LMFDB - Embedded newform 462.2.u.b.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.4
Character	$\chi$	$=$	462.349
Dual form			462.2.u.b.139.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.23816 - 3.08056i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.345808 - 2.62305i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.23816 - 3.08056i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.345808 - 2.62305i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} -3.80779 q^{10} +(-2.45044 - 2.23503i) q^{11} +1.00000i q^{12} +(-3.55934 + 2.58601i) q^{13} +(-2.32536 + 1.26203i) q^{14} +(1.17667 - 3.62142i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.02829 + 2.20018i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(1.91100 + 5.88146i) q^{19} +(2.23816 + 3.08056i) q^{20} +(-0.481686 - 2.60153i) q^{21} +(-0.367849 + 3.29616i) q^{22} -1.81438 q^{23} +(0.809017 - 0.587785i) q^{24} +(-2.93543 - 9.03431i) q^{25} +(4.18425 + 1.35955i) q^{26} +(0.587785 - 0.809017i) q^{27} +(2.38781 + 1.13945i) q^{28} +(5.96527 + 1.93823i) q^{29} +(-3.62142 + 1.17667i) q^{30} +(-4.39239 - 6.04560i) q^{31} +1.00000i q^{32} +(-3.02117 - 1.36842i) q^{33} -3.74317i q^{34} +(-7.30652 - 6.93610i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-0.733252 + 2.25672i) q^{37} +(3.63494 - 5.00306i) q^{38} +(-2.58601 + 3.55934i) q^{39} +(1.17667 - 3.62142i) q^{40} +(1.59239 + 4.90087i) q^{41} +(-1.82156 + 1.91884i) q^{42} -2.46166i q^{43} +(2.88287 - 1.63984i) q^{44} -3.80779i q^{45} +(1.06647 + 1.46786i) q^{46} +(9.32804 - 3.03086i) q^{47} +(-0.951057 - 0.309017i) q^{48} +(-6.76083 - 1.81415i) q^{49} +(-5.58351 + 7.68505i) q^{50} +(3.55997 + 1.15670i) q^{51} +(-1.35955 - 4.18425i) q^{52} +(0.843168 - 0.612598i) q^{53} -1.00000 q^{54} +(-12.3696 + 2.54636i) q^{55} +(-0.481686 - 2.60153i) q^{56} +(3.63494 + 5.00306i) q^{57} +(-1.93823 - 5.96527i) q^{58} +(8.59298 + 2.79203i) q^{59} +(3.08056 + 2.23816i) q^{60} +(2.48147 + 1.80290i) q^{61} +(-2.30921 + 7.10703i) q^{62} +(-1.26203 - 2.32536i) q^{63} +(0.809017 - 0.587785i) q^{64} +16.7527i q^{65} +(0.668725 + 3.24851i) q^{66} +8.07953 q^{67} +(-3.02829 + 2.20018i) q^{68} +(-1.72558 + 0.560674i) q^{69} +(-1.31676 + 9.98803i) q^{70} +(-12.3419 - 8.96690i) q^{71} +(0.587785 - 0.809017i) q^{72} +(0.732686 - 2.25498i) q^{73} +(2.25672 - 0.733252i) q^{74} +(-5.58351 - 7.68505i) q^{75} -6.18413 q^{76} +(-6.70999 + 5.65473i) q^{77} +4.39958 q^{78} +(-4.32990 - 5.95960i) q^{79} +(-3.62142 + 1.17667i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.02891 - 4.16893i) q^{82} +(1.86864 + 1.35765i) q^{83} +(2.62305 + 0.345808i) q^{84} +(13.5556 - 4.40448i) q^{85} +(-1.99153 + 1.44693i) q^{86} +6.27225 q^{87} +(-3.02117 - 1.36842i) q^{88} +2.42774i q^{89} +(-3.08056 + 2.23816i) q^{90} +(5.55240 + 10.2306i) q^{91} +(0.560674 - 1.72558i) q^{92} +(-6.04560 - 4.39239i) q^{93} +(-7.93490 - 5.76504i) q^{94} +(22.3953 + 7.27668i) q^{95} +(0.309017 + 0.951057i) q^{96} +(6.55248 + 9.01871i) q^{97} +(2.50624 + 6.53596i) q^{98} +(-3.29616 - 0.367849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 - 12 * q^17 - 16 * q^19 + 10 * q^20 - 8 * q^21 - 4 * q^22 + 8 * q^23 + 8 * q^24 + 6 * q^25 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * q^49 + 40 * q^51 - 32 * q^54 - 40 * q^55 - 8 * q^56 + 10 * q^58 + 60 * q^59 + 4 * q^60 - 4 * q^61 + 20 * q^62 - 10 * q^63 + 8 * q^64 + 8 * q^66 - 16 * q^67 + 12 * q^68 + 30 * q^69 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * q^77 - 60 * q^79 - 8 * q^81 + 20 * q^82 + 4 * q^83 - 2 * q^84 - 10 * q^85 - 36 * q^86 + 20 * q^87 - 16 * q^88 - 4 * q^90 - 20 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 - 8 * q^96 + 60 * q^97 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	2.23816	−	3.08056i	1.00094	−	1.37767i	0.0761865	−	0.997094i	$-0.475726\pi$
$5$	2.23816	−	3.08056i	1.00094	−	1.37767i	0.924749	−	0.380577i	$-0.124274\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	0.345808	−	2.62305i	0.130703	−	0.991422i
$7$	0.345808	−	2.62305i	0.130703	−	0.991422i
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	−3.80779			−1.20413
$11$	−2.45044	−	2.23503i	−0.738834	−	0.673887i
$11$	−2.45044	−	2.23503i	−0.738834	−	0.673887i
$12$			1.00000i			0.288675i
$13$	−3.55934	+	2.58601i	−0.987183	+	0.717230i	−0.959302	−	0.282381i	$-0.908876\pi$
$13$	−3.55934	+	2.58601i	−0.987183	+	0.717230i	−0.0278803	+	0.999611i	$0.508876\pi$
$14$	−2.32536	+	1.26203i	−0.621478	+	0.337291i
$15$	1.17667	−	3.62142i	0.303815	−	0.935047i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.02829	+	2.20018i	0.734468	+	0.533622i	0.890974	−	0.454055i	$-0.150023\pi$
$17$	3.02829	+	2.20018i	0.734468	+	0.533622i	−0.156506	+	0.987677i	$0.550023\pi$
$18$	−0.951057	−	0.309017i	−0.224166	−	0.0728360i
$19$	1.91100	+	5.88146i	0.438414	+	1.34930i	0.889548	+	0.456842i	$0.151020\pi$
$19$	1.91100	+	5.88146i	0.438414	+	1.34930i	−0.451134	+	0.892456i	$0.648980\pi$
$20$	2.23816	+	3.08056i	0.500468	+	0.688835i
$21$	−0.481686	−	2.60153i	−0.105112	−	0.567701i
$22$	−0.367849	+	3.29616i	−0.0784257	+	0.702744i
$23$	−1.81438			−0.378324			−0.189162	−	0.981946i	$-0.560577\pi$
$23$	−1.81438			−0.378324			−0.189162	+	0.981946i	$0.560577\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	−2.93543	−	9.03431i	−0.587085	−	1.80686i
$26$	4.18425	+	1.35955i	0.820599	+	0.266629i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	2.38781	+	1.13945i	0.451254	+	0.215336i
$29$	5.96527	+	1.93823i	1.10772	+	0.359921i	0.805070	−	0.593180i	$-0.202128\pi$
$29$	5.96527	+	1.93823i	1.10772	+	0.359921i	0.302652	+	0.953101i	$0.402128\pi$
$30$	−3.62142	+	1.17667i	−0.661178	+	0.214830i
$31$	−4.39239	−	6.04560i	−0.788896	−	1.08582i	−0.994245	−	0.107133i	$-0.965833\pi$
$31$	−4.39239	−	6.04560i	−0.788896	−	1.08582i	0.205349	−	0.978689i	$-0.434167\pi$
$32$			1.00000i			0.176777i
$33$	−3.02117	−	1.36842i	−0.525917	−	0.238211i
$34$		−	3.74317i		−	0.641948i
$35$	−7.30652	−	6.93610i	−1.23503	−	1.17242i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−0.733252	+	2.25672i	−0.120546	+	0.371002i	−0.993063	−	0.117581i	$-0.962486\pi$
$37$	−0.733252	+	2.25672i	−0.120546	+	0.371002i	0.872517	+	0.488583i	$0.162486\pi$
$38$	3.63494	−	5.00306i	0.589665	−	0.811604i
$39$	−2.58601	+	3.55934i	−0.414093	+	0.569950i
$40$	1.17667	−	3.62142i	0.186048	−	0.572597i
$41$	1.59239	+	4.90087i	0.248690	+	0.765388i	0.995008	+	0.0997984i	$0.0318198\pi$
$41$	1.59239	+	4.90087i	0.248690	+	0.765388i	−0.746318	+	0.665589i	$0.768180\pi$
$42$	−1.82156	+	1.91884i	−0.281072	+	0.296083i
$43$		−	2.46166i		−	0.375400i	−0.982226	−	0.187700i	$-0.939897\pi$
$43$		−	2.46166i		−	0.375400i	0.982226	−	0.187700i	$-0.0601033\pi$
$44$	2.88287	−	1.63984i	0.434609	−	0.247215i
$45$		−	3.80779i		−	0.567631i
$46$	1.06647	+	1.46786i	0.157242	+	0.216425i
$47$	9.32804	−	3.03086i	1.36063	−	0.442097i	0.464379	−	0.885637i	$-0.346278\pi$
$47$	9.32804	−	3.03086i	1.36063	−	0.442097i	0.896255	+	0.443540i	$0.146278\pi$
$48$	−0.951057	−	0.309017i	−0.137273	−	0.0446028i
$49$	−6.76083	−	1.81415i	−0.965833	−	0.259164i
$50$	−5.58351	+	7.68505i	−0.789628	+	1.08683i
$51$	3.55997	+	1.15670i	0.498495	+	0.161971i
$52$	−1.35955	−	4.18425i	−0.188535	−	0.580251i
$53$	0.843168	−	0.612598i	0.115818	−	0.0841468i	−0.528368	−	0.849015i	$-0.677196\pi$
$53$	0.843168	−	0.612598i	0.115818	−	0.0841468i	0.644187	+	0.764868i	$0.277196\pi$
$54$	−1.00000			−0.136083
$55$	−12.3696	+	2.54636i	−1.66792	+	0.343351i
$56$	−0.481686	−	2.60153i	−0.0643680	−	0.347645i
$57$	3.63494	+	5.00306i	0.481459	+	0.662672i
$58$	−1.93823	−	5.96527i	−0.254502	−	0.783278i
$59$	8.59298	+	2.79203i	1.11871	+	0.363491i	0.809276	−	0.587429i	$-0.199860\pi$
$59$	8.59298	+	2.79203i	1.11871	+	0.363491i	0.309436	+	0.950920i	$0.399860\pi$
$60$	3.08056	+	2.23816i	0.397699	+	0.288945i
$61$	2.48147	+	1.80290i	0.317720	+	0.230837i	0.735202	−	0.677848i	$-0.237087\pi$
$61$	2.48147	+	1.80290i	0.317720	+	0.230837i	−0.417482	+	0.908685i	$0.637087\pi$
$62$	−2.30921	+	7.10703i	−0.293270	+	0.902594i
$63$	−1.26203	−	2.32536i	−0.159001	−	0.292967i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$			16.7527i			2.07791i
$66$	0.668725	+	3.24851i	0.0823143	+	0.399864i
$67$	8.07953			0.987072			0.493536	−	0.869725i	$-0.335704\pi$
$67$	8.07953			0.987072			0.493536	+	0.869725i	$0.335704\pi$
$68$	−3.02829	+	2.20018i	−0.367234	+	0.266811i
$69$	−1.72558	+	0.560674i	−0.207735	+	0.0674973i
$70$	−1.31676	+	9.98803i	−0.157383	+	1.19380i
$71$	−12.3419	−	8.96690i	−1.46471	−	1.06417i	−0.982104	−	0.188338i	$-0.939690\pi$
$71$	−12.3419	−	8.96690i	−1.46471	−	1.06417i	−0.482607	−	0.875837i	$-0.660310\pi$
$72$	0.587785	−	0.809017i	0.0692712	−	0.0953436i
$73$	0.732686	−	2.25498i	0.0857545	−	0.263925i	−0.898980	−	0.437990i	$-0.855690\pi$
$73$	0.732686	−	2.25498i	0.0857545	−	0.263925i	0.984734	+	0.174065i	$0.0556904\pi$
$74$	2.25672	−	0.733252i	0.262338	−	0.0852388i
$75$	−5.58351	−	7.68505i	−0.644729	−	0.887393i
$76$	−6.18413			−0.709368
$77$	−6.70999	+	5.65473i	−0.764674	+	0.644417i
$78$	4.39958			0.498155
$79$	−4.32990	−	5.95960i	−0.487152	−	0.670508i	0.492707	−	0.870195i	$-0.336007\pi$
$79$	−4.32990	−	5.95960i	−0.487152	−	0.670508i	−0.979860	+	0.199688i	$0.936007\pi$
$80$	−3.62142	+	1.17667i	−0.404887	+	0.131556i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	3.02891	−	4.16893i	0.334487	−	0.460381i
$83$	1.86864	+	1.35765i	0.205110	+	0.149021i	0.685599	−	0.727980i	$-0.259541\pi$
$83$	1.86864	+	1.35765i	0.205110	+	0.149021i	−0.480488	+	0.877001i	$0.659541\pi$
$84$	2.62305	+	0.345808i	0.286199	+	0.0377307i
$85$	13.5556	−	4.40448i	1.47031	−	0.477733i
$86$	−1.99153	+	1.44693i	−0.214752	+	0.156026i
$87$	6.27225			0.672456
$88$	−3.02117	−	1.36842i	−0.322057	−	0.145874i
$89$			2.42774i			0.257340i	0.991687	+	0.128670i	$0.0410709\pi$
$89$			2.42774i			0.257340i	−0.991687	+	0.128670i	$0.958929\pi$
$90$	−3.08056	+	2.23816i	−0.324720	+	0.235923i
$91$	5.55240	+	10.2306i	0.582050	+	1.07246i
$92$	0.560674	−	1.72558i	0.0584543	−	0.179904i
$93$	−6.04560	−	4.39239i	−0.626899	−	0.455469i
$94$	−7.93490	−	5.76504i	−0.818423	−	0.594619i
$95$	22.3953	+	7.27668i	2.29771	+	0.746572i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	6.55248	+	9.01871i	0.665303	+	0.915711i	0.999642	−	0.0267416i	$-0.00851312\pi$
$97$	6.55248	+	9.01871i	0.665303	+	0.915711i	−0.334339	+	0.942453i	$0.608513\pi$
$98$	2.50624	+	6.53596i	0.253169	+	0.660231i
$99$	−3.29616	−	0.367849i	−0.331277	−	0.0369702i
$100$	9.49924			0.949924
$101$	5.41471	−	3.93402i	0.538784	−	0.391450i	−0.284849	−	0.958572i	$-0.591943\pi$
$101$	5.41471	−	3.93402i	0.538784	−	0.391450i	0.823633	+	0.567123i	$0.191943\pi$
$102$	−1.15670	−	3.55997i	−0.114531	−	0.352489i
$103$	9.10564	+	2.95860i	0.897206	+	0.291520i	0.721083	−	0.692848i	$-0.243645\pi$
$103$	9.10564	+	2.95860i	0.897206	+	0.291520i	0.176122	+	0.984368i	$0.443645\pi$
$104$	−2.58601	+	3.55934i	−0.253579	+	0.349022i
$105$	−9.09228	−	4.33879i	−0.887316	−	0.423422i
$106$	−0.991204	−	0.322062i	−0.0962742	−	0.0312814i
$107$	1.22336	−	0.397495i	0.118267	−	0.0384272i	−0.249286	−	0.968430i	$-0.580196\pi$
$107$	1.22336	−	0.397495i	0.118267	−	0.0384272i	0.367553	+	0.930003i	$0.380196\pi$
$108$	0.587785	+	0.809017i	0.0565597	+	0.0778477i
$109$			3.30954i			0.316997i	0.987359	+	0.158498i	$0.0506652\pi$
$109$			3.30954i			0.316997i	−0.987359	+	0.158498i	$0.949335\pi$
$110$	9.33073	+	8.51052i	0.889651	+	0.811447i
$111$			2.37285i			0.225221i
$112$	−1.82156	+	1.91884i	−0.172121	+	0.181313i
$113$	3.73258	+	11.4877i	0.351132	+	1.08067i	0.958219	+	0.286037i	$0.0923380\pi$
$113$	3.73258	+	11.4877i	0.351132	+	1.08067i	−0.607087	+	0.794635i	$0.707662\pi$
$114$	1.91100	−	5.88146i	0.178982	−	0.550849i
$115$	−4.06088	+	5.58932i	−0.378679	+	0.521206i
$116$	−3.68674	+	5.07436i	−0.342305	+	0.471142i
$117$	−1.35955	+	4.18425i	−0.125690	+	0.386834i
$118$	−2.79203	−	8.59298i	−0.257027	−	0.791048i
$119$	6.81840	−	7.18253i	0.625042	−	0.658421i
$120$		−	3.80779i		−	0.347602i
$121$	1.00926	+	10.9536i	0.0917513	+	0.995782i
$122$		−	3.06727i		−	0.277698i
$123$	3.02891	+	4.16893i	0.273107	+	0.375900i
$124$	7.10703	−	2.30921i	0.638230	−	0.207373i
$125$	−16.2936	−	5.29412i	−1.45735	−	0.473521i
$126$	−1.13945	+	2.38781i	−0.101510	+	0.212723i
$127$	−7.99968	+	11.0106i	−0.709857	+	0.977034i	0.289944	+	0.957044i	$0.406363\pi$
$127$	−7.99968	+	11.0106i	−0.709857	+	0.977034i	−0.999800	+	0.0199900i	$0.993637\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	−0.760696	−	2.34118i	−0.0669755	−	0.206129i
$130$	13.5532	−	9.84697i	1.18869	−	0.863637i
$131$	−3.73427			−0.326265			−0.163132	−	0.986604i	$-0.552160\pi$
$131$	−3.73427			−0.326265			−0.163132	+	0.986604i	$0.552160\pi$
$132$	2.23503	−	2.45044i	0.194535	−	0.213283i
$133$	16.0882	−	2.97881i	1.39503	−	0.258295i
$134$	−4.74903	−	6.53648i	−0.410254	−	0.564666i
$135$	−1.17667	−	3.62142i	−0.101272	−	0.311682i
$136$	3.55997	+	1.15670i	0.305265	+	0.0991865i
$137$	9.33870	+	6.78497i	0.797859	+	0.579679i	0.910285	−	0.413981i	$-0.135862\pi$
$137$	9.33870	+	6.78497i	0.797859	+	0.579679i	−0.112426	+	0.993660i	$0.535862\pi$
$138$	1.46786	+	1.06647i	0.124953	+	0.0907836i
$139$	−1.50518	+	4.63248i	−0.127668	+	0.392922i	−0.994378	−	0.105891i	$-0.966231\pi$
$139$	−1.50518	+	4.63248i	−0.127668	+	0.392922i	0.866710	+	0.498813i	$0.166231\pi$
$140$	8.85446	−	4.80554i	0.748339	−	0.406142i
$141$	7.93490	−	5.76504i	0.668239	−	0.485504i
$142$			15.2554i			1.28020i
$143$	14.5017	+	1.61838i	1.21270	+	0.135336i
$144$	−1.00000			−0.0833333
$145$	19.3221	−	14.0383i	1.60461	−	1.16582i
$146$	−2.25498	+	0.732686i	−0.186623	+	0.0606376i
$147$	−6.99054	+	0.363858i	−0.576570	+	0.0300105i
$148$	−1.91968	−	1.39473i	−0.157797	−	0.114646i
$149$	14.2835	−	19.6595i	1.17015	−	1.61057i	0.507461	−	0.861675i	$-0.330584\pi$
$149$	14.2835	−	19.6595i	1.17015	−	1.61057i	0.662687	−	0.748896i	$-0.269416\pi$
$150$	−2.93543	+	9.03431i	−0.239677	+	0.737649i
$151$	−19.9073	+	6.46828i	−1.62003	+	0.526381i	−0.971950	−	0.235188i	$-0.924429\pi$
$151$	−19.9073	+	6.46828i	−1.62003	+	0.526381i	−0.648084	+	0.761569i	$0.724429\pi$
$152$	3.63494	+	5.00306i	0.294833	+	0.405802i
$153$	3.74317			0.302617
$154$	8.51881	+	2.10473i	0.686465	+	0.169604i
$155$	−28.4547			−2.28554
$156$	−2.58601	−	3.55934i	−0.207047	−	0.284975i
$157$	−1.03325	+	0.335724i	−0.0824624	+	0.0267937i	−0.349958	−	0.936766i	$-0.613804\pi$
$157$	−1.03325	+	0.335724i	−0.0824624	+	0.0267937i	0.267495	+	0.963559i	$0.413804\pi$
$158$	−2.27637	+	7.00593i	−0.181098	+	0.557362i
$159$	0.612598	−	0.843168i	0.0485822	−	0.0668676i
$160$	3.08056	+	2.23816i	0.243540	+	0.176942i
$161$	−0.627427	+	4.75922i	−0.0494482	+	0.375079i
$162$	−0.951057	+	0.309017i	−0.0747221	+	0.0242787i
$163$	−9.85810	+	7.16233i	−0.772146	+	0.560997i	−0.902612	−	0.430456i	$-0.858353\pi$
$163$	−9.85810	+	7.16233i	−0.772146	+	0.560997i	0.130465	+	0.991453i	$0.458353\pi$
$164$	−5.15308			−0.402388
$165$	−10.9773	+	6.24416i	−0.854585	+	0.486107i
$166$		−	2.30977i		−	0.179273i
$167$	−8.04752	+	5.84686i	−0.622736	+	0.452444i	−0.853876	−	0.520477i	$-0.825754\pi$
$167$	−8.04752	+	5.84686i	−0.622736	+	0.452444i	0.231140	+	0.972920i	$0.425754\pi$
$168$	−1.26203	−	2.32536i	−0.0973676	−	0.179405i
$169$	1.96421	−	6.04523i	0.151093	−	0.465018i
$170$	−11.5311	−	8.37782i	−0.884393	−	0.642549i
$171$	5.00306	+	3.63494i	0.382594	+	0.277971i
$172$	2.34118	+	0.760696i	0.178513	+	0.0580025i
$173$	−6.46391	−	19.8939i	−0.491442	−	1.51250i	−0.822430	−	0.568867i	$-0.807382\pi$
$173$	−6.46391	−	19.8939i	−0.491442	−	1.51250i	0.330988	−	0.943635i	$-0.392618\pi$
$174$	−3.68674	−	5.07436i	−0.279491	−	0.384686i
$175$	−24.7126	+	4.57565i	−1.86810	+	0.345887i
$176$	0.668725	+	3.24851i	0.0504070	+	0.244866i
$177$	9.03520			0.679127
$178$	1.96409	−	1.42699i	0.147214	−	0.106958i
$179$	−6.80156	−	20.9331i	−0.508373	−	1.56461i	−0.795026	−	0.606576i	$-0.792543\pi$
$179$	−6.80156	−	20.9331i	−0.508373	−	1.56461i	0.286653	−	0.958034i	$-0.407457\pi$
$180$	3.62142	+	1.17667i	0.269925	+	0.0877039i
$181$	−11.3341	+	15.6000i	−0.842456	+	1.15954i	0.143019	+	0.989720i	$0.454319\pi$
$181$	−11.3341	+	15.6000i	−0.842456	+	1.15954i	−0.985475	+	0.169821i	$0.945681\pi$
$182$	5.01311	−	10.5054i	0.371596	−	0.778711i
$183$	2.91715	+	0.947839i	0.215642	+	0.0700663i
$184$	−1.72558	+	0.560674i	−0.127211	+	0.0413335i
$185$	5.31083	+	7.30972i	0.390460	+	0.537422i
$186$			7.47277i			0.547930i
$187$	−2.50315	−	12.1597i	−0.183049	−	0.889207i
$188$			9.80808i			0.715328i
$189$	−1.91884	−	1.82156i	−0.139575	−	0.132499i
$190$	−7.27668	−	22.3953i	−0.527906	−	1.62473i
$191$	1.21679	−	3.74489i	0.0880438	−	0.270971i	−0.897335	−	0.441351i	$-0.854499\pi$
$191$	1.21679	−	3.74489i	0.0880438	−	0.270971i	0.985378	+	0.170380i	$0.0544994\pi$
$192$	0.587785	−	0.809017i	0.0424197	−	0.0583858i
$193$	−15.3927	+	21.1862i	−1.10799	+	1.52501i	−0.283641	+	0.958931i	$0.591542\pi$
$193$	−15.3927	+	21.1862i	−1.10799	+	1.52501i	−0.824347	+	0.566084i	$0.808458\pi$
$194$	3.44484	−	10.6021i	0.247325	−	0.761189i
$195$	5.17686	+	15.9327i	0.370723	+	1.14097i
$196$	3.81457	−	5.86933i	0.272469	−	0.419238i
$197$			18.8657i			1.34412i	0.740494	+	0.672062i	$0.234591\pi$
$197$			18.8657i			1.34412i	−0.740494	+	0.672062i	$0.765409\pi$
$198$	1.63984	+	2.88287i	0.116538	+	0.204876i
$199$			19.7274i			1.39844i	0.714907	+	0.699219i	$0.246469\pi$
$199$			19.7274i			1.39844i	−0.714907	+	0.699219i	$0.753531\pi$
$200$	−5.58351	−	7.68505i	−0.394814	−	0.543415i
$201$	7.68409	−	2.49671i	0.541994	−	0.176105i
$202$	−6.36538	−	2.06824i	−0.447867	−	0.145521i
$203$	7.14692	−	14.9770i	0.501616	−	1.05118i
$204$	−2.20018	+	3.02829i	−0.154043	+	0.212023i
$205$	18.6615	+	6.06348i	1.30337	+	0.423492i
$206$	−2.95860	−	9.10564i	−0.206136	−	0.634420i
$207$	−1.46786	+	1.06647i	−0.102024	+	0.0741245i
$208$	4.39958			0.305056
$209$	8.46246	−	18.6833i	0.585360	−	1.29235i
$210$	1.83416	+	9.90609i	0.126569	+	0.683585i
$211$	−8.16270	−	11.2350i	−0.561943	−	0.773448i	0.429629	−	0.903006i	$-0.358644\pi$
$211$	−8.16270	−	11.2350i	−0.561943	−	0.773448i	−0.991572	+	0.129557i	$0.958644\pi$
$212$	0.322062	+	0.991204i	0.0221193	+	0.0680762i
$213$	−14.5087	−	4.71418i	−0.994123	−	0.323010i
$214$	−1.04065	−	0.756080i	−0.0711377	−	0.0516845i
$215$	−7.58331	−	5.50960i	−0.517177	−	0.375751i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	−17.3769	+	9.43085i	−1.17962	+	0.640208i
$218$	2.67748	−	1.94530i	0.181342	−	0.131752i
$219$		−	2.37102i		−	0.160219i
$220$	1.40069	−	12.5511i	0.0944346	−	0.846194i
$221$	−16.4684			−1.10778
$222$	1.91968	−	1.39473i	0.128840	−	0.0936080i
$223$	25.1715	−	8.17871i	1.68561	−	0.547687i	0.699621	−	0.714514i	$-0.253352\pi$
$223$	25.1715	−	8.17871i	1.68561	−	0.547687i	0.985986	+	0.166827i	$0.0533521\pi$
$224$	2.62305	+	0.345808i	0.175260	+	0.0231052i
$225$	−7.68505	−	5.58351i	−0.512336	−	0.372234i
$226$	7.09979	−	9.77202i	0.472271	−	0.650025i
$227$	−7.19176	+	22.1340i	−0.477334	+	1.46908i	0.365450	+	0.930831i	$0.380915\pi$
$227$	−7.19176	+	22.1340i	−0.477334	+	1.46908i	−0.842784	+	0.538252i	$0.819085\pi$
$228$	−5.88146	+	1.91100i	−0.389509	+	0.126559i
$229$	7.14514	+	9.83444i	0.472164	+	0.649878i	0.976975	−	0.213352i	$-0.0684380\pi$
$229$	7.14514	+	9.83444i	0.472164	+	0.649878i	−0.504811	+	0.863230i	$0.668438\pi$
$230$	6.90877			0.455551
$231$	−4.63417	+	7.45147i	−0.304906	+	0.490271i
$232$	6.27225			0.411793
$233$	−7.69492	−	10.5911i	−0.504111	−	0.693849i	0.478801	−	0.877923i	$-0.341071\pi$
$233$	−7.69492	−	10.5911i	−0.504111	−	0.693849i	−0.982912	+	0.184074i	$0.941071\pi$
$234$	4.18425	−	1.35955i	0.273533	−	0.0888763i
$235$	11.5409	−	35.5192i	0.752844	−	2.31702i
$236$	−5.31076	+	7.30963i	−0.345701	+	0.475816i
$237$	−5.95960	−	4.32990i	−0.387118	−	0.281257i
$238$	−9.81854	−	1.29442i	−0.636442	−	0.0839046i
$239$	−4.25633	+	1.38297i	−0.275319	+	0.0894566i	−0.443422	−	0.896313i	$-0.646236\pi$
$239$	−4.25633	+	1.38297i	−0.275319	+	0.0894566i	0.168103	+	0.985769i	$0.446236\pi$
$240$	−3.08056	+	2.23816i	−0.198850	+	0.144473i
$241$	21.2676			1.36997			0.684983	−	0.728559i	$-0.259809\pi$
$241$	21.2676			1.36997			0.684983	+	0.728559i	$0.259809\pi$
$242$	8.26842	−	7.25488i	0.531514	−	0.466361i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.48147	+	1.80290i	−0.158860	+	0.115419i
$245$	−20.7204	+	16.7668i	−1.32378	+	1.07119i
$246$	1.59239	−	4.90087i	0.101527	−	0.312468i
$247$	−22.0114	−	15.9922i	−1.40055	−	1.01756i
$248$	−6.04560	−	4.39239i	−0.383896	−	0.278917i
$249$	2.19672	+	0.713758i	0.139211	+	0.0452326i
$250$	5.29412	+	16.2936i	0.334830	+	1.03050i
$251$	−16.1184	−	22.1850i	−1.01738	−	1.40031i	−0.914022	−	0.405664i	$-0.867040\pi$
$251$	−16.1184	−	22.1850i	−1.01738	−	1.40031i	−0.103361	−	0.994644i	$-0.532960\pi$
$252$	2.60153	−	0.481686i	0.163881	−	0.0303434i
$253$	4.44602	+	4.05520i	0.279519	+	0.254948i
$254$	13.6099			0.853959
$255$	11.5311	−	8.37782i	0.722104	−	0.524639i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−11.1882	−	3.63525i	−0.697898	−	0.226761i	−0.0614834	−	0.998108i	$-0.519583\pi$
$257$	−11.1882	−	3.63525i	−0.697898	−	0.226761i	−0.636414	+	0.771347i	$0.719583\pi$
$258$	−1.44693	+	1.99153i	−0.0900819	+	0.123987i
$259$	5.66593	+	2.70375i	0.352064	+	0.168003i
$260$	−15.9327	−	5.17686i	−0.988107	−	0.321055i
$261$	5.96527	−	1.93823i	0.369241	−	0.119974i
$262$	2.19495	+	3.02109i	0.135605	+	0.186644i
$263$			2.03444i			0.125449i	0.998031	+	0.0627246i	$0.0199790\pi$
$263$			2.03444i			0.125449i	−0.998031	+	0.0627246i	$0.980021\pi$
$264$	−3.29616	−	0.367849i	−0.202865	−	0.0226396i
$265$		−	3.96853i		−	0.243785i
$266$	−11.8663	−	11.2647i	−0.727571	−	0.690686i
$267$	0.750214	+	2.30892i	0.0459124	+	0.141304i
$268$	−2.49671	+	7.68409i	−0.152511	+	0.469381i
$269$	9.02202	−	12.4177i	0.550082	−	0.757123i	−0.439941	−	0.898027i	$-0.645001\pi$
$269$	9.02202	−	12.4177i	0.550082	−	0.757123i	0.990023	+	0.140903i	$0.0450006\pi$
$270$	−2.23816	+	3.08056i	−0.136210	+	0.187477i
$271$	4.09684	−	12.6088i	0.248865	−	0.765928i	−0.746111	−	0.665821i	$-0.768081\pi$
$271$	4.09684	−	12.6088i	0.248865	−	0.765928i	0.994977	−	0.100107i	$-0.0319186\pi$
$272$	−1.15670	−	3.55997i	−0.0701354	−	0.215855i
$273$	8.44208	+	8.01409i	0.510938	+	0.485035i
$274$		−	11.5433i		−	0.697355i
$275$	−12.9989	+	28.6988i	−0.783864	+	1.73060i
$276$		−	1.81438i		−	0.109213i
$277$	−10.5917	−	14.5782i	−0.636394	−	0.875921i	0.362023	−	0.932169i	$-0.382086\pi$
$277$	−10.5917	−	14.5782i	−0.636394	−	0.875921i	−0.998417	+	0.0562481i	$0.982086\pi$
$278$	4.63248	−	1.50518i	0.277838	−	0.0902750i
$279$	−7.10703	−	2.30921i	−0.425487	−	0.138249i
$280$	−9.09228	−	4.33879i	−0.543368	−	0.259292i
$281$	−7.57461	+	10.4256i	−0.451863	+	0.621937i	−0.972797	−	0.231661i	$-0.925584\pi$
$281$	−7.57461	+	10.4256i	−0.451863	+	0.621937i	0.520933	+	0.853597i	$0.325584\pi$
$282$	−9.32804	−	3.03086i	−0.555476	−	0.180485i
$283$	−7.06564	−	21.7458i	−0.420009	−	1.29265i	−0.907693	−	0.419634i	$-0.862158\pi$
$283$	−7.06564	−	21.7458i	−0.420009	−	1.29265i	0.487684	−	0.873020i	$-0.337842\pi$
$284$	12.3419	−	8.96690i	0.732356	−	0.532087i
$285$	23.5478			1.39485
$286$	−7.21461	−	12.6834i	−0.426609	−	0.749986i
$287$	13.4059	−	2.48217i	0.791326	−	0.146518i
$288$	0.587785	+	0.809017i	0.0346356	+	0.0476718i
$289$	−0.923551	−	2.84240i	−0.0543265	−	0.167200i
$290$	−22.7145	−	7.38037i	−1.33384	−	0.433391i
$291$	9.01871	+	6.55248i	0.528686	+	0.384113i
$292$	1.91820	+	1.39365i	0.112254	+	0.0815573i
$293$	−3.62972	+	11.1711i	−0.212050	+	0.652623i	0.787300	+	0.616571i	$0.211478\pi$
$293$	−3.62972	+	11.1711i	−0.212050	+	0.652623i	−0.999350	+	0.0360529i	$0.988522\pi$
$294$	4.40330	+	5.44159i	0.256806	+	0.317360i
$295$	27.8335	−	20.2222i	1.62053	−	1.17738i
$296$			2.37285i			0.137919i
$297$	−3.24851	+	0.668725i	−0.188498	+	0.0388034i
$298$	−24.3005			−1.40769
$299$	6.45799	−	4.69201i	0.373475	−	0.271346i
$300$	9.03431	−	2.93543i	0.521596	−	0.169477i
$301$	−6.45708	−	0.851262i	−0.372180	−	0.0490659i
$302$	16.9342	+	12.3034i	0.974452	+	0.707981i
$303$	3.93402	−	5.41471i	0.226004	−	0.311067i
$304$	1.91100	−	5.88146i	0.109603	−	0.337325i
$305$	11.1079	−	3.60917i	0.636035	−	0.206660i
$306$	−2.20018	−	3.02829i	−0.125776	−	0.173116i
$307$	−5.10040			−0.291095			−0.145548	−	0.989351i	$-0.546494\pi$
$307$	−5.10040			−0.291095			−0.145548	+	0.989351i	$0.546494\pi$
$308$	−3.30447	−	8.12899i	−0.188290	−	0.463192i
$309$	9.57424			0.544660
$310$	16.7253	+	23.0204i	0.949931	+	1.30747i
$311$	−5.83677	+	1.89648i	−0.330973	+	0.107540i	−0.469789	−	0.882779i	$-0.655670\pi$
$311$	−5.83677	+	1.89648i	−0.330973	+	0.107540i	0.138817	+	0.990318i	$0.455670\pi$
$312$	−1.35955	+	4.18425i	−0.0769691	+	0.236887i
$313$	−8.96475	+	12.3389i	−0.506718	+	0.697437i	−0.983362	−	0.181659i	$-0.941853\pi$
$313$	−8.96475	+	12.3389i	−0.506718	+	0.697437i	0.476644	+	0.879097i	$0.341853\pi$
$314$	0.878936	+	0.638584i	0.0496012	+	0.0360374i
$315$	−9.98803	−	1.31676i	−0.562762	−	0.0741911i
$316$	7.00593	−	2.27637i	0.394114	−	0.128056i
$317$	4.83397	−	3.51208i	0.271503	−	0.197258i	−0.443700	−	0.896175i	$-0.646334\pi$
$317$	4.83397	−	3.51208i	0.271503	−	0.197258i	0.715203	+	0.698917i	$0.246334\pi$
$318$	−1.04221			−0.0584444
$319$	−10.2855	−	18.0821i	−0.575877	−	1.01240i
$320$		−	3.80779i		−	0.212862i
$321$	1.04065	−	0.756080i	0.0580837	−	0.0422002i
$322$	4.21908	−	2.28980i	0.235120	−	0.127606i
$323$	−7.15320	+	22.0153i	−0.398015	+	1.22496i
$324$	0.809017	+	0.587785i	0.0449454	+	0.0326547i
$325$	33.8110	+	24.5651i	1.87550	+	1.36263i
$326$	11.5889	+	3.76546i	0.641850	+	0.208550i
$327$	1.02270	+	3.14756i	0.0565557	+	0.174061i
$328$	3.02891	+	4.16893i	0.167243	+	0.230191i
$329$	−4.72441	−	25.5160i	−0.260465	−	1.40675i
$330$	11.5040	+	5.21063i	0.633272	+	0.286836i
$331$	−5.63142			−0.309531			−0.154765	−	0.987951i	$-0.549462\pi$
$331$	−5.63142			−0.309531			−0.154765	+	0.987951i	$0.549462\pi$
$332$	−1.86864	+	1.35765i	−0.102555	+	0.0745106i
$333$	0.733252	+	2.25672i	0.0401820	+	0.123667i
$334$	9.46042	+	3.07388i	0.517651	+	0.168195i
$335$	18.0833	−	24.8895i	0.987996	−	1.35986i
$336$	−1.13945	+	2.38781i	−0.0621622	+	0.130266i
$337$	28.5514	+	9.27692i	1.55529	+	0.505346i	0.955546	−	0.294842i	$-0.0952672\pi$
$337$	28.5514	+	9.27692i	1.55529	+	0.505346i	0.599749	+	0.800188i	$0.295267\pi$
$338$	−6.04523	+	1.96421i	−0.328817	+	0.106839i
$339$	7.09979	+	9.77202i	0.385608	+	0.530744i
$340$			14.2532i			0.772988i
$341$	−2.74885	+	24.6315i	−0.148859	+	1.33387i
$342$		−	6.18413i		−	0.334399i
$343$	−7.09655	+	17.1067i	−0.383178	+	0.923675i
$344$	−0.760696	−	2.34118i	−0.0410140	−	0.126228i
$345$	−2.13493	+	6.57063i	−0.114941	+	0.353751i
$346$	−12.2951	+	16.9227i	−0.660988	+	0.909771i
$347$	−5.38786	+	7.41576i	−0.289236	+	0.398099i	−0.928766	−	0.370667i	$-0.879129\pi$
$347$	−5.38786	+	7.41576i	−0.289236	+	0.398099i	0.639530	+	0.768766i	$0.279129\pi$
$348$	−1.93823	+	5.96527i	−0.103900	+	0.319772i
$349$	2.80491	+	8.63264i	0.150144	+	0.462095i	0.997637	−	0.0687122i	$-0.0218890\pi$
$349$	2.80491	+	8.63264i	0.150144	+	0.462095i	−0.847493	+	0.530807i	$0.821889\pi$
$350$	18.2275	+	17.3034i	0.974300	+	0.924906i
$351$			4.39958i			0.234832i
$352$	2.23503	−	2.45044i	0.119128	−	0.130609i
$353$			12.8657i			0.684775i	0.939559	+	0.342387i	$0.111236\pi$
$353$			12.8657i			0.684775i	−0.939559	+	0.342387i	$0.888764\pi$
$354$	−5.31076	−	7.30963i	−0.282263	−	0.388502i
$355$	−55.2462	+	17.9506i	−2.93216	+	0.952718i
$356$	−2.30892	−	0.750214i	−0.122373	−	0.0397613i
$357$	4.26516	−	8.93799i	0.225736	−	0.473049i
$358$	−12.9373	+	17.8067i	−0.683760	+	0.941114i
$359$	8.82973	+	2.86895i	0.466015	+	0.151418i	0.532607	−	0.846363i	$-0.321212\pi$
$359$	8.82973	+	2.86895i	0.466015	+	0.151418i	−0.0665916	+	0.997780i	$0.521212\pi$
$360$	−1.17667	−	3.62142i	−0.0620160	−	0.190866i
$361$	−15.5683	+	11.3110i	−0.819383	+	0.595316i
$362$	19.2827			1.01348
$363$	4.34472	+	10.1056i	0.228038	+	0.530407i
$364$	−11.4457	+	2.11922i	−0.599916	+	0.111077i
$365$	−5.30673	−	7.30409i	−0.277767	−	0.382314i
$366$	−0.947839	−	2.91715i	−0.0495443	−	0.152482i
$367$	18.6171	+	6.04905i	0.971803	+	0.315758i	0.751544	−	0.659683i	$-0.229310\pi$
$367$	18.6171	+	6.04905i	0.971803	+	0.315758i	0.220259	+	0.975441i	$0.429310\pi$
$368$	1.46786	+	1.06647i	0.0765177	+	0.0555934i
$369$	4.16893	+	3.02891i	0.217026	+	0.157679i
$370$	2.79207	−	8.59310i	0.145153	−	0.446734i
$371$	−1.31530	−	2.42352i	−0.0682871	−	0.125823i
$372$	6.04560	−	4.39239i	0.313450	−	0.227735i
$373$		−	0.574847i		−	0.0297644i	−0.999889	−	0.0148822i	$-0.995263\pi$
$373$		−	0.574847i		−	0.0297644i	0.999889	−	0.0148822i	$-0.00473733\pi$
$374$	−8.36611	+	9.17240i	−0.432601	+	0.474293i
$375$	−17.1321			−0.884700
$376$	7.93490	−	5.76504i	0.409211	−	0.297309i
$377$	−26.2447	+	8.52741i	−1.35167	+	0.439184i
$378$	−0.345808	+	2.62305i	−0.0177864	+	0.134915i
$379$	24.3948	+	17.7239i	1.25308	+	0.910415i	0.998396	−	0.0566098i	$-0.0180291\pi$
$379$	24.3948	+	17.7239i	1.25308	+	0.910415i	0.254682	+	0.967025i	$0.418029\pi$
$380$	−13.8411	+	19.0506i	−0.710032	+	0.977275i
$381$	−4.20568	+	12.9438i	−0.215463	+	0.663128i
$382$	−3.74489	+	1.21679i	−0.191605	+	0.0622564i
$383$	3.94080	+	5.42405i	0.201365	+	0.277156i	0.897743	−	0.440520i	$-0.145206\pi$
$383$	3.94080	+	5.42405i	0.201365	+	0.277156i	−0.696377	+	0.717676i	$0.745206\pi$
$384$	−1.00000			−0.0510310
$385$	2.40173	+	33.3268i	0.122404	+	1.69849i
$386$	26.1876			1.33291
$387$	−1.44693	−	1.99153i	−0.0735515	−	0.101235i
$388$	−10.6021	+	3.44484i	−0.538242	+	0.174885i
$389$	9.33849	−	28.7409i	0.473480	−	1.45722i	−0.374516	−	0.927221i	$-0.622191\pi$
$389$	9.33849	−	28.7409i	0.473480	−	1.45722i	0.847996	−	0.530002i	$-0.177809\pi$
$390$	9.84697	−	13.5532i	0.498621	−	0.686293i
$391$	−5.49447	−	3.99196i	−0.277867	−	0.201882i
$392$	−6.99054	+	0.363858i	−0.353075	+	0.0183776i
$393$	−3.55150	+	1.15395i	−0.179150	+	0.0582093i
$394$	15.2627	−	11.0890i	0.768922	−	0.558655i
$395$	−28.0500			−1.41135
$396$	1.36842	−	3.02117i	0.0687655	−	0.151819i
$397$		−	28.1134i		−	1.41097i	−0.708724	−	0.705486i	$-0.750729\pi$
$397$		−	28.1134i		−	1.41097i	0.708724	−	0.705486i	$-0.249271\pi$
$398$	15.9598	−	11.5955i	0.799993	−	0.581229i
$399$	14.3803	−	7.80455i	0.719916	−	0.390716i
$400$	−2.93543	+	9.03431i	−0.146771	+	0.451716i
$401$	−13.3023	−	9.66470i	−0.664286	−	0.482632i	0.203821	−	0.979008i	$-0.434664\pi$
$401$	−13.3023	−	9.66470i	−0.664286	−	0.482632i	−0.868108	+	0.496376i	$0.834664\pi$
$402$	−6.53648	−	4.74903i	−0.326010	−	0.236860i
$403$	31.2680	+	10.1596i	1.55757	+	0.506085i
$404$	2.06824	+	6.36538i	0.102899	+	0.316689i
$405$	−2.23816	−	3.08056i	−0.111215	−	0.153074i
$406$	−16.3175	+	3.02125i	−0.809823	+	0.149942i
$407$	6.84062	−	3.89110i	0.339077	−	0.192875i
$408$	3.74317			0.185315
$409$	−9.62676	+	6.99425i	−0.476013	+	0.345844i	−0.799780	−	0.600293i	$-0.795051\pi$
$409$	−9.62676	+	6.99425i	−0.476013	+	0.345844i	0.323767	+	0.946137i	$0.395051\pi$
$410$	−6.06348	−	18.6615i	−0.299454	−	0.921625i
$411$	10.9783	+	3.56707i	0.541520	+	0.175950i
$412$	−5.62760	+	7.74572i	−0.277252	+	0.381604i
$413$	10.2952	−	21.5744i	0.506592	−	1.06160i
$414$	1.72558	+	0.560674i	0.0848075	+	0.0275556i
$415$	8.36464	−	2.71784i	0.410604	−	0.133413i
$416$	−2.58601	−	3.55934i	−0.126790	−	0.174511i
$417$			4.87088i			0.238528i
$418$	−20.0892	+	4.13548i	−0.982594	+	0.202273i
$419$			0.0324611i			0.00158583i	1.00000		0.000792914i	$0.000252392\pi$
$419$			0.0324611i			0.00158583i	−1.00000		0.000792914i	$0.999748\pi$
$420$	6.93610	−	7.30652i	0.338447	−	0.356521i
$421$	2.74368	+	8.44416i	0.133719	+	0.411543i	0.995388	−	0.0959257i	$-0.0305811\pi$
$421$	2.74368	+	8.44416i	0.133719	+	0.411543i	−0.861670	+	0.507469i	$0.830581\pi$
$422$	−4.29138	+	13.2075i	−0.208901	+	0.642932i
$423$	5.76504	−	7.93490i	0.280306	−	0.385808i
$424$	0.612598	−	0.843168i	0.0297504	−	0.0409479i
$425$	10.9878	−	33.8170i	0.532987	−	1.64036i
$426$	4.71418	+	14.5087i	0.228403	+	0.702951i
$427$	5.58721	−	5.88559i	0.270384	−	0.284824i
$428$			1.28632i			0.0621766i
$429$	14.2921	−	2.94211i	0.690028	−	0.142046i
$430$			9.37349i			0.452030i
$431$	18.5966	+	25.5960i	0.895766	+	1.23292i	0.971799	+	0.235811i	$0.0757748\pi$
$431$	18.5966	+	25.5960i	0.895766	+	1.23292i	−0.0760324	+	0.997105i	$0.524225\pi$
$432$	−0.951057	+	0.309017i	−0.0457577	+	0.0148676i
$433$	5.77262	+	1.87564i	0.277414	+	0.0901374i	0.444420	−	0.895819i	$-0.353410\pi$
$433$	5.77262	+	1.87564i	0.277414	+	0.0901374i	−0.167006	+	0.985956i	$0.553410\pi$
$434$	17.8436	+	8.51486i	0.856519	+	0.408726i
$435$	14.0383	−	19.3221i	0.673085	−	0.926422i
$436$	−3.14756	−	1.02270i	−0.150741	−	0.0489787i
$437$	−3.46728	−	10.6712i	−0.165863	−	0.510473i
$438$	−1.91820	+	1.39365i	−0.0916551	+	0.0665913i
$439$	−34.1975			−1.63216			−0.816079	−	0.577940i	$-0.803857\pi$
$439$	−34.1975			−1.63216			−0.816079	+	0.577940i	$0.803857\pi$
$440$	−10.9773	+	6.24416i	−0.523324	+	0.297679i
$441$	−6.53596	+	2.50624i	−0.311236	+	0.119345i
$442$	9.67988	+	13.3232i	0.460425	+	0.633720i
$443$	−4.04656	−	12.4540i	−0.192258	−	0.591709i	−0.999998	−	0.00216993i	$-0.999309\pi$
$443$	−4.04656	−	12.4540i	−0.192258	−	0.591709i	0.807740	−	0.589539i	$-0.200691\pi$
$444$	−2.25672	−	0.733252i	−0.107099	−	0.0347986i
$445$	7.47882	+	5.43368i	0.354530	+	0.257581i
$446$	−21.4121	−	15.5568i	−1.01389	−	0.736637i
$447$	7.50927	−	23.1112i	0.355176	−	1.09312i
$448$	−1.26203	−	2.32536i	−0.0596253	−	0.109863i
$449$	−12.5673	+	9.13070i	−0.593089	+	0.430905i	−0.843419	−	0.537256i	$-0.819461\pi$
$449$	−12.5673	+	9.13070i	−0.593089	+	0.430905i	0.250330	+	0.968161i	$0.419461\pi$
$450$			9.49924i			0.447798i
$451$	7.05156	−	15.5683i	0.332045	−	0.733083i
$452$	−12.0789			−0.568143
$453$	−16.9342	+	12.3034i	−0.795637	+	0.578064i
$454$	22.1340	−	7.19176i	1.03880	−	0.337526i
$455$	43.9432	+	5.79320i	2.06009	+	0.271590i
$456$	5.00306	+	3.63494i	0.234290	+	0.170222i
$457$	0.420355	−	0.578570i	0.0196634	−	0.0270643i	−0.799072	−	0.601235i	$-0.794675\pi$
$457$	0.420355	−	0.578570i	0.0196634	−	0.0270643i	0.818736	+	0.574171i	$0.194675\pi$
$458$	3.75642	−	11.5611i	0.175526	−	0.540214i
$459$	3.55997	−	1.15670i	0.166165	−	0.0539903i
$460$	−4.06088	−	5.58932i	−0.189339	−	0.260603i
$461$	35.6235			1.65915			0.829577	−	0.558393i	$-0.188582\pi$
$461$	35.6235			1.65915			0.829577	+	0.558393i	$0.188582\pi$
$462$	8.75227	−	0.630743i	0.407192	−	0.0293448i
$463$	−34.1877			−1.58884			−0.794419	−	0.607370i	$-0.792224\pi$
$463$	−34.1877			−1.58884			−0.794419	+	0.607370i	$0.792224\pi$
$464$	−3.68674	−	5.07436i	−0.171152	−	0.235571i
$465$	−27.0620	+	8.79299i	−1.25497	+	0.407765i
$466$	−4.04546	+	12.4506i	−0.187402	+	0.576765i
$467$	−1.19877	+	1.64997i	−0.0554727	+	0.0763516i	−0.835852	−	0.548955i	$-0.815026\pi$
$467$	−1.19877	+	1.64997i	−0.0554727	+	0.0763516i	0.780379	+	0.625306i	$0.215026\pi$
$468$	−3.55934	−	2.58601i	−0.164530	−	0.119538i
$469$	2.79396	−	21.1931i	0.129013	−	0.978604i
$470$	−35.5192	+	11.5409i	−1.63838	+	0.532341i
$471$	−0.878936	+	0.638584i	−0.0404992	+	0.0294244i
$472$	9.03520			0.415879
$473$	−5.50189	+	6.03214i	−0.252977	+	0.277358i
$474$			7.36647i			0.338353i
$475$	47.5253	−	34.5292i	2.18061	−	1.58431i
$476$	4.72399	+	8.70421i	0.216524	+	0.398957i
$477$	0.322062	−	0.991204i	0.0147462	−	0.0453841i
$478$	3.62065	+	2.63056i	0.165605	+	0.120319i
$479$	−29.2720	−	21.2673i	−1.33747	−	0.971730i	−0.999533	−	0.0305613i	$-0.990271\pi$
$479$	−29.2720	−	21.2673i	−1.33747	−	0.971730i	−0.337938	−	0.941168i	$-0.609729\pi$
$480$	3.62142	+	1.17667i	0.165294	+	0.0537074i
$481$	−3.22600	−	9.92861i	−0.147093	−	0.452706i
$482$	−12.5008	−	17.2059i	−0.569395	−	0.783705i
$483$	0.873961	+	4.72017i	0.0397666	+	0.214775i
$484$	−10.7294	−	2.42498i	−0.487699	−	0.110226i
$485$	42.4482			1.92747
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	8.25448	+	25.4047i	0.374046	+	1.15120i	0.944120	+	0.329603i	$0.106915\pi$
$487$	8.25448	+	25.4047i	0.374046	+	1.15120i	−0.570073	+	0.821594i	$0.693085\pi$
$488$	2.91715	+	0.947839i	0.132053	+	0.0429066i
$489$	−7.16233	+	9.85810i	−0.323892	+	0.445799i
$490$	25.7438	+	6.90788i	1.16299	+	0.312066i
$491$	2.03470	+	0.661113i	0.0918246	+	0.0298356i	0.354569	−	0.935030i	$-0.384628\pi$
$491$	2.03470	+	0.661113i	0.0918246	+	0.0298356i	−0.262744	+	0.964865i	$0.584628\pi$
$492$	−4.90087	+	1.59239i	−0.220948	+	0.0717905i
$493$	13.8001	+	18.9942i	0.621525	+	0.855455i
$494$			27.2076i			1.22413i
$495$	−8.51052	+	9.33073i	−0.382520	+	0.419385i
$496$			7.47277i			0.335537i
$497$	−27.7886	+	29.2726i	−1.24649	+	1.31306i
$498$	−0.713758	−	2.19672i	−0.0319842	−	0.0984374i
$499$	−0.748532	+	2.30375i	−0.0335089	+	0.103130i	−0.966412	−	0.256998i	$-0.917267\pi$
$499$	−0.748532	+	2.30375i	−0.0335089	+	0.103130i	0.932903	+	0.360127i	$0.117267\pi$
$500$	10.0700	−	13.8602i	0.450345	−	0.619847i
$501$	−5.84686	+	8.04752i	−0.261219	+	0.359537i
$502$	−8.47393	+	26.0801i	−0.378210	+	1.16401i
$503$	4.83317	+	14.8750i	0.215500	+	0.663242i	0.999118	+	0.0419979i	$0.0133723\pi$
$503$	4.83317	+	14.8750i	0.215500	+	0.663242i	−0.783617	+	0.621244i	$0.786628\pi$
$504$	−1.91884	−	1.82156i	−0.0854717	−	0.0811386i
$505$		−	25.4853i		−	1.13408i
$506$	0.667418	−	5.98049i	0.0296704	−	0.265865i
$507$		−	6.35633i		−	0.282295i
$508$	−7.99968	−	11.0106i	−0.354928	−	0.488517i
$509$	32.9383	−	10.7023i	1.45997	−	0.474372i	0.531906	−	0.846803i	$-0.321476\pi$
$509$	32.9383	−	10.7023i	1.45997	−	0.474372i	0.928060	+	0.372432i	$0.121476\pi$
$510$	−13.5556	−	4.40448i	−0.600252	−	0.195034i
$511$	−5.66156	−	2.70167i	−0.250453	−	0.119515i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	5.88146	+	1.91100i	0.259673	+	0.0843727i
$514$	3.63525	+	11.1882i	0.160344	+	0.493488i
$515$	29.4941	−	21.4287i	1.29966	−	0.944261i
$516$	2.46166			0.108369
$517$	−29.6318	−	13.4215i	−1.30321	−	0.590278i
$518$	−1.14297	−	6.17306i	−0.0502192	−	0.271229i
$519$	−12.2951	−	16.9227i	−0.539694	−	0.742825i
$520$	5.17686	+	15.9327i	0.227020	+	0.698697i
$521$	0.924165	+	0.300279i	0.0404884	+	0.0131555i	0.329191	−	0.944263i	$-0.393224\pi$
$521$	0.924165	+	0.300279i	0.0404884	+	0.0131555i	−0.288703	+	0.957419i	$0.593224\pi$
$522$	−5.07436	−	3.68674i	−0.222099	−	0.161364i
$523$	−16.8707	−	12.2573i	−0.737704	−	0.535973i	0.154287	−	0.988026i	$-0.450692\pi$
$523$	−16.8707	−	12.2573i	−0.737704	−	0.535973i	−0.891991	+	0.452053i	$0.850692\pi$
$524$	1.15395	−	3.55150i	0.0504107	−	0.155148i
$525$	−22.0891	+	11.9883i	−0.964048	+	0.523213i
$526$	1.64590	−	1.19582i	0.0717646	−	0.0521400i
$527$		−	27.9719i		−	1.21847i
$528$	1.63984	+	2.88287i	0.0713649	+	0.125461i
$529$	−19.7080			−0.856871
$530$	−3.21060	+	2.33264i	−0.139460	+	0.101323i
$531$	8.59298	−	2.79203i	0.372904	−	0.121164i
$532$	−2.13852	+	16.2213i	−0.0927166	+	0.703283i
$533$	−18.3416	−	13.3259i	−0.794461	−	0.577210i
$534$	1.42699	−	1.96409i	0.0617520	−	0.0849943i
$535$	1.51357	−	4.65830i	0.0654375	−	0.201396i
$536$	7.68409	−	2.49671i	0.331902	−	0.107842i
$537$	−12.9373	−	17.8067i	−0.558287	−	0.768417i
$538$	−15.3492			−0.661750
$539$	12.5123	+	19.5561i	0.538943	+	0.842342i
$540$	3.80779			0.163861
$541$	−16.0754	−	22.1259i	−0.691134	−	0.951265i	−1.00000		0.000159059i	$-0.999949\pi$
$541$	−16.0754	−	22.1259i	−0.691134	−	0.951265i	0.308866	−	0.951106i	$-0.400051\pi$
$542$	−12.6088	+	4.09684i	−0.541593	+	0.175974i
$543$	−5.95868	+	18.3389i	−0.255711	+	0.786999i
$544$	−2.20018	+	3.02829i	−0.0943320	+	0.129837i
$545$	10.1953	+	7.40729i	0.436717	+	0.317293i
$546$	1.52141	−	11.5403i	0.0651103	−	0.493881i
$547$	−27.9252	+	9.07344i	−1.19399	+	0.387952i	−0.837548	−	0.546364i	$-0.816012\pi$
$547$	−27.9252	+	9.07344i	−1.19399	+	0.387952i	−0.356446	+	0.934316i	$0.616012\pi$
$548$	−9.33870	+	6.78497i	−0.398930	+	0.289839i
$549$	3.06727			0.130908
$550$	30.8584	−	6.35238i	1.31580	−	0.270866i
$551$			38.7884i			1.65244i
$552$	−1.46786	+	1.06647i	−0.0624765	+	0.0453918i
$553$	−17.1297	+	9.29670i	−0.728428	+	0.395336i
$554$	−5.56839	+	17.1377i	−0.236578	+	0.728113i
$555$	7.30972	+	5.31083i	0.310281	+	0.225432i
$556$	−3.94062	−	2.86303i	−0.167120	−	0.121420i
$557$	−12.0497	−	3.91519i	−0.510563	−	0.165892i	0.0423950	−	0.999101i	$-0.486501\pi$
$557$	−12.0497	−	3.91519i	−0.510563	−	0.165892i	−0.552958	+	0.833209i	$0.686501\pi$
$558$	2.30921	+	7.10703i	0.0977568	+	0.300865i
$559$	6.36588	+	8.76189i	0.269248	+	0.370588i
$560$	1.83416	+	9.90609i	0.0775073	+	0.418609i
$561$	−6.13820	−	10.7911i	−0.259155	−	0.455599i
$562$	12.8867			0.543593
$563$	−3.09436	+	2.24818i	−0.130412	+	0.0947497i	−0.651079	−	0.759010i	$-0.725683\pi$
$563$	−3.09436	+	2.24818i	−0.130412	+	0.0947497i	0.520667	+	0.853760i	$0.325683\pi$
$564$	3.03086	+	9.32804i	0.127622	+	0.392781i
$565$	43.7427	+	14.2129i	1.84027	+	0.597940i
$566$	−13.4396	+	18.4981i	−0.564911	+	0.777533i
$567$	−2.38781	−	1.13945i	−0.100279	−	0.0478525i
$568$	−14.5087	−	4.71418i	−0.608773	−	0.197802i
$569$	−13.2642	+	4.30980i	−0.556065	+	0.180676i	−0.573550	−	0.819171i	$-0.694434\pi$
$569$	−13.2642	+	4.30980i	−0.556065	+	0.180676i	0.0174851	+	0.999847i	$0.494434\pi$
$570$	−13.8411	−	19.0506i	−0.579739	−	0.797942i
$571$		−	30.0162i		−	1.25614i	−0.778157	−	0.628070i	$-0.783845\pi$
$571$		−	30.0162i		−	1.25614i	0.778157	−	0.628070i	$-0.216155\pi$
$572$	−6.02046	+	13.2919i	−0.251728	+	0.555761i
$573$		−	3.93762i		−	0.164496i
$574$	−9.88792	−	9.38664i	−0.412714	−	0.391791i
$575$	5.32598	+	16.3917i	0.222109	+	0.683580i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−4.96793	+	6.83777i	−0.206818	+	0.284660i	−0.899807	−	0.436287i	$-0.856293\pi$
$577$	−4.96793	+	6.83777i	−0.206818	+	0.284660i	0.692990	+	0.720947i	$0.256293\pi$
$578$	−1.75670	+	2.41789i	−0.0730690	+	0.100571i
$579$	−8.09240	+	24.9059i	−0.336309	+	1.03505i
$580$	7.38037	+	22.7145i	0.306453	+	0.943167i
$581$	4.20738	−	4.43207i	0.174551	−	0.183873i
$582$		−	11.1477i		−	0.462089i
$583$	−3.43530	−	0.383377i	−0.142276	−	0.0158779i
$584$		−	2.37102i		−	0.0981136i
$585$	9.84697	+	13.5532i	0.407122	+	0.560356i
$586$	11.1711	−	3.62972i	0.461474	−	0.149942i
$587$	27.0403	+	8.78592i	1.11607	+	0.362634i	0.808267	−	0.588816i	$-0.200406\pi$
$587$	27.0403	+	8.78592i	1.11607	+	0.362634i	0.307805	+	0.951450i	$0.400406\pi$
$588$	1.81415	−	6.76083i	0.0748141	−	0.278812i
$589$	27.1631	−	37.3868i	1.11923	−	1.54049i
$590$	−32.7202	−	10.6315i	−1.34707	−	0.437690i
$591$	5.82982	+	17.9423i	0.239807	+	0.738049i
$592$	1.91968	−	1.39473i	0.0788983	−	0.0573230i
$593$	−45.3591			−1.86267			−0.931337	−	0.364159i	$-0.881356\pi$
$593$	−45.3591			−1.86267			−0.931337	+	0.364159i	$0.881356\pi$
$594$	2.45044	+	2.23503i	0.100543	+	0.0917045i
$595$	−6.86556	−	37.0802i	−0.281461	−	1.52014i
$596$	14.2835	+	19.6595i	0.585074	+	0.805286i
$597$	6.09610	+	18.7619i	0.249497	+	0.767873i
$598$	−7.59182	−	2.46673i	−0.310453	−	0.100872i
$599$	21.2617	+	15.4476i	0.868731	+	0.631170i	0.930246	−	0.366936i	$-0.119593\pi$
$599$	21.2617	+	15.4476i	0.868731	+	0.631170i	−0.0615152	+	0.998106i	$0.519593\pi$
$600$	−7.68505	−	5.58351i	−0.313741	−	0.227946i
$601$	2.09978	−	6.46246i	0.0856519	−	0.263609i	−0.899053	−	0.437840i	$-0.855744\pi$
$601$	2.09978	−	6.46246i	0.0856519	−	0.263609i	0.984705	+	0.174230i	$0.0557437\pi$
$602$	3.10669	+	5.72424i	0.126619	+	0.233303i
$603$	6.53648	−	4.74903i	0.266186	−	0.193395i
$604$		−	20.9318i		−	0.851702i
$605$	36.0022	+	21.4068i	1.46370	+	0.870311i
$606$	−6.69296			−0.271883
$607$	−4.71166	+	3.42322i	−0.191240	+	0.138944i	−0.679285	−	0.733874i	$-0.737710\pi$
$607$	−4.71166	+	3.42322i	−0.191240	+	0.138944i	0.488045	+	0.872818i	$0.337710\pi$
$608$	−5.88146	+	1.91100i	−0.238525	+	0.0775013i
$609$	2.16899	−	16.4525i	0.0878920	−	0.666687i
$610$	−9.44892	−	6.86504i	−0.382576	−	0.277958i
$611$	−25.3638	+	34.9103i	−1.02611	+	1.41232i
$612$	−1.15670	+	3.55997i	−0.0467570	+	0.143903i
$613$	32.9602	−	10.7094i	1.33125	−	0.432549i	0.444906	−	0.895577i	$-0.353237\pi$
$613$	32.9602	−	10.7094i	1.33125	−	0.432549i	0.886343	+	0.463028i	$0.153237\pi$
$614$	2.99794	+	4.12631i	0.120987	+	0.166524i
$615$	19.6218			0.791229
$616$	−4.63417	+	7.45147i	−0.186716	+	0.300228i
$617$	−45.6715			−1.83867			−0.919334	−	0.393479i	$-0.871271\pi$
$617$	−45.6715			−1.83867			−0.919334	+	0.393479i	$0.871271\pi$
$618$	−5.62760	−	7.74572i	−0.226375	−	0.311579i
$619$	−0.169080	+	0.0549375i	−0.00679591	+	0.00220813i	−0.312413	−	0.949946i	$-0.601137\pi$
$619$	−0.169080	+	0.0549375i	−0.00679591	+	0.00220813i	0.305617	+	0.952155i	$0.401137\pi$
$620$	8.79299	−	27.0620i	0.353135	−	1.08684i
$621$	−1.06647	+	1.46786i	−0.0427958	+	0.0589034i
$622$	4.96505	+	3.60732i	0.199080	+	0.144640i
$623$	6.36811	+	0.839532i	0.255133	+	0.0336352i
$624$	4.18425	−	1.35955i	0.167504	−	0.0544254i
$625$	−14.3514	+	10.4269i	−0.574057	+	0.417077i
$626$	15.2517			0.609582
$627$	2.27483	−	20.3839i	0.0908478	−	0.814054i
$628$		−	1.08642i		−	0.0433531i
$629$	−7.18568	+	5.22070i	−0.286512	+	0.208163i
$630$	4.80554	+	8.85446i	0.191457	+	0.352770i
$631$	3.13736	−	9.65580i	0.124896	−	0.384391i	−0.868986	−	0.494837i	$-0.835228\pi$
$631$	3.13736	−	9.65580i	0.124896	−	0.384391i	0.993882	+	0.110446i	$0.0352278\pi$
$632$	−5.95960	−	4.32990i	−0.237060	−	0.172234i
$633$	−11.2350	−	8.16270i	−0.446551	−	0.324438i
$634$	−5.68267	−	1.84641i	−0.225688	−	0.0733303i
$635$	16.0143	+	49.2870i	0.635509	+	1.95590i
$636$	0.612598	+	0.843168i	0.0242911	+	0.0334338i
$637$	28.7555	−	11.0264i	1.13933	−	0.436883i
$638$	−8.58305	+	18.9495i	−0.339806	+	0.750218i
$639$	−15.2554			−0.603494
$640$	−3.08056	+	2.23816i	−0.121770	+	0.0884711i
$641$	0.941638	+	2.89806i	0.0371925	+	0.114467i	0.967929	−	0.251224i	$-0.0808330\pi$
$641$	0.941638	+	2.89806i	0.0371925	+	0.114467i	−0.930737	+	0.365690i	$0.880833\pi$
$642$	−1.22336	−	0.397495i	−0.0482823	−	0.0156879i
$643$	−8.37314	+	11.5246i	−0.330204	+	0.454487i	−0.941548	−	0.336878i	$-0.890629\pi$
$643$	−8.37314	+	11.5246i	−0.330204	+	0.454487i	0.611344	+	0.791365i	$0.290629\pi$
$644$	−4.33240	−	2.06740i	−0.170721	−	0.0814669i
$645$	−8.91471	−	2.89657i	−0.351017	−	0.114052i
$646$	22.0153	−	7.15320i	0.866180	−	0.281439i
$647$	9.01274	+	12.4050i	0.354327	+	0.487690i	0.948557	−	0.316606i	$-0.102543\pi$
$647$	9.01274	+	12.4050i	0.354327	+	0.487690i	−0.594230	+	0.804295i	$0.702543\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−14.8163	−	26.0473i	−0.581590	−	1.02245i
$650$		−	41.7927i		−	1.63924i
$651$	−13.6121	+	14.3390i	−0.533500	+	0.561990i
$652$	−3.76546	−	11.5889i	−0.147467	−	0.453856i
$653$	−4.58461	+	14.1100i	−0.179410	+	0.552166i	−0.999807	−	0.0196270i	$-0.993752\pi$
$653$	−4.58461	+	14.1100i	−0.179410	+	0.552166i	0.820398	+	0.571793i	$0.193752\pi$
$654$	1.94530	−	2.67748i	0.0760672	−	0.104698i
$655$	−8.35790	+	11.5037i	−0.326570	+	0.449485i
$656$	1.59239	−	4.90087i	0.0621724	−	0.191347i
$657$	−0.732686	−	2.25498i	−0.0285848	−	0.0879750i
$658$	−17.8660	+	18.8201i	−0.696488	+	0.733683i
$659$		−	28.6517i		−	1.11611i	−0.829804	−	0.558055i	$-0.811548\pi$
$659$		−	28.6517i		−	1.11611i	0.829804	−	0.558055i	$-0.188452\pi$
$660$	−2.54636	−	12.3696i	−0.0991170	−	0.481487i
$661$		−	5.31877i		−	0.206876i	−0.994636	−	0.103438i	$-0.967016\pi$
$661$		−	5.31877i		−	0.206876i	0.994636	−	0.103438i	$-0.0329844\pi$
$662$	3.31006	+	4.55591i	0.128649	+	0.177071i
$663$	−15.6624	+	5.08901i	−0.608276	+	0.197641i
$664$	2.19672	+	0.713758i	0.0852493	+	0.0276992i
$665$	26.8316	−	56.2278i	1.04049	−	2.18042i
$666$	1.39473	−	1.91968i	0.0540446	−	0.0743860i
$667$	−10.8233	−	3.51669i	−0.419078	−	0.136167i
$668$	−3.07388	−	9.46042i	−0.118932	−	0.366035i
$669$	21.4121	−	15.5568i	0.827841	−	0.601462i
$670$	−30.7651			−1.18856
$671$	−2.05116	−	9.96405i	−0.0791842	−	0.384658i
$672$	2.60153	−	0.481686i	0.100356	−	0.0185814i
$673$	−5.76579	−	7.93593i	−0.222255	−	0.305908i	0.683299	−	0.730138i	$-0.260544\pi$
$673$	−5.76579	−	7.93593i	−0.222255	−	0.305908i	−0.905554	+	0.424231i	$0.860544\pi$
$674$	−9.27692	−	28.5514i	−0.357333	−	1.09976i
$675$	−9.03431	−	2.93543i	−0.347731	−	0.112985i
$676$	5.14238	+	3.73616i	0.197784	+	0.143698i
$677$	−13.1106	−	9.52544i	−0.503883	−	0.366092i	0.306615	−	0.951834i	$-0.400804\pi$
$677$	−13.1106	−	9.52544i	−0.503883	−	0.366092i	−0.810498	+	0.585741i	$0.800804\pi$
$678$	3.73258	−	11.4877i	0.143349	−	0.441183i
$679$	25.9225	−	14.0688i	0.994813	−	0.539910i
$680$	11.5311	−	8.37782i	0.442197	−	0.321275i
$681$			23.2730i			0.891824i
$682$	21.5430	−	12.2541i	0.824925	−	0.469236i
$683$	27.2117			1.04123			0.520613	−	0.853793i	$-0.325703\pi$
$683$	27.2117			1.04123			0.520613	+	0.853793i	$0.325703\pi$
$684$	−5.00306	+	3.63494i	−0.191297	+	0.138985i
$685$	41.8030	−	13.5826i	1.59721	−	0.518966i
$686$	18.0109	−	4.31383i	0.687658	−	0.164703i
$687$	9.83444	+	7.14514i	0.375207	+	0.272604i
$688$	−1.44693	+	1.99153i	−0.0551636	+	0.0759262i
$689$	−1.41694	+	4.36088i	−0.0539810	+	0.166136i
$690$	6.57063	−	2.13493i	0.250140	−	0.0812753i
$691$	−13.9853	−	19.2492i	−0.532027	−	0.732273i	0.455410	−	0.890282i	$-0.349493\pi$
$691$	−13.9853	−	19.2492i	−0.532027	−	0.732273i	−0.987438	+	0.158009i	$0.949493\pi$
$692$	20.9176			0.795169
$693$	−2.10473	+	8.51881i	−0.0799520	+	0.323603i
$694$	9.16638			0.347951
$695$	10.9018	+	15.0051i	0.413529	+	0.569174i
$696$	5.96527	−	1.93823i	0.226113	−	0.0734685i
$697$	−5.96059	+	18.3448i	−0.225773	+	0.694859i
$698$	5.33526	−	7.34336i	0.201943	−	0.277950i
$699$	−10.5911	−	7.69492i	−0.400594	−	0.291049i
$700$	3.28491	−	24.9170i	0.124158	−	0.941775i
$701$	−11.5016	+	3.73709i	−0.434409	+	0.141148i	−0.518054	−	0.855348i	$-0.673344\pi$
$701$	−11.5016	+	3.73709i	−0.434409	+	0.141148i	0.0836458	+	0.996496i	$0.473344\pi$
$702$	3.55934	−	2.58601i	0.134339	−	0.0976027i
$703$	−14.6740			−0.553441
$704$	−3.29616	−	0.367849i	−0.124229	−	0.0138638i
$705$		−	37.3471i		−	1.40657i
$706$	10.4086	−	7.56230i	0.391733	−	0.284611i
$707$	−8.44670	−	15.5635i	−0.317671	−	0.585326i
$708$	−2.79203	+	8.59298i	−0.104931	+	0.322944i
$709$	−29.3886	−	21.3521i	−1.10371	−	0.801894i	−0.122050	−	0.992524i	$-0.538947\pi$
$709$	−29.3886	−	21.3521i	−1.10371	−	0.801894i	−0.981662	+	0.190630i	$0.938947\pi$
$710$	46.9952	+	34.1440i	1.76370	+	1.28140i
$711$	−7.00593	−	2.27637i	−0.262743	−	0.0853704i
$712$	0.750214	+	2.30892i	0.0281155	+	0.0865305i
$713$	7.96946	+	10.9690i	0.298459	+	0.410793i
$714$	−9.73799	+	1.80303i	−0.364435	+	0.0674768i
$715$	37.4428	−	41.0513i	1.40028	−	1.53523i
$716$	22.0103			0.822564
$717$	−3.62065	+	2.63056i	−0.135216	+	0.0982399i
$718$	−2.86895	−	8.82973i	−0.107068	−	0.329523i
$719$	−19.0440	−	6.18777i	−0.710221	−	0.230765i	−0.0684426	−	0.997655i	$-0.521803\pi$
$719$	−19.0440	−	6.18777i	−0.710221	−	0.230765i	−0.641778	+	0.766890i	$0.721803\pi$
$720$	−2.23816	+	3.08056i	−0.0834113	+	0.114806i
$721$	10.9094	−	22.8615i	0.406287	−	0.851407i
$722$	18.3016	+	5.94655i	0.681115	+	0.221308i
$723$	20.2267	−	6.57205i	0.752239	−	0.244417i
$724$	−11.3341	−	15.6000i	−0.421228	−	0.579771i
$725$		−	59.5816i		−	2.21281i
$726$	5.62185	−	9.45488i	0.208647	−	0.350904i
$727$		−	7.87678i		−	0.292134i	−0.989275	−	0.146067i	$-0.953339\pi$
$727$		−	7.87678i		−	0.292134i	0.989275	−	0.146067i	$-0.0466615\pi$
$728$	8.44208	+	8.01409i	0.312884	+	0.297022i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−2.78991	+	8.58647i	−0.103259	+	0.317800i
$731$	5.41610	−	7.45462i	0.200322	−	0.275719i
$732$	−1.80290	+	2.48147i	−0.0666370	+	0.0917179i
$733$	−1.52190	+	4.68391i	−0.0562125	+	0.173004i	−0.975221	−	0.221234i	$-0.928992\pi$
$733$	−1.52190	+	4.68391i	−0.0562125	+	0.173004i	0.919008	+	0.394238i	$0.128992\pi$
$734$	−6.04905	−	18.6171i	−0.223275	−	0.687168i
$735$	−14.5251	+	22.3492i	−0.535765	+	0.824362i
$736$		−	1.81438i		−	0.0668789i
$737$	−19.7984	−	18.0580i	−0.729282	−	0.665175i
$738$		−	5.15308i		−	0.189688i
$739$	14.5457	+	20.0205i	0.535073	+	0.736465i	0.987893	−	0.155137i	$-0.0495819\pi$
$739$	14.5457	+	20.0205i	0.535073	+	0.736465i	−0.452820	+	0.891602i	$0.649582\pi$
$740$	−8.59310	+	2.79207i	−0.315889	+	0.102638i
$741$	−25.8759	−	8.40761i	−0.950577	−	0.308861i
$742$	−1.18755	+	2.48861i	−0.0435964	+	0.0913598i
$743$	3.22493	−	4.43873i	0.118311	−	0.162841i	−0.745754	−	0.666222i	$-0.767911\pi$
$743$	3.22493	−	4.43873i	0.118311	−	0.162841i	0.864065	+	0.503380i	$0.167911\pi$
$744$	−7.10703	−	2.30921i	−0.260556	−	0.0846599i
$745$	−28.5937	−	88.0024i	−1.04759	−	3.22416i
$746$	−0.465061	+	0.337886i	−0.0170271	+	0.0123709i
$747$	2.30977			0.0845100
$748$	12.3381	+	1.37692i	0.451126	+	0.0503453i
$749$	−0.619602	−	3.34640i	−0.0226398	−	0.122275i
$750$	10.0700	+	13.8602i	0.367705	+	0.506103i
$751$	6.05629	+	18.6394i	0.220997	+	0.680160i	0.998673	+	0.0514945i	$0.0163985\pi$
$751$	6.05629	+	18.6394i	0.220997	+	0.680160i	−0.777676	+	0.628665i	$0.783602\pi$
$752$	−9.32804	−	3.03086i	−0.340158	−	0.110524i
$753$	−22.1850	−	16.1184i	−0.808468	−	0.587386i
$754$	22.3251	+	16.2201i	0.813031	+	0.590701i
$755$	−24.6298	+	75.8028i	−0.896371	+	2.75875i
$756$	2.32536	−	1.26203i	0.0845724	−	0.0458995i
$757$	−33.8491	+	24.5928i	−1.23026	+	0.893840i	−0.996910	−	0.0785519i	$-0.974970\pi$
$757$	−33.8491	+	24.5928i	−1.23026	+	0.893840i	−0.233355	+	0.972392i	$0.574970\pi$
$758$		−	30.1537i		−	1.09523i
$759$	5.48154	+	2.48283i	0.198967	+	0.0901209i
$760$	23.5478			0.854170
$761$	−27.5712	+	20.0317i	−0.999457	+	0.726148i	−0.961972	−	0.273149i	$-0.911935\pi$
$761$	−27.5712	+	20.0317i	−0.999457	+	0.726148i	−0.0374852	+	0.999297i	$0.511935\pi$
$762$	12.9438	−	4.20568i	0.468903	−	0.152356i
$763$	8.68111	+	1.14447i	0.314277	+	0.0414324i
$764$	3.18560	+	2.31447i	0.115251	+	0.0837347i
$765$	8.37782	−	11.5311i	0.302901	−	0.416907i
$766$	2.07180	−	6.37635i	0.0748572	−	0.230387i
$767$	−37.8055	+	12.2838i	−1.36508	+	0.443541i
$768$	0.587785	+	0.809017i	0.0212099	+	0.0291929i
$769$	−11.6123			−0.418750			−0.209375	−	0.977835i	$-0.567143\pi$
$769$	−11.6123			−0.418750			−0.209375	+	0.977835i	$0.567143\pi$
$770$	25.5502	−	21.5320i	0.920766	−	0.775960i
$771$	−11.7639			−0.423667
$772$	−15.3927	−	21.1862i	−0.553994	−	0.762507i
$773$	27.3444	−	8.88472i	0.983509	−	0.319561i	0.227252	−	0.973836i	$-0.427026\pi$
$773$	27.3444	−	8.88472i	0.983509	−	0.319561i	0.756257	+	0.654275i	$0.227026\pi$
$774$	−0.760696	+	2.34118i	−0.0273426	+	0.0841520i
$775$	−41.7243	+	57.4286i	−1.49878	+	2.06290i
$776$	9.01871	+	6.55248i	0.323753	+	0.235220i
$777$	6.22412	+	0.820551i	0.223289	+	0.0294371i
$778$	−28.7409	+	9.33849i	−1.03041	+	0.334801i
$779$	−25.7812	+	18.7311i	−0.923708	+	0.671113i
$780$	−16.7527			−0.599842
$781$	10.2017	+	49.5573i	0.365044	+	1.77330i
$782$			6.79154i			0.242865i
$783$	5.07436	−	3.68674i	0.181343	−	0.131753i
$784$	4.40330	+	5.44159i	0.157261	+	0.194343i
$785$	−1.27836	+	3.93440i	−0.0456268	+	0.140425i
$786$	3.02109	+	2.19495i	0.107759	+	0.0782913i
$787$	30.2361	+	21.9678i	1.07780	+	0.783068i	0.977298	−	0.211868i	$-0.0679548\pi$
$787$	30.2361	+	21.9678i	1.07780	+	0.783068i	0.100503	+	0.994937i	$0.467955\pi$
$788$	−17.9423	−	5.82982i	−0.639169	−	0.207679i
$789$	0.628677	+	1.93487i	0.0223815	+	0.0688832i
$790$	16.4874	+	22.6929i	0.586594	+	0.807377i
$791$	31.4236	−	5.81823i	1.11730	−	0.206872i
$792$	−3.24851	+	0.668725i	−0.115431	+	0.0237621i
$793$	−13.4947			−0.479211
$794$	−22.7442	+	16.5247i	−0.807163	+	0.586438i
$795$	−1.22634	−	3.77429i	−0.0434939	−	0.133860i
$796$	−18.7619	−	6.09610i	−0.664997	−	0.216071i
$797$	−19.5235	+	26.8718i	−0.691559	+	0.951849i	0.308441	+	0.951243i	$0.400193\pi$
$797$	−19.5235	+	26.8718i	−0.691559	+	0.951849i	−1.00000		0.000605449i	$0.999807\pi$
$798$	−14.7665	−	7.04651i	−0.522730	−	0.249444i
$799$	34.9164	+	11.3450i	1.23525	+	0.401358i
$800$	9.03431	−	2.93543i	0.319411	−	0.103783i
$801$	1.42699	+	1.96409i	0.0504203	+	0.0693976i
$802$			16.4426i			0.580607i
$803$	−6.83535	+	3.88810i	−0.241214	+	0.137208i
$804$			8.07953i			0.284943i
$805$	13.2568	+	12.5847i	0.467241	+	0.443553i
$806$	−10.1596	−	31.2680i	−0.357856	−	1.10137i
$807$	4.74316	−	14.5979i	0.166967	−	0.513872i
$808$	3.93402	−	5.41471i	0.138398	−	0.190489i
$809$	16.7807	−	23.0966i	0.589977	−	0.812033i	−0.404768	−	0.914419i	$-0.632648\pi$
$809$	16.7807	−	23.0966i	0.589977	−	0.812033i	0.994745	+	0.102386i	$0.0326477\pi$
$810$	−1.17667	+	3.62142i	−0.0413440	+	0.127244i
$811$	−1.27162	−	3.91364i	−0.0446526	−	0.137427i	0.926245	−	0.376923i	$-0.123018\pi$
$811$	−1.27162	−	3.91364i	−0.0446526	−	0.137427i	−0.970897	+	0.239496i	$0.923018\pi$
$812$	12.0354	+	11.4253i	0.422360	+	0.400948i
$813$		−	13.2576i		−	0.464966i
$814$	−7.16878	−	3.24705i	−0.251266	−	0.113809i
$815$			46.3990i			1.62529i
$816$	−2.20018	−	3.02829i	−0.0770217	−	0.106011i
$817$	14.4782	−	4.70424i	0.506527	−	0.164580i
$818$	11.3169	+	3.67710i	0.395687	+	0.128567i
$819$	10.5054	+	5.01311i	0.367088	+	0.175172i
$820$	−11.5334	+	15.8744i	−0.402765	+	0.554358i
$821$	−20.3611	−	6.61571i	−0.710606	−	0.230890i	−0.0686602	−	0.997640i	$-0.521872\pi$
$821$	−20.3611	−	6.61571i	−0.710606	−	0.230890i	−0.641945	+	0.766750i	$0.721872\pi$
$822$	−3.56707	−	10.9783i	−0.124416	−	0.382912i
$823$	−37.5614	+	27.2900i	−1.30931	+	0.951269i	−0.309309	+	0.950962i	$0.600098\pi$
$823$	−37.5614	+	27.2900i	−1.30931	+	0.951269i	−1.00000		0.000307127i	$0.999902\pi$
$824$	9.57424			0.333534
$825$	−3.49429	+	31.3110i	−0.121655	+	1.09011i
$826$	−23.5054	+	4.35213i	−0.817857	+	0.151430i
$827$	−6.74924	−	9.28953i	−0.234694	−	0.323029i	0.675383	−	0.737467i	$-0.263978\pi$
$827$	−6.74924	−	9.28953i	−0.234694	−	0.323029i	−0.910078	+	0.414438i	$0.863978\pi$
$828$	−0.560674	−	1.72558i	−0.0194848	−	0.0599680i
$829$	−29.9782	−	9.74050i	−1.04119	−	0.338302i	−0.261982	−	0.965073i	$-0.584376\pi$
$829$	−29.9782	−	9.74050i	−1.04119	−	0.338302i	−0.779203	+	0.626771i	$0.784376\pi$
$830$	−7.11539	−	5.16963i	−0.246979	−	0.179441i
$831$	−14.5782	−	10.5917i	−0.505713	−	0.367422i
$832$	−1.35955	+	4.18425i	−0.0471338	+	0.145063i
$833$	−16.4823	−	20.3688i	−0.571078	−	0.705737i
$834$	3.94062	−	2.86303i	0.136453	−	0.0991387i
$835$			37.8771i			1.31079i
$836$	15.1538	+	13.8217i	0.524105	+	0.478034i
$837$	−7.47277			−0.258297
$838$	0.0262616	−	0.0190801i	0.000907191	−	0.000659112i
$839$	46.2244	−	15.0192i	1.59584	−	0.518520i	0.629767	−	0.776784i	$-0.283150\pi$
$839$	46.2244	−	15.0192i	1.59584	−	0.518520i	0.966075	+	0.258263i	$0.0831502\pi$
$840$	−9.98803	−	1.31676i	−0.344620	−	0.0454326i
$841$	8.36616	+	6.07837i	0.288488	+	0.209599i
$842$	5.21878	−	7.18304i	0.179851	−	0.247544i
$843$	−3.98221	+	12.2560i	−0.137155	+	0.422118i
$844$	13.2075	−	4.29138i	0.454622	−	0.147716i
$845$	−14.2265	−	19.5811i	−0.489406	−	0.673610i
$846$	−9.80808			−0.337209
$847$	29.0809	+	1.14048i	0.999232	+	0.0391875i
$848$	−1.04221			−0.0357898
$849$	−13.4396	−	18.4981i	−0.461248	−	0.634853i
$850$	−33.8170	+	10.9878i	−1.15991	+	0.376878i
$851$	1.33040	−	4.09454i	0.0456054	−	0.140359i
$852$	8.96690	−	12.3419i	0.307201	−	0.422826i
$853$	11.7279	+	8.52084i	0.401557	+	0.291748i	0.770175	−	0.637833i	$-0.220169\pi$
$853$	11.7279	+	8.52084i	0.401557	+	0.291748i	−0.368618	+	0.929581i	$0.620169\pi$
$854$	−8.04562	−	1.06069i	−0.275315	−	0.0362959i
$855$	22.3953	−	7.27668i	0.765904	−	0.248857i
$856$	1.04065	−	0.756080i	0.0355688	−	0.0258423i
$857$	7.39700			0.252677			0.126338	−	0.991987i	$-0.459677\pi$
$857$	7.39700			0.252677			0.126338	+	0.991987i	$0.459677\pi$
$858$	−10.7809	−	9.83321i	−0.368054	−	0.335700i
$859$			9.37674i			0.319930i	0.987123	+	0.159965i	$0.0511382\pi$
$859$			9.37674i			0.319930i	−0.987123	+	0.159965i	$0.948862\pi$
$860$	7.58331	−	5.50960i	0.258589	−	0.187876i
$861$	11.9828	−	6.50334i	0.408371	−	0.221633i
$862$	9.77681	−	30.0899i	0.332999	−	1.02487i
$863$	40.6925	+	29.5648i	1.38519	+	1.00640i	0.996374	+	0.0850827i	$0.0271154\pi$
$863$	40.6925	+	29.5648i	1.38519	+	1.00640i	0.388815	+	0.921316i	$0.372885\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−75.7516	−	24.6132i	−2.57563	−	0.836873i
$866$	−1.87564	−	5.77262i	−0.0637368	−	0.196162i
$867$	−1.75670	−	2.41789i	−0.0596606	−	0.0821158i
$868$	−3.59953	−	19.4407i	−0.122176	−	0.659859i
$869$	−2.70975	+	24.2811i	−0.0919220	+	0.823680i
$870$	−23.8834			−0.809723
$871$	−28.7578	+	20.8938i	−0.974420	+	0.707958i
$872$	1.02270	+	3.14756i	0.0346332	+	0.106590i
$873$	10.6021	+	3.44484i	0.358828	+	0.116590i
$874$	−6.59516	+	9.07746i	−0.223085	+	0.307050i
$875$	−19.5212	+	40.9084i	−0.659938	+	1.38295i
$876$	2.25498	+	0.732686i	0.0761886	+	0.0247552i
$877$	25.1059	−	8.15739i	0.847765	−	0.275455i	0.147255	−	0.989099i	$-0.452956\pi$
$877$	25.1059	−	8.15739i	0.847765	−	0.275455i	0.700510	+	0.713643i	$0.252956\pi$
$878$	20.1008	+	27.6664i	0.678369	+	0.933695i
$879$			11.7460i			0.396183i
$880$	11.5040	+	5.21063i	0.387798	+	0.175650i
$881$		−	51.9974i		−	1.75184i	−0.482461	−	0.875918i	$-0.660257\pi$
$881$		−	51.9974i		−	1.75184i	0.482461	−	0.875918i	$-0.339743\pi$
$882$	5.86933	+	3.81457i	0.197631	+	0.128443i
$883$	15.4970	+	47.6948i	0.521514	+	1.60506i	0.771107	+	0.636706i	$0.219703\pi$
$883$	15.4970	+	47.6948i	0.521514	+	1.60506i	−0.249592	+	0.968351i	$0.580297\pi$
$884$	5.08901	−	15.6624i	0.171162	−	0.526782i
$885$	20.2222	−	27.8335i	0.679763	−	0.935613i
$886$	−7.69702	+	10.5940i	−0.258586	+	0.355914i
$887$	8.46159	−	26.0421i	0.284113	−	0.874408i	−0.702551	−	0.711634i	$-0.747956\pi$
$887$	8.46159	−	26.0421i	0.284113	−	0.874408i	0.986663	−	0.162775i	$-0.0520444\pi$
$888$	0.733252	+	2.25672i	0.0246063	+	0.0757305i
$889$	26.1151	+	24.7911i	0.875872	+	0.831468i
$890$		−	9.24433i		−	0.309871i
$891$	−2.88287	+	1.63984i	−0.0965797	+	0.0549367i
$892$			26.4669i			0.886176i
$893$	35.6518	+	49.0704i	1.19304	+	1.64208i
$894$	−23.1112	+	7.50927i	−0.772953	+	0.251148i
$895$	−79.7086	−	25.8989i	−2.66436	−	0.865705i
$896$	−1.13945	+	2.38781i	−0.0380664	+	0.0797712i
$897$	4.69201	−	6.45799i	0.156662	−	0.215626i
$898$	14.7738	+	4.80029i	0.493008	+	0.160188i
$899$	−14.4840	−	44.5771i	−0.483067	−	1.48673i
$900$	7.68505	−	5.58351i	0.256168	−	0.186117i
$901$	3.90118			0.129967
$902$	−16.7398	+	3.44599i	−0.557375	+	0.114739i
$903$	−6.40410	+	1.18575i	−0.213115	+	0.0394592i
$904$	7.09979	+	9.77202i	0.236136	+	0.325013i
$905$	22.6894	+	69.8308i	0.754221	+	2.32125i
$906$	19.9073	+	6.46828i	0.661376	+	0.214894i
$907$	−18.3025	−	13.2975i	−0.607724	−	0.441537i	0.240888	−	0.970553i	$-0.422561\pi$
$907$	−18.3025	−	13.2975i	−0.607724	−	0.441537i	−0.848612	+	0.529015i	$0.822561\pi$
$908$	−18.8283	−	13.6795i	−0.624838	−	0.453971i
$909$	2.06824	−	6.36538i	0.0685991	−	0.211126i
$910$	−21.1424	−	38.9559i	−0.700862	−	1.29138i
$911$	−19.2319	+	13.9728i	−0.637182	+	0.462940i	−0.858881	−	0.512175i	$-0.828840\pi$
$911$	−19.2319	+	13.9728i	−0.637182	+	0.462940i	0.221699	+	0.975115i	$0.428840\pi$
$912$		−	6.18413i		−	0.204777i
$913$	−1.54460	−	7.50330i	−0.0511188	−	0.248323i
$914$	−0.715151			−0.0236551
$915$	9.44892	−	6.86504i	0.312372	−	0.226951i
$916$	−11.5611	+	3.75642i	−0.381989	+	0.124116i
$917$	−1.29134	+	9.79520i	−0.0426438	+	0.323466i
$918$	−3.02829	−	2.20018i	−0.0999484	−	0.0726168i
$919$	23.2406	−	31.9880i	0.766637	−	1.05519i	−0.229995	−	0.973192i	$-0.573871\pi$
$919$	23.2406	−	31.9880i	0.766637	−	1.05519i	0.996633	−	0.0819942i	$-0.0261289\pi$
$920$	−2.13493	+	6.57063i	−0.0703865	+	0.216627i
$921$	−4.85077	+	1.57611i	−0.159838	+	0.0519346i
$922$	−20.9390	−	28.8200i	−0.689589	−	0.949138i
$923$	67.1174			2.20920
$924$	−5.65473	−	6.70999i	−0.186027	−	0.220742i
$925$	22.5403			0.741120
$926$	20.0950	+	27.6584i	0.660364	+	0.908913i
$927$	9.10564	−	2.95860i	0.299069	−	0.0971733i
$928$	−1.93823	+	5.96527i	−0.0636256	+	0.195819i
$929$	−12.5648	+	17.2940i	−0.412239	+	0.567398i	−0.963763	−	0.266761i	$-0.914046\pi$
$929$	−12.5648	+	17.2940i	−0.412239	+	0.567398i	0.551524	+	0.834159i	$0.314046\pi$
$930$	23.0204	+	16.7253i	0.754867	+	0.548443i
$931$	−2.25014	−	43.2304i	−0.0737455	−	1.41682i
$932$	12.4506	−	4.04546i	0.407834	−	0.132513i
$933$	−4.96505	+	3.60732i	−0.162548	+	0.118098i
$934$	2.03948			0.0667337
$935$	−43.0613	−	19.5043i	−1.40825	−	0.637859i
$936$			4.39958i			0.143805i
$937$	19.5720	−	14.2199i	0.639391	−	0.464545i	−0.220250	−	0.975443i	$-0.570687\pi$
$937$	19.5720	−	14.2199i	0.639391	−	0.464545i	0.859641	+	0.510899i	$0.170687\pi$
$938$	−18.7878	+	10.1966i	−0.613443	+	0.332931i
$939$	−4.71305	+	14.5053i	−0.153805	+	0.473362i
$940$	30.2144	+	21.9521i	0.985485	+	0.715997i
$941$	−20.9970	−	15.2552i	−0.684482	−	0.497305i	0.190360	−	0.981714i	$-0.439035\pi$
$941$	−20.9970	−	15.2552i	−0.684482	−	0.497305i	−0.874841	+	0.484409i	$0.839035\pi$
$942$	1.03325	+	0.335724i	0.0336651	+	0.0109385i
$943$	−2.88920	−	8.89205i	−0.0940853	−	0.289565i
$944$	−5.31076	−	7.30963i	−0.172850	−	0.237908i
$945$	−9.90609	+	1.83416i	−0.322245	+	0.0596651i
$946$	8.11404	+	0.905521i	0.263810	+	0.0294410i
$947$	13.7871			0.448021			0.224011	−	0.974587i	$-0.428085\pi$
$947$	13.7871			0.448021			0.224011	+	0.974587i	$0.428085\pi$
$948$	5.95960	−	4.32990i	0.193559	−	0.140629i
$949$	3.22352	+	9.92096i	0.104640	+	0.322048i
$950$	−55.8693	−	18.1531i	−1.81264	−	0.588963i
$951$	3.51208	−	4.83397i	0.113887	−	0.156752i
$952$	4.26516	−	8.93799i	0.138235	−	0.289682i
$953$	−22.0070	−	7.15050i	−0.712876	−	0.231628i	−0.0699444	−	0.997551i	$-0.522282\pi$
$953$	−22.0070	−	7.15050i	−0.712876	−	0.231628i	−0.642932	+	0.765923i	$0.722282\pi$
$954$	−0.991204	+	0.322062i	−0.0320914	+	0.0104271i
$955$	−8.81302	−	12.1301i	−0.285182	−	0.392520i
$956$		−	4.47537i		−	0.144744i
$957$	−15.3697	−	14.0187i	−0.496833	−	0.453160i
$958$			36.1822i			1.16899i
$959$	21.0267	−	22.1496i	0.678989	−	0.715249i
$960$	−1.17667	−	3.62142i	−0.0379769	−	0.116881i
$961$	−7.67670	+	23.6265i	−0.247635	+	0.762144i
$962$	−6.13622	+	8.44578i	−0.197840	+	0.272303i
$963$	0.756080	−	1.04065i	0.0243643	−	0.0335346i
$964$	−6.57205	+	20.2267i	−0.211672	+	0.651458i
$965$	30.8141	+	94.8362i	0.991942	+	3.05288i
$966$	3.30500	−	3.48150i	0.106337	−	0.112015i
$967$			19.6383i			0.631524i	0.948838	+	0.315762i	$0.102260\pi$
$967$			19.6383i			0.631524i	−0.948838	+	0.315762i	$0.897740\pi$
$968$	4.34472	+	10.1056i	0.139644	+	0.324807i
$969$			23.1482i			0.743629i
$970$	−24.9504	−	34.3413i	−0.801110	−	1.10263i
$971$	13.8716	−	4.50717i	0.445162	−	0.144642i	−0.0778541	−	0.996965i	$-0.524807\pi$
$971$	13.8716	−	4.50717i	0.445162	−	0.144642i	0.523016	+	0.852323i	$0.324807\pi$
$972$	0.951057	+	0.309017i	0.0305052	+	0.00991172i
$973$	11.6308	+	5.55013i	0.372865	+	0.177929i
$974$	15.7010	−	21.6105i	0.503091	−	0.692446i
$975$	39.7472	+	12.9147i	1.27293	+	0.413600i
$976$	−0.947839	−	2.91715i	−0.0303396	−	0.0933756i
$977$	−26.7498	+	19.4349i	−0.855802	+	0.621777i	−0.926740	−	0.375704i	$-0.877401\pi$
$977$	−26.7498	+	19.4349i	−0.855802	+	0.621777i	0.0709374	+	0.997481i	$0.477401\pi$
$978$	12.1853			0.389642
$979$	5.42609	−	5.94903i	0.173418	−	0.190132i
$980$	−9.54324	−	24.8875i	−0.304848	−	0.795003i
$981$	1.94530	+	2.67748i	0.0621086	+	0.0854852i
$982$	−0.661113	−	2.03470i	−0.0210970	−	0.0649298i
$983$	−32.2841	−	10.4897i	−1.02970	−	0.334571i	−0.255031	−	0.966933i	$-0.582086\pi$
$983$	−32.2841	−	10.4897i	−1.02970	−	0.334571i	−0.774673	+	0.632362i	$0.782086\pi$
$984$	4.16893	+	3.02891i	0.132901	+	0.0965580i
$985$	58.1170	+	42.2245i	1.85176	+	1.34538i
$986$	7.25513	−	22.3290i	0.231051	−	0.711100i
$987$	−12.3781	−	22.8073i	−0.393998	−	0.725964i
$988$	22.0114	−	15.9922i	0.700276	−	0.508780i
$989$			4.46639i			0.142023i
$990$	12.5511	+	1.40069i	0.398900	+	0.0445169i
$991$	39.6288			1.25885			0.629425	−	0.777061i	$-0.283291\pi$
$991$	39.6288			1.25885			0.629425	+	0.777061i	$0.283291\pi$
$992$	6.04560	−	4.39239i	0.191948	−	0.139458i
$993$	−5.35580	+	1.74020i	−0.169961	+	0.0552237i
$994$	40.0157	+	5.27543i	1.26922	+	0.167327i
$995$	60.7715	+	44.1531i	1.92659	+	1.39975i
$996$	−1.35765	+	1.86864i	−0.0430187	+	0.0592102i
$997$	−7.63570	+	23.5003i	−0.241825	+	0.744261i	0.754317	+	0.656510i	$0.227968\pi$
$997$	−7.63570	+	23.5003i	−0.241825	+	0.744261i	−0.996142	+	0.0877510i	$0.972032\pi$
$998$	2.30375	−	0.748532i	0.0729238	−	0.0236944i
$999$	1.39473	+	1.91968i	0.0441272	+	0.0607359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.b.349.4	yes	32
7.6	odd	2		462.2.u.a.349.1	yes	32
11.7	odd	10		462.2.u.a.139.1	✓	32
77.62	even	10	inner	462.2.u.b.139.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.139.1	✓	32	11.7	odd	10
462.2.u.a.349.1	yes	32	7.6	odd	2
462.2.u.b.139.4	yes	32	77.62	even	10	inner
462.2.u.b.349.4	yes	32	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.23816 - 3.08056i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.345808 - 2.62305i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.23816 - 3.08056i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.345808 - 2.62305i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} -3.80779 q^{10} +(-2.45044 - 2.23503i) q^{11} +1.00000i q^{12} +(-3.55934 + 2.58601i) q^{13} +(-2.32536 + 1.26203i) q^{14} +(1.17667 - 3.62142i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.02829 + 2.20018i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(1.91100 + 5.88146i) q^{19} +(2.23816 + 3.08056i) q^{20} +(-0.481686 - 2.60153i) q^{21} +(-0.367849 + 3.29616i) q^{22} -1.81438 q^{23} +(0.809017 - 0.587785i) q^{24} +(-2.93543 - 9.03431i) q^{25} +(4.18425 + 1.35955i) q^{26} +(0.587785 - 0.809017i) q^{27} +(2.38781 + 1.13945i) q^{28} +(5.96527 + 1.93823i) q^{29} +(-3.62142 + 1.17667i) q^{30} +(-4.39239 - 6.04560i) q^{31} +1.00000i q^{32} +(-3.02117 - 1.36842i) q^{33} -3.74317i q^{34} +(-7.30652 - 6.93610i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-0.733252 + 2.25672i) q^{37} +(3.63494 - 5.00306i) q^{38} +(-2.58601 + 3.55934i) q^{39} +(1.17667 - 3.62142i) q^{40} +(1.59239 + 4.90087i) q^{41} +(-1.82156 + 1.91884i) q^{42} -2.46166i q^{43} +(2.88287 - 1.63984i) q^{44} -3.80779i q^{45} +(1.06647 + 1.46786i) q^{46} +(9.32804 - 3.03086i) q^{47} +(-0.951057 - 0.309017i) q^{48} +(-6.76083 - 1.81415i) q^{49} +(-5.58351 + 7.68505i) q^{50} +(3.55997 + 1.15670i) q^{51} +(-1.35955 - 4.18425i) q^{52} +(0.843168 - 0.612598i) q^{53} -1.00000 q^{54} +(-12.3696 + 2.54636i) q^{55} +(-0.481686 - 2.60153i) q^{56} +(3.63494 + 5.00306i) q^{57} +(-1.93823 - 5.96527i) q^{58} +(8.59298 + 2.79203i) q^{59} +(3.08056 + 2.23816i) q^{60} +(2.48147 + 1.80290i) q^{61} +(-2.30921 + 7.10703i) q^{62} +(-1.26203 - 2.32536i) q^{63} +(0.809017 - 0.587785i) q^{64} +16.7527i q^{65} +(0.668725 + 3.24851i) q^{66} +8.07953 q^{67} +(-3.02829 + 2.20018i) q^{68} +(-1.72558 + 0.560674i) q^{69} +(-1.31676 + 9.98803i) q^{70} +(-12.3419 - 8.96690i) q^{71} +(0.587785 - 0.809017i) q^{72} +(0.732686 - 2.25498i) q^{73} +(2.25672 - 0.733252i) q^{74} +(-5.58351 - 7.68505i) q^{75} -6.18413 q^{76} +(-6.70999 + 5.65473i) q^{77} +4.39958 q^{78} +(-4.32990 - 5.95960i) q^{79} +(-3.62142 + 1.17667i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.02891 - 4.16893i) q^{82} +(1.86864 + 1.35765i) q^{83} +(2.62305 + 0.345808i) q^{84} +(13.5556 - 4.40448i) q^{85} +(-1.99153 + 1.44693i) q^{86} +6.27225 q^{87} +(-3.02117 - 1.36842i) q^{88} +2.42774i q^{89} +(-3.08056 + 2.23816i) q^{90} +(5.55240 + 10.2306i) q^{91} +(0.560674 - 1.72558i) q^{92} +(-6.04560 - 4.39239i) q^{93} +(-7.93490 - 5.76504i) q^{94} +(22.3953 + 7.27668i) q^{95} +(0.309017 + 0.951057i) q^{96} +(6.55248 + 9.01871i) q^{97} +(2.50624 + 6.53596i) q^{98} +(-3.29616 - 0.367849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} + 10 q^{5} - 8 q^{6} - 10 q^{7} + 8 q^{9} + 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} - 12 q^{17} - 16 q^{19} + 10 q^{20} - 8 q^{21} - 4 q^{22} + 8 q^{23} + 8 q^{24} + 6 q^{25} + 10 q^{28} + 20 q^{29} - 50 q^{31} - 16 q^{33} - 12 q^{35} - 8 q^{36} - 16 q^{37} + 6 q^{40} + 40 q^{41} + 12 q^{44} + 52 q^{49} + 40 q^{51} - 32 q^{54} - 40 q^{55} - 8 q^{56} + 10 q^{58} + 60 q^{59} + 4 q^{60} - 4 q^{61} + 20 q^{62} - 10 q^{63} + 8 q^{64} + 8 q^{66} - 16 q^{67} + 12 q^{68} + 30 q^{69} - 28 q^{70} - 48 q^{71} - 74 q^{73} - 40 q^{74} - 24 q^{76} + 6 q^{77} - 60 q^{79} - 8 q^{81} + 20 q^{82} + 4 q^{83} - 2 q^{84} - 10 q^{85} - 36 q^{86} + 20 q^{87} - 16 q^{88} - 4 q^{90} - 20 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} - 8 q^{96} + 60 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 + 10 * q^5 - 8 * q^6 - 10 * q^7 + 8 * q^9 + 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 - 12 * q^17 - 16 * q^19 + 10 * q^20 - 8 * q^21 - 4 * q^22 + 8 * q^23 + 8 * q^24 + 6 * q^25 + 10 * q^28 + 20 * q^29 - 50 * q^31 - 16 * q^33 - 12 * q^35 - 8 * q^36 - 16 * q^37 + 6 * q^40 + 40 * q^41 + 12 * q^44 + 52 * q^49 + 40 * q^51 - 32 * q^54 - 40 * q^55 - 8 * q^56 + 10 * q^58 + 60 * q^59 + 4 * q^60 - 4 * q^61 + 20 * q^62 - 10 * q^63 + 8 * q^64 + 8 * q^66 - 16 * q^67 + 12 * q^68 + 30 * q^69 - 28 * q^70 - 48 * q^71 - 74 * q^73 - 40 * q^74 - 24 * q^76 + 6 * q^77 - 60 * q^79 - 8 * q^81 + 20 * q^82 + 4 * q^83 - 2 * q^84 - 10 * q^85 - 36 * q^86 + 20 * q^87 - 16 * q^88 - 4 * q^90 - 20 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 - 8 * q^96 + 60 * q^97 - 40 * q^98 - 8 * q^99

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