LMFDB - Embedded newform 288.2.v.c.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	288.37
Dual form			288.2.v.c.109.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.835415 + 1.14109i) q^{2} +(-0.604162 + 1.90656i) q^{4} +(0.823699 + 0.341187i) q^{5} +(0.760681 + 0.760681i) q^{7} +(-2.68028 + 0.903371i) q^{8} +O(q^{10})$	\(q+(0.835415 + 1.14109i) q^{2} +(-0.604162 + 1.90656i) q^{4} +(0.823699 + 0.341187i) q^{5} +(0.760681 + 0.760681i) q^{7} +(-2.68028 + 0.903371i) q^{8} +(0.298806 + 1.22495i) q^{10} +(-1.76000 + 4.24901i) q^{11} +(2.78781 - 1.15475i) q^{13} +(-0.232519 + 1.50349i) q^{14} +(-3.26998 - 2.30375i) q^{16} +0.00932001i q^{17} +(5.33680 - 2.21057i) q^{19} +(-1.14814 + 1.36430i) q^{20} +(-6.31883 + 1.54138i) q^{22} +(-2.06602 + 2.06602i) q^{23} +(-2.97346 - 2.97346i) q^{25} +(3.64666 + 2.21644i) q^{26} +(-1.90986 + 0.990712i) q^{28} +(-1.24011 - 2.99388i) q^{29} -1.86423 q^{31} +(-0.103008 - 5.65592i) q^{32} +(-0.0106350 + 0.00778608i) q^{34} +(0.367038 + 0.886107i) q^{35} +(4.94247 + 2.04724i) q^{37} +(6.98090 + 4.24301i) q^{38} +(-2.51597 - 0.170373i) q^{40} +(7.21705 - 7.21705i) q^{41} +(2.68885 - 6.49145i) q^{43} +(-7.03769 - 5.92265i) q^{44} +(-4.08349 - 0.631524i) q^{46} +8.24036i q^{47} -5.84273i q^{49} +(0.908905 - 5.87706i) q^{50} +(0.517314 + 6.01281i) q^{52} +(4.21657 - 10.1797i) q^{53} +(-2.89942 + 2.89942i) q^{55} +(-2.72602 - 1.35166i) q^{56} +(2.38028 - 3.91621i) q^{58} +(-4.98906 - 2.06654i) q^{59} +(4.20515 + 10.1521i) q^{61} +(-1.55740 - 2.12725i) q^{62} +(6.36784 - 4.84258i) q^{64} +2.69031 q^{65} +(-1.34088 - 3.23718i) q^{67} +(-0.0177692 - 0.00563080i) q^{68} +(-0.704497 + 1.15909i) q^{70} +(-5.86295 - 5.86295i) q^{71} +(-1.26194 + 1.26194i) q^{73} +(1.79294 + 7.35008i) q^{74} +(0.990309 + 11.5105i) q^{76} +(-4.57094 + 1.89335i) q^{77} +13.6919i q^{79} +(-1.90747 - 3.01327i) q^{80} +(14.2645 + 2.20605i) q^{82} +(6.49900 - 2.69197i) q^{83} +(-0.00317987 + 0.00767689i) q^{85} +(9.65362 - 2.35485i) q^{86} +(0.878862 - 12.9785i) q^{88} +(-10.7468 - 10.7468i) q^{89} +(2.99903 + 1.24224i) q^{91} +(-2.69078 - 5.18720i) q^{92} +(-9.40298 + 6.88412i) q^{94} +5.15013 q^{95} -16.8748 q^{97} +(6.66707 - 4.88111i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 - 8 * q^16 - 24 * q^22 - 40 * q^28 + 48 * q^31 - 40 * q^34 - 72 * q^40 + 16 * q^43 - 32 * q^46 - 8 * q^52 + 32 * q^55 - 32 * q^58 - 32 * q^61 + 72 * q^64 + 16 * q^67 + 120 * q^70 + 72 * q^76 + 120 * q^82 + 128 * q^88 - 48 * q^91 + 80 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.835415	+	1.14109i	0.590728	+	0.806871i
$2$	0.835415	+	1.14109i	0.590728	+	0.806871i
$3$		0			0
$3$		0			0
$4$	−0.604162	+	1.90656i	−0.302081	+	0.953282i
$5$	0.823699	+	0.341187i	0.368369	+	0.152584i	0.559186	−	0.829042i	$-0.311114\pi$
$5$	0.823699	+	0.341187i	0.368369	+	0.152584i	−0.190817	+	0.981626i	$0.561114\pi$
$6$		0			0
$7$	0.760681	+	0.760681i	0.287510	+	0.287510i	0.836095	−	0.548585i	$-0.184833\pi$
$7$	0.760681	+	0.760681i	0.287510	+	0.287510i	−0.548585	+	0.836095i	$0.684833\pi$
$8$	−2.68028	+	0.903371i	−0.947623	+	0.319390i
$9$		0			0
$10$	0.298806	+	1.22495i	0.0944908	+	0.387362i
$11$	−1.76000	+	4.24901i	−0.530660	+	1.28113i	0.400427	+	0.916329i	$0.368862\pi$
$11$	−1.76000	+	4.24901i	−0.530660	+	1.28113i	−0.931087	+	0.364797i	$0.881138\pi$
$12$		0			0
$13$	2.78781	−	1.15475i	0.773201	−	0.320270i	0.0390326	−	0.999238i	$-0.487572\pi$
$13$	2.78781	−	1.15475i	0.773201	−	0.320270i	0.734168	+	0.678968i	$0.237572\pi$
$14$	−0.232519	+	1.50349i	−0.0621434	+	0.401824i
$15$		0			0
$16$	−3.26998	−	2.30375i	−0.817494	−	0.575937i
$17$			0.00932001i			0.00226044i	0.999999	+	0.00113022i	$0.000359760\pi$
$17$			0.00932001i			0.00226044i	−0.999999	+	0.00113022i	$0.999640\pi$
$18$		0			0
$19$	5.33680	−	2.21057i	1.22435	−	0.507140i	0.325556	−	0.945523i	$-0.394448\pi$
$19$	5.33680	−	2.21057i	1.22435	−	0.507140i	0.898789	+	0.438382i	$0.144448\pi$
$20$	−1.14814	+	1.36430i	−0.256733	+	0.305067i
$21$		0			0
$22$	−6.31883	+	1.54138i	−1.34718	+	0.328623i
$23$	−2.06602	+	2.06602i	−0.430794	+	0.430794i	−0.888898	−	0.458104i	$-0.848529\pi$
$23$	−2.06602	+	2.06602i	−0.430794	+	0.430794i	0.458104	+	0.888898i	$0.348529\pi$
$24$		0			0
$25$	−2.97346	−	2.97346i	−0.594692	−	0.594692i
$26$	3.64666	+	2.21644i	0.715168	+	0.434681i
$27$		0			0
$28$	−1.90986	+	0.990712i	−0.360930	+	0.187227i
$29$	−1.24011	−	2.99388i	−0.230282	−	0.555950i	0.765928	−	0.642926i	$-0.222280\pi$
$29$	−1.24011	−	2.99388i	−0.230282	−	0.555950i	−0.996210	+	0.0869758i	$0.972280\pi$
$30$		0			0
$31$	−1.86423			−0.334825			−0.167412	−	0.985887i	$-0.553541\pi$
$31$	−1.86423			−0.334825			−0.167412	+	0.985887i	$0.553541\pi$
$32$	−0.103008	−	5.65592i	−0.0182094	−	0.999834i
$33$		0			0
$34$	−0.0106350	+	0.00778608i	−0.00182388	+	0.00133530i
$35$	0.367038	+	0.886107i	0.0620407	+	0.149779i
$36$		0			0
$37$	4.94247	+	2.04724i	0.812537	+	0.336564i	0.749966	−	0.661477i	$-0.230070\pi$
$37$	4.94247	+	2.04724i	0.812537	+	0.336564i	0.0625711	+	0.998041i	$0.480070\pi$
$38$	6.98090	+	4.24301i	1.13245	+	0.688306i
$39$		0			0
$40$	−2.51597	−	0.170373i	−0.397809	−	0.0269384i
$41$	7.21705	−	7.21705i	1.12711	−	1.12711i	0.136469	−	0.990644i	$-0.456425\pi$
$41$	7.21705	−	7.21705i	1.12711	−	1.12711i	0.990644	−	0.136469i	$-0.0435754\pi$
$42$		0			0
$43$	2.68885	−	6.49145i	0.410045	−	0.989937i	−0.575080	−	0.818097i	$-0.695029\pi$
$43$	2.68885	−	6.49145i	0.410045	−	0.989937i	0.985125	−	0.171839i	$-0.0549710\pi$
$44$	−7.03769	−	5.92265i	−1.06097	−	0.892872i
$45$		0			0
$46$	−4.08349	−	0.631524i	−0.602077	−	0.0931132i
$47$			8.24036i			1.20198i	0.799256	+	0.600990i	$0.205227\pi$
$47$			8.24036i			1.20198i	−0.799256	+	0.600990i	$0.794773\pi$
$48$		0			0
$49$		−	5.84273i		−	0.834676i
$50$	0.908905	−	5.87706i	0.128539	−	0.831141i
$51$		0			0
$52$	0.517314	+	6.01281i	0.0717385	+	0.833826i
$53$	4.21657	−	10.1797i	0.579191	−	1.39829i	−0.314349	−	0.949307i	$-0.601786\pi$
$53$	4.21657	−	10.1797i	0.579191	−	1.39829i	0.893540	−	0.448983i	$-0.148214\pi$
$54$		0			0
$55$	−2.89942	+	2.89942i	−0.390958	+	0.390958i
$56$	−2.72602	−	1.35166i	−0.364279	−	0.180624i
$57$		0			0
$58$	2.38028	−	3.91621i	0.312546	−	0.514223i
$59$	−4.98906	−	2.06654i	−0.649520	−	0.269040i	0.0335009	−	0.999439i	$-0.489334\pi$
$59$	−4.98906	−	2.06654i	−0.649520	−	0.269040i	−0.683021	+	0.730399i	$0.739334\pi$
$60$		0			0
$61$	4.20515	+	10.1521i	0.538414	+	1.29985i	0.925829	+	0.377942i	$0.123368\pi$
$61$	4.20515	+	10.1521i	0.538414	+	1.29985i	−0.387415	+	0.921905i	$0.626632\pi$
$62$	−1.55740	−	2.12725i	−0.197790	−	0.270160i
$63$		0			0
$64$	6.36784	−	4.84258i	0.795980	−	0.605323i
$65$	2.69031			0.333692
$66$		0			0
$67$	−1.34088	−	3.23718i	−0.163815	−	0.395485i	0.820562	−	0.571557i	$-0.193661\pi$
$67$	−1.34088	−	3.23718i	−0.163815	−	0.395485i	−0.984377	+	0.176073i	$0.943661\pi$
$68$	−0.0177692	−	0.00563080i	−0.00215483	−	0.000682835i
$69$		0			0
$70$	−0.704497	+	1.15909i	−0.0842035	+	0.138538i
$71$	−5.86295	−	5.86295i	−0.695804	−	0.695804i	0.267698	−	0.963503i	$-0.413737\pi$
$71$	−5.86295	−	5.86295i	−0.695804	−	0.695804i	−0.963503	+	0.267698i	$0.913737\pi$
$72$		0			0
$73$	−1.26194	+	1.26194i	−0.147699	+	0.147699i	−0.777089	−	0.629390i	$-0.783305\pi$
$73$	−1.26194	+	1.26194i	−0.147699	+	0.147699i	0.629390	+	0.777089i	$0.283305\pi$
$74$	1.79294	+	7.35008i	0.208425	+	0.854430i
$75$		0			0
$76$	0.990309	+	11.5105i	0.113596	+	1.32034i
$77$	−4.57094	+	1.89335i	−0.520907	+	0.215767i
$78$		0			0
$79$			13.6919i			1.54046i	0.637769	+	0.770228i	$0.279857\pi$
$79$			13.6919i			1.54046i	−0.637769	+	0.770228i	$0.720143\pi$
$80$	−1.90747	−	3.01327i	−0.213261	−	0.336894i
$81$		0			0
$82$	14.2645	+	2.20605i	1.57525	+	0.243618i
$83$	6.49900	−	2.69197i	0.713358	−	0.295483i	0.00366477	−	0.999993i	$-0.498833\pi$
$83$	6.49900	−	2.69197i	0.713358	−	0.295483i	0.709693	+	0.704511i	$0.248833\pi$
$84$		0			0
$85$	−0.00317987	+	0.00767689i	−0.000344905	+	0.000832676i
$86$	9.65362	−	2.35485i	1.04098	−	0.253930i
$87$		0			0
$88$	0.878862	−	12.9785i	0.0936870	−	1.38351i
$89$	−10.7468	−	10.7468i	−1.13915	−	1.13915i	−0.988602	−	0.150552i	$-0.951895\pi$
$89$	−10.7468	−	10.7468i	−1.13915	−	1.13915i	−0.150552	−	0.988602i	$-0.548105\pi$
$90$		0			0
$91$	2.99903	+	1.24224i	0.314384	+	0.130222i
$92$	−2.69078	−	5.18720i	−0.280534	−	0.540803i
$93$		0			0
$94$	−9.40298	+	6.88412i	−0.969843	+	0.710043i
$95$	5.15013			0.528393
$96$		0			0
$97$	−16.8748			−1.71337			−0.856687	−	0.515836i	$-0.827481\pi$
$97$	−16.8748			−1.71337			−0.856687	+	0.515836i	$0.827481\pi$
$98$	6.66707	−	4.88111i	0.673475	−	0.493066i
$99$		0			0
$100$	7.46555	−	3.87264i	0.746555	−	0.387264i
$101$	17.0982	+	7.08231i	1.70134	+	0.704716i	0.999967	−	0.00808212i	$-0.00257265\pi$
$101$	17.0982	+	7.08231i	1.70134	+	0.704716i	0.701369	+	0.712799i	$0.252573\pi$
$102$		0			0
$103$	−3.47025	−	3.47025i	−0.341934	−	0.341934i	0.515160	−	0.857094i	$-0.327733\pi$
$103$	−3.47025	−	3.47025i	−0.341934	−	0.341934i	−0.857094	+	0.515160i	$0.827733\pi$
$104$	−6.42897	+	5.61349i	−0.630412	+	0.550448i
$105$		0			0
$106$	15.1385	−	3.69280i	1.47038	−	0.358677i
$107$	−6.02703	+	14.5505i	−0.582655	+	1.40665i	0.307743	+	0.951470i	$0.400426\pi$
$107$	−6.02703	+	14.5505i	−0.582655	+	1.40665i	−0.890398	+	0.455184i	$0.849574\pi$
$108$		0			0
$109$	−2.41743	+	1.00133i	−0.231548	+	0.0959104i	−0.495441	−	0.868642i	$-0.664993\pi$
$109$	−2.41743	+	1.00133i	−0.231548	+	0.0959104i	0.263893	+	0.964552i	$0.414993\pi$
$110$	−5.73071	−	0.886273i	−0.546402	−	0.0845028i
$111$		0			0
$112$	−0.734990	−	4.23983i	−0.0694500	−	0.400626i
$113$			13.2563i			1.24705i	0.781804	+	0.623525i	$0.214300\pi$
$113$			13.2563i			1.24705i	−0.781804	+	0.623525i	$0.785700\pi$
$114$		0			0
$115$	−2.40667	+	0.996877i	−0.224424	+	0.0929593i
$116$	6.45726	−	0.555552i	0.599541	−	0.0515817i
$117$		0			0
$118$	−1.80984	−	7.41937i	−0.166609	−	0.683008i
$119$	−0.00708956	+	0.00708956i	−0.000649899	+	0.000649899i
$120$		0			0
$121$	−7.17835	−	7.17835i	−0.652577	−	0.652577i
$122$	−8.07143	+	13.2797i	−0.730753	+	1.20229i
$123$		0			0
$124$	1.12630	−	3.55427i	0.101144	−	0.319183i
$125$	−3.14067	−	7.58224i	−0.280910	−	0.678176i
$126$		0			0
$127$	−12.6657			−1.12390			−0.561949	−	0.827172i	$-0.689948\pi$
$127$	−12.6657			−1.12390			−0.561949	+	0.827172i	$0.689948\pi$
$128$	10.8456	+	3.22070i	0.958625	+	0.284672i
$129$		0			0
$130$	2.24752	+	3.06988i	0.197121	+	0.269246i
$131$	−2.14148	−	5.17000i	−0.187102	−	0.451705i	0.802297	−	0.596925i	$-0.203611\pi$
$131$	−2.14148	−	5.17000i	−0.187102	−	0.451705i	−0.989399	+	0.145220i	$0.953611\pi$
$132$		0			0
$133$	5.74114	+	2.37806i	0.497820	+	0.206204i
$134$	2.57371	−	4.23446i	0.222335	−	0.365801i
$135$		0			0
$136$	−0.00841943	−	0.0249803i	−0.000721960	−	0.00214204i
$137$	0.607219	−	0.607219i	0.0518782	−	0.0518782i	−0.680692	−	0.732570i	$-0.738321\pi$
$137$	0.607219	−	0.607219i	0.0518782	−	0.0518782i	0.732570	+	0.680692i	$0.238321\pi$
$138$		0			0
$139$	2.58482	−	6.24030i	0.219241	−	0.529296i	−0.775543	−	0.631295i	$-0.782524\pi$
$139$	2.58482	−	6.24030i	0.219241	−	0.529296i	0.994785	+	0.101999i	$0.0325238\pi$
$140$	−1.91117	+	0.164428i	−0.161523	+	0.0138967i
$141$		0			0
$142$	1.79214	−	11.5881i	0.150393	−	0.972455i
$143$			13.8778i			1.16052i
$144$		0			0
$145$		−	2.88917i		−	0.239932i
$146$	−2.49423	−	0.385740i	−0.206424	−	0.0319241i
$147$		0			0
$148$	−6.88924	+	8.18627i	−0.566292	+	0.672907i
$149$	−4.39926	+	10.6207i	−0.360401	+	0.870086i	0.634840	+	0.772644i	$0.281066\pi$
$149$	−4.39926	+	10.6207i	−0.360401	+	0.870086i	−0.995241	+	0.0974420i	$0.968934\pi$
$150$		0			0
$151$	−15.8960	+	15.8960i	−1.29360	+	1.29360i	−0.361052	+	0.932546i	$0.617582\pi$
$151$	−15.8960	+	15.8960i	−1.29360	+	1.29360i	−0.932546	+	0.361052i	$0.882418\pi$
$152$	−12.3072	+	10.7461i	−0.998243	+	0.871621i
$153$		0			0
$154$	−5.97911	−	3.63411i	−0.481810	−	0.292845i
$155$	−1.53556	−	0.636050i	−0.123339	−	0.0510888i
$156$		0			0
$157$	0.263500	+	0.636146i	0.0210296	+	0.0507700i	0.934046	−	0.357154i	$-0.116253\pi$
$157$	0.263500	+	0.636146i	0.0210296	+	0.0507700i	−0.913016	+	0.407924i	$0.866253\pi$
$158$	−15.6236	+	11.4384i	−1.24295	+	0.909990i
$159$		0			0
$160$	1.84488	−	4.69392i	0.145851	−	0.371087i
$161$	−3.14316			−0.247716
$162$		0			0
$163$	−2.46581	−	5.95298i	−0.193137	−	0.466274i	0.797412	−	0.603436i	$-0.206202\pi$
$163$	−2.46581	−	5.95298i	−0.193137	−	0.466274i	−0.990549	+	0.137162i	$0.956202\pi$
$164$	9.39950	+	18.1200i	0.733977	+	1.41494i
$165$		0			0
$166$	8.50115	+	5.16701i	0.659817	+	0.401038i
$167$	−12.5015	−	12.5015i	−0.967397	−	0.967397i	0.0320881	−	0.999485i	$-0.489784\pi$
$167$	−12.5015	−	12.5015i	−0.967397	−	0.967397i	−0.999485	+	0.0320881i	$0.989784\pi$
$168$		0			0
$169$	−2.75393	+	2.75393i	−0.211840	+	0.211840i
$170$	−0.0114165	+	0.00278488i	−0.000875607	+	0.000213590i
$171$		0			0
$172$	10.7519	+	9.04835i	0.819822	+	0.689930i
$173$	−18.5869	+	7.69893i	−1.41313	+	0.585339i	−0.953125	−	0.302575i	$-0.902154\pi$
$173$	−18.5869	+	7.69893i	−1.41313	+	0.585339i	−0.460008	+	0.887915i	$0.652154\pi$
$174$		0			0
$175$		−	4.52371i		−	0.341960i
$176$	15.5438	−	9.83957i	1.17166	−	0.741686i
$177$		0			0
$178$	3.28499	−	21.2410i	0.246220	−	1.59208i
$179$	17.6807	−	7.32357i	1.32151	−	0.547389i	0.393292	−	0.919414i	$-0.371336\pi$
$179$	17.6807	−	7.32357i	1.32151	−	0.547389i	0.928223	+	0.372025i	$0.121336\pi$
$180$		0			0
$181$	−5.30940	+	12.8180i	−0.394645	+	0.952757i	0.594269	+	0.804266i	$0.297441\pi$
$181$	−5.30940	+	12.8180i	−0.394645	+	0.952757i	−0.988914	+	0.148491i	$0.952559\pi$
$182$	1.08793	+	4.45995i	0.0806430	+	0.330593i
$183$		0			0
$184$	3.67113	−	7.40389i	0.270639	−	0.545822i
$185$	3.37262	+	3.37262i	0.247960	+	0.247960i
$186$		0			0
$187$	−0.0396009	−	0.0164032i	−0.00289590	−	0.00119952i
$188$	−15.7108	−	4.97852i	−1.14583	−	0.363096i
$189$		0			0
$190$	4.30250	+	5.87676i	0.312136	+	0.426345i
$191$	21.8841			1.58348			0.791740	−	0.610858i	$-0.209175\pi$
$191$	21.8841			1.58348			0.791740	+	0.610858i	$0.209175\pi$
$192$		0			0
$193$	2.97546			0.214178			0.107089	−	0.994249i	$-0.465847\pi$
$193$	2.97546			0.214178			0.107089	+	0.994249i	$0.465847\pi$
$194$	−14.0974	−	19.2556i	−1.01214	−	1.38247i
$195$		0			0
$196$	11.1395	+	3.52996i	0.795681	+	0.252140i
$197$	1.68346	+	0.697310i	0.119941	+	0.0496813i	0.441847	−	0.897090i	$-0.354323\pi$
$197$	1.68346	+	0.697310i	0.119941	+	0.0496813i	−0.321906	+	0.946772i	$0.604323\pi$
$198$		0			0
$199$	8.85560	+	8.85560i	0.627757	+	0.627757i	0.947503	−	0.319746i	$-0.103598\pi$
$199$	8.85560	+	8.85560i	0.627757	+	0.627757i	−0.319746	+	0.947503i	$0.603598\pi$
$200$	10.6559	+	5.28358i	0.753483	+	0.373606i
$201$		0			0
$202$	6.20257	+	25.4272i	0.436411	+	1.78905i
$203$	1.33406	−	3.22072i	0.0936330	−	0.226050i
$204$		0			0
$205$	8.40704	−	3.48231i	0.587173	−	0.243215i
$206$	1.06076	−	6.85897i	0.0739067	−	0.477887i
$207$		0			0
$208$	−11.7763	−	2.64642i	−0.816542	−	0.183496i
$209$			26.5667i			1.83766i
$210$		0			0
$211$	18.0487	−	7.47601i	1.24252	−	0.514670i	0.338021	−	0.941139i	$-0.390243\pi$
$211$	18.0487	−	7.47601i	1.24252	−	0.514670i	0.904502	+	0.426469i	$0.140243\pi$
$212$	16.8608	+	14.1894i	1.15800	+	0.974530i
$213$		0			0
$214$	−21.6385	+	5.27837i	−1.47918	+	0.360822i
$215$	4.42960	−	4.42960i	0.302096	−	0.302096i
$216$		0			0
$217$	−1.41808	−	1.41808i	−0.0962656	−	0.0962656i
$218$	−3.16217	−	1.92197i	−0.214169	−	0.130173i
$219$		0			0
$220$	−3.77621	−	7.27965i	−0.254592	−	0.490794i
$221$	0.0107623	+	0.0259825i	0.000723950	+	0.00174777i
$222$		0			0
$223$	7.19272			0.481660			0.240830	−	0.970567i	$-0.422580\pi$
$223$	7.19272			0.481660			0.240830	+	0.970567i	$0.422580\pi$
$224$	4.22399	−	4.38070i	0.282227	−	0.292698i
$225$		0			0
$226$	−15.1266	+	11.0745i	−1.00621	+	0.736667i
$227$	−5.74555	−	13.8710i	−0.381346	−	0.920650i	−0.991706	−	0.128526i	$-0.958975\pi$
$227$	−5.74555	−	13.8710i	−0.381346	−	0.920650i	0.610360	−	0.792124i	$-0.291025\pi$
$228$		0			0
$229$	5.60857	+	2.32314i	0.370624	+	0.153518i	0.560218	−	0.828345i	$-0.310717\pi$
$229$	5.60857	+	2.32314i	0.370624	+	0.153518i	−0.189594	+	0.981863i	$0.560717\pi$
$230$	−3.14810	−	1.91342i	−0.207579	−	0.126167i
$231$		0			0
$232$	6.02843	+	6.90418i	0.395786	+	0.453282i
$233$	9.43052	−	9.43052i	0.617814	−	0.617814i	−0.327156	−	0.944970i	$-0.606090\pi$
$233$	9.43052	−	9.43052i	0.617814	−	0.617814i	0.944970	+	0.327156i	$0.106090\pi$
$234$		0			0
$235$	−2.81151	+	6.78758i	−0.183403	+	0.442773i
$236$	6.95419	−	8.26344i	0.452679	−	0.537904i
$237$		0			0
$238$	−0.0140125	−	0.00216708i	−0.000908298	−	0.000140471i
$239$		−	9.20989i		−	0.595739i	−0.954607	−	0.297869i	$-0.903724\pi$
$239$		−	9.20989i		−	0.595739i	0.954607	−	0.297869i	$-0.0962760\pi$
$240$		0			0
$241$			9.50772i			0.612446i	0.951960	+	0.306223i	$0.0990653\pi$
$241$			9.50772i			0.612446i	−0.951960	+	0.306223i	$0.900935\pi$
$242$	2.19422	−	14.1880i	0.141050	−	0.912041i
$243$		0			0
$244$	−21.8963	+	1.88385i	−1.40177	+	0.120601i
$245$	1.99347	−	4.81265i	0.127358	−	0.307469i
$246$		0			0
$247$	12.3253	−	12.3253i	0.784243	−	0.784243i
$248$	4.99666	−	1.68409i	0.317288	−	0.106940i
$249$		0			0
$250$	6.02824	−	9.91810i	0.381260	−	0.627276i
$251$	−6.40268	−	2.65208i	−0.404134	−	0.167398i	0.171351	−	0.985210i	$-0.445187\pi$
$251$	−6.40268	−	2.65208i	−0.404134	−	0.167398i	−0.575485	+	0.817812i	$0.695187\pi$
$252$		0			0
$253$	−5.14234	−	12.4147i	−0.323296	−	0.780507i
$254$	−10.5811	−	14.4527i	−0.663918	−	0.906841i
$255$		0			0
$256$	5.38548	+	15.0664i	0.336592	+	0.941650i
$257$	−8.89106			−0.554609			−0.277304	−	0.960782i	$-0.589441\pi$
$257$	−8.89106			−0.554609			−0.277304	+	0.960782i	$0.589441\pi$
$258$		0			0
$259$	2.20235	+	5.31694i	0.136847	+	0.330378i
$260$	−1.62538	+	5.12924i	−0.100802	+	0.318102i
$261$		0			0
$262$	4.11040	−	6.76272i	0.253941	−	0.417802i
$263$	−17.8779	−	17.8779i	−1.10240	−	1.10240i	−0.994120	−	0.108280i	$-0.965466\pi$
$263$	−17.8779	−	17.8779i	−1.10240	−	1.10240i	−0.108280	−	0.994120i	$-0.534534\pi$
$264$		0			0
$265$	6.94638	−	6.94638i	0.426713	−	0.426713i
$266$	2.08266	+	8.53781i	0.127696	+	0.523487i
$267$		0			0
$268$	6.98201	−	0.600699i	0.426494	−	0.0366935i
$269$	−20.1363	+	8.34075i	−1.22773	+	0.508544i	−0.899861	−	0.436177i	$-0.856332\pi$
$269$	−20.1363	+	8.34075i	−1.22773	+	0.508544i	−0.327874	+	0.944721i	$0.606332\pi$
$270$		0			0
$271$		−	17.1501i		−	1.04179i	−0.853620	−	0.520896i	$-0.825598\pi$
$271$		−	17.1501i		−	1.04179i	0.853620	−	0.520896i	$-0.174402\pi$
$272$	0.0214710	−	0.0304762i	0.00130187	−	0.00184789i
$273$		0			0
$274$	1.20017	+	0.185610i	0.0725050	+	0.0112131i
$275$	17.8676	−	7.40099i	1.07746	−	0.446297i
$276$		0			0
$277$	3.37223	−	8.14128i	0.202617	−	0.489162i	−0.789609	−	0.613611i	$-0.789716\pi$
$277$	3.37223	−	8.14128i	0.202617	−	0.489162i	0.992226	+	0.124449i	$0.0397163\pi$
$278$	9.28013	−	2.26374i	0.556585	−	0.135770i
$279$		0			0
$280$	−1.78425	−	2.04345i	−0.106629	−	0.122119i
$281$	−11.2880	−	11.2880i	−0.673386	−	0.673386i	0.285109	−	0.958495i	$-0.407970\pi$
$281$	−11.2880	−	11.2880i	−0.673386	−	0.673386i	−0.958495	+	0.285109i	$0.907970\pi$
$282$		0			0
$283$	0.558205	+	0.231216i	0.0331819	+	0.0137444i	0.399213	−	0.916858i	$-0.369284\pi$
$283$	0.558205	+	0.231216i	0.0331819	+	0.0137444i	−0.366031	+	0.930603i	$0.619284\pi$
$284$	14.7203	−	7.63592i	0.873487	−	0.453108i
$285$		0			0
$286$	−15.8358	+	11.5937i	−0.936391	+	0.685553i
$287$	10.9797			0.648114
$288$		0			0
$289$	16.9999			0.999995
$290$	3.29679	−	2.41366i	0.193594	−	0.141735i
$291$		0			0
$292$	−1.64355	−	3.16839i	−0.0961816	−	0.185416i
$293$	14.8830	+	6.16475i	0.869476	+	0.360149i	0.772406	−	0.635129i	$-0.219053\pi$
$293$	14.8830	+	6.16475i	0.869476	+	0.360149i	0.0970697	+	0.995278i	$0.469053\pi$
$294$		0			0
$295$	−3.40441	−	3.40441i	−0.198212	−	0.198212i
$296$	−15.0966	−	1.02230i	−0.877474	−	0.0594197i
$297$		0			0
$298$	−15.7944	+	3.85280i	−0.914946	+	0.223187i
$299$	−3.37394	+	8.14541i	−0.195120	+	0.471061i
$300$		0			0
$301$	6.98328	−	2.89257i	0.402509	−	0.166725i
$302$	−31.4185	−	4.85897i	−1.80793	−	0.279602i
$303$		0			0
$304$	−22.5438	−	5.06612i	−1.29298	−	0.290562i
$305$			9.79705i			0.560977i
$306$		0			0
$307$	−20.1046	+	8.32760i	−1.14743	+	0.475281i	−0.873671	−	0.486517i	$-0.838267\pi$
$307$	−20.1046	+	8.32760i	−1.14743	+	0.475281i	−0.273760	+	0.961798i	$0.588267\pi$
$308$	−0.848195	−	9.85868i	−0.0483304	−	0.561751i
$309$		0			0
$310$	−0.557042	−	2.28358i	−0.0316379	−	0.129698i
$311$	19.4536	−	19.4536i	1.10311	−	1.10311i	0.109080	−	0.994033i	$-0.465209\pi$
$311$	19.4536	−	19.4536i	1.10311	−	1.10311i	0.994033	−	0.109080i	$-0.0347906\pi$
$312$		0			0
$313$	8.73135	+	8.73135i	0.493525	+	0.493525i	0.909415	−	0.415890i	$-0.136530\pi$
$313$	8.73135	+	8.73135i	0.493525	+	0.493525i	−0.415890	+	0.909415i	$0.636530\pi$
$314$	−0.505767	+	0.832124i	−0.0285421	+	0.0469595i
$315$		0			0
$316$	−26.1044	−	8.27211i	−1.46849	−	0.465343i
$317$	2.35263	+	5.67975i	0.132137	+	0.319007i	0.976075	−	0.217434i	$-0.0697686\pi$
$317$	2.35263	+	5.67975i	0.132137	+	0.319007i	−0.843938	+	0.536440i	$0.819769\pi$
$318$		0			0
$319$	14.9036			0.834444
$320$	6.89741	−	1.81620i	0.385577	−	0.101529i
$321$		0			0
$322$	−2.62584	−	3.58662i	−0.146332	−	0.199874i
$323$	0.0206026	+	0.0497390i	0.00114636	+	0.00276755i
$324$		0			0
$325$	−11.7231	−	4.85585i	−0.650279	−	0.269354i
$326$	4.73290	−	7.78692i	0.262131	−	0.431277i
$327$		0			0
$328$	−12.8241	+	25.8634i	−0.708091	+	1.42807i
$329$	−6.26829	+	6.26829i	−0.345582	+	0.345582i
$330$		0			0
$331$	1.07290	−	2.59020i	0.0589718	−	0.142370i	−0.891647	−	0.452731i	$-0.850450\pi$
$331$	1.07290	−	2.59020i	0.0589718	−	0.142370i	0.950619	+	0.310361i	$0.100450\pi$
$332$	1.20597	+	14.0172i	0.0661862	+	0.769291i
$333$		0			0
$334$	3.82137	−	24.7093i	0.209096	−	1.35203i
$335$		−	3.12396i		−	0.170680i
$336$		0			0
$337$		−	13.7560i		−	0.749335i	−0.927159	−	0.374667i	$-0.877757\pi$
$337$		−	13.7560i		−	0.749335i	0.927159	−	0.374667i	$-0.122243\pi$
$338$	−5.44314	−	0.841799i	−0.296068	−	0.0457878i
$339$		0			0
$340$	−0.0127153	−	0.0107007i	−0.000689585	−	0.000580328i
$341$	3.28104	−	7.92112i	0.177678	−	0.428953i
$342$		0			0
$343$	9.76922	−	9.76922i	0.527488	−	0.527488i
$344$	−1.34269	+	19.8280i	−0.0723928	+	1.06905i
$345$		0			0
$346$	−24.3129	−	14.7774i	−1.30707	−	0.794440i
$347$	−4.45557	−	1.84556i	−0.239188	−	0.0990748i	0.259870	−	0.965644i	$-0.416320\pi$
$347$	−4.45557	−	1.84556i	−0.239188	−	0.0990748i	−0.499058	+	0.866569i	$0.666320\pi$
$348$		0			0
$349$	3.00002	+	7.24268i	0.160587	+	0.387692i	0.983608	−	0.180319i	$-0.0577131\pi$
$349$	3.00002	+	7.24268i	0.160587	+	0.387692i	−0.823021	+	0.568011i	$0.807713\pi$
$350$	5.16195	−	3.77918i	0.275918	−	0.202006i
$351$		0			0
$352$	24.2134	+	9.51673i	1.29058	+	0.507243i
$353$	5.41049			0.287971			0.143986	−	0.989580i	$-0.454008\pi$
$353$	5.41049			0.287971			0.143986	+	0.989580i	$0.454008\pi$
$354$		0			0
$355$	−2.82894	−	6.82967i	−0.150145	−	0.362481i
$356$	26.9822	−	13.9966i	1.43005	−	0.741818i
$357$		0			0
$358$	23.1275	+	14.0570i	1.22233	+	0.742934i
$359$	13.7364	+	13.7364i	0.724980	+	0.724980i	0.969615	−	0.244635i	$-0.0786682\pi$
$359$	13.7364	+	13.7364i	0.724980	+	0.724980i	−0.244635	+	0.969615i	$0.578668\pi$
$360$		0			0
$361$	10.1597	−	10.1597i	0.534723	−	0.534723i
$362$	−19.0621	+	4.64989i	−1.00188	+	0.244393i
$363$		0			0
$364$	−4.18032	+	4.96734i	−0.219108	+	0.260359i
$365$	−1.47002	+	0.608901i	−0.0769442	+	0.0318713i
$366$		0			0
$367$			14.0989i			0.735955i	0.929835	+	0.367977i	$0.119950\pi$
$367$			14.0989i			0.735955i	−0.929835	+	0.367977i	$0.880050\pi$
$368$	11.5154	−	1.99624i	0.600282	−	0.104061i
$369$		0			0
$370$	−1.03092	+	6.66598i	−0.0535947	+	0.346548i
$371$	10.9510	−	4.53604i	0.568546	−	0.235500i
$372$		0			0
$373$	7.31708	−	17.6650i	0.378864	−	0.914659i	−0.613315	−	0.789838i	$-0.710164\pi$
$373$	7.31708	−	17.6650i	0.378864	−	0.914659i	0.992179	−	0.124821i	$-0.0398355\pi$
$374$	−0.0143657	−	0.0588916i	−0.000742831	−	0.00304521i
$375$		0			0
$376$	−7.44410	−	22.0865i	−0.383900	−	1.13902i
$377$	−6.91438	−	6.91438i	−0.356109	−	0.356109i
$378$		0			0
$379$	8.91380	+	3.69222i	0.457871	+	0.189656i	0.599684	−	0.800237i	$-0.295293\pi$
$379$	8.91380	+	3.69222i	0.457871	+	0.189656i	−0.141813	+	0.989894i	$0.545293\pi$
$380$	−3.11152	+	9.81906i	−0.159618	+	0.503707i
$381$		0			0
$382$	18.2823	+	24.9717i	0.935406	+	1.27766i
$383$	−23.3173			−1.19146			−0.595729	−	0.803186i	$-0.703137\pi$
$383$	−23.3173			−1.19146			−0.595729	+	0.803186i	$0.703137\pi$
$384$		0			0
$385$	−4.41107			−0.224809
$386$	2.48575	+	3.39526i	0.126521	+	0.172814i
$387$		0			0
$388$	10.1951	−	32.1729i	0.517578	−	1.63333i
$389$	6.07617	+	2.51683i	0.308074	+	0.127608i	0.531364	−	0.847144i	$-0.321680\pi$
$389$	6.07617	+	2.51683i	0.308074	+	0.127608i	−0.223290	+	0.974752i	$0.571680\pi$
$390$		0			0
$391$	−0.0192553	−	0.0192553i	−0.000973783	−	0.000973783i
$392$	5.27815	+	15.6602i	0.266587	+	0.790958i
$393$		0			0
$394$	0.610693	+	2.50351i	0.0307663	+	0.126125i
$395$	−4.67149	+	11.2780i	−0.235048	+	0.567457i
$396$		0			0
$397$	−29.6431	+	12.2786i	−1.48775	+	0.616244i	−0.970825	−	0.239789i	$-0.922922\pi$
$397$	−29.6431	+	12.2786i	−1.48775	+	0.616244i	−0.516920	+	0.856034i	$0.672922\pi$
$398$	−2.70691	+	17.5031i	−0.135685	+	0.877352i
$399$		0			0
$400$	2.87304	+	16.5733i	0.143652	+	0.828663i
$401$			1.87076i			0.0934214i	0.998908	+	0.0467107i	$0.0148739\pi$
$401$			1.87076i			0.0934214i	−0.998908	+	0.0467107i	$0.985126\pi$
$402$		0			0
$403$	−5.19712	+	2.15272i	−0.258887	+	0.107234i
$404$	−23.8330	+	28.3200i	−1.18574	+	1.40897i
$405$		0			0
$406$	4.78962	−	1.16835i	0.237705	−	0.0579843i
$407$	−17.3975	+	17.3975i	−0.862361	+	0.862361i
$408$		0			0
$409$	17.6704	+	17.6704i	0.873744	+	0.873744i	0.992878	−	0.119135i	$-0.0380120\pi$
$409$	17.6704	+	17.6704i	0.873744	+	0.873744i	−0.119135	+	0.992878i	$0.538012\pi$
$410$	10.9970	+	6.68400i	0.543103	+	0.330099i
$411$		0			0
$412$	8.71286	−	4.51967i	0.429252	−	0.222668i
$413$	−2.22311	−	5.36706i	−0.109392	−	0.264096i
$414$		0			0
$415$	6.27169			0.307865
$416$	−6.81834	−	15.6487i	−0.334297	−	0.767241i
$417$		0			0
$418$	−30.3150	+	22.1943i	−1.48275	+	1.08556i
$419$	1.39543	+	3.36888i	0.0681715	+	0.164580i	0.954293	−	0.298872i	$-0.0966104\pi$
$419$	1.39543	+	3.36888i	0.0681715	+	0.164580i	−0.886122	+	0.463453i	$0.846610\pi$
$420$		0			0
$421$	−7.92900	−	3.28430i	−0.386436	−	0.160067i	0.181003	−	0.983483i	$-0.442066\pi$
$421$	−7.92900	−	3.28430i	−0.386436	−	0.160067i	−0.567439	+	0.823416i	$0.692066\pi$
$422$	23.6089	+	14.3496i	1.14927	+	0.698526i
$423$		0			0
$424$	−2.10556	+	31.0936i	−0.102255	+	1.51004i
$425$	0.0277127	−	0.0277127i	0.00134426	−	0.00134426i
$426$		0			0
$427$	−4.52376	+	10.9213i	−0.218920	+	0.528519i
$428$	−24.1002	−	20.2818i	−1.16493	−	0.980358i
$429$		0			0
$430$	8.75512	+	1.35401i	0.422209	+	0.0652960i
$431$			28.8420i			1.38927i	0.719363	+	0.694635i	$0.244434\pi$
$431$			28.8420i			1.38927i	−0.719363	+	0.694635i	$0.755566\pi$
$432$		0			0
$433$			20.2379i			0.972569i	0.873800	+	0.486285i	$0.161648\pi$
$433$			20.2379i			0.972569i	−0.873800	+	0.486285i	$0.838352\pi$
$434$	0.433468	−	2.80284i	0.0208071	−	0.134541i
$435$		0			0
$436$	−0.448585	−	5.21396i	−0.0214833	−	0.249703i
$437$	−6.45883	+	15.5930i	−0.308968	+	0.745914i
$438$		0			0
$439$	18.4090	−	18.4090i	0.878613	−	0.878613i	−0.114778	−	0.993391i	$-0.536616\pi$
$439$	18.4090	−	18.4090i	0.878613	−	0.878613i	0.993391	+	0.114778i	$0.0366156\pi$
$440$	5.15202	−	10.3905i	0.245613	−	0.495349i
$441$		0			0
$442$	−0.0206573	+	0.0339869i	−0.000982568	+	0.00161659i
$443$	−6.93861	−	2.87407i	−0.329664	−	0.136551i	0.211712	−	0.977332i	$-0.432096\pi$
$443$	−6.93861	−	2.87407i	−0.329664	−	0.136551i	−0.541375	+	0.840781i	$0.682096\pi$
$444$		0			0
$445$	−5.18544	−	12.5188i	−0.245813	−	0.593446i
$446$	6.00891	+	8.20752i	0.284530	+	0.388637i
$447$		0			0
$448$	8.52755	+	1.16024i	0.402889	+	0.0548161i
$449$	−3.59049			−0.169446			−0.0847229	−	0.996405i	$-0.527000\pi$
$449$	−3.59049			−0.169446			−0.0847229	+	0.996405i	$0.527000\pi$
$450$		0			0
$451$	17.9633	+	43.3673i	0.845860	+	2.04209i
$452$	−25.2740	−	8.00897i	−1.18879	−	0.376710i
$453$		0			0
$454$	11.0281	−	18.1442i	0.517574	−	0.851550i
$455$	2.04647	+	2.04647i	0.0959398	+	0.0959398i
$456$		0			0
$457$	−18.2566	+	18.2566i	−0.854007	+	0.854007i	−0.990624	−	0.136617i	$-0.956377\pi$
$457$	−18.2566	+	18.2566i	−0.854007	+	0.854007i	0.136617	+	0.990624i	$0.456377\pi$
$458$	2.03457	+	8.34065i	0.0950692	+	0.389733i
$459$		0			0
$460$	−0.446588	−	5.19076i	−0.0208223	−	0.242020i
$461$	3.70224	−	1.53352i	0.172431	−	0.0714231i	−0.294798	−	0.955560i	$-0.595252\pi$
$461$	3.70224	−	1.53352i	0.172431	−	0.0714231i	0.467229	+	0.884136i	$0.345252\pi$
$462$		0			0
$463$		−	9.58897i		−	0.445637i	−0.974860	−	0.222819i	$-0.928474\pi$
$463$		−	9.58897i		−	0.445637i	0.974860	−	0.222819i	$-0.0715257\pi$
$464$	−2.84204	+	12.6468i	−0.131938	+	0.587114i
$465$		0			0
$466$	18.6395	+	2.88265i	0.863456	+	0.133536i
$467$	−13.6644	+	5.65999i	−0.632314	+	0.261913i	−0.675736	−	0.737144i	$-0.736174\pi$
$467$	−13.6644	+	5.65999i	−0.632314	+	0.261913i	0.0434217	+	0.999057i	$0.486174\pi$
$468$		0			0
$469$	1.44248	−	3.48245i	0.0666074	−	0.160804i
$470$	−10.0940	+	2.46227i	−0.465601	+	0.113576i
$471$		0			0
$472$	15.2389	+	1.03193i	0.701429	+	0.0474986i
$473$	22.8499	+	22.8499i	1.05064	+	1.05064i
$474$		0			0
$475$	−22.4418	−	9.29571i	−1.02970	−	0.426516i
$476$	−0.00923345	−	0.0177999i	−0.000423215	−	0.000815859i
$477$		0			0
$478$	10.5093	−	7.69409i	0.480684	−	0.351919i
$479$	12.1591			0.555563			0.277781	−	0.960644i	$-0.410401\pi$
$479$	12.1591			0.555563			0.277781	+	0.960644i	$0.410401\pi$
$480$		0			0
$481$	16.1427			0.736045
$482$	−10.8491	+	7.94289i	−0.494165	+	0.361789i
$483$		0			0
$484$	18.0229	−	9.34909i	0.819221	−	0.424959i
$485$	−13.8997	−	5.75746i	−0.631155	−	0.261433i
$486$		0			0
$487$	−27.5188	−	27.5188i	−1.24700	−	1.24700i	−0.957040	−	0.289956i	$-0.906359\pi$
$487$	−27.5188	−	27.5188i	−1.24700	−	1.24700i	−0.289956	−	0.957040i	$-0.593641\pi$
$488$	−20.4421	−	23.4118i	−0.925372	−	1.05980i
$489$		0			0
$490$	7.15703	−	1.74584i	0.323322	−	0.0788692i
$491$	3.09495	−	7.47186i	0.139673	−	0.337200i	−0.838529	−	0.544857i	$-0.816584\pi$
$491$	3.09495	−	7.47186i	0.139673	−	0.337200i	0.978202	+	0.207657i	$0.0665838\pi$
$492$		0			0
$493$	0.0279030	−	0.0115578i	0.00125669	−	0.000520538i
$494$	24.3611	+	3.76752i	1.09606	+	0.169509i
$495$		0			0
$496$	6.09597	+	4.29471i	0.273717	+	0.192838i
$497$		−	8.91967i		−	0.400102i
$498$		0			0
$499$	−25.5827	+	10.5967i	−1.14524	+	0.474373i	−0.872934	−	0.487838i	$-0.837786\pi$
$499$	−25.5827	+	10.5967i	−1.14524	+	0.474373i	−0.272304	+	0.962211i	$0.587786\pi$
$500$	16.3535	−	1.40698i	0.731351	−	0.0629220i
$501$		0			0
$502$	−2.32264	−	9.52161i	−0.103665	−	0.424970i
$503$	−22.2953	+	22.2953i	−0.994096	+	0.994096i	−0.999983	−	0.00588649i	$-0.998126\pi$
$503$	−22.2953	+	22.2953i	−0.994096	+	0.994096i	0.00588649	+	0.999983i	$0.498126\pi$
$504$		0			0
$505$	11.6674	+	11.6674i	0.519192	+	0.519192i
$506$	9.87029	−	16.2393i	0.438788	−	0.721926i
$507$		0			0
$508$	7.65214	−	24.1480i	0.339509	−	1.07139i
$509$	−0.426371	−	1.02935i	−0.0188986	−	0.0456252i	0.914149	−	0.405379i	$-0.132861\pi$
$509$	−0.426371	−	1.02935i	−0.0188986	−	0.0456252i	−0.933047	+	0.359754i	$0.882861\pi$
$510$		0			0
$511$	−1.91987			−0.0849299
$512$	−12.6930	+	18.7320i	−0.560956	+	0.827846i
$513$		0			0
$514$	−7.42772	−	10.1455i	−0.327623	−	0.447498i
$515$	−1.67444	−	4.04245i	−0.0737846	−	0.178132i
$516$		0			0
$517$	−35.0134	−	14.5030i	−1.53989	−	0.637842i
$518$	−4.22722	+	6.95492i	−0.185733	+	0.305582i
$519$		0			0
$520$	−7.21079	+	2.43035i	−0.316214	+	0.106578i
$521$	24.7547	−	24.7547i	1.08452	−	1.08452i	0.0884421	−	0.996081i	$-0.471811\pi$
$521$	24.7547	−	24.7547i	1.08452	−	1.08452i	0.996081	−	0.0884421i	$-0.0281888\pi$
$522$		0			0
$523$	−12.9693	+	31.3107i	−0.567109	+	1.36912i	0.336872	+	0.941550i	$0.390631\pi$
$523$	−12.9693	+	31.3107i	−0.567109	+	1.36912i	−0.903981	+	0.427572i	$0.859369\pi$
$524$	11.1507	−	0.959358i	0.487123	−	0.0419097i
$525$		0			0
$526$	5.46479	−	35.3358i	0.238276	−	1.54071i
$527$		−	0.0173746i		−	0.000756850i
$528$		0			0
$529$			14.4632i			0.628833i
$530$	13.7295	+	2.12332i	0.596373	+	0.0922309i
$531$		0			0
$532$	−8.00250	+	9.50912i	−0.346952	+	0.412273i
$533$	11.7859	−	28.4537i	0.510504	−	1.23247i
$534$		0			0
$535$	−9.92892	+	9.92892i	−0.429265	+	0.429265i
$536$	6.51833	+	7.46525i	0.281549	+	0.322450i
$537$		0			0
$538$	−26.3397	−	16.0093i	−1.13559	−	0.690212i
$539$	24.8258	+	10.2832i	1.06932	+	0.442929i
$540$		0			0
$541$	−5.37276	−	12.9710i	−0.230993	−	0.557667i	0.765302	−	0.643672i	$-0.222590\pi$
$541$	−5.37276	−	12.9710i	−0.230993	−	0.557667i	−0.996295	+	0.0860052i	$0.972590\pi$
$542$	19.5697	−	14.3274i	0.840592	−	0.615416i
$543$		0			0
$544$	0.0527132		0.000960034i	0.00226006		4.11611e-5i
$545$	−2.33288			−0.0999296
$546$		0			0
$547$	−15.7171	−	37.9446i	−0.672017	−	1.62239i	−0.778179	−	0.628043i	$-0.783856\pi$
$547$	−15.7171	−	37.9446i	−0.672017	−	1.62239i	0.106162	−	0.994349i	$-0.466144\pi$
$548$	0.790844	+	1.52456i	0.0337832	+	0.0651260i
$549$		0			0
$550$	23.3720	+	14.2056i	0.996586	+	0.605727i
$551$	−13.2364	−	13.2364i	−0.563890	−	0.563890i
$552$		0			0
$553$	−10.4151	+	10.4151i	−0.442897	+	0.442897i
$554$	12.1071	−	2.95334i	0.514382	−	0.125475i
$555$		0			0
$556$	10.3359	+	8.69828i	0.438339	+	0.368889i
$557$	26.4894	−	10.9723i	1.12239	−	0.464909i	0.257202	−	0.966358i	$-0.417199\pi$
$557$	26.4894	−	10.9723i	1.12239	−	0.464909i	0.865188	+	0.501448i	$0.167199\pi$
$558$		0			0
$559$		−	21.2019i		−	0.896745i
$560$	0.841164	−	3.74311i	0.0355457	−	0.158175i
$561$		0			0
$562$	3.45043	−	22.3108i	0.145548	−	0.941124i
$563$	−32.2109	+	13.3422i	−1.35753	+	0.562307i	−0.938378	−	0.345609i	$-0.887672\pi$
$563$	−32.2109	+	13.3422i	−1.35753	+	0.562307i	−0.419151	+	0.907917i	$0.637672\pi$
$564$		0			0
$565$	−4.52289	+	10.9192i	−0.190279	+	0.459375i
$566$	0.202495	+	0.830123i	0.00851151	+	0.0348927i
$567$		0			0
$568$	21.0108	+	10.4180i	0.881593	+	0.437128i
$569$	−20.7035	−	20.7035i	−0.867936	−	0.867936i	0.124307	−	0.992244i	$-0.460329\pi$
$569$	−20.7035	−	20.7035i	−0.867936	−	0.867936i	−0.992244	+	0.124307i	$0.960329\pi$
$570$		0			0
$571$	−18.7087	−	7.74938i	−0.782933	−	0.324302i	−0.0448347	−	0.998994i	$-0.514276\pi$
$571$	−18.7087	−	7.74938i	−0.782933	−	0.324302i	−0.738099	+	0.674693i	$0.764276\pi$
$572$	−26.4590	−	8.38446i	−1.10630	−	0.350572i
$573$		0			0
$574$	9.17264	+	12.5288i	0.382859	+	0.522944i
$575$	12.2864			0.512380
$576$		0			0
$577$	13.6903			0.569937			0.284968	−	0.958537i	$-0.408017\pi$
$577$	13.6903			0.569937			0.284968	+	0.958537i	$0.408017\pi$
$578$	14.2020	+	19.3984i	0.590725	+	0.806867i
$579$		0			0
$580$	5.50839	+	1.74553i	0.228723	+	0.0724791i
$581$	6.99140	+	2.89593i	0.290052	+	0.120144i
$582$		0			0
$583$	35.8326	+	35.8326i	1.48403	+	1.48403i
$584$	2.24236	−	4.52235i	0.0927894	−	0.187136i
$585$		0			0
$586$	5.39899	+	22.1330i	0.223030	+	0.914305i
$587$	−2.03062	+	4.90234i	−0.0838125	+	0.202341i	−0.960230	−	0.279211i	$-0.909927\pi$
$587$	−2.03062	+	4.90234i	−0.0838125	+	0.202341i	0.876417	+	0.481553i	$0.159927\pi$
$588$		0			0
$589$	−9.94900	+	4.12101i	−0.409941	+	0.169803i
$590$	1.04063	−	6.72882i	0.0428422	−	0.277021i
$591$		0			0
$592$	−11.4454	−	18.0806i	−0.470404	−	0.743109i
$593$		−	37.8785i		−	1.55548i	−0.628584	−	0.777742i	$-0.716365\pi$
$593$		−	37.8785i		−	1.55548i	0.628584	−	0.777742i	$-0.283635\pi$
$594$		0			0
$595$	−0.00825853	+	0.00342080i	−0.000338567	+	0.000140239i
$596$	−17.5913	−	14.8041i	−0.720567	−	0.606401i
$597$		0			0
$598$	−12.1133	+	2.95484i	−0.495348	+	0.120832i
$599$	11.3329	−	11.3329i	0.463049	−	0.463049i	−0.436604	−	0.899654i	$-0.643819\pi$
$599$	11.3329	−	11.3329i	0.463049	−	0.463049i	0.899654	+	0.436604i	$0.143819\pi$
$600$		0			0
$601$	−18.2912	−	18.2912i	−0.746112	−	0.746112i	0.227635	−	0.973747i	$-0.426901\pi$
$601$	−18.2912	−	18.2912i	−0.746112	−	0.746112i	−0.973747	+	0.227635i	$0.926901\pi$
$602$	9.13461	+	5.55203i	0.372299	+	0.226284i
$603$		0			0
$604$	−20.7030	−	39.9105i	−0.842392	−	1.62393i
$605$	−3.46364	−	8.36196i	−0.140817	−	0.339962i
$606$		0			0
$607$	−19.2598			−0.781733			−0.390866	−	0.920447i	$-0.627825\pi$
$607$	−19.2598			−0.781733			−0.390866	+	0.920447i	$0.627825\pi$
$608$	−13.0525	−	29.9568i	−0.529351	−	1.21491i
$609$		0			0
$610$	−11.1793	+	8.18460i	−0.452636	+	0.331385i
$611$	9.51556	+	22.9726i	0.384959	+	0.929372i
$612$		0			0
$613$	−21.1578	−	8.76386i	−0.854557	−	0.353969i	−0.0879805	−	0.996122i	$-0.528041\pi$
$613$	−21.1578	−	8.76386i	−0.854557	−	0.353969i	−0.766576	+	0.642153i	$0.778041\pi$
$614$	−26.2982	−	15.9841i	−1.06131	−	0.645067i
$615$		0			0
$616$	10.5410	−	9.20396i	0.424710	−	0.370838i
$617$	−18.3158	+	18.3158i	−0.737368	+	0.737368i	−0.972068	−	0.234700i	$-0.924589\pi$
$617$	−18.3158	+	18.3158i	−0.737368	+	0.737368i	0.234700	+	0.972068i	$0.424589\pi$
$618$		0			0
$619$	−3.15520	+	7.61733i	−0.126818	+	0.306166i	−0.974518	−	0.224310i	$-0.927987\pi$
$619$	−3.15520	+	7.61733i	−0.126818	+	0.306166i	0.847699	+	0.530477i	$0.177987\pi$
$620$	2.14040	−	2.54337i	0.0859605	−	0.102144i
$621$		0			0
$622$	38.4501	+	5.94643i	1.54171	+	0.238430i
$623$		−	16.3497i		−	0.655037i
$624$		0			0
$625$			13.7085i			0.548340i
$626$	−2.66893	+	17.2575i	−0.106672	+	0.689750i
$627$		0			0
$628$	−1.37205	+	0.118045i	−0.0547508	+	0.00471050i
$629$	−0.0190803	+	0.0460639i	−0.000760781	+	0.00183669i
$630$		0			0
$631$	19.2283	−	19.2283i	0.765466	−	0.765466i	−0.211839	−	0.977305i	$-0.567945\pi$
$631$	19.2283	−	19.2283i	0.765466	−	0.765466i	0.977305	+	0.211839i	$0.0679453\pi$
$632$	−12.3688	−	36.6981i	−0.492006	−	1.45977i
$633$		0			0
$634$	−4.51567	+	7.42951i	−0.179340	+	0.295063i
$635$	−10.4327	−	4.32138i	−0.414010	−	0.171489i
$636$		0			0
$637$	−6.74690	−	16.2884i	−0.267322	−	0.645372i
$638$	12.4507	+	17.0064i	0.492929	+	0.673288i
$639$		0			0
$640$	7.83465	+	6.35327i	0.309692	+	0.251135i
$641$	24.1571			0.954147			0.477074	−	0.878863i	$-0.341698\pi$
$641$	24.1571			0.954147			0.477074	+	0.878863i	$0.341698\pi$
$642$		0			0
$643$	15.5461	+	37.5316i	0.613079	+	1.48010i	0.859601	+	0.510966i	$0.170712\pi$
$643$	15.5461	+	37.5316i	0.613079	+	1.48010i	−0.246522	+	0.969137i	$0.579288\pi$
$644$	1.89898	−	5.99263i	0.0748302	−	0.236143i
$645$		0			0
$646$	−0.0395449	+	0.0650621i	−0.00155587	+	0.00255983i
$647$	16.1361	+	16.1361i	0.634377	+	0.634377i	0.949163	−	0.314786i	$-0.101933\pi$
$647$	16.1361	+	16.1361i	0.634377	+	0.634377i	−0.314786	+	0.949163i	$0.601933\pi$
$648$		0			0
$649$	17.5615	−	17.5615i	0.689348	−	0.689348i
$650$	−4.25268	−	17.4337i	−0.166804	−	0.683806i
$651$		0			0
$652$	12.8395	−	1.10465i	0.502833	−	0.0432614i
$653$	41.9825	−	17.3897i	1.64290	−	0.680513i	0.646316	−	0.763070i	$-0.276309\pi$
$653$	41.9825	−	17.3897i	1.64290	−	0.680513i	0.996586	+	0.0825571i	$0.0263087\pi$
$654$		0			0
$655$		−	4.98917i		−	0.194943i
$656$	−40.2258	+	6.97330i	−1.57055	+	0.272262i
$657$		0			0
$658$	−12.3893	−	1.91604i	−0.482985	−	0.0746951i
$659$	−13.7053	+	5.67693i	−0.533883	+	0.221142i	−0.633303	−	0.773904i	$-0.718301\pi$
$659$	−13.7053	+	5.67693i	−0.533883	+	0.221142i	0.0994199	+	0.995046i	$0.468301\pi$
$660$		0			0
$661$	−8.16833	+	19.7201i	−0.317711	+	0.767022i	0.681664	+	0.731666i	$0.261257\pi$
$661$	−8.16833	+	19.7201i	−0.317711	+	0.767022i	−0.999375	+	0.0353568i	$0.988743\pi$
$662$	3.85196	−	0.939625i	0.149711	−	0.0365196i
$663$		0			0
$664$	−14.9873	+	13.0863i	−0.581621	+	0.507846i
$665$	3.91761	+	3.91761i	0.151918	+	0.151918i
$666$		0			0
$667$	8.74749	+	3.62333i	0.338704	+	0.140296i
$668$	31.3879	−	16.2820i	1.21443	−	0.629970i
$669$		0			0
$670$	3.56471	−	2.60980i	0.137717	−	0.100825i
$671$	−50.5376			−1.95098
$672$		0			0
$673$	3.71057			0.143032			0.0715161	−	0.997439i	$-0.477216\pi$
$673$	3.71057			0.143032			0.0715161	+	0.997439i	$0.477216\pi$
$674$	15.6968	−	11.4919i	0.604617	−	0.442653i
$675$		0			0
$676$	−3.58672	−	6.91435i	−0.137951	−	0.265937i
$677$	−29.7407	−	12.3190i	−1.14303	−	0.473458i	−0.270839	−	0.962625i	$-0.587301\pi$
$677$	−29.7407	−	12.3190i	−1.14303	−	0.473458i	−0.872190	+	0.489167i	$0.837301\pi$
$678$		0			0
$679$	−12.8363	−	12.8363i	−0.492613	−	0.492613i
$680$	0.00158788	−	0.0234488i	6.08925e−5	−	0.000899222i
$681$		0			0
$682$	11.7797	−	2.87348i	0.451069	−	0.110031i
$683$	−4.25617	+	10.2753i	−0.162858	+	0.393173i	−0.984151	−	0.177333i	$-0.943253\pi$
$683$	−4.25617	+	10.2753i	−0.162858	+	0.393173i	0.821293	+	0.570506i	$0.193253\pi$
$684$		0			0
$685$	0.707342	−	0.292990i	0.0270261	−	0.0111946i
$686$	19.3089	+	2.98618i	0.737217	+	0.114013i
$687$		0			0
$688$	−23.7471	+	15.0325i	−0.905351	+	0.573107i
$689$		−	33.2482i		−	1.26666i
$690$		0			0
$691$	6.21462	−	2.57418i	0.236415	−	0.0979265i	−0.261330	−	0.965249i	$-0.584161\pi$
$691$	6.21462	−	2.57418i	0.236415	−	0.0979265i	0.497746	+	0.867323i	$0.334161\pi$
$692$	−3.44902	−	40.0885i	−0.131112	−	1.52394i
$693$		0			0
$694$	−1.61631	−	6.62601i	−0.0613543	−	0.251520i
$695$	4.25823	−	4.25823i	0.161524	−	0.161524i
$696$		0			0
$697$	0.0672630	+	0.0672630i	0.00254777	+	0.00254777i
$698$	−5.75827	+	9.47393i	−0.217954	+	0.358594i
$699$		0			0
$700$	8.62475	+	2.73306i	0.325985	+	0.103300i
$701$	−8.11781	−	19.5981i	−0.306606	−	0.740211i	−0.999810	−	0.0194707i	$-0.993802\pi$
$701$	−8.11781	−	19.5981i	−0.306606	−	0.740211i	0.693205	−	0.720741i	$-0.256198\pi$
$702$		0			0
$703$	30.9025			1.16551
$704$	9.36879	+	35.5800i	0.353100	+	1.34097i
$705$		0			0
$706$	4.52000	+	6.17384i	0.170113	+	0.232356i
$707$	7.61891	+	18.3937i	0.286538	+	0.691765i
$708$		0			0
$709$	42.9936	+	17.8086i	1.61466	+	0.668814i	0.993391	−	0.114783i	$-0.0366172\pi$
$709$	42.9936	+	17.8086i	1.61466	+	0.668814i	0.621270	+	0.783597i	$0.286617\pi$
$710$	5.42991	−	8.93369i	0.203781	−	0.335275i
$711$		0			0
$712$	38.5127	+	19.0961i	1.44332	+	0.715655i
$713$	3.85152	−	3.85152i	0.144241	−	0.144241i
$714$		0			0
$715$	−4.73494	+	11.4312i	−0.177077	+	0.427501i
$716$	3.28087	+	38.1339i	0.122612	+	1.42513i
$717$		0			0
$718$	−4.19884	+	27.1501i	−0.156699	+	1.01323i
$719$		−	11.1345i		−	0.415247i	−0.978209	−	0.207623i	$-0.933427\pi$
$719$		−	11.1345i		−	0.415247i	0.978209	−	0.207623i	$-0.0665729\pi$
$720$		0			0
$721$		−	5.27951i		−	0.196619i
$722$	20.0807	+	3.10555i	0.747328	+	0.115577i
$723$		0			0
$724$	−21.2307	−	17.8669i	−0.789032	−	0.664018i
$725$	−5.21479	+	12.5896i	−0.193672	+	0.467566i
$726$		0			0
$727$	−24.8906	+	24.8906i	−0.923142	+	0.923142i	−0.997250	−	0.0741087i	$-0.976389\pi$
$727$	−24.8906	+	24.8906i	−0.923142	+	0.923142i	0.0741087	+	0.997250i	$0.476389\pi$
$728$	−9.16047	−	0.620318i	−0.339510	−	0.0229905i
$729$		0			0
$730$	−1.92288	−	1.16873i	−0.0711691	−	0.0432567i
$731$	0.0605004	+	0.0250601i	0.00223769	+	0.000926881i
$732$		0			0
$733$	0.0725845	+	0.175234i	0.00268097	+	0.00647243i	0.925214	−	0.379445i	$-0.123885\pi$
$733$	0.0725845	+	0.175234i	0.00268097	+	0.00647243i	−0.922533	+	0.385917i	$0.873885\pi$
$734$	−16.0880	+	11.7784i	−0.593820	+	0.434749i
$735$		0			0
$736$	11.8980	+	11.4724i	0.438567	+	0.422878i
$737$	16.1148			0.593596
$738$		0			0
$739$	−4.22742	−	10.2059i	−0.155508	−	0.375430i	0.826854	−	0.562416i	$-0.190128\pi$
$739$	−4.22742	−	10.2059i	−0.155508	−	0.375430i	−0.982363	+	0.186986i	$0.940128\pi$
$740$	−8.46772	+	4.39250i	−0.311279	+	0.161472i
$741$		0			0
$742$	14.3246	+	8.70655i	0.525874	+	0.319627i
$743$	33.8685	+	33.8685i	1.24252	+	1.24252i	0.958954	+	0.283562i	$0.0915162\pi$
$743$	33.8685	+	33.8685i	1.24252	+	1.24252i	0.283562	+	0.958954i	$0.408484\pi$
$744$		0			0
$745$	−7.24733	+	7.24733i	−0.265522	+	0.265522i
$746$	26.2701	−	6.40818i	0.961817	−	0.234620i
$747$		0			0
$748$	0.0551991	−	0.0655914i	0.00201828	−	0.00239826i
$749$	−15.6530	+	6.48367i	−0.571947	+	0.236908i
$750$		0			0
$751$			1.52241i			0.0555534i	0.999614	+	0.0277767i	$0.00884274\pi$
$751$			1.52241i			0.0555534i	−0.999614	+	0.0277767i	$0.991157\pi$
$752$	18.9837	−	26.9458i	0.692265	−	0.982611i
$753$		0			0
$754$	2.11353	−	13.6663i	0.0769704	−	0.497697i
$755$	−18.5170	+	7.67000i	−0.673904	+	0.279140i
$756$		0			0
$757$	4.47115	−	10.7943i	0.162507	−	0.392326i	−0.821561	−	0.570121i	$-0.806896\pi$
$757$	4.47115	−	10.7943i	0.162507	−	0.392326i	0.984068	+	0.177795i	$0.0568963\pi$
$758$	3.23358	+	13.2560i	0.117449	+	0.481478i
$759$		0			0
$760$	−13.8038	+	4.65248i	−0.500717	+	0.168763i
$761$	21.7341	+	21.7341i	0.787861	+	0.787861i	0.981143	−	0.193282i	$-0.0619132\pi$
$761$	21.7341	+	21.7341i	0.787861	+	0.787861i	−0.193282	+	0.981143i	$0.561913\pi$
$762$		0			0
$763$	−2.60059	−	1.07720i	−0.0941477	−	0.0389973i
$764$	−13.2216	+	41.7235i	−0.478340	+	1.50950i
$765$		0			0
$766$	−19.4796	−	26.6071i	−0.703827	−	0.961353i
$767$	−16.2949			−0.588375
$768$		0			0
$769$	2.99672			0.108064			0.0540322	−	0.998539i	$-0.482793\pi$
$769$	2.99672			0.108064			0.0540322	+	0.998539i	$0.482793\pi$
$770$	−3.68507	−	5.03341i	−0.132801	−	0.181392i
$771$		0			0
$772$	−1.79766	+	5.67291i	−0.0646993	+	0.204172i
$773$	3.94358	+	1.63348i	0.141841	+	0.0587523i	0.452475	−	0.891777i	$-0.350541\pi$
$773$	3.94358	+	1.63348i	0.141841	+	0.0587523i	−0.310634	+	0.950530i	$0.600541\pi$
$774$		0			0
$775$	5.54321	+	5.54321i	0.199118	+	0.199118i
$776$	45.2292	−	15.2442i	1.62363	−	0.547234i
$777$		0			0
$778$	2.20420	+	9.03604i	0.0790244	+	0.323958i
$779$	22.5621	−	54.4697i	0.808371	−	1.95158i
$780$		0			0
$781$	35.2306	−	14.5930i	1.26065	−	0.522178i
$782$	0.00588581	−	0.0380582i	0.000210476	−	0.00136096i
$783$		0			0
$784$	−13.4602	+	19.1056i	−0.480721	+	0.682342i
$785$			0.613896i			0.0219109i
$786$		0			0
$787$	15.2672	−	6.32387i	0.544216	−	0.225422i	−0.0936007	−	0.995610i	$-0.529838\pi$
$787$	15.2672	−	6.32387i	0.544216	−	0.225422i	0.637817	+	0.770188i	$0.279838\pi$
$788$	−2.34655	+	2.78833i	−0.0835923	+	0.0993301i
$789$		0			0
$790$	−16.7718	+	4.09121i	−0.596714	+	0.145559i
$791$	−10.0838	+	10.0838i	−0.358540	+	0.358540i
$792$		0			0
$793$	23.4464	+	23.4464i	0.832605	+	0.832605i
$794$	−38.7752	−	23.5677i	−1.37608	−	0.836386i
$795$		0			0
$796$	−22.2340	+	11.5336i	−0.788063	+	0.408796i
$797$	11.0586	+	26.6979i	0.391717	+	0.945689i	0.989566	+	0.144080i	$0.0460222\pi$
$797$	11.0586	+	26.6979i	0.391717	+	0.945689i	−0.597849	+	0.801609i	$0.703978\pi$
$798$		0			0
$799$	−0.0768003			−0.00271700
$800$	−16.5114	+	17.1239i	−0.583765	+	0.605423i
$801$		0			0
$802$	−2.13470	+	1.56286i	−0.0753790	+	0.0551866i
$803$	−3.14099	−	7.58301i	−0.110843	−	0.267599i
$804$		0			0
$805$	−2.58902	−	1.07241i	−0.0912509	−	0.0377973i
$806$	−6.79819	−	4.13195i	−0.239456	−	0.145542i
$807$		0			0
$808$	−52.2260	−	3.53658i	−1.83731	−	0.124416i
$809$	−31.2884	+	31.2884i	−1.10004	+	1.10004i	−0.105638	+	0.994405i	$0.533688\pi$
$809$	−31.2884	+	31.2884i	−1.10004	+	1.10004i	−0.994405	+	0.105638i	$0.966312\pi$
$810$		0			0
$811$	10.5583	−	25.4901i	0.370753	−	0.895078i	−0.622870	−	0.782326i	$-0.714033\pi$
$811$	10.5583	−	25.4901i	0.370753	−	0.895078i	0.993623	−	0.112752i	$-0.0359667\pi$
$812$	5.33451	+	4.48931i	0.187205	+	0.157544i
$813$		0			0
$814$	−34.3862	−	5.31793i	−1.20523	−	0.186393i
$815$		−	5.74477i		−	0.201231i
$816$		0			0
$817$		−	40.5874i		−	1.41997i
$818$	−5.40134	+	34.9255i	−0.188854	+	1.22114i
$819$		0			0
$820$	1.56003	+	18.1324i	0.0544786	+	0.633213i
$821$	−4.91826	+	11.8737i	−0.171648	+	0.414396i	−0.986170	−	0.165738i	$-0.947000\pi$
$821$	−4.91826	+	11.8737i	−0.171648	+	0.414396i	0.814522	+	0.580133i	$0.197000\pi$
$822$		0			0
$823$	25.9198	−	25.9198i	0.903509	−	0.903509i	−0.0922291	−	0.995738i	$-0.529399\pi$
$823$	25.9198	−	25.9198i	0.903509	−	0.903509i	0.995738	+	0.0922291i	$0.0293992\pi$
$824$	12.4362	+	6.16634i	0.433235	+	0.214815i
$825$		0			0
$826$	4.26706	−	7.02048i	0.148470	−	0.244274i
$827$	29.3813	+	12.1701i	1.02169	+	0.423196i	0.829705	−	0.558202i	$-0.188509\pi$
$827$	29.3813	+	12.1701i	1.02169	+	0.423196i	0.191981	+	0.981399i	$0.438509\pi$
$828$		0			0
$829$	11.4896	+	27.7384i	0.399051	+	0.963395i	0.987892	+	0.155145i	$0.0495846\pi$
$829$	11.4896	+	27.7384i	0.399051	+	0.963395i	−0.588840	+	0.808249i	$0.700415\pi$
$830$	5.23947	+	7.15655i	0.181865	+	0.248407i
$831$		0			0
$832$	12.1604	−	20.8535i	0.421586	−	0.722965i
$833$	0.0544543			0.00188673
$834$		0			0
$835$	−6.03213	−	14.5629i	−0.208751	−	0.503968i
$836$	−50.6512	−	16.0506i	−1.75181	−	0.555122i
$837$		0			0
$838$	−2.67842	+	4.40673i	−0.0925244	+	0.152228i
$839$	11.8856	+	11.8856i	0.410337	+	0.410337i	0.881856	−	0.471519i	$-0.156294\pi$
$839$	11.8856	+	11.8856i	0.410337	+	0.410337i	−0.471519	+	0.881856i	$0.656294\pi$
$840$		0			0
$841$	13.0806	−	13.0806i	0.451056	−	0.451056i
$842$	−2.87634	−	11.7914i	−0.0991251	−	0.406360i
$843$		0			0
$844$	3.34916	+	38.9277i	0.115283	+	1.33995i
$845$	−3.20801	+	1.32880i	−0.110359	+	0.0457122i
$846$		0			0
$847$		−	10.9209i		−	0.375245i
$848$	−37.2396	+	23.5735i	−1.27881	+	0.809516i
$849$		0			0
$850$	0.0547743	+	0.00847101i	0.00187874	+	0.000290553i
$851$	−14.4408	+	5.98159i	−0.495026	+	0.205046i
$852$		0			0
$853$	12.6415	−	30.5194i	0.432838	−	1.04496i	−0.545530	−	0.838091i	$-0.683672\pi$
$853$	12.6415	−	30.5194i	0.432838	−	1.04496i	0.978368	−	0.206872i	$-0.0663283\pi$
$854$	−16.2414	+	3.96183i	−0.555769	+	0.135571i
$855$		0			0
$856$	3.00962	−	44.4442i	0.102867	−	1.51907i
$857$	17.0412	+	17.0412i	0.582117	+	0.582117i	0.935484	−	0.353368i	$-0.114964\pi$
$857$	17.0412	+	17.0412i	0.582117	+	0.582117i	−0.353368	+	0.935484i	$0.614964\pi$
$858$		0			0
$859$	35.0316	+	14.5106i	1.19526	+	0.495094i	0.889465	−	0.457003i	$-0.151077\pi$
$859$	35.0316	+	14.5106i	1.19526	+	0.495094i	0.305797	+	0.952097i	$0.401077\pi$
$860$	5.76912	+	11.1215i	0.196725	+	0.379241i
$861$		0			0
$862$	−32.9112	+	24.0950i	−1.12096	+	0.820680i
$863$	−7.87584			−0.268097			−0.134048	−	0.990975i	$-0.542798\pi$
$863$	−7.87584			−0.268097			−0.134048	+	0.990975i	$0.542798\pi$
$864$		0			0
$865$	−17.9368			−0.609869
$866$	−23.0932	+	16.9070i	−0.784738	+	0.574524i
$867$		0			0
$868$	3.56041	−	1.84691i	0.120848	−	0.0626883i
$869$	−58.1769	−	24.0977i	−1.97352	−	0.817458i
$870$		0			0
$871$	−7.47628	−	7.47628i	−0.253324	−	0.253324i
$872$	5.57483	−	4.86770i	0.188788	−	0.164841i
$873$		0			0
$874$	−23.1888	+	5.65653i	−0.784372	+	0.191335i
$875$	3.37862	−	8.15671i	0.114218	−	0.275747i
$876$		0			0
$877$	−29.9043	+	12.3868i	−1.00980	+	0.418271i	−0.825380	−	0.564577i	$-0.809039\pi$
$877$	−29.9043	+	12.3868i	−1.00980	+	0.418271i	−0.184415	+	0.982848i	$0.559039\pi$
$878$	36.3854	+	5.62712i	1.22795	+	0.189906i
$879$		0			0
$880$	16.1606	−	2.80150i	0.544773	−	0.0944384i
$881$			9.57672i			0.322648i	0.986902	+	0.161324i	$0.0515764\pi$
$881$			9.57672i			0.322648i	−0.986902	+	0.161324i	$0.948424\pi$
$882$		0			0
$883$	−37.4683	+	15.5199i	−1.26091	+	0.522285i	−0.910188	−	0.414196i	$-0.864063\pi$
$883$	−37.4683	+	15.5199i	−1.26091	+	0.522285i	−0.350719	+	0.936481i	$0.614063\pi$
$884$	−0.0560394	+	0.00482137i	−0.00188481	+	0.000162160i
$885$		0			0
$886$	−2.51706	−	10.3186i	−0.0845623	−	0.346660i
$887$	1.97076	−	1.97076i	0.0661717	−	0.0661717i	−0.673246	−	0.739418i	$-0.735101\pi$
$887$	1.97076	−	1.97076i	0.0661717	−	0.0661717i	0.739418	+	0.673246i	$0.235101\pi$
$888$		0			0
$889$	−9.63455	−	9.63455i	−0.323133	−	0.323133i
$890$	9.95301	−	16.3754i	0.333626	−	0.548905i
$891$		0			0
$892$	−4.34557	+	13.7134i	−0.145500	+	0.459158i
$893$	18.2159	+	43.9771i	0.609573	+	1.47164i
$894$		0			0
$895$	17.0623			0.570328
$896$	5.80012	+	10.7000i	0.193768	+	0.357461i
$897$		0			0
$898$	−2.99955	−	4.09707i	−0.100096	−	0.136721i
$899$	2.31184	+	5.58128i	0.0771042	+	0.186146i
$900$		0			0
$901$	0.0948750	+	0.0392985i	0.00316075	+	0.00130922i
$902$	−34.4791	+	56.7275i	−1.14803	+	1.88882i
$903$		0			0
$904$	−11.9754	−	35.5307i	−0.398295	−	1.18173i
$905$	−8.74670	+	8.74670i	−0.290750	+	0.290750i
$906$		0			0
$907$	20.3870	−	49.2187i	0.676940	−	1.63428i	−0.0926174	−	0.995702i	$-0.529523\pi$
$907$	20.3870	−	49.2187i	0.676940	−	1.63428i	0.769558	−	0.638577i	$-0.220477\pi$
$908$	29.9172	−	2.57393i	0.992837	−	0.0854190i
$909$		0			0
$910$	−0.625548	+	4.04485i	−0.0207367	+	0.134085i
$911$		−	4.42493i		−	0.146605i	−0.997310	−	0.0733023i	$-0.976646\pi$
$911$		−	4.42493i		−	0.146605i	0.997310	−	0.0733023i	$-0.0233538\pi$
$912$		0			0
$913$			32.3522i			1.07070i
$914$	−36.0842	−	5.58054i	−1.19356	−	0.184588i
$915$		0			0
$916$	−7.81771	+	9.28953i	−0.258304	+	0.306935i
$917$	2.30374	−	5.56171i	0.0760760	−	0.183664i
$918$		0			0
$919$	−15.6802	+	15.6802i	−0.517241	+	0.517241i	−0.916736	−	0.399495i	$-0.869186\pi$
$919$	−15.6802	+	15.6802i	−0.517241	+	0.517241i	0.399495	+	0.916736i	$0.369186\pi$
$920$	5.55002	−	4.84603i	0.182979	−	0.159769i
$921$		0			0
$922$	4.84279	+	2.94346i	0.159489	+	0.0969376i
$923$	−23.1151	−	9.57458i	−0.760842	−	0.315151i
$924$		0			0
$925$	−8.60886	−	20.7836i	−0.283058	−	0.683361i
$926$	10.9419	−	8.01077i	0.359572	−	0.263250i
$927$		0			0
$928$	−16.8054	+	7.32234i	−0.551665	+	0.240367i
$929$	−25.6774			−0.842447			−0.421224	−	0.906957i	$-0.638399\pi$
$929$	−25.6774			−0.842447			−0.421224	+	0.906957i	$0.638399\pi$
$930$		0			0
$931$	−12.9158	−	31.1815i	−0.423298	−	1.02193i
$932$	12.2823	+	23.6775i	0.402321	+	0.775581i
$933$		0			0
$934$	−17.8740	−	10.8639i	−0.584856	−	0.355477i
$935$	−0.0270226	−	0.0270226i	−0.000883735	−	0.000883735i
$936$		0			0
$937$	24.8836	−	24.8836i	0.812912	−	0.812912i	−0.172157	−	0.985069i	$-0.555074\pi$
$937$	24.8836	−	24.8836i	0.812912	−	0.812912i	0.985069	+	0.172157i	$0.0550737\pi$
$938$	5.17885	−	1.26330i	0.169095	−	0.0412481i
$939$		0			0
$940$	−11.2423	−	9.46112i	−0.366685	−	0.308588i
$941$	39.8725	−	16.5157i	1.29981	−	0.538398i	0.377914	−	0.925841i	$-0.376642\pi$
$941$	39.8725	−	16.5157i	1.29981	−	0.538398i	0.921894	+	0.387443i	$0.126642\pi$
$942$		0			0
$943$			29.8211i			0.971108i
$944$	11.5533	+	18.2511i	0.376029	+	0.594022i
$945$		0			0
$946$	−6.98458	+	45.1629i	−0.227088	+	1.46837i
$947$	−0.260183	+	0.107771i	−0.00845481	+	0.00350210i	−0.386907	−	0.922119i	$-0.626456\pi$
$947$	−0.260183	+	0.107771i	−0.00845481	+	0.00350210i	0.378452	+	0.925621i	$0.376456\pi$
$948$		0			0
$949$	−2.06083	+	4.97528i	−0.0668973	+	0.161504i
$950$	−8.14102	−	33.3739i	−0.264130	−	1.08279i
$951$		0			0
$952$	0.0125975	−	0.0254065i	0.000408288	−	0.000823430i
$953$	−2.34737	−	2.34737i	−0.0760389	−	0.0760389i	0.668064	−	0.744103i	$-0.267123\pi$
$953$	−2.34737	−	2.34737i	−0.0760389	−	0.0760389i	−0.744103	+	0.668064i	$0.767123\pi$
$954$		0			0
$955$	18.0259	+	7.46659i	0.583306	+	0.241613i
$956$	17.5593	+	5.56427i	0.567907	+	0.179961i
$957$		0			0
$958$	10.1579	+	13.8746i	0.328186	+	0.448267i
$959$	0.923800			0.0298311
$960$		0			0
$961$	−27.5247			−0.887892
$962$	13.4859	+	18.4203i	0.434803	+	0.593894i
$963$		0			0
$964$	−18.1271	−	5.74421i	−0.583834	−	0.185008i
$965$	2.45088	+	1.01519i	0.0788968	+	0.0326801i
$966$		0			0
$967$	6.55661	+	6.55661i	0.210846	+	0.210846i	0.804627	−	0.593781i	$-0.202365\pi$
$967$	6.55661	+	6.55661i	0.210846	+	0.210846i	−0.593781	+	0.804627i	$0.702365\pi$
$968$	25.7247	+	12.7553i	0.826824	+	0.409971i
$969$		0			0
$970$	−5.04229	−	20.6707i	−0.161898	−	0.663696i
$971$	5.04308	−	12.1751i	0.161840	−	0.390717i	−0.822069	−	0.569389i	$-0.807180\pi$
$971$	5.04308	−	12.1751i	0.161840	−	0.390717i	0.983909	+	0.178672i	$0.0571800\pi$
$972$		0			0
$973$	6.71310	−	2.78066i	0.215212	−	0.0891438i
$974$	8.41174	−	54.3910i	0.269529	−	1.74280i
$975$		0			0
$976$	9.63723	−	42.8848i	0.308480	−	1.37271i
$977$		−	33.4125i		−	1.06896i	−0.845181	−	0.534480i	$-0.820508\pi$
$977$		−	33.4125i		−	1.06896i	0.845181	−	0.534480i	$-0.179492\pi$
$978$		0			0
$979$	64.5774	−	26.7488i	2.06390	−	0.854897i
$980$	7.97125	+	6.70829i	0.254632	+	0.214289i
$981$		0			0
$982$	11.1116	−	2.71050i	0.354586	−	0.0864956i
$983$	2.61896	−	2.61896i	0.0835317	−	0.0835317i	−0.664106	−	0.747638i	$-0.731188\pi$
$983$	2.61896	−	2.61896i	0.0835317	−	0.0835317i	0.747638	+	0.664106i	$0.231188\pi$
$984$		0			0
$985$	1.14875	+	1.14875i	0.0366022	+	0.0366022i
$986$	0.0364991	+	0.0221842i	0.00116237	+	0.000706490i
$987$		0			0
$988$	16.0525	+	30.9456i	0.510700	+	0.984509i
$989$	7.85624	+	18.9666i	0.249814	+	0.603104i
$990$		0			0
$991$	−14.9171			−0.473856			−0.236928	−	0.971527i	$-0.576141\pi$
$991$	−14.9171			−0.473856			−0.236928	+	0.971527i	$0.576141\pi$
$992$	0.192030	+	10.5439i	0.00609695	+	0.334769i
$993$		0			0
$994$	10.1781	−	7.45163i	0.322831	−	0.236351i
$995$	4.27293	+	10.3158i	0.135461	+	0.327032i
$996$		0			0
$997$	42.1607	+	17.4635i	1.33524	+	0.553076i	0.932146	−	0.362081i	$-0.117934\pi$
$997$	42.1607	+	17.4635i	1.33524	+	0.553076i	0.403097	+	0.915157i	$0.367934\pi$
$998$	−33.4639	−	20.3394i	−1.05928	−	0.643834i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.c.37.6	yes	32
3.2	odd	2	inner	288.2.v.c.37.3	✓	32
4.3	odd	2		1152.2.v.d.1009.5		32
12.11	even	2		1152.2.v.d.1009.4		32
32.13	even	8	inner	288.2.v.c.109.6	yes	32
32.19	odd	8		1152.2.v.d.145.5		32
96.77	odd	8	inner	288.2.v.c.109.3	yes	32
96.83	even	8		1152.2.v.d.145.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.v.c.37.3	✓	32	3.2	odd	2	inner
288.2.v.c.37.6	yes	32	1.1	even	1	trivial
288.2.v.c.109.3	yes	32	96.77	odd	8	inner
288.2.v.c.109.6	yes	32	32.13	even	8	inner
1152.2.v.d.145.4		32	96.83	even	8
1152.2.v.d.145.5		32	32.19	odd	8
1152.2.v.d.1009.4		32	12.11	even	2
1152.2.v.d.1009.5		32	4.3	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.835415 + 1.14109i) q^{2} +(-0.604162 + 1.90656i) q^{4} +(0.823699 + 0.341187i) q^{5} +(0.760681 + 0.760681i) q^{7} +(-2.68028 + 0.903371i) q^{8} +O(q^{10})\)	\(q+(0.835415 + 1.14109i) q^{2} +(-0.604162 + 1.90656i) q^{4} +(0.823699 + 0.341187i) q^{5} +(0.760681 + 0.760681i) q^{7} +(-2.68028 + 0.903371i) q^{8} +(0.298806 + 1.22495i) q^{10} +(-1.76000 + 4.24901i) q^{11} +(2.78781 - 1.15475i) q^{13} +(-0.232519 + 1.50349i) q^{14} +(-3.26998 - 2.30375i) q^{16} +0.00932001i q^{17} +(5.33680 - 2.21057i) q^{19} +(-1.14814 + 1.36430i) q^{20} +(-6.31883 + 1.54138i) q^{22} +(-2.06602 + 2.06602i) q^{23} +(-2.97346 - 2.97346i) q^{25} +(3.64666 + 2.21644i) q^{26} +(-1.90986 + 0.990712i) q^{28} +(-1.24011 - 2.99388i) q^{29} -1.86423 q^{31} +(-0.103008 - 5.65592i) q^{32} +(-0.0106350 + 0.00778608i) q^{34} +(0.367038 + 0.886107i) q^{35} +(4.94247 + 2.04724i) q^{37} +(6.98090 + 4.24301i) q^{38} +(-2.51597 - 0.170373i) q^{40} +(7.21705 - 7.21705i) q^{41} +(2.68885 - 6.49145i) q^{43} +(-7.03769 - 5.92265i) q^{44} +(-4.08349 - 0.631524i) q^{46} +8.24036i q^{47} -5.84273i q^{49} +(0.908905 - 5.87706i) q^{50} +(0.517314 + 6.01281i) q^{52} +(4.21657 - 10.1797i) q^{53} +(-2.89942 + 2.89942i) q^{55} +(-2.72602 - 1.35166i) q^{56} +(2.38028 - 3.91621i) q^{58} +(-4.98906 - 2.06654i) q^{59} +(4.20515 + 10.1521i) q^{61} +(-1.55740 - 2.12725i) q^{62} +(6.36784 - 4.84258i) q^{64} +2.69031 q^{65} +(-1.34088 - 3.23718i) q^{67} +(-0.0177692 - 0.00563080i) q^{68} +(-0.704497 + 1.15909i) q^{70} +(-5.86295 - 5.86295i) q^{71} +(-1.26194 + 1.26194i) q^{73} +(1.79294 + 7.35008i) q^{74} +(0.990309 + 11.5105i) q^{76} +(-4.57094 + 1.89335i) q^{77} +13.6919i q^{79} +(-1.90747 - 3.01327i) q^{80} +(14.2645 + 2.20605i) q^{82} +(6.49900 - 2.69197i) q^{83} +(-0.00317987 + 0.00767689i) q^{85} +(9.65362 - 2.35485i) q^{86} +(0.878862 - 12.9785i) q^{88} +(-10.7468 - 10.7468i) q^{89} +(2.99903 + 1.24224i) q^{91} +(-2.69078 - 5.18720i) q^{92} +(-9.40298 + 6.88412i) q^{94} +5.15013 q^{95} -16.8748 q^{97} +(6.66707 - 4.88111i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 - 8 * q^16 - 24 * q^22 - 40 * q^28 + 48 * q^31 - 40 * q^34 - 72 * q^40 + 16 * q^43 - 32 * q^46 - 8 * q^52 + 32 * q^55 - 32 * q^58 - 32 * q^61 + 72 * q^64 + 16 * q^67 + 120 * q^70 + 72 * q^76 + 120 * q^82 + 128 * q^88 - 48 * q^91 + 80 * q^94

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