LMFDB - Embedded newform 612.2.bd.d.91.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [612,2,Mod(91,612)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(612, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 0, 15]))

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

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

chi := DirichletCharacter("612.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 612 = 2^{2} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	612.bd (of order $16$, degree $8$, 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:	$4.88684460370$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 68)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			91.6
Character	$\chi$	$=$	612.91
Dual form			612.2.bd.d.343.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17748 - 0.783289i) q^{2} +(0.772915 - 1.84461i) q^{4} +(0.561585 - 0.840472i) q^{5} +(-1.73093 + 1.15657i) q^{7} +(-0.534775 - 2.77741i) q^{8} +O(q^{10})$	\(q+(1.17748 - 0.783289i) q^{2} +(0.772915 - 1.84461i) q^{4} +(0.561585 - 0.840472i) q^{5} +(-1.73093 + 1.15657i) q^{7} +(-0.534775 - 2.77741i) q^{8} +(0.00292235 - 1.42952i) q^{10} +(-1.04891 - 0.208641i) q^{11} +(4.36539 - 4.36539i) q^{13} +(-1.13221 + 2.71766i) q^{14} +(-2.80520 - 2.85146i) q^{16} +(-0.0297412 - 4.12300i) q^{17} +(2.55002 - 6.15628i) q^{19} +(-1.11629 - 1.68552i) q^{20} +(-1.39849 + 0.575928i) q^{22} +(-0.773086 + 3.88657i) q^{23} +(1.52240 + 3.67540i) q^{25} +(1.72079 - 8.55953i) q^{26} +(0.795567 + 4.08684i) q^{28} +(3.11609 + 2.08211i) q^{29} +(-5.38553 + 1.07125i) q^{31} +(-5.53659 - 1.16025i) q^{32} +(-3.26452 - 4.83145i) q^{34} +2.10432i q^{35} +(-5.03388 + 1.00130i) q^{37} +(-1.81956 - 9.24630i) q^{38} +(-2.63466 - 1.11029i) q^{40} +(4.02629 + 6.02577i) q^{41} +(0.733065 + 1.76977i) q^{43} +(-1.19558 + 1.77357i) q^{44} +(2.13401 + 5.18190i) q^{46} +(6.00982 + 6.00982i) q^{47} +(-1.02031 + 2.46325i) q^{49} +(4.67150 + 3.13523i) q^{50} +(-4.67839 - 11.4265i) q^{52} +(1.43923 + 0.596147i) q^{53} +(-0.764407 + 0.764407i) q^{55} +(4.13794 + 4.18901i) q^{56} +(5.30003 + 0.0108348i) q^{58} +(-4.31414 + 1.78698i) q^{59} +(6.25751 - 4.18113i) q^{61} +(-5.50225 + 5.47980i) q^{62} +(-7.42803 + 2.97058i) q^{64} +(-1.21745 - 6.12053i) q^{65} +0.616467 q^{67} +(-7.62833 - 3.13187i) q^{68} +(1.64829 + 2.47779i) q^{70} +(-1.17044 - 5.88422i) q^{71} +(0.112327 - 0.168110i) q^{73} +(-5.14298 + 5.12199i) q^{74} +(-9.38502 - 9.46208i) q^{76} +(2.05690 - 0.851995i) q^{77} +(11.4809 + 2.28368i) q^{79} +(-3.97193 + 0.756357i) q^{80} +(9.46080 + 3.94147i) q^{82} +(11.4667 + 4.74966i) q^{83} +(-3.48197 - 2.29042i) q^{85} +(2.24941 + 1.50967i) q^{86} +(-0.0185510 + 3.02482i) q^{88} +(-1.64195 - 1.64195i) q^{89} +(-2.50731 + 12.6051i) q^{91} +(6.57169 + 4.43003i) q^{92} +(11.7839 + 2.36901i) q^{94} +(-3.74213 - 5.60049i) q^{95} +(-4.27885 - 2.85903i) q^{97} +(0.728042 + 3.69963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 8 q^{4} + 16 q^{5} + 8 q^{8}+O(q^{10}) $ 48 * q + 8 * q^2 - 8 * q^4 + 16 * q^5 + 8 * q^8	$ 48 q + 8 q^{2} - 8 q^{4} + 16 q^{5} + 8 q^{8} + 16 q^{10} - 16 q^{13} + 8 q^{14} + 16 q^{17} + 24 q^{20} - 8 q^{22} + 16 q^{25} + 16 q^{26} + 40 q^{28} - 32 q^{32} + 56 q^{34} - 16 q^{37} - 32 q^{38} + 56 q^{40} + 48 q^{41} - 24 q^{44} + 8 q^{46} - 16 q^{49} - 16 q^{52} - 48 q^{53} + 48 q^{56} - 64 q^{58} + 16 q^{61} + 64 q^{62} - 56 q^{64} - 96 q^{65} + 32 q^{68} - 80 q^{70} + 64 q^{73} + 16 q^{74} - 64 q^{76} - 16 q^{77} + 24 q^{80} - 40 q^{82} - 80 q^{85} - 64 q^{86} + 56 q^{88} + 16 q^{89} - 104 q^{92} + 88 q^{94} - 16 q^{97} - 72 q^{98}+O(q^{100}) $ 48 * q + 8 * q^2 - 8 * q^4 + 16 * q^5 + 8 * q^8 + 16 * q^10 - 16 * q^13 + 8 * q^14 + 16 * q^17 + 24 * q^20 - 8 * q^22 + 16 * q^25 + 16 * q^26 + 40 * q^28 - 32 * q^32 + 56 * q^34 - 16 * q^37 - 32 * q^38 + 56 * q^40 + 48 * q^41 - 24 * q^44 + 8 * q^46 - 16 * q^49 - 16 * q^52 - 48 * q^53 + 48 * q^56 - 64 * q^58 + 16 * q^61 + 64 * q^62 - 56 * q^64 - 96 * q^65 + 32 * q^68 - 80 * q^70 + 64 * q^73 + 16 * q^74 - 64 * q^76 - 16 * q^77 + 24 * q^80 - 40 * q^82 - 80 * q^85 - 64 * q^86 + 56 * q^88 + 16 * q^89 - 104 * q^92 + 88 * q^94 - 16 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/612\mathbb{Z}\right)^\times$.

$n$	$37$	$137$	$307$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$1$	$-1$

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 $

$2$	1.17748	−	0.783289i	0.832604	−	0.553869i
$2$	1.17748	−	0.783289i	0.832604	−	0.553869i
$3$		0			0
$3$		0			0
$4$	0.772915	−	1.84461i	0.386458	−	0.922307i
$5$	0.561585	−	0.840472i	0.251149	−	0.375870i	−0.684378	−	0.729128i	$-0.739926\pi$
$5$	0.561585	−	0.840472i	0.251149	−	0.375870i	0.935526	+	0.353257i	$0.114926\pi$
$6$		0			0
$7$	−1.73093	+	1.15657i	−0.654232	+	0.437144i	−0.837885	−	0.545847i	$-0.816208\pi$
$7$	−1.73093	+	1.15657i	−0.654232	+	0.437144i	0.183653	+	0.982991i	$0.441208\pi$
$8$	−0.534775	−	2.77741i	−0.189072	−	0.981963i
$9$		0			0
$10$	0.00292235	−	1.42952i	0.000924130	−	0.452054i
$11$	−1.04891	−	0.208641i	−0.316257	−	0.0629075i	0.0344093	−	0.999408i	$-0.489045\pi$
$11$	−1.04891	−	0.208641i	−0.316257	−	0.0629075i	−0.350667	+	0.936500i	$0.614045\pi$
$12$		0			0
$13$	4.36539	−	4.36539i	1.21074	−	1.21074i	0.239959	−	0.970783i	$-0.422866\pi$
$13$	4.36539	−	4.36539i	1.21074	−	1.21074i	0.970783	−	0.239959i	$-0.0771342\pi$
$14$	−1.13221	+	2.71766i	−0.302595	+	0.726326i
$15$		0			0
$16$	−2.80520	−	2.85146i	−0.701301	−	0.712865i
$17$	−0.0297412	−	4.12300i	−0.00721330	−	0.999974i
$17$	−0.0297412	−	4.12300i	−0.00721330	−	0.999974i
$18$		0			0
$19$	2.55002	−	6.15628i	0.585014	−	1.41235i	−0.303204	−	0.952926i	$-0.598056\pi$
$19$	2.55002	−	6.15628i	0.585014	−	1.41235i	0.888218	−	0.459423i	$-0.151944\pi$
$20$	−1.11629	−	1.68552i	−0.249610	−	0.376894i
$21$		0			0
$22$	−1.39849	+	0.575928i	−0.298160	+	0.122788i
$23$	−0.773086	+	3.88657i	−0.161200	+	0.810405i	0.812569	+	0.582865i	$0.198068\pi$
$23$	−0.773086	+	3.88657i	−0.161200	+	0.810405i	−0.973769	+	0.227540i	$0.926932\pi$
$24$		0			0
$25$	1.52240	+	3.67540i	0.304481	+	0.735081i
$26$	1.72079	−	8.55953i	0.337475	−	1.67866i
$27$		0			0
$28$	0.795567	+	4.08684i	0.150348	+	0.772340i
$29$	3.11609	+	2.08211i	0.578644	+	0.386638i	0.810173	−	0.586190i	$-0.199373\pi$
$29$	3.11609	+	2.08211i	0.578644	+	0.386638i	−0.231529	+	0.972828i	$0.574373\pi$
$30$		0			0
$31$	−5.38553	+	1.07125i	−0.967269	+	0.192402i	−0.653357	−	0.757050i	$-0.726640\pi$
$31$	−5.38553	+	1.07125i	−0.967269	+	0.192402i	−0.313912	+	0.949452i	$0.601640\pi$
$32$	−5.53659	−	1.16025i	−0.978740	−	0.205105i
$33$		0			0
$34$	−3.26452	−	4.83145i	−0.559861	−	0.828587i
$35$			2.10432i			0.355694i
$36$		0			0
$37$	−5.03388	+	1.00130i	−0.827564	+	0.164613i	−0.590660	−	0.806920i	$-0.701133\pi$
$37$	−5.03388	+	1.00130i	−0.827564	+	0.164613i	−0.236904	+	0.971533i	$0.576133\pi$
$38$	−1.81956	−	9.24630i	−0.295172	−	1.49995i
$39$		0			0
$40$	−2.63466	−	1.11029i	−0.416576	−	0.175552i
$41$	4.02629	+	6.02577i	0.628801	+	0.941067i	0.999922	+	0.0124828i	$0.00397351\pi$
$41$	4.02629	+	6.02577i	0.628801	+	0.941067i	−0.371121	+	0.928585i	$0.621026\pi$
$42$		0			0
$43$	0.733065	+	1.76977i	0.111791	+	0.269888i	0.969867	−	0.243635i	$-0.0783400\pi$
$43$	0.733065	+	1.76977i	0.111791	+	0.269888i	−0.858076	+	0.513523i	$0.828340\pi$
$44$	−1.19558	+	1.77357i	−0.180240	+	0.267375i
$45$		0			0
$46$	2.13401	+	5.18190i	0.314643	+	0.764030i
$47$	6.00982	+	6.00982i	0.876622	+	0.876622i	0.993183	−	0.116561i	$-0.0371872\pi$
$47$	6.00982	+	6.00982i	0.876622	+	0.876622i	−0.116561	+	0.993183i	$0.537187\pi$
$48$		0			0
$49$	−1.02031	+	2.46325i	−0.145759	+	0.351893i
$50$	4.67150	+	3.13523i	0.660650	+	0.443389i
$51$		0			0
$52$	−4.67839	−	11.4265i	−0.648776	−	1.58458i
$53$	1.43923	+	0.596147i	0.197693	+	0.0818871i	0.479333	−	0.877633i	$-0.340879\pi$
$53$	1.43923	+	0.596147i	0.197693	+	0.0818871i	−0.281640	+	0.959520i	$0.590879\pi$
$54$		0			0
$55$	−0.764407	+	0.764407i	−0.103073	+	0.103073i
$56$	4.13794	+	4.18901i	0.552956	+	0.559780i
$57$		0			0
$58$	5.30003	+	0.0108348i	0.695928	+	0.00142268i
$59$	−4.31414	+	1.78698i	−0.561653	+	0.232644i	−0.645403	−	0.763842i	$-0.723310\pi$
$59$	−4.31414	+	1.78698i	−0.561653	+	0.232644i	0.0837494	+	0.996487i	$0.473310\pi$
$60$		0			0
$61$	6.25751	−	4.18113i	0.801192	−	0.535339i	−0.0862420	−	0.996274i	$-0.527486\pi$
$61$	6.25751	−	4.18113i	0.801192	−	0.535339i	0.887434	+	0.460935i	$0.152486\pi$
$62$	−5.50225	+	5.47980i	−0.698786	+	0.695935i
$63$		0			0
$64$	−7.42803	+	2.97058i	−0.928504	+	0.371323i
$65$	−1.21745	−	6.12053i	−0.151006	−	0.759158i
$66$		0			0
$67$	0.616467			0.0753134			0.0376567	−	0.999291i	$-0.488011\pi$
$67$	0.616467			0.0753134			0.0376567	+	0.999291i	$0.488011\pi$
$68$	−7.62833	−	3.13187i	−0.925071	−	0.379795i
$69$		0			0
$70$	1.64829	+	2.47779i	0.197008	+	0.296152i
$71$	−1.17044	−	5.88422i	−0.138906	−	0.698329i	−0.985981	−	0.166856i	$-0.946639\pi$
$71$	−1.17044	−	5.88422i	−0.138906	−	0.698329i	0.847075	−	0.531473i	$-0.178361\pi$
$72$		0			0
$73$	0.112327	−	0.168110i	0.0131469	−	0.0196758i	−0.824838	−	0.565369i	$-0.808734\pi$
$73$	0.112327	−	0.168110i	0.0131469	−	0.0196758i	0.837985	+	0.545693i	$0.183734\pi$
$74$	−5.14298	+	5.12199i	−0.597859	+	0.595420i
$75$		0			0
$76$	−9.38502	−	9.46208i	−1.07654	−	1.08538i
$77$	2.05690	−	0.851995i	0.234405	−	0.0970939i
$78$		0			0
$79$	11.4809	+	2.28368i	1.29170	+	0.256935i	0.792670	−	0.609651i	$-0.208691\pi$
$79$	11.4809	+	2.28368i	1.29170	+	0.256935i	0.499028	+	0.866586i	$0.333691\pi$
$80$	−3.97193	+	0.756357i	−0.444076	+	0.0845632i
$81$		0			0
$82$	9.46080	+	3.94147i	1.04477	+	0.435262i
$83$	11.4667	+	4.74966i	1.25863	+	0.521343i	0.909489	−	0.415727i	$-0.136473\pi$
$83$	11.4667	+	4.74966i	1.25863	+	0.521343i	0.349143	+	0.937070i	$0.386473\pi$
$84$		0			0
$85$	−3.48197	−	2.29042i	−0.377672	−	0.248431i
$86$	2.24941	+	1.50967i	0.242561	+	0.162792i
$87$		0			0
$88$	−0.0185510	+	3.02482i	−0.00197755	+	0.322447i
$89$	−1.64195	−	1.64195i	−0.174046	−	0.174046i	0.614708	−	0.788755i	$-0.289274\pi$
$89$	−1.64195	−	1.64195i	−0.174046	−	0.174046i	−0.788755	+	0.614708i	$0.789274\pi$
$90$		0			0
$91$	−2.50731	+	12.6051i	−0.262838	+	1.32137i
$92$	6.57169	+	4.43003i	0.685146	+	0.461863i
$93$		0			0
$94$	11.7839	+	2.36901i	1.21541	+	0.244345i
$95$	−3.74213	−	5.60049i	−0.383934	−	0.574599i
$96$		0			0
$97$	−4.27885	−	2.85903i	−0.434451	−	0.290291i	0.319050	−	0.947738i	$-0.396636\pi$
$97$	−4.27885	−	2.85903i	−0.434451	−	0.290291i	−0.753501	+	0.657447i	$0.771636\pi$
$98$	0.728042	+	3.69963i	0.0735434	+	0.373719i
$99$		0			0
$100$	7.95639	+	0.0325305i	0.795639	+	0.00325305i
$101$			4.66402i			0.464087i	0.972705	+	0.232044i	$0.0745412\pi$
$101$			4.66402i			0.464087i	−0.972705	+	0.232044i	$0.925459\pi$
$102$		0			0
$103$			8.53993i			0.841464i	0.907185	+	0.420732i	$0.138227\pi$
$103$			8.53993i			0.841464i	−0.907185	+	0.420732i	$0.861773\pi$
$104$	−14.4590	−	9.78999i	−1.41782	−	0.959987i
$105$		0			0
$106$	2.16162	−	0.425380i	0.209955	−	0.0413166i
$107$	−3.03293	−	2.02654i	−0.293204	−	0.195913i	0.400264	−	0.916400i	$-0.368918\pi$
$107$	−3.03293	−	2.02654i	−0.293204	−	0.195913i	−0.693469	+	0.720487i	$0.743918\pi$
$108$		0			0
$109$	4.13331	+	6.18594i	0.395899	+	0.592505i	0.974851	−	0.222856i	$-0.0715381\pi$
$109$	4.13331	+	6.18594i	0.395899	+	0.592505i	−0.578952	+	0.815362i	$0.696538\pi$
$110$	−0.301322	+	1.49883i	−0.0287299	+	0.142907i
$111$		0			0
$112$	8.15355	+	1.69127i	0.770438	+	0.159810i
$113$	−0.661577	+	3.32597i	−0.0622359	+	0.312881i	−0.999346	−	0.0361520i	$-0.988490\pi$
$113$	−0.661577	+	3.32597i	−0.0622359	+	0.312881i	0.937110	+	0.349033i	$0.113490\pi$
$114$		0			0
$115$	2.83240	+	2.83240i	0.264122	+	0.264122i
$116$	6.24916	−	4.13870i	0.580220	−	0.384269i
$117$		0			0
$118$	−3.68009	+	5.48335i	−0.338780	+	0.504783i
$119$	4.82003	+	7.10224i	0.441851	+	0.651061i
$120$		0			0
$121$	−9.10600	−	3.77183i	−0.827818	−	0.342893i
$122$	4.09305	−	9.82464i	0.370567	−	0.889481i
$123$		0			0
$124$	−2.18652	+	10.7622i	−0.196355	+	0.966474i
$125$	8.90105	+	1.77053i	0.796134	+	0.158361i
$126$		0			0
$127$	−3.23692	+	1.34078i	−0.287230	+	0.118975i	−0.521647	−	0.853162i	$-0.674682\pi$
$127$	−3.23692	+	1.34078i	−0.287230	+	0.118975i	0.234416	+	0.972136i	$0.424682\pi$
$128$	−6.41953	+	9.31610i	−0.567411	+	0.823435i
$129$		0			0
$130$	−6.22767	−	6.25318i	−0.546203	−	0.548440i
$131$	−8.52460	+	12.7580i	−0.744797	+	1.11467i	0.244627	+	0.969617i	$0.421335\pi$
$131$	−8.52460	+	12.7580i	−0.744797	+	1.11467i	−0.989424	+	0.145051i	$0.953665\pi$
$132$		0			0
$133$	2.70628	+	13.6054i	0.234665	+	1.17974i
$134$	0.725877	−	0.482872i	0.0627062	−	0.0417138i
$135$		0			0
$136$	−11.4354	+	2.28748i	−0.980574	+	0.196150i
$137$	−1.49452			−0.127686			−0.0638429	−	0.997960i	$-0.520336\pi$
$137$	−1.49452			−0.127686			−0.0638429	+	0.997960i	$0.520336\pi$
$138$		0			0
$139$	−3.20590	−	16.1171i	−0.271921	−	1.36704i	−0.839339	−	0.543608i	$-0.817058\pi$
$139$	−3.20590	−	16.1171i	−0.271921	−	1.36704i	0.567419	−	0.823429i	$-0.307942\pi$
$140$	3.88165	+	1.62646i	0.328059	+	0.137461i
$141$		0			0
$142$	−5.98722	−	6.01175i	−0.502437	−	0.504495i
$143$	−5.48969	+	3.66810i	−0.459071	+	0.306742i
$144$		0			0
$145$	3.49990	−	1.44971i	0.290651	−	0.120392i
$146$	0.000584525	−	0.285931i	4.83756e−5	−	0.0236638i
$147$		0			0
$148$	−2.04375	+	10.0595i	−0.167995	+	0.826884i
$149$	4.60411	−	4.60411i	0.377183	−	0.377183i	−0.492902	−	0.870085i	$-0.664064\pi$
$149$	4.60411	−	4.60411i	0.377183	−	0.377183i	0.870085	+	0.492902i	$0.164064\pi$
$150$		0			0
$151$	1.26412	+	0.523616i	0.102873	+	0.0426112i	0.433526	−	0.901141i	$-0.357269\pi$
$151$	1.26412	+	0.523616i	0.102873	+	0.0426112i	−0.330654	+	0.943752i	$0.607269\pi$
$152$	−18.4622	−	3.79022i	−1.49748	−	0.307427i
$153$		0			0
$154$	1.75460	−	2.61435i	0.141389	−	0.210671i
$155$	−2.12408	+	5.12798i	−0.170610	+	0.411889i
$156$		0			0
$157$	3.70126	+	3.70126i	0.295393	+	0.295393i	0.839206	−	0.543813i	$-0.183020\pi$
$157$	3.70126	+	3.70126i	0.295393	+	0.295393i	−0.543813	+	0.839206i	$0.683020\pi$
$158$	15.3073	−	6.30384i	1.21778	−	0.501507i
$159$		0			0
$160$	−4.08442	+	4.00177i	−0.322902	+	0.316367i
$161$	−3.15694	−	7.62153i	−0.248802	−	0.600660i
$162$		0			0
$163$	4.61217	+	6.90260i	0.361253	+	0.540653i	0.966925	−	0.255061i	$-0.0820956\pi$
$163$	4.61217	+	6.90260i	0.361253	+	0.540653i	−0.605672	+	0.795714i	$0.707096\pi$
$164$	14.2272	−	2.76955i	1.11096	−	0.216265i
$165$		0			0
$166$	17.2221	−	3.38911i	1.33670	−	0.263046i
$167$	20.1200	−	4.00211i	1.55693	−	0.309693i	0.659793	−	0.751447i	$-0.270644\pi$
$167$	20.1200	−	4.00211i	1.55693	−	0.309693i	0.897136	+	0.441754i	$0.145644\pi$
$168$		0			0
$169$		−	25.1133i		−	1.93179i
$170$	−5.89400	+	0.0304668i	−0.452049	+	0.00233670i
$171$		0			0
$172$	3.83115	+	0.0156640i	0.292122	+	0.00119437i
$173$	−8.78742	+	1.74793i	−0.668095	+	0.132892i	−0.517474	−	0.855699i	$-0.673127\pi$
$173$	−8.78742	+	1.74793i	−0.668095	+	0.132892i	−0.150621	+	0.988592i	$0.548127\pi$
$174$		0			0
$175$	−6.88606	−	4.60111i	−0.520537	−	0.347812i
$176$	2.34747	+	3.57620i	0.176947	+	0.269566i
$177$		0			0
$178$	−3.21948	−	0.647240i	−0.241310	−	0.0485127i
$179$	−8.09765	−	19.5495i	−0.605247	−	1.46120i	−0.868115	−	0.496364i	$-0.834668\pi$
$179$	−8.09765	−	19.5495i	−0.605247	−	1.46120i	0.262868	−	0.964832i	$-0.415332\pi$
$180$		0			0
$181$	−4.60615	+	23.1567i	−0.342373	+	1.72122i	0.299225	+	0.954182i	$0.403272\pi$
$181$	−4.60615	+	23.1567i	−0.342373	+	1.72122i	−0.641598	+	0.767041i	$0.721728\pi$
$182$	6.92114	+	16.8062i	0.513029	+	1.24576i
$183$		0			0
$184$	11.2080	+	0.0687381i	0.826267	+	0.00506744i
$185$	−1.98539	+	4.79315i	−0.145968	+	0.352399i
$186$		0			0
$187$	−0.829029	+	4.33085i	−0.0606246	+	0.316703i
$188$	15.7309	−	6.44072i	1.14729	−	0.469738i
$189$		0			0
$190$	−8.79309	−	3.66329i	−0.637918	−	0.265763i
$191$	7.02075	−	7.02075i	0.508003	−	0.508003i	−0.405910	−	0.913913i	$-0.633045\pi$
$191$	7.02075	−	7.02075i	0.508003	−	0.508003i	0.913913	+	0.405910i	$0.133045\pi$
$192$		0			0
$193$	−17.6041	−	3.50168i	−1.26717	−	0.252057i	−0.484667	−	0.874699i	$-0.661059\pi$
$193$	−17.6041	−	3.50168i	−1.26717	−	0.252057i	−0.782507	+	0.622642i	$0.786059\pi$
$194$	−7.27771	−	0.0148777i	−0.522509	−	0.00106816i
$195$		0			0
$196$	3.75513	+	3.78597i	0.268224	+	0.270426i
$197$	−1.75750	+	1.17432i	−0.125217	+	0.0836670i	−0.616601	−	0.787276i	$-0.711491\pi$
$197$	−1.75750	+	1.17432i	−0.125217	+	0.0836670i	0.491385	+	0.870943i	$0.336491\pi$
$198$		0			0
$199$	−1.02043	+	1.52719i	−0.0723366	+	0.108259i	−0.865874	−	0.500262i	$-0.833237\pi$
$199$	−1.02043	+	1.52719i	−0.0723366	+	0.108259i	0.793537	+	0.608521i	$0.208237\pi$
$200$	9.39397	−	6.19385i	0.664254	−	0.437972i
$201$		0			0
$202$	3.65328	+	5.49179i	0.257044	+	0.386401i
$203$	−7.80187			−0.547584
$204$		0			0
$205$	7.32559			0.511642
$206$	6.68923	+	10.0556i	0.466061	+	0.700606i
$207$		0			0
$208$	−24.6936	−	0.201927i	−1.71219	−	0.0140011i
$209$	−3.95918	+	5.92534i	−0.273862	+	0.409864i
$210$		0			0
$211$	20.1186	−	13.4428i	1.38502	−	0.925440i	0.385021	−	0.922908i	$-0.374194\pi$
$211$	20.1186	−	13.4428i	1.38502	−	0.925440i	0.999997	−	0.00253193i	$-0.000805940\pi$
$212$	2.21206	−	2.19405i	0.151925	−	0.150688i
$213$		0			0
$214$	−5.15858	−	0.0105456i	−0.352633	−	0.000720884i
$215$	1.89912	+	0.377759i	0.129519	+	0.0257630i
$216$		0			0
$217$	8.08302	−	8.08302i	0.548711	−	0.548711i
$218$	9.71227	+	4.04623i	0.657798	+	0.274046i
$219$		0			0
$220$	0.819215	+	2.00086i	0.0552315	+	0.134898i
$221$	−18.1283	−	17.8687i	−1.21944	−	1.20198i
$222$		0			0
$223$	−5.47542	+	13.2188i	−0.366661	+	0.885199i	0.627631	+	0.778511i	$0.284025\pi$
$223$	−5.47542	+	13.2188i	−0.366661	+	0.885199i	−0.994293	+	0.106688i	$0.965975\pi$
$224$	10.9254	−	4.39516i	0.729983	−	0.293664i
$225$		0			0
$226$	1.82621	+	4.43447i	0.121477	+	0.294977i
$227$	4.02687	−	20.2445i	0.267273	−	1.34367i	−0.580910	−	0.813968i	$-0.697303\pi$
$227$	4.02687	−	20.2445i	0.267273	−	1.34367i	0.848183	−	0.529704i	$-0.177697\pi$
$228$		0			0
$229$	0.275631	+	0.665433i	0.0182142	+	0.0439731i	0.932725	−	0.360589i	$-0.117424\pi$
$229$	0.275631	+	0.665433i	0.0182142	+	0.0439731i	−0.914511	+	0.404562i	$0.867424\pi$
$230$	5.55367	+	1.11650i	0.366198	+	0.0736199i
$231$		0			0
$232$	4.11646	−	9.76814i	0.270259	−	0.641310i
$233$	−15.2485	−	10.1887i	−0.998962	−	0.667485i	−0.0553255	−	0.998468i	$-0.517620\pi$
$233$	−15.2485	−	10.1887i	−0.998962	−	0.667485i	−0.943637	+	0.330983i	$0.892620\pi$
$234$		0			0
$235$	8.42611	−	1.67606i	0.549659	−	0.109334i
$236$	−0.0381838	+	9.33911i	−0.00248556	+	0.607924i
$237$		0			0
$238$	11.2386	+	4.58726i	0.728490	+	0.297348i
$239$		−	10.2504i		−	0.663044i	−0.943447	−	0.331522i	$-0.892438\pi$
$239$		−	10.2504i		−	0.663044i	0.943447	−	0.331522i	$-0.107562\pi$
$240$		0			0
$241$	10.6102	−	2.11050i	0.683462	−	0.135949i	0.158866	−	0.987300i	$-0.449216\pi$
$241$	10.6102	−	2.11050i	0.683462	−	0.135949i	0.524596	+	0.851351i	$0.324216\pi$
$242$	−13.6766	+	2.69138i	−0.879163	+	0.173009i
$243$		0			0
$244$	−2.87606	−	14.7744i	−0.184121	−	0.945831i
$245$	1.49730	+	2.24087i	0.0956590	+	0.143164i
$246$		0			0
$247$	−15.7428	−	38.0064i	−1.00169	−	2.41829i
$248$	5.85534	+	14.3849i	0.371815	+	0.913445i
$249$		0			0
$250$	11.8676	−	4.88734i	0.750575	−	0.309102i
$251$	2.76475	+	2.76475i	0.174509	+	0.174509i	0.788957	−	0.614448i	$-0.210621\pi$
$251$	2.76475	+	2.76475i	0.174509	+	0.174509i	−0.614448	+	0.788957i	$0.710621\pi$
$252$		0			0
$253$	1.62179	−	3.91535i	0.101961	−	0.246156i
$254$	−2.76119	+	4.11418i	−0.173253	+	0.258147i
$255$		0			0
$256$	−0.261657	+	15.9979i	−0.0163536	+	0.999866i
$257$	13.2450	+	5.48626i	0.826201	+	0.342224i	0.755398	−	0.655266i	$-0.227444\pi$
$257$	13.2450	+	5.48626i	0.826201	+	0.342224i	0.0708035	+	0.997490i	$0.477444\pi$
$258$		0			0
$259$	7.55523	−	7.55523i	0.469459	−	0.469459i
$260$	−12.2310	−	2.48493i	−0.758535	−	0.154109i
$261$		0			0
$262$	−0.0443600	+	21.6995i	−0.00274057	+	1.34060i
$263$	−16.6441	+	6.89422i	−1.02632	+	0.425116i	−0.831383	−	0.555700i	$-0.812450\pi$
$263$	−16.6441	+	6.89422i	−1.02632	+	0.425116i	−0.194937	+	0.980816i	$0.562450\pi$
$264$		0			0
$265$	1.30929	−	0.874842i	0.0804292	−	0.0537411i
$266$	13.8436	+	13.9003i	0.848803	+	0.852281i
$267$		0			0
$268$	0.476477	−	1.13714i	0.0291054	−	0.0694621i
$269$	6.36128	+	31.9803i	0.387854	+	1.94987i	0.300879	+	0.953662i	$0.402720\pi$
$269$	6.36128	+	31.9803i	0.387854	+	1.94987i	0.0869746	+	0.996211i	$0.472280\pi$
$270$		0			0
$271$	4.56417			0.277253			0.138627	−	0.990345i	$-0.455731\pi$
$271$	4.56417			0.277253			0.138627	+	0.990345i	$0.455731\pi$
$272$	−11.6731	+	11.6507i	−0.707788	+	0.706425i
$273$		0			0
$274$	−1.75977	+	1.17065i	−0.106312	+	0.0707213i
$275$	−0.830020	−	4.17279i	−0.0500521	−	0.251629i
$276$		0			0
$277$	−7.41492	+	11.0972i	−0.445519	+	0.666767i	−0.984466	−	0.175573i	$-0.943822\pi$
$277$	−7.41492	+	11.0972i	−0.445519	+	0.666767i	0.538947	+	0.842340i	$0.318822\pi$
$278$	−16.3993	−	16.4664i	−0.983562	−	0.987591i
$279$		0			0
$280$	5.84455	−	1.12534i	0.349279	−	0.0672517i
$281$	−3.29326	+	1.36411i	−0.196459	+	0.0813762i	−0.478744	−	0.877955i	$-0.658908\pi$
$281$	−3.29326	+	1.36411i	−0.196459	+	0.0813762i	0.282285	+	0.959331i	$0.408908\pi$
$282$		0			0
$283$	−32.5206	−	6.46874i	−1.93315	−	0.384527i	−0.999664	−	0.0259060i	$-0.991753\pi$
$283$	−32.5206	−	6.46874i	−1.93315	−	0.384527i	−0.933483	−	0.358621i	$-0.883247\pi$
$284$	−11.7588	−	2.38899i	−0.697755	−	0.141760i
$285$		0			0
$286$	−3.59082	+	8.61913i	−0.212330	+	0.509660i
$287$	−13.9385	−	5.77351i	−0.822763	−	0.340800i
$288$		0			0
$289$	−16.9982	+	0.245246i	−0.999896	+	0.0144262i
$290$	2.98552	−	4.44844i	0.175316	−	0.261221i
$291$		0			0
$292$	−0.223278	−	0.337135i	−0.0130664	−	0.0197294i
$293$	−8.72543	−	8.72543i	−0.509745	−	0.509745i	0.404703	−	0.914448i	$-0.367375\pi$
$293$	−8.72543	−	8.72543i	−0.509745	−	0.509745i	−0.914448	+	0.404703i	$0.867375\pi$
$294$		0			0
$295$	−0.920855	+	4.62945i	−0.0536143	+	0.269537i
$296$	5.47302	+	13.4457i	0.318113	+	0.781514i
$297$		0			0
$298$	1.81489	−	9.02759i	0.105134	−	0.522954i
$299$	13.5916	+	20.3412i	0.786021	+	1.17636i
$300$		0			0
$301$	−3.31576	−	2.21552i	−0.191117	−	0.127701i
$302$	1.89862	−	0.373625i	0.109253	−	0.0214997i
$303$		0			0
$304$	−24.7077	+	9.99836i	−1.41708	+	0.573445i
$305$		−	7.60732i		−	0.435594i
$306$		0			0
$307$			1.15950i			0.0661761i	0.999452	+	0.0330881i	$0.0105342\pi$
$307$			1.15950i			0.0661761i	−0.999452	+	0.0330881i	$0.989466\pi$
$308$	0.0182053	−	4.45270i	0.00103734	−	0.253716i
$309$		0			0
$310$	1.51563	+	7.70186i	0.0860822	+	0.437436i
$311$	−6.43138	−	4.29731i	−0.364690	−	0.243678i	0.359701	−	0.933068i	$-0.382879\pi$
$311$	−6.43138	−	4.29731i	−0.364690	−	0.243678i	−0.724391	+	0.689390i	$0.757879\pi$
$312$		0			0
$313$	−6.48916	−	9.71171i	−0.366789	−	0.548938i	0.601468	−	0.798897i	$-0.294583\pi$
$313$	−6.48916	−	9.71171i	−0.366789	−	0.548938i	−0.968256	+	0.249959i	$0.919583\pi$
$314$	7.25732	+	1.45900i	0.409554	+	0.0823361i
$315$		0			0
$316$	13.0862	−	19.4127i	0.736159	−	1.09205i
$317$	−2.37533	+	11.9416i	−0.133412	+	0.670706i	0.854965	+	0.518685i	$0.173578\pi$
$317$	−2.37533	+	11.9416i	−0.133412	+	0.670706i	−0.988377	+	0.152021i	$0.951422\pi$
$318$		0			0
$319$	−2.83408	−	2.83408i	−0.158678	−	0.158678i
$320$	−1.67478	+	7.91128i	−0.0936231	+	0.442254i
$321$		0			0
$322$	−9.68709	−	6.50139i	−0.539840	−	0.362308i
$323$	−25.4582	−	10.3306i	−1.41653	−	0.574811i
$324$		0			0
$325$	22.6905	+	9.39870i	1.25864	+	0.521346i
$326$	10.8375	+	4.51500i	0.600232	+	0.250063i
$327$		0			0
$328$	14.5829	−	14.4051i	0.805205	−	0.795389i
$329$	−17.3534	−	3.45181i	−0.956724	−	0.190304i
$330$		0			0
$331$	1.60439	−	0.664562i	0.0881855	−	0.0365276i	−0.338155	−	0.941091i	$-0.609803\pi$
$331$	1.60439	−	0.664562i	0.0881855	−	0.0365276i	0.426340	+	0.904563i	$0.359803\pi$
$332$	17.6241	−	17.4805i	0.967246	−	0.959369i
$333$		0			0
$334$	20.5560	−	20.4722i	1.12478	−	1.12019i
$335$	0.346199	−	0.518123i	0.0189149	−	0.0283081i
$336$		0			0
$337$	1.90969	+	9.60067i	0.104028	+	0.522982i	0.997298	+	0.0734621i	$0.0234048\pi$
$337$	1.90969	+	9.60067i	0.104028	+	0.522982i	−0.893270	+	0.449520i	$0.851595\pi$
$338$	−19.6710	−	29.5704i	−1.06996	−	1.60842i
$339$		0			0
$340$	−6.91620	+	4.65258i	−0.375084	+	0.252322i
$341$	5.87242			0.318010
$342$		0			0
$343$	−3.92578	−	19.7362i	−0.211972	−	1.06566i
$344$	4.52337	−	2.98245i	0.243884	−	0.160803i
$345$		0			0
$346$	−8.97787	+	8.94124i	−0.482653	+	0.480684i
$347$	23.9344	−	15.9925i	1.28487	−	0.858520i	0.289737	−	0.957106i	$-0.406432\pi$
$347$	23.9344	−	15.9925i	1.28487	−	0.858520i	0.995129	+	0.0985862i	$0.0314320\pi$
$348$		0			0
$349$	1.40518	−	0.582046i	0.0752178	−	0.0311562i	−0.344757	−	0.938692i	$-0.612039\pi$
$349$	1.40518	−	0.582046i	0.0752178	−	0.0311562i	0.419975	+	0.907536i	$0.362039\pi$
$350$	−11.7122	−	0.0239431i	−0.626043	−	0.00127981i
$351$		0			0
$352$	5.56529	+	2.37215i	0.296631	+	0.126436i
$353$	−16.0913	+	16.0913i	−0.856454	+	0.856454i	−0.990918	−	0.134464i	$-0.957069\pi$
$353$	−16.0913	+	16.0913i	−0.856454	+	0.856454i	0.134464	+	0.990918i	$0.457069\pi$
$354$		0			0
$355$	−5.60283	−	2.32077i	−0.297367	−	0.123173i
$356$	−4.29785	+	1.75968i	−0.227786	+	0.0932626i
$357$		0			0
$358$	−24.8477	−	16.6763i	−1.31324	−	0.881369i
$359$	11.2986	−	27.2772i	0.596316	−	1.43963i	−0.280994	−	0.959710i	$-0.590664\pi$
$359$	11.2986	−	27.2772i	0.596316	−	1.43963i	0.877310	−	0.479924i	$-0.159336\pi$
$360$		0			0
$361$	−17.9622	−	17.9622i	−0.945380	−	0.945380i
$362$	12.7147	+	30.8745i	0.668272	+	1.62273i
$363$		0			0
$364$	21.3136	+	14.3677i	1.11714	+	0.753072i
$365$	−0.0782101	−	0.188816i	−0.00409370	−	0.00988308i
$366$		0			0
$367$	5.23108	+	7.82887i	0.273060	+	0.408664i	0.942502	−	0.334201i	$-0.108467\pi$
$367$	5.23108	+	7.82887i	0.273060	+	0.408664i	−0.669441	+	0.742865i	$0.733467\pi$
$368$	13.2511	−	8.69819i	0.690759	−	0.453425i
$369$		0			0
$370$	1.41667	+	7.19896i	0.0736492	+	0.374256i
$371$	−3.18069	+	0.632680i	−0.165133	+	0.0328471i
$372$		0			0
$373$			21.7371i			1.12550i	0.826626	+	0.562751i	$0.190257\pi$
$373$			21.7371i			1.12550i	−0.826626	+	0.562751i	$0.809743\pi$
$374$	2.41614	+	5.74886i	0.124936	+	0.297266i
$375$		0			0
$376$	13.4778	−	19.9056i	0.695066	−	1.02656i
$377$	22.6922	−	4.51376i	1.16871	−	0.232470i
$378$		0			0
$379$	−3.46561	−	2.31565i	−0.178016	−	0.118947i	0.463370	−	0.886165i	$-0.346640\pi$
$379$	−3.46561	−	2.31565i	−0.178016	−	0.118947i	−0.641386	+	0.767218i	$0.721640\pi$
$380$	−13.2231	+	2.57408i	−0.678331	+	0.132048i
$381$		0			0
$382$	2.76751	−	13.7661i	0.141598	−	0.704333i
$383$	−10.4436	−	25.2130i	−0.533642	−	1.28833i	−0.929096	−	0.369839i	$-0.879413\pi$
$383$	−10.4436	−	25.2130i	−0.533642	−	1.28833i	0.395454	−	0.918486i	$-0.370587\pi$
$384$		0			0
$385$	0.439046	−	2.20723i	0.0223758	−	0.112491i
$386$	−23.4713	+	9.66598i	−1.19466	+	0.491985i
$387$		0			0
$388$	−8.58100	+	5.68303i	−0.435634	+	0.288512i
$389$	0.852088	−	2.05712i	0.0432026	−	0.104300i	−0.900805	−	0.434223i	$-0.857023\pi$
$389$	0.852088	−	2.05712i	0.0432026	−	0.104300i	0.944008	+	0.329923i	$0.107023\pi$
$390$		0			0
$391$	16.0473	+	3.07184i	0.811547	+	0.155350i
$392$	7.38710	+	1.51654i	0.373105	+	0.0765968i
$393$		0			0
$394$	−1.14958	+	2.75937i	−0.0579152	+	0.139015i
$395$	8.36685	−	8.36685i	0.420982	−	0.420982i
$396$		0			0
$397$	−5.08689	−	1.01185i	−0.255304	−	0.0507831i	0.0657790	−	0.997834i	$-0.479047\pi$
$397$	−5.08689	−	1.01185i	−0.255304	−	0.0507831i	−0.321083	+	0.947051i	$0.604047\pi$
$398$	−0.00531009	+	2.59753i	−0.000266171	+	0.130202i
$399$		0			0
$400$	6.20962	−	14.6513i	0.310481	−	0.732567i
$401$	11.0979	−	7.41540i	0.554204	−	0.370307i	−0.246708	−	0.969090i	$-0.579349\pi$
$401$	11.0979	−	7.41540i	0.554204	−	0.370307i	0.800912	+	0.598783i	$0.204349\pi$
$402$		0			0
$403$	−18.8335	+	28.1864i	−0.938164	+	1.40406i
$404$	8.60332	+	3.60489i	0.428031	+	0.179350i
$405$		0			0
$406$	−9.18654	+	6.11112i	−0.455920	+	0.303290i
$407$	5.48898			0.272079
$408$		0			0
$409$	−0.0180838			−0.000894186			−0.000447093	−	1.00000i	$-0.500142\pi$
$409$	−0.0180838			−0.000894186			−0.000447093		1.00000i	$0.500142\pi$
$410$	8.62574	−	5.73806i	0.425995	−	0.283383i
$411$		0			0
$412$	15.7529	+	6.60064i	0.776088	+	0.325190i
$413$	5.40073	−	8.08276i	0.265752	−	0.397727i
$414$		0			0
$415$	10.4315	−	6.97009i	0.512061	−	0.342148i
$416$	−29.2343	+	19.1044i	−1.43333	+	0.936673i
$417$		0			0
$418$	−0.0206026	+	10.0781i	−0.00100771	+	0.492938i
$419$	2.09333	+	0.416388i	0.102266	+	0.0203419i	0.245958	−	0.969281i	$-0.420898\pi$
$419$	2.09333	+	0.416388i	0.102266	+	0.0203419i	−0.143692	+	0.989622i	$0.545898\pi$
$420$		0			0
$421$	12.0317	−	12.0317i	0.586391	−	0.586391i	−0.350261	−	0.936652i	$-0.613907\pi$
$421$	12.0317	−	12.0317i	0.586391	−	0.586391i	0.936652	+	0.350261i	$0.113907\pi$
$422$	13.1596	−	31.5873i	0.640599	−	1.53764i
$423$		0			0
$424$	0.886083	−	4.31613i	0.0430320	−	0.209610i
$425$	15.1084	−	6.38617i	0.732866	−	0.309775i
$426$		0			0
$427$	−5.99555	+	14.4745i	−0.290145	+	0.700472i
$428$	−6.08238	+	4.02824i	−0.294003	+	0.194713i
$429$		0			0
$430$	2.53207	−	1.04276i	0.122107	−	0.0502864i
$431$	−7.00428	+	35.2129i	−0.337385	+	1.69615i	0.323965	+	0.946069i	$0.394984\pi$
$431$	−7.00428	+	35.2129i	−0.337385	+	1.69615i	−0.661350	+	0.750078i	$0.730016\pi$
$432$		0			0
$433$	1.25174	+	3.02196i	0.0601546	+	0.145226i	0.951099	−	0.308887i	$-0.0999563\pi$
$433$	1.25174	+	3.02196i	0.0601546	+	0.145226i	−0.890944	+	0.454113i	$0.849956\pi$
$434$	3.18624	−	15.8489i	0.152945	−	0.760773i
$435$		0			0
$436$	14.6054	−	2.84316i	0.699470	−	0.136163i
$437$	21.9554	+	14.6702i	1.05027	+	0.701768i
$438$		0			0
$439$	1.05590	−	0.210032i	0.0503954	−	0.0100243i	−0.169828	−	0.985474i	$-0.554321\pi$
$439$	1.05590	−	0.210032i	0.0503954	−	0.0100243i	0.220224	+	0.975449i	$0.429321\pi$
$440$	2.53186	+	1.71429i	0.120702	+	0.0817255i
$441$		0			0
$442$	−35.3421	−	6.84026i	−1.68105	−	0.325358i
$443$			23.1842i			1.10152i	0.834665	+	0.550758i	$0.185661\pi$
$443$			23.1842i			1.10152i	−0.834665	+	0.550758i	$0.814339\pi$
$444$		0			0
$445$	−2.30211	+	0.457917i	−0.109130	+	0.0217074i
$446$	3.90698	+	19.8537i	0.185001	+	0.940102i
$447$		0			0
$448$	9.42174	−	13.7329i	0.445135	−	0.648821i
$449$	−15.6952	−	23.4895i	−0.740701	−	1.10854i	−0.990131	−	0.140145i	$-0.955243\pi$
$449$	−15.6952	−	23.4895i	−0.740701	−	1.10854i	0.249430	−	0.968393i	$-0.419757\pi$
$450$		0			0
$451$	−2.96599	−	7.16052i	−0.139663	−	0.337176i
$452$	5.62379	+	3.79105i	0.264521	+	0.178316i
$453$		0			0
$454$	−11.1157	−	26.9916i	−0.521686	−	1.26678i
$455$	9.18617	+	9.18617i	0.430654	+	0.430654i
$456$		0			0
$457$	8.21934	−	19.8432i	0.384485	−	0.928228i	−0.606602	−	0.795006i	$-0.707468\pi$
$457$	8.21934	−	19.8432i	0.384485	−	0.928228i	0.991086	−	0.133222i	$-0.0425323\pi$
$458$	0.845777	+	0.567635i	0.0395206	+	0.0265238i
$459$		0			0
$460$	7.41388	−	3.03548i	0.345674	−	0.141530i
$461$	−6.76893	−	2.80378i	−0.315260	−	0.130585i	0.219442	−	0.975626i	$-0.429576\pi$
$461$	−6.76893	−	2.80378i	−0.315260	−	0.130585i	−0.534702	+	0.845040i	$0.679576\pi$
$462$		0			0
$463$	−4.70840	+	4.70840i	−0.218818	+	0.218818i	−0.808000	−	0.589182i	$-0.799450\pi$
$463$	−4.70840	+	4.70840i	−0.218818	+	0.218818i	0.589182	+	0.808000i	$0.299450\pi$
$464$	−2.80423	−	14.7262i	−0.130183	−	0.683645i
$465$		0			0
$466$	−25.9355	−	0.0530197i	−1.20144	−	0.00245609i
$467$	−25.4117	+	10.5259i	−1.17591	+	0.487079i	−0.883143	−	0.469104i	$-0.844577\pi$
$467$	−25.4117	+	10.5259i	−1.17591	+	0.487079i	−0.292770	+	0.956183i	$0.594577\pi$
$468$		0			0
$469$	−1.06706	+	0.712989i	−0.0492724	+	0.0329228i
$470$	8.60873	−	8.57360i	0.397091	−	0.395471i
$471$		0			0
$472$	7.27026	+	11.0265i	0.334641	+	0.507537i
$473$	−0.399670	−	2.00928i	−0.0183769	−	0.0923867i
$474$		0			0
$475$	26.5090			1.21632
$476$	16.8264	−	3.40167i	0.771236	−	0.155915i
$477$		0			0
$478$	−8.02904	−	12.0696i	−0.367240	−	0.552053i
$479$	−2.10832	−	10.5992i	−0.0963315	−	0.484291i	−0.998589	−	0.0530945i	$-0.983092\pi$
$479$	−2.10832	−	10.5992i	−0.0963315	−	0.484291i	0.902258	−	0.431197i	$-0.141908\pi$
$480$		0			0
$481$	−17.6038	+	26.3459i	−0.802664	+	1.20127i
$482$	10.8401	−	10.7959i	0.493755	−	0.491740i
$483$		0			0
$484$	−13.9957	+	13.8818i	−0.636170	+	0.630989i
$485$	−4.80587	+	1.99066i	−0.218224	+	0.0903911i
$486$		0			0
$487$	4.15661	+	0.826801i	0.188354	+	0.0374659i	0.288366	−	0.957520i	$-0.406888\pi$
$487$	4.15661	+	0.826801i	0.188354	+	0.0374659i	−0.100012	+	0.994986i	$0.531888\pi$
$488$	−14.9591	−	15.1437i	−0.677166	−	0.685524i
$489$		0			0
$490$	3.51829	+	1.46576i	0.158940	+	0.0662161i
$491$	−2.21627	−	0.918009i	−0.100019	−	0.0414292i	0.332113	−	0.943240i	$-0.392238\pi$
$491$	−2.21627	−	0.918009i	−0.100019	−	0.0414292i	−0.432132	+	0.901810i	$0.642238\pi$
$492$		0			0
$493$	8.49185	−	12.9096i	0.382454	−	0.581418i
$494$	−48.3068	−	32.4206i	−2.17343	−	1.45867i
$495$		0			0
$496$	18.1621	+	12.3515i	0.815503	+	0.554601i
$497$	8.83150	+	8.83150i	0.396147	+	0.396147i
$498$		0			0
$499$	−0.0192904	+	0.0969795i	−0.000863558	+	0.00434140i	−0.981215	−	0.192919i	$-0.938204\pi$
$499$	−0.0192904	+	0.0969795i	−0.000863558	+	0.00434140i	0.980351	+	0.197261i	$0.0632045\pi$
$500$	10.1457	−	15.0505i	0.453730	−	0.673081i
$501$		0			0
$502$	5.42103	+	1.08984i	0.241952	+	0.0486417i
$503$	13.2387	+	19.8132i	0.590286	+	0.883425i	0.999580	−	0.0289774i	$-0.00922510\pi$
$503$	13.2387	+	19.8132i	0.590286	+	0.883425i	−0.409294	+	0.912402i	$0.634225\pi$
$504$		0			0
$505$	3.91998	+	2.61925i	0.174437	+	0.116555i
$506$	−1.15723	−	5.88058i	−0.0514451	−	0.261424i
$507$		0			0
$508$	−0.0286495	+	7.00718i	−0.00127112	+	0.310893i
$509$		−	4.80674i		−	0.213055i	−0.994310	−	0.106527i	$-0.966027\pi$
$509$		−	4.80674i		−	0.213055i	0.994310	−	0.106527i	$-0.0339732\pi$
$510$		0			0
$511$			0.420902i			0.0186196i
$512$	12.2229	+	19.0421i	0.540179	+	0.841550i
$513$		0			0
$514$	19.8931	−	3.91472i	0.877446	−	0.172671i
$515$	7.17756	+	4.79590i	0.316281	+	0.211332i
$516$		0			0
$517$	−5.04985	−	7.55764i	−0.222092	−	0.332384i
$518$	2.97820	−	14.8141i	0.130854	−	0.650893i
$519$		0			0
$520$	−16.3482	+	6.65447i	−0.716915	+	0.291818i
$521$	6.23757	−	31.3584i	0.273273	−	1.37384i	−0.563423	−	0.826168i	$-0.690516\pi$
$521$	6.23757	−	31.3584i	0.273273	−	1.37384i	0.836696	−	0.547667i	$-0.184484\pi$
$522$		0			0
$523$	4.39174	+	4.39174i	0.192037	+	0.192037i	0.796576	−	0.604538i	$-0.206642\pi$
$523$	4.39174	+	4.39174i	0.192037	+	0.192037i	−0.604538	+	0.796576i	$0.706642\pi$
$524$	16.9447	+	25.5854i	0.740234	+	1.11770i
$525$		0			0
$526$	−14.1979	+	21.1550i	−0.619059	+	0.922400i
$527$	4.57692	+	22.1727i	0.199374	+	0.965856i
$528$		0			0
$529$	6.74148	+	2.79241i	0.293108	+	0.121409i
$530$	0.856411	−	2.05566i	0.0372001	−	0.0892923i
$531$		0			0
$532$	27.1885	+	5.52378i	1.17877	+	0.239486i
$533$	43.8812	+	8.72852i	1.90071	+	0.378074i
$534$		0			0
$535$	−3.40650	+	1.41102i	−0.147276	+	0.0610036i
$536$	−0.329671	−	1.71218i	−0.0142396	−	0.0739550i
$537$		0			0
$538$	32.5401	+	32.6734i	1.40290	+	1.40865i
$539$	1.58415	−	2.37084i	0.0682340	−	0.102119i
$540$		0			0
$541$	−3.65194	−	18.3596i	−0.157009	−	0.789339i	−0.976378	−	0.216072i	$-0.930676\pi$
$541$	−3.65194	−	18.3596i	−0.157009	−	0.789339i	0.819368	−	0.573268i	$-0.194324\pi$
$542$	5.37421	−	3.57506i	0.230842	−	0.153562i
$543$		0			0
$544$	−4.61904	+	22.8619i	−0.198040	+	0.980194i
$545$	7.52031			0.322135
$546$		0			0
$547$	3.86493	+	19.4303i	0.165253	+	0.830781i	0.971103	+	0.238661i	$0.0767086\pi$
$547$	3.86493	+	19.4303i	0.165253	+	0.830781i	−0.805850	+	0.592119i	$0.798291\pi$
$548$	−1.15514	+	2.75682i	−0.0493452	+	0.117766i
$549$		0			0
$550$	−4.24584	−	4.26323i	−0.181043	−	0.181785i
$551$	20.7641	−	13.8742i	0.884582	−	0.591059i
$552$		0			0
$553$	−22.5139	+	9.32555i	−0.957387	+	0.396563i
$554$	−0.0385855	+	18.8748i	−0.00163934	+	0.801912i
$555$		0			0
$556$	−32.2078	−	6.54353i	−1.36591	−	0.277507i
$557$	−2.93149	+	2.93149i	−0.124211	+	0.124211i	−0.766480	−	0.642269i	$-0.777993\pi$
$557$	−2.93149	+	2.93149i	−0.124211	+	0.124211i	0.642269	+	0.766480i	$0.277993\pi$
$558$		0			0
$559$	10.9259	+	4.52565i	0.462116	+	0.191415i
$560$	6.00037	−	5.90304i	0.253562	−	0.249449i
$561$		0			0
$562$	−2.80925	+	4.18579i	−0.118501	+	0.176567i
$563$	−10.2091	+	24.6470i	−0.430264	+	1.03875i	0.548938	+	0.835863i	$0.315032\pi$
$563$	−10.2091	+	24.6470i	−0.430264	+	1.03875i	−0.979202	+	0.202886i	$0.934968\pi$
$564$		0			0
$565$	2.42385	+	2.42385i	0.101972	+	0.101972i
$566$	−43.3592	+	17.8562i	−1.82252	+	0.750553i
$567$		0			0
$568$	−15.7170	+	6.39754i	−0.659470	+	0.268435i
$569$	−12.5588	−	30.3197i	−0.526494	−	1.27107i	−0.933806	−	0.357780i	$-0.883534\pi$
$569$	−12.5588	−	30.3197i	−0.526494	−	1.27107i	0.407312	−	0.913289i	$-0.366466\pi$
$570$		0			0
$571$	−5.97411	−	8.94088i	−0.250009	−	0.374164i	0.685145	−	0.728407i	$-0.259739\pi$
$571$	−5.97411	−	8.94088i	−0.250009	−	0.374164i	−0.935154	+	0.354242i	$0.884739\pi$
$572$	2.52315	+	12.9615i	0.105498	+	0.541947i
$573$		0			0
$574$	−20.9346	+	4.11968i	−0.873794	+	0.171952i
$575$	−15.4617	+	3.07552i	−0.644796	+	0.128258i
$576$		0			0
$577$		−	40.4944i		−	1.68581i	−0.538066	−	0.842903i	$-0.680845\pi$
$577$		−	40.4944i		−	1.68581i	0.538066	−	0.842903i	$-0.319155\pi$
$578$	−19.8230	+	13.6033i	−0.824527	+	0.565823i
$579$		0			0
$580$	0.0309771	−	7.57648i	0.00128626	−	0.314596i
$581$	−25.3414	+	5.04072i	−1.05134	+	0.209124i
$582$		0			0
$583$	−1.38523	−	0.925584i	−0.0573706	−	0.0383338i
$584$	−0.526980	−	0.222078i	−0.0218066	−	0.00918967i
$585$		0			0
$586$	−17.1085	−	3.43947i	−0.706747	−	0.142083i
$587$	−3.22904	−	7.79559i	−0.133277	−	0.321758i	0.843126	−	0.537716i	$-0.180713\pi$
$587$	−3.22904	−	7.79559i	−0.133277	−	0.321758i	−0.976403	+	0.215958i	$0.930713\pi$
$588$		0			0
$589$	−7.13827	+	35.8865i	−0.294127	+	1.47868i
$590$	2.54191	+	6.17238i	0.104649	+	0.254113i
$591$		0			0
$592$	16.9762	+	11.5451i	0.697718	+	0.474499i
$593$	−13.8864	+	33.5247i	−0.570245	+	1.37669i	0.331101	+	0.943595i	$0.392580\pi$
$593$	−13.8864	+	33.5247i	−0.570245	+	1.37669i	−0.901347	+	0.433099i	$0.857420\pi$
$594$		0			0
$595$	8.67609	−	0.0625848i	0.355685	−	0.00256573i
$596$	−4.93422	−	12.0514i	−0.202113	−	0.493644i
$597$		0			0
$598$	31.9369	+	13.3052i	1.30600	+	0.544092i
$599$	−18.2511	+	18.2511i	−0.745722	+	0.745722i	−0.973673	−	0.227951i	$-0.926797\pi$
$599$	−18.2511	+	18.2511i	−0.745722	+	0.745722i	0.227951	+	0.973673i	$0.426797\pi$
$600$		0			0
$601$	29.1388	+	5.79607i	1.18860	+	0.236426i	0.749494	−	0.662011i	$-0.230297\pi$
$601$	29.1388	+	5.79607i	1.18860	+	0.236426i	0.439102	+	0.898437i	$0.355297\pi$
$602$	−5.63964	−	0.0115290i	−0.229854	−	0.000469889i
$603$		0			0
$604$	1.94293	−	1.92710i	0.0790566	−	0.0784127i
$605$	−8.28391	+	5.53513i	−0.336789	+	0.225035i
$606$		0			0
$607$	2.39265	−	3.58085i	0.0971145	−	0.145342i	−0.779730	−	0.626115i	$-0.784644\pi$
$607$	2.39265	−	3.58085i	0.0971145	−	0.145342i	0.876845	+	0.480773i	$0.159644\pi$
$608$	−21.2612	+	31.1262i	−0.862256	+	1.26233i
$609$		0			0
$610$	−5.95874	−	8.95746i	−0.241262	−	0.362677i
$611$	52.4705			2.12273
$612$		0			0
$613$	48.3994			1.95483			0.977417	−	0.211319i	$-0.0677760\pi$
$613$	48.3994			1.95483			0.977417	+	0.211319i	$0.0677760\pi$
$614$	0.908224	+	1.36529i	0.0366529	+	0.0550985i
$615$		0			0
$616$	−3.46632	−	5.25723i	−0.139662	−	0.211820i
$617$	−18.1998	+	27.2379i	−0.732697	+	1.09656i	0.258737	+	0.965948i	$0.416694\pi$
$617$	−18.1998	+	27.2379i	−0.732697	+	1.09656i	−0.991434	+	0.130611i	$0.958306\pi$
$618$		0			0
$619$	7.40715	−	4.94930i	0.297718	−	0.198929i	−0.397735	−	0.917500i	$-0.630204\pi$
$619$	7.40715	−	4.94930i	0.297718	−	0.198929i	0.695453	+	0.718571i	$0.255204\pi$
$620$	7.81741	+	7.88160i	0.313955	+	0.316533i
$621$		0			0
$622$	−10.9389	−	0.0223622i	−0.438608	−	0.000896641i
$623$	4.74114	+	0.943072i	0.189950	+	0.0377834i
$624$		0			0
$625$	−7.57839	+	7.57839i	−0.303136	+	0.303136i
$626$	−15.2479	−	6.35245i	−0.609430	−	0.253895i
$627$		0			0
$628$	9.68816	−	3.96664i	0.386600	−	0.158286i
$629$	4.27807	+	20.7249i	0.170578	+	0.826355i
$630$		0			0
$631$	−12.8274	+	30.9682i	−0.510652	+	1.23282i	0.432853	+	0.901465i	$0.357507\pi$
$631$	−12.8274	+	30.9682i	−0.510652	+	1.23282i	−0.943505	+	0.331359i	$0.892493\pi$
$632$	0.203051	−	33.1083i	0.00807694	−	1.31698i
$633$		0			0
$634$	6.55682	+	15.9215i	0.260404	+	0.632325i
$635$	−0.690922	+	3.47350i	−0.0274184	+	0.137842i
$636$		0			0
$637$	6.29900	+	15.2071i	0.249575	+	0.602528i
$638$	−5.55698	−	1.11717i	−0.220003	−	0.0442290i
$639$		0			0
$640$	4.22481	+	10.6272i	0.167000	+	0.420077i
$641$	−30.1359	−	20.1362i	−1.19030	−	0.795331i	−0.207179	−	0.978303i	$-0.566428\pi$
$641$	−30.1359	−	20.1362i	−1.19030	−	0.795331i	−0.983118	+	0.182972i	$0.941428\pi$
$642$		0			0
$643$	11.5439	−	2.29622i	0.455246	−	0.0905540i	0.0378593	−	0.999283i	$-0.487946\pi$
$643$	11.5439	−	2.29622i	0.455246	−	0.0905540i	0.417387	+	0.908729i	$0.362946\pi$
$644$	−16.4988	−	0.0674570i	−0.650145	−	0.00265818i
$645$		0			0
$646$	−38.0684	+	7.77704i	−1.49778	+	0.305984i
$647$			24.9566i			0.981146i	0.871400	+	0.490573i	$0.163213\pi$
$647$			24.9566i			0.981146i	−0.871400	+	0.490573i	$0.836787\pi$
$648$		0			0
$649$	4.89797	−	0.974267i	0.192262	−	0.0382433i
$650$	34.0795	−	6.70643i	1.33671	−	0.263048i
$651$		0			0
$652$	16.2974	−	3.17255i	0.638257	−	0.124247i
$653$	8.79462	+	13.1621i	0.344160	+	0.515072i	0.962660	−	0.270713i	$-0.0872594\pi$
$653$	8.79462	+	13.1621i	0.344160	+	0.515072i	−0.618500	+	0.785785i	$0.712259\pi$
$654$		0			0
$655$	5.93542	+	14.3294i	0.231916	+	0.559894i
$656$	5.88768	−	28.3843i	0.229875	−	1.10822i
$657$		0			0
$658$	−23.1370	+	9.52831i	−0.901975	+	0.371452i
$659$	14.1892	+	14.1892i	0.552732	+	0.552732i	0.927228	−	0.374496i	$-0.122184\pi$
$659$	14.1892	+	14.1892i	0.552732	+	0.552732i	−0.374496	+	0.927228i	$0.622184\pi$
$660$		0			0
$661$	−8.09850	+	19.5515i	−0.314995	+	0.760466i	0.684510	+	0.729004i	$0.260016\pi$
$661$	−8.09850	+	19.5515i	−0.314995	+	0.760466i	−0.999505	+	0.0314620i	$0.989984\pi$
$662$	1.36860	−	2.03921i	0.0531920	−	0.0792562i
$663$		0			0
$664$	7.05965	−	34.3877i	0.273968	−	1.33450i
$665$	12.9548	+	5.36604i	0.502364	+	0.208086i
$666$		0			0
$667$	−10.5013	+	10.5013i	−0.406611	+	0.406611i
$668$	8.16868	−	40.2069i	0.316056	−	1.55565i
$669$		0			0
$670$	0.00180154	−	0.881253i	6.95994e−5	−	0.0340458i
$671$	−7.43590	+	3.08005i	−0.287060	+	0.118904i
$672$		0			0
$673$	−30.4683	+	20.3583i	−1.17447	+	0.784753i	−0.980551	−	0.196265i	$-0.937119\pi$
$673$	−30.4683	+	20.3583i	−1.17447	+	0.784753i	−0.193916	+	0.981018i	$0.562119\pi$
$674$	9.76872	+	9.80875i	0.376277	+	0.377819i
$675$		0			0
$676$	−46.3244	−	19.4105i	−1.78171	−	0.746557i
$677$	1.76369	+	8.86666i	0.0677840	+	0.340773i	0.999764	−	0.0217372i	$-0.00691970\pi$
$677$	1.76369	+	8.86666i	0.0677840	+	0.340773i	−0.931980	+	0.362510i	$0.881920\pi$
$678$		0			0
$679$	10.7131			0.411131
$680$	−4.49936	+	10.8957i	−0.172543	+	0.417831i
$681$		0			0
$682$	6.91466	−	4.59981i	0.264776	−	0.176136i
$683$	0.887895	+	4.46375i	0.0339744	+	0.170801i	0.994047	−	0.108949i	$-0.0347485\pi$
$683$	0.887895	+	4.46375i	0.0339744	+	0.170801i	−0.960073	+	0.279750i	$0.909749\pi$
$684$		0			0
$685$	−0.839303	+	1.25611i	−0.0320681	+	0.0479933i
$686$	−20.0817	−	20.1640i	−0.766723	−	0.769864i
$687$		0			0
$688$	2.99005	−	7.05489i	0.113994	−	0.268965i
$689$	8.88521	−	3.68037i	0.338499	−	0.140211i
$690$		0			0
$691$	10.1731	+	2.02356i	0.387003	+	0.0769797i	0.384757	−	0.923018i	$-0.374285\pi$
$691$	10.1731	+	2.02356i	0.387003	+	0.0769797i	0.00224577	+	0.999997i	$0.499285\pi$
$692$	−3.56768	+	17.5604i	−0.135623	+	0.667546i
$693$		0			0
$694$	15.6555	−	37.5784i	0.594276	−	1.42645i
$695$	−15.3464	−	6.35667i	−0.582121	−	0.241122i
$696$		0			0
$697$	24.7245	−	16.7796i	0.936507	−	0.635573i
$698$	1.19866	−	1.78601i	0.0453701	−	0.0676016i
$699$		0			0
$700$	−13.8096	+	9.14584i	−0.521955	+	0.345680i
$701$	5.29204	+	5.29204i	0.199878	+	0.199878i	0.799948	−	0.600070i	$-0.204861\pi$
$701$	5.29204	+	5.29204i	0.199878	+	0.199878i	−0.600070	+	0.799948i	$0.704861\pi$
$702$		0			0
$703$	−6.67218	+	33.5433i	−0.251646	+	1.26511i
$704$	8.41110	−	1.56608i	0.317005	−	0.0590238i
$705$		0			0
$706$	−6.34303	+	31.5514i	−0.238723	+	1.18745i
$707$	−5.39428	−	8.07312i	−0.202873	−	0.303621i
$708$		0			0
$709$	18.3393	+	12.2539i	0.688746	+	0.460205i	0.850052	−	0.526699i	$-0.176571\pi$
$709$	18.3393	+	12.2539i	0.688746	+	0.460205i	−0.161306	+	0.986904i	$0.551571\pi$
$710$	−8.41504	+	1.65598i	−0.315811	+	0.0621478i
$711$		0			0
$712$	−3.68229	+	5.43844i	−0.138000	+	0.203814i
$713$		−	21.7594i		−	0.814895i
$714$		0			0
$715$			6.67388i			0.249589i
$716$	−42.3200	−	0.173029i	−1.58157	−	0.00646641i
$717$		0			0
$718$	−8.06208	−	40.9684i	−0.300874	−	1.52893i
$719$	1.76591	+	1.17995i	0.0658575	+	0.0440046i	0.588063	−	0.808815i	$-0.299891\pi$
$719$	1.76591	+	1.17995i	0.0658575	+	0.0440046i	−0.522206	+	0.852820i	$0.674891\pi$
$720$		0			0
$721$	−9.87705	−	14.7821i	−0.367841	−	0.550512i
$722$	−35.2198	−	7.08053i	−1.31074	−	0.263510i
$723$		0			0
$724$	39.1550	+	26.3947i	1.45518	+	0.980953i
$725$	−2.90864	+	14.6227i	−0.108024	+	0.543074i
$726$		0			0
$727$	34.6182	+	34.6182i	1.28392	+	1.28392i	0.938420	+	0.345497i	$0.112290\pi$
$727$	34.6182	+	34.6182i	1.28392	+	1.28392i	0.345497	+	0.938420i	$0.387710\pi$
$728$	36.3504	+	0.222935i	1.34724	+	0.00826251i
$729$		0			0
$730$	−0.239988	−	0.161066i	−0.00888237	−	0.00596131i
$731$	7.27498	−	3.07506i	0.269075	−	0.113735i
$732$		0			0
$733$	−13.6215	−	5.64222i	−0.503122	−	0.208400i	0.116663	−	0.993172i	$-0.462780\pi$
$733$	−13.6215	−	5.64222i	−0.503122	−	0.208400i	−0.619785	+	0.784771i	$0.712780\pi$
$734$	12.2918	+	5.12088i	0.453697	+	0.189015i
$735$		0			0
$736$	8.78965	−	20.6214i	0.323991	−	0.760113i
$737$	−0.646617	−	0.128620i	−0.0238184	−	0.00473778i
$738$		0			0
$739$	−39.7609	+	16.4695i	−1.46263	+	0.605840i	−0.965164	−	0.261646i	$-0.915735\pi$
$739$	−39.7609	+	16.4695i	−1.46263	+	0.605840i	−0.497463	+	0.867485i	$0.665735\pi$
$740$	7.30697	+	7.36697i	0.268610	+	0.270815i
$741$		0			0
$742$	−3.24963	+	3.23637i	−0.119298	+	0.118811i
$743$	−23.1475	+	34.6428i	−0.849201	+	1.27092i	0.111620	+	0.993751i	$0.464396\pi$
$743$	−23.1475	+	34.6428i	−0.849201	+	1.27092i	−0.960821	+	0.277168i	$0.910604\pi$
$744$		0			0
$745$	−1.28402	−	6.45522i	−0.0470430	−	0.236501i
$746$	17.0264	+	25.5949i	0.623381	+	0.937097i
$747$		0			0
$748$	7.34798	+	4.87662i	0.268669	+	0.178307i
$749$	7.59364			0.277466
$750$		0			0
$751$	−6.13003	−	30.8178i	−0.223688	−	1.12456i	−0.915450	−	0.402431i	$-0.868165\pi$
$751$	−6.13003	−	30.8178i	−0.223688	−	1.12456i	0.691762	−	0.722125i	$-0.256835\pi$
$752$	0.277993	−	33.9955i	0.0101373	−	1.23969i
$753$		0			0
$754$	23.1840	−	23.0894i	0.844312	−	0.840867i
$755$	1.15000	−	0.768402i	0.0418526	−	0.0279650i
$756$		0			0
$757$	−6.84851	+	2.83675i	−0.248913	+	0.103103i	−0.503652	−	0.863907i	$-0.668011\pi$
$757$	−6.84851	+	2.83675i	−0.248913	+	0.103103i	0.254739	+	0.967010i	$0.418011\pi$
$758$	−5.89450	−	0.0120501i	−0.214098	−	0.000437678i
$759$		0			0
$760$	−13.5537	+	13.3884i	−0.491644	+	0.485650i
$761$	20.6136	−	20.6136i	0.747242	−	0.747242i	−0.226718	−	0.973960i	$-0.572800\pi$
$761$	20.6136	−	20.6136i	0.747242	−	0.747242i	0.973960	+	0.226718i	$0.0727996\pi$
$762$		0			0
$763$	−14.3090	−	5.92697i	−0.518020	−	0.214571i
$764$	−7.52413	−	18.3770i	−0.272213	−	0.664857i
$765$		0			0
$766$	−32.0462	−	21.5075i	−1.15788	−	0.777096i
$767$	−11.0321	+	26.6338i	−0.398345	+	0.961690i
$768$		0			0
$769$	2.07701	+	2.07701i	0.0748989	+	0.0748989i	0.743564	−	0.668665i	$-0.233134\pi$
$769$	2.07701	+	2.07701i	0.0748989	+	0.0748989i	−0.668665	+	0.743564i	$0.733134\pi$
$770$	−1.21193	−	2.94287i	−0.0436751	−	0.106054i
$771$		0			0
$772$	−20.0658	+	29.7663i	−0.722182	+	1.07131i
$773$	12.4018	+	29.9406i	0.446061	+	1.07689i	0.973785	+	0.227471i	$0.0730457\pi$
$773$	12.4018	+	29.9406i	0.446061	+	1.07689i	−0.527724	+	0.849416i	$0.676954\pi$
$774$		0			0
$775$	−12.1362	−	18.1631i	−0.435945	−	0.652438i
$776$	−5.65249	+	13.4131i	−0.202913	+	0.481501i
$777$		0			0
$778$	−0.608007	−	3.08965i	−0.0217981	−	0.110769i
$779$	47.3635	−	9.42118i	1.69697	−	0.337549i
$780$		0			0
$781$			6.41621i			0.229590i
$782$	21.3015	−	8.95265i	0.761740	−	0.320146i
$783$		0			0
$784$	9.88605	−	4.00054i	0.353073	−	0.142877i
$785$	5.18938	−	1.03223i	0.185217	−	0.0368419i
$786$		0			0
$787$	−30.4237	−	20.3285i	−1.08449	−	0.724632i	−0.121073	−	0.992644i	$-0.538633\pi$
$787$	−30.4237	−	20.3285i	−1.08449	−	0.724632i	−0.963416	+	0.268012i	$0.913633\pi$
$788$	0.807776	+	4.14956i	0.0287758	+	0.147822i
$789$		0			0
$790$	3.29813	−	16.4055i	0.117342	−	0.583680i
$791$	−2.70158	−	6.52220i	−0.0960573	−	0.231903i
$792$		0			0
$793$	9.06420	−	45.5688i	0.321879	−	1.61820i
$794$	−6.78228	+	2.79308i	−0.240694	+	0.0991227i
$795$		0			0
$796$	2.02836	+	3.06269i	0.0718934	+	0.108554i
$797$	16.8463	−	40.6706i	0.596727	−	1.44063i	−0.280171	−	0.959950i	$-0.590391\pi$
$797$	16.8463	−	40.6706i	0.596727	−	1.44063i	0.876898	−	0.480677i	$-0.159609\pi$
$798$		0			0
$799$	24.5997	−	24.9572i	0.870276	−	0.882923i
$800$	−4.16453	−	22.1156i	−0.147238	−	0.781904i
$801$		0			0
$802$	7.25918	−	17.4244i	0.256330	−	0.615276i
$803$	−0.152896	+	0.152896i	−0.00539557	+	0.00539557i
$804$		0			0
$805$	−8.17857	−	1.62682i	−0.288257	−	0.0573378i
$806$	−0.0980051	+	47.9410i	−0.00345208	+	1.68865i
$807$		0			0
$808$	12.9539	−	2.49420i	0.455717	−	0.0877458i
$809$	15.3649	−	10.2665i	0.540202	−	0.360952i	−0.255338	−	0.966852i	$-0.582187\pi$
$809$	15.3649	−	10.2665i	0.540202	−	0.360952i	0.795541	+	0.605900i	$0.207187\pi$
$810$		0			0
$811$	12.0401	−	18.0192i	0.422784	−	0.632740i	−0.557537	−	0.830152i	$-0.688254\pi$
$811$	12.0401	−	18.0192i	0.422784	−	0.632740i	0.980321	+	0.197412i	$0.0632536\pi$
$812$	−6.03018	+	14.3914i	−0.211618	+	0.505040i
$813$		0			0
$814$	6.46316	−	4.29946i	0.226534	−	0.150696i
$815$	8.39156			0.293944
$816$		0			0
$817$	12.7646			0.446576
$818$	−0.0212933	+	0.0141648i	−0.000744502	+	0.000495262i
$819$		0			0
$820$	5.66206	−	13.5129i	0.197728	−	0.471891i
$821$	5.71100	−	8.54712i	0.199315	−	0.298297i	−0.718326	−	0.695707i	$-0.755091\pi$
$821$	5.71100	−	8.54712i	0.199315	−	0.298297i	0.917641	+	0.397411i	$0.130091\pi$
$822$		0			0
$823$	6.33161	−	4.23065i	0.220706	−	0.147471i	−0.440302	−	0.897850i	$-0.645129\pi$
$823$	6.33161	−	4.23065i	0.220706	−	0.147471i	0.661008	+	0.750378i	$0.270129\pi$
$824$	23.7189	−	4.56694i	0.826287	−	0.159097i
$825$		0			0
$826$	0.0281041	−	13.7476i	0.000977866	−	0.478341i
$827$	−15.4121	−	3.06566i	−0.535932	−	0.106603i	−0.0802981	−	0.996771i	$-0.525587\pi$
$827$	−15.4121	−	3.06566i	−0.535932	−	0.106603i	−0.455634	+	0.890167i	$0.650587\pi$
$828$		0			0
$829$	−10.2185	+	10.2185i	−0.354903	+	0.354903i	−0.861930	−	0.507027i	$-0.830744\pi$
$829$	−10.2185	+	10.2185i	−0.354903	+	0.354903i	0.507027	+	0.861930i	$0.330744\pi$
$830$	6.82325	−	16.3780i	0.236838	−	0.568488i
$831$		0			0
$832$	−19.4585	+	45.3940i	−0.674603	+	1.57376i
$833$	10.1863	+	4.13348i	0.352935	+	0.143217i
$834$		0			0
$835$	7.93541	−	19.1578i	0.274616	−	0.662982i
$836$	7.86985	+	11.8829i	0.272184	+	0.410980i
$837$		0			0
$838$	2.79100	−	1.14939i	0.0964135	−	0.0397051i
$839$	4.47721	−	22.5084i	0.154570	−	0.777077i	−0.823258	−	0.567668i	$-0.807846\pi$
$839$	4.47721	−	22.5084i	0.154570	−	0.777077i	0.977828	−	0.209410i	$-0.0671542\pi$
$840$		0			0
$841$	−5.72295	−	13.8164i	−0.197343	−	0.476428i
$842$	4.74279	−	23.5915i	0.163447	−	0.813015i
$843$		0			0
$844$	−9.24682	−	47.5011i	−0.318289	−	1.63506i
$845$	−21.1070	−	14.1033i	−0.726104	−	0.485167i
$846$		0			0
$847$	20.1243	−	4.00297i	0.691479	−	0.137544i
$848$	−2.33743	−	5.77621i	−0.0802678	−	0.198356i
$849$		0			0
$850$	12.7876	−	19.3538i	0.438612	−	0.663831i
$851$		−	20.3386i		−	0.697198i
$852$		0			0
$853$	−18.0315	+	3.58668i	−0.617386	+	0.122806i	−0.493868	−	0.869537i	$-0.664417\pi$
$853$	−18.0315	+	3.58668i	−0.617386	+	0.122806i	−0.123517	+	0.992342i	$0.539417\pi$
$854$	4.27812	+	21.7397i	0.146394	+	0.743918i
$855$		0			0
$856$	−4.00660	+	9.50744i	−0.136943	+	0.324958i
$857$	−8.86432	−	13.2664i	−0.302799	−	0.453171i	0.648601	−	0.761129i	$-0.275355\pi$
$857$	−8.86432	−	13.2664i	−0.302799	−	0.453171i	−0.951400	+	0.307958i	$0.900355\pi$
$858$		0			0
$859$	−13.5362	−	32.6792i	−0.461848	−	1.11500i	−0.967638	−	0.252343i	$-0.918799\pi$
$859$	−13.5362	−	32.6792i	−0.461848	−	1.11500i	0.505789	−	0.862657i	$-0.331201\pi$
$860$	2.16468	−	3.21118i	0.0738150	−	0.109500i
$861$		0			0
$862$	19.3345	+	46.9489i	0.658536	+	1.59908i
$863$	22.3530	+	22.3530i	0.760906	+	0.760906i	0.976486	−	0.215580i	$-0.0691642\pi$
$863$	22.3530	+	22.3530i	0.760906	+	0.760906i	−0.215580	+	0.976486i	$0.569164\pi$
$864$		0			0
$865$	−3.46580	+	8.36718i	−0.117841	+	0.284493i
$866$	3.84096	+	2.57782i	0.130521	+	0.0875980i
$867$		0			0
$868$	−8.66256	−	21.1575i	−0.294026	−	0.718133i
$869$	−11.5659	−	4.79075i	−0.392346	−	0.162515i
$870$		0			0
$871$	2.69112	−	2.69112i	0.0911852	−	0.0911852i
$872$	14.9705	−	14.7880i	0.506965	−	0.500785i
$873$		0			0
$874$	37.3430	+	0.0763400i	1.26315	+	0.00258224i
$875$	−17.4549	+	7.23005i	−0.590083	+	0.244420i
$876$		0			0
$877$	1.36712	−	0.913483i	0.0461645	−	0.0308461i	−0.532274	−	0.846572i	$-0.678662\pi$
$877$	1.36712	−	0.913483i	0.0461645	−	0.0308461i	0.578438	+	0.815726i	$0.303662\pi$
$878$	1.07879	−	1.07438i	0.0364073	−	0.0362587i
$879$		0			0
$880$	4.32400	+	0.0353587i	0.145762	+	0.00119194i
$881$	1.01383	+	5.09688i	0.0341569	+	0.171718i	0.994098	−	0.108482i	$-0.0345990\pi$
$881$	1.01383	+	5.09688i	0.0341569	+	0.171718i	−0.959941	+	0.280200i	$0.909599\pi$
$882$		0			0
$883$	−13.1664			−0.443086			−0.221543	−	0.975151i	$-0.571109\pi$
$883$	−13.1664			−0.443086			−0.221543	+	0.975151i	$0.571109\pi$
$884$	−46.9725	+	19.6288i	−1.57986	+	0.660189i
$885$		0			0
$886$	18.1600	+	27.2990i	0.610096	+	0.917126i
$887$	−8.37931	−	42.1257i	−0.281350	−	1.41444i	−0.820218	−	0.572051i	$-0.806148\pi$
$887$	−8.37931	−	42.1257i	−0.281350	−	1.41444i	0.538868	−	0.842390i	$-0.318852\pi$
$888$		0			0
$889$	4.05219	−	6.06453i	0.135906	−	0.203398i
$890$	−2.35200	+	2.34240i	−0.0788392	+	0.0785176i
$891$		0			0
$892$	20.1516	+	20.3171i	0.674726	+	0.680266i
$893$	52.3233	−	21.6730i	1.75093	−	0.725260i
$894$		0			0
$895$	−20.9783	−	4.17284i	−0.701227	−	0.139483i
$896$	0.337026	−	23.5502i	0.0112593	−	0.786757i
$897$		0			0
$898$	−36.8798	−	15.3645i	−1.23070	−	0.512721i
$899$	−19.0123	−	7.87514i	−0.634094	−	0.262650i
$900$		0			0
$901$	2.41511	−	5.95166i	0.0804590	−	0.198279i
$902$	−9.10115	−	6.10814i	−0.303035	−	0.203379i
$903$		0			0
$904$	9.59139	+	0.0588234i	0.319005	+	0.00195644i
$905$	16.8758	+	16.8758i	0.560970	+	0.560970i
$906$		0			0
$907$	−1.91211	+	9.61281i	−0.0634905	+	0.319188i	−0.999459	−	0.0328961i	$-0.989527\pi$
$907$	−1.91211	+	9.61281i	−0.0634905	+	0.319188i	0.935968	+	0.352084i	$0.114527\pi$
$908$	−34.2308	−	23.0753i	−1.13599	−	0.765780i
$909$		0			0
$910$	18.0119	+	3.62109i	0.597090	+	0.120038i
$911$	−26.4536	−	39.5905i	−0.876445	−	1.31169i	−0.949307	−	0.314351i	$-0.898213\pi$
$911$	−26.4536	−	39.5905i	−0.876445	−	1.31169i	0.0728613	−	0.997342i	$-0.476787\pi$
$912$		0			0
$913$	−11.0365	−	7.37437i	−0.365256	−	0.244056i
$914$	−5.86490	−	29.8031i	−0.193994	−	0.985800i
$915$		0			0
$916$	1.44051	+	0.00588965i	0.0475957	+	0.000194599i
$917$		−	31.9425i		−	1.05483i
$918$		0			0
$919$			38.7851i			1.27940i	0.768624	+	0.639701i	$0.220942\pi$
$919$			38.7851i			1.27940i	−0.768624	+	0.639701i	$0.779058\pi$
$920$	6.35203	−	9.38142i	0.209420	−	0.309296i
$921$		0			0
$922$	−10.1664	+	2.00064i	−0.334814	+	0.0658874i
$923$	−30.7964	−	20.5775i	−1.01368	−	0.677316i
$924$		0			0
$925$	−11.3438	−	16.9772i	−0.372981	−	0.558205i
$926$	−1.85600	+	9.23208i	−0.0609920	+	0.303385i
$927$		0			0
$928$	−14.8368	−	15.1432i	−0.487041	−	0.497101i
$929$	−10.0100	+	50.3239i	−0.328419	+	1.65107i	0.365347	+	0.930872i	$0.380950\pi$
$929$	−10.0100	+	50.3239i	−0.328419	+	1.65107i	−0.693765	+	0.720201i	$0.744050\pi$
$930$		0			0
$931$	12.5627	+	12.5627i	0.411725	+	0.411725i
$932$	−30.5801	+	20.2526i	−1.00168	+	0.663395i
$933$		0			0
$934$	−21.6769	+	32.2987i	−0.709291	+	1.05685i
$935$	3.17438	+	3.12892i	0.103813	+	0.102326i
$936$		0			0
$937$	−5.64323	−	2.33750i	−0.184356	−	0.0763629i	0.288596	−	0.957451i	$-0.406812\pi$
$937$	−5.64323	−	2.33750i	−0.184356	−	0.0763629i	−0.472952	+	0.881088i	$0.656812\pi$
$938$	−0.697969	+	1.67535i	−0.0227895	+	0.0547021i
$939$		0			0
$940$	3.42099	−	16.8384i	0.111580	−	0.549207i
$941$	−20.8412	−	4.14557i	−0.679403	−	0.135142i	−0.156687	−	0.987648i	$-0.550081\pi$
$941$	−20.8412	−	4.14557i	−0.679403	−	0.135142i	−0.522716	+	0.852507i	$0.675081\pi$
$942$		0			0
$943$	−26.5322	+	10.9900i	−0.864009	+	0.357884i
$944$	17.1975	+	7.28877i	0.559732	+	0.237229i
$945$		0			0
$946$	−2.04445	−	2.05283i	−0.0664708	−	0.0667431i
$947$	3.28509	−	4.91648i	0.106751	−	0.159764i	−0.774248	−	0.632882i	$-0.781872\pi$
$947$	3.28509	−	4.91648i	0.106751	−	0.159764i	0.880999	+	0.473118i	$0.156872\pi$
$948$		0			0
$949$	−0.243512	−	1.22422i	−0.00790474	−	0.0397398i
$950$	31.2138	−	20.7642i	1.01271	−	0.673680i
$951$		0			0
$952$	17.1482	−	17.1853i	0.555777	−	0.556979i
$953$	24.7513			0.801774			0.400887	−	0.916127i	$-0.368702\pi$
$953$	24.7513			0.801774			0.400887	+	0.916127i	$0.368702\pi$
$954$		0			0
$955$	−1.95799	−	9.84349i	−0.0633591	−	0.318528i
$956$	−18.9081	−	7.92270i	−0.611530	−	0.256238i
$957$		0			0
$958$	−10.7848	−	10.8289i	−0.348440	−	0.349867i
$959$	2.58692	−	1.72853i	0.0835361	−	0.0558171i
$960$		0			0
$961$	−0.783955	+	0.324725i	−0.0252889	+	0.0104750i
$962$	−0.0916059	+	44.8106i	−0.00295349	+	1.44475i
$963$		0			0
$964$	4.30772	−	21.2029i	0.138742	−	0.682900i
$965$	−12.8293	+	12.8293i	−0.412989	+	0.412989i
$966$		0			0
$967$	−41.5952	−	17.2293i	−1.33761	−	0.554056i	−0.404794	−	0.914408i	$-0.632657\pi$
$967$	−41.5952	−	17.2293i	−1.33761	−	0.554056i	−0.932816	+	0.360352i	$0.882657\pi$
$968$	−5.60625	+	27.3082i	−0.180192	+	0.877718i
$969$		0			0
$970$	−4.09956	+	6.10835i	−0.131629	+	0.196127i
$971$	15.0873	−	36.4239i	0.484174	−	1.16890i	−0.473435	−	0.880829i	$-0.656986\pi$
$971$	15.0873	−	36.4239i	0.484174	−	1.16890i	0.957609	−	0.288071i	$-0.0930139\pi$
$972$		0			0
$973$	24.1898	+	24.1898i	0.775491	+	0.775491i
$974$	5.54194	−	2.28229i	0.177575	−	0.0731292i
$975$		0			0
$976$	−29.4759	−	6.11411i	−0.943502	−	0.195708i
$977$	−6.19856	−	14.9646i	−0.198309	−	0.478761i	0.793174	−	0.608995i	$-0.208427\pi$
$977$	−6.19856	−	14.9646i	−0.198309	−	0.478761i	−0.991483	+	0.130234i	$0.958427\pi$
$978$		0			0
$979$	1.37968	+	2.06483i	0.0440946	+	0.0659923i
$980$	5.29082	−	1.02994i	0.169009	−	0.0329002i
$981$		0			0
$982$	−3.32868	+	0.655044i	−0.106222	+	0.0209033i
$983$	−34.8034	+	6.92283i	−1.11006	+	0.220804i	−0.715875	−	0.698228i	$-0.753972\pi$
$983$	−34.8034	+	6.92283i	−1.11006	+	0.220804i	−0.394182	+	0.919032i	$0.628972\pi$
$984$		0			0
$985$			2.13661i			0.0680780i
$986$	−0.112957	−	21.8523i	−0.00359729	−	0.695920i
$987$		0			0
$988$	−82.2750	−	0.336389i	−2.61752	−	0.0107020i
$989$	−7.44507	+	1.48092i	−0.236740	+	0.0470904i
$990$		0			0
$991$	−15.0339	−	10.0453i	−0.477568	−	0.319101i	0.293383	−	0.955995i	$-0.405219\pi$
$991$	−15.0339	−	10.0453i	−0.477568	−	0.319101i	−0.770951	+	0.636894i	$0.780219\pi$
$992$	31.0604	+	0.317492i	0.986167	+	0.0100804i
$993$		0			0
$994$	17.3165	+	3.48129i	0.549247	+	0.110420i
$995$	0.710497	+	1.71529i	0.0225243	+	0.0543784i
$996$		0			0
$997$	−2.81333	+	14.1436i	−0.0890991	+	0.447932i	0.910322	+	0.413901i	$0.135834\pi$
$997$	−2.81333	+	14.1436i	−0.0890991	+	0.447932i	−0.999421	+	0.0340301i	$0.989166\pi$
$998$	0.0532489	+	0.129301i	0.00168557	+	0.00409296i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	612.2.bd.d.91.6		48
3.2	odd	2		68.2.i.b.23.1	yes	48
4.3	odd	2	inner	612.2.bd.d.91.4		48
12.11	even	2		68.2.i.b.23.3	yes	48
17.3	odd	16	inner	612.2.bd.d.343.4		48
51.20	even	16		68.2.i.b.3.3	yes	48
68.3	even	16	inner	612.2.bd.d.343.6		48
204.71	odd	16		68.2.i.b.3.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.i.b.3.1	✓	48	204.71	odd	16
68.2.i.b.3.3	yes	48	51.20	even	16
68.2.i.b.23.1	yes	48	3.2	odd	2
68.2.i.b.23.3	yes	48	12.11	even	2
612.2.bd.d.91.4		48	4.3	odd	2	inner
612.2.bd.d.91.6		48	1.1	even	1	trivial
612.2.bd.d.343.4		48	17.3	odd	16	inner
612.2.bd.d.343.6		48	68.3	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 612 = 2^{2} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	612.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17748 - 0.783289i) q^{2} +(0.772915 - 1.84461i) q^{4} +(0.561585 - 0.840472i) q^{5} +(-1.73093 + 1.15657i) q^{7} +(-0.534775 - 2.77741i) q^{8} +O(q^{10})\)	\(q+(1.17748 - 0.783289i) q^{2} +(0.772915 - 1.84461i) q^{4} +(0.561585 - 0.840472i) q^{5} +(-1.73093 + 1.15657i) q^{7} +(-0.534775 - 2.77741i) q^{8} +(0.00292235 - 1.42952i) q^{10} +(-1.04891 - 0.208641i) q^{11} +(4.36539 - 4.36539i) q^{13} +(-1.13221 + 2.71766i) q^{14} +(-2.80520 - 2.85146i) q^{16} +(-0.0297412 - 4.12300i) q^{17} +(2.55002 - 6.15628i) q^{19} +(-1.11629 - 1.68552i) q^{20} +(-1.39849 + 0.575928i) q^{22} +(-0.773086 + 3.88657i) q^{23} +(1.52240 + 3.67540i) q^{25} +(1.72079 - 8.55953i) q^{26} +(0.795567 + 4.08684i) q^{28} +(3.11609 + 2.08211i) q^{29} +(-5.38553 + 1.07125i) q^{31} +(-5.53659 - 1.16025i) q^{32} +(-3.26452 - 4.83145i) q^{34} +2.10432i q^{35} +(-5.03388 + 1.00130i) q^{37} +(-1.81956 - 9.24630i) q^{38} +(-2.63466 - 1.11029i) q^{40} +(4.02629 + 6.02577i) q^{41} +(0.733065 + 1.76977i) q^{43} +(-1.19558 + 1.77357i) q^{44} +(2.13401 + 5.18190i) q^{46} +(6.00982 + 6.00982i) q^{47} +(-1.02031 + 2.46325i) q^{49} +(4.67150 + 3.13523i) q^{50} +(-4.67839 - 11.4265i) q^{52} +(1.43923 + 0.596147i) q^{53} +(-0.764407 + 0.764407i) q^{55} +(4.13794 + 4.18901i) q^{56} +(5.30003 + 0.0108348i) q^{58} +(-4.31414 + 1.78698i) q^{59} +(6.25751 - 4.18113i) q^{61} +(-5.50225 + 5.47980i) q^{62} +(-7.42803 + 2.97058i) q^{64} +(-1.21745 - 6.12053i) q^{65} +0.616467 q^{67} +(-7.62833 - 3.13187i) q^{68} +(1.64829 + 2.47779i) q^{70} +(-1.17044 - 5.88422i) q^{71} +(0.112327 - 0.168110i) q^{73} +(-5.14298 + 5.12199i) q^{74} +(-9.38502 - 9.46208i) q^{76} +(2.05690 - 0.851995i) q^{77} +(11.4809 + 2.28368i) q^{79} +(-3.97193 + 0.756357i) q^{80} +(9.46080 + 3.94147i) q^{82} +(11.4667 + 4.74966i) q^{83} +(-3.48197 - 2.29042i) q^{85} +(2.24941 + 1.50967i) q^{86} +(-0.0185510 + 3.02482i) q^{88} +(-1.64195 - 1.64195i) q^{89} +(-2.50731 + 12.6051i) q^{91} +(6.57169 + 4.43003i) q^{92} +(11.7839 + 2.36901i) q^{94} +(-3.74213 - 5.60049i) q^{95} +(-4.27885 - 2.85903i) q^{97} +(0.728042 + 3.69963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 8 q^{4} + 16 q^{5} + 8 q^{8}+O(q^{10}) \) 48 * q + 8 * q^2 - 8 * q^4 + 16 * q^5 + 8 * q^8	\( 48 q + 8 q^{2} - 8 q^{4} + 16 q^{5} + 8 q^{8} + 16 q^{10} - 16 q^{13} + 8 q^{14} + 16 q^{17} + 24 q^{20} - 8 q^{22} + 16 q^{25} + 16 q^{26} + 40 q^{28} - 32 q^{32} + 56 q^{34} - 16 q^{37} - 32 q^{38} + 56 q^{40} + 48 q^{41} - 24 q^{44} + 8 q^{46} - 16 q^{49} - 16 q^{52} - 48 q^{53} + 48 q^{56} - 64 q^{58} + 16 q^{61} + 64 q^{62} - 56 q^{64} - 96 q^{65} + 32 q^{68} - 80 q^{70} + 64 q^{73} + 16 q^{74} - 64 q^{76} - 16 q^{77} + 24 q^{80} - 40 q^{82} - 80 q^{85} - 64 q^{86} + 56 q^{88} + 16 q^{89} - 104 q^{92} + 88 q^{94} - 16 q^{97} - 72 q^{98}+O(q^{100}) \) 48 * q + 8 * q^2 - 8 * q^4 + 16 * q^5 + 8 * q^8 + 16 * q^10 - 16 * q^13 + 8 * q^14 + 16 * q^17 + 24 * q^20 - 8 * q^22 + 16 * q^25 + 16 * q^26 + 40 * q^28 - 32 * q^32 + 56 * q^34 - 16 * q^37 - 32 * q^38 + 56 * q^40 + 48 * q^41 - 24 * q^44 + 8 * q^46 - 16 * q^49 - 16 * q^52 - 48 * q^53 + 48 * q^56 - 64 * q^58 + 16 * q^61 + 64 * q^62 - 56 * q^64 - 96 * q^65 + 32 * q^68 - 80 * q^70 + 64 * q^73 + 16 * q^74 - 64 * q^76 - 16 * q^77 + 24 * q^80 - 40 * q^82 - 80 * q^85 - 64 * q^86 + 56 * q^88 + 16 * q^89 - 104 * q^92 + 88 * q^94 - 16 * q^97 - 72 * q^98

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