LMFDB - Embedded newform 2700.2.s.b.2449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2700,2,Mod(1549,2700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("2700.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2700.s (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:	$21.5596085457$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2449.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2700.2449
Dual form			2700.2.s.b.1549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{7} +O(q^{10})$	$q+(-0.866025 - 0.500000i) q^{7} +(1.50000 - 2.59808i) q^{11} +(-0.866025 + 0.500000i) q^{13} +6.00000i q^{17} +4.00000 q^{19} +(2.59808 - 1.50000i) q^{23} +(-1.50000 + 2.59808i) q^{29} +(-2.50000 - 4.33013i) q^{31} -2.00000i q^{37} +(1.50000 + 2.59808i) q^{41} +(0.866025 + 0.500000i) q^{43} +(7.79423 + 4.50000i) q^{47} +(-3.00000 - 5.19615i) q^{49} +6.00000i q^{53} +(1.50000 + 2.59808i) q^{59} +(6.50000 - 11.2583i) q^{61} +(6.06218 - 3.50000i) q^{67} +12.0000 q^{71} -10.0000i q^{73} +(-2.59808 + 1.50000i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-7.79423 - 4.50000i) q^{83} +6.00000 q^{89} +1.00000 q^{91} +(9.52628 + 5.50000i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q + 6 q^{11} + 16 q^{19} - 6 q^{29} - 10 q^{31} + 6 q^{41} - 12 q^{49} + 6 q^{59} + 26 q^{61} + 48 q^{71} + 22 q^{79} + 24 q^{89} + 4 q^{91}+O(q^{100}) $ 4 * q + 6 * q^11 + 16 * q^19 - 6 * q^29 - 10 * q^31 + 6 * q^41 - 12 * q^49 + 6 * q^59 + 26 * q^61 + 48 * q^71 + 22 * q^79 + 24 * q^89 + 4 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2700\mathbb{Z}\right)^\times$.

$n$	$1001$	$1351$	$2377$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	0.327327	−	0.944911i	$-0.393852\pi$
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	−0.654654	+	0.755929i	$0.727186\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i	−0.615265	−	0.788320i	$-0.710951\pi$
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i	0.375073	+	0.926995i	$0.377618\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			6.00000i			1.45521i	0.685994	+	0.727607i	$0.259367\pi$
$17$			6.00000i			1.45521i	−0.685994	+	0.727607i	$0.740633\pi$
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	−0.204046	−	0.978961i	$-0.565409\pi$
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	0.745782	+	0.666190i	$0.232076\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	0.866025	+	0.500000i	0.132068	+	0.0762493i	0.564578	−	0.825380i	$-0.309039\pi$
$43$	0.866025	+	0.500000i	0.132068	+	0.0762493i	−0.432511	+	0.901629i	$0.642372\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.79423	+	4.50000i	1.13691	+	0.656392i	0.945662	−	0.325150i	$-0.105415\pi$
$47$	7.79423	+	4.50000i	1.13691	+	0.656392i	0.191243	+	0.981543i	$0.438748\pi$
$48$		0			0
$49$	−3.00000	−	5.19615i	−0.428571	−	0.742307i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	−0.0816792	−	0.996659i	$-0.526028\pi$
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	0.822292	+	0.569066i	$0.192695\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.59808	+	1.50000i	−0.296078	+	0.170941i
$78$		0			0
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	−0.370907	−	0.928670i	$-0.620953\pi$
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	0.989705	−	0.143120i	$-0.0457135\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.79423	−	4.50000i	−0.855528	−	0.493939i	0.00698436	−	0.999976i	$-0.497777\pi$
$83$	−7.79423	−	4.50000i	−0.855528	−	0.493939i	−0.862512	+	0.506036i	$0.831110\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	1.00000			0.104828
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	9.52628	+	5.50000i	0.967247	+	0.558440i	0.898396	−	0.439187i	$-0.144733\pi$
$97$	9.52628	+	5.50000i	0.967247	+	0.558440i	0.0688512	+	0.997627i	$0.478067\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	−0.203317	−	0.979113i	$-0.565172\pi$
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	0.949595	−	0.313478i	$-0.101494\pi$
$102$		0			0
$103$	−6.06218	+	3.50000i	−0.597324	+	0.344865i	−0.767988	−	0.640464i	$-0.778742\pi$
$103$	−6.06218	+	3.50000i	−0.597324	+	0.344865i	0.170664	+	0.985329i	$0.445409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.79423	−	4.50000i	0.733219	−	0.423324i	−0.0863794	−	0.996262i	$-0.527530\pi$
$113$	7.79423	−	4.50000i	0.733219	−	0.423324i	0.819599	+	0.572938i	$0.194196\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.00000	−	5.19615i	0.275010	−	0.476331i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.803365	+	0.595487i	$0.203041\pi$
$131$	10.5000	+	18.1865i	0.917389	+	1.58896i	0.114024	+	0.993478i	$0.463626\pi$
$132$		0			0
$133$	−3.46410	−	2.00000i	−0.300376	−	0.173422i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.59808	−	1.50000i	−0.221969	−	0.128154i	0.384893	−	0.922961i	$-0.374238\pi$
$137$	−2.59808	−	1.50000i	−0.221969	−	0.128154i	−0.606861	+	0.794808i	$0.707572\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			3.00000i			0.250873i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	−0.990485	−	0.137619i	$-0.956055\pi$
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	0.376061	−	0.926595i	$-0.377278\pi$
$150$		0			0
$151$	6.50000	−	11.2583i	0.528962	−	0.916190i	−0.470467	−	0.882418i	$-0.655915\pi$
$151$	6.50000	−	11.2583i	0.528962	−	0.916190i	0.999430	−	0.0337724i	$-0.0107521\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.2583	−	6.50000i	0.898513	−	0.518756i	0.0217953	−	0.999762i	$-0.493062\pi$
$157$	11.2583	−	6.50000i	0.898513	−	0.518756i	0.876717	+	0.481006i	$0.159728\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.00000			−0.236433
$162$		0			0
$163$			20.0000i			1.56652i	0.621694	+	0.783260i	$0.286445\pi$
$163$			20.0000i			1.56652i	−0.621694	+	0.783260i	$0.713555\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.79423	−	4.50000i	0.603136	−	0.348220i	−0.167139	−	0.985933i	$-0.553453\pi$
$167$	7.79423	−	4.50000i	0.603136	−	0.348220i	0.770274	+	0.637713i	$0.220119\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.79423	−	4.50000i	−0.592584	−	0.342129i	0.173534	−	0.984828i	$-0.444481\pi$
$173$	−7.79423	−	4.50000i	−0.592584	−	0.342129i	−0.766119	+	0.642699i	$0.777815\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	15.5885	+	9.00000i	1.13994	+	0.658145i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	−0.456068	−	0.889945i	$-0.650743\pi$
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	0.998749	−	0.0500060i	$-0.0159241\pi$
$192$		0			0
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	−0.116289	−	0.993215i	$-0.537100\pi$
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	0.802005	+	0.597317i	$0.203766\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		0			0
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.59808	−	1.50000i	0.182349	−	0.105279i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.00000	−	10.3923i	0.415029	−	0.718851i
$210$		0			0
$211$	−8.50000	−	14.7224i	−0.585164	−	1.01353i	−0.994855	−	0.101310i	$-0.967697\pi$
$211$	−8.50000	−	14.7224i	−0.585164	−	1.01353i	0.409691	−	0.912224i	$-0.365637\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$			5.00000i			0.339422i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$		0			0
$223$	0.866025	+	0.500000i	0.0579934	+	0.0334825i	0.528716	−	0.848799i	$-0.322674\pi$
$223$	0.866025	+	0.500000i	0.0579934	+	0.0334825i	−0.470723	+	0.882281i	$0.656007\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−23.3827	−	13.5000i	−1.55196	−	0.896026i	−0.997982	−	0.0634974i	$-0.979775\pi$
$227$	−23.3827	−	13.5000i	−1.55196	−	0.896026i	−0.553981	−	0.832529i	$-0.686892\pi$
$228$		0			0
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	0.567300	−	0.823511i	$-0.307988\pi$
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	−0.996832	+	0.0795401i	$0.974655\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			6.00000i			0.393073i	0.980497	+	0.196537i	$0.0629694\pi$
$233$			6.00000i			0.393073i	−0.980497	+	0.196537i	$0.937031\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.858623	+	0.512607i	$0.171320\pi$
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.0146191	+	0.999893i	$0.495346\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.46410	+	2.00000i	−0.220416	+	0.127257i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$		−	9.00000i		−	0.565825i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.79423	+	4.50000i	−0.486191	+	0.280702i	−0.722993	−	0.690856i	$-0.757234\pi$
$257$	−7.79423	+	4.50000i	−0.486191	+	0.280702i	0.236802	+	0.971558i	$0.423901\pi$
$258$		0			0
$259$	−1.00000	+	1.73205i	−0.0621370	+	0.107624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−18.1865	−	10.5000i	−1.12143	−	0.647458i	−0.179664	−	0.983728i	$-0.557501\pi$
$263$	−18.1865	−	10.5000i	−1.12143	−	0.647458i	−0.941766	+	0.336270i	$0.890834\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.866025	−	0.500000i	−0.0520344	−	0.0300421i	0.473757	−	0.880656i	$-0.342897\pi$
$277$	−0.866025	−	0.500000i	−0.0520344	−	0.0300421i	−0.525792	+	0.850613i	$0.676231\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$		0			0
$283$	4.33013	−	2.50000i	0.257399	−	0.148610i	−0.365748	−	0.930714i	$-0.619187\pi$
$283$	4.33013	−	2.50000i	0.257399	−	0.148610i	0.623148	+	0.782104i	$0.285854\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	3.00000i		−	0.177084i
$288$		0			0
$289$	−19.0000			−1.11765
$290$		0			0
$291$		0			0
$292$		0			0
$293$	18.1865	−	10.5000i	1.06247	−	0.613417i	0.136355	−	0.990660i	$-0.456461\pi$
$293$	18.1865	−	10.5000i	1.06247	−	0.613417i	0.926114	+	0.377244i	$0.123128\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.50000	+	2.59808i	−0.0867472	+	0.150251i
$300$		0			0
$301$	−0.500000	−	0.866025i	−0.0288195	−	0.0499169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	20.0000i		−	1.14146i	−0.821138	−	0.570730i	$-0.806660\pi$
$307$		−	20.0000i		−	1.14146i	0.821138	−	0.570730i	$-0.193340\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.5000	+	18.1865i	0.595400	+	1.03126i	0.993490	+	0.113917i	$0.0363399\pi$
$311$	10.5000	+	18.1865i	0.595400	+	1.03126i	−0.398090	+	0.917346i	$0.630327\pi$
$312$		0			0
$313$	0.866025	+	0.500000i	0.0489506	+	0.0282617i	0.524276	−	0.851549i	$-0.324336\pi$
$313$	0.866025	+	0.500000i	0.0489506	+	0.0282617i	−0.475325	+	0.879810i	$0.657669\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	18.1865	+	10.5000i	1.02146	+	0.589739i	0.914526	−	0.404528i	$-0.132564\pi$
$317$	18.1865	+	10.5000i	1.02146	+	0.589739i	0.106932	+	0.994266i	$0.465897\pi$
$318$		0			0
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			24.0000i			1.33540i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−4.50000	−	7.79423i	−0.248093	−	0.429710i
$330$		0			0
$331$	−5.50000	+	9.52628i	−0.302307	+	0.523612i	−0.976658	−	0.214799i	$-0.931090\pi$
$331$	−5.50000	+	9.52628i	−0.302307	+	0.523612i	0.674351	+	0.738411i	$0.264424\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−19.9186	+	11.5000i	−1.08503	+	0.626445i	−0.932250	−	0.361815i	$-0.882157\pi$
$337$	−19.9186	+	11.5000i	−1.08503	+	0.626445i	−0.152784	+	0.988260i	$0.548824\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.0000			−0.812296
$342$		0			0
$343$			13.0000i			0.701934i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.79423	−	4.50000i	0.418416	−	0.241573i	−0.275983	−	0.961162i	$-0.589003\pi$
$347$	7.79423	−	4.50000i	0.418416	−	0.241573i	0.694399	+	0.719590i	$0.255670\pi$
$348$		0			0
$349$	−0.500000	+	0.866025i	−0.0267644	+	0.0463573i	−0.879097	−	0.476642i	$-0.841854\pi$
$349$	−0.500000	+	0.866025i	−0.0267644	+	0.0463573i	0.852333	+	0.523000i	$0.175187\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.59808	+	1.50000i	0.138282	+	0.0798369i	0.567545	−	0.823343i	$-0.307893\pi$
$353$	2.59808	+	1.50000i	0.138282	+	0.0798369i	−0.429263	+	0.903179i	$0.641227\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−11.2583	−	6.50000i	−0.587680	−	0.339297i	0.176500	−	0.984301i	$-0.443523\pi$
$367$	−11.2583	−	6.50000i	−0.587680	−	0.339297i	−0.764180	+	0.645003i	$0.776856\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	−0.866025	+	0.500000i	−0.0448411	+	0.0258890i	−0.522253	−	0.852791i	$-0.674908\pi$
$373$	−0.866025	+	0.500000i	−0.0448411	+	0.0258890i	0.477412	+	0.878680i	$0.341575\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	3.00000i		−	0.154508i
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.9904	−	7.50000i	0.663777	−	0.383232i	−0.129937	−	0.991522i	$-0.541478\pi$
$383$	12.9904	−	7.50000i	0.663777	−	0.383232i	0.793715	+	0.608290i	$0.208144\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.50000	+	12.9904i	−0.380265	+	0.658638i	−0.991100	−	0.133120i	$-0.957501\pi$
$389$	−7.50000	+	12.9904i	−0.380265	+	0.658638i	0.610835	+	0.791758i	$0.290834\pi$
$390$		0			0
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	2.00000i		−	0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$		−	2.00000i		−	0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	4.33013	+	2.50000i	0.215699	+	0.124534i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.19615	−	3.00000i	−0.257564	−	0.148704i
$408$		0			0
$409$	11.5000	+	19.9186i	0.568638	+	0.984911i	0.996701	+	0.0811615i	$0.0258630\pi$
$409$	11.5000	+	19.9186i	0.568638	+	0.984911i	−0.428063	+	0.903749i	$0.640804\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	3.00000i		−	0.147620i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$		0			0
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	0.0256838	+	0.999670i	$0.491824\pi$
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	−0.878582	+	0.477592i	$0.841510\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−11.2583	+	6.50000i	−0.544829	+	0.314557i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$		0			0
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.3923	−	6.00000i	0.497131	−	0.287019i
$438$		0			0
$439$	17.5000	−	30.3109i	0.835229	−	1.44666i	−0.0586141	−	0.998281i	$-0.518668\pi$
$439$	17.5000	−	30.3109i	0.835229	−	1.44666i	0.893843	−	0.448379i	$-0.147999\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.79423	−	4.50000i	−0.370315	−	0.213801i	0.303281	−	0.952901i	$-0.401918\pi$
$443$	−7.79423	−	4.50000i	−0.370315	−	0.213801i	−0.673596	+	0.739100i	$0.735251\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	9.00000			0.423793
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−32.0429	−	18.5000i	−1.49891	−	0.865393i	−0.498906	−	0.866656i	$-0.666265\pi$
$457$	−32.0429	−	18.5000i	−1.49891	−	0.865393i	−0.999999	+	0.00126243i	$0.999598\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	−0.828978	−	0.559281i	$-0.811077\pi$
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	0.898840	+	0.438276i	$0.144411\pi$
$462$		0			0
$463$	−16.4545	+	9.50000i	−0.764705	+	0.441502i	−0.830982	−	0.556299i	$-0.812221\pi$
$463$	−16.4545	+	9.50000i	−0.764705	+	0.441502i	0.0662777	+	0.997801i	$0.478888\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$		0			0
$469$	−7.00000			−0.323230
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.59808	−	1.50000i	0.119460	−	0.0689701i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.5000	+	23.3827i	−0.616831	+	1.06838i	0.373230	+	0.927739i	$0.378250\pi$
$479$	−13.5000	+	23.3827i	−0.616831	+	1.06838i	−0.990060	+	0.140643i	$0.955083\pi$
$480$		0			0
$481$	1.00000	+	1.73205i	0.0455961	+	0.0789747i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	32.0000i		−	1.45006i	−0.688718	−	0.725029i	$-0.741826\pi$
$487$		−	32.0000i		−	1.45006i	0.688718	−	0.725029i	$-0.258174\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.50000	−	2.59808i	−0.0676941	−	0.117250i	0.830192	−	0.557478i	$-0.188231\pi$
$491$	−1.50000	−	2.59808i	−0.0676941	−	0.117250i	−0.897886	+	0.440228i	$0.854898\pi$
$492$		0			0
$493$	−15.5885	−	9.00000i	−0.702069	−	0.405340i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.3923	−	6.00000i	−0.466159	−	0.269137i
$498$		0			0
$499$	2.50000	+	4.33013i	0.111915	+	0.193843i	0.916542	−	0.399937i	$-0.130968\pi$
$499$	2.50000	+	4.33013i	0.111915	+	0.193843i	−0.804627	+	0.593780i	$0.797635\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			36.0000i			1.60516i	0.596544	+	0.802580i	$0.296540\pi$
$503$			36.0000i			1.60516i	−0.596544	+	0.802580i	$0.703460\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−19.5000	−	33.7750i	−0.864322	−	1.49705i	−0.867719	−	0.497056i	$-0.834414\pi$
$509$	−19.5000	−	33.7750i	−0.864322	−	1.49705i	0.00339621	−	0.999994i	$-0.498919\pi$
$510$		0			0
$511$	−5.00000	+	8.66025i	−0.221187	+	0.383107i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$	23.3827	−	13.5000i	1.02837	−	0.593729i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$		0			0
$523$			8.00000i			0.349816i	0.984585	+	0.174908i	$0.0559627\pi$
$523$			8.00000i			0.349816i	−0.984585	+	0.174908i	$0.944037\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	25.9808	−	15.0000i	1.13174	−	0.653410i
$528$		0			0
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.59808	−	1.50000i	−0.112535	−	0.0649722i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−18.0000			−0.775315
$540$		0			0
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−11.2583	−	6.50000i	−0.481371	−	0.277920i	0.239616	−	0.970868i	$-0.422978\pi$
$547$	−11.2583	−	6.50000i	−0.481371	−	0.277920i	−0.720988	+	0.692948i	$0.756312\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$		0			0
$553$	−9.52628	+	5.50000i	−0.405099	+	0.233884i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	30.0000i		−	1.27114i	−0.772043	−	0.635570i	$-0.780765\pi$
$557$		−	30.0000i		−	1.27114i	0.772043	−	0.635570i	$-0.219235\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.79423	+	4.50000i	−0.328488	+	0.189652i	−0.655169	−	0.755482i	$-0.727403\pi$
$563$	−7.79423	+	4.50000i	−0.328488	+	0.189652i	0.326682	+	0.945134i	$0.394069\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	−0.979313	−	0.202350i	$-0.935142\pi$
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	0.664897	+	0.746935i	$0.268475\pi$
$570$		0			0
$571$	15.5000	+	26.8468i	0.648655	+	1.12350i	0.983444	+	0.181210i	$0.0580014\pi$
$571$	15.5000	+	26.8468i	0.648655	+	1.12350i	−0.334790	+	0.942293i	$0.608665\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$			10.0000i			0.416305i	0.978096	+	0.208153i	$0.0667451\pi$
$577$			10.0000i			0.416305i	−0.978096	+	0.208153i	$0.933255\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.50000	+	7.79423i	0.186691	+	0.323359i
$582$		0			0
$583$	15.5885	+	9.00000i	0.645608	+	0.372742i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.9904	−	7.50000i	−0.536170	−	0.309558i	0.207355	−	0.978266i	$-0.433514\pi$
$587$	−12.9904	−	7.50000i	−0.536170	−	0.309558i	−0.743525	+	0.668708i	$0.766848\pi$
$588$		0			0
$589$	−10.0000	−	17.3205i	−0.412043	−	0.713679i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	6.00000i		−	0.246390i	−0.992382	−	0.123195i	$-0.960686\pi$
$593$		−	6.00000i		−	0.246390i	0.992382	−	0.123195i	$-0.0393141\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	19.5000	+	33.7750i	0.796748	+	1.38001i	0.921723	+	0.387849i	$0.126782\pi$
$599$	19.5000	+	33.7750i	0.796748	+	1.38001i	−0.124975	+	0.992160i	$0.539885\pi$
$600$		0			0
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	0.249565	+	0.968358i	$0.419712\pi$
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	−0.963405	+	0.268049i	$0.913621\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−35.5070	+	20.5000i	−1.44119	+	0.832069i	−0.997929	−	0.0643251i	$-0.979511\pi$
$607$	−35.5070	+	20.5000i	−1.44119	+	0.832069i	−0.443257	+	0.896394i	$0.646177\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.00000			−0.364101
$612$		0			0
$613$			26.0000i			1.05013i	0.851062	+	0.525065i	$0.175959\pi$
$613$			26.0000i			1.05013i	−0.851062	+	0.525065i	$0.824041\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.59808	−	1.50000i	0.104595	−	0.0603877i	−0.446790	−	0.894639i	$-0.647433\pi$
$617$	2.59808	−	1.50000i	0.104595	−	0.0603877i	0.551385	+	0.834251i	$0.314100\pi$
$618$		0			0
$619$	−6.50000	+	11.2583i	−0.261257	+	0.452510i	−0.966576	−	0.256379i	$-0.917470\pi$
$619$	−6.50000	+	11.2583i	−0.261257	+	0.452510i	0.705319	+	0.708890i	$0.250804\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−5.19615	−	3.00000i	−0.208179	−	0.120192i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$	12.0000			0.478471
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	5.19615	+	3.00000i	0.205879	+	0.118864i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$		0			0
$643$	35.5070	−	20.5000i	1.40026	−	0.808441i	0.405842	−	0.913943i	$-0.366978\pi$
$643$	35.5070	−	20.5000i	1.40026	−	0.808441i	0.994419	+	0.105502i	$0.0336450\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$		0			0
$649$	9.00000			0.353281
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.1865	−	10.5000i	0.711694	−	0.410897i	−0.0999939	−	0.994988i	$-0.531882\pi$
$653$	18.1865	−	10.5000i	0.711694	−	0.410897i	0.811688	+	0.584091i	$0.198549\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10.5000	−	18.1865i	0.409022	−	0.708447i	−0.585758	−	0.810486i	$-0.699203\pi$
$659$	10.5000	−	18.1865i	0.409022	−	0.708447i	0.994780	+	0.102039i	$0.0325366\pi$
$660$		0			0
$661$	−5.50000	−	9.52628i	−0.213925	−	0.370529i	0.739014	−	0.673690i	$-0.235292\pi$
$661$	−5.50000	−	9.52628i	−0.213925	−	0.370529i	−0.952940	+	0.303160i	$0.901958\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$			9.00000i			0.348481i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−19.5000	−	33.7750i	−0.752789	−	1.30387i
$672$		0			0
$673$	−9.52628	−	5.50000i	−0.367211	−	0.212009i	0.305028	−	0.952343i	$-0.401334\pi$
$673$	−9.52628	−	5.50000i	−0.367211	−	0.212009i	−0.672239	+	0.740334i	$0.734667\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.9904	−	7.50000i	−0.499261	−	0.288248i	0.229147	−	0.973392i	$-0.426406\pi$
$677$	−12.9904	−	7.50000i	−0.499261	−	0.288248i	−0.728408	+	0.685143i	$0.759740\pi$
$678$		0			0
$679$	−5.50000	−	9.52628i	−0.211071	−	0.365585i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.00000	−	5.19615i	−0.114291	−	0.197958i
$690$		0			0
$691$	0.500000	−	0.866025i	0.0190209	−	0.0329452i	−0.856358	−	0.516382i	$-0.827278\pi$
$691$	0.500000	−	0.866025i	0.0190209	−	0.0329452i	0.875379	+	0.483437i	$0.160612\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−15.5885	+	9.00000i	−0.590455	+	0.340899i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$		−	8.00000i		−	0.301726i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−12.9904	+	7.50000i	−0.488554	+	0.282067i
$708$		0			0
$709$	−12.5000	+	21.6506i	−0.469447	+	0.813107i	−0.999390	−	0.0349269i	$-0.988880\pi$
$709$	−12.5000	+	21.6506i	−0.469447	+	0.813107i	0.529943	+	0.848034i	$0.322213\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−12.9904	−	7.50000i	−0.486494	−	0.280877i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	7.00000			0.260694
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−32.0429	−	18.5000i	−1.18841	−	0.686127i	−0.230463	−	0.973081i	$-0.574024\pi$
$727$	−32.0429	−	18.5000i	−1.18841	−	0.686127i	−0.957944	+	0.286954i	$0.907357\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.00000	+	5.19615i	−0.110959	+	0.192187i
$732$		0			0
$733$	19.9186	−	11.5000i	0.735710	−	0.424762i	−0.0847976	−	0.996398i	$-0.527024\pi$
$733$	19.9186	−	11.5000i	0.735710	−	0.424762i	0.820507	+	0.571636i	$0.193691\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	21.0000i		−	0.773545i
$738$		0			0
$739$	16.0000			0.588570			0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000			0.588570			0.294285	+	0.955718i	$0.404919\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7.79423	+	4.50000i	−0.285943	+	0.165089i	−0.636111	−	0.771598i	$-0.719458\pi$
$743$	−7.79423	+	4.50000i	−0.285943	+	0.165089i	0.350168	+	0.936687i	$0.386124\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.00000	−	10.3923i	0.219235	−	0.379727i
$750$		0			0
$751$	15.5000	+	26.8468i	0.565603	+	0.979653i	0.996993	+	0.0774878i	$0.0246899\pi$
$751$	15.5000	+	26.8468i	0.565603	+	0.979653i	−0.431390	+	0.902165i	$0.641977\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$			10.0000i			0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$			10.0000i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	0.999925	−	0.0122260i	$-0.00389175\pi$
$761$	13.5000	+	23.3827i	0.489375	+	0.847622i	−0.510551	+	0.859848i	$0.670558\pi$
$762$		0			0
$763$	1.73205	+	1.00000i	0.0627044	+	0.0362024i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.59808	−	1.50000i	−0.0938111	−	0.0541619i
$768$		0			0
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	0.856869	−	0.515534i	$-0.172406\pi$
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	−0.874900	+	0.484304i	$0.839073\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	18.0000i		−	0.647415i	−0.946157	−	0.323708i	$-0.895071\pi$
$773$		−	18.0000i		−	0.647415i	0.946157	−	0.323708i	$-0.104929\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.00000	+	10.3923i	0.214972	+	0.372343i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	37.2391	−	21.5000i	1.32743	−	0.766392i	0.342529	−	0.939507i	$-0.388717\pi$
$787$	37.2391	−	21.5000i	1.32743	−	0.766392i	0.984902	+	0.173115i	$0.0553833\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.00000			−0.320003
$792$		0			0
$793$			13.0000i			0.461644i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.79423	+	4.50000i	−0.276086	+	0.159398i	−0.631650	−	0.775254i	$-0.717622\pi$
$797$	−7.79423	+	4.50000i	−0.276086	+	0.159398i	0.355564	+	0.934652i	$0.384289\pi$
$798$		0			0
$799$	−27.0000	+	46.7654i	−0.955191	+	1.65444i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−25.9808	−	15.0000i	−0.916841	−	0.529339i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	6.00000			0.210949			0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000			0.210949			0.105474	+	0.994422i	$0.466364\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.46410	+	2.00000i	0.121194	+	0.0699711i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	25.5000	−	44.1673i	0.889956	−	1.54145i	0.0500305	−	0.998748i	$-0.484068\pi$
$821$	25.5000	−	44.1673i	0.889956	−	1.54145i	0.839926	−	0.542702i	$-0.182599\pi$
$822$		0			0
$823$	−16.4545	+	9.50000i	−0.573567	+	0.331149i	−0.758573	−	0.651588i	$-0.774103\pi$
$823$	−16.4545	+	9.50000i	−0.573567	+	0.331149i	0.185006	+	0.982737i	$0.440770\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	12.0000i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$		−	12.0000i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$		0			0
$829$	−50.0000			−1.73657			−0.868286	−	0.496064i	$-0.834778\pi$
$829$	−50.0000			−1.73657			−0.868286	+	0.496064i	$0.834778\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	31.1769	−	18.0000i	1.08022	−	0.623663i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	−0.777832	−	0.628473i	$-0.783680\pi$
$839$	4.50000	−	7.79423i	0.155357	−	0.269087i	0.933189	+	0.359386i	$0.117014\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	2.00000i		−	0.0687208i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.00000	−	5.19615i	−0.102839	−	0.178122i
$852$		0			0
$853$	11.2583	+	6.50000i	0.385478	+	0.222556i	0.680199	−	0.733028i	$-0.261893\pi$
$853$	11.2583	+	6.50000i	0.385478	+	0.222556i	−0.294721	+	0.955583i	$0.595227\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.3827	−	13.5000i	−0.798737	−	0.461151i	0.0442921	−	0.999019i	$-0.485897\pi$
$857$	−23.3827	−	13.5000i	−0.798737	−	0.461151i	−0.843029	+	0.537867i	$0.819230\pi$
$858$		0			0
$859$	20.5000	+	35.5070i	0.699451	+	1.21148i	0.968657	+	0.248402i	$0.0799054\pi$
$859$	20.5000	+	35.5070i	0.699451	+	1.21148i	−0.269206	+	0.963083i	$0.586761\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−16.5000	−	28.5788i	−0.559724	−	0.969471i
$870$		0			0
$871$	−3.50000	+	6.06218i	−0.118593	+	0.205409i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−19.9186	+	11.5000i	−0.672603	+	0.388327i	−0.797062	−	0.603897i	$-0.793614\pi$
$877$	−19.9186	+	11.5000i	−0.672603	+	0.388327i	0.124459	+	0.992225i	$0.460280\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$		−	4.00000i		−	0.134611i	−0.997732	−	0.0673054i	$-0.978560\pi$
$883$		−	4.00000i		−	0.134611i	0.997732	−	0.0673054i	$-0.0214402\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.1865	−	10.5000i	0.610644	−	0.352555i	−0.162573	−	0.986696i	$-0.551979\pi$
$887$	18.1865	−	10.5000i	0.610644	−	0.352555i	0.773217	+	0.634141i	$0.218646\pi$
$888$		0			0
$889$	8.00000	−	13.8564i	0.268311	−	0.464729i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	31.1769	+	18.0000i	1.04330	+	0.602347i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$	15.0000			0.500278
$900$		0			0
$901$	−36.0000			−1.19933
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	40.7032	+	23.5000i	1.35153	+	0.780305i	0.988463	−	0.151460i	$-0.0483973\pi$
$907$	40.7032	+	23.5000i	1.35153	+	0.780305i	0.363064	+	0.931764i	$0.381731\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−22.5000	+	38.9711i	−0.745458	+	1.29117i	0.204522	+	0.978862i	$0.434436\pi$
$911$	−22.5000	+	38.9711i	−0.745458	+	1.29117i	−0.949980	+	0.312310i	$0.898897\pi$
$912$		0			0
$913$	−23.3827	+	13.5000i	−0.773854	+	0.446785i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	21.0000i		−	0.693481i
$918$		0			0
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−10.3923	+	6.00000i	−0.342067	+	0.197492i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	−0.997905	−	0.0646999i	$-0.979391\pi$
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	0.554984	+	0.831861i	$0.312724\pi$
$930$		0			0
$931$	−12.0000	−	20.7846i	−0.393284	−	0.681188i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$			34.0000i			1.11073i	0.831606	+	0.555366i	$0.187422\pi$
$937$			34.0000i			1.11073i	−0.831606	+	0.555366i	$0.812578\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	0.642567	−	0.766229i	$-0.277869\pi$
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	−0.984858	+	0.173365i	$0.944536\pi$
$942$		0			0
$943$	7.79423	+	4.50000i	0.253815	+	0.146540i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−23.3827	−	13.5000i	−0.759835	−	0.438691i	0.0694014	−	0.997589i	$-0.477891\pi$
$947$	−23.3827	−	13.5000i	−0.759835	−	0.438691i	−0.829237	+	0.558898i	$0.811224\pi$
$948$		0			0
$949$	5.00000	+	8.66025i	0.162307	+	0.281124i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	54.0000i		−	1.74923i	−0.484817	−	0.874616i	$-0.661114\pi$
$953$		−	54.0000i		−	1.74923i	0.484817	−	0.874616i	$-0.338886\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.50000	+	2.59808i	0.0484375	+	0.0838963i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	37.2391	−	21.5000i	1.19753	−	0.691393i	0.237525	−	0.971381i	$-0.423664\pi$
$967$	37.2391	−	21.5000i	1.19753	−	0.691393i	0.960003	+	0.279988i	$0.0903305\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$		−	5.00000i		−	0.160293i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−49.3634	+	28.5000i	−1.57928	+	0.911796i	−0.584316	+	0.811526i	$0.698637\pi$
$977$	−49.3634	+	28.5000i	−1.57928	+	0.911796i	−0.994960	+	0.100270i	$0.968029\pi$
$978$		0			0
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	44.1673	+	25.5000i	1.40872	+	0.813324i	0.995265	−	0.0972017i	$-0.0309892\pi$
$983$	44.1673	+	25.5000i	1.40872	+	0.813324i	0.413453	+	0.910525i	$0.364323\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.00000			0.0953945
$990$		0			0
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.866025	−	0.500000i	−0.0274273	−	0.0158352i	0.486224	−	0.873834i	$-0.338374\pi$
$997$	−0.866025	−	0.500000i	−0.0274273	−	0.0158352i	−0.513651	+	0.857999i	$0.671707\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2700.2.s.b.2449.1		4
3.2	odd	2		900.2.s.b.349.1		4
5.2	odd	4		108.2.e.a.73.1		2
5.3	odd	4		2700.2.i.b.1801.1		2
5.4	even	2	inner	2700.2.s.b.2449.2		4
9.2	odd	6		8100.2.d.h.649.2		2
9.4	even	3	inner	2700.2.s.b.1549.2		4
9.5	odd	6		900.2.s.b.49.2		4
9.7	even	3		8100.2.d.c.649.2		2
15.2	even	4		36.2.e.a.25.1	yes	2
15.8	even	4		900.2.i.b.601.1		2
15.14	odd	2		900.2.s.b.349.2		4
20.7	even	4		432.2.i.c.289.1		2
35.2	odd	12		5292.2.i.c.2125.1		2
35.12	even	12		5292.2.i.a.2125.1		2
35.17	even	12		5292.2.l.c.3313.1		2
35.27	even	4		5292.2.j.a.3529.1		2
35.32	odd	12		5292.2.l.a.3313.1		2
40.27	even	4		1728.2.i.c.1153.1		2
40.37	odd	4		1728.2.i.d.1153.1		2
45.2	even	12		324.2.a.c.1.1		1
45.4	even	6	inner	2700.2.s.b.1549.1		4
45.7	odd	12		324.2.a.a.1.1		1
45.13	odd	12		2700.2.i.b.901.1		2
45.14	odd	6		900.2.s.b.49.1		4
45.22	odd	12		108.2.e.a.37.1		2
45.23	even	12		900.2.i.b.301.1		2
45.29	odd	6		8100.2.d.h.649.1		2
45.32	even	12		36.2.e.a.13.1	✓	2
45.34	even	6		8100.2.d.c.649.1		2
45.38	even	12		8100.2.a.j.1.1		1
45.43	odd	12		8100.2.a.g.1.1		1
60.47	odd	4		144.2.i.a.97.1		2
105.2	even	12		1764.2.i.a.1537.1		2
105.17	odd	12		1764.2.l.a.961.1		2
105.32	even	12		1764.2.l.c.961.1		2
105.47	odd	12		1764.2.i.c.1537.1		2
105.62	odd	4		1764.2.j.b.1177.1		2
120.77	even	4		576.2.i.f.385.1		2
120.107	odd	4		576.2.i.e.385.1		2
180.7	even	12		1296.2.a.b.1.1		1
180.47	odd	12		1296.2.a.k.1.1		1
180.67	even	12		432.2.i.c.145.1		2
180.167	odd	12		144.2.i.a.49.1		2
315.32	even	12		1764.2.i.a.373.1		2
315.67	odd	12		5292.2.i.c.1549.1		2
315.122	odd	12		1764.2.i.c.373.1		2
315.157	even	12		5292.2.i.a.1549.1		2
315.167	odd	12		1764.2.j.b.589.1		2
315.202	even	12		5292.2.j.a.1765.1		2
315.212	even	12		1764.2.l.c.949.1		2
315.247	odd	12		5292.2.l.a.361.1		2
315.257	odd	12		1764.2.l.a.949.1		2
315.292	even	12		5292.2.l.c.361.1		2
360.67	even	12		1728.2.i.c.577.1		2
360.77	even	12		576.2.i.f.193.1		2
360.157	odd	12		1728.2.i.d.577.1		2
360.187	even	12		5184.2.a.bb.1.1		1
360.227	odd	12		5184.2.a.f.1.1		1
360.277	odd	12		5184.2.a.ba.1.1		1
360.317	even	12		5184.2.a.e.1.1		1
360.347	odd	12		576.2.i.e.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.e.a.13.1	✓	2	45.32	even	12
36.2.e.a.25.1	yes	2	15.2	even	4
108.2.e.a.37.1		2	45.22	odd	12
108.2.e.a.73.1		2	5.2	odd	4
144.2.i.a.49.1		2	180.167	odd	12
144.2.i.a.97.1		2	60.47	odd	4
324.2.a.a.1.1		1	45.7	odd	12
324.2.a.c.1.1		1	45.2	even	12
432.2.i.c.145.1		2	180.67	even	12
432.2.i.c.289.1		2	20.7	even	4
576.2.i.e.193.1		2	360.347	odd	12
576.2.i.e.385.1		2	120.107	odd	4
576.2.i.f.193.1		2	360.77	even	12
576.2.i.f.385.1		2	120.77	even	4
900.2.i.b.301.1		2	45.23	even	12
900.2.i.b.601.1		2	15.8	even	4
900.2.s.b.49.1		4	45.14	odd	6
900.2.s.b.49.2		4	9.5	odd	6
900.2.s.b.349.1		4	3.2	odd	2
900.2.s.b.349.2		4	15.14	odd	2
1296.2.a.b.1.1		1	180.7	even	12
1296.2.a.k.1.1		1	180.47	odd	12
1728.2.i.c.577.1		2	360.67	even	12
1728.2.i.c.1153.1		2	40.27	even	4
1728.2.i.d.577.1		2	360.157	odd	12
1728.2.i.d.1153.1		2	40.37	odd	4
1764.2.i.a.373.1		2	315.32	even	12
1764.2.i.a.1537.1		2	105.2	even	12
1764.2.i.c.373.1		2	315.122	odd	12
1764.2.i.c.1537.1		2	105.47	odd	12
1764.2.j.b.589.1		2	315.167	odd	12
1764.2.j.b.1177.1		2	105.62	odd	4
1764.2.l.a.949.1		2	315.257	odd	12
1764.2.l.a.961.1		2	105.17	odd	12
1764.2.l.c.949.1		2	315.212	even	12
1764.2.l.c.961.1		2	105.32	even	12
2700.2.i.b.901.1		2	45.13	odd	12
2700.2.i.b.1801.1		2	5.3	odd	4
2700.2.s.b.1549.1		4	45.4	even	6	inner
2700.2.s.b.1549.2		4	9.4	even	3	inner
2700.2.s.b.2449.1		4	1.1	even	1	trivial
2700.2.s.b.2449.2		4	5.4	even	2	inner
5184.2.a.e.1.1		1	360.317	even	12
5184.2.a.f.1.1		1	360.227	odd	12
5184.2.a.ba.1.1		1	360.277	odd	12
5184.2.a.bb.1.1		1	360.187	even	12
5292.2.i.a.1549.1		2	315.157	even	12
5292.2.i.a.2125.1		2	35.12	even	12
5292.2.i.c.1549.1		2	315.67	odd	12
5292.2.i.c.2125.1		2	35.2	odd	12
5292.2.j.a.1765.1		2	315.202	even	12
5292.2.j.a.3529.1		2	35.27	even	4
5292.2.l.a.361.1		2	315.247	odd	12
5292.2.l.a.3313.1		2	35.32	odd	12
5292.2.l.c.361.1		2	315.292	even	12
5292.2.l.c.3313.1		2	35.17	even	12
8100.2.a.g.1.1		1	45.43	odd	12
8100.2.a.j.1.1		1	45.38	even	12
8100.2.d.c.649.1		2	45.34	even	6
8100.2.d.c.649.2		2	9.7	even	3
8100.2.d.h.649.1		2	45.29	odd	6
8100.2.d.h.649.2		2	9.2	odd	6

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:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2700.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{7} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{7} +(1.50000 - 2.59808i) q^{11} +(-0.866025 + 0.500000i) q^{13} +6.00000i q^{17} +4.00000 q^{19} +(2.59808 - 1.50000i) q^{23} +(-1.50000 + 2.59808i) q^{29} +(-2.50000 - 4.33013i) q^{31} -2.00000i q^{37} +(1.50000 + 2.59808i) q^{41} +(0.866025 + 0.500000i) q^{43} +(7.79423 + 4.50000i) q^{47} +(-3.00000 - 5.19615i) q^{49} +6.00000i q^{53} +(1.50000 + 2.59808i) q^{59} +(6.50000 - 11.2583i) q^{61} +(6.06218 - 3.50000i) q^{67} +12.0000 q^{71} -10.0000i q^{73} +(-2.59808 + 1.50000i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-7.79423 - 4.50000i) q^{83} +6.00000 q^{89} +1.00000 q^{91} +(9.52628 + 5.50000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q + 6 q^{11} + 16 q^{19} - 6 q^{29} - 10 q^{31} + 6 q^{41} - 12 q^{49} + 6 q^{59} + 26 q^{61} + 48 q^{71} + 22 q^{79} + 24 q^{89} + 4 q^{91}+O(q^{100}) \) 4 * q + 6 * q^11 + 16 * q^19 - 6 * q^29 - 10 * q^31 + 6 * q^41 - 12 * q^49 + 6 * q^59 + 26 * q^61 + 48 * q^71 + 22 * q^79 + 24 * q^89 + 4 * q^91

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