LMFDB - Embedded newform 1305.2.c.k.784.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1305,2,Mod(784,1305)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1305, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1305.784");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 148x^{8} + 502x^{6} + 792x^{4} + 496x^{2} + 45 $ x^12 + 20x^10 + 148x^8 + 502x^6 + 792x^4 + 496*x^2 + 45
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.6
Root			$-0.328889i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.k.784.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.328889i q^{2} +1.89183 q^{4} +(2.20614 + 0.364635i) q^{5} -1.86588i q^{7} -1.27998i q^{8} +(0.119924 - 0.725574i) q^{10} -0.564087 q^{11} +4.95986i q^{13} -0.613668 q^{14} +3.36269 q^{16} +7.06879i q^{17} +3.32971 q^{19} +(4.17364 + 0.689828i) q^{20} +0.185522i q^{22} -2.36471i q^{23} +(4.73408 + 1.60887i) q^{25} +1.63124 q^{26} -3.52994i q^{28} -1.00000 q^{29} +4.87352 q^{31} -3.66591i q^{32} +2.32485 q^{34} +(0.680366 - 4.11639i) q^{35} -8.50474i q^{37} -1.09510i q^{38} +(0.466725 - 2.82381i) q^{40} -7.86030 q^{41} -4.39693i q^{43} -1.06716 q^{44} -0.777727 q^{46} +7.06879i q^{47} +3.51848 q^{49} +(0.529139 - 1.55699i) q^{50} +9.38323i q^{52} -4.18169i q^{53} +(-1.24445 - 0.205686i) q^{55} -2.38829 q^{56} +0.328889i q^{58} -9.01198 q^{59} -1.26059 q^{61} -1.60285i q^{62} +5.51971 q^{64} +(-1.80854 + 10.9421i) q^{65} -6.61254i q^{67} +13.3730i q^{68} +(-1.35384 - 0.223765i) q^{70} +5.46480 q^{71} -5.77659i q^{73} -2.79711 q^{74} +6.29925 q^{76} +1.05252i q^{77} -12.1018 q^{79} +(7.41856 + 1.22616i) q^{80} +2.58516i q^{82} -9.41830i q^{83} +(-2.57753 + 15.5947i) q^{85} -1.44610 q^{86} +0.722020i q^{88} -0.622547 q^{89} +9.25453 q^{91} -4.47364i q^{92} +2.32485 q^{94} +(7.34579 + 1.21413i) q^{95} +19.2638i q^{97} -1.15719i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) $ 12 * q - 16 * q^4 - 10 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^16 + 20 * q^19 + 14 * q^20 + 8 * q^25 - 56 * q^26 - 12 * q^29 - 16 * q^31 - 4 * q^34 - 16 * q^35 + 16 * q^40 - 32 * q^41 + 68 * q^44 + 20 * q^46 + 4 * q^49 - 8 * q^50 + 4 * q^55 - 76 * q^56 + 44 * q^59 - 52 * q^61 - 36 * q^64 - 8 * q^65 - 30 * q^70 - 20 * q^71 + 20 * q^74 - 28 * q^76 + 4 * q^79 + 34 * q^80 + 20 * q^85 - 36 * q^86 + 68 * q^89 + 48 * q^91 - 4 * q^94 - 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	0.328889i		−	0.232560i	−0.993216	−	0.116280i	$-0.962903\pi$
$2$		−	0.328889i		−	0.232560i	0.993216	−	0.116280i	$-0.0370969\pi$
$3$		0			0
$3$		0			0
$4$	1.89183			0.945916
$5$	2.20614	+	0.364635i	0.986615	+	0.163070i
$5$	2.20614	+	0.364635i	0.986615	+	0.163070i
$6$		0			0
$7$		−	1.86588i		−	0.705237i	−0.935767	−	0.352619i	$-0.885291\pi$
$7$		−	1.86588i		−	0.705237i	0.935767	−	0.352619i	$-0.114709\pi$
$8$		−	1.27998i		−	0.452541i
$9$		0			0
$10$	0.119924	−	0.725574i	0.0379234	−	0.229447i
$11$	−0.564087			−0.170079			−0.0850393	−	0.996378i	$-0.527102\pi$
$11$	−0.564087			−0.170079			−0.0850393	+	0.996378i	$0.527102\pi$
$12$		0			0
$13$			4.95986i			1.37562i	0.725891	+	0.687809i	$0.241428\pi$
$13$			4.95986i			1.37562i	−0.725891	+	0.687809i	$0.758572\pi$
$14$	−0.613668			−0.164010
$15$		0			0
$16$	3.36269			0.840673
$17$			7.06879i			1.71443i	0.514956	+	0.857217i	$0.327808\pi$
$17$			7.06879i			1.71443i	−0.514956	+	0.857217i	$0.672192\pi$
$18$		0			0
$19$	3.32971			0.763887			0.381944	−	0.924186i	$-0.375255\pi$
$19$	3.32971			0.763887			0.381944	+	0.924186i	$0.375255\pi$
$20$	4.17364	+	0.689828i	0.933255	+	0.154250i
$21$		0			0
$22$			0.185522i			0.0395534i
$23$		−	2.36471i		−	0.493076i	−0.969133	−	0.246538i	$-0.920707\pi$
$23$		−	2.36471i		−	0.493076i	0.969133	−	0.246538i	$-0.0792931\pi$
$24$		0			0
$25$	4.73408	+	1.60887i	0.946817	+	0.321774i
$26$	1.63124			0.319913
$27$		0			0
$28$		−	3.52994i		−	0.667095i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$		0			0
$31$	4.87352			0.875310			0.437655	−	0.899143i	$-0.355809\pi$
$31$	4.87352			0.875310			0.437655	+	0.899143i	$0.355809\pi$
$32$		−	3.66591i		−	0.648048i
$33$		0			0
$34$	2.32485			0.398708
$35$	0.680366	−	4.11639i	0.115003	−	0.695798i
$36$		0			0
$37$		−	8.50474i		−	1.39817i	−0.715038	−	0.699085i	$-0.753591\pi$
$37$		−	8.50474i		−	1.39817i	0.715038	−	0.699085i	$-0.246409\pi$
$38$		−	1.09510i		−	0.177649i
$39$		0			0
$40$	0.466725	−	2.82381i	0.0737958	−	0.446484i
$41$	−7.86030			−1.22757			−0.613786	−	0.789473i	$-0.710354\pi$
$41$	−7.86030			−1.22757			−0.613786	+	0.789473i	$0.710354\pi$
$42$		0			0
$43$		−	4.39693i		−	0.670526i	−0.942125	−	0.335263i	$-0.891175\pi$
$43$		−	4.39693i		−	0.670526i	0.942125	−	0.335263i	$-0.108825\pi$
$44$	−1.06716			−0.160880
$45$		0			0
$46$	−0.777727			−0.114670
$47$			7.06879i			1.03109i	0.856863	+	0.515544i	$0.172410\pi$
$47$			7.06879i			1.03109i	−0.856863	+	0.515544i	$0.827590\pi$
$48$		0			0
$49$	3.51848			0.502640
$50$	0.529139	−	1.55699i	0.0748316	−	0.220191i
$51$		0			0
$52$			9.38323i			1.30122i
$53$		−	4.18169i		−	0.574400i	−0.957871	−	0.287200i	$-0.907276\pi$
$53$		−	4.18169i		−	0.574400i	0.957871	−	0.287200i	$-0.0927244\pi$
$54$		0			0
$55$	−1.24445	−	0.205686i	−0.167802	−	0.0277346i
$56$	−2.38829			−0.319149
$57$		0			0
$58$			0.328889i			0.0431852i
$59$	−9.01198			−1.17326			−0.586630	−	0.809855i	$-0.699546\pi$
$59$	−9.01198			−1.17326			−0.586630	+	0.809855i	$0.699546\pi$
$60$		0			0
$61$	−1.26059			−0.161402			−0.0807009	−	0.996738i	$-0.525716\pi$
$61$	−1.26059			−0.161402			−0.0807009	+	0.996738i	$0.525716\pi$
$62$		−	1.60285i		−	0.203562i
$63$		0			0
$64$	5.51971			0.689964
$65$	−1.80854	+	10.9421i	−0.224322	+	1.35721i
$66$		0			0
$67$		−	6.61254i		−	0.807851i	−0.914792	−	0.403925i	$-0.867646\pi$
$67$		−	6.61254i		−	0.807851i	0.914792	−	0.403925i	$-0.132354\pi$
$68$			13.3730i			1.62171i
$69$		0			0
$70$	−1.35384	−	0.223765i	−0.161814	−	0.0267450i
$71$	5.46480			0.648552			0.324276	−	0.945962i	$-0.394879\pi$
$71$	5.46480			0.648552			0.324276	+	0.945962i	$0.394879\pi$
$72$		0			0
$73$		−	5.77659i		−	0.676099i	−0.941128	−	0.338049i	$-0.890233\pi$
$73$		−	5.77659i		−	0.676099i	0.941128	−	0.338049i	$-0.109767\pi$
$74$	−2.79711			−0.325158
$75$		0			0
$76$	6.29925			0.722573
$77$			1.05252i			0.119946i
$78$		0			0
$79$	−12.1018			−1.36156			−0.680782	−	0.732486i	$-0.738360\pi$
$79$	−12.1018			−1.36156			−0.680782	+	0.732486i	$0.738360\pi$
$80$	7.41856	+	1.22616i	0.829420	+	0.137088i
$81$		0			0
$82$			2.58516i			0.285484i
$83$		−	9.41830i		−	1.03379i	−0.856048	−	0.516896i	$-0.827087\pi$
$83$		−	9.41830i		−	1.03379i	0.856048	−	0.516896i	$-0.172913\pi$
$84$		0			0
$85$	−2.57753	+	15.5947i	−0.279572	+	1.69148i
$86$	−1.44610			−0.155937
$87$		0			0
$88$			0.722020i			0.0769676i
$89$	−0.622547			−0.0659899			−0.0329949	−	0.999456i	$-0.510505\pi$
$89$	−0.622547			−0.0659899			−0.0329949	+	0.999456i	$0.510505\pi$
$90$		0			0
$91$	9.25453			0.970138
$92$		−	4.47364i		−	0.466409i
$93$		0			0
$94$	2.32485			0.239790
$95$	7.34579	+	1.21413i	0.753662	+	0.124567i
$96$		0			0
$97$			19.2638i			1.95594i	0.208743	+	0.977970i	$0.433063\pi$
$97$			19.2638i			1.95594i	−0.208743	+	0.977970i	$0.566937\pi$
$98$		−	1.15719i		−	0.116894i
$99$		0			0
$100$	8.95609	+	3.04371i	0.895609	+	0.304371i
$101$	−9.33018			−0.928387			−0.464194	−	0.885734i	$-0.653656\pi$
$101$	−9.33018			−0.928387			−0.464194	+	0.885734i	$0.653656\pi$
$102$		0			0
$103$		−	7.79546i		−	0.768110i	−0.923310	−	0.384055i	$-0.874527\pi$
$103$		−	7.79546i		−	0.768110i	0.923310	−	0.384055i	$-0.125473\pi$
$104$	6.34853			0.622524
$105$		0			0
$106$	−1.37531			−0.133582
$107$		−	15.5446i		−	1.50276i	−0.659873	−	0.751378i	$-0.729390\pi$
$107$		−	15.5446i		−	1.50276i	0.659873	−	0.751378i	$-0.270610\pi$
$108$		0			0
$109$	3.89814			0.373374			0.186687	−	0.982419i	$-0.440225\pi$
$109$	3.89814			0.373374			0.186687	+	0.982419i	$0.440225\pi$
$110$	−0.0676477	+	0.409287i	−0.00644996	+	0.0390239i
$111$		0			0
$112$		−	6.27439i		−	0.592874i
$113$			6.89464i			0.648593i	0.945955	+	0.324297i	$0.105128\pi$
$113$			6.89464i			0.648593i	−0.945955	+	0.324297i	$0.894872\pi$
$114$		0			0
$115$	0.862256	−	5.21688i	0.0804058	−	0.486476i
$116$	−1.89183			−0.175652
$117$		0			0
$118$			2.96394i			0.272853i
$119$	13.1895			1.20908
$120$		0			0
$121$	−10.6818			−0.971073
$122$			0.414593i			0.0375355i
$123$		0			0
$124$	9.21989			0.827970
$125$	9.85739	+	5.27560i	0.881671	+	0.471864i
$126$		0			0
$127$		−	6.04498i		−	0.536405i	−0.963363	−	0.268203i	$-0.913570\pi$
$127$		−	6.04498i		−	0.536405i	0.963363	−	0.268203i	$-0.0864296\pi$
$128$		−	9.14720i		−	0.808506i
$129$		0			0
$130$	3.59875	+	0.594808i	0.315631	+	0.0521681i
$131$	−7.99224			−0.698285			−0.349143	−	0.937070i	$-0.613527\pi$
$131$	−7.99224			−0.698285			−0.349143	+	0.937070i	$0.613527\pi$
$132$		0			0
$133$		−	6.21284i		−	0.538722i
$134$	−2.17479			−0.187873
$135$		0			0
$136$	9.04791			0.775852
$137$		−	14.9670i		−	1.27872i	−0.768907	−	0.639361i	$-0.779199\pi$
$137$		−	14.9670i		−	1.27872i	0.768907	−	0.639361i	$-0.220801\pi$
$138$		0			0
$139$	5.25453			0.445683			0.222842	−	0.974855i	$-0.428467\pi$
$139$	5.25453			0.445683			0.222842	+	0.974855i	$0.428467\pi$
$140$	1.28714	−	7.78753i	0.108783	−	0.658166i
$141$		0			0
$142$		−	1.79731i		−	0.150827i
$143$		−	2.79779i		−	0.233963i
$144$		0			0
$145$	−2.20614	−	0.364635i	−0.183210	−	0.0302813i
$146$	−1.89986			−0.157233
$147$		0			0
$148$		−	16.0895i		−	1.32255i
$149$	−2.97589			−0.243795			−0.121897	−	0.992543i	$-0.538898\pi$
$149$	−2.97589			−0.243795			−0.121897	+	0.992543i	$0.538898\pi$
$150$		0			0
$151$	−12.8646			−1.04690			−0.523452	−	0.852055i	$-0.675356\pi$
$151$	−12.8646			−1.04690			−0.523452	+	0.852055i	$0.675356\pi$
$152$		−	4.26196i		−	0.345690i
$153$		0			0
$154$	0.346162			0.0278945
$155$	10.7517	+	1.77706i	0.863594	+	0.142737i
$156$		0			0
$157$			8.72737i			0.696520i	0.937398	+	0.348260i	$0.113227\pi$
$157$			8.72737i			0.696520i	−0.937398	+	0.348260i	$0.886773\pi$
$158$			3.98016i			0.316645i
$159$		0			0
$160$	1.33672	−	8.08751i	0.105677	−	0.639374i
$161$	−4.41227			−0.347736
$162$		0			0
$163$			13.4872i			1.05640i	0.849120	+	0.528199i	$0.177133\pi$
$163$			13.4872i			1.05640i	−0.849120	+	0.528199i	$0.822867\pi$
$164$	−14.8704			−1.16118
$165$		0			0
$166$	−3.09757			−0.240418
$167$			24.7351i			1.91406i	0.289993	+	0.957029i	$0.406347\pi$
$167$			24.7351i			1.91406i	−0.289993	+	0.957029i	$0.593653\pi$
$168$		0			0
$169$	−11.6003			−0.892327
$170$	5.12893	+	0.847720i	0.393371	+	0.0650171i
$171$		0			0
$172$		−	8.31826i		−	0.634262i
$173$			15.4531i			1.17488i	0.809268	+	0.587440i	$0.199864\pi$
$173$			15.4531i			1.17488i	−0.809268	+	0.587440i	$0.800136\pi$
$174$		0			0
$175$	3.00196	−	8.83324i	0.226927	−	0.667730i
$176$	−1.89685			−0.142980
$177$		0			0
$178$			0.204749i			0.0153466i
$179$	17.3358			1.29573			0.647867	−	0.761753i	$-0.275661\pi$
$179$	17.3358			1.29573			0.647867	+	0.761753i	$0.275661\pi$
$180$		0			0
$181$	−2.04972			−0.152355			−0.0761773	−	0.997094i	$-0.524271\pi$
$181$	−2.04972			−0.152355			−0.0761773	+	0.997094i	$0.524271\pi$
$182$		−	3.04371i		−	0.225615i
$183$		0			0
$184$	−3.02678			−0.223137
$185$	3.10112	−	18.7626i	0.227999	−	1.37946i
$186$		0			0
$187$		−	3.98741i		−	0.291588i
$188$			13.3730i			0.975324i
$189$		0			0
$190$	0.399313	−	2.41595i	0.0289692	−	0.175271i
$191$	−1.76575			−0.127765			−0.0638824	−	0.997957i	$-0.520348\pi$
$191$	−1.76575			−0.127765			−0.0638824	+	0.997957i	$0.520348\pi$
$192$		0			0
$193$			8.81831i			0.634756i	0.948299	+	0.317378i	$0.102802\pi$
$193$			8.81831i			0.634756i	−0.948299	+	0.317378i	$0.897198\pi$
$194$	6.33564			0.454873
$195$		0			0
$196$	6.65638			0.475455
$197$		−	13.4231i		−	0.956356i	−0.878263	−	0.478178i	$-0.841297\pi$
$197$		−	13.4231i		−	0.956356i	0.878263	−	0.478178i	$-0.158703\pi$
$198$		0			0
$199$	6.08459			0.431325			0.215663	−	0.976468i	$-0.430809\pi$
$199$	6.08459			0.431325			0.215663	+	0.976468i	$0.430809\pi$
$200$	2.05932	−	6.05953i	0.145616	−	0.428474i
$201$		0			0
$202$			3.06859i			0.215905i
$203$			1.86588i			0.130959i
$204$		0			0
$205$	−17.3409	−	2.86614i	−1.21114	−	0.200180i
$206$	−2.56384			−0.178631
$207$		0			0
$208$			16.6785i			1.15645i
$209$	−1.87824			−0.129921
$210$		0			0
$211$	9.05366			0.623280			0.311640	−	0.950200i	$-0.399122\pi$
$211$	9.05366			0.623280			0.311640	+	0.950200i	$0.399122\pi$
$212$		−	7.91106i		−	0.543334i
$213$		0			0
$214$	−5.11245			−0.349480
$215$	1.60328	−	9.70024i	0.109342	−	0.661551i
$216$		0			0
$217$		−	9.09342i		−	0.617302i
$218$		−	1.28206i		−	0.0868318i
$219$		0			0
$220$	−2.35430	−	0.389123i	−0.158727	−	0.0262346i
$221$	−35.0602			−2.35841
$222$		0			0
$223$			18.5300i			1.24086i	0.784260	+	0.620432i	$0.213043\pi$
$223$			18.5300i			1.24086i	−0.784260	+	0.620432i	$0.786957\pi$
$224$	−6.84016			−0.457028
$225$		0			0
$226$	2.26757			0.150837
$227$			23.6011i			1.56646i	0.621734	+	0.783229i	$0.286429\pi$
$227$			23.6011i			1.56646i	−0.621734	+	0.783229i	$0.713571\pi$
$228$		0			0
$229$	−10.5987			−0.700384			−0.350192	−	0.936678i	$-0.613884\pi$
$229$	−10.5987			−0.700384			−0.350192	+	0.936678i	$0.613884\pi$
$230$	−1.71577	−	0.283586i	−0.113135	−	0.0186991i
$231$		0			0
$232$			1.27998i			0.0840348i
$233$		−	8.62938i		−	0.565329i	−0.959219	−	0.282665i	$-0.908782\pi$
$233$		−	8.62938i		−	0.565329i	0.959219	−	0.282665i	$-0.0912183\pi$
$234$		0			0
$235$	−2.57753	+	15.5947i	−0.168139	+	1.01729i
$236$	−17.0492			−1.10981
$237$		0			0
$238$		−	4.33789i		−	0.281184i
$239$	24.0914			1.55834			0.779171	−	0.626811i	$-0.215640\pi$
$239$	24.0914			1.55834			0.779171	+	0.626811i	$0.215640\pi$
$240$		0			0
$241$	−25.6988			−1.65541			−0.827703	−	0.561166i	$-0.810353\pi$
$241$	−25.6988			−1.65541			−0.827703	+	0.561166i	$0.810353\pi$
$242$			3.51313i			0.225832i
$243$		0			0
$244$	−2.38482			−0.152673
$245$	7.76225	+	1.28296i	0.495912	+	0.0819654i
$246$		0			0
$247$			16.5149i			1.05082i
$248$		−	6.23801i		−	0.396114i
$249$		0			0
$250$	1.73509	−	3.24198i	0.109736	−	0.205041i
$251$	−25.0072			−1.57844			−0.789219	−	0.614112i	$-0.789514\pi$
$251$	−25.0072			−1.57844			−0.789219	+	0.614112i	$0.789514\pi$
$252$		0			0
$253$			1.33390i			0.0838617i
$254$	−1.98813			−0.124746
$255$		0			0
$256$	8.03101			0.501938
$257$			1.73788i			0.108406i	0.998530	+	0.0542030i	$0.0172618\pi$
$257$			1.73788i			0.108406i	−0.998530	+	0.0542030i	$0.982738\pi$
$258$		0			0
$259$	−15.8688			−0.986042
$260$	−3.42145	+	20.7007i	−0.212189	+	1.28380i
$261$		0			0
$262$			2.62856i			0.162393i
$263$		−	8.87689i		−	0.547372i	−0.961819	−	0.273686i	$-0.911757\pi$
$263$		−	8.87689i		−	0.547372i	0.961819	−	0.273686i	$-0.0882430\pi$
$264$		0			0
$265$	1.52479	−	9.22539i	0.0936672	−	0.566711i
$266$	−2.04333			−0.125285
$267$		0			0
$268$		−	12.5098i		−	0.764159i
$269$	6.55657			0.399761			0.199881	−	0.979820i	$-0.435945\pi$
$269$	6.55657			0.399761			0.199881	+	0.979820i	$0.435945\pi$
$270$		0			0
$271$	−20.8413			−1.26602			−0.633008	−	0.774145i	$-0.718180\pi$
$271$	−20.8413			−1.26602			−0.633008	+	0.774145i	$0.718180\pi$
$272$			23.7702i			1.44128i
$273$		0			0
$274$	−4.92250			−0.297379
$275$	−2.67043	−	0.907542i	−0.161033	−	0.0547268i
$276$		0			0
$277$			17.7687i			1.06762i	0.845605	+	0.533810i	$0.179240\pi$
$277$			17.7687i			1.06762i	−0.845605	+	0.533810i	$0.820760\pi$
$278$		−	1.72815i		−	0.103648i
$279$		0			0
$280$	−5.26890	−	0.870855i	−0.314877	−	0.0520435i
$281$	14.8520			0.885995			0.442998	−	0.896523i	$-0.353915\pi$
$281$	14.8520			0.885995			0.442998	+	0.896523i	$0.353915\pi$
$282$		0			0
$283$		−	13.8856i		−	0.825414i	−0.910864	−	0.412707i	$-0.864583\pi$
$283$		−	13.8856i		−	0.825414i	0.910864	−	0.412707i	$-0.135417\pi$
$284$	10.3385			0.613476
$285$		0			0
$286$	−0.920163			−0.0544104
$287$			14.6664i			0.865730i
$288$		0			0
$289$	−32.9678			−1.93928
$290$	−0.119924	+	0.725574i	−0.00704220	+	0.0426072i
$291$		0			0
$292$		−	10.9283i		−	0.639533i
$293$		−	7.21254i		−	0.421361i	−0.977555	−	0.210681i	$-0.932432\pi$
$293$		−	7.21254i		−	0.421361i	0.977555	−	0.210681i	$-0.0675680\pi$
$294$		0			0
$295$	−19.8817	−	3.28608i	−1.15756	−	0.191323i
$296$	−10.8859			−0.632730
$297$		0			0
$298$			0.978738i			0.0566968i
$299$	11.7286			0.678285
$300$		0			0
$301$	−8.20417			−0.472880
$302$			4.23101i			0.243467i
$303$		0			0
$304$	11.1968			0.642179
$305$	−2.78103	−	0.459654i	−0.159241	−	0.0263197i
$306$		0			0
$307$			21.2856i			1.21483i	0.794383	+	0.607417i	$0.207794\pi$
$307$			21.2856i			1.21483i	−0.794383	+	0.607417i	$0.792206\pi$
$308$			1.99119i			0.113459i
$309$		0			0
$310$	0.584454	−	3.53610i	0.0331948	−	0.200837i
$311$	−29.1250			−1.65153			−0.825764	−	0.564015i	$-0.809256\pi$
$311$	−29.1250			−1.65153			−0.825764	+	0.564015i	$0.809256\pi$
$312$		0			0
$313$		−	26.1401i		−	1.47752i	−0.673966	−	0.738762i	$-0.735411\pi$
$313$		−	26.1401i		−	1.47752i	0.673966	−	0.738762i	$-0.264589\pi$
$314$	2.87034			0.161982
$315$		0			0
$316$	−22.8946			−1.28792
$317$			7.83033i			0.439795i	0.975523	+	0.219898i	$0.0705723\pi$
$317$			7.83033i			0.439795i	−0.975523	+	0.219898i	$0.929428\pi$
$318$		0			0
$319$	0.564087			0.0315828
$320$	12.1772	+	2.01268i	0.680728	+	0.112512i
$321$		0			0
$322$			1.45115i			0.0808693i
$323$			23.5370i			1.30963i
$324$		0			0
$325$	−7.97977	+	23.4804i	−0.442638	+	1.30246i
$326$	4.43579			0.245676
$327$		0			0
$328$			10.0610i			0.555527i
$329$	13.1895			0.727163
$330$		0			0
$331$	−18.8874			−1.03814			−0.519072	−	0.854731i	$-0.673722\pi$
$331$	−18.8874			−1.03814			−0.519072	+	0.854731i	$0.673722\pi$
$332$		−	17.8178i		−	0.977881i
$333$		0			0
$334$	8.13509			0.445132
$335$	2.41116	−	14.5882i	0.131736	−	0.797037i
$336$		0			0
$337$		−	8.33059i		−	0.453796i	−0.973919	−	0.226898i	$-0.927142\pi$
$337$		−	8.33059i		−	0.453796i	0.973919	−	0.226898i	$-0.0728584\pi$
$338$			3.81519i			0.207519i
$339$		0			0
$340$	−4.87625	+	29.5026i	−0.264452	+	1.60000i
$341$	−2.74909			−0.148872
$342$		0			0
$343$		−	19.6263i		−	1.05972i
$344$	−5.62799			−0.303441
$345$		0			0
$346$	5.08236			0.273230
$347$		−	32.5993i		−	1.75002i	−0.484104	−	0.875010i	$-0.660854\pi$
$347$		−	32.5993i		−	1.75002i	0.484104	−	0.875010i	$-0.339146\pi$
$348$		0			0
$349$	−33.6370			−1.80055			−0.900273	−	0.435326i	$-0.856633\pi$
$349$	−33.6370			−1.80055			−0.900273	+	0.435326i	$0.856633\pi$
$350$	−2.90516	−	0.987312i	−0.155287	−	0.0527740i
$351$		0			0
$352$			2.06789i			0.110219i
$353$		−	2.85951i		−	0.152196i	−0.997100	−	0.0760982i	$-0.975754\pi$
$353$		−	2.85951i		−	0.152196i	0.997100	−	0.0760982i	$-0.0242463\pi$
$354$		0			0
$355$	12.0561	+	1.99266i	0.639871	+	0.105759i
$356$	−1.17775			−0.0624209
$357$		0			0
$358$		−	5.70154i		−	0.301335i
$359$	33.6883			1.77800			0.889001	−	0.457905i	$-0.151400\pi$
$359$	33.6883			1.77800			0.889001	+	0.457905i	$0.151400\pi$
$360$		0			0
$361$	−7.91305			−0.416477
$362$			0.674130i			0.0354315i
$363$		0			0
$364$	17.5080			0.917669
$365$	2.10635	−	12.7440i	0.110251	−	0.667049i
$366$		0			0
$367$		−	9.63376i		−	0.502878i	−0.967873	−	0.251439i	$-0.919096\pi$
$367$		−	9.63376i		−	0.502878i	0.967873	−	0.251439i	$-0.0809038\pi$
$368$		−	7.95180i		−	0.414516i
$369$		0			0
$370$	−6.17082	−	1.01993i	−0.320805	−	0.0530234i
$371$	−7.80255			−0.405088
$372$		0			0
$373$			5.28344i			0.273566i	0.990601	+	0.136783i	$0.0436763\pi$
$373$			5.28344i			0.273566i	−0.990601	+	0.136783i	$0.956324\pi$
$374$	−1.31141			−0.0678116
$375$		0			0
$376$	9.04791			0.466610
$377$		−	4.95986i		−	0.255446i
$378$		0			0
$379$	2.62792			0.134987			0.0674936	−	0.997720i	$-0.478500\pi$
$379$	2.62792			0.134987			0.0674936	+	0.997720i	$0.478500\pi$
$380$	13.8970	+	2.29692i	0.712901	+	0.117830i
$381$		0			0
$382$			0.580734i			0.0297129i
$383$			0.626829i			0.0320295i	0.999872	+	0.0160147i	$0.00509787\pi$
$383$			0.626829i			0.0320295i	−0.999872	+	0.0160147i	$0.994902\pi$
$384$		0			0
$385$	−0.383785	+	2.32200i	−0.0195595	+	0.118340i
$386$	2.90024			0.147618
$387$		0			0
$388$			36.4438i			1.85016i
$389$	26.3950			1.33828			0.669140	−	0.743136i	$-0.266662\pi$
$389$	26.3950			1.33828			0.669140	+	0.743136i	$0.266662\pi$
$390$		0			0
$391$	16.7156			0.845347
$392$		−	4.50359i		−	0.227465i
$393$		0			0
$394$	−4.41471			−0.222410
$395$	−26.6983	−	4.41275i	−1.34334	−	0.222030i
$396$		0			0
$397$		−	27.8333i		−	1.39691i	−0.715652	−	0.698457i	$-0.753870\pi$
$397$		−	27.8333i		−	1.39691i	0.715652	−	0.698457i	$-0.246130\pi$
$398$		−	2.00115i		−	0.100309i
$399$		0			0
$400$	15.9193	+	5.41013i	0.795963	+	0.270507i
$401$	−11.0561			−0.552117			−0.276058	−	0.961141i	$-0.589028\pi$
$401$	−11.0561			−0.552117			−0.276058	+	0.961141i	$0.589028\pi$
$402$		0			0
$403$			24.1720i			1.20409i
$404$	−17.6511			−0.878176
$405$		0			0
$406$	0.613668			0.0304558
$407$			4.79741i			0.237799i
$408$		0			0
$409$	−1.57317			−0.0777882			−0.0388941	−	0.999243i	$-0.512383\pi$
$409$	−1.57317			−0.0777882			−0.0388941	+	0.999243i	$0.512383\pi$
$410$	−0.942641	+	5.70323i	−0.0465537	+	0.281662i
$411$		0			0
$412$		−	14.7477i		−	0.726567i
$413$			16.8153i			0.827427i
$414$		0			0
$415$	3.43424	−	20.7781i	0.168580	−	1.01996i
$416$	18.1824			0.891467
$417$		0			0
$418$			0.617733i			0.0302143i
$419$	35.9256			1.75508			0.877540	−	0.479504i	$-0.159183\pi$
$419$	35.9256			1.75508			0.877540	+	0.479504i	$0.159183\pi$
$420$		0			0
$421$	−15.5075			−0.755788			−0.377894	−	0.925849i	$-0.623352\pi$
$421$	−15.5075			−0.755788			−0.377894	+	0.925849i	$0.623352\pi$
$422$		−	2.97765i		−	0.144950i
$423$		0			0
$424$	−5.35248			−0.259940
$425$	−11.3728	+	33.4642i	−0.551660	+	1.62325i
$426$		0			0
$427$			2.35211i			0.113827i
$428$		−	29.4078i		−	1.42148i
$429$		0			0
$430$	−3.19030	−	0.527300i	−0.153850	−	0.0254286i
$431$	−16.9390			−0.815924			−0.407962	−	0.912999i	$-0.633760\pi$
$431$	−16.9390			−0.815924			−0.407962	+	0.912999i	$0.633760\pi$
$432$		0			0
$433$		−	40.5136i		−	1.94696i	−0.228772	−	0.973480i	$-0.573471\pi$
$433$		−	40.5136i		−	1.94696i	0.228772	−	0.973480i	$-0.426529\pi$
$434$	−2.99072			−0.143559
$435$		0			0
$436$	7.37463			0.353181
$437$		−	7.87380i		−	0.376655i
$438$		0			0
$439$	23.4655			1.11995			0.559973	−	0.828511i	$-0.310812\pi$
$439$	23.4655			1.11995			0.559973	+	0.828511i	$0.310812\pi$
$440$	−0.263274	+	1.59287i	−0.0125511	+	0.0759373i
$441$		0			0
$442$			11.5309i			0.548470i
$443$			16.3994i			0.779161i	0.920992	+	0.389580i	$0.127380\pi$
$443$			16.3994i			0.779161i	−0.920992	+	0.389580i	$0.872620\pi$
$444$		0			0
$445$	−1.37342	−	0.227002i	−0.0651066	−	0.0107609i
$446$	6.09432			0.288575
$447$		0			0
$448$		−	10.2991i		−	0.486588i
$449$	−8.92984			−0.421425			−0.210713	−	0.977548i	$-0.567578\pi$
$449$	−8.92984			−0.421425			−0.210713	+	0.977548i	$0.567578\pi$
$450$		0			0
$451$	4.43389			0.208784
$452$			13.0435i			0.613515i
$453$		0			0
$454$	7.76213			0.364295
$455$	20.4168	+	3.37452i	0.957152	+	0.158200i
$456$		0			0
$457$			3.16068i			0.147850i	0.997264	+	0.0739252i	$0.0235526\pi$
$457$			3.16068i			0.147850i	−0.997264	+	0.0739252i	$0.976447\pi$
$458$			3.48580i			0.162881i
$459$		0			0
$460$	1.63124	−	9.86946i	0.0760571	−	0.460166i
$461$	−3.85936			−0.179748			−0.0898741	−	0.995953i	$-0.528646\pi$
$461$	−3.85936			−0.179748			−0.0898741	+	0.995953i	$0.528646\pi$
$462$		0			0
$463$			24.5493i			1.14090i	0.821331	+	0.570451i	$0.193232\pi$
$463$			24.5493i			1.14090i	−0.821331	+	0.570451i	$0.806768\pi$
$464$	−3.36269			−0.156109
$465$		0			0
$466$	−2.83811			−0.131473
$467$		−	16.7566i		−	0.775405i	−0.921785	−	0.387703i	$-0.873269\pi$
$467$		−	16.7566i		−	0.775405i	0.921785	−	0.387703i	$-0.126731\pi$
$468$		0			0
$469$	−12.3382			−0.569727
$470$	5.12893	+	0.847720i	0.236580	+	0.0391024i
$471$		0			0
$472$			11.5352i			0.530949i
$473$			2.48025i			0.114042i
$474$		0			0
$475$	15.7631	+	5.35706i	0.723261	+	0.245799i
$476$	24.9524			1.14369
$477$		0			0
$478$		−	7.92339i		−	0.362407i
$479$	−18.4125			−0.841289			−0.420644	−	0.907226i	$-0.638196\pi$
$479$	−18.4125			−0.841289			−0.420644	+	0.907226i	$0.638196\pi$
$480$		0			0
$481$	42.1823			1.92335
$482$			8.45205i			0.384981i
$483$		0			0
$484$	−20.2082			−0.918554
$485$	−7.02425	+	42.4986i	−0.318955	+	1.92976i
$486$		0			0
$487$		−	18.3658i		−	0.832232i	−0.909311	−	0.416116i	$-0.863391\pi$
$487$		−	18.3658i		−	0.832232i	0.909311	−	0.416116i	$-0.136609\pi$
$488$			1.61353i			0.0730410i
$489$		0			0
$490$	0.421952	−	2.55292i	0.0190618	−	0.115329i
$491$	−17.2651			−0.779165			−0.389582	−	0.920992i	$-0.627381\pi$
$491$	−17.2651			−0.779165			−0.389582	+	0.920992i	$0.627381\pi$
$492$		0			0
$493$		−	7.06879i		−	0.318362i
$494$	5.43156			0.244378
$495$		0			0
$496$	16.3882			0.735850
$497$		−	10.1967i		−	0.457383i
$498$		0			0
$499$	22.2484			0.995976			0.497988	−	0.867184i	$-0.334072\pi$
$499$	22.2484			0.995976			0.497988	+	0.867184i	$0.334072\pi$
$500$	18.6485	+	9.98054i	0.833987	+	0.446344i
$501$		0			0
$502$			8.22458i			0.367081i
$503$		−	25.4171i		−	1.13329i	−0.823961	−	0.566646i	$-0.808241\pi$
$503$		−	25.4171i		−	1.13329i	0.823961	−	0.566646i	$-0.191759\pi$
$504$		0			0
$505$	−20.5836	−	3.40211i	−0.915960	−	0.151392i
$506$	0.438706			0.0195028
$507$		0			0
$508$		−	11.4361i		−	0.507394i
$509$	12.5897			0.558028			0.279014	−	0.960287i	$-0.409992\pi$
$509$	12.5897			0.558028			0.279014	+	0.960287i	$0.409992\pi$
$510$		0			0
$511$	−10.7784			−0.476810
$512$		−	20.9357i		−	0.925236i
$513$		0			0
$514$	0.571570			0.0252109
$515$	2.84250	−	17.1979i	0.125255	−	0.757828i
$516$		0			0
$517$		−	3.98741i		−	0.175366i
$518$			5.21909i			0.229313i
$519$		0			0
$520$	14.0057	+	2.31489i	0.614192	+	0.101515i
$521$	−25.3294			−1.10970			−0.554851	−	0.831949i	$-0.687225\pi$
$521$	−25.3294			−1.10970			−0.554851	+	0.831949i	$0.687225\pi$
$522$		0			0
$523$			40.2732i			1.76102i	0.474023	+	0.880512i	$0.342801\pi$
$523$			40.2732i			1.76102i	−0.474023	+	0.880512i	$0.657199\pi$
$524$	−15.1200			−0.660519
$525$		0			0
$526$	−2.91951			−0.127297
$527$			34.4499i			1.50066i
$528$		0			0
$529$	17.4081			0.756876
$530$	−3.03413	−	0.501487i	−0.131794	−	0.0217832i
$531$		0			0
$532$		−	11.7537i		−	0.509586i
$533$		−	38.9860i		−	1.68867i
$534$		0			0
$535$	5.66811	−	34.2936i	0.245054	−	1.48264i
$536$	−8.46393			−0.365586
$537$		0			0
$538$		−	2.15638i		−	0.0929683i
$539$	−1.98473			−0.0854883
$540$		0			0
$541$	10.5720			0.454527			0.227263	−	0.973833i	$-0.427022\pi$
$541$	10.5720			0.454527			0.227263	+	0.973833i	$0.427022\pi$
$542$			6.85446i			0.294424i
$543$		0			0
$544$	25.9136			1.11103
$545$	8.59984	+	1.42140i	0.368377	+	0.0608860i
$546$		0			0
$547$		−	28.0175i		−	1.19794i	−0.800770	−	0.598971i	$-0.795576\pi$
$547$		−	28.0175i		−	1.19794i	0.800770	−	0.598971i	$-0.204424\pi$
$548$		−	28.3151i		−	1.20956i
$549$		0			0
$550$	−0.298480	+	0.878276i	−0.0127272	+	0.0374498i
$551$	−3.32971			−0.141850
$552$		0			0
$553$			22.5806i			0.960225i
$554$	5.84394			0.248285
$555$		0			0
$556$	9.94068			0.421579
$557$			38.8895i			1.64780i	0.566734	+	0.823901i	$0.308207\pi$
$557$			38.8895i			1.64780i	−0.566734	+	0.823901i	$0.691793\pi$
$558$		0			0
$559$	21.8082			0.922389
$560$	2.28786	−	13.8422i	0.0966798	−	0.584938i
$561$		0			0
$562$		−	4.88465i		−	0.206047i
$563$			30.3735i			1.28009i	0.768337	+	0.640045i	$0.221084\pi$
$563$			30.3735i			1.28009i	−0.768337	+	0.640045i	$0.778916\pi$
$564$		0			0
$565$	−2.51403	+	15.2105i	−0.105766	+	0.639912i
$566$	−4.56683			−0.191958
$567$		0			0
$568$		−	6.99483i		−	0.293497i
$569$	−46.3254			−1.94206			−0.971031	−	0.238953i	$-0.923196\pi$
$569$	−46.3254			−1.94206			−0.971031	+	0.238953i	$0.923196\pi$
$570$		0			0
$571$	38.9012			1.62796			0.813982	−	0.580890i	$-0.197295\pi$
$571$	38.9012			1.62796			0.813982	+	0.580890i	$0.197295\pi$
$572$		−	5.29295i		−	0.221310i
$573$		0			0
$574$	4.82361			0.201334
$575$	3.80451	−	11.1947i	0.158659	−	0.466853i
$576$		0			0
$577$			24.5426i			1.02172i	0.859663	+	0.510861i	$0.170673\pi$
$577$			24.5426i			1.02172i	−0.859663	+	0.510861i	$0.829327\pi$
$578$			10.8427i			0.450998i
$579$		0			0
$580$	−4.17364	−	0.689828i	−0.173301	−	0.0286435i
$581$	−17.5734			−0.729069
$582$		0			0
$583$			2.35884i			0.0976931i
$584$	−7.39392			−0.305963
$585$		0			0
$586$	−2.37212			−0.0979915
$587$		−	42.3399i		−	1.74755i	−0.486328	−	0.873777i	$-0.661664\pi$
$587$		−	42.3399i		−	1.74755i	0.486328	−	0.873777i	$-0.338336\pi$
$588$		0			0
$589$	16.2274			0.668638
$590$	−1.08076	+	6.53886i	−0.0444940	+	0.269201i
$591$		0			0
$592$		−	28.5988i		−	1.17540i
$593$			4.17650i			0.171508i	0.996316	+	0.0857541i	$0.0273299\pi$
$593$			4.17650i			0.171508i	−0.996316	+	0.0857541i	$0.972670\pi$
$594$		0			0
$595$	29.0979	+	4.80936i	1.19290	+	0.197165i
$596$	−5.62989			−0.230609
$597$		0			0
$598$		−	3.85742i		−	0.157742i
$599$	−11.9559			−0.488505			−0.244252	−	0.969712i	$-0.578543\pi$
$599$	−11.9559			−0.488505			−0.244252	+	0.969712i	$0.578543\pi$
$600$		0			0
$601$	−25.1790			−1.02707			−0.513537	−	0.858068i	$-0.671665\pi$
$601$	−25.1790			−1.02707			−0.513537	+	0.858068i	$0.671665\pi$
$602$			2.69826i			0.109973i
$603$		0			0
$604$	−24.3376			−0.990282
$605$	−23.5655	−	3.89496i	−0.958075	−	0.158353i
$606$		0			0
$607$			19.4870i			0.790953i	0.918476	+	0.395476i	$0.129420\pi$
$607$			19.4870i			0.790953i	−0.918476	+	0.395476i	$0.870580\pi$
$608$		−	12.2064i		−	0.495035i
$609$		0			0
$610$	−0.151175	+	0.914650i	−0.00612091	+	0.0370331i
$611$	−35.0602			−1.41839
$612$		0			0
$613$			27.7763i			1.12187i	0.827859	+	0.560937i	$0.189559\pi$
$613$			27.7763i			1.12187i	−0.827859	+	0.560937i	$0.810441\pi$
$614$	7.00060			0.282521
$615$		0			0
$616$	1.34720			0.0542804
$617$		−	12.7828i		−	0.514616i	−0.966329	−	0.257308i	$-0.917164\pi$
$617$		−	12.7828i		−	0.514616i	0.966329	−	0.257308i	$-0.0828355\pi$
$618$		0			0
$619$	5.83385			0.234482			0.117241	−	0.993103i	$-0.462595\pi$
$619$	5.83385			0.234482			0.117241	+	0.993103i	$0.462595\pi$
$620$	20.3403	+	3.36189i	0.816887	+	0.135017i
$621$		0			0
$622$			9.57890i			0.384079i
$623$			1.16160i			0.0465385i
$624$		0			0
$625$	19.8231	+	15.2330i	0.792923	+	0.609322i
$626$	−8.59718			−0.343612
$627$		0			0
$628$			16.5107i			0.658850i
$629$	60.1182			2.39707
$630$		0			0
$631$	−9.97085			−0.396933			−0.198467	−	0.980108i	$-0.563596\pi$
$631$	−9.97085			−0.396933			−0.198467	+	0.980108i	$0.563596\pi$
$632$			15.4901i			0.616164i
$633$		0			0
$634$	2.57531			0.102279
$635$	2.20421	−	13.3361i	0.0874714	−	0.529225i
$636$		0			0
$637$			17.4512i			0.691441i
$638$		−	0.185522i		−	0.00734488i
$639$		0			0
$640$	3.33539	−	20.1800i	0.131843	−	0.797683i
$641$	47.6315			1.88133			0.940667	−	0.339332i	$-0.110201\pi$
$641$	47.6315			1.88133			0.940667	+	0.339332i	$0.110201\pi$
$642$		0			0
$643$			7.26701i			0.286583i	0.989681	+	0.143291i	$0.0457686\pi$
$643$			7.26701i			0.286583i	−0.989681	+	0.143291i	$0.954231\pi$
$644$	−8.34728			−0.328929
$645$		0			0
$646$	7.74106			0.304568
$647$		−	17.7415i		−	0.697488i	−0.937218	−	0.348744i	$-0.886608\pi$
$647$		−	17.7415i		−	0.697488i	0.937218	−	0.348744i	$-0.113392\pi$
$648$		0			0
$649$	5.08354			0.199546
$650$	7.72244	+	2.62446i	0.302899	+	0.102940i
$651$		0			0
$652$			25.5155i			0.999264i
$653$		−	23.4342i		−	0.917050i	−0.888682	−	0.458525i	$-0.848378\pi$
$653$		−	23.4342i		−	0.917050i	0.888682	−	0.458525i	$-0.151622\pi$
$654$		0			0
$655$	−17.6320	−	2.91425i	−0.688939	−	0.113869i
$656$	−26.4318			−1.03199
$657$		0			0
$658$		−	4.33789i		−	0.169109i
$659$	−30.4650			−1.18675			−0.593373	−	0.804928i	$-0.702204\pi$
$659$	−30.4650			−1.18675			−0.593373	+	0.804928i	$0.702204\pi$
$660$		0			0
$661$	1.35516			0.0527095			0.0263547	−	0.999653i	$-0.491610\pi$
$661$	1.35516			0.0527095			0.0263547	+	0.999653i	$0.491610\pi$
$662$			6.21184i			0.241430i
$663$		0			0
$664$	−12.0552			−0.467834
$665$	2.26542	−	13.7064i	0.0878492	−	0.531511i
$666$		0			0
$667$			2.36471i			0.0915620i
$668$			46.7946i			1.81054i
$669$		0			0
$670$	−4.79789	−	0.793005i	−0.185359	−	0.0306365i
$671$	0.711081			0.0274510
$672$		0			0
$673$			6.26746i			0.241593i	0.992677	+	0.120796i	$0.0385448\pi$
$673$			6.26746i			0.241593i	−0.992677	+	0.120796i	$0.961455\pi$
$674$	−2.73984			−0.105535
$675$		0			0
$676$	−21.9457			−0.844066
$677$		−	32.3653i		−	1.24390i	−0.783057	−	0.621950i	$-0.786341\pi$
$677$		−	32.3653i		−	1.24390i	0.783057	−	0.621950i	$-0.213659\pi$
$678$		0			0
$679$	35.9440			1.37940
$680$	19.9609	+	3.29918i	0.765467	+	0.126518i
$681$		0			0
$682$			0.904145i			0.0346215i
$683$			29.0003i			1.10967i	0.831962	+	0.554833i	$0.187218\pi$
$683$			29.0003i			1.10967i	−0.831962	+	0.554833i	$0.812782\pi$
$684$		0			0
$685$	5.45751	−	33.0194i	0.208521	−	1.26161i
$686$	−6.45486			−0.246448
$687$		0			0
$688$		−	14.7855i		−	0.563694i
$689$	20.7406			0.790155
$690$		0			0
$691$	39.6602			1.50875			0.754373	−	0.656446i	$-0.227941\pi$
$691$	39.6602			1.50875			0.754373	+	0.656446i	$0.227941\pi$
$692$			29.2347i			1.11134i
$693$		0			0
$694$	−10.7215			−0.406984
$695$	11.5922	+	1.91598i	0.439717	+	0.0726774i
$696$		0			0
$697$		−	55.5628i		−	2.10459i
$698$			11.0628i			0.418734i
$699$		0			0
$700$	5.67921	−	16.7110i	0.214654	−	0.631617i
$701$	1.21005			0.0457029			0.0228514	−	0.999739i	$-0.492726\pi$
$701$	1.21005			0.0457029			0.0228514	+	0.999739i	$0.492726\pi$
$702$		0			0
$703$		−	28.3183i		−	1.06804i
$704$	−3.11359			−0.117348
$705$		0			0
$706$	−0.940462			−0.0353947
$707$			17.4090i			0.654733i
$708$		0			0
$709$	2.37420			0.0891651			0.0445826	−	0.999006i	$-0.485804\pi$
$709$	2.37420			0.0891651			0.0445826	+	0.999006i	$0.485804\pi$
$710$	0.655362	−	3.96511i	0.0245953	−	0.148808i
$711$		0			0
$712$			0.796848i			0.0298631i
$713$		−	11.5245i		−	0.431595i
$714$		0			0
$715$	1.02017	−	6.17232i	0.0381523	−	0.230832i
$716$	32.7963			1.22566
$717$		0			0
$718$		−	11.0797i		−	0.413491i
$719$	3.46098			0.129073			0.0645364	−	0.997915i	$-0.479443\pi$
$719$	3.46098			0.129073			0.0645364	+	0.997915i	$0.479443\pi$
$720$		0			0
$721$	−14.5454			−0.541700
$722$			2.60252i			0.0968556i
$723$		0			0
$724$	−3.87773			−0.144115
$725$	−4.73408	−	1.60887i	−0.175819	−	0.0597519i
$726$		0			0
$727$		−	0.967841i		−	0.0358952i	−0.999839	−	0.0179476i	$-0.994287\pi$
$727$		−	0.967841i		−	0.0358952i	0.999839	−	0.0179476i	$-0.00571321\pi$
$728$		−	11.8456i		−	0.439027i
$729$		0			0
$730$	−4.19134	−	0.692754i	−0.155129	−	0.0256400i
$731$	31.0810			1.14957
$732$		0			0
$733$		−	4.61626i		−	0.170506i	−0.996359	−	0.0852528i	$-0.972830\pi$
$733$		−	4.61626i		−	0.170506i	0.996359	−	0.0852528i	$-0.0271698\pi$
$734$	−3.16844			−0.116949
$735$		0			0
$736$	−8.66883			−0.319537
$737$			3.73005i			0.137398i
$738$		0			0
$739$	5.94453			0.218673			0.109336	−	0.994005i	$-0.465127\pi$
$739$	5.94453			0.218673			0.109336	+	0.994005i	$0.465127\pi$
$740$	5.86681	−	35.4957i	0.215668	−	1.30485i
$741$		0			0
$742$			2.56617i			0.0942071i
$743$		−	11.0789i		−	0.406444i	−0.979133	−	0.203222i	$-0.934859\pi$
$743$		−	11.0789i		−	0.406444i	0.979133	−	0.203222i	$-0.0651414\pi$
$744$		0			0
$745$	−6.56523	−	1.08511i	−0.240531	−	0.0397555i
$746$	1.73766			0.0636204
$747$		0			0
$748$		−	7.54351i		−	0.275818i
$749$	−29.0044			−1.05980
$750$		0			0
$751$	16.3810			0.597750			0.298875	−	0.954292i	$-0.403389\pi$
$751$	16.3810			0.597750			0.298875	+	0.954292i	$0.403389\pi$
$752$			23.7702i			0.866809i
$753$		0			0
$754$	−1.63124			−0.0594064
$755$	−28.3810	−	4.69087i	−1.03289	−	0.170718i
$756$		0			0
$757$			27.9468i			1.01575i	0.861432	+	0.507873i	$0.169568\pi$
$757$			27.9468i			1.01575i	−0.861432	+	0.507873i	$0.830432\pi$
$758$		−	0.864293i		−	0.0313925i
$759$		0			0
$760$	1.55406	−	9.40247i	0.0563716	−	0.341063i
$761$	16.1657			0.586006			0.293003	−	0.956112i	$-0.405345\pi$
$761$	16.1657			0.586006			0.293003	+	0.956112i	$0.405345\pi$
$762$		0			0
$763$		−	7.27348i		−	0.263318i
$764$	−3.34049			−0.120855
$765$		0			0
$766$	0.206157			0.00744876
$767$		−	44.6982i		−	1.61396i
$768$		0			0
$769$	17.8664			0.644279			0.322139	−	0.946692i	$-0.395598\pi$
$769$	17.8664			0.644279			0.322139	+	0.946692i	$0.395598\pi$
$770$	0.763681	+	0.126223i	0.0275211	+	0.00454875i
$771$		0			0
$772$			16.6828i			0.600426i
$773$		−	16.7961i		−	0.604114i	−0.953290	−	0.302057i	$-0.902327\pi$
$773$		−	16.7961i		−	0.604114i	0.953290	−	0.302057i	$-0.0976733\pi$
$774$		0			0
$775$	23.0717	+	7.84086i	0.828758	+	0.281652i
$776$	24.6573			0.885144
$777$		0			0
$778$		−	8.68103i		−	0.311230i
$779$	−26.1725			−0.937726
$780$		0			0
$781$	−3.08262			−0.110305
$782$		−	5.49759i		−	0.196593i
$783$		0			0
$784$	11.8316			0.422556
$785$	−3.18230	+	19.2538i	−0.113581	+	0.687197i
$786$		0			0
$787$		−	43.1607i		−	1.53851i	−0.638941	−	0.769256i	$-0.720627\pi$
$787$		−	43.1607i		−	1.53851i	0.638941	−	0.769256i	$-0.279373\pi$
$788$		−	25.3942i		−	0.904632i
$789$		0			0
$790$	−1.45131	+	8.78078i	−0.0516351	+	0.312406i
$791$	12.8646			0.457412
$792$		0			0
$793$		−	6.25235i		−	0.222027i
$794$	−9.15407			−0.324866
$795$		0			0
$796$	11.5110			0.407998
$797$			19.7554i			0.699772i	0.936792	+	0.349886i	$0.113780\pi$
$797$			19.7554i			0.699772i	−0.936792	+	0.349886i	$0.886220\pi$
$798$		0			0
$799$	−49.9678			−1.76773
$800$	5.89797	−	17.3547i	0.208525	−	0.613583i
$801$		0			0
$802$			3.63624i			0.128400i
$803$			3.25850i			0.114990i
$804$		0			0
$805$	−9.73408	−	1.60887i	−0.343081	−	0.0567052i
$806$	7.94990			0.280023
$807$		0			0
$808$			11.9424i			0.420134i
$809$	23.6721			0.832268			0.416134	−	0.909303i	$-0.363385\pi$
$809$	23.6721			0.832268			0.416134	+	0.909303i	$0.363385\pi$
$810$		0			0
$811$	18.5443			0.651178			0.325589	−	0.945511i	$-0.394437\pi$
$811$	18.5443			0.651178			0.325589	+	0.945511i	$0.394437\pi$
$812$			3.52994i			0.123877i
$813$		0			0
$814$	1.57781			0.0553024
$815$	−4.91790	+	29.7546i	−0.172267	+	1.04226i
$816$		0			0
$817$		−	14.6405i		−	0.512206i
$818$			0.517398i			0.0180904i
$819$		0			0
$820$	−32.8061	−	5.42225i	−1.14564	−	0.189353i
$821$	41.5778			1.45108			0.725538	−	0.688182i	$-0.241591\pi$
$821$	41.5778			1.45108			0.725538	+	0.688182i	$0.241591\pi$
$822$		0			0
$823$		−	31.1276i		−	1.08504i	−0.840043	−	0.542519i	$-0.817471\pi$
$823$		−	31.1276i		−	1.08504i	0.840043	−	0.542519i	$-0.182529\pi$
$824$	−9.97804			−0.347601
$825$		0			0
$826$	5.53037			0.192426
$827$			42.5406i			1.47928i	0.673001	+	0.739641i	$0.265005\pi$
$827$			42.5406i			1.47928i	−0.673001	+	0.739641i	$0.734995\pi$
$828$		0			0
$829$	−2.61307			−0.0907558			−0.0453779	−	0.998970i	$-0.514449\pi$
$829$	−2.61307			−0.0907558			−0.0453779	+	0.998970i	$0.514449\pi$
$830$	−6.83367	−	1.12948i	−0.237200	−	0.0392049i
$831$		0			0
$832$			27.3770i			0.949127i
$833$			24.8714i			0.861743i
$834$		0			0
$835$	−9.01927	+	54.5690i	−0.312125	+	1.88844i
$836$	−3.55332			−0.122894
$837$		0			0
$838$		−	11.8155i		−	0.408161i
$839$	30.9618			1.06892			0.534461	−	0.845193i	$-0.320515\pi$
$839$	30.9618			1.06892			0.534461	+	0.845193i	$0.320515\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$			5.10024i			0.175766i
$843$		0			0
$844$	17.1280			0.589571
$845$	−25.5917	−	4.22986i	−0.880383	−	0.145511i
$846$		0			0
$847$			19.9310i			0.684837i
$848$		−	14.0617i		−	0.482882i
$849$		0			0
$850$	11.0060	+	3.74037i	0.377503	+	0.128294i
$851$	−20.1113			−0.689405
$852$		0			0
$853$			26.3048i			0.900659i	0.892863	+	0.450329i	$0.148693\pi$
$853$			26.3048i			0.900659i	−0.892863	+	0.450329i	$0.851307\pi$
$854$	0.773583			0.0264715
$855$		0			0
$856$	−19.8968			−0.680059
$857$			5.37241i			0.183518i	0.995781	+	0.0917590i	$0.0292489\pi$
$857$			5.37241i			0.183518i	−0.995781	+	0.0917590i	$0.970751\pi$
$858$		0			0
$859$	37.9952			1.29638			0.648189	−	0.761479i	$-0.275527\pi$
$859$	37.9952			1.29638			0.648189	+	0.761479i	$0.275527\pi$
$860$	3.03313	−	18.3512i	0.103429	−	0.625772i
$861$		0			0
$862$			5.57105i			0.189751i
$863$		−	13.5782i		−	0.462206i	−0.972929	−	0.231103i	$-0.925767\pi$
$863$		−	13.5782i		−	0.462206i	0.972929	−	0.231103i	$-0.0742334\pi$
$864$		0			0
$865$	−5.63475	+	34.0917i	−0.191587	+	1.15915i
$866$	−13.3245			−0.452784
$867$		0			0
$868$		−	17.2032i		−	0.583916i
$869$	6.82649			0.231573
$870$		0			0
$871$	32.7973			1.11129
$872$		−	4.98954i		−	0.168967i
$873$		0			0
$874$	−2.58960			−0.0875946
$875$	9.84365	−	18.3927i	0.332776	−	0.621788i
$876$		0			0
$877$		−	32.1671i		−	1.08621i	−0.839666	−	0.543104i	$-0.817249\pi$
$877$		−	32.1671i		−	1.08621i	0.839666	−	0.543104i	$-0.182751\pi$
$878$		−	7.71753i		−	0.260454i
$879$		0			0
$880$	−4.18471	−	0.691658i	−0.141067	−	0.0233158i
$881$	47.6183			1.60430			0.802151	−	0.597121i	$-0.203689\pi$
$881$	47.6183			1.60430			0.802151	+	0.597121i	$0.203689\pi$
$882$		0			0
$883$			17.9986i			0.605701i	0.953038	+	0.302851i	$0.0979384\pi$
$883$			17.9986i			0.605701i	−0.953038	+	0.302851i	$0.902062\pi$
$884$	−66.3281			−2.23085
$885$		0			0
$886$	5.39359			0.181201
$887$		−	28.7126i		−	0.964076i	−0.876150	−	0.482038i	$-0.839897\pi$
$887$		−	28.7126i		−	0.964076i	0.876150	−	0.482038i	$-0.160103\pi$
$888$		0			0
$889$	−11.2792			−0.378293
$890$	−0.0746586	+	0.451704i	−0.00250256	+	0.0151412i
$891$		0			0
$892$			35.0557i			1.17375i
$893$			23.5370i			0.787636i
$894$		0			0
$895$	38.2450	+	6.32122i	1.27839	+	0.211295i
$896$	−17.0676			−0.570188
$897$		0			0
$898$			2.93693i			0.0980065i
$899$	−4.87352			−0.162541
$900$		0			0
$901$	29.5595			0.984770
$902$		−	1.45826i		−	0.0485546i
$903$		0			0
$904$	8.82500			0.293515
$905$	−4.52197	−	0.747400i	−0.150315	−	0.0248444i
$906$		0			0
$907$		−	29.4971i		−	0.979434i	−0.871881	−	0.489717i	$-0.837100\pi$
$907$		−	29.4971i		−	0.979434i	0.871881	−	0.489717i	$-0.162900\pi$
$908$			44.6492i			1.48174i
$909$		0			0
$910$	1.10984	−	6.71484i	0.0367909	−	0.222595i
$911$	33.9486			1.12477			0.562384	−	0.826876i	$-0.309884\pi$
$911$	33.9486			1.12477			0.562384	+	0.826876i	$0.309884\pi$
$912$		0			0
$913$			5.31274i			0.175826i
$914$	1.03951			0.0343840
$915$		0			0
$916$	−20.0510			−0.662504
$917$			14.9126i			0.492457i
$918$		0			0
$919$	17.6898			0.583531			0.291766	−	0.956490i	$-0.405757\pi$
$919$	17.6898			0.583531			0.291766	+	0.956490i	$0.405757\pi$
$920$	−6.67750	−	1.10367i	−0.220151	−	0.0363870i
$921$		0			0
$922$			1.26930i			0.0418022i
$923$			27.1047i			0.892161i
$924$		0			0
$925$	13.6830	−	40.2621i	0.449895	−	1.32381i
$926$	8.07399			0.265328
$927$		0			0
$928$			3.66591i			0.120339i
$929$	−3.74299			−0.122804			−0.0614018	−	0.998113i	$-0.519557\pi$
$929$	−3.74299			−0.122804			−0.0614018	+	0.998113i	$0.519557\pi$
$930$		0			0
$931$	11.7155			0.383960
$932$		−	16.3253i		−	0.534754i
$933$		0			0
$934$	−5.51107			−0.180328
$935$	1.45395	−	8.79677i	0.0475492	−	0.287685i
$936$		0			0
$937$			2.12550i			0.0694369i	0.999397	+	0.0347185i	$0.0110535\pi$
$937$			2.12550i			0.0694369i	−0.999397	+	0.0347185i	$0.988947\pi$
$938$			4.05791i			0.132495i
$939$		0			0
$940$	−4.87625	+	29.5026i	−0.159046	+	0.962268i
$941$	54.9017			1.78974			0.894871	−	0.446324i	$-0.147267\pi$
$941$	54.9017			1.78974			0.894871	+	0.446324i	$0.147267\pi$
$942$		0			0
$943$			18.5873i			0.605287i
$944$	−30.3045			−0.986328
$945$		0			0
$946$	0.815727			0.0265216
$947$			32.5730i			1.05848i	0.848472	+	0.529240i	$0.177523\pi$
$947$			32.5730i			1.05848i	−0.848472	+	0.529240i	$0.822477\pi$
$948$		0			0
$949$	28.6511			0.930054
$950$	1.76188	−	5.18431i	0.0571629	−	0.168201i
$951$		0			0
$952$		−	16.8823i		−	0.547160i
$953$			8.68090i			0.281202i	0.990066	+	0.140601i	$0.0449035\pi$
$953$			8.68090i			0.281202i	−0.990066	+	0.140601i	$0.955097\pi$
$954$		0			0
$955$	−3.89548	−	0.643853i	−0.126055	−	0.0208346i
$956$	45.5769			1.47406
$957$		0			0
$958$			6.05567i			0.195650i
$959$	−27.9268			−0.901802
$960$		0			0
$961$	−7.24878			−0.233832
$962$		−	13.8733i		−	0.447293i
$963$		0			0
$964$	−48.6179			−1.56588
$965$	−3.21546	+	19.4544i	−0.103509	+	0.626259i
$966$		0			0
$967$			53.2460i			1.71228i	0.516747	+	0.856138i	$0.327143\pi$
$967$			53.2460i			1.71228i	−0.516747	+	0.856138i	$0.672857\pi$
$968$			13.6725i			0.439451i
$969$		0			0
$970$	13.9773	+	2.31020i	0.448784	+	0.0741759i
$971$	−53.7614			−1.72529			−0.862643	−	0.505814i	$-0.831192\pi$
$971$	−53.7614			−1.72529			−0.862643	+	0.505814i	$0.831192\pi$
$972$		0			0
$973$		−	9.80433i		−	0.314312i
$974$	−6.04030			−0.193544
$975$		0			0
$976$	−4.23897			−0.135686
$977$			13.2134i			0.422735i	0.977407	+	0.211367i	$0.0677916\pi$
$977$			13.2134i			0.422735i	−0.977407	+	0.211367i	$0.932208\pi$
$978$		0			0
$979$	0.351171			0.0112235
$980$	14.6849	+	2.42715i	0.469091	+	0.0775324i
$981$		0			0
$982$			5.67831i			0.181202i
$983$			31.7530i			1.01276i	0.862310	+	0.506381i	$0.169017\pi$
$983$			31.7530i			1.01276i	−0.862310	+	0.506381i	$0.830983\pi$
$984$		0			0
$985$	4.89453	−	29.6132i	0.155953	−	0.943554i
$986$	−2.32485			−0.0740382
$987$		0			0
$988$			31.2434i			0.993985i
$989$	−10.3975			−0.330621
$990$		0			0
$991$	12.5237			0.397830			0.198915	−	0.980017i	$-0.436258\pi$
$991$	12.5237			0.397830			0.198915	+	0.980017i	$0.436258\pi$
$992$		−	17.8659i		−	0.567243i
$993$		0			0
$994$	−3.35357			−0.106369
$995$	13.4234	+	2.21865i	0.425552	+	0.0703361i
$996$		0			0
$997$			28.9494i			0.916837i	0.888736	+	0.458418i	$0.151584\pi$
$997$			28.9494i			0.916837i	−0.888736	+	0.458418i	$0.848416\pi$
$998$		−	7.31725i		−	0.231624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.k.784.6	✓	12
3.2	odd	2		1305.2.c.l.784.7	yes	12
5.2	odd	4		6525.2.a.ce.1.7		12
5.3	odd	4		6525.2.a.ce.1.6		12
5.4	even	2	inner	1305.2.c.k.784.7	yes	12
15.2	even	4		6525.2.a.cf.1.6		12
15.8	even	4		6525.2.a.cf.1.7		12
15.14	odd	2		1305.2.c.l.784.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1305.2.c.k.784.6	✓	12	1.1	even	1	trivial
1305.2.c.k.784.7	yes	12	5.4	even	2	inner
1305.2.c.l.784.6	yes	12	15.14	odd	2
1305.2.c.l.784.7	yes	12	3.2	odd	2
6525.2.a.ce.1.6		12	5.3	odd	4
6525.2.a.ce.1.7		12	5.2	odd	4
6525.2.a.cf.1.6		12	15.2	even	4
6525.2.a.cf.1.7		12	15.8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.328889i q^{2} +1.89183 q^{4} +(2.20614 + 0.364635i) q^{5} -1.86588i q^{7} -1.27998i q^{8} +(0.119924 - 0.725574i) q^{10} -0.564087 q^{11} +4.95986i q^{13} -0.613668 q^{14} +3.36269 q^{16} +7.06879i q^{17} +3.32971 q^{19} +(4.17364 + 0.689828i) q^{20} +0.185522i q^{22} -2.36471i q^{23} +(4.73408 + 1.60887i) q^{25} +1.63124 q^{26} -3.52994i q^{28} -1.00000 q^{29} +4.87352 q^{31} -3.66591i q^{32} +2.32485 q^{34} +(0.680366 - 4.11639i) q^{35} -8.50474i q^{37} -1.09510i q^{38} +(0.466725 - 2.82381i) q^{40} -7.86030 q^{41} -4.39693i q^{43} -1.06716 q^{44} -0.777727 q^{46} +7.06879i q^{47} +3.51848 q^{49} +(0.529139 - 1.55699i) q^{50} +9.38323i q^{52} -4.18169i q^{53} +(-1.24445 - 0.205686i) q^{55} -2.38829 q^{56} +0.328889i q^{58} -9.01198 q^{59} -1.26059 q^{61} -1.60285i q^{62} +5.51971 q^{64} +(-1.80854 + 10.9421i) q^{65} -6.61254i q^{67} +13.3730i q^{68} +(-1.35384 - 0.223765i) q^{70} +5.46480 q^{71} -5.77659i q^{73} -2.79711 q^{74} +6.29925 q^{76} +1.05252i q^{77} -12.1018 q^{79} +(7.41856 + 1.22616i) q^{80} +2.58516i q^{82} -9.41830i q^{83} +(-2.57753 + 15.5947i) q^{85} -1.44610 q^{86} +0.722020i q^{88} -0.622547 q^{89} +9.25453 q^{91} -4.47364i q^{92} +2.32485 q^{94} +(7.34579 + 1.21413i) q^{95} +19.2638i q^{97} -1.15719i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) \) 12 * q - 16 * q^4 - 10 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^16 + 20 * q^19 + 14 * q^20 + 8 * q^25 - 56 * q^26 - 12 * q^29 - 16 * q^31 - 4 * q^34 - 16 * q^35 + 16 * q^40 - 32 * q^41 + 68 * q^44 + 20 * q^46 + 4 * q^49 - 8 * q^50 + 4 * q^55 - 76 * q^56 + 44 * q^59 - 52 * q^61 - 36 * q^64 - 8 * q^65 - 30 * q^70 - 20 * q^71 + 20 * q^74 - 28 * q^76 + 4 * q^79 + 34 * q^80 + 20 * q^85 - 36 * q^86 + 68 * q^89 + 48 * q^91 - 4 * q^94 - 8 * q^95

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