LMFDB - Embedded newform 875.2.bb.a.243.10

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			243.10
Character	$\chi$	$=$	875.243
Dual form			875.2.bb.a.857.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.263087 + 0.0137878i) q^{2} +(-1.61063 - 1.98896i) q^{3} +(-1.92002 - 0.201802i) q^{4} +(-0.396312 - 0.545476i) q^{6} +(-2.51572 + 0.819241i) q^{7} +(-1.02276 - 0.161989i) q^{8} +(-0.738101 + 3.47249i) q^{9} +(-3.43661 + 0.730475i) q^{11} +(2.69106 + 4.14386i) q^{12} +(3.27037 + 1.66634i) q^{13} +(-0.673149 + 0.180846i) q^{14} +(3.50997 + 0.746068i) q^{16} +(-2.11271 - 5.50381i) q^{17} +(-0.242063 + 0.903391i) q^{18} +(0.817063 + 7.77383i) q^{19} +(5.68132 + 3.68417i) q^{21} +(-0.914201 + 0.144795i) q^{22} +(0.334690 - 6.38626i) q^{23} +(1.32509 + 2.29513i) q^{24} +(0.837417 + 0.483483i) q^{26} +(1.25435 - 0.639125i) q^{27} +(4.99555 - 1.06528i) q^{28} +(-0.147381 + 0.202852i) q^{29} +(0.511405 - 1.14863i) q^{31} +(2.91359 + 0.780694i) q^{32} +(6.98798 + 5.65876i) q^{33} +(-0.479943 - 1.47711i) q^{34} +(2.11792 - 6.51830i) q^{36} +(4.12728 - 2.68029i) q^{37} +(0.107775 + 2.05646i) q^{38} +(-1.95307 - 9.18847i) q^{39} +(0.567075 - 0.184254i) q^{41} +(1.44389 + 1.04759i) q^{42} +(5.65218 + 5.65218i) q^{43} +(6.74578 - 0.709010i) q^{44} +(0.176105 - 1.67553i) q^{46} +(-0.980249 - 0.376282i) q^{47} +(-4.16936 - 8.18282i) q^{48} +(5.65769 - 4.12196i) q^{49} +(-7.54405 + 13.0667i) q^{51} +(-5.94290 - 3.85937i) q^{52} +(2.30142 - 1.86365i) q^{53} +(0.338816 - 0.150851i) q^{54} +(2.70568 - 0.430367i) q^{56} +(14.1458 - 14.1458i) q^{57} +(-0.0415708 + 0.0513357i) q^{58} +(-3.73669 + 4.15002i) q^{59} +(2.91370 - 2.62351i) q^{61} +(0.150381 - 0.295140i) q^{62} +(-0.987952 - 9.34049i) q^{63} +(-6.06975 - 1.97218i) q^{64} +(1.76043 + 1.58510i) q^{66} +(1.10691 - 0.424905i) q^{67} +(2.94577 + 10.9938i) q^{68} +(-13.2411 + 9.62020i) q^{69} +(7.13505 + 5.18392i) q^{71} +(1.31741 - 3.43196i) q^{72} +(-4.36627 + 6.72347i) q^{73} +(1.12279 - 0.648243i) q^{74} -15.0908i q^{76} +(8.04712 - 4.65309i) q^{77} +(-0.387139 - 2.44430i) q^{78} +(4.00368 + 8.99240i) q^{79} +(6.43796 + 2.86636i) q^{81} +(0.151731 - 0.0406561i) q^{82} +(-0.951116 + 6.00511i) q^{83} +(-10.1648 - 8.22017i) q^{84} +(1.40908 + 1.56495i) q^{86} +(0.640839 - 0.0335849i) q^{87} +(3.63316 - 0.190406i) q^{88} +(2.57386 + 2.85856i) q^{89} +(-9.59246 - 1.51281i) q^{91} +(-1.93137 + 12.1942i) q^{92} +(-3.10827 + 0.832857i) q^{93} +(-0.252703 - 0.112511i) q^{94} +(-3.13994 - 7.05242i) q^{96} +(1.59410 + 10.0647i) q^{97} +(1.54530 - 1.00643i) q^{98} -12.4728i 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 $

$2$	0.263087	+	0.0137878i	0.186031	+	0.00974946i	0.145124	−	0.989413i	$-0.453642\pi$
$2$	0.263087	+	0.0137878i	0.186031	+	0.00974946i	0.0409070	+	0.999163i	$0.486975\pi$
$3$	−1.61063	−	1.98896i	−0.929895	−	1.14833i	−0.988678	−	0.150054i	$-0.952055\pi$
$3$	−1.61063	−	1.98896i	−0.929895	−	1.14833i	0.0587824	−	0.998271i	$-0.481278\pi$
$4$	−1.92002	−	0.201802i	−0.960009	−	0.100901i
$5$		0			0
$5$		0			0
$6$	−0.396312	−	0.545476i	−0.161794	−	0.222690i
$7$	−2.51572	+	0.819241i	−0.950853	+	0.309644i
$7$	−2.51572	+	0.819241i	−0.950853	+	0.309644i
$8$	−1.02276	−	0.161989i	−0.361600	−	0.0572718i
$9$	−0.738101	+	3.47249i	−0.246034	+	1.15750i
$10$		0			0
$11$	−3.43661	+	0.730475i	−1.03618	+	0.220246i	−0.694441	−	0.719549i	$-0.744348\pi$
$11$	−3.43661	+	0.730475i	−1.03618	+	0.220246i	−0.341737	+	0.939796i	$0.611015\pi$
$12$	2.69106	+	4.14386i	0.776841	+	1.19623i
$13$	3.27037	+	1.66634i	0.907037	+	0.462159i	0.844300	−	0.535871i	$-0.180017\pi$
$13$	3.27037	+	1.66634i	0.907037	+	0.462159i	0.0627378	+	0.998030i	$0.480017\pi$
$14$	−0.673149	+	0.180846i	−0.179907	+	0.0483330i
$15$		0			0
$16$	3.50997	+	0.746068i	0.877493	+	0.186517i
$17$	−2.11271	−	5.50381i	−0.512408	−	1.33487i	−0.908970	−	0.416862i	$-0.863130\pi$
$17$	−2.11271	−	5.50381i	−0.512408	−	1.33487i	0.396561	−	0.918008i	$-0.370203\pi$
$18$	−0.242063	+	0.903391i	−0.0570548	+	0.212931i
$19$	0.817063	+	7.77383i	0.187447	+	1.78344i	0.534075	+	0.845437i	$0.320660\pi$
$19$	0.817063	+	7.77383i	0.187447	+	1.78344i	−0.346628	+	0.938003i	$0.612673\pi$
$20$		0			0
$21$	5.68132	+	3.68417i	1.23977	+	0.803951i
$22$	−0.914201	+	0.144795i	−0.194908	+	0.0308704i
$23$	0.334690	−	6.38626i	0.0697877	−	1.33163i	−0.709386	−	0.704820i	$-0.751028\pi$
$23$	0.334690	−	6.38626i	0.0697877	−	1.33163i	0.779174	−	0.626808i	$-0.215639\pi$
$24$	1.32509	+	2.29513i	0.270484	+	0.468491i
$25$		0			0
$26$	0.837417	+	0.483483i	0.164231	+	0.0948189i
$27$	1.25435	−	0.639125i	0.241400	−	0.123000i
$28$	4.99555	−	1.06528i	0.944071	−	0.201319i
$29$	−0.147381	+	0.202852i	−0.0273679	+	0.0376687i	−0.822482	−	0.568792i	$-0.807411\pi$
$29$	−0.147381	+	0.202852i	−0.0273679	+	0.0376687i	0.795114	+	0.606460i	$0.207411\pi$
$30$		0			0
$31$	0.511405	−	1.14863i	0.0918510	−	0.206301i	−0.861778	−	0.507286i	$-0.830649\pi$
$31$	0.511405	−	1.14863i	0.0918510	−	0.206301i	0.953629	+	0.300985i	$0.0973155\pi$
$32$	2.91359	+	0.780694i	0.515055	+	0.138009i
$33$	6.98798	+	5.65876i	1.21645	+	0.985063i
$34$	−0.479943	−	1.47711i	−0.0823095	−	0.253323i
$35$		0			0
$36$	2.11792	−	6.51830i	0.352987	−	1.08638i
$37$	4.12728	−	2.68029i	0.678520	−	0.440636i	−0.158828	−	0.987306i	$-0.550771\pi$
$37$	4.12728	−	2.68029i	0.678520	−	0.440636i	0.837348	+	0.546670i	$0.184105\pi$
$38$	0.107775	+	2.05646i	0.0174834	+	0.333602i
$39$	−1.95307	−	9.18847i	−0.312741	−	1.47133i
$40$		0			0
$41$	0.567075	−	0.184254i	0.0885622	−	0.0287756i	−0.264401	−	0.964413i	$-0.585174\pi$
$41$	0.567075	−	0.184254i	0.0885622	−	0.0287756i	0.352963	+	0.935637i	$0.385174\pi$
$42$	1.44389	+	1.04759i	0.222796	+	0.161647i
$43$	5.65218	+	5.65218i	0.861949	+	0.861949i	0.991564	−	0.129616i	$-0.0413743\pi$
$43$	5.65218	+	5.65218i	0.861949	+	0.861949i	−0.129616	+	0.991564i	$0.541374\pi$
$44$	6.74578	−	0.709010i	1.01696	−	0.106887i
$45$		0			0
$46$	0.176105	−	1.67553i	0.0259653	−	0.247043i
$47$	−0.980249	−	0.376282i	−0.142984	−	0.0548864i	0.285824	−	0.958282i	$-0.407733\pi$
$47$	−0.980249	−	0.376282i	−0.142984	−	0.0548864i	−0.428808	+	0.903396i	$0.641066\pi$
$48$	−4.16936	−	8.18282i	−0.601795	−	1.18109i
$49$	5.65769	−	4.12196i	0.808241	−	0.588852i
$50$		0			0
$51$	−7.54405	+	13.0667i	−1.05638	+	1.82970i
$52$	−5.94290	−	3.85937i	−0.824132	−	0.535198i
$53$	2.30142	−	1.86365i	0.316124	−	0.255992i	−0.458104	−	0.888898i	$-0.651471\pi$
$53$	2.30142	−	1.86365i	0.316124	−	0.255992i	0.774229	+	0.632906i	$0.218138\pi$
$54$	0.338816	−	0.150851i	0.0461071	−	0.0205282i
$55$		0			0
$56$	2.70568	−	0.430367i	0.361562	−	0.0575103i
$57$	14.1458	−	14.1458i	1.87366	−	1.87366i
$58$	−0.0415708	+	0.0513357i	−0.00545852	+	0.00674071i
$59$	−3.73669	+	4.15002i	−0.486476	+	0.540286i	−0.935543	−	0.353212i	$-0.885090\pi$
$59$	−3.73669	+	4.15002i	−0.486476	+	0.540286i	0.449068	+	0.893498i	$0.351756\pi$
$60$		0			0
$61$	2.91370	−	2.62351i	0.373062	−	0.335906i	−0.461179	−	0.887307i	$-0.652573\pi$
$61$	2.91370	−	2.62351i	0.373062	−	0.335906i	0.834240	+	0.551401i	$0.185907\pi$
$62$	0.150381	−	0.295140i	0.0190984	−	0.0374828i
$63$	−0.987952	−	9.34049i	−0.124470	−	1.17679i
$64$	−6.06975	−	1.97218i	−0.758719	−	0.246523i
$65$		0			0
$66$	1.76043	+	1.58510i	0.216694	+	0.195112i
$67$	1.10691	−	0.424905i	0.135231	−	0.0519104i	−0.289811	−	0.957084i	$-0.593593\pi$
$67$	1.10691	−	0.424905i	0.135231	−	0.0519104i	0.425042	+	0.905173i	$0.360259\pi$
$68$	2.94577	+	10.9938i	0.357227	+	1.33319i
$69$	−13.2411	+	9.62020i	−1.59404	+	1.15814i
$70$		0			0
$71$	7.13505	+	5.18392i	0.846775	+	0.615218i	0.924255	−	0.381776i	$-0.124687\pi$
$71$	7.13505	+	5.18392i	0.846775	+	0.615218i	−0.0774798	+	0.996994i	$0.524687\pi$
$72$	1.31741	−	3.43196i	0.155258	−	0.404460i
$73$	−4.36627	+	6.72347i	−0.511034	+	0.786923i	−0.996163	−	0.0875197i	$-0.972106\pi$
$73$	−4.36627	+	6.72347i	−0.511034	+	0.786923i	0.485129	+	0.874443i	$0.338773\pi$
$74$	1.12279	−	0.648243i	0.130522	−	0.0753567i
$75$		0			0
$76$		−	15.0908i		−	1.73103i
$77$	8.04712	−	4.65309i	0.917055	−	0.530268i
$78$	−0.387139	−	2.44430i	−0.0438348	−	0.276762i
$79$	4.00368	+	8.99240i	0.450449	+	1.01172i	0.985927	+	0.167176i	$0.0534647\pi$
$79$	4.00368	+	8.99240i	0.450449	+	1.01172i	−0.535478	+	0.844549i	$0.679869\pi$
$80$		0			0
$81$	6.43796	+	2.86636i	0.715329	+	0.318485i
$82$	0.151731	−	0.0406561i	0.0167558	−	0.00448972i
$83$	−0.951116	+	6.00511i	−0.104399	+	0.659146i	0.878881	+	0.477042i	$0.158291\pi$
$83$	−0.951116	+	6.00511i	−0.104399	+	0.659146i	−0.983279	+	0.182105i	$0.941709\pi$
$84$	−10.1648	−	8.22017i	−1.10907	−	0.896895i
$85$		0			0
$86$	1.40908	+	1.56495i	0.151945	+	0.168753i
$87$	0.640839	−	0.0335849i	0.0687051	−	0.00360068i
$88$	3.63316	−	0.190406i	0.387296	−	0.0202973i
$89$	2.57386	+	2.85856i	0.272829	+	0.303007i	0.863952	−	0.503574i	$-0.167982\pi$
$89$	2.57386	+	2.85856i	0.272829	+	0.303007i	−0.591123	+	0.806581i	$0.701315\pi$
$90$		0			0
$91$	−9.59246	−	1.51281i	−1.00556	−	0.158586i
$92$	−1.93137	+	12.1942i	−0.201360	+	1.27133i
$93$	−3.10827	+	0.832857i	−0.322312	+	0.0863633i
$94$	−0.252703	−	0.112511i	−0.0260643	−	0.0116046i
$95$		0			0
$96$	−3.13994	−	7.05242i	−0.320469	−	0.719784i
$97$	1.59410	+	10.0647i	0.161856	+	1.02192i	0.926179	+	0.377085i	$0.123073\pi$
$97$	1.59410	+	10.0647i	0.161856	+	1.02192i	−0.764323	+	0.644834i	$0.776927\pi$
$98$	1.54530	−	1.00643i	0.156099	−	0.101665i
$99$		−	12.4728i		−	1.25356i
$100$		0			0
$101$	9.38700	−	5.41959i	0.934041	−	0.539269i	0.0459539	−	0.998944i	$-0.485367\pi$
$101$	9.38700	−	5.41959i	0.934041	−	0.539269i	0.888087	+	0.459675i	$0.152034\pi$
$102$	−2.16490	+	3.33366i	−0.214357	+	0.330082i
$103$	1.76689	−	4.60289i	0.174096	−	0.453537i	−0.818572	−	0.574403i	$-0.805234\pi$
$103$	1.76689	−	4.60289i	0.174096	−	0.453537i	0.992669	+	0.120867i	$0.0385674\pi$
$104$	−3.07487	−	2.23403i	−0.301516	−	0.219064i
$105$		0			0
$106$	0.631170	−	0.458572i	0.0613046	−	0.0445404i
$107$	2.23275	+	8.33275i	0.215848	+	0.805557i	0.985866	+	0.167535i	$0.0535806\pi$
$107$	2.23275	+	8.33275i	0.215848	+	0.805557i	−0.770018	+	0.638022i	$0.779753\pi$
$108$	−2.53736	+	0.974000i	−0.244157	+	0.0937232i
$109$	6.47269	+	5.82804i	0.619972	+	0.558225i	0.918124	−	0.396293i	$-0.129704\pi$
$109$	6.47269	+	5.82804i	0.619972	+	0.558225i	−0.298152	+	0.954518i	$0.596370\pi$
$110$		0			0
$111$	−11.9785	−	3.89204i	−1.13695	−	0.369416i
$112$	−9.44131	+	0.998616i	−0.892120	+	0.0943604i
$113$	−3.59375	+	7.05314i	−0.338072	+	0.663504i	−0.995978	−	0.0895963i	$-0.971442\pi$
$113$	−3.59375	+	7.05314i	−0.338072	+	0.663504i	0.657906	+	0.753100i	$0.271442\pi$
$114$	3.91663	−	3.52655i	0.366826	−	0.330292i
$115$		0			0
$116$	0.323909	−	0.359738i	0.0300742	−	0.0334008i
$117$	−8.20020	+	10.1264i	−0.758109	+	0.936186i
$118$	−1.04030	+	1.04030i	−0.0957670	+	0.0957670i
$119$	9.82394	+	12.1152i	0.900559	+	1.11060i
$120$		0			0
$121$	1.22772	−	0.546618i	0.111611	−	0.0496925i
$122$	0.802731	−	0.650039i	0.0726759	−	0.0588517i
$123$	−1.27982	−	0.831124i	−0.115397	−	0.0749399i
$124$	−1.21370	+	2.10220i	−0.108994	+	0.188783i
$125$		0			0
$126$	−0.131133	−	2.47099i	−0.0116822	−	0.220133i
$127$	−4.46370	−	8.76051i	−0.396090	−	0.777370i	0.603714	−	0.797201i	$-0.293687\pi$
$127$	−4.46370	−	8.76051i	−0.396090	−	0.777370i	−0.999803	+	0.0198315i	$0.993687\pi$
$128$	−7.20173	−	2.76449i	−0.636549	−	0.244348i
$129$	2.13840	−	20.3455i	0.188275	−	1.79132i
$130$		0			0
$131$	−13.5234	+	1.42136i	−1.18154	+	0.124185i	−0.674858	−	0.737947i	$-0.735795\pi$
$131$	−13.5234	+	1.42136i	−1.18154	+	0.124185i	−0.506683	+	0.862132i	$0.669129\pi$
$132$	−12.2751	−	12.2751i	−1.06841	−	1.06841i
$133$	−8.42415	−	18.8874i	−0.730466	−	1.63775i
$134$	0.297074	−	0.0965251i	0.0256633	−	0.00833850i
$135$		0			0
$136$	1.26924	+	5.97131i	0.108837	+	0.512036i
$137$	0.319201	+	6.09072i	0.0272712	+	0.520365i	0.977776	+	0.209654i	$0.0672338\pi$
$137$	0.319201	+	6.09072i	0.0272712	+	0.520365i	−0.950504	+	0.310711i	$0.899433\pi$
$138$	−3.61620	+	2.34839i	−0.307831	+	0.199908i
$139$	−0.132140	+	0.406687i	−0.0112080	+	0.0344947i	−0.956504	−	0.291719i	$-0.905773\pi$
$139$	−0.132140	+	0.406687i	−0.0112080	+	0.0344947i	0.945296	+	0.326214i	$0.105773\pi$
$140$		0			0
$141$	0.830405	+	2.55572i	0.0699327	+	0.215231i
$142$	1.80567	+	1.46220i	0.151528	+	0.122705i
$143$	−12.4562	−	3.33763i	−1.04164	−	0.279107i
$144$	−5.18142	+	11.6377i	−0.431785	+	0.969806i
$145$		0			0
$146$	−1.24141	+	1.70866i	−0.102740	+	0.141410i
$147$	−17.3108	−	4.61396i	−1.42777	−	0.380553i
$148$	−8.46534	+	4.31331i	−0.695847	+	0.354552i
$149$	2.78363	+	1.60713i	0.228044	+	0.131661i	0.609669	−	0.792656i	$-0.291302\pi$
$149$	2.78363	+	1.60713i	0.228044	+	0.131661i	−0.381626	+	0.924317i	$0.624636\pi$
$150$		0			0
$151$	2.73858	+	4.74335i	0.222862	+	0.386009i	0.955676	−	0.294421i	$-0.0951267\pi$
$151$	2.73858	+	4.74335i	0.222862	+	0.386009i	−0.732814	+	0.680429i	$0.761793\pi$
$152$	0.423618	−	8.08312i	0.0343600	−	0.655628i
$153$	20.6713	−	3.27401i	1.67118	−	0.264688i
$154$	2.18125	−	1.11322i	0.175770	−	0.0897054i
$155$		0			0
$156$	1.89568	+	18.0362i	0.151776	+	1.44405i
$157$	−5.24342	+	19.5687i	−0.418471	+	1.56175i	0.359310	+	0.933218i	$0.383012\pi$
$157$	−5.24342	+	19.5687i	−0.418471	+	1.56175i	−0.777781	+	0.628535i	$0.783655\pi$
$158$	0.929331	+	2.42099i	0.0739336	+	0.192604i
$159$	−7.41345	−	1.57578i	−0.587925	−	0.124967i
$160$		0			0
$161$	4.38990	+	16.3402i	0.345973	+	1.28779i
$162$	1.65422	+	0.842869i	0.129968	+	0.0662221i
$163$	4.74149	+	7.30125i	0.371382	+	0.571878i	0.974112	−	0.226067i	$-0.0725870\pi$
$163$	4.74149	+	7.30125i	0.371382	+	0.571878i	−0.602730	+	0.797945i	$0.705920\pi$
$164$	−1.12598	+	0.239334i	−0.0879241	+	0.0186888i
$165$		0			0
$166$	−0.333024	+	1.56675i	−0.0258477	+	0.121604i
$167$	−19.3182	−	3.05970i	−1.49489	−	0.236767i	−0.645182	−	0.764029i	$-0.723219\pi$
$167$	−19.3182	−	3.05970i	−1.49489	−	0.236767i	−0.849703	+	0.527262i	$0.823219\pi$
$168$	−5.21383	−	4.68833i	−0.402256	−	0.361713i
$169$	0.277432	+	0.381852i	0.0213409	+	0.0293732i
$170$		0			0
$171$	−27.5976	−	2.90063i	−2.11044	−	0.221817i
$172$	−9.71166	−	11.9929i	−0.740507	−	0.914451i
$173$	−8.38638	−	0.439511i	−0.637604	−	0.0334154i	−0.269205	−	0.963083i	$-0.586761\pi$
$173$	−8.38638	−	0.439511i	−0.637604	−	0.0334154i	−0.368400	+	0.929668i	$0.620094\pi$
$174$	0.169060			0.0128164
$175$		0			0
$176$	−12.6074			−0.950319
$177$	14.2726	+	0.747996i	1.07280	+	0.0562229i
$178$	0.637737	+	0.787540i	0.0478004	+	0.0590286i
$179$	15.2840	+	1.60642i	1.14238	+	0.120069i	0.656761	−	0.754099i	$-0.271926\pi$
$179$	15.2840	+	1.60642i	1.14238	+	0.120069i	0.485623	+	0.874168i	$0.338593\pi$
$180$		0			0
$181$	−4.54675	−	6.25807i	−0.337957	−	0.465159i	0.605886	−	0.795551i	$-0.292819\pi$
$181$	−4.54675	−	6.25807i	−0.337957	−	0.465159i	−0.943843	+	0.330393i	$0.892819\pi$
$182$	−2.50280	−	0.530261i	−0.185520	−	0.0393056i
$183$	−9.91094	−	1.56974i	−0.732638	−	0.116038i
$184$	−1.37681	+	6.47740i	−0.101500	+	0.477520i
$185$		0			0
$186$	−0.829229	+	0.176258i	−0.0608020	+	0.0129239i
$187$	11.2810	+	17.3712i	0.824947	+	1.27031i
$188$	1.80616	+	0.920285i	0.131728	+	0.0671187i
$189$	−2.63200	+	2.63548i	−0.191450	+	0.191703i
$190$		0			0
$191$	6.76057	+	1.43700i	0.489178	+	0.103978i	0.445896	−	0.895085i	$-0.352885\pi$
$191$	6.76057	+	1.43700i	0.489178	+	0.103978i	0.0432821	+	0.999063i	$0.486219\pi$
$192$	5.85351	+	15.2489i	0.422441	+	1.10050i
$193$	2.55619	−	9.53984i	0.183999	−	0.686693i	−0.810844	−	0.585262i	$-0.800991\pi$
$193$	2.55619	−	9.53984i	0.183999	−	0.686693i	0.994843	−	0.101430i	$-0.0323419\pi$
$194$	0.280616	+	2.66988i	0.0201470	+	0.191686i
$195$		0			0
$196$	−11.6947	+	6.77251i	−0.835335	+	0.483751i
$197$	5.85802	−	0.927819i	0.417367	−	0.0661044i	0.0557804	−	0.998443i	$-0.482235\pi$
$197$	5.85802	−	0.927819i	0.417367	−	0.0661044i	0.361586	+	0.932339i	$0.382235\pi$
$198$	0.171972	−	3.28143i	0.0122215	−	0.233201i
$199$	−0.710570	−	1.23074i	−0.0503709	−	0.0872450i	0.839741	−	0.542988i	$-0.182707\pi$
$199$	−0.710570	−	1.23074i	−0.0503709	−	0.0872450i	−0.890112	+	0.455743i	$0.849374\pi$
$200$		0			0
$201$	−2.62794	−	1.51724i	−0.185361	−	0.107018i
$202$	2.54432	−	1.29640i	0.179018	−	0.0912142i
$203$	0.204584	−	0.631059i	0.0143589	−	0.0442916i
$204$	17.1216	−	23.5659i	1.19875	−	1.64994i
$205$		0			0
$206$	0.528309	−	1.18660i	0.0368090	−	0.0826744i
$207$	21.9292	+	5.87591i	1.52418	+	0.408404i
$208$	10.2357	+	8.28871i	0.709719	+	0.574719i
$209$	−8.48652	−	26.1188i	−0.587025	−	1.80668i
$210$		0			0
$211$	4.15174	−	12.7778i	0.285818	−	0.879657i	−0.700335	−	0.713815i	$-0.746966\pi$
$211$	4.15174	−	12.7778i	0.285818	−	0.879657i	0.986152	−	0.165842i	$-0.0530341\pi$
$212$	−4.79486	+	3.11382i	−0.329312	+	0.213858i
$213$	−1.18131	−	22.5407i	−0.0809418	−	1.54446i
$214$	0.472518	+	2.22302i	0.0323007	+	0.151963i
$215$		0			0
$216$	−1.38643	+	0.450479i	−0.0943348	+	0.0306512i
$217$	−0.345543	+	3.30861i	−0.0234570	+	0.224603i
$218$	1.62253	+	1.62253i	0.109891	+	0.109891i
$219$	20.4051	−	2.14467i	1.37885	−	0.144923i
$220$		0			0
$221$	2.26184	−	21.5200i	0.152148	−	1.44759i
$222$	−3.09772	−	1.18910i	−0.207905	−	0.0798074i
$223$	9.41051	+	18.4692i	0.630175	+	1.23679i	0.956556	+	0.291549i	$0.0941707\pi$
$223$	9.41051	+	18.4692i	0.630175	+	1.23679i	−0.326381	+	0.945238i	$0.605829\pi$
$224$	−7.96936	+	0.422925i	−0.532475	+	0.0282579i
$225$		0			0
$226$	−1.04272	+	1.80604i	−0.0693606	+	0.120136i
$227$	−12.3279	−	8.00585i	−0.818233	−	0.531367i	0.0663243	−	0.997798i	$-0.478873\pi$
$227$	−12.3279	−	8.00585i	−0.818233	−	0.531367i	−0.884557	+	0.466431i	$0.845539\pi$
$228$	−30.0149	+	24.3056i	−1.98779	+	1.60968i
$229$	18.2779	−	8.13786i	1.20784	−	0.537765i	0.298736	−	0.954336i	$-0.403435\pi$
$229$	18.2779	−	8.13786i	1.20784	−	0.537765i	0.909103	+	0.416571i	$0.136768\pi$
$230$		0			0
$231$	−22.2157	−	8.51100i	−1.46169	−	0.559983i
$232$	0.183595	−	0.183595i	0.0120536	−	0.0120536i
$233$	4.30031	−	5.31044i	0.281723	−	0.347899i	−0.616567	−	0.787303i	$-0.711477\pi$
$233$	4.30031	−	5.31044i	0.281723	−	0.347899i	0.898290	+	0.439404i	$0.144810\pi$
$234$	−2.29699	+	2.55106i	−0.150159	+	0.166768i
$235$		0			0
$236$	8.01200	−	7.21404i	0.521537	−	0.469594i
$237$	11.4371	−	22.4465i	0.742918	−	1.45806i
$238$	2.41751	+	3.32281i	0.156704	+	0.215386i
$239$	−4.07114	−	1.32279i	−0.263340	−	0.0855644i	0.174371	−	0.984680i	$-0.444211\pi$
$239$	−4.07114	−	1.32279i	−0.263340	−	0.0855644i	−0.437711	+	0.899116i	$0.644211\pi$
$240$		0			0
$241$	−2.71942	−	2.44858i	−0.175173	−	0.157727i	0.576880	−	0.816829i	$-0.304270\pi$
$241$	−2.71942	−	2.44858i	−0.175173	−	0.157727i	−0.752054	+	0.659102i	$0.770937\pi$
$242$	0.330535	−	0.126880i	0.0212476	−	0.00815619i
$243$	−5.76116	−	21.5009i	−0.369579	−	1.37929i
$244$	−6.12380	+	4.44920i	−0.392036	+	0.284831i
$245$		0			0
$246$	−0.325245	−	0.236304i	−0.0207368	−	0.0150662i
$247$	−10.2817	+	26.7848i	−0.654211	+	1.70428i
$248$	−0.709111	+	1.09193i	−0.0450286	+	0.0693379i
$249$	13.4758	−	7.78025i	0.853994	−	0.493054i
$250$		0			0
$251$			23.2521i			1.46766i	0.679334	+	0.733829i	$0.262269\pi$
$251$			23.2521i			1.46766i	−0.679334	+	0.733829i	$0.737731\pi$
$252$	0.0119562	+	18.1333i	0.000753172	+	1.14229i
$253$	3.51481	+	22.1916i	0.220974	+	1.39517i
$254$	−1.05356	−	2.36632i	−0.0661059	−	0.148476i
$255$		0			0
$256$	9.80414	+	4.36508i	0.612759	+	0.272818i
$257$	0.313748	−	0.0840686i	0.0195711	−	0.00524406i	−0.249020	−	0.968498i	$-0.580109\pi$
$257$	0.313748	−	0.0840686i	0.0195711	−	0.00524406i	0.268591	+	0.963254i	$0.413442\pi$
$258$	0.843105	−	5.32315i	0.0524894	−	0.331405i
$259$	−8.18727	+	10.1241i	−0.508732	+	0.629080i
$260$		0			0
$261$	−0.595620	−	0.661503i	−0.0368679	−	0.0409460i
$262$	−3.57742	+	0.187485i	−0.221014	+	0.0115828i
$263$	−6.74598	+	0.353542i	−0.415975	+	0.0218003i	−0.259176	−	0.965830i	$-0.583451\pi$
$263$	−6.74598	+	0.353542i	−0.415975	+	0.0218003i	−0.156799	+	0.987631i	$0.550118\pi$
$264$	−6.23037	−	6.91953i	−0.383453	−	0.425867i
$265$		0			0
$266$	−1.95587	−	5.08519i	−0.119922	−	0.311793i
$267$	1.54003	−	9.72338i	0.0942484	−	0.595061i
$268$	−2.21104	+	0.592447i	−0.135061	+	0.0361895i
$269$	0.532457	+	0.237065i	0.0324645	+	0.0144541i	0.422905	−	0.906174i	$-0.361011\pi$
$269$	0.532457	+	0.237065i	0.0324645	+	0.0144541i	−0.390440	+	0.920628i	$0.627677\pi$
$270$		0			0
$271$	7.55674	+	16.9727i	0.459039	+	1.03102i	0.983718	+	0.179719i	$0.0575187\pi$
$271$	7.55674	+	16.9727i	0.459039	+	1.03102i	−0.524679	+	0.851300i	$0.675815\pi$
$272$	−3.30935	−	20.8944i	−0.200659	−	1.26691i
$273$	12.4409	+	21.5156i	0.752960	+	1.30218i
$274$			1.60679i			0.0970698i
$275$		0			0
$276$	27.3645	−	15.7989i	1.64715	−	0.950981i
$277$	0.818099	−	1.25976i	0.0491548	−	0.0756917i	−0.813239	−	0.581930i	$-0.802298\pi$
$277$	0.818099	−	1.25976i	0.0491548	−	0.0756917i	0.862394	+	0.506238i	$0.168964\pi$
$278$	−0.0403718	+	0.105172i	−0.00242134	+	0.00630781i
$279$	3.61115	+	2.62366i	0.216194	+	0.157074i
$280$		0			0
$281$	24.2076	−	17.5878i	1.44410	−	1.04920i	0.456936	−	0.889499i	$-0.348947\pi$
$281$	24.2076	−	17.5878i	1.44410	−	1.04920i	0.987165	−	0.159702i	$-0.0510533\pi$
$282$	0.183231	+	0.683827i	0.0109112	+	0.0407213i
$283$	8.38668	−	3.21935i	0.498537	−	0.191370i	−0.0960894	−	0.995373i	$-0.530633\pi$
$283$	8.38668	−	3.21935i	0.498537	−	0.191370i	0.594626	+	0.804002i	$0.297300\pi$
$284$	−12.6533	−	11.3931i	−0.750836	−	0.676056i
$285$		0			0
$286$	−3.23105	−	1.04983i	−0.191056	−	0.0620779i
$287$	−1.27565	+	0.928102i	−0.0752994	+	0.0547841i
$288$	−4.86148	+	9.54119i	−0.286465	+	0.562220i
$289$	−13.1949	+	11.8807i	−0.776170	+	0.698867i
$290$		0			0
$291$	17.4508	−	19.3811i	1.02299	−	1.13614i
$292$	9.74014	−	12.0281i	0.569998	−	0.703889i
$293$	19.5938	−	19.5938i	1.14468	−	1.14468i	0.157096	−	0.987583i	$-0.449787\pi$
$293$	19.5938	−	19.5938i	1.14468	−	1.14468i	0.987583	−	0.157096i	$-0.0502132\pi$
$294$	−4.49064	−	1.45255i	−0.261900	−	0.0847146i
$295$		0			0
$296$	−4.65539	+	2.07271i	−0.270589	+	0.120474i
$297$	−3.84386	+	3.11270i	−0.223043	+	0.180617i
$298$	0.710179	+	0.461195i	0.0411395	+	0.0267163i
$299$	11.7362	−	20.3277i	0.678723	−	1.17558i
$300$		0			0
$301$	−18.8498	−	9.58879i	−1.08648	−	0.552689i
$302$	0.655084	+	1.28567i	0.0376959	+	0.0739823i
$303$	−25.8983	−	9.94141i	−1.48782	−	0.571119i
$304$	−2.93194	+	27.8955i	−0.168158	+	1.59992i
$305$		0			0
$306$	5.48350	−	0.576339i	0.313471	−	0.0329471i
$307$	4.81162	+	4.81162i	0.274613	+	0.274613i	0.830954	−	0.556341i	$-0.187795\pi$
$307$	4.81162	+	4.81162i	0.274613	+	0.274613i	−0.556341	+	0.830954i	$0.687795\pi$
$308$	−16.3896	+	7.31009i	−0.933886	+	0.416531i
$309$	−12.0008	+	3.89928i	−0.682699	+	0.221822i
$310$		0			0
$311$	6.33562	+	29.8067i	0.359260	+	1.69018i	0.672166	+	0.740401i	$0.265364\pi$
$311$	6.33562	+	29.8067i	0.359260	+	1.69018i	−0.312906	+	0.949784i	$0.601303\pi$
$312$	0.509088	+	9.71397i	0.0288214	+	0.549946i
$313$	−10.4215	+	6.76777i	−0.589055	+	0.382537i	−0.804477	−	0.593984i	$-0.797554\pi$
$313$	−10.4215	+	6.76777i	−0.589055	+	0.382537i	0.215421	+	0.976521i	$0.430888\pi$
$314$	−1.64929	+	5.07598i	−0.0930747	+	0.286454i
$315$		0			0
$316$	−5.87245	−	18.0735i	−0.330351	−	1.01672i
$317$	2.13910	+	1.73221i	0.120144	+	0.0972906i	0.687509	−	0.726175i	$-0.258704\pi$
$317$	2.13910	+	1.73221i	0.120144	+	0.0972906i	−0.567366	+	0.823466i	$0.692037\pi$
$318$	−1.92866	−	0.516782i	−0.108154	−	0.0289797i
$319$	0.358312	−	0.804782i	0.0200616	−	0.0450591i
$320$		0			0
$321$	12.9773	−	17.8618i	0.724325	−	0.996948i
$322$	0.929631	+	4.35944i	0.0518063	+	0.242942i
$323$	41.0595	−	20.9209i	2.28461	−	1.16407i
$324$	−11.7826	−	6.80267i	−0.654587	−	0.377926i
$325$		0			0
$326$	1.14676	+	1.98624i	0.0635130	+	0.110008i
$327$	1.16663	−	22.2607i	0.0645150	−	1.23102i
$328$	−0.609829	+	0.0965874i	−0.0336722	+	0.00533315i
$329$	2.77430	+	0.143560i	0.152952	+	0.00791475i
$330$		0			0
$331$	−2.12996	−	20.2652i	−0.117073	−	1.11388i	−0.882486	−	0.470339i	$-0.844132\pi$
$331$	−2.12996	−	20.2652i	−0.117073	−	1.11388i	0.765413	−	0.643540i	$-0.222535\pi$
$332$	3.03800	−	11.3380i	0.166732	−	0.622253i
$333$	6.26092	+	16.3103i	0.343096	+	0.893796i
$334$	−5.04018	−	1.07132i	−0.275786	−	0.0586202i
$335$		0			0
$336$	17.1926	+	17.1700i	0.937935	+	0.936699i
$337$	12.2954	+	6.26481i	0.669772	+	0.341266i	0.755590	−	0.655045i	$-0.227350\pi$
$337$	12.2954	+	6.26481i	0.669772	+	0.341266i	−0.0858177	+	0.996311i	$0.527350\pi$
$338$	0.0677239	+	0.104286i	0.00368369	+	0.00567239i
$339$	19.8166	−	4.21215i	1.07629	−	0.228772i
$340$		0			0
$341$	−0.918453	+	4.32098i	−0.0497370	+	0.233994i
$342$	−7.22059	−	1.14363i	−0.390445	−	0.0618404i
$343$	−10.8563	+	15.0047i	−0.586184	+	0.810178i
$344$	−4.86523	−	6.69641i	−0.262315	−	0.361046i
$345$		0			0
$346$	−2.20029	−	0.231260i	−0.118288	−	0.0124326i
$347$	−1.58176	−	1.95331i	−0.0849134	−	0.104859i	0.732919	−	0.680316i	$-0.238158\pi$
$347$	−1.58176	−	1.95331i	−0.0849134	−	0.104859i	−0.817832	+	0.575457i	$0.804824\pi$
$348$	−1.23720	−	0.0648389i	−0.0663209	−	0.00347573i
$349$	−27.7478			−1.48531			−0.742654	−	0.669676i	$-0.766433\pi$
$349$	−27.7478			−1.48531			−0.742654	+	0.669676i	$0.766433\pi$
$350$		0			0
$351$	5.16719			0.275804
$352$	−10.5832	−	0.554640i	−0.564085	−	0.0295624i
$353$	15.3616	+	18.9700i	0.817614	+	1.00967i	0.999652	+	0.0263777i	$0.00839724\pi$
$353$	15.3616	+	18.9700i	0.817614	+	1.00967i	−0.182038	+	0.983291i	$0.558269\pi$
$354$	3.74463	+	0.393577i	0.199025	+	0.0209184i
$355$		0			0
$356$	−4.36500	−	6.00791i	−0.231345	−	0.318418i
$357$	8.27395	−	39.0525i	0.437904	−	2.06688i
$358$	3.99889	+	0.633362i	0.211348	+	0.0334742i
$359$	7.52675	−	35.4106i	0.397247	−	1.86890i	−0.0904726	−	0.995899i	$-0.528838\pi$
$359$	7.52675	−	35.4106i	0.397247	−	1.86890i	0.487719	−	0.873000i	$-0.337829\pi$
$360$		0			0
$361$	−41.1801	+	8.75310i	−2.16737	+	0.460690i
$362$	−1.10991	−	1.70911i	−0.0583355	−	0.0898287i
$363$	−3.06460	−	1.56149i	−0.160850	−	0.0819571i
$364$	18.1124	+	4.84041i	0.949349	+	0.253707i
$365$		0			0
$366$	−2.58580	−	0.549628i	−0.135162	−	0.0287295i
$367$	4.23406	+	11.0301i	0.221016	+	0.575766i	0.998593	−	0.0530209i	$-0.0168850\pi$
$367$	4.23406	+	11.0301i	0.221016	+	0.575766i	−0.777577	+	0.628787i	$0.783552\pi$
$368$	5.93934	−	22.1659i	0.309609	−	1.15548i
$369$	0.221261	+	2.10516i	0.0115184	+	0.109590i
$370$		0			0
$371$	−4.26294	+	6.57384i	−0.221321	+	0.341297i
$372$	6.13600	−	0.971847i	0.318137	−	0.0503879i
$373$	−1.03759	+	19.7985i	−0.0537246	+	1.02513i	0.830191	+	0.557479i	$0.188231\pi$
$373$	−1.03759	+	19.7985i	−0.0537246	+	1.02513i	−0.883916	+	0.467647i	$0.845102\pi$
$374$	2.72837	+	4.72568i	0.141081	+	0.244359i
$375$		0			0
$376$	0.941605	+	0.543636i	0.0485596	+	0.0280359i
$377$	−0.820009	+	0.417815i	−0.0422326	+	0.0215186i
$378$	−0.728784	+	0.657070i	−0.0374846	+	0.0337961i
$379$	8.72393	−	12.0075i	0.448118	−	0.616782i	−0.523874	−	0.851796i	$-0.675514\pi$
$379$	8.72393	−	12.0075i	0.448118	−	0.616782i	0.971992	+	0.235014i	$0.0755136\pi$
$380$		0			0
$381$	−10.2349	+	22.9880i	−0.524351	+	1.17771i
$382$	1.75881	+	0.471271i	0.0899884	+	0.0241123i
$383$	−22.0440	−	17.8508i	−1.12639	−	0.912135i	−0.129553	−	0.991572i	$-0.541354\pi$
$383$	−22.0440	−	17.8508i	−1.12639	−	0.912135i	−0.996840	+	0.0794371i	$0.974688\pi$
$384$	6.10085	+	18.7765i	0.311333	+	0.958184i
$385$		0			0
$386$	0.804035	−	2.47457i	0.0409243	−	0.125952i
$387$	−23.7990	+	15.4553i	−1.20977	+	0.785635i
$388$	−1.02961	−	19.6462i	−0.0522706	−	0.997383i
$389$	4.29281	+	20.1961i	0.217654	+	1.02398i	0.942276	+	0.334836i	$0.108681\pi$
$389$	4.29281	+	20.1961i	0.217654	+	1.02398i	−0.724622	+	0.689146i	$0.757986\pi$
$390$		0			0
$391$	−35.8559	+	11.6503i	−1.81331	+	0.589180i
$392$	−6.45417	+	3.29929i	−0.325985	+	0.166639i
$393$	24.6081	+	24.6081i	1.24131	+	1.24131i
$394$	1.55396	−	0.163328i	0.0782875	−	0.00822835i
$395$		0			0
$396$	−2.51703	+	23.9480i	−0.126486	+	1.20343i
$397$	0.983037	+	0.377352i	0.0493372	+	0.0189388i	0.382911	−	0.923785i	$-0.374921\pi$
$397$	0.983037	+	0.377352i	0.0493372	+	0.0189388i	−0.333574	+	0.942724i	$0.608255\pi$
$398$	−0.169973	−	0.333590i	−0.00851996	−	0.0167214i
$399$	−23.9981	+	47.1758i	−1.20141	+	2.36175i
$400$		0			0
$401$	0.184864	−	0.320194i	0.00923166	−	0.0159897i	−0.861373	−	0.507974i	$-0.830395\pi$
$401$	0.184864	−	0.320194i	0.00923166	−	0.0159897i	0.870604	+	0.491984i	$0.163728\pi$
$402$	−0.670459	−	0.435401i	−0.0334395	−	0.0217158i
$403$	3.58649	−	2.90429i	0.178656	−	0.144673i
$404$	−19.1169	+	8.51139i	−0.951101	+	0.423458i
$405$		0			0
$406$	0.0625242	−	0.163203i	0.00310303	−	0.00809962i
$407$	−12.2260	+	12.2260i	−0.606019	+	0.606019i
$408$	9.83241	−	12.1420i	0.486777	−	0.601119i
$409$	−19.6346	+	21.8064i	−0.970868	+	1.07826i	0.0260387	+	0.999661i	$0.491711\pi$
$409$	−19.6346	+	21.8064i	−0.970868	+	1.07826i	−0.996906	+	0.0785970i	$0.974956\pi$
$410$		0			0
$411$	11.6001	−	10.4447i	0.572189	−	0.515201i
$412$	−4.32133	+	8.48108i	−0.212897	+	0.417833i
$413$	6.00060	−	13.5015i	0.295270	−	0.664367i
$414$	5.68828	+	1.84823i	0.279564	+	0.0908357i
$415$		0			0
$416$	8.22762	+	7.40818i	0.403392	+	0.363216i
$417$	1.02171	−	0.392198i	0.0500334	−	0.0192060i
$418$	−1.87257	−	6.98854i	−0.0915906	−	0.341821i
$419$	6.95129	−	5.05041i	0.339593	−	0.246729i	−0.404897	−	0.914362i	$-0.632693\pi$
$419$	6.95129	−	5.05041i	0.339593	−	0.246729i	0.744490	+	0.667634i	$0.232693\pi$
$420$		0			0
$421$	25.8891	+	18.8095i	1.26176	+	0.916720i	0.998843	−	0.0480998i	$-0.0153165\pi$
$421$	25.8891	+	18.8095i	1.26176	+	0.916720i	0.262914	+	0.964819i	$0.415317\pi$
$422$	1.26845	−	3.30442i	0.0617471	−	0.160857i
$423$	2.03016	−	3.12617i	0.0987097	−	0.152000i
$424$	−2.65569	+	1.53326i	−0.128972	+	0.0744619i
$425$		0			0
$426$		−	5.94645i		−	0.288107i
$427$	−5.18077	+	8.98704i	−0.250715	+	0.434914i
$428$	−2.60536	−	16.4496i	−0.125935	−	0.795122i
$429$	13.4239	+	30.1506i	0.648112	+	1.45568i
$430$		0			0
$431$	28.5735	+	12.7218i	1.37634	+	0.612785i	0.955673	−	0.294430i	$-0.0951299\pi$
$431$	28.5735	+	12.7218i	1.37634	+	0.612785i	0.420666	+	0.907216i	$0.361797\pi$
$432$	4.87957	−	1.30748i	0.234769	−	0.0629060i
$433$	−0.266365	+	1.68176i	−0.0128007	+	0.0808204i	−0.993262	−	0.115893i	$-0.963027\pi$
$433$	−0.266365	+	1.68176i	−0.0128007	+	0.0808204i	0.980461	+	0.196714i	$0.0630269\pi$
$434$	−0.136526	+	0.865688i	−0.00655348	+	0.0415543i
$435$		0			0
$436$	−11.2516	−	12.4962i	−0.538853	−	0.598457i
$437$	49.9192	−	2.61616i	2.38796	−	0.125148i
$438$	5.39790	−	0.282892i	0.257922	−	0.0135171i
$439$	−19.8967	−	22.0975i	−0.949616	−	1.05466i	−0.998439	−	0.0558477i	$-0.982214\pi$
$439$	−19.8967	−	22.0975i	−0.949616	−	1.05466i	0.0488236	−	0.998807i	$-0.484453\pi$
$440$		0			0
$441$	10.1375	+	22.6887i	0.482739	+	1.08041i
$442$	0.891775	−	5.63045i	0.0424174	−	0.267813i
$443$	−24.2744	+	6.50431i	−1.15331	+	0.309029i	−0.784292	−	0.620392i	$-0.786974\pi$
$443$	−24.2744	+	6.50431i	−1.15331	+	0.309029i	−0.369021	+	0.929421i	$0.620307\pi$
$444$	22.2135	+	9.89008i	1.05421	+	0.469362i
$445$		0			0
$446$	2.22114	+	4.98876i	0.105174	+	0.236224i
$447$	−1.28687	−	8.12500i	−0.0608671	−	0.384299i
$448$	16.8855	−	0.0111335i	0.797764	−	0.000526008i
$449$			19.5516i			0.922696i	0.887219	+	0.461348i	$0.152634\pi$
$449$			19.5516i			0.922696i	−0.887219	+	0.461348i	$0.847366\pi$
$450$		0			0
$451$	−1.81423	+	1.04744i	−0.0854285	+	0.0493222i
$452$	8.32341	−	12.8169i	0.391500	−	0.602858i
$453$	5.02351	−	13.0867i	0.236025	−	0.614866i
$454$	−3.13294	−	2.27621i	−0.147036	−	0.106828i
$455$		0			0
$456$	−16.7593	+	12.1763i	−0.784825	+	0.570209i
$457$	−1.63299	−	6.09440i	−0.0763880	−	0.285084i	0.917156	−	0.398527i	$-0.130479\pi$
$457$	−1.63299	−	6.09440i	−0.0763880	−	0.285084i	−0.993544	+	0.113443i	$0.963812\pi$
$458$	4.92089	−	1.88895i	0.229938	−	0.0882650i
$459$	−6.16771	−	5.55343i	−0.287884	−	0.259212i
$460$		0			0
$461$	5.06458	+	1.64558i	0.235881	+	0.0766424i	0.424572	−	0.905394i	$-0.360425\pi$
$461$	5.06458	+	1.64558i	0.235881	+	0.0766424i	−0.188691	+	0.982036i	$0.560425\pi$
$462$	−5.72732	−	2.54544i	−0.266459	−	0.118425i
$463$	−10.0937	+	19.8100i	−0.469094	+	0.920649i	0.528338	+	0.849034i	$0.322815\pi$
$463$	−10.0937	+	19.8100i	−0.469094	+	0.920649i	−0.997432	+	0.0716148i	$0.977185\pi$
$464$	−0.668643	+	0.602049i	−0.0310410	+	0.0279494i
$465$		0			0
$466$	1.20458	−	1.33782i	0.0558009	−	0.0619732i
$467$	4.68313	−	5.78319i	0.216709	−	0.267614i	−0.657185	−	0.753729i	$-0.728253\pi$
$467$	4.68313	−	5.78319i	0.216709	−	0.267614i	0.873895	+	0.486115i	$0.161586\pi$
$468$	17.7881	−	17.7881i	0.822254	−	0.822254i
$469$	−2.43659	+	1.97577i	−0.112511	+	0.0912326i
$470$		0			0
$471$	47.3665	−	21.0889i	2.18253	−	0.971727i
$472$	4.49400	−	3.63917i	0.206853	−	0.167506i
$473$	−23.5531	−	15.2956i	−1.08297	−	0.703291i
$474$	3.31844	−	5.74771i	0.152421	−	0.264001i
$475$		0			0
$476$	−16.4173	−	25.2439i	−0.752485	−	1.15705i
$477$	4.77284	+	9.36722i	0.218533	+	0.428895i
$478$	−1.05283	−	0.404142i	−0.0481552	−	0.0184850i
$479$	1.32701	−	12.6257i	0.0606327	−	0.576881i	−0.921459	−	0.388476i	$-0.873002\pi$
$479$	1.32701	−	12.6257i	0.0606327	−	0.576881i	0.982091	−	0.188405i	$-0.0603318\pi$
$480$		0			0
$481$	17.9640	−	1.88809i	0.819087	−	0.0860895i
$482$	−0.681684	−	0.681684i	−0.0310498	−	0.0310498i
$483$	25.4295	−	35.0493i	1.15708	−	1.59480i
$484$	−2.46756	+	0.801759i	−0.112162	+	0.0364436i
$485$		0			0
$486$	−1.21924	−	5.73606i	−0.0553057	−	0.260193i
$487$	−0.821060	−	15.6668i	−0.0372058	−	0.709928i	−0.952017	−	0.306046i	$-0.900994\pi$
$487$	−0.821060	−	15.6668i	−0.0372058	−	0.709928i	0.914811	−	0.403882i	$-0.132339\pi$
$488$	−3.40500	+	2.21123i	−0.154137	+	0.100098i
$489$	6.88511	−	21.1902i	0.311355	−	0.958254i
$490$		0			0
$491$	4.43552	+	13.6511i	0.200172	+	0.616067i	0.999877	+	0.0156736i	$0.00498927\pi$
$491$	4.43552	+	13.6511i	0.200172	+	0.616067i	−0.799705	+	0.600393i	$0.795011\pi$
$492$	2.28955	+	1.85404i	0.103221	+	0.0835868i
$493$	1.42783	+	0.382586i	0.0643063	+	0.0172308i
$494$	−3.07430	+	6.90498i	−0.138319	+	0.310670i
$495$		0			0
$496$	2.65198	−	3.65013i	0.119077	−	0.163896i
$497$	−22.1967	−	7.19596i	−0.995657	−	0.322783i
$498$	3.65258	−	1.86108i	0.163676	−	0.0833972i
$499$	6.68368	+	3.85883i	0.299203	+	0.172745i	0.642085	−	0.766634i	$-0.278070\pi$
$499$	6.68368	+	3.85883i	0.299203	+	0.172745i	−0.342882	+	0.939378i	$0.611403\pi$
$500$		0			0
$501$	25.0287	+	43.3511i	1.11820	+	1.93678i
$502$	−0.320595	+	6.11732i	−0.0143089	+	0.273030i
$503$	−9.64392	+	1.52745i	−0.430001	+	0.0681055i	−0.367684	−	0.929951i	$-0.619849\pi$
$503$	−9.64392	+	1.52745i	−0.430001	+	0.0681055i	−0.0623173	+	0.998056i	$0.519849\pi$
$504$	−0.502621	+	9.71312i	−0.0223885	+	0.432657i
$505$		0			0
$506$	0.618727	+	5.88679i	0.0275058	+	0.261700i
$507$	0.312649	−	1.16682i	0.0138852	−	0.0518203i
$508$	6.80251	+	17.7211i	0.301812	+	0.786248i
$509$	5.47118	+	1.16293i	0.242506	+	0.0515462i	0.327561	−	0.944830i	$-0.393773\pi$
$509$	5.47118	+	1.16293i	0.242506	+	0.0515462i	−0.0850552	+	0.996376i	$0.527107\pi$
$510$		0			0
$511$	5.47617	−	20.4914i	0.242252	−	0.906486i
$512$	16.2658	+	8.28783i	0.718853	+	0.366274i
$513$	5.99333	+	9.22892i	0.264612	+	0.407467i
$514$	0.0837023	−	0.0177915i	0.00369195	−	0.000784748i
$515$		0			0
$516$	−8.21152	+	38.6322i	−0.361492	+	1.70069i
$517$	3.64360	+	0.577090i	0.160245	+	0.0253804i
$518$	−2.29356	+	2.55063i	−0.100773	+	0.112068i
$519$	12.6331	+	17.3880i	0.554534	+	0.763250i
$520$		0			0
$521$	−35.0701	−	3.68601i	−1.53645	−	0.161487i	−0.701841	−	0.712334i	$-0.747638\pi$
$521$	−35.0701	−	3.68601i	−1.53645	−	0.161487i	−0.834606	+	0.550847i	$0.814305\pi$
$522$	−0.147579	−	0.182245i	−0.00645937	−	0.00797666i
$523$	17.6409	+	0.924518i	0.771381	+	0.0404264i	0.433965	−	0.900930i	$-0.357114\pi$
$523$	17.6409	+	0.924518i	0.771381	+	0.0404264i	0.337415	+	0.941356i	$0.390447\pi$
$524$	26.2519			1.14682
$525$		0			0
$526$	−1.77966			−0.0775967
$527$	−7.40232	−	0.387939i	−0.322450	−	0.0168989i
$528$	20.3058	+	25.0756i	0.883697	+	1.09127i
$529$	−17.7983	−	1.87068i	−0.773841	−	0.0813340i
$530$		0			0
$531$	−11.6528	−	16.0388i	−0.505690	−	0.696023i
$532$	12.3630	+	37.9642i	0.536004	+	1.64596i
$533$	2.16157	+	0.342360i	0.0936282	+	0.0148292i
$534$	0.539227	−	2.53686i	0.0233346	−	0.109781i
$535$		0			0
$536$	−1.20094	+	0.255267i	−0.0518726	+	0.0110259i
$537$	−21.4218	−	32.9867i	−0.924418	−	1.42348i
$538$	0.136814	+	0.0697102i	0.00589847	+	0.00300542i
$539$	−16.4323	+	18.2984i	−0.707789	+	0.788167i
$540$		0			0
$541$	14.5992	+	3.10316i	0.627669	+	0.133415i	0.510754	−	0.859727i	$-0.329366\pi$
$541$	14.5992	+	3.10316i	0.627669	+	0.133415i	0.116915	+	0.993142i	$0.462700\pi$
$542$	1.75406	+	4.56950i	0.0753435	+	0.196277i
$543$	−5.12391	+	19.1227i	−0.219888	+	0.820634i
$544$	−1.85879	−	17.6852i	−0.0796951	−	0.758248i
$545$		0			0
$546$	2.97640	+	5.83201i	0.127378	+	0.249587i
$547$	43.4146	−	6.87620i	1.85627	−	0.294005i	0.874639	−	0.484774i	$-0.161098\pi$
$547$	43.4146	−	6.87620i	1.85627	−	0.294005i	0.981635	+	0.190769i	$0.0610981\pi$
$548$	0.616248	−	11.7587i	0.0263248	−	0.502307i
$549$	6.95951	+	12.0542i	0.297025	+	0.514462i
$550$		0			0
$551$	−1.69736	−	0.979969i	−0.0723098	−	0.0417481i
$552$	15.1008	−	7.69424i	0.642733	−	0.327489i
$553$	−17.4391	−	19.3424i	−0.741585	−	0.822522i
$554$	0.232601	−	0.320147i	0.00988226	−	0.0136018i
$555$		0			0
$556$	0.335782	−	0.754180i	0.0142403	−	0.0319843i
$557$	−2.55339	−	0.684178i	−0.108190	−	0.0289895i	0.204318	−	0.978905i	$-0.434502\pi$
$557$	−2.55339	−	0.684178i	−0.108190	−	0.0289895i	−0.312508	+	0.949915i	$0.601169\pi$
$558$	0.913874	+	0.740040i	0.0386874	+	0.0313284i
$559$	9.06628	+	27.9031i	0.383463	+	1.18018i
$560$		0			0
$561$	16.3811	−	50.4159i	0.691611	−	2.12856i
$562$	6.61120	−	4.29336i	0.278877	−	0.181105i
$563$	−1.56885	−	29.9354i	−0.0661191	−	1.26163i	−0.807227	−	0.590241i	$-0.799033\pi$
$563$	−1.56885	−	29.9354i	−0.0661191	−	1.26163i	0.741108	−	0.671386i	$-0.234301\pi$
$564$	−1.07864	−	5.07461i	−0.0454190	−	0.213680i
$565$		0			0
$566$	2.25082	−	0.731335i	0.0946089	−	0.0307403i
$567$	−18.5443	−	1.93673i	−0.778789	−	0.0813349i
$568$	−6.45771	−	6.45771i	−0.270959	−	0.270959i
$569$	−32.8105	+	3.44853i	−1.37549	+	0.144570i	−0.763250	−	0.646103i	$-0.776398\pi$
$569$	−32.8105	+	3.44853i	−1.37549	+	0.144570i	−0.612239	+	0.790673i	$0.709731\pi$
$570$		0			0
$571$	3.39211	−	32.2738i	0.141956	−	1.35062i	−0.659113	−	0.752044i	$-0.729068\pi$
$571$	3.39211	−	32.2738i	0.141956	−	1.35062i	0.801068	−	0.598573i	$-0.204265\pi$
$572$	23.2426	+	8.92201i	0.971823	+	0.373048i
$573$	−8.03061	−	15.7610i	−0.335484	−	0.658424i
$574$	−0.348405	+	0.226583i	−0.0145421	+	0.00945741i
$575$		0			0
$576$	11.3285	−	19.6215i	0.472020	−	0.817562i
$577$	−0.111322	−	0.0722936i	−0.00463441	−	0.00300962i	0.542320	−	0.840172i	$-0.317546\pi$
$577$	−0.111322	−	0.0722936i	−0.00463441	−	0.00300962i	−0.546954	+	0.837163i	$0.684213\pi$
$578$	−3.63522	+	2.94374i	−0.151205	+	0.122443i
$579$	−23.0914	+	10.2810i	−0.959646	+	0.427262i
$580$		0			0
$581$	−2.52689	−	15.8864i	−0.104833	−	0.659077i
$582$	4.85831	−	4.85831i	0.201384	−	0.201384i
$583$	−6.54774	+	8.08578i	−0.271180	+	0.334879i
$584$	5.55478	−	6.16921i	0.229858	−	0.255284i
$585$		0			0
$586$	5.42502	−	4.88471i	0.224106	−	0.201786i
$587$	−12.7376	+	24.9989i	−0.525736	+	1.03182i	0.463584	+	0.886053i	$0.346563\pi$
$587$	−12.7376	+	24.9989i	−0.525736	+	1.03182i	−0.989320	+	0.145762i	$0.953437\pi$
$588$	32.3060	+	12.3523i	1.33228	+	0.509399i
$589$	9.34714	+	3.03707i	0.385142	+	0.125140i
$590$		0			0
$591$	−11.2805	−	10.1570i	−0.464017	−	0.417802i
$592$	16.4863	−	6.32850i	0.677583	−	0.260100i
$593$	11.6217	+	43.3728i	0.477247	+	1.78111i	0.612689	+	0.790324i	$0.290088\pi$
$593$	11.6217	+	43.3728i	0.477247	+	1.78111i	−0.135442	+	0.990785i	$0.543246\pi$
$594$	−1.05419	+	0.765913i	−0.0432539	+	0.0314258i
$595$		0			0
$596$	−5.02030	−	3.64746i	−0.205639	−	0.149406i
$597$	−1.30343	+	3.39556i	−0.0533460	+	0.138971i
$598$	3.36793	−	5.18615i	0.137725	−	0.212078i
$599$	18.7555	−	10.8285i	0.766331	−	0.442441i	−0.0652335	−	0.997870i	$-0.520779\pi$
$599$	18.7555	−	10.8285i	0.766331	−	0.442441i	0.831564	+	0.555429i	$0.187446\pi$
$600$		0			0
$601$			27.1300i			1.10666i	0.832963	+	0.553328i	$0.186643\pi$
$601$			27.1300i			1.10666i	−0.832963	+	0.553328i	$0.813357\pi$
$602$	−4.82693	−	2.78259i	−0.196731	−	0.113410i
$603$	0.658463	+	4.15737i	0.0268147	+	0.169301i
$604$	−4.30090	−	9.65998i	−0.175001	−	0.393059i
$605$		0			0
$606$	−6.67644	−	2.97254i	−0.271212	−	0.120751i
$607$	3.36494	−	0.901633i	0.136579	−	0.0365961i	−0.189882	−	0.981807i	$-0.560811\pi$
$607$	3.36494	−	0.901633i	0.136579	−	0.0365961i	0.326461	+	0.945211i	$0.394144\pi$
$608$	−3.68840	+	23.2877i	−0.149584	+	0.944439i
$609$	−1.58466	+	0.609492i	−0.0642135	+	0.0246979i
$610$		0			0
$611$	−2.57876	−	2.86401i	−0.104326	−	0.115865i
$612$	−40.3500	+	2.11466i	−1.63105	+	0.0854799i
$613$	32.9083	−	1.72465i	1.32916	−	0.0696581i	0.625514	−	0.780213i	$-0.284889\pi$
$613$	32.9083	−	1.72465i	1.32916	−	0.0696581i	0.703642	+	0.710555i	$0.251556\pi$
$614$	1.19953	+	1.33222i	0.0484092	+	0.0537639i
$615$		0			0
$616$	−8.98402	+	3.45544i	−0.361977	+	0.139224i
$617$	6.30591	−	39.8140i	0.253866	−	1.60285i	−0.450342	−	0.892856i	$-0.648698\pi$
$617$	6.30591	−	39.8140i	0.253866	−	1.60285i	0.704208	−	0.709994i	$-0.251302\pi$
$618$	−3.21101	+	0.860387i	−0.129166	+	0.0346098i
$619$	−26.1694	−	11.6513i	−1.05184	−	0.468307i	−0.193342	−	0.981131i	$-0.561933\pi$
$619$	−26.1694	−	11.6513i	−1.05184	−	0.468307i	−0.858494	+	0.512824i	$0.828599\pi$
$620$		0			0
$621$	−3.66180	−	8.22453i	−0.146943	−	0.330039i
$622$	1.25585	+	7.92913i	0.0503550	+	0.317929i
$623$	−8.81697	−	5.08273i	−0.353244	−	0.203635i
$624$		−	33.7084i		−	1.34942i
$625$		0			0
$626$	−2.83506	+	1.63683i	−0.113312	+	0.0654207i
$627$	−38.2806	+	58.9470i	−1.52878	+	2.35412i
$628$	14.0165	−	36.5142i	0.559318	−	1.45707i
$629$	−23.4715	−	17.0531i	−0.935872	−	0.679951i
$630$		0			0
$631$	−34.7400	+	25.2401i	−1.38298	+	1.00479i	−0.386382	+	0.922339i	$0.626275\pi$
$631$	−34.7400	+	25.2401i	−1.38298	+	1.00479i	−0.996595	+	0.0824526i	$0.973725\pi$
$632$	−2.63813	−	9.84562i	−0.104939	−	0.391638i
$633$	−32.1013	+	12.3225i	−1.27591	+	0.489777i
$634$	0.538887	+	0.485216i	0.0214019	+	0.0192704i
$635$		0			0
$636$	13.9160	+	4.52157i	0.551804	+	0.179292i
$637$	25.3713	−	4.05272i	1.00525	−	0.160575i
$638$	0.105363	−	0.206787i	0.00417138	−	0.00818680i
$639$	−23.2675	+	20.9502i	−0.920448	+	0.828775i
$640$		0			0
$641$	20.7202	−	23.0121i	0.818399	−	0.908924i	−0.178787	−	0.983888i	$-0.557217\pi$
$641$	20.7202	−	23.0121i	0.818399	−	0.908924i	0.997186	+	0.0749634i	$0.0238840\pi$
$642$	3.66045	−	4.52028i	0.144466	−	0.178401i
$643$	−10.0822	+	10.0822i	−0.397604	+	0.397604i	−0.877387	−	0.479783i	$-0.840715\pi$
$643$	−10.0822	+	10.0822i	−0.397604	+	0.397604i	0.479783	+	0.877387i	$0.340715\pi$
$644$	−5.13120	−	32.2595i	−0.202198	−	1.27120i
$645$		0			0
$646$	11.0907	−	4.93789i	0.436357	−	0.194279i
$647$	22.0741	−	17.8753i	0.867823	−	0.702749i	−0.0881806	−	0.996105i	$-0.528105\pi$
$647$	22.0741	−	17.8753i	0.867823	−	0.702749i	0.956003	+	0.293355i	$0.0947719\pi$
$648$	−6.12017	−	3.97448i	−0.240423	−	0.156132i
$649$	9.81009	−	16.9916i	0.385080	−	0.666977i
$650$		0			0
$651$	7.13722	−	4.64166i	0.279730	−	0.181921i
$652$	−7.63034	−	14.9754i	−0.298827	−	0.586481i
$653$	−31.5132	−	12.0968i	−1.23321	−	0.473383i	−0.347521	−	0.937672i	$-0.612977\pi$
$653$	−31.5132	−	12.0968i	−1.23321	−	0.473383i	−0.885684	+	0.464289i	$0.846310\pi$
$654$	0.613853	−	5.84042i	0.0240036	−	0.228379i
$655$		0			0
$656$	2.12788	−	0.223650i	0.0830799	−	0.00873205i
$657$	−20.1244	−	20.1244i	−0.785129	−	0.785129i
$658$	0.727903	+	0.0760204i	0.0283766	+	0.00296359i
$659$	1.81381	−	0.589344i	0.0706562	−	0.0229576i	−0.273476	−	0.961879i	$-0.588173\pi$
$659$	1.81381	−	0.589344i	0.0706562	−	0.0229576i	0.344132	+	0.938921i	$0.388173\pi$
$660$		0			0
$661$	2.24221	+	10.5488i	0.0872120	+	0.410300i	0.999998	+	0.00186255i	$0.000592870\pi$
$661$	2.24221	+	10.5488i	0.0872120	+	0.410300i	−0.912786	+	0.408437i	$0.866074\pi$
$662$	−0.280953	−	5.36090i	−0.0109195	−	0.208357i
$663$	−46.4453	+	30.1619i	−1.80379	+	1.17139i
$664$	1.94553	−	5.98771i	0.0755010	−	0.232368i
$665$		0			0
$666$	1.42229	+	4.37734i	0.0551124	+	0.169619i
$667$	1.24614	+	1.00910i	0.0482507	+	0.0390727i
$668$	36.4738	+	9.77313i	1.41121	+	0.378134i
$669$	21.5776	−	48.4640i	0.834238	−	1.87373i
$670$		0			0
$671$	−8.09687	+	11.1444i	−0.312576	+	0.430224i
$672$	13.6768	+	15.1695i	0.527595	+	0.585177i
$673$	−39.2085	+	19.9777i	−1.51138	+	0.770084i	−0.996208	−	0.0870048i	$-0.972270\pi$
$673$	−39.2085	+	19.9777i	−1.51138	+	0.770084i	−0.515168	+	0.857089i	$0.672270\pi$
$674$	3.14838	+	1.81772i	0.121271	+	0.0700159i
$675$		0			0
$676$	−0.455616	−	0.789150i	−0.0175237	−	0.0303519i
$677$	0.476818	−	9.09823i	0.0183256	−	0.349674i	−0.974043	−	0.226364i	$-0.927316\pi$
$677$	0.476818	−	9.09823i	0.0183256	−	0.349674i	0.992368	−	0.123309i	$-0.0393507\pi$
$678$	5.27157	−	0.834934i	0.202453	−	0.0320655i
$679$	−12.2557	−	24.0141i	−0.470332	−	0.921576i
$680$		0			0
$681$	3.93239	+	37.4141i	0.150689	+	1.43371i
$682$	−0.301210	+	1.12413i	−0.0115339	+	0.0430452i
$683$	10.0618	+	26.2120i	0.385006	+	1.00297i	0.979956	+	0.199212i	$0.0638382\pi$
$683$	10.0618	+	26.2120i	0.385006	+	1.00297i	−0.594951	+	0.803762i	$0.702828\pi$
$684$	52.4026	+	11.1385i	2.00366	+	0.425892i
$685$		0			0
$686$	−3.06303	+	3.79786i	−0.116947	+	0.145003i
$687$	−45.6248	−	23.2470i	−1.74069	−	0.886927i
$688$	15.6221	+	24.0559i	0.595586	+	0.917122i
$689$	10.6320	−	2.25989i	0.405046	−	0.0860951i
$690$		0			0
$691$	10.4802	−	49.3056i	0.398686	−	1.87567i	−0.0785710	−	0.996909i	$-0.525036\pi$
$691$	10.4802	−	49.3056i	0.398686	−	1.87567i	0.477257	−	0.878764i	$-0.341631\pi$
$692$	16.0133	+	2.53626i	0.608735	+	0.0964141i
$693$	10.2182	+	31.3780i	0.388158	+	1.19195i
$694$	−0.389209	−	0.535701i	−0.0147742	−	0.0203349i
$695$		0			0
$696$	−0.660865	−	0.0694597i	−0.0250500	−	0.00263286i
$697$	−2.21217	−	2.73180i	−0.0837917	−	0.103474i
$698$	−7.30010	−	0.382582i	−0.276313	−	0.0144809i
$699$	−17.4884			−0.661473
$700$		0			0
$701$	−10.4471			−0.394583			−0.197292	−	0.980345i	$-0.563215\pi$
$701$	−10.4471			−0.394583			−0.197292	+	0.980345i	$0.563215\pi$
$702$	1.35942	+	0.0712443i	0.0513081	+	0.00268894i
$703$	24.2083	+	29.8948i	0.913035	+	1.12750i
$704$	22.3000	+	2.34383i	0.840464	+	0.0883363i
$705$		0			0
$706$	3.77988	+	5.20256i	0.142258	+	0.195801i
$707$	−19.1751	+	21.3244i	−0.721154	+	0.801986i
$708$	−27.2528	−	4.31641i	−1.02422	−	0.162221i
$709$	2.36320	−	11.1180i	0.0887517	−	0.417544i	−0.911232	−	0.411893i	$-0.864868\pi$
$709$	2.36320	−	11.1180i	0.0887517	−	0.417544i	0.999984	−	0.00565112i	$-0.00179882\pi$
$710$		0			0
$711$	−34.1811	+	7.26543i	−1.28189	+	0.272475i
$712$	−2.16939	−	3.34056i	−0.0813012	−	0.125193i
$713$	−7.16432	−	3.65040i	−0.268306	−	0.136709i
$714$	2.71522	−	10.1601i	0.101615	−	0.380233i
$715$		0			0
$716$	−29.0215	−	6.16871i	−1.08458	−	0.230535i
$717$	3.92610	+	10.2279i	0.146623	+	0.381966i
$718$	2.46843	−	9.21230i	0.0921209	−	0.343800i
$719$	4.58882	+	43.6597i	0.171134	+	1.62823i	0.656784	+	0.754078i	$0.271916\pi$
$719$	4.58882	+	43.6597i	0.171134	+	1.62823i	−0.485650	+	0.874153i	$0.661417\pi$
$720$		0			0
$721$	−0.674108	+	13.0271i	−0.0251051	+	0.485154i
$722$	−10.9546	+	1.73505i	−0.407690	+	0.0645717i
$723$	−0.490146	+	9.35255i	−0.0182287	+	0.347825i
$724$	7.46696	+	12.9332i	0.277507	+	0.480657i
$725$		0			0
$726$	−0.784728	−	0.453063i	−0.0291240	−	0.0168147i
$727$	29.7714	−	15.1693i	1.10416	−	0.562598i	0.195740	−	0.980656i	$-0.437289\pi$
$727$	29.7714	−	15.1693i	1.10416	−	0.562598i	0.908420	+	0.418058i	$0.137289\pi$
$728$	9.56573	+	3.10112i	0.354529	+	0.114935i
$729$	−21.0586	+	28.9847i	−0.779949	+	1.07351i
$730$		0			0
$731$	19.1671	−	43.0499i	0.708919	−	1.59226i
$732$	18.7124	+	5.01398i	0.691631	+	0.185322i
$733$	29.5521	+	23.9308i	1.09153	+	0.883904i	0.993786	−	0.111307i	$-0.0355038\pi$
$733$	29.5521	+	23.9308i	1.09153	+	0.883904i	0.0977448	+	0.995212i	$0.468837\pi$
$734$	0.961845	+	2.96026i	0.0355024	+	0.109265i
$735$		0			0
$736$	5.96087	−	18.3457i	0.219721	−	0.676230i
$737$	−3.49366	+	2.26881i	−0.128691	+	0.0835726i
$738$	0.0291854	+	0.556892i	0.00107433	+	0.0204995i
$739$	−6.32030	−	29.7347i	−0.232496	−	1.09381i	−0.927216	−	0.374528i	$-0.877805\pi$
$739$	−6.32030	−	29.7347i	−0.232496	−	1.09381i	0.694720	−	0.719281i	$-0.255528\pi$
$740$		0			0
$741$	69.8339	−	22.6904i	2.56541	−	0.833553i
$742$	−1.21217	+	1.67072i	−0.0445000	+	0.0613340i
$743$	−8.10749	−	8.10749i	−0.297435	−	0.297435i	0.542573	−	0.840008i	$-0.317450\pi$
$743$	−8.10749	−	8.10749i	−0.297435	−	0.297435i	−0.840008	+	0.542573i	$0.817450\pi$
$744$	3.31392	−	0.348307i	0.121494	−	0.0127696i
$745$		0			0
$746$	−0.545955	+	5.19442i	−0.0199888	+	0.190181i
$747$	−20.1507	−	7.73511i	−0.737274	−	0.283013i
$748$	−18.1542	−	35.6295i	−0.663781	−	1.30274i
$749$	−12.4435	−	19.1337i	−0.454676	−	0.699130i
$750$		0			0
$751$	−22.9279	+	39.7123i	−0.836652	+	1.44912i	0.0560263	+	0.998429i	$0.482157\pi$
$751$	−22.9279	+	39.7123i	−0.836652	+	1.44912i	−0.892678	+	0.450694i	$0.851176\pi$
$752$	−3.15991	−	2.05207i	−0.115230	−	0.0748313i
$753$	46.2474	−	37.4504i	1.68535	−	1.36477i
$754$	−0.221495	+	0.0986157i	−0.00806636	+	0.00359137i
$755$		0			0
$756$	5.58534	−	4.52902i	0.203137	−	0.164719i
$757$	−24.8825	+	24.8825i	−0.904371	+	0.904371i	−0.995811	−	0.0914400i	$-0.970853\pi$
$757$	−24.8825	+	24.8825i	−0.904371	+	0.904371i	0.0914400	+	0.995811i	$0.470853\pi$
$758$	2.46071	−	3.03873i	0.0893771	−	0.110372i
$759$	38.4771	−	42.7332i	1.39663	−	1.55112i
$760$		0			0
$761$	−18.8581	+	16.9799i	−0.683606	+	0.615522i	−0.935957	−	0.352114i	$-0.885463\pi$
$761$	−18.8581	+	16.9799i	−0.683606	+	0.615522i	0.252351	+	0.967636i	$0.418796\pi$
$762$	−3.00963	+	5.90674i	−0.109028	+	0.213979i
$763$	−21.0581	−	9.35902i	−0.762353	−	0.338819i
$764$	−12.6904	−	4.12337i	−0.459124	−	0.149178i
$765$		0			0
$766$	−5.55336	−	5.00027i	−0.200651	−	0.180667i
$767$	−19.1357	+	7.34550i	−0.690950	+	0.265231i
$768$	−7.10883	−	26.5305i	−0.256518	−	0.957338i
$769$	−8.55473	+	6.21537i	−0.308491	+	0.224132i	−0.731249	−	0.682111i	$-0.761062\pi$
$769$	−8.55473	+	6.21537i	−0.308491	+	0.224132i	0.422757	+	0.906243i	$0.361062\pi$
$770$		0			0
$771$	−0.672540	−	0.488629i	−0.0242209	−	0.0175975i
$772$	−6.83310	+	17.8008i	−0.245929	+	0.640666i
$773$	3.89062	−	5.99102i	0.139936	−	0.215482i	−0.761753	−	0.647867i	$-0.775661\pi$
$773$	3.89062	−	5.99102i	0.139936	−	0.215482i	0.901689	+	0.432385i	$0.142328\pi$
$774$	−6.47431	+	3.73794i	−0.232714	+	0.134358i
$775$		0			0
$776$		−	10.5520i		−	0.378796i
$777$	33.3230	−	0.0219716i	1.19546	−	0.000788227i
$778$	0.850924	+	5.37252i	0.0305071	+	0.192614i
$779$	1.89569	+	4.25780i	0.0679203	+	0.152552i
$780$		0			0
$781$	−28.3072	−	12.6032i	−1.01291	−	0.450976i
$782$	−9.59386	+	2.57067i	−0.343076	+	0.0919268i
$783$	−0.0552195	+	0.348642i	−0.00197339	+	0.0124595i
$784$	22.9336	−	10.2470i	0.819057	−	0.365963i
$785$		0			0
$786$	6.13479	+	6.81337i	0.218821	+	0.243025i
$787$	−12.8429	+	0.673066i	−0.457799	+	0.0239922i	−0.279842	−	0.960046i	$-0.590282\pi$
$787$	−12.8429	+	0.673066i	−0.457799	+	0.0239922i	−0.177957	+	0.984038i	$0.556949\pi$
$788$	−11.4347	+	0.599270i	−0.407346	+	0.0213481i
$789$	11.5684	+	12.8480i	0.411847	+	0.457402i
$790$		0			0
$791$	3.26266	−	20.6879i	0.116007	−	0.735576i
$792$	−2.02045	+	12.7566i	−0.0717937	+	0.453288i
$793$	13.9005	−	3.72464i	0.493623	−	0.132266i
$794$	0.253422	+	0.112831i	0.00899359	+	0.00400421i
$795$		0			0
$796$	1.11594	+	2.50644i	0.0395535	+	0.0888386i
$797$	2.58451	+	16.3180i	0.0915481	+	0.578012i	0.990234	+	0.139418i	$0.0445233\pi$
$797$	2.58451	+	16.3180i	0.0915481	+	0.578012i	−0.898685	+	0.438594i	$0.855477\pi$
$798$	−6.96405	+	12.0805i	−0.246525	+	0.427644i
$799$			6.19008i			0.218989i
$800$		0			0
$801$	−11.8261	+	6.82780i	−0.417855	+	0.241249i
$802$	0.0530501	−	0.0816900i	0.00187326	−	0.00288457i
$803$	10.0939	−	26.2954i	0.356205	−	0.927946i
$804$	4.73952	+	3.44346i	0.167150	+	0.121442i
$805$		0			0
$806$	0.983605	−	0.714631i	0.0346460	−	0.0251718i
$807$	−0.386077	−	1.44086i	−0.0135905	−	0.0507206i
$808$	−10.4786	+	4.02234i	−0.368634	+	0.141506i
$809$	27.9141	+	25.1340i	0.981407	+	0.883663i	0.993218	−	0.116267i	$-0.0370929\pi$
$809$	27.9141	+	25.1340i	0.981407	+	0.883663i	−0.0118109	+	0.999930i	$0.503760\pi$
$810$		0			0
$811$	−19.9913	−	6.49556i	−0.701989	−	0.228090i	−0.0637922	−	0.997963i	$-0.520319\pi$
$811$	−19.9913	−	6.49556i	−0.701989	−	0.228090i	−0.638197	+	0.769873i	$0.720319\pi$
$812$	−0.520153	+	1.17036i	−0.0182538	+	0.0410716i
$813$	21.5869	−	42.3667i	0.757086	−	1.48587i
$814$	−3.38507	+	3.04793i	−0.118647	+	0.106830i
$815$		0			0
$816$	−36.2280	+	40.2353i	−1.26823	+	1.40852i
$817$	−39.3209	+	48.5573i	−1.37566	+	1.69880i
$818$	−5.46627	+	5.46627i	−0.191124	+	0.191124i
$819$	12.3334	−	32.1931i	0.430965	−	1.12492i
$820$		0			0
$821$	−45.0953	+	20.0777i	−1.57384	+	0.700718i	−0.993518	−	0.113671i	$-0.963739\pi$
$821$	−45.0953	+	20.0777i	−1.57384	+	0.700718i	−0.580320	+	0.814389i	$0.697072\pi$
$822$	3.19584	−	2.58794i	0.111468	−	0.0902648i
$823$	−43.6298	−	28.3335i	−1.52084	−	0.987645i	−0.990139	−	0.140086i	$-0.955262\pi$
$823$	−43.6298	−	28.3335i	−1.52084	−	0.987645i	−0.530701	−	0.847559i	$-0.678071\pi$
$824$	−2.55272	+	4.42144i	−0.0889282	+	0.154028i
$825$		0			0
$826$	1.76484	−	3.46935i	0.0614066	−	0.120714i
$827$	17.1839	+	33.7254i	0.597544	+	1.17275i	0.969637	+	0.244550i	$0.0786404\pi$
$827$	17.1839	+	33.7254i	0.597544	+	1.17275i	−0.372093	+	0.928196i	$0.621360\pi$
$828$	−40.9187	−	15.7072i	−1.42202	−	0.545864i
$829$	−3.99905	+	38.0484i	−0.138893	+	1.32147i	0.673857	+	0.738862i	$0.264636\pi$
$829$	−3.99905	+	38.0484i	−0.138893	+	1.32147i	−0.812750	+	0.582613i	$0.802030\pi$
$830$		0			0
$831$	−3.82326	+	0.401841i	−0.132628	+	0.0139397i
$832$	−16.5640	−	16.5640i	−0.574254	−	0.574254i
$833$	−34.6396	−	22.4303i	−1.20019	−	0.777164i
$834$	0.274207	−	0.0890952i	0.00949500	−	0.00308511i
$835$		0			0
$836$	11.0234	+	51.8612i	0.381254	+	1.79366i
$837$	−0.0926383	−	1.76764i	−0.00320205	−	0.0610987i
$838$	1.89843	−	1.23286i	0.0655802	−	0.0425883i
$839$	5.99213	−	18.4419i	0.206871	−	0.636684i	−0.792760	−	0.609534i	$-0.791357\pi$
$839$	5.99213	−	18.4419i	0.206871	−	0.636684i	0.999631	−	0.0271505i	$-0.00864335\pi$
$840$		0			0
$841$	8.94206	+	27.5208i	0.308347	+	0.948995i
$842$	6.55174	+	5.30550i	0.225788	+	0.182840i
$843$	−73.9707	−	19.8204i	−2.54769	−	0.682651i
$844$	−10.5500	+	23.6957i	−0.363146	+	0.815639i
$845$		0			0
$846$	0.577212	−	0.794464i	0.0198449	−	0.0273142i
$847$	−2.64080	+	2.38094i	−0.0907388	+	0.0818100i
$848$	9.46833	−	4.82435i	0.325144	−	0.165669i
$849$	−19.9110	−	11.4956i	−0.683342	−	0.394528i
$850$		0			0
$851$	−15.7357	−	27.2550i	−0.539411	−	0.934288i
$852$	−2.28062	+	43.5169i	−0.0781329	+	1.49086i
$853$	9.23966	−	1.46342i	0.316360	−	0.0501065i	0.00376463	−	0.999993i	$-0.498802\pi$
$853$	9.23966	−	1.46342i	0.316360	−	0.0501065i	0.312595	+	0.949886i	$0.398802\pi$
$854$	−1.48691	+	2.29295i	−0.0508809	+	0.0784630i
$855$		0			0
$856$	−0.933754	−	8.88408i	−0.0319151	−	0.303652i
$857$	−4.23294	+	15.7975i	−0.144594	+	0.539633i	0.855179	+	0.518333i	$0.173447\pi$
$857$	−4.23294	+	15.7975i	−0.144594	+	0.539633i	−0.999773	+	0.0213003i	$0.993219\pi$
$858$	3.11595	+	8.11731i	0.106377	+	0.277121i
$859$	47.3304	+	10.0604i	1.61489	+	0.343256i	0.924797	−	0.380461i	$-0.124235\pi$
$859$	47.3304	+	10.0604i	1.61489	+	0.343256i	0.690096	+	0.723717i	$0.257568\pi$
$860$		0			0
$861$	3.90056	+	1.04239i	0.132931	+	0.0355247i
$862$	7.34193	+	3.74090i	0.250067	+	0.127416i
$863$	28.6272	+	44.0820i	0.974481	+	1.50057i	0.861996	+	0.506916i	$0.169214\pi$
$863$	28.6272	+	44.0820i	0.974481	+	1.50057i	0.112485	+	0.993653i	$0.464119\pi$
$864$	4.15363	−	0.882882i	0.141309	−	0.0300362i
$865$		0			0
$866$	−0.0932651	+	0.438778i	−0.00316928	+	0.0149103i
$867$	44.8823	+	7.10866i	1.52428	+	0.241423i
$868$	1.33113	−	6.28285i	0.0451816	−	0.213254i
$869$	−20.3278	−	27.9788i	−0.689574	−	0.949117i
$870$		0			0
$871$	4.32806	+	0.454897i	0.146651	+	0.0154136i
$872$	−5.67593	−	7.00919i	−0.192211	−	0.237361i
$873$	−36.1263	−	1.89330i	−1.22269	−	0.0640784i
$874$	13.1692			0.445454
$875$		0			0
$876$	−39.6110			−1.33833
$877$	−27.2293	−	1.42703i	−0.919469	−	0.0481873i	−0.413274	−	0.910607i	$-0.635615\pi$
$877$	−27.2293	−	1.42703i	−0.919469	−	0.0481873i	−0.506195	+	0.862419i	$0.668948\pi$
$878$	−4.92988	−	6.08790i	−0.166375	−	0.205457i
$879$	−70.5293	−	7.41293i	−2.37890	−	0.250032i
$880$		0			0
$881$	−0.398014	−	0.547820i	−0.0134094	−	0.0184565i	0.802260	−	0.596975i	$-0.203631\pi$
$881$	−0.398014	−	0.547820i	−0.0134094	−	0.0184565i	−0.815669	+	0.578519i	$0.803631\pi$
$882$	2.35423	+	6.10888i	0.0792709	+	0.205697i
$883$	−31.4097	−	4.97481i	−1.05702	−	0.167416i	−0.396356	−	0.918097i	$-0.629726\pi$
$883$	−31.4097	−	4.97481i	−1.05702	−	0.167416i	−0.660665	+	0.750681i	$0.729726\pi$
$884$	−8.68556	+	40.8623i	−0.292127	+	1.37435i
$885$		0			0
$886$	−6.47597	+	1.37651i	−0.217565	+	0.0462448i
$887$	−0.370913	−	0.571156i	−0.0124540	−	0.0191775i	0.832389	−	0.554192i	$-0.186973\pi$
$887$	−0.370913	−	0.571156i	−0.0124540	−	0.0191775i	−0.844843	+	0.535015i	$0.820306\pi$
$888$	11.6206	+	5.92101i	0.389963	+	0.198696i
$889$	18.4064	+	18.3821i	0.617331	+	0.616517i
$890$		0			0
$891$	−24.2186	−	5.14782i	−0.811353	−	0.172458i
$892$	−14.3412	−	37.3602i	−0.480180	−	1.25091i
$893$	2.12423	−	7.92774i	0.0710847	−	0.265292i
$894$	−0.226534	−	2.15533i	−0.00757643	−	0.0720849i
$895$		0			0
$896$	20.3823	+	1.05472i	0.680926	+	0.0352356i
$897$	−59.3337	+	9.39753i	−1.98109	+	0.313774i
$898$	−0.269574	+	5.14377i	−0.00899579	+	0.171650i
$899$	0.157632	+	0.273026i	0.00525731	+	0.00910592i
$900$		0			0
$901$	−15.1194	−	8.72921i	−0.503701	−	0.290812i
$902$	−0.491742	+	0.250555i	−0.0163732	+	0.00834256i
$903$	11.2882	+	52.9354i	0.375649	+	1.76158i
$904$	4.81808	−	6.63152i	0.160247	−	0.220561i
$905$		0			0
$906$	1.50206	−	3.37368i	0.0499025	−	0.112083i
$907$	−42.2126	−	11.3108i	−1.40165	−	0.375570i	−0.522710	−	0.852510i	$-0.675079\pi$
$907$	−42.2126	−	11.3108i	−1.40165	−	0.375570i	−0.878936	+	0.476941i	$0.841746\pi$
$908$	22.0543	+	17.8592i	0.731896	+	0.592678i
$909$	11.8909	+	36.5965i	0.394397	+	1.21383i
$910$		0			0
$911$	−8.28755	+	25.5065i	−0.274579	+	0.845067i	0.714752	+	0.699378i	$0.246540\pi$
$911$	−8.28755	+	25.5065i	−0.274579	+	0.845067i	−0.989331	+	0.145689i	$0.953460\pi$
$912$	60.2053	−	39.0978i	1.99360	−	1.29466i
$913$	−1.11796	−	21.3320i	−0.0369992	−	0.705986i
$914$	−0.345590	−	1.62587i	−0.0114311	−	0.0537791i
$915$		0			0
$916$	−36.7362	+	11.9363i	−1.21380	+	0.394387i
$917$	32.8565	−	14.6546i	1.08502	−	0.483939i
$918$	−1.54608	−	1.54608i	−0.0510281	−	0.0510281i
$919$	43.3179	−	4.55289i	1.42892	−	0.150186i	0.641749	−	0.766915i	$-0.278209\pi$
$919$	43.3179	−	4.55289i	1.42892	−	0.150186i	0.787176	+	0.616729i	$0.211542\pi$
$920$		0			0
$921$	1.82039	−	17.3198i	0.0599838	−	0.570707i
$922$	1.30974	+	0.502761i	0.0431339	+	0.0165575i
$923$	14.6961	+	28.8427i	0.483728	+	0.949370i
$924$	40.9370	+	20.8245i	1.34673	+	0.685074i
$925$		0			0
$926$	−2.92866	+	5.07259i	−0.0962417	+	0.166696i
$927$	14.6794	+	9.53289i	0.482134	+	0.313101i
$928$	−0.587772	+	0.475969i	−0.0192946	+	0.0156244i
$929$	−38.1215	+	16.9728i	−1.25073	+	0.556859i	−0.921862	−	0.387519i	$-0.873332\pi$
$929$	−38.1215	+	16.9728i	−1.25073	+	0.556859i	−0.328863	+	0.944378i	$0.606666\pi$
$930$		0			0
$931$	36.6661	+	40.6140i	1.20168	+	1.33107i
$932$	−9.32834	+	9.32834i	−0.305560	+	0.305560i
$933$	49.0800	−	60.6088i	1.60681	−	1.98424i
$934$	1.31181	−	1.45691i	0.0429237	−	0.0476716i
$935$		0			0
$936$	10.0272	−	9.02853i	0.327749	−	0.295107i
$937$	−9.28106	+	18.2151i	−0.303199	+	0.595062i	−0.991461	−	0.130400i	$-0.958374\pi$
$937$	−9.28106	+	18.2151i	−0.303199	+	0.595062i	0.688262	+	0.725462i	$0.258374\pi$
$938$	−0.668277	+	0.486205i	−0.0218200	+	0.0158752i
$939$	30.2459	+	9.82748i	0.987037	+	0.320708i
$940$		0			0
$941$	−2.78647	−	2.50895i	−0.0908362	−	0.0817893i	0.622462	−	0.782650i	$-0.286133\pi$
$941$	−2.78647	−	2.50895i	−0.0908362	−	0.0817893i	−0.713298	+	0.700861i	$0.752799\pi$
$942$	12.7523	−	4.89515i	0.415492	−	0.159493i
$943$	−0.986899	−	3.68316i	−0.0321379	−	0.119940i
$944$	−16.2119	+	11.7786i	−0.527652	+	0.383361i
$945$		0			0
$946$	−5.98563	−	4.34882i	−0.194610	−	0.141392i
$947$	19.6429	−	51.1715i	0.638308	−	1.66285i	−0.105470	−	0.994423i	$-0.533635\pi$
$947$	19.6429	−	51.1715i	0.638308	−	1.66285i	0.743778	−	0.668427i	$-0.233032\pi$
$948$	−26.4892	+	40.7898i	−0.860328	+	1.32479i
$949$	−25.4829	+	14.7126i	−0.827210	+	0.477590i
$950$		0			0
$951$		−	7.04452i		−	0.228434i
$952$	−8.08500	−	13.9823i	−0.262036	−	0.453170i
$953$	−3.77491	−	23.8338i	−0.122281	−	0.772054i	−0.970267	−	0.242036i	$-0.922185\pi$
$953$	−3.77491	−	23.8338i	−0.122281	−	0.772054i	0.847986	−	0.530019i	$-0.177815\pi$
$954$	1.12652	+	2.53020i	0.0364724	+	0.0819183i
$955$		0			0
$956$	7.54972	+	3.36135i	0.244176	+	0.108714i
$957$	−2.17778	+	0.583535i	−0.0703977	+	0.0188630i
$958$	0.523200	−	3.30335i	0.0169038	−	0.106727i
$959$	−5.79279	−	15.0610i	−0.187059	−	0.486346i
$960$		0			0
$961$	19.6852	+	21.8627i	0.635007	+	0.705247i
$962$	4.75213	−	0.249048i	0.153215	−	0.00802965i
$963$	−30.5834	+	1.60281i	−0.985535	+	0.0516497i
$964$	4.72721	+	5.25010i	0.152253	+	0.169094i
$965$		0			0
$966$	7.17344	−	8.87042i	0.230802	−	0.285401i
$967$	0.694147	−	4.38267i	0.0223222	−	0.140937i	−0.974010	−	0.226504i	$-0.927270\pi$
$967$	0.694147	−	4.38267i	0.0223222	−	0.140937i	0.996332	+	0.0855672i	$0.0272702\pi$
$968$	−1.34421	+	0.360181i	−0.0432046	+	0.0115766i
$969$	−107.742	−	47.9699i	−3.46118	−	1.54102i
$970$		0			0
$971$	−1.14821	−	2.57893i	−0.0368479	−	0.0827617i	0.894184	−	0.447700i	$-0.147757\pi$
$971$	−1.14821	−	2.57893i	−0.0368479	−	0.0827617i	−0.931032	+	0.364938i	$0.881090\pi$
$972$	6.72260	+	42.4448i	0.215627	+	1.36142i
$973$	−0.000745968	−	1.13136i	−2.39146e−5	−	0.0362699i
$974$		−	4.13304i		−	0.132431i
$975$		0			0
$976$	12.1843	−	7.03463i	0.390011	−	0.225173i
$977$	12.4592	−	19.1854i	0.398604	−	0.613797i	−0.581199	−	0.813762i	$-0.697416\pi$
$977$	12.4592	−	19.1854i	0.398604	−	0.613797i	0.979803	+	0.199965i	$0.0640828\pi$
$978$	2.10355	−	5.47994i	0.0672642	−	0.175229i
$979$	−10.9335	−	7.94364i	−0.349436	−	0.253880i
$980$		0			0
$981$	−25.0153	+	18.1747i	−0.798677	+	0.580273i
$982$	0.978710	+	3.65259i	0.0312319	+	0.116559i
$983$	−25.3059	+	9.71403i	−0.807133	+	0.309829i	−0.726721	−	0.686932i	$-0.758957\pi$
$983$	−25.3059	+	9.71403i	−0.807133	+	0.309829i	−0.0804117	+	0.996762i	$0.525623\pi$
$984$	1.17431	+	1.05736i	0.0374358	+	0.0337073i
$985$		0			0
$986$	0.370369	+	0.120340i	0.0117950	+	0.00383241i
$987$	−4.18282	−	5.74918i	−0.133141	−	0.182998i
$988$	25.1463	−	49.3525i	0.800012	−	1.57011i
$989$	37.9880	−	34.2046i	1.20795	−	1.08764i
$990$		0			0
$991$	11.0607	−	12.2841i	0.351354	−	0.390219i	−0.541398	−	0.840767i	$-0.682105\pi$
$991$	11.0607	−	12.2841i	0.351354	−	0.390219i	0.892752	+	0.450548i	$0.148771\pi$
$992$	2.38676	−	2.94740i	0.0757796	−	0.0935800i
$993$	−36.8761	+	36.8761i	−1.17023	+	1.17023i
$994$	−5.74045	−	2.19921i	−0.182076	−	0.0697547i
$995$		0			0
$996$	−27.4439	+	12.2188i	−0.869592	+	0.387167i
$997$	−2.37413	+	1.92253i	−0.0751895	+	0.0608872i	−0.666178	−	0.745792i	$-0.732071\pi$
$997$	−2.37413	+	1.92253i	−0.0751895	+	0.0608872i	0.590989	+	0.806680i	$0.298738\pi$
$998$	1.70519	+	1.10736i	0.0539767	+	0.0350529i
$999$	3.46403	−	5.99987i	0.109597	−	0.189827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.243.10		288
5.2	odd	4		875.2.bb.c.257.9		288
5.3	odd	4		175.2.x.a.47.10	yes	288
5.4	even	2		875.2.bb.b.243.9		288
7.3	odd	6	inner	875.2.bb.a.493.9		288
25.6	even	5		875.2.bb.c.768.9		288
25.8	odd	20		875.2.bb.b.607.10		288
25.17	odd	20	inner	875.2.bb.a.607.9		288
25.19	even	10		175.2.x.a.33.10	✓	288
35.3	even	12		175.2.x.a.122.10	yes	288
35.17	even	12		875.2.bb.c.507.9		288
35.24	odd	6		875.2.bb.b.493.10		288
175.17	even	60	inner	875.2.bb.a.857.10		288
175.31	odd	30		875.2.bb.c.143.9		288
175.94	odd	30		175.2.x.a.108.10	yes	288
175.108	even	60		875.2.bb.b.857.9		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.10	✓	288	25.19	even	10
175.2.x.a.47.10	yes	288	5.3	odd	4
175.2.x.a.108.10	yes	288	175.94	odd	30
175.2.x.a.122.10	yes	288	35.3	even	12
875.2.bb.a.243.10		288	1.1	even	1	trivial
875.2.bb.a.493.9		288	7.3	odd	6	inner
875.2.bb.a.607.9		288	25.17	odd	20	inner
875.2.bb.a.857.10		288	175.17	even	60	inner
875.2.bb.b.243.9		288	5.4	even	2
875.2.bb.b.493.10		288	35.24	odd	6
875.2.bb.b.607.10		288	25.8	odd	20
875.2.bb.b.857.9		288	175.108	even	60
875.2.bb.c.143.9		288	175.31	odd	30
875.2.bb.c.257.9		288	5.2	odd	4
875.2.bb.c.507.9		288	35.17	even	12
875.2.bb.c.768.9		288	25.6	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.263087 + 0.0137878i) q^{2} +(-1.61063 - 1.98896i) q^{3} +(-1.92002 - 0.201802i) q^{4} +(-0.396312 - 0.545476i) q^{6} +(-2.51572 + 0.819241i) q^{7} +(-1.02276 - 0.161989i) q^{8} +(-0.738101 + 3.47249i) q^{9} +(-3.43661 + 0.730475i) q^{11} +(2.69106 + 4.14386i) q^{12} +(3.27037 + 1.66634i) q^{13} +(-0.673149 + 0.180846i) q^{14} +(3.50997 + 0.746068i) q^{16} +(-2.11271 - 5.50381i) q^{17} +(-0.242063 + 0.903391i) q^{18} +(0.817063 + 7.77383i) q^{19} +(5.68132 + 3.68417i) q^{21} +(-0.914201 + 0.144795i) q^{22} +(0.334690 - 6.38626i) q^{23} +(1.32509 + 2.29513i) q^{24} +(0.837417 + 0.483483i) q^{26} +(1.25435 - 0.639125i) q^{27} +(4.99555 - 1.06528i) q^{28} +(-0.147381 + 0.202852i) q^{29} +(0.511405 - 1.14863i) q^{31} +(2.91359 + 0.780694i) q^{32} +(6.98798 + 5.65876i) q^{33} +(-0.479943 - 1.47711i) q^{34} +(2.11792 - 6.51830i) q^{36} +(4.12728 - 2.68029i) q^{37} +(0.107775 + 2.05646i) q^{38} +(-1.95307 - 9.18847i) q^{39} +(0.567075 - 0.184254i) q^{41} +(1.44389 + 1.04759i) q^{42} +(5.65218 + 5.65218i) q^{43} +(6.74578 - 0.709010i) q^{44} +(0.176105 - 1.67553i) q^{46} +(-0.980249 - 0.376282i) q^{47} +(-4.16936 - 8.18282i) q^{48} +(5.65769 - 4.12196i) q^{49} +(-7.54405 + 13.0667i) q^{51} +(-5.94290 - 3.85937i) q^{52} +(2.30142 - 1.86365i) q^{53} +(0.338816 - 0.150851i) q^{54} +(2.70568 - 0.430367i) q^{56} +(14.1458 - 14.1458i) q^{57} +(-0.0415708 + 0.0513357i) q^{58} +(-3.73669 + 4.15002i) q^{59} +(2.91370 - 2.62351i) q^{61} +(0.150381 - 0.295140i) q^{62} +(-0.987952 - 9.34049i) q^{63} +(-6.06975 - 1.97218i) q^{64} +(1.76043 + 1.58510i) q^{66} +(1.10691 - 0.424905i) q^{67} +(2.94577 + 10.9938i) q^{68} +(-13.2411 + 9.62020i) q^{69} +(7.13505 + 5.18392i) q^{71} +(1.31741 - 3.43196i) q^{72} +(-4.36627 + 6.72347i) q^{73} +(1.12279 - 0.648243i) q^{74} -15.0908i q^{76} +(8.04712 - 4.65309i) q^{77} +(-0.387139 - 2.44430i) q^{78} +(4.00368 + 8.99240i) q^{79} +(6.43796 + 2.86636i) q^{81} +(0.151731 - 0.0406561i) q^{82} +(-0.951116 + 6.00511i) q^{83} +(-10.1648 - 8.22017i) q^{84} +(1.40908 + 1.56495i) q^{86} +(0.640839 - 0.0335849i) q^{87} +(3.63316 - 0.190406i) q^{88} +(2.57386 + 2.85856i) q^{89} +(-9.59246 - 1.51281i) q^{91} +(-1.93137 + 12.1942i) q^{92} +(-3.10827 + 0.832857i) q^{93} +(-0.252703 - 0.112511i) q^{94} +(-3.13994 - 7.05242i) q^{96} +(1.59410 + 10.0647i) q^{97} +(1.54530 - 1.00643i) q^{98} -12.4728i 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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