LMFDB - Embedded newform 504.2.bf.b.115.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(115,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 1]))

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

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

chi := DirichletCharacter("504.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bf (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.18
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.b.355.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15708 + 0.813118i) q^{2} +(1.26585 + 1.18221i) q^{3} +(0.677678 - 1.88169i) q^{4} +(-0.495626 + 0.858449i) q^{5} +(-2.42597 - 0.338635i) q^{6} +(1.90467 - 1.83636i) q^{7} +(0.745907 + 2.72830i) q^{8} +(0.204739 + 2.99301i) q^{9} +O(q^{10})$	\(q+(-1.15708 + 0.813118i) q^{2} +(1.26585 + 1.18221i) q^{3} +(0.677678 - 1.88169i) q^{4} +(-0.495626 + 0.858449i) q^{5} +(-2.42597 - 0.338635i) q^{6} +(1.90467 - 1.83636i) q^{7} +(0.745907 + 2.72830i) q^{8} +(0.204739 + 2.99301i) q^{9} +(-0.124541 - 1.39630i) q^{10} +(0.420385 + 0.728127i) q^{11} +(3.08240 - 1.58077i) q^{12} +(-0.437200 - 0.757253i) q^{13} +(-0.710686 + 3.67354i) q^{14} +(-1.64226 + 0.500730i) q^{15} +(-3.08151 - 2.55036i) q^{16} +(4.93085 + 2.84683i) q^{17} +(-2.67057 - 3.29668i) q^{18} +(-1.02651 + 0.592657i) q^{19} +(1.27946 + 1.51437i) q^{20} +(4.58200 - 0.0728195i) q^{21} +(-1.07847 - 0.500681i) q^{22} +(2.91432 + 1.68258i) q^{23} +(-2.28123 + 4.33543i) q^{24} +(2.00871 + 3.47919i) q^{25} +(1.12161 + 0.520708i) q^{26} +(-3.27920 + 4.03073i) q^{27} +(-2.16470 - 4.82846i) q^{28} +(-3.76915 - 2.17612i) q^{29} +(1.49307 - 1.91474i) q^{30} +4.33231 q^{31} +(5.63930 + 0.445345i) q^{32} +(-0.328660 + 1.41868i) q^{33} +(-8.02021 + 0.715351i) q^{34} +(0.632417 + 2.54521i) q^{35} +(5.77065 + 1.64304i) q^{36} +(2.44244 - 1.41014i) q^{37} +(0.705859 - 1.52043i) q^{38} +(0.341806 - 1.47543i) q^{39} +(-2.71180 - 0.711894i) q^{40} +(-3.40426 + 1.96545i) q^{41} +(-5.24254 + 3.80996i) q^{42} +(-2.13973 + 3.70612i) q^{43} +(1.65499 - 0.297597i) q^{44} +(-2.67082 - 1.30765i) q^{45} +(-4.74025 + 0.422799i) q^{46} -2.86374 q^{47} +(-0.885647 - 6.87136i) q^{48} +(0.255563 - 6.99533i) q^{49} +(-5.15323 - 2.39239i) q^{50} +(2.87615 + 9.43298i) q^{51} +(-1.72119 + 0.309501i) q^{52} +(-5.27128 - 3.04338i) q^{53} +(0.516846 - 7.33027i) q^{54} -0.833414 q^{55} +(6.43085 + 3.82677i) q^{56} +(-2.00006 - 0.463344i) q^{57} +(6.13065 - 0.546815i) q^{58} -3.71124i q^{59} +(-0.170704 + 3.42955i) q^{60} -10.8074 q^{61} +(-5.01284 + 3.52268i) q^{62} +(5.88620 + 5.32472i) q^{63} +(-6.88725 + 4.07011i) q^{64} +0.866751 q^{65} +(-0.773270 - 1.90877i) q^{66} +12.7544 q^{67} +(8.69838 - 7.34910i) q^{68} +(1.69991 + 5.57525i) q^{69} +(-2.80132 - 2.43079i) q^{70} +13.2223i q^{71} +(-8.01310 + 2.79109i) q^{72} +(-4.18378 - 2.41551i) q^{73} +(-1.67949 + 3.61764i) q^{74} +(-1.57042 + 6.77885i) q^{75} +(0.419552 + 2.33321i) q^{76} +(2.13780 + 0.614868i) q^{77} +(0.804201 + 1.98512i) q^{78} -1.60451i q^{79} +(3.71663 - 1.38129i) q^{80} +(-8.91616 + 1.22557i) q^{81} +(2.34086 - 5.04225i) q^{82} +(1.99016 + 1.14902i) q^{83} +(2.96809 - 8.67124i) q^{84} +(-4.88772 + 2.82193i) q^{85} +(-0.537672 - 6.02815i) q^{86} +(-2.19853 - 7.21057i) q^{87} +(-1.67298 + 1.69005i) q^{88} +(13.3302 - 7.69617i) q^{89} +(4.15363 - 0.658629i) q^{90} +(-2.22331 - 0.639463i) q^{91} +(5.14107 - 4.34360i) q^{92} +(5.48405 + 5.12172i) q^{93} +(3.31358 - 2.32856i) q^{94} -1.17495i q^{95} +(6.61200 + 7.23059i) q^{96} +(-6.38736 - 3.68775i) q^{97} +(5.39232 + 8.30198i) q^{98} +(-2.09322 + 1.40729i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.15708	+	0.813118i	−0.818181	+	0.574961i
$2$	−1.15708	+	0.813118i	−0.818181	+	0.574961i
$3$	1.26585	+	1.18221i	0.730837	+	0.682552i
$3$	1.26585	+	1.18221i	0.730837	+	0.682552i
$4$	0.677678	−	1.88169i	0.338839	−	0.940844i
$5$	−0.495626	+	0.858449i	−0.221651	+	0.383910i	−0.955309	−	0.295608i	$-0.904478\pi$
$5$	−0.495626	+	0.858449i	−0.221651	+	0.383910i	0.733659	+	0.679518i	$0.237811\pi$
$6$	−2.42597	−	0.338635i	−0.990398	−	0.138247i
$7$	1.90467	−	1.83636i	0.719899	−	0.694079i
$7$	1.90467	−	1.83636i	0.719899	−	0.694079i
$8$	0.745907	+	2.72830i	0.263718	+	0.964600i
$9$	0.204739	+	2.99301i	0.0682464	+	0.997668i
$10$	−0.124541	−	1.39630i	−0.0393833	−	0.441549i
$11$	0.420385	+	0.728127i	0.126751	+	0.219539i	0.922416	−	0.386198i	$-0.126212\pi$
$11$	0.420385	+	0.728127i	0.126751	+	0.219539i	−0.795665	+	0.605737i	$0.792879\pi$
$12$	3.08240	−	1.58077i	0.889811	−	0.456329i
$13$	−0.437200	−	0.757253i	−0.121257	−	0.210024i	0.799006	−	0.601323i	$-0.205359\pi$
$13$	−0.437200	−	0.757253i	−0.121257	−	0.210024i	−0.920264	+	0.391298i	$0.872026\pi$
$14$	−0.710686	+	3.67354i	−0.189939	+	0.981796i
$15$	−1.64226	+	0.500730i	−0.424029	+	0.129288i
$16$	−3.08151	−	2.55036i	−0.770376	−	0.637589i
$17$	4.93085	+	2.84683i	1.19591	+	0.690458i	0.959640	−	0.281230i	$-0.0907425\pi$
$17$	4.93085	+	2.84683i	1.19591	+	0.690458i	0.236267	+	0.971688i	$0.424076\pi$
$18$	−2.67057	−	3.29668i	−0.629459	−	0.777034i
$19$	−1.02651	+	0.592657i	−0.235498	+	0.135965i	−0.613106	−	0.790001i	$-0.710080\pi$
$19$	−1.02651	+	0.592657i	−0.235498	+	0.135965i	0.377608	+	0.925966i	$0.376747\pi$
$20$	1.27946	+	1.51437i	0.286096	+	0.338623i
$21$	4.58200	−	0.0728195i	0.999874	−	0.0158905i
$22$	−1.07847	−	0.500681i	−0.229931	−	0.106746i
$23$	2.91432	+	1.68258i	0.607678	+	0.350843i	0.772056	−	0.635554i	$-0.219228\pi$
$23$	2.91432	+	1.68258i	0.607678	+	0.350843i	−0.164378	+	0.986397i	$0.552562\pi$
$24$	−2.28123	+	4.33543i	−0.465654	+	0.884967i
$25$	2.00871	+	3.47919i	0.401742	+	0.695837i
$26$	1.12161	+	0.520708i	0.219966	+	0.102119i
$27$	−3.27920	+	4.03073i	−0.631083	+	0.775715i
$28$	−2.16470	−	4.82846i	−0.409090	−	0.912494i
$29$	−3.76915	−	2.17612i	−0.699913	−	0.404095i	0.107402	−	0.994216i	$-0.465747\pi$
$29$	−3.76915	−	2.17612i	−0.699913	−	0.404095i	−0.807315	+	0.590121i	$0.799080\pi$
$30$	1.49307	−	1.91474i	0.272597	−	0.349581i
$31$	4.33231			0.778107			0.389053	−	0.921215i	$-0.372802\pi$
$31$	4.33231			0.778107			0.389053	+	0.921215i	$0.372802\pi$
$32$	5.63930	+	0.445345i	0.996896	+	0.0787265i
$33$	−0.328660	+	1.41868i	−0.0572123	+	0.246961i
$34$	−8.02021	+	0.715351i	−1.37545	+	0.122682i
$35$	0.632417	+	2.54521i	0.106898	+	0.430220i
$36$	5.77065	+	1.64304i	0.961775	+	0.273840i
$37$	2.44244	−	1.41014i	0.401535	−	0.231826i	−0.285611	−	0.958346i	$-0.592197\pi$
$37$	2.44244	−	1.41014i	0.401535	−	0.231826i	0.687146	+	0.726519i	$0.258863\pi$
$38$	0.705859	−	1.52043i	0.114505	−	0.246646i
$39$	0.341806	−	1.47543i	0.0547328	−	0.236258i
$40$	−2.71180	−	0.711894i	−0.428773	−	0.112560i
$41$	−3.40426	+	1.96545i	−0.531656	+	0.306952i	−0.741690	−	0.670742i	$-0.765976\pi$
$41$	−3.40426	+	1.96545i	−0.531656	+	0.306952i	0.210035	+	0.977694i	$0.432642\pi$
$42$	−5.24254	+	3.80996i	−0.808941	+	0.587890i
$43$	−2.13973	+	3.70612i	−0.326306	+	0.565179i	−0.981776	−	0.190043i	$-0.939137\pi$
$43$	−2.13973	+	3.70612i	−0.326306	+	0.565179i	0.655470	+	0.755221i	$0.272471\pi$
$44$	1.65499	−	0.297597i	0.249500	−	0.0448645i
$45$	−2.67082	−	1.30765i	−0.398142	−	0.194933i
$46$	−4.74025	+	0.422799i	−0.698911	+	0.0623384i
$47$	−2.86374			−0.417719			−0.208859	−	0.977946i	$-0.566975\pi$
$47$	−2.86374			−0.417719			−0.208859	+	0.977946i	$0.566975\pi$
$48$	−0.885647	−	6.87136i	−0.127832	−	0.991796i
$49$	0.255563	−	6.99533i	0.0365091	−	0.999333i
$50$	−5.15323	−	2.39239i	−0.728777	−	0.338335i
$51$	2.87615	+	9.43298i	0.402741	+	1.32088i
$52$	−1.72119	+	0.309501i	−0.238687	+	0.0429201i
$53$	−5.27128	−	3.04338i	−0.724066	−	0.418040i	0.0921812	−	0.995742i	$-0.470616\pi$
$53$	−5.27128	−	3.04338i	−0.724066	−	0.418040i	−0.816247	+	0.577702i	$0.803949\pi$
$54$	0.516846	−	7.33027i	0.0703338	−	0.997524i
$55$	−0.833414			−0.112378
$56$	6.43085	+	3.82677i	0.859359	+	0.511374i
$57$	−2.00006	−	0.463344i	−0.264914	−	0.0613714i
$58$	6.13065	−	0.546815i	0.804994	−	0.0718003i
$59$		−	3.71124i		−	0.483162i	−0.970381	−	0.241581i	$-0.922334\pi$
$59$		−	3.71124i		−	0.483162i	0.970381	−	0.241581i	$-0.0776659\pi$
$60$	−0.170704	+	3.42955i	−0.0220378	+	0.442753i
$61$	−10.8074			−1.38374			−0.691871	−	0.722021i	$-0.743213\pi$
$61$	−10.8074			−1.38374			−0.691871	+	0.722021i	$0.743213\pi$
$62$	−5.01284	+	3.52268i	−0.636632	+	0.447381i
$63$	5.88620	+	5.32472i	0.741591	+	0.670852i
$64$	−6.88725	+	4.07011i	−0.860906	+	0.508764i
$65$	0.866751			0.107507
$66$	−0.773270	−	1.90877i	−0.0951830	−	0.234954i
$67$	12.7544			1.55820			0.779100	−	0.626900i	$-0.215676\pi$
$67$	12.7544			1.55820			0.779100	+	0.626900i	$0.215676\pi$
$68$	8.69838	−	7.34910i	1.05483	−	0.891209i
$69$	1.69991	+	5.57525i	0.204645	+	0.671181i
$70$	−2.80132	−	2.43079i	−0.334821	−	0.290535i
$71$			13.2223i			1.56919i	0.620007	+	0.784596i	$0.287130\pi$
$71$			13.2223i			1.56919i	−0.620007	+	0.784596i	$0.712870\pi$
$72$	−8.01310	+	2.79109i	−0.944353	+	0.328933i
$73$	−4.18378	−	2.41551i	−0.489675	−	0.282714i	0.234765	−	0.972052i	$-0.424568\pi$
$73$	−4.18378	−	2.41551i	−0.489675	−	0.282714i	−0.724440	+	0.689338i	$0.757901\pi$
$74$	−1.67949	+	3.61764i	−0.195237	+	0.420543i
$75$	−1.57042	+	6.77885i	−0.181337	+	0.782754i
$76$	0.419552	+	2.33321i	0.0481259	+	0.267637i
$77$	2.13780	+	0.614868i	0.243625	+	0.0700707i
$78$	0.804201	+	1.98512i	0.0910579	+	0.224771i
$79$		−	1.60451i		−	0.180522i	−0.995918	−	0.0902610i	$-0.971230\pi$
$79$		−	1.60451i		−	0.180522i	0.995918	−	0.0902610i	$-0.0287701\pi$
$80$	3.71663	−	1.38129i	0.415532	−	0.154433i
$81$	−8.91616	+	1.22557i	−0.990685	+	0.136175i
$82$	2.34086	−	5.04225i	0.258505	−	0.556823i
$83$	1.99016	+	1.14902i	0.218448	+	0.126121i	0.605232	−	0.796049i	$-0.293080\pi$
$83$	1.99016	+	1.14902i	0.218448	+	0.126121i	−0.386783	+	0.922171i	$0.626414\pi$
$84$	2.96809	−	8.67124i	0.323846	−	0.946110i
$85$	−4.88772	+	2.82193i	−0.530148	+	0.306081i
$86$	−0.537672	−	6.02815i	−0.0579786	−	0.650032i
$87$	−2.19853	−	7.21057i	−0.235707	−	0.773055i
$88$	−1.67298	+	1.69005i	−0.178341	+	0.180160i
$89$	13.3302	−	7.69617i	1.41299	−	0.815792i	0.417324	−	0.908758i	$-0.362968\pi$
$89$	13.3302	−	7.69617i	1.41299	−	0.815792i	0.995669	+	0.0929654i	$0.0296346\pi$
$90$	4.15363	−	0.658629i	0.437831	−	0.0694256i
$91$	−2.22331	−	0.639463i	−0.233066	−	0.0670339i
$92$	5.14107	−	4.34360i	0.535994	−	0.452851i
$93$	5.48405	+	5.12172i	0.568669	+	0.531098i
$94$	3.31358	−	2.32856i	0.341769	−	0.240172i
$95$		−	1.17495i		−	0.120547i
$96$	6.61200	+	7.23059i	0.674834	+	0.737969i
$97$	−6.38736	−	3.68775i	−0.648539	−	0.374434i	0.139357	−	0.990242i	$-0.455496\pi$
$97$	−6.38736	−	3.68775i	−0.648539	−	0.374434i	−0.787896	+	0.615808i	$0.788830\pi$
$98$	5.39232	+	8.30198i	0.544707	+	0.838626i
$99$	−2.09322	+	1.40729i	−0.210377	+	0.141438i
$100$	7.90801	−	1.42200i	0.790801	−	0.142200i
$101$	−0.278283	−	0.482001i	−0.0276902	−	0.0479609i	0.851848	−	0.523789i	$-0.175482\pi$
$101$	−0.278283	−	0.482001i	−0.0276902	−	0.0479609i	−0.879538	+	0.475828i	$0.842149\pi$
$102$	−10.9981	−	8.57608i	−1.08897	−	0.849159i
$103$	9.58414	−	16.6002i	0.944353	−	1.63567i	0.187312	−	0.982300i	$-0.440022\pi$
$103$	9.58414	−	16.6002i	0.944353	−	1.63567i	0.757041	−	0.653367i	$-0.226644\pi$
$104$	1.73990	−	1.75765i	0.170611	−	0.172352i
$105$	−2.20845	+	3.96950i	−0.215522	+	0.387384i
$106$	8.57393	−	0.764739i	0.832774	−	0.0742780i
$107$	−2.77621	−	4.80854i	−0.268387	−	0.464859i	0.700059	−	0.714085i	$-0.253157\pi$
$107$	−2.77621	−	4.80854i	−0.268387	−	0.464859i	−0.968445	+	0.249226i	$0.919824\pi$
$108$	5.36234	+	8.90198i	0.515992	+	0.856594i
$109$	2.47877	+	1.43112i	0.237423	+	0.137076i	0.613992	−	0.789312i	$-0.289563\pi$
$109$	2.47877	+	1.43112i	0.237423	+	0.137076i	−0.376569	+	0.926389i	$0.622896\pi$
$110$	0.964328	−	0.677664i	0.0919451	−	0.0646127i
$111$	4.75885	+	1.10246i	0.451690	+	0.104641i
$112$	−10.5526	+	0.801156i	−0.997130	+	0.0757021i
$113$	−8.08870	−	14.0100i	−0.760921	−	1.31795i	−0.942376	−	0.334555i	$-0.891414\pi$
$113$	−8.08870	−	14.0100i	−0.760921	−	1.31795i	0.181455	−	0.983399i	$-0.441919\pi$
$114$	2.69098	−	1.09016i	0.252034	−	0.102102i
$115$	−2.88883	+	1.66786i	−0.269384	+	0.155529i
$116$	−6.64904	+	5.61766i	−0.617348	+	0.521586i
$117$	2.17695	−	1.46358i	0.201259	−	0.135308i
$118$	3.01767	+	4.29420i	0.277799	+	0.395314i
$119$	14.6195	−	3.63254i	1.34016	−	0.332995i
$120$	−2.59111	−	4.10708i	−0.236535	−	0.374923i
$121$	5.14655	−	8.91409i	0.467869	−	0.810372i
$122$	12.5050	−	8.78767i	1.13215	−	0.795599i
$123$	−6.63285	−	1.53660i	−0.598064	−	0.138551i
$124$	2.93591	−	8.15207i	0.263653	−	0.732077i
$125$	−8.93854			−0.799487
$126$	−11.1404	−	1.37497i	−0.992470	−	0.122492i
$127$			2.09459i			0.185865i	0.995672	+	0.0929324i	$0.0296240\pi$
$127$			2.09459i			0.185865i	−0.995672	+	0.0929324i	$0.970376\pi$
$128$	4.65963	−	10.3096i	0.411857	−	0.911249i
$129$	−7.09001	+	2.16177i	−0.624240	+	0.190333i
$130$	−1.00290	+	0.704771i	−0.0879603	+	0.0618125i
$131$	−11.1121	−	6.41559i	−0.970871	−	0.560533i	−0.0713694	−	0.997450i	$-0.522737\pi$
$131$	−11.1121	−	6.41559i	−0.970871	−	0.560533i	−0.899502	+	0.436917i	$0.856070\pi$
$132$	2.44679	+	1.57985i	0.212966	+	0.137508i
$133$	−0.866839	+	3.01387i	−0.0751645	+	0.261335i
$134$	−14.7579	+	10.3708i	−1.27489	+	0.895905i
$135$	−1.83492	−	4.81277i	−0.157925	−	0.414217i
$136$	−4.08905	+	15.5763i	−0.350633	+	1.33566i
$137$	−8.49900	−	14.7207i	−0.726118	−	1.25767i	−0.958512	−	0.285052i	$-0.907989\pi$
$137$	−8.49900	−	14.7207i	−0.726118	−	1.25767i	0.232394	−	0.972622i	$-0.425344\pi$
$138$	−6.50027	−	5.06879i	−0.553340	−	0.431484i
$139$	18.7215	−	10.8088i	1.58793	−	0.916793i	0.594286	−	0.804254i	$-0.297435\pi$
$139$	18.7215	−	10.8088i	1.58793	−	0.916793i	0.993647	−	0.112539i	$-0.0358985\pi$
$140$	5.21788	+	0.534824i	0.440991	+	0.0452009i
$141$	−3.62505	−	3.38555i	−0.305285	−	0.285115i
$142$	−10.7513	−	15.2992i	−0.902225	−	1.28388i
$143$	0.367584	−	0.636675i	0.0307389	−	0.0532414i
$144$	7.00233	−	9.74512i	0.583527	−	0.812093i
$145$	3.73618	−	2.15708i	0.310272	−	0.179136i
$146$	6.80508	−	0.606969i	0.563192	−	0.0502331i
$147$	8.59349	−	8.55289i	0.708779	−	0.705431i
$148$	−0.998264	−	5.55154i	−0.0820568	−	0.456333i
$149$	18.5119	+	10.6878i	1.51655	+	0.875581i	0.999811	+	0.0194384i	$0.00618783\pi$
$149$	18.5119	+	10.6878i	1.51655	+	0.875581i	0.516740	+	0.856143i	$0.327146\pi$
$150$	−3.69489	−	9.12062i	−0.301687	−	0.744696i
$151$	20.0250	−	11.5615i	1.62962	−	0.940859i	0.645408	−	0.763838i	$-0.276687\pi$
$151$	20.0250	−	11.5615i	1.62962	−	0.940859i	0.984207	−	0.177021i	$-0.0566461\pi$
$152$	−2.38263	−	2.35857i	−0.193257	−	0.191305i
$153$	−7.51104	+	15.3409i	−0.607231	+	1.24024i
$154$	−2.97357	+	1.02683i	−0.239617	+	0.0827444i
$155$	−2.14721	+	3.71907i	−0.172468	+	0.298723i
$156$	−2.54467	−	1.64304i	−0.203736	−	0.131548i
$157$	−12.5043			−0.997950			−0.498975	−	0.866616i	$-0.666290\pi$
$157$	−12.5043			−0.997950			−0.498975	+	0.866616i	$0.666290\pi$
$158$	1.30466	+	1.85655i	0.103793	+	0.147700i
$159$	−3.07472	−	10.0842i	−0.243841	−	0.799732i
$160$	−3.17729	+	4.62033i	−0.251187	+	0.365269i
$161$	8.64066	−	2.14697i	0.680979	−	0.169205i
$162$	9.32020	−	8.66798i	0.732264	−	0.681021i
$163$	5.81672	+	10.0749i	0.455601	+	0.789124i	0.998723	−	0.0505300i	$-0.0160910\pi$
$163$	5.81672	+	10.0749i	0.455601	+	0.789124i	−0.543122	+	0.839654i	$0.682758\pi$
$164$	1.39137	+	7.73769i	0.108648	+	0.604212i
$165$	−1.05498	−	0.985274i	−0.0821297	−	0.0767035i
$166$	−3.23707	+	0.288725i	−0.251245	+	0.0224094i
$167$	−1.98369	−	3.43585i	−0.153503	−	0.265874i	0.779010	−	0.627011i	$-0.215722\pi$
$167$	−1.98369	−	3.43585i	−0.153503	−	0.265874i	−0.932513	+	0.361137i	$0.882389\pi$
$168$	3.61641	+	12.4467i	0.279012	+	0.960287i
$169$	6.11771	−	10.5962i	0.470593	−	0.815091i
$170$	3.36093	−	7.23949i	0.257772	−	0.555244i
$171$	−1.98399	−	2.95102i	−0.151720	−	0.225670i
$172$	5.52372	+	6.53787i	0.421180	+	0.498508i
$173$	−19.4208			−1.47654			−0.738268	−	0.674508i	$-0.764356\pi$
$173$	−19.4208			−1.47654			−0.738268	+	0.674508i	$0.764356\pi$
$174$	8.40692	+	6.55556i	0.637327	+	0.496976i
$175$	10.2150	+	2.93800i	0.772180	+	0.222092i
$176$	0.561568	−	3.31586i	0.0423298	−	0.249942i
$177$	4.38748	−	4.69786i	0.329783	−	0.353113i
$178$	−9.16619	+	19.7441i	−0.687035	+	1.47988i
$179$	4.41968	−	7.65510i	0.330342	−	0.572169i	−0.652237	−	0.758015i	$-0.726169\pi$
$179$	4.41968	−	7.65510i	0.330342	−	0.572169i	0.982579	+	0.185846i	$0.0595026\pi$
$180$	−4.27055	+	4.13948i	−0.318308	+	0.308539i
$181$	−7.82382			−0.581540			−0.290770	−	0.956793i	$-0.593911\pi$
$181$	−7.82382			−0.581540			−0.290770	+	0.956793i	$0.593911\pi$
$182$	3.09251	−	1.06790i	0.229232	−	0.0791584i
$183$	−13.6805	−	12.7766i	−1.01129	−	0.944476i
$184$	−2.41678	+	9.20619i	−0.178168	+	0.678690i
$185$			2.79562i			0.205538i
$186$	−10.5101	−	1.46707i	−0.770635	−	0.107571i
$187$			4.78705i			0.350064i
$188$	−1.94069	+	5.38866i	−0.141539	+	0.393009i
$189$	1.15606	+	13.6990i	0.0840913	+	0.996458i
$190$	0.955370	+	1.35951i	0.0693098	+	0.0986291i
$191$			11.4052i			0.825251i	0.910901	+	0.412626i	$0.135388\pi$
$191$			11.4052i			0.825251i	−0.910901	+	0.412626i	$0.864612\pi$
$192$	−13.5300	−	2.99006i	−0.976440	−	0.215789i
$193$	−0.997825			−0.0718250			−0.0359125	−	0.999355i	$-0.511434\pi$
$193$	−0.997825			−0.0718250			−0.0359125	+	0.999355i	$0.511434\pi$
$194$	10.3893	−	0.926657i	0.745907	−	0.0665301i
$195$	1.09717	+	1.02469i	0.0785703	+	0.0733792i
$196$	−12.9899	−	5.22147i	−0.927846	−	0.372962i
$197$		−	13.3043i		−	0.947896i	−0.880553	−	0.473948i	$-0.842829\pi$
$197$		−	13.3043i		−	0.947896i	0.880553	−	0.473948i	$-0.157171\pi$
$198$	1.27773	−	3.33038i	0.0908046	−	0.236680i
$199$	−7.99785	+	13.8527i	−0.566953	+	0.981991i	0.429912	+	0.902871i	$0.358545\pi$
$199$	−7.99785	+	13.8527i	−0.566953	+	0.981991i	−0.996865	+	0.0791205i	$0.974789\pi$
$200$	−7.99396	+	8.07551i	−0.565258	+	0.571025i
$201$	16.1451	+	15.0785i	1.13879	+	1.06355i
$202$	0.713921	+	0.331437i	0.0502313	+	0.0233199i
$203$	−11.1751	+	2.77672i	−0.784341	+	0.194887i
$204$	19.6990	+	0.980507i	1.37921	+	0.0686492i
$205$		−	3.89651i		−	0.272144i
$206$	2.40830	+	27.0008i	0.167794	+	1.88124i
$207$	−4.43931	+	9.06707i	−0.308553	+	0.630205i
$208$	−0.584031	+	3.44849i	−0.0404952	+	0.239110i
$209$	−0.863060	−	0.498288i	−0.0596991	−	0.0344673i
$210$	−0.672324	−	6.38877i	−0.0463947	−	0.440867i
$211$	10.8462	+	18.7861i	0.746680	+	1.29329i	0.949406	+	0.314052i	$0.101687\pi$
$211$	10.8462	+	18.7861i	0.746680	+	1.29329i	−0.202726	+	0.979236i	$0.564980\pi$
$212$	−9.29892	+	7.85648i	−0.638652	+	0.539586i
$213$	−15.6315	+	16.7374i	−1.07106	+	1.14682i
$214$	7.12222	+	3.30649i	0.486865	+	0.226027i
$215$	−2.12101	−	3.67370i	−0.144652	−	0.250545i
$216$	−13.4430	−	5.94011i	−0.914683	−	0.404173i
$217$	8.25165	−	7.95569i	0.560158	−	0.540067i
$218$	−4.03181	+	0.359611i	−0.273068	+	0.0243559i
$219$	−2.44038	−	8.00380i	−0.164906	−	0.540846i
$220$	−0.564786	+	1.56823i	−0.0380779	+	0.105730i
$221$		−	4.97854i		−	0.334893i
$222$	−6.40281	+	2.59387i	−0.429728	+	0.174089i
$223$	−7.29437	+	12.6342i	−0.488467	+	0.846050i	−0.999912	−	0.0132661i	$-0.995777\pi$
$223$	−7.29437	+	12.6342i	−0.488467	+	0.846050i	0.511445	+	0.859316i	$0.329110\pi$
$224$	11.5588	−	9.50754i	0.772307	−	0.635249i
$225$	−10.0020	+	6.72441i	−0.666798	+	0.448294i
$226$	20.7511	+	9.63370i	1.38034	+	0.640824i
$227$	−15.8127	+	9.12947i	−1.04953	+	0.605944i	−0.922517	−	0.385957i	$-0.873871\pi$
$227$	−15.8127	+	9.12947i	−1.04953	+	0.605944i	−0.127010	+	0.991901i	$0.540538\pi$
$228$	−2.22726	+	3.44949i	−0.147504	+	0.228448i
$229$	−8.04062	+	13.9268i	−0.531339	+	0.920306i	0.467992	+	0.883733i	$0.344978\pi$
$229$	−8.04062	+	13.9268i	−0.531339	+	0.920306i	−0.999331	+	0.0365734i	$0.988356\pi$
$230$	1.98644	−	4.27881i	0.130982	−	0.282137i
$231$	1.97922	+	3.30567i	0.130223	+	0.217497i
$232$	3.12567	−	11.9065i	0.205210	−	0.781703i
$233$	−8.14132	−	14.1012i	−0.533356	−	0.923799i	−0.999241	−	0.0389541i	$-0.987597\pi$
$233$	−8.14132	−	14.1012i	−0.533356	−	0.923799i	0.465885	−	0.884845i	$-0.345736\pi$
$234$	−1.32884	+	3.46360i	−0.0868693	+	0.226423i
$235$	1.41934	−	2.45837i	0.0925877	−	0.160367i
$236$	−6.98339	−	2.51502i	−0.454580	−	0.163714i
$237$	1.89688	−	2.03107i	0.123216	−	0.131932i
$238$	−13.9622	+	16.0905i	−0.905038	+	1.04299i
$239$	−20.3895	+	11.7719i	−1.31889	+	0.761461i	−0.983550	−	0.180636i	$-0.942184\pi$
$239$	−20.3895	+	11.7719i	−1.31889	+	0.761461i	−0.335340	+	0.942097i	$0.608851\pi$
$240$	6.33767	+	2.64534i	0.409095	+	0.170756i
$241$	−12.0196	+	6.93950i	−0.774248	+	0.447012i	−0.834388	−	0.551177i	$-0.814179\pi$
$241$	−12.0196	+	6.93950i	−0.774248	+	0.447012i	0.0601397	+	0.998190i	$0.480845\pi$
$242$	1.29323	+	14.4991i	0.0831317	+	0.932037i
$243$	−12.7354	−	8.98943i	−0.816976	−	0.576672i
$244$	−7.32392	+	20.3361i	−0.468866	+	1.30189i
$245$	5.87848	+	3.68646i	0.375562	+	0.235519i
$246$	8.92419	−	3.61532i	0.568986	−	0.230504i
$247$	0.897583	+	0.518220i	0.0571118	+	0.0329735i
$248$	3.23150	+	11.8199i	0.205201	+	0.750562i
$249$	1.16085	+	3.80728i	0.0735660	+	0.241276i
$250$	10.3426	−	7.26809i	0.654125	−	0.459674i
$251$		−	15.8907i		−	1.00301i	−0.865153	−	0.501507i	$-0.832779\pi$
$251$		−	15.8907i		−	1.00301i	0.865153	−	0.501507i	$-0.167221\pi$
$252$	14.0084	−	7.46754i	0.882447	−	0.470411i
$253$			2.82933i			0.177878i
$254$	−1.70315	−	2.42361i	−0.106865	−	0.152071i
$255$	−9.52323	−	2.20620i	−0.596368	−	0.138158i
$256$	2.99135	+	15.7179i	0.186960	+	0.982368i
$257$	12.3887	+	7.15263i	0.772787	+	0.446169i	0.833868	−	0.551964i	$-0.186121\pi$
$257$	12.3887	+	7.15263i	0.772787	+	0.446169i	−0.0610808	+	0.998133i	$0.519455\pi$
$258$	6.44595	−	8.26635i	0.401307	−	0.514641i
$259$	2.06252	−	7.17106i	0.128159	−	0.445588i
$260$	0.587378	−	1.63096i	0.0364276	−	0.101148i
$261$	5.74144	−	11.7266i	0.355386	−	0.725859i
$262$	18.0743	−	1.61211i	1.11663	−	0.0995964i
$263$	3.99033	−	2.30382i	0.246055	−	0.142060i	−0.371902	−	0.928272i	$-0.621294\pi$
$263$	3.99033	−	2.30382i	0.246055	−	0.142060i	0.617956	+	0.786212i	$0.287961\pi$
$264$	−4.11574	+	0.161522i	−0.253306	+	0.00994099i
$265$	5.22517	−	3.01675i	0.320980	−	0.185318i
$266$	−1.44762	−	4.19213i	−0.0887596	−	0.257036i
$267$	25.9725	+	6.01692i	1.58949	+	0.368230i
$268$	8.64338	−	23.9998i	0.527979	−	1.46602i
$269$	10.8324	−	18.7623i	0.660464	−	1.14396i	−0.320030	−	0.947407i	$-0.603693\pi$
$269$	10.8324	−	18.7623i	0.660464	−	1.14396i	0.980494	−	0.196549i	$-0.0629735\pi$
$270$	6.03650	+	4.07676i	0.367370	+	0.248104i
$271$	−9.32142	−	16.1452i	−0.566236	−	0.980749i	−0.996934	−	0.0782528i	$-0.975066\pi$
$271$	−9.32142	−	16.1452i	−0.566236	−	0.980749i	0.430698	−	0.902496i	$-0.358267\pi$
$272$	−7.93402	−	21.3480i	−0.481071	−	1.29441i
$273$	−2.05839	−	3.43789i	−0.124580	−	0.208071i
$274$	21.8037	+	10.1224i	1.31721	+	0.611514i
$275$	−1.68886	+	2.92519i	−0.101842	+	0.176396i
$276$	11.6429	+	0.579517i	0.700818	+	0.0348828i
$277$	23.2301	−	13.4119i	1.39576	−	0.805843i	0.401815	−	0.915721i	$-0.368379\pi$
$277$	23.2301	−	13.4119i	1.39576	−	0.805843i	0.993945	+	0.109878i	$0.0350461\pi$
$278$	−12.8734	+	27.7295i	−0.772095	+	1.66310i
$279$	0.886995	+	12.9666i	0.0531030	+	0.776293i
$280$	−6.47238	+	3.62391i	−0.386799	+	0.216570i
$281$	−10.4685	+	18.1319i	−0.624496	+	1.08166i	0.364142	+	0.931343i	$0.381362\pi$
$281$	−10.4685	+	18.1319i	−0.624496	+	1.08166i	−0.988638	+	0.150315i	$0.951971\pi$
$282$	6.94734	+	0.969762i	0.413708	+	0.0577485i
$283$			15.1587i			0.901091i	0.892753	+	0.450546i	$0.148771\pi$
$283$			15.1587i			0.901091i	−0.892753	+	0.450546i	$0.851229\pi$
$284$	24.8802	+	8.96043i	1.47637	+	0.531704i
$285$	1.38904	−	1.48730i	0.0822795	−	0.0881002i
$286$	0.0923665	+	1.03557i	0.00546175	+	0.0612348i
$287$	−2.87473	+	9.99498i	−0.169690	+	0.589985i
$288$	−0.178333	+	16.9696i	−0.0105084	+	0.999945i
$289$	7.70888	+	13.3522i	0.453464	+	0.785422i
$290$	−2.56910	+	5.53387i	−0.150863	+	0.324960i
$291$	−3.72572	−	12.2194i	−0.218406	−	0.716311i
$292$	−7.38049	+	6.23564i	−0.431911	+	0.364913i
$293$	−15.2512	−	26.4159i	−0.890986	−	1.54323i	−0.838696	−	0.544600i	$-0.816681\pi$
$293$	−15.2512	−	26.4159i	−0.890986	−	1.54323i	−0.0522899	−	0.998632i	$-0.516652\pi$
$294$	−2.98886	+	16.8839i	−0.174314	+	0.984690i
$295$	3.18591	+	1.83939i	0.185491	+	0.107093i
$296$	5.66913	+	5.61188i	0.329511	+	0.326184i
$297$	−4.31341	−	0.693221i	−0.250290	−	0.0402247i
$298$	−30.1102	+	2.68564i	−1.74424	+	0.155575i
$299$		−	2.94250i		−	0.170169i
$300$	11.6914	+	7.54892i	0.675005	+	0.435837i
$301$	2.73029	+	10.9883i	0.157371	+	0.633354i
$302$	−13.7698	+	29.6603i	−0.792362	+	1.70676i
$303$	0.217564	−	0.939131i	0.0124987	−	0.0539516i
$304$	4.67469	+	0.791697i	0.268112	+	0.0454070i
$305$	5.35642	−	9.27759i	0.306708	−	0.531233i
$306$	−3.78310	−	23.8581i	−0.216266	−	1.36388i
$307$		−	6.09166i		−	0.347670i	−0.984775	−	0.173835i	$-0.944384\pi$
$307$		−	6.09166i		−	0.347670i	0.984775	−	0.173835i	$-0.0556159\pi$
$308$	2.60573	−	3.60599i	0.148475	−	0.205470i
$309$	31.7571	−	9.68283i	1.80660	−	0.550837i
$310$	−0.539550	−	6.04921i	−0.0306444	−	0.343572i
$311$	−3.67867			−0.208598			−0.104299	−	0.994546i	$-0.533260\pi$
$311$	−3.67867			−0.208598			−0.104299	+	0.994546i	$0.533260\pi$
$312$	4.28037	−	0.167983i	0.242328	−	0.00951016i
$313$			6.50583i			0.367731i	0.982951	+	0.183866i	$0.0588611\pi$
$313$			6.50583i			0.367731i	−0.982951	+	0.183866i	$0.941139\pi$
$314$	14.4685	−	10.1675i	0.816503	−	0.573783i
$315$	−7.48836	+	2.41393i	−0.421921	+	0.136010i
$316$	−3.01920	−	1.08734i	−0.169843	−	0.0611679i
$317$			4.37351i			0.245641i	0.992429	+	0.122820i	$0.0391939\pi$
$317$			4.37351i			0.245641i	−0.992429	+	0.122820i	$0.960806\pi$
$318$	11.7574	+	9.16818i	0.659321	+	0.514126i
$319$		−	3.65923i		−	0.204877i
$320$	−0.0804886	−	7.92961i	−0.00449945	−	0.443279i
$321$	2.17047	−	9.36896i	0.121144	−	0.522924i
$322$	−8.25221	+	9.51010i	−0.459878	+	0.529977i
$323$	−6.74878			−0.375512
$324$	−3.73614	+	17.6080i	−0.207563	+	0.978222i
$325$	1.75642	−	3.04220i	0.0974284	−	0.168751i
$326$	−14.9225	−	6.92776i	−0.826480	−	0.383693i
$327$	1.44586	+	4.74201i	0.0799560	+	0.262234i
$328$	−7.90159	−	7.82179i	−0.436292	−	0.431886i
$329$	−5.45448	+	5.25885i	−0.300715	+	0.289930i
$330$	2.02184	+	0.282223i	0.111298	+	0.0155359i
$331$	−1.38788			−0.0762848			−0.0381424	−	0.999272i	$-0.512144\pi$
$331$	−1.38788			−0.0762848			−0.0381424	+	0.999272i	$0.512144\pi$
$332$	3.51078	−	2.96620i	0.192679	−	0.162791i
$333$	4.72063	+	7.02153i	0.258689	+	0.384777i
$334$	5.08905	+	2.36259i	0.278460	+	0.129275i
$335$	−6.32142	+	10.9490i	−0.345376	+	0.598209i
$336$	−14.3052	−	11.4613i	−0.780411	−	0.625267i
$337$	−6.94844	−	12.0351i	−0.378506	−	0.655591i	0.612339	−	0.790595i	$-0.290229\pi$
$337$	−6.94844	−	12.0351i	−0.378506	−	0.655591i	−0.990845	+	0.135004i	$0.956895\pi$
$338$	1.53726	+	17.2351i	0.0836158	+	0.937465i
$339$	6.32381	−	27.2972i	0.343462	−	1.48258i
$340$	1.99769	+	11.1095i	0.108340	+	0.602498i
$341$	1.82124	+	3.15448i	0.0986256	+	0.170825i
$342$	4.69517	+	1.80135i	0.253886	+	0.0974058i
$343$	−12.3592	−	13.7931i	−0.667333	−	0.744759i
$344$	−11.7075	−	3.07341i	−0.631224	−	0.165707i
$345$	−5.62859	−	1.30395i	−0.303033	−	0.0702023i
$346$	22.4714	−	15.7914i	1.20807	−	0.848951i
$347$	−21.0698			−1.13109			−0.565543	−	0.824719i	$-0.691334\pi$
$347$	−21.0698			−1.13109			−0.565543	+	0.824719i	$0.691334\pi$
$348$	−15.0579	−	0.749500i	−0.807191	−	0.0401774i
$349$	−15.4247	+	26.7164i	−0.825665	+	1.43009i	0.0757442	+	0.997127i	$0.475867\pi$
$349$	−15.4247	+	26.7164i	−0.825665	+	1.43009i	−0.901410	+	0.432967i	$0.857467\pi$
$350$	−14.2085	+	4.90647i	−0.759477	+	0.262262i
$351$	4.48595	+	0.720950i	0.239442	+	0.0384814i
$352$	2.04641	+	4.29334i	0.109074	+	0.228836i
$353$	6.18024	−	3.56816i	0.328941	−	0.189914i	−0.326430	−	0.945221i	$-0.605846\pi$
$353$	6.18024	−	3.56816i	0.328941	−	0.189914i	0.655371	+	0.755307i	$0.272512\pi$
$354$	−1.25676	+	9.00334i	−0.0667958	+	0.478522i
$355$	−11.3506	−	6.55329i	−0.602429	−	0.347813i
$356$	−5.44824	−	30.2987i	−0.288756	−	1.60583i
$357$	22.8005	+	12.6851i	1.20673	+	0.671367i
$358$	1.11058	+	12.4513i	0.0586957	+	0.658072i
$359$	6.96243	−	4.01976i	0.367463	−	0.212155i	−0.304886	−	0.952389i	$-0.598618\pi$
$359$	6.96243	−	4.01976i	0.367463	−	0.212155i	0.672350	+	0.740234i	$0.265285\pi$
$360$	1.57549	−	8.26218i	0.0830356	−	0.435455i
$361$	−8.79751	+	15.2377i	−0.463027	+	0.801986i
$362$	9.05280	−	6.36169i	0.475805	−	0.334363i
$363$	17.0531	−	5.19955i	0.895057	−	0.272906i
$364$	−2.70996	+	3.75023i	−0.142040	+	0.196566i
$365$	4.14719	−	2.39438i	0.217074	−	0.125328i
$366$	26.2184	+	3.65976i	1.37046	+	0.191299i
$367$	−9.76184	−	16.9080i	−0.509564	−	0.882590i	−0.999939	−	0.0110787i	$-0.996473\pi$
$367$	−9.76184	−	16.9080i	−0.509564	−	0.882590i	0.490375	−	0.871512i	$-0.336860\pi$
$368$	−4.68931	−	12.6175i	−0.244447	−	0.657730i
$369$	−6.57958	−	9.78655i	−0.342519	−	0.509468i
$370$	−2.27317	−	3.23476i	−0.118176	−	0.168167i
$371$	−15.6288	+	3.88333i	−0.811407	+	0.201613i
$372$	13.3539	−	6.84840i	0.692368	−	0.355073i
$373$	−30.5547	−	17.6408i	−1.58206	−	0.913404i	−0.994558	−	0.104182i	$-0.966778\pi$
$373$	−30.5547	−	17.6408i	−1.58206	−	0.913404i	−0.587503	−	0.809222i	$-0.699889\pi$
$374$	−3.89244	−	5.53901i	−0.201273	−	0.286416i
$375$	−11.3148	−	10.5673i	−0.584295	−	0.545691i
$376$	−2.13608	−	7.81313i	−0.110160	−	0.402932i
$377$			3.80560i			0.195998i
$378$	−12.4766	−	14.9109i	−0.641727	−	0.766933i
$379$	2.65195			0.136221			0.0681107	−	0.997678i	$-0.478303\pi$
$379$	2.65195			0.136221			0.0681107	+	0.997678i	$0.478303\pi$
$380$	−2.21088	−	0.796235i	−0.113416	−	0.0408460i
$381$	−2.47625	+	2.65143i	−0.126862	+	0.135837i
$382$	−9.27377	−	13.1968i	−0.474488	−	0.675205i
$383$	−17.2901	+	29.9474i	−0.883484	+	1.53024i	−0.0360426	+	0.999350i	$0.511475\pi$
$383$	−17.2901	+	29.9474i	−0.883484	+	1.53024i	−0.847441	+	0.530889i	$0.821858\pi$
$384$	18.0865	−	7.54171i	0.922975	−	0.384861i
$385$	−1.58738	+	1.53045i	−0.0809005	+	0.0779989i
$386$	1.15457	−	0.811349i	0.0587658	−	0.0412966i
$387$	−11.5305	−	5.64544i	−0.586130	−	0.286974i
$388$	−11.2678	+	9.51993i	−0.572034	+	0.483301i
$389$	32.5526	−	18.7943i	1.65048	−	0.952907i	0.673611	−	0.739086i	$-0.264742\pi$
$389$	32.5526	−	18.7943i	1.65048	−	0.952907i	0.976873	−	0.213822i	$-0.0685911\pi$
$390$	−2.10271	−	0.293512i	−0.106475	−	0.0148626i
$391$	9.58006	+	16.5932i	0.484484	+	0.839152i
$392$	19.2760	−	4.52061i	0.973585	−	0.228325i
$393$	−6.48166	−	21.2581i	−0.326956	−	1.07233i
$394$	10.8180	+	15.3942i	0.545003	+	0.775550i
$395$	1.37739	+	0.795239i	0.0693042	+	0.0400128i
$396$	1.22955	+	4.89248i	0.0617873	+	0.245856i
$397$	−3.72508	−	6.45203i	−0.186956	−	0.323818i	0.757278	−	0.653093i	$-0.226529\pi$
$397$	−3.72508	−	6.45203i	−0.186956	−	0.323818i	−0.944234	+	0.329275i	$0.893196\pi$
$398$	−2.00970	−	22.5319i	−0.100737	−	1.12942i
$399$	−4.66032	+	2.79030i	−0.233308	+	0.139690i
$400$	2.68332	−	15.8441i	0.134166	−	0.792203i
$401$	−8.13118	+	14.0836i	−0.406052	+	0.703302i	−0.994443	−	0.105274i	$-0.966428\pi$
$401$	−8.13118	+	14.0836i	−0.406052	+	0.703302i	0.588391	+	0.808576i	$0.299761\pi$
$402$	−30.9418	−	4.31910i	−1.54324	−	0.215417i
$403$	−1.89409	−	3.28066i	−0.0943513	−	0.163421i
$404$	−1.09556	+	0.197001i	−0.0545063	+	0.00980119i
$405$	3.36699	−	8.26150i	0.167307	−	0.410517i
$406$	10.6727	−	12.2996i	0.529680	−	0.610418i
$407$	2.05353	+	1.18561i	0.101790	+	0.0587683i
$408$	−23.5907	+	14.8831i	−1.16791	+	0.736824i
$409$		−	15.4050i		−	0.761726i	−0.924631	−	0.380863i	$-0.875627\pi$
$409$		−	15.4050i		−	0.761726i	0.924631	−	0.380863i	$-0.124373\pi$
$410$	3.16832	+	4.50858i	0.156472	+	0.222663i
$411$	6.64458	−	28.6818i	0.327753	−	1.41477i
$412$	−24.7415	−	29.2840i	−1.21893	−	1.44272i
$413$	−6.81517	−	7.06869i	−0.335352	−	0.347828i
$414$	−2.23596	−	14.1010i	−0.109891	−	0.693028i
$415$	−1.97275	+	1.13897i	−0.0968385	+	0.0559097i
$416$	−2.12826	−	4.46508i	−0.104347	−	0.218918i
$417$	36.4769	+	8.45043i	1.78628	+	0.413819i
$418$	1.40380	−	0.125210i	0.0686620	−	0.00612421i
$419$	12.0628	−	6.96445i	0.589305	−	0.340235i	−0.175518	−	0.984476i	$-0.556160\pi$
$419$	12.0628	−	6.96445i	0.589305	−	0.340235i	0.764823	+	0.644241i	$0.222827\pi$
$420$	5.97276	+	6.84565i	0.291441	+	0.334034i
$421$	25.5483	+	14.7503i	1.24515	+	0.718886i	0.970138	−	0.242555i	$-0.0779856\pi$
$421$	25.5483	+	14.7503i	1.24515	+	0.718886i	0.275010	+	0.961441i	$0.411319\pi$
$422$	−27.8252	−	12.9178i	−1.35451	−	0.628831i
$423$	−0.586319	−	8.57118i	−0.0285078	−	0.416745i
$424$	4.37136	−	16.6517i	0.212292	−	0.808679i
$425$			22.8738i			1.10954i
$426$	4.47752	−	32.0768i	0.216937	−	1.55413i
$427$	−20.5845	+	19.8462i	−0.996155	+	0.960427i
$428$	−10.9296	+	1.96533i	−0.528300	+	0.0949977i
$429$	1.21799	−	0.371370i	0.0588052	−	0.0179299i
$430$	5.44134	+	2.52614i	0.262405	+	0.121821i
$431$	−2.30954	−	1.33341i	−0.111247	−	0.0642283i	0.443344	−	0.896351i	$-0.353792\pi$
$431$	−2.30954	−	1.33341i	−0.111247	−	0.0642283i	−0.554591	+	0.832123i	$0.687125\pi$
$432$	20.3847	−	4.05759i	0.980759	−	0.195221i
$433$			39.6555i			1.90572i	0.303410	+	0.952860i	$0.401875\pi$
$433$			39.6555i			1.90572i	−0.303410	+	0.952860i	$0.598125\pi$
$434$	−3.07892	+	15.9149i	−0.147793	+	0.763942i
$435$	7.27956	+	1.68642i	0.349028	+	0.0808578i
$436$	4.37272	−	3.69443i	0.209416	−	0.176931i
$437$	−3.98878			−0.190809
$438$	9.33176	+	7.27673i	0.445889	+	0.347696i
$439$	−20.2071			−0.964430			−0.482215	−	0.876053i	$-0.660168\pi$
$439$	−20.2071			−0.964430			−0.482215	+	0.876053i	$0.660168\pi$
$440$	−0.621649	−	2.27380i	−0.0296360	−	0.108399i
$441$	20.9894	−	0.667317i	0.999495	−	0.0317770i
$442$	4.04814	+	5.76058i	0.192550	+	0.274003i
$443$	29.7259			1.41232			0.706160	−	0.708053i	$-0.250426\pi$
$443$	29.7259			1.41232			0.706160	+	0.708053i	$0.250426\pi$
$444$	5.29946	−	8.20756i	0.251501	−	0.389514i
$445$			15.2577i			0.723284i
$446$	−1.83293	−	20.5500i	−0.0867917	−	0.973072i
$447$	10.7979	+	35.4141i	0.510723	+	1.67503i
$448$	−5.64376	+	20.3997i	−0.266643	+	0.963795i
$449$	14.8578			0.701184			0.350592	−	0.936528i	$-0.385980\pi$
$449$	14.8578			0.701184			0.350592	+	0.936528i	$0.385980\pi$
$450$	6.10536	−	15.9135i	0.287809	−	0.750168i
$451$	−2.86219	−	1.65249i	−0.134775	−	0.0778126i
$452$	−31.8441	+	5.72612i	−1.49782	+	0.269334i
$453$	39.0168	+	9.03884i	1.83317	+	0.424682i
$454$	10.8733	−	23.4212i	0.510308	−	1.09921i
$455$	1.65088	−	1.59167i	0.0773943	−	0.0746185i
$456$	−0.227713	−	5.80237i	−0.0106637	−	0.271721i
$457$	11.3960			0.533083			0.266541	−	0.963824i	$-0.414119\pi$
$457$	11.3960			0.533083			0.266541	+	0.963824i	$0.414119\pi$
$458$	−2.02045	−	22.6524i	−0.0944092	−	1.05848i
$459$	−27.6441	+	10.5396i	−1.29032	+	0.491947i
$460$	1.18071	+	6.56615i	0.0550508	+	0.306148i
$461$	1.38683	−	2.40206i	0.0645910	−	0.111875i	−0.831921	−	0.554893i	$-0.812759\pi$
$461$	1.38683	−	2.40206i	0.0645910	−	0.111875i	0.896512	+	0.443018i	$0.146092\pi$
$462$	−4.97802	−	2.21558i	−0.231598	−	0.103078i
$463$	17.2262	−	9.94557i	0.800571	−	0.462210i	−0.0430998	−	0.999071i	$-0.513723\pi$
$463$	17.2262	−	9.94557i	0.800571	−	0.462210i	0.843671	+	0.536861i	$0.180390\pi$
$464$	6.06477	+	16.3184i	0.281550	+	0.757562i
$465$	−7.11478	+	2.16932i	−0.329940	+	0.100600i
$466$	20.8861	+	9.69637i	0.967530	+	0.449176i
$467$	−11.4369	+	6.60309i	−0.529236	+	0.305554i	−0.740705	−	0.671830i	$-0.765508\pi$
$467$	−11.4369	+	6.60309i	−0.529236	+	0.305554i	0.211470	+	0.977385i	$0.432175\pi$
$468$	−1.27873	−	5.08818i	−0.0591095	−	0.235201i
$469$	24.2930	−	23.4217i	1.12175	−	1.08151i
$470$	0.356652	+	3.99863i	0.0164511	+	0.184443i
$471$	−15.8285	−	14.7827i	−0.729339	−	0.681152i
$472$	10.1254	−	2.76824i	0.466058	−	0.127418i
$473$	−3.59804			−0.165438
$474$	−0.543345	+	3.89250i	−0.0249567	+	0.178789i
$475$	−4.12393	−	2.38095i	−0.189219	−	0.109246i
$476$	3.07198	−	29.9710i	0.140804	−	1.37372i
$477$	8.02960	−	16.4001i	0.367650	−	0.750908i
$478$	14.0204	−	30.2002i	0.641279	−	1.38132i
$479$	−3.69079	−	6.39264i	−0.168637	−	0.292087i	0.769304	−	0.638883i	$-0.220603\pi$
$479$	−3.69079	−	6.39264i	−0.168637	−	0.292087i	−0.937941	+	0.346796i	$0.887270\pi$
$480$	−9.48418	+	2.09239i	−0.432892	+	0.0955043i
$481$	−2.13567	−	1.23303i	−0.0973782	−	0.0562213i
$482$	8.26499	−	17.8029i	0.376460	−	0.810900i
$483$	13.4759	+	7.49738i	0.613176	+	0.341142i
$484$	−13.2858	−	15.7251i	−0.603902	−	0.714777i
$485$	6.33149	−	3.65549i	0.287498	−	0.165987i
$486$	22.0454	+	0.0461286i	0.999998	+	0.00209244i
$487$	28.8010	+	16.6282i	1.30510	+	0.753498i	0.981273	−	0.192620i	$-0.0616985\pi$
$487$	28.8010	+	16.6282i	1.30510	+	0.753498i	0.323823	+	0.946118i	$0.395032\pi$
$488$	−8.06129	−	29.4858i	−0.364918	−	1.33476i
$489$	−4.54756	+	19.6299i	−0.205648	+	0.887693i
$490$	−9.79941	+	0.514362i	−0.442692	+	0.0232365i
$491$	−1.18434	−	2.05134i	−0.0534487	−	0.0925758i	0.838063	−	0.545573i	$-0.183688\pi$
$491$	−1.18434	−	2.05134i	−0.0534487	−	0.0925758i	−0.891512	+	0.452997i	$0.850355\pi$
$492$	−7.38634	+	11.4396i	−0.333002	+	0.515739i
$493$	−12.3901	−	21.4602i	−0.558021	−	0.966521i
$494$	−1.45995	+	0.130218i	−0.0656863	+	0.00585879i
$495$	−0.170633	−	2.49441i	−0.00766937	−	0.112116i
$496$	−13.3501	−	11.0490i	−0.599435	−	0.496113i
$497$	24.2808	+	25.1841i	1.08914	+	1.12966i
$498$	−4.43897	−	3.46142i	−0.198915	−	0.155110i
$499$	−0.958768	+	1.66063i	−0.0429203	+	0.0743402i	−0.886688	−	0.462369i	$-0.846999\pi$
$499$	−0.958768	+	1.66063i	−0.0429203	+	0.0743402i	0.843767	+	0.536709i	$0.180333\pi$
$500$	−6.05745	+	16.8195i	−0.270897	+	0.752193i
$501$	1.55086	−	6.69441i	0.0692875	−	0.299084i
$502$	12.9210	+	18.3869i	0.576695	+	0.820647i
$503$	−3.22909			−0.143978			−0.0719890	−	0.997405i	$-0.522935\pi$
$503$	−3.22909			−0.143978			−0.0719890	+	0.997405i	$0.522935\pi$
$504$	−10.1369	+	20.0311i	−0.451533	+	0.892254i
$505$	0.551698			0.0245502
$506$	−2.30058	−	3.27377i	−0.102273	−	0.145537i
$507$	20.2711	−	6.18071i	0.900269	−	0.274495i
$508$	3.94137	+	1.41946i	0.174870	+	0.0629782i
$509$	−16.4404	+	28.4757i	−0.728709	+	1.26216i	0.228719	+	0.973492i	$0.426546\pi$
$509$	−16.4404	+	28.4757i	−0.728709	+	1.26216i	−0.957429	+	0.288669i	$0.906787\pi$
$510$	12.8131	−	5.19075i	0.567372	−	0.229850i
$511$	−12.4045	+	3.08218i	−0.548742	+	0.136348i
$512$	−16.2417	−	15.7546i	−0.717790	−	0.696260i
$513$	0.977301	−	6.08105i	0.0431489	−	0.268485i
$514$	−20.1507	+	1.79731i	−0.888809	+	0.0792761i
$515$	9.50030	+	16.4550i	0.418633	+	0.725094i
$516$	−0.736968	+	14.8062i	−0.0324432	+	0.651805i
$517$	−1.20387	−	2.08516i	−0.0529462	−	0.0917054i
$518$	3.44442	+	9.97458i	0.151339	+	0.438258i
$519$	−24.5838	−	22.9595i	−1.07911	−	1.00781i
$520$	0.646515	+	2.36476i	0.0283516	+	0.103701i
$521$	21.5988	+	12.4701i	0.946260	+	0.546323i	0.891917	−	0.452199i	$-0.149360\pi$
$521$	21.5988	+	12.4701i	0.946260	+	0.546323i	0.0543426	+	0.998522i	$0.482694\pi$
$522$	2.89181	+	18.2371i	0.126571	+	0.798217i
$523$	−16.0223	+	9.25045i	−0.700604	+	0.404494i	−0.807572	−	0.589768i	$-0.799219\pi$
$523$	−16.0223	+	9.25045i	−0.700604	+	0.404494i	0.106968	+	0.994262i	$0.465886\pi$
$524$	−19.6026	+	16.5619i	−0.856343	+	0.723508i
$525$	9.45725	+	15.7954i	0.412748	+	0.689366i
$526$	−2.74387	+	5.91032i	−0.119638	+	0.257702i
$527$	21.3620	+	12.3334i	0.930544	+	0.537250i
$528$	4.63091	−	3.53348i	0.201535	−	0.153775i
$529$	−5.83782	−	10.1114i	−0.253818	−	0.439626i
$530$	−3.59297	+	7.73931i	−0.156069	+	0.336174i
$531$	11.1077	−	0.759836i	0.482035	−	0.0329741i
$532$	5.08372	+	3.67355i	0.220407	+	0.159269i
$533$	2.97668	+	1.71859i	0.128934	+	0.0744403i
$534$	−34.9447	+	14.1566i	−1.51221	+	0.612616i
$535$	5.50386			0.237952
$536$	9.51360	+	34.7979i	0.410925	+	1.50304i
$537$	14.6446	−	4.46519i	0.631961	−	0.192687i
$538$	2.72197	+	30.5175i	0.117352	+	1.31570i
$539$	5.20093	−	2.75465i	0.224020	−	0.118651i
$540$	−10.2996	+	0.191246i	−0.443225	+	0.00822994i
$541$	−15.2097	+	8.78132i	−0.653916	+	0.377538i	−0.789955	−	0.613165i	$-0.789896\pi$
$541$	−15.2097	+	8.78132i	−0.653916	+	0.377538i	0.136039	+	0.990703i	$0.456563\pi$
$542$	23.9136	+	11.1019i	1.02718	+	0.476866i
$543$	−9.90376	−	9.24943i	−0.425011	−	0.396931i
$544$	26.5387	+	18.2500i	1.13784	+	0.782464i
$545$	−2.45708	+	1.41860i	−0.105250	+	0.0607661i
$546$	5.17714	+	2.30421i	0.221561	+	0.0986110i
$547$	9.01744	−	15.6187i	0.385558	−	0.667806i	−0.606289	−	0.795245i	$-0.707342\pi$
$547$	9.01744	−	15.6187i	0.385558	−	0.667806i	0.991846	+	0.127439i	$0.0406757\pi$
$548$	−33.4594	+	6.01658i	−1.42931	+	0.257016i
$549$	−2.21269	−	32.3465i	−0.0944355	−	1.38052i
$550$	−0.424377	−	4.75793i	−0.0180955	−	0.202879i
$551$	5.15877			0.219771
$552$	−13.9430	+	8.79648i	−0.593452	+	0.374403i
$553$	−2.94647	−	3.05608i	−0.125296	−	0.129958i
$554$	−15.9737	+	34.4075i	−0.678656	+	1.46183i
$555$	−3.30502	+	3.53882i	−0.140290	+	0.150215i
$556$	−7.65175	−	42.5529i	−0.324507	−	1.80464i
$557$	−12.2341	−	7.06335i	−0.518374	−	0.299284i	0.217895	−	0.975972i	$-0.430081\pi$
$557$	−12.2341	−	7.06335i	−0.518374	−	0.299284i	−0.736269	+	0.676689i	$0.763414\pi$
$558$	−11.5697	−	14.2822i	−0.489786	−	0.604615i
$559$	3.74196			0.158268
$560$	4.54241	−	9.45598i	0.191952	−	0.399588i
$561$	−5.65932	+	6.05968i	−0.238937	+	0.255840i
$562$	−2.63051	−	29.4922i	−0.110961	−	1.24405i
$563$		−	6.71616i		−	0.283052i	−0.989935	−	0.141526i	$-0.954799\pi$
$563$		−	6.71616i		−	0.283052i	0.989935	−	0.141526i	$-0.0452009\pi$
$564$	−8.82717	+	4.52691i	−0.371691	+	0.190617i
$565$	16.0359			0.674635
$566$	−12.3258	−	17.5399i	−0.518093	−	0.737255i
$567$	−14.7318	+	18.7076i	−0.618677	+	0.785645i
$568$	−36.0743	+	9.86257i	−1.51364	+	0.413824i
$569$	9.23666			0.387221			0.193610	−	0.981078i	$-0.437980\pi$
$569$	9.23666			0.387221			0.193610	+	0.981078i	$0.437980\pi$
$570$	−0.397878	+	2.85038i	−0.0166653	+	0.119389i
$571$	−11.3436			−0.474713			−0.237357	−	0.971423i	$-0.576281\pi$
$571$	−11.3436			−0.474713			−0.237357	+	0.971423i	$0.576281\pi$
$572$	−0.948920	−	1.12314i	−0.0396763	−	0.0469608i
$573$	−13.4834	+	14.4372i	−0.563277	+	0.603124i
$574$	−4.80080	−	13.9025i	−0.200382	−	0.580279i
$575$			13.5193i			0.563793i
$576$	−13.5920	−	19.7803i	−0.566332	−	0.824177i
$577$	6.03962	+	3.48698i	0.251433	+	0.145165i	0.620420	−	0.784270i	$-0.286962\pi$
$577$	6.03962	+	3.48698i	0.251433	+	0.145165i	−0.368987	+	0.929434i	$0.620295\pi$
$578$	−19.7767	−	9.18133i	−0.822602	−	0.381893i
$579$	−1.26309	−	1.17964i	−0.0524924	−	0.0490243i
$580$	−1.52703	−	8.49213i	−0.0634066	−	0.352616i
$581$	5.90062	−	1.46614i	0.244799	−	0.0608259i
$582$	14.2467	+	11.1093i	0.590547	+	0.460497i
$583$		−	5.11755i		−	0.211947i
$584$	3.46952	−	13.2164i	0.143570	−	0.546897i
$585$	0.177458	+	2.59419i	0.00733698	+	0.107257i
$586$	39.1261	+	18.1643i	1.61629	+	0.750360i
$587$	31.7895	+	18.3537i	1.31209	+	0.757538i	0.982443	−	0.186565i	$-0.0597355\pi$
$587$	31.7895	+	18.3537i	1.31209	+	0.757538i	0.329651	+	0.944103i	$0.393069\pi$
$588$	−10.2703	−	21.9664i	−0.423539	−	0.905878i
$589$	−4.44718	+	2.56758i	−0.183243	+	0.105795i
$590$	−5.18199	+	0.462200i	−0.213339	+	0.0190285i
$591$	15.7286	−	16.8413i	0.646988	−	0.692757i
$592$	−11.1228	−	1.88373i	−0.457143	−	0.0774208i
$593$	−22.5267	+	13.0058i	−0.925061	+	0.534084i	−0.885246	−	0.465123i	$-0.846010\pi$
$593$	−22.5267	+	13.0058i	−0.925061	+	0.534084i	−0.0398147	+	0.999207i	$0.512677\pi$
$594$	5.55464	−	2.70520i	0.227910	−	0.110996i
$595$	−4.12744	+	14.3505i	−0.169208	+	0.588312i
$596$	32.6562	−	27.5907i	1.33765	−	1.13016i
$597$	−26.5009	+	8.08022i	−1.08461	+	0.330701i
$598$	2.39260	+	3.40472i	0.0978408	+	0.139229i
$599$		−	15.7509i		−	0.643563i	−0.946814	−	0.321781i	$-0.895718\pi$
$599$		−	15.7509i		−	0.643563i	0.946814	−	0.321781i	$-0.104282\pi$
$600$	−19.6661	+	0.771795i	−0.802866	+	0.0315084i
$601$	−21.8384	−	12.6084i	−0.890808	−	0.514308i	−0.0166010	−	0.999862i	$-0.505285\pi$
$601$	−21.8384	−	12.6084i	−0.890808	−	0.514308i	−0.874207	+	0.485554i	$0.838618\pi$
$602$	−12.0939	−	10.4943i	−0.492912	−	0.427715i
$603$	2.61133	+	38.1740i	0.106342	+	1.55457i
$604$	−8.18455	−	45.5159i	−0.333025	−	1.85201i
$605$	5.10153	+	8.83611i	0.207407	+	0.359239i
$606$	0.511885	+	1.26356i	0.0207939	+	0.0513285i
$607$	20.8384	−	36.0932i	0.845805	−	1.46498i	−0.0391158	−	0.999235i	$-0.512454\pi$
$607$	20.8384	−	36.0932i	0.845805	−	1.46498i	0.884921	−	0.465742i	$-0.154213\pi$
$608$	−6.05275	+	2.88502i	−0.245471	+	0.117003i
$609$	−17.4287	−	9.69650i	−0.706246	−	0.392922i
$610$	1.34596	+	15.0903i	0.0544963	+	0.610990i
$611$	1.25203	+	2.16857i	0.0506515	+	0.0877310i
$612$	23.7768	+	24.5296i	0.961120	+	0.991552i
$613$	8.00024	+	4.61894i	0.323126	+	0.186557i	0.652785	−	0.757543i	$-0.273600\pi$
$613$	8.00024	+	4.61894i	0.323126	+	0.186557i	−0.329659	+	0.944100i	$0.606934\pi$
$614$	4.95324	+	7.04856i	0.199897	+	0.284457i
$615$	4.60651	−	4.93239i	0.185752	−	0.198893i
$616$	−0.0829451	+	6.29119i	−0.00334196	+	0.253479i
$617$	−11.9275	−	20.6591i	−0.480184	−	0.831703i	0.519558	−	0.854435i	$-0.326097\pi$
$617$	−11.9275	−	20.6591i	−0.480184	−	0.831703i	−0.999742	+	0.0227325i	$0.992763\pi$
$618$	−28.8722	+	37.0261i	−1.16141	+	1.48941i
$619$	29.5619	−	17.0676i	1.18819	−	0.686004i	0.230298	−	0.973120i	$-0.426030\pi$
$619$	29.5619	−	17.0676i	1.18819	−	0.686004i	0.957896	+	0.287116i	$0.0926967\pi$
$620$	5.54302	+	6.56071i	0.222613	+	0.263484i
$621$	−16.3387	+	6.22931i	−0.655650	+	0.249974i
$622$	4.25652	−	2.99119i	0.170671	−	0.119936i
$623$	11.2567	−	39.1377i	0.450988	−	1.56802i
$624$	−4.81615	+	3.67482i	−0.192800	+	0.147110i
$625$	−5.61338	+	9.72265i	−0.224535	+	0.388906i
$626$	−5.29001	−	7.52778i	−0.211431	−	0.300871i
$627$	−0.503419	−	1.65108i	−0.0201046	−	0.0659377i
$628$	−8.47387	+	23.5292i	−0.338144	+	0.938915i
$629$	16.0578			0.640265
$630$	6.70183	−	8.88204i	0.267007	−	0.353869i
$631$			42.2128i			1.68046i	0.542227	+	0.840232i	$0.317581\pi$
$631$			42.2128i			1.68046i	−0.542227	+	0.840232i	$0.682419\pi$
$632$	4.37760	−	1.19682i	0.174131	−	0.0476069i
$633$	−8.47960	+	36.6028i	−0.337034	+	1.45483i
$634$	−3.55618	−	5.06051i	−0.141234	−	0.200978i
$635$	−1.79810	−	1.03813i	−0.0713554	−	0.0411971i
$636$	−21.0591	−	1.04820i	−0.835046	−	0.0415639i
$637$	−5.40897	+	2.86483i	−0.214311	+	0.113509i
$638$	2.97538	+	4.23402i	0.117797	+	0.167627i
$639$	−39.5743	+	2.70712i	−1.56553	+	0.107092i
$640$	6.54084	+	9.10976i	0.258549	+	0.360095i
$641$	2.27178	+	3.93483i	0.0897298	+	0.155417i	0.907397	−	0.420275i	$-0.138066\pi$
$641$	2.27178	+	3.93483i	0.0897298	+	0.155417i	−0.817667	+	0.575691i	$0.804733\pi$
$642$	5.10667	+	12.6055i	0.201544	+	0.497499i
$643$	−17.3567	+	10.0209i	−0.684482	+	0.395186i	−0.801542	−	0.597939i	$-0.795987\pi$
$643$	−17.3567	+	10.0209i	−0.684482	+	0.395186i	0.117059	+	0.993125i	$0.462653\pi$
$644$	1.81566	−	17.7140i	0.0715468	−	0.698029i
$645$	1.65822	−	7.15784i	0.0652925	−	0.281840i
$646$	7.80889	−	5.48756i	0.307237	−	0.215905i
$647$	15.3908	−	26.6576i	0.605074	−	1.04802i	−0.386966	−	0.922094i	$-0.626477\pi$
$647$	15.3908	−	26.6576i	0.605074	−	1.04802i	0.992040	−	0.125925i	$-0.0401898\pi$
$648$	−9.99435	−	23.4118i	−0.392615	−	0.919703i
$649$	2.70225	−	1.56015i	0.106073	−	0.0612411i
$650$	0.441352	+	4.94825i	0.0173112	+	0.194086i
$651$	19.8507	−	0.315477i	0.778008	−	0.0123645i
$652$	22.8996	−	4.11776i	0.896818	−	0.161264i
$653$	21.6699	+	12.5111i	0.848007	+	0.489597i	0.859978	−	0.510331i	$-0.170477\pi$
$653$	21.6699	+	12.5111i	0.848007	+	0.489597i	−0.0119708	+	0.999928i	$0.503811\pi$
$654$	−5.52879	−	4.31125i	−0.216193	−	0.168583i
$655$	11.0149	−	6.35947i	0.430389	−	0.248485i
$656$	15.5028	+	2.62553i	0.605284	+	0.102510i
$657$	6.37305	−	13.0166i	0.248636	−	0.507828i
$658$	2.03522	−	10.5201i	0.0793410	−	0.410115i
$659$	6.15917	−	10.6680i	0.239927	−	0.415566i	−0.720766	−	0.693178i	$-0.756210\pi$
$659$	6.15917	−	10.6680i	0.239927	−	0.415566i	0.960693	+	0.277613i	$0.0895431\pi$
$660$	−2.56891	+	1.31744i	−0.0999948	+	0.0512811i
$661$	19.9359			0.775418			0.387709	−	0.921782i	$-0.373267\pi$
$661$	19.9359			0.775418			0.387709	+	0.921782i	$0.373267\pi$
$662$	1.60589	−	1.12851i	0.0624147	−	0.0438608i
$663$	5.88570	−	6.30207i	0.228582	−	0.244752i
$664$	−1.65040	+	6.28681i	−0.0640478	+	0.243976i
$665$	−2.15762	−	2.23789i	−0.0836691	−	0.0867816i
$666$	−11.1715	−	4.28605i	−0.432886	−	0.166081i
$667$	−7.32300	−	12.6838i	−0.283548	−	0.491119i
$668$	−7.80951	+	1.40429i	−0.302159	+	0.0543335i
$669$	−24.1699	+	7.36949i	−0.934463	+	0.284921i
$670$	−1.58845	−	17.8090i	−0.0613670	−	0.688021i
$671$	−4.54325	−	7.86915i	−0.175390	−	0.303785i
$672$	25.8717	+	1.62992i	0.998021	+	0.0628754i
$673$	−10.6802	+	18.4986i	−0.411691	+	0.713070i	−0.995075	−	0.0991269i	$-0.968395\pi$
$673$	−10.6802	+	18.4986i	−0.411691	+	0.713070i	0.583384	+	0.812197i	$0.301728\pi$
$674$	17.8258	+	8.27564i	0.686625	+	0.318766i
$675$	−20.6106	−	3.31239i	−0.793304	−	0.127494i
$676$	−15.7929	−	18.6924i	−0.607419	−	0.718940i
$677$	15.5662			0.598259			0.299130	−	0.954213i	$-0.403304\pi$
$677$	15.5662			0.598259			0.299130	+	0.954213i	$0.403304\pi$
$678$	14.8786	+	36.7270i	0.571411	+	1.41049i
$679$	−18.9379	+	4.70555i	−0.726769	+	0.180582i
$680$	−11.3448	−	11.2303i	−0.435055	−	0.430661i
$681$	−30.8095	−	7.13749i	−1.18062	−	0.273509i
$682$	−4.67228	−	2.16911i	−0.178911	−	0.0830594i
$683$	−10.1116	+	17.5138i	−0.386910	+	0.670147i	−0.992032	−	0.125985i	$-0.959791\pi$
$683$	−10.1116	+	17.5138i	−0.386910	+	0.670147i	0.605122	+	0.796132i	$0.293124\pi$
$684$	−6.89741	+	1.73342i	−0.263729	+	0.0662790i
$685$	16.8493			0.643779
$686$	25.5160	+	5.91031i	0.974207	+	0.225657i
$687$	−26.6426	+	8.12342i	−1.01648	+	0.309928i
$688$	16.0455	−	5.96336i	0.611730	−	0.227351i
$689$			5.32226i			0.202762i
$690$	7.57300	−	3.06793i	0.288299	−	0.116794i
$691$			13.8327i			0.526222i	0.964766	+	0.263111i	$0.0847485\pi$
$691$			13.8327i			0.526222i	−0.964766	+	0.263111i	$0.915252\pi$
$692$	−13.1610	+	36.5439i	−0.500308	+	1.38919i
$693$	−1.40261	+	6.52433i	−0.0532808	+	0.247839i
$694$	24.3795	−	17.1322i	0.925433	−	0.650331i
$695$			21.4286i			0.812832i
$696$	18.0327	−	11.3767i	0.683528	−	0.431231i
$697$	−22.3812			−0.847748
$698$	−3.87592	−	43.4551i	−0.146706	−	1.64480i
$699$	6.36495	−	27.4747i	0.240744	−	1.03919i
$700$	12.4509	−	17.2304i	0.470599	−	0.651247i
$701$			10.2555i			0.387346i	0.981066	+	0.193673i	$0.0620401\pi$
$701$			10.2555i			0.387346i	−0.981066	+	0.193673i	$0.937960\pi$
$702$	−5.77683	+	2.81341i	−0.218032	+	0.106185i
$703$	−1.67146	+	2.89506i	−0.0630405	+	0.109189i
$704$	−5.85885	−	3.30378i	−0.220814	−	0.124516i
$705$	4.70299	−	1.43396i	0.177125	−	0.0540060i
$706$	−4.24971	+	9.15392i	−0.159940	+	0.344512i
$707$	−1.41517	−	0.407026i	−0.0532228	−	0.0153078i
$708$	−5.86661	−	11.4395i	−0.220481	−	0.429923i
$709$			23.6352i			0.887640i	0.896116	+	0.443820i	$0.146377\pi$
$709$			23.6352i			0.887640i	−0.896116	+	0.443820i	$0.853623\pi$
$710$	18.4622	−	1.64671i	0.692875	−	0.0618000i
$711$	4.80232	−	0.328507i	0.180101	−	0.0123200i
$712$	30.9405	+	30.6280i	1.15954	+	1.14783i
$713$	12.6258	+	7.28948i	0.472838	+	0.272993i
$714$	−36.6965	+	3.86176i	−1.37333	+	0.144523i
$715$	0.364369	+	0.631105i	0.0136266	+	0.0236020i
$716$	−11.4094	−	13.5041i	−0.426389	−	0.504674i
$717$	−39.7270	−	9.20337i	−1.48363	−	0.343706i
$718$	−4.78757	+	10.3125i	−0.178670	+	0.384858i
$719$	12.7165	+	22.0256i	0.474245	+	0.821416i	0.999565	−	0.0294887i	$-0.00938789\pi$
$719$	12.7165	+	22.0256i	0.474245	+	0.821416i	−0.525320	+	0.850904i	$0.676055\pi$
$720$	4.89516	+	10.8411i	0.182432	+	0.404023i
$721$	−12.2293	−	49.2179i	−0.455443	−	1.83297i
$722$	−2.21064	−	24.7847i	−0.0822714	−	0.922392i
$723$	−23.4189	−	5.42535i	−0.870959	−	0.201771i
$724$	−5.30203	+	14.7220i	−0.197048	+	0.547138i
$725$		−	17.4848i		−	0.649368i
$726$	−15.5040	+	19.8825i	−0.575408	+	0.737909i
$727$	−11.8070	+	20.4502i	−0.437896	+	0.758457i	−0.997527	−	0.0702842i	$-0.977609\pi$
$727$	−11.8070	+	20.4502i	−0.437896	+	0.758457i	0.559631	+	0.828742i	$0.310943\pi$
$728$	0.0862630	−	6.54284i	0.00319712	−	0.242494i
$729$	−5.49363	−	26.4352i	−0.203468	−	0.979082i
$730$	−2.85172	+	6.14264i	−0.105547	+	0.227349i
$731$	−21.1014	+	12.1829i	−0.780464	+	0.450601i
$732$	−33.3126	+	17.0840i	−1.23127	+	0.631442i
$733$	−8.42759	+	14.5970i	−0.311280	+	0.539153i	−0.978640	−	0.205583i	$-0.934091\pi$
$733$	−8.42759	+	14.5970i	−0.311280	+	0.539153i	0.667360	+	0.744736i	$0.267424\pi$
$734$	25.0434	+	11.6264i	0.924370	+	0.429139i
$735$	3.08307	+	11.6161i	0.113721	+	0.428467i
$736$	15.6854	+	10.7865i	0.578171	+	0.397594i
$737$	5.36176	+	9.28684i	0.197503	+	0.342085i
$738$	15.5707	+	5.97387i	0.573167	+	0.219901i
$739$	19.0597	−	33.0123i	0.701122	−	1.21438i	−0.266951	−	0.963710i	$-0.586016\pi$
$739$	19.0597	−	33.0123i	0.701122	−	1.21438i	0.968073	−	0.250668i	$-0.0806504\pi$
$740$	5.26048	+	1.89453i	0.193379	+	0.0696442i
$741$	0.523556	+	1.71712i	0.0192333	+	0.0630801i
$742$	14.9262	−	17.2014i	0.547958	−	0.631483i
$743$	31.2738	−	18.0559i	1.14732	−	0.662408i	0.199090	−	0.979981i	$-0.436201\pi$
$743$	31.2738	−	18.0559i	1.14732	−	0.662408i	0.948234	+	0.317573i	$0.102868\pi$
$744$	−9.88301	+	18.7825i	−0.362329	+	0.688598i
$745$	−18.3499	+	10.5943i	−0.672289	+	0.388146i
$746$	49.6983	−	4.43277i	1.81958	−	0.162295i
$747$	−3.03156	+	6.19181i	−0.110919	+	0.226546i
$748$	9.00774	+	3.24408i	0.329356	+	0.118615i
$749$	−14.1180	−	4.06058i	−0.515860	−	0.148370i
$750$	21.6846	+	3.02690i	0.791810	+	0.110527i
$751$	5.36369	+	3.09673i	0.195724	+	0.113001i	0.594659	−	0.803978i	$-0.297287\pi$
$751$	5.36369	+	3.09673i	0.195724	+	0.113001i	−0.398936	+	0.916979i	$0.630620\pi$
$752$	8.82462	+	7.30355i	0.321801	+	0.266333i
$753$	18.7863	−	20.1152i	0.684609	−	0.733040i
$754$	−3.09440	−	4.40339i	−0.112691	−	0.160362i
$755$			22.9207i			0.834168i
$756$	26.5608	+	7.10818i	0.966005	+	0.258522i
$757$			19.4270i			0.706085i	0.935607	+	0.353042i	$0.114853\pi$
$757$			19.4270i			0.706085i	−0.935607	+	0.353042i	$0.885147\pi$
$758$	−3.06852	+	2.15635i	−0.111454	+	0.0783221i
$759$	−3.34487	+	3.58150i	−0.121411	+	0.130000i
$760$	3.20561	−	0.876400i	0.116280	−	0.0317904i
$761$	17.0651	+	9.85251i	0.618608	+	0.357153i	0.776327	−	0.630331i	$-0.217081\pi$
$761$	17.0651	+	9.85251i	0.618608	+	0.357153i	−0.157719	+	0.987484i	$0.550414\pi$
$762$	0.709302	−	5.08141i	0.0256953	−	0.184080i
$763$	7.34929	−	1.82610i	0.266062	−	0.0661092i
$764$	21.4610	+	7.72905i	0.776433	+	0.279627i
$765$	−9.44675	−	14.0512i	−0.341548	−	0.508023i
$766$	−4.34466	−	48.7105i	−0.156979	−	1.75998i
$767$	−2.81034	+	1.62255i	−0.101476	+	0.0585870i
$768$	−14.7953	+	23.4329i	−0.533880	+	0.845561i
$769$	−21.2636	+	12.2765i	−0.766784	+	0.442703i	−0.831726	−	0.555186i	$-0.812647\pi$
$769$	−21.2636	+	12.2765i	−0.766784	+	0.442703i	0.0649424	+	0.997889i	$0.479314\pi$
$770$	0.592296	−	3.06158i	0.0213449	−	0.110332i
$771$	7.22629	+	23.7003i	0.260248	+	0.853544i
$772$	−0.676204	+	1.87760i	−0.0243371	+	0.0675761i
$773$	−2.39742	+	4.15246i	−0.0862293	+	0.149354i	−0.905914	−	0.423461i	$-0.860815\pi$
$773$	−2.39742	+	4.15246i	−0.0862293	+	0.149354i	0.819685	+	0.572814i	$0.194148\pi$
$774$	17.9322	−	2.84345i	0.644559	−	0.102206i
$775$	8.70236	+	15.0729i	0.312598	+	0.541436i
$776$	5.29690	−	20.1774i	0.190148	−	0.724325i
$777$	11.0886	−	6.63913i	0.397800	−	0.238178i
$778$	−22.3841	+	48.2156i	−0.802509	+	1.72861i
$779$	2.32968	−	4.03512i	0.0834693	−	0.144573i
$780$	2.67167	−	1.37013i	0.0956611	−	0.0490587i
$781$	−9.62748	+	5.55843i	−0.344498	+	0.198896i
$782$	−24.5771	−	11.4099i	−0.878876	−	0.408018i
$783$	21.1312	−	8.05649i	0.755166	−	0.287916i
$784$	−18.6281	+	20.9044i	−0.665290	+	0.746585i
$785$	6.19744	−	10.7343i	0.221196	−	0.383123i
$786$	24.7851	+	19.3270i	0.884056	+	0.689371i
$787$			17.7984i			0.634445i	0.948351	+	0.317222i	$0.102750\pi$
$787$			17.7984i			0.634445i	−0.948351	+	0.317222i	$0.897250\pi$
$788$	−25.0346	−	9.01606i	−0.891822	−	0.321184i
$789$	7.77476	+	1.80114i	0.276789	+	0.0641224i
$790$	−2.24038	+	0.199828i	−0.0797092	+	0.00710955i
$791$	−41.1338	−	11.8308i	−1.46255	−	0.420654i
$792$	−5.40085	−	4.66123i	−0.191911	−	0.165629i
$793$	4.72499	+	8.18391i	0.167789	+	0.290619i
$794$	9.55648	+	4.43659i	0.339147	+	0.157449i
$795$	10.1807	+	2.35852i	0.361073	+	0.0836481i
$796$	20.6465	+	24.4371i	0.731795	+	0.866151i
$797$	−10.9176	−	18.9098i	−0.386721	−	0.669820i	0.605285	−	0.796008i	$-0.293059\pi$
$797$	−10.9176	−	18.9098i	−0.386721	−	0.669820i	−0.992006	+	0.126188i	$0.959726\pi$
$798$	3.12353	−	7.01800i	0.110572	−	0.248435i
$799$	−14.1207	−	8.15257i	−0.499553	−	0.288417i
$800$	9.77827	+	20.5147i	0.345714	+	0.725305i
$801$	25.7639	+	38.3215i	0.910322	+	1.35402i
$802$	−2.04320	−	22.9075i	−0.0721480	−	0.808893i
$803$		−	4.06177i		−	0.143337i
$804$	39.3142	−	20.1618i	1.38650	−	0.711052i
$805$	−2.43947	+	8.48166i	−0.0859801	+	0.298939i
$806$	4.85918	+	2.25587i	0.171157	+	0.0794597i
$807$	35.8932	−	10.9440i	1.26350	−	0.385246i
$808$	1.10747	−	1.11877i	0.0389607	−	0.0393581i
$809$	5.01587	−	8.68774i	0.176348	−	0.305445i	−0.764279	−	0.644886i	$-0.776905\pi$
$809$	5.01587	−	8.68774i	0.176348	−	0.305445i	0.940627	+	0.339442i	$0.110238\pi$
$810$	2.82169	+	12.2970i	0.0991441	+	0.432072i
$811$		−	26.5343i		−	0.931746i	−0.884852	−	0.465873i	$-0.845740\pi$
$811$		−	26.5343i		−	0.931746i	0.884852	−	0.465873i	$-0.154260\pi$
$812$	−2.34822	+	22.9098i	−0.0824064	+	0.803978i
$813$	7.28755	−	31.4572i	0.255586	−	1.10325i
$814$	−3.34014	+	0.297919i	−0.117072	+	0.0104420i
$815$	−11.5317			−0.403937
$816$	15.1946	−	36.4030i	0.531918	−	1.27436i
$817$		−	5.07251i		−	0.177465i
$818$	12.5260	+	17.8248i	0.437963	+	0.623229i
$819$	1.45872	−	6.78531i	0.0509716	−	0.237098i
$820$	−7.33202	−	2.64058i	−0.256045	−	0.0922130i
$821$			19.1406i			0.668013i	0.942571	+	0.334007i	$0.108401\pi$
$821$			19.1406i			0.668013i	−0.942571	+	0.334007i	$0.891599\pi$
$822$	15.6334	+	38.5900i	0.545276	+	1.34598i
$823$			33.5962i			1.17109i	0.810639	+	0.585546i	$0.199120\pi$
$823$			33.5962i			1.17109i	−0.810639	+	0.585546i	$0.800880\pi$
$824$	52.4392	+	13.7662i	1.82681	+	0.479568i
$825$	−5.59604	+	1.70625i	−0.194829	+	0.0594041i
$826$	13.6334	+	2.63752i	0.474366	+	0.0917712i
$827$	54.4458			1.89326			0.946632	−	0.322315i	$-0.104461\pi$
$827$	54.4458			1.89326			0.946632	+	0.322315i	$0.104461\pi$
$828$	14.0530	+	14.4979i	0.488375	+	0.503838i
$829$	8.85983	−	15.3457i	0.307715	−	0.532978i	−0.670147	−	0.742228i	$-0.733769\pi$
$829$	8.85983	−	15.3457i	0.307715	−	0.532978i	0.977862	+	0.209251i	$0.0671024\pi$
$830$	1.35652	−	2.92196i	0.0470854	−	0.101423i
$831$	45.2615	+	10.4855i	1.57010	+	0.363739i
$832$	6.09321	+	3.43593i	0.211244	+	0.119120i
$833$	21.1747	−	33.7654i	0.733659	−	1.16990i
$834$	−49.0779	+	19.8822i	−1.69943	+	0.688463i
$835$	3.93267			0.136096
$836$	−1.52250	+	1.28633i	−0.0526568	+	0.0444887i
$837$	−14.2065	+	17.4624i	−0.491050	+	0.603589i
$838$	−8.29470	+	17.8669i	−0.286536	+	0.617202i
$839$	6.85214	−	11.8683i	0.236562	−	0.409738i	−0.723163	−	0.690677i	$-0.757313\pi$
$839$	6.85214	−	11.8683i	0.236562	−	0.409738i	0.959726	+	0.280939i	$0.0906460\pi$
$840$	−12.4773	−	3.06442i	−0.430508	−	0.105733i
$841$	−5.02902	−	8.71052i	−0.173414	−	0.300363i
$842$	−41.5552	+	3.70646i	−1.43209	+	0.127733i
$843$	−34.6873	+	10.5763i	−1.19469	+	0.364266i
$844$	42.6998	−	7.67817i	1.46979	−	0.264294i
$845$	6.06420	+	10.5035i	0.208615	+	0.361331i
$846$	7.64780	+	9.44081i	0.262937	+	0.324582i
$847$	−6.56698	−	26.4294i	−0.225644	−	0.908124i
$848$	8.48179	+	22.8218i	0.291266	+	0.783705i
$849$	−17.9208	+	19.1886i	−0.615041	+	0.658551i
$850$	−18.5991	−	26.4669i	−0.637944	−	0.907807i
$851$	9.49074			0.325338
$852$	20.9014	+	40.7562i	0.716068	+	1.39629i
$853$	0.235840	−	0.408486i	0.00807499	−	0.0139863i	−0.861960	−	0.506977i	$-0.830763\pi$
$853$	0.235840	−	0.408486i	0.00807499	−	0.0139863i	0.870035	+	0.492991i	$0.164096\pi$
$854$	7.68065	−	39.7014i	0.262826	−	1.35855i
$855$	3.51662	−	0.240558i	0.120266	−	0.00822690i
$856$	11.0484	−	11.1611i	0.377625	−	0.381478i
$857$	27.0405	−	15.6119i	0.923688	−	0.533291i	0.0388780	−	0.999244i	$-0.487622\pi$
$857$	27.0405	−	15.6119i	0.923688	−	0.533291i	0.884810	+	0.465953i	$0.154288\pi$
$858$	−1.10735	+	1.42008i	−0.0378043	+	0.0484806i
$859$	−17.0135	−	9.82276i	−0.580494	−	0.335148i	0.180836	−	0.983513i	$-0.442120\pi$
$859$	−17.0135	−	9.82276i	−0.580494	−	0.335148i	−0.761330	+	0.648365i	$0.775453\pi$
$860$	−8.35013	+	1.50150i	−0.284737	+	0.0512007i
$861$	−15.4552	+	9.25358i	−0.526711	+	0.315361i
$862$	3.75655	−	0.335060i	0.127949	−	0.0114122i
$863$	−0.576611	+	0.332906i	−0.0196281	+	0.0113323i	−0.509782	−	0.860304i	$-0.670274\pi$
$863$	−0.576611	+	0.332906i	−0.0196281	+	0.0113323i	0.490154	+	0.871636i	$0.336941\pi$
$864$	−20.2875	+	21.2701i	−0.690194	+	0.723624i
$865$	9.62545	−	16.6718i	0.327275	−	0.566857i
$866$	−32.2446	−	45.8846i	−1.09572	−	1.55922i
$867$	−6.02686	+	26.0154i	−0.204683	+	0.883528i
$868$	−9.37818	−	20.9184i	−0.318316	−	0.710018i
$869$	1.16829	−	0.674513i	0.0396316	−	0.0228813i
$870$	−9.79431	+	3.96781i	−0.332058	+	0.134521i
$871$	−5.57623	−	9.65832i	−0.188943	−	0.327260i
$872$	−2.05559	+	7.83031i	−0.0696110	+	0.265168i
$873$	9.72970	−	19.8724i	0.329300	−	0.672580i
$874$	4.61535	−	3.24335i	0.156117	−	0.109708i
$875$	−17.0250	+	16.4144i	−0.575550	+	0.554907i
$876$	−16.7144	−	0.831952i	−0.564729	−	0.0281090i
$877$	−26.3948	−	15.2390i	−0.891288	−	0.514585i	−0.0169245	−	0.999857i	$-0.505387\pi$
$877$	−26.3948	−	15.2390i	−0.891288	−	0.514585i	−0.874364	+	0.485271i	$0.838721\pi$
$878$	23.3812	−	16.4307i	0.789078	−	0.554510i
$879$	11.9235	−	51.4687i	0.402170	−	1.73600i
$880$	2.56817	+	2.12550i	0.0865730	+	0.0716507i
$881$		−	3.98506i		−	0.134260i	−0.997744	−	0.0671301i	$-0.978616\pi$
$881$		−	3.98506i		−	0.134260i	0.997744	−	0.0671301i	$-0.0213843\pi$
$882$	−23.7438	+	17.8390i	−0.799497	+	0.600670i
$883$	−53.0792			−1.78626			−0.893129	−	0.449801i	$-0.851495\pi$
$883$	−53.0792			−1.78626			−0.893129	+	0.449801i	$0.851495\pi$
$884$	−9.36806	−	3.37384i	−0.315082	−	0.113475i
$885$	1.85833	+	6.09481i	0.0624670	+	0.204875i
$886$	−34.3953	+	24.1707i	−1.15553	+	0.812029i
$887$	8.34390	−	14.4521i	0.280161	−	0.485253i	−0.691263	−	0.722603i	$-0.742946\pi$
$887$	8.34390	−	14.4521i	0.280161	−	0.485253i	0.971424	+	0.237350i	$0.0762789\pi$
$888$	0.541811	+	13.8059i	0.0181820	+	0.463296i
$889$	3.84642	+	3.98951i	0.129005	+	0.133804i
$890$	−12.4063	−	17.6544i	−0.415860	−	0.591777i
$891$	−4.64059	−	5.97689i	−0.155466	−	0.200233i
$892$	18.8304	+	22.2877i	0.630490	+	0.746246i
$893$	2.93966	−	1.69721i	0.0983720	−	0.0567951i
$894$	−41.2899	−	32.1971i	−1.38094	−	1.07683i
$895$	4.38101	+	7.58814i	0.146441	+	0.253643i
$896$	−10.0571	−	28.1932i	−0.335983	−	0.941868i
$897$	3.47867	−	3.72476i	0.116149	−	0.124366i
$898$	−17.1917	+	12.0812i	−0.573695	+	0.403154i
$899$	−16.3291	−	9.42763i	−0.544607	−	0.314429i
$900$	5.87513	+	23.3776i	0.195838	+	0.779252i
$901$	−17.3279	−	30.0129i	−0.577278	−	0.999874i
$902$	4.65546	−	0.415237i	0.155010	−	0.0138259i
$903$	−9.53437	+	17.1373i	−0.317284	+	0.570292i
$904$	32.1902	−	32.5186i	1.07063	−	1.08155i
$905$	3.87769	−	6.71635i	0.128899	−	0.223259i
$906$	−52.4953	+	21.2666i	−1.74404	+	0.706535i
$907$	−9.13856	−	15.8285i	−0.303441	−	0.525575i	0.673472	−	0.739213i	$-0.264802\pi$
$907$	−9.13856	−	15.8285i	−0.303441	−	0.525575i	−0.976913	+	0.213637i	$0.931469\pi$
$908$	6.46291	+	35.9414i	0.214479	+	1.19276i
$909$	1.38566	−	0.931589i	0.0459593	−	0.0308988i
$910$	−0.615988	+	3.18405i	−0.0204198	+	0.105550i
$911$	−9.23992	−	5.33467i	−0.306132	−	0.176746i	0.339062	−	0.940764i	$-0.389890\pi$
$911$	−9.23992	−	5.33467i	−0.306132	−	0.176746i	−0.645194	+	0.764018i	$0.723224\pi$
$912$	4.98149	+	6.52866i	0.164954	+	0.216185i
$913$			1.93212i			0.0639438i
$914$	−13.1861	+	9.26630i	−0.436158	+	0.306502i
$915$	17.7485	−	5.41158i	0.586747	−	0.178901i
$916$	20.7569	+	24.5678i	0.685827	+	0.811743i
$917$	−32.9463	+	8.18626i	−1.08798	+	0.270334i
$918$	23.4165	−	34.6731i	0.772861	−	1.14438i
$919$	−44.0949	+	25.4582i	−1.45456	+	0.839789i	−0.998735	−	0.0502824i	$-0.983988\pi$
$919$	−44.0949	+	25.4582i	−1.45456	+	0.839789i	−0.455822	+	0.890071i	$0.650655\pi$
$920$	−6.70523	−	6.63752i	−0.221065	−	0.218832i
$921$	7.20165	−	7.71112i	0.237303	−	0.254090i
$922$	0.348482	+	3.90703i	0.0114766	+	0.128671i
$923$	10.0126	−	5.78077i	0.329568	−	0.190276i
$924$	7.56151	−	1.48410i	0.248755	−	0.0488235i
$925$	9.81231	+	5.66514i	0.322627	+	0.186269i
$926$	−11.8452	+	25.5148i	−0.389259	+	0.838469i
$927$	51.6468	+	25.2867i	1.69630	+	0.830523i
$928$	−20.2862	−	13.9503i	−0.665928	−	0.457943i
$929$			14.8017i			0.485629i	0.970073	+	0.242814i	$0.0780706\pi$
$929$			14.8017i			0.485629i	−0.970073	+	0.242814i	$0.921929\pi$
$930$	6.46847	−	8.29524i	0.212109	−	0.272012i
$931$	3.88350	+	7.33226i	0.127276	+	0.240305i
$932$	−32.0512	+	5.76338i	−1.04987	+	0.188786i
$933$	−4.65664	−	4.34898i	−0.152451	−	0.142379i
$934$	7.86432	−	16.9398i	0.257328	−	0.554289i
$935$	−4.10944	−	2.37259i	−0.134393	−	0.0775919i
$936$	5.61689	+	4.84768i	0.183594	+	0.158451i
$937$		−	23.6965i		−	0.774131i	−0.922052	−	0.387066i	$-0.873489\pi$
$937$		−	23.6965i		−	0.774131i	0.922052	−	0.387066i	$-0.126511\pi$
$938$	−9.06439	+	46.8539i	−0.295963	+	1.52983i
$939$	−7.69128	+	8.23539i	−0.250996	+	0.268752i
$940$	−3.66404	−	4.33675i	−0.119508	−	0.141449i
$941$	2.96495			0.0966547			0.0483274	−	0.998832i	$-0.484611\pi$
$941$	2.96495			0.0966547			0.0483274	+	0.998832i	$0.484611\pi$
$942$	30.3350	+	4.23439i	0.988367	+	0.137964i
$943$	−13.2281			−0.430767
$944$	−9.46498	+	11.4362i	−0.308059	+	0.372216i
$945$	−12.3329	−	5.79718i	−0.401189	−	0.188582i
$946$	4.16323	−	2.92563i	0.135358	−	0.0951205i
$947$	11.5450			0.375163			0.187582	−	0.982249i	$-0.439935\pi$
$947$	11.5450			0.375163			0.187582	+	0.982249i	$0.439935\pi$
$948$	−2.53637	−	4.94575i	−0.0823774	−	0.160630i
$949$			4.22424i			0.137125i
$950$	6.70772	−	0.598286i	0.217627	−	0.0194110i
$951$	−5.17042	+	5.53619i	−0.167662	+	0.179523i
$952$	20.8154	+	37.1768i	0.674632	+	1.20491i
$953$	−37.1331			−1.20286			−0.601429	−	0.798926i	$-0.705402\pi$
$953$	−37.1331			−1.20286			−0.601429	+	0.798926i	$0.705402\pi$
$954$	4.04429	+	25.5052i	0.130939	+	0.825763i
$955$	−9.79079	−	5.65271i	−0.316822	−	0.182918i
$956$	8.33353	+	46.3443i	0.269526	+	1.49888i
$957$	4.32599	−	4.63202i	0.139839	−	0.149732i
$958$	9.46852	+	4.39576i	0.305914	+	0.142020i
$959$	−43.2203	−	12.4309i	−1.39566	−	0.401415i
$960$	9.27261	−	10.1328i	0.299272	−	0.327036i
$961$	−12.2310			−0.394550
$962$	3.47374	−	0.309836i	0.111998	−	0.00998950i
$963$	13.8236	−	9.29372i	0.445459	−	0.299486i
$964$	4.91259	+	27.3198i	0.158224	+	0.879912i
$965$	0.494548	−	0.856582i	0.0159201	−	0.0275744i
$966$	−21.6890	+	2.28245i	−0.697833	+	0.0734366i
$967$	−15.2147	+	8.78423i	−0.489273	+	0.282482i	−0.724273	−	0.689514i	$-0.757824\pi$
$967$	−15.2147	+	8.78423i	−0.489273	+	0.282482i	0.235000	+	0.971995i	$0.424491\pi$
$968$	28.1592	+	7.39227i	0.905070	+	0.237596i
$969$	−8.54293	−	7.97850i	−0.274438	−	0.256306i
$970$	−4.35371	+	9.37795i	−0.139789	+	0.301108i
$971$	3.90242	−	2.25306i	0.125235	−	0.0723043i	−0.436074	−	0.899911i	$-0.643631\pi$
$971$	3.90242	−	2.25306i	0.125235	−	0.0723043i	0.561309	+	0.827607i	$0.310298\pi$
$972$	−25.5458	+	17.8721i	−0.819382	+	0.573248i
$973$	15.8093	−	54.9666i	0.506824	−	1.76215i
$974$	−46.8458	+	4.17834i	−1.50104	+	0.133883i
$975$	5.81989	−	1.77450i	0.186386	−	0.0568296i
$976$	33.3030	+	27.5627i	1.06600	+	0.882260i
$977$	−16.3016			−0.521535			−0.260767	−	0.965402i	$-0.583976\pi$
$977$	−16.3016			−0.521535			−0.260767	+	0.965402i	$0.583976\pi$
$978$	−10.6995	−	26.4111i	−0.342132	−	0.844532i
$979$	11.2076	+	6.47070i	0.358196	+	0.206804i
$980$	10.9205	−	8.56323i	0.348842	−	0.273542i
$981$	−3.77584	+	7.71197i	−0.120553	+	0.246224i
$982$	3.03837	+	1.41056i	0.0969582	+	0.0450128i
$983$	17.8822	+	30.9729i	0.570355	+	0.987883i	0.996529	+	0.0832425i	$0.0265276\pi$
$983$	17.8822	+	30.9729i	0.570355	+	0.987883i	−0.426175	+	0.904641i	$0.640139\pi$
$984$	−0.755173	−	19.2426i	−0.0240740	−	0.613431i
$985$	11.4211	+	6.59398i	0.363907	+	0.210102i
$986$	31.7860	+	14.7567i	1.01227	+	0.469948i
$987$	−13.1216	+	0.208536i	−0.417666	+	0.00663777i
$988$	1.58340	−	1.33779i	0.0503747	−	0.0425606i
$989$	−12.4717	+	7.20056i	−0.396578	+	0.228964i
$990$	2.22569	+	2.74750i	0.0707370	+	0.0873212i
$991$	5.86472	+	3.38600i	0.186299	+	0.107560i	0.590249	−	0.807221i	$-0.299030\pi$
$991$	5.86472	+	3.38600i	0.186299	+	0.107560i	−0.403950	+	0.914781i	$0.632363\pi$
$992$	24.4312	+	1.92937i	0.775692	+	0.0612577i
$993$	−1.75684	−	1.64077i	−0.0557518	−	0.0520683i
$994$	−48.5725	−	9.39687i	−1.54063	−	0.298051i
$995$	−7.92789	−	13.7315i	−0.251331	−	0.435318i
$996$	7.95080	+	0.395746i	0.251931	+	0.0125397i
$997$	−0.453891	−	0.786162i	−0.0143749	−	0.0248980i	0.858748	−	0.512397i	$-0.171242\pi$
$997$	−0.453891	−	0.786162i	−0.0143749	−	0.0248980i	−0.873123	+	0.487499i	$0.837909\pi$
$998$	−0.240919	−	2.70108i	−0.00762616	−	0.0855012i
$999$	−2.32535	+	14.4690i	−0.0735708	+	0.457778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bf.b.115.18	yes	180
7.5	odd	6		504.2.cz.b.187.77	yes	180
8.3	odd	2	inner	504.2.bf.b.115.17	✓	180
9.4	even	3		504.2.cz.b.283.44	yes	180
56.19	even	6		504.2.cz.b.187.44	yes	180
63.40	odd	6	inner	504.2.bf.b.355.18	yes	180
72.67	odd	6		504.2.cz.b.283.77	yes	180
504.355	even	6	inner	504.2.bf.b.355.17	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.17	✓	180	8.3	odd	2	inner
504.2.bf.b.115.18	yes	180	1.1	even	1	trivial
504.2.bf.b.355.17	yes	180	504.355	even	6	inner
504.2.bf.b.355.18	yes	180	63.40	odd	6	inner
504.2.cz.b.187.44	yes	180	56.19	even	6
504.2.cz.b.187.77	yes	180	7.5	odd	6
504.2.cz.b.283.44	yes	180	9.4	even	3
504.2.cz.b.283.77	yes	180	72.67	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15708 + 0.813118i) q^{2} +(1.26585 + 1.18221i) q^{3} +(0.677678 - 1.88169i) q^{4} +(-0.495626 + 0.858449i) q^{5} +(-2.42597 - 0.338635i) q^{6} +(1.90467 - 1.83636i) q^{7} +(0.745907 + 2.72830i) q^{8} +(0.204739 + 2.99301i) q^{9} +O(q^{10})\)	\(q+(-1.15708 + 0.813118i) q^{2} +(1.26585 + 1.18221i) q^{3} +(0.677678 - 1.88169i) q^{4} +(-0.495626 + 0.858449i) q^{5} +(-2.42597 - 0.338635i) q^{6} +(1.90467 - 1.83636i) q^{7} +(0.745907 + 2.72830i) q^{8} +(0.204739 + 2.99301i) q^{9} +(-0.124541 - 1.39630i) q^{10} +(0.420385 + 0.728127i) q^{11} +(3.08240 - 1.58077i) q^{12} +(-0.437200 - 0.757253i) q^{13} +(-0.710686 + 3.67354i) q^{14} +(-1.64226 + 0.500730i) q^{15} +(-3.08151 - 2.55036i) q^{16} +(4.93085 + 2.84683i) q^{17} +(-2.67057 - 3.29668i) q^{18} +(-1.02651 + 0.592657i) q^{19} +(1.27946 + 1.51437i) q^{20} +(4.58200 - 0.0728195i) q^{21} +(-1.07847 - 0.500681i) q^{22} +(2.91432 + 1.68258i) q^{23} +(-2.28123 + 4.33543i) q^{24} +(2.00871 + 3.47919i) q^{25} +(1.12161 + 0.520708i) q^{26} +(-3.27920 + 4.03073i) q^{27} +(-2.16470 - 4.82846i) q^{28} +(-3.76915 - 2.17612i) q^{29} +(1.49307 - 1.91474i) q^{30} +4.33231 q^{31} +(5.63930 + 0.445345i) q^{32} +(-0.328660 + 1.41868i) q^{33} +(-8.02021 + 0.715351i) q^{34} +(0.632417 + 2.54521i) q^{35} +(5.77065 + 1.64304i) q^{36} +(2.44244 - 1.41014i) q^{37} +(0.705859 - 1.52043i) q^{38} +(0.341806 - 1.47543i) q^{39} +(-2.71180 - 0.711894i) q^{40} +(-3.40426 + 1.96545i) q^{41} +(-5.24254 + 3.80996i) q^{42} +(-2.13973 + 3.70612i) q^{43} +(1.65499 - 0.297597i) q^{44} +(-2.67082 - 1.30765i) q^{45} +(-4.74025 + 0.422799i) q^{46} -2.86374 q^{47} +(-0.885647 - 6.87136i) q^{48} +(0.255563 - 6.99533i) q^{49} +(-5.15323 - 2.39239i) q^{50} +(2.87615 + 9.43298i) q^{51} +(-1.72119 + 0.309501i) q^{52} +(-5.27128 - 3.04338i) q^{53} +(0.516846 - 7.33027i) q^{54} -0.833414 q^{55} +(6.43085 + 3.82677i) q^{56} +(-2.00006 - 0.463344i) q^{57} +(6.13065 - 0.546815i) q^{58} -3.71124i q^{59} +(-0.170704 + 3.42955i) q^{60} -10.8074 q^{61} +(-5.01284 + 3.52268i) q^{62} +(5.88620 + 5.32472i) q^{63} +(-6.88725 + 4.07011i) q^{64} +0.866751 q^{65} +(-0.773270 - 1.90877i) q^{66} +12.7544 q^{67} +(8.69838 - 7.34910i) q^{68} +(1.69991 + 5.57525i) q^{69} +(-2.80132 - 2.43079i) q^{70} +13.2223i q^{71} +(-8.01310 + 2.79109i) q^{72} +(-4.18378 - 2.41551i) q^{73} +(-1.67949 + 3.61764i) q^{74} +(-1.57042 + 6.77885i) q^{75} +(0.419552 + 2.33321i) q^{76} +(2.13780 + 0.614868i) q^{77} +(0.804201 + 1.98512i) q^{78} -1.60451i q^{79} +(3.71663 - 1.38129i) q^{80} +(-8.91616 + 1.22557i) q^{81} +(2.34086 - 5.04225i) q^{82} +(1.99016 + 1.14902i) q^{83} +(2.96809 - 8.67124i) q^{84} +(-4.88772 + 2.82193i) q^{85} +(-0.537672 - 6.02815i) q^{86} +(-2.19853 - 7.21057i) q^{87} +(-1.67298 + 1.69005i) q^{88} +(13.3302 - 7.69617i) q^{89} +(4.15363 - 0.658629i) q^{90} +(-2.22331 - 0.639463i) q^{91} +(5.14107 - 4.34360i) q^{92} +(5.48405 + 5.12172i) q^{93} +(3.31358 - 2.32856i) q^{94} -1.17495i q^{95} +(6.61200 + 7.23059i) q^{96} +(-6.38736 - 3.68775i) q^{97} +(5.39232 + 8.30198i) q^{98} +(-2.09322 + 1.40729i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

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