LMFDB - Embedded newform 875.2.bb.b.243.11

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			243.11
Character	$\chi$	$=$	875.243
Dual form			875.2.bb.b.857.11

$q$-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	0.376315	−	0.926492i	$-0.377191\pi$
$2$	0.924506	+	0.0484513i	0.653724	+	0.0342602i	0.277409	+	0.960752i	$0.410524\pi$
$3$	−0.831339	−	1.02662i	−0.479974	−	0.592718i	0.478433	−	0.878124i	$-0.341205\pi$
$3$	−0.831339	−	1.02662i	−0.479974	−	0.592718i	−0.958407	+	0.285406i	$0.907872\pi$
$4$	−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	0.552254	−	0.833676i	$-0.313768\pi$
$13$	0.729773	+	0.371838i	0.202403	+	0.103129i	−0.349851	+	0.936805i	$0.613768\pi$
$14$	−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	$0.240974\pi$
$17$	2.66452	+	6.94132i	0.646242	+	1.68352i	−0.0806290	+	0.996744i	$0.525693\pi$
$18$	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	$0.156774\pi$
$23$	−0.213890	+	4.08126i	−0.0445991	+	0.851002i	−0.925743	+	0.378154i	$0.876559\pi$
$24$	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	−0.911075	−	0.412241i	$-0.864746\pi$
$37$	−5.50515	+	3.57509i	−0.905041	+	0.587740i	0.00603374	+	0.999982i	$0.498079\pi$
$38$	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	0.830792	−	0.556583i	$-0.187888\pi$
$43$	1.79811	+	1.79811i	0.274209	+	0.274209i	−0.556583	+	0.830792i	$0.687888\pi$
$44$	−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	−0.590149	−	0.807294i	$-0.700931\pi$
$47$	−10.7558	−	4.12878i	−1.56890	−	0.602244i	−0.978751	+	0.205050i	$0.934264\pi$
$48$	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	−0.975033	−	0.222060i	$-0.928722\pi$
$53$	−6.99289	+	5.66273i	−0.960547	+	0.777836i	0.0144862	+	0.999895i	$0.495389\pi$
$54$	−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	−0.305729	−	0.952119i	$-0.598900\pi$
$67$	0.852602	−	0.327283i	0.104162	−	0.0399840i	0.409891	+	0.912135i	$0.365567\pi$
$68$	−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	−0.700374	−	0.713776i	$-0.746984\pi$
$73$	2.02117	−	3.11233i	0.236560	−	0.364270i	0.936934	+	0.349505i	$0.113650\pi$
$74$	−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	$-0.857790\pi$
$83$	0.814213	−	5.14074i	0.0893715	−	0.564269i	0.991221	−	0.132218i	$-0.0422100\pi$
$84$	−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	$-0.867087\pi$
$97$	−1.67483	−	10.5745i	−0.170054	−	1.07368i	0.744029	−	0.668148i	$-0.232913\pi$
$98$	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	$0.278870\pi$
$103$	−3.54834	+	9.24375i	−0.349629	+	0.910814i	−0.989785	+	0.142569i	$0.954464\pi$
$104$	−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	$0.00141696\pi$
$107$	1.40885	+	5.25791i	0.136199	+	0.508302i	−0.863791	+	0.503850i	$0.831916\pi$
$108$	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	−0.999903	−	0.0139501i	$-0.995559\pi$
$113$	−4.26151	+	8.36368i	−0.400889	+	0.786789i	0.599014	+	0.800739i	$0.295559\pi$
$114$	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	0.824762	−	0.565480i	$-0.191309\pi$
$127$	−1.32420	−	2.59888i	−0.117503	−	0.230613i	−0.942266	+	0.334866i	$0.891309\pi$
$128$	−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	$0.296145\pi$
$137$	1.01934	+	19.4502i	0.0870884	+	1.66175i	−0.510451	+	0.859907i	$0.670521\pi$
$138$	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	$-0.684983\pi$
$157$	4.31493	−	16.1035i	0.344369	−	1.28520i	0.893348	−	0.449365i	$-0.148350\pi$
$158$	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	$-0.885183\pi$
$163$	−11.2033	−	17.2516i	−0.877510	−	1.35125i	0.0581372	−	0.998309i	$-0.481484\pi$
$164$	−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	−0.0269687	−	0.999636i	$-0.508585\pi$
$167$	−4.67190	−	0.739956i	−0.361522	−	0.0572595i	−0.334553	+	0.942377i	$0.608585\pi$
$168$	−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	0.242966	−	0.970035i	$-0.421880\pi$
$173$	5.04027	+	0.264149i	0.383204	+	0.0200829i	0.140239	+	0.990118i	$0.455213\pi$
$174$	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	$0.264123\pi$
$193$	−3.86831	+	14.4367i	−0.278447	+	1.03918i	−0.953496	+	0.301406i	$0.902544\pi$
$194$	−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	−0.209256	−	0.977861i	$-0.567104\pi$
$197$	−1.48910	+	0.235850i	−0.106094	+	0.0168036i	0.103162	+	0.994665i	$0.467104\pi$
$198$	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	0.718725	−	0.695294i	$-0.244726\pi$
$223$	−3.97575	−	7.80285i	−0.266236	−	0.522518i	−0.984961	+	0.172777i	$0.944726\pi$
$224$	−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	0.778882	−	0.627171i	$-0.215787\pi$
$227$	7.87576	+	5.11458i	0.522733	+	0.339467i	−0.256149	+	0.966637i	$0.582454\pi$
$228$	−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	−0.831328	−	0.555782i	$-0.812419\pi$
$233$	−1.75308	+	2.16487i	−0.114848	+	0.141825i	0.716480	+	0.697608i	$0.245752\pi$
$234$	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	0.350129	−	0.936701i	$-0.386138\pi$
$257$	17.9822	−	4.81832i	1.12170	−	0.300559i	0.771571	+	0.636143i	$0.219471\pi$
$258$	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	0.597567	−	0.801819i	$-0.296134\pi$
$263$	20.6879	−	1.08421i	1.27567	−	0.0668552i	0.678106	+	0.734964i	$0.262801\pi$
$264$	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	−0.817972	−	0.575259i	$-0.804901\pi$
$277$	0.669930	−	1.03160i	0.0402522	−	0.0619830i	0.858224	+	0.513276i	$0.171568\pi$
$278$	−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	0.0980061	−	0.995186i	$-0.468754\pi$
$283$	14.0763	−	5.40338i	0.836748	−	0.321198i	0.738742	+	0.673988i	$0.235420\pi$
$284$	−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	−0.782657	−	0.622454i	$-0.786136\pi$
$293$	−2.74224	+	2.74224i	−0.160203	+	0.160203i	0.622454	+	0.782657i	$0.286136\pi$
$294$	−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	$-0.955647\pi$
$307$	−19.7851	−	19.7851i	−1.12920	−	1.12920i	−0.138889	−	0.990308i	$-0.544353\pi$
$308$	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	−0.653494	−	0.756932i	$-0.726698\pi$
$313$	−4.03024	+	2.61727i	−0.227802	+	0.147937i	0.425692	+	0.904868i	$0.360031\pi$
$314$	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	$0.0309055\pi$
$317$	23.0932	+	18.7005i	1.29704	+	1.05033i	0.301754	+	0.953386i	$0.402428\pi$
$318$	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	0.319617	−	0.947547i	$-0.396446\pi$
$337$	−4.75641	−	2.42351i	−0.259098	−	0.132017i	−0.578715	+	0.815530i	$0.696446\pi$
$338$	−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	0.979987	−	0.199061i	$-0.0637893\pi$
$347$	10.8326	+	13.3772i	0.581525	+	0.718124i	−0.398462	+	0.917185i	$0.630456\pi$
$348$	−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	0.514256	−	0.857637i	$-0.328068\pi$
$353$	−8.10825	−	10.0129i	−0.431559	−	0.532931i	−0.945815	+	0.324706i	$0.894735\pi$
$354$	−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	0.961038	−	0.276415i	$-0.0891465\pi$
$367$	1.18564	+	3.08870i	0.0618899	+	0.161229i	−0.899148	+	0.437644i	$0.855813\pi$
$368$	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	$-0.951979\pi$
$373$	0.198805	−	3.79343i	0.0102937	−	0.196416i	0.998936	−	0.0461259i	$-0.0146875\pi$
$374$	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	0.134130	−	0.990964i	$-0.457176\pi$
$383$	−15.7990	−	12.7938i	−0.807291	−	0.653732i	−0.941422	+	0.337232i	$0.890509\pi$
$384$	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	0.0757170	−	0.997129i	$-0.475875\pi$
$397$	−10.6643	−	4.09363i	−0.535224	−	0.205453i	−0.610941	+	0.791676i	$0.709209\pi$
$398$	−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	$-0.878635\pi$
$433$	1.44743	−	9.13869i	0.0695589	−	0.439178i	0.997748	−	0.0670695i	$-0.0213649\pi$
$434$	−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	0.305545	−	0.952178i	$-0.401161\pi$
$443$	22.0209	−	5.90047i	1.04624	−	0.280340i	0.740698	+	0.671838i	$0.234495\pi$
$444$	−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	0.899617	−	0.436679i	$-0.143846\pi$
$457$	−2.09102	−	7.80380i	−0.0978138	−	0.365046i	−0.997431	+	0.0716332i	$0.977179\pi$
$458$	−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	$0.476127\pi$
$463$	−16.6944	+	32.7647i	−0.775856	+	1.52270i	−0.850785	+	0.525514i	$0.823873\pi$
$464$	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	−0.984197	−	0.177075i	$-0.943337\pi$
$467$	−13.1037	+	16.1817i	−0.606366	+	0.748800i	0.377831	+	0.925874i	$0.376670\pi$
$468$	−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	$-0.810763\pi$
$487$	−1.39215	−	26.5638i	−0.0630844	−	1.20372i	0.765342	−	0.643624i	$-0.222570\pi$
$488$	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	−0.228558	−	0.973530i	$-0.573401\pi$
$503$	−3.25409	+	0.515396i	−0.145092	+	0.0229804i	0.0834657	+	0.996511i	$0.473401\pi$
$504$	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	0.892915	−	0.450225i	$-0.148656\pi$
$523$	39.6524	+	2.07809i	1.73388	+	0.0908687i	0.840962	+	0.541094i	$0.181990\pi$
$524$	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	0.318968	−	0.947766i	$-0.396664\pi$
$547$	21.4047	−	3.39018i	0.915200	−	0.144953i	0.596232	+	0.802812i	$0.296664\pi$
$548$	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	0.482147	−	0.876090i	$-0.339857\pi$
$557$	10.8954	+	2.91942i	0.461654	+	0.123700i	−0.0204931	+	0.999790i	$0.506524\pi$
$558$	−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	$-0.983406\pi$
$563$	−0.259044	−	4.94286i	−0.0109174	−	0.208317i	0.987724	−	0.156209i	$-0.0499273\pi$
$564$	−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	0.350624	−	0.936516i	$-0.385970\pi$
$577$	−8.70310	−	5.65186i	−0.362315	−	0.235290i	−0.712939	+	0.701226i	$0.752636\pi$
$578$	−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	−0.929997	−	0.367568i	$-0.880191\pi$
$587$	−2.08337	+	4.08885i	−0.0859899	+	0.168765i	0.844007	+	0.536332i	$0.180191\pi$
$588$	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	$0.0191098\pi$
$593$	3.98715	+	14.8803i	0.163733	+	0.611059i	−0.834466	+	0.551060i	$0.814224\pi$
$594$	−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	−0.0331368	−	0.999451i	$-0.510550\pi$
$607$	10.7885	−	2.89077i	0.437891	−	0.117333i	0.471028	+	0.882118i	$0.343883\pi$
$608$	−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	0.0103446	−	0.999946i	$-0.496707\pi$
$613$	3.09870	−	0.162396i	0.125155	−	0.00655911i	0.114811	+	0.993387i	$0.463374\pi$
$614$	−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	$-0.576641\pi$
$617$	7.16450	−	45.2349i	0.288432	−	1.82109i	0.526888	−	0.849935i	$-0.323359\pi$
$618$	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	−0.161295	−	0.986906i	$-0.551567\pi$
$643$	20.9354	−	20.9354i	0.825611	−	0.825611i	0.986906	+	0.161295i	$0.0515672\pi$
$644$	−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	−0.283324	−	0.959024i	$-0.591437\pi$
$647$	15.1558	−	12.2729i	0.595837	−	0.482499i	0.879161	+	0.476525i	$0.158104\pi$
$648$	−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	0.415393	−	0.909642i	$-0.363644\pi$
$653$	2.94945	+	1.13219i	0.115421	+	0.0443060i	−0.299972	+	0.953948i	$0.596977\pi$
$654$	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	0.214185	−	0.976793i	$-0.431290\pi$
$673$	29.3231	−	14.9409i	1.13032	−	0.575928i	0.916137	+	0.400865i	$0.131290\pi$
$674$	−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	$0.0523223\pi$
$677$	−0.304435	+	5.80896i	−0.0117004	+	0.223256i	−0.998221	+	0.0596203i	$0.981011\pi$
$678$	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	0.757669	−	0.652639i	$-0.226338\pi$
$683$	−6.32684	−	16.4820i	−0.242090	−	0.630666i	−0.999759	+	0.0219738i	$0.993005\pi$
$684$	−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	−0.231580	−	0.972816i	$-0.574390\pi$
$727$	11.3062	−	5.76081i	0.419325	−	0.213657i	0.650905	+	0.759159i	$0.274390\pi$
$728$	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	$-0.946770\pi$
$733$	−36.6547	−	29.6824i	−1.35387	−	1.09634i	−0.367823	−	0.929896i	$-0.619897\pi$
$734$	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	0.881447	−	0.472283i	$-0.156570\pi$
$743$	11.1530	+	11.1530i	0.409164	+	0.409164i	−0.472283	+	0.881447i	$0.656570\pi$
$744$	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	$0.620914\pi$
$757$	−35.7542	+	35.7542i	−1.29951	+	1.29951i	−0.928716	+	0.370793i	$0.879086\pi$
$758$	−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	−0.769290	−	0.638900i	$-0.779390\pi$
$773$	3.53856	−	5.44891i	0.127273	−	0.195984i	0.896563	+	0.442917i	$0.146056\pi$
$774$	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	−0.178874	−	0.983872i	$-0.557246\pi$
$787$	−7.12353	+	0.373328i	−0.253926	+	0.0133077i	−0.0750519	+	0.997180i	$0.523912\pi$
$788$	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	$0.127924\pi$
$797$	4.68404	+	29.5739i	0.165917	+	1.04756i	−0.754408	+	0.656406i	$0.772076\pi$
$798$	−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	0.796944	−	0.604053i	$-0.206448\pi$
$823$	16.3309	+	10.6054i	0.569261	+	0.369682i	−0.227683	+	0.973735i	$0.573115\pi$
$824$	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	0.986099	−	0.166160i	$-0.0531368\pi$
$827$	7.82374	+	15.3550i	0.272058	+	0.533944i	−0.714041	+	0.700104i	$0.753137\pi$
$828$	−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	−0.598954	−	0.800783i	$-0.704417\pi$
$853$	−26.9029	+	4.26100i	−0.921138	+	0.145894i	−0.322184	+	0.946677i	$0.604417\pi$
$854$	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	$-0.689288\pi$
$857$	9.92732	−	37.0493i	0.339111	−	1.26558i	0.899343	−	0.437244i	$-0.144045\pi$
$858$	−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	0.849410	−	0.527733i	$-0.176958\pi$
$863$	0.640865	+	0.986845i	0.0218153	+	0.0335926i	−0.827595	+	0.561326i	$0.810291\pi$
$864$	−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	−0.661694	−	0.749774i	$-0.730162\pi$
$877$	−41.4047	−	2.16993i	−1.39814	−	0.0732732i	−0.736442	+	0.676501i	$0.763496\pi$
$878$	−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	−0.0614522	−	0.998110i	$-0.519573\pi$
$883$	−12.7280	−	2.01591i	−0.428330	−	0.0678407i	−0.366877	+	0.930269i	$0.619573\pi$
$884$	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	$-0.903945\pi$
$887$	−24.9568	−	38.4301i	−0.837968	−	1.29036i	0.116845	−	0.993150i	$-0.462722\pi$
$888$	−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	0.560280	−	0.828303i	$-0.310693\pi$
$907$	19.0139	+	5.09475i	0.631345	+	0.169168i	0.0710652	+	0.997472i	$0.477360\pi$
$908$	−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	−0.804546	−	0.593891i	$-0.797591\pi$
$937$	4.55551	−	8.94070i	0.148822	−	0.292080i	0.953368	+	0.301811i	$0.0975911\pi$
$938$	−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	$-0.506564\pi$
$947$	20.4240	−	53.2064i	0.663692	−	1.72898i	0.684312	−	0.729190i	$-0.260103\pi$
$948$	−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	$-0.966810\pi$
$953$	−2.49558	−	15.7565i	−0.0808399	−	0.510403i	0.913729	−	0.406324i	$-0.133190\pi$
$954$	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	$-0.784796\pi$
$967$	4.82581	−	30.4690i	0.155188	−	0.979817i	0.935217	−	0.354074i	$-0.115204\pi$
$968$	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	−0.985121	−	0.171864i	$-0.945021\pi$
$977$	−13.3602	+	20.5729i	−0.427430	+	0.658184i	0.557691	+	0.830049i	$0.311688\pi$
$978$	−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	0.434590	−	0.900629i	$-0.356893\pi$
$983$	42.6458	−	16.3702i	1.36019	−	0.522128i	0.925601	+	0.378500i	$0.123560\pi$
$984$	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	−0.867495	−	0.497446i	$-0.834271\pi$
$997$	−17.7226	+	14.3515i	−0.561281	+	0.454517i	0.306213	+	0.951963i	$0.400938\pi$
$998$	−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.b.243.11		288
5.2	odd	4		175.2.x.a.47.8	yes	288
5.3	odd	4		875.2.bb.c.257.11		288
5.4	even	2		875.2.bb.a.243.8		288
7.3	odd	6	inner	875.2.bb.b.493.8		288
25.6	even	5		175.2.x.a.33.8	✓	288
25.8	odd	20		875.2.bb.a.607.11		288
25.17	odd	20	inner	875.2.bb.b.607.8		288
25.19	even	10		875.2.bb.c.768.11		288
35.3	even	12		875.2.bb.c.507.11		288
35.17	even	12		175.2.x.a.122.8	yes	288
35.24	odd	6		875.2.bb.a.493.11		288
175.17	even	60	inner	875.2.bb.b.857.11		288
175.31	odd	30		175.2.x.a.108.8	yes	288
175.94	odd	30		875.2.bb.c.143.11		288
175.108	even	60		875.2.bb.a.857.8		288

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

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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