LMFDB - Embedded newform 1722.2.f.e.1639.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1722,2,Mod(1639,1722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1722, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1722.1639");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1722 = 2 \cdot 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1722.f (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:	$13.7502392281$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1639.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1722.1639
Dual form			1722.2.f.e.1639.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} -2.00000 q^{10} +4.00000i q^{11} -1.00000i q^{12} -2.00000i q^{13} -1.00000i q^{14} -2.00000i q^{15} +1.00000 q^{16} -2.00000i q^{17} +1.00000 q^{18} +8.00000i q^{19} +2.00000 q^{20} +1.00000 q^{21} -4.00000i q^{22} +1.00000i q^{24} -1.00000 q^{25} +2.00000i q^{26} +1.00000i q^{27} +1.00000i q^{28} +4.00000i q^{29} +2.00000i q^{30} +2.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} +2.00000i q^{34} +2.00000i q^{35} -1.00000 q^{36} +6.00000 q^{37} -8.00000i q^{38} -2.00000 q^{39} -2.00000 q^{40} +(-4.00000 + 5.00000i) q^{41} -1.00000 q^{42} +4.00000 q^{43} +4.00000i q^{44} -2.00000 q^{45} +4.00000i q^{47} -1.00000i q^{48} -1.00000 q^{49} +1.00000 q^{50} -2.00000 q^{51} -2.00000i q^{52} +8.00000i q^{53} -1.00000i q^{54} +8.00000i q^{55} -1.00000i q^{56} +8.00000 q^{57} -4.00000i q^{58} -6.00000 q^{59} -2.00000i q^{60} -8.00000 q^{61} -2.00000 q^{62} -1.00000i q^{63} +1.00000 q^{64} -4.00000i q^{65} -4.00000 q^{66} +2.00000i q^{67} -2.00000i q^{68} -2.00000i q^{70} +6.00000i q^{71} +1.00000 q^{72} +10.0000 q^{73} -6.00000 q^{74} +1.00000i q^{75} +8.00000i q^{76} -4.00000 q^{77} +2.00000 q^{78} -4.00000i q^{79} +2.00000 q^{80} +1.00000 q^{81} +(4.00000 - 5.00000i) q^{82} -10.0000 q^{83} +1.00000 q^{84} -4.00000i q^{85} -4.00000 q^{86} +4.00000 q^{87} -4.00000i q^{88} -10.0000i q^{89} +2.00000 q^{90} +2.00000 q^{91} -2.00000i q^{93} -4.00000i q^{94} +16.0000i q^{95} +1.00000i q^{96} -14.0000i q^{97} +1.00000 q^{98} -4.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^5 - 2 * q^8 - 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{8} - 2 q^{9} - 4 q^{10} + 2 q^{16} + 2 q^{18} + 4 q^{20} + 2 q^{21} - 2 q^{25} + 4 q^{31} - 2 q^{32} + 8 q^{33} - 2 q^{36} + 12 q^{37} - 4 q^{39} - 4 q^{40} - 8 q^{41} - 2 q^{42} + 8 q^{43} - 4 q^{45} - 2 q^{49} + 2 q^{50} - 4 q^{51} + 16 q^{57} - 12 q^{59} - 16 q^{61} - 4 q^{62} + 2 q^{64} - 8 q^{66} + 2 q^{72} + 20 q^{73} - 12 q^{74} - 8 q^{77} + 4 q^{78} + 4 q^{80} + 2 q^{81} + 8 q^{82} - 20 q^{83} + 2 q^{84} - 8 q^{86} + 8 q^{87} + 4 q^{90} + 4 q^{91} + 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^5 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 2 * q^16 + 2 * q^18 + 4 * q^20 + 2 * q^21 - 2 * q^25 + 4 * q^31 - 2 * q^32 + 8 * q^33 - 2 * q^36 + 12 * q^37 - 4 * q^39 - 4 * q^40 - 8 * q^41 - 2 * q^42 + 8 * q^43 - 4 * q^45 - 2 * q^49 + 2 * q^50 - 4 * q^51 + 16 * q^57 - 12 * q^59 - 16 * q^61 - 4 * q^62 + 2 * q^64 - 8 * q^66 + 2 * q^72 + 20 * q^73 - 12 * q^74 - 8 * q^77 + 4 * q^78 + 4 * q^80 + 2 * q^81 + 8 * q^82 - 20 * q^83 + 2 * q^84 - 8 * q^86 + 8 * q^87 + 4 * q^90 + 4 * q^91 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1722\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$			1.00000i			0.408248i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$	−2.00000			−0.632456
$11$			4.00000i			1.20605i	0.797724	+	0.603023i	$0.206037\pi$
$11$			4.00000i			1.20605i	−0.797724	+	0.603023i	$0.793963\pi$
$12$		−	1.00000i		−	0.288675i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		−	1.00000i		−	0.267261i
$15$		−	2.00000i		−	0.516398i
$16$	1.00000			0.250000
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$	1.00000			0.235702
$19$			8.00000i			1.83533i	0.397360	+	0.917663i	$0.369927\pi$
$19$			8.00000i			1.83533i	−0.397360	+	0.917663i	$0.630073\pi$
$20$	2.00000			0.447214
$21$	1.00000			0.218218
$22$		−	4.00000i		−	0.852803i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$			1.00000i			0.204124i
$25$	−1.00000			−0.200000
$26$			2.00000i			0.392232i
$27$			1.00000i			0.192450i
$28$			1.00000i			0.188982i
$29$			4.00000i			0.742781i	0.928477	+	0.371391i	$0.121119\pi$
$29$			4.00000i			0.742781i	−0.928477	+	0.371391i	$0.878881\pi$
$30$			2.00000i			0.365148i
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000			−0.176777
$33$	4.00000			0.696311
$34$			2.00000i			0.342997i
$35$			2.00000i			0.338062i
$36$	−1.00000			−0.166667
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$		−	8.00000i		−	1.29777i
$39$	−2.00000			−0.320256
$40$	−2.00000			−0.316228
$41$	−4.00000	+	5.00000i	−0.624695	+	0.780869i
$41$	−4.00000	+	5.00000i	−0.624695	+	0.780869i
$42$	−1.00000			−0.154303
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$			4.00000i			0.603023i
$45$	−2.00000			−0.298142
$46$		0			0
$47$			4.00000i			0.583460i	0.956501	+	0.291730i	$0.0942309\pi$
$47$			4.00000i			0.583460i	−0.956501	+	0.291730i	$0.905769\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−1.00000			−0.142857
$50$	1.00000			0.141421
$51$	−2.00000			−0.280056
$52$		−	2.00000i		−	0.277350i
$53$			8.00000i			1.09888i	0.835532	+	0.549442i	$0.185160\pi$
$53$			8.00000i			1.09888i	−0.835532	+	0.549442i	$0.814840\pi$
$54$		−	1.00000i		−	0.136083i
$55$			8.00000i			1.07872i
$56$		−	1.00000i		−	0.133631i
$57$	8.00000			1.05963
$58$		−	4.00000i		−	0.525226i
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$		−	2.00000i		−	0.258199i
$61$	−8.00000			−1.02430			−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000			−1.02430			−0.512148	+	0.858898i	$0.671150\pi$
$62$	−2.00000			−0.254000
$63$		−	1.00000i		−	0.125988i
$64$	1.00000			0.125000
$65$		−	4.00000i		−	0.496139i
$66$	−4.00000			−0.492366
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$		−	2.00000i		−	0.242536i
$69$		0			0
$70$		−	2.00000i		−	0.239046i
$71$			6.00000i			0.712069i	0.934473	+	0.356034i	$0.115871\pi$
$71$			6.00000i			0.712069i	−0.934473	+	0.356034i	$0.884129\pi$
$72$	1.00000			0.117851
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$	−6.00000			−0.697486
$75$			1.00000i			0.115470i
$76$			8.00000i			0.917663i
$77$	−4.00000			−0.455842
$78$	2.00000			0.226455
$79$		−	4.00000i		−	0.450035i	−0.974355	−	0.225018i	$-0.927756\pi$
$79$		−	4.00000i		−	0.450035i	0.974355	−	0.225018i	$-0.0722440\pi$
$80$	2.00000			0.223607
$81$	1.00000			0.111111
$82$	4.00000	−	5.00000i	0.441726	−	0.552158i
$83$	−10.0000			−1.09764			−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000			−1.09764			−0.548821	+	0.835940i	$0.684923\pi$
$84$	1.00000			0.109109
$85$		−	4.00000i		−	0.433861i
$86$	−4.00000			−0.431331
$87$	4.00000			0.428845
$88$		−	4.00000i		−	0.426401i
$89$		−	10.0000i		−	1.06000i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$		−	10.0000i		−	1.06000i	0.847998	−	0.529999i	$-0.177808\pi$
$90$	2.00000			0.210819
$91$	2.00000			0.209657
$92$		0			0
$93$		−	2.00000i		−	0.207390i
$94$		−	4.00000i		−	0.412568i
$95$			16.0000i			1.64157i
$96$			1.00000i			0.102062i
$97$		−	14.0000i		−	1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$		−	14.0000i		−	1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$	1.00000			0.101015
$99$		−	4.00000i		−	0.402015i
$100$	−1.00000			−0.100000
$101$			6.00000i			0.597022i	0.954406	+	0.298511i	$0.0964900\pi$
$101$			6.00000i			0.597022i	−0.954406	+	0.298511i	$0.903510\pi$
$102$	2.00000			0.198030
$103$	10.0000			0.985329			0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000			0.985329			0.492665	+	0.870219i	$0.336023\pi$
$104$			2.00000i			0.196116i
$105$	2.00000			0.195180
$106$		−	8.00000i		−	0.777029i
$107$	8.00000			0.773389			0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000			0.773389			0.386695	+	0.922208i	$0.373617\pi$
$108$			1.00000i			0.0962250i
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$		−	8.00000i		−	0.762770i
$111$		−	6.00000i		−	0.569495i
$112$			1.00000i			0.0944911i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	−8.00000			−0.749269
$115$		0			0
$116$			4.00000i			0.371391i
$117$			2.00000i			0.184900i
$118$	6.00000			0.552345
$119$	2.00000			0.183340
$120$			2.00000i			0.182574i
$121$	−5.00000			−0.454545
$122$	8.00000			0.724286
$123$	5.00000	+	4.00000i	0.450835	+	0.360668i
$124$	2.00000			0.179605
$125$	−12.0000			−1.07331
$126$			1.00000i			0.0890871i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000			−0.0883883
$129$		−	4.00000i		−	0.352180i
$130$			4.00000i			0.350823i
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	4.00000			0.348155
$133$	−8.00000			−0.693688
$134$		−	2.00000i		−	0.172774i
$135$			2.00000i			0.172133i
$136$			2.00000i			0.171499i
$137$			18.0000i			1.53784i	0.639343	+	0.768922i	$0.279207\pi$
$137$			18.0000i			1.53784i	−0.639343	+	0.768922i	$0.720793\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$			2.00000i			0.169031i
$141$	4.00000			0.336861
$142$		−	6.00000i		−	0.503509i
$143$	8.00000			0.668994
$144$	−1.00000			−0.0833333
$145$			8.00000i			0.664364i
$146$	−10.0000			−0.827606
$147$			1.00000i			0.0824786i
$148$	6.00000			0.493197
$149$			12.0000i			0.983078i	0.870855	+	0.491539i	$0.163566\pi$
$149$			12.0000i			0.983078i	−0.870855	+	0.491539i	$0.836434\pi$
$150$		−	1.00000i		−	0.0816497i
$151$			4.00000i			0.325515i	0.986666	+	0.162758i	$0.0520389\pi$
$151$			4.00000i			0.325515i	−0.986666	+	0.162758i	$0.947961\pi$
$152$		−	8.00000i		−	0.648886i
$153$			2.00000i			0.161690i
$154$	4.00000			0.322329
$155$	4.00000			0.321288
$156$	−2.00000			−0.160128
$157$			10.0000i			0.798087i	0.916932	+	0.399043i	$0.130658\pi$
$157$			10.0000i			0.798087i	−0.916932	+	0.399043i	$0.869342\pi$
$158$			4.00000i			0.318223i
$159$	8.00000			0.634441
$160$	−2.00000			−0.158114
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$	−4.00000	+	5.00000i	−0.312348	+	0.390434i
$165$	8.00000			0.622799
$166$	10.0000			0.776151
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$	−1.00000			−0.0771517
$169$	9.00000			0.692308
$170$			4.00000i			0.306786i
$171$		−	8.00000i		−	0.611775i
$172$	4.00000			0.304997
$173$	−10.0000			−0.760286			−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000			−0.760286			−0.380143	+	0.924928i	$0.624125\pi$
$174$	−4.00000			−0.303239
$175$		−	1.00000i		−	0.0755929i
$176$			4.00000i			0.301511i
$177$			6.00000i			0.450988i
$178$			10.0000i			0.749532i
$179$		−	12.0000i		−	0.896922i	−0.893802	−	0.448461i	$-0.851972\pi$
$179$		−	12.0000i		−	0.896922i	0.893802	−	0.448461i	$-0.148028\pi$
$180$	−2.00000			−0.149071
$181$		−	6.00000i		−	0.445976i	−0.974821	−	0.222988i	$-0.928419\pi$
$181$		−	6.00000i		−	0.445976i	0.974821	−	0.222988i	$-0.0715812\pi$
$182$	−2.00000			−0.148250
$183$			8.00000i			0.591377i
$184$		0			0
$185$	12.0000			0.882258
$186$			2.00000i			0.146647i
$187$	8.00000			0.585018
$188$			4.00000i			0.291730i
$189$	−1.00000			−0.0727393
$190$		−	16.0000i		−	1.16076i
$191$			6.00000i			0.434145i	0.976156	+	0.217072i	$0.0696508\pi$
$191$			6.00000i			0.434145i	−0.976156	+	0.217072i	$0.930349\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	4.00000i		−	0.287926i	−0.989583	−	0.143963i	$-0.954015\pi$
$193$		−	4.00000i		−	0.287926i	0.989583	−	0.143963i	$-0.0459847\pi$
$194$			14.0000i			1.00514i
$195$	−4.00000			−0.286446
$196$	−1.00000			−0.0714286
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$			4.00000i			0.284268i
$199$			8.00000i			0.567105i	0.958957	+	0.283552i	$0.0915130\pi$
$199$			8.00000i			0.567105i	−0.958957	+	0.283552i	$0.908487\pi$
$200$	1.00000			0.0707107
$201$	2.00000			0.141069
$202$		−	6.00000i		−	0.422159i
$203$	−4.00000			−0.280745
$204$	−2.00000			−0.140028
$205$	−8.00000	+	10.0000i	−0.558744	+	0.698430i
$206$	−10.0000			−0.696733
$207$		0			0
$208$		−	2.00000i		−	0.138675i
$209$	−32.0000			−2.21349
$210$	−2.00000			−0.138013
$211$		−	10.0000i		−	0.688428i	−0.938891	−	0.344214i	$-0.888145\pi$
$211$		−	10.0000i		−	0.688428i	0.938891	−	0.344214i	$-0.111855\pi$
$212$			8.00000i			0.549442i
$213$	6.00000			0.411113
$214$	−8.00000			−0.546869
$215$	8.00000			0.545595
$216$		−	1.00000i		−	0.0680414i
$217$			2.00000i			0.135769i
$218$			2.00000i			0.135457i
$219$		−	10.0000i		−	0.675737i
$220$			8.00000i			0.539360i
$221$	−4.00000			−0.269069
$222$			6.00000i			0.402694i
$223$	14.0000			0.937509			0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000			0.937509			0.468755	+	0.883328i	$0.344703\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	1.00000			0.0666667
$226$	−6.00000			−0.399114
$227$			20.0000i			1.32745i	0.747978	+	0.663723i	$0.231025\pi$
$227$			20.0000i			1.32745i	−0.747978	+	0.663723i	$0.768975\pi$
$228$	8.00000			0.529813
$229$		−	10.0000i		−	0.660819i	−0.943838	−	0.330409i	$-0.892813\pi$
$229$		−	10.0000i		−	0.660819i	0.943838	−	0.330409i	$-0.107187\pi$
$230$		0			0
$231$			4.00000i			0.263181i
$232$		−	4.00000i		−	0.262613i
$233$		−	10.0000i		−	0.655122i	−0.944830	−	0.327561i	$-0.893773\pi$
$233$		−	10.0000i		−	0.655122i	0.944830	−	0.327561i	$-0.106227\pi$
$234$		−	2.00000i		−	0.130744i
$235$			8.00000i			0.521862i
$236$	−6.00000			−0.390567
$237$	−4.00000			−0.259828
$238$	−2.00000			−0.129641
$239$			2.00000i			0.129369i	0.997906	+	0.0646846i	$0.0206041\pi$
$239$			2.00000i			0.129369i	−0.997906	+	0.0646846i	$0.979396\pi$
$240$		−	2.00000i		−	0.129099i
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$	5.00000			0.321412
$243$		−	1.00000i		−	0.0641500i
$244$	−8.00000			−0.512148
$245$	−2.00000			−0.127775
$246$	−5.00000	−	4.00000i	−0.318788	−	0.255031i
$247$	16.0000			1.01806
$248$	−2.00000			−0.127000
$249$			10.0000i			0.633724i
$250$	12.0000			0.758947
$251$	22.0000			1.38863			0.694314	−	0.719672i	$-0.255708\pi$
$251$	22.0000			1.38863			0.694314	+	0.719672i	$0.255708\pi$
$252$		−	1.00000i		−	0.0629941i
$253$		0			0
$254$	−8.00000			−0.501965
$255$	−4.00000			−0.250490
$256$	1.00000			0.0625000
$257$		−	30.0000i		−	1.87135i	−0.352865	−	0.935674i	$-0.614792\pi$
$257$		−	30.0000i		−	1.87135i	0.352865	−	0.935674i	$-0.385208\pi$
$258$			4.00000i			0.249029i
$259$			6.00000i			0.372822i
$260$		−	4.00000i		−	0.248069i
$261$		−	4.00000i		−	0.247594i
$262$	−10.0000			−0.617802
$263$		−	14.0000i		−	0.863277i	−0.902047	−	0.431638i	$-0.857936\pi$
$263$		−	14.0000i		−	0.863277i	0.902047	−	0.431638i	$-0.142064\pi$
$264$	−4.00000			−0.246183
$265$			16.0000i			0.982872i
$266$	8.00000			0.490511
$267$	−10.0000			−0.611990
$268$			2.00000i			0.122169i
$269$	−30.0000			−1.82913			−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000			−1.82913			−0.914566	+	0.404436i	$0.867468\pi$
$270$		−	2.00000i		−	0.121716i
$271$	22.0000			1.33640			0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000			1.33640			0.668202	+	0.743980i	$0.267064\pi$
$272$		−	2.00000i		−	0.121268i
$273$		−	2.00000i		−	0.121046i
$274$		−	18.0000i		−	1.08742i
$275$		−	4.00000i		−	0.241209i
$276$		0			0
$277$	−22.0000			−1.32185			−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000			−1.32185			−0.660926	+	0.750451i	$0.729836\pi$
$278$		0			0
$279$	−2.00000			−0.119737
$280$		−	2.00000i		−	0.119523i
$281$		−	18.0000i		−	1.07379i	−0.843649	−	0.536895i	$-0.819597\pi$
$281$		−	18.0000i		−	1.07379i	0.843649	−	0.536895i	$-0.180403\pi$
$282$	−4.00000			−0.238197
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$			6.00000i			0.356034i
$285$	16.0000			0.947758
$286$	−8.00000			−0.473050
$287$	−5.00000	−	4.00000i	−0.295141	−	0.236113i
$288$	1.00000			0.0589256
$289$	13.0000			0.764706
$290$		−	8.00000i		−	0.469776i
$291$	−14.0000			−0.820695
$292$	10.0000			0.585206
$293$			2.00000i			0.116841i	0.998292	+	0.0584206i	$0.0186065\pi$
$293$			2.00000i			0.116841i	−0.998292	+	0.0584206i	$0.981394\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	−12.0000			−0.698667
$296$	−6.00000			−0.348743
$297$	−4.00000			−0.232104
$298$		−	12.0000i		−	0.695141i
$299$		0			0
$300$			1.00000i			0.0577350i
$301$			4.00000i			0.230556i
$302$		−	4.00000i		−	0.230174i
$303$	6.00000			0.344691
$304$			8.00000i			0.458831i
$305$	−16.0000			−0.916157
$306$		−	2.00000i		−	0.114332i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	−4.00000			−0.227921
$309$		−	10.0000i		−	0.568880i
$310$	−4.00000			−0.227185
$311$		−	20.0000i		−	1.13410i	−0.823685	−	0.567048i	$-0.808085\pi$
$311$		−	20.0000i		−	1.13410i	0.823685	−	0.567048i	$-0.191915\pi$
$312$	2.00000			0.113228
$313$		−	6.00000i		−	0.339140i	−0.985518	−	0.169570i	$-0.945762\pi$
$313$		−	6.00000i		−	0.339140i	0.985518	−	0.169570i	$-0.0542379\pi$
$314$		−	10.0000i		−	0.564333i
$315$		−	2.00000i		−	0.112687i
$316$		−	4.00000i		−	0.225018i
$317$			8.00000i			0.449325i	0.974437	+	0.224662i	$0.0721279\pi$
$317$			8.00000i			0.449325i	−0.974437	+	0.224662i	$0.927872\pi$
$318$	−8.00000			−0.448618
$319$	−16.0000			−0.895828
$320$	2.00000			0.111803
$321$		−	8.00000i		−	0.446516i
$322$		0			0
$323$	16.0000			0.890264
$324$	1.00000			0.0555556
$325$			2.00000i			0.110940i
$326$	−20.0000			−1.10770
$327$	−2.00000			−0.110600
$328$	4.00000	−	5.00000i	0.220863	−	0.276079i
$329$	−4.00000			−0.220527
$330$	−8.00000			−0.440386
$331$		−	10.0000i		−	0.549650i	−0.961494	−	0.274825i	$-0.911380\pi$
$331$		−	10.0000i		−	0.549650i	0.961494	−	0.274825i	$-0.0886199\pi$
$332$	−10.0000			−0.548821
$333$	−6.00000			−0.328798
$334$		−	12.0000i		−	0.656611i
$335$			4.00000i			0.218543i
$336$	1.00000			0.0545545
$337$	−30.0000			−1.63420			−0.817102	−	0.576493i	$-0.804421\pi$
$337$	−30.0000			−1.63420			−0.817102	+	0.576493i	$0.804421\pi$
$338$	−9.00000			−0.489535
$339$		−	6.00000i		−	0.325875i
$340$		−	4.00000i		−	0.216930i
$341$			8.00000i			0.433224i
$342$			8.00000i			0.432590i
$343$		−	1.00000i		−	0.0539949i
$344$	−4.00000			−0.215666
$345$		0			0
$346$	10.0000			0.537603
$347$			32.0000i			1.71785i	0.512101	+	0.858925i	$0.328867\pi$
$347$			32.0000i			1.71785i	−0.512101	+	0.858925i	$0.671133\pi$
$348$	4.00000			0.214423
$349$	12.0000			0.642345			0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000			0.642345			0.321173	+	0.947021i	$0.395923\pi$
$350$			1.00000i			0.0534522i
$351$	2.00000			0.106752
$352$		−	4.00000i		−	0.213201i
$353$	−24.0000			−1.27739			−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000			−1.27739			−0.638696	+	0.769460i	$0.720526\pi$
$354$		−	6.00000i		−	0.318896i
$355$			12.0000i			0.636894i
$356$		−	10.0000i		−	0.529999i
$357$		−	2.00000i		−	0.105851i
$358$			12.0000i			0.634220i
$359$	−16.0000			−0.844448			−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000			−0.844448			−0.422224	+	0.906492i	$0.638750\pi$
$360$	2.00000			0.105409
$361$	−45.0000			−2.36842
$362$			6.00000i			0.315353i
$363$			5.00000i			0.262432i
$364$	2.00000			0.104828
$365$	20.0000			1.04685
$366$		−	8.00000i		−	0.418167i
$367$	−34.0000			−1.77479			−0.887393	−	0.461014i	$-0.847486\pi$
$367$	−34.0000			−1.77479			−0.887393	+	0.461014i	$0.847486\pi$
$368$		0			0
$369$	4.00000	−	5.00000i	0.208232	−	0.260290i
$370$	−12.0000			−0.623850
$371$	−8.00000			−0.415339
$372$		−	2.00000i		−	0.103695i
$373$	−2.00000			−0.103556			−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000			−0.103556			−0.0517780	+	0.998659i	$0.516489\pi$
$374$	−8.00000			−0.413670
$375$			12.0000i			0.619677i
$376$		−	4.00000i		−	0.206284i
$377$	8.00000			0.412021
$378$	1.00000			0.0514344
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$			16.0000i			0.820783i
$381$		−	8.00000i		−	0.409852i
$382$		−	6.00000i		−	0.306987i
$383$		−	36.0000i		−	1.83951i	−0.392488	−	0.919757i	$-0.628386\pi$
$383$		−	36.0000i		−	1.83951i	0.392488	−	0.919757i	$-0.371614\pi$
$384$			1.00000i			0.0510310i
$385$	−8.00000			−0.407718
$386$			4.00000i			0.203595i
$387$	−4.00000			−0.203331
$388$		−	14.0000i		−	0.710742i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$	4.00000			0.202548
$391$		0			0
$392$	1.00000			0.0505076
$393$		−	10.0000i		−	0.504433i
$394$	6.00000			0.302276
$395$		−	8.00000i		−	0.402524i
$396$		−	4.00000i		−	0.201008i
$397$		−	14.0000i		−	0.702640i	−0.936255	−	0.351320i	$-0.885733\pi$
$397$		−	14.0000i		−	0.702640i	0.936255	−	0.351320i	$-0.114267\pi$
$398$		−	8.00000i		−	0.401004i
$399$			8.00000i			0.400501i
$400$	−1.00000			−0.0500000
$401$	10.0000			0.499376			0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000			0.499376			0.249688	+	0.968326i	$0.419672\pi$
$402$	−2.00000			−0.0997509
$403$		−	4.00000i		−	0.199254i
$404$			6.00000i			0.298511i
$405$	2.00000			0.0993808
$406$	4.00000			0.198517
$407$			24.0000i			1.18964i
$408$	2.00000			0.0990148
$409$	6.00000			0.296681			0.148340	−	0.988936i	$-0.452607\pi$
$409$	6.00000			0.296681			0.148340	+	0.988936i	$0.452607\pi$
$410$	8.00000	−	10.0000i	0.395092	−	0.493865i
$411$	18.0000			0.887875
$412$	10.0000			0.492665
$413$		−	6.00000i		−	0.295241i
$414$		0			0
$415$	−20.0000			−0.981761
$416$			2.00000i			0.0980581i
$417$		0			0
$418$	32.0000			1.56517
$419$	−2.00000			−0.0977064			−0.0488532	−	0.998806i	$-0.515557\pi$
$419$	−2.00000			−0.0977064			−0.0488532	+	0.998806i	$0.515557\pi$
$420$	2.00000			0.0975900
$421$		−	26.0000i		−	1.26716i	−0.773676	−	0.633581i	$-0.781584\pi$
$421$		−	26.0000i		−	1.26716i	0.773676	−	0.633581i	$-0.218416\pi$
$422$			10.0000i			0.486792i
$423$		−	4.00000i		−	0.194487i
$424$		−	8.00000i		−	0.388514i
$425$			2.00000i			0.0970143i
$426$	−6.00000			−0.290701
$427$		−	8.00000i		−	0.387147i
$428$	8.00000			0.386695
$429$		−	8.00000i		−	0.386244i
$430$	−8.00000			−0.385794
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$			1.00000i			0.0481125i
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$		−	2.00000i		−	0.0960031i
$435$	8.00000			0.383571
$436$		−	2.00000i		−	0.0957826i
$437$		0			0
$438$			10.0000i			0.477818i
$439$		−	24.0000i		−	1.14546i	−0.819745	−	0.572729i	$-0.805885\pi$
$439$		−	24.0000i		−	1.14546i	0.819745	−	0.572729i	$-0.194115\pi$
$440$		−	8.00000i		−	0.381385i
$441$	1.00000			0.0476190
$442$	4.00000			0.190261
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$		−	6.00000i		−	0.284747i
$445$		−	20.0000i		−	0.948091i
$446$	−14.0000			−0.662919
$447$	12.0000			0.567581
$448$			1.00000i			0.0472456i
$449$	34.0000			1.60456			0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$	−1.00000			−0.0471405
$451$	−20.0000	−	16.0000i	−0.941763	−	0.753411i
$452$	6.00000			0.282216
$453$	4.00000			0.187936
$454$		−	20.0000i		−	0.938647i
$455$	4.00000			0.187523
$456$	−8.00000			−0.374634
$457$			16.0000i			0.748448i	0.927338	+	0.374224i	$0.122091\pi$
$457$			16.0000i			0.748448i	−0.927338	+	0.374224i	$0.877909\pi$
$458$			10.0000i			0.467269i
$459$	2.00000			0.0933520
$460$		0			0
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		−	4.00000i		−	0.186097i
$463$		−	4.00000i		−	0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$		−	4.00000i		−	0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$			4.00000i			0.185695i
$465$		−	4.00000i		−	0.185496i
$466$			10.0000i			0.463241i
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$			2.00000i			0.0924500i
$469$	−2.00000			−0.0923514
$470$		−	8.00000i		−	0.369012i
$471$	10.0000			0.460776
$472$	6.00000			0.276172
$473$			16.0000i			0.735681i
$474$	4.00000			0.183726
$475$		−	8.00000i		−	0.367065i
$476$	2.00000			0.0916698
$477$		−	8.00000i		−	0.366295i
$478$		−	2.00000i		−	0.0914779i
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$			2.00000i			0.0912871i
$481$		−	12.0000i		−	0.547153i
$482$	−18.0000			−0.819878
$483$		0			0
$484$	−5.00000			−0.227273
$485$		−	28.0000i		−	1.27141i
$486$			1.00000i			0.0453609i
$487$	−4.00000			−0.181257			−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000			−0.181257			−0.0906287	+	0.995885i	$0.528888\pi$
$488$	8.00000			0.362143
$489$		−	20.0000i		−	0.904431i
$490$	2.00000			0.0903508
$491$	−20.0000			−0.902587			−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000			−0.902587			−0.451294	+	0.892375i	$0.649037\pi$
$492$	5.00000	+	4.00000i	0.225417	+	0.180334i
$493$	8.00000			0.360302
$494$	−16.0000			−0.719874
$495$		−	8.00000i		−	0.359573i
$496$	2.00000			0.0898027
$497$	−6.00000			−0.269137
$498$		−	10.0000i		−	0.448111i
$499$			6.00000i			0.268597i	0.990941	+	0.134298i	$0.0428781\pi$
$499$			6.00000i			0.268597i	−0.990941	+	0.134298i	$0.957122\pi$
$500$	−12.0000			−0.536656
$501$	12.0000			0.536120
$502$	−22.0000			−0.981908
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$			1.00000i			0.0445435i
$505$			12.0000i			0.533993i
$506$		0			0
$507$		−	9.00000i		−	0.399704i
$508$	8.00000			0.354943
$509$		−	42.0000i		−	1.86162i	−0.365507	−	0.930809i	$-0.619104\pi$
$509$		−	42.0000i		−	1.86162i	0.365507	−	0.930809i	$-0.380896\pi$
$510$	4.00000			0.177123
$511$			10.0000i			0.442374i
$512$	−1.00000			−0.0441942
$513$	−8.00000			−0.353209
$514$			30.0000i			1.32324i
$515$	20.0000			0.881305
$516$		−	4.00000i		−	0.176090i
$517$	−16.0000			−0.703679
$518$		−	6.00000i		−	0.263625i
$519$			10.0000i			0.438951i
$520$			4.00000i			0.175412i
$521$			38.0000i			1.66481i	0.554168	+	0.832405i	$0.313037\pi$
$521$			38.0000i			1.66481i	−0.554168	+	0.832405i	$0.686963\pi$
$522$			4.00000i			0.175075i
$523$	4.00000			0.174908			0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000			0.174908			0.0874539	+	0.996169i	$0.472127\pi$
$524$	10.0000			0.436852
$525$	−1.00000			−0.0436436
$526$			14.0000i			0.610429i
$527$		−	4.00000i		−	0.174243i
$528$	4.00000			0.174078
$529$	−23.0000			−1.00000
$530$		−	16.0000i		−	0.694996i
$531$	6.00000			0.260378
$532$	−8.00000			−0.346844
$533$	10.0000	+	8.00000i	0.433148	+	0.346518i
$534$	10.0000			0.432742
$535$	16.0000			0.691740
$536$		−	2.00000i		−	0.0863868i
$537$	−12.0000			−0.517838
$538$	30.0000			1.29339
$539$		−	4.00000i		−	0.172292i
$540$			2.00000i			0.0860663i
$541$	−6.00000			−0.257960			−0.128980	−	0.991647i	$-0.541170\pi$
$541$	−6.00000			−0.257960			−0.128980	+	0.991647i	$0.541170\pi$
$542$	−22.0000			−0.944981
$543$	−6.00000			−0.257485
$544$			2.00000i			0.0857493i
$545$		−	4.00000i		−	0.171341i
$546$			2.00000i			0.0855921i
$547$			22.0000i			0.940652i	0.882493	+	0.470326i	$0.155864\pi$
$547$			22.0000i			0.940652i	−0.882493	+	0.470326i	$0.844136\pi$
$548$			18.0000i			0.768922i
$549$	8.00000			0.341432
$550$			4.00000i			0.170561i
$551$	−32.0000			−1.36325
$552$		0			0
$553$	4.00000			0.170097
$554$	22.0000			0.934690
$555$		−	12.0000i		−	0.509372i
$556$		0			0
$557$			4.00000i			0.169485i	0.996403	+	0.0847427i	$0.0270068\pi$
$557$			4.00000i			0.169485i	−0.996403	+	0.0847427i	$0.972993\pi$
$558$	2.00000			0.0846668
$559$		−	8.00000i		−	0.338364i
$560$			2.00000i			0.0845154i
$561$		−	8.00000i		−	0.337760i
$562$			18.0000i			0.759284i
$563$		−	12.0000i		−	0.505740i	−0.967500	−	0.252870i	$-0.918626\pi$
$563$		−	12.0000i		−	0.505740i	0.967500	−	0.252870i	$-0.0813744\pi$
$564$	4.00000			0.168430
$565$	12.0000			0.504844
$566$	4.00000			0.168133
$567$			1.00000i			0.0419961i
$568$		−	6.00000i		−	0.251754i
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$	−16.0000			−0.670166
$571$			18.0000i			0.753277i	0.926360	+	0.376638i	$0.122920\pi$
$571$			18.0000i			0.753277i	−0.926360	+	0.376638i	$0.877080\pi$
$572$	8.00000			0.334497
$573$	6.00000			0.250654
$574$	5.00000	+	4.00000i	0.208696	+	0.166957i
$575$		0			0
$576$	−1.00000			−0.0416667
$577$		−	2.00000i		−	0.0832611i	−0.999133	−	0.0416305i	$-0.986745\pi$
$577$		−	2.00000i		−	0.0832611i	0.999133	−	0.0416305i	$-0.0132552\pi$
$578$	−13.0000			−0.540729
$579$	−4.00000			−0.166234
$580$			8.00000i			0.332182i
$581$		−	10.0000i		−	0.414870i
$582$	14.0000			0.580319
$583$	−32.0000			−1.32530
$584$	−10.0000			−0.413803
$585$			4.00000i			0.165380i
$586$		−	2.00000i		−	0.0826192i
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$			1.00000i			0.0412393i
$589$			16.0000i			0.659269i
$590$	12.0000			0.494032
$591$			6.00000i			0.246807i
$592$	6.00000			0.246598
$593$		−	30.0000i		−	1.23195i	−0.787765	−	0.615976i	$-0.788762\pi$
$593$		−	30.0000i		−	1.23195i	0.787765	−	0.615976i	$-0.211238\pi$
$594$	4.00000			0.164122
$595$	4.00000			0.163984
$596$			12.0000i			0.491539i
$597$	8.00000			0.327418
$598$		0			0
$599$	−32.0000			−1.30748			−0.653742	−	0.756717i	$-0.726802\pi$
$599$	−32.0000			−1.30748			−0.653742	+	0.756717i	$0.726802\pi$
$600$		−	1.00000i		−	0.0408248i
$601$			26.0000i			1.06056i	0.847822	+	0.530281i	$0.177914\pi$
$601$			26.0000i			1.06056i	−0.847822	+	0.530281i	$0.822086\pi$
$602$		−	4.00000i		−	0.163028i
$603$		−	2.00000i		−	0.0814463i
$604$			4.00000i			0.162758i
$605$	−10.0000			−0.406558
$606$	−6.00000			−0.243733
$607$	−30.0000			−1.21766			−0.608831	−	0.793300i	$-0.708361\pi$
$607$	−30.0000			−1.21766			−0.608831	+	0.793300i	$0.708361\pi$
$608$		−	8.00000i		−	0.324443i
$609$			4.00000i			0.162088i
$610$	16.0000			0.647821
$611$	8.00000			0.323645
$612$			2.00000i			0.0808452i
$613$	−34.0000			−1.37325			−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000			−1.37325			−0.686624	+	0.727013i	$0.740908\pi$
$614$		0			0
$615$	10.0000	+	8.00000i	0.403239	+	0.322591i
$616$	4.00000			0.161165
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$			10.0000i			0.402259i
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$	4.00000			0.160644
$621$		0			0
$622$			20.0000i			0.801927i
$623$	10.0000			0.400642
$624$	−2.00000			−0.0800641
$625$	−19.0000			−0.760000
$626$			6.00000i			0.239808i
$627$			32.0000i			1.27796i
$628$			10.0000i			0.399043i
$629$		−	12.0000i		−	0.478471i
$630$			2.00000i			0.0796819i
$631$	12.0000			0.477712			0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000			0.477712			0.238856	+	0.971055i	$0.423228\pi$
$632$			4.00000i			0.159111i
$633$	−10.0000			−0.397464
$634$		−	8.00000i		−	0.317721i
$635$	16.0000			0.634941
$636$	8.00000			0.317221
$637$			2.00000i			0.0792429i
$638$	16.0000			0.633446
$639$		−	6.00000i		−	0.237356i
$640$	−2.00000			−0.0790569
$641$			2.00000i			0.0789953i	0.999220	+	0.0394976i	$0.0125758\pi$
$641$			2.00000i			0.0789953i	−0.999220	+	0.0394976i	$0.987424\pi$
$642$			8.00000i			0.315735i
$643$			24.0000i			0.946468i	0.880937	+	0.473234i	$0.156913\pi$
$643$			24.0000i			0.946468i	−0.880937	+	0.473234i	$0.843087\pi$
$644$		0			0
$645$		−	8.00000i		−	0.315000i
$646$	−16.0000			−0.629512
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$	−1.00000			−0.0392837
$649$		−	24.0000i		−	0.942082i
$650$		−	2.00000i		−	0.0784465i
$651$	2.00000			0.0783862
$652$	20.0000			0.783260
$653$		−	24.0000i		−	0.939193i	−0.882881	−	0.469596i	$-0.844399\pi$
$653$		−	24.0000i		−	0.939193i	0.882881	−	0.469596i	$-0.155601\pi$
$654$	2.00000			0.0782062
$655$	20.0000			0.781465
$656$	−4.00000	+	5.00000i	−0.156174	+	0.195217i
$657$	−10.0000			−0.390137
$658$	4.00000			0.155936
$659$			28.0000i			1.09073i	0.838200	+	0.545363i	$0.183608\pi$
$659$			28.0000i			1.09073i	−0.838200	+	0.545363i	$0.816392\pi$
$660$	8.00000			0.311400
$661$	−8.00000			−0.311164			−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000			−0.311164			−0.155582	+	0.987823i	$0.549725\pi$
$662$			10.0000i			0.388661i
$663$			4.00000i			0.155347i
$664$	10.0000			0.388075
$665$	−16.0000			−0.620453
$666$	6.00000			0.232495
$667$		0			0
$668$			12.0000i			0.464294i
$669$		−	14.0000i		−	0.541271i
$670$		−	4.00000i		−	0.154533i
$671$		−	32.0000i		−	1.23535i
$672$	−1.00000			−0.0385758
$673$			32.0000i			1.23351i	0.787155	+	0.616755i	$0.211553\pi$
$673$			32.0000i			1.23351i	−0.787155	+	0.616755i	$0.788447\pi$
$674$	30.0000			1.15556
$675$		−	1.00000i		−	0.0384900i
$676$	9.00000			0.346154
$677$	34.0000			1.30673			0.653363	−	0.757045i	$-0.273358\pi$
$677$	34.0000			1.30673			0.653363	+	0.757045i	$0.273358\pi$
$678$			6.00000i			0.230429i
$679$	14.0000			0.537271
$680$			4.00000i			0.153393i
$681$	20.0000			0.766402
$682$		−	8.00000i		−	0.306336i
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		−	8.00000i		−	0.305888i
$685$			36.0000i			1.37549i
$686$			1.00000i			0.0381802i
$687$	−10.0000			−0.381524
$688$	4.00000			0.152499
$689$	16.0000			0.609551
$690$		0			0
$691$		−	40.0000i		−	1.52167i	−0.648944	−	0.760836i	$-0.724789\pi$
$691$		−	40.0000i		−	1.52167i	0.648944	−	0.760836i	$-0.275211\pi$
$692$	−10.0000			−0.380143
$693$	4.00000			0.151947
$694$		−	32.0000i		−	1.21470i
$695$		0			0
$696$	−4.00000			−0.151620
$697$	10.0000	+	8.00000i	0.378777	+	0.303022i
$698$	−12.0000			−0.454207
$699$	−10.0000			−0.378235
$700$		−	1.00000i		−	0.0377964i
$701$	−22.0000			−0.830929			−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000			−0.830929			−0.415464	+	0.909610i	$0.636381\pi$
$702$	−2.00000			−0.0754851
$703$			48.0000i			1.81035i
$704$			4.00000i			0.150756i
$705$	8.00000			0.301297
$706$	24.0000			0.903252
$707$	−6.00000			−0.225653
$708$			6.00000i			0.225494i
$709$			14.0000i			0.525781i	0.964826	+	0.262891i	$0.0846758\pi$
$709$			14.0000i			0.525781i	−0.964826	+	0.262891i	$0.915324\pi$
$710$		−	12.0000i		−	0.450352i
$711$			4.00000i			0.150012i
$712$			10.0000i			0.374766i
$713$		0			0
$714$			2.00000i			0.0748481i
$715$	16.0000			0.598366
$716$		−	12.0000i		−	0.448461i
$717$	2.00000			0.0746914
$718$	16.0000			0.597115
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$	−2.00000			−0.0745356
$721$			10.0000i			0.372419i
$722$	45.0000			1.67473
$723$		−	18.0000i		−	0.669427i
$724$		−	6.00000i		−	0.222988i
$725$		−	4.00000i		−	0.148556i
$726$		−	5.00000i		−	0.185567i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	−2.00000			−0.0741249
$729$	−1.00000			−0.0370370
$730$	−20.0000			−0.740233
$731$		−	8.00000i		−	0.295891i
$732$			8.00000i			0.295689i
$733$	44.0000			1.62518			0.812589	−	0.582838i	$-0.198058\pi$
$733$	44.0000			1.62518			0.812589	+	0.582838i	$0.198058\pi$
$734$	34.0000			1.25496
$735$			2.00000i			0.0737711i
$736$		0			0
$737$	−8.00000			−0.294684
$738$	−4.00000	+	5.00000i	−0.147242	+	0.184053i
$739$	−52.0000			−1.91285			−0.956425	−	0.291977i	$-0.905687\pi$
$739$	−52.0000			−1.91285			−0.956425	+	0.291977i	$0.905687\pi$
$740$	12.0000			0.441129
$741$		−	16.0000i		−	0.587775i
$742$	8.00000			0.293689
$743$	8.00000			0.293492			0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000			0.293492			0.146746	+	0.989174i	$0.453120\pi$
$744$			2.00000i			0.0733236i
$745$			24.0000i			0.879292i
$746$	2.00000			0.0732252
$747$	10.0000			0.365881
$748$	8.00000			0.292509
$749$			8.00000i			0.292314i
$750$		−	12.0000i		−	0.438178i
$751$			24.0000i			0.875772i	0.899030	+	0.437886i	$0.144273\pi$
$751$			24.0000i			0.875772i	−0.899030	+	0.437886i	$0.855727\pi$
$752$			4.00000i			0.145865i
$753$		−	22.0000i		−	0.801725i
$754$	−8.00000			−0.291343
$755$			8.00000i			0.291150i
$756$	−1.00000			−0.0363696
$757$		−	46.0000i		−	1.67190i	−0.548807	−	0.835949i	$-0.684918\pi$
$757$		−	46.0000i		−	1.67190i	0.548807	−	0.835949i	$-0.315082\pi$
$758$	12.0000			0.435860
$759$		0			0
$760$		−	16.0000i		−	0.580381i
$761$		0			0			−	1.00000i	$-0.5\pi$
$761$		0			0				1.00000i	$0.5\pi$
$762$			8.00000i			0.289809i
$763$	2.00000			0.0724049
$764$			6.00000i			0.217072i
$765$			4.00000i			0.144620i
$766$			36.0000i			1.30073i
$767$			12.0000i			0.433295i
$768$		−	1.00000i		−	0.0360844i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$	8.00000			0.288300
$771$	−30.0000			−1.08042
$772$		−	4.00000i		−	0.143963i
$773$		−	6.00000i		−	0.215805i	−0.994161	−	0.107903i	$-0.965587\pi$
$773$		−	6.00000i		−	0.215805i	0.994161	−	0.107903i	$-0.0344134\pi$
$774$	4.00000			0.143777
$775$	−2.00000			−0.0718421
$776$			14.0000i			0.502571i
$777$	6.00000			0.215249
$778$	−6.00000			−0.215110
$779$	−40.0000	−	32.0000i	−1.43315	−	1.14652i
$780$	−4.00000			−0.143223
$781$	−24.0000			−0.858788
$782$		0			0
$783$	−4.00000			−0.142948
$784$	−1.00000			−0.0357143
$785$			20.0000i			0.713831i
$786$			10.0000i			0.356688i
$787$	40.0000			1.42585			0.712923	−	0.701242i	$-0.247371\pi$
$787$	40.0000			1.42585			0.712923	+	0.701242i	$0.247371\pi$
$788$	−6.00000			−0.213741
$789$	−14.0000			−0.498413
$790$			8.00000i			0.284627i
$791$			6.00000i			0.213335i
$792$			4.00000i			0.142134i
$793$			16.0000i			0.568177i
$794$			14.0000i			0.496841i
$795$	16.0000			0.567462
$796$			8.00000i			0.283552i
$797$	46.0000			1.62940			0.814702	−	0.579880i	$-0.196901\pi$
$797$	46.0000			1.62940			0.814702	+	0.579880i	$0.196901\pi$
$798$		−	8.00000i		−	0.283197i
$799$	8.00000			0.283020
$800$	1.00000			0.0353553
$801$			10.0000i			0.353333i
$802$	−10.0000			−0.353112
$803$			40.0000i			1.41157i
$804$	2.00000			0.0705346
$805$		0			0
$806$			4.00000i			0.140894i
$807$			30.0000i			1.05605i
$808$		−	6.00000i		−	0.211079i
$809$		−	30.0000i		−	1.05474i	−0.849635	−	0.527372i	$-0.823177\pi$
$809$		−	30.0000i		−	1.05474i	0.849635	−	0.527372i	$-0.176823\pi$
$810$	−2.00000			−0.0702728
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	−4.00000			−0.140372
$813$		−	22.0000i		−	0.771574i
$814$		−	24.0000i		−	0.841200i
$815$	40.0000			1.40114
$816$	−2.00000			−0.0700140
$817$			32.0000i			1.11954i
$818$	−6.00000			−0.209785
$819$	−2.00000			−0.0698857
$820$	−8.00000	+	10.0000i	−0.279372	+	0.349215i
$821$	−6.00000			−0.209401			−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000			−0.209401			−0.104701	+	0.994504i	$0.533388\pi$
$822$	−18.0000			−0.627822
$823$			4.00000i			0.139431i	0.997567	+	0.0697156i	$0.0222092\pi$
$823$			4.00000i			0.139431i	−0.997567	+	0.0697156i	$0.977791\pi$
$824$	−10.0000			−0.348367
$825$	−4.00000			−0.139262
$826$			6.00000i			0.208767i
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$		0			0
$829$	−4.00000			−0.138926			−0.0694629	−	0.997585i	$-0.522129\pi$
$829$	−4.00000			−0.138926			−0.0694629	+	0.997585i	$0.522129\pi$
$830$	20.0000			0.694210
$831$			22.0000i			0.763172i
$832$		−	2.00000i		−	0.0693375i
$833$			2.00000i			0.0692959i
$834$		0			0
$835$			24.0000i			0.830554i
$836$	−32.0000			−1.10674
$837$			2.00000i			0.0691301i
$838$	2.00000			0.0690889
$839$		−	16.0000i		−	0.552381i	−0.961103	−	0.276191i	$-0.910928\pi$
$839$		−	16.0000i		−	0.552381i	0.961103	−	0.276191i	$-0.0890721\pi$
$840$	−2.00000			−0.0690066
$841$	13.0000			0.448276
$842$			26.0000i			0.896019i
$843$	−18.0000			−0.619953
$844$		−	10.0000i		−	0.344214i
$845$	18.0000			0.619219
$846$			4.00000i			0.137523i
$847$		−	5.00000i		−	0.171802i
$848$			8.00000i			0.274721i
$849$			4.00000i			0.137280i
$850$		−	2.00000i		−	0.0685994i
$851$		0			0
$852$	6.00000			0.205557
$853$	44.0000			1.50653			0.753266	−	0.657716i	$-0.228477\pi$
$853$	44.0000			1.50653			0.753266	+	0.657716i	$0.228477\pi$
$854$			8.00000i			0.273754i
$855$		−	16.0000i		−	0.547188i
$856$	−8.00000			−0.273434
$857$	8.00000			0.273275			0.136637	−	0.990621i	$-0.456370\pi$
$857$	8.00000			0.273275			0.136637	+	0.990621i	$0.456370\pi$
$858$			8.00000i			0.273115i
$859$	24.0000			0.818869			0.409435	−	0.912339i	$-0.365726\pi$
$859$	24.0000			0.818869			0.409435	+	0.912339i	$0.365726\pi$
$860$	8.00000			0.272798
$861$	−4.00000	+	5.00000i	−0.136320	+	0.170400i
$862$	−24.0000			−0.817443
$863$	40.0000			1.36162			0.680808	−	0.732462i	$-0.261629\pi$
$863$	40.0000			1.36162			0.680808	+	0.732462i	$0.261629\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	−20.0000			−0.680020
$866$	26.0000			0.883516
$867$		−	13.0000i		−	0.441503i
$868$			2.00000i			0.0678844i
$869$	16.0000			0.542763
$870$	−8.00000			−0.271225
$871$	4.00000			0.135535
$872$			2.00000i			0.0677285i
$873$			14.0000i			0.473828i
$874$		0			0
$875$		−	12.0000i		−	0.405674i
$876$		−	10.0000i		−	0.337869i
$877$	42.0000			1.41824			0.709120	−	0.705088i	$-0.249093\pi$
$877$	42.0000			1.41824			0.709120	+	0.705088i	$0.249093\pi$
$878$			24.0000i			0.809961i
$879$	2.00000			0.0674583
$880$			8.00000i			0.269680i
$881$	24.0000			0.808581			0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000			0.808581			0.404290	+	0.914631i	$0.367519\pi$
$882$	−1.00000			−0.0336718
$883$		−	10.0000i		−	0.336527i	−0.985742	−	0.168263i	$-0.946184\pi$
$883$		−	10.0000i		−	0.336527i	0.985742	−	0.168263i	$-0.0538159\pi$
$884$	−4.00000			−0.134535
$885$			12.0000i			0.403376i
$886$	12.0000			0.403148
$887$		−	32.0000i		−	1.07445i	−0.843437	−	0.537227i	$-0.819472\pi$
$887$		−	32.0000i		−	1.07445i	0.843437	−	0.537227i	$-0.180528\pi$
$888$			6.00000i			0.201347i
$889$			8.00000i			0.268311i
$890$			20.0000i			0.670402i
$891$			4.00000i			0.134005i
$892$	14.0000			0.468755
$893$	−32.0000			−1.07084
$894$	−12.0000			−0.401340
$895$		−	24.0000i		−	0.802232i
$896$		−	1.00000i		−	0.0334077i
$897$		0			0
$898$	−34.0000			−1.13459
$899$			8.00000i			0.266815i
$900$	1.00000			0.0333333
$901$	16.0000			0.533037
$902$	20.0000	+	16.0000i	0.665927	+	0.532742i
$903$	4.00000			0.133112
$904$	−6.00000			−0.199557
$905$		−	12.0000i		−	0.398893i
$906$	−4.00000			−0.132891
$907$	44.0000			1.46100			0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000			1.46100			0.730498	+	0.682915i	$0.239288\pi$
$908$			20.0000i			0.663723i
$909$		−	6.00000i		−	0.199007i
$910$	−4.00000			−0.132599
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$	8.00000			0.264906
$913$		−	40.0000i		−	1.32381i
$914$		−	16.0000i		−	0.529233i
$915$			16.0000i			0.528944i
$916$		−	10.0000i		−	0.330409i
$917$			10.0000i			0.330229i
$918$	−2.00000			−0.0660098
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	−18.0000			−0.592798
$923$	12.0000			0.394985
$924$			4.00000i			0.131590i
$925$	−6.00000			−0.197279
$926$			4.00000i			0.131448i
$927$	−10.0000			−0.328443
$928$		−	4.00000i		−	0.131306i
$929$		−	14.0000i		−	0.459325i	−0.973270	−	0.229663i	$-0.926238\pi$
$929$		−	14.0000i		−	0.459325i	0.973270	−	0.229663i	$-0.0737623\pi$
$930$			4.00000i			0.131165i
$931$		−	8.00000i		−	0.262189i
$932$		−	10.0000i		−	0.327561i
$933$	−20.0000			−0.654771
$934$	−18.0000			−0.588978
$935$	16.0000			0.523256
$936$		−	2.00000i		−	0.0653720i
$937$			54.0000i			1.76410i	0.471153	+	0.882052i	$0.343838\pi$
$937$			54.0000i			1.76410i	−0.471153	+	0.882052i	$0.656162\pi$
$938$	2.00000			0.0653023
$939$	−6.00000			−0.195803
$940$			8.00000i			0.260931i
$941$	38.0000			1.23876			0.619382	−	0.785090i	$-0.287383\pi$
$941$	38.0000			1.23876			0.619382	+	0.785090i	$0.287383\pi$
$942$	−10.0000			−0.325818
$943$		0			0
$944$	−6.00000			−0.195283
$945$	−2.00000			−0.0650600
$946$		−	16.0000i		−	0.520205i
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	−4.00000			−0.129914
$949$		−	20.0000i		−	0.649227i
$950$			8.00000i			0.259554i
$951$	8.00000			0.259418
$952$	−2.00000			−0.0648204
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$			8.00000i			0.259010i
$955$			12.0000i			0.388311i
$956$			2.00000i			0.0646846i
$957$			16.0000i			0.517207i
$958$		0			0
$959$	−18.0000			−0.581250
$960$		−	2.00000i		−	0.0645497i
$961$	−27.0000			−0.870968
$962$			12.0000i			0.386896i
$963$	−8.00000			−0.257796
$964$	18.0000			0.579741
$965$		−	8.00000i		−	0.257529i
$966$		0			0
$967$		−	28.0000i		−	0.900419i	−0.892923	−	0.450210i	$-0.851349\pi$
$967$		−	28.0000i		−	0.900419i	0.892923	−	0.450210i	$-0.148651\pi$
$968$	5.00000			0.160706
$969$		−	16.0000i		−	0.513994i
$970$			28.0000i			0.899026i
$971$			28.0000i			0.898563i	0.893390	+	0.449281i	$0.148320\pi$
$971$			28.0000i			0.898563i	−0.893390	+	0.449281i	$0.851680\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	4.00000			0.128168
$975$	2.00000			0.0640513
$976$	−8.00000			−0.256074
$977$			38.0000i			1.21573i	0.794041	+	0.607864i	$0.207973\pi$
$977$			38.0000i			1.21573i	−0.794041	+	0.607864i	$0.792027\pi$
$978$			20.0000i			0.639529i
$979$	40.0000			1.27841
$980$	−2.00000			−0.0638877
$981$			2.00000i			0.0638551i
$982$	20.0000			0.638226
$983$	28.0000			0.893061			0.446531	−	0.894768i	$-0.352659\pi$
$983$	28.0000			0.893061			0.446531	+	0.894768i	$0.352659\pi$
$984$	−5.00000	−	4.00000i	−0.159394	−	0.127515i
$985$	−12.0000			−0.382352
$986$	−8.00000			−0.254772
$987$			4.00000i			0.127321i
$988$	16.0000			0.509028
$989$		0			0
$990$			8.00000i			0.254257i
$991$			8.00000i			0.254128i	0.991894	+	0.127064i	$0.0405554\pi$
$991$			8.00000i			0.254128i	−0.991894	+	0.127064i	$0.959445\pi$
$992$	−2.00000			−0.0635001
$993$	−10.0000			−0.317340
$994$	6.00000			0.190308
$995$			16.0000i			0.507234i
$996$			10.0000i			0.316862i
$997$		−	42.0000i		−	1.33015i	−0.746775	−	0.665077i	$-0.768399\pi$
$997$		−	42.0000i		−	1.33015i	0.746775	−	0.665077i	$-0.231601\pi$
$998$		−	6.00000i		−	0.189927i
$999$			6.00000i			0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1722.2.f.e.1639.1	✓	2
41.40	even	2	inner	1722.2.f.e.1639.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1722.2.f.e.1639.1	✓	2	1.1	even	1	trivial
1722.2.f.e.1639.2	yes	2	41.40	even	2	inner

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:	\( N \)	\(=\)	\( 1722 = 2 \cdot 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1722.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000 q^{8} -1.00000 q^{9} -2.00000 q^{10} +4.00000i q^{11} -1.00000i q^{12} -2.00000i q^{13} -1.00000i q^{14} -2.00000i q^{15} +1.00000 q^{16} -2.00000i q^{17} +1.00000 q^{18} +8.00000i q^{19} +2.00000 q^{20} +1.00000 q^{21} -4.00000i q^{22} +1.00000i q^{24} -1.00000 q^{25} +2.00000i q^{26} +1.00000i q^{27} +1.00000i q^{28} +4.00000i q^{29} +2.00000i q^{30} +2.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} +2.00000i q^{34} +2.00000i q^{35} -1.00000 q^{36} +6.00000 q^{37} -8.00000i q^{38} -2.00000 q^{39} -2.00000 q^{40} +(-4.00000 + 5.00000i) q^{41} -1.00000 q^{42} +4.00000 q^{43} +4.00000i q^{44} -2.00000 q^{45} +4.00000i q^{47} -1.00000i q^{48} -1.00000 q^{49} +1.00000 q^{50} -2.00000 q^{51} -2.00000i q^{52} +8.00000i q^{53} -1.00000i q^{54} +8.00000i q^{55} -1.00000i q^{56} +8.00000 q^{57} -4.00000i q^{58} -6.00000 q^{59} -2.00000i q^{60} -8.00000 q^{61} -2.00000 q^{62} -1.00000i q^{63} +1.00000 q^{64} -4.00000i q^{65} -4.00000 q^{66} +2.00000i q^{67} -2.00000i q^{68} -2.00000i q^{70} +6.00000i q^{71} +1.00000 q^{72} +10.0000 q^{73} -6.00000 q^{74} +1.00000i q^{75} +8.00000i q^{76} -4.00000 q^{77} +2.00000 q^{78} -4.00000i q^{79} +2.00000 q^{80} +1.00000 q^{81} +(4.00000 - 5.00000i) q^{82} -10.0000 q^{83} +1.00000 q^{84} -4.00000i q^{85} -4.00000 q^{86} +4.00000 q^{87} -4.00000i q^{88} -10.0000i q^{89} +2.00000 q^{90} +2.00000 q^{91} -2.00000i q^{93} -4.00000i q^{94} +16.0000i q^{95} +1.00000i q^{96} -14.0000i q^{97} +1.00000 q^{98} -4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^5 - 2 * q^8 - 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{8} - 2 q^{9} - 4 q^{10} + 2 q^{16} + 2 q^{18} + 4 q^{20} + 2 q^{21} - 2 q^{25} + 4 q^{31} - 2 q^{32} + 8 q^{33} - 2 q^{36} + 12 q^{37} - 4 q^{39} - 4 q^{40} - 8 q^{41} - 2 q^{42} + 8 q^{43} - 4 q^{45} - 2 q^{49} + 2 q^{50} - 4 q^{51} + 16 q^{57} - 12 q^{59} - 16 q^{61} - 4 q^{62} + 2 q^{64} - 8 q^{66} + 2 q^{72} + 20 q^{73} - 12 q^{74} - 8 q^{77} + 4 q^{78} + 4 q^{80} + 2 q^{81} + 8 q^{82} - 20 q^{83} + 2 q^{84} - 8 q^{86} + 8 q^{87} + 4 q^{90} + 4 q^{91} + 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + 4 * q^5 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 2 * q^16 + 2 * q^18 + 4 * q^20 + 2 * q^21 - 2 * q^25 + 4 * q^31 - 2 * q^32 + 8 * q^33 - 2 * q^36 + 12 * q^37 - 4 * q^39 - 4 * q^40 - 8 * q^41 - 2 * q^42 + 8 * q^43 - 4 * q^45 - 2 * q^49 + 2 * q^50 - 4 * q^51 + 16 * q^57 - 12 * q^59 - 16 * q^61 - 4 * q^62 + 2 * q^64 - 8 * q^66 + 2 * q^72 + 20 * q^73 - 12 * q^74 - 8 * q^77 + 4 * q^78 + 4 * q^80 + 2 * q^81 + 8 * q^82 - 20 * q^83 + 2 * q^84 - 8 * q^86 + 8 * q^87 + 4 * q^90 + 4 * q^91 + 2 * q^98

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