LMFDB - Embedded newform 875.2.bb.b.507.18

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			507.18
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.b.768.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.33033 + 1.51333i) q^{2} +(1.23871 + 0.475498i) q^{3} +(2.32679 + 5.22605i) q^{4} +(2.16703 + 2.98265i) q^{6} +(2.14677 - 1.54641i) q^{7} +(-1.61724 + 10.2108i) q^{8} +(-0.921121 - 0.829381i) q^{9} +(-0.0207859 - 0.0230851i) q^{11} +(0.397249 + 7.57996i) q^{12} +(1.24353 - 2.44056i) q^{13} +(7.34292 - 0.354862i) q^{14} +(-11.5654 + 12.8447i) q^{16} +(-3.30746 - 2.67833i) q^{17} +(-0.891386 - 3.32670i) q^{18} +(-2.41099 - 1.07344i) q^{19} +(3.39455 - 0.894773i) q^{21} +(-0.0135026 - 0.0852518i) q^{22} +(1.07668 - 1.65794i) q^{23} +(-6.85853 + 11.8793i) q^{24} +(6.59122 - 3.80544i) q^{26} +(-2.55376 - 5.01203i) q^{27} +(13.0767 + 7.62096i) q^{28} +(-0.472036 + 0.649701i) q^{29} +(-1.14651 + 0.120504i) q^{31} +(-26.4179 + 7.07866i) q^{32} +(-0.0147709 - 0.0384794i) q^{33} +(-3.65427 - 11.2467i) q^{34} +(2.19113 - 6.74362i) q^{36} +(0.469391 - 0.0245997i) q^{37} +(-3.99393 - 6.15012i) q^{38} +(2.70086 - 2.43186i) q^{39} +(3.35339 - 1.08958i) q^{41} +(9.26451 + 3.05197i) q^{42} +(-6.90226 + 6.90226i) q^{43} +(0.0722793 - 0.162342i) q^{44} +(5.01803 - 2.23417i) q^{46} +(2.18830 + 2.70233i) q^{47} +(-20.4339 + 10.4116i) q^{48} +(2.21724 - 6.63957i) q^{49} +(-2.82346 - 4.89037i) q^{51} +(15.6479 + 0.820073i) q^{52} +(-3.78661 + 9.86446i) q^{53} +(1.63378 - 15.5444i) q^{54} +(12.3183 + 24.4212i) q^{56} +(-2.47611 - 2.47611i) q^{57} +(-2.08321 + 0.799671i) q^{58} +(2.31821 + 0.492751i) q^{59} +(-0.182210 - 0.857229i) q^{61} +(-2.85412 - 1.45425i) q^{62} +(-3.26000 - 0.356061i) q^{63} +(-39.3982 - 12.8013i) q^{64} +(0.0238112 - 0.112023i) q^{66} +(6.52995 - 8.06381i) q^{67} +(6.30132 - 23.5169i) q^{68} +(2.12204 - 1.54175i) q^{69} +(-2.26602 - 1.64636i) q^{71} +(9.95835 - 8.06412i) q^{72} +(-0.375203 + 7.15930i) q^{73} +(1.13106 + 0.653020i) q^{74} -15.0976i q^{76} +(-0.0803215 - 0.0174149i) q^{77} +(9.97412 - 1.57974i) q^{78} +(-10.9039 - 1.14605i) q^{79} +(-0.391479 - 3.72467i) q^{81} +(9.46340 + 2.53571i) q^{82} +(14.4760 + 2.29277i) q^{83} +(12.5745 + 15.6581i) q^{84} +(-26.5300 + 5.63912i) q^{86} +(-0.893648 + 0.580342i) q^{87} +(0.269334 - 0.174907i) q^{88} +(4.56856 - 0.971077i) q^{89} +(-1.10454 - 7.16233i) q^{91} +(11.1697 + 1.76910i) q^{92} +(-1.47750 - 0.395896i) q^{93} +(1.00994 + 9.60895i) q^{94} +(-36.0901 - 3.79322i) q^{96} +(-0.258287 + 0.0409086i) q^{97} +(15.2148 - 12.1170i) q^{98} +0.0385036i 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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.33033	+	1.51333i	1.64779	+	1.07009i	0.925676	+	0.378318i	$0.123497\pi$
$2$	2.33033	+	1.51333i	1.64779	+	1.07009i	0.722117	+	0.691771i	$0.243169\pi$
$3$	1.23871	+	0.475498i	0.715172	+	0.274529i	0.688624	−	0.725119i	$-0.258215\pi$
$3$	1.23871	+	0.475498i	0.715172	+	0.274529i	0.0265479	+	0.999648i	$0.491549\pi$
$4$	2.32679	+	5.22605i	1.16339	+	2.61302i
$5$		0			0
$5$		0			0
$6$	2.16703	+	2.98265i	0.884684	+	1.21766i
$7$	2.14677	−	1.54641i	0.811403	−	0.584487i
$7$	2.14677	−	1.54641i	0.811403	−	0.584487i
$8$	−1.61724	+	10.2108i	−0.571780	+	3.61008i
$9$	−0.921121	−	0.829381i	−0.307040	−	0.276460i
$10$		0			0
$11$	−0.0207859	−	0.0230851i	−0.00626718	−	0.00696041i	0.740003	−	0.672603i	$-0.234824\pi$
$11$	−0.0207859	−	0.0230851i	−0.00626718	−	0.00696041i	−0.746270	+	0.665643i	$0.768157\pi$
$12$	0.397249	+	7.57996i	0.114676	+	2.18815i
$13$	1.24353	−	2.44056i	0.344893	−	0.676891i	−0.651779	−	0.758409i	$-0.725977\pi$
$13$	1.24353	−	2.44056i	0.344893	−	0.676891i	0.996672	+	0.0815185i	$0.0259770\pi$
$14$	7.34292	−	0.354862i	1.96248	−	0.0948410i
$15$		0			0
$16$	−11.5654	+	12.8447i	−2.89136	+	3.21118i
$17$	−3.30746	−	2.67833i	−0.802177	−	0.649590i	0.137940	−	0.990441i	$-0.455952\pi$
$17$	−3.30746	−	2.67833i	−0.802177	−	0.649590i	−0.940118	+	0.340850i	$0.889285\pi$
$18$	−0.891386	−	3.32670i	−0.210102	−	0.784110i
$19$	−2.41099	−	1.07344i	−0.553120	−	0.246265i	0.111091	−	0.993810i	$-0.464566\pi$
$19$	−2.41099	−	1.07344i	−0.553120	−	0.246265i	−0.664211	+	0.747545i	$0.731232\pi$
$20$		0			0
$21$	3.39455	−	0.894773i	0.740751	−	0.195256i
$22$	−0.0135026	−	0.0852518i	−0.00287876	−	0.0181758i
$23$	1.07668	−	1.65794i	0.224503	−	0.345704i	−0.708413	−	0.705798i	$-0.750589\pi$
$23$	1.07668	−	1.65794i	0.224503	−	0.345704i	0.932916	+	0.360094i	$0.117255\pi$
$24$	−6.85853	+	11.8793i	−1.39999	+	2.42486i
$25$		0			0
$26$	6.59122	−	3.80544i	1.29265	−	0.746309i
$27$	−2.55376	−	5.01203i	−0.491471	−	0.964566i
$28$	13.0767	+	7.62096i	2.47126	+	1.44023i
$29$	−0.472036	+	0.649701i	−0.0876548	+	0.120646i	−0.850592	−	0.525826i	$-0.823756\pi$
$29$	−0.472036	+	0.649701i	−0.0876548	+	0.120646i	0.762937	+	0.646472i	$0.223756\pi$
$30$		0			0
$31$	−1.14651	+	0.120504i	−0.205920	+	0.0216431i	−0.206927	−	0.978356i	$-0.566346\pi$
$31$	−1.14651	+	0.120504i	−0.205920	+	0.0216431i	0.00100671	+	0.999999i	$0.499680\pi$
$32$	−26.4179	+	7.07866i	−4.67007	+	1.25134i
$33$	−0.0147709	−	0.0384794i	−0.00257128	−	0.00669841i
$34$	−3.65427	−	11.2467i	−0.626702	−	1.92879i
$35$		0			0
$36$	2.19113	−	6.74362i	0.365189	−	1.12394i
$37$	0.469391	−	0.0245997i	0.0771674	−	0.00404417i	−0.0137132	−	0.999906i	$-0.504365\pi$
$37$	0.469391	−	0.0245997i	0.0771674	−	0.00404417i	0.0908806	+	0.995862i	$0.471032\pi$
$38$	−3.99393	−	6.15012i	−0.647902	−	0.997681i
$39$	2.70086	−	2.43186i	0.432484	−	0.389410i
$40$		0			0
$41$	3.35339	−	1.08958i	0.523711	−	0.170164i	−0.0352178	−	0.999380i	$-0.511212\pi$
$41$	3.35339	−	1.08958i	0.523711	−	0.170164i	0.558929	+	0.829216i	$0.311212\pi$
$42$	9.26451	+	3.05197i	1.42954	+	0.470929i
$43$	−6.90226	+	6.90226i	−1.05258	+	1.05258i	−0.0540463	+	0.998538i	$0.517212\pi$
$43$	−6.90226	+	6.90226i	−1.05258	+	1.05258i	−0.998538	+	0.0540463i	$0.982788\pi$
$44$	0.0722793	−	0.162342i	0.0108965	−	0.0244740i
$45$		0			0
$46$	5.01803	−	2.23417i	0.739868	−	0.329410i
$47$	2.18830	+	2.70233i	0.319197	+	0.394175i	0.911338	−	0.411659i	$-0.135051\pi$
$47$	2.18830	+	2.70233i	0.319197	+	0.394175i	−0.592141	+	0.805834i	$0.701717\pi$
$48$	−20.4339	+	10.4116i	−2.94938	+	1.50278i
$49$	2.21724	−	6.63957i	0.316749	−	0.948509i
$50$		0			0
$51$	−2.82346	−	4.89037i	−0.395363	−	0.684789i
$52$	15.6479	+	0.820073i	2.16998	+	0.113724i
$53$	−3.78661	+	9.86446i	−0.520131	+	1.35499i	0.382254	+	0.924057i	$0.375148\pi$
$53$	−3.78661	+	9.86446i	−0.520131	+	1.35499i	−0.902385	+	0.430930i	$0.858185\pi$
$54$	1.63378	−	15.5444i	0.222329	−	2.11532i
$55$		0			0
$56$	12.3183	+	24.4212i	1.64610	+	3.26343i
$57$	−2.47611	−	2.47611i	−0.327969	−	0.327969i
$58$	−2.08321	+	0.799671i	−0.273539	+	0.105002i
$59$	2.31821	+	0.492751i	0.301806	+	0.0641508i	0.356325	−	0.934362i	$-0.384029\pi$
$59$	2.31821	+	0.492751i	0.301806	+	0.0641508i	−0.0545198	+	0.998513i	$0.517363\pi$
$60$		0			0
$61$	−0.182210	−	0.857229i	−0.0233296	−	0.109757i	0.964942	−	0.262463i	$-0.0845347\pi$
$61$	−0.182210	−	0.857229i	−0.0233296	−	0.109757i	−0.988272	+	0.152706i	$0.951201\pi$
$62$	−2.85412	−	1.45425i	−0.362474	−	0.184690i
$63$	−3.26000	−	0.356061i	−0.410721	−	0.0448595i
$64$	−39.3982	−	12.8013i	−4.92478	−	1.60016i
$65$		0			0
$66$	0.0238112	−	0.112023i	0.00293096	−	0.0137891i
$67$	6.52995	−	8.06381i	0.797760	−	0.985152i	−0.202223	−	0.979339i	$-0.564817\pi$
$67$	6.52995	−	8.06381i	0.797760	−	0.985152i	0.999983	−	0.00581217i	$-0.00185008\pi$
$68$	6.30132	−	23.5169i	0.764147	−	2.85184i
$69$	2.12204	−	1.54175i	0.255464	−	0.185605i
$70$		0			0
$71$	−2.26602	−	1.64636i	−0.268927	−	0.195387i	0.445146	−	0.895458i	$-0.353152\pi$
$71$	−2.26602	−	1.64636i	−0.268927	−	0.195387i	−0.714073	+	0.700071i	$0.753152\pi$
$72$	9.95835	−	8.06412i	1.17360	−	0.950365i
$73$	−0.375203	+	7.15930i	−0.0439142	+	0.837933i	0.884535	+	0.466474i	$0.154476\pi$
$73$	−0.375203	+	7.15930i	−0.0439142	+	0.837933i	−0.928449	+	0.371459i	$0.878858\pi$
$74$	1.13106	+	0.653020i	0.131483	+	0.0759120i
$75$		0			0
$76$		−	15.0976i		−	1.73182i
$77$	−0.0803215	−	0.0174149i	−0.00915348	−	0.00198461i
$78$	9.97412	−	1.57974i	1.12935	−	0.178871i
$79$	−10.9039	−	1.14605i	−1.22679	−	0.128941i	−0.531116	−	0.847299i	$-0.678227\pi$
$79$	−10.9039	−	1.14605i	−1.22679	−	0.128941i	−0.695673	+	0.718358i	$0.744894\pi$
$80$		0			0
$81$	−0.391479	−	3.72467i	−0.0434977	−	0.413853i
$82$	9.46340	+	2.53571i	1.04506	+	0.280022i
$83$	14.4760	+	2.29277i	1.58895	+	0.251664i	0.887414	−	0.460974i	$-0.152500\pi$
$83$	14.4760	+	2.29277i	1.58895	+	0.251664i	0.701532	+	0.712638i	$0.252500\pi$
$84$	12.5745	+	15.6581i	1.37199	+	1.70844i
$85$		0			0
$86$	−26.5300	+	5.63912i	−2.86080	+	0.608082i
$87$	−0.893648	+	0.580342i	−0.0958091	+	0.0622192i
$88$	0.269334	−	0.174907i	0.0287111	−	0.0186452i
$89$	4.56856	−	0.971077i	0.484266	−	0.102934i	0.0406923	−	0.999172i	$-0.487044\pi$
$89$	4.56856	−	0.971077i	0.484266	−	0.102934i	0.443574	+	0.896238i	$0.353710\pi$
$90$		0			0
$91$	−1.10454	−	7.16233i	−0.115787	−	0.750816i
$92$	11.1697	+	1.76910i	1.16452	+	0.184441i
$93$	−1.47750	−	0.395896i	−0.153210	−	0.0410525i
$94$	1.00994	+	9.60895i	0.104168	+	0.991088i
$95$		0			0
$96$	−36.0901	−	3.79322i	−3.68343	−	0.387144i
$97$	−0.258287	+	0.0409086i	−0.0262251	+	0.00415364i	−0.169533	−	0.985524i	$-0.554226\pi$
$97$	−0.258287	+	0.0409086i	−0.0262251	+	0.00415364i	0.143308	+	0.989678i	$0.454226\pi$
$98$	15.2148	−	12.1170i	1.53693	−	1.22400i
$99$			0.0385036i			0.00386975i
$100$		0			0
$101$	12.7732	+	7.37464i	1.27099	+	0.733804i	0.975174	−	0.221442i	$-0.0710764\pi$
$101$	12.7732	+	7.37464i	1.27099	+	0.733804i	0.295812	+	0.955246i	$0.404410\pi$
$102$	0.821179	−	15.6690i	0.0813088	−	1.55146i
$103$	−11.2626	+	9.12025i	−1.10973	+	0.898645i	−0.995495	−	0.0948088i	$-0.969776\pi$
$103$	−11.2626	+	9.12025i	−1.10973	+	0.898645i	−0.114238	+	0.993453i	$0.536443\pi$
$104$	22.9091	+	16.6445i	2.24642	+	1.63212i
$105$		0			0
$106$	−23.7523	+	17.2570i	−2.30703	+	1.67615i
$107$	−1.73705	+	6.48278i	−0.167927	+	0.626714i	0.829721	+	0.558178i	$0.188499\pi$
$107$	−1.73705	+	6.48278i	−0.167927	+	0.626714i	−0.997649	+	0.0685357i	$0.978167\pi$
$108$	20.2511	−	25.0080i	1.94866	−	2.40639i
$109$	−0.492676	+	2.31786i	−0.0471898	+	0.222011i	−0.995423	−	0.0955632i	$-0.969535\pi$
$109$	−0.492676	+	2.31786i	−0.0471898	+	0.222011i	0.948234	+	0.317574i	$0.102868\pi$
$110$		0			0
$111$	0.593138	+	0.192722i	0.0562982	+	0.0182924i
$112$	−4.96515	+	45.4595i	−0.469162	+	4.29552i
$113$	4.12905	+	2.10385i	0.388428	+	0.197914i	0.637288	−	0.770625i	$-0.280056\pi$
$113$	4.12905	+	2.10385i	0.388428	+	0.197914i	−0.248860	+	0.968539i	$0.580056\pi$
$114$	−2.02297	−	9.51734i	−0.189469	−	0.891381i
$115$		0			0
$116$	−4.49370	−	0.955164i	−0.417229	−	0.0886848i
$117$	−3.16960	+	1.21669i	−0.293029	+	0.112483i
$118$	4.65651	+	4.65651i	0.428666	+	0.428666i
$119$	−11.2421	−	0.635070i	−1.03057	−	0.0582168i
$120$		0			0
$121$	1.14971	−	10.9388i	0.104519	−	0.994435i
$122$	0.872666	−	2.27337i	0.0790075	−	0.205821i
$123$	4.67198	+	0.244848i	0.421258	+	0.0220772i
$124$	−3.29745	−	5.71136i	−0.296120	−	0.512895i
$125$		0			0
$126$	−7.05803	−	5.76321i	−0.628779	−	0.513427i
$127$	3.12902	−	1.59432i	0.277656	−	0.141473i	−0.309618	−	0.950861i	$-0.600201\pi$
$127$	3.12902	−	1.59432i	0.277656	−	0.141473i	0.587274	+	0.809388i	$0.300201\pi$
$128$	−38.0147	−	46.9442i	−3.36005	−	4.14932i
$129$	−11.8319	+	5.26791i	−1.04174	+	0.463814i
$130$		0			0
$131$	7.81765	−	17.5587i	0.683031	−	1.53411i	−0.154660	−	0.987968i	$-0.549428\pi$
$131$	7.81765	−	17.5587i	0.683031	−	1.53411i	0.837691	−	0.546145i	$-0.183905\pi$
$132$	0.166727	−	0.166727i	0.0145117	−	0.0145117i
$133$	−6.83583	+	1.42395i	−0.592742	+	0.123472i
$134$	27.4202	−	8.90936i	2.36874	−	0.769651i
$135$		0			0
$136$	32.6970	−	29.4405i	2.80374	−	2.52450i
$137$	9.03634	+	13.9147i	0.772027	+	1.18882i	0.977661	+	0.210188i	$0.0674075\pi$
$137$	9.03634	+	13.9147i	0.772027	+	1.18882i	−0.205634	+	0.978629i	$0.565926\pi$
$138$	7.27824	−	0.381436i	0.619565	−	0.0324700i
$139$	1.88349	−	5.79678i	0.159755	−	0.491677i	−0.838856	−	0.544353i	$-0.816775\pi$
$139$	1.88349	−	5.79678i	0.159755	−	0.491677i	0.998612	+	0.0526764i	$0.0167752\pi$
$140$		0			0
$141$	1.42573	+	4.38794i	0.120068	+	0.369532i
$142$	−2.78908	−	7.26580i	−0.234054	−	0.609732i
$143$	−0.0821884	+	0.0220223i	−0.00687294	+	0.00184160i
$144$	21.3063	−	2.23939i	1.77553	−	0.186615i
$145$		0			0
$146$	−11.7088	+	16.1157i	−0.969024	+	1.33375i
$147$	5.90362	−	7.17023i	0.486923	−	0.591390i
$148$	1.22073	+	2.39582i	0.100344	+	0.196935i
$149$	2.64673	−	1.52809i	0.216829	−	0.125186i	−0.387652	−	0.921806i	$-0.626714\pi$
$149$	2.64673	−	1.52809i	0.216829	−	0.125186i	0.604481	+	0.796620i	$0.293381\pi$
$150$		0			0
$151$	−4.01875	+	6.96068i	−0.327041	+	0.566452i	−0.981923	−	0.189279i	$-0.939385\pi$
$151$	−4.01875	+	6.96068i	−0.327041	+	0.566452i	0.654882	+	0.755731i	$0.272718\pi$
$152$	14.8599	−	22.8823i	1.20530	−	1.85600i
$153$	0.825217	+	5.21021i	0.0667148	+	0.421221i
$154$	−0.160821	−	0.162136i	−0.0129593	−	0.0130653i
$155$		0			0
$156$	18.9934	+	8.45639i	1.52069	+	0.677053i
$157$	−0.585981	−	2.18691i	−0.0467664	−	0.174534i	0.938592	−	0.345028i	$-0.112131\pi$
$157$	−0.585981	−	2.18691i	−0.0467664	−	0.174534i	−0.985359	+	0.170493i	$0.945464\pi$
$158$	−23.6754	−	19.1720i	−1.88352	−	1.52524i
$159$	−9.38105	+	10.4187i	−0.743966	+	0.826258i
$160$		0			0
$161$	−0.252471	−	5.22419i	−0.0198975	−	0.411724i
$162$	4.72440	−	9.27216i	0.371184	−	0.728490i
$163$	0.497685	+	9.49640i	0.0389817	+	0.743815i	0.946284	+	0.323337i	$0.104805\pi$
$163$	0.497685	+	9.49640i	0.0389817	+	0.743815i	−0.907302	+	0.420479i	$0.861862\pi$
$164$	13.4968	+	14.9897i	1.05392	+	1.17050i
$165$		0			0
$166$	30.2641	+	27.2499i	2.34895	+	2.11500i
$167$	−1.95260	+	12.3283i	−0.151097	+	0.953989i	0.789324	+	0.613977i	$0.210431\pi$
$167$	−1.95260	+	12.3283i	−0.151097	+	0.953989i	−0.940421	+	0.340012i	$0.889569\pi$
$168$	3.64660	+	36.1082i	0.281341	+	2.78581i
$169$	3.23122	+	4.44740i	0.248556	+	0.342107i
$170$		0			0
$171$	1.33052	+	2.98840i	0.101748	+	0.228529i
$172$	−52.1316	−	20.0115i	−3.97500	−	1.52586i
$173$	−3.13516	−	2.03600i	−0.238362	−	0.154794i	0.419931	−	0.907556i	$-0.362054\pi$
$173$	−3.13516	−	2.03600i	−0.238362	−	0.154794i	−0.658293	+	0.752762i	$0.728721\pi$
$174$	−2.96075			−0.224454
$175$		0			0
$176$	0.536919			0.0404718
$177$	2.63730	+	1.71268i	0.198232	+	0.128733i
$178$	12.1158	+	4.65083i	0.908119	+	0.348594i
$179$	−3.99933	−	8.98264i	−0.298924	−	0.671394i	0.700169	−	0.713977i	$-0.253108\pi$
$179$	−3.99933	−	8.98264i	−0.298924	−	0.671394i	−0.999093	+	0.0425830i	$0.986441\pi$
$180$		0			0
$181$	−7.66282	−	10.5470i	−0.569573	−	0.783950i	0.422931	−	0.906162i	$-0.361001\pi$
$181$	−7.66282	−	10.5470i	−0.569573	−	0.783950i	−0.992504	+	0.122212i	$0.961001\pi$
$182$	8.26507	−	18.3621i	0.612648	−	1.36109i
$183$	0.181905	−	1.14850i	0.0134468	−	0.0848997i
$184$	15.1877	+	13.6751i	1.11965	+	1.00814i
$185$		0			0
$186$	−2.84395	−	3.15852i	−0.208528	−	0.231594i
$187$	0.00691911	+	0.132024i	0.000505975	+	0.00965458i
$188$	−9.03079	+	17.7239i	−0.658638	+	1.29265i
$189$	−13.2330	−	6.81052i	−0.962557	−	0.495393i
$190$		0			0
$191$	6.88905	−	7.65106i	0.498474	−	0.553611i	−0.440432	−	0.897786i	$-0.645175\pi$
$191$	6.88905	−	7.65106i	0.498474	−	0.553611i	0.938906	+	0.344175i	$0.111841\pi$
$192$	−42.7161	−	34.5908i	−3.08277	−	2.49638i
$193$	−4.98675	−	18.6108i	−0.358954	−	1.33963i	−0.875435	−	0.483336i	$-0.839425\pi$
$193$	−4.98675	−	18.6108i	−0.358954	−	1.33963i	0.516481	−	0.856299i	$-0.327242\pi$
$194$	−0.663803	−	0.295544i	−0.0476583	−	0.0212188i
$195$		0			0
$196$	39.8577	−	3.86144i	2.84698	−	0.275817i
$197$	2.80798	+	17.7289i	0.200060	+	1.26313i	0.859407	+	0.511292i	$0.170833\pi$
$197$	2.80798	+	17.7289i	0.200060	+	1.26313i	−0.659347	+	0.751839i	$0.729167\pi$
$198$	−0.0582688	+	0.0897260i	−0.00414098	+	0.00637655i
$199$	3.48571	−	6.03743i	0.247096	−	0.427982i	−0.715623	−	0.698487i	$-0.753857\pi$
$199$	3.48571	−	6.03743i	0.247096	−	0.427982i	0.962719	+	0.270504i	$0.0871904\pi$
$200$		0			0
$201$	11.9231	−	6.88378i	0.840988	−	0.485544i
$202$	18.6056	+	36.5155i	1.30909	+	2.56922i
$203$	−0.00864822	+	2.12472i	−0.000606986	+	0.149126i
$204$	18.9877	−	26.1344i	1.32941	−	1.82977i
$205$		0			0
$206$	−40.0475	+	4.20916i	−2.79024	+	0.293266i
$207$	−2.36681	+	0.634185i	−0.164505	+	0.0440789i
$208$	16.9664	+	44.1990i	1.17641	+	3.06465i
$209$	0.0253341	+	0.0779704i	0.00175240	+	0.00539333i
$210$		0			0
$211$	−4.64578	+	14.2982i	−0.319829	+	0.984332i	0.653892	+	0.756588i	$0.273135\pi$
$211$	−4.64578	+	14.2982i	−0.319829	+	0.984332i	−0.973721	+	0.227744i	$0.926865\pi$
$212$	−60.3628	+	3.16348i	−4.14573	+	0.217269i
$213$	−2.02411	−	3.11685i	−0.138690	−	0.213563i
$214$	−13.8585	+	12.4783i	−0.947349	+	0.852997i
$215$		0			0
$216$	55.3071	−	17.9704i	3.76317	−	1.22273i
$217$	−2.27496	+	2.03167i	−0.154434	+	0.137919i
$218$	−4.65579	+	4.65579i	−0.315330	+	0.315330i
$219$	−3.86900	+	8.68992i	−0.261443	+	0.587210i
$220$		0			0
$221$	−10.6496	+	4.74149i	−0.716367	+	0.318947i
$222$	1.09055	+	1.34672i	0.0731932	+	0.0903861i
$223$	21.1287	−	10.7656i	1.41488	−	0.720919i	0.431441	−	0.902141i	$-0.358005\pi$
$223$	21.1287	−	10.7656i	1.41488	−	0.720919i	0.983442	+	0.181222i	$0.0580052\pi$
$224$	−45.7667	+	56.0491i	−3.05792	+	3.74494i
$225$		0			0
$226$	6.43821	+	11.1513i	0.428263	+	0.741774i
$227$	−27.6051	−	1.44672i	−1.83221	−	0.0960222i	−0.895274	−	0.445516i	$-0.853020\pi$
$227$	−27.6051	−	1.44672i	−1.83221	−	0.0960222i	−0.936939	+	0.349494i	$0.886353\pi$
$228$	7.17889	−	18.7017i	0.475434	−	1.23855i
$229$	1.23146	−	11.7166i	0.0813775	−	0.774255i	−0.875393	−	0.483412i	$-0.839397\pi$
$229$	1.23146	−	11.7166i	0.0813775	−	0.774255i	0.956771	−	0.290843i	$-0.0939359\pi$
$230$		0			0
$231$	−0.0912146	−	0.0597647i	−0.00600148	−	0.00393223i
$232$	−5.87060	−	5.87060i	−0.385424	−	0.385424i
$233$	−18.3944	+	7.06094i	−1.20506	+	0.462578i	−0.876267	−	0.481826i	$-0.839974\pi$
$233$	−18.3944	+	7.06094i	−1.20506	+	0.462578i	−0.328789	+	0.944403i	$0.606640\pi$
$234$	−9.22748	−	1.96136i	−0.603219	−	0.128218i
$235$		0			0
$236$	2.81884	+	13.2616i	0.183491	+	0.863258i
$237$	−12.9619	−	6.60443i	−0.841967	−	0.429004i
$238$	−25.2369	−	18.4931i	−1.63586	−	1.19873i
$239$	−1.79808	−	0.584231i	−0.116308	−	0.0377908i	0.250285	−	0.968172i	$-0.419476\pi$
$239$	−1.79808	−	0.584231i	−0.116308	−	0.0377908i	−0.366593	+	0.930382i	$0.619476\pi$
$240$		0			0
$241$	0.582807	−	2.74189i	0.0375419	−	0.176621i	−0.955382	−	0.295373i	$-0.904556\pi$
$241$	0.582807	−	2.74189i	0.0375419	−	0.176621i	0.992924	+	0.118752i	$0.0378894\pi$
$242$	19.2332	−	23.7511i	1.23636	−	1.52678i
$243$	−3.08153	+	11.5004i	−0.197680	+	0.737753i
$244$	4.05596	−	2.94683i	0.259656	−	0.188651i
$245$		0			0
$246$	10.5167	+	7.64084i	0.670522	+	0.487162i
$247$	−5.61795	+	4.54933i	−0.357462	+	0.289467i
$248$	0.623745	−	11.9018i	0.0396079	−	0.755763i
$249$	16.8414	+	9.72338i	1.06728	+	0.616194i
$250$		0			0
$251$			11.2411i			0.709530i	0.934956	+	0.354765i	$0.115439\pi$
$251$			11.2411i			0.709530i	−0.934956	+	0.354765i	$0.884561\pi$
$252$	−5.72453	−	17.8654i	−0.360611	−	1.12541i
$253$	−0.0606533	+	0.00960654i	−0.00381324	+	0.000603958i
$254$	9.70438	+	1.01997i	0.608907	+	0.0639987i
$255$		0			0
$256$	−8.88413	−	84.5268i	−0.555258	−	5.28293i
$257$	−23.8998	−	6.40393i	−1.49083	−	0.399466i	−0.580812	−	0.814038i	$-0.697265\pi$
$257$	−23.8998	−	6.40393i	−1.49083	−	0.399466i	−0.910017	+	0.414572i	$0.863931\pi$
$258$	−35.5444	−	5.62968i	−2.21290	−	0.350489i
$259$	0.969633	−	0.778680i	0.0602500	−	0.0483848i
$260$		0			0
$261$	0.973652	−	0.206956i	0.0602675	−	0.0128103i
$262$	44.7899	−	29.0869i	2.76713	−	1.79700i
$263$	17.3877	−	11.2917i	1.07217	−	0.696277i	0.117241	−	0.993104i	$-0.462595\pi$
$263$	17.3877	−	11.2917i	1.07217	−	0.696277i	0.954931	+	0.296827i	$0.0959284\pi$
$264$	0.416795	−	0.0885926i	0.0256520	−	0.00545250i
$265$		0			0
$266$	−18.0847	−	7.02664i	−1.10884	−	0.430831i
$267$	6.12088	+	0.969452i	0.374592	+	0.0593295i
$268$	57.3357	+	15.3630i	3.50233	+	0.938447i
$269$	0.884395	+	8.41446i	0.0539225	+	0.513038i	0.987832	+	0.155528i	$0.0497078\pi$
$269$	0.884395	+	8.41446i	0.0539225	+	0.513038i	−0.933909	+	0.357511i	$0.883626\pi$
$270$		0			0
$271$	−16.9599	−	1.78256i	−1.03024	−	0.108283i	−0.425706	−	0.904861i	$-0.639974\pi$
$271$	−16.9599	−	1.78256i	−1.03024	−	0.108283i	−0.604535	+	0.796579i	$0.706641\pi$
$272$	72.6546	−	11.5074i	4.40533	−	0.697736i
$273$	2.03747	−	9.39728i	0.123313	−	0.568749i
$274$			46.1010i			2.78506i
$275$		0			0
$276$	12.9948	+	7.50255i	0.782195	+	0.451601i
$277$	−0.146131	+	2.78835i	−0.00878018	+	0.167536i	0.990720	+	0.135919i	$0.0433988\pi$
$277$	−0.146131	+	2.78835i	−0.00878018	+	0.167536i	−0.999500	+	0.0316164i	$0.989934\pi$
$278$	13.1616	−	10.6581i	0.789382	−	0.639229i
$279$	1.15602	+	0.839900i	0.0692093	+	0.0502835i
$280$		0			0
$281$	4.73304	−	3.43875i	0.282349	−	0.205139i	−0.437592	−	0.899174i	$-0.644169\pi$
$281$	4.73304	−	3.43875i	0.282349	−	0.205139i	0.719941	+	0.694035i	$0.244169\pi$
$282$	−3.31801	+	12.3830i	−0.197584	+	0.737395i
$283$	−10.2523	+	12.6606i	−0.609438	+	0.752593i	−0.984687	−	0.174331i	$-0.944224\pi$
$283$	−10.2523	+	12.6606i	−0.609438	+	0.752593i	0.375249	+	0.926924i	$0.377557\pi$
$284$	3.33141	−	15.6730i	0.197683	−	0.930024i
$285$		0			0
$286$	−0.224853	−	0.0730593i	−0.0132959	−	0.00432009i
$287$	5.51401	−	7.52479i	0.325482	−	0.444174i
$288$	30.2050	+	15.3902i	1.77985	+	0.906877i
$289$	0.231353	+	1.08843i	0.0136090	+	0.0640254i
$290$		0			0
$291$	−0.339396	−	0.0721408i	−0.0198957	−	0.00422897i
$292$	−38.2879	+	14.6973i	−2.24063	+	0.860097i
$293$	−19.7336	−	19.7336i	−1.15285	−	1.15285i	−0.985979	−	0.166868i	$-0.946635\pi$
$293$	−19.7336	−	19.7336i	−1.15285	−	1.15285i	−0.166868	−	0.985979i	$-0.553365\pi$
$294$	24.6083	−	7.77484i	1.43519	−	0.453438i
$295$		0			0
$296$	−0.507933	+	4.83266i	−0.0295230	+	0.280893i
$297$	−0.0626209	+	0.163133i	−0.00363364	+	0.00946595i
$298$	8.48027	+	0.444432i	0.491249	+	0.0257453i
$299$	−2.70742	−	4.68939i	−0.156574	−	0.271195i
$300$		0			0
$301$	−4.14385	+	25.4913i	−0.238848	+	1.46929i
$302$	−19.8989	+	10.1390i	−1.14505	+	0.583432i
$303$	12.3158	+	15.2087i	0.707523	+	0.873718i
$304$	41.6723	−	18.5537i	2.39007	−	1.06413i
$305$		0			0
$306$	−5.96177	+	13.3903i	−0.340811	+	0.765475i
$307$	13.1692	−	13.1692i	0.751604	−	0.751604i	−0.223174	−	0.974779i	$-0.571642\pi$
$307$	13.1692	−	13.1692i	0.751604	−	0.751604i	0.974779	+	0.223174i	$0.0716419\pi$
$308$	−0.0958800	−	0.460284i	−0.00546327	−	0.0262271i
$309$	−18.2877	+	5.94205i	−1.04035	+	0.338031i
$310$		0			0
$311$	8.16224	−	7.34931i	0.462838	−	0.416741i	−0.404440	−	0.914564i	$-0.632534\pi$
$311$	8.16224	−	7.34931i	0.462838	−	0.416741i	0.867279	+	0.497823i	$0.165867\pi$
$312$	20.4634	+	31.5109i	1.15851	+	1.78396i
$313$	−18.8243	+	0.986542i	−1.06401	+	0.0557626i	−0.576298	−	0.817239i	$-0.695503\pi$
$313$	−18.8243	+	0.986542i	−1.06401	+	0.0557626i	−0.487716	+	0.873002i	$0.662170\pi$
$314$	1.94400	−	5.98301i	0.109706	−	0.337641i
$315$		0			0
$316$	−19.3818	−	59.6511i	−1.09031	−	3.35564i
$317$	4.77313	+	12.4344i	0.268086	+	0.698387i	0.999858	+	0.0168381i	$0.00535998\pi$
$317$	4.77313	+	12.4344i	0.268086	+	0.698387i	−0.731773	+	0.681549i	$0.761307\pi$
$318$	−37.6279	+	10.0824i	−2.11007	+	0.565392i
$319$	0.0248101	−	0.00260764i	0.00138910	−	0.000146000i
$320$		0			0
$321$	−5.23426	+	7.20434i	−0.292148	+	0.402107i
$322$	7.31761	−	12.5562i	0.407794	−	0.699728i
$323$	5.09923	+	10.0078i	0.283729	+	0.556849i
$324$	18.5544	−	10.7124i	1.03080	−	0.595134i
$325$		0			0
$326$	−13.2115	+	22.8829i	−0.731715	+	1.26737i
$327$	−1.71242	+	2.63690i	−0.0946971	+	0.145821i
$328$	5.70232	+	36.0030i	0.314858	+	1.98793i
$329$	8.87669	+	2.41727i	0.489388	+	0.133268i
$330$		0			0
$331$	5.57228	+	2.48094i	0.306280	+	0.136365i	0.554121	−	0.832436i	$-0.313054\pi$
$331$	5.57228	+	2.48094i	0.306280	+	0.136365i	−0.247841	+	0.968801i	$0.579721\pi$
$332$	21.7004	+	80.9870i	1.19096	+	4.44474i
$333$	−0.452768	−	0.366645i	−0.0248116	−	0.0200920i
$334$	−23.2070	+	25.7740i	−1.26983	+	1.41029i
$335$		0			0
$336$	−27.7663	+	53.9504i	−1.51478	+	2.94324i
$337$	−3.05339	+	5.99261i	−0.166329	+	0.326438i	−0.959094	−	0.283089i	$-0.908641\pi$
$337$	−3.05339	+	5.99261i	−0.166329	+	0.326438i	0.792765	+	0.609527i	$0.208641\pi$
$338$	0.799419	+	15.2538i	0.0434827	+	0.829699i
$339$	4.11433	+	4.56942i	0.223460	+	0.248177i
$340$		0			0
$341$	0.0266132	+	0.0239626i	0.00144118	+	0.00129765i
$342$	−1.42190	+	8.97750i	−0.0768873	+	0.485448i
$343$	−5.50757	−	17.6824i	−0.297381	−	0.954759i
$344$	−59.3153	−	81.6405i	−3.19807	−	4.40176i
$345$		0			0
$346$	−4.22481	−	9.48909i	−0.227127	−	0.510137i
$347$	16.1508	+	6.19970i	0.867019	+	0.332817i	0.750898	−	0.660418i	$-0.229621\pi$
$347$	16.1508	+	6.19970i	0.867019	+	0.332817i	0.116120	+	0.993235i	$0.462954\pi$
$348$	−5.11222	−	3.31992i	−0.274044	−	0.177966i
$349$	35.3960			1.89470			0.947351	−	0.320196i	$-0.103749\pi$
$349$	35.3960			1.89470			0.947351	+	0.320196i	$0.103749\pi$
$350$		0			0
$351$	−15.4079			−0.822410
$352$	0.712531	+	0.462723i	0.0379780	+	0.0246632i
$353$	22.6287	+	8.68634i	1.20440	+	0.462327i	0.876047	−	0.482226i	$-0.160172\pi$
$353$	22.6287	+	8.68634i	1.20440	+	0.462327i	0.328357	+	0.944554i	$0.393505\pi$
$354$	3.55392	+	7.98223i	0.188889	+	0.424251i
$355$		0			0
$356$	15.7050	+	21.6160i	0.832361	+	1.14565i
$357$	−13.6238	−	6.13229i	−0.721049	−	0.324555i
$358$	4.27398	−	26.9849i	0.225887	−	1.42619i
$359$	12.1908	+	10.9767i	0.643406	+	0.579326i	0.924887	−	0.380241i	$-0.124159\pi$
$359$	12.1908	+	10.9767i	0.643406	+	0.579326i	−0.281481	+	0.959567i	$0.590826\pi$
$360$		0			0
$361$	−8.05287	−	8.94362i	−0.423835	−	0.470717i
$362$	−1.89582	−	36.1743i	−0.0996419	−	1.90128i
$363$	6.62553	−	13.0033i	0.347750	−	0.682498i
$364$	34.8607	−	22.4376i	1.82720	−	1.17605i
$365$		0			0
$366$	2.16197	−	2.40111i	0.113008	−	0.125508i
$367$	−6.64193	−	5.37853i	−0.346706	−	0.280757i	0.440111	−	0.897943i	$-0.354939\pi$
$367$	−6.64193	−	5.37853i	−0.346706	−	0.280757i	−0.786817	+	0.617186i	$0.788272\pi$
$368$	8.84350	+	33.0044i	0.460999	+	1.72047i
$369$	−3.99255	−	1.77760i	−0.207844	−	0.0925381i
$370$		0			0
$371$	7.12550	+	27.0324i	0.369938	+	1.40345i
$372$	−1.36886	−	8.64267i	−0.0709723	−	0.448101i
$373$	13.1589	−	20.2629i	0.681341	−	1.04917i	−0.313682	−	0.949528i	$-0.601563\pi$
$373$	13.1589	−	20.2629i	0.681341	−	1.04917i	0.995023	−	0.0996450i	$-0.0317707\pi$
$374$	−0.183673	+	0.318131i	−0.00949752	+	0.0164502i
$375$		0			0
$376$	−31.1321	+	17.9741i	−1.60551	+	0.926944i
$377$	0.998647	+	1.95996i	0.0514329	+	0.100943i
$378$	−20.5306	−	35.8967i	−1.05598	−	1.84633i
$379$	−7.62907	+	10.5005i	−0.391879	+	0.539375i	−0.958683	−	0.284478i	$-0.908180\pi$
$379$	−7.62907	+	10.5005i	−0.391879	+	0.539375i	0.566804	+	0.823853i	$0.308180\pi$
$380$		0			0
$381$	4.63405	−	0.487059i	0.237410	−	0.0249528i
$382$	27.6324	−	7.40407i	1.41379	−	0.378825i
$383$	−0.809370	−	2.10848i	−0.0413569	−	0.107738i	0.911347	−	0.411640i	$-0.135044\pi$
$383$	−0.809370	−	2.10848i	−0.0413569	−	0.107738i	−0.952703	+	0.303902i	$0.901711\pi$
$384$	−24.7674	−	76.2263i	−1.26391	−	3.88991i
$385$		0			0
$386$	16.5436	−	50.9159i	0.842046	−	2.59155i
$387$	12.0824	−	0.633213i	0.614184	−	0.0321880i
$388$	−0.814769	−	1.25463i	−0.0413636	−	0.0636944i
$389$	20.5361	−	18.4908i	1.04122	−	0.937519i	0.0431167	−	0.999070i	$-0.486271\pi$
$389$	20.5361	−	18.4908i	1.04122	−	0.937519i	0.998104	+	0.0615507i	$0.0196046\pi$
$390$		0			0
$391$	−8.00157	+	2.59987i	−0.404657	+	0.131481i
$392$	64.2098	+	33.3777i	3.24308	+	1.68583i
$393$	18.0330	−	18.0330i	0.909642	−	0.909642i
$394$	−20.2862	+	45.5636i	−1.02200	+	2.29546i
$395$		0			0
$396$	−0.201221	+	0.0895896i	−0.0101118	+	0.00450205i
$397$	−22.4158	−	27.6813i	−1.12502	−	1.38928i	−0.910976	−	0.412459i	$-0.864670\pi$
$397$	−22.4158	−	27.6813i	−1.12502	−	1.38928i	−0.214043	−	0.976824i	$-0.568663\pi$
$398$	17.2595	−	8.79417i	0.865142	−	0.440812i
$399$	−9.14472	−	1.48656i	−0.457809	−	0.0744212i
$400$		0			0
$401$	−18.5807	−	32.1828i	−0.927877	−	1.60713i	−0.786867	−	0.617123i	$-0.788298\pi$
$401$	−18.5807	−	32.1828i	−0.927877	−	1.60713i	−0.141010	−	0.990008i	$-0.545035\pi$
$402$	38.2021	+	2.00209i	1.90535	+	0.0998551i
$403$	−1.13163	+	2.94799i	−0.0563704	+	0.146850i
$404$	−8.81959	+	83.9128i	−0.438791	+	4.17482i
$405$		0			0
$406$	−3.23556	+	4.93821i	−0.160578	+	0.245079i
$407$	−0.0103246	−	0.0103246i	−0.000511771	−	0.000511771i
$408$	54.5010	−	20.9210i	2.69820	−	1.03574i
$409$	17.2690	+	3.67064i	0.853897	+	0.181501i	0.614009	−	0.789299i	$-0.289556\pi$
$409$	17.2690	+	3.67064i	0.853897	+	0.181501i	0.239888	+	0.970801i	$0.422889\pi$
$410$		0			0
$411$	4.57701	+	21.5331i	0.225767	+	1.06215i
$412$	−73.8684	−	37.6378i	−3.63924	−	1.85428i
$413$	5.73867	−	2.52708i	0.282381	−	0.124350i
$414$	−6.47519	−	2.10392i	−0.318238	−	0.103402i
$415$		0			0
$416$	−15.5755	+	73.2771i	−0.763653	+	3.59271i
$417$	5.08946	−	6.28496i	0.249232	−	0.307776i
$418$	−0.0589584	+	0.220036i	−0.00288375	+	0.0107623i
$419$	−19.8377	+	14.4129i	−0.969134	+	0.704117i	−0.955254	−	0.295787i	$-0.904418\pi$
$419$	−19.8377	+	14.4129i	−0.969134	+	0.704117i	−0.0138799	+	0.999904i	$0.504418\pi$
$420$		0			0
$421$	−14.7221	−	10.6962i	−0.717512	−	0.521303i	0.168077	−	0.985774i	$-0.446244\pi$
$421$	−14.7221	−	10.6962i	−0.717512	−	0.521303i	−0.885588	+	0.464471i	$0.846244\pi$
$422$	−32.4642	+	26.2890i	−1.58033	+	1.27973i
$423$	0.225569	−	4.30411i	0.0109675	−	0.209273i
$424$	−94.6006	−	54.6177i	−4.59421	−	2.65247i
$425$		0			0
$426$		−	10.3264i		−	0.500318i
$427$	−1.71679	−	1.55850i	−0.0830813	−	0.0754213i
$428$	−37.9211	+	6.00611i	−1.83298	+	0.290316i
$429$	−0.112279	−	0.0118010i	−0.00542090	−	0.000569760i
$430$		0			0
$431$	1.15577	+	10.9964i	0.0556714	+	0.529678i	0.986446	+	0.164085i	$0.0524671\pi$
$431$	1.15577	+	10.9964i	0.0556714	+	0.529678i	−0.930775	+	0.365593i	$0.880866\pi$
$432$	93.9134	+	25.1640i	4.51841	+	1.21070i
$433$	−37.9980	−	6.01829i	−1.82607	−	0.289221i	−0.853371	−	0.521304i	$-0.825446\pi$
$433$	−37.9980	−	6.01829i	−1.82607	−	0.289221i	−0.972696	+	0.232084i	$0.925446\pi$
$434$	−8.37600	+	1.29170i	−0.402061	+	0.0620037i
$435$		0			0
$436$	−13.2596	+	2.81841i	−0.635019	+	0.134977i
$437$	−4.37556	+	2.84153i	−0.209312	+	0.135929i
$438$	−22.1668	+	14.3953i	−1.05917	+	0.687834i
$439$	−24.7221	+	5.25484i	−1.17992	+	0.250800i	−0.755798	−	0.654805i	$-0.772751\pi$
$439$	−24.7221	+	5.25484i	−1.17992	+	0.250800i	−0.424123	+	0.905605i	$0.639417\pi$
$440$		0			0
$441$	−7.54908	+	4.27691i	−0.359480	+	0.203662i
$442$	−31.9924	−	5.06711i	−1.52173	−	0.241018i
$443$	−7.33193	−	1.96458i	−0.348351	−	0.0933402i	0.0804012	−	0.996763i	$-0.474380\pi$
$443$	−7.33193	−	1.96458i	−0.348351	−	0.0933402i	−0.428752	+	0.903422i	$0.641047\pi$
$444$	0.372930	+	3.54819i	0.0176985	+	0.168390i
$445$		0			0
$446$	65.5289	+	6.88736i	3.10288	+	0.326126i
$447$	4.00514	−	0.634352i	0.189437	−	0.0300038i
$448$	−104.375	+	33.4444i	−4.93125	+	1.58010i
$449$			2.62419i			0.123843i	0.998081	+	0.0619217i	$0.0197229\pi$
$449$			2.62419i			0.123843i	−0.998081	+	0.0619217i	$0.980277\pi$
$450$		0			0
$451$	−0.0948562	−	0.0547652i	−0.00446660	−	0.00257879i
$452$	−1.38743	+	26.4738i	−0.0652594	+	1.24522i
$453$	−8.28787	+	6.71138i	−0.389398	+	0.315328i
$454$	−62.1395	−	45.1470i	−2.91635	−	2.11885i
$455$		0			0
$456$	29.2876	−	21.2787i	1.37152	−	0.996467i
$457$	−7.30752	+	27.2720i	−0.341831	+	1.27573i	0.554440	+	0.832224i	$0.312933\pi$
$457$	−7.30752	+	27.2720i	−0.341831	+	1.27573i	−0.896271	+	0.443507i	$0.853734\pi$
$458$	20.6009	−	25.4399i	0.962615	−	1.18873i
$459$	−4.97742	+	23.4169i	−0.232326	+	1.09301i
$460$		0			0
$461$	20.6080	+	6.69595i	0.959811	+	0.311861i	0.746696	−	0.665166i	$-0.231639\pi$
$461$	20.6080	+	6.69595i	0.959811	+	0.311861i	0.213115	+	0.977027i	$0.431639\pi$
$462$	−0.122116	−	0.277310i	−0.00568136	−	0.0129016i
$463$	2.68099	+	1.36603i	0.124596	+	0.0634850i	0.515178	−	0.857083i	$-0.327726\pi$
$463$	2.68099	+	1.36603i	0.124596	+	0.0634850i	−0.390581	+	0.920568i	$0.627726\pi$
$464$	−2.88593	−	13.5772i	−0.133976	−	0.630307i
$465$		0			0
$466$	−53.5506	−	11.3825i	−2.48068	−	0.527285i
$467$	−29.7707	+	11.4279i	−1.37762	+	0.528820i	−0.930710	−	0.365758i	$-0.880810\pi$
$467$	−29.7707	+	11.4279i	−1.37762	+	0.528820i	−0.446913	+	0.894578i	$0.647477\pi$
$468$	−13.7335	−	13.7335i	−0.634831	−	0.634831i
$469$	1.54834	−	27.4091i	0.0714959	−	1.26564i
$470$		0			0
$471$	0.314008	−	2.98759i	0.0144687	−	0.137661i
$472$	−8.78051	+	22.8740i	−0.404156	+	1.05286i
$473$	0.302809	+	0.0158695i	0.0139232	+	0.000729682i
$474$	−20.2108	−	35.0062i	−0.928315	−	1.60789i
$475$		0			0
$476$	−22.8392	−	60.2297i	−1.04683	−	2.76062i
$477$	11.6693	−	5.94582i	0.534302	−	0.272240i
$478$	−3.30598	−	4.08255i	−0.151212	−	0.186731i
$479$	−3.96929	+	1.76724i	−0.181362	+	0.0807474i	−0.495409	−	0.868660i	$-0.664982\pi$
$479$	−3.96929	+	1.76724i	−0.181362	+	0.0807474i	0.314047	+	0.949407i	$0.398315\pi$
$480$		0			0
$481$	0.523664	−	1.17617i	0.0238770	−	0.0536287i
$482$	5.50753	−	5.50753i	0.250861	−	0.250861i
$483$	2.17135	−	6.59133i	0.0988000	−	0.299916i
$484$	59.8417	−	19.4438i	2.72008	−	0.883807i
$485$		0			0
$486$	−24.5850	+	22.1364i	−1.11520	+	1.00413i
$487$	7.75579	+	11.9429i	0.351448	+	0.541183i	0.969543	−	0.244921i	$-0.0787619\pi$
$487$	7.75579	+	11.9429i	0.351448	+	0.541183i	−0.618095	+	0.786104i	$0.712095\pi$
$488$	9.04771	−	0.474170i	0.409571	−	0.0214647i
$489$	−3.89903	+	12.0000i	−0.176320	+	0.542657i
$490$		0			0
$491$	6.63863	+	20.4316i	0.299597	+	0.922065i	0.981638	+	0.190751i	$0.0610924\pi$
$491$	6.63863	+	20.4316i	0.299597	+	0.922065i	−0.682041	+	0.731314i	$0.738908\pi$
$492$	9.59111	+	24.9857i	0.432401	+	1.12644i
$493$	3.30135	−	0.884595i	0.148685	−	0.0398402i
$494$	−19.9763	+	2.09960i	−0.898778	+	0.0944653i
$495$		0			0
$496$	11.7121	−	16.1203i	0.525889	−	0.723824i
$497$	−7.41056	−	0.0301631i	−0.332409	−	0.00135300i
$498$	24.5313	+	48.1453i	1.09927	+	2.15744i
$499$	−4.04729	+	2.33670i	−0.181182	+	0.104605i	−0.587848	−	0.808972i	$-0.700025\pi$
$499$	−4.04729	+	2.33670i	−0.181182	+	0.104605i	0.406666	+	0.913577i	$0.366691\pi$
$500$		0			0
$501$	−8.28078	+	14.3427i	−0.369958	+	0.640786i
$502$	−17.0115	+	26.1954i	−0.759260	+	1.16916i
$503$	0.677889	+	4.28002i	0.0302256	+	0.190837i	0.998181	−	0.0602844i	$-0.0192007\pi$
$503$	0.677889	+	4.28002i	0.0302256	+	0.190837i	−0.967956	+	0.251121i	$0.919201\pi$
$504$	8.90788	−	32.7115i	0.396788	−	1.45709i
$505$		0			0
$506$	−0.155880	−	0.0694023i	−0.00692972	−	0.00308531i
$507$	1.88783	+	7.04549i	0.0838416	+	0.312901i
$508$	15.6125	+	12.6428i	0.692694	+	0.560933i
$509$	14.7448	−	16.3758i	0.653553	−	0.725844i	−0.321723	−	0.946834i	$-0.604262\pi$
$509$	14.7448	−	16.3758i	0.653553	−	0.725844i	0.975276	+	0.220990i	$0.0709287\pi$
$510$		0			0
$511$	10.2657	+	15.9496i	0.454129	+	0.705568i
$512$	52.3670	−	102.776i	2.31432	−	4.54210i
$513$	0.776961	+	14.8253i	0.0343036	+	0.654553i
$514$	−46.0031	−	51.0917i	−2.02911	−	2.25356i
$515$		0			0
$516$	−55.0608	−	49.5769i	−2.42391	−	2.18250i
$517$	0.0168976	−	0.106687i	0.000743157	−	0.00469211i
$518$	3.43797	−	0.347203i	0.151056	−	0.0152552i
$519$	−2.91545	−	4.01278i	−0.127974	−	0.176141i
$520$		0			0
$521$	−13.2533	−	29.7675i	−0.580639	−	1.30414i	−0.930142	−	0.367201i	$-0.880316\pi$
$521$	−13.2533	−	29.7675i	−0.580639	−	1.30414i	0.349503	−	0.936935i	$-0.386350\pi$
$522$	2.58212	+	0.991185i	0.113017	+	0.0433830i
$523$	−23.5603	−	15.3003i	−1.03022	−	0.669033i	−0.0853081	−	0.996355i	$-0.527187\pi$
$523$	−23.5603	−	15.3003i	−1.03022	−	0.669033i	−0.944913	+	0.327321i	$0.893854\pi$
$524$	109.953			4.80331
$525$		0			0
$526$	57.6072			2.51180
$527$	4.11480	+	2.67218i	0.179244	+	0.116402i
$528$	0.665089	+	0.255304i	0.0289443	+	0.0111107i
$529$	7.76542	+	17.4414i	0.337627	+	0.758323i
$530$		0			0
$531$	−1.72668	−	2.37657i	−0.0749314	−	0.103134i
$532$	−23.3471	−	32.4112i	−1.01223	−	1.40520i
$533$	1.51084	−	9.53908i	0.0654418	−	0.413183i
$534$	12.7966	+	11.5221i	0.553762	+	0.498609i
$535$		0			0
$536$	71.7779	+	79.7174i	3.10033	+	3.44327i
$537$	−0.682800	−	13.0286i	−0.0294650	−	0.562225i
$538$	−10.6730	+	20.9468i	−0.460144	+	0.903083i
$539$	−0.199362	+	0.0868241i	−0.00858714	+	0.00373978i
$540$		0			0
$541$	−3.69792	+	4.10696i	−0.158986	+	0.176572i	−0.817375	−	0.576106i	$-0.804572\pi$
$541$	−3.69792	+	4.10696i	−0.158986	+	0.176572i	0.658389	+	0.752678i	$0.271238\pi$
$542$	−36.8246	−	29.8200i	−1.58175	−	1.28088i
$543$	−4.47698	−	16.7083i	−0.192126	−	0.717023i
$544$	106.335	+	47.3435i	4.55908	+	2.02984i
$545$		0			0
$546$	18.9692	−	18.8154i	0.811807	−	0.805225i
$547$	2.49899	+	15.7780i	0.106849	+	0.674619i	0.981730	+	0.190280i	$0.0609397\pi$
$547$	2.49899	+	15.7780i	0.106849	+	0.674619i	−0.874881	+	0.484339i	$0.839060\pi$
$548$	−51.6935	+	79.6010i	−2.20824	+	3.40039i
$549$	−0.543133	+	0.940733i	−0.0231803	+	0.0401495i
$550$		0			0
$551$	1.83549	−	1.05972i	0.0781946	−	0.0451457i
$552$	12.3107	+	24.1612i	0.523980	+	1.02837i
$553$	−25.1805	+	14.4016i	−1.07078	+	0.612420i
$554$	−4.56025	+	6.27664i	−0.193746	+	0.266669i
$555$		0			0
$556$	34.6767	−	3.64467i	1.47062	−	0.154569i
$557$	−20.7131	+	5.55006i	−0.877642	+	0.235163i	−0.669389	−	0.742912i	$-0.733444\pi$
$557$	−20.7131	+	5.55006i	−0.877642	+	0.235163i	−0.208252	+	0.978075i	$0.566778\pi$
$558$	1.42287	+	3.70669i	0.0602347	+	0.156917i
$559$	8.26224	+	25.4286i	0.349456	+	1.07551i
$560$		0			0
$561$	−0.0542065	+	0.166830i	−0.00228860	+	0.00704359i
$562$	16.2335	−	0.850763i	0.684770	−	0.0358873i
$563$	8.52318	+	13.1246i	0.359209	+	0.553134i	0.971362	−	0.237606i	$-0.0763627\pi$
$563$	8.52318	+	13.1246i	0.359209	+	0.553134i	−0.612152	+	0.790740i	$0.709696\pi$
$564$	−19.6142	+	17.6607i	−0.825908	+	0.743651i
$565$		0			0
$566$	−43.0510	+	13.9881i	−1.80957	+	0.587965i
$567$	−6.60028	−	7.39063i	−0.277186	−	0.310377i
$568$	20.4754	−	20.4754i	0.859128	−	0.859128i
$569$	−9.04485	+	20.3151i	−0.379180	+	0.851652i	0.618641	+	0.785674i	$0.287684\pi$
$569$	−9.04485	+	20.3151i	−0.379180	+	0.851652i	−0.997821	+	0.0659784i	$0.978983\pi$
$570$		0			0
$571$	18.8261	−	8.38193i	0.787849	−	0.350773i	0.0269446	−	0.999637i	$-0.491422\pi$
$571$	18.8261	−	8.38193i	0.787849	−	0.350773i	0.760904	+	0.648864i	$0.224756\pi$
$572$	−0.306325	−	0.378279i	−0.0128081	−	0.0158167i
$573$	12.1716	−	6.20175i	0.508477	−	0.259082i
$574$	24.2370	−	9.19070i	1.01163	−	0.383612i
$575$		0			0
$576$	25.6734	+	44.4677i	1.06973	+	1.85282i
$577$	13.6794	+	0.716908i	0.569482	+	0.0298453i	0.334904	−	0.942252i	$-0.391296\pi$
$577$	13.6794	+	0.716908i	0.569482	+	0.0298453i	0.234578	+	0.972097i	$0.424629\pi$
$578$	−1.10803	+	2.88652i	−0.0460881	+	0.120063i
$579$	2.67224	−	25.4246i	0.111054	−	1.05661i
$580$		0			0
$581$	34.6222	−	17.4637i	1.43637	−	0.724518i
$582$	−0.681731	−	0.681731i	−0.0282587	−	0.0282587i
$583$	0.306430	−	0.117627i	0.0126910	−	0.00487163i
$584$	−72.4957	−	15.4094i	−2.99989	−	0.637647i
$585$		0			0
$586$	−16.1222	−	75.8492i	−0.666004	−	3.13330i
$587$	3.31302	+	1.68807i	0.136743	+	0.0696741i	0.521023	−	0.853542i	$-0.325550\pi$
$587$	3.31302	+	1.68807i	0.136743	+	0.0696741i	−0.384280	+	0.923216i	$0.625550\pi$
$588$	51.2084	+	14.1690i	2.11180	+	0.584321i
$589$	2.89359	+	0.940186i	0.119228	+	0.0387397i
$590$		0			0
$591$	−4.95176	+	23.2962i	−0.203688	+	0.958277i
$592$	−5.11273	+	6.31370i	−0.210132	+	0.259491i
$593$	−0.804417	+	3.00212i	−0.0330334	+	0.123282i	−0.980474	−	0.196650i	$-0.936994\pi$
$593$	−0.804417	+	3.00212i	−0.0330334	+	0.123282i	0.947440	+	0.319933i	$0.103660\pi$
$594$	−0.392803	+	0.285388i	−0.0161169	+	0.0117096i
$595$		0			0
$596$	14.1442	+	10.2764i	0.579371	+	0.420938i
$597$	7.18859	−	5.82120i	0.294209	−	0.238246i
$598$	0.787431	−	15.0251i	0.0322004	−	0.614421i
$599$	3.72331	+	2.14965i	0.152130	+	0.0878325i	0.574133	−	0.818762i	$-0.305339\pi$
$599$	3.72331	+	2.14965i	0.152130	+	0.0878325i	−0.422002	+	0.906595i	$0.638673\pi$
$600$		0			0
$601$		−	24.6722i		−	1.00640i	−0.864169	−	0.503201i	$-0.832156\pi$
$601$		−	24.6722i		−	1.00640i	0.864169	−	0.503201i	$-0.167844\pi$
$602$	−48.2334	+	53.1321i	−1.96585	+	2.16550i
$603$	−12.7028	+	2.01193i	−0.517300	+	0.0819323i
$604$	−45.7276	−	4.80617i	−1.86063	−	0.195560i
$605$		0			0
$606$	5.68395	+	54.0792i	0.230895	+	2.19682i
$607$	21.6785	+	5.80874i	0.879904	+	0.235769i	0.670366	−	0.742031i	$-0.266137\pi$
$607$	21.6785	+	5.80874i	0.879904	+	0.235769i	0.209538	+	0.977800i	$0.432804\pi$
$608$	71.2920	+	11.2915i	2.89127	+	0.457932i
$609$	−1.02101	+	2.62781i	−0.0413735	+	0.106484i
$610$		0			0
$611$	9.31642	−	1.98027i	0.376902	−	0.0801130i
$612$	−25.3087	+	16.4357i	−1.02304	+	0.664373i
$613$	41.3408	−	26.8470i	1.66974	−	1.08434i	0.783076	−	0.621925i	$-0.213649\pi$
$613$	41.3408	−	26.8470i	1.66974	−	1.08434i	0.886663	−	0.462416i	$-0.153017\pi$
$614$	50.6179	−	10.7592i	2.04277	−	0.434204i
$615$		0			0
$616$	0.307719	−	0.791986i	0.0123984	−	0.0319100i
$617$	27.0684	+	4.28721i	1.08973	+	0.172597i	0.675344	−	0.737503i	$-0.263995\pi$
$617$	27.0684	+	4.28721i	1.08973	+	0.172597i	0.414389	+	0.910100i	$0.363995\pi$
$618$	−51.6088	−	13.8285i	−2.07601	−	0.556265i
$619$	1.40408	+	13.3589i	0.0564348	+	0.536941i	0.985817	+	0.167823i	$0.0536736\pi$
$619$	1.40408	+	13.3589i	0.0564348	+	0.536941i	−0.929382	+	0.369118i	$0.879660\pi$
$620$		0			0
$621$	−11.0592	−	1.16237i	−0.443791	−	0.0466443i
$622$	30.1427	−	4.77413i	1.20861	−	0.191425i
$623$	8.30596	−	9.14954i	0.332771	−	0.366568i
$624$			62.8173i			2.51471i
$625$		0			0
$626$	−45.3599	−	26.1886i	−1.81295	−	1.04671i
$627$	−0.00569302	+	0.108629i	−0.000227357	+	0.00433824i
$628$	10.0654	−	8.15084i	0.401655	−	0.325254i
$629$	−1.61838	−	1.17582i	−0.0645290	−	0.0468830i
$630$		0			0
$631$	−5.43708	+	3.95027i	−0.216447	+	0.157258i	−0.690726	−	0.723117i	$-0.742709\pi$
$631$	−5.43708	+	3.95027i	−0.216447	+	0.157258i	0.474279	+	0.880375i	$0.342709\pi$
$632$	29.3364	−	109.485i	1.16694	−	4.35508i
$633$	−12.5536	+	15.5024i	−0.498960	+	0.616164i
$634$	−7.69448	+	36.1997i	−0.305587	+	1.43767i
$635$		0			0
$636$	−76.2764	−	24.7837i	−3.02456	−	0.982738i
$637$	−13.4471	−	13.6678i	−0.532793	−	0.541538i
$638$	0.0617619	+	0.0314693i	0.00244518	+	0.00124588i
$639$	0.721818	+	3.39589i	0.0285547	+	0.134339i
$640$		0			0
$641$	−8.34004	−	1.77273i	−0.329412	−	0.0700186i	0.0402370	−	0.999190i	$-0.487189\pi$
$641$	−8.34004	−	1.77273i	−0.329412	−	0.0700186i	−0.369649	+	0.929172i	$0.620522\pi$
$642$	−23.1001	+	8.86731i	−0.911689	+	0.349965i
$643$	20.6442	+	20.6442i	0.814129	+	0.814129i	0.985250	−	0.171121i	$-0.0547389\pi$
$643$	20.6442	+	20.6442i	0.814129	+	0.814129i	−0.171121	+	0.985250i	$0.554739\pi$
$644$	26.7144	−	13.4750i	1.05270	−	0.530990i
$645$		0			0
$646$	−3.26226	+	31.0384i	−0.128352	+	1.22119i
$647$	−6.19567	+	16.1403i	−0.243577	+	0.634540i	−0.999805	−	0.0197690i	$-0.993707\pi$
$647$	−6.19567	+	16.1403i	−0.243577	+	0.634540i	0.756228	+	0.654309i	$0.227040\pi$
$648$	38.6652	+	2.02636i	1.51891	+	0.0796028i
$649$	−0.0368109	−	0.0637584i	−0.00144495	−	0.00250274i
$650$		0			0
$651$	−3.78407	+	1.43493i	−0.148310	+	0.0562392i
$652$	−48.4706	+	24.6970i	−1.89826	+	0.967210i
$653$	20.0115	+	24.7121i	0.783109	+	0.967059i	0.999958	−	0.00914629i	$-0.00291140\pi$
$653$	20.0115	+	24.7121i	0.783109	+	0.967059i	−0.216849	+	0.976205i	$0.569578\pi$
$654$	−7.98101	+	3.55337i	−0.312082	+	0.138948i
$655$		0			0
$656$	−24.7880	+	55.6748i	−0.967809	+	2.17374i
$657$	6.28340	−	6.28340i	0.245139	−	0.245139i
$658$	17.0275	+	19.0664i	0.663800	+	0.743287i
$659$	11.8279	−	3.84312i	0.460750	−	0.149707i	−0.0694392	−	0.997586i	$-0.522121\pi$
$659$	11.8279	−	3.84312i	0.460750	−	0.149707i	0.530189	+	0.847880i	$0.322121\pi$
$660$		0			0
$661$	−35.0100	+	31.5232i	−1.36173	+	1.22611i	−0.412726	+	0.910855i	$0.635423\pi$
$661$	−35.0100	+	31.5232i	−1.36173	+	1.22611i	−0.949007	+	0.315254i	$0.897910\pi$
$662$	9.23077	+	14.2141i	0.358764	+	0.552448i
$663$	−15.4463	+	0.809507i	−0.599885	+	0.0314387i
$664$	−46.8222	+	144.104i	−1.81705	+	5.59232i
$665$		0			0
$666$	−0.500244	−	1.53959i	−0.0193841	−	0.0596580i
$667$	0.568934	+	1.48212i	0.0220292	+	0.0573881i
$668$	−68.9714	+	18.4808i	−2.66858	+	0.715044i
$669$	31.2915	−	3.28886i	1.20980	−	0.127155i
$670$		0			0
$671$	−0.0160018	+	0.0220246i	−0.000617743	+	0.000850250i
$672$	−83.3430	+	47.6669i	−3.21503	+	1.83879i
$673$	−16.4316	−	32.2488i	−0.633391	−	1.24310i	−0.955106	−	0.296263i	$-0.904259\pi$
$673$	−16.4316	−	32.2488i	−0.633391	−	1.24310i	0.321716	−	0.946836i	$-0.395741\pi$
$674$	−16.1842	+	9.34397i	−0.623393	+	0.359916i
$675$		0			0
$676$	−15.7239	+	27.2347i	−0.604767	+	1.04749i
$677$	20.7843	−	32.0050i	0.798804	−	1.23005i	−0.170784	−	0.985309i	$-0.554630\pi$
$677$	20.7843	−	32.0050i	0.798804	−	1.23005i	0.969588	−	0.244742i	$-0.0787033\pi$
$678$	2.67268	+	16.8746i	0.102644	+	0.648066i
$679$	−0.491221	+	0.487239i	−0.0188513	+	0.0186985i
$680$		0			0
$681$	−33.5069	−	14.9182i	−1.28399	−	0.571667i
$682$	0.0257540	+	0.0961154i	0.000986173	+	0.00368045i
$683$	22.4448	+	18.1754i	0.858825	+	0.695463i	0.953938	−	0.300004i	$-0.0969880\pi$
$683$	22.4448	+	18.1754i	0.858825	+	0.695463i	−0.0951133	+	0.995466i	$0.530321\pi$
$684$	−12.5217	+	13.9068i	−0.478779	+	0.531738i
$685$		0			0
$686$	13.9249	−	49.5406i	0.531655	−	1.89147i
$687$	7.09665	−	13.9280i	0.270754	−	0.531385i
$688$	−8.82993	−	168.485i	−0.336638	−	6.42344i
$689$	19.3661	+	21.5082i	0.737789	+	0.819397i
$690$		0			0
$691$	19.9813	+	17.9913i	0.760125	+	0.684420i	0.955065	−	0.296395i	$-0.0957846\pi$
$691$	19.9813	+	17.9913i	0.760125	+	0.684420i	−0.194940	+	0.980815i	$0.562451\pi$
$692$	3.34537	−	21.1218i	0.127172	−	0.802931i
$693$	0.0595422	+	0.0826583i	0.00226182	+	0.00313993i
$694$	28.2544	+	38.8889i	1.07252	+	1.47620i
$695$		0			0
$696$	−4.48054	−	10.0635i	−0.169834	−	0.381454i
$697$	−14.0095	−	5.37773i	−0.530646	−	0.203696i
$698$	82.4843	+	53.5659i	3.12208	+	2.02750i
$699$	−26.1428			−0.988813
$700$		0			0
$701$	7.94356			0.300024			0.150012	−	0.988684i	$-0.452069\pi$
$701$	7.94356			0.300024			0.150012	+	0.988684i	$0.452069\pi$
$702$	−35.9054	−	23.3172i	−1.35516	−	0.880052i
$703$	−1.15810	−	0.444555i	−0.0436788	−	0.0167667i
$704$	0.523409	+	1.17560i	0.0197267	+	0.0443069i
$705$		0			0
$706$	39.5870	+	54.4868i	1.48988	+	2.05064i
$707$	38.8254	−	3.92101i	1.46018	−	0.147465i
$708$	−2.81413	+	17.7677i	−0.105761	+	0.667751i
$709$	−36.5479	−	32.9078i	−1.37258	−	1.23588i	−0.942974	−	0.332865i	$-0.891985\pi$
$709$	−36.5479	−	32.9078i	−1.37258	−	1.23588i	−0.429610	−	0.903015i	$-0.641349\pi$
$710$		0			0
$711$	9.09334	+	10.0992i	0.341027	+	0.378749i
$712$	2.52707	+	48.2193i	0.0947058	+	1.80709i
$713$	−1.03464	+	2.03059i	−0.0387475	+	0.0760463i
$714$	−22.4678	−	34.9077i	−0.840837	−	1.30639i
$715$		0			0
$716$	37.6381	−	41.8014i	1.40660	−	1.56219i
$717$	−1.94950	−	1.57868i	−0.0728056	−	0.0589568i
$718$	11.7973	+	44.0280i	0.440270	+	1.64311i
$719$	−22.0414	−	9.81347i	−0.822006	−	0.365981i	−0.0477546	−	0.998859i	$-0.515207\pi$
$719$	−22.0414	−	9.81347i	−0.822006	−	0.365981i	−0.774251	+	0.632879i	$0.781873\pi$
$720$		0			0
$721$	−10.0745	+	36.9956i	−0.375194	+	1.37779i
$722$	−5.23116	−	33.0283i	−0.194684	−	1.22919i
$723$	2.02569	−	3.11929i	0.0753363	−	0.116008i
$724$	37.2892	−	64.5868i	1.38584	−	2.40035i
$725$		0			0
$726$	35.1181	−	20.2754i	1.30335	−	0.752491i
$727$	4.10261	+	8.05183i	0.152158	+	0.298626i	0.954485	−	0.298258i	$-0.0964054\pi$
$727$	4.10261	+	8.05183i	0.152158	+	0.298626i	−0.802328	+	0.596884i	$0.796405\pi$
$728$	74.9197	+	0.304945i	2.77671	+	0.0113020i
$729$	−15.8897	+	21.8703i	−0.588506	+	0.810009i
$730$		0			0
$731$	41.3155	−	4.34243i	1.52811	−	0.160611i
$732$	6.42538	−	1.72168i	0.237489	−	0.0636350i
$733$	−6.15103	−	16.0240i	−0.227193	−	0.591859i	0.771840	−	0.635817i	$-0.219337\pi$
$733$	−6.15103	−	16.0240i	−0.227193	−	0.591859i	−0.999033	+	0.0439579i	$0.986003\pi$
$734$	−7.33839	−	22.5852i	−0.270865	−	0.833636i
$735$		0			0
$736$	−16.7076	+	51.4207i	−0.615850	+	1.89539i
$737$	−0.321884	+	0.0168692i	−0.0118568	+	0.000621387i
$738$	−6.61387	−	10.1845i	−0.243460	−	0.374895i
$739$	30.3592	−	27.3356i	1.11678	−	1.00556i	0.116859	−	0.993148i	$-0.462717\pi$
$739$	30.3592	−	27.3356i	1.11678	−	1.00556i	0.999923	−	0.0124069i	$-0.00394934\pi$
$740$		0			0
$741$	−9.12222	+	2.96399i	−0.335113	+	0.108885i
$742$	−24.3042	+	73.7776i	−0.892237	+	2.70846i
$743$	16.4859	−	16.4859i	0.604808	−	0.604808i	−0.336777	−	0.941584i	$-0.609337\pi$
$743$	16.4859	−	16.4859i	0.604808	−	0.604808i	0.941584	+	0.336777i	$0.109337\pi$
$744$	6.43190	−	14.4463i	0.235805	−	0.529627i
$745$		0			0
$746$	61.3291	−	27.3055i	2.24542	−	0.999724i
$747$	−11.4326	−	14.1180i	−0.418295	−	0.516552i
$748$	−0.673867	+	0.343352i	−0.0246390	+	0.0125542i
$749$	6.29596	+	16.6032i	0.230050	+	0.606669i
$750$		0			0
$751$	−8.88707	−	15.3929i	−0.324294	−	0.561693i	0.657075	−	0.753825i	$-0.271793\pi$
$751$	−8.88707	−	15.3929i	−0.324294	−	0.561693i	−0.981369	+	0.192132i	$0.938460\pi$
$752$	−60.0193	−	3.14548i	−2.18868	−	0.114704i
$753$	−5.34510	+	13.9245i	−0.194786	+	0.507435i
$754$	−0.638890	+	6.07863i	−0.0232670	+	0.221371i
$755$		0			0
$756$	4.80182	−	85.0028i	0.174640	−	3.09152i
$757$	−0.545391	−	0.545391i	−0.0198226	−	0.0198226i	0.697126	−	0.716949i	$-0.254462\pi$
$757$	−0.545391	−	0.545391i	−0.0198226	−	0.0198226i	−0.716949	+	0.697126i	$0.754462\pi$
$758$	−33.6690	+	12.9243i	−1.22291	+	0.469433i
$759$	−0.0796999	−	0.0169407i	−0.00289292	−	0.000614910i
$760$		0			0
$761$	−3.53829	−	16.6464i	−0.128263	−	0.603430i	−0.994583	−	0.103941i	$-0.966855\pi$
$761$	−3.53829	−	16.6464i	−0.128263	−	0.603430i	0.866320	−	0.499489i	$-0.166479\pi$
$762$	11.5360	+	5.87786i	0.417904	+	0.212933i
$763$	2.52669	+	5.73779i	0.0914725	+	0.207722i
$764$	56.0141	+	18.2001i	2.02652	+	0.658457i
$765$		0			0
$766$	1.30474	−	6.13830i	0.0471421	−	0.221786i
$767$	4.08536	−	5.04500i	0.147514	−	0.182164i
$768$	29.1874	−	108.929i	1.05321	−	3.93063i
$769$	−5.73647	+	4.16779i	−0.206863	+	0.150294i	−0.686393	−	0.727231i	$-0.740807\pi$
$769$	−5.73647	+	4.16779i	−0.206863	+	0.150294i	0.479530	+	0.877525i	$0.340807\pi$
$770$		0			0
$771$	−26.5599	−	19.2969i	−0.956533	−	0.694962i
$772$	85.6578	−	69.3643i	3.08289	−	2.49648i
$773$	−0.0926275	+	1.76744i	−0.00333158	+	0.0635703i	−0.999789	−	0.0205243i	$-0.993466\pi$
$773$	−0.0926275	+	1.76744i	−0.00333158	+	0.0635703i	0.996458	+	0.0840946i	$0.0267998\pi$
$774$	29.1143	+	16.8091i	1.04649	+	0.604192i
$775$		0			0
$776$		−	2.70349i		−	0.0970495i
$777$	1.57136	−	0.503503i	0.0563721	−	0.0180631i
$778$	75.8386	−	12.0117i	2.71894	−	0.430639i
$779$	−9.25460	−	0.972698i	−0.331581	−	0.0348505i
$780$		0			0
$781$	0.00909490	+	0.0865322i	0.000325441	+	0.00309636i
$782$	−22.5808	−	6.05050i	−0.807487	−	0.216365i
$783$	4.46179	+	0.706678i	0.159451	+	0.0252546i
$784$	59.6400	+	105.269i	2.13000	+	3.75962i
$785$		0			0
$786$	69.3126	−	14.7329i	2.47230	−	0.525504i
$787$	14.6709	−	9.52741i	0.522962	−	0.339616i	−0.256010	−	0.966674i	$-0.582408\pi$
$787$	14.6709	−	9.52741i	0.522962	−	0.339616i	0.778972	+	0.627059i	$0.215741\pi$
$788$	−86.1184	+	55.9260i	−3.06784	+	1.99228i
$789$	26.9076	−	5.71938i	0.957935	−	0.203615i
$790$		0			0
$791$	12.1175	−	1.86870i	0.430850	−	0.0664434i
$792$	−0.393154	−	0.0622694i	−0.0139701	−	0.00221265i
$793$	−2.31871	−	0.621295i	−0.0823397	−	0.0220628i
$794$	−10.3453	−	98.4292i	−0.367142	−	3.49312i
$795$		0			0
$796$	39.6624	+	4.16869i	1.40580	+	0.147755i
$797$	41.0288	−	6.49832i	1.45331	−	0.230182i	0.620706	−	0.784044i	$-0.286846\pi$
$797$	41.0288	−	6.49832i	1.45331	−	0.230182i	0.832609	+	0.553861i	$0.186846\pi$
$798$	−19.0606	−	17.3032i	−0.674736	−	0.612527i
$799$		−	14.7988i		−	0.523545i
$800$		0			0
$801$	−5.01359	−	2.89460i	−0.177146	−	0.102276i
$802$	5.40405	−	103.115i	0.190824	−	3.64113i
$803$	0.173072	−	0.140151i	0.00610757	−	0.00494582i
$804$	63.7174	+	46.2934i	2.24714	+	1.63264i
$805$		0			0
$806$	−7.09837	+	5.15726i	−0.250029	+	0.181657i
$807$	−2.90554	+	10.8436i	−0.102280	+	0.381714i
$808$	−95.9587	+	118.499i	−3.37581	+	4.16878i
$809$	6.92563	−	32.5825i	0.243492	−	1.14554i	−0.671164	−	0.741309i	$-0.734205\pi$
$809$	6.92563	−	32.5825i	0.243492	−	1.14554i	0.914656	−	0.404232i	$-0.132461\pi$
$810$		0			0
$811$	30.7233	+	9.98261i	1.07884	+	0.350537i	0.793925	−	0.608016i	$-0.208034\pi$
$811$	30.7233	+	9.98261i	1.07884	+	0.350537i	0.284916	+	0.958552i	$0.408034\pi$
$812$	−11.1240	+	4.89857i	−0.390376	+	0.171906i
$813$	−20.1609	−	10.2725i	−0.707073	−	0.360272i
$814$	−0.00843515	−	0.0396843i	−0.000295652	−	0.00139093i
$815$		0			0
$816$	95.4700	+	20.2928i	3.34212	+	0.710389i
$817$	24.0505	−	9.23212i	0.841420	−	0.322991i
$818$	34.6876	+	34.6876i	1.21282	+	1.21282i
$819$	−4.92289	+	7.51346i	−0.172020	+	0.262541i
$820$		0			0
$821$	−2.25230	+	21.4292i	−0.0786059	+	0.747885i	0.882240	+	0.470801i	$0.156035\pi$
$821$	−2.25230	+	21.4292i	−0.0786059	+	0.747885i	−0.960846	+	0.277085i	$0.910632\pi$
$822$	−21.9209	+	57.1059i	−0.764579	+	1.99180i
$823$	28.2003	+	1.47792i	0.983002	+	0.0515170i	0.537059	−	0.843545i	$-0.319535\pi$
$823$	28.2003	+	1.47792i	0.983002	+	0.0515170i	0.445943	+	0.895061i	$0.352868\pi$
$824$	−74.9111	−	129.750i	−2.60965	−	4.52005i
$825$		0			0
$826$	17.1973	+	2.79559i	0.598371	+	0.0972709i
$827$	28.0565	−	14.2955i	0.975619	−	0.497103i	0.107902	−	0.994161i	$-0.465587\pi$
$827$	28.0565	−	14.2955i	0.975619	−	0.497103i	0.867717	+	0.497059i	$0.165587\pi$
$828$	−8.82135	−	10.8935i	−0.306563	−	0.378574i
$829$	27.4497	−	12.2214i	0.953368	−	0.424467i	0.129709	−	0.991552i	$-0.458596\pi$
$829$	27.4497	−	12.2214i	0.953368	−	0.424467i	0.823659	+	0.567085i	$0.191929\pi$
$830$		0			0
$831$	−1.50687	+	3.38449i	−0.0522727	+	0.117407i
$832$	−80.2351	+	80.2351i	−2.78165	+	2.78165i
$833$	−25.1164	+	16.0216i	−0.870231	+	0.555116i
$834$	21.3714	−	6.94398i	0.740030	−	0.240450i
$835$		0			0
$836$	−0.348530	+	0.313818i	−0.0120542	+	0.0108536i
$837$	3.53189	+	5.43863i	0.122080	+	0.187987i
$838$	−68.0399	+	3.56582i	−2.35040	+	0.123179i
$839$	13.0052	−	40.0259i	0.448990	−	1.38185i	−0.429058	−	0.903277i	$-0.641155\pi$
$839$	13.0052	−	40.0259i	0.448990	−	1.38185i	0.878048	−	0.478572i	$-0.158845\pi$
$840$		0			0
$841$	8.76220	+	26.9673i	0.302145	+	0.929906i
$842$	−18.1204	−	47.2052i	−0.624470	−	1.62680i
$843$	7.49799	−	2.00908i	0.258245	−	0.0691964i
$844$	−85.5330	+	8.98988i	−2.94417	+	0.309445i
$845$		0			0
$846$	7.03921	−	9.68864i	0.242013	−	0.333102i
$847$	−14.4477	−	25.2610i	−0.496427	−	0.867977i
$848$	−82.9124	−	162.725i	−2.84722	−	5.58799i
$849$	−18.7198	+	10.8079i	−0.642461	+	0.370925i
$850$		0			0
$851$	0.464598	−	0.804706i	0.0159262	−	0.0275850i
$852$	11.5792	−	17.8303i	0.396695	−	0.610857i
$853$	−2.01294	−	12.7092i	−0.0689216	−	0.435154i	−0.997886	−	0.0649853i	$-0.979300\pi$
$853$	−2.01294	−	12.7092i	−0.0689216	−	0.435154i	0.928965	−	0.370168i	$-0.120700\pi$
$854$	−1.64215	−	6.22990i	−0.0561932	−	0.213183i
$855$		0			0
$856$	−63.3854	−	28.2210i	−2.16647	−	0.964574i
$857$	3.02647	+	11.2950i	0.103382	+	0.385828i	0.998157	−	0.0606906i	$-0.0193303\pi$
$857$	3.02647	+	11.2950i	0.103382	+	0.385828i	−0.894774	+	0.446519i	$0.852664\pi$
$858$	−0.243789	−	0.197417i	−0.00832283	−	0.00673970i
$859$	−2.79708	+	3.10647i	−0.0954352	+	0.105992i	−0.788970	−	0.614431i	$-0.789386\pi$
$859$	−2.79708	+	3.10647i	−0.0954352	+	0.105992i	0.693535	+	0.720423i	$0.256052\pi$
$860$		0			0
$861$	10.4083	−	6.69916i	0.354714	−	0.228307i
$862$	−13.9479	+	27.3743i	−0.475068	+	0.932373i
$863$	1.71847	+	32.7905i	0.0584976	+	1.11620i	0.857370	+	0.514700i	$0.172097\pi$
$863$	1.71847	+	32.7905i	0.0584976	+	1.11620i	−0.798873	+	0.601500i	$0.794570\pi$
$864$	102.943	+	114.330i	3.50221	+	3.88959i
$865$		0			0
$866$	−79.4402	−	71.5283i	−2.69949	−	2.43063i
$867$	−0.230966	+	1.45826i	−0.00784403	+	0.0495252i
$868$	−15.9110	−	7.16176i	−0.540053	−	0.243086i
$869$	0.200191	+	0.275540i	0.00679103	+	0.00934705i
$870$		0			0
$871$	−11.5601	−	25.9643i	−0.391698	−	0.879768i
$872$	−22.8705	−	8.77917i	−0.774493	−	0.297300i
$873$	0.271843	+	0.176537i	0.00920047	+	0.00597486i
$874$	−14.4967			−0.490358
$875$		0			0
$876$	−54.4163			−1.83856
$877$	−32.9586	−	21.4036i	−1.11293	−	0.722747i	−0.148985	−	0.988839i	$-0.547601\pi$
$877$	−32.9586	−	21.4036i	−1.11293	−	0.722747i	−0.963947	+	0.266093i	$0.914267\pi$
$878$	−65.5630	−	25.1673i	−2.21264	−	0.849354i
$879$	−15.0610	−	33.8275i	−0.507994	−	1.14097i
$880$		0			0
$881$	−21.0874	−	29.0243i	−0.710453	−	0.977854i	−0.999787	−	0.0206263i	$-0.993434\pi$
$881$	−21.0874	−	29.0243i	−0.710453	−	0.977854i	0.289335	−	0.957228i	$-0.406566\pi$
$882$	−24.0642	−	1.45768i	−0.810285	−	0.0490825i
$883$	−5.89645	+	37.2287i	−0.198431	+	1.25285i	0.664408	+	0.747370i	$0.268684\pi$
$883$	−5.89645	+	37.2287i	−0.198431	+	1.25285i	−0.862840	+	0.505477i	$0.831316\pi$
$884$	−49.5585	−	44.6227i	−1.66683	−	1.50082i
$885$		0			0
$886$	−14.1127	−	15.6738i	−0.474127	−	0.526571i
$887$	2.24377	+	42.8137i	0.0753384	+	1.43754i	0.730943	+	0.682438i	$0.239080\pi$
$887$	2.24377	+	42.8137i	0.0753384	+	1.43754i	−0.655605	+	0.755104i	$0.727586\pi$
$888$	−2.92710	+	5.74476i	−0.0982271	+	0.192781i
$889$	4.25182	−	8.26137i	0.142602	−	0.277078i
$890$		0			0
$891$	−0.0778471	+	0.0864580i	−0.00260798	+	0.00289645i
$892$	105.424	+	85.3704i	3.52985	+	2.85841i
$893$	−2.37519	−	8.86432i	−0.0794826	−	0.296633i
$894$	10.2933	+	4.58287i	0.344259	+	0.153274i
$895$		0			0
$896$	−154.204	−	41.9922i	−5.15158	−	1.40286i
$897$	−1.12393	−	7.09619i	−0.0375268	−	0.236935i
$898$	−3.97128	+	6.11524i	−0.132523	+	0.204068i
$899$	0.462905	−	0.801774i	0.0154387	−	0.0267407i
$900$		0			0
$901$	38.9443	−	22.4845i	1.29742	−	0.749068i
$902$	−0.138168	−	0.271170i	−0.00460050	−	0.00902898i
$903$	−17.2541	+	29.6060i	−0.574180	+	0.985226i
$904$	−28.1598	+	38.7586i	−0.936580	+	1.28909i
$905$		0			0
$906$	−29.4700	+	3.09743i	−0.979077	+	0.102905i
$907$	36.2880	−	9.72335i	1.20492	−	0.322858i	0.400156	−	0.916447i	$-0.368956\pi$
$907$	36.2880	−	9.72335i	1.20492	−	0.322858i	0.804769	+	0.593589i	$0.202289\pi$
$908$	−56.6705	−	147.632i	−1.88068	−	4.89933i
$909$	−5.64932	−	17.3868i	−0.187376	−	0.576685i
$910$		0			0
$911$	−3.26942	+	10.0623i	−0.108321	+	0.333377i	−0.990496	−	0.137545i	$-0.956079\pi$
$911$	−3.26942	+	10.0623i	−0.108321	+	0.333377i	0.882175	+	0.470922i	$0.156079\pi$
$912$	60.4422	−	3.16764i	2.00144	−	0.104891i
$913$	−0.247967	−	0.381836i	−0.00820652	−	0.0126369i
$914$	−58.3006	+	52.4941i	−1.92841	+	1.73635i
$915$		0			0
$916$	64.0969	−	20.8263i	2.11782	−	0.688122i
$917$	−10.3703	−	49.7838i	−0.342456	−	1.64401i
$918$	−47.0366	+	47.0366i	−1.55244	+	1.55244i
$919$	9.54724	−	21.4435i	0.314934	−	0.707354i	−0.684838	−	0.728696i	$-0.740127\pi$
$919$	9.54724	−	21.4435i	0.314934	−	0.707354i	0.999772	+	0.0213412i	$0.00679363\pi$
$920$		0			0
$921$	22.5747	−	10.0509i	0.743863	−	0.331189i
$922$	37.8903	+	46.7906i	1.24785	+	1.54097i
$923$	−6.83590	+	3.48306i	−0.225006	+	0.114646i
$924$	0.100096	−	0.615751i	0.00329292	−	0.0202567i
$925$		0			0
$926$	4.18033	+	7.24055i	0.137374	+	0.237939i
$927$	17.9383	+	0.940109i	0.589173	+	0.0308772i
$928$	7.87118	−	20.5051i	0.258384	−	0.673114i
$929$	3.91001	−	37.2013i	0.128283	−	1.22053i	−0.721127	−	0.692802i	$-0.756376\pi$
$929$	3.91001	−	37.2013i	0.128283	−	1.22053i	0.849411	−	0.527732i	$-0.176958\pi$
$930$		0			0
$931$	−12.4730	+	13.6279i	−0.408785	+	0.446635i
$932$	−79.7006	−	79.7006i	−2.61068	−	2.61068i
$933$	13.6053	−	5.22257i	0.445416	−	0.170979i
$934$	−86.6698	−	18.4222i	−2.83592	−	0.602794i
$935$		0			0
$936$	−7.29748	−	34.3320i	−0.238526	−	1.12218i
$937$	−49.9739	−	25.4630i	−1.63258	−	0.831840i	−0.998272	−	0.0587564i	$-0.981286\pi$
$937$	−49.9739	−	25.4630i	−1.63258	−	0.831840i	−0.634305	−	0.773083i	$-0.718714\pi$
$938$	45.0873	−	61.5291i	1.47215	−	2.00900i
$939$	−23.7871	−	7.72889i	−0.776262	−	0.252223i
$940$		0			0
$941$	1.69048	−	7.95308i	0.0551081	−	0.259263i	−0.941966	−	0.335709i	$-0.891024\pi$
$941$	1.69048	−	7.95308i	0.0551081	−	0.259263i	0.997074	+	0.0764462i	$0.0243574\pi$
$942$	5.25296	−	6.48687i	0.171151	−	0.211354i
$943$	1.80406	−	6.73283i	0.0587482	−	0.219251i
$944$	−33.1404	+	24.0779i	−1.07863	+	0.783669i
$945$		0			0
$946$	0.681628	+	0.495232i	0.0221617	+	0.0161014i
$947$	−12.8803	+	10.4303i	−0.418554	+	0.338939i	−0.815350	−	0.578968i	$-0.803455\pi$
$947$	−12.8803	+	10.4303i	−0.418554	+	0.338939i	0.396796	+	0.917907i	$0.370122\pi$
$948$	4.35544	−	83.1067i	0.141458	−	2.69918i
$949$	17.0062	+	9.81851i	0.552043	+	0.318722i
$950$		0			0
$951$			17.6723i			0.573064i
$952$	24.6658	−	113.765i	0.799424	−	3.68714i
$953$	40.4065	−	6.39977i	1.30890	−	0.207309i	0.537284	−	0.843402i	$-0.319450\pi$
$953$	40.4065	−	6.39977i	1.30890	−	0.207309i	0.771613	+	0.636093i	$0.219450\pi$
$954$	36.1914	+	3.80387i	1.17174	+	0.123155i
$955$		0			0
$956$	−1.13052	−	10.7562i	−0.0365638	−	0.347881i
$957$	0.0319725	+	0.00856701i	0.00103352	+	0.000276932i
$958$	−11.9242	−	1.88861i	−0.385253	−	0.0610181i
$959$	40.9168	+	15.8979i	1.32127	+	0.513369i
$960$		0			0
$961$	−29.0226	+	6.16894i	−0.936213	+	0.198998i
$962$	3.00025	−	1.94838i	0.0967318	−	0.0628184i
$963$	6.97673	−	4.53074i	0.224822	−	0.146001i
$964$	15.6853	−	3.33402i	0.505190	−	0.107381i
$965$		0			0
$966$	15.0349	−	12.0740i	0.483738	−	0.388474i
$967$	33.8150	+	5.35578i	1.08742	+	0.172230i	0.674307	−	0.738451i	$-0.264442\pi$
$967$	33.8150	+	5.35578i	1.08742	+	0.172230i	0.413111	+	0.910681i	$0.364442\pi$
$968$	109.835	+	29.4301i	3.53022	+	0.945921i
$969$	1.55780	+	14.8215i	0.0500438	+	0.476135i
$970$		0			0
$971$	7.80423	+	0.820257i	0.250450	+	0.0263233i	0.228921	−	0.973445i	$-0.426480\pi$
$971$	7.80423	+	0.820257i	0.250450	+	0.0263233i	0.0215283	+	0.999768i	$0.493147\pi$
$972$	−67.2719	+	10.6548i	−2.15775	+	0.341754i
$973$	−4.92078	−	15.3570i	−0.157753	−	0.492323i
$974$			39.5679i			1.26784i
$975$		0			0
$976$	13.1182	+	7.57380i	0.419903	+	0.242431i
$977$	−1.94208	+	37.0572i	−0.0621328	+	1.18556i	0.772594	+	0.634900i	$0.218959\pi$
$977$	−1.94208	+	37.0572i	−0.0621328	+	1.18556i	−0.834727	+	0.550664i	$0.814375\pi$
$978$	−27.2460	+	22.0634i	−0.871230	+	0.705508i
$979$	−0.117379	−	0.0852808i	−0.00375145	−	0.00272559i
$980$		0			0
$981$	2.37620	−	1.72641i	0.0758663	−	0.0551201i
$982$	−15.4496	+	57.6588i	−0.493018	+	1.83997i
$983$	29.9442	−	36.9780i	0.955071	−	1.17941i	−0.0286278	−	0.999590i	$-0.509114\pi$
$983$	29.9442	−	36.9780i	0.955071	−	1.17941i	0.983699	−	0.179824i	$-0.0575529\pi$
$984$	−10.0558	+	47.3089i	−0.320568	+	1.50815i
$985$		0			0
$986$	9.03193	+	2.93465i	0.287635	+	0.0934584i
$987$	9.84627	+	7.21514i	0.313410	+	0.229661i
$988$	−36.8468	−	18.7744i	−1.17225	−	0.597292i
$989$	4.01201	+	18.8750i	0.127574	+	0.600191i
$990$		0			0
$991$	49.8520	+	10.5964i	1.58360	+	0.336605i	0.913872	−	0.406001i	$-0.133077\pi$
$991$	49.8520	+	10.5964i	1.58360	+	0.336605i	0.669728	+	0.742606i	$0.266411\pi$
$992$	29.4355	−	11.2992i	0.934579	−	0.358751i
$993$	5.72278	+	5.72278i	0.181607	+	0.181607i
$994$	−17.2234	−	11.2849i	−0.546293	−	0.357937i
$995$		0			0
$996$	−11.6285	+	110.638i	−0.368464	+	3.50570i
$997$	4.94701	−	12.8874i	0.156673	−	0.408148i	−0.832666	−	0.553775i	$-0.813187\pi$
$997$	4.94701	−	12.8874i	0.156673	−	0.408148i	0.989340	+	0.145627i	$0.0465201\pi$
$998$	−12.9677	−	0.679610i	−0.410487	−	0.0215127i
$999$	−1.32200	−	2.28978i	−0.0418264	−	0.0724454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.507.18		288
5.2	odd	4		875.2.bb.c.493.1		288
5.3	odd	4		175.2.x.a.3.18	✓	288
5.4	even	2		875.2.bb.a.507.1		288
7.5	odd	6	inner	875.2.bb.b.257.18		288
25.6	even	5		175.2.x.a.17.1	yes	288
25.8	odd	20	inner	875.2.bb.b.143.18		288
25.17	odd	20		875.2.bb.a.143.1		288
25.19	even	10		875.2.bb.c.857.18		288
35.12	even	12		875.2.bb.c.243.18		288
35.19	odd	6		875.2.bb.a.257.1		288
35.33	even	12		175.2.x.a.103.1	yes	288
175.19	odd	30		875.2.bb.c.607.1		288
175.33	even	60	inner	875.2.bb.b.768.18		288
175.117	even	60		875.2.bb.a.768.1		288
175.131	odd	30		175.2.x.a.117.18	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.18	✓	288	5.3	odd	4
175.2.x.a.17.1	yes	288	25.6	even	5
175.2.x.a.103.1	yes	288	35.33	even	12
175.2.x.a.117.18	yes	288	175.131	odd	30
875.2.bb.a.143.1		288	25.17	odd	20
875.2.bb.a.257.1		288	35.19	odd	6
875.2.bb.a.507.1		288	5.4	even	2
875.2.bb.a.768.1		288	175.117	even	60
875.2.bb.b.143.18		288	25.8	odd	20	inner
875.2.bb.b.257.18		288	7.5	odd	6	inner
875.2.bb.b.507.18		288	1.1	even	1	trivial
875.2.bb.b.768.18		288	175.33	even	60	inner
875.2.bb.c.243.18		288	35.12	even	12
875.2.bb.c.493.1		288	5.2	odd	4
875.2.bb.c.607.1		288	175.19	odd	30
875.2.bb.c.857.18		288	25.19	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.33033 + 1.51333i) q^{2} +(1.23871 + 0.475498i) q^{3} +(2.32679 + 5.22605i) q^{4} +(2.16703 + 2.98265i) q^{6} +(2.14677 - 1.54641i) q^{7} +(-1.61724 + 10.2108i) q^{8} +(-0.921121 - 0.829381i) q^{9} +(-0.0207859 - 0.0230851i) q^{11} +(0.397249 + 7.57996i) q^{12} +(1.24353 - 2.44056i) q^{13} +(7.34292 - 0.354862i) q^{14} +(-11.5654 + 12.8447i) q^{16} +(-3.30746 - 2.67833i) q^{17} +(-0.891386 - 3.32670i) q^{18} +(-2.41099 - 1.07344i) q^{19} +(3.39455 - 0.894773i) q^{21} +(-0.0135026 - 0.0852518i) q^{22} +(1.07668 - 1.65794i) q^{23} +(-6.85853 + 11.8793i) q^{24} +(6.59122 - 3.80544i) q^{26} +(-2.55376 - 5.01203i) q^{27} +(13.0767 + 7.62096i) q^{28} +(-0.472036 + 0.649701i) q^{29} +(-1.14651 + 0.120504i) q^{31} +(-26.4179 + 7.07866i) q^{32} +(-0.0147709 - 0.0384794i) q^{33} +(-3.65427 - 11.2467i) q^{34} +(2.19113 - 6.74362i) q^{36} +(0.469391 - 0.0245997i) q^{37} +(-3.99393 - 6.15012i) q^{38} +(2.70086 - 2.43186i) q^{39} +(3.35339 - 1.08958i) q^{41} +(9.26451 + 3.05197i) q^{42} +(-6.90226 + 6.90226i) q^{43} +(0.0722793 - 0.162342i) q^{44} +(5.01803 - 2.23417i) q^{46} +(2.18830 + 2.70233i) q^{47} +(-20.4339 + 10.4116i) q^{48} +(2.21724 - 6.63957i) q^{49} +(-2.82346 - 4.89037i) q^{51} +(15.6479 + 0.820073i) q^{52} +(-3.78661 + 9.86446i) q^{53} +(1.63378 - 15.5444i) q^{54} +(12.3183 + 24.4212i) q^{56} +(-2.47611 - 2.47611i) q^{57} +(-2.08321 + 0.799671i) q^{58} +(2.31821 + 0.492751i) q^{59} +(-0.182210 - 0.857229i) q^{61} +(-2.85412 - 1.45425i) q^{62} +(-3.26000 - 0.356061i) q^{63} +(-39.3982 - 12.8013i) q^{64} +(0.0238112 - 0.112023i) q^{66} +(6.52995 - 8.06381i) q^{67} +(6.30132 - 23.5169i) q^{68} +(2.12204 - 1.54175i) q^{69} +(-2.26602 - 1.64636i) q^{71} +(9.95835 - 8.06412i) q^{72} +(-0.375203 + 7.15930i) q^{73} +(1.13106 + 0.653020i) q^{74} -15.0976i q^{76} +(-0.0803215 - 0.0174149i) q^{77} +(9.97412 - 1.57974i) q^{78} +(-10.9039 - 1.14605i) q^{79} +(-0.391479 - 3.72467i) q^{81} +(9.46340 + 2.53571i) q^{82} +(14.4760 + 2.29277i) q^{83} +(12.5745 + 15.6581i) q^{84} +(-26.5300 + 5.63912i) q^{86} +(-0.893648 + 0.580342i) q^{87} +(0.269334 - 0.174907i) q^{88} +(4.56856 - 0.971077i) q^{89} +(-1.10454 - 7.16233i) q^{91} +(11.1697 + 1.76910i) q^{92} +(-1.47750 - 0.395896i) q^{93} +(1.00994 + 9.60895i) q^{94} +(-36.0901 - 3.79322i) q^{96} +(-0.258287 + 0.0409086i) q^{97} +(15.2148 - 12.1170i) q^{98} +0.0385036i 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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