LMFDB - Embedded newform 1710.2.d.f.1369.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1369,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, 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("1710.1369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.d (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1369.6
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	1710.1369
Dual form			1710.2.d.f.1369.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(1.67513 + 1.48119i) q^{5} -3.35026i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.67513 + 1.48119i) q^{5} -3.35026i q^{7} -1.00000i q^{8} +(-1.48119 + 1.67513i) q^{10} +0.962389 q^{11} +1.61213i q^{13} +3.35026 q^{14} +1.00000 q^{16} +0.387873i q^{17} -1.00000 q^{19} +(-1.67513 - 1.48119i) q^{20} +0.962389i q^{22} -0.962389i q^{23} +(0.612127 + 4.96239i) q^{25} -1.61213 q^{26} +3.35026i q^{28} +6.96239 q^{29} +3.35026 q^{31} +1.00000i q^{32} -0.387873 q^{34} +(4.96239 - 5.61213i) q^{35} -1.61213i q^{37} -1.00000i q^{38} +(1.48119 - 1.67513i) q^{40} +9.27504 q^{41} -6.18664i q^{43} -0.962389 q^{44} +0.962389 q^{46} -0.962389i q^{47} -4.22425 q^{49} +(-4.96239 + 0.612127i) q^{50} -1.61213i q^{52} +6.00000i q^{53} +(1.61213 + 1.42548i) q^{55} -3.35026 q^{56} +6.96239i q^{58} +10.3127 q^{59} +11.9248 q^{61} +3.35026i q^{62} -1.00000 q^{64} +(-2.38787 + 2.70052i) q^{65} -7.22425i q^{67} -0.387873i q^{68} +(5.61213 + 4.96239i) q^{70} -7.22425 q^{71} +3.22425i q^{73} +1.61213 q^{74} +1.00000 q^{76} -3.22425i q^{77} +3.35026 q^{79} +(1.67513 + 1.48119i) q^{80} +9.27504i q^{82} +15.0132i q^{83} +(-0.574515 + 0.649738i) q^{85} +6.18664 q^{86} -0.962389i q^{88} +4.64974 q^{89} +5.40105 q^{91} +0.962389i q^{92} +0.962389 q^{94} +(-1.67513 - 1.48119i) q^{95} -10.9624i q^{97} -4.22425i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4}+O(q^{10}) $ 6 * q - 6 * q^4	$ 6 q - 6 q^{4} + 2 q^{10} - 16 q^{11} + 6 q^{16} - 6 q^{19} + 2 q^{25} - 8 q^{26} + 20 q^{29} - 4 q^{34} + 8 q^{35} - 2 q^{40} - 8 q^{41} + 16 q^{44} - 16 q^{46} - 22 q^{49} - 8 q^{50} + 8 q^{55} + 20 q^{59} + 28 q^{61} - 6 q^{64} - 16 q^{65} + 32 q^{70} - 40 q^{71} + 8 q^{74} + 6 q^{76} + 20 q^{85} + 12 q^{86} + 48 q^{89} - 48 q^{91} - 16 q^{94}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^10 - 16 * q^11 + 6 * q^16 - 6 * q^19 + 2 * q^25 - 8 * q^26 + 20 * q^29 - 4 * q^34 + 8 * q^35 - 2 * q^40 - 8 * q^41 + 16 * q^44 - 16 * q^46 - 22 * q^49 - 8 * q^50 + 8 * q^55 + 20 * q^59 + 28 * q^61 - 6 * q^64 - 16 * q^65 + 32 * q^70 - 40 * q^71 + 8 * q^74 + 6 * q^76 + 20 * q^85 + 12 * q^86 + 48 * q^89 - 48 * q^91 - 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$1$

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
$5$	1.67513	+	1.48119i	0.749141	+	0.662410i
$5$	1.67513	+	1.48119i	0.749141	+	0.662410i
$6$		0			0
$7$		−	3.35026i		−	1.26628i	−0.774037	−	0.633140i	$-0.781766\pi$
$7$		−	3.35026i		−	1.26628i	0.774037	−	0.633140i	$-0.218234\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.48119	+	1.67513i	−0.468395	+	0.529723i
$11$	0.962389			0.290171			0.145086	−	0.989419i	$-0.453654\pi$
$11$	0.962389			0.290171			0.145086	+	0.989419i	$0.453654\pi$
$12$		0			0
$13$			1.61213i			0.447124i	0.974690	+	0.223562i	$0.0717684\pi$
$13$			1.61213i			0.447124i	−0.974690	+	0.223562i	$0.928232\pi$
$14$	3.35026			0.895395
$15$		0			0
$16$	1.00000			0.250000
$17$			0.387873i			0.0940731i	0.998893	+	0.0470365i	$0.0149777\pi$
$17$			0.387873i			0.0940731i	−0.998893	+	0.0470365i	$0.985022\pi$
$18$		0			0
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−1.67513	−	1.48119i	−0.374571	−	0.331205i
$21$		0			0
$22$			0.962389i			0.205182i
$23$		−	0.962389i		−	0.200672i	−0.994954	−	0.100336i	$-0.968008\pi$
$23$		−	0.962389i		−	0.200672i	0.994954	−	0.100336i	$-0.0319918\pi$
$24$		0			0
$25$	0.612127	+	4.96239i	0.122425	+	0.992478i
$26$	−1.61213			−0.316164
$27$		0			0
$28$			3.35026i			0.633140i
$29$	6.96239			1.29288			0.646442	−	0.762964i	$-0.276256\pi$
$29$	6.96239			1.29288			0.646442	+	0.762964i	$0.276256\pi$
$30$		0			0
$31$	3.35026			0.601725			0.300862	−	0.953668i	$-0.402726\pi$
$31$	3.35026			0.601725			0.300862	+	0.953668i	$0.402726\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−0.387873			−0.0665197
$35$	4.96239	−	5.61213i	0.838797	−	0.948623i
$36$		0			0
$37$		−	1.61213i		−	0.265032i	−0.991181	−	0.132516i	$-0.957694\pi$
$37$		−	1.61213i		−	0.265032i	0.991181	−	0.132516i	$-0.0423056\pi$
$38$		−	1.00000i		−	0.162221i
$39$		0			0
$40$	1.48119	−	1.67513i	0.234197	−	0.264861i
$41$	9.27504			1.44852			0.724259	−	0.689528i	$-0.242182\pi$
$41$	9.27504			1.44852			0.724259	+	0.689528i	$0.242182\pi$
$42$		0			0
$43$		−	6.18664i		−	0.943454i	−0.881745	−	0.471727i	$-0.843631\pi$
$43$		−	6.18664i		−	0.943454i	0.881745	−	0.471727i	$-0.156369\pi$
$44$	−0.962389			−0.145086
$45$		0			0
$46$	0.962389			0.141896
$47$		−	0.962389i		−	0.140379i	−0.997534	−	0.0701894i	$-0.977640\pi$
$47$		−	0.962389i		−	0.140379i	0.997534	−	0.0701894i	$-0.0223604\pi$
$48$		0			0
$49$	−4.22425			−0.603465
$50$	−4.96239	+	0.612127i	−0.701788	+	0.0865678i
$51$		0			0
$52$		−	1.61213i		−	0.223562i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$	1.61213	+	1.42548i	0.217379	+	0.192212i
$56$	−3.35026			−0.447698
$57$		0			0
$58$			6.96239i			0.914206i
$59$	10.3127			1.34259			0.671296	−	0.741189i	$-0.265738\pi$
$59$	10.3127			1.34259			0.671296	+	0.741189i	$0.265738\pi$
$60$		0			0
$61$	11.9248			1.52681			0.763406	−	0.645919i	$-0.223526\pi$
$61$	11.9248			1.52681			0.763406	+	0.645919i	$0.223526\pi$
$62$			3.35026i			0.425484i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.38787	+	2.70052i	−0.296179	+	0.334959i
$66$		0			0
$67$		−	7.22425i		−	0.882583i	−0.897364	−	0.441292i	$-0.854520\pi$
$67$		−	7.22425i		−	0.882583i	0.897364	−	0.441292i	$-0.145480\pi$
$68$		−	0.387873i		−	0.0470365i
$69$		0			0
$70$	5.61213	+	4.96239i	0.670777	+	0.593119i
$71$	−7.22425			−0.857361			−0.428681	−	0.903456i	$-0.641021\pi$
$71$	−7.22425			−0.857361			−0.428681	+	0.903456i	$0.641021\pi$
$72$		0			0
$73$			3.22425i			0.377370i	0.982038	+	0.188685i	$0.0604226\pi$
$73$			3.22425i			0.377370i	−0.982038	+	0.188685i	$0.939577\pi$
$74$	1.61213			0.187406
$75$		0			0
$76$	1.00000			0.114708
$77$		−	3.22425i		−	0.367438i
$78$		0			0
$79$	3.35026			0.376934			0.188467	−	0.982080i	$-0.439648\pi$
$79$	3.35026			0.376934			0.188467	+	0.982080i	$0.439648\pi$
$80$	1.67513	+	1.48119i	0.187285	+	0.165603i
$81$		0			0
$82$			9.27504i			1.02426i
$83$			15.0132i			1.64791i	0.566655	+	0.823955i	$0.308237\pi$
$83$			15.0132i			1.64791i	−0.566655	+	0.823955i	$0.691763\pi$
$84$		0			0
$85$	−0.574515	+	0.649738i	−0.0623150	+	0.0704740i
$86$	6.18664			0.667123
$87$		0			0
$88$		−	0.962389i		−	0.102591i
$89$	4.64974			0.492871			0.246436	−	0.969159i	$-0.420741\pi$
$89$	4.64974			0.492871			0.246436	+	0.969159i	$0.420741\pi$
$90$		0			0
$91$	5.40105			0.566184
$92$			0.962389i			0.100336i
$93$		0			0
$94$	0.962389			0.0992628
$95$	−1.67513	−	1.48119i	−0.171865	−	0.151967i
$96$		0			0
$97$		−	10.9624i		−	1.11306i	−0.830827	−	0.556531i	$-0.812132\pi$
$97$		−	10.9624i		−	1.11306i	0.830827	−	0.556531i	$-0.187868\pi$
$98$		−	4.22425i		−	0.426714i
$99$		0			0
$100$	−0.612127	−	4.96239i	−0.0612127	−	0.496239i
$101$	−2.72496			−0.271144			−0.135572	−	0.990768i	$-0.543287\pi$
$101$	−2.72496			−0.271144			−0.135572	+	0.990768i	$0.543287\pi$
$102$		0			0
$103$		−	0.574515i		−	0.0566087i	−0.999599	−	0.0283043i	$-0.990989\pi$
$103$		−	0.574515i		−	0.0566087i	0.999599	−	0.0283043i	$-0.00901076\pi$
$104$	1.61213			0.158082
$105$		0			0
$106$	−6.00000			−0.582772
$107$		−	10.7005i		−	1.03446i	−0.855847	−	0.517229i	$-0.826963\pi$
$107$		−	10.7005i		−	1.03446i	0.855847	−	0.517229i	$-0.173037\pi$
$108$		0			0
$109$	−10.1260			−0.969896			−0.484948	−	0.874543i	$-0.661161\pi$
$109$	−10.1260			−0.969896			−0.484948	+	0.874543i	$0.661161\pi$
$110$	−1.42548	+	1.61213i	−0.135915	+	0.153710i
$111$		0			0
$112$		−	3.35026i		−	0.316570i
$113$			20.5501i			1.93319i	0.256311	+	0.966594i	$0.417493\pi$
$113$			20.5501i			1.93319i	−0.256311	+	0.966594i	$0.582507\pi$
$114$		0			0
$115$	1.42548	−	1.61213i	0.132927	−	0.150332i
$116$	−6.96239			−0.646442
$117$		0			0
$118$			10.3127i			0.949356i
$119$	1.29948			0.119123
$120$		0			0
$121$	−10.0738			−0.915801
$122$			11.9248i			1.07962i
$123$		0			0
$124$	−3.35026			−0.300862
$125$	−6.32487	+	9.21933i	−0.565713	+	0.824602i
$126$		0			0
$127$			1.35026i			0.119816i	0.998204	+	0.0599082i	$0.0190808\pi$
$127$			1.35026i			0.119816i	−0.998204	+	0.0599082i	$0.980919\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−2.70052	−	2.38787i	−0.236852	−	0.209430i
$131$	−12.4387			−1.08677			−0.543385	−	0.839483i	$-0.682858\pi$
$131$	−12.4387			−1.08677			−0.543385	+	0.839483i	$0.682858\pi$
$132$		0			0
$133$			3.35026i			0.290505i
$134$	7.22425			0.624080
$135$		0			0
$136$	0.387873			0.0332598
$137$			18.1622i			1.55170i	0.630916	+	0.775851i	$0.282679\pi$
$137$			18.1622i			1.55170i	−0.630916	+	0.775851i	$0.717321\pi$
$138$		0			0
$139$	−8.77575			−0.744349			−0.372175	−	0.928163i	$-0.621388\pi$
$139$	−8.77575			−0.744349			−0.372175	+	0.928163i	$0.621388\pi$
$140$	−4.96239	+	5.61213i	−0.419398	+	0.474311i
$141$		0			0
$142$		−	7.22425i		−	0.606246i
$143$			1.55149i			0.129742i
$144$		0			0
$145$	11.6629	+	10.3127i	0.968552	+	0.856419i
$146$	−3.22425			−0.266841
$147$		0			0
$148$			1.61213i			0.132516i
$149$	15.9756			1.30877			0.654385	−	0.756162i	$-0.272928\pi$
$149$	15.9756			1.30877			0.654385	+	0.756162i	$0.272928\pi$
$150$		0			0
$151$	18.4241			1.49933			0.749665	−	0.661818i	$-0.230215\pi$
$151$	18.4241			1.49933			0.749665	+	0.661818i	$0.230215\pi$
$152$			1.00000i			0.0811107i
$153$		0			0
$154$	3.22425			0.259818
$155$	5.61213	+	4.96239i	0.450777	+	0.398589i
$156$		0			0
$157$		−	13.7889i		−	1.10048i	−0.835008	−	0.550238i	$-0.814537\pi$
$157$		−	13.7889i		−	1.10048i	0.835008	−	0.550238i	$-0.185463\pi$
$158$			3.35026i			0.266533i
$159$		0			0
$160$	−1.48119	+	1.67513i	−0.117099	+	0.132431i
$161$	−3.22425			−0.254107
$162$		0			0
$163$			3.73813i			0.292793i	0.989226	+	0.146397i	$0.0467676\pi$
$163$			3.73813i			0.292793i	−0.989226	+	0.146397i	$0.953232\pi$
$164$	−9.27504			−0.724259
$165$		0			0
$166$	−15.0132			−1.16525
$167$		−	15.4763i		−	1.19759i	−0.800902	−	0.598795i	$-0.795646\pi$
$167$		−	15.4763i		−	1.19759i	0.800902	−	0.598795i	$-0.204354\pi$
$168$		0			0
$169$	10.4010			0.800081
$170$	−0.649738	−	0.574515i	−0.0498326	−	0.0440633i
$171$		0			0
$172$			6.18664i			0.471727i
$173$		−	1.47627i		−	0.112239i	−0.998424	−	0.0561194i	$-0.982127\pi$
$173$		−	1.47627i		−	0.112239i	0.998424	−	0.0561194i	$-0.0178727\pi$
$174$		0			0
$175$	16.6253	−	2.05079i	1.25675	−	0.155025i
$176$	0.962389			0.0725428
$177$		0			0
$178$			4.64974i			0.348513i
$179$	−14.3127			−1.06978			−0.534889	−	0.844922i	$-0.679647\pi$
$179$	−14.3127			−1.06978			−0.534889	+	0.844922i	$0.679647\pi$
$180$		0			0
$181$	−8.82653			−0.656071			−0.328035	−	0.944665i	$-0.606387\pi$
$181$	−8.82653			−0.656071			−0.328035	+	0.944665i	$0.606387\pi$
$182$			5.40105i			0.400352i
$183$		0			0
$184$	−0.962389			−0.0709482
$185$	2.38787	−	2.70052i	0.175560	−	0.198546i
$186$		0			0
$187$			0.373285i			0.0272973i
$188$			0.962389i			0.0701894i
$189$		0			0
$190$	1.48119	−	1.67513i	0.107457	−	0.121527i
$191$	−2.31265			−0.167338			−0.0836688	−	0.996494i	$-0.526664\pi$
$191$	−2.31265			−0.167338			−0.0836688	+	0.996494i	$0.526664\pi$
$192$		0			0
$193$		−	7.58769i		−	0.546174i	−0.961989	−	0.273087i	$-0.911955\pi$
$193$		−	7.58769i		−	0.546174i	0.961989	−	0.273087i	$-0.0880447\pi$
$194$	10.9624			0.787054
$195$		0			0
$196$	4.22425			0.301732
$197$			18.8119i			1.34030i	0.742228	+	0.670148i	$0.233769\pi$
$197$			18.8119i			1.34030i	−0.742228	+	0.670148i	$0.766231\pi$
$198$		0			0
$199$	9.40105			0.666423			0.333211	−	0.942852i	$-0.391868\pi$
$199$	9.40105			0.666423			0.333211	+	0.942852i	$0.391868\pi$
$200$	4.96239	−	0.612127i	0.350894	−	0.0432839i
$201$		0			0
$202$		−	2.72496i		−	0.191728i
$203$		−	23.3258i		−	1.63715i
$204$		0			0
$205$	15.5369	+	13.7381i	1.08514	+	0.959513i
$206$	0.574515			0.0400284
$207$		0			0
$208$			1.61213i			0.111781i
$209$	−0.962389			−0.0665698
$210$		0			0
$211$	4.77575			0.328776			0.164388	−	0.986396i	$-0.447435\pi$
$211$	4.77575			0.328776			0.164388	+	0.986396i	$0.447435\pi$
$212$		−	6.00000i		−	0.412082i
$213$		0			0
$214$	10.7005			0.731473
$215$	9.16362	−	10.3634i	0.624954	−	0.706780i
$216$		0			0
$217$		−	11.2243i		−	0.761952i
$218$		−	10.1260i		−	0.685820i
$219$		0			0
$220$	−1.61213	−	1.42548i	−0.108690	−	0.0961061i
$221$	−0.625301			−0.0420623
$222$		0			0
$223$			24.6761i			1.65243i	0.563353	+	0.826216i	$0.309511\pi$
$223$			24.6761i			1.65243i	−0.563353	+	0.826216i	$0.690489\pi$
$224$	3.35026			0.223849
$225$		0			0
$226$	−20.5501			−1.36697
$227$		−	15.4763i		−	1.02720i	−0.858031	−	0.513598i	$-0.828312\pi$
$227$		−	15.4763i		−	1.02720i	0.858031	−	0.513598i	$-0.171688\pi$
$228$		0			0
$229$	−21.3258			−1.40925			−0.704625	−	0.709580i	$-0.748885\pi$
$229$	−21.3258			−1.40925			−0.704625	+	0.709580i	$0.748885\pi$
$230$	1.61213	+	1.42548i	0.106300	+	0.0939937i
$231$		0			0
$232$		−	6.96239i		−	0.457103i
$233$		−	9.01317i		−	0.590473i	−0.955424	−	0.295236i	$-0.904602\pi$
$233$		−	9.01317i		−	0.590473i	0.955424	−	0.295236i	$-0.0953984\pi$
$234$		0			0
$235$	1.42548	−	1.61213i	0.0929884	−	0.105164i
$236$	−10.3127			−0.671296
$237$		0			0
$238$			1.29948i			0.0842326i
$239$	−0.135857			−0.00878787			−0.00439393	−	0.999990i	$-0.501399\pi$
$239$	−0.135857			−0.00878787			−0.00439393	+	0.999990i	$0.501399\pi$
$240$		0			0
$241$	−25.8496			−1.66512			−0.832558	−	0.553938i	$-0.813125\pi$
$241$	−25.8496			−1.66512			−0.832558	+	0.553938i	$0.813125\pi$
$242$		−	10.0738i		−	0.647569i
$243$		0			0
$244$	−11.9248			−0.763406
$245$	−7.07618	−	6.25694i	−0.452080	−	0.399741i
$246$		0			0
$247$		−	1.61213i		−	0.102577i
$248$		−	3.35026i		−	0.212742i
$249$		0			0
$250$	−9.21933	−	6.32487i	−0.583082	−	0.400020i
$251$	10.1114			0.638227			0.319114	−	0.947716i	$-0.396615\pi$
$251$	10.1114			0.638227			0.319114	+	0.947716i	$0.396615\pi$
$252$		0			0
$253$		−	0.926192i		−	0.0582292i
$254$	−1.35026			−0.0847230
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	26.9986i		−	1.68413i	−0.539380	−	0.842063i	$-0.681341\pi$
$257$		−	26.9986i		−	1.68413i	0.539380	−	0.842063i	$-0.318659\pi$
$258$		0			0
$259$	−5.40105			−0.335605
$260$	2.38787	−	2.70052i	0.148090	−	0.167479i
$261$		0			0
$262$		−	12.4387i		−	0.768463i
$263$			15.0376i			0.927259i	0.886029	+	0.463629i	$0.153453\pi$
$263$			15.0376i			0.927259i	−0.886029	+	0.463629i	$0.846547\pi$
$264$		0			0
$265$	−8.88717	+	10.0508i	−0.545934	+	0.617415i
$266$	−3.35026			−0.205418
$267$		0			0
$268$			7.22425i			0.441292i
$269$	−4.51388			−0.275216			−0.137608	−	0.990487i	$-0.543941\pi$
$269$	−4.51388			−0.275216			−0.137608	+	0.990487i	$0.543941\pi$
$270$		0			0
$271$	15.8496			0.962792			0.481396	−	0.876503i	$-0.340130\pi$
$271$	15.8496			0.962792			0.481396	+	0.876503i	$0.340130\pi$
$272$			0.387873i			0.0235183i
$273$		0			0
$274$	−18.1622			−1.09722
$275$	0.589104	+	4.77575i	0.0355243	+	0.287988i
$276$		0			0
$277$			10.3127i			0.619627i	0.950797	+	0.309814i	$0.100267\pi$
$277$			10.3127i			0.619627i	−0.950797	+	0.309814i	$0.899733\pi$
$278$		−	8.77575i		−	0.526334i
$279$		0			0
$280$	−5.61213	−	4.96239i	−0.335389	−	0.296559i
$281$	−24.3488			−1.45253			−0.726265	−	0.687415i	$-0.758746\pi$
$281$	−24.3488			−1.45253			−0.726265	+	0.687415i	$0.758746\pi$
$282$		0			0
$283$		−	26.2882i		−	1.56267i	−0.624111	−	0.781336i	$-0.714539\pi$
$283$		−	26.2882i		−	1.56267i	0.624111	−	0.781336i	$-0.285461\pi$
$284$	7.22425			0.428681
$285$		0			0
$286$	−1.55149			−0.0917417
$287$		−	31.0738i		−	1.83423i
$288$		0			0
$289$	16.8496			0.991150
$290$	−10.3127	+	11.6629i	−0.605580	+	0.684870i
$291$		0			0
$292$		−	3.22425i		−	0.188685i
$293$		−	13.0738i		−	0.763780i	−0.924208	−	0.381890i	$-0.875273\pi$
$293$		−	13.0738i		−	0.763780i	0.924208	−	0.381890i	$-0.124727\pi$
$294$		0			0
$295$	17.2750	+	15.2750i	1.00579	+	0.889347i
$296$	−1.61213			−0.0937030
$297$		0			0
$298$			15.9756i			0.925439i
$299$	1.55149			0.0897251
$300$		0			0
$301$	−20.7269			−1.19468
$302$			18.4241i			1.06019i
$303$		0			0
$304$	−1.00000			−0.0573539
$305$	19.9756	+	17.6629i	1.14380	+	1.01138i
$306$		0			0
$307$		−	7.07381i		−	0.403724i	−0.979414	−	0.201862i	$-0.935301\pi$
$307$		−	7.07381i		−	0.403724i	0.979414	−	0.201862i	$-0.0646992\pi$
$308$			3.22425i			0.183719i
$309$		0			0
$310$	−4.96239	+	5.61213i	−0.281845	+	0.318747i
$311$	−26.3127			−1.49205			−0.746027	−	0.665916i	$-0.768041\pi$
$311$	−26.3127			−1.49205			−0.746027	+	0.665916i	$0.768041\pi$
$312$		0			0
$313$			18.7005i			1.05702i	0.848928	+	0.528508i	$0.177248\pi$
$313$			18.7005i			1.05702i	−0.848928	+	0.528508i	$0.822752\pi$
$314$	13.7889			0.778154
$315$		0			0
$316$	−3.35026			−0.188467
$317$		−	26.4749i		−	1.48698i	−0.668749	−	0.743488i	$-0.733170\pi$
$317$		−	26.4749i		−	1.48698i	0.668749	−	0.743488i	$-0.266830\pi$
$318$		0			0
$319$	6.70052			0.375157
$320$	−1.67513	−	1.48119i	−0.0936427	−	0.0828013i
$321$		0			0
$322$		−	3.22425i		−	0.179681i
$323$		−	0.387873i		−	0.0215818i
$324$		0			0
$325$	−8.00000	+	0.986826i	−0.443760	+	0.0547393i
$326$	−3.73813			−0.207036
$327$		0			0
$328$		−	9.27504i		−	0.512128i
$329$	−3.22425			−0.177759
$330$		0			0
$331$	−30.7005			−1.68745			−0.843727	−	0.536773i	$-0.819643\pi$
$331$	−30.7005			−1.68745			−0.843727	+	0.536773i	$0.819643\pi$
$332$		−	15.0132i		−	0.823955i
$333$		0			0
$334$	15.4763			0.846824
$335$	10.7005	−	12.1016i	0.584632	−	0.661179i
$336$		0			0
$337$			6.81194i			0.371070i	0.982638	+	0.185535i	$0.0594018\pi$
$337$			6.81194i			0.371070i	−0.982638	+	0.185535i	$0.940598\pi$
$338$			10.4010i			0.565742i
$339$		0			0
$340$	0.574515	−	0.649738i	0.0311575	−	0.0352370i
$341$	3.22425			0.174603
$342$		0			0
$343$		−	9.29948i		−	0.502125i
$344$	−6.18664			−0.333561
$345$		0			0
$346$	1.47627			0.0793648
$347$		−	18.3879i		−	0.987113i	−0.869714	−	0.493556i	$-0.835697\pi$
$347$		−	18.3879i		−	0.987113i	0.869714	−	0.493556i	$-0.164303\pi$
$348$		0			0
$349$	−31.1490			−1.66737			−0.833685	−	0.552241i	$-0.813773\pi$
$349$	−31.1490			−1.66737			−0.833685	+	0.552241i	$0.813773\pi$
$350$	2.05079	+	16.6253i	0.109619	+	0.888660i
$351$		0			0
$352$			0.962389i			0.0512955i
$353$			7.61213i			0.405153i	0.979266	+	0.202576i	$0.0649314\pi$
$353$			7.61213i			0.405153i	−0.979266	+	0.202576i	$0.935069\pi$
$354$		0			0
$355$	−12.1016	−	10.7005i	−0.642285	−	0.567925i
$356$	−4.64974			−0.246436
$357$		0			0
$358$		−	14.3127i		−	0.756447i
$359$	−35.3112			−1.86366			−0.931828	−	0.362901i	$-0.881786\pi$
$359$	−35.3112			−1.86366			−0.931828	+	0.362901i	$0.881786\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		−	8.82653i		−	0.463912i
$363$		0			0
$364$	−5.40105			−0.283092
$365$	−4.77575	+	5.40105i	−0.249974	+	0.282704i
$366$		0			0
$367$			31.9756i			1.66911i	0.550924	+	0.834555i	$0.314275\pi$
$367$			31.9756i			1.66911i	−0.550924	+	0.834555i	$0.685725\pi$
$368$		−	0.962389i		−	0.0501680i
$369$		0			0
$370$	2.70052	+	2.38787i	0.140394	+	0.124140i
$371$	20.1016			1.04362
$372$		0			0
$373$		−	26.4894i		−	1.37157i	−0.727804	−	0.685786i	$-0.759459\pi$
$373$		−	26.4894i		−	1.37157i	0.727804	−	0.685786i	$-0.240541\pi$
$374$	−0.373285			−0.0193021
$375$		0			0
$376$	−0.962389			−0.0496314
$377$			11.2243i			0.578078i
$378$		0			0
$379$	19.3258			0.992701			0.496350	−	0.868122i	$-0.334673\pi$
$379$	19.3258			0.992701			0.496350	+	0.868122i	$0.334673\pi$
$380$	1.67513	+	1.48119i	0.0859324	+	0.0759837i
$381$		0			0
$382$		−	2.31265i		−	0.118325i
$383$			3.37470i			0.172439i	0.996276	+	0.0862195i	$0.0274786\pi$
$383$			3.37470i			0.172439i	−0.996276	+	0.0862195i	$0.972521\pi$
$384$		0			0
$385$	4.77575	−	5.40105i	0.243395	−	0.275263i
$386$	7.58769			0.386203
$387$		0			0
$388$			10.9624i			0.556531i
$389$	−11.3503			−0.575481			−0.287741	−	0.957708i	$-0.592904\pi$
$389$	−11.3503			−0.575481			−0.287741	+	0.957708i	$0.592904\pi$
$390$		0			0
$391$	0.373285			0.0188778
$392$			4.22425i			0.213357i
$393$		0			0
$394$	−18.8119			−0.947732
$395$	5.61213	+	4.96239i	0.282377	+	0.249685i
$396$		0			0
$397$		−	18.8364i		−	0.945371i	−0.881231	−	0.472685i	$-0.843285\pi$
$397$		−	18.8364i		−	0.945371i	0.881231	−	0.472685i	$-0.156715\pi$
$398$			9.40105i			0.471232i
$399$		0			0
$400$	0.612127	+	4.96239i	0.0306063	+	0.248119i
$401$	4.12601			0.206043			0.103022	−	0.994679i	$-0.467149\pi$
$401$	4.12601			0.206043			0.103022	+	0.994679i	$0.467149\pi$
$402$		0			0
$403$			5.40105i			0.269045i
$404$	2.72496			0.135572
$405$		0			0
$406$	23.3258			1.15764
$407$		−	1.55149i		−	0.0769046i
$408$		0			0
$409$	−2.52373			−0.124790			−0.0623952	−	0.998052i	$-0.519874\pi$
$409$	−2.52373			−0.124790			−0.0623952	+	0.998052i	$0.519874\pi$
$410$	−13.7381	+	15.5369i	−0.678478	+	0.767313i
$411$		0			0
$412$			0.574515i			0.0283043i
$413$		−	34.5501i		−	1.70010i
$414$		0			0
$415$	−22.2374	+	25.1490i	−1.09159	+	1.23452i
$416$	−1.61213			−0.0790410
$417$		0			0
$418$		−	0.962389i		−	0.0470720i
$419$	7.51247			0.367008			0.183504	−	0.983019i	$-0.441256\pi$
$419$	7.51247			0.367008			0.183504	+	0.983019i	$0.441256\pi$
$420$		0			0
$421$	3.67750			0.179230			0.0896152	−	0.995976i	$-0.471436\pi$
$421$	3.67750			0.179230			0.0896152	+	0.995976i	$0.471436\pi$
$422$			4.77575i			0.232480i
$423$		0			0
$424$	6.00000			0.291386
$425$	−1.92478	+	0.237428i	−0.0933654	+	0.0115169i
$426$		0			0
$427$		−	39.9511i		−	1.93337i
$428$			10.7005i			0.517229i
$429$		0			0
$430$	10.3634	+	9.16362i	0.499769	+	0.441909i
$431$	10.3272			0.497446			0.248723	−	0.968575i	$-0.419989\pi$
$431$	10.3272			0.497446			0.248723	+	0.968575i	$0.419989\pi$
$432$		0			0
$433$		−	31.5877i		−	1.51801i	−0.651086	−	0.759004i	$-0.725686\pi$
$433$		−	31.5877i		−	1.51801i	0.651086	−	0.759004i	$-0.274314\pi$
$434$	11.2243			0.538781
$435$		0			0
$436$	10.1260			0.484948
$437$			0.962389i			0.0460373i
$438$		0			0
$439$	38.1524			1.82091			0.910456	−	0.413605i	$-0.135731\pi$
$439$	38.1524			1.82091			0.910456	+	0.413605i	$0.135731\pi$
$440$	1.42548	−	1.61213i	0.0679573	−	0.0768551i
$441$		0			0
$442$		−	0.625301i		−	0.0297425i
$443$			16.3127i			0.775037i	0.921862	+	0.387519i	$0.126668\pi$
$443$			16.3127i			0.775037i	−0.921862	+	0.387519i	$0.873332\pi$
$444$		0			0
$445$	7.78892	+	6.88717i	0.369230	+	0.326483i
$446$	−24.6761			−1.16845
$447$		0			0
$448$			3.35026i			0.158285i
$449$	−37.5271			−1.77101			−0.885506	−	0.464629i	$-0.846188\pi$
$449$	−37.5271			−1.77101			−0.885506	+	0.464629i	$0.846188\pi$
$450$		0			0
$451$	8.92619			0.420318
$452$		−	20.5501i		−	0.966594i
$453$		0			0
$454$	15.4763			0.726337
$455$	9.04746	+	8.00000i	0.424151	+	0.375046i
$456$		0			0
$457$		−	8.00000i		−	0.374224i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$		−	8.00000i		−	0.374224i	0.982339	−	0.187112i	$-0.0599128\pi$
$458$		−	21.3258i		−	0.996490i
$459$		0			0
$460$	−1.42548	+	1.61213i	−0.0664636	+	0.0751658i
$461$	−12.3780			−0.576502			−0.288251	−	0.957555i	$-0.593074\pi$
$461$	−12.3780			−0.576502			−0.288251	+	0.957555i	$0.593074\pi$
$462$		0			0
$463$		−	32.4504i		−	1.50810i	−0.656818	−	0.754049i	$-0.728098\pi$
$463$		−	32.4504i		−	1.50810i	0.656818	−	0.754049i	$-0.271902\pi$
$464$	6.96239			0.323221
$465$		0			0
$466$	9.01317			0.417527
$467$		−	7.53690i		−	0.348766i	−0.984678	−	0.174383i	$-0.944207\pi$
$467$		−	7.53690i		−	0.348766i	0.984678	−	0.174383i	$-0.0557931\pi$
$468$		0			0
$469$	−24.2031			−1.11760
$470$	1.61213	+	1.42548i	0.0743619	+	0.0657527i
$471$		0			0
$472$		−	10.3127i		−	0.474678i
$473$		−	5.95395i		−	0.273763i
$474$		0			0
$475$	−0.612127	−	4.96239i	−0.0280863	−	0.227690i
$476$	−1.29948			−0.0595614
$477$		0			0
$478$		−	0.135857i		−	0.00621396i
$479$	15.2097			0.694947			0.347474	−	0.937690i	$-0.387040\pi$
$479$	15.2097			0.694947			0.347474	+	0.937690i	$0.387040\pi$
$480$		0			0
$481$	2.59895			0.118502
$482$		−	25.8496i		−	1.17741i
$483$		0			0
$484$	10.0738			0.457900
$485$	16.2374	−	18.3634i	0.737304	−	0.833841i
$486$		0			0
$487$		−	1.19982i		−	0.0543689i	−0.999630	−	0.0271844i	$-0.991346\pi$
$487$		−	1.19982i		−	0.0543689i	0.999630	−	0.0271844i	$-0.00865414\pi$
$488$		−	11.9248i		−	0.539809i
$489$		0			0
$490$	6.25694	−	7.07618i	0.282660	−	0.319669i
$491$	5.11283			0.230739			0.115369	−	0.993323i	$-0.463195\pi$
$491$	5.11283			0.230739			0.115369	+	0.993323i	$0.463195\pi$
$492$		0			0
$493$			2.70052i			0.121625i
$494$	1.61213			0.0725330
$495$		0			0
$496$	3.35026			0.150431
$497$			24.2031i			1.08566i
$498$		0			0
$499$	−14.2981			−0.640069			−0.320035	−	0.947406i	$-0.603695\pi$
$499$	−14.2981			−0.640069			−0.320035	+	0.947406i	$0.603695\pi$
$500$	6.32487	−	9.21933i	0.282857	−	0.412301i
$501$		0			0
$502$			10.1114i			0.451295i
$503$			11.5125i			0.513316i	0.966502	+	0.256658i	$0.0826213\pi$
$503$			11.5125i			0.513316i	−0.966502	+	0.256658i	$0.917379\pi$
$504$		0			0
$505$	−4.56467	−	4.03620i	−0.203125	−	0.179608i
$506$	0.926192			0.0411742
$507$		0			0
$508$		−	1.35026i		−	0.0599082i
$509$	−31.9610			−1.41665			−0.708323	−	0.705889i	$-0.750548\pi$
$509$	−31.9610			−1.41665			−0.708323	+	0.705889i	$0.750548\pi$
$510$		0			0
$511$	10.8021			0.477857
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	26.9986			1.19086
$515$	0.850969	−	0.962389i	0.0374982	−	0.0424079i
$516$		0			0
$517$		−	0.926192i		−	0.0407339i
$518$		−	5.40105i		−	0.237308i
$519$		0			0
$520$	2.70052	+	2.38787i	0.118426	+	0.104715i
$521$	33.2750			1.45781			0.728903	−	0.684617i	$-0.240031\pi$
$521$	33.2750			1.45781			0.728903	+	0.684617i	$0.240031\pi$
$522$		0			0
$523$			9.29948i			0.406638i	0.979113	+	0.203319i	$0.0651728\pi$
$523$			9.29948i			0.406638i	−0.979113	+	0.203319i	$0.934827\pi$
$524$	12.4387			0.543385
$525$		0			0
$526$	−15.0376			−0.655671
$527$			1.29948i			0.0566061i
$528$		0			0
$529$	22.0738			0.959731
$530$	−10.0508	−	8.88717i	−0.436578	−	0.386034i
$531$		0			0
$532$		−	3.35026i		−	0.145252i
$533$			14.9525i			0.647666i
$534$		0			0
$535$	15.8496	−	17.9248i	0.685236	−	0.774956i
$536$	−7.22425			−0.312040
$537$		0			0
$538$		−	4.51388i		−	0.194607i
$539$	−4.06537			−0.175108
$540$		0			0
$541$	28.5501			1.22746			0.613732	−	0.789515i	$-0.289668\pi$
$541$	28.5501			1.22746			0.613732	+	0.789515i	$0.289668\pi$
$542$			15.8496i			0.680797i
$543$		0			0
$544$	−0.387873			−0.0166299
$545$	−16.9624	−	14.9986i	−0.726589	−	0.642469i
$546$		0			0
$547$		−	28.4749i		−	1.21750i	−0.793363	−	0.608748i	$-0.791672\pi$
$547$		−	28.4749i		−	1.21750i	0.793363	−	0.608748i	$-0.208328\pi$
$548$		−	18.1622i		−	0.775851i
$549$		0			0
$550$	−4.77575	+	0.589104i	−0.203639	+	0.0251195i
$551$	−6.96239			−0.296608
$552$		0			0
$553$		−	11.2243i		−	0.477304i
$554$	−10.3127			−0.438143
$555$		0			0
$556$	8.77575			0.372175
$557$			4.88717i			0.207076i	0.994626	+	0.103538i	$0.0330163\pi$
$557$			4.88717i			0.207076i	−0.994626	+	0.103538i	$0.966984\pi$
$558$		0			0
$559$	9.97365			0.421841
$560$	4.96239	−	5.61213i	0.209699	−	0.237156i
$561$		0			0
$562$		−	24.3488i		−	1.02709i
$563$			30.8021i			1.29815i	0.760723	+	0.649077i	$0.224845\pi$
$563$			30.8021i			1.29815i	−0.760723	+	0.649077i	$0.775155\pi$
$564$		0			0
$565$	−30.4387	+	34.4241i	−1.28056	+	1.44823i
$566$	26.2882			1.10498
$567$		0			0
$568$			7.22425i			0.303123i
$569$	−24.1260			−1.01141			−0.505707	−	0.862705i	$-0.668768\pi$
$569$	−24.1260			−1.01141			−0.505707	+	0.862705i	$0.668768\pi$
$570$		0			0
$571$	−5.67276			−0.237398			−0.118699	−	0.992930i	$-0.537872\pi$
$571$	−5.67276			−0.237398			−0.118699	+	0.992930i	$0.537872\pi$
$572$		−	1.55149i		−	0.0648712i
$573$		0			0
$574$	31.0738			1.29700
$575$	4.77575	−	0.589104i	0.199162	−	0.0245673i
$576$		0			0
$577$		−	32.0000i		−	1.33218i	−0.745873	−	0.666089i	$-0.767967\pi$
$577$		−	32.0000i		−	1.33218i	0.745873	−	0.666089i	$-0.232033\pi$
$578$			16.8496i			0.700849i
$579$		0			0
$580$	−11.6629	−	10.3127i	−0.484276	−	0.428209i
$581$	50.2981			2.08672
$582$		0			0
$583$			5.77433i			0.239148i
$584$	3.22425			0.133421
$585$		0			0
$586$	13.0738			0.540074
$587$			13.6121i			0.561833i	0.959732	+	0.280916i	$0.0906383\pi$
$587$			13.6121i			0.561833i	−0.959732	+	0.280916i	$0.909362\pi$
$588$		0			0
$589$	−3.35026			−0.138045
$590$	−15.2750	+	17.2750i	−0.628863	+	0.711202i
$591$		0			0
$592$		−	1.61213i		−	0.0662580i
$593$			23.4617i			0.963456i	0.876321	+	0.481728i	$0.159991\pi$
$593$			23.4617i			0.963456i	−0.876321	+	0.481728i	$0.840009\pi$
$594$		0			0
$595$	2.17679	+	1.92478i	0.0892398	+	0.0789082i
$596$	−15.9756			−0.654385
$597$		0			0
$598$			1.55149i			0.0634452i
$599$	10.0263			0.409665			0.204833	−	0.978797i	$-0.434335\pi$
$599$	10.0263			0.409665			0.204833	+	0.978797i	$0.434335\pi$
$600$		0			0
$601$	11.7743			0.480285			0.240143	−	0.970738i	$-0.422806\pi$
$601$	11.7743			0.480285			0.240143	+	0.970738i	$0.422806\pi$
$602$		−	20.7269i		−	0.844764i
$603$		0			0
$604$	−18.4241			−0.749665
$605$	−16.8749	−	14.9213i	−0.686064	−	0.606636i
$606$		0			0
$607$			38.4993i			1.56264i	0.624132	+	0.781319i	$0.285453\pi$
$607$			38.4993i			1.56264i	−0.624132	+	0.781319i	$0.714547\pi$
$608$		−	1.00000i		−	0.0405554i
$609$		0			0
$610$	−17.6629	+	19.9756i	−0.715150	+	0.808787i
$611$	1.55149			0.0627667
$612$		0			0
$613$			7.61213i			0.307451i	0.988114	+	0.153725i	$0.0491271\pi$
$613$			7.61213i			0.307451i	−0.988114	+	0.153725i	$0.950873\pi$
$614$	7.07381			0.285476
$615$		0			0
$616$	−3.22425			−0.129909
$617$			29.5369i			1.18911i	0.804055	+	0.594555i	$0.202672\pi$
$617$			29.5369i			1.18911i	−0.804055	+	0.594555i	$0.797328\pi$
$618$		0			0
$619$	22.5501			0.906364			0.453182	−	0.891418i	$-0.350289\pi$
$619$	22.5501			0.906364			0.453182	+	0.891418i	$0.350289\pi$
$620$	−5.61213	−	4.96239i	−0.225388	−	0.199294i
$621$		0			0
$622$		−	26.3127i		−	1.05504i
$623$		−	15.5778i		−	0.624113i
$624$		0			0
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$	−18.7005			−0.747423
$627$		0			0
$628$			13.7889i			0.550238i
$629$	0.625301			0.0249324
$630$		0			0
$631$	−37.9248			−1.50976			−0.754881	−	0.655862i	$-0.772305\pi$
$631$	−37.9248			−1.50976			−0.754881	+	0.655862i	$0.772305\pi$
$632$		−	3.35026i		−	0.133266i
$633$		0			0
$634$	26.4749			1.05145
$635$	−2.00000	+	2.26187i	−0.0793676	+	0.0897594i
$636$		0			0
$637$		−	6.81003i		−	0.269823i
$638$			6.70052i			0.265276i
$639$		0			0
$640$	1.48119	−	1.67513i	0.0585493	−	0.0662154i
$641$	−6.67609			−0.263690			−0.131845	−	0.991270i	$-0.542090\pi$
$641$	−6.67609			−0.263690			−0.131845	+	0.991270i	$0.542090\pi$
$642$		0			0
$643$			25.2605i			0.996175i	0.867127	+	0.498087i	$0.165964\pi$
$643$			25.2605i			0.996175i	−0.867127	+	0.498087i	$0.834036\pi$
$644$	3.22425			0.127053
$645$		0			0
$646$	0.387873			0.0152607
$647$			16.9135i			0.664939i	0.943114	+	0.332469i	$0.107882\pi$
$647$			16.9135i			0.664939i	−0.943114	+	0.332469i	$0.892118\pi$
$648$		0			0
$649$	9.92478			0.389582
$650$	−0.986826	−	8.00000i	−0.0387065	−	0.313786i
$651$		0			0
$652$		−	3.73813i		−	0.146397i
$653$		−	24.1114i		−	0.943553i	−0.881718	−	0.471776i	$-0.843613\pi$
$653$		−	24.1114i		−	0.943553i	0.881718	−	0.471776i	$-0.156387\pi$
$654$		0			0
$655$	−20.8364	−	18.4241i	−0.814145	−	0.719888i
$656$	9.27504			0.362129
$657$		0			0
$658$		−	3.22425i		−	0.125694i
$659$	−20.3879			−0.794199			−0.397099	−	0.917776i	$-0.629983\pi$
$659$	−20.3879			−0.794199			−0.397099	+	0.917776i	$0.629983\pi$
$660$		0			0
$661$	17.6023			0.684649			0.342325	−	0.939582i	$-0.388786\pi$
$661$	17.6023			0.684649			0.342325	+	0.939582i	$0.388786\pi$
$662$		−	30.7005i		−	1.19321i
$663$		0			0
$664$	15.0132			0.582624
$665$	−4.96239	+	5.61213i	−0.192433	+	0.217629i
$666$		0			0
$667$		−	6.70052i		−	0.259445i
$668$			15.4763i			0.598795i
$669$		0			0
$670$	12.1016	+	10.7005i	0.467524	+	0.413397i
$671$	11.4763			0.443036
$672$		0			0
$673$			44.3634i			1.71008i	0.518558	+	0.855042i	$0.326469\pi$
$673$			44.3634i			1.71008i	−0.518558	+	0.855042i	$0.673531\pi$
$674$	−6.81194			−0.262386
$675$		0			0
$676$	−10.4010			−0.400040
$677$			8.70052i			0.334388i	0.985924	+	0.167194i	$0.0534707\pi$
$677$			8.70052i			0.334388i	−0.985924	+	0.167194i	$0.946529\pi$
$678$		0			0
$679$	−36.7269			−1.40945
$680$	0.649738	+	0.574515i	0.0249163	+	0.0220317i
$681$		0			0
$682$			3.22425i			0.123463i
$683$			37.8759i			1.44928i	0.689127	+	0.724641i	$0.257994\pi$
$683$			37.8759i			1.44928i	−0.689127	+	0.724641i	$0.742006\pi$
$684$		0			0
$685$	−26.9018	+	30.4241i	−1.02786	+	1.16244i
$686$	9.29948			0.355056
$687$		0			0
$688$		−	6.18664i		−	0.235864i
$689$	−9.67276			−0.368503
$690$		0			0
$691$	−0.775746			−0.0295108			−0.0147554	−	0.999891i	$-0.504697\pi$
$691$	−0.775746			−0.0295108			−0.0147554	+	0.999891i	$0.504697\pi$
$692$			1.47627i			0.0561194i
$693$		0			0
$694$	18.3879			0.697994
$695$	−14.7005	−	12.9986i	−0.557623	−	0.493064i
$696$		0			0
$697$			3.59754i			0.136266i
$698$		−	31.1490i		−	1.17901i
$699$		0			0
$700$	−16.6253	+	2.05079i	−0.628377	+	0.0775124i
$701$	−42.3752			−1.60049			−0.800245	−	0.599674i	$-0.795297\pi$
$701$	−42.3752			−1.60049			−0.800245	+	0.599674i	$0.795297\pi$
$702$		0			0
$703$			1.61213i			0.0608025i
$704$	−0.962389			−0.0362714
$705$		0			0
$706$	−7.61213			−0.286486
$707$			9.12933i			0.343344i
$708$		0			0
$709$	−36.2784			−1.36246			−0.681231	−	0.732068i	$-0.738555\pi$
$709$	−36.2784			−1.36246			−0.681231	+	0.732068i	$0.738555\pi$
$710$	10.7005	−	12.1016i	0.401583	−	0.454164i
$711$		0			0
$712$		−	4.64974i		−	0.174256i
$713$		−	3.22425i		−	0.120749i
$714$		0			0
$715$	−2.29806	+	2.59895i	−0.0859426	+	0.0971953i
$716$	14.3127			0.534889
$717$		0			0
$718$		−	35.3112i		−	1.31780i
$719$	−42.5355			−1.58631			−0.793153	−	0.609022i	$-0.791562\pi$
$719$	−42.5355			−1.58631			−0.793153	+	0.609022i	$0.791562\pi$
$720$		0			0
$721$	−1.92478			−0.0716824
$722$			1.00000i			0.0372161i
$723$		0			0
$724$	8.82653			0.328035
$725$	4.26187	+	34.5501i	0.158282	+	1.28316i
$726$		0			0
$727$			0.378024i			0.0140201i	0.999975	+	0.00701007i	$0.00223139\pi$
$727$			0.378024i			0.0140201i	−0.999975	+	0.00701007i	$0.997769\pi$
$728$		−	5.40105i		−	0.200176i
$729$		0			0
$730$	−5.40105	−	4.77575i	−0.199902	−	0.176758i
$731$	2.39963			0.0887536
$732$		0			0
$733$			26.0118i			0.960766i	0.877059	+	0.480383i	$0.159502\pi$
$733$			26.0118i			0.960766i	−0.877059	+	0.480383i	$0.840498\pi$
$734$	−31.9756			−1.18024
$735$		0			0
$736$	0.962389			0.0354741
$737$		−	6.95254i		−	0.256100i
$738$		0			0
$739$	44.8773			1.65084			0.825419	−	0.564520i	$-0.190939\pi$
$739$	44.8773			1.65084			0.825419	+	0.564520i	$0.190939\pi$
$740$	−2.38787	+	2.70052i	−0.0877800	+	0.0992732i
$741$		0			0
$742$			20.1016i			0.737952i
$743$			4.67418i			0.171479i	0.996318	+	0.0857394i	$0.0273253\pi$
$743$			4.67418i			0.171479i	−0.996318	+	0.0857394i	$0.972675\pi$
$744$		0			0
$745$	26.7612	+	23.6629i	0.980453	+	0.866942i
$746$	26.4894			0.969847
$747$		0			0
$748$		−	0.373285i		−	0.0136486i
$749$	−35.8496			−1.30991
$750$		0			0
$751$	−6.57452			−0.239907			−0.119954	−	0.992779i	$-0.538275\pi$
$751$	−6.57452			−0.239907			−0.119954	+	0.992779i	$0.538275\pi$
$752$		−	0.962389i		−	0.0350947i
$753$		0			0
$754$	−11.2243			−0.408763
$755$	30.8627	+	27.2896i	1.12321	+	0.993171i
$756$		0			0
$757$			15.5633i			0.565656i	0.959171	+	0.282828i	$0.0912726\pi$
$757$			15.5633i			0.565656i	−0.959171	+	0.282828i	$0.908727\pi$
$758$			19.3258i			0.701946i
$759$		0			0
$760$	−1.48119	+	1.67513i	−0.0537286	+	0.0607634i
$761$	23.8759			0.865501			0.432750	−	0.901514i	$-0.357543\pi$
$761$	23.8759			0.865501			0.432750	+	0.901514i	$0.357543\pi$
$762$		0			0
$763$			33.9248i			1.22816i
$764$	2.31265			0.0836688
$765$		0			0
$766$	−3.37470			−0.121933
$767$			16.6253i			0.600305i
$768$		0			0
$769$	−30.4749			−1.09895			−0.549476	−	0.835510i	$-0.685173\pi$
$769$	−30.4749			−1.09895			−0.549476	+	0.835510i	$0.685173\pi$
$770$	5.40105	+	4.77575i	0.194640	+	0.172106i
$771$		0			0
$772$			7.58769i			0.273087i
$773$		−	16.3272i		−	0.587250i	−0.955921	−	0.293625i	$-0.905138\pi$
$773$		−	16.3272i		−	0.587250i	0.955921	−	0.293625i	$-0.0948617\pi$
$774$		0			0
$775$	2.05079	+	16.6253i	0.0736664	+	0.597198i
$776$	−10.9624			−0.393527
$777$		0			0
$778$		−	11.3503i		−	0.406927i
$779$	−9.27504			−0.332313
$780$		0			0
$781$	−6.95254			−0.248781
$782$			0.373285i			0.0133486i
$783$		0			0
$784$	−4.22425			−0.150866
$785$	20.4241	−	23.0982i	0.728966	−	0.824412i
$786$		0			0
$787$		−	30.9525i		−	1.10334i	−0.834063	−	0.551669i	$-0.813991\pi$
$787$		−	30.9525i		−	1.10334i	0.834063	−	0.551669i	$-0.186009\pi$
$788$		−	18.8119i		−	0.670148i
$789$		0			0
$790$	−4.96239	+	5.61213i	−0.176554	+	0.199671i
$791$	68.8481			2.44796
$792$		0			0
$793$			19.2243i			0.682673i
$794$	18.8364			0.668478
$795$		0			0
$796$	−9.40105			−0.333211
$797$			14.8773i			0.526982i	0.964662	+	0.263491i	$0.0848739\pi$
$797$			14.8773i			0.526982i	−0.964662	+	0.263491i	$0.915126\pi$
$798$		0			0
$799$	0.373285			0.0132059
$800$	−4.96239	+	0.612127i	−0.175447	+	0.0216420i
$801$		0			0
$802$			4.12601i			0.145694i
$803$			3.10299i			0.109502i
$804$		0			0
$805$	−5.40105	−	4.77575i	−0.190362	−	0.168323i
$806$	−5.40105			−0.190244
$807$		0			0
$808$			2.72496i			0.0958638i
$809$	25.4471			0.894672			0.447336	−	0.894366i	$-0.352373\pi$
$809$	25.4471			0.894672			0.447336	+	0.894366i	$0.352373\pi$
$810$		0			0
$811$	−53.3522			−1.87345			−0.936724	−	0.350069i	$-0.886158\pi$
$811$	−53.3522			−1.87345			−0.936724	+	0.350069i	$0.886158\pi$
$812$			23.3258i			0.818576i
$813$		0			0
$814$	1.55149			0.0543798
$815$	−5.53690	+	6.26187i	−0.193949	+	0.219344i
$816$		0			0
$817$			6.18664i			0.216443i
$818$		−	2.52373i		−	0.0882402i
$819$		0			0
$820$	−15.5369	−	13.7381i	−0.542572	−	0.479756i
$821$	27.9756			0.976354			0.488177	−	0.872745i	$-0.337662\pi$
$821$	27.9756			0.976354			0.488177	+	0.872745i	$0.337662\pi$
$822$		0			0
$823$		−	7.87399i		−	0.274470i	−0.990539	−	0.137235i	$-0.956178\pi$
$823$		−	7.87399i		−	0.274470i	0.990539	−	0.137235i	$-0.0438216\pi$
$824$	−0.574515			−0.0200142
$825$		0			0
$826$	34.5501			1.20215
$827$			40.1016i			1.39447i	0.716843	+	0.697234i	$0.245586\pi$
$827$			40.1016i			1.39447i	−0.716843	+	0.697234i	$0.754414\pi$
$828$		0			0
$829$	−47.2262			−1.64023			−0.820116	−	0.572197i	$-0.806091\pi$
$829$	−47.2262			−1.64023			−0.820116	+	0.572197i	$0.806091\pi$
$830$	−25.1490	−	22.2374i	−0.872936	−	0.771872i
$831$		0			0
$832$		−	1.61213i		−	0.0558904i
$833$		−	1.63847i		−	0.0567698i
$834$		0			0
$835$	22.9234	−	25.9248i	0.793296	−	0.897164i
$836$	0.962389			0.0332849
$837$		0			0
$838$			7.51247i			0.259514i
$839$	−3.89843			−0.134589			−0.0672944	−	0.997733i	$-0.521437\pi$
$839$	−3.89843			−0.134589			−0.0672944	+	0.997733i	$0.521437\pi$
$840$		0			0
$841$	19.4749			0.671547
$842$			3.67750i			0.126735i
$843$		0			0
$844$	−4.77575			−0.164388
$845$	17.4231	+	15.4060i	0.599373	+	0.529982i
$846$		0			0
$847$			33.7499i			1.15966i
$848$			6.00000i			0.206041i
$849$		0			0
$850$	−0.237428	−	1.92478i	−0.00814370	−	0.0660193i
$851$	−1.55149			−0.0531845
$852$		0			0
$853$			35.1900i			1.20488i	0.798164	+	0.602441i	$0.205805\pi$
$853$			35.1900i			1.20488i	−0.798164	+	0.602441i	$0.794195\pi$
$854$	39.9511			1.36710
$855$		0			0
$856$	−10.7005			−0.365736
$857$		−	12.1768i		−	0.415951i	−0.978134	−	0.207976i	$-0.933313\pi$
$857$		−	12.1768i		−	0.415951i	0.978134	−	0.207976i	$-0.0666875\pi$
$858$		0			0
$859$	−57.3522			−1.95683			−0.978415	−	0.206648i	$-0.933745\pi$
$859$	−57.3522			−1.95683			−0.978415	+	0.206648i	$0.933745\pi$
$860$	−9.16362	+	10.3634i	−0.312477	+	0.353390i
$861$		0			0
$862$			10.3272i			0.351747i
$863$		−	14.0752i		−	0.479126i	−0.970881	−	0.239563i	$-0.922996\pi$
$863$		−	14.0752i		−	0.479126i	0.970881	−	0.239563i	$-0.0770042\pi$
$864$		0			0
$865$	2.18664	−	2.47295i	0.0743481	−	0.0840827i
$866$	31.5877			1.07339
$867$		0			0
$868$			11.2243i			0.380976i
$869$	3.22425			0.109375
$870$		0			0
$871$	11.6464			0.394624
$872$			10.1260i			0.342910i
$873$		0			0
$874$	−0.962389			−0.0325533
$875$	30.8872	+	21.1900i	1.04418	+	0.716352i
$876$		0			0
$877$			18.8627i			0.636949i	0.947931	+	0.318475i	$0.103171\pi$
$877$			18.8627i			0.636949i	−0.947931	+	0.318475i	$0.896829\pi$
$878$			38.1524i			1.28758i
$879$		0			0
$880$	1.61213	+	1.42548i	0.0543448	+	0.0480531i
$881$	19.1490			0.645147			0.322574	−	0.946544i	$-0.395452\pi$
$881$	19.1490			0.645147			0.322574	+	0.946544i	$0.395452\pi$
$882$		0			0
$883$		−	42.9135i		−	1.44415i	−0.691812	−	0.722077i	$-0.743187\pi$
$883$		−	42.9135i		−	1.44415i	0.691812	−	0.722077i	$-0.256813\pi$
$884$	0.625301			0.0210311
$885$		0			0
$886$	−16.3127			−0.548034
$887$		−	22.7005i		−	0.762209i	−0.924532	−	0.381104i	$-0.875544\pi$
$887$		−	22.7005i		−	0.762209i	0.924532	−	0.381104i	$-0.124456\pi$
$888$		0			0
$889$	4.52373			0.151721
$890$	−6.88717	+	7.78892i	−0.230858	+	0.261085i
$891$		0			0
$892$		−	24.6761i		−	0.826216i
$893$			0.962389i			0.0322051i
$894$		0			0
$895$	−23.9756	−	21.1998i	−0.801415	−	0.708632i
$896$	−3.35026			−0.111924
$897$		0			0
$898$		−	37.5271i		−	1.25229i
$899$	23.3258			0.777960
$900$		0			0
$901$	−2.32724			−0.0775316
$902$			8.92619i			0.297210i
$903$		0			0
$904$	20.5501			0.683485
$905$	−14.7856	−	13.0738i	−0.491490	−	0.434588i
$906$		0			0
$907$			14.5501i			0.483127i	0.970385	+	0.241564i	$0.0776603\pi$
$907$			14.5501i			0.483127i	−0.970385	+	0.241564i	$0.922340\pi$
$908$			15.4763i			0.513598i
$909$		0			0
$910$	−8.00000	+	9.04746i	−0.265197	+	0.299920i
$911$	0.998585			0.0330846			0.0165423	−	0.999863i	$-0.494734\pi$
$911$	0.998585			0.0330846			0.0165423	+	0.999863i	$0.494734\pi$
$912$		0			0
$913$			14.4485i			0.478176i
$914$	8.00000			0.264616
$915$		0			0
$916$	21.3258			0.704625
$917$			41.6728i			1.37616i
$918$		0			0
$919$	33.7743			1.11411			0.557056	−	0.830475i	$-0.311931\pi$
$919$	33.7743			1.11411			0.557056	+	0.830475i	$0.311931\pi$
$920$	−1.61213	−	1.42548i	−0.0531502	−	0.0469968i
$921$		0			0
$922$		−	12.3780i		−	0.407649i
$923$		−	11.6464i		−	0.383346i
$924$		0			0
$925$	8.00000	−	0.986826i	0.263038	−	0.0324466i
$926$	32.4504			1.06639
$927$		0			0
$928$			6.96239i			0.228552i
$929$	14.8773			0.488109			0.244054	−	0.969762i	$-0.421522\pi$
$929$	14.8773			0.488109			0.244054	+	0.969762i	$0.421522\pi$
$930$		0			0
$931$	4.22425			0.138444
$932$			9.01317i			0.295236i
$933$		0			0
$934$	7.53690			0.246615
$935$	−0.552907	+	0.625301i	−0.0180820	+	0.0204495i
$936$		0			0
$937$			22.2981i			0.728446i	0.931312	+	0.364223i	$0.118665\pi$
$937$			22.2981i			0.728446i	−0.931312	+	0.364223i	$0.881335\pi$
$938$		−	24.2031i		−	0.790261i
$939$		0			0
$940$	−1.42548	+	1.61213i	−0.0464942	+	0.0525818i
$941$	36.3634			1.18541			0.592707	−	0.805418i	$-0.298059\pi$
$941$	36.3634			1.18541			0.592707	+	0.805418i	$0.298059\pi$
$942$		0			0
$943$		−	8.92619i		−	0.290677i
$944$	10.3127			0.335648
$945$		0			0
$946$	5.95395			0.193580
$947$		−	50.3390i		−	1.63580i	−0.575362	−	0.817899i	$-0.695139\pi$
$947$		−	50.3390i		−	1.63580i	0.575362	−	0.817899i	$-0.304861\pi$
$948$		0			0
$949$	−5.19791			−0.168731
$950$	4.96239	−	0.612127i	0.161001	−	0.0198600i
$951$		0			0
$952$		−	1.29948i		−	0.0421163i
$953$		−	16.3272i		−	0.528891i	−0.964401	−	0.264446i	$-0.914811\pi$
$953$		−	16.3272i		−	0.528891i	0.964401	−	0.264446i	$-0.0851890\pi$
$954$		0			0
$955$	−3.87399	−	3.42548i	−0.125359	−	0.110846i
$956$	0.135857			0.00439393
$957$		0			0
$958$			15.2097i			0.491402i
$959$	60.8481			1.96489
$960$		0			0
$961$	−19.7757			−0.637927
$962$			2.59895i			0.0837936i
$963$		0			0
$964$	25.8496			0.832558
$965$	11.2388	−	12.7104i	0.361791	−	0.409161i
$966$		0			0
$967$			0.276454i			0.00889015i	0.999990	+	0.00444507i	$0.00141492\pi$
$967$			0.276454i			0.00889015i	−0.999990	+	0.00444507i	$0.998585\pi$
$968$			10.0738i			0.323784i
$969$		0			0
$970$	18.3634	+	16.2374i	0.589614	+	0.521352i
$971$	−37.9102			−1.21660			−0.608298	−	0.793709i	$-0.708147\pi$
$971$	−37.9102			−1.21660			−0.608298	+	0.793709i	$0.708147\pi$
$972$		0			0
$973$			29.4010i			0.942554i
$974$	1.19982			0.0384446
$975$		0			0
$976$	11.9248			0.381703
$977$		−	28.3996i		−	0.908585i	−0.890853	−	0.454292i	$-0.849892\pi$
$977$		−	28.3996i		−	0.908585i	0.890853	−	0.454292i	$-0.150108\pi$
$978$		0			0
$979$	4.47486			0.143017
$980$	7.07618	+	6.25694i	0.226040	+	0.199871i
$981$		0			0
$982$			5.11283i			0.163157i
$983$		−	0.926192i		−	0.0295409i	−0.999891	−	0.0147705i	$-0.995298\pi$
$983$		−	0.926192i		−	0.0295409i	0.999891	−	0.0147705i	$-0.00470176\pi$
$984$		0			0
$985$	−27.8641	+	31.5125i	−0.887825	+	1.00407i
$986$	−2.70052			−0.0860022
$987$		0			0
$988$			1.61213i			0.0512886i
$989$	−5.95395			−0.189325
$990$		0			0
$991$	30.5256			0.969679			0.484839	−	0.874603i	$-0.338878\pi$
$991$	30.5256			0.969679			0.484839	+	0.874603i	$0.338878\pi$
$992$			3.35026i			0.106371i
$993$		0			0
$994$	−24.2031			−0.767677
$995$	15.7480	+	13.9248i	0.499245	+	0.441445i
$996$		0			0
$997$			21.0132i			0.665494i	0.943016	+	0.332747i	$0.107975\pi$
$997$			21.0132i			0.665494i	−0.943016	+	0.332747i	$0.892025\pi$
$998$		−	14.2981i		−	0.452597i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.d.f.1369.6		6
3.2	odd	2		570.2.d.c.229.1	✓	6
5.2	odd	4		8550.2.a.ce.1.3		3
5.3	odd	4		8550.2.a.cq.1.1		3
5.4	even	2	inner	1710.2.d.f.1369.3		6
15.2	even	4		2850.2.a.bm.1.3		3
15.8	even	4		2850.2.a.bl.1.1		3
15.14	odd	2		570.2.d.c.229.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.c.229.1	✓	6	3.2	odd	2
570.2.d.c.229.4	yes	6	15.14	odd	2
1710.2.d.f.1369.3		6	5.4	even	2	inner
1710.2.d.f.1369.6		6	1.1	even	1	trivial
2850.2.a.bl.1.1		3	15.8	even	4
2850.2.a.bm.1.3		3	15.2	even	4
8550.2.a.ce.1.3		3	5.2	odd	4
8550.2.a.cq.1.1		3	5.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.67513 + 1.48119i) q^{5} -3.35026i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.67513 + 1.48119i) q^{5} -3.35026i q^{7} -1.00000i q^{8} +(-1.48119 + 1.67513i) q^{10} +0.962389 q^{11} +1.61213i q^{13} +3.35026 q^{14} +1.00000 q^{16} +0.387873i q^{17} -1.00000 q^{19} +(-1.67513 - 1.48119i) q^{20} +0.962389i q^{22} -0.962389i q^{23} +(0.612127 + 4.96239i) q^{25} -1.61213 q^{26} +3.35026i q^{28} +6.96239 q^{29} +3.35026 q^{31} +1.00000i q^{32} -0.387873 q^{34} +(4.96239 - 5.61213i) q^{35} -1.61213i q^{37} -1.00000i q^{38} +(1.48119 - 1.67513i) q^{40} +9.27504 q^{41} -6.18664i q^{43} -0.962389 q^{44} +0.962389 q^{46} -0.962389i q^{47} -4.22425 q^{49} +(-4.96239 + 0.612127i) q^{50} -1.61213i q^{52} +6.00000i q^{53} +(1.61213 + 1.42548i) q^{55} -3.35026 q^{56} +6.96239i q^{58} +10.3127 q^{59} +11.9248 q^{61} +3.35026i q^{62} -1.00000 q^{64} +(-2.38787 + 2.70052i) q^{65} -7.22425i q^{67} -0.387873i q^{68} +(5.61213 + 4.96239i) q^{70} -7.22425 q^{71} +3.22425i q^{73} +1.61213 q^{74} +1.00000 q^{76} -3.22425i q^{77} +3.35026 q^{79} +(1.67513 + 1.48119i) q^{80} +9.27504i q^{82} +15.0132i q^{83} +(-0.574515 + 0.649738i) q^{85} +6.18664 q^{86} -0.962389i q^{88} +4.64974 q^{89} +5.40105 q^{91} +0.962389i q^{92} +0.962389 q^{94} +(-1.67513 - 1.48119i) q^{95} -10.9624i q^{97} -4.22425i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4}+O(q^{10}) \) 6 * q - 6 * q^4	\( 6 q - 6 q^{4} + 2 q^{10} - 16 q^{11} + 6 q^{16} - 6 q^{19} + 2 q^{25} - 8 q^{26} + 20 q^{29} - 4 q^{34} + 8 q^{35} - 2 q^{40} - 8 q^{41} + 16 q^{44} - 16 q^{46} - 22 q^{49} - 8 q^{50} + 8 q^{55} + 20 q^{59} + 28 q^{61} - 6 q^{64} - 16 q^{65} + 32 q^{70} - 40 q^{71} + 8 q^{74} + 6 q^{76} + 20 q^{85} + 12 q^{86} + 48 q^{89} - 48 q^{91} - 16 q^{94}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^10 - 16 * q^11 + 6 * q^16 - 6 * q^19 + 2 * q^25 - 8 * q^26 + 20 * q^29 - 4 * q^34 + 8 * q^35 - 2 * q^40 - 8 * q^41 + 16 * q^44 - 16 * q^46 - 22 * q^49 - 8 * q^50 + 8 * q^55 + 20 * q^59 + 28 * q^61 - 6 * q^64 - 16 * q^65 + 32 * q^70 - 40 * q^71 + 8 * q^74 + 6 * q^76 + 20 * q^85 + 12 * q^86 + 48 * q^89 - 48 * q^91 - 16 * q^94

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