066i
$315$		0			0
$316$	11.1881			0.629378
$317$	−3.18806			−0.179059			−0.0895297	−	0.995984i	$-0.528536\pi$
$317$	−3.18806			−0.179059			−0.0895297	+	0.995984i	$0.528536\pi$
$318$	31.9042			1.78910
$319$		−	31.3740i		−	1.75661i
$320$		0			0
$321$	4.30604			0.240340
$322$			1.08400i			0.0604091i
$323$	14.6461			0.814929
$324$	3.23596			0.179775
$325$		0			0
$326$	−15.7980			−0.874971
$327$	37.3282			2.06426
$328$		−	5.45800i		−	0.301368i
$329$	−4.62600			−0.255040
$330$		0			0
$331$			9.02219i			0.495904i	0.968772	+	0.247952i	$0.0797576\pi$
$331$			9.02219i			0.495904i	−0.968772	+	0.247952i	$0.920242\pi$
$332$	0.188063			0.0103213
$333$	−48.7523			−2.67161
$334$	−15.5642			−0.851635
$335$		0			0
$336$			5.42402i			0.295905i
$337$		−	16.2921i		−	0.887489i	−0.896153	−	0.443744i	$-0.853650\pi$
$337$		−	16.2921i		−	0.887489i	0.896153	−	0.443744i	$-0.146350\pi$
$338$	−12.8341	−	2.07008i	−0.698084	−	0.112598i
$339$	26.5781			1.44352
$340$		0			0
$341$	45.2103			2.44827
$342$		−	25.9042i		−	1.40074i
$343$	−19.6822			−1.06274
$344$			4.00000i			0.215666i
$345$		0			0
$346$			5.64606i			0.303534i
$347$			12.3421i			0.662561i	0.943532	+	0.331281i	$0.107481\pi$
$347$			12.3421i			0.662561i	−0.943532	+	0.331281i	$0.892519\pi$
$348$		−	14.6121i		−	0.783290i
$349$		−	18.7523i		−	1.00379i	−0.864930	−	0.501893i	$-0.832637\pi$
$349$		−	18.7523i		−	1.00379i	0.864930	−	0.501893i	$-0.167363\pi$
$350$		0			0
$351$	−23.8862	−	1.91399i	−1.27495	−	0.102161i
$352$			6.18806i			0.329825i
$353$	0.707877			0.0376765			0.0188382	−	0.999823i	$-0.494003\pi$
$353$	0.707877			0.0376765			0.0188382	+	0.999823i	$0.494003\pi$
$354$	−25.4601			−1.35319
$355$		0			0
$356$			11.4580i			0.607273i
$357$	16.2721			0.861209
$358$	−13.4941			−0.713186
$359$			0.0221876i			0.00117101i	1.00000		0.000585507i	$0.000186373\pi$
$359$			0.0221876i			0.00117101i	−1.00000		0.000585507i	$0.999814\pi$
$360$		0			0
$361$	−4.83412			−0.254428
$362$	2.73006			0.143489
$363$		−	78.6565i		−	4.12839i
$364$	0.542001	−	6.76404i	0.0284086	−	0.354532i
$365$		0			0
$366$			10.5080i			0.549263i
$367$			15.8363i			0.826646i	0.910585	+	0.413323i	$0.135632\pi$
$367$			15.8363i			0.826646i	−0.910585	+	0.413323i	$0.864368\pi$
$368$			0.575978i			0.0300249i
$369$			28.9604i			1.50762i
$370$		0			0
$371$		−	20.8341i		−	1.08165i
$372$	21.0562			1.09171
$373$		−	4.35394i		−	0.225438i	−0.993627	−	0.112719i	$-0.964044\pi$
$373$		−	4.35394i		−	0.225438i	0.993627	−	0.112719i	$-0.0359560\pi$
$374$	18.5642			0.959931
$375$		0			0
$376$	−2.45800			−0.126762
$377$	−1.46013	+	18.2220i	−0.0752004	+	0.938483i
$378$		−	12.5080i		−	0.643343i
$379$		−	2.42402i		−	0.124514i	−0.998060	−	0.0622568i	$-0.980170\pi$
$379$		−	2.42402i		−	0.124514i	0.998060	−	0.0622568i	$-0.0198298\pi$
$380$		0			0
$381$	−12.6121			−0.646137
$382$	−4.84804			−0.248047
$383$	−7.46013			−0.381195			−0.190597	−	0.981668i	$-0.561042\pi$
$383$	−7.46013			−0.381195			−0.190597	+	0.981668i	$0.561042\pi$
$384$			2.88202i			0.147072i
$385$		0			0
$386$	−10.6822			−0.543708
$387$		−	21.2242i		−	1.07889i
$388$	15.7640			0.800298
$389$	−6.57598			−0.333415			−0.166708	−	0.986006i	$-0.553314\pi$
$389$	−6.57598			−0.333415			−0.166708	+	0.986006i	$0.553314\pi$
$390$		0			0
$391$	1.72793			0.0873854
$392$	−3.45800			−0.174655
$393$			63.8084i			3.21871i
$394$	−15.5642			−0.784113
$395$		0			0
$396$		−	32.8341i		−	1.64998i
$397$	6.95210			0.348916			0.174458	−	0.984665i	$-0.444183\pi$
$397$	6.95210			0.348916			0.174458	+	0.984665i	$0.444183\pi$
$398$	0.272066			0.0136374
$399$	−26.4802			−1.32567
$400$		0			0
$401$			6.91813i			0.345475i	0.984968	+	0.172737i	$0.0552612\pi$
$401$			6.91813i			0.345475i	−0.984968	+	0.172737i	$0.944739\pi$
$402$		−	10.3060i		−	0.514019i
$403$	−26.2581	−	2.10406i	−1.30801	−	0.104811i
$404$	10.4941			0.522101
$405$		0			0
$406$	−9.54200			−0.473562
$407$			56.8563i			2.81826i
$408$	8.64606			0.428044
$409$			15.9299i			0.787684i	0.919178	+	0.393842i	$0.128854\pi$
$409$			15.9299i			0.787684i	−0.919178	+	0.393842i	$0.871146\pi$
$410$		0			0
$411$			16.8141i			0.829377i
$412$		−	17.1881i		−	0.846795i
$413$			16.6260i			0.818112i
$414$		−	3.05616i		−	0.150202i
$415$		0			0
$416$	0.287989	−	3.59403i	0.0141198	−	0.176212i
$417$		−	12.3060i		−	0.602629i
$418$	−30.2103			−1.47763
$419$	22.9500			1.12118			0.560590	−	0.828094i	$-0.310574\pi$
$419$	22.9500			1.12118			0.560590	+	0.828094i	$0.310574\pi$
$420$		0			0
$421$		−	24.7523i		−	1.20635i	−0.797609	−	0.603175i	$-0.793902\pi$
$421$		−	24.7523i		−	1.20635i	0.797609	−	0.603175i	$-0.206098\pi$
$422$	−17.0222			−0.828627
$423$	13.0422			0.634136
$424$		−	11.0701i		−	0.537611i
$425$		0			0
$426$		0			0
$427$	6.86196			0.332074
$428$		−	1.49411i		−	0.0722203i
$429$	−5.13603	+	64.0964i	−0.247970	+	3.09460i
$430$		0			0
$431$			32.1041i			1.54640i	0.634163	+	0.773199i	$0.281345\pi$
$431$			32.1041i			1.54640i	−0.634163	+	0.773199i	$0.718655\pi$
$432$		−	6.64606i		−	0.319759i
$433$		−	16.2103i		−	0.779015i	−0.921023	−	0.389507i	$-0.872645\pi$
$433$		−	16.2103i		−	0.779015i	0.921023	−	0.389507i	$-0.127355\pi$
$434$		−	13.7501i		−	0.660027i
$435$		0			0
$436$		−	12.9521i		−	0.620293i
$437$	−2.81194			−0.134513
$438$			34.1062i			1.62966i
$439$	−22.1041			−1.05497			−0.527485	−	0.849565i	$-0.676865\pi$
$439$	−22.1041			−1.05497			−0.527485	+	0.849565i	$0.676865\pi$
$440$		0			0
$441$	18.3483			0.873728
$442$	−10.7821	−	0.863967i	−0.512852	−	0.0410947i
$443$		−	2.64606i		−	0.125718i	−0.998022	−	0.0628591i	$-0.979978\pi$
$443$		−	2.64606i		−	0.125718i	0.998022	−	0.0628591i	$-0.0200219\pi$
$444$			26.4802i			1.25669i
$445$		0			0
$446$	−1.65998			−0.0786024
$447$	−48.7523			−2.30590
$448$	1.88202			0.0889171
$449$		−	35.1262i		−	1.65771i	−0.559463	−	0.828855i	$-0.688993\pi$
$449$		−	35.1262i		−	1.65771i	0.559463	−	0.828855i	$-0.311007\pi$
$450$		0			0
$451$	33.7744			1.59038
$452$		−	9.22204i		−	0.433768i
$453$	50.2803			2.36238
$454$	8.45800			0.396954
$455$		0			0
$456$	−14.0701			−0.658892
$457$	−18.9181			−0.884953			−0.442476	−	0.896780i	$-0.645900\pi$
$457$	−18.9181			−0.884953			−0.442476	+	0.896780i	$0.645900\pi$
$458$		−	9.38792i		−	0.438668i
$459$	−19.9382			−0.930635
$460$		0			0
$461$		−	8.81194i		−	0.410413i	−0.978719	−	0.205206i	$-0.934213\pi$
$461$		−	8.81194i		−	0.410413i	0.978719	−	0.205206i	$-0.0657866\pi$
$462$	−33.5642			−1.56155
$463$	−28.5621			−1.32739			−0.663696	−	0.748003i	$-0.731013\pi$
$463$	−28.5621			−1.32739			−0.663696	+	0.748003i	$0.731013\pi$
$464$	−5.07008			−0.235373
$465$		0			0
$466$			20.9882i			0.972260i
$467$			22.1402i			1.02452i	0.858829	+	0.512262i	$0.171192\pi$
$467$			22.1402i			1.02452i	−0.858829	+	0.512262i	$0.828808\pi$
$468$	−1.52808	+	19.0701i	−0.0706356	+	0.881515i
$469$	−6.73006			−0.310765
$470$		0			0
$471$	−7.86810			−0.362543
$472$			8.83412i			0.406624i
$473$	−24.7523			−1.13811
$474$			32.2442i			1.48103i
$475$		0			0
$476$		−	5.64606i		−	0.258787i
$477$			58.7383i			2.68944i
$478$		−	14.4580i		−	0.661293i
$479$			19.7501i			0.902406i	0.892421	+	0.451203i	$0.149005\pi$
$479$			19.7501i			0.902406i	−0.892421	+	0.451203i	$0.850995\pi$
$480$		0			0
$481$	2.64606	−	33.0222i	0.120650	−	1.50568i
$482$			9.92992i			0.452295i
$483$	−3.12412			−0.142152
$484$	−27.2921			−1.24055
$485$		0			0
$486$		−	10.6121i		−	0.481374i
$487$	−3.78623			−0.171570			−0.0857852	−	0.996314i	$-0.527340\pi$
$487$	−3.78623			−0.171570			−0.0857852	+	0.996314i	$0.527340\pi$
$488$	3.64606			0.165049
$489$		−	45.5302i		−	2.05895i
$490$		0			0
$491$	18.4441			0.832370			0.416185	−	0.909280i	$-0.363367\pi$
$491$	18.4441			0.832370			0.416185	+	0.909280i	$0.363367\pi$
$492$	15.7301			0.709166
$493$			15.2103i			0.685035i
$494$	17.5461	+	1.40597i	0.789438	+	0.0632575i
$495$		0			0
$496$		−	7.30604i		−	0.328051i
$497$		0			0
$498$			0.542001i			0.0242877i
$499$		−	9.98608i		−	0.447038i	−0.974700	−	0.223519i	$-0.928245\pi$
$499$		−	9.98608i		−	0.447038i	0.974700	−	0.223519i	$-0.0717545\pi$
$500$		0			0
$501$		−	44.8563i		−	2.00403i
$502$	−14.6461			−0.653686
$503$		−	2.30391i		−	0.102726i	−0.998680	−	0.0513632i	$-0.983643\pi$
$503$		−	2.30391i		−	0.102726i	0.998680	−	0.0513632i	$-0.0163566\pi$
$504$	−9.98608			−0.444815
$505$		0			0
$506$	−3.56419			−0.158448
$507$	5.96602	−	36.9882i	0.264960	−	1.64270i
$508$			4.37613i			0.194159i
$509$			19.0201i			0.843049i	0.906817	+	0.421525i	$0.138505\pi$
$509$			19.0201i			0.843049i	−0.906817	+	0.421525i	$0.861495\pi$
$510$		0			0
$511$	22.2721			0.985258
$512$	1.00000			0.0441942
$513$	32.4462			1.43254
$514$		−	23.0701i		−	1.01758i
$515$		0			0
$516$	−11.5281			−0.507496
$517$		−	15.2103i		−	0.668946i
$518$	17.2921			0.759772
$519$	−16.2721			−0.714264
$520$		0			0
$521$	−21.2220			−0.929754			−0.464877	−	0.885375i	$-0.653902\pi$
$521$	−21.2220			−0.929754			−0.464877	+	0.885375i	$0.653902\pi$
$522$	26.9021			1.17747
$523$		−	28.3143i		−	1.23810i	−0.785352	−	0.619049i	$-0.787518\pi$
$523$		−	28.3143i		−	1.23810i	0.785352	−	0.619049i	$-0.212482\pi$
$524$	22.1402			0.967198
$525$		0			0
$526$		−	9.56419i		−	0.417018i
$527$	−21.9181			−0.954769
$528$	−17.8341			−0.776131
$529$	22.6682			0.985576
$530$		0			0
$531$		−	46.8742i		−	2.03417i
$532$			9.18806i			0.398353i
$533$	−19.6162	−	1.57184i	−0.849673	−	0.0680841i
$534$	−33.0222			−1.42901
$535$		0			0
$536$	−3.57598			−0.154459
$537$		−	38.8903i		−	1.67824i
$538$	−5.07008			−0.218587
$539$		−	21.3983i		−	0.921691i
$540$		0			0
$541$			24.6204i			1.05851i	0.848462	+	0.529256i	$0.177529\pi$
$541$			24.6204i			1.05851i	−0.848462	+	0.529256i	$0.822471\pi$
$542$		−	0.730064i		−	0.0313589i
$543$			7.86810i			0.337653i
$544$		−	3.00000i		−	0.128624i
$545$		0			0
$546$	19.4941	+	1.56206i	0.834271	+	0.0668500i
$547$		−	17.9382i		−	0.766981i	−0.923545	−	0.383491i	$-0.874722\pi$
$547$		−	17.9382i		−	0.766981i	0.923545	−	0.383491i	$-0.125278\pi$
$548$	5.83412			0.249221
$549$	−19.3462			−0.825674
$550$		0			0
$551$		−	24.7523i		−	1.05448i
$552$	−1.65998			−0.0706535
$553$	21.0562			0.895399
$554$			5.56419i			0.236400i
$555$		0			0
$556$	−4.26994			−0.181086
$557$	−26.4802			−1.12200			−0.561001	−	0.827815i	$-0.689584\pi$
$557$	−26.4802			−1.12200			−0.561001	+	0.827815i	$0.689584\pi$
$558$			38.7662i			1.64110i
$559$	14.3761	+	1.15196i	0.608045	+	0.0487226i
$560$		0			0
$561$			53.5024i			2.25887i
$562$			23.2921i			0.982519i
$563$			14.2803i			0.601844i	0.953649	+	0.300922i	$0.0972944\pi$
$563$			14.2803i			0.601844i	−0.953649	+	0.300922i	$0.902706\pi$
$564$		−	7.08400i		−	0.298290i
$565$		0			0
$566$		−	14.1062i		−	0.592927i
$567$	6.09014			0.255762
$568$		0			0
$569$	4.85983			0.203735			0.101867	−	0.994798i	$-0.467518\pi$
$569$	4.85983			0.203735			0.101867	+	0.994798i	$0.467518\pi$
$570$		0			0
$571$	−6.53987			−0.273685			−0.136843	−	0.990593i	$-0.543695\pi$
$571$	−6.53987			−0.273685			−0.136843	+	0.990593i	$0.543695\pi$
$572$	22.2401	+	1.78209i	0.929905	+	0.0745131i
$573$		−	13.9722i		−	0.583695i
$574$		−	10.2721i		−	0.428748i
$575$		0			0
$576$	−5.30604			−0.221085
$577$	43.7383			1.82085			0.910425	−	0.413673i	$-0.135754\pi$
$577$	43.7383			1.82085			0.910425	+	0.413673i	$0.135754\pi$
$578$	8.00000			0.332756
$579$		−	30.7862i		−	1.27943i
$580$		0			0
$581$	0.353938			0.0146838
$582$			45.4323i			1.88323i
$583$	68.5024			2.83708
$584$	11.8341			0.489700
$585$		0			0
$586$	−6.00000			−0.247858
$587$	13.2721			0.547797			0.273898	−	0.961759i	$-0.411687\pi$
$587$	13.2721			0.547797			0.273898	+	0.961759i	$0.411687\pi$
$588$		−	9.96602i		−	0.410992i
$589$	35.6682			1.46968
$590$		0			0
$591$		−	44.8563i		−	1.84514i
$592$	9.18806			0.377627
$593$	25.6704			1.05416			0.527078	−	0.849817i	$-0.323288\pi$
$593$	25.6704			1.05416			0.527078	+	0.849817i	$0.323288\pi$
$594$	41.1262			1.68743
$595$		0			0
$596$			16.9160i			0.692906i
$597$			0.784099i			0.0320910i
$598$	2.07008	+	0.165875i	0.0846520	+	0.00678315i
$599$	−16.8480			−0.688392			−0.344196	−	0.938898i	$-0.611849\pi$
$599$	−16.8480			−0.688392			−0.344196	+	0.938898i	$0.611849\pi$
$600$		0			0
$601$	−16.2921			−0.664570			−0.332285	−	0.943179i	$-0.607820\pi$
$601$	−16.2921			−0.664570			−0.332285	+	0.943179i	$0.607820\pi$
$602$			7.52808i			0.306822i
$603$	18.9743			0.772693
$604$		−	17.4462i		−	0.709876i
$605$		0			0
$606$			30.2442i			1.22859i
$607$		−	31.5642i		−	1.28115i	−0.767895	−	0.640575i	$-0.778696\pi$
$607$		−	31.5642i		−	1.28115i	0.767895	−	0.640575i	$-0.221304\pi$
$608$			4.88202i			0.197992i
$609$		−	27.5002i		−	1.11437i
$610$		0			0
$611$	−0.707877	+	8.83412i	−0.0286376	+	0.357390i
$612$			15.9181i			0.643452i
$613$	−27.8320			−1.12412			−0.562062	−	0.827095i	$-0.689992\pi$
$613$	−27.8320			−1.12412			−0.562062	+	0.827095i	$0.689992\pi$
$614$	−9.42189			−0.380237
$615$		0			0
$616$			11.6461i			0.469233i
$617$	−1.08400			−0.0436403			−0.0218202	−	0.999762i	$-0.506946\pi$
$617$	−1.08400			−0.0436403			−0.0218202	+	0.999762i	$0.506946\pi$
$618$	49.5364			1.99264
$619$			27.0562i			1.08748i	0.839254	+	0.543740i	$0.182992\pi$
$619$			27.0562i			1.08748i	−0.839254	+	0.543740i	$0.817008\pi$
$620$		0			0
$621$	3.82799			0.153612
$622$	−31.7044			−1.27123
$623$			21.5642i			0.863951i
$624$	10.3581	+	0.829990i	0.414655	+	0.0332262i
$625$		0			0
$626$			15.3740i			0.614468i
$627$		−	87.0666i		−	3.47710i
$628$			2.73006i			0.108941i
$629$		−	27.5642i		−	1.09906i
$630$		0			0
$631$			23.4240i			0.932496i	0.884654	+	0.466248i	$0.154394\pi$
$631$			23.4240i			0.932496i	−0.884654	+	0.466248i	$0.845606\pi$
$632$	11.1881			0.445037
$633$		−	49.0583i		−	1.94989i
$634$	−3.18806			−0.126614
$635$		0			0
$636$	31.9042			1.26508
$637$	−0.995866	+	12.4282i	−0.0394576	+	0.492421i
$638$		−	31.3740i		−	1.24211i
$639$		0			0
$640$		0			0
$641$	−6.22204			−0.245756			−0.122878	−	0.992422i	$-0.539212\pi$
$641$	−6.22204			−0.245756			−0.122878	+	0.992422i	$0.539212\pi$
$642$	4.30604			0.169946
$643$	37.8363			1.49212			0.746058	−	0.665881i	$-0.231944\pi$
$643$	37.8363			1.49212			0.746058	+	0.665881i	$0.231944\pi$
$644$			1.08400i			0.0427157i
$645$		0			0
$646$	14.6461			0.576242
$647$			38.8563i			1.52760i	0.645453	+	0.763800i	$0.276668\pi$
$647$			38.8563i			1.52760i	−0.645453	+	0.763800i	$0.723332\pi$
$648$	3.23596			0.127120
$649$	−54.6661			−2.14583
$650$		0			0
$651$	39.6281			1.55315
$652$	−15.7980			−0.618698
$653$			25.3740i			0.992961i	0.868048	+	0.496481i	$0.165375\pi$
$653$			25.3740i			0.992961i	−0.868048	+	0.496481i	$0.834625\pi$
$654$	37.3282			1.45965
$655$		0			0
$656$		−	5.45800i		−	0.213099i
$657$	−62.7924			−2.44976
$658$	−4.62600			−0.180340
$659$	−16.5059			−0.642978			−0.321489	−	0.946913i	$-0.604183\pi$
$659$	−16.5059			−0.642978			−0.321489	+	0.946913i	$0.604183\pi$
$660$		0			0
$661$			8.81194i			0.342745i	0.985206	+	0.171372i	$0.0548201\pi$
$661$			8.81194i			0.342745i	−0.985206	+	0.171372i	$0.945180\pi$
$662$			9.02219i			0.350657i
$663$	2.48997	−	31.0742i	0.0967025	−	1.20682i
$664$	0.188063			0.00729826
$665$		0			0
$666$	−48.7523			−1.88911
$667$		−	2.92026i		−	0.113073i
$668$	−15.5642			−0.602197
$669$		−	4.78410i		−	0.184964i
$670$		0			0
$671$			22.5621i			0.870999i
$672$			5.42402i			0.209236i
$673$		−	4.08187i		−	0.157345i	−0.996901	−	0.0786723i	$-0.974932\pi$
$673$		−	4.08187i		−	0.157345i	0.996901	−	0.0786723i	$-0.0250681\pi$
$674$		−	16.2921i		−	0.627549i
$675$		0			0
$676$	−12.8341	−	2.07008i	−0.493620	−	0.0796186i
$677$		−	24.4441i		−	0.939462i	−0.882810	−	0.469731i	$-0.844351\pi$
$677$		−	24.4441i		−	0.939462i	0.882810	−	0.469731i	$-0.155649\pi$
$678$	26.5781			1.02073
$679$	29.6682			1.13856
$680$		0			0
$681$			24.3761i			0.934095i
$682$	45.2103			1.73119
$683$	23.4802			0.898444			0.449222	−	0.893420i	$-0.351701\pi$
$683$	23.4802			0.898444			0.449222	+	0.893420i	$0.351701\pi$
$684$		−	25.9042i		−	0.990472i
$685$		0			0
$686$	−19.6822			−0.751469
$687$	27.0562			1.03226
$688$			4.00000i			0.152499i
$689$	−39.7862	−	3.18806i	−1.51573	−	0.121456i
$690$		0			0
$691$		−	11.4358i		−	0.435039i	−0.976056	−	0.217519i	$-0.930203\pi$
$691$		−	11.4358i		−	0.435039i	0.976056	−	0.217519i	$-0.0697965\pi$
$692$			5.64606i			0.214631i
$693$		−	61.7945i		−	2.34738i
$694$			12.3421i			0.468502i
$695$		0			0
$696$		−	14.6121i		−	0.553870i
$697$	−16.3740			−0.620209
$698$		−	18.7523i		−	0.709783i
$699$	−60.4885			−2.28788
$700$		0			0
$701$	−9.23383			−0.348757			−0.174378	−	0.984679i	$-0.555792\pi$
$701$	−9.23383			−0.348757			−0.174378	+	0.984679i	$0.555792\pi$
$702$	−23.8862	−	1.91399i	−0.901525	−	0.0722390i
$703$			44.8563i			1.69179i
$704$			6.18806i			0.233221i
$705$		0			0
$706$	0.707877			0.0266413
$707$	19.7501			0.742780
$708$	−25.4601			−0.956850
$709$		−	18.1999i		−	0.683510i	−0.939789	−	0.341755i	$-0.888979\pi$
$709$		−	18.1999i		−	0.683510i	0.939789	−	0.341755i	$-0.111021\pi$
$710$		0			0
$711$	−59.3643			−2.22634
$712$			11.4580i			0.429407i
$713$	4.20812			0.157595
$714$	16.2721			0.608967
$715$		0			0
$716$	−13.4941			−0.504298
$717$	41.6682			1.55613
$718$			0.0221876i			0.000828033i
$719$	16.8480			0.628326			0.314163	−	0.949369i	$-0.398276\pi$
$719$	16.8480			0.628326			0.314163	+	0.949369i	$0.398276\pi$
$720$		0			0
$721$		−	32.3483i		−	1.20471i
$722$	−4.83412			−0.179907
$723$	−28.6182			−1.06432
$724$	2.73006			0.101462
$725$		0			0
$726$		−	78.6565i		−	2.91922i
$727$			35.0201i			1.29882i	0.760438	+	0.649411i	$0.224985\pi$
$727$			35.0201i			1.29882i	−0.760438	+	0.649411i	$0.775015\pi$
$728$	0.542001	−	6.76404i	0.0200879	−	0.250692i
$729$	40.2921			1.49230
$730$		0			0
$731$	12.0000			0.443836
$732$			10.5080i			0.388388i
$733$	18.1083			0.668846			0.334423	−	0.942423i	$-0.391459\pi$
$733$	18.1083			0.668846			0.334423	+	0.942423i	$0.391459\pi$
$734$			15.8363i			0.584527i
$735$		0			0
$736$			0.575978i			0.0212308i
$737$		−	22.1284i		−	0.815109i
$738$			28.9604i			1.06605i
$739$		−	15.9181i		−	0.585558i	−0.956180	−	0.292779i	$-0.905420\pi$
$739$		−	15.9181i		−	0.585558i	0.956180	−	0.292779i	$-0.0945800\pi$
$740$		0			0
$741$	−4.05203	+	50.5683i	−0.148855	+	1.85767i
$742$		−	20.8341i		−	0.764845i
$743$	−43.8584			−1.60901			−0.804505	−	0.593946i	$-0.797569\pi$
$743$	−43.8584			−1.60901			−0.804505	+	0.593946i	$0.797569\pi$
$744$	21.0562			0.771956
$745$		0			0
$746$		−	4.35394i		−	0.159409i
$747$	−0.997870			−0.0365102
$748$	18.5642			0.678774
$749$		−	2.81194i		−	0.102746i
$750$		0			0
$751$	39.7723			1.45131			0.725656	−	0.688058i	$-0.241536\pi$
$751$	39.7723			1.45131			0.725656	+	0.688058i	$0.241536\pi$
$752$	−2.45800			−0.0896340
$753$		−	42.2103i		−	1.53823i
$754$	−1.46013	+	18.2220i	−0.0531747	+	0.663608i
$755$		0			0
$756$		−	12.5080i		−	0.454912i
$757$		−	42.2943i		−	1.53721i	−0.639723	−	0.768605i	$-0.720951\pi$
$757$		−	42.2943i		−	1.53721i	0.639723	−	0.768605i	$-0.279049\pi$
$758$		−	2.42402i		−	0.0880444i
$759$		−	10.2721i		−	0.372852i
$760$		0			0
$761$		−	3.99787i		−	0.144923i	−0.997371	−	0.0724613i	$-0.976915\pi$
$761$		−	3.99787i		−	0.144923i	0.997371	−	0.0724613i	$-0.0230854\pi$
$762$	−12.6121			−0.456888
$763$		−	24.3761i		−	0.882475i
$764$	−4.84804			−0.175396
$765$		0			0
$766$	−7.46013			−0.269545
$767$	31.7501	+	2.54413i	1.14643	+	0.0918633i
$768$			2.88202i			0.103996i
$769$			39.9063i			1.43906i	0.694462	+	0.719530i	$0.255643\pi$
$769$			39.9063i			1.43906i	−0.694462	+	0.719530i	$0.744357\pi$
$770$		0			0
$771$	66.4885			2.39452
$772$	−10.6822			−0.384460
$773$	15.1881			0.546277			0.273138	−	0.961975i	$-0.411938\pi$
$773$	15.1881			0.546277			0.273138	+	0.961975i	$0.411938\pi$
$774$		−	21.2242i		−	0.762887i
$775$		0			0
$776$	15.7640			0.565896
$777$			49.8363i			1.78787i
$778$	−6.57598			−0.235760
$779$	26.6461			0.954694
$780$		0			0
$781$		0			0
$782$	1.72793			0.0617908
$783$			33.6961i			1.20420i
$784$	−3.45800			−0.123500
$785$		0			0
$786$			63.8084i			2.27597i
$787$	7.68217			0.273840			0.136920	−	0.990582i	$-0.456280\pi$
$787$	7.68217			0.273840			0.136920	+	0.990582i	$0.456280\pi$
$788$	−15.5642			−0.554451
$789$	27.5642			0.981311
$790$		0			0
$791$		−	17.3561i		−	0.617111i
$792$		−	32.8341i		−	1.16671i
$793$	1.05003	−	13.1041i	0.0372875	−	0.465339i
$794$	6.95210			0.246721
$795$		0			0
$796$	0.272066			0.00964311
$797$		−	33.0784i		−	1.17170i	−0.810421	−	0.585848i	$-0.800762\pi$
$797$		−	33.0784i		−	1.17170i	0.810421	−	0.585848i	$-0.199238\pi$
$798$	−26.4802			−0.937388
$799$			7.37400i			0.260873i
$800$		0			0
$801$		−	60.7966i		−	2.14814i
$802$			6.91813i			0.244288i
$803$			73.2303i			2.58424i
$804$		−	10.3060i		−	0.363466i
$805$		0			0
$806$	−26.2581	−	2.10406i	−0.924904	−	0.0741124i
$807$		−	14.6121i		−	0.514370i
$808$	10.4941			0.369181
$809$	−23.2921			−0.818907			−0.409454	−	0.912331i	$-0.634281\pi$
$809$	−23.2921			−0.818907			−0.409454	+	0.912331i	$0.634281\pi$
$810$		0			0
$811$		−	2.14983i		−	0.0754906i	−0.999287	−	0.0377453i	$-0.987982\pi$
$811$		−	2.14983i		−	0.0754906i	0.999287	−	0.0377453i	$-0.0120176\pi$
$812$	−9.54200			−0.334859
$813$	2.10406			0.0737926
$814$			56.8563i			1.99281i
$815$		0			0
$816$	8.64606			0.302673
$817$	−19.5281			−0.683201
$818$			15.9299i			0.556976i
$819$	−2.87588	+	35.8903i	−0.100491	+	1.25411i
$820$		0			0
$821$		−	26.8563i		−	0.937292i	−0.883386	−	0.468646i	$-0.844742\pi$
$821$		−	26.8563i		−	0.937292i	0.883386	−	0.468646i	$-0.155258\pi$
$822$			16.8141i			0.586458i
$823$			4.00000i			0.139431i	0.997567	+	0.0697156i	$0.0222092\pi$
$823$			4.00000i			0.139431i	−0.997567	+	0.0697156i	$0.977791\pi$
$824$		−	17.1881i		−	0.598775i
$825$		0			0
$826$			16.6260i			0.578493i
$827$	−32.0243			−1.11359			−0.556797	−	0.830648i	$-0.687970\pi$
$827$	−32.0243			−1.11359			−0.556797	+	0.830648i	$0.687970\pi$
$828$		−	3.05616i		−	0.106209i
$829$	19.2699			0.669273			0.334636	−	0.942347i	$-0.391387\pi$
$829$	19.2699			0.669273			0.334636	+	0.942347i	$0.391387\pi$
$830$		0			0
$831$	−16.0361			−0.556286
$832$	0.287989	−	3.59403i	0.00998422	−	0.124601i
$833$			10.3740i			0.359438i
$834$		−	12.3060i		−	0.426123i
$835$		0			0
$836$	−30.2103			−1.04484
$837$	−48.5564			−1.67835
$838$	22.9500			0.792794
$839$			14.8119i			0.511365i	0.966761	+	0.255682i	$0.0823001\pi$
$839$			14.8119i			0.511365i	−0.966761	+	0.255682i	$0.917700\pi$
$840$		0			0
$841$	−3.29425			−0.113595
$842$		−	24.7523i		−	0.853019i
$843$	−67.1284			−2.31202
$844$	−17.0222			−0.585928
$845$		0			0
$846$	13.0422			0.448402
$847$	−51.3643			−1.76490
$848$		−	11.0701i		−	0.380148i
$849$	40.6543			1.39525
$850$		0			0
$851$			5.29212i			0.181412i
$852$		0			0
$853$	−36.5524			−1.25153			−0.625765	−	0.780012i	$-0.715213\pi$
$853$	−36.5524			−1.25153			−0.625765	+	0.780012i	$0.715213\pi$
$854$	6.86196			0.234812
$855$		0			0
$856$		−	1.49411i		−	0.0510675i
$857$		−	27.9299i		−	0.954068i	−0.878885	−	0.477034i	$-0.841712\pi$
$857$		−	27.9299i		−	0.954068i	0.878885	−	0.477034i	$-0.158288\pi$
$858$	−5.13603	+	64.0964i	−0.175341	+	2.18822i
$859$	46.6461			1.59154			0.795772	−	0.605597i	$-0.207066\pi$
$859$	46.6461			1.59154			0.795772	+	0.605597i	$0.207066\pi$
$860$		0			0
$861$	29.6043			1.00891
$862$			32.1041i			1.09347i
$863$	37.1062			1.26311			0.631555	−	0.775331i	$-0.282417\pi$
$863$	37.1062			1.26311			0.631555	+	0.775331i	$0.282417\pi$
$864$		−	6.64606i		−	0.226104i
$865$		0			0
$866$		−	16.2103i		−	0.550847i
$867$			23.0562i			0.783028i
$868$		−	13.7501i		−	0.466710i
$869$			69.2324i			2.34855i
$870$		0			0
$871$	−1.02984	+	12.8522i	−0.0348949	+	0.435479i
$872$		−	12.9521i		−	0.438614i
$873$	−83.6447			−2.83094
$874$	−2.81194			−0.0951152
$875$		0			0
$876$			34.1062i			1.15234i
$877$	−46.8924			−1.58344			−0.791722	−	0.610881i	$-0.790815\pi$
$877$	−46.8924			−1.58344			−0.791722	+	0.610881i	$0.790815\pi$
$878$	−22.1041			−0.745976
$879$		−	17.2921i		−	0.583249i
$880$		0			0
$881$	30.2220			1.01821			0.509103	−	0.860705i	$-0.329977\pi$
$881$	30.2220			1.01821			0.509103	+	0.860705i	$0.329977\pi$
$882$	18.3483			0.617819
$883$			3.93818i			0.132530i	0.997802	+	0.0662652i	$0.0211083\pi$
$883$			3.93818i			0.132530i	−0.997802	+	0.0662652i	$0.978892\pi$
$884$	−10.7821	−	0.863967i	−0.362641	−	0.0290584i
$885$		0			0
$886$		−	2.64606i		−	0.0888962i
$887$		−	4.16375i		−	0.139805i	−0.997554	−	0.0699024i	$-0.977731\pi$
$887$		−	4.16375i		−	0.139805i	0.997554	−	0.0699024i	$-0.0222688\pi$
$888$			26.4802i			0.888617i
$889$			8.23596i			0.276225i
$890$		0			0
$891$			20.0243i			0.670840i
$892$	−1.65998			−0.0555803
$893$		−	12.0000i		−	0.401565i
$894$	−48.7523			−1.63052
$895$		0			0
$896$	1.88202			0.0628739
$897$	−0.478056	+	5.96602i	−0.0159618	+	0.199200i
$898$		−	35.1262i		−	1.17218i
$899$			37.0422i			1.23543i
$900$		0			0
$901$	−33.2103			−1.10639
$902$	33.7744			1.12457
$903$	−21.6961			−0.722001
$904$		−	9.22204i		−	0.306720i
$905$		0			0
$906$	50.2803			1.67045
$907$			27.6682i			0.918709i	0.888253	+	0.459355i	$0.151919\pi$
$907$			27.6682i			0.918709i	−0.888253	+	0.459355i	$0.848081\pi$
$908$	8.45800			0.280689
$909$	−55.6822			−1.84686
$910$		0			0
$911$	−48.5524			−1.60861			−0.804306	−	0.594215i	$-0.797463\pi$
$911$	−48.5524			−1.60861			−0.804306	+	0.594215i	$0.797463\pi$
$912$	−14.0701			−0.465907
$913$			1.16375i			0.0385144i
$914$	−18.9181			−0.625756
$915$		0			0
$916$		−	9.38792i		−	0.310185i
$917$	41.6682			1.37601
$918$	−19.9382			−0.658058
$919$	8.26781			0.272730			0.136365	−	0.990659i	$-0.456458\pi$
$919$	8.26781			0.272730			0.136365	+	0.990659i	$0.456458\pi$
$920$		0			0
$921$		−	27.1541i		−	0.894758i
$922$		−	8.81194i		−	0.290206i
$923$		0			0
$924$	−33.5642			−1.10418
$925$		0			0
$926$	−28.5621			−0.938607
$927$			91.2006i			2.99542i
$928$	−5.07008			−0.166434
$929$		−	24.0000i		−	0.787414i	−0.919236	−	0.393707i	$-0.871192\pi$
$929$		−	24.0000i		−	0.787414i	0.919236	−	0.393707i	$-0.128808\pi$
$930$		0			0
$931$		−	16.8820i		−	0.553286i
$932$			20.9882i			0.687492i
$933$		−	91.3726i		−	2.99140i
$934$			22.1402i			0.724448i
$935$		0			0
$936$	−1.52808	+	19.0701i	−0.0499469	+	0.623325i
$937$			46.8764i			1.53138i	0.643207	+	0.765692i	$0.277603\pi$
$937$			46.8764i			1.53138i	−0.643207	+	0.765692i	$0.722397\pi$
$938$	−6.73006			−0.219744
$939$	−44.3082			−1.44594
$940$		0			0
$941$			10.2721i			0.334860i	0.985884	+	0.167430i	$0.0535468\pi$
$941$			10.2721i			0.334860i	−0.985884	+	0.167430i	$0.946453\pi$
$942$	−7.86810			−0.256357
$943$	3.14369			0.102373
$944$			8.83412i			0.287526i
$945$		0			0
$946$	−24.7523			−0.804765
$947$	−38.1262			−1.23894			−0.619468	−	0.785022i	$-0.712652\pi$
$947$	−38.1262			−1.23894			−0.619468	+	0.785022i	$0.712652\pi$
$948$			32.2442i			1.04724i
$949$	3.40810	−	42.5322i	0.110632	−	1.38065i
$950$		0			0
$951$		−	9.18806i		−	0.297943i
$952$		−	5.64606i		−	0.182990i
$953$		−	44.2921i		−	1.43476i	−0.696681	−	0.717381i	$-0.745341\pi$
$953$		−	44.2921i		−	1.43476i	0.696681	−	0.717381i	$-0.254659\pi$
$954$			58.7383i			1.90172i
$955$		0			0
$956$		−	14.4580i		−	0.467605i
$957$	90.4205			2.92288
$958$			19.7501i			0.638097i
$959$	10.9799			0.354561
$960$		0			0
$961$	−22.3783			−0.721879
$962$	2.64606	−	33.0222i	0.0853125	−	1.06468i
$963$			7.92779i			0.255469i
$964$			9.92992i			0.319821i
$965$		0			0
$966$	−3.12412			−0.100517
$967$	44.1262			1.41900			0.709502	−	0.704703i	$-0.248920\pi$
$967$	44.1262			1.41900			0.709502	+	0.704703i	$0.248920\pi$
$968$	−27.2921			−0.877202
$969$			42.2103i			1.35599i
$970$		0			0
$971$	−0.809807			−0.0259879			−0.0129940	−	0.999916i	$-0.504136\pi$
$971$	−0.809807			−0.0259879			−0.0129940	+	0.999916i	$0.504136\pi$
$972$		−	10.6121i		−	0.340383i
$973$	−8.03611			−0.257626
$974$	−3.78623			−0.121319
$975$		0			0
$976$	3.64606			0.116708
$977$	62.0465			1.98504			0.992522	−	0.122068i	$-0.0389525\pi$
$977$	62.0465			1.98504			0.992522	+	0.122068i	$0.0389525\pi$
$978$		−	45.5302i		−	1.45590i
$979$	−70.9028			−2.26606
$980$		0			0
$981$			68.7244i			2.19420i
$982$	18.4441			0.588574
$983$	2.72580			0.0869397			0.0434698	−	0.999055i	$-0.486159\pi$
$983$	2.72580			0.0869397			0.0434698	+	0.999055i	$0.486159\pi$
$984$	15.7301			0.501456
$985$		0			0
$986$			15.2103i			0.484393i
$987$		−	13.3322i		−	0.424370i
$988$	17.5461	+	1.40597i	0.558217	+	0.0447298i
$989$	−2.30391			−0.0732602
$990$		0			0
$991$	25.2921			0.803431			0.401715	−	0.915765i	$-0.368414\pi$
$991$	25.2921			0.803431			0.401715	+	0.915765i	$0.368414\pi$
$992$		−	7.30604i		−	0.231967i
$993$	−26.0021			−0.825153
$994$		0			0
$995$		0			0
$996$			0.542001i			0.0171740i
$997$		−	2.29425i		−	0.0726597i	−0.999340	−	0.0363299i	$-0.988433\pi$
$997$		−	2.29425i		−	0.0726597i	0.999340	−	0.0363299i	$-0.0115667\pi$
$998$		−	9.98608i		−	0.316104i
$999$		−	61.0644i		−	1.93199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.c.f.649.5		6
5.2	odd	4		650.2.d.c.51.6	yes	6
5.3	odd	4		650.2.d.d.51.1	yes	6
5.4	even	2		650.2.c.e.649.2		6
13.12	even	2		650.2.c.e.649.5		6
65.8	even	4		8450.2.a.ce.1.1		3
65.12	odd	4		650.2.d.c.51.3	✓	6
65.18	even	4		8450.2.a.bq.1.1		3
65.38	odd	4		650.2.d.d.51.4	yes	6
65.47	even	4		8450.2.a.br.1.3		3
65.57	even	4		8450.2.a.cd.1.3		3
65.64	even	2	inner	650.2.c.f.649.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.c.e.649.2		6	5.4	even	2
650.2.c.e.649.5		6	13.12	even	2
650.2.c.f.649.2		6	65.64	even	2	inner
650.2.c.f.649.5		6	1.1	even	1	trivial
650.2.d.c.51.3	✓	6	65.12	odd	4
650.2.d.c.51.6	yes	6	5.2	odd	4
650.2.d.d.51.1	yes	6	5.3	odd	4
650.2.d.d.51.4	yes	6	65.38	odd	4
8450.2.a.bq.1.1		3	65.18	even	4
8450.2.a.br.1.3		3	65.47	even	4
8450.2.a.cd.1.3		3	65.57	even	4
8450.2.a.ce.1.1		3	65.8	even	4

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.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.88202i q^{3} +1.00000 q^{4} +2.88202i q^{6} +1.88202 q^{7} +1.00000 q^{8} -5.30604 q^{9} +6.18806i q^{11} +2.88202i q^{12} +(0.287989 - 3.59403i) q^{13} +1.88202 q^{14} +1.00000 q^{16} -3.00000i q^{17} -5.30604 q^{18} +4.88202i q^{19} +5.42402i q^{21} +6.18806i q^{22} +0.575978i q^{23} +2.88202i q^{24} +(0.287989 - 3.59403i) q^{26} -6.64606i q^{27} +1.88202 q^{28} -5.07008 q^{29} -7.30604i q^{31} +1.00000 q^{32} -17.8341 q^{33} -3.00000i q^{34} -5.30604 q^{36} +9.18806 q^{37} +4.88202i q^{38} +(10.3581 + 0.829990i) q^{39} -5.45800i q^{41} +5.42402i q^{42} +4.00000i q^{43} +6.18806i q^{44} +0.575978i q^{46} -2.45800 q^{47} +2.88202i q^{48} -3.45800 q^{49} +8.64606 q^{51} +(0.287989 - 3.59403i) q^{52} -11.0701i q^{53} -6.64606i q^{54} +1.88202 q^{56} -14.0701 q^{57} -5.07008 q^{58} +8.83412i q^{59} +3.64606 q^{61} -7.30604i q^{62} -9.98608 q^{63} +1.00000 q^{64} -17.8341 q^{66} -3.57598 q^{67} -3.00000i q^{68} -1.65998 q^{69} -5.30604 q^{72} +11.8341 q^{73} +9.18806 q^{74} +4.88202i q^{76} +11.6461i q^{77} +(10.3581 + 0.829990i) q^{78} +11.1881 q^{79} +3.23596 q^{81} -5.45800i q^{82} +0.188063 q^{83} +5.42402i q^{84} +4.00000i q^{86} -14.6121i q^{87} +6.18806i q^{88} +11.4580i q^{89} +(0.542001 - 6.76404i) q^{91} +0.575978i q^{92} +21.0562 q^{93} -2.45800 q^{94} +2.88202i q^{96} +15.7640 q^{97} -3.45800 q^{98} -32.8341i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{7} + 6 q^{8} - 18 q^{9} - 6 q^{14} + 6 q^{16} - 18 q^{18} - 6 q^{28} + 18 q^{29} + 6 q^{32} - 24 q^{33} - 18 q^{36} + 24 q^{37} + 12 q^{39} + 6 q^{47} - 6 q^{56} - 36 q^{57}+ \cdots + 60 q^{97}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^7 + 6 * q^8 - 18 * q^9 - 6 * q^14 + 6 * q^16 - 18 * q^18 - 6 * q^28 + 18 * q^29 + 6 * q^32 - 24 * q^33 - 18 * q^36 + 24 * q^37 + 12 * q^39 + 6 * q^47 - 6 * q^56 - 36 * q^57 + 18 * q^58 - 30 * q^61 + 30 * q^63 + 6 * q^64 - 24 * q^66 - 18 * q^67 - 48 * q^69 - 18 * q^72 - 12 * q^73 + 24 * q^74 + 12 * q^78 + 36 * q^79 + 54 * q^81 - 30 * q^83 + 24 * q^91 - 12 * q^93 + 6 * q^94 + 60 * q^97

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