LMFDB - Embedded newform 336.2.bo.a.173.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

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

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			173.32
Character	$\chi$	$=$	336.173
Dual form			336.2.bo.a.101.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.135895 - 1.40767i) q^{2} +(1.44089 + 0.961162i) q^{3} +(-1.96307 - 0.382590i) q^{4} +(0.495078 + 1.84766i) q^{5} +(1.54881 - 1.89768i) q^{6} +(2.64062 - 0.164729i) q^{7} +(-0.805330 + 2.71135i) q^{8} +(1.15234 + 2.76986i) q^{9} +O(q^{10})$	\(q+(0.135895 - 1.40767i) q^{2} +(1.44089 + 0.961162i) q^{3} +(-1.96307 - 0.382590i) q^{4} +(0.495078 + 1.84766i) q^{5} +(1.54881 - 1.89768i) q^{6} +(2.64062 - 0.164729i) q^{7} +(-0.805330 + 2.71135i) q^{8} +(1.15234 + 2.76986i) q^{9} +(2.66817 - 0.445819i) q^{10} +(-0.781622 + 2.91705i) q^{11} +(-2.46083 - 2.43809i) q^{12} +(-1.32862 + 1.32862i) q^{13} +(0.126963 - 3.73950i) q^{14} +(-1.06254 + 3.13812i) q^{15} +(3.70725 + 1.50210i) q^{16} +(-1.97936 - 3.42835i) q^{17} +(4.05564 - 1.24570i) q^{18} +(-0.595421 - 2.22214i) q^{19} +(-0.264976 - 3.81648i) q^{20} +(3.96318 + 2.30071i) q^{21} +(4.00003 + 1.49668i) q^{22} +(3.20186 - 5.54578i) q^{23} +(-3.76644 + 3.13271i) q^{24} +(1.16140 - 0.670533i) q^{25} +(1.68970 + 2.05081i) q^{26} +(-1.00189 + 5.09865i) q^{27} +(-5.24673 - 0.686901i) q^{28} +(3.37288 - 3.37288i) q^{29} +(4.27304 + 1.92216i) q^{30} +(-0.517256 + 0.298638i) q^{31} +(2.61825 - 5.01445i) q^{32} +(-3.92999 + 3.45189i) q^{33} +(-5.09497 + 2.32039i) q^{34} +(1.61167 + 4.79740i) q^{35} +(-1.20239 - 5.87829i) q^{36} +(-2.37621 - 8.86814i) q^{37} +(-3.20895 + 0.536178i) q^{38} +(-3.19141 + 0.637378i) q^{39} +(-5.40835 - 0.145642i) q^{40} +1.57438i q^{41} +(3.77721 - 5.26619i) q^{42} +(-9.17974 + 9.17974i) q^{43} +(2.65041 - 5.42733i) q^{44} +(-4.54725 + 3.50042i) q^{45} +(-7.37151 - 5.26080i) q^{46} +(0.138984 - 0.240727i) q^{47} +(3.89799 + 5.72763i) q^{48} +(6.94573 - 0.869970i) q^{49} +(-0.786061 - 1.72599i) q^{50} +(0.443158 - 6.84237i) q^{51} +(3.11648 - 2.09985i) q^{52} +(0.638126 - 2.38152i) q^{53} +(7.04106 + 2.10321i) q^{54} -5.77668 q^{55} +(-1.67993 + 7.29231i) q^{56} +(1.27790 - 3.77416i) q^{57} +(-4.28954 - 5.20625i) q^{58} +(-11.6322 - 3.11683i) q^{59} +(3.28645 - 5.75382i) q^{60} +(-0.203540 - 0.759622i) q^{61} +(0.350091 + 0.768709i) q^{62} +(3.49916 + 7.12432i) q^{63} +(-6.70289 - 4.36707i) q^{64} +(-3.11260 - 1.79706i) q^{65} +(4.32506 + 6.00123i) q^{66} +(-1.82956 + 6.82801i) q^{67} +(2.57396 + 7.48736i) q^{68} +(9.94392 - 4.91337i) q^{69} +(6.97217 - 1.61676i) q^{70} +12.7692 q^{71} +(-8.43808 + 0.893741i) q^{72} +(-6.33536 - 10.9732i) q^{73} +(-12.8063 + 2.13978i) q^{74} +(2.31794 + 0.150125i) q^{75} +(0.318681 + 4.59001i) q^{76} +(-1.58344 + 7.83158i) q^{77} +(0.463521 + 4.57907i) q^{78} +(-1.42550 + 2.46903i) q^{79} +(-0.939982 + 7.59338i) q^{80} +(-6.34424 + 6.38362i) q^{81} +(2.21620 + 0.213950i) q^{82} +(9.60276 + 9.60276i) q^{83} +(-6.89974 - 6.03270i) q^{84} +(5.35448 - 5.35448i) q^{85} +(11.6746 + 14.1695i) q^{86} +(8.10183 - 1.61807i) q^{87} +(-7.27970 - 4.46845i) q^{88} +(-10.9145 - 6.30150i) q^{89} +(4.30948 + 6.87671i) q^{90} +(-3.28951 + 3.72724i) q^{91} +(-8.40722 + 9.66173i) q^{92} +(-1.03235 - 0.0668618i) q^{93} +(-0.319976 - 0.228356i) q^{94} +(3.81097 - 2.20027i) q^{95} +(8.59232 - 4.70872i) q^{96} +4.81796i q^{97} +(-0.280742 - 9.89551i) q^{98} +(-8.98052 + 1.19644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.135895	−	1.40767i	0.0960921	−	0.995372i
$2$	0.135895	−	1.40767i	0.0960921	−	0.995372i
$3$	1.44089	+	0.961162i	0.831899	+	0.554927i
$3$	1.44089	+	0.961162i	0.831899	+	0.554927i
$4$	−1.96307	−	0.382590i	−0.981533	−	0.191295i
$5$	0.495078	+	1.84766i	0.221406	+	0.826297i	0.983813	+	0.179199i	$0.0573507\pi$
$5$	0.495078	+	1.84766i	0.221406	+	0.826297i	−0.762407	+	0.647097i	$0.775983\pi$
$6$	1.54881	−	1.89768i	0.632298	−	0.774725i
$7$	2.64062	−	0.164729i	0.998060	−	0.0622615i
$7$	2.64062	−	0.164729i	0.998060	−	0.0622615i
$8$	−0.805330	+	2.71135i	−0.284727	+	0.958609i
$9$	1.15234	+	2.76986i	0.384112	+	0.923286i
$10$	2.66817	−	0.445819i	0.843748	−	0.140980i
$11$	−0.781622	+	2.91705i	−0.235668	+	0.879525i	0.742179	+	0.670202i	$0.233793\pi$
$11$	−0.781622	+	2.91705i	−0.235668	+	0.879525i	−0.977847	+	0.209323i	$0.932874\pi$
$12$	−2.46083	−	2.43809i	−0.710381	−	0.703817i
$13$	−1.32862	+	1.32862i	−0.368492	+	0.368492i	−0.866927	−	0.498435i	$-0.833908\pi$
$13$	−1.32862	+	1.32862i	−0.368492	+	0.368492i	0.498435	+	0.866927i	$0.333908\pi$
$14$	0.126963	−	3.73950i	0.0339323	−	0.999424i
$15$	−1.06254	+	3.13812i	−0.274347	+	0.810259i
$16$	3.70725	+	1.50210i	0.926812	+	0.375524i
$17$	−1.97936	−	3.42835i	−0.480065	−	0.831498i	0.519673	−	0.854365i	$-0.326054\pi$
$17$	−1.97936	−	3.42835i	−0.480065	−	0.831498i	−0.999739	+	0.0228674i	$0.992720\pi$
$18$	4.05564	−	1.24570i	0.955924	−	0.293614i
$19$	−0.595421	−	2.22214i	−0.136599	−	0.509794i	−0.999986	−	0.00525229i	$-0.998328\pi$
$19$	−0.595421	−	2.22214i	−0.136599	−	0.509794i	0.863387	−	0.504542i	$-0.168339\pi$
$20$	−0.264976	−	3.81648i	−0.0592504	−	0.853391i
$21$	3.96318	+	2.30071i	0.864836	+	0.502055i
$22$	4.00003	+	1.49668i	0.852809	+	0.319093i
$23$	3.20186	−	5.54578i	0.667634	−	1.15638i	−0.310931	−	0.950433i	$-0.600641\pi$
$23$	3.20186	−	5.54578i	0.667634	−	1.15638i	0.978564	−	0.205943i	$-0.0660260\pi$
$24$	−3.76644	+	3.13271i	−0.768822	+	0.639463i
$25$	1.16140	−	0.670533i	0.232280	−	0.134107i
$26$	1.68970	+	2.05081i	0.331378	+	0.402196i
$27$	−1.00189	+	5.09865i	−0.192814	+	0.981235i
$28$	−5.24673	−	0.686901i	−0.991539	−	0.129812i
$29$	3.37288	−	3.37288i	0.626328	−	0.626328i	−0.320814	−	0.947142i	$-0.603957\pi$
$29$	3.37288	−	3.37288i	0.626328	−	0.626328i	0.947142	+	0.320814i	$0.103957\pi$
$30$	4.27304	+	1.92216i	0.780147	+	0.350937i
$31$	−0.517256	+	0.298638i	−0.0929019	+	0.0536369i	−0.545731	−	0.837960i	$-0.683748\pi$
$31$	−0.517256	+	0.298638i	−0.0929019	+	0.0536369i	0.452829	+	0.891597i	$0.350415\pi$
$32$	2.61825	−	5.01445i	0.462846	−	0.886439i
$33$	−3.92999	+	3.45189i	−0.684124	+	0.600898i
$34$	−5.09497	+	2.32039i	−0.873781	+	0.397944i
$35$	1.61167	+	4.79740i	0.272422	+	0.810909i
$36$	−1.20239	−	5.87829i	−0.200399	−	0.979714i
$37$	−2.37621	−	8.86814i	−0.390647	−	1.45791i	−0.829070	−	0.559144i	$-0.811130\pi$
$37$	−2.37621	−	8.86814i	−0.390647	−	1.45791i	0.438424	−	0.898768i	$-0.355537\pi$
$38$	−3.20895	+	0.536178i	−0.520561	+	0.0869796i
$39$	−3.19141	+	0.637378i	−0.511035	+	0.102062i
$40$	−5.40835	−	0.145642i	−0.855135	−	0.0230280i
$41$			1.57438i			0.245876i	0.992414	+	0.122938i	$0.0392317\pi$
$41$			1.57438i			0.245876i	−0.992414	+	0.122938i	$0.960768\pi$
$42$	3.77721	−	5.26619i	0.582836	−	0.812590i
$43$	−9.17974	+	9.17974i	−1.39990	+	1.39990i	−0.599592	+	0.800306i	$0.704671\pi$
$43$	−9.17974	+	9.17974i	−1.39990	+	1.39990i	−0.800306	+	0.599592i	$0.795329\pi$
$44$	2.65041	−	5.42733i	0.399565	−	0.818200i
$45$	−4.54725	+	3.50042i	−0.677864	+	0.521811i
$46$	−7.37151	−	5.26080i	−1.08687	−	0.775663i
$47$	0.138984	−	0.240727i	0.0202728	−	0.0351136i	−0.855711	−	0.517454i	$-0.826880\pi$
$47$	0.138984	−	0.240727i	0.0202728	−	0.0351136i	0.875984	+	0.482340i	$0.160213\pi$
$48$	3.89799	+	5.72763i	0.562626	+	0.826712i
$49$	6.94573	−	0.869970i	0.992247	−	0.124281i
$50$	−0.786061	−	1.72599i	−0.111166	−	0.244091i
$51$	0.443158	−	6.84237i	0.0620545	−	0.958124i
$52$	3.11648	−	2.09985i	0.432178	−	0.291197i
$53$	0.638126	−	2.38152i	0.0876534	−	0.327127i	−0.908150	−	0.418645i	$-0.862505\pi$
$53$	0.638126	−	2.38152i	0.0876534	−	0.327127i	0.995803	+	0.0915179i	$0.0291719\pi$
$54$	7.04106	+	2.10321i	0.958167	+	0.286211i
$55$	−5.77668			−0.778927
$56$	−1.67993	+	7.29231i	−0.224490	+	0.974476i
$57$	1.27790	−	3.77416i	0.169262	−	0.499900i
$58$	−4.28954	−	5.20625i	−0.563244	−	0.683614i
$59$	−11.6322	−	3.11683i	−1.51438	−	0.405776i	−0.596492	−	0.802619i	$-0.703439\pi$
$59$	−11.6322	−	3.11683i	−1.51438	−	0.405776i	−0.917887	+	0.396843i	$0.870106\pi$
$60$	3.28645	−	5.75382i	0.424279	−	0.742815i
$61$	−0.203540	−	0.759622i	−0.0260606	−	0.0972596i	0.951671	−	0.307121i	$-0.0993655\pi$
$61$	−0.203540	−	0.759622i	−0.0260606	−	0.0972596i	−0.977731	+	0.209861i	$0.932699\pi$
$62$	0.350091	+	0.768709i	0.0444616	+	0.0976261i
$63$	3.49916	+	7.12432i	0.440852	+	0.897580i
$64$	−6.70289	−	4.36707i	−0.837861	−	0.545884i
$65$	−3.11260	−	1.79706i	−0.386070	−	0.222898i
$66$	4.32506	+	6.00123i	0.532378	+	0.738700i
$67$	−1.82956	+	6.82801i	−0.223516	+	0.834174i	0.759477	+	0.650534i	$0.225455\pi$
$67$	−1.82956	+	6.82801i	−0.223516	+	0.834174i	−0.982994	+	0.183640i	$0.941212\pi$
$68$	2.57396	+	7.48736i	0.312139	+	0.907976i
$69$	9.94392	−	4.91337i	1.19711	−	0.591500i
$70$	6.97217	−	1.61676i	0.833334	−	0.193240i
$71$	12.7692			1.51542			0.757710	−	0.652592i	$-0.226318\pi$
$71$	12.7692			1.51542			0.757710	+	0.652592i	$0.226318\pi$
$72$	−8.43808	+	0.893741i	−0.994437	+	0.105328i
$73$	−6.33536	−	10.9732i	−0.741498	−	1.28431i	−0.951813	−	0.306679i	$-0.900782\pi$
$73$	−6.33536	−	10.9732i	−0.741498	−	1.28431i	0.210315	−	0.977634i	$-0.432551\pi$
$74$	−12.8063	+	2.13978i	−1.48870	+	0.248745i
$75$	2.31794	+	0.150125i	0.267653	+	0.0173350i
$76$	0.318681	+	4.59001i	0.0365553	+	0.526510i
$77$	−1.58344	+	7.83158i	−0.180450	+	0.892492i
$78$	0.463521	+	4.57907i	0.0524834	+	0.518477i
$79$	−1.42550	+	2.46903i	−0.160381	+	0.277788i	−0.935005	−	0.354634i	$-0.884606\pi$
$79$	−1.42550	+	2.46903i	−0.160381	+	0.277788i	0.774624	+	0.632421i	$0.217939\pi$
$80$	−0.939982	+	7.59338i	−0.105093	+	0.848965i
$81$	−6.34424	+	6.38362i	−0.704916	+	0.709291i
$82$	2.21620	+	0.213950i	0.244738	+	0.0236268i
$83$	9.60276	+	9.60276i	1.05404	+	1.05404i	0.998454	+	0.0555860i	$0.0177027\pi$
$83$	9.60276	+	9.60276i	1.05404	+	1.05404i	0.0555860	+	0.998454i	$0.482297\pi$
$84$	−6.89974	−	6.03270i	−0.752824	−	0.658222i
$85$	5.35448	−	5.35448i	0.580775	−	0.580775i
$86$	11.6746	+	14.1695i	1.25890	+	1.52794i
$87$	8.10183	−	1.61807i	0.868607	−	0.173475i
$88$	−7.27970	−	4.46845i	−0.776019	−	0.476338i
$89$	−10.9145	−	6.30150i	−1.15694	−	0.667958i	−0.206369	−	0.978474i	$-0.566165\pi$
$89$	−10.9145	−	6.30150i	−1.15694	−	0.667958i	−0.950568	+	0.310516i	$0.899498\pi$
$90$	4.30948	+	6.87671i	0.454259	+	0.724869i
$91$	−3.28951	+	3.72724i	−0.344835	+	0.390720i
$92$	−8.40722	+	9.66173i	−0.876513	+	1.00731i
$93$	−1.03235	−	0.0668618i	−0.107050	−	0.00693325i
$94$	−0.319976	−	0.228356i	−0.0330030	−	0.0235532i
$95$	3.81097	−	2.20027i	0.390997	−	0.225742i
$96$	8.59232	−	4.70872i	0.876950	−	0.480582i
$97$			4.81796i			0.489190i	0.969625	+	0.244595i	$0.0786550\pi$
$97$			4.81796i			0.489190i	−0.969625	+	0.244595i	$0.921345\pi$
$98$	−0.280742	−	9.89551i	−0.0283592	−	0.999598i
$99$	−8.98052	+	1.19644i	−0.902576	+	0.120247i
$100$	−2.53644	+	0.871962i	−0.253644	+	0.0871962i
$101$	−1.37795	−	0.369220i	−0.137111	−	0.0367388i	0.189611	−	0.981859i	$-0.439277\pi$
$101$	−1.37795	−	0.369220i	−0.137111	−	0.0367388i	−0.326722	+	0.945121i	$0.605944\pi$
$102$	−9.57157	−	1.55366i	−0.947727	−	0.153835i
$103$	−5.26506	+	9.11935i	−0.518782	+	0.898556i	0.480980	+	0.876732i	$0.340281\pi$
$103$	−5.26506	+	9.11935i	−0.518782	+	0.898556i	−0.999762	+	0.0218249i	$0.993052\pi$
$104$	−2.53238	−	4.67233i	−0.248320	−	0.458160i
$105$	−2.28883	+	8.46161i	−0.223367	+	0.825769i
$106$	−3.26567	−	1.22191i	−0.317190	−	0.118682i
$107$	3.93611	−	1.05468i	0.380518	−	0.101960i	−0.0634896	−	0.997983i	$-0.520223\pi$
$107$	3.93611	−	1.05468i	0.380518	−	0.101960i	0.444008	+	0.896023i	$0.353556\pi$
$108$	3.91747	−	9.62567i	0.376959	−	0.926230i
$109$	4.27381	−	15.9501i	0.409356	−	1.52774i	−0.386521	−	0.922281i	$-0.626323\pi$
$109$	4.27381	−	15.9501i	0.409356	−	1.52774i	0.795877	−	0.605458i	$-0.207010\pi$
$110$	−0.785020	+	8.13165i	−0.0748487	+	0.775322i
$111$	5.09985	−	15.0619i	0.484057	−	1.42962i
$112$	10.0369	+	3.35578i	0.948395	+	0.317091i
$113$		−	6.91772i		−	0.650765i	−0.945583	−	0.325382i	$-0.894507\pi$
$113$		−	6.91772i		−	0.650765i	0.945583	−	0.325382i	$-0.105493\pi$
$114$	−5.13911	−	2.31175i	−0.481322	−	0.216515i
$115$	11.8319	+	3.17034i	1.10333	+	0.295636i
$116$	−7.91161	+	5.33075i	−0.734574	+	0.494948i
$117$	−5.21110	−	2.14907i	−0.481766	−	0.198682i
$118$	−5.96821	+	15.9507i	−0.549419	+	1.46838i
$119$	−5.79148	−	8.72692i	−0.530904	−	0.799995i
$120$	−7.65286	−	5.40815i	−0.698607	−	0.493695i
$121$	1.62801	+	0.939930i	0.148001	+	0.0854482i
$122$	−1.09696	+	0.183288i	−0.0993138	+	0.0165942i
$123$	−1.51323	+	2.26850i	−0.136443	+	0.204544i
$124$	1.12966	−	0.388349i	0.101447	−	0.0348747i
$125$	8.57679	+	8.57679i	0.767131	+	0.767131i
$126$	10.5042	−	3.95750i	0.935789	−	0.352562i
$127$	−15.8387			−1.40545			−0.702727	−	0.711459i	$-0.748035\pi$
$127$	−15.8387			−1.40545			−0.702727	+	0.711459i	$0.748035\pi$
$128$	−7.05828	+	8.84198i	−0.623870	+	0.781528i
$129$	−22.0502	+	4.40380i	−1.94141	+	0.387733i
$130$	−2.95265	+	4.13730i	−0.258965	+	0.362865i
$131$	−0.988744	+	0.264933i	−0.0863870	+	0.0231473i	−0.301754	−	0.953386i	$-0.597572\pi$
$131$	−0.988744	+	0.264933i	−0.0863870	+	0.0231473i	0.215367	+	0.976533i	$0.430905\pi$
$132$	9.03549	−	5.27272i	0.786439	−	0.458931i
$133$	−1.93833	−	5.76974i	−0.168074	−	0.500300i
$134$	9.36295	+	3.50331i	0.808836	+	0.302639i
$135$	−9.91656	+	0.673079i	−0.853482	+	0.0579294i
$136$	10.8895	−	2.60579i	0.933769	−	0.223445i
$137$	−0.161917	−	0.280448i	−0.0138335	−	0.0239603i	0.859026	−	0.511932i	$-0.171070\pi$
$137$	−0.161917	−	0.280448i	−0.0138335	−	0.0239603i	−0.872859	+	0.487972i	$0.837737\pi$
$138$	−5.56507	−	14.6655i	−0.473730	−	1.24841i
$139$	6.37163	+	6.37163i	0.540435	+	0.540435i	0.923656	−	0.383222i	$-0.125186\pi$
$139$	6.37163	+	6.37163i	0.540435	+	0.540435i	−0.383222	+	0.923656i	$0.625186\pi$
$140$	−1.32838	−	10.0342i	−0.112269	−	0.848046i
$141$	0.431637	−	0.213275i	0.0363504	−	0.0179610i
$142$	1.73526	−	17.9747i	0.145620	−	1.50841i
$143$	−2.83717	−	4.91413i	−0.237256	−	0.410940i
$144$	0.111400	+	11.9995i	0.00928334	+	0.999957i
$145$	7.90175	+	4.56208i	0.656205	+	0.378860i
$146$	−16.3075	+	7.42690i	−1.34962	+	0.614654i
$147$	10.8442	+	5.42244i	0.894417	+	0.447235i
$148$	1.27180	+	18.3178i	0.104541	+	1.50572i
$149$	9.16037	−	2.45451i	0.750447	−	0.201082i	0.136731	−	0.990608i	$-0.456341\pi$
$149$	9.16037	−	2.45451i	0.750447	−	0.201082i	0.613716	+	0.789527i	$0.289674\pi$
$150$	0.526323	−	3.24249i	0.0429741	−	0.264748i
$151$	9.24406	−	5.33706i	0.752271	−	0.434324i	−0.0742427	−	0.997240i	$-0.523654\pi$
$151$	9.24406	−	5.33706i	0.752271	−	0.434324i	0.826514	+	0.562916i	$0.190321\pi$
$152$	6.50452	+	0.175161i	0.527586	+	0.0142074i
$153$	7.21517	−	9.43317i	0.583312	−	0.762626i
$154$	10.8091	+	3.29324i	0.871022	+	0.265377i
$155$	−0.807862	−	0.807862i	−0.0648890	−	0.0648890i
$156$	6.50880	−	0.0302124i	0.521121	−	0.00241893i
$157$	16.8045	+	4.50275i	1.34115	+	0.359359i	0.856859	−	0.515551i	$-0.172413\pi$
$157$	16.8045	+	4.50275i	1.34115	+	0.359359i	0.484286	+	0.874910i	$0.339079\pi$
$158$	3.28186	+	2.34216i	0.261091	+	0.186332i
$159$	3.20850	−	2.81817i	0.254450	−	0.223495i
$160$	10.5612	+	2.35508i	0.834938	+	0.186186i
$161$	7.54134	−	15.1717i	0.594341	−	1.19570i
$162$	8.12388	+	9.79809i	0.638272	+	0.769811i
$163$	−6.49316	+	1.73984i	−0.508583	+	0.136274i	−0.503981	−	0.863715i	$-0.668132\pi$
$163$	−6.49316	+	1.73984i	−0.508583	+	0.136274i	−0.00460262	+	0.999989i	$0.501465\pi$
$164$	0.602340	−	3.09060i	0.0470349	−	0.241336i
$165$	−8.32356	−	5.55232i	−0.647988	−	0.432247i
$166$	14.8225	−	12.2125i	1.15045	−	0.947877i
$167$		−	20.1663i		−	1.56052i	−0.625458	−	0.780258i	$-0.715088\pi$
$167$		−	20.1663i		−	1.56052i	0.625458	−	0.780258i	$-0.284912\pi$
$168$	−9.42969	+	8.89274i	−0.727517	+	0.686090i
$169$			9.46955i			0.728427i
$170$	−6.80969	−	8.26498i	−0.522279	−	0.633895i
$171$	5.46889	−	4.20989i	0.418217	−	0.321938i
$172$	21.5325	−	14.5084i	1.64184	−	1.10625i
$173$	−3.59859	+	0.964239i	−0.273596	+	0.0733097i	−0.393008	−	0.919535i	$-0.628566\pi$
$173$	−3.59859	+	0.964239i	−0.273596	+	0.0733097i	0.119412	+	0.992845i	$0.461899\pi$
$174$	−1.17671	−	11.6246i	−0.0892062	−	0.881258i
$175$	2.95635	−	1.96194i	0.223479	−	0.148309i
$176$	−7.27937	+	9.64018i	−0.548703	+	0.726656i
$177$	−13.7649	−	15.6714i	−1.03463	−	1.17793i
$178$	−10.3537	+	14.5077i	−0.776039	+	1.08740i
$179$	17.0096	+	4.55771i	1.27136	+	0.340659i	0.830551	−	0.556943i	$-0.188026\pi$
$179$	17.0096	+	4.55771i	1.27136	+	0.340659i	0.440807	+	0.897602i	$0.354692\pi$
$180$	10.2658	−	5.13181i	0.765165	−	0.382503i
$181$	5.93458	+	5.93458i	0.441114	+	0.441114i	0.892386	−	0.451272i	$-0.149030\pi$
$181$	5.93458	+	5.93458i	0.441114	+	0.441114i	−0.451272	+	0.892386i	$0.649030\pi$
$182$	4.79969	+	5.13706i	0.355776	+	0.380784i
$183$	0.436840	−	1.29017i	0.0322922	−	0.0953720i
$184$	12.4580	+	13.1476i	0.918418	+	0.969251i
$185$	15.2089	−	8.78084i	1.11818	−	0.645580i
$186$	−0.234410	+	1.44412i	−0.0171878	+	0.105888i
$187$	11.5478	−	3.09423i	0.844459	−	0.226272i
$188$	−0.364933	+	0.419388i	−0.0266155	+	0.0305870i
$189$	−1.80572	+	13.6286i	−0.131347	+	0.991337i
$190$	−2.57935	−	5.66359i	−0.187126	−	0.410880i
$191$	−18.0708	−	10.4332i	−1.30755	−	0.754917i	−0.325867	−	0.945416i	$-0.605656\pi$
$191$	−18.0708	−	10.4332i	−1.30755	−	0.754917i	−0.981688	+	0.190498i	$0.938990\pi$
$192$	−5.46067	−	12.7350i	−0.394090	−	0.919072i
$193$	−8.59743	−	14.8912i	−0.618856	−	1.07189i	−0.989695	−	0.143193i	$-0.954263\pi$
$193$	−8.59743	−	14.8912i	−0.618856	−	1.07189i	0.370838	−	0.928697i	$-0.379070\pi$
$194$	6.78210	+	0.654736i	0.486926	+	0.0470073i
$195$	−2.75765	−	5.58108i	−0.197480	−	0.399669i
$196$	−13.9678	−	0.949557i	−0.997697	−	0.0678255i
$197$	−6.99696	−	6.99696i	−0.498513	−	0.498513i	0.412462	−	0.910975i	$-0.364669\pi$
$197$	−6.99696	−	6.99696i	−0.498513	−	0.498513i	−0.910975	+	0.412462i	$0.864669\pi$
$198$	0.463792	+	12.8042i	0.0329602	+	0.909955i
$199$	0.686010	+	1.18820i	0.0486300	+	0.0842296i	0.889316	−	0.457294i	$-0.151181\pi$
$199$	0.686010	+	1.18820i	0.0486300	+	0.0842296i	−0.840686	+	0.541523i	$0.817848\pi$
$200$	0.882745	+	3.68896i	0.0624195	+	0.260849i
$201$	−9.19902	+	8.07992i	−0.648849	+	0.569913i
$202$	−0.706996	+	1.88952i	−0.0497441	+	0.132946i
$203$	8.35087	−	9.46209i	0.586116	−	0.664109i
$204$	−3.48777	+	13.2625i	−0.244193	+	0.928559i
$205$	−2.90890	+	0.779439i	−0.203167	+	0.0544384i
$206$	12.1215	+	8.65074i	0.844547	+	0.602725i
$207$	19.0507	+	2.47809i	1.32411	+	0.172239i
$208$	−6.92123	+	2.92981i	−0.479901	+	0.203145i
$209$	6.94750			0.480569
$210$	11.6001	+	4.37181i	0.800484	+	0.301683i
$211$	−10.0240	−	10.0240i	−0.690081	−	0.690081i	0.272169	−	0.962250i	$-0.412259\pi$
$211$	−10.0240	−	10.0240i	−0.690081	−	0.690081i	−0.962250	+	0.272169i	$0.912259\pi$
$212$	−2.16383	+	4.43094i	−0.148612	+	0.304318i
$213$	18.3990	+	12.2732i	1.26068	+	0.840947i
$214$	−0.949740	−	5.68407i	−0.0649229	−	0.388555i
$215$	−21.5057	−	12.4163i	−1.46668	−	0.846786i
$216$	−13.0174	−	6.82258i	−0.885721	−	0.464218i
$217$	−1.31668	+	0.873795i	−0.0893822	+	0.0593171i
$218$	−21.8716	−	8.18364i	−1.48133	−	0.554266i
$219$	1.41842	−	21.9005i	0.0958480	−	1.47990i
$220$	11.3400	+	2.21010i	0.764542	+	0.149005i
$221$	7.18479	+	1.92516i	0.483301	+	0.129500i
$222$	−20.5092	−	9.22575i	−1.37649	−	0.619191i
$223$			15.9831i			1.07031i	0.844755	+	0.535153i	$0.179746\pi$
$223$			15.9831i			1.07031i	−0.844755	+	0.535153i	$0.820254\pi$
$224$	6.08778	−	13.6726i	0.406757	−	0.913536i
$225$	3.19560	+	2.44423i	0.213040	+	0.162949i
$226$	−9.73787	−	0.940083i	−0.647753	−	0.0625334i
$227$	0.684946	−	2.55625i	0.0454614	−	0.169664i	−0.939463	−	0.342651i	$-0.888675\pi$
$227$	0.684946	−	2.55625i	0.0454614	−	0.169664i	0.984924	+	0.172987i	$0.0553418\pi$
$228$	−3.95256	+	6.92001i	−0.261764	+	0.458289i
$229$	−4.66155	+	1.24906i	−0.308044	+	0.0825401i	−0.409529	−	0.912297i	$-0.634307\pi$
$229$	−4.66155	+	1.24906i	−0.308044	+	0.0825401i	0.101486	+	0.994837i	$0.467640\pi$
$230$	6.07068	−	16.2245i	0.400288	−	1.06981i
$231$	−9.80899	+	9.76251i	−0.645384	+	0.642326i
$232$	6.42879	+	11.8613i	0.422070	+	0.778736i
$233$	5.56619	−	9.64092i	0.364653	−	0.631597i	−0.624067	−	0.781370i	$-0.714521\pi$
$233$	5.56619	−	9.64092i	0.364653	−	0.631597i	0.988720	+	0.149773i	$0.0478543\pi$
$234$	−3.73334	+	7.04346i	−0.244056	+	0.460445i
$235$	0.513587	+	0.137615i	0.0335028	+	0.00897704i
$236$	21.6422	+	10.5689i	1.40879	+	0.687976i
$237$	−4.42712	+	2.18747i	−0.287573	+	0.142092i
$238$	−13.0716	+	6.96655i	−0.847309	+	0.451574i
$239$			13.1839i			0.852798i	0.904535	+	0.426399i	$0.140218\pi$
$239$			13.1839i			0.852798i	−0.904535	+	0.426399i	$0.859782\pi$
$240$	−8.65287	+	10.0378i	−0.558541	+	0.647934i
$241$	−11.7674	+	6.79392i	−0.758006	+	0.437635i	−0.828579	−	0.559872i	$-0.810850\pi$
$241$	−11.7674	+	6.79392i	−0.758006	+	0.437635i	0.0705736	+	0.997507i	$0.477517\pi$
$242$	1.54435	−	2.16396i	0.0992745	−	0.139105i
$243$	−15.2771	+	3.10026i	−0.980023	+	0.198882i
$244$	0.108939	+	1.56906i	0.00697409	+	0.100449i
$245$	5.04608	+	12.4026i	0.322382	+	0.792374i
$246$	2.98766	+	2.43841i	0.190487	+	0.155467i
$247$	3.74346	+	2.16129i	0.238191	+	0.137520i
$248$	−0.393151	−	1.64297i	−0.0249651	−	0.104328i
$249$	4.60673	+	23.0663i	0.291940	+	1.46177i
$250$	13.2388	−	10.9077i	0.837296	−	0.689866i
$251$	−19.1295	+	19.1295i	−1.20744	+	1.20744i	−0.235589	+	0.971853i	$0.575702\pi$
$251$	−19.1295	+	19.1295i	−1.20744	+	1.20744i	−0.971853	+	0.235589i	$0.924298\pi$
$252$	−4.14338	−	15.3242i	−0.261008	−	0.965337i
$253$	13.6747	+	13.6747i	0.859721	+	0.859721i
$254$	−2.15239	+	22.2956i	−0.135053	+	1.39895i
$255$	12.8617	−	2.56870i	0.805434	−	0.160858i
$256$	11.4874	+	11.1373i	0.717963	+	0.696081i
$257$	−12.3716	+	21.4282i	−0.771717	+	1.33665i	0.164905	+	0.986309i	$0.447268\pi$
$257$	−12.3716	+	21.4282i	−0.771717	+	1.33665i	−0.936622	+	0.350343i	$0.886065\pi$
$258$	3.20258	+	31.6379i	0.199384	+	1.96969i
$259$	−7.73550	−	23.0259i	−0.480661	−	1.43076i
$260$	5.42270	+	4.71859i	0.336301	+	0.292635i
$261$	13.2291	+	5.45571i	0.818860	+	0.337700i
$262$	0.238573	+	1.42783i	0.0147391	+	0.0882115i
$263$	4.53545	+	7.85563i	0.279668	+	0.484399i	0.971302	−	0.237849i	$-0.0764423\pi$
$263$	4.53545	+	7.85563i	0.279668	+	0.484399i	−0.691634	+	0.722248i	$0.743109\pi$
$264$	−6.19436	−	13.4355i	−0.381237	−	0.826899i
$265$	4.71615			0.289711
$266$	−8.38530	+	1.94445i	−0.514136	+	0.119222i
$267$	−9.66988	−	19.5704i	−0.591787	−	1.19769i
$268$	6.20387	−	12.7039i	0.378962	−	0.776011i
$269$	−6.33202	+	23.6314i	−0.386070	+	1.44083i	0.450404	+	0.892825i	$0.351280\pi$
$269$	−6.33202	+	23.6314i	−0.386070	+	1.44083i	−0.836474	+	0.548007i	$0.815387\pi$
$270$	−0.400137	+	14.0507i	−0.0243515	+	0.855099i
$271$	−11.2425	−	6.49088i	−0.682935	−	0.394293i	0.118025	−	0.993011i	$-0.462344\pi$
$271$	−11.2425	−	6.49088i	−0.682935	−	0.394293i	−0.800960	+	0.598718i	$0.795677\pi$
$272$	−2.18826	−	15.6830i	−0.132683	−	0.950919i
$273$	−8.32231	+	2.20879i	−0.503689	+	0.133682i
$274$	−0.416782	+	0.189814i	−0.0251787	+	0.0114671i
$275$	1.04821	+	3.91196i	0.0632093	+	0.235900i
$276$	−21.4004	+	5.84081i	−1.28815	+	0.351576i
$277$	−6.44637	−	1.72730i	−0.387325	−	0.103783i	0.0599012	−	0.998204i	$-0.480921\pi$
$277$	−6.44637	−	1.72730i	−0.387325	−	0.103783i	−0.447226	+	0.894421i	$0.647588\pi$
$278$	9.83502	−	8.10328i	0.589865	−	0.486002i
$279$	−1.42324	−	1.08860i	−0.0852070	−	0.0651725i
$280$	−14.3054	+	0.506325i	−0.854910	+	0.0302587i
$281$	8.68701			0.518224			0.259112	−	0.965847i	$-0.416570\pi$
$281$	8.68701			0.518224			0.259112	+	0.965847i	$0.416570\pi$
$282$	−0.241564	−	0.636586i	−0.0143849	−	0.0379081i
$283$	4.60476	−	17.1852i	0.273724	−	1.02155i	−0.682967	−	0.730449i	$-0.739311\pi$
$283$	4.60476	−	17.1852i	0.273724	−	1.02155i	0.956691	−	0.291104i	$-0.0940225\pi$
$284$	−25.0667	−	4.88535i	−1.48743	−	0.289892i
$285$	7.60601	+	0.492616i	0.450541	+	0.0291800i
$286$	−7.30303	+	3.32600i	−0.431837	+	0.196670i
$287$	0.259345	+	4.15733i	0.0153086	+	0.245399i
$288$	16.9064	+	1.47385i	0.996222	+	0.0868476i
$289$	0.664262	−	1.15054i	0.0390742	−	0.0676786i
$290$	7.49571	−	10.5031i	0.440163	−	0.616763i
$291$	−4.63084	+	6.94216i	−0.271465	+	0.406957i
$292$	8.23851	+	23.9649i	0.482122	+	1.40244i
$293$	−23.8168	+	23.8168i	−1.39139	+	1.39139i	−0.569180	+	0.822213i	$0.692739\pi$
$293$	−23.8168	+	23.8168i	−1.39139	+	1.39139i	−0.822213	+	0.569180i	$0.807261\pi$
$294$	9.10667	−	14.5282i	0.531112	−	0.847302i
$295$		−	23.0353i		−	1.34117i
$296$	25.9583	+	0.699032i	1.50880	+	0.0406304i
$297$	−14.0899	−	6.90779i	−0.817581	−	0.400830i
$298$	−2.21030	−	13.2283i	−0.128039	−	0.766297i
$299$	3.11418	+	11.6223i	0.180098	+	0.672133i
$300$	−4.49283	−	1.18153i	−0.259394	−	0.0682154i
$301$	−22.7280	+	25.7524i	−1.31002	+	1.48434i
$302$	−6.25660	−	13.7379i	−0.360027	−	0.790525i
$303$	−1.63059	−	1.85644i	−0.0936752	−	0.106650i
$304$	1.13050	−	9.13241i	0.0648386	−	0.523780i
$305$	1.30275	−	0.752144i	0.0745954	−	0.0430676i
$306$	−12.2983	−	11.4385i	−0.703046	−	0.653895i
$307$	2.97137	−	2.97137i	0.169585	−	0.169585i	−0.617212	−	0.786797i	$-0.711738\pi$
$307$	2.97137	−	2.97137i	0.169585	−	0.169585i	0.786797	+	0.617212i	$0.211738\pi$
$308$	6.10469	−	14.7681i	0.347847	−	0.841490i
$309$	−16.3516	+	8.07942i	−0.930207	+	0.459622i
$310$	−1.24699	+	1.02742i	−0.0708241	+	0.0583534i
$311$	6.80884	−	3.93108i	0.386094	−	0.222911i	−0.294372	−	0.955691i	$-0.595111\pi$
$311$	6.80884	−	3.93108i	0.386094	−	0.222911i	0.680466	+	0.732779i	$0.261777\pi$
$312$	0.841984	−	9.16635i	0.0476679	−	0.518942i
$313$	−4.21826	+	7.30624i	−0.238430	+	0.412973i	−0.960264	−	0.279093i	$-0.909966\pi$
$313$	−4.21826	+	7.30624i	−0.238430	+	0.412973i	0.721834	+	0.692066i	$0.243300\pi$
$314$	8.62203	−	23.0433i	0.486569	−	1.30041i
$315$	−11.4309	+	9.99233i	−0.644060	+	0.563004i
$316$	3.74297	−	4.30149i	0.210558	−	0.241978i
$317$	−5.63248	−	21.0207i	−0.316352	−	1.18064i	−0.922725	−	0.385460i	$-0.874043\pi$
$317$	−5.63248	−	21.0207i	−0.316352	−	1.18064i	0.606373	−	0.795180i	$-0.292624\pi$
$318$	−3.53103	−	4.89948i	−0.198010	−	0.274749i
$319$	7.20255	+	12.4752i	0.403265	+	0.698476i
$320$	4.75040	−	14.5467i	0.265555	−	0.813183i
$321$	6.68522	+	2.26356i	0.373133	+	0.126340i
$322$	−20.3319	−	12.6775i	−1.13305	−	0.706488i
$323$	−6.43973	+	6.43973i	−0.358316	+	0.358316i
$324$	14.8965	−	10.1042i	0.827582	−	0.561346i
$325$	−0.652172	+	2.43394i	−0.0361760	+	0.135011i
$326$	1.56673	+	9.37665i	0.0867730	+	0.519325i
$327$	21.4887	−	18.8745i	1.18833	−	1.04376i
$328$	−4.26869	−	1.26789i	−0.235699	−	0.0700077i
$329$	0.327348	−	0.658562i	0.0180473	−	0.0363077i
$330$	−8.94696	+	10.9623i	−0.492514	+	0.603454i
$331$	3.76525	+	14.0521i	0.206957	+	0.772373i	0.988844	+	0.148953i	$0.0475904\pi$
$331$	3.76525	+	14.0521i	0.206957	+	0.772373i	−0.781888	+	0.623419i	$0.785743\pi$
$332$	−15.1769	−	22.5248i	−0.832942	−	1.23621i
$333$	21.8253	−	16.8008i	1.19602	−	0.920681i
$334$	−28.3875	−	2.74050i	−1.55329	−	0.149953i
$335$	−13.5216			−0.738763
$336$	11.2366	+	14.4824i	0.613007	+	0.790078i
$337$	21.9594			1.19620			0.598102	−	0.801420i	$-0.295922\pi$
$337$	21.9594			1.19620			0.598102	+	0.801420i	$0.295922\pi$
$338$	13.3300	+	1.28686i	0.725056	+	0.0699961i
$339$	6.64905	−	9.96769i	0.361127	−	0.541371i
$340$	−12.5598	+	8.46262i	−0.681149	+	0.458950i
$341$	−0.466844	−	1.74229i	−0.0252810	−	0.0943501i
$342$	−5.18293	−	8.27049i	−0.280261	−	0.447217i
$343$	18.1977	−	3.44142i	0.982584	−	0.185819i
$344$	−17.4968	−	32.2823i	−0.943365	−	1.74054i
$345$	14.0012	+	15.9404i	0.753800	+	0.858205i
$346$	0.868300	+	5.19666i	0.0466801	+	0.279374i
$347$	3.03376	−	11.3221i	0.162861	−	0.607805i	−0.835443	−	0.549578i	$-0.814789\pi$
$347$	3.03376	−	11.3221i	0.162861	−	0.607805i	0.998303	−	0.0582269i	$-0.0185447\pi$
$348$	−16.5235	+	0.0766982i	−0.885751	+	0.00411146i
$349$	2.66234	−	2.66234i	0.142512	−	0.142512i	−0.632252	−	0.774763i	$-0.717869\pi$
$349$	2.66234	−	2.66234i	0.142512	−	0.142512i	0.774763	+	0.632252i	$0.217869\pi$
$350$	−2.36001	−	4.42818i	−0.126148	−	0.236696i
$351$	−5.44303	−	8.10529i	−0.290527	−	0.432628i
$352$	12.5810	+	11.5570i	0.670567	+	0.615990i
$353$	7.09545	+	12.2897i	0.377652	+	0.654113i	0.990720	−	0.135917i	$-0.0433981\pi$
$353$	7.09545	+	12.2897i	0.377652	+	0.654113i	−0.613068	+	0.790030i	$0.710065\pi$
$354$	−23.9307	+	17.2468i	−1.27190	+	0.916656i
$355$	6.32172	+	23.5930i	0.335522	+	1.25219i
$356$	19.0150	+	16.5460i	1.00779	+	0.876939i
$357$	0.0430768	−	18.1411i	0.00227986	−	0.960128i
$358$	8.72727	−	23.3245i	0.461250	−	1.23274i
$359$	−16.3675	+	28.3493i	−0.863843	+	1.49622i	0.00434871	+	0.999991i	$0.498616\pi$
$359$	−16.3675	+	28.3493i	−0.863843	+	1.49622i	−0.868192	+	0.496229i	$0.834718\pi$
$360$	−5.82883	−	15.1482i	−0.307206	−	0.798380i
$361$	11.8711	−	6.85378i	0.624795	−	0.360725i
$362$	9.16041	−	7.54745i	0.481460	−	0.396685i
$363$	1.44236	+	2.91911i	0.0757041	+	0.153214i
$364$	7.88353	−	6.05827i	0.413209	−	0.317540i
$365$	17.1381	−	17.1381i	0.897051	−	0.897051i
$366$	−1.75677	−	0.790254i	−0.0918276	−	0.0413072i
$367$	29.1928	−	16.8544i	1.52385	−	0.879795i	0.524248	−	0.851566i	$-0.324347\pi$
$367$	29.1928	−	16.8544i	1.52385	−	0.879795i	0.999601	−	0.0282290i	$-0.00898677\pi$
$368$	20.2004	−	15.7501i	1.05302	−	0.821030i
$369$	−4.36080	+	1.81421i	−0.227014	+	0.0944441i
$370$	−10.2937	−	22.6023i	−0.535144	−	1.17504i
$371$	1.29274	−	6.39380i	0.0671159	−	0.331950i
$372$	2.00099	+	0.526220i	0.103746	+	0.0272833i
$373$	1.92063	+	7.16791i	0.0994467	+	0.371140i	0.997656	−	0.0684277i	$-0.0217983\pi$
$373$	1.92063	+	7.16791i	0.0994467	+	0.371140i	−0.898209	+	0.439568i	$0.855132\pi$
$374$	−2.78636	−	16.6760i	−0.144079	−	0.862294i
$375$	4.11454	+	20.6019i	0.212474	+	1.06388i
$376$	0.540767	+	0.570698i	0.0278879	+	0.0294315i
$377$			8.96253i			0.461594i
$378$	18.9392	+	4.39391i	0.974128	+	0.225998i
$379$	−0.171777	+	0.171777i	−0.00882358	+	0.00882358i	−0.711505	−	0.702681i	$-0.751986\pi$
$379$	−0.171777	+	0.171777i	−0.00882358	+	0.00882358i	0.702681	+	0.711505i	$0.251986\pi$
$380$	−8.32298	+	2.86122i	−0.426960	+	0.146778i
$381$	−22.8218	−	15.2235i	−1.16920	−	0.779925i
$382$	−17.1422	+	24.0198i	−0.877069	+	1.22896i
$383$	−7.21803	+	12.5020i	−0.368824	+	0.638822i	−0.989382	−	0.145338i	$-0.953573\pi$
$383$	−7.21803	+	12.5020i	−0.368824	+	0.638822i	0.620558	+	0.784161i	$0.286906\pi$
$384$	−18.6688	+	5.95619i	−0.952688	+	0.303951i
$385$	−15.2540	+	0.951583i	−0.777416	+	0.0484972i
$386$	−22.1302	+	10.0787i	−1.12640	+	0.512992i
$387$	−36.0048	−	14.8484i	−1.83022	−	0.754789i
$388$	1.84330	−	9.45797i	0.0935795	−	0.480156i
$389$	−7.03189	+	26.2434i	−0.356531	+	1.33059i	0.522016	+	0.852936i	$0.325180\pi$
$389$	−7.03189	+	26.2434i	−0.356531	+	1.33059i	−0.878547	+	0.477656i	$0.841487\pi$
$390$	−8.23106	+	3.12342i	−0.416796	+	0.158161i
$391$	−25.3505			−1.28203
$392$	−3.23481	+	19.5329i	−0.163383	+	0.986563i
$393$	−1.67932	−	0.568603i	−0.0847103	−	0.0286822i
$394$	−10.8003	+	8.89856i	−0.544109	+	0.448303i
$395$	−5.26765	−	1.41146i	−0.265044	−	0.0710184i
$396$	18.0871	+	1.08716i	0.908911	+	0.0546318i
$397$	−0.887355	−	3.31165i	−0.0445350	−	0.166207i	0.940077	−	0.340963i	$-0.110753\pi$
$397$	−0.887355	−	3.31165i	−0.0445350	−	0.166207i	−0.984612	+	0.174756i	$0.944086\pi$
$398$	1.76582	−	0.804205i	0.0885128	−	0.0403111i
$399$	2.75273	−	10.1766i	0.137809	−	0.509468i
$400$	5.31280	−	0.741302i	0.265640	−	0.0370651i
$401$	1.91942	+	1.10818i	0.0958513	+	0.0553398i	0.547159	−	0.837028i	$-0.315709\pi$
$401$	1.91942	+	1.10818i	0.0958513	+	0.0553398i	−0.451308	+	0.892368i	$0.649042\pi$
$402$	10.1238	+	14.0472i	0.504927	+	0.700610i
$403$	0.290460	−	1.08401i	0.0144688	−	0.0539985i
$404$	2.56374	+	1.25199i	0.127551	+	0.0622890i
$405$	−14.9356	−	8.56158i	−0.742157	−	0.425429i
$406$	−12.1847	−	13.0411i	−0.604714	−	0.647220i
$407$	27.7261			1.37433
$408$	18.1952	+	6.71193i	0.900797	+	0.332290i
$409$	9.26494	+	16.0473i	0.458122	+	0.793490i	0.998862	−	0.0476998i	$-0.0151891\pi$
$409$	9.26494	+	16.0473i	0.458122	+	0.793490i	−0.540740	+	0.841190i	$0.681856\pi$
$410$	0.701887	+	4.20070i	0.0346637	+	0.207458i
$411$	0.0362515	−	0.559724i	0.00178815	−	0.0276091i
$412$	13.8246	−	15.8875i	0.681091	−	0.782722i
$413$	−31.2295	−	6.31420i	−1.53670	−	0.310702i
$414$	6.07722	−	26.4803i	0.298679	−	1.30143i
$415$	−12.9885	+	22.4967i	−0.637579	+	1.10432i
$416$	3.18364	+	10.1410i	0.156091	+	0.497201i
$417$	3.05666	+	15.3050i	0.149685	+	0.749489i
$418$	0.944129	−	9.77978i	0.0461789	−	0.478345i
$419$	26.3706	+	26.3706i	1.28829	+	1.28829i	0.935827	+	0.352459i	$0.114654\pi$
$419$	26.3706	+	26.3706i	1.28829	+	1.28829i	0.352459	+	0.935827i	$0.385346\pi$
$420$	7.73045	−	15.7350i	0.377207	−	0.767790i
$421$	5.74913	−	5.74913i	0.280195	−	0.280195i	−0.552992	−	0.833187i	$-0.686514\pi$
$421$	5.74913	−	5.74913i	0.280195	−	0.280195i	0.833187	+	0.552992i	$0.186514\pi$
$422$	−15.4727	+	12.7483i	−0.753199	+	0.620576i
$423$	0.826935	+	0.107567i	0.0402069	+	0.00523008i
$424$	5.94324	+	3.64810i	0.288629	+	0.177167i
$425$	−4.59765	−	2.65445i	−0.223019	−	0.128760i
$426$	19.7770	−	24.2318i	0.958197	−	1.17403i
$427$	−0.662603	−	1.97234i	−0.0320656	−	0.0954484i
$428$	−8.13035	+	0.564485i	−0.392995	+	0.0272854i
$429$	0.635213	−	9.80771i	0.0306684	−	0.473521i
$430$	−20.4006	+	28.5856i	−0.983803	+	1.37852i
$431$	−3.06169	+	1.76767i	−0.147477	+	0.0851456i	−0.571923	−	0.820308i	$-0.693802\pi$
$431$	−3.06169	+	1.76767i	−0.147477	+	0.0851456i	0.424446	+	0.905453i	$0.360469\pi$
$432$	−11.3729	+	17.3970i	−0.547180	+	0.837015i
$433$		−	32.3146i		−	1.55294i	−0.630153	−	0.776471i	$-0.717008\pi$
$433$		−	32.3146i		−	1.55294i	0.630153	−	0.776471i	$-0.282992\pi$
$434$	1.05108	+	1.97220i	0.0504537	+	0.0946684i
$435$	7.00067	+	14.1683i	0.335657	+	0.679319i
$436$	−14.4921	+	29.6759i	−0.694045	+	1.42122i
$437$	−14.2300	−	3.81291i	−0.680711	−	0.182396i
$438$	−30.6358	−	4.97282i	−1.46384	−	0.237611i
$439$	−10.8715	+	18.8299i	−0.518866	+	0.898702i	0.480894	+	0.876779i	$0.340312\pi$
$439$	−10.8715	+	18.8299i	−0.518866	+	0.898702i	−0.999760	+	0.0219234i	$0.993021\pi$
$440$	4.65213	−	15.6626i	0.221782	−	0.746686i
$441$	10.4135	+	18.2362i	0.495882	+	0.868390i
$442$	3.68636	−	9.85219i	0.175342	−	0.468621i
$443$	29.4901	−	7.90185i	1.40112	−	0.375428i	0.522372	−	0.852718i	$-0.325047\pi$
$443$	29.4901	−	7.90185i	1.40112	−	0.375428i	0.878746	+	0.477290i	$0.158381\pi$
$444$	−15.7739	+	27.6164i	−0.748596	+	1.31062i
$445$	6.23947	−	23.2860i	0.295779	−	1.10386i
$446$	22.4989	+	2.17202i	1.06535	+	0.102848i
$447$	15.5583	+	5.26791i	0.735882	+	0.249164i
$448$	−18.4191	−	10.4276i	−0.870223	−	0.492658i
$449$			33.6146i			1.58637i	0.608980	+	0.793185i	$0.291579\pi$
$449$			33.6146i			1.58637i	−0.608980	+	0.793185i	$0.708421\pi$
$450$	3.87493	−	4.16620i	0.182666	−	0.196396i
$451$	−4.59254	−	1.23057i	−0.216254	−	0.0579452i
$452$	−2.64665	+	13.5799i	−0.124488	+	0.638747i
$453$	18.4495	+	1.19491i	0.866832	+	0.0561418i
$454$	−3.50528	−	1.31156i	−0.164511	−	0.0615545i
$455$	−8.51521	−	4.23261i	−0.399199	−	0.198428i
$456$	9.20395	+	6.50428i	0.431015	+	0.304591i
$457$	−18.8296	−	10.8712i	−0.880809	−	0.508535i	−0.00988408	−	0.999951i	$-0.503146\pi$
$457$	−18.8296	−	10.8712i	−0.880809	−	0.508535i	−0.870925	+	0.491416i	$0.836480\pi$
$458$	1.12478	+	6.73166i	0.0525576	+	0.314550i
$459$	19.4631	−	6.65723i	0.908458	−	0.310733i
$460$	−22.0138	−	10.7503i	−1.02640	−	0.501237i
$461$	−23.9734	−	23.9734i	−1.11655	−	1.11655i	−0.992244	−	0.124307i	$-0.960329\pi$
$461$	−23.9734	−	23.9734i	−1.11655	−	1.11655i	−0.124307	−	0.992244i	$-0.539671\pi$
$462$	12.4094	+	15.1345i	0.577338	+	0.704120i
$463$	17.5721			0.816644			0.408322	−	0.912838i	$-0.366114\pi$
$463$	17.5721			0.816644			0.408322	+	0.912838i	$0.366114\pi$
$464$	17.5705	−	7.43771i	0.815690	−	0.345287i
$465$	−0.387555	−	1.94053i	−0.0179725	−	0.0899898i
$466$	−12.8148	−	9.14550i	−0.593634	−	0.423657i
$467$	−23.0721	+	6.18216i	−1.06765	+	0.286076i	−0.749528	−	0.661973i	$-0.769719\pi$
$467$	−23.0721	+	6.18216i	−1.06765	+	0.286076i	−0.318123	+	0.948049i	$0.603053\pi$
$468$	9.40752	+	6.21248i	0.434863	+	0.287172i
$469$	−3.70640	+	18.3315i	−0.171146	+	0.846472i
$470$	0.263511	−	0.704260i	0.0121548	−	0.0324851i
$471$	19.8856	+	22.6398i	0.916280	+	1.04319i
$472$	17.8186	−	29.0288i	0.820166	−	1.33616i
$473$	−19.6027	−	33.9529i	−0.901334	−	1.56116i
$474$	2.47762	+	6.52919i	0.113801	+	0.299896i
$475$	−2.18154	−	2.18154i	−0.100096	−	0.100096i
$476$	8.03023	+	19.3473i	0.368065	+	0.886781i
$477$	7.33181	−	0.976792i	0.335701	−	0.0447243i
$478$	18.5586	+	1.79163i	0.848851	+	0.0819471i
$479$	12.0632	+	20.8940i	0.551180	+	0.954672i	0.998190	+	0.0601429i	$0.0191556\pi$
$479$	12.0632	+	20.8940i	0.551180	+	0.954672i	−0.447010	+	0.894529i	$0.647511\pi$
$480$	12.9540	+	13.5445i	0.591265	+	0.618217i
$481$	14.9394	+	8.62529i	0.681180	+	0.393280i
$482$	7.96446	+	17.4879i	0.362771	+	0.796551i
$483$	25.4487	−	14.6124i	1.15796	−	0.664886i
$484$	−2.83628	−	2.46800i	−0.128922	−	0.112182i
$485$	−8.90193	+	2.38527i	−0.404216	+	0.108309i
$486$	2.28807	+	21.9263i	0.103789	+	0.994599i
$487$	−13.9702	+	8.06568i	−0.633048	+	0.365491i	−0.781932	−	0.623364i	$-0.785765\pi$
$487$	−13.9702	+	8.06568i	−0.633048	+	0.365491i	0.148883	+	0.988855i	$0.452432\pi$
$488$	2.22352	+	0.0598773i	0.100654	+	0.00271052i
$489$	−11.0282	−	3.73406i	−0.498712	−	0.168860i
$490$	18.1445	−	5.41776i	0.819685	−	0.244750i
$491$	1.51321	+	1.51321i	0.0682901	+	0.0682901i	0.740427	−	0.672137i	$-0.234623\pi$
$491$	1.51321	+	1.51321i	0.0682901	+	0.0682901i	−0.672137	+	0.740427i	$0.734623\pi$
$492$	3.83848	−	3.87428i	0.173052	−	0.174666i
$493$	−18.2396	−	4.88727i	−0.821468	−	0.220112i
$494$	3.55110	−	4.97585i	0.159771	−	0.223874i
$495$	−6.65667	−	16.0006i	−0.299195	−	0.719173i
$496$	−2.36618	+	0.330156i	−0.106245	+	0.0148245i
$497$	33.7185	−	2.10344i	1.51248	−	0.0943524i
$498$	33.0958	−	3.35016i	1.48306	−	0.150124i
$499$	6.05235	−	1.62172i	0.270940	−	0.0725982i	−0.120791	−	0.992678i	$-0.538543\pi$
$499$	6.05235	−	1.62172i	0.270940	−	0.0725982i	0.391731	+	0.920080i	$0.371876\pi$
$500$	−13.5554	−	20.1182i	−0.606216	−	0.899712i
$501$	19.3831	−	29.0575i	0.865972	−	1.29819i
$502$	24.3284	+	29.5276i	1.08583	+	1.31788i
$503$		−	11.5892i		−	0.516739i	−0.966046	−	0.258370i	$-0.916815\pi$
$503$		−	11.5892i		−	0.516739i	0.966046	−	0.258370i	$-0.0831852\pi$
$504$	−22.1345	+	3.75002i	−0.985950	+	0.167039i
$505$		−	2.72877i		−	0.121429i
$506$	21.1078	−	17.3911i	0.938355	−	0.773130i
$507$	−9.10177	+	13.6446i	−0.404224	+	0.605977i
$508$	31.0923	+	6.05971i	1.37950	+	0.268856i
$509$	18.9884	−	5.08793i	0.841647	−	0.225519i	0.187858	−	0.982196i	$-0.439845\pi$
$509$	18.9884	−	5.08793i	0.841647	−	0.225519i	0.653788	+	0.756678i	$0.273179\pi$
$510$	−1.86804	−	18.4542i	−0.0827182	−	0.817164i
$511$	−18.5369	−	27.9323i	−0.820023	−	1.23565i
$512$	17.2387	−	14.6570i	0.761851	−	0.647752i
$513$	11.9265	−	0.809499i	0.526566	−	0.0357403i
$514$	28.4825	+	20.3270i	1.25631	+	0.896587i
$515$	−19.4560	−	5.21323i	−0.857335	−	0.229722i
$516$	44.9709	−	0.208745i	1.97973	−	0.00918947i
$517$	0.593580	+	0.593580i	0.0261056	+	0.0261056i
$518$	−33.4641	+	7.75992i	−1.47033	+	0.340951i
$519$	−6.11197	−	2.06946i	−0.268286	−	0.0908393i
$520$	7.37914	−	6.99213i	0.323597	−	0.306625i
$521$	−29.2651	+	16.8962i	−1.28213	+	0.740237i	−0.977237	−	0.212150i	$-0.931954\pi$
$521$	−29.2651	+	16.8962i	−1.28213	+	0.740237i	−0.304892	+	0.952387i	$0.598620\pi$
$522$	9.47759	−	17.8808i	0.414823	−	0.782620i
$523$	2.22795	−	0.596978i	0.0974215	−	0.0261040i	−0.209779	−	0.977749i	$-0.567274\pi$
$523$	2.22795	−	0.596978i	0.0974215	−	0.0261040i	0.307200	+	0.951645i	$0.400608\pi$
$524$	2.04233	−	0.141798i	0.0892196	−	0.00619446i
$525$	6.14552	+	0.0145928i	0.268213	+	0.000636882i
$526$	11.6745	−	5.31687i	0.509031	−	0.231827i
$527$	2.04767	+	1.18222i	0.0891980	+	0.0514985i
$528$	−19.7546	+	6.89380i	−0.859706	+	0.300014i
$529$	−9.00379	−	15.5950i	−0.391469	−	0.678044i
$530$	0.640901	−	6.63878i	0.0278389	−	0.288370i
$531$	−4.77099	−	35.8111i	−0.207043	−	1.55407i
$532$	1.59762	+	12.0680i	0.0692657	+	0.523213i
$533$	−2.09174	−	2.09174i	−0.0906035	−	0.0906035i
$534$	−28.8627	+	10.9525i	−1.24901	+	0.473960i
$535$	3.89736	+	6.75043i	0.168498	+	0.291846i
$536$	−17.0398	−	10.4594i	−0.736005	−	0.451777i
$537$	20.1283	+	22.9162i	0.868600	+	0.988905i
$538$	32.4047	+	12.1248i	1.39707	+	0.522736i
$539$	−2.89119	+	20.9411i	−0.124532	+	0.901995i
$540$	19.7244	+	2.47268i	0.848802	+	0.106407i
$541$	−6.25072	+	1.67488i	−0.268739	+	0.0720085i	−0.390672	−	0.920530i	$-0.627757\pi$
$541$	−6.25072	+	1.67488i	−0.268739	+	0.0720085i	0.121933	+	0.992538i	$0.461091\pi$
$542$	−10.6648	+	14.9437i	−0.458093	+	0.641886i
$543$	2.84700	+	14.2552i	0.122176	+	0.611748i
$544$	−22.3738	+	0.949118i	−0.959268	+	0.0406931i
$545$	31.5861			1.35300
$546$	1.97828	+	12.0152i	0.0846628	+	0.514204i
$547$	−0.941076	−	0.941076i	−0.0402375	−	0.0402375i	0.686702	−	0.726939i	$-0.259058\pi$
$547$	−0.941076	−	0.941076i	−0.0402375	−	0.0402375i	−0.726939	+	0.686702i	$0.759058\pi$
$548$	0.210557	+	0.612486i	0.00899454	+	0.0261641i
$549$	1.86950	−	1.43912i	0.0797883	−	0.0614201i
$550$	5.64920	−	0.943914i	0.240883	−	0.0402486i
$551$	−9.50329	−	5.48673i	−0.404854	−	0.233742i
$552$	5.31373	+	30.9184i	0.226167	+	1.31597i
$553$	−3.35747	+	6.75459i	−0.142774	+	0.287234i
$554$	−3.30750	+	8.83963i	−0.140522	+	0.375560i
$555$	30.3541	+	1.96594i	1.28846	+	0.0834493i
$556$	−10.0702	−	14.9456i	−0.427072	−	0.633837i
$557$	−12.1222	−	3.24812i	−0.513632	−	0.137627i	−0.00731273	−	0.999973i	$-0.502328\pi$
$557$	−12.1222	−	3.24812i	−0.513632	−	0.137627i	−0.506320	+	0.862346i	$0.668994\pi$
$558$	−1.72579	+	1.85551i	−0.0730586	+	0.0785502i
$559$		−	24.3928i		−	1.03170i
$560$	−1.23129	+	20.2060i	−0.0520314	+	0.853861i
$561$	19.6132	+	6.64087i	0.828069	+	0.280378i
$562$	1.18052	−	12.2284i	0.0497972	−	0.515826i
$563$	9.18861	−	34.2923i	0.387254	−	1.44525i	−0.447330	−	0.894369i	$-0.647625\pi$
$563$	9.18861	−	34.2923i	0.387254	−	1.44525i	0.834584	−	0.550881i	$-0.185708\pi$
$564$	−0.928929	+	0.253533i	−0.0391150	+	0.0106757i
$565$	12.7816	−	3.42481i	0.537725	−	0.144083i
$566$	−23.5653	−	8.81735i	−0.990523	−	0.370621i
$567$	−15.7012	+	17.9018i	−0.659386	+	0.751804i
$568$	−10.2834	+	34.6217i	−0.431481	+	1.45269i
$569$	−3.30179	+	5.71887i	−0.138418	+	0.239747i	−0.926898	−	0.375313i	$-0.877535\pi$
$569$	−3.30179	+	5.71887i	−0.138418	+	0.239747i	0.788480	+	0.615061i	$0.210868\pi$
$570$	1.72706	−	10.6398i	0.0723385	−	0.445652i
$571$	−22.0546	−	5.90951i	−0.922957	−	0.247305i	−0.234108	−	0.972211i	$-0.575217\pi$
$571$	−22.0546	−	5.90951i	−0.922957	−	0.247305i	−0.688849	+	0.724905i	$0.741884\pi$
$572$	3.68946	+	10.7322i	0.154264	+	0.448737i
$573$	−16.0101	−	32.4020i	−0.668830	−	1.35361i
$574$	5.88738	+	0.199888i	0.245735	+	0.00834315i
$575$		−	8.58781i		−	0.358136i
$576$	4.37220	−	23.5984i	0.182175	−	0.983266i
$577$	2.00743	−	1.15899i	0.0835706	−	0.0482495i	−0.457632	−	0.889142i	$-0.651302\pi$
$577$	2.00743	−	1.15899i	0.0835706	−	0.0482495i	0.541203	+	0.840892i	$0.317969\pi$
$578$	−1.52930	−	1.09141i	−0.0636107	−	0.0453968i
$579$	1.92487	−	29.7201i	0.0799950	−	1.23513i
$580$	−13.7663	−	11.9788i	−0.571612	−	0.497392i
$581$	26.9391	+	23.7754i	1.11762	+	0.986369i
$582$	9.14296	+	7.46209i	0.378988	+	0.309314i
$583$	6.44825	+	3.72290i	0.267059	+	0.154187i
$584$	34.8542	−	8.34039i	1.44228	−	0.345128i
$585$	1.39084	−	10.6923i	0.0575042	−	0.442071i
$586$	30.2896	+	36.7628i	1.25125	+	1.51866i
$587$	0.612943	−	0.612943i	0.0252988	−	0.0252988i	−0.694344	−	0.719643i	$-0.744305\pi$
$587$	0.612943	−	0.612943i	0.0252988	−	0.0252988i	0.719643	+	0.694344i	$0.244305\pi$
$588$	−19.2133	−	14.7935i	−0.792345	−	0.610073i
$589$	0.971600	+	0.971600i	0.0400341	+	0.0400341i
$590$	−32.4261	−	3.13038i	−1.33496	−	0.128876i
$591$	−3.35665	−	16.8071i	−0.138074	−	0.691351i
$592$	4.51160	−	36.4457i	0.185426	−	1.49791i
$593$	13.6407	−	23.6264i	0.560157	−	0.970221i	−0.437325	−	0.899304i	$-0.644074\pi$
$593$	13.6407	−	23.6264i	0.560157	−	0.970221i	0.997482	−	0.0709174i	$-0.0225927\pi$
$594$	−11.6386	+	18.8952i	−0.477539	+	0.775281i
$595$	13.2571	−	15.0212i	0.543488	−	0.615808i
$596$	−18.9215	+	1.31371i	−0.775054	+	0.0538115i
$597$	−0.153590	+	2.37144i	−0.00628603	+	0.0970566i
$598$	16.7835	−	2.80433i	0.686329	−	0.114677i
$599$	3.58051	+	6.20163i	0.146296	+	0.253392i	0.929856	−	0.367925i	$-0.119932\pi$
$599$	3.58051	+	6.20163i	0.146296	+	0.253392i	−0.783560	+	0.621316i	$0.786598\pi$
$600$	−2.27375	+	6.16385i	−0.0928254	+	0.251638i
$601$	−22.5323			−0.919113			−0.459556	−	0.888149i	$-0.651992\pi$
$601$	−22.5323			−0.919113			−0.459556	+	0.888149i	$0.651992\pi$
$602$	33.1622	+	35.4932i	1.35159	+	1.44659i
$603$	−21.0209	+	2.80054i	−0.856037	+	0.114047i
$604$	−20.1886	+	6.94032i	−0.821463	+	0.282398i
$605$	−0.930677	+	3.47333i	−0.0378374	+	0.141211i
$606$	−2.83484	+	2.04306i	−0.115157	+	0.0829935i
$607$	5.72505	+	3.30536i	0.232373	+	0.134160i	0.611666	−	0.791116i	$-0.290500\pi$
$607$	5.72505	+	3.30536i	0.232373	+	0.134160i	−0.379293	+	0.925276i	$0.623833\pi$
$608$	−12.7018	−	2.83242i	−0.515125	−	0.114870i
$609$	21.1273	−	5.60731i	0.856121	−	0.227220i
$610$	−0.881733	−	1.93606i	−0.0357003	−	0.0783886i
$611$	0.135178	+	0.504490i	0.00546870	+	0.0204095i
$612$	−17.7729	+	15.7575i	−0.718426	+	0.636958i
$613$	0.608136	+	0.162950i	0.0245624	+	0.00658147i	0.271079	−	0.962557i	$-0.412619\pi$
$613$	0.608136	+	0.162950i	0.0245624	+	0.00658147i	−0.246517	+	0.969138i	$0.579286\pi$
$614$	−3.77892	−	4.58651i	−0.152505	−	0.185096i
$615$	−4.94058	−	1.67284i	−0.199224	−	0.0674555i
$616$	−19.9590	−	10.6003i	−0.804171	−	0.427098i
$617$	17.1982			0.692375			0.346187	−	0.938165i	$-0.387476\pi$
$617$	17.1982			0.692375			0.346187	+	0.938165i	$0.387476\pi$
$618$	9.15106	+	24.1155i	0.368110	+	0.970069i
$619$	−9.85653	+	36.7851i	−0.396167	+	1.47852i	0.423616	+	0.905842i	$0.360761\pi$
$619$	−9.85653	+	36.7851i	−0.396167	+	1.47852i	−0.819783	+	0.572674i	$0.805906\pi$
$620$	1.27681	+	1.89497i	0.0512778	+	0.0761036i
$621$	25.0681	+	21.8814i	1.00595	+	0.878071i
$622$	−4.60838	−	10.1188i	−0.184779	−	0.405727i
$623$	−29.8591	−	14.8419i	−1.19628	−	0.594629i
$624$	−12.7888	−	2.43089i	−0.511960	−	0.0973136i
$625$	−8.24810	+	14.2861i	−0.329924	+	0.571445i
$626$	9.71154	+	6.93080i	0.388151	+	0.277010i
$627$	10.0106	+	6.67767i	0.399785	+	0.266680i
$628$	−31.2656	−	15.2684i	−1.24763	−	0.609277i
$629$	−25.6997	+	25.6997i	−1.02472	+	1.02472i
$630$	12.5125	+	17.4489i	0.498509	+	0.695180i
$631$		−	8.66282i		−	0.344861i	−0.985022	−	0.172431i	$-0.944838\pi$
$631$		−	8.66282i		−	0.344861i	0.985022	−	0.172431i	$-0.0551621\pi$
$632$	−5.54642	−	5.85341i	−0.220625	−	0.232836i
$633$	−4.80881	−	24.0782i	−0.191133	−	0.957022i
$634$	−30.3556	+	5.07206i	−1.20558	+	0.201437i
$635$	−7.84137	−	29.2644i	−0.311175	−	1.16132i
$636$	−7.37669	+	4.30471i	−0.292505	+	0.170693i
$637$	−8.07236	+	10.3841i	−0.319839	+	0.411432i
$638$	18.5397	−	8.44350i	0.733995	−	0.334281i
$639$	14.7144	+	35.3688i	0.582091	+	1.39917i
$640$	−19.8313	−	8.66380i	−0.783902	−	0.342467i
$641$	16.3876	−	9.46139i	0.647272	−	0.373703i	−0.140138	−	0.990132i	$-0.544755\pi$
$641$	16.3876	−	9.46139i	0.647272	−	0.373703i	0.787410	+	0.616429i	$0.211421\pi$
$642$	4.09483	−	9.10298i	0.161610	−	0.359266i
$643$	−31.8131	+	31.8131i	−1.25459	+	1.25459i	−0.300947	+	0.953641i	$0.597303\pi$
$643$	−31.8131	+	31.8131i	−1.25459	+	1.25459i	−0.953641	+	0.300947i	$0.902697\pi$
$644$	−20.6087	+	26.8978i	−0.812096	+	1.05992i
$645$	−19.0533	−	38.5610i	−0.750222	−	1.51834i
$646$	8.18988	+	9.94014i	0.322227	+	0.391089i
$647$	−35.5083	+	20.5007i	−1.39598	+	0.805967i	−0.993968	−	0.109670i	$-0.965021\pi$
$647$	−35.5083	+	20.5007i	−1.39598	+	0.805967i	−0.402007	+	0.915636i	$0.631687\pi$
$648$	−12.1990	−	22.3424i	−0.479224	−	0.877693i
$649$	18.1839	−	31.4955i	0.713781	−	1.23631i
$650$	3.33755	+	1.24880i	0.130910	+	0.0489820i
$651$	−2.73705	−	0.00649925i	−0.107274	−	0.000254726i
$652$	13.4121	−	0.931196i	0.525260	−	0.0364684i
$653$	5.86749	+	21.8978i	0.229613	+	0.856926i	0.980504	+	0.196500i	$0.0629577\pi$
$653$	5.86749	+	21.8978i	0.229613	+	0.856926i	−0.750891	+	0.660426i	$0.770376\pi$
$654$	−23.6488	−	32.8139i	−0.924743	−	1.28312i
$655$	−0.979011	−	1.69570i	−0.0382531	−	0.0662563i
$656$	−2.36487	+	5.83661i	−0.0923325	+	0.227881i
$657$	23.0937	−	30.1928i	0.900970	−	1.17794i
$658$	−0.882552	−	0.550293i	−0.0344055	−	0.0214526i
$659$	1.24714	−	1.24714i	0.0485815	−	0.0485815i	−0.682399	−	0.730980i	$-0.739063\pi$
$659$	1.24714	−	1.24714i	0.0485815	−	0.0485815i	0.730980	+	0.682399i	$0.239063\pi$
$660$	14.2154	+	14.0841i	0.553335	+	0.548222i
$661$	−0.195309	+	0.728902i	−0.00759663	+	0.0283510i	−0.969620	−	0.244616i	$-0.921338\pi$
$661$	−0.195309	+	0.728902i	−0.00759663	+	0.0283510i	0.962023	+	0.272967i	$0.0880049\pi$
$662$	20.2924	−	3.39061i	0.788685	−	0.131780i
$663$	8.50211	+	9.67969i	0.330195	+	0.375928i
$664$	−33.7699	+	18.3031i	−1.31053	+	0.710298i
$665$	9.70087	−	6.43784i	0.376184	−	0.249649i
$666$	−20.6841	−	33.0059i	−0.801492	−	1.27895i
$667$	−7.90576	−	29.5047i	−0.306112	−	1.14243i
$668$	−7.71542	+	39.5878i	−0.298519	+	1.53170i
$669$	−15.3623	+	23.0299i	−0.593942	+	0.890387i
$670$	−1.83751	+	19.0339i	−0.0709893	+	0.735344i
$671$	2.37495			0.0916840
$672$	21.9134	−	13.8493i	0.845327	−	0.534250i
$673$	10.6344			0.409926			0.204963	−	0.978770i	$-0.434293\pi$
$673$	10.6344			0.409926			0.204963	+	0.978770i	$0.434293\pi$
$674$	2.98417	−	30.9116i	0.114946	−	1.19067i
$675$	2.25522	+	6.59336i	0.0868035	+	0.253779i
$676$	3.62295	−	18.5893i	0.139344	−	0.714975i
$677$	−9.41125	−	35.1233i	−0.361704	−	1.34990i	−0.871835	−	0.489800i	$-0.837070\pi$
$677$	−9.41125	−	35.1233i	−0.361704	−	1.34990i	0.510131	−	0.860097i	$-0.329597\pi$
$678$	−13.1276	−	10.7142i	−0.504164	−	0.411477i
$679$	0.793656	+	12.7224i	0.0304577	+	0.488241i
$680$	10.2058	+	18.8300i	0.391373	+	0.722098i
$681$	3.44390	−	3.02494i	0.131971	−	0.115916i
$682$	−2.51600	+	0.420394i	−0.0963428	+	0.0160977i
$683$	5.68836	−	21.2293i	0.217659	−	0.812315i	−0.767554	−	0.640984i	$-0.778527\pi$
$683$	5.68836	−	21.2293i	0.217659	−	0.812315i	0.985213	−	0.171331i	$-0.0548068\pi$
$684$	−12.3465	+	6.17194i	−0.472078	+	0.235990i
$685$	0.438010	−	0.438010i	0.0167355	−	0.0167355i
$686$	−2.37141	−	26.0840i	−0.0905407	−	0.995893i
$687$	−7.91734	−	2.68075i	−0.302065	−	0.102277i
$688$	−47.8205	+	20.2427i	−1.82314	+	0.771747i
$689$	2.31631	+	4.01196i	0.0882442	+	0.152843i
$690$	24.3416	−	17.5429i	0.926668	−	0.667845i
$691$	−4.89250	−	18.2590i	−0.186119	−	0.694607i	−0.994388	−	0.105793i	$-0.966262\pi$
$691$	−4.89250	−	18.2590i	−0.186119	−	0.694607i	0.808269	−	0.588814i	$-0.200405\pi$
$692$	7.43317	−	0.516080i	0.282567	−	0.0196184i
$693$	−23.5170	+	4.63870i	−0.893339	+	0.176210i
$694$	−15.5256	−	5.80915i	−0.589342	−	0.220512i
$695$	−8.61812	+	14.9270i	−0.326904	+	0.566214i
$696$	−2.13749	+	23.2700i	−0.0810213	+	0.882048i
$697$	5.39752	−	3.11626i	0.204446	−	0.118037i
$698$	−3.38589	−	4.10949i	−0.128158	−	0.155546i
$699$	17.2867	−	8.54151i	0.653845	−	0.323070i
$700$	−6.55413	+	2.72034i	−0.247723	+	0.102819i
$701$	13.7542	−	13.7542i	0.519490	−	0.519490i	−0.397927	−	0.917417i	$-0.630270\pi$
$701$	13.7542	−	13.7542i	0.519490	−	0.519490i	0.917417	+	0.397927i	$0.130270\pi$
$702$	−12.1492	+	6.56052i	−0.458544	+	0.247611i
$703$	−18.2914	+	10.5605i	−0.689873	+	0.398299i
$704$	17.9781	−	16.1393i	0.677576	−	0.608272i
$705$	0.607753	+	0.691929i	0.0228893	+	0.0260596i
$706$	18.2640	−	8.31794i	0.687376	−	0.313050i
$707$	−3.69946	−	0.747982i	−0.139132	−	0.0281308i
$708$	21.0257	+	36.0303i	0.790194	+	1.35410i
$709$	−11.9099	−	44.4485i	−0.447287	−	1.66930i	−0.709825	−	0.704378i	$-0.751226\pi$
$709$	−11.9099	−	44.4485i	−0.447287	−	1.66930i	0.262538	−	0.964922i	$-0.415440\pi$
$710$	34.0702	−	5.69273i	1.27863	−	0.213644i
$711$	−8.48152	−	1.10327i	−0.318082	−	0.0413758i
$712$	25.8754	−	24.5183i	0.969722	−	0.918864i
$713$			3.82478i			0.143239i
$714$	−25.5308	−	2.52592i	−0.955466	−	0.0945301i
$715$	7.67500	−	7.67500i	0.287029	−	0.287029i
$716$	−31.6472	−	15.4548i	−1.18271	−	0.577573i
$717$	−12.6719	+	18.9966i	−0.473240	+	0.709441i
$718$	37.6822	+	26.8925i	1.40629	+	1.00362i
$719$	0.517463	−	0.896272i	0.0192981	−	0.0334253i	−0.856215	−	0.516620i	$-0.827190\pi$
$719$	0.517463	−	0.896272i	0.0192981	−	0.0334253i	0.875513	+	0.483194i	$0.160524\pi$
$720$	−22.1158	+	6.14651i	−0.824206	+	0.229067i
$721$	−12.4008	+	24.9480i	−0.461830	+	0.929113i
$722$	−8.03464	−	17.6420i	−0.299018	−	0.656566i
$723$	−23.4856	−	1.52109i	−0.873440	−	0.0565698i
$724$	−9.37946	−	13.9205i	−0.348585	−	0.517351i
$725$	1.65563	−	6.17888i	0.0614884	−	0.229478i
$726$	4.30516	−	1.63367i	0.159779	−	0.0606311i
$727$	40.7074			1.50976			0.754878	−	0.655866i	$-0.227696\pi$
$727$	40.7074			1.50976			0.754878	+	0.655866i	$0.227696\pi$
$728$	−7.45671	−	11.9207i	−0.276364	−	0.441810i
$729$	−24.9924	−	10.2166i	−0.925646	−	0.378392i
$730$	−21.7959	−	26.4538i	−0.806701	−	0.979100i
$731$	49.6414	+	13.3014i	1.83605	+	0.491969i
$732$	−1.35115	+	2.36555i	−0.0499400	+	0.0874334i
$733$	−10.2871	−	38.3920i	−0.379963	−	1.41804i	−0.845956	−	0.533253i	$-0.820969\pi$
$733$	−10.2871	−	38.3920i	−0.379963	−	1.41804i	0.465993	−	0.884789i	$-0.345697\pi$
$734$	−19.7583	−	43.3842i	−0.729294	−	1.60134i
$735$	−4.65006	+	22.7209i	−0.171520	+	0.838074i
$736$	−19.4258	−	30.5758i	−0.716044	−	1.12704i
$737$	−18.4876	−	10.6738i	−0.681001	−	0.393176i
$738$	1.96120	+	6.38511i	0.0721927	+	0.235039i
$739$	−11.1639	+	41.6644i	−0.410672	+	1.53265i	0.382676	+	0.923883i	$0.375003\pi$
$739$	−11.1639	+	41.6644i	−0.410672	+	1.53265i	−0.793348	+	0.608768i	$0.791664\pi$
$740$	−33.2154	+	11.4186i	−1.22102	+	0.419756i
$741$	3.31658	+	6.71226i	0.121837	+	0.246581i
$742$	−8.82468	−	2.68864i	−0.323964	−	0.0987031i
$743$	26.3486			0.966635			0.483317	−	0.875445i	$-0.339432\pi$
$743$	26.3486			0.966635			0.483317	+	0.875445i	$0.339432\pi$
$744$	1.01267	−	2.74522i	0.0371262	−	0.100645i
$745$	9.07019	+	15.7100i	0.332306	+	0.575571i
$746$	10.3510	−	1.72954i	0.378979	−	0.0633229i
$747$	−15.5327	+	37.6639i	−0.568311	+	1.37805i
$748$	−23.8529	+	1.65609i	−0.872149	+	0.0605527i
$749$	10.2200	−	3.43339i	0.373432	−	0.125453i
$750$	29.5598	−	2.99222i	1.07937	−	0.109260i
$751$	4.52777	−	7.84232i	0.165221	−	0.286170i	−0.771513	−	0.636213i	$-0.780500\pi$
$751$	4.52777	−	7.84232i	0.165221	−	0.286170i	0.936734	+	0.350043i	$0.113833\pi$
$752$	0.876842	−	0.683667i	0.0319751	−	0.0249308i
$753$	−45.9500	+	9.17698i	−1.67451	+	0.334428i
$754$	12.6163	+	1.21796i	0.459458	+	0.0443556i
$755$	14.4376	+	14.4376i	0.525438	+	0.525438i
$756$	8.75892	−	26.0630i	0.318559	−	0.947903i
$757$	−25.3277	+	25.3277i	−0.920551	+	0.920551i	−0.997068	−	0.0765170i	$-0.975620\pi$
$757$	−25.3277	+	25.3277i	−0.920551	+	0.920551i	0.0765170	+	0.997068i	$0.475620\pi$
$758$	0.218461	+	0.265148i	0.00793487	+	0.00963063i
$759$	6.56016	+	32.8474i	0.238119	+	1.19228i
$760$	2.89661	+	12.1048i	0.105071	+	0.439088i
$761$	−23.2431	−	13.4194i	−0.842561	−	0.486453i	0.0155731	−	0.999879i	$-0.495043\pi$
$761$	−23.2431	−	13.4194i	−0.842561	−	0.486453i	−0.858134	+	0.513426i	$0.828376\pi$
$762$	−24.5310	+	30.0568i	−0.888666	+	1.08884i
$763$	8.65806	−	42.8220i	0.313443	−	1.55026i
$764$	31.4825	+	27.3947i	1.13900	+	0.991104i
$765$	21.0013	+	8.66099i	0.759304	+	0.313139i
$766$	16.6178	+	11.8596i	0.600425	+	0.428503i
$767$	19.5958	−	11.3136i	0.707563	−	0.408511i
$768$	5.84735	+	27.0889i	0.210998	+	0.977486i
$769$		−	5.97807i		−	0.215575i	−0.994174	−	0.107787i	$-0.965623\pi$
$769$		−	5.97807i		−	0.215575i	0.994174	−	0.107787i	$-0.0343766\pi$
$770$	−0.733424	+	21.6019i	−0.0264308	+	0.778478i
$771$	−38.4220	+	18.9846i	−1.38373	+	0.683713i
$772$	11.1801	+	32.5217i	0.402381	+	1.17048i
$773$	−20.9181	−	5.60499i	−0.752372	−	0.201598i	−0.137802	−	0.990460i	$-0.544004\pi$
$773$	−20.9181	−	5.60499i	−0.752372	−	0.201598i	−0.614570	+	0.788862i	$0.710670\pi$
$774$	−25.7946	+	48.6650i	−0.927166	+	1.74923i
$775$	−0.400493	+	0.693675i	−0.0143861	+	0.0249175i
$776$	−13.0632	−	3.88005i	−0.468942	−	0.139286i
$777$	10.9856	−	40.6129i	0.394107	−	1.45698i
$778$	35.9864	+	13.4649i	1.29017	+	0.482741i
$779$	3.49848	−	0.937416i	0.125346	−	0.0335864i
$780$	3.27819	+	12.0111i	0.117378	+	0.430065i
$781$	−9.98066	+	37.2483i	−0.357136	+	1.33285i
$782$	−3.44501	+	35.6852i	−0.123193	+	1.27610i
$783$	13.8179	+	20.5764i	0.493810	+	0.735339i
$784$	27.0563	+	7.20797i	0.966298	+	0.257427i
$785$			33.2781i			1.18775i
$786$	−1.02862	+	2.28665i	−0.0366895	+	0.0815622i
$787$	15.4260	+	4.13339i	0.549879	+	0.147340i	0.523052	−	0.852301i	$-0.324793\pi$
$787$	15.4260	+	4.13339i	0.549879	+	0.147340i	0.0268264	+	0.999640i	$0.491460\pi$
$788$	11.0585	+	16.4125i	0.393944	+	0.584670i
$789$	−1.01544	+	15.6784i	−0.0361506	+	0.558166i
$790$	−2.70272	+	7.22330i	−0.0961584	+	0.256993i
$791$	−1.13955	−	18.2671i	−0.0405176	−	0.649502i
$792$	3.98830	−	25.3129i	0.141718	−	0.899455i
$793$	1.27968	+	0.738821i	0.0454426	+	0.0262363i
$794$	−4.78230	+	0.799065i	−0.169717	+	0.0283578i
$795$	6.79546	+	4.53298i	0.241010	+	0.160768i
$796$	−0.892088	−	2.59498i	−0.0316192	−	0.0919767i
$797$	−4.34882	−	4.34882i	−0.154043	−	0.154043i	0.625878	−	0.779921i	$-0.284741\pi$
$797$	−4.34882	−	4.34882i	−0.154043	−	0.154043i	−0.779921	+	0.625878i	$0.784741\pi$
$798$	−13.9512	−	5.25789i	−0.493868	−	0.186127i
$799$	−1.10039			−0.0389292
$800$	−0.321526	−	7.57940i	−0.0113677	−	0.267972i
$801$	4.87707	−	37.4931i	0.172323	−	1.32475i
$802$	1.82079	−	2.55131i	0.0642942	−	0.0900900i
$803$	36.9612	−	9.90372i	1.30433	−	0.349495i
$804$	21.1496	−	12.3420i	0.745888	−	0.435267i
$805$	31.7657	+	6.42261i	1.11959	+	0.226367i
$806$	−1.48646	−	0.556183i	−0.0523582	−	0.0195907i
$807$	−31.8374	+	27.9642i	−1.12073	+	0.984387i
$808$	2.11079	−	3.43876i	0.0742574	−	0.120975i
$809$	1.23933	+	2.14659i	0.0435726	+	0.0754700i	0.886989	−	0.461790i	$-0.152793\pi$
$809$	1.23933	+	2.14659i	0.0435726	+	0.0754700i	−0.843417	+	0.537260i	$0.819459\pi$
$810$	−14.0816	+	19.8609i	−0.494775	+	0.697842i
$811$	−11.6016	−	11.6016i	−0.407386	−	0.407386i	0.473440	−	0.880826i	$-0.343012\pi$
$811$	−11.6016	−	11.6016i	−0.407386	−	0.407386i	−0.880826	+	0.473440i	$0.843012\pi$
$812$	−20.0134	+	15.3797i	−0.702333	+	0.539723i
$813$	−9.96049	−	20.1585i	−0.349329	−	0.706991i
$814$	3.76784	−	39.0292i	0.132063	−	1.36797i
$815$	−6.42924	−	11.1358i	−0.225206	−	0.390069i
$816$	11.9208	−	24.7007i	0.417312	−	0.864698i
$817$	25.8645	+	14.9329i	0.904884	+	0.522435i
$818$	23.8484	−	10.8612i	0.833840	−	0.379753i
$819$	−14.1145	−	4.81646i	−0.493202	−	0.168301i
$820$	6.00857	−	0.417171i	0.209829	−	0.0145683i
$821$	3.08612	−	0.826924i	0.107706	−	0.0288599i	−0.204563	−	0.978853i	$-0.565577\pi$
$821$	3.08612	−	0.826924i	0.107706	−	0.0288599i	0.312270	+	0.949993i	$0.398911\pi$
$822$	−0.782979	−	0.127094i	−0.0273095	−	0.00443290i
$823$	7.70076	−	4.44604i	0.268432	−	0.154979i	−0.359743	−	0.933051i	$-0.617136\pi$
$823$	7.70076	−	4.44604i	0.268432	−	0.154979i	0.628175	+	0.778072i	$0.283802\pi$
$824$	−20.4857	−	21.6195i	−0.713653	−	0.753152i
$825$	−2.24968	+	6.64421i	−0.0783237	+	0.231322i
$826$	−13.1322	+	43.1028i	−0.456929	+	1.49974i
$827$	−10.6462	−	10.6462i	−0.370206	−	0.370206i	0.497346	−	0.867552i	$-0.334308\pi$
$827$	−10.6462	−	10.6462i	−0.370206	−	0.370206i	−0.867552	+	0.497346i	$0.834308\pi$
$828$	−36.4496	−	12.1532i	−1.26671	−	0.422354i
$829$	−11.3277	−	3.03526i	−0.393429	−	0.105419i	0.0566805	−	0.998392i	$-0.481948\pi$
$829$	−11.3277	−	3.03526i	−0.393429	−	0.105419i	−0.450109	+	0.892973i	$0.648615\pi$
$830$	29.9029	+	21.3407i	1.03794	+	0.740745i
$831$	−7.62831	−	8.68486i	−0.264623	−	0.301274i
$832$	14.7077	−	3.10341i	0.509899	−	0.107591i
$833$	−16.7307	−	22.0904i	−0.579683	−	0.765388i
$834$	21.9598	−	2.22290i	0.760404	−	0.0769727i
$835$	37.2604	−	9.98389i	1.28945	−	0.345507i
$836$	−13.6384	−	2.65804i	−0.471694	−	0.0919303i
$837$	−1.00442	−	2.93651i	−0.0347177	−	0.101501i
$838$	40.7046	−	33.5374i	1.40612	−	1.15853i
$839$		−	26.7713i		−	0.924248i	−0.886815	−	0.462124i	$-0.847088\pi$
$839$		−	26.7713i		−	0.924248i	0.886815	−	0.462124i	$-0.152912\pi$
$840$	−21.0992	−	13.0202i	−0.727990	−	0.449240i
$841$			6.24740i			0.215427i
$842$	−7.31159	−	8.87414i	−0.251974	−	0.305823i
$843$	12.5170	+	8.34962i	0.431110	+	0.287576i
$844$	15.8427	+	23.5129i	0.545328	+	0.809346i
$845$	−17.4965	+	4.68816i	−0.601897	+	0.161278i
$846$	0.263795	−	1.14943i	0.00906945	−	0.0395183i
$847$	4.45378	+	2.21382i	0.153034	+	0.0760677i
$848$	5.94297	−	7.87036i	0.204082	−	0.270269i
$849$	23.1527	−	20.3361i	0.794598	−	0.697932i
$850$	−4.36139	+	6.11124i	−0.149594	+	0.209614i
$851$	−56.7890	−	15.2166i	−1.94670	−	0.521617i
$852$	−31.4228	−	31.1324i	−1.07653	−	1.06658i
$853$	8.42520	+	8.42520i	0.288473	+	0.288473i	0.836476	−	0.548003i	$-0.184612\pi$
$853$	8.42520	+	8.42520i	0.288473	+	0.288473i	−0.548003	+	0.836476i	$0.684612\pi$
$854$	−2.86645	+	0.664695i	−0.0980879	+	0.0227454i
$855$	10.4859	+	8.02041i	0.358612	+	0.274292i
$856$	−0.310264	+	11.5216i	−0.0106046	+	0.393799i
$857$	37.5658	−	21.6886i	1.28322	−	0.740870i	0.305788	−	0.952100i	$-0.401080\pi$
$857$	37.5658	−	21.6886i	1.28322	−	0.740870i	0.977436	+	0.211230i	$0.0677469\pi$
$858$	−13.7197	−	2.22699i	−0.468383	−	0.0760281i
$859$	−36.2216	+	9.70555i	−1.23587	+	0.331149i	−0.816861	−	0.576835i	$-0.804288\pi$
$859$	−36.2216	+	9.70555i	−1.23587	+	0.331149i	−0.419005	+	0.907984i	$0.637621\pi$
$860$	37.4667	+	32.6019i	1.27760	+	1.11172i
$861$	−3.62217	+	6.23953i	−0.123443	+	0.212643i
$862$	2.07223	+	4.55007i	0.0705803	+	0.154976i
$863$	−1.77594	−	1.02534i	−0.0604537	−	0.0349030i	0.469469	−	0.882949i	$-0.344446\pi$
$863$	−1.77594	−	1.02534i	−0.0604537	−	0.0349030i	−0.529922	+	0.848046i	$0.677779\pi$
$864$	22.9437	+	18.3735i	0.780562	+	0.625079i
$865$	−3.56316	−	6.17158i	−0.121151	−	0.209840i
$866$	−45.4883	−	4.39139i	−1.54576	−	0.149226i
$867$	2.06298	−	1.01933i	0.0700625	−	0.0346184i
$868$	2.91904	−	1.21157i	0.0990786	−	0.0411233i
$869$	−6.08810	−	6.08810i	−0.206525	−	0.206525i
$870$	20.8957	−	7.92923i	0.708429	−	0.268826i
$871$	−6.64103	−	11.5026i	−0.225023	−	0.389751i
$872$	39.8044	+	24.4329i	1.34795	+	0.827401i
$873$	−13.3451	+	5.55191i	−0.451662	+	0.187904i
$874$	−7.30109	+	19.5129i	−0.246963	+	0.660034i
$875$	24.0609	+	21.2352i	0.813405	+	0.717880i
$876$	−11.1633	+	42.4493i	−0.377174	+	1.43423i
$877$	20.8306	−	5.58155i	0.703401	−	0.188476i	0.110648	−	0.993860i	$-0.464708\pi$
$877$	20.8306	−	5.58155i	0.703401	−	0.188476i	0.592753	+	0.805384i	$0.298041\pi$
$878$	25.0289	+	17.8623i	0.844685	+	0.602823i
$879$	−57.2092	+	11.4256i	−1.92962	+	0.385377i
$880$	−21.4156	−	8.67713i	−0.721919	−	0.292506i
$881$	16.5133			0.556346			0.278173	−	0.960531i	$-0.410271\pi$
$881$	16.5133			0.556346			0.278173	+	0.960531i	$0.410271\pi$
$882$	27.0857	−	12.1806i	0.912022	−	0.410141i
$883$	20.9255	+	20.9255i	0.704198	+	0.704198i	0.965309	−	0.261111i	$-0.0840887\pi$
$883$	20.9255	+	20.9255i	0.704198	+	0.704198i	−0.261111	+	0.965309i	$0.584089\pi$
$884$	−13.3677	−	6.52804i	−0.449603	−	0.219562i
$885$	22.1406	−	33.1914i	0.744250	−	1.11572i
$886$	−7.11564	−	42.5861i	−0.239055	−	1.43071i
$887$	44.9530	+	25.9536i	1.50937	+	0.871438i	0.999940	+	0.0109283i	$0.00347865\pi$
$887$	44.9530	+	25.9536i	1.50937	+	0.871438i	0.509434	+	0.860510i	$0.329855\pi$
$888$	36.7312	+	25.9573i	1.23262	+	0.871072i
$889$	−41.8239	+	2.60908i	−1.40273	+	0.0875058i
$890$	−31.9311	−	11.9476i	−1.07033	−	0.400483i
$891$	−13.6626	−	23.4961i	−0.457713	−	0.787148i
$892$	6.11497	−	31.3758i	0.204744	−	1.05054i
$893$	−0.617682	−	0.165507i	−0.0206699	−	0.00553849i
$894$	9.52976	−	21.1850i	0.318723	−	0.708534i
$895$			33.6843i			1.12594i
$896$	−17.1817	+	24.5110i	−0.574000	+	0.818855i
$897$	−6.68369	+	19.7397i	−0.223162	+	0.659088i
$898$	47.3182	+	4.56805i	1.57903	+	0.152438i
$899$	−0.737372	+	2.75191i	−0.0245927	+	0.0917813i
$900$	−5.33804	−	6.02079i	−0.177935	−	0.200693i
$901$	−9.42778	+	2.52616i	−0.314085	+	0.0841588i
$902$	−2.35633	+	6.29755i	−0.0784574	+	0.209685i
$903$	−57.5008	+	15.2610i	−1.91351	+	0.507856i
$904$	18.7564	+	5.57105i	0.623829	+	0.185290i
$905$	−8.02698	+	13.9031i	−0.266826	+	0.462156i
$906$	4.18923	−	25.8084i	0.139178	−	0.857426i
$907$	21.0916	+	5.65148i	0.700335	+	0.187654i	0.591381	−	0.806393i	$-0.298583\pi$
$907$	21.0916	+	5.65148i	0.700335	+	0.187654i	0.108954	+	0.994047i	$0.465250\pi$
$908$	−2.32259	+	4.75604i	−0.0770778	+	0.157835i
$909$	−0.565172	−	4.24219i	−0.0187456	−	0.140705i
$910$	−7.11529	+	11.4114i	−0.235870	+	0.378285i
$911$		−	5.98219i		−	0.198199i	−0.995078	−	0.0990994i	$-0.968404\pi$
$911$		−	5.98219i		−	0.198199i	0.995078	−	0.0990994i	$-0.0315962\pi$
$912$	10.4066	−	12.0722i	0.344599	−	0.399751i
$913$	−35.5175	+	20.5060i	−1.17546	+	0.678651i
$914$	−17.8620	+	25.0284i	−0.590821	+	0.827867i
$915$	2.60006	+	0.168397i	0.0859552	+	0.00556703i
$916$	9.62880	−	0.668522i	0.318145	−	0.0220886i
$917$	−2.56725	+	0.862462i	−0.0847782	+	0.0284810i
$918$	−6.72625	−	28.3022i	−0.221999	−	0.934113i
$919$	28.2043	+	16.2838i	0.930374	+	0.537152i	0.886930	−	0.461904i	$-0.152834\pi$
$919$	28.2043	+	16.2838i	0.930374	+	0.537152i	0.0434443	+	0.999056i	$0.486167\pi$
$920$	−18.1245	+	29.5272i	−0.597546	+	0.973483i
$921$	7.13740	−	1.42546i	0.235185	−	0.0469704i
$922$	−37.0044	+	30.4887i	−1.21868	+	1.00409i
$923$	−16.9653	+	16.9653i	−0.558421	+	0.558421i
$924$	22.9907	−	15.4116i	0.756339	−	0.507006i
$925$	−8.70611	−	8.70611i	−0.286255	−	0.286255i
$926$	2.38796	−	24.7357i	0.0784731	−	0.812865i
$927$	−31.3264	−	4.07491i	−1.02890	−	0.133838i
$928$	−8.08209	−	25.7442i	−0.265308	−	0.845094i
$929$	11.9866	−	20.7615i	0.393269	−	0.681162i	−0.599610	−	0.800293i	$-0.704677\pi$
$929$	11.9866	−	20.7615i	0.393269	−	0.681162i	0.992879	+	0.119131i	$0.0380108\pi$
$930$	−2.78429	+	0.281842i	−0.0913004	+	0.00924197i
$931$	−6.06883	−	14.9164i	−0.198898	−	0.488865i
$932$	−14.6153	+	16.7962i	−0.478740	+	0.550177i
$933$	13.5892	+	0.880128i	0.444891	+	0.0288141i
$934$	5.56705	+	33.3181i	0.182160	+	1.09020i
$935$	11.4341	+	19.8045i	0.373936	+	0.647676i
$936$	10.0235	−	12.3984i	0.327630	−	0.405255i
$937$	34.0643			1.11283			0.556416	−	0.830904i	$-0.312176\pi$
$937$	34.0643			1.11283			0.556416	+	0.830904i	$0.312176\pi$
$938$	25.3011	+	7.70855i	0.826109	+	0.251693i
$939$	−13.1005	+	6.47307i	−0.427520	+	0.211241i
$940$	−0.955555	−	0.466641i	−0.0311668	−	0.0152202i
$941$	7.40239	−	27.6261i	0.241311	−	0.900585i	−0.733891	−	0.679267i	$-0.762298\pi$
$941$	7.40239	−	27.6261i	0.241311	−	0.900585i	0.975202	−	0.221317i	$-0.0710357\pi$
$942$	34.5717	−	24.9157i	1.12641	−	0.811797i
$943$	8.73114	+	5.04093i	0.284325	+	0.164155i
$944$	−38.4416	−	29.0275i	−1.25117	−	0.944765i
$945$	−26.0750	+	3.41088i	−0.848219	+	0.110956i
$946$	−50.4584	+	22.9801i	−1.64054	+	0.747148i
$947$	−6.59494	−	24.6127i	−0.214307	−	0.799804i	−0.986409	−	0.164306i	$-0.947462\pi$
$947$	−6.59494	−	24.6127i	−0.214307	−	0.799804i	0.772103	−	0.635498i	$-0.219205\pi$
$948$	9.52764	−	2.60038i	0.309443	−	0.0844565i
$949$	22.9964	+	6.16188i	0.746496	+	0.200023i
$950$	−3.36735	+	2.77443i	−0.109251	+	0.0900143i
$951$	12.0885	−	35.7023i	0.391996	−	1.15773i
$952$	28.3258	−	8.67472i	0.918045	−	0.281149i
$953$	5.93311			0.192192			0.0960962	−	0.995372i	$-0.469364\pi$
$953$	5.93311			0.192192			0.0960962	+	0.995372i	$0.469364\pi$
$954$	−0.378645	−	10.4535i	−0.0122591	−	0.338445i
$955$	10.3305	−	38.5538i	0.334286	−	1.24757i
$956$	5.04404	−	25.8809i	0.163136	−	0.837049i
$957$	−1.61257	+	24.8982i	−0.0521271	+	0.804845i
$958$	31.0512	−	14.1416i	1.00322	−	0.456893i
$959$	−0.473758	−	0.713884i	−0.0152985	−	0.0230525i
$960$	20.8265	−	16.3943i	0.672172	−	0.529123i
$961$	−15.3216	+	26.5378i	−0.494246	+	0.856059i
$962$	14.1718	−	19.8577i	0.456916	−	0.640237i
$963$	7.45703	+	9.68713i	0.240299	+	0.312163i
$964$	25.6995	−	8.83481i	0.827725	−	0.284550i
$965$	23.2574	−	23.2574i	0.748682	−	0.748682i
$966$	−17.1110	−	37.8091i	−0.550538	−	1.21649i
$967$		−	15.0819i		−	0.485002i	−0.970151	−	0.242501i	$-0.922032\pi$
$967$		−	15.0819i		−	0.485002i	0.970151	−	0.242501i	$-0.0779678\pi$
$968$	−3.85957	+	3.65715i	−0.124051	+	0.117545i
$969$	−15.4686	+	3.08933i	−0.496922	+	0.0992436i
$970$	2.14794	+	12.8551i	0.0689662	+	0.412753i
$971$	0.856459	+	3.19635i	0.0274851	+	0.102576i	0.978306	−	0.207166i	$-0.0664241\pi$
$971$	0.856459	+	3.19635i	0.0274851	+	0.102576i	−0.950821	+	0.309742i	$0.899757\pi$
$972$	31.1760	−	0.241172i	0.999970	−	0.00773558i
$973$	17.8746	+	15.7755i	0.573034	+	0.505738i
$974$	9.45533	+	20.7614i	0.302968	+	0.665240i
$975$	−3.27912	+	2.88020i	−0.105016	+	0.0922401i
$976$	0.386453	−	3.12185i	0.0123700	−	0.0999279i
$977$	−34.6710	+	20.0173i	−1.10922	+	0.640411i	−0.938628	−	0.344930i	$-0.887903\pi$
$977$	−34.6710	+	20.0173i	−1.10922	+	0.640411i	−0.170596	+	0.985341i	$0.554569\pi$
$978$	−6.75499	+	15.0166i	−0.216001	+	0.480178i
$979$	26.9129	−	26.9129i	0.860139	−	0.860139i
$980$	−5.16067	−	26.2777i	−0.164852	−	0.839411i
$981$	49.1043	−	6.54200i	1.56778	−	0.208870i
$982$	2.33573	−	1.92446i	0.0745362	−	0.0614119i
$983$	−37.0193	+	21.3731i	−1.18073	+	0.681695i	−0.956184	−	0.292768i	$-0.905424\pi$
$983$	−37.0193	+	21.3731i	−1.18073	+	0.681695i	−0.224548	+	0.974463i	$0.572090\pi$
$984$	−4.93207	−	5.92980i	−0.157229	−	0.189035i
$985$	9.46394	−	16.3920i	0.301546	−	0.522293i
$986$	−9.35833	+	25.0111i	−0.298030	+	0.796516i
$987$	1.10466	−	0.634281i	0.0351616	−	0.0201894i
$988$	−6.52178	−	5.67496i	−0.207485	−	0.180545i
$989$	21.5166	+	80.3011i	0.684188	+	2.55343i
$990$	−23.4281	+	7.19600i	−0.744595	+	0.228704i
$991$	1.32563	+	2.29605i	0.0421099	+	0.0729365i	0.886312	−	0.463088i	$-0.153259\pi$
$991$	1.32563	+	2.29605i	0.0421099	+	0.0729365i	−0.844202	+	0.536025i	$0.819925\pi$
$992$	0.143199	+	3.37567i	0.00454658	+	0.107178i
$993$	−8.08102	+	23.8665i	−0.256443	+	0.757382i
$994$	1.62121	−	47.7503i	0.0514217	−	1.51455i
$995$	−1.85576	+	1.85576i	−0.0588317	+	0.0588317i
$996$	−0.218364	−	47.0432i	−0.00691912	−	1.49062i
$997$	−8.42525	+	31.4435i	−0.266830	+	0.995824i	0.694290	+	0.719695i	$0.255718\pi$
$997$	−8.42525	+	31.4435i	−0.266830	+	0.995824i	−0.961121	+	0.276129i	$0.910948\pi$
$998$	−1.46036	−	8.74008i	−0.0462270	−	0.276663i
$999$	47.5962	−	3.23056i	1.50588	−	0.102210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.173.32	yes	240
3.2	odd	2	inner	336.2.bo.a.173.29	yes	240
7.3	odd	6	inner	336.2.bo.a.269.49	yes	240
16.5	even	4	inner	336.2.bo.a.5.12	✓	240
21.17	even	6	inner	336.2.bo.a.269.12	yes	240
48.5	odd	4	inner	336.2.bo.a.5.49	yes	240
112.101	odd	12	inner	336.2.bo.a.101.29	yes	240
336.101	even	12	inner	336.2.bo.a.101.32	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.12	✓	240	16.5	even	4	inner
336.2.bo.a.5.49	yes	240	48.5	odd	4	inner
336.2.bo.a.101.29	yes	240	112.101	odd	12	inner
336.2.bo.a.101.32	yes	240	336.101	even	12	inner
336.2.bo.a.173.29	yes	240	3.2	odd	2	inner
336.2.bo.a.173.32	yes	240	1.1	even	1	trivial
336.2.bo.a.269.12	yes	240	21.17	even	6	inner
336.2.bo.a.269.49	yes	240	7.3	odd	6	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.135895 - 1.40767i) q^{2} +(1.44089 + 0.961162i) q^{3} +(-1.96307 - 0.382590i) q^{4} +(0.495078 + 1.84766i) q^{5} +(1.54881 - 1.89768i) q^{6} +(2.64062 - 0.164729i) q^{7} +(-0.805330 + 2.71135i) q^{8} +(1.15234 + 2.76986i) q^{9} +O(q^{10})\)	\(q+(0.135895 - 1.40767i) q^{2} +(1.44089 + 0.961162i) q^{3} +(-1.96307 - 0.382590i) q^{4} +(0.495078 + 1.84766i) q^{5} +(1.54881 - 1.89768i) q^{6} +(2.64062 - 0.164729i) q^{7} +(-0.805330 + 2.71135i) q^{8} +(1.15234 + 2.76986i) q^{9} +(2.66817 - 0.445819i) q^{10} +(-0.781622 + 2.91705i) q^{11} +(-2.46083 - 2.43809i) q^{12} +(-1.32862 + 1.32862i) q^{13} +(0.126963 - 3.73950i) q^{14} +(-1.06254 + 3.13812i) q^{15} +(3.70725 + 1.50210i) q^{16} +(-1.97936 - 3.42835i) q^{17} +(4.05564 - 1.24570i) q^{18} +(-0.595421 - 2.22214i) q^{19} +(-0.264976 - 3.81648i) q^{20} +(3.96318 + 2.30071i) q^{21} +(4.00003 + 1.49668i) q^{22} +(3.20186 - 5.54578i) q^{23} +(-3.76644 + 3.13271i) q^{24} +(1.16140 - 0.670533i) q^{25} +(1.68970 + 2.05081i) q^{26} +(-1.00189 + 5.09865i) q^{27} +(-5.24673 - 0.686901i) q^{28} +(3.37288 - 3.37288i) q^{29} +(4.27304 + 1.92216i) q^{30} +(-0.517256 + 0.298638i) q^{31} +(2.61825 - 5.01445i) q^{32} +(-3.92999 + 3.45189i) q^{33} +(-5.09497 + 2.32039i) q^{34} +(1.61167 + 4.79740i) q^{35} +(-1.20239 - 5.87829i) q^{36} +(-2.37621 - 8.86814i) q^{37} +(-3.20895 + 0.536178i) q^{38} +(-3.19141 + 0.637378i) q^{39} +(-5.40835 - 0.145642i) q^{40} +1.57438i q^{41} +(3.77721 - 5.26619i) q^{42} +(-9.17974 + 9.17974i) q^{43} +(2.65041 - 5.42733i) q^{44} +(-4.54725 + 3.50042i) q^{45} +(-7.37151 - 5.26080i) q^{46} +(0.138984 - 0.240727i) q^{47} +(3.89799 + 5.72763i) q^{48} +(6.94573 - 0.869970i) q^{49} +(-0.786061 - 1.72599i) q^{50} +(0.443158 - 6.84237i) q^{51} +(3.11648 - 2.09985i) q^{52} +(0.638126 - 2.38152i) q^{53} +(7.04106 + 2.10321i) q^{54} -5.77668 q^{55} +(-1.67993 + 7.29231i) q^{56} +(1.27790 - 3.77416i) q^{57} +(-4.28954 - 5.20625i) q^{58} +(-11.6322 - 3.11683i) q^{59} +(3.28645 - 5.75382i) q^{60} +(-0.203540 - 0.759622i) q^{61} +(0.350091 + 0.768709i) q^{62} +(3.49916 + 7.12432i) q^{63} +(-6.70289 - 4.36707i) q^{64} +(-3.11260 - 1.79706i) q^{65} +(4.32506 + 6.00123i) q^{66} +(-1.82956 + 6.82801i) q^{67} +(2.57396 + 7.48736i) q^{68} +(9.94392 - 4.91337i) q^{69} +(6.97217 - 1.61676i) q^{70} +12.7692 q^{71} +(-8.43808 + 0.893741i) q^{72} +(-6.33536 - 10.9732i) q^{73} +(-12.8063 + 2.13978i) q^{74} +(2.31794 + 0.150125i) q^{75} +(0.318681 + 4.59001i) q^{76} +(-1.58344 + 7.83158i) q^{77} +(0.463521 + 4.57907i) q^{78} +(-1.42550 + 2.46903i) q^{79} +(-0.939982 + 7.59338i) q^{80} +(-6.34424 + 6.38362i) q^{81} +(2.21620 + 0.213950i) q^{82} +(9.60276 + 9.60276i) q^{83} +(-6.89974 - 6.03270i) q^{84} +(5.35448 - 5.35448i) q^{85} +(11.6746 + 14.1695i) q^{86} +(8.10183 - 1.61807i) q^{87} +(-7.27970 - 4.46845i) q^{88} +(-10.9145 - 6.30150i) q^{89} +(4.30948 + 6.87671i) q^{90} +(-3.28951 + 3.72724i) q^{91} +(-8.40722 + 9.66173i) q^{92} +(-1.03235 - 0.0668618i) q^{93} +(-0.319976 - 0.228356i) q^{94} +(3.81097 - 2.20027i) q^{95} +(8.59232 - 4.70872i) q^{96} +4.81796i q^{97} +(-0.280742 - 9.89551i) q^{98} +(-8.98052 + 1.19644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

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