LMFDB - Embedded newform 875.2.bb.a.243.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			243.8
Character	$\chi$	$=$	875.243
Dual form			875.2.bb.a.857.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.924506 - 0.0484513i) q^{2} +(0.831339 + 1.02662i) q^{3} +(-1.13668 - 0.119470i) q^{4} +(-0.718837 - 0.989394i) q^{6} +(2.64389 - 0.0993238i) q^{7} +(2.87383 + 0.455170i) q^{8} +(0.260915 - 1.22751i) q^{9} +(0.769743 - 0.163614i) q^{11} +(-0.822316 - 1.26626i) q^{12} +(-0.729773 - 0.371838i) q^{13} +(-2.44910 - 0.0362743i) q^{14} +(-0.398891 - 0.0847869i) q^{16} +(-2.66452 - 6.94132i) q^{17} +(-0.300692 + 1.12220i) q^{18} +(0.192403 + 1.83059i) q^{19} +(2.29993 + 2.63169i) q^{21} +(-0.719560 + 0.113967i) q^{22} +(0.213890 - 4.08126i) q^{23} +(1.92184 + 3.32873i) q^{24} +(0.656664 + 0.379125i) q^{26} +(5.00818 - 2.55179i) q^{27} +(-3.01712 - 0.202965i) q^{28} +(-5.50382 + 7.57536i) q^{29} +(1.92037 - 4.31323i) q^{31} +(-5.25635 - 1.40844i) q^{32} +(0.807887 + 0.654214i) q^{33} +(2.12705 + 6.54639i) q^{34} +(-0.443227 + 1.36411i) q^{36} +(5.50515 - 3.57509i) q^{37} +(-0.0891829 - 1.70171i) q^{38} +(-0.224953 - 1.05832i) q^{39} +(2.40999 - 0.783055i) q^{41} +(-1.99879 - 2.54445i) q^{42} +(-1.79811 - 1.79811i) q^{43} +(-0.894499 + 0.0940156i) q^{44} +(-0.395485 + 3.76279i) q^{46} +(10.7558 + 4.12878i) q^{47} +(-0.244570 - 0.479996i) q^{48} +(6.98027 - 0.525202i) q^{49} +(4.91096 - 8.50604i) q^{51} +(0.785095 + 0.509847i) q^{52} +(6.99289 - 5.66273i) q^{53} +(-4.75373 + 2.11650i) q^{54} +(7.64330 + 0.917979i) q^{56} +(-1.71936 + 1.71936i) q^{57} +(5.45535 - 6.73680i) q^{58} +(7.62729 - 8.47097i) q^{59} +(-6.28292 + 5.65717i) q^{61} +(-1.98438 + 3.89456i) q^{62} +(0.567908 - 3.27131i) q^{63} +(5.56698 + 1.80882i) q^{64} +(-0.715198 - 0.643968i) q^{66} +(-0.852602 + 0.327283i) q^{67} +(2.19943 + 8.20839i) q^{68} +(4.36771 - 3.17333i) q^{69} +(0.767293 + 0.557471i) q^{71} +(1.30855 - 3.40889i) q^{72} +(-2.02117 + 3.11233i) q^{73} +(-5.26276 + 3.03846i) q^{74} -2.10378i q^{76} +(2.01886 - 0.509031i) q^{77} +(0.156693 + 0.989324i) q^{78} +(1.98946 + 4.46840i) q^{79} +(3.34390 + 1.48880i) q^{81} +(-2.26599 + 0.607171i) q^{82} +(-0.814213 + 5.14074i) q^{83} +(-2.29988 - 3.26616i) q^{84} +(1.57524 + 1.74948i) q^{86} +(-12.3525 + 0.647369i) q^{87} +(2.28659 - 0.119835i) q^{88} +(-0.386903 - 0.429700i) q^{89} +(-1.96637 - 0.910613i) q^{91} +(-0.730712 + 4.61354i) q^{92} +(6.02451 - 1.61426i) q^{93} +(-9.74379 - 4.33822i) q^{94} +(-2.92389 - 6.56715i) q^{96} +(1.67483 + 10.5745i) q^{97} +(-6.47875 + 0.147349i) q^{98} -0.987555i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.924506	−	0.0484513i	−0.653724	−	0.0342602i	−0.277409	−	0.960752i	$-0.589476\pi$
$2$	−0.924506	−	0.0484513i	−0.653724	−	0.0342602i	−0.376315	+	0.926492i	$0.622809\pi$
$3$	0.831339	+	1.02662i	0.479974	+	0.592718i	0.958407	−	0.285406i	$-0.0921284\pi$
$3$	0.831339	+	1.02662i	0.479974	+	0.592718i	−0.478433	+	0.878124i	$0.658795\pi$
$4$	−1.13668	−	0.119470i	−0.568340	−	0.0597349i
$5$		0			0
$5$		0			0
$6$	−0.718837	−	0.989394i	−0.293464	−	0.403918i
$7$	2.64389	−	0.0993238i	0.999295	−	0.0375409i
$7$	2.64389	−	0.0993238i	0.999295	−	0.0375409i
$8$	2.87383	+	0.455170i	1.01605	+	0.160927i
$9$	0.260915	−	1.22751i	0.0869716	−	0.409169i
$10$		0			0
$11$	0.769743	−	0.163614i	0.232086	−	0.0493315i	−0.0904002	−	0.995906i	$-0.528815\pi$
$11$	0.769743	−	0.163614i	0.232086	−	0.0493315i	0.322487	+	0.946574i	$0.395481\pi$
$12$	−0.822316	−	1.26626i	−0.237382	−	0.365537i
$13$	−0.729773	−	0.371838i	−0.202403	−	0.103129i	0.349851	−	0.936805i	$-0.386232\pi$
$13$	−0.729773	−	0.371838i	−0.202403	−	0.103129i	−0.552254	+	0.833676i	$0.686232\pi$
$14$	−2.44910	−	0.0362743i	−0.654550	−	0.00969470i
$15$		0			0
$16$	−0.398891	−	0.0847869i	−0.0997228	−	0.0211967i
$17$	−2.66452	−	6.94132i	−0.646242	−	1.68352i	−0.726871	−	0.686774i	$-0.759026\pi$
$17$	−2.66452	−	6.94132i	−0.646242	−	1.68352i	0.0806290	−	0.996744i	$-0.474307\pi$
$18$	−0.300692	+	1.12220i	−0.0708737	+	0.264504i
$19$	0.192403	+	1.83059i	0.0441402	+	0.419966i	0.994171	+	0.107811i	$0.0343841\pi$
$19$	0.192403	+	1.83059i	0.0441402	+	0.419966i	−0.950031	+	0.312155i	$0.898949\pi$
$20$		0			0
$21$	2.29993	+	2.63169i	0.501887	+	0.574282i
$22$	−0.719560	+	0.113967i	−0.153411	+	0.0242979i
$23$	0.213890	−	4.08126i	0.0445991	−	0.851002i	−0.881144	−	0.472848i	$-0.843226\pi$
$23$	0.213890	−	4.08126i	0.0445991	−	0.851002i	0.925743	−	0.378154i	$-0.123441\pi$
$24$	1.92184	+	3.32873i	0.392294	+	0.679474i
$25$		0			0
$26$	0.656664	+	0.379125i	0.128782	+	0.0743525i
$27$	5.00818	−	2.55179i	0.963824	−	0.491093i
$28$	−3.01712	−	0.202965i	−0.570182	−	0.0383569i
$29$	−5.50382	+	7.57536i	−1.02203	+	1.40671i	−0.111266	+	0.993791i	$0.535491\pi$
$29$	−5.50382	+	7.57536i	−1.02203	+	1.40671i	−0.910768	+	0.412919i	$0.864509\pi$
$30$		0			0
$31$	1.92037	−	4.31323i	0.344909	−	0.774678i	−0.654911	−	0.755706i	$-0.727294\pi$
$31$	1.92037	−	4.31323i	0.344909	−	0.774678i	0.999820	−	0.0189722i	$-0.00603941\pi$
$32$	−5.25635	−	1.40844i	−0.929201	−	0.248979i
$33$	0.807887	+	0.654214i	0.140635	+	0.113884i
$34$	2.12705	+	6.54639i	0.364786	+	1.12270i
$35$		0			0
$36$	−0.443227	+	1.36411i	−0.0738712	+	0.227352i
$37$	5.50515	−	3.57509i	0.905041	−	0.587740i	−0.00603374	−	0.999982i	$-0.501921\pi$
$37$	5.50515	−	3.57509i	0.905041	−	0.587740i	0.911075	+	0.412241i	$0.135254\pi$
$38$	−0.0891829	−	1.70171i	−0.0144674	−	0.276054i
$39$	−0.224953	−	1.05832i	−0.0360213	−	0.169467i
$40$		0			0
$41$	2.40999	−	0.783055i	0.376378	−	0.122293i	−0.114718	−	0.993398i	$-0.536596\pi$
$41$	2.40999	−	0.783055i	0.376378	−	0.122293i	0.491096	+	0.871106i	$0.336596\pi$
$42$	−1.99879	−	2.54445i	−0.308420	−	0.392617i
$43$	−1.79811	−	1.79811i	−0.274209	−	0.274209i	0.556583	−	0.830792i	$-0.312112\pi$
$43$	−1.79811	−	1.79811i	−0.274209	−	0.274209i	−0.830792	+	0.556583i	$0.812112\pi$
$44$	−0.894499	+	0.0940156i	−0.134851	+	0.0141734i
$45$		0			0
$46$	−0.395485	+	3.76279i	−0.0583111	+	0.554793i
$47$	10.7558	+	4.12878i	1.56890	+	0.602244i	0.978751	−	0.205050i	$-0.0657357\pi$
$47$	10.7558	+	4.12878i	1.56890	+	0.602244i	0.590149	+	0.807294i	$0.299069\pi$
$48$	−0.244570	−	0.479996i	−0.0353006	−	0.0692814i
$49$	6.98027	−	0.525202i	0.997181	−	0.0750288i
$50$		0			0
$51$	4.91096	−	8.50604i	0.687673	−	1.19108i
$52$	0.785095	+	0.509847i	0.108873	+	0.0707030i
$53$	6.99289	−	5.66273i	0.960547	−	0.777836i	−0.0144862	−	0.999895i	$-0.504611\pi$
$53$	6.99289	−	5.66273i	0.960547	−	0.777836i	0.975033	+	0.222060i	$0.0712779\pi$
$54$	−4.75373	+	2.11650i	−0.646900	+	0.288019i
$55$		0			0
$56$	7.64330	+	0.917979i	1.02138	+	0.122670i
$57$	−1.71936	+	1.71936i	−0.227735	+	0.227735i
$58$	5.45535	−	6.73680i	0.716323	−	0.884585i
$59$	7.62729	−	8.47097i	0.992989	−	1.10283i	−0.00171029	−	0.999999i	$-0.500544\pi$
$59$	7.62729	−	8.47097i	0.992989	−	1.10283i	0.994699	−	0.102827i	$-0.0327889\pi$
$60$		0			0
$61$	−6.28292	+	5.65717i	−0.804446	+	0.724326i	−0.964872	−	0.262722i	$-0.915380\pi$
$61$	−6.28292	+	5.65717i	−0.804446	+	0.724326i	0.160426	+	0.987048i	$0.448713\pi$
$62$	−1.98438	+	3.89456i	−0.252016	+	0.494609i
$63$	0.567908	−	3.27131i	0.0715497	−	0.412146i
$64$	5.56698	+	1.80882i	0.695872	+	0.226103i
$65$		0			0
$66$	−0.715198	−	0.643968i	−0.0880348	−	0.0792669i
$67$	−0.852602	+	0.327283i	−0.104162	+	0.0399840i	−0.409891	−	0.912135i	$-0.634433\pi$
$67$	−0.852602	+	0.327283i	−0.104162	+	0.0399840i	0.305729	+	0.952119i	$0.401100\pi$
$68$	2.19943	+	8.20839i	0.266720	+	0.995414i
$69$	4.36771	−	3.17333i	0.525811	−	0.382024i
$70$		0			0
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	0.632384	−	0.774655i	$-0.282076\pi$
$71$	0.767293	+	0.557471i	0.0910610	+	0.0661597i	−0.541323	+	0.840815i	$0.682076\pi$
$72$	1.30855	−	3.40889i	0.154214	−	0.401742i
$73$	−2.02117	+	3.11233i	−0.236560	+	0.364270i	−0.936934	−	0.349505i	$-0.886350\pi$
$73$	−2.02117	+	3.11233i	−0.236560	+	0.364270i	0.700374	+	0.713776i	$0.253016\pi$
$74$	−5.26276	+	3.03846i	−0.611783	+	0.353213i
$75$		0			0
$76$		−	2.10378i		−	0.241320i
$77$	2.01886	−	0.509031i	0.230071	−	0.0580094i
$78$	0.156693	+	0.989324i	0.0177420	+	0.112019i
$79$	1.98946	+	4.46840i	0.223832	+	0.502735i	0.990198	−	0.139669i	$-0.0446039\pi$
$79$	1.98946	+	4.46840i	0.223832	+	0.502735i	−0.766366	+	0.642404i	$0.777937\pi$
$80$		0			0
$81$	3.34390	+	1.48880i	0.371544	+	0.165422i
$82$	−2.26599	+	0.607171i	−0.250237	+	0.0670509i
$83$	−0.814213	+	5.14074i	−0.0893715	+	0.564269i	0.901849	+	0.432051i	$0.142210\pi$
$83$	−0.814213	+	5.14074i	−0.0893715	+	0.564269i	−0.991221	+	0.132218i	$0.957790\pi$
$84$	−2.29988	−	3.26616i	−0.250938	−	0.356367i
$85$		0			0
$86$	1.57524	+	1.74948i	0.169863	+	0.188652i
$87$	−12.3525	+	0.647369i	−1.32433	+	0.0694053i
$88$	2.28659	−	0.119835i	0.243751	−	0.0127744i
$89$	−0.386903	−	0.429700i	−0.0410117	−	0.0455481i	0.722290	−	0.691590i	$-0.243090\pi$
$89$	−0.386903	−	0.429700i	−0.0410117	−	0.0455481i	−0.763302	+	0.646042i	$0.776423\pi$
$90$		0			0
$91$	−1.96637	−	0.910613i	−0.206132	−	0.0954582i
$92$	−0.730712	+	4.61354i	−0.0761820	+	0.480994i
$93$	6.02451	−	1.61426i	0.624713	−	0.167391i
$94$	−9.74379	−	4.33822i	−1.00500	−	0.447453i
$95$		0			0
$96$	−2.92389	−	6.56715i	−0.298418	−	0.670257i
$97$	1.67483	+	10.5745i	0.170054	+	1.07368i	0.914082	+	0.405529i	$0.132913\pi$
$97$	1.67483	+	10.5745i	0.170054	+	1.07368i	−0.744029	+	0.668148i	$0.767087\pi$
$98$	−6.47875	+	0.147349i	−0.654452	+	0.0148845i
$99$		−	0.987555i		−	0.0992530i
$100$		0			0
$101$	−5.47339	+	3.16006i	−0.544622	+	0.314438i	−0.746950	−	0.664880i	$-0.768483\pi$
$101$	−5.47339	+	3.16006i	−0.544622	+	0.314438i	0.202328	+	0.979318i	$0.435149\pi$
$102$	−4.95234	+	7.62594i	−0.490355	+	0.755081i
$103$	3.54834	−	9.24375i	0.349629	−	0.910814i	−0.640156	−	0.768245i	$-0.721130\pi$
$103$	3.54834	−	9.24375i	0.349629	−	0.910814i	0.989785	−	0.142569i	$-0.0455363\pi$
$104$	−1.92800	−	1.40077i	−0.189056	−	0.137357i
$105$		0			0
$106$	−6.73933	+	4.89641i	−0.654582	+	0.475581i
$107$	−1.40885	−	5.25791i	−0.136199	−	0.508302i	−0.999990	−	0.00445150i	$-0.998583\pi$
$107$	−1.40885	−	5.25791i	−0.136199	−	0.508302i	0.863791	−	0.503850i	$-0.168084\pi$
$108$	−5.99756	+	2.30225i	−0.577115	+	0.221534i
$109$	12.1845	+	10.9709i	1.16706	+	1.05083i	0.997869	+	0.0652420i	$0.0207819\pi$
$109$	12.1845	+	10.9709i	1.16706	+	1.05083i	0.169190	+	0.985583i	$0.445885\pi$
$110$		0			0
$111$	8.24689	+	2.67958i	0.782760	+	0.254334i
$112$	−1.06304	−	0.184548i	−0.100448	−	0.0174381i
$113$	4.26151	−	8.36368i	0.400889	−	0.786789i	−0.599014	−	0.800739i	$-0.704441\pi$
$113$	4.26151	−	8.36368i	0.400889	−	0.786789i	0.999903	+	0.0139501i	$0.00444059\pi$
$114$	1.67287	−	1.50626i	0.156678	−	0.141074i
$115$		0			0
$116$	7.16111	−	7.95322i	0.664893	−	0.738438i
$117$	−0.646843	+	0.798784i	−0.0598006	+	0.0738476i
$118$	−7.46191	+	7.46191i	−0.686924	+	0.686924i
$119$	−7.73414	−	18.0874i	−0.708987	−	1.65807i
$120$		0			0
$121$	−9.48326	+	4.22222i	−0.862115	+	0.383838i
$122$	6.08270	−	4.92567i	0.550701	−	0.445949i
$123$	2.80742	+	1.82316i	0.253137	+	0.164389i
$124$	−2.69815	+	4.67333i	−0.242301	+	0.419678i
$125$		0			0
$126$	−0.683534	+	2.99683i	−0.0608940	+	0.266979i
$127$	1.32420	+	2.59888i	0.117503	+	0.230613i	0.942266	−	0.334866i	$-0.108691\pi$
$127$	1.32420	+	2.59888i	0.117503	+	0.230613i	−0.824762	+	0.565480i	$0.808691\pi$
$128$	5.10161	+	1.95833i	0.450923	+	0.173093i
$129$	0.351133	−	3.34081i	0.0309156	−	0.294142i
$130$		0			0
$131$	−6.69495	+	0.703668i	−0.584941	+	0.0614797i	−0.392377	−	0.919805i	$-0.628347\pi$
$131$	−6.69495	+	0.703668i	−0.584941	+	0.0614797i	−0.192564	+	0.981284i	$0.561680\pi$
$132$	−0.840150	−	0.840150i	−0.0731256	−	0.0731256i
$133$	0.690511	+	4.82076i	0.0598749	+	0.418013i
$134$	0.804093	−	0.261266i	0.0694631	−	0.0225699i
$135$		0			0
$136$	−4.49791	−	21.1610i	−0.385693	−	1.81454i
$137$	−1.01934	−	19.4502i	−0.0870884	−	1.66175i	−0.597539	−	0.801840i	$-0.703855\pi$
$137$	−1.01934	−	19.4502i	−0.0870884	−	1.66175i	0.510451	−	0.859907i	$-0.329479\pi$
$138$	−4.19173	+	2.72214i	−0.356824	+	0.231724i
$139$	−0.317252	+	0.976401i	−0.0269090	+	0.0828172i	−0.963609	−	0.267315i	$-0.913863\pi$
$139$	−0.317252	+	0.976401i	−0.0269090	+	0.0828172i	0.936700	+	0.350133i	$0.113863\pi$
$140$		0			0
$141$	4.70307	+	14.4746i	0.396070	+	1.21898i
$142$	−0.682357	−	0.552562i	−0.0572621	−	0.0463700i
$143$	−0.622576	−	0.166819i	−0.0520624	−	0.0139501i
$144$	−0.208153	+	0.467520i	−0.0173461	+	0.0389600i
$145$		0			0
$146$	2.01938	−	2.77944i	0.167125	−	0.230028i
$147$	6.34215	+	6.72945i	0.523092	+	0.555036i
$148$	−6.68471	+	3.40603i	−0.549480	+	0.279974i
$149$	−9.86165	−	5.69362i	−0.807897	−	0.466440i	0.0383277	−	0.999265i	$-0.487797\pi$
$149$	−9.86165	−	5.69362i	−0.807897	−	0.466440i	−0.846225	+	0.532825i	$0.821130\pi$
$150$		0			0
$151$	−5.54607	−	9.60607i	−0.451333	−	0.781731i	0.547136	−	0.837043i	$-0.315718\pi$
$151$	−5.54607	−	9.60607i	−0.451333	−	0.781731i	−0.998469	+	0.0553124i	$0.982385\pi$
$152$	−0.280297	+	5.34838i	−0.0227351	+	0.433811i
$153$	−9.21574	+	1.45963i	−0.745049	+	0.118004i
$154$	−1.89111	+	0.372785i	−0.152390	+	0.0300399i
$155$		0			0
$156$	0.129262	+	1.22985i	0.0103493	+	0.0984667i
$157$	−4.31493	+	16.1035i	−0.344369	+	1.28520i	0.548979	+	0.835836i	$0.315017\pi$
$157$	−4.31493	+	16.1035i	−0.344369	+	1.28520i	−0.893348	+	0.449365i	$0.851650\pi$
$158$	−1.62277	−	4.22746i	−0.129101	−	0.336319i
$159$	11.6269	+	2.47138i	0.922075	+	0.195993i
$160$		0			0
$161$	0.160134	−	10.8116i	0.0126203	−	0.852076i
$162$	−3.01932	−	1.53842i	−0.237220	−	0.120870i
$163$	11.2033	+	17.2516i	0.877510	+	1.35125i	0.935647	+	0.352938i	$0.114817\pi$
$163$	11.2033	+	17.2516i	0.877510	+	1.35125i	−0.0581372	+	0.998309i	$0.518516\pi$
$164$	−2.83294	+	0.602161i	−0.221216	+	0.0470209i
$165$		0			0
$166$	1.00182	−	4.71319i	0.0777563	−	0.365815i
$167$	4.67190	+	0.739956i	0.361522	+	0.0572595i	0.334553	−	0.942377i	$-0.391415\pi$
$167$	4.67190	+	0.739956i	0.361522	+	0.0572595i	0.0269687	+	0.999636i	$0.491415\pi$
$168$	5.41176	+	8.60990i	0.417526	+	0.664268i
$169$	−7.24690	−	9.97451i	−0.557454	−	0.767270i
$170$		0			0
$171$	2.29726	+	0.241452i	0.175676	+	0.0184643i
$172$	1.82906	+	2.25870i	0.139464	+	0.172224i
$173$	−5.04027	−	0.264149i	−0.383204	−	0.0200829i	−0.140239	−	0.990118i	$-0.544787\pi$
$173$	−5.04027	−	0.264149i	−0.383204	−	0.0200829i	−0.242966	+	0.970035i	$0.578120\pi$
$174$	11.4514			0.868126
$175$		0			0
$176$	−0.320916			−0.0241900
$177$	15.0373	+	0.788072i	1.13027	+	0.0592351i
$178$	0.336875	+	0.416006i	0.0252498	+	0.0311810i
$179$	−3.59011	−	0.377335i	−0.268337	−	0.0282034i	−0.0305957	−	0.999532i	$-0.509740\pi$
$179$	−3.59011	−	0.377335i	−0.268337	−	0.0282034i	−0.237741	+	0.971328i	$0.576407\pi$
$180$		0			0
$181$	7.29441	+	10.0399i	0.542189	+	0.746259i	0.988927	−	0.148406i	$-0.0474142\pi$
$181$	7.29441	+	10.0399i	0.542189	+	0.746259i	−0.446737	+	0.894665i	$0.647414\pi$
$182$	1.77380	+	0.937141i	0.131483	+	0.0694655i
$183$	−11.0310	−	1.74714i	−0.815434	−	0.129152i
$184$	2.47235	−	11.6315i	0.182264	−	0.857486i
$185$		0			0
$186$	−5.64791	+	1.20050i	−0.414125	+	0.0880250i
$187$	−3.18670	−	4.90708i	−0.233034	−	0.358841i
$188$	−11.7327	−	5.97810i	−0.855694	−	0.435998i
$189$	12.9876	−	7.24408i	0.944709	−	0.526930i
$190$		0			0
$191$	−22.6901	−	4.82293i	−1.64180	−	0.348975i	−0.707845	−	0.706367i	$-0.750333\pi$
$191$	−22.6901	−	4.82293i	−1.64180	−	0.348975i	−0.933954	+	0.357392i	$0.883666\pi$
$192$	2.77108	+	7.21890i	0.199985	+	0.520979i
$193$	3.86831	−	14.4367i	0.278447	−	1.03918i	−0.675049	−	0.737773i	$-0.735877\pi$
$193$	3.86831	−	14.4367i	0.278447	−	1.03918i	0.953496	−	0.301406i	$-0.0974560\pi$
$194$	−1.03605	−	9.85732i	−0.0743838	−	0.707715i
$195$		0			0
$196$	−7.99708	−	0.236946i	−0.571220	−	0.0169247i
$197$	1.48910	−	0.235850i	0.106094	−	0.0168036i	−0.103162	−	0.994665i	$-0.532896\pi$
$197$	1.48910	−	0.235850i	0.106094	−	0.0168036i	0.209256	+	0.977861i	$0.432896\pi$
$198$	−0.0478483	+	0.913001i	−0.00340043	+	0.0648841i
$199$	−1.75472	−	3.03927i	−0.124389	−	0.215448i	0.797105	−	0.603841i	$-0.206364\pi$
$199$	−1.75472	−	3.03927i	−0.124389	−	0.215448i	−0.921494	+	0.388393i	$0.873030\pi$
$200$		0			0
$201$	−1.04480	−	0.603214i	−0.0736943	−	0.0425474i
$202$	5.21329	−	2.65630i	0.366806	−	0.186897i
$203$	−13.7991	+	20.5751i	−0.968505	+	1.44409i
$204$	−6.59841	+	9.08193i	−0.461981	+	0.635863i
$205$		0			0
$206$	−3.72834	+	8.37398i	−0.259766	+	0.583443i
$207$	−4.95398	−	1.32741i	−0.344325	−	0.0922616i
$208$	0.259573	+	0.210198i	0.0179982	+	0.0145746i
$209$	0.447610	+	1.37760i	0.0309619	+	0.0952908i
$210$		0			0
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	0.478791	+	0.877929i	$0.341075\pi$
$211$	−6.16756	+	18.9818i	−0.424593	+	1.30676i	−0.903384	+	0.428833i	$0.858925\pi$
$212$	−8.62520	+	5.60127i	−0.592381	+	0.384697i
$213$	0.0655708	+	1.25116i	0.00449283	+	0.0857284i
$214$	1.04774	+	4.92923i	0.0716221	+	0.336955i
$215$		0			0
$216$	15.5542	−	5.05385i	1.05833	−	0.343871i
$217$	4.64884	−	11.5944i	0.315584	−	0.787080i
$218$	−10.7331	−	10.7331i	−0.726934	−	0.726934i
$219$	−4.87545	+	0.512430i	−0.329452	+	0.0346268i
$220$		0			0
$221$	−0.636549	+	6.05636i	−0.0428189	+	0.407395i
$222$	−7.49447	−	2.87686i	−0.502996	−	0.193082i
$223$	3.97575	+	7.80285i	0.266236	+	0.522518i	0.984961	−	0.172777i	$-0.0552739\pi$
$223$	3.97575	+	7.80285i	0.266236	+	0.522518i	−0.718725	+	0.695294i	$0.755274\pi$
$224$	−14.0371	−	3.20166i	−0.937893	−	0.213920i
$225$		0			0
$226$	−4.34502	+	7.52579i	−0.289026	+	0.500608i
$227$	−7.87576	−	5.11458i	−0.522733	−	0.339467i	0.256149	−	0.966637i	$-0.417546\pi$
$227$	−7.87576	−	5.11458i	−0.522733	−	0.339467i	−0.778882	+	0.627171i	$0.784213\pi$
$228$	2.15978	−	1.74895i	0.143035	−	0.115827i
$229$	−7.85820	+	3.49870i	−0.519285	+	0.231200i	−0.649606	−	0.760271i	$-0.725066\pi$
$229$	−7.85820	+	3.49870i	−0.519285	+	0.231200i	0.130321	+	0.991472i	$0.458399\pi$
$230$		0			0
$231$	2.20094	+	1.64942i	0.144811	+	0.108524i
$232$	−19.2651	+	19.2651i	−1.26482	+	1.26482i
$233$	1.75308	−	2.16487i	0.114848	−	0.141825i	−0.716480	−	0.697608i	$-0.754248\pi$
$233$	1.75308	−	2.16487i	0.114848	−	0.141825i	0.831328	+	0.555782i	$0.187581\pi$
$234$	0.636712	−	0.707140i	0.0416232	−	0.0462272i
$235$		0			0
$236$	−9.68182	+	8.71755i	−0.630233	+	0.567464i
$237$	−2.93343	+	5.75718i	−0.190547	+	0.373969i
$238$	6.27390	+	17.0967i	0.406676	+	1.10821i
$239$	10.2364	+	3.32600i	0.662136	+	0.215141i	0.620757	−	0.784003i	$-0.286825\pi$
$239$	10.2364	+	3.32600i	0.662136	+	0.215141i	0.0413782	+	0.999144i	$0.486825\pi$
$240$		0			0
$241$	7.84239	+	7.06132i	0.505173	+	0.454860i	0.881881	−	0.471472i	$-0.156277\pi$
$241$	7.84239	+	7.06132i	0.505173	+	0.454860i	−0.376708	+	0.926332i	$0.622944\pi$
$242$	8.97191	−	3.44399i	0.576736	−	0.221388i
$243$	−3.11283	−	11.6172i	−0.199688	−	0.745247i
$244$	7.81753	−	5.67977i	0.500466	−	0.363610i
$245$		0			0
$246$	−2.50714	−	1.82155i	−0.159850	−	0.116137i
$247$	0.540272	−	1.40746i	0.0343767	−	0.0895543i
$248$	7.48208	−	11.5214i	0.475113	−	0.731609i
$249$	−5.95446	+	3.43781i	−0.377349	+	0.217862i
$250$		0			0
$251$			29.0617i			1.83436i	0.398477	+	0.917178i	$0.369539\pi$
$251$			29.0617i			1.83436i	−0.398477	+	0.917178i	$0.630461\pi$
$252$	−1.03635	+	3.65058i	−0.0652841	+	0.229965i
$253$	−0.503111	−	3.17652i	−0.0316303	−	0.199706i
$254$	−1.09831	−	2.46684i	−0.0689140	−	0.154783i
$255$		0			0
$256$	−15.3164	−	6.81930i	−0.957275	−	0.426206i
$257$	−17.9822	+	4.81832i	−1.12170	+	0.300559i	−0.771571	−	0.636143i	$-0.780529\pi$
$257$	−17.9822	+	4.81832i	−1.12170	+	0.300559i	−0.350129	+	0.936701i	$0.613862\pi$
$258$	−0.486492	+	3.07159i	−0.0302876	+	0.191229i
$259$	14.1999	−	9.99891i	0.882339	−	0.621302i
$260$		0			0
$261$	7.86279	+	8.73251i	0.486694	+	0.540529i
$262$	6.22362	−	0.326166i	0.384496	−	0.0201506i
$263$	−20.6879	+	1.08421i	−1.27567	+	0.0668552i	−0.678106	−	0.734964i	$-0.737199\pi$
$263$	−20.6879	+	1.08421i	−1.27567	+	0.0668552i	−0.597567	+	0.801819i	$0.703866\pi$
$264$	2.02395	+	2.24783i	0.124566	+	0.138344i
$265$		0			0
$266$	−0.404810	−	4.49027i	−0.0248205	−	0.275316i
$267$	0.119490	−	0.754428i	0.00731265	−	0.0461702i
$268$	1.00824	−	0.270156i	0.0615879	−	0.0165024i
$269$	−1.17313	−	0.522309i	−0.0715267	−	0.0318458i	0.370661	−	0.928768i	$-0.379131\pi$
$269$	−1.17313	−	0.522309i	−0.0715267	−	0.0318458i	−0.442188	+	0.896922i	$0.645798\pi$
$270$		0			0
$271$	5.04698	+	11.3357i	0.306582	+	0.688594i	0.999473	−	0.0324475i	$-0.0103302\pi$
$271$	5.04698	+	11.3357i	0.306582	+	0.688594i	−0.692891	+	0.721042i	$0.743664\pi$
$272$	0.474322	+	2.99475i	0.0287600	+	0.181583i
$273$	−0.699867	−	2.77574i	−0.0423579	−	0.167995i
$274$			18.0313i			1.08931i
$275$		0			0
$276$	−5.34381	+	3.08525i	−0.321660	+	0.185710i
$277$	−0.669930	+	1.03160i	−0.0402522	+	0.0619830i	−0.858224	−	0.513276i	$-0.828432\pi$
$277$	−0.669930	+	1.03160i	−0.0402522	+	0.0619830i	0.817972	+	0.575259i	$0.195099\pi$
$278$	0.340609	−	0.887317i	0.0204284	−	0.0532177i
$279$	−4.79347	−	3.48266i	−0.286977	−	0.208501i
$280$		0			0
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	−0.544440	−	0.838800i	$-0.683258\pi$
$281$	1.42595	−	1.03602i	0.0850652	−	0.0618035i	0.629505	+	0.776996i	$0.283258\pi$
$282$	−3.64670	−	13.6097i	−0.217158	−	0.810445i
$283$	−14.0763	+	5.40338i	−0.836748	+	0.321198i	−0.738742	−	0.673988i	$-0.764580\pi$
$283$	−14.0763	+	5.40338i	−0.836748	+	0.321198i	−0.0980061	+	0.995186i	$0.531246\pi$
$284$	−0.805566	−	0.725335i	−0.0478016	−	0.0430407i
$285$		0			0
$286$	0.567492	+	0.184389i	0.0335565	+	0.0109032i
$287$	6.29398	−	2.30968i	0.371522	−	0.136336i
$288$	−3.10033	+	6.08473i	−0.182689	+	0.358546i
$289$	−28.4488	+	25.6154i	−1.67346	+	1.50679i
$290$		0			0
$291$	−9.46360	+	10.5104i	−0.554766	+	0.616130i
$292$	2.66925	−	3.29625i	0.156206	−	0.192899i
$293$	2.74224	−	2.74224i	0.160203	−	0.160203i	−0.622454	−	0.782657i	$-0.713864\pi$
$293$	2.74224	−	2.74224i	0.160203	−	0.160203i	0.782657	+	0.622454i	$0.213864\pi$
$294$	−5.53731	−	6.52870i	−0.322942	−	0.380762i
$295$		0			0
$296$	17.4482	−	7.76842i	1.01415	−	0.451530i
$297$	3.43750	−	2.78363i	0.199464	−	0.161523i
$298$	8.84129	+	5.74160i	0.512162	+	0.332602i
$299$	−1.67366	+	2.89886i	−0.0967902	+	0.167646i
$300$		0			0
$301$	−4.93259	−	4.57540i	−0.284310	−	0.263722i
$302$	4.66195	+	9.14958i	0.268265	+	0.526499i
$303$	−7.79441	−	2.99200i	−0.447777	−	0.171886i
$304$	0.0784623	−	0.746519i	0.00450012	−	0.0428158i
$305$		0			0
$306$	8.59073	−	0.902922i	0.491099	−	0.0516166i
$307$	19.7851	+	19.7851i	1.12920	+	1.12920i	0.990308	+	0.138889i	$0.0443532\pi$
$307$	19.7851	+	19.7851i	1.12920	+	1.12920i	0.138889	+	0.990308i	$0.455647\pi$
$308$	−2.35562	+	0.337412i	−0.134224	+	0.0192258i
$309$	12.4397	−	4.04190i	0.707669	−	0.229935i
$310$		0			0
$311$	−4.40295	−	20.7142i	−0.249668	−	1.17460i	−0.907045	−	0.421034i	$-0.861667\pi$
$311$	−4.40295	−	20.7142i	−0.249668	−	1.17460i	0.657377	−	0.753562i	$-0.271666\pi$
$312$	−0.164761	−	3.14383i	−0.00932777	−	0.177984i
$313$	4.03024	−	2.61727i	0.227802	−	0.147937i	−0.425692	−	0.904868i	$-0.639969\pi$
$313$	4.03024	−	2.61727i	0.227802	−	0.147937i	0.653494	+	0.756932i	$0.273302\pi$
$314$	4.76941	−	14.6787i	0.269153	−	0.828369i
$315$		0			0
$316$	−1.72754	−	5.31683i	−0.0971818	−	0.299095i
$317$	−23.0932	−	18.7005i	−1.29704	−	1.05033i	−0.995290	−	0.0969400i	$-0.969095\pi$
$317$	−23.0932	−	18.7005i	−1.29704	−	1.05033i	−0.301754	−	0.953386i	$-0.597572\pi$
$318$	−10.6294	−	2.84814i	−0.596068	−	0.159716i
$319$	−2.99710	+	6.73159i	−0.167805	+	0.376896i
$320$		0			0
$321$	4.22663	−	5.81746i	0.235908	−	0.324699i
$322$	−0.671883	+	9.98766i	−0.0374426	+	0.556591i
$323$	12.1940	−	6.21317i	0.678495	−	0.345710i
$324$	−3.62308	−	2.09178i	−0.201282	−	0.116210i
$325$		0			0
$326$	−9.52165	−	16.4920i	−0.527355	−	0.913406i
$327$	−1.13355	+	21.6294i	−0.0626853	+	1.19611i
$328$	7.28234	−	1.15341i	0.402100	−	0.0636864i
$329$	28.8473	+	9.84771i	1.59040	+	0.542922i
$330$		0			0
$331$	−2.40459	−	22.8781i	−0.132168	−	1.25749i	−0.836636	−	0.547759i	$-0.815481\pi$
$331$	−2.40459	−	22.8781i	−0.132168	−	1.25749i	0.704468	−	0.709735i	$-0.251185\pi$
$332$	1.53966	−	5.74610i	0.0845000	−	0.315358i
$333$	−2.95207	−	7.69041i	−0.161772	−	0.421432i
$334$	−4.28334	−	0.910453i	−0.234374	−	0.0498178i
$335$		0			0
$336$	−0.694290	−	1.24476i	−0.0378766	−	0.0679073i
$337$	4.75641	+	2.42351i	0.259098	+	0.132017i	0.578715	−	0.815530i	$-0.303554\pi$
$337$	4.75641	+	2.42351i	0.259098	+	0.132017i	−0.319617	+	0.947547i	$0.603554\pi$
$338$	6.21653	+	9.57261i	0.338134	+	0.520681i
$339$	12.1291	−	2.57811i	0.658760	−	0.140024i
$340$		0			0
$341$	0.772489	−	3.63428i	0.0418326	−	0.196807i
$342$	−2.11213	−	0.334529i	−0.114211	−	0.0180893i
$343$	18.4029	−	2.08188i	0.993662	−	0.112411i
$344$	−4.34902	−	5.98591i	−0.234484	−	0.322739i
$345$		0			0
$346$	4.64696	+	0.488415i	0.249822	+	0.0262573i
$347$	−10.8326	−	13.3772i	−0.581525	−	0.718124i	0.398462	−	0.917185i	$-0.369544\pi$
$347$	−10.8326	−	13.3772i	−0.581525	−	0.718124i	−0.979987	+	0.199061i	$0.936211\pi$
$348$	14.1182	+	0.739905i	0.756817	+	0.0396631i
$349$	20.0775			1.07472			0.537362	−	0.843351i	$-0.319421\pi$
$349$	20.0775			1.07472			0.537362	+	0.843351i	$0.319421\pi$
$350$		0			0
$351$	−4.60369			−0.245727
$352$	−4.27648	−	0.224121i	−0.227937	−	0.0119457i
$353$	8.10825	+	10.0129i	0.431559	+	0.532931i	0.945815	−	0.324706i	$-0.105265\pi$
$353$	8.10825	+	10.0129i	0.431559	+	0.532931i	−0.514256	+	0.857637i	$0.671932\pi$
$354$	−13.8639	−	1.45715i	−0.736858	−	0.0774469i
$355$		0			0
$356$	0.388449	+	0.534654i	0.0205878	+	0.0283366i
$357$	12.1392	−	22.9768i	0.642473	−	1.21606i
$358$	3.30079	+	0.522794i	0.174452	+	0.0276305i
$359$	1.60689	−	7.55982i	0.0848084	−	0.398992i	−0.915183	−	0.403038i	$-0.867954\pi$
$359$	1.60689	−	7.55982i	0.0848084	−	0.398992i	0.999992	+	0.00404548i	$0.00128772\pi$
$360$		0			0
$361$	15.2708	−	3.24590i	0.803725	−	0.170837i
$362$	−6.25728	−	9.63536i	−0.328875	−	0.506423i
$363$	−12.2184	−	6.22559i	−0.641300	−	0.326759i
$364$	2.12634	+	1.27000i	0.111451	+	0.0665660i
$365$		0			0
$366$	10.1136	+	2.14970i	0.528644	+	0.112367i
$367$	−1.18564	−	3.08870i	−0.0618899	−	0.161229i	0.899148	−	0.437644i	$-0.144187\pi$
$367$	−1.18564	−	3.08870i	−0.0618899	−	0.161229i	−0.961038	+	0.276415i	$0.910854\pi$
$368$	−0.431357	+	1.60984i	−0.0224860	+	0.0839189i
$369$	−0.332402	−	3.16260i	−0.0173042	−	0.164638i
$370$		0			0
$371$	17.9260	−	15.6662i	0.930669	−	0.813347i
$372$	−7.04080	+	1.11515i	−0.365049	+	0.0578180i
$373$	−0.198805	+	3.79343i	−0.0102937	+	0.196416i	0.988642	+	0.150290i	$0.0480209\pi$
$373$	−0.198805	+	3.79343i	−0.0102937	+	0.196416i	−0.998936	+	0.0461259i	$0.985312\pi$
$374$	2.70837	+	4.69103i	0.140046	+	0.242567i
$375$		0			0
$376$	29.0312	+	16.7612i	1.49717	+	0.864391i
$377$	6.83335	−	3.48176i	0.351935	−	0.179320i
$378$	−12.3581	+	6.06793i	−0.635632	+	0.312101i
$379$	−17.8775	+	24.6063i	−0.918306	+	1.26394i	0.0459436	+	0.998944i	$0.485371\pi$
$379$	−17.8775	+	24.6063i	−0.918306	+	1.26394i	−0.964250	+	0.264996i	$0.914629\pi$
$380$		0			0
$381$	−1.56720	+	3.51999i	−0.0802902	+	0.180335i
$382$	20.7435	+	5.55820i	1.06133	+	0.284382i
$383$	15.7990	+	12.7938i	0.807291	+	0.653732i	0.941422	−	0.337232i	$-0.109491\pi$
$383$	15.7990	+	12.7938i	0.807291	+	0.653732i	−0.134130	+	0.990964i	$0.542824\pi$
$384$	2.23072	+	6.86544i	0.113836	+	0.350350i
$385$		0			0
$386$	−4.27576	+	13.1594i	−0.217630	+	0.669797i
$387$	−2.67635	+	1.73804i	−0.136046	+	0.0883496i
$388$	−0.640418	−	12.2199i	−0.0325123	−	0.620372i
$389$	2.32066	+	10.9179i	0.117662	+	0.553558i	0.997003	+	0.0773644i	$0.0246505\pi$
$389$	2.32066	+	10.9179i	0.117662	+	0.553558i	−0.879341	+	0.476194i	$0.842016\pi$
$390$		0			0
$391$	−28.8993	+	9.38994i	−1.46150	+	0.474870i
$392$	20.2992	+	1.66787i	1.02526	+	0.0842401i
$393$	−6.28817	−	6.28817i	−0.317196	−	0.317196i
$394$	−1.38811	+	0.145896i	−0.0699317	+	0.00735012i
$395$		0			0
$396$	−0.117983	+	1.12253i	−0.00592888	+	0.0564095i
$397$	10.6643	+	4.09363i	0.535224	+	0.205453i	0.610941	−	0.791676i	$-0.290791\pi$
$397$	10.6643	+	4.09363i	0.535224	+	0.205453i	−0.0757170	+	0.997129i	$0.524125\pi$
$398$	1.47500	+	2.89484i	0.0739348	+	0.145105i
$399$	−4.37503	+	4.71657i	−0.219025	+	0.236124i
$400$		0			0
$401$	14.5815	−	25.2559i	0.728165	−	1.26122i	−0.229493	−	0.973310i	$-0.573707\pi$
$401$	14.5815	−	25.2559i	0.728165	−	1.26122i	0.957658	−	0.287908i	$-0.0929597\pi$
$402$	0.936694	+	0.608296i	0.0467181	+	0.0303391i
$403$	−3.00526	+	2.43361i	−0.149703	+	0.121227i
$404$	6.59902	−	2.93807i	0.328314	−	0.146175i
$405$		0			0
$406$	13.7542	−	18.3532i	0.682610	−	0.910853i
$407$	3.65262	−	3.65262i	0.181054	−	0.181054i
$408$	17.9850	−	22.2096i	0.890390	−	1.09954i
$409$	−21.5981	+	23.9872i	−1.06796	+	1.18609i	−0.0861370	+	0.996283i	$0.527452\pi$
$409$	−21.5981	+	23.9872i	−1.06796	+	1.18609i	−0.981822	+	0.189805i	$0.939214\pi$
$410$		0			0
$411$	19.1206	−	17.2162i	0.943147	−	0.849214i
$412$	−5.13768	+	10.0833i	−0.253115	+	0.496767i
$413$	19.3243	−	23.1538i	0.950888	−	1.13933i
$414$	4.51566	+	1.46723i	0.221933	+	0.0721103i
$415$		0			0
$416$	3.31224	+	2.98235i	0.162396	+	0.146222i
$417$	−1.26613	+	0.486023i	−0.0620029	+	0.0238007i
$418$	−0.347072	−	1.29529i	−0.0169758	−	0.0633547i
$419$	22.7957	−	16.5620i	1.11364	−	0.809109i	0.130410	−	0.991460i	$-0.458371\pi$
$419$	22.7957	−	16.5620i	1.11364	−	0.809109i	0.983233	+	0.182351i	$0.0583708\pi$
$420$		0			0
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	0.0965173	−	0.995331i	$-0.469230\pi$
$421$	−16.8306	−	12.2282i	−0.820274	−	0.595964i	−0.916791	+	0.399368i	$0.869230\pi$
$422$	6.62164	−	17.2500i	0.322337	−	0.839715i
$423$	7.87447	−	12.1256i	0.382870	−	0.589568i
$424$	22.6739	−	13.0908i	1.10114	−	0.635744i
$425$		0			0
$426$		−	1.15989i		−	0.0561967i
$427$	−16.0494	+	15.5810i	−0.776687	+	0.754015i
$428$	0.973254	+	6.14488i	0.0470440	+	0.297024i
$429$	−0.346312	−	0.777830i	−0.0167201	−	0.0375540i
$430$		0			0
$431$	2.27190	+	1.01151i	0.109434	+	0.0487229i	0.460723	−	0.887544i	$-0.347590\pi$
$431$	2.27190	+	1.01151i	0.109434	+	0.0487229i	−0.351290	+	0.936267i	$0.614257\pi$
$432$	−2.21408	+	0.593260i	−0.106525	+	0.0285432i
$433$	−1.44743	+	9.13869i	−0.0695589	+	0.439178i	0.928189	+	0.372108i	$0.121365\pi$
$433$	−1.44743	+	9.13869i	−0.0695589	+	0.439178i	−0.997748	+	0.0670695i	$0.978635\pi$
$434$	−4.85964	+	10.4939i	−0.233270	+	0.503722i
$435$		0			0
$436$	−12.5391	−	13.9261i	−0.600516	−	0.666940i
$437$	7.51226	−	0.393701i	0.359360	−	0.0188333i
$438$	4.53221	−	0.237523i	0.216557	−	0.0113493i
$439$	−14.2078	−	15.7793i	−0.678099	−	0.753105i	0.301632	−	0.953425i	$-0.402469\pi$
$439$	−14.2078	−	15.7793i	−0.678099	−	0.753105i	−0.979731	+	0.200319i	$0.935802\pi$
$440$		0			0
$441$	1.17657	−	8.70537i	0.0560270	−	0.414541i
$442$	0.881932	−	5.56830i	0.0419492	−	0.264857i
$443$	−22.0209	+	5.90047i	−1.04624	+	0.280340i	−0.740698	−	0.671838i	$-0.765505\pi$
$443$	−22.0209	+	5.90047i	−1.04624	+	0.280340i	−0.305545	+	0.952178i	$0.598839\pi$
$444$	−9.05395	−	4.03108i	−0.429681	−	0.191306i
$445$		0			0
$446$	−3.29755	−	7.40641i	−0.156143	−	0.350704i
$447$	−2.35319	−	14.8575i	−0.111302	−	0.702734i
$448$	14.8981	+	4.22938i	0.703870	+	0.199819i
$449$			32.5816i			1.53762i	0.639478	+	0.768809i	$0.279150\pi$
$449$			32.5816i			1.53762i	−0.639478	+	0.768809i	$0.720850\pi$
$450$		0			0
$451$	1.72696	−	0.997060i	0.0813193	−	0.0469497i
$452$	−5.84318	+	8.99770i	−0.274840	+	0.423216i
$453$	5.25110	−	13.6796i	0.246718	−	0.642723i
$454$	7.03338	+	5.11005i	0.330093	+	0.239827i
$455$		0			0
$456$	−5.72376	+	4.15856i	−0.268040	+	0.194742i
$457$	2.09102	+	7.80380i	0.0978138	+	0.365046i	0.997431	−	0.0716332i	$-0.0228211\pi$
$457$	2.09102	+	7.80380i	0.0978138	+	0.365046i	−0.899617	+	0.436679i	$0.856154\pi$
$458$	7.43447	−	2.85383i	0.347390	−	0.133351i
$459$	−31.0572	−	27.9641i	−1.44963	−	1.30525i
$460$		0			0
$461$	36.2181	+	11.7680i	1.68684	+	0.548089i	0.986220	−	0.165441i	$-0.0529046\pi$
$461$	36.2181	+	11.7680i	1.68684	+	0.548089i	0.700625	+	0.713530i	$0.252905\pi$
$462$	−1.95486	−	1.63154i	−0.0909485	−	0.0759061i
$463$	16.6944	−	32.7647i	0.775856	−	1.52270i	−0.0749286	−	0.997189i	$-0.523873\pi$
$463$	16.6944	−	32.7647i	0.775856	−	1.52270i	0.850785	−	0.525514i	$-0.176127\pi$
$464$	2.83772	−	2.55509i	0.131738	−	0.118617i
$465$		0			0
$466$	−1.72562	+	1.91650i	−0.0799378	+	0.0887799i
$467$	13.1037	−	16.1817i	0.606366	−	0.748800i	−0.377831	−	0.925874i	$-0.623330\pi$
$467$	13.1037	−	16.1817i	0.606366	−	0.748800i	0.984197	+	0.177075i	$0.0566634\pi$
$468$	0.830684	−	0.830684i	0.0383984	−	0.0383984i
$469$	−2.22168	+	0.949984i	−0.102587	+	0.0438662i
$470$		0			0
$471$	−20.1193	+	8.95770i	−0.927050	+	0.412749i
$472$	25.7753	−	20.8724i	1.18640	−	0.960731i
$473$	−1.67828	−	1.08989i	−0.0771674	−	0.0501131i
$474$	2.99091	−	5.18041i	0.137377	−	0.237944i
$475$		0			0
$476$	6.63034	+	21.4836i	0.303901	+	0.984699i
$477$	−5.12650	−	10.0613i	−0.234726	−	0.460676i
$478$	−9.30243	−	3.57087i	−0.425483	−	0.163328i
$479$	0.146303	−	1.39198i	0.00668475	−	0.0636011i	−0.990671	−	0.136276i	$-0.956487\pi$
$479$	0.146303	−	1.39198i	0.00668475	−	0.0636011i	0.997356	+	0.0726744i	$0.0231534\pi$
$480$		0			0
$481$	−5.34686	+	0.561978i	−0.243796	+	0.0256240i
$482$	−6.90821	−	6.90821i	−0.314660	−	0.314660i
$483$	11.2325	−	8.82374i	0.511099	−	0.401494i
$484$	11.2839	−	3.66635i	0.512903	−	0.166652i
$485$		0			0
$486$	2.31496	+	10.8910i	0.105009	+	0.494027i
$487$	1.39215	+	26.5638i	0.0630844	+	1.20372i	0.828426	+	0.560098i	$0.189237\pi$
$487$	1.39215	+	26.5638i	0.0630844	+	1.20372i	−0.765342	+	0.643624i	$0.777430\pi$
$488$	−20.6310	+	13.3980i	−0.933923	+	0.606497i
$489$	−8.39703	+	25.8434i	−0.379727	+	1.16868i
$490$		0			0
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	0.952486	−	0.304582i	$-0.0985166\pi$
$491$	0.0638187	+	0.196414i	0.00288010	+	0.00886403i	−0.949606	+	0.313446i	$0.898517\pi$
$492$	−2.97333	−	2.40775i	−0.134048	−	0.108550i
$493$	67.2481	+	18.0191i	3.02870	+	0.811538i
$494$	−0.567678	+	1.27502i	−0.0255410	+	0.0573661i
$495$		0			0
$496$	−1.13172	+	1.55769i	−0.0508159	+	0.0699421i
$497$	2.08401	+	1.39768i	0.0934805	+	0.0626945i
$498$	5.67150	−	2.88977i	0.254146	−	0.129494i
$499$	−20.4454	−	11.8042i	−0.915262	−	0.528427i	−0.0331413	−	0.999451i	$-0.510551\pi$
$499$	−20.4454	−	11.8042i	−0.915262	−	0.528427i	−0.882120	+	0.471024i	$0.843884\pi$
$500$		0			0
$501$	3.12428	+	5.41141i	0.139582	+	0.241764i
$502$	1.40808	−	26.8677i	0.0628455	−	1.19916i
$503$	3.25409	−	0.515396i	0.145092	−	0.0229804i	−0.0834657	−	0.996511i	$-0.526599\pi$
$503$	3.25409	−	0.515396i	0.145092	−	0.0229804i	0.228558	+	0.973530i	$0.426599\pi$
$504$	3.12108	−	9.14269i	0.139024	−	0.407248i
$505$		0			0
$506$	0.311223	+	2.96109i	0.0138355	+	0.131636i
$507$	4.21538	−	15.7320i	0.187211	−	0.698682i
$508$	−1.19470	−	3.11230i	−0.0530062	−	0.138086i
$509$	13.6817	+	2.90814i	0.606431	+	0.128901i	0.500885	−	0.865514i	$-0.333008\pi$
$509$	13.6817	+	2.90814i	0.606431	+	0.128901i	0.105545	+	0.994414i	$0.466341\pi$
$510$		0			0
$511$	−5.03461	+	8.42939i	−0.222718	+	0.372894i
$512$	4.09177	+	2.08486i	0.180832	+	0.0921387i
$513$	5.63487	+	8.67694i	0.248786	+	0.383096i
$514$	16.8581	−	3.58331i	0.743580	−	0.158053i
$515$		0			0
$516$	−0.798253	+	3.75548i	−0.0351411	+	0.165326i
$517$	8.95476	+	1.41829i	0.393830	+	0.0623765i
$518$	−13.6123	+	8.55605i	−0.598092	+	0.375931i
$519$	−3.91899	−	5.39402i	−0.172024	−	0.236771i
$520$		0			0
$521$	28.2500	+	2.96919i	1.23765	+	0.130083i	0.700655	−	0.713500i	$-0.252891\pi$
$521$	28.2500	+	2.96919i	1.23765	+	0.130083i	0.536999	+	0.843583i	$0.319558\pi$
$522$	−6.84609	−	8.45422i	−0.299645	−	0.370031i
$523$	−39.6524	−	2.07809i	−1.73388	−	0.0908687i	−0.840962	−	0.541094i	$-0.818010\pi$
$523$	−39.6524	−	2.07809i	−1.73388	−	0.0908687i	−0.892915	+	0.450225i	$0.851344\pi$
$524$	7.69409			0.336118
$525$		0			0
$526$	19.1787			0.836229
$527$	−35.0564	−	1.83723i	−1.52708	−	0.0800308i
$528$	−0.266790	−	0.329458i	−0.0116105	−	0.0143378i
$529$	6.26305	+	0.658273i	0.272307	+	0.0286206i
$530$		0			0
$531$	−8.40811	−	11.5728i	−0.364881	−	0.502215i
$532$	−0.208955	−	5.56215i	−0.00905937	−	0.241150i
$533$	−2.04992	−	0.324675i	−0.0887918	−	0.0140632i
$534$	−0.147022	+	0.691684i	−0.00636226	+	0.0299321i
$535$		0			0
$536$	−2.59921	+	0.552478i	−0.112269	+	0.0238634i
$537$	−2.59722	−	3.99936i	−0.112078	−	0.172585i
$538$	1.05926	+	0.539718i	0.0456677	+	0.0232689i
$539$	5.28709	−	1.54634i	0.227731	−	0.0666056i
$540$		0			0
$541$	1.28954	+	0.274100i	0.0554417	+	0.0117845i	0.235549	−	0.971862i	$-0.424311\pi$
$541$	1.28954	+	0.274100i	0.0554417	+	0.0117845i	−0.180107	+	0.983647i	$0.557645\pi$
$542$	−4.11673	−	10.7244i	−0.176829	−	0.460654i
$543$	−4.24301	+	15.8351i	−0.182085	+	0.679550i
$544$	4.22927	+	40.2389i	0.181329	+	1.72523i
$545$		0			0
$546$	0.512543	+	2.60010i	0.0219348	+	0.111274i
$547$	−21.4047	+	3.39018i	−0.915200	+	0.144953i	−0.596232	−	0.802812i	$-0.703336\pi$
$547$	−21.4047	+	3.39018i	−0.915200	+	0.144953i	−0.318968	+	0.947766i	$0.603336\pi$
$548$	−1.16505	+	22.2305i	−0.0497685	+	0.949639i
$549$	5.30491	+	9.18838i	0.226408	+	0.392150i
$550$		0			0
$551$	−14.9263	−	8.61771i	−0.635882	−	0.367127i
$552$	13.9965	−	7.13156i	0.595730	−	0.303539i
$553$	5.70373	+	11.6164i	0.242547	+	0.493978i
$554$	0.669337	−	0.921263i	0.0284374	−	0.0391407i
$555$		0			0
$556$	0.477264	−	1.07195i	0.0202405	−	0.0454609i
$557$	−10.8954	−	2.91942i	−0.461654	−	0.123700i	0.0204931	−	0.999790i	$-0.493476\pi$
$557$	−10.8954	−	2.91942i	−0.461654	−	0.123700i	−0.482147	+	0.876090i	$0.660143\pi$
$558$	4.26285	+	3.45199i	0.180461	+	0.146134i
$559$	0.643607	+	1.98082i	0.0272217	+	0.0837797i
$560$		0			0
$561$	2.38847	−	7.35097i	0.100841	−	0.310358i
$562$	−1.36850	+	0.888713i	−0.0577266	+	0.0374881i
$563$	0.259044	+	4.94286i	0.0109174	+	0.208317i	0.998641	+	0.0521079i	$0.0165940\pi$
$563$	0.259044	+	4.94286i	0.0109174	+	0.208317i	−0.987724	+	0.156209i	$0.950073\pi$
$564$	−3.61661	−	17.0148i	−0.152287	−	0.716453i
$565$		0			0
$566$	13.2754	−	4.31344i	0.558007	−	0.181307i
$567$	8.98876	+	3.60409i	0.377493	+	0.151358i
$568$	1.95133	+	1.95133i	0.0818759	+	0.0818759i
$569$	16.8195	−	1.76780i	0.705109	−	0.0741099i	0.254814	−	0.966990i	$-0.417986\pi$
$569$	16.8195	−	1.76780i	0.705109	−	0.0741099i	0.450295	+	0.892880i	$0.351319\pi$
$570$		0			0
$571$	−3.00592	+	28.5994i	−0.125794	+	1.19685i	0.731434	+	0.681912i	$0.238851\pi$
$571$	−3.00592	+	28.5994i	−0.125794	+	1.19685i	−0.857228	+	0.514937i	$0.827815\pi$
$572$	0.687740	+	0.263999i	0.0287558	+	0.0110383i
$573$	−13.9119	−	27.3036i	−0.581177	−	1.14062i
$574$	−5.93072	+	1.83036i	−0.247544	+	0.0763977i
$575$		0			0
$576$	3.67285	−	6.36156i	0.153035	−	0.265065i
$577$	8.70310	+	5.65186i	0.362315	+	0.235290i	0.712939	−	0.701226i	$-0.247364\pi$
$577$	8.70310	+	5.65186i	0.362315	+	0.235290i	−0.350624	+	0.936516i	$0.614030\pi$
$578$	27.5422	−	22.3032i	1.14560	−	0.927692i
$579$	18.0369	−	8.03054i	0.749588	−	0.333738i
$580$		0			0
$581$	−1.64209	+	13.6724i	−0.0681253	+	0.567227i
$582$	9.25840	−	9.25840i	0.383773	−	0.383773i
$583$	4.45623	−	5.50298i	0.184558	−	0.227910i
$584$	−7.22514	+	8.02433i	−0.298978	+	0.332049i
$585$		0			0
$586$	−2.66808	+	2.40235i	−0.110217	+	0.0992401i
$587$	2.08337	−	4.08885i	0.0859899	−	0.168765i	−0.844007	−	0.536332i	$-0.819809\pi$
$587$	2.08337	−	4.08885i	0.0859899	−	0.168765i	0.929997	+	0.367568i	$0.119809\pi$
$588$	−6.40503	−	8.40693i	−0.264139	−	0.346696i
$589$	8.26522	+	2.68553i	0.340563	+	0.110655i
$590$		0			0
$591$	1.48007	+	1.33266i	0.0608820	+	0.0548184i
$592$	−2.49908	+	0.959305i	−0.102711	+	0.0394272i
$593$	−3.98715	−	14.8803i	−0.163733	−	0.611059i	−0.998198	−	0.0599990i	$-0.980890\pi$
$593$	−3.98715	−	14.8803i	−0.163733	−	0.611059i	0.834466	−	0.551060i	$-0.185776\pi$
$594$	−3.31286	+	2.40693i	−0.135928	+	0.0987577i
$595$		0			0
$596$	10.5293	+	7.65000i	0.431298	+	0.313356i
$597$	1.66140	−	4.32809i	0.0679965	−	0.177137i
$598$	1.68776	−	2.59893i	0.0690177	−	0.106278i
$599$	−13.4466	+	7.76339i	−0.549413	+	0.317204i	−0.748885	−	0.662700i	$-0.769411\pi$
$599$	−13.4466	+	7.76339i	−0.549413	+	0.317204i	0.199472	+	0.979903i	$0.436077\pi$
$600$		0			0
$601$		−	41.2449i		−	1.68241i	−0.540714	−	0.841207i	$-0.681846\pi$
$601$		−	41.2449i		−	1.68241i	0.540714	−	0.841207i	$-0.318154\pi$
$602$	4.33853	+	4.46898i	0.176825	+	0.182142i
$603$	0.179286	+	1.13197i	0.00730110	+	0.0460974i
$604$	5.15647	+	11.5816i	0.209814	+	0.471249i
$605$		0			0
$606$	7.06102	+	3.14377i	0.286834	+	0.127707i
$607$	−10.7885	+	2.89077i	−0.437891	+	0.117333i	−0.471028	−	0.882118i	$-0.656117\pi$
$607$	−10.7885	+	2.89077i	−0.437891	+	0.117333i	0.0331368	+	0.999451i	$0.489450\pi$
$608$	1.56693	−	9.89320i	0.0635474	−	0.401222i
$609$	−32.5944	+	2.93847i	−1.32079	+	0.119073i
$610$		0			0
$611$	−6.31408	−	7.01250i	−0.255441	−	0.283695i
$612$	10.6497	−	0.558129i	0.430490	−	0.0225610i
$613$	−3.09870	+	0.162396i	−0.125155	+	0.00655911i	−0.114811	−	0.993387i	$-0.536626\pi$
$613$	−3.09870	+	0.162396i	−0.125155	+	0.00655911i	−0.0103446	+	0.999946i	$0.503293\pi$
$614$	−17.3329	−	19.2501i	−0.699497	−	0.776870i
$615$		0			0
$616$	6.03357	−	0.543942i	0.243099	−	0.0219161i
$617$	−7.16450	+	45.2349i	−0.288432	+	1.82109i	0.238456	+	0.971153i	$0.423359\pi$
$617$	−7.16450	+	45.2349i	−0.288432	+	1.82109i	−0.526888	+	0.849935i	$0.676641\pi$
$618$	−11.6964	+	3.13404i	−0.470498	+	0.126070i
$619$	16.3273	+	7.26936i	0.656248	+	0.292180i	0.707719	−	0.706494i	$-0.249724\pi$
$619$	16.3273	+	7.26936i	0.656248	+	0.292180i	−0.0514712	+	0.998674i	$0.516391\pi$
$620$		0			0
$621$	−9.34334	−	20.9855i	−0.374935	−	0.842119i
$622$	3.06692	+	19.3638i	0.122972	+	0.776416i
$623$	−1.06561	−	1.09765i	−0.0426927	−	0.0439764i
$624$			0.441228i			0.0176633i
$625$		0			0
$626$	−3.85279	+	2.22441i	−0.153988	+	0.0889052i
$627$	−1.04216	+	1.60478i	−0.0416197	+	0.0640887i
$628$	6.82858	−	17.7891i	0.272490	−	0.709861i
$629$	−39.4844	−	28.6871i	−1.57435	−	1.14383i
$630$		0			0
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	−0.586627	−	0.809857i	$-0.699545\pi$
$631$	0.0581461	−	0.0422456i	0.00231476	−	0.00168177i	0.588942	+	0.808175i	$0.299545\pi$
$632$	3.68350	+	13.7470i	0.146522	+	0.546826i
$633$	−24.6144	+	9.44859i	−0.978335	+	0.375548i
$634$	20.4438	+	18.4076i	0.811925	+	0.731061i
$635$		0			0
$636$	−12.9208	−	4.19823i	−0.512344	−	0.166471i
$637$	−5.28930	−	2.21225i	−0.209570	−	0.0876526i
$638$	3.09699	−	6.07818i	0.122611	−	0.240637i
$639$	0.884499	−	0.796406i	0.0349902	−	0.0315053i
$640$		0			0
$641$	−15.6503	+	17.3814i	−0.618149	+	0.686524i	−0.968192	−	0.250209i	$-0.919501\pi$
$641$	−15.6503	+	17.3814i	−0.618149	+	0.686524i	0.350042	+	0.936734i	$0.386167\pi$
$642$	−4.18941	+	5.17349i	−0.165343	+	0.204181i
$643$	−20.9354	+	20.9354i	−0.825611	+	0.825611i	−0.986906	−	0.161295i	$-0.948433\pi$
$643$	−20.9354	+	20.9354i	−0.825611	+	0.825611i	0.161295	+	0.986906i	$0.448433\pi$
$644$	−1.47369	+	12.2702i	−0.0580714	+	0.483515i
$645$		0			0
$646$	−11.5745	+	5.15330i	−0.455393	+	0.202754i
$647$	−15.1558	+	12.2729i	−0.595837	+	0.482499i	−0.879161	−	0.476525i	$-0.841896\pi$
$647$	−15.1558	+	12.2729i	−0.595837	+	0.482499i	0.283324	+	0.959024i	$0.408563\pi$
$648$	8.93215	+	5.80061i	0.350888	+	0.227869i
$649$	4.48509	−	7.76840i	0.176055	−	0.304936i
$650$		0			0
$651$	15.7678	−	4.86631i	0.617989	−	0.190726i
$652$	−10.6735	−	20.9480i	−0.418007	−	0.820385i
$653$	−2.94945	−	1.13219i	−0.115421	−	0.0443060i	0.299972	−	0.953948i	$-0.403023\pi$
$653$	−2.94945	−	1.13219i	−0.115421	−	0.0443060i	−0.415393	+	0.909642i	$0.636356\pi$
$654$	2.09594	−	19.9415i	0.0819578	−	0.779776i
$655$		0			0
$656$	−1.02772	+	0.108018i	−0.0401257	+	0.00421738i
$657$	3.29305	+	3.29305i	0.128474	+	0.128474i
$658$	−26.1924	−	10.5020i	−1.02108	−	0.409409i
$659$	−13.3517	+	4.33824i	−0.520110	+	0.168994i	−0.557295	−	0.830314i	$-0.688161\pi$
$659$	−13.3517	+	4.33824i	−0.520110	+	0.168994i	0.0371852	+	0.999308i	$0.488161\pi$
$660$		0			0
$661$	2.64972	+	12.4660i	0.103062	+	0.484870i	0.999159	+	0.0410104i	$0.0130577\pi$
$661$	2.64972	+	12.4660i	0.103062	+	0.484870i	−0.896096	+	0.443859i	$0.853609\pi$
$662$	1.11458	+	21.2674i	0.0433194	+	0.826583i
$663$	−6.74676	+	4.38140i	−0.262022	+	0.170159i
$664$	−4.67982	+	14.4030i	−0.181612	+	0.558945i
$665$		0			0
$666$	2.35660	+	7.25286i	0.0913163	+	0.281043i
$667$	29.7398	+	24.0828i	1.15153	+	0.932491i
$668$	−5.22205	−	1.39924i	−0.202047	−	0.0541384i
$669$	−4.70535	+	10.5684i	−0.181919	+	0.408598i
$670$		0			0
$671$	−3.91065	+	5.38254i	−0.150969	+	0.207791i
$672$	−8.38270	−	17.0724i	−0.323369	−	0.658582i
$673$	−29.3231	+	14.9409i	−1.13032	+	0.575928i	−0.916137	−	0.400865i	$-0.868710\pi$
$673$	−29.3231	+	14.9409i	−1.13032	+	0.575928i	−0.214185	+	0.976793i	$0.568710\pi$
$674$	−4.27990	−	2.47100i	−0.164856	−	0.0951795i
$675$		0			0
$676$	7.04576	+	12.2036i	0.270991	+	0.469370i
$677$	0.304435	−	5.80896i	0.0117004	−	0.223256i	−0.986521	−	0.163636i	$-0.947678\pi$
$677$	0.304435	−	5.80896i	0.0117004	−	0.223256i	0.998221	−	0.0596203i	$-0.0189890\pi$
$678$	−11.3383	+	1.79581i	−0.435445	+	0.0689677i
$679$	5.47837	+	27.7914i	0.210241	+	1.06654i
$680$		0			0
$681$	−1.29671	−	12.3373i	−0.0496899	−	0.472768i
$682$	−0.890256	+	3.32248i	−0.0340897	+	0.127224i
$683$	6.32684	+	16.4820i	0.242090	+	0.630666i	0.999759	−	0.0219738i	$-0.00699503\pi$
$683$	6.32684	+	16.4820i	0.242090	+	0.630666i	−0.757669	+	0.652639i	$0.773662\pi$
$684$	−2.58241	−	0.548907i	−0.0987408	−	0.0209880i
$685$		0			0
$686$	−17.1144	+	1.03307i	−0.653432	+	0.0394427i
$687$	−10.1247	−	5.15877i	−0.386280	−	0.196819i
$688$	0.564794	+	0.869707i	0.0215326	+	0.0331572i
$689$	−7.20884	+	1.53229i	−0.274635	+	0.0583754i
$690$		0			0
$691$	−7.24591	+	34.0893i	−0.275647	+	1.29682i	0.594527	+	0.804075i	$0.297339\pi$
$691$	−7.24591	+	34.0893i	−0.275647	+	1.29682i	−0.870175	+	0.492743i	$0.835994\pi$
$692$	5.69761	+	0.902413i	0.216591	+	0.0343046i
$693$	−0.0980878	−	2.61098i	−0.00372605	−	0.0991831i
$694$	9.36667	+	12.8921i	0.355554	+	0.489378i
$695$		0			0
$696$	−35.7938	−	3.76208i	−1.35676	−	0.142601i
$697$	−11.8569	−	14.6421i	−0.449113	−	0.554608i
$698$	−18.5618	−	0.972782i	−0.702574	−	0.0368203i
$699$	3.67989			0.139186
$700$		0			0
$701$	−5.86630			−0.221567			−0.110783	−	0.993845i	$-0.535336\pi$
$701$	−5.86630			−0.221567			−0.110783	+	0.993845i	$0.535336\pi$
$702$	4.25614	+	0.223055i	0.160637	+	0.00841865i
$703$	7.60371	+	9.38980i	0.286779	+	0.354143i
$704$	4.58109	+	0.481492i	0.172656	+	0.0181469i
$705$		0			0
$706$	−7.01099	−	9.64980i	−0.263862	−	0.363175i
$707$	−14.1571	+	8.89848i	−0.532434	+	0.334662i
$708$	−16.9985	−	2.69229i	−0.638841	−	0.101183i
$709$	1.95872	−	9.21505i	0.0735612	−	0.346078i	−0.925940	−	0.377672i	$-0.876725\pi$
$709$	1.95872	−	9.21505i	0.0735612	−	0.346078i	0.999501	+	0.0315933i	$0.0100581\pi$
$710$		0			0
$711$	6.00408	−	1.27621i	0.225171	−	0.0478615i
$712$	−0.916309	−	1.41099i	−0.0343401	−	0.0528792i
$713$	−17.1927	−	8.76010i	−0.643870	−	0.328068i
$714$	−12.3360	+	20.6540i	−0.461663	+	0.772957i
$715$		0			0
$716$	4.03572	+	0.857819i	0.150822	+	0.0320582i
$717$	5.09536	+	13.2739i	0.190290	+	0.495722i
$718$	−1.85186	+	6.91124i	−0.0691109	+	0.257925i
$719$	4.40181	+	41.8805i	0.164160	+	1.56188i	0.697879	+	0.716216i	$0.254127\pi$
$719$	4.40181	+	41.8805i	0.164160	+	1.56188i	−0.533719	+	0.845662i	$0.679206\pi$
$720$		0			0
$721$	8.46329	−	24.7919i	0.315190	−	0.923297i
$722$	−14.2752	+	2.26097i	−0.531267	+	0.0841445i
$723$	−0.729594	+	13.9215i	−0.0271339	+	0.517746i
$724$	−7.09194	−	12.2836i	−0.263570	−	0.456517i
$725$		0			0
$726$	10.9944	+	6.34760i	0.408039	+	0.235581i
$727$	−11.3062	+	5.76081i	−0.419325	+	0.213657i	−0.650905	−	0.759159i	$-0.725610\pi$
$727$	−11.3062	+	5.76081i	−0.419325	+	0.213657i	0.231580	+	0.972816i	$0.425610\pi$
$728$	−5.23653	−	3.51198i	−0.194079	−	0.130163i
$729$	15.7932	−	21.7374i	0.584932	−	0.805090i
$730$		0			0
$731$	−7.69016	+	17.2724i	−0.284431	+	0.638842i
$732$	12.3300	+	3.30381i	0.455729	+	0.122112i
$733$	36.6547	+	29.6824i	1.35387	+	1.09634i	0.986050	+	0.166449i	$0.0532301\pi$
$733$	36.6547	+	29.6824i	1.35387	+	1.09634i	0.367823	+	0.929896i	$0.380103\pi$
$734$	0.946479	+	2.91296i	0.0349352	+	0.107519i
$735$		0			0
$736$	−6.87248	+	21.1513i	−0.253323	+	0.779648i
$737$	−0.602737	+	0.391422i	−0.0222021	+	0.0144182i
$738$	0.154076	+	2.93995i	0.00567162	+	0.108221i
$739$	−9.32981	−	43.8933i	−0.343203	−	1.61464i	−0.723875	−	0.689931i	$-0.757641\pi$
$739$	−9.32981	−	43.8933i	−0.343203	−	1.61464i	0.380673	−	0.924710i	$-0.375692\pi$
$740$		0			0
$741$	1.89407	−	0.615420i	0.0695804	−	0.0226080i
$742$	−17.3317	+	13.6149i	−0.636267	+	0.499820i
$743$	−11.1530	−	11.1530i	−0.409164	−	0.409164i	0.472283	−	0.881447i	$-0.343430\pi$
$743$	−11.1530	−	11.1530i	−0.409164	−	0.409164i	−0.881447	+	0.472283i	$0.843430\pi$
$744$	18.0482	−	1.89694i	0.661680	−	0.0695453i
$745$		0			0
$746$	0.367593	−	3.49741i	0.0134585	−	0.128049i
$747$	6.09786	+	2.34075i	0.223109	+	0.0856435i
$748$	3.03601	+	5.95850i	0.111007	+	0.217864i
$749$	−4.24708	−	13.7614i	−0.155185	−	0.502830i
$750$		0			0
$751$	−21.6997	+	37.5850i	−0.791834	+	1.37150i	0.132996	+	0.991117i	$0.457540\pi$
$751$	−21.6997	+	37.5850i	−0.791834	+	1.37150i	−0.924830	+	0.380380i	$0.875793\pi$
$752$	−3.94034	−	2.55889i	−0.143689	−	0.0933131i
$753$	−29.8352	+	24.1601i	−1.08726	+	0.880443i
$754$	−6.48617	+	2.88783i	−0.236212	+	0.105168i
$755$		0			0
$756$	−15.6282	+	6.68258i	−0.568392	+	0.243043i
$757$	35.7542	−	35.7542i	1.29951	−	1.29951i	0.370793	−	0.928716i	$-0.379086\pi$
$757$	35.7542	−	35.7542i	1.29951	−	1.29951i	0.928716	−	0.370793i	$-0.120914\pi$
$758$	17.7201	−	21.8825i	0.643622	−	0.794807i
$759$	2.84282	−	3.15727i	0.103188	−	0.114602i
$760$		0			0
$761$	3.28308	−	2.95609i	0.119011	−	0.107158i	−0.607476	−	0.794338i	$-0.707818\pi$
$761$	3.28308	−	2.95609i	0.119011	−	0.107158i	0.726488	+	0.687179i	$0.241151\pi$
$762$	1.61944	−	3.17832i	0.0586660	−	0.115138i
$763$	33.3040	+	27.7957i	1.20569	+	1.00627i
$764$	25.2152	+	8.19292i	0.912255	+	0.296409i
$765$		0			0
$766$	−13.9864	−	12.5934i	−0.505349	−	0.455018i
$767$	−8.71602	+	3.34577i	−0.314717	+	0.120809i
$768$	−5.73230	−	21.3932i	−0.206847	−	0.771962i
$769$	−29.9959	+	21.7933i	−1.08168	+	0.785888i	−0.977975	−	0.208720i	$-0.933070\pi$
$769$	−29.9959	+	21.7933i	−1.08168	+	0.785888i	−0.103706	+	0.994608i	$0.533070\pi$
$770$		0			0
$771$	−19.8959	−	14.4552i	−0.716533	−	0.520592i
$772$	−6.12179	+	15.9478i	−0.220328	+	0.573974i
$773$	−3.53856	+	5.44891i	−0.127273	+	0.195984i	−0.896563	−	0.442917i	$-0.853944\pi$
$773$	−3.53856	+	5.44891i	−0.127273	+	0.195984i	0.769290	+	0.638900i	$0.220610\pi$
$774$	2.55851	−	1.47716i	0.0919638	−	0.0530953i
$775$		0			0
$776$			31.1516i			1.11828i
$777$	22.0700	+	6.26539i	0.791756	+	0.224769i
$778$	−1.61648	−	10.2061i	−0.0579537	−	0.365905i
$779$	1.89714	+	4.26104i	0.0679721	+	0.152668i
$780$		0			0
$781$	0.681829	+	0.303570i	0.0243978	+	0.0108626i
$782$	27.1725	−	7.28085i	0.971687	−	0.260363i
$783$	−8.23336	+	51.9834i	−0.294236	+	1.85773i
$784$	−2.82890	−	0.382337i	−0.101032	−	0.0136549i
$785$		0			0
$786$	5.50878	+	6.11812i	0.196492	+	0.218226i
$787$	7.12353	−	0.373328i	0.253926	−	0.0133077i	0.0750519	−	0.997180i	$-0.476088\pi$
$787$	7.12353	−	0.373328i	0.253926	−	0.0133077i	0.178874	+	0.983872i	$0.442754\pi$
$788$	−1.72080	+	0.0901835i	−0.0613011	+	0.00321265i
$789$	−18.3118	−	20.3373i	−0.651916	−	0.724026i
$790$		0			0
$791$	10.4362	−	22.5359i	0.371069	−	0.801284i
$792$	0.449506	−	2.83807i	0.0159725	−	0.100846i
$793$	6.68866	−	1.79222i	0.237521	−	0.0636436i
$794$	−9.66083	−	4.30128i	−0.342850	−	0.152647i
$795$		0			0
$796$	1.63146	+	3.66431i	0.0578255	+	0.129878i
$797$	−4.68404	−	29.5739i	−0.165917	−	1.04756i	−0.920325	−	0.391154i	$-0.872076\pi$
$797$	−4.68404	−	29.5739i	−0.165917	−	1.04756i	0.754408	−	0.656406i	$-0.227924\pi$
$798$	4.27326	−	4.14852i	0.151272	−	0.146856i
$799$		−	85.6610i		−	3.03047i
$800$		0			0
$801$	−0.628409	+	0.362812i	−0.0222037	+	0.0128193i
$802$	−14.7044	+	22.6427i	−0.519229	+	0.799542i
$803$	−1.04656	+	2.72638i	−0.0369323	+	0.0962120i
$804$	1.11553	+	0.810483i	0.0393418	+	0.0285835i
$805$		0			0
$806$	2.89629	−	2.10428i	0.102017	−	0.0741200i
$807$	−0.439053	−	1.63857i	−0.0154554	−	0.0576803i
$808$	−17.1680	+	6.59016i	−0.603967	+	0.231841i
$809$	1.59024	+	1.43186i	0.0559098	+	0.0503414i	0.696612	−	0.717448i	$-0.254690\pi$
$809$	1.59024	+	1.43186i	0.0559098	+	0.0503414i	−0.640702	+	0.767790i	$0.721357\pi$
$810$		0			0
$811$	11.1135	+	3.61100i	0.390248	+	0.126799i	0.497567	−	0.867425i	$-0.334227\pi$
$811$	11.1135	+	3.61100i	0.390248	+	0.126799i	−0.107319	+	0.994225i	$0.534227\pi$
$812$	18.1432	−	21.7387i	0.636702	−	0.762878i
$813$	−7.44168	+	14.6051i	−0.260991	+	0.512224i
$814$	−3.55384	+	3.19989i	−0.124562	+	0.112156i
$815$		0			0
$816$	−2.68014	+	2.97660i	−0.0938237	+	0.104202i
$817$	2.94564	−	3.63756i	0.103055	−	0.127262i
$818$	21.1298	−	21.1298i	0.738786	−	0.738786i
$819$	−1.63084	+	2.17614i	−0.0569862	+	0.0760405i
$820$		0			0
$821$	24.0040	−	10.6873i	0.837744	−	0.372988i	0.0574100	−	0.998351i	$-0.481716\pi$
$821$	24.0040	−	10.6873i	0.837744	−	0.372988i	0.780334	+	0.625363i	$0.215049\pi$
$822$	−18.5112	+	14.9901i	−0.645653	+	0.522839i
$823$	−16.3309	−	10.6054i	−0.569261	−	0.369682i	0.227683	−	0.973735i	$-0.426885\pi$
$823$	−16.3309	−	10.6054i	−0.569261	−	0.369682i	−0.796944	+	0.604053i	$0.793552\pi$
$824$	14.4048	−	24.9499i	0.501816	−	0.869171i
$825$		0			0
$826$	−18.9873	+	20.4696i	−0.660652	+	0.712228i
$827$	−7.82374	−	15.3550i	−0.272058	−	0.533944i	0.714041	−	0.700104i	$-0.246863\pi$
$827$	−7.82374	−	15.3550i	−0.272058	−	0.533944i	−0.986099	+	0.166160i	$0.946863\pi$
$828$	5.47250	+	2.10070i	0.190182	+	0.0730042i
$829$	4.34045	−	41.2966i	0.150750	−	1.43429i	−0.613665	−	0.789567i	$-0.710305\pi$
$829$	4.34045	−	41.2966i	0.150750	−	1.43429i	0.764415	−	0.644725i	$-0.223028\pi$
$830$		0			0
$831$	−1.61600	+	0.169848i	−0.0560584	+	0.00589198i
$832$	−3.39004	−	3.39004i	−0.117529	−	0.117529i
$833$	−22.2447	−	47.0529i	−0.770733	−	1.63029i
$834$	1.19410	−	0.387986i	0.0413482	−	0.0134348i
$835$		0			0
$836$	−0.344208	−	1.61937i	−0.0119047	−	0.0560071i
$837$	−1.38890	−	26.5018i	−0.0480074	−	0.916036i
$838$	−21.8772	+	14.2072i	−0.755736	+	0.490781i
$839$	11.9529	−	36.7873i	0.412660	−	1.27004i	−0.501666	−	0.865061i	$-0.667280\pi$
$839$	11.9529	−	36.7873i	0.412660	−	1.27004i	0.914327	−	0.404977i	$-0.132720\pi$
$840$		0			0
$841$	−18.1325	−	55.8062i	−0.625260	−	1.92435i
$842$	14.9675	+	12.1205i	0.515815	+	0.417699i
$843$	2.24904	+	0.602629i	0.0774612	+	0.0207557i
$844$	9.27830	−	20.8394i	0.319372	−	0.717322i
$845$		0			0
$846$	−7.86749	+	10.8287i	−0.270490	+	0.372298i
$847$	−24.6533	+	12.1050i	−0.847098	+	0.415932i
$848$	−3.26953	+	1.66591i	−0.112276	+	0.0572075i
$849$	−17.2494	−	9.95893i	−0.591997	−	0.341789i
$850$		0			0
$851$	−13.4134	−	23.2326i	−0.459804	−	0.796404i
$852$	0.0749435	−	1.43001i	0.00256752	−	0.0489913i
$853$	26.9029	−	4.26100i	0.921138	−	0.145894i	0.322184	−	0.946677i	$-0.395583\pi$
$853$	26.9029	−	4.26100i	0.921138	−	0.145894i	0.598954	+	0.800783i	$0.295583\pi$
$854$	15.5927	−	13.6271i	0.533572	−	0.466309i
$855$		0			0
$856$	−1.65556	−	15.7516i	−0.0565860	−	0.538380i
$857$	−9.92732	+	37.0493i	−0.339111	+	1.26558i	0.560232	+	0.828336i	$0.310712\pi$
$857$	−9.92732	+	37.0493i	−0.339111	+	1.26558i	−0.899343	+	0.437244i	$0.855955\pi$
$858$	0.282481	+	0.735888i	0.00964374	+	0.0251228i
$859$	−0.881487	−	0.187366i	−0.0300759	−	0.00639284i	0.192849	−	0.981228i	$-0.438227\pi$
$859$	−0.881487	−	0.187366i	−0.0300759	−	0.00639284i	−0.222925	+	0.974836i	$0.571561\pi$
$860$		0			0
$861$	7.60358	+	4.54138i	0.259129	+	0.154770i
$862$	−2.05137	−	1.04523i	−0.0698701	−	0.0356006i
$863$	−0.640865	−	0.986845i	−0.0218153	−	0.0335926i	0.827595	−	0.561326i	$-0.189709\pi$
$863$	−0.640865	−	0.986845i	−0.0218153	−	0.0335926i	−0.849410	+	0.527733i	$0.823042\pi$
$864$	−29.9188	+	6.35943i	−1.01786	+	0.216352i
$865$		0			0
$866$	1.78094	−	8.37865i	0.0605187	−	0.284718i
$867$	−49.9479	−	7.91096i	−1.69632	−	0.268670i
$868$	−6.66943	+	12.6237i	−0.226375	+	0.428478i
$869$	2.26247	+	3.11402i	0.0767490	+	0.105636i
$870$		0			0
$871$	0.743903	+	0.0781873i	0.0252062	+	0.00264928i
$872$	30.0225	+	37.0746i	1.01669	+	1.25551i
$873$	13.4173	+	0.703169i	0.454105	+	0.0237987i
$874$	−6.96421			−0.235568
$875$		0			0
$876$	5.60304			0.189309
$877$	41.4047	+	2.16993i	1.39814	+	0.0732732i	0.736442	−	0.676501i	$-0.236504\pi$
$877$	41.4047	+	2.16993i	1.39814	+	0.0732732i	0.661694	+	0.749774i	$0.269838\pi$
$878$	12.3706	+	15.2764i	0.417488	+	0.515555i
$879$	5.09495	+	0.535501i	0.171849	+	0.0180620i
$880$		0			0
$881$	20.7423	+	28.5494i	0.698827	+	0.961852i	0.999966	+	0.00827221i	$0.00263316\pi$
$881$	20.7423	+	28.5494i	0.698827	+	0.961852i	−0.301139	+	0.953580i	$0.597367\pi$
$882$	−1.50953	+	7.99116i	−0.0508285	+	0.269076i
$883$	12.7280	+	2.01591i	0.428330	+	0.0678407i	0.366877	−	0.930269i	$-0.380427\pi$
$883$	12.7280	+	2.01591i	0.428330	+	0.0678407i	0.0614522	+	0.998110i	$0.480427\pi$
$884$	1.44711	−	6.80810i	0.0486714	−	0.228981i
$885$		0			0
$886$	20.6443	−	4.38808i	0.693559	−	0.147421i
$887$	24.9568	+	38.4301i	0.837968	+	1.29036i	0.954813	+	0.297207i	$0.0960553\pi$
$887$	24.9568	+	38.4301i	0.837968	+	1.29036i	−0.116845	+	0.993150i	$0.537278\pi$
$888$	22.4805	+	11.4544i	0.754397	+	0.384384i
$889$	3.75915	+	6.73962i	0.126078	+	0.226040i
$890$		0			0
$891$	2.81753	+	0.598885i	0.0943909	+	0.0200634i
$892$	−3.58695	−	9.34433i	−0.120100	−	0.312871i
$893$	−5.48864	+	20.4839i	−0.183670	+	0.685467i
$894$	1.45568	+	13.8498i	0.0486851	+	0.463208i
$895$		0			0
$896$	13.6826	+	4.67088i	0.457103	+	0.156043i
$897$	−4.36740	+	0.691729i	−0.145823	+	0.0230961i
$898$	1.57862	−	30.1218i	0.0526792	−	1.00518i
$899$	22.1049	+	38.2867i	0.737238	+	1.27693i
$900$		0			0
$901$	−57.9395	−	33.4514i	−1.93025	−	1.11443i
$902$	−1.64489	+	0.838114i	−0.0547689	+	0.0279062i
$903$	0.596535	−	8.86760i	0.0198514	−	0.295095i
$904$	16.0538	−	22.0961i	0.533940	−	0.734905i
$905$		0			0
$906$	−5.51747	+	12.3924i	−0.183306	+	0.411711i
$907$	−19.0139	−	5.09475i	−0.631345	−	0.169168i	−0.0710652	−	0.997472i	$-0.522640\pi$
$907$	−19.0139	−	5.09475i	−0.631345	−	0.169168i	−0.560280	+	0.828303i	$0.689307\pi$
$908$	8.34119	+	6.75456i	0.276812	+	0.224158i
$909$	2.45091	+	7.54313i	0.0812916	+	0.250190i
$910$		0			0
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	−0.595807	−	0.803128i	$-0.703168\pi$
$911$	10.8138	−	33.2815i	0.358278	−	1.10267i	0.954085	−	0.299537i	$-0.0968323\pi$
$912$	0.831618	−	0.540059i	0.0275376	−	0.0178831i
$913$	0.214362	+	4.09027i	0.00709434	+	0.135368i
$914$	−1.55506	−	7.31597i	−0.0514367	−	0.241991i
$915$		0			0
$916$	9.35025	−	3.03808i	0.308941	−	0.100381i
$917$	−17.6308	+	2.52539i	−0.582220	+	0.0833956i
$918$	27.3577	+	27.3577i	0.902939	+	0.902939i
$919$	36.1268	−	3.79708i	1.19171	−	0.125254i	0.512167	−	0.858886i	$-0.328843\pi$
$919$	36.1268	−	3.79708i	1.19171	−	0.125254i	0.679547	+	0.733632i	$0.262176\pi$
$920$		0			0
$921$	−3.86362	+	36.7599i	−0.127311	+	1.21128i
$922$	−32.9137	−	12.6344i	−1.08395	−	0.416091i
$923$	−0.352661	−	0.692136i	−0.0116080	−	0.0227819i
$924$	−2.30471	−	2.13781i	−0.0758193	−	0.0703289i
$925$		0			0
$926$	−17.0216	+	29.4823i	−0.559364	+	0.968847i
$927$	−10.4210	−	6.76745i	−0.342269	−	0.222272i
$928$	39.5994	−	32.0670i	1.29992	−	1.05265i
$929$	3.00637	−	1.33852i	0.0986357	−	0.0439154i	−0.356826	−	0.934171i	$-0.616141\pi$
$929$	3.00637	−	1.33852i	0.0986357	−	0.0439154i	0.455461	+	0.890256i	$0.349474\pi$
$930$		0			0
$931$	2.30445	+	12.6769i	0.0755253	+	0.415470i
$932$	−2.25132	+	2.25132i	−0.0737446	+	0.0737446i
$933$	17.6053	−	21.7407i	0.576370	−	0.711758i
$934$	−12.8985	+	14.3252i	−0.422050	+	0.468734i
$935$		0			0
$936$	−2.22250	+	2.00115i	−0.0726447	+	0.0654096i
$937$	−4.55551	+	8.94070i	−0.148822	+	0.292080i	−0.953368	−	0.301811i	$-0.902409\pi$
$937$	−4.55551	+	8.94070i	−0.148822	+	0.292080i	0.804546	+	0.593891i	$0.202409\pi$
$938$	2.09998	−	0.770623i	0.0685668	−	0.0251617i
$939$	6.03743	+	1.96168i	0.197024	+	0.0640170i
$940$		0			0
$941$	11.2179	+	10.1007i	0.365694	+	0.329272i	0.831407	−	0.555663i	$-0.187536\pi$
$941$	11.2179	+	10.1007i	0.365694	+	0.329272i	−0.465713	+	0.884936i	$0.654202\pi$
$942$	19.0345	−	7.30664i	0.620176	−	0.238063i
$943$	−2.68038	−	10.0033i	−0.0872851	−	0.325752i
$944$	−3.76069	+	2.73230i	−0.122400	+	0.0889288i
$945$		0			0
$946$	1.49877	+	1.08892i	0.0487293	+	0.0354039i
$947$	−20.4240	+	53.2064i	−0.663692	+	1.72898i	0.0206198	+	0.999787i	$0.493436\pi$
$947$	−20.4240	+	53.2064i	−0.663692	+	1.72898i	−0.684312	+	0.729190i	$0.739897\pi$
$948$	4.02218	−	6.19361i	0.130634	−	0.201159i
$949$	2.63228	−	1.51975i	0.0854473	−	0.0493330i
$950$		0			0
$951$		−	39.2544i		−	1.27291i
$952$	−13.9938	−	55.5006i	−0.453540	−	1.79878i
$953$	2.49558	+	15.7565i	0.0808399	+	0.510403i	0.994569	+	0.104079i	$0.0331895\pi$
$953$	2.49558	+	15.7565i	0.0808399	+	0.510403i	−0.913729	+	0.406324i	$0.866810\pi$
$954$	4.25199	+	9.55013i	0.137663	+	0.309197i
$955$		0			0
$956$	−11.2381	−	5.00353i	−0.363467	−	0.161826i
$957$	−9.40237	+	2.51936i	−0.303935	+	0.0814392i
$958$	−0.202701	+	1.27980i	−0.00654897	+	0.0413486i
$959$	−4.62690	−	51.3230i	−0.149410	−	1.65731i
$960$		0			0
$961$	5.82696	+	6.47150i	0.187966	+	0.208758i
$962$	4.97043	−	0.260489i	0.160253	−	0.00839852i
$963$	−6.82172	+	0.357511i	−0.219827	+	0.0115206i
$964$	−8.07068	−	8.96339i	−0.259939	−	0.288691i
$965$		0			0
$966$	−10.8121	+	7.61337i	−0.347873	+	0.244956i
$967$	−4.82581	+	30.4690i	−0.155188	+	0.979817i	0.780030	+	0.625743i	$0.215204\pi$
$967$	−4.82581	+	30.4690i	−0.155188	+	0.979817i	−0.935217	+	0.354074i	$0.884796\pi$
$968$	−29.1751	+	7.81746i	−0.937725	+	0.251263i
$969$	16.5159	+	7.35337i	0.530568	+	0.236224i
$970$		0			0
$971$	−1.64054	−	3.68471i	−0.0526474	−	0.118248i	0.885307	−	0.465008i	$-0.153949\pi$
$971$	−1.64054	−	3.68471i	−0.0526474	−	0.118248i	−0.937954	+	0.346760i	$0.887282\pi$
$972$	2.15038	+	13.5770i	0.0689736	+	0.435482i
$973$	−0.741798	+	2.61300i	−0.0237810	+	0.0837690i
$974$		−	24.6259i		−	0.789064i
$975$		0			0
$976$	2.98586	−	1.72388i	0.0955749	−	0.0551802i
$977$	13.3602	−	20.5729i	0.427430	−	0.658184i	−0.557691	−	0.830049i	$-0.688312\pi$
$977$	13.3602	−	20.5729i	0.427430	−	0.658184i	0.985121	+	0.171864i	$0.0549791\pi$
$978$	9.01525	−	23.4855i	0.288276	−	0.750984i
$979$	−0.368121	−	0.267456i	−0.0117652	−	0.00854792i
$980$		0			0
$981$	16.6460	−	12.0940i	0.531467	−	0.386133i
$982$	−0.0494843	−	0.184678i	−0.00157911	−	0.00589331i
$983$	−42.6458	+	16.3702i	−1.36019	+	0.522128i	−0.925601	−	0.378500i	$-0.876440\pi$
$983$	−42.6458	+	16.3702i	−1.36019	+	0.522128i	−0.434590	+	0.900629i	$0.643107\pi$
$984$	7.23821	+	6.51731i	0.230746	+	0.207764i
$985$		0			0
$986$	−61.2982	−	19.9170i	−1.95213	−	0.634286i
$987$	13.8720	+	37.8019i	0.441552	+	1.20325i
$988$	−0.782265	+	1.53528i	−0.0248872	+	0.0488438i
$989$	−7.72316	+	6.95396i	−0.245582	+	0.221123i
$990$		0			0
$991$	30.6797	−	34.0732i	0.974571	−	1.08237i	−0.0220102	−	0.999758i	$-0.507007\pi$
$991$	30.6797	−	34.0732i	0.974571	−	1.08237i	0.996582	−	0.0826135i	$-0.0263267\pi$
$992$	−16.1691	+	19.9671i	−0.513368	+	0.633957i
$993$	21.4880	−	21.4880i	0.681902	−	0.681902i
$994$	−1.85896	−	1.39314i	−0.0589625	−	0.0441876i
$995$		0			0
$996$	7.17903	−	3.19631i	0.227476	−	0.101279i
$997$	17.7226	−	14.3515i	0.561281	−	0.454517i	−0.306213	−	0.951963i	$-0.599062\pi$
$997$	17.7226	−	14.3515i	0.561281	−	0.454517i	0.867495	+	0.497446i	$0.165729\pi$
$998$	18.3300	+	11.9036i	0.580225	+	0.376802i
$999$	18.4479	−	31.9527i	0.583665	−	1.01094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.243.8		288
5.2	odd	4		875.2.bb.c.257.11		288
5.3	odd	4		175.2.x.a.47.8	yes	288
5.4	even	2		875.2.bb.b.243.11		288
7.3	odd	6	inner	875.2.bb.a.493.11		288
25.6	even	5		875.2.bb.c.768.11		288
25.8	odd	20		875.2.bb.b.607.8		288
25.17	odd	20	inner	875.2.bb.a.607.11		288
25.19	even	10		175.2.x.a.33.8	✓	288
35.3	even	12		175.2.x.a.122.8	yes	288
35.17	even	12		875.2.bb.c.507.11		288
35.24	odd	6		875.2.bb.b.493.8		288
175.17	even	60	inner	875.2.bb.a.857.8		288
175.31	odd	30		875.2.bb.c.143.11		288
175.94	odd	30		175.2.x.a.108.8	yes	288
175.108	even	60		875.2.bb.b.857.11		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.8	✓	288	25.19	even	10
175.2.x.a.47.8	yes	288	5.3	odd	4
175.2.x.a.108.8	yes	288	175.94	odd	30
175.2.x.a.122.8	yes	288	35.3	even	12
875.2.bb.a.243.8		288	1.1	even	1	trivial
875.2.bb.a.493.11		288	7.3	odd	6	inner
875.2.bb.a.607.11		288	25.17	odd	20	inner
875.2.bb.a.857.8		288	175.17	even	60	inner
875.2.bb.b.243.11		288	5.4	even	2
875.2.bb.b.493.8		288	35.24	odd	6
875.2.bb.b.607.8		288	25.8	odd	20
875.2.bb.b.857.11		288	175.108	even	60
875.2.bb.c.143.11		288	175.31	odd	30
875.2.bb.c.257.11		288	5.2	odd	4
875.2.bb.c.507.11		288	35.17	even	12
875.2.bb.c.768.11		288	25.6	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.924506 - 0.0484513i) q^{2} +(0.831339 + 1.02662i) q^{3} +(-1.13668 - 0.119470i) q^{4} +(-0.718837 - 0.989394i) q^{6} +(2.64389 - 0.0993238i) q^{7} +(2.87383 + 0.455170i) q^{8} +(0.260915 - 1.22751i) q^{9} +(0.769743 - 0.163614i) q^{11} +(-0.822316 - 1.26626i) q^{12} +(-0.729773 - 0.371838i) q^{13} +(-2.44910 - 0.0362743i) q^{14} +(-0.398891 - 0.0847869i) q^{16} +(-2.66452 - 6.94132i) q^{17} +(-0.300692 + 1.12220i) q^{18} +(0.192403 + 1.83059i) q^{19} +(2.29993 + 2.63169i) q^{21} +(-0.719560 + 0.113967i) q^{22} +(0.213890 - 4.08126i) q^{23} +(1.92184 + 3.32873i) q^{24} +(0.656664 + 0.379125i) q^{26} +(5.00818 - 2.55179i) q^{27} +(-3.01712 - 0.202965i) q^{28} +(-5.50382 + 7.57536i) q^{29} +(1.92037 - 4.31323i) q^{31} +(-5.25635 - 1.40844i) q^{32} +(0.807887 + 0.654214i) q^{33} +(2.12705 + 6.54639i) q^{34} +(-0.443227 + 1.36411i) q^{36} +(5.50515 - 3.57509i) q^{37} +(-0.0891829 - 1.70171i) q^{38} +(-0.224953 - 1.05832i) q^{39} +(2.40999 - 0.783055i) q^{41} +(-1.99879 - 2.54445i) q^{42} +(-1.79811 - 1.79811i) q^{43} +(-0.894499 + 0.0940156i) q^{44} +(-0.395485 + 3.76279i) q^{46} +(10.7558 + 4.12878i) q^{47} +(-0.244570 - 0.479996i) q^{48} +(6.98027 - 0.525202i) q^{49} +(4.91096 - 8.50604i) q^{51} +(0.785095 + 0.509847i) q^{52} +(6.99289 - 5.66273i) q^{53} +(-4.75373 + 2.11650i) q^{54} +(7.64330 + 0.917979i) q^{56} +(-1.71936 + 1.71936i) q^{57} +(5.45535 - 6.73680i) q^{58} +(7.62729 - 8.47097i) q^{59} +(-6.28292 + 5.65717i) q^{61} +(-1.98438 + 3.89456i) q^{62} +(0.567908 - 3.27131i) q^{63} +(5.56698 + 1.80882i) q^{64} +(-0.715198 - 0.643968i) q^{66} +(-0.852602 + 0.327283i) q^{67} +(2.19943 + 8.20839i) q^{68} +(4.36771 - 3.17333i) q^{69} +(0.767293 + 0.557471i) q^{71} +(1.30855 - 3.40889i) q^{72} +(-2.02117 + 3.11233i) q^{73} +(-5.26276 + 3.03846i) q^{74} -2.10378i q^{76} +(2.01886 - 0.509031i) q^{77} +(0.156693 + 0.989324i) q^{78} +(1.98946 + 4.46840i) q^{79} +(3.34390 + 1.48880i) q^{81} +(-2.26599 + 0.607171i) q^{82} +(-0.814213 + 5.14074i) q^{83} +(-2.29988 - 3.26616i) q^{84} +(1.57524 + 1.74948i) q^{86} +(-12.3525 + 0.647369i) q^{87} +(2.28659 - 0.119835i) q^{88} +(-0.386903 - 0.429700i) q^{89} +(-1.96637 - 0.910613i) q^{91} +(-0.730712 + 4.61354i) q^{92} +(6.02451 - 1.61426i) q^{93} +(-9.74379 - 4.33822i) q^{94} +(-2.92389 - 6.56715i) q^{96} +(1.67483 + 10.5745i) q^{97} +(-6.47875 + 0.147349i) q^{98} -0.987555i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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