LMFDB - Embedded newform 3330.2.e.b.739.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3330,2,Mod(739,3330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3330, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3330.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3330.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$26.5901838731$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	3330.739
Dual form			3330.2.e.b.739.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +3.00000i q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +3.00000i q^{7} +1.00000 q^{8} +(-2.00000 + 1.00000i) q^{10} +3.00000 q^{11} -4.00000 q^{13} +3.00000i q^{14} +1.00000 q^{16} -7.00000 q^{17} -4.00000i q^{19} +(-2.00000 + 1.00000i) q^{20} +3.00000 q^{22} -6.00000 q^{23} +(3.00000 - 4.00000i) q^{25} -4.00000 q^{26} +3.00000i q^{28} +9.00000i q^{29} -5.00000i q^{31} +1.00000 q^{32} -7.00000 q^{34} +(-3.00000 - 6.00000i) q^{35} +(6.00000 - 1.00000i) q^{37} -4.00000i q^{38} +(-2.00000 + 1.00000i) q^{40} -7.00000 q^{41} +1.00000 q^{43} +3.00000 q^{44} -6.00000 q^{46} -8.00000i q^{47} -2.00000 q^{49} +(3.00000 - 4.00000i) q^{50} -4.00000 q^{52} -1.00000i q^{53} +(-6.00000 + 3.00000i) q^{55} +3.00000i q^{56} +9.00000i q^{58} -6.00000i q^{59} -5.00000i q^{61} -5.00000i q^{62} +1.00000 q^{64} +(8.00000 - 4.00000i) q^{65} -2.00000i q^{67} -7.00000 q^{68} +(-3.00000 - 6.00000i) q^{70} -12.0000 q^{71} -4.00000i q^{73} +(6.00000 - 1.00000i) q^{74} -4.00000i q^{76} +9.00000i q^{77} -4.00000i q^{79} +(-2.00000 + 1.00000i) q^{80} -7.00000 q^{82} +14.0000i q^{83} +(14.0000 - 7.00000i) q^{85} +1.00000 q^{86} +3.00000 q^{88} -6.00000i q^{89} -12.0000i q^{91} -6.00000 q^{92} -8.00000i q^{94} +(4.00000 + 8.00000i) q^{95} +7.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^8	$ 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{8} - 4 q^{10} + 6 q^{11} - 8 q^{13} + 2 q^{16} - 14 q^{17} - 4 q^{20} + 6 q^{22} - 12 q^{23} + 6 q^{25} - 8 q^{26} + 2 q^{32} - 14 q^{34} - 6 q^{35} + 12 q^{37} - 4 q^{40} - 14 q^{41} + 2 q^{43} + 6 q^{44} - 12 q^{46} - 4 q^{49} + 6 q^{50} - 8 q^{52} - 12 q^{55} + 2 q^{64} + 16 q^{65} - 14 q^{68} - 6 q^{70} - 24 q^{71} + 12 q^{74} - 4 q^{80} - 14 q^{82} + 28 q^{85} + 2 q^{86} + 6 q^{88} - 12 q^{92} + 8 q^{95} + 14 q^{97} - 4 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^8 - 4 * q^10 + 6 * q^11 - 8 * q^13 + 2 * q^16 - 14 * q^17 - 4 * q^20 + 6 * q^22 - 12 * q^23 + 6 * q^25 - 8 * q^26 + 2 * q^32 - 14 * q^34 - 6 * q^35 + 12 * q^37 - 4 * q^40 - 14 * q^41 + 2 * q^43 + 6 * q^44 - 12 * q^46 - 4 * q^49 + 6 * q^50 - 8 * q^52 - 12 * q^55 + 2 * q^64 + 16 * q^65 - 14 * q^68 - 6 * q^70 - 24 * q^71 + 12 * q^74 - 4 * q^80 - 14 * q^82 + 28 * q^85 + 2 * q^86 + 6 * q^88 - 12 * q^92 + 8 * q^95 + 14 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$-1$

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
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$		0			0
$7$			3.00000i			1.13389i	0.823754	+	0.566947i	$0.191875\pi$
$7$			3.00000i			1.13389i	−0.823754	+	0.566947i	$0.808125\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.00000	+	1.00000i	−0.632456	+	0.316228i
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$			3.00000i			0.801784i
$15$		0			0
$16$	1.00000			0.250000
$17$	−7.00000			−1.69775			−0.848875	−	0.528594i	$-0.822719\pi$
$17$	−7.00000			−1.69775			−0.848875	+	0.528594i	$0.822719\pi$
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	−2.00000	+	1.00000i	−0.447214	+	0.223607i
$21$		0			0
$22$	3.00000			0.639602
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	−4.00000			−0.784465
$27$		0			0
$28$			3.00000i			0.566947i
$29$			9.00000i			1.67126i	0.549294	+	0.835629i	$0.314897\pi$
$29$			9.00000i			1.67126i	−0.549294	+	0.835629i	$0.685103\pi$
$30$		0			0
$31$		−	5.00000i		−	0.898027i	−0.893525	−	0.449013i	$-0.851776\pi$
$31$		−	5.00000i		−	0.898027i	0.893525	−	0.449013i	$-0.148224\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−7.00000			−1.20049
$35$	−3.00000	−	6.00000i	−0.507093	−	1.01419i
$36$		0			0
$37$	6.00000	−	1.00000i	0.986394	−	0.164399i
$37$	6.00000	−	1.00000i	0.986394	−	0.164399i
$38$		−	4.00000i		−	0.648886i
$39$		0			0
$40$	−2.00000	+	1.00000i	−0.316228	+	0.158114i
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−6.00000			−0.884652
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		0			0
$49$	−2.00000			−0.285714
$50$	3.00000	−	4.00000i	0.424264	−	0.565685i
$51$		0			0
$52$	−4.00000			−0.554700
$53$		−	1.00000i		−	0.137361i	−0.997639	−	0.0686803i	$-0.978121\pi$
$53$		−	1.00000i		−	0.137361i	0.997639	−	0.0686803i	$-0.0218788\pi$
$54$		0			0
$55$	−6.00000	+	3.00000i	−0.809040	+	0.404520i
$56$			3.00000i			0.400892i
$57$		0			0
$58$			9.00000i			1.18176i
$59$		−	6.00000i		−	0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$		0			0
$61$		−	5.00000i		−	0.640184i	−0.947386	−	0.320092i	$-0.896286\pi$
$61$		−	5.00000i		−	0.640184i	0.947386	−	0.320092i	$-0.103714\pi$
$62$		−	5.00000i		−	0.635001i
$63$		0			0
$64$	1.00000			0.125000
$65$	8.00000	−	4.00000i	0.992278	−	0.496139i
$66$		0			0
$67$		−	2.00000i		−	0.244339i	−0.992509	−	0.122169i	$-0.961015\pi$
$67$		−	2.00000i		−	0.244339i	0.992509	−	0.122169i	$-0.0389851\pi$
$68$	−7.00000			−0.848875
$69$		0			0
$70$	−3.00000	−	6.00000i	−0.358569	−	0.717137i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$	6.00000	−	1.00000i	0.697486	−	0.116248i
$75$		0			0
$76$		−	4.00000i		−	0.458831i
$77$			9.00000i			1.02565i
$78$		0			0
$79$		−	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	+	1.00000i	−0.223607	+	0.111803i
$81$		0			0
$82$	−7.00000			−0.773021
$83$			14.0000i			1.53670i	0.640030	+	0.768350i	$0.278922\pi$
$83$			14.0000i			1.53670i	−0.640030	+	0.768350i	$0.721078\pi$
$84$		0			0
$85$	14.0000	−	7.00000i	1.51851	−	0.759257i
$86$	1.00000			0.107833
$87$		0			0
$88$	3.00000			0.319801
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$		0			0
$91$		−	12.0000i		−	1.25794i
$92$	−6.00000			−0.625543
$93$		0			0
$94$		−	8.00000i		−	0.825137i
$95$	4.00000	+	8.00000i	0.410391	+	0.820783i
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	−2.00000			−0.202031
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	−2.00000			−0.199007			−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000			−0.199007			−0.0995037	+	0.995037i	$0.531726\pi$
$102$		0			0
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$		−	1.00000i		−	0.0971286i
$107$		−	18.0000i		−	1.74013i	−0.492941	−	0.870063i	$-0.664078\pi$
$107$		−	18.0000i		−	1.74013i	0.492941	−	0.870063i	$-0.335922\pi$
$108$		0			0
$109$			11.0000i			1.05361i	0.849987	+	0.526804i	$0.176610\pi$
$109$			11.0000i			1.05361i	−0.849987	+	0.526804i	$0.823390\pi$
$110$	−6.00000	+	3.00000i	−0.572078	+	0.286039i
$111$		0			0
$112$			3.00000i			0.283473i
$113$	−1.00000			−0.0940721			−0.0470360	−	0.998893i	$-0.514978\pi$
$113$	−1.00000			−0.0940721			−0.0470360	+	0.998893i	$0.514978\pi$
$114$		0			0
$115$	12.0000	−	6.00000i	1.11901	−	0.559503i
$116$			9.00000i			0.835629i
$117$		0			0
$118$		−	6.00000i		−	0.552345i
$119$		−	21.0000i		−	1.92507i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		−	5.00000i		−	0.452679i
$123$		0			0
$124$		−	5.00000i		−	0.449013i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	8.00000	−	4.00000i	0.701646	−	0.350823i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$	12.0000			1.04053
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$	−7.00000			−0.600245
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$		0			0
$139$	−15.0000			−1.27228			−0.636142	−	0.771572i	$-0.719471\pi$
$139$	−15.0000			−1.27228			−0.636142	+	0.771572i	$0.719471\pi$
$140$	−3.00000	−	6.00000i	−0.253546	−	0.507093i
$141$		0			0
$142$	−12.0000			−1.00702
$143$	−12.0000			−1.00349
$144$		0			0
$145$	−9.00000	−	18.0000i	−0.747409	−	1.49482i
$146$		−	4.00000i		−	0.331042i
$147$		0			0
$148$	6.00000	−	1.00000i	0.493197	−	0.0821995i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$		0			0
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$		−	4.00000i		−	0.324443i
$153$		0			0
$154$			9.00000i			0.725241i
$155$	5.00000	+	10.0000i	0.401610	+	0.803219i
$156$		0			0
$157$		−	7.00000i		−	0.558661i	−0.960195	−	0.279330i	$-0.909888\pi$
$157$		−	7.00000i		−	0.558661i	0.960195	−	0.279330i	$-0.0901125\pi$
$158$		−	4.00000i		−	0.318223i
$159$		0			0
$160$	−2.00000	+	1.00000i	−0.158114	+	0.0790569i
$161$		−	18.0000i		−	1.41860i
$162$		0			0
$163$	−9.00000			−0.704934			−0.352467	−	0.935824i	$-0.614657\pi$
$163$	−9.00000			−0.704934			−0.352467	+	0.935824i	$0.614657\pi$
$164$	−7.00000			−0.546608
$165$		0			0
$166$			14.0000i			1.08661i
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$	14.0000	−	7.00000i	1.07375	−	0.536875i
$171$		0			0
$172$	1.00000			0.0762493
$173$			9.00000i			0.684257i	0.939653	+	0.342129i	$0.111148\pi$
$173$			9.00000i			0.684257i	−0.939653	+	0.342129i	$0.888852\pi$
$174$		0			0
$175$	12.0000	+	9.00000i	0.907115	+	0.680336i
$176$	3.00000			0.226134
$177$		0			0
$178$		−	6.00000i		−	0.449719i
$179$			4.00000i			0.298974i	0.988764	+	0.149487i	$0.0477622\pi$
$179$			4.00000i			0.298974i	−0.988764	+	0.149487i	$0.952238\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		−	12.0000i		−	0.889499i
$183$		0			0
$184$	−6.00000			−0.442326
$185$	−11.0000	+	8.00000i	−0.808736	+	0.588172i
$186$		0			0
$187$	−21.0000			−1.53567
$188$		−	8.00000i		−	0.583460i
$189$		0			0
$190$	4.00000	+	8.00000i	0.290191	+	0.580381i
$191$			15.0000i			1.08536i	0.839939	+	0.542681i	$0.182591\pi$
$191$			15.0000i			1.08536i	−0.839939	+	0.542681i	$0.817409\pi$
$192$		0			0
$193$	−14.0000			−1.00774			−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000			−1.00774			−0.503871	+	0.863779i	$0.668091\pi$
$194$	7.00000			0.502571
$195$		0			0
$196$	−2.00000			−0.142857
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		0			0
$199$			16.0000i			1.13421i	0.823646	+	0.567105i	$0.191937\pi$
$199$			16.0000i			1.13421i	−0.823646	+	0.567105i	$0.808063\pi$
$200$	3.00000	−	4.00000i	0.212132	−	0.282843i
$201$		0			0
$202$	−2.00000			−0.140720
$203$	−27.0000			−1.89503
$204$		0			0
$205$	14.0000	−	7.00000i	0.977802	−	0.488901i
$206$	−14.0000			−0.975426
$207$		0			0
$208$	−4.00000			−0.277350
$209$		−	12.0000i		−	0.830057i
$210$		0			0
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$		−	1.00000i		−	0.0686803i
$213$		0			0
$214$		−	18.0000i		−	1.23045i
$215$	−2.00000	+	1.00000i	−0.136399	+	0.0681994i
$216$		0			0
$217$	15.0000			1.01827
$218$			11.0000i			0.745014i
$219$		0			0
$220$	−6.00000	+	3.00000i	−0.404520	+	0.202260i
$221$	28.0000			1.88348
$222$		0			0
$223$			11.0000i			0.736614i	0.929704	+	0.368307i	$0.120063\pi$
$223$			11.0000i			0.736614i	−0.929704	+	0.368307i	$0.879937\pi$
$224$			3.00000i			0.200446i
$225$		0			0
$226$	−1.00000			−0.0665190
$227$	13.0000			0.862840			0.431420	−	0.902151i	$-0.358013\pi$
$227$	13.0000			0.862840			0.431420	+	0.902151i	$0.358013\pi$
$228$		0			0
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	12.0000	−	6.00000i	0.791257	−	0.395628i
$231$		0			0
$232$			9.00000i			0.590879i
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$		0			0
$235$	8.00000	+	16.0000i	0.521862	+	1.04372i
$236$		−	6.00000i		−	0.390567i
$237$		0			0
$238$		−	21.0000i		−	1.36123i
$239$			9.00000i			0.582162i	0.956698	+	0.291081i	$0.0940149\pi$
$239$			9.00000i			0.582162i	−0.956698	+	0.291081i	$0.905985\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−2.00000			−0.128565
$243$		0			0
$244$		−	5.00000i		−	0.320092i
$245$	4.00000	−	2.00000i	0.255551	−	0.127775i
$246$		0			0
$247$			16.0000i			1.01806i
$248$		−	5.00000i		−	0.317500i
$249$		0			0
$250$	−2.00000	+	11.0000i	−0.126491	+	0.695701i
$251$		−	20.0000i		−	1.26239i	−0.775625	−	0.631194i	$-0.782565\pi$
$251$		−	20.0000i		−	1.26239i	0.775625	−	0.631194i	$-0.217435\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$			8.00000i			0.501965i
$255$		0			0
$256$	1.00000			0.0625000
$257$	18.0000			1.12281			0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000			1.12281			0.561405	+	0.827541i	$0.310261\pi$
$258$		0			0
$259$	3.00000	+	18.0000i	0.186411	+	1.11847i
$260$	8.00000	−	4.00000i	0.496139	−	0.248069i
$261$		0			0
$262$		0			0
$263$		−	31.0000i		−	1.91154i	−0.294112	−	0.955771i	$-0.595024\pi$
$263$		−	31.0000i		−	1.91154i	0.294112	−	0.955771i	$-0.404976\pi$
$264$		0			0
$265$	1.00000	+	2.00000i	0.0614295	+	0.122859i
$266$	12.0000			0.735767
$267$		0			0
$268$		−	2.00000i		−	0.122169i
$269$	−20.0000			−1.21942			−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−20.0000			−1.21942			−0.609711	+	0.792624i	$0.708714\pi$
$270$		0			0
$271$	22.0000			1.33640			0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000			1.33640			0.668202	+	0.743980i	$0.267064\pi$
$272$	−7.00000			−0.424437
$273$		0			0
$274$			12.0000i			0.724947i
$275$	9.00000	−	12.0000i	0.542720	−	0.723627i
$276$		0			0
$277$	−28.0000			−1.68236			−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−28.0000			−1.68236			−0.841178	+	0.540758i	$0.818138\pi$
$278$	−15.0000			−0.899640
$279$		0			0
$280$	−3.00000	−	6.00000i	−0.179284	−	0.358569i
$281$			30.0000i			1.78965i	0.446417	+	0.894825i	$0.352700\pi$
$281$			30.0000i			1.78965i	−0.446417	+	0.894825i	$0.647300\pi$
$282$		0			0
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$	−12.0000			−0.712069
$285$		0			0
$286$	−12.0000			−0.709575
$287$		−	21.0000i		−	1.23959i
$288$		0			0
$289$	32.0000			1.88235
$290$	−9.00000	−	18.0000i	−0.528498	−	1.05700i
$291$		0			0
$292$		−	4.00000i		−	0.234082i
$293$			29.0000i			1.69420i	0.531435	+	0.847099i	$0.321653\pi$
$293$			29.0000i			1.69420i	−0.531435	+	0.847099i	$0.678347\pi$
$294$		0			0
$295$	6.00000	+	12.0000i	0.349334	+	0.698667i
$296$	6.00000	−	1.00000i	0.348743	−	0.0581238i
$297$		0			0
$298$		0			0
$299$	24.0000			1.38796
$300$		0			0
$301$			3.00000i			0.172917i
$302$	2.00000			0.115087
$303$		0			0
$304$		−	4.00000i		−	0.229416i
$305$	5.00000	+	10.0000i	0.286299	+	0.572598i
$306$		0			0
$307$			18.0000i			1.02731i	0.857996	+	0.513657i	$0.171710\pi$
$307$			18.0000i			1.02731i	−0.857996	+	0.513657i	$0.828290\pi$
$308$			9.00000i			0.512823i
$309$		0			0
$310$	5.00000	+	10.0000i	0.283981	+	0.567962i
$311$		−	15.0000i		−	0.850572i	−0.905059	−	0.425286i	$-0.860174\pi$
$311$		−	15.0000i		−	0.850572i	0.905059	−	0.425286i	$-0.139826\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$		−	7.00000i		−	0.395033i
$315$		0			0
$316$		−	4.00000i		−	0.225018i
$317$			27.0000i			1.51647i	0.651981	+	0.758236i	$0.273938\pi$
$317$			27.0000i			1.51647i	−0.651981	+	0.758236i	$0.726062\pi$
$318$		0			0
$319$			27.0000i			1.51171i
$320$	−2.00000	+	1.00000i	−0.111803	+	0.0559017i
$321$		0			0
$322$		−	18.0000i		−	1.00310i
$323$			28.0000i			1.55796i
$324$		0			0
$325$	−12.0000	+	16.0000i	−0.665640	+	0.887520i
$326$	−9.00000			−0.498464
$327$		0			0
$328$	−7.00000			−0.386510
$329$	24.0000			1.32316
$330$		0			0
$331$		−	20.0000i		−	1.09930i	−0.835395	−	0.549650i	$-0.814761\pi$
$331$		−	20.0000i		−	1.09930i	0.835395	−	0.549650i	$-0.185239\pi$
$332$			14.0000i			0.768350i
$333$		0			0
$334$	−12.0000			−0.656611
$335$	2.00000	+	4.00000i	0.109272	+	0.218543i
$336$		0			0
$337$			18.0000i			0.980522i	0.871576	+	0.490261i	$0.163099\pi$
$337$			18.0000i			0.980522i	−0.871576	+	0.490261i	$0.836901\pi$
$338$	3.00000			0.163178
$339$		0			0
$340$	14.0000	−	7.00000i	0.759257	−	0.379628i
$341$		−	15.0000i		−	0.812296i
$342$		0			0
$343$			15.0000i			0.809924i
$344$	1.00000			0.0539164
$345$		0			0
$346$			9.00000i			0.483843i
$347$	28.0000			1.50312			0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000			1.50312			0.751559	+	0.659665i	$0.229302\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	12.0000	+	9.00000i	0.641427	+	0.481070i
$351$		0			0
$352$	3.00000			0.159901
$353$	−31.0000			−1.64996			−0.824982	−	0.565159i	$-0.808815\pi$
$353$	−31.0000			−1.64996			−0.824982	+	0.565159i	$0.808815\pi$
$354$		0			0
$355$	24.0000	−	12.0000i	1.27379	−	0.636894i
$356$		−	6.00000i		−	0.317999i
$357$		0			0
$358$			4.00000i			0.211407i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−18.0000			−0.946059
$363$		0			0
$364$		−	12.0000i		−	0.628971i
$365$	4.00000	+	8.00000i	0.209370	+	0.418739i
$366$		0			0
$367$			23.0000i			1.20059i	0.799779	+	0.600295i	$0.204950\pi$
$367$			23.0000i			1.20059i	−0.799779	+	0.600295i	$0.795050\pi$
$368$	−6.00000			−0.312772
$369$		0			0
$370$	−11.0000	+	8.00000i	−0.571863	+	0.415900i
$371$	3.00000			0.155752
$372$		0			0
$373$		−	14.0000i		−	0.724893i	−0.932005	−	0.362446i	$-0.881942\pi$
$373$		−	14.0000i		−	0.724893i	0.932005	−	0.362446i	$-0.118058\pi$
$374$	−21.0000			−1.08588
$375$		0			0
$376$		−	8.00000i		−	0.412568i
$377$		−	36.0000i		−	1.85409i
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	4.00000	+	8.00000i	0.205196	+	0.410391i
$381$		0			0
$382$			15.0000i			0.767467i
$383$	−6.00000			−0.306586			−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000			−0.306586			−0.153293	+	0.988181i	$0.548988\pi$
$384$		0			0
$385$	−9.00000	−	18.0000i	−0.458682	−	0.917365i
$386$	−14.0000			−0.712581
$387$		0			0
$388$	7.00000			0.355371
$389$		−	31.0000i		−	1.57176i	−0.618378	−	0.785881i	$-0.712210\pi$
$389$		−	31.0000i		−	1.57176i	0.618378	−	0.785881i	$-0.287790\pi$
$390$		0			0
$391$	42.0000			2.12403
$392$	−2.00000			−0.101015
$393$		0			0
$394$		−	18.0000i		−	0.906827i
$395$	4.00000	+	8.00000i	0.201262	+	0.402524i
$396$		0			0
$397$			38.0000i			1.90717i	0.301131	+	0.953583i	$0.402636\pi$
$397$			38.0000i			1.90717i	−0.301131	+	0.953583i	$0.597364\pi$
$398$			16.0000i			0.802008i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$			10.0000i			0.499376i	0.968326	+	0.249688i	$0.0803281\pi$
$401$			10.0000i			0.499376i	−0.968326	+	0.249688i	$0.919672\pi$
$402$		0			0
$403$			20.0000i			0.996271i
$404$	−2.00000			−0.0995037
$405$		0			0
$406$	−27.0000			−1.33999
$407$	18.0000	−	3.00000i	0.892227	−	0.148704i
$408$		0			0
$409$		−	14.0000i		−	0.692255i	−0.938187	−	0.346128i	$-0.887496\pi$
$409$		−	14.0000i		−	0.692255i	0.938187	−	0.346128i	$-0.112504\pi$
$410$	14.0000	−	7.00000i	0.691411	−	0.345705i
$411$		0			0
$412$	−14.0000			−0.689730
$413$	18.0000			0.885722
$414$		0			0
$415$	−14.0000	−	28.0000i	−0.687233	−	1.37447i
$416$	−4.00000			−0.196116
$417$		0			0
$418$		−	12.0000i		−	0.586939i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$			30.0000i			1.46211i	0.682318	+	0.731055i	$0.260972\pi$
$421$			30.0000i			1.46211i	−0.682318	+	0.731055i	$0.739028\pi$
$422$	−13.0000			−0.632830
$423$		0			0
$424$		−	1.00000i		−	0.0485643i
$425$	−21.0000	+	28.0000i	−1.01865	+	1.35820i
$426$		0			0
$427$	15.0000			0.725901
$428$		−	18.0000i		−	0.870063i
$429$		0			0
$430$	−2.00000	+	1.00000i	−0.0964486	+	0.0482243i
$431$			25.0000i			1.20421i	0.798418	+	0.602104i	$0.205671\pi$
$431$			25.0000i			1.20421i	−0.798418	+	0.602104i	$0.794329\pi$
$432$		0			0
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$	15.0000			0.720023
$435$		0			0
$436$			11.0000i			0.526804i
$437$			24.0000i			1.14808i
$438$		0			0
$439$		−	9.00000i		−	0.429547i	−0.976664	−	0.214773i	$-0.931099\pi$
$439$		−	9.00000i		−	0.429547i	0.976664	−	0.214773i	$-0.0689013\pi$
$440$	−6.00000	+	3.00000i	−0.286039	+	0.143019i
$441$		0			0
$442$	28.0000			1.33182
$443$		−	36.0000i		−	1.71041i	−0.518289	−	0.855206i	$-0.673431\pi$
$443$		−	36.0000i		−	1.71041i	0.518289	−	0.855206i	$-0.326569\pi$
$444$		0			0
$445$	6.00000	+	12.0000i	0.284427	+	0.568855i
$446$			11.0000i			0.520865i
$447$		0			0
$448$			3.00000i			0.141737i
$449$		−	6.00000i		−	0.283158i	−0.989927	−	0.141579i	$-0.954782\pi$
$449$		−	6.00000i		−	0.283158i	0.989927	−	0.141579i	$-0.0452178\pi$
$450$		0			0
$451$	−21.0000			−0.988851
$452$	−1.00000			−0.0470360
$453$		0			0
$454$	13.0000			0.610120
$455$	12.0000	+	24.0000i	0.562569	+	1.12514i
$456$		0			0
$457$	−13.0000			−0.608114			−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000			−0.608114			−0.304057	+	0.952654i	$0.598341\pi$
$458$	10.0000			0.467269
$459$		0			0
$460$	12.0000	−	6.00000i	0.559503	−	0.279751i
$461$		−	25.0000i		−	1.16437i	−0.813058	−	0.582183i	$-0.802199\pi$
$461$		−	25.0000i		−	1.16437i	0.813058	−	0.582183i	$-0.197801\pi$
$462$		0			0
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$			9.00000i			0.417815i
$465$		0			0
$466$		−	6.00000i		−	0.277945i
$467$	23.0000			1.06431			0.532157	−	0.846646i	$-0.321382\pi$
$467$	23.0000			1.06431			0.532157	+	0.846646i	$0.321382\pi$
$468$		0			0
$469$	6.00000			0.277054
$470$	8.00000	+	16.0000i	0.369012	+	0.738025i
$471$		0			0
$472$		−	6.00000i		−	0.276172i
$473$	3.00000			0.137940
$474$		0			0
$475$	−16.0000	−	12.0000i	−0.734130	−	0.550598i
$476$		−	21.0000i		−	0.962533i
$477$		0			0
$478$			9.00000i			0.411650i
$479$			24.0000i			1.09659i	0.836286	+	0.548294i	$0.184723\pi$
$479$			24.0000i			1.09659i	−0.836286	+	0.548294i	$0.815277\pi$
$480$		0			0
$481$	−24.0000	+	4.00000i	−1.09431	+	0.182384i
$482$		0			0
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−14.0000	+	7.00000i	−0.635707	+	0.317854i
$486$		0			0
$487$	22.0000			0.996915			0.498458	−	0.866914i	$-0.333900\pi$
$487$	22.0000			0.996915			0.498458	+	0.866914i	$0.333900\pi$
$488$		−	5.00000i		−	0.226339i
$489$		0			0
$490$	4.00000	−	2.00000i	0.180702	−	0.0903508i
$491$	8.00000			0.361035			0.180517	−	0.983572i	$-0.442223\pi$
$491$	8.00000			0.361035			0.180517	+	0.983572i	$0.442223\pi$
$492$		0			0
$493$		−	63.0000i		−	2.83738i
$494$			16.0000i			0.719874i
$495$		0			0
$496$		−	5.00000i		−	0.224507i
$497$		−	36.0000i		−	1.61482i
$498$		0			0
$499$		−	24.0000i		−	1.07439i	−0.843459	−	0.537194i	$-0.819484\pi$
$499$		−	24.0000i		−	1.07439i	0.843459	−	0.537194i	$-0.180516\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$		0			0
$502$		−	20.0000i		−	0.892644i
$503$	14.0000			0.624229			0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000			0.624229			0.312115	+	0.950044i	$0.398963\pi$
$504$		0			0
$505$	4.00000	−	2.00000i	0.177998	−	0.0889988i
$506$	−18.0000			−0.800198
$507$		0			0
$508$			8.00000i			0.354943i
$509$	10.0000			0.443242			0.221621	−	0.975133i	$-0.428865\pi$
$509$	10.0000			0.443242			0.221621	+	0.975133i	$0.428865\pi$
$510$		0			0
$511$	12.0000			0.530849
$512$	1.00000			0.0441942
$513$		0			0
$514$	18.0000			0.793946
$515$	28.0000	−	14.0000i	1.23383	−	0.616914i
$516$		0			0
$517$		−	24.0000i		−	1.05552i
$518$	3.00000	+	18.0000i	0.131812	+	0.790875i
$519$		0			0
$520$	8.00000	−	4.00000i	0.350823	−	0.175412i
$521$	−37.0000			−1.62100			−0.810500	−	0.585739i	$-0.800804\pi$
$521$	−37.0000			−1.62100			−0.810500	+	0.585739i	$0.800804\pi$
$522$		0			0
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$		0			0
$525$		0			0
$526$		−	31.0000i		−	1.35166i
$527$			35.0000i			1.52462i
$528$		0			0
$529$	13.0000			0.565217
$530$	1.00000	+	2.00000i	0.0434372	+	0.0868744i
$531$		0			0
$532$	12.0000			0.520266
$533$	28.0000			1.21281
$534$		0			0
$535$	18.0000	+	36.0000i	0.778208	+	1.55642i
$536$		−	2.00000i		−	0.0863868i
$537$		0			0
$538$	−20.0000			−0.862261
$539$	−6.00000			−0.258438
$540$		0			0
$541$			30.0000i			1.28980i	0.764267	+	0.644900i	$0.223101\pi$
$541$			30.0000i			1.28980i	−0.764267	+	0.644900i	$0.776899\pi$
$542$	22.0000			0.944981
$543$		0			0
$544$	−7.00000			−0.300123
$545$	−11.0000	−	22.0000i	−0.471188	−	0.942376i
$546$		0			0
$547$	−23.0000			−0.983409			−0.491704	−	0.870762i	$-0.663626\pi$
$547$	−23.0000			−0.983409			−0.491704	+	0.870762i	$0.663626\pi$
$548$			12.0000i			0.512615i
$549$		0			0
$550$	9.00000	−	12.0000i	0.383761	−	0.511682i
$551$	36.0000			1.53365
$552$		0			0
$553$	12.0000			0.510292
$554$	−28.0000			−1.18961
$555$		0			0
$556$	−15.0000			−0.636142
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	−3.00000	−	6.00000i	−0.126773	−	0.253546i
$561$		0			0
$562$			30.0000i			1.26547i
$563$	−21.0000			−0.885044			−0.442522	−	0.896758i	$-0.645916\pi$
$563$	−21.0000			−0.885044			−0.442522	+	0.896758i	$0.645916\pi$
$564$		0			0
$565$	2.00000	−	1.00000i	0.0841406	−	0.0420703i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	−12.0000			−0.503509
$569$			24.0000i			1.00613i	0.864248	+	0.503066i	$0.167795\pi$
$569$			24.0000i			1.00613i	−0.864248	+	0.503066i	$0.832205\pi$
$570$		0			0
$571$	−33.0000			−1.38101			−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000			−1.38101			−0.690504	+	0.723329i	$0.742611\pi$
$572$	−12.0000			−0.501745
$573$		0			0
$574$		−	21.0000i		−	0.876523i
$575$	−18.0000	+	24.0000i	−0.750652	+	1.00087i
$576$		0			0
$577$	22.0000			0.915872			0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000			0.915872			0.457936	+	0.888985i	$0.348589\pi$
$578$	32.0000			1.33102
$579$		0			0
$580$	−9.00000	−	18.0000i	−0.373705	−	0.747409i
$581$	−42.0000			−1.74245
$582$		0			0
$583$		−	3.00000i		−	0.124247i
$584$		−	4.00000i		−	0.165521i
$585$		0			0
$586$			29.0000i			1.19798i
$587$	−47.0000			−1.93990			−0.969949	−	0.243309i	$-0.921767\pi$
$587$	−47.0000			−1.93990			−0.969949	+	0.243309i	$0.921767\pi$
$588$		0			0
$589$	−20.0000			−0.824086
$590$	6.00000	+	12.0000i	0.247016	+	0.494032i
$591$		0			0
$592$	6.00000	−	1.00000i	0.246598	−	0.0410997i
$593$		−	46.0000i		−	1.88899i	−0.328521	−	0.944497i	$-0.606550\pi$
$593$		−	46.0000i		−	1.88899i	0.328521	−	0.944497i	$-0.393450\pi$
$594$		0			0
$595$	21.0000	+	42.0000i	0.860916	+	1.72183i
$596$		0			0
$597$		0			0
$598$	24.0000			0.981433
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	−23.0000			−0.938190			−0.469095	−	0.883148i	$-0.655420\pi$
$601$	−23.0000			−0.938190			−0.469095	+	0.883148i	$0.655420\pi$
$602$			3.00000i			0.122271i
$603$		0			0
$604$	2.00000			0.0813788
$605$	4.00000	−	2.00000i	0.162623	−	0.0813116i
$606$		0			0
$607$	32.0000			1.29884			0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000			1.29884			0.649420	+	0.760430i	$0.275012\pi$
$608$		−	4.00000i		−	0.162221i
$609$		0			0
$610$	5.00000	+	10.0000i	0.202444	+	0.404888i
$611$			32.0000i			1.29458i
$612$		0			0
$613$			31.0000i			1.25208i	0.779792	+	0.626039i	$0.215325\pi$
$613$			31.0000i			1.25208i	−0.779792	+	0.626039i	$0.784675\pi$
$614$			18.0000i			0.726421i
$615$		0			0
$616$			9.00000i			0.362620i
$617$		−	8.00000i		−	0.322068i	−0.986949	−	0.161034i	$-0.948517\pi$
$617$		−	8.00000i		−	0.322068i	0.986949	−	0.161034i	$-0.0514829\pi$
$618$		0			0
$619$	25.0000			1.00483			0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000			1.00483			0.502417	+	0.864625i	$0.332444\pi$
$620$	5.00000	+	10.0000i	0.200805	+	0.401610i
$621$		0			0
$622$		−	15.0000i		−	0.601445i
$623$	18.0000			0.721155
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	6.00000			0.239808
$627$		0			0
$628$		−	7.00000i		−	0.279330i
$629$	−42.0000	+	7.00000i	−1.67465	+	0.279108i
$630$		0			0
$631$		−	25.0000i		−	0.995234i	−0.867397	−	0.497617i	$-0.834208\pi$
$631$		−	25.0000i		−	0.995234i	0.867397	−	0.497617i	$-0.165792\pi$
$632$		−	4.00000i		−	0.159111i
$633$		0			0
$634$			27.0000i			1.07231i
$635$	−8.00000	−	16.0000i	−0.317470	−	0.634941i
$636$		0			0
$637$	8.00000			0.316972
$638$			27.0000i			1.06894i
$639$		0			0
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$	−17.0000			−0.671460			−0.335730	−	0.941958i	$-0.608983\pi$
$641$	−17.0000			−0.671460			−0.335730	+	0.941958i	$0.608983\pi$
$642$		0			0
$643$	31.0000			1.22252			0.611260	−	0.791430i	$-0.290663\pi$
$643$	31.0000			1.22252			0.611260	+	0.791430i	$0.290663\pi$
$644$		−	18.0000i		−	0.709299i
$645$		0			0
$646$			28.0000i			1.10165i
$647$	48.0000			1.88707			0.943537	−	0.331266i	$-0.107476\pi$
$647$	48.0000			1.88707			0.943537	+	0.331266i	$0.107476\pi$
$648$		0			0
$649$		−	18.0000i		−	0.706562i
$650$	−12.0000	+	16.0000i	−0.470679	+	0.627572i
$651$		0			0
$652$	−9.00000			−0.352467
$653$	−36.0000			−1.40879			−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000			−1.40879			−0.704394	+	0.709809i	$0.748781\pi$
$654$		0			0
$655$		0			0
$656$	−7.00000			−0.273304
$657$		0			0
$658$	24.0000			0.935617
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$		0			0
$661$		−	35.0000i		−	1.36134i	−0.732589	−	0.680671i	$-0.761688\pi$
$661$		−	35.0000i		−	1.36134i	0.732589	−	0.680671i	$-0.238312\pi$
$662$		−	20.0000i		−	0.777322i
$663$		0			0
$664$			14.0000i			0.543305i
$665$	−24.0000	+	12.0000i	−0.930680	+	0.465340i
$666$		0			0
$667$		−	54.0000i		−	2.09089i
$668$	−12.0000			−0.464294
$669$		0			0
$670$	2.00000	+	4.00000i	0.0772667	+	0.154533i
$671$		−	15.0000i		−	0.579069i
$672$		0			0
$673$			26.0000i			1.00223i	0.865382	+	0.501113i	$0.167076\pi$
$673$			26.0000i			1.00223i	−0.865382	+	0.501113i	$0.832924\pi$
$674$			18.0000i			0.693334i
$675$		0			0
$676$	3.00000			0.115385
$677$			42.0000i			1.61419i	0.590421	+	0.807096i	$0.298962\pi$
$677$			42.0000i			1.61419i	−0.590421	+	0.807096i	$0.701038\pi$
$678$		0			0
$679$			21.0000i			0.805906i
$680$	14.0000	−	7.00000i	0.536875	−	0.268438i
$681$		0			0
$682$		−	15.0000i		−	0.574380i
$683$	−1.00000			−0.0382639			−0.0191320	−	0.999817i	$-0.506090\pi$
$683$	−1.00000			−0.0382639			−0.0191320	+	0.999817i	$0.506090\pi$
$684$		0			0
$685$	−12.0000	−	24.0000i	−0.458496	−	0.916993i
$686$			15.0000i			0.572703i
$687$		0			0
$688$	1.00000			0.0381246
$689$			4.00000i			0.152388i
$690$		0			0
$691$	−43.0000			−1.63580			−0.817899	−	0.575362i	$-0.804861\pi$
$691$	−43.0000			−1.63580			−0.817899	+	0.575362i	$0.804861\pi$
$692$			9.00000i			0.342129i
$693$		0			0
$694$	28.0000			1.06287
$695$	30.0000	−	15.0000i	1.13796	−	0.568982i
$696$		0			0
$697$	49.0000			1.85601
$698$		0			0
$699$		0			0
$700$	12.0000	+	9.00000i	0.453557	+	0.340168i
$701$			10.0000i			0.377695i	0.982006	+	0.188847i	$0.0604752\pi$
$701$			10.0000i			0.377695i	−0.982006	+	0.188847i	$0.939525\pi$
$702$		0			0
$703$	−4.00000	−	24.0000i	−0.150863	−	0.905177i
$704$	3.00000			0.113067
$705$		0			0
$706$	−31.0000			−1.16670
$707$		−	6.00000i		−	0.225653i
$708$		0			0
$709$			11.0000i			0.413114i	0.978435	+	0.206557i	$0.0662258\pi$
$709$			11.0000i			0.413114i	−0.978435	+	0.206557i	$0.933774\pi$
$710$	24.0000	−	12.0000i	0.900704	−	0.450352i
$711$		0			0
$712$		−	6.00000i		−	0.224860i
$713$			30.0000i			1.12351i
$714$		0			0
$715$	24.0000	−	12.0000i	0.897549	−	0.448775i
$716$			4.00000i			0.149487i
$717$		0			0
$718$		0			0
$719$	−50.0000			−1.86469			−0.932343	−	0.361576i	$-0.882239\pi$
$719$	−50.0000			−1.86469			−0.932343	+	0.361576i	$0.882239\pi$
$720$		0			0
$721$		−	42.0000i		−	1.56416i
$722$	3.00000			0.111648
$723$		0			0
$724$	−18.0000			−0.668965
$725$	36.0000	+	27.0000i	1.33701	+	1.00275i
$726$		0			0
$727$	−18.0000			−0.667583			−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000			−0.667583			−0.333792	+	0.942647i	$0.608328\pi$
$728$		−	12.0000i		−	0.444750i
$729$		0			0
$730$	4.00000	+	8.00000i	0.148047	+	0.296093i
$731$	−7.00000			−0.258904
$732$		0			0
$733$			11.0000i			0.406294i	0.979148	+	0.203147i	$0.0651170\pi$
$733$			11.0000i			0.406294i	−0.979148	+	0.203147i	$0.934883\pi$
$734$			23.0000i			0.848945i
$735$		0			0
$736$	−6.00000			−0.221163
$737$		−	6.00000i		−	0.221013i
$738$		0			0
$739$	5.00000			0.183928			0.0919640	−	0.995762i	$-0.470686\pi$
$739$	5.00000			0.183928			0.0919640	+	0.995762i	$0.470686\pi$
$740$	−11.0000	+	8.00000i	−0.404368	+	0.294086i
$741$		0			0
$742$	3.00000			0.110133
$743$		−	51.0000i		−	1.87101i	−0.353315	−	0.935504i	$-0.614946\pi$
$743$		−	51.0000i		−	1.87101i	0.353315	−	0.935504i	$-0.385054\pi$
$744$		0			0
$745$		0			0
$746$		−	14.0000i		−	0.512576i
$747$		0			0
$748$	−21.0000			−0.767836
$749$	54.0000			1.97312
$750$		0			0
$751$	−18.0000			−0.656829			−0.328415	−	0.944534i	$-0.606514\pi$
$751$	−18.0000			−0.656829			−0.328415	+	0.944534i	$0.606514\pi$
$752$		−	8.00000i		−	0.291730i
$753$		0			0
$754$		−	36.0000i		−	1.31104i
$755$	−4.00000	+	2.00000i	−0.145575	+	0.0727875i
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	20.0000			0.726433
$759$		0			0
$760$	4.00000	+	8.00000i	0.145095	+	0.290191i
$761$	13.0000			0.471250			0.235625	−	0.971844i	$-0.424286\pi$
$761$	13.0000			0.471250			0.235625	+	0.971844i	$0.424286\pi$
$762$		0			0
$763$	−33.0000			−1.19468
$764$			15.0000i			0.542681i
$765$		0			0
$766$	−6.00000			−0.216789
$767$			24.0000i			0.866590i
$768$		0			0
$769$			26.0000i			0.937584i	0.883309	+	0.468792i	$0.155311\pi$
$769$			26.0000i			0.937584i	−0.883309	+	0.468792i	$0.844689\pi$
$770$	−9.00000	−	18.0000i	−0.324337	−	0.648675i
$771$		0			0
$772$	−14.0000			−0.503871
$773$		−	11.0000i		−	0.395643i	−0.980238	−	0.197821i	$-0.936613\pi$
$773$		−	11.0000i		−	0.395643i	0.980238	−	0.197821i	$-0.0633866\pi$
$774$		0			0
$775$	−20.0000	−	15.0000i	−0.718421	−	0.538816i
$776$	7.00000			0.251285
$777$		0			0
$778$		−	31.0000i		−	1.11140i
$779$			28.0000i			1.00320i
$780$		0			0
$781$	−36.0000			−1.28818
$782$	42.0000			1.50192
$783$		0			0
$784$	−2.00000			−0.0714286
$785$	7.00000	+	14.0000i	0.249841	+	0.499681i
$786$		0			0
$787$			28.0000i			0.998092i	0.866575	+	0.499046i	$0.166316\pi$
$787$			28.0000i			0.998092i	−0.866575	+	0.499046i	$0.833684\pi$
$788$		−	18.0000i		−	0.641223i
$789$		0			0
$790$	4.00000	+	8.00000i	0.142314	+	0.284627i
$791$		−	3.00000i		−	0.106668i
$792$		0			0
$793$			20.0000i			0.710221i
$794$			38.0000i			1.34857i
$795$		0			0
$796$			16.0000i			0.567105i
$797$	28.0000			0.991811			0.495905	−	0.868377i	$-0.334836\pi$
$797$	28.0000			0.991811			0.495905	+	0.868377i	$0.334836\pi$
$798$		0			0
$799$			56.0000i			1.98114i
$800$	3.00000	−	4.00000i	0.106066	−	0.141421i
$801$		0			0
$802$			10.0000i			0.353112i
$803$		−	12.0000i		−	0.423471i
$804$		0			0
$805$	18.0000	+	36.0000i	0.634417	+	1.26883i
$806$			20.0000i			0.704470i
$807$		0			0
$808$	−2.00000			−0.0703598
$809$		−	6.00000i		−	0.210949i	−0.994422	−	0.105474i	$-0.966364\pi$
$809$		−	6.00000i		−	0.210949i	0.994422	−	0.105474i	$-0.0336361\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−27.0000			−0.947514
$813$		0			0
$814$	18.0000	−	3.00000i	0.630900	−	0.105150i
$815$	18.0000	−	9.00000i	0.630512	−	0.315256i
$816$		0			0
$817$		−	4.00000i		−	0.139942i
$818$		−	14.0000i		−	0.489499i
$819$		0			0
$820$	14.0000	−	7.00000i	0.488901	−	0.244451i
$821$	−52.0000			−1.81481			−0.907406	−	0.420255i	$-0.861941\pi$
$821$	−52.0000			−1.81481			−0.907406	+	0.420255i	$0.861941\pi$
$822$		0			0
$823$			16.0000i			0.557725i	0.960331	+	0.278862i	$0.0899574\pi$
$823$			16.0000i			0.557725i	−0.960331	+	0.278862i	$0.910043\pi$
$824$	−14.0000			−0.487713
$825$		0			0
$826$	18.0000			0.626300
$827$	33.0000			1.14752			0.573761	−	0.819023i	$-0.305484\pi$
$827$	33.0000			1.14752			0.573761	+	0.819023i	$0.305484\pi$
$828$		0			0
$829$		−	19.0000i		−	0.659897i	−0.943999	−	0.329949i	$-0.892969\pi$
$829$		−	19.0000i		−	0.659897i	0.943999	−	0.329949i	$-0.107031\pi$
$830$	−14.0000	−	28.0000i	−0.485947	−	0.971894i
$831$		0			0
$832$	−4.00000			−0.138675
$833$	14.0000			0.485071
$834$		0			0
$835$	24.0000	−	12.0000i	0.830554	−	0.415277i
$836$		−	12.0000i		−	0.415029i
$837$		0			0
$838$		0			0
$839$	40.0000			1.38095			0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000			1.38095			0.690477	+	0.723355i	$0.257401\pi$
$840$		0			0
$841$	−52.0000			−1.79310
$842$			30.0000i			1.03387i
$843$		0			0
$844$	−13.0000			−0.447478
$845$	−6.00000	+	3.00000i	−0.206406	+	0.103203i
$846$		0			0
$847$		−	6.00000i		−	0.206162i
$848$		−	1.00000i		−	0.0343401i
$849$		0			0
$850$	−21.0000	+	28.0000i	−0.720294	+	0.960392i
$851$	−36.0000	+	6.00000i	−1.23406	+	0.205677i
$852$		0			0
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$	15.0000			0.513289
$855$		0			0
$856$		−	18.0000i		−	0.615227i
$857$	43.0000			1.46885			0.734426	−	0.678689i	$-0.237451\pi$
$857$	43.0000			1.46885			0.734426	+	0.678689i	$0.237451\pi$
$858$		0			0
$859$			36.0000i			1.22830i	0.789188	+	0.614152i	$0.210502\pi$
$859$			36.0000i			1.22830i	−0.789188	+	0.614152i	$0.789498\pi$
$860$	−2.00000	+	1.00000i	−0.0681994	+	0.0340997i
$861$		0			0
$862$			25.0000i			0.851503i
$863$			49.0000i			1.66798i	0.551780	+	0.833990i	$0.313949\pi$
$863$			49.0000i			1.66798i	−0.551780	+	0.833990i	$0.686051\pi$
$864$		0			0
$865$	−9.00000	−	18.0000i	−0.306009	−	0.612018i
$866$		−	34.0000i		−	1.15537i
$867$		0			0
$868$	15.0000			0.509133
$869$		−	12.0000i		−	0.407072i
$870$		0			0
$871$			8.00000i			0.271070i
$872$			11.0000i			0.372507i
$873$		0			0
$874$			24.0000i			0.811812i
$875$	−33.0000	−	6.00000i	−1.11560	−	0.202837i
$876$		0			0
$877$		−	27.0000i		−	0.911725i	−0.890050	−	0.455863i	$-0.849331\pi$
$877$		−	27.0000i		−	0.911725i	0.890050	−	0.455863i	$-0.150669\pi$
$878$		−	9.00000i		−	0.303735i
$879$		0			0
$880$	−6.00000	+	3.00000i	−0.202260	+	0.101130i
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$		0			0
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$	28.0000			0.941742
$885$		0			0
$886$		−	36.0000i		−	1.20944i
$887$			27.0000i			0.906571i	0.891365	+	0.453286i	$0.149748\pi$
$887$			27.0000i			0.906571i	−0.891365	+	0.453286i	$0.850252\pi$
$888$		0			0
$889$	−24.0000			−0.804934
$890$	6.00000	+	12.0000i	0.201120	+	0.402241i
$891$		0			0
$892$			11.0000i			0.368307i
$893$	−32.0000			−1.07084
$894$		0			0
$895$	−4.00000	−	8.00000i	−0.133705	−	0.267411i
$896$			3.00000i			0.100223i
$897$		0			0
$898$		−	6.00000i		−	0.200223i
$899$	45.0000			1.50083
$900$		0			0
$901$			7.00000i			0.233204i
$902$	−21.0000			−0.699224
$903$		0			0
$904$	−1.00000			−0.0332595
$905$	36.0000	−	18.0000i	1.19668	−	0.598340i
$906$		0			0
$907$	−28.0000			−0.929725			−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000			−0.929725			−0.464862	+	0.885383i	$0.653896\pi$
$908$	13.0000			0.431420
$909$		0			0
$910$	12.0000	+	24.0000i	0.397796	+	0.795592i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$			42.0000i			1.39000i
$914$	−13.0000			−0.430002
$915$		0			0
$916$	10.0000			0.330409
$917$		0			0
$918$		0			0
$919$		−	24.0000i		−	0.791687i	−0.918318	−	0.395843i	$-0.870452\pi$
$919$		−	24.0000i		−	0.791687i	0.918318	−	0.395843i	$-0.129548\pi$
$920$	12.0000	−	6.00000i	0.395628	−	0.197814i
$921$		0			0
$922$		−	25.0000i		−	0.823331i
$923$	48.0000			1.57994
$924$		0			0
$925$	14.0000	−	27.0000i	0.460317	−	0.887755i
$926$	26.0000			0.854413
$927$		0			0
$928$			9.00000i			0.295439i
$929$	5.00000			0.164045			0.0820223	−	0.996630i	$-0.473862\pi$
$929$	5.00000			0.164045			0.0820223	+	0.996630i	$0.473862\pi$
$930$		0			0
$931$			8.00000i			0.262189i
$932$		−	6.00000i		−	0.196537i
$933$		0			0
$934$	23.0000			0.752583
$935$	42.0000	−	21.0000i	1.37355	−	0.686773i
$936$		0			0
$937$		−	12.0000i		−	0.392023i	−0.980602	−	0.196011i	$-0.937201\pi$
$937$		−	12.0000i		−	0.392023i	0.980602	−	0.196011i	$-0.0627990\pi$
$938$	6.00000			0.195907
$939$		0			0
$940$	8.00000	+	16.0000i	0.260931	+	0.521862i
$941$	−12.0000			−0.391189			−0.195594	−	0.980685i	$-0.562664\pi$
$941$	−12.0000			−0.391189			−0.195594	+	0.980685i	$0.562664\pi$
$942$		0			0
$943$	42.0000			1.36771
$944$		−	6.00000i		−	0.195283i
$945$		0			0
$946$	3.00000			0.0975384
$947$	−27.0000			−0.877382			−0.438691	−	0.898638i	$-0.644558\pi$
$947$	−27.0000			−0.877382			−0.438691	+	0.898638i	$0.644558\pi$
$948$		0			0
$949$			16.0000i			0.519382i
$950$	−16.0000	−	12.0000i	−0.519109	−	0.389331i
$951$		0			0
$952$		−	21.0000i		−	0.680614i
$953$		−	16.0000i		−	0.518291i	−0.965838	−	0.259145i	$-0.916559\pi$
$953$		−	16.0000i		−	0.518291i	0.965838	−	0.259145i	$-0.0834409\pi$
$954$		0			0
$955$	−15.0000	−	30.0000i	−0.485389	−	0.970777i
$956$			9.00000i			0.291081i
$957$		0			0
$958$			24.0000i			0.775405i
$959$	−36.0000			−1.16250
$960$		0			0
$961$	6.00000			0.193548
$962$	−24.0000	+	4.00000i	−0.773791	+	0.128965i
$963$		0			0
$964$		0			0
$965$	28.0000	−	14.0000i	0.901352	−	0.450676i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−2.00000			−0.0642824
$969$		0			0
$970$	−14.0000	+	7.00000i	−0.449513	+	0.224756i
$971$	−57.0000			−1.82922			−0.914609	−	0.404341i	$-0.867501\pi$
$971$	−57.0000			−1.82922			−0.914609	+	0.404341i	$0.867501\pi$
$972$		0			0
$973$		−	45.0000i		−	1.44263i
$974$	22.0000			0.704925
$975$		0			0
$976$		−	5.00000i		−	0.160046i
$977$	3.00000			0.0959785			0.0479893	−	0.998848i	$-0.484719\pi$
$977$	3.00000			0.0959785			0.0479893	+	0.998848i	$0.484719\pi$
$978$		0			0
$979$		−	18.0000i		−	0.575282i
$980$	4.00000	−	2.00000i	0.127775	−	0.0638877i
$981$		0			0
$982$	8.00000			0.255290
$983$			19.0000i			0.606006i	0.952990	+	0.303003i	$0.0979892\pi$
$983$			19.0000i			0.606006i	−0.952990	+	0.303003i	$0.902011\pi$
$984$		0			0
$985$	18.0000	+	36.0000i	0.573528	+	1.14706i
$986$		−	63.0000i		−	2.00633i
$987$		0			0
$988$			16.0000i			0.509028i
$989$	−6.00000			−0.190789
$990$		0			0
$991$			25.0000i			0.794151i	0.917786	+	0.397076i	$0.129975\pi$
$991$			25.0000i			0.794151i	−0.917786	+	0.397076i	$0.870025\pi$
$992$		−	5.00000i		−	0.158750i
$993$		0			0
$994$		−	36.0000i		−	1.14185i
$995$	−16.0000	−	32.0000i	−0.507234	−	1.01447i
$996$		0			0
$997$	42.0000			1.33015			0.665077	−	0.746775i	$-0.268399\pi$
$997$	42.0000			1.33015			0.665077	+	0.746775i	$0.268399\pi$
$998$		−	24.0000i		−	0.759707i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.e.b.739.2		2
3.2	odd	2		1110.2.e.a.739.1	✓	2
5.4	even	2		3330.2.e.a.739.2		2
15.14	odd	2		1110.2.e.b.739.2	yes	2
37.36	even	2		3330.2.e.a.739.1		2
111.110	odd	2		1110.2.e.b.739.1	yes	2
185.184	even	2	inner	3330.2.e.b.739.1		2
555.554	odd	2		1110.2.e.a.739.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.e.a.739.1	✓	2	3.2	odd	2
1110.2.e.a.739.2	yes	2	555.554	odd	2
1110.2.e.b.739.1	yes	2	111.110	odd	2
1110.2.e.b.739.2	yes	2	15.14	odd	2
3330.2.e.a.739.1		2	37.36	even	2
3330.2.e.a.739.2		2	5.4	even	2
3330.2.e.b.739.1		2	185.184	even	2	inner
3330.2.e.b.739.2		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +3.00000i q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +3.00000i q^{7} +1.00000 q^{8} +(-2.00000 + 1.00000i) q^{10} +3.00000 q^{11} -4.00000 q^{13} +3.00000i q^{14} +1.00000 q^{16} -7.00000 q^{17} -4.00000i q^{19} +(-2.00000 + 1.00000i) q^{20} +3.00000 q^{22} -6.00000 q^{23} +(3.00000 - 4.00000i) q^{25} -4.00000 q^{26} +3.00000i q^{28} +9.00000i q^{29} -5.00000i q^{31} +1.00000 q^{32} -7.00000 q^{34} +(-3.00000 - 6.00000i) q^{35} +(6.00000 - 1.00000i) q^{37} -4.00000i q^{38} +(-2.00000 + 1.00000i) q^{40} -7.00000 q^{41} +1.00000 q^{43} +3.00000 q^{44} -6.00000 q^{46} -8.00000i q^{47} -2.00000 q^{49} +(3.00000 - 4.00000i) q^{50} -4.00000 q^{52} -1.00000i q^{53} +(-6.00000 + 3.00000i) q^{55} +3.00000i q^{56} +9.00000i q^{58} -6.00000i q^{59} -5.00000i q^{61} -5.00000i q^{62} +1.00000 q^{64} +(8.00000 - 4.00000i) q^{65} -2.00000i q^{67} -7.00000 q^{68} +(-3.00000 - 6.00000i) q^{70} -12.0000 q^{71} -4.00000i q^{73} +(6.00000 - 1.00000i) q^{74} -4.00000i q^{76} +9.00000i q^{77} -4.00000i q^{79} +(-2.00000 + 1.00000i) q^{80} -7.00000 q^{82} +14.0000i q^{83} +(14.0000 - 7.00000i) q^{85} +1.00000 q^{86} +3.00000 q^{88} -6.00000i q^{89} -12.0000i q^{91} -6.00000 q^{92} -8.00000i q^{94} +(4.00000 + 8.00000i) q^{95} +7.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^8	\( 2 q + 2 q^{2} + 2 q^{4} - 4 q^{5} + 2 q^{8} - 4 q^{10} + 6 q^{11} - 8 q^{13} + 2 q^{16} - 14 q^{17} - 4 q^{20} + 6 q^{22} - 12 q^{23} + 6 q^{25} - 8 q^{26} + 2 q^{32} - 14 q^{34} - 6 q^{35} + 12 q^{37} - 4 q^{40} - 14 q^{41} + 2 q^{43} + 6 q^{44} - 12 q^{46} - 4 q^{49} + 6 q^{50} - 8 q^{52} - 12 q^{55} + 2 q^{64} + 16 q^{65} - 14 q^{68} - 6 q^{70} - 24 q^{71} + 12 q^{74} - 4 q^{80} - 14 q^{82} + 28 q^{85} + 2 q^{86} + 6 q^{88} - 12 q^{92} + 8 q^{95} + 14 q^{97} - 4 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - 4 * q^5 + 2 * q^8 - 4 * q^10 + 6 * q^11 - 8 * q^13 + 2 * q^16 - 14 * q^17 - 4 * q^20 + 6 * q^22 - 12 * q^23 + 6 * q^25 - 8 * q^26 + 2 * q^32 - 14 * q^34 - 6 * q^35 + 12 * q^37 - 4 * q^40 - 14 * q^41 + 2 * q^43 + 6 * q^44 - 12 * q^46 - 4 * q^49 + 6 * q^50 - 8 * q^52 - 12 * q^55 + 2 * q^64 + 16 * q^65 - 14 * q^68 - 6 * q^70 - 24 * q^71 + 12 * q^74 - 4 * q^80 - 14 * q^82 + 28 * q^85 + 2 * q^86 + 6 * q^88 - 12 * q^92 + 8 * q^95 + 14 * q^97 - 4 * q^98

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