LMFDB - Embedded newform 403.2.i.a.216.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(216,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("403.216");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			216.19
Character	$\chi$	$=$	403.216
Dual form			403.2.i.a.278.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.235416 + 0.235416i) q^{2} -2.22877i q^{3} -1.88916i q^{4} +(-2.22025 - 2.22025i) q^{5} +(0.524689 - 0.524689i) q^{6} +(-2.84607 + 2.84607i) q^{7} +(0.915572 - 0.915572i) q^{8} -1.96742 q^{9} +O(q^{10})$	\(q+(0.235416 + 0.235416i) q^{2} -2.22877i q^{3} -1.88916i q^{4} +(-2.22025 - 2.22025i) q^{5} +(0.524689 - 0.524689i) q^{6} +(-2.84607 + 2.84607i) q^{7} +(0.915572 - 0.915572i) q^{8} -1.96742 q^{9} -1.04537i q^{10} +(0.497725 + 0.497725i) q^{11} -4.21050 q^{12} +(3.56922 + 0.510524i) q^{13} -1.34002 q^{14} +(-4.94843 + 4.94843i) q^{15} -3.34724 q^{16} +4.84168 q^{17} +(-0.463162 - 0.463162i) q^{18} +(-3.88979 - 3.88979i) q^{19} +(-4.19440 + 4.19440i) q^{20} +(6.34324 + 6.34324i) q^{21} +0.234345i q^{22} -4.25730 q^{23} +(-2.04060 - 2.04060i) q^{24} +4.85902i q^{25} +(0.720068 + 0.960440i) q^{26} -2.30139i q^{27} +(5.37668 + 5.37668i) q^{28} -0.120104i q^{29} -2.32988 q^{30} +(-4.99945 + 2.45062i) q^{31} +(-2.61914 - 2.61914i) q^{32} +(1.10932 - 1.10932i) q^{33} +(1.13981 + 1.13981i) q^{34} +12.6380 q^{35} +3.71676i q^{36} +(-3.58273 - 3.58273i) q^{37} -1.83144i q^{38} +(1.13784 - 7.95498i) q^{39} -4.06560 q^{40} +(0.324424 + 0.324424i) q^{41} +2.98660i q^{42} +4.84871 q^{43} +(0.940282 - 0.940282i) q^{44} +(4.36816 + 4.36816i) q^{45} +(-1.00224 - 1.00224i) q^{46} +(-0.846778 + 0.846778i) q^{47} +7.46022i q^{48} -9.20023i q^{49} +(-1.14389 + 1.14389i) q^{50} -10.7910i q^{51} +(0.964461 - 6.74283i) q^{52} -12.5024i q^{53} +(0.541785 - 0.541785i) q^{54} -2.21015i q^{55} +5.21156i q^{56} +(-8.66945 + 8.66945i) q^{57} +(0.0282746 - 0.0282746i) q^{58} +(5.77614 - 5.77614i) q^{59} +(9.34836 + 9.34836i) q^{60} -10.6918i q^{61} +(-1.75387 - 0.600036i) q^{62} +(5.59941 - 5.59941i) q^{63} +5.46129i q^{64} +(-6.79108 - 9.05806i) q^{65} +0.522302 q^{66} +(-5.82612 - 5.82612i) q^{67} -9.14671i q^{68} +9.48854i q^{69} +(2.97519 + 2.97519i) q^{70} +(4.46072 + 4.46072i) q^{71} +(-1.80131 + 1.80131i) q^{72} +(5.75131 + 5.75131i) q^{73} -1.68687i q^{74} +10.8296 q^{75} +(-7.34843 + 7.34843i) q^{76} -2.83312 q^{77} +(2.14060 - 1.60487i) q^{78} +7.08435i q^{79} +(7.43170 + 7.43170i) q^{80} -11.0315 q^{81} +0.152749i q^{82} +(7.76851 - 7.76851i) q^{83} +(11.9834 - 11.9834i) q^{84} +(-10.7498 - 10.7498i) q^{85} +(1.14147 + 1.14147i) q^{86} -0.267685 q^{87} +0.911406 q^{88} +(12.7505 + 12.7505i) q^{89} +2.05667i q^{90} +(-11.6113 + 8.70528i) q^{91} +8.04271i q^{92} +(5.46186 + 11.1426i) q^{93} -0.398691 q^{94} +17.2726i q^{95} +(-5.83746 + 5.83746i) q^{96} +(0.0107739 + 0.0107739i) q^{97} +(2.16589 - 2.16589i) q^{98} +(-0.979233 - 0.979233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.235416	+	0.235416i	0.166465	+	0.166465i	0.785423	−	0.618959i	$-0.212445\pi$
$2$	0.235416	+	0.235416i	0.166465	+	0.166465i	−0.618959	+	0.785423i	$0.712445\pi$
$3$		−	2.22877i		−	1.28678i	−0.765538	−	0.643391i	$-0.777527\pi$
$3$		−	2.22877i		−	1.28678i	0.765538	−	0.643391i	$-0.222473\pi$
$4$		−	1.88916i		−	0.944579i
$5$	−2.22025	−	2.22025i	−0.992926	−	0.992926i	0.00704910	−	0.999975i	$-0.497756\pi$
$5$	−2.22025	−	2.22025i	−0.992926	−	0.992926i	−0.999975	+	0.00704910i	$0.997756\pi$
$6$	0.524689	−	0.524689i	0.214203	−	0.214203i
$7$	−2.84607	+	2.84607i	−1.07571	+	1.07571i	−0.0788250	+	0.996888i	$0.525117\pi$
$7$	−2.84607	+	2.84607i	−1.07571	+	1.07571i	−0.996888	+	0.0788250i	$0.974883\pi$
$8$	0.915572	−	0.915572i	0.323703	−	0.323703i
$9$	−1.96742			−0.655806
$10$		−	1.04537i		−	0.330574i
$11$	0.497725	+	0.497725i	0.150070	+	0.150070i	0.778149	−	0.628079i	$-0.216159\pi$
$11$	0.497725	+	0.497725i	0.150070	+	0.150070i	−0.628079	+	0.778149i	$0.716159\pi$
$12$	−4.21050			−1.21547
$13$	3.56922	+	0.510524i	0.989925	+	0.141594i
$13$	3.56922	+	0.510524i	0.989925	+	0.141594i
$14$	−1.34002			−0.358136
$15$	−4.94843	+	4.94843i	−1.27768	+	1.27768i
$16$	−3.34724			−0.836809
$17$	4.84168			1.17428			0.587140	−	0.809485i	$-0.300254\pi$
$17$	4.84168			1.17428			0.587140	+	0.809485i	$0.300254\pi$
$18$	−0.463162	−	0.463162i	−0.109168	−	0.109168i
$19$	−3.88979	−	3.88979i	−0.892379	−	0.892379i	0.102368	−	0.994747i	$-0.467358\pi$
$19$	−3.88979	−	3.88979i	−0.892379	−	0.892379i	−0.994747	+	0.102368i	$0.967358\pi$
$20$	−4.19440	+	4.19440i	−0.937897	+	0.937897i
$21$	6.34324	+	6.34324i	1.38421	+	1.38421i
$22$			0.234345i			0.0499626i
$23$	−4.25730			−0.887708			−0.443854	−	0.896099i	$-0.646389\pi$
$23$	−4.25730			−0.887708			−0.443854	+	0.896099i	$0.646389\pi$
$24$	−2.04060	−	2.04060i	−0.416536	−	0.416536i
$25$			4.85902i			0.971804i
$26$	0.720068	+	0.960440i	0.141217	+	0.188358i
$27$		−	2.30139i		−	0.442903i
$28$	5.37668	+	5.37668i	1.01610	+	1.01610i
$29$		−	0.120104i		−	0.0223028i	−0.999938	−	0.0111514i	$-0.996450\pi$
$29$		−	0.120104i		−	0.0223028i	0.999938	−	0.0111514i	$-0.00354968\pi$
$30$	−2.32988			−0.425376
$31$	−4.99945	+	2.45062i	−0.897927	+	0.440144i
$31$	−4.99945	+	2.45062i	−0.897927	+	0.440144i
$32$	−2.61914	−	2.61914i	−0.463002	−	0.463002i
$33$	1.10932	−	1.10932i	0.193107	−	0.193107i
$34$	1.13981	+	1.13981i	0.195476	+	0.195476i
$35$	12.6380			2.13621
$36$			3.71676i			0.619460i
$37$	−3.58273	−	3.58273i	−0.588997	−	0.588997i	0.348362	−	0.937360i	$-0.386738\pi$
$37$	−3.58273	−	3.58273i	−0.588997	−	0.588997i	−0.937360	+	0.348362i	$0.886738\pi$
$38$		−	1.83144i		−	0.297099i
$39$	1.13784	−	7.95498i	0.182200	−	1.27382i
$40$	−4.06560			−0.642827
$41$	0.324424	+	0.324424i	0.0506665	+	0.0506665i	0.731986	−	0.681320i	$-0.238594\pi$
$41$	0.324424	+	0.324424i	0.0506665	+	0.0506665i	−0.681320	+	0.731986i	$0.738594\pi$
$42$			2.98660i			0.460843i
$43$	4.84871			0.739422			0.369711	−	0.929147i	$-0.379457\pi$
$43$	4.84871			0.739422			0.369711	+	0.929147i	$0.379457\pi$
$44$	0.940282	−	0.940282i	0.141753	−	0.141753i
$45$	4.36816	+	4.36816i	0.651167	+	0.651167i
$46$	−1.00224	−	1.00224i	−0.147772	−	0.147772i
$47$	−0.846778	+	0.846778i	−0.123515	+	0.123515i	−0.766162	−	0.642647i	$-0.777836\pi$
$47$	−0.846778	+	0.846778i	−0.123515	+	0.123515i	0.642647	+	0.766162i	$0.277836\pi$
$48$			7.46022i			1.07679i
$49$		−	9.20023i		−	1.31432i
$50$	−1.14389	+	1.14389i	−0.161771	+	0.161771i
$51$		−	10.7910i		−	1.51104i
$52$	0.964461	−	6.74283i	0.133747	−	0.935062i
$53$		−	12.5024i		−	1.71734i	−0.512526	−	0.858671i	$-0.671290\pi$
$53$		−	12.5024i		−	1.71734i	0.512526	−	0.858671i	$-0.328710\pi$
$54$	0.541785	−	0.541785i	0.0737276	−	0.0737276i
$55$		−	2.21015i		−	0.298016i
$56$			5.21156i			0.696424i
$57$	−8.66945	+	8.66945i	−1.14830	+	1.14830i
$58$	0.0282746	−	0.0282746i	0.00371263	−	0.00371263i
$59$	5.77614	−	5.77614i	0.751989	−	0.751989i	−0.222861	−	0.974850i	$-0.571540\pi$
$59$	5.77614	−	5.77614i	0.751989	−	0.751989i	0.974850	+	0.222861i	$0.0715395\pi$
$60$	9.34836	+	9.34836i	1.20687	+	1.20687i
$61$		−	10.6918i		−	1.36894i	−0.729040	−	0.684471i	$-0.760033\pi$
$61$		−	10.6918i		−	1.36894i	0.729040	−	0.684471i	$-0.239967\pi$
$62$	−1.75387	−	0.600036i	−0.222741	−	0.0762047i
$63$	5.59941	−	5.59941i	0.705459	−	0.705459i
$64$			5.46129i			0.682662i
$65$	−6.79108	−	9.05806i	−0.842330	−	1.12351i
$66$	0.522302			0.0642909
$67$	−5.82612	−	5.82612i	−0.711774	−	0.711774i	0.255132	−	0.966906i	$-0.417881\pi$
$67$	−5.82612	−	5.82612i	−0.711774	−	0.711774i	−0.966906	+	0.255132i	$0.917881\pi$
$68$		−	9.14671i		−	1.10920i
$69$			9.48854i			1.14229i
$70$	2.97519	+	2.97519i	0.355603	+	0.355603i
$71$	4.46072	+	4.46072i	0.529390	+	0.529390i	0.920391	−	0.391000i	$-0.127871\pi$
$71$	4.46072	+	4.46072i	0.529390	+	0.529390i	−0.391000	+	0.920391i	$0.627871\pi$
$72$	−1.80131	+	1.80131i	−0.212287	+	0.212287i
$73$	5.75131	+	5.75131i	0.673140	+	0.673140i	0.958439	−	0.285298i	$-0.0920927\pi$
$73$	5.75131	+	5.75131i	0.673140	+	0.673140i	−0.285298	+	0.958439i	$0.592093\pi$
$74$		−	1.68687i		−	0.196094i
$75$	10.8296			1.25050
$76$	−7.34843	+	7.34843i	−0.842923	+	0.842923i
$77$	−2.83312			−0.322864
$78$	2.14060	−	1.60487i	0.242375	−	0.181715i
$79$			7.08435i			0.797052i	0.917157	+	0.398526i	$0.130478\pi$
$79$			7.08435i			0.797052i	−0.917157	+	0.398526i	$0.869522\pi$
$80$	7.43170	+	7.43170i	0.830889	+	0.830889i
$81$	−11.0315			−1.22572
$82$			0.152749i			0.0168683i
$83$	7.76851	−	7.76851i	0.852704	−	0.852704i	−0.137761	−	0.990465i	$-0.543991\pi$
$83$	7.76851	−	7.76851i	0.852704	−	0.852704i	0.990465	+	0.137761i	$0.0439906\pi$
$84$	11.9834	−	11.9834i	1.30749	−	1.30749i
$85$	−10.7498	−	10.7498i	−1.16597	−	1.16597i
$86$	1.14147	+	1.14147i	0.123088	+	0.123088i
$87$	−0.267685			−0.0286989
$88$	0.911406			0.0971562
$89$	12.7505	+	12.7505i	1.35155	+	1.35155i	0.883926	+	0.467626i	$0.154891\pi$
$89$	12.7505	+	12.7505i	1.35155	+	1.35155i	0.467626	+	0.883926i	$0.345109\pi$
$90$			2.05667i			0.216792i
$91$	−11.6113	+	8.70528i	−1.21719	+	0.912561i
$92$			8.04271i			0.838511i
$93$	5.46186	+	11.1426i	0.566369	+	1.15544i
$94$	−0.398691			−0.0411218
$95$			17.2726i			1.77213i
$96$	−5.83746	+	5.83746i	−0.595783	+	0.595783i
$97$	0.0107739	+	0.0107739i	0.00109392	+	0.00109392i	0.707654	−	0.706560i	$-0.249754\pi$
$97$	0.0107739	+	0.0107739i	0.00109392	+	0.00109392i	−0.706560	+	0.707654i	$0.749754\pi$
$98$	2.16589	−	2.16589i	0.218787	−	0.218787i
$99$	−0.979233	−	0.979233i	−0.0984166	−	0.0984166i
$100$	9.17946			0.917946
$101$			17.4545i			1.73679i	0.495874	+	0.868394i	$0.334848\pi$
$101$			17.4545i			1.73679i	−0.495874	+	0.868394i	$0.665152\pi$
$102$	2.54038	−	2.54038i	0.251535	−	0.251535i
$103$		−	15.3350i		−	1.51100i	−0.655148	−	0.755501i	$-0.727394\pi$
$103$		−	15.3350i		−	1.51100i	0.655148	−	0.755501i	$-0.272606\pi$
$104$	3.73530	−	2.80046i	0.366277	−	0.274608i
$105$		−	28.1671i		−	2.74883i
$106$	2.94328	−	2.94328i	0.285877	−	0.285877i
$107$	7.58399			0.733172			0.366586	−	0.930384i	$-0.380527\pi$
$107$	7.58399			0.733172			0.366586	+	0.930384i	$0.380527\pi$
$108$	−4.34769			−0.418357
$109$	−10.0426	−	10.0426i	−0.961908	−	0.961908i	0.0373925	−	0.999301i	$-0.488095\pi$
$109$	−10.0426	−	10.0426i	−0.961908	−	0.961908i	−0.999301	+	0.0373925i	$0.988095\pi$
$110$	0.520305	−	0.520305i	0.0496092	−	0.0496092i
$111$	−7.98509	+	7.98509i	−0.757911	+	0.757911i
$112$	9.52647	−	9.52647i	0.900166	−	0.900166i
$113$	5.42565			0.510402			0.255201	−	0.966888i	$-0.417858\pi$
$113$	5.42565			0.510402			0.255201	+	0.966888i	$0.417858\pi$
$114$	−4.08186			−0.382301
$115$	9.45227	+	9.45227i	0.881429	+	0.881429i
$116$	−0.226896			−0.0210668
$117$	−7.02215	−	1.00441i	−0.649198	−	0.0928582i
$118$	2.71960			0.250359
$119$	−13.7798	+	13.7798i	−1.26319	+	1.26319i
$120$			9.06128i			0.827178i
$121$		−	10.5045i		−	0.954958i
$122$	2.51702	−	2.51702i	0.227880	−	0.227880i
$123$	0.723066	−	0.723066i	0.0651967	−	0.0651967i
$124$	4.62961	+	9.44475i	0.415751	+	0.848163i
$125$	−0.313007	+	0.313007i	−0.0279962	+	0.0279962i
$126$	2.63639			0.234868
$127$	−8.19721			−0.727385			−0.363693	−	0.931519i	$-0.618484\pi$
$127$	−8.19721			−0.727385			−0.363693	+	0.931519i	$0.618484\pi$
$128$	−6.52395	+	6.52395i	−0.576641	+	0.576641i
$129$		−	10.8067i		−	0.951474i
$130$	0.533685	−	3.73115i	0.0468073	−	0.327243i
$131$	12.0512			1.05292			0.526458	−	0.850201i	$-0.323520\pi$
$131$	12.0512			1.05292			0.526458	+	0.850201i	$0.323520\pi$
$132$	−2.09567	−	2.09567i	−0.182405	−	0.182405i
$133$	22.1412			1.91989
$134$		−	2.74313i		−	0.236970i
$135$	−5.10966	+	5.10966i	−0.439770	+	0.439770i
$136$	4.43291	−	4.43291i	0.380119	−	0.380119i
$137$	4.99440	+	4.99440i	0.426700	+	0.426700i	0.887503	−	0.460803i	$-0.152438\pi$
$137$	4.99440	+	4.99440i	0.426700	+	0.426700i	−0.460803	+	0.887503i	$0.652438\pi$
$138$	−2.23376	+	2.23376i	−0.190150	+	0.190150i
$139$			6.82921i			0.579246i	0.957141	+	0.289623i	$0.0935299\pi$
$139$			6.82921i			0.579246i	−0.957141	+	0.289623i	$0.906470\pi$
$140$		−	23.8751i		−	2.01782i
$141$	1.88727	+	1.88727i	0.158937	+	0.158937i
$142$			2.10025i			0.176249i
$143$	1.52239	+	2.03059i	0.127309	+	0.169807i
$144$	6.58541			0.548784
$145$	−0.266662	+	0.266662i	−0.0221451	+	0.0221451i
$146$			2.70791i			0.224108i
$147$	−20.5052			−1.69124
$148$	−6.76835	+	6.76835i	−0.556355	+	0.556355i
$149$	3.38734	+	3.38734i	0.277502	+	0.277502i	0.832111	−	0.554609i	$-0.187132\pi$
$149$	3.38734	+	3.38734i	0.277502	+	0.277502i	−0.554609	+	0.832111i	$0.687132\pi$
$150$	2.54948	+	2.54948i	0.208164	+	0.208164i
$151$	−3.59949	−	3.59949i	−0.292922	−	0.292922i	0.545311	−	0.838234i	$-0.316411\pi$
$151$	−3.59949	−	3.59949i	−0.292922	−	0.292922i	−0.838234	+	0.545311i	$0.816411\pi$
$152$	−7.12276			−0.577732
$153$	−9.52561			−0.770100
$154$	−0.666963	−	0.666963i	−0.0537454	−	0.0537454i
$155$	16.5410	+	5.65904i	1.32861	+	0.454545i
$156$	−15.0282	−	2.14956i	−1.20322	−	0.172103i
$157$	−2.20267			−0.175792			−0.0878961	−	0.996130i	$-0.528014\pi$
$157$	−2.20267			−0.175792			−0.0878961	+	0.996130i	$0.528014\pi$
$158$	−1.66777	+	1.66777i	−0.132681	+	0.132681i
$159$	−27.8651			−2.20984
$160$			11.6303i			0.919454i
$161$	12.1166	−	12.1166i	0.954920	−	0.954920i
$162$	−2.59700	−	2.59700i	−0.204040	−	0.204040i
$163$	−9.89404	+	9.89404i	−0.774961	+	0.774961i	−0.978969	−	0.204008i	$-0.934603\pi$
$163$	−9.89404	+	9.89404i	−0.774961	+	0.774961i	0.204008	+	0.978969i	$0.434603\pi$
$164$	0.612888	−	0.612888i	0.0478585	−	0.0478585i
$165$	−4.92591			−0.383482
$166$	3.65767			0.283890
$167$	−2.11889	−	2.11889i	−0.163965	−	0.163965i	0.620356	−	0.784321i	$-0.286988\pi$
$167$	−2.11889	−	2.11889i	−0.163965	−	0.163965i	−0.784321	+	0.620356i	$0.786988\pi$
$168$	11.6154			0.896146
$169$	12.4787	+	3.64435i	0.959902	+	0.280335i
$170$		−	5.06134i		−	0.388187i
$171$	7.65284	+	7.65284i	0.585227	+	0.585227i
$172$		−	9.15999i		−	0.698442i
$173$		−	18.0249i		−	1.37040i	−0.728353	−	0.685202i	$-0.759714\pi$
$173$		−	18.0249i		−	1.37040i	0.728353	−	0.685202i	$-0.240286\pi$
$174$	−0.0630175	−	0.0630175i	−0.00477735	−	0.00477735i
$175$	−13.8291	−	13.8291i	−1.04538	−	1.04538i
$176$	−1.66600	−	1.66600i	−0.125580	−	0.125580i
$177$	−12.8737	−	12.8737i	−0.967646	−	0.967646i
$178$			6.00336i			0.449971i
$179$	−6.95479			−0.519825			−0.259913	−	0.965632i	$-0.583694\pi$
$179$	−6.95479			−0.519825			−0.259913	+	0.965632i	$0.583694\pi$
$180$	8.25214	−	8.25214i	0.615078	−	0.615078i
$181$	25.5042			1.89571			0.947856	−	0.318698i	$-0.103246\pi$
$181$	25.5042			1.89571			0.947856	+	0.318698i	$0.103246\pi$
$182$	−4.78284	−	0.684115i	−0.354528	−	0.0507099i
$183$	−23.8295			−1.76153
$184$	−3.89786	+	3.89786i	−0.287354	+	0.287354i
$185$			15.9091i			1.16966i
$186$	−1.33734	+	3.90897i	−0.0980587	+	0.286619i
$187$	2.40983	+	2.40983i	0.176224	+	0.176224i
$188$	1.59970	+	1.59970i	0.116670	+	0.116670i
$189$	6.54992	+	6.54992i	0.476436	+	0.476436i
$190$	−4.06626	+	4.06626i	−0.294997	+	0.294997i
$191$	14.1830			1.02625			0.513123	−	0.858315i	$-0.328489\pi$
$191$	14.1830			1.02625			0.513123	+	0.858315i	$0.328489\pi$
$192$	12.1720			0.878436
$193$	2.77188	−	2.77188i	0.199525	−	0.199525i	−0.600272	−	0.799796i	$-0.704941\pi$
$193$	2.77188	−	2.77188i	0.199525	−	0.199525i	0.799796	+	0.600272i	$0.204941\pi$
$194$			0.00507269i			0.000364198i
$195$	−20.1883	+	15.1358i	−1.44572	+	1.08389i
$196$	−17.3807			−1.24148
$197$	8.50405	−	8.50405i	0.605889	−	0.605889i	−0.335980	−	0.941869i	$-0.609068\pi$
$197$	8.50405	−	8.50405i	0.605889	−	0.605889i	0.941869	+	0.335980i	$0.109068\pi$
$198$		−	0.461055i		−	0.0327658i
$199$	1.47218			0.104360			0.0521800	−	0.998638i	$-0.483383\pi$
$199$	1.47218			0.104360			0.0521800	+	0.998638i	$0.483383\pi$
$200$	4.44878	+	4.44878i	0.314576	+	0.314576i
$201$	−12.9851	+	12.9851i	−0.915898	+	0.915898i
$202$	−4.10908	+	4.10908i	−0.289114	+	0.289114i
$203$	0.341826	+	0.341826i	0.0239915	+	0.0239915i
$204$	−20.3859			−1.42730
$205$		−	1.44060i		−	0.100616i
$206$	3.61011	−	3.61011i	0.251528	−	0.251528i
$207$	8.37588			0.582164
$208$	−11.9470	−	1.70885i	−0.828378	−	0.118487i
$209$		−	3.87209i		−	0.267838i
$210$	6.63101	−	6.63101i	0.457583	−	0.457583i
$211$	−22.3120			−1.53602			−0.768010	−	0.640437i	$-0.778753\pi$
$211$	−22.3120			−1.53602			−0.768010	+	0.640437i	$0.778753\pi$
$212$	−23.6191			−1.62217
$213$	9.94193	−	9.94193i	0.681209	−	0.681209i
$214$	1.78540	+	1.78540i	0.122047	+	0.122047i
$215$	−10.7654	−	10.7654i	−0.734191	−	0.734191i
$216$	−2.10709	−	2.10709i	−0.143369	−	0.143369i
$217$	7.25415	−	21.2034i	0.492444	−	1.43938i
$218$		−	4.72839i		−	0.320247i
$219$	12.8184	−	12.8184i	0.866184	−	0.866184i
$220$	−4.17532			−0.281500
$221$	17.2811	+	2.47180i	1.16245	+	0.166271i
$222$	−3.75964			−0.252331
$223$	−10.1361	+	10.1361i	−0.678761	+	0.678761i	−0.959720	−	0.280959i	$-0.909348\pi$
$223$	−10.1361	+	10.1361i	−0.678761	+	0.678761i	0.280959	+	0.959720i	$0.409348\pi$
$224$	14.9085			0.996116
$225$		−	9.55972i		−	0.637315i
$226$	1.27729	+	1.27729i	0.0849639	+	0.0849639i
$227$	−13.0586	−	13.0586i	−0.866729	−	0.866729i	0.125380	−	0.992109i	$-0.459985\pi$
$227$	−13.0586	−	13.0586i	−0.866729	−	0.866729i	−0.992109	+	0.125380i	$0.959985\pi$
$228$	16.3780	+	16.3780i	1.08466	+	1.08466i
$229$	6.27536	+	6.27536i	0.414687	+	0.414687i	0.883368	−	0.468681i	$-0.155270\pi$
$229$	6.27536	+	6.27536i	0.414687	+	0.414687i	−0.468681	+	0.883368i	$0.655270\pi$
$230$			4.45044i			0.293453i
$231$			6.31438i			0.415456i
$232$	−0.109964	−	0.109964i	−0.00721951	−	0.00721951i
$233$		−	15.0407i		−	0.985350i	−0.870214	−	0.492675i	$-0.836019\pi$
$233$		−	15.0407i		−	0.985350i	0.870214	−	0.492675i	$-0.163981\pi$
$234$	−1.41667	−	1.88959i	−0.0926109	−	0.123526i
$235$	3.76012			0.245283
$236$	−10.9120	−	10.9120i	−0.710314	−	0.710314i
$237$	15.7894			1.02563
$238$	−6.48797			−0.420553
$239$	21.0488	−	21.0488i	1.36154	−	1.36154i	0.489576	−	0.871960i	$-0.337151\pi$
$239$	21.0488	−	21.0488i	1.36154	−	1.36154i	0.871960	−	0.489576i	$-0.162849\pi$
$240$	16.5636	−	16.5636i	1.06917	−	1.06917i
$241$	3.13044	+	3.13044i	0.201650	+	0.201650i	0.800706	−	0.599057i	$-0.204458\pi$
$241$	3.13044	+	3.13044i	0.201650	+	0.201650i	−0.599057	+	0.800706i	$0.704458\pi$
$242$	2.47294	−	2.47294i	0.158967	−	0.158967i
$243$			17.6826i			1.13434i
$244$	−20.1985			−1.29307
$245$	−20.4268	+	20.4268i	−1.30502	+	1.30502i
$246$	0.340443			0.0217059
$247$	−11.8977	−	15.8694i	−0.757033	−	1.00974i
$248$	−2.33364	+	6.82107i	−0.148186	+	0.433138i
$249$	−17.3142	−	17.3142i	−1.09724	−	1.09724i
$250$	−0.147374			−0.00932076
$251$	−0.163849			−0.0103420			−0.00517102	−	0.999987i	$-0.501646\pi$
$251$	−0.163849			−0.0103420			−0.00517102	+	0.999987i	$0.501646\pi$
$252$	−10.5782	−	10.5782i	−0.666362	−	0.666362i
$253$	−2.11896	−	2.11896i	−0.133218	−	0.133218i
$254$	−1.92976	−	1.92976i	−0.121084	−	0.121084i
$255$	−23.9587	+	23.9587i	−1.50035	+	1.50035i
$256$	7.85090			0.490681
$257$			5.06995i			0.316255i	0.987419	+	0.158127i	$0.0505457\pi$
$257$			5.06995i			0.316255i	−0.987419	+	0.158127i	$0.949454\pi$
$258$	2.54407	−	2.54407i	0.158387	−	0.158387i
$259$	20.3934			1.26718
$260$	−17.1121	+	12.8294i	−1.06125	+	0.795647i
$261$			0.236296i			0.0146263i
$262$	2.83704	+	2.83704i	0.175273	+	0.175273i
$263$			8.54232i			0.526742i	0.964695	+	0.263371i	$0.0848343\pi$
$263$			8.54232i			0.526742i	−0.964695	+	0.263371i	$0.915166\pi$
$264$		−	2.03131i		−	0.125019i
$265$	−27.7586	+	27.7586i	−1.70519	+	1.70519i
$266$	5.21241	+	5.21241i	0.319593	+	0.319593i
$267$	28.4180	−	28.4180i	1.73915	−	1.73915i
$268$	−11.0065	+	11.0065i	−0.672327	+	0.672327i
$269$			22.8265i			1.39176i	0.718160	+	0.695878i	$0.244985\pi$
$269$			22.8265i			1.39176i	−0.718160	+	0.695878i	$0.755015\pi$
$270$	−2.40580			−0.146412
$271$	13.8093	+	13.8093i	0.838853	+	0.838853i	0.988708	−	0.149855i	$-0.0478806\pi$
$271$	13.8093	+	13.8093i	0.838853	+	0.838853i	−0.149855	+	0.988708i	$0.547881\pi$
$272$	−16.2063			−0.982649
$273$	19.4021	+	25.8788i	1.17427	+	1.56626i
$274$			2.35153i			0.142061i
$275$	−2.41846	+	2.41846i	−0.145838	+	0.145838i
$276$	17.9254			1.07898
$277$	3.07862			0.184976			0.0924881	−	0.995714i	$-0.470518\pi$
$277$	3.07862			0.184976			0.0924881	+	0.995714i	$0.470518\pi$
$278$	−1.60771	+	1.60771i	−0.0964239	+	0.0964239i
$279$	9.83600	−	4.82139i	0.588866	−	0.288649i
$280$	11.5710	−	11.5710i	0.691498	−	0.691498i
$281$	3.93017	−	3.93017i	0.234455	−	0.234455i	−0.580095	−	0.814549i	$-0.696984\pi$
$281$	3.93017	−	3.93017i	0.234455	−	0.234455i	0.814549	+	0.580095i	$0.196984\pi$
$282$			0.888591i			0.0529148i
$283$			21.9333i			1.30380i	0.758304	+	0.651901i	$0.226028\pi$
$283$			21.9333i			1.30380i	−0.758304	+	0.651901i	$0.773972\pi$
$284$	8.42701	−	8.42701i	0.500051	−	0.500051i
$285$	38.4967			2.28035
$286$	−0.119639	+	0.836431i	−0.00707440	+	0.0494592i
$287$	−1.84667			−0.109005
$288$	5.15294	+	5.15294i	0.303640	+	0.303640i
$289$	6.44191			0.378936
$290$	−0.125553			−0.00737274
$291$	0.0240125	−	0.0240125i	0.00140764	−	0.00140764i
$292$	10.8651	−	10.8651i	0.635834	−	0.635834i
$293$	−1.00403	+	1.00403i	−0.0586561	+	0.0586561i	−0.735826	−	0.677170i	$-0.763206\pi$
$293$	−1.00403	+	1.00403i	−0.0586561	+	0.0586561i	0.677170	+	0.735826i	$0.263206\pi$
$294$	−4.82726	−	4.82726i	−0.281532	−	0.281532i
$295$	−25.6490			−1.49334
$296$	−6.56050			−0.381321
$297$	1.14546	−	1.14546i	0.0664663	−	0.0664663i
$298$			1.59487i			0.0923885i
$299$	−15.1953	−	2.17345i	−0.878764	−	0.125694i
$300$		−	20.4589i		−	1.18120i
$301$	−13.7998	+	13.7998i	−0.795406	+	0.795406i
$302$		−	1.69476i		−	0.0975224i
$303$	38.9021			2.23487
$304$	13.0200	+	13.0200i	0.746751	+	0.746751i
$305$	−23.7384	+	23.7384i	−1.35926	+	1.35926i
$306$	−2.24249	−	2.24249i	−0.128194	−	0.128194i
$307$	12.3916	−	12.3916i	0.707226	−	0.707226i	−0.258725	−	0.965951i	$-0.583302\pi$
$307$	12.3916	−	12.3916i	0.707226	−	0.707226i	0.965951	+	0.258725i	$0.0833024\pi$
$308$			5.35221i			0.304971i
$309$	−34.1782			−1.94433
$310$	2.56179	+	5.22626i	0.145500	+	0.296831i
$311$			14.0855i			0.798716i	0.916795	+	0.399358i	$0.130767\pi$
$311$			14.0855i			0.798716i	−0.916795	+	0.399358i	$0.869233\pi$
$312$	−6.24158	−	8.32513i	−0.353360	−	0.471318i
$313$		−	8.34137i		−	0.471482i	−0.971816	−	0.235741i	$-0.924248\pi$
$313$		−	8.34137i		−	0.471482i	0.971816	−	0.235741i	$-0.0757517\pi$
$314$	−0.518545	−	0.518545i	−0.0292632	−	0.0292632i
$315$	−24.8642			−1.40094
$316$	13.3835			0.752879
$317$	−0.454172	−	0.454172i	−0.0255089	−	0.0255089i	0.694237	−	0.719746i	$-0.255742\pi$
$317$	−0.454172	−	0.454172i	−0.0255089	−	0.0255089i	−0.719746	+	0.694237i	$0.755742\pi$
$318$	−6.55990	−	6.55990i	−0.367861	−	0.367861i
$319$	0.0597790	−	0.0597790i	0.00334698	−	0.00334698i
$320$	12.1254	−	12.1254i	0.677833	−	0.677833i
$321$		−	16.9030i		−	0.943432i
$322$	5.70488			0.317921
$323$	−18.8331	−	18.8331i	−1.04790	−	1.04790i
$324$			20.8403i			1.15779i
$325$	−2.48065	+	17.3429i	−0.137602	+	0.962013i
$326$	−4.65844			−0.258007
$327$	−22.3827	+	22.3827i	−1.23777	+	1.23777i
$328$	0.594066			0.0328018
$329$		−	4.81998i		−	0.265734i
$330$	−1.15964	−	1.15964i	−0.0638361	−	0.0638361i
$331$	13.2691	−	13.2691i	0.729334	−	0.729334i	−0.241153	−	0.970487i	$-0.577526\pi$
$331$	13.2691	−	13.2691i	0.729334	−	0.729334i	0.970487	+	0.241153i	$0.0775256\pi$
$332$	−14.6759	−	14.6759i	−0.805447	−	0.805447i
$333$	7.04873	+	7.04873i	0.386268	+	0.386268i
$334$		−	0.997643i		−	0.0545886i
$335$			25.8709i			1.41348i
$336$	−21.2323	−	21.2323i	−1.15832	−	1.15832i
$337$	17.3761			0.946535			0.473268	−	0.880919i	$-0.343074\pi$
$337$	17.3761			0.946535			0.473268	+	0.880919i	$0.343074\pi$
$338$	2.07976	+	3.79564i	0.113124	+	0.206456i
$339$		−	12.0925i		−	0.656776i
$340$	−20.3080	+	20.3080i	−1.10135	+	1.10135i
$341$	−3.70808	−	1.26862i	−0.200804	−	0.0686994i
$342$			3.60321i			0.194839i
$343$	6.26201	+	6.26201i	0.338117	+	0.338117i
$344$	4.43934	−	4.43934i	0.239353	−	0.239353i
$345$	21.0669	−	21.0669i	1.13421	−	1.13421i
$346$	4.24335	−	4.24335i	0.228124	−	0.228124i
$347$			30.7110i			1.64866i	0.566113	+	0.824328i	$0.308447\pi$
$347$			30.7110i			1.64866i	−0.566113	+	0.824328i	$0.691553\pi$
$348$			0.505700i			0.0271084i
$349$	−14.8249	+	14.8249i	−0.793557	+	0.793557i	−0.982071	−	0.188514i	$-0.939633\pi$
$349$	−14.8249	+	14.8249i	−0.793557	+	0.793557i	0.188514	+	0.982071i	$0.439633\pi$
$350$		−	6.51120i		−	0.348038i
$351$	1.17492	−	8.21418i	0.0627123	−	0.438440i
$352$		−	2.60722i		−	0.138965i
$353$	20.4715	−	20.4715i	1.08959	−	1.08959i	0.0940184	−	0.995570i	$-0.470029\pi$
$353$	20.4715	−	20.4715i	1.08959	−	1.08959i	0.995570	−	0.0940184i	$-0.0299713\pi$
$354$		−	6.06136i		−	0.322157i
$355$		−	19.8078i		−	1.05129i
$356$	24.0877	−	24.0877i	1.27665	−	1.27665i
$357$	30.7120	+	30.7120i	1.62545	+	1.62545i
$358$	−1.63727	−	1.63727i	−0.0865325	−	0.0865325i
$359$	15.9164	−	15.9164i	0.840038	−	0.840038i	−0.148826	−	0.988863i	$-0.547549\pi$
$359$	15.9164	−	15.9164i	0.840038	−	0.840038i	0.988863	+	0.148826i	$0.0475493\pi$
$360$	7.99873			0.421570
$361$			11.2609i			0.592681i
$362$	6.00411	+	6.00411i	0.315569	+	0.315569i
$363$	−23.4122			−1.22882
$364$	16.4456	+	21.9355i	0.861986	+	1.14973i
$365$		−	25.5387i		−	1.33676i
$366$	−5.60986	−	5.60986i	−0.293232	−	0.293232i
$367$		−	15.2166i		−	0.794300i	−0.917754	−	0.397150i	$-0.869999\pi$
$367$		−	15.2166i		−	0.794300i	0.917754	−	0.397150i	$-0.130001\pi$
$368$	14.2502			0.742842
$369$	−0.638277	−	0.638277i	−0.0332274	−	0.0332274i
$370$	−3.74527	+	3.74527i	−0.194707	+	0.194707i
$371$	35.5828	+	35.5828i	1.84737	+	1.84737i
$372$	21.0502	−	10.3183i	1.09140	−	0.534980i
$373$	−17.6696			−0.914897			−0.457448	−	0.889236i	$-0.651237\pi$
$373$	−17.6696			−0.914897			−0.457448	+	0.889236i	$0.651237\pi$
$374$			1.13463i			0.0586701i
$375$	0.697622	+	0.697622i	0.0360250	+	0.0360250i
$376$			1.55057i			0.0799647i
$377$	0.0613163	−	0.428680i	0.00315795	−	0.0220781i
$378$			3.08392i			0.158620i
$379$	−8.79067	−	8.79067i	−0.451547	−	0.451547i	0.444321	−	0.895868i	$-0.353445\pi$
$379$	−8.79067	−	8.79067i	−0.451547	−	0.451547i	−0.895868	+	0.444321i	$0.853445\pi$
$380$	32.6307			1.67392
$381$			18.2697i			0.935986i
$382$	3.33891	+	3.33891i	0.170834	+	0.170834i
$383$	6.16439	−	6.16439i	0.314986	−	0.314986i	−0.531852	−	0.846837i	$-0.678504\pi$
$383$	6.16439	−	6.16439i	0.314986	−	0.314986i	0.846837	+	0.531852i	$0.178504\pi$
$384$	14.5404	+	14.5404i	0.742011	+	0.742011i
$385$	6.29024	+	6.29024i	0.320580	+	0.320580i
$386$	1.30509			0.0664275
$387$	−9.53944			−0.484917
$388$	0.0203535	−	0.0203535i	0.00103329	−	0.00103329i
$389$	−7.20401			−0.365258			−0.182629	−	0.983182i	$-0.558461\pi$
$389$	−7.20401			−0.365258			−0.182629	+	0.983182i	$0.558461\pi$
$390$	−8.31587	−	1.18946i	−0.421091	−	0.0602307i
$391$	−20.6125			−1.04242
$392$	−8.42347	−	8.42347i	−0.425450	−	0.425450i
$393$		−	26.8593i		−	1.35487i
$394$	4.00399			0.201718
$395$	15.7290	−	15.7290i	0.791414	−	0.791414i
$396$	−1.84993	+	1.84993i	−0.0929623	+	0.0929623i
$397$	17.3738	−	17.3738i	0.871967	−	0.871967i	−0.120719	−	0.992687i	$-0.538520\pi$
$397$	17.3738	−	17.3738i	0.871967	−	0.871967i	0.992687	+	0.120719i	$0.0385201\pi$
$398$	0.346575	+	0.346575i	0.0173723	+	0.0173723i
$399$		−	49.3477i		−	2.47048i
$400$		−	16.2643i		−	0.813214i
$401$	−23.9069	−	23.9069i	−1.19385	−	1.19385i	−0.975977	−	0.217875i	$-0.930088\pi$
$401$	−23.9069	−	23.9069i	−1.19385	−	1.19385i	−0.217875	−	0.975977i	$-0.569912\pi$
$402$	−6.11381			−0.304929
$403$	−19.0953	+	6.19447i	−0.951202	+	0.308568i
$404$	32.9743			1.64053
$405$	24.4927	+	24.4927i	1.21705	+	1.21705i
$406$			0.160943i			0.00798746i
$407$		−	3.56643i		−	0.176781i
$408$	−9.87994	−	9.87994i	−0.489130	−	0.489130i
$409$	18.1966	−	18.1966i	0.899766	−	0.899766i	−0.0956493	−	0.995415i	$-0.530493\pi$
$409$	18.1966	−	18.1966i	0.899766	−	0.899766i	0.995415	+	0.0956493i	$0.0304927\pi$
$410$	0.339142	−	0.339142i	0.0167490	−	0.0167490i
$411$	11.1314	−	11.1314i	0.549070	−	0.549070i
$412$	−28.9702			−1.42726
$413$			32.8786i			1.61785i
$414$	1.97182	+	1.97182i	0.0969097	+	0.0969097i
$415$	−34.4961			−1.69334
$416$	−8.01116	−	10.6854i	−0.392779	−	0.523896i
$417$	15.2207			0.745363
$418$	0.911554	−	0.911554i	0.0445856	−	0.0445856i
$419$	11.2739			0.550764			0.275382	−	0.961335i	$-0.411196\pi$
$419$	11.2739			0.550764			0.275382	+	0.961335i	$0.411196\pi$
$420$	−53.2122			−2.59649
$421$	26.1632	+	26.1632i	1.27512	+	1.27512i	0.943368	+	0.331748i	$0.107638\pi$
$421$	26.1632	+	26.1632i	1.27512	+	1.27512i	0.331748	+	0.943368i	$0.392362\pi$
$422$	−5.25261	−	5.25261i	−0.255693	−	0.255693i
$423$	1.66597	−	1.66597i	0.0810020	−	0.0810020i
$424$	−11.4469	−	11.4469i	−0.555910	−	0.555910i
$425$			23.5258i			1.14117i
$426$	4.68098			0.226794
$427$	30.4295	+	30.4295i	1.47259	+	1.47259i
$428$		−	14.3274i		−	0.692539i
$429$	4.52573	−	3.39306i	0.218504	−	0.163819i
$430$		−	5.06868i		−	0.244434i
$431$	25.2731	+	25.2731i	1.21736	+	1.21736i	0.968552	+	0.248813i	$0.0800404\pi$
$431$	25.2731	+	25.2731i	1.21736	+	1.21736i	0.248813	+	0.968552i	$0.419960\pi$
$432$			7.70329i			0.370625i
$433$	−7.24838			−0.348335			−0.174167	−	0.984716i	$-0.555723\pi$
$433$	−7.24838			−0.348335			−0.174167	+	0.984716i	$0.555723\pi$
$434$	6.69938	−	3.28389i	0.321580	−	0.157632i
$435$	0.594328	+	0.594328i	0.0284959	+	0.0284959i
$436$	−18.9721	+	18.9721i	−0.908598	+	0.908598i
$437$	16.5600	+	16.5600i	0.792172	+	0.792172i
$438$	6.03530			0.288378
$439$			33.1344i			1.58142i	0.612192	+	0.790709i	$0.290288\pi$
$439$			33.1344i			1.58142i	−0.612192	+	0.790709i	$0.709712\pi$
$440$	−2.02355	−	2.02355i	−0.0964689	−	0.0964689i
$441$			18.1007i			0.861938i
$442$	3.48634	+	4.65015i	0.165828	+	0.221185i
$443$	−16.8858			−0.802270			−0.401135	−	0.916019i	$-0.631384\pi$
$443$	−16.8858			−0.802270			−0.401135	+	0.916019i	$0.631384\pi$
$444$	15.0851	+	15.0851i	0.715907	+	0.715907i
$445$		−	56.6187i		−	2.68398i
$446$	−4.77239			−0.225979
$447$	7.54961	−	7.54961i	0.357084	−	0.357084i
$448$	−15.5432	−	15.5432i	−0.734348	−	0.734348i
$449$	−12.5092	−	12.5092i	−0.590345	−	0.590345i	0.347380	−	0.937725i	$-0.387072\pi$
$449$	−12.5092	−	12.5092i	−0.590345	−	0.590345i	−0.937725	+	0.347380i	$0.887072\pi$
$450$	2.25052	−	2.25052i	0.106090	−	0.106090i
$451$			0.322948i			0.0152070i
$452$		−	10.2499i		−	0.482115i
$453$	−8.02244	+	8.02244i	−0.376927	+	0.376927i
$454$		−	6.14841i		−	0.288559i
$455$	45.1078	+	6.45199i	2.11469	+	0.302474i
$456$			15.8750i			0.743415i
$457$	−16.0351	+	16.0351i	−0.750089	+	0.750089i	−0.974496	−	0.224407i	$-0.927956\pi$
$457$	−16.0351	+	16.0351i	−0.750089	+	0.750089i	0.224407	+	0.974496i	$0.427956\pi$
$458$			2.95464i			0.138061i
$459$		−	11.1426i		−	0.520092i
$460$	17.8568	−	17.8568i	0.832579	−	0.832579i
$461$	−0.859177	+	0.859177i	−0.0400158	+	0.0400158i	−0.726832	−	0.686816i	$-0.759008\pi$
$461$	−0.859177	+	0.859177i	−0.0400158	+	0.0400158i	0.686816	+	0.726832i	$0.259008\pi$
$462$	−1.48651	+	1.48651i	−0.0691586	+	0.0691586i
$463$	−3.93160	−	3.93160i	−0.182717	−	0.182717i	0.609822	−	0.792539i	$-0.291241\pi$
$463$	−3.93160	−	3.93160i	−0.182717	−	0.182717i	−0.792539	+	0.609822i	$0.791241\pi$
$464$			0.402018i			0.0186632i
$465$	12.6127	−	36.8661i	0.584900	−	1.70962i
$466$	3.54083	−	3.54083i	0.164026	−	0.164026i
$467$			9.26269i			0.428626i	0.976765	+	0.214313i	$0.0687513\pi$
$467$			9.26269i			0.428626i	−0.976765	+	0.214313i	$0.931249\pi$
$468$	−1.89750	+	13.2660i	−0.0877119	+	0.613219i
$469$	33.1631			1.53133
$470$	0.885194	+	0.885194i	0.0408309	+	0.0408309i
$471$			4.90925i			0.226206i
$472$		−	10.5769i		−	0.486843i
$473$	2.41333	+	2.41333i	0.110965	+	0.110965i
$474$	3.71708	+	3.71708i	0.170731	+	0.170731i
$475$	18.9006	−	18.9006i	0.867218	−	0.867218i
$476$	26.0322	+	26.0322i	1.19318	+	1.19318i
$477$			24.5975i			1.12624i
$478$	9.91049			0.453295
$479$	6.14465	−	6.14465i	0.280756	−	0.280756i	−0.552654	−	0.833411i	$-0.686385\pi$
$479$	6.14465	−	6.14465i	0.280756	−	0.280756i	0.833411	+	0.552654i	$0.186385\pi$
$480$	25.9212			1.18314
$481$	−10.9585	−	14.6166i	−0.499665	−	0.666462i
$482$			1.47392i			0.0671350i
$483$	−27.0051	−	27.0051i	−1.22877	−	1.22877i
$484$	−19.8447			−0.902033
$485$		−	0.0478414i		−	0.00217237i
$486$	−4.16276	+	4.16276i	−0.188827	+	0.188827i
$487$	−17.5116	+	17.5116i	−0.793528	+	0.793528i	−0.982066	−	0.188538i	$-0.939625\pi$
$487$	−17.5116	+	17.5116i	−0.793528	+	0.793528i	0.188538	+	0.982066i	$0.439625\pi$
$488$	−9.78909	−	9.78909i	−0.443131	−	0.443131i
$489$	22.0516	+	22.0516i	0.997206	+	0.997206i
$490$	−9.61762			−0.434480
$491$	−16.3080			−0.735971			−0.367985	−	0.929832i	$-0.619952\pi$
$491$	−16.3080			−0.735971			−0.367985	+	0.929832i	$0.619952\pi$
$492$	−1.36599	−	1.36599i	−0.0615834	−	0.0615834i
$493$		−	0.581508i		−	0.0261898i
$494$	0.934995	−	6.53682i	0.0420674	−	0.294106i
$495$			4.34828i			0.195441i
$496$	16.7343	−	8.20279i	0.751393	−	0.368316i
$497$	−25.3911			−1.13894
$498$		−	8.15210i		−	0.365304i
$499$	−28.8200	+	28.8200i	−1.29016	+	1.29016i	−0.355475	+	0.934686i	$0.615681\pi$
$499$	−28.8200	+	28.8200i	−1.29016	+	1.29016i	−0.934686	+	0.355475i	$0.884319\pi$
$500$	0.591320	+	0.591320i	0.0264447	+	0.0264447i
$501$	−4.72252	+	4.72252i	−0.210987	+	0.210987i
$502$	−0.0385727	−	0.0385727i	−0.00172158	−	0.00172158i
$503$	−11.8228			−0.527154			−0.263577	−	0.964638i	$-0.584902\pi$
$503$	−11.8228			−0.527154			−0.263577	+	0.964638i	$0.584902\pi$
$504$		−	10.2533i		−	0.456719i
$505$	38.7534	−	38.7534i	1.72450	−	1.72450i
$506$		−	0.997678i		−	0.0443522i
$507$	8.12242	−	27.8122i	0.360730	−	1.23518i
$508$			15.4858i			0.687073i
$509$	−17.1253	+	17.1253i	−0.759064	+	0.759064i	−0.976152	−	0.217088i	$-0.930344\pi$
$509$	−17.1253	+	17.1253i	−0.759064	+	0.759064i	0.217088	+	0.976152i	$0.430344\pi$
$510$	−11.2806			−0.499511
$511$	−32.7373			−1.44821
$512$	14.8961	+	14.8961i	0.658322	+	0.658322i
$513$	−8.95192	+	8.95192i	−0.395237	+	0.395237i
$514$	−1.19355	+	1.19355i	−0.0526452	+	0.0526452i
$515$	−34.0475	+	34.0475i	−1.50031	+	1.50031i
$516$	−20.4155			−0.898742
$517$	−0.842925			−0.0370718
$518$	4.80094	+	4.80094i	0.210941	+	0.210941i
$519$	−40.1733			−1.76341
$520$	−14.5110	−	2.07559i	−0.636351	−	0.0910205i
$521$	−26.7996			−1.17411			−0.587055	−	0.809547i	$-0.699713\pi$
$521$	−26.7996			−1.17411			−0.587055	+	0.809547i	$0.699713\pi$
$522$	−0.0556279	+	0.0556279i	−0.00243477	+	0.00243477i
$523$		−	9.31036i		−	0.407114i	−0.979063	−	0.203557i	$-0.934750\pi$
$523$		−	9.31036i		−	0.407114i	0.979063	−	0.203557i	$-0.0652501\pi$
$524$		−	22.7666i		−	0.994562i
$525$	−30.8219	+	30.8219i	−1.34518	+	1.34518i
$526$	−2.01100	+	2.01100i	−0.0876838	+	0.0876838i
$527$	−24.2057	+	11.8651i	−1.05442	+	0.516853i
$528$	−3.71314	+	3.71314i	−0.161594	+	0.161594i
$529$	−4.87540			−0.211974
$530$	−13.0696			−0.567709
$531$	−11.3641	+	11.3641i	−0.493159	+	0.493159i
$532$		−	41.8283i		−	1.81349i
$533$	0.992315	+	1.32357i	0.0429819	+	0.0573301i
$534$	13.3801			0.579014
$535$	−16.8384	−	16.8384i	−0.727986	−	0.727986i
$536$	−10.6685			−0.460808
$537$			15.5006i			0.668902i
$538$	−5.37374	+	5.37374i	−0.231678	+	0.231678i
$539$	4.57919	−	4.57919i	0.197240	−	0.197240i
$540$	9.65296	+	9.65296i	0.415397	+	0.415397i
$541$	−21.8712	+	21.8712i	−0.940316	+	0.940316i	−0.998317	−	0.0580003i	$-0.981528\pi$
$541$	−21.8712	+	21.8712i	−0.940316	+	0.940316i	0.0580003	+	0.998317i	$0.481528\pi$
$542$			6.50186i			0.279279i
$543$		−	56.8430i		−	2.43937i
$544$	−12.6810	−	12.6810i	−0.543695	−	0.543695i
$545$			44.5942i			1.91021i
$546$	−1.52473	+	10.6599i	−0.0652526	+	0.456200i
$547$	4.41599			0.188814			0.0944071	−	0.995534i	$-0.469904\pi$
$547$	4.41599			0.188814			0.0944071	+	0.995534i	$0.469904\pi$
$548$	9.43521	−	9.43521i	0.403052	−	0.403052i
$549$			21.0352i			0.897760i
$550$	−1.13869			−0.0485539
$551$	−0.467181	+	0.467181i	−0.0199026	+	0.0199026i
$552$	8.68744	+	8.68744i	0.369762	+	0.369762i
$553$	−20.1626	−	20.1626i	−0.857400	−	0.857400i
$554$	0.724757	+	0.724757i	0.0307920	+	0.0307920i
$555$	35.4578			1.50510
$556$	12.9015			0.547143
$557$	−3.61478	−	3.61478i	−0.153163	−	0.153163i	0.626366	−	0.779529i	$-0.284542\pi$
$557$	−3.61478	−	3.61478i	−0.153163	−	0.153163i	−0.779529	+	0.626366i	$0.784542\pi$
$558$	3.45059	+	1.18052i	0.146075	+	0.0499755i
$559$	17.3061	+	2.47539i	0.731972	+	0.104698i
$560$	−42.3023			−1.78760
$561$	5.37095	−	5.37095i	0.226762	−	0.226762i
$562$	1.85046			0.0780567
$563$			21.1172i			0.889986i	0.895534	+	0.444993i	$0.146794\pi$
$563$			21.1172i			0.889986i	−0.895534	+	0.444993i	$0.853206\pi$
$564$	3.56536	−	3.56536i	0.150129	−	0.150129i
$565$	−12.0463	−	12.0463i	−0.506792	−	0.506792i
$566$	−5.16347	+	5.16347i	−0.217037	+	0.217037i
$567$	31.3965	−	31.3965i	1.31853	−	1.31853i
$568$	8.16822			0.342731
$569$	−14.8534			−0.622686			−0.311343	−	0.950298i	$-0.600779\pi$
$569$	−14.8534			−0.622686			−0.311343	+	0.950298i	$0.600779\pi$
$570$	9.06275	+	9.06275i	0.379597	+	0.379597i
$571$	27.1742			1.13721			0.568603	−	0.822612i	$-0.307484\pi$
$571$	27.1742			1.13721			0.568603	+	0.822612i	$0.307484\pi$
$572$	3.83611	−	2.87604i	0.160396	−	0.120253i
$573$		−	31.6106i		−	1.32055i
$574$	−0.434735	−	0.434735i	−0.0181455	−	0.0181455i
$575$		−	20.6863i		−	0.862679i
$576$		−	10.7446i		−	0.447694i
$577$	20.3070	+	20.3070i	0.845393	+	0.845393i	0.989554	−	0.144162i	$-0.0460485\pi$
$577$	20.3070	+	20.3070i	0.845393	+	0.845393i	−0.144162	+	0.989554i	$0.546049\pi$
$578$	1.51653	+	1.51653i	0.0630794	+	0.0630794i
$579$	−6.17789	−	6.17789i	−0.256744	−	0.256744i
$580$	0.503767	+	0.503767i	0.0209178	+	0.0209178i
$581$			44.2194i			1.83453i
$582$	0.0113059			0.000468643
$583$	6.22278	−	6.22278i	0.257721	−	0.257721i
$584$	10.5315			0.435796
$585$	13.3609	+	17.8210i	0.552405	+	0.736807i
$586$	−0.472731			−0.0195283
$587$	18.9225	−	18.9225i	0.781015	−	0.781015i	−0.198987	−	0.980002i	$-0.563765\pi$
$587$	18.9225	−	18.9225i	0.781015	−	0.781015i	0.980002	+	0.198987i	$0.0637652\pi$
$588$			38.7376i			1.59751i
$589$	28.9792	+	9.91441i	1.19407	+	0.408516i
$590$	−6.03819	−	6.03819i	−0.248588	−	0.248588i
$591$	−18.9536	−	18.9536i	−0.779646	−	0.779646i
$592$	11.9922	+	11.9922i	0.492878	+	0.492878i
$593$	9.74951	−	9.74951i	0.400364	−	0.400364i	−0.477997	−	0.878361i	$-0.658637\pi$
$593$	9.74951	−	9.74951i	0.400364	−	0.400364i	0.878361	+	0.477997i	$0.158637\pi$
$594$	0.539320			0.0221286
$595$	61.1891			2.50851
$596$	6.39923	−	6.39923i	0.262123	−	0.262123i
$597$		−	3.28115i		−	0.134289i
$598$	−3.06555	−	4.08888i	−0.125360	−	0.167207i
$599$	−5.78183			−0.236239			−0.118120	−	0.992999i	$-0.537687\pi$
$599$	−5.78183			−0.236239			−0.118120	+	0.992999i	$0.537687\pi$
$600$	9.91532	−	9.91532i	0.404791	−	0.404791i
$601$			44.4704i			1.81399i	0.421144	+	0.906994i	$0.361629\pi$
$601$			44.4704i			1.81399i	−0.421144	+	0.906994i	$0.638371\pi$
$602$	−6.49739			−0.264814
$603$	11.4624	+	11.4624i	0.466786	+	0.466786i
$604$	−6.80001	+	6.80001i	−0.276688	+	0.276688i
$605$	−23.3227	+	23.3227i	−0.948203	+	0.948203i
$606$	9.15819	+	9.15819i	0.372026	+	0.372026i
$607$	1.91605			0.0777699			0.0388849	−	0.999244i	$-0.487619\pi$
$607$	1.91605			0.0777699			0.0388849	+	0.999244i	$0.487619\pi$
$608$			20.3758i			0.826347i
$609$	0.761851	−	0.761851i	0.0308718	−	0.0308718i
$610$	−11.1768			−0.452536
$611$	−3.45464	+	2.59004i	−0.139760	+	0.104782i
$612$			17.9954i			0.727421i
$613$	29.4023	−	29.4023i	1.18755	−	1.18755i	0.209805	−	0.977743i	$-0.432717\pi$
$613$	29.4023	−	29.4023i	1.18755	−	1.18755i	0.977743	−	0.209805i	$-0.0672828\pi$
$614$	5.83437			0.235456
$615$	−3.21078			−0.129471
$616$	−2.59393	+	2.59393i	−0.104512	+	0.104512i
$617$	−31.3827	−	31.3827i	−1.26342	−	1.26342i	−0.949424	−	0.313996i	$-0.898332\pi$
$617$	−31.3827	−	31.3827i	−1.26342	−	1.26342i	−0.313996	−	0.949424i	$-0.601668\pi$
$618$	−8.04610	−	8.04610i	−0.323662	−	0.323662i
$619$	−30.1654	−	30.1654i	−1.21245	−	1.21245i	−0.970219	−	0.242230i	$-0.922121\pi$
$619$	−30.1654	−	30.1654i	−1.21245	−	1.21245i	−0.242230	−	0.970219i	$-0.577879\pi$
$620$	10.6908	−	31.2486i	0.429354	−	1.25497i
$621$			9.79770i			0.393168i
$622$	−3.31596	+	3.31596i	−0.132958	+	0.132958i
$623$	−72.5778			−2.90777
$624$	−3.80862	+	26.6272i	−0.152467	+	1.06594i
$625$	25.6850			1.02740
$626$	1.96369	−	1.96369i	0.0784850	−	0.0784850i
$627$	−8.63001			−0.344649
$628$			4.16119i			0.166050i
$629$	−17.3465	−	17.3465i	−0.691648	−	0.691648i
$630$	−5.85343	−	5.85343i	−0.233206	−	0.233206i
$631$	−10.3920	−	10.3920i	−0.413700	−	0.413700i	0.469325	−	0.883025i	$-0.344497\pi$
$631$	−10.3920	−	10.3920i	−0.413700	−	0.413700i	−0.883025	+	0.469325i	$0.844497\pi$
$632$	6.48623	+	6.48623i	0.258009	+	0.258009i
$633$			49.7283i			1.97652i
$634$		−	0.213839i		−	0.00849264i
$635$	18.1999	+	18.1999i	0.722240	+	0.722240i
$636$			52.6415i			2.08737i
$637$	4.69694	−	32.8377i	0.186100	−	1.30108i
$638$	0.0281459			0.00111431
$639$	−8.77610	−	8.77610i	−0.347177	−	0.347177i
$640$	28.9696			1.14512
$641$	7.32040			0.289138			0.144569	−	0.989495i	$-0.453820\pi$
$641$	7.32040			0.289138			0.144569	+	0.989495i	$0.453820\pi$
$642$	3.97924	−	3.97924i	0.157048	−	0.157048i
$643$	0.950195	−	0.950195i	0.0374720	−	0.0374720i	−0.688122	−	0.725595i	$-0.741565\pi$
$643$	0.950195	−	0.950195i	0.0374720	−	0.0374720i	0.725595	+	0.688122i	$0.241565\pi$
$644$	−22.8901	−	22.8901i	−0.901997	−	0.901997i
$645$	−23.9935	+	23.9935i	−0.944743	+	0.944743i
$646$		−	8.86726i		−	0.348878i
$647$	34.9070			1.37234			0.686168	−	0.727443i	$-0.259292\pi$
$647$	34.9070			1.37234			0.686168	+	0.727443i	$0.259292\pi$
$648$	−10.1001	+	10.1001i	−0.396771	+	0.396771i
$649$	5.74986			0.225702
$650$	−4.66680	+	3.49883i	−0.183047	+	0.137235i
$651$	−47.2575	−	16.1678i	−1.85217	−	0.633667i
$652$	18.6914	+	18.6914i	0.732012	+	0.732012i
$653$	11.0571			0.432698			0.216349	−	0.976316i	$-0.430585\pi$
$653$	11.0571			0.432698			0.216349	+	0.976316i	$0.430585\pi$
$654$	−10.5385			−0.412088
$655$	−26.7566	−	26.7566i	−1.04547	−	1.04547i
$656$	−1.08592	−	1.08592i	−0.0423982	−	0.0423982i
$657$	−11.3152	−	11.3152i	−0.441449	−	0.441449i
$658$	1.13470	−	1.13470i	0.0442353	−	0.0442353i
$659$	−21.5068			−0.837786			−0.418893	−	0.908036i	$-0.637582\pi$
$659$	−21.5068			−0.837786			−0.418893	+	0.908036i	$0.637582\pi$
$660$			9.30583i			0.362229i
$661$	−16.5380	+	16.5380i	−0.643255	+	0.643255i	−0.951354	−	0.308099i	$-0.900307\pi$
$661$	−16.5380	+	16.5380i	−0.643255	+	0.643255i	0.308099	+	0.951354i	$0.400307\pi$
$662$	6.24751			0.242816
$663$	5.50907	−	38.5155i	0.213955	−	1.49582i
$664$		−	14.2252i		−	0.552047i
$665$	−49.1591	−	49.1591i	−1.90631	−	1.90631i
$666$			3.31877i			0.128600i
$667$			0.511321i			0.0197984i
$668$	−4.00292	+	4.00292i	−0.154878	+	0.154878i
$669$	22.5910	+	22.5910i	0.873417	+	0.873417i
$670$	−6.09044	+	6.09044i	−0.235294	+	0.235294i
$671$	5.32156	−	5.32156i	0.205437	−	0.205437i
$672$		−	33.2276i		−	1.28178i
$673$	21.8019			0.840402			0.420201	−	0.907431i	$-0.361960\pi$
$673$	21.8019			0.840402			0.420201	+	0.907431i	$0.361960\pi$
$674$	4.09061	+	4.09061i	0.157565	+	0.157565i
$675$	11.1825			0.430415
$676$	6.88476	−	23.5743i	0.264798	−	0.906704i
$677$		−	2.65486i		−	0.102034i	−0.998698	−	0.0510172i	$-0.983754\pi$
$677$		−	2.65486i		−	0.102034i	0.998698	−	0.0510172i	$-0.0162463\pi$
$678$	2.84678	−	2.84678i	0.109330	−	0.109330i
$679$	−0.0613264			−0.00235349
$680$	−19.6843			−0.754860
$681$	−29.1046	+	29.1046i	−1.11529	+	1.11529i
$682$	−0.574291	−	1.17160i	−0.0219907	−	0.0448628i
$683$	−6.00534	+	6.00534i	−0.229788	+	0.229788i	−0.812604	−	0.582816i	$-0.801951\pi$
$683$	−6.00534	+	6.00534i	−0.229788	+	0.229788i	0.582816	+	0.812604i	$0.301951\pi$
$684$	14.4574	−	14.4574i	0.552794	−	0.552794i
$685$		−	22.1776i		−	0.847363i
$686$			2.94836i			0.112569i
$687$	13.9863	−	13.9863i	0.533612	−	0.533612i
$688$	−16.2298			−0.618755
$689$	6.38280	−	44.6240i	0.243165	−	1.70004i
$690$	9.91901			0.377610
$691$	9.42402	+	9.42402i	0.358507	+	0.358507i	0.863262	−	0.504756i	$-0.168417\pi$
$691$	9.42402	+	9.42402i	0.358507	+	0.358507i	−0.504756	+	0.863262i	$0.668417\pi$
$692$	−34.0518			−1.29446
$693$	5.57393			0.211736
$694$	−7.22988	+	7.22988i	−0.274443	+	0.274443i
$695$	15.1625	−	15.1625i	0.575148	−	0.575148i
$696$	−0.245085	+	0.245085i	−0.00928993	+	0.00928993i
$697$	1.57076	+	1.57076i	0.0594967	+	0.0594967i
$698$	−6.98003			−0.264198
$699$	−33.5223			−1.26793
$700$	−26.1254	+	26.1254i	−0.987447	+	0.987447i
$701$		−	42.7622i		−	1.61511i	−0.589795	−	0.807553i	$-0.700792\pi$
$701$		−	42.7622i		−	1.61511i	0.589795	−	0.807553i	$-0.299208\pi$
$702$	2.21035	−	1.65716i	0.0834241	−	0.0625454i
$703$			27.8721i			1.05122i
$704$	−2.71822	+	2.71822i	−0.102447	+	0.102447i
$705$		−	8.38044i		−	0.315626i
$706$	9.63866			0.362756
$707$	−49.6768	−	49.6768i	−1.86829	−	1.86829i
$708$	−24.3204	+	24.3204i	−0.914018	+	0.914018i
$709$	8.51126	+	8.51126i	0.319647	+	0.319647i	0.848632	−	0.528984i	$-0.177427\pi$
$709$	8.51126	+	8.51126i	0.319647	+	0.319647i	−0.528984	+	0.848632i	$0.677427\pi$
$710$	4.66309	−	4.66309i	0.175003	−	0.175003i
$711$		−	13.9379i		−	0.522711i
$712$	23.3480			0.875004
$713$	21.2841	−	10.4330i	0.797097	−	0.390719i
$714$			14.4602i			0.541159i
$715$	1.12833	−	7.88852i	0.0421973	−	0.295014i
$716$			13.1387i			0.491016i
$717$	−46.9130	−	46.9130i	−1.75200	−	1.75200i
$718$	7.49399			0.279673
$719$	−40.4860			−1.50987			−0.754936	−	0.655798i	$-0.772332\pi$
$719$	−40.4860			−1.50987			−0.754936	+	0.655798i	$0.772332\pi$
$720$	−14.6213	−	14.6213i	−0.544902	−	0.544902i
$721$	43.6444	+	43.6444i	1.62540	+	1.62540i
$722$	−2.65101	+	2.65101i	−0.0986604	+	0.0986604i
$723$	6.97704	−	6.97704i	0.259479	−	0.259479i
$724$		−	48.1815i		−	1.79065i
$725$	0.583590			0.0216740
$726$	−5.51162	−	5.51162i	−0.204555	−	0.204555i
$727$		−	28.1512i		−	1.04407i	−0.852924	−	0.522034i	$-0.825173\pi$
$727$		−	28.1512i		−	1.04407i	0.852924	−	0.522034i	$-0.174827\pi$
$728$	−2.66063	+	18.6012i	−0.0986095	+	0.689408i
$729$	6.31580			0.233919
$730$	6.01223	−	6.01223i	0.222523	−	0.222523i
$731$	23.4759			0.868289
$732$			45.0177i			1.66390i
$733$	8.79255	+	8.79255i	0.324760	+	0.324760i	0.850590	−	0.525830i	$-0.176245\pi$
$733$	8.79255	+	8.79255i	0.324760	+	0.324760i	−0.525830	+	0.850590i	$0.676245\pi$
$734$	3.58224	−	3.58224i	0.132223	−	0.132223i
$735$	45.5267	+	45.5267i	1.67928	+	1.67928i
$736$	11.1505	+	11.1505i	0.411011	+	0.411011i
$737$		−	5.79962i		−	0.213632i
$738$		−	0.300522i		−	0.0110624i
$739$	−6.16455	−	6.16455i	−0.226767	−	0.226767i	0.584574	−	0.811341i	$-0.301262\pi$
$739$	−6.16455	−	6.16455i	−0.226767	−	0.226767i	−0.811341	+	0.584574i	$0.801262\pi$
$740$	30.0548			1.10484
$741$	−35.3692	+	26.5172i	−1.29932	+	0.974135i
$742$			16.7536i			0.615043i
$743$	−18.1238	+	18.1238i	−0.664898	+	0.664898i	−0.956530	−	0.291633i	$-0.905802\pi$
$743$	−18.1238	+	18.1238i	−0.664898	+	0.664898i	0.291633	+	0.956530i	$0.405802\pi$
$744$	15.2026	+	5.20114i	0.557354	+	0.190683i
$745$		−	15.0415i		−	0.551078i
$746$	−4.15971	−	4.15971i	−0.152298	−	0.152298i
$747$	−15.2839	+	15.2839i	−0.559208	+	0.559208i
$748$	4.55255	−	4.55255i	0.166458	−	0.166458i
$749$	−21.5846	+	21.5846i	−0.788683	+	0.788683i
$750$			0.328463i			0.0119938i
$751$			25.8498i			0.943272i	0.881793	+	0.471636i	$0.156336\pi$
$751$			25.8498i			0.943272i	−0.881793	+	0.471636i	$0.843664\pi$
$752$	2.83437	−	2.83437i	0.103359	−	0.103359i
$753$			0.365181i			0.0133079i
$754$	0.115353	−	0.0864834i	0.00420091	−	0.00314954i
$755$			15.9835i			0.581700i
$756$	12.3738	−	12.3738i	0.450032	−	0.450032i
$757$		−	1.88226i		−	0.0684117i	−0.999415	−	0.0342059i	$-0.989110\pi$
$757$		−	1.88226i		−	0.0684117i	0.999415	−	0.0342059i	$-0.0108902\pi$
$758$		−	4.13894i		−	0.150333i
$759$	−4.72269	+	4.72269i	−0.171423	+	0.171423i
$760$	15.8143	+	15.8143i	0.573646	+	0.573646i
$761$	−3.26309	−	3.26309i	−0.118287	−	0.118287i	0.645486	−	0.763773i	$-0.276655\pi$
$761$	−3.26309	−	3.26309i	−0.118287	−	0.118287i	−0.763773	+	0.645486i	$0.776655\pi$
$762$	−4.30099	+	4.30099i	−0.155808	+	0.155808i
$763$	57.1640			2.06947
$764$		−	26.7939i		−	0.969370i
$765$	21.1492	+	21.1492i	0.764653	+	0.764653i
$766$	2.90240			0.104868
$767$	23.5652	−	17.6675i	0.850890	−	0.637936i
$768$		−	17.4978i		−	0.631399i
$769$	8.28934	+	8.28934i	0.298921	+	0.298921i	0.840591	−	0.541670i	$-0.182208\pi$
$769$	8.28934	+	8.28934i	0.298921	+	0.298921i	−0.541670	+	0.840591i	$0.682208\pi$
$770$			2.96165i			0.106730i
$771$	11.2998			0.406951
$772$	−5.23653	−	5.23653i	−0.188467	−	0.188467i
$773$	−16.7598	+	16.7598i	−0.602807	+	0.602807i	−0.941057	−	0.338249i	$-0.890165\pi$
$773$	−16.7598	+	16.7598i	−0.602807	+	0.602807i	0.338249	+	0.941057i	$0.390165\pi$
$774$	−2.24574	−	2.24574i	−0.0807215	−	0.0807215i
$775$	−11.9076	−	24.2924i	−0.427734	−	0.872610i
$776$	0.0197285			0.000708212
$777$		−	45.4522i		−	1.63059i
$778$	−1.69594	−	1.69594i	−0.0608025	−	0.0608025i
$779$		−	2.52388i		−	0.0904274i
$780$	28.5938	+	38.1390i	1.02382	+	1.36559i
$781$			4.44043i			0.158891i
$782$	−4.85252	−	4.85252i	−0.173526	−	0.173526i
$783$	−0.276407			−0.00987799
$784$			30.7953i			1.09983i
$785$	4.89048	+	4.89048i	0.174549	+	0.174549i
$786$	6.32312	−	6.32312i	0.225538	−	0.225538i
$787$	−5.31948	−	5.31948i	−0.189619	−	0.189619i	0.605912	−	0.795531i	$-0.292808\pi$
$787$	−5.31948	−	5.31948i	−0.189619	−	0.189619i	−0.795531	+	0.605912i	$0.792808\pi$
$788$	−16.0655	−	16.0655i	−0.572310	−	0.572310i
$789$	19.0389			0.677801
$790$	7.40575			0.263485
$791$	−15.4418	+	15.4418i	−0.549047	+	0.549047i
$792$	−1.79312			−0.0637156
$793$	5.45841	−	38.1613i	0.193834	−	1.35515i
$794$	8.18017			0.290303
$795$	61.8674	+	61.8674i	2.19421	+	2.19421i
$796$		−	2.78118i		−	0.0985764i
$797$	23.4630			0.831100			0.415550	−	0.909570i	$-0.363589\pi$
$797$	23.4630			0.831100			0.415550	+	0.909570i	$0.363589\pi$
$798$	11.6173	−	11.6173i	0.411247	−	0.411247i
$799$	−4.09983	+	4.09983i	−0.145042	+	0.145042i
$800$	12.7264	−	12.7264i	0.449948	−	0.449948i
$801$	−25.0856	−	25.0856i	−0.886356	−	0.886356i
$802$		−	11.2561i		−	0.397468i
$803$			5.72515i			0.202036i
$804$	24.5309	+	24.5309i	0.865138	+	0.865138i
$805$	−53.8036			−1.89633
$806$	−5.95361	−	3.03706i	−0.209707	−	0.106976i
$807$	50.8751			1.79089
$808$	15.9809	+	15.9809i	0.562205	+	0.562205i
$809$			19.8820i			0.699012i	0.936934	+	0.349506i	$0.113651\pi$
$809$			19.8820i			0.699012i	−0.936934	+	0.349506i	$0.886349\pi$
$810$			11.5320i			0.405193i
$811$	16.3148	+	16.3148i	0.572890	+	0.572890i	0.932935	−	0.360045i	$-0.117239\pi$
$811$	16.3148	+	16.3148i	0.572890	+	0.572890i	−0.360045	+	0.932935i	$0.617239\pi$
$812$	0.645763	−	0.645763i	0.0226618	−	0.0226618i
$813$	30.7777	−	30.7777i	1.07942	−	1.07942i
$814$	0.839596	−	0.839596i	0.0294278	−	0.0294278i
$815$	43.9345			1.53896
$816$			36.1200i			1.26445i
$817$	−18.8605	−	18.8605i	−0.659845	−	0.659845i
$818$	8.56757			0.299558
$819$	22.8442	−	17.1269i	0.798240	−	0.598463i
$820$	−2.72153			−0.0950399
$821$	−6.71978	+	6.71978i	−0.234522	+	0.234522i	−0.814577	−	0.580055i	$-0.803031\pi$
$821$	−6.71978	+	6.71978i	−0.234522	+	0.234522i	0.580055	+	0.814577i	$0.303031\pi$
$822$	5.24101			0.182801
$823$	34.6057			1.20628			0.603139	−	0.797636i	$-0.293917\pi$
$823$	34.6057			1.20628			0.603139	+	0.797636i	$0.293917\pi$
$824$	−14.0403	−	14.0403i	−0.489116	−	0.489116i
$825$	5.39019	+	5.39019i	0.187662	+	0.187662i
$826$	−7.74016	+	7.74016i	−0.269315	+	0.269315i
$827$	26.3076	+	26.3076i	0.914805	+	0.914805i	0.996645	−	0.0818405i	$-0.0260798\pi$
$827$	26.3076	+	26.3076i	0.914805	+	0.914805i	−0.0818405	+	0.996645i	$0.526080\pi$
$828$		−	15.8234i		−	0.549900i
$829$	−50.1456			−1.74163			−0.870814	−	0.491612i	$-0.836408\pi$
$829$	−50.1456			−1.74163			−0.870814	+	0.491612i	$0.836408\pi$
$830$	−8.12094	−	8.12094i	−0.281882	−	0.281882i
$831$		−	6.86153i		−	0.238024i
$832$	−2.78812	+	19.4926i	−0.0966608	+	0.675784i
$833$		−	44.5446i		−	1.54338i
$834$	3.58321	+	3.58321i	0.124076	+	0.124076i
$835$			9.40894i			0.325610i
$836$	−7.31500			−0.252994
$837$	5.63983	+	11.5057i	0.194941	+	0.397694i
$838$	2.65405	+	2.65405i	0.0916826	+	0.0916826i
$839$	22.2085	−	22.2085i	0.766724	−	0.766724i	−0.210804	−	0.977528i	$-0.567608\pi$
$839$	22.2085	−	22.2085i	0.766724	−	0.766724i	0.977528	+	0.210804i	$0.0676083\pi$
$840$	−25.7890	−	25.7890i	−0.889806	−	0.889806i
$841$	28.9856			0.999503
$842$			12.3185i			0.424523i
$843$	−8.75946	−	8.75946i	−0.301692	−	0.301692i
$844$			42.1509i			1.45089i
$845$	−19.6145	−	35.7973i	−0.674760	−	1.23146i
$846$	0.784391			0.0269679
$847$	29.8967	+	29.8967i	1.02726	+	1.02726i
$848$			41.8486i			1.43709i
$849$	48.8844			1.67771
$850$	−5.53837	+	5.53837i	−0.189965	+	0.189965i
$851$	15.2528	+	15.2528i	0.522858	+	0.522858i
$852$	−18.7819	−	18.7819i	−0.643456	−	0.643456i
$853$	−0.922634	+	0.922634i	−0.0315904	+	0.0315904i	−0.722726	−	0.691135i	$-0.757111\pi$
$853$	−0.922634	+	0.922634i	−0.0315904	+	0.0315904i	0.691135	+	0.722726i	$0.257111\pi$
$854$			14.3272i			0.490268i
$855$		−	33.9824i		−	1.16218i
$856$	6.94369	−	6.94369i	0.237330	−	0.237330i
$857$			23.0546i			0.787531i	0.919211	+	0.393765i	$0.128828\pi$
$857$			23.0546i			0.787531i	−0.919211	+	0.393765i	$0.871172\pi$
$858$	1.86421	+	0.266648i	0.0636432	+	0.00910321i
$859$			36.1492i			1.23339i	0.787201	+	0.616697i	$0.211530\pi$
$859$			36.1492i			1.23339i	−0.787201	+	0.616697i	$0.788470\pi$
$860$	−20.3375	+	20.3375i	−0.693502	+	0.693502i
$861$			4.11579i			0.140266i
$862$			11.8994i			0.405296i
$863$	−21.8790	+	21.8790i	−0.744769	+	0.744769i	−0.973492	−	0.228722i	$-0.926545\pi$
$863$	−21.8790	+	21.8790i	−0.744769	+	0.744769i	0.228722	+	0.973492i	$0.426545\pi$
$864$	−6.02766	+	6.02766i	−0.205065	+	0.205065i
$865$	−40.0197	+	40.0197i	−1.36071	+	1.36071i
$866$	−1.70639	−	1.70639i	−0.0579854	−	0.0579854i
$867$		−	14.3575i		−	0.487607i
$868$	−40.0566	−	13.7042i	−1.35961	−	0.465152i
$869$	−3.52606	+	3.52606i	−0.119613	+	0.119613i
$870$			0.279829i			0.00948710i
$871$	−17.8204	−	23.7691i	−0.603820	−	0.805386i
$872$	−18.3895			−0.622746
$873$	−0.0211967	−	0.0211967i	−0.000717400	−	0.000717400i
$874$			7.79699i			0.263737i
$875$		−	1.78168i		−	0.0602318i
$876$	−24.2159	−	24.2159i	−0.818180	−	0.818180i
$877$	−31.4057	−	31.4057i	−1.06049	−	1.06049i	−0.998048	−	0.0624466i	$-0.980110\pi$
$877$	−31.4057	−	31.4057i	−1.06049	−	1.06049i	−0.0624466	−	0.998048i	$-0.519890\pi$
$878$	−7.80038	+	7.80038i	−0.263250	+	0.263250i
$879$	2.23776	+	2.23776i	0.0754776	+	0.0754776i
$880$			7.39789i			0.249383i
$881$	53.0476			1.78722			0.893610	−	0.448844i	$-0.148164\pi$
$881$	53.0476			1.78722			0.893610	+	0.448844i	$0.148164\pi$
$882$	−4.26120	+	4.26120i	−0.143482	+	0.143482i
$883$	17.6386			0.593587			0.296794	−	0.954942i	$-0.404083\pi$
$883$	17.6386			0.593587			0.296794	+	0.954942i	$0.404083\pi$
$884$	4.66962	−	32.6467i	0.157056	−	1.09803i
$885$			57.1656i			1.92160i
$886$	−3.97520	−	3.97520i	−0.133550	−	0.133550i
$887$	56.3589			1.89235			0.946174	−	0.323660i	$-0.104913\pi$
$887$	56.3589			1.89235			0.946174	+	0.323660i	$0.104913\pi$
$888$			14.6218i			0.490677i
$889$	23.3298	−	23.3298i	0.782458	−	0.782458i
$890$	13.3290	−	13.3290i	0.446788	−	0.446788i
$891$	−5.49067	−	5.49067i	−0.183944	−	0.183944i
$892$	19.1486	+	19.1486i	0.641143	+	0.641143i
$893$	6.58758			0.220445
$894$	3.55461			0.118884
$895$	15.4414	+	15.4414i	0.516148	+	0.516148i
$896$		−	37.1353i		−	1.24060i
$897$	−4.84413	+	33.8667i	−0.161741	+	1.13078i
$898$		−	5.88973i		−	0.196543i
$899$	0.294330	+	0.600456i	0.00981646	+	0.0200263i
$900$	−18.0598			−0.601994
$901$		−	60.5329i		−	2.01664i
$902$	−0.0760272	+	0.0760272i	−0.00253143	+	0.00253143i
$903$	30.7565	+	30.7565i	1.02351	+	1.02351i
$904$	4.96757	−	4.96757i	0.165219	−	0.165219i
$905$	−56.6257	−	56.6257i	−1.88230	−	1.88230i
$906$	−3.77723			−0.125490
$907$		−	37.3283i		−	1.23947i	−0.784813	−	0.619733i	$-0.787241\pi$
$907$		−	37.3283i		−	1.23947i	0.784813	−	0.619733i	$-0.212759\pi$
$908$	−24.6697	+	24.6697i	−0.818694	+	0.818694i
$909$		−	34.3403i		−	1.13900i
$910$	9.10021	+	12.1380i	0.301669	+	0.402371i
$911$			17.5661i			0.581991i	0.956724	+	0.290995i	$0.0939865\pi$
$911$			17.5661i			0.581991i	−0.956724	+	0.290995i	$0.906014\pi$
$912$	29.0187	−	29.0187i	0.960905	−	0.960905i
$913$	7.73316			0.255930
$914$	−7.54984			−0.249726
$915$	52.9075	+	52.9075i	1.74907	+	1.74907i
$916$	11.8551	−	11.8551i	0.391705	−	0.391705i
$917$	−34.2985	+	34.2985i	−1.13264	+	1.13264i
$918$	2.62315	−	2.62315i	0.0865769	−	0.0865769i
$919$	−36.0854			−1.19035			−0.595174	−	0.803597i	$-0.702917\pi$
$919$	−36.0854			−1.19035			−0.595174	+	0.803597i	$0.702917\pi$
$920$	17.3085			0.570643
$921$	−27.6180	−	27.6180i	−0.910045	−	0.910045i
$922$	−0.404529			−0.0133224
$923$	13.6440	+	18.1986i	0.449098	+	0.599015i
$924$	11.9289			0.392431
$925$	17.4086	−	17.4086i	0.572390	−	0.572390i
$926$		−	1.85113i		−	0.0608319i
$927$			30.1703i			0.990923i
$928$	−0.314570	+	0.314570i	−0.0103263	+	0.0103263i
$929$	15.8662	−	15.8662i	0.520554	−	0.520554i	−0.397185	−	0.917739i	$-0.630013\pi$
$929$	15.8662	−	15.8662i	0.520554	−	0.520554i	0.917739	+	0.397185i	$0.130013\pi$
$930$	11.6481	−	5.70965i	0.381957	−	0.187227i
$931$	−35.7870	+	35.7870i	−1.17287	+	1.17287i
$932$	−28.4143			−0.930741
$933$	31.3934			1.02777
$934$	−2.18059	+	2.18059i	−0.0713511	+	0.0713511i
$935$		−	10.7008i		−	0.349955i
$936$	−7.34890	+	5.50967i	−0.240206	+	0.180089i
$937$	28.9361			0.945301			0.472651	−	0.881250i	$-0.343297\pi$
$937$	28.9361			0.945301			0.472651	+	0.881250i	$0.343297\pi$
$938$	7.80714	+	7.80714i	0.254912	+	0.254912i
$939$	−18.5910			−0.606694
$940$		−	7.10346i		−	0.231689i
$941$	33.1907	−	33.1907i	1.08199	−	1.08199i	0.0856608	−	0.996324i	$-0.472700\pi$
$941$	33.1907	−	33.1907i	1.08199	−	1.08199i	0.996324	−	0.0856608i	$-0.0273001\pi$
$942$	−1.15572	+	1.15572i	−0.0376553	+	0.0376553i
$943$	−1.38117	−	1.38117i	−0.0449771	−	0.0449771i
$944$	−19.3341	+	19.3341i	−0.629271	+	0.629271i
$945$		−	29.0849i		−	0.946132i
$946$			1.13627i			0.0369434i
$947$	9.77131	+	9.77131i	0.317525	+	0.317525i	0.847816	−	0.530291i	$-0.177917\pi$
$947$	9.77131	+	9.77131i	0.317525	+	0.317525i	−0.530291	+	0.847816i	$0.677917\pi$
$948$		−	29.8287i		−	0.968790i
$949$	17.5915	+	23.4639i	0.571046	+	0.761671i
$950$	8.89901			0.288722
$951$	−1.01225	+	1.01225i	−0.0328243	+	0.0328243i
$952$			25.2327i			0.817798i
$953$	16.0465			0.519797			0.259898	−	0.965636i	$-0.416311\pi$
$953$	16.0465			0.519797			0.259898	+	0.965636i	$0.416311\pi$
$954$	−5.79066	+	5.79066i	−0.187480	+	0.187480i
$955$	−31.4898	−	31.4898i	−1.01899	−	1.01899i
$956$	−39.7646	−	39.7646i	−1.28608	−	1.28608i
$957$	−0.133234	−	0.133234i	−0.00430683	−	0.00430683i
$958$	2.89310			0.0934719
$959$	−28.4288			−0.918014
$960$	−27.0248	−	27.0248i	−0.872222	−	0.872222i
$961$	18.9889	−	24.5035i	0.612547	−	0.790435i
$962$	0.861187	−	6.02081i	0.0277658	−	0.194119i
$963$	−14.9209			−0.480819
$964$	5.91390	−	5.91390i	0.190474	−	0.190474i
$965$	−12.3085			−0.396226
$966$		−	12.7149i		−	0.409094i
$967$	34.7698	−	34.7698i	1.11812	−	1.11812i	0.126106	−	0.992017i	$-0.459752\pi$
$967$	34.7698	−	34.7698i	1.11812	−	1.11812i	0.992017	−	0.126106i	$-0.0402478\pi$
$968$	−9.61766	−	9.61766i	−0.309123	−	0.309123i
$969$	−41.9747	+	41.9747i	−1.34842	+	1.34842i
$970$	0.0112626	−	0.0112626i	0.000361622	−	0.000361622i
$971$	11.5491			0.370629			0.185315	−	0.982679i	$-0.440670\pi$
$971$	11.5491			0.370629			0.185315	+	0.982679i	$0.440670\pi$
$972$	33.4052			1.07147
$973$	−19.4364	−	19.4364i	−0.623102	−	0.623102i
$974$	−8.24506			−0.264189
$975$	38.6534	+	5.52880i	1.23790	+	0.177063i
$976$			35.7879i			1.14554i
$977$	7.35350	+	7.35350i	0.235259	+	0.235259i	0.814884	−	0.579624i	$-0.196801\pi$
$977$	7.35350	+	7.35350i	0.235259	+	0.235259i	−0.579624	+	0.814884i	$0.696801\pi$
$978$			10.3826i			0.331999i
$979$			12.6925i			0.405654i
$980$	38.5895	+	38.5895i	1.23270	+	1.23270i
$981$	19.7580	+	19.7580i	0.630825	+	0.630825i
$982$	−3.83918	−	3.83918i	−0.122513	−	0.122513i
$983$	−27.0450	−	27.0450i	−0.862602	−	0.862602i	0.129038	−	0.991640i	$-0.458811\pi$
$983$	−27.0450	−	27.0450i	−0.862602	−	0.862602i	−0.991640	+	0.129038i	$0.958811\pi$
$984$		−	1.32404i		−	0.0422088i
$985$	−37.7622			−1.20321
$986$	0.136897	−	0.136897i	0.00435967	−	0.00435967i
$987$	−10.7426			−0.341942
$988$	−29.9797	+	22.4766i	−0.953783	+	0.715077i
$989$	−20.6424			−0.656391
$990$	−1.02366	+	1.02366i	−0.0325340	+	0.0325340i
$991$		−	13.0994i		−	0.416117i	−0.978116	−	0.208058i	$-0.933286\pi$
$991$		−	13.0994i		−	0.416117i	0.978116	−	0.208058i	$-0.0667144\pi$
$992$	19.5127	+	6.67573i	0.619530	+	0.211955i
$993$	−29.5737	−	29.5737i	−0.938493	−	0.938493i
$994$	−5.97747	−	5.97747i	−0.189594	−	0.189594i
$995$	−3.26861	−	3.26861i	−0.103622	−	0.103622i
$996$	−32.7093	+	32.7093i	−1.03643	+	1.03643i
$997$	15.3281			0.485447			0.242724	−	0.970095i	$-0.421959\pi$
$997$	15.3281			0.485447			0.242724	+	0.970095i	$0.421959\pi$
$998$	−13.5694			−0.429532
$999$	−8.24526	+	8.24526i	−0.260868	+	0.260868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.i.a.216.19	✓	68
13.5	odd	4	inner	403.2.i.a.278.19	yes	68
31.30	odd	2	inner	403.2.i.a.216.20	yes	68
403.278	even	4	inner	403.2.i.a.278.20	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.i.a.216.19	✓	68	1.1	even	1	trivial
403.2.i.a.216.20	yes	68	31.30	odd	2	inner
403.2.i.a.278.19	yes	68	13.5	odd	4	inner
403.2.i.a.278.20	yes	68	403.278	even	4	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.235416 + 0.235416i) q^{2} -2.22877i q^{3} -1.88916i q^{4} +(-2.22025 - 2.22025i) q^{5} +(0.524689 - 0.524689i) q^{6} +(-2.84607 + 2.84607i) q^{7} +(0.915572 - 0.915572i) q^{8} -1.96742 q^{9} +O(q^{10})\)	\(q+(0.235416 + 0.235416i) q^{2} -2.22877i q^{3} -1.88916i q^{4} +(-2.22025 - 2.22025i) q^{5} +(0.524689 - 0.524689i) q^{6} +(-2.84607 + 2.84607i) q^{7} +(0.915572 - 0.915572i) q^{8} -1.96742 q^{9} -1.04537i q^{10} +(0.497725 + 0.497725i) q^{11} -4.21050 q^{12} +(3.56922 + 0.510524i) q^{13} -1.34002 q^{14} +(-4.94843 + 4.94843i) q^{15} -3.34724 q^{16} +4.84168 q^{17} +(-0.463162 - 0.463162i) q^{18} +(-3.88979 - 3.88979i) q^{19} +(-4.19440 + 4.19440i) q^{20} +(6.34324 + 6.34324i) q^{21} +0.234345i q^{22} -4.25730 q^{23} +(-2.04060 - 2.04060i) q^{24} +4.85902i q^{25} +(0.720068 + 0.960440i) q^{26} -2.30139i q^{27} +(5.37668 + 5.37668i) q^{28} -0.120104i q^{29} -2.32988 q^{30} +(-4.99945 + 2.45062i) q^{31} +(-2.61914 - 2.61914i) q^{32} +(1.10932 - 1.10932i) q^{33} +(1.13981 + 1.13981i) q^{34} +12.6380 q^{35} +3.71676i q^{36} +(-3.58273 - 3.58273i) q^{37} -1.83144i q^{38} +(1.13784 - 7.95498i) q^{39} -4.06560 q^{40} +(0.324424 + 0.324424i) q^{41} +2.98660i q^{42} +4.84871 q^{43} +(0.940282 - 0.940282i) q^{44} +(4.36816 + 4.36816i) q^{45} +(-1.00224 - 1.00224i) q^{46} +(-0.846778 + 0.846778i) q^{47} +7.46022i q^{48} -9.20023i q^{49} +(-1.14389 + 1.14389i) q^{50} -10.7910i q^{51} +(0.964461 - 6.74283i) q^{52} -12.5024i q^{53} +(0.541785 - 0.541785i) q^{54} -2.21015i q^{55} +5.21156i q^{56} +(-8.66945 + 8.66945i) q^{57} +(0.0282746 - 0.0282746i) q^{58} +(5.77614 - 5.77614i) q^{59} +(9.34836 + 9.34836i) q^{60} -10.6918i q^{61} +(-1.75387 - 0.600036i) q^{62} +(5.59941 - 5.59941i) q^{63} +5.46129i q^{64} +(-6.79108 - 9.05806i) q^{65} +0.522302 q^{66} +(-5.82612 - 5.82612i) q^{67} -9.14671i q^{68} +9.48854i q^{69} +(2.97519 + 2.97519i) q^{70} +(4.46072 + 4.46072i) q^{71} +(-1.80131 + 1.80131i) q^{72} +(5.75131 + 5.75131i) q^{73} -1.68687i q^{74} +10.8296 q^{75} +(-7.34843 + 7.34843i) q^{76} -2.83312 q^{77} +(2.14060 - 1.60487i) q^{78} +7.08435i q^{79} +(7.43170 + 7.43170i) q^{80} -11.0315 q^{81} +0.152749i q^{82} +(7.76851 - 7.76851i) q^{83} +(11.9834 - 11.9834i) q^{84} +(-10.7498 - 10.7498i) q^{85} +(1.14147 + 1.14147i) q^{86} -0.267685 q^{87} +0.911406 q^{88} +(12.7505 + 12.7505i) q^{89} +2.05667i q^{90} +(-11.6113 + 8.70528i) q^{91} +8.04271i q^{92} +(5.46186 + 11.1426i) q^{93} -0.398691 q^{94} +17.2726i q^{95} +(-5.83746 + 5.83746i) q^{96} +(0.0107739 + 0.0107739i) q^{97} +(2.16589 - 2.16589i) q^{98} +(-0.979233 - 0.979233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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