LMFDB - Embedded newform 552.2.f.d.277.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 16 x^{14} - 24 x^{13} + 32 x^{12} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 2x^17 + x^16 - 4x^15 + 16x^14 - 24x^13 + 32x^12 - 16x^11 - 16x^10 - 32x^9 + 128x^8 - 192x^7 + 256x^6 - 128x^5 + 64x^4 - 256x^3 + 512x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.8
Root			$0.585586 - 1.28728i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.d.277.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.585586 + 1.28728i) q^{2} -1.00000i q^{3} +(-1.31418 - 1.50763i) q^{4} +1.66345i q^{5} +(1.28728 + 0.585586i) q^{6} -0.540858 q^{7} +(2.71030 - 0.808871i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.585586 + 1.28728i) q^{2} -1.00000i q^{3} +(-1.31418 - 1.50763i) q^{4} +1.66345i q^{5} +(1.28728 + 0.585586i) q^{6} -0.540858 q^{7} +(2.71030 - 0.808871i) q^{8} -1.00000 q^{9} +(-2.14133 - 0.974093i) q^{10} -3.06212i q^{11} +(-1.50763 + 1.31418i) q^{12} +6.59177i q^{13} +(0.316719 - 0.696236i) q^{14} +1.66345 q^{15} +(-0.545870 + 3.96258i) q^{16} +2.00394 q^{17} +(0.585586 - 1.28728i) q^{18} +4.41914i q^{19} +(2.50786 - 2.18607i) q^{20} +0.540858i q^{21} +(3.94181 + 1.79314i) q^{22} +1.00000 q^{23} +(-0.808871 - 2.71030i) q^{24} +2.23294 q^{25} +(-8.48545 - 3.86005i) q^{26} +1.00000i q^{27} +(0.710784 + 0.815412i) q^{28} +3.35884i q^{29} +(-0.974093 + 2.14133i) q^{30} +1.79028 q^{31} +(-4.78129 - 3.02312i) q^{32} -3.06212 q^{33} +(-1.17348 + 2.57963i) q^{34} -0.899690i q^{35} +(1.31418 + 1.50763i) q^{36} +7.72195i q^{37} +(-5.68867 - 2.58779i) q^{38} +6.59177 q^{39} +(1.34552 + 4.50845i) q^{40} -0.419607 q^{41} +(-0.696236 - 0.316719i) q^{42} +9.98043i q^{43} +(-4.61654 + 4.02418i) q^{44} -1.66345i q^{45} +(-0.585586 + 1.28728i) q^{46} +2.45522 q^{47} +(3.96258 + 0.545870i) q^{48} -6.70747 q^{49} +(-1.30758 + 2.87441i) q^{50} -2.00394i q^{51} +(9.93792 - 8.66277i) q^{52} +7.38930i q^{53} +(-1.28728 - 0.585586i) q^{54} +5.09369 q^{55} +(-1.46589 + 0.437485i) q^{56} +4.41914 q^{57} +(-4.32376 - 1.96689i) q^{58} +5.51942i q^{59} +(-2.18607 - 2.50786i) q^{60} -9.35009i q^{61} +(-1.04836 + 2.30459i) q^{62} +0.540858 q^{63} +(6.69145 - 4.38457i) q^{64} -10.9651 q^{65} +(1.79314 - 3.94181i) q^{66} -4.53065i q^{67} +(-2.63353 - 3.02119i) q^{68} -1.00000i q^{69} +(1.15815 + 0.526846i) q^{70} +6.86922 q^{71} +(-2.71030 + 0.808871i) q^{72} -4.18975 q^{73} +(-9.94031 - 4.52186i) q^{74} -2.23294i q^{75} +(6.66241 - 5.80754i) q^{76} +1.65617i q^{77} +(-3.86005 + 8.48545i) q^{78} -8.69129 q^{79} +(-6.59155 - 0.908027i) q^{80} +1.00000 q^{81} +(0.245716 - 0.540151i) q^{82} -18.0678i q^{83} +(0.815412 - 0.710784i) q^{84} +3.33345i q^{85} +(-12.8476 - 5.84440i) q^{86} +3.35884 q^{87} +(-2.47686 - 8.29927i) q^{88} +4.04171 q^{89} +(2.14133 + 0.974093i) q^{90} -3.56521i q^{91} +(-1.31418 - 1.50763i) q^{92} -1.79028i q^{93} +(-1.43774 + 3.16056i) q^{94} -7.35102 q^{95} +(-3.02312 + 4.78129i) q^{96} +5.61109 q^{97} +(3.92780 - 8.63439i) q^{98} +3.06212i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	$ 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.585586	+	1.28728i	−0.414072	+	0.910244i
$2$	−0.585586	+	1.28728i	−0.414072	+	0.910244i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.31418	−	1.50763i	−0.657089	−	0.753813i
$5$			1.66345i			0.743917i	0.928249	+	0.371959i	$0.121314\pi$
$5$			1.66345i			0.743917i	−0.928249	+	0.371959i	$0.878686\pi$
$6$	1.28728	+	0.585586i	0.525530	+	0.239064i
$7$	−0.540858			−0.204425			−0.102213	−	0.994763i	$-0.532592\pi$
$7$	−0.540858			−0.204425			−0.102213	+	0.994763i	$0.532592\pi$
$8$	2.71030	−	0.808871i	0.958236	−	0.285979i
$9$	−1.00000			−0.333333
$10$	−2.14133	−	0.974093i	−0.677146	−	0.308035i
$11$		−	3.06212i		−	0.923265i	−0.887071	−	0.461632i	$-0.847264\pi$
$11$		−	3.06212i		−	0.923265i	0.887071	−	0.461632i	$-0.152736\pi$
$12$	−1.50763	+	1.31418i	−0.435214	+	0.379371i
$13$			6.59177i			1.82823i	0.405457	+	0.914114i	$0.367113\pi$
$13$			6.59177i			1.82823i	−0.405457	+	0.914114i	$0.632887\pi$
$14$	0.316719	−	0.696236i	0.0846467	−	0.186077i
$15$	1.66345			0.429501
$16$	−0.545870	+	3.96258i	−0.136467	+	0.990645i
$17$	2.00394			0.486027			0.243013	−	0.970023i	$-0.421864\pi$
$17$	2.00394			0.486027			0.243013	+	0.970023i	$0.421864\pi$
$18$	0.585586	−	1.28728i	0.138024	−	0.303415i
$19$			4.41914i			1.01382i	0.861999	+	0.506910i	$0.169213\pi$
$19$			4.41914i			1.01382i	−0.861999	+	0.506910i	$0.830787\pi$
$20$	2.50786	−	2.18607i	0.560774	−	0.488820i
$21$			0.540858i			0.118025i
$22$	3.94181	+	1.79314i	0.840397	+	0.382298i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	−0.808871	−	2.71030i	−0.165110	−	0.553238i
$25$	2.23294			0.446587
$26$	−8.48545	−	3.86005i	−1.66413	−	0.757018i
$27$			1.00000i			0.192450i
$28$	0.710784	+	0.815412i	0.134326	+	0.154098i
$29$			3.35884i			0.623720i	0.950128	+	0.311860i	$0.100952\pi$
$29$			3.35884i			0.623720i	−0.950128	+	0.311860i	$0.899048\pi$
$30$	−0.974093	+	2.14133i	−0.177844	+	0.390951i
$31$	1.79028			0.321544			0.160772	−	0.986992i	$-0.448602\pi$
$31$	1.79028			0.321544			0.160772	+	0.986992i	$0.448602\pi$
$32$	−4.78129	−	3.02312i	−0.845221	−	0.534417i
$33$	−3.06212			−0.533047
$34$	−1.17348	+	2.57963i	−0.201250	+	0.442403i
$35$		−	0.899690i		−	0.152075i
$36$	1.31418	+	1.50763i	0.219030	+	0.251271i
$37$			7.72195i			1.26948i	0.772725	+	0.634740i	$0.218893\pi$
$37$			7.72195i			1.26948i	−0.772725	+	0.634740i	$0.781107\pi$
$38$	−5.68867	−	2.58779i	−0.922825	−	0.419794i
$39$	6.59177			1.05553
$40$	1.34552	+	4.50845i	0.212745	+	0.712848i
$41$	−0.419607			−0.0655316			−0.0327658	−	0.999463i	$-0.510432\pi$
$41$	−0.419607			−0.0655316			−0.0327658	+	0.999463i	$0.510432\pi$
$42$	−0.696236	−	0.316719i	−0.107432	−	0.0488708i
$43$			9.98043i			1.52200i	0.648751	+	0.761001i	$0.275292\pi$
$43$			9.98043i			1.52200i	−0.648751	+	0.761001i	$0.724708\pi$
$44$	−4.61654	+	4.02418i	−0.695969	+	0.606667i
$45$		−	1.66345i		−	0.247972i
$46$	−0.585586	+	1.28728i	−0.0863399	+	0.189799i
$47$	2.45522			0.358131			0.179066	−	0.983837i	$-0.442693\pi$
$47$	2.45522			0.358131			0.179066	+	0.983837i	$0.442693\pi$
$48$	3.96258	+	0.545870i	0.571949	+	0.0787895i
$49$	−6.70747			−0.958210
$50$	−1.30758	+	2.87441i	−0.184919	+	0.406503i
$51$		−	2.00394i		−	0.280608i
$52$	9.93792	−	8.66277i	1.37814	−	1.20131i
$53$			7.38930i			1.01500i	0.861652	+	0.507499i	$0.169430\pi$
$53$			7.38930i			1.01500i	−0.861652	+	0.507499i	$0.830570\pi$
$54$	−1.28728	−	0.585586i	−0.175177	−	0.0796881i
$55$	5.09369			0.686833
$56$	−1.46589	+	0.437485i	−0.195888	+	0.0584613i
$57$	4.41914			0.585330
$58$	−4.32376	−	1.96689i	−0.567738	−	0.258265i
$59$			5.51942i			0.718567i	0.933229	+	0.359283i	$0.116979\pi$
$59$			5.51942i			0.718567i	−0.933229	+	0.359283i	$0.883021\pi$
$60$	−2.18607	−	2.50786i	−0.282220	−	0.323763i
$61$		−	9.35009i		−	1.19716i	−0.801065	−	0.598578i	$-0.795733\pi$
$61$		−	9.35009i		−	1.19716i	0.801065	−	0.598578i	$-0.204267\pi$
$62$	−1.04836	+	2.30459i	−0.133142	+	0.292684i
$63$	0.540858			0.0681417
$64$	6.69145	−	4.38457i	0.836432	−	0.548071i
$65$	−10.9651			−1.36005
$66$	1.79314	−	3.94181i	0.220720	−	0.485203i
$67$		−	4.53065i		−	0.553507i	−0.960941	−	0.276754i	$-0.910741\pi$
$67$		−	4.53065i		−	0.553507i	0.960941	−	0.276754i	$-0.0892585\pi$
$68$	−2.63353	−	3.02119i	−0.319363	−	0.366373i
$69$		−	1.00000i		−	0.120386i
$70$	1.15815	+	0.526846i	0.138426	+	0.0629701i
$71$	6.86922			0.815226			0.407613	−	0.913155i	$-0.366361\pi$
$71$	6.86922			0.815226			0.407613	+	0.913155i	$0.366361\pi$
$72$	−2.71030	+	0.808871i	−0.319412	+	0.0953264i
$73$	−4.18975			−0.490373			−0.245187	−	0.969476i	$-0.578849\pi$
$73$	−4.18975			−0.490373			−0.245187	+	0.969476i	$0.578849\pi$
$74$	−9.94031	−	4.52186i	−1.15554	−	0.525656i
$75$		−	2.23294i		−	0.257837i
$76$	6.66241	−	5.80754i	0.764231	−	0.666171i
$77$			1.65617i			0.188739i
$78$	−3.86005	+	8.48545i	−0.437064	+	0.960789i
$79$	−8.69129			−0.977846			−0.488923	−	0.872327i	$-0.662610\pi$
$79$	−8.69129			−0.977846			−0.488923	+	0.872327i	$0.662610\pi$
$80$	−6.59155	−	0.908027i	−0.736958	−	0.101521i
$81$	1.00000			0.111111
$82$	0.245716	−	0.540151i	0.0271348	−	0.0596498i
$83$		−	18.0678i		−	1.98319i	−0.129367	−	0.991597i	$-0.541294\pi$
$83$		−	18.0678i		−	1.98319i	0.129367	−	0.991597i	$-0.458706\pi$
$84$	0.815412	−	0.710784i	0.0889687	−	0.0775529i
$85$			3.33345i			0.361564i
$86$	−12.8476	−	5.84440i	−1.38539	−	0.630218i
$87$	3.35884			0.360105
$88$	−2.47686	−	8.29927i	−0.264035	−	0.884706i
$89$	4.04171			0.428420			0.214210	−	0.976788i	$-0.431282\pi$
$89$	4.04171			0.428420			0.214210	+	0.976788i	$0.431282\pi$
$90$	2.14133	+	0.974093i	0.225715	+	0.102678i
$91$		−	3.56521i		−	0.373736i
$92$	−1.31418	−	1.50763i	−0.137013	−	0.157181i
$93$		−	1.79028i		−	0.185644i
$94$	−1.43774	+	3.16056i	−0.148292	+	0.325987i
$95$	−7.35102			−0.754199
$96$	−3.02312	+	4.78129i	−0.308546	+	0.487989i
$97$	5.61109			0.569720			0.284860	−	0.958569i	$-0.408053\pi$
$97$	5.61109			0.569720			0.284860	+	0.958569i	$0.408053\pi$
$98$	3.92780	−	8.63439i	0.396768	−	0.872205i
$99$			3.06212i			0.307755i
$100$	−2.93448	−	3.36643i	−0.293448	−	0.336643i
$101$		−	7.53629i		−	0.749889i	−0.927047	−	0.374944i	$-0.877662\pi$
$101$		−	7.53629i		−	0.749889i	0.927047	−	0.374944i	$-0.122338\pi$
$102$	2.57963	+	1.17348i	0.255421	+	0.116192i
$103$	11.3720			1.12052			0.560261	−	0.828316i	$-0.310701\pi$
$103$	11.3720			1.12052			0.560261	+	0.828316i	$0.310701\pi$
$104$	5.33189	+	17.8657i	0.522835	+	1.75187i
$105$	−0.899690			−0.0878008
$106$	−9.51210	−	4.32707i	−0.923897	−	0.420282i
$107$		−	7.86953i		−	0.760776i	−0.924827	−	0.380388i	$-0.875790\pi$
$107$		−	7.86953i		−	0.760776i	0.924827	−	0.380388i	$-0.124210\pi$
$108$	1.50763	−	1.31418i	0.145071	−	0.126457i
$109$			4.04979i			0.387900i	0.981011	+	0.193950i	$0.0621299\pi$
$109$			4.04979i			0.387900i	−0.981011	+	0.193950i	$0.937870\pi$
$110$	−2.98279	+	6.55700i	−0.284398	+	0.625186i
$111$	7.72195			0.732935
$112$	0.295238	−	2.14319i	0.0278974	−	0.202513i
$113$	−5.73624			−0.539620			−0.269810	−	0.962914i	$-0.586961\pi$
$113$	−5.73624			−0.539620			−0.269810	+	0.962914i	$0.586961\pi$
$114$	−2.58779	+	5.68867i	−0.242368	+	0.532793i
$115$			1.66345i			0.155117i
$116$	5.06387	−	4.41411i	0.470168	−	0.409840i
$117$		−	6.59177i		−	0.609410i
$118$	−7.10503	−	3.23209i	−0.654071	−	0.297538i
$119$	−1.08385			−0.0993561
$120$	4.50845	−	1.34552i	0.411563	−	0.122828i
$121$	1.62340			0.147582
$122$	12.0362	+	5.47528i	1.08970	+	0.495708i
$123$			0.419607i			0.0378347i
$124$	−2.35275	−	2.69908i	−0.211283	−	0.242384i
$125$			12.0316i			1.07614i
$126$	−0.316719	+	0.696236i	−0.0282156	+	0.0620256i
$127$	20.7895			1.84477			0.922387	−	0.386267i	$-0.126236\pi$
$127$	20.7895			1.84477			0.922387	+	0.386267i	$0.126236\pi$
$128$	1.72574	+	11.1813i	0.152536	+	0.988298i
$129$	9.98043			0.878728
$130$	6.42100	−	14.1151i	0.563159	−	1.23798i
$131$		−	19.6027i		−	1.71269i	−0.516403	−	0.856346i	$-0.672729\pi$
$131$		−	19.6027i		−	1.71269i	0.516403	−	0.856346i	$-0.327271\pi$
$132$	4.02418	+	4.61654i	0.350260	+	0.401818i
$133$		−	2.39013i		−	0.207250i
$134$	5.83221	+	2.65308i	0.503827	+	0.229192i
$135$	−1.66345			−0.143167
$136$	5.43128	−	1.62093i	0.465728	−	0.138993i
$137$	−3.94399			−0.336958			−0.168479	−	0.985705i	$-0.553885\pi$
$137$	−3.94399			−0.336958			−0.168479	+	0.985705i	$0.553885\pi$
$138$	1.28728	+	0.585586i	0.109581	+	0.0498484i
$139$			20.1633i			1.71023i	0.518439	+	0.855115i	$0.326513\pi$
$139$			20.1633i			1.71023i	−0.518439	+	0.855115i	$0.673487\pi$
$140$	−1.35640	+	1.18235i	−0.114636	+	0.0999271i
$141$		−	2.45522i		−	0.206767i
$142$	−4.02252	+	8.84260i	−0.337562	+	0.742055i
$143$	20.1848			1.68794
$144$	0.545870	−	3.96258i	0.0454892	−	0.330215i
$145$	−5.58726			−0.463996
$146$	2.45346	−	5.39338i	0.203050	−	0.446360i
$147$			6.70747i			0.553223i
$148$	11.6418	−	10.1480i	0.956951	−	0.834162i
$149$		−	12.9404i		−	1.06012i	−0.847959	−	0.530061i	$-0.822169\pi$
$149$		−	12.9404i		−	1.06012i	0.847959	−	0.530061i	$-0.177831\pi$
$150$	2.87441	+	1.30758i	0.234695	+	0.106763i
$151$	−11.2220			−0.913233			−0.456616	−	0.889664i	$-0.650939\pi$
$151$	−11.2220			−0.913233			−0.456616	+	0.889664i	$0.650939\pi$
$152$	3.57452	+	11.9772i	0.289932	+	0.971479i
$153$	−2.00394			−0.162009
$154$	−2.13196	−	0.969832i	−0.171798	−	0.0781513i
$155$			2.97804i			0.239202i
$156$	−8.66277	−	9.93792i	−0.693576	−	0.795671i
$157$		−	21.8873i		−	1.74680i	−0.487003	−	0.873400i	$-0.661910\pi$
$157$		−	21.8873i		−	1.74680i	0.487003	−	0.873400i	$-0.338090\pi$
$158$	5.08949	−	11.1881i	0.404898	−	0.890079i
$159$	7.38930			0.586010
$160$	5.02880	−	7.95344i	0.397562	−	0.628775i
$161$	−0.540858			−0.0426256
$162$	−0.585586	+	1.28728i	−0.0460080	+	0.101138i
$163$			7.38307i			0.578286i	0.957286	+	0.289143i	$0.0933704\pi$
$163$			7.38307i			0.578286i	−0.957286	+	0.289143i	$0.906630\pi$
$164$	0.551438	+	0.632610i	0.0430601	+	0.0493985i
$165$		−	5.09369i		−	0.396543i
$166$	23.2583	+	10.5802i	1.80519	+	0.821184i
$167$	−6.13313			−0.474596			−0.237298	−	0.971437i	$-0.576262\pi$
$167$	−6.13313			−0.474596			−0.237298	+	0.971437i	$0.576262\pi$
$168$	0.437485	+	1.46589i	0.0337527	+	0.113096i
$169$	−30.4515			−2.34242
$170$	−4.29109	−	1.95202i	−0.329111	−	0.149713i
$171$		−	4.41914i		−	0.337940i
$172$	15.0468	−	13.1161i	1.14730	−	1.00009i
$173$		−	10.2877i		−	0.782156i	−0.920358	−	0.391078i	$-0.872102\pi$
$173$		−	10.2877i		−	0.782156i	0.920358	−	0.391078i	$-0.127898\pi$
$174$	−1.96689	+	4.32376i	−0.149109	+	0.327784i
$175$	−1.20770			−0.0912936
$176$	12.1339	+	1.67152i	0.914627	+	0.125996i
$177$	5.51942			0.414865
$178$	−2.36677	+	5.20281i	−0.177397	+	0.389967i
$179$			4.77713i			0.357059i	0.983935	+	0.178530i	$0.0571340\pi$
$179$			4.77713i			0.357059i	−0.983935	+	0.178530i	$0.942866\pi$
$180$	−2.50786	+	2.18607i	−0.186925	+	0.162940i
$181$			19.9141i			1.48020i	0.672495	+	0.740102i	$0.265223\pi$
$181$			19.9141i			1.48020i	−0.672495	+	0.740102i	$0.734777\pi$
$182$	4.58943	+	2.08774i	0.340191	+	0.154753i
$183$	−9.35009			−0.691178
$184$	2.71030	−	0.808871i	0.199806	−	0.0596308i
$185$	−12.8451			−0.944389
$186$	2.30459	+	1.04836i	0.168981	+	0.0768698i
$187$		−	6.13631i		−	0.448731i
$188$	−3.22660	−	3.70156i	−0.235324	−	0.269964i
$189$		−	0.540858i		−	0.0393416i
$190$	4.30465	−	9.46282i	0.312292	−	0.686505i
$191$	3.79817			0.274826			0.137413	−	0.990514i	$-0.456121\pi$
$191$	3.79817			0.274826			0.137413	+	0.990514i	$0.456121\pi$
$192$	−4.38457	−	6.69145i	−0.316429	−	0.482914i
$193$	0.125530			0.00903582			0.00451791	−	0.999990i	$-0.498562\pi$
$193$	0.125530			0.00903582			0.00451791	+	0.999990i	$0.498562\pi$
$194$	−3.28578	+	7.22305i	−0.235905	+	0.518584i
$195$			10.9651i			0.785226i
$196$	8.81482	+	10.1124i	0.629630	+	0.722311i
$197$			14.9989i			1.06862i	0.845287	+	0.534312i	$0.179429\pi$
$197$			14.9989i			1.06862i	−0.845287	+	0.534312i	$0.820571\pi$
$198$	−3.94181	−	1.79314i	−0.280132	−	0.127433i
$199$	6.56442			0.465339			0.232670	−	0.972556i	$-0.425254\pi$
$199$	6.56442			0.465339			0.232670	+	0.972556i	$0.425254\pi$
$200$	6.05192	−	1.80616i	0.427936	−	0.127715i
$201$	−4.53065			−0.319567
$202$	9.70131	+	4.41314i	0.682582	+	0.310508i
$203$		−	1.81665i		−	0.127504i
$204$	−3.02119	+	2.63353i	−0.211526	+	0.184384i
$205$		−	0.697995i		−	0.0487501i
$206$	−6.65931	+	14.6390i	−0.463976	+	1.01995i
$207$	−1.00000			−0.0695048
$208$	−26.1204	−	3.59825i	−1.81112	−	0.249494i
$209$	13.5320			0.936025
$210$	0.526846	−	1.15815i	0.0363558	−	0.0799202i
$211$		−	17.2729i		−	1.18912i	−0.804053	−	0.594558i	$-0.797327\pi$
$211$		−	17.2729i		−	1.18912i	0.804053	−	0.594558i	$-0.202673\pi$
$212$	11.1403	−	9.71086i	0.765119	−	0.666945i
$213$		−	6.86922i		−	0.470671i
$214$	10.1303	+	4.60829i	0.692492	+	0.315016i
$215$	−16.6019			−1.13224
$216$	0.808871	+	2.71030i	0.0550367	+	0.184413i
$217$	−0.968289			−0.0657317
$218$	−5.21321	−	2.37150i	−0.353083	−	0.160618i
$219$			4.18975i			0.283117i
$220$	−6.69402	−	7.67937i	−0.451310	−	0.517743i
$221$			13.2095i			0.888568i
$222$	−4.52186	+	9.94031i	−0.303488	+	0.667150i
$223$	−17.7066			−1.18572			−0.592860	−	0.805305i	$-0.702001\pi$
$223$	−17.7066			−1.18572			−0.592860	+	0.805305i	$0.702001\pi$
$224$	2.58600	+	1.63508i	0.172784	+	0.109248i
$225$	−2.23294			−0.148862
$226$	3.35906	−	7.38414i	0.223441	−	0.491186i
$227$		−	15.0039i		−	0.995843i	−0.867222	−	0.497922i	$-0.834097\pi$
$227$		−	15.0039i		−	0.995843i	0.867222	−	0.497922i	$-0.165903\pi$
$228$	−5.80754	−	6.66241i	−0.384614	−	0.441229i
$229$		−	2.56136i		−	0.169260i	−0.996412	−	0.0846298i	$-0.973029\pi$
$229$		−	2.56136i		−	0.169260i	0.996412	−	0.0846298i	$-0.0269708\pi$
$230$	−2.14133	−	0.974093i	−0.141195	−	0.0642298i
$231$	1.65617			0.108968
$232$	2.71687	+	9.10346i	0.178371	+	0.597671i
$233$	−9.69927			−0.635420			−0.317710	−	0.948188i	$-0.602914\pi$
$233$	−9.69927			−0.635420			−0.317710	+	0.948188i	$0.602914\pi$
$234$	8.48545	+	3.86005i	0.554712	+	0.252339i
$235$			4.08414i			0.266420i
$236$	8.32121	−	7.25350i	0.541665	−	0.472163i
$237$			8.69129i			0.564560i
$238$	0.634685	−	1.39521i	0.0411405	−	0.0904383i
$239$	−11.1353			−0.720280			−0.360140	−	0.932898i	$-0.617271\pi$
$239$	−11.1353			−0.720280			−0.360140	+	0.932898i	$0.617271\pi$
$240$	−0.908027	+	6.59155i	−0.0586129	+	0.425483i
$241$	−20.7556			−1.33699			−0.668494	−	0.743718i	$-0.733061\pi$
$241$	−20.7556			−1.33699			−0.668494	+	0.743718i	$0.733061\pi$
$242$	−0.950640	+	2.08977i	−0.0611094	+	0.134335i
$243$		−	1.00000i		−	0.0641500i
$244$	−14.0964	+	12.2877i	−0.902431	+	0.786638i
$245$		−	11.1575i		−	0.712829i
$246$	−0.540151	−	0.245716i	−0.0344388	−	0.0156663i
$247$	−29.1300			−1.85350
$248$	4.85220	−	1.44811i	0.308115	−	0.0919549i
$249$	−18.0678			−1.14500
$250$	−15.4881	−	7.04555i	−0.979551	−	0.445600i
$251$		−	3.56658i		−	0.225120i	−0.993645	−	0.112560i	$-0.964095\pi$
$251$		−	3.56658i		−	0.225120i	0.993645	−	0.112560i	$-0.0359051\pi$
$252$	−0.710784	−	0.815412i	−0.0447752	−	0.0513661i
$253$		−	3.06212i		−	0.192514i
$254$	−12.1741	+	26.7620i	−0.763869	+	1.67919i
$255$	3.33345			0.208749
$256$	−15.4041	−	4.32610i	−0.962753	−	0.270382i
$257$	28.2626			1.76297			0.881487	−	0.472208i	$-0.156543\pi$
$257$	28.2626			1.76297			0.881487	+	0.472208i	$0.156543\pi$
$258$	−5.84440	+	12.8476i	−0.363856	+	0.799857i
$259$		−	4.17648i		−	0.259514i
$260$	14.4101	+	16.5312i	0.893675	+	1.02522i
$261$		−	3.35884i		−	0.207907i
$262$	25.2341	+	11.4790i	1.55897	+	0.709177i
$263$	−6.10911			−0.376704			−0.188352	−	0.982102i	$-0.560315\pi$
$263$	−6.10911			−0.376704			−0.188352	+	0.982102i	$0.560315\pi$
$264$	−8.29927	+	2.47686i	−0.510785	+	0.152440i
$265$	−12.2917			−0.755075
$266$	3.07676	+	1.39963i	0.188649	+	0.0858166i
$267$		−	4.04171i		−	0.247348i
$268$	−6.83052	+	5.95408i	−0.417241	+	0.363704i
$269$			16.9496i			1.03343i	0.856157	+	0.516716i	$0.172846\pi$
$269$			16.9496i			1.03343i	−0.856157	+	0.516716i	$0.827154\pi$
$270$	0.974093	−	2.14133i	0.0592814	−	0.130317i
$271$	6.88698			0.418354			0.209177	−	0.977878i	$-0.432921\pi$
$271$	6.88698			0.418354			0.209177	+	0.977878i	$0.432921\pi$
$272$	−1.09389	+	7.94077i	−0.0663268	+	0.481480i
$273$	−3.56521			−0.215777
$274$	2.30954	−	5.07701i	0.139525	−	0.306714i
$275$		−	6.83752i		−	0.412318i
$276$	−1.50763	+	1.31418i	−0.0907484	+	0.0791042i
$277$			7.55815i			0.454126i	0.973880	+	0.227063i	$0.0729123\pi$
$277$			7.55815i			0.454126i	−0.973880	+	0.227063i	$0.927088\pi$
$278$	−25.9558	−	11.8073i	−1.55673	−	0.708158i
$279$	−1.79028			−0.107181
$280$	−0.727734	−	2.43843i	−0.0434904	−	0.145724i
$281$	31.5872			1.88433			0.942166	−	0.335146i	$-0.108786\pi$
$281$	31.5872			1.88433			0.942166	+	0.335146i	$0.108786\pi$
$282$	3.16056	+	1.43774i	0.188209	+	0.0856164i
$283$		−	3.00293i		−	0.178505i	−0.996009	−	0.0892527i	$-0.971552\pi$
$283$		−	3.00293i		−	0.178505i	0.996009	−	0.0892527i	$-0.0284479\pi$
$284$	−9.02738	−	10.3562i	−0.535676	−	0.614528i
$285$			7.35102i			0.435437i
$286$	−11.8199	+	25.9835i	−0.698928	+	1.53644i
$287$	0.226948			0.0133963
$288$	4.78129	+	3.02312i	0.281740	+	0.178139i
$289$	−12.9842			−0.763778
$290$	3.27182	−	7.19236i	0.192128	−	0.422350i
$291$		−	5.61109i		−	0.328928i
$292$	5.50608	+	6.31658i	0.322219	+	0.369650i
$293$			5.89926i			0.344639i	0.985041	+	0.172319i	$0.0551261\pi$
$293$			5.89926i			0.344639i	−0.985041	+	0.172319i	$0.944874\pi$
$294$	−8.63439	−	3.92780i	−0.503568	−	0.229074i
$295$	−9.18127			−0.534554
$296$	6.24606	+	20.9288i	0.363045	+	1.21646i
$297$	3.06212			0.177682
$298$	16.6580	+	7.57774i	0.964970	+	0.438967i
$299$			6.59177i			0.381212i
$300$	−3.36643	+	2.93448i	−0.194361	+	0.169422i
$301$		−	5.39800i		−	0.311135i
$302$	6.57144	−	14.4458i	0.378144	−	0.831265i
$303$	−7.53629			−0.432948
$304$	−17.5112	−	2.41228i	−1.00434	−	0.138354i
$305$	15.5534			0.890585
$306$	1.17348	−	2.57963i	0.0670833	−	0.147468i
$307$		−	16.2783i		−	0.929054i	−0.885559	−	0.464527i	$-0.846224\pi$
$307$		−	16.2783i		−	0.929054i	0.885559	−	0.464527i	$-0.153776\pi$
$308$	2.49689	−	2.17651i	0.142274	−	0.124018i
$309$		−	11.3720i		−	0.646933i
$310$	−3.83358	−	1.74390i	−0.217732	−	0.0990469i
$311$	−30.2981			−1.71805			−0.859023	−	0.511937i	$-0.828928\pi$
$311$	−30.2981			−1.71805			−0.859023	+	0.511937i	$0.828928\pi$
$312$	17.8657	−	5.33189i	1.01145	−	0.301859i
$313$	5.49847			0.310792			0.155396	−	0.987852i	$-0.450335\pi$
$313$	5.49847			0.310792			0.155396	+	0.987852i	$0.450335\pi$
$314$	28.1751	+	12.8169i	1.59002	+	0.723301i
$315$			0.899690i			0.0506918i
$316$	11.4219	+	13.1032i	0.642532	+	0.737113i
$317$			28.3465i			1.59210i	0.605233	+	0.796048i	$0.293080\pi$
$317$			28.3465i			1.59210i	−0.605233	+	0.796048i	$0.706920\pi$
$318$	−4.32707	+	9.51210i	−0.242650	+	0.533412i
$319$	10.2852			0.575859
$320$	7.29351	+	11.1309i	0.407719	+	0.622236i
$321$	−7.86953			−0.439234
$322$	0.316719	−	0.696236i	0.0176501	−	0.0387997i
$323$			8.85569i			0.492744i
$324$	−1.31418	−	1.50763i	−0.0730099	−	0.0837570i
$325$			14.7190i			0.816463i
$326$	−9.50407	−	4.32342i	−0.526382	−	0.239452i
$327$	4.04979			0.223954
$328$	−1.13726	+	0.339408i	−0.0627947	+	0.0187407i
$329$	−1.32793			−0.0732110
$330$	6.55700	+	2.98279i	0.360951	+	0.164197i
$331$			31.0062i			1.70426i	0.523332	+	0.852129i	$0.324689\pi$
$331$			31.0062i			1.70426i	−0.523332	+	0.852129i	$0.675311\pi$
$332$	−27.2394	+	23.7443i	−1.49496	+	1.30314i
$333$		−	7.72195i		−	0.423160i
$334$	3.59147	−	7.89506i	0.196517	−	0.431998i
$335$	7.53651			0.411763
$336$	−2.14319	−	0.295238i	−0.116921	−	0.0161066i
$337$	19.0100			1.03554			0.517772	−	0.855519i	$-0.326762\pi$
$337$	19.0100			1.03554			0.517772	+	0.855519i	$0.326762\pi$
$338$	17.8319	−	39.1995i	0.969930	−	2.13217i
$339$			5.73624i			0.311550i
$340$	5.02560	−	4.38075i	0.272551	−	0.237580i
$341$		−	5.48207i		−	0.296870i
$342$	5.68867	+	2.58779i	0.307608	+	0.139931i
$343$	7.41380			0.400307
$344$	8.07288	+	27.0500i	0.435261	+	1.45844i
$345$	1.66345			0.0895571
$346$	13.2431	+	6.02431i	0.711953	+	0.323869i
$347$			20.2224i			1.08559i	0.839864	+	0.542797i	$0.182635\pi$
$347$			20.2224i			1.08559i	−0.839864	+	0.542797i	$0.817365\pi$
$348$	−4.41411	−	5.06387i	−0.236621	−	0.271452i
$349$		−	21.6467i		−	1.15872i	−0.815072	−	0.579360i	$-0.803303\pi$
$349$		−	21.6467i		−	1.15872i	0.815072	−	0.579360i	$-0.196697\pi$
$350$	0.707213	−	1.55465i	0.0378021	−	0.0830995i
$351$	−6.59177			−0.351843
$352$	−9.25716	+	14.6409i	−0.493408	+	0.780363i
$353$	27.7394			1.47642			0.738210	−	0.674571i	$-0.235671\pi$
$353$	27.7394			1.47642			0.738210	+	0.674571i	$0.235671\pi$
$354$	−3.23209	+	7.10503i	−0.171784	+	0.377628i
$355$			11.4266i			0.606461i
$356$	−5.31152	−	6.09338i	−0.281510	−	0.322948i
$357$			1.08385i			0.0573633i
$358$	−6.14950	−	2.79742i	−0.325011	−	0.147848i
$359$	3.72088			0.196381			0.0981904	−	0.995168i	$-0.468695\pi$
$359$	3.72088			0.196381			0.0981904	+	0.995168i	$0.468695\pi$
$360$	−1.34552	−	4.50845i	−0.0709149	−	0.237616i
$361$	−0.528818			−0.0278325
$362$	−25.6350	−	11.6614i	−1.34735	−	0.612910i
$363$		−	1.62340i		−	0.0852064i
$364$	−5.37501	+	4.68533i	−0.281727	+	0.245578i
$365$		−	6.96944i		−	0.364797i
$366$	5.47528	−	12.0362i	0.286197	−	0.629141i
$367$	−20.3726			−1.06344			−0.531720	−	0.846920i	$-0.678454\pi$
$367$	−20.3726			−1.06344			−0.531720	+	0.846920i	$0.678454\pi$
$368$	−0.545870	+	3.96258i	−0.0284554	+	0.206564i
$369$	0.419607			0.0218439
$370$	7.52189	−	16.5352i	0.391045	−	0.859624i
$371$		−	3.99657i		−	0.207491i
$372$	−2.69908	+	2.35275i	−0.139941	+	0.121984i
$373$		−	25.2335i		−	1.30654i	−0.757125	−	0.653270i	$-0.773397\pi$
$373$		−	25.2335i		−	1.30654i	0.757125	−	0.653270i	$-0.226603\pi$
$374$	7.89915	+	3.59334i	0.408455	+	0.185807i
$375$	12.0316			0.621310
$376$	6.65439	−	1.98596i	0.343174	−	0.102418i
$377$	−22.1407			−1.14030
$378$	0.696236	+	0.316719i	0.0358105	+	0.0162903i
$379$		−	1.06548i		−	0.0547298i	−0.999626	−	0.0273649i	$-0.991288\pi$
$379$		−	1.06548i		−	0.0547298i	0.999626	−	0.0273649i	$-0.00871161\pi$
$380$	9.66055	+	11.0826i	0.495576	+	0.568525i
$381$		−	20.7895i		−	1.06508i
$382$	−2.22416	+	4.88931i	−0.113798	+	0.250159i
$383$	11.2671			0.575724			0.287862	−	0.957672i	$-0.407056\pi$
$383$	11.2671			0.575724			0.287862	+	0.957672i	$0.407056\pi$
$384$	11.1813	−	1.72574i	0.570594	−	0.0880665i
$385$	−2.75496			−0.140406
$386$	−0.0735084	+	0.161592i	−0.00374148	+	0.00822481i
$387$		−	9.98043i		−	0.507334i
$388$	−7.37398	−	8.45943i	−0.374357	−	0.429462i
$389$		−	20.1479i		−	1.02154i	−0.859717	−	0.510770i	$-0.829360\pi$
$389$		−	20.1479i		−	1.02154i	0.859717	−	0.510770i	$-0.170640\pi$
$390$	−14.1151	−	6.42100i	−0.714747	−	0.325140i
$391$	2.00394			0.101344
$392$	−18.1793	+	5.42548i	−0.918192	+	0.274028i
$393$	−19.6027			−0.988823
$394$	−19.3077	−	8.78312i	−0.972709	−	0.442487i
$395$		−	14.4575i		−	0.727437i
$396$	4.61654	−	4.02418i	0.231990	−	0.202222i
$397$		−	16.9238i		−	0.849382i	−0.905338	−	0.424691i	$-0.860383\pi$
$397$		−	16.9238i		−	0.849382i	0.905338	−	0.424691i	$-0.139617\pi$
$398$	−3.84403	+	8.45024i	−0.192684	+	0.423572i
$399$	−2.39013			−0.119656
$400$	−1.21889	+	8.84818i	−0.0609446	+	0.442409i
$401$	−2.89317			−0.144478			−0.0722389	−	0.997387i	$-0.523014\pi$
$401$	−2.89317			−0.144478			−0.0722389	+	0.997387i	$0.523014\pi$
$402$	2.65308	−	5.83221i	0.132324	−	0.290884i
$403$			11.8011i			0.587856i
$404$	−11.3619	+	9.90403i	−0.565276	+	0.492744i
$405$			1.66345i			0.0826575i
$406$	2.33854	+	1.06381i	0.116060	+	0.0527959i
$407$	23.6456			1.17207
$408$	−1.62093	−	5.43128i	−0.0802479	−	0.268888i
$409$	33.9250			1.67748			0.838741	−	0.544531i	$-0.183292\pi$
$409$	33.9250			1.67748			0.838741	+	0.544531i	$0.183292\pi$
$410$	0.898515	+	0.408736i	0.0443745	+	0.0201860i
$411$			3.94399i			0.194543i
$412$	−14.9449	−	17.1448i	−0.736282	−	0.844663i
$413$		−	2.98522i		−	0.146893i
$414$	0.585586	−	1.28728i	0.0287800	−	0.0632663i
$415$	30.0548			1.47533
$416$	19.9277	−	31.5172i	0.977036	−	1.54526i
$417$	20.1633			0.987401
$418$	−7.92412	+	17.4194i	−0.387582	+	0.852012i
$419$		−	15.0971i		−	0.737540i	−0.929521	−	0.368770i	$-0.879779\pi$
$419$		−	15.0971i		−	0.737540i	0.929521	−	0.368770i	$-0.120221\pi$
$420$	1.18235	+	1.35640i	0.0576930	+	0.0661854i
$421$			3.98500i			0.194217i	0.995274	+	0.0971084i	$0.0309594\pi$
$421$			3.98500i			0.194217i	−0.995274	+	0.0971084i	$0.969041\pi$
$422$	22.2350	+	10.1148i	1.08239	+	0.492379i
$423$	−2.45522			−0.119377
$424$	5.97699	+	20.0272i	0.290269	+	0.972608i
$425$	4.47467			0.217053
$426$	8.84260	+	4.02252i	0.428425	+	0.194892i
$427$			5.05707i			0.244729i
$428$	−11.8643	+	10.3420i	−0.573483	+	0.499898i
$429$		−	20.1848i		−	0.974532i
$430$	9.72187	−	21.3714i	0.468830	−	1.03062i
$431$	−23.6098			−1.13725			−0.568623	−	0.822598i	$-0.692524\pi$
$431$	−23.6098			−1.13725			−0.568623	+	0.822598i	$0.692524\pi$
$432$	−3.96258	−	0.545870i	−0.190650	−	0.0262632i
$433$	27.5153			1.32230			0.661151	−	0.750253i	$-0.270068\pi$
$433$	27.5153			1.32230			0.661151	+	0.750253i	$0.270068\pi$
$434$	0.567016	−	1.24646i	0.0272176	−	0.0598319i
$435$			5.58726i			0.267888i
$436$	6.10557	−	5.32215i	0.292404	−	0.254885i
$437$			4.41914i			0.211396i
$438$	−5.39338	−	2.45346i	−0.257706	−	0.117231i
$439$	−14.3901			−0.686801			−0.343401	−	0.939189i	$-0.611579\pi$
$439$	−14.3901			−0.686801			−0.343401	+	0.939189i	$0.611579\pi$
$440$	13.8054	−	4.12014i	0.658148	−	0.196420i
$441$	6.70747			0.319403
$442$	−17.0043	−	7.73530i	−0.808814	−	0.367931i
$443$		−	16.9789i		−	0.806694i	−0.915047	−	0.403347i	$-0.867847\pi$
$443$		−	16.9789i		−	0.806694i	0.915047	−	0.403347i	$-0.132153\pi$
$444$	−10.1480	−	11.6418i	−0.481604	−	0.552496i
$445$			6.72317i			0.318709i
$446$	10.3687	−	22.7933i	0.490973	−	1.07930i
$447$	−12.9404			−0.612062
$448$	−3.61913	+	2.37143i	−0.170988	+	0.112039i
$449$	9.72763			0.459075			0.229538	−	0.973300i	$-0.426279\pi$
$449$	9.72763			0.459075			0.229538	+	0.973300i	$0.426279\pi$
$450$	1.30758	−	2.87441i	0.0616397	−	0.135501i
$451$			1.28489i			0.0605030i
$452$	7.53844	+	8.64810i	0.354578	+	0.406772i
$453$			11.2220i			0.527255i
$454$	19.3142	+	8.78607i	0.906461	+	0.412351i
$455$	5.93055			0.278029
$456$	11.9772	−	3.57452i	0.560884	−	0.167392i
$457$	29.3687			1.37381			0.686905	−	0.726747i	$-0.258969\pi$
$457$	29.3687			1.37381			0.686905	+	0.726747i	$0.258969\pi$
$458$	3.29719	+	1.49990i	0.154068	+	0.0700856i
$459$			2.00394i			0.0935359i
$460$	2.50786	−	2.18607i	0.116930	−	0.101926i
$461$			35.9221i			1.67306i	0.547921	+	0.836530i	$0.315419\pi$
$461$			35.9221i			1.67306i	−0.547921	+	0.836530i	$0.684581\pi$
$462$	−0.969832	+	2.13196i	−0.0451207	+	0.0991877i
$463$	8.54804			0.397261			0.198631	−	0.980074i	$-0.436351\pi$
$463$	8.54804			0.397261			0.198631	+	0.980074i	$0.436351\pi$
$464$	−13.3097	−	1.83349i	−0.617885	−	0.0851175i
$465$	2.97804			0.138103
$466$	5.67976	−	12.4857i	0.263110	−	0.578388i
$467$		−	34.2006i		−	1.58261i	−0.611418	−	0.791307i	$-0.709401\pi$
$467$		−	34.2006i		−	1.58261i	0.611418	−	0.791307i	$-0.290599\pi$
$468$	−9.93792	+	8.66277i	−0.459381	+	0.400436i
$469$			2.45044i			0.113151i
$470$	−5.25743	−	2.39162i	−0.242507	−	0.110317i
$471$	−21.8873			−1.00852
$472$	4.46450	+	14.9593i	0.205495	+	0.688556i
$473$	30.5613			1.40521
$474$	−11.1881	−	5.08949i	−0.513887	−	0.233768i
$475$			9.86766i			0.452759i
$476$	1.42437	+	1.63404i	0.0652858	+	0.0748959i
$477$		−	7.38930i		−	0.338333i
$478$	6.52065	−	14.3342i	0.298248	−	0.655631i
$479$	−16.7235			−0.764118			−0.382059	−	0.924138i	$-0.624785\pi$
$479$	−16.7235			−0.764118			−0.382059	+	0.924138i	$0.624785\pi$
$480$	−7.95344	−	5.02880i	−0.363023	−	0.229532i
$481$	−50.9013			−2.32090
$482$	12.1542	−	26.7183i	0.553609	−	1.21699i
$483$			0.540858i			0.0246099i
$484$	−2.13344	−	2.44748i	−0.0969744	−	0.111249i
$485$			9.33377i			0.423825i
$486$	1.28728	+	0.585586i	0.0583922	+	0.0265627i
$487$	−3.66551			−0.166100			−0.0830501	−	0.996545i	$-0.526466\pi$
$487$	−3.66551			−0.166100			−0.0830501	+	0.996545i	$0.526466\pi$
$488$	−7.56302	−	25.3415i	−0.342362	−	1.14716i
$489$	7.38307			0.333874
$490$	14.3629	+	6.53370i	0.648849	+	0.295162i
$491$			27.3384i			1.23376i	0.787056	+	0.616881i	$0.211604\pi$
$491$			27.3384i			1.23376i	−0.787056	+	0.616881i	$0.788396\pi$
$492$	0.632610	−	0.551438i	0.0285203	−	0.0248608i
$493$			6.73090i			0.303145i
$494$	17.0581	−	37.4984i	0.767480	−	1.68713i
$495$	−5.09369			−0.228944
$496$	−0.977261	+	7.09413i	−0.0438803	+	0.318536i
$497$	−3.71527			−0.166653
$498$	10.5802	−	23.2583i	0.474111	−	1.04223i
$499$			31.8088i			1.42396i	0.702200	+	0.711979i	$0.252201\pi$
$499$			31.8088i			1.42396i	−0.702200	+	0.711979i	$0.747799\pi$
$500$	18.1392	−	15.8117i	0.811209	−	0.707121i
$501$			6.13313i			0.274008i
$502$	4.59118	+	2.08854i	0.204914	+	0.0932159i
$503$	5.40464			0.240981			0.120491	−	0.992714i	$-0.461553\pi$
$503$	5.40464			0.240981			0.120491	+	0.992714i	$0.461553\pi$
$504$	1.46589	−	0.437485i	0.0652958	−	0.0194871i
$505$	12.5362			0.557855
$506$	3.94181	+	1.79314i	0.175235	+	0.0797146i
$507$			30.4515i			1.35240i
$508$	−27.3212	−	31.3428i	−1.21218	−	1.39061i
$509$			9.92007i			0.439699i	0.975534	+	0.219850i	$0.0705567\pi$
$509$			9.92007i			0.439699i	−0.975534	+	0.219850i	$0.929443\pi$
$510$	−1.95202	+	4.29109i	−0.0864370	+	0.190012i
$511$	2.26606			0.100245
$512$	14.5893	−	17.2960i	0.644762	−	0.764383i
$513$	−4.41914			−0.195110
$514$	−16.5502	+	36.3819i	−0.729998	+	1.60474i
$515$			18.9168i			0.833575i
$516$	−13.1161	−	15.0468i	−0.577403	−	0.662397i
$517$		−	7.51820i		−	0.330650i
$518$	5.37630	+	2.44569i	0.236221	+	0.107457i
$519$	−10.2877			−0.451578
$520$	−29.7187	+	8.86934i	−1.30325	+	0.388946i
$521$	−30.2152			−1.32375			−0.661876	−	0.749614i	$-0.730239\pi$
$521$	−30.2152			−1.32375			−0.661876	+	0.749614i	$0.730239\pi$
$522$	4.32376	+	1.96689i	0.189246	+	0.0860883i
$523$			12.3649i			0.540679i	0.962765	+	0.270339i	$0.0871359\pi$
$523$			12.3649i			0.540679i	−0.962765	+	0.270339i	$0.912864\pi$
$524$	−29.5535	+	25.7614i	−1.29105	+	1.12539i
$525$			1.20770i			0.0527084i
$526$	3.57741	−	7.86414i	0.155983	−	0.342893i
$527$	3.58762			0.156279
$528$	1.67152	−	12.1339i	0.0727436	−	0.528060i
$529$	1.00000			0.0434783
$530$	7.19787	−	15.8229i	0.312655	−	0.687303i
$531$		−	5.51942i		−	0.239522i
$532$	−3.60342	+	3.14106i	−0.156228	+	0.136182i
$533$		−	2.76595i		−	0.119807i
$534$	5.20281	+	2.36677i	0.225147	+	0.102420i
$535$	13.0906			0.565955
$536$	−3.66471	−	12.2794i	−0.158291	−	0.530390i
$537$	4.77713			0.206148
$538$	−21.8188	−	9.92542i	−0.940676	−	0.427915i
$539$			20.5391i			0.884682i
$540$	2.18607	+	2.50786i	0.0940735	+	0.107921i
$541$			27.7925i			1.19489i	0.801909	+	0.597446i	$0.203818\pi$
$541$			27.7925i			1.19489i	−0.801909	+	0.597446i	$0.796182\pi$
$542$	−4.03292	+	8.86548i	−0.173229	+	0.380805i
$543$	19.9141			0.854596
$544$	−9.58142	−	6.05814i	−0.410800	−	0.259741i
$545$	−6.73662			−0.288565
$546$	2.08774	−	4.58943i	0.0893470	−	0.196409i
$547$		−	32.2695i		−	1.37975i	−0.723930	−	0.689873i	$-0.757666\pi$
$547$		−	32.2695i		−	1.37975i	0.723930	−	0.689873i	$-0.242334\pi$
$548$	5.18310	+	5.94606i	0.221411	+	0.254003i
$549$			9.35009i			0.399052i
$550$	8.80181	+	4.00396i	0.375310	+	0.170729i
$551$	−14.8432			−0.632341
$552$	−0.808871	−	2.71030i	−0.0344278	−	0.115358i
$553$	4.70075			0.199896
$554$	−9.72946	−	4.42595i	−0.413365	−	0.188041i
$555$			12.8451i			0.545243i
$556$	30.3987	−	26.4982i	1.28919	−	1.12377i
$557$		−	25.4267i		−	1.07736i	−0.842509	−	0.538682i	$-0.818922\pi$
$557$		−	25.4267i		−	1.07736i	0.842509	−	0.538682i	$-0.181078\pi$
$558$	1.04836	−	2.30459i	0.0443808	−	0.0975612i
$559$	−65.7887			−2.78257
$560$	3.56509	+	0.491114i	0.150653	+	0.0207533i
$561$	−6.13631			−0.259075
$562$	−18.4970	+	40.6615i	−0.780249	+	1.71520i
$563$		−	40.5459i		−	1.70881i	−0.519610	−	0.854404i	$-0.673923\pi$
$563$		−	40.5459i		−	1.70881i	0.519610	−	0.854404i	$-0.326077\pi$
$564$	−3.70156	+	3.22660i	−0.155864	+	0.135864i
$565$		−	9.54194i		−	0.401433i
$566$	3.86561	+	1.75847i	0.162484	+	0.0739140i
$567$	−0.540858			−0.0227139
$568$	18.6176	−	5.55631i	0.781179	−	0.233138i
$569$	12.1926			0.511141			0.255570	−	0.966790i	$-0.417737\pi$
$569$	12.1926			0.511141			0.255570	+	0.966790i	$0.417737\pi$
$570$	−9.46282	−	4.30465i	−0.396354	−	0.180302i
$571$		−	22.5782i		−	0.944869i	−0.881366	−	0.472435i	$-0.843375\pi$
$571$		−	22.5782i		−	0.944869i	0.881366	−	0.472435i	$-0.156625\pi$
$572$	−26.5265	−	30.4312i	−1.10913	−	1.27239i
$573$		−	3.79817i		−	0.158671i
$574$	−0.132897	+	0.292145i	−0.00554703	+	0.0121939i
$575$	2.23294			0.0931198
$576$	−6.69145	+	4.38457i	−0.278811	+	0.182690i
$577$	45.8244			1.90769			0.953846	−	0.300295i	$-0.0970851\pi$
$577$	45.8244			1.90769			0.953846	+	0.300295i	$0.0970851\pi$
$578$	7.60338	−	16.7143i	0.316259	−	0.695225i
$579$		−	0.125530i		−	0.00521684i
$580$	7.34265	+	8.42349i	0.304887	+	0.349766i
$581$			9.77209i			0.405415i
$582$	7.22305	+	3.28578i	0.299405	+	0.136200i
$583$	22.6270			0.937113
$584$	−11.3555	+	3.38897i	−0.469893	+	0.140237i
$585$	10.9651			0.453350
$586$	−7.59400	−	3.45453i	−0.313705	−	0.142705i
$587$		−	8.89836i		−	0.367275i	−0.982994	−	0.183637i	$-0.941213\pi$
$587$		−	8.89836i		−	0.367275i	0.982994	−	0.183637i	$-0.0587872\pi$
$588$	10.1124	−	8.81482i	0.417027	−	0.363517i
$589$			7.91151i			0.325988i
$590$	5.37642	−	11.8189i	0.221344	−	0.486575i
$591$	14.9989			0.616971
$592$	−30.5988	−	4.21518i	−1.25760	−	0.173243i
$593$	40.2002			1.65083			0.825413	−	0.564530i	$-0.190942\pi$
$593$	40.2002			1.65083			0.825413	+	0.564530i	$0.190942\pi$
$594$	−1.79314	+	3.94181i	−0.0735733	+	0.161734i
$595$		−	1.80292i		−	0.0739127i
$596$	−19.5093	+	17.0061i	−0.799134	+	0.696595i
$597$		−	6.56442i		−	0.268664i
$598$	−8.48545	−	3.86005i	−0.346996	−	0.157849i
$599$	13.4080			0.547835			0.273917	−	0.961753i	$-0.411681\pi$
$599$	13.4080			0.547835			0.273917	+	0.961753i	$0.411681\pi$
$600$	−1.80616	−	6.05192i	−0.0737360	−	0.247069i
$601$	−12.0342			−0.490887			−0.245443	−	0.969411i	$-0.578933\pi$
$601$	−12.0342			−0.490887			−0.245443	+	0.969411i	$0.578933\pi$
$602$	6.94873	+	3.16099i	0.283209	+	0.128832i
$603$			4.53065i			0.184502i
$604$	14.7477	+	16.9186i	0.600076	+	0.688407i
$605$			2.70044i			0.109789i
$606$	4.41314	−	9.70131i	0.179272	−	0.394089i
$607$	−12.2200			−0.495995			−0.247998	−	0.968761i	$-0.579772\pi$
$607$	−12.2200			−0.495995			−0.247998	+	0.968761i	$0.579772\pi$
$608$	13.3596	−	21.1292i	0.541803	−	0.856903i
$609$	−1.81665			−0.0736145
$610$	−9.10785	+	20.0216i	−0.368766	+	0.810650i
$611$			16.1843i			0.654746i
$612$	2.63353	+	3.02119i	0.106454	+	0.122124i
$613$		−	23.0219i		−	0.929845i	−0.885351	−	0.464922i	$-0.846082\pi$
$613$		−	23.0219i		−	0.929845i	0.885351	−	0.464922i	$-0.153918\pi$
$614$	20.9548	+	9.53237i	0.845666	+	0.384695i
$615$	−0.697995			−0.0281459
$616$	1.33963	+	4.48873i	0.0539753	+	0.180856i
$617$	−10.7058			−0.430998			−0.215499	−	0.976504i	$-0.569138\pi$
$617$	−10.7058			−0.430998			−0.215499	+	0.976504i	$0.569138\pi$
$618$	14.6390	+	6.65931i	0.588867	+	0.267877i
$619$		−	16.1383i		−	0.648655i	−0.945945	−	0.324327i	$-0.894862\pi$
$619$		−	16.1383i		−	0.648655i	0.945945	−	0.324327i	$-0.105138\pi$
$620$	4.48978	−	3.91368i	0.180314	−	0.157177i
$621$			1.00000i			0.0401286i
$622$	17.7421	−	39.0021i	0.711394	−	1.56384i
$623$	−2.18599			−0.0875798
$624$	−3.59825	+	26.1204i	−0.144045	+	1.04565i
$625$	−8.84932			−0.353973
$626$	−3.21983	+	7.07807i	−0.128690	+	0.282897i
$627$		−	13.5320i		−	0.540414i
$628$	−32.9979	+	28.7639i	−1.31676	+	1.14780i
$629$			15.4743i			0.617001i
$630$	−1.15815	−	0.526846i	−0.0461419	−	0.0209900i
$631$	26.0052			1.03525			0.517625	−	0.855608i	$-0.326816\pi$
$631$	26.0052			1.03525			0.517625	+	0.855608i	$0.326816\pi$
$632$	−23.5560	+	7.03013i	−0.937007	+	0.279644i
$633$	−17.2729			−0.686536
$634$	−36.4898	−	16.5993i	−1.44920	−	0.659242i
$635$			34.5824i			1.37236i
$636$	−9.71086	−	11.1403i	−0.385061	−	0.441742i
$637$		−	44.2141i		−	1.75183i
$638$	−6.02285	+	13.2399i	−0.238447	+	0.524173i
$639$	−6.86922			−0.271742
$640$	−18.5996	+	2.87069i	−0.735212	+	0.113474i
$641$	5.86562			0.231678			0.115839	−	0.993268i	$-0.463044\pi$
$641$	5.86562			0.231678			0.115839	+	0.993268i	$0.463044\pi$
$642$	4.60829	−	10.1303i	0.181875	−	0.399811i
$643$		−	10.7251i		−	0.422956i	−0.977383	−	0.211478i	$-0.932172\pi$
$643$		−	10.7251i		−	0.422956i	0.977383	−	0.211478i	$-0.0678276\pi$
$644$	0.710784	+	0.815412i	0.0280088	+	0.0321317i
$645$			16.6019i			0.653701i
$646$	−11.3998	−	5.18577i	−0.448517	−	0.204031i
$647$	21.7913			0.856704			0.428352	−	0.903612i	$-0.359094\pi$
$647$	21.7913			0.856704			0.428352	+	0.903612i	$0.359094\pi$
$648$	2.71030	−	0.808871i	0.106471	−	0.0317755i
$649$	16.9011			0.663428
$650$	−18.9475	−	8.61924i	−0.743181	−	0.338074i
$651$			0.968289i			0.0379502i
$652$	11.1309	−	9.70267i	0.435920	−	0.379986i
$653$			11.6358i			0.455343i	0.973738	+	0.227672i	$0.0731113\pi$
$653$			11.6358i			0.455343i	−0.973738	+	0.227672i	$0.926889\pi$
$654$	−2.37150	+	5.21321i	−0.0927330	+	0.203853i
$655$	32.6080			1.27410
$656$	0.229051	−	1.66273i	0.00894293	−	0.0649185i
$657$	4.18975			0.163458
$658$	0.777616	−	1.70941i	0.0303146	−	0.0666399i
$659$		−	8.82961i		−	0.343953i	−0.985101	−	0.171976i	$-0.944985\pi$
$659$		−	8.82961i		−	0.343953i	0.985101	−	0.171976i	$-0.0550153\pi$
$660$	−7.67937	+	6.69402i	−0.298919	+	0.260564i
$661$		−	21.8120i		−	0.848388i	−0.905571	−	0.424194i	$-0.860557\pi$
$661$		−	21.8120i		−	0.848388i	0.905571	−	0.424194i	$-0.139443\pi$
$662$	−39.9137	−	18.1568i	−1.55129	−	0.705685i
$663$	13.2095			0.513015
$664$	−14.6145	−	48.9690i	−0.567152	−	1.90037i
$665$	3.97586			0.154177
$666$	9.94031	+	4.52186i	0.385179	+	0.175219i
$667$			3.35884i			0.130055i
$668$	8.06003	+	9.24646i	0.311852	+	0.357756i
$669$			17.7066i			0.684576i
$670$	−4.41327	+	9.70160i	−0.170500	+	0.374805i
$671$	−28.6311			−1.10529
$672$	1.63508	−	2.58600i	0.0630745	−	0.0997572i
$673$	24.7314			0.953325			0.476662	−	0.879086i	$-0.341846\pi$
$673$	24.7314			0.953325			0.476662	+	0.879086i	$0.341846\pi$
$674$	−11.1320	+	24.4712i	−0.428789	+	0.942597i
$675$			2.23294i			0.0859457i
$676$	40.0187	+	45.9094i	1.53918	+	1.76575i
$677$		−	36.7775i		−	1.41347i	−0.707477	−	0.706736i	$-0.750167\pi$
$677$		−	36.7775i		−	1.41347i	0.707477	−	0.706736i	$-0.249833\pi$
$678$	−7.38414	−	3.35906i	−0.283586	−	0.129004i
$679$	−3.03480			−0.116465
$680$	2.69633	+	9.03466i	0.103400	+	0.346463i
$681$	−15.0039			−0.574950
$682$	7.05695	+	3.21022i	0.270225	+	0.122926i
$683$			41.3201i			1.58107i	0.612417	+	0.790535i	$0.290197\pi$
$683$			41.3201i			1.58107i	−0.612417	+	0.790535i	$0.709803\pi$
$684$	−6.66241	+	5.80754i	−0.254744	+	0.222057i
$685$		−	6.56062i		−	0.250669i
$686$	−4.34142	+	9.54363i	−0.165756	+	0.364378i
$687$	−2.56136			−0.0977220
$688$	−39.5482	−	5.44802i	−1.50776	−	0.207704i
$689$	−48.7086			−1.85565
$690$	−0.974093	+	2.14133i	−0.0370831	+	0.0815189i
$691$		−	14.0504i		−	0.534502i	−0.963627	−	0.267251i	$-0.913885\pi$
$691$		−	14.0504i		−	0.534502i	0.963627	−	0.267251i	$-0.0861153\pi$
$692$	−15.5099	+	13.5198i	−0.589599	+	0.513946i
$693$		−	1.65617i		−	0.0629129i
$694$	−26.0319	−	11.8419i	−0.988156	−	0.449514i
$695$	−33.5406			−1.27227
$696$	9.10346	−	2.71687i	0.345066	−	0.102983i
$697$	−0.840867			−0.0318501
$698$	27.8653	+	12.6760i	1.05472	+	0.479793i
$699$			9.69927i			0.366860i
$700$	1.58713	+	1.82076i	0.0599881	+	0.0688183i
$701$		−	28.6096i		−	1.08057i	−0.841482	−	0.540285i	$-0.818316\pi$
$701$		−	28.6096i		−	1.08057i	0.841482	−	0.540285i	$-0.181684\pi$
$702$	3.86005	−	8.48545i	0.145688	−	0.320263i
$703$	−34.1244			−1.28703
$704$	−13.4261	−	20.4901i	−0.506015	−	0.772248i
$705$	4.08414			0.153818
$706$	−16.2438	+	35.7084i	−0.611344	+	1.34390i
$707$			4.07606i			0.153296i
$708$	−7.25350	−	8.32121i	−0.272603	−	0.312730i
$709$			25.5955i			0.961259i	0.876924	+	0.480629i	$0.159592\pi$
$709$			25.5955i			0.961259i	−0.876924	+	0.480629i	$0.840408\pi$
$710$	−14.7092	−	6.69125i	−0.552027	−	0.251118i
$711$	8.69129			0.325949
$712$	10.9542	−	3.26922i	0.410527	−	0.122519i
$713$	1.79028			0.0670466
$714$	−1.39521	−	0.634685i	−0.0522146	−	0.0237525i
$715$			33.5764i			1.25569i
$716$	7.20212	−	6.27800i	0.269156	−	0.234620i
$717$			11.1353i			0.415854i
$718$	−2.17890	+	4.78982i	−0.0813157	+	0.178754i
$719$	−19.1630			−0.714658			−0.357329	−	0.933979i	$-0.616313\pi$
$719$	−19.1630			−0.714658			−0.357329	+	0.933979i	$0.616313\pi$
$720$	6.59155	+	0.908027i	0.245653	+	0.0338402i
$721$	−6.15067			−0.229063
$722$	0.309669	−	0.680737i	0.0115247	−	0.0253344i
$723$			20.7556i			0.771910i
$724$	30.0230	−	26.1707i	1.11580	−	0.972626i
$725$			7.50007i			0.278545i
$726$	2.08977	+	0.950640i	0.0775586	+	0.0352816i
$727$	8.23463			0.305406			0.152703	−	0.988272i	$-0.451202\pi$
$727$	8.23463			0.305406			0.152703	+	0.988272i	$0.451202\pi$
$728$	−2.88380	−	9.66280i	−0.106881	−	0.358127i
$729$	−1.00000			−0.0370370
$730$	8.97162	+	4.08121i	0.332055	+	0.151052i
$731$			20.0002i			0.739733i
$732$	12.2877	+	14.0964i	0.454166	+	0.521019i
$733$			24.4416i			0.902772i	0.892329	+	0.451386i	$0.149070\pi$
$733$			24.4416i			0.902772i	−0.892329	+	0.451386i	$0.850930\pi$
$734$	11.9299	−	26.2252i	0.440340	−	0.967990i
$735$	−11.1575			−0.411552
$736$	−4.78129	−	3.02312i	−0.176241	−	0.111434i
$737$	−13.8734			−0.511034
$738$	−0.245716	+	0.540151i	−0.00904493	+	0.0198833i
$739$		−	18.6792i		−	0.687124i	−0.939130	−	0.343562i	$-0.888366\pi$
$739$		−	18.6792i		−	0.687124i	0.939130	−	0.343562i	$-0.111634\pi$
$740$	16.8807	+	19.3656i	0.620548	+	0.711892i
$741$			29.1300i			1.07012i
$742$	5.14470	+	2.34033i	0.188868	+	0.0859163i
$743$	27.6138			1.01305			0.506526	−	0.862225i	$-0.330930\pi$
$743$	27.6138			1.01305			0.506526	+	0.862225i	$0.330930\pi$
$744$	−1.44811	−	4.85220i	−0.0530902	−	0.177890i
$745$	21.5258			0.788643
$746$	32.4825	+	14.7764i	1.18927	+	0.541001i
$747$			18.0678i			0.661065i
$748$	−9.25126	+	8.06421i	−0.338259	+	0.294857i
$749$			4.25630i			0.155522i
$750$	−7.04555	+	15.4881i	−0.257267	+	0.565544i
$751$	42.1510			1.53811			0.769056	−	0.639181i	$-0.220726\pi$
$751$	42.1510			1.53811			0.769056	+	0.639181i	$0.220726\pi$
$752$	−1.34023	+	9.72902i	−0.0488733	+	0.354781i
$753$	−3.56658			−0.129973
$754$	12.9653	−	28.5013i	0.472167	−	1.03795i
$755$		−	18.6672i		−	0.679370i
$756$	−0.815412	+	0.710784i	−0.0296562	+	0.0258510i
$757$		−	33.9469i		−	1.23382i	−0.787033	−	0.616911i	$-0.788384\pi$
$757$		−	33.9469i		−	1.23382i	0.787033	−	0.616911i	$-0.211616\pi$
$758$	1.37157	+	0.623928i	0.0498175	+	0.0226621i
$759$	−3.06212			−0.111148
$760$	−19.9235	+	5.94603i	−0.722700	+	0.215685i
$761$	11.8903			0.431024			0.215512	−	0.976501i	$-0.430858\pi$
$761$	11.8903			0.431024			0.215512	+	0.976501i	$0.430858\pi$
$762$	26.7620	+	12.1741i	0.969483	+	0.441020i
$763$		−	2.19036i		−	0.0792965i
$764$	−4.99147	−	5.72622i	−0.180585	−	0.207167i
$765$		−	3.33345i		−	0.120521i
$766$	−6.59788	+	14.5040i	−0.238391	+	0.524049i
$767$	−36.3827			−1.31370
$768$	−4.32610	+	15.4041i	−0.156105	+	0.555846i
$769$	1.89059			0.0681765			0.0340882	−	0.999419i	$-0.489147\pi$
$769$	1.89059			0.0681765			0.0340882	+	0.999419i	$0.489147\pi$
$770$	1.61327	−	3.54641i	0.0581381	−	0.127804i
$771$		−	28.2626i		−	1.01785i
$772$	−0.164968	−	0.189252i	−0.00593734	−	0.00681132i
$773$			49.8527i			1.79308i	0.442965	+	0.896539i	$0.353927\pi$
$773$			49.8527i			1.79308i	−0.442965	+	0.896539i	$0.646073\pi$
$774$	12.8476	+	5.84440i	0.461798	+	0.210073i
$775$	3.99758			0.143597
$776$	15.2077	−	4.53865i	0.545926	−	0.162928i
$777$	−4.17648			−0.149830
$778$	25.9360	+	11.7983i	0.929852	+	0.422991i
$779$		−	1.85430i		−	0.0664373i
$780$	16.5312	−	14.4101i	0.591913	−	0.515963i
$781$		−	21.0344i		−	0.752670i
$782$	−1.17348	+	2.57963i	−0.0419635	+	0.0922474i
$783$	−3.35884			−0.120035
$784$	3.66141	−	26.5789i	0.130765	−	0.949246i
$785$	36.4085			1.29948
$786$	11.4790	−	25.2341i	0.409444	−	0.900070i
$787$			31.3273i			1.11670i	0.829606	+	0.558349i	$0.188565\pi$
$787$			31.3273i			1.11670i	−0.829606	+	0.558349i	$0.811435\pi$
$788$	22.6127	−	19.7112i	0.805543	−	0.702182i
$789$			6.10911i			0.217490i
$790$	18.6109	+	8.46612i	0.662145	+	0.301211i
$791$	3.10249			0.110312
$792$	2.47686	+	8.29927i	0.0880115	+	0.294902i
$793$	61.6336			2.18867
$794$	21.7857	+	9.91035i	0.773145	+	0.351705i
$795$			12.2917i			0.435943i
$796$	−8.62682	−	9.89668i	−0.305769	−	0.350779i
$797$			33.8609i			1.19942i	0.800219	+	0.599708i	$0.204717\pi$
$797$			33.8609i			1.19942i	−0.800219	+	0.599708i	$0.795283\pi$
$798$	1.39963	−	3.07676i	0.0495462	−	0.108916i
$799$	4.92012			0.174061
$800$	−10.6763	−	6.75042i	−0.377465	−	0.238664i
$801$	−4.04171			−0.142807
$802$	1.69420	−	3.72432i	0.0598242	−	0.131510i
$803$			12.8295i			0.452745i
$804$	5.95408	+	6.83052i	0.209984	+	0.240894i
$805$		−	0.899690i		−	0.0317099i
$806$	−15.1914	−	6.91058i	−0.535093	−	0.243415i
$807$	16.9496			0.596653
$808$	−6.09589	−	20.4256i	−0.214453	−	0.718570i
$809$	24.4427			0.859361			0.429680	−	0.902981i	$-0.358626\pi$
$809$	24.4427			0.859361			0.429680	+	0.902981i	$0.358626\pi$
$810$	−2.14133	−	0.974093i	−0.0752385	−	0.0342261i
$811$		−	7.13632i		−	0.250590i	−0.992120	−	0.125295i	$-0.960012\pi$
$811$		−	7.13632i		−	0.250590i	0.992120	−	0.125295i	$-0.0399877\pi$
$812$	−2.73883	+	2.38741i	−0.0961143	+	0.0837816i
$813$		−	6.88698i		−	0.241537i
$814$	−13.8465	+	30.4385i	−0.485320	+	1.06687i
$815$	−12.2814			−0.430197
$816$	7.94077	+	1.09389i	0.277982	+	0.0382938i
$817$	−44.1050			−1.54304
$818$	−19.8660	+	43.6709i	−0.694598	+	1.52692i
$819$			3.56521i			0.124579i
$820$	−1.05232	+	0.917290i	−0.0367484	+	0.0320332i
$821$		−	44.0515i		−	1.53741i	−0.639605	−	0.768703i	$-0.720902\pi$
$821$		−	44.0515i		−	1.53741i	0.639605	−	0.768703i	$-0.279098\pi$
$822$	−5.07701	−	2.30954i	−0.177081	−	0.0805546i
$823$	39.9517			1.39263			0.696314	−	0.717737i	$-0.254822\pi$
$823$	39.9517			1.39263			0.696314	+	0.717737i	$0.254822\pi$
$824$	30.8217	−	9.19852i	1.07372	−	0.320446i
$825$	−6.83752			−0.238052
$826$	3.84281	+	1.74810i	0.133709	+	0.0608243i
$827$		−	24.4489i		−	0.850173i	−0.905153	−	0.425086i	$-0.860244\pi$
$827$		−	24.4489i		−	0.850173i	0.905153	−	0.425086i	$-0.139756\pi$
$828$	1.31418	+	1.50763i	0.0456709	+	0.0523936i
$829$			33.9497i			1.17912i	0.807724	+	0.589561i	$0.200699\pi$
$829$			33.9497i			1.17912i	−0.807724	+	0.589561i	$0.799301\pi$
$830$	−17.5997	+	38.6889i	−0.610893	+	1.34291i
$831$	7.55815			0.262189
$832$	28.9021	+	44.1085i	1.00200	+	1.52919i
$833$	−13.4414			−0.465716
$834$	−11.8073	+	25.9558i	−0.408855	+	0.898777i
$835$		−	10.2022i		−	0.353060i
$836$	−17.7834	−	20.4011i	−0.615052	−	0.705588i
$837$			1.79028i			0.0618812i
$838$	19.4341	+	8.84063i	0.671342	+	0.305394i
$839$	8.65237			0.298713			0.149356	−	0.988783i	$-0.452280\pi$
$839$	8.65237			0.298713			0.149356	+	0.988783i	$0.452280\pi$
$840$	−2.43843	+	0.727734i	−0.0841339	+	0.0251092i
$841$	17.7182			0.610973
$842$	−5.12981	−	2.33356i	−0.176785	−	0.0804197i
$843$		−	31.5872i		−	1.08792i
$844$	−26.0411	+	22.6997i	−0.896370	+	0.781355i
$845$		−	50.6545i		−	1.74257i
$846$	1.43774	−	3.16056i	0.0494307	−	0.108662i
$847$	−0.878029			−0.0301694
$848$	−29.2807	−	4.03360i	−1.00550	−	0.138514i
$849$	−3.00293			−0.103060
$850$	−2.62030	+	5.76015i	−0.0898756	+	0.197571i
$851$			7.72195i			0.264705i
$852$	−10.3562	+	9.02738i	−0.354798	+	0.309273i
$853$		−	37.9367i		−	1.29893i	−0.760393	−	0.649463i	$-0.774994\pi$
$853$		−	37.9367i		−	1.29893i	0.760393	−	0.649463i	$-0.225006\pi$
$854$	−6.50986	−	2.96135i	−0.222763	−	0.101335i
$855$	7.35102			0.251400
$856$	−6.36544	−	21.3288i	−0.217566	−	0.729003i
$857$	−57.0443			−1.94860			−0.974298	−	0.225261i	$-0.927677\pi$
$857$	−57.0443			−1.94860			−0.974298	+	0.225261i	$0.927677\pi$
$858$	25.9835	+	11.8199i	0.887062	+	0.403526i
$859$		−	7.21910i		−	0.246312i	−0.992387	−	0.123156i	$-0.960698\pi$
$859$		−	7.21910i		−	0.246312i	0.992387	−	0.123156i	$-0.0393016\pi$
$860$	21.8179	+	25.0295i	0.743985	+	0.853500i
$861$		−	0.226948i		−	0.00773436i
$862$	13.8256	−	30.3925i	0.470901	−	1.03517i
$863$	−9.00854			−0.306654			−0.153327	−	0.988175i	$-0.548999\pi$
$863$	−9.00854			−0.306654			−0.153327	+	0.988175i	$0.548999\pi$
$864$	3.02312	−	4.78129i	0.102849	−	0.162663i
$865$	17.1130			0.581859
$866$	−16.1126	+	35.4199i	−0.547528	+	1.20362i
$867$			12.9842i			0.440968i
$868$	1.27250	+	1.45982i	0.0431916	+	0.0495494i
$869$			26.6138i			0.902811i
$870$	−7.19236	−	3.27182i	−0.243844	−	0.110925i
$871$	29.8650			1.01194
$872$	3.27576	+	10.9762i	0.110931	+	0.371699i
$873$	−5.61109			−0.189907
$874$	−5.68867	−	2.58779i	−0.192422	−	0.0875332i
$875$		−	6.50740i		−	0.219990i
$876$	6.31658	−	5.50608i	0.213417	−	0.186033i
$877$			17.5025i			0.591019i	0.955340	+	0.295509i	$0.0954894\pi$
$877$			17.5025i			0.591019i	−0.955340	+	0.295509i	$0.904511\pi$
$878$	8.42663	−	18.5241i	0.284385	−	0.625157i
$879$	5.89926			0.198977
$880$	−2.78049	+	20.1841i	−0.0937303	+	0.680407i
$881$	−54.2622			−1.82814			−0.914070	−	0.405556i	$-0.867078\pi$
$881$	−54.2622			−1.82814			−0.914070	+	0.405556i	$0.867078\pi$
$882$	−3.92780	+	8.63439i	−0.132256	+	0.290735i
$883$		−	41.6687i		−	1.40226i	−0.713031	−	0.701132i	$-0.752678\pi$
$883$		−	41.6687i		−	1.40226i	0.713031	−	0.701132i	$-0.247322\pi$
$884$	19.9150	−	17.3597i	0.669814	−	0.583868i
$885$			9.18127i			0.308625i
$886$	21.8567	+	9.94263i	0.734289	+	0.334029i
$887$	−30.8013			−1.03421			−0.517104	−	0.855923i	$-0.672990\pi$
$887$	−30.8013			−1.03421			−0.517104	+	0.855923i	$0.672990\pi$
$888$	20.9288	−	6.24606i	0.702325	−	0.209604i
$889$	−11.2442			−0.377118
$890$	−8.65461	−	3.93700i	−0.290103	−	0.131968i
$891$		−	3.06212i		−	0.102585i
$892$	23.2696	+	26.6949i	0.779124	+	0.893811i
$893$			10.8500i			0.363081i
$894$	7.57774	−	16.6580i	0.253438	−	0.557126i
$895$	−7.94651			−0.265623
$896$	−0.933383	−	6.04751i	−0.0311821	−	0.202033i
$897$	6.59177			0.220093
$898$	−5.69636	+	12.5222i	−0.190090	+	0.417871i
$899$			6.01327i			0.200554i
$900$	2.93448	+	3.36643i	0.0978158	+	0.112214i
$901$			14.8077i			0.493316i
$902$	−1.65401	−	0.752412i	−0.0550725	−	0.0250526i
$903$	−5.39800			−0.179634
$904$	−15.5469	+	4.63988i	−0.517083	+	0.154320i
$905$	−33.1261			−1.10115
$906$	−14.4458	−	6.57144i	−0.479931	−	0.218321i
$907$			15.5665i			0.516877i	0.966028	+	0.258439i	$0.0832080\pi$
$907$			15.5665i			0.516877i	−0.966028	+	0.258439i	$0.916792\pi$
$908$	−22.6203	+	19.7178i	−0.750679	+	0.654358i
$909$			7.53629i			0.249963i
$910$	−3.47285	+	7.63428i	−0.115124	+	0.253074i
$911$	47.5505			1.57542			0.787709	−	0.616048i	$-0.211267\pi$
$911$	47.5505			1.57542			0.787709	+	0.616048i	$0.211267\pi$
$912$	−2.41228	+	17.5112i	−0.0798785	+	0.579854i
$913$	−55.3257			−1.83101
$914$	−17.1979	+	37.8058i	−0.568856	+	1.25050i
$915$		−	15.5534i		−	0.514179i
$916$	−3.86157	+	3.36609i	−0.127590	+	0.111219i
$917$			10.6023i			0.350117i
$918$	−2.57963	−	1.17348i	−0.0851405	−	0.0387306i
$919$	−30.2537			−0.997976			−0.498988	−	0.866609i	$-0.666295\pi$
$919$	−30.2537			−0.997976			−0.498988	+	0.866609i	$0.666295\pi$
$920$	1.34552	+	4.50845i	0.0443604	+	0.148639i
$921$	−16.2783			−0.536390
$922$	−46.2418	−	21.0355i	−1.52289	−	0.692767i
$923$			45.2803i			1.49042i
$924$	−2.17651	−	2.49689i	−0.0716019	−	0.0821417i
$925$			17.2426i			0.566934i
$926$	−5.00561	+	11.0037i	−0.164495	+	0.361605i
$927$	−11.3720			−0.373507
$928$	10.1542	−	16.0596i	0.333327	−	0.527182i
$929$	18.1227			0.594588			0.297294	−	0.954786i	$-0.403916\pi$
$929$	18.1227			0.594588			0.297294	+	0.954786i	$0.403916\pi$
$930$	−1.74390	+	3.83358i	−0.0571848	+	0.125708i
$931$		−	29.6413i		−	0.971454i
$932$	12.7466	+	14.6229i	0.417528	+	0.478988i
$933$			30.2981i			0.991914i
$934$	44.0257	+	20.0274i	1.44057	+	0.655316i
$935$	10.2074			0.333819
$936$	−5.33189	−	17.8657i	−0.174278	−	0.583958i
$937$	46.5891			1.52200			0.761000	−	0.648752i	$-0.224709\pi$
$937$	46.5891			1.52200			0.761000	+	0.648752i	$0.224709\pi$
$938$	−3.15440	−	1.43494i	−0.102995	−	0.0468525i
$939$		−	5.49847i		−	0.179436i
$940$	6.15736	−	5.36729i	0.200831	−	0.175062i
$941$		−	35.5779i		−	1.15981i	−0.814685	−	0.579904i	$-0.803090\pi$
$941$		−	35.5779i		−	1.15981i	0.814685	−	0.579904i	$-0.196910\pi$
$942$	12.8169	−	28.1751i	0.417598	−	0.917996i
$943$	−0.419607			−0.0136643
$944$	−21.8711	−	3.01288i	−0.711844	−	0.0980610i
$945$	0.899690			0.0292669
$946$	−17.8963	+	39.3410i	−0.581858	+	1.27909i
$947$			23.4657i			0.762533i	0.924465	+	0.381267i	$0.124512\pi$
$947$			23.4657i			0.762533i	−0.924465	+	0.381267i	$0.875488\pi$
$948$	13.1032	−	11.4219i	0.425572	−	0.370966i
$949$		−	27.6179i		−	0.896515i
$950$	−12.7024	−	5.77836i	−0.412121	−	0.187475i
$951$	28.3465			0.919198
$952$	−2.93755	+	0.876692i	−0.0952065	+	0.0284138i
$953$	−35.5926			−1.15296			−0.576478	−	0.817113i	$-0.695573\pi$
$953$	−35.5926			−1.15296			−0.576478	+	0.817113i	$0.695573\pi$
$954$	9.51210	+	4.32707i	0.307966	+	0.140094i
$955$			6.31807i			0.204448i
$956$	14.6337	+	16.7878i	0.473288	+	0.542956i
$957$		−	10.2852i		−	0.332472i
$958$	9.79307	−	21.5279i	0.316400	−	0.695534i
$959$	2.13314			0.0688826
$960$	11.1309	−	7.29351i	0.359248	−	0.235397i
$961$	−27.7949			−0.896609
$962$	29.8071	−	65.5243i	0.961020	−	2.11259i
$963$			7.86953i			0.253592i
$964$	27.2766	+	31.2917i	0.878520	+	1.00784i
$965$			0.208812i			0.00672191i
$966$	−0.696236	−	0.316719i	−0.0224010	−	0.0101903i
$967$	5.06186			0.162779			0.0813893	−	0.996682i	$-0.474064\pi$
$967$	5.06186			0.162779			0.0813893	+	0.996682i	$0.474064\pi$
$968$	4.39990	−	1.31312i	0.141418	−	0.0422053i
$969$	8.85569			0.284486
$970$	−12.0152	−	5.46572i	−0.385784	−	0.175494i
$971$		−	15.3319i		−	0.492023i	−0.969267	−	0.246012i	$-0.920880\pi$
$971$		−	15.3319i		−	0.492023i	0.969267	−	0.246012i	$-0.0791201\pi$
$972$	−1.50763	+	1.31418i	−0.0483571	+	0.0421523i
$973$		−	10.9055i		−	0.349614i
$974$	2.14647	−	4.71854i	0.0687774	−	0.151192i
$975$	14.7190			0.471385
$976$	37.0504	+	5.10393i	1.18596	+	0.163373i
$977$	−26.8744			−0.859788			−0.429894	−	0.902879i	$-0.641449\pi$
$977$	−26.8744			−0.859788			−0.429894	+	0.902879i	$0.641449\pi$
$978$	−4.32342	+	9.50407i	−0.138248	+	0.303907i
$979$		−	12.3762i		−	0.395545i
$980$	−16.8214	+	14.6630i	−0.537340	+	0.468392i
$981$		−	4.04979i		−	0.129300i
$982$	−35.1921	−	16.0090i	−1.12303	−	0.510866i
$983$	−2.71868			−0.0867125			−0.0433563	−	0.999060i	$-0.513805\pi$
$983$	−2.71868			−0.0867125			−0.0433563	+	0.999060i	$0.513805\pi$
$984$	0.339408	+	1.13726i	0.0108199	+	0.0362545i
$985$	−24.9498			−0.794968
$986$	−8.66456	−	3.94152i	−0.275936	−	0.125524i
$987$			1.32793i			0.0422684i
$988$	38.2820	+	43.9171i	1.21791	+	1.39719i
$989$			9.98043i			0.317359i
$990$	2.98279	−	6.55700i	0.0947993	−	0.208395i
$991$	−11.6493			−0.370053			−0.185027	−	0.982734i	$-0.559237\pi$
$991$	−11.6493			−0.370053			−0.185027	+	0.982734i	$0.559237\pi$
$992$	−8.55986	−	5.41223i	−0.271776	−	0.171839i
$993$	31.0062			0.983953
$994$	2.17561	−	4.78259i	0.0690062	−	0.151695i
$995$			10.9196i			0.346174i
$996$	23.7443	+	27.2394i	0.752365	+	0.863114i
$997$			6.57669i			0.208286i	0.994562	+	0.104143i	$0.0332099\pi$
$997$			6.57669i			0.208286i	−0.994562	+	0.104143i	$0.966790\pi$
$998$	−40.9469	−	18.6268i	−1.29615	−	0.589621i
$999$	−7.72195			−0.244312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.d.277.8	yes	20
4.3	odd	2		2208.2.f.d.1105.16		20
8.3	odd	2		2208.2.f.d.1105.5		20
8.5	even	2	inner	552.2.f.d.277.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.d.277.7	✓	20	8.5	even	2	inner
552.2.f.d.277.8	yes	20	1.1	even	1	trivial
2208.2.f.d.1105.5		20	8.3	odd	2
2208.2.f.d.1105.16		20	4.3	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.585586 + 1.28728i) q^{2} -1.00000i q^{3} +(-1.31418 - 1.50763i) q^{4} +1.66345i q^{5} +(1.28728 + 0.585586i) q^{6} -0.540858 q^{7} +(2.71030 - 0.808871i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.585586 + 1.28728i) q^{2} -1.00000i q^{3} +(-1.31418 - 1.50763i) q^{4} +1.66345i q^{5} +(1.28728 + 0.585586i) q^{6} -0.540858 q^{7} +(2.71030 - 0.808871i) q^{8} -1.00000 q^{9} +(-2.14133 - 0.974093i) q^{10} -3.06212i q^{11} +(-1.50763 + 1.31418i) q^{12} +6.59177i q^{13} +(0.316719 - 0.696236i) q^{14} +1.66345 q^{15} +(-0.545870 + 3.96258i) q^{16} +2.00394 q^{17} +(0.585586 - 1.28728i) q^{18} +4.41914i q^{19} +(2.50786 - 2.18607i) q^{20} +0.540858i q^{21} +(3.94181 + 1.79314i) q^{22} +1.00000 q^{23} +(-0.808871 - 2.71030i) q^{24} +2.23294 q^{25} +(-8.48545 - 3.86005i) q^{26} +1.00000i q^{27} +(0.710784 + 0.815412i) q^{28} +3.35884i q^{29} +(-0.974093 + 2.14133i) q^{30} +1.79028 q^{31} +(-4.78129 - 3.02312i) q^{32} -3.06212 q^{33} +(-1.17348 + 2.57963i) q^{34} -0.899690i q^{35} +(1.31418 + 1.50763i) q^{36} +7.72195i q^{37} +(-5.68867 - 2.58779i) q^{38} +6.59177 q^{39} +(1.34552 + 4.50845i) q^{40} -0.419607 q^{41} +(-0.696236 - 0.316719i) q^{42} +9.98043i q^{43} +(-4.61654 + 4.02418i) q^{44} -1.66345i q^{45} +(-0.585586 + 1.28728i) q^{46} +2.45522 q^{47} +(3.96258 + 0.545870i) q^{48} -6.70747 q^{49} +(-1.30758 + 2.87441i) q^{50} -2.00394i q^{51} +(9.93792 - 8.66277i) q^{52} +7.38930i q^{53} +(-1.28728 - 0.585586i) q^{54} +5.09369 q^{55} +(-1.46589 + 0.437485i) q^{56} +4.41914 q^{57} +(-4.32376 - 1.96689i) q^{58} +5.51942i q^{59} +(-2.18607 - 2.50786i) q^{60} -9.35009i q^{61} +(-1.04836 + 2.30459i) q^{62} +0.540858 q^{63} +(6.69145 - 4.38457i) q^{64} -10.9651 q^{65} +(1.79314 - 3.94181i) q^{66} -4.53065i q^{67} +(-2.63353 - 3.02119i) q^{68} -1.00000i q^{69} +(1.15815 + 0.526846i) q^{70} +6.86922 q^{71} +(-2.71030 + 0.808871i) q^{72} -4.18975 q^{73} +(-9.94031 - 4.52186i) q^{74} -2.23294i q^{75} +(6.66241 - 5.80754i) q^{76} +1.65617i q^{77} +(-3.86005 + 8.48545i) q^{78} -8.69129 q^{79} +(-6.59155 - 0.908027i) q^{80} +1.00000 q^{81} +(0.245716 - 0.540151i) q^{82} -18.0678i q^{83} +(0.815412 - 0.710784i) q^{84} +3.33345i q^{85} +(-12.8476 - 5.84440i) q^{86} +3.35884 q^{87} +(-2.47686 - 8.29927i) q^{88} +4.04171 q^{89} +(2.14133 + 0.974093i) q^{90} -3.56521i q^{91} +(-1.31418 - 1.50763i) q^{92} -1.79028i q^{93} +(-1.43774 + 3.16056i) q^{94} -7.35102 q^{95} +(-3.02312 + 4.78129i) q^{96} +5.61109 q^{97} +(3.92780 - 8.63439i) q^{98} +3.06212i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9	\( 20 q - 2 q^{2} + 2 q^{6} - 8 q^{7} - 2 q^{8} - 20 q^{9} - 12 q^{10} + 2 q^{14} + 4 q^{15} + 4 q^{16} + 32 q^{17} + 2 q^{18} + 20 q^{20} + 14 q^{22} + 20 q^{23} + 10 q^{24} - 28 q^{25} + 18 q^{28} - 22 q^{32} + 28 q^{33} - 26 q^{34} + 16 q^{38} + 4 q^{40} - 40 q^{41} + 14 q^{42} + 10 q^{44} - 2 q^{46} + 40 q^{47} + 12 q^{49} - 14 q^{50} + 20 q^{52} - 2 q^{54} - 8 q^{55} + 6 q^{56} - 44 q^{57} - 32 q^{58} - 24 q^{60} + 20 q^{62} + 8 q^{63} - 48 q^{64} + 8 q^{65} + 10 q^{66} + 22 q^{68} + 80 q^{70} - 40 q^{71} + 2 q^{72} - 16 q^{73} - 30 q^{74} + 44 q^{76} - 36 q^{78} - 16 q^{79} + 4 q^{80} + 20 q^{81} - 32 q^{82} + 6 q^{84} - 4 q^{86} + 8 q^{87} - 70 q^{88} - 40 q^{89} + 12 q^{90} + 64 q^{94} - 40 q^{95} + 2 q^{96} + 32 q^{97} - 26 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^6 - 8 * q^7 - 2 * q^8 - 20 * q^9 - 12 * q^10 + 2 * q^14 + 4 * q^15 + 4 * q^16 + 32 * q^17 + 2 * q^18 + 20 * q^20 + 14 * q^22 + 20 * q^23 + 10 * q^24 - 28 * q^25 + 18 * q^28 - 22 * q^32 + 28 * q^33 - 26 * q^34 + 16 * q^38 + 4 * q^40 - 40 * q^41 + 14 * q^42 + 10 * q^44 - 2 * q^46 + 40 * q^47 + 12 * q^49 - 14 * q^50 + 20 * q^52 - 2 * q^54 - 8 * q^55 + 6 * q^56 - 44 * q^57 - 32 * q^58 - 24 * q^60 + 20 * q^62 + 8 * q^63 - 48 * q^64 + 8 * q^65 + 10 * q^66 + 22 * q^68 + 80 * q^70 - 40 * q^71 + 2 * q^72 - 16 * q^73 - 30 * q^74 + 44 * q^76 - 36 * q^78 - 16 * q^79 + 4 * q^80 + 20 * q^81 - 32 * q^82 + 6 * q^84 - 4 * q^86 + 8 * q^87 - 70 * q^88 - 40 * q^89 + 12 * q^90 + 64 * q^94 - 40 * q^95 + 2 * q^96 + 32 * q^97 - 26 * q^98

Introduction

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