LMFDB - Embedded newform 280.2.l.a.29.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(29,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("280.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.l (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.16
Character	$\chi$	$=$	280.29
Dual form			280.2.l.a.29.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.269098 + 1.38838i) q^{2} +2.55593 q^{3} +(-1.85517 - 0.747219i) q^{4} +(0.790907 - 2.09152i) q^{5} +(-0.687797 + 3.54859i) q^{6} -1.00000i q^{7} +(1.53664 - 2.37460i) q^{8} +3.53279 q^{9} +O(q^{10})$	\(q+(-0.269098 + 1.38838i) q^{2} +2.55593 q^{3} +(-1.85517 - 0.747219i) q^{4} +(0.790907 - 2.09152i) q^{5} +(-0.687797 + 3.54859i) q^{6} -1.00000i q^{7} +(1.53664 - 2.37460i) q^{8} +3.53279 q^{9} +(2.69099 + 1.66090i) q^{10} +2.94061i q^{11} +(-4.74169 - 1.90984i) q^{12} +1.88215 q^{13} +(1.38838 + 0.269098i) q^{14} +(2.02150 - 5.34579i) q^{15} +(2.88333 + 2.77244i) q^{16} +1.25432i q^{17} +(-0.950667 + 4.90483i) q^{18} +2.48842i q^{19} +(-3.03009 + 3.28915i) q^{20} -2.55593i q^{21} +(-4.08267 - 0.791314i) q^{22} -2.92691i q^{23} +(3.92756 - 6.06931i) q^{24} +(-3.74893 - 3.30840i) q^{25} +(-0.506485 + 2.61314i) q^{26} +1.36176 q^{27} +(-0.747219 + 1.85517i) q^{28} +0.808725i q^{29} +(6.87798 + 4.24515i) q^{30} -10.5159 q^{31} +(-4.62509 + 3.25708i) q^{32} +7.51600i q^{33} +(-1.74147 - 0.337536i) q^{34} +(-2.09152 - 0.790907i) q^{35} +(-6.55392 - 2.63976i) q^{36} +2.08227 q^{37} +(-3.45486 - 0.669629i) q^{38} +4.81066 q^{39} +(-3.75119 - 5.09201i) q^{40} -9.10984 q^{41} +(3.54859 + 0.687797i) q^{42} +11.5541 q^{43} +(2.19728 - 5.45534i) q^{44} +(2.79410 - 7.38890i) q^{45} +(4.06365 + 0.787626i) q^{46} +10.2657i q^{47} +(7.36959 + 7.08617i) q^{48} -1.00000 q^{49} +(5.60213 - 4.31464i) q^{50} +3.20596i q^{51} +(-3.49172 - 1.40638i) q^{52} -9.17072 q^{53} +(-0.366448 + 1.89064i) q^{54} +(6.15036 + 2.32575i) q^{55} +(-2.37460 - 1.53664i) q^{56} +6.36023i q^{57} +(-1.12281 - 0.217627i) q^{58} +10.0070i q^{59} +(-7.74471 + 8.40685i) q^{60} -10.3599i q^{61} +(2.82980 - 14.6000i) q^{62} -3.53279i q^{63} +(-3.27745 - 7.29783i) q^{64} +(1.48861 - 3.93657i) q^{65} +(-10.4350 - 2.02254i) q^{66} -2.89235 q^{67} +(0.937254 - 2.32699i) q^{68} -7.48097i q^{69} +(1.66090 - 2.69099i) q^{70} +11.4191 q^{71} +(5.42863 - 8.38895i) q^{72} -16.4847i q^{73} +(-0.560336 + 2.89098i) q^{74} +(-9.58201 - 8.45604i) q^{75} +(1.85939 - 4.61644i) q^{76} +2.94061 q^{77} +(-1.29454 + 6.67900i) q^{78} -13.0056 q^{79} +(8.07906 - 3.83780i) q^{80} -7.11778 q^{81} +(2.45144 - 12.6479i) q^{82} +8.79990 q^{83} +(-1.90984 + 4.74169i) q^{84} +(2.62344 + 0.992053i) q^{85} +(-3.10919 + 16.0414i) q^{86} +2.06705i q^{87} +(6.98278 + 4.51867i) q^{88} +6.64867 q^{89} +(9.50668 + 5.86761i) q^{90} -1.88215i q^{91} +(-2.18704 + 5.42992i) q^{92} -26.8778 q^{93} +(-14.2526 - 2.76248i) q^{94} +(5.20458 + 1.96811i) q^{95} +(-11.8214 + 8.32488i) q^{96} -7.33203i q^{97} +(0.269098 - 1.38838i) q^{98} +10.3886i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−0.269098	+	1.38838i	−0.190281	+	0.981730i
$2$	−0.269098	+	1.38838i	−0.190281	+	0.981730i
$3$	2.55593			1.47567			0.737834	−	0.674982i	$-0.235849\pi$
$3$	2.55593			1.47567			0.737834	+	0.674982i	$0.235849\pi$
$4$	−1.85517	−	0.747219i	−0.927586	−	0.373609i
$5$	0.790907	−	2.09152i	0.353704	−	0.935357i
$5$	0.790907	−	2.09152i	0.353704	−	0.935357i
$6$	−0.687797	+	3.54859i	−0.280792	+	1.44871i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.53664	−	2.37460i	0.543286	−	0.839548i
$9$	3.53279			1.17760
$10$	2.69099	+	1.66090i	0.850965	+	0.525223i
$11$			2.94061i			0.886628i	0.896366	+	0.443314i	$0.146197\pi$
$11$			2.94061i			0.886628i	−0.896366	+	0.443314i	$0.853803\pi$
$12$	−4.74169	−	1.90984i	−1.36881	−	0.551323i
$13$	1.88215			0.522016			0.261008	−	0.965337i	$-0.415945\pi$
$13$	1.88215			0.522016			0.261008	+	0.965337i	$0.415945\pi$
$14$	1.38838	+	0.269098i	0.371059	+	0.0719196i
$15$	2.02150	−	5.34579i	0.521950	−	1.38028i
$16$	2.88333	+	2.77244i	0.720832	+	0.693110i
$17$			1.25432i			0.304218i	0.988364	+	0.152109i	$0.0486065\pi$
$17$			1.25432i			0.304218i	−0.988364	+	0.152109i	$0.951394\pi$
$18$	−0.950667	+	4.90483i	−0.224074	+	1.15608i
$19$			2.48842i			0.570882i	0.958396	+	0.285441i	$0.0921401\pi$
$19$			2.48842i			0.570882i	−0.958396	+	0.285441i	$0.907860\pi$
$20$	−3.03009	+	3.28915i	−0.677550	+	0.735477i
$21$		−	2.55593i		−	0.557750i
$22$	−4.08267	−	0.791314i	−0.870429	−	0.168709i
$23$		−	2.92691i		−	0.610302i	−0.952304	−	0.305151i	$-0.901293\pi$
$23$		−	2.92691i		−	0.610302i	0.952304	−	0.305151i	$-0.0987070\pi$
$24$	3.92756	−	6.06931i	0.801709	−	1.23889i
$25$	−3.74893	−	3.30840i	−0.749786	−	0.661680i
$26$	−0.506485	+	2.61314i	−0.0993298	+	0.512478i
$27$	1.36176			0.262071
$28$	−0.747219	+	1.85517i	−0.141211	+	0.350595i
$29$			0.808725i			0.150177i	0.997177	+	0.0750883i	$0.0239239\pi$
$29$			0.808725i			0.150177i	−0.997177	+	0.0750883i	$0.976076\pi$
$30$	6.87798	+	4.24515i	1.25574	+	0.775055i
$31$	−10.5159			−1.88870			−0.944352	−	0.328938i	$-0.893309\pi$
$31$	−10.5159			−1.88870			−0.944352	+	0.328938i	$0.893309\pi$
$32$	−4.62509	+	3.25708i	−0.817607	+	0.575776i
$33$			7.51600i			1.30837i
$34$	−1.74147	−	0.337536i	−0.298660	−	0.0578870i
$35$	−2.09152	−	0.790907i	−0.353532	−	0.133688i
$36$	−6.55392	−	2.63976i	−1.09232	−	0.439961i
$37$	2.08227			0.342323			0.171162	−	0.985243i	$-0.445248\pi$
$37$	2.08227			0.342323			0.171162	+	0.985243i	$0.445248\pi$
$38$	−3.45486	−	0.669629i	−0.560452	−	0.108628i
$39$	4.81066			0.770322
$40$	−3.75119	−	5.09201i	−0.593115	−	0.805118i
$41$	−9.10984			−1.42272			−0.711359	−	0.702829i	$-0.751920\pi$
$41$	−9.10984			−1.42272			−0.711359	+	0.702829i	$0.751920\pi$
$42$	3.54859	+	0.687797i	0.547560	+	0.106129i
$43$	11.5541			1.76198			0.880992	−	0.473132i	$-0.156877\pi$
$43$	11.5541			1.76198			0.880992	+	0.473132i	$0.156877\pi$
$44$	2.19728	−	5.45534i	0.331253	−	0.822424i
$45$	2.79410	−	7.38890i	0.416521	−	1.10147i
$46$	4.06365	+	0.787626i	0.599152	+	0.116129i
$47$			10.2657i			1.49740i	0.662907	+	0.748702i	$0.269323\pi$
$47$			10.2657i			1.49740i	−0.662907	+	0.748702i	$0.730677\pi$
$48$	7.36959	+	7.08617i	1.06371	+	1.02280i
$49$	−1.00000			−0.142857
$50$	5.60213	−	4.31464i	0.792261	−	0.610182i
$51$			3.20596i			0.448925i
$52$	−3.49172	−	1.40638i	−0.484215	−	0.195030i
$53$	−9.17072			−1.25970			−0.629848	−	0.776719i	$-0.716883\pi$
$53$	−9.17072			−1.25970			−0.629848	+	0.776719i	$0.716883\pi$
$54$	−0.366448	+	1.89064i	−0.0498672	+	0.257283i
$55$	6.15036	+	2.32575i	0.829314	+	0.313604i
$56$	−2.37460	−	1.53664i	−0.317319	−	0.205343i
$57$			6.36023i			0.842432i
$58$	−1.12281	−	0.217627i	−0.147433	−	0.0285758i
$59$			10.0070i			1.30281i	0.758732	+	0.651403i	$0.225819\pi$
$59$			10.0070i			1.30281i	−0.758732	+	0.651403i	$0.774181\pi$
$60$	−7.74471	+	8.40685i	−0.999838	+	1.08532i
$61$		−	10.3599i		−	1.32645i	−0.748419	−	0.663226i	$-0.769187\pi$
$61$		−	10.3599i		−	1.32645i	0.748419	−	0.663226i	$-0.230813\pi$
$62$	2.82980	−	14.6000i	0.359385	−	1.85420i
$63$		−	3.53279i		−	0.445089i
$64$	−3.27745	−	7.29783i	−0.409681	−	0.912229i
$65$	1.48861	−	3.93657i	0.184639	−	0.488271i
$66$	−10.4350	−	2.02254i	−1.28446	−	0.248958i
$67$	−2.89235			−0.353357			−0.176678	−	0.984269i	$-0.556535\pi$
$67$	−2.89235			−0.353357			−0.176678	+	0.984269i	$0.556535\pi$
$68$	0.937254	−	2.32699i	0.113659	−	0.282188i
$69$		−	7.48097i		−	0.900604i
$70$	1.66090	−	2.69099i	0.198516	−	0.321634i
$71$	11.4191			1.35520			0.677600	−	0.735431i	$-0.263020\pi$
$71$	11.4191			1.35520			0.677600	+	0.735431i	$0.263020\pi$
$72$	5.42863	−	8.38895i	0.639771	−	0.988647i
$73$		−	16.4847i		−	1.92939i	−0.263376	−	0.964693i	$-0.584836\pi$
$73$		−	16.4847i		−	1.92939i	0.263376	−	0.964693i	$-0.415164\pi$
$74$	−0.560336	+	2.89098i	−0.0651377	+	0.336069i
$75$	−9.58201	−	8.45604i	−1.10644	−	0.976420i
$76$	1.85939	−	4.61644i	0.213287	−	0.529542i
$77$	2.94061			0.335114
$78$	−1.29454	+	6.67900i	−0.146578	+	0.756248i
$79$	−13.0056			−1.46325			−0.731623	−	0.681709i	$-0.761237\pi$
$79$	−13.0056			−1.46325			−0.731623	+	0.681709i	$0.761237\pi$
$80$	8.07906	−	3.83780i	0.903267	−	0.429079i
$81$	−7.11778			−0.790865
$82$	2.45144	−	12.6479i	0.270716	−	1.39672i
$83$	8.79990			0.965915			0.482957	−	0.875644i	$-0.339563\pi$
$83$	8.79990			0.965915			0.482957	+	0.875644i	$0.339563\pi$
$84$	−1.90984	+	4.74169i	−0.208381	+	0.517361i
$85$	2.62344	+	0.992053i	0.284553	+	0.107603i
$86$	−3.10919	+	16.0414i	−0.335272	+	1.72979i
$87$			2.06705i			0.221611i
$88$	6.98278	+	4.51867i	0.744367	+	0.481692i
$89$	6.64867			0.704757			0.352379	−	0.935857i	$-0.385373\pi$
$89$	6.64867			0.704757			0.352379	+	0.935857i	$0.385373\pi$
$90$	9.50668	+	5.86761i	1.00209	+	0.618500i
$91$		−	1.88215i		−	0.197303i
$92$	−2.18704	+	5.42992i	−0.228015	+	0.566108i
$93$	−26.8778			−2.78710
$94$	−14.2526	−	2.76248i	−1.47005	−	0.284928i
$95$	5.20458	+	1.96811i	0.533979	+	0.201924i
$96$	−11.8214	+	8.32488i	−1.20652	+	0.849654i
$97$		−	7.33203i		−	0.744455i	−0.928141	−	0.372228i	$-0.878594\pi$
$97$		−	7.33203i		−	0.744455i	0.928141	−	0.372228i	$-0.121406\pi$
$98$	0.269098	−	1.38838i	0.0271830	−	0.140247i
$99$			10.3886i			1.04409i
$100$	4.48282	+	8.93892i	0.448282	+	0.893892i
$101$			8.63542i			0.859256i	0.903006	+	0.429628i	$0.141355\pi$
$101$			8.63542i			0.859256i	−0.903006	+	0.429628i	$0.858645\pi$
$102$	−4.45108	−	0.862719i	−0.440723	−	0.0854220i
$103$			3.41511i			0.336501i	0.985744	+	0.168250i	$0.0538117\pi$
$103$			3.41511i			0.336501i	−0.985744	+	0.168250i	$0.946188\pi$
$104$	2.89220	−	4.46936i	0.283604	−	0.438257i
$105$	−5.34579	−	2.02150i	−0.521695	−	0.197279i
$106$	2.46783	−	12.7324i	0.239696	−	1.23668i
$107$	7.95978			0.769501			0.384751	−	0.923021i	$-0.374287\pi$
$107$	7.95978			0.769501			0.384751	+	0.923021i	$0.374287\pi$
$108$	−2.52630	−	1.01753i	−0.243094	−	0.0979123i
$109$			3.96643i			0.379915i	0.981792	+	0.189957i	$0.0608350\pi$
$109$			3.96643i			0.379915i	−0.981792	+	0.189957i	$0.939165\pi$
$110$	−4.88407	+	7.91315i	−0.465677	+	0.754489i
$111$	5.32214			0.505156
$112$	2.77244	−	2.88333i	0.261971	−	0.272449i
$113$			2.59272i			0.243903i	0.992536	+	0.121951i	$0.0389152\pi$
$113$			2.59272i			0.243903i	−0.992536	+	0.121951i	$0.961085\pi$
$114$	−8.83038	−	1.71153i	−0.827041	−	0.160299i
$115$	−6.12169	−	2.31491i	−0.570851	−	0.215867i
$116$	0.604295	−	1.50032i	0.0561074	−	0.139302i
$117$	6.64925			0.614723
$118$	−13.8935	−	2.69288i	−1.27900	−	0.247900i
$119$	1.25432			0.114984
$120$	−9.58778	−	13.0148i	−0.875240	−	1.18809i
$121$	2.35280			0.213891
$122$	14.3835	+	2.78784i	1.30222	+	0.252399i
$123$	−23.2841			−2.09946
$124$	19.5087	+	7.85765i	1.75193	+	0.705637i
$125$	−9.88465	+	5.22434i	−0.884110	+	0.467279i
$126$	4.90483	+	0.950667i	0.436957	+	0.0846921i
$127$			12.7362i			1.13015i	0.825039	+	0.565076i	$0.191153\pi$
$127$			12.7362i			1.13015i	−0.825039	+	0.565076i	$0.808847\pi$
$128$	11.0141	−	2.58650i	0.973517	−	0.228616i
$129$	29.5315			2.60010
$130$	5.06485	+	3.12607i	0.444217	+	0.274175i
$131$			4.34203i			0.379365i	0.981846	+	0.189682i	$0.0607458\pi$
$131$			4.34203i			0.379365i	−0.981846	+	0.189682i	$0.939254\pi$
$132$	5.61610	−	13.9435i	0.488819	−	1.21362i
$133$	2.48842			0.215773
$134$	0.778326	−	4.01567i	0.0672372	−	0.346901i
$135$	1.07703	−	2.84816i	0.0926958	−	0.245130i
$136$	2.97852	+	1.92745i	0.255406	+	0.165277i
$137$			9.86435i			0.842769i	0.906882	+	0.421384i	$0.138456\pi$
$137$			9.86435i			0.842769i	−0.906882	+	0.421384i	$0.861544\pi$
$138$	10.3864	+	2.01312i	0.884149	+	0.171368i
$139$		−	18.0780i		−	1.53335i	−0.642033	−	0.766677i	$-0.721909\pi$
$139$		−	18.0780i		−	1.53335i	0.642033	−	0.766677i	$-0.278091\pi$
$140$	3.28915	+	3.03009i	0.277984	+	0.256090i
$141$			26.2384i			2.20967i
$142$	−3.07286	+	15.8540i	−0.257869	+	1.33044i
$143$			5.53469i			0.462834i
$144$	10.1862	+	9.79443i	0.848848	+	0.816203i
$145$	1.69147	+	0.639627i	0.140469	+	0.0531181i
$146$	22.8869	+	4.43600i	1.89414	+	0.367126i
$147$	−2.55593			−0.210810
$148$	−3.86297	−	1.55591i	−0.317534	−	0.127895i
$149$		−	12.3350i		−	1.01052i	−0.862968	−	0.505259i	$-0.831397\pi$
$149$		−	12.3350i		−	1.01052i	0.862968	−	0.505259i	$-0.168603\pi$
$150$	14.3187	−	11.0279i	1.16911	−	0.900426i
$151$	9.15338			0.744891			0.372446	−	0.928054i	$-0.378519\pi$
$151$	9.15338			0.744891			0.372446	+	0.928054i	$0.378519\pi$
$152$	5.90900	+	3.82381i	0.479283	+	0.310152i
$153$			4.43125i			0.358246i
$154$	−0.791314	+	4.08267i	−0.0637659	+	0.328991i
$155$	−8.31706	+	21.9941i	−0.668043	+	1.76661i
$156$	−8.92460	−	3.59462i	−0.714540	−	0.287800i
$157$	8.31173			0.663349			0.331674	−	0.943394i	$-0.392387\pi$
$157$	8.31173			0.663349			0.331674	+	0.943394i	$0.392387\pi$
$158$	3.49979	−	18.0567i	0.278428	−	1.43651i
$159$	−23.4397			−1.85889
$160$	3.15425	+	12.2495i	0.249365	+	0.968410i
$161$	−2.92691			−0.230673
$162$	1.91538	−	9.88216i	0.150487	−	0.776416i
$163$	13.4112			1.05045			0.525224	−	0.850964i	$-0.323981\pi$
$163$	13.4112			1.05045			0.525224	+	0.850964i	$0.323981\pi$
$164$	16.9003	+	6.80704i	1.31969	+	0.531541i
$165$	15.7199	+	5.94446i	1.22379	+	0.462776i
$166$	−2.36804	+	12.2176i	−0.183795	+	0.948267i
$167$		−	1.57097i		−	0.121565i	−0.998151	−	0.0607825i	$-0.980640\pi$
$167$		−	1.57097i		−	0.121565i	0.998151	−	0.0607825i	$-0.0193596\pi$
$168$	−6.06931	−	3.92756i	−0.468258	−	0.303018i
$169$	−9.45749			−0.727499
$170$	−2.08331	+	3.37537i	−0.159782	+	0.258879i
$171$			8.79105i			0.672268i
$172$	−21.4348	−	8.63344i	−1.63439	−	0.658294i
$173$	−9.47888			−0.720666			−0.360333	−	0.932824i	$-0.617337\pi$
$173$	−9.47888			−0.720666			−0.360333	+	0.932824i	$0.617337\pi$
$174$	−2.86984	−	0.556239i	−0.217562	−	0.0421683i
$175$	−3.30840	+	3.74893i	−0.250091	+	0.283393i
$176$	−8.15267	+	8.47875i	−0.614531	+	0.639110i
$177$			25.5773i			1.92251i
$178$	−1.78915	+	9.23085i	−0.134102	+	0.691881i
$179$			9.38764i			0.701665i	0.936438	+	0.350832i	$0.114101\pi$
$179$			9.38764i			0.701665i	−0.936438	+	0.350832i	$0.885899\pi$
$180$	−10.7047	+	11.6199i	−0.797879	+	0.866094i
$181$		−	7.48170i		−	0.556110i	−0.960565	−	0.278055i	$-0.910310\pi$
$181$		−	7.48170i		−	0.556110i	0.960565	−	0.278055i	$-0.0896898\pi$
$182$	2.61314	+	0.506485i	0.193699	+	0.0375431i
$183$		−	26.4793i		−	1.95740i
$184$	−6.95023	−	4.49761i	−0.512378	−	0.331569i
$185$	1.64688	−	4.35512i	0.121081	−	0.320195i
$186$	7.23277	−	37.3165i	0.530333	−	2.73618i
$187$	−3.68848			−0.269728
$188$	7.67071	−	19.0446i	0.559444	−	1.38897i
$189$		−	1.36176i		−	0.0990536i
$190$	−4.13302	+	6.69630i	−0.299840	+	0.485801i
$191$	−8.88648			−0.643003			−0.321501	−	0.946909i	$-0.604187\pi$
$191$	−8.88648			−0.643003			−0.321501	+	0.946909i	$0.604187\pi$
$192$	−8.37694	−	18.6528i	−0.604553	−	1.34615i
$193$			9.02977i			0.649977i	0.945718	+	0.324989i	$0.105360\pi$
$193$			9.02977i			0.649977i	−0.945718	+	0.324989i	$0.894640\pi$
$194$	10.1796	+	1.97304i	0.730854	+	0.141656i
$195$	3.80478	−	10.0616i	0.272466	−	0.720526i
$196$	1.85517	+	0.747219i	0.132512	+	0.0533728i
$197$	9.67307			0.689178			0.344589	−	0.938754i	$-0.388018\pi$
$197$	9.67307			0.689178			0.344589	+	0.938754i	$0.388018\pi$
$198$	−14.4232	−	2.79554i	−1.02501	−	0.198671i
$199$	−4.59836			−0.325969			−0.162984	−	0.986629i	$-0.552112\pi$
$199$	−4.59836			−0.325969			−0.162984	+	0.986629i	$0.552112\pi$
$200$	−13.6169	+	3.81838i	−0.962860	+	0.270000i
$201$	−7.39265			−0.521437
$202$	−11.9892	−	2.32378i	−0.843557	−	0.163500i
$203$	0.808725			0.0567614
$204$	2.39556	−	5.94761i	0.167723	−	0.416416i
$205$	−7.20503	+	19.0534i	−0.503221	+	1.33075i
$206$	−4.74145	−	0.919000i	−0.330353	−	0.0640298i
$207$		−	10.3401i		−	0.718689i
$208$	5.42687	+	5.21816i	0.376286	+	0.361814i
$209$	−7.31747			−0.506160
$210$	4.24515	−	6.87798i	0.292943	−	0.474625i
$211$		−	27.2554i		−	1.87634i	−0.346176	−	0.938170i	$-0.612520\pi$
$211$		−	27.2554i		−	1.87634i	0.346176	−	0.938170i	$-0.387480\pi$
$212$	17.0133	+	6.85254i	1.16848	+	0.470634i
$213$	29.1865			1.99982
$214$	−2.14196	+	11.0512i	−0.146422	+	0.755442i
$215$	9.13822	−	24.1657i	0.623221	−	1.64808i
$216$	2.09254	−	3.23364i	0.142380	−	0.220021i
$217$			10.5159i			0.713863i
$218$	−5.50689	−	1.06736i	−0.372974	−	0.0722906i
$219$		−	42.1337i		−	2.84713i
$220$	−9.67213	−	8.91033i	−0.652095	−	0.600734i
$221$			2.36083i			0.158807i
$222$	−1.43218	+	7.38913i	−0.0961216	+	0.495926i
$223$		−	10.6823i		−	0.715338i	−0.933848	−	0.357669i	$-0.883572\pi$
$223$		−	10.6823i		−	0.715338i	0.933848	−	0.357669i	$-0.116428\pi$
$224$	3.25708	+	4.62509i	0.217623	+	0.309027i
$225$	−13.2442	−	11.6879i	−0.882945	−	0.779191i
$226$	−3.59967	−	0.697697i	−0.239447	−	0.0464101i
$227$	−15.4722			−1.02692			−0.513461	−	0.858113i	$-0.671637\pi$
$227$	−15.4722			−1.02692			−0.513461	+	0.858113i	$0.671637\pi$
$228$	4.75248	−	11.7993i	0.314741	−	0.781429i
$229$			6.60688i			0.436595i	0.975882	+	0.218298i	$0.0700503\pi$
$229$			6.60688i			0.436595i	−0.975882	+	0.218298i	$0.929950\pi$
$230$	4.86130	−	7.87627i	0.320545	−	0.519346i
$231$	7.51600			0.494517
$232$	1.92040	+	1.24272i	0.126080	+	0.0815888i
$233$		−	11.7981i		−	0.772920i	−0.922306	−	0.386460i	$-0.873698\pi$
$233$		−	11.7981i		−	0.772920i	0.922306	−	0.386460i	$-0.126302\pi$
$234$	−1.78930	+	9.23165i	−0.116970	+	0.603492i
$235$	21.4709	+	8.11920i	1.40061	+	0.529638i
$236$	7.47745	−	18.5648i	0.486741	−	1.20847i
$237$	−33.2415			−2.15927
$238$	−0.337536	+	1.74147i	−0.0218792	+	0.112883i
$239$	−10.1827			−0.658662			−0.329331	−	0.944214i	$-0.606823\pi$
$239$	−10.1827			−0.658662			−0.329331	+	0.944214i	$0.606823\pi$
$240$	20.6495	−	9.80916i	1.33292	−	0.633179i
$241$	−2.99359			−0.192834			−0.0964169	−	0.995341i	$-0.530738\pi$
$241$	−2.99359			−0.192834			−0.0964169	+	0.995341i	$0.530738\pi$
$242$	−0.633134	+	3.26657i	−0.0406994	+	0.209983i
$243$	−22.2779			−1.42913
$244$	−7.74113	+	19.2194i	−0.495575	+	1.23040i
$245$	−0.790907	+	2.09152i	−0.0505292	+	0.133622i
$246$	6.26572	−	32.3271i	0.399488	−	2.06110i
$247$			4.68359i			0.298010i
$248$	−16.1591	+	24.9709i	−1.02611	+	1.58566i
$249$	22.4919			1.42537
$250$	−4.59340	−	15.1295i	−0.290512	−	0.956871i
$251$		−	6.60133i		−	0.416672i	−0.978057	−	0.208336i	$-0.933195\pi$
$251$		−	6.60133i		−	0.416672i	0.978057	−	0.208336i	$-0.0668048\pi$
$252$	−2.63976	+	6.55392i	−0.166289	+	0.412858i
$253$	8.60690			0.541111
$254$	−17.6826	−	3.42728i	−1.10950	−	0.215047i
$255$	6.70535	+	2.53562i	0.419905	+	0.158787i
$256$	0.627158	+	15.9877i	0.0391973	+	0.999231i
$257$		−	16.2700i		−	1.01489i	−0.861683	−	0.507447i	$-0.830589\pi$
$257$		−	16.2700i		−	1.01489i	0.861683	−	0.507447i	$-0.169411\pi$
$258$	−7.94687	+	41.0008i	−0.494751	+	2.55260i
$259$		−	2.08227i		−	0.129386i
$260$	−5.70311	+	6.19070i	−0.353692	+	0.383931i
$261$			2.85705i			0.176847i
$262$	−6.02836	−	1.16843i	−0.372433	−	0.0721860i
$263$			12.2577i			0.755844i	0.925837	+	0.377922i	$0.123361\pi$
$263$			12.2577i			0.755844i	−0.925837	+	0.377922i	$0.876639\pi$
$264$	17.8475	+	11.5494i	1.09844	+	0.710818i
$265$	−7.25319	+	19.1808i	−0.445560	+	1.17827i
$266$	−0.669629	+	3.45486i	−0.0410576	+	0.211831i
$267$	16.9935			1.03999
$268$	5.36581	+	2.16122i	0.327769	+	0.132017i
$269$		−	6.84495i		−	0.417344i	−0.977986	−	0.208672i	$-0.933086\pi$
$269$		−	6.84495i		−	0.417344i	0.977986	−	0.208672i	$-0.0669141\pi$
$270$	3.66448	+	2.26175i	0.223013	+	0.137646i
$271$	12.8200			0.778761			0.389380	−	0.921077i	$-0.372689\pi$
$271$	12.8200			0.778761			0.389380	+	0.921077i	$0.372689\pi$
$272$	−3.47754	+	3.61662i	−0.210857	+	0.219290i
$273$		−	4.81066i		−	0.291154i
$274$	−13.6954	−	2.65448i	−0.827371	−	0.160363i
$275$	9.72872	−	11.0242i	0.586664	−	0.664782i
$276$	−5.58993	+	13.8785i	−0.336474	+	0.835387i
$277$	25.3722			1.52447			0.762234	−	0.647302i	$-0.224103\pi$
$277$	25.3722			1.52447			0.762234	+	0.647302i	$0.224103\pi$
$278$	25.0990	+	4.86476i	1.50534	+	0.291769i
$279$	−37.1503			−2.22413
$280$	−5.09201	+	3.75119i	−0.304306	+	0.224176i
$281$	20.2795			1.20978			0.604888	−	0.796311i	$-0.293218\pi$
$281$	20.2795			1.20978			0.604888	+	0.796311i	$0.293218\pi$
$282$	−36.4287	−	7.06071i	−2.16930	−	0.420459i
$283$	0.643568			0.0382561			0.0191281	−	0.999817i	$-0.493911\pi$
$283$	0.643568			0.0382561			0.0191281	+	0.999817i	$0.493911\pi$
$284$	−21.1844	−	8.53258i	−1.25706	−	0.506315i
$285$	13.3026	+	5.03035i	0.787975	+	0.297972i
$286$	−7.68422	−	1.48938i	−0.454378	−	0.0880686i
$287$			9.10984i			0.537737i
$288$	−16.3394	+	11.5066i	−0.962810	+	0.678031i
$289$	15.4267			0.907451
$290$	−1.34321	+	2.17627i	−0.0788762	+	0.127795i
$291$		−	18.7402i		−	1.09857i
$292$	−12.3177	+	30.5819i	−0.720837	+	1.78967i
$293$	24.5015			1.43139			0.715696	−	0.698412i	$-0.246110\pi$
$293$	24.5015			1.43139			0.715696	+	0.698412i	$0.246110\pi$
$294$	0.687797	−	3.54859i	0.0401131	−	0.206958i
$295$	20.9300	+	7.91464i	1.21859	+	0.460808i
$296$	3.19971	−	4.94456i	0.185979	−	0.287397i
$297$			4.00442i			0.232360i
$298$	17.1255	+	3.31931i	0.992056	+	0.192283i
$299$		−	5.50889i		−	0.318588i
$300$	11.4578	+	22.8473i	0.661515	+	1.31909i
$301$		−	11.5541i		−	0.665967i
$302$	−2.46316	+	12.7083i	−0.141739	+	0.731282i
$303$			22.0715i			1.26798i
$304$	−6.89899	+	7.17492i	−0.395684	+	0.411510i
$305$	−21.6680	−	8.19374i	−1.24071	−	0.469172i
$306$	−6.15224	−	1.19244i	−0.351700	−	0.0681674i
$307$	−9.53860			−0.544396			−0.272198	−	0.962241i	$-0.587751\pi$
$307$	−9.53860			−0.544396			−0.272198	+	0.962241i	$0.587751\pi$
$308$	−5.45534	−	2.19728i	−0.310847	−	0.125202i
$309$			8.72878i			0.496563i
$310$	−28.2980	−	17.4658i	−1.60722	−	0.991990i
$311$	0.978866			0.0555064			0.0277532	−	0.999615i	$-0.491165\pi$
$311$	0.978866			0.0555064			0.0277532	+	0.999615i	$0.491165\pi$
$312$	7.39227	−	11.4234i	0.418505	−	0.646722i
$313$		−	26.7540i		−	1.51223i	−0.654441	−	0.756113i	$-0.727096\pi$
$313$		−	26.7540i		−	1.51223i	0.654441	−	0.756113i	$-0.272904\pi$
$314$	−2.23667	+	11.5398i	−0.126223	+	0.651229i
$315$	−7.38890	−	2.79410i	−0.416317	−	0.157430i
$316$	24.1277	+	9.71804i	1.35729	+	0.546683i
$317$	−21.1277			−1.18665			−0.593326	−	0.804962i	$-0.702186\pi$
$317$	−21.1277			−1.18665			−0.593326	+	0.804962i	$0.702186\pi$
$318$	6.30759	−	32.5431i	0.353712	−	1.82493i
$319$	−2.37815			−0.133151
$320$	−17.8557	+	1.08296i	−0.998166	+	0.0605391i
$321$	20.3447			1.13553
$322$	0.787626	−	4.06365i	0.0438927	−	0.226458i
$323$	−3.12128			−0.173673
$324$	13.2047	+	5.31854i	0.733595	+	0.295475i
$325$	−7.05607	−	6.22692i	−0.391400	−	0.345407i
$326$	−3.60894	+	18.6198i	−0.199881	+	1.03126i
$327$			10.1379i			0.560628i
$328$	−13.9986	+	21.6322i	−0.772942	+	1.19444i
$329$	10.2657			0.565966
$330$	−12.4833	+	20.2255i	−0.687185	+	1.11338i
$331$			1.68575i			0.0926572i	0.998926	+	0.0463286i	$0.0147521\pi$
$331$			1.68575i			0.0926572i	−0.998926	+	0.0463286i	$0.985248\pi$
$332$	−16.3253	−	6.57545i	−0.895969	−	0.360875i
$333$	7.35622			0.403118
$334$	2.18109	+	0.422744i	0.119344	+	0.0231315i
$335$	−2.28758	+	6.04941i	−0.124984	+	0.330515i
$336$	7.08617	−	7.36959i	0.386582	−	0.402044i
$337$		−	24.1464i		−	1.31534i	−0.753306	−	0.657670i	$-0.771542\pi$
$337$		−	24.1464i		−	1.31534i	0.753306	−	0.657670i	$-0.228458\pi$
$338$	2.54500	−	13.1306i	0.138430	−	0.714208i
$339$			6.62682i			0.359920i
$340$	−4.12566	−	3.80072i	−0.223745	−	0.206123i
$341$		−	30.9231i		−	1.67458i
$342$	−12.2053	−	2.36566i	−0.659985	−	0.127920i
$343$			1.00000i			0.0539949i
$344$	17.7545	−	27.4364i	0.957260	−	1.47927i
$345$	−15.6466	−	5.91676i	−0.842386	−	0.318547i
$346$	2.55075	−	13.1602i	0.137129	−	0.707499i
$347$	11.1598			0.599089			0.299544	−	0.954082i	$-0.403165\pi$
$347$	11.1598			0.599089			0.299544	+	0.954082i	$0.403165\pi$
$348$	1.54454	−	3.83473i	0.0827958	−	0.205563i
$349$			28.1101i			1.50470i	0.658765	+	0.752348i	$0.271079\pi$
$349$			28.1101i			1.50470i	−0.658765	+	0.752348i	$0.728921\pi$
$350$	−4.31464	−	5.60213i	−0.230627	−	0.299447i
$351$	2.56305			0.136805
$352$	−9.57782	−	13.6006i	−0.510499	−	0.724914i
$353$			5.06143i			0.269393i	0.990887	+	0.134696i	$0.0430059\pi$
$353$			5.06143i			0.269393i	−0.990887	+	0.134696i	$0.956994\pi$
$354$	−35.5109	−	6.88281i	−1.88738	−	0.365817i
$355$	9.03146	−	23.8833i	0.479340	−	1.26760i
$356$	−12.3344	−	4.96801i	−0.653723	−	0.263304i
$357$	3.20596			0.169678
$358$	−13.0336	−	2.52620i	−0.688845	−	0.133514i
$359$	12.8005			0.675583			0.337792	−	0.941221i	$-0.390320\pi$
$359$	12.8005			0.675583			0.337792	+	0.941221i	$0.390320\pi$
$360$	−13.2521	−	17.9890i	−0.698449	−	0.948103i
$361$	12.8078			0.674094
$362$	10.3874	+	2.01331i	0.545950	+	0.105817i
$363$	6.01359			0.315632
$364$	−1.40638	+	3.49172i	−0.0737144	+	0.183016i
$365$	−34.4781	−	13.0379i	−1.80467	−	0.682432i
$366$	36.7632	+	7.12553i	1.92164	+	0.372457i
$367$		−	18.0163i		−	0.940444i	−0.882548	−	0.470222i	$-0.844174\pi$
$367$		−	18.0163i		−	0.940444i	0.882548	−	0.470222i	$-0.155826\pi$
$368$	8.11467	−	8.43923i	0.423007	−	0.439925i
$369$	−32.1831			−1.67539
$370$	5.60337	+	3.45845i	0.291305	+	0.179796i
$371$			9.17072i			0.476120i
$372$	49.8630	+	20.0836i	2.58527	+	1.04129i
$373$	−0.704850			−0.0364957			−0.0182479	−	0.999833i	$-0.505809\pi$
$373$	−0.704850			−0.0364957			−0.0182479	+	0.999833i	$0.505809\pi$
$374$	0.992563	−	5.12099i	0.0513242	−	0.264800i
$375$	−25.2645	+	13.3531i	−1.30465	+	0.689549i
$376$	24.3769	+	15.7747i	1.25714	+	0.813518i
$377$			1.52215i			0.0783945i
$378$	1.89064	+	0.366448i	0.0972439	+	0.0188480i
$379$			23.4356i			1.20381i	0.798569	+	0.601903i	$0.205591\pi$
$379$			23.4356i			1.20381i	−0.798569	+	0.601903i	$0.794409\pi$
$380$	−8.18479	−	7.54014i	−0.419871	−	0.386801i
$381$			32.5527i			1.66773i
$382$	2.39134	−	12.3378i	0.122351	−	0.631255i
$383$		−	0.732839i		−	0.0374463i	−0.999825	−	0.0187232i	$-0.994040\pi$
$383$		−	0.732839i		−	0.0374463i	0.999825	−	0.0187232i	$-0.00596012\pi$
$384$	28.1512	−	6.61091i	1.43659	−	0.337362i
$385$	2.32575	−	6.15036i	0.118531	−	0.313451i
$386$	−12.5367	−	2.42990i	−0.638102	−	0.123678i
$387$	40.8181			2.07490
$388$	−5.47863	+	13.6022i	−0.278136	+	0.690546i
$389$		−	17.3775i		−	0.881075i	−0.897734	−	0.440537i	$-0.854788\pi$
$389$		−	17.3775i		−	0.881075i	0.897734	−	0.440537i	$-0.145212\pi$
$390$	12.9454	+	7.99003i	0.655517	+	0.404591i
$391$	3.67129			0.185665
$392$	−1.53664	+	2.37460i	−0.0776122	+	0.119935i
$393$			11.0979i			0.559816i
$394$	−2.60301	+	13.4299i	−0.131138	+	0.676586i
$395$	−10.2862	+	27.2015i	−0.517557	+	1.36866i
$396$	7.76252	−	19.2726i	0.390081	−	0.968482i
$397$	14.0231			0.703799			0.351899	−	0.936038i	$-0.385536\pi$
$397$	14.0231			0.703799			0.351899	+	0.936038i	$0.385536\pi$
$398$	1.23741	−	6.38424i	0.0620258	−	0.320013i
$399$	6.36023			0.318410
$400$	−1.63706	−	19.9329i	−0.0818531	−	0.996644i
$401$	−26.1322			−1.30498			−0.652491	−	0.757797i	$-0.726276\pi$
$401$	−26.1322			−1.30498			−0.652491	+	0.757797i	$0.726276\pi$
$402$	1.98935	−	10.2638i	0.0992197	−	0.511910i
$403$	−19.7925			−0.985933
$404$	6.45255	−	16.0202i	0.321026	−	0.797034i
$405$	−5.62951	+	14.8870i	−0.279732	+	0.739741i
$406$	−0.217627	+	1.12281i	−0.0108006	+	0.0557243i
$407$			6.12315i			0.303514i
$408$	7.61288	+	4.92643i	0.376894	+	0.243894i
$409$	−18.6724			−0.923289			−0.461645	−	0.887065i	$-0.652740\pi$
$409$	−18.6724			−0.923289			−0.461645	+	0.887065i	$0.652740\pi$
$410$	−24.5144	−	15.1305i	−1.21068	−	0.747244i
$411$			25.2126i			1.24365i
$412$	2.55183	−	6.33562i	0.125720	−	0.312133i
$413$	10.0070			0.492414
$414$	14.3560	+	2.78251i	0.705558	+	0.136753i
$415$	6.95991	−	18.4052i	0.341648	−	0.903475i
$416$	−8.70513	+	6.13033i	−0.426804	+	0.300564i
$417$		−	46.2061i		−	2.26272i
$418$	1.96912	−	10.1594i	0.0963128	−	0.496912i
$419$			28.6856i			1.40138i	0.713465	+	0.700691i	$0.247125\pi$
$419$			28.6856i			1.40138i	−0.713465	+	0.700691i	$0.752875\pi$
$420$	8.40685	+	7.74471i	0.410212	+	0.377903i
$421$			24.1272i			1.17589i	0.808902	+	0.587943i	$0.200062\pi$
$421$			24.1272i			1.17589i	−0.808902	+	0.587943i	$0.799938\pi$
$422$	37.8407	+	7.33438i	1.84206	+	0.357032i
$423$			36.2665i			1.76334i
$424$	−14.0921	+	21.7768i	−0.684375	+	1.05757i
$425$	4.14980	−	4.70237i	0.201295	−	0.228099i
$426$	−7.85403	+	40.5218i	−0.380529	+	1.96329i
$427$	−10.3599			−0.501352
$428$	−14.7668	−	5.94770i	−0.713779	−	0.287493i
$429$			14.1463i			0.682989i
$430$	31.0919	+	19.1902i	1.49939	+	0.925434i
$431$	−2.64788			−0.127544			−0.0637721	−	0.997964i	$-0.520313\pi$
$431$	−2.64788			−0.127544			−0.0637721	+	0.997964i	$0.520313\pi$
$432$	3.92641	+	3.77540i	0.188909	+	0.181644i
$433$			9.61670i			0.462149i	0.972936	+	0.231075i	$0.0742241\pi$
$433$			9.61670i			0.462149i	−0.972936	+	0.231075i	$0.925776\pi$
$434$	−14.6000	−	2.82980i	−0.700820	−	0.135835i
$435$	4.32327	+	1.63484i	0.207285	+	0.0783847i
$436$	2.96379	−	7.35840i	0.141940	−	0.352404i
$437$	7.28337			0.348411
$438$	58.4974	+	11.3381i	2.79511	+	0.541756i
$439$	−12.6264			−0.602624			−0.301312	−	0.953526i	$-0.597425\pi$
$439$	−12.6264			−0.602624			−0.301312	+	0.953526i	$0.597425\pi$
$440$	14.9736	−	11.0308i	0.713840	−	0.525872i
$441$	−3.53279			−0.168228
$442$	−3.27772	−	0.635295i	−0.155905	−	0.0302179i
$443$	12.0850			0.574178			0.287089	−	0.957904i	$-0.407313\pi$
$443$	12.0850			0.574178			0.287089	+	0.957904i	$0.407313\pi$
$444$	−9.87349	−	3.97681i	−0.468575	−	0.188731i
$445$	5.25848	−	13.9058i	0.249276	−	0.659200i
$446$	14.8310	+	2.87458i	0.702268	+	0.136115i
$447$		−	31.5273i		−	1.49119i
$448$	−7.29783	+	3.27745i	−0.344790	+	0.154845i
$449$	25.6294			1.20953			0.604763	−	0.796406i	$-0.293268\pi$
$449$	25.6294			1.20953			0.604763	+	0.796406i	$0.293268\pi$
$450$	19.7911	−	15.2427i	0.932963	−	0.718548i
$451$		−	26.7885i		−	1.26142i
$452$	1.93733	−	4.80995i	0.0911244	−	0.226241i
$453$	23.3954			1.09921
$454$	4.16353	−	21.4812i	0.195404	−	1.00816i
$455$	−3.93657	−	1.48861i	−0.184549	−	0.0697871i
$456$	15.1030	+	9.77340i	0.707262	+	0.457681i
$457$			1.44766i			0.0677186i	0.999427	+	0.0338593i	$0.0107798\pi$
$457$			1.44766i			0.0677186i	−0.999427	+	0.0338593i	$0.989220\pi$
$458$	−9.17284	−	1.77790i	−0.428618	−	0.0830759i
$459$			1.70809i			0.0797268i
$460$	9.62705	+	8.86880i	0.448863	+	0.413510i
$461$		−	40.8669i		−	1.90336i	−0.307090	−	0.951681i	$-0.599355\pi$
$461$		−	40.8669i		−	1.90336i	0.307090	−	0.951681i	$-0.400645\pi$
$462$	−2.02254	+	10.4350i	−0.0940973	+	0.485482i
$463$			1.57368i			0.0731352i	0.999331	+	0.0365676i	$0.0116424\pi$
$463$			1.57368i			0.0731352i	−0.999331	+	0.0365676i	$0.988358\pi$
$464$	−2.24214	+	2.33182i	−0.104089	+	0.108252i
$465$	−21.2578	+	56.2155i	−0.985809	+	2.60693i
$466$	16.3802	+	3.17485i	0.758799	+	0.147072i
$467$	−8.12109			−0.375799			−0.187900	−	0.982188i	$-0.560168\pi$
$467$	−8.12109			−0.375799			−0.187900	+	0.982188i	$0.560168\pi$
$468$	−12.3355	−	4.96844i	−0.570209	−	0.229666i
$469$			2.89235i			0.133556i
$470$	−17.0503	+	27.6248i	−0.786471	+	1.27424i
$471$	21.2442			0.978882
$472$	23.7627	+	15.3773i	1.09377	+	0.707796i
$473$			33.9761i			1.56222i
$474$	8.94522	−	46.1516i	0.410868	−	2.11981i
$475$	8.23268	−	9.32891i	0.377741	−	0.428040i
$476$	−2.32699	−	0.937254i	−0.106657	−	0.0429590i
$477$	−32.3982			−1.48341
$478$	2.74014	−	14.1374i	0.125331	−	0.646628i
$479$	24.9788			1.14131			0.570656	−	0.821189i	$-0.306689\pi$
$479$	24.9788			1.14131			0.570656	+	0.821189i	$0.306689\pi$
$480$	8.06204	+	31.3089i	0.367980	+	1.42905i
$481$	3.91916			0.178698
$482$	0.805569	−	4.15622i	0.0366927	−	0.189311i
$483$	−7.48097			−0.340396
$484$	−4.36485	−	1.75806i	−0.198402	−	0.0799116i
$485$	−15.3351	−	5.79896i	−0.696332	−	0.263317i
$486$	5.99493	−	30.9300i	0.271936	−	1.40301i
$487$		−	18.3021i		−	0.829346i	−0.909970	−	0.414673i	$-0.863896\pi$
$487$		−	18.3021i		−	0.829346i	0.909970	−	0.414673i	$-0.136104\pi$
$488$	−24.6007	−	15.9195i	−1.11362	−	0.720643i
$489$	34.2782			1.55011
$490$	−2.69099	−	1.66090i	−0.121566	−	0.0750319i
$491$		−	29.6186i		−	1.33667i	−0.743861	−	0.668334i	$-0.767008\pi$
$491$		−	29.6186i		−	1.33667i	0.743861	−	0.668334i	$-0.232992\pi$
$492$	43.1960	+	17.3983i	1.94743	+	0.784377i
$493$	−1.01440			−0.0456864
$494$	−6.50258	−	1.26035i	−0.292565	−	0.0567056i
$495$	21.7279	+	8.21638i	0.976596	+	0.369299i
$496$	−30.3207	−	29.1546i	−1.36144	−	1.30908i
$497$		−	11.4191i		−	0.512217i
$498$	−6.05255	+	31.2273i	−0.271221	+	1.39933i
$499$			41.5006i			1.85782i	0.370303	+	0.928911i	$0.379254\pi$
$499$			41.5006i			1.85782i	−0.370303	+	0.928911i	$0.620746\pi$
$500$	22.2415	−	2.30605i	0.994668	−	0.103130i
$501$		−	4.01528i		−	0.179390i
$502$	9.16513	+	1.77641i	0.409060	+	0.0792849i
$503$			3.43798i			0.153292i	0.997058	+	0.0766461i	$0.0244212\pi$
$503$			3.43798i			0.153292i	−0.997058	+	0.0766461i	$0.975579\pi$
$504$	−8.38895	−	5.42863i	−0.373674	−	0.241811i
$505$	18.0612	+	6.82981i	0.803712	+	0.303923i
$506$	−2.31610	+	11.9496i	−0.102963	+	0.531225i
$507$	−24.1727			−1.07355
$508$	9.51670	−	23.6278i	0.422235	−	1.04831i
$509$			1.09479i			0.0485259i	0.999706	+	0.0242630i	$0.00772390\pi$
$509$			1.09479i			0.0485259i	−0.999706	+	0.0242630i	$0.992276\pi$
$510$	−5.32479	+	8.62720i	−0.235786	+	0.382019i
$511$	−16.4847			−0.729239
$512$	−22.3657	−	3.43153i	−0.988434	−	0.151654i
$513$			3.38863i			0.149612i
$514$	22.5888	+	4.37823i	0.996351	+	0.193115i
$515$	7.14278	+	2.70103i	0.314748	+	0.119022i
$516$	−54.7860	−	22.0665i	−2.41182	−	0.971423i
$517$	−30.1874			−1.32764
$518$	2.89098	+	0.560336i	0.127022	+	0.0246197i
$519$	−24.2274			−1.06346
$520$	−7.06031	−	9.58396i	−0.309615	−	0.420284i
$521$	−33.8624			−1.48354			−0.741768	−	0.670656i	$-0.766013\pi$
$521$	−33.8624			−1.48354			−0.741768	+	0.670656i	$0.766013\pi$
$522$	−3.96666	−	0.768828i	−0.173616	−	0.0336507i
$523$	−34.8079			−1.52204			−0.761021	−	0.648728i	$-0.775301\pi$
$523$	−34.8079			−1.52204			−0.761021	+	0.648728i	$0.775301\pi$
$524$	3.24444	−	8.05521i	0.141734	−	0.351893i
$525$	−8.45604	+	9.58201i	−0.369052	+	0.418193i
$526$	−17.0183	−	3.29854i	−0.742035	−	0.143823i
$527$		−	13.1903i		−	0.574578i
$528$	−20.8377	+	21.6711i	−0.906843	+	0.943114i
$529$	14.4332			0.627531
$530$	−24.6783	−	15.2317i	−1.07196	−	0.661621i
$531$			35.3527i			1.53418i
$532$	−4.61644	−	1.85939i	−0.200148	−	0.0806149i
$533$	−17.1461			−0.742681
$534$	−4.57293	+	23.5934i	−0.197890	+	1.02099i
$535$	6.29545	−	16.6481i	0.272176	−	0.719759i
$536$	−4.44451	+	6.86817i	−0.191974	+	0.296660i
$537$			23.9942i			1.03542i
$538$	9.50336	+	1.84196i	0.409719	+	0.0794127i
$539$		−	2.94061i		−	0.126661i
$540$	−4.12627	+	4.47905i	−0.177566	+	0.192747i
$541$		−	1.30956i		−	0.0563023i	−0.999604	−	0.0281512i	$-0.991038\pi$
$541$		−	1.30956i		−	0.0563023i	0.999604	−	0.0281512i	$-0.00896198\pi$
$542$	−3.44985	+	17.7990i	−0.148184	+	0.764532i
$543$		−	19.1227i		−	0.820634i
$544$	−4.08543	−	5.80135i	−0.175162	−	0.248731i
$545$	8.29587	+	3.13707i	0.355356	+	0.134377i
$546$	6.67900	+	1.29454i	0.285835	+	0.0554012i
$547$	13.8227			0.591016			0.295508	−	0.955340i	$-0.404511\pi$
$547$	13.8227			0.591016			0.295508	+	0.955340i	$0.404511\pi$
$548$	7.37083	−	18.3001i	0.314866	−	0.781740i
$549$		−	36.5994i		−	1.56202i
$550$	12.6877	+	16.4737i	0.541005	+	0.702441i
$551$	−2.01245			−0.0857331
$552$	−17.7643	−	11.4956i	−0.756100	−	0.489285i
$553$			13.0056i			0.553055i
$554$	−6.82762	+	35.2261i	−0.290078	+	1.49662i
$555$	4.20932	−	11.1314i	0.178676	−	0.472501i
$556$	−13.5082	+	33.5378i	−0.572876	+	1.42232i
$557$	−18.8897			−0.800384			−0.400192	−	0.916431i	$-0.631057\pi$
$557$	−18.8897			−0.800384			−0.400192	+	0.916431i	$0.631057\pi$
$558$	9.99707	−	51.5785i	0.423210	−	2.18349i
$559$	21.7466			0.919783
$560$	−3.83780	−	8.07906i	−0.162177	−	0.341403i
$561$	−9.42750			−0.398029
$562$	−5.45719	+	28.1556i	−0.230198	+	1.18767i
$563$	−17.9673			−0.757232			−0.378616	−	0.925554i	$-0.623600\pi$
$563$	−17.9673			−0.757232			−0.378616	+	0.925554i	$0.623600\pi$
$564$	19.6058	−	48.6767i	0.825554	−	2.04966i
$565$	5.42274	+	2.05060i	0.228136	+	0.0862695i
$566$	−0.173183	+	0.893514i	−0.00727943	+	0.0375572i
$567$			7.11778i			0.298919i
$568$	17.5471	−	27.1158i	0.736260	−	1.13775i
$569$	25.3482			1.06265			0.531327	−	0.847167i	$-0.321694\pi$
$569$	25.3482			1.06265			0.531327	+	0.847167i	$0.321694\pi$
$570$	−10.5637	+	17.1153i	−0.442465	+	0.716880i
$571$			8.06376i			0.337458i	0.985662	+	0.168729i	$0.0539663\pi$
$571$			8.06376i			0.337458i	−0.985662	+	0.168729i	$0.946034\pi$
$572$	4.13562	−	10.2678i	0.172919	−	0.429318i
$573$	−22.7132			−0.948858
$574$	−12.6479	−	2.45144i	−0.527912	−	0.102321i
$575$	−9.68338	+	10.9728i	−0.403825	+	0.457596i
$576$	−11.5785	−	25.7817i	−0.482439	−	1.07424i
$577$			18.1057i			0.753748i	0.926264	+	0.376874i	$0.123001\pi$
$577$			18.1057i			0.753748i	−0.926264	+	0.376874i	$0.876999\pi$
$578$	−4.15129	+	21.4180i	−0.172671	+	0.890872i
$579$			23.0795i			0.959150i
$580$	−2.66002	−	2.45051i	−0.110451	−	0.101752i
$581$		−	8.79990i		−	0.365081i
$582$	26.0184	+	5.04295i	1.07850	+	0.209037i
$583$		−	26.9675i		−	1.11688i
$584$	−39.1445	−	25.3311i	−1.61981	−	1.04821i
$585$	5.25894	−	13.9071i	0.217430	−	0.574986i
$586$	−6.59331	+	34.0173i	−0.272367	+	1.40524i
$587$	−18.0269			−0.744051			−0.372025	−	0.928223i	$-0.621337\pi$
$587$	−18.0269			−0.744051			−0.372025	+	0.928223i	$0.621337\pi$
$588$	4.74169	+	1.90984i	0.195544	+	0.0787605i
$589$		−	26.1678i		−	1.07823i
$590$	−16.6207	+	26.9288i	−0.684264	+	1.10864i
$591$	24.7237			1.01700
$592$	6.00387	+	5.77297i	0.246758	+	0.237268i
$593$			23.3814i			0.960159i	0.877225	+	0.480079i	$0.159392\pi$
$593$			23.3814i			0.960159i	−0.877225	+	0.480079i	$0.840608\pi$
$594$	−5.55963	−	1.07758i	−0.228114	−	0.0442137i
$595$	0.992053	−	2.62344i	0.0406702	−	0.107551i
$596$	−9.21691	+	22.8835i	−0.377539	+	0.937343i
$597$	−11.7531			−0.481022
$598$	7.64841	+	1.48243i	0.312767	+	0.0606212i
$599$	−9.26472			−0.378546			−0.189273	−	0.981924i	$-0.560613\pi$
$599$	−9.26472			−0.378546			−0.189273	+	0.981924i	$0.560613\pi$
$600$	−34.8039	+	9.75952i	−1.42086	+	0.398431i
$601$	3.78965			0.154583			0.0772915	−	0.997009i	$-0.475373\pi$
$601$	3.78965			0.154583			0.0772915	+	0.997009i	$0.475373\pi$
$602$	16.0414	+	3.10919i	0.653800	+	0.126721i
$603$	−10.2180			−0.416111
$604$	−16.9811	−	6.83958i	−0.690951	−	0.278298i
$605$	1.86084	−	4.92093i	0.0756541	−	0.200064i
$606$	−30.6436	−	5.93941i	−1.24481	−	0.241272i
$607$		−	4.77766i		−	0.193919i	−0.995288	−	0.0969596i	$-0.969088\pi$
$607$		−	4.77766i		−	0.193919i	0.995288	−	0.0969596i	$-0.0309118\pi$
$608$	−8.10498	−	11.5091i	−0.328700	−	0.466757i
$609$	2.06705			0.0837610
$610$	17.2068	−	27.8784i	0.696684	−	1.12876i
$611$			19.3216i			0.781669i
$612$	3.31112	−	8.22074i	0.133844	−	0.332304i
$613$	11.7814			0.475847			0.237923	−	0.971284i	$-0.423533\pi$
$613$	11.7814			0.475847			0.237923	+	0.971284i	$0.423533\pi$
$614$	2.56682	−	13.2432i	0.103588	−	0.534450i
$615$	−18.4156	+	48.6993i	−0.742588	+	1.96374i
$616$	4.51867	−	6.98278i	0.182063	−	0.281344i
$617$			39.7114i			1.59872i	0.600853	+	0.799360i	$0.294828\pi$
$617$			39.7114i			1.59872i	−0.600853	+	0.799360i	$0.705172\pi$
$618$	−12.1188	−	2.34890i	−0.487491	−	0.0944867i
$619$		−	24.2590i		−	0.975052i	−0.873108	−	0.487526i	$-0.837899\pi$
$619$		−	24.2590i		−	0.975052i	0.873108	−	0.487526i	$-0.162101\pi$
$620$	31.8640	−	34.5883i	1.27969	−	1.38910i
$621$		−	3.98575i		−	0.159943i
$622$	−0.263411	+	1.35903i	−0.0105618	+	0.0544923i
$623$		−	6.64867i		−	0.266373i
$624$	13.8707	+	13.3373i	0.555273	+	0.533918i
$625$	3.10898	+	24.8059i	0.124359	+	0.992237i
$626$	37.1446	+	7.19946i	1.48460	+	0.287748i
$627$	−18.7030			−0.746924
$628$	−15.4197	−	6.21068i	−0.615313	−	0.247833i
$629$			2.61184i			0.104141i
$630$	5.86761	−	9.50668i	0.233771	−	0.378755i
$631$	−41.9840			−1.67136			−0.835678	−	0.549219i	$-0.814925\pi$
$631$	−41.9840			−1.67136			−0.835678	+	0.549219i	$0.814925\pi$
$632$	−19.9850	+	30.8831i	−0.794961	+	1.22847i
$633$		−	69.6629i		−	2.76885i
$634$	5.68544	−	29.3332i	0.225798	−	1.16497i
$635$	26.6380	+	10.0731i	1.05710	+	0.399739i
$636$	43.4847	+	17.5146i	1.72428	+	0.694500i
$637$	−1.88215			−0.0745737
$638$	0.639956	−	3.30176i	0.0253361	−	0.130718i
$639$	40.3413			1.59588
$640$	3.30140	−	25.0819i	0.130499	−	0.991448i
$641$	−4.48888			−0.177300			−0.0886500	−	0.996063i	$-0.528255\pi$
$641$	−4.48888			−0.177300			−0.0886500	+	0.996063i	$0.528255\pi$
$642$	−5.47471	+	28.2460i	−0.216070	+	1.11478i
$643$	29.8174			1.17589			0.587943	−	0.808903i	$-0.299938\pi$
$643$	29.8174			1.17589			0.587943	+	0.808903i	$0.299938\pi$
$644$	5.42992	+	2.18704i	0.213969	+	0.0861815i
$645$	23.3567	−	61.7657i	0.919667	−	2.43202i
$646$	0.839931	−	4.33351i	0.0330467	−	0.170500i
$647$		−	31.9284i		−	1.25523i	−0.778523	−	0.627617i	$-0.784031\pi$
$647$		−	31.9284i		−	1.25523i	0.778523	−	0.627617i	$-0.215969\pi$
$648$	−10.9375	+	16.9019i	−0.429666	+	0.663969i
$649$	−29.4268			−1.15510
$650$	10.5441	−	8.12082i	0.413573	−	0.318525i
$651$			26.8778i			1.05342i
$652$	−24.8801	−	10.0211i	−0.974381	−	0.392457i
$653$	−12.0375			−0.471063			−0.235531	−	0.971867i	$-0.575683\pi$
$653$	−12.0375			−0.471063			−0.235531	+	0.971867i	$0.575683\pi$
$654$	−14.0752	−	2.72810i	−0.550385	−	0.106677i
$655$	9.08145	+	3.43414i	0.354841	+	0.134183i
$656$	−26.2666	−	25.2565i	−1.02554	−	0.986100i
$657$		−	58.2368i		−	2.27204i
$658$	−2.76248	+	14.2526i	−0.107693	+	0.555625i
$659$			23.0181i			0.896657i	0.893869	+	0.448329i	$0.147981\pi$
$659$			23.0181i			0.896657i	−0.893869	+	0.448329i	$0.852019\pi$
$660$	−24.7213	−	22.7742i	−0.962275	−	0.886484i
$661$		−	17.1643i		−	0.667613i	−0.942642	−	0.333806i	$-0.891667\pi$
$661$		−	17.1643i		−	0.667613i	0.942642	−	0.333806i	$-0.108333\pi$
$662$	−2.34045	−	0.453633i	−0.0909644	−	0.0176309i
$663$			6.03412i			0.234346i
$664$	13.5223	−	20.8962i	0.524768	−	0.810932i
$665$	1.96811	−	5.20458i	0.0763199	−	0.201825i
$666$	−1.97955	+	10.2132i	−0.0767059	+	0.395753i
$667$	2.36706			0.0916531
$668$	−1.17386	+	2.91441i	−0.0454179	+	0.112762i
$669$		−	27.3031i		−	1.05560i
$670$	−7.78327	−	4.80391i	−0.300694	−	0.185591i
$671$	30.4645			1.17607
$672$	8.32488	+	11.8214i	0.321139	+	0.456020i
$673$		−	11.2759i		−	0.434655i	−0.976099	−	0.217327i	$-0.930266\pi$
$673$		−	11.2759i		−	0.434655i	0.976099	−	0.217327i	$-0.0697339\pi$
$674$	33.5243	+	6.49776i	1.29131	+	0.250285i
$675$	−5.10515	−	4.50525i	−0.196497	−	0.173407i
$676$	17.5453	+	7.06682i	0.674818	+	0.271801i
$677$	24.3448			0.935648			0.467824	−	0.883822i	$-0.345038\pi$
$677$	24.3448			0.935648			0.467824	+	0.883822i	$0.345038\pi$
$678$	−9.20052	−	1.78327i	−0.353344	−	0.0684859i
$679$	−7.33203			−0.281378
$680$	6.38703	−	4.70520i	0.244931	−	0.180436i
$681$	−39.5458			−1.51540
$682$	42.9328	+	8.32134i	1.64398	+	0.318641i
$683$	21.4971			0.822563			0.411281	−	0.911508i	$-0.365081\pi$
$683$	21.4971			0.822563			0.411281	+	0.911508i	$0.365081\pi$
$684$	6.56884	−	16.3089i	0.251166	−	0.623586i
$685$	20.6315	+	7.80179i	0.788290	+	0.298091i
$686$	−1.38838	−	0.269098i	−0.0530084	−	0.0102742i
$687$			16.8867i			0.644269i
$688$	33.3142	+	32.0330i	1.27009	+	1.22125i
$689$	−17.2607			−0.657581
$690$	12.4252	−	20.1312i	0.473018	−	0.766382i
$691$			13.8322i			0.526203i	0.964768	+	0.263102i	$0.0847455\pi$
$691$			13.8322i			0.526203i	−0.964768	+	0.263102i	$0.915255\pi$
$692$	17.5850	+	7.08280i	0.668480	+	0.269248i
$693$	10.3886			0.394628
$694$	−3.00308	+	15.4940i	−0.113995	+	0.588143i
$695$	−37.8105	−	14.2980i	−1.43423	−	0.542354i
$696$	4.90841	+	3.17631i	0.186053	+	0.120398i
$697$		−	11.4267i		−	0.432816i
$698$	−39.0273	−	7.56437i	−1.47721	−	0.286316i
$699$		−	30.1552i		−	1.14057i
$700$	8.93892	−	4.48282i	0.337860	−	0.169435i
$701$			9.72271i			0.367222i	0.982999	+	0.183611i	$0.0587786\pi$
$701$			9.72271i			0.367222i	−0.982999	+	0.183611i	$0.941221\pi$
$702$	−0.689712	+	3.55847i	−0.0260315	+	0.134306i
$703$			5.18156i			0.195426i
$704$	21.4601	−	9.63771i	0.808808	−	0.363235i
$705$	54.8782	+	20.7521i	2.06683	+	0.781570i
$706$	−7.02717	−	1.36202i	−0.264471	−	0.0512604i
$707$	8.63542			0.324768
$708$	19.1119	−	47.4503i	0.718268	−	1.78329i
$709$			50.6713i			1.90300i	0.307650	+	0.951500i	$0.400457\pi$
$709$			50.6713i			1.90300i	−0.307650	+	0.951500i	$0.599543\pi$
$710$	30.7287	+	18.9660i	1.15323	+	0.711782i
$711$	−45.9461			−1.72311
$712$	10.2166	−	15.7879i	0.382885	−	0.591678i
$713$			30.7789i			1.15268i
$714$	−0.862719	+	4.45108i	−0.0322865	+	0.166578i
$715$	11.5759	+	4.37742i	0.432915	+	0.163706i
$716$	7.01462	−	17.4157i	0.262149	−	0.650855i
$717$	−26.0262			−0.971967
$718$	−3.44459	+	17.7719i	−0.128551	+	0.663240i
$719$	−34.1239			−1.27261			−0.636304	−	0.771439i	$-0.719537\pi$
$719$	−34.1239			−1.27261			−0.636304	+	0.771439i	$0.719537\pi$
$720$	28.5416	−	13.5581i	1.06368	−	0.505282i
$721$	3.41511			0.127185
$722$	−3.44655	+	17.7820i	−0.128267	+	0.661778i
$723$	−7.65140			−0.284559
$724$	−5.59047	+	13.8798i	−0.207768	+	0.515840i
$725$	2.67559	−	3.03186i	0.0993688	−	0.112600i
$726$	−1.61825	+	8.34912i	−0.0600588	+	0.309865i
$727$			16.2343i			0.602098i	0.953609	+	0.301049i	$0.0973367\pi$
$727$			16.2343i			0.602098i	−0.953609	+	0.301049i	$0.902663\pi$
$728$	−4.46936	−	2.89220i	−0.165646	−	0.107192i
$729$	−35.5873			−1.31805
$730$	27.3794	−	44.3601i	1.01336	−	1.64184i
$731$			14.4926i			0.536027i
$732$	−19.7858	+	49.1236i	−0.731304	+	1.81566i
$733$	−27.2740			−1.00739			−0.503695	−	0.863882i	$-0.668026\pi$
$733$	−27.2740			−1.00739			−0.503695	+	0.863882i	$0.668026\pi$
$734$	25.0134	+	4.84816i	0.923262	+	0.178949i
$735$	−2.02150	+	5.34579i	−0.0745643	+	0.197182i
$736$	9.53318	+	13.5372i	0.351398	+	0.498988i
$737$		−	8.50528i		−	0.313296i
$738$	8.66042	−	44.6822i	0.318794	−	1.64478i
$739$		−	20.7791i		−	0.764372i	−0.924085	−	0.382186i	$-0.875171\pi$
$739$		−	20.7791i		−	0.764372i	0.924085	−	0.382186i	$-0.124829\pi$
$740$	−6.30948	+	6.84891i	−0.231941	+	0.251771i
$741$			11.9709i			0.439763i
$742$	−12.7324	−	2.46783i	−0.467421	−	0.0905967i
$743$			15.7586i			0.578128i	0.957310	+	0.289064i	$0.0933441\pi$
$743$			15.7586i			0.578128i	−0.957310	+	0.289064i	$0.906656\pi$
$744$	−41.3016	+	63.8240i	−1.51419	+	2.33990i
$745$	−25.7988	−	9.75580i	−0.945196	−	0.357425i
$746$	0.189674	−	0.978596i	0.00694445	−	0.0358289i
$747$	31.0882			1.13746
$748$	6.84276	+	2.75610i	0.250196	+	0.100773i
$749$		−	7.95978i		−	0.290844i
$750$	−11.7404	−	38.6699i	−0.428699	−	1.41202i
$751$	−33.4985			−1.22238			−0.611189	−	0.791484i	$-0.709309\pi$
$751$	−33.4985			−1.22238			−0.611189	+	0.791484i	$0.709309\pi$
$752$	−28.4610	+	29.5993i	−1.03787	+	1.07938i
$753$		−	16.8726i		−	0.614870i
$754$	−2.11331	−	0.409607i	−0.0769622	−	0.0149170i
$755$	7.23947	−	19.1445i	0.263471	−	0.696740i
$756$	−1.01753	+	2.52630i	−0.0370074	+	0.0918808i
$757$	18.2255			0.662417			0.331209	−	0.943558i	$-0.392544\pi$
$757$	18.2255			0.662417			0.331209	+	0.943558i	$0.392544\pi$
$758$	−32.5374	−	6.30648i	−1.18181	−	0.229062i
$759$	21.9986			0.798500
$760$	12.6711	−	9.33452i	0.459628	−	0.338599i
$761$	16.6248			0.602647			0.301323	−	0.953522i	$-0.402572\pi$
$761$	16.6248			0.602647			0.301323	+	0.953522i	$0.402572\pi$
$762$	−45.1954	−	8.75989i	−1.63726	−	0.317337i
$763$	3.96643			0.143594
$764$	16.4859	+	6.64014i	0.596440	+	0.240232i
$765$	9.26807	+	3.50471i	0.335088	+	0.126713i
$766$	1.01746	+	0.197206i	0.0367622	+	0.00712533i
$767$			18.8348i			0.680086i
$768$	1.60297	+	40.8635i	0.0578423	+	1.47453i
$769$	−32.4549			−1.17035			−0.585176	−	0.810906i	$-0.698975\pi$
$769$	−32.4549			−1.17035			−0.585176	+	0.810906i	$0.698975\pi$
$770$	7.91315	+	4.88407i	0.285170	+	0.176010i
$771$		−	41.5850i		−	1.49765i
$772$	6.74722	−	16.7518i	0.242838	−	0.602910i
$773$	−13.5416			−0.487059			−0.243529	−	0.969894i	$-0.578305\pi$
$773$	−13.5416			−0.487059			−0.243529	+	0.969894i	$0.578305\pi$
$774$	−10.9841	+	56.6709i	−0.394815	+	2.03699i
$775$	39.4232	+	34.7907i	1.41612	+	1.24972i
$776$	−17.4106	−	11.2667i	−0.625006	−	0.404452i
$777$		−	5.32214i		−	0.190931i
$778$	24.1265	+	4.67626i	0.864977	+	0.167652i
$779$		−	22.6691i		−	0.812204i
$780$	−14.5767	+	15.8230i	−0.521931	+	0.566554i
$781$			33.5792i			1.20156i
$782$	−0.987937	+	5.09713i	−0.0353286	+	0.182273i
$783$			1.10129i			0.0393570i
$784$	−2.88333	−	2.77244i	−0.102976	−	0.0990157i
$785$	6.57381	−	17.3842i	0.234629	−	0.620468i
$786$	−15.4081	−	2.98643i	−0.549588	−	0.106523i
$787$	−12.4651			−0.444334			−0.222167	−	0.975009i	$-0.571313\pi$
$787$	−12.4651			−0.444334			−0.222167	+	0.975009i	$0.571313\pi$
$788$	−17.9452	−	7.22790i	−0.639272	−	0.257483i
$789$			31.3299i			1.11538i
$790$	−34.9979	−	21.6010i	−1.24517	−	0.768531i
$791$	2.59272			0.0921866
$792$	24.6687	+	15.9635i	0.876563	+	0.567239i
$793$		−	19.4990i		−	0.692429i
$794$	−3.77359	+	19.4693i	−0.133920	+	0.690940i
$795$	−18.5387	+	49.0247i	−0.657498	+	1.73873i
$796$	8.53074	+	3.43598i	0.302364	+	0.121785i
$797$	40.8982			1.44869			0.724345	−	0.689438i	$-0.242142\pi$
$797$	40.8982			1.44869			0.724345	+	0.689438i	$0.242142\pi$
$798$	−1.71153	+	8.83038i	−0.0605874	+	0.312592i
$799$	−12.8765			−0.455537
$800$	28.1149	+	3.09105i	0.994010	+	0.109285i
$801$	23.4883			0.829919
$802$	7.03214	−	36.2814i	0.248314	−	1.28114i
$803$	48.4751			1.71065
$804$	13.7146	+	5.52393i	0.483678	+	0.194814i
$805$	−2.31491	+	6.12169i	−0.0815899	+	0.215761i
$806$	5.32612	−	27.4794i	0.187605	−	0.967920i
$807$		−	17.4952i		−	0.615861i
$808$	20.5057	+	13.2696i	0.721387	+	0.466822i
$809$	−0.753530			−0.0264927			−0.0132464	−	0.999912i	$-0.504217\pi$
$809$	−0.753530			−0.0264927			−0.0132464	+	0.999912i	$0.504217\pi$
$810$	−19.1539	−	11.8219i	−0.672998	−	0.415380i
$811$			34.2923i			1.20416i	0.798434	+	0.602082i	$0.205662\pi$
$811$			34.2923i			1.20416i	−0.798434	+	0.602082i	$0.794338\pi$
$812$	−1.50032	−	0.604295i	−0.0526511	−	0.0212066i
$813$	32.7671			1.14919
$814$	−8.50124	−	1.64773i	−0.297968	−	0.0577529i
$815$	10.6070	−	28.0499i	0.371548	−	0.982544i
$816$	−8.88834	+	9.24384i	−0.311154	+	0.323599i
$817$			28.7514i			1.00588i
$818$	5.02470	−	25.9243i	0.175685	−	0.906421i
$819$		−	6.64925i		−	0.232344i
$820$	27.6037	−	29.9637i	0.963962	−	1.04638i
$821$		−	12.0734i		−	0.421364i	−0.977555	−	0.210682i	$-0.932431\pi$
$821$		−	12.0734i		−	0.421364i	0.977555	−	0.210682i	$-0.0675685\pi$
$822$	−35.0046	−	6.78467i	−1.22092	−	0.236643i
$823$		−	1.07789i		−	0.0375728i	−0.999824	−	0.0187864i	$-0.994020\pi$
$823$		−	1.07789i		−	0.0375728i	0.999824	−	0.0187864i	$-0.00598024\pi$
$824$	8.10952	+	5.24781i	0.282508	+	0.182816i
$825$	24.8659	−	28.1770i	0.865721	−	0.980997i
$826$	−2.69288	+	13.8935i	−0.0936972	+	0.483418i
$827$	−37.5289			−1.30501			−0.652504	−	0.757786i	$-0.726281\pi$
$827$	−37.5289			−1.30501			−0.652504	+	0.757786i	$0.726281\pi$
$828$	−7.72634	+	19.1827i	−0.268509	+	0.666646i
$829$		−	5.64579i		−	0.196086i	−0.995182	−	0.0980432i	$-0.968742\pi$
$829$		−	5.64579i		−	0.196086i	0.995182	−	0.0980432i	$-0.0312583\pi$
$830$	23.6804	+	14.6158i	0.821959	+	0.507321i
$831$	64.8496			2.24961
$832$	−6.16867	−	13.7356i	−0.213860	−	0.476198i
$833$		−	1.25432i		−	0.0434597i
$834$	64.1514	+	12.4340i	2.22138	+	0.430554i
$835$	−3.28571	−	1.24249i	−0.113707	−	0.0429981i
$836$	13.5752	+	5.46775i	0.469507	+	0.189106i
$837$	−14.3201			−0.494975
$838$	−39.8263	−	7.71924i	−1.37578	−	0.266657i
$839$	5.03287			0.173754			0.0868769	−	0.996219i	$-0.472311\pi$
$839$	5.03287			0.173754			0.0868769	+	0.996219i	$0.472311\pi$
$840$	−13.0148	+	9.58778i	−0.449055	+	0.330810i
$841$	28.3460			0.977447
$842$	−33.4976	−	6.49258i	−1.15440	−	0.223749i
$843$	51.8331			1.78523
$844$	−20.3658	+	50.5635i	−0.701018	+	1.74047i
$845$	−7.48000	+	19.7806i	−0.257320	+	0.680472i
$846$	−50.3515	−	9.75924i	−1.73112	−	0.335530i
$847$		−	2.35280i		−	0.0808431i
$848$	−26.4422	−	25.4253i	−0.908029	−	0.873107i
$849$	1.64492			0.0564534
$850$	5.41195	+	7.02688i	0.185628	+	0.241020i
$851$		−	6.09462i		−	0.208921i
$852$	−54.1459	−	21.8087i	−1.85501	−	0.747153i
$853$	−17.2705			−0.591331			−0.295666	−	0.955291i	$-0.595541\pi$
$853$	−17.2705			−0.591331			−0.295666	+	0.955291i	$0.595541\pi$
$854$	2.78784	−	14.3835i	0.0953979	−	0.492192i
$855$	18.3867	+	6.95290i	0.628811	+	0.237784i
$856$	12.2314	−	18.9013i	0.418059	−	0.646033i
$857$		−	42.2647i		−	1.44374i	−0.692031	−	0.721868i	$-0.743284\pi$
$857$		−	42.2647i		−	1.44374i	0.692031	−	0.721868i	$-0.256716\pi$
$858$	−19.6404	−	3.80674i	−0.670510	−	0.129960i
$859$		−	13.9037i		−	0.474390i	−0.971462	−	0.237195i	$-0.923772\pi$
$859$		−	13.9037i		−	0.474390i	0.971462	−	0.237195i	$-0.0762280\pi$
$860$	−35.0100	+	38.0032i	−1.19383	+	1.29590i
$861$			23.2841i			0.793521i
$862$	0.712541	−	3.67626i	0.0242693	−	0.125214i
$863$			24.9334i			0.848743i	0.905488	+	0.424371i	$0.139505\pi$
$863$			24.9334i			0.848743i	−0.905488	+	0.424371i	$0.860495\pi$
$864$	−6.29827	+	4.43537i	−0.214271	+	0.150894i
$865$	−7.49691	+	19.8253i	−0.254903	+	0.674080i
$866$	−13.3516	−	2.58784i	−0.453705	−	0.0879383i
$867$	39.4295			1.33910
$868$	7.85765	−	19.5087i	0.266706	−	0.662169i
$869$		−	38.2445i		−	1.29736i
$870$	−3.43316	+	5.56239i	−0.116395	+	0.188583i
$871$	−5.44385			−0.184458
$872$	9.41867	+	6.09498i	0.318957	+	0.206402i
$873$		−	25.9025i		−	0.876667i
$874$	−1.95994	+	10.1120i	−0.0662960	+	0.342045i
$875$	5.22434	+	9.88465i	0.176615	+	0.334162i
$876$	−31.4831	+	78.1653i	−1.06372	+	2.64096i
$877$	25.7939			0.870998			0.435499	−	0.900189i	$-0.356572\pi$
$877$	25.7939			0.870998			0.435499	+	0.900189i	$0.356572\pi$
$878$	3.39774	−	17.5302i	0.114668	−	0.591614i
$879$	62.6241			2.11226
$880$	11.2855	+	23.7574i	0.380434	+	0.800862i
$881$	−38.4580			−1.29568			−0.647841	−	0.761776i	$-0.724328\pi$
$881$	−38.4580			−1.29568			−0.647841	+	0.761776i	$0.724328\pi$
$882$	0.950667	−	4.90483i	0.0320106	−	0.165154i
$883$	−7.28866			−0.245283			−0.122641	−	0.992451i	$-0.539137\pi$
$883$	−7.28866			−0.245283			−0.122641	+	0.992451i	$0.539137\pi$
$884$	1.76406	−	4.37975i	0.0593317	−	0.147307i
$885$	53.4955	+	20.2293i	1.79823	+	0.680000i
$886$	−3.25206	+	16.7786i	−0.109255	+	0.563687i
$887$		−	50.2855i		−	1.68842i	−0.536010	−	0.844212i	$-0.680069\pi$
$887$		−	50.2855i		−	1.68842i	0.536010	−	0.844212i	$-0.319931\pi$
$888$	8.17824	−	12.6380i	0.274444	−	0.424102i
$889$	12.7362			0.427157
$890$	17.8915	+	11.0428i	0.599724	+	0.370155i
$891$		−	20.9306i		−	0.701203i
$892$	−7.98199	+	19.8175i	−0.267257	+	0.663537i
$893$	−25.5453			−0.854841
$894$	43.7717	+	8.48394i	1.46394	+	0.283745i
$895$	19.6345	+	7.42475i	0.656307	+	0.248182i
$896$	−2.58650	−	11.0141i	−0.0864088	−	0.367955i
$897$		−	14.0804i		−	0.470129i
$898$	−6.89683	+	35.5832i	−0.230150	+	1.18743i
$899$		−	8.50444i		−	0.283639i
$900$	15.8368	+	31.5793i	0.527894	+	1.05264i
$901$		−	11.5030i		−	0.383222i
$902$	37.1925	+	7.20874i	1.23837	+	0.240025i
$903$		−	29.5315i		−	0.982746i
$904$	6.15668	+	3.98409i	0.204768	+	0.132509i
$905$	−15.6481	−	5.91733i	−0.520162	−	0.196699i
$906$	−6.29567	+	32.4816i	−0.209159	+	1.07913i
$907$	−38.3879			−1.27465			−0.637324	−	0.770596i	$-0.719959\pi$
$907$	−38.3879			−1.27465			−0.637324	+	0.770596i	$0.719959\pi$
$908$	28.7035	+	11.5611i	0.952559	+	0.383668i
$909$			30.5071i			1.01186i
$910$	3.12607	−	5.06485i	0.103628	−	0.167898i
$911$	−14.7552			−0.488862			−0.244431	−	0.969667i	$-0.578601\pi$
$911$	−14.7552			−0.488862			−0.244431	+	0.969667i	$0.578601\pi$
$912$	−17.6333	+	18.3386i	−0.583898	+	0.607252i
$913$			25.8771i			0.856407i
$914$	−2.00989	−	0.389562i	−0.0664813	−	0.0128856i
$915$	−55.3820	−	20.9426i	−1.83087	−	0.692342i
$916$	4.93679	−	12.2569i	0.163116	−	0.404980i
$917$	4.34203			0.143386
$918$	−2.37147	−	0.459644i	−0.0782702	−	0.0151705i
$919$	30.3228			1.00026			0.500129	−	0.865951i	$-0.333286\pi$
$919$	30.3228			1.00026			0.500129	+	0.865951i	$0.333286\pi$
$920$	−14.9039	+	10.9794i	−0.491365	+	0.361979i
$921$	−24.3800			−0.803348
$922$	56.7386	+	10.9972i	1.86859	+	0.362174i
$923$	21.4925			0.707436
$924$	−13.9435	−	5.61610i	−0.458707	−	0.184756i
$925$	−7.80630	−	6.88899i	−0.256669	−	0.226509i
$926$	−2.18486	−	0.423475i	−0.0717990	−	0.0139163i
$927$			12.0648i			0.396262i
$928$	−2.63409	−	3.74042i	−0.0864681	−	0.122785i
$929$	−10.3022			−0.338004			−0.169002	−	0.985616i	$-0.554054\pi$
$929$	−10.3022			−0.338004			−0.169002	+	0.985616i	$0.554054\pi$
$930$	−72.3278	−	44.6414i	−2.37172	−	1.46385i
$931$		−	2.48842i		−	0.0815546i
$932$	−8.81577	+	21.8875i	−0.288770	+	0.716950i
$933$	2.50192			0.0819090
$934$	2.18537	−	11.2751i	0.0715076	−	0.368933i
$935$	−2.91724	+	7.71453i	−0.0954041	+	0.252292i
$936$	10.2175	−	15.7893i	0.333970	−	0.516090i
$937$			3.63881i			0.118875i	0.998232	+	0.0594374i	$0.0189307\pi$
$937$			3.63881i			0.118875i	−0.998232	+	0.0594374i	$0.981069\pi$
$938$	−4.01567	−	0.778326i	−0.131116	−	0.0254133i
$939$		−	68.3814i		−	2.23154i
$940$	−33.7654	−	31.1060i	−1.10131	−	1.01457i
$941$		−	12.2350i		−	0.398851i	−0.979913	−	0.199426i	$-0.936092\pi$
$941$		−	12.2350i		−	0.398851i	0.979913	−	0.199426i	$-0.0639076\pi$
$942$	−5.71678	+	29.4950i	−0.186263	+	0.960997i
$943$			26.6636i			0.868288i
$944$	−27.7439	+	28.8536i	−0.902988	+	0.939104i
$945$	−2.84816	−	1.07703i	−0.0926505	−	0.0350357i
$946$	−47.1716	−	9.14292i	−1.53368	−	0.297262i
$947$	−18.5100			−0.601496			−0.300748	−	0.953704i	$-0.597236\pi$
$947$	−18.5100			−0.601496			−0.300748	+	0.953704i	$0.597236\pi$
$948$	61.6686	+	24.8387i	2.00290	+	0.806722i
$949$		−	31.0267i		−	1.00717i
$950$	10.7366	+	13.9404i	0.348342	+	0.452288i
$951$	−54.0011			−1.75110
$952$	1.92745	−	2.97852i	0.0624690	−	0.0965342i
$953$			56.4219i			1.82769i	0.406069	+	0.913843i	$0.366899\pi$
$953$			56.4219i			1.82769i	−0.406069	+	0.913843i	$0.633101\pi$
$954$	8.71830	−	44.9808i	0.282265	−	1.45631i
$955$	−7.02838	+	18.5863i	−0.227433	+	0.601437i
$956$	18.8906	+	7.60868i	0.610966	+	0.246082i
$957$	−6.07838			−0.196486
$958$	−6.72177	+	34.6800i	−0.217170	+	1.12046i
$959$	9.86435			0.318537
$960$	−45.6380	+	2.76796i	−1.47296	+	0.0893355i
$961$	79.5832			2.56720
$962$	−1.05464	+	5.44126i	−0.0340029	+	0.175433i
$963$	28.1202			0.906161
$964$	5.55362	+	2.23686i	0.178870	+	0.0720446i
$965$	18.8860	+	7.14171i	0.607961	+	0.229900i
$966$	2.01312	−	10.3864i	0.0647710	−	0.334177i
$967$		−	14.5778i		−	0.468790i	−0.972141	−	0.234395i	$-0.924689\pi$
$967$		−	14.5778i		−	0.468790i	0.972141	−	0.234395i	$-0.0753109\pi$
$968$	3.61541	−	5.58695i	0.116204	−	0.179572i
$969$	−7.97778			−0.256283
$970$	12.1778	−	19.7304i	0.391005	−	0.633505i
$971$			44.2799i			1.42101i	0.703692	+	0.710505i	$0.251533\pi$
$971$			44.2799i			1.42101i	−0.703692	+	0.710505i	$0.748467\pi$
$972$	41.3293	+	16.6464i	1.32564	+	0.533935i
$973$	−18.0780			−0.579554
$974$	25.4101	+	4.92506i	0.814194	+	0.157809i
$975$	−18.0348	−	15.9156i	−0.577577	−	0.509707i
$976$	28.7223	−	29.8711i	0.919378	−	0.956150i
$977$		−	29.7021i		−	0.950253i	−0.879917	−	0.475127i	$-0.842402\pi$
$977$		−	29.7021i		−	0.950253i	0.879917	−	0.475127i	$-0.157598\pi$
$978$	−9.22420	+	47.5910i	−0.294957	+	1.52179i
$979$			19.5512i			0.624858i
$980$	3.03009	−	3.28915i	0.0967928	−	0.105068i
$981$			14.0125i			0.447386i
$982$	41.1217	+	7.97031i	1.31225	+	0.254343i
$983$			47.8429i			1.52595i	0.646427	+	0.762976i	$0.276263\pi$
$983$			47.8429i			1.52595i	−0.646427	+	0.762976i	$0.723737\pi$
$984$	−35.7794	+	55.2905i	−1.14061	+	1.76260i
$985$	7.65050	−	20.2314i	0.243765	−	0.644627i
$986$	0.272974	−	1.40837i	0.00869327	−	0.0448517i
$987$	26.2384			0.835177
$988$	3.49967	−	8.68886i	0.111339	−	0.276430i
$989$		−	33.8178i		−	1.07534i
$990$	−17.2544	+	27.9555i	−0.548379	+	0.888483i
$991$	−31.1700			−0.990149			−0.495074	−	0.868851i	$-0.664859\pi$
$991$	−31.1700			−0.990149			−0.495074	+	0.868851i	$0.664859\pi$
$992$	48.6367	−	34.2510i	1.54422	−	1.08747i
$993$			4.30866i			0.136731i
$994$	15.8540	+	3.07286i	0.502859	+	0.0974653i
$995$	−3.63687	+	9.61757i	−0.115297	+	0.304897i
$996$	−41.7264	−	16.8064i	−1.32215	−	0.532531i
$997$	29.8134			0.944201			0.472101	−	0.881545i	$-0.343496\pi$
$997$	29.8134			0.944201			0.472101	+	0.881545i	$0.343496\pi$
$998$	−57.6184	−	11.1677i	−1.82388	−	0.353509i
$999$	2.83556			0.0897131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.l.a.29.16	yes	36
4.3	odd	2		1120.2.l.a.1009.6		36
5.4	even	2	inner	280.2.l.a.29.21	yes	36
8.3	odd	2		1120.2.l.a.1009.31		36
8.5	even	2	inner	280.2.l.a.29.22	yes	36
20.19	odd	2		1120.2.l.a.1009.32		36
40.19	odd	2		1120.2.l.a.1009.5		36
40.29	even	2	inner	280.2.l.a.29.15	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.l.a.29.15	✓	36	40.29	even	2	inner
280.2.l.a.29.16	yes	36	1.1	even	1	trivial
280.2.l.a.29.21	yes	36	5.4	even	2	inner
280.2.l.a.29.22	yes	36	8.5	even	2	inner
1120.2.l.a.1009.5		36	40.19	odd	2
1120.2.l.a.1009.6		36	4.3	odd	2
1120.2.l.a.1009.31		36	8.3	odd	2
1120.2.l.a.1009.32		36	20.19	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.269098 + 1.38838i) q^{2} +2.55593 q^{3} +(-1.85517 - 0.747219i) q^{4} +(0.790907 - 2.09152i) q^{5} +(-0.687797 + 3.54859i) q^{6} -1.00000i q^{7} +(1.53664 - 2.37460i) q^{8} +3.53279 q^{9} +O(q^{10})\)	\(q+(-0.269098 + 1.38838i) q^{2} +2.55593 q^{3} +(-1.85517 - 0.747219i) q^{4} +(0.790907 - 2.09152i) q^{5} +(-0.687797 + 3.54859i) q^{6} -1.00000i q^{7} +(1.53664 - 2.37460i) q^{8} +3.53279 q^{9} +(2.69099 + 1.66090i) q^{10} +2.94061i q^{11} +(-4.74169 - 1.90984i) q^{12} +1.88215 q^{13} +(1.38838 + 0.269098i) q^{14} +(2.02150 - 5.34579i) q^{15} +(2.88333 + 2.77244i) q^{16} +1.25432i q^{17} +(-0.950667 + 4.90483i) q^{18} +2.48842i q^{19} +(-3.03009 + 3.28915i) q^{20} -2.55593i q^{21} +(-4.08267 - 0.791314i) q^{22} -2.92691i q^{23} +(3.92756 - 6.06931i) q^{24} +(-3.74893 - 3.30840i) q^{25} +(-0.506485 + 2.61314i) q^{26} +1.36176 q^{27} +(-0.747219 + 1.85517i) q^{28} +0.808725i q^{29} +(6.87798 + 4.24515i) q^{30} -10.5159 q^{31} +(-4.62509 + 3.25708i) q^{32} +7.51600i q^{33} +(-1.74147 - 0.337536i) q^{34} +(-2.09152 - 0.790907i) q^{35} +(-6.55392 - 2.63976i) q^{36} +2.08227 q^{37} +(-3.45486 - 0.669629i) q^{38} +4.81066 q^{39} +(-3.75119 - 5.09201i) q^{40} -9.10984 q^{41} +(3.54859 + 0.687797i) q^{42} +11.5541 q^{43} +(2.19728 - 5.45534i) q^{44} +(2.79410 - 7.38890i) q^{45} +(4.06365 + 0.787626i) q^{46} +10.2657i q^{47} +(7.36959 + 7.08617i) q^{48} -1.00000 q^{49} +(5.60213 - 4.31464i) q^{50} +3.20596i q^{51} +(-3.49172 - 1.40638i) q^{52} -9.17072 q^{53} +(-0.366448 + 1.89064i) q^{54} +(6.15036 + 2.32575i) q^{55} +(-2.37460 - 1.53664i) q^{56} +6.36023i q^{57} +(-1.12281 - 0.217627i) q^{58} +10.0070i q^{59} +(-7.74471 + 8.40685i) q^{60} -10.3599i q^{61} +(2.82980 - 14.6000i) q^{62} -3.53279i q^{63} +(-3.27745 - 7.29783i) q^{64} +(1.48861 - 3.93657i) q^{65} +(-10.4350 - 2.02254i) q^{66} -2.89235 q^{67} +(0.937254 - 2.32699i) q^{68} -7.48097i q^{69} +(1.66090 - 2.69099i) q^{70} +11.4191 q^{71} +(5.42863 - 8.38895i) q^{72} -16.4847i q^{73} +(-0.560336 + 2.89098i) q^{74} +(-9.58201 - 8.45604i) q^{75} +(1.85939 - 4.61644i) q^{76} +2.94061 q^{77} +(-1.29454 + 6.67900i) q^{78} -13.0056 q^{79} +(8.07906 - 3.83780i) q^{80} -7.11778 q^{81} +(2.45144 - 12.6479i) q^{82} +8.79990 q^{83} +(-1.90984 + 4.74169i) q^{84} +(2.62344 + 0.992053i) q^{85} +(-3.10919 + 16.0414i) q^{86} +2.06705i q^{87} +(6.98278 + 4.51867i) q^{88} +6.64867 q^{89} +(9.50668 + 5.86761i) q^{90} -1.88215i q^{91} +(-2.18704 + 5.42992i) q^{92} -26.8778 q^{93} +(-14.2526 - 2.76248i) q^{94} +(5.20458 + 1.96811i) q^{95} +(-11.8214 + 8.32488i) q^{96} -7.33203i q^{97} +(0.269098 - 1.38838i) q^{98} +10.3886i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Introduction

L-functions

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