LMFDB - Embedded newform 250.2.g.b.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(11,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([38]))

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

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

chi := DirichletCharacter("250.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.g (of order $25$, degree $20$, 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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$7$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	250.11
Dual form			250.2.g.b.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.728969 - 0.684547i) q^{2} +(-0.914190 - 1.44053i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-1.63487 - 1.52552i) q^{5} +(-1.65253 - 0.424297i) q^{6} +(-0.0421220 + 0.129638i) q^{7} +(-0.637424 - 0.770513i) q^{8} +(0.0379457 - 0.0806388i) q^{9} +O(q^{10})$	\(q+(0.728969 - 0.684547i) q^{2} +(-0.914190 - 1.44053i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-1.63487 - 1.52552i) q^{5} +(-1.65253 - 0.424297i) q^{6} +(-0.0421220 + 0.129638i) q^{7} +(-0.637424 - 0.770513i) q^{8} +(0.0379457 - 0.0806388i) q^{9} +(-2.23606 + 0.00708737i) q^{10} +(-1.29213 + 1.21339i) q^{11} +(-1.49509 + 0.821934i) q^{12} +(-2.46426 + 5.23682i) q^{13} +(0.0580378 + 0.123337i) q^{14} +(-0.702983 + 3.74969i) q^{15} +(-0.992115 - 0.125333i) q^{16} +(-0.434578 - 6.90741i) q^{17} +(-0.0275398 - 0.0847588i) q^{18} +(4.15697 - 6.55033i) q^{19} +(-1.62516 + 1.53585i) q^{20} +(0.225255 - 0.0578358i) q^{21} +(-0.111299 + 1.76905i) q^{22} +(0.833755 - 4.37070i) q^{23} +(-0.527223 + 1.62263i) q^{24} +(0.345579 + 4.98804i) q^{25} +(1.78848 + 5.50438i) q^{26} +(-5.22888 + 0.660561i) q^{27} +(0.126737 + 0.0501789i) q^{28} +(9.16935 + 3.63040i) q^{29} +(2.05439 + 3.21463i) q^{30} +(-0.0733328 - 1.16559i) q^{31} +(-0.809017 + 0.587785i) q^{32} +(2.92918 + 0.752086i) q^{33} +(-5.04524 - 4.73780i) q^{34} +(0.266629 - 0.147683i) q^{35} +(-0.0780970 - 0.0429342i) q^{36} +(6.94871 + 0.877826i) q^{37} +(-1.45371 - 7.62063i) q^{38} +(9.79662 - 1.23760i) q^{39} +(-0.133330 + 2.23209i) q^{40} +(-0.364789 - 1.91229i) q^{41} +(0.124613 - 0.196358i) q^{42} +(-6.37996 - 4.63531i) q^{43} +(1.12986 + 1.36577i) q^{44} +(-0.185052 + 0.0739467i) q^{45} +(-2.38417 - 3.75685i) q^{46} +(2.01383 - 2.43431i) q^{47} +(0.726435 + 1.54375i) q^{48} +(5.64809 + 4.10358i) q^{49} +(3.66647 + 3.39956i) q^{50} +(-9.55307 + 6.94071i) q^{51} +(5.07176 + 2.78822i) q^{52} +(2.26880 - 0.582530i) q^{53} +(-3.35951 + 4.06094i) q^{54} +(3.96351 - 0.0125627i) q^{55} +(0.126737 - 0.0501789i) q^{56} -13.2362 q^{57} +(9.16935 - 3.63040i) q^{58} +(4.23830 - 2.33003i) q^{59} +(3.69816 + 0.937041i) q^{60} +(-0.985561 + 5.16649i) q^{61} +(-0.851359 - 0.799480i) q^{62} +(0.00885551 + 0.00831588i) q^{63} +(-0.187381 + 0.982287i) q^{64} +(12.0176 - 4.80223i) q^{65} +(2.65012 - 1.45692i) q^{66} +(-8.05875 + 3.19068i) q^{67} -6.92107 q^{68} +(-7.05835 + 2.79460i) q^{69} +(0.0932683 - 0.290177i) q^{70} +(3.60701 - 4.36013i) q^{71} +(-0.0863208 + 0.0221634i) q^{72} +(4.18040 + 2.29819i) q^{73} +(5.66630 - 4.11681i) q^{74} +(6.86952 - 5.05784i) q^{75} +(-6.27639 - 4.56006i) q^{76} +(-0.102875 - 0.218620i) q^{77} +(6.29423 - 7.60842i) q^{78} +(2.57819 + 4.06258i) q^{79} +(1.43078 + 1.71839i) q^{80} +(5.56133 + 6.72249i) q^{81} +(-1.57497 - 1.14429i) q^{82} +(-6.43442 + 10.1390i) q^{83} +(-0.0435777 - 0.228443i) q^{84} +(-9.82692 + 11.9557i) q^{85} +(-7.82388 + 0.988386i) q^{86} +(-3.15281 - 16.5276i) q^{87} +(1.75857 + 0.222159i) q^{88} +(-8.51631 - 4.68188i) q^{89} +(-0.0842773 + 0.180582i) q^{90} +(-0.575092 - 0.540048i) q^{91} +(-4.30972 - 1.10655i) q^{92} +(-1.61203 + 1.17121i) q^{93} +(-0.198376 - 3.15310i) q^{94} +(-16.7887 + 4.36739i) q^{95} +(1.58632 + 0.628068i) q^{96} +(9.93362 + 3.93300i) q^{97} +(6.92637 - 0.875004i) q^{98} +(0.0488155 + 0.150239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9}+O(q^{10}) $ 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9	$ 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9} + 20 q^{10} - 10 q^{11} + 20 q^{12} + 20 q^{14} - 10 q^{15} - 5 q^{17} - 50 q^{18} + 40 q^{19} - 10 q^{20} - 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} - 5 q^{25} - 35 q^{26} + 30 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} + 35 q^{31} - 35 q^{32} - 55 q^{33} - 15 q^{34} - 25 q^{35} - 10 q^{36} - 25 q^{37} - 30 q^{39} + 25 q^{41} - 5 q^{42} - 45 q^{43} + 40 q^{44} - 5 q^{45} + 90 q^{47} - 5 q^{48} - 65 q^{49} + 30 q^{50} - 80 q^{51} - 50 q^{53} - 5 q^{54} - 35 q^{55} - 5 q^{56} + 40 q^{57} - 10 q^{58} + 45 q^{59} + 15 q^{60} + 45 q^{61} - 45 q^{62} - 75 q^{63} - 60 q^{65} + 15 q^{66} - 45 q^{67} + 10 q^{68} - 125 q^{69} - 15 q^{70} - 5 q^{71} - 5 q^{72} - 50 q^{73} + 20 q^{74} - 130 q^{75} - 5 q^{76} + 10 q^{77} + 10 q^{78} - 50 q^{79} - 5 q^{80} + 15 q^{81} + 40 q^{82} + 25 q^{83} - 50 q^{84} - 95 q^{85} - 10 q^{86} + 80 q^{87} - 10 q^{88} - 65 q^{89} - 10 q^{90} + 65 q^{91} - 25 q^{92} - 10 q^{93} - 35 q^{94} + 80 q^{95} - 40 q^{97} - 25 q^{98} + 90 q^{99}+O(q^{100}) $ 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9 + 20 * q^10 - 10 * q^11 + 20 * q^12 + 20 * q^14 - 10 * q^15 - 5 * q^17 - 50 * q^18 + 40 * q^19 - 10 * q^20 - 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 - 5 * q^25 - 35 * q^26 + 30 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 + 35 * q^31 - 35 * q^32 - 55 * q^33 - 15 * q^34 - 25 * q^35 - 10 * q^36 - 25 * q^37 - 30 * q^39 + 25 * q^41 - 5 * q^42 - 45 * q^43 + 40 * q^44 - 5 * q^45 + 90 * q^47 - 5 * q^48 - 65 * q^49 + 30 * q^50 - 80 * q^51 - 50 * q^53 - 5 * q^54 - 35 * q^55 - 5 * q^56 + 40 * q^57 - 10 * q^58 + 45 * q^59 + 15 * q^60 + 45 * q^61 - 45 * q^62 - 75 * q^63 - 60 * q^65 + 15 * q^66 - 45 * q^67 + 10 * q^68 - 125 * q^69 - 15 * q^70 - 5 * q^71 - 5 * q^72 - 50 * q^73 + 20 * q^74 - 130 * q^75 - 5 * q^76 + 10 * q^77 + 10 * q^78 - 50 * q^79 - 5 * q^80 + 15 * q^81 + 40 * q^82 + 25 * q^83 - 50 * q^84 - 95 * q^85 - 10 * q^86 + 80 * q^87 - 10 * q^88 - 65 * q^89 - 10 * q^90 + 65 * q^91 - 25 * q^92 - 10 * q^93 - 35 * q^94 + 80 * q^95 - 40 * q^97 - 25 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{19}{25}\right)$

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 $

$2$	0.728969	−	0.684547i	0.515459	−	0.484048i
$2$	0.728969	−	0.684547i	0.515459	−	0.484048i
$3$	−0.914190	−	1.44053i	−0.527808	−	0.831692i	0.470917	−	0.882178i	$-0.343923\pi$
$3$	−0.914190	−	1.44053i	−0.527808	−	0.831692i	−0.998725	+	0.0504854i	$0.983923\pi$
$4$	0.0627905	−	0.998027i	0.0313953	−	0.499013i
$5$	−1.63487	−	1.52552i	−0.731135	−	0.682233i
$5$	−1.63487	−	1.52552i	−0.731135	−	0.682233i
$6$	−1.65253	−	0.424297i	−0.674642	−	0.173219i
$7$	−0.0421220	+	0.129638i	−0.0159206	+	0.0489986i	−0.958701	−	0.284415i	$-0.908201\pi$
$7$	−0.0421220	+	0.129638i	−0.0159206	+	0.0489986i	0.942781	+	0.333414i	$0.108201\pi$
$8$	−0.637424	−	0.770513i	−0.225363	−	0.272418i
$9$	0.0379457	−	0.0806388i	0.0126486	−	0.0268796i
$10$	−2.23606	+	0.00708737i	−0.707103	+	0.00224122i
$11$	−1.29213	+	1.21339i	−0.389592	+	0.365851i	−0.854450	−	0.519534i	$-0.826105\pi$
$11$	−1.29213	+	1.21339i	−0.389592	+	0.365851i	0.464858	+	0.885385i	$0.346105\pi$
$12$	−1.49509	+	0.821934i	−0.431596	+	0.237272i
$13$	−2.46426	+	5.23682i	−0.683463	+	1.45243i	0.198010	+	0.980200i	$0.436552\pi$
$13$	−2.46426	+	5.23682i	−0.683463	+	1.45243i	−0.881473	+	0.472234i	$0.843448\pi$
$14$	0.0580378	+	0.123337i	0.0155113	+	0.0329631i
$15$	−0.702983	+	3.74969i	−0.181509	+	0.968167i
$16$	−0.992115	−	0.125333i	−0.248029	−	0.0313333i
$17$	−0.434578	−	6.90741i	−0.105401	−	1.67529i	−0.595291	−	0.803510i	$-0.702963\pi$
$17$	−0.434578	−	6.90741i	−0.105401	−	1.67529i	0.489891	−	0.871784i	$-0.337037\pi$
$18$	−0.0275398	−	0.0847588i	−0.00649119	−	0.0199778i
$19$	4.15697	−	6.55033i	0.953674	−	1.50275i	0.0917057	−	0.995786i	$-0.470768\pi$
$19$	4.15697	−	6.55033i	0.953674	−	1.50275i	0.861968	−	0.506963i	$-0.169232\pi$
$20$	−1.62516	+	1.53585i	−0.363398	+	0.343427i
$21$	0.225255	−	0.0578358i	0.0491548	−	0.0126208i
$22$	−0.111299	+	1.76905i	−0.0237290	+	0.377162i
$23$	0.833755	−	4.37070i	0.173850	−	0.911354i	−0.783274	−	0.621676i	$-0.786452\pi$
$23$	0.833755	−	4.37070i	0.173850	−	0.911354i	0.957124	−	0.289677i	$-0.0935480\pi$
$24$	−0.527223	+	1.62263i	−0.107619	+	0.331217i
$25$	0.345579	+	4.98804i	0.0691159	+	0.997609i
$26$	1.78848	+	5.50438i	0.350750	+	1.07950i
$27$	−5.22888	+	0.660561i	−1.00630	+	0.127125i
$28$	0.126737	+	0.0501789i	0.0239511	+	0.00948292i
$29$	9.16935	+	3.63040i	1.70271	+	0.674149i	0.999328	−	0.0366666i	$-0.0116740\pi$
$29$	9.16935	+	3.63040i	1.70271	+	0.674149i	0.703378	+	0.710816i	$0.251674\pi$
$30$	2.05439	+	3.21463i	0.375079	+	0.586909i
$31$	−0.0733328	−	1.16559i	−0.0131710	−	0.209346i	−0.999108	−	0.0422290i	$-0.986554\pi$
$31$	−0.0733328	−	1.16559i	−0.0131710	−	0.209346i	0.985937	−	0.167117i	$-0.0534459\pi$
$32$	−0.809017	+	0.587785i	−0.143015	+	0.103907i
$33$	2.92918	+	0.752086i	0.509905	+	0.130921i
$34$	−5.04524	−	4.73780i	−0.865252	−	0.812526i
$35$	0.266629	−	0.147683i	0.0450686	−	0.0249630i
$36$	−0.0780970	−	0.0429342i	−0.0130162	−	0.00715570i
$37$	6.94871	+	0.877826i	1.14236	+	0.144314i	0.673659	−	0.739043i	$-0.264722\pi$
$37$	6.94871	+	0.877826i	1.14236	+	0.144314i	0.468702	+	0.883356i	$0.344722\pi$
$38$	−1.45371	−	7.62063i	−0.235823	−	1.23623i
$39$	9.79662	−	1.23760i	1.56871	−	0.198175i
$40$	−0.133330	+	2.23209i	−0.0210813	+	0.352924i
$41$	−0.364789	−	1.91229i	−0.0569705	−	0.298650i	0.942386	−	0.334528i	$-0.108577\pi$
$41$	−0.364789	−	1.91229i	−0.0569705	−	0.298650i	−0.999356	+	0.0358786i	$0.988577\pi$
$42$	0.124613	−	0.196358i	0.0192282	−	0.0302988i
$43$	−6.37996	−	4.63531i	−0.972935	−	0.706879i	−0.0168164	−	0.999859i	$-0.505353\pi$
$43$	−6.37996	−	4.63531i	−0.972935	−	0.706879i	−0.956119	+	0.292980i	$0.905353\pi$
$44$	1.12986	+	1.36577i	0.170333	+	0.205898i
$45$	−0.185052	+	0.0739467i	−0.0275860	+	0.0110233i
$46$	−2.38417	−	3.75685i	−0.351526	−	0.553917i
$47$	2.01383	−	2.43431i	0.293748	−	0.355080i	−0.602906	−	0.797812i	$-0.705991\pi$
$47$	2.01383	−	2.43431i	0.293748	−	0.355080i	0.896654	+	0.442732i	$0.145991\pi$
$48$	0.726435	+	1.54375i	0.104852	+	0.222821i
$49$	5.64809	+	4.10358i	0.806870	+	0.586225i
$50$	3.66647	+	3.39956i	0.518517	+	0.480771i
$51$	−9.55307	+	6.94071i	−1.33770	+	0.971894i
$52$	5.07176	+	2.78822i	0.703326	+	0.386657i
$53$	2.26880	−	0.582530i	0.311644	−	0.0800166i	−0.0896285	−	0.995975i	$-0.528568\pi$
$53$	2.26880	−	0.582530i	0.311644	−	0.0800166i	0.401273	+	0.915959i	$0.368568\pi$
$54$	−3.35951	+	4.06094i	−0.457171	+	0.552625i
$55$	3.96351	−	0.0125627i	0.534440	−	0.00169395i
$56$	0.126737	−	0.0501789i	0.0169360	−	0.00670544i
$57$	−13.2362			−1.75318
$58$	9.16935	−	3.63040i	1.20399	−	0.476695i
$59$	4.23830	−	2.33003i	0.551780	−	0.303344i	−0.181365	−	0.983416i	$-0.558052\pi$
$59$	4.23830	−	2.33003i	0.551780	−	0.303344i	0.733145	+	0.680072i	$0.238052\pi$
$60$	3.69816	+	0.937041i	0.477430	+	0.120971i
$61$	−0.985561	+	5.16649i	−0.126188	+	0.661501i	0.861834	+	0.507190i	$0.169316\pi$
$61$	−0.985561	+	5.16649i	−0.126188	+	0.661501i	−0.988022	+	0.154311i	$0.950684\pi$
$62$	−0.851359	−	0.799480i	−0.108123	−	0.101534i
$63$	0.00885551	+	0.00831588i	0.00111569	+	0.00104770i
$64$	−0.187381	+	0.982287i	−0.0234227	+	0.122786i
$65$	12.0176	−	4.80223i	1.49060	−	0.595643i
$66$	2.65012	−	1.45692i	0.326207	−	0.179334i
$67$	−8.05875	+	3.19068i	−0.984533	+	0.389804i	−0.804563	−	0.593868i	$-0.797600\pi$
$67$	−8.05875	+	3.19068i	−0.984533	+	0.389804i	−0.179970	+	0.983672i	$0.557600\pi$
$68$	−6.92107			−0.839303
$69$	−7.05835	+	2.79460i	−0.849725	+	0.336430i
$70$	0.0932683	−	0.290177i	0.0111477	−	0.0346827i
$71$	3.60701	−	4.36013i	0.428073	−	0.517452i	−0.511740	−	0.859140i	$-0.670999\pi$
$71$	3.60701	−	4.36013i	0.428073	−	0.517452i	0.939813	+	0.341689i	$0.110999\pi$
$72$	−0.0863208	+	0.0221634i	−0.0101730	+	0.00261198i
$73$	4.18040	+	2.29819i	0.489278	+	0.268983i	0.707239	−	0.706974i	$-0.249940\pi$
$73$	4.18040	+	2.29819i	0.489278	+	0.268983i	−0.217961	+	0.975958i	$0.569940\pi$
$74$	5.66630	−	4.11681i	0.658694	−	0.478569i
$75$	6.86952	−	5.05784i	0.793223	−	0.584029i
$76$	−6.27639	−	4.56006i	−0.719951	−	0.523075i
$77$	−0.102875	−	0.218620i	−0.0117237	−	0.0249140i
$78$	6.29423	−	7.60842i	0.712682	−	0.861484i
$79$	2.57819	+	4.06258i	0.290069	+	0.457076i	0.957845	−	0.287287i	$-0.0927533\pi$
$79$	2.57819	+	4.06258i	0.290069	+	0.457076i	−0.667775	+	0.744363i	$0.732753\pi$
$80$	1.43078	+	1.71839i	0.159966	+	0.192122i
$81$	5.56133	+	6.72249i	0.617926	+	0.746944i
$82$	−1.57497	−	1.14429i	−0.173927	−	0.126365i
$83$	−6.43442	+	10.1390i	−0.706270	+	1.11290i	0.281886	+	0.959448i	$0.409040\pi$
$83$	−6.43442	+	10.1390i	−0.706270	+	1.11290i	−0.988156	+	0.153455i	$0.950960\pi$
$84$	−0.0435777	−	0.228443i	−0.00475472	−	0.0249251i
$85$	−9.82692	+	11.9557i	−1.06588	+	1.29677i
$86$	−7.82388	+	0.988386i	−0.843671	+	0.106580i
$87$	−3.15281	−	16.5276i	−0.338017	−	1.77195i
$88$	1.75857	+	0.222159i	0.187464	+	0.0236822i
$89$	−8.51631	−	4.68188i	−0.902727	−	0.496278i	−0.0384307	−	0.999261i	$-0.512236\pi$
$89$	−8.51631	−	4.68188i	−0.902727	−	0.496278i	−0.864296	+	0.502983i	$0.832236\pi$
$90$	−0.0842773	+	0.180582i	−0.00888361	+	0.0190350i
$91$	−0.575092	−	0.540048i	−0.0602861	−	0.0566124i
$92$	−4.30972	−	1.10655i	−0.449320	−	0.115366i
$93$	−1.61203	+	1.17121i	−0.167160	+	0.121449i
$94$	−0.198376	−	3.15310i	−0.0204609	−	0.325217i
$95$	−16.7887	+	4.36739i	−1.72249	+	0.448084i
$96$	1.58632	+	0.628068i	0.161903	+	0.0641020i
$97$	9.93362	+	3.93300i	1.00861	+	0.399336i	0.813574	−	0.581461i	$-0.197519\pi$
$97$	9.93362	+	3.93300i	1.00861	+	0.399336i	0.195033	+	0.980797i	$0.437519\pi$
$98$	6.92637	−	0.875004i	0.699669	−	0.0883887i
$99$	0.0488155	+	0.150239i	0.00490615	+	0.0150996i
$100$	4.99990	−	0.0316955i	0.499990	−	0.00316955i
$101$	−1.73240	+	5.33179i	−0.172380	+	0.530533i	−0.999504	−	0.0314874i	$-0.989976\pi$
$101$	−1.73240	+	5.33179i	−0.172380	+	0.530533i	0.827124	+	0.562020i	$0.189976\pi$
$102$	−2.21264	+	11.5991i	−0.219084	+	1.14848i
$103$	1.17054	−	18.6053i	0.115337	−	1.83323i	−0.337140	−	0.941455i	$-0.609459\pi$
$103$	1.17054	−	18.6053i	0.115337	−	1.83323i	0.452477	−	0.891776i	$-0.350541\pi$
$104$	5.60582	−	1.43933i	0.549696	−	0.141138i
$105$	−0.456492	−	0.249078i	−0.0445491	−	0.0243075i
$106$	1.25512	−	1.97775i	0.121908	−	0.192096i
$107$	0.715514	+	2.20213i	0.0691714	+	0.212888i	0.979667	−	0.200632i	$-0.0642994\pi$
$107$	0.715514	+	2.20213i	0.0691714	+	0.212888i	−0.910495	+	0.413519i	$0.864299\pi$
$108$	0.330934	+	5.26004i	0.0318441	+	0.506148i
$109$	−9.16059	−	1.15725i	−0.877426	−	0.110845i	−0.326299	−	0.945266i	$-0.605802\pi$
$109$	−9.16059	−	1.15725i	−0.877426	−	0.110845i	−0.551126	+	0.834422i	$0.685802\pi$
$110$	2.88068	−	2.72237i	0.274662	−	0.259568i
$111$	−5.08790	−	10.8123i	−0.482922	−	1.02626i
$112$	0.0580378	−	0.123337i	0.00548406	−	0.0116542i
$113$	2.50715	−	1.37832i	0.235853	−	0.129661i	−0.359445	−	0.933166i	$-0.617034\pi$
$113$	2.50715	−	1.37832i	0.235853	−	0.129661i	0.595298	+	0.803505i	$0.297034\pi$
$114$	−9.64879	+	9.06082i	−0.903692	+	0.848624i
$115$	−8.03067	+	5.87360i	−0.748864	+	0.547716i
$116$	4.19899	−	8.92330i	0.389866	−	0.828508i
$117$	0.328783	+	0.397430i	0.0303960	+	0.0367424i
$118$	1.49458	−	4.59983i	0.137587	−	0.423449i
$119$	0.913769	+	0.234616i	0.0837651	+	0.0215072i
$120$	3.33729	−	1.84849i	0.304651	−	0.168743i
$121$	−0.493413	+	7.84258i	−0.0448557	+	0.712962i
$122$	2.81826	+	4.44087i	0.255154	+	0.402058i
$123$	−2.42123	+	2.27369i	−0.218315	+	0.205012i
$124$	−1.16790			−0.104880
$125$	7.04438	−	8.68197i	0.630069	−	0.776539i
$126$	0.0121480			0.00108223
$127$	−2.32626	+	2.18450i	−0.206422	+	0.193843i	−0.780862	−	0.624704i	$-0.785220\pi$
$127$	−2.32626	+	2.18450i	−0.206422	+	0.193843i	0.574440	+	0.818547i	$0.305220\pi$
$128$	0.535827	+	0.844328i	0.0473608	+	0.0746288i
$129$	−0.844825	+	13.4281i	−0.0743827	+	1.18228i
$130$	5.47311	−	11.7273i	0.480024	−	1.02855i
$131$	−1.02131	−	0.262227i	−0.0892320	−	0.0229109i	0.203810	−	0.979010i	$-0.434668\pi$
$131$	−1.02131	−	0.262227i	−0.0892320	−	0.0229109i	−0.293042	+	0.956100i	$0.594668\pi$
$132$	0.934527	−	2.87618i	0.0813401	−	0.250339i
$133$	0.674073	+	0.814814i	0.0584495	+	0.0706533i
$134$	−3.69040	+	7.84250i	−0.318802	+	0.677489i
$135$	9.55623	+	6.89683i	0.822469	+	0.593585i
$136$	−5.04524	+	4.73780i	−0.432626	+	0.406263i
$137$	−2.72263	+	1.49678i	−0.232610	+	0.127878i	−0.593797	−	0.804615i	$-0.702372\pi$
$137$	−2.72263	+	1.49678i	−0.232610	+	0.127878i	0.361187	+	0.932493i	$0.382372\pi$
$138$	−3.23228	+	6.86895i	−0.275150	+	0.584723i
$139$	0.541708	+	1.15119i	0.0459471	+	0.0976425i	0.926483	−	0.376338i	$-0.122817\pi$
$139$	0.541708	+	1.15119i	0.0459471	+	0.0976425i	−0.880535	+	0.473980i	$0.842817\pi$
$140$	−0.130650	−	0.275376i	−0.0110419	−	0.0232735i
$141$	−5.34773	−	0.675575i	−0.450360	−	0.0568937i
$142$	−0.355314	−	5.64756i	−0.0298173	−	0.473933i
$143$	−3.17017	−	9.75677i	−0.265103	−	0.815902i
$144$	−0.0477532	+	0.0752471i	−0.00397944	+	0.00627059i
$145$	−9.45242	−	19.9233i	−0.784981	−	1.65454i
$146$	4.62060	−	1.18637i	0.382404	−	0.0981845i
$147$	0.747911	−	11.8877i	0.0616867	−	0.980481i
$148$	1.31241	−	6.87988i	0.107879	−	0.565522i
$149$	2.03762	−	6.27116i	0.166928	−	0.513753i	−0.832245	−	0.554408i	$-0.812945\pi$
$149$	2.03762	−	6.27116i	0.166928	−	0.513753i	0.999173	+	0.0406554i	$0.0129446\pi$
$150$	1.54533	−	8.38951i	0.126176	−	0.685001i
$151$	6.46727	+	19.9042i	0.526299	+	1.61978i	0.761733	+	0.647891i	$0.224349\pi$
$151$	6.46727	+	19.9042i	0.526299	+	1.61978i	−0.235434	+	0.971890i	$0.575651\pi$
$152$	−7.69687	+	0.972340i	−0.624298	+	0.0788672i
$153$	−0.573496	−	0.227063i	−0.0463644	−	0.0183570i
$154$	−0.224648	−	0.0889444i	−0.0181026	−	0.00716734i
$155$	−1.65824	+	2.01746i	−0.133193	+	0.162046i
$156$	−0.620024	−	9.85500i	−0.0496417	−	0.789031i
$157$	−12.5046	+	9.08511i	−0.997974	+	0.725071i	−0.961653	−	0.274270i	$-0.911564\pi$
$157$	−12.5046	+	9.08511i	−0.997974	+	0.725071i	−0.0363211	+	0.999340i	$0.511564\pi$
$158$	4.66045	+	1.19660i	0.370765	+	0.0951964i
$159$	−2.91327	−	2.73574i	−0.231037	−	0.216959i
$160$	2.21931	+	0.273221i	0.175452	+	0.0216000i
$161$	0.531490	+	0.292189i	0.0418873	+	0.0230277i
$162$	8.65590	+	1.09349i	0.680072	+	0.0859130i
$163$	3.38814	+	17.7612i	0.265379	+	1.39117i	0.826269	+	0.563276i	$0.190459\pi$
$163$	3.38814	+	17.7612i	0.265379	+	1.39117i	−0.560889	+	0.827891i	$0.689541\pi$
$164$	−1.93142	+	0.243996i	−0.150819	+	0.0190529i
$165$	−3.64150	−	5.69809i	−0.283490	−	0.443595i
$166$	2.25015	+	11.7957i	0.174646	+	0.915524i
$167$	11.3651	−	17.9086i	0.879459	−	1.38581i	−0.0427381	−	0.999086i	$-0.513608\pi$
$167$	11.3651	−	17.9086i	0.879459	−	1.38581i	0.922197	−	0.386720i	$-0.126392\pi$
$168$	−0.188146	−	0.136696i	−0.0145158	−	0.0105464i
$169$	−13.0652	−	15.7931i	−1.00502	−	1.21486i
$170$	1.02070	+	15.4423i	0.0782838	+	1.18437i
$171$	−0.370472	−	0.583770i	−0.0283307	−	0.0446420i
$172$	−5.02677	+	6.07632i	−0.383287	+	0.463315i
$173$	4.57950	+	9.73194i	0.348173	+	0.739906i	0.999827	−	0.0186110i	$-0.00592440\pi$
$173$	4.57950	+	9.73194i	0.348173	+	0.739906i	−0.651654	+	0.758517i	$0.725924\pi$
$174$	−13.6122	−	9.88988i	−1.03194	−	0.749750i
$175$	−0.661197	−	0.165306i	−0.0499818	−	0.0124960i
$176$	1.43402	−	1.04188i	0.108093	−	0.0785344i
$177$	−7.23109	−	3.97533i	−0.543522	−	0.298804i
$178$	−9.41309	+	2.41687i	−0.705541	+	0.181152i
$179$	2.02608	−	2.44911i	0.151436	−	0.183055i	−0.689340	−	0.724438i	$-0.742099\pi$
$179$	2.02608	−	2.44911i	0.151436	−	0.183055i	0.840776	+	0.541383i	$0.182099\pi$
$180$	0.0621813	+	0.189330i	0.00463472	+	0.0141118i
$181$	−13.1897	+	5.22218i	−0.980385	+	0.388162i	−0.802999	−	0.595980i	$-0.796764\pi$
$181$	−13.1897	+	5.22218i	−0.980385	+	0.388162i	−0.177385	+	0.984142i	$0.556764\pi$
$182$	−0.788912			−0.0584781
$183$	8.34349	−	3.30342i	0.616769	−	0.244196i
$184$	−3.89914	+	2.14357i	−0.287448	+	0.158026i
$185$	−10.0211	−	12.0355i	−0.736764	−	0.884869i
$186$	−0.373373	+	1.95729i	−0.0273770	+	0.143515i
$187$	8.94292	+	8.39796i	0.653971	+	0.614120i
$188$	−2.30305	−	2.16271i	−0.167967	−	0.157732i
$189$	0.134617	−	0.705687i	0.00979194	−	0.0513311i
$190$	−9.24879	+	14.6764i	−0.670978	+	1.06474i
$191$	7.79859	−	4.28731i	0.564286	−	0.310219i	−0.173957	−	0.984753i	$-0.555656\pi$
$191$	7.79859	−	4.28731i	0.564286	−	0.310219i	0.738244	+	0.674534i	$0.235656\pi$
$192$	1.58632	−	0.628068i	0.114483	−	0.0453269i
$193$	−4.27871			−0.307988			−0.153994	−	0.988072i	$-0.549214\pi$
$193$	−4.27871			−0.307988			−0.153994	+	0.988072i	$0.549214\pi$
$194$	9.93362	−	3.93300i	0.713193	−	0.282373i
$195$	−17.9042	−	12.9216i	−1.28214	−	0.925337i
$196$	4.45012	−	5.37928i	0.317866	−	0.384234i
$197$	15.5171	−	3.98412i	1.10555	−	0.283857i	0.348561	−	0.937286i	$-0.386670\pi$
$197$	15.5171	−	3.98412i	1.10555	−	0.283857i	0.756987	+	0.653429i	$0.226670\pi$
$198$	0.138431	+	0.0761028i	0.00983783	+	0.00540839i
$199$	2.54527	−	1.84925i	0.180430	−	0.131090i	−0.493904	−	0.869516i	$-0.664431\pi$
$199$	2.54527	−	1.84925i	0.180430	−	0.131090i	0.674334	+	0.738426i	$0.264431\pi$
$200$	3.62307	−	3.44577i	0.256190	−	0.243653i
$201$	11.9635	+	8.69200i	0.843841	+	0.613087i
$202$	2.38699	+	5.07262i	0.167948	+	0.356908i
$203$	−0.856870	+	1.03578i	−0.0601405	+	0.0726973i
$204$	6.32717	+	9.97003i	0.442991	+	0.698042i
$205$	−2.32086	+	3.68284i	−0.162096	+	0.257220i
$206$	−11.8829	−	14.3639i	−0.827920	−	1.00078i
$207$	−0.320810	−	0.233082i	−0.0222979	−	0.0162003i
$208$	3.10118	−	4.88668i	0.215028	−	0.338830i
$209$	2.57677	+	13.5079i	0.178239	+	0.934361i
$210$	−0.503274	+	0.130921i	−0.0347292	+	0.00903438i
$211$	22.1115	−	2.79333i	1.52222	−	0.192301i	0.680713	−	0.732550i	$-0.261670\pi$
$211$	22.1115	−	2.79333i	1.52222	−	0.192301i	0.841505	+	0.540249i	$0.181670\pi$
$212$	−0.438921	−	2.30090i	−0.0301452	−	0.158027i
$213$	−9.57840	−	1.21003i	−0.656301	−	0.0829101i
$214$	2.02905	+	1.11548i	0.138703	+	0.0762525i
$215$	3.35913	+	17.3109i	0.229090	+	1.18059i
$216$	3.84199	+	3.60787i	0.261414	+	0.245484i
$217$	0.154194	+	0.0395903i	0.0104674	+	0.00268756i
$218$	−7.46998	+	5.42726i	−0.505931	+	0.367580i
$219$	−0.511055	−	8.12299i	−0.0345339	−	0.548900i
$220$	0.236333	−	3.95648i	0.0159336	−	0.266746i
$221$	37.2438	+	14.7459i	2.50529	+	0.991914i
$222$	−11.1105	−	4.39895i	−0.745687	−	0.295238i
$223$	1.52678	−	0.192878i	0.102241	−	0.0129160i	−0.0740463	−	0.997255i	$-0.523591\pi$
$223$	1.52678	−	0.192878i	0.102241	−	0.0129160i	0.176287	+	0.984339i	$0.443591\pi$
$224$	−0.0421220	−	0.129638i	−0.00281439	−	0.00866181i
$225$	0.415343	+	0.161408i	0.0276895	+	0.0107605i
$226$	0.884110	−	2.72101i	0.0588101	−	0.180999i
$227$	0.955822	−	5.01060i	0.0634402	−	0.332565i	−0.936391	−	0.350959i	$-0.885855\pi$
$227$	0.955822	−	5.01060i	0.0634402	−	0.332565i	0.999831	+	0.0183945i	$0.00585549\pi$
$228$	−0.831110	+	13.2101i	−0.0550416	+	0.874861i
$229$	2.00005	−	0.513527i	0.132167	−	0.0339348i	−0.182027	−	0.983294i	$-0.558266\pi$
$229$	2.00005	−	0.513527i	0.132167	−	0.0339348i	0.314194	+	0.949359i	$0.398266\pi$
$230$	−1.83335	+	9.77904i	−0.120887	+	0.644811i
$231$	−0.220882	+	0.348054i	−0.0145330	+	0.0229003i
$232$	−3.04749	−	9.37921i	−0.200078	−	0.615776i
$233$	0.753154	+	11.9710i	0.0493407	+	0.784249i	0.942437	+	0.334383i	$0.108528\pi$
$233$	0.753154	+	11.9710i	0.0493407	+	0.784249i	−0.893096	+	0.449865i	$0.851472\pi$
$234$	0.511732	+	0.0646468i	0.0334530	+	0.00422609i
$235$	−7.00593	+	0.907624i	−0.457017	+	0.0592069i
$236$	−2.05930	−	4.37624i	−0.134049	−	0.284869i
$237$	3.49532	−	7.42794i	0.227046	−	0.482497i
$238$	0.826715	−	0.454490i	0.0535880	−	0.0294602i
$239$	11.6117	−	10.9042i	0.751101	−	0.705331i	−0.211162	−	0.977451i	$-0.567725\pi$
$239$	11.6117	−	10.9042i	0.751101	−	0.705331i	0.962263	+	0.272120i	$0.0877248\pi$
$240$	1.16740	−	3.63202i	0.0753554	−	0.234446i
$241$	12.3730	−	26.2939i	0.797014	−	1.69374i	0.0798822	−	0.996804i	$-0.474546\pi$
$241$	12.3730	−	26.2939i	0.797014	−	1.69374i	0.717132	−	0.696937i	$-0.245454\pi$
$242$	5.00893	+	6.05476i	0.321986	+	0.389215i
$243$	−0.286106	+	0.880545i	−0.0183537	+	0.0564870i
$244$	5.09441	+	1.30802i	0.326136	+	0.0837376i
$245$	−2.97379	−	15.3251i	−0.189988	−	0.979083i
$246$	−0.208556	+	3.31490i	−0.0132970	+	0.211350i
$247$	24.0591	+	37.9110i	1.53084	+	2.41222i
$248$	−0.851359	+	0.799480i	−0.0540614	+	0.0507670i
$249$	20.4879			1.29837
$250$	−0.808087	−	11.1511i	−0.0511079	−	0.705257i
$251$	−20.4329			−1.28971			−0.644856	−	0.764304i	$-0.723083\pi$
$251$	−20.4329			−1.28971			−0.644856	+	0.764304i	$0.723083\pi$
$252$	0.00885551	−	0.00831588i	0.000557845	−	0.000523851i
$253$	4.22605	+	6.65918i	0.265689	+	0.418659i
$254$	−0.200375	+	3.18486i	−0.0125726	+	0.199836i
$255$	26.2062	+	3.22626i	1.64110	+	0.202036i
$256$	0.968583	+	0.248690i	0.0605364	+	0.0155431i
$257$	5.58255	−	17.1813i	0.348230	−	1.07174i	−0.611602	−	0.791166i	$-0.709475\pi$
$257$	5.58255	−	17.1813i	0.348230	−	1.07174i	0.959832	−	0.280576i	$-0.0905254\pi$
$258$	8.57632	+	10.3670i	0.533938	+	0.645421i
$259$	−0.406493	+	0.863842i	−0.0252582	+	0.0536765i
$260$	−4.03816	−	12.2954i	−0.250436	−	0.762531i
$261$	0.640689	−	0.601647i	0.0396577	−	0.0372410i
$262$	−0.924008	+	0.507977i	−0.0570854	+	0.0313830i
$263$	−12.5967	+	26.7693i	−0.776745	+	1.65067i	−0.0175136	+	0.999847i	$0.505575\pi$
$263$	−12.5967	+	26.7693i	−0.776745	+	1.65067i	−0.759231	+	0.650821i	$0.774425\pi$
$264$	−1.28764	−	2.73637i	−0.0792487	−	0.168412i
$265$	−4.59785	−	2.50875i	−0.282444	−	0.154111i
$266$	1.04916	+	0.132539i	0.0643279	+	0.00812651i
$267$	1.04112	+	16.5482i	0.0637156	+	1.01273i
$268$	2.67838	+	8.24319i	0.163608	+	0.503533i
$269$	−2.43965	+	3.84428i	−0.148748	+	0.234390i	−0.910529	−	0.413445i	$-0.864325\pi$
$269$	−2.43965	+	3.84428i	−0.148748	+	0.234390i	0.761781	+	0.647835i	$0.224325\pi$
$270$	11.6874	−	1.51411i	0.711272	−	0.0921459i
$271$	−5.23879	+	1.34509i	−0.318234	+	0.0817086i	−0.404428	−	0.914570i	$-0.632529\pi$
$271$	−5.23879	+	1.34509i	−0.318234	+	0.0817086i	0.0861942	+	0.996278i	$0.472529\pi$
$272$	−0.434578	+	6.90741i	−0.0263501	+	0.418823i
$273$	−0.252213	+	1.32215i	−0.0152646	+	0.0800199i
$274$	−0.960097	+	2.95487i	−0.0580016	+	0.178510i
$275$	−6.49898	−	6.02588i	−0.391903	−	0.363374i
$276$	2.34589	+	7.21989i	0.141206	+	0.434587i
$277$	17.1533	−	2.16697i	1.03064	−	0.130200i	0.408221	−	0.912883i	$-0.366149\pi$
$277$	17.1533	−	2.16697i	1.03064	−	0.130200i	0.622421	+	0.782683i	$0.286149\pi$
$278$	1.18293	+	0.468355i	0.0709474	+	0.0280901i
$279$	−0.0967745	−	0.0383157i	−0.00579374	−	0.00229390i
$280$	−0.283748	−	0.111305i	−0.0169572	−	0.00665172i
$281$	0.0225271	+	0.358059i	0.00134386	+	0.0213600i	0.998642	−	0.0521069i	$-0.0165937\pi$
$281$	0.0225271	+	0.358059i	0.00134386	+	0.0213600i	−0.997298	+	0.0734669i	$0.976594\pi$
$282$	−4.36079	+	3.16830i	−0.259681	+	0.188669i
$283$	−2.67344	−	0.686424i	−0.158920	−	0.0408037i	0.168392	−	0.985720i	$-0.446143\pi$
$283$	−2.67344	−	0.686424i	−0.158920	−	0.0408037i	−0.327311	+	0.944916i	$0.606143\pi$
$284$	−4.12504	−	3.87367i	−0.244776	−	0.229860i
$285$	21.6395	+	20.1921i	1.28181	+	1.19608i
$286$	−8.98992	−	4.94225i	−0.531585	−	0.292241i
$287$	0.263272	+	0.0332589i	0.0155404	+	0.00196321i
$288$	0.0166995	+	0.0875421i	0.000984030	+	0.00515847i
$289$	−30.6575	+	3.87295i	−1.80338	+	0.227820i
$290$	−20.5289	−	8.05280i	−1.20550	−	0.472877i
$291$	−3.41560	−	17.9052i	−0.200226	−	1.04962i
$292$	2.55615	−	4.02784i	0.149587	−	0.235712i
$293$	1.01335	+	0.736240i	0.0592004	+	0.0430116i	0.616992	−	0.786969i	$-0.288351\pi$
$293$	1.01335	+	0.736240i	0.0592004	+	0.0430116i	−0.557791	+	0.829981i	$0.688351\pi$
$294$	−7.59249	−	9.17774i	−0.442803	−	0.535257i
$295$	−10.4836	−	2.65633i	−0.610377	−	0.154658i
$296$	−3.75290	−	5.91362i	−0.218133	−	0.343722i
$297$	5.95488	−	7.19821i	0.345537	−	0.417682i
$298$	−2.80754	−	5.96632i	−0.162636	−	0.345620i
$299$	20.8340	+	15.1368i	1.20486	+	0.875382i
$300$	−4.61652	−	7.17355i	−0.266535	−	0.414165i
$301$	0.869650	−	0.631838i	0.0501258	−	0.0364185i
$302$	18.3398	+	10.0824i	1.05534	+	0.580177i
$303$	9.26436	−	2.37868i	0.532224	−	0.136652i
$304$	−4.94516	+	5.97767i	−0.283624	+	0.342843i
$305$	9.49284	−	6.94303i	0.543559	−	0.397557i
$306$	−0.573496	+	0.227063i	−0.0327846	+	0.0129803i
$307$	−8.16890			−0.466224			−0.233112	−	0.972450i	$-0.574891\pi$
$307$	−8.16890			−0.466224			−0.233112	+	0.972450i	$0.574891\pi$
$308$	−0.224648	+	0.0889444i	−0.0128005	+	0.00506808i
$309$	−27.8716	+	15.3225i	−1.58556	+	0.871669i
$310$	0.172237	+	2.60581i	0.00978242	+	0.148000i
$311$	1.84939	−	9.69485i	0.104869	−	0.549744i	−0.890610	−	0.454768i	$-0.849722\pi$
$311$	1.84939	−	9.69485i	0.104869	−	0.549744i	0.995479	−	0.0949768i	$-0.0302777\pi$
$312$	−7.19819	−	6.75955i	−0.407517	−	0.382684i
$313$	14.2597	+	13.3908i	0.806008	+	0.756892i	0.973428	−	0.228994i	$-0.0735436\pi$
$313$	14.2597	+	13.3908i	0.806008	+	0.756892i	−0.167420	+	0.985886i	$0.553544\pi$
$314$	−2.89626	+	15.1827i	−0.163445	+	0.856811i
$315$	−0.00179155	−	0.0271046i	−0.000100942	−	0.00152717i
$316$	4.21645	−	2.31801i	0.237194	−	0.130398i
$317$	−0.284137	+	0.112498i	−0.0159587	+	0.00631851i	−0.376090	−	0.926583i	$-0.622732\pi$
$317$	−0.284137	+	0.112498i	−0.0159587	+	0.00631851i	0.360132	+	0.932902i	$0.382732\pi$
$318$	−3.99643			−0.224109
$319$	−16.2531	+	6.43505i	−0.909998	+	0.360294i
$320$	1.80484	−	1.32005i	0.100894	−	0.0737933i
$321$	2.51812	−	3.04388i	0.140548	−	0.169893i
$322$	0.587456	−	0.150833i	0.0327377	−	0.00840560i
$323$	−47.0524	−	25.8673i	−2.61806	−	1.43929i
$324$	7.05843	−	5.12825i	0.392135	−	0.284903i
$325$	−26.9731	−	10.4821i	−1.49620	−	0.581443i
$326$	14.6282	+	10.6280i	0.810184	+	0.588633i
$327$	6.70746	+	14.2541i	0.370924	+	0.788253i
$328$	−1.24092	+	1.50002i	−0.0685184	+	0.0828245i
$329$	0.230752	+	0.363607i	0.0127218	+	0.0200463i
$330$	−6.55515	−	1.66095i	−0.360849	−	0.0914321i
$331$	−5.91945	−	7.15539i	−0.325362	−	0.393296i	0.582316	−	0.812963i	$-0.302147\pi$
$331$	−5.91945	−	7.15539i	−0.325362	−	0.393296i	−0.907678	+	0.419667i	$0.862147\pi$
$332$	9.71500	+	7.05836i	0.533180	+	0.387378i
$333$	0.334461	−	0.527026i	0.0183283	−	0.0288808i
$334$	−3.97444	−	20.8347i	−0.217472	−	1.14003i
$335$	18.0424	+	7.07744i	0.985764	+	0.386682i
$336$	−0.230728	+	0.0291477i	−0.0125872	+	0.00159014i
$337$	−0.313565	−	1.64377i	−0.0170810	−	0.0895417i	0.972726	−	0.231957i	$-0.0745130\pi$
$337$	−0.313565	−	1.64377i	−0.0170810	−	0.0895417i	−0.989807	+	0.142416i	$0.954513\pi$
$338$	−20.3353	−	2.56894i	−1.10609	−	0.139732i
$339$	−4.27752	−	2.35159i	−0.232323	−	0.127721i
$340$	11.3150	+	10.5582i	0.613644	+	0.572600i
$341$	1.50907	+	1.41711i	0.0817209	+	0.0767410i
$342$	−0.669680	−	0.171945i	−0.0362122	−	0.00929770i
$343$	−1.54183	+	1.12020i	−0.0832508	+	0.0604852i
$344$	0.495170	+	7.87051i	0.0266978	+	0.424349i
$345$	15.8027	+	6.19885i	0.850787	+	0.333735i
$346$	10.0003	+	3.95939i	0.537619	+	0.212858i
$347$	−3.12390	−	1.23684i	−0.167700	−	0.0663970i	0.282775	−	0.959186i	$-0.408745\pi$
$347$	−3.12390	−	1.23684i	−0.167700	−	0.0663970i	−0.450474	+	0.892789i	$0.648745\pi$
$348$	−16.6930	+	2.10881i	−0.894838	+	0.113044i
$349$	−8.96275	−	27.5845i	−0.479765	−	1.47656i	−0.839422	−	0.543480i	$-0.817106\pi$
$349$	−8.96275	−	27.5845i	−0.479765	−	1.47656i	0.359657	−	0.933085i	$-0.382894\pi$
$350$	−0.595152	+	0.332118i	−0.0318122	+	0.0177524i
$351$	9.42609	−	29.0105i	0.503128	−	1.54847i
$352$	0.332142	−	1.74115i	0.0177032	−	0.0928035i
$353$	−0.556170	+	8.84006i	−0.0296019	+	0.470509i	0.955102	+	0.296276i	$0.0957447\pi$
$353$	−0.556170	+	8.84006i	−0.0296019	+	0.470509i	−0.984704	+	0.174233i	$0.944255\pi$
$354$	−7.99254	+	2.05214i	−0.424799	+	0.109070i
$355$	−12.5484	+	1.62566i	−0.666002	+	0.0862811i
$356$	−5.20739	+	8.20553i	−0.275991	+	0.434892i
$357$	−0.497387	−	1.53080i	−0.0263245	−	0.0810184i
$358$	−0.199582	−	3.17227i	−0.0105483	−	0.167660i
$359$	−4.55615	−	0.575575i	−0.240464	−	0.0303777i	0.00417736	−	0.999991i	$-0.498670\pi$
$359$	−4.55615	−	0.575575i	−0.240464	−	0.0303777i	−0.244642	+	0.969614i	$0.578670\pi$
$360$	0.174934	+	0.0954498i	0.00921982	+	0.00503065i
$361$	−17.5367	−	37.2673i	−0.922982	−	1.96144i
$362$	−6.04007	+	12.8358i	−0.317459	+	0.674634i
$363$	11.7486	−	6.45883i	0.616640	−	0.339001i
$364$	−0.575092	+	0.540048i	−0.0301430	+	0.0283062i
$365$	−3.32845	−	10.1345i	−0.174219	−	0.530465i
$366$	3.82080	−	8.11960i	0.199716	−	0.424418i
$367$	17.5859	+	21.2577i	0.917975	+	1.10964i	0.993651	+	0.112508i	$0.0358885\pi$
$367$	17.5859	+	21.2577i	0.917975	+	1.10964i	−0.0756760	+	0.997132i	$0.524111\pi$
$368$	−1.37497	+	4.23174i	−0.0716755	+	0.220595i
$369$	−0.168047	−	0.0431472i	−0.00874819	−	0.00224615i
$370$	−15.5439	−	1.91362i	−0.808090	−	0.0994844i
$371$	−0.0200484	+	0.318661i	−0.00104086	+	0.0165440i
$372$	1.06768	+	1.68239i	0.0553566	+	0.0872280i
$373$	15.9098	−	14.9403i	0.823780	−	0.773581i	−0.152909	−	0.988240i	$-0.548864\pi$
$373$	15.9098	−	14.9403i	0.823780	−	0.773581i	0.976689	+	0.214659i	$0.0688641\pi$
$374$	12.2679			0.634358
$375$	−18.9466	−	2.21069i	−0.978397	−	0.114160i
$376$	−3.15933			−0.162930
$377$	−41.6075	+	39.0720i	−2.14289	+	2.01231i
$378$	−0.384944	−	0.606575i	−0.0197994	−	0.0311988i
$379$	1.03191	−	16.4018i	0.0530058	−	0.842503i	−0.878265	−	0.478174i	$-0.841299\pi$
$379$	1.03191	−	16.4018i	0.0530058	−	0.842503i	0.931271	−	0.364328i	$-0.118701\pi$
$380$	3.30459	+	17.0298i	0.169522	+	0.873613i
$381$	5.27348	+	1.35400i	0.270169	+	0.0693675i
$382$	2.75006	−	8.46382i	0.140705	−	0.433046i
$383$	1.23935	+	1.49811i	0.0633276	+	0.0765500i	0.801226	−	0.598362i	$-0.204182\pi$
$383$	1.23935	+	1.49811i	0.0633276	+	0.0765500i	−0.737898	+	0.674912i	$0.764182\pi$
$384$	0.726435	−	1.54375i	0.0370707	−	0.0787793i
$385$	−0.165322	+	0.514351i	−0.00842561	+	0.0262138i
$386$	−3.11905	+	2.92898i	−0.158755	+	0.149081i
$387$	−0.615878	+	0.338582i	−0.0313069	+	0.0172111i
$388$	4.54898	−	9.66707i	0.230939	−	0.490771i
$389$	−4.45411	−	9.46547i	−0.225832	−	0.479918i	0.759512	−	0.650493i	$-0.225438\pi$
$389$	−4.45411	−	9.46547i	−0.225832	−	0.479918i	−0.985345	+	0.170575i	$0.945438\pi$
$390$	−21.8970	+	2.83678i	−1.10880	+	0.143646i
$391$	−30.5526	−	3.85968i	−1.54511	−	0.195193i
$392$	−0.438367	−	6.96764i	−0.0221409	−	0.351919i
$393$	0.555922	+	1.71095i	0.0280426	+	0.0863061i
$394$	8.58417	−	13.5265i	0.432464	−	0.681455i
$395$	1.98255	−	10.5749i	0.0997527	−	0.532079i
$396$	0.153007	−	0.0392856i	0.00768892	−	0.00197418i
$397$	0.879197	−	13.9744i	0.0441256	−	0.701357i	−0.912326	−	0.409465i	$-0.865715\pi$
$397$	0.879197	−	13.9744i	0.0441256	−	0.701357i	0.956451	−	0.291892i	$-0.0942847\pi$
$398$	0.589526	−	3.09041i	0.0295503	−	0.154908i
$399$	0.557536	−	1.71592i	0.0279117	−	0.0859034i
$400$	0.282313	−	4.99202i	0.0141157	−	0.249601i
$401$	−6.58282	−	20.2598i	−0.328730	−	1.01173i	−0.969728	−	0.244186i	$-0.921479\pi$
$401$	−6.58282	−	20.2598i	−0.328730	−	1.01173i	0.640998	−	0.767542i	$-0.278521\pi$
$402$	14.6711	−	1.85339i	0.731729	−	0.0924388i
$403$	6.28471	+	2.48829i	0.313064	+	0.123951i
$404$	5.21249	+	2.06377i	0.259331	+	0.102676i
$405$	1.16326	−	19.4743i	0.0578029	−	0.967686i
$406$	0.0844074	+	1.34162i	0.00418907	+	0.0665833i
$407$	−10.0438	+	7.29723i	−0.497852	+	0.361710i
$408$	11.4373	+	2.93659i	0.566229	+	0.145383i
$409$	18.3165	+	17.2004i	0.905694	+	0.850503i	0.989285	−	0.145997i	$-0.0466390\pi$
$409$	18.3165	+	17.2004i	0.905694	+	0.850503i	−0.0835913	+	0.996500i	$0.526639\pi$
$410$	0.829243	+	4.27341i	0.0409534	+	0.211049i
$411$	4.64516	+	2.55370i	0.229129	+	0.125965i
$412$	−18.4950	−	2.33647i	−0.911186	−	0.115110i
$413$	0.123535	+	0.647591i	0.00607874	+	0.0318659i
$414$	−0.393417	+	0.0497001i	−0.0193354	+	0.00244263i
$415$	25.9867	−	6.76012i	1.27564	−	0.331841i
$416$	−1.08450	−	5.68514i	−0.0531719	−	0.278737i
$417$	1.16310	−	1.83275i	0.0569573	−	0.0897503i
$418$	11.1252	+	8.08292i	0.544150	+	0.395348i
$419$	1.34413	+	1.62478i	0.0656651	+	0.0793755i	0.802323	−	0.596890i	$-0.203597\pi$
$419$	1.34413	+	1.62478i	0.0656651	+	0.0793755i	−0.736658	+	0.676266i	$0.763597\pi$
$420$	−0.277250	+	0.439952i	−0.0135284	+	0.0214675i
$421$	4.56057	+	7.18630i	0.222268	+	0.350239i	0.937102	−	0.349056i	$-0.113498\pi$
$421$	4.56057	+	7.18630i	0.222268	+	0.350239i	−0.714834	+	0.699295i	$0.753498\pi$
$422$	14.2064	−	17.1726i	0.691558	−	0.835950i
$423$	−0.119883	−	0.254765i	−0.00582892	−	0.0123871i
$424$	−1.89504	−	1.37682i	−0.0920311	−	0.0668645i
$425$	34.3043	−	4.55475i	1.66400	−	0.220938i
$426$	−7.81068	+	5.67479i	−0.378428	+	0.274944i
$427$	−0.628260	−	0.345389i	−0.0304036	−	0.0167145i
$428$	2.24271	−	0.575830i	0.108405	−	0.0278338i
$429$	−11.1568	+	13.4863i	−0.538656	+	0.651123i
$430$	14.2988	+	10.3196i	0.689550	+	0.497656i
$431$	−18.9452	+	7.50093i	−0.912558	+	0.361307i	−0.777028	−	0.629466i	$-0.783274\pi$
$431$	−18.9452	+	7.50093i	−0.912558	+	0.361307i	−0.135530	+	0.990773i	$0.543274\pi$
$432$	5.27044			0.253574
$433$	−9.57613	+	3.79146i	−0.460199	+	0.182206i	−0.586773	−	0.809751i	$-0.699602\pi$
$433$	−9.57613	+	3.79146i	−0.460199	+	0.182206i	0.126574	+	0.991957i	$0.459602\pi$
$434$	0.139504	−	0.0766929i	0.00669640	−	0.00368138i
$435$	−20.0588	+	31.8302i	−0.961746	+	1.52614i
$436$	−1.73017	+	9.06985i	−0.0828600	+	0.434367i
$437$	−25.1636	−	23.6302i	−1.20374	−	1.13039i
$438$	−5.93311	−	5.57156i	−0.283495	−	0.266219i
$439$	3.41790	−	17.9172i	0.163127	−	0.855143i	−0.802784	−	0.596270i	$-0.796649\pi$
$439$	3.41790	−	17.9172i	0.163127	−	0.855143i	0.965911	−	0.258873i	$-0.0833512\pi$
$440$	−2.53612	−	3.04593i	−0.120905	−	0.145209i
$441$	0.545228	−	0.299742i	0.0259632	−	0.0142734i
$442$	37.2438	−	14.7459i	1.77151	−	0.701389i
$443$	−33.5721			−1.59506			−0.797529	−	0.603280i	$-0.793860\pi$
$443$	−33.5721			−1.59506			−0.797529	+	0.603280i	$0.793860\pi$
$444$	−11.1105	+	4.39895i	−0.527280	+	0.208765i
$445$	6.78073	+	20.6461i	0.321438	+	0.978717i
$446$	0.980943	−	1.18576i	0.0464490	−	0.0561472i
$447$	−10.8966	+	2.79777i	−0.515391	+	0.132330i
$448$	−0.119449	−	0.0656676i	−0.00564343	−	0.00310250i
$449$	−14.5639	+	10.5813i	−0.687314	+	0.499363i	−0.875776	−	0.482717i	$-0.839650\pi$
$449$	−14.5639	+	10.5813i	−0.687314	+	0.499363i	0.188462	+	0.982081i	$0.439650\pi$
$450$	0.413263	−	0.166661i	0.0194814	−	0.00785646i
$451$	2.79171	+	2.02830i	0.131457	+	0.0955088i
$452$	−1.21817	−	2.58875i	−0.0572980	−	0.121764i
$453$	22.7604	−	27.5126i	1.06938	−	1.29265i
$454$	−2.73322	−	4.30687i	−0.128277	−	0.202132i
$455$	0.116346	+	1.76022i	0.00545439	+	0.0825204i
$456$	8.43709	+	10.1987i	0.395103	+	0.477597i
$457$	18.8146	+	13.6696i	0.880109	+	0.639436i	0.933280	−	0.359149i	$-0.116933\pi$
$457$	18.8146	+	13.6696i	0.880109	+	0.639436i	−0.0531716	+	0.998585i	$0.516933\pi$
$458$	1.10644	−	1.74348i	0.0517007	−	0.0814673i
$459$	6.83513	+	35.8310i	0.319036	+	1.67245i
$460$	5.35776	+	8.38363i	0.249807	+	0.390889i
$461$	−4.76336	+	0.601753i	−0.221852	+	0.0280264i	−0.235473	−	0.971881i	$-0.575664\pi$
$461$	−4.76336	+	0.601753i	−0.221852	+	0.0280264i	0.0136214	+	0.999907i	$0.495664\pi$
$462$	0.0772435	+	0.404925i	0.00359369	+	0.0188388i
$463$	−13.1339	−	1.65920i	−0.610385	−	0.0771095i	−0.185937	−	0.982562i	$-0.559532\pi$
$463$	−13.1339	−	1.65920i	−0.610385	−	0.0771095i	−0.424448	+	0.905452i	$0.639532\pi$
$464$	−8.64204	−	4.75100i	−0.401197	−	0.220560i
$465$	4.42216	+	0.544415i	0.205073	+	0.0252466i
$466$	8.74376	+	8.21094i	0.405047	+	0.380365i
$467$	8.08231	+	2.07518i	0.374005	+	0.0960281i	0.431013	−	0.902346i	$-0.358156\pi$
$467$	8.08231	+	2.07518i	0.374005	+	0.0960281i	−0.0570085	+	0.998374i	$0.518156\pi$
$468$	0.417290	−	0.303179i	0.0192893	−	0.0140145i
$469$	−0.0741839	−	1.17912i	−0.00342549	−	0.0544467i
$470$	−4.48579	+	5.45752i	−0.206914	+	0.251737i
$471$	24.5190	+	9.70774i	1.12977	+	0.447309i
$472$	−4.49691	−	1.78045i	−0.206987	−	0.0819520i
$473$	13.8682	−	1.75196i	0.637660	−	0.0805552i
$474$	−2.53679	−	7.80745i	−0.116519	−	0.358608i
$475$	34.1099	+	18.4715i	1.56507	+	0.847529i
$476$	0.291529	−	0.897234i	0.0133622	−	0.0411247i
$477$	0.0391169	−	0.205058i	0.00179104	−	0.00938897i
$478$	1.00019	−	15.8976i	0.0457476	−	0.727138i
$479$	−39.8500	+	10.2317i	−1.82079	+	0.467500i	−0.995294	−	0.0969021i	$-0.969107\pi$
$479$	−39.8500	+	10.2317i	−1.82079	+	0.467500i	−0.825500	+	0.564402i	$0.809107\pi$
$480$	−1.63529	−	3.44677i	−0.0746405	−	0.157323i
$481$	−21.7205	+	34.2260i	−0.990368	+	1.56057i
$482$	−8.97992	−	27.6374i	−0.409024	−	1.25885i
$483$	−0.0649748	−	1.03274i	−0.00295646	−	0.0469915i
$484$	7.79612	+	0.984879i	0.354369	+	0.0447672i
$485$	−10.2403	−	21.5839i	−0.464987	−	0.980073i
$486$	0.394212	+	0.837743i	0.0178818	+	0.0380008i
$487$	−1.21690	+	2.58605i	−0.0551432	+	0.117185i	−0.930500	−	0.366293i	$-0.880627\pi$
$487$	−1.21690	+	2.58605i	−0.0551432	+	0.117185i	0.875356	+	0.483478i	$0.160627\pi$
$488$	4.60907	−	2.53386i	0.208643	−	0.114702i
$489$	22.4882	−	21.1179i	1.01695	−	0.954983i
$490$	−12.6585	−	9.13580i	−0.571854	−	0.412713i
$491$	−13.5044	+	28.6984i	−0.609447	+	1.29514i	0.327230	+	0.944945i	$0.393885\pi$
$491$	−13.5044	+	28.6984i	−0.609447	+	1.29514i	−0.936677	+	0.350195i	$0.886115\pi$
$492$	2.11717	+	2.55922i	0.0954495	+	0.115379i
$493$	21.0919	−	64.9142i	0.949931	−	2.92359i
$494$	43.4902	+	11.1664i	1.95672	+	0.502399i
$495$	0.149385	−	0.320090i	0.00671437	−	0.0143870i
$496$	−0.0733328	+	1.16559i	−0.00329274	+	0.0523366i
$497$	0.413304	+	0.651263i	0.0185392	+	0.0292131i
$498$	14.9350	−	14.0249i	0.669255	−	0.628472i
$499$	22.7068			1.01650			0.508249	−	0.861210i	$-0.330293\pi$
$499$	22.7068			1.01650			0.508249	+	0.861210i	$0.330293\pi$
$500$	−8.22252	−	7.57563i	−0.367722	−	0.338792i
$501$	−36.1878			−1.61675
$502$	−14.8949	+	13.9873i	−0.664793	+	0.624282i
$503$	11.5378	+	18.1806i	0.514444	+	0.810633i	0.997903	−	0.0647336i	$-0.0206198\pi$
$503$	11.5378	+	18.1806i	0.514444	+	0.810633i	−0.483459	+	0.875367i	$0.660620\pi$
$504$	0.000762779	−	0.0121240i	3.39769e−5	−	0.000540047i
$505$	10.9660	−	6.07395i	0.487980	−	0.270287i
$506$	7.63918	+	1.96141i	0.339603	+	0.0871952i
$507$	−10.8064	+	33.2588i	−0.479931	+	1.47708i
$508$	2.03412	+	2.45883i	0.0902496	+	0.109093i
$509$	−14.4965	+	30.8066i	−0.642545	+	1.36548i	0.272511	+	0.962153i	$0.412146\pi$
$509$	−14.4965	+	30.8066i	−0.642545	+	1.36548i	−0.915057	+	0.403326i	$0.867854\pi$
$510$	21.3120	−	15.5875i	0.943712	−	0.690227i
$511$	−0.474020	+	0.445134i	−0.0209694	+	0.0196916i
$512$	0.876307	−	0.481754i	0.0387276	−	0.0212907i
$513$	−17.4094	+	36.9968i	−0.768643	+	1.63345i
$514$	−7.69192	−	16.3462i	−0.339276	−	0.720998i
$515$	−30.2964	+	28.6314i	−1.33502	+	1.26165i
$516$	13.3486	+	1.68632i	0.587638	+	0.0742359i
$517$	0.351630	+	5.58901i	0.0154647	+	0.245804i
$518$	0.295020	+	0.907977i	0.0129624	+	0.0398942i
$519$	9.83265	−	15.4938i	0.431605	−	0.680101i
$520$	−11.3605	−	6.19868i	−0.498191	−	0.271830i
$521$	−23.9965	+	6.16124i	−1.05130	+	0.269929i	−0.734533	−	0.678573i	$-0.762599\pi$
$521$	−23.9965	+	6.16124i	−1.05130	+	0.269929i	−0.316771	+	0.948502i	$0.602599\pi$
$522$	0.0551865	−	0.877164i	0.00241545	−	0.0383924i
$523$	0.0420279	−	0.220318i	0.00183775	−	0.00963383i	−0.981357	−	0.192196i	$-0.938439\pi$
$523$	0.0420279	−	0.220318i	0.00183775	−	0.00963383i	0.983194	+	0.182562i	$0.0584391\pi$
$524$	−0.325838	+	1.00283i	−0.0142343	+	0.0438087i
$525$	0.366331	+	1.10360i	0.0159880	+	0.0481649i
$526$	9.14227	+	28.1370i	0.398622	+	1.22683i
$527$	−8.01935	+	1.01308i	−0.349328	+	0.0441304i
$528$	−2.81182	−	1.11328i	−0.122369	−	0.0484493i
$529$	2.97700	+	1.17868i	0.129435	+	0.0512468i
$530$	−5.06904	+	1.31865i	−0.220185	+	0.0572785i
$531$	−0.0270650	−	0.430186i	−0.00117452	−	0.0186685i
$532$	0.855532	−	0.621580i	0.0370920	−	0.0269489i
$533$	10.9133	+	2.80205i	0.472706	+	0.121370i
$534$	12.0869	+	11.3504i	0.523053	+	0.491179i
$535$	2.18962	−	4.69171i	0.0946654	−	0.202841i
$536$	7.59531	+	4.17555i	0.328067	+	0.180356i
$537$	−5.38025	−	0.679683i	−0.232175	−	0.0293305i
$538$	0.853159	+	4.47242i	0.0367823	+	0.192820i
$539$	−12.2773	+	1.55098i	−0.528821	+	0.0668056i
$540$	7.48326	−	9.10431i	0.322028	−	0.391787i
$541$	8.29863	+	43.5029i	0.356786	+	1.87034i	0.478972	+	0.877830i	$0.341009\pi$
$541$	8.29863	+	43.5029i	0.356786	+	1.87034i	−0.122186	+	0.992507i	$0.538991\pi$
$542$	−2.89814	+	4.56673i	−0.124486	+	0.196158i
$543$	19.5806	+	14.2262i	0.840286	+	0.610503i
$544$	4.41166	+	5.33278i	0.189148	+	0.228641i
$545$	13.2109	+	15.8666i	0.565894	+	0.679651i
$546$	0.721216	+	1.13645i	0.0308652	+	0.0486358i
$547$	11.0748	−	13.3872i	0.473525	−	0.572394i	−0.478627	−	0.878019i	$-0.658865\pi$
$547$	11.0748	−	13.3872i	0.473525	−	0.572394i	0.952152	+	0.305625i	$0.0988652\pi$
$548$	1.32287	+	2.81124i	0.0565102	+	0.120090i
$549$	0.379222	+	0.275521i	0.0161848	+	0.0117589i
$550$	−8.86255	+	0.0561817i	−0.377900	+	0.00239560i
$551$	61.8970	−	44.9708i	2.63690	−	1.91582i
$552$	6.65243	+	3.65721i	0.283146	+	0.155661i
$553$	−0.635264	+	0.163108i	−0.0270142	+	0.00693606i
$554$	11.0208	−	13.3219i	0.468230	−	0.565993i
$555$	−8.17640	+	25.4384i	−0.347069	+	1.07980i
$556$	1.18293	−	0.468355i	0.0501674	−	0.0198627i
$557$	0.799840			0.0338903			0.0169451	−	0.999856i	$-0.494606\pi$
$557$	0.799840			0.0338903			0.0169451	+	0.999856i	$0.494606\pi$
$558$	−0.0967745	+	0.0383157i	−0.00409679	+	0.00162203i
$559$	39.9962	−	21.9881i	1.69166	−	0.929998i
$560$	−0.283036	+	0.113101i	−0.0119605	+	0.00477939i
$561$	3.92201	−	20.5599i	0.165587	−	0.868040i
$562$	0.261530	+	0.245593i	0.0110320	+	0.0103597i
$563$	10.2182	+	9.59551i	0.430645	+	0.404403i	0.869325	−	0.494241i	$-0.164554\pi$
$563$	10.2182	+	9.59551i	0.430645	+	0.404403i	−0.438680	+	0.898643i	$0.644554\pi$
$564$	−1.01003	+	5.29475i	−0.0425299	+	0.222949i
$565$	−6.20150	−	1.57134i	−0.260899	−	0.0661068i
$566$	−2.41875	+	1.32972i	−0.101667	+	0.0558922i
$567$	−1.10575	+	0.437796i	−0.0464369	+	0.0183857i
$568$	−5.65873			−0.237435
$569$	−15.5158	+	6.14313i	−0.650455	+	0.257533i	−0.670097	−	0.742274i	$-0.733747\pi$
$569$	−15.5158	+	6.14313i	−0.650455	+	0.257533i	0.0196419	+	0.999807i	$0.493747\pi$
$570$	29.5970	−	0.0938100i	1.23968	−	0.00392927i
$571$	20.3791	−	24.6341i	0.852840	−	1.03091i	−0.146291	−	0.989242i	$-0.546734\pi$
$571$	20.3791	−	24.6341i	0.852840	−	1.03091i	0.999132	−	0.0416653i	$-0.0132663\pi$
$572$	−9.93657	+	2.55128i	−0.415469	+	0.106674i
$573$	−13.3054	−	7.31471i	−0.555841	−	0.305576i
$574$	0.214684	−	0.155977i	0.00896074	−	0.00651036i
$575$	22.0894	+	2.64839i	0.921190	+	0.110445i
$576$	0.0721001	+	0.0523838i	0.00300417	+	0.00218266i
$577$	−17.6023	−	37.4067i	−0.732792	−	1.55726i	−0.827314	−	0.561739i	$-0.810132\pi$
$577$	−17.6023	−	37.4067i	−0.732792	−	1.55726i	0.0945222	−	0.995523i	$-0.469868\pi$
$578$	−19.6972	+	23.8098i	−0.819294	+	0.990357i
$579$	3.91156	+	6.16363i	0.162559	+	0.256152i
$580$	−20.4775	+	8.18277i	−0.850280	+	0.339771i
$581$	−1.04337	−	1.26122i	−0.0432864	−	0.0523243i
$582$	−14.7468	−	10.7142i	−0.611276	−	0.444118i
$583$	−2.22475	+	3.50565i	−0.0921398	+	0.145189i
$584$	−0.893897	−	4.68597i	−0.0369897	−	0.193907i
$585$	0.0687714	−	1.15131i	0.00284335	−	0.0476008i
$586$	1.24269	−	0.156988i	0.0513351	−	0.00648513i
$587$	−8.38051	−	43.9322i	−0.345901	−	1.81328i	−0.550967	−	0.834527i	$-0.685741\pi$
$587$	−8.38051	−	43.9322i	−0.345901	−	1.81328i	0.205066	−	0.978748i	$-0.434259\pi$
$588$	−11.8173	−	1.49287i	−0.487337	−	0.0615649i
$589$	−7.93985	−	4.36497i	−0.327156	−	0.179855i
$590$	−9.46057	+	5.24011i	−0.389486	+	0.215732i
$591$	−19.9248	−	18.7107i	−0.819599	−	0.769654i
$592$	−6.78389	−	1.74181i	−0.278816	−	0.0715879i
$593$	14.9746	−	10.8797i	0.614935	−	0.446776i	−0.236214	−	0.971701i	$-0.575907\pi$
$593$	14.9746	−	10.8797i	0.614935	−	0.446776i	0.851149	+	0.524925i	$0.175907\pi$
$594$	−0.586595	−	9.32366i	−0.0240683	−	0.382554i
$595$	−1.13598	−	1.77754i	−0.0465706	−	0.0728720i
$596$	−6.13084	−	2.42737i	−0.251129	−	0.0994290i
$597$	−4.99077	−	1.97599i	−0.204259	−	0.0808717i
$598$	25.5492	−	3.22761i	1.04478	−	0.131987i
$599$	12.6735	+	39.0049i	0.517823	+	1.59370i	0.778086	+	0.628158i	$0.216191\pi$
$599$	12.6735	+	39.0049i	0.517823	+	1.59370i	−0.260262	+	0.965538i	$0.583809\pi$
$600$	−8.27593	−	2.06907i	−0.337863	−	0.0844693i
$601$	−10.1717	+	31.3053i	−0.414912	+	1.27697i	0.497417	+	0.867511i	$0.334282\pi$
$601$	−10.1717	+	31.3053i	−0.414912	+	1.27697i	−0.912330	+	0.409457i	$0.865718\pi$
$602$	0.201425	−	1.05591i	0.00820946	−	0.0430355i
$603$	−0.0485022	+	0.770921i	−0.00197516	+	0.0313943i
$604$	20.2710	−	5.20471i	0.824816	−	0.211777i
$605$	12.7707	−	12.0689i	0.519202	−	0.490669i
$606$	5.12511	−	8.07588i	0.208193	−	0.328060i
$607$	3.59286	+	11.0577i	0.145830	+	0.448818i	0.997117	−	0.0758825i	$-0.0241774\pi$
$607$	3.59286	+	11.0577i	0.145830	+	0.448818i	−0.851287	+	0.524700i	$0.824177\pi$
$608$	0.487131	+	7.74273i	0.0197558	+	0.314009i
$609$	2.27541	+	0.287452i	0.0922044	+	0.0116481i
$610$	2.16715	−	11.5596i	0.0877455	−	0.468033i
$611$	7.78542	+	16.5449i	0.314964	+	0.669333i
$612$	−0.262625	+	0.558107i	−0.0106160	+	0.0225601i
$613$	32.3682	−	17.7946i	1.30734	−	0.718716i	0.332814	−	0.942993i	$-0.392002\pi$
$613$	32.3682	−	17.7946i	1.30734	−	0.718716i	0.974525	+	0.224277i	$0.0720020\pi$
$614$	−5.95487	+	5.59200i	−0.240319	+	0.225675i
$615$	7.42695	−	0.0235404i	0.299484	−	0.000949239i
$616$	−0.102875	+	0.218620i	−0.00414494	+	0.00880844i
$617$	−31.6001	−	38.1979i	−1.27217	−	1.53779i	−0.685996	−	0.727605i	$-0.740633\pi$
$617$	−31.6001	−	38.1979i	−1.27217	−	1.53779i	−0.586175	−	0.810185i	$-0.699367\pi$
$618$	−9.82852	+	30.2491i	−0.395361	+	1.21680i
$619$	13.5958	+	3.49081i	0.546462	+	0.140307i	0.511821	−	0.859092i	$-0.328971\pi$
$619$	13.5958	+	3.49081i	0.546462	+	0.140307i	0.0346409	+	0.999400i	$0.488971\pi$
$620$	1.90935	+	1.78165i	0.0766815	+	0.0715527i
$621$	−1.47249	+	23.4046i	−0.0590891	+	0.939195i
$622$	−5.28843	−	8.33323i	−0.212047	−	0.334132i
$623$	0.965674	−	0.906828i	0.0386889	−	0.0363313i
$624$	−9.87449			−0.395296
$625$	−24.7611	+	3.44753i	−0.990446	+	0.137901i
$626$	19.5615			0.781835
$627$	17.1029	−	16.0607i	0.683025	−	0.641403i
$628$	8.28201	+	13.0504i	0.330488	+	0.520766i
$629$	3.04375	−	48.3791i	0.121362	−	1.92900i
$630$	−0.0198604	−	0.0185320i	−0.000791256	−	0.000738333i
$631$	5.87887	+	1.50944i	0.234034	+	0.0600898i	0.363885	−	0.931444i	$-0.381450\pi$
$631$	5.87887	+	1.50944i	0.234034	+	0.0600898i	−0.129851	+	0.991533i	$0.541450\pi$
$632$	1.48687	−	4.57612i	0.0591445	−	0.182028i
$633$	−24.2380	−	29.2987i	−0.963374	−	1.16452i
$634$	−0.130117	+	0.276513i	−0.00516761	+	0.0109817i
$635$	7.13561	−	0.0226169i	0.283168	−	0.000897525i
$636$	−2.91327	+	2.73574i	−0.115519	+	0.108479i
$637$	−35.4081	+	19.4657i	−1.40292	+	0.771261i
$638$	−7.44290	+	15.8170i	−0.294667	+	0.626199i
$639$	−0.214725	−	0.456313i	−0.00849437	−	0.0180515i
$640$	0.412033	−	2.19778i	0.0162871	−	0.0868748i
$641$	−13.8529	−	1.75003i	−0.547156	−	0.0691219i	−0.153104	−	0.988210i	$-0.548927\pi$
$641$	−13.8529	−	1.75003i	−0.547156	−	0.0691219i	−0.394052	+	0.919088i	$0.628927\pi$
$642$	−0.248052	−	3.94267i	−0.00978982	−	0.155605i
$643$	11.1017	+	34.1675i	0.437807	+	1.34743i	0.890182	+	0.455605i	$0.150577\pi$
$643$	11.1017	+	34.1675i	0.437807	+	1.34743i	−0.452375	+	0.891828i	$0.649423\pi$
$644$	0.324985	−	0.512094i	0.0128062	−	0.0201793i
$645$	21.8660	−	20.6644i	0.860973	−	0.813659i
$646$	−52.0071	+	13.3531i	−2.04619	+	0.525372i
$647$	−2.56757	+	40.8104i	−0.100942	+	1.60442i	0.543258	+	0.839566i	$0.317191\pi$
$647$	−2.56757	+	40.8104i	−0.100942	+	1.60442i	−0.644200	+	0.764857i	$0.722809\pi$
$648$	1.63484	−	8.57016i	0.0642228	−	0.336668i
$649$	−2.64920	+	8.15341i	−0.103990	+	0.320049i
$650$	−26.8380	+	10.8232i	−1.05267	+	0.424522i
$651$	−0.0839315	−	0.258315i	−0.00328953	−	0.0101241i
$652$	17.9389	−	2.26621i	0.702543	−	0.0887518i
$653$	17.7870	+	7.04237i	0.696059	+	0.275589i	0.689392	−	0.724388i	$-0.257878\pi$
$653$	17.7870	+	7.04237i	0.696059	+	0.275589i	0.00666712	+	0.999978i	$0.497878\pi$
$654$	14.6471	+	5.79921i	0.572748	+	0.226767i
$655$	1.26967	+	1.98673i	0.0496101	+	0.0776280i
$656$	0.122239	+	1.94293i	0.00477263	+	0.0758588i
$657$	0.343952	−	0.249896i	0.0134188	−	0.00974935i
$658$	0.417117	+	0.107098i	0.0162609	+	0.00417510i
$659$	−28.4329	−	26.7003i	−1.10759	−	1.04010i	−0.998941	−	0.0460152i	$-0.985348\pi$
$659$	−28.4329	−	26.7003i	−1.10759	−	1.04010i	−0.108648	−	0.994080i	$-0.534652\pi$
$660$	−5.91549	+	3.27653i	−0.230260	+	0.127539i
$661$	4.66953	+	2.56710i	0.181624	+	0.0998484i	0.569972	−	0.821664i	$-0.306954\pi$
$661$	4.66953	+	2.56710i	0.181624	+	0.0998484i	−0.388348	+	0.921513i	$0.626954\pi$
$662$	−9.21329	−	1.16391i	−0.358085	−	0.0452366i
$663$	−12.8060	−	67.1315i	−0.497344	−	2.60717i
$664$	11.9137	−	1.50505i	0.462342	−	0.0584073i
$665$	0.140996	−	2.36042i	0.00546758	−	0.0915333i
$666$	−0.116963	−	0.613139i	−0.00453221	−	0.0237587i
$667$	23.5124	−	37.0496i	0.910404	−	1.43457i
$668$	−17.1596	−	12.4672i	−0.663925	−	0.482370i
$669$	−1.67362	−	2.02306i	−0.0647058	−	0.0782158i
$670$	17.9972	−	7.19167i	0.695293	−	0.277838i
$671$	−4.99550	−	7.87165i	−0.192849	−	0.303882i
$672$	−0.148240	+	0.179192i	−0.00571850	+	0.00691248i
$673$	−8.27948	−	17.5948i	−0.319151	−	0.678230i	0.679301	−	0.733860i	$-0.262283\pi$
$673$	−8.27948	−	17.5948i	−0.319151	−	0.678230i	−0.998451	+	0.0556304i	$0.982283\pi$
$674$	−1.35382	−	0.983604i	−0.0521470	−	0.0378870i
$675$	−5.10190	−	25.8536i	−0.196372	−	0.995106i
$676$	−16.5823	+	12.0478i	−0.637783	+	0.463376i
$677$	13.4582	+	7.39870i	0.517240	+	0.284355i	0.718916	−	0.695097i	$-0.244639\pi$
$677$	13.4582	+	7.39870i	0.517240	+	0.284355i	−0.201676	+	0.979452i	$0.564639\pi$
$678$	−4.72795	+	1.21393i	−0.181576	+	0.0466208i
$679$	−0.928291	+	1.12211i	−0.0356245	+	0.0430627i
$680$	15.4759	−	0.0490522i	0.593474	−	0.00188106i
$681$	−8.09173	+	3.20374i	−0.310076	+	0.122768i
$682$	2.07015			0.0792701
$683$	30.3949	−	12.0342i	1.16303	−	0.460476i	0.294276	−	0.955720i	$-0.404922\pi$
$683$	30.3949	−	12.0342i	1.16303	−	0.460476i	0.868754	+	0.495245i	$0.164922\pi$
$684$	−0.605880	+	0.333085i	−0.0231664	+	0.0127358i
$685$	6.73450	+	1.70639i	0.257312	+	0.0651979i
$686$	−0.357112	+	1.87204i	−0.0136346	+	0.0714750i
$687$	−2.56818	−	2.41168i	−0.0979822	−	0.0920115i
$688$	5.74869	+	5.39838i	0.219167	+	0.205811i
$689$	−2.54032	+	13.3168i	−0.0967785	+	0.507331i
$690$	15.7631	−	6.29890i	0.600089	−	0.239795i
$691$	−2.20279	+	1.21099i	−0.0837981	+	0.0460684i	−0.523102	−	0.852270i	$-0.675225\pi$
$691$	−2.20279	+	1.21099i	−0.0837981	+	0.0460684i	0.439304	+	0.898339i	$0.355225\pi$
$692$	10.0003	−	3.95939i	0.380154	−	0.150514i
$693$	−0.0215329			−0.000817967
$694$	−3.12390	+	1.23684i	−0.118582	+	0.0469497i
$695$	0.870539	−	2.70842i	0.0330214	−	0.102736i
$696$	−10.7251	+	12.9644i	−0.406533	+	0.491414i
$697$	−13.0505	+	3.35079i	−0.494322	+	0.126920i
$698$	−25.4165	−	13.9728i	−0.962027	−	0.528879i
$699$	16.5562	−	12.0287i	0.626211	−	0.454969i
$700$	−0.206497	+	0.649513i	−0.00780484	+	0.0245493i
$701$	16.1397	+	11.7262i	0.609588	+	0.442892i	0.849269	−	0.527960i	$-0.177043\pi$
$701$	16.1397	+	11.7262i	0.609588	+	0.442892i	−0.239681	+	0.970852i	$0.577043\pi$
$702$	−12.9877	−	27.6004i	−0.490191	−	1.04171i
$703$	34.6356	−	41.8672i	1.30631	−	1.57905i
$704$	−0.949777	−	1.49661i	−0.0357961	−	0.0564056i
$705$	7.71222	+	9.26254i	0.290459	+	0.348847i
$706$	5.64601	+	6.82485i	0.212490	+	0.256857i
$707$	−0.618230	−	0.449171i	−0.0232509	−	0.0168928i
$708$	−4.42153	+	6.96721i	−0.166171	+	0.261844i
$709$	0.387264	+	2.03011i	0.0145440	+	0.0762423i	0.988819	−	0.149119i	$-0.0476438\pi$
$709$	0.387264	+	2.03011i	0.0145440	+	0.0762423i	−0.974275	+	0.225361i	$0.927644\pi$
$710$	−8.03458	+	9.77505i	−0.301532	+	0.366851i
$711$	0.425433	−	0.0537447i	0.0159550	−	0.00201558i
$712$	1.82105	+	9.54627i	0.0682467	+	0.357762i
$713$	−5.15559	−	0.651302i	−0.193078	−	0.0243915i
$714$	−1.41048	−	0.775419i	−0.0527860	−	0.0290193i
$715$	−9.70134	+	20.7872i	−0.362810	+	0.777396i
$716$	−2.31706	−	2.17586i	−0.0865926	−	0.0813158i
$717$	−26.3231	−	6.75863i	−0.983056	−	0.252406i
$718$	−3.71530	+	2.69932i	−0.138654	+	0.100738i
$719$	2.06003	+	32.7432i	0.0768260	+	1.22111i	0.827892	+	0.560887i	$0.189540\pi$
$719$	2.06003	+	32.7432i	0.0768260	+	1.22111i	−0.751066	+	0.660227i	$0.770460\pi$
$720$	0.192861	−	0.0501704i	0.00718751	−	0.00186974i
$721$	2.36265	+	0.935437i	0.0879895	+	0.0348375i
$722$	−38.2949	−	15.1620i	−1.42519	−	0.564272i
$723$	−49.1886	+	6.21396i	−1.82934	+	0.231100i
$724$	4.38369	+	13.4916i	0.162918	+	0.501411i
$725$	−14.9399	+	46.9917i	−0.554853	+	1.74523i
$726$	4.14296	−	12.7507i	0.153760	−	0.473224i
$727$	−5.35209	+	28.0566i	−0.198498	+	1.04056i	0.733935	+	0.679220i	$0.237682\pi$
$727$	−5.35209	+	28.0566i	−0.198498	+	1.04056i	−0.932433	+	0.361343i	$0.882318\pi$
$728$	−0.0495362	+	0.787355i	−0.00183593	+	0.0291813i
$729$	26.8818	−	6.90207i	0.995622	−	0.255632i
$730$	−9.36389	−	5.10926i	−0.346573	−	0.189102i
$731$	−29.2454	+	46.0834i	−1.08168	+	1.70446i
$732$	−2.77301	−	8.53445i	−0.102493	−	0.315442i
$733$	1.04631	+	16.6306i	0.0386462	+	0.614264i	0.968916	+	0.247388i	$0.0795724\pi$
$733$	1.04631	+	16.6306i	0.0386462	+	0.614264i	−0.930270	+	0.366875i	$0.880428\pi$
$734$	27.3714	+	3.45781i	1.01030	+	0.127630i
$735$	−19.3577	+	18.2939i	−0.714018	+	0.674779i
$736$	1.89451	+	4.02604i	0.0698326	+	0.148402i
$737$	6.54140	−	13.9012i	0.240956	−	0.512057i
$738$	−0.152037	+	0.0835833i	−0.00559657	+	0.00307674i
$739$	−26.7104	+	25.0828i	−0.982559	+	0.922684i	−0.997015	−	0.0772111i	$-0.975398\pi$
$739$	−26.7104	+	25.0828i	−0.982559	+	0.922684i	0.0144557	+	0.999896i	$0.495398\pi$
$740$	−12.6410	+	9.24558i	−0.464692	+	0.339874i
$741$	32.6175	−	69.3158i	1.19824	−	2.54638i
$742$	0.203524	+	0.246018i	0.00747159	+	0.00903159i
$743$	−9.34490	+	28.7606i	−0.342831	+	1.05513i	0.619904	+	0.784678i	$0.287172\pi$
$743$	−9.34490	+	28.7606i	−0.342831	+	1.05513i	−0.962735	+	0.270448i	$0.912828\pi$
$744$	1.92998	+	0.495535i	0.0707565	+	0.0181672i
$745$	−12.8980	+	7.14407i	−0.472547	+	0.261739i
$746$	1.37041	−	21.7821i	0.0501743	−	0.797498i
$747$	0.573440	+	0.903597i	0.0209811	+	0.0330609i
$748$	8.94292	−	8.39796i	0.326986	−	0.307060i
$749$	−0.315618			−0.0115324
$750$	−15.3248	+	11.3583i	−0.559582	+	0.414746i
$751$	−39.5732			−1.44405			−0.722023	−	0.691869i	$-0.756787\pi$
$751$	−39.5732			−1.44405			−0.722023	+	0.691869i	$0.756787\pi$
$752$	−2.30305	+	2.16271i	−0.0839837	+	0.0788659i
$753$	18.6795	+	29.4342i	0.680720	+	1.07264i
$754$	−3.58391	+	56.9645i	−0.130518	+	2.07453i
$755$	19.7911	−	42.4067i	0.720273	−	1.54334i
$756$	−0.695841	−	0.178662i	−0.0253075	−	0.00649786i
$757$	4.52046	−	13.9125i	0.164299	−	0.505660i	−0.834685	−	0.550728i	$-0.814350\pi$
$757$	4.52046	−	13.9125i	0.164299	−	0.505660i	0.998984	+	0.0450676i	$0.0143503\pi$
$758$	−10.4756	−	12.6628i	−0.380489	−	0.459933i
$759$	5.72936	−	12.1755i	0.207963	−	0.441943i
$760$	14.0667	+	10.1521i	0.510252	+	0.368254i
$761$	−17.0018	+	15.9658i	−0.616315	+	0.578758i	−0.928532	−	0.371253i	$-0.878928\pi$
$761$	−17.0018	+	15.9658i	−0.616315	+	0.578758i	0.312217	+	0.950011i	$0.398928\pi$
$762$	4.77108	−	2.62292i	0.172838	−	0.0950185i
$763$	0.535886	−	1.13882i	0.0194004	−	0.0412279i
$764$	−3.78917	−	8.05240i	−0.137087	−	0.291326i
$765$	0.591200	+	1.24610i	0.0213749	+	0.0450527i
$766$	1.92897	+	0.243686i	0.0696966	+	0.00880473i
$767$	1.75765	+	27.9370i	0.0634650	+	1.00875i
$768$	−0.527223	−	1.62263i	−0.0190245	−	0.0585515i
$769$	18.5699	−	29.2615i	0.669648	−	1.05520i	−0.324365	−	0.945932i	$-0.605151\pi$
$769$	18.5699	−	29.2615i	0.669648	−	1.05520i	0.994013	−	0.109264i	$-0.0348493\pi$
$770$	0.231583	+	0.488117i	0.00834567	+	0.0175905i
$771$	−29.8538	+	7.66515i	−1.07516	+	0.276054i
$772$	−0.268663	+	4.27027i	−0.00966938	+	0.153690i
$773$	−3.66890	+	19.2330i	−0.131961	+	0.691764i	0.853396	+	0.521262i	$0.174539\pi$
$773$	−3.66890	+	19.2330i	−0.131961	+	0.691764i	−0.985357	+	0.170501i	$0.945461\pi$
$774$	−0.217181	+	0.668413i	−0.00780640	+	0.0240256i
$775$	5.78868	−	0.768591i	0.207935	−	0.0276086i
$776$	−3.30150	−	10.1610i	−0.118517	−	0.364758i
$777$	1.61600	−	0.204149i	0.0579738	−	0.00732380i
$778$	−9.72646	−	3.85098i	−0.348711	−	0.138064i
$779$	−14.0426	−	5.55985i	−0.503127	−	0.199202i
$780$	−14.0203	+	17.0575i	−0.502009	+	0.610755i
$781$	0.629811	+	10.0106i	0.0225364	+	0.358206i
$782$	−24.9140	+	18.1011i	−0.890922	+	0.647293i
$783$	−50.3436	−	12.9260i	−1.79913	−	0.461939i
$784$	−5.08924	−	4.77911i	−0.181758	−	0.170683i
$785$	34.3028	+	4.22304i	1.22432	+	0.150727i
$786$	1.57648	+	0.866676i	0.0562311	+	0.0309133i
$787$	31.9907	+	4.04137i	1.14035	+	0.144059i	0.672741	−	0.739878i	$-0.265117\pi$
$787$	31.9907	+	4.04137i	1.14035	+	0.144059i	0.467605	+	0.883937i	$0.345117\pi$
$788$	−3.00193	−	15.7367i	−0.106939	−	0.560595i
$789$	50.0779	−	6.32631i	1.78282	−	0.225222i
$790$	−5.79378	−	9.06589i	−0.206133	−	0.322550i
$791$	0.0730763	+	0.383079i	0.00259829	+	0.0136207i
$792$	0.0846448	−	0.133379i	0.00300772	−	0.00473941i
$793$	−24.6273	−	17.8928i	−0.874542	−	0.635392i
$794$	−8.92526	−	10.7888i	−0.316745	−	0.382879i
$795$	0.589379	+	8.91683i	0.0209031	+	0.316247i
$796$	−1.68578	−	2.65637i	−0.0597510	−	0.0941525i
$797$	−11.6095	+	14.0335i	−0.411231	+	0.497093i	−0.934941	−	0.354804i	$-0.884548\pi$
$797$	−11.6095	+	14.0335i	−0.411231	+	0.497093i	0.523710	+	0.851897i	$0.324548\pi$
$798$	−0.768201	−	1.63251i	−0.0271940	−	0.0577903i
$799$	−17.6899	−	12.8525i	−0.625825	−	0.454688i
$800$	−3.21148	−	3.83229i	−0.113543	−	0.135492i
$801$	−0.700699	+	0.509088i	−0.0247580	+	0.0179877i
$802$	−18.6675	−	10.2625i	−0.659172	−	0.362383i
$803$	−8.19022	+	2.10289i	−0.289027	+	0.0742094i
$804$	9.42605	−	11.3941i	0.332431	−	0.401840i
$805$	−0.423175	−	1.28849i	−0.0149150	−	0.0454132i
$806$	6.28471	−	2.48829i	0.221369	−	0.0876463i
$807$	7.76812			0.273451
$808$	5.21249	−	2.06377i	0.183375	−	0.0726032i
$809$	−0.478779	+	0.263211i	−0.0168330	+	0.00925401i	−0.490148	−	0.871639i	$-0.663057\pi$
$809$	−0.478779	+	0.263211i	−0.0168330	+	0.00925401i	0.473315	+	0.880893i	$0.343057\pi$
$810$	−12.4831	−	14.9925i	−0.438611	−	0.526781i
$811$	0.556254	−	2.91599i	0.0195327	−	0.102394i	−0.971186	−	0.238324i	$-0.923402\pi$
$811$	0.556254	−	2.91599i	0.0195327	−	0.102394i	0.990719	+	0.135930i	$0.0434021\pi$
$812$	0.979931	+	0.920216i	0.0343888	+	0.0322933i
$813$	6.72691	+	6.31699i	0.235923	+	0.221546i
$814$	−2.32630	+	12.1949i	−0.0815368	+	0.427431i
$815$	21.5560	−	34.2059i	0.755072	−	1.19818i
$816$	10.3476	−	5.68866i	0.362240	−	0.199143i
$817$	−56.8841	+	22.5220i	−1.99012	+	0.787946i
$818$	25.1266			0.878532
$819$	−0.0653711	+	0.0258822i	−0.00228425	+	0.000904399i
$820$	3.52984	+	2.54753i	0.123267	+	0.0889635i
$821$	−17.3488	+	20.9711i	−0.605478	+	0.731897i	−0.980804	−	0.194996i	$-0.937531\pi$
$821$	−17.3488	+	20.9711i	−0.605478	+	0.731897i	0.375326	+	0.926893i	$0.377531\pi$
$822$	5.13430	−	1.31827i	0.179079	−	0.0459798i
$823$	47.4022	+	26.0596i	1.65234	+	0.908381i	0.986786	+	0.162029i	$0.0518039\pi$
$823$	47.4022	+	26.0596i	1.65234	+	0.908381i	0.665552	+	0.746351i	$0.268196\pi$
$824$	−15.0817	+	10.9575i	−0.525397	+	0.381723i
$825$	−2.73917	+	14.8708i	−0.0953658	+	0.517735i
$826$	0.533359	+	0.387508i	0.0185579	+	0.0134831i
$827$	−14.0938	−	29.9509i	−0.490091	−	1.04150i	−0.985001	−	0.172551i	$-0.944799\pi$
$827$	−14.0938	−	29.9509i	−0.490091	−	1.04150i	0.494910	−	0.868944i	$-0.335201\pi$
$828$	−0.252766	+	0.305542i	−0.00878424	+	0.0106183i
$829$	−9.76672	−	15.3899i	−0.339212	−	0.534513i	0.631308	−	0.775532i	$-0.282518\pi$
$829$	−9.76672	−	15.3899i	−0.339212	−	0.534513i	−0.970520	+	0.241019i	$0.922518\pi$
$830$	14.3159	−	22.7170i	0.496911	−	0.788520i
$831$	−18.8030	−	22.7289i	−0.652267	−	0.788456i
$832$	−4.68231	−	3.40190i	−0.162330	−	0.117940i
$833$	25.8906	−	40.7970i	0.897055	−	1.41353i
$834$	−0.406742	−	2.13222i	−0.0140843	−	0.0738326i
$835$	−45.9003	+	11.9404i	−1.58845	+	0.413215i
$836$	13.6430	−	1.72352i	0.471855	−	0.0596091i
$837$	1.15339	+	6.04630i	0.0398671	+	0.208991i
$838$	2.09206	+	0.264289i	0.0722692	+	0.00912972i
$839$	13.6507	+	7.50454i	0.471275	+	0.259085i	0.699647	−	0.714488i	$-0.253340\pi$
$839$	13.6507	+	7.50454i	0.471275	+	0.259085i	−0.228373	+	0.973574i	$0.573340\pi$
$840$	0.0990614	+	0.510502i	0.00341794	+	0.0176140i
$841$	49.7571	+	46.7250i	1.71576	+	1.61121i
$842$	8.24387	+	2.11667i	0.284103	+	0.0729451i
$843$	0.495201	−	0.359785i	0.0170556	−	0.0123916i
$844$	−1.39943	−	22.2433i	−0.0481703	−	0.765645i
$845$	−2.73285	+	45.7509i	−0.0940128	+	1.57388i
$846$	−0.261789	−	0.103650i	−0.00900051	−	0.00356355i
$847$	−0.995913	−	0.394310i	−0.0342200	−	0.0135487i
$848$	−2.32392	+	0.293580i	−0.0798039	+	0.0100816i
$849$	1.45522	+	4.47871i	0.0499430	+	0.153709i
$850$	21.8888	−	26.8032i	0.750780	−	0.919341i
$851$	9.63024	−	29.6388i	0.330120	−	1.01601i
$852$	−1.80908	+	9.48352i	−0.0619780	+	0.324900i
$853$	1.04824	−	16.6613i	0.0358910	−	0.570471i	−0.938453	−	0.345407i	$-0.887741\pi$
$853$	1.04824	−	16.6613i	0.0358910	−	0.570471i	0.974344	−	0.225064i	$-0.0722591\pi$
$854$	−0.694417	+	0.178296i	−0.0237625	+	0.00610116i
$855$	−0.284881	+	1.51955i	−0.00974271	+	0.0519674i
$856$	1.24068	−	1.95500i	0.0424056	−	0.0668206i
$857$	12.8253	+	39.4722i	0.438103	+	1.34834i	0.889873	+	0.456209i	$0.150793\pi$
$857$	12.8253	+	39.4722i	0.438103	+	1.34834i	−0.451770	+	0.892135i	$0.649207\pi$
$858$	1.09902	+	17.4684i	0.0375199	+	0.596363i
$859$	−16.4475	−	2.07781i	−0.561183	−	0.0708939i	−0.160375	−	0.987056i	$-0.551270\pi$
$859$	−16.4475	−	2.07781i	−0.561183	−	0.0708939i	−0.400808	+	0.916162i	$0.631270\pi$
$860$	17.4876	−	2.26554i	0.596324	−	0.0772542i
$861$	−0.192770	−	0.409657i	−0.00656957	−	0.0139611i
$862$	−8.67571	+	18.4368i	−0.295496	+	0.627960i
$863$	43.6991	−	24.0238i	1.48753	−	0.817779i	0.489021	−	0.872272i	$-0.337354\pi$
$863$	43.6991	−	24.0238i	1.48753	−	0.817779i	0.998514	+	0.0544930i	$0.0173542\pi$
$864$	3.84199	−	3.60787i	0.130707	−	0.122742i
$865$	7.35939	−	22.8966i	0.250227	−	0.778506i
$866$	−4.38527	+	9.31917i	−0.149017	+	0.316678i
$867$	33.6059	+	40.6226i	1.14132	+	1.37962i
$868$	0.0491941	−	0.151404i	0.00166976	−	0.00513898i
$869$	−8.26086	−	2.12103i	−0.280230	−	0.0719509i
$870$	7.16701	+	36.9344i	0.242984	+	1.25219i
$871$	3.14982	−	50.0649i	0.106728	−	1.69639i
$872$	4.94750	+	7.79602i	0.167544	+	0.264006i
$873$	0.694091	−	0.651795i	0.0234914	−	0.0220599i
$874$	−34.5195			−1.16764
$875$	0.828791	+	1.27892i	0.0280183	+	0.0432355i
$876$	−8.13905			−0.274993
$877$	38.6032	−	36.2508i	1.30354	−	1.22410i	0.345177	−	0.938537i	$-0.387819\pi$
$877$	38.6032	−	36.2508i	1.30354	−	1.22410i	0.958359	−	0.285565i	$-0.0921812\pi$
$878$	−9.77366	−	15.4008i	−0.329845	−	0.519752i
$879$	0.134186	−	2.13283i	0.00452598	−	0.0719384i
$880$	−3.93383	−	0.484296i	−0.132609	−	0.0163256i
$881$	16.7963	+	4.31256i	0.565882	+	0.145294i	0.520784	−	0.853689i	$-0.325640\pi$
$881$	16.7963	+	4.31256i	0.565882	+	0.145294i	0.0450985	+	0.998983i	$0.485640\pi$
$882$	0.192267	−	0.591737i	0.00647396	−	0.0199248i
$883$	−25.7403	−	31.1147i	−0.866231	−	1.04709i	−0.998438	−	0.0558710i	$-0.982206\pi$
$883$	−25.7403	−	31.1147i	−0.866231	−	1.04709i	0.132207	−	0.991222i	$-0.457794\pi$
$884$	17.0553	−	36.2444i	0.573633	−	1.21903i
$885$	5.75744	+	17.5303i	0.193534	+	0.589275i
$886$	−24.4730	+	22.9817i	−0.822187	+	0.772085i
$887$	32.6161	−	17.9308i	1.09514	−	0.602058i	0.171448	−	0.985193i	$-0.445156\pi$
$887$	32.6161	−	17.9308i	1.09514	−	0.602058i	0.923692	+	0.383135i	$0.125156\pi$
$888$	−5.08790	+	10.8123i	−0.170739	+	0.362839i
$889$	−0.185208	−	0.393587i	−0.00621167	−	0.0132005i
$890$	19.0761	+	10.4086i	0.639434	+	0.348897i
$891$	−15.3430	−	1.93827i	−0.514009	−	0.0649344i
$892$	−0.0966295	−	1.53588i	−0.00323539	−	0.0514251i
$893$	−7.57407	−	23.3106i	−0.253457	−	0.780060i
$894$	−6.02806	+	9.49871i	−0.201609	+	0.317684i
$895$	−7.04854	+	0.913144i	−0.235607	+	0.0305230i
$896$	−0.132027	+	0.0338988i	−0.00441072	+	0.00113248i
$897$	2.75880	−	43.8499i	0.0921138	−	1.46411i
$898$	−3.37324	+	17.6831i	−0.112566	+	0.590094i
$899$	3.55915	−	10.9539i	0.118704	−	0.365334i
$900$	0.187169	−	0.404389i	0.00623897	−	0.0134796i
$901$	−5.00974	−	15.4184i	−0.166899	−	0.513662i
$902$	3.42354	−	0.432493i	0.113991	−	0.0144005i
$903$	−1.70521	−	0.675140i	−0.0567458	−	0.0224672i
$904$	−2.66013	−	1.05322i	−0.0884745	−	0.0350295i
$905$	29.5300	+	11.5836i	0.981610	+	0.385052i
$906$	−2.24205	−	35.6363i	−0.0744870	−	1.18394i
$907$	15.6500	−	11.3704i	0.519650	−	0.377548i	−0.296822	−	0.954933i	$-0.595927\pi$
$907$	15.6500	−	11.3704i	0.519650	−	0.377548i	0.816472	+	0.577385i	$0.195927\pi$
$908$	−4.94069	−	1.26855i	−0.163963	−	0.0420984i
$909$	0.364212	+	0.342017i	0.0120801	+	0.0113440i
$910$	1.28977	+	1.20350i	0.0427553	+	0.0398957i
$911$	−3.08368	−	1.69526i	−0.102167	−	0.0561666i	0.429851	−	0.902900i	$-0.358566\pi$
$911$	−3.08368	−	1.69526i	−0.102167	−	0.0561666i	−0.532018	+	0.846733i	$0.678566\pi$
$912$	13.1319	+	1.65894i	0.434839	+	0.0549330i
$913$	−3.98849	−	20.9084i	−0.132000	−	0.691967i
$914$	23.0727	−	2.91476i	0.763177	−	0.0964117i
$915$	−18.6799	−	7.32750i	−0.617539	−	0.242240i
$916$	−0.386929	−	2.02835i	−0.0127845	−	0.0670186i
$917$	0.0770141	−	0.121355i	0.00254323	−	0.00400749i
$918$	29.5106	+	21.4407i	0.973994	+	0.707648i
$919$	−13.5611	−	16.3925i	−0.447338	−	0.540739i	0.497851	−	0.867263i	$-0.334123\pi$
$919$	−13.5611	−	16.3925i	−0.447338	−	0.540739i	−0.945189	+	0.326524i	$0.894123\pi$
$920$	9.64463	+	2.44376i	0.317974	+	0.0805684i
$921$	7.46793	+	11.7676i	0.246077	+	0.387755i
$922$	−3.06041	+	3.69941i	−0.100789	+	0.121833i
$923$	13.9446	+	29.6338i	0.458992	+	0.975407i
$924$	0.333498	+	0.242301i	0.0109713	+	0.00797110i
$925$	−1.97730	+	34.9638i	−0.0650134	+	1.14960i
$926$	−10.7100	+	7.78128i	−0.351953	+	0.255709i
$927$	−1.45589	−	0.800382i	−0.0478177	−	0.0262880i
$928$	−9.55206	+	2.45255i	−0.313562	+	0.0805090i
$929$	2.39199	−	2.89142i	0.0784787	−	0.0948644i	−0.729813	−	0.683647i	$-0.760393\pi$
$929$	2.39199	−	2.89142i	0.0784787	−	0.0948644i	0.808291	+	0.588783i	$0.200393\pi$
$930$	3.59630	−	2.63032i	0.117927	−	0.0862515i
$931$	50.3587	−	19.9384i	1.65044	−	0.653455i
$932$	11.9947			0.392900
$933$	−15.6564	+	6.19882i	−0.512569	+	0.202940i
$934$	7.31231	−	4.01998i	0.239266	−	0.131538i
$935$	−1.80923	−	27.3722i	−0.0591681	−	0.895165i
$936$	0.0966512	−	0.506663i	0.00315914	−	0.0165608i
$937$	33.5414	+	31.4974i	1.09575	+	1.02898i	0.999435	+	0.0336251i	$0.0107052\pi$
$937$	33.5414	+	31.4974i	1.09575	+	1.02898i	0.0963138	+	0.995351i	$0.469295\pi$
$938$	−0.861240	−	0.808758i	−0.0281205	−	0.0264069i
$939$	6.25376	−	32.7833i	0.204084	−	1.06984i
$940$	0.465927	+	7.04910i	0.0151969	+	0.229916i
$941$	−34.0763	+	18.7336i	−1.11086	+	0.610699i	−0.928052	−	0.372451i	$-0.878518\pi$
$941$	−34.0763	+	18.7336i	−1.11086	+	0.610699i	−0.182805	+	0.983149i	$0.558518\pi$
$942$	24.5190	−	9.70774i	0.798871	−	0.316295i
$943$	−8.66220			−0.282080
$944$	−4.49691	+	1.78045i	−0.146362	+	0.0579488i
$945$	−1.29662	+	0.948343i	−0.0421790	+	0.0308496i
$946$	8.91017	−	10.7705i	0.289695	−	0.350181i
$947$	−13.4715	+	3.45890i	−0.437766	+	0.112399i	−0.461139	−	0.887328i	$-0.652559\pi$
$947$	−13.4715	+	3.45890i	−0.437766	+	0.112399i	0.0233738	+	0.999727i	$0.492559\pi$
$948$	−7.19381	−	3.95483i	−0.233644	−	0.128447i
$949$	−22.3368	+	16.2287i	−0.725084	+	0.526804i
$950$	37.5096	−	9.88471i	1.21697	−	0.320702i
$951$	0.421812	+	0.306465i	0.0136782	+	0.00993780i
$952$	−0.401684	−	0.853621i	−0.0130186	−	0.0276660i
$953$	−16.4284	+	19.8585i	−0.532169	+	0.643281i	−0.966254	−	0.257590i	$-0.917072\pi$
$953$	−16.4284	+	19.8585i	−0.532169	+	0.643281i	0.434086	+	0.900872i	$0.357072\pi$
$954$	−0.111857	−	0.176258i	−0.00362150	−	0.00570657i
$955$	−19.2900	−	4.88772i	−0.624211	−	0.158163i
$956$	−10.1535	−	12.2735i	−0.328389	−	0.396954i
$957$	24.1283	+	17.5303i	0.779958	+	0.566673i
$958$	−22.0453	+	34.7378i	−0.712251	+	1.12233i
$959$	−0.0793570	−	0.416004i	−0.00256257	−	0.0134335i
$960$	−3.55155	−	1.39315i	−0.114626	−	0.0449638i
$961$	29.4023	−	3.71438i	0.948462	−	0.119819i
$962$	7.59575	+	39.8183i	0.244897	+	1.28379i
$963$	0.204728	+	0.0258631i	0.00659725	+	0.000833427i
$964$	−25.4651	−	13.9996i	−0.820177	−	0.450896i
$965$	6.99512	+	6.52726i	0.225181	+	0.210120i
$966$	−0.754327	−	0.708360i	−0.0242701	−	0.0227911i
$967$	1.88757	+	0.484645i	0.0607001	+	0.0155851i	0.278918	−	0.960315i	$-0.410024\pi$
$967$	1.88757	+	0.484645i	0.0607001	+	0.0155851i	−0.218218	+	0.975900i	$0.570024\pi$
$968$	6.35732	−	4.61887i	0.204332	−	0.148456i
$969$	5.75217	+	91.4281i	0.184786	+	2.93709i
$970$	−22.2400	−	8.72401i	−0.714084	−	0.280111i
$971$	12.6553	+	5.01059i	0.406128	+	0.160798i	0.562302	−	0.826932i	$-0.309916\pi$
$971$	12.6553	+	5.01059i	0.406128	+	0.160798i	−0.156174	+	0.987730i	$0.549916\pi$
$972$	0.860842	+	0.340832i	0.0276115	+	0.0109322i
$973$	−0.172056	+	0.0217357i	−0.00551585	+	0.000696814i
$974$	0.883190	+	2.71818i	0.0282992	+	0.0870960i
$975$	9.55872	+	48.4383i	0.306124	+	1.55127i
$976$	1.62532	−	5.00223i	0.0520253	−	0.160117i
$977$	1.06591	−	5.58771i	0.0341015	−	0.178767i	−0.961161	−	0.275987i	$-0.910995\pi$
$977$	1.06591	−	5.58771i	0.0341015	−	0.178767i	0.995263	+	0.0972207i	$0.0309953\pi$
$978$	1.93705	−	30.7885i	0.0619400	−	0.984509i
$979$	16.6851	−	4.28401i	0.533259	−	0.136918i
$980$	−15.4816	+	2.00565i	−0.494540	+	0.0640681i
$981$	−0.440925	+	0.694786i	−0.0140776	+	0.0221828i
$982$	9.80109	+	30.1646i	0.312765	+	0.962593i
$983$	0.0947301	+	1.50569i	0.00302142	+	0.0480241i	0.999249	−	0.0387603i	$-0.0123409\pi$
$983$	0.0947301	+	1.50569i	0.00302142	+	0.0480241i	−0.996227	+	0.0867844i	$0.972341\pi$
$984$	3.29526	+	0.416288i	0.105049	+	0.0132708i
$985$	−31.4463	−	17.1582i	−1.00196	−	0.546704i
$986$	−29.0615	−	61.7588i	−0.925506	−	1.96680i
$987$	0.312837	−	0.664812i	0.00995771	−	0.0211612i
$988$	39.3469	−	21.6311i	1.25179	−	0.688178i
$989$	−25.5789	+	24.0202i	−0.813361	+	0.763797i
$990$	−0.110219	−	0.335597i	−0.00350299	−	0.0106660i
$991$	−10.9375	+	23.2435i	−0.347443	+	0.738353i	−0.999809	−	0.0195507i	$-0.993776\pi$
$991$	−10.9375	+	23.2435i	−0.347443	+	0.738353i	0.652366	+	0.757904i	$0.273776\pi$
$992$	0.744445	+	0.899879i	0.0236361	+	0.0285712i
$993$	−4.89607	+	15.0685i	−0.155372	+	0.478186i
$994$	0.747106	+	0.191824i	0.0236968	+	0.00608429i
$995$	−6.98225	−	0.859589i	−0.221352	−	0.0272508i
$996$	1.28645	−	20.4475i	0.0407626	−	0.647903i
$997$	18.3536	+	28.9206i	0.581264	+	0.915925i	0.999970	+	0.00780334i	$0.00248390\pi$
$997$	18.3536	+	28.9206i	0.581264	+	0.915925i	−0.418706	+	0.908122i	$0.637516\pi$
$998$	16.5526	−	15.5439i	0.523963	−	0.492034i
$999$	−36.9138			−1.16790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.g.b.11.2	✓	140
125.91	even	25	inner	250.2.g.b.91.2	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.g.b.11.2	✓	140	1.1	even	1	trivial
250.2.g.b.91.2	yes	140	125.91	even	25	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.728969 - 0.684547i) q^{2} +(-0.914190 - 1.44053i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-1.63487 - 1.52552i) q^{5} +(-1.65253 - 0.424297i) q^{6} +(-0.0421220 + 0.129638i) q^{7} +(-0.637424 - 0.770513i) q^{8} +(0.0379457 - 0.0806388i) q^{9} +O(q^{10})\)	\(q+(0.728969 - 0.684547i) q^{2} +(-0.914190 - 1.44053i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-1.63487 - 1.52552i) q^{5} +(-1.65253 - 0.424297i) q^{6} +(-0.0421220 + 0.129638i) q^{7} +(-0.637424 - 0.770513i) q^{8} +(0.0379457 - 0.0806388i) q^{9} +(-2.23606 + 0.00708737i) q^{10} +(-1.29213 + 1.21339i) q^{11} +(-1.49509 + 0.821934i) q^{12} +(-2.46426 + 5.23682i) q^{13} +(0.0580378 + 0.123337i) q^{14} +(-0.702983 + 3.74969i) q^{15} +(-0.992115 - 0.125333i) q^{16} +(-0.434578 - 6.90741i) q^{17} +(-0.0275398 - 0.0847588i) q^{18} +(4.15697 - 6.55033i) q^{19} +(-1.62516 + 1.53585i) q^{20} +(0.225255 - 0.0578358i) q^{21} +(-0.111299 + 1.76905i) q^{22} +(0.833755 - 4.37070i) q^{23} +(-0.527223 + 1.62263i) q^{24} +(0.345579 + 4.98804i) q^{25} +(1.78848 + 5.50438i) q^{26} +(-5.22888 + 0.660561i) q^{27} +(0.126737 + 0.0501789i) q^{28} +(9.16935 + 3.63040i) q^{29} +(2.05439 + 3.21463i) q^{30} +(-0.0733328 - 1.16559i) q^{31} +(-0.809017 + 0.587785i) q^{32} +(2.92918 + 0.752086i) q^{33} +(-5.04524 - 4.73780i) q^{34} +(0.266629 - 0.147683i) q^{35} +(-0.0780970 - 0.0429342i) q^{36} +(6.94871 + 0.877826i) q^{37} +(-1.45371 - 7.62063i) q^{38} +(9.79662 - 1.23760i) q^{39} +(-0.133330 + 2.23209i) q^{40} +(-0.364789 - 1.91229i) q^{41} +(0.124613 - 0.196358i) q^{42} +(-6.37996 - 4.63531i) q^{43} +(1.12986 + 1.36577i) q^{44} +(-0.185052 + 0.0739467i) q^{45} +(-2.38417 - 3.75685i) q^{46} +(2.01383 - 2.43431i) q^{47} +(0.726435 + 1.54375i) q^{48} +(5.64809 + 4.10358i) q^{49} +(3.66647 + 3.39956i) q^{50} +(-9.55307 + 6.94071i) q^{51} +(5.07176 + 2.78822i) q^{52} +(2.26880 - 0.582530i) q^{53} +(-3.35951 + 4.06094i) q^{54} +(3.96351 - 0.0125627i) q^{55} +(0.126737 - 0.0501789i) q^{56} -13.2362 q^{57} +(9.16935 - 3.63040i) q^{58} +(4.23830 - 2.33003i) q^{59} +(3.69816 + 0.937041i) q^{60} +(-0.985561 + 5.16649i) q^{61} +(-0.851359 - 0.799480i) q^{62} +(0.00885551 + 0.00831588i) q^{63} +(-0.187381 + 0.982287i) q^{64} +(12.0176 - 4.80223i) q^{65} +(2.65012 - 1.45692i) q^{66} +(-8.05875 + 3.19068i) q^{67} -6.92107 q^{68} +(-7.05835 + 2.79460i) q^{69} +(0.0932683 - 0.290177i) q^{70} +(3.60701 - 4.36013i) q^{71} +(-0.0863208 + 0.0221634i) q^{72} +(4.18040 + 2.29819i) q^{73} +(5.66630 - 4.11681i) q^{74} +(6.86952 - 5.05784i) q^{75} +(-6.27639 - 4.56006i) q^{76} +(-0.102875 - 0.218620i) q^{77} +(6.29423 - 7.60842i) q^{78} +(2.57819 + 4.06258i) q^{79} +(1.43078 + 1.71839i) q^{80} +(5.56133 + 6.72249i) q^{81} +(-1.57497 - 1.14429i) q^{82} +(-6.43442 + 10.1390i) q^{83} +(-0.0435777 - 0.228443i) q^{84} +(-9.82692 + 11.9557i) q^{85} +(-7.82388 + 0.988386i) q^{86} +(-3.15281 - 16.5276i) q^{87} +(1.75857 + 0.222159i) q^{88} +(-8.51631 - 4.68188i) q^{89} +(-0.0842773 + 0.180582i) q^{90} +(-0.575092 - 0.540048i) q^{91} +(-4.30972 - 1.10655i) q^{92} +(-1.61203 + 1.17121i) q^{93} +(-0.198376 - 3.15310i) q^{94} +(-16.7887 + 4.36739i) q^{95} +(1.58632 + 0.628068i) q^{96} +(9.93362 + 3.93300i) q^{97} +(6.92637 - 0.875004i) q^{98} +(0.0488155 + 0.150239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9}+O(q^{10}) \) 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9	\( 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9} + 20 q^{10} - 10 q^{11} + 20 q^{12} + 20 q^{14} - 10 q^{15} - 5 q^{17} - 50 q^{18} + 40 q^{19} - 10 q^{20} - 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} - 5 q^{25} - 35 q^{26} + 30 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} + 35 q^{31} - 35 q^{32} - 55 q^{33} - 15 q^{34} - 25 q^{35} - 10 q^{36} - 25 q^{37} - 30 q^{39} + 25 q^{41} - 5 q^{42} - 45 q^{43} + 40 q^{44} - 5 q^{45} + 90 q^{47} - 5 q^{48} - 65 q^{49} + 30 q^{50} - 80 q^{51} - 50 q^{53} - 5 q^{54} - 35 q^{55} - 5 q^{56} + 40 q^{57} - 10 q^{58} + 45 q^{59} + 15 q^{60} + 45 q^{61} - 45 q^{62} - 75 q^{63} - 60 q^{65} + 15 q^{66} - 45 q^{67} + 10 q^{68} - 125 q^{69} - 15 q^{70} - 5 q^{71} - 5 q^{72} - 50 q^{73} + 20 q^{74} - 130 q^{75} - 5 q^{76} + 10 q^{77} + 10 q^{78} - 50 q^{79} - 5 q^{80} + 15 q^{81} + 40 q^{82} + 25 q^{83} - 50 q^{84} - 95 q^{85} - 10 q^{86} + 80 q^{87} - 10 q^{88} - 65 q^{89} - 10 q^{90} + 65 q^{91} - 25 q^{92} - 10 q^{93} - 35 q^{94} + 80 q^{95} - 40 q^{97} - 25 q^{98} + 90 q^{99}+O(q^{100}) \) 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9 + 20 * q^10 - 10 * q^11 + 20 * q^12 + 20 * q^14 - 10 * q^15 - 5 * q^17 - 50 * q^18 + 40 * q^19 - 10 * q^20 - 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 - 5 * q^25 - 35 * q^26 + 30 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 + 35 * q^31 - 35 * q^32 - 55 * q^33 - 15 * q^34 - 25 * q^35 - 10 * q^36 - 25 * q^37 - 30 * q^39 + 25 * q^41 - 5 * q^42 - 45 * q^43 + 40 * q^44 - 5 * q^45 + 90 * q^47 - 5 * q^48 - 65 * q^49 + 30 * q^50 - 80 * q^51 - 50 * q^53 - 5 * q^54 - 35 * q^55 - 5 * q^56 + 40 * q^57 - 10 * q^58 + 45 * q^59 + 15 * q^60 + 45 * q^61 - 45 * q^62 - 75 * q^63 - 60 * q^65 + 15 * q^66 - 45 * q^67 + 10 * q^68 - 125 * q^69 - 15 * q^70 - 5 * q^71 - 5 * q^72 - 50 * q^73 + 20 * q^74 - 130 * q^75 - 5 * q^76 + 10 * q^77 + 10 * q^78 - 50 * q^79 - 5 * q^80 + 15 * q^81 + 40 * q^82 + 25 * q^83 - 50 * q^84 - 95 * q^85 - 10 * q^86 + 80 * q^87 - 10 * q^88 - 65 * q^89 - 10 * q^90 + 65 * q^91 - 25 * q^92 - 10 * q^93 - 35 * q^94 + 80 * q^95 - 40 * q^97 - 25 * q^98 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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