LMFDB - Embedded newform 1275.2.d.i.424.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1275,2,Mod(424,1275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1275.424"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1275 = 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1275.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-12,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.1809262577$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 144x^{8} + 452x^{6} + 604x^{4} + 268x^{2} + 36 $ x^12 + 20x^10 + 144x^8 + 452x^6 + 604x^4 + 268*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			424.10
Root			$1.74480i$ of defining polynomial
Character	$\chi$	$=$	1275.424
Dual form			1275.2.d.i.424.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.74480i q^{2} -1.00000 q^{3} -1.04434 q^{4} -1.74480i q^{6} -4.98357 q^{7} +1.66744i q^{8} +1.00000 q^{9} +2.23877i q^{11} +1.04434 q^{12} +2.92477i q^{13} -8.69535i q^{14} -4.99803 q^{16} +(-1.15455 - 3.95816i) q^{17} +1.74480i q^{18} +1.52050 q^{19} +4.98357 q^{21} -3.90621 q^{22} +1.30964 q^{23} -1.66744i q^{24} -5.10314 q^{26} -1.00000 q^{27} +5.20454 q^{28} -1.82004i q^{29} +1.39136i q^{31} -5.38571i q^{32} -2.23877i q^{33} +(6.90621 - 2.01446i) q^{34} -1.04434 q^{36} -3.54628 q^{37} +2.65298i q^{38} -2.92477i q^{39} -8.48551i q^{41} +8.69535i q^{42} -9.13105i q^{43} -2.33803i q^{44} +2.28507i q^{46} -0.166519i q^{47} +4.99803 q^{48} +17.8360 q^{49} +(1.15455 + 3.95816i) q^{51} -3.05445i q^{52} -7.58067i q^{53} -1.74480i q^{54} -8.30981i q^{56} -1.52050 q^{57} +3.17561 q^{58} -13.7233 q^{59} -4.50092i q^{61} -2.42765 q^{62} -4.98357 q^{63} -0.599071 q^{64} +3.90621 q^{66} +1.03226i q^{67} +(1.20574 + 4.13366i) q^{68} -1.30964 q^{69} -1.78218i q^{71} +1.66744i q^{72} +11.6402 q^{73} -6.18756i q^{74} -1.58792 q^{76} -11.1570i q^{77} +5.10314 q^{78} -13.9481i q^{79} +1.00000 q^{81} +14.8055 q^{82} +4.47514i q^{83} -5.20454 q^{84} +15.9319 q^{86} +1.82004i q^{87} -3.73301 q^{88} -14.6490 q^{89} -14.5758i q^{91} -1.36771 q^{92} -1.39136i q^{93} +0.290543 q^{94} +5.38571i q^{96} -14.7821 q^{97} +31.1203i q^{98} +2.23877i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} - 16 q^{4} + 12 q^{9} + 16 q^{12} + 32 q^{16} - 6 q^{17} + 4 q^{19} + 12 q^{22} - 16 q^{23} - 36 q^{26} - 12 q^{27} - 36 q^{28} + 24 q^{34} - 16 q^{36} - 4 q^{37} - 32 q^{48} + 16 q^{49}+ \cdots - 16 q^{97}+O(q^{100}) $ 12 * q - 12 * q^3 - 16 * q^4 + 12 * q^9 + 16 * q^12 + 32 * q^16 - 6 * q^17 + 4 * q^19 + 12 * q^22 - 16 * q^23 - 36 * q^26 - 12 * q^27 - 36 * q^28 + 24 * q^34 - 16 * q^36 - 4 * q^37 - 32 * q^48 + 16 * q^49 + 6 * q^51 - 4 * q^57 + 4 * q^58 - 32 * q^59 - 56 * q^62 - 56 * q^64 - 12 * q^66 - 20 * q^68 + 16 * q^69 + 44 * q^73 + 64 * q^76 + 36 * q^78 + 12 * q^81 - 40 * q^82 + 36 * q^84 + 20 * q^86 - 8 * q^88 - 4 * q^89 - 40 * q^94 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1275\mathbb{Z}\right)^\times$.

$n$	$52$	$751$	$851$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.74480i			1.23376i	0.787056	+	0.616881i	$0.211604\pi$
$2$			1.74480i			1.23376i	−0.787056	+	0.616881i	$0.788396\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.04434			−0.522169
$5$		0			0
$5$		0			0
$6$		−	1.74480i		−	0.712313i
$7$	−4.98357			−1.88361			−0.941806	−	0.336157i	$-0.890873\pi$
$7$	−4.98357			−1.88361			−0.941806	+	0.336157i	$0.890873\pi$
$8$			1.66744i			0.589529i
$9$	1.00000			0.333333
$10$		0			0
$11$			2.23877i			0.675013i	0.941323	+	0.337507i	$0.109584\pi$
$11$			2.23877i			0.675013i	−0.941323	+	0.337507i	$0.890416\pi$
$12$	1.04434			0.301475
$13$			2.92477i			0.811184i	0.914054	+	0.405592i	$0.132935\pi$
$13$			2.92477i			0.811184i	−0.914054	+	0.405592i	$0.867065\pi$
$14$		−	8.69535i		−	2.32393i
$15$		0			0
$16$	−4.99803			−1.24951
$17$	−1.15455	−	3.95816i	−0.280020	−	0.959994i
$17$	−1.15455	−	3.95816i	−0.280020	−	0.959994i
$18$			1.74480i			0.411254i
$19$	1.52050			0.348827			0.174413	−	0.984673i	$-0.444197\pi$
$19$	1.52050			0.348827			0.174413	+	0.984673i	$0.444197\pi$
$20$		0			0
$21$	4.98357			1.08750
$22$	−3.90621			−0.832806
$23$	1.30964			0.273080			0.136540	−	0.990635i	$-0.456402\pi$
$23$	1.30964			0.273080			0.136540	+	0.990635i	$0.456402\pi$
$24$		−	1.66744i		−	0.340365i
$25$		0			0
$26$	−5.10314			−1.00081
$27$	−1.00000			−0.192450
$28$	5.20454			0.983565
$29$		−	1.82004i		−	0.337972i	−0.985618	−	0.168986i	$-0.945951\pi$
$29$		−	1.82004i		−	0.337972i	0.985618	−	0.168986i	$-0.0540493\pi$
$30$		0			0
$31$			1.39136i			0.249896i	0.992163	+	0.124948i	$0.0398764\pi$
$31$			1.39136i			0.249896i	−0.992163	+	0.124948i	$0.960124\pi$
$32$		−	5.38571i		−	0.952067i
$33$		−	2.23877i		−	0.389719i
$34$	6.90621	−	2.01446i	1.18440	−	0.345478i
$35$		0			0
$36$	−1.04434			−0.174056
$37$	−3.54628			−0.583005			−0.291503	−	0.956570i	$-0.594155\pi$
$37$	−3.54628			−0.583005			−0.291503	+	0.956570i	$0.594155\pi$
$38$			2.65298i			0.430370i
$39$		−	2.92477i		−	0.468337i
$40$		0			0
$41$		−	8.48551i		−	1.32521i	−0.748967	−	0.662607i	$-0.769450\pi$
$41$		−	8.48551i		−	1.32521i	0.748967	−	0.662607i	$-0.230550\pi$
$42$			8.69535i			1.34172i
$43$		−	9.13105i		−	1.39247i	−0.717813	−	0.696236i	$-0.754857\pi$
$43$		−	9.13105i		−	1.39247i	0.717813	−	0.696236i	$-0.245143\pi$
$44$		−	2.33803i		−	0.352471i
$45$		0			0
$46$			2.28507i			0.336915i
$47$		−	0.166519i		−	0.0242893i	−0.999926	−	0.0121446i	$-0.996134\pi$
$47$		−	0.166519i		−	0.0242893i	0.999926	−	0.0121446i	$-0.00386585\pi$
$48$	4.99803			0.721404
$49$	17.8360			2.54800
$50$		0			0
$51$	1.15455	+	3.95816i	0.161669	+	0.554253i
$52$		−	3.05445i		−	0.423576i
$53$		−	7.58067i		−	1.04129i	−0.853775	−	0.520643i	$-0.825692\pi$
$53$		−	7.58067i		−	1.04129i	0.853775	−	0.520643i	$-0.174308\pi$
$54$		−	1.74480i		−	0.237438i
$55$		0			0
$56$		−	8.30981i		−	1.11044i
$57$	−1.52050			−0.201395
$58$	3.17561			0.416978
$59$	−13.7233			−1.78662			−0.893308	−	0.449445i	$-0.851622\pi$
$59$	−13.7233			−1.78662			−0.893308	+	0.449445i	$0.851622\pi$
$60$		0			0
$61$		−	4.50092i		−	0.576284i	−0.957588	−	0.288142i	$-0.906962\pi$
$61$		−	4.50092i		−	0.576284i	0.957588	−	0.288142i	$-0.0930375\pi$
$62$	−2.42765			−0.308312
$63$	−4.98357			−0.627871
$64$	−0.599071			−0.0748839
$65$		0			0
$66$	3.90621			0.480821
$67$			1.03226i			0.126111i	0.998010	+	0.0630556i	$0.0200845\pi$
$67$			1.03226i			0.126111i	−0.998010	+	0.0630556i	$0.979915\pi$
$68$	1.20574	+	4.13366i	0.146218	+	0.501280i
$69$	−1.30964			−0.157663
$70$		0			0
$71$		−	1.78218i		−	0.211506i	−0.994392	−	0.105753i	$-0.966275\pi$
$71$		−	1.78218i		−	0.211506i	0.994392	−	0.105753i	$-0.0337253\pi$
$72$			1.66744i			0.196510i
$73$	11.6402			1.36238			0.681189	−	0.732107i	$-0.261463\pi$
$73$	11.6402			1.36238			0.681189	+	0.732107i	$0.261463\pi$
$74$		−	6.18756i		−	0.719290i
$75$		0			0
$76$	−1.58792			−0.182147
$77$		−	11.1570i		−	1.27146i
$78$	5.10314			0.577817
$79$		−	13.9481i		−	1.56928i	−0.619949	−	0.784642i	$-0.712847\pi$
$79$		−	13.9481i		−	1.56928i	0.619949	−	0.784642i	$-0.287153\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	14.8055			1.63500
$83$			4.47514i			0.491211i	0.969370	+	0.245605i	$0.0789867\pi$
$83$			4.47514i			0.491211i	−0.969370	+	0.245605i	$0.921013\pi$
$84$	−5.20454			−0.567861
$85$		0			0
$86$	15.9319			1.71798
$87$			1.82004i			0.195128i
$88$	−3.73301			−0.397940
$89$	−14.6490			−1.55280			−0.776398	−	0.630243i	$-0.782955\pi$
$89$	−14.6490			−1.55280			−0.776398	+	0.630243i	$0.782955\pi$
$90$		0			0
$91$		−	14.5758i		−	1.52796i
$92$	−1.36771			−0.142594
$93$		−	1.39136i		−	0.144278i
$94$	0.290543			0.0299672
$95$		0			0
$96$			5.38571i			0.549676i
$97$	−14.7821			−1.50089			−0.750445	−	0.660932i	$-0.770161\pi$
$97$	−14.7821			−1.50089			−0.750445	+	0.660932i	$0.770161\pi$
$98$			31.1203i			3.14362i
$99$			2.23877i			0.225004i
$100$		0			0
$101$	−9.91167			−0.986248			−0.493124	−	0.869959i	$-0.664145\pi$
$101$	−9.91167			−0.986248			−0.493124	+	0.869959i	$0.664145\pi$
$102$	−6.90621	+	2.01446i	−0.683816	+	0.199462i
$103$			11.0014i			1.08400i	0.840379	+	0.541999i	$0.182332\pi$
$103$			11.0014i			1.08400i	−0.840379	+	0.541999i	$0.817668\pi$
$104$	−4.87687			−0.478217
$105$		0			0
$106$	13.2268			1.28470
$107$	3.68292			0.356041			0.178021	−	0.984027i	$-0.443031\pi$
$107$	3.68292			0.356041			0.178021	+	0.984027i	$0.443031\pi$
$108$	1.04434			0.100492
$109$			17.1471i			1.64239i	0.570644	+	0.821197i	$0.306693\pi$
$109$			17.1471i			1.64239i	−0.570644	+	0.821197i	$0.693307\pi$
$110$		0			0
$111$	3.54628			0.336598
$112$	24.9081			2.35359
$113$	16.1338			1.51774			0.758868	−	0.651245i	$-0.225753\pi$
$113$	16.1338			1.51774			0.758868	+	0.651245i	$0.225753\pi$
$114$		−	2.65298i		−	0.248474i
$115$		0			0
$116$			1.90074i			0.176479i
$117$			2.92477i			0.270395i
$118$		−	23.9444i		−	2.20426i
$119$	5.75379	+	19.7258i	0.527449	+	1.80826i
$120$		0			0
$121$	5.98793			0.544357
$122$	7.85322			0.710997
$123$			8.48551i			0.765113i
$124$		−	1.45305i		−	0.130488i
$125$		0			0
$126$		−	8.69535i		−	0.774643i
$127$			11.6766i			1.03613i	0.855341	+	0.518065i	$0.173348\pi$
$127$			11.6766i			1.03613i	−0.855341	+	0.518065i	$0.826652\pi$
$128$		−	11.8167i		−	1.04446i
$129$			9.13105i			0.803944i
$130$		0			0
$131$			8.14138i			0.711315i	0.934616	+	0.355658i	$0.115743\pi$
$131$			8.14138i			0.711315i	−0.934616	+	0.355658i	$0.884257\pi$
$132$			2.33803i			0.203499i
$133$	−7.57753			−0.657055
$134$	−1.80110			−0.155591
$135$		0			0
$136$	6.59999	−	1.92515i	0.565945	−	0.165080i
$137$		−	3.47912i		−	0.297241i	−0.988894	−	0.148621i	$-0.952517\pi$
$137$		−	3.47912i		−	0.297241i	0.988894	−	0.148621i	$-0.0474833\pi$
$138$		−	2.28507i		−	0.194518i
$139$			9.56541i			0.811328i	0.914022	+	0.405664i	$0.132960\pi$
$139$			9.56541i			0.811328i	−0.914022	+	0.405664i	$0.867040\pi$
$140$		0			0
$141$			0.166519i			0.0140234i
$142$	3.10956			0.260948
$143$	−6.54787			−0.547560
$144$	−4.99803			−0.416503
$145$		0			0
$146$			20.3098i			1.68085i
$147$	−17.8360			−1.47109
$148$	3.70352			0.304427
$149$	14.6107			1.19696			0.598478	−	0.801139i	$-0.295772\pi$
$149$	14.6107			1.19696			0.598478	+	0.801139i	$0.295772\pi$
$150$		0			0
$151$	−13.6611			−1.11172			−0.555860	−	0.831276i	$-0.687611\pi$
$151$	−13.6611			−1.11172			−0.555860	+	0.831276i	$0.687611\pi$
$152$			2.53535i			0.205644i
$153$	−1.15455	−	3.95816i	−0.0933399	−	0.319998i
$154$	19.4669			1.56868
$155$		0			0
$156$			3.05445i			0.244552i
$157$		−	21.1926i		−	1.69135i	−0.533698	−	0.845675i	$-0.679198\pi$
$157$		−	21.1926i		−	1.69135i	0.533698	−	0.845675i	$-0.320802\pi$
$158$	24.3367			1.93612
$159$			7.58067i			0.601187i
$160$		0			0
$161$	−6.52670			−0.514376
$162$			1.74480i			0.137085i
$163$	4.86075			0.380724			0.190362	−	0.981714i	$-0.439034\pi$
$163$	4.86075			0.380724			0.190362	+	0.981714i	$0.439034\pi$
$164$			8.86175i			0.691986i
$165$		0			0
$166$	−7.80824			−0.606037
$167$	−21.1447			−1.63622			−0.818111	−	0.575060i	$-0.804979\pi$
$167$	−21.1447			−1.63622			−0.818111	+	0.575060i	$0.804979\pi$
$168$			8.30981i			0.641116i
$169$	4.44574			0.341980
$170$		0			0
$171$	1.52050			0.116276
$172$			9.53591i			0.727106i
$173$	−14.8666			−1.13029			−0.565143	−	0.824993i	$-0.691179\pi$
$173$	−14.8666			−1.13029			−0.565143	+	0.824993i	$0.691179\pi$
$174$	−3.17561			−0.240742
$175$		0			0
$176$		−	11.1894i		−	0.843435i
$177$	13.7233			1.03150
$178$		−	25.5597i		−	1.91578i
$179$	−24.1387			−1.80421			−0.902104	−	0.431519i	$-0.857978\pi$
$179$	−24.1387			−1.80421			−0.902104	+	0.431519i	$0.857978\pi$
$180$		0			0
$181$		−	20.1402i		−	1.49701i	−0.663128	−	0.748506i	$-0.730771\pi$
$181$		−	20.1402i		−	1.49701i	0.663128	−	0.748506i	$-0.269229\pi$
$182$	25.4319			1.88514
$183$			4.50092i			0.332718i
$184$			2.18375i			0.160988i
$185$		0			0
$186$	2.42765			0.178004
$187$	8.86139	−	2.58477i	0.648009	−	0.189017i
$188$			0.173902i			0.0126831i
$189$	4.98357			0.362501
$190$		0			0
$191$	−16.0837			−1.16377			−0.581886	−	0.813270i	$-0.697685\pi$
$191$	−16.0837			−1.16377			−0.581886	+	0.813270i	$0.697685\pi$
$192$	0.599071			0.0432342
$193$	17.6995			1.27404			0.637018	−	0.770849i	$-0.280168\pi$
$193$	17.6995			1.27404			0.637018	+	0.770849i	$0.280168\pi$
$194$		−	25.7918i		−	1.85174i
$195$		0			0
$196$	−18.6268			−1.33049
$197$	3.66995			0.261473			0.130737	−	0.991417i	$-0.458266\pi$
$197$	3.66995			0.261473			0.130737	+	0.991417i	$0.458266\pi$
$198$	−3.90621			−0.277602
$199$			18.6289i			1.32057i	0.751015	+	0.660286i	$0.229565\pi$
$199$			18.6289i			1.32057i	−0.751015	+	0.660286i	$0.770435\pi$
$200$		0			0
$201$		−	1.03226i		−	0.0728103i
$202$		−	17.2939i		−	1.21680i
$203$			9.07028i			0.636609i
$204$	−1.20574	−	4.13366i	−0.0844189	−	0.289414i
$205$		0			0
$206$	−19.1952			−1.33739
$207$	1.30964			0.0910265
$208$		−	14.6181i		−	1.01358i
$209$			3.40405i			0.235463i
$210$		0			0
$211$			5.66739i			0.390159i	0.980787	+	0.195079i	$0.0624965\pi$
$211$			5.66739i			0.390159i	−0.980787	+	0.195079i	$0.937504\pi$
$212$			7.91679i			0.543728i
$213$			1.78218i			0.122113i
$214$			6.42597i			0.439270i
$215$		0			0
$216$		−	1.66744i		−	0.113455i
$217$		−	6.93395i		−	0.470707i
$218$	−29.9183			−2.02632
$219$	−11.6402			−0.786570
$220$		0			0
$221$	11.5767	−	3.37679i	0.778732	−	0.227148i
$222$			6.18756i			0.415282i
$223$			3.65155i			0.244526i	0.992498	+	0.122263i	$0.0390151\pi$
$223$			3.65155i			0.244526i	−0.992498	+	0.122263i	$0.960985\pi$
$224$			26.8400i			1.79333i
$225$		0			0
$226$			28.1502i			1.87253i
$227$	−13.7100			−0.909967			−0.454983	−	0.890500i	$-0.650355\pi$
$227$	−13.7100			−0.909967			−0.454983	+	0.890500i	$0.650355\pi$
$228$	1.58792			0.105163
$229$	8.65352			0.571841			0.285920	−	0.958253i	$-0.407701\pi$
$229$	8.65352			0.571841			0.285920	+	0.958253i	$0.407701\pi$
$230$		0			0
$231$			11.1570i			0.734080i
$232$	3.03480			0.199245
$233$	−22.0694			−1.44581			−0.722906	−	0.690947i	$-0.757194\pi$
$233$	−22.0694			−1.44581			−0.722906	+	0.690947i	$0.757194\pi$
$234$	−5.10314			−0.333603
$235$		0			0
$236$	14.3317			0.932916
$237$			13.9481i			0.906027i
$238$	−34.4176	+	10.0392i	−2.23096	+	0.650746i
$239$	−7.58610			−0.490704			−0.245352	−	0.969434i	$-0.578904\pi$
$239$	−7.58610			−0.490704			−0.245352	+	0.969434i	$0.578904\pi$
$240$		0			0
$241$			19.9526i			1.28526i	0.766178	+	0.642628i	$0.222156\pi$
$241$			19.9526i			1.28526i	−0.766178	+	0.642628i	$0.777844\pi$
$242$			10.4478i			0.671607i
$243$	−1.00000			−0.0641500
$244$			4.70049i			0.300918i
$245$		0			0
$246$	−14.8055			−0.943967
$247$			4.44711i			0.282963i
$248$	−2.32001			−0.147321
$249$		−	4.47514i		−	0.283601i
$250$		0			0
$251$	10.6807			0.674162			0.337081	−	0.941476i	$-0.390560\pi$
$251$	10.6807			0.674162			0.337081	+	0.941476i	$0.390560\pi$
$252$	5.20454			0.327855
$253$			2.93199i			0.184332i
$254$	−20.3734			−1.27834
$255$		0			0
$256$	19.4196			1.21373
$257$			5.59173i			0.348803i	0.984675	+	0.174401i	$0.0557990\pi$
$257$			5.59173i			0.348803i	−0.984675	+	0.174401i	$0.944201\pi$
$258$	−15.9319			−0.991876
$259$	17.6731			1.09816
$260$		0			0
$261$		−	1.82004i		−	0.112657i
$262$	−14.2051			−0.877594
$263$		−	13.8769i		−	0.855686i	−0.903853	−	0.427843i	$-0.859274\pi$
$263$		−	13.8769i		−	0.855686i	0.903853	−	0.427843i	$-0.140726\pi$
$264$	3.73301			0.229751
$265$		0			0
$266$		−	13.2213i		−	0.810649i
$267$	14.6490			0.896507
$268$		−	1.07803i		−	0.0658514i
$269$		−	30.2465i		−	1.84416i	−0.386997	−	0.922081i	$-0.626488\pi$
$269$		−	30.2465i		−	1.84416i	0.386997	−	0.922081i	$-0.373512\pi$
$270$		0			0
$271$	−17.6456			−1.07190			−0.535948	−	0.844251i	$-0.680046\pi$
$271$	−17.6456			−1.07190			−0.535948	+	0.844251i	$0.680046\pi$
$272$	5.77048	+	19.7830i	0.349887	+	1.19952i
$273$			14.5758i			0.882166i
$274$	6.07038			0.366725
$275$		0			0
$276$	1.36771			0.0823266
$277$	−16.5619			−0.995111			−0.497556	−	0.867432i	$-0.665769\pi$
$277$	−16.5619			−0.995111			−0.497556	+	0.867432i	$0.665769\pi$
$278$	−16.6898			−1.00099
$279$			1.39136i			0.0832987i
$280$		0			0
$281$	8.40360			0.501317			0.250658	−	0.968076i	$-0.419353\pi$
$281$	8.40360			0.501317			0.250658	+	0.968076i	$0.419353\pi$
$282$	−0.290543			−0.0173016
$283$	−16.2345			−0.965038			−0.482519	−	0.875885i	$-0.660278\pi$
$283$	−16.2345			−0.965038			−0.482519	+	0.875885i	$0.660278\pi$
$284$			1.86120i			0.110442i
$285$		0			0
$286$		−	11.4247i		−	0.675559i
$287$			42.2881i			2.49619i
$288$		−	5.38571i		−	0.317356i
$289$	−14.3340	+	9.13979i	−0.843178	+	0.537635i
$290$		0			0
$291$	14.7821			0.866540
$292$	−12.1563			−0.711393
$293$		−	21.3036i		−	1.24457i	−0.782791	−	0.622284i	$-0.786205\pi$
$293$		−	21.3036i		−	1.24457i	0.782791	−	0.622284i	$-0.213795\pi$
$294$		−	31.1203i		−	1.81497i
$295$		0			0
$296$		−	5.91321i		−	0.343699i
$297$		−	2.23877i		−	0.129906i
$298$			25.4928i			1.47676i
$299$			3.83040i			0.221518i
$300$		0			0
$301$			45.5052i			2.62288i
$302$		−	23.8358i		−	1.37160i
$303$	9.91167			0.569411
$304$	−7.59952			−0.435862
$305$		0			0
$306$	6.90621	−	2.01446i	0.394802	−	0.115159i
$307$		−	23.9979i		−	1.36963i	−0.728715	−	0.684817i	$-0.759882\pi$
$307$		−	23.9979i		−	1.36963i	0.728715	−	0.684817i	$-0.240118\pi$
$308$			11.6517i			0.663919i
$309$		−	11.0014i		−	0.625846i
$310$		0			0
$311$			1.60781i			0.0911708i	0.998960	+	0.0455854i	$0.0145153\pi$
$311$			1.60781i			0.0911708i	−0.998960	+	0.0455854i	$0.985485\pi$
$312$	4.87687			0.276099
$313$	10.5247			0.594893			0.297447	−	0.954738i	$-0.403865\pi$
$313$	10.5247			0.594893			0.297447	+	0.954738i	$0.403865\pi$
$314$	36.9768			2.08672
$315$		0			0
$316$			14.5665i			0.819432i
$317$	−21.3111			−1.19695			−0.598475	−	0.801142i	$-0.704226\pi$
$317$	−21.3111			−1.19695			−0.598475	+	0.801142i	$0.704226\pi$
$318$	−13.2268			−0.741721
$319$	4.07464			0.228136
$320$		0			0
$321$	−3.68292			−0.205560
$322$		−	11.3878i		−	0.634618i
$323$	−1.75550	−	6.01838i	−0.0976784	−	0.334872i
$324$	−1.04434			−0.0580188
$325$		0			0
$326$			8.48106i			0.469722i
$327$		−	17.1471i		−	0.948237i
$328$	14.1491			0.781253
$329$			0.829858i			0.0457515i
$330$		0			0
$331$	−0.393709			−0.0216402			−0.0108201	−	0.999941i	$-0.503444\pi$
$331$	−0.393709			−0.0216402			−0.0108201	+	0.999941i	$0.503444\pi$
$332$		−	4.67357i		−	0.256495i
$333$	−3.54628			−0.194335
$334$		−	36.8933i		−	2.01871i
$335$		0			0
$336$	−24.9081			−1.35885
$337$	3.90176			0.212542			0.106271	−	0.994337i	$-0.466109\pi$
$337$	3.90176			0.212542			0.106271	+	0.994337i	$0.466109\pi$
$338$			7.75695i			0.421922i
$339$	−16.1338			−0.876265
$340$		0			0
$341$	−3.11494			−0.168683
$342$			2.65298i			0.143457i
$343$	−54.0018			−2.91582
$344$	15.2255			0.820903
$345$		0			0
$346$		−	25.9393i		−	1.39451i
$347$	−3.96587			−0.212899			−0.106449	−	0.994318i	$-0.533948\pi$
$347$	−3.96587			−0.212899			−0.106449	+	0.994318i	$0.533948\pi$
$348$		−	1.90074i		−	0.101890i
$349$	−32.5572			−1.74275			−0.871374	−	0.490620i	$-0.836770\pi$
$349$	−32.5572			−1.74275			−0.871374	+	0.490620i	$0.836770\pi$
$350$		0			0
$351$		−	2.92477i		−	0.156112i
$352$	12.0573			0.642658
$353$		−	18.6270i		−	0.991416i	−0.868489	−	0.495708i	$-0.834909\pi$
$353$		−	18.6270i		−	0.991416i	0.868489	−	0.495708i	$-0.165091\pi$
$354$			23.9444i			1.27263i
$355$		0			0
$356$	15.2986			0.810822
$357$	−5.75379	−	19.7258i	−0.304523	−	1.04400i
$358$		−	42.1172i		−	2.22596i
$359$	16.2989			0.860221			0.430111	−	0.902776i	$-0.358475\pi$
$359$	16.2989			0.860221			0.430111	+	0.902776i	$0.358475\pi$
$360$		0			0
$361$	−16.6881			−0.878320
$362$	35.1408			1.84696
$363$	−5.98793			−0.314285
$364$			15.2221i			0.797852i
$365$		0			0
$366$	−7.85322			−0.410495
$367$	25.8123			1.34739			0.673696	−	0.739009i	$-0.264706\pi$
$367$	25.8123			1.34739			0.673696	+	0.739009i	$0.264706\pi$
$368$	−6.54564			−0.341215
$369$		−	8.48551i		−	0.441738i
$370$		0			0
$371$			37.7788i			1.96138i
$372$			1.45305i			0.0753373i
$373$			2.29788i			0.118980i	0.998229	+	0.0594900i	$0.0189474\pi$
$373$			2.29788i			0.118980i	−0.998229	+	0.0594900i	$0.981053\pi$
$374$	4.50991	+	15.4614i	0.233202	+	0.799489i
$375$		0			0
$376$	0.277660			0.0143192
$377$	5.32318			0.274158
$378$			8.69535i			0.447241i
$379$		−	25.0126i		−	1.28481i	−0.766365	−	0.642405i	$-0.777937\pi$
$379$		−	25.0126i		−	1.28481i	0.766365	−	0.642405i	$-0.222063\pi$
$380$		0			0
$381$		−	11.6766i		−	0.598210i
$382$		−	28.0628i		−	1.43582i
$383$		−	8.85151i		−	0.452291i	−0.974094	−	0.226145i	$-0.927388\pi$
$383$		−	8.85151i		−	0.452291i	0.974094	−	0.226145i	$-0.0726124\pi$
$384$			11.8167i			0.603017i
$385$		0			0
$386$			30.8821i			1.57186i
$387$		−	9.13105i		−	0.464157i
$388$	15.4375			0.783719
$389$	−8.05651			−0.408481			−0.204241	−	0.978921i	$-0.565472\pi$
$389$	−8.05651			−0.408481			−0.204241	+	0.978921i	$0.565472\pi$
$390$		0			0
$391$	−1.51205	−	5.18378i	−0.0764677	−	0.262155i
$392$			29.7404i			1.50212i
$393$		−	8.14138i		−	0.410678i
$394$			6.40334i			0.322596i
$395$		0			0
$396$		−	2.33803i		−	0.117490i
$397$	−30.6558			−1.53857			−0.769286	−	0.638904i	$-0.779388\pi$
$397$	−30.6558			−1.53857			−0.769286	+	0.638904i	$0.779388\pi$
$398$	−32.5039			−1.62927
$399$	7.57753			0.379351
$400$		0			0
$401$			23.1614i			1.15663i	0.815815	+	0.578313i	$0.196289\pi$
$401$			23.1614i			1.15663i	−0.815815	+	0.578313i	$0.803711\pi$
$402$	1.80110			0.0898306
$403$	−4.06941			−0.202712
$404$	10.3511			0.514989
$405$		0			0
$406$	−15.8259			−0.785424
$407$		−	7.93929i		−	0.393536i
$408$	−6.59999	+	1.92515i	−0.326748	+	0.0953089i
$409$	10.9627			0.542072			0.271036	−	0.962569i	$-0.412634\pi$
$409$	10.9627			0.542072			0.271036	+	0.962569i	$0.412634\pi$
$410$		0			0
$411$			3.47912i			0.171612i
$412$		−	11.4892i		−	0.566030i
$413$	68.3908			3.36529
$414$			2.28507i			0.112305i
$415$		0			0
$416$	15.7519			0.772302
$417$		−	9.56541i		−	0.468420i
$418$	−5.93939			−0.290505
$419$		−	14.7089i		−	0.718576i	−0.933227	−	0.359288i	$-0.883020\pi$
$419$		−	14.7089i		−	0.718576i	0.933227	−	0.359288i	$-0.116980\pi$
$420$		0			0
$421$	1.85001			0.0901638			0.0450819	−	0.998983i	$-0.485645\pi$
$421$	1.85001			0.0901638			0.0450819	+	0.998983i	$0.485645\pi$
$422$	−9.88848			−0.481363
$423$		−	0.166519i		−	0.00809642i
$424$	12.6403			0.613868
$425$		0			0
$426$	−3.10956			−0.150659
$427$			22.4307i			1.08550i
$428$	−3.84622			−0.185914
$429$	6.54787			0.316134
$430$		0			0
$431$		−	7.41116i		−	0.356983i	−0.983941	−	0.178491i	$-0.942878\pi$
$431$		−	7.41116i		−	0.356983i	0.983941	−	0.178491i	$-0.0571217\pi$
$432$	4.99803			0.240468
$433$			5.01269i			0.240894i	0.992720	+	0.120447i	$0.0384328\pi$
$433$			5.01269i			0.240894i	−0.992720	+	0.120447i	$0.961567\pi$
$434$	12.0984			0.580741
$435$		0			0
$436$		−	17.9074i		−	0.857608i
$437$	1.99132			0.0952575
$438$		−	20.3098i		−	0.970440i
$439$			21.2169i			1.01263i	0.862349	+	0.506315i	$0.168993\pi$
$439$			21.2169i			1.01263i	−0.862349	+	0.506315i	$0.831007\pi$
$440$		0			0
$441$	17.8360			0.849332
$442$	5.89184	+	20.1990i	0.280246	+	0.960770i
$443$		−	22.8512i		−	1.08569i	−0.839832	−	0.542846i	$-0.817347\pi$
$443$		−	22.8512i		−	1.08569i	0.839832	−	0.542846i	$-0.182653\pi$
$444$	−3.70352			−0.175761
$445$		0			0
$446$	−6.37124			−0.301687
$447$	−14.6107			−0.691063
$448$	2.98551			0.141052
$449$		−	20.1999i		−	0.953294i	−0.879095	−	0.476647i	$-0.841852\pi$
$449$		−	20.1999i		−	0.953294i	0.879095	−	0.476647i	$-0.158148\pi$
$450$		0			0
$451$	18.9971			0.894537
$452$	−16.8491			−0.792515
$453$	13.6611			0.641852
$454$		−	23.9213i		−	1.12268i
$455$		0			0
$456$		−	2.53535i		−	0.118728i
$457$			27.4808i			1.28550i	0.766077	+	0.642749i	$0.222206\pi$
$457$			27.4808i			1.28550i	−0.766077	+	0.642749i	$0.777794\pi$
$458$			15.0987i			0.705515i
$459$	1.15455	+	3.95816i	0.0538898	+	0.184751i
$460$		0			0
$461$	27.5990			1.28541			0.642706	−	0.766113i	$-0.277812\pi$
$461$	27.5990			1.28541			0.642706	+	0.766113i	$0.277812\pi$
$462$	−19.4669			−0.905680
$463$			20.5387i			0.954516i	0.878763	+	0.477258i	$0.158369\pi$
$463$			20.5387i			0.954516i	−0.878763	+	0.477258i	$0.841631\pi$
$464$			9.09661i			0.422299i
$465$		0			0
$466$		−	38.5067i		−	1.78379i
$467$		−	12.6544i		−	0.585576i	−0.956177	−	0.292788i	$-0.905417\pi$
$467$		−	12.6544i		−	0.585576i	0.956177	−	0.292788i	$-0.0945831\pi$
$468$		−	3.05445i		−	0.141192i
$469$		−	5.14436i		−	0.237545i
$470$		0			0
$471$			21.1926i			0.976501i
$472$		−	22.8827i		−	1.05326i
$473$	20.4423			0.939937
$474$	−24.3367			−1.11782
$475$		0			0
$476$	−6.00890	−	20.6004i	−0.275418	−	0.944217i
$477$		−	7.58067i		−	0.347095i
$478$		−	13.2363i		−	0.605412i
$479$			25.6921i			1.17390i	0.809622	+	0.586952i	$0.199672\pi$
$479$			25.6921i			1.17390i	−0.809622	+	0.586952i	$0.800328\pi$
$480$		0			0
$481$		−	10.3720i		−	0.472924i
$482$	−34.8133			−1.58570
$483$	6.52670			0.296975
$484$	−6.25342			−0.284247
$485$		0			0
$486$		−	1.74480i		−	0.0791459i
$487$	7.98736			0.361942			0.180971	−	0.983488i	$-0.442076\pi$
$487$	7.98736			0.361942			0.180971	+	0.983488i	$0.442076\pi$
$488$	7.50502			0.339736
$489$	−4.86075			−0.219811
$490$		0			0
$491$	23.4535			1.05844			0.529221	−	0.848484i	$-0.322484\pi$
$491$	23.4535			1.05844			0.529221	+	0.848484i	$0.322484\pi$
$492$		−	8.86175i		−	0.399519i
$493$	−7.20399	+	2.10133i	−0.324452	+	0.0946389i
$494$	−7.75934			−0.349109
$495$		0			0
$496$		−	6.95408i		−	0.312247i
$497$			8.88163i			0.398396i
$498$	7.80824			0.349896
$499$			2.55509i			0.114381i	0.998363	+	0.0571907i	$0.0182143\pi$
$499$			2.55509i			0.114381i	−0.998363	+	0.0571907i	$0.981786\pi$
$500$		0			0
$501$	21.1447			0.944674
$502$			18.6358i			0.831756i
$503$	−22.5894			−1.00721			−0.503605	−	0.863934i	$-0.667993\pi$
$503$	−22.5894			−1.00721			−0.503605	+	0.863934i	$0.667993\pi$
$504$		−	8.30981i		−	0.370148i
$505$		0			0
$506$	−5.11574			−0.227422
$507$	−4.44574			−0.197442
$508$		−	12.1943i		−	0.541036i
$509$	−12.4294			−0.550921			−0.275461	−	0.961312i	$-0.588830\pi$
$509$	−12.4294			−0.550921			−0.275461	+	0.961312i	$0.588830\pi$
$510$		0			0
$511$	−58.0096			−2.56619
$512$			10.2501i			0.452994i
$513$	−1.52050			−0.0671318
$514$	−9.75647			−0.430340
$515$		0			0
$516$		−	9.53591i		−	0.419795i
$517$	0.372797			0.0163956
$518$			30.8362i			1.35486i
$519$	14.8666			0.652571
$520$		0			0
$521$		−	15.6804i		−	0.686969i	−0.939158	−	0.343485i	$-0.888393\pi$
$521$		−	15.6804i		−	0.686969i	0.939158	−	0.343485i	$-0.111607\pi$
$522$	3.17561			0.138993
$523$		−	9.60165i		−	0.419851i	−0.977717	−	0.209925i	$-0.932678\pi$
$523$		−	9.60165i		−	0.419851i	0.977717	−	0.209925i	$-0.0673221\pi$
$524$		−	8.50236i		−	0.371427i
$525$		0			0
$526$	24.2125			1.05571
$527$	5.50723	−	1.60640i	0.239899	−	0.0699758i
$528$			11.1894i			0.486957i
$529$	−21.2848			−0.925428
$530$		0			0
$531$	−13.7233			−0.595539
$532$	7.91350			0.343094
$533$	24.8181			1.07499
$534$			25.5597i			1.10608i
$535$		0			0
$536$	−1.72124			−0.0743462
$537$	24.1387			1.04166
$538$	52.7742			2.27526
$539$			39.9306i			1.71993i
$540$		0			0
$541$			32.9544i			1.41682i	0.705801	+	0.708410i	$0.250587\pi$
$541$			32.9544i			1.41682i	−0.705801	+	0.708410i	$0.749413\pi$
$542$		−	30.7882i		−	1.32247i
$543$			20.1402i			0.864300i
$544$	−21.3175	+	6.21807i	−0.913979	+	0.266598i
$545$		0			0
$546$	−25.4319			−1.08838
$547$	18.9841			0.811701			0.405850	−	0.913940i	$-0.366975\pi$
$547$	18.9841			0.811701			0.405850	+	0.913940i	$0.366975\pi$
$548$			3.63338i			0.155210i
$549$		−	4.50092i		−	0.192095i
$550$		0			0
$551$		−	2.76737i		−	0.117894i
$552$		−	2.18375i		−	0.0929467i
$553$			69.5113i			2.95592i
$554$		−	28.8973i		−	1.22773i
$555$		0			0
$556$		−	9.98953i		−	0.423651i
$557$			44.5929i			1.88946i	0.327847	+	0.944731i	$0.393677\pi$
$557$			44.5929i			1.88946i	−0.327847	+	0.944731i	$0.606323\pi$
$558$	−2.42765			−0.102771
$559$	26.7062			1.12955
$560$		0			0
$561$	−8.86139	+	2.58477i	−0.374128	+	0.109129i
$562$			14.6626i			0.618506i
$563$			4.26474i			0.179737i	0.995954	+	0.0898686i	$0.0286447\pi$
$563$			4.26474i			0.179737i	−0.995954	+	0.0898686i	$0.971355\pi$
$564$		−	0.173902i		−	0.00732260i
$565$		0			0
$566$		−	28.3259i		−	1.19063i
$567$	−4.98357			−0.209290
$568$	2.97168			0.124689
$569$	−5.81934			−0.243959			−0.121980	−	0.992533i	$-0.538924\pi$
$569$	−5.81934			−0.243959			−0.121980	+	0.992533i	$0.538924\pi$
$570$		0			0
$571$			10.0595i			0.420976i	0.977596	+	0.210488i	$0.0675053\pi$
$571$			10.0595i			0.420976i	−0.977596	+	0.210488i	$0.932495\pi$
$572$	6.83819			0.285919
$573$	16.0837			0.671905
$574$	−73.7845			−3.07971
$575$		0			0
$576$	−0.599071			−0.0249613
$577$		−	15.7300i		−	0.654847i	−0.944878	−	0.327423i	$-0.893820\pi$
$577$		−	15.7300i		−	0.654847i	0.944878	−	0.327423i	$-0.106180\pi$
$578$	−15.9471	−	25.0101i	−0.663313	−	1.04028i
$579$	−17.6995			−0.735566
$580$		0			0
$581$		−	22.3022i		−	0.925250i
$582$			25.7918i			1.06910i
$583$	16.9714			0.702882
$584$			19.4093i			0.803162i
$585$		0			0
$586$	37.1706			1.53550
$587$		−	30.6657i		−	1.26571i	−0.774271	−	0.632854i	$-0.781883\pi$
$587$		−	30.6657i		−	1.26571i	0.774271	−	0.632854i	$-0.218117\pi$
$588$	18.6268			0.768156
$589$			2.11557i			0.0871705i
$590$		0			0
$591$	−3.66995			−0.150962
$592$	17.7244			0.728470
$593$			9.22665i			0.378893i	0.981891	+	0.189447i	$0.0606694\pi$
$593$			9.22665i			0.378893i	−0.981891	+	0.189447i	$0.939331\pi$
$594$	3.90621			0.160274
$595$		0			0
$596$	−15.2585			−0.625014
$597$		−	18.6289i		−	0.762432i
$598$	−6.68330			−0.273300
$599$	−12.2310			−0.499745			−0.249873	−	0.968279i	$-0.580389\pi$
$599$	−12.2310			−0.499745			−0.249873	+	0.968279i	$0.580389\pi$
$600$		0			0
$601$		−	36.4552i		−	1.48704i	−0.668715	−	0.743519i	$-0.733155\pi$
$601$		−	36.4552i		−	1.48704i	0.668715	−	0.743519i	$-0.266845\pi$
$602$	−79.3977			−3.23601
$603$			1.03226i			0.0420371i
$604$	14.2668			0.580507
$605$		0			0
$606$			17.2939i			0.702517i
$607$	35.4434			1.43860			0.719302	−	0.694697i	$-0.244462\pi$
$607$	35.4434			1.43860			0.719302	+	0.694697i	$0.244462\pi$
$608$		−	8.18897i		−	0.332107i
$609$		−	9.07028i		−	0.367546i
$610$		0			0
$611$	0.487029			0.0197031
$612$	1.20574	+	4.13366i	0.0487393	+	0.167093i
$613$			31.2013i			1.26021i	0.776511	+	0.630104i	$0.216988\pi$
$613$			31.2013i			1.26021i	−0.776511	+	0.630104i	$0.783012\pi$
$614$	41.8716			1.68980
$615$		0			0
$616$	18.6037			0.749565
$617$	19.2867			0.776452			0.388226	−	0.921564i	$-0.373088\pi$
$617$	19.2867			0.776452			0.388226	+	0.921564i	$0.373088\pi$
$618$	19.1952			0.772145
$619$			5.51660i			0.221731i	0.993835	+	0.110865i	$0.0353622\pi$
$619$			5.51660i			0.221731i	−0.993835	+	0.110865i	$0.964638\pi$
$620$		0			0
$621$	−1.30964			−0.0525542
$622$	−2.80532			−0.112483
$623$	73.0045			2.92486
$624$			14.6181i			0.585192i
$625$		0			0
$626$			18.3636i			0.733957i
$627$		−	3.40405i		−	0.135945i
$628$			22.1322i			0.883171i
$629$	4.09436	+	14.0367i	0.163253	+	0.559681i
$630$		0			0
$631$	−2.66900			−0.106251			−0.0531257	−	0.998588i	$-0.516918\pi$
$631$	−2.66900			−0.106251			−0.0531257	+	0.998588i	$0.516918\pi$
$632$	23.2576			0.925139
$633$		−	5.66739i		−	0.225258i
$634$		−	37.1837i		−	1.47675i
$635$		0			0
$636$		−	7.91679i		−	0.313921i
$637$			52.1660i			2.06689i
$638$			7.10944i			0.281465i
$639$		−	1.78218i		−	0.0705021i
$640$		0			0
$641$		−	22.4010i		−	0.884787i	−0.896821	−	0.442393i	$-0.854129\pi$
$641$		−	22.4010i		−	0.884787i	0.896821	−	0.442393i	$-0.145871\pi$
$642$		−	6.42597i		−	0.253613i
$643$	−9.24620			−0.364635			−0.182317	−	0.983240i	$-0.558360\pi$
$643$	−9.24620			−0.364635			−0.182317	+	0.983240i	$0.558360\pi$
$644$	6.81609			0.268592
$645$		0			0
$646$	10.5009	−	3.06300i	0.413152	−	0.120512i
$647$			34.6465i			1.36209i	0.732239	+	0.681047i	$0.238475\pi$
$647$			34.6465i			1.36209i	−0.732239	+	0.681047i	$0.761525\pi$
$648$			1.66744i			0.0655033i
$649$		−	30.7232i		−	1.20599i
$650$		0			0
$651$			6.93395i			0.271763i
$652$	−5.07627			−0.198802
$653$	−0.981384			−0.0384045			−0.0192023	−	0.999816i	$-0.506113\pi$
$653$	−0.981384			−0.0384045			−0.0192023	+	0.999816i	$0.506113\pi$
$654$	29.9183			1.16990
$655$		0			0
$656$			42.4109i			1.65587i
$657$	11.6402			0.454126
$658$	−1.44794			−0.0564465
$659$	18.3247			0.713828			0.356914	−	0.934137i	$-0.383829\pi$
$659$	18.3247			0.713828			0.356914	+	0.934137i	$0.383829\pi$
$660$		0			0
$661$	−22.4177			−0.871946			−0.435973	−	0.899960i	$-0.643596\pi$
$661$	−22.4177			−0.871946			−0.435973	+	0.899960i	$0.643596\pi$
$662$		−	0.686944i		−	0.0266989i
$663$	−11.5767	+	3.37679i	−0.449601	+	0.131144i
$664$	−7.46203			−0.289583
$665$		0			0
$666$		−	6.18756i		−	0.239763i
$667$		−	2.38360i		−	0.0922934i
$668$	22.0822			0.854386
$669$		−	3.65155i		−	0.141177i
$670$		0			0
$671$	10.0765			0.388999
$672$		−	26.8400i		−	1.03538i
$673$	50.8202			1.95898			0.979488	−	0.201504i	$-0.0645828\pi$
$673$	50.8202			1.95898			0.979488	+	0.201504i	$0.0645828\pi$
$674$			6.80780i			0.262227i
$675$		0			0
$676$	−4.64286			−0.178572
$677$	5.48996			0.210996			0.105498	−	0.994419i	$-0.466356\pi$
$677$	5.48996			0.210996			0.105498	+	0.994419i	$0.466356\pi$
$678$		−	28.1502i		−	1.08110i
$679$	73.6674			2.82710
$680$		0			0
$681$	13.7100			0.525370
$682$		−	5.43495i		−	0.208115i
$683$	−23.8590			−0.912940			−0.456470	−	0.889739i	$-0.650886\pi$
$683$	−23.8590			−0.912940			−0.456470	+	0.889739i	$0.650886\pi$
$684$	−1.58792			−0.0607156
$685$		0			0
$686$		−	94.2225i		−	3.59743i
$687$	−8.65352			−0.330152
$688$			45.6373i			1.73991i
$689$	22.1717			0.844675
$690$		0			0
$691$			11.9837i			0.455882i	0.973675	+	0.227941i	$0.0731993\pi$
$691$			11.9837i			0.455882i	−0.973675	+	0.227941i	$0.926801\pi$
$692$	15.5258			0.590201
$693$		−	11.1570i		−	0.423821i
$694$		−	6.91966i		−	0.262667i
$695$		0			0
$696$	−3.03480			−0.115034
$697$	−33.5870	+	9.79696i	−1.27220	+	0.371086i
$698$		−	56.8059i		−	2.15014i
$699$	22.0694			0.834740
$700$		0			0
$701$	−21.9970			−0.830816			−0.415408	−	0.909635i	$-0.636361\pi$
$701$	−21.9970			−0.830816			−0.415408	+	0.909635i	$0.636361\pi$
$702$	5.10314			0.192606
$703$	−5.39213			−0.203368
$704$		−	1.34118i		−	0.0505476i
$705$		0			0
$706$	32.5005			1.22317
$707$	49.3955			1.85771
$708$	−14.3317			−0.538619
$709$			13.6855i			0.513969i	0.966416	+	0.256984i	$0.0827289\pi$
$709$			13.6855i			0.513969i	−0.966416	+	0.256984i	$0.917271\pi$
$710$		0			0
$711$		−	13.9481i		−	0.523095i
$712$		−	24.4264i		−	0.915419i
$713$			1.82219i			0.0682415i
$714$	34.4176	−	10.0392i	1.28804	−	0.375709i
$715$		0			0
$716$	25.2089			0.942102
$717$	7.58610			0.283308
$718$			28.4383i			1.06131i
$719$		−	22.9414i		−	0.855568i	−0.903881	−	0.427784i	$-0.859294\pi$
$719$		−	22.9414i		−	0.855568i	0.903881	−	0.427784i	$-0.140706\pi$
$720$		0			0
$721$		−	54.8261i		−	2.04183i
$722$		−	29.1174i		−	1.08364i
$723$		−	19.9526i		−	0.742043i
$724$			21.0332i			0.781694i
$725$		0			0
$726$		−	10.4478i		−	0.387752i
$727$			30.6381i			1.13630i	0.822923	+	0.568152i	$0.192342\pi$
$727$			30.6381i			1.13630i	−0.822923	+	0.568152i	$0.807658\pi$
$728$	24.3042			0.900775
$729$	1.00000			0.0370370
$730$		0			0
$731$	−36.1421	+	10.5423i	−1.33677	+	0.389920i
$732$		−	4.70049i		−	0.173735i
$733$			30.3471i			1.12090i	0.828189	+	0.560449i	$0.189371\pi$
$733$			30.3471i			1.12090i	−0.828189	+	0.560449i	$0.810629\pi$
$734$			45.0374i			1.66236i
$735$		0			0
$736$		−	7.05336i		−	0.259990i
$737$	−2.31100			−0.0851267
$738$	14.8055			0.545000
$739$	−17.7291			−0.652174			−0.326087	−	0.945340i	$-0.605730\pi$
$739$	−17.7291			−0.652174			−0.326087	+	0.945340i	$0.605730\pi$
$740$		0			0
$741$		−	4.44711i		−	0.163369i
$742$	−65.9166			−2.41988
$743$	−11.0856			−0.406693			−0.203346	−	0.979107i	$-0.565182\pi$
$743$	−11.0856			−0.406693			−0.203346	+	0.979107i	$0.565182\pi$
$744$	2.32001			0.0850559
$745$		0			0
$746$	−4.00936			−0.146793
$747$			4.47514i			0.163737i
$748$	−9.25429	+	2.69938i	−0.338371	+	0.0986989i
$749$	−18.3541			−0.670644
$750$		0			0
$751$			10.3719i			0.378474i	0.981931	+	0.189237i	$0.0606015\pi$
$751$			10.3719i			0.378474i	−0.981931	+	0.189237i	$0.939399\pi$
$752$			0.832267i			0.0303496i
$753$	−10.6807			−0.389228
$754$			9.28791i			0.338246i
$755$		0			0
$756$	−5.20454			−0.189287
$757$			5.08248i			0.184726i	0.995725	+	0.0923629i	$0.0294420\pi$
$757$			5.08248i			0.184726i	−0.995725	+	0.0923629i	$0.970558\pi$
$758$	43.6421			1.58515
$759$		−	2.93199i		−	0.106424i
$760$		0			0
$761$	25.5981			0.927931			0.463965	−	0.885853i	$-0.346426\pi$
$761$	25.5981			0.927931			0.463965	+	0.885853i	$0.346426\pi$
$762$	20.3734			0.738049
$763$		−	85.4538i		−	3.09363i
$764$	16.7968			0.607687
$765$		0			0
$766$	15.4441			0.558019
$767$		−	40.1373i		−	1.44927i
$768$	−19.4196			−0.700745
$769$	−15.0057			−0.541121			−0.270560	−	0.962703i	$-0.587209\pi$
$769$	−15.0057			−0.541121			−0.270560	+	0.962703i	$0.587209\pi$
$770$		0			0
$771$		−	5.59173i		−	0.201381i
$772$	−18.4843			−0.665263
$773$			39.0295i			1.40379i	0.712278	+	0.701897i	$0.247664\pi$
$773$			39.0295i			1.40379i	−0.712278	+	0.701897i	$0.752336\pi$
$774$	15.9319			0.572660
$775$		0			0
$776$		−	24.6482i		−	0.884819i
$777$	−17.6731			−0.634020
$778$		−	14.0570i		−	0.503969i
$779$		−	12.9022i		−	0.462271i
$780$		0			0
$781$	3.98989			0.142770
$782$	9.04467	−	2.63823i	0.323437	−	0.0943429i
$783$			1.82004i			0.0650428i
$784$	−89.1448			−3.18374
$785$		0			0
$786$	14.2051			0.506679
$787$	21.7701			0.776020			0.388010	−	0.921655i	$-0.373163\pi$
$787$	21.7701			0.776020			0.388010	+	0.921655i	$0.373163\pi$
$788$	−3.83267			−0.136533
$789$			13.8769i			0.494031i
$790$		0			0
$791$	−80.4037			−2.85883
$792$	−3.73301			−0.132647
$793$	13.1641			0.467472
$794$		−	53.4884i		−	1.89823i
$795$		0			0
$796$		−	19.4549i		−	0.689562i
$797$		−	40.0932i		−	1.42017i	−0.704114	−	0.710087i	$-0.748656\pi$
$797$		−	40.0932i		−	1.42017i	0.704114	−	0.710087i	$-0.251344\pi$
$798$			13.2213i			0.468029i
$799$	−0.659108	+	0.192254i	−0.0233175	+	0.00680147i
$800$		0			0
$801$	−14.6490			−0.517599
$802$	−40.4122			−1.42700
$803$			26.0596i			0.919624i
$804$			1.07803i			0.0380193i
$805$		0			0
$806$		−	7.10032i		−	0.250098i
$807$			30.2465i			1.06473i
$808$		−	16.5271i		−	0.581422i
$809$		−	33.2747i		−	1.16988i	−0.811078	−	0.584938i	$-0.801119\pi$
$809$		−	33.2747i		−	1.16988i	0.811078	−	0.584938i	$-0.198881\pi$
$810$		0			0
$811$			1.18314i			0.0415456i	0.999784	+	0.0207728i	$0.00661266\pi$
$811$			1.18314i			0.0415456i	−0.999784	+	0.0207728i	$0.993387\pi$
$812$		−	9.47245i		−	0.332418i
$813$	17.6456			0.618860
$814$	13.8525			0.485530
$815$		0			0
$816$	−5.77048	−	19.7830i	−0.202007	−	0.692544i
$817$		−	13.8838i		−	0.485732i
$818$			19.1278i			0.668788i
$819$		−	14.5758i		−	0.509319i
$820$		0			0
$821$			50.4742i			1.76156i	0.473525	+	0.880780i	$0.342981\pi$
$821$			50.4742i			1.76156i	−0.473525	+	0.880780i	$0.657019\pi$
$822$	−6.07038			−0.211729
$823$	−19.7606			−0.688810			−0.344405	−	0.938821i	$-0.611919\pi$
$823$	−19.7606			−0.688810			−0.344405	+	0.938821i	$0.611919\pi$
$824$	−18.3441			−0.639048
$825$		0			0
$826$			119.329i			4.15197i
$827$	50.1878			1.74520			0.872601	−	0.488434i	$-0.162432\pi$
$827$	50.1878			1.74520			0.872601	+	0.488434i	$0.162432\pi$
$828$	−1.36771			−0.0475313
$829$	−43.5230			−1.51162			−0.755809	−	0.654793i	$-0.772756\pi$
$829$	−43.5230			−1.51162			−0.755809	+	0.654793i	$0.772756\pi$
$830$		0			0
$831$	16.5619			0.574528
$832$		−	1.75214i		−	0.0607446i
$833$	−20.5925	−	70.5976i	−0.713489	−	2.44606i
$834$	16.6898			0.577919
$835$		0			0
$836$		−	3.55498i		−	0.122952i
$837$		−	1.39136i		−	0.0480925i
$838$	25.6641			0.886552
$839$		−	36.9007i		−	1.27395i	−0.770884	−	0.636976i	$-0.780185\pi$
$839$		−	36.9007i		−	1.27395i	0.770884	−	0.636976i	$-0.219815\pi$
$840$		0			0
$841$	25.6875			0.885775
$842$			3.22790i			0.111241i
$843$	−8.40360			−0.289435
$844$		−	5.91867i		−	0.203729i
$845$		0			0
$846$	0.290543			0.00998906
$847$	−29.8412			−1.02536
$848$			37.8885i			1.30110i
$849$	16.2345			0.557165
$850$		0			0
$851$	−4.64437			−0.159207
$852$		−	1.86120i		−	0.0637638i
$853$	−29.8013			−1.02038			−0.510189	−	0.860062i	$-0.670425\pi$
$853$	−29.8013			−1.02038			−0.510189	+	0.860062i	$0.670425\pi$
$854$	−39.1371			−1.33924
$855$		0			0
$856$			6.14105i			0.209897i
$857$	−5.32427			−0.181874			−0.0909368	−	0.995857i	$-0.528986\pi$
$857$	−5.32427			−0.181874			−0.0909368	+	0.995857i	$0.528986\pi$
$858$			11.4247i			0.390034i
$859$	−24.3062			−0.829316			−0.414658	−	0.909977i	$-0.636099\pi$
$859$	−24.3062			−0.829316			−0.414658	+	0.909977i	$0.636099\pi$
$860$		0			0
$861$		−	42.2881i		−	1.44118i
$862$	12.9310			0.440432
$863$		−	25.1361i		−	0.855642i	−0.903863	−	0.427821i	$-0.859281\pi$
$863$		−	25.1361i		−	0.855642i	0.903863	−	0.427821i	$-0.140719\pi$
$864$			5.38571i			0.183225i
$865$		0			0
$866$	−8.74615			−0.297206
$867$	14.3340	−	9.13979i	0.486809	−	0.310404i
$868$			7.24140i			0.245789i
$869$	31.2265			1.05929
$870$		0			0
$871$	−3.01913			−0.102299
$872$	−28.5918			−0.968240
$873$	−14.7821			−0.500297
$874$			3.47445i			0.117525i
$875$		0			0
$876$	12.1563			0.410723
$877$	−25.5005			−0.861090			−0.430545	−	0.902569i	$-0.641679\pi$
$877$	−25.5005			−0.861090			−0.430545	+	0.902569i	$0.641679\pi$
$878$	−37.0194			−1.24934
$879$			21.3036i			0.718552i
$880$		0			0
$881$		−	46.7352i		−	1.57455i	−0.616603	−	0.787274i	$-0.711492\pi$
$881$		−	46.7352i		−	1.57455i	0.616603	−	0.787274i	$-0.288508\pi$
$882$			31.1203i			1.04787i
$883$			11.2968i			0.380166i	0.981768	+	0.190083i	$0.0608757\pi$
$883$			11.2968i			0.380166i	−0.981768	+	0.190083i	$0.939124\pi$
$884$	−12.0900	+	3.52651i	−0.406630	+	0.118610i
$885$		0			0
$886$	39.8708			1.33949
$887$	1.07297			0.0360266			0.0180133	−	0.999838i	$-0.494266\pi$
$887$	1.07297			0.0360266			0.0180133	+	0.999838i	$0.494266\pi$
$888$			5.91321i			0.198434i
$889$		−	58.1911i		−	1.95167i
$890$		0			0
$891$			2.23877i			0.0750015i
$892$		−	3.81346i		−	0.127684i
$893$		−	0.253192i		−	0.00847275i
$894$		−	25.4928i		−	0.852607i
$895$		0			0
$896$			58.8892i			1.96735i
$897$		−	3.83040i		−	0.127893i
$898$	35.2449			1.17614
$899$	2.53233			0.0844580
$900$		0			0
$901$	−30.0055	+	8.75228i	−0.999628	+	0.291581i
$902$			33.1462i			1.10365i
$903$		−	45.5052i		−	1.51432i
$904$			26.9021i			0.894750i
$905$		0			0
$906$			23.8358i			0.791893i
$907$	−46.6720			−1.54972			−0.774860	−	0.632133i	$-0.782180\pi$
$907$	−46.6720			−1.54972			−0.774860	+	0.632133i	$0.782180\pi$
$908$	14.3179			0.475157
$909$	−9.91167			−0.328749
$910$		0			0
$911$			8.14382i			0.269817i	0.990858	+	0.134908i	$0.0430740\pi$
$911$			8.14382i			0.269817i	−0.990858	+	0.134908i	$0.956926\pi$
$912$	7.59952			0.251645
$913$	−10.0188			−0.331574
$914$	−47.9486			−1.58600
$915$		0			0
$916$	−9.03721			−0.298598
$917$		−	40.5731i		−	1.33984i
$918$	−6.90621	+	2.01446i	−0.227939	+	0.0664872i
$919$	−3.96126			−0.130670			−0.0653350	−	0.997863i	$-0.520812\pi$
$919$	−3.96126			−0.130670			−0.0653350	+	0.997863i	$0.520812\pi$
$920$		0			0
$921$			23.9979i			0.790758i
$922$			48.1548i			1.58589i
$923$	5.21247			0.171571
$924$		−	11.6517i		−	0.383314i
$925$		0			0
$926$	−35.8360			−1.17765
$927$			11.0014i			0.361332i
$928$	−9.80218			−0.321772
$929$		−	32.9616i		−	1.08143i	−0.841205	−	0.540717i	$-0.818153\pi$
$929$		−	32.9616i		−	1.08143i	0.841205	−	0.540717i	$-0.181847\pi$
$930$		0			0
$931$	27.1196			0.888809
$932$	23.0479			0.754959
$933$		−	1.60781i		−	0.0526375i
$934$	22.0795			0.722462
$935$		0			0
$936$	−4.87687			−0.159406
$937$			49.6837i			1.62310i	0.584285	+	0.811548i	$0.301375\pi$
$937$			49.6837i			1.62310i	−0.584285	+	0.811548i	$0.698625\pi$
$938$	8.97590			0.293074
$939$	−10.5247			−0.343462
$940$		0			0
$941$			28.8461i			0.940356i	0.882572	+	0.470178i	$0.155810\pi$
$941$			28.8461i			0.940356i	−0.882572	+	0.470178i	$0.844190\pi$
$942$	−36.9768			−1.20477
$943$		−	11.1130i		−	0.361889i
$944$	68.5893			2.23239
$945$		0			0
$946$			35.6678i			1.15966i
$947$	−49.1958			−1.59865			−0.799324	−	0.600900i	$-0.794809\pi$
$947$	−49.1958			−1.59865			−0.799324	+	0.600900i	$0.794809\pi$
$948$		−	14.5665i		−	0.473099i
$949$			34.0448i			1.10514i
$950$		0			0
$951$	21.3111			0.691059
$952$	−32.8915	+	9.59410i	−1.06602	+	0.310946i
$953$			44.1137i			1.42898i	0.699644	+	0.714492i	$0.253342\pi$
$953$			44.1137i			1.42898i	−0.699644	+	0.714492i	$0.746658\pi$
$954$	13.2268			0.428233
$955$		0			0
$956$	7.92246			0.256231
$957$	−4.07464			−0.131714
$958$	−44.8277			−1.44832
$959$			17.3384i			0.559887i
$960$		0			0
$961$	29.0641			0.937552
$962$	18.0972			0.583476
$963$	3.68292			0.118680
$964$		−	20.8372i		−	0.671122i
$965$		0			0
$966$			11.3878i			0.366397i
$967$		−	49.7270i		−	1.59911i	−0.600591	−	0.799557i	$-0.705068\pi$
$967$		−	49.7270i		−	1.59911i	0.600591	−	0.799557i	$-0.294932\pi$
$968$			9.98451i			0.320914i
$969$	1.75550	+	6.01838i	0.0563947	+	0.193338i
$970$		0			0
$971$	37.0067			1.18760			0.593801	−	0.804612i	$-0.297627\pi$
$971$	37.0067			1.18760			0.593801	+	0.804612i	$0.297627\pi$
$972$	1.04434			0.0334972
$973$		−	47.6699i		−	1.52823i
$974$			13.9364i			0.446550i
$975$		0			0
$976$			22.4958i			0.720072i
$977$		−	28.1018i		−	0.899056i	−0.893266	−	0.449528i	$-0.851592\pi$
$977$		−	28.1018i		−	0.899056i	0.893266	−	0.449528i	$-0.148408\pi$
$978$		−	8.48106i		−	0.271194i
$979$		−	32.7958i		−	1.04816i
$980$		0			0
$981$			17.1471i			0.547465i
$982$			40.9218i			1.30587i
$983$	−57.8272			−1.84440			−0.922200	−	0.386714i	$-0.873610\pi$
$983$	−57.8272			−1.84440			−0.922200	+	0.386714i	$0.873610\pi$
$984$	−14.1491			−0.451056
$985$		0			0
$986$	−3.66640	−	12.5696i	−0.116762	−	0.400296i
$987$		−	0.829858i		−	0.0264147i
$988$		−	4.64429i		−	0.147755i
$989$		−	11.9584i		−	0.380256i
$990$		0			0
$991$		−	24.8426i		−	0.789151i	−0.918863	−	0.394576i	$-0.870892\pi$
$991$		−	24.8426i		−	0.789151i	0.918863	−	0.394576i	$-0.129108\pi$
$992$	7.49347			0.237918
$993$	0.393709			0.0124940
$994$	−15.4967			−0.491526
$995$		0			0
$996$			4.67357i			0.148088i
$997$	−15.3101			−0.484877			−0.242438	−	0.970167i	$-0.577947\pi$
$997$	−15.3101			−0.484877			−0.242438	+	0.970167i	$0.577947\pi$
$998$	−4.45813			−0.141119
$999$	3.54628			0.112199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1275.2.d.i.424.10		12
5.2	odd	4		1275.2.g.f.526.4	yes	12
5.3	odd	4		1275.2.g.e.526.9	✓	12
5.4	even	2		1275.2.d.j.424.3		12
17.16	even	2		1275.2.d.j.424.10		12
85.33	odd	4		1275.2.g.e.526.10	yes	12
85.67	odd	4		1275.2.g.f.526.3	yes	12
85.84	even	2	inner	1275.2.d.i.424.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1275.2.d.i.424.3		12	85.84	even	2	inner
1275.2.d.i.424.10		12	1.1	even	1	trivial
1275.2.d.j.424.3		12	5.4	even	2
1275.2.d.j.424.10		12	17.16	even	2
1275.2.g.e.526.9	✓	12	5.3	odd	4
1275.2.g.e.526.10	yes	12	85.33	odd	4
1275.2.g.f.526.3	yes	12	85.67	odd	4
1275.2.g.f.526.4	yes	12	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1275.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.74480i q^{2} -1.00000 q^{3} -1.04434 q^{4} -1.74480i q^{6} -4.98357 q^{7} +1.66744i q^{8} +1.00000 q^{9} +2.23877i q^{11} +1.04434 q^{12} +2.92477i q^{13} -8.69535i q^{14} -4.99803 q^{16} +(-1.15455 - 3.95816i) q^{17} +1.74480i q^{18} +1.52050 q^{19} +4.98357 q^{21} -3.90621 q^{22} +1.30964 q^{23} -1.66744i q^{24} -5.10314 q^{26} -1.00000 q^{27} +5.20454 q^{28} -1.82004i q^{29} +1.39136i q^{31} -5.38571i q^{32} -2.23877i q^{33} +(6.90621 - 2.01446i) q^{34} -1.04434 q^{36} -3.54628 q^{37} +2.65298i q^{38} -2.92477i q^{39} -8.48551i q^{41} +8.69535i q^{42} -9.13105i q^{43} -2.33803i q^{44} +2.28507i q^{46} -0.166519i q^{47} +4.99803 q^{48} +17.8360 q^{49} +(1.15455 + 3.95816i) q^{51} -3.05445i q^{52} -7.58067i q^{53} -1.74480i q^{54} -8.30981i q^{56} -1.52050 q^{57} +3.17561 q^{58} -13.7233 q^{59} -4.50092i q^{61} -2.42765 q^{62} -4.98357 q^{63} -0.599071 q^{64} +3.90621 q^{66} +1.03226i q^{67} +(1.20574 + 4.13366i) q^{68} -1.30964 q^{69} -1.78218i q^{71} +1.66744i q^{72} +11.6402 q^{73} -6.18756i q^{74} -1.58792 q^{76} -11.1570i q^{77} +5.10314 q^{78} -13.9481i q^{79} +1.00000 q^{81} +14.8055 q^{82} +4.47514i q^{83} -5.20454 q^{84} +15.9319 q^{86} +1.82004i q^{87} -3.73301 q^{88} -14.6490 q^{89} -14.5758i q^{91} -1.36771 q^{92} -1.39136i q^{93} +0.290543 q^{94} +5.38571i q^{96} -14.7821 q^{97} +31.1203i q^{98} +2.23877i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} - 16 q^{4} + 12 q^{9} + 16 q^{12} + 32 q^{16} - 6 q^{17} + 4 q^{19} + 12 q^{22} - 16 q^{23} - 36 q^{26} - 12 q^{27} - 36 q^{28} + 24 q^{34} - 16 q^{36} - 4 q^{37} - 32 q^{48} + 16 q^{49}+ \cdots - 16 q^{97}+O(q^{100}) \) 12 * q - 12 * q^3 - 16 * q^4 + 12 * q^9 + 16 * q^12 + 32 * q^16 - 6 * q^17 + 4 * q^19 + 12 * q^22 - 16 * q^23 - 36 * q^26 - 12 * q^27 - 36 * q^28 + 24 * q^34 - 16 * q^36 - 4 * q^37 - 32 * q^48 + 16 * q^49 + 6 * q^51 - 4 * q^57 + 4 * q^58 - 32 * q^59 - 56 * q^62 - 56 * q^64 - 12 * q^66 - 20 * q^68 + 16 * q^69 + 44 * q^73 + 64 * q^76 + 36 * q^78 + 12 * q^81 - 40 * q^82 + 36 * q^84 + 20 * q^86 - 8 * q^88 - 4 * q^89 - 40 * q^94 - 16 * q^97

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