LMFDB - Embedded newform 288.2.bf.a.11.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, 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:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.37
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10744 + 0.879538i) q^{2} +(1.40359 - 1.01486i) q^{3} +(0.452825 + 1.94806i) q^{4} +(-0.419211 - 3.18422i) q^{5} +(2.44699 + 0.110619i) q^{6} +(0.973946 + 3.63481i) q^{7} +(-1.21192 + 2.55563i) q^{8} +(0.940122 - 2.84889i) q^{9} +O(q^{10})$	\(q+(1.10744 + 0.879538i) q^{2} +(1.40359 - 1.01486i) q^{3} +(0.452825 + 1.94806i) q^{4} +(-0.419211 - 3.18422i) q^{5} +(2.44699 + 0.110619i) q^{6} +(0.973946 + 3.63481i) q^{7} +(-1.21192 + 2.55563i) q^{8} +(0.940122 - 2.84889i) q^{9} +(2.33640 - 3.89503i) q^{10} +(-1.02481 + 0.786367i) q^{11} +(2.61259 + 2.27473i) q^{12} +(1.17309 - 1.52880i) q^{13} +(-2.11838 + 4.88194i) q^{14} +(-3.81994 - 4.04390i) q^{15} +(-3.58990 + 1.76426i) q^{16} -2.44375 q^{17} +(3.54683 - 2.32809i) q^{18} +(5.23452 - 2.16821i) q^{19} +(6.01324 - 2.25855i) q^{20} +(5.05584 + 4.11337i) q^{21} +(-1.82655 - 0.0305121i) q^{22} +(-1.73706 - 0.465443i) q^{23} +(0.892566 + 4.81698i) q^{24} +(-5.13391 + 1.37563i) q^{25} +(2.64375 - 0.661268i) q^{26} +(-1.57168 - 4.95276i) q^{27} +(-6.63982 + 3.54324i) q^{28} +(-6.70769 - 0.883084i) q^{29} +(-0.673570 - 7.83814i) q^{30} +(-8.25551 + 4.76632i) q^{31} +(-5.52732 - 1.20365i) q^{32} +(-0.640365 + 2.14378i) q^{33} +(-2.70630 - 2.14937i) q^{34} +(11.1658 - 4.62501i) q^{35} +(5.97553 + 0.541367i) q^{36} +(-4.39219 + 10.6037i) q^{37} +(7.70391 + 2.20281i) q^{38} +(0.0950179 - 3.33632i) q^{39} +(8.64575 + 2.78768i) q^{40} +(-0.643399 + 2.40120i) q^{41} +(1.98116 + 9.00210i) q^{42} +(-2.28752 - 2.98116i) q^{43} +(-1.99595 - 1.64031i) q^{44} +(-9.46561 - 1.79927i) q^{45} +(-1.51430 - 2.04326i) q^{46} +(0.888261 + 0.512838i) q^{47} +(-3.24826 + 6.11954i) q^{48} +(-6.20113 + 3.58023i) q^{49} +(-6.89539 - 2.99205i) q^{50} +(-3.43002 + 2.48006i) q^{51} +(3.50939 + 1.59297i) q^{52} +(3.57267 - 8.62519i) q^{53} +(2.61561 - 6.86721i) q^{54} +(2.93358 + 2.93358i) q^{55} +(-10.4696 - 1.91606i) q^{56} +(5.14668 - 8.35557i) q^{57} +(-6.65162 - 6.87763i) q^{58} +(11.3931 - 1.49993i) q^{59} +(6.14801 - 9.27266i) q^{60} +(-0.590311 + 4.48386i) q^{61} +(-13.3346 - 1.98264i) q^{62} +(11.2708 + 0.642504i) q^{63} +(-5.06249 - 6.19445i) q^{64} +(-5.35980 - 3.09448i) q^{65} +(-2.59470 + 1.81087i) q^{66} +(0.582863 - 0.759602i) q^{67} +(-1.10659 - 4.76058i) q^{68} +(-2.91047 + 1.10958i) q^{69} +(16.4332 + 4.69882i) q^{70} +(8.30320 + 8.30320i) q^{71} +(6.14136 + 5.85523i) q^{72} +(11.7673 - 11.7673i) q^{73} +(-14.1904 + 7.87980i) q^{74} +(-5.80983 + 7.14101i) q^{75} +(6.59413 + 9.21535i) q^{76} +(-3.85641 - 2.95913i) q^{77} +(3.03964 - 3.61118i) q^{78} +(2.72426 - 4.71855i) q^{79} +(7.12273 + 10.6914i) q^{80} +(-7.23234 - 5.35660i) q^{81} +(-2.82447 + 2.09328i) q^{82} +(-6.31259 - 0.831068i) q^{83} +(-5.72368 + 11.7117i) q^{84} +(1.02445 + 7.78145i) q^{85} +(0.0887590 - 5.31341i) q^{86} +(-10.3110 + 5.56787i) q^{87} +(-0.767670 - 3.57206i) q^{88} +(-2.10274 + 2.10274i) q^{89} +(-8.90002 - 10.3179i) q^{90} +(6.69941 + 2.77499i) q^{91} +(0.120129 - 3.59466i) q^{92} +(-6.75019 + 15.0681i) q^{93} +(0.532631 + 1.34919i) q^{94} +(-9.09843 - 15.7589i) q^{95} +(-8.97961 + 3.92003i) q^{96} +(2.69208 - 4.66282i) q^{97} +(-10.0163 - 1.48927i) q^{98} +(1.27682 + 3.65886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.10744	+	0.879538i	0.783075	+	0.621927i
$2$	1.10744	+	0.879538i	0.783075	+	0.621927i
$3$	1.40359	−	1.01486i	0.810362	−	0.585929i
$3$	1.40359	−	1.01486i	0.810362	−	0.585929i
$4$	0.452825	+	1.94806i	0.226413	+	0.974031i
$5$	−0.419211	−	3.18422i	−0.187477	−	1.42403i	−0.783665	−	0.621183i	$-0.786652\pi$
$5$	−0.419211	−	3.18422i	−0.187477	−	1.42403i	0.596188	−	0.802845i	$-0.296681\pi$
$6$	2.44699	+	0.110619i	0.998980	+	0.0451600i
$7$	0.973946	+	3.63481i	0.368117	+	1.37383i	0.863146	+	0.504955i	$0.168491\pi$
$7$	0.973946	+	3.63481i	0.368117	+	1.37383i	−0.495029	+	0.868876i	$0.664843\pi$
$8$	−1.21192	+	2.55563i	−0.428479	+	0.903552i
$9$	0.940122	−	2.84889i	0.313374	−	0.949630i
$10$	2.33640	−	3.89503i	0.738834	−	1.23172i
$11$	−1.02481	+	0.786367i	−0.308993	+	0.237099i	−0.751603	−	0.659615i	$-0.770719\pi$
$11$	−1.02481	+	0.786367i	−0.308993	+	0.237099i	0.442610	+	0.896714i	$0.354052\pi$
$12$	2.61259	+	2.27473i	0.754190	+	0.656657i
$13$	1.17309	−	1.52880i	0.325356	−	0.424012i	−0.601824	−	0.798629i	$-0.705559\pi$
$13$	1.17309	−	1.52880i	0.325356	−	0.424012i	0.927180	+	0.374617i	$0.122226\pi$
$14$	−2.11838	+	4.88194i	−0.566160	+	1.30475i
$15$	−3.81994	−	4.04390i	−0.986304	−	1.04413i
$16$	−3.58990	+	1.76426i	−0.897475	+	0.441066i
$17$	−2.44375			−0.592697			−0.296348	−	0.955080i	$-0.595769\pi$
$17$	−2.44375			−0.592697			−0.296348	+	0.955080i	$0.595769\pi$
$18$	3.54683	−	2.32809i	0.835996	−	0.548736i
$19$	5.23452	−	2.16821i	1.20088	−	0.497421i	0.309597	−	0.950868i	$-0.399806\pi$
$19$	5.23452	−	2.16821i	1.20088	−	0.497421i	0.891283	+	0.453447i	$0.149806\pi$
$20$	6.01324	−	2.25855i	1.34460	−	0.505026i
$21$	5.05584	+	4.11337i	1.10328	+	0.897610i
$22$	−1.82655	−	0.0305121i	−0.389423	−	0.00650520i
$23$	−1.73706	−	0.465443i	−0.362202	−	0.0970516i	0.0731285	−	0.997323i	$-0.476702\pi$
$23$	−1.73706	−	0.465443i	−0.362202	−	0.0970516i	−0.435330	+	0.900271i	$0.643368\pi$
$24$	0.892566	+	4.81698i	0.182194	+	0.983263i
$25$	−5.13391	+	1.37563i	−1.02678	+	0.275125i
$26$	2.64375	−	0.661268i	0.518482	−	0.129685i
$27$	−1.57168	−	4.95276i	−0.302470	−	0.953159i
$28$	−6.63982	+	3.54324i	−1.25481	+	0.669610i
$29$	−6.70769	−	0.883084i	−1.24559	−	0.163985i	−0.521234	−	0.853414i	$-0.674528\pi$
$29$	−6.70769	−	0.883084i	−1.24559	−	0.163985i	−0.724353	+	0.689430i	$0.757861\pi$
$30$	−0.673570	−	7.83814i	−0.122976	−	1.43104i
$31$	−8.25551	+	4.76632i	−1.48273	+	0.856056i	−0.999808	−	0.0196051i	$-0.993759\pi$
$31$	−8.25551	+	4.76632i	−1.48273	+	0.856056i	−0.482925	+	0.875662i	$0.660426\pi$
$32$	−5.52732	−	1.20365i	−0.977101	−	0.212776i
$33$	−0.640365	+	2.14378i	−0.111473	+	0.373184i
$34$	−2.70630	−	2.14937i	−0.464126	−	0.368614i
$35$	11.1658	−	4.62501i	1.88736	−	0.781770i
$36$	5.97553	+	0.541367i	0.995921	+	0.0902278i
$37$	−4.39219	+	10.6037i	−0.722072	+	1.74324i	−0.0547100	+	0.998502i	$0.517423\pi$
$37$	−4.39219	+	10.6037i	−0.722072	+	1.74324i	−0.667362	+	0.744734i	$0.732577\pi$
$38$	7.70391	+	2.20281i	1.24974	+	0.357343i
$39$	0.0950179	−	3.33632i	0.0152150	−	0.534238i
$40$	8.64575	+	2.78768i	1.36701	+	0.440771i
$41$	−0.643399	+	2.40120i	−0.100482	+	0.375004i	−0.997793	−	0.0663940i	$-0.978851\pi$
$41$	−0.643399	+	2.40120i	−0.100482	+	0.375004i	0.897312	+	0.441398i	$0.145517\pi$
$42$	1.98116	+	9.00210i	0.305699	+	1.38905i
$43$	−2.28752	−	2.98116i	−0.348844	−	0.454623i	0.585669	−	0.810550i	$-0.300832\pi$
$43$	−2.28752	−	2.98116i	−0.348844	−	0.454623i	−0.934514	+	0.355927i	$0.884165\pi$
$44$	−1.99595	−	1.64031i	−0.300901	−	0.247287i
$45$	−9.46561	−	1.79927i	−1.41105	−	0.268219i
$46$	−1.51430	−	2.04326i	−0.223272	−	0.301262i
$47$	0.888261	+	0.512838i	0.129566	+	0.0748051i	0.563382	−	0.826196i	$-0.309500\pi$
$47$	0.888261	+	0.512838i	0.129566	+	0.0748051i	−0.433816	+	0.901001i	$0.642833\pi$
$48$	−3.24826	+	6.11954i	−0.468846	+	0.883280i
$49$	−6.20113	+	3.58023i	−0.885876	+	0.511461i
$50$	−6.89539	−	2.99205i	−0.975155	−	0.423140i
$51$	−3.43002	+	2.48006i	−0.480299	+	0.347278i
$52$	3.50939	+	1.59297i	0.486665	+	0.220905i
$53$	3.57267	−	8.62519i	0.490744	−	1.18476i	−0.463598	−	0.886046i	$-0.653442\pi$
$53$	3.57267	−	8.62519i	0.490744	−	1.18476i	0.954342	−	0.298716i	$-0.0965582\pi$
$54$	2.61561	−	6.86721i	0.355939	−	0.934509i
$55$	2.93358	+	2.93358i	0.395564	+	0.395564i
$56$	−10.4696	−	1.91606i	−1.39906	−	0.256045i
$57$	5.14668	−	8.35557i	0.681695	−	1.10672i
$58$	−6.65162	−	6.87763i	−0.873401	−	0.903076i
$59$	11.3931	−	1.49993i	1.48325	−	0.195274i	0.655001	−	0.755628i	$-0.272668\pi$
$59$	11.3931	−	1.49993i	1.48325	−	0.195274i	0.828253	+	0.560354i	$0.189335\pi$
$60$	6.14801	−	9.27266i	0.793704	−	1.19710i
$61$	−0.590311	+	4.48386i	−0.0755816	+	0.574100i	0.911190	+	0.411986i	$0.135165\pi$
$61$	−0.590311	+	4.48386i	−0.0755816	+	0.574100i	−0.986772	+	0.162114i	$0.948169\pi$
$62$	−13.3346	−	1.98264i	−1.69350	−	0.251796i
$63$	11.2708	+	0.642504i	1.41999	+	0.0809479i
$64$	−5.06249	−	6.19445i	−0.632812	−	0.774306i
$65$	−5.35980	−	3.09448i	−0.664801	−	0.383823i
$66$	−2.59470	+	1.81087i	−0.319385	+	0.222903i
$67$	0.582863	−	0.759602i	0.0712081	−	0.0928002i	−0.756391	−	0.654119i	$-0.773039\pi$
$67$	0.582863	−	0.759602i	0.0712081	−	0.0928002i	0.827599	+	0.561319i	$0.189706\pi$
$68$	−1.10659	−	4.76058i	−0.134194	−	0.577305i
$69$	−2.91047	+	1.10958i	−0.350380	+	0.133578i
$70$	16.4332	+	4.69882i	1.96415	+	0.561616i
$71$	8.30320	+	8.30320i	0.985409	+	0.985409i	0.999895	−	0.0144865i	$-0.00461136\pi$
$71$	8.30320	+	8.30320i	0.985409	+	0.985409i	−0.0144865	+	0.999895i	$0.504611\pi$
$72$	6.14136	+	5.85523i	0.723766	+	0.690046i
$73$	11.7673	−	11.7673i	1.37726	−	1.37726i	0.528045	−	0.849216i	$-0.322925\pi$
$73$	11.7673	−	11.7673i	1.37726	−	1.37726i	0.849216	−	0.528045i	$-0.177075\pi$
$74$	−14.1904	+	7.87980i	−1.64960	+	0.916008i
$75$	−5.80983	+	7.14101i	−0.670861	+	0.824573i
$76$	6.59413	+	9.21535i	0.756398	+	1.05707i
$77$	−3.85641	−	2.95913i	−0.439479	−	0.337224i
$78$	3.03964	−	3.61118i	0.344172	−	0.408886i
$79$	2.72426	−	4.71855i	0.306503	−	0.530879i	−0.671092	−	0.741374i	$-0.734174\pi$
$79$	2.72426	−	4.71855i	0.306503	−	0.530879i	0.977595	+	0.210496i	$0.0675077\pi$
$80$	7.12273	+	10.6914i	0.796346	+	1.19534i
$81$	−7.23234	−	5.35660i	−0.803594	−	0.595178i
$82$	−2.82447	+	2.09328i	−0.311910	+	0.231164i
$83$	−6.31259	−	0.831068i	−0.692897	−	0.0912216i	−0.224151	−	0.974555i	$-0.571961\pi$
$83$	−6.31259	−	0.831068i	−0.692897	−	0.0912216i	−0.468746	+	0.883333i	$0.655294\pi$
$84$	−5.72368	+	11.7117i	−0.624505	+	1.27786i
$85$	1.02445	+	7.78145i	0.111117	+	0.844016i
$86$	0.0887590	−	5.31341i	0.00957113	−	0.572959i
$87$	−10.3110	+	5.56787i	−1.10546	+	0.596939i
$88$	−0.767670	−	3.57206i	−0.0818339	−	0.380783i
$89$	−2.10274	+	2.10274i	−0.222890	+	0.222890i	−0.809714	−	0.586824i	$-0.800378\pi$
$89$	−2.10274	+	2.10274i	−0.222890	+	0.222890i	0.586824	+	0.809714i	$0.300378\pi$
$90$	−8.90002	−	10.3179i	−0.938145	−	1.08761i
$91$	6.69941	+	2.77499i	0.702289	+	0.290898i
$92$	0.120129	−	3.59466i	0.0125243	−	0.374770i
$93$	−6.75019	+	15.0681i	−0.699962	+	1.56249i
$94$	0.532631	+	1.34919i	0.0549367	+	0.139159i
$95$	−9.09843	−	15.7589i	−0.933479	−	1.61683i
$96$	−8.97961	+	3.92003i	−0.916478	+	0.400086i
$97$	2.69208	−	4.66282i	0.273339	−	0.473438i	−0.696375	−	0.717678i	$-0.745205\pi$
$97$	2.69208	−	4.66282i	0.273339	−	0.473438i	0.969715	+	0.244240i	$0.0785385\pi$
$98$	−10.0163	−	1.48927i	−1.01180	−	0.150438i
$99$	1.27682	+	3.65886i	0.128326	+	0.367729i
$100$	−5.00457	−	9.37826i	−0.500457	−	0.937826i
$101$	3.98400	−	3.05703i	0.396423	−	0.304186i	−0.391245	−	0.920287i	$-0.627955\pi$
$101$	3.98400	−	3.05703i	0.396423	−	0.304186i	0.787667	+	0.616101i	$0.211289\pi$
$102$	−5.97984	−	0.270325i	−0.592092	−	0.0267662i
$103$	−0.380734	−	0.102017i	−0.0375148	−	0.0100521i	0.240013	−	0.970770i	$-0.422848\pi$
$103$	−0.380734	−	0.102017i	−0.0375148	−	0.0100521i	−0.277528	+	0.960718i	$0.589515\pi$
$104$	2.48535	+	4.85075i	0.243708	+	0.475656i
$105$	10.9784	−	17.8233i	1.07138	−	1.73938i
$106$	11.5427	−	6.40954i	1.12113	−	0.622550i
$107$	15.4203	+	6.38728i	1.49073	+	0.617482i	0.971476	−	0.237136i	$-0.0762088\pi$
$107$	15.4203	+	6.38728i	1.49073	+	0.617482i	0.519257	+	0.854618i	$0.326209\pi$
$108$	8.93659	−	5.30446i	0.859924	−	0.510422i
$109$	−2.26817	−	5.47584i	−0.217251	−	0.524491i	0.777253	−	0.629188i	$-0.216613\pi$
$109$	−2.26817	−	5.47584i	−0.217251	−	0.524491i	−0.994504	+	0.104697i	$0.966613\pi$
$110$	0.668554	+	5.82895i	0.0637441	+	0.555768i
$111$	4.59642	+	19.3407i	0.436273	+	1.83574i
$112$	−9.90914	−	11.3303i	−0.936326	−	1.07061i
$113$	−1.04765	−	1.81458i	−0.0985545	−	0.170701i	0.812532	−	0.582917i	$-0.198089\pi$
$113$	−1.04765	−	1.81458i	−0.0985545	−	0.170701i	−0.911087	+	0.412215i	$0.864755\pi$
$114$	13.0487	−	4.72655i	1.22212	−	0.442682i
$115$	−0.753882	+	5.72630i	−0.0702998	+	0.533980i
$116$	−1.31711	−	13.4669i	−0.122290	−	1.25037i
$117$	−3.25253	−	4.77925i	−0.300696	−	0.441841i
$118$	13.9364	+	8.35958i	1.28295	+	0.769562i
$119$	−2.38008	−	8.88258i	−0.218182	−	0.814265i
$120$	14.9642	−	4.86146i	1.36604	−	0.443789i
$121$	−2.41514	+	9.01343i	−0.219558	+	0.819402i
$122$	−4.59746	+	4.44638i	−0.416234	+	0.402557i
$123$	1.53381	+	4.02325i	0.138299	+	0.362764i
$124$	−13.0234	−	13.9239i	−1.16954	−	1.25041i
$125$	0.387173	+	0.934718i	0.0346298	+	0.0836037i
$126$	11.9166	+	10.6246i	1.06161	+	0.946518i
$127$		−	17.4797i		−	1.55107i	−0.631305	−	0.775535i	$-0.717480\pi$
$127$		−	17.4797i		−	1.55107i	0.631305	−	0.775535i	$-0.282520\pi$
$128$	−0.158132	−	11.3126i	−0.0139770	−	0.999902i
$129$	−6.23620	−	1.86281i	−0.549067	−	0.164011i
$130$	−3.21391	−	8.14108i	−0.281879	−	0.714020i
$131$	1.31575	+	1.00961i	0.114957	+	0.0882098i	0.664640	−	0.747164i	$-0.268585\pi$
$131$	1.31575	+	1.00961i	0.114957	+	0.0882098i	−0.549683	+	0.835373i	$0.685251\pi$
$132$	−4.46619	−	0.276714i	−0.388732	−	0.0240849i
$133$	12.9792	+	16.9148i	1.12544	+	1.46670i
$134$	1.31358	−	0.328560i	0.113476	−	0.0283832i
$135$	−15.1118	+	7.08082i	−1.30062	+	0.609420i
$136$	2.96163	−	6.24532i	0.253958	−	0.535532i
$137$	−4.90988	+	1.31560i	−0.419479	+	0.112399i	−0.462384	−	0.886680i	$-0.653006\pi$
$137$	−4.90988	+	1.31560i	−0.419479	+	0.112399i	0.0429042	+	0.999079i	$0.486339\pi$
$138$	−4.19908	−	1.33109i	−0.357449	−	0.113310i
$139$	0.172627	−	0.0227268i	0.0146421	−	0.00192766i	−0.123202	−	0.992382i	$-0.539316\pi$
$139$	0.172627	−	0.0227268i	0.0146421	−	0.00192766i	0.137844	+	0.990454i	$0.455983\pi$
$140$	14.0660	+	19.6573i	1.18879	+	1.66135i
$141$	1.76721	−	0.181647i	0.148826	−	0.0152974i
$142$	1.89227	+	16.4982i	0.158796	+	1.38450i
$143$			2.48921i			0.208158i
$144$	1.65125	+	11.8858i	0.137604	+	0.990487i
$145$			21.7290i			1.80449i
$146$	23.3814	−	2.68174i	1.93506	−	0.221942i
$147$	−5.07041	+	11.3184i	−0.418201	+	0.933529i
$148$	−22.6456	−	3.75465i	−1.86145	−	0.308630i
$149$	4.14956	−	0.546300i	0.339945	−	0.0447546i	0.0413788	−	0.999144i	$-0.486825\pi$
$149$	4.14956	−	0.546300i	0.339945	−	0.0447546i	0.298566	+	0.954389i	$0.403492\pi$
$150$	−12.7148	+	2.79824i	−1.03816	+	0.228475i
$151$	13.3245	−	3.57030i	1.08433	−	0.290547i	0.327964	−	0.944690i	$-0.393637\pi$
$151$	13.3245	−	3.57030i	1.08433	−	0.290547i	0.756370	+	0.654144i	$0.226971\pi$
$152$	−0.802685	+	16.0052i	−0.0651063	+	1.29819i
$153$	−2.29742	+	6.96198i	−0.185736	+	0.562842i
$154$	−1.66806	−	6.66890i	−0.134416	−	0.537396i
$155$	18.6378	+	24.2893i	1.49703	+	1.95096i
$156$	6.54238	−	1.32567i	0.523810	−	0.106138i
$157$	15.5560	+	11.9365i	1.24150	+	0.952638i	0.999843	−	0.0177228i	$-0.00564162\pi$
$157$	15.5560	+	11.9365i	1.24150	+	0.952638i	0.241660	+	0.970361i	$0.422308\pi$
$158$	7.16709	−	2.82940i	0.570183	−	0.225095i
$159$	−3.73880	−	15.7320i	−0.296506	−	1.24763i
$160$	−1.51556	+	18.1048i	−0.119816	+	1.43131i
$161$		−	6.76720i		−	0.533330i
$162$	−3.29801	−	12.2932i	−0.259116	−	0.965846i
$163$	3.12060	+	7.53379i	0.244424	+	0.590092i	0.997713	−	0.0675981i	$-0.0215336\pi$
$163$	3.12060	+	7.53379i	0.244424	+	0.590092i	−0.753288	+	0.657690i	$0.771534\pi$
$164$	−4.96903	−	0.166059i	−0.388016	−	0.0129670i
$165$	7.09471	+	1.14037i	0.552323	+	0.0887776i
$166$	−6.25983	−	6.47252i	−0.485857	−	0.502365i
$167$	−4.70505	+	17.5595i	−0.364088	+	1.35879i	0.504565	+	0.863374i	$0.331653\pi$
$167$	−4.70505	+	17.5595i	−0.364088	+	1.35879i	−0.868653	+	0.495421i	$0.835014\pi$
$168$	−16.6395	+	7.93579i	−1.28377	+	0.612260i
$169$	2.40356	+	8.97022i	0.184889	+	0.690017i
$170$	−5.70957	+	9.51849i	−0.437904	+	0.730035i
$171$	−1.25590	−	16.9509i	−0.0960413	−	1.29627i
$172$	4.77164	−	5.80619i	0.363834	−	0.442718i
$173$	−1.42003	+	10.7862i	−0.107963	+	0.820062i	0.848702	+	0.528871i	$0.177385\pi$
$173$	−1.42003	+	10.7862i	−0.107963	+	0.820062i	−0.956665	+	0.291190i	$0.905949\pi$
$174$	−16.3160	−	2.90290i	−1.23691	−	0.220068i
$175$	−10.0003	−	17.3210i	−0.755952	−	1.30935i
$176$	2.29162	−	4.63102i	0.172737	−	0.349076i
$177$	14.4690	−	13.6677i	1.08756	−	1.02732i
$178$	−4.17809	+	0.479208i	−0.313161	+	0.0359181i
$179$	−2.08225	−	5.02699i	−0.155635	−	0.375735i	0.826759	−	0.562556i	$-0.190182\pi$
$179$	−2.08225	−	5.02699i	−0.155635	−	0.375735i	−0.982394	+	0.186820i	$0.940182\pi$
$180$	−0.781173	−	19.2544i	−0.0582252	−	1.43514i
$181$	−17.0152	−	7.04792i	−1.26473	−	0.523868i	−0.353371	−	0.935483i	$-0.614965\pi$
$181$	−17.0152	−	7.04792i	−1.26473	−	0.523868i	−0.911358	+	0.411615i	$0.864965\pi$
$182$	4.97846	+	8.96551i	0.369028	+	0.664568i
$183$	3.72193	+	6.89258i	0.275133	+	0.509514i
$184$	3.29468	−	3.87520i	0.242887	−	0.285683i
$185$	35.6058	+	9.54054i	2.61779	+	0.701434i
$186$	−20.7284	+	10.7499i	−1.51988	+	0.788223i
$187$	2.50439	−	1.92168i	0.183139	−	0.140528i
$188$	−0.596813	+	1.96261i	−0.0435271	+	0.143138i
$189$	16.4716	−	10.5365i	1.19814	−	0.766416i
$190$	3.78467	−	25.4544i	0.274569	−	1.84666i
$191$	−0.0514297	+	0.0890788i	−0.00372132	+	0.00644552i	−0.867880	−	0.496774i	$-0.834518\pi$
$191$	−0.0514297	+	0.0890788i	−0.00372132	+	0.00644552i	0.864159	+	0.503219i	$0.167851\pi$
$192$	−13.3921	−	3.55673i	−0.966495	−	0.256685i
$193$	−1.11792	−	1.93630i	−0.0804697	−	0.139378i	0.822982	−	0.568067i	$-0.192309\pi$
$193$	−1.11792	−	1.93630i	−0.0804697	−	0.139378i	−0.903452	+	0.428690i	$0.858975\pi$
$194$	7.08243	−	2.79598i	0.508489	−	0.200740i
$195$	−10.6634	+	1.09606i	−0.763623	+	0.0784907i
$196$	−9.78253	−	10.4590i	−0.698752	−	0.747070i
$197$	−4.55396	−	1.88631i	−0.324457	−	0.134394i	0.214509	−	0.976722i	$-0.431185\pi$
$197$	−4.55396	−	1.88631i	−0.324457	−	0.134394i	−0.538966	+	0.842328i	$0.681185\pi$
$198$	−1.80411	+	5.17497i	−0.128212	+	0.367769i
$199$	2.90444	−	2.90444i	0.205890	−	0.205890i	−0.596628	−	0.802518i	$-0.703493\pi$
$199$	2.90444	−	2.90444i	0.205890	−	0.205890i	0.802518	+	0.596628i	$0.203493\pi$
$200$	2.70630	−	14.7875i	0.191364	−	1.04564i
$201$	0.0472109	−	1.65769i	0.00333000	−	0.116925i
$202$	7.10080	+	0.118617i	0.499610	+	0.00834585i
$203$	−3.32308	−	25.2413i	−0.233234	−	1.77159i
$204$	−6.38452	−	5.55886i	−0.447006	−	0.389198i
$205$	7.91566	+	1.04212i	0.552854	+	0.0727846i
$206$	−0.331910	−	0.447848i	−0.0231253	−	0.0312030i
$207$	−2.95904	+	4.51111i	−0.205668	+	0.313544i
$208$	−1.51406	+	7.55785i	−0.104981	+	0.524043i
$209$	−3.65940	+	6.33826i	−0.253126	+	0.438427i
$210$	27.8342	−	10.0822i	1.92074	−	0.695739i
$211$	−8.65617	−	6.64211i	−0.595915	−	0.457262i	0.266240	−	0.963907i	$-0.414219\pi$
$211$	−8.65617	−	6.64211i	−0.595915	−	0.457262i	−0.862155	+	0.506645i	$0.830885\pi$
$212$	18.4202	+	3.05409i	1.26511	+	0.209755i
$213$	20.0809	+	3.22770i	1.37592	+	0.221158i
$214$	11.4591	+	20.6362i	0.783327	+	1.41066i
$215$	−8.53372	+	8.53372i	−0.581995	+	0.581995i
$216$	14.5622	+	1.98573i	0.990830	+	0.135112i
$217$	−25.3651	−	25.3651i	−1.72190	−	1.72190i
$218$	2.30436	−	8.05908i	0.156071	−	0.545830i
$219$	4.57431	−	28.4587i	0.309103	−	1.92306i
$220$	−4.38640	+	7.04320i	−0.295731	+	0.474852i
$221$	−2.86673	+	3.73600i	−0.192837	+	0.251310i
$222$	−11.9206	+	25.4613i	−0.800060	+	1.70885i
$223$	−5.87067	−	3.38943i	−0.393129	−	0.226973i	0.290386	−	0.956910i	$-0.406216\pi$
$223$	−5.87067	−	3.38943i	−0.393129	−	0.226973i	−0.683515	+	0.729936i	$0.739550\pi$
$224$	−1.00828	−	21.2631i	−0.0673685	−	1.42070i
$225$	−0.907490	+	15.9192i	−0.0604993	+	1.06128i
$226$	0.435790	−	2.93098i	0.0289883	−	0.194966i
$227$	0.0883921	−	0.671405i	0.00586679	−	0.0445627i	−0.988261	−	0.152775i	$-0.951179\pi$
$227$	0.0883921	−	0.671405i	0.00586679	−	0.0445627i	0.994128	+	0.108212i	$0.0345125\pi$
$228$	18.6077	+	6.24245i	1.23233	+	0.413416i
$229$	9.95243	−	1.31026i	0.657675	−	0.0865846i	0.205700	−	0.978615i	$-0.434053\pi$
$229$	9.95243	−	1.31026i	0.657675	−	0.0865846i	0.451975	+	0.892031i	$0.350720\pi$
$230$	−5.87137	+	5.67844i	−0.387147	+	0.374425i
$231$	−8.41591	−	0.239684i	−0.553726	−	0.0157701i
$232$	10.3860	−	16.0721i	0.681876	−	1.05519i
$233$	−7.12109	−	7.12109i	−0.466518	−	0.466518i	0.434266	−	0.900784i	$-0.357008\pi$
$233$	−7.12109	−	7.12109i	−0.466518	−	0.466518i	−0.900784	+	0.434266i	$0.857008\pi$
$234$	0.601568	−	8.15343i	0.0393257	−	0.533006i
$235$	1.26062	−	3.04341i	0.0822339	−	0.198530i
$236$	8.08103	+	21.5153i	0.526031	+	1.40052i
$237$	−0.964930	−	9.38765i	−0.0626789	−	0.609793i
$238$	5.17678	−	11.9303i	0.335561	−	0.773324i
$239$	−14.6247	+	8.44355i	−0.945991	+	0.546168i	−0.891833	−	0.452364i	$-0.850581\pi$
$239$	−14.6247	+	8.44355i	−0.945991	+	0.546168i	−0.0541574	+	0.998532i	$0.517247\pi$
$240$	20.8477	+	7.77781i	1.34571	+	0.502055i
$241$	0.391811	+	0.226212i	0.0252387	+	0.0145716i	0.512566	−	0.858648i	$-0.328695\pi$
$241$	0.391811	+	0.226212i	0.0252387	+	0.0145716i	−0.487328	+	0.873219i	$0.662028\pi$
$242$	−10.6023	+	7.85758i	−0.681539	+	0.505104i
$243$	−15.5874	−	0.178659i	−0.999934	−	0.0114610i
$244$	−9.00215	+	0.880441i	−0.576304	+	0.0563645i
$245$	13.9998	+	18.2449i	0.894416	+	1.16563i
$246$	−1.84001	+	5.80453i	−0.117315	+	0.370083i
$247$	2.82579	−	10.5460i	0.179801	−	0.671026i
$248$	−2.17593	−	26.8744i	−0.138171	−	1.70653i
$249$	−9.70370	+	5.23991i	−0.614947	+	0.332066i
$250$	−0.393351	+	1.37567i	−0.0248777	+	0.0870052i
$251$	−2.36095	+	5.69983i	−0.149022	+	0.359770i	−0.980709	−	0.195474i	$-0.937375\pi$
$251$	−2.36095	+	5.69983i	−0.149022	+	0.359770i	0.831687	+	0.555245i	$0.187375\pi$
$252$	3.85207	+	22.2472i	0.242658	+	1.40144i
$253$	2.14617	−	0.888973i	0.134929	−	0.0558892i
$254$	15.3740	−	19.3576i	0.964652	−	1.21460i
$255$	9.33498	+	9.88228i	0.584579	+	0.618852i
$256$	9.77475	−	12.6671i	0.610922	−	0.791691i
$257$	−13.8423	+	7.99188i	−0.863462	+	0.498520i	−0.865170	−	0.501479i	$-0.832790\pi$
$257$	−13.8423	+	7.99188i	−0.863462	+	0.498520i	0.00170822	+	0.999999i	$0.499456\pi$
$258$	−5.26778	−	7.54791i	−0.327958	−	0.469913i
$259$	−42.8202	−	5.63739i	−2.66072	−	0.350290i
$260$	3.60119	−	11.8425i	0.223336	−	0.734439i
$261$	−8.82185	+	18.2793i	−0.546059	+	1.13146i
$262$	0.569115	+	2.27532i	0.0351601	+	0.140570i
$263$	−8.54387	+	2.28932i	−0.526837	+	0.141166i	−0.512427	−	0.858731i	$-0.671254\pi$
$263$	−8.54387	+	2.28932i	−0.526837	+	0.141166i	−0.0144099	+	0.999896i	$0.504587\pi$
$264$	−4.70263	−	4.23462i	−0.289427	−	0.260623i
$265$	−28.9622	−	7.76041i	−1.77914	−	0.476718i
$266$	−0.503609	+	30.1477i	−0.0308783	+	1.84847i
$267$	−0.817396	+	5.08537i	−0.0500238	+	0.311219i
$268$	1.74369	+	0.791488i	0.106513	+	0.0483478i
$269$	5.55830	−	2.30232i	0.338895	−	0.140375i	−0.206744	−	0.978395i	$-0.566287\pi$
$269$	5.55830	−	2.30232i	0.338895	−	0.140375i	0.545640	+	0.838020i	$0.316287\pi$
$270$	−22.9632	−	5.44988i	−1.39750	−	0.331669i
$271$	5.81106			0.352997			0.176498	−	0.984301i	$-0.443523\pi$
$271$	5.81106			0.352997			0.176498	+	0.984301i	$0.443523\pi$
$272$	8.77282	−	4.31142i	0.531930	−	0.261418i
$273$	12.2194	−	2.90402i	0.739554	−	0.175759i
$274$	−6.59449	−	2.86149i	−0.398388	−	0.172869i
$275$	4.17955	−	5.44690i	0.252036	−	0.328460i
$276$	−3.47946	−	5.16734i	−0.209439	−	0.311037i
$277$	12.1870	−	9.35138i	0.732243	−	0.561870i	−0.173940	−	0.984756i	$-0.555650\pi$
$277$	12.1870	−	9.35138i	0.732243	−	0.561870i	0.906183	+	0.422887i	$0.138983\pi$
$278$	0.211163	+	0.126664i	0.0126647	+	0.00759680i
$279$	5.81754	+	28.0000i	0.348287	+	1.67631i
$280$	−1.71221	+	34.1407i	−0.102324	+	2.04030i
$281$	−4.96835	−	18.5422i	−0.296387	−	1.10613i	−0.940109	−	0.340873i	$-0.889277\pi$
$281$	−4.96835	−	18.5422i	−0.296387	−	1.10613i	0.643722	−	0.765259i	$-0.277389\pi$
$282$	2.11684	+	1.35317i	0.126056	+	0.0805800i
$283$	2.98876	+	22.7019i	0.177664	+	1.34949i	0.815250	+	0.579110i	$0.196600\pi$
$283$	2.98876	+	22.7019i	0.177664	+	1.34949i	−0.637586	+	0.770379i	$0.720067\pi$
$284$	−12.4153	+	19.9351i	−0.736710	+	1.18293i
$285$	−28.7636	−	12.8854i	−1.70381	−	0.763268i
$286$	−2.18935	+	2.75663i	−0.129459	+	0.163003i
$287$	−9.35454			−0.552181
$288$	−8.62540	+	14.6151i	−0.508257	+	0.861206i
$289$	−11.0281			−0.648711
$290$	−19.1115	+	24.0634i	−1.12226	+	1.41305i
$291$	−0.953533	−	9.27677i	−0.0558971	−	0.543814i
$292$	28.2520	+	17.5950i	1.65333	+	1.02967i
$293$	−3.23019	−	24.5357i	−0.188710	−	1.43339i	−0.779416	−	0.626507i	$-0.784484\pi$
$293$	−3.23019	−	24.5357i	−0.188710	−	1.43339i	0.590706	−	0.806887i	$-0.298849\pi$
$294$	−15.5702	+	8.07482i	−0.908070	+	0.470933i
$295$	−9.55222	−	35.6494i	−0.556152	−	2.07559i
$296$	−21.7761	−	24.0757i	−1.26571	−	1.39937i
$297$	5.50536	+	3.83974i	0.319454	+	0.222804i
$298$	5.07586	+	3.04470i	0.294037	+	0.176375i
$299$	−2.74929	+	2.10960i	−0.158995	+	0.122001i
$300$	−16.5420	−	8.08428i	−0.955051	−	0.466746i
$301$	8.60804	−	11.2182i	0.496159	−	0.646607i
$302$	17.8963	+	7.76556i	1.02981	+	0.446858i
$303$	2.48944	−	8.33401i	0.143015	−	0.478776i
$304$	−14.9661	+	17.0187i	−0.858365	+	0.976091i
$305$	14.5251			0.831704
$306$	−8.66757	+	5.68927i	−0.495492	+	0.325234i
$307$	−23.5556	+	9.75704i	−1.34439	+	0.556864i	−0.934725	−	0.355373i	$-0.884354\pi$
$307$	−23.5556	+	9.75704i	−1.34439	+	0.556864i	−0.409664	+	0.912237i	$0.634354\pi$
$308$	4.01829	−	8.85250i	0.228963	−	0.504418i
$309$	−0.637927	+	0.243201i	−0.0362904	+	0.0138352i
$310$	−0.723173	+	43.2915i	−0.0410734	+	2.45879i
$311$	25.1329	+	6.73434i	1.42516	+	0.381869i	0.887310	−	0.461173i	$-0.152571\pi$
$311$	25.1329	+	6.73434i	1.42516	+	0.381869i	0.537846	+	0.843043i	$0.319238\pi$
$312$	8.41124	+	4.28618i	0.476193	+	0.242657i
$313$	22.4873	−	6.02546i	1.27106	−	0.340579i	0.440622	−	0.897693i	$-0.354758\pi$
$313$	22.4873	−	6.02546i	1.27106	−	0.340579i	0.830436	+	0.557114i	$0.188091\pi$
$314$	6.72861	+	26.9010i	0.379718	+	1.51811i
$315$	−2.67897	−	36.1581i	−0.150943	−	2.03728i
$316$	10.4257	+	3.17035i	0.586489	+	0.178346i
$317$	−20.8109	−	2.73981i	−1.16886	−	0.153883i	−0.478991	−	0.877820i	$-0.658997\pi$
$317$	−20.8109	−	2.73981i	−1.16886	−	0.153883i	−0.689866	+	0.723937i	$0.742331\pi$
$318$	9.69641	−	20.7106i	0.543747	−	1.16139i
$319$	7.56856	−	4.36971i	0.423758	−	0.244657i
$320$	−17.6022	+	18.7169i	−0.983995	+	1.04631i
$321$	28.1259	−	6.68428i	1.56983	−	0.373080i
$322$	5.95201	−	7.49424i	0.331693	−	0.417637i
$323$	−12.7919	+	5.29856i	−0.711758	+	0.294820i
$324$	7.16002	−	16.5147i	0.397779	−	0.917481i
$325$	−3.91947	+	9.46243i	−0.217413	+	0.524881i
$326$	−3.17040	+	11.0879i	−0.175592	+	0.614101i
$327$	−8.74079	−	5.38396i	−0.483367	−	0.297734i
$328$	−5.35682	−	4.55435i	−0.295781	−	0.251472i
$329$	−0.998953	+	3.72814i	−0.0550740	+	0.205539i
$330$	6.85394	+	7.50295i	0.377297	+	0.413024i
$331$	6.87790	+	8.96346i	0.378044	+	0.492676i	0.943162	−	0.332334i	$-0.107836\pi$
$331$	6.87790	+	8.96346i	0.378044	+	0.492676i	−0.565118	+	0.825010i	$0.691169\pi$
$332$	−1.23953	−	12.6737i	−0.0680278	−	0.695557i
$333$	26.0795	+	22.4816i	1.42915	+	1.23199i
$334$	−20.6548	+	15.3077i	−1.13018	+	0.837602i
$335$	−2.66309	−	1.53753i	−0.145500	−	0.0840044i
$336$	−25.4070	−	5.84673i	−1.38607	−	0.318965i
$337$	6.81169	−	3.93273i	0.371056	−	0.214229i	−0.302863	−	0.953034i	$-0.597943\pi$
$337$	6.81169	−	3.93273i	0.371056	−	0.214229i	0.673920	+	0.738804i	$0.264609\pi$
$338$	−5.22786	+	12.0480i	−0.284358	+	0.655323i
$339$	−3.31201	−	1.48371i	−0.179884	−	0.0805840i
$340$	−14.6949	+	5.51932i	−0.796940	+	0.299327i
$341$	4.71228	−	11.3764i	0.255184	−	0.616069i
$342$	13.5182	−	19.8767i	0.730979	−	1.07481i
$343$	−0.426938	−	0.426938i	−0.0230525	−	0.0230525i
$344$	10.3910	−	2.23314i	0.560247	−	0.120403i
$345$	4.75325	+	8.80245i	0.255906	+	0.473908i
$346$	−11.0595	+	10.6961i	−0.594562	+	0.575024i
$347$	−21.1220	+	2.78077i	−1.13389	+	0.149279i	−0.674024	−	0.738709i	$-0.735436\pi$
$347$	−21.1220	+	2.78077i	−1.13389	+	0.149279i	−0.459866	+	0.887988i	$0.652102\pi$
$348$	−15.5157	−	17.5653i	−0.831727	−	0.941598i
$349$	3.14994	−	23.9262i	0.168612	−	1.28074i	−0.672589	−	0.740016i	$-0.734818\pi$
$349$	3.14994	−	23.9262i	0.168612	−	1.28074i	0.841202	−	0.540722i	$-0.181849\pi$
$350$	4.15982	−	27.9776i	0.222352	−	1.49546i
$351$	−9.41547	−	3.40724i	−0.502561	−	0.181865i
$352$	6.61098	−	3.11299i	0.352366	−	0.165923i
$353$	−9.54087	−	5.50842i	−0.507809	−	0.293184i	0.224124	−	0.974561i	$-0.428048\pi$
$353$	−9.54087	−	5.50842i	−0.507809	−	0.293184i	−0.731933	+	0.681377i	$0.761381\pi$
$354$	28.0447	−	2.41002i	1.49056	−	0.128091i
$355$	22.9584	−	29.9200i	1.21851	−	1.58799i
$356$	−5.04844	−	3.14410i	−0.267567	−	0.166637i
$357$	−12.3552	−	10.0520i	−0.653908	−	0.532011i
$358$	2.11548	−	7.39849i	0.111806	−	0.391022i
$359$	20.6681	+	20.6681i	1.09082	+	1.09082i	0.995441	+	0.0953785i	$0.0304061\pi$
$359$	20.6681	+	20.6681i	1.09082	+	1.09082i	0.0953785	+	0.995441i	$0.469594\pi$
$360$	16.0698	−	22.0100i	0.846955	−	1.16003i
$361$	9.26403	−	9.26403i	0.487580	−	0.487580i
$362$	−12.6443	−	22.7706i	−0.664570	−	1.19680i
$363$	5.75749	+	15.1022i	0.302190	+	0.792658i
$364$	−2.37219	+	14.3075i	−0.124336	+	0.749915i
$365$	−42.4028	−	32.5368i	−2.21946	−	1.70305i
$366$	−1.94049	+	10.9067i	−0.101431	+	0.570101i
$367$	−3.78150	+	6.54975i	−0.197393	+	0.341894i	−0.947682	−	0.319215i	$-0.896581\pi$
$367$	−3.78150	+	6.54975i	−0.197393	+	0.341894i	0.750290	+	0.661109i	$0.229914\pi$
$368$	7.05703	−	1.39373i	0.367873	−	0.0726534i
$369$	6.23587	+	4.09039i	0.324626	+	0.212937i
$370$	31.0398	+	41.8822i	1.61368	+	2.17735i
$371$	34.8306	+	4.58553i	1.80831	+	0.238069i
$372$	−32.4103	−	6.32657i	−1.68040	−	0.328018i
$373$	0.164870	+	1.25231i	0.00853662	+	0.0648421i	0.995183	−	0.0980353i	$-0.0312558\pi$
$373$	0.164870	+	1.25231i	0.00853662	+	0.0648421i	−0.986646	+	0.162877i	$0.947922\pi$
$374$	4.46364	+	0.0745639i	0.230809	+	0.00385561i
$375$	1.49204	+	0.919033i	0.0770485	+	0.0474587i
$376$	−2.38713	+	1.64855i	−0.123107	+	0.0850174i
$377$	−9.21875	+	9.21875i	−0.474790	+	0.474790i
$378$	27.5085	+	2.81897i	1.41488	+	0.144992i
$379$	35.1550	+	14.5617i	1.80579	+	0.747982i	0.983995	+	0.178198i	$0.0570268\pi$
$379$	35.1550	+	14.5617i	1.80579	+	0.747982i	0.821794	+	0.569784i	$0.192973\pi$
$380$	26.5794	−	24.8604i	1.36349	−	1.27531i
$381$	−17.7394	−	24.5343i	−0.908817	−	1.25693i
$382$	−0.135303	+	0.0534147i	−0.00692272	+	0.00273293i
$383$	−7.86652	−	13.6252i	−0.401960	−	0.696216i	0.592002	−	0.805936i	$-0.298338\pi$
$383$	−7.86652	−	13.6252i	−0.401960	−	0.696216i	−0.993962	+	0.109721i	$0.965004\pi$
$384$	−11.7027	−	15.7178i	−0.597198	−	0.802094i
$385$	−7.80588	+	13.5202i	−0.397824	+	0.689052i
$386$	0.465021	−	3.12758i	0.0236690	−	0.159189i
$387$	−10.6435	+	3.71425i	−0.541042	+	0.188806i
$388$	10.3025	+	3.13290i	0.523031	+	0.159049i
$389$	−19.6892	+	15.1080i	−0.998280	+	0.766007i	−0.972319	−	0.233656i	$-0.924931\pi$
$389$	−19.6892	+	15.1080i	−0.998280	+	0.766007i	−0.0259608	+	0.999663i	$0.508265\pi$
$390$	−12.7731	−	8.16506i	−0.646789	−	0.413454i
$391$	4.24494	+	1.13743i	0.214676	+	0.0575222i
$392$	−1.63445	−	20.1868i	−0.0825521	−	1.01958i
$393$	2.87138	+	0.0817765i	0.144842	+	0.00412508i
$394$	−3.38413	−	6.09436i	−0.170490	−	0.307029i
$395$	−16.1670	−	6.69658i	−0.813448	−	0.336941i
$396$	−6.54951	+	4.14416i	−0.329125	+	0.208252i
$397$	−5.82110	−	14.0534i	−0.292153	−	0.705319i	0.707847	−	0.706366i	$-0.249667\pi$
$397$	−5.82110	−	14.0534i	−0.292153	−	0.705319i	−0.999999	+	0.00104722i	$0.999667\pi$
$398$	5.77105	−	0.661913i	0.289276	−	0.0331787i
$399$	35.3835	+	10.5694i	1.77139	+	0.529130i
$400$	16.0032	−	13.9959i	0.800162	−	0.699797i
$401$	1.50912	+	2.61388i	0.0753621	+	0.130531i	0.901244	−	0.433313i	$-0.142655\pi$
$401$	1.50912	+	2.61388i	0.0753621	+	0.130531i	−0.825882	+	0.563844i	$0.809322\pi$
$402$	1.51029	−	1.79426i	0.0753263	−	0.0894898i
$403$	−2.39769	+	18.2123i	−0.119438	+	0.907219i
$404$	7.75934	+	6.37678i	0.386042	+	0.317257i
$405$	−14.0247	+	25.2749i	−0.696895	+	1.25592i
$406$	18.5206	−	30.8759i	0.919161	−	1.53234i
$407$	−3.83721	−	14.3207i	−0.190204	−	0.709850i
$408$	−2.18121	−	11.7715i	−0.107986	−	0.582776i
$409$	−1.62883	+	6.07888i	−0.0805406	+	0.300582i	−0.994432	−	0.105376i	$-0.966395\pi$
$409$	−1.62883	+	6.07888i	−0.0805406	+	0.300582i	0.913892	+	0.405958i	$0.133062\pi$
$410$	7.84950	+	8.11621i	0.387659	+	0.400831i
$411$	−5.55630	+	6.82940i	−0.274072	+	0.336869i
$412$	0.0263303	−	0.787890i	0.00129720	−	0.0388166i
$413$	16.5482	+	39.9509i	0.814285	+	1.96586i
$414$	−7.24464	+	2.39317i	−0.356055	+	0.117618i
$415$			20.4491i			1.00381i
$416$	−8.32415	+	7.03816i	−0.408125	+	0.345074i
$417$	0.219233	−	0.207092i	0.0107359	−	0.0101413i
$418$	−9.62729	+	3.80063i	−0.470886	+	0.185895i
$419$	24.9293	+	19.1289i	1.21788	+	0.934509i	0.999148	−	0.0412774i	$-0.0131427\pi$
$419$	24.9293	+	19.1289i	1.21788	+	0.934509i	0.218728	+	0.975786i	$0.429809\pi$
$420$	39.6922	+	13.3158i	1.93678	+	0.649744i
$421$	1.55025	+	2.02033i	0.0755546	+	0.0984647i	0.829602	−	0.558356i	$-0.188568\pi$
$421$	1.55025	+	2.02033i	0.0755546	+	0.0984647i	−0.754047	+	0.656820i	$0.771901\pi$
$422$	−3.74415	−	14.9691i	−0.182263	−	0.728686i
$423$	2.29609	−	2.04843i	0.111640	−	0.0995980i
$424$	17.7130	+	19.5835i	0.860220	+	0.951058i
$425$	12.5460	−	3.36169i	0.608570	−	0.163066i
$426$	19.3994	+	21.2363i	0.939902	+	1.02890i
$427$	−16.8729	+	2.22136i	−0.816539	+	0.107499i
$428$	−5.46014	+	32.9320i	−0.263926	+	1.59183i
$429$	2.52619	+	3.49382i	0.121966	+	0.168683i
$430$	−16.9563	+	1.94481i	−0.817704	+	0.0937870i
$431$			2.30404i			0.110982i	0.998459	+	0.0554908i	$0.0176723\pi$
$431$			2.30404i			0.110982i	−0.998459	+	0.0554908i	$0.982328\pi$
$432$	14.3801	+	15.0071i	0.691865	+	0.722027i
$433$			18.6470i			0.896120i	0.894004	+	0.448060i	$0.147885\pi$
$433$			18.6470i			0.896120i	−0.894004	+	0.448060i	$0.852115\pi$
$434$	−5.78063	−	50.3998i	−0.277479	−	2.41927i
$435$	22.0518	+	30.4985i	1.05731	+	1.46229i
$436$	9.64021	−	6.89814i	0.461682	−	0.330361i
$437$	−10.1018	+	1.32993i	−0.483237	+	0.0636193i
$438$	30.0962	−	27.4929i	1.43805	−	1.31366i
$439$	−28.3583	+	7.59860i	−1.35347	+	0.362661i	−0.861415	−	0.507903i	$-0.830421\pi$
$439$	−28.3583	+	7.59860i	−1.35347	+	0.362661i	−0.492056	+	0.870564i	$0.663754\pi$
$440$	−11.0524	+	3.94188i	−0.526903	+	0.187922i
$441$	4.36985	+	21.0322i	0.208088	+	1.00153i
$442$	−6.46067	+	1.61597i	−0.307303	+	0.0768640i
$443$	−20.9937	−	27.3595i	−0.997441	−	1.29989i	−0.953672	−	0.300848i	$-0.902730\pi$
$443$	−20.9937	−	27.3595i	−0.997441	−	1.29989i	−0.0437688	−	0.999042i	$-0.513936\pi$
$444$	−35.5955	+	17.7121i	−1.68929	+	0.840577i
$445$	7.57708	+	5.81410i	0.359188	+	0.275615i
$446$	−3.52025	−	8.91706i	−0.166689	−	0.422235i
$447$	5.26986	−	4.97800i	0.249256	−	0.235451i
$448$	17.5851	−	24.4343i	0.830816	−	1.15441i
$449$			29.4219i			1.38850i	0.719732	+	0.694252i	$0.244265\pi$
$449$			29.4219i			1.38850i	−0.719732	+	0.694252i	$0.755735\pi$
$450$	−15.0065	+	16.8313i	−0.707415	+	0.793435i
$451$	−1.22886	−	2.96673i	−0.0578647	−	0.139698i
$452$	3.06052	−	2.86257i	0.143955	−	0.134644i
$453$	15.0788	−	18.5337i	0.708464	−	0.870791i
$454$	0.688414	−	0.665793i	0.0323089	−	0.0312472i
$455$	6.02771	−	22.4957i	0.282583	−	1.05462i
$456$	15.1164	+	23.2793i	0.707889	+	1.09015i
$457$	−6.95597	−	25.9600i	−0.325386	−	1.21436i	−0.913923	−	0.405888i	$-0.866962\pi$
$457$	−6.95597	−	25.9600i	−0.325386	−	1.21436i	0.588536	−	0.808471i	$-0.299704\pi$
$458$	12.1741	+	7.30251i	0.568858	+	0.341224i
$459$	3.84079	+	12.1033i	0.179273	+	0.564934i
$460$	−11.4966	+	1.12440i	−0.536030	+	0.0524256i
$461$	5.21635	−	39.6221i	0.242950	−	1.84539i	−0.241294	−	0.970452i	$-0.577572\pi$
$461$	5.21635	−	39.6221i	0.242950	−	1.84539i	0.484244	−	0.874933i	$-0.339095\pi$
$462$	−9.10927	−	7.66755i	−0.423801	−	0.356727i
$463$	−0.150055	−	0.259903i	−0.00697364	−	0.0120787i	0.862518	−	0.506027i	$-0.168886\pi$
$463$	−0.150055	−	0.259903i	−0.00697364	−	0.0120787i	−0.869491	+	0.493948i	$0.835553\pi$
$464$	25.6379	−	8.66395i	1.19021	−	0.402214i
$465$	50.8100	+	15.1774i	2.35626	+	0.703835i
$466$	−1.62287	−	14.1494i	−0.0751782	−	0.655459i
$467$	−13.8195	−	33.3633i	−0.639492	−	1.54387i	−0.827358	−	0.561675i	$-0.810157\pi$
$467$	−13.8195	−	33.3633i	−0.639492	−	1.54387i	0.187866	−	0.982195i	$-0.439843\pi$
$468$	7.83745	−	8.50029i	0.362286	−	0.392926i
$469$	3.32869	+	1.37879i	0.153705	+	0.0636666i
$470$	4.07285	−	2.26161i	0.187867	−	0.104320i
$471$	33.9481	+	0.966838i	1.56425	+	0.0445495i
$472$	−9.97427	+	30.9343i	−0.459103	+	1.42387i
$473$	4.68857	+	1.25630i	0.215581	+	0.0577647i
$474$	7.18820	−	11.2449i	0.330165	−	0.516495i
$475$	−23.8909	+	18.3321i	−1.09619	+	0.841136i
$476$	16.2261	−	8.65880i	0.743721	−	0.396876i
$477$	−21.2135	−	18.2869i	−0.971298	−	0.837299i
$478$	−23.6223	−	3.51226i	−1.08046	−	0.160647i
$479$	−4.03805	+	6.99410i	−0.184503	+	0.319569i	−0.943409	−	0.331632i	$-0.892401\pi$
$479$	−4.03805	+	6.99410i	−0.184503	+	0.319569i	0.758906	+	0.651200i	$0.225734\pi$
$480$	16.2466	+	26.9498i	0.741552	+	1.23008i
$481$	11.0585	+	19.1538i	0.504222	+	0.873338i
$482$	0.234943	+	0.595128i	0.0107014	+	0.0271073i
$483$	−6.86776	−	9.49837i	−0.312494	−	0.432191i
$484$	−18.6524	−	0.623339i	−0.847834	−	0.0283336i
$485$	−15.9760	−	6.61748i	−0.725433	−	0.300484i
$486$	−17.1049	−	13.9076i	−0.775896	−	0.630861i
$487$	−0.0938311	+	0.0938311i	−0.00425189	+	0.00425189i	−0.709230	−	0.704978i	$-0.750957\pi$
$487$	−0.0938311	+	0.0938311i	−0.00425189	+	0.00425189i	0.704978	+	0.709230i	$0.250957\pi$
$488$	−10.7437	−	6.94270i	−0.486344	−	0.314281i
$489$	12.0258	+	7.40738i	0.543824	+	0.334973i
$490$	−0.543212	+	32.5184i	−0.0245398	+	1.46903i
$491$	2.77403	+	21.0708i	0.125190	+	0.950913i	0.932597	+	0.360919i	$0.117537\pi$
$491$	2.77403	+	21.0708i	0.125190	+	0.950913i	−0.807407	+	0.589995i	$0.799130\pi$
$492$	−7.14300	+	4.80979i	−0.322031	+	0.216842i
$493$	16.3919	+	2.15804i	0.738255	+	0.0971931i
$494$	12.4050	−	9.19362i	0.558127	−	0.413641i
$495$	11.1154	−	5.59953i	0.499599	−	0.251680i
$496$	21.2274	−	31.6755i	0.953138	−	1.42227i
$497$	−22.0937	+	38.2675i	−0.991039	+	1.71653i
$498$	−15.3549	−	2.73191i	−0.688070	−	0.122420i
$499$	13.7644	+	10.5618i	0.616177	+	0.472809i	0.869073	−	0.494684i	$-0.164716\pi$
$499$	13.7644	+	10.5618i	0.616177	+	0.472809i	−0.252896	+	0.967494i	$0.581383\pi$
$500$	−1.64557	+	1.17750i	−0.0735920	+	0.0526594i
$501$	11.2165	+	29.4213i	0.501114	+	1.31445i
$502$	−7.62781	+	4.23565i	−0.340446	+	0.189046i
$503$	−7.72924	+	7.72924i	−0.344630	+	0.344630i	−0.858105	−	0.513475i	$-0.828358\pi$
$503$	−7.72924	+	7.72924i	−0.344630	+	0.344630i	0.513475	+	0.858105i	$0.328358\pi$
$504$	−15.3013	+	28.0254i	−0.681576	+	1.24835i
$505$	−11.4044	−	11.4044i	−0.507489	−	0.507489i
$506$	3.15863	+	0.903159i	0.140418	+	0.0401503i
$507$	12.4771	+	10.1512i	0.554128	+	0.450831i
$508$	34.0515	−	7.91523i	1.51079	−	0.351182i
$509$	16.8969	−	22.0205i	0.748944	−	0.976043i	−0.251024	−	0.967981i	$-0.580767\pi$
$509$	16.8969	−	22.0205i	0.748944	−	0.976043i	0.999968	−	0.00806166i	$-0.00256613\pi$
$510$	1.64604	+	19.1545i	0.0728877	+	0.848173i
$511$	54.2328	+	31.3113i	2.39912	+	1.38513i
$512$	21.9661	−	5.43068i	0.970772	−	0.240005i
$513$	−18.9656	−	22.5176i	−0.837351	−	0.994176i
$514$	−22.3587	−	3.32438i	−0.986198	−	0.146632i
$515$	−0.165238	+	1.25511i	−0.00728127	+	0.0553067i
$516$	0.804956	−	12.9920i	0.0354362	−	0.571943i
$517$	−1.31358	+	0.172936i	−0.0577712	+	0.00760573i
$518$	−42.4623	−	43.9050i	−1.86569	−	1.92908i
$519$	8.95336	+	16.5806i	0.393009	+	0.727806i
$520$	14.4040	−	9.94739i	0.631657	−	0.436222i
$521$	28.7448	+	28.7448i	1.25933	+	1.25933i	0.951412	+	0.307922i	$0.0996334\pi$
$521$	28.7448	+	28.7448i	1.25933	+	1.25933i	0.307922	+	0.951412i	$0.400367\pi$
$522$	−25.8469	+	12.4839i	−1.13129	+	0.546407i
$523$	8.39463	−	20.2664i	0.367072	−	0.886189i	−0.627156	−	0.778894i	$-0.715781\pi$
$523$	8.39463	−	20.2664i	0.367072	−	0.886189i	0.994227	−	0.107295i	$-0.0342190\pi$
$524$	−1.37098	+	3.02033i	−0.0598914	+	0.131944i
$525$	−31.6147	−	14.1627i	−1.37978	−	0.618111i
$526$	−11.4753	−	4.97938i	−0.500348	−	0.217111i
$527$	20.1744	−	11.6477i	0.878811	−	0.507382i
$528$	−1.48334	−	8.82571i	−0.0645543	−	0.384090i
$529$	−17.1179	−	9.88300i	−0.744254	−	0.429695i
$530$	−25.2482	−	34.0675i	−1.09671	−	1.47980i
$531$	6.43776	−	33.8678i	0.279375	−	1.46974i
$532$	−27.0738	+	32.9437i	−1.17380	+	1.42829i
$533$	2.91618	+	3.80044i	0.126314	+	0.164615i
$534$	−5.37799	+	4.91278i	−0.232728	+	0.212597i
$535$	13.8742	−	51.7792i	0.599833	−	2.23861i
$536$	1.23488	+	2.41016i	0.0533386	+	0.104103i
$537$	−8.02431	−	4.94264i	−0.346275	−	0.213291i
$538$	8.18043	+	2.33906i	0.352684	+	0.100844i
$539$	3.53963	−	8.54543i	0.152463	−	0.368078i
$540$	−20.6369	−	26.2324i	−0.888071	−	1.12886i
$541$	13.1359	−	5.44108i	0.564758	−	0.233930i	−0.0819915	−	0.996633i	$-0.526128\pi$
$541$	13.1359	−	5.44108i	0.564758	−	0.233930i	0.646749	+	0.762703i	$0.276128\pi$
$542$	6.43537	+	5.11105i	0.276423	+	0.219538i
$543$	−31.0350	+	7.37564i	−1.33184	+	0.316519i
$544$	13.5074	+	2.94141i	0.579124	+	0.126112i
$545$	−16.4855	+	9.51789i	−0.706160	+	0.407702i
$546$	16.0864	+	7.53145i	0.688436	+	0.322316i
$547$	−23.6808	−	3.11763i	−1.01252	−	0.133300i	−0.394031	−	0.919097i	$-0.628920\pi$
$547$	−23.6808	−	3.11763i	−1.01252	−	0.133300i	−0.618485	+	0.785797i	$0.712253\pi$
$548$	−4.78619	−	8.96902i	−0.204456	−	0.383138i
$549$	12.2191	+	5.89711i	0.521497	+	0.251682i
$550$	9.41934	−	2.35601i	0.401642	−	0.100461i
$551$	−37.0262	+	9.92115i	−1.57737	+	0.422655i
$552$	0.691593	−	8.78282i	0.0294362	−	0.373822i
$553$	19.8043	+	5.30656i	0.842166	+	0.225658i
$554$	21.7212	+	0.362846i	0.922843	+	0.0154158i
$555$	59.6581	−	22.7439i	2.53235	−	0.965423i
$556$	0.122443	+	0.325998i	0.00519275	+	0.0138254i
$557$	−7.59861	+	3.14745i	−0.321963	+	0.133362i	−0.537811	−	0.843065i	$-0.680749\pi$
$557$	−7.59861	+	3.14745i	−0.321963	+	0.133362i	0.215848	+	0.976427i	$0.430749\pi$
$558$	−18.1845	+	36.1249i	−0.769810	+	1.52929i
$559$	−7.24105			−0.306264
$560$	−31.9242	+	36.3027i	−1.34905	+	1.53407i
$561$	1.56489	−	5.23886i	0.0660698	−	0.221185i
$562$	10.8064	−	24.9041i	0.455840	−	1.05052i
$563$	−10.6287	+	13.8516i	−0.447945	+	0.583774i	−0.961680	−	0.274176i	$-0.911595\pi$
$563$	−10.6287	+	13.8516i	−0.447945	+	0.583774i	0.513734	+	0.857949i	$0.328262\pi$
$564$	1.15410	+	3.36039i	0.0485963	+	0.141498i
$565$	−5.33885	+	4.09664i	−0.224607	+	0.172347i
$566$	−16.6573	+	27.7696i	−0.700160	+	1.16724i
$567$	12.4264	−	31.5053i	0.521858	−	1.32310i
$568$	−31.2827	+	11.1571i	−1.31259	+	0.468141i
$569$	5.78055	+	21.5733i	0.242333	+	0.904401i	0.974705	+	0.223496i	$0.0717468\pi$
$569$	5.78055	+	21.5733i	0.242333	+	0.904401i	−0.732371	+	0.680905i	$0.761587\pi$
$570$	−20.5205	−	39.5684i	−0.859510	−	1.65734i
$571$	−2.15606	−	16.3769i	−0.0902285	−	0.685354i	−0.975456	−	0.220195i	$-0.929331\pi$
$571$	−2.15606	−	16.3769i	−0.0902285	−	0.685354i	0.885227	−	0.465159i	$-0.154003\pi$
$572$	−4.84913	+	1.12718i	−0.202752	+	0.0471296i
$573$	0.0182164	+	0.177224i	0.000760999	+	0.00740364i
$574$	−10.3595	−	8.22767i	−0.432399	−	0.343417i
$575$	9.55818			0.398603
$576$	−22.4067	+	8.59895i	−0.933610	+	0.358290i
$577$	2.01096			0.0837175			0.0418587	−	0.999124i	$-0.486672\pi$
$577$	2.01096			0.0837175			0.0418587	+	0.999124i	$0.486672\pi$
$578$	−12.2129	−	9.69962i	−0.507989	−	0.403451i
$579$	−3.53417	−	1.58323i	−0.146875	−	0.0657968i
$580$	−42.3294	+	9.83943i	−1.75763	+	0.408560i
$581$	−3.12734	−	23.7545i	−0.129744	−	0.985503i
$582$	7.10329	−	11.1121i	0.294441	−	0.460611i
$583$	3.12125	+	11.6486i	0.129269	+	0.482438i
$584$	15.8119	+	44.3340i	0.654300	+	1.83455i
$585$	−13.8547	+	12.3603i	−0.572821	+	0.511035i
$586$	18.0029	−	30.0128i	0.743693	−	1.23982i
$587$	−3.62263	+	2.77974i	−0.149522	+	0.114732i	−0.680814	−	0.732457i	$-0.738374\pi$
$587$	−3.62263	+	2.77974i	−0.149522	+	0.114732i	0.531291	+	0.847189i	$0.321707\pi$
$588$	−24.3450	−	4.75221i	−1.00397	−	0.195978i
$589$	−32.8792	+	42.8491i	−1.35477	+	1.76556i
$590$	20.7765	−	47.8809i	0.855355	−	1.97123i
$591$	−8.30623	+	1.97402i	−0.341673	+	0.0812005i
$592$	−2.94018	−	45.8152i	−0.120841	−	1.88299i
$593$	−44.9511			−1.84592			−0.922960	−	0.384896i	$-0.874237\pi$
$593$	−44.9511			−1.84592			−0.922960	+	0.384896i	$0.874237\pi$
$594$	2.71964	+	9.09444i	0.111588	+	0.373149i
$595$	−27.2864	+	11.3024i	−1.11863	+	0.463353i
$596$	2.94325	+	7.83622i	0.120560	+	0.320984i
$597$	1.12904	−	7.02424i	0.0462086	−	0.287483i
$598$	−4.90013	−	0.0818554i	−0.200381	−	0.00334732i
$599$	−12.3060	−	3.29740i	−0.502811	−	0.134728i	−0.00150696	−	0.999999i	$-0.500480\pi$
$599$	−12.3060	−	3.29740i	−0.502811	−	0.134728i	−0.501304	+	0.865271i	$0.667146\pi$
$600$	−11.2087	−	23.5021i	−0.457594	−	0.959470i
$601$	−27.6001	+	7.39542i	−1.12583	+	0.301666i	−0.773241	−	0.634112i	$-0.781366\pi$
$601$	−27.6001	+	7.39542i	−1.12583	+	0.301666i	−0.352590	+	0.935778i	$0.614699\pi$
$602$	19.3997	−	4.85235i	0.790673	−	0.197767i
$603$	−1.61606	−	2.37463i	−0.0658111	−	0.0967025i
$604$	12.9888	+	24.3403i	0.528509	+	0.990393i
$605$	29.7132	+	3.91182i	1.20801	+	0.159038i
$606$	10.0870	−	7.03982i	0.409755	−	0.285973i
$607$	−14.3589	+	8.29012i	−0.582810	+	0.336485i	−0.762249	−	0.647284i	$-0.775905\pi$
$607$	−14.3589	+	8.29012i	−0.582810	+	0.336485i	0.179439	+	0.983769i	$0.442572\pi$
$608$	−31.5426	+	5.68387i	−1.27922	+	0.230512i
$609$	−30.2806	−	32.0559i	−1.22703	−	1.29897i
$610$	16.0856	+	12.7754i	0.651286	+	0.517259i
$611$	1.82603	−	0.756367i	0.0738733	−	0.0305993i
$612$	−14.6027	−	1.32297i	−0.590279	−	0.0534777i
$613$	10.6730	−	25.7669i	0.431078	−	1.04071i	−0.547863	−	0.836568i	$-0.684558\pi$
$613$	10.6730	−	25.7669i	0.431078	−	1.04071i	0.978941	−	0.204146i	$-0.0654417\pi$
$614$	−34.6680	−	9.91274i	−1.39909	−	0.400046i
$615$	12.1679	−	6.57058i	0.490659	−	0.264951i
$616$	12.2361	−	6.26933i	0.493007	−	0.252599i
$617$	−10.0842	+	37.6348i	−0.405975	+	1.51512i	0.396275	+	0.918132i	$0.370303\pi$
$617$	−10.0842	+	37.6348i	−0.405975	+	1.51512i	−0.802250	+	0.596988i	$0.796364\pi$
$618$	−0.920368	−	0.291752i	−0.0370226	−	0.0117360i
$619$	11.0940	+	14.4580i	0.445906	+	0.581116i	0.961184	−	0.275907i	$-0.0889782\pi$
$619$	11.0940	+	14.4580i	0.445906	+	0.581116i	−0.515278	+	0.857023i	$0.672312\pi$
$620$	−38.8774	+	47.3065i	−1.56135	+	1.89987i
$621$	0.424867	+	9.33476i	0.0170493	+	0.374591i
$622$	21.9100	+	29.5632i	0.878509	+	1.18538i
$623$	−9.69102	−	5.59511i	−0.388263	−	0.224164i
$624$	5.54504	+	12.1447i	0.221979	+	0.486176i
$625$	−20.2006	+	11.6628i	−0.808026	+	0.466514i
$626$	30.2029	+	13.1056i	1.20715	+	0.523807i
$627$	1.29616	+	12.6101i	0.0517635	+	0.503598i
$628$	−16.2090	+	35.7092i	−0.646808	+	1.42495i
$629$	10.7334	−	25.9128i	0.427970	−	1.03321i
$630$	28.8357	−	42.3990i	1.14884	−	1.68922i
$631$	20.2757	+	20.2757i	0.807163	+	0.807163i	0.984203	−	0.177041i	$-0.0566525\pi$
$631$	20.2757	+	20.2757i	0.807163	+	0.807163i	−0.177041	+	0.984203i	$0.556653\pi$
$632$	8.75729	+	12.6807i	0.348346	+	0.504412i
$633$	−18.8905	−	0.537999i	−0.750830	−	0.0213836i
$634$	−20.6370	−	21.3381i	−0.819599	−	0.847446i
$635$	−55.6591	+	7.32766i	−2.20877	+	0.290790i
$636$	28.9539	−	14.4072i	1.14810	−	0.571284i
$637$	−1.80103	+	13.6802i	−0.0713594	+	0.542028i
$638$	12.2250	+	1.81767i	0.483993	+	0.0719621i
$639$	31.4609	−	15.8489i	1.24457	−	0.626972i
$640$	−35.9556	+	5.24589i	−1.42127	+	0.207362i
$641$	29.3783	+	16.9616i	1.16037	+	0.669942i	0.951393	−	0.307979i	$-0.0996525\pi$
$641$	29.3783	+	16.9616i	1.16037	+	0.669942i	0.208979	+	0.977920i	$0.432986\pi$
$642$	37.0267	+	17.3354i	1.46133	+	0.684173i
$643$	4.76413	−	6.20873i	0.187879	−	0.244848i	−0.689911	−	0.723894i	$-0.742350\pi$
$643$	4.76413	−	6.20873i	0.187879	−	0.244848i	0.877790	+	0.479046i	$0.159017\pi$
$644$	13.1829	−	3.06436i	0.519480	−	0.120753i
$645$	−3.31731	+	20.6384i	−0.130619	+	0.812635i
$646$	−18.8264	−	5.38311i	−0.740716	−	0.211796i
$647$	11.0515	+	11.0515i	0.434479	+	0.434479i	0.890149	−	0.455670i	$-0.150600\pi$
$647$	11.0515	+	11.0515i	0.434479	+	0.434479i	−0.455670	+	0.890149i	$0.650600\pi$
$648$	22.4545	−	11.9914i	0.882097	−	0.471067i
$649$	−10.4963	+	10.4963i	−0.412016	+	0.412016i
$650$	−12.6631	+	7.03170i	−0.496688	+	0.275806i
$651$	−61.3442	−	9.86016i	−2.40427	−	0.386450i
$652$	−13.2632	+	9.49062i	−0.519428	+	0.371681i
$653$	22.3060	+	17.1160i	0.872900	+	0.669800i	0.944813	−	0.327611i	$-0.106244\pi$
$653$	22.3060	+	17.1160i	0.872900	+	0.669800i	−0.0719126	+	0.997411i	$0.522910\pi$
$654$	−4.94446	−	13.6502i	−0.193344	−	0.533767i
$655$	2.66324	−	4.61287i	0.104061	−	0.180240i
$656$	−1.92661	−	9.75518i	−0.0752214	−	0.380876i
$657$	−22.4611	−	44.5865i	−0.876291	−	1.73949i
$658$	−4.38532	+	3.25006i	−0.170957	+	0.126700i
$659$	35.6105	+	4.68822i	1.38719	+	0.182627i	0.786863	−	0.617128i	$-0.211704\pi$
$659$	35.6105	+	4.68822i	1.38719	+	0.182627i	0.600327	+	0.799755i	$0.295037\pi$
$660$	0.991154	+	14.3373i	0.0385806	+	0.558080i
$661$	−5.30869	−	40.3235i	−0.206484	−	1.56840i	−0.709866	−	0.704337i	$-0.751244\pi$
$661$	−5.30869	−	40.3235i	−0.206484	−	1.56840i	0.503382	−	0.864064i	$-0.332089\pi$
$662$	−0.266872	+	15.9758i	−0.0103723	+	0.620918i
$663$	−0.232200	+	8.15313i	−0.00901791	+	0.316641i
$664$	9.77427	−	15.1255i	0.379315	−	0.586982i
$665$	48.4194	−	48.4194i	1.87763	−	1.87763i
$666$	9.10796	+	47.8349i	0.352926	+	1.85356i
$667$	11.2406	+	4.65602i	0.435238	+	0.180282i
$668$	−36.3376	−	1.21436i	−1.40594	−	0.0469849i
$669$	−11.6798	+	1.20054i	−0.451567	+	0.0464154i
$670$	−1.59688	−	4.04500i	−0.0616927	−	0.156272i
$671$	−2.92100	−	5.05932i	−0.112764	−	0.195313i
$672$	−22.9942	−	28.8213i	−0.887021	−	1.11181i
$673$	12.1383	−	21.0242i	0.467898	−	0.810423i	−0.531429	−	0.847103i	$-0.678345\pi$
$673$	12.1383	−	21.0242i	0.467898	−	0.810423i	0.999327	+	0.0366796i	$0.0116781\pi$
$674$	11.0025	+	1.63590i	0.423800	+	0.0630124i
$675$	14.8820	+	23.2650i	0.572809	+	0.895469i
$676$	−16.3862	+	8.74423i	−0.630237	+	0.336317i
$677$	19.1999	−	14.7326i	0.737911	−	0.566219i	−0.169969	−	0.985449i	$-0.554367\pi$
$677$	19.1999	−	14.7326i	0.737911	−	0.566219i	0.907880	+	0.419230i	$0.137700\pi$
$678$	−2.36286	−	4.55615i	−0.0907451	−	0.174978i
$679$	19.5704	+	5.24388i	0.751044	+	0.201242i
$680$	−21.1281	−	6.81239i	−0.810224	−	0.261243i
$681$	−0.557315	−	1.03208i	−0.0213564	−	0.0395494i
$682$	15.2246	−	8.45405i	0.582979	−	0.323722i
$683$	0.949161	+	0.393155i	0.0363186	+	0.0150437i	0.400769	−	0.916179i	$-0.368743\pi$
$683$	0.949161	+	0.393155i	0.0363186	+	0.0150437i	−0.364450	+	0.931223i	$0.618743\pi$
$684$	32.4528	−	10.1224i	1.24086	−	0.387039i
$685$	6.24743	+	15.0826i	0.238702	+	0.576278i
$686$	−0.0972978	−	0.848313i	−0.00371485	−	0.0323888i
$687$	12.6394	−	11.9394i	0.482223	−	0.455516i
$688$	13.4715	+	6.66627i	0.513597	+	0.254149i
$689$	−8.99511	−	15.5800i	−0.342686	−	0.593550i
$690$	−2.47818	+	13.9288i	−0.0943426	+	0.530261i
$691$	0.336311	−	2.55454i	0.0127939	−	0.0971792i	−0.983857	−	0.178959i	$-0.942727\pi$
$691$	0.336311	−	2.55454i	0.0127939	−	0.0971792i	0.996650	+	0.0817797i	$0.0260604\pi$
$692$	−21.6553	+	2.11796i	−0.823210	+	0.0805128i
$693$	−12.0557	+	8.20455i	−0.457959	+	0.311665i
$694$	−25.8371	−	15.4981i	−0.980762	−	0.588300i
$695$	−0.144735	−	0.540157i	−0.00549010	−	0.0204893i
$696$	−1.73326	−	33.0990i	−0.0656989	−	1.25462i
$697$	1.57231	−	5.86793i	0.0595553	−	0.222264i
$698$	24.5323	−	23.7262i	0.928562	−	0.898049i
$699$	−17.2220	−	2.76818i	−0.651395	−	0.104702i
$700$	29.2141	−	27.3246i	1.10419	−	1.03277i
$701$	8.65081	+	20.8849i	0.326737	+	0.788812i	0.998831	+	0.0483463i	$0.0153951\pi$
$701$	8.65081	+	20.8849i	0.326737	+	0.788812i	−0.672094	+	0.740466i	$0.734605\pi$
$702$	−7.43023	−	12.0546i	−0.280436	−	0.454970i
$703$			65.0284i			2.45259i
$704$	10.0592	+	2.36717i	0.379121	+	0.0892162i
$705$	−1.31924	−	5.55105i	−0.0496854	−	0.209065i
$706$	−5.72102	−	14.4918i	−0.215314	−	0.545405i
$707$	14.9919	+	11.5037i	0.563830	+	0.432642i
$708$	33.1774	+	21.9975i	1.24688	+	0.826715i
$709$	−23.7243	−	30.9181i	−0.890985	−	1.16115i	−0.986177	−	0.165696i	$-0.947013\pi$
$709$	−23.7243	−	30.9181i	−0.890985	−	1.16115i	0.0951916	−	0.995459i	$-0.469654\pi$
$710$	51.7408	−	12.9417i	1.94180	−	0.485692i
$711$	−10.8815	−	12.1971i	−0.408088	−	0.457428i
$712$	−2.82547	−	7.92218i	−0.105889	−	0.296896i
$713$	16.5588	−	4.43690i	0.620130	−	0.166163i
$714$	−4.84145	−	21.9989i	−0.181187	−	0.823287i
$715$	7.92619	−	1.04350i	0.296423	−	0.0390248i
$716$	8.85001	−	6.33270i	0.330740	−	0.236664i
$717$	−11.9580	+	26.6932i	−0.446579	+	0.996877i
$718$	4.71019	+	41.0669i	0.175783	+	1.53260i
$719$		−	7.23335i		−	0.269758i	−0.990862	−	0.134879i	$-0.956935\pi$
$719$		−	7.23335i		−	0.269758i	0.990862	−	0.134879i	$-0.0430646\pi$
$720$	37.1550	−	10.2406i	1.38468	−	0.381646i
$721$		−	1.48326i		−	0.0552394i
$722$	18.4074	−	2.11124i	0.685051	−	0.0785723i
$723$	0.779514	−	0.0801241i	0.0289905	−	0.00297985i
$724$	6.02489	−	36.3381i	0.223913	−	1.35050i
$725$	35.6515	−	4.69360i	1.32406	−	0.174316i
$726$	−6.90688	+	21.7886i	−0.256338	+	0.808651i
$727$	−7.87070	+	2.10895i	−0.291908	+	0.0782166i	−0.401801	−	0.915727i	$-0.631616\pi$
$727$	−7.87070	+	2.10895i	−0.291908	+	0.0782166i	0.109893	+	0.993943i	$0.464949\pi$
$728$	−15.2110	+	13.7582i	−0.563757	+	0.509911i
$729$	−22.0597	+	15.5683i	−0.817024	+	0.576603i
$730$	−18.3410	−	73.3273i	−0.678830	−	2.71396i
$731$	5.59014	+	7.28521i	0.206759	+	0.269453i
$732$	−11.7418	+	10.3717i	−0.433989	+	0.383349i
$733$	9.30258	+	7.13812i	0.343599	+	0.263653i	0.766116	−	0.642702i	$-0.222187\pi$
$733$	9.30258	+	7.13812i	0.343599	+	0.263653i	−0.422517	+	0.906355i	$0.638853\pi$
$734$	−9.94852	+	3.92745i	−0.367206	+	0.144965i
$735$	38.1660	+	11.4005i	1.40777	+	0.420514i
$736$	9.04104	+	4.66345i	0.333257	+	0.171897i
$737$			1.23680i			0.0455579i
$738$	3.30817	+	10.0145i	0.121775	+	0.368640i
$739$	−11.5905	−	27.9819i	−0.426362	−	1.02933i	−0.980432	−	0.196859i	$-0.936926\pi$
$739$	−11.5905	−	27.9819i	−0.426362	−	1.02933i	0.554069	−	0.832470i	$-0.313074\pi$
$740$	−2.46238	+	73.6825i	−0.0905188	+	2.70862i
$741$	−6.73646	−	17.6700i	−0.247470	−	0.649125i
$742$	34.5394	+	35.7130i	1.26798	+	1.31107i
$743$	−5.83707	+	21.7843i	−0.214141	+	0.799187i	0.772326	+	0.635227i	$0.219093\pi$
$743$	−5.83707	+	21.7843i	−0.214141	+	0.799187i	−0.986467	+	0.163960i	$0.947573\pi$
$744$	−30.3279	−	35.5124i	−1.11187	−	1.30195i
$745$	−3.47908	−	12.9841i	−0.127464	−	0.475701i
$746$	−0.918871	+	1.53186i	−0.0336423	+	0.0560854i
$747$	−8.30222	+	17.2026i	−0.303762	+	0.629409i
$748$	4.87761	+	4.00852i	0.178343	+	0.146566i
$749$	−8.19809	+	62.2707i	−0.299552	+	2.27532i
$750$	0.844011	+	2.33007i	0.0308189	+	0.0850823i
$751$	−6.06106	−	10.4981i	−0.221171	−	0.383080i	0.733993	−	0.679157i	$-0.237655\pi$
$751$	−6.06106	−	10.4981i	−0.221171	−	0.383080i	−0.955164	+	0.296078i	$0.904321\pi$
$752$	−4.09355	−	0.273909i	−0.149276	−	0.00998843i
$753$	2.47073	+	10.3962i	0.0900383	+	0.378860i
$754$	−18.3174	+	2.10093i	−0.667081	+	0.0765112i
$755$	−16.9544	−	40.9316i	−0.617034	−	1.48965i
$756$	27.9845	+	27.3166i	1.01779	+	0.993495i
$757$	−17.1015	−	7.08365i	−0.621563	−	0.257460i	0.0496007	−	0.998769i	$-0.484205\pi$
$757$	−17.1015	−	7.08365i	−0.621563	−	0.257460i	−0.671163	+	0.741309i	$0.734205\pi$
$758$	26.1243	+	47.0462i	0.948877	+	1.70880i
$759$	2.11016	−	3.42581i	0.0765939	−	0.124349i
$760$	51.3006	−	4.15362i	1.86087	−	0.150668i
$761$	−1.95979	−	0.525123i	−0.0710422	−	0.0190357i	0.223123	−	0.974790i	$-0.428375\pi$
$761$	−1.95979	−	0.525123i	−0.0710422	−	0.0190357i	−0.294165	+	0.955755i	$0.595042\pi$
$762$	1.93358	−	42.7726i	0.0700463	−	1.54949i
$763$	17.6946	−	13.5776i	0.640588	−	0.491540i
$764$	−0.196820	−	0.0598511i	−0.00712069	−	0.00216534i
$765$	23.1316	+	4.39697i	0.836324	+	0.158973i
$766$	3.27223	−	22.0079i	0.118231	−	0.795179i
$767$	11.0720	−	19.1773i	0.399786	−	0.692450i
$768$	0.864441	−	27.6993i	0.0311928	−	0.999513i
$769$	−9.01703	−	15.6179i	−0.325162	−	0.563198i	0.656383	−	0.754428i	$-0.272086\pi$
$769$	−9.01703	−	15.6179i	−0.325162	−	0.563198i	−0.981545	+	0.191230i	$0.938752\pi$
$770$	−20.5360	+	8.10715i	−0.740066	+	0.292161i
$771$	−11.3183	+	25.2653i	−0.407619	+	0.909909i
$772$	3.26580	−	3.05458i	0.117539	−	0.109937i
$773$	2.09089	+	0.866073i	0.0752039	+	0.0311505i	0.419968	−	0.907539i	$-0.362041\pi$
$773$	2.09089	+	0.866073i	0.0752039	+	0.0311505i	−0.344764	+	0.938689i	$0.612041\pi$
$774$	−15.0539	−	5.24811i	−0.541100	−	0.188639i
$775$	35.8264	−	35.8264i	1.28692	−	1.28692i
$776$	8.65386	+	12.5309i	0.310655	+	0.449834i
$777$	−65.8231	+	35.5439i	−2.36139	+	1.27513i
$778$	−35.0926	−	0.586212i	−1.25813	−	0.0210167i
$779$	1.83841	+	13.9641i	0.0658680	+	0.500317i
$780$	−6.96386	−	20.2767i	−0.249346	−	0.726021i
$781$	−15.0386	−	1.97987i	−0.538123	−	0.0708453i
$782$	3.70058	+	4.99321i	0.132333	+	0.178557i
$783$	6.16862	+	34.6095i	0.220449	+	1.23684i
$784$	15.9450	−	23.7931i	0.569463	−	0.849753i
$785$	31.4873	−	54.5376i	1.12383	−	1.94653i
$786$	3.10794	+	2.61605i	0.110856	+	0.0933113i
$787$	8.71861	+	6.69002i	0.310785	+	0.238474i	0.752362	−	0.658750i	$-0.228914\pi$
$787$	8.71861	+	6.69002i	0.310785	+	0.238474i	−0.441577	+	0.897223i	$0.645581\pi$
$788$	1.61251	−	9.72558i	0.0574432	−	0.346459i
$789$	−9.66873	+	11.8841i	−0.344216	+	0.423085i
$790$	−12.0140	−	21.6355i	−0.427438	−	0.769756i
$791$	5.57531	−	5.57531i	0.198235	−	0.198235i
$792$	−10.8981	−	1.17116i	−0.387247	−	0.0416154i
$793$	6.16242	+	6.16242i	0.218834	+	0.218834i
$794$	5.91399	−	20.6831i	0.209880	−	0.734015i
$795$	−48.5268	+	18.5002i	−1.72107	+	0.656134i
$796$	6.97324	+	4.34283i	0.247160	+	0.153928i
$797$	9.77983	−	12.7453i	0.346419	−	0.451463i	−0.587352	−	0.809331i	$-0.699830\pi$
$797$	9.77983	−	12.7453i	0.346419	−	0.451463i	0.933772	+	0.357869i	$0.116496\pi$
$798$	29.8888	+	42.8261i	1.05805	+	1.51603i
$799$	−2.17069	−	1.25325i	−0.0767935	−	0.0443367i
$800$	30.0325	−	1.42412i	1.06181	−	0.0503503i
$801$	4.01364	+	7.96730i	0.141815	+	0.281511i
$802$	−0.627750	+	4.22204i	−0.0221666	+	0.149085i
$803$	−2.80588	+	21.3128i	−0.0990173	+	0.752111i
$804$	3.25067	−	0.658675i	0.114642	−	0.0232297i
$805$	−21.5483	+	2.83688i	−0.759477	+	0.0999871i
$806$	−18.6737	+	18.0601i	−0.657753	+	0.636139i
$807$	5.46503	−	8.87240i	0.192378	−	0.312323i
$808$	2.98435	+	13.8865i	0.104989	+	0.488526i
$809$	−23.8607	−	23.8607i	−0.838896	−	0.838896i	0.149818	−	0.988714i	$-0.452131\pi$
$809$	−23.8607	−	23.8607i	−0.838896	−	0.838896i	−0.988714	+	0.149818i	$0.952131\pi$
$810$	−37.7618	+	15.6551i	−1.32681	+	0.550063i
$811$	5.02188	−	12.1239i	0.176342	−	0.425727i	−0.810852	−	0.585251i	$-0.800996\pi$
$811$	5.02188	−	12.1239i	0.176342	−	0.425727i	0.987194	+	0.159524i	$0.0509959\pi$
$812$	47.6668	−	17.9035i	1.67278	−	0.628288i
$813$	8.15634	−	5.89741i	0.286055	−	0.206831i
$814$	8.34612	−	19.2342i	0.292531	−	0.674158i
$815$	22.6811	−	13.0949i	0.794484	−	0.458696i
$816$	7.93794	−	14.9546i	0.277884	−	0.523517i
$817$	−18.4379	−	10.6451i	−0.645059	−	0.372425i
$818$	−7.15044	+	5.29935i	−0.250009	+	0.185287i
$819$	14.2039	−	16.4771i	0.496324	−	0.575755i
$820$	1.55430	+	15.8921i	0.0542786	+	0.554977i
$821$	−19.7757	−	25.7722i	−0.690177	−	0.899457i	0.308481	−	0.951230i	$-0.400179\pi$
$821$	−19.7757	−	25.7722i	−0.690177	−	0.899457i	−0.998659	+	0.0517736i	$0.983513\pi$
$822$	−12.1600	+	2.67613i	−0.424127	+	0.0933408i
$823$	−2.01580	+	7.52305i	−0.0702662	+	0.262237i	−0.992118	−	0.125305i	$-0.960009\pi$
$823$	−2.01580	+	7.52305i	−0.0702662	+	0.262237i	0.921852	+	0.387542i	$0.126676\pi$
$824$	0.722139	−	0.849379i	0.0251569	−	0.0295895i
$825$	0.338536	−	11.8869i	0.0117863	−	0.413847i
$826$	−16.8123	+	58.7979i	−0.584974	+	2.04584i
$827$	0.777600	−	1.87729i	0.0270398	−	0.0652799i	−0.909783	−	0.415084i	$-0.863752\pi$
$827$	0.777600	−	1.87729i	0.0270398	−	0.0652799i	0.936823	+	0.349805i	$0.113752\pi$
$828$	−10.1279	−	3.72166i	−0.351968	−	0.129336i
$829$	−14.3083	+	5.92669i	−0.496947	+	0.205842i	−0.617057	−	0.786918i	$-0.711675\pi$
$829$	−14.3083	+	5.92669i	−0.496947	+	0.205842i	0.120110	+	0.992761i	$0.461675\pi$
$830$	−17.9858	+	22.6460i	−0.624295	+	0.786055i
$831$	7.61513	−	25.4935i	0.264166	−	0.884361i
$832$	−15.4088	+	0.472900i	−0.534203	+	0.0163949i
$833$	15.1540	−	8.74918i	0.525056	−	0.303141i
$834$	0.424932	−	0.0365165i	0.0147142	−	0.00126446i
$835$	57.8858	+	7.62080i	2.00322	+	0.263729i
$836$	−14.0044	−	4.25861i	−0.484352	−	0.147287i
$837$	36.5814	+	33.3964i	1.26444	+	1.15435i
$838$	10.7830	+	43.1103i	0.372491	+	1.48922i
$839$	−7.73654	+	2.07300i	−0.267095	+	0.0715679i	−0.389881	−	0.920865i	$-0.627484\pi$
$839$	−7.73654	+	2.07300i	−0.267095	+	0.0715679i	0.122786	+	0.992433i	$0.460817\pi$
$840$	32.2448	+	49.6572i	1.11255	+	1.71334i
$841$	16.2014	+	4.34115i	0.558669	+	0.149695i
$842$	−0.0601518	+	3.60088i	−0.00207297	+	0.124095i
$843$	−25.7912	−	20.9834i	−0.888296	−	0.722706i
$844$	9.01952	−	19.8705i	0.310465	−	0.683970i
$845$	27.5556	−	11.4139i	0.947941	−	0.392650i
$846$	4.34444	−	0.249001i	0.149365	−	0.00856083i
$847$	−35.1143			−1.20654
$848$	2.39159	+	37.2667i	0.0821274	+	1.27974i
$849$	27.2342	+	28.8310i	0.934677	+	0.989476i
$850$	16.8506	+	7.31183i	0.577971	+	0.250794i
$851$	12.5649	−	16.3749i	0.430720	−	0.561325i
$852$	2.80536	+	40.5804i	0.0961100	+	1.39026i
$853$	−30.0605	+	23.0662i	−1.02925	+	0.789773i	−0.977935	−	0.208910i	$-0.933009\pi$
$853$	−30.0605	+	23.0662i	−1.02925	+	0.789773i	−0.0513169	+	0.998682i	$0.516342\pi$
$854$	−20.6395	−	12.3804i	−0.706268	−	0.423648i
$855$	−53.4491	+	11.1051i	−1.82792	+	0.379786i
$856$	−35.0117	+	31.6676i	−1.19667	+	1.08238i
$857$	−10.2036	−	38.0803i	−0.348548	−	1.30080i	−0.888412	−	0.459047i	$-0.848191\pi$
$857$	−10.2036	−	38.0803i	−0.348548	−	1.30080i	0.539864	−	0.841752i	$-0.318476\pi$
$858$	−0.275353	+	6.09106i	−0.00940041	+	0.207946i
$859$	5.58281	+	42.4056i	0.190483	+	1.44686i	0.773187	+	0.634178i	$0.218661\pi$
$859$	5.58281	+	42.4056i	0.190483	+	1.44686i	−0.582704	+	0.812684i	$0.698005\pi$
$860$	−20.4885	−	12.7599i	−0.698653	−	0.435111i
$861$	−13.1299	+	9.49354i	−0.447467	+	0.323539i
$862$	−2.02649	+	2.55157i	−0.0690225	+	0.0869069i
$863$	−48.0984			−1.63729			−0.818644	−	0.574302i	$-0.805274\pi$
$863$	−48.0984			−1.63729			−0.818644	+	0.574302i	$0.805274\pi$
$864$	2.72580	+	29.2672i	0.0927335	+	0.995691i
$865$	34.9410			1.18803
$866$	−16.4008	+	20.6504i	−0.557321	+	0.701729i
$867$	−15.4789	+	11.1920i	−0.525691	+	0.380099i
$868$	37.9269	−	60.8988i	1.28732	−	2.06704i
$869$	0.918658	+	6.97790i	0.0311633	+	0.236709i
$870$	−2.40364	+	53.1706i	−0.0814909	+	1.80265i
$871$	−0.477528	−	1.78216i	−0.0161804	−	0.0603861i
$872$	16.7431	+	0.839691i	0.566992	+	0.0284355i
$873$	−10.7530	−	12.0531i	−0.363933	−	0.407934i
$874$	−12.3569	−	7.41214i	−0.417977	−	0.250719i
$875$	−3.02044	+	2.31767i	−0.102110	+	0.0783514i
$876$	57.5106	−	3.97577i	1.94310	−	0.134329i
$877$	23.3875	−	30.4792i	0.789740	−	1.02921i	−0.208944	−	0.977928i	$-0.567003\pi$
$877$	23.3875	−	30.4792i	0.789740	−	1.02921i	0.998684	−	0.0512818i	$-0.0163307\pi$
$878$	−38.0883	−	16.5273i	−1.28542	−	0.557769i
$879$	−29.4342	−	31.1599i	−0.992790	−	1.05100i
$880$	−15.7069	−	5.35565i	−0.529478	−	0.180539i
$881$	3.98433			0.134236			0.0671178	−	0.997745i	$-0.478620\pi$
$881$	3.98433			0.134236			0.0671178	+	0.997745i	$0.478620\pi$
$882$	−13.6593	+	27.1352i	−0.459932	+	0.913691i
$883$	−23.9492	+	9.92007i	−0.805954	+	0.333837i	−0.747338	−	0.664444i	$-0.768669\pi$
$883$	−23.9492	+	9.92007i	−0.805954	+	0.333837i	−0.0586153	+	0.998281i	$0.518669\pi$
$884$	−8.57608	−	3.89282i	−0.288445	−	0.130930i
$885$	−49.5865	−	40.3429i	−1.66683	−	1.35611i
$886$	0.814584	−	48.7637i	0.0273665	−	1.63825i
$887$	35.4419	+	9.49662i	1.19002	+	0.318865i	0.798894	−	0.601471i	$-0.205419\pi$
$887$	35.4419	+	9.49662i	1.19002	+	0.318865i	0.391127	+	0.920337i	$0.372085\pi$
$888$	−54.9981	−	11.6926i	−1.84562	−	0.392379i
$889$	63.5353	−	17.0242i	2.13091	−	0.570975i
$890$	3.27740	+	13.1031i	0.109859	+	0.439216i
$891$	11.6241	−	0.197755i	0.389421	−	0.00662505i
$892$	3.94444	−	12.9713i	0.132070	−	0.434310i
$893$	5.76156	+	0.758524i	0.192803	+	0.0253830i
$894$	10.2144	−	0.877771i	0.341619	−	0.0293570i
$895$	−15.1342	+	8.73772i	−0.505879	+	0.292070i
$896$	40.9652	−	11.5926i	1.36855	−	0.387283i
$897$	−1.71792	+	5.75115i	−0.0573596	+	0.192025i
$898$	−25.8777	+	32.5828i	−0.863549	+	1.08730i
$899$	59.5844	−	24.6807i	1.98725	−	0.823147i
$900$	−31.4225	+	5.44077i	−1.04742	+	0.181359i
$901$	−8.73072	+	21.0778i	−0.290862	+	0.702204i
$902$	1.24847	−	4.36628i	0.0415694	−	0.145381i
$903$	0.697236	−	24.4817i	0.0232026	−	0.814700i
$904$	5.90707	−	0.478274i	0.196466	−	0.0159072i
$905$	−15.3092	+	57.1347i	−0.508895	+	1.89922i
$906$	32.9999	−	7.26254i	1.09635	−	0.241282i
$907$	−4.03861	−	5.26322i	−0.134100	−	0.174762i	0.721477	−	0.692439i	$-0.243464\pi$
$907$	−4.03861	−	5.26322i	−0.134100	−	0.174762i	−0.855576	+	0.517676i	$0.826797\pi$
$908$	1.34796	−	0.131836i	0.0447338	−	0.00437512i
$909$	−4.96370	−	14.2240i	−0.164635	−	0.471779i
$910$	26.4611	−	19.6110i	0.877179	−	0.650097i
$911$	−33.3217	−	19.2383i	−1.10400	−	0.637394i	−0.166730	−	0.986003i	$-0.553321\pi$
$911$	−33.3217	−	19.2383i	−1.10400	−	0.637394i	−0.937268	+	0.348609i	$0.886654\pi$
$912$	−3.73464	+	39.0758i	−0.123666	+	1.29393i
$913$	7.12275	−	4.11232i	0.235729	−	0.136098i
$914$	15.1296	−	34.8671i	0.500441	−	1.15330i
$915$	20.3872	−	14.7409i	0.673981	−	0.487319i
$916$	7.05919	+	18.7946i	0.233242	+	0.620993i
$917$	−2.38827	+	5.76580i	−0.0788677	+	0.190403i
$918$	−6.39190	+	16.7818i	−0.210964	+	0.553880i
$919$	8.04799	+	8.04799i	0.265479	+	0.265479i	0.827275	−	0.561797i	$-0.189890\pi$
$919$	8.04799	+	8.04799i	0.265479	+	0.265479i	−0.561797	+	0.827275i	$0.689890\pi$
$920$	−13.7207	−	8.86647i	−0.452357	−	0.292319i
$921$	−23.1603	+	37.6005i	−0.763159	+	1.23898i
$922$	40.6259	−	39.2909i	1.33794	−	1.29398i
$923$	22.4343	−	2.95353i	0.738433	−	0.0972165i
$924$	−3.34402	−	16.5033i	−0.110010	−	0.542918i
$925$	7.96240	−	60.4804i	0.261802	−	1.98858i
$926$	0.0624183	−	0.419804i	0.00205119	−	0.0137956i
$927$	−0.648573	+	0.988761i	−0.0213019	+	0.0324752i
$928$	36.0126	+	12.9548i	1.18217	+	0.425261i
$929$	10.3735	+	5.98911i	0.340342	+	0.196496i	0.660423	−	0.750894i	$-0.270377\pi$
$929$	10.3735	+	5.98911i	0.340342	+	0.196496i	−0.320081	+	0.947390i	$0.603710\pi$
$930$	42.9197	+	61.4974i	1.40739	+	2.01658i
$931$	−24.6973	+	32.1861i	−0.809420	+	1.05486i
$932$	10.6477	−	17.0969i	0.348778	−	0.560029i
$933$	42.1107	−	16.0541i	1.37864	−	0.525588i
$934$	14.0401	−	49.1025i	0.459405	−	1.60668i
$935$	−7.16894	−	7.16894i	−0.234449	−	0.234449i
$936$	16.1558	−	2.52018i	0.528069	−	0.0823748i
$937$	−5.66970	+	5.66970i	−0.185221	+	0.185221i	−0.793626	−	0.608405i	$-0.791810\pi$
$937$	−5.66970	+	5.66970i	−0.185221	+	0.185221i	0.608405	+	0.793626i	$0.291810\pi$
$938$	2.47361	+	4.45463i	0.0807663	+	0.145449i
$939$	25.4479	−	31.2787i	0.830462	−	1.02074i
$940$	6.49959	+	1.07764i	0.211993	+	0.0351487i
$941$	30.1113	+	23.1052i	0.981599	+	0.753207i	0.969088	−	0.246714i	$-0.0793509\pi$
$941$	30.1113	+	23.1052i	0.981599	+	0.753207i	0.0125108	+	0.999922i	$0.496018\pi$
$942$	36.7449	+	30.9294i	1.19721	+	1.00773i
$943$	2.23524	−	3.87155i	0.0727895	−	0.126075i
$944$	−38.2538	+	25.4850i	−1.24505	+	0.829466i
$945$	−40.4556	−	48.0324i	−1.31602	−	1.56249i
$946$	4.08733	+	5.51505i	0.132890	+	0.179310i
$947$	−17.7602	−	2.33818i	−0.577129	−	0.0759805i	−0.163689	−	0.986512i	$-0.552339\pi$
$947$	−17.7602	−	2.33818i	−0.577129	−	0.0759805i	−0.413440	+	0.910531i	$0.635673\pi$
$948$	17.8508	−	6.13071i	0.579766	−	0.199116i
$949$	−4.18575	−	31.7939i	−0.135875	−	1.03207i
$950$	−42.5814	−	0.711311i	−1.38152	−	0.0230780i
$951$	−31.9905	+	17.2746i	−1.03736	+	0.560167i
$952$	25.5851	+	4.68238i	0.829217	+	0.151757i
$953$	−29.5459	+	29.5459i	−0.957087	+	0.957087i	−0.999116	−	0.0420295i	$-0.986618\pi$
$953$	−29.5459	+	29.5459i	−0.957087	+	0.957087i	0.0420295	+	0.999116i	$0.486618\pi$
$954$	−7.40854	−	38.9096i	−0.239860	−	1.25974i
$955$	0.305207	+	0.126421i	0.00987626	+	0.00409088i
$956$	−23.0710	−	24.6663i	−0.746169	−	0.797765i
$957$	6.18850	−	13.8143i	0.200046	−	0.446553i
$958$	−10.6235	+	4.19390i	−0.343228	+	0.135499i
$959$	−9.56391	−	16.5652i	−0.308835	−	0.534918i
$960$	−5.71130	+	44.1346i	−0.184331	+	1.42444i
$961$	29.9356	−	51.8500i	0.965665	−	1.67258i
$962$	−4.59998	+	30.9379i	−0.148309	+	0.997479i
$963$	32.6936	−	37.9258i	1.05354	−	1.22214i
$964$	−0.263254	+	0.865706i	−0.00847882	+	0.0278825i
$965$	−5.69695	+	4.37143i	−0.183391	+	0.140721i
$966$	0.748581	−	16.5593i	0.0240852	−	0.532786i
$967$	15.1177	+	4.05078i	0.486153	+	0.130264i	0.493566	−	0.869708i	$-0.335693\pi$
$967$	15.1177	+	4.05078i	0.486153	+	0.130264i	−0.00741330	+	0.999973i	$0.502360\pi$
$968$	−20.1080	−	17.0958i	−0.646296	−	0.549479i
$969$	−12.5772	+	20.4189i	−0.404038	+	0.655951i
$970$	−11.8721	−	21.3799i	−0.381189	−	0.686469i
$971$	−29.3632	−	12.1626i	−0.942309	−	0.390317i	−0.141974	−	0.989870i	$-0.545345\pi$
$971$	−29.3632	−	12.1626i	−0.942309	−	0.390317i	−0.800335	+	0.599553i	$0.795345\pi$
$972$	−6.71034	−	30.4462i	−0.215234	−	0.976562i
$973$	0.250738	+	0.605334i	0.00803828	+	0.0194061i
$974$	−0.186440	+	0.0213838i	−0.00597392	+	0.000685182i
$975$	4.10171	+	17.2591i	0.131360	+	0.552732i
$976$	−5.79156	−	17.1381i	−0.185383	−	0.548576i
$977$	−1.07803	−	1.86720i	−0.0344892	−	0.0597371i	0.848266	−	0.529571i	$-0.177647\pi$
$977$	−1.07803	−	1.86720i	−0.0344892	−	0.0597371i	−0.882755	+	0.469834i	$0.844314\pi$
$978$	6.80270	+	18.7803i	0.217526	+	0.600528i
$979$	0.501391	−	3.80844i	0.0160245	−	0.121718i
$980$	−29.2028	+	35.5343i	−0.932849	+	1.13510i
$981$	−17.7324	+	1.31380i	−0.566153	+	0.0419465i
$982$	−15.4605	+	25.7744i	−0.493366	+	0.822495i
$983$	0.497815	+	1.85787i	0.0158778	+	0.0592568i	0.973410	−	0.229069i	$-0.0735681\pi$
$983$	0.497815	+	1.85787i	0.0158778	+	0.0592568i	−0.957532	+	0.288326i	$0.906901\pi$
$984$	−12.1408	−	0.956013i	−0.387034	−	0.0304766i
$985$	−4.09737	+	15.2916i	−0.130553	+	0.487231i
$986$	16.2549	+	16.8072i	0.517662	+	0.535250i
$987$	2.38142	+	6.24657i	0.0758015	+	0.198831i
$988$	21.8239	+	0.729327i	0.694310	+	0.0232030i
$989$	2.58600	+	6.24316i	0.0822301	+	0.198521i
$990$	17.2345	+	3.57528i	0.547750	+	0.113630i
$991$			0.996907i			0.0316678i	0.999875	+	0.0158339i	$0.00504030\pi$
$991$			0.996907i			0.0316678i	−0.999875	+	0.0158339i	$0.994960\pi$
$992$	51.3678	−	16.4083i	1.63093	−	0.520963i
$993$	18.7504	+	5.60090i	0.595026	+	0.177739i
$994$	−58.1251	+	22.9465i	−1.84362	+	0.727817i
$995$	−10.4660	−	8.03082i	−0.331793	−	0.254594i
$996$	−14.6018	−	16.5306i	−0.462674	−	0.523794i
$997$	16.9581	+	22.1002i	0.537067	+	0.699919i	0.980529	−	0.196374i	$-0.0629166\pi$
$997$	16.9581	+	22.1002i	0.537067	+	0.699919i	−0.443462	+	0.896293i	$0.646250\pi$
$998$	5.95366	+	23.8027i	0.188460	+	0.753463i
$999$	59.4206	+	5.08789i	1.87999	+	0.160974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.37	✓	368
3.2	odd	2		864.2.bn.a.683.10		368
9.4	even	3		864.2.bn.a.395.6		368
9.5	odd	6	inner	288.2.bf.a.203.41	yes	368
32.3	odd	8	inner	288.2.bf.a.227.41	yes	368
96.35	even	8		864.2.bn.a.35.6		368
288.67	odd	24		864.2.bn.a.611.10		368
288.131	even	24	inner	288.2.bf.a.131.37	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.37	✓	368	1.1	even	1	trivial
288.2.bf.a.131.37	yes	368	288.131	even	24	inner
288.2.bf.a.203.41	yes	368	9.5	odd	6	inner
288.2.bf.a.227.41	yes	368	32.3	odd	8	inner
864.2.bn.a.35.6		368	96.35	even	8
864.2.bn.a.395.6		368	9.4	even	3
864.2.bn.a.611.10		368	288.67	odd	24
864.2.bn.a.683.10		368	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10744 + 0.879538i) q^{2} +(1.40359 - 1.01486i) q^{3} +(0.452825 + 1.94806i) q^{4} +(-0.419211 - 3.18422i) q^{5} +(2.44699 + 0.110619i) q^{6} +(0.973946 + 3.63481i) q^{7} +(-1.21192 + 2.55563i) q^{8} +(0.940122 - 2.84889i) q^{9} +O(q^{10})\)	\(q+(1.10744 + 0.879538i) q^{2} +(1.40359 - 1.01486i) q^{3} +(0.452825 + 1.94806i) q^{4} +(-0.419211 - 3.18422i) q^{5} +(2.44699 + 0.110619i) q^{6} +(0.973946 + 3.63481i) q^{7} +(-1.21192 + 2.55563i) q^{8} +(0.940122 - 2.84889i) q^{9} +(2.33640 - 3.89503i) q^{10} +(-1.02481 + 0.786367i) q^{11} +(2.61259 + 2.27473i) q^{12} +(1.17309 - 1.52880i) q^{13} +(-2.11838 + 4.88194i) q^{14} +(-3.81994 - 4.04390i) q^{15} +(-3.58990 + 1.76426i) q^{16} -2.44375 q^{17} +(3.54683 - 2.32809i) q^{18} +(5.23452 - 2.16821i) q^{19} +(6.01324 - 2.25855i) q^{20} +(5.05584 + 4.11337i) q^{21} +(-1.82655 - 0.0305121i) q^{22} +(-1.73706 - 0.465443i) q^{23} +(0.892566 + 4.81698i) q^{24} +(-5.13391 + 1.37563i) q^{25} +(2.64375 - 0.661268i) q^{26} +(-1.57168 - 4.95276i) q^{27} +(-6.63982 + 3.54324i) q^{28} +(-6.70769 - 0.883084i) q^{29} +(-0.673570 - 7.83814i) q^{30} +(-8.25551 + 4.76632i) q^{31} +(-5.52732 - 1.20365i) q^{32} +(-0.640365 + 2.14378i) q^{33} +(-2.70630 - 2.14937i) q^{34} +(11.1658 - 4.62501i) q^{35} +(5.97553 + 0.541367i) q^{36} +(-4.39219 + 10.6037i) q^{37} +(7.70391 + 2.20281i) q^{38} +(0.0950179 - 3.33632i) q^{39} +(8.64575 + 2.78768i) q^{40} +(-0.643399 + 2.40120i) q^{41} +(1.98116 + 9.00210i) q^{42} +(-2.28752 - 2.98116i) q^{43} +(-1.99595 - 1.64031i) q^{44} +(-9.46561 - 1.79927i) q^{45} +(-1.51430 - 2.04326i) q^{46} +(0.888261 + 0.512838i) q^{47} +(-3.24826 + 6.11954i) q^{48} +(-6.20113 + 3.58023i) q^{49} +(-6.89539 - 2.99205i) q^{50} +(-3.43002 + 2.48006i) q^{51} +(3.50939 + 1.59297i) q^{52} +(3.57267 - 8.62519i) q^{53} +(2.61561 - 6.86721i) q^{54} +(2.93358 + 2.93358i) q^{55} +(-10.4696 - 1.91606i) q^{56} +(5.14668 - 8.35557i) q^{57} +(-6.65162 - 6.87763i) q^{58} +(11.3931 - 1.49993i) q^{59} +(6.14801 - 9.27266i) q^{60} +(-0.590311 + 4.48386i) q^{61} +(-13.3346 - 1.98264i) q^{62} +(11.2708 + 0.642504i) q^{63} +(-5.06249 - 6.19445i) q^{64} +(-5.35980 - 3.09448i) q^{65} +(-2.59470 + 1.81087i) q^{66} +(0.582863 - 0.759602i) q^{67} +(-1.10659 - 4.76058i) q^{68} +(-2.91047 + 1.10958i) q^{69} +(16.4332 + 4.69882i) q^{70} +(8.30320 + 8.30320i) q^{71} +(6.14136 + 5.85523i) q^{72} +(11.7673 - 11.7673i) q^{73} +(-14.1904 + 7.87980i) q^{74} +(-5.80983 + 7.14101i) q^{75} +(6.59413 + 9.21535i) q^{76} +(-3.85641 - 2.95913i) q^{77} +(3.03964 - 3.61118i) q^{78} +(2.72426 - 4.71855i) q^{79} +(7.12273 + 10.6914i) q^{80} +(-7.23234 - 5.35660i) q^{81} +(-2.82447 + 2.09328i) q^{82} +(-6.31259 - 0.831068i) q^{83} +(-5.72368 + 11.7117i) q^{84} +(1.02445 + 7.78145i) q^{85} +(0.0887590 - 5.31341i) q^{86} +(-10.3110 + 5.56787i) q^{87} +(-0.767670 - 3.57206i) q^{88} +(-2.10274 + 2.10274i) q^{89} +(-8.90002 - 10.3179i) q^{90} +(6.69941 + 2.77499i) q^{91} +(0.120129 - 3.59466i) q^{92} +(-6.75019 + 15.0681i) q^{93} +(0.532631 + 1.34919i) q^{94} +(-9.09843 - 15.7589i) q^{95} +(-8.97961 + 3.92003i) q^{96} +(2.69208 - 4.66282i) q^{97} +(-10.0163 - 1.48927i) q^{98} +(1.27682 + 3.65886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more