LMFDB - Embedded newform 960.3.c.k.449.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,3,Mod(449,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("960.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.c (of order $2$, degree $1$, not 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:	$26.1581053786$
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} + 34x^{10} + 305x^{8} + 616x^{6} + 305x^{4} + 34x^{2} + 1 $ x^12 + 34x^10 + 305x^8 + 616x^6 + 305x^4 + 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.10
Root			$0.304307i$ of defining polynomial
Character	$\chi$	$=$	960.449
Dual form			960.3.c.k.449.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.49147 + 1.67109i) q^{3} +(4.19906 + 2.71439i) q^{5} +12.7692i q^{7} +(3.41489 + 8.32698i) q^{9} +O(q^{10})$	\(q+(2.49147 + 1.67109i) q^{3} +(4.19906 + 2.71439i) q^{5} +12.7692i q^{7} +(3.41489 + 8.32698i) q^{9} -12.6296i q^{11} +7.44085i q^{13} +(5.92583 + 13.7799i) q^{15} -14.0550 q^{17} +31.0176 q^{19} +(-21.3386 + 31.8142i) q^{21} +7.50423 q^{23} +(10.2641 + 22.7958i) q^{25} +(-5.40707 + 26.4530i) q^{27} -15.7298i q^{29} -20.4893 q^{31} +(21.1053 - 31.4663i) q^{33} +(-34.6607 + 53.6186i) q^{35} +12.9261i q^{37} +(-12.4344 + 18.5387i) q^{39} -13.8451i q^{41} -30.0797i q^{43} +(-8.26340 + 44.2348i) q^{45} +20.2570 q^{47} -114.053 q^{49} +(-35.0176 - 23.4872i) q^{51} -29.1185 q^{53} +(34.2817 - 53.0324i) q^{55} +(77.2795 + 51.8333i) q^{57} -47.6333i q^{59} -43.0176 q^{61} +(-106.329 + 43.6054i) q^{63} +(-20.1974 + 31.2445i) q^{65} -0.630153i q^{67} +(18.6966 + 12.5403i) q^{69} -90.4047i q^{71} +46.2193i q^{73} +(-12.5211 + 73.9474i) q^{75} +161.270 q^{77} +37.9610 q^{79} +(-57.6771 + 56.8713i) q^{81} +80.2267 q^{83} +(-59.0176 - 38.1507i) q^{85} +(26.2860 - 39.1904i) q^{87} +140.923i q^{89} -95.0138 q^{91} +(-51.0486 - 34.2396i) q^{93} +(130.245 + 84.1939i) q^{95} -10.3429i q^{97} +(105.166 - 43.1286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{9}+O(q^{10}) $ 12 * q + 8 * q^9	$ 12 q + 8 q^{9} + 16 q^{15} - 4 q^{21} + 36 q^{25} - 48 q^{31} - 128 q^{39} + 68 q^{45} - 252 q^{49} - 48 q^{51} - 48 q^{55} - 144 q^{61} - 268 q^{69} - 304 q^{75} + 432 q^{79} - 188 q^{81} - 336 q^{85} + 560 q^{99}+O(q^{100}) $ 12 * q + 8 * q^9 + 16 * q^15 - 4 * q^21 + 36 * q^25 - 48 * q^31 - 128 * q^39 + 68 * q^45 - 252 * q^49 - 48 * q^51 - 48 * q^55 - 144 * q^61 - 268 * q^69 - 304 * q^75 + 432 * q^79 - 188 * q^81 - 336 * q^85 + 560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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			0
$2$		0			0
$3$	2.49147	+	1.67109i	0.830491	+	0.557032i
$3$	2.49147	+	1.67109i	0.830491	+	0.557032i
$4$		0			0
$5$	4.19906	+	2.71439i	0.839811	+	0.542879i
$5$	4.19906	+	2.71439i	0.839811	+	0.542879i
$6$		0			0
$7$			12.7692i			1.82417i	0.409998	+	0.912086i	$0.365529\pi$
$7$			12.7692i			1.82417i	−0.409998	+	0.912086i	$0.634471\pi$
$8$		0			0
$9$	3.41489	+	8.32698i	0.379432	+	0.925220i
$10$		0			0
$11$		−	12.6296i		−	1.14815i	−0.818804	−	0.574073i	$-0.805363\pi$
$11$		−	12.6296i		−	1.14815i	0.818804	−	0.574073i	$-0.194637\pi$
$12$		0			0
$13$			7.44085i			0.572373i	0.958174	+	0.286187i	$0.0923877\pi$
$13$			7.44085i			0.572373i	−0.958174	+	0.286187i	$0.907612\pi$
$14$		0			0
$15$	5.92583	+	13.7799i	0.395055	+	0.918657i
$16$		0			0
$17$	−14.0550			−0.826763			−0.413381	−	0.910558i	$-0.635652\pi$
$17$	−14.0550			−0.826763			−0.413381	+	0.910558i	$0.635652\pi$
$18$		0			0
$19$	31.0176			1.63250			0.816252	−	0.577696i	$-0.196048\pi$
$19$	31.0176			1.63250			0.816252	+	0.577696i	$0.196048\pi$
$20$		0			0
$21$	−21.3386	+	31.8142i	−1.01612	+	1.51496i
$22$		0			0
$23$	7.50423			0.326271			0.163135	−	0.986604i	$-0.447839\pi$
$23$	7.50423			0.326271			0.163135	+	0.986604i	$0.447839\pi$
$24$		0			0
$25$	10.2641	+	22.7958i	0.410565	+	0.911831i
$26$		0			0
$27$	−5.40707	+	26.4530i	−0.200262	+	0.979742i
$28$		0			0
$29$		−	15.7298i		−	0.542407i	−0.962522	−	0.271204i	$-0.912578\pi$
$29$		−	15.7298i		−	0.542407i	0.962522	−	0.271204i	$-0.0874217\pi$
$30$		0			0
$31$	−20.4893			−0.660945			−0.330473	−	0.943816i	$-0.607208\pi$
$31$	−20.4893			−0.660945			−0.330473	+	0.943816i	$0.607208\pi$
$32$		0			0
$33$	21.1053	−	31.4663i	0.639553	−	0.953525i
$34$		0			0
$35$	−34.6607	+	53.6186i	−0.990305	+	1.53196i
$36$		0			0
$37$			12.9261i			0.349355i	0.984626	+	0.174677i	$0.0558883\pi$
$37$			12.9261i			0.349355i	−0.984626	+	0.174677i	$0.944112\pi$
$38$		0			0
$39$	−12.4344	+	18.5387i	−0.318830	+	0.475351i
$40$		0			0
$41$		−	13.8451i		−	0.337685i	−0.985643	−	0.168843i	$-0.945997\pi$
$41$		−	13.8451i		−	0.337685i	0.985643	−	0.168843i	$-0.0540029\pi$
$42$		0			0
$43$		−	30.0797i		−	0.699528i	−0.936838	−	0.349764i	$-0.886262\pi$
$43$		−	30.0797i		−	0.699528i	0.936838	−	0.349764i	$-0.113738\pi$
$44$		0			0
$45$	−8.26340	+	44.2348i	−0.183631	+	0.982995i
$46$		0			0
$47$	20.2570			0.431000			0.215500	−	0.976504i	$-0.430862\pi$
$47$	20.2570			0.431000			0.215500	+	0.976504i	$0.430862\pi$
$48$		0			0
$49$	−114.053			−2.32761
$50$		0			0
$51$	−35.0176	−	23.4872i	−0.686619	−	0.460533i
$52$		0			0
$53$	−29.1185			−0.549406			−0.274703	−	0.961529i	$-0.588580\pi$
$53$	−29.1185			−0.549406			−0.274703	+	0.961529i	$0.588580\pi$
$54$		0			0
$55$	34.2817	−	53.0324i	0.623304	−	0.964226i
$56$		0			0
$57$	77.2795	+	51.8333i	1.35578	+	0.909356i
$58$		0			0
$59$		−	47.6333i		−	0.807344i	−0.914904	−	0.403672i	$-0.867734\pi$
$59$		−	47.6333i		−	0.807344i	0.914904	−	0.403672i	$-0.132266\pi$
$60$		0			0
$61$	−43.0176			−0.705206			−0.352603	−	0.935773i	$-0.614703\pi$
$61$	−43.0176			−0.705206			−0.352603	+	0.935773i	$0.614703\pi$
$62$		0			0
$63$	−106.329	+	43.6054i	−1.68776	+	0.692149i
$64$		0			0
$65$	−20.1974	+	31.2445i	−0.310729	+	0.480685i
$66$		0			0
$67$		−	0.630153i		−	0.00940527i	−0.999989	−	0.00470264i	$-0.998503\pi$
$67$		−	0.630153i		−	0.00940527i	0.999989	−	0.00470264i	$-0.00149690\pi$
$68$		0			0
$69$	18.6966	+	12.5403i	0.270965	+	0.181743i
$70$		0			0
$71$		−	90.4047i		−	1.27330i	−0.771151	−	0.636652i	$-0.780319\pi$
$71$		−	90.4047i		−	1.27330i	0.771151	−	0.636652i	$-0.219681\pi$
$72$		0			0
$73$			46.2193i			0.633140i	0.948569	+	0.316570i	$0.102531\pi$
$73$			46.2193i			0.633140i	−0.948569	+	0.316570i	$0.897469\pi$
$74$		0			0
$75$	−12.5211	+	73.9474i	−0.166948	+	0.985966i
$76$		0			0
$77$	161.270			2.09442
$78$		0			0
$79$	37.9610			0.480519			0.240260	−	0.970709i	$-0.422767\pi$
$79$	37.9610			0.480519			0.240260	+	0.970709i	$0.422767\pi$
$80$		0			0
$81$	−57.6771	+	56.8713i	−0.712063	+	0.702115i
$82$		0			0
$83$	80.2267			0.966587			0.483294	−	0.875458i	$-0.339440\pi$
$83$	80.2267			0.966587			0.483294	+	0.875458i	$0.339440\pi$
$84$		0			0
$85$	−59.0176	−	38.1507i	−0.694324	−	0.448832i
$86$		0			0
$87$	26.2860	−	39.1904i	0.302138	−	0.450465i
$88$		0			0
$89$			140.923i			1.58341i	0.610907	+	0.791703i	$0.290805\pi$
$89$			140.923i			1.58341i	−0.610907	+	0.791703i	$0.709195\pi$
$90$		0			0
$91$	−95.0138			−1.04411
$92$		0			0
$93$	−51.0486	−	34.2396i	−0.548909	−	0.368168i
$94$		0			0
$95$	130.245	+	84.1939i	1.37100	+	0.886252i
$96$		0			0
$97$		−	10.3429i		−	0.106628i	−0.998578	−	0.0533138i	$-0.983022\pi$
$97$		−	10.3429i		−	0.106628i	0.998578	−	0.0533138i	$-0.0169784\pi$
$98$		0			0
$99$	105.166	−	43.1286i	1.06229	−	0.435643i
$100$		0			0
$101$		−	19.2739i		−	0.190830i	−0.995438	−	0.0954152i	$-0.969582\pi$
$101$		−	19.2739i		−	0.190830i	0.995438	−	0.0954152i	$-0.0304179\pi$
$102$		0			0
$103$			6.97008i			0.0676707i	0.999427	+	0.0338353i	$0.0107722\pi$
$103$			6.97008i			0.0676707i	−0.999427	+	0.0338353i	$0.989228\pi$
$104$		0			0
$105$	−175.958	+	75.6682i	−1.67579	+	0.720649i
$106$		0			0
$107$	73.7731			0.689468			0.344734	−	0.938700i	$-0.387969\pi$
$107$	73.7731			0.689468			0.344734	+	0.938700i	$0.387969\pi$
$108$		0			0
$109$	−74.0314			−0.679187			−0.339593	−	0.940572i	$-0.610289\pi$
$109$	−74.0314			−0.679187			−0.339593	+	0.940572i	$0.610289\pi$
$110$		0			0
$111$	−21.6008	+	32.2051i	−0.194602	+	0.290136i
$112$		0			0
$113$	147.215			1.30279			0.651394	−	0.758739i	$-0.274184\pi$
$113$	147.215			1.30279			0.651394	+	0.758739i	$0.274184\pi$
$114$		0			0
$115$	31.5107	+	20.3694i	0.274006	+	0.177126i
$116$		0			0
$117$	−61.9598	+	25.4096i	−0.529571	+	0.217176i
$118$		0			0
$119$		−	179.471i		−	1.50816i
$120$		0			0
$121$	−38.5069			−0.318239
$122$		0			0
$123$	23.1364	−	34.4947i	0.188101	−	0.280444i
$124$		0			0
$125$	−18.7770	+	123.582i	−0.150216	+	0.988653i
$126$		0			0
$127$		−	90.0171i		−	0.708796i	−0.935095	−	0.354398i	$-0.884686\pi$
$127$		−	90.0171i		−	0.708796i	0.935095	−	0.354398i	$-0.115314\pi$
$128$		0			0
$129$	50.2660	−	74.9428i	0.389659	−	0.580952i
$130$		0			0
$131$			11.2911i			0.0861917i	0.999071	+	0.0430958i	$0.0137221\pi$
$131$			11.2911i			0.0861917i	−0.999071	+	0.0430958i	$0.986278\pi$
$132$		0			0
$133$			396.070i			2.97797i
$134$		0			0
$135$	−94.5086	+	96.4009i	−0.700063	+	0.714081i
$136$		0			0
$137$	−22.4905			−0.164164			−0.0820822	−	0.996626i	$-0.526157\pi$
$137$	−22.4905			−0.164164			−0.0820822	+	0.996626i	$0.526157\pi$
$138$		0			0
$139$	−91.0955			−0.655363			−0.327682	−	0.944788i	$-0.606267\pi$
$139$	−91.0955			−0.655363			−0.327682	+	0.944788i	$0.606267\pi$
$140$		0			0
$141$	50.4698	+	33.8514i	0.357942	+	0.240081i
$142$		0			0
$143$	93.9750			0.657168
$144$		0			0
$145$	42.6969	−	66.0504i	0.294461	−	0.455520i
$146$		0			0
$147$	−284.159	−	190.593i	−1.93306	−	1.29655i
$148$		0			0
$149$			228.330i			1.53242i	0.642593	+	0.766208i	$0.277859\pi$
$149$			228.330i			1.53242i	−0.642593	+	0.766208i	$0.722141\pi$
$150$		0			0
$151$	−74.0390			−0.490324			−0.245162	−	0.969482i	$-0.578841\pi$
$151$	−74.0390			−0.490324			−0.245162	+	0.969482i	$0.578841\pi$
$152$		0			0
$153$	−47.9961	−	117.035i	−0.313700	−	0.764937i
$154$		0			0
$155$	−86.0358	−	55.6161i	−0.555069	−	0.358813i
$156$		0			0
$157$		−	245.742i		−	1.56523i	−0.622504	−	0.782616i	$-0.713885\pi$
$157$		−	245.742i		−	1.56523i	0.622504	−	0.782616i	$-0.286115\pi$
$158$		0			0
$159$	−72.5481	−	48.6598i	−0.456277	−	0.306037i
$160$		0			0
$161$			95.8231i			0.595175i
$162$		0			0
$163$		−	60.1570i		−	0.369061i	−0.982827	−	0.184531i	$-0.940924\pi$
$163$		−	60.1570i		−	0.369061i	0.982827	−	0.184531i	$-0.0590765\pi$
$164$		0			0
$165$	174.034	−	74.8409i	1.05475	−	0.453581i
$166$		0			0
$167$	−81.5664			−0.488421			−0.244211	−	0.969722i	$-0.578529\pi$
$167$	−81.5664			−0.488421			−0.244211	+	0.969722i	$0.578529\pi$
$168$		0			0
$169$	113.634			0.672389
$170$		0			0
$171$	105.921	+	258.283i	0.619424	+	1.51043i
$172$		0			0
$173$	−167.064			−0.965687			−0.482843	−	0.875707i	$-0.660396\pi$
$173$	−167.064			−0.965687			−0.482843	+	0.875707i	$0.660396\pi$
$174$		0			0
$175$	−291.084	+	131.065i	−1.66334	+	0.748942i
$176$		0			0
$177$	79.5997	−	118.677i	0.449716	−	0.670492i
$178$		0			0
$179$		−	270.104i		−	1.50896i	−0.656322	−	0.754481i	$-0.727889\pi$
$179$		−	270.104i		−	1.50896i	0.656322	−	0.754481i	$-0.272111\pi$
$180$		0			0
$181$	−86.9786			−0.480545			−0.240272	−	0.970705i	$-0.577237\pi$
$181$	−86.9786			−0.480545			−0.240272	+	0.970705i	$0.577237\pi$
$182$		0			0
$183$	−107.177	−	71.8865i	−0.585668	−	0.392822i
$184$		0			0
$185$	−35.0866	+	54.2776i	−0.189657	+	0.293392i
$186$		0			0
$187$			177.509i			0.949244i
$188$		0			0
$189$	−337.785	−	69.0440i	−1.78722	−	0.365312i
$190$		0			0
$191$			302.223i			1.58232i	0.611610	+	0.791159i	$0.290522\pi$
$191$			302.223i			1.58232i	−0.611610	+	0.791159i	$0.709478\pi$
$192$		0			0
$193$			306.780i			1.58953i	0.606916	+	0.794766i	$0.292407\pi$
$193$			306.780i			1.58953i	−0.606916	+	0.794766i	$0.707593\pi$
$194$		0			0
$195$	−102.534	+	44.0932i	−0.525815	+	0.226119i
$196$		0			0
$197$	289.956			1.47186			0.735930	−	0.677058i	$-0.236745\pi$
$197$	289.956			1.47186			0.735930	+	0.677058i	$0.236745\pi$
$198$		0			0
$199$	382.595			1.92259			0.961293	−	0.275527i	$-0.0888522\pi$
$199$	382.595			1.92259			0.961293	+	0.275527i	$0.0888522\pi$
$200$		0			0
$201$	1.05305	−	1.57001i	0.00523903	−	0.00781100i
$202$		0			0
$203$	200.857			0.989445
$204$		0			0
$205$	37.5810	−	58.1363i	0.183322	−	0.283592i
$206$		0			0
$207$	25.6261	+	62.4876i	0.123798	+	0.301872i
$208$		0			0
$209$		−	391.740i		−	1.87435i
$210$		0			0
$211$	321.115			1.52187			0.760937	−	0.648826i	$-0.224740\pi$
$211$	321.115			1.52187			0.760937	+	0.648826i	$0.224740\pi$
$212$		0			0
$213$	151.075	−	225.241i	0.709271	−	1.05747i
$214$		0			0
$215$	81.6482	−	126.306i	0.379759	−	0.587471i
$216$		0			0
$217$		−	261.632i		−	1.20568i
$218$		0			0
$219$	−77.2368	+	115.154i	−0.352679	+	0.525818i
$220$		0			0
$221$		−	104.581i		−	0.473217i
$222$		0			0
$223$			292.432i			1.31135i	0.755042	+	0.655676i	$0.227616\pi$
$223$			292.432i			1.31135i	−0.755042	+	0.655676i	$0.772384\pi$
$224$		0			0
$225$	−154.769	+	163.314i	−0.687863	+	0.725841i
$226$		0			0
$227$	370.155			1.63064			0.815319	−	0.579013i	$-0.196562\pi$
$227$	370.155			1.63064			0.815319	+	0.579013i	$0.196562\pi$
$228$		0			0
$229$	381.985			1.66806			0.834028	−	0.551722i	$-0.186029\pi$
$229$	381.985			1.66806			0.834028	+	0.551722i	$0.186029\pi$
$230$		0			0
$231$	401.800	+	269.498i	1.73939	+	1.16666i
$232$		0			0
$233$	−144.262			−0.619150			−0.309575	−	0.950875i	$-0.600187\pi$
$233$	−144.262			−0.619150			−0.309575	+	0.950875i	$0.600187\pi$
$234$		0			0
$235$	85.0603	+	54.9855i	0.361959	+	0.233981i
$236$		0			0
$237$	94.5789	+	63.4365i	0.399067	+	0.267665i
$238$		0			0
$239$		−	249.478i		−	1.04384i	−0.852994	−	0.521921i	$-0.825216\pi$
$239$		−	249.478i		−	1.04384i	0.852994	−	0.521921i	$-0.174784\pi$
$240$		0			0
$241$	30.4541			0.126366			0.0631829	−	0.998002i	$-0.479875\pi$
$241$	30.4541			0.126366			0.0631829	+	0.998002i	$0.479875\pi$
$242$		0			0
$243$	−238.738	+	45.3095i	−0.982463	+	0.186459i
$244$		0			0
$245$	−478.914	−	309.584i	−1.95475	−	1.26361i
$246$		0			0
$247$			230.797i			0.934401i
$248$		0			0
$249$	199.883	+	134.066i	0.802742	+	0.538420i
$250$		0			0
$251$			68.9183i			0.274575i	0.990531	+	0.137287i	$0.0438384\pi$
$251$			68.9183i			0.274575i	−0.990531	+	0.137287i	$0.956162\pi$
$252$		0			0
$253$		−	94.7755i		−	0.374607i
$254$		0			0
$255$	−83.2873	−	193.675i	−0.326617	−	0.759512i
$256$		0			0
$257$	362.374			1.41002			0.705009	−	0.709199i	$-0.250943\pi$
$257$	362.374			1.41002			0.705009	+	0.709199i	$0.250943\pi$
$258$		0			0
$259$	−165.057			−0.637284
$260$		0			0
$261$	130.982	−	53.7155i	0.501846	−	0.205807i
$262$		0			0
$263$	−23.4485			−0.0891580			−0.0445790	−	0.999006i	$-0.514195\pi$
$263$	−23.4485			−0.0891580			−0.0445790	+	0.999006i	$0.514195\pi$
$264$		0			0
$265$	−122.270	−	79.0391i	−0.461397	−	0.298261i
$266$		0			0
$267$	−235.496	+	351.106i	−0.882007	+	1.31500i
$268$		0			0
$269$		−	396.738i		−	1.47486i	−0.675421	−	0.737432i	$-0.736038\pi$
$269$		−	396.738i		−	1.47486i	0.675421	−	0.737432i	$-0.263962\pi$
$270$		0			0
$271$	−143.926			−0.531092			−0.265546	−	0.964098i	$-0.585552\pi$
$271$	−143.926			−0.531092			−0.265546	+	0.964098i	$0.585552\pi$
$272$		0			0
$273$	−236.724	−	158.777i	−0.867122	−	0.581601i
$274$		0			0
$275$	287.902	−	129.632i	1.04692	−	0.471389i
$276$		0			0
$277$		−	360.884i		−	1.30283i	−0.758722	−	0.651415i	$-0.774176\pi$
$277$		−	360.884i		−	1.30283i	0.758722	−	0.651415i	$-0.225824\pi$
$278$		0			0
$279$	−69.9686	−	170.614i	−0.250784	−	0.611520i
$280$		0			0
$281$		−	531.655i		−	1.89201i	−0.324149	−	0.946006i	$-0.605078\pi$
$281$		−	531.655i		−	1.89201i	0.324149	−	0.946006i	$-0.394922\pi$
$282$		0			0
$283$			257.400i			0.909541i	0.890609	+	0.454770i	$0.150279\pi$
$283$			257.400i			0.909541i	−0.890609	+	0.454770i	$0.849721\pi$
$284$		0			0
$285$	183.805	+	427.418i	0.644929	+	1.49971i
$286$		0			0
$287$	176.791			0.615996
$288$		0			0
$289$	−91.4579			−0.316463
$290$		0			0
$291$	17.2839	−	25.7690i	0.0593949	−	0.0885533i
$292$		0			0
$293$	−310.456			−1.05958			−0.529789	−	0.848130i	$-0.677729\pi$
$293$	−310.456			−1.05958			−0.529789	+	0.848130i	$0.677729\pi$
$294$		0			0
$295$	129.295	−	200.015i	0.438290	−	0.678016i
$296$		0			0
$297$	334.091	+	68.2892i	1.12489	+	0.229930i
$298$		0			0
$299$			55.8379i			0.186749i
$300$		0			0
$301$	384.094			1.27606
$302$		0			0
$303$	32.2085	−	48.0204i	0.106299	−	0.158483i
$304$		0			0
$305$	−180.633	−	116.767i	−0.592240	−	0.382841i
$306$		0			0
$307$		−	266.169i		−	0.866999i	−0.901154	−	0.433499i	$-0.857279\pi$
$307$		−	266.169i		−	0.866999i	0.901154	−	0.433499i	$-0.142721\pi$
$308$		0			0
$309$	−11.6477	+	17.3658i	−0.0376947	+	0.0561999i
$310$		0			0
$311$		−	186.580i		−	0.599934i	−0.953950	−	0.299967i	$-0.903024\pi$
$311$		−	186.580i		−	0.599934i	0.953950	−	0.299967i	$-0.0969757\pi$
$312$		0			0
$313$			20.5021i			0.0655019i	0.999464	+	0.0327510i	$0.0104268\pi$
$313$			20.5021i			0.0655019i	−0.999464	+	0.0327510i	$0.989573\pi$
$314$		0			0
$315$	−564.843	−	105.517i	−1.79315	−	0.334975i
$316$		0			0
$317$	−18.9792			−0.0598711			−0.0299356	−	0.999552i	$-0.509530\pi$
$317$	−18.9792			−0.0598711			−0.0299356	+	0.999552i	$0.509530\pi$
$318$		0			0
$319$	−198.661			−0.622763
$320$		0			0
$321$	183.804	+	123.282i	0.572597	+	0.384055i
$322$		0			0
$323$	−435.951			−1.34969
$324$		0			0
$325$	−169.620	+	76.3739i	−0.521908	+	0.234997i
$326$		0			0
$327$	−184.447	−	123.713i	−0.564059	−	0.378328i
$328$		0			0
$329$			258.666i			0.786219i
$330$		0			0
$331$	−413.193			−1.24832			−0.624159	−	0.781297i	$-0.714558\pi$
$331$	−413.193			−1.24832			−0.624159	+	0.781297i	$0.714558\pi$
$332$		0			0
$333$	−107.636	+	44.1413i	−0.323230	+	0.132556i
$334$		0			0
$335$	1.71048	−	2.64605i	0.00510592	−	0.00789865i
$336$		0			0
$337$		−	484.733i		−	1.43838i	−0.694816	−	0.719188i	$-0.744514\pi$
$337$		−	484.733i		−	1.43838i	0.694816	−	0.719188i	$-0.255486\pi$
$338$		0			0
$339$	366.783	+	246.010i	1.08195	+	0.725694i
$340$		0			0
$341$			258.772i			0.758862i
$342$		0			0
$343$		−	830.672i		−	2.42178i
$344$		0			0
$345$	44.4688	+	103.407i	0.128895	+	0.299731i
$346$		0			0
$347$	336.214			0.968915			0.484457	−	0.874815i	$-0.339017\pi$
$347$	336.214			0.968915			0.484457	+	0.874815i	$0.339017\pi$
$348$		0			0
$349$	428.261			1.22711			0.613555	−	0.789652i	$-0.289739\pi$
$349$	428.261			1.22711			0.613555	+	0.789652i	$0.289739\pi$
$350$		0			0
$351$	−196.833	−	40.2332i	−0.560778	−	0.114625i
$352$		0			0
$353$	−558.817			−1.58305			−0.791525	−	0.611137i	$-0.790713\pi$
$353$	−558.817			−1.58305			−0.791525	+	0.611137i	$0.790713\pi$
$354$		0			0
$355$	245.394	−	379.614i	0.691250	−	1.06934i
$356$		0			0
$357$	299.913	−	447.147i	0.840092	−	1.25251i
$358$		0			0
$359$			206.915i			0.576365i	0.957576	+	0.288182i	$0.0930509\pi$
$359$			206.915i			0.576365i	−0.957576	+	0.288182i	$0.906949\pi$
$360$		0			0
$361$	601.090			1.66507
$362$		0			0
$363$	−95.9389	−	64.3487i	−0.264295	−	0.177269i
$364$		0			0
$365$	−125.457	+	194.077i	−0.343718	+	0.531718i
$366$		0			0
$367$		−	185.425i		−	0.505246i	−0.967565	−	0.252623i	$-0.918707\pi$
$367$		−	185.425i		−	0.505246i	0.967565	−	0.252623i	$-0.0812932\pi$
$368$		0			0
$369$	115.288	−	47.2794i	0.312433	−	0.128128i
$370$		0			0
$371$		−	371.821i		−	1.00221i
$372$		0			0
$373$		−	427.345i		−	1.14570i	−0.819661	−	0.572848i	$-0.805838\pi$
$373$		−	427.345i		−	1.14570i	0.819661	−	0.572848i	$-0.194162\pi$
$374$		0			0
$375$	−253.299	+	276.522i	−0.675464	+	0.737393i
$376$		0			0
$377$	117.043			0.310459
$378$		0			0
$379$	−117.727			−0.310626			−0.155313	−	0.987865i	$-0.549639\pi$
$379$	−117.727			−0.310626			−0.155313	+	0.987865i	$0.549639\pi$
$380$		0			0
$381$	150.427	−	224.275i	0.394822	−	0.588649i
$382$		0			0
$383$	470.016			1.22720			0.613598	−	0.789619i	$-0.289722\pi$
$383$	470.016			1.22720			0.613598	+	0.789619i	$0.289722\pi$
$384$		0			0
$385$	677.182	+	437.750i	1.75891	+	1.13701i
$386$		0			0
$387$	250.473	−	102.719i	0.647217	−	0.265423i
$388$		0			0
$389$		−	128.160i		−	0.329461i	−0.986339	−	0.164730i	$-0.947325\pi$
$389$		−	128.160i		−	0.329461i	0.986339	−	0.164730i	$-0.0526754\pi$
$390$		0			0
$391$	−105.472			−0.269749
$392$		0			0
$393$	−18.8685	+	28.1315i	−0.0480115	+	0.0715814i
$394$		0			0
$395$	159.401	+	103.041i	0.403546	+	0.260864i
$396$		0			0
$397$			276.316i			0.696011i	0.937493	+	0.348005i	$0.113141\pi$
$397$			276.316i			0.696011i	−0.937493	+	0.348005i	$0.886859\pi$
$398$		0			0
$399$	−661.871	+	986.798i	−1.65882	+	2.47318i
$400$		0			0
$401$			549.912i			1.37135i	0.727907	+	0.685675i	$0.240493\pi$
$401$			549.912i			1.37135i	−0.727907	+	0.685675i	$0.759507\pi$
$402$		0			0
$403$		−	152.458i		−	0.378307i
$404$		0			0
$405$	−396.561	+	82.2475i	−0.979162	+	0.203080i
$406$		0			0
$407$	163.252			0.401110
$408$		0			0
$409$	−219.166			−0.535858			−0.267929	−	0.963439i	$-0.586339\pi$
$409$	−219.166			−0.535858			−0.267929	+	0.963439i	$0.586339\pi$
$410$		0			0
$411$	−56.0346	−	37.5838i	−0.136337	−	0.0914448i
$412$		0			0
$413$	608.240			1.47273
$414$		0			0
$415$	336.877	+	217.767i	0.811751	+	0.524740i
$416$		0			0
$417$	−226.962	−	152.229i	−0.544274	−	0.365058i
$418$		0			0
$419$		−	204.522i		−	0.488119i	−0.969760	−	0.244060i	$-0.921521\pi$
$419$		−	204.522i		−	0.488119i	0.969760	−	0.244060i	$-0.0784792\pi$
$420$		0			0
$421$	−577.186			−1.37099			−0.685494	−	0.728078i	$-0.740414\pi$
$421$	−577.186			−1.37099			−0.685494	+	0.728078i	$0.740414\pi$
$422$		0			0
$423$	69.1754	+	168.680i	0.163535	+	0.398770i
$424$		0			0
$425$	−144.262	−	320.394i	−0.339440	−	0.753868i
$426$		0			0
$427$		−	549.301i		−	1.28642i
$428$		0			0
$429$	234.136	+	157.041i	0.545772	+	0.366063i
$430$		0			0
$431$		−	663.363i		−	1.53913i	−0.638571	−	0.769563i	$-0.720474\pi$
$431$		−	663.363i		−	1.53913i	0.638571	−	0.769563i	$-0.279526\pi$
$432$		0			0
$433$		−	226.876i		−	0.523964i	−0.965073	−	0.261982i	$-0.915624\pi$
$433$		−	226.876i		−	0.523964i	0.965073	−	0.261982i	$-0.0843760\pi$
$434$		0			0
$435$	216.755	−	93.2122i	0.498287	−	0.214281i
$436$		0			0
$437$	232.763			0.532639
$438$		0			0
$439$	282.524			0.643564			0.321782	−	0.946814i	$-0.395718\pi$
$439$	282.524			0.643564			0.321782	+	0.946814i	$0.395718\pi$
$440$		0			0
$441$	−389.477	−	949.715i	−0.883168	−	2.15355i
$442$		0			0
$443$	455.605			1.02845			0.514227	−	0.857654i	$-0.328079\pi$
$443$	455.605			1.02845			0.514227	+	0.857654i	$0.328079\pi$
$444$		0			0
$445$	−382.521	+	591.744i	−0.859597	+	1.32976i
$446$		0			0
$447$	−381.561	+	568.878i	−0.853604	+	1.27266i
$448$		0			0
$449$		−	157.206i		−	0.350124i	−0.984557	−	0.175062i	$-0.943987\pi$
$449$		−	157.206i		−	0.350124i	0.984557	−	0.175062i	$-0.0560127\pi$
$450$		0			0
$451$	−174.858			−0.387712
$452$		0			0
$453$	−184.466	−	123.726i	−0.407210	−	0.273126i
$454$		0			0
$455$	−398.968	−	257.905i	−0.876853	−	0.566824i
$456$		0			0
$457$		−	397.152i		−	0.869041i	−0.900662	−	0.434520i	$-0.856918\pi$
$457$		−	397.152i		−	0.869041i	0.900662	−	0.434520i	$-0.143082\pi$
$458$		0			0
$459$	75.9962	−	371.797i	0.165569	−	0.810014i
$460$		0			0
$461$		−	350.730i		−	0.760803i	−0.924821	−	0.380401i	$-0.875786\pi$
$461$		−	350.730i		−	0.760803i	0.924821	−	0.380401i	$-0.124214\pi$
$462$		0			0
$463$			308.385i			0.666058i	0.942917	+	0.333029i	$0.108071\pi$
$463$			308.385i			0.666058i	−0.942917	+	0.333029i	$0.891929\pi$
$464$		0			0
$465$	−121.416	−	282.340i	−0.261110	−	0.607182i
$466$		0			0
$467$	−800.129			−1.71334			−0.856669	−	0.515866i	$-0.827470\pi$
$467$	−800.129			−1.71334			−0.856669	+	0.515866i	$0.827470\pi$
$468$		0			0
$469$	8.04656			0.0171568
$470$		0			0
$471$	410.657	−	612.259i	0.871884	−	1.29991i
$472$		0			0
$473$	−379.895			−0.803160
$474$		0			0
$475$	318.369	+	707.070i	0.670250	+	1.48857i
$476$		0			0
$477$	−99.4364	−	242.469i	−0.208462	−	0.508321i
$478$		0			0
$479$			630.135i			1.31552i	0.753227	+	0.657761i	$0.228496\pi$
$479$			630.135i			1.31552i	−0.753227	+	0.657761i	$0.771504\pi$
$480$		0			0
$481$	−96.1814			−0.199961
$482$		0			0
$483$	−160.130	+	238.741i	−0.331531	+	0.494287i
$484$		0			0
$485$	28.0746	−	43.4303i	0.0578858	−	0.0895470i
$486$		0			0
$487$		−	103.952i		−	0.213454i	−0.994288	−	0.106727i	$-0.965963\pi$
$487$		−	103.952i		−	0.213454i	0.994288	−	0.106727i	$-0.0340372\pi$
$488$		0			0
$489$	100.528	−	149.879i	0.205579	−	0.306502i
$490$		0			0
$491$		−	286.049i		−	0.582585i	−0.956634	−	0.291292i	$-0.905915\pi$
$491$		−	286.049i		−	0.582585i	0.956634	−	0.291292i	$-0.0940853\pi$
$492$		0			0
$493$			221.082i			0.448442i
$494$		0			0
$495$	558.668	+	104.364i	1.12862	+	0.210835i
$496$		0			0
$497$	1154.40			2.32273
$498$		0			0
$499$	528.285			1.05869			0.529344	−	0.848407i	$-0.322438\pi$
$499$	528.285			1.05869			0.529344	+	0.848407i	$0.322438\pi$
$500$		0			0
$501$	−203.220	−	136.305i	−0.405630	−	0.272066i
$502$		0			0
$503$	733.418			1.45809			0.729044	−	0.684467i	$-0.239965\pi$
$503$	733.418			1.45809			0.729044	+	0.684467i	$0.239965\pi$
$504$		0			0
$505$	52.3169	−	80.9321i	0.103598	−	0.160262i
$506$		0			0
$507$	283.116	+	189.893i	0.558413	+	0.374542i
$508$		0			0
$509$			312.619i			0.614183i	0.951680	+	0.307092i	$0.0993558\pi$
$509$			312.619i			0.614183i	−0.951680	+	0.307092i	$0.900644\pi$
$510$		0			0
$511$	−590.183			−1.15496
$512$		0			0
$513$	−167.714	+	820.509i	−0.326928	+	1.59943i
$514$		0			0
$515$	−18.9195	+	29.2677i	−0.0367370	+	0.0568306i
$516$		0			0
$517$		−	255.838i		−	0.494851i
$518$		0			0
$519$	−416.235	−	279.179i	−0.801995	−	0.537918i
$520$		0			0
$521$			715.719i			1.37374i	0.726780	+	0.686870i	$0.241016\pi$
$521$			715.719i			1.37374i	−0.726780	+	0.686870i	$0.758984\pi$
$522$		0			0
$523$			109.080i			0.208567i	0.994548	+	0.104283i	$0.0332549\pi$
$523$			109.080i			0.208567i	−0.994548	+	0.104283i	$0.966745\pi$
$524$		0			0
$525$	−944.250	−	159.884i	−1.79857	−	0.304542i
$526$		0			0
$527$	287.977			0.546445
$528$		0			0
$529$	−472.686			−0.893547
$530$		0			0
$531$	396.641	−	162.662i	0.746971	−	0.306332i
$532$		0			0
$533$	103.019			0.193282
$534$		0			0
$535$	309.777	+	200.249i	0.579023	+	0.374297i
$536$		0			0
$537$	451.370	−	672.958i	0.840540	−	1.25318i
$538$		0			0
$539$			1440.44i			2.67243i
$540$		0			0
$541$	14.9710			0.0276729			0.0138364	−	0.999904i	$-0.495596\pi$
$541$	14.9710			0.0276729			0.0138364	+	0.999904i	$0.495596\pi$
$542$		0			0
$543$	−216.705	−	145.350i	−0.399088	−	0.267679i
$544$		0			0
$545$	−310.862	−	200.950i	−0.570389	−	0.368716i
$546$		0			0
$547$			842.765i			1.54070i	0.637618	+	0.770352i	$0.279920\pi$
$547$			842.765i			1.54070i	−0.637618	+	0.770352i	$0.720080\pi$
$548$		0			0
$549$	−146.900	−	358.206i	−0.267578	−	0.652471i
$550$		0			0
$551$		−	487.901i		−	0.885482i
$552$		0			0
$553$			484.733i			0.876551i
$554$		0			0
$555$	−178.120	+	76.5981i	−0.320938	+	0.138015i
$556$		0			0
$557$	845.989			1.51883			0.759415	−	0.650606i	$-0.225485\pi$
$557$	845.989			1.51883			0.759415	+	0.650606i	$0.225485\pi$
$558$		0			0
$559$	223.819			0.400391
$560$		0			0
$561$	−296.634	+	442.258i	−0.528759	+	0.788339i
$562$		0			0
$563$	−336.509			−0.597707			−0.298853	−	0.954299i	$-0.596604\pi$
$563$	−336.509			−0.597707			−0.298853	+	0.954299i	$0.596604\pi$
$564$		0			0
$565$	618.164	+	399.600i	1.09410	+	0.707256i
$566$		0			0
$567$	−726.202	−	736.491i	−1.28078	−	1.29893i
$568$		0			0
$569$			552.736i			0.971416i	0.874121	+	0.485708i	$0.161438\pi$
$569$			552.736i			0.971416i	−0.874121	+	0.485708i	$0.838562\pi$
$570$		0			0
$571$	−772.222			−1.35240			−0.676202	−	0.736717i	$-0.736375\pi$
$571$	−772.222			−1.35240			−0.676202	+	0.736717i	$0.736375\pi$
$572$		0			0
$573$	−505.043	+	752.980i	−0.881401	+	1.31410i
$574$		0			0
$575$	77.0245	+	171.065i	0.133956	+	0.297504i
$576$		0			0
$577$			848.557i			1.47064i	0.677722	+	0.735318i	$0.262967\pi$
$577$			848.557i			1.47064i	−0.677722	+	0.735318i	$0.737033\pi$
$578$		0			0
$579$	−512.658	+	764.334i	−0.885420	+	1.32009i
$580$		0			0
$581$			1024.43i			1.76322i
$582$		0			0
$583$			367.755i			0.630798i
$584$		0			0
$585$	−329.144	−	61.4867i	−0.562640	−	0.105106i
$586$		0			0
$587$	−575.536			−0.980470			−0.490235	−	0.871590i	$-0.663089\pi$
$587$	−575.536			−0.980470			−0.490235	+	0.871590i	$0.663089\pi$
$588$		0			0
$589$	−635.529			−1.07900
$590$		0			0
$591$	722.419	+	484.544i	1.22237	+	0.819872i
$592$		0			0
$593$	156.935			0.264646			0.132323	−	0.991207i	$-0.457756\pi$
$593$	156.935			0.264646			0.132323	+	0.991207i	$0.457756\pi$
$594$		0			0
$595$	487.154	−	753.608i	0.818747	−	1.26657i
$596$		0			0
$597$	953.225	+	639.352i	1.59669	+	1.07094i
$598$		0			0
$599$			517.564i			0.864047i	0.901862	+	0.432024i	$0.142200\pi$
$599$			517.564i			0.864047i	−0.901862	+	0.432024i	$0.857800\pi$
$600$		0			0
$601$	−883.588			−1.47020			−0.735098	−	0.677961i	$-0.762864\pi$
$601$	−883.588			−1.47020			−0.735098	+	0.677961i	$0.762864\pi$
$602$		0			0
$603$	5.24727	−	2.15190i	0.00870194	−	0.00356866i
$604$		0			0
$605$	−161.693	−	104.523i	−0.267260	−	0.172765i
$606$		0			0
$607$		−	242.929i		−	0.400212i	−0.979774	−	0.200106i	$-0.935871\pi$
$607$		−	242.929i		−	0.400212i	0.979774	−	0.200106i	$-0.0641287\pi$
$608$		0			0
$609$	500.431	+	335.652i	0.821725	+	0.551152i
$610$		0			0
$611$			150.729i			0.246693i
$612$		0			0
$613$		−	157.263i		−	0.256546i	−0.991739	−	0.128273i	$-0.959057\pi$
$613$		−	157.263i		−	0.256546i	0.991739	−	0.128273i	$-0.0409434\pi$
$614$		0			0
$615$	190.783	−	82.0436i	0.310217	−	0.133404i
$616$		0			0
$617$	471.040			0.763436			0.381718	−	0.924279i	$-0.375333\pi$
$617$	471.040			0.763436			0.381718	+	0.924279i	$0.375333\pi$
$618$		0			0
$619$	−550.320			−0.889047			−0.444524	−	0.895767i	$-0.646627\pi$
$619$	−550.320			−0.889047			−0.444524	+	0.895767i	$0.646627\pi$
$620$		0			0
$621$	−40.5759	+	198.510i	−0.0653396	+	0.319662i
$622$		0			0
$623$	−1799.48			−2.88841
$624$		0			0
$625$	−414.295	+	467.958i	−0.662872	+	0.748733i
$626$		0			0
$627$	654.634	−	976.009i	1.04407	−	1.55663i
$628$		0			0
$629$		−	181.676i		−	0.288834i
$630$		0			0
$631$	−347.362			−0.550495			−0.275248	−	0.961373i	$-0.588760\pi$
$631$	−347.362			−0.550495			−0.275248	+	0.961373i	$0.588760\pi$
$632$		0			0
$633$	800.051	+	536.614i	1.26390	+	0.847732i
$634$		0			0
$635$	244.342	−	377.987i	0.384790	−	0.595255i
$636$		0			0
$637$		−	848.649i		−	1.33226i
$638$		0			0
$639$	752.798	−	308.721i	1.17809	−	0.483132i
$640$		0			0
$641$		−	333.802i		−	0.520752i	−0.965507	−	0.260376i	$-0.916153\pi$
$641$		−	333.802i		−	0.520752i	0.965507	−	0.260376i	$-0.0838465\pi$
$642$		0			0
$643$			495.512i			0.770625i	0.922786	+	0.385313i	$0.125906\pi$
$643$			495.512i			0.770625i	−0.922786	+	0.385313i	$0.874094\pi$
$644$		0			0
$645$	414.494	−	178.247i	0.642627	−	0.276352i
$646$		0			0
$647$	−149.493			−0.231056			−0.115528	−	0.993304i	$-0.536856\pi$
$647$	−149.493			−0.231056			−0.115528	+	0.993304i	$0.536856\pi$
$648$		0			0
$649$	−601.590			−0.926948
$650$		0			0
$651$	437.212	−	651.850i	0.671601	−	1.00131i
$652$		0			0
$653$	−261.846			−0.400990			−0.200495	−	0.979695i	$-0.564255\pi$
$653$	−261.846			−0.400990			−0.200495	+	0.979695i	$0.564255\pi$
$654$		0			0
$655$	−30.6485	+	47.4120i	−0.0467916	+	0.0723847i
$656$		0			0
$657$	−384.867	+	157.833i	−0.585794	+	0.240234i
$658$		0			0
$659$		−	148.718i		−	0.225672i	−0.993614	−	0.112836i	$-0.964006\pi$
$659$		−	148.718i		−	0.225672i	0.993614	−	0.112836i	$-0.0359935\pi$
$660$		0			0
$661$	535.548			0.810209			0.405104	−	0.914270i	$-0.367235\pi$
$661$	535.548			0.810209			0.405104	+	0.914270i	$0.367235\pi$
$662$		0			0
$663$	174.765	−	260.561i	0.263597	−	0.393002i
$664$		0			0
$665$	−1075.09	+	1663.12i	−1.61668	+	2.50093i
$666$		0			0
$667$		−	118.040i		−	0.176972i
$668$		0			0
$669$	−488.681	+	728.586i	−0.730465	+	1.08907i
$670$		0			0
$671$			543.295i			0.809680i
$672$		0			0
$673$		−	678.388i		−	1.00801i	−0.863702	−	0.504003i	$-0.831860\pi$
$673$		−	678.388i		−	1.00801i	0.863702	−	0.504003i	$-0.168140\pi$
$674$		0			0
$675$	−658.517	+	148.259i	−0.975580	+	0.219643i
$676$		0			0
$677$	−809.743			−1.19608			−0.598038	−	0.801468i	$-0.704053\pi$
$677$	−809.743			−1.19608			−0.598038	+	0.801468i	$0.704053\pi$
$678$		0			0
$679$	132.070			0.194507
$680$		0			0
$681$	922.231	+	618.563i	1.35423	+	0.908316i
$682$		0			0
$683$	150.099			0.219764			0.109882	−	0.993945i	$-0.464953\pi$
$683$	150.099			0.219764			0.109882	+	0.993945i	$0.464953\pi$
$684$		0			0
$685$	−94.4390	−	61.0481i	−0.137867	−	0.0891214i
$686$		0			0
$687$	951.705	+	638.333i	1.38531	+	0.929160i
$688$		0			0
$689$		−	216.667i		−	0.314465i
$690$		0			0
$691$	334.001			0.483359			0.241679	−	0.970356i	$-0.422302\pi$
$691$	334.001			0.483359			0.241679	+	0.970356i	$0.422302\pi$
$692$		0			0
$693$	550.719	+	1342.89i	0.794688	+	1.93780i
$694$		0			0
$695$	−382.515	−	247.269i	−0.550381	−	0.355783i
$696$		0			0
$697$			194.592i			0.279185i
$698$		0			0
$699$	−359.425	−	241.076i	−0.514199	−	0.344886i
$700$		0			0
$701$		−	924.471i		−	1.31879i	−0.751797	−	0.659394i	$-0.770813\pi$
$701$		−	924.471i		−	1.31879i	0.751797	−	0.659394i	$-0.229187\pi$
$702$		0			0
$703$			400.937i			0.570324i
$704$		0			0
$705$	120.040	+	279.139i	0.170269	+	0.395942i
$706$		0			0
$707$	246.112			0.348108
$708$		0			0
$709$	−797.459			−1.12477			−0.562383	−	0.826877i	$-0.690115\pi$
$709$	−797.459			−1.12477			−0.562383	+	0.826877i	$0.690115\pi$
$710$		0			0
$711$	129.633	+	316.101i	0.182324	+	0.444586i
$712$		0			0
$713$	−153.757			−0.215647
$714$		0			0
$715$	394.606	+	255.085i	0.551897	+	0.356762i
$716$		0			0
$717$	416.902	−	621.568i	0.581453	−	0.866902i
$718$		0			0
$719$		−	907.966i		−	1.26282i	−0.775450	−	0.631409i	$-0.782477\pi$
$719$		−	907.966i		−	1.26282i	0.775450	−	0.631409i	$-0.217523\pi$
$720$		0			0
$721$	−89.0024			−0.123443
$722$		0			0
$723$	75.8757	+	50.8918i	0.104946	+	0.0703897i
$724$		0			0
$725$	358.573	−	161.453i	0.494584	−	0.222694i
$726$		0			0
$727$			1038.16i			1.42801i	0.700140	+	0.714005i	$0.253121\pi$
$727$			1038.16i			1.42801i	−0.700140	+	0.714005i	$0.746879\pi$
$728$		0			0
$729$	−670.527	−	286.067i	−0.919790	−	0.392410i
$730$		0			0
$731$			422.769i			0.578344i
$732$		0			0
$733$			399.107i			0.544485i	0.962229	+	0.272242i	$0.0877652\pi$
$733$			399.107i			0.544485i	−0.962229	+	0.272242i	$0.912235\pi$
$734$		0			0
$735$	−675.857	−	1571.63i	−0.919533	−	2.13827i
$736$		0			0
$737$	−7.95858			−0.0107986
$738$		0			0
$739$	−452.504			−0.612319			−0.306159	−	0.951980i	$-0.599044\pi$
$739$	−452.504			−0.612319			−0.306159	+	0.951980i	$0.599044\pi$
$740$		0			0
$741$	−385.684	+	575.025i	−0.520491	+	0.776012i
$742$		0			0
$743$	486.909			0.655328			0.327664	−	0.944794i	$-0.393739\pi$
$743$	486.909			0.655328			0.327664	+	0.944794i	$0.393739\pi$
$744$		0			0
$745$	−619.777	+	958.770i	−0.831916	+	1.28694i
$746$		0			0
$747$	273.965	+	668.046i	0.366754	+	0.894306i
$748$		0			0
$749$			942.024i			1.25771i
$750$		0			0
$751$	−470.899			−0.627029			−0.313515	−	0.949583i	$-0.601506\pi$
$751$	−470.899			−0.627029			−0.313515	+	0.949583i	$0.601506\pi$
$752$		0			0
$753$	−115.169	+	171.708i	−0.152947	+	0.228032i
$754$		0			0
$755$	−310.894	−	200.971i	−0.411780	−	0.266187i
$756$		0			0
$757$			886.264i			1.17076i	0.810760	+	0.585379i	$0.199054\pi$
$757$			886.264i			1.17076i	−0.810760	+	0.585379i	$0.800946\pi$
$758$		0			0
$759$	158.379	−	236.131i	0.208668	−	0.311108i
$760$		0			0
$761$		−	1022.30i		−	1.34336i	−0.740841	−	0.671680i	$-0.765573\pi$
$761$		−	1022.30i		−	1.34336i	0.740841	−	0.671680i	$-0.234427\pi$
$762$		0			0
$763$		−	945.322i		−	1.23895i
$764$		0			0
$765$	116.142	−	621.718i	0.151819	−	0.812704i
$766$		0			0
$767$	354.432			0.462102
$768$		0			0
$769$	1051.96			1.36796			0.683982	−	0.729499i	$-0.260247\pi$
$769$	1051.96			1.36796			0.683982	+	0.729499i	$0.260247\pi$
$770$		0			0
$771$	902.847	+	605.562i	1.17101	+	0.785424i
$772$		0			0
$773$	−983.554			−1.27238			−0.636192	−	0.771530i	$-0.719492\pi$
$773$	−983.554			−1.27238			−0.636192	+	0.771530i	$0.719492\pi$
$774$		0			0
$775$	−210.305	−	467.070i	−0.271361	−	0.602671i
$776$		0			0
$777$	−411.234	−	275.825i	−0.529259	−	0.354987i
$778$		0			0
$779$		−	429.441i		−	0.551272i
$780$		0			0
$781$	−1141.77			−1.46194
$782$		0			0
$783$	416.101	+	85.0522i	0.531419	+	0.108624i
$784$		0			0
$785$	667.039	−	1031.88i	0.849731	−	1.31450i
$786$		0			0
$787$			984.726i			1.25124i	0.780128	+	0.625620i	$0.215154\pi$
$787$			984.726i			1.25124i	−0.780128	+	0.625620i	$0.784846\pi$
$788$		0			0
$789$	−58.4214	−	39.1847i	−0.0740449	−	0.0496638i
$790$		0			0
$791$			1879.82i			2.37651i
$792$		0			0
$793$		−	320.087i		−	0.403641i
$794$		0			0
$795$	−172.551	−	401.249i	−0.217046	−	0.504716i
$796$		0			0
$797$	359.710			0.451330			0.225665	−	0.974205i	$-0.427544\pi$
$797$	359.710			0.451330			0.225665	+	0.974205i	$0.427544\pi$
$798$		0			0
$799$	−284.712			−0.356335
$800$		0			0
$801$	−1173.46	+	481.236i	−1.46500	+	0.600794i
$802$		0			0
$803$	583.731			0.726938
$804$		0			0
$805$	−260.102	+	402.367i	−0.323108	+	0.499834i
$806$		0			0
$807$	662.987	−	988.463i	0.821546	−	1.22486i
$808$		0			0
$809$		−	1174.75i		−	1.45211i	−0.687638	−	0.726053i	$-0.741352\pi$
$809$		−	1174.75i		−	1.45211i	0.687638	−	0.726053i	$-0.258648\pi$
$810$		0			0
$811$	1000.55			1.23373			0.616863	−	0.787071i	$-0.288403\pi$
$811$	1000.55			1.23373			0.616863	+	0.787071i	$0.288403\pi$
$812$		0			0
$813$	−358.588	−	240.514i	−0.441067	−	0.295835i
$814$		0			0
$815$	163.290	−	252.602i	0.200355	−	0.309942i
$816$		0			0
$817$		−	933.000i		−	1.14198i
$818$		0			0
$819$	−324.461	−	791.178i	−0.396167	−	0.966029i
$820$		0			0
$821$			536.992i			0.654071i	0.945012	+	0.327036i	$0.106050\pi$
$821$			536.992i			0.654071i	−0.945012	+	0.327036i	$0.893950\pi$
$822$		0			0
$823$		−	563.712i		−	0.684948i	−0.939527	−	0.342474i	$-0.888735\pi$
$823$		−	563.712i		−	0.684948i	0.939527	−	0.342474i	$-0.111265\pi$
$824$		0			0
$825$	933.927	+	158.136i	1.13203	+	0.191680i
$826$		0			0
$827$	−976.487			−1.18076			−0.590379	−	0.807126i	$-0.701022\pi$
$827$	−976.487			−1.18076			−0.590379	+	0.807126i	$0.701022\pi$
$828$		0			0
$829$	358.250			0.432147			0.216074	−	0.976377i	$-0.430675\pi$
$829$	358.250			0.432147			0.216074	+	0.976377i	$0.430675\pi$
$830$		0			0
$831$	603.071	−	899.133i	0.725718	−	1.08199i
$832$		0			0
$833$	1603.01			1.92438
$834$		0			0
$835$	−342.502	−	221.403i	−0.410182	−	0.265154i
$836$		0			0
$837$	110.787	−	542.005i	0.132362	−	0.647556i
$838$		0			0
$839$			98.9138i			0.117895i	0.998261	+	0.0589474i	$0.0187744\pi$
$839$			98.9138i			0.117895i	−0.998261	+	0.0589474i	$0.981226\pi$
$840$		0			0
$841$	593.573			0.705794
$842$		0			0
$843$	888.447	−	1324.61i	1.05391	−	1.57130i
$844$		0			0
$845$	477.154	+	308.447i	0.564680	+	0.365026i
$846$		0			0
$847$		−	491.703i		−	0.580523i
$848$		0			0
$849$	−430.140	+	641.305i	−0.506643	+	0.755366i
$850$		0			0
$851$			97.0007i			0.113984i
$852$		0			0
$853$		−	262.197i		−	0.307383i	−0.988119	−	0.153691i	$-0.950884\pi$
$853$		−	262.197i		−	0.307383i	0.988119	−	0.153691i	$-0.0491161\pi$
$854$		0			0
$855$	−256.311	+	1372.06i	−0.299779	+	1.60474i
$856$		0			0
$857$	−41.1542			−0.0480212			−0.0240106	−	0.999712i	$-0.507644\pi$
$857$	−41.1542			−0.0480212			−0.0240106	+	0.999712i	$0.507644\pi$
$858$		0			0
$859$	414.736			0.482813			0.241406	−	0.970424i	$-0.422391\pi$
$859$	414.736			0.482813			0.241406	+	0.970424i	$0.422391\pi$
$860$		0			0
$861$	440.470	+	295.434i	0.511579	+	0.343129i
$862$		0			0
$863$	−1253.21			−1.45216			−0.726078	−	0.687613i	$-0.758659\pi$
$863$	−1253.21			−1.45216			−0.726078	+	0.687613i	$0.758659\pi$
$864$		0			0
$865$	−701.510	−	453.477i	−0.810995	−	0.524251i
$866$		0			0
$867$	−227.865	−	152.835i	−0.262820	−	0.176280i
$868$		0			0
$869$		−	479.433i		−	0.551706i
$870$		0			0
$871$	4.68888			0.00538332
$872$		0			0
$873$	86.1249	−	35.3197i	0.0986539	−	0.0404579i
$874$		0			0
$875$	−1578.04	−	239.768i	−1.80347	−	0.274021i
$876$		0			0
$877$			861.957i			0.982847i	0.870921	+	0.491424i	$0.163523\pi$
$877$			861.957i			0.982847i	−0.870921	+	0.491424i	$0.836477\pi$
$878$		0			0
$879$	−773.494	−	518.802i	−0.879970	−	0.590218i
$880$		0			0
$881$		−	87.0009i		−	0.0987524i	−0.998780	−	0.0493762i	$-0.984277\pi$
$881$		−	87.0009i		−	0.0987524i	0.998780	−	0.0493762i	$-0.0157233\pi$
$882$		0			0
$883$		−	1022.42i		−	1.15789i	−0.815366	−	0.578945i	$-0.803464\pi$
$883$		−	1022.42i		−	1.15789i	0.815366	−	0.578945i	$-0.196536\pi$
$884$		0			0
$885$	656.380	−	282.267i	0.741672	−	0.318945i
$886$		0			0
$887$	−669.924			−0.755269			−0.377634	−	0.925955i	$-0.623262\pi$
$887$	−669.924			−0.755269			−0.377634	+	0.925955i	$0.623262\pi$
$888$		0			0
$889$	1149.45			1.29297
$890$		0			0
$891$	718.263	+	728.439i	0.806131	+	0.817552i
$892$		0			0
$893$	628.324			0.703610
$894$		0			0
$895$	733.169	−	1134.18i	0.819183	−	1.26724i
$896$		0			0
$897$	−93.3104	+	139.119i	−0.104025	+	0.155093i
$898$		0			0
$899$			322.293i			0.358502i
$900$		0			0
$901$	409.260			0.454229
$902$		0			0
$903$	956.960	+	641.858i	1.05976	+	0.710806i
$904$		0			0
$905$	−365.228	−	236.094i	−0.403567	−	0.260878i
$906$		0			0
$907$		−	1296.52i		−	1.42946i	−0.699402	−	0.714729i	$-0.746550\pi$
$907$		−	1296.52i		−	1.42946i	0.699402	−	0.714729i	$-0.253450\pi$
$908$		0			0
$909$	160.493	−	65.8181i	0.176560	−	0.0724071i
$910$		0			0
$911$			926.622i			1.01715i	0.861018	+	0.508574i	$0.169827\pi$
$911$			926.622i			1.01715i	−0.861018	+	0.508574i	$0.830173\pi$
$912$		0			0
$913$		−	1013.23i		−	1.10978i
$914$		0			0
$915$	−254.915	−	592.776i	−0.278595	−	0.647843i
$916$		0			0
$917$	−144.179			−0.157229
$918$		0			0
$919$	−478.391			−0.520556			−0.260278	−	0.965534i	$-0.583814\pi$
$919$	−478.391			−0.520556			−0.260278	+	0.965534i	$0.583814\pi$
$920$		0			0
$921$	444.793	−	663.152i	0.482946	−	0.720035i
$922$		0			0
$923$	672.687			0.728805
$924$		0			0
$925$	−294.661	+	132.676i	−0.318553	+	0.143433i
$926$		0			0
$927$	−58.0397	+	23.8020i	−0.0626102	+	0.0256764i
$928$		0			0
$929$			1452.00i			1.56297i	0.623923	+	0.781486i	$0.285538\pi$
$929$			1452.00i			1.56297i	−0.623923	+	0.781486i	$0.714462\pi$
$930$		0			0
$931$	−3537.64			−3.79983
$932$		0			0
$933$	311.792	−	464.858i	0.334182	−	0.498240i
$934$		0			0
$935$	−481.828	+	745.369i	−0.515324	+	0.797186i
$936$		0			0
$937$			1535.86i			1.63912i	0.572991	+	0.819562i	$0.305783\pi$
$937$			1535.86i			1.63912i	−0.572991	+	0.819562i	$0.694217\pi$
$938$		0			0
$939$	−34.2610	+	51.0805i	−0.0364866	+	0.0543988i
$940$		0			0
$941$		−	1237.50i		−	1.31509i	−0.753415	−	0.657545i	$-0.771595\pi$
$941$		−	1237.50i		−	1.31509i	0.753415	−	0.657545i	$-0.228405\pi$
$942$		0			0
$943$		−	103.897i		−	0.110177i
$944$		0			0
$945$	−1230.96	−	1206.80i	−1.30261	−	1.27704i
$946$		0			0
$947$	603.800			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$947$	603.800			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$948$		0			0
$949$	−343.911			−0.362393
$950$		0			0
$951$	−47.2861	−	31.7160i	−0.0497225	−	0.0333501i
$952$		0			0
$953$	−534.553			−0.560916			−0.280458	−	0.959866i	$-0.590486\pi$
$953$	−534.553			−0.560916			−0.280458	+	0.959866i	$0.590486\pi$
$954$		0			0
$955$	−820.352	+	1269.05i	−0.859007	+	1.32885i
$956$		0			0
$957$	−494.959	−	331.982i	−0.517199	−	0.346899i
$958$		0			0
$959$		−	287.186i		−	0.299464i
$960$		0			0
$961$	−541.188			−0.563151
$962$		0			0
$963$	251.927	+	614.307i	0.261606	+	0.637909i
$964$		0			0
$965$	−832.721	+	1288.19i	−0.862923	+	1.33491i
$966$		0			0
$967$			271.601i			0.280870i	0.990090	+	0.140435i	$0.0448500\pi$
$967$			271.601i			0.280870i	−0.990090	+	0.140435i	$0.955150\pi$
$968$		0			0
$969$	−1086.16	−	728.515i	−1.12091	−	0.751822i
$970$		0			0
$971$			912.176i			0.939419i	0.882821	+	0.469709i	$0.155641\pi$
$971$			912.176i			0.939419i	−0.882821	+	0.469709i	$0.844359\pi$
$972$		0			0
$973$		−	1163.22i		−	1.19550i
$974$		0			0
$975$	−550.232	−	93.1675i	−0.564340	−	0.0955564i
$976$		0			0
$977$	−333.628			−0.341482			−0.170741	−	0.985316i	$-0.554616\pi$
$977$	−333.628			−0.341482			−0.170741	+	0.985316i	$0.554616\pi$
$978$		0			0
$979$	1779.80			1.81798
$980$		0			0
$981$	−252.809	−	616.458i	−0.257705	−	0.628397i
$982$		0			0
$983$	−1600.35			−1.62803			−0.814013	−	0.580847i	$-0.802722\pi$
$983$	−1600.35			−1.62803			−0.814013	+	0.580847i	$0.802722\pi$
$984$		0			0
$985$	1217.54	+	787.056i	1.23608	+	0.799041i
$986$		0			0
$987$	−432.256	+	644.460i	−0.437949	+	0.652948i
$988$		0			0
$989$		−	225.725i		−	0.228236i
$990$		0			0
$991$	−69.3757			−0.0700057			−0.0350029	−	0.999387i	$-0.511144\pi$
$991$	−69.3757			−0.0700057			−0.0350029	+	0.999387i	$0.511144\pi$
$992$		0			0
$993$	−1029.46	−	690.485i	−1.03672	−	0.695353i
$994$		0			0
$995$	1606.54	+	1038.51i	1.61461	+	1.04373i
$996$		0			0
$997$		−	482.497i		−	0.483949i	−0.970283	−	0.241974i	$-0.922205\pi$
$997$		−	482.497i		−	0.483949i	0.970283	−	0.241974i	$-0.0777950\pi$
$998$		0			0
$999$	−341.936	−	69.8925i	−0.342278	−	0.0699625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.c.k.449.10		12
3.2	odd	2	inner	960.3.c.k.449.4		12
4.3	odd	2		960.3.c.j.449.3		12
5.4	even	2	inner	960.3.c.k.449.3		12
8.3	odd	2		240.3.c.e.209.10		12
8.5	even	2		120.3.c.a.89.3	✓	12
12.11	even	2		960.3.c.j.449.9		12
15.14	odd	2	inner	960.3.c.k.449.9		12
20.19	odd	2		960.3.c.j.449.10		12
24.5	odd	2		120.3.c.a.89.9	yes	12
24.11	even	2		240.3.c.e.209.4		12
40.3	even	4		1200.3.l.y.401.4		12
40.13	odd	4		600.3.l.g.401.9		12
40.19	odd	2		240.3.c.e.209.3		12
40.27	even	4		1200.3.l.y.401.9		12
40.29	even	2		120.3.c.a.89.10	yes	12
40.37	odd	4		600.3.l.g.401.4		12
60.59	even	2		960.3.c.j.449.4		12
120.29	odd	2		120.3.c.a.89.4	yes	12
120.53	even	4		600.3.l.g.401.10		12
120.59	even	2		240.3.c.e.209.9		12
120.77	even	4		600.3.l.g.401.3		12
120.83	odd	4		1200.3.l.y.401.3		12
120.107	odd	4		1200.3.l.y.401.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.c.a.89.3	✓	12	8.5	even	2
120.3.c.a.89.4	yes	12	120.29	odd	2
120.3.c.a.89.9	yes	12	24.5	odd	2
120.3.c.a.89.10	yes	12	40.29	even	2
240.3.c.e.209.3		12	40.19	odd	2
240.3.c.e.209.4		12	24.11	even	2
240.3.c.e.209.9		12	120.59	even	2
240.3.c.e.209.10		12	8.3	odd	2
600.3.l.g.401.3		12	120.77	even	4
600.3.l.g.401.4		12	40.37	odd	4
600.3.l.g.401.9		12	40.13	odd	4
600.3.l.g.401.10		12	120.53	even	4
960.3.c.j.449.3		12	4.3	odd	2
960.3.c.j.449.4		12	60.59	even	2
960.3.c.j.449.9		12	12.11	even	2
960.3.c.j.449.10		12	20.19	odd	2
960.3.c.k.449.3		12	5.4	even	2	inner
960.3.c.k.449.4		12	3.2	odd	2	inner
960.3.c.k.449.9		12	15.14	odd	2	inner
960.3.c.k.449.10		12	1.1	even	1	trivial
1200.3.l.y.401.3		12	120.83	odd	4
1200.3.l.y.401.4		12	40.3	even	4
1200.3.l.y.401.9		12	40.27	even	4
1200.3.l.y.401.10		12	120.107	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.49147 + 1.67109i) q^{3} +(4.19906 + 2.71439i) q^{5} +12.7692i q^{7} +(3.41489 + 8.32698i) q^{9} +O(q^{10})\)	\(q+(2.49147 + 1.67109i) q^{3} +(4.19906 + 2.71439i) q^{5} +12.7692i q^{7} +(3.41489 + 8.32698i) q^{9} -12.6296i q^{11} +7.44085i q^{13} +(5.92583 + 13.7799i) q^{15} -14.0550 q^{17} +31.0176 q^{19} +(-21.3386 + 31.8142i) q^{21} +7.50423 q^{23} +(10.2641 + 22.7958i) q^{25} +(-5.40707 + 26.4530i) q^{27} -15.7298i q^{29} -20.4893 q^{31} +(21.1053 - 31.4663i) q^{33} +(-34.6607 + 53.6186i) q^{35} +12.9261i q^{37} +(-12.4344 + 18.5387i) q^{39} -13.8451i q^{41} -30.0797i q^{43} +(-8.26340 + 44.2348i) q^{45} +20.2570 q^{47} -114.053 q^{49} +(-35.0176 - 23.4872i) q^{51} -29.1185 q^{53} +(34.2817 - 53.0324i) q^{55} +(77.2795 + 51.8333i) q^{57} -47.6333i q^{59} -43.0176 q^{61} +(-106.329 + 43.6054i) q^{63} +(-20.1974 + 31.2445i) q^{65} -0.630153i q^{67} +(18.6966 + 12.5403i) q^{69} -90.4047i q^{71} +46.2193i q^{73} +(-12.5211 + 73.9474i) q^{75} +161.270 q^{77} +37.9610 q^{79} +(-57.6771 + 56.8713i) q^{81} +80.2267 q^{83} +(-59.0176 - 38.1507i) q^{85} +(26.2860 - 39.1904i) q^{87} +140.923i q^{89} -95.0138 q^{91} +(-51.0486 - 34.2396i) q^{93} +(130.245 + 84.1939i) q^{95} -10.3429i q^{97} +(105.166 - 43.1286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{9}+O(q^{10}) \) 12 * q + 8 * q^9	\( 12 q + 8 q^{9} + 16 q^{15} - 4 q^{21} + 36 q^{25} - 48 q^{31} - 128 q^{39} + 68 q^{45} - 252 q^{49} - 48 q^{51} - 48 q^{55} - 144 q^{61} - 268 q^{69} - 304 q^{75} + 432 q^{79} - 188 q^{81} - 336 q^{85} + 560 q^{99}+O(q^{100}) \) 12 * q + 8 * q^9 + 16 * q^15 - 4 * q^21 + 36 * q^25 - 48 * q^31 - 128 * q^39 + 68 * q^45 - 252 * q^49 - 48 * q^51 - 48 * q^55 - 144 * q^61 - 268 * q^69 - 304 * q^75 + 432 * q^79 - 188 * q^81 - 336 * q^85 + 560 * q^99

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