LMFDB - Embedded newform 847.2.f.z.148.6

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			148.6
Character	$\chi$	$=$	847.148
Dual form			847.2.f.z.372.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.428283 + 1.31812i) q^{2} +(0.0990877 + 0.0719914i) q^{3} +(0.0640220 - 0.0465147i) q^{4} +(-0.0411006 + 0.126495i) q^{5} +(-0.0524557 + 0.161442i) q^{6} +(0.809017 - 0.587785i) q^{7} +(2.33125 + 1.69375i) q^{8} +(-0.922415 - 2.83890i) q^{9} +O(q^{10})$	\(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	$0.0630062\pi$
$2$	0.428283	+	1.31812i	0.302842	+	0.932051i	−0.677632	+	0.735401i	$0.736994\pi$
$3$	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	0.974774	−	0.223194i	$-0.0716485\pi$
$13$	0.198215	+	0.610042i	0.0549749	+	0.169195i	−0.919799	+	0.392390i	$0.871648\pi$
$14$	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	−0.883359	−	0.468697i	$-0.844723\pi$
$17$	0.440294	−	1.35508i	0.106787	−	0.328656i	0.990146	+	0.140041i	$0.0447235\pi$
$18$	3.34696	−	2.43171i	0.788885	−	0.573159i
$19$	5.81115	+	4.22204i	1.33317	+	0.968603i	0.999666	+	0.0258541i	$0.00823055\pi$
$19$	5.81115	+	4.22204i	1.33317	+	0.968603i	0.333502	+	0.942749i	$0.391769\pi$
$20$	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	−0.198349	−	0.980131i	$-0.563558\pi$
$29$	3.62162	−	2.63126i	0.672518	−	0.488613i	0.870867	+	0.491519i	$0.163558\pi$
$30$	−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	0.904956	−	0.425505i	$-0.139904\pi$
$41$	4.99395	+	3.62832i	0.779924	+	0.566648i	−0.125032	+	0.992153i	$0.539904\pi$
$42$	0.0524557	+	0.161442i	0.00809409	+	0.0249110i
$43$	1.03970			0.158553			0.0792764	−	0.996853i	$-0.474739\pi$
$43$	1.03970			0.158553			0.0792764	+	0.996853i	$0.474739\pi$
$44$		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	$0.308049\pi$
$61$	−2.93506	+	9.03320i	−0.375796	+	1.15658i	−0.942940	+	0.332963i	$0.891951\pi$
$62$	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	−0.922007	−	0.387173i	$-0.873452\pi$
$73$	−7.16585	+	5.20629i	−0.838699	+	0.609351i	0.0833078	+	0.996524i	$0.473452\pi$
$74$	−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	$-0.876274\pi$
$79$	−3.55081	−	10.9283i	−0.399497	−	1.22953i	0.525906	−	0.850543i	$-0.323726\pi$
$80$	−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	$0.276223\pi$
$83$	−2.96038	+	9.11111i	−0.324944	+	1.00007i	−0.971466	+	0.237179i	$0.923777\pi$
$84$	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	$-0.722887\pi$
$101$	−5.75402	−	17.7091i	−0.572547	−	1.76212i	0.0718388	−	0.997416i	$-0.477113\pi$
$102$	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	0.354159	−	0.935185i	$-0.384767\pi$
$107$	−4.40466	−	3.20017i	−0.425814	−	0.309372i	−0.779973	+	0.625813i	$0.784767\pi$
$108$	−0.0179259	−	0.0551701i	−0.00172492	−	0.00530875i
$109$	9.22316			0.883419			0.441709	−	0.897158i	$-0.354372\pi$
$109$	9.22316			0.883419			0.441709	+	0.897158i	$0.354372\pi$
$110$		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	$0.340525\pi$
$127$	−4.77616	+	14.6995i	−0.423816	+	1.30437i	−0.904123	+	0.427271i	$0.859475\pi$
$128$	−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	$-0.780648\pi$
$131$	−17.6675			−1.54362			−0.771810	+	0.635854i	$0.780648\pi$
$132$		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	−0.954362	−	0.298652i	$-0.903463\pi$
$139$	−11.3800	+	8.26808i	−0.965242	+	0.701289i	−0.0108796	+	0.999941i	$0.503463\pi$
$140$	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	$-0.750682\pi$
$149$	3.41052	−	10.4965i	0.279401	−	0.859907i	0.988021	−	0.154317i	$-0.0493178\pi$
$150$	−0.684225	+	0.497118i	−0.0558667	+	0.0405895i
$151$	−13.0535	−	9.48391i	−1.06228	−	0.771789i	−0.0877688	−	0.996141i	$-0.527974\pi$
$151$	−13.0535	−	9.48391i	−1.06228	−	0.771789i	−0.974508	+	0.224351i	$0.927974\pi$
$152$	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	$0.165652\pi$
$167$	5.91825	+	18.2145i	0.457968	+	1.40948i	−0.409648	+	0.912244i	$0.634348\pi$
$168$	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	0.947561	−	0.319575i	$-0.103540\pi$
$173$	12.3169	+	8.94879i	0.936440	+	0.680364i	−0.0111210	+	0.999938i	$0.503540\pi$
$174$	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	−0.948085	−	0.318017i	$-0.896983\pi$
$193$	0.0813717	−	0.250436i	0.00585726	−	0.0180268i	0.953942	+	0.299990i	$0.0969833\pi$
$194$	−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	$-0.713792\pi$
$197$	−17.4681			−1.24455			−0.622276	+	0.782798i	$0.713792\pi$
$198$		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	$0.0610567\pi$
$211$	4.35102	+	13.3911i	0.299536	+	0.921879i	−0.682123	+	0.731237i	$0.738943\pi$
$212$	−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	−0.831069	−	0.556170i	$-0.812270\pi$
$227$	−8.42119	+	6.11835i	−0.558934	+	0.406089i	0.272135	+	0.962259i	$0.412270\pi$
$228$	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	$-0.912560\pi$
$233$	−5.23969	−	16.1261i	−0.343264	−	1.05646i	0.619243	−	0.785199i	$-0.287440\pi$
$234$	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	0.782960	−	0.622073i	$-0.213709\pi$
$239$	6.69837	+	4.86665i	0.433281	+	0.314797i	−0.349678	+	0.936870i	$0.613709\pi$
$240$	−0.0193076	−	0.0594228i	−0.00124630	−	0.00383572i
$241$	−9.31212			−0.599846			−0.299923	−	0.953963i	$-0.596961\pi$
$241$	−9.31212			−0.599846			−0.299923	+	0.953963i	$0.596961\pi$
$242$		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	$-0.540460\pi$
$263$	−4.11162			−0.253533			−0.126767	+	0.991933i	$0.540460\pi$
$264$		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	−0.725544	−	0.688176i	$-0.758412\pi$
$271$	−4.86050	+	3.53136i	−0.295254	+	0.214515i	0.430289	+	0.902691i	$0.358412\pi$
$272$	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	0.999377	−	0.0353050i	$-0.0112403\pi$
$277$	2.83123	+	8.71363i	0.170112	+	0.523552i	−0.829264	+	0.558857i	$0.811240\pi$
$278$	−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	$0.226317\pi$
$281$	−4.00423	+	12.3237i	−0.238872	+	0.735173i	−0.996584	+	0.0825836i	$0.973683\pi$
$282$	1.30318	−	0.946818i	0.0776034	−	0.0563822i
$283$	−3.06440	−	2.22642i	−0.182160	−	0.132347i	0.492969	−	0.870047i	$-0.335912\pi$
$283$	−3.06440	−	2.22642i	−0.182160	−	0.132347i	−0.675128	+	0.737700i	$0.735912\pi$
$284$	−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	0.0457656	−	0.998952i	$-0.485427\pi$
$293$	17.2879	−	12.5604i	1.00997	−	0.733785i	0.964202	+	0.265168i	$0.0854273\pi$
$294$	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	$-0.422511\pi$
$307$	8.44677			0.482082			0.241041	+	0.970515i	$0.422511\pi$
$308$		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	0.228138	−	0.973629i	$-0.426736\pi$
$337$	22.4809	−	16.3333i	1.22461	−	0.889733i	0.996475	+	0.0838961i	$0.0267364\pi$
$338$	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	$0.416762\pi$
$347$	−9.65724	+	29.7219i	−0.518428	+	1.59556i	−0.776958	+	0.629553i	$0.783238\pi$
$348$	0.0351024	−	0.0255034i	0.00188168	−	0.00136712i
$349$	−0.439651	−	0.319425i	−0.0235340	−	0.0170984i	0.575956	−	0.817481i	$-0.304630\pi$
$349$	−0.439651	−	0.319425i	−0.0235340	−	0.0170984i	−0.599490	+	0.800382i	$0.704630\pi$
$350$	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	−0.813578	−	0.581456i	$-0.802483\pi$
$359$	−9.70081	+	7.04805i	−0.511989	+	0.371982i	0.301588	+	0.953438i	$0.402483\pi$
$360$	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	$-0.587810\pi$
$373$	−10.5209			−0.544753			−0.272377	+	0.962191i	$0.587810\pi$
$374$		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	$-0.968033\pi$
$409$	−5.03471	−	15.4952i	−0.248950	−	0.766190i	0.746011	−	0.665933i	$-0.231967\pi$
$410$	−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	0.972083	−	0.234639i	$-0.0753906\pi$
$431$	0.990988	+	3.04995i	0.0477342	+	0.146911i	−0.924348	+	0.381549i	$0.875391\pi$
$432$	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	$-0.441276\pi$
$439$	7.68712			0.366886			0.183443	+	0.983030i	$0.441276\pi$
$440$		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	$0.331209\pi$
$457$	−8.77488	+	27.0063i	−0.410472	+	1.26330i	−0.916239	+	0.400632i	$0.868791\pi$
$458$	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	$-0.295381\pi$
$461$	25.7420			1.19892			0.599462	+	0.800403i	$0.295381\pi$
$462$		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	−0.946730	−	0.322028i	$-0.895635\pi$
$479$	0.185465	−	0.570803i	0.00847412	−	0.0260807i	0.955204	+	0.295948i	$0.0956354\pi$
$480$	−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	−0.756580	−	0.653901i	$-0.773131\pi$
$491$	−8.16497	+	5.93220i	−0.368480	+	0.267716i	0.388100	+	0.921617i	$0.373131\pi$
$492$	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	0.299122	−	0.954215i	$-0.403306\pi$
$503$	−11.5717	−	8.40733i	−0.515956	−	0.374864i	−0.815078	+	0.579351i	$0.803306\pi$
$504$	−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	$-0.616122\pi$
$523$	10.9993	−	33.8525i	0.480968	−	1.48027i	0.837737	−	0.546074i	$-0.183878\pi$
$524$	−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	$-0.981395\pi$
$541$	−5.23320	−	16.1061i	−0.224993	−	0.692457i	0.773300	−	0.634041i	$-0.218605\pi$
$542$	−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	0.425270	−	0.905067i	$-0.360179\pi$
$547$	−7.11192	−	5.16711i	−0.304084	−	0.220930i	−0.729354	+	0.684137i	$0.760179\pi$
$548$	−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	−0.149407	−	0.988776i	$-0.547737\pi$
$557$	17.5780	−	12.7712i	0.744805	−	0.541132i	0.894212	+	0.447643i	$0.147737\pi$
$558$	−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	0.962216	−	0.272288i	$-0.0877802\pi$
$563$	0.562827	+	1.73220i	0.0237203	+	0.0730036i	−0.938496	+	0.345291i	$0.887780\pi$
$564$	−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	0.983789	−	0.179328i	$-0.0573924\pi$
$569$	26.6505	+	19.3627i	1.11725	+	0.811726i	0.133456	+	0.991055i	$0.457392\pi$
$570$	−0.0501145	−	0.154236i	−0.00209906	−	0.00646025i
$571$	23.4394			0.980908			0.490454	−	0.871467i	$-0.336831\pi$
$571$	23.4394			0.980908			0.490454	+	0.871467i	$0.336831\pi$
$572$		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	$-0.684210\pi$
$593$	−26.6381			−1.09389			−0.546947	+	0.837167i	$0.684210\pi$
$594$		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	−0.666430	−	0.745568i	$-0.732178\pi$
$601$	−4.00312	+	2.90843i	−0.163290	+	0.118637i	0.503139	+	0.864205i	$0.332178\pi$
$602$	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	$0.0893142\pi$
$607$	8.53154	+	26.2574i	0.346285	+	1.06575i	−0.614608	+	0.788833i	$0.710686\pi$
$608$	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	0.699014	−	0.715108i	$-0.253623\pi$
$613$	5.81617	+	4.22570i	0.234913	+	0.170674i	−0.464101	+	0.885782i	$0.653623\pi$
$614$	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	$-0.550669\pi$
$659$	−8.13829			−0.317023			−0.158511	+	0.987357i	$0.550669\pi$
$660$		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	$0.0223099\pi$
$673$	6.01023	+	18.4976i	0.231677	+	0.713030i	−0.765867	+	0.642999i	$0.777690\pi$
$674$	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	$-0.654232\pi$
$677$	11.2186	−	34.5274i	0.431167	−	1.32699i	0.896964	−	0.442103i	$-0.145768\pi$
$678$	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	0.309780	−	0.950808i	$-0.399745\pi$
$701$	−13.2055	−	9.59437i	−0.498765	−	0.362374i	−0.808545	+	0.588434i	$0.799745\pi$
$702$	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	−0.246149	−	0.969232i	$-0.579165\pi$
$733$	16.2330	−	11.7940i	0.599581	−	0.435621i	0.845730	+	0.533611i	$0.179165\pi$
$734$	−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	$0.0351497\pi$
$739$	6.92104	+	21.3008i	0.254595	+	0.783562i	−0.739315	+	0.673360i	$0.764850\pi$
$740$	−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	$-0.668296\pi$
$743$	11.2082	−	34.4953i	0.411189	−	1.26551i	0.915616	−	0.402054i	$-0.131704\pi$
$744$	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	0.918048	−	0.396469i	$-0.129765\pi$
$761$	−1.59192	−	4.89941i	−0.0577069	−	0.177604i	−0.975755	+	0.218865i	$0.929765\pi$
$762$	−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	$-0.255578\pi$
$769$	38.5242			1.38922			0.694608	+	0.719388i	$0.255578\pi$
$770$		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	$0.288966\pi$
$787$	−9.69877	+	29.8497i	−0.345724	+	1.06403i	−0.961195	+	0.275869i	$0.911034\pi$
$788$	−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	−0.994401	−	0.105670i	$-0.966301\pi$
$809$	−3.63508	+	11.1876i	−0.127802	+	0.393336i	0.866599	+	0.499006i	$0.166301\pi$
$810$	1.32209	−	0.960556i	0.0464536	−	0.0337505i
$811$	−6.69303	−	4.86277i	−0.235024	−	0.170755i	0.464040	−	0.885814i	$-0.346400\pi$
$811$	−6.69303	−	4.86277i	−0.235024	−	0.170755i	−0.699064	+	0.715060i	$0.746400\pi$
$812$	−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	−0.687143	−	0.726522i	$-0.741135\pi$
$821$	−5.97470	+	4.34087i	−0.208518	+	0.151497i	0.478625	+	0.878020i	$0.341135\pi$
$822$	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	$-0.967633\pi$
$827$	−7.17967	−	22.0968i	−0.249662	−	0.768380i	0.745173	−	0.666871i	$-0.232367\pi$
$828$	−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	$-0.659516\pi$
$853$	12.3763	−	38.0904i	0.423758	−	1.30419i	0.904179	−	0.427154i	$-0.140484\pi$
$854$	−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	$-0.317839\pi$
$857$	31.7070			1.08309			0.541546	+	0.840671i	$0.317839\pi$
$858$		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	$-0.997703\pi$
$877$	−38.9677	−	28.3117i	−1.31584	−	0.956017i	−0.315871	−	0.948802i	$-0.602297\pi$
$878$	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	−0.647622	−	0.761962i	$-0.724236\pi$
$887$	−3.66562	+	2.66323i	−0.123079	+	0.0894224i	0.524543	+	0.851384i	$0.324236\pi$
$888$	−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	$0.214590\pi$
$919$	−6.60003	+	20.3128i	−0.217715	+	0.670057i	−0.998950	+	0.0458201i	$0.985410\pi$
$920$	−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	0.971443	−	0.237271i	$-0.0762530\pi$
$937$	1.41006	+	4.33973i	0.0460648	+	0.141773i	−0.925379	+	0.379044i	$0.876253\pi$
$938$	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	−0.994159	−	0.107929i	$-0.965578\pi$
$941$	−3.87827	+	11.9361i	−0.126428	+	0.389106i	0.867730	+	0.497035i	$0.165578\pi$
$942$	−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	−0.570321	−	0.821422i	$-0.693181\pi$
$953$	1.06993	−	0.777352i	0.0346585	−	0.0251809i	0.604980	+	0.796241i	$0.293181\pi$
$954$	−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	$-0.248955\pi$
$967$	44.1214			1.41885			0.709425	+	0.704781i	$0.248955\pi$
$968$		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	−0.388680	−	0.921373i	$-0.627069\pi$
$997$	11.6036	−	8.43050i	0.367489	−	0.266996i	0.756169	+	0.654376i	$0.227069\pi$
$998$	−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.z.148.6		24
11.2	odd	10		847.2.f.y.372.1		24
11.3	even	5		847.2.a.m.1.6	✓	6
11.4	even	5	inner	847.2.f.z.729.1		24
11.5	even	5	inner	847.2.f.z.323.1		24
11.6	odd	10		847.2.f.y.323.6		24
11.7	odd	10		847.2.f.y.729.6		24
11.8	odd	10		847.2.a.n.1.1	yes	6
11.9	even	5	inner	847.2.f.z.372.6		24
11.10	odd	2		847.2.f.y.148.1		24
33.8	even	10		7623.2.a.cp.1.6		6
33.14	odd	10		7623.2.a.cs.1.1		6
77.41	even	10		5929.2.a.bm.1.1		6
77.69	odd	10		5929.2.a.bj.1.6		6

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

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