LMFDB - Embedded newform 1170.2.e.f.469.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(469,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1170.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.e (of order $2$, degree $1$, 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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.3534400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 3x^{4} + 16x^{3} + x^{2} - 12x + 40 $ x^6 - 2x^5 - 3x^4 + 16x^3 + x^2 - 12x + 40
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.1
Root			$2.19082 - 1.44755i$ of defining polynomial
Character	$\chi$	$=$	1170.469
Dual form			1170.2.e.f.469.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(-1.44755 - 1.70429i) q^{5} -4.38164i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.44755 - 1.70429i) q^{5} -4.38164i q^{7} +1.00000i q^{8} +(-1.70429 + 1.44755i) q^{10} -2.00000 q^{11} -1.00000i q^{13} -4.38164 q^{14} +1.00000 q^{16} -5.86818i q^{17} +0.973070 q^{19} +(1.44755 + 1.70429i) q^{20} +2.00000i q^{22} +7.79021i q^{23} +(-0.809179 + 4.93409i) q^{25} -1.00000 q^{26} +4.38164i q^{28} +0.973070 q^{29} -1.79021 q^{31} -1.00000i q^{32} -5.86818 q^{34} +(-7.46757 + 6.34266i) q^{35} -0.591429i q^{37} -0.973070i q^{38} +(1.70429 - 1.44755i) q^{40} -4.81714 q^{41} -4.68532i q^{43} +2.00000 q^{44} +7.79021 q^{46} -0.381642i q^{47} -12.1988 q^{49} +(4.93409 + 0.809179i) q^{50} +1.00000i q^{52} +7.79021i q^{53} +(2.89511 + 3.40857i) q^{55} +4.38164 q^{56} -0.973070i q^{58} -0.973070 q^{59} -0.817143 q^{61} +1.79021i q^{62} -1.00000 q^{64} +(-1.70429 + 1.44755i) q^{65} +1.79021i q^{67} +5.86818i q^{68} +(6.34266 + 7.46757i) q^{70} +3.92204 q^{71} +6.00000i q^{73} -0.591429 q^{74} -0.973070 q^{76} +8.76328i q^{77} -10.9731 q^{79} +(-1.44755 - 1.70429i) q^{80} +4.81714i q^{82} -6.97307i q^{83} +(-10.0010 + 8.49450i) q^{85} -4.68532 q^{86} -2.00000i q^{88} +0.973070 q^{89} -4.38164 q^{91} -7.79021i q^{92} -0.381642 q^{94} +(-1.40857 - 1.65839i) q^{95} -18.6074i q^{97} +12.1988i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4}+O(q^{10}) $ 6 * q - 6 * q^4	$ 6 q - 6 q^{4} - 4 q^{10} - 12 q^{11} - 4 q^{14} + 6 q^{16} - 4 q^{19} - 16 q^{25} - 6 q^{26} - 4 q^{29} + 24 q^{31} - 8 q^{34} + 6 q^{35} + 4 q^{40} - 4 q^{41} + 12 q^{44} + 12 q^{46} - 26 q^{49} + 16 q^{50} + 4 q^{56} + 4 q^{59} + 20 q^{61} - 6 q^{64} - 4 q^{65} + 12 q^{70} + 16 q^{71} - 16 q^{74} + 4 q^{76} - 56 q^{79} + 28 q^{85} + 24 q^{86} - 4 q^{89} - 4 q^{91} + 20 q^{94} + 4 q^{95}+O(q^{100}) $ 6 * q - 6 * q^4 - 4 * q^10 - 12 * q^11 - 4 * q^14 + 6 * q^16 - 4 * q^19 - 16 * q^25 - 6 * q^26 - 4 * q^29 + 24 * q^31 - 8 * q^34 + 6 * q^35 + 4 * q^40 - 4 * q^41 + 12 * q^44 + 12 * q^46 - 26 * q^49 + 16 * q^50 + 4 * q^56 + 4 * q^59 + 20 * q^61 - 6 * q^64 - 4 * q^65 + 12 * q^70 + 16 * q^71 - 16 * q^74 + 4 * q^76 - 56 * q^79 + 28 * q^85 + 24 * q^86 - 4 * q^89 - 4 * q^91 + 20 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.44755	−	1.70429i	−0.647365	−	0.762180i
$5$	−1.44755	−	1.70429i	−0.647365	−	0.762180i
$6$		0			0
$7$		−	4.38164i		−	1.65610i	−0.560651	−	0.828052i	$-0.689449\pi$
$7$		−	4.38164i		−	1.65610i	0.560651	−	0.828052i	$-0.310551\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.70429	+	1.44755i	−0.538942	+	0.457757i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−4.38164			−1.17104
$15$		0			0
$16$	1.00000			0.250000
$17$		−	5.86818i		−	1.42324i	−0.702564	−	0.711621i	$-0.747961\pi$
$17$		−	5.86818i		−	1.42324i	0.702564	−	0.711621i	$-0.252039\pi$
$18$		0			0
$19$	0.973070			0.223238			0.111619	−	0.993751i	$-0.464396\pi$
$19$	0.973070			0.223238			0.111619	+	0.993751i	$0.464396\pi$
$20$	1.44755	+	1.70429i	0.323683	+	0.381090i
$21$		0			0
$22$			2.00000i			0.426401i
$23$			7.79021i			1.62437i	0.583399	+	0.812186i	$0.301722\pi$
$23$			7.79021i			1.62437i	−0.583399	+	0.812186i	$0.698278\pi$
$24$		0			0
$25$	−0.809179	+	4.93409i	−0.161836	+	0.986818i
$26$	−1.00000			−0.196116
$27$		0			0
$28$			4.38164i			0.828052i
$29$	0.973070			0.180695			0.0903473	−	0.995910i	$-0.471202\pi$
$29$	0.973070			0.180695			0.0903473	+	0.995910i	$0.471202\pi$
$30$		0			0
$31$	−1.79021			−0.321532			−0.160766	−	0.986993i	$-0.551396\pi$
$31$	−1.79021			−0.321532			−0.160766	+	0.986993i	$0.551396\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−5.86818			−1.00638
$35$	−7.46757	+	6.34266i	−1.26225	+	1.07211i
$36$		0			0
$37$		−	0.591429i		−	0.0972303i	−0.998818	−	0.0486151i	$-0.984519\pi$
$37$		−	0.591429i		−	0.0972303i	0.998818	−	0.0486151i	$-0.0154808\pi$
$38$		−	0.973070i		−	0.157853i
$39$		0			0
$40$	1.70429	−	1.44755i	0.269471	−	0.228878i
$41$	−4.81714			−0.752311			−0.376156	−	0.926556i	$-0.622754\pi$
$41$	−4.81714			−0.752311			−0.376156	+	0.926556i	$0.622754\pi$
$42$		0			0
$43$		−	4.68532i		−	0.714505i	−0.934008	−	0.357252i	$-0.883714\pi$
$43$		−	4.68532i		−	0.714505i	0.934008	−	0.357252i	$-0.116286\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	7.79021			1.14860
$47$		−	0.381642i		−	0.0556682i	−0.999613	−	0.0278341i	$-0.991139\pi$
$47$		−	0.381642i		−	0.0556682i	0.999613	−	0.0278341i	$-0.00886101\pi$
$48$		0			0
$49$	−12.1988			−1.74268
$50$	4.93409	+	0.809179i	0.697785	+	0.114435i
$51$		0			0
$52$			1.00000i			0.138675i
$53$			7.79021i			1.07007i	0.844831	+	0.535034i	$0.179701\pi$
$53$			7.79021i			1.07007i	−0.844831	+	0.535034i	$0.820299\pi$
$54$		0			0
$55$	2.89511	+	3.40857i	0.390376	+	0.459612i
$56$	4.38164			0.585522
$57$		0			0
$58$		−	0.973070i		−	0.127770i
$59$	−0.973070			−0.126683			−0.0633415	−	0.997992i	$-0.520176\pi$
$59$	−0.973070			−0.126683			−0.0633415	+	0.997992i	$0.520176\pi$
$60$		0			0
$61$	−0.817143			−0.104624			−0.0523122	−	0.998631i	$-0.516659\pi$
$61$	−0.817143			−0.104624			−0.0523122	+	0.998631i	$0.516659\pi$
$62$			1.79021i			0.227357i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.70429	+	1.44755i	−0.211391	+	0.179547i
$66$		0			0
$67$			1.79021i			0.218709i	0.994003	+	0.109355i	$0.0348784\pi$
$67$			1.79021i			0.218709i	−0.994003	+	0.109355i	$0.965122\pi$
$68$			5.86818i			0.711621i
$69$		0			0
$70$	6.34266	+	7.46757i	0.758093	+	0.892545i
$71$	3.92204			0.465460			0.232730	−	0.972541i	$-0.425234\pi$
$71$	3.92204			0.465460			0.232730	+	0.972541i	$0.425234\pi$
$72$		0			0
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$	−0.591429			−0.0687522
$75$		0			0
$76$	−0.973070			−0.111619
$77$			8.76328i			0.998669i
$78$		0			0
$79$	−10.9731			−1.23457			−0.617283	−	0.786741i	$-0.711767\pi$
$79$	−10.9731			−1.23457			−0.617283	+	0.786741i	$0.711767\pi$
$80$	−1.44755	−	1.70429i	−0.161841	−	0.190545i
$81$		0			0
$82$			4.81714i			0.531964i
$83$		−	6.97307i		−	0.765394i	−0.923874	−	0.382697i	$-0.874995\pi$
$83$		−	6.97307i		−	0.765394i	0.923874	−	0.382697i	$-0.125005\pi$
$84$		0			0
$85$	−10.0010	+	8.49450i	−1.08477	+	0.921358i
$86$	−4.68532			−0.505231
$87$		0			0
$88$		−	2.00000i		−	0.213201i
$89$	0.973070			0.103145			0.0515726	−	0.998669i	$-0.483577\pi$
$89$	0.973070			0.103145			0.0515726	+	0.998669i	$0.483577\pi$
$90$		0			0
$91$	−4.38164			−0.459321
$92$		−	7.79021i		−	0.812186i
$93$		0			0
$94$	−0.381642			−0.0393633
$95$	−1.40857	−	1.65839i	−0.144516	−	0.170147i
$96$		0			0
$97$		−	18.6074i		−	1.88929i	−0.328093	−	0.944645i	$-0.606406\pi$
$97$		−	18.6074i		−	1.88929i	0.328093	−	0.944645i	$-0.393594\pi$
$98$			12.1988i			1.23226i
$99$		0			0
$100$	0.809179	−	4.93409i	0.0809179	−	0.493409i
$101$	−14.3437			−1.42725			−0.713626	−	0.700527i	$-0.752948\pi$
$101$	−14.3437			−1.42725			−0.713626	+	0.700527i	$0.752948\pi$
$102$		0			0
$103$		−	9.73635i		−	0.959351i	−0.877446	−	0.479676i	$-0.840754\pi$
$103$		−	9.73635i		−	0.959351i	0.877446	−	0.479676i	$-0.159246\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	7.79021			0.756652
$107$			5.79021i			0.559761i	0.960035	+	0.279881i	$0.0902949\pi$
$107$			5.79021i			0.559761i	−0.960035	+	0.279881i	$0.909705\pi$
$108$		0			0
$109$	0.685320			0.0656417			0.0328209	−	0.999461i	$-0.489551\pi$
$109$	0.685320			0.0656417			0.0328209	+	0.999461i	$0.489551\pi$
$110$	3.40857	−	2.89511i	0.324995	−	0.276038i
$111$		0			0
$112$		−	4.38164i		−	0.414026i
$113$			4.00000i			0.376288i	0.982141	+	0.188144i	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$		0			0
$115$	13.2767	−	11.2767i	1.23806	−	1.05156i
$116$	−0.973070			−0.0903473
$117$		0			0
$118$			0.973070i			0.0895784i
$119$	−25.7122			−2.35704
$120$		0			0
$121$	−7.00000			−0.636364
$122$			0.817143i			0.0739806i
$123$		0			0
$124$	1.79021			0.160766
$125$	9.58043	−	5.76328i	0.856899	−	0.515484i
$126$		0			0
$127$			11.7902i			1.04621i	0.852268	+	0.523106i	$0.175227\pi$
$127$			11.7902i			1.04621i	−0.852268	+	0.523106i	$0.824773\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	1.44755	+	1.70429i	0.126959	+	0.149476i
$131$	16.9890			1.48434			0.742168	−	0.670214i	$-0.233798\pi$
$131$	16.9890			1.48434			0.742168	+	0.670214i	$0.233798\pi$
$132$		0			0
$133$		−	4.26365i		−	0.369705i
$134$	1.79021			0.154651
$135$		0			0
$136$	5.86818			0.503192
$137$		−	4.20979i		−	0.359666i	−0.983697	−	0.179833i	$-0.942444\pi$
$137$		−	4.20979i		−	0.359666i	0.983697	−	0.179833i	$-0.0575558\pi$
$138$		0			0
$139$	6.17185			0.523490			0.261745	−	0.965137i	$-0.415702\pi$
$139$	6.17185			0.523490			0.261745	+	0.965137i	$0.415702\pi$
$140$	7.46757	−	6.34266i	0.631125	−	0.536053i
$141$		0			0
$142$		−	3.92204i		−	0.329130i
$143$			2.00000i			0.167248i
$144$		0			0
$145$	−1.40857	−	1.65839i	−0.116975	−	0.137722i
$146$	6.00000			0.496564
$147$		0			0
$148$			0.591429i			0.0486151i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$		0			0
$151$	15.5025			1.26157			0.630786	−	0.775957i	$-0.282732\pi$
$151$	15.5025			1.26157			0.630786	+	0.775957i	$0.282732\pi$
$152$			0.973070i			0.0789264i
$153$		0			0
$154$	8.76328			0.706166
$155$	2.59143	+	3.05103i	0.208149	+	0.245065i
$156$		0			0
$157$			8.97307i			0.716129i	0.933697	+	0.358064i	$0.116563\pi$
$157$			8.97307i			0.716129i	−0.933697	+	0.358064i	$0.883437\pi$
$158$			10.9731i			0.872971i
$159$		0			0
$160$	−1.70429	+	1.44755i	−0.134736	+	0.114439i
$161$	34.1339			2.69013
$162$		0			0
$163$			12.6074i			0.987484i	0.869608	+	0.493742i	$0.164371\pi$
$163$			12.6074i			0.987484i	−0.869608	+	0.493742i	$0.835629\pi$
$164$	4.81714			0.376156
$165$		0			0
$166$	−6.97307			−0.541215
$167$		−	23.1609i		−	1.79224i	−0.443811	−	0.896120i	$-0.646374\pi$
$167$		−	23.1609i		−	1.79224i	0.443811	−	0.896120i	$-0.353626\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	8.49450	+	10.0010i	0.651498	+	0.767046i
$171$		0			0
$172$			4.68532i			0.357252i
$173$		−	19.7902i		−	1.50462i	−0.658808	−	0.752311i	$-0.728939\pi$
$173$		−	19.7902i		−	1.50462i	0.658808	−	0.752311i	$-0.271061\pi$
$174$		0			0
$175$	21.6194	+	3.54553i	1.63427	+	0.268017i
$176$	−2.00000			−0.150756
$177$		0			0
$178$		−	0.973070i		−	0.0729347i
$179$	6.17185			0.461306			0.230653	−	0.973036i	$-0.425914\pi$
$179$	6.17185			0.461306			0.230653	+	0.973036i	$0.425914\pi$
$180$		0			0
$181$	−19.3706			−1.43981			−0.719904	−	0.694074i	$-0.755814\pi$
$181$	−19.3706			−1.43981			−0.719904	+	0.694074i	$0.755814\pi$
$182$			4.38164i			0.324789i
$183$		0			0
$184$	−7.79021			−0.574302
$185$	−1.00796	+	0.856125i	−0.0741069	+	0.0629435i
$186$		0			0
$187$			11.7364i			0.858247i
$188$			0.381642i			0.0278341i
$189$		0			0
$190$	−1.65839	+	1.40857i	−0.120312	+	0.102189i
$191$	3.73635			0.270353			0.135177	−	0.990822i	$-0.456840\pi$
$191$	3.73635			0.270353			0.135177	+	0.990822i	$0.456840\pi$
$192$		0			0
$193$		−	15.3706i		−	1.10640i	−0.833048	−	0.553201i	$-0.813406\pi$
$193$		−	15.3706i		−	1.10640i	0.833048	−	0.553201i	$-0.186594\pi$
$194$	−18.6074			−1.33593
$195$		0			0
$196$	12.1988			0.871342
$197$		−	26.9890i		−	1.92289i	−0.275004	−	0.961443i	$-0.588679\pi$
$197$		−	26.9890i		−	1.92289i	0.275004	−	0.961443i	$-0.411321\pi$
$198$		0			0
$199$	−23.3168			−1.65288			−0.826441	−	0.563023i	$-0.809638\pi$
$199$	−23.3168			−1.65288			−0.826441	+	0.563023i	$0.809638\pi$
$200$	−4.93409	−	0.809179i	−0.348893	−	0.0572176i
$201$		0			0
$202$			14.3437i			1.00922i
$203$		−	4.26365i		−	0.299249i
$204$		0			0
$205$	6.97307	+	8.20979i	0.487020	+	0.573396i
$206$	−9.73635			−0.678364
$207$		0			0
$208$		−	1.00000i		−	0.0693375i
$209$	−1.94614			−0.134617
$210$		0			0
$211$	15.3547			1.05706			0.528531	−	0.848914i	$-0.322743\pi$
$211$	15.3547			1.05706			0.528531	+	0.848914i	$0.322743\pi$
$212$		−	7.79021i		−	0.535034i
$213$		0			0
$214$	5.79021			0.395811
$215$	−7.98512	+	6.78225i	−0.544581	+	0.462546i
$216$		0			0
$217$			7.84407i			0.532490i
$218$		−	0.685320i		−	0.0464157i
$219$		0			0
$220$	−2.89511	−	3.40857i	−0.195188	−	0.229806i
$221$	−5.86818			−0.394736
$222$		0			0
$223$		−	24.8331i		−	1.66295i	−0.555566	−	0.831473i	$-0.687498\pi$
$223$		−	24.8331i		−	1.66295i	0.555566	−	0.831473i	$-0.312502\pi$
$224$	−4.38164			−0.292761
$225$		0			0
$226$	4.00000			0.266076
$227$			21.5266i			1.42877i	0.699754	+	0.714384i	$0.253293\pi$
$227$			21.5266i			1.42877i	−0.699754	+	0.714384i	$0.746707\pi$
$228$		0			0
$229$	2.63146			0.173892			0.0869459	−	0.996213i	$-0.472289\pi$
$229$	2.63146			0.173892			0.0869459	+	0.996213i	$0.472289\pi$
$230$	−11.2767	−	13.2767i	−0.743567	−	0.875443i
$231$		0			0
$232$			0.973070i			0.0638852i
$233$		−	29.0290i		−	1.90175i	−0.309568	−	0.950877i	$-0.600184\pi$
$233$		−	29.0290i		−	1.90175i	0.309568	−	0.950877i	$-0.399816\pi$
$234$		0			0
$235$	−0.650427	+	0.552447i	−0.0424291	+	0.0360377i
$236$	0.973070			0.0633415
$237$		0			0
$238$			25.7122i			1.66668i
$239$	2.13182			0.137896			0.0689481	−	0.997620i	$-0.478036\pi$
$239$	2.13182			0.137896			0.0689481	+	0.997620i	$0.478036\pi$
$240$		0			0
$241$	22.4996			1.44933			0.724665	−	0.689102i	$-0.241995\pi$
$241$	22.4996			1.44933			0.724665	+	0.689102i	$0.241995\pi$
$242$			7.00000i			0.449977i
$243$		0			0
$244$	0.817143			0.0523122
$245$	17.6584	+	20.7902i	1.12815	+	1.32824i
$246$		0			0
$247$		−	0.973070i		−	0.0619150i
$248$		−	1.79021i		−	0.113679i
$249$		0			0
$250$	−5.76328	−	9.58043i	−0.364502	−	0.605919i
$251$	0.419574			0.0264833			0.0132416	−	0.999912i	$-0.495785\pi$
$251$	0.419574			0.0264833			0.0132416	+	0.999912i	$0.495785\pi$
$252$		0			0
$253$		−	15.5804i		−	0.979533i
$254$	11.7902			0.739784
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	19.6584i		−	1.22626i	−0.789983	−	0.613128i	$-0.789911\pi$
$257$		−	19.6584i		−	1.22626i	0.789983	−	0.613128i	$-0.210089\pi$
$258$		0			0
$259$	−2.59143			−0.161024
$260$	1.70429	−	1.44755i	0.105695	−	0.0897734i
$261$		0			0
$262$		−	16.9890i		−	1.04958i
$263$		−	10.7633i		−	0.663692i	−0.943333	−	0.331846i	$-0.892328\pi$
$263$		−	10.7633i		−	0.663692i	0.943333	−	0.331846i	$-0.107672\pi$
$264$		0			0
$265$	13.2767	−	11.2767i	0.815584	−	0.692725i
$266$	−4.26365			−0.261421
$267$		0			0
$268$		−	1.79021i		−	0.109355i
$269$	−14.7633			−0.900133			−0.450067	−	0.892995i	$-0.648600\pi$
$269$	−14.7633			−0.900133			−0.450067	+	0.892995i	$0.648600\pi$
$270$		0			0
$271$	−27.2388			−1.65464			−0.827320	−	0.561731i	$-0.810136\pi$
$271$	−27.2388			−1.65464			−0.827320	+	0.561731i	$0.810136\pi$
$272$		−	5.86818i		−	0.355810i
$273$		0			0
$274$	−4.20979			−0.254323
$275$	1.61836	−	9.86818i	0.0975907	−	0.595073i
$276$		0			0
$277$		−	2.87100i		−	0.172502i	−0.996273	−	0.0862509i	$-0.972511\pi$
$277$		−	2.87100i		−	0.172502i	0.996273	−	0.0862509i	$-0.0274887\pi$
$278$		−	6.17185i		−	0.370163i
$279$		0			0
$280$	−6.34266	−	7.46757i	−0.379046	−	0.446273i
$281$	−5.39264			−0.321698			−0.160849	−	0.986979i	$-0.551423\pi$
$281$	−5.39264			−0.321698			−0.160849	+	0.986979i	$0.551423\pi$
$282$		0			0
$283$			24.9511i			1.48319i	0.670850	+	0.741593i	$0.265930\pi$
$283$			24.9511i			1.48319i	−0.670850	+	0.741593i	$0.734070\pi$
$284$	−3.92204			−0.232730
$285$		0			0
$286$	2.00000			0.118262
$287$			21.1070i			1.24591i
$288$		0			0
$289$	−17.4355			−1.02562
$290$	−1.65839	+	1.40857i	−0.0973840	+	0.0827142i
$291$		0			0
$292$		−	6.00000i		−	0.351123i
$293$			24.9351i			1.45673i	0.685191	+	0.728363i	$0.259719\pi$
$293$			24.9351i			1.45673i	−0.685191	+	0.728363i	$0.740281\pi$
$294$		0			0
$295$	1.40857	+	1.65839i	0.0820102	+	0.0965552i
$296$	0.591429			0.0343761
$297$		0			0
$298$		0			0
$299$	7.79021			0.450520
$300$		0			0
$301$	−20.5294			−1.18329
$302$		−	15.5025i		−	0.892066i
$303$		0			0
$304$	0.973070			0.0558094
$305$	1.18286	+	1.39264i	0.0677302	+	0.0797426i
$306$		0			0
$307$		−	14.8171i		−	0.845659i	−0.906209	−	0.422829i	$-0.861037\pi$
$307$		−	14.8171i		−	0.845659i	0.906209	−	0.422829i	$-0.138963\pi$
$308$		−	8.76328i		−	0.499334i
$309$		0			0
$310$	3.05103	−	2.59143i	0.173287	−	0.147183i
$311$	−12.8710			−0.729848			−0.364924	−	0.931037i	$-0.618905\pi$
$311$	−12.8710			−0.729848			−0.364924	+	0.931037i	$0.618905\pi$
$312$		0			0
$313$		−	19.9220i		−	1.12606i	−0.826436	−	0.563030i	$-0.809636\pi$
$313$		−	19.9220i		−	1.12606i	0.826436	−	0.563030i	$-0.190364\pi$
$314$	8.97307			0.506380
$315$		0			0
$316$	10.9731			0.617283
$317$			3.94614i			0.221637i	0.993841	+	0.110819i	$0.0353473\pi$
$317$			3.94614i			0.221637i	−0.993841	+	0.110819i	$0.964653\pi$
$318$		0			0
$319$	−1.94614			−0.108963
$320$	1.44755	+	1.70429i	0.0809207	+	0.0952725i
$321$		0			0
$322$		−	34.1339i		−	1.90221i
$323$		−	5.71015i		−	0.317721i
$324$		0			0
$325$	4.93409	+	0.809179i	0.273694	+	0.0448852i
$326$	12.6074			0.698257
$327$		0			0
$328$		−	4.81714i		−	0.265982i
$329$	−1.67222			−0.0921923
$330$		0			0
$331$	21.4245			1.17760			0.588798	−	0.808280i	$-0.299601\pi$
$331$	21.4245			1.17760			0.588798	+	0.808280i	$0.299601\pi$
$332$			6.97307i			0.382697i
$333$		0			0
$334$	−23.1609			−1.26731
$335$	3.05103	−	2.59143i	0.166696	−	0.141585i
$336$		0			0
$337$		−	11.2388i		−	0.612217i	−0.951997	−	0.306109i	$-0.900973\pi$
$337$		−	11.2388i		−	0.612217i	0.951997	−	0.306109i	$-0.0990271\pi$
$338$			1.00000i			0.0543928i
$339$		0			0
$340$	10.0010	−	8.49450i	0.542383	−	0.460679i
$341$	3.58043			0.193891
$342$		0			0
$343$			22.7792i			1.22996i
$344$	4.68532			0.252616
$345$		0			0
$346$	−19.7902			−1.06393
$347$			16.9490i			0.909868i	0.890525	+	0.454934i	$0.150337\pi$
$347$			16.9490i			0.909868i	−0.890525	+	0.454934i	$0.849663\pi$
$348$		0			0
$349$	10.2119			0.546630			0.273315	−	0.961925i	$-0.411880\pi$
$349$	10.2119			0.546630			0.273315	+	0.961925i	$0.411880\pi$
$350$	3.54553	−	21.6194i	0.189517	−	1.15561i
$351$		0			0
$352$			2.00000i			0.106600i
$353$		−	14.9511i		−	0.795765i	−0.917436	−	0.397882i	$-0.869745\pi$
$353$		−	14.9511i		−	0.795765i	0.917436	−	0.397882i	$-0.130255\pi$
$354$		0			0
$355$	−5.67736	−	6.68427i	−0.301323	−	0.354764i
$356$	−0.973070			−0.0515726
$357$		0			0
$358$		−	6.17185i		−	0.326193i
$359$	11.8441			0.625106			0.312553	−	0.949900i	$-0.398816\pi$
$359$	11.8441			0.625106			0.312553	+	0.949900i	$0.398816\pi$
$360$		0			0
$361$	−18.0531			−0.950165
$362$			19.3706i			1.01810i
$363$		0			0
$364$	4.38164			0.229660
$365$	10.2257	−	8.68532i	0.535238	−	0.454610i
$366$		0			0
$367$			16.0539i			0.838005i	0.907985	+	0.419002i	$0.137620\pi$
$367$			16.0539i			0.838005i	−0.907985	+	0.419002i	$0.862380\pi$
$368$			7.79021i			0.406093i
$369$		0			0
$370$	0.856125	+	1.00796i	0.0445078	+	0.0524015i
$371$	34.1339			1.77214
$372$		0			0
$373$			6.87100i			0.355767i	0.984052	+	0.177883i	$0.0569250\pi$
$373$			6.87100i			0.355767i	−0.984052	+	0.177883i	$0.943075\pi$
$374$	11.7364			0.606872
$375$		0			0
$376$	0.381642			0.0196817
$377$		−	0.973070i		−	0.0501157i
$378$		0			0
$379$	−1.84407			−0.0947236			−0.0473618	−	0.998878i	$-0.515081\pi$
$379$	−1.84407			−0.0947236			−0.0473618	+	0.998878i	$0.515081\pi$
$380$	1.40857	+	1.65839i	0.0722582	+	0.0850736i
$381$		0			0
$382$		−	3.73635i		−	0.191168i
$383$		−	9.25264i		−	0.472788i	−0.971657	−	0.236394i	$-0.924034\pi$
$383$		−	9.25264i		−	0.472788i	0.971657	−	0.236394i	$-0.0759656\pi$
$384$		0			0
$385$	14.9351	−	12.6853i	0.761165	−	0.646504i
$386$	−15.3706			−0.782345
$387$		0			0
$388$			18.6074i			0.944645i
$389$	−21.2686			−1.07836			−0.539180	−	0.842191i	$-0.681266\pi$
$389$	−21.2686			−1.07836			−0.539180	+	0.842191i	$0.681266\pi$
$390$		0			0
$391$	45.7143			2.31187
$392$		−	12.1988i		−	0.616132i
$393$		0			0
$394$	−26.9890			−1.35969
$395$	15.8841	+	18.7012i	0.799216	+	0.940962i
$396$		0			0
$397$		−	33.4727i		−	1.67995i	−0.542627	−	0.839974i	$-0.682570\pi$
$397$		−	33.4727i		−	1.67995i	0.542627	−	0.839974i	$-0.317430\pi$
$398$			23.3168i			1.16876i
$399$		0			0
$400$	−0.809179	+	4.93409i	−0.0404590	+	0.246704i
$401$	−17.7364			−0.885711			−0.442856	−	0.896593i	$-0.646035\pi$
$401$	−17.7364			−0.885711			−0.442856	+	0.896593i	$0.646035\pi$
$402$		0			0
$403$			1.79021i			0.0891769i
$404$	14.3437			0.713626
$405$		0			0
$406$	−4.26365			−0.211601
$407$			1.18286i			0.0586321i
$408$		0			0
$409$	−7.68249			−0.379875			−0.189937	−	0.981796i	$-0.560829\pi$
$409$	−7.68249			−0.379875			−0.189937	+	0.981796i	$0.560829\pi$
$410$	8.20979	−	6.97307i	0.405452	−	0.344375i
$411$		0			0
$412$			9.73635i			0.479676i
$413$			4.26365i			0.209800i
$414$		0			0
$415$	−11.8841	+	10.0939i	−0.583368	+	0.495490i
$416$	−1.00000			−0.0490290
$417$		0			0
$418$			1.94614i			0.0951889i
$419$	11.8061			0.576768			0.288384	−	0.957515i	$-0.406882\pi$
$419$	11.8061			0.576768			0.288384	+	0.957515i	$0.406882\pi$
$420$		0			0
$421$	−26.3678			−1.28509			−0.642544	−	0.766249i	$-0.722121\pi$
$421$	−26.3678			−1.28509			−0.642544	+	0.766249i	$0.722121\pi$
$422$		−	15.3547i		−	0.747456i
$423$		0			0
$424$	−7.79021			−0.378326
$425$	28.9541	+	4.74841i	1.40448	+	0.230332i
$426$		0			0
$427$			3.58043i			0.173269i
$428$		−	5.79021i		−	0.279881i
$429$		0			0
$430$	6.78225	+	7.98512i	0.327069	+	0.385077i
$431$	−1.71225			−0.0824761			−0.0412381	−	0.999149i	$-0.513130\pi$
$431$	−1.71225			−0.0824761			−0.0412381	+	0.999149i	$0.513130\pi$
$432$		0			0
$433$			11.9220i			0.572936i	0.958090	+	0.286468i	$0.0924813\pi$
$433$			11.9220i			0.572936i	−0.958090	+	0.286468i	$0.907519\pi$
$434$	7.84407			0.376528
$435$		0			0
$436$	−0.685320			−0.0328209
$437$			7.58043i			0.362621i
$438$		0			0
$439$	12.3437			0.589133			0.294567	−	0.955631i	$-0.404825\pi$
$439$	12.3437			0.589133			0.294567	+	0.955631i	$0.404825\pi$
$440$	−3.40857	+	2.89511i	−0.162497	+	0.138019i
$441$		0			0
$442$			5.86818i			0.279121i
$443$		−	28.1580i		−	1.33783i	−0.743340	−	0.668914i	$-0.766759\pi$
$443$		−	28.1580i		−	1.33783i	0.743340	−	0.668914i	$-0.233241\pi$
$444$		0			0
$445$	−1.40857	−	1.65839i	−0.0667727	−	0.0786152i
$446$	−24.8331			−1.17588
$447$		0			0
$448$			4.38164i			0.207013i
$449$	−29.0531			−1.37110			−0.685551	−	0.728025i	$-0.740439\pi$
$449$	−29.0531			−1.37110			−0.685551	+	0.728025i	$0.740439\pi$
$450$		0			0
$451$	9.63429			0.453661
$452$		−	4.00000i		−	0.188144i
$453$		0			0
$454$	21.5266			1.01029
$455$	6.34266	+	7.46757i	0.297348	+	0.350085i
$456$		0			0
$457$		−	11.5266i		−	0.539190i	−0.962974	−	0.269595i	$-0.913110\pi$
$457$		−	11.5266i		−	0.539190i	0.962974	−	0.269595i	$-0.0868898\pi$
$458$		−	2.63146i		−	0.122960i
$459$		0			0
$460$	−13.2767	+	11.2767i	−0.619032	+	0.525781i
$461$	−28.4217			−1.32373			−0.661865	−	0.749623i	$-0.730235\pi$
$461$	−28.4217			−1.32373			−0.661865	+	0.749623i	$0.730235\pi$
$462$		0			0
$463$			27.4727i			1.27677i	0.769719	+	0.638383i	$0.220396\pi$
$463$			27.4727i			1.27677i	−0.769719	+	0.638383i	$0.779604\pi$
$464$	0.973070			0.0451737
$465$		0			0
$466$	−29.0290			−1.34474
$467$			18.2098i			0.842648i	0.906910	+	0.421324i	$0.138435\pi$
$467$			18.2098i			0.842648i	−0.906910	+	0.421324i	$0.861565\pi$
$468$		0			0
$469$	7.84407			0.362206
$470$	0.552447	+	0.650427i	0.0254825	+	0.0300019i
$471$		0			0
$472$		−	0.973070i		−	0.0447892i
$473$			9.37064i			0.430862i
$474$		0			0
$475$	−0.787388	+	4.80122i	−0.0361279	+	0.220295i
$476$	25.7122			1.17852
$477$		0			0
$478$		−	2.13182i		−	0.0975073i
$479$	−33.6045			−1.53543			−0.767715	−	0.640791i	$-0.778606\pi$
$479$	−33.6045			−1.53543			−0.767715	+	0.640791i	$0.778606\pi$
$480$		0			0
$481$	−0.591429			−0.0269668
$482$		−	22.4996i		−	1.02483i
$483$		0			0
$484$	7.00000			0.318182
$485$	−31.7122	+	26.9351i	−1.43998	+	1.22306i
$486$		0			0
$487$			8.00000i			0.362515i	0.983436	+	0.181257i	$0.0580167\pi$
$487$			8.00000i			0.362515i	−0.983436	+	0.181257i	$0.941983\pi$
$488$		−	0.817143i		−	0.0369903i
$489$		0			0
$490$	20.7902	−	17.6584i	0.939206	−	0.797725i
$491$	19.8061			0.893839			0.446919	−	0.894574i	$-0.352521\pi$
$491$	19.8061			0.893839			0.446919	+	0.894574i	$0.352521\pi$
$492$		0			0
$493$		−	5.71015i		−	0.257172i
$494$	−0.973070			−0.0437805
$495$		0			0
$496$	−1.79021			−0.0803829
$497$		−	17.1850i		−	0.770851i
$498$		0			0
$499$	−9.12900			−0.408670			−0.204335	−	0.978901i	$-0.565503\pi$
$499$	−9.12900			−0.408670			−0.204335	+	0.978901i	$0.565503\pi$
$500$	−9.58043	+	5.76328i	−0.428450	+	0.257742i
$501$		0			0
$502$		−	0.419574i		−	0.0187265i
$503$			10.6074i			0.472959i	0.971637	+	0.236479i	$0.0759935\pi$
$503$			10.6074i			0.472959i	−0.971637	+	0.236479i	$0.924006\pi$
$504$		0			0
$505$	20.7633	+	24.4458i	0.923954	+	1.08782i
$506$	−15.5804			−0.692634
$507$		0			0
$508$		−	11.7902i		−	0.523106i
$509$	−5.63429			−0.249735			−0.124868	−	0.992173i	$-0.539851\pi$
$509$	−5.63429			−0.249735			−0.124868	+	0.992173i	$0.539851\pi$
$510$		0			0
$511$	26.2899			1.16299
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−19.6584			−0.867094
$515$	−16.5935	+	14.0939i	−0.731198	+	0.621051i
$516$		0			0
$517$			0.763283i			0.0335692i
$518$			2.59143i			0.113861i
$519$		0			0
$520$	−1.44755	−	1.70429i	−0.0634794	−	0.0747379i
$521$	22.8012			0.998939			0.499470	−	0.866331i	$-0.333528\pi$
$521$	22.8012			0.998939			0.499470	+	0.866331i	$0.333528\pi$
$522$		0			0
$523$		−	23.6286i		−	1.03321i	−0.856224	−	0.516604i	$-0.827196\pi$
$523$		−	23.6286i		−	1.03321i	0.856224	−	0.516604i	$-0.172804\pi$
$524$	−16.9890			−0.742168
$525$		0			0
$526$	−10.7633			−0.469301
$527$			10.5053i			0.457617i
$528$		0			0
$529$	−37.6874			−1.63858
$530$	−11.2767	−	13.2767i	−0.489831	−	0.576705i
$531$		0			0
$532$			4.26365i			0.184853i
$533$			4.81714i			0.208654i
$534$		0			0
$535$	9.86818	−	8.38164i	0.426638	−	0.362370i
$536$	−1.79021			−0.0773254
$537$		0			0
$538$			14.7633i			0.636490i
$539$	24.3976			1.05088
$540$		0			0
$541$	11.3147			0.486456			0.243228	−	0.969969i	$-0.421794\pi$
$541$	11.3147			0.486456			0.243228	+	0.969969i	$0.421794\pi$
$542$			27.2388i			1.17001i
$543$		0			0
$544$	−5.86818			−0.251596
$545$	−0.992037	−	1.16798i	−0.0424942	−	0.0500308i
$546$		0			0
$547$			16.8412i			0.720080i	0.932937	+	0.360040i	$0.117237\pi$
$547$			16.8412i			0.720080i	−0.932937	+	0.360040i	$0.882763\pi$
$548$			4.20979i			0.179833i
$549$		0			0
$550$	−9.86818	−	1.61836i	−0.420780	−	0.0690070i
$551$	0.946866			0.0403379
$552$		0			0
$553$			48.0801i			2.04457i
$554$	−2.87100			−0.121977
$555$		0			0
$556$	−6.17185			−0.261745
$557$			35.7523i			1.51487i	0.652909	+	0.757436i	$0.273548\pi$
$557$			35.7523i			1.51487i	−0.652909	+	0.757436i	$0.726452\pi$
$558$		0			0
$559$	−4.68532			−0.198168
$560$	−7.46757	+	6.34266i	−0.315562	+	0.268026i
$561$		0			0
$562$			5.39264i			0.227475i
$563$		−	13.3685i		−	0.563417i	−0.959500	−	0.281708i	$-0.909099\pi$
$563$		−	13.3685i		−	0.563417i	0.959500	−	0.281708i	$-0.0909011\pi$
$564$		0			0
$565$	6.81714	−	5.79021i	0.286799	−	0.243596i
$566$	24.9511			1.04877
$567$		0			0
$568$			3.92204i			0.164565i
$569$	−29.9621			−1.25608			−0.628038	−	0.778183i	$-0.716142\pi$
$569$	−29.9621			−1.25608			−0.628038	+	0.778183i	$0.716142\pi$
$570$		0			0
$571$	30.5156			1.27704			0.638518	−	0.769607i	$-0.279548\pi$
$571$	30.5156			1.27704			0.638518	+	0.769607i	$0.279548\pi$
$572$		−	2.00000i		−	0.0836242i
$573$		0			0
$574$	21.1070			0.880989
$575$	−38.4376	−	6.30368i	−1.60296	−	0.262882i
$576$		0			0
$577$			33.1609i			1.38050i	0.723569	+	0.690252i	$0.242500\pi$
$577$			33.1609i			1.38050i	−0.723569	+	0.690252i	$0.757500\pi$
$578$			17.4355i			0.725221i
$579$		0			0
$580$	1.40857	+	1.65839i	0.0584877	+	0.0688609i
$581$	−30.5535			−1.26757
$582$		0			0
$583$		−	15.5804i		−	0.645275i
$584$	−6.00000			−0.248282
$585$		0			0
$586$	24.9351			1.03006
$587$		−	14.1339i		−	0.583369i	−0.956515	−	0.291685i	$-0.905784\pi$
$587$		−	14.1339i		−	0.583369i	0.956515	−	0.291685i	$-0.0942158\pi$
$588$		0			0
$589$	−1.74200			−0.0717780
$590$	1.65839	−	1.40857i	0.0682748	−	0.0579900i
$591$		0			0
$592$		−	0.591429i		−	0.0243076i
$593$		−	9.39264i		−	0.385710i	−0.981227	−	0.192855i	$-0.938225\pi$
$593$		−	9.39264i		−	0.385710i	0.981227	−	0.192855i	$-0.0617746\pi$
$594$		0			0
$595$	37.2198	+	43.8210i	1.52587	+	1.79649i
$596$		0			0
$597$		0			0
$598$		−	7.79021i		−	0.318566i
$599$	45.5584			1.86147			0.930733	−	0.365699i	$-0.119170\pi$
$599$	45.5584			1.86147			0.930733	+	0.365699i	$0.119170\pi$
$600$		0			0
$601$	26.7254			1.09015			0.545075	−	0.838387i	$-0.316501\pi$
$601$	26.7254			1.09015			0.545075	+	0.838387i	$0.316501\pi$
$602$			20.5294i			0.836716i
$603$		0			0
$604$	−15.5025			−0.630786
$605$	10.1329	+	11.9300i	0.411960	+	0.485023i
$606$		0			0
$607$		−	30.0801i		−	1.22091i	−0.792050	−	0.610456i	$-0.790986\pi$
$607$		−	30.0801i		−	1.22091i	0.792050	−	0.610456i	$-0.209014\pi$
$608$		−	0.973070i		−	0.0394632i
$609$		0			0
$610$	1.39264	−	1.18286i	0.0563865	−	0.0478925i
$611$	−0.381642			−0.0154396
$612$		0			0
$613$			17.2686i			0.697471i	0.937221	+	0.348735i	$0.113389\pi$
$613$			17.2686i			0.697471i	−0.937221	+	0.348735i	$0.886611\pi$
$614$	−14.8171			−0.597971
$615$		0			0
$616$	−8.76328			−0.353083
$617$			14.3437i			0.577456i	0.957411	+	0.288728i	$0.0932323\pi$
$617$			14.3437i			0.577456i	−0.957411	+	0.288728i	$0.906768\pi$
$618$		0			0
$619$	38.4514			1.54549			0.772747	−	0.634715i	$-0.218882\pi$
$619$	38.4514			1.54549			0.772747	+	0.634715i	$0.218882\pi$
$620$	−2.59143	−	3.05103i	−0.104074	−	0.122532i
$621$		0			0
$622$			12.8710i			0.516080i
$623$		−	4.26365i		−	0.170819i
$624$		0			0
$625$	−23.6905	−	7.98512i	−0.947618	−	0.319405i
$626$	−19.9220			−0.796245
$627$		0			0
$628$		−	8.97307i		−	0.358064i
$629$	−3.47061			−0.138382
$630$		0			0
$631$	−8.18568			−0.325867			−0.162933	−	0.986637i	$-0.552096\pi$
$631$	−8.18568			−0.325867			−0.162933	+	0.986637i	$0.552096\pi$
$632$		−	10.9731i		−	0.436485i
$633$		0			0
$634$	3.94614			0.156721
$635$	20.0939	−	17.0670i	0.797402	−	0.677282i
$636$		0			0
$637$			12.1988i			0.483333i
$638$			1.94614i			0.0770485i
$639$		0			0
$640$	1.70429	−	1.44755i	0.0673678	−	0.0572196i
$641$	12.3657			0.488416			0.244208	−	0.969723i	$-0.421472\pi$
$641$	12.3657			0.488416			0.244208	+	0.969723i	$0.421472\pi$
$642$		0			0
$643$			46.8972i			1.84945i	0.380642	+	0.924723i	$0.375703\pi$
$643$			46.8972i			1.84945i	−0.380642	+	0.924723i	$0.624297\pi$
$644$	−34.1339			−1.34506
$645$		0			0
$646$	−5.71015			−0.224663
$647$			26.1878i			1.02955i	0.857326	+	0.514774i	$0.172124\pi$
$647$			26.1878i			1.02955i	−0.857326	+	0.514774i	$0.827876\pi$
$648$		0			0
$649$	1.94614			0.0763927
$650$	0.809179	−	4.93409i	0.0317386	−	0.193531i
$651$		0			0
$652$		−	12.6074i		−	0.493742i
$653$		−	10.7633i		−	0.421200i	−0.977572	−	0.210600i	$-0.932458\pi$
$653$		−	10.7633i		−	0.421200i	0.977572	−	0.210600i	$-0.0675417\pi$
$654$		0			0
$655$	−24.5925	−	28.9541i	−0.960908	−	1.13133i
$656$	−4.81714			−0.188078
$657$		0			0
$658$			1.67222i			0.0651898i
$659$	31.4727			1.22600			0.613001	−	0.790082i	$-0.289962\pi$
$659$	31.4727			1.22600			0.613001	+	0.790082i	$0.289962\pi$
$660$		0			0
$661$	25.2147			0.980739			0.490369	−	0.871515i	$-0.336862\pi$
$661$	25.2147			0.980739			0.490369	+	0.871515i	$0.336862\pi$
$662$		−	21.4245i		−	0.832687i
$663$		0			0
$664$	6.97307			0.270608
$665$	−7.26647	+	6.17185i	−0.281782	+	0.239334i
$666$		0			0
$667$			7.58043i			0.293515i
$668$			23.1609i			0.896120i
$669$		0			0
$670$	−2.59143	−	3.05103i	−0.100116	−	0.117872i
$671$	1.63429			0.0630909
$672$		0			0
$673$		−	23.2388i		−	0.895791i	−0.894086	−	0.447895i	$-0.852174\pi$
$673$		−	23.2388i		−	0.895791i	0.894086	−	0.447895i	$-0.147826\pi$
$674$	−11.2388			−0.432903
$675$		0			0
$676$	1.00000			0.0384615
$677$			47.2629i			1.81646i	0.418470	+	0.908231i	$0.362567\pi$
$677$			47.2629i			1.81646i	−0.418470	+	0.908231i	$0.637433\pi$
$678$		0			0
$679$	−81.5308			−3.12886
$680$	−8.49450	−	10.0010i	−0.325749	−	0.383523i
$681$		0			0
$682$		−	3.58043i		−	0.137102i
$683$		−	6.97307i		−	0.266817i	−0.991061	−	0.133409i	$-0.957408\pi$
$683$		−	6.97307i		−	0.266817i	0.991061	−	0.133409i	$-0.0425922\pi$
$684$		0			0
$685$	−7.17468	+	6.09389i	−0.274130	+	0.232836i
$686$	22.7792			0.869714
$687$		0			0
$688$		−	4.68532i		−	0.178626i
$689$	7.79021			0.296783
$690$		0			0
$691$	−32.2899			−1.22836			−0.614182	−	0.789164i	$-0.710514\pi$
$691$	−32.2899			−1.22836			−0.614182	+	0.789164i	$0.710514\pi$
$692$			19.7902i			0.752311i
$693$		0			0
$694$	16.9490			0.643374
$695$	−8.93409	−	10.5186i	−0.338889	−	0.398993i
$696$		0			0
$697$			28.2678i			1.07072i
$698$		−	10.2119i		−	0.386526i
$699$		0			0
$700$	−21.6194	−	3.54553i	−0.817137	−	0.134009i
$701$	0.521643			0.0197022			0.00985109	−	0.999951i	$-0.496864\pi$
$701$	0.521643			0.0197022			0.00985109	+	0.999951i	$0.496864\pi$
$702$		0			0
$703$		−	0.575502i		−	0.0217055i
$704$	2.00000			0.0753778
$705$		0			0
$706$	−14.9511			−0.562691
$707$			62.8490i			2.36368i
$708$		0			0
$709$	33.2147			1.24740			0.623702	−	0.781662i	$-0.285628\pi$
$709$	33.2147			1.24740			0.623702	+	0.781662i	$0.285628\pi$
$710$	−6.68427	+	5.67736i	−0.250856	+	0.213067i
$711$		0			0
$712$			0.973070i			0.0364674i
$713$		−	13.9461i		−	0.522287i
$714$		0			0
$715$	3.40857	−	2.89511i	0.127473	−	0.108271i
$716$	−6.17185			−0.230653
$717$		0			0
$718$		−	11.8441i		−	0.442017i
$719$	−4.26365			−0.159007			−0.0795036	−	0.996835i	$-0.525334\pi$
$719$	−4.26365			−0.159007			−0.0795036	+	0.996835i	$0.525334\pi$
$720$		0			0
$721$	−42.6612			−1.58879
$722$			18.0531i			0.671868i
$723$		0			0
$724$	19.3706			0.719904
$725$	−0.787388	+	4.80122i	−0.0292429	+	0.178313i
$726$		0			0
$727$			47.5266i			1.76266i	0.472499	+	0.881331i	$0.343352\pi$
$727$			47.5266i			1.76266i	−0.472499	+	0.881331i	$0.656648\pi$
$728$		−	4.38164i		−	0.162394i
$729$		0			0
$730$	−8.68532	−	10.2257i	−0.321458	−	0.378471i
$731$	−27.4943			−1.01691
$732$		0			0
$733$		−	44.8593i		−	1.65692i	−0.560052	−	0.828458i	$-0.689219\pi$
$733$		−	44.8593i		−	1.65692i	0.560052	−	0.828458i	$-0.310781\pi$
$734$	16.0539			0.592559
$735$		0			0
$736$	7.79021			0.287151
$737$		−	3.58043i		−	0.131887i
$738$		0			0
$739$	18.4514			0.678747			0.339373	−	0.940652i	$-0.389785\pi$
$739$	18.4514			0.678747			0.339373	+	0.940652i	$0.389785\pi$
$740$	1.00796	−	0.856125i	0.0370535	−	0.0314718i
$741$		0			0
$742$		−	34.1339i		−	1.25310i
$743$		−	14.2201i		−	0.521684i	−0.965382	−	0.260842i	$-0.916000\pi$
$743$		−	14.2201i		−	0.521684i	0.965382	−	0.260842i	$-0.0840001\pi$
$744$		0			0
$745$		0			0
$746$	6.87100			0.251565
$747$		0			0
$748$		−	11.7364i		−	0.429124i
$749$	25.3706			0.927023
$750$		0			0
$751$	−28.7951			−1.05075			−0.525375	−	0.850871i	$-0.676075\pi$
$751$	−28.7951			−1.05075			−0.525375	+	0.850871i	$0.676075\pi$
$752$		−	0.381642i		−	0.0139170i
$753$		0			0
$754$	−0.973070			−0.0354371
$755$	−22.4406	−	26.4206i	−0.816698	−	0.961545i
$756$		0			0
$757$			13.7364i			0.499256i	0.968342	+	0.249628i	$0.0803084\pi$
$757$			13.7364i			0.499256i	−0.968342	+	0.249628i	$0.919692\pi$
$758$			1.84407i			0.0669797i
$759$		0			0
$760$	1.65839	−	1.40857i	0.0601561	−	0.0510943i
$761$	−5.39264			−0.195483			−0.0977416	−	0.995212i	$-0.531162\pi$
$761$	−5.39264			−0.195483			−0.0977416	+	0.995212i	$0.531162\pi$
$762$		0			0
$763$		−	3.00282i		−	0.108710i
$764$	−3.73635			−0.135177
$765$		0			0
$766$	−9.25264			−0.334312
$767$			0.973070i			0.0351355i
$768$		0			0
$769$	2.34371			0.0845163			0.0422582	−	0.999107i	$-0.486545\pi$
$769$	2.34371			0.0845163			0.0422582	+	0.999107i	$0.486545\pi$
$770$	−12.6853	−	14.9351i	−0.457147	−	0.538225i
$771$		0			0
$772$			15.3706i			0.553201i
$773$		−	29.3547i		−	1.05582i	−0.849302	−	0.527908i	$-0.822977\pi$
$773$		−	29.3547i		−	1.05582i	0.849302	−	0.527908i	$-0.177023\pi$
$774$		0			0
$775$	1.44860	−	8.83307i	0.0520354	−	0.317293i
$776$	18.6074			0.667965
$777$		0			0
$778$			21.2686i			0.762515i
$779$	−4.68742			−0.167944
$780$		0			0
$781$	−7.84407			−0.280683
$782$		−	45.7143i		−	1.63474i
$783$		0			0
$784$	−12.1988			−0.435671
$785$	15.2927	−	12.9890i	0.545819	−	0.463597i
$786$		0			0
$787$			34.6336i			1.23455i	0.786746	+	0.617277i	$0.211764\pi$
$787$			34.6336i			1.23455i	−0.786746	+	0.617277i	$0.788236\pi$
$788$			26.9890i			0.961443i
$789$		0			0
$790$	18.7012	−	15.8841i	0.665360	−	0.565131i
$791$	17.5266			0.623173
$792$		0			0
$793$			0.817143i			0.0290176i
$794$	−33.4727			−1.18790
$795$		0			0
$796$	23.3168			0.826441
$797$		−	27.8221i		−	0.985508i	−0.870169	−	0.492754i	$-0.835990\pi$
$797$		−	27.8221i		−	0.985508i	0.870169	−	0.492754i	$-0.164010\pi$
$798$		0			0
$799$	−2.23954			−0.0792293
$800$	4.93409	+	0.809179i	0.174446	+	0.0286088i
$801$		0			0
$802$			17.7364i			0.626292i
$803$		−	12.0000i		−	0.423471i
$804$		0			0
$805$	−49.4107	−	58.1740i	−1.74150	−	2.05036i
$806$	1.79021			0.0630576
$807$		0			0
$808$		−	14.3437i		−	0.504610i
$809$	−23.1768			−0.814852			−0.407426	−	0.913238i	$-0.633574\pi$
$809$	−23.1768			−0.814852			−0.407426	+	0.913238i	$0.633574\pi$
$810$		0			0
$811$	36.0857			1.26714			0.633570	−	0.773685i	$-0.281589\pi$
$811$	36.0857			1.26714			0.633570	+	0.773685i	$0.281589\pi$
$812$			4.26365i			0.149625i
$813$		0			0
$814$	1.18286			0.0414591
$815$	21.4865	−	18.2498i	0.752641	−	0.639263i
$816$		0			0
$817$		−	4.55915i		−	0.159504i
$818$			7.68249i			0.268612i
$819$		0			0
$820$	−6.97307	−	8.20979i	−0.243510	−	0.286698i
$821$	−38.3196			−1.33736			−0.668682	−	0.743549i	$-0.733141\pi$
$821$	−38.3196			−1.33736			−0.668682	+	0.743549i	$0.733141\pi$
$822$		0			0
$823$		−	53.3486i		−	1.85962i	−0.368044	−	0.929808i	$-0.619973\pi$
$823$		−	53.3486i		−	1.85962i	0.368044	−	0.929808i	$-0.380027\pi$
$824$	9.73635			0.339182
$825$		0			0
$826$	4.26365			0.148351
$827$		−	14.5053i		−	0.504398i	−0.967675	−	0.252199i	$-0.918846\pi$
$827$		−	14.5053i		−	0.504398i	0.967675	−	0.252199i	$-0.0811538\pi$
$828$		0			0
$829$	13.3926			0.465146			0.232573	−	0.972579i	$-0.425286\pi$
$829$	13.3926			0.465146			0.232573	+	0.972579i	$0.425286\pi$
$830$	10.0939	+	11.8841i	0.350364	+	0.412503i
$831$		0			0
$832$			1.00000i			0.0346688i
$833$			71.5846i			2.48026i
$834$		0			0
$835$	−39.4727	+	33.5266i	−1.36601	+	1.16023i
$836$	1.94614			0.0673087
$837$		0			0
$838$		−	11.8061i		−	0.407836i
$839$	2.52164			0.0870568			0.0435284	−	0.999052i	$-0.486140\pi$
$839$	2.52164			0.0870568			0.0435284	+	0.999052i	$0.486140\pi$
$840$		0			0
$841$	−28.0531			−0.967349
$842$			26.3678i			0.908695i
$843$		0			0
$844$	−15.3547			−0.528531
$845$	1.44755	+	1.70429i	0.0497973	+	0.0586292i
$846$		0			0
$847$			30.6715i			1.05388i
$848$			7.79021i			0.267517i
$849$		0			0
$850$	4.74841	−	28.9541i	0.162869	−	0.993118i
$851$	4.60736			0.157938
$852$		0			0
$853$		−	36.4078i		−	1.24658i	−0.781990	−	0.623290i	$-0.785795\pi$
$853$		−	36.4078i		−	1.24658i	0.781990	−	0.623290i	$-0.214205\pi$
$854$	3.58043			0.122520
$855$		0			0
$856$	−5.79021			−0.197905
$857$		−	21.4188i		−	0.731654i	−0.930683	−	0.365827i	$-0.880786\pi$
$857$		−	21.4188i		−	0.731654i	0.930683	−	0.365827i	$-0.119214\pi$
$858$		0			0
$859$	41.9461			1.43118			0.715592	−	0.698519i	$-0.246157\pi$
$859$	41.9461			1.43118			0.715592	+	0.698519i	$0.246157\pi$
$860$	7.98512	−	6.78225i	0.272290	−	0.231273i
$861$		0			0
$862$			1.71225i			0.0583194i
$863$			38.3278i			1.30469i	0.757921	+	0.652346i	$0.226215\pi$
$863$			38.3278i			1.30469i	−0.757921	+	0.652346i	$0.773785\pi$
$864$		0			0
$865$	−33.7282	+	28.6474i	−1.14679	+	0.974040i
$866$	11.9220			0.405127
$867$		0			0
$868$		−	7.84407i		−	0.266245i
$869$	21.9461			0.744472
$870$		0			0
$871$	1.79021			0.0606591
$872$			0.685320i			0.0232078i
$873$		0			0
$874$	7.58043			0.256412
$875$	−25.2526	−	41.9780i	−0.853695	−	1.41912i
$876$		0			0
$877$		−	43.3327i		−	1.46324i	−0.681712	−	0.731621i	$-0.738764\pi$
$877$		−	43.3327i		−	1.46324i	0.681712	−	0.731621i	$-0.261236\pi$
$878$		−	12.3437i		−	0.416580i
$879$		0			0
$880$	2.89511	+	3.40857i	0.0975940	+	0.114903i
$881$	−1.09107			−0.0367590			−0.0183795	−	0.999831i	$-0.505851\pi$
$881$	−1.09107			−0.0367590			−0.0183795	+	0.999831i	$0.505851\pi$
$882$		0			0
$883$		−	28.3735i		−	0.954843i	−0.878674	−	0.477422i	$-0.841571\pi$
$883$		−	28.3735i		−	0.954843i	0.878674	−	0.477422i	$-0.158429\pi$
$884$	5.86818			0.197368
$885$		0			0
$886$	−28.1580			−0.945987
$887$		−	4.50529i		−	0.151273i	−0.997135	−	0.0756364i	$-0.975901\pi$
$887$		−	4.50529i		−	0.151273i	0.997135	−	0.0756364i	$-0.0240988\pi$
$888$		0			0
$889$	51.6605			1.73264
$890$	−1.65839	+	1.40857i	−0.0555894	+	0.0472154i
$891$		0			0
$892$			24.8331i			0.831473i
$893$		−	0.371364i		−	0.0124272i
$894$		0			0
$895$	−8.93409	−	10.5186i	−0.298634	−	0.351598i
$896$	4.38164			0.146380
$897$		0			0
$898$			29.0531i			0.969516i
$899$	−1.74200			−0.0580991
$900$		0			0
$901$	45.7143			1.52297
$902$		−	9.63429i		−	0.320787i
$903$		0			0
$904$	−4.00000			−0.133038
$905$	28.0400	+	33.0131i	0.932082	+	1.09739i
$906$		0			0
$907$		−	48.0503i		−	1.59548i	−0.602999	−	0.797742i	$-0.706028\pi$
$907$		−	48.0503i		−	1.59548i	0.602999	−	0.797742i	$-0.293972\pi$
$908$		−	21.5266i		−	0.714384i
$909$		0			0
$910$	7.46757	−	6.34266i	0.247548	−	0.210257i
$911$	−12.5755			−0.416645			−0.208322	−	0.978060i	$-0.566800\pi$
$911$	−12.5755			−0.416645			−0.208322	+	0.978060i	$0.566800\pi$
$912$		0			0
$913$			13.9461i			0.461550i
$914$	−11.5266			−0.381265
$915$		0			0
$916$	−2.63146			−0.0869459
$917$		−	74.4397i		−	2.45822i
$918$		0			0
$919$	−23.6881			−0.781400			−0.390700	−	0.920518i	$-0.627767\pi$
$919$	−23.6881			−0.781400			−0.390700	+	0.920518i	$0.627767\pi$
$920$	11.2767	+	13.2767i	0.371783	+	0.437721i
$921$		0			0
$922$			28.4217i			0.936018i
$923$		−	3.92204i		−	0.129095i
$924$		0			0
$925$	2.91816	+	0.478572i	0.0959486	+	0.0157353i
$926$	27.4727			0.902809
$927$		0			0
$928$		−	0.973070i		−	0.0319426i
$929$	45.0850			1.47919			0.739595	−	0.673052i	$-0.235017\pi$
$929$	45.0850			1.47919			0.739595	+	0.673052i	$0.235017\pi$
$930$		0			0
$931$	−11.8703			−0.389033
$932$			29.0290i			0.950877i
$933$		0			0
$934$	18.2098			0.595842
$935$	20.0021	−	16.9890i	0.654139	−	0.555600i
$936$		0			0
$937$			28.7951i			0.940696i	0.882481	+	0.470348i	$0.155872\pi$
$937$			28.7951i			0.940696i	−0.882481	+	0.470348i	$0.844128\pi$
$938$		−	7.84407i		−	0.256118i
$939$		0			0
$940$	0.650427	−	0.552447i	0.0212146	−	0.0180188i
$941$	2.84690			0.0928062			0.0464031	−	0.998923i	$-0.485224\pi$
$941$	2.84690			0.0928062			0.0464031	+	0.998923i	$0.485224\pi$
$942$		0			0
$943$		−	37.5266i		−	1.22203i
$944$	−0.973070			−0.0316707
$945$		0			0
$946$	9.37064			0.304666
$947$		−	11.3168i		−	0.367746i	−0.982950	−	0.183873i	$-0.941136\pi$
$947$		−	11.3168i		−	0.367746i	0.982950	−	0.183873i	$-0.0588635\pi$
$948$		0			0
$949$	6.00000			0.194768
$950$	4.80122	+	0.787388i	0.155772	+	0.0255462i
$951$		0			0
$952$		−	25.7122i		−	0.833339i
$953$		−	28.4535i		−	0.921700i	−0.887478	−	0.460850i	$-0.847545\pi$
$953$		−	28.4535i		−	0.921700i	0.887478	−	0.460850i	$-0.152455\pi$
$954$		0			0
$955$	−5.40857	−	6.36781i	−0.175017	−	0.206058i
$956$	−2.13182			−0.0689481
$957$		0			0
$958$			33.6045i			1.08571i
$959$	−18.4458			−0.595645
$960$		0			0
$961$	−27.7951			−0.896617
$962$			0.591429i			0.0190684i
$963$		0			0
$964$	−22.4996			−0.724665
$965$	−26.1960	+	22.2498i	−0.843278	+	0.716247i
$966$		0			0
$967$		−	1.48863i		−	0.0478713i	−0.999714	−	0.0239356i	$-0.992380\pi$
$967$		−	1.48863i		−	0.0478713i	0.999714	−	0.0239356i	$-0.00761968\pi$
$968$		−	7.00000i		−	0.224989i
$969$		0			0
$970$	26.9351	+	31.7122i	0.864835	+	1.01822i
$971$	−49.6446			−1.59317			−0.796585	−	0.604527i	$-0.793362\pi$
$971$	−49.6446			−1.59317			−0.796585	+	0.604527i	$0.793362\pi$
$972$		0			0
$973$		−	27.0429i		−	0.866954i
$974$	8.00000			0.256337
$975$		0			0
$976$	−0.817143			−0.0261561
$977$			39.6066i			1.26713i	0.773690	+	0.633564i	$0.218409\pi$
$977$			39.6066i			1.26713i	−0.773690	+	0.633564i	$0.781591\pi$
$978$		0			0
$979$	−1.94614			−0.0621989
$980$	−17.6584	−	20.7902i	−0.564077	−	0.664119i
$981$		0			0
$982$		−	19.8061i		−	0.632039i
$983$		−	0.725351i		−	0.0231351i	−0.999933	−	0.0115676i	$-0.996318\pi$
$983$		−	0.725351i		−	0.0231351i	0.999933	−	0.0115676i	$-0.00368215\pi$
$984$		0			0
$985$	−45.9970	+	39.0680i	−1.46559	+	1.24481i
$986$	−5.71015			−0.181848
$987$		0			0
$988$			0.973070i			0.0309575i
$989$	36.4996			1.16062
$990$		0			0
$991$	−35.5046			−1.12784			−0.563920	−	0.825830i	$-0.690707\pi$
$991$	−35.5046			−1.12784			−0.563920	+	0.825830i	$0.690707\pi$
$992$			1.79021i			0.0568393i
$993$		0			0
$994$	−17.1850			−0.545074
$995$	33.7523	+	39.7385i	1.07002	+	1.25979i
$996$		0			0
$997$			10.4196i			0.329991i	0.986294	+	0.164996i	$0.0527610\pi$
$997$			10.4196i			0.329991i	−0.986294	+	0.164996i	$0.947239\pi$
$998$			9.12900i			0.288973i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.e.f.469.1		6
3.2	odd	2		130.2.b.a.79.6	yes	6
5.2	odd	4		5850.2.a.cs.1.3		3
5.3	odd	4		5850.2.a.cp.1.1		3
5.4	even	2	inner	1170.2.e.f.469.4		6
12.11	even	2		1040.2.d.b.209.1		6
15.2	even	4		650.2.a.n.1.3		3
15.8	even	4		650.2.a.o.1.1		3
15.14	odd	2		130.2.b.a.79.1	✓	6
39.5	even	4		1690.2.c.d.1689.6		6
39.8	even	4		1690.2.c.a.1689.6		6
39.38	odd	2		1690.2.b.a.339.3		6
60.23	odd	4		5200.2.a.cf.1.3		3
60.47	odd	4		5200.2.a.ce.1.1		3
60.59	even	2		1040.2.d.b.209.6		6
195.38	even	4		8450.2.a.bs.1.1		3
195.44	even	4		1690.2.c.a.1689.1		6
195.77	even	4		8450.2.a.cc.1.3		3
195.164	even	4		1690.2.c.d.1689.1		6
195.194	odd	2		1690.2.b.a.339.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.b.a.79.1	✓	6	15.14	odd	2
130.2.b.a.79.6	yes	6	3.2	odd	2
650.2.a.n.1.3		3	15.2	even	4
650.2.a.o.1.1		3	15.8	even	4
1040.2.d.b.209.1		6	12.11	even	2
1040.2.d.b.209.6		6	60.59	even	2
1170.2.e.f.469.1		6	1.1	even	1	trivial
1170.2.e.f.469.4		6	5.4	even	2	inner
1690.2.b.a.339.3		6	39.38	odd	2
1690.2.b.a.339.4		6	195.194	odd	2
1690.2.c.a.1689.1		6	195.44	even	4
1690.2.c.a.1689.6		6	39.8	even	4
1690.2.c.d.1689.1		6	195.164	even	4
1690.2.c.d.1689.6		6	39.5	even	4
5200.2.a.ce.1.1		3	60.47	odd	4
5200.2.a.cf.1.3		3	60.23	odd	4
5850.2.a.cp.1.1		3	5.3	odd	4
5850.2.a.cs.1.3		3	5.2	odd	4
8450.2.a.bs.1.1		3	195.38	even	4
8450.2.a.cc.1.3		3	195.77	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.44755 - 1.70429i) q^{5} -4.38164i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-1.44755 - 1.70429i) q^{5} -4.38164i q^{7} +1.00000i q^{8} +(-1.70429 + 1.44755i) q^{10} -2.00000 q^{11} -1.00000i q^{13} -4.38164 q^{14} +1.00000 q^{16} -5.86818i q^{17} +0.973070 q^{19} +(1.44755 + 1.70429i) q^{20} +2.00000i q^{22} +7.79021i q^{23} +(-0.809179 + 4.93409i) q^{25} -1.00000 q^{26} +4.38164i q^{28} +0.973070 q^{29} -1.79021 q^{31} -1.00000i q^{32} -5.86818 q^{34} +(-7.46757 + 6.34266i) q^{35} -0.591429i q^{37} -0.973070i q^{38} +(1.70429 - 1.44755i) q^{40} -4.81714 q^{41} -4.68532i q^{43} +2.00000 q^{44} +7.79021 q^{46} -0.381642i q^{47} -12.1988 q^{49} +(4.93409 + 0.809179i) q^{50} +1.00000i q^{52} +7.79021i q^{53} +(2.89511 + 3.40857i) q^{55} +4.38164 q^{56} -0.973070i q^{58} -0.973070 q^{59} -0.817143 q^{61} +1.79021i q^{62} -1.00000 q^{64} +(-1.70429 + 1.44755i) q^{65} +1.79021i q^{67} +5.86818i q^{68} +(6.34266 + 7.46757i) q^{70} +3.92204 q^{71} +6.00000i q^{73} -0.591429 q^{74} -0.973070 q^{76} +8.76328i q^{77} -10.9731 q^{79} +(-1.44755 - 1.70429i) q^{80} +4.81714i q^{82} -6.97307i q^{83} +(-10.0010 + 8.49450i) q^{85} -4.68532 q^{86} -2.00000i q^{88} +0.973070 q^{89} -4.38164 q^{91} -7.79021i q^{92} -0.381642 q^{94} +(-1.40857 - 1.65839i) q^{95} -18.6074i q^{97} +12.1988i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4}+O(q^{10}) \) 6 * q - 6 * q^4	\( 6 q - 6 q^{4} - 4 q^{10} - 12 q^{11} - 4 q^{14} + 6 q^{16} - 4 q^{19} - 16 q^{25} - 6 q^{26} - 4 q^{29} + 24 q^{31} - 8 q^{34} + 6 q^{35} + 4 q^{40} - 4 q^{41} + 12 q^{44} + 12 q^{46} - 26 q^{49} + 16 q^{50} + 4 q^{56} + 4 q^{59} + 20 q^{61} - 6 q^{64} - 4 q^{65} + 12 q^{70} + 16 q^{71} - 16 q^{74} + 4 q^{76} - 56 q^{79} + 28 q^{85} + 24 q^{86} - 4 q^{89} - 4 q^{91} + 20 q^{94} + 4 q^{95}+O(q^{100}) \) 6 * q - 6 * q^4 - 4 * q^10 - 12 * q^11 - 4 * q^14 + 6 * q^16 - 4 * q^19 - 16 * q^25 - 6 * q^26 - 4 * q^29 + 24 * q^31 - 8 * q^34 + 6 * q^35 + 4 * q^40 - 4 * q^41 + 12 * q^44 + 12 * q^46 - 26 * q^49 + 16 * q^50 + 4 * q^56 + 4 * q^59 + 20 * q^61 - 6 * q^64 - 4 * q^65 + 12 * q^70 + 16 * q^71 - 16 * q^74 + 4 * q^76 - 56 * q^79 + 28 * q^85 + 24 * q^86 - 4 * q^89 - 4 * q^91 + 20 * q^94 + 4 * q^95

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