LMFDB - Embedded newform 462.2.u.b.139.4

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			139.4
Character	$\chi$	$=$	462.139
Dual form			462.2.u.b.349.4

$q$-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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{10}\right)$

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	0.924749	+	0.380577i	$0.124274\pi$
$5$	2.23816	+	3.08056i	1.00094	+	1.37767i	0.0761865	+	0.997094i	$0.475726\pi$
$6$	−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	−0.0278803	−	0.999611i	$-0.508876\pi$
$13$	−3.55934	−	2.58601i	−0.987183	−	0.717230i	−0.959302	+	0.282381i	$0.908876\pi$
$14$	−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	−0.156506	−	0.987677i	$-0.550023\pi$
$17$	3.02829	−	2.20018i	0.734468	−	0.533622i	0.890974	+	0.454055i	$0.150023\pi$
$18$	−0.951057	+	0.309017i	−0.224166	+	0.0728360i
$19$	1.91100	−	5.88146i	0.438414	−	1.34930i	−0.451134	−	0.892456i	$-0.648980\pi$
$19$	1.91100	−	5.88146i	0.438414	−	1.34930i	0.889548	−	0.456842i	$-0.151020\pi$
$20$	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	0.302652	−	0.953101i	$-0.402128\pi$
$29$	5.96527	−	1.93823i	1.10772	−	0.359921i	0.805070	+	0.593180i	$0.202128\pi$
$30$	−3.62142	−	1.17667i	−0.661178	−	0.214830i
$31$	−4.39239	+	6.04560i	−0.788896	+	1.08582i	0.205349	+	0.978689i	$0.434167\pi$
$31$	−4.39239	+	6.04560i	−0.788896	+	1.08582i	−0.994245	+	0.107133i	$0.965833\pi$
$32$		−	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	0.872517	−	0.488583i	$-0.162486\pi$
$37$	−0.733252	−	2.25672i	−0.120546	−	0.371002i	−0.993063	+	0.117581i	$0.962486\pi$
$38$	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	−0.746318	−	0.665589i	$-0.768180\pi$
$41$	1.59239	−	4.90087i	0.248690	−	0.765388i	0.995008	−	0.0997984i	$-0.0318198\pi$
$42$	−1.82156	−	1.91884i	−0.281072	−	0.296083i
$43$			2.46166i			0.375400i	0.982226	+	0.187700i	$0.0601033\pi$
$43$			2.46166i			0.375400i	−0.982226	+	0.187700i	$0.939897\pi$
$44$	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	0.896255	−	0.443540i	$-0.146278\pi$
$47$	9.32804	+	3.03086i	1.36063	+	0.442097i	0.464379	+	0.885637i	$0.346278\pi$
$48$	−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	0.644187	−	0.764868i	$-0.277196\pi$
$53$	0.843168	+	0.612598i	0.115818	+	0.0841468i	−0.528368	+	0.849015i	$0.677196\pi$
$54$	−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	0.309436	−	0.950920i	$-0.399860\pi$
$59$	8.59298	−	2.79203i	1.11871	−	0.363491i	0.809276	+	0.587429i	$0.199860\pi$
$60$	3.08056	−	2.23816i	0.397699	−	0.288945i
$61$	2.48147	−	1.80290i	0.317720	−	0.230837i	−0.417482	−	0.908685i	$-0.637087\pi$
$61$	2.48147	−	1.80290i	0.317720	−	0.230837i	0.735202	+	0.677848i	$0.237087\pi$
$62$	−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	−0.482607	+	0.875837i	$0.660310\pi$
$71$	−12.3419	+	8.96690i	−1.46471	+	1.06417i	−0.982104	+	0.188338i	$0.939690\pi$
$72$	0.587785	+	0.809017i	0.0692712	+	0.0953436i
$73$	0.732686	+	2.25498i	0.0857545	+	0.263925i	0.984734	−	0.174065i	$-0.0556904\pi$
$73$	0.732686	+	2.25498i	0.0857545	+	0.263925i	−0.898980	+	0.437990i	$0.855690\pi$
$74$	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	−0.979860	−	0.199688i	$-0.936007\pi$
$79$	−4.32990	+	5.95960i	−0.487152	+	0.670508i	0.492707	+	0.870195i	$0.336007\pi$
$80$	−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	−0.480488	−	0.877001i	$-0.659541\pi$
$83$	1.86864	−	1.35765i	0.205110	−	0.149021i	0.685599	+	0.727980i	$0.259541\pi$
$84$	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	$-0.958929\pi$
$89$		−	2.42774i		−	0.257340i	0.991687	−	0.128670i	$-0.0410709\pi$
$90$	−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	−0.334339	−	0.942453i	$-0.608513\pi$
$97$	6.55248	−	9.01871i	0.665303	−	0.915711i	0.999642	+	0.0267416i	$0.00851312\pi$
$98$	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	0.823633	−	0.567123i	$-0.191943\pi$
$101$	5.41471	+	3.93402i	0.538784	+	0.391450i	−0.284849	+	0.958572i	$0.591943\pi$
$102$	−1.15670	+	3.55997i	−0.114531	+	0.352489i
$103$	9.10564	−	2.95860i	0.897206	−	0.291520i	0.176122	−	0.984368i	$-0.443645\pi$
$103$	9.10564	−	2.95860i	0.897206	−	0.291520i	0.721083	+	0.692848i	$0.243645\pi$
$104$	−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	0.367553	−	0.930003i	$-0.380196\pi$
$107$	1.22336	+	0.397495i	0.118267	+	0.0384272i	−0.249286	+	0.968430i	$0.580196\pi$
$108$	0.587785	−	0.809017i	0.0565597	−	0.0778477i
$109$		−	3.30954i		−	0.316997i	−0.987359	−	0.158498i	$-0.949335\pi$
$109$		−	3.30954i		−	0.316997i	0.987359	−	0.158498i	$-0.0506652\pi$
$110$	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	−0.607087	−	0.794635i	$-0.707662\pi$
$113$	3.73258	−	11.4877i	0.351132	−	1.08067i	0.958219	−	0.286037i	$-0.0923380\pi$
$114$	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	−0.999800	−	0.0199900i	$-0.993637\pi$
$127$	−7.99968	−	11.0106i	−0.709857	−	0.977034i	0.289944	−	0.957044i	$-0.406363\pi$
$128$	−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	−0.112426	−	0.993660i	$-0.535862\pi$
$137$	9.33870	−	6.78497i	0.797859	−	0.579679i	0.910285	+	0.413981i	$0.135862\pi$
$138$	1.46786	−	1.06647i	0.124953	−	0.0907836i
$139$	−1.50518	−	4.63248i	−0.127668	−	0.392922i	0.866710	−	0.498813i	$-0.166231\pi$
$139$	−1.50518	−	4.63248i	−0.127668	−	0.392922i	−0.994378	+	0.105891i	$0.966231\pi$
$140$	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	0.662687	+	0.748896i	$0.269416\pi$
$149$	14.2835	+	19.6595i	1.17015	+	1.61057i	0.507461	+	0.861675i	$0.330584\pi$
$150$	−2.93543	−	9.03431i	−0.239677	−	0.737649i
$151$	−19.9073	−	6.46828i	−1.62003	−	0.526381i	−0.648084	−	0.761569i	$-0.724429\pi$
$151$	−19.9073	−	6.46828i	−1.62003	−	0.526381i	−0.971950	+	0.235188i	$0.924429\pi$
$152$	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	0.267495	−	0.963559i	$-0.413804\pi$
$157$	−1.03325	−	0.335724i	−0.0824624	−	0.0267937i	−0.349958	+	0.936766i	$0.613804\pi$
$158$	−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	0.130465	−	0.991453i	$-0.458353\pi$
$163$	−9.85810	−	7.16233i	−0.772146	−	0.560997i	−0.902612	+	0.430456i	$0.858353\pi$
$164$	−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	0.231140	−	0.972920i	$-0.425754\pi$
$167$	−8.04752	−	5.84686i	−0.622736	−	0.452444i	−0.853876	+	0.520477i	$0.825754\pi$
$168$	−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	0.330988	+	0.943635i	$0.392618\pi$
$173$	−6.46391	+	19.8939i	−0.491442	+	1.51250i	−0.822430	+	0.568867i	$0.807382\pi$
$174$	−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	0.286653	+	0.958034i	$0.407457\pi$
$179$	−6.80156	+	20.9331i	−0.508373	+	1.56461i	−0.795026	+	0.606576i	$0.792543\pi$
$180$	3.62142	−	1.17667i	0.269925	−	0.0877039i
$181$	−11.3341	−	15.6000i	−0.842456	−	1.15954i	−0.985475	−	0.169821i	$-0.945681\pi$
$181$	−11.3341	−	15.6000i	−0.842456	−	1.15954i	0.143019	−	0.989720i	$-0.454319\pi$
$182$	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	0.985378	−	0.170380i	$-0.0544994\pi$
$191$	1.21679	+	3.74489i	0.0880438	+	0.270971i	−0.897335	+	0.441351i	$0.854499\pi$
$192$	0.587785	+	0.809017i	0.0424197	+	0.0583858i
$193$	−15.3927	−	21.1862i	−1.10799	−	1.52501i	−0.824347	−	0.566084i	$-0.808458\pi$
$193$	−15.3927	−	21.1862i	−1.10799	−	1.52501i	−0.283641	−	0.958931i	$-0.591542\pi$
$194$	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	$-0.765409\pi$
$197$		−	18.8657i		−	1.34412i	0.740494	−	0.672062i	$-0.234591\pi$
$198$	1.63984	−	2.88287i	0.116538	−	0.204876i
$199$		−	19.7274i		−	1.39844i	−0.714907	−	0.699219i	$-0.753531\pi$
$199$		−	19.7274i		−	1.39844i	0.714907	−	0.699219i	$-0.246469\pi$
$200$	−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	−0.991572	−	0.129557i	$-0.958644\pi$
$211$	−8.16270	+	11.2350i	−0.561943	+	0.773448i	0.429629	+	0.903006i	$0.358644\pi$
$212$	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	0.985986	−	0.166827i	$-0.0533521\pi$
$223$	25.1715	+	8.17871i	1.68561	+	0.547687i	0.699621	+	0.714514i	$0.253352\pi$
$224$	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	−0.842784	−	0.538252i	$-0.819085\pi$
$227$	−7.19176	−	22.1340i	−0.477334	−	1.46908i	0.365450	−	0.930831i	$-0.380915\pi$
$228$	−5.88146	−	1.91100i	−0.389509	−	0.126559i
$229$	7.14514	−	9.83444i	0.472164	−	0.649878i	−0.504811	−	0.863230i	$-0.668438\pi$
$229$	7.14514	−	9.83444i	0.472164	−	0.649878i	0.976975	+	0.213352i	$0.0684380\pi$
$230$	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	−0.982912	−	0.184074i	$-0.941071\pi$
$233$	−7.69492	+	10.5911i	−0.504111	+	0.693849i	0.478801	+	0.877923i	$0.341071\pi$
$234$	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	0.168103	−	0.985769i	$-0.446236\pi$
$239$	−4.25633	−	1.38297i	−0.275319	−	0.0894566i	−0.443422	+	0.896313i	$0.646236\pi$
$240$	−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	−0.103361	+	0.994644i	$0.532960\pi$
$251$	−16.1184	+	22.1850i	−1.01738	+	1.40031i	−0.914022	+	0.405664i	$0.867040\pi$
$252$	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	−0.636414	−	0.771347i	$-0.719583\pi$
$257$	−11.1882	+	3.63525i	−0.697898	+	0.226761i	−0.0614834	+	0.998108i	$0.519583\pi$
$258$	−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	$-0.980021\pi$
$263$		−	2.03444i		−	0.125449i	0.998031	−	0.0627246i	$-0.0199790\pi$
$264$	−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	0.990023	−	0.140903i	$-0.0450006\pi$
$269$	9.02202	+	12.4177i	0.550082	+	0.757123i	−0.439941	+	0.898027i	$0.645001\pi$
$270$	−2.23816	−	3.08056i	−0.136210	−	0.187477i
$271$	4.09684	+	12.6088i	0.248865	+	0.765928i	0.994977	+	0.100107i	$0.0319186\pi$
$271$	4.09684	+	12.6088i	0.248865	+	0.765928i	−0.746111	+	0.665821i	$0.768081\pi$
$272$	−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	−0.998417	−	0.0562481i	$-0.982086\pi$
$277$	−10.5917	+	14.5782i	−0.636394	+	0.875921i	0.362023	+	0.932169i	$0.382086\pi$
$278$	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	0.520933	−	0.853597i	$-0.325584\pi$
$281$	−7.57461	−	10.4256i	−0.451863	−	0.621937i	−0.972797	+	0.231661i	$0.925584\pi$
$282$	−9.32804	+	3.03086i	−0.555476	+	0.180485i
$283$	−7.06564	+	21.7458i	−0.420009	+	1.29265i	0.487684	+	0.873020i	$0.337842\pi$
$283$	−7.06564	+	21.7458i	−0.420009	+	1.29265i	−0.907693	+	0.419634i	$0.862158\pi$
$284$	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	−0.999350	−	0.0360529i	$-0.988522\pi$
$293$	−3.62972	−	11.1711i	−0.212050	−	0.652623i	0.787300	−	0.616571i	$-0.211478\pi$
$294$	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	0.138817	−	0.990318i	$-0.455670\pi$
$311$	−5.83677	−	1.89648i	−0.330973	−	0.107540i	−0.469789	+	0.882779i	$0.655670\pi$
$312$	−1.35955	−	4.18425i	−0.0769691	−	0.236887i
$313$	−8.96475	−	12.3389i	−0.506718	−	0.697437i	0.476644	−	0.879097i	$-0.341853\pi$
$313$	−8.96475	−	12.3389i	−0.506718	−	0.697437i	−0.983362	+	0.181659i	$0.941853\pi$
$314$	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	0.715203	−	0.698917i	$-0.246334\pi$
$317$	4.83397	+	3.51208i	0.271503	+	0.197258i	−0.443700	+	0.896175i	$0.646334\pi$
$318$	−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	0.599749	−	0.800188i	$-0.295267\pi$
$337$	28.5514	−	9.27692i	1.55529	−	0.505346i	0.955546	+	0.294842i	$0.0952672\pi$
$338$	−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	0.639530	−	0.768766i	$-0.279129\pi$
$347$	−5.38786	−	7.41576i	−0.289236	−	0.398099i	−0.928766	+	0.370667i	$0.879129\pi$
$348$	−1.93823	−	5.96527i	−0.103900	−	0.319772i
$349$	2.80491	−	8.63264i	0.150144	−	0.462095i	−0.847493	−	0.530807i	$-0.821889\pi$
$349$	2.80491	−	8.63264i	0.150144	−	0.462095i	0.997637	+	0.0687122i	$0.0218890\pi$
$350$	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	$-0.888764\pi$
$353$		−	12.8657i		−	0.684775i	0.939559	−	0.342387i	$-0.111236\pi$
$354$	−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	−0.0665916	−	0.997780i	$-0.521212\pi$
$359$	8.82973	−	2.86895i	0.466015	−	0.151418i	0.532607	+	0.846363i	$0.321212\pi$
$360$	−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	0.220259	−	0.975441i	$-0.429310\pi$
$367$	18.6171	−	6.04905i	0.971803	−	0.315758i	0.751544	+	0.659683i	$0.229310\pi$
$368$	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	$0.00473733\pi$
$373$			0.574847i			0.0297644i	−0.999889	+	0.0148822i	$0.995263\pi$
$374$	−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	0.254682	−	0.967025i	$-0.418029\pi$
$379$	24.3948	−	17.7239i	1.25308	−	0.910415i	0.998396	+	0.0566098i	$0.0180291\pi$
$380$	−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	−0.696377	−	0.717676i	$-0.745206\pi$
$383$	3.94080	−	5.42405i	0.201365	−	0.277156i	0.897743	+	0.440520i	$0.145206\pi$
$384$	−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	0.847996	+	0.530002i	$0.177809\pi$
$389$	9.33849	+	28.7409i	0.473480	+	1.45722i	−0.374516	+	0.927221i	$0.622191\pi$
$390$	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	$0.249271\pi$
$397$			28.1134i			1.41097i	−0.708724	+	0.705486i	$0.750729\pi$
$398$	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	−0.868108	−	0.496376i	$-0.834664\pi$
$401$	−13.3023	+	9.66470i	−0.664286	+	0.482632i	0.203821	+	0.979008i	$0.434664\pi$
$402$	−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	0.323767	−	0.946137i	$-0.395051\pi$
$409$	−9.62676	−	6.99425i	−0.476013	−	0.345844i	−0.799780	+	0.600293i	$0.795051\pi$
$410$	−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	$-0.999748\pi$
$419$		−	0.0324611i		−	0.00158583i	1.00000		0.000792914i	$-0.000252392\pi$
$420$	6.93610	+	7.30652i	0.338447	+	0.356521i
$421$	2.74368	−	8.44416i	0.133719	−	0.411543i	−0.861670	−	0.507469i	$-0.830581\pi$
$421$	2.74368	−	8.44416i	0.133719	−	0.411543i	0.995388	+	0.0959257i	$0.0305811\pi$
$422$	−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	−0.0760324	−	0.997105i	$-0.524225\pi$
$431$	18.5966	−	25.5960i	0.895766	−	1.23292i	0.971799	−	0.235811i	$-0.0757748\pi$
$432$	−0.951057	−	0.309017i	−0.0457577	−	0.0148676i
$433$	5.77262	−	1.87564i	0.277414	−	0.0901374i	−0.167006	−	0.985956i	$-0.553410\pi$
$433$	5.77262	−	1.87564i	0.277414	−	0.0901374i	0.444420	+	0.895819i	$0.353410\pi$
$434$	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	0.807740	+	0.589539i	$0.200691\pi$
$443$	−4.04656	+	12.4540i	−0.192258	+	0.591709i	−0.999998	+	0.00216993i	$0.999309\pi$
$444$	−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	0.250330	−	0.968161i	$-0.419461\pi$
$449$	−12.5673	−	9.13070i	−0.593089	−	0.430905i	−0.843419	+	0.537256i	$0.819461\pi$
$450$		−	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	0.818736	−	0.574171i	$-0.194675\pi$
$457$	0.420355	+	0.578570i	0.0196634	+	0.0270643i	−0.799072	+	0.601235i	$0.794675\pi$
$458$	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	0.780379	−	0.625306i	$-0.215026\pi$
$467$	−1.19877	−	1.64997i	−0.0554727	−	0.0763516i	−0.835852	+	0.548955i	$0.815026\pi$
$468$	−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	−0.337938	+	0.941168i	$0.609729\pi$
$479$	−29.2720	+	21.2673i	−1.33747	+	0.971730i	−0.999533	+	0.0305613i	$0.990271\pi$
$480$	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	−0.570073	−	0.821594i	$-0.693085\pi$
$487$	8.25448	−	25.4047i	0.374046	−	1.15120i	0.944120	−	0.329603i	$-0.106915\pi$
$488$	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	−0.262744	−	0.964865i	$-0.584628\pi$
$491$	2.03470	−	0.661113i	0.0918246	−	0.0298356i	0.354569	+	0.935030i	$0.384628\pi$
$492$	−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	0.932903	−	0.360127i	$-0.117267\pi$
$499$	−0.748532	−	2.30375i	−0.0335089	−	0.103130i	−0.966412	+	0.256998i	$0.917267\pi$
$500$	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	−0.783617	−	0.621244i	$-0.786628\pi$
$503$	4.83317	−	14.8750i	0.215500	−	0.663242i	0.999118	−	0.0419979i	$-0.0133723\pi$
$504$	−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	0.928060	−	0.372432i	$-0.121476\pi$
$509$	32.9383	+	10.7023i	1.45997	+	0.474372i	0.531906	+	0.846803i	$0.321476\pi$
$510$	−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	−0.288703	−	0.957419i	$-0.593224\pi$
$521$	0.924165	−	0.300279i	0.0404884	−	0.0131555i	0.329191	+	0.944263i	$0.393224\pi$
$522$	−5.07436	+	3.68674i	−0.222099	+	0.161364i
$523$	−16.8707	+	12.2573i	−0.737704	+	0.535973i	−0.891991	−	0.452053i	$-0.850692\pi$
$523$	−16.8707	+	12.2573i	−0.737704	+	0.535973i	0.154287	+	0.988026i	$0.450692\pi$
$524$	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	0.308866	+	0.951106i	$0.400051\pi$
$541$	−16.0754	+	22.1259i	−0.691134	+	0.951265i	−1.00000		0.000159059i	$0.999949\pi$
$542$	−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	−0.356446	−	0.934316i	$-0.616012\pi$
$547$	−27.9252	−	9.07344i	−1.19399	−	0.387952i	−0.837548	+	0.546364i	$0.816012\pi$
$548$	−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	−0.552958	−	0.833209i	$-0.686501\pi$
$557$	−12.0497	+	3.91519i	−0.510563	+	0.165892i	0.0423950	+	0.999101i	$0.486501\pi$
$558$	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	0.520667	−	0.853760i	$-0.325683\pi$
$563$	−3.09436	−	2.24818i	−0.130412	−	0.0947497i	−0.651079	+	0.759010i	$0.725683\pi$
$564$	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	0.0174851	−	0.999847i	$-0.494434\pi$
$569$	−13.2642	−	4.30980i	−0.556065	−	0.180676i	−0.573550	+	0.819171i	$0.694434\pi$
$570$	−13.8411	+	19.0506i	−0.579739	+	0.797942i
$571$			30.0162i			1.25614i	0.778157	+	0.628070i	$0.216155\pi$
$571$			30.0162i			1.25614i	−0.778157	+	0.628070i	$0.783845\pi$
$572$	−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	0.692990	−	0.720947i	$-0.256293\pi$
$577$	−4.96793	−	6.83777i	−0.206818	−	0.284660i	−0.899807	+	0.436287i	$0.856293\pi$
$578$	−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	0.307805	−	0.951450i	$-0.400406\pi$
$587$	27.0403	−	8.78592i	1.11607	−	0.362634i	0.808267	+	0.588816i	$0.200406\pi$
$588$	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	−0.0615152	−	0.998106i	$-0.519593\pi$
$599$	21.2617	−	15.4476i	0.868731	−	0.631170i	0.930246	+	0.366936i	$0.119593\pi$
$600$	−7.68505	+	5.58351i	−0.313741	+	0.227946i
$601$	2.09978	+	6.46246i	0.0856519	+	0.263609i	0.984705	−	0.174230i	$-0.0557437\pi$
$601$	2.09978	+	6.46246i	0.0856519	+	0.263609i	−0.899053	+	0.437840i	$0.855744\pi$
$602$	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	0.488045	−	0.872818i	$-0.337710\pi$
$607$	−4.71166	−	3.42322i	−0.191240	−	0.138944i	−0.679285	+	0.733874i	$0.737710\pi$
$608$	−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	0.886343	−	0.463028i	$-0.153237\pi$
$613$	32.9602	+	10.7094i	1.33125	+	0.432549i	0.444906	+	0.895577i	$0.353237\pi$
$614$	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	0.305617	−	0.952155i	$-0.401137\pi$
$619$	−0.169080	−	0.0549375i	−0.00679591	−	0.00220813i	−0.312413	+	0.949946i	$0.601137\pi$
$620$	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	0.993882	−	0.110446i	$-0.0352278\pi$
$631$	3.13736	+	9.65580i	0.124896	+	0.384391i	−0.868986	+	0.494837i	$0.835228\pi$
$632$	−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	−0.930737	−	0.365690i	$-0.880833\pi$
$641$	0.941638	−	2.89806i	0.0371925	−	0.114467i	0.967929	+	0.251224i	$0.0808330\pi$
$642$	−1.22336	+	0.397495i	−0.0482823	+	0.0156879i
$643$	−8.37314	−	11.5246i	−0.330204	−	0.454487i	0.611344	−	0.791365i	$-0.290629\pi$
$643$	−8.37314	−	11.5246i	−0.330204	−	0.454487i	−0.941548	+	0.336878i	$0.890629\pi$
$644$	−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	−0.594230	−	0.804295i	$-0.702543\pi$
$647$	9.01274	−	12.4050i	0.354327	−	0.487690i	0.948557	+	0.316606i	$0.102543\pi$
$648$			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	0.820398	−	0.571793i	$-0.193752\pi$
$653$	−4.58461	−	14.1100i	−0.179410	−	0.552166i	−0.999807	+	0.0196270i	$0.993752\pi$
$654$	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	$0.188452\pi$
$659$			28.6517i			1.11611i	−0.829804	+	0.558055i	$0.811548\pi$
$660$	−2.54636	+	12.3696i	−0.0991170	+	0.481487i
$661$			5.31877i			0.206876i	0.994636	+	0.103438i	$0.0329844\pi$
$661$			5.31877i			0.206876i	−0.994636	+	0.103438i	$0.967016\pi$
$662$	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	−0.905554	−	0.424231i	$-0.860544\pi$
$673$	−5.76579	+	7.93593i	−0.222255	+	0.305908i	0.683299	+	0.730138i	$0.260544\pi$
$674$	−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	−0.810498	−	0.585741i	$-0.800804\pi$
$677$	−13.1106	+	9.52544i	−0.503883	+	0.366092i	0.306615	+	0.951834i	$0.400804\pi$
$678$	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	−0.987438	−	0.158009i	$-0.949493\pi$
$691$	−13.9853	+	19.2492i	−0.532027	+	0.732273i	0.455410	+	0.890282i	$0.349493\pi$
$692$	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	0.0836458	−	0.996496i	$-0.473344\pi$
$701$	−11.5016	−	3.73709i	−0.434409	−	0.141148i	−0.518054	+	0.855348i	$0.673344\pi$
$702$	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	−0.981662	−	0.190630i	$-0.938947\pi$
$709$	−29.3886	+	21.3521i	−1.10371	+	0.801894i	−0.122050	+	0.992524i	$0.538947\pi$
$710$	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	−0.641778	−	0.766890i	$-0.721803\pi$
$719$	−19.0440	+	6.18777i	−0.710221	+	0.230765i	−0.0684426	+	0.997655i	$0.521803\pi$
$720$	−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	$0.0466615\pi$
$727$			7.87678i			0.292134i	−0.989275	+	0.146067i	$0.953339\pi$
$728$	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	0.919008	−	0.394238i	$-0.128992\pi$
$733$	−1.52190	−	4.68391i	−0.0562125	−	0.173004i	−0.975221	+	0.221234i	$0.928992\pi$
$734$	−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	−0.452820	−	0.891602i	$-0.649582\pi$
$739$	14.5457	−	20.0205i	0.535073	−	0.736465i	0.987893	+	0.155137i	$0.0495819\pi$
$740$	−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	0.864065	−	0.503380i	$-0.167911\pi$
$743$	3.22493	+	4.43873i	0.118311	+	0.162841i	−0.745754	+	0.666222i	$0.767911\pi$
$744$	−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	−0.777676	−	0.628665i	$-0.783602\pi$
$751$	6.05629	−	18.6394i	0.220997	−	0.680160i	0.998673	−	0.0514945i	$-0.0163985\pi$
$752$	−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	−0.233355	−	0.972392i	$-0.574970\pi$
$757$	−33.8491	−	24.5928i	−1.23026	−	0.893840i	−0.996910	+	0.0785519i	$0.974970\pi$
$758$			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	−0.0374852	−	0.999297i	$-0.511935\pi$
$761$	−27.5712	−	20.0317i	−0.999457	−	0.726148i	−0.961972	+	0.273149i	$0.911935\pi$
$762$	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	0.756257	−	0.654275i	$-0.227026\pi$
$773$	27.3444	+	8.88472i	0.983509	+	0.319561i	0.227252	+	0.973836i	$0.427026\pi$
$774$	−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	0.100503	−	0.994937i	$-0.467955\pi$
$787$	30.2361	−	21.9678i	1.07780	−	0.783068i	0.977298	+	0.211868i	$0.0679548\pi$
$788$	−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	−1.00000		0.000605449i	$-0.999807\pi$
$797$	−19.5235	−	26.8718i	−0.691559	−	0.951849i	0.308441	−	0.951243i	$-0.400193\pi$
$798$	−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	0.994745	−	0.102386i	$-0.0326477\pi$
$809$	16.7807	+	23.0966i	0.589977	+	0.812033i	−0.404768	+	0.914419i	$0.632648\pi$
$810$	−1.17667	−	3.62142i	−0.0413440	−	0.127244i
$811$	−1.27162	+	3.91364i	−0.0446526	+	0.137427i	−0.970897	−	0.239496i	$-0.923018\pi$
$811$	−1.27162	+	3.91364i	−0.0446526	+	0.137427i	0.926245	+	0.376923i	$0.123018\pi$
$812$	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	−0.641945	−	0.766750i	$-0.721872\pi$
$821$	−20.3611	+	6.61571i	−0.710606	+	0.230890i	−0.0686602	+	0.997640i	$0.521872\pi$
$822$	−3.56707	+	10.9783i	−0.124416	+	0.382912i
$823$	−37.5614	−	27.2900i	−1.30931	−	0.951269i	−1.00000		0.000307127i	$-0.999902\pi$
$823$	−37.5614	−	27.2900i	−1.30931	−	0.951269i	−0.309309	−	0.950962i	$-0.600098\pi$
$824$	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	−0.910078	−	0.414438i	$-0.863978\pi$
$827$	−6.74924	+	9.28953i	−0.234694	+	0.323029i	0.675383	+	0.737467i	$0.263978\pi$
$828$	−0.560674	+	1.72558i	−0.0194848	+	0.0599680i
$829$	−29.9782	+	9.74050i	−1.04119	+	0.338302i	−0.779203	−	0.626771i	$-0.784376\pi$
$829$	−29.9782	+	9.74050i	−1.04119	+	0.338302i	−0.261982	+	0.965073i	$0.584376\pi$
$830$	−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	0.966075	−	0.258263i	$-0.0831502\pi$
$839$	46.2244	+	15.0192i	1.59584	+	0.518520i	0.629767	+	0.776784i	$0.283150\pi$
$840$	−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	−0.368618	−	0.929581i	$-0.620169\pi$
$853$	11.7279	−	8.52084i	0.401557	−	0.291748i	0.770175	+	0.637833i	$0.220169\pi$
$854$	−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	$-0.948862\pi$
$859$		−	9.37674i		−	0.319930i	0.987123	−	0.159965i	$-0.0511382\pi$
$860$	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	0.388815	−	0.921316i	$-0.372885\pi$
$863$	40.6925	−	29.5648i	1.38519	−	1.00640i	0.996374	−	0.0850827i	$-0.0271154\pi$
$864$	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	0.700510	−	0.713643i	$-0.252956\pi$
$877$	25.1059	+	8.15739i	0.847765	+	0.275455i	0.147255	+	0.989099i	$0.452956\pi$
$878$	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	$0.339743\pi$
$881$			51.9974i			1.75184i	−0.482461	+	0.875918i	$0.660257\pi$
$882$	5.86933	−	3.81457i	0.197631	−	0.128443i
$883$	15.4970	−	47.6948i	0.521514	−	1.60506i	−0.249592	−	0.968351i	$-0.580297\pi$
$883$	15.4970	−	47.6948i	0.521514	−	1.60506i	0.771107	−	0.636706i	$-0.219703\pi$
$884$	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	0.986663	+	0.162775i	$0.0520444\pi$
$887$	8.46159	+	26.0421i	0.284113	+	0.874408i	−0.702551	+	0.711634i	$0.747956\pi$
$888$	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	−0.848612	−	0.529015i	$-0.822561\pi$
$907$	−18.3025	+	13.2975i	−0.607724	+	0.441537i	0.240888	+	0.970553i	$0.422561\pi$
$908$	−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	0.221699	−	0.975115i	$-0.428840\pi$
$911$	−19.2319	−	13.9728i	−0.637182	−	0.462940i	−0.858881	+	0.512175i	$0.828840\pi$
$912$			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	0.996633	+	0.0819942i	$0.0261289\pi$
$919$	23.2406	+	31.9880i	0.766637	+	1.05519i	−0.229995	+	0.973192i	$0.573871\pi$
$920$	−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	0.551524	−	0.834159i	$-0.314046\pi$
$929$	−12.5648	−	17.2940i	−0.412239	−	0.567398i	−0.963763	+	0.266761i	$0.914046\pi$
$930$	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	0.859641	−	0.510899i	$-0.170687\pi$
$937$	19.5720	+	14.2199i	0.639391	+	0.464545i	−0.220250	+	0.975443i	$0.570687\pi$
$938$	−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	−0.874841	−	0.484409i	$-0.839035\pi$
$941$	−20.9970	+	15.2552i	−0.684482	+	0.497305i	0.190360	+	0.981714i	$0.439035\pi$
$942$	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	−0.642932	−	0.765923i	$-0.722282\pi$
$953$	−22.0070	+	7.15050i	−0.712876	+	0.231628i	−0.0699444	+	0.997551i	$0.522282\pi$
$954$	−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	$-0.897740\pi$
$967$		−	19.6383i		−	0.631524i	0.948838	−	0.315762i	$-0.102260\pi$
$968$	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	0.523016	−	0.852323i	$-0.324807\pi$
$971$	13.8716	+	4.50717i	0.445162	+	0.144642i	−0.0778541	+	0.996965i	$0.524807\pi$
$972$	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	0.0709374	−	0.997481i	$-0.477401\pi$
$977$	−26.7498	−	19.4349i	−0.855802	−	0.621777i	−0.926740	+	0.375704i	$0.877401\pi$
$978$	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	−0.774673	−	0.632362i	$-0.782086\pi$
$983$	−32.2841	+	10.4897i	−1.02970	+	0.334571i	−0.255031	+	0.966933i	$0.582086\pi$
$984$	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	−0.996142	−	0.0877510i	$-0.972032\pi$
$997$	−7.63570	−	23.5003i	−0.241825	−	0.744261i	0.754317	−	0.656510i	$-0.227968\pi$
$998$	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.139.4	yes	32
7.6	odd	2		462.2.u.a.139.1	✓	32
11.8	odd	10		462.2.u.a.349.1	yes	32
77.41	even	10	inner	462.2.u.b.349.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.139.1	✓	32	7.6	odd	2
462.2.u.a.349.1	yes	32	11.8	odd	10
462.2.u.b.139.4	yes	32	1.1	even	1	trivial
462.2.u.b.349.4	yes	32	77.41	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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