LMFDB - Embedded newform 504.2.bf.b.115.17

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			115.17
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.b.355.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15708 - 0.813118i) q^{2} +(1.26585 + 1.18221i) q^{3} +(0.677678 + 1.88169i) q^{4} +(0.495626 - 0.858449i) q^{5} +(-0.503410 - 2.39720i) q^{6} +(-1.90467 + 1.83636i) q^{7} +(0.745907 - 2.72830i) q^{8} +(0.204739 + 2.99301i) q^{9} +O(q^{10})$	\(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} +(-0.503410 - 2.39720i) q^{6} +(-1.90467 + 1.83636i) q^{7} +(0.745907 - 2.72830i) q^{8} +(0.204739 + 2.99301i) q^{9} +(-1.27150 + 0.590294i) q^{10} +(0.420385 + 0.728127i) q^{11} +(-1.36672 + 3.18309i) q^{12} +(0.437200 + 0.757253i) q^{13} +(3.69704 - 0.576095i) q^{14} +(1.64226 - 0.500730i) q^{15} +(-3.08151 + 2.55036i) q^{16} +(4.93085 + 2.84683i) q^{17} +(2.19677 - 3.62963i) q^{18} +(-1.02651 + 0.592657i) q^{19} +(1.95121 + 0.350862i) q^{20} +(-4.58200 + 0.0728195i) q^{21} +(0.105634 - 1.18433i) q^{22} +(-2.91432 - 1.68258i) q^{23} +(4.16964 - 2.57179i) q^{24} +(2.00871 + 3.47919i) q^{25} +(0.109860 - 1.23170i) q^{26} +(-3.27920 + 4.03073i) q^{27} +(-4.74621 - 2.33954i) q^{28} +(3.76915 + 2.17612i) q^{29} +(-2.30738 - 0.755964i) q^{30} -4.33231 q^{31} +(5.63930 - 0.445345i) q^{32} +(-0.328660 + 1.41868i) q^{33} +(-3.39059 - 7.30338i) q^{34} +(0.632417 + 2.54521i) q^{35} +(-5.49316 + 2.41355i) q^{36} +(-2.44244 + 1.41014i) q^{37} +(1.66966 + 0.148923i) q^{38} +(-0.341806 + 1.47543i) q^{39} +(-1.97242 - 1.99254i) q^{40} +(-3.40426 + 1.96545i) q^{41} +(5.36096 + 3.64145i) q^{42} +(-2.13973 + 3.70612i) q^{43} +(-1.08522 + 1.28447i) q^{44} +(2.67082 + 1.30765i) q^{45} +(2.00397 + 4.31657i) q^{46} +2.86374 q^{47} +(-6.91578 - 0.414636i) q^{48} +(0.255563 - 6.99533i) q^{49} +(0.504748 - 5.65902i) q^{50} +(2.87615 + 9.43298i) q^{51} +(-1.12863 + 1.33585i) q^{52} +(5.27128 + 3.04338i) q^{53} +(7.07177 - 1.99751i) q^{54} +0.833414 q^{55} +(3.58943 + 6.56627i) q^{56} +(-2.00006 - 0.463344i) q^{57} +(-2.59177 - 5.58271i) q^{58} -3.71124i q^{59} +(2.05514 + 2.75089i) 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} +(1.53384 - 1.37429i) q^{66} +12.7544 q^{67} +(-2.01532 + 11.2076i) q^{68} +(-1.69991 - 5.57525i) q^{69} +(1.33780 - 3.45925i) q^{70} -13.2223i q^{71} +(8.31853 + 1.67391i) q^{72} +(-4.18378 - 2.41551i) q^{73} +(3.97272 + 0.354341i) q^{74} +(-1.57042 + 6.77885i) q^{75} +(-1.81084 - 1.52995i) q^{76} +(-2.13780 - 0.614868i) q^{77} +(1.59520 - 1.42927i) q^{78} +1.60451i q^{79} +(0.662079 + 3.90934i) q^{80} +(-8.91616 + 1.22557i) q^{81} +(5.53715 + 0.493878i) q^{82} +(1.99016 + 1.14902i) q^{83} +(-3.24214 - 8.57254i) q^{84} +(4.88772 - 2.82193i) q^{85} +(5.48936 - 2.54844i) q^{86} +(2.19853 + 7.21057i) q^{87} +(2.30012 - 0.603820i) q^{88} +(13.3302 - 7.69617i) q^{89} +(-2.02708 - 3.68475i) q^{90} +(-2.22331 - 0.639463i) q^{91} +(1.19113 - 6.62409i) q^{92} +(-5.48405 - 5.12172i) q^{93} +(-3.31358 - 2.32856i) q^{94} +1.17495i q^{95} +(7.66498 + 6.10312i) q^{96} +(-6.38736 - 3.68775i) q^{97} +(-5.98374 + 7.88637i) 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	−0.733659	−	0.679518i	$-0.762189\pi$
$5$	0.495626	−	0.858449i	0.221651	−	0.383910i	0.955309	+	0.295608i	$0.0955222\pi$
$6$	−0.503410	−	2.39720i	−0.205516	−	0.978654i
$7$	−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
$10$	−1.27150	+	0.590294i	−0.402084	+	0.186667i
$11$	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	$0.792879\pi$
$12$	−1.36672	+	3.18309i	−0.394539	+	0.918879i
$13$	0.437200	+	0.757253i	0.121257	+	0.210024i	0.920264	−	0.391298i	$-0.127974\pi$
$13$	0.437200	+	0.757253i	0.121257	+	0.210024i	−0.799006	+	0.601323i	$0.794641\pi$
$14$	3.69704	−	0.576095i	0.988076	−	0.153968i
$15$	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	$0.424076\pi$
$18$	2.19677	−	3.62963i	0.517783	−	0.855512i
$19$	−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	$0.376747\pi$
$20$	1.95121	+	0.350862i	0.436304	+	0.0784551i
$21$	−4.58200	+	0.0728195i	−0.999874	+	0.0158905i
$22$	0.105634	−	1.18433i	0.0225213	−	0.252499i
$23$	−2.91432	−	1.68258i	−0.607678	−	0.350843i	0.164378	−	0.986397i	$-0.447438\pi$
$23$	−2.91432	−	1.68258i	−0.607678	−	0.350843i	−0.772056	+	0.635554i	$0.780772\pi$
$24$	4.16964	−	2.57179i	0.851124	−	0.524965i
$25$	2.00871	+	3.47919i	0.401742	+	0.695837i
$26$	0.109860	−	1.23170i	0.0215452	−	0.241556i
$27$	−3.27920	+	4.03073i	−0.631083	+	0.775715i
$28$	−4.74621	−	2.33954i	−0.896950	−	0.442132i
$29$	3.76915	+	2.17612i	0.699913	+	0.404095i	0.807315	−	0.590121i	$-0.200920\pi$
$29$	3.76915	+	2.17612i	0.699913	+	0.404095i	−0.107402	+	0.994216i	$0.534253\pi$
$30$	−2.30738	−	0.755964i	−0.421268	−	0.138020i
$31$	−4.33231			−0.778107			−0.389053	−	0.921215i	$-0.627198\pi$
$31$	−4.33231			−0.778107			−0.389053	+	0.921215i	$0.627198\pi$
$32$	5.63930	−	0.445345i	0.996896	−	0.0787265i
$33$	−0.328660	+	1.41868i	−0.0572123	+	0.246961i
$34$	−3.39059	−	7.30338i	−0.581482	−	1.25252i
$35$	0.632417	+	2.54521i	0.106898	+	0.430220i
$36$	−5.49316	+	2.41355i	−0.915526	+	0.402258i
$37$	−2.44244	+	1.41014i	−0.401535	+	0.231826i	−0.687146	−	0.726519i	$-0.741137\pi$
$37$	−2.44244	+	1.41014i	−0.401535	+	0.231826i	0.285611	+	0.958346i	$0.407803\pi$
$38$	1.66966	+	0.148923i	0.270855	+	0.0241585i
$39$	−0.341806	+	1.47543i	−0.0547328	+	0.236258i
$40$	−1.97242	−	1.99254i	−0.311867	−	0.315048i
$41$	−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	$0.432642\pi$
$42$	5.36096	+	3.64145i	0.827214	+	0.561887i
$43$	−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	$0.272471\pi$
$44$	−1.08522	+	1.28447i	−0.163604	+	0.193641i
$45$	2.67082	+	1.30765i	0.398142	+	0.194933i
$46$	2.00397	+	4.31657i	0.295469	+	0.636444i
$47$	2.86374			0.417719			0.208859	−	0.977946i	$-0.433025\pi$
$47$	2.86374			0.417719			0.208859	+	0.977946i	$0.433025\pi$
$48$	−6.91578	−	0.414636i	−0.998208	−	0.0598476i
$49$	0.255563	−	6.99533i	0.0365091	−	0.999333i
$50$	0.504748	−	5.65902i	0.0713822	−	0.800307i
$51$	2.87615	+	9.43298i	0.402741	+	1.32088i
$52$	−1.12863	+	1.33585i	−0.156513	+	0.185249i
$53$	5.27128	+	3.04338i	0.724066	+	0.418040i	0.816247	−	0.577702i	$-0.196051\pi$
$53$	5.27128	+	3.04338i	0.724066	+	0.418040i	−0.0921812	+	0.995742i	$0.529384\pi$
$54$	7.07177	−	1.99751i	0.962346	−	0.271827i
$55$	0.833414			0.112378
$56$	3.58943	+	6.56627i	0.479658	+	0.877455i
$57$	−2.00006	−	0.463344i	−0.264914	−	0.0613714i
$58$	−2.59177	−	5.58271i	−0.340316	−	0.733046i
$59$		−	3.71124i		−	0.483162i	−0.970381	−	0.241581i	$-0.922334\pi$
$59$		−	3.71124i		−	0.483162i	0.970381	−	0.241581i	$-0.0776659\pi$
$60$	2.05514	+	2.75089i	0.265317	+	0.355138i
$61$	10.8074			1.38374			0.691871	−	0.722021i	$-0.256787\pi$
$61$	10.8074			1.38374			0.691871	+	0.722021i	$0.256787\pi$
$62$	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
$66$	1.53384	−	1.37429i	0.188803	−	0.169164i
$67$	12.7544			1.55820			0.779100	−	0.626900i	$-0.215676\pi$
$67$	12.7544			1.55820			0.779100	+	0.626900i	$0.215676\pi$
$68$	−2.01532	+	11.2076i	−0.244393	+	1.35912i
$69$	−1.69991	−	5.57525i	−0.204645	−	0.671181i
$70$	1.33780	−	3.45925i	0.159898	−	0.413460i
$71$		−	13.2223i		−	1.56919i	−0.620007	−	0.784596i	$-0.712870\pi$
$71$		−	13.2223i		−	1.56919i	0.620007	−	0.784596i	$-0.287130\pi$
$72$	8.31853	+	1.67391i	0.980349	+	0.197272i
$73$	−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	$0.757901\pi$
$74$	3.97272	+	0.354341i	0.461819	+	0.0411913i
$75$	−1.57042	+	6.77885i	−0.181337	+	0.782754i
$76$	−1.81084	−	1.52995i	−0.207718	−	0.175497i
$77$	−2.13780	−	0.614868i	−0.243625	−	0.0700707i
$78$	1.59520	−	1.42927i	0.180621	−	0.161832i
$79$			1.60451i			0.180522i	0.995918	+	0.0902610i	$0.0287701\pi$
$79$			1.60451i			0.180522i	−0.995918	+	0.0902610i	$0.971230\pi$
$80$	0.662079	+	3.90934i	0.0740226	+	0.437078i
$81$	−8.91616	+	1.22557i	−0.990685	+	0.136175i
$82$	5.53715	+	0.493878i	0.611476	+	0.0545397i
$83$	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	$0.626414\pi$
$84$	−3.24214	−	8.57254i	−0.353747	−	0.935341i
$85$	4.88772	−	2.82193i	0.530148	−	0.306081i
$86$	5.48936	−	2.54844i	0.591933	−	0.274805i
$87$	2.19853	+	7.21057i	0.235707	+	0.773055i
$88$	2.30012	−	0.603820i	0.245193	−	0.0643675i
$89$	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	$0.0296346\pi$
$90$	−2.02708	−	3.68475i	−0.213673	−	0.388407i
$91$	−2.22331	−	0.639463i	−0.233066	−	0.0670339i
$92$	1.19113	−	6.62409i	0.124184	−	0.690610i
$93$	−5.48405	−	5.12172i	−0.568669	−	0.531098i
$94$	−3.31358	−	2.32856i	−0.341769	−	0.240172i
$95$			1.17495i			0.120547i
$96$	7.66498	+	6.10312i	0.782304	+	0.622897i
$97$	−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	$0.788830\pi$
$98$	−5.98374	+	7.88637i	−0.604449	+	0.796644i
$99$	−2.09322	+	1.40729i	−0.210377	+	0.141438i
$100$	−5.18549	+	6.13753i	−0.518549	+	0.613753i
$101$	0.278283	+	0.482001i	0.0276902	+	0.0479609i	0.879538	−	0.475828i	$-0.157851\pi$
$101$	0.278283	+	0.482001i	0.0276902	+	0.0479609i	−0.851848	+	0.523789i	$0.824518\pi$
$102$	4.34219	−	13.2534i	0.429941	−	1.31228i
$103$	−9.58414	+	16.6002i	−0.944353	+	1.63567i	−0.187312	+	0.982300i	$0.559978\pi$
$103$	−9.58414	+	16.6002i	−0.944353	+	1.63567i	−0.757041	+	0.653367i	$0.773356\pi$
$104$	2.39212	−	0.627973i	0.234567	−	0.0615779i
$105$	−2.20845	+	3.96950i	−0.215522	+	0.387384i
$106$	−3.62468	−	7.80761i	−0.352060	−	0.758342i
$107$	−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	$0.919824\pi$
$108$	−9.80683	−	3.43890i	−0.943663	−	0.330909i
$109$	−2.47877	−	1.43112i	−0.237423	−	0.137076i	0.376569	−	0.926389i	$-0.377104\pi$
$109$	−2.47877	−	1.43112i	−0.237423	−	0.137076i	−0.613992	+	0.789312i	$0.710437\pi$
$110$	−0.964328	−	0.677664i	−0.0919451	−	0.0646127i
$111$	−4.75885	−	1.10246i	−0.451690	−	0.104641i
$112$	1.18589	−	10.5164i	0.112056	−	0.993702i
$113$	−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	$-0.441919\pi$
$114$	1.93748	+	2.16241i	0.181461	+	0.202528i
$115$	−2.88883	+	1.66786i	−0.269384	+	0.155529i
$116$	−1.54051	+	8.56707i	−0.143033	+	0.795432i
$117$	−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
$120$	−0.141171	−	4.85407i	−0.0128871	−	0.443114i
$121$	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
$126$	2.48118	+	10.9473i	0.221041	+	0.975264i
$127$		−	2.09459i		−	0.185865i	−0.995672	−	0.0929324i	$-0.970376\pi$
$127$		−	2.09459i		−	0.185865i	0.995672	−	0.0929324i	$-0.0296240\pi$
$128$	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	$0.856070\pi$
$132$	−2.89224	+	0.342974i	−0.251738	+	0.0298521i
$133$	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
$136$	11.4450	−	11.3294i	0.981398	−	0.971487i
$137$	−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	$-0.425344\pi$
$138$	−2.56640	+	7.83325i	−0.218466	+	0.666810i
$139$	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	$-0.0358985\pi$
$140$	−4.36073	+	2.91485i	−0.368549	+	0.246349i
$141$	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
$144$	−8.26414	−	8.70080i	−0.688678	−	0.725067i
$145$	3.73618	−	2.15708i	0.310272	−	0.179136i
$146$	2.87689	+	6.19685i	0.238093	+	0.512855i
$147$	8.59349	−	8.55289i	0.708779	−	0.705431i
$148$	−4.30864	−	3.64029i	−0.354168	−	0.299230i
$149$	−18.5119	−	10.6878i	−1.51655	−	0.875581i	−0.999811	−	0.0194384i	$-0.993812\pi$
$149$	−18.5119	−	10.6878i	−1.51655	−	0.875581i	−0.516740	−	0.856143i	$-0.672854\pi$
$150$	7.32911	−	6.56674i	0.598419	−	0.536172i
$151$	−20.0250	+	11.5615i	−1.62962	+	0.940859i	−0.645408	+	0.763838i	$0.723313\pi$
$151$	−20.0250	+	11.5615i	−1.62962	+	0.940859i	−0.984207	+	0.177021i	$0.943354\pi$
$152$	0.851265	+	3.24270i	0.0690467	+	0.263018i
$153$	−7.51104	+	15.3409i	−0.607231	+	1.24024i
$154$	1.97365	+	2.44974i	0.159041	+	0.197405i
$155$	−2.14721	+	3.71907i	−0.172468	+	0.298723i
$156$	−3.00794	+	0.356693i	−0.240828	+	0.0285583i
$157$	12.5043			0.997950			0.498975	−	0.866616i	$-0.333710\pi$
$157$	12.5043			0.997950			0.498975	+	0.866616i	$0.333710\pi$
$158$	1.30466	−	1.85655i	0.103793	−	0.147700i
$159$	3.07472	+	10.0842i	0.243841	+	0.799732i
$160$	2.41268	−	5.06178i	0.190739	−	0.400169i
$161$	8.64066	−	2.14697i	0.680979	−	0.169205i
$162$	11.3133	+	5.83181i	0.888854	+	0.458190i
$163$	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	$0.682758\pi$
$164$	−6.00535	−	5.07381i	−0.468939	−	0.396198i
$165$	1.05498	+	0.985274i	0.0821297	+	0.0767035i
$166$	−1.36849	−	2.94774i	−0.106215	−	0.228789i
$167$	1.98369	+	3.43585i	0.153503	+	0.265874i	0.932513	−	0.361137i	$-0.117611\pi$
$167$	1.98369	+	3.43585i	0.153503	+	0.265874i	−0.779010	+	0.627011i	$0.784278\pi$
$168$	−3.21907	+	12.5554i	−0.248357	+	0.968669i
$169$	6.11771	−	10.5962i	0.470593	−	0.815091i
$170$	−7.95005	−	0.709093i	−0.609741	−	0.0543850i
$171$	−1.98399	−	2.95102i	−0.151720	−	0.225670i
$172$	−8.42382	−	1.51475i	−0.642310	−	0.115499i
$173$	19.4208			1.47654			0.738268	−	0.674508i	$-0.235644\pi$
$173$	19.4208			1.47654			0.738268	+	0.674508i	$0.235644\pi$
$174$	3.31917	−	10.1309i	0.251626	−	0.768021i
$175$	−10.2150	−	2.93800i	−0.772180	−	0.222092i
$176$	−3.15240	−	1.17160i	−0.237621	−	0.0883125i
$177$	4.38748	−	4.69786i	0.329783	−	0.353113i
$178$	−21.6820	−	1.93389i	−1.62513	−	0.144951i
$179$	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	$0.0595026\pi$
$180$	−0.650642	+	5.91182i	−0.0484960	+	0.440641i
$181$	7.82382			0.581540			0.290770	−	0.956793i	$-0.406089\pi$
$181$	7.82382			0.581540			0.290770	+	0.956793i	$0.406089\pi$
$182$	2.05260	+	2.54773i	0.152149	+	0.188850i
$183$	13.6805	+	12.7766i	1.01129	+	0.944476i
$184$	−6.76441	+	6.69609i	−0.498679	+	0.493643i
$185$			2.79562i			0.205538i
$186$	2.18093	+	10.3854i	0.159913	+	0.761497i
$187$			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	$-0.864612\pi$
$191$		−	11.4052i		−	0.825251i	0.910901	−	0.412626i	$-0.135388\pi$
$192$	−3.90646	−	13.2943i	−0.281924	−	0.959437i
$193$	−0.997825			−0.0718250			−0.0359125	−	0.999355i	$-0.511434\pi$
$193$	−0.997825			−0.0718250			−0.0359125	+	0.999355i	$0.511434\pi$
$194$	4.39213	+	9.46071i	0.315337	+	0.679239i
$195$	1.09717	+	1.02469i	0.0785703	+	0.0733792i
$196$	13.3362	−	4.25969i	0.952588	−	0.304264i
$197$			13.3043i			0.947896i	0.880553	+	0.473948i	$0.157171\pi$
$197$			13.3043i			0.947896i	−0.880553	+	0.473948i	$0.842829\pi$
$198$	3.56632	+	0.0736857i	0.253447	+	0.00523661i
$199$	7.99785	−	13.8527i	0.566953	−	0.981991i	−0.429912	−	0.902871i	$-0.641455\pi$
$199$	7.99785	−	13.8527i	0.566953	−	0.981991i	0.996865	−	0.0791205i	$-0.0252112\pi$
$200$	10.9906	−	2.88522i	0.777151	−	0.204016i
$201$	16.1451	+	15.0785i	1.13879	+	1.06355i
$202$	0.0699270	−	0.783992i	0.00492005	−	0.0551615i
$203$	−11.1751	+	2.77672i	−0.784341	+	0.194887i
$204$	−15.8008	+	11.8045i	−1.10628	+	0.826483i
$205$			3.89651i			0.272144i
$206$	24.5876	−	11.4148i	1.71310	−	0.795305i
$207$	4.43931	−	9.06707i	0.308553	−	0.630205i
$208$	−3.27850	−	1.21846i	−0.227323	−	0.0844851i
$209$	−0.863060	−	0.498288i	−0.0596991	−	0.0344673i
$210$	5.78303	−	2.79732i	0.399067	−	0.193033i
$211$	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	$0.564980\pi$
$212$	−2.15446	+	11.9813i	−0.147969	+	0.822882i
$213$	15.6315	−	16.7374i	1.07106	−	1.14682i
$214$	−0.697607	+	7.82127i	−0.0476874	+	0.534651i
$215$	2.12101	+	3.67370i	0.144652	+	0.250545i
$216$	8.55107	+	11.9532i	0.581827	+	0.813313i
$217$	8.25165	−	7.95569i	0.560158	−	0.540067i
$218$	1.70447	+	3.67145i	0.115441	+	0.248662i
$219$	−2.44038	−	8.00380i	−0.164906	−	0.540846i
$220$	0.564786	+	1.56823i	0.0380779	+	0.105730i
$221$			4.97854i			0.334893i
$222$	4.60995	+	5.14514i	0.309399	+	0.345319i
$223$	7.29437	−	12.6342i	0.488467	−	0.846050i	−0.511445	−	0.859316i	$-0.670890\pi$
$223$	7.29437	−	12.6342i	0.488467	−	0.846050i	0.999912	+	0.0132661i	$0.00422284\pi$
$224$	−9.92321	+	11.2040i	−0.663022	+	0.748600i
$225$	−10.0020	+	6.72441i	−0.666798	+	0.448294i
$226$	−2.03253	+	22.7878i	−0.135202	+	1.51582i
$227$	−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	$0.540538\pi$
$228$	−0.483525	−	4.07748i	−0.0320222	−	0.270038i
$229$	8.04062	−	13.9268i	0.531339	−	0.920306i	−0.467992	−	0.883733i	$-0.655022\pi$
$229$	8.04062	−	13.9268i	0.531339	−	0.920306i	0.999331	−	0.0365734i	$-0.0116443\pi$
$230$	4.69878	+	0.419101i	0.309828	+	0.0276347i
$231$	−1.97922	−	3.30567i	−0.130223	−	0.217497i
$232$	8.74854	−	8.66019i	0.574370	−	0.568569i
$233$	−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	$-0.345736\pi$
$234$	3.70897	+	0.0766331i	0.242463	+	0.00500967i
$235$	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
$238$	19.8696	+	7.68421i	1.28796	+	0.498093i
$239$	20.3895	−	11.7719i	1.31889	−	0.761461i	0.335340	−	0.942097i	$-0.391149\pi$
$239$	20.3895	−	11.7719i	1.31889	−	0.761461i	0.983550	+	0.180636i	$0.0578155\pi$
$240$	−3.78359	+	5.73135i	−0.244230	+	0.369957i
$241$	−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	$0.480845\pi$
$242$	−13.2032	+	6.12958i	−0.848734	+	0.394024i
$243$	−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
$246$	6.42531	+	7.17127i	0.409663	+	0.457223i
$247$	−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	$-0.167221\pi$
$252$	6.03053	−	14.6844i	0.379888	−	0.925033i
$253$		−	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	$0.519455\pi$
$258$	9.96149	+	3.26367i	0.620175	+	0.203187i
$259$	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
$262$	7.64101	+	16.4588i	0.472063	+	1.01683i
$263$	−3.99033	+	2.30382i	−0.246055	+	0.142060i	−0.617956	−	0.786212i	$-0.712039\pi$
$263$	−3.99033	+	2.30382i	−0.246055	+	0.142060i	0.371902	+	0.928272i	$0.378706\pi$
$264$	3.62544	+	1.95489i	0.223131	+	0.120315i
$265$	5.22517	−	3.01675i	0.320980	−	0.185318i
$266$	−3.45363	+	2.78245i	−0.211756	+	0.170603i
$267$	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	$0.396307\pi$
$269$	−10.8324	+	18.7623i	−0.660464	+	1.14396i	−0.980494	+	0.196549i	$0.937026\pi$
$270$	1.79019	−	7.06078i	0.108948	−	0.429705i
$271$	9.32142	+	16.1452i	0.566236	+	0.980749i	0.996934	+	0.0782528i	$0.0249341\pi$
$271$	9.32142	+	16.1452i	0.566236	+	0.980749i	−0.430698	+	0.902496i	$0.641733\pi$
$272$	−22.4549	+	3.80292i	−1.36153	+	0.230586i
$273$	−2.05839	−	3.43789i	−0.124580	−	0.208071i
$274$	−2.13563	+	23.9437i	−0.129018	+	1.44649i
$275$	−1.68886	+	2.92519i	−0.101842	+	0.176396i
$276$	9.33889	−	6.97692i	0.562135	−	0.419961i
$277$	−23.2301	+	13.4119i	−1.39576	+	0.805843i	−0.993945	−	0.109878i	$-0.964954\pi$
$277$	−23.2301	+	13.4119i	−1.39576	+	0.805843i	−0.401815	+	0.915721i	$0.631621\pi$
$278$	−30.4511	−	2.71604i	−1.82634	−	0.162897i
$279$	−0.886995	−	12.9666i	−0.0531030	−	0.776293i
$280$	7.41583	+	0.173069i	0.443181	+	0.0103429i
$281$	−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	$0.951971\pi$
$282$	−1.44163	−	6.86496i	−0.0858480	−	0.408802i
$283$			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
$286$	0.943017	−	0.437795i	0.0557618	−	0.0258874i
$287$	2.87473	−	9.99498i	0.169690	−	0.589985i
$288$	2.48750	+	16.7873i	0.146578	+	0.989199i
$289$	7.70888	+	13.3522i	0.453464	+	0.785422i
$290$	−6.07702	−	0.542031i	−0.356855	−	0.0318292i
$291$	−3.72572	−	12.2194i	−0.218406	−	0.716311i
$292$	1.70998	−	9.50952i	0.100069	−	0.556502i
$293$	15.2512	+	26.4159i	0.890986	+	1.54323i	0.838696	+	0.544600i	$0.183319\pi$
$293$	15.2512	+	26.4159i	0.890986	+	1.54323i	0.0522899	+	0.998632i	$0.483348\pi$
$294$	−16.8979	+	2.90888i	−0.985504	+	0.169649i
$295$	−3.18591	−	1.83939i	−0.185491	−	0.107093i
$296$	2.02546	+	7.71555i	0.117728	+	0.448457i
$297$	−4.31341	−	0.693221i	−0.250290	−	0.0402247i
$298$	12.7293	+	27.4190i	0.737387	+	1.58834i
$299$		−	2.94250i		−	0.170169i
$300$	−13.8199	+	1.63882i	−0.797893	+	0.0946175i
$301$	−2.73029	−	10.9883i	−0.157371	−	0.633354i
$302$	32.5715	+	2.90516i	1.87428	+	0.167173i
$303$	−0.217564	+	0.939131i	−0.0124987	+	0.0539516i
$304$	1.65172	−	4.44425i	0.0947325	−	0.254895i
$305$	5.35642	−	9.27759i	0.306708	−	0.531233i
$306$	21.1649	−	11.6434i	1.20992	−	0.665606i
$307$		−	6.09166i		−	0.347670i	−0.984775	−	0.173835i	$-0.944384\pi$
$307$		−	6.09166i		−	0.347670i	0.984775	−	0.173835i	$-0.0556159\pi$
$308$	−0.291750	−	4.43936i	−0.0166240	−	0.252956i
$309$	−31.7571	+	9.68283i	−1.80660	+	0.550837i
$310$	5.50854	−	2.55734i	0.312864	−	0.145247i
$311$	3.67867			0.208598			0.104299	−	0.994546i	$-0.466740\pi$
$311$	3.67867			0.208598			0.104299	+	0.994546i	$0.466740\pi$
$312$	3.77046	+	2.03308i	0.213460	+	0.115101i
$313$			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	$-0.960806\pi$
$317$		−	4.37351i		−	0.245641i	0.992429	−	0.122820i	$-0.0391939\pi$
$318$	4.64197	−	14.1684i	0.260309	−	0.794524i
$319$			3.65923i			0.204877i
$320$	−6.90749	+	3.89510i	−0.386140	+	0.217743i
$321$	2.17047	−	9.36896i	0.121144	−	0.522924i
$322$	−11.7437	−	4.54166i	−0.654450	−	0.253097i
$323$	−6.74878			−0.375512
$324$	−8.34843	−	15.9469i	−0.463802	−	0.885939i
$325$	−1.75642	+	3.04220i	−0.0974284	+	0.168751i
$326$	1.46163	−	16.3871i	0.0809520	−	0.907599i
$327$	−1.44586	−	4.74201i	−0.0799560	−	0.262234i
$328$	2.82308	+	10.7539i	0.155878	+	0.593783i
$329$	−5.45448	+	5.25885i	−0.300715	+	0.289930i
$330$	−0.419549	−	1.99786i	−0.0230954	−	0.109979i
$331$	−1.38788			−0.0762848			−0.0381424	−	0.999272i	$-0.512144\pi$
$331$	−1.38788			−0.0762848			−0.0381424	+	0.999272i	$0.512144\pi$
$332$	−0.813410	+	4.52353i	−0.0446417	+	0.248261i
$333$	−4.72063	−	7.02153i	−0.258689	−	0.384777i
$334$	0.498461	−	5.58854i	0.0272746	−	0.305791i
$335$	6.32142	−	10.9490i	0.345376	−	0.598209i
$336$	13.9337	−	11.9101i	0.760148	−	0.649751i
$337$	−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	$0.956895\pi$
$338$	−15.6946	+	7.28624i	−0.853676	+	0.396319i
$339$	6.32381	−	27.2972i	0.343462	−	1.48258i
$340$	8.62229	+	7.28481i	0.467609	+	0.395074i
$341$	−1.82124	−	3.15448i	−0.0986256	−	0.170825i
$342$	−0.103882	+	5.02779i	−0.00561729	+	0.271872i
$343$	12.3592	+	13.7931i	0.667333	+	0.744759i
$344$	8.51538	+	8.60225i	0.459119	+	0.463802i
$345$	−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	$0.691334\pi$
$348$	−12.0782	+	9.02339i	−0.647457	+	0.483704i
$349$	15.4247	−	26.7164i	0.825665	−	1.43009i	−0.0757442	−	0.997127i	$-0.524133\pi$
$349$	15.4247	−	26.7164i	0.825665	−	1.43009i	0.901410	−	0.432967i	$-0.142533\pi$
$350$	9.43062	+	11.7055i	0.504088	+	0.625685i
$351$	−4.48595	−	0.720950i	−0.239442	−	0.0384814i
$352$	2.69494	+	3.91891i	0.143641	+	0.208879i
$353$	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	$0.272512\pi$
$354$	−8.89658	+	1.86827i	−0.472848	+	0.0992975i
$355$	−11.3506	−	6.55329i	−0.602429	−	0.347813i
$356$	23.5153	+	19.8677i	1.24631	+	1.05299i
$357$	−22.8005	−	12.6851i	−1.20673	−	0.671367i
$358$	−11.3384	+	5.26386i	−0.599255	+	0.278204i
$359$	−6.96243	+	4.01976i	−0.367463	+	0.212155i	−0.672350	−	0.740234i	$-0.734715\pi$
$359$	−6.96243	+	4.01976i	−0.367463	+	0.212155i	0.304886	+	0.952389i	$0.401382\pi$
$360$	5.55985	−	6.31141i	0.293030	−	0.332640i
$361$	−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
$364$	−0.303420	−	4.61693i	−0.0159035	−	0.241993i
$365$	−4.14719	+	2.39438i	−0.217074	+	0.125328i
$366$	−5.44054	−	25.9075i	−0.284381	−	1.35421i
$367$	9.76184	+	16.9080i	0.509564	+	0.882590i	0.999939	+	0.0110787i	$0.00352652\pi$
$367$	9.76184	+	16.9080i	0.509564	+	0.882590i	−0.490375	+	0.871512i	$0.663140\pi$
$368$	13.2717	−	2.24767i	0.691834	−	0.117168i
$369$	−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
$372$	5.92107	−	13.7902i	0.306993	−	0.714986i
$373$	30.5547	+	17.6408i	1.58206	+	0.913404i	0.994558	+	0.104182i	$0.0332224\pi$
$373$	30.5547	+	17.6408i	1.58206	+	0.913404i	0.587503	+	0.809222i	$0.300111\pi$
$374$	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
$378$	−9.80127	+	16.7909i	−0.504123	+	0.863632i
$379$	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	$-0.488525\pi$
$383$	17.2901	−	29.9474i	0.883484	−	1.53024i	0.847441	−	0.530889i	$-0.178142\pi$
$384$	−6.28978	+	18.5591i	−0.320974	+	0.947088i
$385$	−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
$388$	2.61062	−	14.5181i	0.132534	−	0.737047i
$389$	−32.5526	+	18.7943i	−1.65048	+	0.952907i	−0.673611	+	0.739086i	$0.735258\pi$
$389$	−32.5526	+	18.7943i	−1.65048	+	0.952907i	−0.976873	+	0.213822i	$0.931409\pi$
$390$	−0.436331	−	2.07778i	−0.0220945	−	0.105212i
$391$	−9.58006	−	16.5932i	−0.484484	−	0.839152i
$392$	−18.8947	−	5.91512i	−0.954329	−	0.298759i
$393$	−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
$396$	−4.06661	−	2.98510i	−0.204355	−	0.150007i
$397$	3.72508	+	6.45203i	0.186956	+	0.323818i	0.944234	−	0.329275i	$-0.106804\pi$
$397$	3.72508	+	6.45203i	0.186956	+	0.323818i	−0.757278	+	0.653093i	$0.773471\pi$
$398$	−20.5180	+	9.52550i	−1.02848	+	0.477470i
$399$	4.66032	−	2.79030i	0.233308	−	0.139690i
$400$	−15.0630	−	5.59821i	−0.753151	−	0.279910i
$401$	−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	$0.299761\pi$
$402$	−6.42070	−	30.5749i	−0.320235	−	1.52494i
$403$	−1.89409	−	3.28066i	−0.0943513	−	0.163421i
$404$	−0.718390	+	0.850284i	−0.0357412	+	0.0423032i
$405$	−3.36699	+	8.26150i	−0.167307	+	0.410517i
$406$	15.1883	+	5.87381i	0.753785	+	0.291512i
$407$	−2.05353	−	1.18561i	−0.101790	−	0.0587683i
$408$	27.8813	−	0.810871i	1.38033	−	0.0401441i
$409$		−	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
$412$	−37.7314	−	6.78477i	−1.85889	−	0.334262i
$413$	6.81517	+	7.06869i	0.335352	+	0.347828i
$414$	−12.5092	+	6.88166i	−0.614796	+	0.338215i
$415$	1.97275	−	1.13897i	0.0968385	−	0.0559097i
$416$	2.80274	+	4.07567i	0.137416	+	0.199826i
$417$	36.4769	+	8.45043i	1.78628	+	0.413819i
$418$	0.593464	+	1.27833i	0.0290273	+	0.0625252i
$419$	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	$0.222827\pi$
$420$	−8.96599	−	1.46556i	−0.437495	−	0.0715121i
$421$	−25.5483	−	14.7503i	−1.24515	−	0.718886i	−0.275010	−	0.961441i	$-0.588681\pi$
$421$	−25.5483	−	14.7503i	−1.24515	−	0.718886i	−0.970138	+	0.242555i	$0.922014\pi$
$422$	2.72542	−	30.5562i	0.132671	−	1.48745i
$423$	0.586319	+	8.57118i	0.0285078	+	0.416745i
$424$	12.2351	−	12.1116i	0.594190	−	0.588190i
$425$			22.8738i			1.10954i
$426$	−31.6964	+	6.65621i	−1.53570	+	0.322494i
$427$	−20.5845	+	19.8462i	−0.996155	+	0.960427i
$428$	7.16680	−	8.48261i	0.346421	−	0.410023i
$429$	−1.21799	+	0.371370i	−0.0588052	+	0.0179299i
$430$	0.532968	−	5.97541i	0.0257020	−	0.288160i
$431$	2.30954	+	1.33341i	0.111247	+	0.0642283i	0.554591	−	0.832123i	$-0.312875\pi$
$431$	2.30954	+	1.33341i	0.111247	+	0.0642283i	−0.443344	+	0.896351i	$0.646208\pi$
$432$	−0.174924	−	20.7839i	−0.00841603	−	0.999965i
$433$			39.6555i			1.90572i	0.303410	+	0.952860i	$0.401875\pi$
$433$			39.6555i			1.90572i	−0.303410	+	0.952860i	$0.598125\pi$
$434$	−16.0167	+	2.49582i	−0.768828	+	0.119803i
$435$	7.27956	+	1.68642i	0.349028	+	0.0808578i
$436$	1.01311	−	5.63411i	0.0485193	−	0.269825i
$437$	3.98878			0.190809
$438$	−3.68431	+	11.2454i	−0.176043	+	0.537325i
$439$	20.2071			0.964430			0.482215	−	0.876053i	$-0.339832\pi$
$439$	20.2071			0.964430			0.482215	+	0.876053i	$0.339832\pi$
$440$	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	$0.250426\pi$
$444$	−1.15048	−	9.70179i	−0.0545992	−	0.460426i
$445$		−	15.2577i		−	0.723284i
$446$	−18.7133	+	8.68765i	−0.886101	+	0.411372i
$447$	−10.7979	−	35.4141i	−0.510723	−	1.67503i
$448$	20.5922	−	4.89523i	0.972888	−	0.231278i
$449$	14.8578			0.701184			0.350592	−	0.936528i	$-0.385980\pi$
$449$	14.8578			0.701184			0.350592	+	0.936528i	$0.385980\pi$
$450$	17.0408	+	0.352090i	0.803312	+	0.0165977i
$451$	−2.86219	−	1.65249i	−0.134775	−	0.0778126i
$452$	20.8810	−	24.7147i	0.982160	−	1.16248i
$453$	−39.0168	−	9.03884i	−1.83317	−	0.424682i
$454$	25.7199	+	2.29405i	1.20710	+	0.107665i
$455$	−1.65088	+	1.59167i	−0.0773943	+	0.0746185i
$456$	−2.75600	+	5.11114i	−0.129061	+	0.239351i
$457$	11.3960			0.533083			0.266541	−	0.963824i	$-0.414119\pi$
$457$	11.3960			0.533083			0.266541	+	0.963824i	$0.414119\pi$
$458$	−20.6278	+	9.57643i	−0.963872	+	0.447477i
$459$	−27.6441	+	10.5396i	−1.29032	+	0.491947i
$460$	−5.09610	−	4.30560i	−0.237607	−	0.200750i
$461$	−1.38683	+	2.40206i	−0.0645910	+	0.111875i	−0.896512	−	0.443018i	$-0.853908\pi$
$461$	−1.38683	+	2.40206i	−0.0645910	+	0.111875i	0.831921	+	0.554893i	$0.187241\pi$
$462$	−0.397774	+	5.43427i	−0.0185061	+	0.252825i
$463$	−17.2262	+	9.94557i	−0.800571	+	0.462210i	−0.843671	−	0.536861i	$-0.819610\pi$
$463$	−17.2262	+	9.94557i	−0.800571	+	0.462210i	0.0430998	+	0.999071i	$0.486277\pi$
$464$	−17.1645	+	2.90695i	−0.796843	+	0.134952i
$465$	−7.11478	+	2.16932i	−0.329940	+	0.100600i
$466$	−2.04575	+	22.9361i	−0.0947676	+	1.06249i
$467$	−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	$0.432175\pi$
$468$	−4.22928	−	3.10450i	−0.195498	−	0.143506i
$469$	−24.2930	+	23.4217i	−1.12175	+	1.08151i
$470$	−3.64124	+	1.69045i	−0.167958	+	0.0779745i
$471$	15.8285	+	14.7827i	0.729339	+	0.681152i
$472$	−10.1254	−	2.76824i	−0.466058	−	0.127418i
$473$	−3.59804			−0.165438
$474$	3.84635	−	0.807728i	0.176669	−	0.0371002i
$475$	−4.12393	−	2.38095i	−0.189219	−	0.109246i
$476$	−16.7426	−	25.0476i	−0.767396	−	1.14806i
$477$	−8.02960	+	16.4001i	−0.367650	+	0.750908i
$478$	−33.1643	−	2.95804i	−1.51690	−	0.135298i
$479$	3.69079	+	6.39264i	0.168637	+	0.292087i	0.937941	−	0.346796i	$-0.112730\pi$
$479$	3.69079	+	6.39264i	0.168637	+	0.292087i	−0.769304	+	0.638883i	$0.779397\pi$
$480$	9.03818	−	3.55514i	0.412535	−	0.162269i
$481$	−2.13567	−	1.23303i	−0.0973782	−	0.0562213i
$482$	19.5503	+	1.74376i	0.890490	+	0.0794259i
$483$	13.4759	+	7.49738i	0.613176	+	0.341142i
$484$	20.2613	+	3.64333i	0.920966	+	0.165606i
$485$	−6.33149	+	3.65549i	−0.287498	+	0.165987i
$486$	7.42643	+	20.7569i	0.336869	+	0.941551i
$487$	−28.8010	−	16.6282i	−1.30510	−	0.753498i	−0.323823	−	0.946118i	$-0.604968\pi$
$487$	−28.8010	−	16.6282i	−1.30510	−	0.753498i	−0.981273	+	0.192620i	$0.938302\pi$
$488$	8.06129	−	29.4858i	0.364918	−	1.33476i
$489$	−4.54756	+	19.6299i	−0.205648	+	0.887693i
$490$	3.80435	+	9.04543i	0.171863	+	0.408631i
$491$	−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	$0.850355\pi$
$492$	−1.60353	−	13.5223i	−0.0722926	−	0.609632i
$493$	12.3901	+	21.4602i	0.558021	+	0.966521i
$494$	0.617203	+	1.32946i	0.0277693	+	0.0598154i
$495$	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
$498$	1.75257	−	5.34924i	0.0785344	−	0.239705i
$499$	−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	$-0.477065\pi$
$503$	3.22909			0.143978			0.0719890	+	0.997405i	$0.477065\pi$
$504$	−18.9180	+	12.0876i	−0.842675	+	0.538423i
$505$	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	$-0.573454\pi$
$509$	16.4404	−	28.4757i	0.728709	−	1.26216i	0.957429	−	0.288669i	$-0.0932129\pi$
$510$	−9.22525	−	10.2963i	−0.408501	−	0.455926i
$511$	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
$514$	−8.51883	−	18.3497i	−0.375750	−	0.809370i
$515$	9.50030	+	16.4550i	0.418633	+	0.725094i
$516$	−8.87251	−	11.8762i	−0.390591	−	0.522821i
$517$	1.20387	+	2.08516i	0.0529462	+	0.0917054i
$518$	−8.21743	+	6.62044i	−0.361053	+	0.290885i
$519$	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	$0.482694\pi$
$522$	16.1784	−	8.90019i	0.708111	−	0.389551i
$523$	−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	$0.465886\pi$
$524$	4.54170	−	25.2573i	0.198405	−	1.10337i
$525$	−9.45725	−	15.7954i	−0.412748	−	0.689366i
$526$	6.49042	+	0.578904i	0.282996	+	0.0252414i
$527$	−21.3620	−	12.3334i	−0.930544	−	0.537250i
$528$	−2.60538	−	5.20988i	−0.113385	−	0.226731i
$529$	−5.83782	−	10.1114i	−0.253818	−	0.439626i
$530$	−8.49893	−	0.758049i	−0.369170	−	0.0329276i
$531$	11.1077	−	0.759836i	0.482035	−	0.0329741i
$532$	6.25860	−	0.411308i	0.271345	−	0.0178325i
$533$	−2.97668	−	1.71859i	−0.128934	−	0.0744403i
$534$	−25.1598	−	28.0808i	−1.08877	−	1.21517i
$535$	−5.50386			−0.237952
$536$	9.51360	−	34.7979i	0.410925	−	1.50304i
$537$	14.6446	−	4.46519i	0.631961	−	0.192687i
$538$	27.7899	−	12.9015i	1.19811	−	0.556222i
$539$	5.20093	−	2.75465i	0.224020	−	0.118651i
$540$	−7.81265	+	6.71426i	−0.336203	+	0.288936i
$541$	15.2097	−	8.78132i	0.653916	−	0.377538i	−0.136039	−	0.990703i	$-0.543437\pi$
$541$	15.2097	−	8.78132i	0.653916	−	0.377538i	0.789955	+	0.613165i	$0.210104\pi$
$542$	2.34228	−	26.2607i	0.100610	−	1.12799i
$543$	9.90376	+	9.24943i	0.425011	+	0.396931i
$544$	29.0744	+	13.8582i	1.24655	+	0.594165i
$545$	−2.45708	+	1.41860i	−0.105250	+	0.0607661i
$546$	−0.413685	+	5.65164i	−0.0177041	+	0.241868i
$547$	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	$0.0406757\pi$
$548$	21.9402	−	25.9684i	0.937238	−	1.10931i
$549$	2.21269	+	32.3465i	0.0944355	+	1.38052i
$550$	4.33268	−	2.01144i	0.184746	−	0.0857683i
$551$	−5.15877			−0.219771
$552$	−16.4789	+	0.479255i	−0.701389	+	0.0203985i
$553$	−2.94647	−	3.05608i	−0.125296	−	0.129958i
$554$	37.7846	+	3.37014i	1.60531	+	0.143183i
$555$	−3.30502	+	3.53882i	−0.140290	+	0.150215i
$556$	33.0260	+	27.9030i	1.40061	+	1.18335i
$557$	12.2341	+	7.06335i	0.518374	+	0.299284i	0.736269	−	0.676689i	$-0.236586\pi$
$557$	12.2341	+	7.06335i	0.518374	+	0.299284i	−0.217895	+	0.975972i	$0.569919\pi$
$558$	−9.51709	+	15.7247i	−0.402890	+	0.665680i
$559$	−3.74196			−0.158268
$560$	−8.44000	−	6.23020i	−0.356655	−	0.263274i
$561$	−5.65932	+	6.05968i	−0.238937	+	0.255840i
$562$	26.8562	−	12.4680i	1.13286	−	0.525931i
$563$		−	6.71616i		−	0.283052i	−0.989935	−	0.141526i	$-0.954799\pi$
$563$		−	6.71616i		−	0.283052i	0.989935	−	0.141526i	$-0.0452009\pi$
$564$	−3.91393	+	9.11553i	−0.164806	+	0.383833i
$565$	−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	$0.437980\pi$
$570$	2.81658	−	0.591479i	0.117974	−	0.0247743i
$571$	−11.3436			−0.474713			−0.237357	−	0.971423i	$-0.576281\pi$
$571$	−11.3436			−0.474713			−0.237357	+	0.971423i	$0.576281\pi$
$572$	−1.44713	−	0.260219i	−0.0605074	−	0.0108803i
$573$	13.4834	−	14.4372i	0.563277	−	0.603124i
$574$	−11.4534	+	9.22752i	−0.478055	+	0.385149i
$575$		−	13.5193i		−	0.563793i
$576$	10.7718	−	21.4469i	0.448824	−	0.893620i
$577$	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	$0.620295\pi$
$578$	1.93709	−	21.7178i	0.0805722	−	0.903341i
$579$	−1.26309	−	1.17964i	−0.0524924	−	0.0490243i
$580$	6.59088	+	5.56851i	0.273671	+	0.231220i
$581$	−5.90062	+	1.46614i	−0.244799	+	0.0608259i
$582$	−5.62481	+	17.1683i	−0.233156	+	0.711647i
$583$			5.11755i			0.211947i
$584$	−9.71095	+	9.61288i	−0.401842	+	0.397784i
$585$	0.177458	+	2.59419i	0.00733698	+	0.107257i
$586$	3.83232	−	42.9664i	0.158312	−	1.77492i
$587$	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	$0.393069\pi$
$588$	21.9175	+	10.3742i	0.903862	+	0.427823i
$589$	4.44718	−	2.56758i	0.183243	−	0.105795i
$590$	2.19072	+	4.71884i	0.0901905	+	0.194272i
$591$	−15.7286	+	16.8413i	−0.646988	+	0.692757i
$592$	3.93002	−	10.5745i	0.161523	−	0.434608i
$593$	−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	$0.512677\pi$
$594$	4.42730	+	4.30943i	0.181654	+	0.176818i
$595$	−4.12744	+	14.3505i	−0.169208	+	0.588312i
$596$	7.56609	−	42.0765i	0.309919	−	1.72352i
$597$	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	$0.104282\pi$
$599$			15.7509i			0.643563i	−0.946814	+	0.321781i	$0.895718\pi$
$600$	17.3233	+	9.34097i	0.707222	+	0.381344i
$601$	−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	$0.838618\pi$
$602$	−5.77560	+	14.9344i	−0.235396	+	0.608680i
$603$	2.61133	+	38.1740i	0.106342	+	1.55457i
$604$	−35.3256	−	29.8460i	−1.43738	−	1.21441i
$605$	−5.10153	−	8.83611i	−0.207407	−	0.359239i
$606$	1.01536	−	0.909746i	0.0412463	−	0.0369559i
$607$	−20.8384	+	36.0932i	−0.845805	+	1.46498i	0.0391158	+	0.999235i	$0.487546\pi$
$607$	−20.8384	+	36.0932i	−0.845805	+	1.46498i	−0.884921	+	0.465742i	$0.845787\pi$
$608$	−5.52487	+	3.79932i	−0.224063	+	0.154083i
$609$	−17.4287	−	9.69650i	−0.706246	−	0.392922i
$610$	−13.7416	+	6.37953i	−0.556381	+	0.258300i
$611$	1.25203	+	2.16857i	0.0506515	+	0.0877310i
$612$	−33.9569	−	3.73723i	−1.37263	−	0.151068i
$613$	−8.00024	−	4.61894i	−0.323126	−	0.186557i	0.329659	−	0.944100i	$-0.393066\pi$
$613$	−8.00024	−	4.61894i	−0.323126	−	0.186557i	−0.652785	+	0.757543i	$0.726400\pi$
$614$	−4.95324	+	7.04856i	−0.199897	+	0.284457i
$615$	−4.60651	+	4.93239i	−0.185752	+	0.198893i
$616$	−3.27214	+	5.37393i	−0.131838	+	0.216522i
$617$	−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	$0.992763\pi$
$618$	44.6188	+	14.6184i	1.79483	+	0.588039i
$619$	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	$0.0926967\pi$
$620$	−8.45325	−	1.52004i	−0.339491	−	0.0610464i
$621$	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
$624$	−2.70960	−	5.41828i	−0.108471	−	0.216905i
$625$	−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
$630$	10.6275	+	3.29580i	0.423408	+	0.131308i
$631$		−	42.2128i		−	1.68046i	−0.542227	−	0.840232i	$-0.682419\pi$
$631$		−	42.2128i		−	1.68046i	0.542227	−	0.840232i	$-0.317581\pi$
$632$	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
$636$	−16.8917	+	12.6195i	−0.669800	+	0.500397i
$637$	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
$640$	11.1597	+	1.10965i	0.441126	+	0.0438629i
$641$	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	$0.804733\pi$
$642$	−10.1295	+	9.07581i	−0.399779	+	0.358194i
$643$	−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	$0.462653\pi$
$644$	9.89551	+	14.8041i	0.389938	+	0.583362i
$645$	−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	$0.373523\pi$
$647$	−15.3908	+	26.6576i	−0.605074	+	1.04802i	−0.992040	+	0.125925i	$0.959810\pi$
$648$	−3.30690	+	25.2401i	−0.129907	+	0.991526i
$649$	2.70225	−	1.56015i	0.106073	−	0.0612411i
$650$	4.50599	−	2.09190i	0.176739	−	0.0820512i
$651$	19.8507	−	0.315477i	0.778008	−	0.0123645i
$652$	−15.0159	+	17.7728i	−0.588068	+	0.696036i
$653$	−21.6699	−	12.5111i	−0.848007	−	0.489597i	0.0119708	−	0.999928i	$-0.496189\pi$
$653$	−21.6699	−	12.5111i	−0.848007	−	0.489597i	−0.859978	+	0.510331i	$0.829523\pi$
$654$	−2.18284	+	6.66255i	−0.0853559	+	0.260526i
$655$	−11.0149	+	6.35947i	−0.430389	+	0.248485i
$656$	5.47764	−	14.7386i	0.213866	−	0.575446i
$657$	6.37305	−	13.0166i	0.248636	−	0.507828i
$658$	10.5874	−	1.64978i	0.412738	−	0.0643152i
$659$	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	$0.0895431\pi$
$660$	−1.13905	+	2.65283i	−0.0443373	+	0.103261i
$661$	−19.9359			−0.775418			−0.387709	−	0.921782i	$-0.626733\pi$
$661$	−19.9359			−0.775418			−0.387709	+	0.921782i	$0.626733\pi$
$662$	1.60589	+	1.12851i	0.0624147	+	0.0438608i
$663$	−5.88570	+	6.30207i	−0.228582	+	0.244752i
$664$	4.61934	−	4.57269i	0.179265	−	0.177455i
$665$	−2.15762	−	2.23789i	−0.0836691	−	0.0867816i
$666$	−0.247172	+	11.9629i	−0.00957773	+	0.463553i
$667$	−7.32300	−	12.6838i	−0.283548	−	0.491119i
$668$	−5.12090	+	6.06109i	−0.198134	+	0.234511i
$669$	24.1699	−	7.36949i	0.934463	−	0.284921i
$670$	−16.2173	+	7.52886i	−0.626527	+	0.290865i
$671$	4.54325	+	7.86915i	0.175390	+	0.303785i
$672$	−25.8068	+	2.45122i	−0.995519	+	0.0945578i
$673$	−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	$0.301728\pi$
$674$	−1.74600	+	19.5754i	−0.0672535	+	0.754018i
$675$	−20.6106	−	3.31239i	−0.793304	−	0.127494i
$676$	24.0846	+	4.33083i	0.926330	+	0.166570i
$677$	−15.5662			−0.598259			−0.299130	−	0.954213i	$-0.596696\pi$
$677$	−15.5662			−0.598259			−0.299130	+	0.954213i	$0.596696\pi$
$678$	−29.5130	+	26.4430i	−1.13344	+	1.01554i
$679$	18.9379	−	4.70555i	0.726769	−	0.180582i
$680$	−4.05328	−	15.4401i	−0.155436	−	0.592099i
$681$	−30.8095	−	7.13749i	−1.18062	−	0.273509i
$682$	−0.457640	+	5.13087i	−0.0175240	+	0.196471i
$683$	−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	$0.293124\pi$
$684$	4.20839	−	5.73310i	0.160912	−	0.219211i
$685$	−16.8493			−0.643779
$686$	−3.08515	−	26.0093i	−0.117791	−	0.993038i
$687$	26.6426	−	8.12342i	1.01648	−	0.309928i
$688$	−2.85835	−	16.8775i	−0.108973	−	0.643450i
$689$			5.32226i			0.202762i
$690$	5.45247	+	6.08548i	0.207572	+	0.231670i
$691$			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
$696$	21.3125	−	0.619830i	0.807848	−	0.0234946i
$697$	−22.3812			−0.847748
$698$	−39.5712	+	18.3709i	−1.49779	+	0.695350i
$699$	6.36495	−	27.4747i	0.240744	−	1.03919i
$700$	−1.39406	−	21.2124i	−0.0526904	−	0.801754i
$701$		−	10.2555i		−	0.387346i	−0.981066	−	0.193673i	$-0.937960\pi$
$701$		−	10.2555i		−	0.387346i	0.981066	−	0.193673i	$-0.0620401\pi$
$702$	4.60440	+	4.48181i	0.173782	+	0.169155i
$703$	1.67146	−	2.89506i	0.0630405	−	0.109189i
$704$	0.0682695	−	6.72581i	0.00257300	−	0.253488i
$705$	4.70299	−	1.43396i	0.177125	−	0.0540060i
$706$	−10.0524	−	0.896607i	−0.378326	−	0.0337443i
$707$	−1.41517	−	0.407026i	−0.0532228	−	0.0153078i
$708$	11.8132	+	5.07223i	0.443967	+	0.190626i
$709$		−	23.6352i		−	0.887640i	−0.896116	−	0.443820i	$-0.853623\pi$
$709$		−	23.6352i		−	0.887640i	0.896116	−	0.443820i	$-0.146377\pi$
$710$	7.80502	+	16.8121i	0.292917	+	0.630947i
$711$	−4.80232	+	0.328507i	−0.180101	+	0.0123200i
$712$	−11.0544	−	42.1093i	−0.414282	−	1.57811i
$713$	12.6258	+	7.28948i	0.472838	+	0.272993i
$714$	16.0675	+	33.2172i	0.601312	+	1.24312i
$715$	0.364369	+	0.631105i	0.0136266	+	0.0236020i
$716$	17.3996	+	3.12876i	0.650255	+	0.116927i
$717$	39.7270	+	9.20337i	1.48363	+	0.343706i
$718$	11.3247	+	1.01009i	0.422632	+	0.0376961i
$719$	−12.7165	−	22.0256i	−0.474245	−	0.821416i	0.525320	−	0.850904i	$-0.323945\pi$
$719$	−12.7165	−	22.0256i	−0.474245	−	0.821416i	−0.999565	+	0.0294887i	$0.990612\pi$
$720$	−11.5651	+	2.78200i	−0.431007	+	0.103679i
$721$	−12.2293	−	49.2179i	−0.455443	−	1.83297i
$722$	22.5695	−	10.4779i	0.839951	−	0.389947i
$723$	−23.4189	−	5.42535i	−0.870959	−	0.201771i
$724$	5.30203	+	14.7220i	0.197048	+	0.547138i
$725$			17.4848i			0.649368i
$726$	−23.9597	−	7.84989i	−0.889228	−	0.291337i
$727$	11.8070	−	20.4502i	0.437896	−	0.758457i	−0.559631	−	0.828742i	$-0.689057\pi$
$727$	11.8070	−	20.4502i	0.437896	−	0.758457i	0.997527	+	0.0702842i	$0.0223906\pi$
$728$	−3.40303	+	5.58888i	−0.126125	+	0.207138i
$729$	−5.49363	−	26.4352i	−0.203468	−	0.979082i
$730$	6.74555	+	0.601659i	0.249664	+	0.0222684i
$731$	−21.1014	+	12.1829i	−0.780464	+	0.450601i
$732$	−14.7707	+	34.4009i	−0.545940	+	1.27149i
$733$	8.42759	−	14.5970i	0.311280	−	0.539153i	−0.667360	−	0.744736i	$-0.732576\pi$
$733$	8.42759	−	14.5970i	0.311280	−	0.539153i	0.978640	+	0.205583i	$0.0659089\pi$
$734$	2.45295	−	27.5015i	0.0905401	−	1.01510i
$735$	−3.08307	−	11.6161i	−0.113721	−	0.428467i
$736$	−17.1841	−	8.19071i	−0.633412	−	0.301914i
$737$	5.36176	+	9.28684i	0.197503	+	0.342085i
$738$	−0.344507	+	16.6738i	−0.0126815	+	0.613772i
$739$	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
$742$	21.2414	+	8.21473i	0.779797	+	0.301572i
$743$	−31.2738	+	18.0559i	−1.14732	+	0.662408i	−0.948234	−	0.317573i	$-0.897132\pi$
$743$	−31.2738	+	18.0559i	−1.14732	+	0.662408i	−0.199090	+	0.979981i	$0.563799\pi$
$744$	−18.0642	+	11.1418i	−0.662265	+	0.408478i
$745$	−18.3499	+	10.5943i	−0.672289	+	0.388146i
$746$	−21.0103	−	45.2564i	−0.769240	−	1.65695i
$747$	−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
$750$	−4.49974	−	21.4275i	−0.164307	−	0.782421i
$751$	−5.36369	−	3.09673i	−0.195724	−	0.113001i	0.398936	−	0.916979i	$-0.369380\pi$
$751$	−5.36369	−	3.09673i	−0.195724	−	0.113001i	−0.594659	+	0.803978i	$0.702713\pi$
$752$	−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
$756$	24.9939	−	11.4589i	0.909019	−	0.416756i
$757$		−	19.4270i		−	0.706085i	−0.935607	−	0.353042i	$-0.885147\pi$
$757$		−	19.4270i		−	0.706085i	0.935607	−	0.353042i	$-0.114853\pi$
$758$	−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	$0.550414\pi$
$762$	−5.02116	+	1.05444i	−0.181897	+	0.0381982i
$763$	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
$766$	−44.3568	+	20.5927i	−1.60268	+	0.744043i
$767$	2.81034	−	1.62255i	0.101476	−	0.0585870i
$768$	22.3685	−	16.3600i	0.807154	−	0.590341i
$769$	−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	$0.479314\pi$
$770$	3.08117	−	0.480125i	0.111038	−	0.0173025i
$771$	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	−0.819685	−	0.572814i	$-0.805852\pi$
$773$	2.39742	−	4.15246i	0.0862293	−	0.149354i	0.905914	+	0.423461i	$0.139185\pi$
$774$	8.75137	+	15.9079i	0.314561	+	0.571799i
$775$	−8.70236	−	15.0729i	−0.312598	−	0.541436i
$776$	−14.8257	+	14.6759i	−0.532210	+	0.526835i
$777$	11.0886	−	6.63913i	0.397800	−	0.238178i
$778$	52.9480	+	4.72262i	1.89828	+	0.169314i
$779$	2.32968	−	4.03512i	0.0834693	−	0.144573i
$780$	−1.18461	+	2.75895i	−0.0424158	+	0.0987862i
$781$	9.62748	−	5.55843i	0.344498	−	0.198896i
$782$	−2.40728	+	26.9894i	−0.0860840	+	0.965138i
$783$	−21.1312	+	8.05649i	−0.755166	+	0.287916i
$784$	17.0531	+	22.2079i	0.609039	+	0.793141i
$785$	6.19744	−	10.7343i	0.221196	−	0.383123i
$786$	−9.78552	+	29.8677i	−0.349038	+	1.06535i
$787$			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
$790$	−0.947135	−	2.04014i	−0.0336976	−	0.0725850i
$791$	41.1338	+	11.8308i	1.46255	+	0.420654i
$792$	2.27816	+	6.76064i	0.0809510	+	0.240229i
$793$	4.72499	+	8.18391i	0.167789	+	0.290619i
$794$	0.936037	−	10.4945i	0.0332187	−	0.372434i
$795$	10.1807	+	2.35852i	0.361073	+	0.0836481i
$796$	31.4864	+	5.66181i	1.11601	+	0.200678i
$797$	10.9176	+	18.9098i	0.386721	+	0.669820i	0.992006	−	0.126188i	$-0.0402744\pi$
$797$	10.9176	+	18.9098i	0.386721	+	0.669820i	−0.605285	+	0.796008i	$0.706941\pi$
$798$	−7.66122	−	0.560781i	−0.271204	−	0.0198514i
$799$	14.1207	+	8.15257i	0.499553	+	0.288417i
$800$	12.8771	+	18.7256i	0.455276	+	0.662050i
$801$	25.7639	+	38.3215i	0.910322	+	1.35402i
$802$	20.8601	−	9.68429i	0.736595	−	0.341964i
$803$		−	4.06177i		−	0.143337i
$804$	−17.4317	+	40.5985i	−0.614770	+	1.43180i
$805$	2.43947	−	8.48166i	0.0859801	−	0.298939i
$806$	−0.475946	+	5.33611i	−0.0167645	+	0.187956i
$807$	−35.8932	+	10.9440i	−1.26350	+	0.385246i
$808$	1.52262	−	0.399713i	0.0535655	−	0.0140619i
$809$	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	$0.110238\pi$
$810$	10.6135	−	6.82147i	0.372919	−	0.239682i
$811$		−	26.5343i		−	0.931746i	−0.884852	−	0.465873i	$-0.845740\pi$
$811$		−	26.5343i		−	0.931746i	0.884852	−	0.465873i	$-0.154260\pi$
$812$	−12.7981	−	19.1464i	−0.449124	−	0.671907i
$813$	−7.28755	+	31.4572i	−0.255586	+	1.10325i
$814$	1.41206	+	3.04160i	0.0494928	+	0.106608i
$815$	11.5317			0.403937
$816$	−32.9203	−	21.7326i	−1.15244	−	0.760792i
$817$		−	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	$-0.891599\pi$
$821$		−	19.1406i		−	0.668013i	0.942571	−	0.334007i	$-0.108401\pi$
$822$	−31.0100	+	27.7844i	−1.08160	+	0.969091i
$823$		−	33.5962i		−	1.17109i	−0.810639	−	0.585546i	$-0.800880\pi$
$823$		−	33.5962i		−	1.17109i	0.810639	−	0.585546i	$-0.199120\pi$
$824$	38.1415	+	38.5306i	1.32872	+	1.34228i
$825$	−5.59604	+	1.70625i	−0.194829	+	0.0594041i
$826$	−2.13802	−	13.7206i	−0.0743913	−	0.477400i
$827$	54.4458			1.89326			0.946632	−	0.322315i	$-0.104461\pi$
$827$	54.4458			1.89326			0.946632	+	0.322315i	$0.104461\pi$
$828$	20.0698	+	2.20884i	0.697475	+	0.0767626i
$829$	−8.85983	+	15.3457i	−0.307715	+	0.532978i	−0.977862	−	0.209251i	$-0.932898\pi$
$829$	−8.85983	+	15.3457i	−0.307715	+	0.532978i	0.670147	+	0.742228i	$0.266231\pi$
$830$	−3.20875	−	0.286200i	−0.111377	−	0.00993413i
$831$	−45.2615	−	10.4855i	−1.57010	−	0.363739i
$832$	0.0710003	−	6.99484i	0.00246149	−	0.242502i
$833$	21.1747	−	33.7654i	0.733659	−	1.16990i
$834$	−35.3355	−	39.4378i	−1.22357	−	1.36562i
$835$	3.93267			0.136096
$836$	0.352746	−	1.96169i	0.0122000	−	0.0678464i
$837$	14.2065	−	17.4624i	0.491050	−	0.603589i
$838$	−19.6205	−	1.75003i	−0.677780	−	0.0604536i
$839$	−6.85214	+	11.8683i	−0.236562	+	0.409738i	−0.959726	−	0.280939i	$-0.909354\pi$
$839$	−6.85214	+	11.8683i	−0.236562	+	0.409738i	0.723163	+	0.690677i	$0.242687\pi$
$840$	9.18271	+	8.98618i	0.316833	+	0.310053i
$841$	−5.02902	−	8.71052i	−0.173414	−	0.300363i
$842$	17.5677	+	37.8411i	0.605424	+	1.30409i
$843$	−34.6873	+	10.5763i	−1.19469	+	0.364266i
$844$	−27.9994	+	33.1400i	−0.963778	+	1.14073i
$845$	−6.06420	−	10.5035i	−0.208615	−	0.361331i
$846$	6.29096	−	10.3943i	0.216288	−	0.357364i
$847$	6.56698	+	26.4294i	0.225644	+	0.908124i
$848$	−24.0052	+	4.06547i	−0.824341	+	0.139609i
$849$	−17.9208	+	19.1886i	−0.615041	+	0.658551i
$850$	18.5991	−	26.4669i	0.637944	−	0.907807i
$851$	9.49074			0.325338
$852$	42.0876	+	18.0712i	1.44190	+	0.619107i
$853$	−0.235840	+	0.408486i	−0.00807499	+	0.0139863i	−0.870035	−	0.492991i	$-0.835904\pi$
$853$	−0.235840	+	0.408486i	−0.00807499	+	0.0139863i	0.861960	+	0.506977i	$0.169237\pi$
$854$	39.9553	−	6.22607i	1.36724	−	0.213052i
$855$	−3.51662	+	0.240558i	−0.120266	+	0.00822690i
$856$	−15.1899	+	3.98762i	−0.519182	+	0.136294i
$857$	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	$0.154288\pi$
$858$	1.71128	+	0.560666i	0.0584222	+	0.0191408i
$859$	−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	$0.775453\pi$
$860$	−5.47540	+	6.48068i	−0.186710	+	0.220989i
$861$	15.4552	−	9.25358i	0.526711	−	0.315361i
$862$	−1.58811	−	3.42080i	−0.0540911	−	0.116513i
$863$	0.576611	−	0.332906i	0.0196281	−	0.0113323i	−0.490154	−	0.871636i	$-0.663059\pi$
$863$	0.576611	−	0.332906i	0.0196281	−	0.0113323i	0.509782	+	0.860304i	$0.329726\pi$
$864$	−16.6973	+	24.1909i	−0.568055	+	0.822990i
$865$	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
$868$	20.5621	+	10.1356i	0.697923	+	0.344026i
$869$	−1.16829	+	0.674513i	−0.0396316	+	0.0228813i
$870$	−7.05179	−	7.87047i	−0.239078	−	0.266834i
$871$	5.57623	+	9.65832i	0.188943	+	0.327260i
$872$	−5.75345	+	5.69535i	−0.194836	+	0.192869i
$873$	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
$876$	13.4069	−	10.0160i	0.452976	−	0.338411i
$877$	26.3948	+	15.2390i	0.891288	+	0.514585i	0.874364	−	0.485271i	$-0.161279\pi$
$877$	26.3948	+	15.2390i	0.891288	+	0.514585i	0.0169245	+	0.999857i	$0.494613\pi$
$878$	−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	$-0.0213843\pi$
$882$	−24.8291	−	16.2947i	−0.836038	−	0.548672i
$883$	−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	−0.971424	−	0.237350i	$-0.923721\pi$
$887$	−8.34390	+	14.4521i	−0.280161	+	0.485253i	0.691263	+	0.722603i	$0.257054\pi$
$888$	−6.55750	+	12.1612i	−0.220055	+	0.408104i
$889$	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
$892$	28.7169	+	5.16381i	0.961513	+	0.172897i
$893$	−2.93966	+	1.69721i	−0.0983720	+	0.0567951i
$894$	−16.3018	+	49.7570i	−0.545215	+	1.66412i
$895$	−4.38101	−	7.58814i	−0.146441	−	0.253643i
$896$	−27.8072	−	11.0797i	−0.928974	−	0.370146i
$897$	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
$900$	−19.4313	−	14.2636i	−0.647712	−	0.475453i
$901$	17.3279	+	30.0129i	0.577278	+	0.999874i
$902$	1.96812	+	4.23937i	0.0655314	+	0.141155i
$903$	9.53437	−	17.1373i	0.317284	−	0.570292i
$904$	−44.2570	+	11.6182i	−1.47197	+	0.386416i
$905$	3.87769	−	6.71635i	0.128899	−	0.223259i
$906$	37.7960	+	42.1839i	1.25569	+	1.40147i
$907$	−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	$0.931469\pi$
$908$	−27.8948	−	23.5678i	−0.925720	−	0.782124i
$909$	−1.38566	+	0.931589i	−0.0459593	+	0.0308988i
$910$	3.20441	−	0.499330i	0.106225	−	0.0165526i
$911$	9.23992	+	5.33467i	0.306132	+	0.176746i	0.645194	−	0.764018i	$-0.276776\pi$
$911$	9.23992	+	5.33467i	0.306132	+	0.176746i	−0.339062	+	0.940764i	$0.610110\pi$
$912$	7.34488	−	3.67306i	0.243213	−	0.121627i
$913$			1.93212i			0.0639438i
$914$	−13.1861	−	9.26630i	−0.436158	−	0.306502i
$915$	17.7485	−	5.41158i	0.586747	−	0.178901i
$916$	31.6548	+	5.69209i	1.04590	+	0.188072i
$917$	32.9463	−	8.18626i	1.08798	−	0.270334i
$918$	40.5564	+	10.2827i	1.33856	+	0.339380i
$919$	44.0949	−	25.4582i	1.45456	−	0.839789i	0.455822	−	0.890071i	$-0.349345\pi$
$919$	44.0949	−	25.4582i	1.45456	−	0.839789i	0.998735	+	0.0502824i	$0.0160121\pi$
$920$	2.39564	+	9.12566i	0.0789820	+	0.300864i
$921$	7.20165	−	7.71112i	0.237303	−	0.254090i
$922$	3.55783	−	1.65172i	0.117171	−	0.0543966i
$923$	10.0126	−	5.78077i	0.329568	−	0.190276i
$924$	4.87896	−	5.96446i	0.160506	−	0.196216i
$925$	−9.81231	−	5.66514i	−0.322627	−	0.186269i
$926$	28.0191	+	2.49912i	0.920764	+	0.0821262i
$927$	−51.6468	−	25.2867i	−1.69630	−	0.830523i
$928$	22.2245	+	10.5932i	0.729554	+	0.347739i
$929$			14.8017i			0.485629i	0.970073	+	0.242814i	$0.0780706\pi$
$929$			14.8017i			0.485629i	−0.970073	+	0.242814i	$0.921929\pi$
$930$	9.99630	+	3.27508i	0.327791	+	0.107394i
$931$	3.88350	+	7.33226i	0.127276	+	0.240305i
$932$	21.0168	−	24.8755i	0.688430	−	0.814824i
$933$	4.65664	+	4.34898i	0.152451	+	0.142379i
$934$	18.6025	+	1.65922i	0.608692	+	0.0542914i
$935$	4.10944	+	2.37259i	0.134393	+	0.0775919i
$936$	2.36929	+	7.03107i	0.0774426	+	0.229818i
$937$		−	23.6965i		−	0.774131i	−0.922052	−	0.387066i	$-0.873489\pi$
$937$		−	23.6965i		−	0.774131i	0.922052	−	0.387066i	$-0.126511\pi$
$938$	47.1536	−	7.34775i	1.53962	−	0.239913i
$939$	−7.69128	+	8.23539i	−0.250996	+	0.268752i
$940$	5.58775	+	1.00478i	0.182252	+	0.0327722i
$941$	−2.96495			−0.0966547			−0.0483274	−	0.998832i	$-0.515389\pi$
$941$	−2.96495			−0.0966547			−0.0483274	+	0.998832i	$0.515389\pi$
$942$	−6.29477	−	29.9753i	−0.205095	−	0.976647i
$943$	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	$0.439935\pi$
$948$	−5.10732	−	2.19293i	−0.165878	−	0.0712229i
$949$		−	4.22424i		−	0.137125i
$950$	2.83573	+	6.10820i	0.0920033	+	0.198176i
$951$	5.17042	−	5.53619i	0.167662	−	0.179523i
$952$	−0.994095	+	42.5958i	−0.0322188	+	1.38054i
$953$	−37.1331			−1.20286			−0.601429	−	0.798926i	$-0.705402\pi$
$953$	−37.1331			−1.20286			−0.601429	+	0.798926i	$0.705402\pi$
$954$	22.6261	−	12.4472i	0.732547	−	0.402994i
$955$	−9.79079	−	5.65271i	−0.316822	−	0.182918i
$956$	35.9686	+	30.3892i	1.16331	+	0.982857i
$957$	−4.32599	+	4.63202i	−0.139839	+	0.149732i
$958$	0.927421	−	10.3979i	0.0299636	−	0.335939i
$959$	43.2203	+	12.4309i	1.39566	+	0.401415i
$960$	−13.3487	−	3.23553i	−0.430826	−	0.104426i
$961$	−12.2310			−0.394550
$962$	1.46855	+	3.16327i	0.0473478	+	0.101988i
$963$	13.8236	−	9.29372i	0.445459	−	0.299486i
$964$	−21.2034	−	17.9143i	−0.682915	−	0.576982i
$965$	−0.494548	+	0.856582i	−0.0159201	+	0.0275744i
$966$	−9.49651	−	19.6326i	−0.305545	−	0.631669i
$967$	15.2147	−	8.78423i	0.489273	−	0.282482i	−0.235000	−	0.971995i	$-0.575509\pi$
$967$	15.2147	−	8.78423i	0.489273	−	0.282482i	0.724273	+	0.689514i	$0.242176\pi$
$968$	−20.4815	−	20.6904i	−0.658300	−	0.665015i
$969$	−8.54293	−	7.97850i	−0.274438	−	0.256306i
$970$	10.2984	+	0.918550i	0.330662	+	0.0294929i
$971$	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	$0.310298\pi$
$972$	8.28482	−	30.0560i	0.265736	−	0.964046i
$973$	−15.8093	+	54.9666i	−0.506824	+	1.76215i
$974$	19.8044	+	42.6588i	0.634572	+	1.36688i
$975$	−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	$0.583976\pi$
$978$	21.2233	−	19.0156i	0.678646	−	0.608053i
$979$	11.2076	+	6.47070i	0.358196	+	0.206804i
$980$	2.95305	−	13.5597i	0.0943318	−	0.433149i
$981$	3.77584	−	7.71197i	0.120553	−	0.246224i
$982$	−0.297602	+	3.33658i	−0.00949685	+	0.106475i
$983$	−17.8822	−	30.9729i	−0.570355	−	0.987883i	−0.996529	−	0.0832425i	$-0.973472\pi$
$983$	−17.8822	−	30.9729i	−0.570355	−	0.987883i	0.426175	−	0.904641i	$-0.359861\pi$
$984$	−9.13980	+	16.9502i	−0.291366	+	0.540354i
$985$	11.4211	+	6.59398i	0.363907	+	0.210102i
$986$	3.11338	−	34.9059i	0.0991501	−	1.11163i
$987$	−13.1216	+	0.208536i	−0.417666	+	0.00663777i
$988$	0.366856	−	2.04016i	0.0116713	−	0.0649061i
$989$	12.4717	−	7.20056i	0.396578	−	0.228964i
$990$	1.83082	−	3.02498i	0.0581872	−	0.0961403i
$991$	−5.86472	−	3.38600i	−0.186299	−	0.107560i	0.403950	−	0.914781i	$-0.367637\pi$
$991$	−5.86472	−	3.38600i	−0.186299	−	0.107560i	−0.590249	+	0.807221i	$0.700970\pi$
$992$	−24.4312	+	1.92937i	−0.775692	+	0.0612577i
$993$	−1.75684	−	1.64077i	−0.0557518	−	0.0520683i
$994$	−7.61727	−	48.8832i	−0.241605	−	1.55048i
$995$	−7.92789	−	13.7315i	−0.251331	−	0.435318i
$996$	−6.37743	+	4.76447i	−0.202077	+	0.150968i
$997$	0.453891	+	0.786162i	0.0143749	+	0.0248980i	0.873123	−	0.487499i	$-0.162091\pi$
$997$	0.453891	+	0.786162i	0.0143749	+	0.0248980i	−0.858748	+	0.512397i	$0.828758\pi$
$998$	2.45966	−	1.14190i	0.0778593	−	0.0361462i
$999$	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.115.17	✓	180
7.5	odd	6		504.2.cz.b.187.44	yes	180
8.3	odd	2	inner	504.2.bf.b.115.18	yes	180
9.4	even	3		504.2.cz.b.283.77	yes	180
56.19	even	6		504.2.cz.b.187.77	yes	180
63.40	odd	6	inner	504.2.bf.b.355.17	yes	180
72.67	odd	6		504.2.cz.b.283.44	yes	180
504.355	even	6	inner	504.2.bf.b.355.18	yes	180

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

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)

\(f(q)\)	\(=\)	\(q+(-1.15708 - 0.813118i) q^{2} +(1.26585 + 1.18221i) q^{3} +(0.677678 + 1.88169i) q^{4} +(0.495626 - 0.858449i) q^{5} +(-0.503410 - 2.39720i) q^{6} +(-1.90467 + 1.83636i) q^{7} +(0.745907 - 2.72830i) q^{8} +(0.204739 + 2.99301i) q^{9} +O(q^{10})\)	\(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} +(-0.503410 - 2.39720i) q^{6} +(-1.90467 + 1.83636i) q^{7} +(0.745907 - 2.72830i) q^{8} +(0.204739 + 2.99301i) q^{9} +(-1.27150 + 0.590294i) q^{10} +(0.420385 + 0.728127i) q^{11} +(-1.36672 + 3.18309i) q^{12} +(0.437200 + 0.757253i) q^{13} +(3.69704 - 0.576095i) q^{14} +(1.64226 - 0.500730i) q^{15} +(-3.08151 + 2.55036i) q^{16} +(4.93085 + 2.84683i) q^{17} +(2.19677 - 3.62963i) q^{18} +(-1.02651 + 0.592657i) q^{19} +(1.95121 + 0.350862i) q^{20} +(-4.58200 + 0.0728195i) q^{21} +(0.105634 - 1.18433i) q^{22} +(-2.91432 - 1.68258i) q^{23} +(4.16964 - 2.57179i) q^{24} +(2.00871 + 3.47919i) q^{25} +(0.109860 - 1.23170i) q^{26} +(-3.27920 + 4.03073i) q^{27} +(-4.74621 - 2.33954i) q^{28} +(3.76915 + 2.17612i) q^{29} +(-2.30738 - 0.755964i) q^{30} -4.33231 q^{31} +(5.63930 - 0.445345i) q^{32} +(-0.328660 + 1.41868i) q^{33} +(-3.39059 - 7.30338i) q^{34} +(0.632417 + 2.54521i) q^{35} +(-5.49316 + 2.41355i) q^{36} +(-2.44244 + 1.41014i) q^{37} +(1.66966 + 0.148923i) q^{38} +(-0.341806 + 1.47543i) q^{39} +(-1.97242 - 1.99254i) q^{40} +(-3.40426 + 1.96545i) q^{41} +(5.36096 + 3.64145i) q^{42} +(-2.13973 + 3.70612i) q^{43} +(-1.08522 + 1.28447i) q^{44} +(2.67082 + 1.30765i) q^{45} +(2.00397 + 4.31657i) q^{46} +2.86374 q^{47} +(-6.91578 - 0.414636i) q^{48} +(0.255563 - 6.99533i) q^{49} +(0.504748 - 5.65902i) q^{50} +(2.87615 + 9.43298i) q^{51} +(-1.12863 + 1.33585i) q^{52} +(5.27128 + 3.04338i) q^{53} +(7.07177 - 1.99751i) q^{54} +0.833414 q^{55} +(3.58943 + 6.56627i) q^{56} +(-2.00006 - 0.463344i) q^{57} +(-2.59177 - 5.58271i) q^{58} -3.71124i q^{59} +(2.05514 + 2.75089i) 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} +(1.53384 - 1.37429i) q^{66} +12.7544 q^{67} +(-2.01532 + 11.2076i) q^{68} +(-1.69991 - 5.57525i) q^{69} +(1.33780 - 3.45925i) q^{70} -13.2223i q^{71} +(8.31853 + 1.67391i) q^{72} +(-4.18378 - 2.41551i) q^{73} +(3.97272 + 0.354341i) q^{74} +(-1.57042 + 6.77885i) q^{75} +(-1.81084 - 1.52995i) q^{76} +(-2.13780 - 0.614868i) q^{77} +(1.59520 - 1.42927i) q^{78} +1.60451i q^{79} +(0.662079 + 3.90934i) q^{80} +(-8.91616 + 1.22557i) q^{81} +(5.53715 + 0.493878i) q^{82} +(1.99016 + 1.14902i) q^{83} +(-3.24214 - 8.57254i) q^{84} +(4.88772 - 2.82193i) q^{85} +(5.48936 - 2.54844i) q^{86} +(2.19853 + 7.21057i) q^{87} +(2.30012 - 0.603820i) q^{88} +(13.3302 - 7.69617i) q^{89} +(-2.02708 - 3.68475i) q^{90} +(-2.22331 - 0.639463i) q^{91} +(1.19113 - 6.62409i) q^{92} +(-5.48405 - 5.12172i) q^{93} +(-3.31358 - 2.32856i) q^{94} +1.17495i q^{95} +(7.66498 + 6.10312i) q^{96} +(-6.38736 - 3.68775i) q^{97} +(-5.98374 + 7.88637i) 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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