LMFDB - Embedded newform 1680.2.f.l.881.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(881,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1680.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.f (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:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + x^{14} - 4 x^{13} + 10 x^{12} - 32 x^{11} + 71 x^{10} - 70 x^{9} + 74 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + x^14 - 4x^13 + 10x^12 - 32x^11 + 71x^10 - 70x^9 + 74x^8 - 210x^7 + 639x^6 - 864x^5 + 810x^4 - 972x^3 + 729x^2 - 4374x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.4
Root			$1.14188 - 1.30235i$ of defining polynomial
Character	$\chi$	$=$	1680.881
Dual form			1680.2.f.l.881.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30235 + 1.14188i) q^{3} +1.00000 q^{5} +(1.35345 + 2.27336i) q^{7} +(0.392236 - 2.97425i) q^{9} +O(q^{10})$	\(q+(-1.30235 + 1.14188i) q^{3} +1.00000 q^{5} +(1.35345 + 2.27336i) q^{7} +(0.392236 - 2.97425i) q^{9} +5.73062i q^{11} +2.24338i q^{13} +(-1.30235 + 1.14188i) q^{15} -6.50062 q^{17} -0.217877i q^{19} +(-4.35857 - 1.41524i) q^{21} -5.57998i q^{23} +1.00000 q^{25} +(2.88539 + 4.32140i) q^{27} +1.11432i q^{29} +5.49827i q^{31} +(-6.54366 - 7.46328i) q^{33} +(1.35345 + 2.27336i) q^{35} +10.0863 q^{37} +(-2.56167 - 2.92167i) q^{39} +1.11802 q^{41} -5.89592 q^{43} +(0.392236 - 2.97425i) q^{45} -7.70789 q^{47} +(-3.33633 + 6.15377i) q^{49} +(8.46609 - 7.42291i) q^{51} -8.37883i q^{53} +5.73062i q^{55} +(0.248789 + 0.283753i) q^{57} +13.4209 q^{59} -1.33454i q^{61} +(7.29241 - 3.13381i) q^{63} +2.24338i q^{65} -14.5144 q^{67} +(6.37165 + 7.26709i) q^{69} +7.41245i q^{71} +12.1828i q^{73} +(-1.30235 + 1.14188i) q^{75} +(-13.0278 + 7.75612i) q^{77} -4.54501 q^{79} +(-8.69230 - 2.33322i) q^{81} -10.9184 q^{83} -6.50062 q^{85} +(-1.27242 - 1.45124i) q^{87} -4.45092 q^{89} +(-5.10002 + 3.03631i) q^{91} +(-6.27835 - 7.16068i) q^{93} -0.217877i q^{95} -9.33620i q^{97} +(17.0443 + 2.24776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^5 - 2 * q^7 - 2 * q^9	$ 16 q + 16 q^{5} - 2 q^{7} - 2 q^{9} + 10 q^{21} + 16 q^{25} - 6 q^{27} + 6 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} + 32 q^{41} - 32 q^{43} - 2 q^{45} - 4 q^{47} - 4 q^{49} - 6 q^{51} + 24 q^{59} + 24 q^{63} + 8 q^{69} - 32 q^{77} + 4 q^{79} - 6 q^{81} - 20 q^{83} - 6 q^{87} - 24 q^{89} - 20 q^{91} - 32 q^{93} + 58 q^{99}+O(q^{100}) $ 16 * q + 16 * q^5 - 2 * q^7 - 2 * q^9 + 10 * q^21 + 16 * q^25 - 6 * q^27 + 6 * q^33 - 2 * q^35 + 12 * q^37 - 6 * q^39 + 32 * q^41 - 32 * q^43 - 2 * q^45 - 4 * q^47 - 4 * q^49 - 6 * q^51 + 24 * q^59 + 24 * q^63 + 8 * q^69 - 32 * q^77 + 4 * q^79 - 6 * q^81 - 20 * q^83 - 6 * q^87 - 24 * q^89 - 20 * q^91 - 32 * q^93 + 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$-1$	$1$	$1$	$-1$	$1$

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
$3$	−1.30235	+	1.14188i	−0.751913	+	0.659263i
$3$	−1.30235	+	1.14188i	−0.751913	+	0.659263i
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	1.35345	+	2.27336i	0.511557	+	0.859249i
$7$	1.35345	+	2.27336i	0.511557	+	0.859249i
$8$		0			0
$9$	0.392236	−	2.97425i	0.130745	−	0.991416i
$10$		0			0
$11$			5.73062i			1.72785i	0.503624	+	0.863923i	$0.332000\pi$
$11$			5.73062i			1.72785i	−0.503624	+	0.863923i	$0.668000\pi$
$12$		0			0
$13$			2.24338i			0.622202i	0.950377	+	0.311101i	$0.100698\pi$
$13$			2.24338i			0.622202i	−0.950377	+	0.311101i	$0.899302\pi$
$14$		0			0
$15$	−1.30235	+	1.14188i	−0.336266	+	0.294831i
$16$		0			0
$17$	−6.50062			−1.57663			−0.788316	−	0.615270i	$-0.789047\pi$
$17$	−6.50062			−1.57663			−0.788316	+	0.615270i	$0.789047\pi$
$18$		0			0
$19$		−	0.217877i		−	0.0499845i	−0.999688	−	0.0249923i	$-0.992044\pi$
$19$		−	0.217877i		−	0.0499845i	0.999688	−	0.0249923i	$-0.00795611\pi$
$20$		0			0
$21$	−4.35857	−	1.41524i	−0.951117	−	0.308830i
$22$		0			0
$23$		−	5.57998i		−	1.16351i	−0.813365	−	0.581753i	$-0.802367\pi$
$23$		−	5.57998i		−	1.16351i	0.813365	−	0.581753i	$-0.197633\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	2.88539	+	4.32140i	0.555294	+	0.831654i
$28$		0			0
$29$			1.11432i			0.206925i	0.994633	+	0.103462i	$0.0329921\pi$
$29$			1.11432i			0.206925i	−0.994633	+	0.103462i	$0.967008\pi$
$30$		0			0
$31$			5.49827i			0.987519i	0.869599	+	0.493759i	$0.164378\pi$
$31$			5.49827i			0.987519i	−0.869599	+	0.493759i	$0.835622\pi$
$32$		0			0
$33$	−6.54366	−	7.46328i	−1.13910	−	1.29919i
$34$		0			0
$35$	1.35345	+	2.27336i	0.228775	+	0.384268i
$36$		0			0
$37$	10.0863			1.65818			0.829091	−	0.559113i	$-0.188858\pi$
$37$	10.0863			1.65818			0.829091	+	0.559113i	$0.188858\pi$
$38$		0			0
$39$	−2.56167	−	2.92167i	−0.410195	−	0.467842i
$40$		0			0
$41$	1.11802			0.174606			0.0873030	−	0.996182i	$-0.472175\pi$
$41$	1.11802			0.174606			0.0873030	+	0.996182i	$0.472175\pi$
$42$		0			0
$43$	−5.89592			−0.899119			−0.449560	−	0.893250i	$-0.648419\pi$
$43$	−5.89592			−0.899119			−0.449560	+	0.893250i	$0.648419\pi$
$44$		0			0
$45$	0.392236	−	2.97425i	0.0584712	−	0.443375i
$46$		0			0
$47$	−7.70789			−1.12431			−0.562156	−	0.827031i	$-0.690028\pi$
$47$	−7.70789			−1.12431			−0.562156	+	0.827031i	$0.690028\pi$
$48$		0			0
$49$	−3.33633	+	6.15377i	−0.476618	+	0.879110i
$50$		0			0
$51$	8.46609	−	7.42291i	1.18549	−	1.03941i
$52$		0			0
$53$		−	8.37883i		−	1.15092i	−0.817829	−	0.575461i	$-0.804823\pi$
$53$		−	8.37883i		−	1.15092i	0.817829	−	0.575461i	$-0.195177\pi$
$54$		0			0
$55$			5.73062i			0.772716i
$56$		0			0
$57$	0.248789	+	0.283753i	0.0329529	+	0.0375840i
$58$		0			0
$59$	13.4209			1.74725			0.873624	−	0.486602i	$-0.161764\pi$
$59$	13.4209			1.74725			0.873624	+	0.486602i	$0.161764\pi$
$60$		0			0
$61$		−	1.33454i		−	0.170870i	−0.996344	−	0.0854349i	$-0.972772\pi$
$61$		−	1.33454i		−	0.170870i	0.996344	−	0.0854349i	$-0.0272280\pi$
$62$		0			0
$63$	7.29241	−	3.13381i	0.918757	−	0.394823i
$64$		0			0
$65$			2.24338i			0.278257i
$66$		0			0
$67$	−14.5144			−1.77322			−0.886610	−	0.462517i	$-0.846946\pi$
$67$	−14.5144			−1.77322			−0.886610	+	0.462517i	$0.846946\pi$
$68$		0			0
$69$	6.37165	+	7.26709i	0.767056	+	0.874855i
$70$		0			0
$71$			7.41245i			0.879696i	0.898072	+	0.439848i	$0.144968\pi$
$71$			7.41245i			0.879696i	−0.898072	+	0.439848i	$0.855032\pi$
$72$		0			0
$73$			12.1828i			1.42589i	0.701220	+	0.712945i	$0.252639\pi$
$73$			12.1828i			1.42589i	−0.701220	+	0.712945i	$0.747361\pi$
$74$		0			0
$75$	−1.30235	+	1.14188i	−0.150383	+	0.131853i
$76$		0			0
$77$	−13.0278	+	7.75612i	−1.48465	+	0.883892i
$78$		0			0
$79$	−4.54501			−0.511354			−0.255677	−	0.966762i	$-0.582298\pi$
$79$	−4.54501			−0.511354			−0.255677	+	0.966762i	$0.582298\pi$
$80$		0			0
$81$	−8.69230	−	2.33322i	−0.965811	−	0.259246i
$82$		0			0
$83$	−10.9184			−1.19845			−0.599223	−	0.800582i	$-0.704524\pi$
$83$	−10.9184			−1.19845			−0.599223	+	0.800582i	$0.704524\pi$
$84$		0			0
$85$	−6.50062			−0.705091
$86$		0			0
$87$	−1.27242	−	1.45124i	−0.136418	−	0.155589i
$88$		0			0
$89$	−4.45092			−0.471797			−0.235898	−	0.971778i	$-0.575803\pi$
$89$	−4.45092			−0.471797			−0.235898	+	0.971778i	$0.575803\pi$
$90$		0			0
$91$	−5.10002	+	3.03631i	−0.534627	+	0.318292i
$92$		0			0
$93$	−6.27835	−	7.16068i	−0.651034	−	0.742528i
$94$		0			0
$95$		−	0.217877i		−	0.0223537i
$96$		0			0
$97$		−	9.33620i		−	0.947948i	−0.880539	−	0.473974i	$-0.842819\pi$
$97$		−	9.33620i		−	0.947948i	0.880539	−	0.473974i	$-0.157181\pi$
$98$		0			0
$99$	17.0443	+	2.24776i	1.71301	+	0.225908i
$100$		0			0
$101$	−8.12564			−0.808531			−0.404266	−	0.914642i	$-0.632473\pi$
$101$	−8.12564			−0.808531			−0.404266	+	0.914642i	$0.632473\pi$
$102$		0			0
$103$		−	3.21987i		−	0.317263i	−0.987338	−	0.158632i	$-0.949292\pi$
$103$		−	3.21987i		−	0.317263i	0.987338	−	0.158632i	$-0.0507082\pi$
$104$		0			0
$105$	−4.35857	−	1.41524i	−0.425353	−	0.138113i
$106$		0			0
$107$		−	0.352062i		−	0.0340351i	−0.999855	−	0.0170175i	$-0.994583\pi$
$107$		−	0.352062i		−	0.0340351i	0.999855	−	0.0170175i	$-0.00541711\pi$
$108$		0			0
$109$	13.8035			1.32214			0.661069	−	0.750325i	$-0.270103\pi$
$109$	13.8035			1.32214			0.661069	+	0.750325i	$0.270103\pi$
$110$		0			0
$111$	−13.1359	+	11.5173i	−1.24681	+	1.09318i
$112$		0			0
$113$			2.52753i			0.237770i	0.992908	+	0.118885i	$0.0379320\pi$
$113$			2.52753i			0.237770i	−0.992908	+	0.118885i	$0.962068\pi$
$114$		0			0
$115$		−	5.57998i		−	0.520336i
$116$		0			0
$117$	6.67238	+	0.879936i	0.616861	+	0.0813502i
$118$		0			0
$119$	−8.79829	−	14.7783i	−0.806538	−	1.35472i
$120$		0			0
$121$	−21.8400			−1.98545
$122$		0			0
$123$	−1.45606	+	1.27664i	−0.131288	+	0.115111i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−13.2059			−1.17183			−0.585916	−	0.810372i	$-0.699265\pi$
$127$	−13.2059			−1.17183			−0.585916	+	0.810372i	$0.699265\pi$
$128$		0			0
$129$	7.67856	−	6.73241i	0.676059	−	0.592756i
$130$		0			0
$131$	−10.2780			−0.897992			−0.448996	−	0.893534i	$-0.648218\pi$
$131$	−10.2780			−0.897992			−0.448996	+	0.893534i	$0.648218\pi$
$132$		0			0
$133$	0.495314	−	0.294887i	0.0429491	−	0.0255699i
$134$		0			0
$135$	2.88539	+	4.32140i	0.248335	+	0.371927i
$136$		0			0
$137$		−	5.43330i		−	0.464198i	−0.972692	−	0.232099i	$-0.925441\pi$
$137$		−	5.43330i		−	0.464198i	0.972692	−	0.232099i	$-0.0745594\pi$
$138$		0			0
$139$		−	16.2976i		−	1.38235i	−0.722689	−	0.691173i	$-0.757094\pi$
$139$		−	16.2976i		−	1.38235i	0.722689	−	0.691173i	$-0.242906\pi$
$140$		0			0
$141$	10.0384	−	8.80146i	0.845384	−	0.741217i
$142$		0			0
$143$	−12.8560			−1.07507
$144$		0			0
$145$			1.11432i			0.0925395i
$146$		0			0
$147$	−2.68178	−	11.8240i	−0.221189	−	0.975231i
$148$		0			0
$149$			9.85697i			0.807514i	0.914866	+	0.403757i	$0.132296\pi$
$149$			9.85697i			0.807514i	−0.914866	+	0.403757i	$0.867704\pi$
$150$		0			0
$151$	−5.96893			−0.485744			−0.242872	−	0.970058i	$-0.578090\pi$
$151$	−5.96893			−0.485744			−0.242872	+	0.970058i	$0.578090\pi$
$152$		0			0
$153$	−2.54978	+	19.3345i	−0.206138	+	1.56310i
$154$		0			0
$155$			5.49827i			0.441632i
$156$		0			0
$157$			7.94202i			0.633842i	0.948452	+	0.316921i	$0.102649\pi$
$157$			7.94202i			0.633842i	−0.948452	+	0.316921i	$0.897351\pi$
$158$		0			0
$159$	9.56759	+	10.9122i	0.758759	+	0.865392i
$160$		0			0
$161$	12.6853	−	7.55224i	0.999742	−	0.595200i
$162$		0			0
$163$	18.4764			1.44718			0.723591	−	0.690229i	$-0.242490\pi$
$163$	18.4764			1.44718			0.723591	+	0.690229i	$0.242490\pi$
$164$		0			0
$165$	−6.54366	−	7.46328i	−0.509423	−	0.581015i
$166$		0			0
$167$	−2.29590			−0.177662			−0.0888310	−	0.996047i	$-0.528313\pi$
$167$	−2.29590			−0.177662			−0.0888310	+	0.996047i	$0.528313\pi$
$168$		0			0
$169$	7.96723			0.612864
$170$		0			0
$171$	−0.648021	−	0.0854595i	−0.0495554	−	0.00653525i
$172$		0			0
$173$	−1.10485			−0.0839999			−0.0420000	−	0.999118i	$-0.513373\pi$
$173$	−1.10485			−0.0839999			−0.0420000	+	0.999118i	$0.513373\pi$
$174$		0			0
$175$	1.35345	+	2.27336i	0.102311	+	0.171850i
$176$		0			0
$177$	−17.4787	+	15.3250i	−1.31378	+	1.15190i
$178$		0			0
$179$			14.4797i			1.08227i	0.840937	+	0.541133i	$0.182004\pi$
$179$			14.4797i			1.08227i	−0.840937	+	0.541133i	$0.817996\pi$
$180$		0			0
$181$			11.5405i			0.857800i	0.903352	+	0.428900i	$0.141099\pi$
$181$			11.5405i			0.857800i	−0.903352	+	0.428900i	$0.858901\pi$
$182$		0			0
$183$	1.52388	+	1.73803i	0.112648	+	0.128479i
$184$		0			0
$185$	10.0863			0.741562
$186$		0			0
$187$		−	37.2526i		−	2.72418i
$188$		0			0
$189$	−5.91885	+	12.4084i	−0.430533	+	0.902575i
$190$		0			0
$191$			10.8880i			0.787828i	0.919147	+	0.393914i	$0.128879\pi$
$191$			10.8880i			0.787828i	−0.919147	+	0.393914i	$0.871121\pi$
$192$		0			0
$193$	5.56607			0.400654			0.200327	−	0.979729i	$-0.435800\pi$
$193$	5.56607			0.400654			0.200327	+	0.979729i	$0.435800\pi$
$194$		0			0
$195$	−2.56167	−	2.92167i	−0.183445	−	0.209225i
$196$		0			0
$197$			22.6465i			1.61349i	0.590898	+	0.806746i	$0.298774\pi$
$197$			22.6465i			1.61349i	−0.590898	+	0.806746i	$0.701226\pi$
$198$		0			0
$199$		−	0.111663i		−	0.00791557i	−0.999992	−	0.00395778i	$-0.998740\pi$
$199$		−	0.111663i		−	0.00791557i	0.999992	−	0.00395778i	$-0.00125980\pi$
$200$		0			0
$201$	18.9029	−	16.5737i	1.33331	−	1.16902i
$202$		0			0
$203$	−2.53326	+	1.50818i	−0.177800	+	0.105854i
$204$		0			0
$205$	1.11802			0.0780861
$206$		0			0
$207$	−16.5962	−	2.18867i	−1.15352	−	0.152123i
$208$		0			0
$209$	1.24857			0.0863655
$210$		0			0
$211$	21.8842			1.50657			0.753284	−	0.657696i	$-0.228469\pi$
$211$	21.8842			1.50657			0.753284	+	0.657696i	$0.228469\pi$
$212$		0			0
$213$	−8.46410	−	9.65361i	−0.579951	−	0.661454i
$214$		0			0
$215$	−5.89592			−0.402098
$216$		0			0
$217$	−12.4995	+	7.44165i	−0.848525	+	0.505172i
$218$		0			0
$219$	−13.9113	−	15.8663i	−0.940036	−	1.07214i
$220$		0			0
$221$		−	14.5834i		−	0.980984i
$222$		0			0
$223$			21.6804i			1.45183i	0.687787	+	0.725913i	$0.258582\pi$
$223$			21.6804i			1.45183i	−0.687787	+	0.725913i	$0.741418\pi$
$224$		0			0
$225$	0.392236	−	2.97425i	0.0261491	−	0.198283i
$226$		0			0
$227$	5.04028			0.334535			0.167268	−	0.985912i	$-0.446506\pi$
$227$	5.04028			0.334535			0.167268	+	0.985912i	$0.446506\pi$
$228$		0			0
$229$			12.7545i			0.842838i	0.906866	+	0.421419i	$0.138468\pi$
$229$			12.7545i			0.842838i	−0.906866	+	0.421419i	$0.861532\pi$
$230$		0			0
$231$	8.11018	−	24.9773i	0.533611	−	1.64338i
$232$		0			0
$233$			26.1291i			1.71178i	0.517161	+	0.855888i	$0.326989\pi$
$233$			26.1291i			1.71178i	−0.517161	+	0.855888i	$0.673011\pi$
$234$		0			0
$235$	−7.70789			−0.502807
$236$		0			0
$237$	5.91920	−	5.18984i	0.384494	−	0.337117i
$238$		0			0
$239$		−	1.92107i		−	0.124264i	−0.998068	−	0.0621319i	$-0.980210\pi$
$239$		−	1.92107i		−	0.124264i	0.998068	−	0.0621319i	$-0.0197899\pi$
$240$		0			0
$241$		−	10.6464i		−	0.685795i	−0.939373	−	0.342898i	$-0.888592\pi$
$241$		−	10.6464i		−	0.685795i	0.939373	−	0.342898i	$-0.111408\pi$
$242$		0			0
$243$	13.9847	−	6.88687i	0.897117	−	0.441793i
$244$		0			0
$245$	−3.33633	+	6.15377i	−0.213150	+	0.393150i
$246$		0			0
$247$	0.488782			0.0311005
$248$		0			0
$249$	14.2195	−	12.4674i	0.901127	−	0.790091i
$250$		0			0
$251$	12.6445			0.798113			0.399056	−	0.916926i	$-0.369338\pi$
$251$	12.6445			0.798113			0.399056	+	0.916926i	$0.369338\pi$
$252$		0			0
$253$	31.9767			2.01036
$254$		0			0
$255$	8.46609	−	7.42291i	0.530167	−	0.464840i
$256$		0			0
$257$	−7.25380			−0.452479			−0.226240	−	0.974072i	$-0.572643\pi$
$257$	−7.25380			−0.452479			−0.226240	+	0.974072i	$0.572643\pi$
$258$		0			0
$259$	13.6514	+	22.9299i	0.848255	+	1.42479i
$260$		0			0
$261$	3.31427	+	0.437078i	0.205148	+	0.0270545i
$262$		0			0
$263$		−	19.7889i		−	1.22024i	−0.792311	−	0.610118i	$-0.791122\pi$
$263$		−	19.7889i		−	1.22024i	0.792311	−	0.610118i	$-0.208878\pi$
$264$		0			0
$265$		−	8.37883i		−	0.514708i
$266$		0			0
$267$	5.79666	−	5.08240i	0.354750	−	0.311038i
$268$		0			0
$269$	23.0527			1.40555			0.702773	−	0.711415i	$-0.251945\pi$
$269$	23.0527			1.40555			0.702773	+	0.711415i	$0.251945\pi$
$270$		0			0
$271$		−	18.2292i		−	1.10734i	−0.832735	−	0.553672i	$-0.813226\pi$
$271$		−	18.2292i		−	1.10734i	0.832735	−	0.553672i	$-0.186774\pi$
$272$		0			0
$273$	3.17492	−	9.77793i	0.192155	−	0.591787i
$274$		0			0
$275$			5.73062i			0.345569i
$276$		0			0
$277$	−19.8032			−1.18986			−0.594928	−	0.803779i	$-0.702819\pi$
$277$	−19.8032			−1.18986			−0.594928	+	0.803779i	$0.702819\pi$
$278$		0			0
$279$	16.3532	+	2.15662i	0.979042	+	0.129114i
$280$		0			0
$281$		−	0.0541878i		−	0.00323257i	−0.999999	−	0.00161629i	$-0.999486\pi$
$281$		−	0.0541878i		−	0.00323257i	0.999999	−	0.00161629i	$-0.000514480\pi$
$282$		0			0
$283$			2.74845i			0.163378i	0.996658	+	0.0816891i	$0.0260315\pi$
$283$			2.74845i			0.163378i	−0.996658	+	0.0816891i	$0.973969\pi$
$284$		0			0
$285$	0.248789	+	0.283753i	0.0147370	+	0.0168081i
$286$		0			0
$287$	1.51319	+	2.54167i	0.0893209	+	0.150030i
$288$		0			0
$289$	25.2581			1.48577
$290$		0			0
$291$	10.6608	+	12.1590i	0.624947	+	0.712774i
$292$		0			0
$293$	4.46410			0.260795			0.130398	−	0.991462i	$-0.458375\pi$
$293$	4.46410			0.260795			0.130398	+	0.991462i	$0.458375\pi$
$294$		0			0
$295$	13.4209			0.781393
$296$		0			0
$297$	−24.7643	+	16.5351i	−1.43697	+	0.959463i
$298$		0			0
$299$	12.5180			0.723937
$300$		0			0
$301$	−7.97985	−	13.4035i	−0.459951	−	0.772568i
$302$		0			0
$303$	10.5824	−	9.27848i	0.607945	−	0.533034i
$304$		0			0
$305$		−	1.33454i		−	0.0764153i
$306$		0			0
$307$		−	3.39682i		−	0.193867i	−0.995291	−	0.0969334i	$-0.969097\pi$
$307$		−	3.39682i		−	0.193867i	0.995291	−	0.0969334i	$-0.0309034\pi$
$308$		0			0
$309$	3.67670	+	4.19340i	0.209160	+	0.238554i
$310$		0			0
$311$	0.473808			0.0268672			0.0134336	−	0.999910i	$-0.495724\pi$
$311$	0.473808			0.0268672			0.0134336	+	0.999910i	$0.495724\pi$
$312$		0			0
$313$		−	12.5169i		−	0.707497i	−0.935341	−	0.353749i	$-0.884907\pi$
$313$		−	12.5169i		−	0.707497i	0.935341	−	0.353749i	$-0.115093\pi$
$314$		0			0
$315$	7.29241	−	3.13381i	0.410881	−	0.176570i
$316$		0			0
$317$			30.3962i			1.70722i	0.520913	+	0.853610i	$0.325592\pi$
$317$			30.3962i			1.70722i	−0.520913	+	0.853610i	$0.674408\pi$
$318$		0			0
$319$	−6.38576			−0.357534
$320$		0			0
$321$	0.402011	+	0.458508i	0.0224381	+	0.0255914i
$322$		0			0
$323$			1.41634i			0.0788072i
$324$		0			0
$325$			2.24338i			0.124440i
$326$		0			0
$327$	−17.9770	+	15.7619i	−0.994132	+	0.871636i
$328$		0			0
$329$	−10.4323	−	17.5228i	−0.575150	−	0.966064i
$330$		0			0
$331$	19.8653			1.09190			0.545948	−	0.837819i	$-0.316169\pi$
$331$	19.8653			1.09190			0.545948	+	0.837819i	$0.316169\pi$
$332$		0			0
$333$	3.95623	−	29.9992i	0.216800	−	1.64395i
$334$		0			0
$335$	−14.5144			−0.793008
$336$		0			0
$337$	32.7104			1.78185			0.890924	−	0.454153i	$-0.150058\pi$
$337$	32.7104			1.78185			0.890924	+	0.454153i	$0.150058\pi$
$338$		0			0
$339$	−2.88613	−	3.29173i	−0.156753	−	0.178782i
$340$		0			0
$341$	−31.5085			−1.70628
$342$		0			0
$343$	−18.5053	+	0.744166i	−0.999192	+	0.0401812i
$344$		0			0
$345$	6.37165	+	7.26709i	0.343038	+	0.391247i
$346$		0			0
$347$			22.7318i			1.22031i	0.792283	+	0.610154i	$0.208893\pi$
$347$			22.7318i			1.22031i	−0.792283	+	0.610154i	$0.791107\pi$
$348$		0			0
$349$		−	8.77997i		−	0.469981i	−0.971998	−	0.234990i	$-0.924494\pi$
$349$		−	8.77997i		−	0.469981i	0.971998	−	0.234990i	$-0.0755059\pi$
$350$		0			0
$351$	−9.69455	+	6.47304i	−0.517457	+	0.345505i
$352$		0			0
$353$	12.5148			0.666098			0.333049	−	0.942910i	$-0.391923\pi$
$353$	12.5148			0.666098			0.333049	+	0.942910i	$0.391923\pi$
$354$		0			0
$355$			7.41245i			0.393412i
$356$		0			0
$357$	28.3334	+	9.19991i	1.49956	+	0.486911i
$358$		0			0
$359$		−	5.22814i		−	0.275931i	−0.990437	−	0.137965i	$-0.955944\pi$
$359$		−	5.22814i		−	0.275931i	0.990437	−	0.137965i	$-0.0440563\pi$
$360$		0			0
$361$	18.9525			0.997502
$362$		0			0
$363$	28.4433	−	24.9386i	1.49289	−	1.30894i
$364$		0			0
$365$			12.1828i			0.637677i
$366$		0			0
$367$		−	29.7583i		−	1.55337i	−0.629888	−	0.776686i	$-0.716899\pi$
$367$		−	29.7583i		−	1.55337i	0.629888	−	0.776686i	$-0.283101\pi$
$368$		0			0
$369$	0.438530	−	3.32528i	0.0228289	−	0.173107i
$370$		0			0
$371$	19.0481	−	11.3404i	0.988928	−	0.588762i
$372$		0			0
$373$	−14.0263			−0.726256			−0.363128	−	0.931739i	$-0.618291\pi$
$373$	−14.0263			−0.726256			−0.363128	+	0.931739i	$0.618291\pi$
$374$		0			0
$375$	−1.30235	+	1.14188i	−0.0672531	+	0.0589662i
$376$		0			0
$377$	−2.49985			−0.128749
$378$		0			0
$379$	14.5017			0.744902			0.372451	−	0.928052i	$-0.378517\pi$
$379$	14.5017			0.744902			0.372451	+	0.928052i	$0.378517\pi$
$380$		0			0
$381$	17.1987	−	15.0795i	0.881115	−	0.772545i
$382$		0			0
$383$	−9.35624			−0.478081			−0.239041	−	0.971010i	$-0.576833\pi$
$383$	−9.35624			−0.478081			−0.239041	+	0.971010i	$0.576833\pi$
$384$		0			0
$385$	−13.0278	+	7.75612i	−0.663956	+	0.395289i
$386$		0			0
$387$	−2.31259	+	17.5359i	−0.117556	+	0.891401i
$388$		0			0
$389$		−	7.16415i		−	0.363237i	−0.983369	−	0.181618i	$-0.941866\pi$
$389$		−	7.16415i		−	0.363237i	0.983369	−	0.181618i	$-0.0581336\pi$
$390$		0			0
$391$			36.2733i			1.83442i
$392$		0			0
$393$	13.3855	−	11.7362i	0.675211	−	0.592012i
$394$		0			0
$395$	−4.54501			−0.228684
$396$		0			0
$397$		−	23.2936i		−	1.16907i	−0.811367	−	0.584537i	$-0.801276\pi$
$397$		−	23.2936i		−	1.16907i	0.811367	−	0.584537i	$-0.198724\pi$
$398$		0			0
$399$	−0.308348	+	0.949633i	−0.0154367	+	0.0475411i
$400$		0			0
$401$		−	14.2990i		−	0.714060i	−0.934093	−	0.357030i	$-0.883789\pi$
$401$		−	14.2990i		−	0.714060i	0.934093	−	0.357030i	$-0.116211\pi$
$402$		0			0
$403$	−12.3347			−0.614436
$404$		0			0
$405$	−8.69230	−	2.33322i	−0.431924	−	0.115938i
$406$		0			0
$407$			57.8009i			2.86508i
$408$		0			0
$409$		−	21.0357i		−	1.04015i	−0.854120	−	0.520075i	$-0.825904\pi$
$409$		−	21.0357i		−	1.04015i	0.854120	−	0.520075i	$-0.174096\pi$
$410$		0			0
$411$	6.20416	+	7.07607i	0.306029	+	0.349037i
$412$		0			0
$413$	18.1645	+	30.5105i	0.893817	+	1.50132i
$414$		0			0
$415$	−10.9184			−0.535962
$416$		0			0
$417$	18.6099	+	21.2252i	0.911330	+	1.03940i
$418$		0			0
$419$	32.7044			1.59771			0.798857	−	0.601521i	$-0.205439\pi$
$419$	32.7044			1.59771			0.798857	+	0.601521i	$0.205439\pi$
$420$		0			0
$421$	−19.1758			−0.934569			−0.467285	−	0.884107i	$-0.654768\pi$
$421$	−19.1758			−0.934569			−0.467285	+	0.884107i	$0.654768\pi$
$422$		0			0
$423$	−3.02332	+	22.9252i	−0.146999	+	1.11466i
$424$		0			0
$425$	−6.50062			−0.315326
$426$		0			0
$427$	3.03388	−	1.80623i	0.146820	−	0.0874097i
$428$		0			0
$429$	16.7430	−	14.6799i	0.808359	−	0.708754i
$430$		0			0
$431$			19.3591i			0.932495i	0.884654	+	0.466248i	$0.154394\pi$
$431$			19.3591i			0.932495i	−0.884654	+	0.466248i	$0.845606\pi$
$432$		0			0
$433$		−	4.02981i		−	0.193660i	−0.995301	−	0.0968302i	$-0.969130\pi$
$433$		−	4.02981i		−	0.193660i	0.995301	−	0.0968302i	$-0.0308704\pi$
$434$		0			0
$435$	−1.27242	−	1.45124i	−0.0610079	−	0.0695817i
$436$		0			0
$437$	−1.21575			−0.0581573
$438$		0			0
$439$			3.28426i			0.156749i	0.996924	+	0.0783746i	$0.0249730\pi$
$439$			3.28426i			0.156749i	−0.996924	+	0.0783746i	$0.975027\pi$
$440$		0			0
$441$	16.9942	+	12.3368i	0.809248	+	0.587467i
$442$		0			0
$443$			20.2006i			0.959760i	0.877334	+	0.479880i	$0.159320\pi$
$443$			20.2006i			0.959760i	−0.877334	+	0.479880i	$0.840680\pi$
$444$		0			0
$445$	−4.45092			−0.210994
$446$		0			0
$447$	−11.2554	−	12.8372i	−0.532364	−	0.607180i
$448$		0			0
$449$		−	2.84898i		−	0.134452i	−0.997738	−	0.0672259i	$-0.978585\pi$
$449$		−	2.84898i		−	0.134452i	0.997738	−	0.0672259i	$-0.0214148\pi$
$450$		0			0
$451$			6.40697i			0.301692i
$452$		0			0
$453$	7.77364	−	6.81578i	0.365237	−	0.320233i
$454$		0			0
$455$	−5.10002	+	3.03631i	−0.239092	+	0.142345i
$456$		0			0
$457$	−22.6864			−1.06123			−0.530613	−	0.847614i	$-0.678038\pi$
$457$	−22.6864			−1.06123			−0.530613	+	0.847614i	$0.678038\pi$
$458$		0			0
$459$	−18.7569	−	28.0918i	−0.875495	−	1.31121i
$460$		0			0
$461$	−16.6309			−0.774579			−0.387290	−	0.921958i	$-0.626589\pi$
$461$	−16.6309			−0.774579			−0.387290	+	0.921958i	$0.626589\pi$
$462$		0			0
$463$	16.8319			0.782247			0.391123	−	0.920338i	$-0.372087\pi$
$463$	16.8319			0.782247			0.391123	+	0.920338i	$0.372087\pi$
$464$		0			0
$465$	−6.27835	−	7.16068i	−0.291151	−	0.332069i
$466$		0			0
$467$	40.2591			1.86297			0.931484	−	0.363782i	$-0.118515\pi$
$467$	40.2591			1.86297			0.931484	+	0.363782i	$0.118515\pi$
$468$		0			0
$469$	−19.6446	−	32.9965i	−0.907104	−	1.52364i
$470$		0			0
$471$	−9.06880	−	10.3433i	−0.417868	−	0.476594i
$472$		0			0
$473$		−	33.7873i		−	1.55354i
$474$		0			0
$475$		−	0.217877i		−	0.00999690i
$476$		0			0
$477$	−24.9207	−	3.28648i	−1.14104	−	0.150478i
$478$		0			0
$479$	−6.90837			−0.315651			−0.157826	−	0.987467i	$-0.550448\pi$
$479$	−6.90837			−0.315651			−0.157826	+	0.987467i	$0.550448\pi$
$480$		0			0
$481$			22.6275i			1.03173i
$482$		0			0
$483$	−7.89699	+	24.3207i	−0.359326	+	1.10663i
$484$		0			0
$485$		−	9.33620i		−	0.423935i
$486$		0			0
$487$	−4.57854			−0.207473			−0.103737	−	0.994605i	$-0.533080\pi$
$487$	−4.57854			−0.207473			−0.103737	+	0.994605i	$0.533080\pi$
$488$		0			0
$489$	−24.0627	+	21.0977i	−1.08815	+	0.954073i
$490$		0			0
$491$			20.0323i			0.904046i	0.892006	+	0.452023i	$0.149297\pi$
$491$			20.0323i			0.904046i	−0.892006	+	0.452023i	$0.850703\pi$
$492$		0			0
$493$		−	7.24380i		−	0.326244i
$494$		0			0
$495$	17.0443	+	2.24776i	0.766083	+	0.101029i
$496$		0			0
$497$	−16.8512	+	10.0324i	−0.755878	+	0.450015i
$498$		0			0
$499$	14.4917			0.648739			0.324369	−	0.945930i	$-0.394848\pi$
$499$	14.4917			0.648739			0.324369	+	0.945930i	$0.394848\pi$
$500$		0			0
$501$	2.99007	−	2.62163i	0.133586	−	0.117126i
$502$		0			0
$503$	44.1442			1.96829			0.984145	−	0.177363i	$-0.0567568\pi$
$503$	44.1442			1.96829			0.984145	+	0.177363i	$0.0567568\pi$
$504$		0			0
$505$	−8.12564			−0.361586
$506$		0			0
$507$	−10.3761	+	9.09760i	−0.460820	+	0.404038i
$508$		0			0
$509$	27.8389			1.23394			0.616968	−	0.786988i	$-0.288361\pi$
$509$	27.8389			1.23394			0.616968	+	0.786988i	$0.288361\pi$
$510$		0			0
$511$	−27.6959	+	16.4889i	−1.22519	+	0.729424i
$512$		0			0
$513$	0.941535	−	0.628662i	0.0415698	−	0.0277561i
$514$		0			0
$515$		−	3.21987i		−	0.141884i
$516$		0			0
$517$		−	44.1710i		−	1.94264i
$518$		0			0
$519$	1.43890	−	1.26160i	0.0631606	−	0.0553780i
$520$		0			0
$521$	15.5640			0.681873			0.340936	−	0.940086i	$-0.389256\pi$
$521$	15.5640			0.681873			0.340936	+	0.940086i	$0.389256\pi$
$522$		0			0
$523$		−	40.3413i		−	1.76400i	−0.471246	−	0.882002i	$-0.656196\pi$
$523$		−	40.3413i		−	1.76400i	0.471246	−	0.882002i	$-0.343804\pi$
$524$		0			0
$525$	−4.35857	−	1.41524i	−0.190223	−	0.0617660i
$526$		0			0
$527$		−	35.7422i		−	1.55695i
$528$		0			0
$529$	−8.13619			−0.353748
$530$		0			0
$531$	5.26415	−	39.9170i	0.228445	−	1.73225i
$532$		0			0
$533$			2.50815i			0.108640i
$534$		0			0
$535$		−	0.352062i		−	0.0152209i
$536$		0			0
$537$	−16.5341	−	18.8577i	−0.713498	−	0.813770i
$538$		0			0
$539$	−35.2649	−	19.1192i	−1.51897	−	0.823523i
$540$		0			0
$541$	8.24259			0.354377			0.177188	−	0.984177i	$-0.443300\pi$
$541$	8.24259			0.354377			0.177188	+	0.984177i	$0.443300\pi$
$542$		0			0
$543$	−13.1778	−	15.0298i	−0.565515	−	0.644990i
$544$		0			0
$545$	13.8035			0.591278
$546$		0			0
$547$	13.2243			0.565430			0.282715	−	0.959204i	$-0.408765\pi$
$547$	13.2243			0.565430			0.282715	+	0.959204i	$0.408765\pi$
$548$		0			0
$549$	−3.96924	−	0.523454i	−0.169403	−	0.0223405i
$550$		0			0
$551$	0.242786			0.0103430
$552$		0			0
$553$	−6.15146	−	10.3324i	−0.261587	−	0.439380i
$554$		0			0
$555$	−13.1359	+	11.5173i	−0.557590	+	0.488884i
$556$		0			0
$557$		−	4.39173i		−	0.186083i	−0.995662	−	0.0930417i	$-0.970341\pi$
$557$		−	4.39173i		−	0.186083i	0.995662	−	0.0930417i	$-0.0296590\pi$
$558$		0			0
$559$		−	13.2268i		−	0.559434i
$560$		0			0
$561$	42.5378	+	48.5159i	1.79595	+	2.04834i
$562$		0			0
$563$	−5.30197			−0.223451			−0.111726	−	0.993739i	$-0.535638\pi$
$563$	−5.30197			−0.223451			−0.111726	+	0.993739i	$0.535638\pi$
$564$		0			0
$565$			2.52753i			0.106334i
$566$		0			0
$567$	−6.46038	−	22.9186i	−0.271310	−	0.962492i
$568$		0			0
$569$		−	16.1380i		−	0.676541i	−0.941049	−	0.338271i	$-0.890158\pi$
$569$		−	16.1380i		−	0.676541i	0.941049	−	0.338271i	$-0.109842\pi$
$570$		0			0
$571$	−18.4724			−0.773044			−0.386522	−	0.922280i	$-0.626324\pi$
$571$	−18.4724			−0.773044			−0.386522	+	0.922280i	$0.626324\pi$
$572$		0			0
$573$	−12.4327	−	14.1800i	−0.519385	−	0.592378i
$574$		0			0
$575$		−	5.57998i		−	0.232701i
$576$		0			0
$577$		−	16.2609i		−	0.676950i	−0.940975	−	0.338475i	$-0.890089\pi$
$577$		−	16.2609i		−	0.676950i	0.940975	−	0.338475i	$-0.109911\pi$
$578$		0			0
$579$	−7.24897	+	6.35576i	−0.301257	+	0.264136i
$580$		0			0
$581$	−14.7775	−	24.8214i	−0.613074	−	1.02976i
$582$		0			0
$583$	48.0159			1.98862
$584$		0			0
$585$	6.67238	+	0.879936i	0.275869	+	0.0363809i
$586$		0			0
$587$	−43.2616			−1.78560			−0.892798	−	0.450456i	$-0.851261\pi$
$587$	−43.2616			−1.78560			−0.892798	+	0.450456i	$0.851261\pi$
$588$		0			0
$589$	1.19795			0.0493606
$590$		0			0
$591$	−25.8594	−	29.4936i	−1.06372	−	1.21321i
$592$		0			0
$593$	18.6653			0.766490			0.383245	−	0.923647i	$-0.374806\pi$
$593$	18.6653			0.766490			0.383245	+	0.923647i	$0.374806\pi$
$594$		0			0
$595$	−8.79829	−	14.7783i	−0.360695	−	0.605849i
$596$		0			0
$597$	0.127505	+	0.145424i	0.00521844	+	0.00595181i
$598$		0			0
$599$		−	2.16911i		−	0.0886273i	−0.999018	−	0.0443136i	$-0.985890\pi$
$599$		−	2.16911i		−	0.0886273i	0.999018	−	0.0443136i	$-0.0141101\pi$
$600$		0			0
$601$			22.6531i			0.924040i	0.886870	+	0.462020i	$0.152875\pi$
$601$			22.6531i			0.924040i	−0.886870	+	0.462020i	$0.847125\pi$
$602$		0			0
$603$	−5.69309	+	43.1695i	−0.231841	+	1.75800i
$604$		0			0
$605$	−21.8400			−0.887922
$606$		0			0
$607$			38.7693i			1.57360i	0.617210	+	0.786798i	$0.288263\pi$
$607$			38.7693i			1.57360i	−0.617210	+	0.786798i	$0.711737\pi$
$608$		0			0
$609$	1.57703	−	4.85685i	0.0639045	−	0.196810i
$610$		0			0
$611$		−	17.2918i		−	0.699549i
$612$		0			0
$613$	−31.8640			−1.28697			−0.643486	−	0.765458i	$-0.722513\pi$
$613$	−31.8640			−1.28697			−0.643486	+	0.765458i	$0.722513\pi$
$614$		0			0
$615$	−1.45606	+	1.27664i	−0.0587140	+	0.0514793i
$616$		0			0
$617$			11.0328i			0.444164i	0.975028	+	0.222082i	$0.0712853\pi$
$617$			11.0328i			0.444164i	−0.975028	+	0.222082i	$0.928715\pi$
$618$		0			0
$619$			22.0902i			0.887881i	0.896056	+	0.443941i	$0.146420\pi$
$619$			22.0902i			0.887881i	−0.896056	+	0.443941i	$0.853580\pi$
$620$		0			0
$621$	24.1133	−	16.1004i	0.967635	−	0.646089i
$622$		0			0
$623$	−6.02412	−	10.1185i	−0.241351	−	0.405391i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−1.62608	+	1.42572i	−0.0649394	+	0.0569376i
$628$		0			0
$629$	−65.5674			−2.61434
$630$		0			0
$631$	−10.3052			−0.410244			−0.205122	−	0.978736i	$-0.565759\pi$
$631$	−10.3052			−0.410244			−0.205122	+	0.978736i	$0.565759\pi$
$632$		0			0
$633$	−28.5008	+	24.9890i	−1.13281	+	0.993223i
$634$		0			0
$635$	−13.2059			−0.524059
$636$		0			0
$637$	−13.8053	−	7.48466i	−0.546985	−	0.296553i
$638$		0			0
$639$	22.0465	+	2.90743i	0.872144	+	0.115016i
$640$		0			0
$641$			49.4982i			1.95506i	0.210790	+	0.977531i	$0.432396\pi$
$641$			49.4982i			1.95506i	−0.210790	+	0.977531i	$0.567604\pi$
$642$		0			0
$643$		−	11.6429i		−	0.459150i	−0.973291	−	0.229575i	$-0.926266\pi$
$643$		−	11.6429i		−	0.459150i	0.973291	−	0.229575i	$-0.0737336\pi$
$644$		0			0
$645$	7.67856	−	6.73241i	0.302343	−	0.265088i
$646$		0			0
$647$	18.0790			0.710757			0.355379	−	0.934722i	$-0.384352\pi$
$647$	18.0790			0.710757			0.355379	+	0.934722i	$0.384352\pi$
$648$		0			0
$649$			76.9099i			3.01898i
$650$		0			0
$651$	7.78135	−	23.9646i	0.304975	−	0.939246i
$652$		0			0
$653$			30.6974i			1.20128i	0.799518	+	0.600642i	$0.205088\pi$
$653$			30.6974i			1.20128i	−0.799518	+	0.600642i	$0.794912\pi$
$654$		0			0
$655$	−10.2780			−0.401594
$656$		0			0
$657$	36.2347	+	4.77854i	1.41365	+	0.186429i
$658$		0			0
$659$			0.244430i			0.00952164i	0.999989	+	0.00476082i	$0.00151542\pi$
$659$			0.244430i			0.00952164i	−0.999989	+	0.00476082i	$0.998485\pi$
$660$		0			0
$661$			24.0272i			0.934550i	0.884112	+	0.467275i	$0.154764\pi$
$661$			24.0272i			0.934550i	−0.884112	+	0.467275i	$0.845236\pi$
$662$		0			0
$663$	16.6524	+	18.9927i	0.646726	+	0.737615i
$664$		0			0
$665$	0.495314	−	0.294887i	0.0192074	−	0.0114352i
$666$		0			0
$667$	6.21790			0.240758
$668$		0			0
$669$	−24.7563	−	28.2355i	−0.957134	−	1.09165i
$670$		0			0
$671$	7.64772			0.295237
$672$		0			0
$673$	−10.2656			−0.395712			−0.197856	−	0.980231i	$-0.563398\pi$
$673$	−10.2656			−0.395712			−0.197856	+	0.980231i	$0.563398\pi$
$674$		0			0
$675$	2.88539	+	4.32140i	0.111059	+	0.166331i
$676$		0			0
$677$	−4.72154			−0.181463			−0.0907317	−	0.995875i	$-0.528921\pi$
$677$	−4.72154			−0.181463			−0.0907317	+	0.995875i	$0.528921\pi$
$678$		0			0
$679$	21.2245	−	12.6361i	0.814523	−	0.484930i
$680$		0			0
$681$	−6.56422	+	5.75538i	−0.251541	+	0.220547i
$682$		0			0
$683$		−	34.9227i		−	1.33628i	−0.744036	−	0.668139i	$-0.767091\pi$
$683$		−	34.9227i		−	1.33628i	0.744036	−	0.668139i	$-0.232909\pi$
$684$		0			0
$685$		−	5.43330i		−	0.207596i
$686$		0			0
$687$	−14.5640	−	16.6108i	−0.555652	−	0.633741i
$688$		0			0
$689$	18.7969			0.716106
$690$		0			0
$691$			42.9041i			1.63215i	0.577948	+	0.816074i	$0.303854\pi$
$691$			42.9041i			1.63215i	−0.577948	+	0.816074i	$0.696146\pi$
$692$		0			0
$693$	17.9587	+	41.7900i	0.682194	+	1.58747i
$694$		0			0
$695$		−	16.2976i		−	0.618204i
$696$		0			0
$697$	−7.26785			−0.275289
$698$		0			0
$699$	−29.8362	−	34.0293i	−1.12851	−	1.28711i
$700$		0			0
$701$			14.1880i			0.535874i	0.963436	+	0.267937i	$0.0863419\pi$
$701$			14.1880i			0.535874i	−0.963436	+	0.267937i	$0.913658\pi$
$702$		0			0
$703$		−	2.19758i		−	0.0828834i
$704$		0			0
$705$	10.0384	−	8.80146i	0.378067	−	0.331482i
$706$		0			0
$707$	−10.9977	−	18.4725i	−0.413610	−	0.694730i
$708$		0			0
$709$	43.7048			1.64137			0.820684	−	0.571382i	$-0.193593\pi$
$709$	43.7048			1.64137			0.820684	+	0.571382i	$0.193593\pi$
$710$		0			0
$711$	−1.78272	+	13.5180i	−0.0668572	+	0.506964i
$712$		0			0
$713$	30.6803			1.14898
$714$		0			0
$715$	−12.8560			−0.480786
$716$		0			0
$717$	2.19363	+	2.50191i	0.0819225	+	0.0934355i
$718$		0			0
$719$	−9.64243			−0.359602			−0.179801	−	0.983703i	$-0.557545\pi$
$719$	−9.64243			−0.359602			−0.179801	+	0.983703i	$0.557545\pi$
$720$		0			0
$721$	7.31993	−	4.35794i	0.272608	−	0.162298i
$722$		0			0
$723$	12.1569	+	13.8654i	0.452119	+	0.515658i
$724$		0			0
$725$			1.11432i			0.0413849i
$726$		0			0
$727$			47.0202i			1.74388i	0.489611	+	0.871941i	$0.337139\pi$
$727$			47.0202i			1.74388i	−0.489611	+	0.871941i	$0.662861\pi$
$728$		0			0
$729$	−10.3490	+	24.9379i	−0.383296	+	0.923625i
$730$		0			0
$731$	38.3271			1.41758
$732$		0			0
$733$			40.3873i			1.49174i	0.666093	+	0.745869i	$0.267965\pi$
$733$			40.3873i			1.49174i	−0.666093	+	0.745869i	$0.732035\pi$
$734$		0			0
$735$	−2.68178	−	11.8240i	−0.0989188	−	0.436137i
$736$		0			0
$737$		−	83.1767i		−	3.06385i
$738$		0			0
$739$	12.5093			0.460160			0.230080	−	0.973172i	$-0.426101\pi$
$739$	12.5093			0.460160			0.230080	+	0.973172i	$0.426101\pi$
$740$		0			0
$741$	−0.636566	+	0.558129i	−0.0233848	+	0.0205034i
$742$		0			0
$743$		−	37.6376i		−	1.38079i	−0.723433	−	0.690395i	$-0.757437\pi$
$743$		−	37.6376i		−	1.38079i	0.723433	−	0.690395i	$-0.242563\pi$
$744$		0			0
$745$			9.85697i			0.361131i
$746$		0			0
$747$	−4.28258	+	32.4739i	−0.156691	+	1.18816i
$748$		0			0
$749$	0.800363	−	0.476499i	0.0292446	−	0.0174109i
$750$		0			0
$751$	−1.45321			−0.0530282			−0.0265141	−	0.999648i	$-0.508441\pi$
$751$	−1.45321			−0.0530282			−0.0265141	+	0.999648i	$0.508441\pi$
$752$		0			0
$753$	−16.4676	+	14.4384i	−0.600111	+	0.526166i
$754$		0			0
$755$	−5.96893			−0.217231
$756$		0			0
$757$	11.1113			0.403848			0.201924	−	0.979401i	$-0.435281\pi$
$757$	11.1113			0.403848			0.201924	+	0.979401i	$0.435281\pi$
$758$		0			0
$759$	−41.6449	+	36.5135i	−1.51162	+	1.32536i
$760$		0			0
$761$	−23.4744			−0.850946			−0.425473	−	0.904971i	$-0.639892\pi$
$761$	−23.4744			−0.850946			−0.425473	+	0.904971i	$0.639892\pi$
$762$		0			0
$763$	18.6824	+	31.3804i	0.676349	+	1.13605i
$764$		0			0
$765$	−2.54978	+	19.3345i	−0.0921875	+	0.699039i
$766$		0			0
$767$			30.1081i			1.08714i
$768$		0			0
$769$		−	13.1458i		−	0.474051i	−0.971503	−	0.237026i	$-0.923827\pi$
$769$		−	13.1458i		−	0.474051i	0.971503	−	0.237026i	$-0.0761725\pi$
$770$		0			0
$771$	9.44699	−	8.28294i	0.340225	−	0.298303i
$772$		0			0
$773$	34.2816			1.23302			0.616512	−	0.787346i	$-0.288545\pi$
$773$	34.2816			1.23302			0.616512	+	0.787346i	$0.288545\pi$
$774$		0			0
$775$			5.49827i			0.197504i
$776$		0			0
$777$	−43.9619	−	14.2745i	−1.57713	−	0.512096i
$778$		0			0
$779$		−	0.243592i		−	0.00872759i
$780$		0			0
$781$	−42.4779			−1.51998
$782$		0			0
$783$	−4.81544	+	3.21526i	−0.172090	+	0.114904i
$784$		0			0
$785$			7.94202i			0.283463i
$786$		0			0
$787$		−	17.1687i		−	0.611996i	−0.952032	−	0.305998i	$-0.901010\pi$
$787$		−	17.1687i		−	0.611996i	0.952032	−	0.305998i	$-0.0989901\pi$
$788$		0			0
$789$	22.5965	+	25.7721i	0.804456	+	0.917511i
$790$		0			0
$791$	−5.74599	+	3.42089i	−0.204304	+	0.121633i
$792$		0			0
$793$	2.99387			0.106316
$794$		0			0
$795$	9.56759	+	10.9122i	0.339328	+	0.387015i
$796$		0			0
$797$	43.9928			1.55830			0.779152	−	0.626834i	$-0.215650\pi$
$797$	43.9928			1.55830			0.779152	+	0.626834i	$0.215650\pi$
$798$		0			0
$799$	50.1061			1.77263
$800$		0			0
$801$	−1.74581	+	13.2381i	−0.0616853	+	0.467747i
$802$		0			0
$803$	−69.8150			−2.46372
$804$		0			0
$805$	12.6853	−	7.55224i	0.447098	−	0.266182i
$806$		0			0
$807$	−30.0226	+	26.3233i	−1.05685	+	0.926623i
$808$		0			0
$809$		−	27.6874i		−	0.973436i	−0.873559	−	0.486718i	$-0.838194\pi$
$809$		−	27.6874i		−	0.973436i	0.873559	−	0.486718i	$-0.161806\pi$
$810$		0			0
$811$			6.48782i			0.227818i	0.993491	+	0.113909i	$0.0363372\pi$
$811$			6.48782i			0.227818i	−0.993491	+	0.113909i	$0.963663\pi$
$812$		0			0
$813$	20.8155	+	23.7408i	0.730031	+	0.832627i
$814$		0			0
$815$	18.4764			0.647199
$816$		0			0
$817$			1.28459i			0.0449420i
$818$		0			0
$819$	7.03034	+	16.3597i	0.245660	+	0.571653i
$820$		0			0
$821$		−	2.97361i		−	0.103780i	−0.998653	−	0.0518899i	$-0.983476\pi$
$821$		−	2.97361i		−	0.103780i	0.998653	−	0.0518899i	$-0.0165245\pi$
$822$		0			0
$823$	21.0592			0.734078			0.367039	−	0.930206i	$-0.380372\pi$
$823$	21.0592			0.734078			0.367039	+	0.930206i	$0.380372\pi$
$824$		0			0
$825$	−6.54366	−	7.46328i	−0.227821	−	0.259838i
$826$		0			0
$827$			8.53762i			0.296882i	0.988921	+	0.148441i	$0.0474255\pi$
$827$			8.53762i			0.296882i	−0.988921	+	0.148441i	$0.952574\pi$
$828$		0			0
$829$			38.7564i			1.34607i	0.739612	+	0.673033i	$0.235009\pi$
$829$			38.7564i			1.34607i	−0.739612	+	0.673033i	$0.764991\pi$
$830$		0			0
$831$	25.7907	−	22.6128i	0.894668	−	0.784428i
$832$		0			0
$833$	21.6882	−	40.0033i	0.751452	−	1.38603i
$834$		0			0
$835$	−2.29590			−0.0794529
$836$		0			0
$837$	−23.7602	+	15.8647i	−0.821274	+	0.548364i
$838$		0			0
$839$	−25.5028			−0.880455			−0.440228	−	0.897886i	$-0.645102\pi$
$839$	−25.5028			−0.880455			−0.440228	+	0.897886i	$0.645102\pi$
$840$		0			0
$841$	27.7583			0.957182
$842$		0			0
$843$	0.0618758	+	0.0705715i	0.00213111	+	0.00243061i
$844$		0			0
$845$	7.96723			0.274081
$846$		0			0
$847$	−29.5594	−	49.6501i	−1.01567	−	1.70600i
$848$		0			0
$849$	−3.13839	−	3.57944i	−0.107709	−	0.122846i
$850$		0			0
$851$		−	56.2815i		−	1.92931i
$852$		0			0
$853$			33.9572i			1.16267i	0.813664	+	0.581336i	$0.197470\pi$
$853$			33.9572i			1.16267i	−0.813664	+	0.581336i	$0.802530\pi$
$854$		0			0
$855$	−0.648021	−	0.0854595i	−0.0221619	−	0.00292265i
$856$		0			0
$857$	−15.7208			−0.537012			−0.268506	−	0.963278i	$-0.586530\pi$
$857$	−15.7208			−0.537012			−0.268506	+	0.963278i	$0.586530\pi$
$858$		0			0
$859$		−	12.3593i		−	0.421693i	−0.977519	−	0.210846i	$-0.932378\pi$
$859$		−	12.3593i		−	0.421693i	0.977519	−	0.210846i	$-0.0676220\pi$
$860$		0			0
$861$	−4.87298	−	1.58227i	−0.166071	−	0.0539235i
$862$		0			0
$863$			31.4856i			1.07178i	0.844287	+	0.535892i	$0.180024\pi$
$863$			31.4856i			1.07178i	−0.844287	+	0.535892i	$0.819976\pi$
$864$		0			0
$865$	−1.10485			−0.0375659
$866$		0			0
$867$	−32.8949	+	28.8416i	−1.11717	+	0.979512i
$868$		0			0
$869$		−	26.0457i		−	0.883541i
$870$		0			0
$871$		−	32.5614i		−	1.10330i
$872$		0			0
$873$	−27.7682	−	3.66200i	−0.939811	−	0.123940i
$874$		0			0
$875$	1.35345	+	2.27336i	0.0457551	+	0.0768536i
$876$		0			0
$877$	−5.74226			−0.193902			−0.0969511	−	0.995289i	$-0.530909\pi$
$877$	−5.74226			−0.193902			−0.0969511	+	0.995289i	$0.530909\pi$
$878$		0			0
$879$	−5.81382	+	5.09745i	−0.196095	+	0.171933i
$880$		0			0
$881$	16.8840			0.568835			0.284417	−	0.958701i	$-0.408200\pi$
$881$	16.8840			0.568835			0.284417	+	0.958701i	$0.408200\pi$
$882$		0			0
$883$	−29.1875			−0.982236			−0.491118	−	0.871093i	$-0.663412\pi$
$883$	−29.1875			−0.982236			−0.491118	+	0.871093i	$0.663412\pi$
$884$		0			0
$885$	−17.4787	+	15.3250i	−0.587539	+	0.515143i
$886$		0			0
$887$	−50.3734			−1.69137			−0.845687	−	0.533680i	$-0.820809\pi$
$887$	−50.3734			−1.69137			−0.845687	+	0.533680i	$0.820809\pi$
$888$		0			0
$889$	−17.8735	−	30.0217i	−0.599459	−	1.00690i
$890$		0			0
$891$	13.3708	−	49.8123i	0.447938	−	1.66877i
$892$		0			0
$893$			1.67938i			0.0561982i
$894$		0			0
$895$			14.4797i			0.484004i
$896$		0			0
$897$	−16.3029	+	14.2940i	−0.544337	+	0.477264i
$898$		0			0
$899$	−6.12685			−0.204342
$900$		0			0
$901$			54.4676i			1.81458i
$902$		0			0
$903$	25.6978	+	8.34412i	0.855168	+	0.277675i
$904$		0			0
$905$			11.5405i			0.383620i
$906$		0			0
$907$	48.7202			1.61773			0.808864	−	0.587996i	$-0.200083\pi$
$907$	48.7202			1.61773			0.808864	+	0.587996i	$0.200083\pi$
$908$		0			0
$909$	−3.18717	+	24.1677i	−0.105712	+	0.801591i
$910$		0			0
$911$		−	0.0878283i		−	0.00290988i	−0.999999	−	0.00145494i	$-0.999537\pi$
$911$		−	0.0878283i		−	0.00290988i	0.999999	−	0.00145494i	$-0.000463122\pi$
$912$		0			0
$913$		−	62.5690i		−	2.07073i
$914$		0			0
$915$	1.52388	+	1.73803i	0.0503778	+	0.0574576i
$916$		0			0
$917$	−13.9108	−	23.3656i	−0.459374	−	0.771599i
$918$		0			0
$919$	−53.5379			−1.76605			−0.883026	−	0.469325i	$-0.844497\pi$
$919$	−53.5379			−1.76605			−0.883026	+	0.469325i	$0.844497\pi$
$920$		0			0
$921$	3.87875	+	4.42385i	0.127809	+	0.145771i
$922$		0			0
$923$	−16.6290			−0.547349
$924$		0			0
$925$	10.0863			0.331637
$926$		0			0
$927$	−9.57670	−	1.26295i	−0.314540	−	0.0414808i
$928$		0			0
$929$	5.34086			0.175228			0.0876140	−	0.996155i	$-0.472076\pi$
$929$	5.34086			0.175228			0.0876140	+	0.996155i	$0.472076\pi$
$930$		0			0
$931$	1.34077	+	0.726911i	0.0439419	+	0.0238235i
$932$		0			0
$933$	−0.617065	+	0.541031i	−0.0202018	+	0.0177126i
$934$		0			0
$935$		−	37.2526i		−	1.21829i
$936$		0			0
$937$		−	34.5412i		−	1.12841i	−0.825634	−	0.564206i	$-0.809182\pi$
$937$		−	34.5412i		−	1.12841i	0.825634	−	0.564206i	$-0.190818\pi$
$938$		0			0
$939$	14.2928	+	16.3014i	0.466427	+	0.531976i
$940$		0			0
$941$	−11.7648			−0.383522			−0.191761	−	0.981442i	$-0.561420\pi$
$941$	−11.7648			−0.383522			−0.191761	+	0.981442i	$0.561420\pi$
$942$		0			0
$943$		−	6.23855i		−	0.203155i
$944$		0			0
$945$	−5.91885	+	12.4084i	−0.192540	+	0.403644i
$946$		0			0
$947$			9.67044i			0.314247i	0.987579	+	0.157124i	$0.0502221\pi$
$947$			9.67044i			0.314247i	−0.987579	+	0.157124i	$0.949778\pi$
$948$		0			0
$949$	−27.3307			−0.887192
$950$		0			0
$951$	−34.7087	−	39.5865i	−1.12551	−	1.28368i
$952$		0			0
$953$		−	14.9312i		−	0.483667i	−0.970318	−	0.241834i	$-0.922251\pi$
$953$		−	14.9312i		−	0.483667i	0.970318	−	0.241834i	$-0.0777489\pi$
$954$		0			0
$955$			10.8880i			0.352327i
$956$		0			0
$957$	8.31651	−	7.29175i	0.268834	−	0.235709i
$958$		0			0
$959$	12.3518	−	7.35372i	0.398862	−	0.237464i
$960$		0			0
$961$	0.769012			0.0248068
$962$		0			0
$963$	−1.04712	−	0.138091i	−0.0337429	−	0.00444993i
$964$		0			0
$965$	5.56607			0.179178
$966$		0			0
$967$	60.0002			1.92948			0.964738	−	0.263211i	$-0.0847815\pi$
$967$	60.0002			1.92948			0.964738	+	0.263211i	$0.0847815\pi$
$968$		0			0
$969$	−1.61728	−	1.84457i	−0.0519546	−	0.0592561i
$970$		0			0
$971$	−14.8832			−0.477623			−0.238812	−	0.971066i	$-0.576758\pi$
$971$	−14.8832			−0.477623			−0.238812	+	0.971066i	$0.576758\pi$
$972$		0			0
$973$	37.0504	−	22.0581i	1.18778	−	0.707150i
$974$		0			0
$975$	−2.56167	−	2.92167i	−0.0820390	−	0.0935684i
$976$		0			0
$977$			4.39064i			0.140469i	0.997531	+	0.0702345i	$0.0223748\pi$
$977$			4.39064i			0.140469i	−0.997531	+	0.0702345i	$0.977625\pi$
$978$		0			0
$979$		−	25.5065i		−	0.815192i
$980$		0			0
$981$	5.41424	−	41.0551i	0.172863	−	1.31079i
$982$		0			0
$983$	35.2167			1.12324			0.561620	−	0.827396i	$-0.310178\pi$
$983$	35.2167			1.12324			0.561620	+	0.827396i	$0.310178\pi$
$984$		0			0
$985$			22.6465i			0.721576i
$986$		0			0
$987$	33.5954	+	10.9085i	1.06935	+	0.347221i
$988$		0			0
$989$			32.8991i			1.04613i
$990$		0			0
$991$	−36.1235			−1.14750			−0.573750	−	0.819030i	$-0.694512\pi$
$991$	−36.1235			−1.14750			−0.573750	+	0.819030i	$0.694512\pi$
$992$		0			0
$993$	−25.8716	+	22.6837i	−0.821011	+	0.719847i
$994$		0			0
$995$		−	0.111663i		−	0.00353995i
$996$		0			0
$997$			36.1961i			1.14634i	0.819436	+	0.573170i	$0.194287\pi$
$997$			36.1961i			1.14634i	−0.819436	+	0.573170i	$0.805713\pi$
$998$		0			0
$999$	29.1030	+	43.5871i	0.920779	+	1.37903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.f.l.881.4		16
3.2	odd	2		1680.2.f.k.881.14		16
4.3	odd	2		840.2.f.b.41.13	yes	16
7.6	odd	2		1680.2.f.k.881.13		16
12.11	even	2		840.2.f.a.41.3	✓	16
21.20	even	2	inner	1680.2.f.l.881.3		16
28.27	even	2		840.2.f.a.41.4	yes	16
84.83	odd	2		840.2.f.b.41.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.f.a.41.3	✓	16	12.11	even	2
840.2.f.a.41.4	yes	16	28.27	even	2
840.2.f.b.41.13	yes	16	4.3	odd	2
840.2.f.b.41.14	yes	16	84.83	odd	2
1680.2.f.k.881.13		16	7.6	odd	2
1680.2.f.k.881.14		16	3.2	odd	2
1680.2.f.l.881.3		16	21.20	even	2	inner
1680.2.f.l.881.4		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30235 + 1.14188i) q^{3} +1.00000 q^{5} +(1.35345 + 2.27336i) q^{7} +(0.392236 - 2.97425i) q^{9} +O(q^{10})\)	\(q+(-1.30235 + 1.14188i) q^{3} +1.00000 q^{5} +(1.35345 + 2.27336i) q^{7} +(0.392236 - 2.97425i) q^{9} +5.73062i q^{11} +2.24338i q^{13} +(-1.30235 + 1.14188i) q^{15} -6.50062 q^{17} -0.217877i q^{19} +(-4.35857 - 1.41524i) q^{21} -5.57998i q^{23} +1.00000 q^{25} +(2.88539 + 4.32140i) q^{27} +1.11432i q^{29} +5.49827i q^{31} +(-6.54366 - 7.46328i) q^{33} +(1.35345 + 2.27336i) q^{35} +10.0863 q^{37} +(-2.56167 - 2.92167i) q^{39} +1.11802 q^{41} -5.89592 q^{43} +(0.392236 - 2.97425i) q^{45} -7.70789 q^{47} +(-3.33633 + 6.15377i) q^{49} +(8.46609 - 7.42291i) q^{51} -8.37883i q^{53} +5.73062i q^{55} +(0.248789 + 0.283753i) q^{57} +13.4209 q^{59} -1.33454i q^{61} +(7.29241 - 3.13381i) q^{63} +2.24338i q^{65} -14.5144 q^{67} +(6.37165 + 7.26709i) q^{69} +7.41245i q^{71} +12.1828i q^{73} +(-1.30235 + 1.14188i) q^{75} +(-13.0278 + 7.75612i) q^{77} -4.54501 q^{79} +(-8.69230 - 2.33322i) q^{81} -10.9184 q^{83} -6.50062 q^{85} +(-1.27242 - 1.45124i) q^{87} -4.45092 q^{89} +(-5.10002 + 3.03631i) q^{91} +(-6.27835 - 7.16068i) q^{93} -0.217877i q^{95} -9.33620i q^{97} +(17.0443 + 2.24776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^5 - 2 * q^7 - 2 * q^9	\( 16 q + 16 q^{5} - 2 q^{7} - 2 q^{9} + 10 q^{21} + 16 q^{25} - 6 q^{27} + 6 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} + 32 q^{41} - 32 q^{43} - 2 q^{45} - 4 q^{47} - 4 q^{49} - 6 q^{51} + 24 q^{59} + 24 q^{63} + 8 q^{69} - 32 q^{77} + 4 q^{79} - 6 q^{81} - 20 q^{83} - 6 q^{87} - 24 q^{89} - 20 q^{91} - 32 q^{93} + 58 q^{99}+O(q^{100}) \) 16 * q + 16 * q^5 - 2 * q^7 - 2 * q^9 + 10 * q^21 + 16 * q^25 - 6 * q^27 + 6 * q^33 - 2 * q^35 + 12 * q^37 - 6 * q^39 + 32 * q^41 - 32 * q^43 - 2 * q^45 - 4 * q^47 - 4 * q^49 - 6 * q^51 + 24 * q^59 + 24 * q^63 + 8 * q^69 - 32 * q^77 + 4 * q^79 - 6 * q^81 - 20 * q^83 - 6 * q^87 - 24 * q^89 - 20 * q^91 - 32 * q^93 + 58 * q^99

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