LMFDB - Embedded newform 405.2.e.j.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.1
Root			$1.15139 + 1.99426i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.2.e.j.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15139 - 1.99426i) q^{2} +(-1.65139 + 2.86029i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.30278 + 2.25647i) q^{7} +3.00000 q^{8} +O(q^{10})$	\(q+(-1.15139 - 1.99426i) q^{2} +(-1.65139 + 2.86029i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.30278 + 2.25647i) q^{7} +3.00000 q^{8} -2.30278 q^{10} +(2.30278 + 3.98852i) q^{11} +(-3.30278 + 5.72058i) q^{13} +(3.00000 - 5.19615i) q^{14} +(-0.151388 - 0.262211i) q^{16} -1.60555 q^{17} +3.60555 q^{19} +(1.65139 + 2.86029i) q^{20} +(5.30278 - 9.18468i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +15.2111 q^{26} -8.60555 q^{28} +(0.697224 + 1.20763i) q^{29} +(2.80278 - 4.85455i) q^{31} +(2.65139 - 4.59234i) q^{32} +(1.84861 + 3.20189i) q^{34} +2.60555 q^{35} +2.00000 q^{37} +(-4.15139 - 7.19041i) q^{38} +(1.50000 - 2.59808i) q^{40} +(-2.30278 + 3.98852i) q^{41} +(-0.302776 - 0.524423i) q^{43} -15.2111 q^{44} +6.90833 q^{46} +(-4.60555 - 7.97705i) q^{47} +(0.105551 - 0.182820i) q^{49} +(-1.15139 + 1.99426i) q^{50} +(-10.9083 - 18.8938i) q^{52} -1.60555 q^{53} +4.60555 q^{55} +(3.90833 + 6.76942i) q^{56} +(1.60555 - 2.78090i) q^{58} +(-0.697224 + 1.20763i) q^{59} +(2.10555 + 3.64692i) q^{61} -12.9083 q^{62} -12.8167 q^{64} +(3.30278 + 5.72058i) q^{65} +(0.394449 - 0.683205i) q^{67} +(2.65139 - 4.59234i) q^{68} +(-3.00000 - 5.19615i) q^{70} -7.39445 q^{71} +12.6056 q^{73} +(-2.30278 - 3.98852i) q^{74} +(-5.95416 + 10.3129i) q^{76} +(-6.00000 + 10.3923i) q^{77} +(5.80278 + 10.0507i) q^{79} -0.302776 q^{80} +10.6056 q^{82} +(1.50000 + 2.59808i) q^{83} +(-0.802776 + 1.39045i) q^{85} +(-0.697224 + 1.20763i) q^{86} +(6.90833 + 11.9656i) q^{88} +13.8167 q^{89} -17.2111 q^{91} +(-4.95416 - 8.58086i) q^{92} +(-10.6056 + 18.3694i) q^{94} +(1.80278 - 3.12250i) q^{95} +(-4.00000 - 6.92820i) q^{97} -0.486122 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q - q^2 - 3 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8	$ 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} - 2 q^{10} + 2 q^{11} - 6 q^{13} + 12 q^{14} + 3 q^{16} + 8 q^{17} + 3 q^{20} + 14 q^{22} - 6 q^{23} - 2 q^{25} + 32 q^{26} - 20 q^{28} + 10 q^{29} + 4 q^{31} + 7 q^{32} + 11 q^{34} - 4 q^{35} + 8 q^{37} - 13 q^{38} + 6 q^{40} - 2 q^{41} + 6 q^{43} - 32 q^{44} + 6 q^{46} - 4 q^{47} - 14 q^{49} - q^{50} - 22 q^{52} + 8 q^{53} + 4 q^{55} - 6 q^{56} - 8 q^{58} - 10 q^{59} - 6 q^{61} - 30 q^{62} - 8 q^{64} + 6 q^{65} + 16 q^{67} + 7 q^{68} - 12 q^{70} - 44 q^{71} + 36 q^{73} - 2 q^{74} - 13 q^{76} - 24 q^{77} + 16 q^{79} + 6 q^{80} + 28 q^{82} + 6 q^{83} + 4 q^{85} - 10 q^{86} + 6 q^{88} + 12 q^{89} - 40 q^{91} - 9 q^{92} - 28 q^{94} - 16 q^{97} - 38 q^{98}+O(q^{100}) $ 4 * q - q^2 - 3 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8 - 2 * q^10 + 2 * q^11 - 6 * q^13 + 12 * q^14 + 3 * q^16 + 8 * q^17 + 3 * q^20 + 14 * q^22 - 6 * q^23 - 2 * q^25 + 32 * q^26 - 20 * q^28 + 10 * q^29 + 4 * q^31 + 7 * q^32 + 11 * q^34 - 4 * q^35 + 8 * q^37 - 13 * q^38 + 6 * q^40 - 2 * q^41 + 6 * q^43 - 32 * q^44 + 6 * q^46 - 4 * q^47 - 14 * q^49 - q^50 - 22 * q^52 + 8 * q^53 + 4 * q^55 - 6 * q^56 - 8 * q^58 - 10 * q^59 - 6 * q^61 - 30 * q^62 - 8 * q^64 + 6 * q^65 + 16 * q^67 + 7 * q^68 - 12 * q^70 - 44 * q^71 + 36 * q^73 - 2 * q^74 - 13 * q^76 - 24 * q^77 + 16 * q^79 + 6 * q^80 + 28 * q^82 + 6 * q^83 + 4 * q^85 - 10 * q^86 + 6 * q^88 + 12 * q^89 - 40 * q^91 - 9 * q^92 - 28 * q^94 - 16 * q^97 - 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.15139	−	1.99426i	−0.814154	−	1.41016i	−0.909934	−	0.414754i	$-0.863868\pi$
$2$	−1.15139	−	1.99426i	−0.814154	−	1.41016i	0.0957796	−	0.995403i	$-0.469466\pi$
$3$		0			0
$3$		0			0
$4$	−1.65139	+	2.86029i	−0.825694	+	1.43014i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.30278	+	2.25647i	0.492403	+	0.852867i	0.999962	−	0.00875026i	$-0.00278533\pi$
$7$	1.30278	+	2.25647i	0.492403	+	0.852867i	−0.507559	+	0.861617i	$0.669452\pi$
$8$	3.00000			1.06066
$9$		0			0
$10$	−2.30278			−0.728202
$11$	2.30278	+	3.98852i	0.694313	+	1.20259i	0.970412	+	0.241456i	$0.0776250\pi$
$11$	2.30278	+	3.98852i	0.694313	+	1.20259i	−0.276099	+	0.961129i	$0.589042\pi$
$12$		0			0
$13$	−3.30278	+	5.72058i	−0.916025	+	1.58660i	−0.110632	+	0.993861i	$0.535287\pi$
$13$	−3.30278	+	5.72058i	−0.916025	+	1.58660i	−0.805393	+	0.592741i	$0.798046\pi$
$14$	3.00000	−	5.19615i	0.801784	−	1.38873i
$15$		0			0
$16$	−0.151388	−	0.262211i	−0.0378470	−	0.0655528i
$17$	−1.60555			−0.389403			−0.194702	−	0.980863i	$-0.562374\pi$
$17$	−1.60555			−0.389403			−0.194702	+	0.980863i	$0.562374\pi$
$18$		0			0
$19$	3.60555			0.827170			0.413585	−	0.910465i	$-0.364276\pi$
$19$	3.60555			0.827170			0.413585	+	0.910465i	$0.364276\pi$
$20$	1.65139	+	2.86029i	0.369262	+	0.639580i
$21$		0			0
$22$	5.30278	−	9.18468i	1.13056	−	1.95818i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	15.2111			2.98314
$27$		0			0
$28$	−8.60555			−1.62630
$29$	0.697224	+	1.20763i	0.129471	+	0.224251i	0.923472	−	0.383666i	$-0.125339\pi$
$29$	0.697224	+	1.20763i	0.129471	+	0.224251i	−0.794001	+	0.607917i	$0.792005\pi$
$30$		0			0
$31$	2.80278	−	4.85455i	0.503393	−	0.871903i	−0.496599	−	0.867980i	$-0.665418\pi$
$31$	2.80278	−	4.85455i	0.503393	−	0.871903i	0.999992	−	0.00392276i	$-0.00124866\pi$
$32$	2.65139	−	4.59234i	0.468704	−	0.811818i
$33$		0			0
$34$	1.84861	+	3.20189i	0.317034	+	0.549120i
$35$	2.60555			0.440419
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−4.15139	−	7.19041i	−0.673444	−	1.16644i
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	−2.30278	+	3.98852i	−0.359633	+	0.622903i	−0.987899	−	0.155095i	$-0.950431\pi$
$41$	−2.30278	+	3.98852i	−0.359633	+	0.622903i	0.628266	+	0.777998i	$0.283765\pi$
$42$		0			0
$43$	−0.302776	−	0.524423i	−0.0461729	−	0.0799737i	0.842015	−	0.539454i	$-0.181369\pi$
$43$	−0.302776	−	0.524423i	−0.0461729	−	0.0799737i	−0.888188	+	0.459480i	$0.848036\pi$
$44$	−15.2111			−2.29316
$45$		0			0
$46$	6.90833			1.01858
$47$	−4.60555	−	7.97705i	−0.671789	−	1.16357i	−0.977396	−	0.211415i	$-0.932193\pi$
$47$	−4.60555	−	7.97705i	−0.671789	−	1.16357i	0.305608	−	0.952157i	$-0.401140\pi$
$48$		0			0
$49$	0.105551	−	0.182820i	0.0150788	−	0.0261172i
$50$	−1.15139	+	1.99426i	−0.162831	+	0.282031i
$51$		0			0
$52$	−10.9083	−	18.8938i	−1.51271	−	2.62010i
$53$	−1.60555			−0.220539			−0.110270	−	0.993902i	$-0.535171\pi$
$53$	−1.60555			−0.220539			−0.110270	+	0.993902i	$0.535171\pi$
$54$		0			0
$55$	4.60555			0.621012
$56$	3.90833	+	6.76942i	0.522272	+	0.904602i
$57$		0			0
$58$	1.60555	−	2.78090i	0.210819	−	0.365150i
$59$	−0.697224	+	1.20763i	−0.0907709	+	0.157220i	−0.907836	−	0.419326i	$-0.862266\pi$
$59$	−0.697224	+	1.20763i	−0.0907709	+	0.157220i	0.817065	+	0.576546i	$0.195600\pi$
$60$		0			0
$61$	2.10555	+	3.64692i	0.269588	+	0.466940i	0.968756	−	0.248018i	$-0.0797791\pi$
$61$	2.10555	+	3.64692i	0.269588	+	0.466940i	−0.699167	+	0.714958i	$0.746446\pi$
$62$	−12.9083			−1.63936
$63$		0			0
$64$	−12.8167			−1.60208
$65$	3.30278	+	5.72058i	0.409659	+	0.709550i
$66$		0			0
$67$	0.394449	−	0.683205i	0.0481896	−	0.0834668i	−0.840924	−	0.541153i	$-0.817988\pi$
$67$	0.394449	−	0.683205i	0.0481896	−	0.0834668i	0.889114	+	0.457686i	$0.151322\pi$
$68$	2.65139	−	4.59234i	0.321528	−	0.556903i
$69$		0			0
$70$	−3.00000	−	5.19615i	−0.358569	−	0.621059i
$71$	−7.39445			−0.877560			−0.438780	−	0.898595i	$-0.644589\pi$
$71$	−7.39445			−0.877560			−0.438780	+	0.898595i	$0.644589\pi$
$72$		0			0
$73$	12.6056			1.47537			0.737684	−	0.675146i	$-0.235919\pi$
$73$	12.6056			1.47537			0.737684	+	0.675146i	$0.235919\pi$
$74$	−2.30278	−	3.98852i	−0.267692	−	0.463657i
$75$		0			0
$76$	−5.95416	+	10.3129i	−0.682989	+	1.18297i
$77$	−6.00000	+	10.3923i	−0.683763	+	1.18431i
$78$		0			0
$79$	5.80278	+	10.0507i	0.652863	+	1.13079i	0.982425	+	0.186658i	$0.0597657\pi$
$79$	5.80278	+	10.0507i	0.652863	+	1.13079i	−0.329562	+	0.944134i	$0.606901\pi$
$80$	−0.302776			−0.0338513
$81$		0			0
$82$	10.6056			1.17119
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	0.936530	−	0.350588i	$-0.114018\pi$
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	−0.771883	+	0.635764i	$0.780685\pi$
$84$		0			0
$85$	−0.802776	+	1.39045i	−0.0870732	+	0.150815i
$86$	−0.697224	+	1.20763i	−0.0751836	+	0.130222i
$87$		0			0
$88$	6.90833	+	11.9656i	0.736430	+	1.27553i
$89$	13.8167			1.46456			0.732281	−	0.681002i	$-0.238456\pi$
$89$	13.8167			1.46456			0.732281	+	0.681002i	$0.238456\pi$
$90$		0			0
$91$	−17.2111			−1.80421
$92$	−4.95416	−	8.58086i	−0.516507	−	0.894617i
$93$		0			0
$94$	−10.6056	+	18.3694i	−1.09388	+	1.89465i
$95$	1.80278	−	3.12250i	0.184961	−	0.320362i
$96$		0			0
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	−0.486122			−0.0491057
$99$		0			0
$100$	3.30278			0.330278
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−9.90833	+	17.1617i	−0.971591	+	1.68285i
$105$		0			0
$106$	1.84861	+	3.20189i	0.179553	+	0.310995i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$	−5.30278	−	9.18468i	−0.505600	−	0.875725i
$111$		0			0
$112$	0.394449	−	0.683205i	0.0372719	−	0.0645568i
$113$	−7.60555	+	13.1732i	−0.715470	+	1.23923i	0.247308	+	0.968937i	$0.420454\pi$
$113$	−7.60555	+	13.1732i	−0.715470	+	1.23923i	−0.962778	+	0.270294i	$0.912879\pi$
$114$		0			0
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$	−4.60555			−0.427615
$117$		0			0
$118$	3.21110			0.295606
$119$	−2.09167	−	3.62288i	−0.191743	−	0.332109i
$120$		0			0
$121$	−5.10555	+	8.84307i	−0.464141	+	0.803916i
$122$	4.84861	−	8.39804i	0.438973	−	0.760323i
$123$		0			0
$124$	9.25694	+	16.0335i	0.831298	+	1.43985i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−19.2111			−1.70471			−0.852355	−	0.522964i	$-0.824826\pi$
$127$	−19.2111			−1.70471			−0.852355	+	0.522964i	$0.824826\pi$
$128$	9.45416	+	16.3751i	0.835638	+	1.44737i
$129$		0			0
$130$	7.60555	−	13.1732i	0.667051	−	1.15537i
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$		0			0
$133$	4.69722	+	8.13583i	0.407301	+	0.705466i
$134$	−1.81665			−0.156935
$135$		0			0
$136$	−4.81665			−0.413025
$137$	8.40833	+	14.5636i	0.718372	+	1.24426i	0.961645	+	0.274299i	$0.0884457\pi$
$137$	8.40833	+	14.5636i	0.718372	+	1.24426i	−0.243273	+	0.969958i	$0.578221\pi$
$138$		0			0
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	−4.30278	+	7.45263i	−0.363651	+	0.629862i
$141$		0			0
$142$	8.51388	+	14.7465i	0.714469	+	1.23750i
$143$	−30.4222			−2.54403
$144$		0			0
$145$	1.39445			0.115803
$146$	−14.5139	−	25.1388i	−1.20118	−	2.08050i
$147$		0			0
$148$	−3.30278	+	5.72058i	−0.271486	+	0.470228i
$149$	11.5139	−	19.9426i	0.943254	−	1.63376i	0.184043	−	0.982918i	$-0.441081\pi$
$149$	11.5139	−	19.9426i	0.943254	−	1.63376i	0.759211	−	0.650845i	$-0.225585\pi$
$150$		0			0
$151$	−7.21110	−	12.4900i	−0.586831	−	1.01642i	−0.994644	−	0.103356i	$-0.967042\pi$
$151$	−7.21110	−	12.4900i	−0.586831	−	1.01642i	0.407813	−	0.913065i	$-0.366291\pi$
$152$	10.8167			0.877346
$153$		0			0
$154$	27.6333			2.22676
$155$	−2.80278	−	4.85455i	−0.225124	−	0.389927i
$156$		0			0
$157$	8.90833	−	15.4297i	0.710962	−	1.23142i	−0.253535	−	0.967326i	$-0.581593\pi$
$157$	8.90833	−	15.4297i	0.710962	−	1.23142i	0.964496	−	0.264096i	$-0.0850735\pi$
$158$	13.3625	−	23.1445i	1.06306	−	1.84128i
$159$		0			0
$160$	−2.65139	−	4.59234i	−0.209611	−	0.363056i
$161$	−7.81665			−0.616039
$162$		0			0
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	−7.60555	−	13.1732i	−0.593894	−	1.02865i
$165$		0			0
$166$	3.45416	−	5.98279i	0.268095	−	0.464354i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$		0			0
$169$	−15.3167	−	26.5292i	−1.17820	−	2.04071i
$170$	3.69722			0.283564
$171$		0			0
$172$	2.00000			0.152499
$173$	−5.40833	−	9.36750i	−0.411187	−	0.712198i	0.583832	−	0.811874i	$-0.301553\pi$
$173$	−5.40833	−	9.36750i	−0.411187	−	0.712198i	−0.995020	+	0.0996766i	$0.968219\pi$
$174$		0			0
$175$	1.30278	−	2.25647i	0.0984806	−	0.170573i
$176$	0.697224	−	1.20763i	0.0525553	−	0.0910284i
$177$		0			0
$178$	−15.9083	−	27.5540i	−1.19238	−	2.06526i
$179$	21.2111			1.58539			0.792696	−	0.609617i	$-0.208677\pi$
$179$	21.2111			1.58539			0.792696	+	0.609617i	$0.208677\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	19.8167	+	34.3235i	1.46891	+	2.54422i
$183$		0			0
$184$	−4.50000	+	7.79423i	−0.331744	+	0.574598i
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$		0			0
$187$	−3.69722	−	6.40378i	−0.270368	−	0.468291i
$188$	30.4222			2.21877
$189$		0			0
$190$	−8.30278			−0.602347
$191$	−6.21110	−	10.7579i	−0.449420	−	0.778418i	0.548929	−	0.835869i	$-0.315036\pi$
$191$	−6.21110	−	10.7579i	−0.449420	−	0.778418i	−0.998348	+	0.0574516i	$0.981703\pi$
$192$		0			0
$193$	−0.0916731	+	0.158782i	−0.00659877	+	0.0114294i	−0.869306	−	0.494274i	$-0.835434\pi$
$193$	−0.0916731	+	0.158782i	−0.00659877	+	0.0114294i	0.862707	+	0.505704i	$0.168767\pi$
$194$	−9.21110	+	15.9541i	−0.661319	+	1.14544i
$195$		0			0
$196$	0.348612	+	0.603814i	0.0249009	+	0.0431296i
$197$	22.8167			1.62562			0.812810	−	0.582529i	$-0.197937\pi$
$197$	22.8167			1.62562			0.812810	+	0.582529i	$0.197937\pi$
$198$		0			0
$199$	−1.21110			−0.0858528			−0.0429264	−	0.999078i	$-0.513668\pi$
$199$	−1.21110			−0.0858528			−0.0429264	+	0.999078i	$0.513668\pi$
$200$	−1.50000	−	2.59808i	−0.106066	−	0.183712i
$201$		0			0
$202$	13.8167	−	23.9311i	0.972136	−	1.68379i
$203$	−1.81665	+	3.14654i	−0.127504	+	0.220844i
$204$		0			0
$205$	2.30278	+	3.98852i	0.160833	+	0.278571i
$206$	−9.21110			−0.641768
$207$		0			0
$208$	2.00000			0.138675
$209$	8.30278	+	14.3808i	0.574315	+	0.994743i
$210$		0			0
$211$	4.40833	−	7.63545i	0.303482	−	0.525646i	−0.673440	−	0.739242i	$-0.735184\pi$
$211$	4.40833	−	7.63545i	0.303482	−	0.525646i	0.976922	+	0.213596i	$0.0685175\pi$
$212$	2.65139	−	4.59234i	0.182098	−	0.315403i
$213$		0			0
$214$		0			0
$215$	−0.605551			−0.0412983
$216$		0			0
$217$	14.6056			0.991489
$218$	8.05971	+	13.9598i	0.545873	+	0.945479i
$219$		0			0
$220$	−7.60555	+	13.1732i	−0.512766	+	0.888137i
$221$	5.30278	−	9.18468i	0.356703	−	0.617828i
$222$		0			0
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	0.983451	−	0.181173i	$-0.0579895\pi$
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	−0.648626	+	0.761107i	$0.724656\pi$
$224$	13.8167			0.923164
$225$		0			0
$226$	35.0278			2.33001
$227$	−5.89445	−	10.2095i	−0.391228	−	0.677627i	0.601384	−	0.798960i	$-0.294616\pi$
$227$	−5.89445	−	10.2095i	−0.391228	−	0.677627i	−0.992612	+	0.121333i	$0.961283\pi$
$228$		0			0
$229$	−4.10555	+	7.11102i	−0.271302	+	0.469910i	−0.969196	−	0.246292i	$-0.920788\pi$
$229$	−4.10555	+	7.11102i	−0.271302	+	0.469910i	0.697893	+	0.716202i	$0.254121\pi$
$230$	3.45416	−	5.98279i	0.227761	−	0.394493i
$231$		0			0
$232$	2.09167	+	3.62288i	0.137325	+	0.237854i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	−9.21110			−0.600866
$236$	−2.30278	−	3.98852i	−0.149898	−	0.259631i
$237$		0			0
$238$	−4.81665	+	8.34269i	−0.312217	+	0.540776i
$239$	−7.60555	+	13.1732i	−0.491962	+	0.852104i	−0.999957	−	0.00925650i	$-0.997054\pi$
$239$	−7.60555	+	13.1732i	−0.491962	+	0.852104i	0.507995	+	0.861360i	$0.330387\pi$
$240$		0			0
$241$	−6.89445	−	11.9415i	−0.444110	−	0.769222i	0.553879	−	0.832597i	$-0.313147\pi$
$241$	−6.89445	−	11.9415i	−0.444110	−	0.769222i	−0.997990	+	0.0633751i	$0.979814\pi$
$242$	23.5139			1.51153
$243$		0			0
$244$	−13.9083			−0.890389
$245$	−0.105551	−	0.182820i	−0.00674342	−	0.0116800i
$246$		0			0
$247$	−11.9083	+	20.6258i	−0.757709	+	1.31239i
$248$	8.40833	−	14.5636i	0.533929	−	0.924793i
$249$		0			0
$250$	1.15139	+	1.99426i	0.0728202	+	0.126128i
$251$	−27.6333			−1.74420			−0.872099	−	0.489329i	$-0.837242\pi$
$251$	−27.6333			−1.74420			−0.872099	+	0.489329i	$0.837242\pi$
$252$		0			0
$253$	−13.8167			−0.868646
$254$	22.1194	+	38.3120i	1.38790	+	2.40391i
$255$		0			0
$256$	8.95416	−	15.5091i	0.559635	−	0.969317i
$257$	0.591673	−	1.02481i	0.0369076	−	0.0639258i	−0.846982	−	0.531622i	$-0.821583\pi$
$257$	0.591673	−	1.02481i	0.0369076	−	0.0639258i	0.883889	+	0.467696i	$0.154916\pi$
$258$		0			0
$259$	2.60555	+	4.51295i	0.161901	+	0.280421i
$260$	−21.8167			−1.35301
$261$		0			0
$262$	−13.8167			−0.853596
$263$	−1.39445	−	2.41526i	−0.0859854	−	0.148931i	0.819825	−	0.572614i	$-0.194071\pi$
$263$	−1.39445	−	2.41526i	−0.0859854	−	0.148931i	−0.905811	+	0.423683i	$0.860737\pi$
$264$		0			0
$265$	−0.802776	+	1.39045i	−0.0493141	+	0.0854146i
$266$	10.8167	−	18.7350i	0.663212	−	1.14872i
$267$		0			0
$268$	1.30278	+	2.25647i	0.0795797	+	0.137836i
$269$	3.21110			0.195784			0.0978922	−	0.995197i	$-0.468790\pi$
$269$	3.21110			0.195784			0.0978922	+	0.995197i	$0.468790\pi$
$270$		0			0
$271$	31.2389			1.89763			0.948813	−	0.315839i	$-0.102286\pi$
$271$	31.2389			1.89763			0.948813	+	0.315839i	$0.102286\pi$
$272$	0.243061	+	0.420994i	0.0147377	+	0.0255265i
$273$		0			0
$274$	19.3625	−	33.5368i	1.16973	−	2.02603i
$275$	2.30278	−	3.98852i	0.138863	−	0.240517i
$276$		0			0
$277$	−3.51388	−	6.08622i	−0.211128	−	0.365685i	0.740939	−	0.671572i	$-0.234381\pi$
$277$	−3.51388	−	6.08622i	−0.211128	−	0.365685i	−0.952068	+	0.305887i	$0.901047\pi$
$278$	−9.21110			−0.552445
$279$		0			0
$280$	7.81665			0.467134
$281$	−9.90833	−	17.1617i	−0.591081	−	1.02378i	−0.994087	−	0.108585i	$-0.965368\pi$
$281$	−9.90833	−	17.1617i	−0.591081	−	1.02378i	0.403006	−	0.915197i	$-0.367965\pi$
$282$		0			0
$283$	−1.69722	+	2.93968i	−0.100890	+	0.174746i	−0.912051	−	0.410076i	$-0.865502\pi$
$283$	−1.69722	+	2.93968i	−0.100890	+	0.174746i	0.811162	+	0.584822i	$0.198836\pi$
$284$	12.2111	−	21.1503i	0.724596	−	1.25504i
$285$		0			0
$286$	35.0278	+	60.6699i	2.07123	+	3.58748i
$287$	−12.0000			−0.708338
$288$		0			0
$289$	−14.4222			−0.848365
$290$	−1.60555	−	2.78090i	−0.0942812	−	0.163300i
$291$		0			0
$292$	−20.8167	+	36.0555i	−1.21820	+	2.10999i
$293$	−3.59167	+	6.22096i	−0.209828	+	0.363432i	−0.951660	−	0.307153i	$-0.900624\pi$
$293$	−3.59167	+	6.22096i	−0.209828	+	0.363432i	0.741832	+	0.670585i	$0.233957\pi$
$294$		0			0
$295$	0.697224	+	1.20763i	0.0405940	+	0.0703108i
$296$	6.00000			0.348743
$297$		0			0
$298$	−53.0278			−3.07182
$299$	−9.90833	−	17.1617i	−0.573013	−	0.992488i
$300$		0			0
$301$	0.788897	−	1.36641i	0.0454713	−	0.0787586i
$302$	−16.6056	+	28.7617i	−0.955542	+	1.65505i
$303$		0			0
$304$	−0.545837	−	0.945417i	−0.0313059	−	0.0542234i
$305$	4.21110			0.241127
$306$		0			0
$307$	8.42221			0.480681			0.240340	−	0.970689i	$-0.422741\pi$
$307$	8.42221			0.480681			0.240340	+	0.970689i	$0.422741\pi$
$308$	−19.8167	−	34.3235i	−1.12916	−	1.95576i
$309$		0			0
$310$	−6.45416	+	11.1789i	−0.366572	+	0.634921i
$311$	−3.90833	+	6.76942i	−0.221621	+	0.383859i	−0.955300	−	0.295637i	$-0.904468\pi$
$311$	−3.90833	+	6.76942i	−0.221621	+	0.383859i	0.733679	+	0.679496i	$0.237801\pi$
$312$		0			0
$313$	9.81665	+	17.0029i	0.554870	+	0.961063i	0.997914	+	0.0645631i	$0.0205654\pi$
$313$	9.81665	+	17.0029i	0.554870	+	0.961063i	−0.443044	+	0.896500i	$0.646101\pi$
$314$	−41.0278			−2.31533
$315$		0			0
$316$	−38.3305			−2.15626
$317$	−3.80278	−	6.58660i	−0.213585	−	0.369940i	0.739249	−	0.673432i	$-0.235181\pi$
$317$	−3.80278	−	6.58660i	−0.213585	−	0.369940i	−0.952834	+	0.303492i	$0.901847\pi$
$318$		0			0
$319$	−3.21110	+	5.56179i	−0.179787	+	0.311401i
$320$	−6.40833	+	11.0995i	−0.358236	+	0.620484i
$321$		0			0
$322$	9.00000	+	15.5885i	0.501550	+	0.868711i
$323$	−5.78890			−0.322103
$324$		0			0
$325$	6.60555			0.366410
$326$	−2.30278	−	3.98852i	−0.127539	−	0.220904i
$327$		0			0
$328$	−6.90833	+	11.9656i	−0.381449	+	0.660688i
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	−14.6056	−	25.2976i	−0.802794	−	1.39048i	−0.917770	−	0.397111i	$-0.870013\pi$
$331$	−14.6056	−	25.2976i	−0.802794	−	1.39048i	0.114977	−	0.993368i	$-0.463321\pi$
$332$	−9.90833			−0.543790
$333$		0			0
$334$	6.90833			0.378007
$335$	−0.394449	−	0.683205i	−0.0215510	−	0.0373275i
$336$		0			0
$337$	−3.30278	+	5.72058i	−0.179914	+	0.311620i	−0.941851	−	0.336031i	$-0.890915\pi$
$337$	−3.30278	+	5.72058i	−0.179914	+	0.311620i	0.761937	+	0.647651i	$0.224249\pi$
$338$	−35.2708	+	61.0908i	−1.91848	+	3.32290i
$339$		0			0
$340$	−2.65139	−	4.59234i	−0.143792	−	0.249055i
$341$	25.8167			1.39805
$342$		0			0
$343$	18.7889			1.01451
$344$	−0.908327	−	1.57327i	−0.0489737	−	0.0848249i
$345$		0			0
$346$	−12.4542	+	21.5712i	−0.669540	+	1.15968i
$347$	15.2111	−	26.3464i	0.816575	−	1.41435i	−0.0916168	−	0.995794i	$-0.529203\pi$
$347$	15.2111	−	26.3464i	0.816575	−	1.41435i	0.908192	−	0.418555i	$-0.137463\pi$
$348$		0			0
$349$	15.9222	+	27.5781i	0.852296	+	1.47622i	0.879131	+	0.476580i	$0.158124\pi$
$349$	15.9222	+	27.5781i	0.852296	+	1.47622i	−0.0268349	+	0.999640i	$0.508543\pi$
$350$	−6.00000			−0.320713
$351$		0			0
$352$	24.4222			1.30171
$353$	10.8167	+	18.7350i	0.575712	+	0.997163i	0.995964	+	0.0897554i	$0.0286085\pi$
$353$	10.8167	+	18.7350i	0.575712	+	0.997163i	−0.420251	+	0.907408i	$0.638058\pi$
$354$		0			0
$355$	−3.69722	+	6.40378i	−0.196228	+	0.339877i
$356$	−22.8167	+	39.5196i	−1.20928	+	2.09453i
$357$		0			0
$358$	−24.4222	−	42.3005i	−1.29075	−	2.23565i
$359$	9.63331			0.508427			0.254213	−	0.967148i	$-0.418183\pi$
$359$	9.63331			0.508427			0.254213	+	0.967148i	$0.418183\pi$
$360$		0			0
$361$	−6.00000			−0.315789
$362$	8.05971	+	13.9598i	0.423609	+	0.733713i
$363$		0			0
$364$	28.4222	−	49.2287i	1.48973	−	2.58029i
$365$	6.30278	−	10.9167i	0.329902	−	0.571408i
$366$		0			0
$367$	1.30278	+	2.25647i	0.0680043	+	0.117787i	0.898023	−	0.439949i	$-0.145003\pi$
$367$	1.30278	+	2.25647i	0.0680043	+	0.117787i	−0.830018	+	0.557736i	$0.811670\pi$
$368$	0.908327			0.0473498
$369$		0			0
$370$	−4.60555			−0.239431
$371$	−2.09167	−	3.62288i	−0.108594	−	0.188091i
$372$		0			0
$373$	12.6056	−	21.8335i	0.652691	−	1.13049i	−0.329777	−	0.944059i	$-0.606973\pi$
$373$	12.6056	−	21.8335i	0.652691	−	1.13049i	0.982467	−	0.186434i	$-0.0596932\pi$
$374$	−8.51388	+	14.7465i	−0.440242	+	0.762522i
$375$		0			0
$376$	−13.8167	−	23.9311i	−0.712540	−	1.23415i
$377$	−9.21110			−0.474396
$378$		0			0
$379$	21.6056			1.10980			0.554901	−	0.831916i	$-0.312756\pi$
$379$	21.6056			1.10980			0.554901	+	0.831916i	$0.312756\pi$
$380$	5.95416	+	10.3129i	0.305442	+	0.529041i
$381$		0			0
$382$	−14.3028	+	24.7731i	−0.731794	+	1.26750i
$383$	12.3167	−	21.3331i	0.629352	−	1.09007i	−0.358330	−	0.933595i	$-0.616654\pi$
$383$	12.3167	−	21.3331i	0.629352	−	1.09007i	0.987682	−	0.156474i	$-0.0500128\pi$
$384$		0			0
$385$	6.00000	+	10.3923i	0.305788	+	0.529641i
$386$	0.422205			0.0214897
$387$		0			0
$388$	26.4222			1.34138
$389$	12.9083	+	22.3579i	0.654478	+	1.13359i	0.982024	+	0.188754i	$0.0604450\pi$
$389$	12.9083	+	22.3579i	0.654478	+	1.13359i	−0.327546	+	0.944835i	$0.606222\pi$
$390$		0			0
$391$	2.40833	−	4.17134i	0.121794	−	0.210954i
$392$	0.316654	−	0.548461i	0.0159934	−	0.0277014i
$393$		0			0
$394$	−26.2708	−	45.5024i	−1.32350	−	2.29238i
$395$	11.6056			0.583939
$396$		0			0
$397$	−5.39445			−0.270740			−0.135370	−	0.990795i	$-0.543222\pi$
$397$	−5.39445			−0.270740			−0.135370	+	0.990795i	$0.543222\pi$
$398$	1.39445	+	2.41526i	0.0698974	+	0.121066i
$399$		0			0
$400$	−0.151388	+	0.262211i	−0.00756939	+	0.0131106i
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	0.199207	+	0.979957i	$0.436163\pi$
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	−0.948272	+	0.317460i	$0.897170\pi$
$402$		0			0
$403$	18.5139	+	32.0670i	0.922242	+	1.59737i
$404$	−39.6333			−1.97183
$405$		0			0
$406$	8.36669			0.415232
$407$	4.60555	+	7.97705i	0.228289	+	0.395408i
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$	5.30278	−	9.18468i	0.261885	−	0.453599i
$411$		0			0
$412$	6.60555	+	11.4412i	0.325432	+	0.563665i
$413$	−3.63331			−0.178783
$414$		0			0
$415$	3.00000			0.147264
$416$	17.5139	+	30.3349i	0.858689	+	1.48729i
$417$		0			0
$418$	19.1194	−	33.1158i	0.935162	−	1.61975i
$419$	11.5139	−	19.9426i	0.562490	−	0.974261i	−0.434789	−	0.900533i	$-0.643177\pi$
$419$	11.5139	−	19.9426i	0.562490	−	0.974261i	0.997278	−	0.0737283i	$-0.0234898\pi$
$420$		0			0
$421$	−2.71110	−	4.69577i	−0.132131	−	0.228858i	0.792367	−	0.610045i	$-0.208849\pi$
$421$	−2.71110	−	4.69577i	−0.132131	−	0.228858i	−0.924498	+	0.381187i	$0.875515\pi$
$422$	−20.3028			−0.988324
$423$		0			0
$424$	−4.81665			−0.233917
$425$	0.802776	+	1.39045i	0.0389403	+	0.0674466i
$426$		0			0
$427$	−5.48612	+	9.50224i	−0.265492	+	0.459846i
$428$		0			0
$429$		0			0
$430$	0.697224	+	1.20763i	0.0336231	+	0.0582370i
$431$	−4.18335			−0.201505			−0.100752	−	0.994912i	$-0.532125\pi$
$431$	−4.18335			−0.201505			−0.100752	+	0.994912i	$0.532125\pi$
$432$		0			0
$433$	22.2389			1.06873			0.534366	−	0.845253i	$-0.320551\pi$
$433$	22.2389			1.06873			0.534366	+	0.845253i	$0.320551\pi$
$434$	−16.8167	−	29.1273i	−0.807225	−	1.39816i
$435$		0			0
$436$	11.5597	−	20.0220i	0.553610	−	0.958881i
$437$	−5.40833	+	9.36750i	−0.258715	+	0.448108i
$438$		0			0
$439$	−13.8028	−	23.9071i	−0.658771	−	1.14102i	−0.980934	−	0.194340i	$-0.937743\pi$
$439$	−13.8028	−	23.9071i	−0.658771	−	1.14102i	0.322164	−	0.946684i	$-0.395590\pi$
$440$	13.8167			0.658683
$441$		0			0
$442$	−24.4222			−1.16165
$443$	−12.3167	−	21.3331i	−0.585182	−	1.01356i	−0.994853	−	0.101331i	$-0.967690\pi$
$443$	−12.3167	−	21.3331i	−0.585182	−	1.01356i	0.409671	−	0.912233i	$-0.365644\pi$
$444$		0			0
$445$	6.90833	−	11.9656i	0.327486	−	0.567223i
$446$	11.5139	−	19.9426i	0.545198	−	0.944311i
$447$		0			0
$448$	−16.6972	−	28.9204i	−0.788870	−	1.36636i
$449$	−38.2389			−1.80460			−0.902302	−	0.431105i	$-0.858124\pi$
$449$	−38.2389			−1.80460			−0.902302	+	0.431105i	$0.858124\pi$
$450$		0			0
$451$	−21.2111			−0.998792
$452$	−25.1194	−	43.5081i	−1.18152	−	2.04645i
$453$		0			0
$454$	−13.5736	+	23.5102i	−0.637040	+	1.10339i
$455$	−8.60555	+	14.9053i	−0.403434	+	0.698769i
$456$		0			0
$457$	6.60555	+	11.4412i	0.308995	+	0.535194i	0.978143	−	0.207935i	$-0.0666741\pi$
$457$	6.60555	+	11.4412i	0.308995	+	0.535194i	−0.669148	+	0.743129i	$0.733341\pi$
$458$	18.9083			0.883528
$459$		0			0
$460$	−9.90833			−0.461978
$461$	10.8167	+	18.7350i	0.503782	+	0.872576i	0.999990	+	0.00437236i	$0.00139177\pi$
$461$	10.8167	+	18.7350i	0.503782	+	0.872576i	−0.496209	+	0.868203i	$0.665275\pi$
$462$		0			0
$463$	0.394449	−	0.683205i	0.0183316	−	0.0317512i	−0.856714	−	0.515792i	$-0.827498\pi$
$463$	0.394449	−	0.683205i	0.0183316	−	0.0317512i	0.875046	+	0.484040i	$0.160831\pi$
$464$	0.211103	−	0.365640i	0.00980019	−	0.0169744i
$465$		0			0
$466$	−20.7250	−	35.8967i	−0.960066	−	1.66288i
$467$	−12.2111			−0.565062			−0.282531	−	0.959258i	$-0.591174\pi$
$467$	−12.2111			−0.565062			−0.282531	+	0.959258i	$0.591174\pi$
$468$		0			0
$469$	2.05551			0.0949148
$470$	10.6056	+	18.3694i	0.489198	+	0.847315i
$471$		0			0
$472$	−2.09167	+	3.62288i	−0.0962771	+	0.166757i
$473$	1.39445	−	2.41526i	0.0641168	−	0.111054i
$474$		0			0
$475$	−1.80278	−	3.12250i	−0.0827170	−	0.143270i
$476$	13.8167			0.633285
$477$		0			0
$478$	35.0278			1.60213
$479$	−18.9083	−	32.7502i	−0.863944	−	1.49639i	−0.868092	−	0.496403i	$-0.834654\pi$
$479$	−18.9083	−	32.7502i	−0.863944	−	1.49639i	0.00414888	−	0.999991i	$-0.498679\pi$
$480$		0			0
$481$	−6.60555	+	11.4412i	−0.301187	+	0.521672i
$482$	−15.8764	+	27.4987i	−0.723149	+	1.25253i
$483$		0			0
$484$	−16.8625	−	29.2067i	−0.766477	−	1.32758i
$485$	−8.00000			−0.363261
$486$		0			0
$487$	−29.8167			−1.35112			−0.675561	−	0.737304i	$-0.736098\pi$
$487$	−29.8167			−1.35112			−0.675561	+	0.737304i	$0.736098\pi$
$488$	6.31665	+	10.9408i	0.285941	+	0.495265i
$489$		0			0
$490$	−0.243061	+	0.420994i	−0.0109804	+	0.0190186i
$491$	13.6056	−	23.5655i	0.614010	−	1.06350i	−0.376547	−	0.926397i	$-0.622889\pi$
$491$	13.6056	−	23.5655i	0.614010	−	1.06350i	0.990557	−	0.137099i	$-0.0437779\pi$
$492$		0			0
$493$	−1.11943	−	1.93891i	−0.0504166	−	0.0873241i
$494$	54.8444			2.46757
$495$		0			0
$496$	−1.69722			−0.0762076
$497$	−9.63331	−	16.6854i	−0.432113	−	0.748442i
$498$		0			0
$499$	10.1972	−	17.6621i	0.456490	−	0.790665i	−0.542282	−	0.840196i	$-0.682440\pi$
$499$	10.1972	−	17.6621i	0.456490	−	0.790665i	0.998773	+	0.0495318i	$0.0157729\pi$
$500$	1.65139	−	2.86029i	0.0738523	−	0.127916i
$501$		0			0
$502$	31.8167	+	55.1081i	1.42005	+	2.45959i
$503$	−2.57779			−0.114938			−0.0574691	−	0.998347i	$-0.518303\pi$
$503$	−2.57779			−0.114938			−0.0574691	+	0.998347i	$0.518303\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$	15.9083	+	27.5540i	0.707211	+	1.22493i
$507$		0			0
$508$	31.7250	−	54.9493i	1.40757	−	2.43798i
$509$	−12.4222	+	21.5159i	−0.550605	+	0.953675i	0.447626	+	0.894221i	$0.352269\pi$
$509$	−12.4222	+	21.5159i	−0.550605	+	0.953675i	−0.998231	+	0.0594544i	$0.981064\pi$
$510$		0			0
$511$	16.4222	+	28.4441i	0.726476	+	1.25829i
$512$	−3.42221			−0.151242
$513$		0			0
$514$	−2.72498			−0.120194
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$		0			0
$517$	21.2111	−	36.7387i	0.932863	−	1.61577i
$518$	6.00000	−	10.3923i	0.263625	−	0.456612i
$519$		0			0
$520$	9.90833	+	17.1617i	0.434509	+	0.752591i
$521$	28.6056			1.25323			0.626616	−	0.779328i	$-0.284439\pi$
$521$	28.6056			1.25323			0.626616	+	0.779328i	$0.284439\pi$
$522$		0			0
$523$	30.6056			1.33829			0.669144	−	0.743133i	$-0.266661\pi$
$523$	30.6056			1.33829			0.669144	+	0.743133i	$0.266661\pi$
$524$	9.90833	+	17.1617i	0.432847	+	0.749713i
$525$		0			0
$526$	−3.21110	+	5.56179i	−0.140011	+	0.242506i
$527$	−4.50000	+	7.79423i	−0.196023	+	0.339522i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	3.69722			0.160597
$531$		0			0
$532$	−31.0278			−1.34522
$533$	−15.2111	−	26.3464i	−0.658866	−	1.14119i
$534$		0			0
$535$		0			0
$536$	1.18335	−	2.04962i	0.0511128	−	0.0885299i
$537$		0			0
$538$	−3.69722	−	6.40378i	−0.159399	−	0.276087i
$539$	0.972244			0.0418775
$540$		0			0
$541$	−40.4222			−1.73789			−0.868943	−	0.494912i	$-0.835200\pi$
$541$	−40.4222			−1.73789			−0.868943	+	0.494912i	$0.835200\pi$
$542$	−35.9680	−	62.2985i	−1.54496	−	2.67595i
$543$		0			0
$544$	−4.25694	+	7.37323i	−0.182515	+	0.316125i
$545$	−3.50000	+	6.06218i	−0.149924	+	0.259675i
$546$		0			0
$547$	−0.302776	−	0.524423i	−0.0129458	−	0.0224227i	0.859480	−	0.511169i	$-0.170788\pi$
$547$	−0.302776	−	0.524423i	−0.0129458	−	0.0224227i	−0.872426	+	0.488747i	$0.837454\pi$
$548$	−55.5416			−2.37262
$549$		0			0
$550$	−10.6056			−0.452222
$551$	2.51388	+	4.35416i	0.107095	+	0.185494i
$552$		0			0
$553$	−15.1194	+	26.1876i	−0.642944	+	1.11361i
$554$	−8.09167	+	14.0152i	−0.343782	+	0.595448i
$555$		0			0
$556$	6.60555	+	11.4412i	0.280138	+	0.485213i
$557$	−9.63331			−0.408176			−0.204088	−	0.978953i	$-0.565423\pi$
$557$	−9.63331			−0.408176			−0.204088	+	0.978953i	$0.565423\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$	−0.394449	−	0.683205i	−0.0166685	−	0.0288707i
$561$		0			0
$562$	−22.8167	+	39.5196i	−0.962462	+	1.66703i
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$		0			0
$565$	7.60555	+	13.1732i	0.319968	+	0.554201i
$566$	7.81665			0.328558
$567$		0			0
$568$	−22.1833			−0.930793
$569$	8.09167	+	14.0152i	0.339221	+	0.587547i	0.984286	−	0.176580i	$-0.0565034\pi$
$569$	8.09167	+	14.0152i	0.339221	+	0.587547i	−0.645066	+	0.764127i	$0.723170\pi$
$570$		0			0
$571$	−14.2250	+	24.6384i	−0.595297	+	1.03108i	0.398208	+	0.917295i	$0.369632\pi$
$571$	−14.2250	+	24.6384i	−0.595297	+	1.03108i	−0.993505	+	0.113789i	$0.963701\pi$
$572$	50.2389	−	87.0163i	2.10059	−	3.63833i
$573$		0			0
$574$	13.8167	+	23.9311i	0.576696	+	0.998867i
$575$	3.00000			0.125109
$576$		0			0
$577$	6.18335			0.257416			0.128708	−	0.991683i	$-0.458917\pi$
$577$	6.18335			0.257416			0.128708	+	0.991683i	$0.458917\pi$
$578$	16.6056	+	28.7617i	0.690700	+	1.19633i
$579$		0			0
$580$	−2.30278	+	3.98852i	−0.0956176	+	0.165614i
$581$	−3.90833	+	6.76942i	−0.162145	+	0.280843i
$582$		0			0
$583$	−3.69722	−	6.40378i	−0.153123	−	0.265217i
$584$	37.8167			1.56486
$585$		0			0
$586$	16.5416			0.683329
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	0.997162	−	0.0752860i	$-0.0239870\pi$
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	−0.563781	+	0.825925i	$0.690654\pi$
$588$		0			0
$589$	10.1056	−	17.5033i	0.416392	−	0.721212i
$590$	1.60555	−	2.78090i	0.0660995	−	0.114488i
$591$		0			0
$592$	−0.302776	−	0.524423i	−0.0124440	−	0.0215536i
$593$	29.2389			1.20070			0.600348	−	0.799739i	$-0.295029\pi$
$593$	29.2389			1.20070			0.600348	+	0.799739i	$0.295029\pi$
$594$		0			0
$595$	−4.18335			−0.171500
$596$	38.0278	+	65.8660i	1.55768	+	2.69798i
$597$		0			0
$598$	−22.8167	+	39.5196i	−0.933042	+	1.61608i
$599$	−11.3028	+	19.5770i	−0.461819	+	0.799894i	−0.999052	−	0.0435402i	$-0.986136\pi$
$599$	−11.3028	+	19.5770i	−0.461819	+	0.799894i	0.537233	+	0.843434i	$0.319470\pi$
$600$		0			0
$601$	5.31665	+	9.20871i	0.216871	+	0.375631i	0.953850	−	0.300285i	$-0.0970816\pi$
$601$	5.31665	+	9.20871i	0.216871	+	0.375631i	−0.736979	+	0.675916i	$0.763748\pi$
$602$	−3.63331			−0.148083
$603$		0			0
$604$	47.6333			1.93817
$605$	5.10555	+	8.84307i	0.207570	+	0.359522i
$606$		0			0
$607$	−12.3028	+	21.3090i	−0.499354	+	0.864907i	−1.00000		0.000745477i	$-0.999763\pi$
$607$	−12.3028	+	21.3090i	−0.499354	+	0.864907i	0.500645	+	0.865652i	$0.333096\pi$
$608$	9.55971	−	16.5579i	0.387698	−	0.671512i
$609$		0			0
$610$	−4.84861	−	8.39804i	−0.196315	−	0.340027i
$611$	60.8444			2.46150
$612$		0			0
$613$	−28.8444			−1.16501			−0.582507	−	0.812825i	$-0.697928\pi$
$613$	−28.8444			−1.16501			−0.582507	+	0.812825i	$0.697928\pi$
$614$	−9.69722	−	16.7961i	−0.391348	−	0.677835i
$615$		0			0
$616$	−18.0000	+	31.1769i	−0.725241	+	1.25615i
$617$	19.2250	−	33.2986i	0.773969	−	1.34055i	−0.161404	−	0.986888i	$-0.551602\pi$
$617$	19.2250	−	33.2986i	0.773969	−	1.34055i	0.935372	−	0.353664i	$-0.115065\pi$
$618$		0			0
$619$	−17.8167	−	30.8593i	−0.716112	−	1.24034i	−0.962529	−	0.271178i	$-0.912587\pi$
$619$	−17.8167	−	30.8593i	−0.716112	−	1.24034i	0.246417	−	0.969164i	$-0.420747\pi$
$620$	18.5139			0.743535
$621$		0			0
$622$	18.0000			0.721734
$623$	18.0000	+	31.1769i	0.721155	+	1.24908i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	22.6056	−	39.1540i	0.903500	−	1.56491i
$627$		0			0
$628$	29.4222	+	50.9608i	1.17407	+	2.03356i
$629$	−3.21110			−0.128035
$630$		0			0
$631$	−6.02776			−0.239961			−0.119981	−	0.992776i	$-0.538283\pi$
$631$	−6.02776			−0.239961			−0.119981	+	0.992776i	$0.538283\pi$
$632$	17.4083	+	30.1521i	0.692466	+	1.19939i
$633$		0			0
$634$	−8.75694	+	15.1675i	−0.347782	+	0.602377i
$635$	−9.60555	+	16.6373i	−0.381185	+	0.660231i
$636$		0			0
$637$	0.697224	+	1.20763i	0.0276250	+	0.0478480i
$638$	14.7889			0.585498
$639$		0			0
$640$	18.9083			0.747417
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	0.525584	−	0.850741i	$-0.323847\pi$
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	−0.999556	+	0.0297987i	$0.990513\pi$
$642$		0			0
$643$	−6.51388	+	11.2824i	−0.256882	+	0.444933i	−0.965405	−	0.260755i	$-0.916029\pi$
$643$	−6.51388	+	11.2824i	−0.256882	+	0.444933i	0.708523	+	0.705688i	$0.249362\pi$
$644$	12.9083	−	22.3579i	0.508659	−	0.881024i
$645$		0			0
$646$	6.66527	+	11.5446i	0.262241	+	0.454215i
$647$	−23.7889			−0.935238			−0.467619	−	0.883930i	$-0.654888\pi$
$647$	−23.7889			−0.935238			−0.467619	+	0.883930i	$0.654888\pi$
$648$		0			0
$649$	−6.42221			−0.252094
$650$	−7.60555	−	13.1732i	−0.298314	−	0.516695i
$651$		0			0
$652$	−3.30278	+	5.72058i	−0.129347	+	0.224035i
$653$	−11.6194	+	20.1254i	−0.454703	+	0.787569i	−0.998671	−	0.0515368i	$-0.983588\pi$
$653$	−11.6194	+	20.1254i	−0.454703	+	0.787569i	0.543968	+	0.839106i	$0.316921\pi$
$654$		0			0
$655$	−3.00000	−	5.19615i	−0.117220	−	0.203030i
$656$	1.39445			0.0544441
$657$		0			0
$658$	−55.2666			−2.15452
$659$	−6.69722	−	11.5999i	−0.260887	−	0.451869i	0.705591	−	0.708619i	$-0.250682\pi$
$659$	−6.69722	−	11.5999i	−0.260887	−	0.451869i	−0.966478	+	0.256750i	$0.917348\pi$
$660$		0			0
$661$	17.4222	−	30.1761i	0.677645	−	1.17372i	−0.298043	−	0.954552i	$-0.596334\pi$
$661$	17.4222	−	30.1761i	0.677645	−	1.17372i	0.975688	−	0.219164i	$-0.0703328\pi$
$662$	−33.6333	+	58.2546i	−1.30720	+	2.26413i
$663$		0			0
$664$	4.50000	+	7.79423i	0.174634	+	0.302475i
$665$	9.39445			0.364301
$666$		0			0
$667$	−4.18335			−0.161980
$668$	−4.95416	−	8.58086i	−0.191682	−	0.332004i
$669$		0			0
$670$	−0.908327	+	1.57327i	−0.0350917	+	0.0607807i
$671$	−9.69722	+	16.7961i	−0.374357	+	0.648406i
$672$		0			0
$673$	−12.5139	−	21.6747i	−0.482375	−	0.835497i	0.517421	−	0.855731i	$-0.326892\pi$
$673$	−12.5139	−	21.6747i	−0.482375	−	0.835497i	−0.999795	+	0.0202339i	$0.993559\pi$
$674$	15.2111			0.585910
$675$		0			0
$676$	101.175			3.89134
$677$	10.8167	+	18.7350i	0.415718	+	0.720044i	0.995504	−	0.0947247i	$-0.0301971\pi$
$677$	10.8167	+	18.7350i	0.415718	+	0.720044i	−0.579786	+	0.814769i	$0.696864\pi$
$678$		0			0
$679$	10.4222	−	18.0518i	0.399968	−	0.692764i
$680$	−2.40833	+	4.17134i	−0.0923551	+	0.159964i
$681$		0			0
$682$	−29.7250	−	51.4852i	−1.13823	−	1.97147i
$683$	9.00000			0.344375			0.172188	−	0.985064i	$-0.444916\pi$
$683$	9.00000			0.344375			0.172188	+	0.985064i	$0.444916\pi$
$684$		0			0
$685$	16.8167			0.642531
$686$	−21.6333	−	37.4700i	−0.825964	−	1.43061i
$687$		0			0
$688$	−0.0916731	+	0.158782i	−0.00349500	+	0.00605352i
$689$	5.30278	−	9.18468i	0.202020	−	0.349908i
$690$		0			0
$691$	−4.80278	−	8.31865i	−0.182706	−	0.316456i	0.760095	−	0.649812i	$-0.225152\pi$
$691$	−4.80278	−	8.31865i	−0.182706	−	0.316456i	−0.942801	+	0.333356i	$0.891819\pi$
$692$	35.7250			1.35806
$693$		0			0
$694$	−70.0555			−2.65927
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$		0			0
$697$	3.69722	−	6.40378i	0.140042	−	0.242560i
$698$	36.6653	−	63.5061i	1.38780	−	2.40374i
$699$		0			0
$700$	4.30278	+	7.45263i	0.162630	+	0.281683i
$701$	−11.5778			−0.437287			−0.218644	−	0.975805i	$-0.570163\pi$
$701$	−11.5778			−0.437287			−0.218644	+	0.975805i	$0.570163\pi$
$702$		0			0
$703$	7.21110			0.271972
$704$	−29.5139	−	51.1195i	−1.11235	−	1.92664i
$705$		0			0
$706$	24.9083	−	43.1425i	0.937437	−	1.62369i
$707$	−15.6333	+	27.0777i	−0.587951	+	1.01836i
$708$		0			0
$709$	11.4222	+	19.7838i	0.428970	+	0.742998i	0.996782	−	0.0801605i	$-0.0255433\pi$
$709$	11.4222	+	19.7838i	0.428970	+	0.742998i	−0.567812	+	0.823158i	$0.692210\pi$
$710$	17.0278			0.639040
$711$		0			0
$712$	41.4500			1.55340
$713$	8.40833	+	14.5636i	0.314894	+	0.545413i
$714$		0			0
$715$	−15.2111	+	26.3464i	−0.568863	+	0.985300i
$716$	−35.0278	+	60.6699i	−1.30905	+	2.26734i
$717$		0			0
$718$	−11.0917	−	19.2113i	−0.413938	−	0.716961i
$719$	−37.2666			−1.38981			−0.694905	−	0.719101i	$-0.744554\pi$
$719$	−37.2666			−1.38981			−0.694905	+	0.719101i	$0.744554\pi$
$720$		0			0
$721$	10.4222			0.388143
$722$	6.90833	+	11.9656i	0.257101	+	0.445313i
$723$		0			0
$724$	11.5597	−	20.0220i	0.429613	−	0.744112i
$725$	0.697224	−	1.20763i	0.0258943	−	0.0448502i
$726$		0			0
$727$	−17.8167	−	30.8593i	−0.660783	−	1.14451i	−0.980410	−	0.196967i	$-0.936891\pi$
$727$	−17.8167	−	30.8593i	−0.660783	−	1.14451i	0.319627	−	0.947543i	$-0.396442\pi$
$728$	−51.6333			−1.91366
$729$		0			0
$730$	−29.0278			−1.07437
$731$	0.486122	+	0.841988i	0.0179799	+	0.0311420i
$732$		0			0
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	0.403128	+	0.915144i	$0.367923\pi$
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	−0.994102	+	0.108453i	$0.965410\pi$
$734$	3.00000	−	5.19615i	0.110732	−	0.191793i
$735$		0			0
$736$	7.95416	+	13.7770i	0.293194	+	0.507828i
$737$	3.63331			0.133835
$738$		0			0
$739$	−6.02776			−0.221735			−0.110867	−	0.993835i	$-0.535363\pi$
$739$	−6.02776			−0.221735			−0.110867	+	0.993835i	$0.535363\pi$
$740$	3.30278	+	5.72058i	0.121412	+	0.210293i
$741$		0			0
$742$	−4.81665	+	8.34269i	−0.176825	+	0.306270i
$743$	−2.78890	+	4.83051i	−0.102315	+	0.177214i	−0.912638	−	0.408769i	$-0.865958\pi$
$743$	−2.78890	+	4.83051i	−0.102315	+	0.177214i	0.810323	+	0.585983i	$0.199292\pi$
$744$		0			0
$745$	−11.5139	−	19.9426i	−0.421836	−	0.730641i
$746$	−58.0555			−2.12556
$747$		0			0
$748$	24.4222			0.892964
$749$		0			0
$750$		0			0
$751$	15.0139	−	26.0048i	0.547864	−	0.948929i	−0.450556	−	0.892748i	$-0.648774\pi$
$751$	15.0139	−	26.0048i	0.547864	−	0.948929i	0.998421	−	0.0561807i	$-0.0178923\pi$
$752$	−1.39445	+	2.41526i	−0.0508503	+	0.0880753i
$753$		0			0
$754$	10.6056	+	18.3694i	0.386231	+	0.668972i
$755$	−14.4222			−0.524878
$756$		0			0
$757$	16.7889			0.610203			0.305101	−	0.952320i	$-0.401310\pi$
$757$	16.7889			0.610203			0.305101	+	0.952320i	$0.401310\pi$
$758$	−24.8764	−	43.0871i	−0.903550	−	1.56500i
$759$		0			0
$760$	5.40833	−	9.36750i	0.196181	−	0.339795i
$761$	5.72498	−	9.91596i	0.207530	−	0.359453i	−0.743406	−	0.668841i	$-0.766791\pi$
$761$	5.72498	−	9.91596i	0.207530	−	0.359453i	0.950936	+	0.309388i	$0.100124\pi$
$762$		0			0
$763$	−9.11943	−	15.7953i	−0.330146	−	0.571829i
$764$	41.0278			1.48433
$765$		0			0
$766$	−56.7250			−2.04956
$767$	−4.60555	−	7.97705i	−0.166297	−	0.288035i
$768$		0			0
$769$	−20.5000	+	35.5070i	−0.739249	+	1.28042i	0.213585	+	0.976924i	$0.431486\pi$
$769$	−20.5000	+	35.5070i	−0.739249	+	1.28042i	−0.952834	+	0.303492i	$0.901847\pi$
$770$	13.8167	−	23.9311i	0.497918	−	0.862419i
$771$		0			0
$772$	−0.302776	−	0.524423i	−0.0108971	−	0.0188744i
$773$	4.81665			0.173243			0.0866215	−	0.996241i	$-0.472393\pi$
$773$	4.81665			0.173243			0.0866215	+	0.996241i	$0.472393\pi$
$774$		0			0
$775$	−5.60555			−0.201357
$776$	−12.0000	−	20.7846i	−0.430775	−	0.746124i
$777$		0			0
$778$	29.7250	−	51.4852i	1.06569	−	1.84583i
$779$	−8.30278	+	14.3808i	−0.297478	+	0.515247i
$780$		0			0
$781$	−17.0278	−	29.4929i	−0.609301	−	1.05534i
$782$	−11.0917			−0.396637
$783$		0			0
$784$	−0.0639167			−0.00228274
$785$	−8.90833	−

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.15139 - 1.99426i) q^{2} +(-1.65139 + 2.86029i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.30278 + 2.25647i) q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q+(-1.15139 - 1.99426i) q^{2} +(-1.65139 + 2.86029i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.30278 + 2.25647i) q^{7} +3.00000 q^{8} -2.30278 q^{10} +(2.30278 + 3.98852i) q^{11} +(-3.30278 + 5.72058i) q^{13} +(3.00000 - 5.19615i) q^{14} +(-0.151388 - 0.262211i) q^{16} -1.60555 q^{17} +3.60555 q^{19} +(1.65139 + 2.86029i) q^{20} +(5.30278 - 9.18468i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +15.2111 q^{26} -8.60555 q^{28} +(0.697224 + 1.20763i) q^{29} +(2.80278 - 4.85455i) q^{31} +(2.65139 - 4.59234i) q^{32} +(1.84861 + 3.20189i) q^{34} +2.60555 q^{35} +2.00000 q^{37} +(-4.15139 - 7.19041i) q^{38} +(1.50000 - 2.59808i) q^{40} +(-2.30278 + 3.98852i) q^{41} +(-0.302776 - 0.524423i) q^{43} -15.2111 q^{44} +6.90833 q^{46} +(-4.60555 - 7.97705i) q^{47} +(0.105551 - 0.182820i) q^{49} +(-1.15139 + 1.99426i) q^{50} +(-10.9083 - 18.8938i) q^{52} -1.60555 q^{53} +4.60555 q^{55} +(3.90833 + 6.76942i) q^{56} +(1.60555 - 2.78090i) q^{58} +(-0.697224 + 1.20763i) q^{59} +(2.10555 + 3.64692i) q^{61} -12.9083 q^{62} -12.8167 q^{64} +(3.30278 + 5.72058i) q^{65} +(0.394449 - 0.683205i) q^{67} +(2.65139 - 4.59234i) q^{68} +(-3.00000 - 5.19615i) q^{70} -7.39445 q^{71} +12.6056 q^{73} +(-2.30278 - 3.98852i) q^{74} +(-5.95416 + 10.3129i) q^{76} +(-6.00000 + 10.3923i) q^{77} +(5.80278 + 10.0507i) q^{79} -0.302776 q^{80} +10.6056 q^{82} +(1.50000 + 2.59808i) q^{83} +(-0.802776 + 1.39045i) q^{85} +(-0.697224 + 1.20763i) q^{86} +(6.90833 + 11.9656i) q^{88} +13.8167 q^{89} -17.2111 q^{91} +(-4.95416 - 8.58086i) q^{92} +(-10.6056 + 18.3694i) q^{94} +(1.80278 - 3.12250i) q^{95} +(-4.00000 - 6.92820i) q^{97} -0.486122 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q - q^2 - 3 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8	\( 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} - 2 q^{10} + 2 q^{11} - 6 q^{13} + 12 q^{14} + 3 q^{16} + 8 q^{17} + 3 q^{20} + 14 q^{22} - 6 q^{23} - 2 q^{25} + 32 q^{26} - 20 q^{28} + 10 q^{29} + 4 q^{31} + 7 q^{32} + 11 q^{34} - 4 q^{35} + 8 q^{37} - 13 q^{38} + 6 q^{40} - 2 q^{41} + 6 q^{43} - 32 q^{44} + 6 q^{46} - 4 q^{47} - 14 q^{49} - q^{50} - 22 q^{52} + 8 q^{53} + 4 q^{55} - 6 q^{56} - 8 q^{58} - 10 q^{59} - 6 q^{61} - 30 q^{62} - 8 q^{64} + 6 q^{65} + 16 q^{67} + 7 q^{68} - 12 q^{70} - 44 q^{71} + 36 q^{73} - 2 q^{74} - 13 q^{76} - 24 q^{77} + 16 q^{79} + 6 q^{80} + 28 q^{82} + 6 q^{83} + 4 q^{85} - 10 q^{86} + 6 q^{88} + 12 q^{89} - 40 q^{91} - 9 q^{92} - 28 q^{94} - 16 q^{97} - 38 q^{98}+O(q^{100}) \) 4 * q - q^2 - 3 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8 - 2 * q^10 + 2 * q^11 - 6 * q^13 + 12 * q^14 + 3 * q^16 + 8 * q^17 + 3 * q^20 + 14 * q^22 - 6 * q^23 - 2 * q^25 + 32 * q^26 - 20 * q^28 + 10 * q^29 + 4 * q^31 + 7 * q^32 + 11 * q^34 - 4 * q^35 + 8 * q^37 - 13 * q^38 + 6 * q^40 - 2 * q^41 + 6 * q^43 - 32 * q^44 + 6 * q^46 - 4 * q^47 - 14 * q^49 - q^50 - 22 * q^52 + 8 * q^53 + 4 * q^55 - 6 * q^56 - 8 * q^58 - 10 * q^59 - 6 * q^61 - 30 * q^62 - 8 * q^64 + 6 * q^65 + 16 * q^67 + 7 * q^68 - 12 * q^70 - 44 * q^71 + 36 * q^73 - 2 * q^74 - 13 * q^76 - 24 * q^77 + 16 * q^79 + 6 * q^80 + 28 * q^82 + 6 * q^83 + 4 * q^85 - 10 * q^86 + 6 * q^88 + 12 * q^89 - 40 * q^91 - 9 * q^92 - 28 * q^94 - 16 * q^97 - 38 * q^98

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