LMFDB - Embedded newform 650.2.d.c.51.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(51,650)] 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([0, 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("650.51"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-6,0,0,0,0,18,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == 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			51.3
Root			$-2.88202i$ of defining polynomial
Character	$\chi$	$=$	650.51
Dual form			650.2.d.c.51.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	2.88202			1.66394			0.831968	−	0.554824i	$-0.187214\pi$
$3$	2.88202			1.66394			0.831968	+	0.554824i	$0.187214\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	2.88202i		−	1.17658i
$7$		−	1.88202i		−	0.711337i	−0.934612	−	0.355668i	$-0.884253\pi$
$7$		−	1.88202i		−	0.711337i	0.934612	−	0.355668i	$-0.115747\pi$
$8$			1.00000i			0.353553i
$9$	5.30604			1.76868
$10$		0			0
$11$		−	6.18806i		−	1.86577i	−0.360173	−	0.932886i	$-0.617282\pi$
$11$		−	6.18806i		−	1.86577i	0.360173	−	0.932886i	$-0.382718\pi$
$12$	−2.88202			−0.831968
$13$	−3.59403	+	0.287989i	−0.996805	+	0.0798738i
$13$	−3.59403	+	0.287989i	−0.996805	+	0.0798738i
$14$	−1.88202			−0.502991
$15$		0			0
$16$	1.00000			0.250000
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		−	5.30604i		−	1.25065i
$19$			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
$22$	−6.18806			−1.31930
$23$	0.575978			0.120100			0.0600499	−	0.998195i	$-0.480874\pi$
$23$	0.575978			0.120100			0.0600499	+	0.998195i	$0.480874\pi$
$24$			2.88202i			0.588290i
$25$		0			0
$26$	0.287989	+	3.59403i	0.0564793	+	0.704848i
$27$	6.64606			1.27904
$28$			1.88202i			0.355668i
$29$	5.07008			0.941491			0.470745	−	0.882269i	$-0.343985\pi$
$29$	5.07008			0.941491			0.470745	+	0.882269i	$0.343985\pi$
$30$		0			0
$31$			7.30604i			1.31220i	0.754672	+	0.656102i	$0.227796\pi$
$31$			7.30604i			1.31220i	−0.754672	+	0.656102i	$0.772204\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	17.8341i		−	3.10452i
$34$		−	3.00000i		−	0.514496i
$35$		0			0
$36$	−5.30604			−0.884340
$37$		−	9.18806i		−	1.51051i	−0.655432	−	0.755254i	$-0.727513\pi$
$37$		−	9.18806i		−	1.51051i	0.655432	−	0.755254i	$-0.272487\pi$
$38$	4.88202			0.791968
$39$	−10.3581	+	0.829990i	−1.65862	+	0.132905i
$40$		0			0
$41$			5.45800i			0.852396i	0.904630	+	0.426198i	$0.140147\pi$
$41$			5.45800i			0.852396i	−0.904630	+	0.426198i	$0.859853\pi$
$42$	−5.42402			−0.836945
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$			6.18806i			0.932886i
$45$		0			0
$46$		−	0.575978i		−	0.0849233i
$47$			2.45800i			0.358536i	0.983800	+	0.179268i	$0.0573729\pi$
$47$			2.45800i			0.358536i	−0.983800	+	0.179268i	$0.942627\pi$
$48$	2.88202			0.415984
$49$	3.45800			0.494000
$50$		0			0
$51$	8.64606			1.21069
$52$	3.59403	−	0.287989i	0.498402	−	0.0399369i
$53$	−11.0701			−1.52059			−0.760296	−	0.649576i	$-0.774946\pi$
$53$	−11.0701			−1.52059			−0.760296	+	0.649576i	$0.774946\pi$
$54$		−	6.64606i		−	0.904414i
$55$		0			0
$56$	1.88202			0.251496
$57$			14.0701i			1.86363i
$58$		−	5.07008i		−	0.665735i
$59$			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	$0.425010\pi$
$62$	7.30604			0.927868
$63$		−	9.98608i		−	1.25813i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−17.8341			−2.19523
$67$			3.57598i			0.436875i	0.975851	+	0.218438i	$0.0700960\pi$
$67$			3.57598i			0.436875i	−0.975851	+	0.218438i	$0.929904\pi$
$68$	−3.00000			−0.363803
$69$	1.65998			0.199838
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$			5.30604i			0.625323i
$73$			11.8341i			1.38508i	0.721380	+	0.692540i	$0.243508\pi$
$73$			11.8341i			1.38508i	−0.721380	+	0.692540i	$0.756492\pi$
$74$	−9.18806			−1.06809
$75$		0			0
$76$		−	4.88202i		−	0.560006i
$77$	−11.6461			−1.32719
$78$	0.829990	+	10.3581i	0.0939779	+	1.17282i
$79$	−11.1881			−1.25876			−0.629378	−	0.777100i	$-0.716690\pi$
$79$	−11.1881			−1.25876			−0.629378	+	0.777100i	$0.716690\pi$
$80$		0			0
$81$	3.23596			0.359551
$82$	5.45800			0.602735
$83$			0.188063i			0.0206426i	0.999947	+	0.0103213i	$0.00328543\pi$
$83$			0.188063i			0.0206426i	−0.999947	+	0.0103213i	$0.996715\pi$
$84$			5.42402i			0.591809i
$85$		0			0
$86$		−	4.00000i		−	0.431331i
$87$	14.6121			1.56658
$88$	6.18806			0.659650
$89$			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
$92$	−0.575978			−0.0600499
$93$			21.0562i			2.18342i
$94$	2.45800			0.253523
$95$		0			0
$96$		−	2.88202i		−	0.294145i
$97$		−	15.7640i		−	1.60060i	−0.599603	−	0.800298i	$-0.704675\pi$
$97$		−	15.7640i		−	1.60060i	0.599603	−	0.800298i	$-0.295325\pi$
$98$		−	3.45800i		−	0.349311i
$99$		−	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	$0.325148\pi$
$102$		−	8.64606i		−	0.856088i
$103$	−17.1881			−1.69359			−0.846795	−	0.531919i	$-0.821471\pi$
$103$	−17.1881			−1.69359			−0.846795	+	0.531919i	$0.821471\pi$
$104$	−0.287989	−	3.59403i	−0.0282397	−	0.352424i
$105$		0			0
$106$			11.0701i			1.07522i
$107$	1.49411			0.144441			0.0722203	−	0.997389i	$-0.476992\pi$
$107$	1.49411			0.144441			0.0722203	+	0.997389i	$0.476992\pi$
$108$	−6.64606			−0.639518
$109$		−	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
$112$		−	1.88202i		−	0.177834i
$113$	−9.22204			−0.867537			−0.433768	−	0.901024i	$-0.642816\pi$
$113$	−9.22204			−0.867537			−0.433768	+	0.901024i	$0.642816\pi$
$114$	14.0701			1.31778
$115$		0			0
$116$	−5.07008			−0.470745
$117$	−19.0701	+	1.52808i	−1.76303	+	0.141271i
$118$	8.83412			0.813247
$119$		−	5.64606i		−	0.517574i
$120$		0			0
$121$	−27.2921			−2.48110
$122$		−	3.64606i		−	0.330099i
$123$			15.7301i			1.41833i
$124$		−	7.30604i		−	0.656102i
$125$		0			0
$126$	−9.98608			−0.889631
$127$	−4.37613			−0.388318			−0.194159	−	0.980970i	$-0.562198\pi$
$127$	−4.37613			−0.388318			−0.194159	+	0.980970i	$0.562198\pi$
$128$			1.00000i			0.0883883i
$129$	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	$0.0817545\pi$
$132$			17.8341i			1.55226i
$133$	9.18806			0.796706
$134$	3.57598			0.308917
$135$		0			0
$136$			3.00000i			0.257248i
$137$		−	5.83412i		−	0.498443i	−0.968447	−	0.249221i	$-0.919825\pi$
$137$		−	5.83412i		−	0.498443i	0.968447	−	0.249221i	$-0.0801747\pi$
$138$		−	1.65998i		−	0.141307i
$139$	4.26994			0.362171			0.181086	−	0.983467i	$-0.442039\pi$
$139$	4.26994			0.362171			0.181086	+	0.983467i	$0.442039\pi$
$140$		0			0
$141$			7.08400i			0.596581i
$142$		0			0
$143$	1.78209	+	22.2401i	0.149026	+	1.85981i
$144$	5.30604			0.442170
$145$		0			0
$146$	11.8341			0.979399
$147$	9.96602			0.821984
$148$			9.18806i			0.755254i
$149$			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	$0.251249\pi$
$151$			17.4462i			1.41975i	−0.704326	+	0.709876i	$0.748751\pi$
$152$	−4.88202			−0.395984
$153$	15.9181			1.28690
$154$			11.6461i			0.938466i
$155$		0			0
$156$	10.3581	−	0.829990i	0.829310	−	0.0664524i
$157$	−2.73006			−0.217883			−0.108941	−	0.994048i	$-0.534746\pi$
$157$	−2.73006			−0.217883			−0.108941	+	0.994048i	$0.534746\pi$
$158$			11.1881i			0.890074i
$159$	−31.9042			−2.53017
$160$		0			0
$161$		−	1.08400i		−	0.0854314i
$162$		−	3.23596i		−	0.254241i
$163$		−	15.7980i		−	1.23740i	−0.785629	−	0.618698i	$-0.787660\pi$
$163$		−	15.7980i		−	1.23740i	0.785629	−	0.618698i	$-0.212340\pi$
$164$		−	5.45800i		−	0.426198i
$165$		0			0
$166$	0.188063			0.0145965
$167$			15.5642i			1.20439i	0.798348	+	0.602197i	$0.205708\pi$
$167$			15.5642i			1.20439i	−0.798348	+	0.602197i	$0.794292\pi$
$168$	5.42402			0.418472
$169$	12.8341	−	2.07008i	0.987240	−	0.159237i
$170$		0			0
$171$			25.9042i			1.98094i
$172$	−4.00000			−0.304997
$173$	5.64606			0.429262			0.214631	−	0.976695i	$-0.431145\pi$
$173$	5.64606			0.429262			0.214631	+	0.976695i	$0.431145\pi$
$174$		−	14.6121i		−	1.10774i
$175$		0			0
$176$		−	6.18806i		−	0.466443i
$177$			25.4601i			1.91370i
$178$	11.4580			0.858813
$179$	13.4941			1.00860			0.504298	−	0.863529i	$-0.331751\pi$
$179$	13.4941			1.00860			0.504298	+	0.863529i	$0.331751\pi$
$180$		0			0
$181$	2.73006			0.202924			0.101462	−	0.994839i	$-0.467648\pi$
$181$	2.73006			0.202924			0.101462	+	0.994839i	$0.467648\pi$
$182$	6.76404	−	0.542001i	0.501384	−	0.0401758i
$183$	10.5080			0.776776
$184$			0.575978i			0.0424617i
$185$		0			0
$186$	21.0562			1.54391
$187$		−	18.5642i		−	1.35755i
$188$		−	2.45800i		−	0.179268i
$189$		−	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	$0.556121\pi$
$192$	−2.88202			−0.207992
$193$		−	10.6822i		−	0.768919i	−0.923142	−	0.384460i	$-0.874388\pi$
$193$		−	10.6822i		−	0.768919i	0.923142	−	0.384460i	$-0.125612\pi$
$194$	−15.7640			−1.13179
$195$		0			0
$196$	−3.45800			−0.247000
$197$			15.5642i			1.10890i	0.832216	+	0.554451i	$0.187072\pi$
$197$			15.5642i			1.10890i	−0.832216	+	0.554451i	$0.812928\pi$
$198$	−32.8341			−2.33342
$199$	−0.272066			−0.0192862			−0.00964311	−	0.999954i	$-0.503070\pi$
$199$	−0.272066			−0.0192862			−0.00964311	+	0.999954i	$0.503070\pi$
$200$		0			0
$201$			10.3060i			0.726932i
$202$		−	10.4941i		−	0.738363i
$203$		−	9.54200i		−	0.669717i
$204$	−8.64606			−0.605345
$205$		0			0
$206$			17.1881i			1.19755i
$207$	3.05616			0.212418
$208$	−3.59403	+	0.287989i	−0.249201	+	0.0199684i
$209$	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	$0.699270\pi$
$212$	11.0701			0.760296
$213$		0			0
$214$		−	1.49411i		−	0.102135i
$215$		0			0
$216$			6.64606i			0.452207i
$217$	13.7501			0.933419
$218$	−12.9521			−0.877227
$219$			34.1062i			2.30468i
$220$		0			0
$221$	−10.7821	+	0.863967i	−0.725282	+	0.0581167i
$222$	−26.4802			−1.77723
$223$		−	1.65998i		−	0.111161i	−0.998454	−	0.0555803i	$-0.982299\pi$
$223$		−	1.65998i		−	0.111161i	0.998454	−	0.0555803i	$-0.0177009\pi$
$224$	−1.88202			−0.125748
$225$		0			0
$226$			9.22204i			0.613441i
$227$		−	8.45800i		−	0.561377i	−0.959799	−	0.280689i	$-0.909437\pi$
$227$		−	8.45800i		−	0.561377i	0.959799	−	0.280689i	$-0.0905628\pi$
$228$		−	14.0701i		−	0.931814i
$229$		−	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
$232$			5.07008i			0.332867i
$233$	20.9882			1.37498			0.687492	−	0.726192i	$-0.258712\pi$
$233$	20.9882			1.37498			0.687492	+	0.726192i	$0.258712\pi$
$234$	1.52808	+	19.0701i	0.0998939	+	1.24665i
$235$		0			0
$236$		−	8.83412i		−	0.575053i
$237$	−32.2442			−2.09449
$238$	−5.64606			−0.365980
$239$		−	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	$-0.896377\pi$
$241$		−	9.92992i		−	0.639642i	0.947478	−	0.319821i	$-0.103623\pi$
$242$			27.2921i			1.75440i
$243$	−10.6121			−0.680766
$244$	−3.64606			−0.233415
$245$		0			0
$246$	15.7301			1.00291
$247$	−1.40597	−	17.5461i	−0.0894596	−	1.11643i
$248$	−7.30604			−0.463934
$249$			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	$0.652949\pi$
$252$			9.98608i			0.629064i
$253$		−	3.56419i		−	0.224079i
$254$			4.37613i			0.274583i
$255$		0			0
$256$	1.00000			0.0625000
$257$	23.0701			1.43907			0.719536	−	0.694455i	$-0.244354\pi$
$257$	23.0701			1.43907			0.719536	+	0.694455i	$0.244354\pi$
$258$		−	11.5281i		−	0.717707i
$259$	−17.2921			−1.07448
$260$		0			0
$261$	26.9021			1.66520
$262$		−	22.1402i		−	1.36782i
$263$	−9.56419			−0.589753			−0.294877	−	0.955535i	$-0.595279\pi$
$263$	−9.56419			−0.589753			−0.294877	+	0.955535i	$0.595279\pi$
$264$	17.8341			1.09761
$265$		0			0
$266$		−	9.18806i		−	0.563356i
$267$			33.0222i			2.02093i
$268$		−	3.57598i		−	0.218438i
$269$	5.07008			0.309128			0.154564	−	0.987983i	$-0.450603\pi$
$269$	5.07008			0.309128			0.154564	+	0.987983i	$0.450603\pi$
$270$		0			0
$271$			0.730064i			0.0443482i	0.999754	+	0.0221741i	$0.00705882\pi$
$271$			0.730064i			0.0443482i	−0.999754	+	0.0221741i	$0.992941\pi$
$272$	3.00000			0.181902
$273$	1.56206	+	19.4941i	0.0945401	+	1.17984i
$274$	−5.83412			−0.352452
$275$		0			0
$276$	−1.65998			−0.0999191
$277$	−5.56419			−0.334320			−0.167160	−	0.985930i	$-0.553460\pi$
$277$	−5.56419			−0.334320			−0.167160	+	0.985930i	$0.553460\pi$
$278$		−	4.26994i		−	0.256094i
$279$			38.7662i			2.32087i
$280$		0			0
$281$		−	23.2921i		−	1.38949i	−0.719255	−	0.694746i	$-0.755517\pi$
$281$		−	23.2921i		−	1.38949i	0.719255	−	0.694746i	$-0.244483\pi$
$282$	7.08400			0.421846
$283$	−14.1062			−0.838526			−0.419263	−	0.907865i	$-0.637711\pi$
$283$	−14.1062			−0.838526			−0.419263	+	0.907865i	$0.637711\pi$
$284$		0			0
$285$		0			0
$286$	22.2401	−	1.78209i	1.31508	−	0.105377i
$287$	10.2721			0.606341
$288$		−	5.30604i		−	0.312662i
$289$	−8.00000			−0.470588
$290$		0			0
$291$		−	45.4323i		−	2.66329i
$292$		−	11.8341i		−	0.692540i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		−	9.96602i		−	0.581230i
$295$		0			0
$296$	9.18806			0.534045
$297$		−	41.1262i		−	2.38639i
$298$	16.9160			0.979917
$299$	−2.07008	+	0.165875i	−0.119716	+	0.00959282i
$300$		0			0
$301$		−	7.52808i		−	0.433911i
$302$	17.4462			1.00392
$303$	30.2442			1.73749
$304$			4.88202i			0.280003i
$305$		0			0
$306$		−	15.9181i		−	0.909979i
$307$			9.42189i			0.537736i	0.963177	+	0.268868i	$0.0866495\pi$
$307$			9.42189i			0.537736i	−0.963177	+	0.268868i	$0.913350\pi$
$308$	11.6461			0.663596
$309$	−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	$0.855629\pi$
$312$	−0.829990	−	10.3581i	−0.0469890	−	0.586410i
$313$	15.3740			0.868990			0.434495	−	0.900674i	$-0.356927\pi$
$313$	15.3740			0.868990			0.434495	+	0.900674i	$0.356927\pi$
$314$			2.73006i			0.154066i
$315$		0			0
$316$	11.1881			0.629378
$317$			3.18806i			0.179059i	0.995984	+	0.0895297i	$0.0285364\pi$
$317$			3.18806i			0.179059i	−0.995984	+	0.0895297i	$0.971464\pi$
$318$			31.9042i			1.78910i
$319$		−	31.3740i		−	1.75661i
$320$		0			0
$321$	4.30604			0.240340
$322$	−1.08400			−0.0604091
$323$			14.6461i			0.814929i
$324$	−3.23596			−0.179775
$325$		0			0
$326$	−15.7980			−0.874971
$327$		−	37.3282i		−	2.06426i
$328$	−5.45800			−0.301368
$329$	4.62600			0.255040
$330$		0			0
$331$		−	9.02219i		−	0.495904i	−0.968772	−	0.247952i	$-0.920242\pi$
$331$		−	9.02219i		−	0.495904i	0.968772	−	0.247952i	$-0.0797576\pi$
$332$		−	0.188063i		−	0.0103213i
$333$		−	48.7523i		−	2.67161i
$334$	15.5642			0.851635
$335$		0			0
$336$		−	5.42402i		−	0.295905i
$337$	16.2921			0.887489			0.443744	−	0.896153i	$-0.353650\pi$
$337$	16.2921			0.887489			0.443744	+	0.896153i	$0.353650\pi$
$338$	−2.07008	−	12.8341i	−0.112598	−	0.698084i
$339$	−26.5781			−1.44352
$340$		0			0
$341$	45.2103			2.44827
$342$	25.9042			1.40074
$343$		−	19.6822i		−	1.06274i
$344$			4.00000i			0.215666i
$345$		0			0
$346$		−	5.64606i		−	0.303534i
$347$	−12.3421			−0.662561			−0.331281	−	0.943532i	$-0.607481\pi$
$347$	−12.3421			−0.662561			−0.331281	+	0.943532i	$0.607481\pi$
$348$	−14.6121			−0.783290
$349$		−	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
$352$	−6.18806			−0.329825
$353$			0.707877i			0.0376765i	0.999823	+	0.0188382i	$0.00599675\pi$
$353$			0.707877i			0.0376765i	−0.999823	+	0.0188382i	$0.994003\pi$
$354$	25.4601			1.35319
$355$		0			0
$356$		−	11.4580i		−	0.607273i
$357$		−	16.2721i		−	0.861209i
$358$		−	13.4941i		−	0.713186i
$359$			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
$362$		−	2.73006i		−	0.143489i
$363$	−78.6565			−4.12839
$364$	−0.542001	−	6.76404i	−0.0284086	−	0.354532i
$365$		0			0
$366$		−	10.5080i		−	0.549263i
$367$	−15.8363			−0.826646			−0.413323	−	0.910585i	$-0.635632\pi$
$367$	−15.8363			−0.826646			−0.413323	+	0.910585i	$0.635632\pi$
$368$	0.575978			0.0300249
$369$			28.9604i			1.50762i
$370$		0			0
$371$			20.8341i			1.08165i
$372$		−	21.0562i		−	1.09171i
$373$	−4.35394			−0.225438			−0.112719	−	0.993627i	$-0.535956\pi$
$373$	−4.35394			−0.225438			−0.112719	+	0.993627i	$0.535956\pi$
$374$	−18.5642			−0.959931
$375$		0			0
$376$	−2.45800			−0.126762
$377$	−18.2220	+	1.46013i	−0.938483	+	0.0752004i
$378$	−12.5080			−0.643343
$379$		−	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
$382$			4.84804i			0.248047i
$383$		−	7.46013i		−	0.381195i	−0.981668	−	0.190597i	$-0.938958\pi$
$383$		−	7.46013i		−	0.381195i	0.981668	−	0.190597i	$-0.0610425\pi$
$384$			2.88202i			0.147072i
$385$		0			0
$386$	−10.6822			−0.543708
$387$	21.2242			1.07889
$388$			15.7640i			0.800298i
$389$	6.57598			0.333415			0.166708	−	0.986006i	$-0.446686\pi$
$389$	6.57598			0.333415			0.166708	+	0.986006i	$0.446686\pi$
$390$		0			0
$391$	1.72793			0.0873854
$392$			3.45800i			0.174655i
$393$	63.8084			3.21871
$394$	15.5642			0.784113
$395$		0			0
$396$			32.8341i			1.64998i
$397$		−	6.95210i		−	0.348916i	−0.984665	−	0.174458i	$-0.944183\pi$
$397$		−	6.95210i		−	0.348916i	0.984665	−	0.174458i	$-0.0558173\pi$
$398$			0.272066i			0.0136374i
$399$	26.4802			1.32567
$400$		0			0
$401$		−	6.91813i		−	0.345475i	−0.984968	−	0.172737i	$-0.944739\pi$
$401$		−	6.91813i		−	0.345475i	0.984968	−	0.172737i	$-0.0552612\pi$
$402$	10.3060			0.514019
$403$	−2.10406	−	26.2581i	−0.104811	−	1.30801i
$404$	−10.4941			−0.522101
$405$		0			0
$406$	−9.54200			−0.473562
$407$	−56.8563			−2.81826
$408$			8.64606i			0.428044i
$409$			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
$412$	17.1881			0.846795
$413$	16.6260			0.818112
$414$		−	3.05616i		−	0.150202i
$415$		0			0
$416$	0.287989	+	3.59403i	0.0141198	+	0.176212i
$417$	12.3060			0.602629
$418$		−	30.2103i		−	1.47763i
$419$	−22.9500			−1.12118			−0.560590	−	0.828094i	$-0.689426\pi$
$419$	−22.9500			−1.12118			−0.560590	+	0.828094i	$0.689426\pi$
$420$		0			0
$421$			24.7523i			1.20635i	0.797609	+	0.603175i	$0.206098\pi$
$421$			24.7523i			1.20635i	−0.797609	+	0.603175i	$0.793902\pi$
$422$			17.0222i			0.828627i
$423$			13.0422i			0.634136i
$424$		−	11.0701i		−	0.537611i
$425$		0			0
$426$		0			0
$427$		−	6.86196i		−	0.332074i
$428$	−1.49411			−0.0722203
$429$	5.13603	+	64.0964i	0.247970	+	3.09460i
$430$		0			0
$431$		−	32.1041i		−	1.54640i	−0.634163	−	0.773199i	$-0.718655\pi$
$431$		−	32.1041i		−	1.54640i	0.634163	−	0.773199i	$-0.281345\pi$
$432$	6.64606			0.319759
$433$	−16.2103			−0.779015			−0.389507	−	0.921023i	$-0.627355\pi$
$433$	−16.2103			−0.779015			−0.389507	+	0.921023i	$0.627355\pi$
$434$		−	13.7501i		−	0.660027i
$435$		0			0
$436$			12.9521i			0.620293i
$437$			2.81194i			0.134513i
$438$	34.1062			1.62966
$439$	22.1041			1.05497			0.527485	−	0.849565i	$-0.323135\pi$
$439$	22.1041			1.05497			0.527485	+	0.849565i	$0.323135\pi$
$440$		0			0
$441$	18.3483			0.873728
$442$	0.863967	+	10.7821i	0.0410947	+	0.512852i
$443$	−2.64606			−0.125718			−0.0628591	−	0.998022i	$-0.520022\pi$
$443$	−2.64606			−0.125718			−0.0628591	+	0.998022i	$0.520022\pi$
$444$			26.4802i			1.25669i
$445$		0			0
$446$	−1.65998			−0.0786024
$447$			48.7523i			2.30590i
$448$			1.88202i			0.0889171i
$449$		−	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
$452$	9.22204			0.433768
$453$			50.2803i			2.36238i
$454$	−8.45800			−0.396954
$455$		0			0
$456$	−14.0701			−0.658892
$457$			18.9181i			0.884953i	0.896780	+	0.442476i	$0.145900\pi$
$457$			18.9181i			0.884953i	−0.896780	+	0.442476i	$0.854100\pi$
$458$	−9.38792			−0.438668
$459$	19.9382			0.930635
$460$		0			0
$461$			8.81194i			0.410413i	0.978719	+	0.205206i	$0.0657866\pi$
$461$			8.81194i			0.410413i	−0.978719	+	0.205206i	$0.934213\pi$
$462$			33.5642i			1.56155i
$463$		−	28.5621i		−	1.32739i	−0.748003	−	0.663696i	$-0.768987\pi$
$463$		−	28.5621i		−	1.32739i	0.748003	−	0.663696i	$-0.231013\pi$
$464$	5.07008			0.235373
$465$		0			0
$466$		−	20.9882i		−	0.972260i
$467$	−22.1402			−1.02452			−0.512262	−	0.858829i	$-0.671192\pi$
$467$	−22.1402			−1.02452			−0.512262	+	0.858829i	$0.671192\pi$
$468$	19.0701	−	1.52808i	0.881515	−	0.0706356i
$469$	6.73006			0.310765
$470$		0			0
$471$	−7.86810			−0.362543
$472$	−8.83412			−0.406624
$473$		−	24.7523i		−	1.13811i
$474$			32.2442i			1.48103i
$475$		0			0
$476$			5.64606i			0.258787i
$477$	−58.7383			−2.68944
$478$	−14.4580			−0.661293
$479$			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
$482$	−9.92992			−0.452295
$483$		−	3.12412i		−	0.142152i
$484$	27.2921			1.24055
$485$		0			0
$486$			10.6121i			0.481374i
$487$			3.78623i			0.171570i	0.996314	+	0.0857852i	$0.0273399\pi$
$487$			3.78623i			0.171570i	−0.996314	+	0.0857852i	$0.972660\pi$
$488$			3.64606i			0.165049i
$489$		−	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	$0.363367\pi$
$492$		−	15.7301i		−	0.709166i
$493$	15.2103			0.685035
$494$	−17.5461	+	1.40597i	−0.789438	+	0.0632575i
$495$		0			0
$496$			7.30604i			0.328051i
$497$		0			0
$498$	0.542001			0.0242877
$499$		−	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
$502$			14.6461i			0.653686i
$503$	−2.30391			−0.102726			−0.0513632	−	0.998680i	$-0.516357\pi$
$503$	−2.30391			−0.102726			−0.0513632	+	0.998680i	$0.516357\pi$
$504$	9.98608			0.444815
$505$		0			0
$506$	−3.56419			−0.158448
$507$	36.9882	−	5.96602i	1.64270	−	0.264960i
$508$	4.37613			0.194159
$509$			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
$512$		−	1.00000i		−	0.0441942i
$513$			32.4462i			1.43254i
$514$		−	23.0701i		−	1.01758i
$515$		0			0
$516$	−11.5281			−0.507496
$517$	15.2103			0.668946
$518$			17.2921i			0.759772i
$519$	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	$0.653902\pi$
$522$		−	26.9021i		−	1.17747i
$523$	−28.3143			−1.23810			−0.619049	−	0.785352i	$-0.712482\pi$
$523$	−28.3143			−1.23810			−0.619049	+	0.785352i	$0.712482\pi$
$524$	−22.1402			−0.967198
$525$		0			0
$526$			9.56419i			0.417018i
$527$			21.9181i			0.954769i
$528$		−	17.8341i		−	0.776131i
$529$	−22.6682			−0.985576
$530$		0			0
$531$			46.8742i			2.03417i
$532$	−9.18806			−0.398353
$533$	−1.57184	−	19.6162i	−0.0680841	−	0.849673i
$534$	33.0222			1.42901
$535$		0			0
$536$	−3.57598			−0.154459
$537$	38.8903			1.67824
$538$		−	5.07008i		−	0.218587i
$539$		−	21.3983i		−	0.921691i
$540$		0			0
$541$		−	24.6204i		−	1.05851i	−0.848462	−	0.529256i	$-0.822471\pi$
$541$		−	24.6204i		−	1.05851i	0.848462	−	0.529256i	$-0.177529\pi$
$542$	0.730064			0.0313589
$543$	7.86810			0.337653
$544$		−	3.00000i		−	0.128624i
$545$		0			0
$546$	19.4941	−	1.56206i	0.834271	−	0.0668500i
$547$	17.9382			0.766981			0.383491	−	0.923545i	$-0.374722\pi$
$547$	17.9382			0.766981			0.383491	+	0.923545i	$0.374722\pi$
$548$			5.83412i			0.249221i
$549$	19.3462			0.825674
$550$		0			0
$551$			24.7523i			1.05448i
$552$			1.65998i			0.0706535i
$553$			21.0562i			0.895399i
$554$			5.56419i			0.236400i
$555$		0			0
$556$	−4.26994			−0.181086
$557$			26.4802i			1.12200i	0.827815	+	0.561001i	$0.189584\pi$
$557$			26.4802i			1.12200i	−0.827815	+	0.561001i	$0.810416\pi$
$558$	38.7662			1.64110
$559$	−14.3761	+	1.15196i	−0.608045	+	0.0487226i
$560$		0			0
$561$		−	53.5024i		−	2.25887i
$562$	−23.2921			−0.982519
$563$	14.2803			0.601844			0.300922	−	0.953649i	$-0.402706\pi$
$563$	14.2803			0.601844			0.300922	+	0.953649i	$0.402706\pi$
$564$		−	7.08400i		−	0.298290i
$565$		0			0
$566$			14.1062i			0.592927i
$567$		−	6.09014i		−	0.255762i
$568$		0			0
$569$	−4.85983			−0.203735			−0.101867	−	0.994798i	$-0.532482\pi$
$569$	−4.85983			−0.203735			−0.101867	+	0.994798i	$0.532482\pi$
$570$		0			0
$571$	−6.53987			−0.273685			−0.136843	−	0.990593i	$-0.543695\pi$
$571$	−6.53987			−0.273685			−0.136843	+	0.990593i	$0.543695\pi$
$572$	−1.78209	−	22.2401i	−0.0745131	−	0.929905i
$573$	−13.9722			−0.583695
$574$		−	10.2721i		−	0.428748i
$575$		0			0
$576$	−5.30604			−0.221085
$577$		−	43.7383i		−	1.82085i	−0.413673	−	0.910425i	$-0.635754\pi$
$577$		−	43.7383i		−	1.82085i	0.413673	−	0.910425i	$-0.364246\pi$
$578$			8.00000i			0.332756i
$579$		−	30.7862i		−	1.27943i
$580$		0			0
$581$	0.353938			0.0146838
$582$	−45.4323			−1.88323
$583$			68.5024i			2.83708i
$584$	−11.8341			−0.489700
$585$		0			0
$586$	−6.00000			−0.247858
$587$		−	13.2721i		−	0.547797i	−0.961759	−	0.273898i	$-0.911687\pi$
$587$		−	13.2721i		−	0.547797i	0.961759	−	0.273898i	$-0.0883132\pi$
$588$	−9.96602			−0.410992
$589$	−35.6682			−1.46968
$590$		0			0
$591$			44.8563i			1.84514i
$592$		−	9.18806i		−	0.377627i
$593$			25.6704i			1.05416i	0.849817	+	0.527078i	$0.176712\pi$
$593$			25.6704i			1.05416i	−0.849817	+	0.527078i	$0.823288\pi$
$594$	−41.1262			−1.68743
$595$		0			0
$596$		−	16.9160i		−	0.692906i
$597$	−0.784099			−0.0320910
$598$	0.165875	+	2.07008i	0.00678315	+	0.0846520i
$599$	16.8480			0.688392			0.344196	−	0.938898i	$-0.388151\pi$
$599$	16.8480			0.688392			0.344196	+	0.938898i	$0.388151\pi$
$600$		0			0
$601$	−16.2921			−0.664570			−0.332285	−	0.943179i	$-0.607820\pi$
$601$	−16.2921			−0.664570			−0.332285	+	0.943179i	$0.607820\pi$
$602$	−7.52808			−0.306822
$603$			18.9743i			0.772693i
$604$		−	17.4462i		−	0.709876i
$605$		0			0
$606$		−	30.2442i		−	1.22859i
$607$	31.5642			1.28115			0.640575	−	0.767895i	$-0.278696\pi$
$607$	31.5642			1.28115			0.640575	+	0.767895i	$0.278696\pi$
$608$	4.88202			0.197992
$609$		−	27.5002i		−	1.11437i
$610$		0			0
$611$	−0.707877	−	8.83412i	−0.0286376	−	0.357390i
$612$	−15.9181			−0.643452
$613$		−	27.8320i		−	1.12412i	−0.827095	−	0.562062i	$-0.810008\pi$
$613$		−	27.8320i		−	1.12412i	0.827095	−	0.562062i	$-0.189992\pi$
$614$	9.42189			0.380237
$615$		0			0
$616$		−	11.6461i		−	0.469233i
$617$			1.08400i			0.0436403i	0.999762	+	0.0218202i	$0.00694612\pi$
$617$			1.08400i			0.0436403i	−0.999762	+	0.0218202i	$0.993054\pi$
$618$			49.5364i			1.99264i
$619$			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
$622$			31.7044i			1.27123i
$623$	21.5642			0.863951
$624$	−10.3581	+	0.829990i	−0.414655	+	0.0332262i
$625$		0			0
$626$		−	15.3740i		−	0.614468i
$627$	87.0666			3.47710
$628$	2.73006			0.108941
$629$		−	27.5642i		−	1.09906i
$630$		0			0
$631$		−	23.4240i		−	0.932496i	−0.884654	−	0.466248i	$-0.845606\pi$
$631$		−	23.4240i		−	0.932496i	0.884654	−	0.466248i	$-0.154394\pi$
$632$		−	11.1881i		−	0.445037i
$633$	−49.0583			−1.94989
$634$	3.18806			0.126614
$635$		0			0
$636$	31.9042			1.26508
$637$	−12.4282	+	0.995866i	−0.492421	+	0.0394576i
$638$	−31.3740			−1.24211
$639$		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	$0.539212\pi$
$642$		−	4.30604i		−	0.169946i
$643$			37.8363i			1.49212i	0.665881	+	0.746058i	$0.268056\pi$
$643$			37.8363i			1.49212i	−0.665881	+	0.746058i	$0.731944\pi$
$644$			1.08400i			0.0427157i
$645$		0			0
$646$	14.6461			0.576242
$647$	−38.8563			−1.52760			−0.763800	−	0.645453i	$-0.776668\pi$
$647$	−38.8563			−1.52760			−0.763800	+	0.645453i	$0.776668\pi$
$648$			3.23596i			0.127120i
$649$	54.6661			2.14583
$650$		0			0
$651$	39.6281			1.55315
$652$			15.7980i			0.618698i
$653$	25.3740			0.992961			0.496481	−	0.868048i	$-0.334625\pi$
$653$	25.3740			0.992961			0.496481	+	0.868048i	$0.334625\pi$
$654$	−37.3282			−1.45965
$655$		0			0
$656$			5.45800i			0.213099i
$657$			62.7924i			2.44976i
$658$		−	4.62600i		−	0.180340i
$659$	16.5059			0.642978			0.321489	−	0.946913i	$-0.395817\pi$
$659$	16.5059			0.642978			0.321489	+	0.946913i	$0.395817\pi$
$660$		0			0
$661$		−	8.81194i		−	0.342745i	−0.985206	−	0.171372i	$-0.945180\pi$
$661$		−	8.81194i		−	0.342745i	0.985206	−	0.171372i	$-0.0548201\pi$
$662$	−9.02219			−0.350657
$663$	−31.0742	+	2.48997i	−1.20682	+	0.0967025i
$664$	−0.188063			−0.00729826
$665$		0			0
$666$	−48.7523			−1.88911
$667$	2.92026			0.113073
$668$		−	15.5642i		−	0.602197i
$669$		−	4.78410i		−	0.184964i
$670$		0			0
$671$		−	22.5621i		−	0.870999i
$672$	−5.42402			−0.209236
$673$	−4.08187			−0.157345			−0.0786723	−	0.996901i	$-0.525068\pi$
$673$	−4.08187			−0.157345			−0.0786723	+	0.996901i	$0.525068\pi$
$674$		−	16.2921i		−	0.627549i
$675$		0			0
$676$	−12.8341	+	2.07008i	−0.493620	+	0.0796186i
$677$	24.4441			0.939462			0.469731	−	0.882810i	$-0.344351\pi$
$677$	24.4441			0.939462			0.469731	+	0.882810i	$0.344351\pi$
$678$			26.5781i			1.02073i
$679$	−29.6682			−1.13856
$680$		0			0
$681$		−	24.3761i		−	0.934095i
$682$		−	45.2103i		−	1.73119i
$683$			23.4802i			0.898444i	0.893420	+	0.449222i	$0.148299\pi$
$683$			23.4802i			0.898444i	−0.893420	+	0.449222i	$0.851701\pi$
$684$		−	25.9042i		−	0.990472i
$685$		0			0
$686$	−19.6822			−0.751469
$687$		−	27.0562i		−	1.03226i
$688$	4.00000			0.152499
$689$	39.7862	−	3.18806i	1.51573	−	0.121456i
$690$		0			0
$691$			11.4358i			0.435039i	0.976056	+	0.217519i	$0.0697965\pi$
$691$			11.4358i			0.435039i	−0.976056	+	0.217519i	$0.930203\pi$
$692$	−5.64606			−0.214631
$693$	−61.7945			−2.34738
$694$			12.3421i			0.468502i
$695$		0			0
$696$			14.6121i			0.553870i
$697$			16.3740i			0.620209i
$698$	−18.7523			−0.709783
$699$	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	$0.555792\pi$
$702$	1.91399	+	23.8862i	0.0722390	+	0.901525i
$703$	44.8563			1.69179
$704$			6.18806i			0.233221i
$705$		0			0
$706$	0.707877			0.0266413
$707$		−	19.7501i		−	0.742780i
$708$		−	25.4601i		−	0.956850i
$709$		−	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
$712$	−11.4580			−0.429407
$713$			4.20812i			0.157595i
$714$	−16.2721			−0.608967
$715$		0			0
$716$	−13.4941			−0.504298
$717$		−	41.6682i		−	1.55613i
$718$	0.0221876			0.000828033
$719$	−16.8480			−0.628326			−0.314163	−	0.949369i	$-0.601724\pi$
$719$	−16.8480			−0.628326			−0.314163	+	0.949369i	$0.601724\pi$
$720$		0			0
$721$			32.3483i			1.20471i
$722$			4.83412i			0.179907i
$723$		−	28.6182i		−	1.06432i
$724$	−2.73006			−0.101462
$725$		0			0
$726$			78.6565i			2.91922i
$727$	−35.0201			−1.29882			−0.649411	−	0.760438i	$-0.724985\pi$
$727$	−35.0201			−1.29882			−0.649411	+	0.760438i	$0.724985\pi$
$728$	−6.76404	+	0.542001i	−0.250692	+	0.0200879i
$729$	−40.2921			−1.49230
$730$		0			0
$731$	12.0000			0.443836
$732$	−10.5080			−0.388388
$733$			18.1083i			0.668846i	0.942423	+	0.334423i	$0.108541\pi$
$733$			18.1083i			0.668846i	−0.942423	+	0.334423i	$0.891459\pi$
$734$			15.8363i			0.584527i
$735$		0			0
$736$		−	0.575978i		−	0.0212308i
$737$	22.1284			0.815109
$738$	28.9604			1.06605
$739$		−	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
$742$	20.8341			0.764845
$743$		−	43.8584i		−	1.60901i	−0.593946	−	0.804505i	$-0.702431\pi$
$743$		−	43.8584i		−	1.60901i	0.593946	−	0.804505i	$-0.297569\pi$
$744$	−21.0562			−0.771956
$745$		0			0
$746$			4.35394i			0.159409i
$747$			0.997870i			0.0365102i
$748$			18.5642i			0.678774i
$749$		−	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	$0.241536\pi$
$752$			2.45800i			0.0896340i
$753$	−42.2103			−1.53823
$754$	1.46013	+	18.2220i	0.0531747	+	0.663608i
$755$		0			0
$756$			12.5080i			0.454912i
$757$	42.2943			1.53721			0.768605	−	0.639723i	$-0.220951\pi$
$757$	42.2943			1.53721			0.768605	+	0.639723i	$0.220951\pi$
$758$	−2.42402			−0.0880444
$759$		−	10.2721i		−	0.372852i
$760$		0			0
$761$			3.99787i			0.144923i	0.997371	+	0.0724613i	$0.0230854\pi$
$761$			3.99787i			0.144923i	−0.997371	+	0.0724613i	$0.976915\pi$
$762$			12.6121i			0.456888i
$763$	−24.3761			−0.882475
$764$	4.84804			0.175396
$765$		0			0
$766$	−7.46013			−0.269545
$767$	−2.54413	−	31.7501i	−0.0918633	−	1.14643i
$768$	2.88202			0.103996
$769$			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
$772$			10.6822i			0.384460i
$773$			15.1881i			0.546277i	0.961975	+	0.273138i	$0.0880617\pi$
$773$			15.1881i			0.546277i	−0.961975	+	0.273138i	$0.911938\pi$
$774$		−	21.2242i		−	0.762887i
$775$		0			0
$776$	15.7640			0.565896
$777$	−49.8363			−1.78787
$778$		−	6.57598i		−	0.235760i
$779$	−26.6461			−0.954694
$780$		0			0
$781$		0			0
$782$		−	1.72793i		−	0.0617908i
$783$	33.6961			1.20420
$784$	3.45800			0.123500
$785$		0			0
$786$		−	63.8084i		−	2.27597i
$787$		−	7.68217i		−	0.273840i	−0.990582	−	0.136920i	$-0.956280\pi$
$787$		−	7.68217i		−	0.273840i	0.990582	−	0.136920i	$-0.0437203\pi$
$788$		−	15.5642i		−	0.554451i
$789$	−27.5642			−0.981311
$790$		0			0
$791$			17.3561i			0.617111i
$792$	32.8341			1.16671
$793$	−13.1041	+	1.05003i	−0.465339	+	0.0372875i
$794$	−6.95210			−0.246721
$795$		0			0
$796$	0.272066			0.00964311
$797$	33.0784			1.17170			0.585848	−	0.810421i	$-0.300762\pi$
$797$	33.0784			1.17170			0.585848	+	0.810421i	$0.300762\pi$
$798$		−	26.4802i		−	0.937388i
$799$			7.37400i			0.260873i
$800$		0			0
$801$			60.7966i			2.14814i
$802$	−6.91813			−0.244288
$803$	73.2303			2.58424
$804$		−	10.3060i		−	0.363466i
$805$		0			0
$806$	−26.2581	+	2.10406i	−0.924904	+	0.0741124i
$807$	14.6121			0.514370
$808$			10.4941i			0.369181i
$809$	23.2921			0.818907			0.409454	−	0.912331i	$-0.365719\pi$
$809$	23.2921			0.818907			0.409454	+	0.912331i	$0.365719\pi$
$810$		0			0
$811$			2.14983i			0.0754906i	0.999287	+	0.0377453i	$0.0120176\pi$
$811$			2.14983i			0.0754906i	−0.999287	+	0.0377453i	$0.987982\pi$
$812$			9.54200i			0.334859i
$813$			2.10406i			0.0737926i
$814$			56.8563i			1.99281i
$815$		0			0
$816$	8.64606			0.302673
$817$			19.5281i			0.683201i
$818$	15.9299			0.556976
$819$	2.87588	+	35.8903i	0.100491	+	1.25411i
$820$		0			0
$821$			26.8563i			0.937292i	0.883386	+	0.468646i	$0.155258\pi$
$821$			26.8563i			0.937292i	−0.883386	+	0.468646i	$0.844742\pi$
$822$	−16.8141			−0.586458
$823$	4.00000			0.139431			0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000			0.139431			0.0697156	+	0.997567i	$0.477791\pi$
$824$		−	17.1881i		−	0.598775i
$825$		0			0
$826$		−	16.6260i		−	0.578493i
$827$			32.0243i			1.11359i	0.830648	+	0.556797i	$0.187970\pi$
$827$			32.0243i			1.11359i	−0.830648	+	0.556797i	$0.812030\pi$
$828$	−3.05616			−0.106209
$829$	−19.2699			−0.669273			−0.334636	−	0.942347i	$-0.608613\pi$
$829$	−19.2699			−0.669273			−0.334636	+	0.942347i	$0.608613\pi$
$830$		0			0
$831$	−16.0361			−0.556286
$832$	3.59403	−	0.287989i	0.124601	−	0.00998422i
$833$	10.3740			0.359438
$834$		−	12.3060i		−	0.426123i
$835$		0			0
$836$	−30.2103			−1.04484
$837$			48.5564i			1.67835i
$838$			22.9500i			0.792794i
$839$			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
$842$	24.7523			0.853019
$843$		−	67.1284i		−	2.31202i
$844$	17.0222			0.585928
$845$		0			0
$846$	13.0422			0.448402
$847$			51.3643i			1.76490i
$848$	−11.0701			−0.380148
$849$	−40.6543			−1.39525
$850$		0			0
$851$		−	5.29212i		−	0.181412i
$852$		0			0
$853$		−	36.5524i		−	1.25153i	−0.780012	−	0.625765i	$-0.784787\pi$
$853$		−	36.5524i		−	1.25153i	0.780012	−	0.625765i	$-0.215213\pi$
$854$	−6.86196			−0.234812
$855$		0			0
$856$			1.49411i			0.0510675i
$857$	27.9299			0.954068			0.477034	−	0.878885i	$-0.341712\pi$
$857$	27.9299			0.954068			0.477034	+	0.878885i	$0.341712\pi$
$858$	64.0964	−	5.13603i	2.18822	−	0.175341i
$859$	−46.6461			−1.59154			−0.795772	−	0.605597i	$-0.792934\pi$
$859$	−46.6461			−1.59154			−0.795772	+	0.605597i	$0.792934\pi$
$860$		0			0
$861$	29.6043			1.00891
$862$	−32.1041			−1.09347
$863$			37.1062i			1.26311i	0.775331	+	0.631555i	$0.217583\pi$
$863$			37.1062i			1.26311i	−0.775331	+	0.631555i	$0.782417\pi$
$864$		−	6.64606i		−	0.226104i
$865$		0			0
$866$			16.2103i			0.550847i
$867$	−23.0562			−0.783028
$868$	−13.7501			−0.466710
$869$			69.2324i			2.34855i
$870$		0			0
$871$	−1.02984	−	12.8522i	−0.0348949	−	0.435479i
$872$	12.9521			0.438614
$873$		−	83.6447i		−	2.83094i
$874$	2.81194			0.0951152
$875$		0			0
$876$		−	34.1062i		−	1.15234i
$877$			46.8924i			1.58344i	0.610881	+	0.791722i	$0.290815\pi$
$877$			46.8924i			1.58344i	−0.610881	+	0.791722i	$0.709185\pi$
$878$		−	22.1041i		−	0.745976i
$879$		−	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	$0.329977\pi$
$882$		−	18.3483i		−	0.617819i
$883$	3.93818			0.132530			0.0662652	−	0.997802i	$-0.478892\pi$
$883$	3.93818			0.132530			0.0662652	+	0.997802i	$0.478892\pi$
$884$	10.7821	−	0.863967i	0.362641	−	0.0290584i
$885$		0			0
$886$			2.64606i			0.0888962i
$887$	4.16375			0.139805			0.0699024	−	0.997554i	$-0.477731\pi$
$887$	4.16375			0.139805			0.0699024	+	0.997554i	$0.477731\pi$
$888$	26.4802			0.888617
$889$			8.23596i			0.276225i
$890$		0			0
$891$		−	20.0243i		−	0.670840i
$892$			1.65998i			0.0555803i
$893$	−12.0000			−0.401565
$894$	48.7523			1.63052
$895$		0			0
$896$	1.88202			0.0628739
$897$	−5.96602	+	0.478056i	−0.199200	+	0.0159618i
$898$	−35.1262			−1.17218
$899$			37.0422i			1.23543i
$900$		0			0
$901$	−33.2103			−1.10639
$902$		−	33.7744i		−	1.12457i
$903$		−	21.6961i		−	0.722001i
$904$		−	9.22204i		−	0.306720i
$905$		0			0
$906$	50.2803			1.67045
$907$	−27.6682			−0.918709			−0.459355	−	0.888253i	$-0.651919\pi$
$907$	−27.6682			−0.918709			−0.459355	+	0.888253i	$0.651919\pi$
$908$			8.45800i			0.280689i
$909$	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	$0.797463\pi$
$912$			14.0701i			0.465907i
$913$	1.16375			0.0385144
$914$	18.9181			0.625756
$915$		0			0
$916$			9.38792i			0.310185i
$917$		−	41.6682i		−	1.37601i
$918$		−	19.9382i		−	0.658058i
$919$	−8.26781			−0.272730			−0.136365	−	0.990659i	$-0.543542\pi$
$919$	−8.26781			−0.272730			−0.136365	+	0.990659i	$0.543542\pi$
$920$		0			0
$921$			27.1541i			0.894758i
$922$	8.81194			0.290206
$923$		0			0
$924$	33.5642			1.10418
$925$		0			0
$926$	−28.5621			−0.938607
$927$	−91.2006			−2.99542
$928$		−	5.07008i		−	0.166434i
$929$		−	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
$932$	−20.9882			−0.687492
$933$	−91.3726			−2.99140
$934$			22.1402i			0.724448i
$935$		0			0
$936$	−1.52808	−	19.0701i	−0.0499469	−	0.623325i
$937$	−46.8764			−1.53138			−0.765692	−	0.643207i	$-0.777603\pi$
$937$	−46.8764			−1.53138			−0.765692	+	0.643207i	$0.777603\pi$
$938$		−	6.73006i		−	0.219744i
$939$	44.3082			1.44594
$940$		0			0
$941$		−	10.2721i		−	0.334860i	−0.985884	−	0.167430i	$-0.946453\pi$
$941$		−	10.2721i		−	0.334860i	0.985884	−	0.167430i	$-0.0535468\pi$
$942$			7.86810i			0.256357i
$943$			3.14369i			0.102373i
$944$			8.83412i			0.287526i
$945$		0			0
$946$	−24.7523			−0.804765
$947$			38.1262i			1.23894i	0.785022	+	0.619468i	$0.212652\pi$
$947$			38.1262i			1.23894i	−0.785022	+	0.619468i	$0.787348\pi$
$948$	32.2442			1.04724
$949$	−3.40810	−	42.5322i	−0.110632	−	1.38065i
$950$		0			0
$951$			9.18806i			0.297943i
$952$	5.64606			0.182990
$953$	−44.2921			−1.43476			−0.717381	−	0.696681i	$-0.754659\pi$
$953$	−44.2921			−1.43476			−0.717381	+	0.696681i	$0.754659\pi$
$954$			58.7383i			1.90172i
$955$		0			0
$956$			14.4580i			0.467605i
$957$		−	90.4205i		−	2.92288i
$958$	19.7501			0.638097
$959$	−10.9799			−0.354561
$960$		0			0
$961$	−22.3783			−0.721879
$962$	33.0222	−	2.64606i	1.06468	−	0.0853125i
$963$	7.92779			0.255469
$964$			9.92992i			0.319821i
$965$		0			0
$966$	−3.12412			−0.100517
$967$		−	44.1262i		−	1.41900i	−0.704703	−	0.709502i	$-0.748920\pi$
$967$		−	44.1262i		−	1.41900i	0.704703	−	0.709502i	$-0.251080\pi$
$968$		−	27.2921i		−	0.877202i
$969$			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	$0.504136\pi$
$972$	10.6121			0.340383
$973$		−	8.03611i		−	0.257626i
$974$	3.78623			0.121319
$975$		0			0
$976$	3.64606			0.116708
$977$		−	62.0465i		−	1.98504i	−0.122068	−	0.992522i	$-0.538952\pi$
$977$		−	62.0465i		−	1.98504i	0.122068	−	0.992522i	$-0.461048\pi$
$978$	−45.5302			−1.45590
$979$	70.9028			2.26606
$980$		0			0
$981$		−	68.7244i		−	2.19420i
$982$		−	18.4441i		−	0.588574i
$983$			2.72580i			0.0869397i	0.999055	+	0.0434698i	$0.0138412\pi$
$983$			2.72580i			0.0869397i	−0.999055	+	0.0434698i	$0.986159\pi$
$984$	−15.7301			−0.501456
$985$		0			0
$986$		−	15.2103i		−	0.484393i
$987$	13.3322			0.424370
$988$	1.40597	+	17.5461i	0.0447298	+	0.558217i
$989$	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	$0.368414\pi$
$992$	7.30604			0.231967
$993$		−	26.0021i		−	0.825153i
$994$		0			0
$995$		0			0
$996$		−	0.542001i		−	0.0171740i
$997$	2.29425			0.0726597			0.0363299	−	0.999340i	$-0.488433\pi$
$997$	2.29425			0.0726597			0.0363299	+	0.999340i	$0.488433\pi$
$998$	−9.98608			−0.316104
$999$		−	61.0644i		−	1.93199i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.c.e.649.2		6	65.12	odd	4
650.2.c.e.649.5		6	5.3	odd	4
650.2.c.f.649.2		6	5.2	odd	4
650.2.c.f.649.5		6	65.38	odd	4
650.2.d.c.51.3	✓	6	1.1	even	1	trivial
650.2.d.c.51.6	yes	6	13.12	even	2	inner
650.2.d.d.51.1	yes	6	65.64	even	2
650.2.d.d.51.4	yes	6	5.4	even	2
8450.2.a.bq.1.1		3	65.34	odd	4
8450.2.a.br.1.3		3	13.5	odd	4
8450.2.a.cd.1.3		3	13.8	odd	4
8450.2.a.ce.1.1		3	65.44	odd	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.d (of order \(2\), degree \(1\), minimal)

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

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