LMFDB - Embedded newform 143.2.h.a.53.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [143,2,Mod(14,143)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("143.14"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(143, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			53.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	143.53
Dual form			143.2.h.a.27.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.690983 + 2.12663i) q^{2} +(-1.00000 + 0.726543i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-1.00000 - 3.07768i) q^{5} +(-0.854102 - 2.62866i) q^{6} +(-3.11803 - 2.26538i) q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.454915 + 1.40008i) q^{9} +7.23607 q^{10} +(-2.80902 + 1.76336i) q^{11} +3.70820 q^{12} +(-0.309017 + 0.951057i) q^{13} +(6.97214 - 5.06555i) q^{14} +(3.23607 + 2.35114i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.42705 + 4.39201i) q^{17} +(-2.66312 - 1.93487i) q^{18} +(1.30902 - 0.951057i) q^{19} +(-3.00000 + 9.23305i) q^{20} +4.76393 q^{21} +(-1.80902 - 7.19218i) q^{22} -8.00000 q^{23} +(-0.854102 + 2.62866i) q^{24} +(-4.42705 + 3.21644i) q^{25} +(-1.80902 - 1.31433i) q^{26} +(-1.70820 - 5.25731i) q^{27} +(3.57295 + 10.9964i) q^{28} +(4.54508 + 3.30220i) q^{29} +(-7.23607 + 5.25731i) q^{30} +(1.73607 - 5.34307i) q^{31} +6.70820 q^{32} +(1.52786 - 3.80423i) q^{33} -10.3262 q^{34} +(-3.85410 + 11.8617i) q^{35} +(3.57295 - 2.59590i) q^{36} +(-3.23607 - 2.35114i) q^{37} +(1.11803 + 3.44095i) q^{38} +(-0.381966 - 1.17557i) q^{39} +(-5.85410 - 4.25325i) q^{40} +(-3.29180 + 10.1311i) q^{42} -4.00000 q^{43} +(9.92705 + 0.673542i) q^{44} +4.76393 q^{45} +(5.52786 - 17.0130i) q^{46} +(-5.11803 + 3.71847i) q^{47} +(1.00000 + 0.726543i) q^{48} +(2.42705 + 7.46969i) q^{49} +(-3.78115 - 11.6372i) q^{50} +(-4.61803 - 3.35520i) q^{51} +(2.42705 - 1.76336i) q^{52} +(0.0278640 - 0.0857567i) q^{53} +12.3607 q^{54} +(8.23607 + 6.88191i) q^{55} -8.61803 q^{56} +(-0.618034 + 1.90211i) q^{57} +(-10.1631 + 7.38394i) q^{58} +(7.78115 + 5.65334i) q^{59} +(-3.70820 - 11.4127i) q^{60} +(-2.26393 - 6.96767i) q^{61} +(10.1631 + 7.38394i) q^{62} +(4.59017 - 3.33495i) q^{63} +(-4.01722 + 12.3637i) q^{64} +3.23607 q^{65} +(7.03444 + 5.87785i) q^{66} -1.52786 q^{67} +(4.28115 - 13.1760i) q^{68} +(8.00000 - 5.81234i) q^{69} +(-22.5623 - 16.3925i) q^{70} +(-3.57295 - 10.9964i) q^{71} +(1.01722 + 3.13068i) q^{72} +(-4.61803 - 3.35520i) q^{73} +(7.23607 - 5.25731i) q^{74} +(2.09017 - 6.43288i) q^{75} -4.85410 q^{76} +(12.7533 + 0.865300i) q^{77} +2.76393 q^{78} +(-0.618034 + 1.90211i) q^{79} +(-2.61803 + 1.90211i) q^{80} +(1.95492 + 1.42033i) q^{81} +(2.50000 + 7.69421i) q^{83} +(-11.5623 - 8.40051i) q^{84} +(12.0902 - 8.78402i) q^{85} +(2.76393 - 8.50651i) q^{86} -6.94427 q^{87} +(-2.76393 + 6.88191i) q^{88} -15.4164 q^{89} +(-3.29180 + 10.1311i) q^{90} +(3.11803 - 2.26538i) q^{91} +(19.4164 + 14.1068i) q^{92} +(2.14590 + 6.60440i) q^{93} +(-4.37132 - 13.4535i) q^{94} +(-4.23607 - 3.07768i) q^{95} +(-6.70820 + 4.87380i) q^{96} +(-3.00000 + 9.23305i) q^{97} -17.5623 q^{98} +(-1.19098 - 4.73504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 4 q^{3} - 3 q^{4} - 4 q^{5} + 10 q^{6} - 8 q^{7} + 5 q^{8} - 13 q^{9} + 20 q^{10} - 9 q^{11} - 12 q^{12} + q^{13} + 10 q^{14} + 4 q^{15} + q^{16} - q^{17} + 5 q^{18} + 3 q^{19} - 12 q^{20}+ \cdots - 7 q^{99}+O(q^{100}) $ 4 * q - 5 * q^2 - 4 * q^3 - 3 * q^4 - 4 * q^5 + 10 * q^6 - 8 * q^7 + 5 * q^8 - 13 * q^9 + 20 * q^10 - 9 * q^11 - 12 * q^12 + q^13 + 10 * q^14 + 4 * q^15 + q^16 - q^17 + 5 * q^18 + 3 * q^19 - 12 * q^20 + 28 * q^21 - 5 * q^22 - 32 * q^23 + 10 * q^24 - 11 * q^25 - 5 * q^26 + 20 * q^27 + 21 * q^28 + 7 * q^29 - 20 * q^30 - 2 * q^31 + 24 * q^33 - 10 * q^34 - 2 * q^35 + 21 * q^36 - 4 * q^37 - 6 * q^39 - 10 * q^40 - 40 * q^42 - 16 * q^43 + 33 * q^44 + 28 * q^45 + 40 * q^46 - 16 * q^47 + 4 * q^48 + 3 * q^49 + 5 * q^50 - 14 * q^51 + 3 * q^52 + 18 * q^53 - 40 * q^54 + 24 * q^55 - 30 * q^56 + 2 * q^57 - 25 * q^58 + 11 * q^59 + 12 * q^60 - 18 * q^61 + 25 * q^62 - 4 * q^63 + 13 * q^64 + 4 * q^65 - 30 * q^66 - 24 * q^67 - 3 * q^68 + 32 * q^69 - 50 * q^70 - 21 * q^71 - 25 * q^72 - 14 * q^73 + 20 * q^74 - 14 * q^75 - 6 * q^76 + 13 * q^77 + 20 * q^78 + 2 * q^79 - 6 * q^80 + 19 * q^81 + 10 * q^83 - 6 * q^84 + 26 * q^85 + 20 * q^86 + 8 * q^87 - 20 * q^88 - 8 * q^89 - 40 * q^90 + 8 * q^91 + 24 * q^92 + 22 * q^93 + 25 * q^94 - 8 * q^95 - 12 * q^97 - 30 * q^98 - 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.690983	+	2.12663i	−0.488599	+	1.50375i	0.338101	+	0.941110i	$0.390215\pi$
$2$	−0.690983	+	2.12663i	−0.488599	+	1.50375i	−0.826700	+	0.562643i	$0.809785\pi$
$3$	−1.00000	+	0.726543i	−0.577350	+	0.419470i	−0.837768	−	0.546027i	$-0.816140\pi$
$3$	−1.00000	+	0.726543i	−0.577350	+	0.419470i	0.260418	+	0.965496i	$0.416140\pi$
$4$	−2.42705	−	1.76336i	−1.21353	−	0.881678i
$5$	−1.00000	−	3.07768i	−0.447214	−	1.37638i	−0.880038	−	0.474904i	$-0.842483\pi$
$5$	−1.00000	−	3.07768i	−0.447214	−	1.37638i	0.432824	−	0.901478i	$-0.357517\pi$
$6$	−0.854102	−	2.62866i	−0.348686	−	1.07314i
$7$	−3.11803	−	2.26538i	−1.17851	−	0.856235i	−0.186504	−	0.982454i	$-0.559716\pi$
$7$	−3.11803	−	2.26538i	−1.17851	−	0.856235i	−0.992002	+	0.126219i	$0.959716\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	−0.454915	+	1.40008i	−0.151638	+	0.466695i
$10$	7.23607			2.28825
$11$	−2.80902	+	1.76336i	−0.846950	+	0.531672i
$11$	−2.80902	+	1.76336i	−0.846950	+	0.531672i
$12$	3.70820			1.07047
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	6.97214	−	5.06555i	1.86338	−	1.35383i
$15$	3.23607	+	2.35114i	0.835549	+	0.607062i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	1.42705	+	4.39201i	0.346111	+	1.06522i	0.960987	+	0.276595i	$0.0892061\pi$
$17$	1.42705	+	4.39201i	0.346111	+	1.06522i	−0.614876	+	0.788624i	$0.710794\pi$
$18$	−2.66312	−	1.93487i	−0.627703	−	0.456053i
$19$	1.30902	−	0.951057i	0.300309	−	0.218187i	−0.427418	−	0.904054i	$-0.640577\pi$
$19$	1.30902	−	0.951057i	0.300309	−	0.218187i	0.727727	+	0.685867i	$0.240577\pi$
$20$	−3.00000	+	9.23305i	−0.670820	+	2.06457i
$21$	4.76393			1.03958
$22$	−1.80902	−	7.19218i	−0.385684	−	1.53338i
$23$	−8.00000			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$	−0.854102	+	2.62866i	−0.174343	+	0.536572i
$25$	−4.42705	+	3.21644i	−0.885410	+	0.643288i
$26$	−1.80902	−	1.31433i	−0.354777	−	0.257761i
$27$	−1.70820	−	5.25731i	−0.328744	−	1.01177i
$28$	3.57295	+	10.9964i	0.675224	+	2.07813i
$29$	4.54508	+	3.30220i	0.844001	+	0.613203i	0.923485	−	0.383633i	$-0.125327\pi$
$29$	4.54508	+	3.30220i	0.844001	+	0.613203i	−0.0794844	+	0.996836i	$0.525327\pi$
$30$	−7.23607	+	5.25731i	−1.32112	+	0.959849i
$31$	1.73607	−	5.34307i	0.311807	−	0.959643i	−0.665242	−	0.746628i	$-0.731672\pi$
$31$	1.73607	−	5.34307i	0.311807	−	0.959643i	0.977049	−	0.213015i	$-0.0683284\pi$
$32$	6.70820			1.18585
$33$	1.52786	−	3.80423i	0.265967	−	0.662231i
$34$	−10.3262			−1.77094
$35$	−3.85410	+	11.8617i	−0.651462	+	2.00499i
$36$	3.57295	−	2.59590i	0.595492	−	0.432650i
$37$	−3.23607	−	2.35114i	−0.532006	−	0.386525i	0.289101	−	0.957298i	$-0.406644\pi$
$37$	−3.23607	−	2.35114i	−0.532006	−	0.386525i	−0.821108	+	0.570773i	$0.806644\pi$
$38$	1.11803	+	3.44095i	0.181369	+	0.558197i
$39$	−0.381966	−	1.17557i	−0.0611635	−	0.188242i
$40$	−5.85410	−	4.25325i	−0.925615	−	0.672499i
$41$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$41$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$42$	−3.29180	+	10.1311i	−0.507935	+	1.56326i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	9.92705	+	0.673542i	1.49656	+	0.101540i
$45$	4.76393			0.710165
$46$	5.52786	−	17.0130i	0.815039	−	2.50843i
$47$	−5.11803	+	3.71847i	−0.746542	+	0.542395i	−0.894753	−	0.446561i	$-0.852648\pi$
$47$	−5.11803	+	3.71847i	−0.746542	+	0.542395i	0.148211	+	0.988956i	$0.452648\pi$
$48$	1.00000	+	0.726543i	0.144338	+	0.104867i
$49$	2.42705	+	7.46969i	0.346722	+	1.06710i
$50$	−3.78115	−	11.6372i	−0.534736	−	1.64575i
$51$	−4.61803	−	3.35520i	−0.646654	−	0.469822i
$52$	2.42705	−	1.76336i	0.336571	−	0.244533i
$53$	0.0278640	−	0.0857567i	0.00382742	−	0.0117796i	−0.949125	−	0.314901i	$-0.898029\pi$
$53$	0.0278640	−	0.0857567i	0.00382742	−	0.0117796i	0.952952	+	0.303121i	$0.0980287\pi$
$54$	12.3607			1.68208
$55$	8.23607	+	6.88191i	1.11055	+	0.927957i
$56$	−8.61803			−1.15163
$57$	−0.618034	+	1.90211i	−0.0818606	+	0.251941i
$58$	−10.1631	+	7.38394i	−1.33448	+	0.969559i
$59$	7.78115	+	5.65334i	1.01302	+	0.736002i	0.964840	−	0.262837i	$-0.0846581\pi$
$59$	7.78115	+	5.65334i	1.01302	+	0.736002i	0.0481795	+	0.998839i	$0.484658\pi$
$60$	−3.70820	−	11.4127i	−0.478727	−	1.47337i
$61$	−2.26393	−	6.96767i	−0.289867	−	0.892118i	−0.984898	−	0.173138i	$-0.944609\pi$
$61$	−2.26393	−	6.96767i	−0.289867	−	0.892118i	0.695031	−	0.718980i	$-0.255391\pi$
$62$	10.1631	+	7.38394i	1.29072	+	0.937761i
$63$	4.59017	−	3.33495i	0.578307	−	0.420165i
$64$	−4.01722	+	12.3637i	−0.502153	+	1.54547i
$65$	3.23607			0.401385
$66$	7.03444	+	5.87785i	0.865880	+	0.723514i
$67$	−1.52786			−0.186658			−0.0933292	−	0.995635i	$-0.529751\pi$
$67$	−1.52786			−0.186658			−0.0933292	+	0.995635i	$0.529751\pi$
$68$	4.28115	−	13.1760i	0.519166	−	1.59783i
$69$	8.00000	−	5.81234i	0.963087	−	0.699724i
$70$	−22.5623	−	16.3925i	−2.69671	−	1.95928i
$71$	−3.57295	−	10.9964i	−0.424031	−	1.30503i	−0.903919	−	0.427704i	$-0.859323\pi$
$71$	−3.57295	−	10.9964i	−0.424031	−	1.30503i	0.479888	−	0.877330i	$-0.340677\pi$
$72$	1.01722	+	3.13068i	0.119881	+	0.368955i
$73$	−4.61803	−	3.35520i	−0.540500	−	0.392696i	0.283771	−	0.958892i	$-0.408415\pi$
$73$	−4.61803	−	3.35520i	−0.540500	−	0.392696i	−0.824271	+	0.566196i	$0.808415\pi$
$74$	7.23607	−	5.25731i	0.841176	−	0.611150i
$75$	2.09017	−	6.43288i	0.241352	−	0.742805i
$76$	−4.85410			−0.556804
$77$	12.7533	+	0.865300i	1.45337	+	0.0986101i
$78$	2.76393			0.312954
$79$	−0.618034	+	1.90211i	−0.0695343	+	0.214004i	−0.979785	−	0.200053i	$-0.935889\pi$
$79$	−0.618034	+	1.90211i	−0.0695343	+	0.214004i	0.910251	+	0.414057i	$0.135889\pi$
$80$	−2.61803	+	1.90211i	−0.292705	+	0.212663i
$81$	1.95492	+	1.42033i	0.217213	+	0.157814i
$82$		0			0
$83$	2.50000	+	7.69421i	0.274411	+	0.844549i	0.989375	+	0.145388i	$0.0464430\pi$
$83$	2.50000	+	7.69421i	0.274411	+	0.844549i	−0.714964	+	0.699161i	$0.753557\pi$
$84$	−11.5623	−	8.40051i	−1.26155	−	0.916570i
$85$	12.0902	−	8.78402i	1.31136	−	0.952761i
$86$	2.76393	−	8.50651i	0.298042	−	0.917280i
$87$	−6.94427			−0.744504
$88$	−2.76393	+	6.88191i	−0.294636	+	0.733614i
$89$	−15.4164			−1.63414			−0.817068	−	0.576541i	$-0.804402\pi$
$89$	−15.4164			−1.63414			−0.817068	+	0.576541i	$0.804402\pi$
$90$	−3.29180	+	10.1311i	−0.346986	+	1.06791i
$91$	3.11803	−	2.26538i	0.326859	−	0.237477i
$92$	19.4164	+	14.1068i	2.02430	+	1.47074i
$93$	2.14590	+	6.60440i	0.222519	+	0.684844i
$94$	−4.37132	−	13.4535i	−0.450868	−	1.38763i
$95$	−4.23607	−	3.07768i	−0.434611	−	0.315764i
$96$	−6.70820	+	4.87380i	−0.684653	+	0.497430i
$97$	−3.00000	+	9.23305i	−0.304604	+	0.937474i	0.675221	+	0.737616i	$0.264048\pi$
$97$	−3.00000	+	9.23305i	−0.304604	+	0.937474i	−0.979825	+	0.199859i	$0.935952\pi$
$98$	−17.5623			−1.77406
$99$	−1.19098	−	4.73504i	−0.119698	−	0.475889i
$100$	16.4164			1.64164
$101$	−1.04508	+	3.21644i	−0.103990	+	0.320048i	−0.989492	−	0.144587i	$-0.953815\pi$
$101$	−1.04508	+	3.21644i	−0.103990	+	0.320048i	0.885502	+	0.464635i	$0.153815\pi$
$102$	10.3262	−	7.50245i	1.02245	−	0.742853i
$103$	1.61803	+	1.17557i	0.159430	+	0.115832i	0.664640	−	0.747164i	$-0.268585\pi$
$103$	1.61803	+	1.17557i	0.159430	+	0.115832i	−0.505210	+	0.862996i	$0.668585\pi$
$104$	0.690983	+	2.12663i	0.0677565	+	0.208533i
$105$	−4.76393	−	14.6619i	−0.464912	−	1.43085i
$106$	0.163119	+	0.118513i	0.0158435	+	0.0115110i
$107$	−5.09017	+	3.69822i	−0.492085	+	0.357521i	−0.805986	−	0.591935i	$-0.798364\pi$
$107$	−5.09017	+	3.69822i	−0.492085	+	0.357521i	0.313900	+	0.949456i	$0.398364\pi$
$108$	−5.12461	+	15.7719i	−0.493116	+	1.51765i
$109$	10.1803			0.975100			0.487550	−	0.873095i	$-0.337891\pi$
$109$	10.1803			0.975100			0.487550	+	0.873095i	$0.337891\pi$
$110$	−20.3262	+	12.7598i	−1.93803	+	1.21660i
$111$	4.94427			0.469290
$112$	−1.19098	+	3.66547i	−0.112537	+	0.346354i
$113$	−1.50000	+	1.08981i	−0.141108	+	0.102521i	−0.656100	−	0.754674i	$-0.727795\pi$
$113$	−1.50000	+	1.08981i	−0.141108	+	0.102521i	0.514992	+	0.857195i	$0.327795\pi$
$114$	−3.61803	−	2.62866i	−0.338860	−	0.246196i
$115$	8.00000	+	24.6215i	0.746004	+	2.29596i
$116$	−5.20820	−	16.0292i	−0.483570	−	1.48827i
$117$	−1.19098	−	0.865300i	−0.110106	−	0.0799970i
$118$	−17.3992	+	12.6412i	−1.60172	+	1.16372i
$119$	5.50000	−	16.9273i	0.504184	−	1.55172i
$120$	8.94427			0.816497
$121$	4.78115	−	9.90659i	0.434650	−	0.900599i
$122$	16.3820			1.48315
$123$		0			0
$124$	−13.6353	+	9.90659i	−1.22448	+	0.889638i
$125$	1.23607	+	0.898056i	0.110557	+	0.0803246i
$126$	3.92047	+	12.0660i	0.349264	+	1.07492i
$127$	1.47214	+	4.53077i	0.130631	+	0.402041i	0.994885	−	0.101015i	$-0.0322090\pi$
$127$	1.47214	+	4.53077i	0.130631	+	0.402041i	−0.864254	+	0.503056i	$0.832209\pi$
$128$	−12.6631	−	9.20029i	−1.11927	−	0.813199i
$129$	4.00000	−	2.90617i	0.352180	−	0.255874i
$130$	−2.23607	+	6.88191i	−0.196116	+	0.603583i
$131$	−19.8885			−1.73767			−0.868835	−	0.495102i	$-0.835131\pi$
$131$	−19.8885			−1.73767			−0.868835	+	0.495102i	$0.835131\pi$
$132$	−10.4164	+	6.53888i	−0.906632	+	0.569137i
$133$	−6.23607			−0.540736
$134$	1.05573	−	3.24920i	0.0912010	−	0.280688i
$135$	−14.4721	+	10.5146i	−1.24556	+	0.904955i
$136$	8.35410	+	6.06961i	0.716358	+	0.520465i
$137$	−4.23607	−	13.0373i	−0.361912	−	1.11385i	−0.951892	−	0.306432i	$-0.900865\pi$
$137$	−4.23607	−	13.0373i	−0.361912	−	1.11385i	0.589981	−	0.807417i	$-0.299135\pi$
$138$	6.83282	+	21.0292i	0.581648	+	1.79013i
$139$	14.7082	+	10.6861i	1.24753	+	0.906386i	0.998076	−	0.0619996i	$-0.0197477\pi$
$139$	14.7082	+	10.6861i	1.24753	+	0.906386i	0.249457	+	0.968386i	$0.419748\pi$
$140$	30.2705	−	21.9928i	2.55833	−	1.85873i
$141$	2.41641	−	7.43694i	0.203498	−	0.626303i
$142$	25.8541			2.16963
$143$	−0.809017	−	3.21644i	−0.0676534	−	0.268972i
$144$	1.47214			0.122678
$145$	5.61803	−	17.2905i	0.466552	−	1.43590i
$146$	10.3262	−	7.50245i	0.854606	−	0.620907i
$147$	−7.85410	−	5.70634i	−0.647795	−	0.470651i
$148$	3.70820	+	11.4127i	0.304812	+	0.938116i
$149$	−2.38197	−	7.33094i	−0.195138	−	0.600574i	−0.999975	−	0.00707748i	$-0.997747\pi$
$149$	−2.38197	−	7.33094i	−0.195138	−	0.600574i	0.804837	−	0.593496i	$-0.202253\pi$
$150$	12.2361	+	8.89002i	0.999071	+	0.725867i
$151$	−9.78115	+	7.10642i	−0.795979	+	0.578313i	−0.909732	−	0.415197i	$-0.863713\pi$
$151$	−9.78115	+	7.10642i	−0.795979	+	0.578313i	0.113753	+	0.993509i	$0.463713\pi$
$152$	1.11803	−	3.44095i	0.0906845	−	0.279098i
$153$	−6.79837			−0.549616
$154$	−10.6525	+	26.5236i	−0.858401	+	2.13733i
$155$	−18.1803			−1.46028
$156$	−1.14590	+	3.52671i	−0.0917453	+	0.282363i
$157$	11.9721	−	8.69827i	0.955480	−	0.694197i	0.00338376	−	0.999994i	$-0.498923\pi$
$157$	11.9721	−	8.69827i	0.955480	−	0.694197i	0.952097	+	0.305797i	$0.0989229\pi$
$158$	−3.61803	−	2.62866i	−0.287835	−	0.209125i
$159$	0.0344419	+	0.106001i	0.00273142	+	0.00840644i
$160$	−6.70820	−	20.6457i	−0.530330	−	1.63219i
$161$	24.9443	+	18.1231i	1.96588	+	1.42830i
$162$	−4.37132	+	3.17595i	−0.343444	+	0.249526i
$163$	−1.66312	+	5.11855i	−0.130266	+	0.400916i	−0.994824	−	0.101617i	$-0.967598\pi$
$163$	−1.66312	+	5.11855i	−0.130266	+	0.400916i	0.864558	+	0.502533i	$0.167598\pi$
$164$		0			0
$165$	−13.2361	−	0.898056i	−1.03043	−	0.0699136i
$166$	−18.0902			−1.40407
$167$	0.972136	−	2.99193i	0.0752261	−	0.231522i	−0.906372	−	0.422480i	$-0.861160\pi$
$167$	0.972136	−	2.99193i	0.0752261	−	0.231522i	0.981598	+	0.190958i	$0.0611595\pi$
$168$	8.61803	−	6.26137i	0.664896	−	0.483075i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	10.3262	+	31.7809i	0.791986	+	2.43748i
$171$	0.736068	+	2.26538i	0.0562885	+	0.173238i
$172$	9.70820	+	7.05342i	0.740244	+	0.537818i
$173$	10.0902	−	7.33094i	0.767141	−	0.557361i	−0.133951	−	0.990988i	$-0.542766\pi$
$173$	10.0902	−	7.33094i	0.767141	−	0.557361i	0.901092	+	0.433627i	$0.142766\pi$
$174$	4.79837	−	14.7679i	0.363764	−	1.11955i
$175$	21.0902			1.59427
$176$	2.54508	+	2.12663i	0.191843	+	0.160301i
$177$	−11.8885			−0.893598
$178$	10.6525	−	32.7849i	0.798437	−	2.45734i
$179$	17.5623	−	12.7598i	1.31267	−	0.953709i	0.312676	−	0.949860i	$-0.398775\pi$
$179$	17.5623	−	12.7598i	1.31267	−	0.953709i	0.999993	−	0.00384949i	$-0.00122533\pi$
$180$	−11.5623	−	8.40051i	−0.861803	−	0.626137i
$181$	1.04508	+	3.21644i	0.0776806	+	0.239076i	0.982355	−	0.187028i	$-0.0598856\pi$
$181$	1.04508	+	3.21644i	0.0776806	+	0.239076i	−0.904674	+	0.426104i	$0.859886\pi$
$182$	2.66312	+	8.19624i	0.197404	+	0.607546i
$183$	7.32624	+	5.32282i	0.541571	+	0.393474i
$184$	−14.4721	+	10.5146i	−1.06690	+	0.775148i
$185$	−4.00000	+	12.3107i	−0.294086	+	0.905103i
$186$	−15.5279			−1.13856
$187$	−11.7533	−	9.82084i	−0.859486	−	0.718171i
$188$	18.9787			1.38416
$189$	−6.58359	+	20.2622i	−0.478886	+	1.47386i
$190$	9.47214	−	6.88191i	0.687181	−	0.499266i
$191$	−7.23607	−	5.25731i	−0.523584	−	0.380406i	0.294369	−	0.955692i	$-0.404891\pi$
$191$	−7.23607	−	5.25731i	−0.523584	−	0.380406i	−0.817952	+	0.575286i	$0.804891\pi$
$192$	−4.96556	−	15.2824i	−0.358358	−	1.10291i
$193$	−4.32624	−	13.3148i	−0.311409	−	0.958420i	−0.977207	−	0.212287i	$-0.931909\pi$
$193$	−4.32624	−	13.3148i	−0.311409	−	0.958420i	0.665798	−	0.746132i	$-0.268091\pi$
$194$	−17.5623	−	12.7598i	−1.26090	−	0.916098i
$195$	−3.23607	+	2.35114i	−0.231740	+	0.168369i
$196$	7.28115	−	22.4091i	0.520082	−	1.60065i
$197$	−17.8885			−1.27451			−0.637253	−	0.770655i	$-0.719929\pi$
$197$	−17.8885			−1.27451			−0.637253	+	0.770655i	$0.719929\pi$
$198$	10.8926	+	0.739054i	0.774104	+	0.0525223i
$199$	−12.9443			−0.917595			−0.458798	−	0.888541i	$-0.651720\pi$
$199$	−12.9443			−0.917595			−0.458798	+	0.888541i	$0.651720\pi$
$200$	−3.78115	+	11.6372i	−0.267368	+	0.822874i
$201$	1.52786	−	1.11006i	0.107767	−	0.0782975i
$202$	−6.11803	−	4.44501i	−0.430463	−	0.312750i
$203$	−6.69098	−	20.5927i	−0.469615	−	1.44533i
$204$	5.29180	+	16.2865i	0.370500	+	1.14028i
$205$		0			0
$206$	−3.61803	+	2.62866i	−0.252080	+	0.183147i
$207$	3.63932	−	11.2007i	0.252950	−	0.778501i
$208$	1.00000			0.0693375
$209$	−2.00000	+	4.97980i	−0.138343	+	0.344460i
$210$	34.4721			2.37880
$211$	−2.94427	+	9.06154i	−0.202692	+	0.623822i	0.797108	+	0.603836i	$0.206362\pi$
$211$	−2.94427	+	9.06154i	−0.202692	+	0.623822i	−0.999800	+	0.0199855i	$0.993638\pi$
$212$	−0.218847	+	0.159002i	−0.0150305	+	0.0109203i
$213$	11.5623	+	8.40051i	0.792236	+	0.575593i
$214$	−4.34752	−	13.3803i	−0.297191	−	0.914659i
$215$	4.00000	+	12.3107i	0.272798	+	0.839585i
$216$	−10.0000	−	7.26543i	−0.680414	−	0.494350i
$217$	−17.5172	+	12.7270i	−1.18915	+	0.863965i
$218$	−7.03444	+	21.6498i	−0.476433	+	1.46631i
$219$	7.05573			0.476782
$220$	−7.85410	−	31.2259i	−0.529523	−	2.10525i
$221$	−4.61803			−0.310643
$222$	−3.41641	+	10.5146i	−0.229294	+	0.705695i
$223$	7.23607	−	5.25731i	0.484563	−	0.352056i	−0.318527	−	0.947914i	$-0.603188\pi$
$223$	7.23607	−	5.25731i	0.484563	−	0.352056i	0.803090	+	0.595858i	$0.203188\pi$
$224$	−20.9164	−	15.1967i	−1.39754	−	1.01537i
$225$	−2.48936	−	7.66145i	−0.165957	−	0.510764i
$226$	−1.28115	−	3.94298i	−0.0852210	−	0.262283i
$227$	−3.35410	−	2.43690i	−0.222620	−	0.161743i	0.470885	−	0.882194i	$-0.343934\pi$
$227$	−3.35410	−	2.43690i	−0.222620	−	0.161743i	−0.693505	+	0.720452i	$0.743934\pi$
$228$	4.85410	−	3.52671i	0.321471	−	0.233562i
$229$	−5.47214	+	16.8415i	−0.361609	+	1.11292i	0.590468	+	0.807061i	$0.298943\pi$
$229$	−5.47214	+	16.8415i	−0.361609	+	1.11292i	−0.952077	+	0.305857i	$0.901057\pi$
$230$	−57.8885			−3.81706
$231$	−13.3820	+	8.40051i	−0.880469	+	0.552713i
$232$	12.5623			0.824756
$233$	2.68034	−	8.24924i	0.175595	−	0.540426i	−0.824065	−	0.566495i	$-0.808299\pi$
$233$	2.68034	−	8.24924i	0.175595	−	0.540426i	0.999660	+	0.0260694i	$0.00829908\pi$
$234$	2.66312	−	1.93487i	0.174094	−	0.126486i
$235$	16.5623	+	12.0332i	1.08041	+	0.784961i
$236$	−8.91641	−	27.4419i	−0.580409	−	1.78631i
$237$	−0.763932	−	2.35114i	−0.0496227	−	0.152723i
$238$	32.1976	+	23.3929i	2.08706	+	1.51634i
$239$	−8.35410	+	6.06961i	−0.540382	+	0.392610i	−0.824227	−	0.566260i	$-0.808390\pi$
$239$	−8.35410	+	6.06961i	−0.540382	+	0.392610i	0.283845	+	0.958870i	$0.408390\pi$
$240$	1.23607	−	3.80423i	0.0797878	−	0.245562i
$241$	−12.7639			−0.822197			−0.411099	−	0.911591i	$-0.634855\pi$
$241$	−12.7639			−0.822197			−0.411099	+	0.911591i	$0.634855\pi$
$242$	17.7639	+	17.0130i	1.14191	+	1.09364i
$243$	13.5967			0.872232
$244$	−6.79180	+	20.9030i	−0.434800	+	1.33818i
$245$	20.5623	−	14.9394i	1.31368	−	0.954443i
$246$		0			0
$247$	0.500000	+	1.53884i	0.0318142	+	0.0979142i
$248$	−3.88197	−	11.9475i	−0.246505	−	0.758665i
$249$	−8.09017	−	5.87785i	−0.512694	−	0.372494i
$250$	−2.76393	+	2.00811i	−0.174806	+	0.127004i
$251$	7.70820	−	23.7234i	0.486538	−	1.49741i	−0.343204	−	0.939261i	$-0.611512\pi$
$251$	7.70820	−	23.7234i	0.486538	−	1.49741i	0.829742	−	0.558148i	$-0.188488\pi$
$252$	−17.0213			−1.07224
$253$	22.4721	−	14.1068i	1.41281	−	0.886890i
$254$	−10.6525			−0.668396
$255$	−5.70820	+	17.5680i	−0.357462	+	1.10015i
$256$	7.28115	−	5.29007i	0.455072	−	0.330629i
$257$	14.9721	+	10.8779i	0.933936	+	0.678544i	0.946953	−	0.321371i	$-0.104144\pi$
$257$	14.9721	+	10.8779i	0.933936	+	0.678544i	−0.0130172	+	0.999915i	$0.504144\pi$
$258$	3.41641	+	10.5146i	0.212696	+	0.654612i
$259$	4.76393	+	14.6619i	0.296016	+	0.911045i
$260$	−7.85410	−	5.70634i	−0.487091	−	0.353892i
$261$	−6.69098	+	4.86128i	−0.414161	+	0.300906i
$262$	13.7426	−	42.2955i	0.849023	−	2.61303i
$263$	2.65248			0.163559			0.0817793	−	0.996650i	$-0.473940\pi$
$263$	2.65248			0.163559			0.0817793	+	0.996650i	$0.473940\pi$
$264$	−2.23607	−	8.89002i	−0.137620	−	0.547143i
$265$	−0.291796			−0.0179249
$266$	4.30902	−	13.2618i	0.264203	−	0.813133i
$267$	15.4164	−	11.2007i	0.943469	−	0.685470i
$268$	3.70820	+	2.69417i	0.226515	+	0.164572i
$269$	7.50000	+	23.0826i	0.457283	+	1.40737i	0.868434	+	0.495805i	$0.165127\pi$
$269$	7.50000	+	23.0826i	0.457283	+	1.40737i	−0.411151	+	0.911567i	$0.634873\pi$
$270$	−12.3607	−	38.0423i	−0.752247	−	2.31518i
$271$	9.11803	+	6.62464i	0.553881	+	0.402418i	0.829214	−	0.558931i	$-0.188788\pi$
$271$	9.11803	+	6.62464i	0.553881	+	0.402418i	−0.275333	+	0.961349i	$0.588788\pi$
$272$	3.73607	−	2.71441i	0.226532	−	0.164585i
$273$	−1.47214	+	4.53077i	−0.0890977	+	0.274215i
$274$	30.6525			1.85178
$275$	6.76393	−	16.8415i	0.407880	−	1.01558i
$276$	−29.6656			−1.78566
$277$	−6.86475	+	21.1275i	−0.412463	+	1.26943i	0.502038	+	0.864845i	$0.332584\pi$
$277$	−6.86475	+	21.1275i	−0.412463	+	1.26943i	−0.914501	+	0.404584i	$0.867416\pi$
$278$	−32.8885	+	23.8949i	−1.97252	+	1.43312i
$279$	6.69098	+	4.86128i	0.400579	+	0.291037i
$280$	8.61803	+	26.5236i	0.515026	+	1.58509i
$281$	9.38197	+	28.8747i	0.559681	+	1.72252i	0.683249	+	0.730185i	$0.260566\pi$
$281$	9.38197	+	28.8747i	0.559681	+	1.72252i	−0.123568	+	0.992336i	$0.539434\pi$
$282$	14.1459	+	10.2776i	0.842376	+	0.612022i
$283$	6.38197	−	4.63677i	0.379369	−	0.275627i	−0.381717	−	0.924279i	$-0.624667\pi$
$283$	6.38197	−	4.63677i	0.379369	−	0.275627i	0.761085	+	0.648652i	$0.224667\pi$
$284$	−10.7188	+	32.9892i	−0.636047	+	1.95755i
$285$	6.47214			0.383376
$286$	7.39919	+	0.502029i	0.437523	+	0.0296856i
$287$		0			0
$288$	−3.05166	+	9.39205i	−0.179821	+	0.553432i
$289$	−3.50000	+	2.54290i	−0.205882	+	0.149582i
$290$	32.8885	+	23.8949i	1.93128	+	1.40316i
$291$	−3.70820	−	11.4127i	−0.217379	−	0.669023i
$292$	5.29180	+	16.2865i	0.309679	+	0.953094i
$293$	4.85410	+	3.52671i	0.283580	+	0.206033i	0.720477	−	0.693479i	$-0.243923\pi$
$293$	4.85410	+	3.52671i	0.283580	+	0.206033i	−0.436898	+	0.899511i	$0.643923\pi$
$294$	17.5623	−	12.7598i	1.02425	−	0.744164i
$295$	9.61803	−	29.6013i	0.559984	−	1.72345i
$296$	−8.94427			−0.519875
$297$	14.0689	+	11.7557i	0.816359	+	0.682135i
$298$	17.2361			0.998459
$299$	2.47214	−	7.60845i	0.142967	−	0.440008i
$300$	−16.4164	+	11.9272i	−0.947802	+	0.688618i
$301$	12.4721	+	9.06154i	0.718882	+	0.522298i
$302$	−8.35410	−	25.7113i	−0.480725	−	1.47952i
$303$	−1.29180	−	3.97574i	−0.0742117	−	0.228400i
$304$	−1.30902	−	0.951057i	−0.0750773	−	0.0545468i
$305$	−19.1803	+	13.9353i	−1.09826	+	0.797935i
$306$	4.69756	−	14.4576i	0.268542	−	0.826486i
$307$	4.79837			0.273858			0.136929	−	0.990581i	$-0.456277\pi$
$307$	4.79837			0.273858			0.136929	+	0.990581i	$0.456277\pi$
$308$	−29.4271	−	24.5887i	−1.67676	−	1.40107i
$309$	−2.47214			−0.140635
$310$	12.5623	−	38.6628i	0.713491	−	2.19590i
$311$	−23.1803	+	16.8415i	−1.31444	+	0.954994i	−0.314453	+	0.949273i	$0.601821\pi$
$311$	−23.1803	+	16.8415i	−1.31444	+	0.954994i	−0.999984	+	0.00572091i	$0.998179\pi$
$312$	−2.23607	−	1.62460i	−0.126592	−	0.0919748i
$313$	−7.42705	−	22.8581i	−0.419802	−	1.29202i	−0.907885	−	0.419220i	$-0.862304\pi$
$313$	−7.42705	−	22.8581i	−0.419802	−	1.29202i	0.488083	−	0.872797i	$-0.337696\pi$
$314$	10.2254	+	31.4706i	0.577054	+	1.77599i
$315$	−14.8541	−	10.7921i	−0.836934	−	0.608068i
$316$	4.85410	−	3.52671i	0.273065	−	0.198393i
$317$	−1.32624	+	4.08174i	−0.0744889	+	0.229253i	−0.981368	−	0.192138i	$-0.938458\pi$
$317$	−1.32624	+	4.08174i	−0.0744889	+	0.229253i	0.906879	+	0.421391i	$0.138458\pi$
$318$	−0.249224			−0.0139758
$319$	−18.5902	−	1.26133i	−1.04085	−	0.0706208i
$320$	42.0689			2.35172
$321$	2.40325	−	7.39645i	0.134136	−	0.412830i
$322$	−55.7771	+	40.5244i	−3.10834	+	2.25834i
$323$	6.04508	+	4.39201i	0.336358	+	0.244378i
$324$	−2.24013	−	6.89442i	−0.124452	−	0.383023i
$325$	−1.69098	−	5.20431i	−0.0937989	−	0.288683i
$326$	−9.73607	−	7.07367i	−0.539231	−	0.391774i
$327$	−10.1803	+	7.39645i	−0.562974	+	0.409025i
$328$		0			0
$329$	24.3820			1.34422
$330$	11.0557	−	27.5276i	0.608598	−	1.51535i
$331$	8.27051			0.454588			0.227294	−	0.973826i	$-0.427012\pi$
$331$	8.27051			0.454588			0.227294	+	0.973826i	$0.427012\pi$
$332$	7.50000	−	23.0826i	0.411616	−	1.26682i
$333$	4.76393	−	3.46120i	0.261062	−	0.189673i
$334$	5.69098	+	4.13474i	0.311397	+	0.226243i
$335$	1.52786	+	4.70228i	0.0834761	+	0.256913i
$336$	−1.47214	−	4.53077i	−0.0803116	−	0.247174i
$337$	−24.1074	−	17.5150i	−1.31321	−	0.954105i	−0.999990	−	0.00442569i	$-0.998591\pi$
$337$	−24.1074	−	17.5150i	−1.31321	−	0.954105i	−0.313223	−	0.949680i	$-0.601409\pi$
$338$	1.80902	−	1.31433i	0.0983976	−	0.0714900i
$339$	0.708204	−	2.17963i	0.0384644	−	0.118381i
$340$	−44.8328			−2.43140
$341$	4.54508	+	18.0701i	0.246130	+	0.978549i
$342$	−5.32624			−0.288010
$343$	1.01722	−	3.13068i	0.0549248	−	0.169041i
$344$	−7.23607	+	5.25731i	−0.390143	+	0.283455i
$345$	−25.8885	−	18.8091i	−1.39379	−	1.01265i
$346$	8.61803	+	26.5236i	0.463308	+	1.42592i
$347$	8.00000	+	24.6215i	0.429463	+	1.32175i	0.898656	+	0.438654i	$0.144545\pi$
$347$	8.00000	+	24.6215i	0.429463	+	1.32175i	−0.469193	+	0.883095i	$0.655455\pi$
$348$	16.8541	+	12.2452i	0.903475	+	0.656413i
$349$	−9.85410	+	7.15942i	−0.527478	+	0.383235i	−0.819414	−	0.573203i	$-0.805701\pi$
$349$	−9.85410	+	7.15942i	−0.527478	+	0.383235i	0.291936	+	0.956438i	$0.405701\pi$
$350$	−14.5729	+	44.8509i	−0.778957	+	2.39738i
$351$	5.52786			0.295056
$352$	−18.8435	+	11.8290i	−1.00436	+	0.630485i
$353$	−5.52786			−0.294219			−0.147109	−	0.989120i	$-0.546997\pi$
$353$	−5.52786			−0.294219			−0.147109	+	0.989120i	$0.546997\pi$
$354$	8.21478	−	25.2825i	0.436611	−	1.34375i
$355$	−30.2705	+	21.9928i	−1.60659	+	1.16726i
$356$	37.4164	+	27.1846i	1.98307	+	1.44078i
$357$	6.79837	+	20.9232i	0.359808	+	1.10738i
$358$	15.0000	+	46.1653i	0.792775	+	2.43991i
$359$	−24.8713	−	18.0701i	−1.31266	−	0.953702i	−0.999993	−	0.00383875i	$-0.998778\pi$
$359$	−24.8713	−	18.0701i	−1.31266	−	0.953702i	−0.312666	−	0.949863i	$-0.601222\pi$
$360$	8.61803	−	6.26137i	0.454210	−	0.330003i
$361$	−5.06231	+	15.5802i	−0.266437	+	0.820009i
$362$	−7.56231			−0.397466
$363$	2.41641	+	13.3803i	0.126829	+	0.702284i
$364$	−11.5623			−0.606029
$365$	−5.70820	+	17.5680i	−0.298781	+	0.919554i
$366$	−16.3820	+	11.9022i	−0.856299	+	0.622138i
$367$	−7.85410	−	5.70634i	−0.409981	−	0.297868i	0.363613	−	0.931550i	$-0.381543\pi$
$367$	−7.85410	−	5.70634i	−0.409981	−	0.297868i	−0.773594	+	0.633682i	$0.781543\pi$
$368$	2.47214	+	7.60845i	0.128869	+	0.396618i
$369$		0			0
$370$	−23.4164	−	17.0130i	−1.21736	−	0.884465i
$371$	−0.281153	+	0.204270i	−0.0145967	+	0.0106051i
$372$	6.43769	−	19.8132i	0.333779	−	1.02727i
$373$	−9.85410			−0.510226			−0.255113	−	0.966911i	$-0.582113\pi$
$373$	−9.85410			−0.510226			−0.255113	+	0.966911i	$0.582113\pi$
$374$	29.0066	−	18.2088i	1.49989	−	0.941556i
$375$	−1.88854			−0.0975240
$376$	−4.37132	+	13.4535i	−0.225434	+	0.693814i
$377$	−4.54508	+	3.30220i	−0.234084	+	0.170072i
$378$	−38.5410	−	28.0017i	−1.98234	−	1.44025i
$379$	5.05573	+	15.5599i	0.259695	+	0.799260i	0.992868	+	0.119218i	$0.0380386\pi$
$379$	5.05573	+	15.5599i	0.259695	+	0.799260i	−0.733173	+	0.680042i	$0.761961\pi$
$380$	4.85410	+	14.9394i	0.249010	+	0.766375i
$381$	−4.76393	−	3.46120i	−0.244064	−	0.177323i
$382$	16.1803	−	11.7557i	0.827858	−	0.601474i
$383$	−4.62868	+	14.2456i	−0.236514	+	0.727916i	0.760403	+	0.649452i	$0.225002\pi$
$383$	−4.62868	+	14.2456i	−0.236514	+	0.727916i	−0.996917	+	0.0784643i	$0.974998\pi$
$384$	19.3475			0.987324
$385$	−10.0902	−	40.1159i	−0.514243	−	2.04449i
$386$	31.3050			1.59338
$387$	1.81966	−	5.60034i	0.0924985	−	0.284681i
$388$	23.5623	−	17.1190i	1.19619	−	0.869086i
$389$	−17.0172	−	12.3637i	−0.862807	−	0.626866i	0.0658399	−	0.997830i	$-0.479027\pi$
$389$	−17.0172	−	12.3637i	−0.862807	−	0.626866i	−0.928647	+	0.370964i	$0.879027\pi$
$390$	−2.76393	−	8.50651i	−0.139957	−	0.430744i
$391$	−11.4164	−	35.1361i	−0.577353	−	1.77691i
$392$	14.2082	+	10.3229i	0.717623	+	0.521383i
$393$	19.8885	−	14.4499i	1.00324	−	0.728900i
$394$	12.3607	−	38.0423i	0.622722	−	1.91654i
$395$	6.47214			0.325649
$396$	−5.45898	+	13.5923i	−0.274324	+	0.683039i
$397$	18.1803			0.912445			0.456223	−	0.889866i	$-0.349202\pi$
$397$	18.1803			0.912445			0.456223	+	0.889866i	$0.349202\pi$
$398$	8.94427	−	27.5276i	0.448336	−	1.37984i
$399$	6.23607	−	4.53077i	0.312194	−	0.226822i
$400$	4.42705	+	3.21644i	0.221353	+	0.160822i
$401$	−11.0902	−	34.1320i	−0.553817	−	1.70447i	−0.699048	−	0.715075i	$-0.746393\pi$
$401$	−11.0902	−	34.1320i	−0.553817	−	1.70447i	0.145231	−	0.989398i	$-0.453607\pi$
$402$	1.30495	+	4.01623i	0.0650851	+	0.200311i
$403$	4.54508	+	3.30220i	0.226407	+	0.164494i
$404$	8.20820	−	5.96361i	0.408373	−	0.296701i
$405$	2.41641	−	7.43694i	0.120072	−	0.369544i
$406$	48.4164			2.40287
$407$	13.2361	+	0.898056i	0.656088	+	0.0445150i
$408$	−12.7639			−0.631909
$409$	−5.43769	+	16.7355i	−0.268877	+	0.827517i	0.721898	+	0.691999i	$0.243270\pi$
$409$	−5.43769	+	16.7355i	−0.268877	+	0.827517i	−0.990775	+	0.135518i	$0.956730\pi$
$410$		0			0
$411$	13.7082	+	9.95959i	0.676176	+	0.491271i
$412$	−1.85410	−	5.70634i	−0.0913450	−	0.281131i
$413$	−11.4549	−	35.2546i	−0.563660	−	1.73477i
$414$	21.3050	+	15.4790i	1.04708	+	0.760749i
$415$	21.1803	−	15.3884i	1.03970	−	0.755388i
$416$	−2.07295	+	6.37988i	−0.101635	+	0.312799i
$417$	−22.4721			−1.10047
$418$	−9.20820	−	7.69421i	−0.450388	−	0.376336i
$419$	28.1803			1.37670			0.688350	−	0.725379i	$-0.258335\pi$
$419$	28.1803			1.37670			0.688350	+	0.725379i	$0.258335\pi$
$420$	−14.2918	+	43.9856i	−0.697368	+	2.14628i
$421$	5.23607	−	3.80423i	0.255190	−	0.185407i	−0.452834	−	0.891595i	$-0.649587\pi$
$421$	5.23607	−	3.80423i	0.255190	−	0.185407i	0.708024	+	0.706188i	$0.249587\pi$
$422$	−17.2361	−	12.5227i	−0.839039	−	0.609597i
$423$	−2.87790	−	8.85727i	−0.139928	−	0.430655i
$424$	−0.0623059	−	0.191758i	−0.00302584	−	0.00931258i
$425$	−20.4443	−	14.8536i	−0.991693	−	0.720507i
$426$	−25.8541	+	18.7841i	−1.25264	+	0.910093i
$427$	−8.72542	+	26.8541i	−0.422253	+	1.29956i
$428$	18.8754			0.912376
$429$	3.14590	+	2.62866i	0.151885	+	0.126913i
$430$	−28.9443			−1.39582
$431$	2.13525	−	6.57164i	0.102852	−	0.316545i	−0.886369	−	0.462980i	$-0.846780\pi$
$431$	2.13525	−	6.57164i	0.102852	−	0.316545i	0.989220	+	0.146436i	$0.0467801\pi$
$432$	−4.47214	+	3.24920i	−0.215166	+	0.156327i
$433$	−15.6803	−	11.3924i	−0.753549	−	0.547485i	0.143376	−	0.989668i	$-0.454204\pi$
$433$	−15.6803	−	11.3924i	−0.753549	−	0.547485i	−0.896925	+	0.442183i	$0.854204\pi$
$434$	−14.9615	−	46.0467i	−0.718175	−	2.21031i
$435$	6.94427	+	21.3723i	0.332952	+	1.02472i
$436$	−24.7082	−	17.9516i	−1.18331	−	0.859724i
$437$	−10.4721	+	7.60845i	−0.500950	+	0.363962i
$438$	−4.87539	+	15.0049i	−0.232955	+	0.716962i
$439$	10.4721			0.499808			0.249904	−	0.968271i	$-0.419601\pi$
$439$	10.4721			0.499808			0.249904	+	0.968271i	$0.419601\pi$
$440$	23.9443	+	1.62460i	1.14150	+	0.0774497i
$441$	−11.5623			−0.550586
$442$	3.19098	−	9.82084i	0.151780	−	0.467130i
$443$	16.7984	−	12.2047i	0.798115	−	0.579864i	−0.112246	−	0.993680i	$-0.535804\pi$
$443$	16.7984	−	12.2047i	0.798115	−	0.579864i	0.910360	+	0.413816i	$0.135804\pi$
$444$	−12.0000	−	8.71851i	−0.569495	−	0.413762i
$445$	15.4164	+	47.4468i	0.730808	+	2.24920i
$446$	6.18034	+	19.0211i	0.292648	+	0.900677i
$447$	7.70820	+	5.60034i	0.364586	+	0.264887i
$448$	40.5344	−	29.4500i	1.91507	−	1.39138i
$449$	9.61803	−	29.6013i	0.453903	−	1.39697i	−0.418515	−	0.908210i	$-0.637449\pi$
$449$	9.61803	−	29.6013i	0.453903	−	1.39697i	0.872418	−	0.488760i	$-0.162551\pi$
$450$	18.0132			0.849148
$451$		0			0
$452$	5.56231			0.261629
$453$	4.61803	−	14.2128i	0.216974	−	0.667778i
$454$	7.50000	−	5.44907i	0.351992	−	0.255737i
$455$	−10.0902	−	7.33094i	−0.473034	−	0.343680i
$456$	1.38197	+	4.25325i	0.0647165	+	0.199177i
$457$	10.1803	+	31.3319i	0.476216	+	1.46564i	0.844310	+	0.535854i	$0.180010\pi$
$457$	10.1803	+	31.3319i	0.476216	+	1.46564i	−0.368094	+	0.929788i	$0.619990\pi$
$458$	−32.0344	−	23.2744i	−1.49687	−	1.08754i
$459$	20.6525	−	15.0049i	0.963975	−	0.700369i
$460$	24.0000	−	73.8644i	1.11901	−	3.44395i
$461$	−20.6525			−0.961882			−0.480941	−	0.876753i	$-0.659705\pi$
$461$	−20.6525			−0.961882			−0.480941	+	0.876753i	$0.659705\pi$
$462$	−8.61803	−	34.2631i	−0.400947	−	1.59406i
$463$	−4.85410			−0.225589			−0.112795	−	0.993618i	$-0.535980\pi$
$463$	−4.85410			−0.225589			−0.112795	+	0.993618i	$0.535980\pi$
$464$	1.73607	−	5.34307i	0.0805949	−	0.248046i
$465$	18.1803	−	13.2088i	0.843093	−	0.612543i
$466$	15.6910	+	11.4002i	0.726871	+	0.528103i
$467$	−6.94427	−	21.3723i	−0.321343	−	0.988991i	−0.973065	−	0.230533i	$-0.925953\pi$
$467$	−6.94427	−	21.3723i	−0.321343	−	0.988991i	0.651722	−	0.758458i	$-0.274047\pi$
$468$	1.36475	+	4.20025i	0.0630854	+	0.194157i
$469$	4.76393	+	3.46120i	0.219978	+	0.159823i
$470$	−37.0344	+	26.9071i	−1.70827	+	1.24113i
$471$	−5.65248	+	17.3965i	−0.260452	+	0.801590i
$472$	21.5066			0.989920
$473$	11.2361	−	7.05342i	0.516635	−	0.324317i
$474$	5.52786			0.253903
$475$	−2.73607	+	8.42075i	−0.125539	+	0.386371i
$476$	−43.1976	+	31.3849i	−1.97996	+	1.43852i
$477$	0.107391	+	0.0780240i	0.00491709	+	0.00357248i
$478$	−7.13525	−	21.9601i	−0.326359	−	1.00443i
$479$	8.62461	+	26.5438i	0.394069	+	1.21282i	0.929685	+	0.368357i	$0.120079\pi$
$479$	8.62461	+	26.5438i	0.394069	+	1.21282i	−0.535616	+	0.844462i	$0.679921\pi$
$480$	21.7082	+	15.7719i	0.990839	+	0.719887i
$481$	3.23607	−	2.35114i	0.147552	−	0.107203i
$482$	8.81966	−	27.1441i	0.401725	−	1.23638i
$483$	−38.1115			−1.73413
$484$	−29.0729	+	15.6129i	−1.32150	+	0.709679i
$485$	31.4164			1.42655
$486$	−9.39512	+	28.9152i	−0.426171	+	1.31162i
$487$	−8.35410	+	6.06961i	−0.378560	+	0.275040i	−0.760752	−	0.649043i	$-0.775170\pi$
$487$	−8.35410	+	6.06961i	−0.378560	+	0.275040i	0.382191	+	0.924083i	$0.375170\pi$
$488$	−13.2533	−	9.62908i	−0.599948	−	0.435888i
$489$	−2.05573	−	6.32688i	−0.0929632	−	0.286111i
$490$	17.5623	+	54.0512i	0.793384	+	2.44179i
$491$	−13.3262	−	9.68208i	−0.601405	−	0.436946i	0.244972	−	0.969530i	$-0.421221\pi$
$491$	−13.3262	−	9.68208i	−0.601405	−	0.436946i	−0.846377	+	0.532584i	$0.821221\pi$
$492$		0			0
$493$	−8.01722	+	24.6745i	−0.361077	+	1.11128i
$494$	−3.61803			−0.162783
$495$	−13.3820	+	8.40051i	−0.601475	+	0.377575i
$496$	−5.61803			−0.252257
$497$	−13.7705	+	42.3813i	−0.617692	+	1.90106i
$498$	18.0902	−	13.1433i	0.810640	−	0.588964i
$499$	−7.59017	−	5.51458i	−0.339783	−	0.246867i	0.404787	−	0.914411i	$-0.367346\pi$
$499$	−7.59017	−	5.51458i	−0.339783	−	0.246867i	−0.744570	+	0.667544i	$0.767346\pi$
$500$	−1.41641	−	4.35926i	−0.0633437	−	0.194952i
$501$	1.20163	+	3.69822i	0.0536847	+	0.165225i
$502$	45.1246	+	32.7849i	2.01401	+	1.46326i
$503$	15.3262	−	11.1352i	0.683363	−	0.496492i	−0.191109	−	0.981569i	$-0.561208\pi$
$503$	15.3262	−	11.1352i	0.683363	−	0.496492i	0.874472	+	0.485077i	$0.161208\pi$
$504$	3.92047	−	12.0660i	0.174632	−	0.537461i
$505$	10.9443			0.487014
$506$	14.4721	+	57.5374i	0.643365	+	2.55785i
$507$	1.23607			0.0548957
$508$	4.41641	−	13.5923i	0.195946	−	0.603061i
$509$	−24.0902	+	17.5025i	−1.06778	+	0.775786i	−0.975512	−	0.219948i	$-0.929411\pi$
$509$	−24.0902	+	17.5025i	−1.06778	+	0.775786i	−0.0922665	+	0.995734i	$0.529411\pi$
$510$	−33.4164	−	24.2784i	−1.47970	−	1.07507i
$511$	6.79837	+	20.9232i	0.300742	+	0.925590i
$512$	−3.45492	−	10.6331i	−0.152687	−	0.469923i
$513$	−7.23607	−	5.25731i	−0.319480	−	0.232116i
$514$	−33.4787	+	24.3237i	−1.47668	+	1.07287i
$515$	2.00000	−	6.15537i	0.0881305	−	0.271238i
$516$	−14.8328			−0.652978
$517$	7.81966	−	19.4702i	0.343908	−	0.856297i
$518$	−34.4721			−1.51462
$519$	−4.76393	+	14.6619i	−0.209113	+	0.643585i
$520$	5.85410	−	4.25325i	0.256719	−	0.186518i
$521$	−4.83688	−	3.51420i	−0.211908	−	0.153960i	0.476769	−	0.879029i	$-0.341808\pi$
$521$	−4.83688	−	3.51420i	−0.211908	−	0.153960i	−0.688676	+	0.725069i	$0.741808\pi$
$522$	−5.71478	−	17.5883i	−0.250129	−	0.769819i
$523$	−8.14590	−	25.0705i	−0.356195	−	1.09626i	−0.955313	−	0.295595i	$-0.904482\pi$
$523$	−8.14590	−	25.0705i	−0.356195	−	1.09626i	0.599118	−	0.800661i	$-0.295518\pi$
$524$	48.2705	+	35.0706i	2.10871	+	1.53207i
$525$	−21.0902	+	15.3229i	−0.920450	+	0.668746i
$526$	−1.83282	+	5.64083i	−0.0799146	+	0.245952i
$527$	25.9443			1.13015
$528$	−4.09017	−	0.277515i	−0.178002	−	0.0120773i
$529$	41.0000			1.78261
$530$	0.201626	−	0.620541i	0.00875808	−	0.0269546i
$531$	−11.4549	+	8.32248i	−0.497101	+	0.361165i
$532$	15.1353	+	10.9964i	0.656197	+	0.476755i
$533$		0			0
$534$	13.1672	+	40.5244i	0.569800	+	1.75366i
$535$	16.4721	+	11.9677i	0.712153	+	0.517409i
$536$	−2.76393	+	2.00811i	−0.119384	+	0.0867373i
$537$	−8.29180	+	25.5195i	−0.357817	+	1.10125i
$538$	−54.2705			−2.33977
$539$	−19.9894	−	16.7027i	−0.861003	−	0.719438i
$540$	53.6656			2.30940
$541$	11.1803	−	34.4095i	0.480680	−	1.47938i	−0.357461	−	0.933928i	$-0.616357\pi$
$541$	11.1803	−	34.4095i	0.480680	−	1.47938i	0.838141	−	0.545454i	$-0.183643\pi$
$542$	−20.3885	+	14.8131i	−0.875763	+	0.636279i
$543$	−3.38197	−	2.45714i	−0.145134	−	0.105446i
$544$	9.57295	+	29.4625i	0.410437	+	1.26319i
$545$	−10.1803	−	31.3319i	−0.436078	−	1.34211i
$546$	−8.61803	−	6.26137i	−0.368818	−	0.267962i
$547$	11.0902	−	8.05748i	0.474181	−	0.344513i	−0.324887	−	0.945753i	$-0.605326\pi$
$547$	11.0902	−	8.05748i	0.474181	−	0.344513i	0.799069	+	0.601240i	$0.205326\pi$
$548$	−12.7082	+	39.1118i	−0.542868	+	1.67077i
$549$	10.7852			0.460302
$550$	31.1418	+	26.0216i	1.32789	+	1.10956i
$551$	9.09017			0.387254
$552$	6.83282	−	21.0292i	0.290824	−	0.895064i
$553$	6.23607	−	4.53077i	0.265185	−	0.192668i
$554$	−40.1869	−	29.1975i	−1.70738	−	1.24048i
$555$	−4.94427	−	15.2169i	−0.209873	−	0.645922i
$556$	−16.8541	−	51.8716i	−0.714773	−	2.19985i
$557$	−27.7984	−	20.1967i	−1.17785	−	0.855762i	−0.185927	−	0.982564i	$-0.559529\pi$
$557$	−27.7984	−	20.1967i	−1.17785	−	0.855762i	−0.991928	+	0.126802i	$0.959529\pi$
$558$	−14.9615	+	10.8702i	−0.633370	+	0.460171i
$559$	1.23607	−	3.80423i	0.0522801	−	0.160902i
$560$	12.4721			0.527044
$561$	18.8885	+	1.28157i	0.797475	+	0.0541080i
$562$	−67.8885			−2.86371
$563$	3.72949	−	11.4782i	0.157179	−	0.483748i	−0.841196	−	0.540730i	$-0.818148\pi$
$563$	3.72949	−	11.4782i	0.157179	−	0.483748i	0.998375	+	0.0569824i	$0.0181479\pi$
$564$	−18.9787	+	13.7888i	−0.799148	+	0.580615i
$565$	4.85410	+	3.52671i	0.204214	+	0.148370i
$566$	5.45085	+	16.7760i	0.229116	+	0.705147i
$567$	−2.87790	−	8.85727i	−0.120860	−	0.371970i
$568$	−20.9164	−	15.1967i	−0.877633	−	0.637638i
$569$	−18.4443	+	13.4005i	−0.773224	+	0.561780i	−0.902938	−	0.429771i	$-0.858594\pi$
$569$	−18.4443	+	13.4005i	−0.773224	+	0.561780i	0.129714	+	0.991551i	$0.458594\pi$
$570$	−4.47214	+	13.7638i	−0.187317	+	0.576503i
$571$	9.59675			0.401611			0.200806	−	0.979631i	$-0.435644\pi$
$571$	9.59675			0.401611			0.200806	+	0.979631i	$0.435644\pi$
$572$	−3.70820	+	9.23305i	−0.155048	+	0.386053i
$573$	11.0557			0.461860
$574$		0			0
$575$	35.4164	−	25.7315i	1.47697	−	1.07308i
$576$	−15.4828	−	11.2489i	−0.645116	−	0.468704i
$577$	−6.03444	−	18.5721i	−0.251217	−	0.773167i	−0.994551	−	0.104247i	$-0.966757\pi$
$577$	−6.03444	−	18.5721i	−0.251217	−	0.773167i	0.743334	−	0.668920i	$-0.233243\pi$
$578$	−2.98936	−	9.20029i	−0.124341	−	0.382682i
$579$	14.0000	+	10.1716i	0.581820	+	0.422717i
$580$	−44.1246	+	32.0584i	−1.83217	+	1.33115i
$581$	9.63525	−	29.6543i	0.399738	−	1.23027i
$582$	26.8328			1.11226
$583$	0.0729490	+	0.290026i	0.00302124	+	0.0120117i
$584$	−12.7639			−0.528175
$585$	−1.47214	+	4.53077i	−0.0608653	+	0.187324i
$586$	−10.8541	+	7.88597i	−0.448379	+	0.325766i
$587$	14.1803	+	10.3026i	0.585285	+	0.425235i	0.840626	−	0.541617i	$-0.182188\pi$
$587$	14.1803	+	10.3026i	0.585285	+	0.425235i	−0.255340	+	0.966851i	$0.582188\pi$
$588$	9.00000	+	27.6992i	0.371154	+	1.14229i
$589$	−2.80902	−	8.64527i	−0.115744	−	0.356222i
$590$	56.3050	+	40.9079i	2.31804	+	1.68415i
$591$	17.8885	−	12.9968i	0.735836	−	0.534616i
$592$	−1.23607	+	3.80423i	−0.0508021	+	0.156353i
$593$	20.8328			0.855501			0.427751	−	0.903897i	$-0.359306\pi$
$593$	20.8328			0.855501			0.427751	+	0.903897i	$0.359306\pi$
$594$	−34.7214	+	21.7963i	−1.42463	+	0.894312i
$595$	−57.5967			−2.36124
$596$	−7.14590	+	21.9928i	−0.292707	+	0.900861i
$597$	12.9443	−	9.40456i	0.529774	−	0.384903i
$598$	14.4721	+	10.5146i	0.591810	+	0.429975i
$599$	−4.09017	−	12.5882i	−0.167120	−	0.514342i	0.832066	−	0.554676i	$-0.187158\pi$
$599$	−4.09017	−	12.5882i	−0.167120	−	0.514342i	−0.999186	+	0.0403341i	$0.987158\pi$
$600$	−4.67376	−	14.3844i	−0.190806	−	0.587239i
$601$	−15.6180	−	11.3472i	−0.637073	−	0.462861i	0.221770	−	0.975099i	$-0.428816\pi$
$601$	−15.6180	−	11.3472i	−0.637073	−	0.462861i	−0.858843	+	0.512238i	$0.828816\pi$
$602$	−27.8885	+	20.2622i	−1.13665	+	0.825826i
$603$	0.695048	−	2.13914i	0.0283046	−	0.0871125i
$604$	36.2705			1.47583
$605$	−35.2705	−	4.80828i	−1.43395	−	0.195485i
$606$	9.34752			0.379717
$607$	4.05573	−	12.4822i	0.164617	−	0.506639i	−0.834391	−	0.551173i	$-0.814180\pi$
$607$	4.05573	−	12.4822i	0.164617	−	0.506639i	0.999008	+	0.0445343i	$0.0141804\pi$
$608$	8.78115	−	6.37988i	0.356123	−	0.258738i
$609$	21.6525	+	15.7314i	0.877403	+	0.637470i
$610$	−16.3820	−	50.4185i	−0.663286	−	2.04139i
$611$	−1.95492	−	6.01661i	−0.0790874	−	0.243406i
$612$	16.5000	+	11.9880i	0.666973	+	0.484584i
$613$	4.70820	−	3.42071i	0.190163	−	0.138161i	−0.488630	−	0.872491i	$-0.662503\pi$
$613$	4.70820	−	3.42071i	0.190163	−	0.138161i	0.678793	+	0.734330i	$0.262503\pi$
$614$	−3.31559	+	10.2044i	−0.133807	+	0.411814i
$615$		0			0
$616$	24.2082	−	15.1967i	0.975376	−	0.612291i
$617$	15.4164			0.620641			0.310321	−	0.950632i	$-0.399564\pi$
$617$	15.4164			0.620641			0.310321	+	0.950632i	$0.399564\pi$
$618$	1.70820	−	5.25731i	0.0687140	−	0.211480i
$619$	27.0066	−	19.6214i	1.08549	−	0.788652i	0.106855	−	0.994275i	$-0.465922\pi$
$619$	27.0066	−	19.6214i	1.08549	−	0.788652i	0.978631	+	0.205623i	$0.0659220\pi$
$620$	44.1246	+	32.0584i	1.77209	+	1.28750i
$621$	13.6656	+	42.0585i	0.548383	+	1.68775i
$622$	−19.7984	−	60.9331i	−0.793842	−	2.44320i
$623$	48.0689	+	34.9241i	1.92584	+	1.39920i
$624$	−1.00000	+	0.726543i	−0.0400320	+	0.0290850i
$625$	−6.92705	+	21.3193i	−0.277082	+	0.852771i
$626$	53.7426			2.14799
$627$	−1.61803	−	6.43288i	−0.0646181	−	0.256905i
$628$	−44.3951			−1.77156
$629$	5.70820	−	17.5680i	0.227601	−	0.700484i
$630$	33.2148	−	24.1320i	1.32331	−	0.961440i
$631$	14.1180	+	10.2574i	0.562030	+	0.408339i	0.832201	−	0.554474i	$-0.187080\pi$
$631$	14.1180	+	10.2574i	0.562030	+	0.408339i	−0.270171	+	0.962812i	$0.587080\pi$
$632$	1.38197	+	4.25325i	0.0549717	+	0.169185i
$633$	−3.63932	−	11.2007i	−0.144650	−	0.445187i
$634$	−7.76393	−	5.64083i	−0.308345	−	0.224026i
$635$	12.4721	−	9.06154i	0.494942	−	0.359596i
$636$	0.103326	−	0.318003i	0.00409713	−	0.0126097i
$637$	−7.85410			−0.311191
$638$	15.5279	−	38.6628i	0.614754	−	1.53067i
$639$	17.0213			0.673352
$640$	−15.6525	+	48.1734i	−0.618718	+	1.90422i
$641$	−19.3435	+	14.0538i	−0.764021	+	0.555094i	−0.900141	−	0.435599i	$-0.856537\pi$
$641$	−19.3435	+	14.0538i	−0.764021	+	0.555094i	0.136120	+	0.990692i	$0.456537\pi$
$642$	14.0689	+	10.2216i	0.555255	+	0.403416i
$643$	5.08359	+	15.6457i	0.200477	+	0.617006i	0.999869	+	0.0161953i	$0.00515534\pi$
$643$	5.08359	+	15.6457i	0.200477	+	0.617006i	−0.799392	+	0.600810i	$0.794845\pi$
$644$	−28.5836	−	87.9713i	−1.12635	−	3.46655i
$645$	−12.9443	−	9.40456i	−0.509680	−	0.370304i
$646$	−13.5172	+	9.82084i	−0.531828	+	0.386396i
$647$	3.09017	−	9.51057i	0.121487	−	0.373899i	−0.871758	−	0.489937i	$-0.837020\pi$
$647$	3.09017	−	9.51057i	0.121487	−	0.373899i	0.993245	+	0.116039i	$0.0370196\pi$
$648$	5.40325			0.212260
$649$	−31.8262	−	2.15938i	−1.24929	−	0.0847632i
$650$	12.2361			0.479938
$651$	8.27051	−	25.4540i	0.324147	−	0.997621i
$652$	13.0623	−	9.49032i	0.511559	−	0.371670i
$653$	27.3885	+	19.8989i	1.07180	+	0.778706i	0.976234	−	0.216718i	$-0.0695351\pi$
$653$	27.3885	+	19.8989i	1.07180	+	0.778706i	0.0955622	+	0.995423i	$0.469535\pi$
$654$	−8.69505	−	26.7606i	−0.340003	−	1.04642i
$655$	19.8885	+	61.2106i	0.777110	+	2.39170i
$656$		0			0
$657$	6.79837	−	4.93931i	0.265230	−	0.192701i
$658$	−16.8475	+	51.8513i	−0.656785	+	2.02138i
$659$	−37.4164			−1.45754			−0.728768	−	0.684761i	$-0.759907\pi$
$659$	−37.4164			−1.45754			−0.728768	+	0.684761i	$0.759907\pi$
$660$	30.5410	+	25.5195i	1.18881	+	0.993346i
$661$	21.1246			0.821652			0.410826	−	0.911714i	$-0.365240\pi$
$661$	21.1246			0.821652			0.410826	+	0.911714i	$0.365240\pi$
$662$	−5.71478	+	17.5883i	−0.222111	+	0.683588i
$663$	4.61803	−	3.35520i	0.179350	−	0.130305i
$664$	14.6353	+	10.6331i	0.567958	+	0.412646i
$665$	6.23607	+	19.1926i	0.241824	+	0.744259i
$666$	4.06888	+	12.5227i	0.157666	+	0.485246i
$667$	−36.3607	−	26.4176i	−1.40789	−	1.02289i
$668$	−7.63525	+	5.54734i	−0.295417	+	0.214633i
$669$	−3.41641	+	10.5146i	−0.132086	+	0.406519i
$670$	−11.0557			−0.427120
$671$	18.6459	+	15.5802i	0.719817	+	0.601466i
$672$	31.9574			1.23278
$673$	−7.84752	+	24.1522i	−0.302500	+	0.930999i	0.678099	+	0.734971i	$0.262804\pi$
$673$	−7.84752	+	24.1522i	−0.302500	+	0.930999i	−0.980598	+	0.196028i	$0.937196\pi$
$674$	53.9058	−	39.1648i	2.07637	−	1.50857i
$675$	24.4721	+	17.7800i	0.941933	+	0.684354i
$676$	0.927051	+	2.85317i	0.0356558	+	0.109737i
$677$	4.02786	+	12.3965i	0.154803	+	0.476436i	0.998141	−	0.0609484i	$-0.0194125\pi$
$677$	4.02786	+	12.3965i	0.154803	+	0.476436i	−0.843338	+	0.537384i	$0.819413\pi$
$678$	4.14590	+	3.01217i	0.159222	+	0.115682i
$679$	30.2705	−	21.9928i	1.16168	−	0.844007i
$680$	10.3262	−	31.7809i	0.395993	−	1.21874i
$681$	5.12461			0.196376
$682$	−41.5689	−	2.82041i	−1.59175	−	0.107999i
$683$	−29.9787			−1.14710			−0.573552	−	0.819169i	$-0.694435\pi$
$683$	−29.9787			−1.14710			−0.573552	+	0.819169i	$0.694435\pi$
$684$	2.20820	−	6.79615i	0.0844328	−	0.259857i
$685$	−35.8885	+	26.0746i	−1.37123	+	0.996257i
$686$	5.95492	+	4.32650i	0.227360	+	0.165187i
$687$	−6.76393	−	20.8172i	−0.258060	−	0.794227i
$688$	1.23607	+	3.80423i	0.0471246	+	0.145035i
$689$	0.0729490	+	0.0530006i	0.00277914	+	0.00201916i
$690$	57.8885	−	42.0585i	2.20378	−	1.60114i
$691$	−1.44427	+	4.44501i	−0.0549427	+	0.169096i	−0.974762	−	0.223245i	$-0.928335\pi$
$691$	−1.44427	+	4.44501i	−0.0549427	+	0.169096i	0.919820	+	0.392342i	$0.128335\pi$
$692$	−37.4164			−1.42236
$693$	−7.01316	+	17.4620i	−0.266408	+	0.663328i
$694$	−57.8885			−2.19742
$695$	18.1803	−	55.9533i	0.689620	−	2.12243i
$696$	−12.5623	+	9.12705i	−0.476173	+	0.345960i
$697$		0			0
$698$	−8.41641	−	25.9030i	−0.318566	−	0.980445i
$699$	3.31308	+	10.1966i	0.125312	+	0.385672i
$700$	−51.1869	−	37.1895i	−1.93468	−	1.40563i
$701$	9.73607	−	7.07367i	0.367726	−	0.267169i	−0.388541	−	0.921431i	$-0.627021\pi$
$701$	9.73607	−	7.07367i	0.367726	−	0.267169i	0.756267	+	0.654263i	$0.227021\pi$
$702$	−3.81966	+	11.7557i	−0.144164	+	0.443690i
$703$	−6.47214			−0.244101
$704$	−10.5172	−	41.8137i	−0.396383	−	1.57591i
$705$	−25.3050			−0.953040
$706$	3.81966	−	11.7557i	0.143755	−	0.442432i
$707$	10.5451	−	7.66145i	0.396589	−	0.288139i
$708$	28.8541	+	20.9637i	1.08440	+	0.787865i
$709$	4.47214	+	13.7638i	0.167955	+	0.516911i	0.999242	−	0.0389319i	$-0.0123956\pi$
$709$	4.47214	+	13.7638i	0.167955	+	0.516911i	−0.831287	+	0.555843i	$0.812396\pi$
$710$	−25.8541	−	79.5707i	−0.970287	−	2.98624i
$711$	−2.38197	−	1.73060i	−0.0893307	−	0.0649026i
$712$	−27.8885	+	20.2622i	−1.04517	+	0.759359i
$713$	−13.8885	+	42.7445i	−0.520130	+	1.60080i
$714$	−49.1935			−1.84102
$715$	−9.09017	+	5.70634i	−0.339953	+	0.213405i
$716$	−65.1246			−2.43382
$717$	3.94427	−	12.1392i	0.147302	−	0.453348i
$718$	55.6140	−	40.4059i	2.07549	−	1.50794i
$719$	−6.85410	−	4.97980i	−0.255615	−	0.185715i	0.452597	−	0.891715i	$-0.350498\pi$
$719$	−6.85410	−	4.97980i	−0.255615	−	0.185715i	−0.708212	+	0.706000i	$0.750498\pi$
$720$	−1.47214	−	4.53077i	−0.0548633	−	0.168852i
$721$	−2.38197	−	7.33094i	−0.0887090	−	0.273018i
$722$	−29.6353	−	21.5313i	−1.10291	−	0.801311i
$723$	12.7639	−	9.27354i	0.474696	−	0.344887i
$724$	3.13525	−	9.64932i	0.116521	−	0.358614i
$725$	−30.7426			−1.14175
$726$	−30.1246	−	4.10676i	−1.11803	−	0.152416i
$727$	−3.88854			−0.144218			−0.0721091	−	0.997397i	$-0.522973\pi$
$727$	−3.88854			−0.144218			−0.0721091	+	0.997397i	$0.522973\pi$
$728$	2.66312	−	8.19624i	0.0987018	−	0.303773i
$729$	−19.4615	+	14.1396i	−0.720796	+	0.523689i
$730$	−33.4164	−	24.2784i	−1.23680	−	0.898585i
$731$	−5.70820	−	17.5680i	−0.211126	−	0.649778i
$732$	−8.39512	−	25.8375i	−0.310293	−	0.954983i
$733$	26.0344	+	18.9151i	0.961604	+	0.698646i	0.953523	−	0.301321i	$-0.0974276\pi$
$733$	26.0344	+	18.9151i	0.961604	+	0.698646i	0.00808132	+	0.999967i	$0.497428\pi$
$734$	17.5623	−	12.7598i	0.648237	−	0.470971i
$735$	−9.70820	+	29.8788i	−0.358092	+	1.10210i
$736$	−53.6656			−1.97814
$737$	4.29180	−	2.69417i	0.158090	−	0.0992409i
$738$		0			0
$739$	−9.86475	+	30.3606i	−0.362881	+	1.11683i	0.588417	+	0.808558i	$0.299751\pi$
$739$	−9.86475	+	30.3606i	−0.362881	+	1.11683i	−0.951298	+	0.308274i	$0.900249\pi$
$740$	31.4164	−	22.8254i	1.15489	−	0.839077i
$741$	−1.61803	−	1.17557i	−0.0594400	−	0.0431857i
$742$	−0.240133	−	0.739054i	−0.00881557	−	0.0271315i
$743$	−6.02786	−	18.5519i	−0.221141	−	0.680602i	−0.998660	−	0.0517429i	$-0.983522\pi$
$743$	−6.02786	−	18.5519i	−0.221141	−	0.680602i	0.777520	−	0.628859i	$-0.216478\pi$
$744$	12.5623	+	9.12705i	0.460556	+	0.334614i
$745$	−20.1803	+	14.6619i	−0.739350	+	0.537170i
$746$	6.80902	−	20.9560i	0.249296	−	0.767254i
$747$	−11.9098			−0.435758
$748$	11.2082	+	44.5609i	0.409813	+	1.62931i
$749$	24.2492			0.886047
$750$	1.30495	−	4.01623i	0.0476501	−	0.146652i
$751$	29.9443	−	21.7558i	1.09268	−	0.793880i	0.112832	−	0.993614i	$-0.464008\pi$
$751$	29.9443	−	21.7558i	1.09268	−	0.793880i	0.979850	+	0.199734i	$0.0640079\pi$
$752$	5.11803	+	3.71847i	0.186635	+	0.135599i
$753$	9.52786	+	29.3238i	0.347215	+	1.06862i
$754$	−3.88197	−	11.9475i	−0.141373	−	0.435101i
$755$	31.6525	+	22.9969i	1.15195	+	0.836942i
$756$	51.7082	−	37.5682i	1.88061	−	1.36634i
$757$	14.1697	−	43.6098i	0.515006	−	1.58503i	−0.268264	−	0.963345i	$-0.586450\pi$
$757$	14.1697	−	43.6098i	0.515006	−	1.58503i	0.783270	−	0.621681i	$-0.213550\pi$
$758$	−36.5836			−1.32878
$759$	−12.2229	+	30.4338i	−0.443664	+	1.10468i
$760$	−11.7082			−0.424701
$761$	−4.65248	+	14.3188i	−0.168652	+	0.519058i	−0.999287	−	0.0377599i	$-0.987978\pi$
$761$	−4.65248	+	14.3188i	−0.168652	+	0.519058i	0.830635	+	0.556818i	$0.187978\pi$
$762$	10.6525	−	7.73948i	0.385898	−	0.280372i
$763$	−31.7426	−	23.0624i	−1.14916	−	0.834914i
$764$	8.29180	+	25.5195i	0.299987	+	0.923264i
$765$	6.79837	+	20.9232i	0.245796	+	0.756481i
$766$	−27.0967	−	19.6869i	−0.979045	−	0.711318i
$767$	−7.78115	+	5.65334i	−0.280961	+	0.204130i
$768$	−3.43769	+	10.5801i	−0.124047	+	0.381778i
$769$	−51.3050			−1.85010			−0.925052	−	0.379841i	$-0.875979\pi$
$769$	−51.3050			−1.85010			−0.925052	+	0.379841i	$0.875979\pi$
$770$	92.2837	+	6.26137i	3.32567	+	0.225644i
$771$	−22.8754			−0.823837
$772$	−12.9787	+	39.9444i	−0.467114	+	1.43763i
$773$	−8.94427	+	6.49839i	−0.321703	+	0.233731i	−0.736902	−	0.676000i	$-0.763712\pi$
$773$	−8.94427	+	6.49839i	−0.321703	+	0.233731i	0.415199	+	0.909731i	$0.363712\pi$
$774$	10.6525	+	7.73948i	0.382895	+	0.278190i
$775$	9.50000	+	29.2380i	0.341250	+	1.05026i
$776$	6.70820	+	20.6457i	0.240810	+	0.741138i
$777$	−15.4164	−	11.2007i	−0.553061	−	0.401822i
$778$	38.0517	−	27.6462i	1.36422	−	0.991163i
$779$		0			0
$780$	12.0000			0.429669
$781$	29.4271	+	24.5887i	1.05298	+	0.879853i
$782$	82.6099			2.95412
$783$	9.59675	−	29.5358i	0.342960	−	1.05552i
$784$	6.35410	−	4.61653i	0.226932	−	0.164876i
$785$	−38.7426	−	28.1482i	−1.38278	−	1.00465i
$786$	16.9868	+	52.2801i	0.605901	+	1.86477i
$787$	9.23607	+	28.4257i	0.329230	+	1.01327i	0.969495	+	0.245112i	$0.0788248\pi$
$787$	9.23607	+	28.4257i	0.329230	+	1.01327i	−0.640264	+	0.768155i	$0.721175\pi$
$788$	43.4164	+	31.5439i	1.54665	+	1.12370i
$789$	−2.65248	+	1.92714i	−0.0944306	+	0.0686079i
$790$	−4.47214	+	13.7638i	−0.159111	+	0.489695i
$791$	7.14590			0.254079
$792$	−8.37790	−	7.00042i	−0.297696	−	0.248749i
$793$	7.32624			0.260162
$794$	−12.5623	+	38.6628i	−0.445820	+	1.37209i
$795$	0.291796	−	0.212002i	0.0103489	−	0.00751895i
$796$	31.4164	+	22.8254i	1.11353	+	0.809023i
$797$	0.0278640	+	0.0857567i	0.000986995	+	0.00303766i	0.951549	−	0.307498i	$-0.0994917\pi$
$797$	0.0278640	+	0.0857567i	0.000986995	+	0.00303766i	−0.950562	+	0.310535i	$0.899492\pi$
$798$	5.32624	+	16.3925i	0.188547	+	0.580287i
$799$	−23.6353	−	17.1720i	−0.836155	−	0.607502i
$800$	−29.6976	+	21.5765i	−1.04997	+	0.762846i
$801$	7.01316	−	21.5843i	0.247798	−	0.762643i
$802$	80.2492			2.83370
$803$	18.8885	+	1.28157i	0.666562	+	0.0452257i
$804$	−5.66563			−0.199811
$805$	30.8328	−	94.8936i	1.08671	−	3.34456i
$806$	−10.1631	+	7.38394i	−0.357981	+	0.260088i
$807$	−24.2705	−	17.6336i	−0.854362	−	0.620731i
$808$	2.33688	+	7.19218i	0.0822112	+	0.253020i
$809$	−10.7984	−	33.2340i	−0.379651	−	1.16844i	−0.940287	−	0.340382i	$-0.889443\pi$
$809$	−10.7984	−	33.2340i	−0.379651	−	1.16844i	0.560636	−	0.828062i	$-0.310557\pi$
$810$	14.1459	+	10.2776i	0.497036	+	0.361118i
$811$	−4.94427	+	3.59222i	−0.173617	+	0.126140i	−0.671200	−	0.741276i	$-0.734221\pi$
$811$	−4.94427	+	3.59222i	−0.173617	+	0.126140i	0.497583	+	0.867416i	$0.334221\pi$
$812$	−20.0729	+	61.7782i	−0.704422	+	2.16799i
$813$	−13.9311			−0.488586
$814$	−11.0557	+	27.5276i	−0.387503	+	0.964843i
$815$	17.4164			0.610070
$816$	−1.76393	+	5.42882i	−0.0617500	+	0.190047i
$817$	−5.23607	+	3.80423i	−0.183187	+	0.133093i
$818$	−31.8328	−	23.1279i	−1.11301	−	0.808648i
$819$	1.75329	+	5.39607i	0.0612649	+	0.188554i
$820$		0			0
$821$	−22.8885	−	16.6295i	−0.798816	−	0.580374i	0.111751	−	0.993736i	$-0.464354\pi$
$821$	−22.8885	−	16.6295i	−0.798816	−	0.580374i	−0.910566	+	0.413363i	$0.864354\pi$
$822$	−30.6525	+	22.2703i	−1.06913	+	0.776767i
$823$	2.58359	−	7.95148i	0.0900584	−	0.277171i	−0.895876	−	0.444304i	$-0.853451\pi$
$823$	2.58359	−	7.95148i	0.0900584	−	0.277171i	0.985934	+	0.167133i	$0.0534509\pi$
$824$	4.47214			0.155794
$825$	5.47214	+	21.7558i	0.190515	+	0.757439i
$826$	82.8885			2.88406
$827$	−8.94427	+	27.5276i	−0.311023	+	0.957230i	0.666338	+	0.745650i	$0.267861\pi$
$827$	−8.94427	+	27.5276i	−0.311023	+	0.957230i	−0.977361	+	0.211580i	$0.932139\pi$
$828$	−28.5836	+	20.7672i	−0.993348	+	0.721710i
$829$	−6.69098	−	4.86128i	−0.232387	−	0.168839i	0.465498	−	0.885049i	$-0.345875\pi$
$829$	−6.69098	−	4.86128i	−0.232387	−	0.168839i	−0.697885	+	0.716210i	$0.745875\pi$
$830$	18.0902	+	55.6758i	0.627919	+	1.93254i
$831$	−8.48529	−	26.1150i	−0.294352	−	0.905921i
$832$	−10.5172	−	7.64121i	−0.364619	−	0.264911i
$833$	−29.3435	+	21.3193i	−1.01669	+	0.738669i
$834$	15.5279	−	47.7899i	0.537686	−	1.65483i
$835$	−10.1803			−0.352305
$836$	13.6353	−	8.55951i	0.471585	−	0.296037i
$837$	−31.0557			−1.07344
$838$	−19.4721	+	59.9291i	−0.672654	+	2.07022i
$839$	−5.45492	+	3.96323i	−0.188325	+	0.136826i	−0.677953	−	0.735106i	$-0.737133\pi$
$839$	−5.45492	+	3.96323i	−0.188325	+	0.136826i	0.489628	+	0.871931i	$0.337133\pi$
$840$	−27.8885	−	20.2622i	−0.962246	−	0.699113i
$841$	0.791796	+	2.43690i	0.0273033	+	0.0840310i
$842$	4.47214	+	13.7638i	0.154120	+	0.474333i
$843$	−30.3607	−	22.0583i	−1.04568	−	0.759729i
$844$	23.1246	−	16.8010i	0.795982	−	0.578315i
$845$	−1.00000	+	3.07768i	−0.0344010	+	0.105876i
$846$	20.8247			0.715967
$847$	−37.3500	+	20.0579i	−1.28336	+	0.689199i
$848$	−0.0901699			−0.00309645
$849$	−3.01316	+	9.27354i	−0.103411	+	0.318267i
$850$	45.7148	−	33.2137i	1.56800	−	1.13922i
$851$	25.8885	+	18.8091i	0.887448	+	0.644769i
$852$	−13.2492	−	40.7769i	−0.453911	−	1.39699i
$853$	−1.50658	−	4.63677i	−0.0515842	−	0.158760i	0.921946	−	0.387319i	$-0.126599\pi$
$853$	−1.50658	−	4.63677i	−0.0515842	−	0.158760i	−0.973530	+	0.228559i	$0.926599\pi$
$854$	−51.0795	−	37.1114i	−1.74791	−	1.26993i
$855$	6.23607	−	4.53077i	0.213269	−	0.154949i
$856$	−4.34752	+	13.3803i	−0.148595	+	0.457329i
$857$	35.1591			1.20101			0.600505	−	0.799621i	$-0.294966\pi$
$857$	35.1591			1.20101			0.600505	+	0.799621i	$0.294966\pi$
$858$	−7.76393	+	4.87380i	−0.265056	+	0.166389i
$859$	2.87539			0.0981070			0.0490535	−	0.998796i	$-0.484380\pi$
$859$	2.87539			0.0981070			0.0490535	+	0.998796i	$0.484380\pi$
$860$	12.0000	−	36.9322i	0.409197	−	1.25938i
$861$		0			0
$862$	12.5000	+	9.08178i	0.425752	+	0.309327i
$863$	14.8328	+	45.6507i	0.504915	+	1.55397i	0.800914	+	0.598780i	$0.204348\pi$
$863$	14.8328	+	45.6507i	0.504915	+	1.55397i	−0.295999	+	0.955188i	$0.595652\pi$
$864$	−11.4590	−	35.2671i	−0.389842	−	1.19981i
$865$	−32.6525	−	23.7234i	−1.11022	−	0.806620i
$866$	35.0623	−	25.4743i	1.19147	−	0.865650i
$867$	1.65248	−	5.08580i	0.0561210	−	0.172723i
$868$	64.9574			2.20480
$869$	−1.61803	−	6.43288i	−0.0548880	−	0.218221i
$870$	−50.2492			−1.70361
$871$	0.472136	−	1.45309i	0.0159977	−	0.0492359i
$872$	18.4164	−	13.3803i	0.623658	−	0.453114i
$873$	−11.5623	−	8.40051i	−0.391325	−	0.284314i
$874$	−8.94427	−	27.5276i	−0.302545	−	0.931136i
$875$	−1.81966	−	5.60034i	−0.0615157	−	0.189326i
$876$	−17.1246	−	12.4418i	−0.578587	−	0.420368i
$877$	−15.9443	+	11.5842i	−0.538400	+	0.391170i	−0.823490	−	0.567330i	$-0.807976\pi$
$877$	−15.9443	+	11.5842i	−0.538400	+	0.391170i	0.285091	+	0.958501i	$0.407976\pi$
$878$	−7.23607	+	22.2703i	−0.244205	+	0.751587i
$879$	−7.41641			−0.250149
$880$	4.00000	−	9.95959i	0.134840	−	0.335738i
$881$	27.1459			0.914569			0.457284	−	0.889321i	$-0.348822\pi$
$881$	27.1459			0.914569			0.457284	+	0.889321i	$0.348822\pi$
$882$	7.98936	−	24.5887i	0.269016	−	0.827945i
$883$	−5.61803	+	4.08174i	−0.189062	+	0.137362i	−0.678290	−	0.734794i	$-0.737279\pi$
$883$	−5.61803	+	4.08174i	−0.189062	+	0.137362i	0.489228	+	0.872156i	$0.337279\pi$
$884$	11.2082	+	8.14324i	0.376973	+	0.273887i
$885$	11.8885	+	36.5892i	0.399629	+	1.22993i
$886$	14.3475	+	44.1571i	0.482015	+	1.48349i
$887$	14.0344	+	10.1966i	0.471230	+	0.342369i	0.797921	−	0.602763i	$-0.205933\pi$
$887$	14.0344	+	10.1966i	0.471230	+	0.342369i	−0.326690	+	0.945131i	$0.605933\pi$
$888$	8.94427	−	6.49839i	0.300150	−	0.218072i
$889$	5.67376	−	17.4620i	0.190292	−	0.585658i
$890$	−111.554			−3.73930
$891$	−7.99593	−	0.542517i	−0.267874	−	0.0181750i
$892$	−26.8328			−0.898429
$893$	−3.16312	+	9.73508i	−0.105850	+	0.325772i
$894$	−17.2361	+	12.5227i	−0.576460	+	0.418823i
$895$	−56.8328	−	41.2915i	−1.89971	−	1.38022i
$896$	18.6418	+	57.3737i	0.622780	+	1.91672i
$897$	3.05573	+	9.40456i	0.102028	+	0.314009i
$898$	56.3050	+	40.9079i	1.87892	+	1.36512i
$899$	25.5344	−	18.5519i	0.851621	−	0.618739i
$900$	−7.46807	+	22.9844i	−0.248936	+	0.766145i
$901$	0.416408			0.0138726
$902$		0			0
$903$	−19.0557			−0.634135
$904$	−1.28115	+	3.94298i	−0.0426105	+	0.131142i
$905$	8.85410	−	6.43288i	0.294320	−	0.213836i
$906$	27.0344	+	19.6417i	0.898159	+	0.652551i
$907$	−8.85410	−	27.2501i	−0.293996	−	0.904826i	−0.983557	−	0.180598i	$-0.942197\pi$
$907$	−8.85410	−	27.2501i	−0.293996	−	0.904826i	0.689561	−	0.724227i	$-0.257803\pi$
$908$	3.84346	+	11.8290i	0.127550	+	0.392557i
$909$	−4.02786	−	2.92641i	−0.133596	−	0.0970630i
$910$	22.5623	−	16.3925i	0.747933	−	0.543405i
$911$	−18.5279	+	57.0229i	−0.613856	+	1.88925i	−0.196523	+	0.980499i	$0.562965\pi$
$911$	−18.5279	+	57.0229i	−0.613856	+	1.88925i	−0.417333	+	0.908754i	$0.637035\pi$
$912$	2.00000			0.0662266
$913$	−20.5902	−	17.2048i	−0.681435	−	0.569395i
$914$	−73.6656			−2.43664
$915$	9.05573	−	27.8707i	0.299373	−	0.921376i
$916$	42.9787	−	31.2259i	1.42006	−	1.03173i
$917$	62.0132	+	45.0552i	2.04785	+	1.48785i
$918$	17.6393	+	54.2882i	0.582184	+	1.79178i
$919$	6.50658	+	20.0252i	0.214632	+	0.660570i	0.999179	+	0.0405010i	$0.0128954\pi$
$919$	6.50658	+	20.0252i	0.214632	+	0.660570i	−0.784547	+	0.620069i	$0.787105\pi$
$920$	46.8328	+	34.0260i	1.54403	+	1.12181i
$921$	−4.79837	+	3.48622i	−0.158112	+	0.114875i
$922$	14.2705	−	43.9201i	0.469974	−	1.44643i
$923$	11.5623			0.380578
$924$	47.2918	+	3.20871i	1.55579	+	0.105559i
$925$	21.8885			0.719691
$926$	3.35410	−	10.3229i	0.110223	−	0.339230i
$927$	−2.38197	+	1.73060i	−0.0782340	+	0.0568403i
$928$	30.4894	+	22.1518i	1.00086	+	0.727169i
$929$	1.74265	+	5.36331i	0.0571744	+	0.175965i	0.975565	−	0.219710i	$-0.0705110\pi$
$929$	1.74265	+	5.36331i	0.0571744	+	0.175965i	−0.918391	+	0.395674i	$0.870511\pi$
$930$	15.5279	+	47.7899i	0.509179	+	1.56709i
$931$	10.2812	+	7.46969i	0.336951	+	0.244809i
$932$	−21.0517	+	15.2949i	−0.689570	+	0.501002i
$933$	10.9443	−	33.6830i	0.358299	−	1.10273i
$934$	50.2492			1.64420
$935$	−18.4721	+	45.9937i	−0.604103	+	1.50416i
$936$	−3.29180			−0.107596
$937$	14.4443	−	44.4549i	0.471874	−	1.45228i	−0.378254	−	0.925702i	$-0.623475\pi$
$937$	14.4443	−	44.4549i	0.471874	−	1.45228i	0.850128	−	0.526576i	$-0.176525\pi$
$938$	−10.6525	+	7.73948i	−0.347816	+	0.252703i
$939$	24.0344	+	17.4620i	0.784334	+	0.569852i
$940$	−18.9787	−	58.4105i	−0.619017	−	1.90514i
$941$	−14.6180	−	44.9897i	−0.476534	−	1.46662i	−0.843877	−	0.536536i	$-0.819732\pi$
$941$	−14.6180	−	44.9897i	−0.476534	−	1.46662i	0.367343	−	0.930086i	$-0.380268\pi$
$942$	−33.0902	−	24.0414i	−1.07814	−	0.783312i
$943$		0			0
$944$	2.97214	−	9.14729i	0.0967348	−	0.297719i
$945$	68.9443			2.24276
$946$	7.23607	+	28.7687i	0.235265	+	0.935352i
$947$	−40.5066			−1.31629			−0.658143	−	0.752893i	$-0.728658\pi$
$947$	−40.5066			−1.31629			−0.658143	+	0.752893i	$0.728658\pi$
$948$	−2.29180	+	7.05342i	−0.0744341	+	0.229085i
$949$	4.61803	−	3.35520i	0.149908	−	0.108914i
$950$	−16.0172	−	11.6372i	−0.519667	−	0.377560i
$951$	−1.63932	−	5.04531i	−0.0531586	−	0.163605i
$952$	−12.2984	−	37.8505i	−0.398593	−	1.22674i
$953$	10.8541	+	7.88597i	0.351599	+	0.255452i	0.749539	−	0.661960i	$-0.230275\pi$
$953$	10.8541	+	7.88597i	0.351599	+	0.255452i	−0.397941	+	0.917411i	$0.630275\pi$
$954$	−0.240133	+	0.174467i	−0.00777460	+	0.00564858i
$955$	−8.94427	+	27.5276i	−0.289430	+	0.890773i
$956$	30.9787			1.00192
$957$	19.5066	−	12.2452i	0.630558	−	0.395832i
$958$	−62.4083			−2.01632
$959$	−16.3262	+	50.2470i	−0.527202	+	1.62256i
$960$	−42.0689	+	30.5648i	−1.35777	+	0.986476i
$961$	−0.454915	−	0.330515i	−0.0146747	−	0.0106618i
$962$	2.76393	+	8.50651i	0.0891127	+	0.274261i
$963$	−2.86223	−	8.80905i	−0.0922342	−	0.283868i
$964$	30.9787	+	22.5074i	0.997757	+	0.724913i
$965$	−36.6525	+	26.6296i	−1.17988	+	0.857237i
$966$	26.3344	−	81.0489i	0.847294	−	2.60770i
$967$	13.5279			0.435027			0.217513	−	0.976057i	$-0.430205\pi$
$967$	13.5279			0.435027			0.217513	+	0.976057i	$0.430205\pi$
$968$	−4.37132	−	24.2052i	−0.140500	−	0.777984i
$969$	−9.23607			−0.296705
$970$	−21.7082	+	66.8110i	−0.697008	+	2.14517i
$971$	10.4721	−	7.60845i	0.336067	−	0.244167i	−0.406934	−	0.913458i	$-0.633402\pi$
$971$	10.4721	−	7.60845i	0.336067	−	0.244167i	0.743000	+	0.669291i	$0.233402\pi$
$972$	−33.0000	−	23.9759i	−1.05848	−	0.769027i
$973$	−21.6525	−	66.6395i	−0.694147	−	2.13636i
$974$	−7.13525	−	21.9601i	−0.228628	−	0.703646i
$975$	5.47214	+	3.97574i	0.175249	+	0.127326i
$976$	−5.92705	+	4.30625i	−0.189720	+	0.137840i
$977$	3.56231	−	10.9637i	0.113968	−	0.350758i	−0.877762	−	0.479097i	$-0.840964\pi$
$977$	3.56231	−	10.9637i	0.113968	−	0.350758i	0.991730	+	0.128338i	$0.0409644\pi$
$978$	14.8754			0.475662
$979$	43.3050	−	27.1846i	1.38403	−	0.868824i
$980$	−76.2492			−2.43569
$981$	−4.63119	+	14.2533i	−0.147863	+	0.455074i
$982$	29.7984	−	21.6498i	0.950904	−	0.690872i
$983$	−7.01722	−	5.09831i	−0.223815	−	0.162611i	0.470228	−	0.882545i	$-0.344172\pi$
$983$	−7.01722	−	5.09831i	−0.223815	−	0.162611i	−0.694042	+	0.719934i	$0.744172\pi$
$984$		0			0
$985$	17.8885	+	55.0553i	0.569976	+	1.75421i
$986$	−46.9336	−	34.0993i	−1.49467	−	1.08594i
$987$	−24.3820	+	17.7145i	−0.776087	+	0.563860i
$988$	1.50000	−	4.61653i	0.0477214	−	0.146871i
$989$	32.0000			1.01754
$990$	−8.61803	−	34.2631i	−0.273899	−	1.08895i
$991$	−7.34752			−0.233402			−0.116701	−	0.993167i	$-0.537232\pi$
$991$	−7.34752			−0.233402			−0.116701	+	0.993167i	$0.537232\pi$
$992$	11.6459	−	35.8424i	0.369758	−	1.13800i
$993$	−8.27051	+	6.00888i	−0.262457	+	0.190686i
$994$	−80.6140	−	58.5695i	−2.55692	−	1.85771i
$995$	12.9443	+	39.8384i	0.410361	+	1.26296i
$996$	9.27051	+	28.5317i	0.293747	+	0.904061i
$997$	18.9721	+	13.7841i	0.600854	+	0.436546i	0.846182	−	0.532894i	$-0.178896\pi$
$997$	18.9721	+	13.7841i	0.600854	+	0.436546i	−0.245328	+	0.969440i	$0.578896\pi$
$998$	16.9721	−	12.3310i	0.537244	−	0.390330i
$999$	−6.83282	+	21.0292i	−0.216181	+	0.665336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.a.53.1	yes	4
11.4	even	5		1573.2.a.d.1.1		2
11.5	even	5	inner	143.2.h.a.27.1	✓	4
11.7	odd	10		1573.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.a.27.1	✓	4	11.5	even	5	inner
143.2.h.a.53.1	yes	4	1.1	even	1	trivial
1573.2.a.d.1.1		2	11.4	even	5
1573.2.a.e.1.2		2	11.7	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.690983 + 2.12663i) q^{2} +(-1.00000 + 0.726543i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(-1.00000 - 3.07768i) q^{5} +(-0.854102 - 2.62866i) q^{6} +(-3.11803 - 2.26538i) q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.454915 + 1.40008i) q^{9} +7.23607 q^{10} +(-2.80902 + 1.76336i) q^{11} +3.70820 q^{12} +(-0.309017 + 0.951057i) q^{13} +(6.97214 - 5.06555i) q^{14} +(3.23607 + 2.35114i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.42705 + 4.39201i) q^{17} +(-2.66312 - 1.93487i) q^{18} +(1.30902 - 0.951057i) q^{19} +(-3.00000 + 9.23305i) q^{20} +4.76393 q^{21} +(-1.80902 - 7.19218i) q^{22} -8.00000 q^{23} +(-0.854102 + 2.62866i) q^{24} +(-4.42705 + 3.21644i) q^{25} +(-1.80902 - 1.31433i) q^{26} +(-1.70820 - 5.25731i) q^{27} +(3.57295 + 10.9964i) q^{28} +(4.54508 + 3.30220i) q^{29} +(-7.23607 + 5.25731i) q^{30} +(1.73607 - 5.34307i) q^{31} +6.70820 q^{32} +(1.52786 - 3.80423i) q^{33} -10.3262 q^{34} +(-3.85410 + 11.8617i) q^{35} +(3.57295 - 2.59590i) q^{36} +(-3.23607 - 2.35114i) q^{37} +(1.11803 + 3.44095i) q^{38} +(-0.381966 - 1.17557i) q^{39} +(-5.85410 - 4.25325i) q^{40} +(-3.29180 + 10.1311i) q^{42} -4.00000 q^{43} +(9.92705 + 0.673542i) q^{44} +4.76393 q^{45} +(5.52786 - 17.0130i) q^{46} +(-5.11803 + 3.71847i) q^{47} +(1.00000 + 0.726543i) q^{48} +(2.42705 + 7.46969i) q^{49} +(-3.78115 - 11.6372i) q^{50} +(-4.61803 - 3.35520i) q^{51} +(2.42705 - 1.76336i) q^{52} +(0.0278640 - 0.0857567i) q^{53} +12.3607 q^{54} +(8.23607 + 6.88191i) q^{55} -8.61803 q^{56} +(-0.618034 + 1.90211i) q^{57} +(-10.1631 + 7.38394i) q^{58} +(7.78115 + 5.65334i) q^{59} +(-3.70820 - 11.4127i) q^{60} +(-2.26393 - 6.96767i) q^{61} +(10.1631 + 7.38394i) q^{62} +(4.59017 - 3.33495i) q^{63} +(-4.01722 + 12.3637i) q^{64} +3.23607 q^{65} +(7.03444 + 5.87785i) q^{66} -1.52786 q^{67} +(4.28115 - 13.1760i) q^{68} +(8.00000 - 5.81234i) q^{69} +(-22.5623 - 16.3925i) q^{70} +(-3.57295 - 10.9964i) q^{71} +(1.01722 + 3.13068i) q^{72} +(-4.61803 - 3.35520i) q^{73} +(7.23607 - 5.25731i) q^{74} +(2.09017 - 6.43288i) q^{75} -4.85410 q^{76} +(12.7533 + 0.865300i) q^{77} +2.76393 q^{78} +(-0.618034 + 1.90211i) q^{79} +(-2.61803 + 1.90211i) q^{80} +(1.95492 + 1.42033i) q^{81} +(2.50000 + 7.69421i) q^{83} +(-11.5623 - 8.40051i) q^{84} +(12.0902 - 8.78402i) q^{85} +(2.76393 - 8.50651i) q^{86} -6.94427 q^{87} +(-2.76393 + 6.88191i) q^{88} -15.4164 q^{89} +(-3.29180 + 10.1311i) q^{90} +(3.11803 - 2.26538i) q^{91} +(19.4164 + 14.1068i) q^{92} +(2.14590 + 6.60440i) q^{93} +(-4.37132 - 13.4535i) q^{94} +(-4.23607 - 3.07768i) q^{95} +(-6.70820 + 4.87380i) q^{96} +(-3.00000 + 9.23305i) q^{97} -17.5623 q^{98} +(-1.19098 - 4.73504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 4 q^{3} - 3 q^{4} - 4 q^{5} + 10 q^{6} - 8 q^{7} + 5 q^{8} - 13 q^{9} + 20 q^{10} - 9 q^{11} - 12 q^{12} + q^{13} + 10 q^{14} + 4 q^{15} + q^{16} - q^{17} + 5 q^{18} + 3 q^{19} - 12 q^{20}+ \cdots - 7 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 4 * q^3 - 3 * q^4 - 4 * q^5 + 10 * q^6 - 8 * q^7 + 5 * q^8 - 13 * q^9 + 20 * q^10 - 9 * q^11 - 12 * q^12 + q^13 + 10 * q^14 + 4 * q^15 + q^16 - q^17 + 5 * q^18 + 3 * q^19 - 12 * q^20 + 28 * q^21 - 5 * q^22 - 32 * q^23 + 10 * q^24 - 11 * q^25 - 5 * q^26 + 20 * q^27 + 21 * q^28 + 7 * q^29 - 20 * q^30 - 2 * q^31 + 24 * q^33 - 10 * q^34 - 2 * q^35 + 21 * q^36 - 4 * q^37 - 6 * q^39 - 10 * q^40 - 40 * q^42 - 16 * q^43 + 33 * q^44 + 28 * q^45 + 40 * q^46 - 16 * q^47 + 4 * q^48 + 3 * q^49 + 5 * q^50 - 14 * q^51 + 3 * q^52 + 18 * q^53 - 40 * q^54 + 24 * q^55 - 30 * q^56 + 2 * q^57 - 25 * q^58 + 11 * q^59 + 12 * q^60 - 18 * q^61 + 25 * q^62 - 4 * q^63 + 13 * q^64 + 4 * q^65 - 30 * q^66 - 24 * q^67 - 3 * q^68 + 32 * q^69 - 50 * q^70 - 21 * q^71 - 25 * q^72 - 14 * q^73 + 20 * q^74 - 14 * q^75 - 6 * q^76 + 13 * q^77 + 20 * q^78 + 2 * q^79 - 6 * q^80 + 19 * q^81 + 10 * q^83 - 6 * q^84 + 26 * q^85 + 20 * q^86 + 8 * q^87 - 20 * q^88 - 8 * q^89 - 40 * q^90 + 8 * q^91 + 24 * q^92 + 22 * q^93 + 25 * q^94 - 8 * q^95 - 12 * q^97 - 30 * q^98 - 7 * q^99

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