LMFDB - Embedded newform 1710.2.d.e.1369.4

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			1369.4
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1710.1369
Dual form			1710.2.d.e.1369.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-2.17009 - 0.539189i) q^{5} -1.07838i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.17009 - 0.539189i) q^{5} -1.07838i q^{7} -1.00000i q^{8} +(0.539189 - 2.17009i) q^{10} -3.41855 q^{11} +0.921622i q^{13} +1.07838 q^{14} +1.00000 q^{16} -0.340173i q^{17} +1.00000 q^{19} +(2.17009 + 0.539189i) q^{20} -3.41855i q^{22} -0.921622i q^{23} +(4.41855 + 2.34017i) q^{25} -0.921622 q^{26} +1.07838i q^{28} -1.41855 q^{29} +7.26180 q^{31} +1.00000i q^{32} +0.340173 q^{34} +(-0.581449 + 2.34017i) q^{35} +5.60197i q^{37} +1.00000i q^{38} +(-0.539189 + 2.17009i) q^{40} +1.07838 q^{41} -0.738205i q^{43} +3.41855 q^{44} +0.921622 q^{46} +7.75872i q^{47} +5.83710 q^{49} +(-2.34017 + 4.41855i) q^{50} -0.921622i q^{52} +2.68035i q^{53} +(7.41855 + 1.84324i) q^{55} -1.07838 q^{56} -1.41855i q^{58} +8.34017 q^{59} +2.00000 q^{61} +7.26180i q^{62} -1.00000 q^{64} +(0.496928 - 2.00000i) q^{65} -4.68035i q^{67} +0.340173i q^{68} +(-2.34017 - 0.581449i) q^{70} +10.8371 q^{71} +6.83710i q^{73} -5.60197 q^{74} -1.00000 q^{76} +3.68649i q^{77} -4.73820 q^{79} +(-2.17009 - 0.539189i) q^{80} +1.07838i q^{82} +11.0205i q^{83} +(-0.183417 + 0.738205i) q^{85} +0.738205 q^{86} +3.41855i q^{88} +9.75872 q^{89} +0.993857 q^{91} +0.921622i q^{92} -7.75872 q^{94} +(-2.17009 - 0.539189i) q^{95} +16.2557i q^{97} +5.83710i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 2 q^{5}+O(q^{10}) $ 6 * q - 6 * q^4 - 2 * q^5	$ 6 q - 6 q^{4} - 2 q^{5} + 8 q^{11} + 6 q^{16} + 6 q^{19} + 2 q^{20} - 2 q^{25} - 12 q^{26} + 20 q^{29} + 28 q^{31} - 20 q^{34} - 32 q^{35} - 8 q^{44} + 12 q^{46} - 22 q^{49} + 8 q^{50} + 16 q^{55} + 28 q^{59} + 12 q^{61} - 6 q^{64} - 32 q^{65} + 8 q^{70} + 8 q^{71} + 4 q^{74} - 6 q^{76} - 44 q^{79} - 2 q^{80} + 8 q^{85} + 20 q^{86} + 8 q^{89} - 64 q^{91} + 4 q^{94} - 2 q^{95}+O(q^{100}) $ 6 * q - 6 * q^4 - 2 * q^5 + 8 * q^11 + 6 * q^16 + 6 * q^19 + 2 * q^20 - 2 * q^25 - 12 * q^26 + 20 * q^29 + 28 * q^31 - 20 * q^34 - 32 * q^35 - 8 * q^44 + 12 * q^46 - 22 * q^49 + 8 * q^50 + 16 * q^55 + 28 * q^59 + 12 * q^61 - 6 * q^64 - 32 * q^65 + 8 * q^70 + 8 * q^71 + 4 * q^74 - 6 * q^76 - 44 * q^79 - 2 * q^80 + 8 * q^85 + 20 * q^86 + 8 * q^89 - 64 * q^91 + 4 * q^94 - 2 * q^95

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
$5$	−2.17009	−	0.539189i	−0.970492	−	0.241133i
$5$	−2.17009	−	0.539189i	−0.970492	−	0.241133i
$6$		0			0
$7$		−	1.07838i		−	0.407588i	−0.979014	−	0.203794i	$-0.934673\pi$
$7$		−	1.07838i		−	0.407588i	0.979014	−	0.203794i	$-0.0653274\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.539189	−	2.17009i	0.170506	−	0.686242i
$11$	−3.41855			−1.03073			−0.515366	−	0.856970i	$-0.672344\pi$
$11$	−3.41855			−1.03073			−0.515366	+	0.856970i	$0.672344\pi$
$12$		0			0
$13$			0.921622i			0.255612i	0.991799	+	0.127806i	$0.0407935\pi$
$13$			0.921622i			0.255612i	−0.991799	+	0.127806i	$0.959207\pi$
$14$	1.07838			0.288209
$15$		0			0
$16$	1.00000			0.250000
$17$		−	0.340173i		−	0.0825041i	−0.999149	−	0.0412520i	$-0.986865\pi$
$17$		−	0.340173i		−	0.0825041i	0.999149	−	0.0412520i	$-0.0131347\pi$
$18$		0			0
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	2.17009	+	0.539189i	0.485246	+	0.120566i
$21$		0			0
$22$		−	3.41855i		−	0.728837i
$23$		−	0.921622i		−	0.192172i	−0.995373	−	0.0960858i	$-0.969368\pi$
$23$		−	0.921622i		−	0.192172i	0.995373	−	0.0960858i	$-0.0306323\pi$
$24$		0			0
$25$	4.41855	+	2.34017i	0.883710	+	0.468035i
$26$	−0.921622			−0.180745
$27$		0			0
$28$			1.07838i			0.203794i
$29$	−1.41855			−0.263418			−0.131709	−	0.991288i	$-0.542046\pi$
$29$	−1.41855			−0.263418			−0.131709	+	0.991288i	$0.542046\pi$
$30$		0			0
$31$	7.26180			1.30426			0.652128	−	0.758108i	$-0.273876\pi$
$31$	7.26180			1.30426			0.652128	+	0.758108i	$0.273876\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	0.340173			0.0583392
$35$	−0.581449	+	2.34017i	−0.0982829	+	0.395561i
$36$		0			0
$37$			5.60197i			0.920958i	0.887671	+	0.460479i	$0.152322\pi$
$37$			5.60197i			0.920958i	−0.887671	+	0.460479i	$0.847678\pi$
$38$			1.00000i			0.162221i
$39$		0			0
$40$	−0.539189	+	2.17009i	−0.0852532	+	0.343121i
$41$	1.07838			0.168414			0.0842072	−	0.996448i	$-0.473164\pi$
$41$	1.07838			0.168414			0.0842072	+	0.996448i	$0.473164\pi$
$42$		0			0
$43$		−	0.738205i		−	0.112575i	−0.998415	−	0.0562876i	$-0.982074\pi$
$43$		−	0.738205i		−	0.112575i	0.998415	−	0.0562876i	$-0.0179264\pi$
$44$	3.41855			0.515366
$45$		0			0
$46$	0.921622			0.135886
$47$			7.75872i			1.13173i	0.824499	+	0.565863i	$0.191457\pi$
$47$			7.75872i			1.13173i	−0.824499	+	0.565863i	$0.808543\pi$
$48$		0			0
$49$	5.83710			0.833872
$50$	−2.34017	+	4.41855i	−0.330950	+	0.624877i
$51$		0			0
$52$		−	0.921622i		−	0.127806i
$53$			2.68035i			0.368174i	0.982910	+	0.184087i	$0.0589328\pi$
$53$			2.68035i			0.368174i	−0.982910	+	0.184087i	$0.941067\pi$
$54$		0			0
$55$	7.41855	+	1.84324i	1.00032	+	0.248543i
$56$	−1.07838			−0.144104
$57$		0			0
$58$		−	1.41855i		−	0.186265i
$59$	8.34017			1.08580			0.542899	−	0.839798i	$-0.317327\pi$
$59$	8.34017			1.08580			0.542899	+	0.839798i	$0.317327\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$			7.26180i			0.922249i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.496928	−	2.00000i	0.0616364	−	0.248069i
$66$		0			0
$67$		−	4.68035i		−	0.571795i	−0.958260	−	0.285898i	$-0.907708\pi$
$67$		−	4.68035i		−	0.571795i	0.958260	−	0.285898i	$-0.0922917\pi$
$68$			0.340173i			0.0412520i
$69$		0			0
$70$	−2.34017	−	0.581449i	−0.279704	−	0.0694965i
$71$	10.8371			1.28613			0.643064	−	0.765813i	$-0.277663\pi$
$71$	10.8371			1.28613			0.643064	+	0.765813i	$0.277663\pi$
$72$		0			0
$73$			6.83710i			0.800222i	0.916467	+	0.400111i	$0.131028\pi$
$73$			6.83710i			0.800222i	−0.916467	+	0.400111i	$0.868972\pi$
$74$	−5.60197			−0.651216
$75$		0			0
$76$	−1.00000			−0.114708
$77$			3.68649i			0.420114i
$78$		0			0
$79$	−4.73820			−0.533090			−0.266545	−	0.963823i	$-0.585882\pi$
$79$	−4.73820			−0.533090			−0.266545	+	0.963823i	$0.585882\pi$
$80$	−2.17009	−	0.539189i	−0.242623	−	0.0602831i
$81$		0			0
$82$			1.07838i			0.119087i
$83$			11.0205i			1.20966i	0.796355	+	0.604830i	$0.206759\pi$
$83$			11.0205i			1.20966i	−0.796355	+	0.604830i	$0.793241\pi$
$84$		0			0
$85$	−0.183417	+	0.738205i	−0.0198944	+	0.0800695i
$86$	0.738205			0.0796027
$87$		0			0
$88$			3.41855i			0.364419i
$89$	9.75872			1.03442			0.517211	−	0.855858i	$-0.326970\pi$
$89$	9.75872			1.03442			0.517211	+	0.855858i	$0.326970\pi$
$90$		0			0
$91$	0.993857			0.104185
$92$			0.921622i			0.0960858i
$93$		0			0
$94$	−7.75872			−0.800251
$95$	−2.17009	−	0.539189i	−0.222646	−	0.0553196i
$96$		0			0
$97$			16.2557i			1.65051i	0.564759	+	0.825256i	$0.308969\pi$
$97$			16.2557i			1.65051i	−0.564759	+	0.825256i	$0.691031\pi$
$98$			5.83710i			0.589636i
$99$		0			0
$100$	−4.41855	−	2.34017i	−0.441855	−	0.234017i
$101$	13.0205			1.29559			0.647795	−	0.761815i	$-0.275691\pi$
$101$	13.0205			1.29559			0.647795	+	0.761815i	$0.275691\pi$
$102$		0			0
$103$		−	14.3402i		−	1.41298i	−0.707723	−	0.706490i	$-0.750278\pi$
$103$		−	14.3402i		−	1.41298i	0.707723	−	0.706490i	$-0.249722\pi$
$104$	0.921622			0.0903725
$105$		0			0
$106$	−2.68035			−0.260338
$107$			10.8371i			1.04766i	0.851822	+	0.523831i	$0.175498\pi$
$107$			10.8371i			1.04766i	−0.851822	+	0.523831i	$0.824502\pi$
$108$		0			0
$109$	−18.6225			−1.78371			−0.891855	−	0.452321i	$-0.850596\pi$
$109$	−18.6225			−1.78371			−0.891855	+	0.452321i	$0.850596\pi$
$110$	−1.84324	+	7.41855i	−0.175746	+	0.707331i
$111$		0			0
$112$		−	1.07838i		−	0.101897i
$113$		−	13.5174i		−	1.27161i	−0.771848	−	0.635807i	$-0.780667\pi$
$113$		−	13.5174i		−	1.27161i	0.771848	−	0.635807i	$-0.219333\pi$
$114$		0			0
$115$	−0.496928	+	2.00000i	−0.0463388	+	0.186501i
$116$	1.41855			0.131709
$117$		0			0
$118$			8.34017i			0.767775i
$119$	−0.366835			−0.0336277
$120$		0			0
$121$	0.686489			0.0624081
$122$			2.00000i			0.181071i
$123$		0			0
$124$	−7.26180			−0.652128
$125$	−8.32684	−	7.46081i	−0.744775	−	0.667315i
$126$		0			0
$127$			16.4969i			1.46387i	0.681377	+	0.731933i	$0.261382\pi$
$127$			16.4969i			1.46387i	−0.681377	+	0.731933i	$0.738618\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	2.00000	+	0.496928i	0.175412	+	0.0435835i
$131$	−0.581449			−0.0508015			−0.0254007	−	0.999677i	$-0.508086\pi$
$131$	−0.581449			−0.0508015			−0.0254007	+	0.999677i	$0.508086\pi$
$132$		0			0
$133$		−	1.07838i		−	0.0935072i
$134$	4.68035			0.404320
$135$		0			0
$136$	−0.340173			−0.0291696
$137$			5.81658i			0.496944i	0.968639	+	0.248472i	$0.0799284\pi$
$137$			5.81658i			0.496944i	−0.968639	+	0.248472i	$0.920072\pi$
$138$		0			0
$139$	−6.15676			−0.522209			−0.261105	−	0.965311i	$-0.584087\pi$
$139$	−6.15676			−0.522209			−0.261105	+	0.965311i	$0.584087\pi$
$140$	0.581449	−	2.34017i	0.0491414	−	0.197781i
$141$		0			0
$142$			10.8371i			0.909429i
$143$		−	3.15061i		−	0.263467i
$144$		0			0
$145$	3.07838	+	0.764867i	0.255645	+	0.0635187i
$146$	−6.83710			−0.565843
$147$		0			0
$148$		−	5.60197i		−	0.460479i
$149$	8.34017			0.683254			0.341627	−	0.939836i	$-0.389022\pi$
$149$	8.34017			0.683254			0.341627	+	0.939836i	$0.389022\pi$
$150$		0			0
$151$	16.2557			1.32287			0.661433	−	0.750004i	$-0.269949\pi$
$151$	16.2557			1.32287			0.661433	+	0.750004i	$0.269949\pi$
$152$		−	1.00000i		−	0.0811107i
$153$		0			0
$154$	−3.68649			−0.297066
$155$	−15.7587	−	3.91548i	−1.26577	−	0.314499i
$156$		0			0
$157$			3.65983i			0.292086i	0.989278	+	0.146043i	$0.0466538\pi$
$157$			3.65983i			0.292086i	−0.989278	+	0.146043i	$0.953346\pi$
$158$		−	4.73820i		−	0.376951i
$159$		0			0
$160$	0.539189	−	2.17009i	0.0426266	−	0.171560i
$161$	−0.993857			−0.0783269
$162$		0			0
$163$		−	6.89496i		−	0.540055i	−0.962853	−	0.270027i	$-0.912967\pi$
$163$		−	6.89496i		−	0.540055i	0.962853	−	0.270027i	$-0.0870328\pi$
$164$	−1.07838			−0.0842072
$165$		0			0
$166$	−11.0205			−0.855358
$167$			4.68035i			0.362176i	0.983467	+	0.181088i	$0.0579619\pi$
$167$			4.68035i			0.362176i	−0.983467	+	0.181088i	$0.942038\pi$
$168$		0			0
$169$	12.1506			0.934662
$170$	−0.738205	−	0.183417i	−0.0566177	−	0.0140675i
$171$		0			0
$172$			0.738205i			0.0562876i
$173$		−	4.52359i		−	0.343922i	−0.985104	−	0.171961i	$-0.944990\pi$
$173$		−	4.52359i		−	0.343922i	0.985104	−	0.171961i	$-0.0550103\pi$
$174$		0			0
$175$	2.52359	−	4.76487i	0.190766	−	0.360190i
$176$	−3.41855			−0.257683
$177$		0			0
$178$			9.75872i			0.731447i
$179$	14.4969			1.08355			0.541776	−	0.840523i	$-0.317752\pi$
$179$	14.4969			1.08355			0.541776	+	0.840523i	$0.317752\pi$
$180$		0			0
$181$	−12.7792			−0.949874			−0.474937	−	0.880020i	$-0.657529\pi$
$181$	−12.7792			−0.949874			−0.474937	+	0.880020i	$0.657529\pi$
$182$			0.993857i			0.0736696i
$183$		0			0
$184$	−0.921622			−0.0679429
$185$	3.02052	−	12.1568i	0.222073	−	0.893782i
$186$		0			0
$187$			1.16290i			0.0850396i
$188$		−	7.75872i		−	0.565863i
$189$		0			0
$190$	0.539189	−	2.17009i	0.0391169	−	0.157435i
$191$	4.39803			0.318230			0.159115	−	0.987260i	$-0.449136\pi$
$191$	4.39803			0.318230			0.159115	+	0.987260i	$0.449136\pi$
$192$		0			0
$193$		−	24.6225i		−	1.77237i	−0.463336	−	0.886183i	$-0.653348\pi$
$193$		−	24.6225i		−	1.77237i	0.463336	−	0.886183i	$-0.346652\pi$
$194$	−16.2557			−1.16709
$195$		0			0
$196$	−5.83710			−0.416936
$197$			3.91548i			0.278966i	0.990224	+	0.139483i	$0.0445441\pi$
$197$			3.91548i			0.278966i	−0.990224	+	0.139483i	$0.955456\pi$
$198$		0			0
$199$	−8.99386			−0.637558			−0.318779	−	0.947829i	$-0.603273\pi$
$199$	−8.99386			−0.637558			−0.318779	+	0.947829i	$0.603273\pi$
$200$	2.34017	−	4.41855i	0.165475	−	0.312439i
$201$		0			0
$202$			13.0205i			0.916121i
$203$			1.52973i			0.107366i
$204$		0			0
$205$	−2.34017	−	0.581449i	−0.163445	−	0.0406102i
$206$	14.3402			0.999127
$207$		0			0
$208$			0.921622i			0.0639030i
$209$	−3.41855			−0.236466
$210$		0			0
$211$	−4.68035			−0.322208			−0.161104	−	0.986937i	$-0.551506\pi$
$211$	−4.68035			−0.322208			−0.161104	+	0.986937i	$0.551506\pi$
$212$		−	2.68035i		−	0.184087i
$213$		0			0
$214$	−10.8371			−0.740809
$215$	−0.398032	+	1.60197i	−0.0271455	+	0.109253i
$216$		0			0
$217$		−	7.83096i		−	0.531600i
$218$		−	18.6225i		−	1.26127i
$219$		0			0
$220$	−7.41855	−	1.84324i	−0.500159	−	0.124272i
$221$	0.313511			0.0210890
$222$		0			0
$223$		−	14.3402i		−	0.960289i	−0.877189	−	0.480145i	$-0.840584\pi$
$223$		−	14.3402i		−	0.960289i	0.877189	−	0.480145i	$-0.159416\pi$
$224$	1.07838			0.0720521
$225$		0			0
$226$	13.5174			0.899167
$227$		−	19.2039i		−	1.27461i	−0.770612	−	0.637305i	$-0.780049\pi$
$227$		−	19.2039i		−	1.27461i	0.770612	−	0.637305i	$-0.219951\pi$
$228$		0			0
$229$	−2.31351			−0.152881			−0.0764406	−	0.997074i	$-0.524356\pi$
$229$	−2.31351			−0.152881			−0.0764406	+	0.997074i	$0.524356\pi$
$230$	−2.00000	−	0.496928i	−0.131876	−	0.0327665i
$231$		0			0
$232$			1.41855i			0.0931324i
$233$			25.6475i			1.68023i	0.542411	+	0.840113i	$0.317511\pi$
$233$			25.6475i			1.68023i	−0.542411	+	0.840113i	$0.682489\pi$
$234$		0			0
$235$	4.18342	−	16.8371i	0.272896	−	1.09833i
$236$	−8.34017			−0.542899
$237$		0			0
$238$		−	0.366835i		−	0.0237784i
$239$	3.60197			0.232992			0.116496	−	0.993191i	$-0.462834\pi$
$239$	3.60197			0.232992			0.116496	+	0.993191i	$0.462834\pi$
$240$		0			0
$241$	−2.36683			−0.152461			−0.0762306	−	0.997090i	$-0.524289\pi$
$241$	−2.36683			−0.152461			−0.0762306	+	0.997090i	$0.524289\pi$
$242$			0.686489i			0.0441292i
$243$		0			0
$244$	−2.00000			−0.128037
$245$	−12.6670	−	3.14730i	−0.809266	−	0.201074i
$246$		0			0
$247$			0.921622i			0.0586414i
$248$		−	7.26180i		−	0.461124i
$249$		0			0
$250$	7.46081	−	8.32684i	0.471863	−	0.526636i
$251$	−6.73820			−0.425312			−0.212656	−	0.977127i	$-0.568211\pi$
$251$	−6.73820			−0.425312			−0.212656	+	0.977127i	$0.568211\pi$
$252$		0			0
$253$			3.15061i			0.198077i
$254$	−16.4969			−1.03511
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	9.20394i		−	0.574126i	−0.957912	−	0.287063i	$-0.907321\pi$
$257$		−	9.20394i		−	0.574126i	0.957912	−	0.287063i	$-0.0926789\pi$
$258$		0			0
$259$	6.04104			0.375372
$260$	−0.496928	+	2.00000i	−0.0308182	+	0.124035i
$261$		0			0
$262$		−	0.581449i		−	0.0359221i
$263$			25.7998i			1.59088i	0.606031	+	0.795441i	$0.292761\pi$
$263$			25.7998i			1.59088i	−0.606031	+	0.795441i	$0.707239\pi$
$264$		0			0
$265$	1.44521	−	5.81658i	0.0887787	−	0.357310i
$266$	1.07838			0.0661196
$267$		0			0
$268$			4.68035i			0.285898i
$269$	4.73820			0.288893			0.144447	−	0.989513i	$-0.453860\pi$
$269$	4.73820			0.288893			0.144447	+	0.989513i	$0.453860\pi$
$270$		0			0
$271$	16.3668			0.994214			0.497107	−	0.867689i	$-0.334396\pi$
$271$	16.3668			0.994214			0.497107	+	0.867689i	$0.334396\pi$
$272$		−	0.340173i		−	0.0206260i
$273$		0			0
$274$	−5.81658			−0.351393
$275$	−15.1050	−	8.00000i	−0.910868	−	0.482418i
$276$		0			0
$277$			12.6537i			0.760286i	0.924928	+	0.380143i	$0.124125\pi$
$277$			12.6537i			0.760286i	−0.924928	+	0.380143i	$0.875875\pi$
$278$		−	6.15676i		−	0.369258i
$279$		0			0
$280$	2.34017	+	0.581449i	0.139852	+	0.0347482i
$281$	−9.44521			−0.563454			−0.281727	−	0.959495i	$-0.590907\pi$
$281$	−9.44521			−0.563454			−0.281727	+	0.959495i	$0.590907\pi$
$282$		0			0
$283$		−	15.8888i		−	0.944492i	−0.881467	−	0.472246i	$-0.843443\pi$
$283$		−	15.8888i		−	0.944492i	0.881467	−	0.472246i	$-0.156557\pi$
$284$	−10.8371			−0.643064
$285$		0			0
$286$	3.15061			0.186300
$287$		−	1.16290i		−	0.0686437i
$288$		0			0
$289$	16.8843			0.993193
$290$	−0.764867	+	3.07838i	−0.0449145	+	0.180769i
$291$		0			0
$292$		−	6.83710i		−	0.400111i
$293$			4.47027i			0.261156i	0.991438	+	0.130578i	$0.0416833\pi$
$293$			4.47027i			0.261156i	−0.991438	+	0.130578i	$0.958317\pi$
$294$		0			0
$295$	−18.0989	−	4.49693i	−1.05376	−	0.261821i
$296$	5.60197			0.325608
$297$		0			0
$298$			8.34017i			0.483133i
$299$	0.849388			0.0491214
$300$		0			0
$301$	−0.796064			−0.0458843
$302$			16.2557i			0.935408i
$303$		0			0
$304$	1.00000			0.0573539
$305$	−4.34017	−	1.07838i	−0.248518	−	0.0617477i
$306$		0			0
$307$			15.3197i			0.874339i	0.899379	+	0.437169i	$0.144019\pi$
$307$			15.3197i			0.874339i	−0.899379	+	0.437169i	$0.855981\pi$
$308$		−	3.68649i		−	0.210057i
$309$		0			0
$310$	3.91548	−	15.7587i	0.222384	−	0.895035i
$311$	4.39803			0.249390			0.124695	−	0.992195i	$-0.460205\pi$
$311$	4.39803			0.249390			0.124695	+	0.992195i	$0.460205\pi$
$312$		0			0
$313$		−	8.31351i		−	0.469907i	−0.972007	−	0.234954i	$-0.924506\pi$
$313$		−	8.31351i		−	0.469907i	0.972007	−	0.234954i	$-0.0754939\pi$
$314$	−3.65983			−0.206536
$315$		0			0
$316$	4.73820			0.266545
$317$		−	0.470266i		−	0.0264128i	−0.999913	−	0.0132064i	$-0.995796\pi$
$317$		−	0.470266i		−	0.0264128i	0.999913	−	0.0132064i	$-0.00420385\pi$
$318$		0			0
$319$	4.84939			0.271514
$320$	2.17009	+	0.539189i	0.121312	+	0.0301416i
$321$		0			0
$322$		−	0.993857i		−	0.0553855i
$323$		−	0.340173i		−	0.0189277i
$324$		0			0
$325$	−2.15676	+	4.07223i	−0.119635	+	0.225887i
$326$	6.89496			0.381877
$327$		0			0
$328$		−	1.07838i		−	0.0595435i
$329$	8.36683			0.461279
$330$		0			0
$331$	31.5174			1.73236			0.866178	−	0.499736i	$-0.166570\pi$
$331$	31.5174			1.73236			0.866178	+	0.499736i	$0.166570\pi$
$332$		−	11.0205i		−	0.604830i
$333$		0			0
$334$	−4.68035			−0.256097
$335$	−2.52359	+	10.1568i	−0.137878	+	0.554923i
$336$		0			0
$337$			0.0578588i			0.00315177i	0.999999	+	0.00157589i	$0.000501620\pi$
$337$			0.0578588i			0.00315177i	−0.999999	+	0.00157589i	$0.999498\pi$
$338$			12.1506i			0.660906i
$339$		0			0
$340$	0.183417	−	0.738205i	0.00994721	−	0.0400348i
$341$	−24.8248			−1.34434
$342$		0			0
$343$		−	13.8432i		−	0.747465i
$344$	−0.738205			−0.0398013
$345$		0			0
$346$	4.52359			0.243190
$347$			6.34017i			0.340358i	0.985413	+	0.170179i	$0.0544346\pi$
$347$			6.34017i			0.340358i	−0.985413	+	0.170179i	$0.945565\pi$
$348$		0			0
$349$	20.5236			1.09860			0.549301	−	0.835624i	$-0.314894\pi$
$349$	20.5236			1.09860			0.549301	+	0.835624i	$0.314894\pi$
$350$	4.76487	+	2.52359i	0.254693	+	0.134892i
$351$		0			0
$352$		−	3.41855i		−	0.182209i
$353$		−	22.3812i		−	1.19123i	−0.803269	−	0.595616i	$-0.796908\pi$
$353$		−	22.3812i		−	1.19123i	0.803269	−	0.595616i	$-0.203092\pi$
$354$		0			0
$355$	−23.5174	−	5.84324i	−1.24818	−	0.310127i
$356$	−9.75872			−0.517211
$357$		0			0
$358$			14.4969i			0.766186i
$359$	−0.282314			−0.0149000			−0.00744999	−	0.999972i	$-0.502371\pi$
$359$	−0.282314			−0.0149000			−0.00744999	+	0.999972i	$0.502371\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		−	12.7792i		−	0.671662i
$363$		0			0
$364$	−0.993857			−0.0520923
$365$	3.68649	−	14.8371i	0.192960	−	0.776609i
$366$		0			0
$367$			27.9155i			1.45718i	0.684952	+	0.728588i	$0.259823\pi$
$367$			27.9155i			1.45718i	−0.684952	+	0.728588i	$0.740177\pi$
$368$		−	0.921622i		−	0.0480429i
$369$		0			0
$370$	12.1568	+	3.02052i	0.632000	+	0.157029i
$371$	2.89043			0.150063
$372$		0			0
$373$		−	3.44521i		−	0.178386i	−0.996014	−	0.0891932i	$-0.971571\pi$
$373$		−	3.44521i		−	0.178386i	0.996014	−	0.0891932i	$-0.0284288\pi$
$374$	−1.16290			−0.0601321
$375$		0			0
$376$	7.75872			0.400126
$377$		−	1.30737i		−	0.0673329i
$378$		0			0
$379$	28.5113			1.46453			0.732264	−	0.681021i	$-0.238464\pi$
$379$	28.5113			1.46453			0.732264	+	0.681021i	$0.238464\pi$
$380$	2.17009	+	0.539189i	0.111323	+	0.0276598i
$381$		0			0
$382$			4.39803i			0.225023i
$383$			2.63931i			0.134862i	0.997724	+	0.0674312i	$0.0214803\pi$
$383$			2.63931i			0.134862i	−0.997724	+	0.0674312i	$0.978520\pi$
$384$		0			0
$385$	1.98771	−	8.00000i	0.101303	−	0.407718i
$386$	24.6225			1.25325
$387$		0			0
$388$		−	16.2557i		−	0.825256i
$389$	−22.1834			−1.12474			−0.562372	−	0.826884i	$-0.690111\pi$
$389$	−22.1834			−1.12474			−0.562372	+	0.826884i	$0.690111\pi$
$390$		0			0
$391$	−0.313511			−0.0158549
$392$		−	5.83710i		−	0.294818i
$393$		0			0
$394$	−3.91548			−0.197259
$395$	10.2823	+	2.55479i	0.517359	+	0.128545i
$396$		0			0
$397$			24.2245i			1.21579i	0.794017	+	0.607895i	$0.207986\pi$
$397$			24.2245i			1.21579i	−0.794017	+	0.607895i	$0.792014\pi$
$398$		−	8.99386i		−	0.450821i
$399$		0			0
$400$	4.41855	+	2.34017i	0.220928	+	0.117009i
$401$	−12.7649			−0.637447			−0.318724	−	0.947848i	$-0.603254\pi$
$401$	−12.7649			−0.637447			−0.318724	+	0.947848i	$0.603254\pi$
$402$		0			0
$403$			6.69263i			0.333384i
$404$	−13.0205			−0.647795
$405$		0			0
$406$	−1.52973			−0.0759194
$407$		−	19.1506i		−	0.949261i
$408$		0			0
$409$	−22.8781			−1.13125			−0.565626	−	0.824662i	$-0.691365\pi$
$409$	−22.8781			−1.13125			−0.565626	+	0.824662i	$0.691365\pi$
$410$	0.581449	−	2.34017i	0.0287157	−	0.115573i
$411$		0			0
$412$			14.3402i			0.706490i
$413$		−	8.99386i		−	0.442559i
$414$		0			0
$415$	5.94214	−	23.9155i	0.291688	−	1.17396i
$416$	−0.921622			−0.0451862
$417$		0			0
$418$		−	3.41855i		−	0.167207i
$419$	3.47187			0.169612			0.0848061	−	0.996397i	$-0.472973\pi$
$419$	3.47187			0.169612			0.0848061	+	0.996397i	$0.472973\pi$
$420$		0			0
$421$	−20.4657			−0.997439			−0.498719	−	0.866764i	$-0.666196\pi$
$421$	−20.4657			−0.997439			−0.498719	+	0.866764i	$0.666196\pi$
$422$		−	4.68035i		−	0.227836i
$423$		0			0
$424$	2.68035			0.130169
$425$	0.796064	−	1.50307i	0.0386148	−	0.0729097i
$426$		0			0
$427$		−	2.15676i		−	0.104373i
$428$		−	10.8371i		−	0.523831i
$429$		0			0
$430$	−1.60197	−	0.398032i	−0.0772538	−	0.0191948i
$431$	33.1917			1.59879			0.799393	−	0.600809i	$-0.205155\pi$
$431$	33.1917			1.59879			0.799393	+	0.600809i	$0.205155\pi$
$432$		0			0
$433$			41.1338i			1.97676i	0.151991	+	0.988382i	$0.451432\pi$
$433$			41.1338i			1.97676i	−0.151991	+	0.988382i	$0.548568\pi$
$434$	7.83096			0.375898
$435$		0			0
$436$	18.6225			0.891855
$437$		−	0.921622i		−	0.0440872i
$438$		0			0
$439$	−19.1461			−0.913792			−0.456896	−	0.889520i	$-0.651039\pi$
$439$	−19.1461			−0.913792			−0.456896	+	0.889520i	$0.651039\pi$
$440$	1.84324	−	7.41855i	0.0878732	−	0.353666i
$441$		0			0
$442$			0.313511i			0.0149122i
$443$		−	37.4908i		−	1.78124i	−0.454747	−	0.890620i	$-0.650270\pi$
$443$		−	37.4908i		−	1.78124i	0.454747	−	0.890620i	$-0.349730\pi$
$444$		0			0
$445$	−21.1773	−	5.26180i	−1.00390	−	0.249433i
$446$	14.3402			0.679027
$447$		0			0
$448$			1.07838i			0.0509486i
$449$	6.43907			0.303878			0.151939	−	0.988390i	$-0.451448\pi$
$449$	6.43907			0.303878			0.151939	+	0.988390i	$0.451448\pi$
$450$		0			0
$451$	−3.68649			−0.173590
$452$			13.5174i			0.635807i
$453$		0			0
$454$	19.2039			0.901285
$455$	−2.15676	−	0.535877i	−0.101110	−	0.0251223i
$456$		0			0
$457$		−	13.6742i		−	0.639652i	−0.947476	−	0.319826i	$-0.896376\pi$
$457$		−	13.6742i		−	0.639652i	0.947476	−	0.319826i	$-0.103624\pi$
$458$		−	2.31351i		−	0.108103i
$459$		0			0
$460$	0.496928	−	2.00000i	0.0231694	−	0.0932505i
$461$	−27.5441			−1.28286			−0.641429	−	0.767183i	$-0.721658\pi$
$461$	−27.5441			−1.28286			−0.641429	+	0.767183i	$0.721658\pi$
$462$		0			0
$463$		−	28.5958i		−	1.32896i	−0.747306	−	0.664480i	$-0.768653\pi$
$463$		−	28.5958i		−	1.32896i	0.747306	−	0.664480i	$-0.231347\pi$
$464$	−1.41855			−0.0658546
$465$		0			0
$466$	−25.6475			−1.18810
$467$		−	35.5318i		−	1.64422i	−0.569331	−	0.822108i	$-0.692798\pi$
$467$		−	35.5318i		−	1.64422i	0.569331	−	0.822108i	$-0.307202\pi$
$468$		0			0
$469$	−5.04718			−0.233057
$470$	16.8371	+	4.18342i	0.776638	+	0.192967i
$471$		0			0
$472$		−	8.34017i		−	0.383888i
$473$			2.52359i			0.116035i
$474$		0			0
$475$	4.41855	+	2.34017i	0.202737	+	0.107375i
$476$	0.366835			0.0168139
$477$		0			0
$478$			3.60197i			0.164750i
$479$	24.6491			1.12625			0.563124	−	0.826372i	$-0.309599\pi$
$479$	24.6491			1.12625			0.563124	+	0.826372i	$0.309599\pi$
$480$		0			0
$481$	−5.16290			−0.235408
$482$		−	2.36683i		−	0.107806i
$483$		0			0
$484$	−0.686489			−0.0312040
$485$	8.76487	−	35.2762i	0.397992	−	1.60181i
$486$		0			0
$487$		−	15.3340i		−	0.694851i	−0.937708	−	0.347426i	$-0.887056\pi$
$487$		−	15.3340i		−	0.694851i	0.937708	−	0.347426i	$-0.112944\pi$
$488$		−	2.00000i		−	0.0905357i
$489$		0			0
$490$	3.14730	−	12.6670i	0.142181	−	0.572237i
$491$	32.7792			1.47931			0.739653	−	0.672988i	$-0.234990\pi$
$491$	32.7792			1.47931			0.739653	+	0.672988i	$0.234990\pi$
$492$		0			0
$493$			0.482553i			0.0217331i
$494$	−0.921622			−0.0414657
$495$		0			0
$496$	7.26180			0.326064
$497$		−	11.6865i		−	0.524211i
$498$		0			0
$499$	25.6742			1.14934			0.574668	−	0.818387i	$-0.305131\pi$
$499$	25.6742			1.14934			0.574668	+	0.818387i	$0.305131\pi$
$500$	8.32684	+	7.46081i	0.372388	+	0.333658i
$501$		0			0
$502$		−	6.73820i		−	0.300741i
$503$			24.7526i			1.10366i	0.833956	+	0.551832i	$0.186071\pi$
$503$			24.7526i			1.10366i	−0.833956	+	0.551832i	$0.813929\pi$
$504$		0			0
$505$	−28.2557	−	7.02052i	−1.25736	−	0.312409i
$506$	−3.15061			−0.140062
$507$		0			0
$508$		−	16.4969i		−	0.731933i
$509$	−20.9360			−0.927972			−0.463986	−	0.885843i	$-0.653581\pi$
$509$	−20.9360			−0.927972			−0.463986	+	0.885843i	$0.653581\pi$
$510$		0			0
$511$	7.37298			0.326161
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	9.20394			0.405968
$515$	−7.73206	+	31.1194i	−0.340715	+	1.37129i
$516$		0			0
$517$		−	26.5236i		−	1.16651i
$518$			6.04104i			0.265428i
$519$		0			0
$520$	−2.00000	−	0.496928i	−0.0877058	−	0.0217918i
$521$	−23.5486			−1.03168			−0.515842	−	0.856683i	$-0.672521\pi$
$521$	−23.5486			−1.03168			−0.515842	+	0.856683i	$0.672521\pi$
$522$		0			0
$523$			14.7838i			0.646449i	0.946322	+	0.323225i	$0.104767\pi$
$523$			14.7838i			0.646449i	−0.946322	+	0.323225i	$0.895233\pi$
$524$	0.581449			0.0254007
$525$		0			0
$526$	−25.7998			−1.12492
$527$		−	2.47027i		−	0.107606i
$528$		0			0
$529$	22.1506			0.963070
$530$	5.81658	+	1.44521i	0.252656	+	0.0627760i
$531$		0			0
$532$			1.07838i			0.0467536i
$533$			0.993857i			0.0430487i
$534$		0			0
$535$	5.84324	−	23.5174i	0.252625	−	1.01675i
$536$	−4.68035			−0.202160
$537$		0			0
$538$			4.73820i			0.204279i
$539$	−19.9544			−0.859498
$540$		0			0
$541$	−40.8371			−1.75572			−0.877862	−	0.478914i	$-0.841031\pi$
$541$	−40.8371			−1.75572			−0.877862	+	0.478914i	$0.841031\pi$
$542$			16.3668i			0.703016i
$543$		0			0
$544$	0.340173			0.0145848
$545$	40.4124	+	10.0410i	1.73108	+	0.430111i
$546$		0			0
$547$			42.0410i			1.79754i	0.438415	+	0.898772i	$0.355540\pi$
$547$			42.0410i			1.79754i	−0.438415	+	0.898772i	$0.644460\pi$
$548$		−	5.81658i		−	0.248472i
$549$		0			0
$550$	8.00000	−	15.1050i	0.341121	−	0.644081i
$551$	−1.41855			−0.0604323
$552$		0			0
$553$			5.10957i			0.217281i
$554$	−12.6537			−0.537604
$555$		0			0
$556$	6.15676			0.261105
$557$			26.7526i			1.13354i	0.823875	+	0.566772i	$0.191808\pi$
$557$			26.7526i			1.13354i	−0.823875	+	0.566772i	$0.808192\pi$
$558$		0			0
$559$	0.680346			0.0287756
$560$	−0.581449	+	2.34017i	−0.0245707	+	0.0988904i
$561$		0			0
$562$		−	9.44521i		−	0.398422i
$563$		−	21.9877i		−	0.926672i	−0.886183	−	0.463336i	$-0.846652\pi$
$563$		−	21.9877i		−	0.926672i	0.886183	−	0.463336i	$-0.153348\pi$
$564$		0			0
$565$	−7.28846	+	29.3340i	−0.306628	+	1.23409i
$566$	15.8888			0.667857
$567$		0			0
$568$		−	10.8371i		−	0.454715i
$569$	−32.5958			−1.36649			−0.683244	−	0.730190i	$-0.739431\pi$
$569$	−32.5958			−1.36649			−0.683244	+	0.730190i	$0.739431\pi$
$570$		0			0
$571$	−32.1445			−1.34520			−0.672602	−	0.740004i	$-0.734823\pi$
$571$	−32.1445			−1.34520			−0.672602	+	0.740004i	$0.734823\pi$
$572$			3.15061i			0.131734i
$573$		0			0
$574$	1.16290			0.0485384
$575$	2.15676	−	4.07223i	0.0899429	−	0.169824i
$576$		0			0
$577$		−	13.6742i		−	0.569265i	−0.958637	−	0.284632i	$-0.908129\pi$
$577$		−	13.6742i		−	0.569265i	0.958637	−	0.284632i	$-0.0918715\pi$
$578$			16.8843i			0.702294i
$579$		0			0
$580$	−3.07838	−	0.764867i	−0.127823	−	0.0317594i
$581$	11.8843			0.493043
$582$		0			0
$583$		−	9.16290i		−	0.379488i
$584$	6.83710			0.282921
$585$		0			0
$586$	−4.47027			−0.184665
$587$			30.9672i			1.27815i	0.769143	+	0.639076i	$0.220683\pi$
$587$			30.9672i			1.27815i	−0.769143	+	0.639076i	$0.779317\pi$
$588$		0			0
$589$	7.26180			0.299217
$590$	4.49693	−	18.0989i	0.185136	−	0.745120i
$591$		0			0
$592$			5.60197i			0.230239i
$593$		−	42.3812i		−	1.74039i	−0.492709	−	0.870194i	$-0.663993\pi$
$593$		−	42.3812i		−	1.74039i	0.492709	−	0.870194i	$-0.336007\pi$
$594$		0			0
$595$	0.796064	+	0.197793i	0.0326354	+	0.00810874i
$596$	−8.34017			−0.341627
$597$		0			0
$598$			0.849388i			0.0347340i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	11.4764			0.468133			0.234066	−	0.972221i	$-0.424797\pi$
$601$	11.4764			0.468133			0.234066	+	0.972221i	$0.424797\pi$
$602$		−	0.796064i		−	0.0324451i
$603$		0			0
$604$	−16.2557			−0.661433
$605$	−1.48974	−	0.370147i	−0.0605666	−	0.0150486i
$606$		0			0
$607$		−	15.3340i		−	0.622389i	−0.950346	−	0.311195i	$-0.899271\pi$
$607$		−	15.3340i		−	0.622389i	0.950346	−	0.311195i	$-0.100729\pi$
$608$			1.00000i			0.0405554i
$609$		0			0
$610$	1.07838	−	4.34017i	0.0436622	−	0.175728i
$611$	−7.15061			−0.289283
$612$		0			0
$613$		−	4.34017i		−	0.175298i	−0.996151	−	0.0876490i	$-0.972065\pi$
$613$		−	4.34017i		−	0.175298i	0.996151	−	0.0876490i	$-0.0279354\pi$
$614$	−15.3197			−0.618251
$615$		0			0
$616$	3.68649			0.148533
$617$			30.1834i			1.21514i	0.794267	+	0.607569i	$0.207855\pi$
$617$			30.1834i			1.21514i	−0.794267	+	0.607569i	$0.792145\pi$
$618$		0			0
$619$	7.94668			0.319404			0.159702	−	0.987165i	$-0.448947\pi$
$619$	7.94668			0.319404			0.159702	+	0.987165i	$0.448947\pi$
$620$	15.7587	+	3.91548i	0.632886	+	0.157249i
$621$		0			0
$622$			4.39803i			0.176345i
$623$		−	10.5236i		−	0.421619i
$624$		0			0
$625$	14.0472	+	20.6803i	0.561887	+	0.827214i
$626$	8.31351			0.332275
$627$		0			0
$628$		−	3.65983i		−	0.146043i
$629$	1.90564			0.0759828
$630$		0			0
$631$	8.68035			0.345559			0.172780	−	0.984961i	$-0.444725\pi$
$631$	8.68035			0.345559			0.172780	+	0.984961i	$0.444725\pi$
$632$			4.73820i			0.188476i
$633$		0			0
$634$	0.470266			0.0186767
$635$	8.89496	−	35.7998i	0.352986	−	1.42067i
$636$		0			0
$637$			5.37960i			0.213148i
$638$			4.84939i			0.191989i
$639$		0			0
$640$	−0.539189	+	2.17009i	−0.0213133	+	0.0857802i
$641$	41.6430			1.64480			0.822400	−	0.568910i	$-0.192635\pi$
$641$	41.6430			1.64480			0.822400	+	0.568910i	$0.192635\pi$
$642$		0			0
$643$			29.7854i			1.17462i	0.809362	+	0.587310i	$0.199813\pi$
$643$			29.7854i			1.17462i	−0.809362	+	0.587310i	$0.800187\pi$
$644$	0.993857			0.0391634
$645$		0			0
$646$	0.340173			0.0133839
$647$		−	28.9216i		−	1.13703i	−0.822674	−	0.568513i	$-0.807519\pi$
$647$		−	28.9216i		−	1.13703i	0.822674	−	0.568513i	$-0.192481\pi$
$648$		0			0
$649$	−28.5113			−1.11917
$650$	−4.07223	−	2.15676i	−0.159726	−	0.0845949i
$651$		0			0
$652$			6.89496i			0.270027i
$653$			41.9565i			1.64189i	0.571011	+	0.820943i	$0.306552\pi$
$653$			41.9565i			1.64189i	−0.571011	+	0.820943i	$0.693448\pi$
$654$		0			0
$655$	1.26180	+	0.313511i	0.0493024	+	0.0122499i
$656$	1.07838			0.0421036
$657$		0			0
$658$			8.36683i			0.326173i
$659$	43.0082			1.67536			0.837681	−	0.546159i	$-0.183911\pi$
$659$	43.0082			1.67536			0.837681	+	0.546159i	$0.183911\pi$
$660$		0			0
$661$	−34.3090			−1.33446			−0.667232	−	0.744850i	$-0.732521\pi$
$661$	−34.3090			−1.33446			−0.667232	+	0.744850i	$0.732521\pi$
$662$			31.5174i			1.22496i
$663$		0			0
$664$	11.0205			0.427679
$665$	−0.581449	+	2.34017i	−0.0225476	+	0.0907480i
$666$		0			0
$667$			1.30737i			0.0506215i
$668$		−	4.68035i		−	0.181088i
$669$		0			0
$670$	−10.1568	−	2.52359i	−0.392390	−	0.0974948i
$671$	−6.83710			−0.263943
$672$		0			0
$673$			31.0928i			1.19854i	0.800548	+	0.599269i	$0.204542\pi$
$673$			31.0928i			1.19854i	−0.800548	+	0.599269i	$0.795458\pi$
$674$	−0.0578588			−0.00222864
$675$		0			0
$676$	−12.1506			−0.467331
$677$			35.9877i			1.38312i	0.722319	+	0.691560i	$0.243076\pi$
$677$			35.9877i			1.38312i	−0.722319	+	0.691560i	$0.756924\pi$
$678$		0			0
$679$	17.5297			0.672729
$680$	0.738205	+	0.183417i	0.0283089	+	0.00703374i
$681$		0			0
$682$		−	24.8248i		−	0.950591i
$683$		−	27.4017i		−	1.04850i	−0.851565	−	0.524249i	$-0.824346\pi$
$683$		−	27.4017i		−	1.04850i	0.851565	−	0.524249i	$-0.175654\pi$
$684$		0			0
$685$	3.13624	−	12.6225i	0.119829	−	0.482280i
$686$	13.8432			0.528538
$687$		0			0
$688$		−	0.738205i		−	0.0281438i
$689$	−2.47027			−0.0941097
$690$		0			0
$691$	3.83096			0.145737			0.0728683	−	0.997342i	$-0.476785\pi$
$691$	3.83096			0.145737			0.0728683	+	0.997342i	$0.476785\pi$
$692$			4.52359i			0.171961i
$693$		0			0
$694$	−6.34017			−0.240670
$695$	13.3607	+	3.31965i	0.506800	+	0.125922i
$696$		0			0
$697$		−	0.366835i		−	0.0138949i
$698$			20.5236i			0.776829i
$699$		0			0
$700$	−2.52359	+	4.76487i	−0.0953828	+	0.180095i
$701$	−46.5790			−1.75926			−0.879632	−	0.475654i	$-0.842211\pi$
$701$	−46.5790			−1.75926			−0.879632	+	0.475654i	$0.842211\pi$
$702$		0			0
$703$			5.60197i			0.211282i
$704$	3.41855			0.128841
$705$		0			0
$706$	22.3812			0.842328
$707$		−	14.0410i		−	0.528068i
$708$		0			0
$709$	−15.1917			−0.570534			−0.285267	−	0.958448i	$-0.592082\pi$
$709$	−15.1917			−0.570534			−0.285267	+	0.958448i	$0.592082\pi$
$710$	5.84324	−	23.5174i	0.219293	−	0.882594i
$711$		0			0
$712$		−	9.75872i		−	0.365724i
$713$		−	6.69263i		−	0.250641i
$714$		0			0
$715$	−1.69878	+	6.83710i	−0.0635306	+	0.255693i
$716$	−14.4969			−0.541776
$717$		0			0
$718$		−	0.282314i		−	0.0105359i
$719$	−8.45136			−0.315182			−0.157591	−	0.987504i	$-0.550373\pi$
$719$	−8.45136			−0.315182			−0.157591	+	0.987504i	$0.550373\pi$
$720$		0			0
$721$	−15.4641			−0.575914
$722$			1.00000i			0.0372161i
$723$		0			0
$724$	12.7792			0.474937
$725$	−6.26794	−	3.31965i	−0.232785	−	0.123289i
$726$		0			0
$727$			39.9688i			1.48236i	0.671306	+	0.741180i	$0.265734\pi$
$727$			39.9688i			1.48236i	−0.671306	+	0.741180i	$0.734266\pi$
$728$		−	0.993857i		−	0.0368348i
$729$		0			0
$730$	14.8371	+	3.68649i	0.549146	+	0.136443i
$731$	−0.251117			−0.00928791
$732$		0			0
$733$		−	38.7480i		−	1.43119i	−0.698515	−	0.715596i	$-0.746155\pi$
$733$		−	38.7480i		−	1.43119i	0.698515	−	0.715596i	$-0.253845\pi$
$734$	−27.9155			−1.03038
$735$		0			0
$736$	0.921622			0.0339714
$737$			16.0000i			0.589368i
$738$		0			0
$739$	15.1506			0.557324			0.278662	−	0.960389i	$-0.410109\pi$
$739$	15.1506			0.557324			0.278662	+	0.960389i	$0.410109\pi$
$740$	−3.02052	+	12.1568i	−0.111036	+	0.446891i
$741$		0			0
$742$			2.89043i			0.106111i
$743$			28.8781i			1.05944i	0.848174	+	0.529718i	$0.177702\pi$
$743$			28.8781i			1.05944i	−0.848174	+	0.529718i	$0.822298\pi$
$744$		0			0
$745$	−18.0989	−	4.49693i	−0.663092	−	0.164755i
$746$	3.44521			0.126138
$747$		0			0
$748$		−	1.16290i		−	0.0425198i
$749$	11.6865			0.427015
$750$		0			0
$751$	−14.2679			−0.520644			−0.260322	−	0.965522i	$-0.583829\pi$
$751$	−14.2679			−0.520644			−0.260322	+	0.965522i	$0.583829\pi$
$752$			7.75872i			0.282932i
$753$		0			0
$754$	1.30737			0.0476115
$755$	−35.2762	−	8.76487i	−1.28383	−	0.318986i
$756$		0			0
$757$			22.2122i			0.807315i	0.914910	+	0.403658i	$0.132261\pi$
$757$			22.2122i			0.807315i	−0.914910	+	0.403658i	$0.867739\pi$
$758$			28.5113i			1.03558i
$759$		0			0
$760$	−0.539189	+	2.17009i	−0.0195584	+	0.0787173i
$761$	−2.48255			−0.0899925			−0.0449962	−	0.998987i	$-0.514328\pi$
$761$	−2.48255			−0.0899925			−0.0449962	+	0.998987i	$0.514328\pi$
$762$		0			0
$763$			20.0821i			0.727020i
$764$	−4.39803			−0.159115
$765$		0			0
$766$	−2.63931			−0.0953621
$767$			7.68649i			0.277543i
$768$		0			0
$769$	22.3135			0.804646			0.402323	−	0.915498i	$-0.368203\pi$
$769$	22.3135			0.804646			0.402323	+	0.915498i	$0.368203\pi$
$770$	8.00000	+	1.98771i	0.288300	+	0.0716322i
$771$		0			0
$772$			24.6225i			0.886183i
$773$			24.2101i			0.870776i	0.900243	+	0.435388i	$0.143389\pi$
$773$			24.2101i			0.870776i	−0.900243	+	0.435388i	$0.856611\pi$
$774$		0			0
$775$	32.0866	+	16.9939i	1.15259	+	0.610437i
$776$	16.2557			0.583544
$777$		0			0
$778$		−	22.1834i		−	0.795314i
$779$	1.07838			0.0386369
$780$		0			0
$781$	−37.0472			−1.32565
$782$		−	0.313511i		−	0.0112111i
$783$		0			0
$784$	5.83710			0.208468
$785$	1.97334	−	7.94214i	0.0704315	−	0.283467i
$786$		0			0
$787$			31.0349i			1.10627i	0.833090	+	0.553137i	$0.186569\pi$
$787$			31.0349i			1.10627i	−0.833090	+	0.553137i	$0.813431\pi$
$788$		−	3.91548i		−	0.139483i
$789$		0			0
$790$	−2.55479	+	10.2823i	−0.0908953	+	0.365828i
$791$	−14.5769			−0.518295
$792$		0			0
$793$			1.84324i			0.0654555i
$794$	−24.2245			−0.859694
$795$		0			0
$796$	8.99386			0.318779
$797$			25.2039i			0.892769i	0.894841	+	0.446385i	$0.147289\pi$
$797$			25.2039i			0.892769i	−0.894841	+	0.446385i	$0.852711\pi$
$798$		0			0
$799$	2.63931			0.0933720
$800$	−2.34017	+	4.41855i	−0.0827376	+	0.156219i
$801$		0			0
$802$		−	12.7649i		−	0.450743i
$803$		−	23.3730i		−	0.824814i
$804$		0			0
$805$	2.15676	+	0.535877i	0.0760156	+	0.0188872i
$806$	−6.69263			−0.235738
$807$		0			0
$808$		−	13.0205i		−	0.458060i
$809$	17.9467			0.630972			0.315486	−	0.948930i	$-0.397833\pi$
$809$	17.9467			0.630972			0.315486	+	0.948930i	$0.397833\pi$
$810$		0			0
$811$	40.5113			1.42254			0.711272	−	0.702917i	$-0.248119\pi$
$811$	40.5113			1.42254			0.711272	+	0.702917i	$0.248119\pi$
$812$		−	1.52973i		−	0.0536831i
$813$		0			0
$814$	19.1506			0.671229
$815$	−3.71769	+	14.9627i	−0.130225	+	0.524119i
$816$		0			0
$817$		−	0.738205i		−	0.0258265i
$818$		−	22.8781i		−	0.799915i
$819$		0			0
$820$	2.34017	+	0.581449i	0.0817224	+	0.0203051i
$821$	−49.3340			−1.72177			−0.860885	−	0.508800i	$-0.830089\pi$
$821$	−49.3340			−1.72177			−0.860885	+	0.508800i	$0.830089\pi$
$822$		0			0
$823$			5.24742i			0.182914i	0.995809	+	0.0914568i	$0.0291523\pi$
$823$			5.24742i			0.182914i	−0.995809	+	0.0914568i	$0.970848\pi$
$824$	−14.3402			−0.499564
$825$		0			0
$826$	8.99386			0.312936
$827$		−	22.5236i		−	0.783222i	−0.920131	−	0.391611i	$-0.871918\pi$
$827$		−	22.5236i		−	0.783222i	0.920131	−	0.391611i	$-0.128082\pi$
$828$		0			0
$829$	−43.2495			−1.50212			−0.751059	−	0.660235i	$-0.770457\pi$
$829$	−43.2495			−1.50212			−0.751059	+	0.660235i	$0.770457\pi$
$830$	23.9155	+	5.94214i	0.830118	+	0.206255i
$831$		0			0
$832$		−	0.921622i		−	0.0319515i
$833$		−	1.98562i		−	0.0687978i
$834$		0			0
$835$	2.52359	−	10.1568i	0.0873324	−	0.351489i
$836$	3.41855			0.118233
$837$		0			0
$838$			3.47187i			0.119934i
$839$	−34.6681			−1.19687			−0.598437	−	0.801170i	$-0.704211\pi$
$839$	−34.6681			−1.19687			−0.598437	+	0.801170i	$0.704211\pi$
$840$		0			0
$841$	−26.9877			−0.930611
$842$		−	20.4657i		−	0.705296i
$843$		0			0
$844$	4.68035			0.161104
$845$	−26.3679	−	6.55148i	−0.907083	−	0.225378i
$846$		0			0
$847$		−	0.740294i		−	0.0254368i
$848$			2.68035i			0.0920435i
$849$		0			0
$850$	1.50307	+	0.796064i	0.0515549	+	0.0273048i
$851$	5.16290			0.176982
$852$		0			0
$853$			28.0554i			0.960599i	0.877105	+	0.480300i	$0.159472\pi$
$853$			28.0554i			0.960599i	−0.877105	+	0.480300i	$0.840528\pi$
$854$	2.15676			0.0738027
$855$		0			0
$856$	10.8371			0.370405
$857$			49.0882i			1.67682i	0.545039	+	0.838411i	$0.316515\pi$
$857$			49.0882i			1.67682i	−0.545039	+	0.838411i	$0.683485\pi$
$858$		0			0
$859$	37.7275			1.28725			0.643623	−	0.765342i	$-0.277430\pi$
$859$	37.7275			1.28725			0.643623	+	0.765342i	$0.277430\pi$
$860$	0.398032	−	1.60197i	0.0135728	−	0.0546267i
$861$		0			0
$862$			33.1917i			1.13051i
$863$			44.9939i			1.53161i	0.643074	+	0.765804i	$0.277659\pi$
$863$			44.9939i			1.53161i	−0.643074	+	0.765804i	$0.722341\pi$
$864$		0			0
$865$	−2.43907	+	9.81658i	−0.0829309	+	0.333774i
$866$	−41.1338			−1.39778
$867$		0			0
$868$			7.83096i			0.265800i
$869$	16.1978			0.549473
$870$		0			0
$871$	4.31351			0.146158
$872$			18.6225i			0.630637i
$873$		0			0
$874$	0.921622			0.0311743
$875$	−8.04557	+	8.97948i	−0.271990	+	0.303562i
$876$		0			0
$877$		−	2.64915i		−	0.0894554i	−0.998999	−	0.0447277i	$-0.985758\pi$
$877$		−	2.64915i		−	0.0894554i	0.998999	−	0.0447277i	$-0.0142420\pi$
$878$		−	19.1461i		−	0.646149i
$879$		0			0
$880$	7.41855	+	1.84324i	0.250079	+	0.0621358i
$881$	−30.2511			−1.01919			−0.509593	−	0.860416i	$-0.670204\pi$
$881$	−30.2511			−1.01919			−0.509593	+	0.860416i	$0.670204\pi$
$882$		0			0
$883$		−	19.9955i		−	0.672901i	−0.941701	−	0.336450i	$-0.890774\pi$
$883$		−	19.9955i		−	0.672901i	0.941701	−	0.336450i	$-0.109226\pi$
$884$	−0.313511			−0.0105445
$885$		0			0
$886$	37.4908			1.25953
$887$			57.0759i			1.91642i	0.286062	+	0.958211i	$0.407654\pi$
$887$			57.0759i			1.91642i	−0.286062	+	0.958211i	$0.592346\pi$
$888$		0			0
$889$	17.7899			0.596655
$890$	5.26180	−	21.1773i	0.176376	−	0.709864i
$891$		0			0
$892$			14.3402i			0.480145i
$893$			7.75872i			0.259636i
$894$		0			0
$895$	−31.4596	−	7.81658i	−1.05158	−	0.261280i
$896$	−1.07838			−0.0360261
$897$		0			0
$898$			6.43907i			0.214875i
$899$	−10.3012			−0.343565
$900$		0			0
$901$	0.911781			0.0303758
$902$		−	3.68649i		−	0.122747i
$903$		0			0
$904$	−13.5174			−0.449584
$905$	27.7321	+	6.89043i	0.921845	+	0.229045i
$906$		0			0
$907$			15.4017i			0.511406i	0.966755	+	0.255703i	$0.0823069\pi$
$907$			15.4017i			0.511406i	−0.966755	+	0.255703i	$0.917693\pi$
$908$			19.2039i			0.637305i
$909$		0			0
$910$	0.535877	−	2.15676i	0.0177641	−	0.0714957i
$911$	37.5585			1.24437			0.622184	−	0.782871i	$-0.286246\pi$
$911$	37.5585			1.24437			0.622184	+	0.782871i	$0.286246\pi$
$912$		0			0
$913$		−	37.6742i		−	1.24683i
$914$	13.6742			0.452302
$915$		0			0
$916$	2.31351			0.0764406
$917$			0.627022i			0.0207061i
$918$		0			0
$919$	10.0410			0.331223			0.165612	−	0.986191i	$-0.447040\pi$
$919$	10.0410			0.331223			0.165612	+	0.986191i	$0.447040\pi$
$920$	2.00000	+	0.496928i	0.0659380	+	0.0163832i
$921$		0			0
$922$		−	27.5441i		−	0.907117i
$923$			9.98771i			0.328750i
$924$		0			0
$925$	−13.1096	+	24.7526i	−0.431040	+	0.813860i
$926$	28.5958			0.939717
$927$		0			0
$928$		−	1.41855i		−	0.0465662i
$929$	1.26633			0.0415469			0.0207735	−	0.999784i	$-0.493387\pi$
$929$	1.26633			0.0415469			0.0207735	+	0.999784i	$0.493387\pi$
$930$		0			0
$931$	5.83710			0.191303
$932$		−	25.6475i		−	0.840113i
$933$		0			0
$934$	35.5318			1.16264
$935$	0.627022	−	2.52359i	0.0205058	−	0.0825302i
$936$		0			0
$937$		−	14.1568i		−	0.462481i	−0.972897	−	0.231241i	$-0.925722\pi$
$937$		−	14.1568i		−	0.462481i	0.972897	−	0.231241i	$-0.0742784\pi$
$938$		−	5.04718i		−	0.164796i
$939$		0			0
$940$	−4.18342	+	16.8371i	−0.136448	+	0.549166i
$941$	−15.2085			−0.495782			−0.247891	−	0.968788i	$-0.579737\pi$
$941$	−15.2085			−0.495782			−0.247891	+	0.968788i	$0.579737\pi$
$942$		0			0
$943$		−	0.993857i		−	0.0323644i
$944$	8.34017			0.271450
$945$		0			0
$946$	−2.52359			−0.0820490
$947$			2.53797i			0.0824728i	0.999149	+	0.0412364i	$0.0131297\pi$
$947$			2.53797i			0.0824728i	−0.999149	+	0.0412364i	$0.986870\pi$
$948$		0			0
$949$	−6.30122			−0.204546
$950$	−2.34017	+	4.41855i	−0.0759252	+	0.143357i
$951$		0			0
$952$			0.366835i			0.0118892i
$953$			55.0759i			1.78408i	0.451952	+	0.892042i	$0.350728\pi$
$953$			55.0759i			1.78408i	−0.451952	+	0.892042i	$0.649272\pi$
$954$		0			0
$955$	−9.54411	−	2.37137i	−0.308840	−	0.0767357i
$956$	−3.60197			−0.116496
$957$		0			0
$958$			24.6491i			0.796378i
$959$	6.27247			0.202549
$960$		0			0
$961$	21.7337			0.701086
$962$		−	5.16290i		−	0.166459i
$963$		0			0
$964$	2.36683			0.0762306
$965$	−13.2762	+	53.4329i	−0.427375	+	1.72007i
$966$		0			0
$967$		−	12.6491i		−	0.406769i	−0.979099	−	0.203385i	$-0.934806\pi$
$967$		−	12.6491i		−	0.406769i	0.979099	−	0.203385i	$-0.0651942\pi$
$968$		−	0.686489i		−	0.0220646i
$969$		0			0
$970$	35.2762	+	8.76487i	1.13265	+	0.281423i
$971$	−38.0677			−1.22165			−0.610825	−	0.791765i	$-0.709162\pi$
$971$	−38.0677			−1.22165			−0.610825	+	0.791765i	$0.709162\pi$
$972$		0			0
$973$			6.63931i			0.212846i
$974$	15.3340			0.491334
$975$		0			0
$976$	2.00000			0.0640184
$977$			6.16904i			0.197365i	0.995119	+	0.0986826i	$0.0314628\pi$
$977$			6.16904i			0.197365i	−0.995119	+	0.0986826i	$0.968537\pi$
$978$		0			0
$979$	−33.3607			−1.06621
$980$	12.6670	+	3.14730i	0.404633	+	0.100537i
$981$		0			0
$982$			32.7792i			1.04603i
$983$		−	1.98771i		−	0.0633982i	−0.999497	−	0.0316991i	$-0.989908\pi$
$983$		−	1.98771i		−	0.0633982i	0.999497	−	0.0316991i	$-0.0100918\pi$
$984$		0			0
$985$	2.11118	−	8.49693i	0.0672679	−	0.270735i
$986$	−0.482553			−0.0153676
$987$		0			0
$988$		−	0.921622i		−	0.0293207i
$989$	−0.680346			−0.0216337
$990$		0			0
$991$	−0.907246			−0.0288196			−0.0144098	−	0.999896i	$-0.504587\pi$
$991$	−0.907246			−0.0288196			−0.0144098	+	0.999896i	$0.504587\pi$
$992$			7.26180i			0.230562i
$993$		0			0
$994$	11.6865			0.370673
$995$	19.5174	+	4.84939i	0.618745	+	0.153736i
$996$		0			0
$997$		−	17.3874i		−	0.550663i	−0.961349	−	0.275332i	$-0.911212\pi$
$997$		−	17.3874i		−	0.550663i	0.961349	−	0.275332i	$-0.0887876\pi$
$998$			25.6742i			0.812703i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.d.e.1369.4		6
3.2	odd	2		570.2.d.d.229.3	✓	6
5.2	odd	4		8550.2.a.cf.1.2		3
5.3	odd	4		8550.2.a.cr.1.2		3
5.4	even	2	inner	1710.2.d.e.1369.1		6
15.2	even	4		2850.2.a.bn.1.2		3
15.8	even	4		2850.2.a.bk.1.2		3
15.14	odd	2		570.2.d.d.229.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.d.229.3	✓	6	3.2	odd	2
570.2.d.d.229.6	yes	6	15.14	odd	2
1710.2.d.e.1369.1		6	5.4	even	2	inner
1710.2.d.e.1369.4		6	1.1	even	1	trivial
2850.2.a.bk.1.2		3	15.8	even	4
2850.2.a.bn.1.2		3	15.2	even	4
8550.2.a.cf.1.2		3	5.2	odd	4
8550.2.a.cr.1.2		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.17009 - 0.539189i) q^{5} -1.07838i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.17009 - 0.539189i) q^{5} -1.07838i q^{7} -1.00000i q^{8} +(0.539189 - 2.17009i) q^{10} -3.41855 q^{11} +0.921622i q^{13} +1.07838 q^{14} +1.00000 q^{16} -0.340173i q^{17} +1.00000 q^{19} +(2.17009 + 0.539189i) q^{20} -3.41855i q^{22} -0.921622i q^{23} +(4.41855 + 2.34017i) q^{25} -0.921622 q^{26} +1.07838i q^{28} -1.41855 q^{29} +7.26180 q^{31} +1.00000i q^{32} +0.340173 q^{34} +(-0.581449 + 2.34017i) q^{35} +5.60197i q^{37} +1.00000i q^{38} +(-0.539189 + 2.17009i) q^{40} +1.07838 q^{41} -0.738205i q^{43} +3.41855 q^{44} +0.921622 q^{46} +7.75872i q^{47} +5.83710 q^{49} +(-2.34017 + 4.41855i) q^{50} -0.921622i q^{52} +2.68035i q^{53} +(7.41855 + 1.84324i) q^{55} -1.07838 q^{56} -1.41855i q^{58} +8.34017 q^{59} +2.00000 q^{61} +7.26180i q^{62} -1.00000 q^{64} +(0.496928 - 2.00000i) q^{65} -4.68035i q^{67} +0.340173i q^{68} +(-2.34017 - 0.581449i) q^{70} +10.8371 q^{71} +6.83710i q^{73} -5.60197 q^{74} -1.00000 q^{76} +3.68649i q^{77} -4.73820 q^{79} +(-2.17009 - 0.539189i) q^{80} +1.07838i q^{82} +11.0205i q^{83} +(-0.183417 + 0.738205i) q^{85} +0.738205 q^{86} +3.41855i q^{88} +9.75872 q^{89} +0.993857 q^{91} +0.921622i q^{92} -7.75872 q^{94} +(-2.17009 - 0.539189i) q^{95} +16.2557i q^{97} +5.83710i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{5}+O(q^{10}) \) 6 * q - 6 * q^4 - 2 * q^5	\( 6 q - 6 q^{4} - 2 q^{5} + 8 q^{11} + 6 q^{16} + 6 q^{19} + 2 q^{20} - 2 q^{25} - 12 q^{26} + 20 q^{29} + 28 q^{31} - 20 q^{34} - 32 q^{35} - 8 q^{44} + 12 q^{46} - 22 q^{49} + 8 q^{50} + 16 q^{55} + 28 q^{59} + 12 q^{61} - 6 q^{64} - 32 q^{65} + 8 q^{70} + 8 q^{71} + 4 q^{74} - 6 q^{76} - 44 q^{79} - 2 q^{80} + 8 q^{85} + 20 q^{86} + 8 q^{89} - 64 q^{91} + 4 q^{94} - 2 q^{95}+O(q^{100}) \) 6 * q - 6 * q^4 - 2 * q^5 + 8 * q^11 + 6 * q^16 + 6 * q^19 + 2 * q^20 - 2 * q^25 - 12 * q^26 + 20 * q^29 + 28 * q^31 - 20 * q^34 - 32 * q^35 - 8 * q^44 + 12 * q^46 - 22 * q^49 + 8 * q^50 + 16 * q^55 + 28 * q^59 + 12 * q^61 - 6 * q^64 - 32 * q^65 + 8 * q^70 + 8 * q^71 + 4 * q^74 - 6 * q^76 - 44 * q^79 - 2 * q^80 + 8 * q^85 + 20 * q^86 + 8 * q^89 - 64 * q^91 + 4 * q^94 - 2 * q^95

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