LMFDB - Embedded newform 525.2.bg.b.16.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.12
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.b.361.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.811470 - 0.361290i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.810308 + 0.899939i) q^{4} +(-1.71756 - 1.43178i) q^{5} +(0.274489 - 0.844789i) q^{6} +(-1.96006 - 1.77712i) q^{7} +(-0.881380 + 2.71261i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.811470 - 0.361290i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.810308 + 0.899939i) q^{4} +(-1.71756 - 1.43178i) q^{5} +(0.274489 - 0.844789i) q^{6} +(-1.96006 - 1.77712i) q^{7} +(-0.881380 + 2.71261i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-1.91103 - 0.541305i) q^{10} +(0.408551 - 3.88710i) q^{11} +(0.126583 + 1.20435i) q^{12} +(-0.281222 + 0.204320i) q^{13} +(-2.23258 - 0.733931i) q^{14} +(-2.21329 + 0.318353i) q^{15} +(0.0116587 + 0.110925i) q^{16} +(-6.85359 + 1.45678i) q^{17} +(-0.444132 - 0.769259i) q^{18} +(-1.32916 - 1.47618i) q^{19} +(2.68027 - 0.385521i) q^{20} +(-2.63220 + 0.267482i) q^{21} +(-1.07284 - 3.30187i) q^{22} +(3.80456 - 1.69390i) q^{23} +(1.42610 + 2.47008i) q^{24} +(0.900040 + 4.91833i) q^{25} +(-0.154384 + 0.267402i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(3.18755 - 0.323917i) q^{28} +(-2.45504 - 7.55584i) q^{29} +(-1.68100 + 1.05797i) q^{30} +(-6.39862 + 1.36007i) q^{31} +(-2.80267 - 4.85436i) q^{32} +(-2.61531 - 2.90459i) q^{33} +(-5.03516 + 3.65826i) q^{34} +(0.822086 + 5.85868i) q^{35} +(0.979709 + 0.711800i) q^{36} +(0.00303566 + 0.0288823i) q^{37} +(-1.61190 - 0.717666i) q^{38} +(-0.0363351 + 0.345705i) q^{39} +(5.39767 - 3.39713i) q^{40} +(1.31525 - 0.955582i) q^{41} +(-2.03931 + 1.16804i) q^{42} +9.69534 q^{43} +(3.16710 + 3.51742i) q^{44} +(-1.24440 + 1.85781i) q^{45} +(2.47529 - 2.74909i) q^{46} +(12.1376 + 2.57992i) q^{47} +(0.0902349 + 0.0655595i) q^{48} +(0.683672 + 6.96653i) q^{49} +(2.50729 + 3.66590i) q^{50} +(-3.50335 + 6.06798i) q^{51} +(0.0440013 - 0.418644i) q^{52} +(6.07085 - 6.74236i) q^{53} +(-0.868853 - 0.184680i) q^{54} +(-6.26717 + 6.09139i) q^{55} +(6.54819 - 3.75055i) q^{56} -1.98640 q^{57} +(-4.72204 - 5.24435i) q^{58} +(-2.54376 - 1.13255i) q^{59} +(1.50695 - 2.24979i) q^{60} +(-4.00317 + 1.78233i) q^{61} +(-4.70090 + 3.41541i) q^{62} +(-1.56251 + 2.13508i) q^{63} +(-4.20858 - 3.05771i) q^{64} +(0.775556 + 0.0517147i) q^{65} +(-3.17164 - 1.41210i) q^{66} +(9.61596 - 2.04393i) q^{67} +(4.24251 - 7.34825i) q^{68} +(1.28693 - 3.96078i) q^{69} +(2.78378 + 4.45713i) q^{70} +(2.06401 + 6.35238i) q^{71} +(2.78988 + 0.593007i) q^{72} +(-0.426100 + 4.05407i) q^{73} +(0.0128982 + 0.0223404i) q^{74} +(4.25727 + 2.62214i) q^{75} +2.40551 q^{76} +(-7.70864 + 6.89291i) q^{77} +(0.0954148 + 0.293657i) q^{78} +(-13.8498 - 2.94387i) q^{79} +(0.138796 - 0.207214i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.722040 - 1.25061i) q^{82} +(2.83044 - 8.71121i) q^{83} +(1.89217 - 2.58556i) q^{84} +(13.8572 + 7.31070i) q^{85} +(7.86747 - 3.50283i) q^{86} +(-7.25783 - 3.23139i) q^{87} +(10.1841 + 4.53425i) q^{88} +(2.51137 - 1.11814i) q^{89} +(-0.338582 + 1.95715i) q^{90} +(0.914313 + 0.0992868i) q^{91} +(-1.55846 + 4.79645i) q^{92} +(-3.27078 + 5.66516i) q^{93} +(10.7814 - 2.29165i) q^{94} +(0.169355 + 4.43850i) q^{95} +(-5.48284 - 1.16541i) q^{96} +(-0.829208 - 2.55204i) q^{97} +(3.07171 + 5.40613i) q^{98} -3.90851 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.811470	−	0.361290i	0.573796	−	0.255470i	−0.0992607	−	0.995061i	$-0.531648\pi$
$2$	0.811470	−	0.361290i	0.573796	−	0.255470i	0.673056	+	0.739591i	$0.264981\pi$
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−0.810308	+	0.899939i	−0.405154	+	0.449969i
$5$	−1.71756	−	1.43178i	−0.768117	−	0.640309i
$5$	−1.71756	−	1.43178i	−0.768117	−	0.640309i
$6$	0.274489	−	0.844789i	0.112060	−	0.344884i
$7$	−1.96006	−	1.77712i	−0.740833	−	0.671689i
$7$	−1.96006	−	1.77712i	−0.740833	−	0.671689i
$8$	−0.881380	+	2.71261i	−0.311615	+	0.959052i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−1.91103	−	0.541305i	−0.604322	−	0.171176i
$11$	0.408551	−	3.88710i	0.123183	−	1.17201i	−0.741948	−	0.670458i	$-0.766098\pi$
$11$	0.408551	−	3.88710i	0.123183	−	1.17201i	0.865130	−	0.501547i	$-0.167236\pi$
$12$	0.126583	+	1.20435i	0.0365413	+	0.347667i
$13$	−0.281222	+	0.204320i	−0.0779969	+	0.0566681i	−0.626100	−	0.779742i	$-0.715350\pi$
$13$	−0.281222	+	0.204320i	−0.0779969	+	0.0566681i	0.548103	+	0.836411i	$0.315350\pi$
$14$	−2.23258	−	0.733931i	−0.596683	−	0.196151i
$15$	−2.21329	+	0.318353i	−0.571469	+	0.0821984i
$16$	0.0116587	+	0.110925i	0.00291468	+	0.0277314i
$17$	−6.85359	+	1.45678i	−1.66224	+	0.353320i	−0.940749	−	0.339104i	$-0.889876\pi$
$17$	−6.85359	+	1.45678i	−1.66224	+	0.353320i	−0.721491	+	0.692424i	$0.756543\pi$
$18$	−0.444132	−	0.769259i	−0.104683	−	0.181316i
$19$	−1.32916	−	1.47618i	−0.304931	−	0.338660i	0.571131	−	0.820859i	$-0.306505\pi$
$19$	−1.32916	−	1.47618i	−0.304931	−	0.338660i	−0.876062	+	0.482199i	$0.839838\pi$
$20$	2.68027	−	0.385521i	0.599325	−	0.0862052i
$21$	−2.63220	+	0.267482i	−0.574392	+	0.0583693i
$22$	−1.07284	−	3.30187i	−0.228731	−	0.703961i
$23$	3.80456	−	1.69390i	0.793305	−	0.353202i	0.0302555	−	0.999542i	$-0.490368\pi$
$23$	3.80456	−	1.69390i	0.793305	−	0.353202i	0.763049	+	0.646340i	$0.223701\pi$
$24$	1.42610	+	2.47008i	0.291102	+	0.504203i
$25$	0.900040	+	4.91833i	0.180008	+	0.983665i
$26$	−0.154384	+	0.267402i	−0.0302773	+	0.0524418i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	3.18755	−	0.323917i	0.602391	−	0.0612145i
$29$	−2.45504	−	7.55584i	−0.455890	−	1.40308i	−0.870087	−	0.492897i	$-0.835938\pi$
$29$	−2.45504	−	7.55584i	−0.455890	−	1.40308i	0.414198	−	0.910187i	$-0.364062\pi$
$30$	−1.68100	+	1.05797i	−0.306907	+	0.193158i
$31$	−6.39862	+	1.36007i	−1.14923	+	0.244275i	−0.742867	−	0.669439i	$-0.766535\pi$
$31$	−6.39862	+	1.36007i	−1.14923	+	0.244275i	−0.406358	+	0.913714i	$0.633201\pi$
$32$	−2.80267	−	4.85436i	−0.495446	−	0.858138i
$33$	−2.61531	−	2.90459i	−0.455266	−	0.505624i
$34$	−5.03516	+	3.65826i	−0.863523	+	0.627386i
$35$	0.822086	+	5.85868i	0.138958	+	0.990298i
$36$	0.979709	+	0.711800i	0.163285	+	0.118633i
$37$	0.00303566	+	0.0288823i	0.000499059	+	0.00474823i	0.994769	−	0.102154i	$-0.0325735\pi$
$37$	0.00303566	+	0.0288823i	0.000499059	+	0.00474823i	−0.994270	+	0.106902i	$0.965907\pi$
$38$	−1.61190	−	0.717666i	−0.261485	−	0.116421i
$39$	−0.0363351	+	0.345705i	−0.00581827	+	0.0553571i
$40$	5.39767	−	3.39713i	0.853446	−	0.537134i
$41$	1.31525	−	0.955582i	0.205407	−	0.149237i	−0.480326	−	0.877090i	$-0.659482\pi$
$41$	1.31525	−	0.955582i	0.205407	−	0.149237i	0.685733	+	0.727853i	$0.259482\pi$
$42$	−2.03931	+	1.16804i	−0.314672	+	0.180232i
$43$	9.69534			1.47853			0.739263	−	0.673417i	$-0.235174\pi$
$43$	9.69534			1.47853			0.739263	+	0.673417i	$0.235174\pi$
$44$	3.16710	+	3.51742i	0.477458	+	0.530271i
$45$	−1.24440	+	1.85781i	−0.185504	+	0.276947i
$46$	2.47529	−	2.74909i	0.364962	−	0.405332i
$47$	12.1376	+	2.57992i	1.77045	+	0.376321i	0.973672	−	0.227952i	$-0.0732030\pi$
$47$	12.1376	+	2.57992i	1.77045	+	0.376321i	0.796777	+	0.604273i	$0.206536\pi$
$48$	0.0902349	+	0.0655595i	0.0130243	+	0.00946270i
$49$	0.683672	+	6.96653i	0.0976675	+	0.995219i
$50$	2.50729	+	3.66590i	0.354585	+	0.518436i
$51$	−3.50335	+	6.06798i	−0.490567	+	0.849688i
$52$	0.0440013	−	0.418644i	0.00610188	−	0.0580555i
$53$	6.07085	−	6.74236i	0.833895	−	0.926135i	−0.164286	−	0.986413i	$-0.552532\pi$
$53$	6.07085	−	6.74236i	0.833895	−	0.926135i	0.998182	+	0.0602781i	$0.0191987\pi$
$54$	−0.868853	−	0.184680i	−0.118236	−	0.0251318i
$55$	−6.26717	+	6.09139i	−0.845065	+	0.821362i
$56$	6.54819	−	3.75055i	0.875039	−	0.501189i
$57$	−1.98640			−0.263105
$58$	−4.72204	−	5.24435i	−0.620034	−	0.688617i
$59$	−2.54376	−	1.13255i	−0.331169	−	0.147446i	0.234415	−	0.972137i	$-0.424683\pi$
$59$	−2.54376	−	1.13255i	−0.331169	−	0.147446i	−0.565584	+	0.824691i	$0.691349\pi$
$60$	1.50695	−	2.24979i	0.194546	−	0.290447i
$61$	−4.00317	+	1.78233i	−0.512553	+	0.228203i	−0.646681	−	0.762761i	$-0.723843\pi$
$61$	−4.00317	+	1.78233i	−0.512553	+	0.228203i	0.134128	+	0.990964i	$0.457177\pi$
$62$	−4.70090	+	3.41541i	−0.597015	+	0.433757i
$63$	−1.56251	+	2.13508i	−0.196857	+	0.268995i
$64$	−4.20858	−	3.05771i	−0.526072	−	0.382214i
$65$	0.775556	+	0.0517147i	0.0961959	+	0.00641443i
$66$	−3.17164	−	1.41210i	−0.390402	−	0.173818i
$67$	9.61596	−	2.04393i	1.17478	−	0.249706i	0.421138	−	0.906996i	$-0.361631\pi$
$67$	9.61596	−	2.04393i	1.17478	−	0.249706i	0.753638	+	0.657290i	$0.228297\pi$
$68$	4.24251	−	7.34825i	0.514480	−	0.891106i
$69$	1.28693	−	3.96078i	0.154929	−	0.476821i
$70$	2.78378	+	4.45713i	0.332725	+	0.532729i
$71$	2.06401	+	6.35238i	0.244953	+	0.753889i	0.995644	+	0.0932354i	$0.0297209\pi$
$71$	2.06401	+	6.35238i	0.244953	+	0.753889i	−0.750691	+	0.660654i	$0.770279\pi$
$72$	2.78988	+	0.593007i	0.328790	+	0.0698865i
$73$	−0.426100	+	4.05407i	−0.0498712	+	0.474493i	0.940874	+	0.338757i	$0.110007\pi$
$73$	−0.426100	+	4.05407i	−0.0498712	+	0.474493i	−0.990745	+	0.135736i	$0.956660\pi$
$74$	0.0128982	+	0.0223404i	0.00149939	+	0.00259702i
$75$	4.25727	+	2.62214i	0.491588	+	0.302779i
$76$	2.40551			0.275930
$77$	−7.70864	+	6.89291i	−0.878481	+	0.785520i
$78$	0.0954148	+	0.293657i	0.0108036	+	0.0332501i
$79$	−13.8498	−	2.94387i	−1.55823	−	0.331211i	−0.653407	−	0.757007i	$-0.726661\pi$
$79$	−13.8498	−	2.94387i	−1.55823	−	0.331211i	−0.904819	+	0.425795i	$0.859994\pi$
$80$	0.138796	−	0.207214i	0.0155178	−	0.0231672i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	0.722040	−	1.25061i	0.0797360	−	0.138107i
$83$	2.83044	−	8.71121i	0.310682	−	0.956179i	−0.666814	−	0.745224i	$-0.732343\pi$
$83$	2.83044	−	8.71121i	0.310682	−	0.956179i	0.977496	−	0.210955i	$-0.0676575\pi$
$84$	1.89217	−	2.58556i	0.206453	−	0.282107i
$85$	13.8572	+	7.31070i	1.50303	+	0.792956i
$86$	7.86747	−	3.50283i	0.848372	−	0.377719i
$87$	−7.25783	−	3.23139i	−0.778121	−	0.346442i
$88$	10.1841	+	4.53425i	1.08563	+	0.483353i
$89$	2.51137	−	1.11814i	0.266205	−	0.118522i	−0.269294	−	0.963058i	$-0.586790\pi$
$89$	2.51137	−	1.11814i	0.266205	−	0.118522i	0.535499	+	0.844536i	$0.320124\pi$
$90$	−0.338582	+	1.95715i	−0.0356897	+	0.206301i
$91$	0.914313	+	0.0992868i	0.0958460	+	0.0104081i
$92$	−1.55846	+	4.79645i	−0.162481	+	0.500064i
$93$	−3.27078	+	5.66516i	−0.339164	+	0.587450i
$94$	10.7814	−	2.29165i	1.11202	−	0.236366i
$95$	0.169355	+	4.43850i	0.0173755	+	0.455380i
$96$	−5.48284	−	1.16541i	−0.559590	−	0.118945i
$97$	−0.829208	−	2.55204i	−0.0841933	−	0.259120i	0.900094	−	0.435696i	$-0.143498\pi$
$97$	−0.829208	−	2.55204i	−0.0841933	−	0.259120i	−0.984287	+	0.176576i	$0.943498\pi$
$98$	3.07171	+	5.40613i	0.310290	+	0.546101i
$99$	−3.90851			−0.392820
$100$	−5.15550	−	3.17538i	−0.515550	−	0.317538i
$101$	1.05964	+	1.83535i	0.105438	+	0.182625i	0.913917	−	0.405901i	$-0.133042\pi$
$101$	1.05964	+	1.83535i	0.105438	+	0.182625i	−0.808479	+	0.588525i	$0.799709\pi$
$102$	−0.650564	+	6.18971i	−0.0644155	+	0.612872i
$103$	−10.5683	−	2.24637i	−1.04133	−	0.221341i	−0.344654	−	0.938730i	$-0.612004\pi$
$103$	−10.5683	−	2.24637i	−1.04133	−	0.221341i	−0.696673	+	0.717389i	$0.745337\pi$
$104$	−0.306376	−	0.942928i	−0.0300426	−	0.0924617i
$105$	4.90393	+	3.30930i	0.478575	+	0.322954i
$106$	2.49037	−	7.66456i	0.241886	−	0.744447i
$107$	−7.92505	+	13.7266i	−0.766143	+	1.32700i	0.173497	+	0.984834i	$0.444493\pi$
$107$	−7.92505	+	13.7266i	−0.766143	+	1.32700i	−0.939640	+	0.342164i	$0.888840\pi$
$108$	1.18452	−	0.251778i	0.113981	−	0.0242274i
$109$	−9.55855	−	4.25574i	−0.915543	−	0.407626i	−0.105785	−	0.994389i	$-0.533735\pi$
$109$	−9.55855	−	4.25574i	−0.915543	−	0.407626i	−0.809759	+	0.586763i	$0.800402\pi$
$110$	−2.88486	+	7.20724i	−0.275061	+	0.687183i
$111$	0.0234950	+	0.0170701i	0.00223005	+	0.00162022i
$112$	0.174276	−	0.238140i	0.0164676	−	0.0225021i
$113$	15.6506	−	11.3708i	1.47229	−	1.06968i	0.492343	−	0.870401i	$-0.336140\pi$
$113$	15.6506	−	11.3708i	1.47229	−	1.06968i	0.979943	−	0.199278i	$-0.0638595\pi$
$114$	−1.61190	+	0.717666i	−0.150969	+	0.0672156i
$115$	−8.95984	−	2.53789i	−0.835510	−	0.236660i
$116$	8.78913	+	3.91317i	0.816051	+	0.363329i
$117$	0.232596	+	0.258324i	0.0215035	+	0.0238821i
$118$	−2.47336			−0.227691
$119$	16.0223	+	9.32430i	1.46876	+	0.854757i
$120$	1.08718	−	6.28438i	0.0992457	−	0.573682i
$121$	−4.18302	−	0.889129i	−0.380275	−	0.0808299i
$122$	−2.60452	+	2.89261i	−0.235802	+	0.261884i
$123$	0.169935	−	1.61683i	0.0153226	−	0.145784i
$124$	3.96087	−	6.86044i	0.355697	−	0.616085i
$125$	5.49606	−	9.73619i	0.491583	−	0.870831i
$126$	−0.496542	+	2.29707i	−0.0442355	+	0.204639i
$127$	−5.77958	−	4.19911i	−0.512854	−	0.372611i	0.301051	−	0.953608i	$-0.402663\pi$
$127$	−5.77958	−	4.19911i	−0.512854	−	0.372611i	−0.813905	+	0.580998i	$0.802663\pi$
$128$	6.44584	+	1.37010i	0.569737	+	0.121101i
$129$	6.48745	−	7.20504i	0.571188	−	0.634369i
$130$	0.648024	−	0.238235i	0.0568355	−	0.0208946i
$131$	−12.3462	−	13.7118i	−1.07869	−	1.19801i	−0.979185	−	0.202972i	$-0.934940\pi$
$131$	−12.3462	−	13.7118i	−1.07869	−	1.19801i	−0.0995076	−	0.995037i	$-0.531727\pi$
$132$	4.73316			0.411969
$133$	−0.0181219	+	5.25549i	−0.00157137	+	0.455709i
$134$	7.06460	−	5.13273i	0.610289	−	0.443401i
$135$	0.547961	+	2.16789i	0.0471610	+	0.186582i
$136$	2.08895	−	19.8751i	0.179126	−	1.70427i
$137$	−9.92127	−	4.41723i	−0.847631	−	0.377390i	−0.0634977	−	0.997982i	$-0.520226\pi$
$137$	−9.92127	−	4.41723i	−0.847631	−	0.377390i	−0.784133	+	0.620592i	$0.786892\pi$
$138$	−0.386679	−	3.67900i	−0.0329163	−	0.313178i
$139$	−0.0819599	−	0.0595473i	−0.00695175	−	0.00505074i	0.584304	−	0.811535i	$-0.301368\pi$
$139$	−0.0819599	−	0.0595473i	−0.00695175	−	0.00505074i	−0.591256	+	0.806484i	$0.701368\pi$
$140$	−5.93860	−	4.00751i	−0.501903	−	0.338697i
$141$	10.0389	−	7.29368i	0.845427	−	0.614239i
$142$	3.96993	+	4.40906i	0.333150	+	0.370000i
$143$	0.679318	+	1.17661i	0.0568074	+	0.0983933i
$144$	0.109099	−	0.0231897i	0.00909159	−	0.00193248i
$145$	−6.60158	+	16.4927i	−0.548231	+	1.36964i
$146$	1.11893	+	3.44370i	0.0926030	+	0.285003i
$147$	5.63461	+	4.15345i	0.464735	+	0.342571i
$148$	−0.0284522	−	0.0206717i	−0.00233875	−	0.00169920i
$149$	0.377883	−	0.654512i	0.0309574	−	0.0536197i	−0.850132	−	0.526570i	$-0.823478\pi$
$149$	0.377883	−	0.654512i	0.0309574	−	0.0536197i	0.881089	+	0.472950i	$0.156811\pi$
$150$	4.40200	+	0.589680i	0.359422	+	0.0481472i
$151$	2.95000	+	5.10954i	0.240067	+	0.415809i	0.960733	−	0.277474i	$-0.0894972\pi$
$151$	2.95000	+	5.10954i	0.240067	+	0.415809i	−0.720666	+	0.693282i	$0.756164\pi$
$152$	5.17580	−	2.30442i	0.419813	−	0.186913i
$153$	2.16519	+	6.66377i	0.175045	+	0.538734i
$154$	−3.76499	+	8.37844i	−0.303392	+	0.675154i
$155$	12.9373	+	6.82538i	1.03915	+	0.548228i
$156$	−0.281671	−	0.312827i	−0.0225517	−	0.0250462i
$157$	−4.02625	−	6.97367i	−0.321330	−	0.556560i	0.659433	−	0.751764i	$-0.270797\pi$
$157$	−4.02625	−	6.97367i	−0.321330	−	0.556560i	−0.980763	+	0.195204i	$0.937463\pi$
$158$	−12.3023	+	2.61493i	−0.978718	+	0.208033i
$159$	−0.948360	−	9.02304i	−0.0752098	−	0.715574i
$160$	−2.13660	+	12.3505i	−0.168913	+	0.976389i
$161$	−10.4674	−	3.44102i	−0.824949	−	0.271190i
$162$	−0.718621	+	0.522108i	−0.0564602	+	0.0410207i
$163$	1.71237	+	16.2921i	0.134123	+	1.27610i	0.829930	+	0.557868i	$0.188380\pi$
$163$	1.71237	+	16.2921i	0.134123	+	1.27610i	−0.695807	+	0.718229i	$0.744953\pi$
$164$	−0.205790	+	1.95796i	−0.0160695	+	0.152891i
$165$	0.333229	+	8.73335i	0.0259418	+	0.679890i
$166$	−0.850450	−	8.09149i	−0.0660077	−	0.628021i
$167$	4.54101	−	13.9758i	0.351394	−	1.08148i	−0.606678	−	0.794948i	$-0.707498\pi$
$167$	4.54101	−	13.9758i	0.351394	−	1.08148i	0.958071	−	0.286530i	$-0.0925019\pi$
$168$	1.59439	−	7.37587i	0.123010	−	0.569060i
$169$	−3.97988	+	12.2488i	−0.306145	+	0.942217i
$170$	13.8860	+	0.925931i	1.06501	+	0.0710157i
$171$	−1.32916	+	1.47618i	−0.101644	+	0.112887i
$172$	−7.85622	+	8.72521i	−0.599031	+	0.665291i
$173$	15.8550	−	7.05909i	1.20543	−	0.536693i	0.297061	−	0.954858i	$-0.403993\pi$
$173$	15.8550	−	7.05909i	1.20543	−	0.536693i	0.908371	+	0.418166i	$0.137327\pi$
$174$	−7.05697			−0.534988
$175$	6.97633	−	11.2397i	0.527361	−	0.849641i
$176$	0.435942			0.0328603
$177$	−2.54376	+	1.13255i	−0.191200	+	0.0851279i
$178$	1.63393	−	1.81467i	0.122468	−	0.136015i
$179$	8.11783	−	9.01577i	0.606755	−	0.673870i	−0.358996	−	0.933339i	$-0.616881\pi$
$179$	8.11783	−	9.01577i	0.606755	−	0.673870i	0.965751	+	0.259469i	$0.0835475\pi$
$180$	−0.663573	−	2.62528i	−0.0494598	−	0.195677i
$181$	4.21389	−	12.9690i	0.313216	−	0.963980i	−0.663266	−	0.748383i	$-0.730830\pi$
$181$	4.21389	−	12.9690i	0.313216	−	0.963980i	0.976483	−	0.215597i	$-0.0691696\pi$
$182$	0.777808	−	0.249763i	0.0576550	−	0.0185137i
$183$	−1.35412	+	4.16754i	−0.100099	+	0.308074i
$184$	1.24162	+	11.8132i	0.0915335	+	0.870883i
$185$	0.0361391	−	0.0539536i	0.00265700	−	0.00396675i
$186$	−0.607377	+	5.77881i	−0.0445350	+	0.423723i
$187$	2.86259	+	27.2358i	0.209334	+	1.99168i
$188$	−12.1570	+	8.83255i	−0.886638	+	0.644180i
$189$	0.541156	+	2.58982i	0.0393633	+	0.188381i
$190$	1.74101	+	3.54052i	0.126306	+	0.256856i
$191$	0.223193	+	2.12354i	0.0161497	+	0.153654i	0.999625	−	0.0273891i	$-0.00871932\pi$
$191$	0.223193	+	2.12354i	0.0161497	+	0.153654i	−0.983475	+	0.181043i	$0.942053\pi$
$192$	−5.08841	+	1.08158i	−0.367225	+	0.0780560i
$193$	7.14320	+	12.3724i	0.514179	+	0.890584i	0.999865	+	0.0164507i	$0.00523667\pi$
$193$	7.14320	+	12.3724i	0.514179	+	0.890584i	−0.485686	+	0.874134i	$0.661430\pi$
$194$	−1.59490	−	1.77132i	−0.114507	−	0.127173i
$195$	0.557380	−	0.541746i	0.0399148	−	0.0387953i
$196$	−6.82344	−	5.02978i	−0.487388	−	0.359270i
$197$	−2.94822	−	9.07370i	−0.210052	−	0.646475i	−0.999468	−	0.0326155i	$-0.989616\pi$
$197$	−2.94822	−	9.07370i	−0.210052	−	0.646475i	0.789416	−	0.613859i	$-0.210384\pi$
$198$	−3.17164	+	1.41210i	−0.225399	+	0.100354i
$199$	−5.55375	−	9.61938i	−0.393695	−	0.681900i	0.599239	−	0.800570i	$-0.295470\pi$
$199$	−5.55375	−	9.61938i	−0.393695	−	0.681900i	−0.992934	+	0.118671i	$0.962137\pi$
$200$	−14.1348	−	1.89346i	−0.999479	−	0.133888i
$201$	4.91539	−	8.51371i	0.346705	−	0.600511i
$202$	1.52296	+	1.10650i	0.107155	+	0.0778528i
$203$	−8.61562	+	19.1728i	−0.604698	+	1.34567i
$204$	−2.62202	−	8.06974i	−0.183578	−	0.564995i
$205$	−3.62720	−	0.241865i	−0.253334	−	0.0168926i
$206$	−9.38746	+	1.99537i	−0.654055	+	0.139024i
$207$	−2.08230	−	3.60665i	−0.144730	−	0.250680i
$208$	−0.0259429	−	0.0288125i	−0.00179882	−	0.00199779i
$209$	−6.28111	+	4.56349i	−0.434473	+	0.315663i
$210$	5.17501	+	0.913653i	0.357109	+	0.0630480i
$211$	−7.01531	−	5.09692i	−0.482954	−	0.350887i	0.319514	−	0.947582i	$-0.396480\pi$
$211$	−7.01531	−	5.09692i	−0.482954	−	0.350887i	−0.802468	+	0.596695i	$0.796480\pi$
$212$	1.14845	+	10.9268i	0.0788760	+	0.750455i
$213$	6.10184	+	2.71671i	0.418091	+	0.186146i
$214$	−1.47166	+	14.0019i	−0.100601	+	0.957153i
$215$	−16.6524	−	13.8815i	−1.13568	−	0.946714i
$216$	2.30748	−	1.67648i	0.157004	−	0.114070i
$217$	14.9587	+	8.70531i	1.01546	+	0.590955i
$218$	−9.29403			−0.629471
$219$	2.72765	+	3.02936i	0.184317	+	0.204705i
$220$	−0.403536	−	10.5760i	−0.0272064	−	0.713032i
$221$	1.62973	−	1.81000i	0.109628	−	0.121754i
$222$	0.0252327	+	0.00536339i	0.00169351	+	0.000359967i
$223$	17.8782	+	12.9893i	1.19722	+	0.869828i	0.994008	−	0.109308i	$-0.0348635\pi$
$223$	17.8782	+	12.9893i	1.19722	+	0.869828i	0.203207	+	0.979136i	$0.434863\pi$
$224$	−3.13340	+	14.4955i	−0.209359	+	0.968523i
$225$	4.79730	−	1.40921i	0.319820	−	0.0939476i
$226$	8.59184	−	14.8815i	0.571520	−	0.989902i
$227$	−0.569420	+	5.41767i	−0.0377937	+	0.359583i	0.959238	+	0.282598i	$0.0911962\pi$
$227$	−0.569420	+	5.41767i	−0.0377937	+	0.359583i	−0.997032	+	0.0769856i	$0.975470\pi$
$228$	1.60960	−	1.78764i	0.106598	−	0.118389i
$229$	−17.7637	−	3.77578i	−1.17386	−	0.249511i	−0.420605	−	0.907244i	$-0.638182\pi$
$229$	−17.7637	−	3.77578i	−1.17386	−	0.249511i	−0.753251	+	0.657733i	$0.771516\pi$
$230$	−8.18756	+	1.17767i	−0.539871	+	0.0776535i
$231$	−0.0356574	+	10.3409i	−0.00234608	+	0.680381i
$232$	22.6599			1.48769
$233$	−7.25849	−	8.06137i	−0.475519	−	0.528118i	0.456889	−	0.889524i	$-0.348964\pi$
$233$	−7.25849	−	8.06137i	−0.475519	−	0.528118i	−0.932409	+	0.361406i	$0.882297\pi$
$234$	0.282074	+	0.125588i	0.0184398	+	0.00820992i
$235$	−17.1532	−	21.8095i	−1.11895	−	1.42269i
$236$	3.08046	−	1.37151i	0.200521	−	0.0892775i
$237$	−11.4551	+	8.32259i	−0.744086	+	0.540610i
$238$	16.3704	+	1.77769i	1.06114	+	0.115231i
$239$	−9.60876	−	6.98118i	−0.621539	−	0.451575i	0.231920	−	0.972735i	$-0.425499\pi$
$239$	−9.60876	−	6.98118i	−0.621539	−	0.451575i	−0.853459	+	0.521160i	$0.825499\pi$
$240$	−0.0611176	−	0.241799i	−0.00394512	−	0.0156080i
$241$	−4.64166	−	2.06660i	−0.298995	−	0.133121i	0.251756	−	0.967791i	$-0.418992\pi$
$241$	−4.64166	−	2.06660i	−0.298995	−	0.133121i	−0.550751	+	0.834669i	$0.685659\pi$
$242$	−3.71563	+	0.789781i	−0.238850	+	0.0507690i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.63982	−	5.04684i	0.104979	−	0.323091i
$245$	8.80026	−	12.9443i	0.562228	−	0.826982i
$246$	−0.446245	−	1.37340i	−0.0284516	−	0.0875649i
$247$	0.675403	+	0.143561i	0.0429748	+	0.00913458i
$248$	1.95028	−	18.5557i	0.123843	−	1.17829i
$249$	−4.57975	−	7.93237i	−0.290230	−	0.502693i
$250$	0.942305	−	9.88629i	0.0595966	−	0.625264i
$251$	5.36801			0.338826			0.169413	−	0.985545i	$-0.445813\pi$
$251$	5.36801			0.338826			0.169413	+	0.985545i	$0.445813\pi$
$252$	−0.655333	−	3.13623i	−0.0412821	−	0.197564i
$253$	−5.03000	−	15.4807i	−0.316233	−	0.973266i
$254$	−6.20704	−	1.31935i	−0.389465	−	0.0827832i
$255$	14.7052	−	5.40613i	0.920876	−	0.338545i
$256$	15.9024	−	3.38017i	0.993902	−	0.211260i
$257$	−7.41799	+	12.8483i	−0.462721	+	0.801457i	−0.999095	−	0.0425234i	$-0.986460\pi$
$257$	−7.41799	+	12.8483i	−0.462721	+	0.801457i	0.536374	+	0.843980i	$0.319794\pi$
$258$	2.66126	−	8.19052i	0.165683	−	0.509920i
$259$	0.0453774	−	0.0620059i	0.00281961	−	0.00385286i
$260$	−0.674979	+	0.656048i	−0.0418605	+	0.0406864i
$261$	−7.25783	+	3.23139i	−0.449248	+	0.200018i
$262$	−14.9725	−	6.66619i	−0.925004	−	0.411839i
$263$	−6.10762	−	2.71929i	−0.376612	−	0.167678i	0.209696	−	0.977767i	$-0.432753\pi$
$263$	−6.10762	−	2.71929i	−0.376612	−	0.167678i	−0.586308	+	0.810088i	$0.699419\pi$
$264$	10.1841	−	4.53425i	0.626788	−	0.279064i
$265$	−20.0806	+	2.88833i	−1.23354	+	0.177429i
$266$	1.88405	+	4.27122i	0.115518	+	0.261885i
$267$	0.849501	−	2.61449i	0.0519886	−	0.160004i
$268$	−5.95247	+	10.3100i	−0.363605	+	0.629783i
$269$	−7.00711	+	1.48941i	−0.427231	+	0.0908107i	−0.416509	−	0.909132i	$-0.636746\pi$
$269$	−7.00711	+	1.48941i	−0.427231	+	0.0908107i	−0.0107223	+	0.999943i	$0.503413\pi$
$270$	1.22789	+	1.56120i	0.0747269	+	0.0950118i
$271$	−4.76415	−	1.01265i	−0.289402	−	0.0615142i	0.0609233	−	0.998142i	$-0.480595\pi$
$271$	−4.76415	−	1.01265i	−0.289402	−	0.0615142i	−0.350325	+	0.936628i	$0.613929\pi$
$272$	−0.241498	−	0.743253i	−0.0146429	−	0.0450663i
$273$	0.685579	−	0.613031i	0.0414931	−	0.0371023i
$274$	−9.64671			−0.582779
$275$	19.4857	−	1.48916i	1.17503	−	0.0897998i
$276$	2.52164	+	4.36761i	0.151785	+	0.262899i
$277$	1.95148	−	18.5671i	0.117253	−	1.11559i	−0.764745	−	0.644333i	$-0.777135\pi$
$277$	1.95148	−	18.5671i	0.117253	−	1.11559i	0.881998	−	0.471253i	$-0.156198\pi$
$278$	−0.0880218	−	0.0187096i	−0.00527920	−	0.00112213i
$279$	2.02145	+	6.22140i	0.121021	+	0.372465i
$280$	−16.6169	−	2.93373i	−0.993048	−	0.175324i
$281$	−4.56443	+	14.0479i	−0.272291	+	0.838026i	0.717632	+	0.696422i	$0.245226\pi$
$281$	−4.56443	+	14.0479i	−0.272291	+	0.838026i	−0.989923	+	0.141604i	$0.954774\pi$
$282$	5.51112	−	9.54555i	0.328183	−	0.568429i
$283$	−18.4529	+	3.92228i	−1.09691	+	0.233155i	−0.720609	−	0.693342i	$-0.756138\pi$
$283$	−18.4529	+	3.92228i	−1.09691	+	0.233155i	−0.376301	+	0.926497i	$0.622804\pi$
$284$	−7.38924	−	3.28990i	−0.438471	−	0.195220i
$285$	3.41177	+	2.84408i	0.202096	+	0.168469i
$286$	0.976344	+	0.709355i	0.0577324	+	0.0419450i
$287$	−4.27615	−	0.464355i	−0.252413	−	0.0274100i
$288$	−4.53481	+	3.29473i	−0.267216	+	0.194144i
$289$	29.3192	−	13.0538i	1.72466	−	0.767868i
$290$	0.601658	+	15.7684i	0.0353306	+	0.925952i
$291$	−2.45138	−	1.09143i	−0.143703	−	0.0639805i
$292$	−3.30314	−	3.66851i	−0.193302	−	0.214683i
$293$	−17.3460			−1.01336			−0.506682	−	0.862133i	$-0.669128\pi$
$293$	−17.3460			−1.01336			−0.506682	+	0.862133i	$0.669128\pi$
$294$	6.07291	+	1.33468i	0.354180	+	0.0778399i
$295$	2.74750	+	5.58732i	0.159966	+	0.325306i
$296$	−0.0810220	−	0.0172218i	−0.00470931	−	0.00100099i
$297$	−2.61531	+	2.90459i	−0.151755	+	0.168541i
$298$	0.0701720	−	0.667642i	0.00406495	−	0.0386754i
$299$	−0.723828	+	1.25371i	−0.0418600	+	0.0725037i
$300$	−5.80947	+	1.70654i	−0.335410	+	0.0985272i
$301$	−19.0035	−	17.2298i	−1.09534	−	0.993110i
$302$	4.23986	+	3.08044i	0.243976	+	0.177259i
$303$	2.07297	+	0.440624i	0.119089	+	0.0253132i
$304$	0.148250	−	0.164648i	0.00850272	−	0.00944323i
$305$	9.42758	+	2.67038i	0.539822	+	0.152906i
$306$	4.16454	+	4.62519i	0.238071	+	0.264404i
$307$	5.80262			0.331173			0.165587	−	0.986195i	$-0.447048\pi$
$307$	5.80262			0.331173			0.165587	+	0.986195i	$0.447048\pi$
$308$	0.0431806	−	12.5227i	0.00246044	−	0.713546i
$309$	−8.74096	+	6.35068i	−0.497256	+	0.361278i
$310$	12.9642	+	0.864464i	0.736316	+	0.0490982i
$311$	−1.03081	+	9.80747i	−0.0584517	+	0.556130i	0.925632	+	0.378425i	$0.123534\pi$
$311$	−1.03081	+	9.80747i	−0.0584517	+	0.556130i	−0.984084	+	0.177706i	$0.943133\pi$
$312$	−0.905737	−	0.403260i	−0.0512773	−	0.0228301i
$313$	−0.407680	−	3.87882i	−0.0230435	−	0.219244i	−0.999984	−	0.00573042i	$-0.998176\pi$
$313$	−0.407680	−	3.87882i	−0.0230435	−	0.219244i	0.976940	−	0.213513i	$-0.0684907\pi$
$314$	−5.78670	−	4.20428i	−0.326562	−	0.237261i
$315$	5.74066	−	1.42998i	0.323449	−	0.0805703i
$316$	13.8719	−	10.0785i	0.780357	−	0.566963i
$317$	−17.2067	−	19.1099i	−0.966423	−	1.07332i	−0.997273	−	0.0737976i	$-0.976488\pi$
$317$	−17.2067	−	19.1099i	−0.966423	−	1.07332i	0.0308501	−	0.999524i	$-0.490179\pi$
$318$	−4.02950	−	6.97929i	−0.225963	−	0.391379i
$319$	−30.3733	+	6.45605i	−1.70058	+	0.361469i
$320$	2.85054	+	11.2775i	0.159350	+	0.630434i
$321$	4.89795	+	15.0743i	0.273377	+	0.841367i
$322$	−9.73720	+	0.989487i	−0.542633	+	0.0551419i
$323$	11.2600	+	8.18087i	0.626523	+	0.455196i
$324$	0.605494	−	1.04875i	0.0336385	−	0.0582636i
$325$	−1.25802	−	1.19924i	−0.0697825	−	0.0665221i
$326$	7.27570	+	12.6019i	0.402964	+	0.697954i
$327$	−9.55855	+	4.25574i	−0.528589	+	0.235343i
$328$	1.43289	+	4.40998i	0.0791180	+	0.243500i
$329$	−19.2056	−	26.6268i	−1.05884	−	1.46798i
$330$	3.42567	+	6.96645i	0.188577	+	0.383491i
$331$	19.5987	+	21.7665i	1.07724	+	1.19640i	0.979554	+	0.201180i	$0.0644776\pi$
$331$	19.5987	+	21.7665i	1.07724	+	1.19640i	0.0976865	+	0.995217i	$0.468856\pi$
$332$	5.54602	+	9.60599i	0.304377	+	0.527197i
$333$	0.0284068	−	0.00603805i	0.00155668	−	0.000330883i
$334$	−1.36441	−	12.9815i	−0.0746575	−	0.710318i
$335$	−19.4425	−	10.2573i	−1.06225	−	0.560416i
$336$	−0.0603586	−	0.288859i	−0.00329283	−	0.0157585i
$337$	25.1365	−	18.2628i	1.36927	−	0.994836i	0.371481	−	0.928441i	$-0.378850\pi$
$337$	25.1365	−	18.2628i	1.36927	−	0.994836i	0.997793	−	0.0663954i	$-0.0211499\pi$
$338$	1.19582	+	11.3774i	0.0650438	+	0.618851i
$339$	2.02213	−	19.2393i	0.109827	−	1.04493i
$340$	−17.8078	+	6.54675i	−0.965765	+	0.355047i
$341$	2.67256	+	25.4277i	0.144727	+	1.37699i
$342$	−0.545245	+	1.67809i	−0.0294834	+	0.0907407i
$343$	11.0403	−	14.8698i	0.596123	−	0.802893i
$344$	−8.54528	+	26.2997i	−0.460730	+	1.41798i
$345$	−7.88133	+	4.96028i	−0.424317	+	0.267052i
$346$	10.3155	−	11.4565i	0.554563	−	0.615904i
$347$	−9.13462	+	10.1450i	−0.490372	+	0.544614i	−0.936643	−	0.350284i	$-0.886085\pi$
$347$	−9.13462	+	10.1450i	−0.490372	+	0.544614i	0.446271	+	0.894898i	$0.352752\pi$
$348$	8.78913	−	3.91317i	0.471147	−	0.209768i
$349$	37.2611			1.99454			0.997270	−	0.0738347i	$-0.0235237\pi$
$349$	37.2611			1.99454			0.997270	+	0.0738347i	$0.0235237\pi$
$350$	1.60030	−	11.6411i	0.0855395	−	0.622246i
$351$	0.347609			0.0185540
$352$	−20.0144	+	8.91100i	−1.06677	+	0.474958i
$353$	−16.9573	+	18.8330i	−0.902546	+	1.00238i	0.0974284	+	0.995243i	$0.468938\pi$
$353$	−16.9573	+	18.8330i	−0.902546	+	1.00238i	−0.999975	+	0.00713649i	$0.997728\pi$
$354$	−1.65500	+	1.83807i	−0.0879623	+	0.0976921i
$355$	5.55011	−	13.8658i	0.294569	−	0.735921i
$356$	−1.02873	+	3.16612i	−0.0545228	+	0.167804i
$357$	17.6503	−	5.66773i	0.934154	−	0.299968i
$358$	3.33007	−	10.2489i	0.176000	−	0.541672i
$359$	−0.0961788	−	0.915080i	−0.00507612	−	0.0482961i	0.991691	−	0.128646i	$-0.0410630\pi$
$359$	−0.0961788	−	0.915080i	−0.00507612	−	0.0482961i	−0.996767	+	0.0803496i	$0.974396\pi$
$360$	−3.94273	−	5.01300i	−0.207800	−	0.264208i
$361$	1.57359	−	14.9717i	0.0828207	−	0.787986i
$362$	−1.26613	−	12.0464i	−0.0665462	−	0.633145i
$363$	−3.45974	+	2.51365i	−0.181589	+	0.131932i
$364$	−0.830227	+	0.742372i	−0.0435157	+	0.0389109i
$365$	6.53637	−	6.35304i	0.342129	−	0.332533i
$366$	0.406865	+	3.87106i	0.0212672	+	0.202344i
$367$	15.1478	−	3.21977i	0.790710	−	0.168071i	0.205183	−	0.978724i	$-0.434221\pi$
$367$	15.1478	−	3.21977i	0.790710	−	0.168071i	0.585527	+	0.810653i	$0.300888\pi$
$368$	0.232253	+	0.402273i	0.0121070	+	0.0209700i
$369$	−1.08783	−	1.20816i	−0.0566301	−	0.0628941i
$370$	0.00983290	−	0.0568384i	0.000511188	−	0.00295489i
$371$	−23.8812	+	2.42679i	−1.23985	+	0.125993i
$372$	−2.44796	−	7.53403i	−0.126921	−	0.390621i
$373$	11.0768	−	4.93172i	0.573536	−	0.255355i	−0.0994097	−	0.995047i	$-0.531695\pi$
$373$	11.0768	−	4.93172i	0.573536	−	0.255355i	0.672946	+	0.739692i	$0.265029\pi$
$374$	12.1629	+	21.0668i	0.628929	+	1.08934i
$375$	−3.55781	−	10.5991i	−0.183725	−	0.547338i
$376$	−17.6961	+	30.6506i	−0.912609	+	1.58069i
$377$	2.23422	+	1.62325i	0.115068	+	0.0836018i
$378$	1.37481	+	1.90604i	0.0707123	+	0.0980363i
$379$	5.91851	+	18.2153i	0.304013	+	0.935656i	0.980044	+	0.198783i	$0.0636988\pi$
$379$	5.91851	+	18.2153i	0.304013	+	0.935656i	−0.676030	+	0.736874i	$0.736301\pi$
$380$	−4.13161	−	3.44414i	−0.211947	−	0.176681i
$381$	−6.98784	+	1.48531i	−0.357998	+	0.0760948i
$382$	0.948327	+	1.64255i	0.0485206	+	0.0840402i
$383$	−1.11859	−	1.24232i	−0.0571571	−	0.0634794i	0.713888	−	0.700260i	$-0.246932\pi$
$383$	−1.11859	−	1.24232i	−0.0571571	−	0.0634794i	−0.771045	+	0.636780i	$0.780266\pi$
$384$	5.33129	−	3.87341i	0.272061	−	0.197664i
$385$	23.1092	−	0.801961i	1.17775	−	0.0408717i
$386$	10.2665	+	7.45906i	0.522552	+	0.379656i
$387$	−1.01344	−	9.64223i	−0.0515160	−	0.490142i
$388$	2.96859	+	1.32170i	0.150707	+	0.0670993i
$389$	3.01431	−	28.6792i	0.152831	−	1.45409i	−0.602169	−	0.798369i	$-0.705697\pi$
$389$	3.01431	−	28.6792i	0.152831	−	1.45409i	0.755000	−	0.655724i	$-0.227637\pi$
$390$	0.256569	−	0.640986i	0.0129919	−	0.0324576i
$391$	−23.6072	+	17.1517i	−1.19387	+	0.867397i
$392$	−19.5000	−	4.28563i	−0.984901	−	0.216457i
$393$	−18.4511			−0.930735
$394$	−5.67063	−	6.29787i	−0.285682	−	0.317282i
$395$	19.5730	+	24.8861i	0.984823	+	1.25216i
$396$	3.16710	−	3.51742i	0.159153	−	0.176757i
$397$	38.2632	+	8.13310i	1.92038	+	0.408189i	0.999847	+	0.0175192i	$0.00557681\pi$
$397$	38.2632	+	8.13310i	1.92038	+	0.408189i	0.920531	+	0.390670i	$0.127757\pi$
$398$	−7.98208	−	5.79932i	−0.400106	−	0.290694i
$399$	3.89347	+	3.53008i	0.194917	+	0.176725i
$400$	−0.535074	+	0.157179i	−0.0267537	+	0.00785894i
$401$	14.6950	−	25.4526i	0.733836	−	1.27104i	−0.221397	−	0.975184i	$-0.571062\pi$
$401$	14.6950	−	25.4526i	0.733836	−	1.27104i	0.955232	−	0.295857i	$-0.0956051\pi$
$402$	0.912777	−	8.68449i	0.0455252	−	0.433143i
$403$	1.52154	−	1.68984i	0.0757934	−	0.0841771i
$404$	−2.51034	−	0.533590i	−0.124894	−	0.0265471i
$405$	1.97771	+	1.04339i	0.0982733	+	0.0518463i
$406$	−0.0643808	+	18.6709i	−0.00319516	+	0.926621i
$407$	0.113509			0.00562642
$408$	−13.3723	−	14.8514i	−0.662026	−	0.735255i
$409$	3.25261	+	1.44816i	0.160831	+	0.0716067i	0.485573	−	0.874196i	$-0.338611\pi$
$409$	3.25261	+	1.44816i	0.160831	+	0.0716067i	−0.324742	+	0.945803i	$0.605278\pi$
$410$	−3.03074	+	1.11420i	−0.149678	+	0.0550265i
$411$	−9.92127	+	4.41723i	−0.489380	+	0.217886i
$412$	10.5852	−	7.69059i	0.521495	−	0.378888i
$413$	2.97323	+	6.74044i	0.146303	+	0.331675i
$414$	−2.99277	−	2.17438i	−0.147087	−	0.106865i
$415$	−17.3340	+	10.9095i	−0.850890	+	0.535526i
$416$	1.78001	+	0.792513i	0.0872723	+	0.0388561i
$417$	−0.0990942	+	0.0210631i	−0.00485266	+	0.00103147i
$418$	−3.44818	+	5.97243i	−0.168656	+	0.292121i
$419$	−7.06648	+	21.7484i	−0.345220	+	1.06248i	0.616246	+	0.787554i	$0.288653\pi$
$419$	−7.06648	+	21.7484i	−0.345220	+	1.06248i	−0.961466	+	0.274924i	$0.911347\pi$
$420$	−6.95186	+	1.73169i	−0.339216	+	0.0844978i
$421$	2.31069	+	7.11157i	0.112616	+	0.346597i	0.991442	−	0.130545i	$-0.0416728\pi$
$421$	2.31069	+	7.11157i	0.112616	+	0.346597i	−0.878826	+	0.477142i	$0.841673\pi$
$422$	−7.53418	−	1.60144i	−0.366758	−	0.0779569i
$423$	1.29707	−	12.3408i	0.0630656	−	0.600029i
$424$	12.9387	+	22.4104i	0.628357	+	1.08835i
$425$	−13.3334	−	32.3970i	−0.646765	−	1.57149i
$426$	5.93297			0.287454
$427$	11.0139	+	3.62066i	0.532998	+	0.175216i
$428$	−5.93135	−	18.2548i	−0.286703	−	0.882380i
$429$	1.32895	+	0.282476i	0.0641621	+	0.0136381i
$430$	−18.5281	−	5.24813i	−0.893506	−	0.253087i
$431$	20.3968	−	4.33548i	0.982480	−	0.208833i	0.311450	−	0.950263i	$-0.399185\pi$
$431$	20.3968	−	4.33548i	0.982480	−	0.208833i	0.671030	+	0.741430i	$0.265852\pi$
$432$	0.0557682	−	0.0965934i	0.00268315	−	0.00464735i
$433$	−0.783821	+	2.41235i	−0.0376680	+	0.115930i	−0.968122	−	0.250477i	$-0.919412\pi$
$433$	−0.783821	+	2.41235i	−0.0376680	+	0.115930i	0.930454	+	0.366408i	$0.119412\pi$
$434$	15.2836	+	1.65968i	0.733639	+	0.0796671i
$435$	7.83914	+	15.9417i	0.375858	+	0.764346i
$436$	11.5753	−	5.15365i	0.554356	−	0.246815i
$437$	−7.55738	−	3.36476i	−0.361518	−	0.160958i
$438$	3.30788	+	1.47276i	0.158056	+	0.0703713i
$439$	1.66629	−	0.741879i	0.0795276	−	0.0354080i	−0.366587	−	0.930384i	$-0.619474\pi$
$439$	1.66629	−	0.741879i	0.0795276	−	0.0354080i	0.446115	+	0.894976i	$0.352807\pi$
$440$	−10.9998	−	22.3692i	−0.524394	−	1.06641i
$441$	6.85691	−	1.40813i	0.326519	−	0.0670537i
$442$	0.668543	−	2.05756i	0.0317994	−	0.0978684i
$443$	−19.7949	+	34.2858i	−0.940485	+	1.62897i	−0.175937	+	0.984402i	$0.556295\pi$
$443$	−19.7949	+	34.2858i	−0.940485	+	1.62897i	−0.764548	+	0.644566i	$0.777038\pi$
$444$	−0.0344003	+	0.00731200i	−0.00163256	+	0.000347012i
$445$	−5.91436	−	1.67526i	−0.280368	−	0.0794147i
$446$	19.2005	+	4.08120i	0.909172	+	0.193250i
$447$	−0.233544	−	0.718776i	−0.0110463	−	0.0339969i
$448$	2.81514	+	13.4725i	0.133003	+	0.636514i
$449$	19.9440			0.941215			0.470608	−	0.882343i	$-0.344035\pi$
$449$	19.9440			0.941215			0.470608	+	0.882343i	$0.344035\pi$
$450$	3.38373	−	2.87675i	0.159511	−	0.135611i
$451$	−3.17710	−	5.50290i	−0.149604	−	0.259121i
$452$	−2.44877	+	23.2985i	−0.115180	+	1.09587i
$453$	5.77106	+	1.22668i	0.271148	+	0.0576343i
$454$	1.49528	+	4.60200i	0.0701770	+	0.215983i
$455$	−1.42823	−	1.47962i	−0.0669566	−	0.0693657i
$456$	1.75077	−	5.38833i	0.0819875	−	0.252331i
$457$	−2.34063	+	4.05410i	−0.109490	+	0.189643i	−0.915564	−	0.402173i	$-0.868255\pi$
$457$	−2.34063	+	4.05410i	−0.109490	+	0.189643i	0.806074	+	0.591815i	$0.201589\pi$
$458$	−15.7788	+	3.35389i	−0.737296	+	0.156717i
$459$	6.40094	+	2.84988i	0.298770	+	0.133021i
$460$	9.54419	−	6.00683i	0.445000	−	0.280070i
$461$	−1.19424	−	0.867665i	−0.0556212	−	0.0404112i	0.559627	−	0.828744i	$-0.310944\pi$
$461$	−1.19424	−	0.867665i	−0.0556212	−	0.0404112i	−0.615248	+	0.788333i	$0.710944\pi$
$462$	3.70712	+	8.40420i	0.172471	+	0.390999i
$463$	−25.1695	+	18.2867i	−1.16973	+	0.849856i	−0.990976	−	0.134039i	$-0.957205\pi$
$463$	−25.1695	+	18.2867i	−1.16973	+	0.849856i	−0.178750	+	0.983895i	$0.557205\pi$
$464$	0.809512	−	0.360418i	0.0375807	−	0.0167320i
$465$	13.7290	−	5.04724i	0.636668	−	0.234060i
$466$	−8.80253	−	3.91914i	−0.407769	−	0.181551i
$467$	27.8254	+	30.9032i	1.28761	+	1.43003i	0.846330	+	0.532658i	$0.178807\pi$
$467$	27.8254	+	30.9032i	1.28761	+	1.43003i	0.441275	+	0.897372i	$0.354526\pi$
$468$	−0.420950			−0.0194584
$469$	−22.4802	−	13.0825i	−1.03804	−	0.604093i
$470$	−21.7988	−	11.5005i	−1.00551	−	0.530477i
$471$	−7.87654	−	1.67421i	−0.362932	−	0.0771435i
$472$	5.31419	−	5.90200i	0.244605	−	0.271662i
$473$	3.96104	−	37.6868i	0.182129	−	1.73284i
$474$	−6.28857	+	10.8921i	−0.288844	+	0.500292i
$475$	6.06405	−	7.86587i	0.278238	−	0.360911i
$476$	−21.3743	+	6.86354i	−0.979690	+	0.314590i
$477$	−7.34000	−	5.33282i	−0.336076	−	0.244173i
$478$	−10.3194	−	2.19347i	−0.472000	−	0.100327i
$479$	−8.55571	+	9.50208i	−0.390920	+	0.434161i	−0.906192	−	0.422866i	$-0.861024\pi$
$479$	−8.55571	+	9.50208i	−0.390920	+	0.434161i	0.515272	+	0.857027i	$0.327691\pi$
$480$	7.74852	+	9.85187i	0.353670	+	0.449674i
$481$	−0.00675492	−	0.00750210i	−0.000307998	−	0.000342066i
$482$	−4.51321			−0.205571
$483$	−9.56125	+	5.47632i	−0.435052	+	0.249181i
$484$	4.18970	−	3.04399i	0.190441	−	0.138363i
$485$	−2.22973	+	5.57052i	−0.101247	+	0.252944i
$486$	−0.0928489	+	0.883398i	−0.00421171	+	0.0400717i
$487$	15.7587	+	7.01620i	0.714093	+	0.317935i	0.731431	−	0.681915i	$-0.238853\pi$
$487$	15.7587	+	7.01620i	0.714093	+	0.317935i	−0.0173386	+	0.999850i	$0.505519\pi$
$488$	−1.30644	−	12.4299i	−0.0591397	−	0.562677i
$489$	13.2532	+	9.62901i	0.599330	+	0.435439i
$490$	2.46450	−	13.6834i	0.111335	−	0.618151i
$491$	21.9135	−	15.9211i	0.988941	−	0.718507i	0.0292519	−	0.999572i	$-0.490688\pi$
$491$	21.9135	−	15.9211i	0.988941	−	0.718507i	0.959689	+	0.281065i	$0.0906875\pi$
$492$	1.31735	+	1.46306i	0.0593905	+	0.0659599i
$493$	27.8330	+	48.2082i	1.25354	+	2.17119i
$494$	0.599936	−	0.127520i	0.0269924	−	0.00573741i
$495$	6.71311	+	5.59611i	0.301732	+	0.251526i
$496$	−0.225466	−	0.693913i	−0.0101237	−	0.0311576i
$497$	7.24337	−	16.1191i	0.324910	−	0.723039i
$498$	−6.58221	−	4.78226i	−0.294956	−	0.214298i
$499$	−12.3848	+	21.4511i	−0.554420	+	0.960283i	0.443529	+	0.896260i	$0.353726\pi$
$499$	−12.3848	+	21.4511i	−0.554420	+	0.960283i	−0.997948	+	0.0640231i	$0.979607\pi$
$500$	4.30847	+	12.8354i	0.192680	+	0.574018i
$501$	−7.34750	−	12.7262i	−0.328262	−	0.568567i
$502$	4.35597	−	1.93941i	0.194417	−	0.0865599i
$503$	−9.21397	−	28.3577i	−0.410831	−	1.26441i	−0.915927	−	0.401344i	$-0.868543\pi$
$503$	−9.21397	−	28.3577i	−0.410831	−	1.26441i	0.505096	−	0.863063i	$-0.331457\pi$
$504$	−4.41448	−	6.12028i	−0.196637	−	0.272619i
$505$	0.807813	−	4.66951i	0.0359472	−	0.207790i
$506$	−9.67472	−	10.7449i	−0.430094	−	0.477668i
$507$	6.43958	+	11.1537i	0.285992	+	0.495353i
$508$	8.46218	−	1.79869i	0.375448	−	0.0798040i
$509$	−1.41166	−	13.4310i	−0.0625705	−	0.595319i	−0.980218	−	0.197923i	$-0.936581\pi$
$509$	−1.41166	−	13.4310i	−0.0625705	−	0.595319i	0.917647	−	0.397396i	$-0.130086\pi$
$510$	9.97965	−	9.69975i	0.441906	−	0.429512i
$511$	8.03976	−	7.18899i	0.355658	−	0.318022i
$512$	1.02053	−	0.741461i	0.0451016	−	0.0327682i
$513$	0.207635	+	1.97552i	0.00916733	+	0.0872213i
$514$	−1.37750	+	13.1061i	−0.0607591	+	0.578084i
$515$	14.9355	+	18.9897i	0.658135	+	0.836787i
$516$	1.22726	+	11.6766i	0.0540272	+	0.514034i
$517$	14.9873	−	46.1260i	0.659139	−	2.02862i
$518$	0.0144203	−	0.0667102i	0.000633592	−	0.00293108i
$519$	5.36313	−	16.5060i	0.235415	−	0.724533i
$520$	−0.823841	+	2.05820i	−0.0361278	+	0.0902580i
$521$	10.6378	−	11.8145i	0.466050	−	0.517601i	−0.463600	−	0.886045i	$-0.653442\pi$
$521$	10.6378	−	11.8145i	0.466050	−	0.517601i	0.929650	+	0.368443i	$0.120109\pi$
$522$	−4.72204	+	5.24435i	−0.206678	+	0.229539i
$523$	27.8714	−	12.4091i	1.21873	−	0.542613i	0.306334	−	0.951924i	$-0.400897\pi$
$523$	27.8714	−	12.4091i	1.21873	−	0.542613i	0.912395	+	0.409311i	$0.134231\pi$
$524$	22.3440			0.976104
$525$	−3.68464	−	12.7053i	−0.160811	−	0.554503i
$526$	−5.93860			−0.258935
$527$	41.8722	−	18.6427i	1.82398	−	0.812088i
$528$	0.291702	−	0.323968i	0.0126947	−	0.0140989i
$529$	−3.78464	+	4.20327i	−0.164550	+	0.182751i
$530$	−15.2513	+	9.59871i	−0.662473	+	0.416941i
$531$	−0.860454	+	2.64821i	−0.0373405	+	0.114922i
$532$	−4.71494	−	4.27488i	−0.204418	−	0.185339i
$533$	−0.174632	+	0.537461i	−0.00756414	+	0.0232800i
$534$	−0.255245	−	2.42850i	−0.0110456	−	0.105091i
$535$	33.2651	−	12.2294i	1.43818	−	0.528722i
$536$	−2.93092	+	27.8858i	−0.126596	+	1.20448i
$537$	−1.26813	−	12.0655i	−0.0547238	−	0.520663i
$538$	−5.14795	+	3.74020i	−0.221944	+	0.161252i
$539$	27.3589	+	0.188680i	1.17843	+	0.00812702i
$540$	−2.39498	−	1.26353i	−0.103064	−	0.0543735i
$541$	−0.283370	−	2.69609i	−0.0121830	−	0.115914i	0.986740	−	0.162308i	$-0.0518937\pi$
$541$	−0.283370	−	2.69609i	−0.0121830	−	0.115914i	−0.998923	+	0.0463939i	$0.985227\pi$
$542$	−4.23182	+	0.899502i	−0.181772	+	0.0386369i
$543$	−6.81822	−	11.8095i	−0.292598	−	0.506794i
$544$	26.2800	+	29.1869i	1.12675	+	1.25138i
$545$	10.3241	+	20.9952i	0.442238	+	0.899336i
$546$	0.334845	−	0.745148i	0.0143300	−	0.0318894i
$547$	3.38387	+	10.4145i	0.144684	+	0.445291i	0.996970	−	0.0777845i	$-0.0247846\pi$
$547$	3.38387	+	10.4145i	0.144684	+	0.445291i	−0.852286	+	0.523075i	$0.824785\pi$
$548$	12.0145	−	5.34921i	0.513235	−	0.228507i
$549$	2.19101	+	3.79494i	0.0935099	+	0.161964i
$550$	15.2741	−	8.24840i	0.651289	−	0.351713i
$551$	−7.89066	+	13.6670i	−0.336153	+	0.582235i
$552$	9.60975	+	6.98189i	0.409018	+	0.297169i
$553$	21.9149	+	30.3830i	0.931915	+	1.29202i
$554$	−5.12452	−	15.7716i	−0.217720	−	0.670073i
$555$	−0.0159136	−	0.0629586i	−0.000675493	−	0.00267244i
$556$	0.120002	−	0.0255072i	0.00508921	−	0.00108174i
$557$	−3.62526	−	6.27914i	−0.153607	−	0.266056i	0.778944	−	0.627094i	$-0.215756\pi$
$557$	−3.62526	−	6.27914i	−0.153607	−	0.266056i	−0.932551	+	0.361038i	$0.882422\pi$
$558$	3.88807	+	4.31814i	0.164595	+	0.182802i
$559$	−2.72654	+	1.98095i	−0.115320	+	0.0837852i
$560$	−0.640293	+	0.159495i	−0.0270573	+	0.00673990i
$561$	22.1556	+	16.0970i	0.935409	+	0.679614i
$562$	1.37145	+	13.0485i	0.0578513	+	0.550418i
$563$	17.7588	+	7.90675i	0.748446	+	0.333230i	0.745268	−	0.666765i	$-0.232322\pi$
$563$	17.7588	+	7.90675i	0.748446	+	0.333230i	0.00317821	+	0.999995i	$0.498988\pi$
$564$	−1.57073	+	14.9445i	−0.0661398	+	0.629278i
$565$	−43.1614	−	2.87804i	−1.81581	−	0.121080i
$566$	−13.5569	+	9.84964i	−0.569838	+	0.414011i
$567$	2.28671	+	1.33077i	0.0960329	+	0.0558870i
$568$	−19.0507			−0.799350
$569$	26.7476	+	29.7062i	1.12132	+	1.24535i	0.966295	+	0.257438i	$0.0828785\pi$
$569$	26.7476	+	29.7062i	1.12132	+	1.24535i	0.155023	+	0.987911i	$0.450455\pi$
$570$	3.79608	+	1.07525i	0.159000	+	0.0450372i
$571$	−20.7881	+	23.0876i	−0.869957	+	0.966185i	−0.999678	−	0.0253658i	$-0.991925\pi$
$571$	−20.7881	+	23.0876i	−0.869957	+	0.966185i	0.129722	+	0.991550i	$0.458592\pi$
$572$	−1.60934	−	0.342075i	−0.0672897	−	0.0143029i
$573$	1.72744	+	1.25506i	0.0721650	+	0.0524309i
$574$	−3.63773	+	1.16812i	−0.151836	+	0.0487563i
$575$	11.7554	+	17.1875i	0.490234	+	0.716767i
$576$	−2.60105	+	4.50514i	−0.108377	+	0.187714i
$577$	3.80439	−	36.1964i	0.158379	−	1.50687i	−0.569968	−	0.821667i	$-0.693045\pi$
$577$	3.80439	−	36.1964i	0.158379	−	1.50687i	0.728347	−	0.685208i	$-0.240289\pi$
$578$	19.0755	−	21.1855i	0.793435	−	0.881199i
$579$	13.9742	+	2.97031i	0.580749	+	0.123442i
$580$	−9.49310	−	19.3052i	−0.394179	−	0.801604i
$581$	−21.0287	+	12.0444i	−0.872418	+	0.499688i
$582$	−2.38354			−0.0988010
$583$	−23.7280	−	26.3526i	−0.982713	−	1.09141i
$584$	−10.6215	−	4.72902i	−0.439523	−	0.195688i
$585$	−0.0296362	−	0.776713i	−0.00122531	−	0.0321131i
$586$	−14.0757	+	6.26693i	−0.581464	+	0.258884i
$587$	16.2681	−	11.8195i	0.671456	−	0.487842i	−0.199056	−	0.979988i	$-0.563788\pi$
$587$	16.2681	−	11.8195i	0.671456	−	0.487842i	0.870512	+	0.492146i	$0.163788\pi$
$588$	−8.30363	+	1.70522i	−0.342436	+	0.0703223i
$589$	10.5125	+	7.63778i	0.433160	+	0.314709i
$590$	4.24815	+	3.54130i	0.174894	+	0.145793i
$591$	−8.71582	−	3.88053i	−0.358521	−	0.159624i
$592$	−0.00316839		0.000673463i	−0.000130220		2.76792e-5i
$593$	−8.69805	+	15.0655i	−0.357186	+	0.618665i	−0.987490	−	0.157684i	$-0.949597\pi$
$593$	−8.69805	+	15.0655i	−0.357186	+	0.618665i	0.630303	+	0.776349i	$0.282930\pi$
$594$	−1.07284	+	3.30187i	−0.0440193	+	0.135477i
$595$	−14.1690	−	38.9554i	−0.580873	−	1.59702i
$596$	0.282819	+	0.870428i	0.0115847	+	0.0356541i
$597$	−10.8648	−	2.30938i	−0.444666	−	0.0945166i
$598$	−0.134413	+	1.27886i	−0.00549657	+	0.0522963i
$599$	−12.1413	−	21.0294i	−0.496081	−	0.859238i	0.503908	−	0.863757i	$-0.331895\pi$
$599$	−12.1413	−	21.0294i	−0.496081	−	0.859238i	−0.999990	+	0.00451883i	$0.998562\pi$
$600$	−10.8651	+	9.23721i	−0.443566	+	0.377107i
$601$	18.3124			0.746978			0.373489	−	0.927635i	$-0.378161\pi$
$601$	18.3124			0.746978			0.373489	+	0.927635i	$0.378161\pi$
$602$	−21.6457	−	7.11572i	−0.882212	−	0.290015i
$603$	−3.03788	−	9.34963i	−0.123712	−	0.380746i
$604$	−6.98868	−	1.48549i	−0.284365	−	0.0604437i
$605$	5.91157	+	7.51628i	0.240339	+	0.305580i
$606$	1.84135	−	0.391391i	0.0747996	−	0.0158992i
$607$	−2.45267	+	4.24815i	−0.0995509	+	0.172427i	−0.911499	−	0.411303i	$-0.865074\pi$
$607$	−2.45267	+	4.24815i	−0.0995509	+	0.172427i	0.811948	+	0.583730i	$0.198407\pi$
$608$	−3.44073	+	10.5895i	−0.139540	+	0.429460i
$609$	8.48320	+	19.2318i	0.343757	+	0.779311i
$610$	8.61498	−	1.23915i	0.348810	−	0.0501718i
$611$	−3.94048	+	1.75442i	−0.159415	+	0.0709761i
$612$	−7.75146	−	3.45117i	−0.313334	−	0.139505i
$613$	22.6626	+	10.0900i	0.915333	+	0.407532i	0.809681	−	0.586871i	$-0.199640\pi$
$613$	22.6626	+	10.0900i	0.915333	+	0.407532i	0.105652	+	0.994403i	$0.466307\pi$
$614$	4.70865	−	2.09643i	0.190026	−	0.0846049i
$615$	−2.60681	+	2.53369i	−0.105117	+	0.102168i
$616$	−11.9035	−	26.9858i	−0.479606	−	1.08729i
$617$	5.28926	−	16.2787i	0.212938	−	0.655355i	−0.786356	−	0.617774i	$-0.788035\pi$
$617$	5.28926	−	16.2787i	0.212938	−	0.655355i	0.999294	−	0.0375810i	$-0.0119652\pi$
$618$	−4.79859	+	8.31140i	−0.193028	+	0.334334i
$619$	39.5754	−	8.41200i	1.59067	−	0.338107i	0.674305	−	0.738453i	$-0.264444\pi$
$619$	39.5754	−	8.41200i	1.59067	−	0.338107i	0.916364	+	0.400346i	$0.131110\pi$
$620$	−16.6257	+	6.11214i	−0.667702	+	0.245470i
$621$	−4.07360	−	0.865870i	−0.163468	−	0.0347462i
$622$	2.70687	+	8.33088i	0.108535	+	0.334038i
$623$	−6.90951	−	2.27141i	−0.276824	−	0.0910020i
$624$	−0.0387711			−0.00155209
$625$	−23.3799	+	8.85338i	−0.935194	+	0.354135i
$626$	−1.73220	−	3.00025i	−0.0692325	−	0.119914i
$627$	−0.811546	+	7.72134i	−0.0324100	+	0.308361i
$628$	9.53838	+	2.02745i	0.380623	+	0.0809039i
$629$	−0.0628802	−	0.193525i	−0.00250720	−	0.00771637i
$630$	4.14173	−	3.23443i	0.165011	−	0.128863i
$631$	−4.59899	+	14.1542i	−0.183083	+	0.563471i	−0.999910	−	0.0134115i	$-0.995731\pi$
$631$	−4.59899	+	14.1542i	−0.183083	+	0.563471i	0.816827	+	0.576882i	$0.195731\pi$
$632$	20.1925	−	34.9745i	0.803215	−	1.39121i
$633$	−8.48192	+	1.80289i	−0.337126	+	0.0716583i
$634$	−20.8669	−	9.29055i	−0.828731	−	0.368975i
$635$	3.91460	+	15.4873i	0.155346	+	0.614594i
$636$	8.88865	+	6.45798i	0.352458	+	0.256076i
$637$	−1.61566	−	1.81945i	−0.0640149	−	0.0720894i
$638$	−22.3145	+	16.2125i	−0.883441	+	0.641857i
$639$	6.10184	−	2.71671i	0.241385	−	0.107471i
$640$	−9.10944	−	11.5822i	−0.360082	−	0.457828i
$641$	−1.76129	−	0.784178i	−0.0695669	−	0.0309732i	0.371658	−	0.928370i	$-0.378789\pi$
$641$	−1.76129	−	0.784178i	−0.0695669	−	0.0309732i	−0.441225	+	0.897396i	$0.645456\pi$
$642$	9.42073	+	10.4628i	0.371807	+	0.412933i
$643$	−13.3895			−0.528029			−0.264014	−	0.964519i	$-0.585047\pi$
$643$	−13.3895			−0.528029			−0.264014	+	0.964519i	$0.585047\pi$
$644$	11.5786	−	6.63175i	0.456259	−	0.261328i
$645$	−21.4586	+	3.08654i	−0.844932	+	0.121532i
$646$	12.0928	+	2.57041i	0.475785	+	0.101131i
$647$	−17.0696	+	18.9577i	−0.671073	+	0.745302i	−0.978495	−	0.206271i	$-0.933867\pi$
$647$	−17.0696	+	18.9577i	−0.671073	+	0.745302i	0.307422	+	0.951573i	$0.400534\pi$
$648$	0.298137	−	2.83658i	0.0117119	−	0.111431i
$649$	−5.44160	+	9.42513i	−0.213602	+	0.369969i
$650$	−1.45412	−	0.518641i	−0.0570353	−	0.0203428i
$651$	16.4786	−	5.29148i	0.645848	−	0.207389i
$652$	−16.0494	−	11.6606i	−0.628545	−	0.456665i
$653$	−8.12197	−	1.72638i	−0.317837	−	0.0675584i	0.0462307	−	0.998931i	$-0.485279\pi$
$653$	−8.12197	−	1.72638i	−0.317837	−	0.0675584i	−0.364068	+	0.931372i	$0.618612\pi$
$654$	−6.21892	+	6.90681i	−0.243179	+	0.270078i
$655$	1.57309	+	41.2279i	0.0614657	+	1.61091i
$656$	0.121332	+	0.134753i	0.00473724	+	0.00526123i
$657$	4.07640			0.159036
$658$	−25.2047	−	14.6681i	−0.982582	−	0.571821i
$659$	−2.76749	+	2.01070i	−0.107806	+	0.0783257i	−0.640382	−	0.768056i	$-0.721224\pi$
$659$	−2.76749	+	2.01070i	−0.107806	+	0.0783257i	0.532576	+	0.846382i	$0.321224\pi$
$660$	−8.12949	−	6.77682i	−0.316440	−	0.263787i
$661$	0.224603	−	2.13696i	0.00873605	−	0.0831180i	−0.989285	−	0.145996i	$-0.953361\pi$
$661$	0.224603	−	2.13696i	0.00873605	−	0.0831180i	0.998021	+	0.0628782i	$0.0200280\pi$
$662$	23.7678	+	10.5821i	0.923760	+	0.411284i
$663$	−0.254589	−	2.42225i	−0.00988742	−	0.0940725i
$664$	21.1354	+	15.3558i	0.820212	+	0.595919i
$665$	7.55581	−	9.00069i	0.293002	−	0.349032i
$666$	0.0208698	−	0.0151628i	0.000808687	−	0.000587546i
$667$	−22.1392	−	24.5880i	−0.857232	−	0.952053i
$668$	8.89773	+	15.4113i	0.344264	+	0.596282i
$669$	21.6158	−	4.59458i	0.835715	−	0.177637i
$670$	−19.4828	−	1.29913i	−0.752687	−	0.0501898i
$671$	5.29258	+	16.2889i	0.204318	+	0.628826i
$672$	8.67562	+	12.0280i	0.334669	+	0.463989i
$673$	−24.2563	−	17.6232i	−0.935010	−	0.679324i	0.0122045	−	0.999926i	$-0.496115\pi$
$673$	−24.2563	−	17.6232i	−0.935010	−	0.679324i	−0.947214	+	0.320601i	$0.896115\pi$
$674$	13.7994	−	23.9012i	0.531533	−	0.920641i
$675$	2.16277	−	4.50804i	0.0832451	−	0.173515i
$676$	−7.79825	−	13.5070i	−0.299933	−	0.519499i
$677$	23.9588	−	10.6671i	0.920811	−	0.409971i	0.109100	−	0.994031i	$-0.465203\pi$
$677$	23.9588	−	10.6671i	0.920811	−	0.409971i	0.811711	+	0.584059i	$0.198536\pi$
$678$	−5.31005	−	16.3426i	−0.203931	−	0.627635i
$679$	−2.90999	+	6.47575i	−0.111675	+	0.248517i
$680$	−32.0445	+	31.1458i	−1.22885	+	1.19439i
$681$	3.64510	+	4.04829i	0.139680	+	0.155131i
$682$	11.3555	+	19.6683i	0.434824	+	0.753137i
$683$	−10.1301	+	2.15321i	−0.387616	+	0.0823904i	−0.397598	−	0.917560i	$-0.630156\pi$
$683$	−10.1301	+	2.15321i	−0.387616	+	0.0823904i	0.00998143	+	0.999950i	$0.496823\pi$
$684$	−0.251444	−	2.39233i	−0.00961419	−	0.0914730i
$685$	10.7159	+	21.7919i	0.409434	+	0.832626i
$686$	3.58660	−	16.0551i	0.136937	−	0.612988i
$687$	−14.6922	+	10.6745i	−0.560541	+	0.407257i
$688$	0.113035	+	1.07546i	0.00430943	+	0.0410015i
$689$	−0.329659	+	3.13649i	−0.0125590	+	0.119491i
$690$	−4.60336	+	6.87256i	−0.175247	+	0.261634i
$691$	1.75300	+	16.6787i	0.0666872	+	0.634486i	0.975910	+	0.218175i	$0.0700105\pi$
$691$	1.75300	+	16.6787i	0.0666872	+	0.634486i	−0.909222	+	0.416311i	$0.863323\pi$
$692$	−6.49468	+	19.9886i	−0.246891	+	0.759851i
$693$	7.66092	+	6.94591i	0.291014	+	0.263853i
$694$	−3.74718	+	11.5326i	−0.142241	+	0.437772i
$695$	0.0555128	+	0.219624i	0.00210572	+	0.00833083i
$696$	15.1624	−	16.8396i	0.574729	−	0.638302i
$697$	−7.62209	+	8.46519i	−0.288707	+	0.320642i
$698$	30.2362	−	13.4620i	1.14446	−	0.509546i
$699$	−10.8476			−0.410295
$700$	4.46206	+	15.3859i	0.168650	+	0.581532i
$701$	−10.5136			−0.397094			−0.198547	−	0.980091i	$-0.563622\pi$
$701$	−10.5136			−0.397094			−0.198547	+	0.980091i	$0.563622\pi$
$702$	0.282074	−	0.125588i	0.0106462	−	0.00474000i
$703$	0.0386008	−	0.0428705i	0.00145586	−	0.00161689i
$704$	−13.6051	+	15.1099i	−0.512760	+	0.569477i
$705$	−27.6853	−	1.84608i	−1.04269	−	0.0695275i
$706$	−6.95617	+	21.4089i	−0.261799	+	0.805734i
$707$	1.18469	−	5.48052i	0.0445547	−	0.206116i
$708$	1.04200	−	3.20694i	0.0391607	−	0.120524i
$709$	−3.69847	−	35.1886i	−0.138899	−	1.32154i	−0.812726	−	0.582646i	$-0.802017\pi$
$709$	−3.69847	−	35.1886i	−0.138899	−	1.32154i	0.673827	−	0.738889i	$-0.264649\pi$
$710$	−0.505829	−	13.2569i	−0.0189834	−	0.497522i
$711$	−1.48004	+	14.0817i	−0.0555059	+	0.528104i
$712$	0.819590	+	7.79788i	0.0307154	+	0.292238i
$713$	−22.0401	+	16.0131i	−0.825408	+	0.599694i
$714$	12.2750	−	10.9761i	0.459381	−	0.410769i
$715$	0.517874	−	2.99354i	0.0193674	−	0.111952i
$716$	1.53569	+	14.6111i	0.0573914	+	0.546043i
$717$	−11.6175	+	2.46938i	−0.433865	+	0.0922209i
$718$	−0.408655	−	0.707811i	−0.0152509	−	0.0264153i
$719$	−13.7099	−	15.2264i	−0.511294	−	0.567850i	0.431121	−	0.902294i	$-0.358118\pi$
$719$	−13.7099	−	15.2264i	−0.511294	−	0.567850i	−0.942416	+	0.334444i	$0.891451\pi$
$720$	−0.220587	−	0.116376i	−0.00822079	−	0.00433706i
$721$	16.7225	+	23.1842i	0.622778	+	0.863425i
$722$	−4.13221	−	12.7176i	−0.153785	−	0.473301i
$723$	−4.64166	+	2.06660i	−0.172625	+	0.0768577i
$724$	8.25677	+	14.3012i	0.306861	+	0.531498i
$725$	34.9524	−	18.8753i	1.29810	−	0.701009i
$726$	−1.89932	+	3.28972i	−0.0704903	+	0.122093i
$727$	−4.52642	−	3.28864i	−0.167876	−	0.121969i	0.500675	−	0.865635i	$-0.333085\pi$
$727$	−4.52642	−	3.28864i	−0.167876	−	0.121969i	−0.668551	+	0.743666i	$0.733085\pi$
$728$	−1.07518	+	2.39266i	−0.0398489	+	0.0886780i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	3.00878	−	7.51682i	0.111360	−	0.278210i
$731$	−66.4479	+	14.1239i	−2.45766	+	0.522393i
$732$	−2.65328	−	4.59562i	−0.0980681	−	0.169859i
$733$	−4.64706	−	5.16109i	−0.171643	−	0.190629i	0.651185	−	0.758919i	$-0.274272\pi$
$733$	−4.64706	−	5.16109i	−0.171643	−	0.190629i	−0.822829	+	0.568290i	$0.807605\pi$
$734$	11.1287	−	8.08550i	0.410769	−	0.298441i
$735$	−3.73098	−	15.2013i	−0.137619	−	0.560709i
$736$	−18.8857	−	13.7213i	−0.696136	−	0.505773i
$737$	−4.01637	−	38.2132i	−0.147945	−	1.40760i
$738$	−1.31923	−	0.587361i	−0.0485616	−	0.0216210i
$739$	1.73799	−	16.5358i	0.0639328	−	0.608280i	−0.914909	−	0.403661i	$-0.867738\pi$
$739$	1.73799	−	16.5358i	0.0639328	−	0.608280i	0.978842	−	0.204619i	$-0.0655957\pi$
$740$	0.0192711	+	0.0762420i	0.000708421	+	0.00280271i
$741$	0.558619	−	0.405861i	0.0205214	−	0.0149097i
$742$	−18.5021	+	10.5973i	−0.679234	+	0.389039i
$743$	−2.57141			−0.0943359			−0.0471680	−	0.998887i	$-0.515020\pi$
$743$	−2.57141			−0.0943359			−0.0471680	+	0.998887i	$0.515020\pi$
$744$	−12.4846	−	13.8655i	−0.457706	−	0.508334i
$745$	−1.58615	+	0.583122i	−0.0581121	+	0.0213639i
$746$	7.20672	−	8.00388i	0.263857	−	0.293043i
$747$	−8.95935	−	1.90437i	−0.327805	−	0.0696772i
$748$	−26.8301	−	19.4932i	−0.981006	−	0.712742i
$749$	39.9274	−	12.8212i	1.45891	−	0.468475i
$750$	−6.71642	−	7.31549i	−0.245249	−	0.267124i
$751$	14.9856	−	25.9559i	0.546834	−	0.947144i	−0.451655	−	0.892193i	$-0.649166\pi$
$751$	14.9856	−	25.9559i	0.546834	−	0.947144i	0.998489	−	0.0549516i	$-0.0175005\pi$
$752$	−0.144670	+	1.37645i	−0.00527558	+	0.0501938i
$753$	3.59190	−	3.98921i	0.130896	−	0.145375i
$754$	2.39946	+	0.510022i	0.0873833	+	0.0185739i
$755$	2.24891	−	12.9997i	0.0818464	−	0.473107i
$756$	−2.76918	−	1.61154i	−0.100714	−	0.0586113i
$757$	−11.9825			−0.435510			−0.217755	−	0.976003i	$-0.569873\pi$
$757$	−11.9825			−0.435510			−0.217755	+	0.976003i	$0.569873\pi$
$758$	11.3837	+	12.6429i	0.413474	+	0.459209i
$759$	−14.8702	−	6.62062i	−0.539753	−	0.240313i
$760$	−12.1892	−	3.45261i	−0.442148	−	0.125239i
$761$	14.7710	−	6.57647i	0.535448	−	0.238397i	−0.121154	−	0.992634i	$-0.538660\pi$
$761$	14.7710	−	6.57647i	0.535448	−	0.238397i	0.656603	+	0.754237i	$0.271993\pi$
$762$	−5.13379	+	3.72992i	−0.185978	+	0.135121i
$763$	11.1724	+	25.3282i	0.404467	+	0.916943i
$764$	−2.09191	−	1.51986i	−0.0756827	−	0.0549867i
$765$	5.82217	−	14.5455i	0.210501	−	0.525894i
$766$	−1.35653	−	0.603968i	−0.0490136	−	0.0218223i
$767$	0.946763	−	0.201241i	0.0341856	−	0.00726638i
$768$	8.12885	−	14.0796i	0.293325	−	0.508053i
$769$	6.37384	−	19.6167i	0.229846	−	0.707395i	−0.767917	−	0.640549i	$-0.778707\pi$
$769$	6.37384	−	19.6167i	0.229846	−	0.707395i	0.997763	−	0.0668451i	$-0.0212933\pi$
$770$	18.4626	−	8.99987i	0.665347	−	0.324333i
$771$	4.58457	+	14.1099i	0.165109	+	0.508154i
$772$	−16.9226	−	3.59701i	−0.609057	−	0.129459i
$773$	−2.26812	+	21.5797i	−0.0815785	+	0.776168i	0.874888	+	0.484325i	$0.160935\pi$
$773$	−2.26812	+	21.5797i	−0.0815785	+	0.776168i	−0.956466	+	0.291842i	$0.905732\pi$
$774$	−4.30601	−	7.45823i	−0.154776	−	0.268081i
$775$	−12.4483	−	30.2464i	−0.447155	−	1.08648i
$776$	7.65353			0.274746
$777$	−0.0157159	−	0.0752120i	−0.000563806	−	0.00269822i
$778$	−7.91548	−	24.3613i	−0.283784	−	0.873396i
$779$	−3.15879	−	0.671421i	−0.113175	−	0.0240562i
$780$	0.0358891	+	0.940589i	0.00128503	+	0.0336785i
$781$	25.5356	−	5.42776i	0.913736	−	0.194221i
$782$	−12.9598	+	22.4471i	−0.463443	+	0.802707i
$783$	−2.45504	+	7.55584i	−0.0877360	+	0.270024i
$784$	−0.764795	+	0.157058i	−0.0273141	+	0.00560920i
$785$	−3.06939	+	17.7424i	−0.109551	+	0.633254i
$786$	−14.9725	+	6.66619i	−0.534052	+	0.237775i
$787$	35.7655	+	15.9238i	1.27490	+	0.567623i	0.928803	−	0.370575i	$-0.120839\pi$
$787$	35.7655	+	15.9238i	1.27490	+	0.567623i	0.346099	+	0.938198i	$0.387506\pi$
$788$	10.5547	+	4.69928i	0.375997	+	0.167405i
$789$	−6.10762	+	2.71929i	−0.217437	+	0.0968092i
$790$	24.8740	+	13.1228i	0.884976	+	0.466889i
$791$	−50.8835	−	5.52553i	−1.80921	−	0.196465i
$792$	3.44488	−	10.6023i	0.122409	−	0.376735i
$793$	0.761615	−	1.31916i	0.0270457	−	0.0468446i
$794$	33.9879	−	7.22434i	1.20618	−	0.256382i
$795$	−11.2901	+	16.8555i	−0.400419	+	0.597802i
$796$	13.1571	+	2.79663i	0.466341	+	0.0991239i
$797$	−7.66151	−	23.5797i	−0.271384	−	0.835236i	−0.990153	−	0.139987i	$-0.955294\pi$
$797$	−7.66151	−	23.5797i	−0.271384	−	0.835236i	0.718769	−	0.695249i	$-0.244706\pi$
$798$	4.43481	+	1.45788i	0.156991	+	0.0516085i
$799$	−86.9444			−3.07587
$800$	21.3528	−	18.1536i	0.754936	−	0.641825i
$801$	−1.37452	−	2.38074i	−0.0485663	−	0.0841193i
$802$	2.72884	−	25.9632i	0.0963586	−	0.916791i
$803$	15.5845	+	3.31259i	0.549965	+	0.116899i
$804$	3.67883	+	11.3223i	0.129742	+	0.399306i
$805$	13.0517	+	20.8972i	0.460011	+	0.736528i
$806$	0.624162	−	1.92097i	0.0219852	−	0.0676634i
$807$	−3.58183	+	6.20390i	−0.126086	+	0.218388i
$808$	−5.91254	+	1.25675i	−0.208003	+	0.0442123i
$809$	1.15819	+	0.515659i	0.0407198	+	0.0181296i	0.426996	−	0.904254i	$-0.359572\pi$
$809$	1.15819	+	0.515659i	0.0407198	+	0.0181296i	−0.386276	+	0.922383i	$0.626239\pi$
$810$	1.98182	+	0.132149i	0.0696340	+	0.00464326i
$811$	−5.01792	−	3.64573i	−0.176203	−	0.128019i	0.496188	−	0.868215i	$-0.334733\pi$
$811$	−5.01792	−	3.64573i	−0.176203	−	0.128019i	−0.672391	+	0.740196i	$0.734733\pi$
$812$	−10.2730	−	23.2894i	−0.360513	−	0.817299i
$813$	−3.94039	+	2.86286i	−0.138195	+	0.100405i
$814$	0.0921090	−	0.0410095i	0.00322842	−	0.00143738i
$815$	20.3855	−	30.4344i	0.714074	−	1.06607i
$816$	−0.713938	−	0.317866i	−0.0249928	−	0.0111275i
$817$	−12.8867	−	14.3121i	−0.450848	−	0.500717i
$818$	3.16260			0.110578
$819$	0.00317124	−	0.919682i	0.000110812	−	0.0321363i
$820$	3.15681	−	3.06827i	0.110241	−	0.107149i
$821$	13.4559	+	2.86013i	0.469613	+	0.0998193i	0.436639	−	0.899637i	$-0.356169\pi$
$821$	13.4559	+	2.86013i	0.469613	+	0.0998193i	0.0329741	+	0.999456i	$0.489502\pi$
$822$	−6.45491	+	7.16890i	−0.225141	+	0.250044i
$823$	3.01140	−	28.6516i	0.104971	−	0.998731i	−0.807577	−	0.589762i	$-0.799222\pi$
$823$	3.01140	−	28.6516i	0.104971	−	0.998731i	0.912548	−	0.408969i	$-0.134112\pi$
$824$	15.4082	−	26.6878i	0.536770	−	0.929714i
$825$	11.9318	−	15.4772i	0.415414	−	0.538846i
$826$	4.84794	+	4.39546i	0.168681	+	0.152938i
$827$	0.799136	+	0.580607i	0.0277887	+	0.0201897i	0.601593	−	0.798803i	$-0.294533\pi$
$827$	0.799136	+	0.580607i	0.0277887	+	0.0201897i	−0.573804	+	0.818993i	$0.694533\pi$
$828$	4.93308	+	1.04856i	0.171436	+	0.0364399i
$829$	6.06048	−	6.73085i	0.210489	−	0.233772i	−0.628650	−	0.777688i	$-0.716392\pi$
$829$	6.06048	−	6.73085i	0.210489	−	0.233772i	0.839140	+	0.543916i	$0.183059\pi$
$830$	−10.1245	+	15.1153i	−0.351426	+	0.524659i
$831$	−12.4922	−	13.8740i	−0.433350	−	0.481284i
$832$	1.80829			0.0626913
$833$	−14.8343	−	46.7498i	−0.513977	−	1.61978i
$834$	−0.0728020	+	0.0528938i	−0.00252093	+	0.00183156i
$835$	−27.8096	+	17.5026i	−0.962392	+	0.605702i
$836$	0.982771	−	9.35045i	0.0339899	−	0.323392i
$837$	5.97602	+	2.66069i	0.206561	+	0.0919670i
$838$	2.12323	+	20.2012i	0.0733458	+	0.697839i
$839$	−17.9461	−	13.0386i	−0.619568	−	0.450143i	0.233203	−	0.972428i	$-0.425079\pi$
$839$	−17.9461	−	13.0386i	−0.619568	−	0.450143i	−0.852771	+	0.522286i	$0.825079\pi$
$840$	−13.2990	+	10.3857i	−0.458861	+	0.358341i
$841$	−27.6020	+	20.0540i	−0.951793	+	0.691518i
$842$	4.44439	+	4.93599i	0.153164	+	0.170106i
$843$	7.38541	+	12.7919i	0.254367	+	0.440576i
$844$	10.2715	−	2.18327i	0.353559	−	0.0751513i
$845$	24.3732	−	15.3398i	0.838465	−	0.527705i
$846$	−3.40606	−	10.4828i	−0.117103	−	0.360405i
$847$	6.61888	+	9.17649i	0.227428	+	0.315308i
$848$	0.818678	+	0.594804i	0.0281135	+	0.0204257i
$849$	−9.43256	+	16.3377i	−0.323725	+	0.560708i
$850$	−22.5244	−	21.4720i	−0.772579	−	0.736483i
$851$	0.0604731	+	0.104742i	0.00207299	+	0.00359052i
$852$	−7.38924	+	3.28990i	−0.253151	+	0.112710i
$853$	6.26861	+	19.2928i	0.214633	+	0.660573i	0.999179	+	0.0405028i	$0.0128960\pi$
$853$	6.26861	+	19.2928i	0.214633	+	0.660573i	−0.784546	+	0.620070i	$0.787104\pi$
$854$	10.2455	−	1.04114i	0.350595	−	0.0356271i
$855$	4.39648	−	0.632377i	0.150356	−	0.0216268i
$856$	−30.2499	−	33.5959i	−1.03392	−	1.14828i
$857$	−9.94251	−	17.2209i	−0.339630	−	0.588256i	0.644733	−	0.764408i	$-0.276968\pi$
$857$	−9.94251	−	17.2209i	−0.339630	−	0.588256i	−0.984363	+	0.176152i	$0.943635\pi$
$858$	1.18045	−	0.250913i	0.0403001	−	0.00856604i
$859$	−4.77233	−	45.4057i	−0.162830	−	1.54922i	−0.705154	−	0.709054i	$-0.749122\pi$
$859$	−4.77233	−	45.4057i	−0.162830	−	1.54922i	0.542324	−	0.840169i	$-0.317544\pi$
$860$	25.9861	−	3.73776i	0.886118	−	0.127457i
$861$	−3.20638	+	2.86708i	−0.109273	+	0.0977099i
$862$	14.9850	−	10.8873i	0.510392	−	0.370822i
$863$	−2.09294	−	19.9130i	−0.0712445	−	0.677846i	−0.970612	−	0.240652i	$-0.922639\pi$
$863$	−2.09294	−	19.9130i	−0.0712445	−	0.677846i	0.899367	−	0.437194i	$-0.144028\pi$
$864$	−0.585917	+	5.57463i	−0.0199333	+	0.189653i
$865$	−37.3390	−	10.5763i	−1.26956	−	0.359606i
$866$	0.235511	+	2.24074i	0.00800299	+	0.0761433i
$867$	9.91756	−	30.5231i	0.336818	−	1.03662i
$868$	−19.9554	+	6.40791i	−0.677330	+	0.217499i
$869$	−17.1015	+	52.6329i	−0.580128	+	1.78545i
$870$	12.1208	+	10.1040i	0.410933	+	0.342558i
$871$	−2.28660	+	2.53953i	−0.0774785	+	0.0860486i
$872$	19.9689	−	22.1777i	0.676231	−	0.751031i
$873$	−2.45138	+	1.09143i	−0.0829667	+	0.0369392i
$874$	−7.34823			−0.248558
$875$	−28.0750	+	9.31634i	−0.949108	+	0.314950i
$876$	−4.93647			−0.166788
$877$	−18.1424	+	8.07753i	−0.612627	+	0.272759i	−0.689504	−	0.724282i	$-0.742172\pi$
$877$	−18.1424	+	8.07753i	−0.612627	+	0.272759i	0.0768777	+	0.997041i	$0.475505\pi$
$878$	1.08411	−	1.20402i	0.0365869	−	0.0406339i
$879$	−11.6067	+	12.8906i	−0.391485	+	0.434789i
$880$	−0.748757	−	0.624170i	−0.0252406	−	0.0210408i
$881$	15.1350	−	46.5807i	0.509911	−	1.56935i	−0.282443	−	0.959284i	$-0.591145\pi$
$881$	15.1350	−	46.5807i	0.509911	−	1.56935i	0.792354	−	0.610061i	$-0.208855\pi$
$882$	5.05543	−	3.61998i	0.170225	−	0.121891i
$883$	13.5931	−	41.8354i	0.457446	−	1.40787i	−0.410794	−	0.911728i	$-0.634748\pi$
$883$	13.5931	−	41.8354i	0.457446	−	1.40787i	0.868240	−	0.496145i	$-0.165252\pi$
$884$	0.308304	+	2.93332i	0.0103694	+	0.0986581i
$885$	5.99062	+	1.69686i	0.201373	+	0.0570392i
$886$	−3.67587	+	34.9736i	−0.123493	+	1.17496i
$887$	1.83467	+	17.4557i	0.0616023	+	0.586106i	0.981166	+	0.193166i	$0.0618755\pi$
$887$	1.83467	+	17.4557i	0.0616023	+	0.586106i	−0.919564	+	0.392941i	$0.871458\pi$
$888$	−0.0670126	+	0.0486875i	−0.00224879	+	0.00163385i
$889$	3.86599	+	18.5015i	0.129661	+	0.620521i
$890$	−5.40458	+	0.777378i	−0.181162	+	0.0260578i
$891$	0.408551	+	3.88710i	0.0136870	+	0.130223i
$892$	−26.1765	+	5.56398i	−0.876453	+	0.186296i
$893$	−12.3244	−	21.3464i	−0.412420	−	0.714332i
$894$	−0.449200	−	0.498887i	−0.0150235	−	0.0166853i
$895$	−26.8514	+	3.86223i	−0.897544	+	0.129100i
$896$	−10.1994	−	14.1405i	−0.340737	−	0.472402i
$897$	0.447350	+	1.37680i	0.0149366	+	0.0459701i
$898$	16.1839	−	7.20556i	0.540065	−	0.240453i
$899$	25.9853	+	45.0079i	0.866659	+	1.50110i
$900$	−2.61909	+	5.45918i	−0.0873029	+	0.181973i
$901$	−31.7850	+	55.0532i	−1.05891	+	1.83409i
$902$	−4.56626	−	3.31758i	−0.152040	−	0.110463i
$903$	−25.5200	+	2.59333i	−0.849254	+	0.0863005i
$904$	17.0505	+	52.4760i	0.567091	+	1.74533i
$905$	−25.8063	+	16.2418i	−0.857832	+	0.539894i
$906$	5.12623	−	1.08961i	0.170307	−	0.0362000i
$907$	−16.1726	−	28.0118i	−0.537003	−	0.930117i	−0.999063	−	0.0432682i	$-0.986223\pi$
$907$	−16.1726	−	28.0118i	−0.537003	−	0.930117i	0.462060	−	0.886848i	$-0.347110\pi$
$908$	−4.41417	−	4.90243i	−0.146489	−	0.162693i
$909$	1.71454	−	1.24568i	0.0568676	−	0.0413167i
$910$	−1.69354	−	0.684662i	−0.0561403	−	0.0226963i
$911$	6.43956	+	4.67861i	0.213352	+	0.155009i	0.689329	−	0.724448i	$-0.257905\pi$
$911$	6.43956	+	4.67861i	0.213352	+	0.155009i	−0.475977	+	0.879458i	$0.657905\pi$
$912$	−0.0231589	−	0.220342i	−0.000766868	−	0.00729627i
$913$	−32.7050	−	14.5612i	−1.08238	−	0.481905i
$914$	−0.434651	+	4.13542i	−0.0143770	+	0.136788i
$915$	8.29277	−	5.21923i	0.274150	−	0.172542i
$916$	17.7920	−	12.9267i	0.587865	−	0.427109i
$917$	−0.168329	+	48.8167i	−0.00555873	+	1.61207i
$918$	6.22380			0.205416
$919$	22.3535	+	24.8261i	0.737375	+	0.818938i	0.988848	−	0.148926i	$-0.0475816\pi$
$919$	22.3535	+	24.8261i	0.737375	+	0.818938i	−0.251473	+	0.967864i	$0.580915\pi$
$920$	14.7813	−	22.0677i	0.487326	−	0.727550i
$921$	3.88271	−	4.31219i	0.127940	−	0.142091i
$922$	−1.28257	−	0.272618i	−0.0422391	−	0.00897819i
$923$	−1.87836	−	1.36471i	−0.0618271	−	0.0449200i
$924$	−9.27728	−	8.41140i	−0.305200	−	0.276715i
$925$	−0.139321	+	0.0409256i	−0.00458083	+	0.00134563i
$926$	−13.8175	+	23.9326i	−0.454071	+	0.786474i
$927$	−1.12937	+	10.7452i	−0.0370934	+	0.352920i
$928$	−29.7981	+	33.0942i	−0.978171	+	1.08637i
$929$	−18.6989	−	3.97457i	−0.613490	−	0.130401i	−0.109321	−	0.994006i	$-0.534868\pi$
$929$	−18.6989	−	3.97457i	−0.613490	−	0.130401i	−0.504169	+	0.863605i	$0.668201\pi$
$930$	9.31716	−	9.05583i	0.305522	−	0.296952i
$931$	9.37517	−	10.2689i	0.307259	−	0.336549i
$932$	13.1364			0.430295
$933$	6.59862	+	7.32851i	0.216029	+	0.239925i
$934$	33.7445	+	15.0240i	1.10415	+	0.491600i
$935$	34.0788	−	50.8777i	1.11450	−	1.66388i
$936$	−0.905737	+	0.403260i	−0.0296049	+	0.0131810i
$937$	−16.3004	+	11.8430i	−0.532512	+	0.386893i	−0.821297	−	0.570501i	$-0.806749\pi$
$937$	−16.3004	+	11.8430i	−0.532512	+	0.386893i	0.288784	+	0.957394i	$0.406749\pi$
$938$	−22.9685	−	2.49420i	−0.749950	−	0.0814384i
$939$	−3.15532	−	2.29247i	−0.102970	−	0.0748120i
$940$	33.5266	+	2.23558i	1.09352	+	0.0729166i
$941$	6.53136	+	2.90795i	0.212916	+	0.0947964i	0.510424	−	0.859923i	$-0.329489\pi$
$941$	6.53136	+	2.90795i	0.212916	+	0.0947964i	−0.297507	+	0.954720i	$0.596155\pi$
$942$	−6.99645	+	1.48714i	−0.227956	+	0.0484536i
$943$	3.38527	−	5.86346i	0.110240	−	0.190941i
$944$	0.0959720	−	0.295371i	0.00312362	−	0.00961352i
$945$	2.77857	−	5.22298i	0.0903868	−	0.169904i
$946$	−10.4016	−	32.0128i	−0.338184	−	1.04082i
$947$	25.7879	+	5.48139i	0.837994	+	0.178121i	0.606868	−	0.794803i	$-0.292426\pi$
$947$	25.7879	+	5.48139i	0.837994	+	0.178121i	0.231126	+	0.972924i	$0.425759\pi$
$948$	1.79231	−	17.0527i	0.0582116	−	0.553847i
$949$	−0.708498	−	1.22715i	−0.0229988	−	0.0398351i
$950$	2.07894	−	8.57380i	0.0674496	−	0.278171i
$951$	−25.7150			−0.833865
$952$	−39.4149	+	35.2440i	−1.27744	+	1.14226i
$953$	11.7204	+	36.0718i	0.379662	+	1.16848i	0.940279	+	0.340404i	$0.110564\pi$
$953$	11.7204	+	36.0718i	0.379662	+	1.16848i	−0.560617	+	0.828075i	$0.689436\pi$
$954$	−7.88288	−	1.67556i	−0.255218	−	0.0542482i
$955$	2.65708	−	3.96687i	0.0859812	−	0.128365i
$956$	14.0687	−	2.99039i	0.455014	−	0.0967162i
$957$	−15.5259	+	26.8917i	−0.501882	+	0.869286i
$958$	−3.50970	+	10.8017i	−0.113393	+	0.348988i
$959$	11.5963	+	26.2894i	0.374465	+	0.848927i
$960$	10.2882	+	5.42779i	0.332051	+	0.175181i
$961$	10.7726	−	4.79627i	0.347503	−	0.154718i
$962$	−0.00819184	−	0.00364724i	−0.000264116	−	0.000117592i
$963$	14.4798	+	6.44681i	0.466604	+	0.207746i
$964$	5.62099	−	2.50262i	0.181040	−	0.0806041i
$965$	5.44559	−	31.4778i	0.175300	−	1.01331i
$966$	−5.78013	+	7.89825i	−0.185973	+	0.254122i
$967$	−10.0603	+	30.9624i	−0.323517	+	0.995684i	0.648588	+	0.761140i	$0.275360\pi$
$967$	−10.0603	+	30.9624i	−0.323517	+	0.995684i	−0.972105	+	0.234544i	$0.924640\pi$
$968$	6.09869	−	10.5632i	0.196019	−	0.339515i
$969$	13.6140	−	2.89374i	0.437344	−	0.0929603i
$970$	0.203214	+	5.32589i	0.00652482	+	0.171004i
$971$	−50.9501	−	10.8298i	−1.63507	−	0.347544i	−0.703382	−	0.710812i	$-0.748328\pi$
$971$	−50.9501	−	10.8298i	−1.63507	−	0.347544i	−0.931685	+	0.363268i	$0.881661\pi$
$972$	−0.374216	−	1.15172i	−0.0120030	−	0.0369413i
$973$	0.0548234	+	0.262369i	0.00175756	+	0.00841117i
$974$	15.3225			0.490966
$975$	−1.73299	+	0.132441i	−0.0555002	+	0.00424150i
$976$	−0.244377	−	0.423274i	−0.00782232	−	0.0135487i
$977$	−1.36787	+	13.0144i	−0.0437620	+	0.416368i	0.950607	+	0.310397i	$0.100462\pi$
$977$	−1.36787	+	13.0144i	−0.0437620	+	0.416368i	−0.994369	+	0.105971i	$0.966205\pi$
$978$	14.2334	+	3.02541i	0.455135	+	0.0967419i
$979$	−3.32028	−	10.2188i	−0.106117	−	0.326594i
$980$	4.51817	+	18.4086i	0.144328	+	0.588041i
$981$	−3.23329	+	9.95104i	−0.103231	+	0.317712i
$982$	12.0300	−	20.8366i	0.383893	−	0.664921i
$983$	45.6583	−	9.70497i	1.45627	−	0.309540i	0.589308	−	0.807909i	$-0.299401\pi$
$983$	45.6583	−	9.70497i	1.45627	−	0.309540i	0.866965	+	0.498368i	$0.166067\pi$
$984$	4.23604	+	1.88601i	0.135040	+	0.0601237i
$985$	−7.92774	+	19.8058i	−0.252599	+	0.631067i
$986$	40.0028	+	29.0637i	1.27395	+	0.925577i
$987$	−32.6386	−	3.54428i	−1.03890	−	0.112816i
$988$	−0.676481	+	0.491492i	−0.0215217	+	0.0156364i
$989$	36.8865	−	16.4229i	1.17292	−	0.522218i
$990$	7.46930	+	2.11570i	0.237390	+	0.0672412i
$991$	−4.80424	−	2.13898i	−0.152612	−	0.0679470i	0.329010	−	0.944327i	$-0.393285\pi$
$991$	−4.80424	−	2.13898i	−0.152612	−	0.0679470i	−0.481621	+	0.876380i	$0.659952\pi$
$992$	24.5355	+	27.2494i	0.779001	+	0.865169i
$993$	29.2898			0.929483
$994$	0.0541265	−	15.6971i	0.00171679	−	0.497881i
$995$	−4.23388	+	24.4736i	−0.134223	+	0.775866i
$996$	10.8497	+	2.30617i	0.343785	+	0.0730737i
$997$	−37.4523	+	41.5950i	−1.18613	+	1.31733i	−0.248932	+	0.968521i	$0.580080\pi$
$997$	−37.4523	+	41.5950i	−1.18613	+	1.31733i	−0.937195	+	0.348806i	$0.886587\pi$
$998$	−2.29983	+	21.8814i	−0.0727998	+	0.692644i
$999$	0.0145207	−	0.0251506i	0.000459415	−	0.000795730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.b.16.12	✓	160
7.4	even	3	inner	525.2.bg.b.466.9	yes	160
25.11	even	5	inner	525.2.bg.b.436.9	yes	160
175.11	even	15	inner	525.2.bg.b.361.12	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.b.16.12	✓	160	1.1	even	1	trivial
525.2.bg.b.361.12	yes	160	175.11	even	15	inner
525.2.bg.b.436.9	yes	160	25.11	even	5	inner
525.2.bg.b.466.9	yes	160	7.4	even	3	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.811470 - 0.361290i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.810308 + 0.899939i) q^{4} +(-1.71756 - 1.43178i) q^{5} +(0.274489 - 0.844789i) q^{6} +(-1.96006 - 1.77712i) q^{7} +(-0.881380 + 2.71261i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.811470 - 0.361290i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.810308 + 0.899939i) q^{4} +(-1.71756 - 1.43178i) q^{5} +(0.274489 - 0.844789i) q^{6} +(-1.96006 - 1.77712i) q^{7} +(-0.881380 + 2.71261i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-1.91103 - 0.541305i) q^{10} +(0.408551 - 3.88710i) q^{11} +(0.126583 + 1.20435i) q^{12} +(-0.281222 + 0.204320i) q^{13} +(-2.23258 - 0.733931i) q^{14} +(-2.21329 + 0.318353i) q^{15} +(0.0116587 + 0.110925i) q^{16} +(-6.85359 + 1.45678i) q^{17} +(-0.444132 - 0.769259i) q^{18} +(-1.32916 - 1.47618i) q^{19} +(2.68027 - 0.385521i) q^{20} +(-2.63220 + 0.267482i) q^{21} +(-1.07284 - 3.30187i) q^{22} +(3.80456 - 1.69390i) q^{23} +(1.42610 + 2.47008i) q^{24} +(0.900040 + 4.91833i) q^{25} +(-0.154384 + 0.267402i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(3.18755 - 0.323917i) q^{28} +(-2.45504 - 7.55584i) q^{29} +(-1.68100 + 1.05797i) q^{30} +(-6.39862 + 1.36007i) q^{31} +(-2.80267 - 4.85436i) q^{32} +(-2.61531 - 2.90459i) q^{33} +(-5.03516 + 3.65826i) q^{34} +(0.822086 + 5.85868i) q^{35} +(0.979709 + 0.711800i) q^{36} +(0.00303566 + 0.0288823i) q^{37} +(-1.61190 - 0.717666i) q^{38} +(-0.0363351 + 0.345705i) q^{39} +(5.39767 - 3.39713i) q^{40} +(1.31525 - 0.955582i) q^{41} +(-2.03931 + 1.16804i) q^{42} +9.69534 q^{43} +(3.16710 + 3.51742i) q^{44} +(-1.24440 + 1.85781i) q^{45} +(2.47529 - 2.74909i) q^{46} +(12.1376 + 2.57992i) q^{47} +(0.0902349 + 0.0655595i) q^{48} +(0.683672 + 6.96653i) q^{49} +(2.50729 + 3.66590i) q^{50} +(-3.50335 + 6.06798i) q^{51} +(0.0440013 - 0.418644i) q^{52} +(6.07085 - 6.74236i) q^{53} +(-0.868853 - 0.184680i) q^{54} +(-6.26717 + 6.09139i) q^{55} +(6.54819 - 3.75055i) q^{56} -1.98640 q^{57} +(-4.72204 - 5.24435i) q^{58} +(-2.54376 - 1.13255i) q^{59} +(1.50695 - 2.24979i) q^{60} +(-4.00317 + 1.78233i) q^{61} +(-4.70090 + 3.41541i) q^{62} +(-1.56251 + 2.13508i) q^{63} +(-4.20858 - 3.05771i) q^{64} +(0.775556 + 0.0517147i) q^{65} +(-3.17164 - 1.41210i) q^{66} +(9.61596 - 2.04393i) q^{67} +(4.24251 - 7.34825i) q^{68} +(1.28693 - 3.96078i) q^{69} +(2.78378 + 4.45713i) q^{70} +(2.06401 + 6.35238i) q^{71} +(2.78988 + 0.593007i) q^{72} +(-0.426100 + 4.05407i) q^{73} +(0.0128982 + 0.0223404i) q^{74} +(4.25727 + 2.62214i) q^{75} +2.40551 q^{76} +(-7.70864 + 6.89291i) q^{77} +(0.0954148 + 0.293657i) q^{78} +(-13.8498 - 2.94387i) q^{79} +(0.138796 - 0.207214i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.722040 - 1.25061i) q^{82} +(2.83044 - 8.71121i) q^{83} +(1.89217 - 2.58556i) q^{84} +(13.8572 + 7.31070i) q^{85} +(7.86747 - 3.50283i) q^{86} +(-7.25783 - 3.23139i) q^{87} +(10.1841 + 4.53425i) q^{88} +(2.51137 - 1.11814i) q^{89} +(-0.338582 + 1.95715i) q^{90} +(0.914313 + 0.0992868i) q^{91} +(-1.55846 + 4.79645i) q^{92} +(-3.27078 + 5.66516i) q^{93} +(10.7814 - 2.29165i) q^{94} +(0.169355 + 4.43850i) q^{95} +(-5.48284 - 1.16541i) q^{96} +(-0.829208 - 2.55204i) q^{97} +(3.07171 + 5.40613i) q^{98} -3.90851 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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