LMFDB - Embedded newform 156.2.p.b.107.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(35,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("156.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.p (of order $6$, degree $2$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.7
Character	$\chi$	$=$	156.107
Dual form			156.2.p.b.35.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.863590 + 1.11992i) q^{2} +(1.29017 - 1.15562i) q^{3} +(-0.508424 - 1.93430i) q^{4} -1.98084i q^{5} +(0.180026 + 2.44287i) q^{6} +(-2.42516 - 1.40017i) q^{7} +(2.60532 + 1.10105i) q^{8} +(0.329066 - 2.98190i) q^{9} +(2.21838 + 1.71064i) q^{10} +(-2.01615 - 3.49208i) q^{11} +(-2.89127 - 1.90802i) q^{12} +(0.235350 + 3.59786i) q^{13} +(3.66242 - 1.50681i) q^{14} +(-2.28911 - 2.55562i) q^{15} +(-3.48301 + 1.96689i) q^{16} +(6.77232 + 3.91000i) q^{17} +(3.05530 + 2.94366i) q^{18} +(3.36616 + 1.94345i) q^{19} +(-3.83154 + 1.00711i) q^{20} +(-4.74693 + 0.996124i) q^{21} +(5.65196 + 0.757803i) q^{22} +(0.939991 + 1.62811i) q^{23} +(4.63370 - 1.59024i) q^{24} +1.07626 q^{25} +(-4.23255 - 2.84351i) q^{26} +(-3.02140 - 4.22742i) q^{27} +(-1.47533 + 5.40286i) q^{28} +(1.74420 - 1.00701i) q^{29} +(4.83893 - 0.356604i) q^{30} +4.09815i q^{31} +(0.805143 - 5.59926i) q^{32} +(-6.63670 - 2.17545i) q^{33} +(-10.2274 + 4.20779i) q^{34} +(-2.77351 + 4.80386i) q^{35} +(-5.93518 + 0.879559i) q^{36} +(-2.61536 - 4.52993i) q^{37} +(-5.08348 + 2.09147i) q^{38} +(4.46142 + 4.36987i) q^{39} +(2.18100 - 5.16073i) q^{40} +(-3.61265 + 2.08577i) q^{41} +(2.98383 - 6.17641i) q^{42} +(-2.06494 - 1.19219i) q^{43} +(-5.72966 + 5.67529i) q^{44} +(-5.90667 - 0.651827i) q^{45} +(-2.63512 - 0.353310i) q^{46} +2.72193 q^{47} +(-2.22068 + 6.56266i) q^{48} +(0.420938 + 0.729086i) q^{49} +(-0.929448 + 1.20532i) q^{50} +(13.2559 - 2.78170i) q^{51} +(6.83968 - 2.28448i) q^{52} -1.24793i q^{53} +(7.34362 + 0.267043i) q^{54} +(-6.91726 + 3.99368i) q^{55} +(-4.77667 - 6.31810i) q^{56} +(6.58881 - 1.38263i) q^{57} +(-0.378501 + 2.82300i) q^{58} +(-0.420977 + 0.729153i) q^{59} +(-3.77949 + 5.72716i) q^{60} +(-1.28690 + 2.22897i) q^{61} +(-4.58959 - 3.53912i) q^{62} +(-4.97319 + 6.77084i) q^{63} +(5.57539 + 5.73716i) q^{64} +(7.12680 - 0.466192i) q^{65} +(8.16772 - 5.55385i) q^{66} +(6.50853 - 3.75770i) q^{67} +(4.11989 - 15.0876i) q^{68} +(3.09423 + 1.01426i) q^{69} +(-2.98475 - 7.25467i) q^{70} +(-7.46100 + 12.9228i) q^{71} +(4.14053 - 7.40648i) q^{72} +2.63433 q^{73} +(7.33174 + 0.983023i) q^{74} +(1.38856 - 1.24375i) q^{75} +(2.04778 - 7.49925i) q^{76} +11.2918i q^{77} +(-8.74672 + 1.22264i) q^{78} -7.13890i q^{79} +(3.89610 + 6.89930i) q^{80} +(-8.78343 - 1.96248i) q^{81} +(0.783968 - 5.84712i) q^{82} +13.6116 q^{83} +(4.34026 + 8.67552i) q^{84} +(7.74510 - 13.4149i) q^{85} +(3.11842 - 1.28299i) q^{86} +(1.08658 - 3.31485i) q^{87} +(-1.40778 - 11.3179i) q^{88} +(2.80518 - 1.61957i) q^{89} +(5.83094 - 6.05207i) q^{90} +(4.46685 - 9.05493i) q^{91} +(2.67134 - 2.64599i) q^{92} +(4.73593 + 5.28731i) q^{93} +(-2.35064 + 3.04834i) q^{94} +(3.84967 - 6.66783i) q^{95} +(-5.43187 - 8.15443i) q^{96} +(-6.30978 + 10.9289i) q^{97} +(-1.18003 - 0.158216i) q^{98} +(-11.0765 + 4.86284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{4} + 2 q^{6} - 10 q^{9} + 6 q^{10} - 16 q^{12} + 16 q^{13} + 18 q^{16} - 20 q^{18} - 60 q^{21} + 20 q^{22} - 20 q^{24} - 32 q^{25} - 24 q^{28} - 26 q^{30} - 2 q^{33} - 28 q^{34} + 6 q^{36} + 16 q^{37}+ \cdots - 56 q^{97}+O(q^{100}) $ 40 * q + 6 * q^4 + 2 * q^6 - 10 * q^9 + 6 * q^10 - 16 * q^12 + 16 * q^13 + 18 * q^16 - 20 * q^18 - 60 * q^21 + 20 * q^22 - 20 * q^24 - 32 * q^25 - 24 * q^28 - 26 * q^30 - 2 * q^33 - 28 * q^34 + 6 * q^36 + 16 * q^37 + 20 * q^40 - 4 * q^42 + 28 * q^45 + 48 * q^46 - 24 * q^48 - 28 * q^49 + 12 * q^52 - 4 * q^54 + 44 * q^57 - 50 * q^58 - 12 * q^60 - 12 * q^61 + 12 * q^64 + 24 * q^66 - 6 * q^69 + 48 * q^72 - 16 * q^73 + 30 * q^78 - 14 * q^81 - 2 * q^82 - 6 * q^84 + 52 * q^85 - 12 * q^88 + 156 * q^90 + 40 * q^93 - 8 * q^94 + 128 * q^96 - 56 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.863590	+	1.11992i	−0.610650	+	0.791900i
$2$	−0.863590	+	1.11992i	−0.610650	+	0.791900i
$3$	1.29017	−	1.15562i	0.744879	−	0.667200i
$3$	1.29017	−	1.15562i	0.744879	−	0.667200i
$4$	−0.508424	−	1.93430i	−0.254212	−	0.967148i
$5$		−	1.98084i		−	0.885860i	−0.896556	−	0.442930i	$-0.853939\pi$
$5$		−	1.98084i		−	0.885860i	0.896556	−	0.442930i	$-0.146061\pi$
$6$	0.180026	+	2.44287i	0.0734954	+	0.997296i
$7$	−2.42516	−	1.40017i	−0.916625	−	0.529214i	−0.0340681	−	0.999420i	$-0.510846\pi$
$7$	−2.42516	−	1.40017i	−0.916625	−	0.529214i	−0.882557	+	0.470206i	$0.844180\pi$
$8$	2.60532	+	1.10105i	0.921120	+	0.389279i
$9$	0.329066	−	2.98190i	0.109689	−	0.993966i
$10$	2.21838	+	1.71064i	0.701513	+	0.540951i
$11$	−2.01615	−	3.49208i	−0.607893	−	1.05290i	−0.991587	−	0.129441i	$-0.958682\pi$
$11$	−2.01615	−	3.49208i	−0.607893	−	1.05290i	0.383694	−	0.923460i	$-0.374652\pi$
$12$	−2.89127	−	1.90802i	−0.834639	−	0.550798i
$13$	0.235350	+	3.59786i	0.0652744	+	0.997867i
$13$	0.235350	+	3.59786i	0.0652744	+	0.997867i
$14$	3.66242	−	1.50681i	0.978822	−	0.402711i
$15$	−2.28911	−	2.55562i	−0.591046	−	0.659858i
$16$	−3.48301	+	1.96689i	−0.870752	+	0.491722i
$17$	6.77232	+	3.91000i	1.64253	+	0.948314i	0.979931	+	0.199339i	$0.0638795\pi$
$17$	6.77232	+	3.91000i	1.64253	+	0.948314i	0.662598	+	0.748975i	$0.269454\pi$
$18$	3.05530	+	2.94366i	0.720141	+	0.693828i
$19$	3.36616	+	1.94345i	0.772250	+	0.445858i	0.833677	−	0.552253i	$-0.186232\pi$
$19$	3.36616	+	1.94345i	0.772250	+	0.445858i	−0.0614269	+	0.998112i	$0.519565\pi$
$20$	−3.83154	+	1.00711i	−0.856758	+	0.225196i
$21$	−4.74693	+	0.996124i	−1.03587	+	0.217372i
$22$	5.65196	+	0.757803i	1.20500	+	0.161564i
$23$	0.939991	+	1.62811i	0.196002	+	0.339485i	0.947228	−	0.320559i	$-0.103871\pi$
$23$	0.939991	+	1.62811i	0.196002	+	0.339485i	−0.751227	+	0.660044i	$0.770538\pi$
$24$	4.63370	−	1.59024i	0.945849	−	0.324606i
$25$	1.07626			0.215252
$26$	−4.23255	−	2.84351i	−0.830071	−	0.557657i
$27$	−3.02140	−	4.22742i	−0.581469	−	0.813568i
$28$	−1.47533	+	5.40286i	−0.278811	+	1.02104i
$29$	1.74420	−	1.00701i	0.323889	−	0.186998i	−0.329236	−	0.944248i	$-0.606791\pi$
$29$	1.74420	−	1.00701i	0.323889	−	0.186998i	0.653125	+	0.757250i	$0.273458\pi$
$30$	4.83893	−	0.356604i	0.883464	−	0.0651066i
$31$			4.09815i			0.736050i	0.929816	+	0.368025i	$0.119966\pi$
$31$			4.09815i			0.736050i	−0.929816	+	0.368025i	$0.880034\pi$
$32$	0.805143	−	5.59926i	0.142331	−	0.989819i
$33$	−6.63670	−	2.17545i	−1.15530	−	0.378698i
$34$	−10.2274	+	4.20779i	−1.75398	+	0.721630i
$35$	−2.77351	+	4.80386i	−0.468809	+	0.812001i
$36$	−5.93518	+	0.879559i	−0.989197	+	0.146593i
$37$	−2.61536	−	4.52993i	−0.429962	−	0.744716i	0.566907	−	0.823782i	$-0.308140\pi$
$37$	−2.61536	−	4.52993i	−0.429962	−	0.744716i	−0.996869	+	0.0790655i	$0.974806\pi$
$38$	−5.08348	+	2.09147i	−0.824650	+	0.339281i
$39$	4.46142	+	4.36987i	0.714399	+	0.699739i
$40$	2.18100	−	5.16073i	0.344847	−	0.815983i
$41$	−3.61265	+	2.08577i	−0.564202	+	0.325742i	−0.754830	−	0.655920i	$-0.772281\pi$
$41$	−3.61265	+	2.08577i	−0.564202	+	0.325742i	0.190629	+	0.981662i	$0.438947\pi$
$42$	2.98383	−	6.17641i	0.460415	−	0.953041i
$43$	−2.06494	−	1.19219i	−0.314900	−	0.181808i	0.334217	−	0.942496i	$-0.391528\pi$
$43$	−2.06494	−	1.19219i	−0.314900	−	0.181808i	−0.649117	+	0.760688i	$0.724862\pi$
$44$	−5.72966	+	5.67529i	−0.863778	+	0.855583i
$45$	−5.90667	−	0.651827i	−0.880515	−	0.0971687i
$46$	−2.63512	−	0.353310i	−0.388527	−	0.0520928i
$47$	2.72193			0.397035			0.198518	−	0.980097i	$-0.436387\pi$
$47$	2.72193			0.397035			0.198518	+	0.980097i	$0.436387\pi$
$48$	−2.22068	+	6.56266i	−0.320528	+	0.947239i
$49$	0.420938	+	0.729086i	0.0601340	+	0.104155i
$50$	−0.929448	+	1.20532i	−0.131444	+	0.170458i
$51$	13.2559	−	2.78170i	1.85620	−	0.389516i
$52$	6.83968	−	2.28448i	0.948492	−	0.316800i
$53$		−	1.24793i		−	0.171417i	−0.996320	−	0.0857084i	$-0.972685\pi$
$53$		−	1.24793i		−	0.171417i	0.996320	−	0.0857084i	$-0.0273153\pi$
$54$	7.34362	+	0.267043i	0.999339	+	0.0363400i
$55$	−6.91726	+	3.99368i	−0.932723	+	0.538508i
$56$	−4.77667	−	6.31810i	−0.638310	−	0.844292i
$57$	6.58881	−	1.38263i	0.872709	−	0.183134i
$58$	−0.378501	+	2.82300i	−0.0496997	+	0.370678i
$59$	−0.420977	+	0.729153i	−0.0548065	+	0.0949276i	−0.892127	−	0.451785i	$-0.850788\pi$
$59$	−0.420977	+	0.729153i	−0.0548065	+	0.0949276i	0.837321	+	0.546712i	$0.184121\pi$
$60$	−3.77949	+	5.72716i	−0.487930	+	0.739373i
$61$	−1.28690	+	2.22897i	−0.164770	+	0.285391i	−0.936574	−	0.350471i	$-0.886022\pi$
$61$	−1.28690	+	2.22897i	−0.164770	+	0.285391i	0.771803	+	0.635861i	$0.219355\pi$
$62$	−4.58959	−	3.53912i	−0.582878	−	0.449469i
$63$	−4.97319	+	6.77084i	−0.626564	+	0.853045i
$64$	5.57539	+	5.73716i	0.696924	+	0.717145i
$65$	7.12680	−	0.466192i	0.883971	−	0.0578240i
$66$	8.16772	−	5.55385i	1.00538	−	0.683632i
$67$	6.50853	−	3.75770i	0.795144	−	0.459076i	−0.0466265	−	0.998912i	$-0.514847\pi$
$67$	6.50853	−	3.75770i	0.795144	−	0.459076i	0.841770	+	0.539836i	$0.181514\pi$
$68$	4.11989	−	15.0876i	0.499610	−	1.82964i
$69$	3.09423	+	1.01426i	0.372502	+	0.122103i
$70$	−2.98475	−	7.25467i	−0.356746	−	0.867099i
$71$	−7.46100	+	12.9228i	−0.885458	+	1.53366i	−0.0402702	+	0.999189i	$0.512822\pi$
$71$	−7.46100	+	12.9228i	−0.885458	+	1.53366i	−0.845188	+	0.534469i	$0.820511\pi$
$72$	4.14053	−	7.40648i	0.487966	−	0.872862i
$73$	2.63433			0.308325			0.154162	−	0.988046i	$-0.450732\pi$
$73$	2.63433			0.308325			0.154162	+	0.988046i	$0.450732\pi$
$74$	7.33174	+	0.983023i	0.852297	+	0.114274i
$75$	1.38856	−	1.24375i	0.160337	−	0.143616i
$76$	2.04778	−	7.49925i	0.234896	−	0.860223i
$77$			11.2918i			1.28682i
$78$	−8.74672	+	1.22264i	−0.990371	+	0.138437i
$79$		−	7.13890i		−	0.803188i	−0.915818	−	0.401594i	$-0.868456\pi$
$79$		−	7.13890i		−	0.803188i	0.915818	−	0.401594i	$-0.131544\pi$
$80$	3.89610	+	6.89930i	0.435597	+	0.771365i
$81$	−8.78343	−	1.96248i	−0.975937	−	0.218053i
$82$	0.783968	−	5.84712i	0.0865748	−	0.645706i
$83$	13.6116			1.49407			0.747035	−	0.664784i	$-0.231477\pi$
$83$	13.6116			1.49407			0.747035	+	0.664784i	$0.231477\pi$
$84$	4.34026	+	8.67552i	0.473561	+	0.946577i
$85$	7.74510	−	13.4149i	0.840074	−	1.45505i
$86$	3.11842	−	1.28299i	0.336268	−	0.138349i
$87$	1.08658	−	3.31485i	0.116493	−	0.355389i
$88$	−1.40778	−	11.3179i	−0.150070	−	1.20649i
$89$	2.80518	−	1.61957i	0.297349	−	0.171675i	−0.343902	−	0.939005i	$-0.611749\pi$
$89$	2.80518	−	1.61957i	0.297349	−	0.171675i	0.641251	+	0.767331i	$0.278416\pi$
$90$	5.83094	−	6.05207i	0.614635	−	0.637944i
$91$	4.46685	−	9.05493i	0.468253	−	0.949214i
$92$	2.67134	−	2.64599i	0.278506	−	0.275864i
$93$	4.73593	+	5.28731i	0.491093	+	0.548268i
$94$	−2.35064	+	3.04834i	−0.242450	+	0.314412i
$95$	3.84967	−	6.66783i	0.394968	−	0.684105i
$96$	−5.43187	−	8.15443i	−0.554388	−	0.832258i
$97$	−6.30978	+	10.9289i	−0.640661	+	1.10966i	0.344625	+	0.938740i	$0.388006\pi$
$97$	−6.30978	+	10.9289i	−0.640661	+	1.10966i	−0.985286	+	0.170916i	$0.945327\pi$
$98$	−1.18003	−	0.158216i	−0.119201	−	0.0159823i
$99$	−11.0765	+	4.86284i	−1.11323	+	0.488734i
$100$	−0.547197	−	2.08181i	−0.0547197	−	0.208181i
$101$	−4.54040	+	2.62140i	−0.451787	+	0.260839i	−0.708584	−	0.705626i	$-0.750666\pi$
$101$	−4.54040	+	2.62140i	−0.451787	+	0.260839i	0.256798	+	0.966465i	$0.417333\pi$
$102$	−8.33241	+	17.2478i	−0.825031	+	1.70778i
$103$			4.31171i			0.424845i	0.977178	+	0.212423i	$0.0681353\pi$
$103$			4.31171i			0.424845i	−0.977178	+	0.212423i	$0.931865\pi$
$104$	−3.34825	+	9.63272i	−0.328323	+	0.944565i
$105$	1.97317	+	9.40293i	0.192561	+	0.917632i
$106$	1.39758	+	1.07770i	0.135745	+	0.104676i
$107$	6.91701	+	11.9806i	0.668692	+	1.15821i	0.978270	+	0.207335i	$0.0664789\pi$
$107$	6.91701	+	11.9806i	0.668692	+	1.15821i	−0.309578	+	0.950874i	$0.600188\pi$
$108$	−6.64094	+	7.99362i	−0.639025	+	0.769186i
$109$	−9.47620			−0.907656			−0.453828	−	0.891089i	$-0.649942\pi$
$109$	−9.47620			−0.907656			−0.453828	+	0.891089i	$0.649942\pi$
$110$	1.50109	−	11.1957i	0.143123	−	1.06746i
$111$	−8.60915	−	2.82200i	−0.817144	−	0.267852i
$112$	11.2008	+	0.106777i	1.05838	+	0.0100895i
$113$	−10.6484	−	6.14784i	−1.00171	−	0.578340i	−0.0929592	−	0.995670i	$-0.529633\pi$
$113$	−10.6484	−	6.14784i	−1.00171	−	0.578340i	−0.908755	+	0.417330i	$0.862966\pi$
$114$	−4.14160	+	8.57294i	−0.387896	+	0.802930i
$115$	3.22503	−	1.86197i	0.300736	−	0.173630i
$116$	−2.83465	−	2.86180i	−0.263191	−	0.265712i
$117$	10.8059	+	0.482142i	0.999006	+	0.0445740i
$118$	−0.453039	−	1.10115i	−0.0417056	−	0.101369i
$119$	−10.9493	−	18.9648i	−1.00372	−	1.73850i
$120$	−3.15001	−	9.17863i	−0.287555	−	0.837890i
$121$	−2.62974	+	4.55484i	−0.239067	+	0.414077i
$122$	−1.38491	−	3.36614i	−0.125384	−	0.304756i
$123$	−2.25057	+	6.86586i	−0.202927	+	0.619073i
$124$	7.92705	−	2.08360i	0.711870	−	0.187113i
$125$		−	12.0361i		−	1.07654i
$126$	−3.28797	−	11.4168i	−0.292916	−	1.01709i
$127$	−6.70906	+	3.87348i	−0.595333	+	0.343716i	−0.767203	−	0.641404i	$-0.778352\pi$
$127$	−6.70906	+	3.87348i	−0.595333	+	0.343716i	0.171870	+	0.985120i	$0.445019\pi$
$128$	−11.2400	+	1.28942i	−0.993484	+	0.113969i
$129$	−4.04185	+	0.848165i	−0.355865	+	0.0746768i
$130$	−5.63254	+	8.38402i	−0.494006	+	0.735327i
$131$	−11.4093			−0.996839			−0.498420	−	0.866936i	$-0.666086\pi$
$131$	−11.4093			−0.996839			−0.498420	+	0.866936i	$0.666086\pi$
$132$	−0.833708	+	13.9434i	−0.0725650	+	1.21362i
$133$	−5.44232	−	9.42637i	−0.471909	−	0.817370i
$134$	−1.41239	+	10.5341i	−0.122012	+	0.910010i
$135$	−8.37387	+	5.98493i	−0.720708	+	0.515100i
$136$	13.3390	+	17.6434i	1.14381	+	1.51291i
$137$	4.71225	+	2.72062i	0.402595	+	0.232438i	0.687603	−	0.726087i	$-0.258663\pi$
$137$	4.71225	+	2.72062i	0.402595	+	0.232438i	−0.285008	+	0.958525i	$0.591996\pi$
$138$	−3.80803	+	2.58937i	−0.324161	+	0.220422i
$139$	3.44882	+	1.99118i	0.292525	+	0.168889i	0.639080	−	0.769140i	$-0.279315\pi$
$139$	3.44882	+	1.99118i	0.292525	+	0.168889i	−0.346555	+	0.938030i	$0.612649\pi$
$140$	10.7022	+	2.92239i	0.904503	+	0.246987i
$141$	3.51175	−	3.14553i	0.295743	−	0.264902i
$142$	−8.02924	−	19.5157i	−0.673799	−	1.63772i
$143$	12.0895	−	8.07570i	1.01098	−	0.675324i
$144$	4.71892	+	11.0332i	0.393243	+	0.919434i
$145$	−1.99473	−	3.45498i	−0.165654	−	0.286920i
$146$	−2.27498	+	2.95022i	−0.188279	+	0.244162i
$147$	1.38563	+	0.454197i	0.114285	+	0.0374616i
$148$	−7.43252	+	7.36200i	−0.610949	+	0.605153i
$149$	0.634052	+	0.366070i	0.0519435	+	0.0299896i	0.525747	−	0.850641i	$-0.323786\pi$
$149$	0.634052	+	0.366070i	0.0519435	+	0.0299896i	−0.473803	+	0.880631i	$0.657119\pi$
$150$	0.193755	+	2.62916i	0.0158200	+	0.214670i
$151$			12.7204i			1.03517i	0.855631	+	0.517587i	$0.173170\pi$
$151$			12.7204i			1.03517i	−0.855631	+	0.517587i	$0.826830\pi$
$152$	6.63009	+	8.76961i	0.537771	+	0.711310i
$153$	13.8878	−	18.9077i	1.12276	−	1.52860i
$154$	−12.6459	−	9.75149i	−1.01903	−	0.785797i
$155$	8.11780			0.652037
$156$	6.18433	−	10.8515i	0.495143	−	0.868812i
$157$	17.1422			1.36810			0.684048	−	0.729437i	$-0.260218\pi$
$157$	17.1422			1.36810			0.684048	+	0.729437i	$0.260218\pi$
$158$	7.99496	+	6.16508i	0.636045	+	0.490467i
$159$	−1.44214	−	1.61004i	−0.114369	−	0.127685i
$160$	−11.0913	−	1.59486i	−0.876841	−	0.126085i
$161$		−	5.26458i		−	0.414907i
$162$	9.78310	−	8.14193i	0.768633	−	0.639690i
$163$	13.8016	+	7.96836i	1.08102	+	0.624130i	0.931173	−	0.364579i	$-0.118787\pi$
$163$	13.8016	+	7.96836i	1.08102	+	0.624130i	0.149852	+	0.988708i	$0.452120\pi$
$164$	5.87125	+	5.92749i	0.458468	+	0.462859i
$165$	−4.30923	+	13.1463i	−0.335473	+	1.02344i
$166$	−11.7549	+	15.2439i	−0.912355	+	1.18316i
$167$	−9.26053	−	16.0397i	−0.716601	−	1.24119i	−0.962339	−	0.271853i	$-0.912363\pi$
$167$	−9.26053	−	16.0397i	−0.716601	−	1.24119i	0.245738	−	0.969336i	$-0.420970\pi$
$168$	−13.4641	−	2.63137i	−1.03877	−	0.203015i
$169$	−12.8892	+	1.69352i	−0.991478	+	0.130270i
$170$	8.33498	+	20.2588i	0.639263	+	1.55378i
$171$	6.90286	−	9.39802i	0.527875	−	0.718684i
$172$	−1.25619	+	4.60035i	−0.0957837	+	0.350773i
$173$	−12.1103	−	6.99189i	−0.920730	−	0.531584i	−0.0368619	−	0.999320i	$-0.511736\pi$
$173$	−12.1103	−	6.99189i	−0.920730	−	0.531584i	−0.883868	+	0.467737i	$0.845070\pi$
$174$	2.77400	+	4.07955i	0.210296	+	0.309270i
$175$	−2.61010	−	1.50694i	−0.197305	−	0.113914i
$176$	13.8908	+	8.19740i	1.04706	+	0.617902i
$177$	0.299496	+	1.42722i	0.0225115	+	0.107276i
$178$	−0.608742	+	4.54022i	−0.0456272	+	0.340304i
$179$	−8.30296	−	14.3811i	−0.620592	−	1.07490i	−0.989376	−	0.145382i	$-0.953559\pi$
$179$	−8.30296	−	14.3811i	−0.620592	−	1.07490i	0.368784	−	0.929515i	$-0.379774\pi$
$180$	1.74227	+	11.7567i	0.129861	+	0.876290i
$181$	10.2752			0.763750			0.381875	−	0.924214i	$-0.375278\pi$
$181$	10.2752			0.763750			0.381875	+	0.924214i	$0.375278\pi$
$182$	6.28323	+	12.8222i	0.465744	+	0.950447i
$183$	0.915540	+	4.36292i	0.0676787	+	0.322516i
$184$	0.656350	+	5.27673i	0.0483867	+	0.389005i
$185$	−8.97308	+	5.18061i	−0.659714	+	0.380886i
$186$	−10.0112	+	0.737775i	−0.734059	+	0.0540963i
$187$		−	31.5326i		−	2.30589i
$188$	−1.38390	−	5.26503i	−0.100931	−	0.383992i
$189$	1.40829	+	14.4827i	0.102438	+	1.05346i
$190$	4.14287	+	10.0696i	0.300555	+	0.730524i
$191$	−10.0558	+	17.4171i	−0.727611	+	1.26026i	0.230280	+	0.973124i	$0.426036\pi$
$191$	−10.0558	+	17.4171i	−0.727611	+	1.26026i	−0.957890	+	0.287134i	$0.907297\pi$
$192$	13.8232	+	0.958843i	0.997603	+	0.0691985i
$193$	3.99386	+	6.91758i	0.287485	+	0.497938i	0.973209	−	0.229924i	$-0.0738476\pi$
$193$	3.99386	+	6.91758i	0.287485	+	0.497938i	−0.685724	+	0.727862i	$0.740514\pi$
$194$	−6.79034	−	16.5045i	−0.487518	−	1.18495i
$195$	8.65602	−	8.83737i	0.619871	−	0.632857i
$196$	1.19625	−	1.18490i	0.0854467	−	0.0846360i
$197$	13.2446	−	7.64680i	0.943642	−	0.544812i	0.0525419	−	0.998619i	$-0.483268\pi$
$197$	13.2446	−	7.64680i	0.943642	−	0.544812i	0.891100	+	0.453807i	$0.149934\pi$
$198$	4.11956	−	16.6042i	0.292764	−	1.18001i
$199$	−2.39424	−	1.38231i	−0.169723	−	0.0979896i	0.412732	−	0.910852i	$-0.364575\pi$
$199$	−2.39424	−	1.38231i	−0.169723	−	0.0979896i	−0.582455	+	0.812863i	$0.697908\pi$
$200$	2.80400	+	1.18501i	0.198273	+	0.0837931i
$201$	4.05461	−	12.3695i	0.285990	−	0.872476i
$202$	0.985295	−	7.34868i	0.0693251	−	0.517051i
$203$	−5.63994			−0.395846
$204$	−12.1203	−	24.2266i	−0.848588	−	1.69620i
$205$	4.13158	+	7.15610i	0.288562	+	0.499804i
$206$	−4.82875	−	3.72355i	−0.336435	−	0.259432i
$207$	5.16418	−	2.26720i	0.358935	−	0.157581i
$208$	−7.89632	−	12.0685i	−0.547511	−	0.836798i
$209$		−	15.6732i		−	1.08414i
$210$	−12.2345	−	5.91050i	−0.844261	−	0.407863i
$211$	−17.9842	+	10.3832i	−1.23808	+	0.714808i	−0.968702	−	0.248226i	$-0.920152\pi$
$211$	−17.9842	+	10.3832i	−1.23808	+	0.714808i	−0.269381	+	0.963034i	$0.586819\pi$
$212$	−2.41387	+	0.634480i	−0.165785	+	0.0435762i
$213$	5.30800	+	25.2947i	0.363698	+	1.73317i
$214$	−19.3907	−	2.59987i	−1.32552	−	0.177723i
$215$	−2.36155	+	4.09032i	−0.161056	+	0.278958i
$216$	−3.21713	−	14.3405i	−0.218898	−	0.975748i
$217$	5.73810	−	9.93868i	0.389528	−	0.674682i
$218$	8.18355	−	10.6126i	0.554260	−	0.718773i
$219$	3.39872	−	3.04429i	0.229664	−	0.205714i
$220$	11.2419	+	11.3495i	0.757927	+	0.765186i
$221$	−12.4738	+	25.2861i	−0.839077	+	1.70093i
$222$	10.5952	−	7.20447i	0.711102	−	0.483532i
$223$	−0.964251	+	0.556711i	−0.0645710	+	0.0372801i	−0.531938	−	0.846783i	$-0.678536\pi$
$223$	−0.964251	+	0.556711i	−0.0645710	+	0.0372801i	0.467367	+	0.884063i	$0.345203\pi$
$224$	−9.79251	+	12.4518i	−0.654289	+	0.831970i
$225$	0.354160	−	3.20930i	0.0236107	−	0.213953i
$226$	16.0809	−	6.61607i	1.06968	−	0.440094i
$227$	−1.97871	+	3.42722i	−0.131331	+	0.227473i	−0.924190	−	0.381933i	$-0.875259\pi$
$227$	−1.97871	+	3.42722i	−0.131331	+	0.227473i	0.792859	+	0.609406i	$0.208592\pi$
$228$	−6.02434	−	12.0417i	−0.398971	−	0.797484i
$229$	−3.59696			−0.237694			−0.118847	−	0.992913i	$-0.537920\pi$
$229$	−3.59696			−0.237694			−0.118847	+	0.992913i	$0.537920\pi$
$230$	−0.699852	+	5.21975i	−0.0461469	+	0.344180i
$231$	13.0491	+	14.5683i	0.858567	+	0.958525i
$232$	5.65296	−	0.703148i	0.371135	−	0.0461639i
$233$			0.850018i			0.0556865i	0.999612	+	0.0278433i	$0.00886393\pi$
$233$			0.850018i			0.0556865i	−0.999612	+	0.0278433i	$0.991136\pi$
$234$	−9.87183	+	11.6853i	−0.645342	+	0.763894i
$235$		−	5.39173i		−	0.351717i
$236$	1.62443	+	0.443575i	0.105742	+	0.0288743i
$237$	−8.24988	−	9.21037i	−0.535887	−	0.598278i
$238$	30.6947	+	4.11547i	1.98964	+	0.266766i
$239$	2.44269			0.158005			0.0790023	−	0.996874i	$-0.474827\pi$
$239$	2.44269			0.158005			0.0790023	+	0.996874i	$0.474827\pi$
$240$	12.9996	+	4.39883i	0.839121	+	0.283943i
$241$	−6.95115	+	12.0397i	−0.447763	+	0.775548i	−0.998240	−	0.0593022i	$-0.981112\pi$
$241$	−6.95115	+	12.0397i	−0.447763	+	0.775548i	0.550477	+	0.834850i	$0.314446\pi$
$242$	−2.83003	−	6.87861i	−0.181921	−	0.442174i
$243$	−13.6000	+	7.61842i	−0.872440	+	0.488722i
$244$	4.96578	+	1.35598i	0.317902	+	0.0868076i
$245$	1.44421	−	0.833812i	0.0922669	−	0.0532703i
$246$	−5.74562	−	8.44973i	−0.366327	−	0.538735i
$247$	−6.20005	+	12.5684i	−0.394499	+	0.799706i
$248$	−4.51226	+	10.6770i	−0.286529	+	0.677990i
$249$	17.5613	−	15.7299i	1.11290	−	0.996844i
$250$	13.4794	+	10.3943i	0.852515	+	0.657392i
$251$	9.31600	−	16.1358i	0.588021	−	1.01848i	−0.406471	−	0.913664i	$-0.633241\pi$
$251$	9.31600	−	16.1358i	0.588021	−	1.01848i	0.994491	−	0.104818i	$-0.0334260\pi$
$252$	15.6253	+	6.17718i	0.984301	+	0.389125i
$253$	3.79033	−	6.56504i	0.238296	−	0.412741i
$254$	1.45591	−	10.8587i	0.0913518	−	0.681334i
$255$	−5.51011	−	26.2579i	−0.345056	−	1.64433i
$256$	8.26271	−	13.7014i	0.516419	−	0.856336i
$257$	−24.1583	+	13.9478i	−1.50695	+	0.870039i	−0.506984	+	0.861955i	$0.669240\pi$
$257$	−24.1583	+	13.9478i	−1.50695	+	0.870039i	−0.999967	+	0.00808340i	$0.997427\pi$
$258$	2.54063	−	5.25900i	0.158172	−	0.327411i
$259$			14.6477i			0.910167i
$260$	−4.52519	−	13.5483i	−0.280641	−	0.840231i
$261$	−2.42885	−	5.53239i	−0.150342	−	0.342446i
$262$	9.85300	−	12.7775i	0.608720	−	0.789397i
$263$	14.0576	+	24.3485i	0.866828	+	1.50139i	0.865220	+	0.501392i	$0.167179\pi$
$263$	14.0576	+	24.3485i	0.866828	+	1.50139i	0.00160803	+	0.999999i	$0.499488\pi$
$264$	−14.8955	−	12.9751i	−0.916753	−	0.798561i
$265$	−2.47196			−0.151851
$266$	15.2567	+	2.04558i	0.935447	+	0.125423i
$267$	1.74754	−	5.33126i	0.106948	−	0.326268i
$268$	−10.5776	−	10.6789i	−0.646130	−	0.652319i
$269$	−5.29540	−	3.05730i	−0.322866	−	0.186407i	0.329803	−	0.944050i	$-0.393018\pi$
$269$	−5.29540	−	3.05730i	−0.322866	−	0.186407i	−0.652669	+	0.757643i	$0.726351\pi$
$270$	0.528971	−	14.5466i	0.0321921	−	0.885275i
$271$	5.91118	−	3.41282i	0.359079	−	0.207314i	−0.309598	−	0.950868i	$-0.600194\pi$
$271$	5.91118	−	3.41282i	0.359079	−	0.207314i	0.668677	+	0.743553i	$0.266861\pi$
$272$	−31.2786	−	0.298178i	−1.89654	−	0.0180797i
$273$	−4.70111	−	16.8444i	−0.284524	−	1.01947i
$274$	−7.11632	+	2.92783i	−0.429913	+	0.176877i
$275$	−2.16990	−	3.75839i	−0.130850	−	0.226639i
$276$	0.388700	−	6.50084i	0.0233970	−	0.391304i
$277$	10.8046	−	18.7141i	0.649186	−	1.12442i	−0.334132	−	0.942526i	$-0.608443\pi$
$277$	10.8046	−	18.7141i	0.649186	−	1.12442i	0.983318	−	0.181897i	$-0.0582236\pi$
$278$	−5.20831	+	2.14283i	−0.312374	+	0.128518i
$279$	12.2203	+	1.34856i	0.731609	+	0.0807362i
$280$	−12.5152	+	9.46184i	−0.747924	+	0.565453i
$281$		−	0.713464i		−	0.0425617i	−0.999774	−	0.0212808i	$-0.993226\pi$
$281$		−	0.713464i		−	0.0425617i	0.999774	−	0.0212808i	$-0.00677441\pi$
$282$	0.490019	+	6.64932i	0.0291802	+	0.395961i
$283$	1.60203	−	0.924935i	0.0952310	−	0.0549817i	−0.451628	−	0.892206i	$-0.649157\pi$
$283$	1.60203	−	0.924935i	0.0952310	−	0.0549817i	0.546859	+	0.837225i	$0.315823\pi$
$284$	28.7900	+	7.86151i	1.70837	+	0.466495i
$285$	−2.73878	−	13.0514i	−0.162231	−	0.773098i
$286$	−1.39628	+	20.5133i	−0.0825636	+	1.21298i
$287$	11.6817			0.689548
$288$	−16.4315	−	4.24338i	−0.968235	−	0.250044i
$289$	22.0762	+	38.2371i	1.29860	+	2.24924i
$290$	5.59192	+	0.749752i	0.328369	+	0.0440270i
$291$	4.48898	+	21.3918i	0.263148	+	1.25401i
$292$	−1.33936	−	5.09557i	−0.0783799	−	0.298196i
$293$	5.46613	+	3.15587i	0.319335	+	0.184368i	0.651096	−	0.758995i	$-0.274310\pi$
$293$	5.46613	+	3.15587i	0.319335	+	0.184368i	−0.331761	+	0.943363i	$0.607643\pi$
$294$	−1.70528	+	1.15955i	−0.0994539	+	0.0676263i
$295$	1.44434	+	0.833889i	0.0840926	+	0.0485509i
$296$	−1.82618	−	14.6816i	−0.106144	−	0.853348i
$297$	−8.67089	+	19.0741i	−0.503136	+	1.10679i
$298$	−0.957528	+	0.393950i	−0.0554681	+	0.0228209i
$299$	−5.63649	+	3.76513i	−0.325967	+	0.217743i
$300$	−3.11176	−	2.05353i	−0.179658	−	0.118560i
$301$	3.33854	+	5.78252i	0.192430	+	0.333299i
$302$	−14.2458	−	10.9852i	−0.819755	−	0.632129i
$303$	−2.82852	+	8.62904i	−0.162494	+	0.495725i
$304$	−15.5469	−	0.148208i	−0.891676	−	0.00850033i
$305$	4.41524	+	2.54914i	0.252816	+	0.145963i
$306$	9.18173	+	31.8816i	0.524884	+	1.82255i
$307$			2.21488i			0.126410i	0.998001	+	0.0632050i	$0.0201322\pi$
$307$			2.21488i			0.126410i	−0.998001	+	0.0632050i	$0.979868\pi$
$308$	21.8417	−	5.74103i	1.24455	−	0.327125i
$309$	4.98271	+	5.56283i	0.283457	+	0.316458i
$310$	−7.01045	+	9.09125i	−0.398167	+	0.516349i
$311$	25.4362			1.44235			0.721177	−	0.692750i	$-0.243601\pi$
$311$	25.4362			1.44235			0.721177	+	0.692750i	$0.243601\pi$
$312$	6.81199	+	16.2971i	0.385653	+	0.922644i
$313$	−27.4174			−1.54972			−0.774861	−	0.632131i	$-0.782180\pi$
$313$	−27.4174			−1.54972			−0.774861	+	0.632131i	$0.782180\pi$
$314$	−14.8038	+	19.1978i	−0.835428	+	1.08339i
$315$	13.4120	+	9.85112i	0.755679	+	0.555048i
$316$	−13.8087	+	3.62959i	−0.776803	+	0.204180i
$317$		−	13.2937i		−	0.746646i	−0.927701	−	0.373323i	$-0.878218\pi$
$317$		−	13.2937i		−	0.746646i	0.927701	−	0.373323i	$-0.121782\pi$
$318$	3.04853	−	0.224661i	0.170953	−	0.0125983i
$319$	−7.03313	−	4.06058i	−0.393780	−	0.227349i
$320$	11.3644	−	11.0440i	0.635290	−	0.617377i
$321$	22.7692	+	7.46353i	1.27085	+	0.416574i
$322$	5.89589	+	4.54644i	0.328565	+	0.253363i
$323$	15.1978	+	26.3234i	0.845628	+	1.46467i
$324$	0.669692	+	17.9875i	0.0372051	+	0.999308i
$325$	0.253298	+	3.87224i	0.0140505	+	0.214793i
$326$	−20.8428	+	8.57524i	−1.15438	+	0.474939i
$327$	−12.2259	+	10.9509i	−0.676093	+	0.605588i
$328$	−11.7086	+	1.45639i	−0.646502	+	0.0804156i
$329$	−6.60113	−	3.81116i	−0.363932	−	0.210116i
$330$	−11.0013	−	16.1790i	−0.605602	−	0.890623i
$331$	−28.0738	−	16.2084i	−1.54307	−	0.890894i	−0.998642	−	0.0520889i	$-0.983412\pi$
$331$	−28.0738	−	16.2084i	−1.54307	−	0.890894i	−0.544432	−	0.838805i	$-0.683255\pi$
$332$	−6.92049	−	26.3289i	−0.379811	−	1.44499i
$333$	−14.3684	+	6.30808i	−0.787384	+	0.345681i
$334$	25.9604	+	3.48071i	1.42049	+	0.190456i
$335$	−7.44342	−	12.8924i	−0.406677	−	0.704386i
$336$	14.5743	−	12.8062i	0.795096	−	0.698635i
$337$	−23.3411			−1.27147			−0.635736	−	0.771906i	$-0.719303\pi$
$337$	−23.3411			−1.27147			−0.635736	+	0.771906i	$0.719303\pi$
$338$	9.23441	−	15.8973i	0.502286	−	0.864702i
$339$	−20.8428	+	4.37377i	−1.13202	+	0.237551i
$340$	−29.8862	−	8.16085i	−1.62081	−	0.442584i
$341$	14.3111	−	8.26250i	0.774988	−	0.447440i
$342$	4.56375	+	15.8467i	0.246779	+	0.856889i
$343$			17.2448i			0.931132i
$344$	−4.06717	−	5.37964i	−0.219287	−	0.290051i
$345$	2.00909	−	6.12919i	0.108166	−	0.329984i
$346$	18.2887	−	7.52440i	0.983205	−	0.404514i
$347$	4.49629	−	7.78780i	0.241374	−	0.418071i	−0.719732	−	0.694252i	$-0.755735\pi$
$347$	4.49629	−	7.78780i	0.241374	−	0.418071i	0.961106	+	0.276181i	$0.0890688\pi$
$348$	−6.96435	−	0.416414i	−0.373328	−	0.0223221i
$349$	−13.8208	−	23.9383i	−0.739809	−	1.28139i	−0.952581	−	0.304285i	$-0.901582\pi$
$349$	−13.8208	−	23.9383i	−0.739809	−	1.28139i	0.212772	−	0.977102i	$-0.431751\pi$
$350$	3.94171	−	1.62172i	0.210693	−	0.0866844i
$351$	14.4986	−	11.8655i	0.773878	−	0.633335i
$352$	−21.1764	+	8.47734i	−1.12870	+	0.451844i
$353$	1.88888	−	1.09054i	0.100535	−	0.0580438i	−0.448890	−	0.893587i	$-0.648180\pi$
$353$	1.88888	−	1.09054i	0.100535	−	0.0580438i	0.549424	+	0.835543i	$0.314847\pi$
$354$	−1.85701	−	0.897123i	−0.0986989	−	0.0476815i
$355$	25.5981	+	14.7791i	1.35861	+	0.784392i
$356$	−4.55896	−	4.60263i	−0.241624	−	0.243939i
$357$	−36.0426	−	11.8144i	−1.90758	−	0.625286i
$358$	23.2760	+	3.12080i	1.23018	+	0.164939i
$359$	−3.58192			−0.189046			−0.0945231	−	0.995523i	$-0.530133\pi$
$359$	−3.58192			−0.189046			−0.0945231	+	0.995523i	$0.530133\pi$
$360$	−14.6711	−	8.20174i	−0.773234	−	0.432270i
$361$	−1.94599	−	3.37055i	−0.102420	−	0.177397i
$362$	−8.87357	+	11.5074i	−0.466384	+	0.604814i
$363$	1.87088	+	8.91550i	0.0981958	+	0.467943i
$364$	−19.7860	−	4.03646i	−1.03707	−	0.211568i
$365$		−	5.21819i		−	0.273132i
$366$	−5.67675	−	2.74244i	−0.296729	−	0.143350i
$367$	29.3819	−	16.9636i	1.53372	−	0.885495i	0.534537	−	0.845145i	$-0.320486\pi$
$367$	29.3819	−	16.9636i	1.53372	−	0.885495i	0.999186	−	0.0403498i	$-0.0128472\pi$
$368$	−6.47631	−	3.82187i	−0.337601	−	0.199229i
$369$	5.03074	+	11.4589i	0.261890	+	0.596527i
$370$	1.94721	−	14.5230i	0.101231	−	0.755016i
$371$	−1.74732	+	3.02644i	−0.0907161	+	0.157125i
$372$	7.81936	−	11.8489i	0.405415	−	0.614336i
$373$	1.94382	−	3.36679i	0.100647	−	0.174326i	−0.811304	−	0.584624i	$-0.801242\pi$
$373$	1.94382	−	3.36679i	0.100647	−	0.174326i	0.911951	+	0.410298i	$0.134575\pi$
$374$	35.3139	+	27.2313i	1.82604	+	1.40809i
$375$	−13.9092	−	15.5286i	−0.718270	−	0.801894i
$376$	7.09151	+	2.99698i	0.365717	+	0.154557i
$377$	4.03359	+	6.03838i	0.207740	+	0.310992i
$378$	−17.4355	−	10.9299i	−0.896788	−	0.562174i
$379$	−15.2264	+	8.79094i	−0.782125	+	0.451560i	−0.837183	−	0.546923i	$-0.815799\pi$
$379$	−15.2264	+	8.79094i	−0.782125	+	0.451560i	0.0550576	+	0.998483i	$0.482466\pi$
$380$	−14.8548	−	4.05632i	−0.762037	−	0.208085i
$381$	−4.17953	+	12.7506i	−0.214124	+	0.653232i
$382$	−10.8216	−	26.3029i	−0.553683	−	1.34577i
$383$	−5.29523	+	9.17162i	−0.270574	+	0.468648i	−0.969009	−	0.247026i	$-0.920547\pi$
$383$	−5.29523	+	9.17162i	−0.270574	+	0.468648i	0.698435	+	0.715673i	$0.253880\pi$
$384$	−13.0114	+	14.6528i	−0.663985	+	0.747746i
$385$	22.3673			1.13994
$386$	−11.1962	−	1.50116i	−0.569870	−	0.0764069i
$387$	−4.23450	+	5.76513i	−0.215252	+	0.293058i
$388$	24.3477	+	6.64848i	1.23607	+	0.337526i
$389$			13.7221i			0.695737i	0.937543	+	0.347868i	$0.113094\pi$
$389$			13.7221i			0.695737i	−0.937543	+	0.347868i	$0.886906\pi$
$390$	2.42185	+	17.3259i	0.122635	+	0.877330i
$391$			14.7015i			0.743485i
$392$	0.293921	+	2.36298i	0.0148452	+	0.119348i
$393$	−14.7200	+	13.1849i	−0.742524	+	0.665091i
$394$	−2.87417	+	21.4366i	−0.144799	+	1.07996i
$395$	−14.1410			−0.711513
$396$	15.0377	+	18.9528i	0.755674	+	0.952414i
$397$	3.61632	−	6.26365i	0.181498	−	0.314364i	−0.760893	−	0.648878i	$-0.775239\pi$
$397$	3.61632	−	6.26365i	0.181498	−	0.314364i	0.942391	+	0.334514i	$0.108572\pi$
$398$	3.61571	−	1.48759i	0.181239	−	0.0745663i
$399$	−17.9148	−	5.87232i	−0.896864	−	0.293984i
$400$	−3.74862	+	2.11688i	−0.187431	+	0.105844i
$401$	8.45838	−	4.88345i	0.422391	−	0.243868i	−0.273709	−	0.961813i	$-0.588250\pi$
$401$	8.45838	−	4.88345i	0.422391	−	0.243868i	0.696100	+	0.717945i	$0.254917\pi$
$402$	10.3513	+	15.2230i	0.516274	+	0.759253i
$403$	−14.7446	+	0.964502i	−0.734480	+	0.0480453i
$404$	7.37902	+	7.44970i	0.367120	+	0.370636i
$405$	−3.88736	+	17.3986i	−0.193165	+	0.864543i
$406$	4.87060	−	6.31626i	0.241724	−	0.313471i
$407$	−10.5459	+	18.2661i	−0.522742	+	0.905415i
$408$	37.5987	+	7.34817i	1.86141	+	0.363789i
$409$	13.0347	−	22.5767i	0.644524	−	1.11635i	−0.339887	−	0.940466i	$-0.610389\pi$
$409$	13.0347	−	22.5767i	0.644524	−	1.11635i	0.984411	−	0.175882i	$-0.0562777\pi$
$410$	−11.5822	−	1.55292i	−0.572005	−	0.0766931i
$411$	9.22361	−	1.93554i	0.454967	−	0.0954730i
$412$	8.34012	−	2.19218i	0.410888	−	0.108001i
$413$	2.04187	−	1.17888i	0.100474	−	0.0580087i
$414$	−1.92066	+	7.74138i	−0.0943953	+	0.380468i
$415$		−	26.9625i		−	1.32354i
$416$	20.3349	+	1.57901i	0.996999	+	0.0774171i
$417$	6.75060	−	1.41659i	0.330578	−	0.0693705i
$418$	17.5526	+	13.5352i	0.858528	+	0.662028i
$419$	−14.5467	−	25.1957i	−0.710655	−	1.23089i	−0.964612	−	0.263675i	$-0.915065\pi$
$419$	−14.5467	−	25.1957i	−0.710655	−	1.23089i	0.253956	−	0.967216i	$-0.418268\pi$
$420$	17.1848	−	8.59737i	0.838535	−	0.419509i
$421$	−15.6745			−0.763927			−0.381964	−	0.924177i	$-0.624752\pi$
$421$	−15.6745			−0.763927			−0.381964	+	0.924177i	$0.624752\pi$
$422$	3.90268	−	29.1076i	0.189980	−	1.41694i
$423$	0.895695	−	8.11653i	0.0435502	−	0.394639i
$424$	1.37403	−	3.25127i	0.0667289	−	0.157895i
$425$	7.28878	+	4.20818i	0.353558	+	0.204127i
$426$	−32.9119	−	15.8998i	−1.59459	−	0.770347i
$427$	6.24187	−	3.60374i	0.302065	−	0.174397i
$428$	19.6573	−	19.4708i	0.950170	−	0.941155i
$429$	6.26503	−	24.3899i	0.302478	−	1.17756i
$430$	−2.54141	−	6.17710i	−0.122558	−	0.297886i
$431$	−3.63631	−	6.29827i	−0.175155	−	0.303377i	0.765060	−	0.643959i	$-0.222709\pi$
$431$	−3.63631	−	6.29827i	−0.175155	−	0.303377i	−0.940215	+	0.340582i	$0.889376\pi$
$432$	18.8384	+	8.78140i	0.906365	+	0.422495i
$433$	−6.50796	+	11.2721i	−0.312753	+	0.541704i	−0.978957	−	0.204066i	$-0.934584\pi$
$433$	−6.50796	+	11.2721i	−0.312753	+	0.541704i	0.666205	+	0.745769i	$0.267918\pi$
$434$	6.17512	+	15.0091i	0.296415	+	0.720462i
$435$	−6.56620	−	2.15234i	−0.314825	−	0.103197i
$436$	4.81793	+	18.3298i	0.230737	+	0.877838i
$437$			7.30731i			0.349556i
$438$	0.474248	+	6.43530i	0.0226604	+	0.307491i
$439$	23.4044	−	13.5125i	1.11703	−	0.644918i	0.176390	−	0.984320i	$-0.443558\pi$
$439$	23.4044	−	13.5125i	1.11703	−	0.644918i	0.940641	+	0.339402i	$0.110225\pi$
$440$	−22.4189	+	2.78859i	−1.06878	+	0.132941i
$441$	2.31258	−	1.01528i	0.110123	−	0.0483465i
$442$	−17.5461	−	35.8064i	−0.834582	−	1.70314i
$443$	7.59619			0.360906			0.180453	−	0.983584i	$-0.442244\pi$
$443$	7.59619			0.360906			0.180453	+	0.983584i	$0.442244\pi$
$444$	−1.08149	+	18.0874i	−0.0513252	+	0.858391i
$445$	−3.20812	−	5.55663i	−0.152080	−	0.263410i
$446$	0.209248	−	1.56065i	0.00990820	−	0.0738989i
$447$	1.24107	−	0.260434i	0.0587007	−	0.0123181i
$448$	−5.48824	−	21.7200i	−0.259295	−	1.02617i
$449$	−6.82867	−	3.94253i	−0.322265	−	0.186060i	0.330137	−	0.943933i	$-0.392905\pi$
$449$	−6.82867	−	3.94253i	−0.322265	−	0.186060i	−0.652402	+	0.757873i	$0.726238\pi$
$450$	3.28830	+	3.16815i	0.155012	+	0.149348i
$451$	14.5673	+	8.41044i	0.685948	+	0.396032i
$452$	−6.47785	+	23.7228i	−0.304693	+	1.11583i
$453$	14.7000	+	16.4115i	0.690668	+	0.771079i
$454$	−2.12941	−	5.17570i	−0.0999380	−	0.242908i
$455$	−17.9364	−	8.84812i	−0.840871	−	0.414806i
$456$	18.6883	+	3.65238i	0.875160	+	0.171038i
$457$	7.82778	+	13.5581i	0.366168	+	0.634222i	0.988963	−	0.148164i	$-0.0473362\pi$
$457$	7.82778	+	13.5581i	0.366168	+	0.634222i	−0.622795	+	0.782385i	$0.714003\pi$
$458$	3.10630	−	4.02829i	0.145148	−	0.188230i
$459$	−3.93268	−	40.4432i	−0.183562	−	1.88772i
$460$	−5.24130	−	5.29150i	−0.244377	−	0.246717i
$461$	34.1273	+	19.7034i	1.58947	+	0.917679i	0.993395	+	0.114749i	$0.0366063\pi$
$461$	34.1273	+	19.7034i	1.58947	+	0.917679i	0.596072	+	0.802931i	$0.296727\pi$
$462$	−27.5844	+	2.03282i	−1.28334	+	0.0945753i
$463$		−	34.9373i		−	1.62367i	−0.583884	−	0.811837i	$-0.698468\pi$
$463$		−	34.9373i		−	1.62367i	0.583884	−	0.811837i	$-0.301532\pi$
$464$	−4.09437	+	6.93807i	−0.190076	+	0.322092i
$465$	10.4733	−	9.38113i	0.485689	−	0.435039i
$466$	−0.951949	−	0.734067i	−0.0440982	−	0.0340050i
$467$	−22.6893			−1.04994			−0.524969	−	0.851121i	$-0.675923\pi$
$467$	−22.6893			−1.04994			−0.524969	+	0.851121i	$0.675923\pi$
$468$	−4.56138	−	21.1470i	−0.210850	−	0.977518i
$469$	−21.0457			−0.971798
$470$	6.03828	+	4.65624i	0.278525	+	0.214776i
$471$	22.1163	−	19.8099i	1.01906	−	0.912793i
$472$	−1.89961	+	1.43616i	−0.0874367	+	0.0661047i
$473$			9.61458i			0.442079i
$474$	17.4394	−	1.28519i	0.801016	−	0.0590306i
$475$	3.62286	+	2.09166i	0.166228	+	0.0959720i
$476$	−31.1166	+	30.8214i	−1.42623	+	1.41269i
$477$	−3.72121	−	0.410652i	−0.170382	−	0.0188025i
$478$	−2.10948	+	2.73561i	−0.0964856	+	0.125124i
$479$	−3.31239	−	5.73723i	−0.151347	−	0.262141i	0.780376	−	0.625311i	$-0.215028\pi$
$479$	−3.31239	−	5.73723i	−0.151347	−	0.262141i	−0.931723	+	0.363170i	$0.881694\pi$
$480$	−16.1526	+	10.7597i	−0.737264	+	0.491110i
$481$	15.6825	−	10.4758i	0.715062	−	0.477656i
$482$	−7.48056	−	18.1821i	−0.340730	−	0.828172i
$483$	−6.08387	−	6.79219i	−0.276826	−	0.309055i
$484$	10.1474	+	2.77090i	0.461247	+	0.125950i
$485$	21.6483	+	12.4987i	0.983001	+	0.567536i
$486$	3.21283	−	21.8100i	0.145737	−	0.989323i
$487$	2.69276	+	1.55467i	0.122021	+	0.0704487i	0.559768	−	0.828649i	$-0.310890\pi$
$487$	2.69276	+	1.55467i	0.122021	+	0.0704487i	−0.437747	+	0.899098i	$0.644224\pi$
$488$	−5.80698	+	4.39025i	−0.262870	+	0.198737i
$489$	27.0148	−	5.66894i	1.22165	−	0.256359i
$490$	−0.313401	+	2.33746i	−0.0141580	+	0.105596i
$491$	2.24938	+	3.89604i	0.101513	+	0.175826i	0.912308	−	0.409504i	$-0.134298\pi$
$491$	2.24938	+	3.89604i	0.101513	+	0.175826i	−0.810795	+	0.585330i	$0.800965\pi$
$492$	14.4248	+	0.862495i	0.650322	+	0.0388843i
$493$	15.7497			0.709330
$494$	−8.72121	−	17.7974i	−0.392386	−	0.800745i
$495$	9.63252	+	21.9407i	0.432950	+	0.986163i
$496$	−8.06061	−	14.2739i	−0.361932	−	0.640917i
$497$	36.1883	−	20.8933i	1.62327	−	0.937193i
$498$	2.45045	+	33.2514i	0.109807	+	1.49003i
$499$		−	6.63001i		−	0.296800i	−0.988927	−	0.148400i	$-0.952588\pi$
$499$		−	6.63001i		−	0.296800i	0.988927	−	0.148400i	$-0.0474123\pi$
$500$	−23.2814	+	6.11946i	−1.04118	+	0.273670i
$501$	−30.4835	−	9.99222i	−1.36190	−	0.446419i
$502$	10.0255	+	24.3678i	0.447461	+	1.08759i
$503$	21.1482	−	36.6298i	0.942952	−	1.63324i	0.183152	−	0.983085i	$-0.441370\pi$
$503$	21.1482	−	36.6298i	0.942952	−	1.63324i	0.759800	−	0.650157i	$-0.225297\pi$
$504$	−20.4118	+	12.1645i	−0.909213	+	0.541849i
$505$	5.19258	+	8.99382i	0.231067	+	0.400220i
$506$	4.07901	+	9.91436i	0.181334	+	0.440747i
$507$	−14.6722	+	17.0800i	−0.651615	+	0.758550i
$508$	10.9035	+	11.0079i	0.483765	+	0.488399i
$509$	−12.2759	+	7.08748i	−0.544118	+	0.314147i	−0.746746	−	0.665109i	$-0.768385\pi$
$509$	−12.2759	+	7.08748i	−0.544118	+	0.314147i	0.202628	+	0.979256i	$0.435052\pi$
$510$	34.1651	+	16.5052i	1.51286	+	0.730862i
$511$	−6.38867	−	3.68850i	−0.282618	−	0.163170i
$512$	8.20880	+	21.0859i	0.362781	+	0.931874i
$513$	−1.95472	−	20.1021i	−0.0863032	−	0.887531i
$514$	5.24249	−	39.1004i	0.231236	−	1.72464i
$515$	8.54082			0.376353
$516$	3.69558	+	7.38691i	0.162689	+	0.325190i
$517$	−5.48784	−	9.50521i	−0.241355	−	0.418039i
$518$	−16.4043	−	12.6497i	−0.720761	−	0.555794i
$519$	−23.7043	+	4.97425i	−1.04050	+	0.218346i
$520$	19.0809	+	6.63236i	0.836753	+	0.290848i
$521$		−	33.0887i		−	1.44964i	−0.688938	−	0.724820i	$-0.741923\pi$
$521$		−	33.0887i		−	1.44964i	0.688938	−	0.724820i	$-0.258077\pi$
$522$	8.29335	+	2.05760i	0.362990	+	0.0900589i
$523$	−24.6943	+	14.2572i	−1.07981	+	0.623426i	−0.930844	−	0.365417i	$-0.880926\pi$
$523$	−24.6943	+	14.2572i	−1.07981	+	0.623426i	−0.148961	+	0.988843i	$0.547593\pi$
$524$	5.80079	+	22.0691i	0.253409	+	0.964091i
$525$	−5.10893	+	1.07209i	−0.222972	+	0.0467898i
$526$	−39.4082	−	5.28377i	−1.71828	−	0.230383i
$527$	−16.0238	+	27.7540i	−0.698007	+	1.20898i
$528$	27.3946	−	5.47653i	1.19220	−	0.238335i
$529$	9.73284	−	16.8578i	0.423167	−	0.732946i
$530$	2.13476	−	2.76839i	0.0927280	−	0.120251i
$531$	2.03573	+	1.49525i	0.0883432	+	0.0648883i
$532$	−15.4664	+	15.3197i	−0.670553	+	0.664191i
$533$	−8.35454	−	12.5069i	−0.361875	−	0.541736i
$534$	4.46141	+	6.56112i	0.193064	+	0.283928i
$535$	23.7317	−	13.7015i	1.02601	−	0.592368i
$536$	21.0942	−	2.62382i	0.911132	−	0.113332i
$537$	−27.3314	−	8.95899i	−1.17944	−	0.386609i
$538$	7.99697	−	3.29015i	0.344774	−	0.141848i
$539$	1.69735	−	2.93990i	0.0731101	−	0.126630i
$540$	15.8341	+	13.1547i	0.681391	+	0.566086i
$541$	9.76861			0.419985			0.209993	−	0.977703i	$-0.432656\pi$
$541$	9.76861			0.419985			0.209993	+	0.977703i	$0.432656\pi$
$542$	−1.28276	+	9.56731i	−0.0550994	+	0.410951i
$543$	13.2567	−	11.8743i	0.568901	−	0.509574i
$544$	27.3458	−	34.7719i	1.17244	−	1.49083i
$545$			18.7709i			0.804056i
$546$	22.9241	+	9.28178i	0.981061	+	0.397224i
$547$			18.5829i			0.794549i	0.917700	+	0.397275i	$0.130044\pi$
$547$			18.5829i			0.794549i	−0.917700	+	0.397275i	$0.869956\pi$
$548$	2.86666	−	10.4981i	0.122458	−	0.448458i
$549$	6.22309	+	4.57088i	0.265595	+	0.195080i
$550$	6.08298	+	0.815593i	0.259379	+	0.0347770i
$551$	7.82832			0.333498
$552$	6.94471	+	6.04937i	0.295587	+	0.257478i
$553$	−9.99565	+	17.3130i	−0.425058	+	0.736222i
$554$	11.6275	+	28.2616i	0.494005	+	1.20072i
$555$	−5.58994	+	17.0534i	−0.237280	+	0.723875i
$556$	2.09806	−	7.68340i	0.0889776	−	0.325849i
$557$	16.0205	−	9.24946i	0.678812	−	0.391912i	−0.120595	−	0.992702i	$-0.538480\pi$
$557$	16.0205	−	9.24946i	0.678812	−	0.391912i	0.799407	+	0.600790i	$0.205147\pi$
$558$	−12.0636	+	12.5211i	−0.510692	+	0.530060i
$559$	3.80336	−	7.70995i	0.160865	−	0.326096i
$560$	0.211509	−	22.1871i	0.00893789	−	0.937576i
$561$	−36.4399	−	40.6824i	−1.53849	−	1.71761i
$562$	0.799020	+	0.616140i	0.0337046	+	0.0259903i
$563$	−9.52361	+	16.4954i	−0.401372	+	0.695198i	−0.993892	−	0.110359i	$-0.964800\pi$
$563$	−9.52361	+	16.4954i	−0.401372	+	0.695198i	0.592519	+	0.805556i	$0.298133\pi$
$564$	−7.86986	−	5.19351i	−0.331381	−	0.218686i
$565$	−12.1779	+	21.0927i	−0.512328	+	0.887379i
$566$	−0.347651	+	2.59291i	−0.0146129	+	0.108988i
$567$	18.5534	+	17.0576i	0.779171	+	0.716352i
$568$	−33.6669	+	25.4532i	−1.41263	+	1.06799i
$569$	−16.6680	+	9.62328i	−0.698759	+	0.403429i	−0.806885	−	0.590708i	$-0.798848\pi$
$569$	−16.6680	+	9.62328i	−0.698759	+	0.403429i	0.108126	+	0.994137i	$0.465515\pi$
$570$	16.9817	+	8.20385i	0.711283	+	0.343621i
$571$			14.9433i			0.625357i	0.949859	+	0.312678i	$0.101226\pi$
$571$			14.9433i			0.625357i	−0.949859	+	0.312678i	$0.898774\pi$
$572$	−21.7674	−	19.2788i	−0.910141	−	0.806088i
$573$	7.15400	+	34.0917i	0.298863	+	1.42420i
$574$	−10.0882	+	13.0825i	−0.421073	+	0.546053i
$575$	1.01167	+	1.75227i	0.0421898	+	0.0730748i
$576$	18.9423	−	14.7373i	0.789262	−	0.614056i
$577$	−10.5158			−0.437777			−0.218889	−	0.975750i	$-0.570243\pi$
$577$	−10.5158			−0.437777			−0.218889	+	0.975750i	$0.570243\pi$
$578$	−61.8871	−	8.29769i	−2.57417	−	0.345138i
$579$	13.1469	+	4.30943i	0.546365	+	0.179094i
$580$	−5.66879	+	5.61500i	−0.235384	+	0.233150i
$581$	−33.0104	−	19.0586i	−1.36950	−	0.790683i
$582$	−27.8336	−	13.4465i	−1.15374	−	0.557373i
$583$	−4.35788	+	2.51602i	−0.180485	+	0.104203i
$584$	6.86327	+	2.90052i	0.284004	+	0.120024i
$585$	0.955047	−	21.4048i	0.0394863	−	0.884980i
$586$	−8.25480	+	3.39623i	−0.341003	+	0.140297i
$587$	10.4007	+	18.0146i	0.429284	+	0.743542i	0.996810	−	0.0798138i	$-0.0254326\pi$
$587$	10.4007	+	18.0146i	0.429284	+	0.743542i	−0.567526	+	0.823356i	$0.692099\pi$
$588$	0.174064	−	2.91115i	0.00717828	−	0.120054i
$589$	−7.96457	+	13.7950i	−0.328174	+	0.568414i
$590$	−2.18120	+	0.897399i	−0.0897986	+	0.0369453i
$591$	8.25099	−	25.1715i	0.339400	−	1.03542i
$592$	18.0192	+	10.6337i	0.740584	+	0.437041i
$593$			33.8531i			1.39018i	0.718922	+	0.695090i	$0.244636\pi$
$593$			33.8531i			1.39018i	−0.718922	+	0.695090i	$0.755364\pi$
$594$	−13.8733	−	26.1829i	−0.569229	−	1.07430i
$595$	−37.5662	+	21.6889i	−1.54006	+	0.889157i
$596$	0.385721	−	1.41256i	0.0157997	−	0.0578608i
$597$	−4.68640	+	0.983422i	−0.191802	+	0.0402488i
$598$	0.650986	−	9.56393i	0.0266208	−	0.391098i
$599$	−13.5256			−0.552642			−0.276321	−	0.961065i	$-0.589115\pi$
$599$	−13.5256			−0.552642			−0.276321	+	0.961065i	$0.589115\pi$
$600$	4.98706	−	1.71151i	0.203596	−	0.0698720i
$601$	4.97195	+	8.61168i	0.202810	+	0.351278i	0.949433	−	0.313970i	$-0.101659\pi$
$601$	4.97195	+	8.61168i	0.202810	+	0.351278i	−0.746623	+	0.665248i	$0.768326\pi$
$602$	−9.35907	−	1.25484i	−0.381447	−	0.0511436i
$603$	−9.06335	−	20.6443i	−0.369088	−	0.840701i
$604$	24.6051	−	6.46738i	1.00117	−	0.263154i
$605$	9.02243	+	5.20910i	0.366814	+	0.211780i
$606$	−7.22112	−	10.6197i	−0.293338	−	0.431394i
$607$	−20.0249	−	11.5614i	−0.812786	−	0.469262i	0.0351367	−	0.999383i	$-0.488813\pi$
$607$	−20.0249	−	11.5614i	−0.812786	−	0.469262i	−0.847922	+	0.530121i	$0.822147\pi$
$608$	13.5921	−	17.2832i	0.551234	−	0.700928i
$609$	−7.27647	+	6.51766i	−0.294858	+	0.264109i
$610$	−6.66779	+	2.74329i	−0.269971	+	0.111073i
$611$	0.640608	+	9.79315i	0.0259162	+	0.396188i
$612$	−43.6340	−	17.2499i	−1.76380	−	0.697286i
$613$	−13.2467	−	22.9439i	−0.535029	−	0.926697i	−0.999162	−	0.0409317i	$-0.986967\pi$
$613$	−13.2467	−	22.9439i	−0.535029	−	0.926697i	0.464133	−	0.885765i	$-0.346366\pi$
$614$	−2.48048	−	1.91275i	−0.100104	−	0.0771923i
$615$	13.6002	+	4.45802i	0.548412	+	0.179765i
$616$	−12.4328	+	29.4188i	−0.500932	+	1.18532i
$617$	29.4281	+	16.9903i	1.18473	+	0.684003i	0.957104	−	0.289745i	$-0.0935706\pi$
$617$	29.4281	+	16.9903i	1.18473	+	0.684003i	0.227625	+	0.973749i	$0.426904\pi$
$618$	−10.5329	+	0.776220i	−0.423696	+	0.0312242i
$619$			13.2158i			0.531187i	0.964085	+	0.265593i	$0.0855678\pi$
$619$			13.2158i			0.531187i	−0.964085	+	0.265593i	$0.914432\pi$
$620$	−4.12729	−	15.7022i	−0.165756	−	0.630617i
$621$	4.04263	−	8.89292i	0.162225	−	0.356861i
$622$	−21.9665	+	28.4864i	−0.880775	+	1.14220i
$623$	−9.07070			−0.363410
$624$	−24.1342	−	6.44519i	−0.966141	−	0.258014i
$625$	−18.4604			−0.738414
$626$	23.6774	−	30.7052i	0.946339	−	1.22723i
$627$	−18.1123	−	20.2210i	−0.723336	−	0.807550i
$628$	−8.71550	−	33.1581i	−0.347786	−	1.32315i
$629$		−	40.9042i		−	1.63096i
$630$	−22.6149	+	6.51295i	−0.900998	+	0.259482i
$631$	7.34162	+	4.23869i	0.292265	+	0.168739i	0.638963	−	0.769238i	$-0.279364\pi$
$631$	7.34162	+	4.23869i	0.292265	+	0.168739i	−0.346698	+	0.937977i	$0.612697\pi$
$632$	7.86026	−	18.5991i	0.312664	−	0.739833i
$633$	−11.2036	+	34.1790i	−0.445302	+	1.35849i
$634$	14.8878	+	11.4803i	0.591269	+	0.455940i
$635$	7.67275	+	13.2896i	0.304484	+	0.527382i
$636$	−2.38108	+	3.60812i	−0.0944160	+	0.143071i
$637$	−2.52408	+	1.68607i	−0.100008	+	0.0668044i
$638$	10.6213	−	4.36984i	0.420499	−	0.173004i
$639$	36.0794	+	26.5004i	1.42728	+	1.04834i
$640$	2.55413	+	22.2647i	0.100961	+	0.880088i
$641$	12.4529	+	7.18968i	0.491860	+	0.283975i	0.725346	−	0.688385i	$-0.241680\pi$
$641$	12.4529	+	7.18968i	0.491860	+	0.283975i	−0.233486	+	0.972360i	$0.575013\pi$
$642$	−28.0218	+	19.0541i	−1.10593	+	0.752007i
$643$	7.39212	+	4.26784i	0.291517	+	0.168307i	0.638626	−	0.769518i	$-0.279503\pi$
$643$	7.39212	+	4.26784i	0.291517	+	0.168307i	−0.347109	+	0.937825i	$0.612837\pi$
$644$	−10.1833	+	2.67664i	−0.401277	+	0.105474i
$645$	1.68008	+	8.00627i	0.0661532	+	0.315246i
$646$	−42.6046	−	5.71233i	−1.67626	−	0.224749i
$647$	16.2864	+	28.2089i	0.640285	+	1.10901i	0.985369	+	0.170435i	$0.0545172\pi$
$647$	16.2864	+	28.2089i	0.640285	+	1.10901i	−0.345084	+	0.938572i	$0.612149\pi$
$648$	−20.7229	−	14.7839i	−0.814071	−	0.580765i
$649$	3.39501			0.133266
$650$	−4.55533	−	3.06035i	−0.178675	−	0.120037i
$651$	−4.08227	−	19.4537i	−0.159997	−	0.762449i
$652$	8.39610	−	30.7477i	0.328817	−	1.20417i
$653$	−33.8257	+	19.5293i	−1.32370	+	0.764240i	−0.984317	−	0.176407i	$-0.943553\pi$
$653$	−33.8257	+	19.5293i	−1.32370	+	0.764240i	−0.339386	+	0.940647i	$0.610219\pi$
$654$	−1.70596	−	23.1491i	−0.0667085	−	0.905201i
$655$			22.6001i			0.883060i
$656$	8.48044	−	14.3704i	0.331105	−	0.561071i
$657$	0.866866	−	7.85529i	0.0338197	−	0.306464i
$658$	9.96886	−	4.10143i	0.388626	−	0.159890i
$659$	6.42459	−	11.1277i	0.250266	−	0.433474i	−0.713333	−	0.700826i	$-0.752815\pi$
$659$	6.42459	−	11.1277i	0.250266	−	0.433474i	0.963599	+	0.267351i	$0.0861485\pi$
$660$	27.6197	+	1.65145i	1.07510	+	0.0642824i
$661$	11.7808	+	20.4049i	0.458219	+	0.793658i	0.998867	−	0.0475909i	$-0.0151544\pi$
$661$	11.7808	+	20.4049i	0.458219	+	0.793658i	−0.540648	+	0.841249i	$0.681821\pi$
$662$	42.3963	−	17.4429i	1.64778	−	0.677936i
$663$	13.1280	+	47.0383i	0.509848	+	1.82682i
$664$	35.4627	+	14.9870i	1.37622	+	0.581610i
$665$	−18.6722	+	10.7804i	−0.724075	+	0.418045i
$666$	5.34390	−	21.5390i	0.207072	−	0.834620i
$667$	3.27906	+	1.89316i	0.126966	+	0.0733036i
$668$	−26.3173	+	26.0676i	−1.01825	+	1.00859i
$669$	−0.600698	+	1.83256i	−0.0232243	+	0.0708510i
$670$	20.8665	+	2.79773i	0.806141	+	0.108086i
$671$	10.3783			0.400651
$672$	1.75560	+	27.3813i	0.0677237	+	1.05626i
$673$	11.7674	+	20.3818i	0.453602	+	0.785661i	0.998607	−	0.0527718i	$-0.0168056\pi$
$673$	11.7674	+	20.3818i	0.453602	+	0.785661i	−0.545005	+	0.838433i	$0.683472\pi$
$674$	20.1572	−	26.1401i	0.776425	−	1.00688i
$675$	−3.25182	−	4.54981i	−0.125162	−	0.175122i
$676$	9.82896	+	24.0706i	0.378037	+	0.925791i
$677$			28.4274i			1.09255i	0.837605	+	0.546276i	$0.183955\pi$
$677$			28.4274i			1.09255i	−0.837605	+	0.546276i	$0.816045\pi$
$678$	13.1014	−	27.1193i	0.503155	−	1.04151i
$679$	30.6044	−	17.6695i	1.17449	−	0.678093i
$680$	34.9489	−	26.4224i	1.34023	−	1.01325i
$681$	1.40771	+	6.70833i	0.0539438	+	0.257064i
$682$	−3.10559	+	23.1626i	−0.118919	+	0.886942i
$683$	12.6467	−	21.9047i	0.483911	−	0.838158i	−0.515918	−	0.856638i	$-0.672549\pi$
$683$	12.6467	−	21.9047i	0.483911	−	0.838158i	0.999829	+	0.0184794i	$0.00588250\pi$
$684$	−21.6881	−	8.57401i	−0.829267	−	0.327835i
$685$	5.38912	−	9.33424i	0.205908	−	0.356643i
$686$	−19.3127	−	14.8924i	−0.737364	−	0.568596i
$687$	−4.64068	+	4.15673i	−0.177053	+	0.158589i
$688$	9.53712	+	0.0909171i	0.363599	+	0.00346618i
$689$	4.48989	−	0.293701i	0.171051	−	0.0111891i
$690$	5.12914	+	7.54312i	0.195263	+	0.287162i
$691$	−35.7171	+	20.6213i	−1.35874	+	0.784471i	−0.989455	−	0.144843i	$-0.953732\pi$
$691$	−35.7171	+	20.6213i	−1.35874	+	0.784471i	−0.369290	+	0.929314i	$0.620399\pi$
$692$	−7.36722	+	26.9798i	−0.280060	+	1.02562i
$693$	33.6710	+	3.71574i	1.27906	+	0.141149i
$694$	4.83874	+	11.7609i	0.183676	+	0.446439i
$695$	3.94421	−	6.83157i	0.149612	−	0.259136i
$696$	6.48069	−	7.43988i	0.245650	−	0.282008i
$697$	−32.6214			−1.23562
$698$	38.7444	+	5.19476i	1.46650	+	0.196624i
$699$	0.982301	+	1.09667i	0.0371541	+	0.0414797i
$700$	−1.58784	+	5.81489i	−0.0600146	+	0.219782i
$701$		−	17.2824i		−	0.652747i	−0.945241	−	0.326374i	$-0.894173\pi$
$701$		−	17.2824i		−	0.652747i	0.945241	−	0.326374i	$-0.105827\pi$
$702$	0.767538	+	26.4842i	0.0289688	+	0.999580i
$703$		−	20.3313i		−	0.766809i
$704$	8.79378	−	31.0367i	0.331428	−	1.16974i
$705$	−6.23081	−	6.95623i	−0.234666	−	0.261987i
$706$	−0.409898	+	3.05717i	−0.0154267	+	0.115058i
$707$	14.6816			0.552158
$708$	2.60840	−	1.30495i	0.0980296	−	0.0490430i
$709$	16.5524	−	28.6696i	0.621639	−	1.07671i	−0.367542	−	0.930007i	$-0.619801\pi$
$709$	16.5524	−	28.6696i	0.621639	−	1.07671i	0.989181	−	0.146703i	$-0.0468661\pi$
$710$	−38.6576	+	15.9047i	−1.45079	+	0.596892i
$711$	−21.2875	−	2.34916i	−0.798342	−	0.0881006i
$712$	9.09163	−	1.13087i	0.340723	−	0.0423811i
$713$	−6.67225	+	3.85223i	−0.249878	+	0.144267i
$714$	44.3572	−	30.1618i	1.66003	−	1.12878i
$715$	−15.9967	−	23.9474i	−0.598242	−	0.895583i
$716$	−23.5960	+	23.3721i	−0.881823	+	0.873456i
$717$	3.15148	−	2.82283i	0.117694	−	0.105421i
$718$	3.09331	−	4.01144i	0.115441	−	0.149706i
$719$	−0.122727	+	0.212570i	−0.00457695	+	0.00792751i	−0.868305	−	0.496031i	$-0.834790\pi$
$719$	−0.122727	+	0.212570i	−0.00457695	+	0.00792751i	0.863728	+	0.503959i	$0.168124\pi$
$720$	21.8551	−	9.34744i	0.814490	−	0.348358i
$721$	6.03711	−	10.4566i	0.224834	−	0.389424i
$722$	5.45527	+	0.731430i	0.203024	+	0.0272210i
$723$	4.94527	+	23.5662i	0.183917	+	0.876436i
$724$	−5.22417	−	19.8753i	−0.194155	−	0.738660i
$725$	1.87721	−	1.08381i	0.0697178	−	0.0402516i
$726$	−11.6003	−	5.60411i	−0.430527	−	0.207988i
$727$			22.0505i			0.817806i	0.912578	+	0.408903i	$0.134089\pi$
$727$			22.0505i			0.817806i	−0.912578	+	0.408903i	$0.865911\pi$
$728$	21.6075	−	18.6728i	0.800826	−	0.692059i
$729$	−8.74224	+	25.5455i	−0.323787	+	0.946130i
$730$	5.84393	+	4.50638i	0.216294	+	0.166788i
$731$	−9.32296	−	16.1478i	−0.344822	−	0.597249i
$732$	7.97370	−	3.98914i	0.294716	−	0.147443i
$733$	53.3800			1.97164			0.985818	−	0.167818i	$-0.0536722\pi$
$733$	53.3800			1.97164			0.985818	+	0.167818i	$0.0536722\pi$
$734$	−6.37605	+	47.5549i	−0.235344	+	1.75528i
$735$	0.899693	−	2.74472i	0.0331857	−	0.101240i
$736$	9.87305	−	3.95239i	0.363926	−	0.145687i
$737$	−26.2444	−	15.1522i	−0.966724	−	0.558139i
$738$	−17.1775	−	4.26180i	−0.632313	−	0.156879i
$739$	23.7188	−	13.6941i	0.872510	−	0.503744i	0.00432869	−	0.999991i	$-0.498622\pi$
$739$	23.7188	−	13.6941i	0.872510	−	0.503744i	0.868182	+	0.496247i	$0.165289\pi$
$740$	14.5830	+	14.7227i	0.536081	+	0.541216i
$741$	6.52520	+	23.3802i	0.239709	+	0.858894i
$742$	−1.88039	−	4.57045i	−0.0690314	−	0.167786i
$743$	15.7175	+	27.2235i	0.576619	+	0.998733i	0.995864	+	0.0908602i	$0.0289616\pi$
$743$	15.7175	+	27.2235i	0.576619	+	0.998733i	−0.419245	+	0.907873i	$0.637705\pi$
$744$	6.51703	+	18.9896i	0.238926	+	0.696193i
$745$	0.725127	−	1.25596i	0.0265666	−	0.0460147i
$746$	2.09186	+	5.08443i	0.0765884	+	0.186154i
$747$	4.47912	−	40.5885i	0.163882	−	1.48506i
$748$	−60.9935	+	16.0320i	−2.23014	+	0.586186i
$749$		−	38.7399i		−	1.41552i
$750$	29.4026	−	2.16682i	1.07363	−	0.0791209i
$751$	−17.5626	+	10.1398i	−0.640868	+	0.370005i	−0.784949	−	0.619561i	$-0.787311\pi$
$751$	−17.5626	+	10.1398i	−0.640868	+	0.370005i	0.144081	+	0.989566i	$0.453977\pi$
$752$	−9.48052	+	5.35374i	−0.345719	+	0.195231i
$753$	−6.62770	−	31.5837i	−0.241527	−	1.15097i
$754$	−10.2458	−	0.697402i	−0.373132	−	0.0253979i
$755$	25.1972			0.917019
$756$	27.2978	−	10.0874i	0.992810	−	0.366875i
$757$	−4.57964	−	7.93216i	−0.166450	−	0.288299i	0.770719	−	0.637175i	$-0.219897\pi$
$757$	−4.57964	−	7.93216i	−0.166450	−	0.288299i	−0.937169	+	0.348875i	$0.886564\pi$
$758$	3.30421	−	24.6440i	0.120014	−	0.895111i
$759$	−2.69656	−	12.8502i	−0.0978790	−	0.466433i
$760$	17.3712	−	13.1332i	0.630121	−	0.476390i
$761$	−3.99740	−	2.30790i	−0.144905	−	0.0836612i	0.425794	−	0.904820i	$-0.359995\pi$
$761$	−3.99740	−	2.30790i	−0.144905	−	0.0836612i	−0.570700	+	0.821159i	$0.693328\pi$
$762$	−10.6702	−	15.6920i	−0.386540	−	0.568461i
$763$	22.9813	+	13.2683i	0.831980	+	0.480344i
$764$	38.8025	+	10.5956i	1.40382	+	0.383334i
$765$	−37.4532	−	27.5095i	−1.35412	−	0.994607i
$766$	−5.69853	−	13.8507i	−0.205896	−	0.500447i
$767$	−2.72247	−	1.34301i	−0.0983027	−	0.0484933i
$768$	−5.17336	−	27.2257i	−0.186678	−	0.982421i
$769$	6.18090	+	10.7056i	0.222889	+	0.386055i	0.955684	−	0.294394i	$-0.0951179\pi$
$769$	6.18090	+	10.7056i	0.222889	+	0.386055i	−0.732795	+	0.680450i	$0.761785\pi$
$770$	−19.3162	+	25.0495i	−0.696107	+	0.902721i
$771$	−15.0498	+	45.9129i	−0.542006	+	1.65351i
$772$	11.3501	−	11.2424i	0.408498	−	0.404622i
$773$	−2.81129	−	1.62310i	−0.101115	−	0.0583788i	0.448590	−	0.893738i	$-0.351926\pi$
$773$	−2.81129	−	1.62310i	−0.101115	−	0.0583788i	−0.549705	+	0.835359i	$0.685260\pi$
$774$	−2.79959	−	9.72100i	−0.100629	−	0.349414i
$775$			4.41068i			0.158436i
$776$	−28.4722	+	21.5258i	−1.02209	+	0.772731i
$777$	16.9273	+	18.8981i	0.607263	+	0.677964i
$778$	−15.3676	−	11.8502i	−0.550954	−	0.424852i
$779$	−16.2143			−0.580939
$780$	−21.4950	−	12.2502i	−0.769645	−	0.438627i
$781$	60.1701			2.15305
$782$	−16.4644	−	12.6960i	−0.588766	−	0.454009i
$783$	−9.52699	−	4.33087i	−0.340467	−	0.154773i
$784$	−2.90016	−	1.71148i	−0.103577	−	0.0611241i
$785$		−	33.9560i		−	1.21194i
$786$	−2.05398	−	27.8715i	−0.0732631	−	0.994143i
$787$	1.24966	+	0.721491i	0.0445455	+	0.0257184i	0.522107	−	0.852880i	$-0.325146\pi$
$787$	1.24966	+	0.721491i	0.0445455	+	0.0257184i	−0.477562	+	0.878598i	$0.658479\pi$
$788$	−21.5251	−	21.7313i	−0.766799	−	0.774144i
$789$	46.2743	+	15.1683i	1.64741	+	0.540006i
$790$	12.2121	−	15.8368i	0.434485	−	0.563447i
$791$	17.2160	+	29.8190i	0.612131	+	1.06024i
$792$	−34.2120	+	0.473541i	−1.21567	+	0.0168266i
$793$	−8.32241	−	4.10549i	−0.295537	−	0.145790i
$794$	3.89175	+	9.45921i	0.138113	+	0.335695i
$795$	−3.18924	+	2.85666i	−0.113111	+	0.101315i
$796$	−1.45652	+	5.33397i	−0.0516248	+	0.189057i
$797$	2.03875	+	1.17707i	0.0722162	+	0.0416940i	0.535673	−	0.844425i	$-0.320058\pi$
$797$	2.03875	+	1.17707i	0.0722162	+	0.0416940i	−0.463457	+	0.886119i	$0.653391\pi$
$798$	22.0476	−	14.9918i	0.780476	−	0.530705i
$799$	18.4338	+	10.6428i	0.652141	+	0.376514i
$800$	0.866544	−	6.02626i	0.0306369	−	0.213061i
$801$	−3.90631	−	8.89772i	−0.138023	−	0.314385i
$802$	−1.83552	+	13.6900i	−0.0648145	+	0.483410i
$803$	−5.31120	−	9.19927i	−0.187428	−	0.324635i
$804$	−25.9877	−	1.55386i	−0.916516	−	0.0548006i
$805$	−10.4283			−0.367549
$806$	11.6531	−	17.3456i	0.410464	−	0.610974i
$807$	−10.3650	+	2.17506i	−0.364867	+	0.0765657i
$808$	−14.7155	+	1.83040i	−0.517689	+	0.0643931i
$809$	9.09309	−	5.24990i	0.319696	−	0.184577i	−0.331561	−	0.943434i	$-0.607575\pi$
$809$	9.09309	−	5.24990i	0.319696	−	0.184577i	0.651257	+	0.758857i	$0.274242\pi$
$810$	−16.1279	−	19.3788i	−0.566676	−	0.680901i
$811$		−	38.1116i		−	1.33828i	−0.743137	−	0.669139i	$-0.766663\pi$
$811$		−	38.1116i		−	1.33828i	0.743137	−	0.669139i	$-0.233337\pi$
$812$	2.86749	+	10.9093i	0.100629	+	0.382842i
$813$	3.68248	−	11.2342i	0.129150	−	0.394001i
$814$	−11.3491	−	27.5849i	−0.397786	−	0.966851i
$815$	15.7841	−	27.3388i	0.552892	−	0.957636i
$816$	−40.6992	+	35.7616i	−1.42476	+	1.25191i
$817$	−4.63394	−	8.02623i	−0.162121	−	0.280802i
$818$	14.0274	+	34.0948i	0.490458	+	1.19210i
$819$	−25.5310	−	16.2993i	−0.892125	−	0.569545i
$820$	11.7414	−	11.6300i	0.410028	−	0.406138i
$821$	−48.0908	+	27.7652i	−1.67838	+	0.969013i	−0.715686	+	0.698422i	$0.753886\pi$
$821$	−48.0908	+	27.7652i	−1.67838	+	0.969013i	−0.962694	+	0.270591i	$0.912781\pi$
$822$	−5.79778	+	12.0012i	−0.202221	+	0.418589i
$823$	−40.4499	−	23.3538i	−1.40999	−	0.814061i	−0.414607	−	0.910000i	$-0.636081\pi$
$823$	−40.4499	−	23.3538i	−1.40999	−	0.814061i	−0.995387	+	0.0959396i	$0.969414\pi$
$824$	−4.74739	+	11.2334i	−0.165383	+	0.391333i
$825$	−7.14282	−	2.34135i	−0.248681	−	0.0815155i
$826$	−0.443099	+	3.30479i	−0.0154174	+	0.114988i
$827$	−22.0817			−0.767857			−0.383928	−	0.923363i	$-0.625429\pi$
$827$	−22.0817			−0.767857			−0.383928	+	0.923363i	$0.625429\pi$
$828$	−7.01104	−	8.83636i	−0.243650	−	0.307085i
$829$	−0.0585429	−	0.101399i	−0.00203328	−	0.00352174i	0.865007	−	0.501760i	$-0.167314\pi$
$829$	−0.0585429	−	0.101399i	−0.00203328	−	0.00352174i	−0.867040	+	0.498238i	$0.833981\pi$
$830$	30.1958	+	23.2846i	1.04811	+	0.808219i
$831$	−7.68674	−	36.6304i	−0.266650	−	1.27070i
$832$	−19.3293	+	21.4097i	−0.670124	+	0.742249i
$833$			6.58347i			0.228104i
$834$	−4.24330	+	8.78346i	−0.146933	+	0.304146i
$835$	−31.7721	+	18.3437i	−1.09952	+	0.634808i
$836$	−30.3166	+	7.96863i	−1.04852	+	0.275601i
$837$	17.3246	−	12.3822i	0.598827	−	0.427991i
$838$	40.7795	+	5.46762i	1.40870	+	0.188876i
$839$	21.6203	−	37.4475i	0.746416	−	1.29283i	−0.203114	−	0.979155i	$-0.565106\pi$
$839$	21.6203	−	37.4475i	0.746416	−	1.29283i	0.949530	−	0.313676i	$-0.101561\pi$
$840$	−5.21234	+	26.6702i	−0.179843	+	0.920209i
$841$	−12.4719	+	21.6019i	−0.430064	+	0.744892i
$842$	13.5363	−	17.5541i	0.466493	−	0.604954i
$843$	−0.824496	−	0.920488i	−0.0283972	−	0.0317033i
$844$	29.2278	+	29.5077i	1.00606	+	1.01570i
$845$	3.35459	+	25.5315i	0.115401	+	0.878311i
$846$	8.31632	+	8.01246i	0.285921	+	0.275474i
$847$	12.7551	−	7.36415i	0.438270	−	0.253035i
$848$	2.45454	+	4.34656i	0.0842894	+	0.149262i
$849$	0.998016	−	3.04467i	0.0342518	−	0.104493i
$850$	−11.0073	+	4.52868i	−0.377548	+	0.155332i
$851$	4.91682	−	8.51619i	0.168546	−	0.291931i
$852$	46.2288	−	23.1277i	1.58377	−	0.792342i
$853$	−25.9640			−0.888990			−0.444495	−	0.895781i	$-0.646617\pi$
$853$	−25.9640			−0.888990			−0.444495	+	0.895781i	$0.646617\pi$
$854$	−1.35452	+	10.1025i	−0.0463509	+	0.345701i
$855$	−18.6160	−	13.6735i	−0.636654	−	0.467623i
$856$	4.82981	+	38.8293i	0.165079	+	1.32716i
$857$		−	33.7371i		−	1.15244i	−0.817296	−	0.576218i	$-0.804528\pi$
$857$		−	33.7371i		−	1.15244i	0.817296	−	0.576218i	$-0.195472\pi$
$858$	21.9043	+	28.0792i	0.747800	+	0.958609i
$859$		−	9.97263i		−	0.340262i	−0.985421	−	0.170131i	$-0.945581\pi$
$859$		−	9.97263i		−	0.340262i	0.985421	−	0.170131i	$-0.0544191\pi$
$860$	9.11257	+	2.48832i	0.310736	+	0.0848509i
$861$	15.0713	−	13.4996i	0.513630	−	0.460067i
$862$	10.1938	+	1.36676i	0.347203	+	0.0465522i
$863$	−19.5813			−0.666554			−0.333277	−	0.942829i	$-0.608154\pi$
$863$	−19.5813			−0.666554			−0.333277	+	0.942829i	$0.608154\pi$
$864$	−26.1031	+	13.5140i	−0.888046	+	0.459754i
$865$	−13.8498	+	23.9886i	−0.470909	+	0.815638i
$866$	−7.00362	−	17.0229i	−0.237993	−	0.578460i
$867$	72.6697	+	23.8205i	2.46799	+	0.808986i
$868$	−22.1418	−	6.04612i	−0.751540	−	0.205219i
$869$	−24.9296	+	14.3931i	−0.845678	+	0.488252i
$870$	8.08095	−	5.49485i	0.273970	−	0.186293i
$871$	15.0515	+	22.5324i	0.510000	+	0.763482i
$872$	−24.6885	−	10.4337i	−0.836060	−	0.353331i
$873$	30.5124	+	22.4114i	1.03269	+	0.758511i
$874$	−8.18357	−	6.31052i	−0.276813	−	0.213456i
$875$	−16.8526	+	29.1895i	−0.569721	+	0.986786i
$876$	−7.61656	−	5.02635i	−0.257340	−	0.169825i
$877$	−17.0141	+	29.4693i	−0.574525	+	0.995106i	0.421568	+	0.906797i	$0.361480\pi$
$877$	−17.0141	+	29.4693i	−0.574525	+	0.995106i	−0.996093	+	0.0883096i	$0.971854\pi$
$878$	−5.07890	+	37.8803i	−0.171405	+	1.27840i
$879$	10.6992	−	2.24519i	0.360876	−	0.0757283i
$880$	16.2378	−	27.5155i	0.547375	−	0.927547i
$881$	−15.0990	+	8.71742i	−0.508699	+	0.293697i	−0.732299	−	0.680984i	$-0.761552\pi$
$881$	−15.0990	+	8.71742i	−0.508699	+	0.293697i	0.223600	+	0.974681i	$0.428219\pi$
$882$	−0.860093	+	3.46668i	−0.0289608	+	0.116729i
$883$		−	24.3615i		−	0.819829i	−0.912124	−	0.409914i	$-0.865559\pi$
$883$		−	24.3615i		−	0.819829i	0.912124	−	0.409914i	$-0.134441\pi$
$884$	55.2528	+	11.2719i	1.85835	+	0.379116i
$885$	2.82710	−	0.593255i	0.0950319	−	0.0199421i
$886$	−6.56000	+	8.50710i	−0.220387	+	0.285802i
$887$	−23.0104	−	39.8552i	−0.772613	−	1.33821i	−0.936126	−	0.351664i	$-0.885616\pi$
$887$	−23.0104	−	39.8552i	−0.772613	−	1.33821i	0.163513	−	0.986541i	$-0.447717\pi$
$888$	−19.3224	−	16.8313i	−0.648418	−	0.564821i
$889$	21.6941			0.727596
$890$	8.99346	+	1.20582i	0.301462	+	0.0404193i
$891$	10.8556	+	34.6291i	0.363676	+	1.16012i
$892$	1.56709	+	1.58210i	0.0524701	+	0.0529727i
$893$	9.16246	+	5.28995i	0.306610	+	0.177021i
$894$	−0.780114	+	1.61481i	−0.0260909	+	0.0540072i
$895$	−28.4868	+	16.4469i	−0.952208	+	0.549758i
$896$	29.0642	+	12.6108i	0.970966	+	0.421298i
$897$	−2.92094	+	11.3713i	−0.0975275	+	0.379677i
$898$	10.3125	−	4.24280i	0.344132	−	0.141584i
$899$	4.12689	+	7.14799i	0.137640	+	0.238399i
$900$	−6.38780	+	0.946635i	−0.212927	+	0.0315545i
$901$	4.87942	−	8.45140i	0.162557	−	0.281557i
$902$	−21.9992	+	9.05100i	−0.732493	+	0.301365i
$903$	10.9897	+	3.60233i	0.365714	+	0.119878i
$904$	−20.9734	−	27.7414i	−0.697563	−	0.922667i
$905$		−	20.3536i		−	0.676576i
$906$	−31.0743	+	2.29001i	−1.03237	+	0.0760805i
$907$	45.0566	−	26.0134i	1.49608	−	0.863762i	0.496089	−	0.868271i	$-0.334769\pi$
$907$	45.0566	−	26.0134i	1.49608	−	0.863762i	0.999990	+	0.00450965i	$0.00143547\pi$
$908$	7.63528	+	2.08492i	0.253386	+	0.0691906i
$909$	6.32266	+	14.4016i	0.209709	+	0.477672i
$910$	25.3988	−	12.4461i	0.841963	−	0.412584i
$911$	20.2998			0.672564			0.336282	−	0.941761i	$-0.390831\pi$
$911$	20.2998			0.672564			0.336282	+	0.941761i	$0.390831\pi$
$912$	−20.2294	+	17.7752i	−0.669862	+	0.588595i
$913$	−27.4431	−	47.5329i	−0.908235	−	1.57311i
$914$	−21.9439	−	2.94219i	−0.725841	−	0.0973191i
$915$	8.64226	−	1.81354i	0.285704	−	0.0599538i
$916$	1.82878	+	6.95759i	0.0604247	+	0.229885i
$917$	27.6695	+	15.9750i	0.913728	+	0.527541i
$918$	48.6892	+	30.5220i	1.60698	+	1.00738i
$919$	−5.11593	−	2.95368i	−0.168759	−	0.0974330i	0.413242	−	0.910621i	$-0.364397\pi$
$919$	−5.11593	−	2.95368i	−0.168759	−	0.0974330i	−0.582001	+	0.813188i	$0.697730\pi$
$920$	10.4524	−	1.30013i	0.344604	−	0.0428639i
$921$	2.55957	+	2.85757i	0.0843407	+	0.0941600i
$922$	−51.5382	+	21.2041i	−1.69732	+	0.698318i
$923$	−48.2505	−	23.8023i	−1.58819	−	0.783461i
$924$	21.5450	−	32.6477i	0.708778	−	1.07403i
$925$	−2.81480	−	4.87538i	−0.0925502	−	0.160302i
$926$	39.1268	+	30.1715i	1.28579	+	0.991497i
$927$	12.8571	+	1.41883i	0.422282	+	0.0466006i
$928$	−4.23420	−	10.5770i	−0.138994	−	0.347207i
$929$	11.5057	+	6.64281i	0.377489	+	0.217943i	0.676725	−	0.736236i	$-0.263399\pi$
$929$	11.5057	+	6.64281i	0.377489	+	0.217943i	−0.299236	+	0.954179i	$0.596732\pi$
$930$	1.46142	+	19.8307i	0.0479217	+	0.650274i
$931$			3.27229i			0.107245i
$932$	1.64419	−	0.432170i	0.0538571	−	0.0141562i
$933$	32.8170	−	29.3947i	1.07438	−	0.962339i
$934$	19.5943	−	25.4102i	0.641145	−	0.831446i
$935$	−62.4612			−2.04270
$936$	27.6220	+	13.1539i	0.902853	+	0.429950i
$937$	−35.4819			−1.15914			−0.579572	−	0.814921i	$-0.696780\pi$
$937$	−35.4819			−1.15914			−0.579572	+	0.814921i	$0.696780\pi$
$938$	18.1748	−	23.5694i	0.593429	−	0.769567i
$939$	−35.3730	+	31.6842i	−1.15436	+	1.03397i
$940$	−10.4292	+	2.74128i	−0.340163	+	0.0894109i
$941$			6.71658i			0.218954i	0.993989	+	0.109477i	$0.0349177\pi$
$941$			6.71658i			0.218954i	−0.993989	+	0.109477i	$0.965082\pi$
$942$	3.08604	+	41.8760i	0.100549	+	1.36440i
$943$	−6.79172	−	3.92120i	−0.221169	−	0.127692i
$944$	0.0321038	−	3.36766i	0.00104489	−	0.109608i
$945$	28.6879	−	2.78960i	0.933217	−	0.0907456i
$946$	−10.7675	−	8.30305i	−0.350082	−	0.269956i
$947$	−17.9692	−	31.1236i	−0.583921	−	1.01138i	−0.995009	−	0.0997857i	$-0.968184\pi$
$947$	−17.9692	−	31.1236i	−0.583921	−	1.01138i	0.411087	−	0.911596i	$-0.365149\pi$
$948$	−13.6212	+	20.6405i	−0.442395	+	0.670372i
$949$	0.619990	+	9.47794i	0.0201257	+	0.307667i
$950$	−5.47115	+	2.25096i	−0.177508	+	0.0730309i
$951$	−15.3625	−	17.1510i	−0.498162	−	0.556161i
$952$	−7.64537	−	61.4650i	−0.247788	−	1.99209i
$953$	−7.45821	−	4.30600i	−0.241595	−	0.139485i	0.374314	−	0.927302i	$-0.377878\pi$
$953$	−7.45821	−	4.30600i	−0.241595	−	0.139485i	−0.615910	+	0.787817i	$0.711211\pi$
$954$	3.67349	−	3.81281i	0.118934	−	0.123444i
$955$	34.5006	+	19.9189i	1.11641	+	0.644561i
$956$	−1.24192	−	4.72489i	−0.0401667	−	0.152814i
$957$	−13.7664	+	2.88883i	−0.445005	+	0.0933825i
$958$	9.28576	+	1.24501i	0.300009	+	0.0402246i
$959$	−7.61865	−	13.1959i	−0.246019	−	0.426117i
$960$	1.89932	−	27.3816i	0.0613002	−	0.883737i
$961$	14.2051			0.458230
$962$	−1.81125	+	26.6099i	−0.0583972	+	0.857939i
$963$	38.0011	−	16.6834i	1.22457	−	0.537615i
$964$	26.8226	+	7.32429i	0.863897	+	0.235899i
$965$	13.7026	−	7.91122i	0.441103	−	0.254671i
$966$	12.8607	−	0.947762i	0.413785	−	0.0304937i
$967$			39.9079i			1.28335i	0.766975	+	0.641676i	$0.221761\pi$
$967$			39.9079i			1.28335i	−0.766975	+	0.641676i	$0.778239\pi$
$968$	−11.8664	+	8.97136i	−0.381401	+	0.288350i
$969$	50.0276	+	16.3986i	1.60712	+	0.526799i
$970$	−32.6928	+	13.4506i	−1.04970	+	0.431873i
$971$	4.39573	−	7.61362i	0.141066	−	0.244333i	−0.786833	−	0.617167i	$-0.788280\pi$
$971$	4.39573	−	7.61362i	0.141066	−	0.244333i	0.927898	+	0.372834i	$0.121614\pi$
$972$	21.6508	+	22.4330i	0.694451	+	0.719540i
$973$	−5.57596	−	9.65784i	−0.178757	−	0.309616i
$974$	−4.06654	+	1.67307i	−0.130300	+	0.0536088i
$975$	4.80165	+	4.70312i	0.153776	+	0.150620i
$976$	0.0981393	−	10.2947i	0.00314136	−	0.329526i
$977$	27.1638	−	15.6830i	0.869047	−	0.501745i	0.00201588	−	0.999998i	$-0.499358\pi$
$977$	27.1638	−	15.6830i	0.869047	−	0.501745i	0.867032	+	0.498253i	$0.166025\pi$
$978$	−16.9810	+	35.1500i	−0.542992	+	1.12397i
$979$	−11.3114	−	6.53062i	−0.361513	−	0.208719i
$980$	−2.34711	−	2.36959i	−0.0749757	−	0.0756938i
$981$	−3.11829	+	28.2571i	−0.0995594	+	0.902179i
$982$	−6.30578	−	0.845465i	−0.201226	−	0.0269799i
$983$	−25.0538			−0.799092			−0.399546	−	0.916713i	$-0.630832\pi$
$983$	−25.0538			−0.799092			−0.399546	+	0.916713i	$0.630832\pi$
$984$	−13.4231	+	15.4098i	−0.427912	+	0.491246i
$985$	−15.1471	−	26.2356i	−0.482627	−	0.835935i
$986$	−13.6013	+	17.6383i	−0.433152	+	0.561718i
$987$	−12.9208	+	2.71138i	−0.411275	+	0.0863043i
$988$	27.4632	+	5.60267i	0.873721	+	0.178245i
$989$		−	4.48260i		−	0.142539i
$990$	−32.8903	−	8.16020i	−1.04532	−	0.259348i
$991$	9.47381	−	5.46971i	0.300945	−	0.173751i	−0.341922	−	0.939728i	$-0.611078\pi$
$991$	9.47381	−	5.46971i	0.300945	−	0.173751i	0.642868	+	0.765977i	$0.277745\pi$
$992$	22.9466	+	3.29960i	0.728557	+	0.104762i
$993$	−54.9507	+	11.5312i	−1.74381	+	0.365931i
$994$	−7.85308	+	58.5711i	−0.249084	+	1.85776i
$995$	−2.73815	+	4.74261i	−0.0868050	+	0.150351i
$996$	−39.3549	−	25.9713i	−1.24701	−	0.822931i
$997$	−17.0806	+	29.5845i	−0.540948	+	0.936950i	0.457902	+	0.889003i	$0.348601\pi$
$997$	−17.0806	+	29.5845i	−0.540948	+	0.936950i	−0.998850	+	0.0479470i	$0.984732\pi$
$998$	7.42505	+	5.72561i	0.235036	+	0.181241i
$999$	−11.2479	+	24.7430i	−0.355868	+	0.782833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.p.b.107.7	yes	40
3.2	odd	2	inner	156.2.p.b.107.14	yes	40
4.3	odd	2	inner	156.2.p.b.107.1	yes	40
12.11	even	2	inner	156.2.p.b.107.20	yes	40
13.9	even	3	inner	156.2.p.b.35.20	yes	40
39.35	odd	6	inner	156.2.p.b.35.1	✓	40
52.35	odd	6	inner	156.2.p.b.35.14	yes	40
156.35	even	6	inner	156.2.p.b.35.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.p.b.35.1	✓	40	39.35	odd	6	inner
156.2.p.b.35.7	yes	40	156.35	even	6	inner
156.2.p.b.35.14	yes	40	52.35	odd	6	inner
156.2.p.b.35.20	yes	40	13.9	even	3	inner
156.2.p.b.107.1	yes	40	4.3	odd	2	inner
156.2.p.b.107.7	yes	40	1.1	even	1	trivial
156.2.p.b.107.14	yes	40	3.2	odd	2	inner
156.2.p.b.107.20	yes	40	12.11	even	2	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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.863590 + 1.11992i) q^{2} +(1.29017 - 1.15562i) q^{3} +(-0.508424 - 1.93430i) q^{4} -1.98084i q^{5} +(0.180026 + 2.44287i) q^{6} +(-2.42516 - 1.40017i) q^{7} +(2.60532 + 1.10105i) q^{8} +(0.329066 - 2.98190i) q^{9} +(2.21838 + 1.71064i) q^{10} +(-2.01615 - 3.49208i) q^{11} +(-2.89127 - 1.90802i) q^{12} +(0.235350 + 3.59786i) q^{13} +(3.66242 - 1.50681i) q^{14} +(-2.28911 - 2.55562i) q^{15} +(-3.48301 + 1.96689i) q^{16} +(6.77232 + 3.91000i) q^{17} +(3.05530 + 2.94366i) q^{18} +(3.36616 + 1.94345i) q^{19} +(-3.83154 + 1.00711i) q^{20} +(-4.74693 + 0.996124i) q^{21} +(5.65196 + 0.757803i) q^{22} +(0.939991 + 1.62811i) q^{23} +(4.63370 - 1.59024i) q^{24} +1.07626 q^{25} +(-4.23255 - 2.84351i) q^{26} +(-3.02140 - 4.22742i) q^{27} +(-1.47533 + 5.40286i) q^{28} +(1.74420 - 1.00701i) q^{29} +(4.83893 - 0.356604i) q^{30} +4.09815i q^{31} +(0.805143 - 5.59926i) q^{32} +(-6.63670 - 2.17545i) q^{33} +(-10.2274 + 4.20779i) q^{34} +(-2.77351 + 4.80386i) q^{35} +(-5.93518 + 0.879559i) q^{36} +(-2.61536 - 4.52993i) q^{37} +(-5.08348 + 2.09147i) q^{38} +(4.46142 + 4.36987i) q^{39} +(2.18100 - 5.16073i) q^{40} +(-3.61265 + 2.08577i) q^{41} +(2.98383 - 6.17641i) q^{42} +(-2.06494 - 1.19219i) q^{43} +(-5.72966 + 5.67529i) q^{44} +(-5.90667 - 0.651827i) q^{45} +(-2.63512 - 0.353310i) q^{46} +2.72193 q^{47} +(-2.22068 + 6.56266i) q^{48} +(0.420938 + 0.729086i) q^{49} +(-0.929448 + 1.20532i) q^{50} +(13.2559 - 2.78170i) q^{51} +(6.83968 - 2.28448i) q^{52} -1.24793i q^{53} +(7.34362 + 0.267043i) q^{54} +(-6.91726 + 3.99368i) q^{55} +(-4.77667 - 6.31810i) q^{56} +(6.58881 - 1.38263i) q^{57} +(-0.378501 + 2.82300i) q^{58} +(-0.420977 + 0.729153i) q^{59} +(-3.77949 + 5.72716i) q^{60} +(-1.28690 + 2.22897i) q^{61} +(-4.58959 - 3.53912i) q^{62} +(-4.97319 + 6.77084i) q^{63} +(5.57539 + 5.73716i) q^{64} +(7.12680 - 0.466192i) q^{65} +(8.16772 - 5.55385i) q^{66} +(6.50853 - 3.75770i) q^{67} +(4.11989 - 15.0876i) q^{68} +(3.09423 + 1.01426i) q^{69} +(-2.98475 - 7.25467i) q^{70} +(-7.46100 + 12.9228i) q^{71} +(4.14053 - 7.40648i) q^{72} +2.63433 q^{73} +(7.33174 + 0.983023i) q^{74} +(1.38856 - 1.24375i) q^{75} +(2.04778 - 7.49925i) q^{76} +11.2918i q^{77} +(-8.74672 + 1.22264i) q^{78} -7.13890i q^{79} +(3.89610 + 6.89930i) q^{80} +(-8.78343 - 1.96248i) q^{81} +(0.783968 - 5.84712i) q^{82} +13.6116 q^{83} +(4.34026 + 8.67552i) q^{84} +(7.74510 - 13.4149i) q^{85} +(3.11842 - 1.28299i) q^{86} +(1.08658 - 3.31485i) q^{87} +(-1.40778 - 11.3179i) q^{88} +(2.80518 - 1.61957i) q^{89} +(5.83094 - 6.05207i) q^{90} +(4.46685 - 9.05493i) q^{91} +(2.67134 - 2.64599i) q^{92} +(4.73593 + 5.28731i) q^{93} +(-2.35064 + 3.04834i) q^{94} +(3.84967 - 6.66783i) q^{95} +(-5.43187 - 8.15443i) q^{96} +(-6.30978 + 10.9289i) q^{97} +(-1.18003 - 0.158216i) q^{98} +(-11.0765 + 4.86284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{4} + 2 q^{6} - 10 q^{9} + 6 q^{10} - 16 q^{12} + 16 q^{13} + 18 q^{16} - 20 q^{18} - 60 q^{21} + 20 q^{22} - 20 q^{24} - 32 q^{25} - 24 q^{28} - 26 q^{30} - 2 q^{33} - 28 q^{34} + 6 q^{36} + 16 q^{37}+ \cdots - 56 q^{97}+O(q^{100}) \) 40 * q + 6 * q^4 + 2 * q^6 - 10 * q^9 + 6 * q^10 - 16 * q^12 + 16 * q^13 + 18 * q^16 - 20 * q^18 - 60 * q^21 + 20 * q^22 - 20 * q^24 - 32 * q^25 - 24 * q^28 - 26 * q^30 - 2 * q^33 - 28 * q^34 + 6 * q^36 + 16 * q^37 + 20 * q^40 - 4 * q^42 + 28 * q^45 + 48 * q^46 - 24 * q^48 - 28 * q^49 + 12 * q^52 - 4 * q^54 + 44 * q^57 - 50 * q^58 - 12 * q^60 - 12 * q^61 + 12 * q^64 + 24 * q^66 - 6 * q^69 + 48 * q^72 - 16 * q^73 + 30 * q^78 - 14 * q^81 - 2 * q^82 - 6 * q^84 + 52 * q^85 - 12 * q^88 + 156 * q^90 + 40 * q^93 - 8 * q^94 + 128 * q^96 - 56 * q^97

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