LMFDB - Embedded newform 2610.2.e.i.2089.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2610,2,Mod(2089,2610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2610, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2610.2089");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2610 = 2 \cdot 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2610.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:	$20.8409549276$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 24x^{8} + 152x^{6} + 377x^{4} + 352x^{2} + 64 $ x^10 + 24x^8 + 152x^6 + 377x^4 + 352x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2089.7
Root			$1.35864i$ of defining polynomial
Character	$\chi$	$=$	2610.2089
Dual form			2610.2.e.i.2089.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-1.32739 + 1.79945i) q^{5} -4.21797i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.32739 + 1.79945i) q^{5} -4.21797i q^{7} -1.00000i q^{8} +(-1.79945 - 1.32739i) q^{10} -3.59890 q^{11} +0.585478i q^{13} +4.21797 q^{14} +1.00000 q^{16} -4.93525i q^{17} +5.60690 q^{19} +(1.32739 - 1.79945i) q^{20} -3.59890i q^{22} +6.62033i q^{23} +(-1.47606 - 4.77716i) q^{25} -0.585478 q^{26} +4.21797i q^{28} +1.00000 q^{29} -5.81688 q^{31} +1.00000i q^{32} +4.93525 q^{34} +(7.59004 + 5.59890i) q^{35} +11.1532i q^{37} +5.60690i q^{38} +(1.79945 + 1.32739i) q^{40} +4.48053 q^{41} +1.26586i q^{43} +3.59890 q^{44} -6.62033 q^{46} +10.2617i q^{47} -10.7913 q^{49} +(4.77716 - 1.47606i) q^{50} -0.585478i q^{52} +0.507305i q^{53} +(4.77716 - 6.47606i) q^{55} -4.21797 q^{56} +1.00000i q^{58} +3.90304 q^{59} -3.25018 q^{61} -5.81688i q^{62} -1.00000 q^{64} +(-1.05354 - 0.777160i) q^{65} -0.0605750i q^{67} +4.93525i q^{68} +(-5.59890 + 7.59004i) q^{70} -10.0428 q^{71} +7.57213i q^{73} -11.1532 q^{74} -5.60690 q^{76} +15.1801i q^{77} -5.73870 q^{79} +(-1.32739 + 1.79945i) q^{80} +4.48053i q^{82} -15.4506i q^{83} +(8.88075 + 6.55102i) q^{85} -1.26586 q^{86} +3.59890i q^{88} +0.111762 q^{89} +2.46953 q^{91} -6.62033i q^{92} -10.2617 q^{94} +(-7.44256 + 10.0893i) q^{95} +12.3836i q^{97} -10.7913i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{4}+O(q^{10}) $ 10 * q - 10 * q^4	$ 10 q - 10 q^{4} + 10 q^{14} + 10 q^{16} + 8 q^{19} - 4 q^{25} - 14 q^{26} + 10 q^{29} + 10 q^{31} - 18 q^{34} - 18 q^{35} + 8 q^{41} + 26 q^{46} - 32 q^{49} + 16 q^{50} + 16 q^{55} - 10 q^{56} - 18 q^{59} + 10 q^{61} - 10 q^{64} - 20 q^{65} - 20 q^{70} + 12 q^{71} - 12 q^{74} - 8 q^{76} + 34 q^{79} + 18 q^{85} - 2 q^{86} + 20 q^{89} - 44 q^{91} - 28 q^{94} + 8 q^{95}+O(q^{100}) $ 10 * q - 10 * q^4 + 10 * q^14 + 10 * q^16 + 8 * q^19 - 4 * q^25 - 14 * q^26 + 10 * q^29 + 10 * q^31 - 18 * q^34 - 18 * q^35 + 8 * q^41 + 26 * q^46 - 32 * q^49 + 16 * q^50 + 16 * q^55 - 10 * q^56 - 18 * q^59 + 10 * q^61 - 10 * q^64 - 20 * q^65 - 20 * q^70 + 12 * q^71 - 12 * q^74 - 8 * q^76 + 34 * q^79 + 18 * q^85 - 2 * q^86 + 20 * q^89 - 44 * q^91 - 28 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2610\mathbb{Z}\right)^\times$.

$n$	$901$	$1451$	$1567$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.32739	+	1.79945i	−0.593628	+	0.804740i
$5$	−1.32739	+	1.79945i	−0.593628	+	0.804740i
$6$		0			0
$7$		−	4.21797i		−	1.59424i	−0.603819	−	0.797122i	$-0.706355\pi$
$7$		−	4.21797i		−	1.59424i	0.603819	−	0.797122i	$-0.293645\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.79945	−	1.32739i	−0.569037	−	0.419758i
$11$	−3.59890			−1.08511			−0.542555	−	0.840020i	$-0.682543\pi$
$11$	−3.59890			−1.08511			−0.542555	+	0.840020i	$0.682543\pi$
$12$		0			0
$13$			0.585478i			0.162382i	0.996699	+	0.0811912i	$0.0258725\pi$
$13$			0.585478i			0.162382i	−0.996699	+	0.0811912i	$0.974128\pi$
$14$	4.21797			1.12730
$15$		0			0
$16$	1.00000			0.250000
$17$		−	4.93525i		−	1.19697i	−0.801132	−	0.598487i	$-0.795769\pi$
$17$		−	4.93525i		−	1.19697i	0.801132	−	0.598487i	$-0.204231\pi$
$18$		0			0
$19$	5.60690			1.28631			0.643155	−	0.765736i	$-0.277625\pi$
$19$	5.60690			1.28631			0.643155	+	0.765736i	$0.277625\pi$
$20$	1.32739	−	1.79945i	0.296814	−	0.402370i
$21$		0			0
$22$		−	3.59890i		−	0.767289i
$23$			6.62033i			1.38043i	0.723603	+	0.690217i	$0.242485\pi$
$23$			6.62033i			1.38043i	−0.723603	+	0.690217i	$0.757515\pi$
$24$		0			0
$25$	−1.47606	−	4.77716i	−0.295211	−	0.955432i
$26$	−0.585478			−0.114822
$27$		0			0
$28$			4.21797i			0.797122i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$		0			0
$31$	−5.81688			−1.04474			−0.522371	−	0.852718i	$-0.674952\pi$
$31$	−5.81688			−1.04474			−0.522371	+	0.852718i	$0.674952\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	4.93525			0.846389
$35$	7.59004	+	5.59890i	1.28295	+	0.946388i
$36$		0			0
$37$			11.1532i			1.83358i	0.399371	+	0.916789i	$0.369229\pi$
$37$			11.1532i			1.83358i	−0.399371	+	0.916789i	$0.630771\pi$
$38$			5.60690i			0.909559i
$39$		0			0
$40$	1.79945	+	1.32739i	0.284518	+	0.209879i
$41$	4.48053			0.699741			0.349870	−	0.936798i	$-0.386226\pi$
$41$	4.48053			0.699741			0.349870	+	0.936798i	$0.386226\pi$
$42$		0			0
$43$			1.26586i			0.193041i	0.995331	+	0.0965207i	$0.0307714\pi$
$43$			1.26586i			0.193041i	−0.995331	+	0.0965207i	$0.969229\pi$
$44$	3.59890			0.542555
$45$		0			0
$46$	−6.62033			−0.976114
$47$			10.2617i			1.49682i	0.663236	+	0.748410i	$0.269183\pi$
$47$			10.2617i			1.49682i	−0.663236	+	0.748410i	$0.730817\pi$
$48$		0			0
$49$	−10.7913			−1.54161
$50$	4.77716	−	1.47606i	0.675592	−	0.208746i
$51$		0			0
$52$		−	0.585478i		−	0.0811912i
$53$			0.507305i			0.0696837i	0.999393	+	0.0348419i	$0.0110928\pi$
$53$			0.507305i			0.0696837i	−0.999393	+	0.0348419i	$0.988907\pi$
$54$		0			0
$55$	4.77716	−	6.47606i	0.644152	−	0.873231i
$56$	−4.21797			−0.563650
$57$		0			0
$58$			1.00000i			0.131306i
$59$	3.90304			0.508133			0.254067	−	0.967187i	$-0.418232\pi$
$59$	3.90304			0.508133			0.254067	+	0.967187i	$0.418232\pi$
$60$		0			0
$61$	−3.25018			−0.416143			−0.208071	−	0.978114i	$-0.566719\pi$
$61$	−3.25018			−0.416143			−0.208071	+	0.978114i	$0.566719\pi$
$62$		−	5.81688i		−	0.738744i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.05354	−	0.777160i	−0.130676	−	0.0963948i
$66$		0			0
$67$		−	0.0605750i		−	0.00740041i	−0.999993	−	0.00370021i	$-0.998822\pi$
$67$		−	0.0605750i		−	0.00740041i	0.999993	−	0.00370021i	$-0.00117782\pi$
$68$			4.93525i			0.598487i
$69$		0			0
$70$	−5.59890	+	7.59004i	−0.669197	+	0.907183i
$71$	−10.0428			−1.19187			−0.595933	−	0.803034i	$-0.703218\pi$
$71$	−10.0428			−1.19187			−0.595933	+	0.803034i	$0.703218\pi$
$72$		0			0
$73$			7.57213i			0.886250i	0.896460	+	0.443125i	$0.146130\pi$
$73$			7.57213i			0.886250i	−0.896460	+	0.443125i	$0.853870\pi$
$74$	−11.1532			−1.29654
$75$		0			0
$76$	−5.60690			−0.643155
$77$			15.1801i			1.72993i
$78$		0			0
$79$	−5.73870			−0.645654			−0.322827	−	0.946458i	$-0.604633\pi$
$79$	−5.73870			−0.645654			−0.322827	+	0.946458i	$0.604633\pi$
$80$	−1.32739	+	1.79945i	−0.148407	+	0.201185i
$81$		0			0
$82$			4.48053i			0.494792i
$83$		−	15.4506i		−	1.69592i	−0.530061	−	0.847959i	$-0.677831\pi$
$83$		−	15.4506i		−	1.69592i	0.530061	−	0.847959i	$-0.322169\pi$
$84$		0			0
$85$	8.88075	+	6.55102i	0.963253	+	0.710558i
$86$	−1.26586			−0.136501
$87$		0			0
$88$			3.59890i			0.383645i
$89$	0.111762			0.0118467			0.00592336	−	0.999982i	$-0.498115\pi$
$89$	0.111762			0.0118467			0.00592336	+	0.999982i	$0.498115\pi$
$90$		0			0
$91$	2.46953			0.258877
$92$		−	6.62033i		−	0.690217i
$93$		0			0
$94$	−10.2617			−1.05841
$95$	−7.44256	+	10.0893i	−0.763590	+	1.03515i
$96$		0			0
$97$			12.3836i			1.25736i	0.777664	+	0.628681i	$0.216405\pi$
$97$			12.3836i			1.25736i	−0.777664	+	0.628681i	$0.783595\pi$
$98$		−	10.7913i		−	1.09008i
$99$		0			0
$100$	1.47606	+	4.77716i	0.147606	+	0.477716i
$101$	9.73071			0.968242			0.484121	−	0.875001i	$-0.339140\pi$
$101$	9.73071			0.968242			0.484121	+	0.875001i	$0.339140\pi$
$102$		0			0
$103$			16.4628i			1.62213i	0.584958	+	0.811064i	$0.301111\pi$
$103$			16.4628i			1.62213i	−0.584958	+	0.811064i	$0.698889\pi$
$104$	0.585478			0.0574109
$105$		0			0
$106$	−0.507305			−0.0492738
$107$			17.9151i			1.73192i	0.500116	+	0.865959i	$0.333291\pi$
$107$			17.9151i			1.73192i	−0.500116	+	0.865959i	$0.666709\pi$
$108$		0			0
$109$	6.77978			0.649385			0.324692	−	0.945820i	$-0.394739\pi$
$109$	6.77978			0.649385			0.324692	+	0.945820i	$0.394739\pi$
$110$	6.47606	+	4.77716i	0.617468	+	0.455484i
$111$		0			0
$112$		−	4.21797i		−	0.398561i
$113$		−	4.94199i		−	0.464903i	−0.972608	−	0.232452i	$-0.925325\pi$
$113$		−	4.94199i		−	0.464903i	0.972608	−	0.232452i	$-0.0746747\pi$
$114$		0			0
$115$	−11.9130	−	8.78777i	−1.11089	−	0.819464i
$116$	−1.00000			−0.0928477
$117$		0			0
$118$			3.90304i			0.359304i
$119$	−20.8168			−1.90827
$120$		0			0
$121$	1.95211			0.177465
$122$		−	3.25018i		−	0.294257i
$123$		0			0
$124$	5.81688			0.522371
$125$	10.5556	+	3.68507i	0.944120	+	0.329603i
$126$		0			0
$127$			10.7779i			0.956380i	0.878256	+	0.478190i	$0.158707\pi$
$127$			10.7779i			0.956380i	−0.878256	+	0.478190i	$0.841293\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	0.777160	−	1.05354i	0.0681614	−	0.0924016i
$131$	2.39310			0.209086			0.104543	−	0.994520i	$-0.466662\pi$
$131$	2.39310			0.209086			0.104543	+	0.994520i	$0.466662\pi$
$132$		0			0
$133$		−	23.6497i		−	2.05069i
$134$	0.0605750			0.00523288
$135$		0			0
$136$	−4.93525			−0.423194
$137$			0.452492i			0.0386590i	0.999813	+	0.0193295i	$0.00615315\pi$
$137$			0.452492i			0.0386590i	−0.999813	+	0.0193295i	$0.993847\pi$
$138$		0			0
$139$	−0.401171			−0.0340268			−0.0170134	−	0.999855i	$-0.505416\pi$
$139$	−0.401171			−0.0340268			−0.0170134	+	0.999855i	$0.505416\pi$
$140$	−7.59004	−	5.59890i	−0.641475	−	0.473194i
$141$		0			0
$142$		−	10.0428i		−	0.842777i
$143$		−	2.10708i		−	0.176203i
$144$		0			0
$145$	−1.32739	+	1.79945i	−0.110234	+	0.149436i
$146$	−7.57213			−0.626674
$147$		0			0
$148$		−	11.1532i		−	0.916789i
$149$	−8.71536			−0.713990			−0.356995	−	0.934106i	$-0.616199\pi$
$149$	−8.71536			−0.713990			−0.356995	+	0.934106i	$0.616199\pi$
$150$		0			0
$151$	−13.7455			−1.11859			−0.559297	−	0.828967i	$-0.688929\pi$
$151$	−13.7455			−1.11859			−0.559297	+	0.828967i	$0.688929\pi$
$152$		−	5.60690i		−	0.454780i
$153$		0			0
$154$	−15.1801			−1.22325
$155$	7.72128	−	10.4672i	0.620188	−	0.840745i
$156$		0			0
$157$		−	10.2124i		−	0.815040i	−0.913196	−	0.407520i	$-0.866394\pi$
$157$		−	10.2124i		−	0.815040i	0.913196	−	0.407520i	$-0.133606\pi$
$158$		−	5.73870i		−	0.456547i
$159$		0			0
$160$	−1.79945	−	1.32739i	−0.142259	−	0.104940i
$161$	27.9243			2.20075
$162$		0			0
$163$			3.18887i			0.249771i	0.992171	+	0.124886i	$0.0398564\pi$
$163$			3.18887i			0.249771i	−0.992171	+	0.124886i	$0.960144\pi$
$164$	−4.48053			−0.349870
$165$		0			0
$166$	15.4506			1.19920
$167$			14.3297i			1.10887i	0.832228	+	0.554434i	$0.187065\pi$
$167$			14.3297i			1.10887i	−0.832228	+	0.554434i	$0.812935\pi$
$168$		0			0
$169$	12.6572			0.973632
$170$	−6.55102	+	8.88075i	−0.502440	+	0.681123i
$171$		0			0
$172$		−	1.26586i		−	0.0965207i
$173$		−	7.76443i		−	0.590319i	−0.955448	−	0.295159i	$-0.904627\pi$
$173$		−	7.76443i		−	0.590319i	0.955448	−	0.295159i	$-0.0953727\pi$
$174$		0			0
$175$	−20.1499	+	6.22597i	−1.52319	+	0.470639i
$176$	−3.59890			−0.271278
$177$		0			0
$178$			0.111762i			0.00837690i
$179$	−10.5935			−0.791793			−0.395897	−	0.918295i	$-0.629566\pi$
$179$	−10.5935			−0.791793			−0.395897	+	0.918295i	$0.629566\pi$
$180$		0			0
$181$	21.1176			1.56966			0.784829	−	0.619713i	$-0.212751\pi$
$181$	21.1176			1.56966			0.784829	+	0.619713i	$0.212751\pi$
$182$			2.46953i			0.183054i
$183$		0			0
$184$	6.62033			0.488057
$185$	−20.0697	−	14.8047i	−1.47555	−	1.08846i
$186$		0			0
$187$			17.7615i			1.29885i
$188$		−	10.2617i		−	0.748410i
$189$		0			0
$190$	−10.0893	−	7.44256i	−0.731958	−	0.539940i
$191$	−2.49931			−0.180844			−0.0904219	−	0.995904i	$-0.528822\pi$
$191$	−2.49931			−0.180844			−0.0904219	+	0.995904i	$0.528822\pi$
$192$		0			0
$193$		−	8.57748i		−	0.617421i	−0.951156	−	0.308710i	$-0.900103\pi$
$193$		−	8.57748i		−	0.617421i	0.951156	−	0.308710i	$-0.0998974\pi$
$194$	−12.3836			−0.889089
$195$		0			0
$196$	10.7913			0.770806
$197$			7.51392i			0.535345i	0.963510	+	0.267672i	$0.0862545\pi$
$197$			7.51392i			0.535345i	−0.963510	+	0.267672i	$0.913746\pi$
$198$		0			0
$199$	7.49277			0.531148			0.265574	−	0.964090i	$-0.414438\pi$
$199$	7.49277			0.531148			0.265574	+	0.964090i	$0.414438\pi$
$200$	−4.77716	+	1.47606i	−0.337796	+	0.104373i
$201$		0			0
$202$			9.73071i			0.684650i
$203$		−	4.21797i		−	0.296044i
$204$		0			0
$205$	−5.94742	+	8.06250i	−0.415386	+	0.563109i
$206$	−16.4628			−1.14702
$207$		0			0
$208$			0.585478i			0.0405956i
$209$	−20.1787			−1.39579
$210$		0			0
$211$	−22.0617			−1.51879			−0.759395	−	0.650630i	$-0.774505\pi$
$211$	−22.0617			−1.51879			−0.759395	+	0.650630i	$0.774505\pi$
$212$		−	0.507305i		−	0.0348419i
$213$		0			0
$214$	−17.9151			−1.22465
$215$	−2.27785	−	1.68029i	−0.155348	−	0.114595i
$216$		0			0
$217$			24.5354i			1.66557i
$218$			6.77978i			0.459184i
$219$		0			0
$220$	−4.77716	+	6.47606i	−0.322076	+	0.436616i
$221$	2.88948			0.194368
$222$		0			0
$223$			10.0120i			0.670456i	0.942137	+	0.335228i	$0.108813\pi$
$223$			10.0120i			0.670456i	−0.942137	+	0.335228i	$0.891187\pi$
$224$	4.21797			0.281825
$225$		0			0
$226$	4.94199			0.328736
$227$		−	8.61914i		−	0.572073i	−0.958219	−	0.286036i	$-0.907662\pi$
$227$		−	8.61914i		−	0.572073i	0.958219	−	0.286036i	$-0.0923378\pi$
$228$		0			0
$229$	−23.0871			−1.52564			−0.762819	−	0.646612i	$-0.776185\pi$
$229$	−23.0871			−1.52564			−0.762819	+	0.646612i	$0.776185\pi$
$230$	8.78777	−	11.9130i	0.579449	−	0.785517i
$231$		0			0
$232$		−	1.00000i		−	0.0656532i
$233$			0.106134i			0.00695310i	0.999994	+	0.00347655i	$0.00110662\pi$
$233$			0.106134i			0.00695310i	−0.999994	+	0.00347655i	$0.998893\pi$
$234$		0			0
$235$	−18.4654	−	13.6213i	−1.20455	−	0.888555i
$236$	−3.90304			−0.254067
$237$		0			0
$238$		−	20.8168i		−	1.34935i
$239$	6.95404			0.449819			0.224910	−	0.974380i	$-0.427791\pi$
$239$	6.95404			0.449819			0.224910	+	0.974380i	$0.427791\pi$
$240$		0			0
$241$	4.25348			0.273991			0.136995	−	0.990572i	$-0.456255\pi$
$241$	4.25348			0.273991			0.136995	+	0.990572i	$0.456255\pi$
$242$			1.95211i			0.125487i
$243$		0			0
$244$	3.25018			0.208071
$245$	14.3243	−	19.4184i	0.915144	−	1.24060i
$246$		0			0
$247$			3.28272i			0.208874i
$248$			5.81688i			0.369372i
$249$		0			0
$250$	−3.68507	+	10.5556i	−0.233064	+	0.667593i
$251$	−20.6832			−1.30551			−0.652756	−	0.757568i	$-0.726387\pi$
$251$	−20.6832			−1.30551			−0.652756	+	0.757568i	$0.726387\pi$
$252$		0			0
$253$		−	23.8259i		−	1.49792i
$254$	−10.7779			−0.676263
$255$		0			0
$256$	1.00000			0.0625000
$257$			12.3834i			0.772453i	0.922404	+	0.386226i	$0.126222\pi$
$257$			12.3834i			0.772453i	−0.922404	+	0.386226i	$0.873778\pi$
$258$		0			0
$259$	47.0440			2.92317
$260$	1.05354	+	0.777160i	0.0653378	+	0.0481974i
$261$		0			0
$262$			2.39310i			0.147846i
$263$			23.6587i			1.45886i	0.684057	+	0.729428i	$0.260214\pi$
$263$			23.6587i			1.45886i	−0.684057	+	0.729428i	$0.739786\pi$
$264$		0			0
$265$	−0.912871	−	0.673393i	−0.0560772	−	0.0413662i
$266$	23.6497			1.45006
$267$		0			0
$268$			0.0605750i			0.00370021i
$269$	22.4886			1.37115			0.685577	−	0.728000i	$-0.259550\pi$
$269$	22.4886			1.37115			0.685577	+	0.728000i	$0.259550\pi$
$270$		0			0
$271$	15.1964			0.923117			0.461558	−	0.887110i	$-0.347291\pi$
$271$	15.1964			0.923117			0.461558	+	0.887110i	$0.347291\pi$
$272$		−	4.93525i		−	0.299244i
$273$		0			0
$274$	−0.452492			−0.0273360
$275$	5.31219	+	17.1925i	0.320337	+	1.03675i
$276$		0			0
$277$			16.2101i			0.973968i	0.873411	+	0.486984i	$0.161903\pi$
$277$			16.2101i			0.973968i	−0.873411	+	0.486984i	$0.838097\pi$
$278$		−	0.401171i		−	0.0240606i
$279$		0			0
$280$	5.59890	−	7.59004i	0.334599	−	0.453592i
$281$	−5.87138			−0.350257			−0.175128	−	0.984546i	$-0.556034\pi$
$281$	−5.87138			−0.350257			−0.175128	+	0.984546i	$0.556034\pi$
$282$		0			0
$283$		−	8.01086i		−	0.476196i	−0.971241	−	0.238098i	$-0.923476\pi$
$283$		−	8.01086i		−	0.476196i	0.971241	−	0.238098i	$-0.0765240\pi$
$284$	10.0428			0.595933
$285$		0			0
$286$	2.10708			0.124594
$287$		−	18.8987i		−	1.11556i
$288$		0			0
$289$	−7.35672			−0.432748
$290$	−1.79945	−	1.32739i	−0.105667	−	0.0779472i
$291$		0			0
$292$		−	7.57213i		−	0.443125i
$293$			6.66373i			0.389299i	0.980873	+	0.194650i	$0.0623570\pi$
$293$			6.66373i			0.389299i	−0.980873	+	0.194650i	$0.937643\pi$
$294$		0			0
$295$	−5.18087	+	7.02334i	−0.301642	+	0.408915i
$296$	11.1532			0.648268
$297$		0			0
$298$		−	8.71536i		−	0.504867i
$299$	−3.87606			−0.224158
$300$		0			0
$301$	5.33935			0.307755
$302$		−	13.7455i		−	0.790965i
$303$		0			0
$304$	5.60690			0.321578
$305$	4.31427	−	5.84854i	0.247034	−	0.334887i
$306$		0			0
$307$		−	24.6733i		−	1.40818i	−0.710111	−	0.704090i	$-0.751355\pi$
$307$		−	24.6733i		−	1.40818i	0.710111	−	0.704090i	$-0.248645\pi$
$308$		−	15.1801i		−	0.864965i
$309$		0			0
$310$	10.4672	+	7.72128i	0.594496	+	0.438539i
$311$	−16.8304			−0.954363			−0.477182	−	0.878805i	$-0.658342\pi$
$311$	−16.8304			−0.954363			−0.477182	+	0.878805i	$0.658342\pi$
$312$		0			0
$313$			22.7950i			1.28845i	0.764837	+	0.644224i	$0.222820\pi$
$313$			22.7950i			1.28845i	−0.764837	+	0.644224i	$0.777180\pi$
$314$	10.2124			0.576320
$315$		0			0
$316$	5.73870			0.322827
$317$			8.76187i			0.492115i	0.969255	+	0.246058i	$0.0791353\pi$
$317$			8.76187i			0.492115i	−0.969255	+	0.246058i	$0.920865\pi$
$318$		0			0
$319$	−3.59890			−0.201500
$320$	1.32739	−	1.79945i	0.0742035	−	0.100592i
$321$		0			0
$322$			27.9243i			1.55616i
$323$		−	27.6715i		−	1.53968i
$324$		0			0
$325$	2.79692	−	0.864200i	0.155145	−	0.0479372i
$326$	−3.18887			−0.176615
$327$		0			0
$328$		−	4.48053i		−	0.247396i
$329$	43.2835			2.38630
$330$		0			0
$331$	−13.5206			−0.743159			−0.371580	−	0.928401i	$-0.621184\pi$
$331$	−13.5206			−0.743159			−0.371580	+	0.928401i	$0.621184\pi$
$332$			15.4506i			0.847959i
$333$		0			0
$334$	−14.3297			−0.784088
$335$	0.109002	+	0.0804068i	0.00595541	+	0.00439309i
$336$		0			0
$337$		−	0.935253i		−	0.0509465i	−0.999676	−	0.0254732i	$-0.991891\pi$
$337$		−	0.935253i		−	0.0509465i	0.999676	−	0.0254732i	$-0.00810926\pi$
$338$			12.6572i			0.688462i
$339$		0			0
$340$	−8.88075	−	6.55102i	−0.481626	−	0.355279i
$341$	20.9344			1.13366
$342$		0			0
$343$			15.9915i			0.863461i
$344$	1.26586			0.0682505
$345$		0			0
$346$	7.76443			0.417418
$347$			29.4910i			1.58316i	0.611065	+	0.791581i	$0.290742\pi$
$347$			29.4910i			1.58316i	−0.611065	+	0.791581i	$0.709258\pi$
$348$		0			0
$349$	8.89406			0.476088			0.238044	−	0.971254i	$-0.423494\pi$
$349$	8.89406			0.476088			0.238044	+	0.971254i	$0.423494\pi$
$350$	−6.22597	−	20.1499i	−0.332792	−	1.07706i
$351$		0			0
$352$		−	3.59890i		−	0.191822i
$353$			27.0440i			1.43941i	0.694282	+	0.719703i	$0.255722\pi$
$353$			27.0440i			1.43941i	−0.694282	+	0.719703i	$0.744278\pi$
$354$		0			0
$355$	13.3308	−	18.0716i	0.707525	−	0.959142i
$356$	−0.111762			−0.00592336
$357$		0			0
$358$		−	10.5935i		−	0.559882i
$359$	12.3442			0.651503			0.325752	−	0.945455i	$-0.394383\pi$
$359$	12.3442			0.651503			0.325752	+	0.945455i	$0.394383\pi$
$360$		0			0
$361$	12.4373			0.654596
$362$			21.1176i			1.10992i
$363$		0			0
$364$	−2.46953			−0.129439
$365$	−13.6257	−	10.0512i	−0.713201	−	0.526103i
$366$		0			0
$367$			24.2124i			1.26388i	0.775018	+	0.631939i	$0.217741\pi$
$367$			24.2124i			1.26388i	−0.775018	+	0.631939i	$0.782259\pi$
$368$			6.62033i			0.345108i
$369$		0			0
$370$	14.8047	−	20.0697i	0.769660	−	1.04337i
$371$	2.13980			0.111093
$372$		0			0
$373$			14.1543i			0.732881i	0.930441	+	0.366441i	$0.119424\pi$
$373$			14.1543i			0.732881i	−0.930441	+	0.366441i	$0.880576\pi$
$374$	−17.7615			−0.918425
$375$		0			0
$376$	10.2617			0.529206
$377$			0.585478i			0.0301537i
$378$		0			0
$379$	19.0415			0.978094			0.489047	−	0.872257i	$-0.337345\pi$
$379$	19.0415			0.978094			0.489047	+	0.872257i	$0.337345\pi$
$380$	7.44256	−	10.0893i	0.381795	−	0.517573i
$381$		0			0
$382$		−	2.49931i		−	0.127876i
$383$		−	31.2620i		−	1.59741i	−0.601722	−	0.798706i	$-0.705519\pi$
$383$		−	31.2620i		−	1.59741i	0.601722	−	0.798706i	$-0.294481\pi$
$384$		0			0
$385$	−27.3158	−	20.1499i	−1.39214	−	1.02694i
$386$	8.57748			0.436582
$387$		0			0
$388$		−	12.3836i		−	0.628681i
$389$	23.0860			1.17051			0.585255	−	0.810850i	$-0.300995\pi$
$389$	23.0860			1.17051			0.585255	+	0.810850i	$0.300995\pi$
$390$		0			0
$391$	32.6730			1.65234
$392$			10.7913i			0.545042i
$393$		0			0
$394$	−7.51392			−0.378546
$395$	7.61751	−	10.3265i	0.383279	−	0.519584i
$396$		0			0
$397$		−	3.04076i		−	0.152611i	−0.997084	−	0.0763057i	$-0.975687\pi$
$397$		−	3.04076i		−	0.152611i	0.997084	−	0.0763057i	$-0.0243125\pi$
$398$			7.49277i			0.375579i
$399$		0			0
$400$	−1.47606	−	4.77716i	−0.0738029	−	0.238858i
$401$	22.3657			1.11689			0.558444	−	0.829542i	$-0.311399\pi$
$401$	22.3657			1.11689			0.558444	+	0.829542i	$0.311399\pi$
$402$		0			0
$403$		−	3.40566i		−	0.169648i
$404$	−9.73071			−0.484121
$405$		0			0
$406$	4.21797			0.209334
$407$		−	40.1394i		−	1.98964i
$408$		0			0
$409$	31.4906			1.55711			0.778556	−	0.627575i	$-0.215953\pi$
$409$	31.4906			1.55711			0.778556	+	0.627575i	$0.215953\pi$
$410$	−8.06250	−	5.94742i	−0.398178	−	0.293722i
$411$		0			0
$412$		−	16.4628i		−	0.811064i
$413$		−	16.4629i		−	0.810088i
$414$		0			0
$415$	27.8025	+	20.5090i	1.36477	+	1.00674i
$416$	−0.585478			−0.0287054
$417$		0			0
$418$		−	20.1787i		−	0.986972i
$419$	−38.6091			−1.88618			−0.943089	−	0.332541i	$-0.892094\pi$
$419$	−38.6091			−1.88618			−0.943089	+	0.332541i	$0.892094\pi$
$420$		0			0
$421$	−30.7181			−1.49711			−0.748553	−	0.663075i	$-0.769251\pi$
$421$	−30.7181			−1.49711			−0.748553	+	0.663075i	$0.769251\pi$
$422$		−	22.0617i		−	1.07395i
$423$		0			0
$424$	0.507305			0.0246369
$425$	−23.5765	+	7.28471i	−1.14363	+	0.353361i
$426$		0			0
$427$			13.7092i			0.663433i
$428$		−	17.9151i		−	0.865959i
$429$		0			0
$430$	1.68029	−	2.27785i	0.0810308	−	0.109848i
$431$	11.5648			0.557058			0.278529	−	0.960428i	$-0.410153\pi$
$431$	11.5648			0.557058			0.278529	+	0.960428i	$0.410153\pi$
$432$		0			0
$433$		−	12.4942i		−	0.600431i	−0.953871	−	0.300215i	$-0.902941\pi$
$433$		−	12.4942i		−	0.600431i	0.953871	−	0.300215i	$-0.0970585\pi$
$434$	−24.5354			−1.17774
$435$		0			0
$436$	−6.77978			−0.324692
$437$			37.1195i			1.77567i
$438$		0			0
$439$	−35.7773			−1.70756			−0.853778	−	0.520638i	$-0.825694\pi$
$439$	−35.7773			−1.70756			−0.853778	+	0.520638i	$0.825694\pi$
$440$	−6.47606	−	4.77716i	−0.308734	−	0.227742i
$441$		0			0
$442$			2.88948i			0.137439i
$443$			26.3836i			1.25352i	0.779212	+	0.626761i	$0.215620\pi$
$443$			26.3836i			1.25352i	−0.779212	+	0.626761i	$0.784380\pi$
$444$		0			0
$445$	−0.148352	+	0.201110i	−0.00703255	+	0.00953353i
$446$	−10.0120			−0.474084
$447$		0			0
$448$			4.21797i			0.199280i
$449$	−22.4028			−1.05726			−0.528628	−	0.848854i	$-0.677293\pi$
$449$	−22.4028			−1.05726			−0.528628	+	0.848854i	$0.677293\pi$
$450$		0			0
$451$	−16.1250			−0.759296
$452$			4.94199i			0.232452i
$453$		0			0
$454$	8.61914			0.404516
$455$	−3.27804	+	4.44380i	−0.153677	+	0.208329i
$456$		0			0
$457$		−	24.6460i		−	1.15289i	−0.817136	−	0.576445i	$-0.804439\pi$
$457$		−	24.6460i		−	1.15289i	0.817136	−	0.576445i	$-0.195561\pi$
$458$		−	23.0871i		−	1.07879i
$459$		0			0
$460$	11.9130	+	8.78777i	0.555445	+	0.409732i
$461$	26.5959			1.23869			0.619346	−	0.785118i	$-0.287398\pi$
$461$	26.5959			1.23869			0.619346	+	0.785118i	$0.287398\pi$
$462$		0			0
$463$		−	10.9099i		−	0.507025i	−0.967332	−	0.253512i	$-0.918414\pi$
$463$		−	10.9099i		−	0.507025i	0.967332	−	0.253512i	$-0.0815858\pi$
$464$	1.00000			0.0464238
$465$		0			0
$466$	−0.106134			−0.00491659
$467$		−	1.47828i		−	0.0684065i	−0.999415	−	0.0342032i	$-0.989111\pi$
$467$		−	1.47828i		−	0.0684065i	0.999415	−	0.0342032i	$-0.0108894\pi$
$468$		0			0
$469$	−0.255504			−0.0117981
$470$	13.6213	−	18.4654i	0.628303	−	0.851746i
$471$		0			0
$472$		−	3.90304i		−	0.179652i
$473$		−	4.55570i		−	0.209471i
$474$		0			0
$475$	−8.27610	−	26.7851i	−0.379734	−	1.22898i
$476$	20.8168			0.954134
$477$		0			0
$478$			6.95404i			0.318070i
$479$	8.80715			0.402409			0.201205	−	0.979549i	$-0.435514\pi$
$479$	8.80715			0.402409			0.201205	+	0.979549i	$0.435514\pi$
$480$		0			0
$481$	−6.52997			−0.297741
$482$			4.25348i			0.193741i
$483$		0			0
$484$	−1.95211			−0.0887325
$485$	−22.2836	−	16.4379i	−1.01185	−	0.746405i
$486$		0			0
$487$		−	34.8847i		−	1.58078i	−0.612606	−	0.790388i	$-0.709879\pi$
$487$		−	34.8847i		−	1.58078i	0.612606	−	0.790388i	$-0.290121\pi$
$488$			3.25018i			0.147129i
$489$		0			0
$490$	19.4184	+	14.3243i	0.877234	+	0.647105i
$491$	40.5780			1.83126			0.915631	−	0.402020i	$-0.131692\pi$
$491$	40.5780			1.83126			0.915631	+	0.402020i	$0.131692\pi$
$492$		0			0
$493$		−	4.93525i		−	0.222273i
$494$	−3.28272			−0.147696
$495$		0			0
$496$	−5.81688			−0.261185
$497$			42.3604i			1.90012i
$498$		0			0
$499$	−0.495334			−0.0221742			−0.0110871	−	0.999939i	$-0.503529\pi$
$499$	−0.495334			−0.0221742			−0.0110871	+	0.999939i	$0.503529\pi$
$500$	−10.5556	−	3.68507i	−0.472060	−	0.164801i
$501$		0			0
$502$		−	20.6832i		−	0.923137i
$503$			11.5713i			0.515937i	0.966153	+	0.257968i	$0.0830530\pi$
$503$			11.5713i			0.515937i	−0.966153	+	0.257968i	$0.916947\pi$
$504$		0			0
$505$	−12.9165	+	17.5099i	−0.574775	+	0.779182i
$506$	23.8259			1.05919
$507$		0			0
$508$		−	10.7779i		−	0.478190i
$509$	−39.7077			−1.76001			−0.880007	−	0.474960i	$-0.842462\pi$
$509$	−39.7077			−1.76001			−0.880007	+	0.474960i	$0.842462\pi$
$510$		0			0
$511$	31.9390			1.41290
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−12.3834			−0.546207
$515$	−29.6240	−	21.8526i	−1.30539	−	0.962940i
$516$		0			0
$517$		−	36.9308i		−	1.62422i
$518$			47.0440i			2.06699i
$519$		0			0
$520$	−0.777160	+	1.05354i	−0.0340807	+	0.0462008i
$521$	11.7380			0.514253			0.257126	−	0.966378i	$-0.417224\pi$
$521$	11.7380			0.514253			0.257126	+	0.966378i	$0.417224\pi$
$522$		0			0
$523$		−	9.58641i		−	0.419184i	−0.977789	−	0.209592i	$-0.932786\pi$
$523$		−	9.58641i		−	0.419184i	0.977789	−	0.209592i	$-0.0672136\pi$
$524$	−2.39310			−0.104543
$525$		0			0
$526$	−23.6587			−1.03157
$527$			28.7078i			1.25053i
$528$		0			0
$529$	−20.8287			−0.905596
$530$	0.673393	−	0.912871i	0.0292503	−	0.0396526i
$531$		0			0
$532$			23.6497i			1.02535i
$533$			2.62325i			0.113626i
$534$		0			0
$535$	−32.2374	−	23.7804i	−1.39374	−	1.02811i
$536$	−0.0605750			−0.00261644
$537$		0			0
$538$			22.4886i			0.969552i
$539$	38.8368			1.67282
$540$		0			0
$541$	−1.76880			−0.0760466			−0.0380233	−	0.999277i	$-0.512106\pi$
$541$	−1.76880			−0.0760466			−0.0380233	+	0.999277i	$0.512106\pi$
$542$			15.1964i			0.652742i
$543$		0			0
$544$	4.93525			0.211597
$545$	−8.99943	+	12.1999i	−0.385493	+	0.522586i
$546$		0			0
$547$		−	10.5746i		−	0.452135i	−0.974112	−	0.226068i	$-0.927413\pi$
$547$		−	10.5746i		−	0.452135i	0.974112	−	0.226068i	$-0.0725871\pi$
$548$		−	0.452492i		−	0.0193295i
$549$		0			0
$550$	−17.1925	+	5.31219i	−0.733092	+	0.226512i
$551$	5.60690			0.238862
$552$		0			0
$553$			24.2057i			1.02933i
$554$	−16.2101			−0.688699
$555$		0			0
$556$	0.401171			0.0170134
$557$		−	24.3213i		−	1.03052i	−0.857033	−	0.515262i	$-0.827695\pi$
$557$		−	24.3213i		−	1.03052i	0.857033	−	0.515262i	$-0.172305\pi$
$558$		0			0
$559$	−0.741132			−0.0313465
$560$	7.59004	+	5.59890i	0.320738	+	0.236597i
$561$		0			0
$562$		−	5.87138i		−	0.247669i
$563$		−	17.0670i		−	0.719286i	−0.933090	−	0.359643i	$-0.882898\pi$
$563$		−	17.0670i		−	0.719286i	0.933090	−	0.359643i	$-0.117102\pi$
$564$		0			0
$565$	8.89287	+	6.55996i	0.374126	+	0.275980i
$566$	8.01086			0.336722
$567$		0			0
$568$			10.0428i			0.421388i
$569$	−3.39937			−0.142509			−0.0712544	−	0.997458i	$-0.522700\pi$
$569$	−3.39937			−0.142509			−0.0712544	+	0.997458i	$0.522700\pi$
$570$		0			0
$571$	39.1927			1.64017			0.820083	−	0.572245i	$-0.193927\pi$
$571$	39.1927			1.64017			0.820083	+	0.572245i	$0.193927\pi$
$572$			2.10708i			0.0881015i
$573$		0			0
$574$	18.8987			0.788818
$575$	31.6264	−	9.77198i	1.31891	−	0.407520i
$576$		0			0
$577$			37.8963i			1.57764i	0.614622	+	0.788822i	$0.289309\pi$
$577$			37.8963i			1.57764i	−0.614622	+	0.788822i	$0.710691\pi$
$578$		−	7.35672i		−	0.305999i
$579$		0			0
$580$	1.32739	−	1.79945i	0.0551170	−	0.0747182i
$581$	−65.1700			−2.70371
$582$		0			0
$583$		−	1.82574i		−	0.0756145i
$584$	7.57213			0.313337
$585$		0			0
$586$	−6.66373			−0.275276
$587$			7.04981i			0.290977i	0.989360	+	0.145488i	$0.0464753\pi$
$587$			7.04981i			0.290977i	−0.989360	+	0.145488i	$0.953525\pi$
$588$		0			0
$589$	−32.6146			−1.34386
$590$	−7.02334	−	5.18087i	−0.289146	−	0.213293i
$591$		0			0
$592$			11.1532i			0.458395i
$593$			4.05258i			0.166420i	0.996532	+	0.0832098i	$0.0265171\pi$
$593$			4.05258i			0.166420i	−0.996532	+	0.0832098i	$0.973483\pi$
$594$		0			0
$595$	27.6320	−	37.4588i	1.13280	−	1.53566i
$596$	8.71536			0.356995
$597$		0			0
$598$		−	3.87606i		−	0.158504i
$599$	14.3976			0.588272			0.294136	−	0.955764i	$-0.404968\pi$
$599$	14.3976			0.588272			0.294136	+	0.955764i	$0.404968\pi$
$600$		0			0
$601$	−0.797688			−0.0325384			−0.0162692	−	0.999868i	$-0.505179\pi$
$601$	−0.797688			−0.0325384			−0.0162692	+	0.999868i	$0.505179\pi$
$602$			5.33935i			0.217616i
$603$		0			0
$604$	13.7455			0.559297
$605$	−2.59122	+	3.51274i	−0.105348	+	0.142813i
$606$		0			0
$607$		−	28.7799i		−	1.16814i	−0.811703	−	0.584071i	$-0.801459\pi$
$607$		−	28.7799i		−	1.16814i	0.811703	−	0.584071i	$-0.198541\pi$
$608$			5.60690i			0.227390i
$609$		0			0
$610$	5.84854	+	4.31427i	0.236801	+	0.174679i
$611$	−6.00799			−0.243057
$612$		0			0
$613$		−	12.6981i		−	0.512873i	−0.966561	−	0.256437i	$-0.917451\pi$
$613$		−	12.6981i		−	0.512873i	0.966561	−	0.256437i	$-0.0825485\pi$
$614$	24.6733			0.995733
$615$		0			0
$616$	15.1801			0.611623
$617$			10.3500i			0.416675i	0.978057	+	0.208337i	$0.0668052\pi$
$617$			10.3500i			0.416675i	−0.978057	+	0.208337i	$0.933195\pi$
$618$		0			0
$619$	40.3304			1.62102			0.810508	−	0.585727i	$-0.199191\pi$
$619$	40.3304			1.62102			0.810508	+	0.585727i	$0.199191\pi$
$620$	−7.72128	+	10.4672i	−0.310094	+	0.420372i
$621$		0			0
$622$		−	16.8304i		−	0.674837i
$623$		−	0.471408i		−	0.0188866i
$624$		0			0
$625$	−20.6425	+	14.1027i	−0.825700	+	0.564109i
$626$	−22.7950			−0.911070
$627$		0			0
$628$			10.2124i			0.407520i
$629$	55.0440			2.19475
$630$		0			0
$631$	−4.57867			−0.182274			−0.0911369	−	0.995838i	$-0.529050\pi$
$631$	−4.57867			−0.182274			−0.0911369	+	0.995838i	$0.529050\pi$
$632$			5.73870i			0.228273i
$633$		0			0
$634$	−8.76187			−0.347978
$635$	−19.3942	−	14.3064i	−0.769637	−	0.567734i
$636$		0			0
$637$		−	6.31806i		−	0.250331i
$638$		−	3.59890i		−	0.142482i
$639$		0			0
$640$	1.79945	+	1.32739i	0.0711296	+	0.0524698i
$641$	−12.7267			−0.502673			−0.251337	−	0.967900i	$-0.580870\pi$
$641$	−12.7267			−0.502673			−0.251337	+	0.967900i	$0.580870\pi$
$642$		0			0
$643$		−	28.0411i		−	1.10583i	−0.833237	−	0.552917i	$-0.813515\pi$
$643$		−	28.0411i		−	1.10583i	0.833237	−	0.552917i	$-0.186485\pi$
$644$	−27.9243			−1.10037
$645$		0			0
$646$	27.6715			1.08872
$647$		−	35.7498i		−	1.40547i	−0.711452	−	0.702734i	$-0.751962\pi$
$647$		−	35.7498i		−	1.40547i	0.711452	−	0.702734i	$-0.248038\pi$
$648$		0			0
$649$	−14.0467			−0.551381
$650$	0.864200	+	2.79692i	0.0338967	+	0.109704i
$651$		0			0
$652$		−	3.18887i		−	0.124886i
$653$		−	43.3319i		−	1.69571i	−0.530229	−	0.847855i	$-0.677894\pi$
$653$		−	43.3319i		−	1.69571i	0.530229	−	0.847855i	$-0.322106\pi$
$654$		0			0
$655$	−3.17658	+	4.30627i	−0.124119	+	0.168260i
$656$	4.48053			0.174935
$657$		0			0
$658$			43.2835i			1.68737i
$659$	−16.0189			−0.624006			−0.312003	−	0.950081i	$-0.601000\pi$
$659$	−16.0189			−0.624006			−0.312003	+	0.950081i	$0.601000\pi$
$660$		0			0
$661$	26.8719			1.04520			0.522598	−	0.852579i	$-0.324963\pi$
$661$	26.8719			1.04520			0.522598	+	0.852579i	$0.324963\pi$
$662$		−	13.5206i		−	0.525493i
$663$		0			0
$664$	−15.4506			−0.599598
$665$	42.5566	+	31.3925i	1.65027	+	1.21735i
$666$		0			0
$667$			6.62033i			0.256340i
$668$		−	14.3297i		−	0.554434i
$669$		0			0
$670$	−0.0804068	+	0.109002i	−0.00310639	+	0.00421111i
$671$	11.6971			0.451561
$672$		0			0
$673$			25.4871i			0.982457i	0.871031	+	0.491229i	$0.163452\pi$
$673$			25.4871i			0.982457i	−0.871031	+	0.491229i	$0.836548\pi$
$674$	0.935253			0.0360246
$675$		0			0
$676$	−12.6572			−0.486816
$677$			46.4367i			1.78471i	0.451336	+	0.892354i	$0.350948\pi$
$677$			46.4367i			1.78471i	−0.451336	+	0.892354i	$0.649052\pi$
$678$		0			0
$679$	52.2336			2.00454
$680$	6.55102	−	8.88075i	0.251220	−	0.340561i
$681$		0			0
$682$			20.9344i			0.801619i
$683$			3.71590i			0.142185i	0.997470	+	0.0710925i	$0.0226486\pi$
$683$			3.71590i			0.142185i	−0.997470	+	0.0710925i	$0.977351\pi$
$684$		0			0
$685$	−0.814237	−	0.600634i	−0.0311104	−	0.0229490i
$686$	−15.9915			−0.610559
$687$		0			0
$688$			1.26586i			0.0482604i
$689$	−0.297016			−0.0113154
$690$		0			0
$691$	−23.8562			−0.907534			−0.453767	−	0.891120i	$-0.649920\pi$
$691$	−23.8562			−0.907534			−0.453767	+	0.891120i	$0.649920\pi$
$692$			7.76443i			0.295159i
$693$		0			0
$694$	−29.4910			−1.11946
$695$	0.532511	−	0.721887i	0.0201993	−	0.0273827i
$696$		0			0
$697$		−	22.1125i		−	0.837572i
$698$			8.89406i			0.336645i
$699$		0			0
$700$	20.1499	−	6.22597i	0.761596	−	0.235319i
$701$	30.7287			1.16061			0.580304	−	0.814400i	$-0.302934\pi$
$701$	30.7287			1.16061			0.580304	+	0.814400i	$0.302934\pi$
$702$		0			0
$703$			62.5350i			2.35855i
$704$	3.59890			0.135639
$705$		0			0
$706$	−27.0440			−1.01781
$707$		−	41.0438i		−	1.54361i
$708$		0			0
$709$	32.7488			1.22991			0.614954	−	0.788563i	$-0.289175\pi$
$709$	32.7488			1.22991			0.614954	+	0.788563i	$0.289175\pi$
$710$	18.0716	+	13.3308i	0.678216	+	0.500296i
$711$		0			0
$712$		−	0.111762i		−	0.00418845i
$713$		−	38.5096i		−	1.44220i
$714$		0			0
$715$	3.79159	+	2.79692i	0.141797	+	0.104599i
$716$	10.5935			0.395897
$717$		0			0
$718$			12.3442i			0.460682i
$719$	17.8545			0.665861			0.332931	−	0.942951i	$-0.391963\pi$
$719$	17.8545			0.665861			0.332931	+	0.942951i	$0.391963\pi$
$720$		0			0
$721$	69.4396			2.58607
$722$			12.4373i			0.462869i
$723$		0			0
$724$	−21.1176			−0.784829
$725$	−1.47606	−	4.77716i	−0.0548194	−	0.177419i
$726$		0			0
$727$			16.7021i			0.619445i	0.950827	+	0.309723i	$0.100236\pi$
$727$			16.7021i			0.619445i	−0.950827	+	0.309723i	$0.899764\pi$
$728$		−	2.46953i		−	0.0915269i
$729$		0			0
$730$	10.0512	−	13.6257i	0.372011	−	0.504309i
$731$	6.24733			0.231066
$732$		0			0
$733$		−	19.2744i		−	0.711915i	−0.934502	−	0.355958i	$-0.884155\pi$
$733$		−	19.2744i		−	0.711915i	0.934502	−	0.355958i	$-0.115845\pi$
$734$	−24.2124			−0.893697
$735$		0			0
$736$	−6.62033			−0.244028
$737$			0.218004i			0.00803027i
$738$		0			0
$739$	−31.3423			−1.15294			−0.576472	−	0.817117i	$-0.695571\pi$
$739$	−31.3423			−1.15294			−0.576472	+	0.817117i	$0.695571\pi$
$740$	20.0697	+	14.8047i	0.737777	+	0.544232i
$741$		0			0
$742$			2.13980i			0.0785545i
$743$			5.44803i			0.199869i	0.994994	+	0.0999345i	$0.0318633\pi$
$743$			5.44803i			0.199869i	−0.994994	+	0.0999345i	$0.968137\pi$
$744$		0			0
$745$	11.5687	−	15.6829i	0.423845	−	0.574576i
$746$	−14.1543			−0.518225
$747$		0			0
$748$		−	17.7615i		−	0.649425i
$749$	75.5653			2.76110
$750$		0			0
$751$	24.2445			0.884696			0.442348	−	0.896843i	$-0.354146\pi$
$751$	24.2445			0.884696			0.442348	+	0.896843i	$0.354146\pi$
$752$			10.2617i			0.374205i
$753$		0			0
$754$	−0.585478			−0.0213219
$755$	18.2457	−	24.7344i	0.664029	−	0.900177i
$756$		0			0
$757$		−	27.0868i		−	0.984487i	−0.870457	−	0.492244i	$-0.836177\pi$
$757$		−	27.0868i		−	0.984487i	0.870457	−	0.492244i	$-0.163823\pi$
$758$			19.0415i			0.691617i
$759$		0			0
$760$	10.0893	+	7.44256i	0.365979	+	0.269970i
$761$	−28.7119			−1.04080			−0.520402	−	0.853921i	$-0.674218\pi$
$761$	−28.7119			−1.04080			−0.520402	+	0.853921i	$0.674218\pi$
$762$		0			0
$763$		−	28.5969i		−	1.03528i
$764$	2.49931			0.0904219
$765$		0			0
$766$	31.2620			1.12954
$767$			2.28515i			0.0825119i
$768$		0			0
$769$	−27.7598			−1.00104			−0.500521	−	0.865724i	$-0.666858\pi$
$769$	−27.7598			−1.00104			−0.500521	+	0.865724i	$0.666858\pi$
$770$	20.1499	−	27.3158i	0.726153	−	0.984394i
$771$		0			0
$772$			8.57748i			0.308710i
$773$		−	51.5763i		−	1.85507i	−0.373735	−	0.927536i	$-0.621923\pi$
$773$		−	51.5763i		−	1.85507i	0.373735	−	0.927536i	$-0.378077\pi$
$774$		0			0
$775$	8.58604	+	27.7881i	0.308420	+	0.998180i
$776$	12.3836			0.444544
$777$		0			0
$778$			23.0860i			0.827675i
$779$	25.1219			0.900084
$780$		0			0
$781$	36.1432			1.29331
$782$			32.6730i			1.16838i
$783$		0			0
$784$	−10.7913			−0.385403
$785$	18.3768	+	13.5559i	0.655895	+	0.483830i
$786$		0			0
$787$			22.7340i			0.810381i	0.914232	+	0.405191i	$0.132795\pi$
$787$			22.7340i			0.810381i	−0.914232	+	0.405191i	$0.867205\pi$
$788$		−	7.51392i		−	0.267672i
$789$		0			0
$790$	10.3265	+	7.61751i	0.367401	+	0.271019i
$791$	−20.8452			−0.741169
$792$		0			0
$793$		−	1.90291i		−	0.0675743i
$794$	3.04076			0.107913
$795$		0			0
$796$	−7.49277			−0.265574
$797$			29.0656i			1.02955i	0.857324	+	0.514777i	$0.172125\pi$
$797$			29.0656i			1.02955i	−0.857324	+	0.514777i	$0.827875\pi$
$798$		0			0
$799$	50.6440			1.79166
$800$	4.77716	−	1.47606i	0.168898	−	0.0521865i
$801$		0			0
$802$			22.3657i			0.789759i
$803$		−	27.2514i		−	0.961680i
$804$		0			0
$805$	−37.0666	+	50.2485i	−1.30643	+	1.77103i
$806$	3.40566			0.119959
$807$		0			0
$808$		−	9.73071i		−	0.342325i
$809$	5.69142			0.200100			0.100050	−	0.994982i	$-0.468100\pi$
$809$	5.69142			0.200100			0.100050	+	0.994982i	$0.468100\pi$
$810$		0			0
$811$	−34.9471			−1.22716			−0.613580	−	0.789633i	$-0.710271\pi$
$811$	−34.9471			−1.22716			−0.613580	+	0.789633i	$0.710271\pi$
$812$			4.21797i			0.148022i
$813$		0			0
$814$	40.1394			1.40688
$815$	−5.73822	−	4.23288i	−0.201001	−	0.148271i
$816$		0			0
$817$			7.09753i			0.248311i
$818$			31.4906i			1.10104i
$819$		0			0
$820$	5.94742	−	8.06250i	0.207693	−	0.281555i
$821$	−9.99358			−0.348778			−0.174389	−	0.984677i	$-0.555795\pi$
$821$	−9.99358			−0.348778			−0.174389	+	0.984677i	$0.555795\pi$
$822$		0			0
$823$		−	55.1352i		−	1.92189i	−0.276733	−	0.960947i	$-0.589252\pi$
$823$		−	55.1352i		−	1.92189i	0.276733	−	0.960947i	$-0.410748\pi$
$824$	16.4628			0.573509
$825$		0			0
$826$	16.4629			0.572819
$827$			25.8946i			0.900443i	0.892917	+	0.450222i	$0.148655\pi$
$827$			25.8946i			0.900443i	−0.892917	+	0.450222i	$0.851345\pi$
$828$		0			0
$829$	24.3911			0.847137			0.423569	−	0.905864i	$-0.360777\pi$
$829$	24.3911			0.847137			0.423569	+	0.905864i	$0.360777\pi$
$830$	−20.5090	+	27.8025i	−0.711876	+	0.965040i
$831$		0			0
$832$		−	0.585478i		−	0.0202978i
$833$			53.2577i			1.84527i
$834$		0			0
$835$	−25.7857	−	19.0212i	−0.892350	−	0.658255i
$836$	20.1787			0.697895
$837$		0			0
$838$		−	38.6091i		−	1.33373i
$839$	−44.1267			−1.52342			−0.761712	−	0.647916i	$-0.775641\pi$
$839$	−44.1267			−1.52342			−0.761712	+	0.647916i	$0.775641\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$		−	30.7181i		−	1.05861i
$843$		0			0
$844$	22.0617			0.759395
$845$	−16.8011	+	22.7761i	−0.577975	+	0.783520i
$846$		0			0
$847$		−	8.23396i		−	0.282922i
$848$			0.507305i			0.0174209i
$849$		0			0
$850$	−7.28471	−	23.5765i	−0.249864	−	0.808667i
$851$	−73.8380			−2.53113
$852$		0			0
$853$			40.4474i			1.38489i	0.721469	+	0.692447i	$0.243467\pi$
$853$			40.4474i			1.38489i	−0.721469	+	0.692447i	$0.756533\pi$
$854$	−13.7092			−0.469118
$855$		0			0
$856$	17.9151			0.612325
$857$			2.65531i			0.0907038i	0.998971	+	0.0453519i	$0.0144409\pi$
$857$			2.65531i			0.0907038i	−0.998971	+	0.0453519i	$0.985559\pi$
$858$		0			0
$859$	2.39597			0.0817494			0.0408747	−	0.999164i	$-0.486986\pi$
$859$	2.39597			0.0817494			0.0408747	+	0.999164i	$0.486986\pi$
$860$	2.27785	+	1.68029i	0.0776740	+	0.0572974i
$861$		0			0
$862$			11.5648i			0.393900i
$863$		−	50.5829i		−	1.72186i	−0.508721	−	0.860931i	$-0.669882\pi$
$863$		−	50.5829i		−	1.72186i	0.508721	−	0.860931i	$-0.330118\pi$
$864$		0			0
$865$	13.9717	+	10.3064i	0.475053	+	0.350430i
$866$	12.4942			0.424569
$867$		0			0
$868$		−	24.5354i		−	0.832786i
$869$	20.6530			0.700606
$870$		0			0
$871$	0.0354654			0.00120170
$872$		−	6.77978i		−	0.229592i
$873$		0			0
$874$	−37.1195			−1.25559
$875$	15.5435	−	44.5231i	0.525467	−	1.50516i
$876$		0			0
$877$		−	1.70498i		−	0.0575731i	−0.999586	−	0.0287865i	$-0.990836\pi$
$877$		−	1.70498i		−	0.0575731i	0.999586	−	0.0287865i	$-0.00916431\pi$
$878$		−	35.7773i		−	1.20742i
$879$		0			0
$880$	4.77716	−	6.47606i	0.161038	−	0.218308i
$881$	−15.6044			−0.525725			−0.262862	−	0.964833i	$-0.584667\pi$
$881$	−15.6044			−0.525725			−0.262862	+	0.964833i	$0.584667\pi$
$882$		0			0
$883$		−	5.89658i		−	0.198436i	−0.995066	−	0.0992179i	$-0.968366\pi$
$883$		−	5.89658i		−	0.198436i	0.995066	−	0.0992179i	$-0.0316341\pi$
$884$	−2.88948			−0.0971839
$885$		0			0
$886$	−26.3836			−0.886373
$887$			25.2648i			0.848309i	0.905590	+	0.424155i	$0.139429\pi$
$887$			25.2648i			0.848309i	−0.905590	+	0.424155i	$0.860571\pi$
$888$		0			0
$889$	45.4607			1.52470
$890$	−0.201110	−	0.148352i	−0.00674122	−	0.00497276i
$891$		0			0
$892$		−	10.0120i		−	0.335228i
$893$			57.5362i			1.92538i
$894$		0			0
$895$	14.0617	−	19.0624i	0.470031	−	0.637187i
$896$	−4.21797			−0.140913
$897$		0			0
$898$		−	22.4028i		−	0.747593i
$899$	−5.81688			−0.194004
$900$		0			0
$901$	2.50368			0.0834096
$902$		−	16.1250i		−	0.536903i
$903$		0			0
$904$	−4.94199			−0.164368
$905$	−28.0313	+	38.0001i	−0.931793	+	1.26317i
$906$		0			0
$907$			18.6397i			0.618920i	0.950912	+	0.309460i	$0.100148\pi$
$907$			18.6397i			0.618920i	−0.950912	+	0.309460i	$0.899852\pi$
$908$			8.61914i			0.286036i
$909$		0			0
$910$	−4.44380	−	3.27804i	−0.147311	−	0.108666i
$911$	−17.5023			−0.579878			−0.289939	−	0.957045i	$-0.593635\pi$
$911$	−17.5023			−0.579878			−0.289939	+	0.957045i	$0.593635\pi$
$912$		0			0
$913$			55.6051i			1.84026i
$914$	24.6460			0.815217
$915$		0			0
$916$	23.0871			0.762819
$917$		−	10.0940i		−	0.333334i
$918$		0			0
$919$	−22.7616			−0.750836			−0.375418	−	0.926856i	$-0.622501\pi$
$919$	−22.7616			−0.750836			−0.375418	+	0.926856i	$0.622501\pi$
$920$	−8.78777	+	11.9130i	−0.289724	+	0.392759i
$921$		0			0
$922$			26.5959i			0.875888i
$923$		−	5.87987i		−	0.193538i
$924$		0			0
$925$	53.2807	−	16.4628i	1.75186	−	0.541293i
$926$	10.9099			0.358521
$927$		0			0
$928$			1.00000i			0.0328266i
$929$	−0.424031			−0.0139120			−0.00695600	−	0.999976i	$-0.502214\pi$
$929$	−0.424031			−0.0139120			−0.00695600	+	0.999976i	$0.502214\pi$
$930$		0			0
$931$	−60.5056			−1.98299
$932$		−	0.106134i		−	0.00347655i
$933$		0			0
$934$	1.47828			0.0483707
$935$	−31.9610	−	23.5765i	−1.04524	−	0.771034i
$936$		0			0
$937$			20.3685i			0.665410i	0.943031	+	0.332705i	$0.107961\pi$
$937$			20.3685i			0.665410i	−0.943031	+	0.332705i	$0.892039\pi$
$938$		−	0.255504i		−	0.00834249i
$939$		0			0
$940$	18.4654	+	13.6213i	0.602275	+	0.444277i
$941$	−14.6037			−0.476069			−0.238034	−	0.971257i	$-0.576503\pi$
$941$	−14.6037			−0.476069			−0.238034	+	0.971257i	$0.576503\pi$
$942$		0			0
$943$			29.6626i			0.965946i
$944$	3.90304			0.127033
$945$		0			0
$946$	4.55570			0.148119
$947$		−	13.7126i		−	0.445601i	−0.974864	−	0.222801i	$-0.928480\pi$
$947$		−	13.7126i		−	0.445601i	0.974864	−	0.222801i	$-0.0715199\pi$
$948$		0			0
$949$	−4.43332			−0.143912
$950$	26.7851	−	8.27610i	0.869022	−	0.268512i
$951$		0			0
$952$			20.8168i			0.674675i
$953$			30.3398i			0.982803i	0.870933	+	0.491402i	$0.163515\pi$
$953$			30.3398i			0.982803i	−0.870933	+	0.491402i	$0.836485\pi$
$954$		0			0
$955$	3.31757	−	4.49739i	0.107354	−	0.145532i
$956$	−6.95404			−0.224910
$957$		0			0
$958$			8.80715i			0.284546i
$959$	1.90860			0.0616318
$960$		0			0
$961$	2.83605			0.0914853
$962$		−	6.52997i		−	0.210535i
$963$		0			0
$964$	−4.25348			−0.136995
$965$	15.4348	+	11.3857i	0.496863	+	0.366518i
$966$		0			0
$967$			31.8547i			1.02438i	0.858873	+	0.512189i	$0.171165\pi$
$967$			31.8547i			1.02438i	−0.858873	+	0.512189i	$0.828835\pi$
$968$		−	1.95211i		−	0.0627433i
$969$		0			0
$970$	16.4379	−	22.2836i	0.527788	−	0.715485i
$971$	−23.7009			−0.760599			−0.380299	−	0.924863i	$-0.624179\pi$
$971$	−23.7009			−0.760599			−0.380299	+	0.924863i	$0.624179\pi$
$972$		0			0
$973$			1.69213i			0.0542471i
$974$	34.8847			1.11778
$975$		0			0
$976$	−3.25018			−0.104036
$977$			1.16746i			0.0373505i	0.999826	+	0.0186752i	$0.00594486\pi$
$977$			1.16746i			0.0373505i	−0.999826	+	0.0186752i	$0.994055\pi$
$978$		0			0
$979$	−0.402220			−0.0128550
$980$	−14.3243	+	19.4184i	−0.457572	+	0.620298i
$981$		0			0
$982$			40.5780i			1.29490i
$983$			33.4104i			1.06563i	0.846233	+	0.532813i	$0.178865\pi$
$983$			33.4104i			1.06563i	−0.846233	+	0.532813i	$0.821135\pi$
$984$		0			0
$985$	−13.5209	−	9.97392i	−0.430813	−	0.317796i
$986$	4.93525			0.157170
$987$		0			0
$988$		−	3.28272i		−	0.104437i
$989$	−8.38039			−0.266481
$990$		0			0
$991$	−40.3062			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$991$	−40.3062			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$992$		−	5.81688i		−	0.184686i
$993$		0			0
$994$	−42.3604			−1.34359
$995$	−9.94585	+	13.4829i	−0.315305	+	0.427436i
$996$		0			0
$997$		−	25.7965i		−	0.816982i	−0.912762	−	0.408491i	$-0.866055\pi$
$997$		−	25.7965i		−	0.816982i	0.912762	−	0.408491i	$-0.133945\pi$
$998$		−	0.495334i		−	0.0156795i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2610.2.e.i.2089.7		10
3.2	odd	2		290.2.b.b.59.4	✓	10
5.4	even	2	inner	2610.2.e.i.2089.2		10
12.11	even	2		2320.2.d.h.929.3		10
15.2	even	4		1450.2.a.u.1.4		5
15.8	even	4		1450.2.a.t.1.2		5
15.14	odd	2		290.2.b.b.59.7	yes	10
60.59	even	2		2320.2.d.h.929.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.b.b.59.4	✓	10	3.2	odd	2
290.2.b.b.59.7	yes	10	15.14	odd	2
1450.2.a.t.1.2		5	15.8	even	4
1450.2.a.u.1.4		5	15.2	even	4
2320.2.d.h.929.3		10	12.11	even	2
2320.2.d.h.929.8		10	60.59	even	2
2610.2.e.i.2089.2		10	5.4	even	2	inner
2610.2.e.i.2089.7		10	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:	\( N \)	\(=\)	\( 2610 = 2 \cdot 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2610.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.32739 + 1.79945i) q^{5} -4.21797i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.32739 + 1.79945i) q^{5} -4.21797i q^{7} -1.00000i q^{8} +(-1.79945 - 1.32739i) q^{10} -3.59890 q^{11} +0.585478i q^{13} +4.21797 q^{14} +1.00000 q^{16} -4.93525i q^{17} +5.60690 q^{19} +(1.32739 - 1.79945i) q^{20} -3.59890i q^{22} +6.62033i q^{23} +(-1.47606 - 4.77716i) q^{25} -0.585478 q^{26} +4.21797i q^{28} +1.00000 q^{29} -5.81688 q^{31} +1.00000i q^{32} +4.93525 q^{34} +(7.59004 + 5.59890i) q^{35} +11.1532i q^{37} +5.60690i q^{38} +(1.79945 + 1.32739i) q^{40} +4.48053 q^{41} +1.26586i q^{43} +3.59890 q^{44} -6.62033 q^{46} +10.2617i q^{47} -10.7913 q^{49} +(4.77716 - 1.47606i) q^{50} -0.585478i q^{52} +0.507305i q^{53} +(4.77716 - 6.47606i) q^{55} -4.21797 q^{56} +1.00000i q^{58} +3.90304 q^{59} -3.25018 q^{61} -5.81688i q^{62} -1.00000 q^{64} +(-1.05354 - 0.777160i) q^{65} -0.0605750i q^{67} +4.93525i q^{68} +(-5.59890 + 7.59004i) q^{70} -10.0428 q^{71} +7.57213i q^{73} -11.1532 q^{74} -5.60690 q^{76} +15.1801i q^{77} -5.73870 q^{79} +(-1.32739 + 1.79945i) q^{80} +4.48053i q^{82} -15.4506i q^{83} +(8.88075 + 6.55102i) q^{85} -1.26586 q^{86} +3.59890i q^{88} +0.111762 q^{89} +2.46953 q^{91} -6.62033i q^{92} -10.2617 q^{94} +(-7.44256 + 10.0893i) q^{95} +12.3836i q^{97} -10.7913i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4}+O(q^{10}) \) 10 * q - 10 * q^4	\( 10 q - 10 q^{4} + 10 q^{14} + 10 q^{16} + 8 q^{19} - 4 q^{25} - 14 q^{26} + 10 q^{29} + 10 q^{31} - 18 q^{34} - 18 q^{35} + 8 q^{41} + 26 q^{46} - 32 q^{49} + 16 q^{50} + 16 q^{55} - 10 q^{56} - 18 q^{59} + 10 q^{61} - 10 q^{64} - 20 q^{65} - 20 q^{70} + 12 q^{71} - 12 q^{74} - 8 q^{76} + 34 q^{79} + 18 q^{85} - 2 q^{86} + 20 q^{89} - 44 q^{91} - 28 q^{94} + 8 q^{95}+O(q^{100}) \) 10 * q - 10 * q^4 + 10 * q^14 + 10 * q^16 + 8 * q^19 - 4 * q^25 - 14 * q^26 + 10 * q^29 + 10 * q^31 - 18 * q^34 - 18 * q^35 + 8 * q^41 + 26 * q^46 - 32 * q^49 + 16 * q^50 + 16 * q^55 - 10 * q^56 - 18 * q^59 + 10 * q^61 - 10 * q^64 - 20 * q^65 - 20 * q^70 + 12 * q^71 - 12 * q^74 - 8 * q^76 + 34 * q^79 + 18 * q^85 - 2 * q^86 + 20 * q^89 - 44 * q^91 - 28 * q^94 + 8 * q^95

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