LMFDB - Embedded newform 1728.3.q.b.449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(449,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1728.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.q (of order $6$, degree $2$, 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:	$47.0845896815$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1728.449
Dual form			1728.3.q.b.1601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +O(q^{10})$	$q+(3.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 0.866025i) q^{11} +(-2.00000 + 3.46410i) q^{13} -15.5885i q^{17} +11.0000 q^{19} +(-24.0000 - 13.8564i) q^{23} +(-6.50000 - 11.2583i) q^{25} +(39.0000 - 22.5167i) q^{29} +(16.0000 - 27.7128i) q^{31} +6.92820i q^{35} +34.0000 q^{37} +(10.5000 + 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +(-42.0000 + 24.2487i) q^{47} +(22.5000 - 38.9711i) q^{49} +6.00000 q^{55} +(-43.5000 - 25.1147i) q^{59} +(28.0000 + 48.4974i) q^{61} +(-12.0000 + 6.92820i) q^{65} +(15.5000 - 26.8468i) q^{67} -31.1769i q^{71} +65.0000 q^{73} +(3.00000 + 1.73205i) q^{77} +(19.0000 + 32.9090i) q^{79} +(42.0000 - 24.2487i) q^{83} +(27.0000 - 46.7654i) q^{85} -124.708i q^{89} -8.00000 q^{91} +(33.0000 + 19.0526i) q^{95} +(57.5000 + 99.5929i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{5} + 2 q^{7}+O(q^{10}) $ 2 * q + 6 * q^5 + 2 * q^7	$ 2 q + 6 q^{5} + 2 q^{7} + 3 q^{11} - 4 q^{13} + 22 q^{19} - 48 q^{23} - 13 q^{25} + 78 q^{29} + 32 q^{31} + 68 q^{37} + 21 q^{41} + 61 q^{43} - 84 q^{47} + 45 q^{49} + 12 q^{55} - 87 q^{59} + 56 q^{61} - 24 q^{65} + 31 q^{67} + 130 q^{73} + 6 q^{77} + 38 q^{79} + 84 q^{83} + 54 q^{85} - 16 q^{91} + 66 q^{95} + 115 q^{97}+O(q^{100}) $ 2 * q + 6 * q^5 + 2 * q^7 + 3 * q^11 - 4 * q^13 + 22 * q^19 - 48 * q^23 - 13 * q^25 + 78 * q^29 + 32 * q^31 + 68 * q^37 + 21 * q^41 + 61 * q^43 - 84 * q^47 + 45 * q^49 + 12 * q^55 - 87 * q^59 + 56 * q^61 - 24 * q^65 + 31 * q^67 + 130 * q^73 + 6 * q^77 + 38 * q^79 + 84 * q^83 + 54 * q^85 - 16 * q^91 + 66 * q^95 + 115 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	3.00000	+	1.73205i	0.600000	+	0.346410i	0.769042	−	0.639199i	$-0.220734\pi$
$5$	3.00000	+	1.73205i	0.600000	+	0.346410i	−0.169042	+	0.985609i	$0.554067\pi$
$6$		0			0
$7$	1.00000	+	1.73205i	0.142857	+	0.247436i	0.928571	−	0.371154i	$-0.121038\pi$
$7$	1.00000	+	1.73205i	0.142857	+	0.247436i	−0.785714	+	0.618590i	$0.787704\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.50000	−	0.866025i	0.136364	−	0.0787296i	−0.430266	−	0.902702i	$-0.641580\pi$
$11$	1.50000	−	0.866025i	0.136364	−	0.0787296i	0.566630	+	0.823972i	$0.308247\pi$
$12$		0			0
$13$	−2.00000	+	3.46410i	−0.153846	+	0.266469i	−0.932638	−	0.360813i	$-0.882499\pi$
$13$	−2.00000	+	3.46410i	−0.153846	+	0.266469i	0.778792	+	0.627282i	$0.215833\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	15.5885i		−	0.916968i	−0.888703	−	0.458484i	$-0.848393\pi$
$17$		−	15.5885i		−	0.916968i	0.888703	−	0.458484i	$-0.151607\pi$
$18$		0			0
$19$	11.0000			0.578947			0.289474	−	0.957186i	$-0.406520\pi$
$19$	11.0000			0.578947			0.289474	+	0.957186i	$0.406520\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−24.0000	−	13.8564i	−1.04348	−	0.602452i	−0.122662	−	0.992449i	$-0.539143\pi$
$23$	−24.0000	−	13.8564i	−1.04348	−	0.602452i	−0.920817	+	0.389996i	$0.872476\pi$
$24$		0			0
$25$	−6.50000	−	11.2583i	−0.260000	−	0.450333i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	39.0000	−	22.5167i	1.34483	−	0.776437i	0.357316	−	0.933984i	$-0.383692\pi$
$29$	39.0000	−	22.5167i	1.34483	−	0.776437i	0.987511	+	0.157547i	$0.0503586\pi$
$30$		0			0
$31$	16.0000	−	27.7128i	0.516129	−	0.893962i	−0.483696	−	0.875236i	$-0.660706\pi$
$31$	16.0000	−	27.7128i	0.516129	−	0.893962i	0.999825	−	0.0187254i	$-0.00596084\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			6.92820i			0.197949i
$36$		0			0
$37$	34.0000			0.918919			0.459459	−	0.888199i	$-0.348043\pi$
$37$	34.0000			0.918919			0.459459	+	0.888199i	$0.348043\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	10.5000	+	6.06218i	0.256098	+	0.147858i	0.622553	−	0.782578i	$-0.286095\pi$
$41$	10.5000	+	6.06218i	0.256098	+	0.147858i	−0.366456	+	0.930436i	$0.619429\pi$
$42$		0			0
$43$	30.5000	+	52.8275i	0.709302	+	1.22855i	0.965116	+	0.261822i	$0.0843232\pi$
$43$	30.5000	+	52.8275i	0.709302	+	1.22855i	−0.255814	+	0.966726i	$0.582343\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−42.0000	+	24.2487i	−0.893617	+	0.515930i	−0.875124	−	0.483899i	$-0.839220\pi$
$47$	−42.0000	+	24.2487i	−0.893617	+	0.515930i	−0.0184931	+	0.999829i	$0.505887\pi$
$48$		0			0
$49$	22.5000	−	38.9711i	0.459184	−	0.795329i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$	6.00000			0.109091
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−43.5000	−	25.1147i	−0.737288	−	0.425674i	0.0837943	−	0.996483i	$-0.473296\pi$
$59$	−43.5000	−	25.1147i	−0.737288	−	0.425674i	−0.821082	+	0.570810i	$0.806629\pi$
$60$		0			0
$61$	28.0000	+	48.4974i	0.459016	+	0.795040i	0.998909	−	0.0466940i	$-0.0148686\pi$
$61$	28.0000	+	48.4974i	0.459016	+	0.795040i	−0.539893	+	0.841734i	$0.681535\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−12.0000	+	6.92820i	−0.184615	+	0.106588i
$66$		0			0
$67$	15.5000	−	26.8468i	0.231343	−	0.400698i	−0.726860	−	0.686785i	$-0.759021\pi$
$67$	15.5000	−	26.8468i	0.231343	−	0.400698i	0.958204	+	0.286087i	$0.0923546\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	31.1769i		−	0.439111i	−0.975600	−	0.219556i	$-0.929539\pi$
$71$		−	31.1769i		−	0.439111i	0.975600	−	0.219556i	$-0.0704608\pi$
$72$		0			0
$73$	65.0000			0.890411			0.445205	−	0.895428i	$-0.353131\pi$
$73$	65.0000			0.890411			0.445205	+	0.895428i	$0.353131\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.00000	+	1.73205i	0.0389610	+	0.0224942i
$78$		0			0
$79$	19.0000	+	32.9090i	0.240506	+	0.416569i	0.960859	−	0.277039i	$-0.0893532\pi$
$79$	19.0000	+	32.9090i	0.240506	+	0.416569i	−0.720352	+	0.693608i	$0.756020\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	42.0000	−	24.2487i	0.506024	−	0.292153i	−0.225174	−	0.974319i	$-0.572295\pi$
$83$	42.0000	−	24.2487i	0.506024	−	0.292153i	0.731198	+	0.682165i	$0.238962\pi$
$84$		0			0
$85$	27.0000	−	46.7654i	0.317647	−	0.550181i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	124.708i		−	1.40121i	−0.713549	−	0.700605i	$-0.752914\pi$
$89$		−	124.708i		−	1.40121i	0.713549	−	0.700605i	$-0.247086\pi$
$90$		0			0
$91$	−8.00000			−0.0879121
$92$		0			0
$93$		0			0
$94$		0			0
$95$	33.0000	+	19.0526i	0.347368	+	0.200553i
$96$		0			0
$97$	57.5000	+	99.5929i	0.592784	+	1.02673i	0.993856	+	0.110685i	$0.0353044\pi$
$97$	57.5000	+	99.5929i	0.592784	+	1.02673i	−0.401072	+	0.916047i	$0.631362\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	39.0000	−	22.5167i	0.386139	−	0.222937i	−0.294347	−	0.955699i	$-0.595102\pi$
$101$	39.0000	−	22.5167i	0.386139	−	0.222937i	0.680486	+	0.732761i	$0.261769\pi$
$102$		0			0
$103$	−20.0000	+	34.6410i	−0.194175	+	0.336321i	−0.946630	−	0.322323i	$-0.895536\pi$
$103$	−20.0000	+	34.6410i	−0.194175	+	0.336321i	0.752455	+	0.658644i	$0.228870\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			140.296i			1.31118i	0.755118	+	0.655589i	$0.227580\pi$
$107$			140.296i			1.31118i	−0.755118	+	0.655589i	$0.772420\pi$
$108$		0			0
$109$	52.0000			0.477064			0.238532	−	0.971135i	$-0.423334\pi$
$109$	52.0000			0.477064			0.238532	+	0.971135i	$0.423334\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	78.0000	+	45.0333i	0.690265	+	0.398525i	0.803711	−	0.595019i	$-0.202856\pi$
$113$	78.0000	+	45.0333i	0.690265	+	0.398525i	−0.113446	+	0.993544i	$0.536189\pi$
$114$		0			0
$115$	−48.0000	−	83.1384i	−0.417391	−	0.722943i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	27.0000	−	15.5885i	0.226891	−	0.130995i
$120$		0			0
$121$	−59.0000	+	102.191i	−0.487603	+	0.844554i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	131.636i		−	1.05309i
$126$		0			0
$127$	16.0000			0.125984			0.0629921	−	0.998014i	$-0.479936\pi$
$127$	16.0000			0.125984			0.0629921	+	0.998014i	$0.479936\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−138.000	−	79.6743i	−1.05344	−	0.608201i	−0.129826	−	0.991537i	$-0.541442\pi$
$131$	−138.000	−	79.6743i	−1.05344	−	0.608201i	−0.923609	+	0.383336i	$0.874775\pi$
$132$		0			0
$133$	11.0000	+	19.0526i	0.0827068	+	0.143252i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	163.500	−	94.3968i	1.19343	−	0.689028i	0.234348	−	0.972153i	$-0.424705\pi$
$137$	163.500	−	94.3968i	1.19343	−	0.689028i	0.959083	+	0.283125i	$0.0913712\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.0179856	+	0.0311520i	−0.874878	−	0.484343i	$-0.839059\pi$
$139$	−2.50000	+	4.33013i	−0.0179856	+	0.0311520i	0.856893	+	0.515495i	$0.172392\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			6.92820i			0.0484490i
$144$		0			0
$145$	156.000			1.07586
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−132.000	−	76.2102i	−0.885906	−	0.511478i	−0.0133049	−	0.999911i	$-0.504235\pi$
$149$	−132.000	−	76.2102i	−0.885906	−	0.511478i	−0.872601	+	0.488433i	$0.837569\pi$
$150$		0			0
$151$	10.0000	+	17.3205i	0.0662252	+	0.114705i	0.897237	−	0.441550i	$-0.145571\pi$
$151$	10.0000	+	17.3205i	0.0662252	+	0.114705i	−0.831012	+	0.556255i	$0.812238\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	96.0000	−	55.4256i	0.619355	−	0.357585i
$156$		0			0
$157$	−20.0000	+	34.6410i	−0.127389	+	0.220643i	−0.922664	−	0.385605i	$-0.873993\pi$
$157$	−20.0000	+	34.6410i	−0.127389	+	0.220643i	0.795276	+	0.606248i	$0.207326\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	55.4256i		−	0.344259i
$162$		0			0
$163$	−106.000			−0.650307			−0.325153	−	0.945661i	$-0.605416\pi$
$163$	−106.000			−0.650307			−0.325153	+	0.945661i	$0.605416\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	165.000	+	95.2628i	0.988024	+	0.570436i	0.904683	−	0.426085i	$-0.140108\pi$
$167$	165.000	+	95.2628i	0.988024	+	0.570436i	0.0833409	+	0.996521i	$0.473441\pi$
$168$		0			0
$169$	76.5000	+	132.502i	0.452663	+	0.784035i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	201.000	−	116.047i	1.16185	−	0.670794i	0.210103	−	0.977679i	$-0.432620\pi$
$173$	201.000	−	116.047i	1.16185	−	0.670794i	0.951747	+	0.306885i	$0.0992867\pi$
$174$		0			0
$175$	13.0000	−	22.5167i	0.0742857	−	0.128667i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	62.3538i		−	0.348345i	−0.984715	−	0.174173i	$-0.944275\pi$
$179$		−	62.3538i		−	0.348345i	0.984715	−	0.174173i	$-0.0557251\pi$
$180$		0			0
$181$	232.000			1.28177			0.640884	−	0.767638i	$-0.278568\pi$
$181$	232.000			1.28177			0.640884	+	0.767638i	$0.278568\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	102.000	+	58.8897i	0.551351	+	0.318323i
$186$		0			0
$187$	−13.5000	−	23.3827i	−0.0721925	−	0.125041i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	201.000	−	116.047i	1.05236	−	0.607578i	0.129048	−	0.991638i	$-0.458808\pi$
$191$	201.000	−	116.047i	1.05236	−	0.607578i	0.923308	+	0.384060i	$0.125475\pi$
$192$		0			0
$193$	132.500	−	229.497i	0.686528	−	1.18910i	−0.286425	−	0.958103i	$-0.592467\pi$
$193$	132.500	−	229.497i	0.686528	−	1.18910i	0.972954	−	0.231000i	$-0.0741996\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			124.708i			0.633034i	0.948587	+	0.316517i	$0.102513\pi$
$197$			124.708i			0.633034i	−0.948587	+	0.316517i	$0.897487\pi$
$198$		0			0
$199$	−290.000			−1.45729			−0.728643	−	0.684893i	$-0.759849\pi$
$199$	−290.000			−1.45729			−0.728643	+	0.684893i	$0.759849\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	78.0000	+	45.0333i	0.384236	+	0.221839i
$204$		0			0
$205$	21.0000	+	36.3731i	0.102439	+	0.177430i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	16.5000	−	9.52628i	0.0789474	−	0.0455803i
$210$		0			0
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	−0.732893	−	0.680344i	$-0.761830\pi$
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	0.955642	+	0.294532i	$0.0951637\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			211.310i			0.982838i
$216$		0			0
$217$	64.0000			0.294931
$218$		0			0
$219$		0			0
$220$		0			0
$221$	54.0000	+	31.1769i	0.244344	+	0.141072i
$222$		0			0
$223$	−26.0000	−	45.0333i	−0.116592	−	0.201943i	0.801823	−	0.597562i	$-0.203864\pi$
$223$	−26.0000	−	45.0333i	−0.116592	−	0.201943i	−0.918415	+	0.395618i	$0.870530\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	163.500	−	94.3968i	0.720264	−	0.415845i	−0.0945856	−	0.995517i	$-0.530153\pi$
$227$	163.500	−	94.3968i	0.720264	−	0.415845i	0.814850	+	0.579672i	$0.196819\pi$
$228$		0			0
$229$	133.000	−	230.363i	0.580786	−	1.00595i	−0.414600	−	0.910004i	$-0.636079\pi$
$229$	133.000	−	230.363i	0.580786	−	1.00595i	0.995386	−	0.0959473i	$-0.0305880\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	202.650i		−	0.869742i	−0.900493	−	0.434871i	$-0.856794\pi$
$233$		−	202.650i		−	0.869742i	0.900493	−	0.434871i	$-0.143206\pi$
$234$		0			0
$235$	−168.000			−0.714894
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−348.000	−	200.918i	−1.45607	−	0.840661i	−0.457252	−	0.889337i	$-0.651166\pi$
$239$	−348.000	−	200.918i	−1.45607	−	0.840661i	−0.998815	+	0.0486764i	$0.984500\pi$
$240$		0			0
$241$	−59.5000	−	103.057i	−0.246888	−	0.427623i	0.715773	−	0.698333i	$-0.246075\pi$
$241$	−59.5000	−	103.057i	−0.246888	−	0.427623i	−0.962661	+	0.270711i	$0.912741\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	135.000	−	77.9423i	0.551020	−	0.318132i
$246$		0			0
$247$	−22.0000	+	38.1051i	−0.0890688	+	0.154272i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			389.711i			1.55264i	0.630342	+	0.776318i	$0.282915\pi$
$251$			389.711i			1.55264i	−0.630342	+	0.776318i	$0.717085\pi$
$252$		0			0
$253$	−48.0000			−0.189723
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−151.500	−	87.4686i	−0.589494	−	0.340345i	0.175403	−	0.984497i	$-0.443877\pi$
$257$	−151.500	−	87.4686i	−0.589494	−	0.340345i	−0.764897	+	0.644152i	$0.777210\pi$
$258$		0			0
$259$	34.0000	+	58.8897i	0.131274	+	0.227373i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	39.0000	−	22.5167i	0.148289	−	0.0856147i	−0.424020	−	0.905653i	$-0.639381\pi$
$263$	39.0000	−	22.5167i	0.148289	−	0.0856147i	0.572309	+	0.820038i	$0.306048\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	187.061i		−	0.695396i	−0.937607	−	0.347698i	$-0.886963\pi$
$269$		−	187.061i		−	0.695396i	0.937607	−	0.347698i	$-0.113037\pi$
$270$		0			0
$271$	268.000			0.988930			0.494465	−	0.869198i	$-0.335364\pi$
$271$	268.000			0.988930			0.494465	+	0.869198i	$0.335364\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−19.5000	−	11.2583i	−0.0709091	−	0.0409394i
$276$		0			0
$277$	28.0000	+	48.4974i	0.101083	+	0.175081i	0.912131	−	0.409899i	$-0.134436\pi$
$277$	28.0000	+	48.4974i	0.101083	+	0.175081i	−0.811048	+	0.584979i	$0.801103\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	42.0000	−	24.2487i	0.149466	−	0.0862943i	−0.423402	−	0.905942i	$-0.639164\pi$
$281$	42.0000	−	24.2487i	0.149466	−	0.0862943i	0.572868	+	0.819648i	$0.305831\pi$
$282$		0			0
$283$	−187.000	+	323.894i	−0.660777	+	1.14450i	0.319634	+	0.947541i	$0.396440\pi$
$283$	−187.000	+	323.894i	−0.660777	+	1.14450i	−0.980412	+	0.196959i	$0.936893\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			24.2487i			0.0844903i
$288$		0			0
$289$	46.0000			0.159170
$290$		0			0
$291$		0			0
$292$		0			0
$293$	219.000	+	126.440i	0.747440	+	0.431535i	0.824768	−	0.565471i	$-0.191306\pi$
$293$	219.000	+	126.440i	0.747440	+	0.431535i	−0.0773280	+	0.997006i	$0.524639\pi$
$294$		0			0
$295$	−87.0000	−	150.688i	−0.294915	−	0.510808i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	96.0000	−	55.4256i	0.321070	−	0.185370i
$300$		0			0
$301$	−61.0000	+	105.655i	−0.202658	+	0.351014i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			193.990i			0.636032i
$306$		0			0
$307$	533.000			1.73616			0.868078	−	0.496428i	$-0.165355\pi$
$307$	533.000			1.73616			0.868078	+	0.496428i	$0.165355\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−213.000	−	122.976i	−0.684887	−	0.395420i	0.116806	−	0.993155i	$-0.462734\pi$
$311$	−213.000	−	122.976i	−0.684887	−	0.395420i	−0.801694	+	0.597735i	$0.796068\pi$
$312$		0			0
$313$	−77.5000	−	134.234i	−0.247604	−	0.428862i	0.715257	−	0.698862i	$-0.246310\pi$
$313$	−77.5000	−	134.234i	−0.247604	−	0.428862i	−0.962860	+	0.269999i	$0.912976\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−42.0000	+	24.2487i	−0.132492	+	0.0764944i	−0.564781	−	0.825241i	$-0.691039\pi$
$317$	−42.0000	+	24.2487i	−0.132492	+	0.0764944i	0.432289	+	0.901735i	$0.357706\pi$
$318$		0			0
$319$	39.0000	−	67.5500i	0.122257	−	0.211755i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	171.473i		−	0.530876i
$324$		0			0
$325$	52.0000			0.160000
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−84.0000	−	48.4974i	−0.255319	−	0.147409i
$330$		0			0
$331$	−1.00000	−	1.73205i	−0.00302115	−	0.00523278i	0.864511	−	0.502614i	$-0.167628\pi$
$331$	−1.00000	−	1.73205i	−0.00302115	−	0.00523278i	−0.867532	+	0.497381i	$0.834295\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	93.0000	−	53.6936i	0.277612	−	0.160279i
$336$		0			0
$337$	−38.5000	+	66.6840i	−0.114243	+	0.197875i	−0.917477	−	0.397789i	$-0.869778\pi$
$337$	−38.5000	+	66.6840i	−0.114243	+	0.197875i	0.803234	+	0.595664i	$0.203111\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	55.4256i		−	0.162538i
$342$		0			0
$343$	188.000			0.548105
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−97.5000	−	56.2917i	−0.280980	−	0.162224i	0.352887	−	0.935666i	$-0.385200\pi$
$347$	−97.5000	−	56.2917i	−0.280980	−	0.162224i	−0.633867	+	0.773442i	$0.718533\pi$
$348$		0			0
$349$	208.000	+	360.267i	0.595989	+	1.03228i	0.993407	+	0.114645i	$0.0365730\pi$
$349$	208.000	+	360.267i	0.595989	+	1.03228i	−0.397418	+	0.917638i	$0.630094\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.50000	−	0.866025i	0.00424929	−	0.00245333i	−0.497874	−	0.867249i	$-0.665886\pi$
$353$	1.50000	−	0.866025i	0.00424929	−	0.00245333i	0.502123	+	0.864796i	$0.332552\pi$
$354$		0			0
$355$	54.0000	−	93.5307i	0.152113	−	0.263467i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			592.361i			1.65003i	0.565110	+	0.825016i	$0.308834\pi$
$359$			592.361i			1.65003i	−0.565110	+	0.825016i	$0.691166\pi$
$360$		0			0
$361$	−240.000			−0.664820
$362$		0			0
$363$		0			0
$364$		0			0
$365$	195.000	+	112.583i	0.534247	+	0.308447i
$366$		0			0
$367$	−179.000	−	310.037i	−0.487738	−	0.844788i	0.512162	−	0.858889i	$-0.328845\pi$
$367$	−179.000	−	310.037i	−0.487738	−	0.844788i	−0.999901	+	0.0141011i	$0.995511\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−290.000	+	502.295i	−0.777480	+	1.34663i	0.155910	+	0.987771i	$0.450169\pi$
$373$	−290.000	+	502.295i	−0.777480	+	1.34663i	−0.933390	+	0.358863i	$0.883164\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			180.133i			0.477807i
$378$		0			0
$379$	83.0000			0.218997			0.109499	−	0.993987i	$-0.465075\pi$
$379$	83.0000			0.218997			0.109499	+	0.993987i	$0.465075\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−483.000	−	278.860i	−1.26110	−	0.728094i	−0.287810	−	0.957688i	$-0.592927\pi$
$383$	−483.000	−	278.860i	−1.26110	−	0.728094i	−0.973287	+	0.229593i	$0.926260\pi$
$384$		0			0
$385$	6.00000	+	10.3923i	0.0155844	+	0.0269930i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−447.000	+	258.076i	−1.14910	+	0.663433i	−0.948668	−	0.316274i	$-0.897568\pi$
$389$	−447.000	+	258.076i	−1.14910	+	0.663433i	−0.200432	+	0.979708i	$0.564235\pi$
$390$		0			0
$391$	−216.000	+	374.123i	−0.552430	+	0.956836i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			131.636i			0.333255i
$396$		0			0
$397$	−362.000			−0.911839			−0.455919	−	0.890021i	$-0.650689\pi$
$397$	−362.000			−0.911839			−0.455919	+	0.890021i	$0.650689\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−340.500	−	196.588i	−0.849127	−	0.490244i	0.0112291	−	0.999937i	$-0.496426\pi$
$401$	−340.500	−	196.588i	−0.849127	−	0.490244i	−0.860356	+	0.509693i	$0.829759\pi$
$402$		0			0
$403$	64.0000	+	110.851i	0.158809	+	0.275065i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	51.0000	−	29.4449i	0.125307	−	0.0723461i
$408$		0			0
$409$	−110.500	+	191.392i	−0.270171	+	0.467950i	−0.968905	−	0.247431i	$-0.920414\pi$
$409$	−110.500	+	191.392i	−0.270171	+	0.467950i	0.698734	+	0.715381i	$0.253747\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	100.459i		−	0.243242i
$414$		0			0
$415$	168.000			0.404819
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−678.000	−	391.443i	−1.61814	−	0.934233i	−0.987401	−	0.158236i	$-0.949419\pi$
$419$	−678.000	−	391.443i	−1.61814	−	0.934233i	−0.630737	−	0.775997i	$-0.717247\pi$
$420$		0			0
$421$	−341.000	−	590.629i	−0.809976	−	1.40292i	−0.912880	−	0.408229i	$-0.866147\pi$
$421$	−341.000	−	590.629i	−0.809976	−	1.40292i	0.102903	−	0.994691i	$-0.467187\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−175.500	+	101.325i	−0.412941	+	0.238412i
$426$		0			0
$427$	−56.0000	+	96.9948i	−0.131148	+	0.227154i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	280.592i		−	0.651026i	−0.945538	−	0.325513i	$-0.894463\pi$
$431$		−	280.592i		−	0.651026i	0.945538	−	0.325513i	$-0.105537\pi$
$432$		0			0
$433$	−295.000			−0.681293			−0.340647	−	0.940191i	$-0.610646\pi$
$433$	−295.000			−0.681293			−0.340647	+	0.940191i	$0.610646\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−264.000	−	152.420i	−0.604119	−	0.348788i
$438$		0			0
$439$	406.000	+	703.213i	0.924829	+	1.60185i	0.791836	+	0.610734i	$0.209126\pi$
$439$	406.000	+	703.213i	0.924829	+	1.60185i	0.132993	+	0.991117i	$0.457541\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−79.5000	+	45.8993i	−0.179458	+	0.103610i	−0.587038	−	0.809559i	$-0.699706\pi$
$443$	−79.5000	+	45.8993i	−0.179458	+	0.103610i	0.407580	+	0.913170i	$0.366373\pi$
$444$		0			0
$445$	216.000	−	374.123i	0.485393	−	0.840726i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			639.127i			1.42344i	0.702461	+	0.711722i	$0.252085\pi$
$449$			639.127i			1.42344i	−0.702461	+	0.711722i	$0.747915\pi$
$450$		0			0
$451$	21.0000			0.0465632
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−24.0000	−	13.8564i	−0.0527473	−	0.0304536i
$456$		0			0
$457$	−32.5000	−	56.2917i	−0.0711160	−	0.123176i	0.828275	−	0.560322i	$-0.189323\pi$
$457$	−32.5000	−	56.2917i	−0.0711160	−	0.123176i	−0.899391	+	0.437146i	$0.855989\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−690.000	+	398.372i	−1.49675	+	0.864147i	−0.999993	−	0.00374501i	$-0.998808\pi$
$461$	−690.000	+	398.372i	−1.49675	+	0.864147i	−0.496753	+	0.867892i	$0.665475\pi$
$462$		0			0
$463$	367.000	−	635.663i	0.792657	−	1.37292i	−0.131660	−	0.991295i	$-0.542031\pi$
$463$	367.000	−	635.663i	0.792657	−	1.37292i	0.924317	−	0.381627i	$-0.124636\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			202.650i			0.433940i	0.976178	+	0.216970i	$0.0696174\pi$
$467$			202.650i			0.433940i	−0.976178	+	0.216970i	$0.930383\pi$
$468$		0			0
$469$	62.0000			0.132196
$470$		0			0
$471$		0			0
$472$		0			0
$473$	91.5000	+	52.8275i	0.193446	+	0.111686i
$474$		0			0
$475$	−71.5000	−	123.842i	−0.150526	−	0.260719i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	525.000	−	303.109i	1.09603	−	0.632795i	0.160857	−	0.986978i	$-0.448574\pi$
$479$	525.000	−	303.109i	1.09603	−	0.632795i	0.935176	+	0.354183i	$0.115241\pi$
$480$		0			0
$481$	−68.0000	+	117.779i	−0.141372	+	0.244864i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			398.372i			0.821385i
$486$		0			0
$487$	106.000			0.217659			0.108830	−	0.994060i	$-0.465290\pi$
$487$	106.000			0.217659			0.108830	+	0.994060i	$0.465290\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	199.500	+	115.181i	0.406314	+	0.234585i	0.689205	−	0.724567i	$-0.257960\pi$
$491$	199.500	+	115.181i	0.406314	+	0.234585i	−0.282891	+	0.959152i	$0.591293\pi$
$492$		0			0
$493$	−351.000	−	607.950i	−0.711968	−	1.23316i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	54.0000	−	31.1769i	0.108652	−	0.0627302i
$498$		0			0
$499$	393.500	−	681.562i	0.788577	−	1.36586i	−0.138261	−	0.990396i	$-0.544151\pi$
$499$	393.500	−	681.562i	0.788577	−	1.36586i	0.926839	−	0.375460i	$-0.122515\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			623.538i			1.23964i	0.784745	+	0.619819i	$0.212794\pi$
$503$			623.538i			1.23964i	−0.784745	+	0.619819i	$0.787206\pi$
$504$		0			0
$505$	156.000			0.308911
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−186.000	−	107.387i	−0.365422	−	0.210977i	0.306034	−	0.952020i	$-0.400998\pi$
$509$	−186.000	−	107.387i	−0.365422	−	0.210977i	−0.671457	+	0.741044i	$0.734331\pi$
$510$		0			0
$511$	65.0000	+	112.583i	0.127202	+	0.220320i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−120.000	+	69.2820i	−0.233010	+	0.134528i
$516$		0			0
$517$	−42.0000	+	72.7461i	−0.0812379	+	0.140708i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			202.650i			0.388963i	0.980906	+	0.194482i	$0.0623025\pi$
$521$			202.650i			0.388963i	−0.980906	+	0.194482i	$0.937698\pi$
$522$		0			0
$523$	−250.000			−0.478011			−0.239006	−	0.971018i	$-0.576821\pi$
$523$	−250.000			−0.478011			−0.239006	+	0.971018i	$0.576821\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−432.000	−	249.415i	−0.819734	−	0.473274i
$528$		0			0
$529$	119.500	+	206.980i	0.225898	+	0.391267i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−42.0000	+	24.2487i	−0.0787992	+	0.0454948i
$534$		0			0
$535$	−243.000	+	420.888i	−0.454206	+	0.786707i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	77.9423i		−	0.144605i
$540$		0			0
$541$	−650.000			−1.20148			−0.600739	−	0.799445i	$-0.705127\pi$
$541$	−650.000			−1.20148			−0.600739	+	0.799445i	$0.705127\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	156.000	+	90.0666i	0.286239	+	0.165260i
$546$		0			0
$547$	−311.500	−	539.534i	−0.569470	−	0.986351i	−0.996618	−	0.0821692i	$-0.973815\pi$
$547$	−311.500	−	539.534i	−0.569470	−	0.986351i	0.427149	−	0.904181i	$-0.359518\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	429.000	−	247.683i	0.778584	−	0.449516i
$552$		0			0
$553$	−38.0000	+	65.8179i	−0.0687161	+	0.119020i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			530.008i			0.951540i	0.879570	+	0.475770i	$0.157830\pi$
$557$			530.008i			0.951540i	−0.879570	+	0.475770i	$0.842170\pi$
$558$		0			0
$559$	−244.000			−0.436494
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−97.5000	−	56.2917i	−0.173179	−	0.0999852i	0.410905	−	0.911678i	$-0.365213\pi$
$563$	−97.5000	−	56.2917i	−0.173179	−	0.0999852i	−0.584084	+	0.811693i	$0.698546\pi$
$564$		0			0
$565$	156.000	+	270.200i	0.276106	+	0.478230i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−565.500	+	326.492i	−0.993849	+	0.573799i	−0.906423	−	0.422372i	$-0.861198\pi$
$569$	−565.500	+	326.492i	−0.993849	+	0.573799i	−0.0874263	+	0.996171i	$0.527864\pi$
$570$		0			0
$571$	−272.500	+	471.984i	−0.477233	+	0.826592i	−0.999660	−	0.0260926i	$-0.991694\pi$
$571$	−272.500	+	471.984i	−0.477233	+	0.826592i	0.522427	+	0.852684i	$0.325027\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			360.267i			0.626551i
$576$		0			0
$577$	−871.000			−1.50953			−0.754766	−	0.655994i	$-0.772250\pi$
$577$	−871.000			−1.50953			−0.754766	+	0.655994i	$0.772250\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	84.0000	+	48.4974i	0.144578	+	0.0834723i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.50000	−	0.866025i	0.00255537	−	0.00147534i	−0.498722	−	0.866762i	$-0.666197\pi$
$587$	1.50000	−	0.866025i	0.00255537	−	0.00147534i	0.501277	+	0.865287i	$0.332864\pi$
$588$		0			0
$589$	176.000	−	304.841i	0.298812	−	0.517557i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	187.061i		−	0.315449i	−0.987483	−	0.157725i	$-0.949584\pi$
$593$		−	187.061i		−	0.315449i	0.987483	−	0.157725i	$-0.0504159\pi$
$594$		0			0
$595$	108.000			0.181513
$596$		0			0
$597$		0			0
$598$		0			0
$599$	489.000	+	282.324i	0.816361	+	0.471326i	0.849160	−	0.528136i	$-0.177109\pi$
$599$	489.000	+	282.324i	0.816361	+	0.471326i	−0.0327992	+	0.999462i	$0.510442\pi$
$600$		0			0
$601$	−230.500	−	399.238i	−0.383527	−	0.664289i	0.608036	−	0.793909i	$-0.291958\pi$
$601$	−230.500	−	399.238i	−0.383527	−	0.664289i	−0.991564	+	0.129620i	$0.958624\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−354.000	+	204.382i	−0.585124	+	0.337821i
$606$		0			0
$607$	−56.0000	+	96.9948i	−0.0922570	+	0.159794i	−0.908461	−	0.417971i	$-0.862741\pi$
$607$	−56.0000	+	96.9948i	−0.0922570	+	0.159794i	0.816204	+	0.577765i	$0.196075\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	193.990i		−	0.317495i
$612$		0			0
$613$	−902.000			−1.47145			−0.735726	−	0.677279i	$-0.763159\pi$
$613$	−902.000			−1.47145			−0.735726	+	0.677279i	$0.763159\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	307.500	+	177.535i	0.498379	+	0.287739i	0.728044	−	0.685530i	$-0.240430\pi$
$617$	307.500	+	177.535i	0.498379	+	0.287739i	−0.229665	+	0.973270i	$0.573763\pi$
$618$		0			0
$619$	399.500	+	691.954i	0.645396	+	1.11786i	0.984210	+	0.177005i	$0.0566409\pi$
$619$	399.500	+	691.954i	0.645396	+	1.11786i	−0.338814	+	0.940853i	$0.610026\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	216.000	−	124.708i	0.346709	−	0.200173i
$624$		0			0
$625$	65.5000	−	113.449i	0.104800	−	0.181519i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	530.008i		−	0.842619i
$630$		0			0
$631$	−830.000			−1.31537			−0.657686	−	0.753292i	$-0.728465\pi$
$631$	−830.000			−1.31537			−0.657686	+	0.753292i	$0.728465\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	48.0000	+	27.7128i	0.0755906	+	0.0436422i
$636$		0			0
$637$	90.0000	+	155.885i	0.141287	+	0.244717i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	325.500	−	187.928i	0.507800	−	0.293179i	−0.224129	−	0.974560i	$-0.571954\pi$
$641$	325.500	−	187.928i	0.507800	−	0.293179i	0.731929	+	0.681381i	$0.238620\pi$
$642$		0			0
$643$	6.50000	−	11.2583i	0.0101089	−	0.0175091i	−0.860927	−	0.508729i	$-0.830116\pi$
$643$	6.50000	−	11.2583i	0.0101089	−	0.0175091i	0.871036	+	0.491220i	$0.163449\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			467.654i			0.722803i	0.932410	+	0.361402i	$0.117702\pi$
$647$			467.654i			0.722803i	−0.932410	+	0.361402i	$0.882298\pi$
$648$		0			0
$649$	−87.0000			−0.134052
$650$		0			0
$651$		0			0
$652$		0			0
$653$	327.000	+	188.794i	0.500766	+	0.289117i	0.729030	−	0.684482i	$-0.239972\pi$
$653$	327.000	+	188.794i	0.500766	+	0.289117i	−0.228264	+	0.973599i	$0.573305\pi$
$654$		0			0
$655$	−276.000	−	478.046i	−0.421374	−	0.729841i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	852.000	−	491.902i	1.29287	−	0.746438i	0.313706	−	0.949520i	$-0.398429\pi$
$659$	852.000	−	491.902i	1.29287	−	0.746438i	0.979162	+	0.203082i	$0.0650959\pi$
$660$		0			0
$661$	−191.000	+	330.822i	−0.288956	+	0.500487i	−0.973561	−	0.228428i	$-0.926642\pi$
$661$	−191.000	+	330.822i	−0.288956	+	0.500487i	0.684605	+	0.728915i	$0.259975\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			76.2102i			0.114602i
$666$		0			0
$667$	−1248.00			−1.87106
$668$		0			0
$669$		0			0
$670$		0			0
$671$	84.0000	+	48.4974i	0.125186	+	0.0722763i
$672$		0			0
$673$	−289.000	−	500.563i	−0.429421	−	0.743778i	0.567401	−	0.823441i	$-0.307949\pi$
$673$	−289.000	−	500.563i	−0.429421	−	0.743778i	−0.996822	+	0.0796633i	$0.974615\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	606.000	−	349.874i	0.895126	−	0.516801i	0.0195100	−	0.999810i	$-0.493789\pi$
$677$	606.000	−	349.874i	0.895126	−	0.516801i	0.875616	+	0.483009i	$0.160456\pi$
$678$		0			0
$679$	−115.000	+	199.186i	−0.169367	+	0.293352i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			1044.43i			1.52918i	0.644520	+	0.764588i	$0.277057\pi$
$683$			1044.43i			1.52918i	−0.644520	+	0.764588i	$0.722943\pi$
$684$		0			0
$685$	654.000			0.954745
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−91.0000	−	157.617i	−0.131693	−	0.228099i	0.792636	−	0.609695i	$-0.208708\pi$
$691$	−91.0000	−	157.617i	−0.131693	−	0.228099i	−0.924329	+	0.381596i	$0.875375\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−15.0000	+	8.66025i	−0.0215827	+	0.0124608i
$696$		0			0
$697$	94.5000	−	163.679i	0.135581	−	0.234833i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	374.000			0.532006
$704$		0			0
$705$		0			0
$706$		0			0
$707$	78.0000	+	45.0333i	0.110325	+	0.0636964i
$708$		0			0
$709$	−350.000	−	606.218i	−0.493653	−	0.855032i	0.506320	−	0.862346i	$-0.331005\pi$
$709$	−350.000	−	606.218i	−0.493653	−	0.855032i	−0.999973	+	0.00731341i	$0.997672\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−768.000	+	443.405i	−1.07714	+	0.621886i
$714$		0			0
$715$	−12.0000	+	20.7846i	−0.0167832	+	0.0290694i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	592.361i		−	0.823868i	−0.911214	−	0.411934i	$-0.864853\pi$
$719$		−	592.361i		−	0.823868i	0.911214	−	0.411934i	$-0.135147\pi$
$720$		0			0
$721$	−80.0000			−0.110957
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−507.000	−	292.717i	−0.699310	−	0.403747i
$726$		0			0
$727$	−332.000	−	575.041i	−0.456671	−	0.790978i	0.542111	−	0.840307i	$-0.317625\pi$
$727$	−332.000	−	575.041i	−0.456671	−	0.790978i	−0.998783	+	0.0493289i	$0.984292\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	823.500	−	475.448i	1.12654	−	0.650408i
$732$		0			0
$733$	−335.000	+	580.237i	−0.457026	+	0.791592i	−0.998802	−	0.0489306i	$-0.984419\pi$
$733$	−335.000	+	580.237i	−0.457026	+	0.791592i	0.541776	+	0.840523i	$0.317752\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	53.6936i		−	0.0728542i
$738$		0			0
$739$	317.000			0.428958			0.214479	−	0.976729i	$-0.431195\pi$
$739$	317.000			0.428958			0.214479	+	0.976729i	$0.431195\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−537.000	−	310.037i	−0.722746	−	0.417277i	0.0930168	−	0.995665i	$-0.470349\pi$
$743$	−537.000	−	310.037i	−0.722746	−	0.417277i	−0.815762	+	0.578387i	$0.803682\pi$
$744$		0			0
$745$	−264.000	−	457.261i	−0.354362	−	0.613774i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−243.000	+	140.296i	−0.324433	+	0.187311i
$750$		0			0
$751$	655.000	−	1134.49i	0.872170	−	1.51064i	0.0124237	−	0.999923i	$-0.496045\pi$
$751$	655.000	−	1134.49i	0.872170	−	1.51064i	0.859747	−	0.510721i	$-0.170621\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			69.2820i			0.0917643i
$756$		0			0
$757$	−218.000			−0.287979			−0.143989	−	0.989579i	$-0.545993\pi$
$757$	−218.000			−0.287979			−0.143989	+	0.989579i	$0.545993\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−570.000	−	329.090i	−0.749014	−	0.432444i	0.0763232	−	0.997083i	$-0.475682\pi$
$761$	−570.000	−	329.090i	−0.749014	−	0.432444i	−0.825338	+	0.564639i	$0.809015\pi$
$762$		0			0
$763$	52.0000	+	90.0666i	0.0681520	+	0.118043i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	174.000	−	100.459i	0.226858	−	0.130976i
$768$		0			0
$769$	−511.000	+	885.078i	−0.664499	+	1.15095i	0.314921	+	0.949118i	$0.398022\pi$
$769$	−511.000	+	885.078i	−0.664499	+	1.15095i	−0.979421	+	0.201829i	$0.935312\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			1184.72i			1.53263i	0.642465	+	0.766315i	$0.277912\pi$
$773$			1184.72i			1.53263i	−0.642465	+	0.766315i	$0.722088\pi$
$774$		0			0
$775$	−416.000			−0.536774
$776$		0			0
$777$		0			0
$778$		0			0
$779$	115.500	+	66.6840i	0.148267	+	0.0856020i
$780$		0			0
$781$	−27.0000	−	46.7654i	−0.0345711	−	0.0598788i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−120.000	+	69.2820i	−0.152866	+	0.0882574i
$786$		0			0
$787$	65.0000	−	112.583i	0.0825921	−	0.143054i	−0.821771	−	0.569819i	$-0.807013\pi$
$787$	65.0000	−	112.583i	0.0825921	−	0.143054i	0.904363	+	0.426765i	$0.140347\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			180.133i			0.227729i
$792$		0			0
$793$	−224.000			−0.282472
$794$		0			0
$795$		0			0
$796$		0			0
$797$	273.000	+	157.617i	0.342535	+	0.197762i	0.661392	−	0.750040i	$-0.269966\pi$
$797$	273.000	+	157.617i	0.342535	+	0.197762i	−0.318858	+	0.947803i	$0.603299\pi$
$798$		0			0
$799$	378.000	+	654.715i	0.473091	+	0.819418i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	97.5000	−	56.2917i	0.121420	−	0.0701017i
$804$		0			0
$805$	96.0000	−	166.277i	0.119255	−	0.206555i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			140.296i			0.173419i	0.996234	+	0.0867096i	$0.0276352\pi$
$809$			140.296i			0.173419i	−0.996234	+	0.0867096i	$0.972365\pi$
$810$		0			0
$811$	299.000			0.368681			0.184340	−	0.982862i	$-0.440985\pi$
$811$	299.000			0.368681			0.184340	+	0.982862i	$0.440985\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−318.000	−	183.597i	−0.390184	−	0.225273i
$816$		0			0
$817$	335.500	+	581.103i	0.410649	+	0.711264i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	525.000	−	303.109i	0.639464	−	0.369195i	−0.144944	−	0.989440i	$-0.546300\pi$
$821$	525.000	−	303.109i	0.639464	−	0.369195i	0.784408	+	0.620245i	$0.212967\pi$
$822$		0			0
$823$	−407.000	+	704.945i	−0.494532	+	0.856555i	−0.999980	−	0.00630221i	$-0.997994\pi$
$823$	−407.000	+	704.945i	−0.494532	+	0.856555i	0.505448	+	0.862857i	$0.331327\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			1434.14i			1.73415i	0.498182	+	0.867073i	$0.334001\pi$
$827$			1434.14i			1.73415i	−0.498182	+	0.867073i	$0.665999\pi$
$828$		0			0
$829$	718.000			0.866104			0.433052	−	0.901369i	$-0.357437\pi$
$829$	718.000			0.866104			0.433052	+	0.901369i	$0.357437\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−607.500	−	350.740i	−0.729292	−	0.421057i
$834$		0			0
$835$	330.000	+	571.577i	0.395210	+	0.684523i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−690.000	+	398.372i	−0.822408	+	0.474817i	−0.851246	−	0.524767i	$-0.824153\pi$
$839$	−690.000	+	398.372i	−0.822408	+	0.474817i	0.0288384	+	0.999584i	$0.490819\pi$
$840$		0			0
$841$	593.500	−	1027.97i	0.705707	−	1.22232i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			530.008i			0.627228i
$846$		0			0
$847$	−236.000			−0.278630
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−816.000	−	471.118i	−0.958872	−	0.553605i
$852$		0			0
$853$	712.000	+	1233.22i	0.834701	+	1.44574i	0.894274	+	0.447521i	$0.147693\pi$
$853$	712.000	+	1233.22i	0.834701	+	1.44574i	−0.0595725	+	0.998224i	$0.518974\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−606.000	+	349.874i	−0.707118	+	0.408255i	−0.809993	−	0.586440i	$-0.800529\pi$
$857$	−606.000	+	349.874i	−0.707118	+	0.408255i	0.102875	+	0.994694i	$0.467196\pi$
$858$		0			0
$859$	−155.500	+	269.334i	−0.181024	+	0.313544i	−0.942230	−	0.334968i	$-0.891275\pi$
$859$	−155.500	+	269.334i	−0.181024	+	0.313544i	0.761205	+	0.648511i	$0.224608\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	1028.84i		−	1.19216i	−0.802923	−	0.596082i	$-0.796723\pi$
$863$		−	1028.84i		−	1.19216i	0.802923	−	0.596082i	$-0.203277\pi$
$864$		0			0
$865$	804.000			0.929480
$866$		0			0
$867$		0			0
$868$		0			0
$869$	57.0000	+	32.9090i	0.0655926	+	0.0378699i
$870$		0			0
$871$	62.0000	+	107.387i	0.0711825	+	0.123292i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	228.000	−	131.636i	0.260571	−	0.150441i
$876$		0			0
$877$	52.0000	−	90.0666i	0.0592930	−	0.102699i	−0.834855	−	0.550470i	$-0.814449\pi$
$877$	52.0000	−	90.0666i	0.0592930	−	0.102699i	0.894148	+	0.447771i	$0.147782\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	62.3538i		−	0.0707762i	−0.999374	−	0.0353881i	$-0.988733\pi$
$881$		−	62.3538i		−	0.0707762i	0.999374	−	0.0353881i	$-0.0112667\pi$
$882$		0			0
$883$	119.000			0.134768			0.0673839	−	0.997727i	$-0.478535\pi$
$883$	119.000			0.134768			0.0673839	+	0.997727i	$0.478535\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1029.00	+	594.093i	1.16009	+	0.669778i	0.951326	−	0.308188i	$-0.0997224\pi$
$887$	1029.00	+	594.093i	1.16009	+	0.669778i	0.208765	+	0.977966i	$0.433056\pi$
$888$		0			0
$889$	16.0000	+	27.7128i	0.0179978	+	0.0311730i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−462.000	+	266.736i	−0.517357	+	0.298696i
$894$		0			0
$895$	108.000	−	187.061i	0.120670	−	0.209007i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	1441.07i		−	1.60297i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	696.000	+	401.836i	0.769061	+	0.444017i
$906$		0			0
$907$	−347.500	−	601.888i	−0.383131	−	0.663603i	0.608377	−	0.793648i	$-0.291821\pi$
$907$	−347.500	−	601.888i	−0.383131	−	0.663603i	−0.991508	+	0.130046i	$0.958488\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1500.00	+	866.025i	−1.64654	+	0.950632i	−0.668110	+	0.744062i	$0.732897\pi$
$911$	−1500.00	+	866.025i	−1.64654	+	0.950632i	−0.978432	+	0.206569i	$0.933770\pi$
$912$		0			0
$913$	42.0000	−	72.7461i	0.0460022	−	0.0796781i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	318.697i		−	0.347543i
$918$		0			0
$919$	−56.0000			−0.0609358			−0.0304679	−	0.999536i	$-0.509700\pi$
$919$	−56.0000			−0.0609358			−0.0304679	+	0.999536i	$0.509700\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	108.000	+	62.3538i	0.117010	+	0.0675556i
$924$		0			0
$925$	−221.000	−	382.783i	−0.238919	−	0.413820i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	690.000	−	398.372i	0.742734	−	0.428818i	−0.0803285	−	0.996768i	$-0.525597\pi$
$929$	690.000	−	398.372i	0.742734	−	0.428818i	0.823063	+	0.567951i	$0.192264\pi$
$930$		0			0
$931$	247.500	−	428.683i	0.265843	−	0.460454i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	93.5307i		−	0.100033i
$936$		0			0
$937$	470.000			0.501601			0.250800	−	0.968039i	$-0.419306\pi$
$937$	470.000			0.501601			0.250800	+	0.968039i	$0.419306\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−348.000	−	200.918i	−0.369819	−	0.213515i	0.303560	−	0.952812i	$-0.401825\pi$
$941$	−348.000	−	200.918i	−0.369819	−	0.213515i	−0.673380	+	0.739297i	$0.735158\pi$
$942$		0			0
$943$	−168.000	−	290.985i	−0.178155	−	0.308573i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.50000	−	0.866025i	0.00158395	−	0.000914494i	−0.499208	−	0.866482i	$-0.666376\pi$
$947$	1.50000	−	0.866025i	0.00158395	−	0.000914494i	0.500792	+	0.865568i	$0.333042\pi$
$948$		0			0
$949$	−130.000	+	225.167i	−0.136986	+	0.237267i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	826.188i		−	0.866934i	−0.901169	−	0.433467i	$-0.857290\pi$
$953$		−	826.188i		−	0.866934i	0.901169	−	0.433467i	$-0.142710\pi$
$954$		0			0
$955$	804.000			0.841885
$956$		0			0
$957$		0			0
$958$		0			0
$959$	327.000	+	188.794i	0.340980	+	0.196865i
$960$		0			0
$961$	−31.5000	−	54.5596i	−0.0327784	−	0.0567738i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	795.000	−	458.993i	0.823834	−	0.475641i
$966$		0			0
$967$	601.000	−	1040.96i	0.621510	−	1.07649i	−0.367695	−	0.929946i	$-0.619853\pi$
$967$	601.000	−	1040.96i	0.621510	−	1.07649i	0.989205	−	0.146540i	$-0.0468137\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			187.061i			0.192648i	0.995350	+	0.0963241i	$0.0307085\pi$
$971$			187.061i			0.192648i	−0.995350	+	0.0963241i	$0.969291\pi$
$972$		0			0
$973$	−10.0000			−0.0102775
$974$		0			0
$975$		0			0
$976$		0			0
$977$	361.500	+	208.712i	0.370010	+	0.213626i	0.673463	−	0.739221i	$-0.264806\pi$
$977$	361.500	+	208.712i	0.370010	+	0.213626i	−0.303453	+	0.952847i	$0.598139\pi$
$978$		0			0
$979$	−108.000	−	187.061i	−0.110317	−	0.191074i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1011.00	−	583.701i	1.02848	−	0.593796i	0.111934	−	0.993716i	$-0.464295\pi$
$983$	1011.00	−	583.701i	1.02848	−	0.593796i	0.916550	+	0.399920i	$0.130962\pi$
$984$		0			0
$985$	−216.000	+	374.123i	−0.219289	+	0.379820i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	1690.48i		−	1.70928i
$990$		0			0
$991$	1420.00			1.43290			0.716448	−	0.697640i	$-0.245767\pi$
$991$	1420.00			1.43290			0.716448	+	0.697640i	$0.245767\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−870.000	−	502.295i	−0.874372	−	0.504819i
$996$		0			0
$997$	262.000	+	453.797i	0.262788	+	0.455163i	0.966982	−	0.254845i	$-0.0820246\pi$
$997$	262.000	+	453.797i	0.262788	+	0.455163i	−0.704193	+	0.710008i	$0.748691\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.q.b.449.1		2
3.2	odd	2		576.3.q.a.257.1		2
4.3	odd	2		1728.3.q.a.449.1		2
8.3	odd	2		27.3.d.a.17.1		2
8.5	even	2		432.3.q.a.17.1		2
9.2	odd	6	inner	1728.3.q.b.1601.1		2
9.7	even	3		576.3.q.a.65.1		2
12.11	even	2		576.3.q.b.257.1		2
24.5	odd	2		144.3.q.a.113.1		2
24.11	even	2		9.3.d.a.5.1	yes	2
36.7	odd	6		576.3.q.b.65.1		2
36.11	even	6		1728.3.q.a.1601.1		2
40.3	even	4		675.3.i.a.449.1		4
40.19	odd	2		675.3.j.a.476.1		2
40.27	even	4		675.3.i.a.449.2		4
72.5	odd	6		1296.3.e.a.161.1		2
72.11	even	6		27.3.d.a.8.1		2
72.13	even	6		1296.3.e.a.161.2		2
72.29	odd	6		432.3.q.a.305.1		2
72.43	odd	6		9.3.d.a.2.1	✓	2
72.59	even	6		81.3.b.a.80.1		2
72.61	even	6		144.3.q.a.65.1		2
72.67	odd	6		81.3.b.a.80.2		2
120.59	even	2		225.3.j.a.176.1		2
120.83	odd	4		225.3.i.a.149.2		4
120.107	odd	4		225.3.i.a.149.1		4
168.11	even	6		441.3.j.a.275.1		2
168.59	odd	6		441.3.j.b.275.1		2
168.83	odd	2		441.3.r.a.50.1		2
168.107	even	6		441.3.n.b.410.1		2
168.131	odd	6		441.3.n.a.410.1		2
360.43	even	12		225.3.i.a.74.1		4
360.83	odd	12		675.3.i.a.224.2		4
360.187	even	12		225.3.i.a.74.2		4
360.227	odd	12		675.3.i.a.224.1		4
360.259	odd	6		225.3.j.a.101.1		2
360.299	even	6		675.3.j.a.251.1		2
504.115	even	6		441.3.n.a.128.1		2
504.187	even	6		441.3.j.b.263.1		2
504.331	odd	6		441.3.j.a.263.1		2
504.403	odd	6		441.3.n.b.128.1		2
504.475	even	6		441.3.r.a.344.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.3.d.a.2.1	✓	2	72.43	odd	6
9.3.d.a.5.1	yes	2	24.11	even	2
27.3.d.a.8.1		2	72.11	even	6
27.3.d.a.17.1		2	8.3	odd	2
81.3.b.a.80.1		2	72.59	even	6
81.3.b.a.80.2		2	72.67	odd	6
144.3.q.a.65.1		2	72.61	even	6
144.3.q.a.113.1		2	24.5	odd	2
225.3.i.a.74.1		4	360.43	even	12
225.3.i.a.74.2		4	360.187	even	12
225.3.i.a.149.1		4	120.107	odd	4
225.3.i.a.149.2		4	120.83	odd	4
225.3.j.a.101.1		2	360.259	odd	6
225.3.j.a.176.1		2	120.59	even	2
432.3.q.a.17.1		2	8.5	even	2
432.3.q.a.305.1		2	72.29	odd	6
441.3.j.a.263.1		2	504.331	odd	6
441.3.j.a.275.1		2	168.11	even	6
441.3.j.b.263.1		2	504.187	even	6
441.3.j.b.275.1		2	168.59	odd	6
441.3.n.a.128.1		2	504.115	even	6
441.3.n.a.410.1		2	168.131	odd	6
441.3.n.b.128.1		2	504.403	odd	6
441.3.n.b.410.1		2	168.107	even	6
441.3.r.a.50.1		2	168.83	odd	2
441.3.r.a.344.1		2	504.475	even	6
576.3.q.a.65.1		2	9.7	even	3
576.3.q.a.257.1		2	3.2	odd	2
576.3.q.b.65.1		2	36.7	odd	6
576.3.q.b.257.1		2	12.11	even	2
675.3.i.a.224.1		4	360.227	odd	12
675.3.i.a.224.2		4	360.83	odd	12
675.3.i.a.449.1		4	40.3	even	4
675.3.i.a.449.2		4	40.27	even	4
675.3.j.a.251.1		2	360.299	even	6
675.3.j.a.476.1		2	40.19	odd	2
1296.3.e.a.161.1		2	72.5	odd	6
1296.3.e.a.161.2		2	72.13	even	6
1728.3.q.a.449.1		2	4.3	odd	2
1728.3.q.a.1601.1		2	36.11	even	6
1728.3.q.b.449.1		2	1.1	even	1	trivial
1728.3.q.b.1601.1		2	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +O(q^{10})\)	\(q+(3.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 0.866025i) q^{11} +(-2.00000 + 3.46410i) q^{13} -15.5885i q^{17} +11.0000 q^{19} +(-24.0000 - 13.8564i) q^{23} +(-6.50000 - 11.2583i) q^{25} +(39.0000 - 22.5167i) q^{29} +(16.0000 - 27.7128i) q^{31} +6.92820i q^{35} +34.0000 q^{37} +(10.5000 + 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +(-42.0000 + 24.2487i) q^{47} +(22.5000 - 38.9711i) q^{49} +6.00000 q^{55} +(-43.5000 - 25.1147i) q^{59} +(28.0000 + 48.4974i) q^{61} +(-12.0000 + 6.92820i) q^{65} +(15.5000 - 26.8468i) q^{67} -31.1769i q^{71} +65.0000 q^{73} +(3.00000 + 1.73205i) q^{77} +(19.0000 + 32.9090i) q^{79} +(42.0000 - 24.2487i) q^{83} +(27.0000 - 46.7654i) q^{85} -124.708i q^{89} -8.00000 q^{91} +(33.0000 + 19.0526i) q^{95} +(57.5000 + 99.5929i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{5} + 2 q^{7}+O(q^{10}) \) 2 * q + 6 * q^5 + 2 * q^7	\( 2 q + 6 q^{5} + 2 q^{7} + 3 q^{11} - 4 q^{13} + 22 q^{19} - 48 q^{23} - 13 q^{25} + 78 q^{29} + 32 q^{31} + 68 q^{37} + 21 q^{41} + 61 q^{43} - 84 q^{47} + 45 q^{49} + 12 q^{55} - 87 q^{59} + 56 q^{61} - 24 q^{65} + 31 q^{67} + 130 q^{73} + 6 q^{77} + 38 q^{79} + 84 q^{83} + 54 q^{85} - 16 q^{91} + 66 q^{95} + 115 q^{97}+O(q^{100}) \) 2 * q + 6 * q^5 + 2 * q^7 + 3 * q^11 - 4 * q^13 + 22 * q^19 - 48 * q^23 - 13 * q^25 + 78 * q^29 + 32 * q^31 + 68 * q^37 + 21 * q^41 + 61 * q^43 - 84 * q^47 + 45 * q^49 + 12 * q^55 - 87 * q^59 + 56 * q^61 - 24 * q^65 + 31 * q^67 + 130 * q^73 + 6 * q^77 + 38 * q^79 + 84 * q^83 + 54 * q^85 - 16 * q^91 + 66 * q^95 + 115 * q^97

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