LMFDB - Embedded newform 961.2.d.l.531.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			531.1
Root			$1.14412 + 0.831254i$ of defining polynomial
Character	$\chi$	$=$	961.531
Dual form			961.2.d.l.628.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.746033 - 2.29605i) q^{2} +(-0.746033 + 2.29605i) q^{3} +(-3.09726 + 2.25029i) q^{4} +1.00000 q^{5} +5.82843 q^{6} +(-1.95314 + 1.41904i) q^{7} +(3.57117 + 2.59461i) q^{8} +(-2.28825 - 1.66251i) q^{9} +(-0.746033 - 2.29605i) q^{10} +(4.24139 - 3.08155i) q^{11} +(-2.85613 - 8.79027i) q^{12} +(0.565015 - 1.73894i) q^{13} +(4.71530 + 3.42586i) q^{14} +(-0.746033 + 2.29605i) q^{15} +(0.927051 - 2.85317i) q^{16} +(0.138805 + 0.100848i) q^{17} +(-2.11010 + 6.49422i) q^{18} +(0.490035 + 1.50817i) q^{19} +(-3.09726 + 2.25029i) q^{20} +(-1.80108 - 5.54316i) q^{21} +(-10.2396 - 7.43951i) q^{22} +(3.23607 + 2.35114i) q^{23} +(-8.62158 + 6.26394i) q^{24} -4.00000 q^{25} -4.41421 q^{26} +(-0.335106 + 0.243469i) q^{27} +(2.85613 - 8.79027i) q^{28} +(-0.362036 - 1.11423i) q^{29} +5.82843 q^{30} +1.58579 q^{32} +(3.91118 + 12.0374i) q^{33} +(0.127999 - 0.393941i) q^{34} +(-1.95314 + 1.41904i) q^{35} +10.8284 q^{36} +1.00000 q^{37} +(3.09726 - 2.25029i) q^{38} +(3.57117 + 2.59461i) q^{39} +(3.57117 + 2.59461i) q^{40} +(2.93111 + 9.02104i) q^{41} +(-11.3837 + 8.27077i) q^{42} +(2.75010 + 8.46392i) q^{43} +(-6.20230 + 19.0887i) q^{44} +(-2.28825 - 1.66251i) q^{45} +(2.98413 - 9.18421i) q^{46} +(-0.511996 + 1.57576i) q^{47} +(5.85942 + 4.25712i) q^{48} +(-0.362036 + 1.11423i) q^{49} +(2.98413 + 9.18421i) q^{50} +(-0.335106 + 0.243469i) q^{51} +(2.16312 + 6.65740i) q^{52} +(-0.138805 - 0.100848i) q^{53} +(0.809017 + 0.587785i) q^{54} +(4.24139 - 3.08155i) q^{55} -10.6569 q^{56} -3.82843 q^{57} +(-2.28825 + 1.66251i) q^{58} +(-3.11213 + 9.57815i) q^{59} +(-2.85613 - 8.79027i) q^{60} +2.82843 q^{61} +6.82843 q^{63} +(-3.03715 - 9.34739i) q^{64} +(0.565015 - 1.73894i) q^{65} +(24.7206 - 17.9606i) q^{66} -5.24264 q^{67} -0.656854 q^{68} +(-7.81256 + 5.67616i) q^{69} +(4.71530 + 3.42586i) q^{70} +(11.3837 + 8.27077i) q^{71} +(-3.85816 - 11.8742i) q^{72} +(-3.09726 + 2.25029i) q^{73} +(-0.746033 - 2.29605i) q^{74} +(2.98413 - 9.18421i) q^{75} +(-4.91160 - 3.56848i) q^{76} +(-3.91118 + 12.0374i) q^{77} +(3.29315 - 10.1353i) q^{78} +(12.3316 + 8.95940i) q^{79} +(0.927051 - 2.85317i) q^{80} +(-2.93111 - 9.02104i) q^{81} +(18.5261 - 13.4600i) q^{82} +(1.25803 + 3.87182i) q^{83} +(18.0522 + 13.1157i) q^{84} +(0.138805 + 0.100848i) q^{85} +(17.3820 - 12.6287i) q^{86} +2.82843 q^{87} +23.1421 q^{88} +(10.1008 - 7.33866i) q^{89} +(-2.11010 + 6.49422i) q^{90} +(1.36407 + 4.19817i) q^{91} -15.3137 q^{92} +4.00000 q^{94} +(0.490035 + 1.50817i) q^{95} +(-1.18305 + 3.64105i) q^{96} +(-8.76038 + 6.36479i) q^{97} +2.82843 q^{98} -14.8284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} + 24 q^{6} - 2 q^{7} + 6 q^{8} + 2 q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} + 6 q^{14} + 2 q^{15} - 6 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} - 2 q^{20} + 6 q^{21}+ \cdots - 96 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 + 24 * q^6 - 2 * q^7 + 6 * q^8 + 2 * q^10 + 2 * q^11 + 10 * q^12 + 2 * q^13 + 6 * q^14 + 2 * q^15 - 6 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 - 2 * q^20 + 6 * q^21 - 14 * q^22 + 8 * q^23 - 10 * q^24 - 32 * q^25 - 24 * q^26 + 2 * q^27 - 10 * q^28 + 8 * q^29 + 24 * q^30 + 24 * q^32 - 14 * q^33 + 2 * q^34 - 2 * q^35 + 64 * q^36 + 8 * q^37 + 2 * q^38 + 6 * q^39 + 6 * q^40 - 2 * q^41 - 14 * q^42 + 2 * q^43 + 26 * q^44 - 8 * q^46 - 8 * q^47 + 6 * q^48 + 8 * q^49 - 8 * q^50 + 2 * q^51 - 14 * q^52 - 6 * q^53 + 2 * q^54 + 2 * q^55 - 40 * q^56 - 8 * q^57 + 6 * q^59 + 10 * q^60 + 32 * q^63 + 14 * q^64 + 2 * q^65 + 30 * q^66 - 8 * q^67 + 40 * q^68 - 8 * q^69 + 6 * q^70 + 14 * q^71 + 8 * q^72 - 2 * q^73 + 2 * q^74 - 8 * q^75 + 2 * q^76 + 14 * q^77 - 10 * q^78 + 22 * q^79 - 6 * q^80 + 2 * q^81 + 26 * q^82 + 6 * q^83 + 22 * q^84 + 6 * q^85 + 26 * q^86 + 72 * q^88 + 8 * q^89 + 8 * q^90 - 6 * q^91 - 32 * q^92 + 32 * q^94 - 6 * q^95 + 2 * q^96 - 16 * q^97 - 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.746033	−	2.29605i	−0.527525	−	1.62356i	−0.759268	−	0.650778i	$-0.774443\pi$
$2$	−0.746033	−	2.29605i	−0.527525	−	1.62356i	0.231743	−	0.972777i	$-0.425557\pi$
$3$	−0.746033	+	2.29605i	−0.430722	+	1.32563i	0.466685	+	0.884424i	$0.345448\pi$
$3$	−0.746033	+	2.29605i	−0.430722	+	1.32563i	−0.897407	+	0.441203i	$0.854552\pi$
$4$	−3.09726	+	2.25029i	−1.54863	+	1.12515i
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	5.82843			2.37945
$7$	−1.95314	+	1.41904i	−0.738217	+	0.536346i	−0.892152	−	0.451735i	$-0.850805\pi$
$7$	−1.95314	+	1.41904i	−0.738217	+	0.536346i	0.153935	+	0.988081i	$0.450805\pi$
$8$	3.57117	+	2.59461i	1.26260	+	0.917333i
$9$	−2.28825	−	1.66251i	−0.762749	−	0.554169i
$10$	−0.746033	−	2.29605i	−0.235916	−	0.726076i
$11$	4.24139	−	3.08155i	1.27883	−	0.929121i	0.279309	−	0.960201i	$-0.409895\pi$
$11$	4.24139	−	3.08155i	1.27883	−	0.929121i	0.999517	+	0.0310800i	$0.00989465\pi$
$12$	−2.85613	−	8.79027i	−0.824495	−	2.53753i
$13$	0.565015	−	1.73894i	0.156707	−	0.482294i	−0.841623	−	0.540066i	$-0.818399\pi$
$13$	0.565015	−	1.73894i	0.156707	−	0.482294i	0.998330	+	0.0577712i	$0.0183994\pi$
$14$	4.71530	+	3.42586i	1.26022	+	0.915601i
$15$	−0.746033	+	2.29605i	−0.192625	+	0.592838i
$16$	0.927051	−	2.85317i	0.231763	−	0.713292i
$17$	0.138805	+	0.100848i	0.0336652	+	0.0244592i	0.604491	−	0.796612i	$-0.293377\pi$
$17$	0.138805	+	0.100848i	0.0336652	+	0.0244592i	−0.570825	+	0.821071i	$0.693377\pi$
$18$	−2.11010	+	6.49422i	−0.497355	+	1.53070i
$19$	0.490035	+	1.50817i	0.112422	+	0.345999i	0.991401	−	0.130862i	$-0.0417746\pi$
$19$	0.490035	+	1.50817i	0.112422	+	0.345999i	−0.878979	+	0.476861i	$0.841775\pi$
$20$	−3.09726	+	2.25029i	−0.692569	+	0.503181i
$21$	−1.80108	−	5.54316i	−0.393029	−	1.20962i
$22$	−10.2396	−	7.43951i	−2.18309	−	1.58611i
$23$	3.23607	+	2.35114i	0.674767	+	0.490247i	0.871617	−	0.490187i	$-0.163071\pi$
$23$	3.23607	+	2.35114i	0.674767	+	0.490247i	−0.196851	+	0.980433i	$0.563071\pi$
$24$	−8.62158	+	6.26394i	−1.75987	+	1.27862i
$25$	−4.00000			−0.800000
$26$	−4.41421			−0.865699
$27$	−0.335106	+	0.243469i	−0.0644911	+	0.0468556i
$28$	2.85613	−	8.79027i	0.539758	−	1.66121i
$29$	−0.362036	−	1.11423i	−0.0672284	−	0.206908i	0.911799	−	0.410637i	$-0.134694\pi$
$29$	−0.362036	−	1.11423i	−0.0672284	−	0.206908i	−0.979027	+	0.203729i	$0.934694\pi$
$30$	5.82843			1.06412
$31$		0			0
$31$		0			0
$32$	1.58579			0.280330
$33$	3.91118	+	12.0374i	0.680850	+	2.09544i
$34$	0.127999	−	0.393941i	0.0219517	−	0.0675602i
$35$	−1.95314	+	1.41904i	−0.330141	+	0.239861i
$36$	10.8284			1.80474
$37$	1.00000			0.164399			0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000			0.164399			0.0821995	+	0.996616i	$0.473806\pi$
$38$	3.09726	−	2.25029i	0.502442	−	0.365046i
$39$	3.57117	+	2.59461i	0.571845	+	0.415470i
$40$	3.57117	+	2.59461i	0.564652	+	0.410244i
$41$	2.93111	+	9.02104i	0.457763	+	1.40885i	0.867861	+	0.496808i	$0.165495\pi$
$41$	2.93111	+	9.02104i	0.457763	+	1.40885i	−0.410098	+	0.912042i	$0.634505\pi$
$42$	−11.3837	+	8.27077i	−1.75655	+	1.27621i
$43$	2.75010	+	8.46392i	0.419386	+	1.29074i	0.908269	+	0.418387i	$0.137404\pi$
$43$	2.75010	+	8.46392i	0.419386	+	1.29074i	−0.488883	+	0.872349i	$0.662596\pi$
$44$	−6.20230	+	19.0887i	−0.935032	+	2.87773i
$45$	−2.28825	−	1.66251i	−0.341112	−	0.247832i
$46$	2.98413	−	9.18421i	0.439986	−	1.35414i
$47$	−0.511996	+	1.57576i	−0.0746823	+	0.229849i	−0.981428	−	0.191828i	$-0.938558\pi$
$47$	−0.511996	+	1.57576i	−0.0746823	+	0.229849i	0.906746	+	0.421677i	$0.138558\pi$
$48$	5.85942	+	4.25712i	0.845734	+	0.614462i
$49$	−0.362036	+	1.11423i	−0.0517194	+	0.159176i
$50$	2.98413	+	9.18421i	0.422020	+	1.29884i
$51$	−0.335106	+	0.243469i	−0.0469242	+	0.0340924i
$52$	2.16312	+	6.65740i	0.299971	+	0.923215i
$53$	−0.138805	−	0.100848i	−0.0190664	−	0.0138525i	0.578211	−	0.815887i	$-0.303751\pi$
$53$	−0.138805	−	0.100848i	−0.0190664	−	0.0138525i	−0.597278	+	0.802035i	$0.703751\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	4.24139	−	3.08155i	0.571908	−	0.415516i
$56$	−10.6569			−1.42408
$57$	−3.82843			−0.507088
$58$	−2.28825	+	1.66251i	−0.300461	+	0.218298i
$59$	−3.11213	+	9.57815i	−0.405165	+	1.24697i	0.515592	+	0.856834i	$0.327572\pi$
$59$	−3.11213	+	9.57815i	−0.405165	+	1.24697i	−0.920757	+	0.390136i	$0.872428\pi$
$60$	−2.85613	−	8.79027i	−0.368725	−	1.13482i
$61$	2.82843			0.362143			0.181071	−	0.983470i	$-0.442043\pi$
$61$	2.82843			0.362143			0.181071	+	0.983470i	$0.442043\pi$
$62$		0			0
$63$	6.82843			0.860301
$64$	−3.03715	−	9.34739i	−0.379644	−	1.16842i
$65$	0.565015	−	1.73894i	0.0700815	−	0.215689i
$66$	24.7206	−	17.9606i	3.04290	−	2.21079i
$67$	−5.24264			−0.640490			−0.320245	−	0.947335i	$-0.603765\pi$
$67$	−5.24264			−0.640490			−0.320245	+	0.947335i	$0.603765\pi$
$68$	−0.656854			−0.0796553
$69$	−7.81256	+	5.67616i	−0.940522	+	0.683329i
$70$	4.71530	+	3.42586i	0.563586	+	0.409469i
$71$	11.3837	+	8.27077i	1.35100	+	0.981559i	0.998961	+	0.0455742i	$0.0145118\pi$
$71$	11.3837	+	8.27077i	1.35100	+	0.981559i	0.352040	+	0.935985i	$0.385488\pi$
$72$	−3.85816	−	11.8742i	−0.454689	−	1.39939i
$73$	−3.09726	+	2.25029i	−0.362507	+	0.263377i	−0.754097	−	0.656763i	$-0.771925\pi$
$73$	−3.09726	+	2.25029i	−0.362507	+	0.263377i	0.391590	+	0.920140i	$0.371925\pi$
$74$	−0.746033	−	2.29605i	−0.0867246	−	0.266911i
$75$	2.98413	−	9.18421i	0.344578	−	1.06050i
$76$	−4.91160	−	3.56848i	−0.563399	−	0.409333i
$77$	−3.91118	+	12.0374i	−0.445721	+	1.37179i
$78$	3.29315	−	10.1353i	0.372876	−	1.14759i
$79$	12.3316	+	8.95940i	1.38741	+	1.00801i	0.996144	+	0.0877328i	$0.0279622\pi$
$79$	12.3316	+	8.95940i	1.38741	+	1.00801i	0.391264	+	0.920278i	$0.372038\pi$
$80$	0.927051	−	2.85317i	0.103647	−	0.318994i
$81$	−2.93111	−	9.02104i	−0.325679	−	1.00234i
$82$	18.5261	−	13.4600i	2.04586	−	1.48641i
$83$	1.25803	+	3.87182i	0.138087	+	0.424987i	0.996057	−	0.0887116i	$-0.0282750\pi$
$83$	1.25803	+	3.87182i	0.138087	+	0.424987i	−0.857971	+	0.513699i	$0.828275\pi$
$84$	18.0522	+	13.1157i	1.96965	+	1.43104i
$85$	0.138805	+	0.100848i	0.0150556	+	0.0109385i
$86$	17.3820	−	12.6287i	1.87434	−	1.36179i
$87$	2.82843			0.303239
$88$	23.1421			2.46696
$89$	10.1008	−	7.33866i	1.07068	−	0.777897i	0.0946482	−	0.995511i	$-0.469827\pi$
$89$	10.1008	−	7.33866i	1.07068	−	0.777897i	0.976035	+	0.217614i	$0.0698274\pi$
$90$	−2.11010	+	6.49422i	−0.222424	+	0.684551i
$91$	1.36407	+	4.19817i	0.142993	+	0.440087i
$92$	−15.3137			−1.59656
$93$		0			0
$94$	4.00000			0.412568
$95$	0.490035	+	1.50817i	0.0502765	+	0.154735i
$96$	−1.18305	+	3.64105i	−0.120744	+	0.371613i
$97$	−8.76038	+	6.36479i	−0.889482	+	0.646246i	−0.935743	−	0.352683i	$-0.885269\pi$
$97$	−8.76038	+	6.36479i	−0.889482	+	0.646246i	0.0462609	+	0.998929i	$0.485269\pi$
$98$	2.82843			0.285714
$99$	−14.8284			−1.49031
$100$	12.3891	−	9.00117i	1.23891	−	0.900117i
$101$	−6.86474	−	4.98752i	−0.683067	−	0.496277i	0.191307	−	0.981530i	$-0.438727\pi$
$101$	−6.86474	−	4.98752i	−0.683067	−	0.496277i	−0.874374	+	0.485253i	$0.838727\pi$
$102$	0.809017	+	0.587785i	0.0801046	+	0.0581994i
$103$	−3.73017	−	11.4803i	−0.367544	−	1.13118i	−0.948373	−	0.317158i	$-0.897271\pi$
$103$	−3.73017	−	11.4803i	−0.367544	−	1.13118i	0.580828	−	0.814026i	$-0.302729\pi$
$104$	6.52963	−	4.74405i	0.640283	−	0.465193i
$105$	−1.80108	−	5.54316i	−0.175768	−	0.540957i
$106$	−0.127999	+	0.393941i	−0.0124324	+	0.0382629i
$107$	−7.75506	−	5.63438i	−0.749710	−	0.544696i	0.146027	−	0.989281i	$-0.453351\pi$
$107$	−7.75506	−	5.63438i	−0.749710	−	0.544696i	−0.895737	+	0.444584i	$0.853351\pi$
$108$	0.490035	−	1.50817i	0.0471536	−	0.145124i
$109$	−1.59810	+	4.91846i	−0.153071	+	0.471103i	−0.997960	−	0.0638377i	$-0.979666\pi$
$109$	−1.59810	+	4.91846i	−0.153071	+	0.471103i	0.844890	+	0.534941i	$0.179666\pi$
$110$	−10.2396	−	7.43951i	−0.976309	−	0.709330i
$111$	−0.746033	+	2.29605i	−0.0708103	+	0.217932i
$112$	2.23810	+	6.88816i	0.211480	+	0.650870i
$113$	−4.32270	+	3.14062i	−0.406645	+	0.295445i	−0.772242	−	0.635328i	$-0.780865\pi$
$113$	−4.32270	+	3.14062i	−0.406645	+	0.295445i	0.365597	+	0.930773i	$0.380865\pi$
$114$	2.85613	+	8.79027i	0.267501	+	0.823285i
$115$	3.23607	+	2.35114i	0.301765	+	0.219245i
$116$	3.62867	+	2.63638i	0.336913	+	0.244782i
$117$	−4.18389	+	3.03977i	−0.386801	+	0.281027i
$118$	24.3137			2.23826
$119$	−0.414214			−0.0379709
$120$	−8.62158	+	6.26394i	−0.787039	+	0.571817i
$121$	5.09423	−	15.6784i	0.463112	−	1.42531i
$122$	−2.11010	−	6.49422i	−0.191039	−	0.587959i
$123$	−22.8995			−2.06478
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−5.09423	−	15.6784i	−0.453830	−	1.39675i
$127$	−3.36813	+	10.3660i	−0.298873	+	0.919837i	0.683020	+	0.730400i	$0.260666\pi$
$127$	−3.36813	+	10.3660i	−0.298873	+	0.919837i	−0.981893	+	0.189437i	$0.939334\pi$
$128$	−16.6304	+	12.0827i	−1.46994	+	1.06797i
$129$	−21.4853			−1.89167
$130$	−4.41421			−0.387152
$131$	3.84878	−	2.79631i	0.336270	−	0.244314i	−0.406816	−	0.913510i	$-0.633361\pi$
$131$	3.84878	−	2.79631i	0.336270	−	0.244314i	0.743086	+	0.669196i	$0.233361\pi$
$132$	−39.2016	−	28.4816i	−3.41206	−	2.47901i
$133$	−3.09726	−	2.25029i	−0.268567	−	0.195125i
$134$	3.91118	+	12.0374i	0.337875	+	1.03987i
$135$	−0.335106	+	0.243469i	−0.0288413	+	0.0209544i
$136$	0.234037	+	0.720292i	0.0200685	+	0.0617645i
$137$	−2.31308	+	7.11893i	−0.197620	+	0.608211i	0.802316	+	0.596899i	$0.203601\pi$
$137$	−2.31308	+	7.11893i	−0.197620	+	0.608211i	−0.999936	+	0.0113118i	$0.996399\pi$
$138$	18.8612	+	13.7035i	1.60557	+	1.16652i
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$	2.85613	−	8.79027i	0.241387	−	0.742914i
$141$	−3.23607	−	2.35114i	−0.272526	−	0.198002i
$142$	10.4975	−	32.3079i	0.880929	−	2.71122i
$143$	−2.96217	−	9.11662i	−0.247709	−	0.762370i
$144$	−6.86474	+	4.98752i	−0.572061	+	0.415627i
$145$	−0.362036	−	1.11423i	−0.0300654	−	0.0925319i
$146$	7.47745	+	5.43269i	0.618838	+	0.449612i
$147$	−2.28825	−	1.66251i	−0.188731	−	0.137121i
$148$	−3.09726	+	2.25029i	−0.254593	+	0.184973i
$149$	1.00000			0.0819232			0.0409616	−	0.999161i	$-0.486958\pi$
$149$	1.00000			0.0819232			0.0409616	+	0.999161i	$0.486958\pi$
$150$	−23.3137			−1.90356
$151$	14.0071	−	10.1767i	1.13988	−	0.828172i	0.152778	−	0.988261i	$-0.451178\pi$
$151$	14.0071	−	10.1767i	1.13988	−	0.828172i	0.987103	+	0.160089i	$0.0511781\pi$
$152$	−2.16312	+	6.65740i	−0.175452	+	0.539986i
$153$	−0.149960	−	0.461530i	−0.0121236	−	0.0373125i
$154$	30.5563			2.46230
$155$		0			0
$156$	−16.8995			−1.35304
$157$	4.58224	+	14.1027i	0.365702	+	1.12552i	0.949540	+	0.313646i	$0.101550\pi$
$157$	4.58224	+	14.1027i	0.365702	+	1.12552i	−0.583838	+	0.811870i	$0.698450\pi$
$158$	11.3715	−	34.9979i	0.904669	−	2.78428i
$159$	0.335106	−	0.243469i	0.0265756	−	0.0193083i
$160$	1.58579			0.125367
$161$	−9.65685			−0.761067
$162$	−18.5261	+	13.4600i	−1.45555	+	1.05752i
$163$	10.4934	+	7.62391i	0.821907	+	0.597150i	0.917258	−	0.398293i	$-0.130397\pi$
$163$	10.4934	+	7.62391i	0.821907	+	0.597150i	−0.0953511	+	0.995444i	$0.530397\pi$
$164$	−29.3784	−	21.3447i	−2.29407	−	1.66674i
$165$	3.91118	+	12.0374i	0.304485	+	0.937109i
$166$	7.95136	−	5.77700i	0.617146	−	0.448383i
$167$	−2.64406	−	8.13757i	−0.204603	−	0.629704i	−0.999729	−	0.0232601i	$-0.992595\pi$
$167$	−2.64406	−	8.13757i	−0.204603	−	0.629704i	0.795126	−	0.606444i	$-0.207405\pi$
$168$	7.95037	−	24.4687i	0.613384	−	1.88780i
$169$	7.81256	+	5.67616i	0.600966	+	0.436627i
$170$	0.127999	−	0.393941i	0.00981708	−	0.0302139i
$171$	1.38603	−	4.26576i	0.105992	−	0.326211i
$172$	−27.5641	−	20.0265i	−2.10174	−	1.52700i
$173$	−4.42318	+	13.6131i	−0.336288	+	1.03499i	0.629796	+	0.776761i	$0.283138\pi$
$173$	−4.42318	+	13.6131i	−0.336288	+	1.03499i	−0.966084	+	0.258228i	$0.916862\pi$
$174$	−2.11010	−	6.49422i	−0.159966	−	0.492326i
$175$	7.81256	−	5.67616i	0.590574	−	0.429077i
$176$	−4.86020	−	14.9581i	−0.366351	−	1.12751i
$177$	−19.6702	−	14.2912i	−1.47850	−	1.07420i
$178$	−24.3855	−	17.7171i	−1.82777	−	1.32795i
$179$	5.46682	−	3.97188i	0.408609	−	0.296872i	−0.364429	−	0.931231i	$-0.618736\pi$
$179$	5.46682	−	3.97188i	0.408609	−	0.296872i	0.773039	+	0.634359i	$0.218736\pi$
$180$	10.8284			0.807103
$181$	−10.3137			−0.766612			−0.383306	−	0.923621i	$-0.625215\pi$
$181$	−10.3137			−0.766612			−0.383306	+	0.923621i	$0.625215\pi$
$182$	8.62158	−	6.26394i	0.639074	−	0.464314i
$183$	−2.11010	+	6.49422i	−0.155983	+	0.480067i
$184$	5.45627	+	16.7927i	0.402241	+	1.23797i
$185$	1.00000			0.0735215
$186$		0			0
$187$	0.899495			0.0657776
$188$	−1.96014	−	6.03269i	−0.142958	−	0.439979i
$189$	0.309017	−	0.951057i	0.0224777	−	0.0691792i
$190$	3.09726	−	2.25029i	0.224699	−	0.163253i
$191$	−1.10051			−0.0796298			−0.0398149	−	0.999207i	$-0.512677\pi$
$191$	−1.10051			−0.0796298			−0.0398149	+	0.999207i	$0.512677\pi$
$192$	23.7279			1.71242
$193$	17.1043	−	12.4270i	1.23120	−	0.894518i	0.234218	−	0.972184i	$-0.424747\pi$
$193$	17.1043	−	12.4270i	1.23120	−	0.894518i	0.996979	+	0.0776664i	$0.0247469\pi$
$194$	21.1494	+	15.3660i	1.51844	+	1.10321i
$195$	3.57117	+	2.59461i	0.255737	+	0.185804i
$196$	−1.38603	−	4.26576i	−0.0990020	−	0.304697i
$197$	−2.81965	+	2.04860i	−0.200892	+	0.145956i	−0.683683	−	0.729779i	$-0.739623\pi$
$197$	−2.81965	+	2.04860i	−0.200892	+	0.145956i	0.482791	+	0.875735i	$0.339623\pi$
$198$	11.0625	+	34.0469i	0.786177	+	2.41961i
$199$	4.81627	−	14.8230i	0.341417	−	1.05077i	−0.622058	−	0.782971i	$-0.713703\pi$
$199$	4.81627	−	14.8230i	0.341417	−	1.05077i	0.963474	−	0.267801i	$-0.0862969\pi$
$200$	−14.2847	−	10.3784i	−1.01008	−	0.733866i
$201$	3.91118	−	12.0374i	0.275874	−	0.849052i
$202$	−6.33030	+	19.4827i	−0.445398	+	1.37080i
$203$	2.28825	+	1.66251i	0.160603	+	0.116685i
$204$	0.490035	−	1.50817i	0.0343093	−	0.105593i
$205$	2.93111	+	9.02104i	0.204718	+	0.630057i
$206$	−23.5765	+	17.1293i	−1.64265	+	1.19346i
$207$	−3.49613	−	10.7600i	−0.242998	−	0.747870i
$208$	−4.43769	−	3.22417i	−0.307698	−	0.223556i
$209$	6.72593	+	4.88668i	0.465242	+	0.338018i
$210$	−11.3837	+	8.27077i	−0.785552	+	0.570737i
$211$	7.58579			0.522227			0.261114	−	0.965308i	$-0.415910\pi$
$211$	7.58579			0.522227			0.261114	+	0.965308i	$0.415910\pi$
$212$	0.656854			0.0451129
$213$	−27.4828	+	19.9674i	−1.88309	+	1.36814i
$214$	−7.15131	+	22.0095i	−0.488854	+	1.50454i
$215$	2.75010	+	8.46392i	0.187555	+	0.577235i
$216$	−1.82843			−0.124409
$217$		0			0
$218$	12.4853			0.845610
$219$	−2.85613	−	8.79027i	−0.193000	−	0.593992i
$220$	−6.20230	+	19.0887i	−0.418159	+	1.28696i
$221$	0.253796	−	0.184393i	0.0170721	−	0.0124036i
$222$	5.82843			0.391178
$223$	1.72792			0.115710			0.0578551	−	0.998325i	$-0.481574\pi$
$223$	1.72792			0.115710			0.0578551	+	0.998325i	$0.481574\pi$
$224$	−3.09726	+	2.25029i	−0.206945	+	0.150354i
$225$	9.15298	+	6.65003i	0.610199	+	0.443335i
$226$	10.4359	+	7.58213i	0.694186	+	0.504356i
$227$	−4.81627	−	14.8230i	−0.319667	−	0.983835i	−0.973791	−	0.227447i	$-0.926962\pi$
$227$	−4.81627	−	14.8230i	−0.319667	−	0.983835i	0.654123	−	0.756388i	$-0.273038\pi$
$228$	11.8576	−	8.61508i	0.785292	−	0.570548i
$229$	3.54915	+	10.9232i	0.234534	+	0.721822i	0.997183	+	0.0750091i	$0.0238986\pi$
$229$	3.54915	+	10.9232i	0.234534	+	0.721822i	−0.762649	+	0.646813i	$0.776101\pi$
$230$	2.98413	−	9.18421i	0.196768	−	0.605589i
$231$	−24.7206	−	17.9606i	−1.62650	−	1.18172i
$232$	1.59810	−	4.91846i	0.104921	−	0.322913i
$233$	−4.58224	+	14.1027i	−0.300192	+	0.923897i	0.681235	+	0.732064i	$0.261443\pi$
$233$	−4.58224	+	14.1027i	−0.300192	+	0.923897i	−0.981428	+	0.191832i	$0.938557\pi$
$234$	10.1008	+	7.33866i	0.660310	+	0.479743i
$235$	−0.511996	+	1.57576i	−0.0333989	+	0.102791i
$236$	−11.9146	−	36.6693i	−0.775572	−	2.38697i
$237$	−29.7710	+	21.6299i	−1.93383	+	1.40501i
$238$	0.309017	+	0.951057i	0.0200306	+	0.0616478i
$239$	10.3209	+	7.49859i	0.667605	+	0.485043i	0.869223	−	0.494421i	$-0.164620\pi$
$239$	10.3209	+	7.49859i	0.667605	+	0.485043i	−0.201618	+	0.979464i	$0.564620\pi$
$240$	5.85942	+	4.25712i	0.378224	+	0.274796i
$241$	−19.9478	+	14.4929i	−1.28495	+	0.933572i	−0.999690	−	0.0248778i	$-0.992080\pi$
$241$	−19.9478	+	14.4929i	−1.28495	+	0.933572i	−0.285261	+	0.958450i	$0.592080\pi$
$242$	−39.7990			−2.55838
$243$	21.6569			1.38929
$244$	−8.76038	+	6.36479i	−0.560826	+	0.407464i
$245$	−0.362036	+	1.11423i	−0.0231296	+	0.0711857i
$246$	17.0838	+	52.5785i	1.08922	+	3.35228i
$247$	2.89949			0.184490
$248$		0			0
$249$	−9.82843			−0.622851
$250$	6.71430	+	20.6645i	0.424649	+	1.30694i
$251$	1.10807	−	3.41029i	0.0699407	−	0.215255i	−0.909977	−	0.414660i	$-0.863901\pi$
$251$	1.10807	−	3.41029i	0.0699407	−	0.215255i	0.979917	+	0.199404i	$0.0639007\pi$
$252$	−21.1494	+	15.3660i	−1.33229	+	0.967965i
$253$	20.9706			1.31841
$254$	26.3137			1.65107
$255$	−0.335106	+	0.243469i	−0.0209851	+	0.0152466i
$256$	24.2467	+	17.6163i	1.51542	+	1.10102i
$257$	0.253796	+	0.184393i	0.0158313	+	0.0115021i	0.595673	−	0.803227i	$-0.296886\pi$
$257$	0.253796	+	0.184393i	0.0158313	+	0.0115021i	−0.579841	+	0.814729i	$0.696886\pi$
$258$	16.0287	+	49.3314i	0.997905	+	3.07124i
$259$	−1.95314	+	1.41904i	−0.121362	+	0.0881748i
$260$	2.16312	+	6.65740i	0.134151	+	0.412874i
$261$	−1.02399	+	3.15152i	−0.0633835	+	0.195074i
$262$	−9.29179	−	6.75088i	−0.574049	−	0.417071i
$263$	−0.212076	+	0.652702i	−0.0130772	+	0.0402473i	−0.957382	−	0.288824i	$-0.906736\pi$
$263$	−0.212076	+	0.652702i	−0.0130772	+	0.0402473i	0.944305	+	0.329071i	$0.106736\pi$
$264$	−17.2648	+	53.1356i	−1.06257	+	3.27027i
$265$	−0.138805	−	0.100848i	−0.00852675	−	0.00619504i
$266$	−2.85613	+	8.79027i	−0.175121	+	0.538966i
$267$	9.31443	+	28.6669i	0.570034	+	1.75438i
$268$	16.2378	−	11.7975i	0.991884	−	0.720646i
$269$	−9.83552	−	30.2706i	−0.599683	−	1.84563i	−0.529881	−	0.848072i	$-0.677763\pi$
$269$	−9.83552	−	30.2706i	−0.599683	−	1.84563i	−0.0698018	−	0.997561i	$-0.522237\pi$
$270$	0.809017	+	0.587785i	0.0492352	+	0.0357715i
$271$	18.8612	+	13.7035i	1.14574	+	0.832426i	0.987908	−	0.155041i	$-0.0495510\pi$
$271$	18.8612	+	13.7035i	1.14574	+	0.832426i	0.157827	+	0.987467i	$0.449551\pi$
$272$	0.416416	−	0.302544i	0.0252489	−	0.0183444i
$273$	−10.6569			−0.644982
$274$	18.0711			1.09171
$275$	−16.9655	+	12.3262i	−1.02306	+	0.743297i
$276$	11.4245	−	35.1611i	0.687676	−	2.11645i
$277$	−4.37016	−	13.4500i	−0.262577	−	0.808130i	−0.992242	−	0.124325i	$-0.960324\pi$
$277$	−4.37016	−	13.4500i	−0.262577	−	0.808130i	0.729664	−	0.683806i	$-0.239676\pi$
$278$		0			0
$279$		0			0
$280$	−10.6569			−0.636869
$281$	0.618034	+	1.90211i	0.0368688	+	0.113471i	0.967797	−	0.251731i	$-0.0809999\pi$
$281$	0.618034	+	1.90211i	0.0368688	+	0.113471i	−0.930928	+	0.365202i	$0.881000\pi$
$282$	−2.98413	+	9.18421i	−0.177702	+	0.546912i
$283$	1.89564	−	1.37727i	0.112684	−	0.0818700i	−0.530016	−	0.847988i	$-0.677814\pi$
$283$	1.89564	−	1.37727i	0.112684	−	0.0818700i	0.642700	+	0.766118i	$0.277814\pi$
$284$	−53.8701			−3.19660
$285$	−3.82843			−0.226776
$286$	−18.7224	+	13.6026i	−1.10708	+	0.804339i
$287$	−18.5261	−	13.4600i	−1.09356	−	0.794518i
$288$	−3.62867	−	2.63638i	−0.213821	−	0.155350i
$289$	−5.24419	−	16.1400i	−0.308482	−	0.949410i
$290$	−2.28825	+	1.66251i	−0.134370	+	0.0976258i
$291$	−8.07836	−	24.8626i	−0.473562	−	1.45747i
$292$	4.52922	−	13.9395i	0.265052	−	0.815747i
$293$	20.0628	+	14.5765i	1.17208	+	0.851567i	0.991257	−	0.131948i	$-0.0421233\pi$
$293$	20.0628	+	14.5765i	1.17208	+	0.851567i	0.180825	+	0.983515i	$0.442123\pi$
$294$	−2.11010	+	6.49422i	−0.123064	+	0.378751i
$295$	−3.11213	+	9.57815i	−0.181195	+	0.557662i
$296$	3.57117	+	2.59461i	0.207570	+	0.150809i
$297$	−0.671053	+	2.06529i	−0.0389384	+	0.119840i
$298$	−0.746033	−	2.29605i	−0.0432165	−	0.133007i
$299$	5.91691	−	4.29889i	0.342184	−	0.248611i
$300$	11.4245	+	35.1611i	0.659596	+	2.03003i
$301$	−17.3820	−	12.6287i	−1.00188	−	0.727908i
$302$	−33.8161	−	24.5688i	−1.94590	−	1.41378i
$303$	16.5729	−	12.0409i	0.952091	−	0.691734i
$304$	4.75736			0.272853
$305$	2.82843			0.161955
$306$	−0.947822	+	0.688633i	−0.0541834	+	0.0393665i
$307$	−0.852071	+	2.62240i	−0.0486303	+	0.149669i	−0.972423	−	0.233225i	$-0.925072\pi$
$307$	−0.852071	+	2.62240i	−0.0486303	+	0.149669i	0.923793	+	0.382893i	$0.125072\pi$
$308$	−14.9737	−	46.0842i	−0.853205	−	2.62589i
$309$	29.1421			1.65784
$310$		0			0
$311$	−11.3137			−0.641542			−0.320771	−	0.947157i	$-0.603942\pi$
$311$	−11.3137			−0.641542			−0.320771	+	0.947157i	$0.603942\pi$
$312$	6.02128	+	18.5316i	0.340888	+	1.04915i
$313$	1.18305	−	3.64105i	0.0668699	−	0.205804i	−0.912038	−	0.410105i	$-0.865492\pi$
$313$	1.18305	−	3.64105i	0.0668699	−	0.205804i	0.978908	+	0.204301i	$0.0654920\pi$
$314$	28.9620	−	21.0421i	1.63442	−	1.18748i
$315$	6.82843			0.384738
$316$	−58.3553			−3.28274
$317$	1.75684	−	1.27642i	0.0986739	−	0.0716908i	−0.537354	−	0.843357i	$-0.680576\pi$
$317$	1.75684	−	1.27642i	0.0986739	−	0.0716908i	0.636028	+	0.771666i	$0.280576\pi$
$318$	−0.809017	−	0.587785i	−0.0453674	−	0.0329614i
$319$	−4.96909	−	3.61026i	−0.278216	−	0.202136i
$320$	−3.03715	−	9.34739i	−0.169782	−	0.522535i
$321$	18.7224	−	13.6026i	1.04498	−	0.759223i
$322$	7.20433	+	22.1727i	0.401482	+	1.23563i
$323$	−0.0840767	+	0.258761i	−0.00467815	+	0.0143979i
$324$	29.3784	+	21.3447i	1.63213	+	1.18581i
$325$	−2.26006	+	6.95575i	−0.125366	+	0.385836i
$326$	9.67647	−	29.7811i	0.535930	−	1.64942i
$327$	−10.1008	−	7.33866i	−0.558576	−	0.405829i
$328$	−12.9386	+	39.8208i	−0.714412	+	2.19874i
$329$	−1.23607	−	3.80423i	−0.0681466	−	0.209734i
$330$	24.7206	−	17.9606i	1.36082	−	0.988697i
$331$	0.234037	+	0.720292i	0.0128638	+	0.0395908i	0.957282	−	0.289155i	$-0.0933742\pi$
$331$	0.234037	+	0.720292i	0.0128638	+	0.0395908i	−0.944419	+	0.328745i	$0.893374\pi$
$332$	−12.6092	−	9.16110i	−0.692018	−	0.502780i
$333$	−2.28825	−	1.66251i	−0.125395	−	0.0911049i
$334$	−16.7117	+	12.1418i	−0.914426	+	0.664369i
$335$	−5.24264			−0.286436
$336$	−17.4853			−0.953900
$337$	10.7710	−	7.82560i	0.586735	−	0.426288i	−0.254411	−	0.967096i	$-0.581882\pi$
$337$	10.7710	−	7.82560i	0.586735	−	0.426288i	0.841146	+	0.540808i	$0.181882\pi$
$338$	7.20433	−	22.1727i	0.391864	−	1.20603i
$339$	−3.98616	−	12.2681i	−0.216499	−	0.666314i
$340$	−0.656854			−0.0356229
$341$		0			0
$342$	−10.8284			−0.585534
$343$	−6.09626	−	18.7624i	−0.329167	−	1.01307i
$344$	−12.1395	+	37.3616i	−0.654518	+	2.01440i
$345$	−7.81256	+	5.67616i	−0.420614	+	0.305594i
$346$	34.5563			1.85776
$347$	22.5563			1.21089			0.605444	−	0.795888i	$-0.292996\pi$
$347$	22.5563			1.21089			0.605444	+	0.795888i	$0.292996\pi$
$348$	−8.76038	+	6.36479i	−0.469606	+	0.341189i
$349$	−28.4068	−	20.6387i	−1.52058	−	1.10477i	−0.961199	−	0.275854i	$-0.911039\pi$
$349$	−28.4068	−	20.6387i	−1.52058	−	1.10477i	−0.559380	−	0.828911i	$-0.688961\pi$
$350$	−18.8612	−	13.7035i	−1.00817	−	0.732480i
$351$	0.234037	+	0.720292i	0.0124920	+	0.0384463i
$352$	6.72593	−	4.88668i	0.358493	−	0.260461i
$353$	0.927051	+	2.85317i	0.0493419	+	0.151859i	0.972692	−	0.232101i	$-0.0745600\pi$
$353$	0.927051	+	2.85317i	0.0493419	+	0.151859i	−0.923350	+	0.383960i	$0.874560\pi$
$354$	−18.1388	+	55.8256i	−0.964068	+	2.96710i
$355$	11.3837	+	8.27077i	0.604186	+	0.438967i
$356$	−14.7707	+	45.4595i	−0.782846	+	2.40935i
$357$	0.309017	−	0.951057i	0.0163549	−	0.0503352i
$358$	−13.1981	−	9.58896i	−0.697540	−	0.506792i
$359$	8.31240	−	25.5829i	0.438712	−	1.35022i	−0.450523	−	0.892765i	$-0.648762\pi$
$359$	8.31240	−	25.5829i	0.438712	−	1.35022i	0.889235	−	0.457451i	$-0.151238\pi$
$360$	−3.85816	−	11.8742i	−0.203343	−	0.625826i
$361$	13.3369	−	9.68981i	0.701941	−	0.509990i
$362$	7.69437	+	23.6808i	0.404407	+	1.24464i
$363$	32.1981	+	23.3933i	1.68996	+	1.22783i
$364$	−13.6720	−	9.93327i	−0.716606	−	0.520645i
$365$	−3.09726	+	2.25029i	−0.162118	+	0.117786i
$366$	16.4853			0.861699
$367$	18.2132			0.950721			0.475361	−	0.879791i	$-0.342318\pi$
$367$	18.2132			0.950721			0.475361	+	0.879791i	$0.342318\pi$
$368$	9.70820	−	7.05342i	0.506075	−	0.367685i
$369$	8.29044	−	25.5154i	0.431583	−	1.32828i
$370$	−0.746033	−	2.29605i	−0.0387844	−	0.119366i
$371$	0.414214			0.0215049
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	−0.671053	−	2.06529i	−0.0346993	−	0.106794i
$375$	6.71430	−	20.6645i	0.346725	−	1.06711i
$376$	−5.91691	+	4.29889i	−0.305142	+	0.221698i
$377$	−2.14214			−0.110326
$378$	−2.41421			−0.124174
$379$	23.7728	−	17.2719i	1.22113	−	0.887200i	0.224933	−	0.974374i	$-0.427784\pi$
$379$	23.7728	−	17.2719i	1.22113	−	0.887200i	0.996193	+	0.0871744i	$0.0277837\pi$
$380$	−4.91160	−	3.56848i	−0.251960	−	0.183059i
$381$	−21.2882	−	15.4668i	−1.09063	−	0.792389i
$382$	0.821013	+	2.52682i	0.0420067	+	0.129283i
$383$	−20.1441	+	14.6356i	−1.02932	+	0.747842i	−0.968172	−	0.250287i	$-0.919475\pi$
$383$	−20.1441	+	14.6356i	−1.02932	+	0.747842i	−0.0611445	+	0.998129i	$0.519475\pi$
$384$	−15.3357	−	47.1985i	−0.782597	−	2.40859i
$385$	−3.91118	+	12.0374i	−0.199332	+	0.613482i
$386$	−41.2935	−	30.0015i	−2.10179	−	1.52704i
$387$	7.77844	−	23.9396i	0.395401	−	1.21692i
$388$	12.8106	−	39.4269i	0.650358	−	2.00160i
$389$	−13.8683	−	10.0759i	−0.703150	−	0.510868i	0.177807	−	0.984065i	$-0.443100\pi$
$389$	−13.8683	−	10.0759i	−0.703150	−	0.510868i	−0.880956	+	0.473197i	$0.843100\pi$
$390$	3.29315	−	10.1353i	0.166755	−	0.513219i
$391$	0.212076	+	0.652702i	0.0107251	+	0.0330086i
$392$	−4.18389	+	3.03977i	−0.211318	+	0.153532i
$393$	3.54915	+	10.9232i	0.179031	+	0.551000i
$394$	6.80724	+	4.94575i	0.342944	+	0.249163i
$395$	12.3316	+	8.95940i	0.620468	+	0.450796i
$396$	45.9275	−	33.3683i	2.30795	−	1.67682i
$397$	−16.5147			−0.828850			−0.414425	−	0.910083i	$-0.636017\pi$
$397$	−16.5147			−0.828850			−0.414425	+	0.910083i	$0.636017\pi$
$398$	−37.6274			−1.88609
$399$	7.47745	−	5.43269i	0.374341	−	0.271975i
$400$	−3.70820	+	11.4127i	−0.185410	+	0.570634i
$401$	−6.54238	−	20.1354i	−0.326711	−	1.00551i	−0.970663	−	0.240446i	$-0.922706\pi$
$401$	−6.54238	−	20.1354i	−0.326711	−	1.00551i	0.643952	−	0.765066i	$-0.277294\pi$
$402$	−30.5563			−1.52401
$403$		0			0
$404$	32.4853			1.61620
$405$	−2.93111	−	9.02104i	−0.145648	−	0.448259i
$406$	2.11010	−	6.49422i	0.104723	−	0.322303i
$407$	4.24139	−	3.08155i	0.210238	−	0.152747i
$408$	−1.82843			−0.0905206
$409$	9.34315			0.461989			0.230994	−	0.972955i	$-0.425802\pi$
$409$	9.34315			0.461989			0.230994	+	0.972955i	$0.425802\pi$
$410$	18.5261	−	13.4600i	0.914938	−	0.664741i
$411$	−14.6198	−	10.6219i	−0.721142	−	0.523940i
$412$	37.3873	+	27.1634i	1.84194	+	1.33825i
$413$	−7.51335	−	23.1237i	−0.369708	−	1.13784i
$414$	−22.0973	+	16.0546i	−1.08602	+	0.789040i
$415$	1.25803	+	3.87182i	0.0617542	+	0.190060i
$416$	0.895993	−	2.75758i	0.0439297	−	0.135202i
$417$		0			0
$418$	6.20230	−	19.0887i	0.303364	−	0.933660i
$419$	8.65248	−	26.6296i	0.422701	−	1.30094i	−0.482477	−	0.875908i	$-0.660263\pi$
$419$	8.65248	−	26.6296i	0.422701	−	1.30094i	0.905178	−	0.425032i	$-0.139737\pi$
$420$	18.0522	+	13.1157i	0.880856	+	0.639979i
$421$	−0.883129	+	2.71799i	−0.0430411	+	0.132467i	−0.970268	−	0.242033i	$-0.922186\pi$
$421$	−0.883129	+	2.71799i	−0.0430411	+	0.132467i	0.927227	+	0.374500i	$0.122186\pi$
$422$	−5.65925	−	17.4174i	−0.275488	−	0.847864i
$423$	3.79129	−	2.75453i	0.184339	−	0.133930i
$424$	−0.234037	−	0.720292i	−0.0113658	−	0.0349804i
$425$	−0.555221	−	0.403392i	−0.0269322	−	0.0195674i
$426$	66.3493	+	48.2056i	3.21463	+	2.33557i
$427$	−5.52431	+	4.01365i	−0.267340	+	0.194234i
$428$	36.6985			1.77389
$429$	23.1421			1.11731
$430$	17.3820	−	12.6287i	0.838232	−	0.609012i
$431$	−7.80040	+	24.0072i	−0.375732	+	1.15639i	0.567251	+	0.823545i	$0.308007\pi$
$431$	−7.80040	+	24.0072i	−0.375732	+	1.15639i	−0.942983	+	0.332840i	$0.891993\pi$
$432$	0.383997	+	1.18182i	0.0184751	+	0.0568604i
$433$	−35.1127			−1.68741			−0.843704	−	0.536808i	$-0.819630\pi$
$433$	−35.1127			−1.68741			−0.843704	+	0.536808i	$0.819630\pi$
$434$		0			0
$435$	2.82843			0.135613
$436$	−6.11822	−	18.8300i	−0.293010	−	0.901791i
$437$	−1.96014	+	6.03269i	−0.0937662	+	0.288583i
$438$	−18.0522	+	13.1157i	−0.862566	+	0.626691i
$439$	−12.0711			−0.576121			−0.288060	−	0.957612i	$-0.593010\pi$
$439$	−12.0711			−0.576121			−0.288060	+	0.957612i	$0.593010\pi$
$440$	23.1421			1.10326
$441$	2.68085	−	1.94775i	0.127659	−	0.0927500i
$442$	−0.612717	−	0.445165i	−0.0291440	−	0.0211743i
$443$	10.7135	+	7.78383i	0.509015	+	0.369821i	0.812450	−	0.583031i	$-0.198134\pi$
$443$	10.7135	+	7.78383i	0.509015	+	0.369821i	−0.303435	+	0.952852i	$0.598134\pi$
$444$	−2.85613	−	8.79027i	−0.135546	−	0.417168i
$445$	10.1008	−	7.33866i	0.478824	−	0.347886i
$446$	−1.28909	−	3.96740i	−0.0610400	−	0.187862i
$447$	−0.746033	+	2.29605i	−0.0352862	+	0.108600i
$448$	19.1963	+	13.9469i	0.906940	+	0.658930i
$449$	1.42995	−	4.40094i	0.0674835	−	0.207693i	−0.911628	−	0.411016i	$-0.865174\pi$
$449$	1.42995	−	4.40094i	0.0674835	−	0.207693i	0.979112	+	0.203323i	$0.0651741\pi$
$450$	8.44040	−	25.9769i	0.397884	−	1.22456i
$451$	40.2307	+	29.2293i	1.89439	+	1.37636i
$452$	6.32120	−	19.4547i	0.297324	−	0.915070i
$453$	12.9166	+	39.7532i	0.606875	+	1.86777i
$454$	−30.4412	+	22.1168i	−1.42868	+	1.03799i
$455$	1.36407	+	4.19817i	0.0639484	+	0.196813i
$456$	−13.6720	−	9.93327i	−0.640249	−	0.465168i
$457$	−25.1707	−	18.2876i	−1.17744	−	0.855457i	−0.185556	−	0.982634i	$-0.559409\pi$
$457$	−25.1707	−	18.2876i	−1.17744	−	0.855457i	−0.991880	+	0.127177i	$0.959409\pi$
$458$	22.4324	−	16.2981i	1.04820	−	0.761559i
$459$	−0.0710678			−0.00331716
$460$	−15.3137			−0.714005
$461$	−21.1494	+	15.3660i	−0.985027	+	0.715664i	−0.958826	−	0.283993i	$-0.908341\pi$
$461$	−21.1494	+	15.3660i	−0.985027	+	0.715664i	−0.0262008	+	0.999657i	$0.508341\pi$
$462$	−22.7960	+	70.1590i	−1.06057	+	3.26409i
$463$	7.71633	+	23.7484i	0.358608	+	1.10368i	0.953888	+	0.300164i	$0.0970413\pi$
$463$	7.71633	+	23.7484i	0.358608	+	1.10368i	−0.595279	+	0.803519i	$0.702959\pi$
$464$	−3.51472			−0.163167
$465$		0			0
$466$	35.7990			1.65836
$467$	−2.47214	−	7.60845i	−0.114397	−	0.352077i	0.877424	−	0.479716i	$-0.159260\pi$
$467$	−2.47214	−	7.60845i	−0.114397	−	0.352077i	−0.991821	+	0.127639i	$0.959260\pi$
$468$	6.11822	−	18.8300i	0.282815	−	0.870415i
$469$	10.2396	−	7.43951i	0.472821	−	0.343525i
$470$	4.00000			0.184506
$471$	−35.7990			−1.64953
$472$	−35.9655	+	26.1305i	−1.65545	+	1.20275i
$473$	37.7462	+	27.4242i	1.73557	+	1.26097i
$474$	71.8736	+	52.2192i	3.30126	+	2.39851i
$475$	−1.96014	−	6.03269i	−0.0899374	−	0.276799i
$476$	1.28293	−	0.932102i	0.0588029	−	0.0427228i
$477$	0.149960	+	0.461530i	0.00686621	+	0.0211320i
$478$	9.51741	−	29.2916i	0.435316	−	1.33977i
$479$	−7.87005	−	5.71793i	−0.359592	−	0.261259i	0.393290	−	0.919415i	$-0.371337\pi$
$479$	−7.87005	−	5.71793i	−0.359592	−	0.261259i	−0.752882	+	0.658156i	$0.771337\pi$
$480$	−1.18305	+	3.64105i	−0.0539986	+	0.166190i
$481$	0.565015	−	1.73894i	0.0257625	−	0.0792887i
$482$	48.1583	+	34.9890i	2.19355	+	1.59371i
$483$	7.20433	−	22.1727i	0.327808	−	1.00889i
$484$	19.5029	+	60.0237i	0.886495	+	2.72835i
$485$	−8.76038	+	6.36479i	−0.397788	+	0.289010i
$486$	−16.1567	−	49.7253i	−0.732884	−	2.25559i
$487$	14.0646	+	10.2185i	0.637327	+	0.463045i	0.858931	−	0.512092i	$-0.171129\pi$
$487$	14.0646	+	10.2185i	0.637327	+	0.463045i	−0.221604	+	0.975137i	$0.571129\pi$
$488$	10.1008	+	7.33866i	0.457242	+	0.332206i
$489$	−25.3333	+	18.4057i	−1.14561	+	0.832336i
$490$	2.82843			0.127775
$491$	4.41421			0.199211			0.0996053	−	0.995027i	$-0.468242\pi$
$491$	4.41421			0.199211			0.0996053	+	0.995027i	$0.468242\pi$
$492$	70.9257	−	51.5306i	3.19758	−	2.32318i
$493$	0.0621155	−	0.191172i	0.00279754	−	0.00860995i
$494$	−2.16312	−	6.65740i	−0.0973233	−	0.299530i
$495$	−14.8284			−0.666488
$496$		0			0
$497$	−33.9706			−1.52379
$498$	7.33233	+	22.5666i	0.328570	+	1.01123i
$499$	12.4266	−	38.2450i	0.556289	−	1.71208i	−0.136224	−	0.990678i	$-0.543497\pi$
$499$	12.4266	−	38.2450i	0.556289	−	1.71208i	0.692514	−	0.721405i	$-0.256503\pi$
$500$	27.8754	−	20.2526i	1.24662	−	0.905725i
$501$	20.6569			0.922880
$502$	−8.65685			−0.386374
$503$	−18.9187	+	13.7452i	−0.843542	+	0.612869i	−0.923358	−	0.383940i	$-0.874567\pi$
$503$	−18.9187	+	13.7452i	−0.843542	+	0.612869i	0.0798156	+	0.996810i	$0.474567\pi$
$504$	24.3855	+	17.7171i	1.08622	+	0.789182i
$505$	−6.86474	−	4.98752i	−0.305477	−	0.221942i
$506$	−15.6447	−	48.1495i	−0.695493	−	2.14051i
$507$	−18.8612	+	13.7035i	−0.837655	+	0.608592i
$508$	−12.8946	−	39.6856i	−0.572107	−	1.76076i
$509$	2.10100	−	6.46622i	0.0931253	−	0.286610i	−0.893635	−	0.448794i	$-0.851854\pi$
$509$	2.10100	−	6.46622i	0.0931253	−	0.286610i	0.986761	+	0.162184i	$0.0518537\pi$
$510$	0.809017	+	0.587785i	0.0358239	+	0.0260276i
$511$	2.85613	−	8.79027i	0.126348	−	0.388859i
$512$	9.65451	−	29.7135i	0.426673	−	1.31316i
$513$	−0.531406	−	0.386089i	−0.0234622	−	0.0170463i
$514$	0.234037	−	0.720292i	0.0103229	−	0.0317707i
$515$	−3.73017	−	11.4803i	−0.164371	−	0.505881i
$516$	66.5456	−	48.3482i	2.92950	−	2.12841i
$517$	2.68421	+	8.26115i	0.118051	+	0.363325i
$518$	4.71530	+	3.42586i	0.207178	+	0.150524i
$519$	−27.9567	−	20.3117i	−1.22716	−	0.891585i
$520$	6.52963	−	4.74405i	0.286343	−	0.208041i
$521$	30.4558			1.33429			0.667147	−	0.744926i	$-0.267515\pi$
$521$	30.4558			1.33429			0.667147	+	0.744926i	$0.267515\pi$
$522$	8.00000			0.350150
$523$	6.47214	−	4.70228i	0.283007	−	0.205616i	−0.437221	−	0.899354i	$-0.644037\pi$
$523$	6.47214	−	4.70228i	0.283007	−	0.205616i	0.720228	+	0.693738i	$0.244037\pi$
$524$	−5.62819	+	17.3218i	−0.245869	+	0.756706i
$525$	7.20433	+	22.1727i	0.314423	+	0.967694i
$526$	1.65685			0.0722423
$527$		0			0
$528$	37.9706			1.65246
$529$	−2.16312	−	6.65740i	−0.0940487	−	0.289452i
$530$	−0.127999	+	0.393941i	−0.00555992	+	0.0171117i
$531$	23.0451	−	16.7432i	1.00007	−	0.726594i
$532$	14.6569			0.635455
$533$	17.3431			0.751215
$534$	58.8718	−	42.7729i	2.54763	−	1.85096i
$535$	−7.75506	−	5.63438i	−0.335281	−	0.243596i
$536$	−18.7224	−	13.6026i	−0.808684	−	0.587543i
$537$	5.04121	+	15.5153i	0.217544	+	0.669533i
$538$	−62.1654	+	45.1658i	−2.68014	+	1.94724i
$539$	1.89802	+	5.84152i	0.0817537	+	0.251612i
$540$	0.490035	−	1.50817i	0.0210877	−	0.0649014i
$541$	−20.4554	−	14.8617i	−0.879447	−	0.638955i	0.0536584	−	0.998559i	$-0.482912\pi$
$541$	−20.4554	−	14.8617i	−0.879447	−	0.638955i	−0.933105	+	0.359604i	$0.882912\pi$
$542$	17.3928	−	53.5295i	0.747085	−	2.29929i
$543$	7.69437	−	23.6808i	0.330197	−	1.01624i
$544$	0.220116	+	0.159923i	0.00943738	+	0.00685666i
$545$	−1.59810	+	4.91846i	−0.0684553	+	0.210684i
$546$	7.95037	+	24.4687i	0.340244	+	1.04716i
$547$	−4.63399	+	3.36679i	−0.198135	+	0.143953i	−0.682429	−	0.730952i	$-0.739076\pi$
$547$	−4.63399	+	3.36679i	−0.198135	+	0.143953i	0.484294	+	0.874905i	$0.339076\pi$
$548$	−8.85545	−	27.2543i	−0.378286	−	1.16425i
$549$	−6.47214	−	4.70228i	−0.276224	−	0.200689i
$550$	40.9584	+	29.7580i	1.74647	+	1.26889i
$551$	1.50304	−	1.09203i	0.0640318	−	0.0465218i
$552$	−42.6274			−1.81434
$553$	−36.7990			−1.56485
$554$	−27.6216	+	20.0682i	−1.17353	+	0.852618i
$555$	−0.746033	+	2.29605i	−0.0316673	+	0.0974620i
$556$		0			0
$557$	44.4853			1.88490			0.942451	−	0.334344i	$-0.108515\pi$
$557$	44.4853			1.88490			0.942451	+	0.334344i	$0.108515\pi$
$558$		0			0
$559$	16.2721			0.688236
$560$	2.23810	+	6.88816i	0.0945769	+	0.291078i
$561$	−0.671053	+	2.06529i	−0.0283319	+	0.0871966i
$562$	3.90628	−	2.83808i	0.164776	−	0.119717i
$563$	4.75736			0.200499			0.100249	−	0.994962i	$-0.468036\pi$
$563$	4.75736			0.200499			0.100249	+	0.994962i	$0.468036\pi$
$564$	15.3137			0.644823
$565$	−4.32270	+	3.14062i	−0.181857	+	0.132127i
$566$	−4.57649	−	3.32502i	−0.192364	−	0.139761i
$567$	18.5261	+	13.4600i	0.778022	+	0.565266i
$568$	19.1939	+	59.0727i	0.805357	+	2.47863i
$569$	−12.2502	+	8.90032i	−0.513557	+	0.373121i	−0.814171	−	0.580625i	$-0.802808\pi$
$569$	−12.2502	+	8.90032i	−0.513557	+	0.373121i	0.300614	+	0.953746i	$0.402808\pi$
$570$	2.85613	+	8.79027i	0.119630	+	0.368184i
$571$	−12.6386	+	38.8977i	−0.528911	+	1.62782i	0.227540	+	0.973769i	$0.426932\pi$
$571$	−12.6386	+	38.8977i	−0.528911	+	1.62782i	−0.756451	+	0.654051i	$0.773068\pi$
$572$	29.6897	+	21.5708i	1.24139	+	0.901922i
$573$	0.821013	−	2.52682i	0.0342983	−	0.105559i
$574$	−17.0838	+	52.5785i	−0.713063	+	2.19458i
$575$	−12.9443	−	9.40456i	−0.539813	−	0.392197i
$576$	−8.59036	+	26.4384i	−0.357932	+	1.10160i
$577$	−10.4975	−	32.3079i	−0.437016	−	1.34500i	−0.891007	−	0.453990i	$-0.850000\pi$
$577$	−10.4975	−	32.3079i	−0.437016	−	1.34500i	0.453991	−	0.891006i	$-0.350000\pi$
$578$	−33.1459	+	24.0819i	−1.37869	+	1.00167i
$579$	15.7727	+	48.5435i	0.655492	+	2.01740i
$580$	3.62867	+	2.63638i	0.150672	+	0.109470i
$581$	−7.95136	−	5.77700i	−0.329878	−	0.239671i
$582$	−51.0592	+	37.0967i	−2.11647	+	1.53771i
$583$	−0.899495			−0.0372533
$584$	−16.8995			−0.699306
$585$	−4.18389	+	3.03977i	−0.172983	+	0.125679i
$586$	18.5009	−	56.9398i	0.764264	−	2.35216i
$587$	−6.28638	−	19.3475i	−0.259467	−	0.798556i	−0.992917	−	0.118813i	$-0.962091\pi$
$587$	−6.28638	−	19.3475i	−0.259467	−	0.798556i	0.733450	−	0.679743i	$-0.237909\pi$
$588$	10.8284			0.446557
$589$		0			0
$590$	24.3137			1.00098
$591$	−2.60013	−	8.00239i	−0.106955	−	0.329174i
$592$	0.927051	−	2.85317i	0.0381016	−	0.117265i
$593$	−17.2432	+	12.5279i	−0.708091	+	0.514459i	−0.882557	−	0.470205i	$-0.844180\pi$
$593$	−17.2432	+	12.5279i	−0.708091	+	0.514459i	0.174466	+	0.984663i	$0.444180\pi$
$594$	5.24264			0.215108
$595$	−0.414214			−0.0169811
$596$	−3.09726	+	2.25029i	−0.126869	+	0.0921756i
$597$	30.4412	+	22.1168i	1.24588	+	0.905182i
$598$	−14.2847	−	10.3784i	−0.584145	−	0.424406i
$599$	10.7845	+	33.1914i	0.440644	+	1.35616i	0.887191	+	0.461403i	$0.152654\pi$
$599$	10.7845	+	33.1914i	0.440644	+	1.35616i	−0.446546	+	0.894760i	$0.647346\pi$
$600$	34.4863	−	25.0558i	1.40790	−	1.02290i
$601$	−7.25735	−	22.3358i	−0.296034	−	0.911098i	−0.982872	−	0.184288i	$-0.941002\pi$
$601$	−7.25735	−	22.3358i	−0.296034	−	0.911098i	0.686839	−	0.726810i	$-0.258998\pi$
$602$	−16.0287	+	49.3314i	−0.653282	+	2.01060i
$603$	11.9964	+	8.71593i	0.488533	+	0.354940i
$604$	−20.4830	+	63.0401i	−0.833440	+	2.56506i
$605$	5.09423	−	15.6784i	0.207110	−	0.637419i
$606$	−40.0106	−	29.0694i	−1.62532	−	1.18086i
$607$	−1.36407	+	4.19817i	−0.0553658	+	0.170398i	−0.974915	−	0.222575i	$-0.928554\pi$
$607$	−1.36407	+	4.19817i	−0.0553658	+	0.170398i	0.919550	+	0.392974i	$0.128554\pi$
$608$	0.777091	+	2.39164i	0.0315152	+	0.0969938i
$609$	−5.52431	+	4.01365i	−0.223856	+	0.162641i
$610$	−2.11010	−	6.49422i	−0.0854355	−	0.262943i
$611$	2.45087	+	1.78066i	0.0991514	+	0.0720377i
$612$	1.50304	+	1.09203i	0.0607569	+	0.0441425i
$613$	8.34397	−	6.06225i	0.337010	−	0.244852i	−0.406389	−	0.913700i	$-0.633212\pi$
$613$	8.34397	−	6.06225i	0.337010	−	0.244852i	0.743399	+	0.668848i	$0.233212\pi$
$614$	6.65685			0.268649
$615$	−22.8995			−0.923397
$616$	−45.1998	+	32.8396i	−1.82115	+	1.32315i
$617$	7.19524	−	22.1447i	0.289669	−	0.891510i	−0.695291	−	0.718728i	$-0.744724\pi$
$617$	7.19524	−	22.1447i	0.289669	−	0.891510i	0.984960	−	0.172782i	$-0.0552756\pi$
$618$	−21.7410	−	66.9119i	−0.874551	−	2.69159i
$619$	−31.6569			−1.27240			−0.636198	−	0.771526i	$-0.719494\pi$
$619$	−31.6569			−1.27240			−0.636198	+	0.771526i	$0.719494\pi$
$620$		0			0
$621$	−1.65685			−0.0664873
$622$	8.44040	+	25.9769i	0.338429	+	1.04158i
$623$	−9.31443	+	28.6669i	−0.373175	+	1.14851i
$624$	10.7135	−	7.78383i	0.428884	−	0.311603i
$625$	11.0000			0.440000
$626$	−9.24264			−0.369410
$627$	−16.2378	+	11.7975i	−0.648477	+	0.471146i
$628$	−45.9275	−	33.3683i	−1.83271	−	1.33154i
$629$	0.138805	+	0.100848i	0.00553453	+	0.00402107i
$630$	−5.09423	−	15.6784i	−0.202959	−	0.624644i
$631$	25.8984	−	18.8163i	1.03100	−	0.749065i	0.0624909	−	0.998046i	$-0.480096\pi$
$631$	25.8984	−	18.8163i	1.03100	−	0.749065i	0.968508	+	0.248981i	$0.0800956\pi$
$632$	20.7920	+	63.9911i	0.827061	+	2.54543i
$633$	−5.65925	+	17.4174i	−0.224935	+	0.692278i
$634$	−4.24139	−	3.08155i	−0.168447	−	0.122384i
$635$	−3.36813	+	10.3660i	−0.133660	+	0.411364i
$636$	−0.490035	+	1.50817i	−0.0194312	+	0.0598029i
$637$	1.73302	+	1.25912i	0.0686649	+	0.0498880i
$638$	−4.58224	+	14.1027i	−0.181412	+	0.558330i
$639$	−12.2986	−	37.8511i	−0.486524	−	1.49737i
$640$	−16.6304	+	12.0827i	−0.657376	+	0.477611i
$641$	6.17124	+	18.9931i	0.243749	+	0.750184i	0.995840	+	0.0911234i	$0.0290458\pi$
$641$	6.17124	+	18.9931i	0.243749	+	0.750184i	−0.752090	+	0.659060i	$0.770954\pi$
$642$	−45.1998	−	32.8396i	−1.78389	−	1.29608i
$643$	−10.2634	−	7.45682i	−0.404750	−	0.294068i	0.366723	−	0.930330i	$-0.380480\pi$
$643$	−10.2634	−	7.45682i	−0.404750	−	0.294068i	−0.771473	+	0.636262i	$0.780480\pi$
$644$	29.9098	−	21.7308i	1.17861	−	0.856312i
$645$	−21.4853			−0.845982
$646$	0.656854			0.0258436
$647$	18.3536	−	13.3347i	0.721554	−	0.524240i	−0.165326	−	0.986239i	$-0.552868\pi$
$647$	18.3536	−	13.3347i	0.721554	−	0.524240i	0.886880	+	0.461999i	$0.152868\pi$
$648$	12.9386	−	39.8208i	0.508275	−	1.56431i
$649$	16.3158	+	50.2148i	0.640451	+	1.97110i
$650$	17.6569			0.692559
$651$		0			0
$652$	−49.6569			−1.94471
$653$	6.84230	+	21.0584i	0.267760	+	0.824080i	0.991045	+	0.133530i	$0.0426313\pi$
$653$	6.84230	+	21.0584i	0.267760	+	0.824080i	−0.723285	+	0.690550i	$0.757369\pi$
$654$	−9.31443	+	28.6669i	−0.364223	+	1.12096i
$655$	3.84878	−	2.79631i	0.150384	−	0.109261i
$656$	28.4558			1.11101
$657$	10.8284			0.422457
$658$	−7.81256	+	5.67616i	−0.304565	+	0.221280i
$659$	−7.81256	−	5.67616i	−0.304334	−	0.221112i	0.425127	−	0.905134i	$-0.360229\pi$
$659$	−7.81256	−	5.67616i	−0.304334	−	0.221112i	−0.729462	+	0.684022i	$0.760229\pi$
$660$	−39.2016	−	28.4816i	−1.52592	−	1.10865i
$661$	10.2415	+	31.5200i	0.398348	+	1.22599i	0.926324	+	0.376728i	$0.122951\pi$
$661$	10.2415	+	31.5200i	0.398348	+	1.22599i	−0.527976	+	0.849259i	$0.677049\pi$
$662$	1.47923	−	1.07472i	0.0574919	−	0.0417703i
$663$	0.234037	+	0.720292i	0.00908924	+	0.0279738i
$664$	−5.55321	+	17.0910i	−0.215506	+	0.663260i
$665$	−3.09726	−	2.25029i	−0.120107	−	0.0872626i
$666$	−2.11010	+	6.49422i	−0.0817647	+	0.251646i
$667$	1.44814	−	4.45693i	0.0560723	−	0.172573i
$668$	26.5013	+	19.2543i	1.02536	+	0.744971i
$669$	−1.28909	+	3.96740i	−0.0498390	+	0.153389i
$670$	3.91118	+	12.0374i	0.151102	+	0.465045i
$671$	11.9964	−	8.71593i	0.463118	−	0.336475i
$672$	−2.85613	−	8.79027i	−0.110178	−	0.339092i
$673$	−16.7117	−	12.1418i	−0.644190	−	0.468032i	0.217097	−	0.976150i	$-0.430341\pi$
$673$	−16.7117	−	12.1418i	−0.644190	−	0.468032i	−0.861287	+	0.508118i	$0.830341\pi$
$674$	−26.0035	−	18.8927i	−1.00162	−	0.727719i
$675$	1.34042	−	0.973874i	0.0515929	−	0.0374844i
$676$	−36.9706			−1.42194
$677$	40.5980			1.56031			0.780154	−	0.625588i	$-0.215141\pi$
$677$	40.5980			1.56031			0.780154	+	0.625588i	$0.215141\pi$
$678$	−25.1945	+	18.3049i	−0.967590	+	0.702995i
$679$	8.07836	−	24.8626i	0.310019	−	0.954141i
$680$	0.234037	+	0.720292i	0.00897491	+	0.0276219i
$681$	37.6274			1.44189
$682$		0			0
$683$	−46.6274			−1.78415			−0.892074	−	0.451889i	$-0.850750\pi$
$683$	−46.6274			−1.78415			−0.892074	+	0.451889i	$0.850750\pi$
$684$	5.30631	+	16.3311i	0.202892	+	0.624437i
$685$	−2.31308	+	7.11893i	−0.0883782	+	0.272000i
$686$	−38.5314	+	27.9947i	−1.47114	+	1.06884i
$687$	−27.7279			−1.05789
$688$	26.6985			1.01787
$689$	−0.253796	+	0.184393i	−0.00966884	+	0.00702482i
$690$	18.8612	+	13.7035i	0.718033	+	0.521682i
$691$	−11.3837	−	8.27077i	−0.433058	−	0.314635i	0.349813	−	0.936820i	$-0.386245\pi$
$691$	−11.3837	−	8.27077i	−0.433058	−	0.314635i	−0.782870	+	0.622185i	$0.786245\pi$
$692$	−16.9338	−	52.1169i	−0.643727	−	1.98119i
$693$	28.9620	−	21.0421i	1.10018	−	0.799324i
$694$	−16.8278	−	51.7906i	−0.638774	−	1.96594i
$695$		0			0
$696$	10.1008	+	7.33866i	0.382870	+	0.278171i
$697$	−0.502900	+	1.54777i	−0.0190487	+	0.0586258i
$698$	−26.1952	+	80.6206i	−0.991504	+	3.05154i
$699$	−28.9620	−	21.0421i	−1.09544	−	0.795886i
$700$	−11.4245	+	35.1611i	−0.431807	+	1.32896i
$701$	1.07701	+	3.31470i	0.0406782	+	0.125194i	0.969333	−	0.245750i	$-0.0790341\pi$
$701$	1.07701	+	3.31470i	0.0406782	+	0.125194i	−0.928655	+	0.370944i	$0.879034\pi$
$702$	1.47923	−	1.07472i	0.0558299	−	0.0405628i
$703$	0.490035	+	1.50817i	0.0184820	+	0.0568818i
$704$	−41.6861	−	30.2868i	−1.57111	−	1.14148i
$705$	−3.23607	−	2.35114i	−0.121877	−	0.0885491i
$706$	5.85942	−	4.25712i	0.220522	−	0.160219i
$707$	20.4853			0.770428
$708$	93.0833			3.49828
$709$	4.29888	−	3.12332i	0.161448	−	0.117299i	−0.504128	−	0.863629i	$-0.668186\pi$
$709$	4.29888	−	3.12332i	0.161448	−	0.117299i	0.665576	+	0.746330i	$0.268186\pi$
$710$	10.4975	−	32.3079i	0.393963	−	1.21249i
$711$	−13.3226	−	41.0026i	−0.499635	−	1.53772i
$712$	55.1127			2.06544
$713$		0			0
$714$	−2.41421			−0.0903497
$715$	−2.96217	−	9.11662i	−0.110779	−	0.340942i
$716$	−7.99429	+	24.6039i	−0.298761	+	0.919490i
$717$	−24.9169	+	18.1032i	−0.930539	+	0.676076i
$718$	−64.9411			−2.42358
$719$	6.07107			0.226413			0.113206	−	0.993572i	$-0.463888\pi$
$719$	6.07107			0.226413			0.113206	+	0.993572i	$0.463888\pi$
$720$	−6.86474	+	4.98752i	−0.255834	+	0.185874i
$721$	23.5765	+	17.1293i	0.878034	+	0.637929i
$722$	−32.1981	−	23.3933i	−1.19829	−	0.870607i
$723$	−18.3948	−	56.6135i	−0.684111	−	2.10548i
$724$	31.9443	−	23.2089i	1.18720	−	0.862551i
$725$	1.44814	+	4.45693i	0.0537827	+	0.165526i
$726$	29.6914	−	91.3806i	1.10195	−	3.39145i
$727$	37.8949	+	27.5322i	1.40544	+	1.02111i	0.993965	+	0.109694i	$0.0349870\pi$
$727$	37.8949	+	27.5322i	1.40544	+	1.02111i	0.411477	+	0.911420i	$0.365013\pi$
$728$	−6.02128	+	18.5316i	−0.223164	+	0.686827i
$729$	−7.36339	+	22.6622i	−0.272718	+	0.839340i
$730$	7.47745	+	5.43269i	0.276753	+	0.201073i
$731$	−0.471842	+	1.45218i	−0.0174517	+	0.0537108i
$732$	−8.07836	−	24.8626i	−0.298585	−	0.918950i
$733$	23.9691	−	17.4146i	0.885318	−	0.643221i	−0.0493348	−	0.998782i	$-0.515710\pi$
$733$	23.9691	−	17.4146i	0.885318	−	0.643221i	0.934653	+	0.355561i	$0.115710\pi$
$734$	−13.5877	−	41.8185i	−0.501529	−	1.54355i
$735$	−2.28825	−	1.66251i	−0.0844032	−	0.0613225i
$736$	5.13171	+	3.72841i	0.189157	+	0.137431i
$737$	−22.2361	+	16.1554i	−0.819076	+	0.595093i
$738$	−64.7696			−2.38420
$739$	−7.87006			−0.289505			−0.144752	−	0.989468i	$-0.546239\pi$
$739$	−7.87006			−0.289505			−0.144752	+	0.989468i	$0.546239\pi$
$740$	−3.09726	+	2.25029i	−0.113858	+	0.0827224i
$741$	−2.16312	+	6.65740i	−0.0794642	+	0.244566i
$742$	−0.309017	−	0.951057i	−0.0113444	−	0.0349144i
$743$	−5.65685			−0.207530			−0.103765	−	0.994602i	$-0.533089\pi$
$743$	−5.65685			−0.207530			−0.103765	+	0.994602i	$0.533089\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$	−7.46033	−	22.9605i	−0.273142	−	0.840645i
$747$	3.55824	−	10.9511i	0.130189	−	0.400682i
$748$	−2.78597	+	2.02413i	−0.101865	+	0.0740094i
$749$	23.1421			0.845595
$750$	−52.4558			−1.91542
$751$	1.00532	−	0.730406i	0.0366846	−	0.0266529i	−0.569292	−	0.822135i	$-0.692783\pi$
$751$	1.00532	−	0.730406i	0.0366846	−	0.0266529i	0.605976	+	0.795483i	$0.292783\pi$
$752$	4.02127	+	2.92162i	0.146641	+	0.106541i
$753$	7.00354	+	5.08837i	0.255223	+	0.185431i
$754$	1.59810	+	4.91846i	0.0581995	+	0.179120i
$755$	14.0071	−	10.1767i	0.509770	−	0.370370i
$756$	1.18305	+	3.64105i	0.0430271	+	0.132424i
$757$	10.7096	−	32.9606i	0.389245	−	1.19797i	−0.544108	−	0.839015i	$-0.683132\pi$
$757$	10.7096	−	32.9606i	0.389245	−	1.19797i	0.933353	−	0.358959i	$-0.116868\pi$
$758$	−57.3926	−	41.6981i	−2.08459	−	1.51454i
$759$	−15.6447	+	48.1495i	−0.567868	+	1.74772i
$760$	−2.16312	+	6.65740i	−0.0784646	+	0.241489i
$761$	16.5491	+	12.0236i	0.599905	+	0.435857i	0.845845	−	0.533428i	$-0.179097\pi$
$761$	16.5491	+	12.0236i	0.599905	+	0.435857i	−0.245940	+	0.969285i	$0.579097\pi$
$762$	−19.6309	+	60.4177i	−0.711152	+	2.18870i
$763$	−3.85816	−	11.8742i	−0.139675	−	0.429875i
$764$	3.40855	−	2.47646i	0.123317	−	0.0895951i
$765$	−0.149960	−	0.461530i	−0.00542182	−	0.0166867i
$766$	48.6322	+	35.3334i	1.75715	+	1.27665i
$767$	14.8974	+	10.8236i	0.537914	+	0.390818i
$768$	−58.5367	+	42.5294i	−2.11226	+	1.53465i
$769$	−26.1127			−0.941648			−0.470824	−	0.882227i	$-0.656043\pi$
$769$	−26.1127			−0.941648			−0.470824	+	0.882227i	$0.656043\pi$
$770$	30.5563			1.10117
$771$	−0.612717	+	0.445165i	−0.0220664	+	0.0160322i
$772$	−25.0122	+	76.9796i	−0.900208	+	2.77056i
$773$	5.56231	+	17.1190i	0.200062	+	0.615728i	0.999880	+	0.0154855i	$0.00492938\pi$
$773$	5.56231	+	17.1190i	0.200062	+	0.615728i	−0.799818	+	0.600243i	$0.795071\pi$
$774$	−60.7696			−2.18432
$775$		0			0
$776$	−47.7990			−1.71588
$777$	−1.80108	−	5.54316i	−0.0646135	−	0.198860i
$778$	−12.7886	+	39.3593i	−0.458493	+	1.41110i
$779$	−12.1689	+	8.84125i	−0.435997	+	0.316771i
$780$	−16.8995			−0.605099
$781$	73.7696			2.63968
$782$	1.34042	−	0.973874i	0.0479334	−	0.0348257i
$783$	0.392601	+	0.285241i	0.0140304	+	0.0101937i
$784$	2.84347	+	2.06590i	0.101552	+	0.0737821i
$785$	4.58224	+	14.1027i	0.163547	+	0.503346i
$786$	22.4324	−	16.2981i	0.800136	−	0.581333i
$787$	12.2327	+	37.6483i	0.436048	+	1.34202i	0.892009	+	0.452018i	$0.149296\pi$
$787$	12.2327	+	37.6483i	0.436048	+	1.34202i	−0.455961	+	0.890000i	$0.650704\pi$
$788$	4.12326	−	12.6901i	0.146885	−	0.452066i
$789$	−1.34042	−	0.973874i	−0.0477203	−	0.0346709i
$790$	11.3715	−	34.9979i	0.404580	−	1.24517i
$791$	3.98616	−	12.2681i	0.141732	−	0.436205i
$792$	−52.9549	−	38.4740i	−1.88167	−	1.36711i
$793$	1.59810	−	4.91846i	0.0567503	−	0.174660i
$794$	12.3205	+	37.9187i	0.437239	+	1.34568i
$795$	0.335106	−	0.243469i	0.0118850	−	0.00863494i
$796$	18.4387	+	56.7486i	0.653544	+	2.01140i
$797$	18.1672	+	13.1992i	0.643514	+	0.467540i	0.861056	−	0.508511i	$-0.169804\pi$
$797$	18.1672	+	13.1992i	0.643514	+	0.467540i	−0.217542	+	0.976051i	$0.569804\pi$
$798$	−18.0522	−	13.1157i	−0.639040	−	0.464290i
$799$	−0.229980	+	0.167090i	−0.00813612	+	0.00591124i
$800$	−6.34315			−0.224264
$801$	−35.3137			−1.24775
$802$	−41.3510	+	30.0433i	−1.46016	+	1.06087i
$803$	−6.20230	+	19.0887i	−0.218874	+	0.673626i
$804$	14.9737	+	46.0842i	0.528081	+	1.62527i
$805$	−9.65685			−0.340359
$806$		0			0
$807$	76.8406			2.70492
$808$	−11.5745	−	35.6226i	−0.407189	−	1.25320i
$809$	−14.2057	+	43.7206i	−0.499445	+	1.53713i	0.310467	+	0.950584i	$0.399514\pi$
$809$	−14.2057	+	43.7206i	−0.499445	+	1.53713i	−0.809913	+	0.586551i	$0.800486\pi$
$810$	−18.5261	+	13.4600i	−0.650940	+	0.472936i
$811$	11.7279			0.411823			0.205912	−	0.978571i	$-0.433984\pi$
$811$	11.7279			0.411823			0.205912	+	0.978571i	$0.433984\pi$
$812$	−10.8284			−0.380003
$813$	−45.5349	+	33.0831i	−1.59698	+	1.16027i
$814$	−10.2396	−	7.43951i	−0.358898	−	0.260755i
$815$	10.4934	+	7.62391i	0.367568	+	0.267054i
$816$	0.383997	+	1.18182i	0.0134426	+	0.0413720i
$817$	−11.4174	+	8.29524i	−0.399445	+	0.290214i
$818$	−6.97030	−	21.4524i	−0.243711	−	0.750064i
$819$	3.85816	−	11.8742i	0.134815	−	0.414918i
$820$	−29.3784	−	21.3447i	−1.02594	−	0.745388i
$821$	−2.62210	+	8.06998i	−0.0915118	+	0.281644i	−0.986329	−	0.164789i	$-0.947306\pi$
$821$	−2.62210	+	8.06998i	−0.0915118	+	0.281644i	0.894817	+	0.446433i	$0.147306\pi$
$822$	−13.4816	+	41.4921i	−0.470225	+	1.44720i
$823$	5.02659	+	3.65203i	0.175216	+	0.127302i	0.671937	−	0.740609i	$-0.265463\pi$
$823$	5.02659	+	3.65203i	0.175216	+	0.127302i	−0.496721	+	0.867910i	$0.665463\pi$
$824$	16.4657	−	50.6764i	0.573611	−	1.76539i
$825$	−15.6447	−	48.1495i	−0.544680	−	1.67635i
$826$	−47.4881	+	34.5021i	−1.65232	+	1.20048i
$827$	5.28435	+	16.2635i	0.183755	+	0.565539i	0.999925	−	0.0122730i	$-0.00390671\pi$
$827$	5.28435	+	16.2635i	0.183755	+	0.565539i	−0.816170	+	0.577812i	$0.803907\pi$
$828$	35.0415	+	25.4592i	1.21778	+	0.884767i
$829$	37.5598	+	27.2888i	1.30450	+	0.947778i	0.999989	−	0.00472973i	$-0.00150553\pi$
$829$	37.5598	+	27.2888i	1.30450	+	0.947778i	0.304515	+	0.952507i	$0.401506\pi$
$830$	7.95136	−	5.77700i	0.275996	−	0.200523i
$831$	34.1421			1.18438
$832$	−17.9706			−0.623017
$833$	−0.162621	+	0.118151i	−0.00563447	+	0.00409368i
$834$		0			0
$835$	−2.64406	−	8.13757i	−0.0915014	−	0.281612i
$836$	−31.8284			−1.10081
$837$		0			0
$838$	−67.5980			−2.33513
$839$	9.46439	+	29.1284i	0.326747	+	1.00562i	0.970646	+	0.240513i	$0.0773158\pi$
$839$	9.46439	+	29.1284i	0.326747	+	1.00562i	−0.643899	+	0.765111i	$0.722684\pi$
$840$	7.95037	−	24.4687i	0.274314	−	0.844251i
$841$	22.3510	−	16.2390i	0.770726	−	0.559965i
$842$	6.89949			0.237772
$843$	−4.82843			−0.166300
$844$	−23.4952	+	17.0702i	−0.808737	+	0.587582i
$845$	7.81256	+	5.67616i	0.268760	+	0.195266i
$846$	−9.15298	−	6.65003i	−0.314686	−	0.228633i
$847$	12.2986	+	37.8511i	0.422584	+	1.30058i
$848$	−0.416416	+	0.302544i	−0.0142998	+	0.0103894i
$849$	1.74806	+	5.37999i	0.0599934	+	0.184641i
$850$	−0.511996	+	1.57576i	−0.0175613	+	0.0540482i
$851$	3.23607	+	2.35114i	0.110931	+	0.0805961i
$852$	40.1888	−	123.689i	1.37685	−	4.23750i
$853$	−10.0385	+	30.8953i	−0.343712	+	1.05784i	0.618558	+	0.785739i	$0.287717\pi$
$853$	−10.0385	+	30.8953i	−0.343712	+	1.05784i	−0.962270	+	0.272097i	$0.912283\pi$
$854$	13.3369	+	9.68981i	0.456378	+	0.331578i
$855$	1.38603	−	4.26576i	0.0474012	−	0.145886i
$856$	−13.0757	−	40.2427i	−0.446917	−	1.37547i
$857$	2.03445	−	1.47811i	0.0694955	−	0.0504914i	−0.552495	−	0.833516i	$-0.686324\pi$
$857$	2.03445	−	1.47811i	0.0694955	−	0.0504914i	0.621991	+	0.783025i	$0.286324\pi$
$858$	−17.2648	−	53.1356i	−0.589410	−	1.81402i
$859$	10.2059	+	7.41504i	0.348222	+	0.252998i	0.748123	−	0.663560i	$-0.230955\pi$
$859$	10.2059	+	7.41504i	0.348222	+	0.252998i	−0.399901	+	0.916558i	$0.630955\pi$
$860$	−27.5641	−	20.0265i	−0.939927	−	0.682897i
$861$	44.7259	−	32.4953i	1.52426	−	1.10744i
$862$	60.9411			2.07566
$863$	−39.3848			−1.34067			−0.670337	−	0.742057i	$-0.733850\pi$
$863$	−39.3848			−1.34067			−0.670337	+	0.742057i	$0.733850\pi$
$864$	−0.531406	+	0.386089i	−0.0180788	+	0.0131350i
$865$	−4.42318	+	13.6131i	−0.150393	+	0.462861i
$866$	26.1952	+	80.6206i	0.890150	+	2.73960i
$867$	40.9706			1.39143
$868$		0			0
$869$	79.9117			2.71082
$870$	−2.11010	−	6.49422i	−0.0715391	−	0.220175i
$871$	−2.96217	+	9.11662i	−0.100369	+	0.308905i
$872$	−18.4686	+	13.4182i	−0.625425	+	0.454398i
$873$	30.6274			1.03658
$874$	15.3137			0.517994
$875$	17.5783	−	12.7714i	0.594254	−	0.431751i
$876$	28.6269	+	20.7986i	0.967213	+	0.702721i
$877$	−38.9716	−	28.3145i	−1.31598	−	0.956114i	−0.999973	−	0.00735663i	$-0.997658\pi$
$877$	−38.9716	−	28.3145i	−1.31598	−	0.956114i	−0.316005	−	0.948757i	$-0.602342\pi$
$878$	9.00542	+	27.7158i	0.303918	+	0.935364i
$879$	−48.4359	+	35.1907i	−1.63370	+	1.18695i
$880$	−4.86020	−	14.9581i	−0.163837	−	0.504239i
$881$	10.6035	−	32.6343i	0.357242	−	1.09948i	−0.597457	−	0.801901i	$-0.703822\pi$
$881$	10.6035	−	32.6343i	0.357242	−	1.09948i	0.954698	−	0.297575i	$-0.0961780\pi$
$882$	−6.47214	−	4.70228i	−0.217928	−	0.158334i
$883$	8.12229	−	24.9978i	0.273337	−	0.841244i	−0.716318	−	0.697774i	$-0.754174\pi$
$883$	8.12229	−	24.9978i	0.273337	−	0.841244i	0.989655	−	0.143470i	$-0.0458260\pi$
$884$	−0.371133	+	1.14223i	−0.0124825	+	0.0384173i
$885$	−19.6702	−	14.2912i	−0.661207	−	0.480395i
$886$	9.87945	−	30.4058i	0.331907	−	1.02150i
$887$	16.4786	+	50.7159i	0.553298	+	1.70287i	0.700397	+	0.713753i	$0.253006\pi$
$887$	16.4786	+	50.7159i	0.553298	+	1.70287i	−0.147100	+	0.989122i	$0.546994\pi$
$888$	−8.62158	+	6.26394i	−0.289321	+	0.210204i
$889$	−8.13138	−	25.0258i	−0.272718	−	0.839339i
$890$	−24.3855	−	17.7171i	−0.817404	−	0.593879i
$891$	−40.2307	−	29.2293i	−1.34778	−	0.979220i
$892$	−5.35183	+	3.88833i	−0.179192	+	0.130191i
$893$	−2.62742			−0.0879232
$894$	5.82843			0.194932
$895$	5.46682	−	3.97188i	0.182736	−	0.132765i
$896$	15.3357	−	47.1985i	0.512330	−	1.57679i
$897$	5.45627	+	16.7927i	0.182179	+	0.560691i
$898$	−11.1716			−0.372800
$899$		0			0
$900$	−43.3137			−1.44379
$901$	−0.00909661	−	0.0279965i	−0.000303052	−	0.000932698i
$902$	37.0987	−	114.178i	1.23525	−	3.80171i
$903$	41.9638	−	30.4885i	1.39647	−	1.01459i
$904$	−23.5858			−0.784452
$905$	−10.3137			−0.342839
$906$	81.6393	−	59.3144i	2.71228	−	1.97059i
$907$	−44.7497	−	32.5126i	−1.48589	−	1.07956i	−0.975599	−	0.219561i	$-0.929537\pi$
$907$	−44.7497	−	32.5126i	−1.48589	−	1.07956i	−0.510292	−	0.860001i	$-0.670463\pi$
$908$	48.2733	+	35.0726i	1.60200	+	1.16392i
$909$	7.41641	+	22.8254i	0.245987	+	0.757069i
$910$	8.62158	−	6.26394i	0.285802	−	0.207648i
$911$	15.1547	+	46.6414i	0.502098	+	1.54530i	0.805596	+	0.592465i	$0.201845\pi$
$911$	15.1547	+	46.6414i	0.502098	+	1.54530i	−0.303498	+	0.952832i	$0.598155\pi$
$912$	−3.54915	+	10.9232i	−0.117524	+	0.361702i
$913$	17.2670	+	12.5452i	0.571453	+	0.415185i
$914$	−23.2111	+	71.4364i	−0.767755	+	2.36291i
$915$	−2.11010	+	6.49422i	−0.0697578	+	0.214692i
$916$	−35.5729	−	25.8452i	−1.17536	−	0.853951i
$917$	−3.54915	+	10.9232i	−0.117203	+	0.360714i
$918$	0.0530189	+	0.163176i	0.00174989	+	0.00538559i
$919$	12.2166	−	8.87585i	0.402987	−	0.292787i	−0.367769	−	0.929917i	$-0.619878\pi$
$919$	12.2166	−	8.87585i	0.402987	−	0.292787i	0.770757	+	0.637130i	$0.219878\pi$
$920$	5.45627	+	16.7927i	0.179888	+	0.553638i
$921$	−5.38551	−	3.91280i	−0.177459	−	0.128931i
$922$	51.0592	+	37.0967i	1.68155	+	1.22172i
$923$	20.8143	−	15.1225i	0.685112	−	0.497763i
$924$	116.983			3.84845
$925$	−4.00000			−0.131519
$926$	48.7710	−	35.4342i	1.60271	−	1.16444i
$927$	−10.5505	+	32.4711i	−0.346524	+	1.06649i
$928$	−0.574112	−	1.76693i	−0.0188461	−	0.0580025i
$929$	24.4853			0.803336			0.401668	−	0.915785i	$-0.368431\pi$
$929$	24.4853			0.803336			0.401668	+	0.915785i	$0.368431\pi$
$930$		0			0
$931$	−1.85786			−0.0608890
$932$	−17.5428	−	53.9911i	−0.574632	−	1.76854i
$933$	8.44040	−	25.9769i	0.276326	−	0.850445i
$934$	−15.6251	+	11.3523i	−0.511269	+	0.371459i
$935$	0.899495			0.0294166
$936$	−22.8284			−0.746170
$937$	−30.9964	+	22.5202i	−1.01261	+	0.735704i	−0.964755	−	0.263150i	$-0.915238\pi$
$937$	−30.9964	+	22.5202i	−1.01261	+	0.735704i	−0.0478548	+	0.998854i	$0.515238\pi$
$938$	−24.7206	−	17.9606i	−0.807156	−	0.586433i
$939$	7.47745	+	5.43269i	0.244017	+	0.177289i
$940$	−1.96014	−	6.03269i	−0.0639327	−	0.196765i
$941$	28.3156	−	20.5725i	0.923062	−	0.670644i	−0.0212223	−	0.999775i	$-0.506756\pi$
$941$	28.3156	−	20.5725i	0.923062	−	0.670644i	0.944284	+	0.329131i	$0.106756\pi$
$942$	26.7072	+	82.1964i	0.870169	+	2.67810i
$943$	−11.7245	+	36.0842i	−0.381801	+	1.17506i
$944$	24.4430	+	17.7589i	0.795552	+	0.578002i
$945$	0.309017	−	0.951057i	0.0100523	−	0.0309379i
$946$	34.8076	−	107.127i	1.13169	−	3.48299i
$947$	−31.4704	−	22.8645i	−1.02265	−	0.742998i	−0.0558248	−	0.998441i	$-0.517779\pi$
$947$	−31.4704	−	22.8645i	−1.02265	−	0.742998i	−0.966824	+	0.255443i	$0.917779\pi$
$948$	43.5350	−	133.987i	1.41395	−	4.35169i
$949$	2.16312	+	6.65740i	0.0702178	+	0.216108i
$950$	−12.3891	+	9.00117i	−0.401954	+	0.292037i
$951$	1.62007	+	4.98605i	0.0525342	+	0.161684i
$952$	−1.47923	−	1.07472i	−0.0479421	−	0.0348320i
$953$	−16.5729	−	12.0409i	−0.536850	−	0.390045i	0.286064	−	0.958211i	$-0.407653\pi$
$953$	−16.5729	−	12.0409i	−0.536850	−	0.390045i	−0.822914	+	0.568166i	$0.807653\pi$
$954$	0.947822	−	0.688633i	0.0306869	−	0.0222953i
$955$	−1.10051			−0.0356115
$956$	−48.8406			−1.57962
$957$	11.9964	−	8.71593i	0.387790	−	0.281746i
$958$	−7.25735	+	22.3358i	−0.234474	+	0.721638i
$959$	−5.58427	−	17.1866i	−0.180325	−	0.554984i
$960$	23.7279			0.765815
$961$		0			0
$962$	−4.41421			−0.142320
$963$	8.37828	+	25.7857i	0.269986	+	0.830933i
$964$	29.1703	−	89.7769i	0.939511	−	2.89152i
$965$	17.1043	−	12.4270i	0.550608	−	0.400040i
$966$	−56.2843			−1.81092
$967$	−46.5563			−1.49715			−0.748576	−	0.663049i	$-0.769262\pi$
$967$	−46.5563			−1.49715			−0.748576	+	0.663049i	$0.769262\pi$
$968$	58.8718	−	42.7729i	1.89221	−	1.37477i
$969$	−0.531406	−	0.386089i	−0.0170712	−	0.0124030i
$970$	21.1494	+	15.3660i	0.679067	+	0.493371i
$971$	18.1388	+	55.8256i	0.582103	+	1.79153i	0.610606	+	0.791934i	$0.290926\pi$
$971$	18.1388	+	55.8256i	0.582103	+	1.79153i	−0.0285036	+	0.999594i	$0.509074\pi$
$972$	−67.0770	+	48.7343i	−2.15149	+	1.56315i
$973$		0			0
$974$	12.9696	−	39.9164i	0.415573	−	1.27900i
$975$	−14.2847	−	10.3784i	−0.457476	−	0.332376i
$976$	2.62210	−	8.06998i	0.0839313	−	0.258314i
$977$	5.09423	−	15.6784i	0.162979	−	0.501598i	−0.835903	−	0.548878i	$-0.815055\pi$
$977$	5.09423	−	15.6784i	0.162979	−	0.501598i	0.998882	+	0.0472800i	$0.0150553\pi$
$978$	61.1601	+	44.4354i	1.95568	+	1.42089i
$979$	20.2270	−	62.2522i	0.646457	−	1.98959i
$980$	−1.38603	−	4.26576i	−0.0442750	−	0.136265i
$981$	11.8338	−	8.59778i	0.377825	−	0.274506i
$982$	−3.29315	−	10.1353i	−0.105089	−	0.323429i
$983$	−39.5129	−	28.7078i	−1.26027	−	0.915637i	−0.261495	−	0.965205i	$-0.584215\pi$
$983$	−39.5129	−	28.7078i	−1.26027	−	0.915637i	−0.998771	+	0.0495684i	$0.984215\pi$
$984$	−81.7781	−	59.4153i	−2.60699	−	1.89409i
$985$	−2.81965	+	2.04860i	−0.0898416	+	0.0652737i
$986$	−0.485281			−0.0154545
$987$	9.65685			0.307381
$988$	−8.98050	+	6.52471i	−0.285708	+	0.207579i
$989$	−11.0004	+	33.8557i	−0.349792	+	1.07655i
$990$	11.0625	+	34.0469i	0.351589	+	1.08208i
$991$	−19.9411			−0.633451			−0.316725	−	0.948517i	$-0.602583\pi$
$991$	−19.9411			−0.633451			−0.316725	+	0.948517i	$0.602583\pi$
$992$		0			0
$993$	−1.82843			−0.0580234
$994$	25.3432	+	77.9982i	0.803836	+	2.47395i
$995$	4.81627	−	14.8230i	0.152686	−	0.469920i
$996$	30.4412	−	22.1168i	0.964567	−	0.700799i
$997$	−46.5980			−1.47577			−0.737886	−	0.674925i	$-0.764176\pi$
$997$	−46.5980			−1.47577			−0.737886	+	0.674925i	$0.764176\pi$
$998$	−97.0833			−3.07312
$999$	−0.335106	+	0.243469i	−0.0106023	+	0.00770301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.l.531.1		8
31.2	even	5	inner	961.2.d.l.388.2		8
31.3	odd	30		961.2.c.a.439.1		4
31.4	even	5	inner	961.2.d.l.374.2		8
31.5	even	3		961.2.g.o.844.1		16
31.6	odd	6		961.2.g.r.547.1		16
31.7	even	15		961.2.g.o.816.2		16
31.8	even	5	inner	961.2.d.l.628.1		8
31.9	even	15		961.2.g.o.448.1		16
31.10	even	15		961.2.g.o.338.2		16
31.11	odd	30		961.2.g.r.732.2		16
31.12	odd	30		961.2.g.r.235.2		16
31.13	odd	30		961.2.c.a.521.1		4
31.14	even	15		961.2.g.o.846.1		16
31.15	odd	10		961.2.a.c.1.1		2
31.16	even	5		961.2.a.a.1.1		2
31.17	odd	30		961.2.g.r.846.1		16
31.18	even	15		31.2.c.a.25.1	yes	4
31.19	even	15		961.2.g.o.235.2		16
31.20	even	15		961.2.g.o.732.2		16
31.21	odd	30		961.2.g.r.338.2		16
31.22	odd	30		961.2.g.r.448.1		16
31.23	odd	10		961.2.d.i.628.1		8
31.24	odd	30		961.2.g.r.816.2		16
31.25	even	3		961.2.g.o.547.1		16
31.26	odd	6		961.2.g.r.844.1		16
31.27	odd	10		961.2.d.i.374.2		8
31.28	even	15		31.2.c.a.5.1	✓	4
31.29	odd	10		961.2.d.i.388.2		8
31.30	odd	2		961.2.d.i.531.1		8
93.47	odd	10		8649.2.a.l.1.2		2
93.59	odd	30		279.2.h.c.253.2		4
93.77	even	10		8649.2.a.k.1.2		2
93.80	odd	30		279.2.h.c.118.2		4
124.59	odd	30		496.2.i.h.129.1		4
124.111	odd	30		496.2.i.h.273.1		4
155.18	odd	60		775.2.o.d.149.4		8
155.28	odd	60		775.2.o.d.749.4		8
155.49	even	30		775.2.e.e.676.2		4
155.59	even	30		775.2.e.e.501.2		4
155.142	odd	60		775.2.o.d.149.1		8
155.152	odd	60		775.2.o.d.749.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.1	✓	4	31.28	even	15
31.2.c.a.25.1	yes	4	31.18	even	15
279.2.h.c.118.2		4	93.80	odd	30
279.2.h.c.253.2		4	93.59	odd	30
496.2.i.h.129.1		4	124.59	odd	30
496.2.i.h.273.1		4	124.111	odd	30
775.2.e.e.501.2		4	155.59	even	30
775.2.e.e.676.2		4	155.49	even	30
775.2.o.d.149.1		8	155.142	odd	60
775.2.o.d.149.4		8	155.18	odd	60
775.2.o.d.749.1		8	155.152	odd	60
775.2.o.d.749.4		8	155.28	odd	60
961.2.a.a.1.1		2	31.16	even	5
961.2.a.c.1.1		2	31.15	odd	10
961.2.c.a.439.1		4	31.3	odd	30
961.2.c.a.521.1		4	31.13	odd	30
961.2.d.i.374.2		8	31.27	odd	10
961.2.d.i.388.2		8	31.29	odd	10
961.2.d.i.531.1		8	31.30	odd	2
961.2.d.i.628.1		8	31.23	odd	10
961.2.d.l.374.2		8	31.4	even	5	inner
961.2.d.l.388.2		8	31.2	even	5	inner
961.2.d.l.531.1		8	1.1	even	1	trivial
961.2.d.l.628.1		8	31.8	even	5	inner
961.2.g.o.235.2		16	31.19	even	15
961.2.g.o.338.2		16	31.10	even	15
961.2.g.o.448.1		16	31.9	even	15
961.2.g.o.547.1		16	31.25	even	3
961.2.g.o.732.2		16	31.20	even	15
961.2.g.o.816.2		16	31.7	even	15
961.2.g.o.844.1		16	31.5	even	3
961.2.g.o.846.1		16	31.14	even	15
961.2.g.r.235.2		16	31.12	odd	30
961.2.g.r.338.2		16	31.21	odd	30
961.2.g.r.448.1		16	31.22	odd	30
961.2.g.r.547.1		16	31.6	odd	6
961.2.g.r.732.2		16	31.11	odd	30
961.2.g.r.816.2		16	31.24	odd	30
961.2.g.r.844.1		16	31.26	odd	6
961.2.g.r.846.1		16	31.17	odd	30
8649.2.a.k.1.2		2	93.77	even	10
8649.2.a.l.1.2		2	93.47	odd	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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.746033 - 2.29605i) q^{2} +(-0.746033 + 2.29605i) q^{3} +(-3.09726 + 2.25029i) q^{4} +1.00000 q^{5} +5.82843 q^{6} +(-1.95314 + 1.41904i) q^{7} +(3.57117 + 2.59461i) q^{8} +(-2.28825 - 1.66251i) q^{9} +(-0.746033 - 2.29605i) q^{10} +(4.24139 - 3.08155i) q^{11} +(-2.85613 - 8.79027i) q^{12} +(0.565015 - 1.73894i) q^{13} +(4.71530 + 3.42586i) q^{14} +(-0.746033 + 2.29605i) q^{15} +(0.927051 - 2.85317i) q^{16} +(0.138805 + 0.100848i) q^{17} +(-2.11010 + 6.49422i) q^{18} +(0.490035 + 1.50817i) q^{19} +(-3.09726 + 2.25029i) q^{20} +(-1.80108 - 5.54316i) q^{21} +(-10.2396 - 7.43951i) q^{22} +(3.23607 + 2.35114i) q^{23} +(-8.62158 + 6.26394i) q^{24} -4.00000 q^{25} -4.41421 q^{26} +(-0.335106 + 0.243469i) q^{27} +(2.85613 - 8.79027i) q^{28} +(-0.362036 - 1.11423i) q^{29} +5.82843 q^{30} +1.58579 q^{32} +(3.91118 + 12.0374i) q^{33} +(0.127999 - 0.393941i) q^{34} +(-1.95314 + 1.41904i) q^{35} +10.8284 q^{36} +1.00000 q^{37} +(3.09726 - 2.25029i) q^{38} +(3.57117 + 2.59461i) q^{39} +(3.57117 + 2.59461i) q^{40} +(2.93111 + 9.02104i) q^{41} +(-11.3837 + 8.27077i) q^{42} +(2.75010 + 8.46392i) q^{43} +(-6.20230 + 19.0887i) q^{44} +(-2.28825 - 1.66251i) q^{45} +(2.98413 - 9.18421i) q^{46} +(-0.511996 + 1.57576i) q^{47} +(5.85942 + 4.25712i) q^{48} +(-0.362036 + 1.11423i) q^{49} +(2.98413 + 9.18421i) q^{50} +(-0.335106 + 0.243469i) q^{51} +(2.16312 + 6.65740i) q^{52} +(-0.138805 - 0.100848i) q^{53} +(0.809017 + 0.587785i) q^{54} +(4.24139 - 3.08155i) q^{55} -10.6569 q^{56} -3.82843 q^{57} +(-2.28825 + 1.66251i) q^{58} +(-3.11213 + 9.57815i) q^{59} +(-2.85613 - 8.79027i) q^{60} +2.82843 q^{61} +6.82843 q^{63} +(-3.03715 - 9.34739i) q^{64} +(0.565015 - 1.73894i) q^{65} +(24.7206 - 17.9606i) q^{66} -5.24264 q^{67} -0.656854 q^{68} +(-7.81256 + 5.67616i) q^{69} +(4.71530 + 3.42586i) q^{70} +(11.3837 + 8.27077i) q^{71} +(-3.85816 - 11.8742i) q^{72} +(-3.09726 + 2.25029i) q^{73} +(-0.746033 - 2.29605i) q^{74} +(2.98413 - 9.18421i) q^{75} +(-4.91160 - 3.56848i) q^{76} +(-3.91118 + 12.0374i) q^{77} +(3.29315 - 10.1353i) q^{78} +(12.3316 + 8.95940i) q^{79} +(0.927051 - 2.85317i) q^{80} +(-2.93111 - 9.02104i) q^{81} +(18.5261 - 13.4600i) q^{82} +(1.25803 + 3.87182i) q^{83} +(18.0522 + 13.1157i) q^{84} +(0.138805 + 0.100848i) q^{85} +(17.3820 - 12.6287i) q^{86} +2.82843 q^{87} +23.1421 q^{88} +(10.1008 - 7.33866i) q^{89} +(-2.11010 + 6.49422i) q^{90} +(1.36407 + 4.19817i) q^{91} -15.3137 q^{92} +4.00000 q^{94} +(0.490035 + 1.50817i) q^{95} +(-1.18305 + 3.64105i) q^{96} +(-8.76038 + 6.36479i) q^{97} +2.82843 q^{98} -14.8284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} + 24 q^{6} - 2 q^{7} + 6 q^{8} + 2 q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} + 6 q^{14} + 2 q^{15} - 6 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} - 2 q^{20} + 6 q^{21}+ \cdots - 96 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 + 24 * q^6 - 2 * q^7 + 6 * q^8 + 2 * q^10 + 2 * q^11 + 10 * q^12 + 2 * q^13 + 6 * q^14 + 2 * q^15 - 6 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 - 2 * q^20 + 6 * q^21 - 14 * q^22 + 8 * q^23 - 10 * q^24 - 32 * q^25 - 24 * q^26 + 2 * q^27 - 10 * q^28 + 8 * q^29 + 24 * q^30 + 24 * q^32 - 14 * q^33 + 2 * q^34 - 2 * q^35 + 64 * q^36 + 8 * q^37 + 2 * q^38 + 6 * q^39 + 6 * q^40 - 2 * q^41 - 14 * q^42 + 2 * q^43 + 26 * q^44 - 8 * q^46 - 8 * q^47 + 6 * q^48 + 8 * q^49 - 8 * q^50 + 2 * q^51 - 14 * q^52 - 6 * q^53 + 2 * q^54 + 2 * q^55 - 40 * q^56 - 8 * q^57 + 6 * q^59 + 10 * q^60 + 32 * q^63 + 14 * q^64 + 2 * q^65 + 30 * q^66 - 8 * q^67 + 40 * q^68 - 8 * q^69 + 6 * q^70 + 14 * q^71 + 8 * q^72 - 2 * q^73 + 2 * q^74 - 8 * q^75 + 2 * q^76 + 14 * q^77 - 10 * q^78 + 22 * q^79 - 6 * q^80 + 2 * q^81 + 26 * q^82 + 6 * q^83 + 22 * q^84 + 6 * q^85 + 26 * q^86 + 72 * q^88 + 8 * q^89 + 8 * q^90 - 6 * q^91 - 32 * q^92 + 32 * q^94 - 6 * q^95 + 2 * q^96 - 16 * q^97 - 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more