LMFDB - Embedded newform 847.2.f.y.148.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.1
Character	$\chi$	$=$	847.148
Dual form			847.2.f.y.372.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.428283 - 1.31812i) q^{2} +(0.0990877 + 0.0719914i) q^{3} +(0.0640220 - 0.0465147i) q^{4} +(-0.0411006 + 0.126495i) q^{5} +(0.0524557 - 0.161442i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-2.33125 - 1.69375i) q^{8} +(-0.922415 - 2.83890i) q^{9} +O(q^{10})$	\(q+(-0.428283 - 1.31812i) q^{2} +(0.0990877 + 0.0719914i) q^{3} +(0.0640220 - 0.0465147i) q^{4} +(-0.0411006 + 0.126495i) q^{5} +(0.0524557 - 0.161442i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-2.33125 - 1.69375i) q^{8} +(-0.922415 - 2.83890i) q^{9} +0.184338 q^{10} +0.00969245 q^{12} +(-0.198215 - 0.610042i) q^{13} +(1.12126 + 0.814642i) q^{14} +(-0.0131791 + 0.00957518i) q^{15} +(-1.18522 + 3.64775i) q^{16} +(-0.440294 + 1.35508i) q^{17} +(-3.34696 + 2.43171i) q^{18} +(-5.81115 - 4.22204i) q^{19} +(0.00325252 + 0.0100102i) q^{20} -0.122479 q^{21} +1.66655 q^{23} +(-0.109063 - 0.335660i) q^{24} +(4.03077 + 2.92853i) q^{25} +(-0.719216 + 0.522541i) q^{26} +(0.226521 - 0.697160i) q^{27} +(-0.0244542 + 0.0752624i) q^{28} +(-3.62162 + 2.63126i) q^{29} +(0.0182656 + 0.0132707i) q^{30} +(-2.11115 - 6.49745i) q^{31} -0.447392 q^{32} +1.97473 q^{34} +(-0.0411006 - 0.126495i) q^{35} +(-0.191106 - 0.138846i) q^{36} +(-3.04890 + 2.21515i) q^{37} +(-3.07634 + 9.46801i) q^{38} +(0.0242772 - 0.0747174i) q^{39} +(0.310067 - 0.225277i) q^{40} +(-4.99395 - 3.62832i) q^{41} +(0.0524557 + 0.161442i) q^{42} -1.03970 q^{43} +0.397018 q^{45} +(-0.713755 - 2.19671i) q^{46} +(-7.67707 - 5.57771i) q^{47} +(-0.380047 + 0.276121i) q^{48} +(0.309017 - 0.951057i) q^{49} +(2.13384 - 6.56728i) q^{50} +(-0.141182 + 0.102575i) q^{51} +(-0.0410660 - 0.0298362i) q^{52} +(-0.205975 - 0.633926i) q^{53} -1.01595 q^{54} +2.88158 q^{56} +(-0.271862 - 0.836705i) q^{57} +(5.01939 + 3.64680i) q^{58} +(-6.62338 + 4.81217i) q^{59} +(-0.000398366 + 0.00122604i) q^{60} +(2.93506 - 9.03320i) q^{61} +(-7.66024 + 5.56549i) q^{62} +(2.41491 + 1.75454i) q^{63} +(2.56206 + 7.88521i) q^{64} +0.0853139 q^{65} +12.0398 q^{67} +(0.0348429 + 0.107235i) q^{68} +(0.165134 + 0.119977i) q^{69} +(-0.149132 + 0.108351i) q^{70} +(1.49384 - 4.59758i) q^{71} +(-2.65802 + 8.18053i) q^{72} +(7.16585 - 5.20629i) q^{73} +(4.22563 + 3.07010i) q^{74} +(0.188571 + 0.580362i) q^{75} -0.568428 q^{76} -0.108884 q^{78} +(3.55081 + 10.9283i) q^{79} +(-0.412707 - 0.299849i) q^{80} +(-7.17211 + 5.21084i) q^{81} +(-2.64373 + 8.13656i) q^{82} +(2.96038 - 9.11111i) q^{83} +(-0.00784136 + 0.00569708i) q^{84} +(-0.153315 - 0.111390i) q^{85} +(0.445286 + 1.37045i) q^{86} -0.548286 q^{87} -17.7001 q^{89} +(-0.170036 - 0.523317i) q^{90} +(0.518933 + 0.377027i) q^{91} +(0.106696 - 0.0775190i) q^{92} +(0.258572 - 0.795802i) q^{93} +(-4.06414 + 12.5081i) q^{94} +(0.772908 - 0.561551i) q^{95} +(-0.0443310 - 0.0322084i) q^{96} +(2.03376 + 6.25927i) q^{97} -1.38595 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.428283	−	1.31812i	−0.302842	−	0.932051i	−0.980474	−	0.196650i	$-0.936994\pi$
$2$	−0.428283	−	1.31812i	−0.302842	−	0.932051i	0.677632	−	0.735401i	$-0.263006\pi$
$3$	0.0990877	+	0.0719914i	0.0572083	+	0.0415643i	0.616022	−	0.787729i	$-0.288743\pi$
$3$	0.0990877	+	0.0719914i	0.0572083	+	0.0415643i	−0.558814	+	0.829293i	$0.688743\pi$
$4$	0.0640220	−	0.0465147i	0.0320110	−	0.0232574i
$5$	−0.0411006	+	0.126495i	−0.0183808	+	0.0565702i	−0.959826	−	0.280595i	$-0.909468\pi$
$5$	−0.0411006	+	0.126495i	−0.0183808	+	0.0565702i	0.941445	+	0.337165i	$0.109468\pi$
$6$	0.0524557	−	0.161442i	0.0214150	−	0.0659084i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−2.33125	−	1.69375i	−0.824221	−	0.598832i
$9$	−0.922415	−	2.83890i	−0.307472	−	0.946301i
$10$	0.184338			0.0582928
$11$		0			0
$11$		0			0
$12$	0.00969245			0.00279797
$13$	−0.198215	−	0.610042i	−0.0549749	−	0.169195i	0.919799	−	0.392390i	$-0.128352\pi$
$13$	−0.198215	−	0.610042i	−0.0549749	−	0.169195i	−0.974774	+	0.223194i	$0.928352\pi$
$14$	1.12126	+	0.814642i	0.299669	+	0.217722i
$15$	−0.0131791	+	0.00957518i	−0.00340283	+	0.00247230i
$16$	−1.18522	+	3.64775i	−0.296306	+	0.911936i
$17$	−0.440294	+	1.35508i	−0.106787	+	0.328656i	−0.990146	−	0.140041i	$-0.955277\pi$
$17$	−0.440294	+	1.35508i	−0.106787	+	0.328656i	0.883359	+	0.468697i	$0.155277\pi$
$18$	−3.34696	+	2.43171i	−0.788885	+	0.573159i
$19$	−5.81115	−	4.22204i	−1.33317	−	0.968603i	−0.999666	−	0.0258541i	$-0.991769\pi$
$19$	−5.81115	−	4.22204i	−1.33317	−	0.968603i	−0.333502	−	0.942749i	$-0.608231\pi$
$20$	0.00325252	+	0.0100102i	0.000727286	+	0.00223836i
$21$	−0.122479			−0.0267271
$22$		0			0
$23$	1.66655			0.347500			0.173750	−	0.984790i	$-0.444412\pi$
$23$	1.66655			0.347500			0.173750	+	0.984790i	$0.444412\pi$
$24$	−0.109063	−	0.335660i	−0.0222623	−	0.0685163i
$25$	4.03077	+	2.92853i	0.806155	+	0.585706i
$26$	−0.719216	+	0.522541i	−0.141050	+	0.102479i
$27$	0.226521	−	0.697160i	0.0435940	−	0.134168i
$28$	−0.0244542	+	0.0752624i	−0.00462141	+	0.0142233i
$29$	−3.62162	+	2.63126i	−0.672518	+	0.488613i	−0.870867	−	0.491519i	$-0.836442\pi$
$29$	−3.62162	+	2.63126i	−0.672518	+	0.488613i	0.198349	+	0.980131i	$0.436442\pi$
$30$	0.0182656	+	0.0132707i	0.00333483	+	0.00242290i
$31$	−2.11115	−	6.49745i	−0.379174	−	1.16698i	−0.940619	−	0.339463i	$-0.889755\pi$
$31$	−2.11115	−	6.49745i	−0.379174	−	1.16698i	0.561446	−	0.827514i	$-0.310245\pi$
$32$	−0.447392			−0.0790885
$33$		0			0
$34$	1.97473			0.338664
$35$	−0.0411006	−	0.126495i	−0.00694728	−	0.0213815i
$36$	−0.191106	−	0.138846i	−0.0318509	−	0.0231411i
$37$	−3.04890	+	2.21515i	−0.501235	+	0.364169i	−0.809489	−	0.587135i	$-0.800256\pi$
$37$	−3.04890	+	2.21515i	−0.501235	+	0.364169i	0.308253	+	0.951304i	$0.400256\pi$
$38$	−3.07634	+	9.46801i	−0.499049	+	1.53591i
$39$	0.0242772	−	0.0747174i	0.00388746	−	0.0119644i
$40$	0.310067	−	0.225277i	0.0490258	−	0.0356194i
$41$	−4.99395	−	3.62832i	−0.779924	−	0.566648i	0.125032	−	0.992153i	$-0.460096\pi$
$41$	−4.99395	−	3.62832i	−0.779924	−	0.566648i	−0.904956	+	0.425505i	$0.860096\pi$
$42$	0.0524557	+	0.161442i	0.00809409	+	0.0249110i
$43$	−1.03970			−0.158553			−0.0792764	−	0.996853i	$-0.525261\pi$
$43$	−1.03970			−0.158553			−0.0792764	+	0.996853i	$0.525261\pi$
$44$		0			0
$45$	0.397018			0.0591840
$46$	−0.713755	−	2.19671i	−0.105237	−	0.323887i
$47$	−7.67707	−	5.57771i	−1.11982	−	0.813593i	−0.135634	−	0.990759i	$-0.543307\pi$
$47$	−7.67707	−	5.57771i	−1.11982	−	0.813593i	−0.984181	+	0.177166i	$0.943307\pi$
$48$	−0.380047	+	0.276121i	−0.0548551	+	0.0398546i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	2.13384	−	6.56728i	0.301770	−	0.928753i
$51$	−0.141182	+	0.102575i	−0.0197695	+	0.0143633i
$52$	−0.0410660	−	0.0298362i	−0.00569483	−	0.00413754i
$53$	−0.205975	−	0.633926i	−0.0282928	−	0.0870764i	0.935913	−	0.352231i	$-0.114577\pi$
$53$	−0.205975	−	0.633926i	−0.0282928	−	0.0870764i	−0.964206	+	0.265155i	$0.914577\pi$
$54$	−1.01595			−0.138254
$55$		0			0
$56$	2.88158			0.385068
$57$	−0.271862	−	0.836705i	−0.0360090	−	0.110824i
$58$	5.01939	+	3.64680i	0.659078	+	0.478849i
$59$	−6.62338	+	4.81217i	−0.862291	+	0.626491i	−0.928507	−	0.371314i	$-0.878907\pi$
$59$	−6.62338	+	4.81217i	−0.862291	+	0.626491i	0.0662165	+	0.997805i	$0.478907\pi$
$60$	−0.000398366		0.00122604i	−5.14288e−5		0.000158282i
$61$	2.93506	−	9.03320i	0.375796	−	1.15658i	−0.567143	−	0.823619i	$-0.691951\pi$
$61$	2.93506	−	9.03320i	0.375796	−	1.15658i	0.942940	−	0.332963i	$-0.108049\pi$
$62$	−7.66024	+	5.56549i	−0.972852	+	0.706818i
$63$	2.41491	+	1.75454i	0.304251	+	0.221051i
$64$	2.56206	+	7.88521i	0.320257	+	0.985651i
$65$	0.0853139			0.0105819
$66$		0			0
$67$	12.0398			1.47089			0.735446	−	0.677583i	$-0.236973\pi$
$67$	12.0398			1.47089			0.735446	+	0.677583i	$0.236973\pi$
$68$	0.0348429	+	0.107235i	0.00422532	+	0.0130042i
$69$	0.165134	+	0.119977i	0.0198799	+	0.0144436i
$70$	−0.149132	+	0.108351i	−0.0178247	+	0.0129504i
$71$	1.49384	−	4.59758i	0.177287	−	0.545632i	−0.822444	−	0.568846i	$-0.807390\pi$
$71$	1.49384	−	4.59758i	0.177287	−	0.545632i	0.999731	+	0.0232143i	$0.00738999\pi$
$72$	−2.65802	+	8.18053i	−0.313250	+	0.964085i
$73$	7.16585	−	5.20629i	0.838699	−	0.609351i	−0.0833078	−	0.996524i	$-0.526548\pi$
$73$	7.16585	−	5.20629i	0.838699	−	0.609351i	0.922007	+	0.387173i	$0.126548\pi$
$74$	4.22563	+	3.07010i	0.491219	+	0.356891i
$75$	0.188571	+	0.580362i	0.0217743	+	0.0670144i
$76$	−0.568428			−0.0652032
$77$		0			0
$78$	−0.108884			−0.0123287
$79$	3.55081	+	10.9283i	0.399497	+	1.22953i	0.925403	+	0.378984i	$0.123726\pi$
$79$	3.55081	+	10.9283i	0.399497	+	1.22953i	−0.525906	+	0.850543i	$0.676274\pi$
$80$	−0.412707	−	0.299849i	−0.0461421	−	0.0335242i
$81$	−7.17211	+	5.21084i	−0.796901	+	0.578983i
$82$	−2.64373	+	8.13656i	−0.291951	+	0.898533i
$83$	2.96038	−	9.11111i	0.324944	−	1.00007i	−0.646522	−	0.762895i	$-0.723777\pi$
$83$	2.96038	−	9.11111i	0.324944	−	1.00007i	0.971466	−	0.237179i	$-0.0762227\pi$
$84$	−0.00784136	+	0.00569708i	−0.000855562	+	0.000621602i
$85$	−0.153315	−	0.111390i	−0.0166293	−	0.0120819i
$86$	0.445286	+	1.37045i	0.0480164	+	0.147779i
$87$	−0.548286			−0.0587824
$88$		0			0
$89$	−17.7001			−1.87621			−0.938104	−	0.346353i	$-0.887420\pi$
$89$	−17.7001			−1.87621			−0.938104	+	0.346353i	$0.887420\pi$
$90$	−0.170036	−	0.523317i	−0.0179234	−	0.0551625i
$91$	0.518933	+	0.377027i	0.0543989	+	0.0395231i
$92$	0.106696	−	0.0775190i	0.0111238	−	0.00808192i
$93$	0.258572	−	0.795802i	0.0268126	−	0.0825208i
$94$	−4.06414	+	12.5081i	−0.419184	+	1.29011i
$95$	0.772908	−	0.561551i	0.0792987	−	0.0576139i
$96$	−0.0443310	−	0.0322084i	−0.00452452	−	0.00328725i
$97$	2.03376	+	6.25927i	0.206497	+	0.635533i	0.999649	+	0.0265084i	$0.00843888\pi$
$97$	2.03376	+	6.25927i	0.206497	+	0.635533i	−0.793151	+	0.609024i	$0.791561\pi$
$98$	−1.38595			−0.140002
$99$		0			0
$100$	0.394278			0.0394278
$101$	5.75402	+	17.7091i	0.572547	+	1.76212i	0.644385	+	0.764701i	$0.277113\pi$
$101$	5.75402	+	17.7091i	0.572547	+	1.76212i	−0.0718388	+	0.997416i	$0.522887\pi$
$102$	0.195672	+	0.142164i	0.0193744	+	0.0140763i
$103$	5.60128	−	4.06957i	0.551910	−	0.400986i	−0.276579	−	0.960991i	$-0.589201\pi$
$103$	5.60128	−	4.06957i	0.551910	−	0.400986i	0.828489	+	0.560005i	$0.189201\pi$
$104$	−0.571172	+	1.75789i	−0.0560080	+	0.172375i
$105$	0.00503397	−	0.0154930i	0.000491265	−	0.00151196i
$106$	−0.747374	+	0.542999i	−0.0725914	+	0.0527408i
$107$	4.40466	+	3.20017i	0.425814	+	0.309372i	0.779973	−	0.625813i	$-0.215233\pi$
$107$	4.40466	+	3.20017i	0.425814	+	0.309372i	−0.354159	+	0.935185i	$0.615233\pi$
$108$	−0.0179259	−	0.0551701i	−0.00172492	−	0.00530875i
$109$	−9.22316			−0.883419			−0.441709	−	0.897158i	$-0.645628\pi$
$109$	−9.22316			−0.883419			−0.441709	+	0.897158i	$0.645628\pi$
$110$		0			0
$111$	−0.461580			−0.0438112
$112$	−1.18522	−	3.64775i	−0.111993	−	0.344680i
$113$	−7.59038	−	5.51474i	−0.714043	−	0.518783i	0.170432	−	0.985369i	$-0.445484\pi$
$113$	−7.59038	−	5.51474i	−0.714043	−	0.518783i	−0.884476	+	0.466587i	$0.845484\pi$
$114$	−0.986443	+	0.716693i	−0.0923889	+	0.0671244i
$115$	−0.0684962	+	0.210810i	−0.00638731	+	0.0196581i
$116$	−0.109471	+	0.336917i	−0.0101641	+	0.0312820i
$117$	−1.54901	+	1.12542i	−0.143206	+	0.104046i
$118$	9.17969	+	6.66944i	0.845059	+	0.613971i
$119$	−0.440294	−	1.35508i	−0.0403617	−	0.124220i
$120$	0.0469418			0.00428518
$121$		0			0
$122$	−13.1639			−1.19180
$123$	−0.233631	−	0.719043i	−0.0210658	−	0.0648339i
$124$	−0.437387	−	0.317780i	−0.0392785	−	0.0285375i
$125$	−1.07413	+	0.780398i	−0.0960727	+	0.0698009i
$126$	1.27842	−	3.93458i	0.113891	−	0.350521i
$127$	4.77616	−	14.6995i	0.423816	−	1.30437i	−0.480308	−	0.877100i	$-0.659475\pi$
$127$	4.77616	−	14.6995i	0.423816	−	1.30437i	0.904123	−	0.427271i	$-0.140525\pi$
$128$	8.57246	−	6.22826i	0.757706	−	0.550505i
$129$	−0.103022	−	0.0748495i	−0.00907054	−	0.00659013i
$130$	−0.0365385	−	0.112454i	−0.00320464	−	0.00986286i
$131$	17.6675			1.54362			0.771810	−	0.635854i	$-0.219352\pi$
$131$	17.6675			1.54362			0.771810	+	0.635854i	$0.219352\pi$
$132$		0			0
$133$	7.18297			0.622843
$134$	−5.15643	−	15.8699i	−0.445448	−	1.37095i
$135$	0.0788769	+	0.0573074i	0.00678865	+	0.00493224i
$136$	3.32161	−	2.41329i	0.284826	−	0.206938i
$137$	5.88131	−	18.1008i	0.502474	−	1.54646i	−0.302501	−	0.953149i	$-0.597822\pi$
$137$	5.88131	−	18.1008i	0.502474	−	1.54646i	0.804975	−	0.593308i	$-0.202178\pi$
$138$	0.0874200	−	0.269051i	0.00744169	−	0.0229032i
$139$	11.3800	−	8.26808i	0.965242	−	0.701289i	0.0108796	−	0.999941i	$-0.496537\pi$
$139$	11.3800	−	8.26808i	0.965242	−	0.701289i	0.954362	+	0.298652i	$0.0965369\pi$
$140$	−0.00851521	−	0.00618666i	−0.000719667	−	0.000522869i
$141$	−0.359155	−	1.10537i	−0.0302463	−	0.0930886i
$142$	−6.69994			−0.562247
$143$		0			0
$144$	11.4489			0.954072
$145$	−0.183990	−	0.566262i	−0.0152795	−	0.0470255i
$146$	−9.93153	−	7.21568i	−0.821939	−	0.597174i
$147$	0.0990877	−	0.0719914i	0.00817261	−	0.00593775i
$148$	−0.0921593	+	0.283637i	−0.00757544	+	0.0233148i
$149$	−3.41052	+	10.4965i	−0.279401	+	0.859907i	0.708621	+	0.705590i	$0.249318\pi$
$149$	−3.41052	+	10.4965i	−0.279401	+	0.859907i	−0.988021	+	0.154317i	$0.950682\pi$
$150$	0.684225	−	0.497118i	0.0558667	−	0.0405895i
$151$	13.0535	+	9.48391i	1.06228	+	0.771789i	0.974508	−	0.224351i	$-0.0720263\pi$
$151$	13.0535	+	9.48391i	1.06228	+	0.771789i	0.0877688	+	0.996141i	$0.472026\pi$
$152$	6.39614	+	19.6853i	0.518795	+	1.59669i
$153$	4.25309			0.343842
$154$		0			0
$155$	0.908663			0.0729856
$156$	−0.00192119	−	0.00591280i	−0.000153818	−	0.000473403i
$157$	12.0300	+	8.74029i	0.960096	+	0.697551i	0.953173	−	0.302425i	$-0.0977962\pi$
$157$	12.0300	+	8.74029i	0.960096	+	0.697551i	0.00692325	+	0.999976i	$0.497796\pi$
$158$	12.8840	−	9.36078i	1.02500	−	0.744704i
$159$	0.0252276	−	0.0776427i	0.00200068	−	0.00615747i
$160$	0.0183881	−	0.0565927i	0.00145371	−	0.00447405i
$161$	−1.34827	+	0.979573i	−0.106258	+	0.0772012i
$162$	9.94020	+	7.22198i	0.780976	+	0.567412i
$163$	−5.08454	−	15.6486i	−0.398252	−	1.22569i	−0.926400	−	0.376541i	$-0.877113\pi$
$163$	−5.08454	−	15.6486i	−0.398252	−	1.22569i	0.528148	−	0.849152i	$-0.322887\pi$
$164$	−0.488493			−0.0381449
$165$		0			0
$166$	−13.2774			−1.03053
$167$	−5.91825	−	18.2145i	−0.457968	−	1.40948i	−0.867615	−	0.497236i	$-0.834348\pi$
$167$	−5.91825	−	18.2145i	−0.457968	−	1.40948i	0.409648	−	0.912244i	$-0.365652\pi$
$168$	0.285529	+	0.207449i	0.0220291	+	0.0160051i
$169$	10.1844	−	7.39937i	0.783412	−	0.569182i
$170$	−0.0811628	+	0.249793i	−0.00622490	+	0.0191583i
$171$	−6.62568	+	20.3918i	−0.506679	+	1.55940i
$172$	−0.0665637	+	0.0483614i	−0.00507544	+	0.00368752i
$173$	−12.3169	−	8.94879i	−0.936440	−	0.680364i	0.0111210	−	0.999938i	$-0.496460\pi$
$173$	−12.3169	−	8.94879i	−0.936440	−	0.680364i	−0.947561	+	0.319575i	$0.896460\pi$
$174$	0.234821	+	0.722706i	0.0178018	+	0.0547882i
$175$	−4.98231			−0.376627
$176$		0			0
$177$	−1.00273			−0.0753698
$178$	7.58066	+	23.3309i	0.568194	+	1.74872i
$179$	−0.913077	−	0.663389i	−0.0682465	−	0.0495840i	0.553139	−	0.833089i	$-0.313430\pi$
$179$	−0.913077	−	0.663389i	−0.0682465	−	0.0495840i	−0.621385	+	0.783505i	$0.713430\pi$
$180$	0.0254179	−	0.0184672i	0.00189454	−	0.00137646i
$181$	5.70986	−	17.5731i	0.424410	−	1.30620i	−0.479147	−	0.877735i	$-0.659054\pi$
$181$	5.70986	−	17.5731i	0.424410	−	1.30620i	0.903558	−	0.428466i	$-0.140946\pi$
$182$	0.274716	−	0.845489i	0.0203633	−	0.0626718i
$183$	0.941141	−	0.683779i	0.0695712	−	0.0505464i
$184$	−3.88514	−	2.82272i	−0.286416	−	0.208094i
$185$	−0.154894	−	0.476714i	−0.0113880	−	0.0350487i
$186$	−1.15970			−0.0850336
$187$		0			0
$188$	−0.750947			−0.0547684
$189$	0.226521	+	0.697160i	0.0164770	+	0.0507109i
$190$	−1.07121	−	0.778283i	−0.0777141	−	0.0564626i
$191$	1.96576	−	1.42821i	0.142237	−	0.103342i	−0.514391	−	0.857556i	$-0.671982\pi$
$191$	1.96576	−	1.42821i	0.142237	−	0.103342i	0.656628	+	0.754214i	$0.271982\pi$
$192$	−0.313799	+	0.965773i	−0.0226465	+	0.0696987i
$193$	−0.0813717	+	0.250436i	−0.00585726	+	0.0180268i	−0.953942	−	0.299990i	$-0.903017\pi$
$193$	−0.0813717	+	0.250436i	−0.00585726	+	0.0180268i	0.948085	+	0.318017i	$0.103017\pi$
$194$	7.37944	−	5.36148i	0.529813	−	0.384932i
$195$	0.00845355	+	0.00614187i	0.000605372	+	0.000439828i
$196$	−0.0244542	−	0.0752624i	−0.00174673	−	0.00537588i
$197$	17.4681			1.24455			0.622276	−	0.782798i	$-0.286208\pi$
$197$	17.4681			1.24455			0.622276	+	0.782798i	$0.286208\pi$
$198$		0			0
$199$	−20.1415			−1.42780			−0.713898	−	0.700250i	$-0.753072\pi$
$199$	−20.1415			−1.42780			−0.713898	+	0.700250i	$0.753072\pi$
$200$	−4.43654	−	13.6543i	−0.313711	−	0.965502i
$201$	1.19299	+	0.866760i	0.0841473	+	0.0611366i
$202$	20.8783	−	15.1690i	1.46899	−	1.06729i
$203$	1.38334	−	4.25747i	0.0970911	−	0.298816i
$204$	−0.00426752	+	0.0131341i	−0.000298786	+	0.000919570i
$205$	0.664217	−	0.482582i	0.0463910	−	0.0337050i
$206$	−7.76310	−	5.64023i	−0.540881	−	0.392973i
$207$	−1.53725	−	4.73117i	−0.106846	−	0.328839i
$208$	2.46021			0.170585
$209$		0			0
$210$	−0.0225775			−0.00155800
$211$	−4.35102	−	13.3911i	−0.299536	−	0.921879i	−0.981660	−	0.190641i	$-0.938943\pi$
$211$	−4.35102	−	13.3911i	−0.299536	−	0.921879i	0.682123	−	0.731237i	$-0.261057\pi$
$212$	−0.0426738	−	0.0310043i	−0.00293085	−	0.00212939i
$213$	0.479007	−	0.348019i	0.0328210	−	0.0238459i
$214$	2.33177	−	7.17644i	0.159396	−	0.490572i
$215$	0.0427324	−	0.131517i	0.00291432	−	0.00896937i
$216$	−1.70889	+	1.24158i	−0.116275	+	0.0844791i
$217$	5.52706	+	4.01565i	0.375201	+	0.272600i
$218$	3.95012	+	12.1572i	0.267536	+	0.823391i
$219$	1.08486			0.0733078
$220$		0			0
$221$	0.913931			0.0614777
$222$	0.197687	+	0.608417i	0.0132679	+	0.0408343i
$223$	7.79378	+	5.66251i	0.521910	+	0.379190i	0.817323	−	0.576180i	$-0.195457\pi$
$223$	7.79378	+	5.66251i	0.521910	+	0.379190i	−0.295413	+	0.955370i	$0.595457\pi$
$224$	0.361948	−	0.262970i	0.0241836	−	0.0175704i
$225$	4.59576	−	14.1443i	0.306384	−	0.942953i
$226$	−4.01825	+	12.3669i	−0.267290	+	0.822634i
$227$	8.42119	−	6.11835i	0.558934	−	0.406089i	−0.272135	−	0.962259i	$-0.587730\pi$
$227$	8.42119	−	6.11835i	0.558934	−	0.406089i	0.831069	+	0.556170i	$0.187730\pi$
$228$	−0.0563242	−	0.0409220i	−0.00373016	−	0.00271012i
$229$	−2.88167	−	8.86887i	−0.190426	−	0.586072i	0.809573	−	0.587019i	$-0.199699\pi$
$229$	−2.88167	−	8.86887i	−0.190426	−	0.586072i	−1.00000		0.000947117i	$0.999699\pi$
$230$	0.307208			0.0202567
$231$		0			0
$232$	12.8996			0.846900
$233$	5.23969	+	16.1261i	0.343264	+	1.05646i	0.962507	+	0.271258i	$0.0874396\pi$
$233$	5.23969	+	16.1261i	0.343264	+	1.05646i	−0.619243	+	0.785199i	$0.712560\pi$
$234$	2.14686	+	1.55978i	0.140345	+	0.101966i
$235$	1.02108	−	0.741861i	0.0666082	−	0.0483937i
$236$	−0.200206	+	0.616169i	−0.0130323	+	0.0401092i
$237$	−0.434900	+	1.33848i	−0.0282498	+	0.0869439i
$238$	−1.59759	+	1.16072i	−0.103557	+	0.0752382i
$239$	−6.69837	−	4.86665i	−0.433281	−	0.314797i	0.349678	−	0.936870i	$-0.386291\pi$
$239$	−6.69837	−	4.86665i	−0.433281	−	0.314797i	−0.782960	+	0.622073i	$0.786291\pi$
$240$	−0.0193076	−	0.0594228i	−0.00124630	−	0.00383572i
$241$	9.31212			0.599846			0.299923	−	0.953963i	$-0.403039\pi$
$241$	9.31212			0.599846			0.299923	+	0.953963i	$0.403039\pi$
$242$		0			0
$243$	−3.28492			−0.210727
$244$	−0.232268	−	0.714847i	−0.0148694	−	0.0457634i
$245$	0.107603	+	0.0781781i	0.00687450	+	0.00499461i
$246$	−0.847724	+	0.615907i	−0.0540489	+	0.0392688i
$247$	−1.42377	+	4.38191i	−0.0905923	+	0.278815i
$248$	−6.08345	+	18.7229i	−0.386300	+	1.18891i
$249$	0.949258	−	0.689676i	0.0601568	−	0.0437065i
$250$	1.48869	+	1.08159i	0.0941528	+	0.0684060i
$251$	−1.52510	−	4.69377i	−0.0962633	−	0.296268i	0.891318	−	0.453379i	$-0.149782\pi$
$251$	−1.52510	−	4.69377i	−0.0962633	−	0.296268i	−0.987581	+	0.157112i	$0.949782\pi$
$252$	0.236220			0.0148804
$253$		0			0
$254$	−21.4213			−1.34409
$255$	−0.00717250	−	0.0220747i	−0.000449160	−	0.00138237i
$256$	1.53409	+	1.11458i	0.0958807	+	0.0696614i
$257$	13.6044	−	9.88415i	0.848617	−	0.616556i	−0.0761474	−	0.997097i	$-0.524262\pi$
$257$	13.6044	−	9.88415i	0.848617	−	0.616556i	0.924764	+	0.380540i	$0.124262\pi$
$258$	−0.0545382	+	0.167851i	−0.00339540	+	0.0104500i
$259$	1.16457	−	3.58419i	0.0723632	−	0.222711i
$260$	0.00546197	−	0.00396835i	0.000338737	−	0.000246107i
$261$	10.8105	+	7.85431i	0.669155	+	0.486170i
$262$	−7.56670	−	23.2879i	−0.467472	−	1.43873i
$263$	4.11162			0.253533			0.126767	−	0.991933i	$-0.459540\pi$
$263$	4.11162			0.253533			0.126767	+	0.991933i	$0.459540\pi$
$264$		0			0
$265$	0.0886540			0.00544597
$266$	−3.07634	−	9.46801i	−0.188623	−	0.580521i
$267$	−1.75386	−	1.27426i	−0.107335	−	0.0779832i
$268$	0.770811	−	0.560027i	0.0470847	−	0.0342091i
$269$	−7.40664	+	22.7953i	−0.451591	+	1.38985i	0.423500	+	0.905896i	$0.360801\pi$
$269$	−7.40664	+	22.7953i	−0.451591	+	1.38985i	−0.875091	+	0.483958i	$0.839199\pi$
$270$	0.0417564	−	0.128513i	0.00254121	−	0.00782105i
$271$	4.86050	−	3.53136i	0.295254	−	0.214515i	−0.430289	−	0.902691i	$-0.641588\pi$
$271$	4.86050	−	3.53136i	0.295254	−	0.214515i	0.725544	+	0.688176i	$0.241588\pi$
$272$	−4.42116	−	3.21216i	−0.268072	−	0.194766i
$273$	0.0242772	+	0.0747174i	0.00146932	+	0.00452210i
$274$	−26.3779			−1.59355
$275$		0			0
$276$	0.0161529			0.000972293
$277$	−2.83123	−	8.71363i	−0.170112	−	0.523552i	0.829264	−	0.558857i	$-0.188760\pi$
$277$	−2.83123	−	8.71363i	−0.170112	−	0.523552i	−0.999377	+	0.0353050i	$0.988760\pi$
$278$	−15.7722	−	11.4592i	−0.945953	−	0.687275i
$279$	−16.4983	+	11.9867i	−0.987726	+	0.717625i
$280$	−0.118435	+	0.364505i	−0.00707784	+	0.0217834i
$281$	4.00423	−	12.3237i	0.238872	−	0.735173i	−0.757712	−	0.652589i	$-0.773683\pi$
$281$	4.00423	−	12.3237i	0.238872	−	0.735173i	0.996584	−	0.0825836i	$-0.0263172\pi$
$282$	−1.30318	+	0.946818i	−0.0776034	+	0.0563822i
$283$	3.06440	+	2.22642i	0.182160	+	0.132347i	0.675128	−	0.737700i	$-0.264088\pi$
$283$	3.06440	+	2.22642i	0.182160	+	0.132347i	−0.492969	+	0.870047i	$0.664088\pi$
$284$	−0.118216	−	0.363832i	−0.00701483	−	0.0215894i
$285$	0.117013			0.00693122
$286$		0			0
$287$	6.17286			0.364372
$288$	0.412681	+	1.27010i	0.0243175	+	0.0748415i
$289$	12.1109	+	8.79908i	0.712405	+	0.517593i
$290$	−0.667602	+	0.485041i	−0.0392029	+	0.0284826i
$291$	−0.249093	+	0.766630i	−0.0146021	+	0.0449407i
$292$	0.216603	−	0.666635i	0.0126757	−	0.0390118i
$293$	−17.2879	+	12.5604i	−1.00997	+	0.733785i	−0.964202	−	0.265168i	$-0.914573\pi$
$293$	−17.2879	+	12.5604i	−1.00997	+	0.733785i	−0.0457656	+	0.998952i	$0.514573\pi$
$294$	−0.137331	−	0.0997767i	−0.00800930	−	0.00581909i
$295$	−0.336489	−	1.03561i	−0.0195911	−	0.0602953i
$296$	10.8597			0.631205
$297$		0			0
$298$	15.2963			0.886091
$299$	−0.330334	−	1.01667i	−0.0191037	−	0.0587953i
$300$	0.0390681	+	0.0283846i	0.00225560	+	0.00163879i
$301$	0.841136	−	0.611121i	0.0484822	−	0.0352244i
$302$	6.91034	−	21.2678i	0.397645	−	1.22383i
$303$	−0.704747	+	2.16899i	−0.0404867	+	0.124605i
$304$	22.2885	−	16.1935i	1.27833	−	0.928761i
$305$	1.02202	+	0.742540i	0.0585207	+	0.0425177i
$306$	−1.82152	−	5.60608i	−0.104130	−	0.320478i
$307$	−8.44677			−0.482082			−0.241041	−	0.970515i	$-0.577489\pi$
$307$	−8.44677			−0.482082			−0.241041	+	0.970515i	$0.577489\pi$
$308$		0			0
$309$	0.847991			0.0482405
$310$	−0.389165	−	1.19773i	−0.0221031	−	0.0680263i
$311$	−14.5777	−	10.5913i	−0.826624	−	0.600577i	0.0919783	−	0.995761i	$-0.470681\pi$
$311$	−14.5777	−	10.5913i	−0.826624	−	0.600577i	−0.918602	+	0.395184i	$0.870681\pi$
$312$	−0.183149	+	0.133065i	−0.0103688	+	0.00753335i
$313$	0.0730332	−	0.224773i	0.00412808	−	0.0127049i	−0.948971	−	0.315363i	$-0.897874\pi$
$313$	0.0730332	−	0.224773i	0.00412808	−	0.0127049i	0.953099	+	0.302658i	$0.0978739\pi$
$314$	6.36851	−	19.6003i	0.359396	−	1.10611i
$315$	−0.321194	+	0.233361i	−0.0180973	+	0.0131484i
$316$	0.735655	+	0.534485i	0.0413838	+	0.0300671i
$317$	5.28206	+	16.2565i	0.296670	+	0.913056i	0.982655	+	0.185441i	$0.0593714\pi$
$317$	5.28206	+	16.2565i	0.296670	+	0.913056i	−0.685985	+	0.727615i	$0.740629\pi$
$318$	−0.113147			−0.00634496
$319$		0			0
$320$	−1.10274			−0.0616450
$321$	0.206062	+	0.634195i	0.0115013	+	0.0353973i
$322$	1.86863	+	1.35764i	0.104135	+	0.0756584i
$323$	8.27984	−	6.01565i	0.460703	−	0.334720i
$324$	−0.216792	+	0.667217i	−0.0120440	+	0.0370676i
$325$	0.987567	−	3.03942i	0.0547804	−	0.168597i
$326$	−18.4491	+	13.4041i	−1.02180	+	0.742382i
$327$	−0.913902	−	0.663988i	−0.0505389	−	0.0367186i
$328$	5.49667	+	16.9170i	0.303503	+	0.934086i
$329$	9.48937			0.523166
$330$		0			0
$331$	4.41186			0.242498			0.121249	−	0.992622i	$-0.461310\pi$
$331$	4.41186			0.242498			0.121249	+	0.992622i	$0.461310\pi$
$332$	−0.234271	−	0.721012i	−0.0128573	−	0.0395707i
$333$	9.10095	+	6.61223i	0.498729	+	0.362348i
$334$	−21.4742	+	15.6019i	−1.17502	+	0.853699i
$335$	−0.494843	+	1.52297i	−0.0270361	+	0.0832087i
$336$	0.145165	−	0.446773i	0.00791941	−	0.0243734i
$337$	−22.4809	+	16.3333i	−1.22461	+	0.889733i	−0.996475	−	0.0838961i	$-0.973264\pi$
$337$	−22.4809	+	16.3333i	−1.22461	+	0.889733i	−0.228138	+	0.973629i	$0.573264\pi$
$338$	−14.1150	−	10.2552i	−0.767757	−	0.557808i
$339$	−0.355100	−	1.09289i	−0.0192864	−	0.0593574i
$340$	−0.0149968			−0.000813315
$341$		0			0
$342$	29.7164			1.60688
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	2.42380	+	1.76100i	0.130683	+	0.0949465i
$345$	−0.0219636	+	0.0159575i	−0.00118248	+	0.000859123i
$346$	−6.52043	+	20.0678i	−0.350540	+	1.07885i
$347$	9.65724	−	29.7219i	0.518428	−	1.59556i	−0.258530	−	0.966003i	$-0.583238\pi$
$347$	9.65724	−	29.7219i	0.518428	−	1.59556i	0.776958	−	0.629553i	$-0.216762\pi$
$348$	−0.0351024	+	0.0255034i	−0.00188168	+	0.00136712i
$349$	0.439651	+	0.319425i	0.0235340	+	0.0170984i	0.599490	−	0.800382i	$-0.295370\pi$
$349$	0.439651	+	0.319425i	0.0235340	+	0.0170984i	−0.575956	+	0.817481i	$0.695370\pi$
$350$	2.13384	+	6.56728i	0.114058	+	0.351036i
$351$	−0.470197			−0.0250972
$352$		0			0
$353$	−17.8517			−0.950148			−0.475074	−	0.879946i	$-0.657579\pi$
$353$	−17.8517			−0.950148			−0.475074	+	0.879946i	$0.657579\pi$
$354$	0.429452	+	1.32172i	0.0228251	+	0.0702485i
$355$	0.520171	+	0.377927i	0.0276078	+	0.0200583i
$356$	−1.13320	+	0.823316i	−0.0600593	+	0.0436356i
$357$	0.0539268	−	0.165970i	0.00285411	−	0.00878404i
$358$	−0.483371	+	1.48766i	−0.0255469	+	0.0786254i
$359$	9.70081	−	7.04805i	0.511989	−	0.371982i	−0.301588	−	0.953438i	$-0.597517\pi$
$359$	9.70081	−	7.04805i	0.511989	−	0.371982i	0.813578	+	0.581456i	$0.197517\pi$
$360$	−0.925549	−	0.672450i	−0.0487807	−	0.0354413i
$361$	10.0724	+	30.9998i	0.530128	+	1.63157i
$362$	−25.6089			−1.34598
$363$		0			0
$364$	0.0507604			0.00266057
$365$	0.364048	+	1.12042i	0.0190551	+	0.0586457i
$366$	−1.30438	−	0.947685i	−0.0681809	−	0.0495363i
$367$	−23.9435	+	17.3960i	−1.24984	+	0.908062i	−0.998213	−	0.0597620i	$-0.980966\pi$
$367$	−23.9435	+	17.3960i	−1.24984	+	0.908062i	−0.251628	+	0.967824i	$0.580966\pi$
$368$	−1.97523	+	6.07915i	−0.102966	+	0.316897i
$369$	−5.69394	+	17.5241i	−0.296415	+	0.912271i
$370$	−0.562027	+	0.408337i	−0.0292184	+	0.0212284i
$371$	0.539250	+	0.391788i	0.0279964	+	0.0203406i
$372$	−0.0204622	−	0.0629762i	−0.00106092	−	0.00326516i
$373$	10.5209			0.544753			0.272377	−	0.962191i	$-0.412190\pi$
$373$	10.5209			0.544753			0.272377	+	0.962191i	$0.412190\pi$
$374$		0			0
$375$	−0.162615			−0.00839738
$376$	8.44989	+	26.0061i	0.435770	+	1.34116i
$377$	2.32304	+	1.68779i	0.119643	+	0.0869254i
$378$	0.821925	−	0.597163i	0.0422752	−	0.0307148i
$379$	−2.58002	+	7.94050i	−0.132527	+	0.407876i	−0.995197	−	0.0978908i	$-0.968790\pi$
$379$	−2.58002	+	7.94050i	−0.132527	+	0.407876i	0.862670	+	0.505767i	$0.168790\pi$
$380$	0.0233628	−	0.0719032i	0.00119848	−	0.00368856i
$381$	1.53150	−	1.11270i	0.0784610	−	0.0570053i
$382$	−2.72445	−	1.97943i	−0.139395	−	0.101276i
$383$	−5.70870	−	17.5696i	−0.291701	−	0.897764i	−0.984310	−	0.176450i	$-0.943539\pi$
$383$	−5.70870	−	17.5696i	−0.291701	−	0.897764i	0.692609	−	0.721314i	$-0.256461\pi$
$384$	1.29781			0.0662284
$385$		0			0
$386$	0.364955			0.0185757
$387$	0.959036	+	2.95161i	0.0487505	+	0.150039i
$388$	0.421354	+	0.306131i	0.0213910	+	0.0155415i
$389$	−18.8145	+	13.6695i	−0.953934	+	0.693074i	−0.951734	−	0.306924i	$-0.900700\pi$
$389$	−18.8145	+	13.6695i	−0.953934	+	0.693074i	−0.00219987	+	0.999998i	$0.500700\pi$
$390$	0.00447520	−	0.0137732i	0.000226611	−	0.000697436i
$391$	−0.733771	+	2.25832i	−0.0371084	+	0.114208i
$392$	−2.33125	+	1.69375i	−0.117746	+	0.0855474i
$393$	1.75063	+	1.27191i	0.0883078	+	0.0641594i
$394$	−7.48130	−	23.0251i	−0.376902	−	1.15999i
$395$	−1.52831			−0.0768976
$396$		0			0
$397$	21.6794			1.08806			0.544029	−	0.839066i	$-0.316898\pi$
$397$	21.6794			1.08806			0.544029	+	0.839066i	$0.316898\pi$
$398$	8.62627	+	26.5489i	0.432396	+	1.33078i
$399$	0.711744	+	0.517112i	0.0356318	+	0.0258880i
$400$	−15.4599	+	11.2323i	−0.772995	+	0.561614i
$401$	−10.7561	+	33.1039i	−0.537135	+	1.65313i	0.201855	+	0.979415i	$0.435303\pi$
$401$	−10.7561	+	33.1039i	−0.537135	+	1.65313i	−0.738990	+	0.673717i	$0.764697\pi$
$402$	0.631555	−	1.94373i	0.0314991	−	0.0969443i
$403$	−3.54526	+	2.57578i	−0.176602	+	0.128309i
$404$	1.19212	+	0.866123i	0.0593100	+	0.0430912i
$405$	−0.364366	−	1.12140i	−0.0181055	−	0.0557230i
$406$	−6.20431			−0.307915
$407$		0			0
$408$	0.502867			0.0248956
$409$	5.03471	+	15.4952i	0.248950	+	0.766190i	0.994962	+	0.100257i	$0.0319665\pi$
$409$	5.03471	+	15.4952i	0.248950	+	0.766190i	−0.746011	+	0.665933i	$0.768033\pi$
$410$	−0.920574	−	0.668836i	−0.0454639	−	0.0330315i
$411$	1.88587	−	1.37016i	0.0930231	−	0.0675852i
$412$	0.169310	−	0.521084i	0.00834132	−	0.0256719i
$413$	2.52991	−	7.78625i	0.124489	−	0.383136i
$414$	−5.57787	+	4.05256i	−0.274137	+	0.199172i
$415$	1.03083	+	0.748945i	0.0506016	+	0.0367642i
$416$	0.0886796	+	0.272928i	0.00434788	+	0.0133814i
$417$	1.72285			0.0843684
$418$		0			0
$419$	−22.6536			−1.10670			−0.553350	−	0.832949i	$-0.686651\pi$
$419$	−22.6536			−1.10670			−0.553350	+	0.832949i	$0.686651\pi$
$420$	−0.000398366	−	0.00122604i	−1.94383e−5	−	5.98248e-5i
$421$	12.3020	+	8.93795i	0.599564	+	0.435609i	0.845724	−	0.533620i	$-0.179169\pi$
$421$	12.3020	+	8.93795i	0.599564	+	0.435609i	−0.246160	+	0.969229i	$0.579169\pi$
$422$	−15.7875	+	11.4703i	−0.768526	+	0.558367i
$423$	−8.75314	+	26.9394i	−0.425592	+	1.30984i
$424$	−0.593534	+	1.82671i	−0.0288246	+	0.0887129i
$425$	−5.74313	+	4.17263i	−0.278583	+	0.202402i
$426$	−0.663882	−	0.482338i	−0.0321652	−	0.0233694i
$427$	2.93506	+	9.03320i	0.142038	+	0.437147i
$428$	0.430850			0.0208259
$429$		0			0
$430$	−0.191656			−0.00924249
$431$	−0.990988	−	3.04995i	−0.0477342	−	0.146911i	0.924348	−	0.381549i	$-0.124609\pi$
$431$	−0.990988	−	3.04995i	−0.0477342	−	0.146911i	−0.972083	+	0.234639i	$0.924609\pi$
$432$	2.27458	+	1.65258i	0.109436	+	0.0795099i
$433$	−4.84800	+	3.52228i	−0.232980	+	0.169270i	−0.698150	−	0.715951i	$-0.745993\pi$
$433$	−4.84800	+	3.52228i	−0.232980	+	0.169270i	0.465170	+	0.885221i	$0.345993\pi$
$434$	2.92595	−	9.00516i	0.140450	−	0.432261i
$435$	0.0225349	−	0.0693553i	0.00108047	−	0.00332533i
$436$	−0.590485	+	0.429013i	−0.0282791	+	0.0205460i
$437$	−9.68456	−	7.03624i	−0.463275	−	0.336589i
$438$	−0.464625	−	1.42997i	−0.0222007	−	0.0683266i
$439$	−7.68712			−0.366886			−0.183443	−	0.983030i	$-0.558724\pi$
$439$	−7.68712			−0.366886			−0.183443	+	0.983030i	$0.558724\pi$
$440$		0			0
$441$	−2.98500			−0.142143
$442$	−0.391421	−	1.20467i	−0.0186180	−	0.0573003i
$443$	−30.1358	−	21.8950i	−1.43180	−	1.04026i	−0.989679	−	0.143303i	$-0.954228\pi$
$443$	−30.1358	−	21.8950i	−1.43180	−	1.04026i	−0.442117	−	0.896957i	$-0.645772\pi$
$444$	−0.0295513	+	0.0214703i	−0.00140244	+	0.00101893i
$445$	0.727486	−	2.23897i	0.0344861	−	0.106137i
$446$	4.12592	−	12.6983i	0.195368	−	0.601281i
$447$	−1.09360	+	0.794546i	−0.0517254	+	0.0375807i
$448$	−6.70756	−	4.87333i	−0.316902	−	0.230243i
$449$	3.42156	+	10.5305i	0.161473	+	0.496964i	0.998759	−	0.0498016i	$-0.0158589\pi$
$449$	3.42156	+	10.5305i	0.161473	+	0.496964i	−0.837286	+	0.546766i	$0.815859\pi$
$450$	−20.6121			−0.971666
$451$		0			0
$452$	−0.742468			−0.0349228
$453$	0.610679	+	1.87948i	0.0286922	+	0.0883055i
$454$	−11.6714	−	8.47975i	−0.547764	−	0.397974i
$455$	−0.0690204	+	0.0501462i	−0.00323573	+	0.00235089i
$456$	−0.783393	+	2.41104i	−0.0366857	+	0.112907i
$457$	8.77488	−	27.0063i	0.410472	−	1.26330i	−0.505768	−	0.862670i	$-0.668791\pi$
$457$	8.77488	−	27.0063i	0.410472	−	1.26330i	0.916239	−	0.400632i	$-0.131209\pi$
$458$	−10.4561	+	7.59677i	−0.488580	+	0.354974i
$459$	0.844975	+	0.613910i	0.0394401	+	0.0286549i
$460$	0.00542049	+	0.0166825i	0.000252732	+	0.000777828i
$461$	−25.7420			−1.19892			−0.599462	−	0.800403i	$-0.704619\pi$
$461$	−25.7420			−1.19892			−0.599462	+	0.800403i	$0.704619\pi$
$462$		0			0
$463$	37.6543			1.74995			0.874973	−	0.484172i	$-0.160879\pi$
$463$	37.6543			1.74995			0.874973	+	0.484172i	$0.160879\pi$
$464$	−5.30574	−	16.3294i	−0.246313	−	0.758072i
$465$	0.0900373	+	0.0654159i	0.00417538	+	0.00303359i
$466$	19.0121	−	13.8131i	0.880717	−	0.639879i
$467$	−4.75498	+	14.6343i	−0.220034	+	0.677196i	0.778723	+	0.627367i	$0.215868\pi$
$467$	−4.75498	+	14.6343i	−0.220034	+	0.677196i	−0.998758	+	0.0498289i	$0.984132\pi$
$468$	−0.0468222	+	0.144104i	−0.00216436	+	0.00666120i
$469$	−9.74038	+	7.07680i	−0.449769	+	0.326776i
$470$	−1.41517	−	1.02818i	−0.0652771	−	0.0474266i
$471$	0.562796	+	1.73211i	0.0259323	+	0.0798114i
$472$	23.5914			1.08588
$473$		0			0
$474$	1.95054			0.0895914
$475$	−11.0590	−	34.0362i	−0.507423	−	1.56169i
$476$	−0.0912198	−	0.0662751i	−0.00418105	−	0.00303771i
$477$	−1.60966	+	1.16949i	−0.0737012	+	0.0535471i
$478$	−3.54603	+	10.9135i	−0.162191	+	0.499174i
$479$	−0.185465	+	0.570803i	−0.00847412	+	0.0260807i	−0.955204	−	0.295948i	$-0.904365\pi$
$479$	−0.185465	+	0.570803i	−0.00847412	+	0.0260807i	0.946730	+	0.322028i	$0.104365\pi$
$480$	0.00589622	−	0.00428386i	0.000269125	−	0.000195530i
$481$	1.95567	+	1.42088i	0.0891710	+	0.0647865i
$482$	−3.98822	−	12.2745i	−0.181658	−	0.559087i
$483$	−0.204117			−0.00928767
$484$		0			0
$485$	−0.875354			−0.0397478
$486$	1.40687	+	4.32991i	0.0638171	+	0.196409i
$487$	−8.33216	−	6.05367i	−0.377566	−	0.274318i	0.382775	−	0.923842i	$-0.374968\pi$
$487$	−8.33216	−	6.05367i	−0.377566	−	0.274318i	−0.760341	+	0.649524i	$0.774968\pi$
$488$	−22.1424	+	16.0874i	−1.00234	+	0.728241i
$489$	0.622750	−	1.91663i	0.0281617	−	0.0866729i
$490$	0.0569635	−	0.175316i	0.00257335	−	0.00791996i
$491$	8.16497	−	5.93220i	0.368480	−	0.267716i	−0.388100	−	0.921617i	$-0.626869\pi$
$491$	8.16497	−	5.93220i	0.368480	−	0.267716i	0.756580	+	0.653901i	$0.226869\pi$
$492$	−0.0484036	−	0.0351673i	−0.00218220	−	0.00158546i
$493$	−1.97100	−	6.06613i	−0.0887696	−	0.273205i
$494$	6.38566			0.287304
$495$		0			0
$496$	26.2032			1.17656
$497$	1.49384	+	4.59758i	0.0670080	+	0.206229i
$498$	−1.31563	−	0.955859i	−0.0589546	−	0.0428331i
$499$	−16.0149	+	11.6355i	−0.716926	+	0.520877i	−0.885401	−	0.464829i	$-0.846116\pi$
$499$	−16.0149	+	11.6355i	−0.716926	+	0.520877i	0.168474	+	0.985706i	$0.446116\pi$
$500$	−0.0324677	+	0.0999252i	−0.00145200	+	0.00446879i
$501$	0.724862	−	2.23089i	0.0323844	−	0.0996690i
$502$	−5.53377	+	4.02052i	−0.246984	+	0.179445i
$503$	11.5717	+	8.40733i	0.515956	+	0.374864i	0.815078	−	0.579351i	$-0.196694\pi$
$503$	11.5717	+	8.40733i	0.515956	+	0.374864i	−0.299122	+	0.954215i	$0.596694\pi$
$504$	−2.65802	−	8.18053i	−0.118397	−	0.364390i
$505$	−2.47660			−0.110207
$506$		0			0
$507$	1.54184			0.0684753
$508$	−0.377964	−	1.16325i	−0.0167695	−	0.0516111i
$509$	34.0576	+	24.7443i	1.50958	+	1.09677i	0.966364	+	0.257178i	$0.0827927\pi$
$509$	34.0576	+	24.7443i	1.50958	+	1.09677i	0.543214	+	0.839594i	$0.317207\pi$
$510$	−0.0260252	+	0.0189084i	−0.00115242	+	0.000837279i
$511$	−2.73711	+	8.42396i	−0.121083	+	0.372654i
$512$	7.36090	−	22.6545i	0.325309	−	1.00120i
$513$	−4.25979	+	3.09492i	−0.188074	+	0.136644i
$514$	−18.8550	−	13.6990i	−0.831659	−	0.604235i
$515$	0.284563	+	0.875794i	0.0125393	+	0.0385921i
$516$	−0.0100772			−0.000443626
$517$		0			0
$518$	−5.22316			−0.229492
$519$	−0.576222	−	1.77343i	−0.0252933	−	0.0778449i
$520$	−0.198888	−	0.144501i	−0.00872181	−	0.00633677i
$521$	17.3512	−	12.6064i	0.760168	−	0.552294i	−0.138794	−	0.990321i	$-0.544323\pi$
$521$	17.3512	−	12.6064i	0.760168	−	0.552294i	0.898962	+	0.438027i	$0.144323\pi$
$522$	5.72295	−	17.6134i	0.250487	−	0.770919i
$523$	−10.9993	+	33.8525i	−0.480968	+	1.48027i	0.356769	+	0.934193i	$0.383878\pi$
$523$	−10.9993	+	33.8525i	−0.480968	+	1.48027i	−0.837737	+	0.546074i	$0.816122\pi$
$524$	1.13111	−	0.821800i	0.0494128	−	0.0359005i
$525$	−0.493685	−	0.358684i	−0.0215462	−	0.0156542i
$526$	−1.76094	−	5.41960i	−0.0767804	−	0.236306i
$527$	9.73412			0.424025
$528$		0			0
$529$	−20.2226			−0.879244
$530$	−0.0379690	−	0.116857i	−0.00164927	−	0.00507593i
$531$	19.7708	+	14.3643i	0.857979	+	0.623358i
$532$	0.459868	−	0.334114i	0.0199378	−	0.0144857i
$533$	−1.22355	+	3.76570i	−0.0529979	+	0.163111i
$534$	−0.928472	+	2.85754i	−0.0401789	+	0.123658i
$535$	−0.585839	+	0.425637i	−0.0253280	+	0.0184019i
$536$	−28.0677	−	20.3924i	−1.21234	−	0.880817i
$537$	−0.0427163	−	0.131467i	−0.00184335	−	0.00567323i
$538$	33.2191			1.43218
$539$		0			0
$540$	0.00771550			0.000332022
$541$	5.23320	+	16.1061i	0.224993	+	0.692457i	0.998292	+	0.0584158i	$0.0186049\pi$
$541$	5.23320	+	16.1061i	0.224993	+	0.692457i	−0.773300	+	0.634041i	$0.781395\pi$
$542$	−6.73642	−	4.89430i	−0.289354	−	0.210228i
$543$	1.83089	−	1.33022i	0.0785711	−	0.0570852i
$544$	0.196984	−	0.606254i	0.00844561	−	0.0259929i
$545$	0.379078	−	1.16668i	0.0162379	−	0.0499752i
$546$	0.0880889	−	0.0640004i	0.00376986	−	0.00273896i
$547$	7.11192	+	5.16711i	0.304084	+	0.220930i	0.729354	−	0.684137i	$-0.239821\pi$
$547$	7.11192	+	5.16711i	0.304084	+	0.220930i	−0.425270	+	0.905067i	$0.639821\pi$
$548$	−0.465421	−	1.43242i	−0.0198818	−	0.0611899i
$549$	−28.3517			−1.21002
$550$		0			0
$551$	32.1551			1.36985
$552$	−0.181758	−	0.559394i	−0.00773614	−	0.0238094i
$553$	−9.29614	−	6.75404i	−0.395312	−	0.287211i
$554$	−10.2730	+	7.46380i	−0.436460	+	0.317107i
$555$	0.0189712	−	0.0583875i	0.000805284	−	0.00247841i
$556$	0.343985	−	1.05868i	0.0145882	−	0.0448979i
$557$	−17.5780	+	12.7712i	−0.744805	+	0.541132i	−0.894212	−	0.447643i	$-0.852263\pi$
$557$	−17.5780	+	12.7712i	−0.744805	+	0.541132i	0.149407	+	0.988776i	$0.452263\pi$
$558$	22.8658	+	16.6130i	0.967987	+	0.703284i
$559$	0.206084	+	0.634261i	0.00871642	+	0.0268264i
$560$	0.510134			0.0215571
$561$		0			0
$562$	−17.9591			−0.757559
$563$	−0.562827	−	1.73220i	−0.0237203	−	0.0730036i	0.938496	−	0.345291i	$-0.112220\pi$
$563$	−0.562827	−	1.73220i	−0.0237203	−	0.0730036i	−0.962216	+	0.272288i	$0.912220\pi$
$564$	−0.0744096	−	0.0540617i	−0.00313321	−	0.00227641i
$565$	1.00956	−	0.733485i	0.0424723	−	0.0308579i
$566$	1.62225	−	4.99278i	0.0681884	−	0.209862i
$567$	2.73950	−	8.43132i	0.115048	−	0.354082i
$568$	−11.2697	+	8.18790i	−0.472865	+	0.343557i
$569$	−26.6505	−	19.3627i	−1.11725	−	0.811726i	−0.133456	−	0.991055i	$-0.542608\pi$
$569$	−26.6505	−	19.3627i	−1.11725	−	0.811726i	−0.983789	+	0.179328i	$0.942608\pi$
$570$	−0.0501145	−	0.154236i	−0.00209906	−	0.00646025i
$571$	−23.4394			−0.980908			−0.490454	−	0.871467i	$-0.663169\pi$
$571$	−23.4394			−0.980908			−0.490454	+	0.871467i	$0.663169\pi$
$572$		0			0
$573$	0.297601			0.0124325
$574$	−2.64373	−	8.13656i	−0.110347	−	0.339614i
$575$	6.71748	+	4.88054i	0.280138	+	0.203532i
$576$	20.0221	−	14.5469i	0.834252	−	0.606120i
$577$	10.6468	−	32.7676i	0.443233	−	1.36413i	−0.441177	−	0.897420i	$-0.645439\pi$
$577$	10.6468	−	32.7676i	0.443233	−	1.36413i	0.884410	−	0.466711i	$-0.154561\pi$
$578$	6.41135	−	19.7321i	0.266677	−	0.820747i
$579$	−0.0260922	+	0.0189571i	−0.00108435	+	0.000787830i
$580$	−0.0381189	−	0.0276950i	−0.00158280	−	0.00114997i
$581$	2.96038	+	9.11111i	0.122817	+	0.377992i
$582$	1.11719			0.0463091
$583$		0			0
$584$	−25.5236			−1.05617
$585$	−0.0786948	−	0.242198i	−0.00325363	−	0.0100136i
$586$	23.9602	+	17.4081i	0.989785	+	0.719121i
$587$	16.8818	−	12.2653i	0.696786	−	0.506244i	−0.182098	−	0.983280i	$-0.558289\pi$
$587$	16.8818	−	12.2653i	0.696786	−	0.506244i	0.878884	+	0.477036i	$0.158289\pi$
$588$	0.00299513	−	0.00921807i	0.000123517	−	0.000380147i
$589$	−15.1643	+	46.6710i	−0.624835	+	1.92304i
$590$	−1.22094	+	0.887065i	−0.0502653	+	0.0365199i
$591$	1.73088	+	1.25755i	0.0711987	+	0.0517289i
$592$	−4.46669	−	13.7471i	−0.183580	−	0.565000i
$593$	26.6381			1.09389			0.546947	−	0.837167i	$-0.315790\pi$
$593$	26.6381			1.09389			0.546947	+	0.837167i	$0.315790\pi$
$594$		0			0
$595$	0.189507			0.00776905
$596$	0.269893	+	0.830646i	0.0110553	+	0.0340246i
$597$	−1.99578	−	1.45002i	−0.0816817	−	0.0593453i
$598$	−1.19861	+	0.870840i	−0.0490148	+	0.0356113i
$599$	−6.38775	+	19.6595i	−0.260996	+	0.803264i	0.731592	+	0.681742i	$0.238777\pi$
$599$	−6.38775	+	19.6595i	−0.260996	+	0.803264i	−0.992589	+	0.121522i	$0.961223\pi$
$600$	0.543383	−	1.67236i	0.0221835	−	0.0682739i
$601$	4.00312	−	2.90843i	0.163290	−	0.118637i	−0.503139	−	0.864205i	$-0.667822\pi$
$601$	4.00312	−	2.90843i	0.163290	−	0.118637i	0.666430	+	0.745568i	$0.267822\pi$
$602$	−1.16577	−	0.846984i	−0.0475134	−	0.0345205i
$603$	−11.1057	−	34.1798i	−0.452258	−	1.39191i
$604$	1.27685			0.0519543
$605$		0			0
$606$	3.16082			0.128399
$607$	−8.53154	−	26.2574i	−0.346285	−	1.06575i	−0.960893	−	0.276922i	$-0.910686\pi$
$607$	−8.53154	−	26.2574i	−0.346285	−	1.06575i	0.614608	−	0.788833i	$-0.289314\pi$
$608$	2.59986	+	1.88891i	0.105438	+	0.0766053i
$609$	0.443573	−	0.322274i	0.0179745	−	0.0130592i
$610$	0.541043	−	1.66516i	0.0219062	−	0.0674204i
$611$	−1.88093	+	5.78892i	−0.0760944	+	0.234195i
$612$	0.272291	−	0.197831i	0.0110067	−	0.00799685i
$613$	−5.81617	−	4.22570i	−0.234913	−	0.170674i	0.464101	−	0.885782i	$-0.346377\pi$
$613$	−5.81617	−	4.22570i	−0.234913	−	0.170674i	−0.699014	+	0.715108i	$0.746377\pi$
$614$	3.61760	+	11.1338i	0.145995	+	0.449325i
$615$	0.100558			0.00405487
$616$		0			0
$617$	21.1215			0.850320			0.425160	−	0.905118i	$-0.360218\pi$
$617$	21.1215			0.850320			0.425160	+	0.905118i	$0.360218\pi$
$618$	−0.363180	−	1.11775i	−0.0146092	−	0.0449626i
$619$	−2.24431	−	1.63059i	−0.0902064	−	0.0655388i	0.541768	−	0.840528i	$-0.317755\pi$
$619$	−2.24431	−	1.63059i	−0.0902064	−	0.0655388i	−0.631974	+	0.774989i	$0.717755\pi$
$620$	0.0581744	−	0.0422662i	0.00233634	−	0.00169745i
$621$	0.377508	−	1.16185i	0.0151489	−	0.0466235i
$622$	−7.71723	+	23.7512i	−0.309433	+	0.952336i
$623$	14.3197	−	10.4039i	0.573706	−	0.416822i
$624$	0.243776	+	0.177114i	0.00975886	+	0.00709022i
$625$	7.64352	+	23.5243i	0.305741	+	0.940974i
$626$	−0.327556			−0.0130918
$627$		0			0
$628$	1.17673			0.0469568
$629$	−1.65931	−	5.10683i	−0.0661610	−	0.203623i
$630$	0.445160	+	0.323428i	0.0177356	+	0.0128857i
$631$	19.5855	−	14.2297i	0.779685	−	0.566474i	−0.125200	−	0.992132i	$-0.539957\pi$
$631$	19.5855	−	14.2297i	0.779685	−	0.566474i	0.904884	+	0.425657i	$0.139957\pi$
$632$	10.2320	−	31.4907i	0.407005	−	1.25263i
$633$	0.532909	−	1.64012i	0.0211812	−	0.0651891i
$634$	19.1658	−	13.9248i	0.761171	−	0.553023i
$635$	1.66311	+	1.20832i	0.0659985	+	0.0479507i
$636$	−0.00199640	−	0.00614430i	−7.91625e−5	−	0.000243637i
$637$	−0.641436			−0.0254146
$638$		0			0
$639$	−14.4300			−0.570843
$640$	0.435508	+	1.34036i	0.0172150	+	0.0529823i
$641$	−35.1839	−	25.5626i	−1.38968	−	1.00966i	−0.995900	−	0.0904593i	$-0.971166\pi$
$641$	−35.1839	−	25.5626i	−1.38968	−	1.00966i	−0.393782	−	0.919204i	$-0.628834\pi$
$642$	0.747692	−	0.543230i	0.0295090	−	0.0214396i
$643$	−5.30017	+	16.3122i	−0.209018	+	0.643292i	0.790506	+	0.612454i	$0.209818\pi$
$643$	−5.30017	+	16.3122i	−0.209018	+	0.643292i	−0.999524	+	0.0308379i	$0.990182\pi$
$644$	−0.0407542	+	0.125428i	−0.00160594	+	0.00494257i
$645$	0.0137023	−	0.00995532i	0.000539529	−	0.000391990i
$646$	−11.4755	−	8.33741i	−0.451496	−	0.328031i
$647$	4.41613	+	13.5914i	0.173616	+	0.534335i	0.999568	−	0.0294062i	$-0.00936164\pi$
$647$	4.41613	+	13.5914i	0.173616	+	0.534335i	−0.825952	+	0.563741i	$0.809362\pi$
$648$	25.5459			1.00354
$649$		0			0
$650$	−4.42927			−0.173730
$651$	0.258572	+	0.795802i	0.0101342	+	0.0311899i
$652$	−1.05341	−	0.765349i	−0.0412548	−	0.0299734i
$653$	30.6228	−	22.2487i	1.19836	−	0.870660i	0.204239	−	0.978921i	$-0.434528\pi$
$653$	30.6228	−	22.2487i	1.19836	−	0.870660i	0.994123	+	0.108261i	$0.0345282\pi$
$654$	−0.483807	+	1.48901i	−0.0189184	+	0.0582247i
$655$	−0.726147	+	2.23485i	−0.0283729	+	0.0873228i
$656$	19.1541	−	13.9163i	0.747843	−	0.543340i
$657$	−21.3901	−	15.5408i	−0.834505	−	0.606304i
$658$	−4.06414	−	12.5081i	−0.158437	−	0.487618i
$659$	8.13829			0.317023			0.158511	−	0.987357i	$-0.449331\pi$
$659$	8.13829			0.317023			0.158511	+	0.987357i	$0.449331\pi$
$660$		0			0
$661$	−5.33161			−0.207375			−0.103688	−	0.994610i	$-0.533064\pi$
$661$	−5.33161			−0.207375			−0.103688	+	0.994610i	$0.533064\pi$
$662$	−1.88952	−	5.81535i	−0.0734384	−	0.226020i
$663$	0.0905593	+	0.0657952i	0.00351703	+	0.00255527i
$664$	−22.3333	+	16.2261i	−0.866701	+	0.629695i
$665$	−0.295225	+	0.908608i	−0.0114483	+	0.0352343i
$666$	4.81792	−	14.8280i	0.186691	−	0.574575i
$667$	−6.03561	+	4.38512i	−0.233700	+	0.169793i
$668$	−1.22614	−	0.890843i	−0.0474408	−	0.0344677i
$669$	0.364615	+	1.12217i	0.0140968	+	0.0433856i
$670$	2.21939			0.0857424
$671$		0			0
$672$	0.0547962			0.00211381
$673$	−6.01023	−	18.4976i	−0.231677	−	0.713030i	−0.997545	−	0.0700313i	$-0.977690\pi$
$673$	−6.01023	−	18.4976i	−0.231677	−	0.713030i	0.765867	−	0.642999i	$-0.222310\pi$
$674$	31.1574	+	22.6372i	1.20014	+	0.871953i
$675$	2.95471	−	2.14672i	0.113727	−	0.0826273i
$676$	0.307844	−	0.947445i	0.0118401	−	0.0364402i
$677$	−11.2186	+	34.5274i	−0.431167	+	1.32699i	0.465797	+	0.884891i	$0.345768\pi$
$677$	−11.2186	+	34.5274i	−0.431167	+	1.32699i	−0.896964	+	0.442103i	$0.854232\pi$
$678$	−1.28847	+	0.936128i	−0.0494834	+	0.0359518i
$679$	−5.32446	−	3.86844i	−0.204334	−	0.148457i
$680$	0.168748	+	0.519354i	0.00647121	+	0.0199163i
$681$	1.27490			0.0488545
$682$		0			0
$683$	−20.7805			−0.795142			−0.397571	−	0.917571i	$-0.630147\pi$
$683$	−20.7805			−0.795142			−0.397571	+	0.917571i	$0.630147\pi$
$684$	0.524327	+	1.61371i	0.0200481	+	0.0617018i
$685$	2.04793	+	1.48791i	0.0782475	+	0.0568501i
$686$	1.12126	−	0.814642i	0.0428099	−	0.0311032i
$687$	0.352945	−	1.08625i	0.0134657	−	0.0414431i
$688$	1.23228	−	3.79256i	0.0469802	−	0.144590i
$689$	−0.345894	+	0.251307i	−0.0131775	+	0.00957403i
$690$	0.0304405	+	0.0221163i	0.00115885	+	0.000841955i
$691$	−15.4833	−	47.6527i	−0.589012	−	1.81279i	−0.582522	−	0.812815i	$-0.697934\pi$
$691$	−15.4833	−	47.6527i	−0.589012	−	1.81279i	−0.00649001	−	0.999979i	$-0.502066\pi$
$692$	−1.20481			−0.0457998
$693$		0			0
$694$	−43.3131			−1.64414
$695$	0.578142	+	1.77934i	0.0219302	+	0.0674941i
$696$	1.27819	+	0.928660i	0.0484497	+	0.0352008i
$697$	7.11548	−	5.16970i	0.269518	−	0.195816i
$698$	0.232745	−	0.716316i	0.00880954	−	0.0271130i
$699$	−0.641753	+	1.97511i	−0.0242733	+	0.0747056i
$700$	−0.318977	+	0.231751i	−0.0120562	+	0.00875935i
$701$	13.2055	+	9.59437i	0.498765	+	0.362374i	0.808545	−	0.588434i	$-0.200255\pi$
$701$	13.2055	+	9.59437i	0.498765	+	0.362374i	−0.309780	+	0.950808i	$0.600255\pi$
$702$	0.201377	+	0.619775i	0.00760049	+	0.0233919i
$703$	27.0701			1.02097
$704$		0			0
$705$	0.154584			0.00582199
$706$	7.64556	+	23.5306i	0.287745	+	0.885587i
$707$	−15.0642	−	10.9448i	−0.566548	−	0.411622i
$708$	−0.0641968	+	0.0466417i	−0.00241266	+	0.00175290i
$709$	10.2686	−	31.6035i	0.385646	−	1.18690i	−0.550365	−	0.834924i	$-0.685511\pi$
$709$	10.2686	−	31.6035i	0.385646	−	1.18690i	0.936011	−	0.351971i	$-0.114489\pi$
$710$	0.275372	−	0.847507i	0.0103345	−	0.0318064i
$711$	27.7490	−	20.1608i	1.04067	−	0.756089i
$712$	41.2634	+	29.9796i	1.54641	+	1.12353i
$713$	−3.51833	−	10.8283i	−0.131763	−	0.405524i
$714$	−0.241864			−0.00905152
$715$		0			0
$716$	−0.0893143			−0.00333783
$717$	−0.313369	−	0.964450i	−0.0117030	−	0.0360180i
$718$	−13.4449	−	9.76827i	−0.501758	−	0.364548i
$719$	20.4240	−	14.8389i	0.761688	−	0.553399i	−0.137740	−	0.990468i	$-0.543984\pi$
$719$	20.4240	−	14.8389i	0.761688	−	0.553399i	0.899428	+	0.437070i	$0.143984\pi$
$720$	−0.470556	+	1.44822i	−0.0175366	+	0.0539720i
$721$	−2.13950	+	6.58470i	−0.0796791	+	0.245227i
$722$	36.5475	−	26.5533i	1.36016	−	0.988212i
$723$	0.922716	+	0.670392i	0.0343162	+	0.0249322i
$724$	−0.451853	−	1.39066i	−0.0167930	−	0.0516835i
$725$	−22.3036			−0.828337
$726$		0			0
$727$	1.86242			0.0690733			0.0345366	−	0.999403i	$-0.489004\pi$
$727$	1.86242			0.0690733			0.0345366	+	0.999403i	$0.489004\pi$
$728$	−0.571172	−	1.75789i	−0.0211690	−	0.0651516i
$729$	21.1908	+	15.3960i	0.784846	+	0.570224i
$730$	1.32094	−	0.959717i	0.0488901	−	0.0355207i
$731$	0.457774	−	1.40888i	0.0169314	−	0.0521094i
$732$	0.0284480	−	0.0875538i	0.00105147	−	0.00323608i
$733$	−16.2330	+	11.7940i	−0.599581	+	0.435621i	−0.845730	−	0.533611i	$-0.820835\pi$
$733$	−16.2330	+	11.7940i	−0.599581	+	0.435621i	0.246149	+	0.969232i	$0.420835\pi$
$734$	33.1845	+	24.1100i	1.22486	+	0.889916i
$735$	0.00503397	+	0.0154930i	0.000185681	+	0.000571467i
$736$	−0.745601			−0.0274832
$737$		0			0
$738$	25.5375			0.940049
$739$	−6.92104	−	21.3008i	−0.254595	−	0.783562i	−0.993909	−	0.110202i	$-0.964850\pi$
$739$	−6.92104	−	21.3008i	−0.254595	−	0.783562i	0.739315	−	0.673360i	$-0.235150\pi$
$740$	−0.0320908	−	0.0233153i	−0.00117968	−	0.000857089i
$741$	−0.456538	+	0.331694i	−0.0167714	+	0.0121851i
$742$	0.285472	−	0.878591i	0.0104800	−	0.0322541i
$743$	−11.2082	+	34.4953i	−0.411189	+	1.26551i	0.504427	+	0.863454i	$0.331704\pi$
$743$	−11.2082	+	34.4953i	−0.411189	+	1.26551i	−0.915616	+	0.402054i	$0.868296\pi$
$744$	−1.95069	+	1.41726i	−0.0715156	+	0.0519591i
$745$	−1.18758	−	0.862826i	−0.0435095	−	0.0316115i
$746$	−4.50593	−	13.8678i	−0.164974	−	0.507738i
$747$	−28.5962			−1.04628
$748$		0			0
$749$	−5.44446			−0.198936
$750$	0.0696450	+	0.214345i	0.00254308	+	0.00782678i
$751$	−36.1013	−	26.2291i	−1.31736	−	0.957115i	−0.999961	−	0.00882107i	$-0.997192\pi$
$751$	−36.1013	−	26.2291i	−1.31736	−	0.957115i	−0.317394	−	0.948294i	$-0.602808\pi$
$752$	29.4451	−	21.3931i	1.07375	−	0.780127i
$753$	0.186793	−	0.574888i	0.00680710	−	0.0209501i
$754$	1.22979	−	3.78489i	0.0447861	−	0.137838i
$755$	−1.73617	+	1.26140i	−0.0631857	+	0.0459071i
$756$	0.0469305	+	0.0340970i	0.00170685	+	0.00124010i
$757$	2.78104	+	8.55916i	0.101079	+	0.311088i	0.988790	−	0.149312i	$-0.0477059\pi$
$757$	2.78104	+	8.55916i	0.101079	+	0.311088i	−0.887711	+	0.460400i	$0.847706\pi$
$758$	11.5715			0.420296
$759$		0			0
$760$	−2.75297			−0.0998607
$761$	1.59192	+	4.89941i	0.0577069	+	0.177604i	0.975755	−	0.218865i	$-0.0702355\pi$
$761$	1.59192	+	4.89941i	0.0577069	+	0.177604i	−0.918048	+	0.396469i	$0.870235\pi$
$762$	−2.12258	−	1.54215i	−0.0768931	−	0.0558661i
$763$	7.46169	−	5.42124i	0.270131	−	0.196262i
$764$	0.0594192	−	0.182874i	0.00214971	−	0.00661613i
$765$	−0.174805	+	0.537993i	−0.00632007	+	0.0194512i
$766$	−20.7139	+	15.0495i	−0.748422	+	0.543761i
$767$	4.24848	+	3.08670i	0.153404	+	0.111454i
$768$	0.0717691	+	0.220883i	0.00258975	+	0.00797042i
$769$	−38.5242			−1.38922			−0.694608	−	0.719388i	$-0.744422\pi$
$769$	−38.5242			−1.38922			−0.694608	+	0.719388i	$0.744422\pi$
$770$		0			0
$771$	2.05960			0.0741746
$772$	0.00643939	+	0.0198184i	0.000231759	+	0.000713280i
$773$	5.65522	+	4.10876i	0.203404	+	0.147782i	0.684824	−	0.728708i	$-0.259879\pi$
$773$	5.65522	+	4.10876i	0.203404	+	0.147782i	−0.481420	+	0.876490i	$0.659879\pi$
$774$	3.47983	−	2.52825i	0.125080	−	0.0908760i
$775$	10.5184	−	32.3723i	0.377832	−	1.16285i
$776$	5.86045	−	18.0366i	0.210378	−	0.647477i
$777$	0.373426	−	0.271310i	0.0133966	−	0.00973319i
$778$	26.0760	+	18.9453i	0.934871	+	0.679223i
$779$	13.7016	+	42.1693i	0.490912	+	1.51087i
$780$	0.000826901	0		2.96078e−5	0
$781$		0			0
$782$	3.29099			0.117686
$783$	1.01404	+	3.12088i	0.0362387	+	0.111531i
$784$	3.10296	+	2.25443i	0.110820	+	0.0805154i
$785$	−1.60004	+	1.16250i	−0.0571079	+	0.0414913i
$786$	0.926763	−	2.85228i	0.0330565	−	0.101738i
$787$	9.69877	−	29.8497i	0.345724	−	1.06403i	−0.615471	−	0.788159i	$-0.711034\pi$
$787$	9.69877	−	29.8497i	0.345724	−	1.06403i	0.961195	−	0.275869i	$-0.0889656\pi$
$788$	1.11834	−	0.812524i	0.0398394	−	0.0289450i
$789$	0.407411	+	0.296001i	0.0145042	+	0.0105379i
$790$	0.654549	+	2.01449i	0.0232878	+	0.0716725i
$791$	9.38223			0.333594
$792$		0			0
$793$	−6.09240			−0.216348
$794$	−9.28492	−	28.5760i	−0.329509	−	1.01413i
$795$	0.00878452	+	0.00638233i	0.000311555	+	0.000226358i
$796$	−1.28950	+	0.936878i	−0.0457052	+	0.0332067i
$797$	8.12629	−	25.0102i	0.287848	−	0.885905i	−0.697682	−	0.716407i	$-0.745785\pi$
$797$	8.12629	−	25.0102i	0.287848	−	0.885905i	0.985531	−	0.169498i	$-0.0542147\pi$
$798$	0.376788	−	1.15963i	0.0133381	−	0.0410506i
$799$	10.9384	−	7.94724i	0.386974	−	0.281153i
$800$	−1.80334	−	1.31020i	−0.0637575	−	0.0463226i
$801$	16.3269	+	50.2489i	0.576881	+	1.77546i
$802$	48.2416			1.70347
$803$		0			0
$804$	0.116695			0.00411551
$805$	−0.0684962	−	0.210810i	−0.00241418	−	0.00743007i
$806$	4.91356	+	3.56991i	0.173073	+	0.125745i
$807$	−2.37497	+	1.72552i	−0.0836030	+	0.0607412i
$808$	16.5807	−	51.0301i	0.583307	−	1.79523i
$809$	3.63508	−	11.1876i	0.127802	−	0.393336i	−0.866599	−	0.499006i	$-0.833699\pi$
$809$	3.63508	−	11.1876i	0.127802	−	0.393336i	0.994401	+	0.105670i	$0.0336987\pi$
$810$	−1.32209	+	0.960556i	−0.0464536	+	0.0337505i
$811$	6.69303	+	4.86277i	0.235024	+	0.170755i	0.699064	−	0.715060i	$-0.253600\pi$
$811$	6.69303	+	4.86277i	0.235024	+	0.170755i	−0.464040	+	0.885814i	$0.653600\pi$
$812$	−0.109471	−	0.336917i	−0.00384168	−	0.0118235i
$813$	0.735843			0.0258071
$814$		0			0
$815$	2.18844			0.0766579
$816$	−0.206834	−	0.636571i	−0.00724065	−	0.0222844i
$817$	6.04185	+	4.38966i	0.211378	+	0.153575i
$818$	18.2683	−	13.2727i	0.638736	−	0.464069i
$819$	0.591671	−	1.82097i	0.0206746	−	0.0636300i
$820$	0.0200774	−	0.0617918i	0.000701132	−	0.00215786i
$821$	5.97470	−	4.34087i	0.208518	−	0.151497i	−0.478625	−	0.878020i	$-0.658865\pi$
$821$	5.97470	−	4.34087i	0.208518	−	0.151497i	0.687143	+	0.726522i	$0.258865\pi$
$822$	−2.61372	−	1.89898i	−0.0911641	−	0.0662346i
$823$	15.2788	+	47.0234i	0.532587	+	1.63913i	0.748807	+	0.662788i	$0.230627\pi$
$823$	15.2788	+	47.0234i	0.532587	+	1.63913i	−0.216220	+	0.976345i	$0.569373\pi$
$824$	−19.9508			−0.695019
$825$		0			0
$826$	−11.3467			−0.394803
$827$	7.17967	+	22.0968i	0.249662	+	0.768380i	0.994835	+	0.101509i	$0.0323669\pi$
$827$	7.17967	+	22.0968i	0.249662	+	0.768380i	−0.745173	+	0.666871i	$0.767633\pi$
$828$	−0.318487	−	0.231394i	−0.0110682	−	0.00804151i
$829$	−24.4273	+	17.7474i	−0.848394	+	0.616394i	−0.924703	−	0.380690i	$-0.875686\pi$
$829$	−24.4273	+	17.7474i	−0.848394	+	0.616394i	0.0763089	+	0.997084i	$0.475686\pi$
$830$	0.545710	−	1.67952i	0.0189419	−	0.0582971i
$831$	0.346767	−	1.06724i	0.0120292	−	0.0370221i
$832$	4.30247	−	3.12593i	0.149161	−	0.108372i
$833$	1.15270	+	0.837488i	0.0399388	+	0.0290173i
$834$	−0.737868	−	2.27092i	−0.0255503	−	0.0786357i
$835$	2.54728			0.0881523
$836$		0			0
$837$	−5.00798			−0.173101
$838$	9.70214	+	29.8601i	0.335155	+	1.03150i
$839$	−13.4398	−	9.76461i	−0.463995	−	0.337112i	0.331102	−	0.943595i	$-0.392580\pi$
$839$	−13.4398	−	9.76461i	−0.463995	−	0.337112i	−0.795096	+	0.606483i	$0.792580\pi$
$840$	−0.0379767	+	0.0275917i	−0.00131032	+	0.000952003i
$841$	−2.76890	+	8.52180i	−0.0954793	+	0.293855i
$842$	6.51253	−	20.0435i	0.224437	−	0.690745i
$843$	1.28397	−	0.932861i	0.0442224	−	0.0321294i
$844$	−0.901442	−	0.654936i	−0.0310289	−	0.0225438i
$845$	0.517398	+	1.59239i	0.0177990	+	0.0547798i
$846$	39.2582			1.34972
$847$		0			0
$848$	2.55653			0.0877915
$849$	0.143361	+	0.441221i	0.00492015	+	0.0151427i
$850$	7.95970	+	5.78306i	0.273016	+	0.198357i
$851$	−5.08114	+	3.69166i	−0.174179	+	0.126549i
$852$	0.0144790	−	0.0445618i	0.000496042	−	0.00152666i
$853$	−12.3763	+	38.0904i	−0.423758	+	1.30419i	0.480421	+	0.877038i	$0.340484\pi$
$853$	−12.3763	+	38.0904i	−0.423758	+	1.30419i	−0.904179	+	0.427154i	$0.859516\pi$
$854$	10.6498	−	7.73753i	0.364428	−	0.264773i
$855$	−2.30713	−	1.67623i	−0.0789022	−	0.0573258i
$856$	−4.84806	−	14.9208i	−0.165703	−	0.509982i
$857$	−31.7070			−1.08309			−0.541546	−	0.840671i	$-0.682161\pi$
$857$	−31.7070			−1.08309			−0.541546	+	0.840671i	$0.682161\pi$
$858$		0			0
$859$	1.63654			0.0558381			0.0279190	−	0.999610i	$-0.491112\pi$
$859$	1.63654			0.0558381			0.0279190	+	0.999610i	$0.491112\pi$
$860$	−0.00338165	−	0.0104076i	−0.000115313	−	0.000354898i
$861$	0.611654	+	0.444393i	0.0208451	+	0.0151449i
$862$	−3.59577	+	2.61248i	−0.122472	+	0.0889815i
$863$	−5.37858	+	16.5536i	−0.183089	+	0.563490i	−0.999910	−	0.0134007i	$-0.995734\pi$
$863$	−5.37858	+	16.5536i	−0.183089	+	0.563490i	0.816821	+	0.576891i	$0.195734\pi$
$864$	−0.101344	+	0.311904i	−0.00344778	+	0.0106112i
$865$	1.63821	−	1.19023i	0.0557008	−	0.0404690i
$866$	6.71910	+	4.88171i	0.228324	+	0.165887i
$867$	0.566582	+	1.74376i	0.0192421	+	0.0592212i
$868$	0.540640			0.0183505
$869$		0			0
$870$	−0.101070			−0.00342659
$871$	−2.38646	−	7.34477i	−0.0808621	−	0.248868i
$872$	21.5015	+	15.6217i	0.728132	+	0.529019i
$873$	15.8935	−	11.5473i	0.537913	−	0.390817i
$874$	−5.12688	+	15.7789i	−0.173419	+	0.533729i
$875$	0.410279	−	1.26271i	0.0138700	−	0.0426874i
$876$	0.0694546	−	0.0504617i	0.00234665	−	0.00170494i
$877$	38.9677	+	28.3117i	1.31584	+	0.956017i	0.999974	+	0.00721510i	$0.00229666\pi$
$877$	38.9677	+	28.3117i	1.31584	+	0.956017i	0.315871	+	0.948802i	$0.397703\pi$
$878$	3.29226	+	10.1325i	0.111108	+	0.341957i
$879$	−2.61725			−0.0882778
$880$		0			0
$881$	−30.0141			−1.01120			−0.505601	−	0.862767i	$-0.668729\pi$
$881$	−30.0141			−1.01120			−0.505601	+	0.862767i	$0.668729\pi$
$882$	1.27842	+	3.93458i	0.0430468	+	0.132484i
$883$	−45.5764	−	33.1132i	−1.53377	−	1.11435i	−0.954097	−	0.299497i	$-0.903181\pi$
$883$	−45.5764	−	33.1132i	−1.53377	−	1.11435i	−0.579671	−	0.814851i	$-0.696819\pi$
$884$	0.0585117	−	0.0425112i	0.00196796	−	0.00142981i
$885$	0.0412129	−	0.126840i	0.00138536	−	0.00426368i
$886$	−15.9535	+	49.0998i	−0.535968	+	1.64954i
$887$	3.66562	−	2.66323i	0.123079	−	0.0894224i	−0.524543	−	0.851384i	$-0.675764\pi$
$887$	3.66562	−	2.66323i	0.123079	−	0.0894224i	0.647622	+	0.761962i	$0.275764\pi$
$888$	1.07606	+	0.781802i	0.0361102	+	0.0262356i
$889$	4.77616	+	14.6995i	0.160187	+	0.493006i
$890$	−3.26280			−0.109369
$891$		0			0
$892$	0.762363			0.0255258
$893$	21.0632	+	64.8258i	0.704853	+	2.16931i
$894$	1.51568	+	1.10120i	0.0506918	+	0.0368297i
$895$	0.121443	−	0.0882337i	0.00405940	−	0.00294933i
$896$	−3.27439	+	10.0775i	−0.109390	+	0.336667i
$897$	0.0404591	−	0.124520i	0.00135089	−	0.00415761i
$898$	12.4150	−	9.02005i	0.414295	−	0.301003i
$899$	24.7423	+	17.9763i	0.825201	+	0.599543i
$900$	−0.363688	−	1.11932i	−0.0121229	−	0.0373105i
$901$	0.949713			0.0316395
$902$		0			0
$903$	0.127342			0.00423766
$904$	8.35448	+	25.7125i	0.277866	+	0.855184i
$905$	1.98823	+	1.44453i	0.0660910	+	0.0480180i
$906$	2.21583	−	1.60990i	0.0736161	−	0.0534852i
$907$	−6.41548	+	19.7448i	−0.213023	+	0.655616i	0.786266	+	0.617889i	$0.212012\pi$
$907$	−6.41548	+	19.7448i	−0.213023	+	0.655616i	−0.999288	+	0.0377272i	$0.987988\pi$
$908$	0.254548	−	0.783418i	0.00844747	−	0.0259986i
$909$	44.9667	−	32.6702i	1.49145	−	1.08360i
$910$	0.0956590	+	0.0695003i	0.00317106	+	0.00230391i
$911$	−4.75738	−	14.6417i	−0.157619	−	0.485102i	0.840798	−	0.541349i	$-0.182086\pi$
$911$	−4.75738	−	14.6417i	−0.157619	−	0.485102i	−0.998417	+	0.0562476i	$0.982086\pi$
$912$	3.37430			0.111734
$913$		0			0
$914$	−39.3557			−1.30177
$915$	0.0478130	+	0.147153i	0.00158065	+	0.00486474i
$916$	−0.597023	−	0.433763i	−0.0197262	−	0.0143319i
$917$	−14.2933	+	10.3847i	−0.472007	+	0.342933i
$918$	0.447319	−	1.37670i	0.0147637	−	0.0454380i
$919$	6.60003	−	20.3128i	0.217715	−	0.670057i	−0.781235	−	0.624237i	$-0.785410\pi$
$919$	6.60003	−	20.3128i	0.217715	−	0.670057i	0.998950	−	0.0458201i	$-0.0145901\pi$
$920$	0.516741	−	0.375435i	0.0170365	−	0.0123777i
$921$	−0.836970	−	0.608095i	−0.0275791	−	0.0200374i
$922$	11.0248	+	33.9310i	0.363084	+	1.11746i
$923$	−3.10082			−0.102065
$924$		0			0
$925$	−18.7765			−0.617369
$926$	−16.1267	−	49.6329i	−0.529956	−	1.63104i
$927$	−16.7198	−	12.1477i	−0.549150	−	0.398981i
$928$	1.62028	−	1.17720i	0.0531884	−	0.0386436i
$929$	4.98554	−	15.3439i	0.163570	−	0.503418i	−0.835358	−	0.549707i	$-0.814739\pi$
$929$	4.98554	−	15.3439i	0.163570	−	0.503418i	0.998928	+	0.0462888i	$0.0147395\pi$
$930$	0.0476646	−	0.146696i	0.00156298	−	0.00481037i
$931$	−5.81115	+	4.22204i	−0.190453	+	0.138372i
$932$	1.08556	+	0.788704i	0.0355586	+	0.0258348i
$933$	−0.681985	−	2.09893i	−0.0223272	−	0.0687160i
$934$	21.3263			0.697817
$935$		0			0
$936$	5.51733			0.180339
$937$	−1.41006	−	4.33973i	−0.0460648	−	0.141773i	0.925379	−	0.379044i	$-0.123747\pi$
$937$	−1.41006	−	4.33973i	−0.0460648	−	0.141773i	−0.971443	+	0.237271i	$0.923747\pi$
$938$	13.4997	+	9.80811i	0.440781	+	0.320246i
$939$	0.0234184	−	0.0170145i	0.000764231	−	0.000555246i
$940$	0.0308644	−	0.0949908i	0.00100669	−	0.00309826i
$941$	3.87827	−	11.9361i	0.126428	−	0.389106i	−0.867730	−	0.497035i	$-0.834422\pi$
$941$	3.87827	−	11.9361i	0.126428	−	0.389106i	0.994159	+	0.107929i	$0.0344220\pi$
$942$	2.04209	−	1.48367i	0.0665349	−	0.0483404i
$943$	−8.32266	−	6.04677i	−0.271023	−	0.196910i
$944$	−9.70337	−	29.8639i	−0.315818	−	0.971987i
$945$	−0.0974972			−0.00317159
$946$		0			0
$947$	51.6790			1.67934			0.839672	−	0.543094i	$-0.182747\pi$
$947$	51.6790			1.67934			0.839672	+	0.543094i	$0.182747\pi$
$948$	0.0344161	+	0.105922i	0.00111778	+	0.00344018i
$949$	−4.59643	−	3.33951i	−0.149207	−	0.108405i
$950$	−40.1274	+	29.1542i	−1.30190	+	0.945889i
$951$	−0.646942	+	1.99108i	−0.0209785	+	0.0645653i
$952$	−1.26874	+	3.90479i	−0.0411202	+	0.126555i
$953$	−1.06993	+	0.777352i	−0.0346585	+	0.0251809i	−0.604980	−	0.796241i	$-0.706819\pi$
$953$	−1.06993	+	0.777352i	−0.0346585	+	0.0251809i	0.570321	+	0.821422i	$0.306819\pi$
$954$	2.23091	+	1.62085i	0.0722284	+	0.0524770i
$955$	0.0998669	+	0.307359i	0.00323162	+	0.00994589i
$956$	−0.655213			−0.0211911
$957$		0			0
$958$	0.831818			0.0268748
$959$	5.88131	+	18.1008i	0.189917	+	0.584506i
$960$	−0.109268	−	0.0793878i	−0.00352661	−	0.00256223i
$961$	−12.6804	+	9.21284i	−0.409045	+	0.297188i
$962$	1.03531	−	3.18635i	0.0333796	−	0.102732i
$963$	5.02205	−	15.4563i	0.161833	−	0.498072i
$964$	0.596180	−	0.433150i	0.0192017	−	0.0139508i
$965$	−0.0283345	−	0.0205862i	−0.000912118	−	0.000662693i
$966$	0.0874200	+	0.269051i	0.00281269	+	0.00865658i
$967$	−44.1214			−1.41885			−0.709425	−	0.704781i	$-0.751045\pi$
$967$	−44.1214			−1.41885			−0.709425	+	0.704781i	$0.751045\pi$
$968$		0			0
$969$	1.25351			0.0402684
$970$	0.374899	+	1.15382i	0.0120373	+	0.0370470i
$971$	1.06119	+	0.770998i	0.0340551	+	0.0247425i	0.604683	−	0.796467i	$-0.293300\pi$
$971$	1.06119	+	0.770998i	0.0340551	+	0.0247425i	−0.570627	+	0.821209i	$0.693300\pi$
$972$	−0.210307	+	0.152797i	−0.00674560	+	0.00490096i
$973$	−4.34679	+	13.3780i	−0.139352	+	0.428880i
$974$	−4.41094	+	13.5755i	−0.141335	+	0.434986i
$975$	0.316668	−	0.230073i	0.0101415	−	0.00736822i
$976$	29.4721	+	21.4127i	0.943379	+	0.685405i
$977$	−3.83495	−	11.8028i	−0.122691	−	0.377604i	0.870782	−	0.491669i	$-0.163613\pi$
$977$	−3.83495	−	11.8028i	−0.122691	−	0.377604i	−0.993473	+	0.114065i	$0.963613\pi$
$978$	−2.79306			−0.0893121
$979$		0			0
$980$	0.0105254			0.000336221
$981$	8.50758	+	26.1837i	0.271626	+	0.835980i
$982$	−11.3163	−	8.22174i	−0.361116	−	0.262366i
$983$	25.8533	−	18.7836i	0.824594	−	0.599102i	−0.0934309	−	0.995626i	$-0.529783\pi$
$983$	25.8533	−	18.7836i	0.824594	−	0.599102i	0.918025	+	0.396523i	$0.129783\pi$
$984$	−0.673228	+	2.07198i	−0.0214617	+	0.0660523i
$985$	−0.717951	+	2.20963i	−0.0228758	+	0.0704045i
$986$	−7.15173	+	5.19604i	−0.227758	+	0.165476i
$987$	0.940280	+	0.683153i	0.0299294	+	0.0217450i
$988$	0.112671	+	0.346765i	0.00358454	+	0.0110321i
$989$	−1.73271			−0.0550970
$990$		0			0
$991$	−9.17926			−0.291589			−0.145794	−	0.989315i	$-0.546574\pi$
$991$	−9.17926			−0.291589			−0.145794	+	0.989315i	$0.546574\pi$
$992$	0.944511	+	2.90691i	0.0299883	+	0.0922944i
$993$	0.437161	+	0.317616i	0.0138729	+	0.0100792i
$994$	5.42037	−	3.93813i	0.171924	−	0.124910i
$995$	0.827830	−	2.54780i	0.0262440	−	0.0807707i
$996$	0.0286933	−	0.0883089i	0.000909182	−	0.00279818i
$997$	−11.6036	+	8.43050i	−0.367489	+	0.266996i	−0.756169	−	0.654376i	$-0.772931\pi$
$997$	−11.6036	+	8.43050i	−0.367489	+	0.266996i	0.388680	+	0.921373i	$0.372931\pi$
$998$	22.1959	+	16.1263i	0.702600	+	0.510468i
$999$	0.853677	+	2.62735i	0.0270091	+	0.0831256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.y.148.1		24
11.2	odd	10		847.2.f.z.372.6		24
11.3	even	5		847.2.a.n.1.1	yes	6
11.4	even	5	inner	847.2.f.y.729.6		24
11.5	even	5	inner	847.2.f.y.323.6		24
11.6	odd	10		847.2.f.z.323.1		24
11.7	odd	10		847.2.f.z.729.1		24
11.8	odd	10		847.2.a.m.1.6	✓	6
11.9	even	5	inner	847.2.f.y.372.1		24
11.10	odd	2		847.2.f.z.148.6		24
33.8	even	10		7623.2.a.cs.1.1		6
33.14	odd	10		7623.2.a.cp.1.6		6
77.41	even	10		5929.2.a.bj.1.6		6
77.69	odd	10		5929.2.a.bm.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.6	✓	6	11.8	odd	10
847.2.a.n.1.1	yes	6	11.3	even	5
847.2.f.y.148.1		24	1.1	even	1	trivial
847.2.f.y.323.6		24	11.5	even	5	inner
847.2.f.y.372.1		24	11.9	even	5	inner
847.2.f.y.729.6		24	11.4	even	5	inner
847.2.f.z.148.6		24	11.10	odd	2
847.2.f.z.323.1		24	11.6	odd	10
847.2.f.z.372.6		24	11.2	odd	10
847.2.f.z.729.1		24	11.7	odd	10
5929.2.a.bj.1.6		6	77.41	even	10
5929.2.a.bm.1.1		6	77.69	odd	10
7623.2.a.cp.1.6		6	33.14	odd	10
7623.2.a.cs.1.1		6	33.8	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.428283 - 1.31812i) q^{2} +(0.0990877 + 0.0719914i) q^{3} +(0.0640220 - 0.0465147i) q^{4} +(-0.0411006 + 0.126495i) q^{5} +(0.0524557 - 0.161442i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-2.33125 - 1.69375i) q^{8} +(-0.922415 - 2.83890i) q^{9} +O(q^{10})\)	\(q+(-0.428283 - 1.31812i) q^{2} +(0.0990877 + 0.0719914i) q^{3} +(0.0640220 - 0.0465147i) q^{4} +(-0.0411006 + 0.126495i) q^{5} +(0.0524557 - 0.161442i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(-2.33125 - 1.69375i) q^{8} +(-0.922415 - 2.83890i) q^{9} +0.184338 q^{10} +0.00969245 q^{12} +(-0.198215 - 0.610042i) q^{13} +(1.12126 + 0.814642i) q^{14} +(-0.0131791 + 0.00957518i) q^{15} +(-1.18522 + 3.64775i) q^{16} +(-0.440294 + 1.35508i) q^{17} +(-3.34696 + 2.43171i) q^{18} +(-5.81115 - 4.22204i) q^{19} +(0.00325252 + 0.0100102i) q^{20} -0.122479 q^{21} +1.66655 q^{23} +(-0.109063 - 0.335660i) q^{24} +(4.03077 + 2.92853i) q^{25} +(-0.719216 + 0.522541i) q^{26} +(0.226521 - 0.697160i) q^{27} +(-0.0244542 + 0.0752624i) q^{28} +(-3.62162 + 2.63126i) q^{29} +(0.0182656 + 0.0132707i) q^{30} +(-2.11115 - 6.49745i) q^{31} -0.447392 q^{32} +1.97473 q^{34} +(-0.0411006 - 0.126495i) q^{35} +(-0.191106 - 0.138846i) q^{36} +(-3.04890 + 2.21515i) q^{37} +(-3.07634 + 9.46801i) q^{38} +(0.0242772 - 0.0747174i) q^{39} +(0.310067 - 0.225277i) q^{40} +(-4.99395 - 3.62832i) q^{41} +(0.0524557 + 0.161442i) q^{42} -1.03970 q^{43} +0.397018 q^{45} +(-0.713755 - 2.19671i) q^{46} +(-7.67707 - 5.57771i) q^{47} +(-0.380047 + 0.276121i) q^{48} +(0.309017 - 0.951057i) q^{49} +(2.13384 - 6.56728i) q^{50} +(-0.141182 + 0.102575i) q^{51} +(-0.0410660 - 0.0298362i) q^{52} +(-0.205975 - 0.633926i) q^{53} -1.01595 q^{54} +2.88158 q^{56} +(-0.271862 - 0.836705i) q^{57} +(5.01939 + 3.64680i) q^{58} +(-6.62338 + 4.81217i) q^{59} +(-0.000398366 + 0.00122604i) q^{60} +(2.93506 - 9.03320i) q^{61} +(-7.66024 + 5.56549i) q^{62} +(2.41491 + 1.75454i) q^{63} +(2.56206 + 7.88521i) q^{64} +0.0853139 q^{65} +12.0398 q^{67} +(0.0348429 + 0.107235i) q^{68} +(0.165134 + 0.119977i) q^{69} +(-0.149132 + 0.108351i) q^{70} +(1.49384 - 4.59758i) q^{71} +(-2.65802 + 8.18053i) q^{72} +(7.16585 - 5.20629i) q^{73} +(4.22563 + 3.07010i) q^{74} +(0.188571 + 0.580362i) q^{75} -0.568428 q^{76} -0.108884 q^{78} +(3.55081 + 10.9283i) q^{79} +(-0.412707 - 0.299849i) q^{80} +(-7.17211 + 5.21084i) q^{81} +(-2.64373 + 8.13656i) q^{82} +(2.96038 - 9.11111i) q^{83} +(-0.00784136 + 0.00569708i) q^{84} +(-0.153315 - 0.111390i) q^{85} +(0.445286 + 1.37045i) q^{86} -0.548286 q^{87} -17.7001 q^{89} +(-0.170036 - 0.523317i) q^{90} +(0.518933 + 0.377027i) q^{91} +(0.106696 - 0.0775190i) q^{92} +(0.258572 - 0.795802i) q^{93} +(-4.06414 + 12.5081i) q^{94} +(0.772908 - 0.561551i) q^{95} +(-0.0443310 - 0.0322084i) q^{96} +(2.03376 + 6.25927i) q^{97} -1.38595 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Introduction

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