LMFDB - Embedded newform 495.2.c.d.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(199,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, 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("495.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.c (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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.4
Root			$1.45161 - 1.45161i$ of defining polynomial
Character	$\chi$	$=$	495.199
Dual form			495.2.c.d.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.21432i q^{2} +0.525428 q^{4} +(-0.311108 - 2.21432i) q^{5} +4.90321i q^{7} +3.06668i q^{8} +O(q^{10})$	\(q+1.21432i q^{2} +0.525428 q^{4} +(-0.311108 - 2.21432i) q^{5} +4.90321i q^{7} +3.06668i q^{8} +(2.68889 - 0.377784i) q^{10} +1.00000 q^{11} -4.14764i q^{13} -5.95407 q^{14} -2.67307 q^{16} +5.33185i q^{17} +5.18421 q^{19} +(-0.163465 - 1.16346i) q^{20} +1.21432i q^{22} +4.00000i q^{23} +(-4.80642 + 1.37778i) q^{25} +5.03657 q^{26} +2.57628i q^{28} +1.80642 q^{29} +2.62222 q^{31} +2.88739i q^{32} -6.47457 q^{34} +(10.8573 - 1.52543i) q^{35} +5.80642i q^{37} +6.29529i q^{38} +(6.79060 - 0.954067i) q^{40} -1.80642 q^{41} -4.90321i q^{43} +0.525428 q^{44} -4.85728 q^{46} -7.05086i q^{47} -17.0415 q^{49} +(-1.67307 - 5.83654i) q^{50} -2.17929i q^{52} -7.18421i q^{53} +(-0.311108 - 2.21432i) q^{55} -15.0366 q^{56} +2.19358i q^{58} +1.67307 q^{59} +0.755569 q^{61} +3.18421i q^{62} -8.85236 q^{64} +(-9.18421 + 1.29036i) q^{65} -4.85728i q^{67} +2.80150i q^{68} +(1.85236 + 13.1842i) q^{70} -0.428639 q^{71} -12.7096i q^{73} -7.05086 q^{74} +2.72393 q^{76} +4.90321i q^{77} +6.42864 q^{79} +(0.831613 + 5.91903i) q^{80} -2.19358i q^{82} -2.90321i q^{83} +(11.8064 - 1.65878i) q^{85} +5.95407 q^{86} +3.06668i q^{88} +0.622216 q^{89} +20.3368 q^{91} +2.10171i q^{92} +8.56199 q^{94} +(-1.61285 - 11.4795i) q^{95} -2.75557i q^{97} -20.6938i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} - 2 q^{5}+O(q^{10}) $ 6 * q - 10 * q^4 - 2 * q^5	$ 6 q - 10 q^{4} - 2 q^{5} + 16 q^{10} + 6 q^{11} + 4 q^{14} + 10 q^{16} + 4 q^{19} - 14 q^{20} - 2 q^{25} + 16 q^{26} - 16 q^{29} + 16 q^{31} - 52 q^{34} + 12 q^{35} - 12 q^{40} + 16 q^{41} - 10 q^{44} + 24 q^{46} - 22 q^{49} + 16 q^{50} - 2 q^{55} - 76 q^{56} - 16 q^{59} + 4 q^{61} - 66 q^{64} - 28 q^{65} + 24 q^{70} + 24 q^{71} - 16 q^{74} - 36 q^{76} + 12 q^{79} + 58 q^{80} + 44 q^{85} - 4 q^{86} + 4 q^{89} + 16 q^{91} + 24 q^{94} + 44 q^{95}+O(q^{100}) $ 6 * q - 10 * q^4 - 2 * q^5 + 16 * q^10 + 6 * q^11 + 4 * q^14 + 10 * q^16 + 4 * q^19 - 14 * q^20 - 2 * q^25 + 16 * q^26 - 16 * q^29 + 16 * q^31 - 52 * q^34 + 12 * q^35 - 12 * q^40 + 16 * q^41 - 10 * q^44 + 24 * q^46 - 22 * q^49 + 16 * q^50 - 2 * q^55 - 76 * q^56 - 16 * q^59 + 4 * q^61 - 66 * q^64 - 28 * q^65 + 24 * q^70 + 24 * q^71 - 16 * q^74 - 36 * q^76 + 12 * q^79 + 58 * q^80 + 44 * q^85 - 4 * q^86 + 4 * q^89 + 16 * q^91 + 24 * q^94 + 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.21432i			0.858654i	0.903149	+	0.429327i	$0.141249\pi$
$2$			1.21432i			0.858654i	−0.903149	+	0.429327i	$0.858751\pi$
$3$		0			0
$3$		0			0
$4$	0.525428			0.262714
$5$	−0.311108	−	2.21432i	−0.139132	−	0.990274i
$5$	−0.311108	−	2.21432i	−0.139132	−	0.990274i
$6$		0			0
$7$			4.90321i			1.85324i	0.375999	+	0.926620i	$0.377300\pi$
$7$			4.90321i			1.85324i	−0.375999	+	0.926620i	$0.622700\pi$
$8$			3.06668i			1.08423i
$9$		0			0
$10$	2.68889	−	0.377784i	0.850302	−	0.119466i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		0			0
$13$		−	4.14764i		−	1.15035i	−0.818031	−	0.575175i	$-0.804934\pi$
$13$		−	4.14764i		−	1.15035i	0.818031	−	0.575175i	$-0.195066\pi$
$14$	−5.95407			−1.59129
$15$		0			0
$16$	−2.67307			−0.668268
$17$			5.33185i			1.29316i	0.762845	+	0.646582i	$0.223802\pi$
$17$			5.33185i			1.29316i	−0.762845	+	0.646582i	$0.776198\pi$
$18$		0			0
$19$	5.18421			1.18934			0.594669	−	0.803970i	$-0.297283\pi$
$19$	5.18421			1.18934			0.594669	+	0.803970i	$0.297283\pi$
$20$	−0.163465	−	1.16346i	−0.0365518	−	0.260159i
$21$		0			0
$22$			1.21432i			0.258894i
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$		0			0
$25$	−4.80642	+	1.37778i	−0.961285	+	0.275557i
$26$	5.03657			0.987752
$27$		0			0
$28$			2.57628i			0.486872i
$29$	1.80642			0.335444			0.167722	−	0.985834i	$-0.446359\pi$
$29$	1.80642			0.335444			0.167722	+	0.985834i	$0.446359\pi$
$30$		0			0
$31$	2.62222			0.470964			0.235482	−	0.971879i	$-0.424333\pi$
$31$	2.62222			0.470964			0.235482	+	0.971879i	$0.424333\pi$
$32$			2.88739i			0.510423i
$33$		0			0
$34$	−6.47457			−1.11038
$35$	10.8573	−	1.52543i	1.83522	−	0.257844i
$36$		0			0
$37$			5.80642i			0.954570i	0.878749	+	0.477285i	$0.158379\pi$
$37$			5.80642i			0.954570i	−0.878749	+	0.477285i	$0.841621\pi$
$38$			6.29529i			1.02123i
$39$		0			0
$40$	6.79060	−	0.954067i	1.07369	−	0.150851i
$41$	−1.80642			−0.282116			−0.141058	−	0.990001i	$-0.545050\pi$
$41$	−1.80642			−0.282116			−0.141058	+	0.990001i	$0.545050\pi$
$42$		0			0
$43$		−	4.90321i		−	0.747733i	−0.927483	−	0.373866i	$-0.878032\pi$
$43$		−	4.90321i		−	0.747733i	0.927483	−	0.373866i	$-0.121968\pi$
$44$	0.525428			0.0792112
$45$		0			0
$46$	−4.85728			−0.716167
$47$		−	7.05086i		−	1.02847i	−0.857648	−	0.514236i	$-0.828075\pi$
$47$		−	7.05086i		−	1.02847i	0.857648	−	0.514236i	$-0.171925\pi$
$48$		0			0
$49$	−17.0415			−2.43450
$50$	−1.67307	−	5.83654i	−0.236608	−	0.825411i
$51$		0			0
$52$		−	2.17929i		−	0.302213i
$53$		−	7.18421i		−	0.986827i	−0.869795	−	0.493413i	$-0.835749\pi$
$53$		−	7.18421i		−	0.986827i	0.869795	−	0.493413i	$-0.164251\pi$
$54$		0			0
$55$	−0.311108	−	2.21432i	−0.0419498	−	0.298579i
$56$	−15.0366			−2.00935
$57$		0			0
$58$			2.19358i			0.288031i
$59$	1.67307			0.217815			0.108908	−	0.994052i	$-0.465265\pi$
$59$	1.67307			0.217815			0.108908	+	0.994052i	$0.465265\pi$
$60$		0			0
$61$	0.755569			0.0967407			0.0483703	−	0.998829i	$-0.484597\pi$
$61$	0.755569			0.0967407			0.0483703	+	0.998829i	$0.484597\pi$
$62$			3.18421i			0.404395i
$63$		0			0
$64$	−8.85236			−1.10654
$65$	−9.18421	+	1.29036i	−1.13916	+	0.160050i
$66$		0			0
$67$		−	4.85728i		−	0.593411i	−0.954969	−	0.296706i	$-0.904112\pi$
$67$		−	4.85728i		−	0.593411i	0.954969	−	0.296706i	$-0.0958880\pi$
$68$			2.80150i			0.339732i
$69$		0			0
$70$	1.85236	+	13.1842i	0.221399	+	1.57581i
$71$	−0.428639			−0.0508701			−0.0254351	−	0.999676i	$-0.508097\pi$
$71$	−0.428639			−0.0508701			−0.0254351	+	0.999676i	$0.508097\pi$
$72$		0			0
$73$		−	12.7096i		−	1.48755i	−0.668430	−	0.743775i	$-0.733033\pi$
$73$		−	12.7096i		−	1.48755i	0.668430	−	0.743775i	$-0.266967\pi$
$74$	−7.05086			−0.819645
$75$		0			0
$76$	2.72393			0.312456
$77$			4.90321i			0.558773i
$78$		0			0
$79$	6.42864			0.723278			0.361639	−	0.932318i	$-0.382217\pi$
$79$	6.42864			0.723278			0.361639	+	0.932318i	$0.382217\pi$
$80$	0.831613	+	5.91903i	0.0929772	+	0.661768i
$81$		0			0
$82$		−	2.19358i		−	0.242240i
$83$		−	2.90321i		−	0.318669i	−0.987225	−	0.159334i	$-0.949065\pi$
$83$		−	2.90321i		−	0.318669i	0.987225	−	0.159334i	$-0.0509348\pi$
$84$		0			0
$85$	11.8064	−	1.65878i	1.28059	−	0.179920i
$86$	5.95407			0.642044
$87$		0			0
$88$			3.06668i			0.326909i
$89$	0.622216			0.0659547			0.0329774	−	0.999456i	$-0.489501\pi$
$89$	0.622216			0.0659547			0.0329774	+	0.999456i	$0.489501\pi$
$90$		0			0
$91$	20.3368			2.13187
$92$			2.10171i			0.219118i
$93$		0			0
$94$	8.56199			0.883102
$95$	−1.61285	−	11.4795i	−0.165475	−	1.17777i
$96$		0			0
$97$		−	2.75557i		−	0.279786i	−0.990167	−	0.139893i	$-0.955324\pi$
$97$		−	2.75557i		−	0.279786i	0.990167	−	0.139893i	$-0.0446758\pi$
$98$		−	20.6938i		−	2.09039i
$99$		0			0
$100$	−2.52543	+	0.723926i	−0.252543	+	0.0723926i
$101$	17.8064			1.77181			0.885903	−	0.463871i	$-0.153540\pi$
$101$	17.8064			1.77181			0.885903	+	0.463871i	$0.153540\pi$
$102$		0			0
$103$		−	4.94914i		−	0.487654i	−0.969819	−	0.243827i	$-0.921597\pi$
$103$		−	4.94914i		−	0.487654i	0.969819	−	0.243827i	$-0.0784029\pi$
$104$	12.7195			1.24725
$105$		0			0
$106$	8.72393			0.847343
$107$		−	11.1985i		−	1.08260i	−0.840830	−	0.541300i	$-0.817932\pi$
$107$		−	11.1985i		−	1.08260i	0.840830	−	0.541300i	$-0.182068\pi$
$108$		0			0
$109$	−15.7146			−1.50518			−0.752591	−	0.658488i	$-0.771196\pi$
$109$	−15.7146			−1.50518			−0.752591	+	0.658488i	$0.771196\pi$
$110$	2.68889	−	0.377784i	0.256376	−	0.0360203i
$111$		0			0
$112$		−	13.1066i		−	1.23846i
$113$		−	1.76494i		−	0.166031i	−0.996548	−	0.0830156i	$-0.973545\pi$
$113$		−	1.76494i		−	0.166031i	0.996548	−	0.0830156i	$-0.0264551\pi$
$114$		0			0
$115$	8.85728	−	1.24443i	0.825946	−	0.116044i
$116$	0.949145			0.0881259
$117$		0			0
$118$			2.03164i			0.187028i
$119$	−26.1432			−2.39654
$120$		0			0
$121$	1.00000			0.0909091
$122$			0.917502i			0.0830667i
$123$		0			0
$124$	1.37778			0.123729
$125$	4.54617	+	10.2143i	0.406622	+	0.913597i
$126$		0			0
$127$			18.7096i			1.66021i	0.557606	+	0.830106i	$0.311720\pi$
$127$			18.7096i			1.66021i	−0.557606	+	0.830106i	$0.688280\pi$
$128$		−	4.97481i		−	0.439715i
$129$		0			0
$130$	−1.56691	−	11.1526i	−0.137428	−	0.978145i
$131$	1.24443			0.108726			0.0543632	−	0.998521i	$-0.482687\pi$
$131$	1.24443			0.108726			0.0543632	+	0.998521i	$0.482687\pi$
$132$		0			0
$133$			25.4193i			2.20413i
$134$	5.89829			0.509535
$135$		0			0
$136$	−16.3511			−1.40209
$137$		−	18.7971i		−	1.60594i	−0.596019	−	0.802970i	$-0.703252\pi$
$137$		−	18.7971i		−	1.60594i	0.596019	−	0.802970i	$-0.296748\pi$
$138$		0			0
$139$	−14.0415			−1.19098			−0.595492	−	0.803361i	$-0.703043\pi$
$139$	−14.0415			−1.19098			−0.595492	+	0.803361i	$0.703043\pi$
$140$	5.70471	−	0.801502i	0.482136	−	0.0677393i
$141$		0			0
$142$		−	0.520505i		−	0.0436798i
$143$		−	4.14764i		−	0.346843i
$144$		0			0
$145$	−0.561993	−	4.00000i	−0.0466709	−	0.332182i
$146$	15.4336			1.27729
$147$		0			0
$148$			3.05086i			0.250779i
$149$	−3.05086			−0.249936			−0.124968	−	0.992161i	$-0.539883\pi$
$149$	−3.05086			−0.249936			−0.124968	+	0.992161i	$0.539883\pi$
$150$		0			0
$151$	−0.326929			−0.0266051			−0.0133026	−	0.999912i	$-0.504234\pi$
$151$	−0.326929			−0.0266051			−0.0133026	+	0.999912i	$0.504234\pi$
$152$			15.8983i			1.28952i
$153$		0			0
$154$	−5.95407			−0.479792
$155$	−0.815792	−	5.80642i	−0.0655260	−	0.466383i
$156$		0			0
$157$		−	19.9081i		−	1.58884i	−0.607367	−	0.794421i	$-0.707774\pi$
$157$		−	19.9081i		−	1.58884i	0.607367	−	0.794421i	$-0.292226\pi$
$158$			7.80642i			0.621046i
$159$		0			0
$160$	6.39361	−	0.898290i	0.505459	−	0.0710160i
$161$	−19.6128			−1.54571
$162$		0			0
$163$		−	12.1748i		−	0.953607i	−0.879010	−	0.476804i	$-0.841795\pi$
$163$		−	12.1748i		−	0.953607i	0.879010	−	0.476804i	$-0.158205\pi$
$164$	−0.949145			−0.0741158
$165$		0			0
$166$	3.52543			0.273626
$167$		−	13.0049i		−	1.00635i	−0.864184	−	0.503176i	$-0.832165\pi$
$167$		−	13.0049i		−	1.00635i	0.864184	−	0.503176i	$-0.167835\pi$
$168$		0			0
$169$	−4.20294			−0.323303
$170$	2.01429	+	14.3368i	0.154489	+	1.09958i
$171$		0			0
$172$		−	2.57628i		−	0.196440i
$173$			13.8938i			1.05633i	0.849142	+	0.528165i	$0.177120\pi$
$173$			13.8938i			1.05633i	−0.849142	+	0.528165i	$0.822880\pi$
$174$		0			0
$175$	−6.75557	−	23.5669i	−0.510673	−	1.78149i
$176$	−2.67307			−0.201490
$177$		0			0
$178$			0.755569i			0.0566323i
$179$	12.8573			0.960998			0.480499	−	0.876995i	$-0.340456\pi$
$179$	12.8573			0.960998			0.480499	+	0.876995i	$0.340456\pi$
$180$		0			0
$181$	0.917502			0.0681974			0.0340987	−	0.999418i	$-0.489144\pi$
$181$	0.917502			0.0681974			0.0340987	+	0.999418i	$0.489144\pi$
$182$			24.6953i			1.83054i
$183$		0			0
$184$	−12.2667			−0.904314
$185$	12.8573	−	1.80642i	0.945286	−	0.132811i
$186$		0			0
$187$			5.33185i			0.389904i
$188$		−	3.70471i		−	0.270194i
$189$		0			0
$190$	13.9398	−	1.95851i	1.01130	−	0.142085i
$191$	−14.3684			−1.03966			−0.519831	−	0.854269i	$-0.674005\pi$
$191$	−14.3684			−1.03966			−0.519831	+	0.854269i	$0.674005\pi$
$192$		0			0
$193$			11.7605i			0.846539i	0.906004	+	0.423269i	$0.139118\pi$
$193$			11.7605i			0.846539i	−0.906004	+	0.423269i	$0.860882\pi$
$194$	3.34614			0.240239
$195$		0			0
$196$	−8.95407			−0.639576
$197$			3.82071i			0.272215i	0.990694	+	0.136107i	$0.0434592\pi$
$197$			3.82071i			0.272215i	−0.990694	+	0.136107i	$0.956541\pi$
$198$		0			0
$199$	13.7146			0.972199			0.486100	−	0.873903i	$-0.338419\pi$
$199$	13.7146			0.972199			0.486100	+	0.873903i	$0.338419\pi$
$200$	−4.22522	−	14.7397i	−0.298768	−	1.04226i
$201$		0			0
$202$			21.6227i			1.52137i
$203$			8.85728i			0.621659i
$204$		0			0
$205$	0.561993	+	4.00000i	0.0392513	+	0.279372i
$206$	6.00984			0.418726
$207$		0			0
$208$			11.0869i			0.768741i
$209$	5.18421			0.358599
$210$		0			0
$211$	1.95851			0.134830			0.0674148	−	0.997725i	$-0.478525\pi$
$211$	1.95851			0.134830			0.0674148	+	0.997725i	$0.478525\pi$
$212$		−	3.77478i		−	0.259253i
$213$		0			0
$214$	13.5986			0.929578
$215$	−10.8573	+	1.52543i	−0.740460	+	0.104033i
$216$		0			0
$217$			12.8573i			0.872809i
$218$		−	19.0825i		−	1.29243i
$219$		0			0
$220$	−0.163465	−	1.16346i	−0.0110208	−	0.0784408i
$221$	22.1146			1.48759
$222$		0			0
$223$			26.0098i			1.74175i	0.491506	+	0.870874i	$0.336446\pi$
$223$			26.0098i			1.74175i	−0.491506	+	0.870874i	$0.663554\pi$
$224$	−14.1575			−0.945937
$225$		0			0
$226$	2.14320			0.142563
$227$			6.34122i			0.420882i	0.977607	+	0.210441i	$0.0674899\pi$
$227$			6.34122i			0.420882i	−0.977607	+	0.210441i	$0.932510\pi$
$228$		0			0
$229$	23.3274			1.54152			0.770759	−	0.637127i	$-0.219877\pi$
$229$	23.3274			1.54152			0.770759	+	0.637127i	$0.219877\pi$
$230$	1.51114	+	10.7556i	0.0996415	+	0.709201i
$231$		0			0
$232$			5.53972i			0.363700i
$233$		−	1.42372i		−	0.0932708i	−0.998912	−	0.0466354i	$-0.985150\pi$
$233$		−	1.42372i		−	0.0932708i	0.998912	−	0.0466354i	$-0.0148499\pi$
$234$		0			0
$235$	−15.6128	+	2.19358i	−1.01847	+	0.143093i
$236$	0.879077			0.0572231
$237$		0			0
$238$		−	31.7462i		−	2.05780i
$239$	−18.9590			−1.22636			−0.613178	−	0.789945i	$-0.710109\pi$
$239$	−18.9590			−1.22636			−0.613178	+	0.789945i	$0.710109\pi$
$240$		0			0
$241$	−1.34614			−0.0867126			−0.0433563	−	0.999060i	$-0.513805\pi$
$241$	−1.34614			−0.0867126			−0.0433563	+	0.999060i	$0.513805\pi$
$242$			1.21432i			0.0780594i
$243$		0			0
$244$	0.396997			0.0254151
$245$	5.30174	+	37.7353i	0.338716	+	2.41082i
$246$		0			0
$247$		−	21.5022i		−	1.36816i
$248$			8.04149i			0.510635i
$249$		0			0
$250$	−12.4035	+	5.52051i	−0.784463	+	0.349147i
$251$	−1.08250			−0.0683267			−0.0341633	−	0.999416i	$-0.510877\pi$
$251$	−1.08250			−0.0683267			−0.0341633	+	0.999416i	$0.510877\pi$
$252$		0			0
$253$			4.00000i			0.251478i
$254$	−22.7195			−1.42555
$255$		0			0
$256$	−11.6637			−0.728981
$257$			0.133353i			0.00831834i	0.999991	+	0.00415917i	$0.00132391\pi$
$257$			0.133353i			0.00831834i	−0.999991	+	0.00415917i	$0.998676\pi$
$258$		0			0
$259$	−28.4701			−1.76905
$260$	−4.82564	+	0.677993i	−0.299273	+	0.0420473i
$261$		0			0
$262$			1.51114i			0.0933584i
$263$		−	0.147643i		−	0.00910407i	−0.999990	−	0.00455203i	$-0.998551\pi$
$263$		−	0.147643i		−	0.00910407i	0.999990	−	0.00455203i	$-0.00144896\pi$
$264$		0			0
$265$	−15.9081	+	2.23506i	−0.977229	+	0.137299i
$266$	−30.8671			−1.89258
$267$		0			0
$268$		−	2.55215i		−	0.155897i
$269$	−26.8573			−1.63752			−0.818759	−	0.574138i	$-0.805337\pi$
$269$	−26.8573			−1.63752			−0.818759	+	0.574138i	$0.805337\pi$
$270$		0			0
$271$	3.08250			0.187248			0.0936242	−	0.995608i	$-0.470155\pi$
$271$	3.08250			0.187248			0.0936242	+	0.995608i	$0.470155\pi$
$272$		−	14.2524i		−	0.864180i
$273$		0			0
$274$	22.8256			1.37895
$275$	−4.80642	+	1.37778i	−0.289838	+	0.0830835i
$276$		0			0
$277$		−	8.70964i		−	0.523311i	−0.965161	−	0.261656i	$-0.915732\pi$
$277$		−	8.70964i		−	0.523311i	0.965161	−	0.261656i	$-0.0842685\pi$
$278$		−	17.0509i		−	1.02264i
$279$		0			0
$280$	4.67799	+	33.2958i	0.279564	+	1.98980i
$281$	20.3783			1.21567			0.607833	−	0.794065i	$-0.292039\pi$
$281$	20.3783			1.21567			0.607833	+	0.794065i	$0.292039\pi$
$282$		0			0
$283$			6.32248i			0.375833i	0.982185	+	0.187916i	$0.0601734\pi$
$283$			6.32248i			0.375833i	−0.982185	+	0.187916i	$0.939827\pi$
$284$	−0.225219			−0.0133643
$285$		0			0
$286$	5.03657			0.297818
$287$		−	8.85728i		−	0.522829i
$288$		0			0
$289$	−11.4286			−0.672273
$290$	4.85728	−	0.682439i	0.285229	−	0.0400742i
$291$		0			0
$292$		−	6.67799i		−	0.390800i
$293$			16.6780i			0.974339i	0.873308	+	0.487169i	$0.161971\pi$
$293$			16.6780i			0.974339i	−0.873308	+	0.487169i	$0.838029\pi$
$294$		0			0
$295$	−0.520505	−	3.70471i	−0.0303050	−	0.215697i
$296$	−17.8064			−1.03498
$297$		0			0
$298$		−	3.70471i		−	0.214608i
$299$	16.5906			0.959458
$300$		0			0
$301$	24.0415			1.38573
$302$		−	0.396997i		−	0.0228446i
$303$		0			0
$304$	−13.8578			−0.794797
$305$	−0.235063	−	1.67307i	−0.0134597	−	0.0957998i
$306$		0			0
$307$		−	9.58565i		−	0.547082i	−0.961860	−	0.273541i	$-0.911805\pi$
$307$		−	9.58565i		−	0.547082i	0.961860	−	0.273541i	$-0.0881949\pi$
$308$			2.57628i			0.146797i
$309$		0			0
$310$	7.05086	−	0.990632i	0.400462	−	0.0562641i
$311$	−14.5303			−0.823941			−0.411970	−	0.911197i	$-0.635159\pi$
$311$	−14.5303			−0.823941			−0.411970	+	0.911197i	$0.635159\pi$
$312$		0			0
$313$			21.0321i			1.18881i	0.804167	+	0.594403i	$0.202612\pi$
$313$			21.0321i			1.18881i	−0.804167	+	0.594403i	$0.797388\pi$
$314$	24.1748			1.36427
$315$		0			0
$316$	3.37778			0.190015
$317$			0.990632i			0.0556394i	0.999613	+	0.0278197i	$0.00885643\pi$
$317$			0.990632i			0.0556394i	−0.999613	+	0.0278197i	$0.991144\pi$
$318$		0			0
$319$	1.80642			0.101140
$320$	2.75404	+	19.6019i	0.153955	+	1.09578i
$321$		0			0
$322$		−	23.8163i		−	1.32723i
$323$			27.6414i			1.53801i
$324$		0			0
$325$	5.71456	+	19.9353i	0.316987	+	1.10581i
$326$	14.7841			0.818818
$327$		0			0
$328$		−	5.53972i		−	0.305880i
$329$	34.5718			1.90601
$330$		0			0
$331$	−17.5812			−0.966350			−0.483175	−	0.875524i	$-0.660517\pi$
$331$	−17.5812			−0.966350			−0.483175	+	0.875524i	$0.660517\pi$
$332$		−	1.52543i		−	0.0837187i
$333$		0			0
$334$	15.7921			0.864107
$335$	−10.7556	+	1.51114i	−0.587639	+	0.0825623i
$336$		0			0
$337$		−	3.16992i		−	0.172676i	−0.996266	−	0.0863382i	$-0.972483\pi$
$337$		−	3.16992i		−	0.172676i	0.996266	−	0.0863382i	$-0.0275166\pi$
$338$		−	5.10372i		−	0.277606i
$339$		0			0
$340$	6.20342	−	0.871569i	0.336428	−	0.0472675i
$341$	2.62222			0.142001
$342$		0			0
$343$		−	49.2355i		−	2.65847i
$344$	15.0366			0.810717
$345$		0			0
$346$	−16.8716			−0.907021
$347$		−	4.97634i		−	0.267144i	−0.991039	−	0.133572i	$-0.957355\pi$
$347$		−	4.97634i		−	0.267144i	0.991039	−	0.133572i	$-0.0426447\pi$
$348$		0			0
$349$	−18.2034			−0.974407			−0.487203	−	0.873289i	$-0.661983\pi$
$349$	−18.2034			−0.974407			−0.487203	+	0.873289i	$0.661983\pi$
$350$	28.6178	−	8.20342i	1.52968	−	0.438491i
$351$		0			0
$352$			2.88739i			0.153898i
$353$			22.4099i			1.19276i	0.802703	+	0.596379i	$0.203395\pi$
$353$			22.4099i			1.19276i	−0.802703	+	0.596379i	$0.796605\pi$
$354$		0			0
$355$	0.133353	+	0.949145i	0.00707765	+	0.0503754i
$356$	0.326929			0.0173272
$357$		0			0
$358$			15.6128i			0.825165i
$359$	21.3274			1.12562			0.562809	−	0.826587i	$-0.309721\pi$
$359$	21.3274			1.12562			0.562809	+	0.826587i	$0.309721\pi$
$360$		0			0
$361$	7.87601			0.414527
$362$			1.11414i			0.0585579i
$363$		0			0
$364$	10.6855			0.560072
$365$	−28.1432	+	3.95407i	−1.47308	+	0.206965i
$366$		0			0
$367$			35.1338i			1.83397i	0.398921	+	0.916985i	$0.369385\pi$
$367$			35.1338i			1.83397i	−0.398921	+	0.916985i	$0.630615\pi$
$368$		−	10.6923i		−	0.557374i
$369$		0			0
$370$	2.19358	+	15.6128i	0.114039	+	0.811673i
$371$	35.2257			1.82883
$372$		0			0
$373$			17.0049i			0.880481i	0.897880	+	0.440241i	$0.145107\pi$
$373$			17.0049i			0.880481i	−0.897880	+	0.440241i	$0.854893\pi$
$374$	−6.47457			−0.334792
$375$		0			0
$376$	21.6227			1.11511
$377$		−	7.49240i		−	0.385878i
$378$		0			0
$379$	−2.36842			−0.121657			−0.0608287	−	0.998148i	$-0.519374\pi$
$379$	−2.36842			−0.121657			−0.0608287	+	0.998148i	$0.519374\pi$
$380$	−0.847435	−	6.03164i	−0.0434725	−	0.309417i
$381$		0			0
$382$		−	17.4479i		−	0.892710i
$383$			1.21585i			0.0621271i	0.999517	+	0.0310635i	$0.00988942\pi$
$383$			1.21585i			0.0621271i	−0.999517	+	0.0310635i	$0.990111\pi$
$384$		0			0
$385$	10.8573	−	1.52543i	0.553338	−	0.0777430i
$386$	−14.2810			−0.726884
$387$		0			0
$388$		−	1.44785i		−	0.0735035i
$389$	2.26671			0.114927			0.0574633	−	0.998348i	$-0.481699\pi$
$389$	2.26671			0.114927			0.0574633	+	0.998348i	$0.481699\pi$
$390$		0			0
$391$	−21.3274			−1.07857
$392$		−	52.2607i		−	2.63957i
$393$		0			0
$394$	−4.63957			−0.233738
$395$	−2.00000	−	14.2351i	−0.100631	−	0.716244i
$396$		0			0
$397$		−	18.4889i		−	0.927929i	−0.885854	−	0.463965i	$-0.846426\pi$
$397$		−	18.4889i		−	0.927929i	0.885854	−	0.463965i	$-0.153574\pi$
$398$			16.6539i			0.834782i
$399$		0			0
$400$	12.8479	−	3.68292i	0.642396	−	0.184146i
$401$	−17.5625			−0.877028			−0.438514	−	0.898724i	$-0.644495\pi$
$401$	−17.5625			−0.877028			−0.438514	+	0.898724i	$0.644495\pi$
$402$		0			0
$403$		−	10.8760i		−	0.541773i
$404$	9.35599			0.465478
$405$		0			0
$406$	−10.7556			−0.533790
$407$			5.80642i			0.287814i
$408$		0			0
$409$	21.3461			1.05550			0.527749	−	0.849400i	$-0.323036\pi$
$409$	21.3461			1.05550			0.527749	+	0.849400i	$0.323036\pi$
$410$	−4.85728	+	0.682439i	−0.239884	+	0.0337032i
$411$		0			0
$412$		−	2.60042i		−	0.128113i
$413$			8.20342i			0.403664i
$414$		0			0
$415$	−6.42864	+	0.903212i	−0.315570	+	0.0443369i
$416$	11.9759			0.587165
$417$		0			0
$418$			6.29529i			0.307913i
$419$	28.8573			1.40977			0.704885	−	0.709321i	$-0.250999\pi$
$419$	28.8573			1.40977			0.704885	+	0.709321i	$0.250999\pi$
$420$		0			0
$421$	−35.4893			−1.72964			−0.864822	−	0.502078i	$-0.832569\pi$
$421$	−35.4893			−1.72964			−0.864822	+	0.502078i	$0.832569\pi$
$422$			2.37826i			0.115772i
$423$		0			0
$424$	22.0316			1.06995
$425$	−7.34614	−	25.6271i	−0.356340	−	1.24310i
$426$		0			0
$427$			3.70471i			0.179284i
$428$		−	5.88400i		−	0.284414i
$429$		0			0
$430$	−1.85236	−	13.1842i	−0.0893286	−	0.635799i
$431$	−9.24443			−0.445289			−0.222644	−	0.974900i	$-0.571469\pi$
$431$	−9.24443			−0.445289			−0.222644	+	0.974900i	$0.571469\pi$
$432$		0			0
$433$			6.28544i			0.302059i	0.988529	+	0.151030i	$0.0482589\pi$
$433$			6.28544i			0.302059i	−0.988529	+	0.151030i	$0.951741\pi$
$434$	−15.6128			−0.749441
$435$		0			0
$436$	−8.25686			−0.395432
$437$			20.7368i			0.991977i
$438$		0			0
$439$	36.5303			1.74350			0.871749	−	0.489952i	$-0.162986\pi$
$439$	36.5303			1.74350			0.871749	+	0.489952i	$0.162986\pi$
$440$	6.79060	−	0.954067i	0.323729	−	0.0454834i
$441$		0			0
$442$			26.8542i			1.27732i
$443$		−	38.2766i		−	1.81857i	−0.416170	−	0.909287i	$-0.636628\pi$
$443$		−	38.2766i		−	1.81857i	0.416170	−	0.909287i	$-0.363372\pi$
$444$		0			0
$445$	−0.193576	−	1.37778i	−0.00917639	−	0.0653132i
$446$	−31.5843			−1.49556
$447$		0			0
$448$		−	43.4050i		−	2.05069i
$449$	−31.8479			−1.50300			−0.751498	−	0.659735i	$-0.770668\pi$
$449$	−31.8479			−1.50300			−0.751498	+	0.659735i	$0.770668\pi$
$450$		0			0
$451$	−1.80642			−0.0850612
$452$		−	0.927346i		−	0.0436187i
$453$		0			0
$454$	−7.70027			−0.361391
$455$	−6.32693	−	45.0321i	−0.296611	−	2.11114i
$456$		0			0
$457$			1.39207i			0.0651185i	0.999470	+	0.0325592i	$0.0103658\pi$
$457$			1.39207i			0.0651185i	−0.999470	+	0.0325592i	$0.989634\pi$
$458$			28.3269i			1.32363i
$459$		0			0
$460$	4.65386	−	0.653858i	0.216987	−	0.0304863i
$461$	7.70471			0.358844			0.179422	−	0.983772i	$-0.442577\pi$
$461$	7.70471			0.358844			0.179422	+	0.983772i	$0.442577\pi$
$462$		0			0
$463$		−	4.68244i		−	0.217611i	−0.994063	−	0.108806i	$-0.965297\pi$
$463$		−	4.68244i		−	0.217611i	0.994063	−	0.108806i	$-0.0347026\pi$
$464$	−4.82870			−0.224167
$465$		0			0
$466$	1.72885			0.0800873
$467$		−	12.8573i		−	0.594964i	−0.954727	−	0.297482i	$-0.903853\pi$
$467$		−	12.8573i		−	0.594964i	0.954727	−	0.297482i	$-0.0961468\pi$
$468$		0			0
$469$	23.8163			1.09973
$470$	−2.66370	−	18.9590i	−0.122867	−	0.874513i
$471$		0			0
$472$			5.13077i			0.236163i
$473$		−	4.90321i		−	0.225450i
$474$		0			0
$475$	−24.9175	+	7.14272i	−1.14329	+	0.327731i
$476$	−13.7364			−0.629605
$477$		0			0
$478$		−	23.0223i		−	1.05301i
$479$	8.38715			0.383219			0.191609	−	0.981471i	$-0.438629\pi$
$479$	8.38715			0.383219			0.191609	+	0.981471i	$0.438629\pi$
$480$		0			0
$481$	24.0830			1.09809
$482$		−	1.63465i		−	0.0744561i
$483$		0			0
$484$	0.525428			0.0238831
$485$	−6.10171	+	0.857279i	−0.277064	+	0.0389270i
$486$		0			0
$487$			9.83500i			0.445667i	0.974857	+	0.222833i	$0.0715306\pi$
$487$			9.83500i			0.445667i	−0.974857	+	0.222833i	$0.928469\pi$
$488$			2.31708i			0.104890i
$489$		0			0
$490$	−45.8227	+	6.43801i	−2.07006	+	0.290840i
$491$	32.9403			1.48657			0.743286	−	0.668973i	$-0.233266\pi$
$491$	32.9403			1.48657			0.743286	+	0.668973i	$0.233266\pi$
$492$		0			0
$493$			9.63158i			0.433785i
$494$	26.1106			1.17477
$495$		0			0
$496$	−7.00937			−0.314730
$497$		−	2.10171i		−	0.0942746i
$498$		0			0
$499$	1.63158			0.0730397			0.0365199	−	0.999333i	$-0.488373\pi$
$499$	1.63158			0.0730397			0.0365199	+	0.999333i	$0.488373\pi$
$500$	2.38868	+	5.36689i	0.106825	+	0.240014i
$501$		0			0
$502$		−	1.31450i		−	0.0586689i
$503$			41.8622i			1.86654i	0.359171	+	0.933272i	$0.383059\pi$
$503$			41.8622i			1.86654i	−0.359171	+	0.933272i	$0.616941\pi$
$504$		0			0
$505$	−5.53972	−	39.4291i	−0.246514	−	1.75457i
$506$	−4.85728			−0.215932
$507$		0			0
$508$			9.83056i			0.436160i
$509$	−38.8573			−1.72232			−0.861159	−	0.508335i	$-0.830261\pi$
$509$	−38.8573			−1.72232			−0.861159	+	0.508335i	$0.830261\pi$
$510$		0			0
$511$	62.3180			2.75679
$512$		−	24.1131i		−	1.06566i
$513$		0			0
$514$	−0.161933			−0.00714257
$515$	−10.9590	+	1.53972i	−0.482911	+	0.0678481i
$516$		0			0
$517$		−	7.05086i		−	0.310096i
$518$		−	34.5718i		−	1.51900i
$519$		0			0
$520$	−3.95713	−	28.1650i	−0.173532	−	1.23512i
$521$	−11.1111			−0.486785			−0.243393	−	0.969928i	$-0.578260\pi$
$521$	−11.1111			−0.486785			−0.243393	+	0.969928i	$0.578260\pi$
$522$		0			0
$523$		−	27.3002i		−	1.19375i	−0.802332	−	0.596877i	$-0.796408\pi$
$523$		−	27.3002i		−	1.19375i	0.802332	−	0.596877i	$-0.203592\pi$
$524$	0.653858			0.0285639
$525$		0			0
$526$	0.179286			0.00781724
$527$			13.9813i			0.609033i
$528$		0			0
$529$	7.00000			0.304348
$530$	−2.71408	−	19.3176i	−0.117892	−	0.839101i
$531$		0			0
$532$			13.3560i			0.579055i
$533$			7.49240i			0.324532i
$534$		0			0
$535$	−24.7971	+	3.48394i	−1.07207	+	0.150624i
$536$	14.8957			0.643396
$537$		0			0
$538$		−	32.6133i		−	1.40606i
$539$	−17.0415			−0.734029
$540$		0			0
$541$	−16.1017			−0.692267			−0.346133	−	0.938185i	$-0.612506\pi$
$541$	−16.1017			−0.692267			−0.346133	+	0.938185i	$0.612506\pi$
$542$			3.74314i			0.160782i
$543$		0			0
$544$	−15.3951			−0.660061
$545$	4.88892	+	34.7971i	0.209418	+	1.49054i
$546$		0			0
$547$			40.0370i			1.71186i	0.517091	+	0.855930i	$0.327015\pi$
$547$			40.0370i			1.71186i	−0.517091	+	0.855930i	$0.672985\pi$
$548$		−	9.87649i		−	0.421903i
$549$		0			0
$550$	−1.67307	−	5.83654i	−0.0713400	−	0.248871i
$551$	9.36488			0.398957
$552$		0			0
$553$			31.5210i			1.34041i
$554$	10.5763			0.449343
$555$		0			0
$556$	−7.37778			−0.312888
$557$			28.2908i			1.19872i	0.800479	+	0.599361i	$0.204578\pi$
$557$			28.2908i			1.19872i	−0.800479	+	0.599361i	$0.795422\pi$
$558$		0			0
$559$	−20.3368			−0.860154
$560$	−29.0223	+	4.07758i	−1.22641	+	0.172309i
$561$		0			0
$562$			24.7457i			1.04384i
$563$		−	32.7926i		−	1.38204i	−0.722834	−	0.691022i	$-0.757161\pi$
$563$		−	32.7926i		−	1.38204i	0.722834	−	0.691022i	$-0.242839\pi$
$564$		0			0
$565$	−3.90813	+	0.549086i	−0.164416	+	0.0231002i
$566$	−7.67752			−0.322710
$567$		0			0
$568$		−	1.31450i		−	0.0551551i
$569$	−8.88586			−0.372515			−0.186257	−	0.982501i	$-0.559636\pi$
$569$	−8.88586			−0.372515			−0.186257	+	0.982501i	$0.559636\pi$
$570$		0			0
$571$	−10.6953			−0.447586			−0.223793	−	0.974637i	$-0.571844\pi$
$571$	−10.6953			−0.447586			−0.223793	+	0.974637i	$0.571844\pi$
$572$		−	2.17929i		−	0.0911205i
$573$		0			0
$574$	10.7556			0.448929
$575$	−5.51114	−	19.2257i	−0.229830	−	0.801767i
$576$		0			0
$577$		−	27.1338i		−	1.12960i	−0.825229	−	0.564798i	$-0.808954\pi$
$577$		−	27.1338i		−	1.12960i	0.825229	−	0.564798i	$-0.191046\pi$
$578$		−	13.8780i		−	0.577250i
$579$		0			0
$580$	−0.295286	−	2.10171i	−0.0122611	−	0.0872688i
$581$	14.2351			0.590570
$582$		0			0
$583$		−	7.18421i		−	0.297540i
$584$	38.9763			1.61285
$585$		0			0
$586$	−20.2524			−0.836620
$587$			10.9590i			0.452326i	0.974089	+	0.226163i	$0.0726182\pi$
$587$			10.9590i			0.452326i	−0.974089	+	0.226163i	$0.927382\pi$
$588$		0			0
$589$	13.5941			0.560136
$590$	4.49871	−	0.632060i	0.185209	−	0.0260215i
$591$		0			0
$592$		−	15.5210i		−	0.637908i
$593$		−	23.7003i		−	0.973253i	−0.873610	−	0.486627i	$-0.838227\pi$
$593$		−	23.7003i		−	0.973253i	0.873610	−	0.486627i	$-0.161773\pi$
$594$		0			0
$595$	8.13335	+	57.8894i	0.333435	+	2.37323i
$596$	−1.60300			−0.0656616
$597$		0			0
$598$			20.1463i			0.823842i
$599$	41.7146			1.70441			0.852205	−	0.523208i	$-0.175265\pi$
$599$	41.7146			1.70441			0.852205	+	0.523208i	$0.175265\pi$
$600$		0			0
$601$	14.5906			0.595162			0.297581	−	0.954697i	$-0.403820\pi$
$601$	14.5906			0.595162			0.297581	+	0.954697i	$0.403820\pi$
$602$			29.1941i			1.18986i
$603$		0			0
$604$	−0.171778			−0.00698953
$605$	−0.311108	−	2.21432i	−0.0126483	−	0.0900249i
$606$		0			0
$607$		−	19.9826i		−	0.811071i	−0.914079	−	0.405535i	$-0.867085\pi$
$607$		−	19.9826i		−	0.811071i	0.914079	−	0.405535i	$-0.132915\pi$
$608$			14.9688i			0.607066i
$609$		0			0
$610$	2.03164	−	0.285442i	0.0822588	−	0.0115572i
$611$	−29.2444			−1.18310
$612$		0			0
$613$		−	19.0781i		−	0.770555i	−0.922801	−	0.385278i	$-0.874106\pi$
$613$		−	19.0781i		−	0.770555i	0.922801	−	0.385278i	$-0.125894\pi$
$614$	11.6400			0.469754
$615$		0			0
$616$	−15.0366			−0.605840
$617$			39.3590i			1.58454i	0.610174	+	0.792268i	$0.291100\pi$
$617$			39.3590i			1.58454i	−0.610174	+	0.792268i	$0.708900\pi$
$618$		0			0
$619$	23.0923			0.928160			0.464080	−	0.885793i	$-0.346385\pi$
$619$	23.0923			0.928160			0.464080	+	0.885793i	$0.346385\pi$
$620$	−0.428639	−	3.05086i	−0.0172146	−	0.122525i
$621$		0			0
$622$		−	17.6445i		−	0.707480i
$623$			3.05086i			0.122230i
$624$		0			0
$625$	21.2034	−	13.2444i	0.848137	−	0.529777i
$626$	−25.5397			−1.02077
$627$		0			0
$628$		−	10.4603i		−	0.417411i
$629$	−30.9590			−1.23442
$630$		0			0
$631$	−25.5111			−1.01558			−0.507791	−	0.861480i	$-0.669538\pi$
$631$	−25.5111			−1.01558			−0.507791	+	0.861480i	$0.669538\pi$
$632$			19.7146i			0.784203i
$633$		0			0
$634$	−1.20294			−0.0477750
$635$	41.4291	−	5.82071i	1.64406	−	0.230988i
$636$		0			0
$637$			70.6820i			2.80052i
$638$			2.19358i			0.0868445i
$639$		0			0
$640$	−11.0158	+	1.54770i	−0.435439	+	0.0611783i
$641$	6.25380			0.247010			0.123505	−	0.992344i	$-0.460586\pi$
$641$	6.25380			0.247010			0.123505	+	0.992344i	$0.460586\pi$
$642$		0			0
$643$		−	6.84743i		−	0.270036i	−0.990843	−	0.135018i	$-0.956891\pi$
$643$		−	6.84743i		−	0.270036i	0.990843	−	0.135018i	$-0.0431093\pi$
$644$	−10.3051			−0.406079
$645$		0			0
$646$	−33.5655			−1.32062
$647$		−	20.2953i		−	0.797890i	−0.916975	−	0.398945i	$-0.869376\pi$
$647$		−	20.2953i		−	0.797890i	0.916975	−	0.398945i	$-0.130624\pi$
$648$		0			0
$649$	1.67307			0.0656738
$650$	−24.2079	+	6.93930i	−0.949511	+	0.272182i
$651$		0			0
$652$		−	6.39700i		−	0.250526i
$653$		−	10.6222i		−	0.415679i	−0.978163	−	0.207840i	$-0.933357\pi$
$653$		−	10.6222i		−	0.415679i	0.978163	−	0.207840i	$-0.0666432\pi$
$654$		0			0
$655$	−0.387152	−	2.75557i	−0.0151273	−	0.107669i
$656$	4.82870			0.188529
$657$		0			0
$658$			41.9813i			1.63660i
$659$	10.1017			0.393507			0.196753	−	0.980453i	$-0.436960\pi$
$659$	10.1017			0.393507			0.196753	+	0.980453i	$0.436960\pi$
$660$		0			0
$661$	21.6128			0.840642			0.420321	−	0.907375i	$-0.361917\pi$
$661$	21.6128			0.840642			0.420321	+	0.907375i	$0.361917\pi$
$662$		−	21.3492i		−	0.829760i
$663$		0			0
$664$	8.90321			0.345512
$665$	56.2864	−	7.90813i	2.18269	−	0.306664i
$666$		0			0
$667$			7.22570i			0.279780i
$668$		−	6.83314i		−	0.264382i
$669$		0			0
$670$	−1.83500	−	13.0607i	−0.0708924	−	0.504579i
$671$	0.755569			0.0291684
$672$		0			0
$673$		−	10.2208i		−	0.393982i	−0.980405	−	0.196991i	$-0.936883\pi$
$673$		−	10.2208i		−	0.393982i	0.980405	−	0.196991i	$-0.0631170\pi$
$674$	3.84929			0.148269
$675$		0			0
$676$	−2.20834			−0.0849363
$677$		−	13.9224i		−	0.535082i	−0.963546	−	0.267541i	$-0.913789\pi$
$677$		−	13.9224i		−	0.535082i	0.963546	−	0.267541i	$-0.0862111\pi$
$678$		0			0
$679$	13.5111			0.518510
$680$	5.08694	+	36.2065i	0.195075	+	1.38846i
$681$		0			0
$682$			3.18421i			0.121930i
$683$		−	10.3970i		−	0.397830i	−0.980017	−	0.198915i	$-0.936258\pi$
$683$		−	10.3970i		−	0.397830i	0.980017	−	0.198915i	$-0.0637418\pi$
$684$		0			0
$685$	−41.6227	+	5.84791i	−1.59032	+	0.223437i
$686$	59.7877			2.28270
$687$		0			0
$688$			13.1066i			0.499686i
$689$	−29.7975			−1.13520
$690$		0			0
$691$	−0.977725			−0.0371944			−0.0185972	−	0.999827i	$-0.505920\pi$
$691$	−0.977725			−0.0371944			−0.0185972	+	0.999827i	$0.505920\pi$
$692$			7.30021i			0.277512i
$693$		0			0
$694$	6.04287			0.229384
$695$	4.36842	+	31.0923i	0.165703	+	1.17940i
$696$		0			0
$697$		−	9.63158i		−	0.364822i
$698$		−	22.1048i		−	0.836678i
$699$		0			0
$700$	−3.54956	−	12.3827i	−0.134161	−	0.468022i
$701$	−48.9688			−1.84953			−0.924764	−	0.380542i	$-0.875737\pi$
$701$	−48.9688			−1.84953			−0.924764	+	0.380542i	$0.875737\pi$
$702$		0			0
$703$			30.1017i			1.13531i
$704$	−8.85236			−0.333636
$705$		0			0
$706$	−27.2128			−1.02417
$707$			87.3087i			3.28358i
$708$		0			0
$709$	37.2672			1.39960			0.699799	−	0.714340i	$-0.253273\pi$
$709$	37.2672			1.39960			0.699799	+	0.714340i	$0.253273\pi$
$710$	−1.15257	+	0.161933i	−0.0432550	+	0.00607725i
$711$		0			0
$712$			1.90813i			0.0715103i
$713$			10.4889i			0.392811i
$714$		0			0
$715$	−9.18421	+	1.29036i	−0.343470	+	0.0482569i
$716$	6.75557			0.252467
$717$		0			0
$718$			25.8983i			0.966516i
$719$	5.83500			0.217609			0.108804	−	0.994063i	$-0.465298\pi$
$719$	5.83500			0.217609			0.108804	+	0.994063i	$0.465298\pi$
$720$		0			0
$721$	24.2667			0.903739
$722$			9.56400i			0.355935i
$723$		0			0
$724$	0.482081			0.0179164
$725$	−8.68244	+	2.48886i	−0.322458	+	0.0924340i
$726$		0			0
$727$		−	46.8385i		−	1.73715i	−0.495562	−	0.868573i	$-0.665038\pi$
$727$		−	46.8385i		−	1.73715i	0.495562	−	0.868573i	$-0.334962\pi$
$728$			62.3663i			2.31145i
$729$		0			0
$730$	−4.80150	−	34.1748i	−0.177712	−	1.26487i
$731$	26.1432			0.966941
$732$		0			0
$733$			45.2083i			1.66981i	0.550395	+	0.834904i	$0.314477\pi$
$733$			45.2083i			1.66981i	−0.550395	+	0.834904i	$0.685523\pi$
$734$	−42.6637			−1.57475
$735$		0			0
$736$	−11.5496			−0.425723
$737$		−	4.85728i		−	0.178920i
$738$		0			0
$739$	−5.65433			−0.207998			−0.103999	−	0.994577i	$-0.533164\pi$
$739$	−5.65433			−0.207998			−0.103999	+	0.994577i	$0.533164\pi$
$740$	6.75557	−	0.949145i	0.248340	−	0.0348913i
$741$		0			0
$742$			42.7753i			1.57033i
$743$			4.50622i			0.165317i	0.996578	+	0.0826585i	$0.0263411\pi$
$743$			4.50622i			0.165317i	−0.996578	+	0.0826585i	$0.973659\pi$
$744$		0			0
$745$	0.949145	+	6.75557i	0.0347740	+	0.247505i
$746$	−20.6494			−0.756029
$747$		0			0
$748$			2.80150i			0.102433i
$749$	54.9086			2.00632
$750$		0			0
$751$	47.5121			1.73374			0.866870	−	0.498534i	$-0.166128\pi$
$751$	47.5121			1.73374			0.866870	+	0.498534i	$0.166128\pi$
$752$			18.8474i			0.687295i
$753$		0			0
$754$	9.09817			0.331336
$755$	0.101710	+	0.723926i	0.00370161	+	0.0263464i
$756$		0			0
$757$		−	46.6637i		−	1.69602i	−0.529979	−	0.848011i	$-0.677800\pi$
$757$		−	46.6637i		−	1.69602i	0.529979	−	0.848011i	$-0.322200\pi$
$758$		−	2.87601i		−	0.104462i
$759$		0			0
$760$	35.2039	−	4.94608i	1.27698	−	0.179413i
$761$	−14.9304			−0.541227			−0.270613	−	0.962688i	$-0.587227\pi$
$761$	−14.9304			−0.541227			−0.270613	+	0.962688i	$0.587227\pi$
$762$		0			0
$763$		−	77.0518i		−	2.78946i
$764$	−7.54956			−0.273134
$765$		0			0
$766$	−1.47643			−0.0533457
$767$		−	6.93930i		−	0.250564i
$768$		0			0
$769$	−38.8573			−1.40123			−0.700615	−	0.713540i	$-0.747091\pi$
$769$	−38.8573			−1.40123			−0.700615	+	0.713540i	$0.747091\pi$
$770$	1.85236	+	13.1842i	0.0667543	+	0.475126i
$771$		0			0
$772$			6.17929i			0.222397i
$773$		−	36.3368i		−	1.30694i	−0.756951	−	0.653471i	$-0.773312\pi$
$773$		−	36.3368i		−	1.30694i	0.756951	−	0.653471i	$-0.226688\pi$
$774$		0			0
$775$	−12.6035	+	3.61285i	−0.452730	+	0.129777i
$776$	8.45044			0.303353
$777$		0			0
$778$			2.75251i			0.0986821i
$779$	−9.36488			−0.335532
$780$		0			0
$781$	−0.428639			−0.0153379
$782$		−	25.8983i		−	0.926121i
$783$		0			0
$784$	45.5531			1.62690
$785$	−44.0830	+	6.19358i	−1.57339	+	0.221058i
$786$		0			0
$787$		−	33.5482i		−	1.19586i	−0.801547	−	0.597932i	$-0.795989\pi$
$787$		−	33.5482i		−	1.19586i	0.801547	−	0.597932i	$-0.204011\pi$
$788$			2.00751i			0.0715145i
$789$		0			0
$790$	17.2859	−	2.42864i	0.615005	−	0.0864071i
$791$	8.65386			0.307696
$792$		0			0
$793$		−	3.13383i		−	0.111286i
$794$	22.4514			0.796770
$795$		0			0
$796$	7.20601			0.255410
$797$			16.1334i			0.571473i	0.958308	+	0.285736i	$0.0922382\pi$
$797$			16.1334i			0.571473i	−0.958308	+	0.285736i	$0.907762\pi$
$798$		0			0
$799$	37.5941			1.32998
$800$	−3.97820	−	13.8780i	−0.140651	−	0.490662i
$801$		0			0
$802$		−	21.3265i		−	0.753063i
$803$		−	12.7096i		−	0.448513i
$804$		0			0
$805$	6.10171	+	43.4291i	0.215057	+	1.53068i
$806$	13.2070			0.465195
$807$		0			0
$808$			54.6065i			1.92105i
$809$	25.7431			0.905081			0.452540	−	0.891744i	$-0.350518\pi$
$809$	25.7431			0.905081			0.452540	+	0.891744i	$0.350518\pi$
$810$		0			0
$811$	13.4509			0.472325			0.236163	−	0.971714i	$-0.424110\pi$
$811$	13.4509			0.472325			0.236163	+	0.971714i	$0.424110\pi$
$812$			4.65386i			0.163318i
$813$		0			0
$814$	−7.05086			−0.247132
$815$	−26.9590	+	3.78769i	−0.944332	+	0.132677i
$816$		0			0
$817$		−	25.4193i		−	0.889308i
$818$			25.9210i			0.906308i
$819$		0			0
$820$	0.295286	+	2.10171i	0.0103118	+	0.0733949i
$821$	−24.1748			−0.843708			−0.421854	−	0.906664i	$-0.638620\pi$
$821$	−24.1748			−0.843708			−0.421854	+	0.906664i	$0.638620\pi$
$822$		0			0
$823$			40.9117i			1.42609i	0.701118	+	0.713046i	$0.252685\pi$
$823$			40.9117i			1.42609i	−0.701118	+	0.713046i	$0.747315\pi$
$824$	15.1774			0.528731
$825$		0			0
$826$	−9.96158			−0.346608
$827$			20.1476i			0.700602i	0.936637	+	0.350301i	$0.113921\pi$
$827$			20.1476i			0.700602i	−0.936637	+	0.350301i	$0.886079\pi$
$828$		0			0
$829$	−31.4322			−1.09168			−0.545842	−	0.837888i	$-0.683790\pi$
$829$	−31.4322			−1.09168			−0.545842	+	0.837888i	$0.683790\pi$
$830$	−1.09679	−	7.80642i	−0.0380701	−	0.270965i
$831$		0			0
$832$			36.7164i			1.27291i
$833$		−	90.8627i		−	3.14821i
$834$		0			0
$835$	−28.7971	+	4.04593i	−0.996563	+	0.140015i
$836$	2.72393			0.0942089
$837$		0			0
$838$			35.0420i			1.21050i
$839$	−52.8988			−1.82627			−0.913134	−	0.407659i	$-0.866345\pi$
$839$	−52.8988			−1.82627			−0.913134	+	0.407659i	$0.866345\pi$
$840$		0			0
$841$	−25.7368			−0.887477
$842$		−	43.0954i		−	1.48517i
$843$		0			0
$844$	1.02906			0.0354216
$845$	1.30757	+	9.30666i	0.0449817	+	0.320159i
$846$		0			0
$847$			4.90321i			0.168476i
$848$			19.2039i			0.659465i
$849$		0			0
$850$	31.1195	−	8.92056i	1.06739	−	0.305973i
$851$	−23.2257			−0.796167
$852$		0			0
$853$			46.9229i			1.60661i	0.595568	+	0.803305i	$0.296927\pi$
$853$			46.9229i			1.60661i	−0.595568	+	0.803305i	$0.703073\pi$
$854$	−4.49871			−0.153943
$855$		0			0
$856$	34.3422			1.17379
$857$			25.1481i			0.859043i	0.903057	+	0.429522i	$0.141318\pi$
$857$			25.1481i			0.859043i	−0.903057	+	0.429522i	$0.858682\pi$
$858$		0			0
$859$	−1.84791			−0.0630499			−0.0315250	−	0.999503i	$-0.510036\pi$
$859$	−1.84791			−0.0630499			−0.0315250	+	0.999503i	$0.510036\pi$
$860$	−5.70471	+	0.801502i	−0.194529	+	0.0273310i
$861$		0			0
$862$		−	11.2257i		−	0.382349i
$863$			32.6824i			1.11252i	0.831007	+	0.556262i	$0.187765\pi$
$863$			32.6824i			1.11252i	−0.831007	+	0.556262i	$0.812235\pi$
$864$		0			0
$865$	30.7654	−	4.32248i	1.04606	−	0.146969i
$866$	−7.63254			−0.259364
$867$		0			0
$868$			6.75557i			0.229299i
$869$	6.42864			0.218077
$870$		0			0
$871$	−20.1463			−0.682630
$872$		−	48.1915i		−	1.63197i
$873$		0			0
$874$	−25.1811			−0.851765
$875$	−50.0830	+	22.2908i	−1.69311	+	0.753568i
$876$		0			0
$877$			49.1798i			1.66068i	0.557255	+	0.830341i	$0.311855\pi$
$877$			49.1798i			1.66068i	−0.557255	+	0.830341i	$0.688145\pi$
$878$			44.3595i			1.49706i
$879$		0			0
$880$	0.831613	+	5.91903i	0.0280337	+	0.199531i
$881$	−33.8163			−1.13930			−0.569650	−	0.821888i	$-0.692921\pi$
$881$	−33.8163			−1.13930			−0.569650	+	0.821888i	$0.692921\pi$
$882$		0			0
$883$		−	24.7368i		−	0.832461i	−0.909259	−	0.416230i	$-0.863351\pi$
$883$		−	24.7368i		−	0.832461i	0.909259	−	0.416230i	$-0.136649\pi$
$884$	11.6196			0.390810
$885$		0			0
$886$	46.4800			1.56153
$887$		−	7.64004i		−	0.256528i	−0.991740	−	0.128264i	$-0.959060\pi$
$887$		−	7.64004i		−	0.256528i	0.991740	−	0.128264i	$-0.0409404\pi$
$888$		0			0
$889$	−91.7373			−3.07677
$890$	1.67307	−	0.235063i	0.0560815	−	0.00787934i
$891$		0			0
$892$			13.6663i			0.457581i
$893$		−	36.5531i		−	1.22320i
$894$		0			0
$895$	−4.00000	−	28.4701i	−0.133705	−	0.951651i
$896$	24.3926			0.814898
$897$		0			0
$898$		−	38.6735i		−	1.29055i
$899$	4.73683			0.157982
$900$		0			0
$901$	38.3051			1.27613
$902$		−	2.19358i		−	0.0730381i
$903$		0			0
$904$	5.41249			0.180017
$905$	−0.285442	−	2.03164i	−0.00948841	−	0.0675341i
$906$		0			0
$907$		−	30.3970i		−	1.00932i	−0.863319	−	0.504658i	$-0.831619\pi$
$907$		−	30.3970i		−	1.00932i	0.863319	−	0.504658i	$-0.168381\pi$
$908$			3.33185i			0.110571i
$909$		0			0
$910$	54.6834	−	7.68292i	1.81274	−	0.254686i
$911$	45.3274			1.50176			0.750882	−	0.660436i	$-0.229629\pi$
$911$	45.3274			1.50176			0.750882	+	0.660436i	$0.229629\pi$
$912$		0			0
$913$		−	2.90321i		−	0.0960823i
$914$	−1.69042			−0.0559142
$915$		0			0
$916$	12.2569			0.404978
$917$			6.10171i			0.201496i
$918$		0			0
$919$	16.3269			0.538576			0.269288	−	0.963060i	$-0.413212\pi$
$919$	16.3269			0.538576			0.269288	+	0.963060i	$0.413212\pi$
$920$	3.81627	+	27.1624i	0.125819	+	0.895518i
$921$		0			0
$922$			9.35599i			0.308123i
$923$			1.77784i			0.0585184i
$924$		0			0
$925$	−8.00000	−	27.9081i	−0.263038	−	0.917614i
$926$	5.68598			0.186853
$927$		0			0
$928$			5.21585i			0.171219i
$929$	−29.6128			−0.971566			−0.485783	−	0.874079i	$-0.661465\pi$
$929$	−29.6128			−0.971566			−0.485783	+	0.874079i	$0.661465\pi$
$930$		0			0
$931$	−88.3466			−2.89544
$932$		−	0.748060i		−	0.0245035i
$933$		0			0
$934$	15.6128			0.510868
$935$	11.8064	−	1.65878i	0.386111	−	0.0542479i
$936$		0			0
$937$			8.92195i			0.291467i	0.989324	+	0.145734i	$0.0465543\pi$
$937$			8.92195i			0.291467i	−0.989324	+	0.145734i	$0.953446\pi$
$938$			28.9206i			0.944290i
$939$		0			0
$940$	−8.20342	+	1.15257i	−0.267566	+	0.0375925i
$941$	22.2766			0.726195			0.363097	−	0.931751i	$-0.381719\pi$
$941$	22.2766			0.726195			0.363097	+	0.931751i	$0.381719\pi$
$942$		0			0
$943$		−	7.22570i		−	0.235301i
$944$	−4.47224			−0.145559
$945$		0			0
$946$	5.95407			0.193583
$947$		−	44.4612i		−	1.44480i	−0.691477	−	0.722398i	$-0.743040\pi$
$947$		−	44.4612i		−	1.44480i	0.691477	−	0.722398i	$-0.256960\pi$
$948$		0			0
$949$	−52.7150			−1.71120
$950$	−8.67355	−	30.2578i	−0.281407	−	0.981693i
$951$		0			0
$952$		−	80.1727i		−	2.59841i
$953$			20.5575i			0.665924i	0.942940	+	0.332962i	$0.108048\pi$
$953$			20.5575i			0.665924i	−0.942940	+	0.332962i	$0.891952\pi$
$954$		0			0
$955$	4.47013	+	31.8163i	0.144650	+	1.02955i
$956$	−9.96158			−0.322180
$957$		0			0
$958$			10.1847i			0.329052i
$959$	92.1659			2.97619
$960$		0			0
$961$	−24.1240			−0.778193
$962$			29.2444i			0.942878i
$963$		0			0
$964$	−0.707300			−0.0227806
$965$	26.0415	−	3.65878i	0.838305	−	0.117780i
$966$		0			0
$967$			27.4839i			0.883824i	0.897058	+	0.441912i	$0.145700\pi$
$967$			27.4839i			0.883824i	−0.897058	+	0.441912i	$0.854300\pi$
$968$			3.06668i			0.0985667i
$969$		0			0
$970$	−1.04101	−	7.40943i	−0.0334248	−	0.237902i
$971$	5.81532			0.186622			0.0933112	−	0.995637i	$-0.470255\pi$
$971$	5.81532			0.186622			0.0933112	+	0.995637i	$0.470255\pi$
$972$		0			0
$973$		−	68.8484i		−	2.20718i
$974$	−11.9428			−0.382673
$975$		0			0
$976$	−2.01969			−0.0646487
$977$		−	48.3912i		−	1.54817i	−0.633081	−	0.774085i	$-0.718210\pi$
$977$		−	48.3912i		−	1.54817i	0.633081	−	0.774085i	$-0.281790\pi$
$978$		0			0
$979$	0.622216			0.0198861
$980$	2.78568	+	19.8272i	0.0889853	+	0.633356i
$981$		0			0
$982$			40.0000i			1.27645i
$983$		−	49.9724i		−	1.59387i	−0.604064	−	0.796936i	$-0.706453\pi$
$983$		−	49.9724i		−	1.59387i	0.604064	−	0.796936i	$-0.293547\pi$
$984$		0			0
$985$	8.46028	−	1.18865i	0.269567	−	0.0378737i
$986$	−11.6958			−0.372471
$987$		0			0
$988$		−	11.2979i		−	0.359433i
$989$	19.6128			0.623652
$990$		0			0
$991$	−7.35905			−0.233768			−0.116884	−	0.993146i	$-0.537291\pi$
$991$	−7.35905			−0.233768			−0.116884	+	0.993146i	$0.537291\pi$
$992$			7.57136i			0.240391i
$993$		0			0
$994$	2.55215			0.0809492
$995$	−4.26671	−	30.3684i	−0.135264	−	0.962744i
$996$		0			0
$997$		−	4.33138i		−	0.137176i	−0.997645	−	0.0685880i	$-0.978151\pi$
$997$		−	4.33138i		−	0.137176i	0.997645	−	0.0685880i	$-0.0218494\pi$
$998$			1.98126i			0.0627158i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.c.d.199.4		6
3.2	odd	2		165.2.c.a.34.3	✓	6
5.2	odd	4		2475.2.a.be.1.1		3
5.3	odd	4		2475.2.a.y.1.3		3
5.4	even	2	inner	495.2.c.d.199.3		6
12.11	even	2		2640.2.d.i.529.2		6
15.2	even	4		825.2.a.h.1.3		3
15.8	even	4		825.2.a.n.1.1		3
15.14	odd	2		165.2.c.a.34.4	yes	6
33.32	even	2		1815.2.c.d.364.4		6
60.59	even	2		2640.2.d.i.529.5		6
165.32	odd	4		9075.2.a.ck.1.1		3
165.98	odd	4		9075.2.a.cc.1.3		3
165.164	even	2		1815.2.c.d.364.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.c.a.34.3	✓	6	3.2	odd	2
165.2.c.a.34.4	yes	6	15.14	odd	2
495.2.c.d.199.3		6	5.4	even	2	inner
495.2.c.d.199.4		6	1.1	even	1	trivial
825.2.a.h.1.3		3	15.2	even	4
825.2.a.n.1.1		3	15.8	even	4
1815.2.c.d.364.3		6	165.164	even	2
1815.2.c.d.364.4		6	33.32	even	2
2475.2.a.y.1.3		3	5.3	odd	4
2475.2.a.be.1.1		3	5.2	odd	4
2640.2.d.i.529.2		6	12.11	even	2
2640.2.d.i.529.5		6	60.59	even	2
9075.2.a.cc.1.3		3	165.98	odd	4
9075.2.a.ck.1.1		3	165.32	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.21432i q^{2} +0.525428 q^{4} +(-0.311108 - 2.21432i) q^{5} +4.90321i q^{7} +3.06668i q^{8} +O(q^{10})\)	\(q+1.21432i q^{2} +0.525428 q^{4} +(-0.311108 - 2.21432i) q^{5} +4.90321i q^{7} +3.06668i q^{8} +(2.68889 - 0.377784i) q^{10} +1.00000 q^{11} -4.14764i q^{13} -5.95407 q^{14} -2.67307 q^{16} +5.33185i q^{17} +5.18421 q^{19} +(-0.163465 - 1.16346i) q^{20} +1.21432i q^{22} +4.00000i q^{23} +(-4.80642 + 1.37778i) q^{25} +5.03657 q^{26} +2.57628i q^{28} +1.80642 q^{29} +2.62222 q^{31} +2.88739i q^{32} -6.47457 q^{34} +(10.8573 - 1.52543i) q^{35} +5.80642i q^{37} +6.29529i q^{38} +(6.79060 - 0.954067i) q^{40} -1.80642 q^{41} -4.90321i q^{43} +0.525428 q^{44} -4.85728 q^{46} -7.05086i q^{47} -17.0415 q^{49} +(-1.67307 - 5.83654i) q^{50} -2.17929i q^{52} -7.18421i q^{53} +(-0.311108 - 2.21432i) q^{55} -15.0366 q^{56} +2.19358i q^{58} +1.67307 q^{59} +0.755569 q^{61} +3.18421i q^{62} -8.85236 q^{64} +(-9.18421 + 1.29036i) q^{65} -4.85728i q^{67} +2.80150i q^{68} +(1.85236 + 13.1842i) q^{70} -0.428639 q^{71} -12.7096i q^{73} -7.05086 q^{74} +2.72393 q^{76} +4.90321i q^{77} +6.42864 q^{79} +(0.831613 + 5.91903i) q^{80} -2.19358i q^{82} -2.90321i q^{83} +(11.8064 - 1.65878i) q^{85} +5.95407 q^{86} +3.06668i q^{88} +0.622216 q^{89} +20.3368 q^{91} +2.10171i q^{92} +8.56199 q^{94} +(-1.61285 - 11.4795i) q^{95} -2.75557i q^{97} -20.6938i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} - 2 q^{5}+O(q^{10}) \) 6 * q - 10 * q^4 - 2 * q^5	\( 6 q - 10 q^{4} - 2 q^{5} + 16 q^{10} + 6 q^{11} + 4 q^{14} + 10 q^{16} + 4 q^{19} - 14 q^{20} - 2 q^{25} + 16 q^{26} - 16 q^{29} + 16 q^{31} - 52 q^{34} + 12 q^{35} - 12 q^{40} + 16 q^{41} - 10 q^{44} + 24 q^{46} - 22 q^{49} + 16 q^{50} - 2 q^{55} - 76 q^{56} - 16 q^{59} + 4 q^{61} - 66 q^{64} - 28 q^{65} + 24 q^{70} + 24 q^{71} - 16 q^{74} - 36 q^{76} + 12 q^{79} + 58 q^{80} + 44 q^{85} - 4 q^{86} + 4 q^{89} + 16 q^{91} + 24 q^{94} + 44 q^{95}+O(q^{100}) \) 6 * q - 10 * q^4 - 2 * q^5 + 16 * q^10 + 6 * q^11 + 4 * q^14 + 10 * q^16 + 4 * q^19 - 14 * q^20 - 2 * q^25 + 16 * q^26 - 16 * q^29 + 16 * q^31 - 52 * q^34 + 12 * q^35 - 12 * q^40 + 16 * q^41 - 10 * q^44 + 24 * q^46 - 22 * q^49 + 16 * q^50 - 2 * q^55 - 76 * q^56 - 16 * q^59 + 4 * q^61 - 66 * q^64 - 28 * q^65 + 24 * q^70 + 24 * q^71 - 16 * q^74 - 36 * q^76 + 12 * q^79 + 58 * q^80 + 44 * q^85 - 4 * q^86 + 4 * q^89 + 16 * q^91 + 24 * q^94 + 44 * q^95

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