LMFDB - Embedded newform 1305.2.c.e.784.2

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:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.e.784.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.73205i q^{2} -1.00000 q^{4} +(2.18614 + 0.469882i) q^{5} -1.58457i q^{7} -1.73205i q^{8} +(0.813859 - 3.78651i) q^{10} -6.37228 q^{11} -0.939764i q^{13} -2.74456 q^{14} -5.00000 q^{16} -5.04868i q^{17} -4.00000 q^{19} +(-2.18614 - 0.469882i) q^{20} +11.0371i q^{22} +3.46410i q^{23} +(4.55842 + 2.05446i) q^{25} -1.62772 q^{26} +1.58457i q^{28} -1.00000 q^{29} +2.37228 q^{31} +5.19615i q^{32} -8.74456 q^{34} +(0.744563 - 3.46410i) q^{35} -10.0974i q^{37} +6.92820i q^{38} +(0.813859 - 3.78651i) q^{40} -6.74456 q^{41} -5.69349i q^{43} +6.37228 q^{44} +6.00000 q^{46} -5.69349i q^{47} +4.48913 q^{49} +(3.55842 - 7.89542i) q^{50} +0.939764i q^{52} +0.939764i q^{53} +(-13.9307 - 2.99422i) q^{55} -2.74456 q^{56} +1.73205i q^{58} +0.744563 q^{59} +6.00000 q^{61} -4.10891i q^{62} -1.00000 q^{64} +(0.441578 - 2.05446i) q^{65} -8.51278i q^{67} +5.04868i q^{68} +(-6.00000 - 1.28962i) q^{70} +4.74456 q^{71} +6.92820i q^{73} -17.4891 q^{74} +4.00000 q^{76} +10.0974i q^{77} -5.62772 q^{79} +(-10.9307 - 2.34941i) q^{80} +11.6819i q^{82} +16.7306i q^{83} +(2.37228 - 11.0371i) q^{85} -9.86141 q^{86} +11.0371i q^{88} +10.7446 q^{89} -1.48913 q^{91} -3.46410i q^{92} -9.86141 q^{94} +(-8.74456 - 1.87953i) q^{95} -6.92820i q^{97} -7.77539i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 3 q^{5} + 9 q^{10} - 14 q^{11} + 12 q^{14} - 20 q^{16} - 16 q^{19} - 3 q^{20} + q^{25} - 18 q^{26} - 4 q^{29} - 2 q^{31} - 12 q^{34} - 20 q^{35} + 9 q^{40} - 4 q^{41} + 14 q^{44} + 24 q^{46}+ \cdots - 12 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 + 3 * q^5 + 9 * q^10 - 14 * q^11 + 12 * q^14 - 20 * q^16 - 16 * q^19 - 3 * q^20 + q^25 - 18 * q^26 - 4 * q^29 - 2 * q^31 - 12 * q^34 - 20 * q^35 + 9 * q^40 - 4 * q^41 + 14 * q^44 + 24 * q^46 - 28 * q^49 - 3 * q^50 - 27 * q^55 + 12 * q^56 - 20 * q^59 + 24 * q^61 - 4 * q^64 + 19 * q^65 - 24 * q^70 - 4 * q^71 - 24 * q^74 + 16 * q^76 - 34 * q^79 - 15 * q^80 - 2 * q^85 + 18 * q^86 + 20 * q^89 + 40 * q^91 + 18 * q^94 - 12 * 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 $

$2$		−	1.73205i		−	1.22474i	−0.790569	−	0.612372i	$-0.790215\pi$
$2$		−	1.73205i		−	1.22474i	0.790569	−	0.612372i	$-0.209785\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	2.18614	+	0.469882i	0.977672	+	0.210138i
$5$	2.18614	+	0.469882i	0.977672	+	0.210138i
$6$		0			0
$7$		−	1.58457i		−	0.598913i	−0.954110	−	0.299456i	$-0.903195\pi$
$7$		−	1.58457i		−	0.598913i	0.954110	−	0.299456i	$-0.0968053\pi$
$8$		−	1.73205i		−	0.612372i
$9$		0			0
$10$	0.813859	−	3.78651i	0.257365	−	1.19740i
$11$	−6.37228			−1.92132			−0.960658	−	0.277736i	$-0.910416\pi$
$11$	−6.37228			−1.92132			−0.960658	+	0.277736i	$0.910416\pi$
$12$		0			0
$13$		−	0.939764i		−	0.260644i	−0.991472	−	0.130322i	$-0.958399\pi$
$13$		−	0.939764i		−	0.260644i	0.991472	−	0.130322i	$-0.0416010\pi$
$14$	−2.74456			−0.733515
$15$		0			0
$16$	−5.00000			−1.25000
$17$		−	5.04868i		−	1.22448i	−0.790671	−	0.612242i	$-0.790268\pi$
$17$		−	5.04868i		−	1.22448i	0.790671	−	0.612242i	$-0.209732\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	−2.18614	−	0.469882i	−0.488836	−	0.105069i
$21$		0			0
$22$			11.0371i			2.35312i
$23$			3.46410i			0.722315i	0.932505	+	0.361158i	$0.117618\pi$
$23$			3.46410i			0.722315i	−0.932505	+	0.361158i	$0.882382\pi$
$24$		0			0
$25$	4.55842	+	2.05446i	0.911684	+	0.410891i
$26$	−1.62772			−0.319222
$27$		0			0
$28$			1.58457i			0.299456i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$		0			0
$31$	2.37228			0.426074			0.213037	−	0.977044i	$-0.431664\pi$
$31$	2.37228			0.426074			0.213037	+	0.977044i	$0.431664\pi$
$32$			5.19615i			0.918559i
$33$		0			0
$34$	−8.74456			−1.49968
$35$	0.744563	−	3.46410i	0.125854	−	0.585540i
$36$		0			0
$37$		−	10.0974i		−	1.65999i	−0.557768	−	0.829997i	$-0.688342\pi$
$37$		−	10.0974i		−	1.65999i	0.557768	−	0.829997i	$-0.311658\pi$
$38$			6.92820i			1.12390i
$39$		0			0
$40$	0.813859	−	3.78651i	0.128682	−	0.598699i
$41$	−6.74456			−1.05332			−0.526662	−	0.850075i	$-0.676557\pi$
$41$	−6.74456			−1.05332			−0.526662	+	0.850075i	$0.676557\pi$
$42$		0			0
$43$		−	5.69349i		−	0.868248i	−0.900853	−	0.434124i	$-0.857058\pi$
$43$		−	5.69349i		−	0.868248i	0.900853	−	0.434124i	$-0.142942\pi$
$44$	6.37228			0.960658
$45$		0			0
$46$	6.00000			0.884652
$47$		−	5.69349i		−	0.830480i	−0.909712	−	0.415240i	$-0.863698\pi$
$47$		−	5.69349i		−	0.830480i	0.909712	−	0.415240i	$-0.136302\pi$
$48$		0			0
$49$	4.48913			0.641304
$50$	3.55842	−	7.89542i	0.503237	−	1.11658i
$51$		0			0
$52$			0.939764i			0.130322i
$53$			0.939764i			0.129086i	0.997915	+	0.0645432i	$0.0205590\pi$
$53$			0.939764i			0.129086i	−0.997915	+	0.0645432i	$0.979441\pi$
$54$		0			0
$55$	−13.9307	−	2.99422i	−1.87842	−	0.403741i
$56$	−2.74456			−0.366758
$57$		0			0
$58$			1.73205i			0.227429i
$59$	0.744563			0.0969338			0.0484669	−	0.998825i	$-0.484566\pi$
$59$	0.744563			0.0969338			0.0484669	+	0.998825i	$0.484566\pi$
$60$		0			0
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$		−	4.10891i		−	0.521832i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.441578	−	2.05446i	0.0547710	−	0.254824i
$66$		0			0
$67$		−	8.51278i		−	1.04000i	−0.854166	−	0.520001i	$-0.825932\pi$
$67$		−	8.51278i		−	1.04000i	0.854166	−	0.520001i	$-0.174068\pi$
$68$			5.04868i			0.612242i
$69$		0			0
$70$	−6.00000	−	1.28962i	−0.717137	−	0.154139i
$71$	4.74456			0.563076			0.281538	−	0.959550i	$-0.409155\pi$
$71$	4.74456			0.563076			0.281538	+	0.959550i	$0.409155\pi$
$72$		0			0
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$	−17.4891			−2.03307
$75$		0			0
$76$	4.00000			0.458831
$77$			10.0974i			1.15070i
$78$		0			0
$79$	−5.62772			−0.633168			−0.316584	−	0.948565i	$-0.602536\pi$
$79$	−5.62772			−0.633168			−0.316584	+	0.948565i	$0.602536\pi$
$80$	−10.9307	−	2.34941i	−1.22209	−	0.262672i
$81$		0			0
$82$			11.6819i			1.29005i
$83$			16.7306i			1.83642i	0.396092	+	0.918211i	$0.370366\pi$
$83$			16.7306i			1.83642i	−0.396092	+	0.918211i	$0.629634\pi$
$84$		0			0
$85$	2.37228	−	11.0371i	0.257310	−	1.19714i
$86$	−9.86141			−1.06338
$87$		0			0
$88$			11.0371i			1.17656i
$89$	10.7446			1.13892			0.569461	−	0.822019i	$-0.307152\pi$
$89$	10.7446			1.13892			0.569461	+	0.822019i	$0.307152\pi$
$90$		0			0
$91$	−1.48913			−0.156103
$92$		−	3.46410i		−	0.361158i
$93$		0			0
$94$	−9.86141			−1.01713
$95$	−8.74456	−	1.87953i	−0.897173	−	0.192835i
$96$		0			0
$97$		−	6.92820i		−	0.703452i	−0.936103	−	0.351726i	$-0.885595\pi$
$97$		−	6.92820i		−	0.703452i	0.936103	−	0.351726i	$-0.114405\pi$
$98$		−	7.77539i		−	0.785433i
$99$		0			0
$100$	−4.55842	−	2.05446i	−0.455842	−	0.205446i
$101$	14.7446			1.46714			0.733569	−	0.679615i	$-0.237853\pi$
$101$	14.7446			1.46714			0.733569	+	0.679615i	$0.237853\pi$
$102$		0			0
$103$		−	3.46410i		−	0.341328i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$		−	3.46410i		−	0.341328i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	−1.62772			−0.159611
$105$		0			0
$106$	1.62772			0.158098
$107$		−	1.58457i		−	0.153187i	−0.997062	−	0.0765933i	$-0.975596\pi$
$107$		−	1.58457i		−	0.153187i	0.997062	−	0.0765933i	$-0.0244043\pi$
$108$		0			0
$109$	−1.11684			−0.106974			−0.0534871	−	0.998569i	$-0.517034\pi$
$109$	−1.11684			−0.106974			−0.0534871	+	0.998569i	$0.517034\pi$
$110$	−5.18614	+	24.1287i	−0.494479	+	2.30058i
$111$		0			0
$112$			7.92287i			0.748641i
$113$		−	8.80773i		−	0.828562i	−0.910149	−	0.414281i	$-0.864033\pi$
$113$		−	8.80773i		−	0.828562i	0.910149	−	0.414281i	$-0.135967\pi$
$114$		0			0
$115$	−1.62772	+	7.57301i	−0.151786	+	0.706187i
$116$	1.00000			0.0928477
$117$		0			0
$118$		−	1.28962i		−	0.118719i
$119$	−8.00000			−0.733359
$120$		0			0
$121$	29.6060			2.69145
$122$		−	10.3923i		−	0.940875i
$123$		0			0
$124$	−2.37228			−0.213037
$125$	9.00000	+	6.63325i	0.804984	+	0.593296i
$126$		0			0
$127$			3.46410i			0.307389i	0.988118	+	0.153695i	$0.0491172\pi$
$127$			3.46410i			0.307389i	−0.988118	+	0.153695i	$0.950883\pi$
$128$			12.1244i			1.07165i
$129$		0			0
$130$	−3.55842	−	0.764836i	−0.312094	−	0.0670805i
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		0			0
$133$			6.33830i			0.549600i
$134$	−14.7446			−1.27374
$135$		0			0
$136$	−8.74456			−0.749840
$137$		−	6.92820i		−	0.591916i	−0.955201	−	0.295958i	$-0.904361\pi$
$137$		−	6.92820i		−	0.591916i	0.955201	−	0.295958i	$-0.0956389\pi$
$138$		0			0
$139$	−8.74456			−0.741704			−0.370852	−	0.928692i	$-0.620934\pi$
$139$	−8.74456			−0.741704			−0.370852	+	0.928692i	$0.620934\pi$
$140$	−0.744563	+	3.46410i	−0.0629270	+	0.292770i
$141$		0			0
$142$		−	8.21782i		−	0.689624i
$143$			5.98844i			0.500778i
$144$		0			0
$145$	−2.18614	−	0.469882i	−0.181549	−	0.0390216i
$146$	12.0000			0.993127
$147$		0			0
$148$			10.0974i			0.829997i
$149$	−21.1168			−1.72996			−0.864980	−	0.501807i	$-0.832669\pi$
$149$	−21.1168			−1.72996			−0.864980	+	0.501807i	$0.832669\pi$
$150$		0			0
$151$	−9.48913			−0.772214			−0.386107	−	0.922454i	$-0.626180\pi$
$151$	−9.48913			−0.772214			−0.386107	+	0.922454i	$0.626180\pi$
$152$			6.92820i			0.561951i
$153$		0			0
$154$	17.4891			1.40931
$155$	5.18614	+	1.11469i	0.416561	+	0.0895342i
$156$		0			0
$157$			13.8564i			1.10586i	0.833227	+	0.552931i	$0.186491\pi$
$157$			13.8564i			1.10586i	−0.833227	+	0.552931i	$0.813509\pi$
$158$			9.74749i			0.775469i
$159$		0			0
$160$	−2.44158	+	11.3595i	−0.193024	+	0.898049i
$161$	5.48913			0.432604
$162$		0			0
$163$			6.28339i			0.492153i	0.969250	+	0.246077i	$0.0791415\pi$
$163$			6.28339i			0.492153i	−0.969250	+	0.246077i	$0.920858\pi$
$164$	6.74456			0.526662
$165$		0			0
$166$	28.9783			2.24915
$167$			9.80240i			0.758532i	0.925288	+	0.379266i	$0.123824\pi$
$167$			9.80240i			0.758532i	−0.925288	+	0.379266i	$0.876176\pi$
$168$		0			0
$169$	12.1168			0.932065
$170$	−19.1168	−	4.10891i	−1.46620	−	0.315139i
$171$		0			0
$172$			5.69349i			0.434124i
$173$			10.6873i			0.812537i	0.913754	+	0.406269i	$0.133170\pi$
$173$			10.6873i			0.812537i	−0.913754	+	0.406269i	$0.866830\pi$
$174$		0			0
$175$	3.25544	−	7.22316i	0.246088	−	0.546019i
$176$	31.8614			2.40164
$177$		0			0
$178$		−	18.6101i		−	1.39489i
$179$	16.7446			1.25155			0.625774	−	0.780005i	$-0.284783\pi$
$179$	16.7446			1.25155			0.625774	+	0.780005i	$0.284783\pi$
$180$		0			0
$181$	−13.8614			−1.03031			−0.515155	−	0.857097i	$-0.672266\pi$
$181$	−13.8614			−1.03031			−0.515155	+	0.857097i	$0.672266\pi$
$182$			2.57924i			0.191186i
$183$		0			0
$184$	6.00000			0.442326
$185$	4.74456	−	22.0742i	0.348827	−	1.62293i
$186$		0			0
$187$			32.1716i			2.35262i
$188$			5.69349i			0.415240i
$189$		0			0
$190$	−3.25544	+	15.1460i	−0.236174	+	1.09881i
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$		0			0
$193$		−	6.92820i		−	0.498703i	−0.968413	−	0.249351i	$-0.919783\pi$
$193$		−	6.92820i		−	0.498703i	0.968413	−	0.249351i	$-0.0802174\pi$
$194$	−12.0000			−0.861550
$195$		0			0
$196$	−4.48913			−0.320652
$197$		−	27.1229i		−	1.93243i	−0.257743	−	0.966214i	$-0.582979\pi$
$197$		−	27.1229i		−	1.93243i	0.257743	−	0.966214i	$-0.417021\pi$
$198$		0			0
$199$	9.48913			0.672666			0.336333	−	0.941743i	$-0.390813\pi$
$199$	9.48913			0.672666			0.336333	+	0.941743i	$0.390813\pi$
$200$	3.55842	−	7.89542i	0.251618	−	0.558290i
$201$		0			0
$202$		−	25.5383i		−	1.79687i
$203$			1.58457i			0.111215i
$204$		0			0
$205$	−14.7446	−	3.16915i	−1.02980	−	0.221343i
$206$	−6.00000			−0.418040
$207$		0			0
$208$			4.69882i			0.325804i
$209$	25.4891			1.76312
$210$		0			0
$211$	−11.1168			−0.765315			−0.382658	−	0.923890i	$-0.624991\pi$
$211$	−11.1168			−0.765315			−0.382658	+	0.923890i	$0.624991\pi$
$212$		−	0.939764i		−	0.0645432i
$213$		0			0
$214$	−2.74456			−0.187614
$215$	2.67527	−	12.4468i	0.182452	−	0.848862i
$216$		0			0
$217$		−	3.75906i		−	0.255181i
$218$			1.93443i			0.131016i
$219$		0			0
$220$	13.9307	+	2.99422i	0.939208	+	0.201870i
$221$	−4.74456			−0.319154
$222$		0			0
$223$			10.3923i			0.695920i	0.937509	+	0.347960i	$0.113126\pi$
$223$			10.3923i			0.695920i	−0.937509	+	0.347960i	$0.886874\pi$
$224$	8.23369			0.550136
$225$		0			0
$226$	−15.2554			−1.01478
$227$		−	13.5615i		−	0.900105i	−0.893002	−	0.450053i	$-0.851405\pi$
$227$		−	13.5615i		−	0.900105i	0.893002	−	0.450053i	$-0.148595\pi$
$228$		0			0
$229$	1.25544			0.0829616			0.0414808	−	0.999139i	$-0.486792\pi$
$229$	1.25544			0.0829616			0.0414808	+	0.999139i	$0.486792\pi$
$230$	13.1168	+	2.81929i	0.864899	+	0.185899i
$231$		0			0
$232$			1.73205i			0.113715i
$233$		−	16.0858i		−	1.05382i	−0.849923	−	0.526908i	$-0.823351\pi$
$233$		−	16.0858i		−	1.05382i	0.849923	−	0.526908i	$-0.176649\pi$
$234$		0			0
$235$	2.67527	−	12.4468i	0.174515	−	0.811937i
$236$	−0.744563			−0.0484669
$237$		0			0
$238$			13.8564i			0.898177i
$239$	−6.23369			−0.403224			−0.201612	−	0.979465i	$-0.564618\pi$
$239$	−6.23369			−0.403224			−0.201612	+	0.979465i	$0.564618\pi$
$240$		0			0
$241$	12.3723			0.796969			0.398484	−	0.917175i	$-0.369536\pi$
$241$	12.3723			0.796969			0.398484	+	0.917175i	$0.369536\pi$
$242$		−	51.2790i		−	3.29634i
$243$		0			0
$244$	−6.00000			−0.384111
$245$	9.81386	+	2.10936i	0.626984	+	0.134762i
$246$		0			0
$247$			3.75906i			0.239183i
$248$		−	4.10891i		−	0.260916i
$249$		0			0
$250$	11.4891	−	15.5885i	0.726636	−	0.985901i
$251$	−1.62772			−0.102741			−0.0513703	−	0.998680i	$-0.516359\pi$
$251$	−1.62772			−0.102741			−0.0513703	+	0.998680i	$0.516359\pi$
$252$		0			0
$253$		−	22.0742i		−	1.38779i
$254$	6.00000			0.376473
$255$		0			0
$256$	19.0000			1.18750
$257$			12.3267i			0.768921i	0.923142	+	0.384460i	$0.125612\pi$
$257$			12.3267i			0.768921i	−0.923142	+	0.384460i	$0.874388\pi$
$258$		0			0
$259$	−16.0000			−0.994192
$260$	−0.441578	+	2.05446i	−0.0273855	+	0.127412i
$261$		0			0
$262$		−	6.92820i		−	0.428026i
$263$			26.4781i			1.63271i	0.577551	+	0.816355i	$0.304008\pi$
$263$			26.4781i			1.63271i	−0.577551	+	0.816355i	$0.695992\pi$
$264$		0			0
$265$	−0.441578	+	2.05446i	−0.0271259	+	0.126204i
$266$	10.9783			0.673120
$267$		0			0
$268$			8.51278i			0.520001i
$269$	0.510875			0.0311486			0.0155743	−	0.999879i	$-0.495042\pi$
$269$	0.510875			0.0311486			0.0155743	+	0.999879i	$0.495042\pi$
$270$		0			0
$271$	19.8614			1.20649			0.603247	−	0.797554i	$-0.293873\pi$
$271$	19.8614			1.20649			0.603247	+	0.797554i	$0.293873\pi$
$272$			25.2434i			1.53060i
$273$		0			0
$274$	−12.0000			−0.724947
$275$	−29.0475	−	13.0916i	−1.75163	−	0.789451i
$276$		0			0
$277$		−	6.92820i		−	0.416275i	−0.978100	−	0.208138i	$-0.933260\pi$
$277$		−	6.92820i		−	0.416275i	0.978100	−	0.208138i	$-0.0667402\pi$
$278$			15.1460i			0.908398i
$279$		0			0
$280$	−6.00000	−	1.28962i	−0.358569	−	0.0770696i
$281$	−4.37228			−0.260828			−0.130414	−	0.991460i	$-0.541631\pi$
$281$	−4.37228			−0.260828			−0.130414	+	0.991460i	$0.541631\pi$
$282$		0			0
$283$		−	30.5870i		−	1.81821i	−0.416568	−	0.909104i	$-0.636767\pi$
$283$		−	30.5870i		−	1.81821i	0.416568	−	0.909104i	$-0.363233\pi$
$284$	−4.74456			−0.281538
$285$		0			0
$286$	10.3723			0.613326
$287$			10.6873i			0.630849i
$288$		0			0
$289$	−8.48913			−0.499360
$290$	−0.813859	+	3.78651i	−0.0477915	+	0.222351i
$291$		0			0
$292$		−	6.92820i		−	0.405442i
$293$		−	22.0742i		−	1.28959i	−0.764355	−	0.644795i	$-0.776943\pi$
$293$		−	22.0742i		−	1.28959i	0.764355	−	0.644795i	$-0.223057\pi$
$294$		0			0
$295$	1.62772	+	0.349857i	0.0947694	+	0.0203694i
$296$	−17.4891			−1.01653
$297$		0			0
$298$			36.5754i			2.11876i
$299$	3.25544			0.188267
$300$		0			0
$301$	−9.02175			−0.520005
$302$			16.4356i			0.945765i
$303$		0			0
$304$	20.0000			1.14708
$305$	13.1168	+	2.81929i	0.751068	+	0.161432i
$306$		0			0
$307$		−	15.7908i		−	0.901231i	−0.892718	−	0.450615i	$-0.851205\pi$
$307$		−	15.7908i		−	0.901231i	0.892718	−	0.450615i	$-0.148795\pi$
$308$		−	10.0974i		−	0.575350i
$309$		0			0
$310$	1.93070	−	8.98266i	0.109657	−	0.510181i
$311$	18.9783			1.07616			0.538079	−	0.842894i	$-0.319150\pi$
$311$	18.9783			1.07616			0.538079	+	0.842894i	$0.319150\pi$
$312$		0			0
$313$		−	2.22938i		−	0.126012i	−0.998013	−	0.0630061i	$-0.979931\pi$
$313$		−	2.22938i		−	0.126012i	0.998013	−	0.0630061i	$-0.0200688\pi$
$314$	24.0000			1.35440
$315$		0			0
$316$	5.62772			0.316584
$317$			15.7359i			0.883818i	0.897060	+	0.441909i	$0.145699\pi$
$317$			15.7359i			0.883818i	−0.897060	+	0.441909i	$0.854301\pi$
$318$		0			0
$319$	6.37228			0.356779
$320$	−2.18614	−	0.469882i	−0.122209	−	0.0262672i
$321$		0			0
$322$		−	9.50744i		−	0.529829i
$323$			20.1947i			1.12366i
$324$		0			0
$325$	1.93070	−	4.28384i	0.107096	−	0.237625i
$326$	10.8832			0.602762
$327$		0			0
$328$			11.6819i			0.645026i
$329$	−9.02175			−0.497385
$330$		0			0
$331$	0.138593			0.00761778			0.00380889	−	0.999993i	$-0.498788\pi$
$331$	0.138593			0.00761778			0.00380889	+	0.999993i	$0.498788\pi$
$332$		−	16.7306i		−	0.918211i
$333$		0			0
$334$	16.9783			0.929009
$335$	4.00000	−	18.6101i	0.218543	−	1.01678i
$336$		0			0
$337$			25.2434i			1.37509i	0.726140	+	0.687547i	$0.241313\pi$
$337$			25.2434i			1.37509i	−0.726140	+	0.687547i	$0.758687\pi$
$338$		−	20.9870i		−	1.14154i
$339$		0			0
$340$	−2.37228	+	11.0371i	−0.128655	+	0.598572i
$341$	−15.1168			−0.818623
$342$		0			0
$343$		−	18.2054i		−	0.982998i
$344$	−9.86141			−0.531691
$345$		0			0
$346$	18.5109			0.995151
$347$		−	19.8997i		−	1.06827i	−0.845398	−	0.534137i	$-0.820637\pi$
$347$		−	19.8997i		−	1.06827i	0.845398	−	0.534137i	$-0.179363\pi$
$348$		0			0
$349$	1.86141			0.0996388			0.0498194	−	0.998758i	$-0.484135\pi$
$349$	1.86141			0.0996388			0.0498194	+	0.998758i	$0.484135\pi$
$350$	−12.5109	−	5.63858i	−0.668734	−	0.301395i
$351$		0			0
$352$		−	33.1113i		−	1.76484i
$353$		−	23.9538i		−	1.27493i	−0.770479	−	0.637465i	$-0.779983\pi$
$353$		−	23.9538i		−	1.27493i	0.770479	−	0.637465i	$-0.220017\pi$
$354$		0			0
$355$	10.3723	+	2.22938i	0.550504	+	0.118323i
$356$	−10.7446			−0.569461
$357$		0			0
$358$		−	29.0024i		−	1.53283i
$359$	−31.1168			−1.64228			−0.821142	−	0.570724i	$-0.806663\pi$
$359$	−31.1168			−1.64228			−0.821142	+	0.570724i	$0.806663\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$			24.0087i			1.26187i
$363$		0			0
$364$	1.48913			0.0780514
$365$	−3.25544	+	15.1460i	−0.170397	+	0.792779i
$366$		0			0
$367$		−	10.3923i		−	0.542474i	−0.962513	−	0.271237i	$-0.912567\pi$
$367$		−	10.3923i		−	0.542474i	0.962513	−	0.271237i	$-0.0874327\pi$
$368$		−	17.3205i		−	0.902894i
$369$		0			0
$370$	−38.2337	−	8.21782i	−1.98767	−	0.427224i
$371$	1.48913			0.0773115
$372$		0			0
$373$			5.39853i			0.279525i	0.990185	+	0.139763i	$0.0446340\pi$
$373$			5.39853i			0.279525i	−0.990185	+	0.139763i	$0.955366\pi$
$374$	55.7228			2.88136
$375$		0			0
$376$	−9.86141			−0.508563
$377$			0.939764i			0.0484003i
$378$		0			0
$379$	21.4891			1.10382			0.551911	−	0.833903i	$-0.313899\pi$
$379$	21.4891			1.10382			0.551911	+	0.833903i	$0.313899\pi$
$380$	8.74456	+	1.87953i	0.448587	+	0.0964177i
$381$		0			0
$382$		−	27.7128i		−	1.41791i
$383$		−	18.6101i		−	0.950933i	−0.879734	−	0.475467i	$-0.842279\pi$
$383$		−	18.6101i		−	0.950933i	0.879734	−	0.475467i	$-0.157721\pi$
$384$		0			0
$385$	−4.74456	+	22.0742i	−0.241805	+	1.12501i
$386$	−12.0000			−0.610784
$387$		0			0
$388$			6.92820i			0.351726i
$389$	−2.74456			−0.139155			−0.0695774	−	0.997577i	$-0.522165\pi$
$389$	−2.74456			−0.139155			−0.0695774	+	0.997577i	$0.522165\pi$
$390$		0			0
$391$	17.4891			0.884463
$392$		−	7.77539i		−	0.392717i
$393$		0			0
$394$	−46.9783			−2.36673
$395$	−12.3030	−	2.64436i	−0.619030	−	0.133052i
$396$		0			0
$397$			7.27806i			0.365275i	0.983180	+	0.182638i	$0.0584635\pi$
$397$			7.27806i			0.365275i	−0.983180	+	0.182638i	$0.941536\pi$
$398$		−	16.4356i		−	0.823845i
$399$		0			0
$400$	−22.7921	−	10.2723i	−1.13961	−	0.513614i
$401$	13.1168			0.655024			0.327512	−	0.944847i	$-0.393790\pi$
$401$	13.1168			0.655024			0.327512	+	0.944847i	$0.393790\pi$
$402$		0			0
$403$		−	2.22938i		−	0.111054i
$404$	−14.7446			−0.733569
$405$		0			0
$406$	2.74456			0.136210
$407$			64.3432i			3.18937i
$408$		0			0
$409$	30.4674			1.50651			0.753257	−	0.657726i	$-0.228481\pi$
$409$	30.4674			1.50651			0.753257	+	0.657726i	$0.228481\pi$
$410$	−5.48913	+	25.5383i	−0.271089	+	1.26125i
$411$		0			0
$412$			3.46410i			0.170664i
$413$		−	1.17981i		−	0.0580549i
$414$		0			0
$415$	−7.86141	+	36.5754i	−0.385901	+	1.79542i
$416$	4.88316			0.239416
$417$		0			0
$418$		−	44.1485i		−	2.15937i
$419$	24.7446			1.20885			0.604425	−	0.796662i	$-0.293403\pi$
$419$	24.7446			1.20885			0.604425	+	0.796662i	$0.293403\pi$
$420$		0			0
$421$	−20.9783			−1.02242			−0.511209	−	0.859457i	$-0.670802\pi$
$421$	−20.9783			−1.02242			−0.511209	+	0.859457i	$0.670802\pi$
$422$			19.2549i			0.937316i
$423$		0			0
$424$	1.62772			0.0790490
$425$	10.3723	−	23.0140i	0.503130	−	1.11634i
$426$		0			0
$427$		−	9.50744i		−	0.460097i
$428$			1.58457i			0.0765933i
$429$		0			0
$430$	−21.5584	−	4.63370i	−1.03964	−	0.223457i
$431$	11.2554			0.542155			0.271078	−	0.962557i	$-0.412620\pi$
$431$	11.2554			0.542155			0.271078	+	0.962557i	$0.412620\pi$
$432$		0			0
$433$			14.4463i			0.694246i	0.937820	+	0.347123i	$0.112841\pi$
$433$			14.4463i			0.694246i	−0.937820	+	0.347123i	$0.887159\pi$
$434$	−6.51087			−0.312532
$435$		0			0
$436$	1.11684			0.0534871
$437$		−	13.8564i		−	0.662842i
$438$		0			0
$439$	−30.2337			−1.44298			−0.721488	−	0.692427i	$-0.756541\pi$
$439$	−30.2337			−1.44298			−0.721488	+	0.692427i	$0.756541\pi$
$440$	−5.18614	+	24.1287i	−0.247240	+	1.15029i
$441$		0			0
$442$			8.21782i			0.390882i
$443$			7.22316i			0.343183i	0.985168	+	0.171591i	$0.0548908\pi$
$443$			7.22316i			0.343183i	−0.985168	+	0.171591i	$0.945109\pi$
$444$		0			0
$445$	23.4891	+	5.04868i	1.11349	+	0.239330i
$446$	18.0000			0.852325
$447$		0			0
$448$			1.58457i			0.0748641i
$449$	34.4674			1.62662			0.813308	−	0.581833i	$-0.197664\pi$
$449$	34.4674			1.62662			0.813308	+	0.581833i	$0.197664\pi$
$450$		0			0
$451$	42.9783			2.02377
$452$			8.80773i			0.414281i
$453$		0			0
$454$	−23.4891			−1.10240
$455$	−3.25544	−	0.699713i	−0.152617	−	0.0328031i
$456$		0			0
$457$		−	2.57924i		−	0.120652i	−0.998179	−	0.0603259i	$-0.980786\pi$
$457$		−	2.57924i		−	0.120652i	0.998179	−	0.0603259i	$-0.0192140\pi$
$458$		−	2.17448i		−	0.101607i
$459$		0			0
$460$	1.62772	−	7.57301i	0.0758928	−	0.353094i
$461$	−4.51087			−0.210092			−0.105046	−	0.994467i	$-0.533499\pi$
$461$	−4.51087			−0.210092			−0.105046	+	0.994467i	$0.533499\pi$
$462$		0			0
$463$			20.4897i			0.952235i	0.879382	+	0.476118i	$0.157956\pi$
$463$			20.4897i			0.952235i	−0.879382	+	0.476118i	$0.842044\pi$
$464$	5.00000			0.232119
$465$		0			0
$466$	−27.8614			−1.29065
$467$			39.7446i			1.83916i	0.392902	+	0.919580i	$0.371471\pi$
$467$			39.7446i			1.83916i	−0.392902	+	0.919580i	$0.628529\pi$
$468$		0			0
$469$	−13.4891			−0.622870
$470$	−21.5584	−	4.63370i	−0.994416	−	0.213736i
$471$		0			0
$472$		−	1.28962i		−	0.0593596i
$473$			36.2805i			1.66818i
$474$		0			0
$475$	−18.2337	−	8.21782i	−0.836619	−	0.377060i
$476$	8.00000			0.366679
$477$		0			0
$478$			10.7971i			0.493846i
$479$	−10.3723			−0.473922			−0.236961	−	0.971519i	$-0.576151\pi$
$479$	−10.3723			−0.473922			−0.236961	+	0.971519i	$0.576151\pi$
$480$		0			0
$481$	−9.48913			−0.432667
$482$		−	21.4294i		−	0.976083i
$483$		0			0
$484$	−29.6060			−1.34573
$485$	3.25544	−	15.1460i	0.147822	−	0.687746i
$486$		0			0
$487$		−	9.10268i		−	0.412482i	−0.978501	−	0.206241i	$-0.933877\pi$
$487$		−	9.10268i		−	0.412482i	0.978501	−	0.206241i	$-0.0661231\pi$
$488$		−	10.3923i		−	0.470438i
$489$		0			0
$490$	3.65352	−	16.9981i	0.165049	−	0.767896i
$491$	17.6277			0.795528			0.397764	−	0.917488i	$-0.369786\pi$
$491$	17.6277			0.795528			0.397764	+	0.917488i	$0.369786\pi$
$492$		0			0
$493$			5.04868i			0.227381i
$494$	6.51087			0.292938
$495$		0			0
$496$	−11.8614			−0.532593
$497$		−	7.51811i		−	0.337233i
$498$		0			0
$499$	−16.7446			−0.749590			−0.374795	−	0.927108i	$-0.622287\pi$
$499$	−16.7446			−0.749590			−0.374795	+	0.927108i	$0.622287\pi$
$500$	−9.00000	−	6.63325i	−0.402492	−	0.296648i
$501$		0			0
$502$			2.81929i			0.125831i
$503$		−	39.7446i		−	1.77212i	−0.463567	−	0.886062i	$-0.653431\pi$
$503$		−	39.7446i		−	1.77212i	0.463567	−	0.886062i	$-0.346569\pi$
$504$		0			0
$505$	32.2337	+	6.92820i	1.43438	+	0.308301i
$506$	−38.2337			−1.69969
$507$		0			0
$508$		−	3.46410i		−	0.153695i
$509$	5.86141			0.259802			0.129901	−	0.991527i	$-0.458534\pi$
$509$	5.86141			0.259802			0.129901	+	0.991527i	$0.458534\pi$
$510$		0			0
$511$	10.9783			0.485649
$512$		−	8.66025i		−	0.382733i
$513$		0			0
$514$	21.3505			0.941732
$515$	1.62772	−	7.57301i	0.0717259	−	0.333707i
$516$		0			0
$517$			36.2805i			1.59561i
$518$			27.7128i			1.21763i
$519$		0			0
$520$	−3.55842	−	0.764836i	−0.156047	−	0.0335403i
$521$	25.8614			1.13301			0.566504	−	0.824059i	$-0.308295\pi$
$521$	25.8614			1.13301			0.566504	+	0.824059i	$0.308295\pi$
$522$		0			0
$523$		−	4.75372i		−	0.207866i	−0.994584	−	0.103933i	$-0.966857\pi$
$523$		−	4.75372i		−	0.207866i	0.994584	−	0.103933i	$-0.0331427\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	45.8614			1.99965
$527$		−	11.9769i		−	0.521721i
$528$		0			0
$529$	11.0000			0.478261
$530$	3.55842	+	0.764836i	0.154568	+	0.0332223i
$531$		0			0
$532$		−	6.33830i		−	0.274800i
$533$			6.33830i			0.274542i
$534$		0			0
$535$	0.744563	−	3.46410i	0.0321903	−	0.149766i
$536$	−14.7446			−0.636868
$537$		0			0
$538$		−	0.884861i		−	0.0381491i
$539$	−28.6060			−1.23215
$540$		0			0
$541$	34.7446			1.49379			0.746893	−	0.664945i	$-0.231545\pi$
$541$	34.7446			1.49379			0.746893	+	0.664945i	$0.231545\pi$
$542$		−	34.4010i		−	1.47765i
$543$		0			0
$544$	26.2337			1.12476
$545$	−2.44158	−	0.524785i	−0.104586	−	0.0224793i
$546$		0			0
$547$		−	4.75372i		−	0.203254i	−0.994823	−	0.101627i	$-0.967595\pi$
$547$		−	4.75372i		−	0.203254i	0.994823	−	0.101627i	$-0.0324049\pi$
$548$			6.92820i			0.295958i
$549$		0			0
$550$	−22.6753	+	50.3118i	−0.966877	+	2.14530i
$551$	4.00000			0.170406
$552$		0			0
$553$			8.91754i			0.379212i
$554$	−12.0000			−0.509831
$555$		0			0
$556$	8.74456			0.370852
$557$		−	30.8820i		−	1.30851i	−0.756274	−	0.654255i	$-0.772982\pi$
$557$		−	30.8820i		−	1.30851i	0.756274	−	0.654255i	$-0.227018\pi$
$558$		0			0
$559$	−5.35053			−0.226303
$560$	−3.72281	+	17.3205i	−0.157318	+	0.731925i
$561$		0			0
$562$			7.57301i			0.319448i
$563$			1.23472i			0.0520371i	0.999661	+	0.0260186i	$0.00828290\pi$
$563$			1.23472i			0.0520371i	−0.999661	+	0.0260186i	$0.991717\pi$
$564$		0			0
$565$	4.13859	−	19.2549i	0.174112	−	0.810061i
$566$	−52.9783			−2.22684
$567$		0			0
$568$		−	8.21782i		−	0.344812i
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$		0			0
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$		−	5.98844i		−	0.250389i
$573$		0			0
$574$	18.5109			0.772629
$575$	−7.11684	+	15.7908i	−0.296793	+	0.658523i
$576$		0			0
$577$		−	8.80773i		−	0.366671i	−0.983050	−	0.183335i	$-0.941311\pi$
$577$		−	8.80773i		−	0.366671i	0.983050	−	0.183335i	$-0.0586894\pi$
$578$			14.7036i			0.611589i
$579$		0			0
$580$	2.18614	+	0.469882i	0.0907746	+	0.0195108i
$581$	26.5109			1.09986
$582$		0			0
$583$		−	5.98844i		−	0.248016i
$584$	12.0000			0.496564
$585$		0			0
$586$	−38.2337			−1.57942
$587$			36.9253i			1.52407i	0.647536	+	0.762035i	$0.275800\pi$
$587$			36.9253i			1.52407i	−0.647536	+	0.762035i	$0.724200\pi$
$588$		0			0
$589$	−9.48913			−0.390993
$590$	0.605969	−	2.81929i	0.0249474	−	0.116068i
$591$		0			0
$592$			50.4868i			2.07499i
$593$			14.2063i			0.583381i	0.956513	+	0.291691i	$0.0942178\pi$
$593$			14.2063i			0.583381i	−0.956513	+	0.291691i	$0.905782\pi$
$594$		0			0
$595$	−17.4891	−	3.75906i	−0.716984	−	0.154106i
$596$	21.1168			0.864980
$597$		0			0
$598$		−	5.63858i		−	0.230579i
$599$	−21.3505			−0.872359			−0.436180	−	0.899860i	$-0.643669\pi$
$599$	−21.3505			−0.872359			−0.436180	+	0.899860i	$0.643669\pi$
$600$		0			0
$601$	−18.7446			−0.764607			−0.382303	−	0.924037i	$-0.624869\pi$
$601$	−18.7446			−0.764607			−0.382303	+	0.924037i	$0.624869\pi$
$602$			15.6261i			0.636873i
$603$		0			0
$604$	9.48913			0.386107
$605$	64.7228	+	13.9113i	2.63136	+	0.565575i
$606$		0			0
$607$			25.8882i			1.05077i	0.850865	+	0.525385i	$0.176079\pi$
$607$			25.8882i			1.05077i	−0.850865	+	0.525385i	$0.823921\pi$
$608$		−	20.7846i		−	0.842927i
$609$		0			0
$610$	4.88316	−	22.7190i	0.197713	−	0.919867i
$611$	−5.35053			−0.216459
$612$		0			0
$613$			39.4496i			1.59336i	0.604404	+	0.796678i	$0.293411\pi$
$613$			39.4496i			1.59336i	−0.604404	+	0.796678i	$0.706589\pi$
$614$	−27.3505			−1.10378
$615$		0			0
$616$	17.4891			0.704657
$617$			24.5437i			0.988091i	0.869436	+	0.494045i	$0.164482\pi$
$617$			24.5437i			0.988091i	−0.869436	+	0.494045i	$0.835518\pi$
$618$		0			0
$619$	−25.6277			−1.03006			−0.515032	−	0.857171i	$-0.672220\pi$
$619$	−25.6277			−1.03006			−0.515032	+	0.857171i	$0.672220\pi$
$620$	−5.18614	−	1.11469i	−0.208280	−	0.0447671i
$621$		0			0
$622$		−	32.8713i		−	1.31802i
$623$		−	17.0256i		−	0.682114i
$624$		0			0
$625$	16.5584	+	18.7302i	0.662337	+	0.749206i
$626$	−3.86141			−0.154333
$627$		0			0
$628$		−	13.8564i		−	0.552931i
$629$	−50.9783			−2.03264
$630$		0			0
$631$	6.23369			0.248159			0.124080	−	0.992272i	$-0.460402\pi$
$631$	6.23369			0.248159			0.124080	+	0.992272i	$0.460402\pi$
$632$			9.74749i			0.387735i
$633$		0			0
$634$	27.2554			1.08245
$635$	−1.62772	+	7.57301i	−0.0645940	+	0.300526i
$636$		0			0
$637$		−	4.21872i		−	0.167152i
$638$		−	11.0371i		−	0.436964i
$639$		0			0
$640$	−5.69702	+	26.5055i	−0.225194	+	1.04772i
$641$	−3.48913			−0.137812			−0.0689061	−	0.997623i	$-0.521951\pi$
$641$	−3.48913			−0.137812			−0.0689061	+	0.997623i	$0.521951\pi$
$642$		0			0
$643$		−	4.75372i		−	0.187468i	−0.995597	−	0.0937342i	$-0.970120\pi$
$643$		−	4.75372i		−	0.187468i	0.995597	−	0.0937342i	$-0.0298804\pi$
$644$	−5.48913			−0.216302
$645$		0			0
$646$	34.9783			1.37620
$647$			27.4179i			1.07791i	0.842335	+	0.538954i	$0.181180\pi$
$647$			27.4179i			1.07791i	−0.842335	+	0.538954i	$0.818820\pi$
$648$		0			0
$649$	−4.74456			−0.186240
$650$	−7.41983	−	3.34408i	−0.291030	−	0.131165i
$651$		0			0
$652$		−	6.28339i		−	0.246077i
$653$		−	17.6155i		−	0.689346i	−0.938723	−	0.344673i	$-0.887990\pi$
$653$		−	17.6155i		−	0.689346i	0.938723	−	0.344673i	$-0.112010\pi$
$654$		0			0
$655$	8.74456	+	1.87953i	0.341678	+	0.0734392i
$656$	33.7228			1.31665
$657$		0			0
$658$			15.6261i			0.609170i
$659$	−41.3505			−1.61079			−0.805394	−	0.592740i	$-0.798046\pi$
$659$	−41.3505			−1.61079			−0.805394	+	0.592740i	$0.798046\pi$
$660$		0			0
$661$	−16.5109			−0.642199			−0.321099	−	0.947046i	$-0.604052\pi$
$661$	−16.5109			−0.642199			−0.321099	+	0.947046i	$0.604052\pi$
$662$		−	0.240051i		−	0.00932984i
$663$		0			0
$664$	28.9783			1.12457
$665$	−2.97825	+	13.8564i	−0.115492	+	0.537328i
$666$		0			0
$667$		−	3.46410i		−	0.134131i
$668$		−	9.80240i		−	0.379266i
$669$		0			0
$670$	−32.2337	−	6.92820i	−1.24530	−	0.267660i
$671$	−38.2337			−1.47600
$672$		0			0
$673$			3.40920i			0.131415i	0.997839	+	0.0657075i	$0.0209304\pi$
$673$			3.40920i			0.131415i	−0.997839	+	0.0657075i	$0.979070\pi$
$674$	43.7228			1.68414
$675$		0			0
$676$	−12.1168			−0.466032
$677$		−	0.699713i		−	0.0268922i	−0.999910	−	0.0134461i	$-0.995720\pi$
$677$		−	0.699713i		−	0.0268922i	0.999910	−	0.0134461i	$-0.00428015\pi$
$678$		0			0
$679$	−10.9783			−0.421307
$680$	−19.1168	−	4.10891i	−0.733098	−	0.157570i
$681$		0			0
$682$			26.1831i			1.00260i
$683$		−	31.8766i		−	1.21973i	−0.792507	−	0.609863i	$-0.791225\pi$
$683$		−	31.8766i		−	1.21973i	0.792507	−	0.609863i	$-0.208775\pi$
$684$		0			0
$685$	3.25544	−	15.1460i	0.124384	−	0.578700i
$686$	−31.5326			−1.20392
$687$		0			0
$688$			28.4674i			1.08531i
$689$	0.883156			0.0336456
$690$		0			0
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$		−	10.6873i		−	0.406269i
$693$		0			0
$694$	−34.4674			−1.30836
$695$	−19.1168	−	4.10891i	−0.725143	−	0.155860i
$696$		0			0
$697$			34.0511i			1.28978i
$698$		−	3.22405i		−	0.122032i
$699$		0			0
$700$	−3.25544	+	7.22316i	−0.123044	+	0.273010i
$701$	17.1168			0.646494			0.323247	−	0.946315i	$-0.395225\pi$
$701$	17.1168			0.646494			0.323247	+	0.946315i	$0.395225\pi$
$702$		0			0
$703$			40.3894i			1.52332i
$704$	6.37228			0.240164
$705$		0			0
$706$	−41.4891			−1.56146
$707$		−	23.3639i		−	0.878688i
$708$		0			0
$709$	−28.0951			−1.05513			−0.527567	−	0.849514i	$-0.676896\pi$
$709$	−28.0951			−1.05513			−0.527567	+	0.849514i	$0.676896\pi$
$710$	3.86141	−	17.9653i	0.144916	−	0.674226i
$711$		0			0
$712$		−	18.6101i		−	0.697444i
$713$			8.21782i			0.307760i
$714$		0			0
$715$	−2.81386	+	13.0916i	−0.105232	+	0.489597i
$716$	−16.7446			−0.625774
$717$		0			0
$718$			53.8960i			2.01138i
$719$	3.25544			0.121407			0.0607037	−	0.998156i	$-0.480666\pi$
$719$	3.25544			0.121407			0.0607037	+	0.998156i	$0.480666\pi$
$720$		0			0
$721$	−5.48913			−0.204426
$722$			5.19615i			0.193381i
$723$		0			0
$724$	13.8614			0.515155
$725$	−4.55842	−	2.05446i	−0.169296	−	0.0763006i
$726$		0			0
$727$		−	0.294954i		−	0.0109392i	−0.999985	−	0.00546961i	$-0.998259\pi$
$727$		−	0.294954i		−	0.0109392i	0.999985	−	0.00546961i	$-0.00174104\pi$
$728$			2.57924i			0.0955930i
$729$		0			0
$730$	26.2337	+	5.63858i	0.970952	+	0.208693i
$731$	−28.7446			−1.06316
$732$		0			0
$733$		−	27.7128i		−	1.02360i	−0.859106	−	0.511798i	$-0.828980\pi$
$733$		−	27.7128i		−	1.02360i	0.859106	−	0.511798i	$-0.171020\pi$
$734$	−18.0000			−0.664392
$735$		0			0
$736$	−18.0000			−0.663489
$737$			54.2458i			1.99817i
$738$		0			0
$739$	−9.62772			−0.354161			−0.177081	−	0.984196i	$-0.556665\pi$
$739$	−9.62772			−0.354161			−0.177081	+	0.984196i	$0.556665\pi$
$740$	−4.74456	+	22.0742i	−0.174414	+	0.811465i
$741$		0			0
$742$		−	2.57924i		−	0.0946869i
$743$		−	17.3205i		−	0.635428i	−0.948187	−	0.317714i	$-0.897085\pi$
$743$		−	17.3205i		−	0.635428i	0.948187	−	0.317714i	$-0.102915\pi$
$744$		0			0
$745$	−46.1644	−	9.92242i	−1.69133	−	0.363529i
$746$	9.35053			0.342347
$747$		0			0
$748$		−	32.1716i		−	1.17631i
$749$	−2.51087			−0.0917454
$750$		0			0
$751$	−20.4674			−0.746865			−0.373433	−	0.927657i	$-0.621819\pi$
$751$	−20.4674			−0.746865			−0.373433	+	0.927657i	$0.621819\pi$
$752$			28.4674i			1.03810i
$753$		0			0
$754$	1.62772			0.0592780
$755$	−20.7446	−	4.45877i	−0.754972	−	0.162271i
$756$		0			0
$757$		−	29.5923i		−	1.07555i	−0.843088	−	0.537776i	$-0.819265\pi$
$757$		−	29.5923i		−	1.07555i	0.843088	−	0.537776i	$-0.180735\pi$
$758$		−	37.2203i		−	1.35190i
$759$		0			0
$760$	−3.25544	+	15.1460i	−0.118087	+	0.549404i
$761$	−38.4674			−1.39444			−0.697221	−	0.716857i	$-0.745580\pi$
$761$	−38.4674			−1.39444			−0.697221	+	0.716857i	$0.745580\pi$
$762$		0			0
$763$			1.76972i			0.0640682i
$764$	−16.0000			−0.578860
$765$		0			0
$766$	−32.2337			−1.16465
$767$		−	0.699713i		−	0.0252652i
$768$		0			0
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$	38.2337	+	8.21782i	1.37785	+	0.296150i
$771$		0			0
$772$			6.92820i			0.249351i
$773$			51.6666i			1.85832i	0.369681	+	0.929159i	$0.379467\pi$
$773$			51.6666i			1.85832i	−0.369681	+	0.929159i	$0.620533\pi$
$774$		0			0
$775$	10.8139	+	4.87375i	0.388445	+	0.175070i
$776$	−12.0000			−0.430775
$777$		0			0
$778$			4.75372i			0.170429i
$779$	26.9783			0.966596
$780$		0			0
$781$	−30.2337			−1.08185
$782$		−	30.2921i		−	1.08324i
$783$		0			0
$784$	−22.4456			−0.801630
$785$	−6.51087	+	30.2921i	−0.232383	+	1.08117i
$786$		0			0
$787$			13.5615i			0.483414i	0.970349	+	0.241707i	$0.0777072\pi$
$787$			13.5615i			0.483414i	−0.970349	+	0.241707i	$0.922293\pi$
$788$			27.1229i			0.966214i
$789$		0			0
$790$	−4.58017	+	21.3094i	−0.162955	+	0.758154i
$791$	−13.9565			−0.496236
$792$		0			0
$793$		−	5.63858i		−	0.200232i
$794$	12.6060			0.447369
$795$		0			0
$796$	−9.48913			−0.336333
$797$		−	4.45877i		−	0.157938i	−0.996877	−	0.0789688i	$-0.974837\pi$
$797$		−	4.45877i		−	0.157938i	0.996877	−	0.0789688i	$-0.0251628\pi$
$798$		0			0
$799$	−28.7446			−1.01691
$800$	−10.6753	+	23.6863i	−0.377428	+	0.837436i
$801$		0			0
$802$		−	22.7190i		−	0.802237i
$803$		−	44.1485i		−	1.55797i
$804$		0			0
$805$	12.0000	+	2.57924i	0.422944	+	0.0909063i
$806$	−3.86141			−0.136012
$807$		0			0
$808$		−	25.5383i		−	0.898435i
$809$	1.25544			0.0441388			0.0220694	−	0.999756i	$-0.492975\pi$
$809$	1.25544			0.0441388			0.0220694	+	0.999756i	$0.492975\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		−	1.58457i		−	0.0556076i
$813$		0			0
$814$	111.446			3.90617
$815$	−2.95245	+	13.7364i	−0.103420	+	0.481164i
$816$		0			0
$817$			22.7739i			0.796759i
$818$		−	52.7710i		−	1.84510i
$819$		0			0
$820$	14.7446	+	3.16915i	0.514902	+	0.110671i
$821$	−11.6277			−0.405810			−0.202905	−	0.979198i	$-0.565038\pi$
$821$	−11.6277			−0.405810			−0.202905	+	0.979198i	$0.565038\pi$
$822$		0			0
$823$		−	33.1662i		−	1.15610i	−0.816000	−	0.578051i	$-0.803813\pi$
$823$		−	33.1662i		−	1.15610i	0.816000	−	0.578051i	$-0.196187\pi$
$824$	−6.00000			−0.209020
$825$		0			0
$826$	−2.04350			−0.0711024
$827$			33.4063i			1.16165i	0.814028	+	0.580825i	$0.197270\pi$
$827$			33.4063i			1.16165i	−0.814028	+	0.580825i	$0.802730\pi$
$828$		0			0
$829$	−26.0000			−0.903017			−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000			−0.903017			−0.451509	+	0.892267i	$0.649114\pi$
$830$	63.3505	+	13.6164i	2.19893	+	0.472631i
$831$		0			0
$832$			0.939764i			0.0325804i
$833$		−	22.6641i		−	0.785266i
$834$		0			0
$835$	−4.60597	+	21.4294i	−0.159396	+	0.741596i
$836$	−25.4891			−0.881560
$837$		0			0
$838$		−	42.8588i		−	1.48053i
$839$	−13.6277			−0.470481			−0.235241	−	0.971937i	$-0.575588\pi$
$839$	−13.6277			−0.470481			−0.235241	+	0.971937i	$0.575588\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$			36.3354i			1.25220i
$843$		0			0
$844$	11.1168			0.382658
$845$	26.4891	+	5.69349i	0.911254	+	0.195862i
$846$		0			0
$847$		−	46.9128i		−	1.61194i
$848$		−	4.69882i		−	0.161358i
$849$		0			0
$850$	−39.8614	−	17.9653i	−1.36723	−	0.616205i
$851$	34.9783			1.19904
$852$		0			0
$853$		−	5.63858i		−	0.193061i	−0.995330	−	0.0965307i	$-0.969225\pi$
$853$		−	5.63858i		−	0.193061i	0.995330	−	0.0965307i	$-0.0307746\pi$
$854$	−16.4674			−0.563502
$855$		0			0
$856$	−2.74456			−0.0938072
$857$		−	29.9422i		−	1.02281i	−0.859341	−	0.511403i	$-0.829126\pi$
$857$		−	29.9422i		−	1.02281i	0.859341	−	0.511403i	$-0.170874\pi$
$858$		0			0
$859$	−11.3940			−0.388759			−0.194380	−	0.980926i	$-0.562269\pi$
$859$	−11.3940			−0.388759			−0.194380	+	0.980926i	$0.562269\pi$
$860$	−2.67527	+	12.4468i	−0.0912258	+	0.424431i
$861$		0			0
$862$		−	19.4950i		−	0.664002i
$863$		−	6.63325i		−	0.225798i	−0.993606	−	0.112899i	$-0.963986\pi$
$863$		−	6.63325i		−	0.225798i	0.993606	−	0.112899i	$-0.0360137\pi$
$864$		0			0
$865$	−5.02175	+	23.3639i	−0.170745	+	0.794395i
$866$	25.0217			0.850274
$867$		0			0
$868$			3.75906i			0.127591i
$869$	35.8614			1.21651
$870$		0			0
$871$	−8.00000			−0.271070
$872$			1.93443i			0.0655081i
$873$		0			0
$874$	−24.0000			−0.811812
$875$	10.5109	−	14.2612i	0.355332	−	0.482115i
$876$		0			0
$877$			41.3292i			1.39559i	0.716299	+	0.697793i	$0.245835\pi$
$877$			41.3292i			1.39559i	−0.716299	+	0.697793i	$0.754165\pi$
$878$			52.3663i			1.76728i
$879$		0			0
$880$	69.6535	+	14.9711i	2.34802	+	0.504676i
$881$	8.97825			0.302485			0.151242	−	0.988497i	$-0.451673\pi$
$881$	8.97825			0.302485			0.151242	+	0.988497i	$0.451673\pi$
$882$		0			0
$883$		−	18.6101i		−	0.626281i	−0.949707	−	0.313140i	$-0.898619\pi$
$883$		−	18.6101i		−	0.626281i	0.949707	−	0.313140i	$-0.101381\pi$
$884$	4.74456			0.159577
$885$		0			0
$886$	12.5109			0.420311
$887$		−	32.2265i		−	1.08206i	−0.841003	−	0.541030i	$-0.818035\pi$
$887$		−	32.2265i		−	1.08206i	0.841003	−	0.541030i	$-0.181965\pi$
$888$		0			0
$889$	5.48913			0.184099
$890$	8.74456	−	40.6844i	0.293118	−	1.36374i
$891$		0			0
$892$		−	10.3923i		−	0.347960i
$893$			22.7739i			0.762101i
$894$		0			0
$895$	36.6060	+	7.86797i	1.22360	+	0.262997i
$896$	19.2119			0.641826
$897$		0			0
$898$		−	59.6992i		−	1.99219i
$899$	−2.37228			−0.0791200
$900$		0			0
$901$	4.74456			0.158064
$902$		−	74.4405i		−	2.47860i
$903$		0			0
$904$	−15.2554			−0.507388
$905$	−30.3030	−	6.51322i	−1.00731	−	0.216507i
$906$		0			0
$907$			33.1662i			1.10127i	0.834747	+	0.550634i	$0.185614\pi$
$907$			33.1662i			1.10127i	−0.834747	+	0.550634i	$0.814386\pi$
$908$			13.5615i			0.450053i
$909$		0			0
$910$	−1.21194	+	5.63858i	−0.0401754	+	0.186917i
$911$	8.88316			0.294312			0.147156	−	0.989113i	$-0.452988\pi$
$911$	8.88316			0.294312			0.147156	+	0.989113i	$0.452988\pi$
$912$		0			0
$913$		−	106.612i		−	3.52835i
$914$	−4.46738			−0.147768
$915$		0			0
$916$	−1.25544			−0.0414808
$917$		−	6.33830i		−	0.209309i
$918$		0			0
$919$	−17.7663			−0.586057			−0.293028	−	0.956104i	$-0.594663\pi$
$919$	−17.7663			−0.586057			−0.293028	+	0.956104i	$0.594663\pi$
$920$	13.1168	+	2.81929i	0.432450	+	0.0929493i
$921$		0			0
$922$			7.81306i			0.257310i
$923$		−	4.45877i		−	0.146762i
$924$		0			0
$925$	20.7446	−	46.0280i	0.682077	−	1.51339i
$926$	35.4891			1.16625
$927$		0			0
$928$		−	5.19615i		−	0.170572i
$929$	−24.5109			−0.804176			−0.402088	−	0.915601i	$-0.631715\pi$
$929$	−24.5109			−0.804176			−0.402088	+	0.915601i	$0.631715\pi$
$930$		0			0
$931$	−17.9565			−0.588501
$932$			16.0858i			0.526908i
$933$		0			0
$934$	68.8397			2.25250
$935$	−15.1168	+	70.3316i	−0.494374	+	2.30009i
$936$		0			0
$937$		−	21.3745i		−	0.698275i	−0.937071	−	0.349138i	$-0.886475\pi$
$937$		−	21.3745i		−	0.698275i	0.937071	−	0.349138i	$-0.113525\pi$
$938$			23.3639i			0.762857i
$939$		0			0
$940$	−2.67527	+	12.4468i	−0.0872576	+	0.405969i
$941$	−19.6277			−0.639845			−0.319923	−	0.947444i	$-0.603657\pi$
$941$	−19.6277			−0.639845			−0.319923	+	0.947444i	$0.603657\pi$
$942$		0			0
$943$		−	23.3639i		−	0.760832i
$944$	−3.72281			−0.121167
$945$		0			0
$946$	62.8397			2.04309
$947$		−	41.0342i		−	1.33343i	−0.745311	−	0.666716i	$-0.767699\pi$
$947$		−	41.0342i		−	1.33343i	0.745311	−	0.666716i	$-0.232301\pi$
$948$		0			0
$949$	6.51087			0.211352
$950$	−14.2337	+	31.5817i	−0.461802	+	1.02464i
$951$		0			0
$952$			13.8564i			0.449089i
$953$		−	40.0395i		−	1.29701i	−0.761211	−	0.648504i	$-0.775395\pi$
$953$		−	40.0395i		−	1.29701i	0.761211	−	0.648504i	$-0.224605\pi$
$954$		0			0
$955$	34.9783	+	7.51811i	1.13187	+	0.243280i
$956$	6.23369			0.201612
$957$		0			0
$958$			17.9653i			0.580433i
$959$	−10.9783			−0.354506
$960$		0			0
$961$	−25.3723			−0.818461
$962$			16.4356i			0.529907i
$963$		0			0
$964$	−12.3723			−0.398484
$965$	3.25544	−	15.1460i	0.104796	−	0.487568i
$966$		0			0
$967$			4.99377i			0.160589i	0.996771	+	0.0802945i	$0.0255861\pi$
$967$			4.99377i			0.160589i	−0.996771	+	0.0802945i	$0.974414\pi$
$968$		−	51.2790i		−	1.64817i
$969$		0			0
$970$	−26.2337	−	5.63858i	−0.842313	−	0.181044i
$971$	−38.9783			−1.25087			−0.625436	−	0.780276i	$-0.715079\pi$
$971$	−38.9783			−1.25087			−0.625436	+	0.780276i	$0.715079\pi$
$972$		0			0
$973$			13.8564i			0.444216i
$974$	−15.7663			−0.505185
$975$		0			0
$976$	−30.0000			−0.960277
$977$			8.56768i			0.274104i	0.990564	+	0.137052i	$0.0437628\pi$
$977$			8.56768i			0.274104i	−0.990564	+	0.137052i	$0.956237\pi$
$978$		0			0
$979$	−68.4674			−2.18823
$980$	−9.81386	−	2.10936i	−0.313492	−	0.0673810i
$981$		0			0
$982$		−	30.5321i		−	0.974319i
$983$		−	56.1802i		−	1.79187i	−0.444184	−	0.895936i	$-0.646506\pi$
$983$		−	56.1802i		−	1.79187i	0.444184	−	0.895936i	$-0.353494\pi$
$984$		0			0
$985$	12.7446	−	59.2945i	0.406076	−	1.88928i
$986$	8.74456			0.278484
$987$		0			0
$988$		−	3.75906i		−	0.119591i
$989$	19.7228			0.627149
$990$		0			0
$991$	28.7446			0.913101			0.456551	−	0.889697i	$-0.349085\pi$
$991$	28.7446			0.913101			0.456551	+	0.889697i	$0.349085\pi$
$992$			12.3267i			0.391374i
$993$		0			0
$994$	−13.0217			−0.413025
$995$	20.7446	+	4.45877i	0.657647	+	0.141352i
$996$		0			0
$997$		−	2.57924i		−	0.0816854i	−0.999166	−	0.0408427i	$-0.986996\pi$
$997$		−	2.57924i		−	0.0816854i	0.999166	−	0.0408427i	$-0.0130042\pi$
$998$			29.0024i			0.918056i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.e.784.2		4
3.2	odd	2		145.2.b.a.59.4	yes	4
5.2	odd	4		6525.2.a.bk.1.4		4
5.3	odd	4		6525.2.a.bk.1.1		4
5.4	even	2	inner	1305.2.c.e.784.4		4
12.11	even	2		2320.2.d.c.929.1		4
15.2	even	4		725.2.a.g.1.2		4
15.8	even	4		725.2.a.g.1.3		4
15.14	odd	2		145.2.b.a.59.1	✓	4
60.59	even	2		2320.2.d.c.929.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.b.a.59.1	✓	4	15.14	odd	2
145.2.b.a.59.4	yes	4	3.2	odd	2
725.2.a.g.1.2		4	15.2	even	4
725.2.a.g.1.3		4	15.8	even	4
1305.2.c.e.784.2		4	1.1	even	1	trivial
1305.2.c.e.784.4		4	5.4	even	2	inner
2320.2.d.c.929.1		4	12.11	even	2
2320.2.d.c.929.4		4	60.59	even	2
6525.2.a.bk.1.1		4	5.3	odd	4
6525.2.a.bk.1.4		4	5.2	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.73205i q^{2} -1.00000 q^{4} +(2.18614 + 0.469882i) q^{5} -1.58457i q^{7} -1.73205i q^{8} +(0.813859 - 3.78651i) q^{10} -6.37228 q^{11} -0.939764i q^{13} -2.74456 q^{14} -5.00000 q^{16} -5.04868i q^{17} -4.00000 q^{19} +(-2.18614 - 0.469882i) q^{20} +11.0371i q^{22} +3.46410i q^{23} +(4.55842 + 2.05446i) q^{25} -1.62772 q^{26} +1.58457i q^{28} -1.00000 q^{29} +2.37228 q^{31} +5.19615i q^{32} -8.74456 q^{34} +(0.744563 - 3.46410i) q^{35} -10.0974i q^{37} +6.92820i q^{38} +(0.813859 - 3.78651i) q^{40} -6.74456 q^{41} -5.69349i q^{43} +6.37228 q^{44} +6.00000 q^{46} -5.69349i q^{47} +4.48913 q^{49} +(3.55842 - 7.89542i) q^{50} +0.939764i q^{52} +0.939764i q^{53} +(-13.9307 - 2.99422i) q^{55} -2.74456 q^{56} +1.73205i q^{58} +0.744563 q^{59} +6.00000 q^{61} -4.10891i q^{62} -1.00000 q^{64} +(0.441578 - 2.05446i) q^{65} -8.51278i q^{67} +5.04868i q^{68} +(-6.00000 - 1.28962i) q^{70} +4.74456 q^{71} +6.92820i q^{73} -17.4891 q^{74} +4.00000 q^{76} +10.0974i q^{77} -5.62772 q^{79} +(-10.9307 - 2.34941i) q^{80} +11.6819i q^{82} +16.7306i q^{83} +(2.37228 - 11.0371i) q^{85} -9.86141 q^{86} +11.0371i q^{88} +10.7446 q^{89} -1.48913 q^{91} -3.46410i q^{92} -9.86141 q^{94} +(-8.74456 - 1.87953i) q^{95} -6.92820i q^{97} -7.77539i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 3 q^{5} + 9 q^{10} - 14 q^{11} + 12 q^{14} - 20 q^{16} - 16 q^{19} - 3 q^{20} + q^{25} - 18 q^{26} - 4 q^{29} - 2 q^{31} - 12 q^{34} - 20 q^{35} + 9 q^{40} - 4 q^{41} + 14 q^{44} + 24 q^{46}+ \cdots - 12 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 + 3 * q^5 + 9 * q^10 - 14 * q^11 + 12 * q^14 - 20 * q^16 - 16 * q^19 - 3 * q^20 + q^25 - 18 * q^26 - 4 * q^29 - 2 * q^31 - 12 * q^34 - 20 * q^35 + 9 * q^40 - 4 * q^41 + 14 * q^44 + 24 * q^46 - 28 * q^49 - 3 * q^50 - 27 * q^55 + 12 * q^56 - 20 * q^59 + 24 * q^61 - 4 * q^64 + 19 * q^65 - 24 * q^70 - 4 * q^71 - 24 * q^74 + 16 * q^76 - 34 * q^79 - 15 * q^80 - 2 * q^85 + 18 * q^86 + 20 * q^89 + 40 * q^91 + 18 * q^94 - 12 * q^95

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