LMFDB - Embedded newform 875.2.bb.c.143.1

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 = [288,8] 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			143.1
Character	$\chi$	$=$	875.143
Dual form			875.2.bb.c.257.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.127170 - 2.42654i) q^{2} +(1.78675 + 1.44688i) q^{3} +(-3.88289 + 0.408108i) q^{4} +(3.28370 - 4.51962i) q^{6} +(-1.54352 + 2.14884i) q^{7} +(0.723845 + 4.57018i) q^{8} +(0.475273 + 2.23598i) q^{9} +(-0.0163732 - 0.00348022i) q^{11} +(-7.52823 - 4.88889i) q^{12} +(1.39124 + 2.73047i) q^{13} +(5.41055 + 3.47216i) q^{14} +(3.35976 - 0.714139i) q^{16} +(6.59423 + 2.53129i) q^{17} +(5.36527 - 1.43762i) q^{18} +(0.331948 - 3.15828i) q^{19} +(-5.86701 + 1.60615i) q^{21} +(-0.00636273 + 0.0401727i) q^{22} +(5.46923 - 0.286630i) q^{23} +(-5.31918 + 9.21308i) q^{24} +(6.44868 - 3.72315i) q^{26} +(0.745322 - 1.46278i) q^{27} +(5.11637 - 8.97365i) q^{28} +(-0.0353871 - 0.0487062i) q^{29} +(3.66733 + 8.23697i) q^{31} +(0.235039 + 0.877177i) q^{32} +(-0.0242193 - 0.0299083i) q^{33} +(5.30369 - 16.3231i) q^{34} +(-2.75796 - 8.48811i) q^{36} +(-4.57608 + 7.04654i) q^{37} +(-7.70591 - 0.403850i) q^{38} +(-1.46486 + 6.89163i) q^{39} +(5.83738 + 1.89668i) q^{41} +(4.64350 + 14.0323i) q^{42} +(3.18681 + 3.18681i) q^{43} +(0.0649954 + 0.00683130i) q^{44} +(-1.39104 - 13.2349i) q^{46} +(-1.64959 - 4.29732i) q^{47} +(7.03633 + 3.58519i) q^{48} +(-2.23507 - 6.63359i) q^{49} +(8.11977 + 14.0639i) q^{51} +(-6.51638 - 10.0343i) q^{52} +(-2.73861 + 3.38191i) q^{53} +(-3.64427 - 1.62253i) q^{54} +(-10.9379 - 5.49875i) q^{56} +(5.16276 - 5.16276i) q^{57} +(-0.113687 + 0.0920622i) q^{58} +(1.67651 + 1.86195i) q^{59} +(-9.91649 - 8.92884i) q^{61} +(19.5210 - 9.94643i) q^{62} +(-5.53838 - 2.43001i) q^{63} +(8.63203 - 2.80472i) q^{64} +(-0.0694938 + 0.0625725i) q^{66} +(-0.113980 + 0.296929i) q^{67} +(-26.6377 - 7.13755i) q^{68} +(10.1869 + 7.40119i) q^{69} +(-6.35569 + 4.61768i) q^{71} +(-9.87482 + 3.79059i) q^{72} +(2.80391 - 1.82088i) q^{73} +(17.6807 + 10.2079i) q^{74} +12.3987i q^{76} +(0.0327508 - 0.0298116i) q^{77} +(16.9091 + 2.67814i) q^{78} +(2.17913 - 4.89441i) q^{79} +(9.71309 - 4.32455i) q^{81} +(3.86003 - 14.4058i) q^{82} +(-8.63403 + 1.36750i) q^{83} +(22.1255 - 8.63088i) q^{84} +(7.32766 - 8.13819i) q^{86} +(0.00724415 - 0.138227i) q^{87} +(0.00405361 - 0.0773474i) q^{88} +(5.60082 - 6.22034i) q^{89} +(-8.01478 - 1.22498i) q^{91} +(-21.1194 + 3.34499i) q^{92} +(-5.36531 + 20.0236i) q^{93} +(-10.2178 + 4.54928i) q^{94} +(-0.849216 + 1.90737i) q^{96} +(-6.79613 - 1.07640i) q^{97} +(-15.8124 + 6.26707i) q^{98} -0.0382642i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.127170	−	2.42654i	−0.0899225	−	1.71582i	−0.556085	−	0.831125i	$-0.687697\pi$
$2$	−0.127170	−	2.42654i	−0.0899225	−	1.71582i	0.466163	−	0.884699i	$-0.345636\pi$
$3$	1.78675	+	1.44688i	1.03158	+	0.835357i	0.986522	−	0.163627i	$-0.0523194\pi$
$3$	1.78675	+	1.44688i	1.03158	+	0.835357i	0.0450579	+	0.998984i	$0.485653\pi$
$4$	−3.88289	+	0.408108i	−1.94144	+	0.204054i
$5$		0			0
$5$		0			0
$6$	3.28370	−	4.51962i	1.34056	−	1.84513i
$7$	−1.54352	+	2.14884i	−0.583397	+	0.812187i
$7$	−1.54352	+	2.14884i	−0.583397	+	0.812187i
$8$	0.723845	+	4.57018i	0.255918	+	1.61580i
$9$	0.475273	+	2.23598i	0.158424	+	0.745328i
$10$		0			0
$11$	−0.0163732	−	0.00348022i	−0.00493669	−	0.00104933i	0.205443	−	0.978669i	$-0.434137\pi$
$11$	−0.0163732	−	0.00348022i	−0.00493669	−	0.00104933i	−0.210379	+	0.977620i	$0.567470\pi$
$12$	−7.52823	−	4.88889i	−2.17321	−	1.41130i
$13$	1.39124	+	2.73047i	0.385862	+	0.757297i	0.999478	−	0.0323079i	$-0.0102857\pi$
$13$	1.39124	+	2.73047i	0.385862	+	0.757297i	−0.613616	+	0.789605i	$0.710286\pi$
$14$	5.41055	+	3.47216i	1.44603	+	0.927973i
$15$		0			0
$16$	3.35976	−	0.714139i	0.839940	−	0.178535i
$17$	6.59423	+	2.53129i	1.59934	+	0.613928i	0.984603	−	0.174807i	$-0.0559300\pi$
$17$	6.59423	+	2.53129i	1.59934	+	0.613928i	0.614734	+	0.788735i	$0.289263\pi$
$18$	5.36527	−	1.43762i	1.26461	−	0.338850i
$19$	0.331948	−	3.15828i	0.0761542	−	0.724559i	−0.888113	−	0.459626i	$-0.847984\pi$
$19$	0.331948	−	3.15828i	0.0761542	−	0.724559i	0.964267	−	0.264933i	$-0.0853498\pi$
$20$		0			0
$21$	−5.86701	+	1.60615i	−1.28029	+	0.350491i
$22$	−0.00636273	+	0.0401727i	−0.00135654	+	0.00856485i
$23$	5.46923	−	0.286630i	1.14041	−	0.0597665i	0.527241	−	0.849716i	$-0.323226\pi$
$23$	5.46923	−	0.286630i	1.14041	−	0.0597665i	0.613172	+	0.789949i	$0.289893\pi$
$24$	−5.31918	+	9.21308i	−1.08577	+	1.88061i
$25$		0			0
$26$	6.44868	−	3.72315i	1.26469	−	0.730169i
$27$	0.745322	−	1.46278i	0.143437	−	0.281512i
$28$	5.11637	−	8.97365i	0.966903	−	1.69586i
$29$	−0.0353871	−	0.0487062i	−0.00657122	−	0.00904451i	0.805719	−	0.592298i	$-0.201779\pi$
$29$	−0.0353871	−	0.0487062i	−0.00657122	−	0.00904451i	−0.812290	+	0.583254i	$0.801779\pi$
$30$		0			0
$31$	3.66733	+	8.23697i	0.658673	+	1.47940i	0.865440	+	0.501013i	$0.167039\pi$
$31$	3.66733	+	8.23697i	0.658673	+	1.47940i	−0.206767	+	0.978390i	$0.566294\pi$
$32$	0.235039	+	0.877177i	0.0415494	+	0.155065i
$33$	−0.0242193	−	0.0299083i	−0.00421603	−	0.00520637i
$34$	5.30369	−	16.3231i	0.909576	−	2.79939i
$35$		0			0
$36$	−2.75796	−	8.48811i	−0.459659	−	1.41469i
$37$	−4.57608	+	7.04654i	−0.752302	+	1.15844i	0.230372	+	0.973103i	$0.426006\pi$
$37$	−4.57608	+	7.04654i	−0.752302	+	1.15844i	−0.982674	+	0.185341i	$0.940661\pi$
$38$	−7.70591	−	0.403850i	−1.25006	−	0.0655130i
$39$	−1.46486	+	6.89163i	−0.234566	+	1.10354i
$40$		0			0
$41$	5.83738	+	1.89668i	0.911646	+	0.296212i	0.727035	−	0.686600i	$-0.240898\pi$
$41$	5.83738	+	1.89668i	0.911646	+	0.296212i	0.184610	+	0.982812i	$0.440898\pi$
$42$	4.64350	+	14.0323i	0.716507	+	2.16523i
$43$	3.18681	+	3.18681i	0.485984	+	0.485984i	0.907036	−	0.421052i	$-0.138339\pi$
$43$	3.18681	+	3.18681i	0.485984	+	0.485984i	−0.421052	+	0.907036i	$0.638339\pi$
$44$	0.0649954	+	0.00683130i	0.00979843	+	0.00102986i
$45$		0			0
$46$	−1.39104	−	13.2349i	−0.205098	−	1.95137i
$47$	−1.64959	−	4.29732i	−0.240617	−	0.626828i	0.759091	−	0.650984i	$-0.225644\pi$
$47$	−1.64959	−	4.29732i	−0.240617	−	0.626828i	−0.999708	+	0.0241558i	$0.992310\pi$
$48$	7.03633	+	3.58519i	1.01561	+	0.517477i
$49$	−2.23507	−	6.63359i	−0.319295	−	0.947655i
$50$		0			0
$51$	8.11977	+	14.0639i	1.13700	+	1.96933i
$52$	−6.51638	−	10.0343i	−0.903659	−	1.39151i
$53$	−2.73861	+	3.38191i	−0.376178	+	0.464541i	−0.929713	−	0.368285i	$-0.879945\pi$
$53$	−2.73861	+	3.38191i	−0.376178	+	0.464541i	0.553535	+	0.832826i	$0.313278\pi$
$54$	−3.64427	−	1.62253i	−0.495923	−	0.220799i
$55$		0			0
$56$	−10.9379	−	5.49875i	−1.46164	−	0.734802i
$57$	5.16276	−	5.16276i	0.683825	−	0.683825i
$58$	−0.113687	+	0.0920622i	−0.0149279	+	0.0120884i
$59$	1.67651	+	1.86195i	0.218263	+	0.242406i	0.842326	−	0.538968i	$-0.181186\pi$
$59$	1.67651	+	1.86195i	0.218263	+	0.242406i	−0.624063	+	0.781374i	$0.714519\pi$
$60$		0			0
$61$	−9.91649	−	8.92884i	−1.26968	−	1.14322i	−0.982684	−	0.185288i	$-0.940678\pi$
$61$	−9.91649	−	8.92884i	−1.26968	−	1.14322i	−0.286992	−	0.957933i	$-0.592655\pi$
$62$	19.5210	−	9.94643i	2.47917	−	1.26320i
$63$	−5.53838	−	2.43001i	−0.697770	−	0.306152i
$64$	8.63203	−	2.80472i	1.07900	−	0.350590i
$65$		0			0
$66$	−0.0694938	+	0.0625725i	−0.00855409	+	0.00770214i
$67$	−0.113980	+	0.296929i	−0.0139249	+	0.0362757i	−0.940367	−	0.340162i	$-0.889518\pi$
$67$	−0.113980	+	0.296929i	−0.0139249	+	0.0362757i	0.926442	+	0.376438i	$0.122851\pi$
$68$	−26.6377	−	7.13755i	−3.23030	−	0.865556i
$69$	10.1869	+	7.40119i	1.22635	+	0.890999i
$70$		0			0
$71$	−6.35569	+	4.61768i	−0.754282	+	0.548018i	−0.897151	−	0.441724i	$-0.854367\pi$
$71$	−6.35569	+	4.61768i	−0.754282	+	0.548018i	0.142869	+	0.989742i	$0.454367\pi$
$72$	−9.87482	+	3.79059i	−1.16376	+	0.446725i
$73$	2.80391	−	1.82088i	0.328173	−	0.213118i	−0.370027	−	0.929021i	$-0.620651\pi$
$73$	2.80391	−	1.82088i	0.328173	−	0.213118i	0.698200	+	0.715903i	$0.253985\pi$
$74$	17.6807	+	10.2079i	2.05533	+	1.18665i
$75$		0			0
$76$			12.3987i			1.42223i
$77$	0.0327508	−	0.0298116i	0.00373230	−	0.00339734i
$78$	16.9091	+	2.67814i	1.91458	+	0.303240i
$79$	2.17913	−	4.89441i	0.245171	−	0.550664i	−0.748481	−	0.663156i	$-0.769217\pi$
$79$	2.17913	−	4.89441i	0.245171	−	0.550664i	0.993653	+	0.112492i	$0.0358833\pi$
$80$		0			0
$81$	9.71309	−	4.32455i	1.07923	−	0.480505i
$82$	3.86003	−	14.4058i	0.426270	−	1.59086i
$83$	−8.63403	+	1.36750i	−0.947708	+	0.150102i	−0.611110	−	0.791546i	$-0.709277\pi$
$83$	−8.63403	+	1.36750i	−0.947708	+	0.150102i	−0.336599	+	0.941648i	$0.609277\pi$
$84$	22.1255	−	8.63088i	2.41409	−	0.941706i
$85$		0			0
$86$	7.32766	−	8.13819i	0.790162	−	0.877564i
$87$	0.00724415	−	0.138227i	0.000776654	−	0.0148194i
$88$	0.00405361	−	0.0773474i	0.000432116	−	0.00824526i
$89$	5.60082	−	6.22034i	0.593686	−	0.659355i	−0.369173	−	0.929361i	$-0.620359\pi$
$89$	5.60082	−	6.22034i	0.593686	−	0.659355i	0.962859	+	0.270006i	$0.0870257\pi$
$90$		0			0
$91$	−8.01478	−	1.22498i	−0.840177	−	0.128413i
$92$	−21.1194	+	3.34499i	−2.20185	+	0.348739i
$93$	−5.36531	+	20.0236i	−0.556356	+	2.07635i
$94$	−10.2178	+	4.54928i	−1.05389	+	0.469222i
$95$		0			0
$96$	−0.849216	+	1.90737i	−0.0866727	+	0.194670i
$97$	−6.79613	−	1.07640i	−0.690043	−	0.109292i	−0.198442	−	0.980113i	$-0.563588\pi$
$97$	−6.79613	−	1.07640i	−0.690043	−	0.109292i	−0.491601	+	0.870821i	$0.663588\pi$
$98$	−15.8124	+	6.26707i	−1.59730	+	0.633070i
$99$		−	0.0382642i		−	0.00384569i
$100$		0			0
$101$	−9.18326	−	5.30196i	−0.913768	−	0.527564i	−0.0321267	−	0.999484i	$-0.510228\pi$
$101$	−9.18326	−	5.30196i	−0.913768	−	0.527564i	−0.881642	+	0.471919i	$0.843561\pi$
$102$	33.0939	−	21.4915i	3.27679	−	2.12797i
$103$	−0.204272	+	0.0784125i	−0.0201275	+	0.00772622i	−0.368411	−	0.929663i	$-0.620098\pi$
$103$	−0.204272	+	0.0784125i	−0.0201275	+	0.00772622i	0.348283	+	0.937389i	$0.386765\pi$
$104$	−11.4717	+	8.33468i	−1.12489	+	0.817282i
$105$		0			0
$106$	8.55461	+	6.21528i	0.830897	+	0.603682i
$107$	−4.72847	−	1.26699i	−0.457119	−	0.122485i	0.0229097	−	0.999738i	$-0.492707\pi$
$107$	−4.72847	−	1.26699i	−0.457119	−	0.122485i	−0.480028	+	0.877253i	$0.659374\pi$
$108$	−2.29703	+	5.98397i	−0.221032	+	0.575808i
$109$	−5.73459	+	5.16345i	−0.549274	+	0.494569i	−0.896398	−	0.443251i	$-0.853825\pi$
$109$	−5.73459	+	5.16345i	−0.549274	+	0.494569i	0.347123	+	0.937819i	$0.387158\pi$
$110$		0			0
$111$	−18.3718	+	5.96936i	−1.74377	+	0.566587i
$112$	−3.65130	+	8.32190i	−0.345015	+	0.786345i
$113$	3.56746	−	1.81771i	0.335599	−	0.170996i	−0.278068	−	0.960561i	$-0.589694\pi$
$113$	3.56746	−	1.81771i	0.335599	−	0.170996i	0.613666	+	0.789565i	$0.289694\pi$
$114$	−13.1842	−	11.8711i	−1.23481	−	1.11183i
$115$		0			0
$116$	0.157282	+	0.174679i	0.0146032	+	0.0162185i
$117$	−5.44407	+	4.40852i	−0.503304	+	0.407568i
$118$	4.30491	−	4.30491i	0.396299	−	0.396299i
$119$	−15.6177	+	10.2629i	−1.43167	+	0.940796i
$120$		0			0
$121$	−10.0487	−	4.47399i	−0.913522	−	0.406726i
$122$	−20.4051	+	25.1982i	−1.84739	+	2.28134i
$123$	7.68566	+	11.8349i	0.692993	+	1.06712i
$124$	−17.6014	−	30.4866i	−1.58065	−	2.73777i
$125$		0			0
$126$	−5.19220	+	13.7481i	−0.462558	+	1.22478i
$127$	−6.49211	−	3.30790i	−0.576082	−	0.293528i	0.141572	−	0.989928i	$-0.454784\pi$
$127$	−6.49211	−	3.30790i	−0.576082	−	0.293528i	−0.717654	+	0.696399i	$0.754784\pi$
$128$	−7.25261	−	18.8937i	−0.641047	−	1.66998i
$129$	1.08310	+	10.3050i	0.0953612	+	0.907301i
$130$		0			0
$131$	−11.7655	−	1.23661i	−1.02796	−	0.108043i	−0.424493	−	0.905431i	$-0.639548\pi$
$131$	−11.7655	−	1.23661i	−1.02796	−	0.108043i	−0.603466	+	0.797389i	$0.706214\pi$
$132$	0.106246	+	0.106246i	0.00924757	+	0.00924757i
$133$	6.27428	+	5.58819i	0.544049	+	0.484557i
$134$	0.735006	+	0.238818i	0.0634949	+	0.0206307i
$135$		0			0
$136$	−6.79524	+	31.9691i	−0.582687	+	2.74133i
$137$	−3.28970	−	0.172406i	−0.281058	−	0.0147296i	−0.0887140	−	0.996057i	$-0.528276\pi$
$137$	−3.28970	−	0.172406i	−0.281058	−	0.0147296i	−0.192344	+	0.981327i	$0.561609\pi$
$138$	16.6638	−	25.6601i	1.41852	−	2.18433i
$139$	−1.40509	−	4.32443i	−0.119179	−	0.366794i	0.873617	−	0.486614i	$-0.161768\pi$
$139$	−1.40509	−	4.32443i	−0.119179	−	0.366794i	−0.992796	+	0.119820i	$0.961768\pi$
$140$		0			0
$141$	3.27031	−	10.0650i	0.275410	−	0.847625i
$142$	12.0133	+	14.8351i	1.00813	+	1.24494i
$143$	−0.0132764	−	0.0495483i	−0.00111023	−	0.00414344i
$144$	3.19361	+	7.17296i	0.266134	+	0.597747i
$145$		0			0
$146$	−4.77502	−	6.57225i	−0.395183	−	0.543923i
$147$	5.60451	−	15.0864i	0.462252	−	1.24431i
$148$	14.8926	−	29.2285i	1.22417	−	2.40256i
$149$	15.7486	−	9.09246i	1.29018	−	0.744884i	0.311491	−	0.950249i	$-0.399172\pi$
$149$	15.7486	−	9.09246i	1.29018	−	0.744884i	0.978685	+	0.205366i	$0.0658384\pi$
$150$		0			0
$151$	9.44990	−	16.3677i	0.769022	−	1.33198i	−0.169072	−	0.985604i	$-0.554077\pi$
$151$	9.44990	−	16.3677i	0.769022	−	1.33198i	0.938094	−	0.346381i	$-0.112590\pi$
$152$	14.6742	−	0.769041i	1.19023	−	0.0623775i
$153$	−2.52586	+	15.9477i	−0.204204	+	1.28929i
$154$	−0.0765039	−	0.0756801i	−0.00616486	−	0.00609848i
$155$		0			0
$156$	2.87536	−	27.3573i	0.230213	−	2.19033i
$157$	15.7038	−	4.20781i	1.25330	−	0.335820i	0.429688	−	0.902978i	$-0.358624\pi$
$157$	15.7038	−	4.20781i	1.25330	−	0.335820i	0.823609	+	0.567158i	$0.191957\pi$
$158$	−12.1536	−	4.66533i	−0.966889	−	0.371154i
$159$	−9.78643	+	2.08017i	−0.776115	+	0.164968i
$160$		0			0
$161$	−7.82597	+	12.1950i	−0.616773	+	0.961097i
$162$	−11.7289	−	23.0193i	−0.921510	−	1.80856i
$163$	−7.85580	−	5.10162i	−0.615314	−	0.399590i	0.199012	−	0.979997i	$-0.436227\pi$
$163$	−7.85580	−	5.10162i	−0.615314	−	0.399590i	−0.814326	+	0.580407i	$0.802893\pi$
$164$	−23.4399	−	4.98231i	−1.83035	−	0.389053i
$165$		0			0
$166$	4.41627	+	20.7769i	0.342769	+	1.61260i
$167$	−1.18224	−	7.46435i	−0.0914842	−	0.577608i	−0.990263	−	0.139207i	$-0.955545\pi$
$167$	−1.18224	−	7.46435i	−0.0914842	−	0.577608i	0.898779	−	0.438402i	$-0.144455\pi$
$168$	−11.5872	−	25.6507i	−0.893972	−	1.97899i
$169$	2.12129	−	2.91971i	0.163177	−	0.224593i
$170$		0			0
$171$	7.21963	−	0.758813i	0.552099	−	0.0580279i
$172$	−13.6746	−	11.0735i	−1.04268	−	0.844343i
$173$	1.22482	+	23.3710i	0.0931217	+	1.77687i	0.502572	+	0.864535i	$0.332387\pi$
$173$	1.22482	+	23.3710i	0.0931217	+	1.77687i	−0.409451	+	0.912332i	$0.634280\pi$
$174$	−0.336334			−0.0254974
$175$		0			0
$176$	−0.0574953			−0.00433387
$177$	0.301479	+	5.75255i	0.0226605	+	0.432388i
$178$	−15.8062	−	12.7996i	−1.18472	−	0.959369i
$179$	−13.5506	+	1.42423i	−1.01282	+	0.106452i	−0.596373	−	0.802707i	$-0.703392\pi$
$179$	−13.5506	+	1.42423i	−1.01282	+	0.106452i	−0.416449	+	0.909159i	$0.636726\pi$
$180$		0			0
$181$	3.38018	−	4.65241i	0.251247	−	0.345811i	−0.664701	−	0.747110i	$-0.731441\pi$
$181$	3.38018	−	4.65241i	0.251247	−	0.345811i	0.915947	+	0.401298i	$0.131441\pi$
$182$	−1.95323	+	19.6040i	−0.144783	+	1.45314i
$183$	−4.79930	−	30.3016i	−0.354774	−	2.23996i
$184$	5.26883	+	24.7879i	0.388423	+	1.82739i
$185$		0			0
$186$	49.2704	+	10.4727i	3.61268	+	0.767899i
$187$	−0.0991590	−	0.0643946i	−0.00725122	−	0.00470900i
$188$	8.15893	+	16.0128i	0.595051	+	1.16785i
$189$	1.99286	+	3.85941i	0.144959	+	0.280731i
$190$		0			0
$191$	14.4947	−	3.08094i	1.04880	−	0.222929i	0.348892	−	0.937163i	$-0.386558\pi$
$191$	14.4947	−	3.08094i	1.04880	−	0.222929i	0.699907	+	0.714234i	$0.253225\pi$
$192$	19.4814	+	7.47820i	1.40595	+	0.539693i
$193$	16.0726	−	4.30663i	1.15693	−	0.309998i	0.371191	−	0.928557i	$-0.378950\pi$
$193$	16.0726	−	4.30663i	1.15693	−	0.309998i	0.785739	+	0.618558i	$0.212283\pi$
$194$	−1.74767	+	16.6280i	−0.125475	+	1.19382i
$195$		0			0
$196$	11.3857	+	24.8453i	0.813266	+	1.77467i
$197$	−2.43376	+	15.3662i	−0.173398	+	1.09479i	0.735423	+	0.677608i	$0.236983\pi$
$197$	−2.43376	+	15.3662i	−0.173398	+	1.09479i	−0.908821	+	0.417185i	$0.863017\pi$
$198$	−0.0928496	+	0.00486604i	−0.00659854	+	0.000345815i
$199$	0.988951	−	1.71291i	0.0701049	−	0.121425i	−0.828842	−	0.559482i	$-0.811000\pi$
$199$	0.988951	−	1.71291i	0.0701049	−	0.121425i	0.898947	+	0.438057i	$0.144333\pi$
$200$		0			0
$201$	−0.633276	+	0.365622i	−0.0446678	+	0.0257890i
$202$	−11.6976	+	22.9578i	−0.823039	+	1.61531i
$203$	0.159283		0.000862231i	0.0111795		6.05168e-5i
$204$	−37.2677	−	51.2946i	−2.60926	−	3.59134i
$205$		0			0
$206$	0.216248	+	0.485702i	0.0150667	+	0.0338405i
$207$	3.24028	+	12.0929i	0.225215	+	0.840514i
$208$	6.62419	+	8.18019i	0.459305	+	0.567194i
$209$	−0.0164266	+	0.0505557i	−0.00113625	+	0.00349701i
$210$		0			0
$211$	2.82445	+	8.69276i	0.194443	+	0.598434i	0.999983	+	0.00589215i	$0.00187554\pi$
$211$	2.82445	+	8.69276i	0.194443	+	0.598434i	−0.805540	+	0.592542i	$0.798124\pi$
$212$	9.25355	−	14.2492i	0.635536	−	0.978640i
$213$	−18.0373	−	0.945293i	−1.23589	−	0.0647704i
$214$	−2.47309	+	11.6350i	−0.169057	+	0.795349i
$215$		0			0
$216$	7.22465	+	2.34743i	0.491575	+	0.159722i
$217$	−23.3606	−	4.83343i	−1.58582	−	0.328115i
$218$	13.2586	+	13.2586i	0.897985	+	0.897985i
$219$	7.64448	+	0.803468i	0.516566	+	0.0542933i
$220$		0			0
$221$	2.26258	+	21.5270i	0.152198	+	1.44806i
$222$	16.8212	+	43.8208i	1.12897	+	2.94106i
$223$	−6.62726	−	3.37676i	−0.443794	−	0.226124i	0.217789	−	0.975996i	$-0.430115\pi$
$223$	−6.62726	−	3.37676i	−0.443794	−	0.226124i	−0.661584	+	0.749871i	$0.730115\pi$
$224$	−2.24771	−	0.848882i	−0.150181	−	0.0567183i
$225$		0			0
$226$	−4.86443	−	8.42544i	−0.323577	−	0.560452i
$227$	6.38180	+	9.82711i	0.423575	+	0.652249i	0.984453	−	0.175650i	$-0.0562028\pi$
$227$	6.38180	+	9.82711i	0.423575	+	0.652249i	−0.560877	+	0.827899i	$0.689536\pi$
$228$	−17.9395	+	22.1534i	−1.18807	+	1.46714i
$229$	24.6116	+	10.9578i	1.62638	+	0.724110i	0.998529	−	0.0542256i	$-0.0172690\pi$
$229$	24.6116	+	10.9578i	1.62638	+	0.724110i	0.627849	+	0.778335i	$0.283936\pi$
$230$		0			0
$231$	0.101651	−	0.00587925i	0.00668816	−	0.000386826i
$232$	0.196981	−	0.196981i	0.0129324	−	0.0129324i
$233$	16.9779	−	13.7484i	1.11226	−	0.900689i	0.116546	−	0.993185i	$-0.462818\pi$
$233$	16.9779	−	13.7484i	1.11226	−	0.900689i	0.995713	+	0.0924959i	$0.0294845\pi$
$234$	11.3898	+	12.6496i	0.744573	+	0.826932i
$235$		0			0
$236$	−7.26958	−	6.54556i	−0.473209	−	0.426080i
$237$	10.9752	−	5.59214i	0.712915	−	0.363248i
$238$	26.8894	+	36.5919i	1.74298	+	2.37190i
$239$	−4.05851	+	1.31869i	−0.262523	+	0.0852989i	−0.437321	−	0.899305i	$-0.644073\pi$
$239$	−4.05851	+	1.31869i	−0.262523	+	0.0852989i	0.174798	+	0.984604i	$0.444073\pi$
$240$		0			0
$241$	−0.122038	+	0.109884i	−0.00786117	+	0.00707823i	−0.673052	−	0.739595i	$-0.735017\pi$
$241$	−0.122038	+	0.109884i	−0.00786117	+	0.00707823i	0.665191	+	0.746674i	$0.268350\pi$
$242$	−9.57843	+	24.9527i	−0.615725	+	1.60402i
$243$	18.8546	+	5.05209i	1.20953	+	0.324092i
$244$	42.1485	+	30.6227i	2.69828	+	1.96042i
$245$		0			0
$246$	27.7405	−	20.1546i	1.76867	−	1.28501i
$247$	9.08541	−	3.48756i	0.578091	−	0.221908i
$248$	−34.9898	+	22.7227i	−2.22186	+	1.44289i
$249$	−17.4055	−	10.0490i	−1.10303	−	0.636832i
$250$		0			0
$251$		−	0.132304i		−	0.00835098i	−0.999991	−	0.00417549i	$-0.998671\pi$
$251$		−	0.132304i		−	0.00835098i	0.999991	−	0.00417549i	$-0.00132910\pi$
$252$	22.4966	+	7.17519i	1.41715	+	0.451995i
$253$	−0.0905461	−	0.0143411i	−0.00569259	−	0.000901617i
$254$	−7.20115	+	16.1741i	−0.451840	+	1.01485i
$255$		0			0
$256$	−28.3409	+	12.6182i	−1.77131	+	0.788637i
$257$	2.37849	−	8.87663i	0.148366	−	0.553709i	−0.851217	−	0.524815i	$-0.824135\pi$
$257$	2.37849	−	8.87663i	0.148366	−	0.553709i	0.999582	−	0.0288944i	$-0.00919866\pi$
$258$	24.8677	−	3.93865i	1.54819	−	0.245210i
$259$	−8.07863	−	20.7098i	−0.501982	−	1.28684i
$260$		0			0
$261$	0.0920877	−	0.102274i	0.00570008	−	0.00633058i
$262$	−1.50446	+	28.7068i	−0.0929458	+	1.77351i
$263$	−1.09475	+	20.8891i	−0.0675052	+	1.28808i	0.729449	+	0.684036i	$0.239777\pi$
$263$	−1.09475	+	20.8891i	−0.0675052	+	1.28808i	−0.796954	+	0.604040i	$0.793557\pi$
$264$	0.119155	−	0.132335i	0.00733350	−	0.00814468i
$265$		0			0
$266$	12.7621	−	15.9354i	0.782492	−	0.977065i
$267$	19.0074	−	3.01047i	1.16323	−	0.184238i
$268$	0.321394	−	1.19946i	0.0196323	−	0.0732687i
$269$	1.38180	−	0.615216i	0.0842497	−	0.0375104i	−0.364179	−	0.931329i	$-0.618650\pi$
$269$	1.38180	−	0.615216i	0.0842497	−	0.0375104i	0.448429	+	0.893819i	$0.351984\pi$
$270$		0			0
$271$	3.69590	−	8.30112i	0.224510	−	0.504257i	−0.765809	−	0.643068i	$-0.777661\pi$
$271$	3.69590	−	8.30112i	0.224510	−	0.504257i	0.990319	+	0.138811i	$0.0443279\pi$
$272$	23.9627	+	3.79533i	1.45295	+	0.230125i
$273$	−12.5480	−	13.7852i	−0.759439	−	0.834316i
$274$			8.00453i			0.483571i
$275$		0			0
$276$	−42.5749	−	24.5807i	−2.56271	−	1.47958i
$277$	11.4597	−	7.44201i	0.688546	−	0.447147i	−0.152362	−	0.988325i	$-0.548688\pi$
$277$	11.4597	−	7.44201i	0.688546	−	0.447147i	0.840908	+	0.541177i	$0.182021\pi$
$278$	−10.3147	+	3.95946i	−0.618637	+	0.237472i
$279$	−16.6747	+	12.1149i	−0.998291	+	0.725301i
$280$		0			0
$281$	−3.22462	−	2.34282i	−0.192365	−	0.139761i	0.487434	−	0.873160i	$-0.337933\pi$
$281$	−3.22462	−	2.34282i	−0.192365	−	0.139761i	−0.679799	+	0.733399i	$0.737933\pi$
$282$	−24.8390	−	6.65559i	−1.47914	−	0.396334i
$283$	6.77206	−	17.6418i	0.402557	−	1.04870i	−0.571140	−	0.820853i	$-0.693499\pi$
$283$	6.77206	−	17.6418i	0.402557	−	1.04870i	0.973697	−	0.227845i	$-0.0731680\pi$
$284$	22.7939	−	20.5238i	1.35257	−	1.21786i
$285$		0			0
$286$	−0.118543	+	0.0385168i	−0.00700957	+	0.00227755i
$287$	−13.0858	+	9.61605i	−0.772431	+	0.567618i
$288$	−1.84965	+	0.942442i	−0.108991	+	0.0555339i
$289$	24.4430	+	22.0086i	1.43783	+	1.29462i
$290$		0			0
$291$	−10.5856	−	11.7565i	−0.620536	−	0.689176i
$292$	−10.1442	+	8.21458i	−0.593642	+	0.480722i
$293$	−4.94524	+	4.94524i	−0.288904	+	0.288904i	−0.836647	−	0.547743i	$-0.815487\pi$
$293$	−4.94524	+	4.94524i	−0.288904	+	0.288904i	0.547743	+	0.836647i	$0.315487\pi$
$294$	−37.3206	−	11.6810i	−2.17658	−	0.681252i
$295$		0			0
$296$	−35.5163	−	15.8129i	−2.06434	−	0.919105i
$297$	−0.0172941	+	0.0213564i	−0.00100350	+	0.00123922i
$298$	−24.0660	−	37.0584i	−1.39410	−	2.14673i
$299$	8.39168	+	14.5348i	0.485303	+	0.840570i
$300$		0			0
$301$	−11.7669	+	1.92904i	−0.678231	+	0.111188i
$302$	−40.9187	−	20.8491i	−2.35460	−	1.19973i
$303$	−8.73688	−	22.7604i	−0.501921	−	1.30755i
$304$	−1.14018	−	10.8481i	−0.0653940	−	0.622182i
$305$		0			0
$306$	39.0189	+	4.10105i	2.23056	+	0.234441i
$307$	−4.76473	−	4.76473i	−0.271938	−	0.271938i	0.557942	−	0.829880i	$-0.311591\pi$
$307$	−4.76473	−	4.76473i	−0.271938	−	0.271938i	−0.829880	+	0.557942i	$0.811591\pi$
$308$	−0.115001	+	0.129121i	−0.00655282	+	0.00735734i
$309$	−0.478436	−	0.155453i	−0.0272173	−	0.00884342i
$310$		0			0
$311$	−0.546587	+	2.57149i	−0.0309941	+	0.145816i	−0.990924	−	0.134425i	$-0.957081\pi$
$311$	−0.546587	+	2.57149i	−0.0309941	+	0.145816i	0.959930	+	0.280241i	$0.0904145\pi$
$312$	−32.5563	−	1.70621i	−1.84314	−	0.0965948i
$313$	2.36870	−	3.64748i	0.133887	−	0.206168i	−0.765368	−	0.643593i	$-0.777443\pi$
$313$	2.36870	−	3.64748i	0.133887	−	0.206168i	0.899255	+	0.437425i	$0.144110\pi$
$314$	−12.2075	−	37.5707i	−0.688908	−	2.12024i
$315$		0			0
$316$	−6.46387	+	19.8938i	−0.363621	+	1.11911i
$317$	−13.0585	−	16.1259i	−0.733440	−	0.905723i	0.264844	−	0.964291i	$-0.414680\pi$
$317$	−13.0585	−	16.1259i	−0.733440	−	0.905723i	−0.998283	+	0.0585688i	$0.981346\pi$
$318$	6.29216	+	23.4827i	0.352847	+	1.31684i
$319$	0.000409890	0	0.000920629i	2.29494e−5	0	5.15453e-5i
$320$		0			0
$321$	−6.61541	−	9.10533i	−0.369236	−	0.508210i
$322$	30.5868	+	17.4392i	1.70453	+	0.971849i
$323$	10.1835	−	19.9862i	0.566623	−	1.11206i
$324$	−35.9500	+	20.7557i	−1.99722	+	1.15310i
$325$		0			0
$326$	−11.3803	+	19.7112i	−0.630295	+	1.09170i
$327$	−17.7172	+	0.928518i	−0.979762	+	0.0513471i
$328$	−4.44281	+	28.0508i	−0.245313	+	1.54884i
$329$	11.7804	+	3.08831i	0.649477	+	0.170264i
$330$		0			0
$331$	−1.66114	+	15.8047i	−0.0913045	+	0.868705i	0.849005	+	0.528385i	$0.177202\pi$
$331$	−1.66114	+	15.8047i	−0.0913045	+	0.868705i	−0.940310	+	0.340320i	$0.889465\pi$
$332$	32.9669	−	8.83346i	1.80929	−	0.484799i
$333$	−17.9308	−	6.88300i	−0.982604	−	0.377186i
$334$	−17.9622	+	3.81798i	−0.982848	+	0.208911i
$335$		0			0
$336$	−18.5647	+	9.58615i	−1.01279	+	0.522967i
$337$	11.6113	+	22.7884i	0.632508	+	1.24137i	0.955507	+	0.294967i	$0.0953086\pi$
$337$	11.6113	+	22.7884i	0.632508	+	1.24137i	−0.323000	+	0.946399i	$0.604691\pi$
$338$	−7.35457	−	4.77611i	−0.400036	−	0.259786i
$339$	9.00418	+	1.91390i	0.489040	+	0.103949i
$340$		0			0
$341$	−0.0313794	−	0.147628i	−0.00169929	−	0.00799452i
$342$	−2.75941	−	17.4222i	−0.149212	−	0.942086i
$343$	17.7044	+	5.43629i	0.955949	+	0.293532i
$344$	−12.2575	+	16.8710i	−0.660882	+	0.909626i
$345$		0			0
$346$	56.5550	−	5.94418i	3.04042	−	0.319561i
$347$	−11.7761	−	9.53608i	−0.632173	−	0.511923i	0.258829	−	0.965923i	$-0.416663\pi$
$347$	−11.7761	−	9.53608i	−0.632173	−	0.511923i	−0.891002	+	0.454000i	$0.849997\pi$
$348$	0.0282832	+	0.539675i	0.00151614	+	0.0289296i
$349$	1.48928			0.0797192			0.0398596	−	0.999205i	$-0.487309\pi$
$349$	1.48928			0.0797192			0.0398596	+	0.999205i	$0.487309\pi$
$350$		0			0
$351$	5.03100			0.268535
$352$	−0.000795558	−	0.0151802i	−4.24034e−5	−	0.000809105i
$353$	7.30497	+	5.91545i	0.388804	+	0.314847i	0.803715	−	0.595015i	$-0.202854\pi$
$353$	7.30497	+	5.91545i	0.388804	+	0.314847i	−0.414911	+	0.909862i	$0.636187\pi$
$354$	13.9205	−	1.46310i	0.739865	−	0.0777629i
$355$		0			0
$356$	−19.2088	+	26.4386i	−1.01806	+	1.40124i
$357$	−42.7541	−	4.25978i	−2.26279	−	0.225451i
$358$	5.17918	+	32.7001i	0.273728	+	1.72825i
$359$	−1.27728	−	6.00914i	−0.0674124	−	0.317150i	0.931502	−	0.363736i	$-0.118499\pi$
$359$	−1.27728	−	6.00914i	−0.0674124	−	0.317150i	−0.998914	+	0.0465862i	$0.985166\pi$
$360$		0			0
$361$	8.72027	+	1.85355i	0.458962	+	0.0975553i
$362$	−11.7191	−	7.61049i	−0.615944	−	0.399999i
$363$	−11.4813	−	22.5332i	−0.602610	−	1.18269i
$364$	31.6204	+	1.48557i	1.65736	+	0.0778648i
$365$		0			0
$366$	−72.9177	+	15.4991i	−3.81147	+	0.810153i
$367$	−33.6866	−	12.9311i	−1.75843	−	0.674997i	−0.999722	−	0.0235632i	$-0.992499\pi$
$367$	−33.6866	−	12.9311i	−1.75843	−	0.674997i	−0.758705	−	0.651434i	$-0.774168\pi$
$368$	18.1706	−	4.86880i	0.947209	−	0.253804i
$369$	−1.46660	+	13.9537i	−0.0763479	+	0.726402i
$370$		0			0
$371$	−3.04007	−	11.1049i	−0.157833	−	0.576538i
$372$	12.6611	−	79.9390i	0.656447	−	4.14464i
$373$	18.5645	−	0.972924i	0.961233	−	0.0503761i	0.434741	−	0.900556i	$-0.356840\pi$
$373$	18.5645	−	0.972924i	0.961233	−	0.0503761i	0.526493	+	0.850180i	$0.323507\pi$
$374$	−0.143646	+	0.248802i	−0.00742777	+	0.0128653i
$375$		0			0
$376$	18.4455	−	10.6495i	0.951252	−	0.549206i
$377$	0.0837587	−	0.164386i	0.00431379	−	0.00846629i
$378$	9.11160	−	5.32655i	0.468650	−	0.273968i
$379$	−13.0838	−	18.0083i	−0.672068	−	0.925022i	0.327737	−	0.944769i	$-0.393714\pi$
$379$	−13.0838	−	18.0083i	−0.672068	−	0.925022i	−0.999805	+	0.0197466i	$0.993714\pi$
$380$		0			0
$381$	−6.81365	−	15.3037i	−0.349074	−	0.784032i
$382$	−9.31932	−	34.7802i	−0.476818	−	1.77951i
$383$	9.68844	+	11.9642i	0.495056	+	0.611344i	0.962035	−	0.272925i	$-0.0879910\pi$
$383$	9.68844	+	11.9642i	0.495056	+	0.611344i	−0.466979	+	0.884268i	$0.654658\pi$
$384$	14.3783	−	44.2520i	0.733742	−	2.25822i
$385$		0			0
$386$	−12.4942	−	38.4531i	−0.635937	−	1.95721i
$387$	−5.61105	+	8.64026i	−0.285226	+	0.439209i
$388$	26.8279	+	1.40599i	1.36198	+	0.0713784i
$389$	2.47851	−	11.6605i	0.125666	−	0.591211i	−0.869578	−	0.493795i	$-0.835609\pi$
$389$	2.47851	−	11.6605i	0.125666	−	0.591211i	0.995244	−	0.0974152i	$-0.0310575\pi$
$390$		0			0
$391$	36.7909	+	11.9541i	1.86060	+	0.604545i
$392$	28.6988	−	15.0163i	1.44951	−	0.758440i
$393$	−19.2328	−	19.2328i	−0.970168	−	0.970168i
$394$	37.5961	+	3.95151i	1.89407	+	0.199074i
$395$		0			0
$396$	0.0156159	+	0.148576i	0.000784729	+	0.00746620i
$397$	2.42929	+	6.32850i	0.121922	+	0.317619i	0.980935	−	0.194336i	$-0.0622551\pi$
$397$	2.42929	+	6.32850i	0.121922	+	0.317619i	−0.859013	+	0.511954i	$0.828922\pi$
$398$	−4.28222	−	2.18190i	−0.214648	−	0.109369i
$399$	3.12512	+	19.0628i	0.156452	+	0.954335i
$400$		0			0
$401$	−9.14254	−	15.8353i	−0.456557	−	0.790779i	0.542220	−	0.840237i	$-0.317584\pi$
$401$	−9.14254	−	15.8353i	−0.456557	−	0.790779i	−0.998776	+	0.0494575i	$0.984251\pi$
$402$	0.967730	+	1.49017i	0.0482660	+	0.0743231i
$403$	−17.3887	+	21.4732i	−0.866190	+	1.06966i
$404$	37.8213	+	16.8391i	1.88168	+	0.837779i
$405$		0			0
$406$	−0.0223482	−	0.386397i	−0.00110912	−	0.0191765i
$407$	0.0994483	−	0.0994483i	0.00492947	−	0.00492947i
$408$	−58.3969	+	47.2888i	−2.89108	+	2.34115i
$409$	−10.6452	−	11.8226i	−0.526369	−	0.584592i	0.420063	−	0.907495i	$-0.362008\pi$
$409$	−10.6452	−	11.8226i	−0.526369	−	0.584592i	−0.946432	+	0.322903i	$0.895341\pi$
$410$		0			0
$411$	−5.62843	−	5.06786i	−0.277630	−	0.249979i
$412$	0.761163	−	0.387832i	0.0374998	−	0.0191071i
$413$	−6.58878	+	0.728590i	−0.324213	+	0.0358516i
$414$	28.9318	−	9.40052i	1.42192	−	0.462010i
$415$		0			0
$416$	−2.06811	+	1.86214i	−0.101397	+	0.0912987i
$417$	3.74639	−	9.75968i	0.183462	−	0.477934i
$418$	0.124765	+	0.0334306i	0.00610243	+	0.00163514i
$419$	−28.7560	−	20.8925i	−1.40482	−	1.02066i	−0.994050	−	0.108926i	$-0.965259\pi$
$419$	−28.7560	−	20.8925i	−1.40482	−	1.02066i	−0.410773	−	0.911738i	$-0.634741\pi$
$420$		0			0
$421$	−11.3679	+	8.25925i	−0.554037	+	0.402531i	−0.829272	−	0.558846i	$-0.811244\pi$
$421$	−11.3679	+	8.25925i	−0.554037	+	0.402531i	0.275235	+	0.961377i	$0.411244\pi$
$422$	20.7342	−	7.95910i	1.00932	−	0.387443i
$423$	8.82473	−	5.73085i	0.429073	−	0.278643i
$424$	−17.4383	−	10.0680i	−0.846876	−	0.488944i
$425$		0			0
$426$			43.8884i			2.12640i
$427$	34.4930	−	7.52710i	1.66923	−	0.364262i
$428$	18.8772	+	2.98985i	0.912464	+	0.144520i
$429$	0.0479688	−	0.107740i	0.00231596	−	0.00520172i
$430$		0			0
$431$	3.47670	−	1.54793i	0.167467	−	0.0745610i	−0.321291	−	0.946980i	$-0.604117\pi$
$431$	3.47670	−	1.54793i	0.167467	−	0.0745610i	0.488758	+	0.872419i	$0.337450\pi$
$432$	1.45948	−	5.44685i	0.0702192	−	0.262061i
$433$	1.22529	−	0.194066i	0.0588836	−	0.00932624i	−0.126923	−	0.991913i	$-0.540510\pi$
$433$	1.22529	−	0.194066i	0.0588836	−	0.00932624i	0.185807	+	0.982586i	$0.440510\pi$
$434$	−8.75776	+	57.3001i	−0.420386	+	2.75049i
$435$		0			0
$436$	20.1595	−	22.3894i	0.965467	−	1.07226i
$437$	0.910245	−	17.3685i	0.0435429	−	0.830848i
$438$	0.977501	−	18.6518i	0.0467068	−	0.891219i
$439$	−3.64427	+	4.04738i	−0.173932	+	0.193171i	−0.823807	−	0.566870i	$-0.808154\pi$
$439$	−3.64427	+	4.04738i	−0.173932	+	0.193171i	0.649876	+	0.760041i	$0.274821\pi$
$440$		0			0
$441$	13.7703	−	8.15034i	0.655730	−	0.388111i
$442$	51.9485	−	8.22783i	2.47094	−	0.391358i
$443$	4.73507	−	17.6715i	0.224970	−	0.839599i	−0.757447	−	0.652897i	$-0.773553\pi$
$443$	4.73507	−	17.6715i	0.224970	−	0.839599i	0.982417	−	0.186702i	$-0.0597799\pi$
$444$	68.8995	−	30.6760i	3.26983	−	1.45582i
$445$		0			0
$446$	−7.35106	+	16.5107i	−0.348083	+	0.781807i
$447$	41.2945	+	6.54041i	1.95316	+	0.309351i
$448$	−7.29685	+	22.8780i	−0.344744	+	1.08089i
$449$		−	7.28927i		−	0.344002i	−0.985097	−	0.172001i	$-0.944977\pi$
$449$		−	7.28927i		−	0.344002i	0.985097	−	0.172001i	$-0.0550232\pi$
$450$		0			0
$451$	−0.0889755	−	0.0513700i	−0.00418969	−	0.00241892i
$452$	−13.1102	+	8.51389i	−0.616654	+	0.400460i
$453$	40.5667	−	15.5721i	1.90599	−	0.731641i
$454$	23.0343	−	16.7354i	1.08105	−	0.785432i
$455$		0			0
$456$	27.3318	+	19.8577i	1.27993	+	0.929922i
$457$	11.4145	+	3.05849i	0.533946	+	0.143070i	0.515710	−	0.856763i	$-0.327528\pi$
$457$	11.4145	+	3.05849i	0.533946	+	0.143070i	0.0182361	+	0.999834i	$0.494195\pi$
$458$	23.4596	−	61.1145i	1.09620	−	2.85569i
$459$	8.61754	−	7.75927i	0.402232	−	0.362172i
$460$		0			0
$461$	0.809532	−	0.263033i	0.0377037	−	0.0122507i	−0.290104	−	0.956995i	$-0.593690\pi$
$461$	0.809532	−	0.263033i	0.0377037	−	0.0122507i	0.327808	+	0.944744i	$0.393690\pi$
$462$	−0.0271932	−	0.245913i	−0.00126514	−	0.0114409i
$463$	−34.4372	+	17.5466i	−1.60043	+	0.815460i	−0.600557	+	0.799582i	$0.705055\pi$
$463$	−34.4372	+	17.5466i	−1.60043	+	0.815460i	−0.999874	+	0.0158788i	$0.994945\pi$
$464$	−0.153675	−	0.138370i	−0.00713419	−	0.00642365i
$465$		0			0
$466$	−35.5202	−	39.4492i	−1.64544	−	1.82745i
$467$	6.95024	−	5.62819i	0.321619	−	0.260442i	−0.454891	−	0.890547i	$-0.650322\pi$
$467$	6.95024	−	5.62819i	0.321619	−	0.260442i	0.776509	+	0.630106i	$0.216988\pi$
$468$	19.3396	−	19.3396i	0.893972	−	0.893972i
$469$	−0.462123	−	0.703244i	−0.0213389	−	0.0324728i
$470$		0			0
$471$	34.1469	+	15.2032i	1.57341	+	0.700525i
$472$	−7.29593	+	9.00972i	−0.335822	+	0.414706i
$473$	−0.0410873	−	0.0632689i	−0.00188920	−	0.00290911i
$474$	−14.9653	−	25.9206i	−0.687377	−	1.19057i
$475$		0			0
$476$	56.4535	−	46.2233i	2.58754	−	2.11864i
$477$	−8.86348	−	4.51617i	−0.405831	−	0.206781i
$478$	3.71597	+	9.68044i	0.169965	+	0.442773i
$479$	0.101310	+	0.963902i	0.00462898	+	0.0440418i	0.996593	−	0.0824819i	$-0.0262847\pi$
$479$	0.101310	+	0.963902i	0.00462898	+	0.0440418i	−0.991964	+	0.126524i	$0.959618\pi$
$480$		0			0
$481$	−25.6068	−	2.69138i	−1.16757	−	0.122717i
$482$	0.282157	+	0.282157i	0.0128519	+	0.0128519i
$483$	−31.6277	+	10.4661i	−1.43911	+	0.476223i
$484$	40.8440	+	13.2710i	1.85655	+	0.603228i
$485$		0			0
$486$	9.86136	−	46.3941i	0.447320	−	2.10448i
$487$	−34.6240	−	1.81457i	−1.56896	−	0.0822258i	−0.752096	−	0.659053i	$-0.770957\pi$
$487$	−34.6240	−	1.81457i	−1.56896	−	0.0822258i	−0.816866	+	0.576827i	$0.804291\pi$
$488$	33.6284	−	51.7832i	1.52229	−	2.34412i
$489$	−6.65491	−	20.4817i	−0.300946	−	0.926215i
$490$		0			0
$491$	1.58176	−	4.86817i	0.0713840	−	0.219697i	−0.908999	−	0.416798i	$-0.863152\pi$
$491$	1.58176	−	4.86817i	0.0713840	−	0.219697i	0.980383	+	0.197100i	$0.0631524\pi$
$492$	−34.6725	−	42.8170i	−1.56316	−	1.93034i
$493$	−0.110061	−	0.410755i	−0.00495692	−	0.0184995i
$494$	−9.61810	−	21.6026i	−0.432739	−	0.971948i
$495$		0			0
$496$	18.2037	+	25.0553i	0.817371	+	1.12501i
$497$	−0.112513	−	20.7849i	−0.00504690	−	0.932330i
$498$	−22.1710	+	43.5130i	−0.993506	+	1.94986i
$499$	−31.5502	+	18.2155i	−1.41238	+	0.815438i	−0.995612	−	0.0935745i	$-0.970171\pi$
$499$	−31.5502	+	18.2155i	−1.41238	+	0.815438i	−0.416768	+	0.909013i	$0.636837\pi$
$500$		0			0
$501$	8.68766	−	15.0475i	0.388136	−	0.672271i
$502$	−0.321042	+	0.0168251i	−0.0143288	+	0.000750941i
$503$	0.209162	−	1.32059i	0.00932605	−	0.0588824i	−0.982586	−	0.185806i	$-0.940510\pi$
$503$	0.209162	−	1.32059i	0.00932605	−	0.0588824i	0.991912	+	0.126924i	$0.0405104\pi$
$504$	7.09664	−	27.0703i	0.316110	−	1.20581i
$505$		0			0
$506$	−0.0232846	+	0.221538i	−0.00103512	+	0.00984855i
$507$	8.01470	−	2.14753i	0.355945	−	0.0953752i
$508$	26.5581	+	10.1947i	1.17833	+	0.452317i
$509$	−18.7407	+	3.98347i	−0.830669	+	0.176564i	−0.603573	−	0.797308i	$-0.706257\pi$
$509$	−18.7407	+	3.98347i	−0.830669	+	0.176564i	−0.227097	+	0.973872i	$0.572923\pi$
$510$		0			0
$511$	−0.415114	+	8.83574i	−0.0183636	+	0.390870i
$512$	15.8470	+	31.1015i	0.700346	+	1.37451i
$513$	−4.37245	−	2.83950i	−0.193048	−	0.125367i
$514$	−21.8420	−	4.64266i	−0.963409	−	0.204779i
$515$		0			0
$516$	−8.41107	−	39.5710i	−0.370277	−	1.74202i
$517$	0.0120533	+	0.0761016i	0.000530104	+	0.00334694i
$518$	−49.2258	+	22.2368i	−2.16286	+	0.977028i
$519$	−31.6267	+	43.5304i	−1.38826	+	1.91077i
$520$		0			0
$521$	14.5325	−	1.52742i	0.636678	−	0.0669176i	0.219310	−	0.975655i	$-0.429619\pi$
$521$	14.5325	−	1.52742i	0.636678	−	0.0669176i	0.417368	+	0.908738i	$0.362953\pi$
$522$	−0.259882	−	0.210448i	−0.0113747	−	0.00921108i
$523$	−1.82151	−	34.7566i	−0.0796493	−	1.51980i	−0.687755	−	0.725943i	$-0.741404\pi$
$523$	−1.82151	−	34.7566i	−0.0796493	−	1.51980i	0.608106	−	0.793856i	$-0.291930\pi$
$524$	46.1889			2.01777
$525$		0			0
$526$	50.8274			2.21618
$527$	3.33311	+	63.5996i	0.145193	+	2.77044i
$528$	−0.102730	−	0.0831888i	−0.00447073	−	0.00362033i
$529$	6.95634	−	0.731141i	0.302449	−	0.0317887i
$530$		0			0
$531$	−3.36650	+	4.63359i	−0.146094	+	0.201081i
$532$	−26.6429	−	19.1377i	−1.15512	−	0.829725i
$533$	2.94239	+	18.5775i	0.127449	+	0.804683i
$534$	−9.72219	−	45.7393i	−0.420720	−	1.97933i
$535$		0			0
$536$	−1.43952	−	0.305980i	−0.0621780	−	0.0132163i
$537$	−26.2723	−	17.0614i	−1.13373	−	0.736255i
$538$	−1.66857	−	3.27475i	−0.0719372	−	0.141185i
$539$	0.0135087	+	0.116391i	0.000581862	+	0.00501333i
$540$		0			0
$541$	16.9335	−	3.59933i	0.728028	−	0.154747i	0.171036	−	0.985265i	$-0.445289\pi$
$541$	16.9335	−	3.59933i	0.728028	−	0.154747i	0.556992	+	0.830518i	$0.311955\pi$
$542$	−20.6130	−	7.91260i	−0.885405	−	0.339875i
$543$	12.7710	−	3.42198i	0.548057	−	0.146851i
$544$	−0.670488	+	6.37926i	−0.0287469	+	0.273509i
$545$		0			0
$546$	−31.8546	+	32.2013i	−1.36325	+	1.37809i
$547$	−1.54775	+	9.77211i	−0.0661770	+	0.417825i	0.932253	+	0.361808i	$0.117840\pi$
$547$	−1.54775	+	9.77211i	−0.0661770	+	0.417825i	−0.998430	+	0.0560177i	$0.982160\pi$
$548$	12.8439	−	0.673121i	0.548665	−	0.0287543i
$549$	15.2517	−	26.4167i	0.650927	−	1.12744i
$550$		0			0
$551$	−0.165574	+	0.0955944i	−0.00705370	+	0.00407246i
$552$	−26.4511	+	51.9131i	−1.12583	+	2.20957i
$553$	7.15378	+	12.2373i	0.304210	+	0.520381i
$554$	−19.5157	−	26.8610i	−0.829142	−	1.14122i
$555$		0			0
$556$	7.22066	+	16.2179i	0.306224	+	0.687791i
$557$	4.19928	+	15.6719i	0.177929	+	0.664041i	0.996034	+	0.0889717i	$0.0283581\pi$
$557$	4.19928	+	15.6719i	0.177929	+	0.664041i	−0.818105	+	0.575069i	$0.804975\pi$
$558$	31.5179	+	38.9213i	1.33426	+	1.64767i
$559$	−4.26786	+	13.1351i	−0.180511	+	0.555557i
$560$		0			0
$561$	−0.0840009	−	0.258528i	−0.00354652	−	0.0109151i
$562$	−5.27488	+	8.12260i	−0.222507	+	0.342631i
$563$	−30.9666	−	1.62289i	−1.30509	−	0.0683966i	−0.612925	−	0.790141i	$-0.710007\pi$
$563$	−30.9666	−	1.62289i	−1.30509	−	0.0683966i	−0.692160	+	0.721744i	$0.743341\pi$
$564$	−8.59065	+	40.4158i	−0.361732	+	1.70181i
$565$		0			0
$566$	−43.6698	−	14.1892i	−1.83558	−	0.596416i
$567$	−5.69961	+	27.5470i	−0.239361	+	1.15686i
$568$	−25.7042	−	25.7042i	−1.07852	−	1.07852i
$569$	−13.2566	−	1.39333i	−0.555746	−	0.0584112i	−0.177507	−	0.984119i	$-0.556803\pi$
$569$	−13.2566	−	1.39333i	−0.555746	−	0.0584112i	−0.378238	+	0.925708i	$0.623470\pi$
$570$		0			0
$571$	−0.872701	−	8.30320i	−0.0365214	−	0.347478i	−0.997489	−	0.0708179i	$-0.977439\pi$
$571$	−0.872701	−	8.30320i	−0.0365214	−	0.347478i	0.960968	−	0.276660i	$-0.0892276\pi$
$572$	0.0717719	+	0.186972i	0.00300093	+	0.00781770i
$573$	30.3562	+	15.4672i	1.26815	+	0.646153i
$574$	24.9979	+	30.5304i	1.04339	+	1.27431i
$575$		0			0
$576$	10.3739	+	17.9681i	0.432245	+	0.748670i
$577$	−18.8463	−	29.0208i	−0.784582	−	1.20815i	−0.974065	−	0.226267i	$-0.927348\pi$
$577$	−18.8463	−	29.0208i	−0.784582	−	1.20815i	0.189483	−	0.981884i	$-0.439319\pi$
$578$	50.2964	−	62.1109i	2.09205	−	2.58347i
$579$	34.9489	+	15.5602i	1.45242	+	0.646661i
$580$		0			0
$581$	10.3883	−	20.6640i	0.430979	−	0.857286i
$582$	−27.1814	+	27.1814i	−1.12670	+	1.12670i
$583$	0.0566095	−	0.0458415i	0.00234453	−	0.00189856i
$584$	10.3514	+	11.4963i	0.428342	+	0.475722i
$585$		0			0
$586$	12.6287	+	11.3709i	0.521687	+	0.469729i
$587$	17.8813	−	9.11097i	0.738039	−	0.376050i	−0.0442042	−	0.999023i	$-0.514075\pi$
$587$	17.8813	−	9.11097i	0.738039	−	0.376050i	0.782244	+	0.622973i	$0.214075\pi$
$588$	−15.6048	+	60.8662i	−0.643531	+	2.51008i
$589$	27.2320	−	8.84822i	1.12208	−	0.364584i
$590$		0			0
$591$	−26.5815	+	23.9341i	−1.09342	+	0.984518i
$592$	−10.3423	+	26.9426i	−0.425066	+	1.10734i
$593$	−17.9557	−	4.81121i	−0.737352	−	0.197573i	−0.129451	−	0.991586i	$-0.541322\pi$
$593$	−17.9557	−	4.81121i	−0.737352	−	0.197573i	−0.607901	+	0.794013i	$0.707988\pi$
$594$	0.0540215	+	0.0392489i	0.00221653	+	0.00161040i
$595$		0			0
$596$	−57.4394	+	41.7321i	−2.35281	+	1.70942i
$597$	4.24539	−	1.62965i	0.173752	−	0.0666972i
$598$	34.2022	−	22.2111i	1.39863	−	0.908281i
$599$	−30.6038	−	17.6691i	−1.25044	−	0.721941i	−0.279241	−	0.960221i	$-0.590083\pi$
$599$	−30.6038	−	17.6691i	−1.25044	−	0.721941i	−0.971196	+	0.238280i	$0.923416\pi$
$600$		0			0
$601$		−	0.819532i		−	0.0334294i	−0.999860	−	0.0167147i	$-0.994679\pi$
$601$		−	0.819532i		−	0.0334294i	0.999860	−	0.0167147i	$-0.00532070\pi$
$602$	6.17729	+	28.3075i	0.251767	+	1.15373i
$603$	−0.718101	−	0.113736i	−0.0292433	−	0.00463169i
$604$	−30.0131	+	67.4105i	−1.22122	+	2.74290i
$605$		0			0
$606$	−54.1179	+	24.0948i	−2.19839	+	0.978786i
$607$	−3.58282	+	13.3713i	−0.145422	+	0.542724i	0.854314	+	0.519757i	$0.173978\pi$
$607$	−3.58282	+	13.3713i	−0.145422	+	0.542724i	−0.999736	+	0.0229662i	$0.992689\pi$
$608$	2.84839	−	0.451141i	0.115518	−	0.0182962i
$609$	0.285846	+	0.228923i	0.0115831	+	0.00927642i
$610$		0			0
$611$	9.43873	−	10.4828i	0.381850	−	0.424087i
$612$	3.29927	−	62.9538i	0.133365	−	2.54476i
$613$	2.00609	−	38.2785i	0.0810253	−	1.54605i	−0.591697	−	0.806160i	$-0.701542\pi$
$613$	2.00609	−	38.2785i	0.0810253	−	1.54605i	0.672723	−	0.739895i	$-0.265125\pi$
$614$	−10.9559	+	12.1678i	−0.442144	+	0.491051i
$615$		0			0
$616$	0.159951	+	0.128098i	0.00644460	+	0.00516122i
$617$	16.5933	−	2.62812i	0.668022	−	0.105804i	0.186793	−	0.982399i	$-0.440191\pi$
$617$	16.5933	−	2.62812i	0.668022	−	0.105804i	0.481229	+	0.876595i	$0.340191\pi$
$618$	−0.316371	+	1.18071i	−0.0127263	+	0.0474952i
$619$	−5.67928	+	2.52858i	−0.228269	+	0.101632i	−0.517685	−	0.855572i	$-0.673206\pi$
$619$	−5.67928	+	2.52858i	−0.228269	+	0.101632i	0.289415	+	0.957204i	$0.406539\pi$
$620$		0			0
$621$	3.65706	−	8.21390i	0.146753	−	0.329612i
$622$	6.30933	+	0.999300i	0.252981	+	0.0400683i
$623$	4.72154	+	21.6365i	0.189165	+	0.866850i
$624$			24.2004i			0.968790i
$625$		0			0
$626$	−9.15199	−	5.28391i	−0.365787	−	0.211187i
$627$	−0.102498	+	0.0665632i	−0.00409339	+	0.00265828i
$628$	−59.2587	+	22.7473i	−2.36468	+	0.907716i
$629$	−48.0125	+	34.8832i	−1.91439	+	1.39088i
$630$		0			0
$631$	−16.6120	−	12.0693i	−0.661312	−	0.480471i	0.205794	−	0.978595i	$-0.434022\pi$
$631$	−16.6120	−	12.0693i	−0.661312	−	0.480471i	−0.867106	+	0.498124i	$0.834022\pi$
$632$	23.9457	+	6.41622i	0.952508	+	0.255224i
$633$	−7.53080	+	19.6184i	−0.299323	+	0.779762i
$634$	−37.4696	+	33.7378i	−1.48811	+	1.33990i
$635$		0			0
$636$	37.1507	−	12.0710i	1.47312	−	0.478646i
$637$	15.0033	−	15.3317i	0.594452	−	0.607465i
$638$	0.00218182	−	0.00111169i	8.63790e−5	−	4.40123e-5i
$639$	−13.3458	−	12.0166i	−0.527950	−	0.475368i
$640$		0			0
$641$	6.22319	+	6.91155i	0.245801	+	0.272990i	0.853403	−	0.521252i	$-0.174535\pi$
$641$	6.22319	+	6.91155i	0.245801	+	0.272990i	−0.607602	+	0.794242i	$0.707868\pi$
$642$	−21.2532	+	17.2105i	−0.838796	+	0.679244i
$643$	−10.6811	+	10.6811i	−0.421223	+	0.421223i	−0.885625	−	0.464402i	$-0.846269\pi$
$643$	−10.6811	+	10.6811i	−0.421223	+	0.421223i	0.464402	+	0.885625i	$0.346269\pi$
$644$	25.4105	−	50.5455i	1.00131	−	1.99177i
$645$		0			0
$646$	−49.7923	−	22.1690i	−1.95905	−	0.872226i
$647$	−9.53557	+	11.7754i	−0.374882	+	0.462940i	−0.929315	−	0.369288i	$-0.879602\pi$
$647$	−9.53557	+	11.7754i	−0.374882	+	0.462940i	0.554433	+	0.832228i	$0.312935\pi$
$648$	26.7947	+	41.2603i	1.05260	+	1.62086i
$649$	−0.0209698	−	0.0363207i	−0.000823135	−	0.00142571i
$650$		0			0
$651$	−34.7461	−	42.4361i	−1.36181	−	1.66320i
$652$	32.5852	+	16.6030i	1.27614	+	0.650223i
$653$	12.9236	+	33.6671i	0.505740	+	1.31750i	0.914401	+	0.404811i	$0.132663\pi$
$653$	12.9236	+	33.6671i	0.505740	+	1.31750i	−0.408661	+	0.912686i	$0.634004\pi$
$654$	4.50617	+	42.8734i	0.176205	+	1.67648i
$655$		0			0
$656$	20.9667	+	2.20369i	0.818612	+	0.0860396i
$657$	5.40409	+	5.40409i	0.210833	+	0.210833i
$658$	5.99580	−	28.9785i	0.233741	−	1.12970i
$659$	30.6779	+	9.96786i	1.19504	+	0.388293i	0.837935	−	0.545771i	$-0.183763\pi$
$659$	30.6779	+	9.96786i	1.19504	+	0.388293i	0.357107	+	0.934063i	$0.383763\pi$
$660$		0			0
$661$	3.78793	−	17.8208i	0.147333	−	0.693149i	−0.841024	−	0.540998i	$-0.818047\pi$
$661$	3.78793	−	17.8208i	0.147333	−	0.693149i	0.988357	−	0.152151i	$-0.0486199\pi$
$662$	38.5620	+	2.02095i	1.49875	+	0.0785464i
$663$	−27.1044	+	41.7371i	−1.05265	+	1.62093i
$664$	−12.4994	−	38.4692i	−0.485071	−	1.49290i
$665$		0			0
$666$	−14.4216	+	44.3852i	−0.558827	+	1.71989i
$667$	−0.207501	−	0.256242i	−0.00803447	−	0.00992174i
$668$	7.63675	+	28.5007i	0.295475	+	1.10273i
$669$	−6.95549	−	15.6223i	−0.268915	−	0.603992i
$670$		0			0
$671$	0.131290	+	0.180705i	0.00506839	+	0.00697604i
$672$	−2.78786	−	4.76890i	−0.107544	−	0.183964i
$673$	8.71675	−	17.1076i	0.336006	−	0.659449i	−0.659750	−	0.751485i	$-0.729338\pi$
$673$	8.71675	−	17.1076i	0.336006	−	0.659449i	0.995756	+	0.0920367i	$0.0293377\pi$
$674$	53.8205	−	31.0733i	2.07309	−	1.19690i
$675$		0			0
$676$	−7.04519	+	12.2026i	−0.270969	+	0.469332i
$677$	−35.4419	+	1.85743i	−1.36214	+	0.0713870i	−0.719348	−	0.694650i	$-0.755559\pi$
$677$	−35.4419	+	1.85743i	−1.36214	+	0.0713870i	−0.642797	+	0.766037i	$0.722226\pi$
$678$	3.49909	−	22.0924i	0.134382	−	0.848453i
$679$	12.8030	−	12.9424i	0.491335	−	0.496683i
$680$		0			0
$681$	−2.81598	+	26.7923i	−0.107909	+	1.02668i
$682$	−0.354236	+	0.0949172i	−0.0135644	+	0.00363457i
$683$	−8.91129	−	3.42072i	−0.340981	−	0.130890i	0.181851	−	0.983326i	$-0.441791\pi$
$683$	−8.91129	−	3.42072i	−0.340981	−	0.130890i	−0.522832	+	0.852436i	$0.675124\pi$
$684$	−27.7233	+	5.89278i	−1.06003	+	0.225316i
$685$		0			0
$686$	10.9399	−	43.6519i	0.417688	−	1.66664i
$687$	28.1201	+	55.1888i	1.07285	+	2.10558i
$688$	12.9827	+	8.43109i	0.494962	+	0.321432i
$689$	−13.0443	−	2.77265i	−0.496948	−	0.105629i
$690$		0			0
$691$	10.4781	+	49.2956i	0.398606	+	1.87529i	0.477855	+	0.878439i	$0.341415\pi$
$691$	10.4781	+	49.2956i	0.398606	+	1.87529i	−0.0792486	+	0.996855i	$0.525252\pi$
$692$	−14.2938	−	90.2473i	−0.543367	−	3.43069i
$693$	0.0822238	+	0.0590617i	0.00312342	+	0.00224357i
$694$	−21.6421	+	29.7878i	−0.821524	+	1.13073i
$695$		0			0
$696$	0.636964	−	0.0669476i	0.0241441	−	0.00253764i
$697$	33.6920	+	27.2832i	1.27618	+	1.03343i
$698$	−0.189391	−	3.61379i	−0.00716855	−	0.136784i
$699$	50.2276			1.89978
$700$		0			0
$701$	41.2864			1.55936			0.779682	−	0.626176i	$-0.215381\pi$
$701$	41.2864			1.55936			0.779682	+	0.626176i	$0.215381\pi$
$702$	−0.639790	−	12.2079i	−0.0241473	−	0.460758i
$703$	20.7359	+	16.7916i	0.782070	+	0.633307i
$704$	−0.151095	+	0.0158807i	−0.00569460	+	0.000598526i
$705$		0			0
$706$	13.4251	−	18.4781i	0.505261	−	0.695431i
$707$	25.5677	−	11.5497i	0.961571	−	0.434371i
$708$	−3.51827	−	22.2135i	−0.132225	−	0.834834i
$709$	0.400572	+	1.88454i	0.0150438	+	0.0707755i	0.985029	−	0.172388i	$-0.0551482\pi$
$709$	0.400572	+	1.88454i	0.0150438	+	0.0707755i	−0.969985	+	0.243163i	$0.921815\pi$
$710$		0			0
$711$	11.9795	+	2.54632i	0.449266	+	0.0954945i
$712$	32.4822	+	21.0942i	1.21732	+	0.790538i
$713$	22.4185	+	43.9987i	0.839578	+	1.64777i
$714$	−4.89950	+	104.286i	−0.183359	+	3.90282i
$715$		0			0
$716$	52.0344	−	11.0603i	1.94462	−	0.413341i
$717$	−9.15952	−	3.51601i	−0.342069	−	0.131308i
$718$	−14.4190	+	3.86356i	−0.538112	+	0.144187i
$719$	5.06873	−	48.2257i	0.189032	−	1.79852i	−0.330230	−	0.943900i	$-0.607126\pi$
$719$	5.06873	−	48.2257i	0.189032	−	1.79852i	0.519262	−	0.854615i	$-0.326207\pi$
$720$		0			0
$721$	0.146802	−	0.559980i	0.00546719	−	0.0208547i
$722$	3.38876	−	21.3958i	0.126117	−	0.796270i
$723$	−0.377040	+	0.0197598i	−0.0140223	+	0.000734876i
$724$	−11.2262	+	19.4443i	−0.417217	+	0.722641i
$725$		0			0
$726$	−53.2178	+	30.7253i	−1.97510	+	1.14032i
$727$	−3.31875	+	6.51342i	−0.123086	+	0.241569i	−0.944325	−	0.329015i	$-0.893283\pi$
$727$	−3.31875	+	6.51342i	−0.123086	+	0.241569i	0.821239	+	0.570584i	$0.193283\pi$
$728$	−0.203080	−	37.5157i	−0.00752665	−	1.39042i
$729$	7.63022	+	10.5021i	0.282601	+	0.388967i
$730$		0			0
$731$	12.9478	+	29.0813i	0.478893	+	1.07561i
$732$	31.0015	+	115.699i	1.14585	+	4.27636i
$733$	6.48565	+	8.00911i	0.239553	+	0.295823i	0.882717	−	0.469905i	$-0.155712\pi$
$733$	6.48565	+	8.00911i	0.239553	+	0.295823i	−0.643164	+	0.765729i	$0.722379\pi$
$734$	−27.0939	+	83.3864i	−1.00005	+	3.07785i
$735$		0			0
$736$	1.53691	+	4.73012i	0.0566512	+	0.174354i
$737$	0.00289960	−	0.00446499i	0.000106808	−	0.000164470i
$738$	34.0458	+	1.78427i	1.25324	+	0.0656797i
$739$	4.57499	−	21.5236i	0.168294	−	0.791759i	−0.810309	−	0.586002i	$-0.800701\pi$
$739$	4.57499	−	21.5236i	0.168294	−	0.791759i	0.978603	−	0.205757i	$-0.0659657\pi$
$740$		0			0
$741$	21.2794	+	6.91411i	0.781720	+	0.253996i
$742$	−26.5599	+	8.78907i	−0.975045	+	0.322657i
$743$	32.3075	+	32.3075i	1.18525	+	1.18525i	0.978366	+	0.206883i	$0.0663319\pi$
$743$	32.3075	+	32.3075i	1.18525	+	1.18525i	0.206883	+	0.978366i	$0.433668\pi$
$744$	−95.3951	−	10.0264i	−3.49735	−	0.367587i
$745$		0			0
$746$	−4.72168	−	44.9238i	−0.172873	−	1.64478i
$747$	−7.16123	−	18.6556i	−0.262016	−	0.682574i
$748$	0.411303	+	0.209569i	0.0150387	+	0.00766262i
$749$	10.0211	−	8.20512i	0.366162	−	0.299809i
$750$		0			0
$751$	−11.0388	−	19.1197i	−0.402810	−	0.697687i	0.591254	−	0.806485i	$-0.298633\pi$
$751$	−11.0388	−	19.1197i	−0.402810	−	0.697687i	−0.994064	+	0.108798i	$0.965300\pi$
$752$	−8.61110	−	13.2599i	−0.314014	−	0.483540i
$753$	0.191429	−	0.236395i	0.00697605	−	0.00861471i
$754$	−0.409540	−	0.182339i	−0.0149146	−	0.00664040i
$755$		0			0
$756$	−9.31310	−	14.1724i	−0.338714	−	0.515444i
$757$	−2.36580	+	2.36580i	−0.0859865	+	0.0859865i	−0.748792	−	0.662805i	$-0.769366\pi$
$757$	−2.36580	+	2.36580i	−0.0859865	+	0.0859865i	0.662805	+	0.748792i	$0.269366\pi$
$758$	−42.0339	+	34.0384i	−1.52674	+	1.23633i
$759$	−0.141033	−	0.156633i	−0.00511919	−	0.00568543i
$760$		0			0
$761$	27.8157	+	25.0454i	1.00832	+	0.907895i	0.995757	−	0.0920256i	$-0.0293342\pi$
$761$	27.8157	+	25.0454i	1.00832	+	0.907895i	0.0125634	+	0.999921i	$0.496001\pi$
$762$	−36.2686	+	18.4798i	−1.31387	+	0.669451i
$763$	−2.24397	−	20.2927i	−0.0812371	−	0.734643i
$764$	−55.0239	+	17.8784i	−1.99070	+	0.646816i
$765$		0			0
$766$	27.7996	−	25.0309i	1.00444	−	0.904403i
$767$	−2.75157	+	7.16810i	−0.0993536	+	0.258825i
$768$	−68.8951	−	18.4604i	−2.48604	−	0.666132i
$769$	31.5396	+	22.9148i	1.13735	+	0.826330i	0.986747	−	0.162264i	$-0.0518798\pi$
$769$	31.5396	+	22.9148i	1.13735	+	0.826330i	0.150599	+	0.988595i	$0.451880\pi$
$770$		0			0
$771$	17.0932	−	12.4189i	0.615596	−	0.447257i
$772$	−60.6505	+	23.2815i	−2.18286	+	0.837920i
$773$	−19.4971	+	12.6616i	−0.701263	+	0.455405i	−0.845387	−	0.534154i	$-0.820630\pi$
$773$	−19.4971	+	12.6616i	−0.701263	+	0.455405i	0.144124	+	0.989560i	$0.453963\pi$
$774$	21.6795	+	12.5167i	0.779254	+	0.449902i
$775$		0			0
$776$		−	31.8387i		−	1.14294i
$777$	15.5301	−	48.6920i	0.557139	−	1.74682i
$778$	−28.6099	−	4.53136i	−1.02571	−	0.162457i
$779$	7.92795	−	17.8065i	0.284048	−	0.637983i
$780$		0			0
$781$	0.120133	−	0.0534868i	0.00429871	−	0.00191391i
$782$	24.3284	−	90.7949i	0.869983	−	3.24682i
$783$	−0.0976210	+	0.0154617i	−0.00348869	+	0.000552554i
$784$	−12.2466	−	20.6911i	−0.437378	−	0.738969i
$785$		0			0
$786$	−44.2234	+	49.1151i	−1.57740	+	1.75188i
$787$	−0.863994	+	16.4860i	−0.0307981	+	0.587662i	0.939024	+	0.343850i	$0.111731\pi$
$787$	−0.863994	+	16.4860i	−0.0307981	+	0.587662i	−0.969823	+	0.243812i	$0.921602\pi$
$788$	3.17897	−	60.6583i	0.113246	−	2.16086i
$789$	−32.1801	+	35.7396i	−1.14564	+	1.27236i
$790$		0			0
$791$	−1.60048	+	10.4716i	−0.0569066	+	0.372327i
$792$	0.174874	−	0.0276973i	0.00621388	−	0.000984182i
$793$	10.5837	−	39.4989i	0.375838	−	1.40265i
$794$	15.0474	−	6.69956i	0.534014	−	0.237758i
$795$		0			0
$796$	−3.14093	+	7.05465i	−0.111327	+	0.250045i
$797$	−43.0687	−	6.82142i	−1.52557	−	0.241627i	−0.663409	−	0.748257i	$-0.730891\pi$
$797$	−43.0687	−	6.82142i	−1.52557	−	0.241627i	−0.862164	+	0.506630i	$0.830891\pi$
$798$	45.8593	−	10.0075i	1.62340	−	0.354260i
$799$		−	32.5131i		−	1.15023i
$800$		0			0
$801$	16.5705	+	9.56698i	0.585490	+	0.338033i
$802$	−37.2625	+	24.1985i	−1.31578	+	0.854480i
$803$	−0.0522459	+	0.0200553i	−0.00184372	+	0.000707738i
$804$	2.30973	−	1.67811i	0.0814578	−	0.0591825i
$805$		0			0
$806$	54.3169	+	39.4635i	1.91323	+	1.39004i
$807$	3.35907	+	0.900061i	0.118245	+	0.0316836i
$808$	17.5836	−	45.8069i	0.618590	−	1.61148i
$809$	10.9422	−	9.85244i	0.384709	−	0.346393i	−0.453973	−	0.891016i	$-0.649994\pi$
$809$	10.9422	−	9.85244i	0.384709	−	0.346393i	0.838681	+	0.544622i	$0.183327\pi$
$810$		0			0
$811$	−24.6251	+	8.00118i	−0.864704	+	0.280959i	−0.707592	−	0.706621i	$-0.750218\pi$
$811$	−24.6251	+	8.00118i	−0.864704	+	0.280959i	−0.157112	+	0.987581i	$0.550218\pi$
$812$	−0.618125	+	0.0683525i	−0.0216920	+	0.00239870i
$813$	18.6144	−	9.48450i	0.652835	−	0.332636i
$814$	−0.253962	−	0.228669i	−0.00890137	−	0.00801483i
$815$		0			0
$816$	37.3240	+	41.4525i	1.30660	+	1.45113i
$817$	11.1227	−	9.00697i	0.389134	−	0.315114i
$818$	−27.3344	+	27.3344i	−0.955725	+	0.955725i
$819$	−1.07017	−	18.5031i	−0.0373948	−	0.646551i
$820$		0			0
$821$	44.7779	+	19.9364i	1.56276	+	0.695785i	0.992106	−	0.125406i	$-0.0400233\pi$
$821$	44.7779	+	19.9364i	1.56276	+	0.695785i	0.570653	+	0.821191i	$0.306690\pi$
$822$	−11.5816	+	14.3021i	−0.403955	+	0.498843i
$823$	−28.8436	−	44.4153i	−1.00543	−	1.54822i	−0.825393	−	0.564558i	$-0.809047\pi$
$823$	−28.8436	−	44.4153i	−1.00543	−	1.54822i	−0.180032	−	0.983661i	$-0.557620\pi$
$824$	−0.506220	−	0.876799i	−0.0176350	−	0.0305447i
$825$		0			0
$826$	2.60585	+	15.8953i	0.0906690	+	0.553068i
$827$	−4.78458	−	2.43786i	−0.166376	−	0.0847728i	0.368819	−	0.929501i	$-0.379762\pi$
$827$	−4.78458	−	2.43786i	−0.166376	−	0.0847728i	−0.535196	+	0.844728i	$0.679762\pi$
$828$	−17.5168	−	45.6330i	−0.608753	−	1.58585i
$829$	−3.66391	−	34.8598i	−0.127253	−	1.21073i	−0.852681	−	0.522432i	$-0.825025\pi$
$829$	−3.66391	−	34.8598i	−0.127253	−	1.21073i	0.725428	−	0.688298i	$-0.241642\pi$
$830$		0			0
$831$	31.2433	+	3.28380i	1.08382	+	0.113914i
$832$	19.6675	+	19.6675i	0.681847	+	0.681847i
$833$	2.05298	−	49.4010i	0.0711316	−	1.71164i
$834$	−24.1587	−	7.84964i	−0.836548	−	0.271811i
$835$		0			0
$836$	0.0431503	−	0.203006i	0.00149238	−	0.00702111i
$837$	14.7822	+	0.774702i	0.510947	+	0.0267776i
$838$	−47.0395	+	72.4345i	−1.62495	+	2.50221i
$839$	4.17081	+	12.8364i	0.143992	+	0.443163i	0.996880	−	0.0789314i	$-0.0251508\pi$
$839$	4.17081	+	12.8364i	0.143992	+	0.443163i	−0.852888	+	0.522095i	$0.825151\pi$
$840$		0			0
$841$	8.96037	−	27.5772i	0.308978	−	0.950938i
$842$	21.4871	+	26.5343i	0.740493	+	0.914433i
$843$	−2.37180	−	8.85167i	−0.0816891	−	0.304868i
$844$	−14.5146	−	32.6003i	−0.499613	−	1.12215i
$845$		0			0
$846$	−15.0284	−	20.6848i	−0.516686	−	0.711158i
$847$	25.1244	−	14.6875i	0.863284	−	0.504668i
$848$	−6.78594	+	13.3182i	−0.233030	+	0.457347i
$849$	37.6256	−	21.7232i	1.29131	−	0.745537i
$850$		0			0
$851$	−23.0079	+	39.8508i	−0.788699	+	1.36607i
$852$	70.4225	−	3.69069i	2.41263	−	0.126441i
$853$	5.33840	−	33.7053i	0.182783	−	1.15405i	−0.710214	−	0.703986i	$-0.751402\pi$
$853$	5.33840	−	33.7053i	0.182783	−	1.15405i	0.892997	−	0.450063i	$-0.148598\pi$
$854$	−22.6513	−	82.7416i	−0.775111	−	2.83136i
$855$		0			0
$856$	2.36769	−	22.5271i	0.0809260	−	0.769960i
$857$	−6.63141	+	1.77688i	−0.226525	+	0.0606971i	−0.370296	−	0.928914i	$-0.620744\pi$
$857$	−6.63141	+	1.77688i	−0.226525	+	0.0606971i	0.143771	+	0.989611i	$0.454077\pi$
$858$	−0.267535	−	0.102697i	−0.00913350	−	0.00350602i
$859$	43.3468	−	9.21364i	1.47897	−	0.314365i	0.603395	−	0.797442i	$-0.293814\pi$
$859$	43.3468	−	9.21364i	1.47897	−	0.314365i	0.875578	+	0.483077i	$0.160481\pi$
$860$		0			0
$861$	−37.2943	−	1.75213i	−1.27099	−	0.0597126i
$862$	−4.19824	−	8.23950i	−0.142993	−	0.280639i
$863$	−1.69343	−	1.09973i	−0.0576452	−	0.0374352i	0.515495	−	0.856893i	$-0.327608\pi$
$863$	−1.69343	−	1.09973i	−0.0576452	−	0.0374352i	−0.573140	+	0.819458i	$0.694275\pi$
$864$	1.45829	+	0.309970i	0.0496122	+	0.0105454i
$865$		0			0
$866$	−0.626730	−	2.94853i	−0.0212971	−	0.100195i
$867$	11.8297	+	74.6900i	0.401759	+	2.53661i
$868$	92.6791	+	9.23402i	3.14573	+	0.313423i
$869$	−0.0527129	+	0.0725531i	−0.00178816	+	0.00246119i
$870$		0			0
$871$	−0.969332	+	0.101881i	−0.0328446	+	0.00345210i
$872$	−27.7488	−	22.4706i	−0.939694	−	0.760950i
$873$	−0.823202	−	15.7076i	−0.0278612	−	0.531623i
$874$	−42.2612			−1.42950
$875$		0			0
$876$	−30.0106			−1.01396
$877$	2.45627	+	46.8683i	0.0829422	+	1.58263i	0.650635	+	0.759391i	$0.274503\pi$
$877$	2.45627	+	46.8683i	0.0829422	+	1.58263i	−0.567693	+	0.823240i	$0.692164\pi$
$878$	10.2846	+	8.32828i	0.347087	+	0.281066i
$879$	−15.9911	+	1.68073i	−0.539365	+	0.0566896i
$880$		0			0
$881$	12.9945	−	17.8855i	0.437797	−	0.602576i	−0.531924	−	0.846792i	$-0.678531\pi$
$881$	12.9945	−	17.8855i	0.437797	−	0.602576i	0.969721	+	0.244216i	$0.0785306\pi$
$882$	−21.5283	−	32.3778i	−0.724896	−	1.09022i
$883$	−2.48456	−	15.6869i	−0.0836122	−	0.527906i	−0.993571	−	0.113208i	$-0.963887\pi$
$883$	−2.48456	−	15.6869i	−0.0836122	−	0.527906i	0.909959	−	0.414698i	$-0.136113\pi$
$884$	−17.5707	−	82.6636i	−0.590966	−	2.78028i
$885$		0			0
$886$	−43.4828	−	9.24256i	−1.46083	−	0.310510i
$887$	14.7196	+	9.55901i	0.494236	+	0.320960i	0.767577	−	0.640957i	$-0.221462\pi$
$887$	14.7196	+	9.55901i	0.494236	+	0.320960i	−0.273341	+	0.961917i	$0.588129\pi$
$888$	−40.5794	−	79.6415i	−1.36175	−	2.67259i
$889$	17.1289	−	8.84473i	0.574485	−	0.296643i
$890$		0			0
$891$	−0.174084	+	0.0370028i	−0.00583205	+	0.00123964i
$892$	27.1110	+	10.4069i	0.907743	+	0.348450i
$893$	−14.1197	+	3.78336i	−0.472498	+	0.126605i
$894$	10.6192	−	101.035i	0.355158	−	3.37910i
$895$		0			0
$896$	51.7942	+	13.5782i	1.73032	+	0.453614i
$897$	−6.03632	+	38.1118i	−0.201547	+	1.27252i
$898$	−17.6877	+	0.926974i	−0.590246	+	0.0309335i
$899$	0.271415	−	0.470104i	0.00905219	−	0.0156789i
$900$		0			0
$901$	−26.6196	+	15.3689i	−0.886829	+	0.512011i
$902$	−0.113336	+	0.222435i	−0.00377369	+	0.00740629i
$903$	−23.8155	−	13.5786i	−0.792532	−	0.451866i
$904$	10.8896	+	14.9882i	0.362182	+	0.498500i
$905$		0			0
$906$	−42.9452	−	96.4565i	−1.42676	−	3.20455i
$907$	−7.69450	−	28.7163i	−0.255492	−	0.953508i	−0.967816	−	0.251658i	$-0.919024\pi$
$907$	−7.69450	−	28.7163i	−0.255492	−	0.953508i	0.712325	−	0.701850i	$-0.247642\pi$
$908$	−28.7904	−	35.5531i	−0.955441	−	1.17987i
$909$	7.49054	−	23.0535i	0.248445	−	0.764636i
$910$		0			0
$911$	12.1969	+	37.5382i	0.404101	+	1.24370i	0.921643	+	0.388038i	$0.126847\pi$
$911$	12.1969	+	37.5382i	0.404101	+	1.24370i	−0.517542	+	0.855658i	$0.673153\pi$
$912$	13.6587	−	21.0326i	0.452285	−	0.696458i
$913$	0.146126	+	0.00765812i	0.00483605	+	0.000253447i
$914$	5.96999	−	28.0866i	0.197470	−	0.929022i
$915$		0			0
$916$	−100.036	−	32.5036i	−3.30528	−	1.07395i
$917$	20.8177	−	23.3736i	0.687459	−	0.771863i
$918$	−19.9241	−	19.9241i	−0.657593	−	0.657593i
$919$	−14.7138	−	1.54648i	−0.485363	−	0.0510137i	−0.141313	−	0.989965i	$-0.545132\pi$
$919$	−14.7138	−	1.54648i	−0.485363	−	0.0510137i	−0.344050	+	0.938951i	$0.611799\pi$
$920$		0			0
$921$	−1.61938	−	15.4074i	−0.0533605	−	0.507691i
$922$	−0.741208	−	1.93091i	−0.0244104	−	0.0635912i
$923$	−21.4508	−	10.9297i	−0.706061	−	0.359756i
$924$	−0.392301	+	0.0643132i	−0.0129058	+	0.00211575i
$925$		0			0
$926$	46.9570	+	81.3318i	1.54310	+	2.67273i
$927$	−0.272414	−	0.419481i	−0.00894725	−	0.0137776i
$928$	0.0344066	−	0.0424886i	0.00112945	−	0.00139476i
$929$	15.8211	+	7.04399i	0.519072	+	0.231106i	0.649513	−	0.760350i	$-0.274973\pi$
$929$	15.8211	+	7.04399i	0.519072	+	0.231106i	−0.130441	+	0.991456i	$0.541639\pi$
$930$		0			0
$931$	−21.6926	+	4.85695i	−0.710948	+	0.159180i
$932$	−60.3124	+	60.3124i	−1.97560	+	1.97560i
$933$	−4.69725	+	3.80376i	−0.153781	+	0.124530i
$934$	−14.5409	−	16.1493i	−0.475793	−	0.528421i
$935$		0			0
$936$	−24.0884	−	21.6893i	−0.787354	−	0.708937i
$937$	29.8820	−	15.2256i	0.976202	−	0.497400i	0.108291	−	0.994119i	$-0.465462\pi$
$937$	29.8820	−	15.2256i	0.976202	−	0.497400i	0.867911	+	0.496719i	$0.165462\pi$
$938$	−1.64768	+	1.21079i	−0.0537987	+	0.0395338i
$939$	9.50975	−	3.08990i	0.310339	−	0.100835i
$940$		0			0
$941$	−32.3887	+	29.1630i	−1.05584	+	0.950685i	−0.998862	−	0.0476900i	$-0.984814\pi$
$941$	−32.3887	+	29.1630i	−1.05584	+	0.950685i	−0.0569808	+	0.998375i	$0.518147\pi$
$942$	32.5487	−	84.7923i	1.06049	−	2.76268i
$943$	32.4696	+	8.70021i	1.05736	+	0.283318i
$944$	6.96237	+	5.05846i	0.226606	+	0.164639i
$945$		0			0
$946$	−0.148300	+	0.107746i	−0.00482164	+	0.00350312i
$947$	−5.14526	+	1.97508i	−0.167199	+	0.0641815i	−0.440528	−	0.897739i	$-0.645209\pi$
$947$	−5.14526	+	1.97508i	−0.167199	+	0.0641815i	0.273329	+	0.961921i	$0.411875\pi$
$948$	−40.3332	+	26.1927i	−1.30996	+	0.850699i
$949$	8.87279	+	5.12271i	0.288023	+	0.166290i
$950$		0			0
$951$		−	47.7071i		−	1.54701i
$952$	−58.2080	−	63.9470i	−1.88653	−	2.07253i
$953$	6.68823	+	1.05931i	0.216653	+	0.0343145i	0.263817	−	0.964573i	$-0.415018\pi$
$953$	6.68823	+	1.05931i	0.216653	+	0.0343145i	−0.0471642	+	0.998887i	$0.515018\pi$
$954$	−9.83150	+	22.0819i	−0.318307	+	0.714929i
$955$		0			0
$956$	15.2206	−	6.77663i	0.492268	−	0.219172i
$957$	−0.000599669		0.00223799i	−1.93845e−5		7.23441e-5i
$958$	2.32607	−	0.368413i	0.0751518	−	0.0119029i
$959$	5.44821	−	6.80295i	0.175932	−	0.219679i
$960$		0			0
$961$	−33.6553	+	37.3780i	−1.08565	+	1.20574i
$962$	−3.27435	+	62.4783i	−0.105569	+	2.01438i
$963$	0.585655	−	11.1750i	0.0188725	−	0.360108i
$964$	0.429016	−	0.476471i	0.0138177	−	0.0153461i
$965$		0			0
$966$	29.4184	+	75.4149i	0.946523	+	2.42644i
$967$	57.0421	−	9.03458i	1.83435	−	0.290533i	0.859128	−	0.511760i	$-0.171006\pi$
$967$	57.0421	−	9.03458i	1.83435	−	0.290533i	0.975222	+	0.221228i	$0.0710065\pi$
$968$	13.1732	−	49.1630i	0.423403	−	1.58016i
$969$	47.1129	−	20.9760i	1.51348	−	0.673847i
$970$		0			0
$971$	−7.98460	+	17.9337i	−0.256238	+	0.575520i	−0.995160	−	0.0982714i	$-0.968669\pi$
$971$	−7.98460	+	17.9337i	−0.256238	+	0.575520i	0.738922	+	0.673791i	$0.235335\pi$
$972$	−75.2723	−	11.9220i	−2.41436	−	0.382397i
$973$	11.4613	+	3.65554i	0.367434	+	0.117191i
$974$			84.2473i			2.69946i
$975$		0			0
$976$	−39.6935	−	22.9170i	−1.27056	−	0.733556i
$977$	20.6393	−	13.4033i	0.660309	−	0.428810i	−0.170507	−	0.985356i	$-0.554541\pi$
$977$	20.6393	−	13.4033i	0.660309	−	0.428810i	0.830816	+	0.556547i	$0.187874\pi$
$978$	−48.8534	+	18.7531i	−1.56216	+	0.599657i
$979$	−0.113351	+	0.0823545i	−0.00362272	+	0.00263206i
$980$		0			0
$981$	−14.2709	−	10.3684i	−0.455634	−	0.331038i
$982$	−12.0140	−	3.21913i	−0.383381	−	0.102727i
$983$	−16.0960	+	41.9315i	−0.513382	+	1.33741i	0.394775	+	0.918778i	$0.370823\pi$
$983$	−16.0960	+	41.9315i	−0.513382	+	1.33741i	−0.908157	+	0.418629i	$0.862511\pi$
$984$	−48.5243	+	43.6915i	−1.54690	+	1.39283i
$985$		0			0
$986$	−0.982717	+	0.319304i	−0.0312961	+	0.0101687i
$987$	16.5803	+	22.5629i	0.527756	+	0.718186i
$988$	−33.8543	+	17.2496i	−1.07705	+	0.548784i
$989$	18.3428	+	16.5160i	0.583268	+	0.525177i
$990$		0			0
$991$	−31.0000	−	34.4290i	−0.984747	−	1.09367i	−0.995598	−	0.0937308i	$-0.970121\pi$
$991$	−31.0000	−	34.4290i	−0.984747	−	1.09367i	0.0108510	−	0.999941i	$-0.496546\pi$
$992$	−6.36332	+	5.15291i	−0.202035	+	0.163605i
$993$	−25.8356	+	25.8356i	−0.819867	+	0.819867i
$994$	−50.4211	+	2.91623i	−1.59926	+	0.0924971i
$995$		0			0
$996$	71.6845	+	31.9160i	2.27141	+	1.01130i
$997$	15.5757	−	19.2344i	0.493286	−	0.609158i	−0.468331	−	0.883553i	$-0.655144\pi$
$997$	15.5757	−	19.2344i	0.493286	−	0.609158i	0.961617	+	0.274395i	$0.0884777\pi$
$998$	48.2129	+	74.2414i	1.52615	+	2.35007i
$999$	6.89686	+	11.9457i	0.218207	+	0.377946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.c.143.1		288
5.2	odd	4		875.2.bb.a.857.18		288
5.3	odd	4		875.2.bb.b.857.1		288
5.4	even	2		175.2.x.a.108.18	yes	288
7.5	odd	6	inner	875.2.bb.c.768.1		288
25.3	odd	20		175.2.x.a.122.18	yes	288
25.4	even	10		875.2.bb.b.493.18		288
25.21	even	5		875.2.bb.a.493.1		288
25.22	odd	20	inner	875.2.bb.c.507.1		288
35.12	even	12		875.2.bb.a.607.1		288
35.19	odd	6		175.2.x.a.33.18	✓	288
35.33	even	12		875.2.bb.b.607.18		288
175.47	even	60	inner	875.2.bb.c.257.1		288
175.54	odd	30		875.2.bb.b.243.1		288
175.96	odd	30		875.2.bb.a.243.18		288
175.103	even	60		175.2.x.a.47.18	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.18	✓	288	35.19	odd	6
175.2.x.a.47.18	yes	288	175.103	even	60
175.2.x.a.108.18	yes	288	5.4	even	2
175.2.x.a.122.18	yes	288	25.3	odd	20
875.2.bb.a.243.18		288	175.96	odd	30
875.2.bb.a.493.1		288	25.21	even	5
875.2.bb.a.607.1		288	35.12	even	12
875.2.bb.a.857.18		288	5.2	odd	4
875.2.bb.b.243.1		288	175.54	odd	30
875.2.bb.b.493.18		288	25.4	even	10
875.2.bb.b.607.18		288	35.33	even	12
875.2.bb.b.857.1		288	5.3	odd	4
875.2.bb.c.143.1		288	1.1	even	1	trivial
875.2.bb.c.257.1		288	175.47	even	60	inner
875.2.bb.c.507.1		288	25.22	odd	20	inner
875.2.bb.c.768.1		288	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(-0.127170 - 2.42654i) q^{2} +(1.78675 + 1.44688i) q^{3} +(-3.88289 + 0.408108i) q^{4} +(3.28370 - 4.51962i) q^{6} +(-1.54352 + 2.14884i) q^{7} +(0.723845 + 4.57018i) q^{8} +(0.475273 + 2.23598i) q^{9} +(-0.0163732 - 0.00348022i) q^{11} +(-7.52823 - 4.88889i) q^{12} +(1.39124 + 2.73047i) q^{13} +(5.41055 + 3.47216i) q^{14} +(3.35976 - 0.714139i) q^{16} +(6.59423 + 2.53129i) q^{17} +(5.36527 - 1.43762i) q^{18} +(0.331948 - 3.15828i) q^{19} +(-5.86701 + 1.60615i) q^{21} +(-0.00636273 + 0.0401727i) q^{22} +(5.46923 - 0.286630i) q^{23} +(-5.31918 + 9.21308i) q^{24} +(6.44868 - 3.72315i) q^{26} +(0.745322 - 1.46278i) q^{27} +(5.11637 - 8.97365i) q^{28} +(-0.0353871 - 0.0487062i) q^{29} +(3.66733 + 8.23697i) q^{31} +(0.235039 + 0.877177i) q^{32} +(-0.0242193 - 0.0299083i) q^{33} +(5.30369 - 16.3231i) q^{34} +(-2.75796 - 8.48811i) q^{36} +(-4.57608 + 7.04654i) q^{37} +(-7.70591 - 0.403850i) q^{38} +(-1.46486 + 6.89163i) q^{39} +(5.83738 + 1.89668i) q^{41} +(4.64350 + 14.0323i) q^{42} +(3.18681 + 3.18681i) q^{43} +(0.0649954 + 0.00683130i) q^{44} +(-1.39104 - 13.2349i) q^{46} +(-1.64959 - 4.29732i) q^{47} +(7.03633 + 3.58519i) q^{48} +(-2.23507 - 6.63359i) q^{49} +(8.11977 + 14.0639i) q^{51} +(-6.51638 - 10.0343i) q^{52} +(-2.73861 + 3.38191i) q^{53} +(-3.64427 - 1.62253i) q^{54} +(-10.9379 - 5.49875i) q^{56} +(5.16276 - 5.16276i) q^{57} +(-0.113687 + 0.0920622i) q^{58} +(1.67651 + 1.86195i) q^{59} +(-9.91649 - 8.92884i) q^{61} +(19.5210 - 9.94643i) q^{62} +(-5.53838 - 2.43001i) q^{63} +(8.63203 - 2.80472i) q^{64} +(-0.0694938 + 0.0625725i) q^{66} +(-0.113980 + 0.296929i) q^{67} +(-26.6377 - 7.13755i) q^{68} +(10.1869 + 7.40119i) q^{69} +(-6.35569 + 4.61768i) q^{71} +(-9.87482 + 3.79059i) q^{72} +(2.80391 - 1.82088i) q^{73} +(17.6807 + 10.2079i) q^{74} +12.3987i q^{76} +(0.0327508 - 0.0298116i) q^{77} +(16.9091 + 2.67814i) q^{78} +(2.17913 - 4.89441i) q^{79} +(9.71309 - 4.32455i) q^{81} +(3.86003 - 14.4058i) q^{82} +(-8.63403 + 1.36750i) q^{83} +(22.1255 - 8.63088i) q^{84} +(7.32766 - 8.13819i) q^{86} +(0.00724415 - 0.138227i) q^{87} +(0.00405361 - 0.0773474i) q^{88} +(5.60082 - 6.22034i) q^{89} +(-8.01478 - 1.22498i) q^{91} +(-21.1194 + 3.34499i) q^{92} +(-5.36531 + 20.0236i) q^{93} +(-10.2178 + 4.54928i) q^{94} +(-0.849216 + 1.90737i) q^{96} +(-6.79613 - 1.07640i) q^{97} +(-15.8124 + 6.26707i) q^{98} -0.0382642i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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