LMFDB - Embedded newform 378.2.bf.a.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(5,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("378.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	378.101
Dual form			378.2.bf.a.131.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 + 0.766044i) q^{2} +(-1.02900 + 1.39326i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.192211 - 0.161284i) q^{5} +(-0.405868 - 1.68383i) q^{6} +(1.12093 - 2.39657i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.882323 - 2.86732i) q^{9} +O(q^{10})$	\(q+(-0.642788 + 0.766044i) q^{2} +(-1.02900 + 1.39326i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.192211 - 0.161284i) q^{5} +(-0.405868 - 1.68383i) q^{6} +(1.12093 - 2.39657i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.882323 - 2.86732i) q^{9} +0.250914i q^{10} +(0.990049 - 1.17989i) q^{11} +(1.55077 + 0.771430i) q^{12} +(0.561675 - 1.54319i) q^{13} +(1.11536 + 2.39916i) q^{14} +(0.0269253 + 0.433761i) q^{15} +(-0.939693 + 0.342020i) q^{16} +3.55225 q^{17} +(2.76364 + 1.16718i) q^{18} -7.87949i q^{19} +(-0.192211 - 0.161284i) q^{20} +(2.18560 + 4.02780i) q^{21} +(0.267460 + 1.51684i) q^{22} +(-0.889699 + 2.44443i) q^{23} +(-1.58777 + 0.692095i) q^{24} +(-0.857308 + 4.86204i) q^{25} +(0.821115 + 1.42221i) q^{26} +(4.90281 + 1.72116i) q^{27} +(-2.55480 - 0.687738i) q^{28} +(2.08247 + 5.72155i) q^{29} +(-0.349587 - 0.258190i) q^{30} +(5.24515 - 0.924861i) q^{31} +(0.342020 - 0.939693i) q^{32} +(0.625136 + 2.59350i) q^{33} +(-2.28334 + 2.72118i) q^{34} +(-0.171074 - 0.641435i) q^{35} +(-2.67054 + 1.36682i) q^{36} +(1.66215 - 2.87894i) q^{37} +(6.03604 + 5.06484i) q^{38} +(1.57210 + 2.37050i) q^{39} +(0.247102 - 0.0435707i) q^{40} +(-0.882623 - 0.321249i) q^{41} +(-4.49035 - 0.914756i) q^{42} +(0.314905 - 1.78592i) q^{43} +(-1.33389 - 0.770122i) q^{44} +(-0.632046 - 0.408826i) q^{45} +(-1.30065 - 2.25280i) q^{46} +(1.20488 - 6.83324i) q^{47} +(0.490421 - 1.66117i) q^{48} +(-4.48705 - 5.37275i) q^{49} +(-3.17347 - 3.78199i) q^{50} +(-3.65526 + 4.94920i) q^{51} +(-1.61728 - 0.285170i) q^{52} +(8.07580 + 4.66257i) q^{53} +(-4.46996 + 2.64943i) q^{54} -0.386469i q^{55} +(2.16903 - 1.51502i) q^{56} +(10.9781 + 8.10798i) q^{57} +(-5.72155 - 2.08247i) q^{58} +(-7.02021 - 2.55515i) q^{59} +(0.422495 - 0.101838i) q^{60} +(-7.43170 - 1.31041i) q^{61} +(-2.66303 + 4.61251i) q^{62} +(-7.86073 - 1.09951i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.140932 - 0.387208i) q^{65} +(-2.38857 - 1.18819i) q^{66} +(-1.29464 + 1.08633i) q^{67} +(-0.616842 - 3.49829i) q^{68} +(-2.49022 - 3.75489i) q^{69} +(0.601332 + 0.281256i) q^{70} +(9.53352 - 5.50418i) q^{71} +(0.669544 - 2.92433i) q^{72} +(10.9243 - 6.30714i) q^{73} +(1.13698 + 3.12383i) q^{74} +(-5.89189 - 6.19748i) q^{75} +(-7.75978 + 1.36826i) q^{76} +(-1.71792 - 3.69529i) q^{77} +(-2.82643 - 0.319432i) q^{78} +(-9.72988 - 8.16434i) q^{79} +(-0.125457 + 0.217298i) q^{80} +(-7.44301 + 5.05980i) q^{81} +(0.813430 - 0.469634i) q^{82} +(-8.82507 + 3.21206i) q^{83} +(3.58708 - 2.85181i) q^{84} +(0.682783 - 0.572923i) q^{85} +(1.16567 + 1.38920i) q^{86} +(-10.1144 - 2.98605i) q^{87} +(1.44736 - 0.526794i) q^{88} +6.25145 q^{89} +(0.719450 - 0.221387i) q^{90} +(-3.06876 - 3.07589i) q^{91} +(2.56179 + 0.451712i) q^{92} +(-4.10868 + 8.25951i) q^{93} +(4.46008 + 5.31532i) q^{94} +(-1.27084 - 1.51453i) q^{95} +(0.957294 + 1.44346i) q^{96} +(14.9961 + 2.64422i) q^{97} +(6.99998 + 0.0162556i) q^{98} +(-4.25668 - 1.79774i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) $ 144 * q + 18 * q^6 - 12 * q^9	$ 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) $ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	−1.02900	+	1.39326i	−0.594093	+	0.804397i
$3$	−1.02900	+	1.39326i	−0.594093	+	0.804397i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	0.192211	−	0.161284i	0.0859595	−	0.0721286i	−0.598795	−	0.800902i	$-0.704354\pi$
$5$	0.192211	−	0.161284i	0.0859595	−	0.0721286i	0.684755	+	0.728774i	$0.259909\pi$
$6$	−0.405868	−	1.68383i	−0.165695	−	0.687419i
$7$	1.12093	−	2.39657i	0.423670	−	0.905816i
$7$	1.12093	−	2.39657i	0.423670	−	0.905816i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−0.882323	−	2.86732i	−0.294108	−	0.955772i
$10$			0.250914i			0.0793460i
$11$	0.990049	−	1.17989i	0.298511	−	0.355752i	−0.595851	−	0.803095i	$-0.703185\pi$
$11$	0.990049	−	1.17989i	0.298511	−	0.355752i	0.894362	+	0.447343i	$0.147630\pi$
$12$	1.55077	+	0.771430i	0.447670	+	0.222693i
$13$	0.561675	−	1.54319i	0.155781	−	0.428004i	−0.837110	−	0.547035i	$-0.815756\pi$
$13$	0.561675	−	1.54319i	0.155781	−	0.428004i	0.992891	+	0.119031i	$0.0379787\pi$
$14$	1.11536	+	2.39916i	0.298092	+	0.641203i
$15$	0.0269253	+	0.433761i	0.00695207	+	0.111997i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.55225			0.861548			0.430774	−	0.902460i	$-0.358241\pi$
$17$	3.55225			0.861548			0.430774	+	0.902460i	$0.358241\pi$
$18$	2.76364	+	1.16718i	0.651396	+	0.275106i
$19$		−	7.87949i		−	1.80768i	−0.427872	−	0.903839i	$-0.640737\pi$
$19$		−	7.87949i		−	1.80768i	0.427872	−	0.903839i	$-0.359263\pi$
$20$	−0.192211	−	0.161284i	−0.0429797	−	0.0360643i
$21$	2.18560	+	4.02780i	0.476936	+	0.878938i
$22$	0.267460	+	1.51684i	0.0570228	+	0.323392i
$23$	−0.889699	+	2.44443i	−0.185515	+	0.509699i	−0.997232	−	0.0743524i	$-0.976311\pi$
$23$	−0.889699	+	2.44443i	−0.185515	+	0.509699i	0.811717	+	0.584051i	$0.198533\pi$
$24$	−1.58777	+	0.692095i	−0.324102	+	0.141273i
$25$	−0.857308	+	4.86204i	−0.171462	+	0.972407i
$26$	0.821115	+	1.42221i	0.161034	+	0.278919i
$27$	4.90281	+	1.72116i	0.943547	+	0.331238i
$28$	−2.55480	−	0.687738i	−0.482812	−	0.129970i
$29$	2.08247	+	5.72155i	0.386705	+	1.06246i	0.968475	+	0.249111i	$0.0801383\pi$
$29$	2.08247	+	5.72155i	0.386705	+	1.06246i	−0.581770	+	0.813354i	$0.697639\pi$
$30$	−0.349587	−	0.258190i	−0.0638256	−	0.0471389i
$31$	5.24515	−	0.924861i	0.942056	−	0.166110i	0.318530	−	0.947913i	$-0.396811\pi$
$31$	5.24515	−	0.924861i	0.942056	−	0.166110i	0.623526	+	0.781803i	$0.285700\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	0.625136	+	2.59350i	0.108822	+	0.451471i
$34$	−2.28334	+	2.72118i	−0.391590	+	0.466679i
$35$	−0.171074	−	0.641435i	−0.0289168	−	0.108422i
$36$	−2.67054	+	1.36682i	−0.445090	+	0.227804i
$37$	1.66215	−	2.87894i	0.273257	−	0.473294i	−0.696437	−	0.717618i	$-0.745233\pi$
$37$	1.66215	−	2.87894i	0.273257	−	0.473294i	0.969694	+	0.244323i	$0.0785659\pi$
$38$	6.03604	+	5.06484i	0.979175	+	0.821625i
$39$	1.57210	+	2.37050i	0.251737	+	0.379584i
$40$	0.247102	−	0.0435707i	0.0390703	−	0.00688914i
$41$	−0.882623	−	0.321249i	−0.137843	−	0.0501706i	0.272178	−	0.962247i	$-0.412256\pi$
$41$	−0.882623	−	0.321249i	−0.137843	−	0.0501706i	−0.410020	+	0.912076i	$0.634478\pi$
$42$	−4.49035	−	0.914756i	−0.692876	−	0.141150i
$43$	0.314905	−	1.78592i	0.0480226	−	0.272350i	−0.951336	−	0.308155i	$-0.900288\pi$
$43$	0.314905	−	1.78592i	0.0480226	−	0.272350i	0.999359	+	0.0358053i	$0.0113996\pi$
$44$	−1.33389	−	0.770122i	−0.201091	−	0.116100i
$45$	−0.632046	−	0.408826i	−0.0942198	−	0.0609441i
$46$	−1.30065	−	2.25280i	−0.191771	−	0.332157i
$47$	1.20488	−	6.83324i	0.175750	−	0.996731i	−0.761524	−	0.648137i	$-0.775548\pi$
$47$	1.20488	−	6.83324i	0.175750	−	0.996731i	0.937274	−	0.348593i	$-0.113341\pi$
$48$	0.490421	−	1.66117i	0.0707862	−	0.239769i
$49$	−4.48705	−	5.37275i	−0.641007	−	0.767535i
$50$	−3.17347	−	3.78199i	−0.448796	−	0.534855i
$51$	−3.65526	+	4.94920i	−0.511839	+	0.693026i
$52$	−1.61728	−	0.285170i	−0.224276	−	0.0395460i
$53$	8.07580	+	4.66257i	1.10930	+	0.640453i	0.938647	−	0.344879i	$-0.112080\pi$
$53$	8.07580	+	4.66257i	1.10930	+	0.640453i	0.170649	+	0.985332i	$0.445413\pi$
$54$	−4.46996	+	2.64943i	−0.608284	+	0.360542i
$55$		−	0.386469i		−	0.0521114i
$56$	2.16903	−	1.51502i	0.289849	−	0.202453i
$57$	10.9781	+	8.10798i	1.45409	+	1.07393i
$58$	−5.72155	−	2.08247i	−0.751276	−	0.273442i
$59$	−7.02021	−	2.55515i	−0.913953	−	0.332652i	−0.158123	−	0.987419i	$-0.550544\pi$
$59$	−7.02021	−	2.55515i	−0.913953	−	0.332652i	−0.755830	+	0.654768i	$0.772767\pi$
$60$	0.422495	−	0.101838i	0.0545439	−	0.0131472i
$61$	−7.43170	−	1.31041i	−0.951532	−	0.167781i	−0.323726	−	0.946151i	$-0.604936\pi$
$61$	−7.43170	−	1.31041i	−0.951532	−	0.167781i	−0.627806	+	0.778370i	$0.716047\pi$
$62$	−2.66303	+	4.61251i	−0.338205	+	0.585789i
$63$	−7.86073	−	1.09951i	−0.990359	−	0.138525i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.140932	−	0.387208i	−0.0174805	−	0.0480272i
$66$	−2.38857	−	1.18819i	−0.294012	−	0.146256i
$67$	−1.29464	+	1.08633i	−0.158165	+	0.132716i	−0.718436	−	0.695593i	$-0.755142\pi$
$67$	−1.29464	+	1.08633i	−0.158165	+	0.132716i	0.560271	+	0.828310i	$0.310697\pi$
$68$	−0.616842	−	3.49829i	−0.0748031	−	0.424230i
$69$	−2.49022	−	3.75489i	−0.299787	−	0.452036i
$70$	0.601332	+	0.281256i	0.0718729	+	0.0336165i
$71$	9.53352	−	5.50418i	1.13142	−	0.653226i	0.187129	−	0.982335i	$-0.440082\pi$
$71$	9.53352	−	5.50418i	1.13142	−	0.653226i	0.944292	+	0.329109i	$0.106748\pi$
$72$	0.669544	−	2.92433i	0.0789065	−	0.344636i
$73$	10.9243	−	6.30714i	1.27859	−	0.738195i	0.302002	−	0.953307i	$-0.402345\pi$
$73$	10.9243	−	6.30714i	1.27859	−	0.738195i	0.976589	+	0.215112i	$0.0690117\pi$
$74$	1.13698	+	3.12383i	0.132171	+	0.363138i
$75$	−5.89189	−	6.19748i	−0.680337	−	0.715623i
$76$	−7.75978	+	1.36826i	−0.890108	+	0.156950i
$77$	−1.71792	−	3.69529i	−0.195775	−	0.421118i
$78$	−2.82643	−	0.319432i	−0.320030	−	0.0361686i
$79$	−9.72988	−	8.16434i	−1.09470	−	0.918560i	−0.0976395	−	0.995222i	$-0.531129\pi$
$79$	−9.72988	−	8.16434i	−1.09470	−	0.918560i	−0.997057	+	0.0766623i	$0.975574\pi$
$80$	−0.125457	+	0.217298i	−0.0140265	+	0.0242946i
$81$	−7.44301	+	5.05980i	−0.827001	+	0.562200i
$82$	0.813430	−	0.469634i	0.0898283	−	0.0518624i
$83$	−8.82507	+	3.21206i	−0.968678	+	0.352570i	−0.777428	−	0.628972i	$-0.783476\pi$
$83$	−8.82507	+	3.21206i	−0.968678	+	0.352570i	−0.191249	+	0.981541i	$0.561254\pi$
$84$	3.58708	−	2.85181i	0.391383	−	0.311158i
$85$	0.682783	−	0.572923i	0.0740582	−	0.0621422i
$86$	1.16567	+	1.38920i	0.125698	+	0.149801i
$87$	−10.1144	−	2.98605i	−1.08438	−	0.320138i
$88$	1.44736	−	0.526794i	0.154289	−	0.0561565i
$89$	6.25145			0.662652			0.331326	−	0.943516i	$-0.392504\pi$
$89$	6.25145			0.662652			0.331326	+	0.943516i	$0.392504\pi$
$90$	0.719450	−	0.221387i	0.0758367	−	0.0233363i
$91$	−3.06876	−	3.07589i	−0.321693	−	0.322441i
$92$	2.56179	+	0.451712i	0.267085	+	0.0470943i
$93$	−4.10868	+	8.25951i	−0.426051	+	0.856472i
$94$	4.46008	+	5.31532i	0.460022	+	0.548233i
$95$	−1.27084	−	1.51453i	−0.130385	−	0.155387i
$96$	0.957294	+	1.44346i	0.0977034	+	0.147323i
$97$	14.9961	+	2.64422i	1.52262	+	0.268480i	0.871463	−	0.490461i	$-0.163172\pi$
$97$	14.9961	+	2.64422i	1.52262	+	0.268480i	0.651160	+	0.758940i	$0.274283\pi$
$98$	6.99998	+	0.0162556i	0.707105	+	0.00164207i
$99$	−4.25668	−	1.79774i	−0.427812	−	0.180679i
$100$	4.93704			0.493704
$101$	−16.1765	+	5.88776i	−1.60962	+	0.585854i	−0.981365	−	0.192152i	$-0.938453\pi$
$101$	−16.1765	+	5.88776i	−1.60962	+	0.585854i	−0.628257	+	0.778006i	$0.716231\pi$
$102$	−1.44175	−	5.98138i	−0.142754	−	0.592245i
$103$	−2.16141	−	2.57587i	−0.212970	−	0.253808i	0.648975	−	0.760810i	$-0.275198\pi$
$103$	−2.16141	−	2.57587i	−0.212970	−	0.253808i	−0.861945	+	0.507002i	$0.830754\pi$
$104$	1.25802	−	1.05560i	0.123359	−	0.103511i
$105$	1.06972	+	0.421686i	0.104394	+	0.0411523i
$106$	−8.76276	+	3.18938i	−0.851114	+	0.309780i
$107$	0.822027	−	0.474597i	0.0794683	−	0.0458811i	−0.459739	−	0.888054i	$-0.652057\pi$
$107$	0.822027	−	0.474597i	0.0794683	−	0.0458811i	0.539208	+	0.842173i	$0.318724\pi$
$108$	0.843651	−	5.12721i	0.0811803	−	0.493366i
$109$	−0.947993	+	1.64197i	−0.0908012	+	0.157272i	−0.907849	−	0.419298i	$-0.862276\pi$
$109$	−0.947993	+	1.64197i	−0.0908012	+	0.157272i	0.817047	+	0.576571i	$0.195609\pi$
$110$	0.296052	+	0.248417i	0.0282275	+	0.0236857i
$111$	2.30074	+	5.27823i	0.218377	+	0.500987i
$112$	−0.233653	+	2.63541i	−0.0220781	+	0.249023i
$113$	−8.76558	+	1.54561i	−0.824596	+	0.145399i	−0.569996	−	0.821648i	$-0.693055\pi$
$113$	−8.76558	+	1.54561i	−0.824596	+	0.145399i	−0.254601	+	0.967046i	$0.581944\pi$
$114$	−13.2677	+	3.19803i	−1.24263	+	0.299523i
$115$	0.223238	+	0.613341i	0.0208170	+	0.0571944i
$116$	5.27301	−	3.04437i	0.489586	−	0.282663i
$117$	−4.92040	−	0.248909i	−0.454891	−	0.0230116i
$118$	6.46986	−	3.73538i	0.595599	−	0.343869i
$119$	3.98181	−	8.51321i	0.365012	−	0.780404i
$120$	−0.193562	+	0.389111i	−0.0176698	+	0.0355208i
$121$	1.49818	+	8.49658i	0.136198	+	0.772416i
$122$	5.78084	−	4.85070i	0.523372	−	0.439161i
$123$	1.35580	−	0.899155i	0.122248	−	0.0810741i
$124$	−1.82162	−	5.00486i	−0.163586	−	0.449450i
$125$	1.24667	+	2.15930i	0.111506	+	0.193133i
$126$	5.89505	−	5.31492i	0.525173	−	0.473491i
$127$	−2.36151	+	4.09025i	−0.209550	+	0.362951i	−0.951573	−	0.307423i	$-0.900533\pi$
$127$	−2.36151	+	4.09025i	−0.209550	+	0.362951i	0.742023	+	0.670374i	$0.233867\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	2.16420	+	2.27645i	0.190547	+	0.200430i
$130$	0.387208	+	0.140932i	0.0339604	+	0.0123606i
$131$	−12.9652	−	4.71896i	−1.13278	−	0.412297i	−0.293478	−	0.955966i	$-0.594813\pi$
$131$	−12.9652	−	4.71896i	−1.13278	−	0.412297i	−0.839300	+	0.543669i	$0.817035\pi$
$132$	2.44555	−	1.06600i	0.212858	−	0.0927830i
$133$	−18.8837	−	8.83232i	−1.63742	−	0.765860i
$134$		−	1.69003i		−	0.145996i
$135$	1.21997	−	0.459920i	0.104999	−	0.0395836i
$136$	3.07634	+	1.77613i	0.263794	+	0.152302i
$137$	14.3772	+	2.53509i	1.22833	+	0.216587i	0.749906	−	0.661544i	$-0.230099\pi$
$137$	14.3772	+	2.53509i	1.22833	+	0.216587i	0.478420	+	0.878131i	$0.341210\pi$
$138$	4.47709	+	0.505983i	0.381116	+	0.0430722i
$139$	11.7026	+	13.9467i	0.992604	+	1.18294i	0.983116	+	0.182985i	$0.0585759\pi$
$139$	11.7026	+	13.9467i	0.992604	+	1.18294i	0.00948857	+	0.999955i	$0.496980\pi$
$140$	−0.601983	+	0.279859i	−0.0508769	+	0.0236524i
$141$	8.28063	+	8.71011i	0.697355	+	0.733523i
$142$	−1.91158	+	10.8411i	−0.160416	+	0.909767i
$143$	−1.26472	−	2.19055i	−0.105761	−	0.183183i
$144$	1.80979	+	2.39262i	0.150816	+	0.199385i
$145$	1.32307	+	0.763875i	0.109875	+	0.0634364i
$146$	−2.19045	+	12.4226i	−0.181283	+	1.02811i
$147$	12.1028	−	0.723058i	0.998220	−	0.0596368i
$148$	−3.12383	−	1.13698i	−0.256777	−	0.0934593i
$149$	−12.7882	+	2.25491i	−1.04765	+	0.184729i	−0.670872	−	0.741573i	$-0.734080\pi$
$149$	−12.7882	+	2.25491i	−1.04765	+	0.184729i	−0.376780	+	0.926303i	$0.622969\pi$
$150$	8.53478	−	0.529788i	0.696862	−	0.0432570i
$151$	8.83099	+	7.41008i	0.718656	+	0.603024i	0.927013	−	0.375029i	$-0.122367\pi$
$151$	8.83099	+	7.41008i	0.718656	+	0.603024i	−0.208357	+	0.978053i	$0.566812\pi$
$152$	3.93974	−	6.82384i	0.319555	−	0.553486i
$153$	−3.13424	−	10.1854i	−0.253388	−	0.823444i
$154$	3.93502	+	1.05928i	0.317093	+	0.0853595i
$155$	0.859011	−	1.02373i	0.0689974	−	0.0822279i
$156$	2.06149	−	1.95985i	0.165052	−	0.156913i
$157$	−2.06342	+	5.66920i	−0.164679	+	0.452451i	−0.994394	−	0.105735i	$-0.966280\pi$
$157$	−2.06342	+	5.66920i	−0.164679	+	0.452451i	0.829715	+	0.558187i	$0.188503\pi$
$158$	12.5085	−	2.20558i	0.995122	−	0.175467i
$159$	−14.8061	+	6.45388i	−1.17420	+	0.511826i
$160$	−0.0858176	−	0.235782i	−0.00678448	−	0.0186402i
$161$	4.86095	+	4.87225i	0.383096	+	0.383987i
$162$	0.908245	−	8.95405i	0.0713584	−	0.703497i
$163$	2.51123	+	4.34957i	0.196694	+	0.340685i	0.947455	−	0.319890i	$-0.103646\pi$
$163$	2.51123	+	4.34957i	0.196694	+	0.340685i	−0.750760	+	0.660575i	$0.770313\pi$
$164$	−0.163102	+	0.924998i	−0.0127361	+	0.0722302i
$165$	0.538450	+	0.397676i	0.0419182	+	0.0309590i
$166$	3.21206	−	8.82507i	0.249305	−	0.684959i
$167$	−0.680744	−	3.86069i	−0.0526776	−	0.298749i	0.947075	−	0.321014i	$-0.104024\pi$
$167$	−0.680744	−	3.86069i	−0.0526776	−	0.298749i	−0.999752	+	0.0222643i	$0.992912\pi$
$168$	−0.121118	+	4.58097i	−0.00934444	+	0.353430i
$169$	7.89262	+	6.62269i	0.607125	+	0.509438i
$170$			0.891310i			0.0683603i
$171$	−22.5930	+	6.95225i	−1.72773	+	0.531652i
$172$	−1.81347			−0.138276
$173$	11.2134	−	4.08134i	0.852539	−	0.310299i	0.121464	−	0.992596i	$-0.461241\pi$
$173$	11.2134	−	4.08134i	0.852539	−	0.310299i	0.731075	+	0.682297i	$0.239019\pi$
$174$	8.78888	−	5.82872i	0.666283	−	0.441874i
$175$	10.6912	+	7.50458i	0.808179	+	0.567293i
$176$	−0.526794	+	1.44736i	−0.0397086	+	0.109099i
$177$	10.7838	−	7.15170i	0.810557	−	0.537555i
$178$	−4.01835	+	4.78889i	−0.301188	+	0.358942i
$179$		−	4.48399i		−	0.335149i	−0.985859	−	0.167574i	$-0.946407\pi$
$179$		−	4.48399i		−	0.335149i	0.985859	−	0.167574i	$-0.0535935\pi$
$180$	−0.292861	+	0.693435i	−0.0218286	+	0.0516856i
$181$	0.930546	+	0.537251i	0.0691670	+	0.0399336i	0.534185	−	0.845368i	$-0.320619\pi$
$181$	0.930546	+	0.537251i	0.0691670	+	0.0399336i	−0.465018	+	0.885301i	$0.653952\pi$
$182$	4.32883	−	0.373660i	0.320874	−	0.0276975i
$183$	9.47294	−	9.00585i	0.700260	−	0.665731i
$184$	−1.99272	+	1.67209i	−0.146905	+	0.123268i
$185$	−0.144843	−	0.821444i	−0.0106490	−	0.0603937i
$186$	−3.68614	−	8.45655i	−0.270281	−	0.620064i
$187$	3.51691	−	4.19129i	0.257182	−	0.306497i
$188$	−6.93865			−0.506053
$189$	9.62058	−	9.82062i	0.699794	−	0.714345i
$190$	1.97707			0.143432
$191$	−11.6429	+	13.8755i	−0.842454	+	1.00400i	0.157411	+	0.987533i	$0.449685\pi$
$191$	−11.6429	+	13.8755i	−0.842454	+	1.00400i	−0.999864	+	0.0164641i	$0.994759\pi$
$192$	−1.72109	−	0.194511i	−0.124209	−	0.0140376i
$193$	1.60155	+	9.08284i	0.115282	+	0.653797i	0.986610	+	0.163096i	$0.0521481\pi$
$193$	1.60155	+	9.08284i	0.115282	+	0.653797i	−0.871328	+	0.490701i	$0.836741\pi$
$194$	−11.6649	+	9.78801i	−0.837491	+	0.702738i
$195$	0.684499	+	0.202082i	0.0490180	+	0.0144714i
$196$	−4.51195	+	5.35185i	−0.322282	+	0.382275i
$197$	−19.8315	−	11.4497i	−1.41293	−	0.815757i	−0.417269	−	0.908783i	$-0.637013\pi$
$197$	−19.8315	−	11.4497i	−1.41293	−	0.815757i	−0.995664	+	0.0930262i	$0.970346\pi$
$198$	4.11329	−	2.10524i	0.292318	−	0.149613i
$199$		−	7.80352i		−	0.553177i	−0.960988	−	0.276589i	$-0.910796\pi$
$199$		−	7.80352i		−	0.553177i	0.960988	−	0.276589i	$-0.0892039\pi$
$200$	−3.17347	+	3.78199i	−0.224398	+	0.267427i
$201$	−0.181355	−	2.92160i	−0.0127918	−	0.206073i
$202$	5.88776	−	16.1765i	0.414262	−	1.13817i
$203$	16.0464	+	1.42265i	1.12623	+	0.0998505i
$204$	5.50874	+	2.74031i	0.385689	+	0.191860i
$205$	−0.221462	+	0.0806057i	−0.0154676	+	0.00562975i
$206$	3.36256			0.234280
$207$	7.79395	+	0.394274i	0.541717	+	0.0274039i
$208$			1.64223i			0.113868i
$209$	−9.29697	−	7.80108i	−0.643085	−	0.539612i
$210$	−1.01063	+	0.548397i	−0.0697402	+	0.0378430i
$211$	4.79231	+	27.1785i	0.329916	+	1.87105i	0.472598	+	0.881278i	$0.343316\pi$
$211$	4.79231	+	27.1785i	0.329916	+	1.87105i	−0.142682	+	0.989769i	$0.545573\pi$
$212$	3.18938	−	8.76276i	0.219048	−	0.601829i
$213$	−2.14125	+	18.9464i	−0.146716	+	1.29819i
$214$	−0.164826	+	0.934775i	−0.0112673	+	0.0638999i
$215$	−0.227512	−	0.394062i	−0.0155162	−	0.0268748i
$216$	3.38538	+	3.94198i	0.230346	+	0.268218i
$217$	3.66293	−	13.6070i	0.248656	−	0.923706i
$218$	−0.648465	−	1.78164i	−0.0439196	−	0.120668i
$219$	−2.45362	+	21.7104i	−0.165800	+	1.46705i
$220$	−0.380597	+	0.0671096i	−0.0256599	+	0.00452453i
$221$	1.99521	−	5.48180i	0.134213	−	0.368746i
$222$	−5.52225	−	1.63031i	−0.370629	−	0.109419i
$223$	5.81563	−	6.93080i	0.389444	−	0.464121i	−0.535328	−	0.844645i	$-0.679812\pi$
$223$	5.81563	−	6.93080i	0.389444	−	0.464121i	0.924771	+	0.380524i	$0.124256\pi$
$224$	−1.86866	−	1.87300i	−0.124855	−	0.125145i
$225$	14.6974	−	1.83171i	0.979828	−	0.122114i
$226$	4.45040	−	7.70832i	0.296036	−	0.512750i
$227$	−15.0604	−	12.6372i	−0.999594	−	0.838759i	−0.0126661	−	0.999920i	$-0.504032\pi$
$227$	−15.0604	−	12.6372i	−0.999594	−	0.838759i	−0.986928	+	0.161161i	$0.948476\pi$
$228$	6.07847	−	12.2193i	0.402557	−	0.809243i
$229$	13.6972	−	2.41518i	0.905135	−	0.159600i	0.298342	−	0.954459i	$-0.403567\pi$
$229$	13.6972	−	2.41518i	0.905135	−	0.159600i	0.606794	+	0.794859i	$0.292455\pi$
$230$	−0.613341	−	0.223238i	−0.0404425	−	0.0147199i
$231$	6.91623	+	1.40895i	0.455054	+	0.0927019i
$232$	−1.05730	+	5.99624i	−0.0694151	+	0.393672i
$233$	21.4009	+	12.3558i	1.40202	+	0.809455i	0.994599	−	0.103788i	$-0.0330962\pi$
$233$	21.4009	+	12.3558i	1.40202	+	0.809455i	0.407417	+	0.913242i	$0.366430\pi$
$234$	3.35344	−	3.60925i	0.219222	−	0.235944i
$235$	−0.870503	−	1.50775i	−0.0567853	−	0.0983551i
$236$	−1.29728	+	7.35725i	−0.0844459	+	0.478916i
$237$	21.3870	−	5.15511i	1.38924	−	0.334861i
$238$	3.96203	+	8.52243i	0.256821	+	0.552427i
$239$	−12.0988	−	14.4188i	−0.782606	−	0.932674i	0.216442	−	0.976296i	$-0.430555\pi$
$239$	−12.0988	−	14.4188i	−0.782606	−	0.932674i	−0.999048	+	0.0436217i	$0.986110\pi$
$240$	−0.173656	−	0.398393i	−0.0112095	−	0.0257161i
$241$	−25.8643	−	4.56057i	−1.66607	−	0.293772i	−0.740415	−	0.672150i	$-0.765371\pi$
$241$	−25.8643	−	4.56057i	−1.66607	−	0.293772i	−0.925651	+	0.378378i	$0.876482\pi$
$242$	−7.47176	−	4.31382i	−0.480303	−	0.277303i
$243$	0.609256	−	15.5765i	0.0390838	−	0.999236i
$244$			7.54635i			0.483105i
$245$	−1.72900	−	0.309011i	−0.110462	−	0.0197420i
$246$	−0.182698	+	1.61657i	−0.0116484	+	0.103069i
$247$	−12.1596	−	4.42572i	−0.773694	−	0.281602i
$248$	5.00486	+	1.82162i	0.317809	+	0.115673i
$249$	4.60576	−	15.6008i	0.291878	−	0.988660i
$250$	−2.45546	−	0.432964i	−0.155297	−	0.0273831i
$251$	−7.97673	+	13.8161i	−0.503487	+	0.872065i	0.496505	+	0.868034i	$0.334616\pi$
$251$	−7.97673	+	13.8161i	−0.503487	+	0.872065i	−0.999992	+	0.00403107i	$0.998717\pi$
$252$	0.282199	+	7.93224i	0.0177769	+	0.499684i
$253$	2.00332	+	3.46986i	0.125948	+	0.218148i
$254$	−1.61537	−	4.43818i	−0.101357	−	0.278476i
$255$	0.0956453	+	1.54083i	0.00598954	+	0.0964904i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	4.18389	+	23.7280i	0.260984	+	1.48011i	0.780233	+	0.625489i	$0.215100\pi$
$257$	4.18389	+	23.7280i	0.260984	+	1.48011i	−0.519249	+	0.854623i	$0.673788\pi$
$258$	−3.13498	+	0.194601i	−0.195175	+	0.0121153i
$259$	−5.03641	−	7.21054i	−0.312947	−	0.448041i
$260$	−0.356853	+	0.206029i	−0.0221311	+	0.0127774i
$261$	14.5681	−	11.0194i	0.901741	−	0.682081i
$262$	11.9488	−	6.89866i	0.738201	−	0.426200i
$263$	6.13787	+	16.8636i	0.378477	+	1.03986i	0.971988	+	0.235031i	$0.0755192\pi$
$263$	6.13787	+	16.8636i	0.378477	+	1.03986i	−0.593511	+	0.804826i	$0.702259\pi$
$264$	−0.755368	+	2.55861i	−0.0464897	+	0.157471i
$265$	2.30426	−	0.406303i	0.141549	−	0.0249590i
$266$	18.9042	−	8.78845i	1.15909	−	0.538854i
$267$	−6.43273	+	8.70986i	−0.393677	+	0.533035i
$268$	1.29464	+	1.08633i	0.0790826	+	0.0663582i
$269$	−3.18737	+	5.52070i	−0.194338	+	0.336603i	−0.946683	−	0.322166i	$-0.895589\pi$
$269$	−3.18737	+	5.52070i	−0.194338	+	0.336603i	0.752346	+	0.658769i	$0.228922\pi$
$270$	−0.431864	+	1.23018i	−0.0262824	+	0.0748666i
$271$	−2.85403	+	1.64778i	−0.173370	+	0.100095i	−0.584174	−	0.811628i	$-0.698581\pi$
$271$	−2.85403	+	1.64778i	−0.173370	+	0.100095i	0.410804	+	0.911724i	$0.365248\pi$
$272$	−3.33803	+	1.21494i	−0.202398	+	0.0736667i
$273$	7.44326	−	1.11048i	0.450487	−	0.0672090i
$274$	−11.1835	+	9.38404i	−0.675618	+	0.566911i
$275$	4.88792	+	5.82519i	0.294752	+	0.351272i
$276$	−3.26543	+	3.10441i	−0.196556	+	0.186864i
$277$	1.76181	−	0.641247i	0.105857	−	0.0385288i	−0.288549	−	0.957465i	$-0.593173\pi$
$277$	1.76181	−	0.641247i	0.105857	−	0.0385288i	0.394406	+	0.918936i	$0.370950\pi$
$278$	−18.2061			−1.09193
$279$	−7.27978	−	14.2235i	−0.435829	−	0.851537i
$280$	0.172563	−	0.641036i	0.0103126	−	0.0383092i
$281$	−11.4439	−	2.01786i	−0.682685	−	0.120376i	−0.178459	−	0.983947i	$-0.557111\pi$
$281$	−11.4439	−	2.01786i	−0.682685	−	0.120376i	−0.504226	+	0.863572i	$0.668222\pi$
$282$	−11.9950	+	0.744578i	−0.714293	+	0.0443390i
$283$	15.1419	+	18.0454i	0.900094	+	1.07269i	0.997000	+	0.0773963i	$0.0246607\pi$
$283$	15.1419	+	18.0454i	0.900094	+	1.07269i	−0.0969068	+	0.995293i	$0.530895\pi$
$284$	−7.07604	−	8.43290i	−0.419886	−	0.500400i
$285$	3.41781	−	0.212157i	0.202454	−	0.0125671i
$286$	2.49101	+	0.439231i	0.147296	+	0.0259723i
$287$	−1.75925	+	1.75517i	−0.103845	+	0.103604i
$288$	−2.99617	−	0.151568i	−0.176551	−	0.00893121i
$289$	−4.38150			−0.257735
$290$	−1.43562	+	0.522521i	−0.0843023	+	0.0306835i
$291$	−19.1150	+	18.1725i	−1.12054	+	1.06529i
$292$	−8.10831	−	9.66310i	−0.474503	−	0.565490i
$293$	−17.9999	+	15.1037i	−1.05156	+	0.882366i	−0.993257	−	0.115933i	$-0.963014\pi$
$293$	−17.9999	+	15.1037i	−1.05156	+	0.882366i	−0.0583059	+	0.998299i	$0.518570\pi$
$294$	−7.22562	+	9.73604i	−0.421407	+	0.567817i
$295$	−1.76147	+	0.641122i	−0.102557	+	0.0373276i
$296$	2.87894	−	1.66215i	0.167335	−	0.0966108i
$297$	6.88482	−	4.08077i	0.399498	−	0.236790i
$298$	6.49275	−	11.2458i	0.376115	−	0.651450i
$299$	3.27250	+	2.74595i	0.189253	+	0.158802i
$300$	−5.08021	+	6.87856i	−0.293306	+	0.397134i
$301$	−3.92708	−	2.75657i	−0.226353	−	0.158886i
$302$	−11.3529	+	2.00182i	−0.653286	+	0.115192i
$303$	8.44244	−	28.5965i	0.485005	−	1.64283i
$304$	2.69494	+	7.40430i	0.154566	+	0.424666i
$305$	−1.63980	+	0.946742i	−0.0938949	+	0.0542103i
$306$	9.81714	+	4.14611i	0.561209	+	0.237017i
$307$	−7.21564	+	4.16595i	−0.411818	+	0.237763i	−0.691571	−	0.722309i	$-0.743081\pi$
$307$	−7.21564	+	4.16595i	−0.411818	+	0.237763i	0.279752	+	0.960072i	$0.409748\pi$
$308$	−3.34084	+	2.33350i	−0.190362	+	0.132964i
$309$	5.81293	−	0.360832i	0.330686	−	0.0205270i
$310$	0.232061	+	1.31608i	0.0131802	+	0.0747484i
$311$	10.8306	−	9.08795i	0.614147	−	0.515330i	−0.281811	−	0.959470i	$-0.590935\pi$
$311$	10.8306	−	9.08795i	0.614147	−	0.515330i	0.895958	+	0.444140i	$0.146491\pi$
$312$	0.176226	+	2.83896i	0.00997681	+	0.160724i
$313$	−3.92655	−	10.7881i	−0.221942	−	0.609780i	0.777885	−	0.628407i	$-0.216293\pi$
$313$	−3.92655	−	10.7881i	−0.221942	−	0.609780i	−0.999827	+	0.0186267i	$0.994071\pi$
$314$	−3.01652	−	5.22476i	−0.170232	−	0.294850i
$315$	−1.68825	+	1.05648i	−0.0951223	+	0.0595257i
$316$	−6.35073	+	10.9998i	−0.357256	+	0.618786i
$317$	−6.36740	−	1.12275i	−0.357629	−	0.0630596i	−0.00805281	−	0.999968i	$-0.502563\pi$
$317$	−6.36740	−	1.12275i	−0.357629	−	0.0630596i	−0.349576	+	0.936908i	$0.613674\pi$
$318$	4.57324	−	15.4906i	0.256455	−	0.868672i
$319$	8.81257	+	3.20751i	0.493409	+	0.179586i
$320$	0.235782	+	0.0858176i	0.0131806	+	0.00479735i
$321$	−0.184629	+	1.63365i	−0.0103050	+	0.0911817i
$322$	−6.85691	+	0.591880i	−0.382121	+	0.0329842i
$323$		−	27.9899i		−	1.55740i
$324$	6.27540	+	6.45131i	0.348633	+	0.358406i
$325$	7.02152	+	4.05388i	0.389484	+	0.224869i
$326$	−4.94615	−	0.872140i	−0.273942	−	0.0483034i
$327$	−1.31220	−	3.01038i	−0.0725650	−	0.166475i
$328$	−0.603750	−	0.719521i	−0.0333365	−	0.0397289i
$329$	−15.0257	−	10.5471i	−0.828395	−	0.581483i
$330$	−0.650746	+	0.156855i	−0.0358224	+	0.00863460i
$331$	−4.76308	+	27.0128i	−0.261803	+	1.48476i	0.516185	+	0.856477i	$0.327352\pi$
$331$	−4.76308	+	27.0128i	−0.261803	+	1.48476i	−0.777987	+	0.628280i	$0.783759\pi$
$332$	4.69572	+	8.13323i	0.257711	+	0.446369i
$333$	−9.72138	−	2.22577i	−0.532728	−	0.121972i
$334$	3.39504	+	1.96013i	0.185768	+	0.107253i
$335$	−0.0736359	+	0.417610i	−0.00402316	+	0.0228165i
$336$	−3.43138	−	3.03738i	−0.187197	−	0.165702i
$337$	−28.4533	−	10.3562i	−1.54995	−	0.564136i	−0.581546	−	0.813514i	$-0.697552\pi$
$337$	−28.4533	−	10.3562i	−1.54995	−	0.564136i	−0.968406	+	0.249377i	$0.919774\pi$
$338$	−10.1466	+	1.78911i	−0.551900	+	0.0973148i
$339$	6.86634	−	13.8031i	0.372929	−	0.749683i
$340$	−0.682783	−	0.572923i	−0.0370291	−	0.0310711i
$341$	4.10172	−	7.10438i	0.222120	−	0.384724i
$342$	9.19676	−	21.7761i	0.497304	−	1.17751i
$343$	−17.9058	+	4.73105i	−0.966822	+	0.255453i
$344$	1.16567	−	1.38920i	0.0628489	−	0.0749004i
$345$	−1.08425	−	0.320100i	−0.0583742	−	0.0172336i
$346$	−4.08134	+	11.2134i	−0.219414	+	0.602836i
$347$	0.0561624	−	0.00990294i	0.00301495	−	0.000531618i	−0.172140	−	0.985072i	$-0.555068\pi$
$347$	0.0561624	−	0.00990294i	0.00301495	−	0.000531618i	0.175155	+	0.984541i	$0.443957\pi$
$348$	−1.18433	+	10.4793i	−0.0634867	+	0.561749i
$349$	−3.76424	−	10.3422i	−0.201495	−	0.553603i	0.797252	−	0.603647i	$-0.206286\pi$
$349$	−3.76424	−	10.3422i	−0.201495	−	0.553603i	−0.998747	+	0.0500436i	$0.984064\pi$
$350$	−12.6210	+	3.36609i	−0.674622	+	0.179925i
$351$	5.40988	−	6.59924i	0.288758	−	0.352242i
$352$	−0.770122	−	1.33389i	−0.0410476	−	0.0710966i
$353$	1.50093	−	8.51222i	0.0798866	−	0.453060i	−0.918457	−	0.395522i	$-0.870564\pi$
$353$	1.50093	−	8.51222i	0.0798866	−	0.453060i	0.998343	−	0.0575380i	$-0.0183250\pi$
$354$	−1.45314	+	12.8579i	−0.0772338	+	0.683388i
$355$	0.944712	−	2.59557i	0.0501401	−	0.137759i
$356$	−1.08555	−	6.15647i	−0.0575342	−	0.326292i
$357$	7.76379	+	14.3078i	0.410903	+	0.757247i
$358$	3.43493	+	2.88225i	0.181542	+	0.152332i
$359$		−	20.2231i		−	1.06733i	−0.845695	−	0.533666i	$-0.820814\pi$
$359$		−	20.2231i		−	1.06733i	0.845695	−	0.533666i	$-0.179186\pi$
$360$	−0.342955	−	0.670076i	−0.0180753	−	0.0353161i
$361$	−43.0863			−2.26770
$362$	−1.00970	+	0.367501i	−0.0530688	+	0.0193154i
$363$	−13.3795	−	6.65562i	−0.702243	−	0.349330i
$364$	−2.49628	+	3.55626i	−0.130841	+	0.186399i
$365$	1.08253	−	2.97422i	0.0566621	−	0.155678i
$366$	0.809789	+	13.0455i	0.0423283	+	0.681902i
$367$	9.70146	−	11.5617i	0.506412	−	0.603518i	−0.450900	−	0.892574i	$-0.648897\pi$
$367$	9.70146	−	11.5617i	0.506412	−	0.603518i	0.957312	+	0.289056i	$0.0933414\pi$
$368$		−	2.60131i		−	0.135603i
$369$	−0.142363	+	2.81421i	−0.00741110	+	0.146502i
$370$	0.722365	+	0.417058i	0.0375540	+	0.0216818i
$371$	20.2265	−	14.1278i	1.05011	−	0.733478i
$372$	8.84750	+	2.61201i	0.458721	+	0.135427i
$373$	23.3464	−	19.5899i	1.20883	−	1.01433i	0.209497	−	0.977809i	$-0.432817\pi$
$373$	23.3464	−	19.5899i	1.20883	−	1.01433i	0.999333	−	0.0365195i	$-0.0116271\pi$
$374$	0.950087	+	5.38821i	0.0491279	+	0.278618i
$375$	−4.29128	−	0.484983i	−0.221601	−	0.0250444i
$376$	4.46008	−	5.31532i	0.230011	−	0.274117i
$377$	9.99911			0.514980
$378$	1.33904	+	13.6824i	0.0688729	+	0.703745i
$379$	−9.40461			−0.483083			−0.241541	−	0.970391i	$-0.577653\pi$
$379$	−9.40461			−0.483083			−0.241541	+	0.970391i	$0.577653\pi$
$380$	−1.27084	+	1.51453i	−0.0651926	+	0.0776935i
$381$	−3.26878	−	7.49905i	−0.167465	−	0.384188i
$382$	−3.14532	−	17.8380i	−0.160929	−	0.912673i
$383$	8.63996	−	7.24979i	0.441481	−	0.370447i	−0.394782	−	0.918775i	$-0.629180\pi$
$383$	8.63996	−	7.24979i	0.441481	−	0.370447i	0.836263	+	0.548328i	$0.184735\pi$
$384$	1.25530	−	1.19341i	0.0640594	−	0.0609007i
$385$	−0.926197	−	0.433203i	−0.0472034	−	0.0220781i
$386$	−7.98732	−	4.61148i	−0.406544	−	0.234718i
$387$	−5.39863	+	0.672822i	−0.274428	+	0.0342015i
$388$		−	15.2274i		−	0.773056i
$389$	−18.1419	+	21.6207i	−0.919830	+	1.09621i	0.0752524	+	0.997165i	$0.476024\pi$
$389$	−18.1419	+	21.6207i	−0.919830	+	1.09621i	−0.995083	+	0.0990466i	$0.968421\pi$
$390$	−0.594791	+	0.394461i	−0.0301184	+	0.0199743i
$391$	−3.16044	+	8.68323i	−0.159830	+	0.439130i
$392$	−1.19953	−	6.89646i	−0.0605852	−	0.348324i
$393$	19.9159	−	13.2081i	1.00463	−	0.666260i
$394$	21.5184	−	7.83205i	1.08408	−	0.394573i
$395$	−3.18697			−0.160354
$396$	−1.03126	+	4.50418i	−0.0518228	+	0.226344i
$397$			14.9822i			0.751933i	0.926633	+	0.375967i	$0.122689\pi$
$397$			14.9822i			0.751933i	−0.926633	+	0.375967i	$0.877311\pi$
$398$	5.97785	+	5.01601i	0.299642	+	0.251430i
$399$	31.7370	−	17.2214i	1.58884	−	0.862147i
$400$	−0.857308	−	4.86204i	−0.0428654	−	0.243102i
$401$	−9.25605	+	25.4308i	−0.462225	+	1.26995i	0.461583	+	0.887097i	$0.347282\pi$
$401$	−9.25605	+	25.4308i	−0.462225	+	1.26995i	−0.923808	+	0.382856i	$0.874941\pi$
$402$	2.35464	+	1.73904i	0.117439	+	0.0867354i
$403$	1.51883	−	8.61374i	0.0756585	−	0.429081i
$404$	8.60734	+	14.9083i	0.428231	+	0.741718i
$405$	−0.614564	+	2.17299i	−0.0305379	+	0.107977i
$406$	−11.4042	+	11.3778i	−0.565982	+	0.564669i
$407$	−1.75123	−	4.81146i	−0.0868051	−	0.238495i
$408$	−5.64015	+	2.45850i	−0.279229	+	0.121714i
$409$	31.8274	−	5.61203i	1.57376	−	0.277497i	0.682467	−	0.730917i	$-0.260907\pi$
$409$	31.8274	−	5.61203i	1.57376	−	0.277497i	0.891297	+	0.453420i	$0.149796\pi$
$410$	0.0806057	−	0.221462i	0.00398083	−	0.0109373i
$411$	−18.3261	+	17.4225i	−0.903961	+	0.859388i
$412$	−2.16141	+	2.57587i	−0.106485	+	0.126904i
$413$	−13.9927	+	13.9603i	−0.688536	+	0.686939i
$414$	−5.31189	+	5.71708i	−0.261065	+	0.280979i
$415$	−1.17822	+	2.04074i	−0.0578367	+	0.100176i
$416$	−1.25802	−	1.05560i	−0.0616795	−	0.0517553i
$417$	−31.4732	+	1.95367i	−1.54125	+	0.0956716i
$418$	11.9520	−	2.10745i	0.584589	−	0.103079i
$419$	−17.2669	−	6.28465i	−0.843545	−	0.307025i	−0.116139	−	0.993233i	$-0.537052\pi$
$419$	−17.2669	−	6.28465i	−0.843545	−	0.307025i	−0.727406	+	0.686208i	$0.759274\pi$
$420$	0.229525	−	1.12669i	0.0111997	−	0.0549769i
$421$	4.30946	−	24.4401i	0.210030	−	1.19114i	−0.679295	−	0.733865i	$-0.737714\pi$
$421$	4.30946	−	24.4401i	0.210030	−	1.19114i	0.889325	−	0.457275i	$-0.151174\pi$
$422$	−23.9004	−	13.7989i	−1.16345	−	0.671720i
$423$	−20.6562	+	2.57434i	−1.00434	+	0.125169i
$424$	4.66257	+	8.07580i	0.226434	+	0.392196i
$425$	−3.04538	+	17.2712i	−0.147722	+	0.837776i
$426$	−13.1374	−	13.8188i	−0.636511	−	0.669524i
$427$	−11.4709	+	16.3417i	−0.555114	+	0.790829i
$428$	−0.610131	−	0.727125i	−0.0294918	−	0.0351469i
$429$	4.35339	+	0.492003i	0.210184	+	0.0237541i
$430$	0.448111	+	0.0790141i	0.0216098	+	0.00381040i
$431$	14.6107	+	8.43552i	0.703775	+	0.406325i	0.808752	−	0.588150i	$-0.200144\pi$
$431$	14.6107	+	8.43552i	0.703775	+	0.406325i	−0.104977	+	0.994475i	$0.533477\pi$
$432$	−5.19581	+	0.0594965i	−0.249984	+	0.00286253i
$433$			7.54427i			0.362554i	0.983432	+	0.181277i	$0.0580231\pi$
$433$			7.54427i			0.362554i	−0.983432	+	0.181277i	$0.941977\pi$
$434$	8.06911	+	11.5524i	0.387330	+	0.554533i
$435$	−2.42571	+	1.05735i	−0.116304	+	0.0506960i
$436$	1.78164	+	0.648465i	0.0853253	+	0.0310559i
$437$	19.2608	+	7.01038i	0.921371	+	0.335352i
$438$	−15.0540	−	15.8347i	−0.719306	−	0.756613i
$439$	8.29449	+	1.46254i	0.395874	+	0.0698033i	0.368042	−	0.929809i	$-0.380028\pi$
$439$	8.29449	+	1.46254i	0.395874	+	0.0698033i	0.0278326	+	0.999613i	$0.491139\pi$
$440$	0.193234	−	0.334692i	0.00921208	−	0.0159558i
$441$	−11.4463	+	17.6063i	−0.545064	+	0.838395i
$442$	2.91681	+	5.05206i	0.138738	+	0.240302i
$443$	10.1523	+	27.8932i	0.482350	+	1.32525i	0.907473	+	0.420111i	$0.138009\pi$
$443$	10.1523	+	27.8932i	0.482350	+	1.32525i	−0.425123	+	0.905136i	$0.639769\pi$
$444$	4.79852	−	3.18234i	0.227728	−	0.151027i
$445$	1.20160	−	1.00826i	0.0569612	−	0.0477961i
$446$	1.57109	+	8.91007i	0.0743930	+	0.421904i
$447$	10.0174	−	20.1376i	0.473807	−	0.952474i
$448$	2.63595	−	0.227532i	0.124537	−	0.0107499i
$449$	14.3123	−	8.26319i	0.675438	−	0.389964i	−0.122696	−	0.992444i	$-0.539154\pi$
$449$	14.3123	−	8.26319i	0.675438	−	0.389964i	0.798134	+	0.602480i	$0.205821\pi$
$450$	−8.04415	+	12.4363i	−0.379205	+	0.586252i
$451$	−1.25288	+	0.723351i	−0.0589958	+	0.0340613i
$452$	3.04425	+	8.36402i	0.143190	+	0.393410i
$453$	−19.4112	+	4.67886i	−0.912018	+	0.219832i
$454$	19.3613	−	3.41392i	0.908670	−	0.160223i
$455$	−1.08594	−	0.0962785i	−0.0509098	−	0.00451360i
$456$	5.45336	+	12.5108i	0.255377	+	0.585871i
$457$	−4.38345	−	3.67815i	−0.205049	−	0.172057i	0.534480	−	0.845181i	$-0.320507\pi$
$457$	−4.38345	−	3.67815i	−0.205049	−	0.172057i	−0.739529	+	0.673124i	$0.764952\pi$
$458$	−6.95424	+	12.0451i	−0.324950	+	0.562831i
$459$	17.4160	+	6.11401i	0.812911	+	0.285378i
$460$	0.565258	−	0.326352i	0.0263553	−	0.0152162i
$461$	1.54167	−	0.561121i	0.0718026	−	0.0261340i	−0.305869	−	0.952074i	$-0.598947\pi$
$461$	1.54167	−	0.561121i	0.0718026	−	0.0261340i	0.377672	+	0.925940i	$0.376725\pi$
$462$	−5.52498	+	4.39249i	−0.257045	+	0.204357i
$463$	−15.4751	+	12.9852i	−0.719189	+	0.603471i	−0.927161	−	0.374664i	$-0.877758\pi$
$463$	−15.4751	+	12.9852i	−0.719189	+	0.603471i	0.207972	+	0.978135i	$0.433314\pi$
$464$	−3.91377	−	4.66425i	−0.181692	−	0.216532i
$465$	0.542395	+	2.25024i	0.0251530	+	0.104352i
$466$	−23.2213	+	8.45186i	−1.07571	+	0.391525i
$467$	32.4447			1.50136			0.750681	−	0.660664i	$-0.229725\pi$
$467$	32.4447			1.50136			0.750681	+	0.660664i	$0.229725\pi$
$468$	0.609290	+	4.88887i	0.0281645	+	0.225988i
$469$	1.15227	+	4.32038i	0.0532068	+	0.199497i
$470$	1.71456	+	0.302322i	0.0790865	+	0.0139451i
$471$	−5.77539	−	8.70847i	−0.266116	−	0.401265i
$472$	−4.80211	−	5.72293i	−0.221035	−	0.263419i
$473$	−1.79542	−	2.13970i	−0.0825536	−	0.0983835i
$474$	−9.79828	+	19.6971i	−0.450050	+	0.904716i
$475$	38.3104	+	6.75515i	1.75780	+	0.309948i
$476$	−9.07531	−	2.44302i	−0.415966	−	0.111976i
$477$	6.24359	−	27.2698i	0.285874	−	1.24860i
$478$	18.8224			0.860916
$479$	5.48548	−	1.99655i	0.250638	−	0.0912247i	−0.213646	−	0.976911i	$-0.568534\pi$
$479$	5.48548	−	1.99655i	0.250638	−	0.0912247i	0.464284	+	0.885686i	$0.346312\pi$
$480$	0.416811	+	0.123053i	0.0190247	+	0.00561660i
$481$	−3.50916	−	4.18205i	−0.160004	−	0.190685i
$482$	20.1189	−	16.8817i	0.916389	−	0.768942i
$483$	−11.7902	+	1.75900i	−0.536472	+	0.0800375i
$484$	8.10734	−	2.95083i	0.368515	−	0.134129i
$485$	3.30889	−	1.91039i	0.150249	−	0.0867463i
$486$	11.5407	+	10.4791i	0.523497	+	0.475343i
$487$	4.12510	−	7.14488i	0.186926	−	0.323765i	−0.757298	−	0.653070i	$-0.773481\pi$
$487$	4.12510	−	7.14488i	0.186926	−	0.323765i	0.944224	+	0.329304i	$0.106814\pi$
$488$	−5.78084	−	4.85070i	−0.261686	−	0.219581i
$489$	−8.64412	−	0.976924i	−0.390900	−	0.0441780i
$490$	1.34810	−	1.12586i	0.0609008	−	0.0508613i
$491$	22.8417	−	4.02761i	1.03083	−	0.181764i	0.367449	−	0.930044i	$-0.380231\pi$
$491$	22.8417	−	4.02761i	1.03083	−	0.181764i	0.663383	+	0.748280i	$0.269120\pi$
$492$	−1.12093	−	1.17907i	−0.0505353	−	0.0531564i
$493$	7.39747	+	20.3244i	0.333165	+	0.915364i
$494$	11.2063	−	6.46996i	0.504195	−	0.291097i
$495$	−1.10813	+	0.340990i	−0.0498066	+	0.0153264i
$496$	−4.61251	+	2.66303i	−0.207108	+	0.119574i
$497$	−2.50475	−	29.0175i	−0.112354	−	1.30161i
$498$	8.99037	+	13.5562i	0.402868	+	0.607469i
$499$	−2.79438	−	15.8477i	−0.125093	−	0.709440i	−0.981252	−	0.192728i	$-0.938267\pi$
$499$	−2.79438	−	15.8477i	−0.125093	−	0.709440i	0.856159	−	0.516713i	$-0.172844\pi$
$500$	1.91001	−	1.60269i	0.0854183	−	0.0716745i
$501$	6.07942	+	3.02420i	0.271608	+	0.135111i
$502$	−5.45641	−	14.9914i	−0.243531	−	0.669097i
$503$	7.34194	+	12.7166i	0.327361	+	0.567006i	0.981987	−	0.188947i	$-0.0605074\pi$
$503$	7.34194	+	12.7166i	0.327361	+	0.567006i	−0.654626	+	0.755953i	$0.727174\pi$
$504$	−6.25784	−	4.88257i	−0.278746	−	0.217487i
$505$	−2.15970	+	3.74071i	−0.0961054	+	0.166459i
$506$	−3.94578	−	0.695747i	−0.175411	−	0.0309297i
$507$	−17.3486	+	4.18169i	−0.770478	+	0.185716i
$508$	4.43818	+	1.61537i	0.196912	+	0.0716703i
$509$	27.8540	+	10.1380i	1.23461	+	0.449361i	0.875174	−	0.483809i	$-0.160747\pi$
$509$	27.8540	+	10.1380i	1.23461	+	0.449361i	0.359435	+	0.933170i	$0.382969\pi$
$510$	−1.24182	−	0.917157i	−0.0549888	−	0.0406124i
$511$	−2.87015	−	33.2506i	−0.126968	−	1.47092i
$512$			1.00000i			0.0441942i
$513$	13.5619	−	38.6317i	0.598772	−	1.70563i
$514$	−20.8661	−	12.0470i	−0.920362	−	0.531371i
$515$	−0.830894	−	0.146509i	−0.0366136	−	0.00645596i
$516$	1.86605	−	2.52662i	0.0821485	−	0.111228i
$517$	−6.86961	−	8.18688i	−0.302125	−	0.360059i
$518$	8.76093	+	0.776734i	0.384933	+	0.0341277i
$519$	−5.85222	+	19.8228i	−0.256884	+	0.870126i
$520$	0.0715532	−	0.405798i	0.00313781	−	0.0177954i
$521$	5.09642	+	8.82725i	0.223278	+	0.386729i	0.955801	−	0.294013i	$-0.0949909\pi$
$521$	5.09642	+	8.82725i	0.223278	+	0.386729i	−0.732523	+	0.680742i	$0.761658\pi$
$522$	−0.922856	+	18.2429i	−0.0403923	+	0.798470i
$523$	18.6114	+	10.7453i	0.813822	+	0.469860i	0.848281	−	0.529546i	$-0.177638\pi$
$523$	18.6114	+	10.7453i	0.813822	+	0.469860i	−0.0344596	+	0.999406i	$0.510971\pi$
$524$	−2.39588	+	13.5877i	−0.104664	+	0.593581i
$525$	−21.4570	+	7.17338i	−0.936462	+	0.313072i
$526$	−16.8636	−	6.13787i	−0.735290	−	0.267624i
$527$	18.6321	−	3.28534i	0.811627	−	0.143112i
$528$	−1.47447	−	2.22329i	−0.0641679	−	0.0967561i
$529$	12.4354	+	10.4345i	0.540668	+	0.453674i
$530$	−1.16990	+	2.02633i	−0.0508173	+	0.0880182i
$531$	−1.13232	+	22.3836i	−0.0491387	+	0.971367i
$532$	−5.41902	+	20.1305i	−0.234944	+	0.872769i
$533$	−0.991496	+	1.18162i	−0.0429464	+	0.0511816i
$534$	−2.53726	−	10.5264i	−0.109798	−	0.455520i
$535$	0.0814576	−	0.223803i	0.00352172	−	0.00967585i
$536$	−1.66436	+	0.293471i	−0.0718892	+	0.0126760i
$537$	6.24734	+	4.61402i	0.269593	+	0.199110i
$538$	−2.18029	−	5.99031i	−0.0939991	−	0.258260i
$539$	−10.7817	−	0.0250377i	−0.464400	−	0.00107845i
$540$	−0.664779	−	1.12157i	−0.0286075	−	0.0482649i
$541$	9.76509	+	16.9136i	0.419834	+	0.727174i	0.995922	−	0.0902134i	$-0.0287549\pi$
$541$	9.76509	+	16.9136i	0.419834	+	0.727174i	−0.576088	+	0.817387i	$0.695422\pi$
$542$	0.572267	−	3.24549i	0.0245810	−	0.139406i
$543$	−1.70606	+	0.743658i	−0.0732140	+	0.0319134i
$544$	1.21494	−	3.33803i	0.0520902	−	0.143117i
$545$	0.0826095	+	0.468502i	0.00353860	+	0.0200684i
$546$	−3.93376	+	6.41567i	−0.168349	+	0.274565i
$547$	12.7092	+	10.6643i	0.543406	+	0.455972i	0.872701	−	0.488255i	$-0.162367\pi$
$547$	12.7092	+	10.6643i	0.543406	+	0.455972i	−0.329295	+	0.944227i	$0.606811\pi$
$548$		−	14.5990i		−	0.623637i
$549$	2.79980	+	22.4652i	0.119493	+	0.958793i
$550$	−7.60425			−0.324246
$551$	45.0829	−	16.4088i	1.92059	−	0.699039i
$552$	−0.279143	−	4.49694i	−0.0118811	−	0.191403i
$553$	−30.4728	+	14.1667i	−1.29584	+	0.602428i
$554$	−0.641247	+	1.76181i	−0.0272440	+	0.0748522i
$555$	1.29352	+	0.643462i	0.0549070	+	0.0273134i
$556$	11.7026	−	13.9467i	0.496302	−	0.591470i
$557$		−	18.9001i		−	0.800821i	−0.916336	−	0.400411i	$-0.868868\pi$
$557$		−	18.9001i		−	0.800821i	0.916336	−	0.400411i	$-0.131132\pi$
$558$	15.5752	+	3.56603i	0.659350	+	0.150962i
$559$	−2.57913	−	1.48906i	−0.109086	−	0.0629807i
$560$	0.380140	+	0.544241i	0.0160639	+	0.0229984i
$561$	2.22064	+	9.21278i	0.0937555	+	0.388964i
$562$	8.90176	−	7.46946i	0.375498	−	0.315080i
$563$	1.24712	+	7.07275i	0.0525597	+	0.298081i	0.999744	−	0.0226077i	$-0.00719688\pi$
$563$	1.24712	+	7.07275i	0.0525597	+	0.298081i	−0.947185	+	0.320688i	$0.896086\pi$
$564$	7.13987	−	9.66732i	0.300643	−	0.407068i
$565$	−1.43556	+	1.71083i	−0.0603945	+	0.0719753i
$566$	−23.5566			−0.990160
$567$	3.78307	+	23.5093i	0.158874	+	0.987299i
$568$	11.0084			0.461901
$569$	25.0091	−	29.8047i	1.04844	−	1.24948i	0.0809076	−	0.996722i	$-0.474218\pi$
$569$	25.0091	−	29.8047i	1.04844	−	1.24948i	0.967530	−	0.252757i	$-0.0813374\pi$
$570$	−2.03441	+	2.75457i	−0.0852119	+	0.115376i
$571$	1.26153	+	7.15447i	0.0527933	+	0.299405i	0.999760	−	0.0219274i	$-0.00698028\pi$
$571$	1.26153	+	7.15447i	0.0527933	+	0.299405i	−0.946966	+	0.321333i	$0.895869\pi$
$572$	−1.93766	+	1.62589i	−0.0810176	+	0.0679818i
$573$	−7.35157	−	30.4995i	−0.307116	−	1.27413i
$574$	−0.213713	−	2.47586i	−0.00892023	−	0.103341i
$575$	−11.1222	−	6.42138i	−0.463826	−	0.267790i
$576$	2.04201	−	2.19777i	0.0850837	−	0.0915739i
$577$		−	11.2124i		−	0.466779i	−0.972383	−	0.233389i	$-0.925018\pi$
$577$		−	11.2124i		−	0.466779i	0.972383	−	0.233389i	$-0.0749816\pi$
$578$	2.81637	−	3.35642i	0.117146	−	0.139609i
$579$	−14.3027	−	7.11487i	−0.594401	−	0.295684i
$580$	0.522521	−	1.43562i	0.0216965	−	0.0596107i
$581$	−2.19434	+	24.7503i	−0.0910364	+	1.02682i
$582$	−1.63404	−	26.3240i	−0.0677330	−	1.09117i
$583$	13.4968	−	4.91243i	0.558980	−	0.203452i
$584$	12.6143			0.521983
$585$	−0.985900	+	0.745740i	−0.0407620	+	0.0308325i
$586$		−	23.4971i		−	0.970658i
$587$	−15.8859	−	13.3299i	−0.655683	−	0.550183i	0.253107	−	0.967438i	$-0.418548\pi$
$587$	−15.8859	−	13.3299i	−0.655683	−	0.550183i	−0.908789	+	0.417255i	$0.862992\pi$
$588$	−2.81370	−	11.7934i	−0.116035	−	0.486350i
$589$	−7.28743	−	41.3291i	−0.300273	−	1.70294i
$590$	0.641122	−	1.76147i	0.0263946	−	0.0725185i
$591$	36.3589	−	15.8486i	1.49560	−	0.651923i
$592$	−0.577260	+	3.27381i	−0.0237253	+	0.134553i
$593$	19.2800	+	33.3939i	0.791733	+	1.37132i	0.924893	+	0.380228i	$0.124154\pi$
$593$	19.2800	+	33.3939i	0.791733	+	1.37132i	−0.133160	+	0.991095i	$0.542512\pi$
$594$	−1.29943	+	7.89715i	−0.0533162	+	0.324024i
$595$	−0.607698	−	2.27854i	−0.0249132	−	0.0934110i
$596$	4.44131	+	12.2024i	0.181923	+	0.499829i
$597$	10.8723	+	8.02982i	0.444974	+	0.328639i
$598$	−4.20704	+	0.741815i	−0.172039	+	0.0303351i
$599$	15.7038	−	43.1459i	0.641641	−	1.76289i	−0.00486983	−	0.999988i	$-0.501550\pi$
$599$	15.7038	−	43.1459i	0.641641	−	1.76289i	0.646510	−	0.762905i	$-0.276228\pi$
$600$	−2.00379	−	8.31312i	−0.0818043	−	0.339382i
$601$	−24.6258	+	29.3479i	−1.00451	+	1.19712i	−0.0241872	+	0.999707i	$0.507700\pi$
$601$	−24.6258	+	29.3479i	−1.00451	+	1.19712i	−0.980320	+	0.197417i	$0.936745\pi$
$602$	4.63593	−	1.23643i	0.188947	−	0.0503930i
$603$	4.25714	+	2.75364i	0.173364	+	0.112137i
$604$	5.76402	−	9.98357i	0.234535	−	0.406226i
$605$	1.65833	+	1.39151i	0.0674207	+	0.0565727i
$606$	16.4795	+	24.8488i	0.669434	+	1.00941i
$607$	5.64099	−	0.994660i	0.228961	−	0.0403720i	−0.0579905	−	0.998317i	$-0.518469\pi$
$607$	5.64099	−	0.994660i	0.228961	−	0.0403720i	0.286951	+	0.957945i	$0.407358\pi$
$608$	−7.40430	−	2.69494i	−0.300284	−	0.109294i
$609$	−18.4938	+	20.8928i	−0.749406	+	0.846618i
$610$	0.328800	−	1.86472i	0.0133127	−	0.0755002i
$611$	−9.86824	−	5.69743i	−0.399226	−	0.230493i
$612$	−9.48644	+	4.85530i	−0.383467	+	0.196264i
$613$	−21.5459	−	37.3186i	−0.870230	−	1.50728i	−0.861759	−	0.507318i	$-0.830637\pi$
$613$	−21.5459	−	37.3186i	−0.870230	−	1.50728i	−0.00847119	−	0.999964i	$-0.502696\pi$
$614$	1.44682	−	8.20532i	0.0583889	−	0.331140i
$615$	0.115580	−	0.391497i	0.00466064	−	0.0157867i
$616$	0.359882	−	4.05918i	0.0145001	−	0.163549i
$617$	28.9863	+	34.5446i	1.16695	+	1.39071i	0.904882	+	0.425662i	$0.139959\pi$
$617$	28.9863	+	34.5446i	1.16695	+	1.39071i	0.262064	+	0.965050i	$0.415597\pi$
$618$	−3.46007	+	4.68490i	−0.139184	+	0.188454i
$619$	−16.2774	−	2.87014i	−0.654242	−	0.115361i	−0.163333	−	0.986571i	$-0.552224\pi$
$619$	−16.2774	−	2.87014i	−0.654242	−	0.115361i	−0.490910	+	0.871210i	$0.663336\pi$
$620$	−1.15734	−	0.668192i	−0.0464800	−	0.0268352i
$621$	−8.56929	+	10.4533i	−0.343874	+	0.419475i
$622$			14.1383i			0.566896i
$623$	7.00741	−	14.9820i	0.280746	−	0.600241i
$624$	−2.28805	−	1.68985i	−0.0915951	−	0.0676482i
$625$	−22.6086	−	8.22887i	−0.904345	−	0.329155i
$626$	10.7881	+	3.92655i	0.431180	+	0.156937i
$627$	20.4355	−	4.92575i	0.816114	−	0.196715i
$628$	5.94138	+	1.04763i	0.237087	+	0.0418048i
$629$	5.90440	−	10.2267i	0.235424	−	0.407766i
$630$	0.275881	−	1.97237i	0.0109914	−	0.0785810i
$631$	21.8965	+	37.9258i	0.871685	+	1.50980i	0.860253	+	0.509868i	$0.170306\pi$
$631$	21.8965	+	37.9258i	0.871685	+	1.50980i	0.0114324	+	0.999935i	$0.496361\pi$
$632$	−4.34415	−	11.9355i	−0.172801	−	0.474767i
$633$	−42.7979	−	21.2898i	−1.70106	−	0.846192i
$634$	4.95296	−	4.15603i	0.196707	−	0.165057i
$635$	0.205785	+	1.16707i	0.00816634	+	0.0463136i
$636$	8.92689	+	13.4605i	0.353974	+	0.533743i
$637$	−10.8114	+	3.90663i	−0.428365	+	0.154786i
$638$	−8.12171	+	4.68907i	−0.321542	+	0.185642i
$639$	−24.1939	−	22.4792i	−0.957095	−	0.889262i
$640$	−0.217298	+	0.125457i	−0.00858945	+	0.00495912i
$641$	−1.96200	−	5.39056i	−0.0774945	−	0.212914i	0.894896	−	0.446275i	$-0.147250\pi$
$641$	−1.96200	−	5.39056i	−0.0774945	−	0.212914i	−0.972390	+	0.233361i	$0.925028\pi$
$642$	−1.13277	−	1.19153i	−0.0447070	−	0.0470258i
$643$	8.69859	−	1.53380i	0.343039	−	0.0604870i	0.000525273	−	1.00000i	$-0.499833\pi$
$643$	8.69859	−	1.53380i	0.343039	−	0.0604870i	0.342514	+	0.939513i	$0.388722\pi$
$644$	3.95413	−	5.63315i	0.155815	−	0.221977i
$645$	0.783139	+	0.0885073i	0.0308361	+	0.00348497i
$646$	21.4415	+	17.9916i	0.843606	+	0.707869i
$647$	−17.5715	+	30.4347i	−0.690807	+	1.19651i	0.280767	+	0.959776i	$0.409411\pi$
$647$	−17.5715	+	30.4347i	−0.690807	+	1.19651i	−0.971574	+	0.236737i	$0.923922\pi$
$648$	−8.97574	+	0.660409i	−0.352600	+	0.0259433i
$649$	−9.96516	+	5.75339i	−0.391167	+	0.225840i
$650$	−7.61880	+	2.77302i	−0.298834	+	0.108767i
$651$	15.1889	+	19.1050i	0.595301	+	0.748785i
$652$	3.84742	−	3.22837i	0.150677	−	0.126433i
$653$	18.3630	+	21.8841i	0.718598	+	0.856392i	0.994494	−	0.104796i	$-0.0334188\pi$
$653$	18.3630	+	21.8841i	0.718598	+	0.856392i	−0.275896	+	0.961188i	$0.588974\pi$
$654$	3.14956	+	0.929831i	0.123157	+	0.0363593i
$655$	−3.25316	+	1.18405i	−0.127111	+	0.0462648i
$656$	0.939268			0.0366723
$657$	−27.7233	−	25.7585i	−1.08159	−	1.00493i
$658$	17.7379	−	4.73080i	0.691496	−	0.184426i
$659$	3.67168	+	0.647415i	0.143028	+	0.0252197i	0.244704	−	0.969598i	$-0.421309\pi$
$659$	3.67168	+	0.647415i	0.143028	+	0.0252197i	−0.101676	+	0.994818i	$0.532420\pi$
$660$	0.298133	−	0.599325i	0.0116048	−	0.0233287i
$661$	−23.0640	−	27.4865i	−0.897084	−	1.06910i	−0.997248	−	0.0741320i	$-0.976381\pi$
$661$	−23.0640	−	27.4865i	−0.897084	−	1.06910i	0.100165	−	0.994971i	$-0.468063\pi$
$662$	−17.6313	−	21.0122i	−0.685262	−	0.816663i
$663$	5.58448	+	8.42061i	0.216883	+	0.327030i
$664$	−9.24877	−	1.63081i	−0.358922	−	0.0632876i
$665$	−5.05418	+	1.34797i	−0.195993	+	0.0522722i
$666$	7.95382	−	6.01631i	0.308204	−	0.233127i
$667$	−15.8387			−0.613276
$668$	−3.68383	+	1.34080i	−0.142532	+	0.0518773i
$669$	3.67210	+	15.2344i	0.141972	+	0.588998i
$670$	−0.272575	−	0.324843i	−0.0105305	−	0.0125498i
$671$	−8.90389	+	7.47125i	−0.343731	+	0.288425i
$672$	4.53241	−	0.676200i	0.174842	−	0.0260850i
$673$	8.46322	−	3.08036i	0.326233	−	0.118739i	−0.173711	−	0.984797i	$-0.555576\pi$
$673$	8.46322	−	3.08036i	0.326233	−	0.118739i	0.499945	+	0.866057i	$0.333354\pi$
$674$	26.2227	−	15.1397i	1.01006	−	0.583160i
$675$	−12.5716	+	22.3621i	−0.483881	+	0.860718i
$676$	5.15154	−	8.92273i	0.198136	−	0.343182i
$677$	−13.7698	−	11.5542i	−0.529215	−	0.444064i	0.338615	−	0.940925i	$-0.390042\pi$
$677$	−13.7698	−	11.5542i	−0.529215	−	0.444064i	−0.867830	+	0.496861i	$0.834486\pi$
$678$	6.16021	+	14.1324i	0.236581	+	0.542752i
$679$	23.1466	−	32.9752i	0.888283	−	1.26547i
$680$	0.877769	−	0.154774i	0.0336609	−	0.00593532i
$681$	33.1040	−	7.97935i	1.26855	−	0.305769i
$682$	2.80574	+	7.70871i	0.107437	+	0.295182i
$683$	0.0195816	−	0.0113054i	0.000749268	−	0.000432590i	−0.499625	−	0.866242i	$-0.666529\pi$
$683$	0.0195816	−	0.0113054i	0.000749268	−	0.000432590i	0.500375	+	0.865809i	$0.333196\pi$
$684$	10.7699	+	21.0425i	0.411796	+	0.804580i
$685$	3.17233	−	1.83154i	0.121208	−	0.0699797i
$686$	7.88542	−	16.7577i	0.301067	−	0.639812i
$687$	−10.7294	+	21.5689i	−0.409353	+	0.822905i
$688$	0.314905	+	1.78592i	0.0120056	+	0.0680874i
$689$	11.7312	−	9.84365i	0.446923	−	0.375013i
$690$	0.942155	−	0.624830i	0.0358672	−	0.0237869i
$691$	−8.70951	−	23.9292i	−0.331325	−	0.910309i	−0.987768	−	0.155933i	$-0.950162\pi$
$691$	−8.70951	−	23.9292i	−0.331325	−	0.910309i	0.656442	−	0.754376i	$-0.272061\pi$
$692$	−5.96653	−	10.3343i	−0.226813	−	0.392852i
$693$	−9.07981	+	8.18627i	−0.344914	+	0.310971i
$694$	−0.0285144	+	0.0493884i	−0.00108239	+	0.00187476i
$695$	4.49875	+	0.793252i	0.170647	+	0.0300898i
$696$	−7.26634	−	7.64321i	−0.275430	−	0.289715i
$697$	−3.13530	−	1.14116i	−0.118758	−	0.0432244i
$698$	10.3422	+	3.76424i	0.391456	+	0.142478i
$699$	−39.2362	+	17.1028i	−1.48405	+	0.646886i
$700$	5.53406	−	11.8319i	0.209168	−	0.447205i
$701$		−	41.2322i		−	1.55732i	−0.627446	−	0.778660i	$-0.715900\pi$
$701$		−	41.2322i		−	1.55732i	0.627446	−	0.778660i	$-0.284100\pi$
$702$	1.57791	+	8.38612i	0.0595545	+	0.316514i
$703$	−22.6845	−	13.0969i	−0.855564	−	0.493960i
$704$	1.51684	+	0.267460i	0.0571682	+	0.0100803i
$705$	2.99643	+	0.338645i	0.112852	+	0.0127541i
$706$	5.55595	+	6.62133i	0.209101	+	0.249197i
$707$	−4.02225	+	45.3678i	−0.151272	+	1.70623i
$708$	−8.91563	−	9.37805i	−0.335070	−	0.352449i
$709$	0.823016	−	4.66756i	0.0309090	−	0.175294i	−0.965445	−	0.260606i	$-0.916078\pi$
$709$	0.823016	−	4.66756i	0.0309090	−	0.175294i	0.996354	+	0.0853122i	$0.0271888\pi$
$710$	1.38108	+	2.39209i	0.0518309	+	0.0897737i
$711$	−14.8248	+	35.1022i	−0.555975	+	1.31644i
$712$	5.41391	+	3.12572i	0.202895	+	0.117141i
$713$	−2.40585	+	13.6442i	−0.0900997	+	0.510981i
$714$	−15.9509	−	3.24944i	−0.596946	−	0.121607i
$715$	−0.596395	−	0.217070i	−0.0223039	−	0.00811795i
$716$	−4.41587	+	0.778636i	−0.165029	+	0.0290990i
$717$	32.5387	−	2.01981i	1.21518	−	0.0754311i
$718$	15.4918	+	12.9991i	0.578147	+	0.485123i
$719$	−21.3477	+	36.9753i	−0.796135	+	1.37895i	0.125981	+	0.992033i	$0.459792\pi$
$719$	−21.3477	+	36.9753i	−0.796135	+	1.37895i	−0.922116	+	0.386913i	$0.873541\pi$
$720$	0.733755	+	0.167998i	0.0273454	+	0.00626092i
$721$	−8.59601	+	2.29260i	−0.320132	+	0.0853809i
$722$	27.6954	−	33.0060i	1.03071	−	1.22836i
$723$	32.9684	−	31.3428i	1.22611	−	1.16565i
$724$	0.367501	−	1.00970i	0.0136581	−	0.0375253i
$725$	−29.6037	+	5.21993i	−1.09945	+	0.193863i
$726$	13.6987	−	5.97116i	0.508406	−	0.221610i
$727$	16.1245	+	44.3016i	0.598023	+	1.64305i	0.755208	+	0.655485i	$0.227536\pi$
$727$	16.1245	+	44.3016i	0.598023	+	1.64305i	−0.157185	+	0.987569i	$0.550242\pi$
$728$	−1.11968	−	4.19818i	−0.0414980	−	0.155595i
$729$	21.0752	+	16.8771i	0.780563	+	0.625078i
$730$	1.58255	+	2.74106i	0.0585728	+	0.101451i
$731$	1.11862	−	6.34403i	0.0413738	−	0.234642i
$732$	−10.5140	−	7.76518i	−0.388608	−	0.287009i
$733$	−12.7790	+	35.1100i	−0.472002	+	1.29682i	0.444138	+	0.895958i	$0.353510\pi$
$733$	−12.7790	+	35.1100i	−0.472002	+	1.29682i	−0.916140	+	0.400858i	$0.868712\pi$
$734$	2.62083	+	14.8635i	0.0967368	+	0.548622i
$735$	2.20967	−	2.09097i	0.0815050	−	0.0771265i
$736$	1.99272	+	1.67209i	0.0734525	+	0.0616340i
$737$			2.60306i			0.0958849i
$738$	−2.06430	−	1.91799i	−0.0759878	−	0.0706023i
$739$	−27.1302			−0.998000			−0.499000	−	0.866602i	$-0.666299\pi$
$739$	−27.1302			−0.998000			−0.499000	+	0.866602i	$0.666299\pi$
$740$	−0.783812	+	0.285284i	−0.0288135	+	0.0104873i
$741$	18.6783	−	12.3873i	0.686165	−	0.455059i
$742$	−2.17884	+	24.5756i	−0.0799878	+	0.902198i
$743$	−7.49055	+	20.5801i	−0.274802	+	0.755011i	0.723129	+	0.690713i	$0.242703\pi$
$743$	−7.49055	+	20.5801i	−0.274802	+	0.755011i	−0.997931	+	0.0642983i	$0.979519\pi$
$744$	−7.68798	+	5.09861i	−0.281855	+	0.186924i
$745$	−2.09436	+	2.49596i	−0.0767314	+	0.0914449i
$746$			30.4765i			1.11583i
$747$	16.9966	+	22.4702i	0.621872	+	0.822142i
$748$	−4.73832	−	2.73567i	−0.173250	−	0.100026i
$749$	−0.215972	−	2.50203i	−0.00789145	−	0.0914222i
$750$	3.12990	−	2.97557i	0.114288	−	0.108652i
$751$	1.58726	−	1.33187i	0.0579198	−	0.0486005i	−0.613368	−	0.789797i	$-0.710186\pi$
$751$	1.58726	−	1.33187i	0.0579198	−	0.0486005i	0.671288	+	0.741197i	$0.265741\pi$
$752$	1.20488	+	6.83324i	0.0439376	+	0.249183i
$753$	−11.0413	−	25.3304i	−0.402368	−	0.923091i
$754$	−6.42730	+	7.65976i	−0.234069	+	0.278952i
$755$	2.89255			0.105271
$756$	−11.3420	−	7.76908i	−0.412505	−	0.282559i
$757$	−16.3207			−0.593187			−0.296594	−	0.955004i	$-0.595851\pi$
$757$	−16.3207			−0.593187			−0.296594	+	0.955004i	$0.595851\pi$
$758$	6.04517	−	7.20435i	0.219570	−	0.261674i
$759$	−6.89582	−	0.779338i	−0.250302	−	0.0282882i
$760$	−0.343315	−	1.94704i	−0.0124533	−	0.0706265i
$761$	8.45586	−	7.09531i	0.306525	−	0.257205i	−0.476529	−	0.879159i	$-0.658105\pi$
$761$	8.45586	−	7.09531i	0.306525	−	0.257205i	0.783054	+	0.621954i	$0.213661\pi$
$762$	7.84573	+	2.31627i	0.284221	+	0.0839094i
$763$	2.87246	+	4.11246i	0.103990	+	0.148881i
$764$	15.6865	+	9.05660i	0.567517	+	0.327656i
$765$	−2.24519	−	1.45225i	−0.0811749	−	0.0525063i
$766$			11.2787i			0.407515i
$767$	−7.88616	+	9.39836i	−0.284753	+	0.339355i
$768$	0.107309	+	1.72872i	0.00387217	+	0.0623799i
$769$	−6.63833	+	18.2386i	−0.239384	+	0.657703i	0.760580	+	0.649244i	$0.224915\pi$
$769$	−6.63833	+	18.2386i	−0.239384	+	0.657703i	−0.999964	+	0.00845840i	$0.997308\pi$
$770$	0.927201	−	0.431051i	0.0334140	−	0.0155340i
$771$	−37.3644	−	18.5869i	−1.34565	−	0.669389i
$772$	8.66675	−	3.15444i	0.311923	−	0.113531i
$773$	−30.0969			−1.08251			−0.541256	−	0.840858i	$-0.682051\pi$
$773$	−30.0969			−1.08251			−0.541256	+	0.840858i	$0.682051\pi$
$774$	2.95476	−	4.56808i	0.106207	−	0.164196i
$775$			26.2950i			0.944544i
$776$	11.6649	+	9.78801i	0.418745	+	0.351369i
$777$	15.2286	+	0.402633i	0.546322	+	0.0144444i
$778$	−4.90101	−	27.7950i	−0.175710	−	0.996499i
$779$	−2.53127	+	6.95462i	−0.0906923	+	0.249175i
$780$	0.0801499	−	0.709191i	0.00286983	−	0.0253931i
$781$	2.94430	−	16.6980i	0.105355	−	0.597500i
$782$	−4.62025	−	8.00251i	−0.165220	−	0.286169i
$783$	0.362259	+	31.6360i	0.0129461	+	1.13058i
$784$	6.05403	+	3.51407i	0.216215	+	0.125502i
$785$	0.517741	+	1.42248i	0.0184790	+	0.0507705i
$786$	−2.68373	+	23.7465i	−0.0957256	+	0.847009i
$787$	10.7017	−	1.88700i	0.381475	−	0.0672644i	0.0203774	−	0.999792i	$-0.493513\pi$
$787$	10.7017	−	1.88700i	0.381475	−	0.0672644i	0.361098	+	0.932528i	$0.382402\pi$
$788$	−7.83205	+	21.5184i	−0.279005	+	0.766561i
$789$	−29.8112	−	8.80106i	−1.06131	−	0.313326i
$790$	2.04855	−	2.44136i	0.0728840	−	0.0868597i
$791$	−6.12142	+	22.7398i	−0.217653	+	0.808534i
$792$	−2.78752	−	3.68522i	−0.0990503	−	0.130949i
$793$	−6.19641	+	10.7325i	−0.220041	+	0.381122i
$794$	−11.4770	−	9.63035i	−0.407304	−	0.341768i
$795$	−1.80500	+	3.62851i	−0.0640166	+	0.128690i
$796$	−7.68497	+	1.35507i	−0.272387	+	0.0480291i
$797$	21.2866	+	7.74770i	0.754012	+	0.274438i	0.690293	−	0.723530i	$-0.257482\pi$
$797$	21.2866	+	7.74770i	0.754012	+	0.274438i	0.0637187	+	0.997968i	$0.479704\pi$
$798$	−7.20781	+	35.3816i	−0.255154	+	1.25250i
$799$	4.28006	−	24.2734i	0.151417	−	0.858731i
$800$	4.27560	+	2.46852i	0.151165	+	0.0872754i
$801$	−5.51580	−	17.9249i	−0.194891	−	0.633344i
$802$	−13.5314	−	23.4371i	−0.477812	−	0.827594i
$803$	3.37382	−	19.1339i	0.119060	−	0.675221i
$804$	−2.84572	+	0.685930i	−0.100361	+	0.0241909i
$805$	1.72015	+	0.152506i	0.0606272	+	0.00537513i
$806$	5.62222	+	6.70030i	0.198034	+	0.236008i
$807$	−4.41194	−	10.1216i	−0.155307	−	0.356298i
$808$	−16.9531	−	2.98930i	−0.596409	−	0.105163i
$809$	−4.54825	−	2.62593i	−0.159908	−	0.0923229i	0.417911	−	0.908488i	$-0.362763\pi$
$809$	−4.54825	−	2.62593i	−0.159908	−	0.0923229i	−0.577819	+	0.816165i	$0.696096\pi$
$810$	−1.26957	−	1.86756i	−0.0446083	−	0.0656192i
$811$		−	7.40478i		−	0.260017i	−0.991513	−	0.130008i	$-0.958500\pi$
$811$		−	7.40478i		−	0.260017i	0.991513	−	0.130008i	$-0.0415004\pi$
$812$	−1.38538	−	16.0496i	−0.0486174	−	0.563231i
$813$	0.641022	−	5.67196i	0.0224816	−	0.198924i
$814$	4.81146	+	1.75123i	0.168642	+	0.0613805i
$815$	1.18420	+	0.431015i	0.0414809	+	0.0150978i
$816$	1.74210	−	5.90090i	0.0609857	−	0.206573i
$817$	−14.0721	−	2.48129i	−0.492320	−	0.0868094i
$818$	−16.1592	+	27.9885i	−0.564993	+	0.978597i
$819$	−6.11193	+	11.5130i	−0.213568	+	0.402298i
$820$	0.117838	+	0.204101i	0.00411507	+	0.00712751i
$821$	−0.846629	−	2.32609i	−0.0295476	−	0.0811812i	0.924042	−	0.382292i	$-0.124865\pi$
$821$	−0.846629	−	2.32609i	−0.0295476	−	0.0811812i	−0.953589	+	0.301110i	$0.902643\pi$
$822$	−1.56660	−	25.2376i	−0.0546414	−	0.880262i
$823$	37.5270	−	31.4889i	1.30811	−	1.09763i	0.319428	−	0.947611i	$-0.396509\pi$
$823$	37.5270	−	31.4889i	1.30811	−	1.09763i	0.988682	−	0.150024i	$-0.0479350\pi$
$824$	−0.583902	−	3.31147i	−0.0203412	−	0.115361i
$825$	−13.1456	+	0.816002i	−0.457672	+	0.0284095i
$826$	−1.69983	−	19.6925i	−0.0591448	−	0.685190i
$827$	−47.8693	+	27.6374i	−1.66458	+	0.961045i	−0.694093	+	0.719885i	$0.744195\pi$
$827$	−47.8693	+	27.6374i	−1.66458	+	0.961045i	−0.970485	+	0.241160i	$0.922472\pi$
$828$	−0.965122	−	7.74401i	−0.0335403	−	0.269123i
$829$	46.8241	−	27.0339i	1.62627	−	0.938926i	0.641075	−	0.767478i	$-0.278489\pi$
$829$	46.8241	−	27.0339i	1.62627	−	0.938926i	0.985193	−	0.171448i	$-0.0548445\pi$
$830$	−0.805952	−	2.21433i	−0.0279750	−	0.0768606i
$831$	−0.919481	+	3.11450i	−0.0318964	+	0.108041i
$832$	1.61728	−	0.285170i	0.0560691	−	0.00988650i
$833$	−15.9391	−	19.0854i	−0.552258	−	0.661268i
$834$	18.7340	−	25.3657i	0.648706	−	0.878342i
$835$	−0.753516	−	0.632275i	−0.0260765	−	0.0218808i
$836$	−6.06816	+	10.5104i	−0.209872	+	0.363509i
$837$	27.3078	+	4.49334i	0.943897	+	0.155312i
$838$	15.9133	−	9.18754i	0.549715	−	0.317378i
$839$	28.3190	−	10.3073i	0.977681	−	0.355847i	0.196743	−	0.980455i	$-0.436964\pi$
$839$	28.3190	−	10.3073i	0.977681	−	0.355847i	0.780938	+	0.624608i	$0.214741\pi$
$840$	0.715559	+	0.900049i	0.0246891	+	0.0310546i
$841$	−6.18411	+	5.18909i	−0.213245	+	0.178934i
$842$	15.9522	+	19.0111i	0.549748	+	0.655164i
$843$	14.5871	−	13.8679i	0.502408	−	0.477635i
$844$	25.9334	−	9.43900i	0.892666	−	0.324904i
$845$	2.58519			0.0889331
$846$	11.3055	−	17.4783i	0.388690	−	0.600916i
$847$	22.0419	+	5.93356i	0.757370	+	0.203880i
$848$	−9.18346	−	1.61929i	−0.315361	−	0.0556067i
$849$	−40.7229	+	2.52783i	−1.39761	+	0.0867550i
$850$	−11.2730	−	13.4346i	−0.386660	−	0.460803i
$851$	5.55854	+	6.62441i	0.190544	+	0.227082i
$852$	19.0304	−	1.18129i	0.651971	−	0.0404705i
$853$	0.722674	+	0.127427i	0.0247439	+	0.00436301i	0.186006	−	0.982549i	$-0.440445\pi$
$853$	0.722674	+	0.127427i	0.0247439	+	0.00436301i	−0.161263	+	0.986912i	$0.551557\pi$
$854$	−5.14512	−	19.2914i	−0.176062	−	0.660139i
$855$	−3.22134	+	4.98020i	−0.110167	+	0.170319i
$856$	0.949195			0.0324428
$857$	−30.0713	+	10.9451i	−1.02722	+	0.373876i	−0.800020	−	0.599973i	$-0.795178\pi$
$857$	−30.0713	+	10.9451i	−1.02722	+	0.373876i	−0.227196	+	0.973849i	$0.572956\pi$
$858$	−3.17520	+	3.01864i	−0.108400	+	0.103055i
$859$	−25.2640	−	30.1085i	−0.861998	−	1.02729i	−0.999324	−	0.0367632i	$-0.988295\pi$
$859$	−25.2640	−	30.1085i	−0.861998	−	1.02729i	0.137326	−	0.990526i	$-0.456149\pi$
$860$	−0.348569	+	0.292484i	−0.0118861	+	0.00997361i
$861$	−0.635133	−	4.25715i	−0.0216453	−	0.145083i
$862$	−15.8536	+	5.77023i	−0.539975	+	0.196535i
$863$	−18.1263	+	10.4653i	−0.617028	+	0.356241i	−0.775711	−	0.631088i	$-0.782609\pi$
$863$	−18.1263	+	10.4653i	−0.617028	+	0.356241i	0.158683	+	0.987330i	$0.449275\pi$
$864$	3.29423	−	4.01847i	0.112072	−	0.136711i
$865$	1.49708	−	2.59303i	0.0509024	−	0.0881656i
$866$	−5.77924	−	4.84936i	−0.196387	−	0.164788i
$867$	4.50855	−	6.10454i	0.153118	−	0.207321i
$868$	−14.0364	−	1.24445i	−0.476426	−	0.0422393i
$869$	−19.2661	+	3.39714i	−0.653558	+	0.115240i
$870$	0.749241	−	2.53785i	0.0254016	−	0.0860413i
$871$	0.949249	+	2.60804i	0.0321641	+	0.0883700i
$872$	−1.64197	+	0.947993i	−0.0556042	+	0.0321031i
$873$	−5.64960	−	45.3316i	−0.191210	−	1.53424i
$874$	−17.7509	+	10.2485i	−0.600433	+	0.346660i
$875$	6.57232	−	0.567315i	0.222185	−	0.0191787i
$876$	21.8066	−	1.35362i	0.736777	−	0.0457347i
$877$	−4.93965	−	28.0142i	−0.166800	−	0.945971i	−0.947189	−	0.320676i	$-0.896090\pi$
$877$	−4.93965	−	28.0142i	−0.166800	−	0.945971i	0.780389	−	0.625295i	$-0.215021\pi$
$878$	−6.45197	+	5.41384i	−0.217743	+	0.182708i
$879$	−2.52145	−	40.6201i	−0.0850464	−	1.37008i
$880$	0.132180	+	0.363162i	0.00445579	+	0.0122422i
$881$	−1.96192	−	3.39815i	−0.0660989	−	0.114487i	0.831082	−	0.556150i	$-0.187722\pi$
$881$	−1.96192	−	3.39815i	−0.0660989	−	0.114487i	−0.897181	+	0.441663i	$0.854389\pi$
$882$	−6.12963	−	20.0855i	−0.206396	−	0.676314i
$883$	−16.8539	+	29.1917i	−0.567178	+	0.982380i	0.429666	+	0.902988i	$0.358631\pi$
$883$	−16.8539	+	29.1917i	−0.567178	+	0.982380i	−0.996843	+	0.0793924i	$0.974702\pi$
$884$	−5.74499	−	1.01300i	−0.193225	−	0.0340708i
$885$	0.919302	−	3.11389i	0.0309020	−	0.104672i
$886$	−27.8932	−	10.1523i	−0.937091	−	0.341073i
$887$	−35.7819	−	13.0236i	−1.20144	−	0.437288i	−0.337713	−	0.941249i	$-0.609653\pi$
$887$	−35.7819	−	13.0236i	−1.20144	−	0.437288i	−0.863726	+	0.503961i	$0.831875\pi$
$888$	−0.646616	+	5.72145i	−0.0216990	+	0.191999i
$889$	7.15548	+	10.2444i	0.239987	+	0.343585i
$890$			1.56858i			0.0525788i
$891$	−1.39892	+	13.7914i	−0.0468655	+	0.462030i
$892$	−7.83538	−	4.52376i	−0.262348	−	0.151467i
$893$	−53.8424	−	9.49387i	−1.80177	−	0.317700i
$894$	8.98721	+	20.6180i	0.300577	+	0.689568i
$895$	−0.723197	−	0.861873i	−0.0241738	−	0.0288092i
$896$	−1.52006	+	2.16551i	−0.0507815	+	0.0723446i
$897$	−7.19321	+	1.73385i	−0.240174	+	0.0578914i
$898$	−2.86978	+	16.2753i	−0.0957657	+	0.543114i
$899$	16.2145	+	28.0844i	0.540784	+	0.936666i
$900$	−4.35607	−	14.1561i	−0.145202	−	0.471869i
$901$	28.6873	+	16.5626i	0.955712	+	0.551781i
$902$	0.251217	−	1.42472i	0.00836461	−	0.0474381i
$903$	7.88157	−	2.63492i	0.262282	−	0.0876845i
$904$	−8.36402	−	3.04425i	−0.278183	−	0.101250i
$905$	0.265512	−	0.0468169i	0.00882591	−	0.00155625i
$906$	8.89307	−	17.8774i	0.295452	−	0.593936i
$907$	11.4505	+	9.60810i	0.380207	+	0.319032i	0.812784	−	0.582565i	$-0.197951\pi$
$907$	11.4505	+	9.60810i	0.380207	+	0.319032i	−0.432577	+	0.901597i	$0.642395\pi$
$908$	−9.82998	+	17.0260i	−0.326219	+	0.565029i
$909$	31.1550	+	41.1882i	1.03335	+	1.36613i
$910$	0.771785	−	0.769995i	0.0255844	−	0.0255251i
$911$	37.5881	−	44.7958i	1.24535	−	1.48415i	0.432545	−	0.901612i	$-0.357616\pi$
$911$	37.5881	−	44.7958i	1.24535	−	1.48415i	0.812804	−	0.582537i	$-0.197940\pi$
$912$	−13.0892	−	3.86427i	−0.433426	−	0.127959i
$913$	−4.94736	+	13.5928i	−0.163734	+	0.449855i
$914$	5.63525	−	0.993647i	0.186398	−	0.0328669i
$915$	0.368304	−	3.25886i	0.0121757	−	0.107735i
$916$	−4.75698	−	13.0697i	−0.157175	−	0.431835i
$917$	−25.8424	+	25.7824i	−0.853390	+	0.851411i
$918$	−15.8784	+	9.41145i	−0.524066	+	0.310624i
$919$	−10.2860	−	17.8158i	−0.339303	−	0.587690i	0.644999	−	0.764184i	$-0.276858\pi$
$919$	−10.2860	−	17.8158i	−0.339303	−	0.587690i	−0.984302	+	0.176493i	$0.943525\pi$
$920$	−0.113341	+	0.642788i	−0.00373674	+	0.0211921i
$921$	1.62065	−	14.3400i	0.0534022	−	0.472519i
$922$	−0.561121	+	1.54167i	−0.0184795	+	0.0507721i
$923$	−3.13926	−	17.8036i	−0.103330	−	0.586013i
$924$	0.186551	−	7.05582i	0.00613708	−	0.232119i
$925$	12.5725	+	10.5496i	0.413382	+	0.346869i
$926$		−	20.2013i		−	0.663856i
$927$	−5.47877	+	8.47019i	−0.179946	+	0.278198i
$928$	6.08874			0.199873
$929$	4.51969	−	1.64503i	0.148286	−	0.0539718i	−0.266811	−	0.963749i	$-0.585970\pi$
$929$	4.51969	−	1.64503i	0.148286	−	0.0539718i	0.415097	+	0.909777i	$0.363748\pi$
$930$	−2.07243	−	1.03093i	−0.0679576	−	0.0338054i
$931$	−42.3345	+	35.3556i	−1.38746	+	1.15873i
$932$	8.45186	−	23.2213i	0.276850	−	0.760639i
$933$	1.51717	+	24.4413i	0.0496698	+	0.800172i
$934$	−20.8551	+	24.8541i	−0.682399	+	0.813251i
$935$		−	1.37283i		−	0.0448965i
$936$	−4.13673	−	2.67576i	−0.135213	−	0.0874599i
$937$	−20.7843	−	11.9998i	−0.678992	−	0.392016i	0.120483	−	0.992715i	$-0.461556\pi$
$937$	−20.7843	−	11.9998i	−0.678992	−	0.392016i	−0.799475	+	0.600699i	$0.794889\pi$
$938$	−4.05027	−	1.89440i	−0.132246	−	0.0618543i
$939$	19.0710	+	5.63027i	0.622359	+	0.183737i
$940$	−1.33369	+	1.11910i	−0.0435001	+	0.0365009i
$941$	−2.84843	−	16.1543i	−0.0928562	−	0.526614i	−0.995383	−	0.0959805i	$-0.969401\pi$
$941$	−2.84843	−	16.1543i	−0.0928562	−	0.526614i	0.902527	−	0.430633i	$-0.141710\pi$
$942$	10.3834	+	1.17349i	0.338310	+	0.0382345i
$943$	1.57054	−	1.87170i	0.0511438	−	0.0609508i
$944$	7.47075			0.243152
$945$	0.265271	−	3.43928i	0.00862925	−	0.111880i
$946$	2.79318			0.0908141
$947$	−13.8492	+	16.5048i	−0.450037	+	0.536334i	−0.942591	−	0.333948i	$-0.891619\pi$
$947$	−13.8492	+	16.5048i	−0.450037	+	0.536334i	0.492554	+	0.870282i	$0.336063\pi$
$948$	−8.79062	−	20.1669i	−0.285506	−	0.654992i
$949$	−3.59722	−	20.4008i	−0.116771	−	0.662239i
$950$	−29.8002	+	25.0053i	−0.966845	+	0.811280i
$951$	8.11632	−	7.71612i	0.263190	−	0.250212i
$952$	7.70496	−	5.38175i	0.249719	−	0.174423i
$953$	−25.5793	−	14.7682i	−0.828595	−	0.478390i	0.0247763	−	0.999693i	$-0.492113\pi$
$953$	−25.5793	−	14.7682i	−0.828595	−	0.478390i	−0.853371	+	0.521303i	$0.825446\pi$
$954$	16.8766	+	22.3115i	0.546399	+	0.722363i
$955$			4.54486i			0.147068i
$956$	−12.0988	+	14.4188i	−0.391303	+	0.466337i
$957$	−13.5370	+	8.97764i	−0.437590	+	0.290206i
$958$	−1.99655	+	5.48548i	−0.0645056	+	0.177228i
$959$	22.1913	−	31.6142i	0.716593	−	1.02088i
$960$	−0.362185	+	0.240198i	−0.0116895	+	0.00775237i
$961$	−2.47426	+	0.900557i	−0.0798149	+	0.0290502i
$962$	5.45928			0.176014
$963$	−2.08611	−	1.93826i	−0.0672241	−	0.0624597i
$964$			26.2633i			0.845884i
$965$	1.77276	+	1.48752i	0.0570671	+	0.0478849i
$966$	6.23112	−	10.1625i	0.200483	−	0.326972i
$967$	3.10597	+	17.6148i	0.0998811	+	0.566454i	0.993142	+	0.116915i	$0.0373006\pi$
$967$	3.10597	+	17.6148i	0.0998811	+	0.566454i	−0.893261	+	0.449539i	$0.851588\pi$
$968$	−2.95083	+	8.10734i	−0.0948433	+	0.260580i
$969$	38.9971	+	28.8016i	1.25277	+	0.925241i
$970$	−0.663471	+	3.76273i	−0.0213028	+	0.120814i
$971$	−14.8842	−	25.7802i	−0.477656	−	0.827325i	0.522016	−	0.852936i	$-0.325180\pi$
$971$	−14.8842	−	25.7802i	−0.477656	−	0.827325i	−0.999672	+	0.0256112i	$0.991847\pi$
$972$	−15.4457	+	2.10484i	−0.495421	+	0.0675128i
$973$	46.5419	−	12.4129i	1.49206	−	0.397941i
$974$	2.82173	+	7.75265i	0.0904141	+	0.248411i
$975$	−12.8732	+	5.61134i	−0.412273	+	0.179707i
$976$	7.43170	−	1.31041i	0.237883	−	0.0419452i
$977$	17.3156	−	47.5741i	0.553974	−	1.52203i	−0.274264	−	0.961655i	$-0.588434\pi$
$977$	17.3156	−	47.5741i	0.553974	−	1.52203i	0.828238	−	0.560377i	$-0.189344\pi$
$978$	6.30470	−	5.99382i	0.201602	−	0.191661i
$979$	6.18924	−	7.37605i	0.197809	−	0.235740i
$980$	−0.00407877	+	1.75639i	−0.000130291	+	0.0561059i
$981$	5.54449	+	1.26945i	0.177022	+	0.0405303i
$982$	−11.5970	+	20.0867i	−0.370077	+	0.640991i
$983$	−17.0628	−	14.3174i	−0.544218	−	0.456653i	0.328759	−	0.944414i	$-0.393370\pi$
$983$	−17.0628	−	14.3174i	−0.544218	−	0.456653i	−0.872978	+	0.487760i	$0.837814\pi$
$984$	1.62373	−	0.100792i	0.0517628	−	0.00321312i
$985$	−5.65848	+	0.997743i	−0.180294	+	0.0317907i
$986$	−20.3244	−	7.39747i	−0.647260	−	0.235583i
$987$	30.1563	−	10.0817i	0.959886	−	0.320903i
$988$	−2.24699	+	12.7433i	−0.0714864	+	0.405420i
$989$	4.08537	+	2.35869i	0.129907	+	0.0750020i
$990$	0.451077	−	1.06806i	0.0143362	−	0.0339452i
$991$	6.10101	+	10.5673i	0.193805	+	0.335680i	0.946508	−	0.322680i	$-0.104584\pi$
$991$	6.10101	+	10.5673i	0.193805	+	0.335680i	−0.752703	+	0.658360i	$0.771250\pi$
$992$	0.924861	−	5.24515i	0.0293644	−	0.166534i
$993$	−32.7345	−	34.4323i	−1.03880	−	1.09268i
$994$	23.8387	+	16.7333i	0.756118	+	0.530749i
$995$	−1.25859	−	1.49992i	−0.0398999	−	0.0475508i
$996$	−16.1636	−	1.82674i	−0.512162	−	0.0578825i
$997$	−7.79280	−	1.37408i	−0.246801	−	0.0435176i	0.0488793	−	0.998805i	$-0.484435\pi$
$997$	−7.79280	−	1.37408i	−0.246801	−	0.0435176i	−0.295680	+	0.955287i	$0.595546\pi$
$998$	13.9362	+	8.04609i	0.441144	+	0.254694i
$999$	13.1044	−	11.2541i	0.414604	−	0.356062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.101.4	yes	144
7.5	odd	6		378.2.ba.a.47.20	✓	144
27.23	odd	18		378.2.ba.a.185.20	yes	144
189.131	even	18	inner	378.2.bf.a.131.4	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.20	✓	144	7.5	odd	6
378.2.ba.a.185.20	yes	144	27.23	odd	18
378.2.bf.a.101.4	yes	144	1.1	even	1	trivial
378.2.bf.a.131.4	yes	144	189.131	even	18	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-1.02900 + 1.39326i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.192211 - 0.161284i) q^{5} +(-0.405868 - 1.68383i) q^{6} +(1.12093 - 2.39657i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.882323 - 2.86732i) q^{9} +O(q^{10})\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-1.02900 + 1.39326i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.192211 - 0.161284i) q^{5} +(-0.405868 - 1.68383i) q^{6} +(1.12093 - 2.39657i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.882323 - 2.86732i) q^{9} +0.250914i q^{10} +(0.990049 - 1.17989i) q^{11} +(1.55077 + 0.771430i) q^{12} +(0.561675 - 1.54319i) q^{13} +(1.11536 + 2.39916i) q^{14} +(0.0269253 + 0.433761i) q^{15} +(-0.939693 + 0.342020i) q^{16} +3.55225 q^{17} +(2.76364 + 1.16718i) q^{18} -7.87949i q^{19} +(-0.192211 - 0.161284i) q^{20} +(2.18560 + 4.02780i) q^{21} +(0.267460 + 1.51684i) q^{22} +(-0.889699 + 2.44443i) q^{23} +(-1.58777 + 0.692095i) q^{24} +(-0.857308 + 4.86204i) q^{25} +(0.821115 + 1.42221i) q^{26} +(4.90281 + 1.72116i) q^{27} +(-2.55480 - 0.687738i) q^{28} +(2.08247 + 5.72155i) q^{29} +(-0.349587 - 0.258190i) q^{30} +(5.24515 - 0.924861i) q^{31} +(0.342020 - 0.939693i) q^{32} +(0.625136 + 2.59350i) q^{33} +(-2.28334 + 2.72118i) q^{34} +(-0.171074 - 0.641435i) q^{35} +(-2.67054 + 1.36682i) q^{36} +(1.66215 - 2.87894i) q^{37} +(6.03604 + 5.06484i) q^{38} +(1.57210 + 2.37050i) q^{39} +(0.247102 - 0.0435707i) q^{40} +(-0.882623 - 0.321249i) q^{41} +(-4.49035 - 0.914756i) q^{42} +(0.314905 - 1.78592i) q^{43} +(-1.33389 - 0.770122i) q^{44} +(-0.632046 - 0.408826i) q^{45} +(-1.30065 - 2.25280i) q^{46} +(1.20488 - 6.83324i) q^{47} +(0.490421 - 1.66117i) q^{48} +(-4.48705 - 5.37275i) q^{49} +(-3.17347 - 3.78199i) q^{50} +(-3.65526 + 4.94920i) q^{51} +(-1.61728 - 0.285170i) q^{52} +(8.07580 + 4.66257i) q^{53} +(-4.46996 + 2.64943i) q^{54} -0.386469i q^{55} +(2.16903 - 1.51502i) q^{56} +(10.9781 + 8.10798i) q^{57} +(-5.72155 - 2.08247i) q^{58} +(-7.02021 - 2.55515i) q^{59} +(0.422495 - 0.101838i) q^{60} +(-7.43170 - 1.31041i) q^{61} +(-2.66303 + 4.61251i) q^{62} +(-7.86073 - 1.09951i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.140932 - 0.387208i) q^{65} +(-2.38857 - 1.18819i) q^{66} +(-1.29464 + 1.08633i) q^{67} +(-0.616842 - 3.49829i) q^{68} +(-2.49022 - 3.75489i) q^{69} +(0.601332 + 0.281256i) q^{70} +(9.53352 - 5.50418i) q^{71} +(0.669544 - 2.92433i) q^{72} +(10.9243 - 6.30714i) q^{73} +(1.13698 + 3.12383i) q^{74} +(-5.89189 - 6.19748i) q^{75} +(-7.75978 + 1.36826i) q^{76} +(-1.71792 - 3.69529i) q^{77} +(-2.82643 - 0.319432i) q^{78} +(-9.72988 - 8.16434i) q^{79} +(-0.125457 + 0.217298i) q^{80} +(-7.44301 + 5.05980i) q^{81} +(0.813430 - 0.469634i) q^{82} +(-8.82507 + 3.21206i) q^{83} +(3.58708 - 2.85181i) q^{84} +(0.682783 - 0.572923i) q^{85} +(1.16567 + 1.38920i) q^{86} +(-10.1144 - 2.98605i) q^{87} +(1.44736 - 0.526794i) q^{88} +6.25145 q^{89} +(0.719450 - 0.221387i) q^{90} +(-3.06876 - 3.07589i) q^{91} +(2.56179 + 0.451712i) q^{92} +(-4.10868 + 8.25951i) q^{93} +(4.46008 + 5.31532i) q^{94} +(-1.27084 - 1.51453i) q^{95} +(0.957294 + 1.44346i) q^{96} +(14.9961 + 2.64422i) q^{97} +(6.99998 + 0.0162556i) q^{98} +(-4.25668 - 1.79774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) \) 144 * q + 18 * q^6 - 12 * q^9	\( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) \) 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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