LMFDB - Embedded newform 156.2.p.b.107.14

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			107.14
Character	$\chi$	$=$	156.107
Dual form			156.2.p.b.35.14

$q$ -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} +(1.64588 - 0.539506i) q^{3} +(-0.508424 - 1.93430i) q^{4} +1.98084i q^{5} +(0.817167 - 2.30916i) q^{6} +(-2.42516 - 1.40017i) q^{7} +(-2.60532 - 1.10105i) q^{8} +(2.41787 - 1.77593i) q^{9} +(2.21838 + 1.71064i) q^{10} +(2.01615 + 3.49208i) q^{11} +(-1.88037 - 2.90933i) q^{12} +(0.235350 + 3.59786i) q^{13} +(-3.66242 + 1.50681i) q^{14} +(1.06868 + 3.26024i) q^{15} +(-3.48301 + 1.96689i) q^{16} +(-6.77232 - 3.91000i) q^{17} +(0.0991550 - 4.24148i) 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} +(-4.88208 - 0.406609i) 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} +(4.57409 + 1.61868i) q^{30} +4.09815i q^{31} +(-0.805143 + 5.59926i) q^{32} +(5.20235 + 4.65983i) q^{33} +(-10.2274 + 4.20779i) q^{34} +(2.77351 - 4.80386i) q^{35} +(-4.66447 - 3.77395i) q^{36} +(-2.61536 - 4.52993i) q^{37} +(5.08348 - 2.09147i) q^{38} +(2.32843 + 5.79469i) q^{39} +(2.18100 - 5.16073i) q^{40} +(3.61265 - 2.08577i) q^{41} +(-5.21498 + 4.45592i) q^{42} +(-2.06494 - 1.19219i) q^{43} +(5.72966 - 5.67529i) q^{44} +(3.51784 + 4.78941i) q^{45} +(-2.63512 - 0.353310i) q^{46} -2.72193 q^{47} +(-4.67148 + 5.11637i) 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} +(-2.12511 - 7.03448i) 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} +(5.76293 - 3.72472i) q^{60} +(-1.28690 + 2.22897i) q^{61} +(4.58959 + 3.53912i) q^{62} +(-8.35031 + 0.921494i) q^{63} +(5.57539 + 5.73716i) q^{64} +(-7.12680 + 0.466192i) q^{65} +(9.71131 - 1.80201i) q^{66} +(6.50853 - 3.75770i) q^{67} +(-4.11989 + 15.0876i) q^{68} +(-2.42549 - 2.17255i) q^{69} +(-2.98475 - 7.25467i) q^{70} +(7.46100 - 12.9228i) q^{71} +(-8.25470 + 1.96468i) q^{72} +2.63433 q^{73} +(-7.33174 - 0.983023i) q^{74} +(1.77140 - 0.580649i) q^{75} +(2.04778 - 7.49925i) q^{76} -11.2918i q^{77} +(8.50037 + 2.39659i) q^{78} -7.13890i q^{79} +(-3.89610 - 6.89930i) q^{80} +(2.69216 - 8.58791i) q^{81} +(0.783968 - 5.84712i) q^{82} -13.6116 q^{83} +(0.486656 + 9.68843i) q^{84} +(7.74510 - 13.4149i) q^{85} +(-3.11842 + 1.28299i) q^{86} +(-2.32746 + 2.59843i) q^{87} +(-1.40778 - 11.3179i) q^{88} +(-2.80518 + 1.61957i) q^{89} +(8.40171 + 0.196411i) q^{90} +(4.46685 - 9.05493i) q^{91} +(-2.67134 + 2.64599i) q^{92} +(2.21098 + 6.74508i) q^{93} +(-2.35064 + 3.04834i) q^{94} +(-3.84967 + 6.66783i) q^{95} +(1.69566 + 9.65012i) 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
$3$	1.64588	−	0.539506i	0.950251	−	0.311484i
$3$	1.64588	−	0.539506i	0.950251	−	0.311484i
$4$	−0.508424	−	1.93430i	−0.254212	−	0.967148i
$5$			1.98084i			0.885860i	0.896556	+	0.442930i	$0.146061\pi$
$5$			1.98084i			0.885860i	−0.896556	+	0.442930i	$0.853939\pi$
$6$	0.817167	−	2.30916i	0.333607	−	0.942712i
$7$	−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
$9$	2.41787	−	1.77593i	0.805956	−	0.591976i
$10$	2.21838	+	1.71064i	0.701513	+	0.540951i
$11$	2.01615	+	3.49208i	0.607893	+	1.05290i	0.991587	+	0.129441i	$0.0413183\pi$
$11$	2.01615	+	3.49208i	0.607893	+	1.05290i	−0.383694	+	0.923460i	$0.625348\pi$
$12$	−1.88037	−	2.90933i	−0.542817	−	0.839851i
$13$	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
$15$	1.06868	+	3.26024i	0.275931	+	0.841790i
$16$	−3.48301	+	1.96689i	−0.870752	+	0.491722i
$17$	−6.77232	−	3.91000i	−1.64253	−	0.948314i	−0.979931	−	0.199339i	$-0.936120\pi$
$17$	−6.77232	−	3.91000i	−1.64253	−	0.948314i	−0.662598	−	0.748975i	$-0.730546\pi$
$18$	0.0991550	−	4.24148i	0.0233711	−	0.999727i
$19$	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	0.751227	−	0.660044i	$-0.229462\pi$
$23$	−0.939991	−	1.62811i	−0.196002	−	0.339485i	−0.947228	+	0.320559i	$0.896129\pi$
$24$	−4.88208	−	0.406609i	−0.996550	−	0.0829988i
$25$	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	−0.653125	−	0.757250i	$-0.726542\pi$
$29$	−1.74420	+	1.00701i	−0.323889	+	0.186998i	0.329236	+	0.944248i	$0.393209\pi$
$30$	4.57409	+	1.61868i	0.835111	+	0.295529i
$31$			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
$33$	5.20235	+	4.65983i	0.905613	+	0.811172i
$34$	−10.2274	+	4.20779i	−1.75398	+	0.721630i
$35$	2.77351	−	4.80386i	0.468809	−	0.812001i
$36$	−4.66447	−	3.77395i	−0.777412	−	0.628991i
$37$	−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
$39$	2.32843	+	5.79469i	0.372847	+	0.927893i
$40$	2.18100	−	5.16073i	0.344847	−	0.815983i
$41$	3.61265	−	2.08577i	0.564202	−	0.325742i	−0.190629	−	0.981662i	$-0.561053\pi$
$41$	3.61265	−	2.08577i	0.564202	−	0.325742i	0.754830	+	0.655920i	$0.227719\pi$
$42$	−5.21498	+	4.45592i	−0.804689	+	0.687564i
$43$	−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
$45$	3.51784	+	4.78941i	0.524408	+	0.713964i
$46$	−2.63512	−	0.353310i	−0.388527	−	0.0520928i
$47$	−2.72193			−0.397035			−0.198518	−	0.980097i	$-0.563613\pi$
$47$	−2.72193			−0.397035			−0.198518	+	0.980097i	$0.563613\pi$
$48$	−4.67148	+	5.11637i	−0.674270	+	0.738485i
$49$	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	$0.0273153\pi$
$53$			1.24793i			0.171417i	−0.996320	+	0.0857084i	$0.972685\pi$
$54$	−2.12511	−	7.03448i	−0.289190	−	0.957272i
$55$	−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	−0.837321	−	0.546712i	$-0.815879\pi$
$59$	0.420977	−	0.729153i	0.0548065	−	0.0949276i	0.892127	+	0.451785i	$0.149212\pi$
$60$	5.76293	−	3.72472i	0.743991	−	0.480860i
$61$	−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
$63$	−8.35031	+	0.921494i	−1.05204	+	0.116097i
$64$	5.57539	+	5.73716i	0.696924	+	0.717145i
$65$	−7.12680	+	0.466192i	−0.883971	+	0.0578240i
$66$	9.71131	−	1.80201i	1.19538	−	0.221812i
$67$	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
$69$	−2.42549	−	2.17255i	−0.291995	−	0.261545i
$70$	−2.98475	−	7.25467i	−0.356746	−	0.867099i
$71$	7.46100	−	12.9228i	0.885458	−	1.53366i	0.0402702	−	0.999189i	$-0.487178\pi$
$71$	7.46100	−	12.9228i	0.885458	−	1.53366i	0.845188	−	0.534469i	$-0.179489\pi$
$72$	−8.25470	+	1.96468i	−0.972826	+	0.231539i
$73$	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
$75$	1.77140	−	0.580649i	0.204544	−	0.0670476i
$76$	2.04778	−	7.49925i	0.234896	−	0.860223i
$77$		−	11.2918i		−	1.28682i
$78$	8.50037	+	2.39659i	0.962478	+	0.271361i
$79$		−	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
$81$	2.69216	−	8.58791i	0.299129	−	0.954213i
$82$	0.783968	−	5.84712i	0.0865748	−	0.645706i
$83$	−13.6116			−1.49407			−0.747035	−	0.664784i	$-0.768523\pi$
$83$	−13.6116			−1.49407			−0.747035	+	0.664784i	$0.768523\pi$
$84$	0.486656	+	9.68843i	0.0530986	+	1.05709i
$85$	7.74510	−	13.4149i	0.840074	−	1.45505i
$86$	−3.11842	+	1.28299i	−0.336268	+	0.138349i
$87$	−2.32746	+	2.59843i	−0.249529	+	0.278581i
$88$	−1.40778	−	11.3179i	−0.150070	−	1.20649i
$89$	−2.80518	+	1.61957i	−0.297349	+	0.171675i	−0.641251	−	0.767331i	$-0.721584\pi$
$89$	−2.80518	+	1.61957i	−0.297349	+	0.171675i	0.343902	+	0.939005i	$0.388251\pi$
$90$	8.40171	+	0.196411i	0.885618	+	0.0207035i
$91$	4.46685	−	9.05493i	0.468253	−	0.949214i
$92$	−2.67134	+	2.64599i	−0.278506	+	0.275864i
$93$	2.21098	+	6.74508i	0.229268	+	0.699433i
$94$	−2.35064	+	3.04834i	−0.242450	+	0.314412i
$95$	−3.84967	+	6.66783i	−0.394968	+	0.684105i
$96$	1.69566	+	9.65012i	0.173063	+	0.984911i
$97$	−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	−0.256798	−	0.966465i	$-0.582667\pi$
$101$	4.54040	−	2.62140i	0.451787	−	0.260839i	0.708584	+	0.705626i	$0.249334\pi$
$102$	−14.5629	+	12.4433i	−1.44195	+	1.23207i
$103$			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	$-0.933521\pi$
$107$	−6.91701	−	11.9806i	−0.668692	−	1.15821i	0.309578	−	0.950874i	$-0.399812\pi$
$108$	−9.71325	−	3.69497i	−0.934658	−	0.355548i
$109$	−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
$111$	−6.74850	−	6.04474i	−0.640539	−	0.573741i
$112$	11.2008	+	0.106777i	1.05838	+	0.0100895i
$113$	10.6484	+	6.14784i	1.00171	+	0.578340i	0.908755	−	0.417330i	$-0.137034\pi$
$113$	10.6484	+	6.14784i	1.00171	+	0.578340i	0.0929592	+	0.995670i	$0.470367\pi$
$114$	7.23846	−	6.18488i	0.677944	−	0.579267i
$115$	3.22503	−	1.86197i	0.300736	−	0.173630i
$116$	2.83465	+	2.86180i	0.263191	+	0.265712i
$117$	6.95859	+	8.28119i	0.643322	+	0.765596i
$118$	−0.453039	−	1.10115i	−0.0417056	−	0.101369i
$119$	10.9493	+	18.9648i	1.00372	+	1.73850i
$120$	0.805429	−	9.67063i	0.0735253	−	0.882803i
$121$	−2.62974	+	4.55484i	−0.239067	+	0.414077i
$122$	1.38491	+	3.36614i	0.125384	+	0.304756i
$123$	4.82072	−	5.38198i	0.434670	−	0.485276i
$124$	7.92705	−	2.08360i	0.711870	−	0.187113i
$125$			12.0361i			1.07654i
$126$	−6.17925	+	10.1474i	−0.550492	+	0.904006i
$127$	−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	$-0.333914\pi$
$131$	11.4093			0.996839			0.498420	+	0.866936i	$0.333914\pi$
$132$	6.36849	−	12.4321i	0.554306	−	1.08207i
$133$	−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	0.285008	−	0.958525i	$-0.408004\pi$
$137$	−4.71225	−	2.72062i	−0.402595	−	0.232438i	−0.687603	+	0.726087i	$0.741337\pi$
$138$	−4.52771	+	0.840153i	−0.385424	+	0.0715185i
$139$	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
$141$	−4.47999	+	1.46850i	−0.377283	+	0.123670i
$142$	−8.02924	−	19.5157i	−0.673799	−	1.63772i
$143$	−12.0895	+	8.07570i	−1.01098	+	0.675324i
$144$	−4.92840	+	10.9412i	−0.410700	+	0.911770i
$145$	−1.99473	−	3.45498i	−0.165654	−	0.286920i
$146$	2.27498	−	2.95022i	0.188279	−	0.244162i
$147$	1.08616	+	0.972892i	0.0895851	+	0.0802428i
$148$	−7.43252	+	7.36200i	−0.610949	+	0.605153i
$149$	−0.634052	−	0.366070i	−0.0519435	−	0.0299896i	0.473803	−	0.880631i	$-0.342881\pi$
$149$	−0.634052	−	0.366070i	−0.0519435	−	0.0299896i	−0.525747	+	0.850641i	$0.676214\pi$
$150$	0.879485	−	2.48526i	0.0718096	−	0.202921i
$151$			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
$153$	−23.3184	+	2.57329i	−1.88518	+	0.208038i
$154$	−12.6459	−	9.75149i	−1.01903	−	0.785797i
$155$	−8.11780			−0.652037
$156$	10.0248	−	7.45003i	0.802628	−	0.596480i
$157$	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
$159$	0.673267	+	2.05395i	0.0533936	+	0.162889i
$160$	−11.0913	−	1.59486i	−0.876841	−	0.126085i
$161$			5.26458i			0.414907i
$162$	−7.29282	−	10.4314i	−0.572978	−	0.819571i
$163$	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
$165$	−9.23039	+	10.3050i	−0.718585	+	0.802246i
$166$	−11.7549	+	15.2439i	−0.912355	+	1.18316i
$167$	9.26053	+	16.0397i	0.716601	+	1.24119i	0.962339	+	0.271853i	$0.0876365\pi$
$167$	9.26053	+	16.0397i	0.716601	+	1.24119i	−0.245738	+	0.969336i	$0.579030\pi$
$168$	11.2705	+	7.82182i	0.869538	+	0.603466i
$169$	−12.8892	+	1.69352i	−0.991478	+	0.130270i
$170$	−8.33498	−	20.2588i	−0.639263	−	1.55378i
$171$	11.5904	−	1.27905i	0.886336	−	0.0978111i
$172$	−1.25619	+	4.60035i	−0.0957837	+	0.350773i
$173$	12.1103	+	6.99189i	0.920730	+	0.531584i	0.883868	−	0.467737i	$-0.154930\pi$
$173$	12.1103	+	6.99189i	0.920730	+	0.531584i	0.0368619	+	0.999320i	$0.488264\pi$
$174$	0.900056	+	4.85053i	0.0682331	+	0.367718i
$175$	−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	$0.0464410\pi$
$179$	8.30296	+	14.3811i	0.620592	+	1.07490i	−0.368784	+	0.929515i	$0.620226\pi$
$180$	7.47560	−	9.23959i	0.557198	−	0.688679i
$181$	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
$186$	9.46331	+	3.34888i	0.693883	+	0.245552i
$187$		−	31.5326i		−	2.30589i
$188$	1.38390	+	5.26503i	0.100931	+	0.383992i
$189$	−13.2465	+	6.02172i	−0.963541	+	0.438015i
$190$	4.14287	+	10.0696i	0.300555	+	0.730524i
$191$	10.0558	−	17.4171i	0.727611	−	1.26026i	−0.230280	−	0.973124i	$-0.573964\pi$
$191$	10.0558	−	17.4171i	0.727611	−	1.26026i	0.957890	−	0.287134i	$-0.0927025\pi$
$192$	12.2717	+	6.43474i	0.885632	+	0.464388i
$193$	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
$195$	−11.4784	+	4.61225i	−0.821983	+	0.330290i
$196$	1.19625	−	1.18490i	0.0854467	−	0.0846360i
$197$	−13.2446	+	7.64680i	−0.943642	+	0.544812i	−0.891100	−	0.453807i	$-0.850066\pi$
$197$	−13.2446	+	7.64680i	−0.943642	+	0.544812i	−0.0525419	+	0.998619i	$0.516732\pi$
$198$	15.0115	−	8.20522i	1.06682	−	0.583119i
$199$	−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
$201$	8.68498	−	9.69613i	0.612592	−	0.683913i
$202$	0.985295	−	7.34868i	0.0693251	−	0.517051i
$203$	5.63994			0.395846
$204$	1.35900	+	27.0552i	0.0951490	+	1.89424i
$205$	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
$210$	−8.82649	−	10.3301i	−0.609085	−	0.712842i
$211$	−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
$216$	−12.5263	+	7.68709i	−0.852308	+	0.523040i
$217$	5.73810	−	9.93868i	0.389528	−	0.674682i
$218$	−8.18355	+	10.6126i	−0.554260	+	0.718773i
$219$	4.33580	−	1.42123i	0.292986	−	0.0960382i
$220$	11.2419	+	11.3495i	0.757927	+	0.765186i
$221$	12.4738	−	25.2861i	0.839077	−	1.70093i
$222$	−12.5975	+	2.33758i	−0.845491	+	0.156888i
$223$	−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
$225$	2.60225	−	1.91136i	0.173484	−	0.127424i
$226$	16.0809	−	6.61607i	1.06968	−	0.440094i
$227$	1.97871	−	3.42722i	0.131331	−	0.227473i	−0.792859	−	0.609406i	$-0.791408\pi$
$227$	1.97871	−	3.42722i	0.131331	−	0.227473i	0.924190	+	0.381933i	$0.124741\pi$
$228$	−0.675486	−	13.4477i	−0.0447351	−	0.890594i
$229$	−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
$231$	−6.09200	−	18.5850i	−0.400824	−	1.22280i
$232$	5.65296	−	0.703148i	0.371135	−	0.0461639i
$233$		−	0.850018i		−	0.0556865i	−0.999612	−	0.0278433i	$-0.991136\pi$
$233$		−	0.850018i		−	0.0556865i	0.999612	−	0.0278433i	$-0.00886393\pi$
$234$	15.2836	−	0.641488i	0.999120	−	0.0419354i
$235$		−	5.39173i		−	0.351717i
$236$	−1.62443	−	0.443575i	−0.105742	−	0.0288743i
$237$	−3.85148	−	11.7498i	−0.250180	−	0.763231i
$238$	30.6947	+	4.11547i	1.98964	+	0.266766i
$239$	−2.44269			−0.158005			−0.0790023	−	0.996874i	$-0.525173\pi$
$239$	−2.44269			−0.158005			−0.0790023	+	0.996874i	$0.525173\pi$
$240$	−10.1347	−	9.25347i	−0.654194	−	0.597309i
$241$	−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
$243$	−0.202251	−	15.5871i	−0.0129744	−	0.999916i
$244$	4.96578	+	1.35598i	0.317902	+	0.0868076i
$245$	−1.44421	+	0.833812i	−0.0922669	+	0.0532703i
$246$	−1.86423	−	10.0466i	−0.118859	−	0.640550i
$247$	−6.20005	+	12.5684i	−0.394499	+	0.799706i
$248$	4.51226	−	10.6770i	0.286529	−	0.677990i
$249$	−22.4032	+	7.34356i	−1.41974	+	0.465379i
$250$	13.4794	+	10.3943i	0.852515	+	0.657392i
$251$	−9.31600	+	16.1358i	−0.588021	+	1.01848i	0.406471	+	0.913664i	$0.366759\pi$
$251$	−9.31600	+	16.1358i	−0.588021	+	1.01848i	−0.994491	+	0.104818i	$0.966574\pi$
$252$	6.02795	+	15.6835i	0.379725	+	0.987966i
$253$	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	$-0.330760\pi$
$257$	24.1583	−	13.9478i	1.50695	−	0.870039i	0.999967	−	0.00808340i	$-0.00257305\pi$
$258$	−4.44037	+	3.79406i	−0.276446	+	0.236208i
$259$			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	$-0.832821\pi$
$263$	−14.0576	−	24.3485i	−0.866828	−	1.50139i	−0.00160803	−	0.999999i	$-0.500512\pi$
$264$	−8.42310	−	17.8684i	−0.518406	−	1.09972i
$265$	−2.47196			−0.151851
$266$	−15.2567	−	2.04558i	−0.935447	−	0.125423i
$267$	−3.74324	+	4.17904i	−0.229082	+	0.255753i
$268$	−10.5776	−	10.6789i	−0.646130	−	0.652319i
$269$	5.29540	+	3.05730i	0.322866	+	0.186407i	0.652669	−	0.757643i	$-0.273649\pi$
$269$	5.29540	+	3.05730i	0.322866	+	0.186407i	−0.329803	+	0.944050i	$0.606982\pi$
$270$	13.9342	−	4.20950i	0.848009	−	0.256182i
$271$	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
$273$	2.46672	−	17.3132i	0.149293	−	1.04785i
$274$	−7.11632	+	2.92783i	−0.429913	+	0.176877i
$275$	2.16990	+	3.75839i	0.130850	+	0.226639i
$276$	−2.96918	+	5.79620i	−0.178724	+	0.348890i
$277$	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
$279$	7.27803	+	9.90879i	0.435724	+	0.593224i
$280$	−12.5152	+	9.46184i	−0.747924	+	0.565453i
$281$			0.713464i			0.0425617i	0.999774	+	0.0212808i	$0.00677441\pi$
$281$			0.713464i			0.0425617i	−0.999774	+	0.0212808i	$0.993226\pi$
$282$	−2.22428	+	6.28539i	−0.132454	+	0.374290i
$283$	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
$288$	7.99716	+	14.9681i	0.471237	+	0.882007i
$289$	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	0.331761	−	0.943363i	$-0.392357\pi$
$293$	−5.46613	−	3.15587i	−0.319335	−	0.184368i	−0.651096	+	0.758995i	$0.725690\pi$
$294$	2.02756	−	0.376230i	0.118249	−	0.0219422i
$295$	1.44434	+	0.833889i	0.0840926	+	0.0485509i
$296$	1.82618	+	14.6816i	0.106144	+	0.853348i
$297$	20.8541	+	2.02785i	1.21008	+	0.117668i
$298$	−0.957528	+	0.393950i	−0.0554681	+	0.0228209i
$299$	5.63649	−	3.76513i	0.325967	−	0.217743i
$300$	−2.02377	−	3.13120i	−0.116842	−	0.180780i
$301$	3.33854	+	5.78252i	0.192430	+	0.333299i
$302$	14.2458	+	10.9852i	0.819755	+	0.632129i
$303$	6.05871	−	6.76409i	0.348064	−	0.388587i
$304$	−15.5469	−	0.148208i	−0.891676	−	0.00850033i
$305$	−4.41524	−	2.54914i	−0.252816	−	0.145963i
$306$	−17.2557	+	28.3370i	−0.986443	+	1.61992i
$307$			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
$309$	2.32619	+	7.09657i	0.132332	+	0.403710i
$310$	−7.01045	+	9.09125i	−0.398167	+	0.516349i
$311$	−25.4362			−1.44235			−0.721177	−	0.692750i	$-0.756399\pi$
$311$	−25.4362			−1.44235			−0.721177	+	0.692750i	$0.756399\pi$
$312$	0.313926	−	17.6607i	0.0177726	−	0.999842i
$313$	−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
$315$	−1.82533	−	16.5407i	−0.102846	−	0.931961i
$316$	−13.8087	+	3.62959i	−0.776803	+	0.204180i
$317$			13.2937i			0.746646i	0.927701	+	0.373323i	$0.121782\pi$
$317$			13.2937i			0.746646i	−0.927701	+	0.373323i	$0.878218\pi$
$318$	2.88168	+	1.01977i	0.161597	+	0.0571859i
$319$	−7.03313	−	4.06058i	−0.393780	−	0.227349i
$320$	−11.3644	+	11.0440i	−0.635290	+	0.617377i
$321$	−17.8482	−	15.9869i	−0.996189	−	0.892303i
$322$	5.89589	+	4.54644i	0.328565	+	0.253363i
$323$	−15.1978	−	26.3234i	−0.845628	−	1.46467i
$324$	−17.9803	−	0.841129i	−0.998908	−	0.0467294i
$325$	0.253298	+	3.87224i	0.0140505	+	0.214793i
$326$	20.8428	−	8.57524i	1.15438	−	0.474939i
$327$	−15.5967	+	5.11247i	−0.862501	+	0.282720i
$328$	−11.7086	+	1.45639i	−0.646502	+	0.0804156i
$329$	6.60113	+	3.81116i	0.363932	+	0.210116i
$330$	3.56951	+	19.2366i	0.196495	+	1.05894i
$331$	−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
$336$	18.4929	−	5.86717i	1.00887	−	0.320080i
$337$	−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
$342$	8.57689	−	14.0848i	0.463785	−	0.761618i
$343$			17.2448i			0.931132i
$344$	4.06717	+	5.37964i	0.219287	+	0.290051i
$345$	4.30348	−	4.80452i	0.231692	−	0.258667i
$346$	18.2887	−	7.52440i	0.983205	−	0.404514i
$347$	−4.49629	+	7.78780i	−0.241374	+	0.418071i	−0.961106	−	0.276181i	$-0.910931\pi$
$347$	−4.49629	+	7.78780i	−0.241374	+	0.418071i	0.719732	+	0.694252i	$0.244265\pi$
$348$	6.20947	+	3.18089i	0.332863	+	0.170513i
$349$	−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
$351$	15.9208	+	9.87567i	0.849788	+	0.527124i
$352$	−21.1764	+	8.47734i	−1.12870	+	0.451844i
$353$	−1.88888	+	1.09054i	−0.100535	+	0.0580438i	−0.549424	−	0.835543i	$-0.685153\pi$
$353$	−1.88888	+	1.09054i	−0.100535	+	0.0580438i	0.448890	+	0.893587i	$0.351820\pi$
$354$	−1.33973	−	1.56794i	−0.0712056	−	0.0833353i
$355$	25.5981	+	14.7791i	1.35861	+	0.784392i
$356$	4.55896	+	4.60263i	0.241624	+	0.243939i
$357$	28.2529	+	25.3066i	1.49530	+	1.33937i
$358$	23.2760	+	3.12080i	1.23018	+	0.164939i
$359$	3.58192			0.189046			0.0945231	−	0.995523i	$-0.469867\pi$
$359$	3.58192			0.189046			0.0945231	+	0.995523i	$0.469867\pi$
$360$	−3.89172	−	16.3513i	−0.205112	−	0.861787i
$361$	−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
$366$	4.09545	+	4.79310i	0.214073	+	0.250539i
$367$	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
$372$	11.9229	−	7.70605i	0.618173	−	0.399540i
$373$	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
$375$	6.49356	+	19.8101i	0.335326	+	1.02299i
$376$	7.09151	+	2.99698i	0.365717	+	0.154557i
$377$	−4.03359	−	6.03838i	−0.207740	−	0.310992i
$378$	−4.69572	+	20.0353i	−0.241522	+	1.03050i
$379$	−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
$381$	−8.95257	+	9.99487i	−0.458654	+	0.512053i
$382$	−10.8216	−	26.3029i	−0.553683	−	1.34577i
$383$	5.29523	−	9.17162i	0.270574	−	0.468648i	−0.698435	−	0.715673i	$-0.746120\pi$
$383$	5.29523	−	9.17162i	0.270574	−	0.468648i	0.969009	+	0.247026i	$0.0794532\pi$
$384$	17.8041	−	8.18627i	0.908560	−	0.417754i
$385$	22.3673			1.13994
$386$	11.1962	+	1.50116i	0.569870	+	0.0764069i
$387$	−7.11000	+	0.784620i	−0.361422	+	0.0398845i
$388$	24.3477	+	6.64848i	1.23607	+	0.337526i
$389$		−	13.7221i		−	0.695737i	−0.937543	−	0.347868i	$-0.886906\pi$
$389$		−	13.7221i		−	0.695737i	0.937543	−	0.347868i	$-0.113094\pi$
$390$	−4.74728	+	16.8379i	−0.240388	+	0.852621i
$391$			14.7015i			0.743485i
$392$	−0.293921	−	2.36298i	−0.0148452	−	0.119348i
$393$	18.7785	−	6.15541i	0.947248	−	0.310499i
$394$	−2.87417	+	21.4366i	−0.144799	+	1.07996i
$395$	14.1410			0.711513
$396$	3.77463	−	23.8976i	0.189682	−	1.20090i
$397$	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
$399$	−14.0430	−	12.5785i	−0.703030	−	0.629715i
$400$	−3.74862	+	2.11688i	−0.187431	+	0.105844i
$401$	−8.45838	+	4.88345i	−0.422391	+	0.243868i	−0.696100	−	0.717945i	$-0.745083\pi$
$401$	−8.45838	+	4.88345i	−0.422391	+	0.243868i	0.273709	+	0.961813i	$0.411750\pi$
$402$	−3.35859	−	18.0999i	−0.167511	−	0.902743i
$403$	−14.7446	+	0.964502i	−0.734480	+	0.0480453i
$404$	−7.37902	−	7.44970i	−0.367120	−	0.370636i
$405$	17.0113	+	5.33274i	0.845299	+	0.264986i
$406$	4.87060	−	6.31626i	0.241724	−	0.313471i
$407$	10.5459	−	18.2661i	0.522742	−	0.905415i
$408$	31.4731	+	21.8426i	1.55815	+	1.08137i
$409$	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
$414$	−6.99881	+	3.82552i	−0.343973	+	0.188014i
$415$		−	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	$0.0849347\pi$
$419$	14.5467	+	25.1957i	0.710655	+	1.23089i	−0.253956	+	0.967216i	$0.581732\pi$
$420$	−19.1913	+	0.963990i	−0.936438	+	0.0470379i
$421$	−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
$423$	−6.58128	+	4.83396i	−0.319993	+	0.235035i
$424$	1.37403	−	3.25127i	0.0667289	−	0.157895i
$425$	−7.28878	−	4.20818i	−0.353558	−	0.204127i
$426$	−23.7441	−	27.7888i	−1.15040	−	1.34637i
$427$	6.24187	−	3.60374i	0.302065	−	0.174397i
$428$	−19.6573	+	19.4708i	−0.950170	+	0.941155i
$429$	−15.5410	+	19.8140i	−0.750329	+	0.956630i
$430$	−2.54141	−	6.17710i	−0.122558	−	0.297886i
$431$	3.63631	+	6.29827i	0.175155	+	0.303377i	0.940215	−	0.340582i	$-0.110624\pi$
$431$	3.63631	+	6.29827i	0.175155	+	0.303377i	−0.765060	+	0.643959i	$0.777291\pi$
$432$	−2.20871	+	20.6669i	−0.106267	+	0.994338i
$433$	−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
$435$	−5.14708	−	4.61032i	−0.246784	−	0.221048i
$436$	4.81793	+	18.3298i	0.230737	+	0.877838i
$437$		−	7.30731i		−	0.349556i
$438$	2.15269	−	6.08309i	0.102859	−	0.290661i
$439$	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	$-0.557756\pi$
$443$	−7.59619			−0.360906			−0.180453	+	0.983584i	$0.557756\pi$
$444$	−8.26122	+	16.1269i	−0.392060	+	0.765348i
$445$	−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	0.652402	−	0.757873i	$-0.273762\pi$
$449$	6.82867	+	3.94253i	0.322265	+	0.186060i	−0.330137	+	0.943933i	$0.607095\pi$
$450$	0.106717	−	4.56494i	0.00503067	−	0.215193i
$451$	14.5673	+	8.41044i	0.685948	+	0.396032i
$452$	6.47785	−	23.7228i	0.304693	−	1.11583i
$453$	6.86275	+	20.9363i	0.322440	+	0.983675i
$454$	−2.12941	−	5.17570i	−0.0999380	−	0.242908i
$455$	17.9364	+	8.84812i	0.840871	+	0.414806i
$456$	−15.6436	−	10.8568i	−0.732579	−	0.508416i
$457$	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
$459$	−36.9911	+	16.8158i	−1.72660	+	0.784893i
$460$	−5.24130	−	5.29150i	−0.244377	−	0.246717i
$461$	−34.1273	−	19.7034i	−1.58947	−	0.917679i	−0.993395	−	0.114749i	$-0.963394\pi$
$461$	−34.1273	−	19.7034i	−1.58947	−	0.917679i	−0.596072	−	0.802931i	$-0.703273\pi$
$462$	−26.0746	−	9.22729i	−1.21310	−	0.429293i
$463$		−	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
$465$	−13.3610	+	4.37960i	−0.619599	+	0.203099i
$466$	−0.951949	−	0.734067i	−0.0440982	−	0.0340050i
$467$	22.6893			1.04994			0.524969	−	0.851121i	$-0.324077\pi$
$467$	22.6893			1.04994			0.524969	+	0.851121i	$0.324077\pi$
$468$	12.4804	−	17.6703i	0.576905	−	0.816812i
$469$	−21.0457			−0.971798
$470$	−6.03828	−	4.65624i	−0.278525	−	0.214776i
$471$	28.2140	−	9.24831i	1.30003	−	0.426140i
$472$	−1.89961	+	1.43616i	−0.0874367	+	0.0661047i
$473$		−	9.61458i		−	0.442079i
$474$	−16.4849	−	5.83367i	−0.757176	−	0.267949i
$475$	3.62286	+	2.09166i	0.166228	+	0.0959720i
$476$	31.1166	−	30.8214i	1.42623	−	1.41269i
$477$	2.21624	+	3.01734i	0.101475	+	0.138154i
$478$	−2.10948	+	2.73561i	−0.0964856	+	0.125124i
$479$	3.31239	+	5.73723i	0.151347	+	0.262141i	0.931723	−	0.363170i	$-0.118306\pi$
$479$	3.31239	+	5.73723i	0.151347	+	0.262141i	−0.780376	+	0.625311i	$0.784972\pi$
$480$	−19.1154	+	3.35884i	−0.872493	+	0.153310i
$481$	15.6825	−	10.4758i	0.715062	−	0.477656i
$482$	7.48056	+	18.1821i	0.340730	+	0.828172i
$483$	2.84027	+	8.66488i	0.129237	+	0.394266i
$484$	10.1474	+	2.77090i	0.461247	+	0.125950i
$485$	−21.6483	−	12.4987i	−0.983001	−	0.567536i
$486$	−17.6310	−	13.2344i	−0.799756	−	0.600325i
$487$	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	0.810795	−	0.585330i	$-0.199035\pi$
$491$	−2.24938	−	3.89604i	−0.101513	−	0.175826i	−0.912308	+	0.409504i	$0.865702\pi$
$492$	−12.8613	−	6.58838i	−0.579833	−	0.297027i
$493$	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
$498$	−11.1230	+	31.4315i	−0.498433	+	1.40848i
$499$		−	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
$501$	23.8953	+	21.4034i	1.06756	+	0.956232i
$502$	10.0255	+	24.3678i	0.447461	+	1.08759i
$503$	−21.1482	+	36.6298i	−0.942952	+	1.63324i	−0.183152	+	0.983085i	$0.558630\pi$
$503$	−21.1482	+	36.6298i	−0.942952	+	1.63324i	−0.759800	+	0.650157i	$0.774703\pi$
$504$	22.7699	+	6.79330i	1.01425	+	0.302598i
$505$	5.19258	+	8.99382i	0.231067	+	0.400220i
$506$	−4.07901	−	9.91436i	−0.181334	−	0.440747i
$507$	−20.3005	+	9.74114i	−0.901577	+	0.432619i
$508$	10.9035	+	11.0079i	0.483765	+	0.488399i
$509$	12.2759	−	7.08748i	0.544118	−	0.314147i	−0.202628	−	0.979256i	$-0.564948\pi$
$509$	12.2759	−	7.08748i	0.544118	−	0.314147i	0.746746	+	0.665109i	$0.231615\pi$
$510$	−24.6482	−	28.8469i	−1.09144	−	1.27736i
$511$	−6.38867	−	3.68850i	−0.282618	−	0.163170i
$512$	−8.20880	−	21.0859i	−0.362781	−	0.931874i
$513$	18.3863	−	8.35823i	0.811776	−	0.369025i
$514$	5.24249	−	39.1004i	0.231236	−	1.72464i
$515$	−8.54082			−0.376353
$516$	0.414371	+	8.24936i	0.0182417	+	0.363158i
$517$	−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	$0.258077\pi$
$521$			33.0887i			1.44964i	−0.688938	+	0.724820i	$0.741923\pi$
$522$	4.09828	+	7.49783i	0.179377	+	0.328171i
$523$	−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
$528$	−27.2852	−	5.99779i	−1.18744	−	0.261020i
$529$	9.73284	−	16.8578i	0.423167	−	0.732946i
$530$	−2.13476	+	2.76839i	−0.0927280	+	0.120251i
$531$	−0.277058	−	2.51062i	−0.0120233	−	0.108952i
$532$	−15.4664	+	15.3197i	−0.670553	+	0.664191i
$533$	8.35454	+	12.5069i	0.361875	+	0.541736i
$534$	1.44756	+	7.80109i	0.0626419	+	0.337586i
$535$	23.7317	−	13.7015i	1.02601	−	0.592368i
$536$	−21.0942	+	2.62382i	−0.911132	+	0.113332i
$537$	21.4244	+	19.1902i	0.924532	+	0.828118i
$538$	7.99697	−	3.29015i	0.344774	−	0.141848i
$539$	−1.69735	+	2.93990i	−0.0731101	+	0.126630i
$540$	7.31915	−	19.2404i	0.314966	−	0.827976i
$541$	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
$543$	16.9118	−	5.54354i	0.725755	−	0.237896i
$544$	27.3458	−	34.7719i	1.17244	−	1.49083i
$545$		−	18.7709i		−	0.804056i
$546$	−17.2591	−	17.7141i	−0.738623	−	0.758092i
$547$			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
$549$	0.846947	+	7.67480i	0.0361468	+	0.327552i
$550$	6.08298	+	0.815593i	0.259379	+	0.0347770i
$551$	−7.82832			−0.333498
$552$	3.92710	+	8.33077i	0.167149	+	0.354581i
$553$	−9.99565	+	17.3130i	−0.425058	+	0.736222i
$554$	−11.6275	−	28.2616i	−0.494005	−	1.20072i
$555$	11.9737	−	13.3677i	0.508254	−	0.567428i
$556$	2.09806	−	7.68340i	0.0889776	−	0.325849i
$557$	−16.0205	+	9.24946i	−0.678812	+	0.391912i	−0.799407	−	0.600790i	$-0.794853\pi$
$557$	−16.0205	+	9.24946i	−0.678812	+	0.391912i	0.120595	+	0.992702i	$0.461520\pi$
$558$	17.3822	+	0.406353i	0.735849	+	0.0172023i
$559$	3.80336	−	7.70995i	0.160865	−	0.326096i
$560$	−0.211509	+	22.1871i	−0.00893789	+	0.937576i
$561$	−17.0120	−	51.8990i	−0.718249	−	2.19118i
$562$	0.799020	+	0.616140i	0.0337046	+	0.0259903i
$563$	9.52361	−	16.4954i	0.401372	−	0.695198i	−0.592519	−	0.805556i	$-0.701867\pi$
$563$	9.52361	−	16.4954i	0.401372	−	0.695198i	0.993892	+	0.110359i	$0.0352000\pi$
$564$	5.11825	+	7.91901i	0.215517	+	0.333450i
$565$	−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	−0.108126	−	0.994137i	$-0.534485\pi$
$569$	16.6680	−	9.62328i	0.698759	−	0.403429i	0.806885	+	0.590708i	$0.201152\pi$
$570$	12.2513	+	14.3383i	0.513150	+	0.600564i
$571$			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
$576$	23.6693	+	3.97020i	0.986222	+	0.165425i
$577$	−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
$579$	10.3055	+	9.23081i	0.428282	+	0.383619i
$580$	−5.66879	+	5.61500i	−0.235384	+	0.233150i
$581$	33.0104	+	19.0586i	1.36950	+	0.790683i
$582$	20.0804	+	23.5010i	0.832358	+	0.974148i
$583$	−4.35788	+	2.51602i	−0.180485	+	0.104203i
$584$	−6.86327	−	2.90052i	−0.284004	−	0.120024i
$585$	−16.4037	+	13.7839i	−0.678211	+	0.569893i
$586$	−8.25480	+	3.39623i	−0.341003	+	0.140297i
$587$	−10.4007	−	18.0146i	−0.429284	−	0.743542i	0.567526	−	0.823356i	$-0.307901\pi$
$587$	−10.4007	−	18.0146i	−0.429284	−	0.743542i	−0.996810	+	0.0798138i	$0.974567\pi$
$588$	1.32963	−	2.59560i	0.0548331	−	0.107041i
$589$	−7.96457	+	13.7950i	−0.328174	+	0.568414i
$590$	2.18120	−	0.897399i	0.0897986	−	0.0369453i
$591$	−17.6737	+	19.7313i	−0.726997	+	0.811638i
$592$	18.0192	+	10.6337i	0.740584	+	0.437041i
$593$		−	33.8531i		−	1.39018i	−0.718922	−	0.695090i	$-0.755364\pi$
$593$		−	33.8531i		−	1.39018i	0.718922	−	0.695090i	$-0.244636\pi$
$594$	20.2804	−	21.6036i	0.832116	−	0.886407i
$595$	−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	$-0.410885\pi$
$599$	13.5256			0.552642			0.276321	+	0.961065i	$0.410885\pi$
$600$	−5.25439	−	0.437618i	−0.214509	−	0.0178657i
$601$	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
$606$	−2.34298	−	12.6266i	−0.0951769	−	0.512922i
$607$	−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
$609$	9.28269	−	3.04278i	0.376154	−	0.123300i
$610$	−6.66779	+	2.74329i	−0.269971	+	0.111073i
$611$	−0.640608	−	9.79315i	−0.0259162	−	0.396188i
$612$	16.8332	+	43.7965i	0.680441	+	1.77037i
$613$	−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
$615$	10.6609	+	9.54910i	0.429887	+	0.385057i
$616$	−12.4328	+	29.4188i	−0.500932	+	1.18532i
$617$	−29.4281	−	16.9903i	−1.18473	−	0.684003i	−0.227625	−	0.973749i	$-0.573096\pi$
$617$	−29.4281	−	16.9903i	−1.18473	−	0.684003i	−0.957104	+	0.289745i	$0.906429\pi$
$618$	9.95644	+	3.52339i	0.400507	+	0.141731i
$619$			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
$621$	−9.72281	−	0.945443i	−0.390163	−	0.0379393i
$622$	−21.9665	+	28.4864i	−0.880775	+	1.14220i
$623$	9.07070			0.363410
$624$	−19.5074	−	15.6032i	−0.780922	−	0.624628i
$625$	−18.4604			−0.738414
$626$	−23.6774	+	30.7052i	−0.946339	+	1.22723i
$627$	8.45577	+	25.7962i	0.337691	+	1.03020i
$628$	−8.71550	−	33.1581i	−0.347786	−	1.32315i
$629$			40.9042i			1.63096i
$630$	−20.1005	−	12.2401i	−0.800823	−	0.487658i
$631$	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
$633$	−23.9981	+	26.7921i	−0.953839	+	1.06489i
$634$	14.8878	+	11.4803i	0.591269	+	0.455940i
$635$	−7.67275	−	13.2896i	−0.304484	−	0.527382i
$636$	3.63065	−	2.34658i	0.143965	−	0.0930479i
$637$	−2.52408	+	1.68607i	−0.100008	+	0.0668044i
$638$	−10.6213	+	4.36984i	−0.420499	+	0.173004i
$639$	−4.91032	−	44.4959i	−0.194249	−	1.76023i
$640$	2.55413	+	22.2647i	0.100961	+	0.880088i
$641$	−12.4529	−	7.18968i	−0.491860	−	0.283975i	0.233486	−	0.972360i	$-0.424987\pi$
$641$	−12.4529	−	7.18968i	−0.491860	−	0.283975i	−0.725346	+	0.688385i	$0.758320\pi$
$642$	−33.3175	+	6.18234i	−1.31494	+	0.243997i
$643$	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	$-0.945483\pi$
$647$	−16.2864	−	28.2089i	−0.640285	−	1.10901i	0.345084	−	0.938572i	$-0.387851\pi$
$648$	−16.4696	+	19.4101i	−0.646988	+	0.762500i
$649$	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	0.339386	−	0.940647i	$-0.389781\pi$
$653$	33.8257	−	19.5293i	1.32370	−	0.764240i	0.984317	+	0.176407i	$0.0564474\pi$
$654$	−7.74364	+	21.8821i	−0.302800	+	0.855658i
$655$			22.6001i			0.883060i
$656$	−8.48044	+	14.3704i	−0.331105	+	0.561071i
$657$	6.36945	−	4.67837i	0.248496	−	0.182521i
$658$	9.96886	−	4.10143i	0.388626	−	0.159890i
$659$	−6.42459	+	11.1277i	−0.250266	+	0.433474i	−0.963599	−	0.267351i	$-0.913852\pi$
$659$	−6.42459	+	11.1277i	−0.250266	+	0.433474i	0.713333	+	0.700826i	$0.247185\pi$
$660$	24.6260	+	12.6150i	0.958564	+	0.491038i
$661$	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
$663$	6.88839	−	48.3476i	0.267523	−	1.87767i
$664$	35.4627	+	14.9870i	1.37622	+	0.581610i
$665$	18.6722	−	10.7804i	0.724075	−	0.418045i
$666$	−19.4729	+	10.6438i	−0.754561	+	0.412440i
$667$	3.27906	+	1.89316i	0.126966	+	0.0733036i
$668$	26.3173	−	26.0676i	1.01825	−	1.00859i
$669$	−1.28670	+	1.43650i	−0.0497466	+	0.0555383i
$670$	20.8665	+	2.79773i	0.806141	+	0.108086i
$671$	−10.3783			−0.400651
$672$	9.39952	−	25.7773i	0.362594	−	0.994381i
$673$	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	$-0.816045\pi$
$677$		−	28.4274i		−	1.09255i	0.837605	−	0.546276i	$-0.183955\pi$
$678$	22.8979	−	19.5650i	0.879387	−	0.751390i
$679$	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	−0.999829	−	0.0184794i	$-0.994118\pi$
$683$	−12.6467	+	21.9047i	−0.483911	+	0.838158i	0.515918	+	0.856638i	$0.327451\pi$
$684$	−8.36687	−	21.7689i	−0.319915	−	0.832354i
$685$	5.38912	−	9.33424i	0.205908	−	0.356643i
$686$	19.3127	+	14.8924i	0.737364	+	0.568596i
$687$	−5.92018	+	1.94058i	−0.225869	+	0.0740378i
$688$	9.53712	+	0.0909171i	0.363599	+	0.00346618i
$689$	−4.48989	+	0.293701i	−0.171051	+	0.0111891i
$690$	−1.66421	−	8.96868i	−0.0633554	−	0.341432i
$691$	−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
$693$	−20.0534	−	27.3021i	−0.761767	−	1.03712i
$694$	4.83874	+	11.7609i	0.183676	+	0.446439i
$695$	−3.94421	+	6.83157i	−0.149612	+	0.259136i
$696$	8.92476	−	4.20710i	0.338292	−	0.159470i
$697$	−32.6214			−1.23562
$698$	−38.7444	−	5.19476i	−1.46650	−	0.196624i
$699$	−0.458590	−	1.39903i	−0.0173455	−	0.0529162i
$700$	−1.58784	+	5.81489i	−0.0600146	+	0.219782i
$701$			17.2824i			0.652747i	0.945241	+	0.326374i	$0.105827\pi$
$701$			17.2824i			0.652747i	−0.945241	+	0.326374i	$0.894173\pi$
$702$	24.8089	−	9.30141i	0.936353	−	0.351059i
$703$		−	20.3313i		−	0.766809i
$704$	−8.79378	+	31.0367i	−0.331428	+	1.16974i
$705$	−2.90887	−	8.87415i	−0.109554	−	0.334220i
$706$	−0.409898	+	3.05717i	−0.0154267	+	0.115058i
$707$	−14.6816			−0.552158
$708$	−2.91294	+	0.146319i	−0.109475	+	0.00549900i
$709$	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
$711$	−12.6782	−	17.2609i	−0.475468	−	0.647334i
$712$	9.09163	−	1.13087i	0.340723	−	0.0423811i
$713$	6.67225	−	3.85223i	0.249878	−	0.144267i
$714$	52.7402	−	9.78636i	1.97375	−	0.366245i
$715$	−15.9967	−	23.9474i	−0.598242	−	0.895583i
$716$	23.5960	−	23.3721i	0.881823	−	0.873456i
$717$	−4.02039	+	1.31785i	−0.150144	+	0.0492159i
$718$	3.09331	−	4.01144i	0.115441	−	0.149706i
$719$	0.122727	−	0.212570i	0.00457695	−	0.00792751i	−0.863728	−	0.503959i	$-0.831876\pi$
$719$	0.122727	−	0.212570i	0.00457695	−	0.00792751i	0.868305	+	0.496031i	$0.165210\pi$
$720$	−21.6729	−	9.76239i	−0.807701	−	0.363823i
$721$	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
$726$	8.36894	+	9.79457i	0.310601	+	0.363511i
$727$			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
$732$	8.90466	−	0.447287i	0.329126	−	0.0165322i
$733$	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
$735$	−1.92715	+	2.15152i	−0.0710839	+	0.0793598i
$736$	9.87305	−	3.95239i	0.363926	−	0.145687i
$737$	26.2444	+	15.1522i	0.966724	+	0.558139i
$738$	−8.48853	−	15.5298i	−0.312467	−	0.571660i
$739$	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
$741$	−3.42385	+	24.0310i	−0.125778	+	0.882802i
$742$	−1.88039	−	4.57045i	−0.0690314	−	0.167786i
$743$	−15.7175	−	27.2235i	−0.576619	−	0.998733i	−0.995864	−	0.0908602i	$-0.971038\pi$
$743$	−15.7175	−	27.2235i	−0.576619	−	0.998733i	0.419245	−	0.907873i	$-0.362295\pi$
$744$	1.66635	−	20.0075i	0.0610913	−	0.733510i
$745$	0.725127	−	1.25596i	0.0265666	−	0.0460147i
$746$	−2.09186	−	5.08443i	−0.0765884	−	0.186154i
$747$	−32.9111	+	24.1733i	−1.20415	+	0.884454i
$748$	−60.9935	+	16.0320i	−2.23014	+	0.586186i
$749$			38.7399i			1.41552i
$750$	27.7934	+	9.83552i	1.01487	+	0.359143i
$751$	−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
$756$	18.3826	+	22.5611i	0.668570	+	0.820538i
$757$	−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	0.570700	−	0.821159i	$-0.306672\pi$
$761$	3.99740	+	2.30790i	0.144905	+	0.0836612i	−0.425794	+	0.904820i	$0.640005\pi$
$762$	3.46207	+	18.6576i	0.125418	+	0.675894i
$763$	22.9813	+	13.2683i	0.831980	+	0.480344i
$764$	−38.8025	−	10.5956i	−1.40382	−	0.383334i
$765$	−5.09729	−	46.1902i	−0.184293	−	1.67001i
$766$	−5.69853	−	13.8507i	−0.205896	−	0.500447i
$767$	2.72247	+	1.34301i	0.0983027	+	0.0484933i
$768$	6.20748	−	27.0086i	0.223993	−	0.974591i
$769$	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
$771$	32.2368	−	35.9900i	1.16098	−	1.29615i
$772$	11.3501	−	11.2424i	0.408498	−	0.404622i
$773$	2.81129	+	1.62310i	0.101115	+	0.0583788i	0.549705	−	0.835359i	$-0.314740\pi$
$773$	2.81129	+	1.62310i	0.101115	+	0.0583788i	−0.448590	+	0.893738i	$0.648074\pi$
$774$	−5.26142	+	8.64019i	−0.189118	+	0.310565i
$775$			4.41068i			0.158436i
$776$	28.4722	−	21.5258i	1.02209	−	0.772731i
$777$	7.90255	+	24.1085i	0.283502	+	0.864887i
$778$	−15.3676	−	11.8502i	−0.550954	−	0.424852i
$779$	16.2143			0.580939
$780$	14.7573	+	19.8576i	0.528398	+	0.711016i
$781$	60.1701			2.15305
$782$	16.4644	+	12.6960i	0.588766	+	0.454009i
$783$	−1.01285	+	10.4161i	−0.0361964	+	0.372239i
$784$	−2.90016	−	1.71148i	−0.103577	−	0.0611241i
$785$			33.9560i			1.21194i
$786$	9.32335	−	26.3460i	0.332553	−	0.939732i
$787$	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
$789$	−36.2733	−	32.4906i	−1.29136	−	1.15670i
$790$	12.2121	−	15.8368i	0.434485	−	0.563447i
$791$	−17.2160	−	29.8190i	−0.612131	−	1.06024i
$792$	−23.5035	−	24.8650i	−0.835162	−	0.883538i
$793$	−8.32241	−	4.10549i	−0.295537	−	0.145790i
$794$	−3.89175	−	9.45921i	−0.138113	−	0.335695i
$795$	−4.06856	+	1.33364i	−0.144297	+	0.0472992i
$796$	−1.45652	+	5.33397i	−0.0516248	+	0.189057i
$797$	−2.03875	−	1.17707i	−0.0722162	−	0.0416940i	0.463457	−	0.886119i	$-0.346609\pi$
$797$	−2.03875	−	1.17707i	−0.0722162	−	0.0416940i	−0.535673	+	0.844425i	$0.679942\pi$
$798$	−26.2143	+	4.86428i	−0.927977	+	0.172194i
$799$	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
$804$	−23.1709	−	11.8696i	−0.817173	−	0.418608i
$805$	−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	−0.651257	−	0.758857i	$-0.725758\pi$
$809$	−9.09309	+	5.24990i	−0.319696	+	0.184577i	0.331561	+	0.943434i	$0.392425\pi$
$810$	20.6630	−	14.4459i	0.726025	−	0.507579i
$811$		−	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
$813$	7.88788	−	8.80623i	0.276640	−	0.308848i
$814$	−11.3491	−	27.5849i	−0.397786	−	0.966851i
$815$	−15.7841	+	27.3388i	−0.552892	+	0.957636i
$816$	51.6418	−	16.3842i	1.80782	−	0.573562i
$817$	−4.63394	−	8.02623i	−0.162121	−	0.280802i
$818$	−14.0274	−	34.0948i	−0.490458	−	1.19210i
$819$	−5.28066	−	29.8264i	−0.184521	−	1.04222i
$820$	11.7414	−	11.6300i	0.410028	−	0.406138i
$821$	48.0908	−	27.7652i	1.67838	−	0.969013i	0.715686	−	0.698422i	$-0.246114\pi$
$821$	48.0908	−	27.7652i	1.67838	−	0.969013i	0.962694	−	0.270591i	$-0.0872190\pi$
$822$	−10.1331	+	8.65816i	−0.353431	+	0.301988i
$823$	−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
$825$	5.59908	+	5.01519i	0.194935	+	0.174606i
$826$	−0.443099	+	3.30479i	−0.0154174	+	0.114988i
$827$	22.0817			0.767857			0.383928	−	0.923363i	$-0.374571\pi$
$827$	22.0817			0.767857			0.383928	+	0.923363i	$0.374571\pi$
$828$	−1.75984	+	11.1418i	−0.0611588	+	0.387203i
$829$	−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
$834$	7.41621	−	6.33676i	0.256802	−	0.219424i
$835$	−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	$0.434894\pi$
$839$	−21.6203	+	37.4475i	−0.746416	+	1.29283i	−0.949530	+	0.313676i	$0.898439\pi$
$840$	−15.4938	+	22.3251i	−0.534587	+	0.770289i
$841$	−12.4719	+	21.6019i	−0.430064	+	0.744892i
$842$	−13.5363	+	17.5541i	−0.466493	+	0.604954i
$843$	0.384918	+	1.17428i	0.0132573	+	0.0404443i
$844$	29.2278	+	29.5077i	1.00606	+	1.01570i
$845$	−3.35459	−	25.5315i	−0.115401	−	0.878311i
$846$	−0.269894	+	11.5450i	−0.00927913	+	0.396927i
$847$	12.7551	−	7.36415i	0.438270	−	0.253035i
$848$	−2.45454	−	4.34656i	−0.0842894	−	0.149262i
$849$	2.13775	−	2.38664i	0.0733675	−	0.0819093i
$850$	−11.0073	+	4.52868i	−0.377548	+	0.155332i
$851$	−4.91682	+	8.51619i	−0.168546	+	0.291931i
$852$	−51.6262	+	2.59322i	−1.76869	+	0.0888423i
$853$	−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
$855$	2.53359	+	22.9587i	0.0866470	+	0.785170i
$856$	4.82981	+	38.8293i	0.165079	+	1.32716i
$857$			33.7371i			1.15244i	0.817296	+	0.576218i	$0.195472\pi$
$857$			33.7371i			1.15244i	−0.817296	+	0.576218i	$0.804528\pi$
$858$	8.76896	+	34.5159i	0.299367	+	1.17835i
$859$		−	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
$861$	−19.2267	+	6.30234i	−0.655244	+	0.214783i
$862$	10.1938	+	1.36676i	0.347203	+	0.0465522i
$863$	19.5813			0.666554			0.333277	−	0.942829i	$-0.391846\pi$
$863$	19.5813			0.666554			0.333277	+	0.942829i	$0.391846\pi$
$864$	21.2378	+	20.3213i	0.722525	+	0.691345i
$865$	−13.8498	+	23.9886i	−0.470909	+	0.815638i
$866$	7.00362	+	17.0229i	0.237993	+	0.578460i
$867$	56.9640	+	51.0236i	1.93460	+	1.73285i
$868$	−22.1418	−	6.04612i	−0.751540	−	0.205219i
$869$	24.9296	−	14.3931i	0.845678	−	0.488252i
$870$	−9.60815	+	1.78287i	−0.325747	+	0.0604449i
$871$	15.0515	+	22.5324i	0.510000	+	0.763482i
$872$	24.6885	+	10.4337i	0.836060	+	0.353331i
$873$	4.15266	+	37.6302i	0.140546	+	1.27359i
$874$	−8.18357	−	6.31052i	−0.276813	−	0.213456i
$875$	16.8526	−	29.1895i	0.569721	−	0.986786i
$876$	−4.95351	−	7.66413i	−0.167364	−	0.258947i
$877$	−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	−0.223600	−	0.974681i	$-0.571781\pi$
$881$	15.0990	−	8.71742i	0.508699	−	0.293697i	0.732299	+	0.680984i	$0.238448\pi$
$882$	3.13414	−	1.71311i	0.105532	−	0.0576834i
$883$		−	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	$0.114384\pi$
$887$	23.0104	+	39.8552i	0.772613	+	1.33821i	−0.163513	+	0.986541i	$0.552283\pi$
$888$	10.9265	+	23.1789i	0.366668	+	0.777833i
$889$	21.6941			0.727596
$890$	−8.99346	−	1.20582i	−0.301462	−	0.0404193i
$891$	35.4175	−	7.91332i	1.18653	−	0.265106i
$892$	1.56709	+	1.58210i	0.0524701	+	0.0529727i
$893$	−9.16246	−	5.28995i	−0.306610	−	0.177021i
$894$	−1.36344	+	1.16499i	−0.0456003	+	0.0389631i
$895$	−28.4868	+	16.4469i	−0.952208	+	0.549758i
$896$	−29.0642	−	12.6108i	−0.970966	−	0.421298i
$897$	7.24570	−	9.23789i	0.241927	−	0.308444i
$898$	10.3125	−	4.24280i	0.344132	−	0.141584i
$899$	−4.12689	−	7.14799i	−0.137640	−	0.238399i
$900$	−5.02019	−	4.06175i	−0.167340	−	0.135392i
$901$	4.87942	−	8.45140i	0.162557	−	0.281557i
$902$	21.9992	−	9.05100i	0.732493	−	0.301365i
$903$	8.61456	+	7.71620i	0.286675	+	0.256779i
$904$	−20.9734	−	27.7414i	−0.697563	−	0.922667i
$905$			20.3536i			0.676576i
$906$	29.3736	+	10.3947i	0.975871	+	0.345341i
$907$	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	$-0.609169\pi$
$911$	−20.2998			−0.672564			−0.336282	+	0.941761i	$0.609169\pi$
$912$	−25.6684	+	8.14372i	−0.849965	+	0.269665i
$913$	−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
$918$	−13.1129	+	55.9489i	−0.432791	+	1.84659i
$919$	−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
$921$	1.19494	+	3.64544i	0.0393747	+	0.120121i
$922$	−51.5382	+	21.2041i	−1.69732	+	0.698318i
$923$	48.2505	+	23.8023i	1.58819	+	0.783461i
$924$	−32.8516	+	21.2328i	−1.08074	+	0.698508i
$925$	−2.81480	−	4.87538i	−0.0925502	−	0.160302i
$926$	−39.1268	−	30.1715i	−1.28579	−	0.991497i
$927$	7.65728	+	10.4251i	0.251498	+	0.342406i
$928$	−4.23420	−	10.5770i	−0.138994	−	0.347207i
$929$	−11.5057	−	6.64281i	−0.377489	−	0.217943i	0.299236	−	0.954179i	$-0.403268\pi$
$929$	−11.5057	−	6.64281i	−0.377489	−	0.217943i	−0.676725	+	0.736236i	$0.736601\pi$
$930$	−6.63360	+	18.7453i	−0.217524	+	0.614684i
$931$			3.27229i			0.107245i
$932$	−1.64419	+	0.432170i	−0.0538571	+	0.0141562i
$933$	−41.8650	+	13.7230i	−1.37060	+	0.449270i
$934$	19.5943	−	25.4102i	0.641145	−	0.831446i
$935$	62.4612			2.04270
$936$	−9.01138	−	29.2369i	−0.294546	−	0.955637i
$937$	−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
$939$	−45.1258	+	14.7918i	−1.47263	+	0.482714i
$940$	−10.4292	+	2.74128i	−0.340163	+	0.0894109i
$941$		−	6.71658i		−	0.218954i	−0.993989	−	0.109477i	$-0.965082\pi$
$941$		−	6.71658i		−	0.218954i	0.993989	−	0.109477i	$-0.0349177\pi$
$942$	14.0080	−	39.5841i	0.456406	−	1.28972i
$943$	−6.79172	−	3.92120i	−0.221169	−	0.127692i
$944$	−0.0321038	+	3.36766i	−0.00104489	+	0.109608i
$945$	−11.9281	−	26.2392i	−0.388020	−	0.853562i
$946$	−10.7675	−	8.30305i	−0.350082	−	0.269956i
$947$	17.9692	+	31.1236i	0.583921	+	1.01138i	0.995009	+	0.0997857i	$0.0318157\pi$
$947$	17.9692	+	31.1236i	0.583921	+	1.01138i	−0.411087	+	0.911596i	$0.634851\pi$
$948$	−20.7694	+	13.4238i	−0.674559	+	0.435984i
$949$	0.619990	+	9.47794i	0.0201257	+	0.307667i
$950$	5.47115	−	2.25096i	0.177508	−	0.0730309i
$951$	7.17201	+	21.8798i	0.232568	+	0.709501i
$952$	−7.64537	−	61.4650i	−0.247788	−	1.99209i
$953$	7.45821	+	4.30600i	0.241595	+	0.139485i	0.615910	−	0.787817i	$-0.288789\pi$
$953$	7.45821	+	4.30600i	0.241595	+	0.139485i	−0.374314	+	0.927302i	$0.622122\pi$
$954$	5.29309	+	0.123739i	0.171370	+	0.00400619i
$955$	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
$960$	−12.7462	+	24.3083i	−0.411382	+	0.784546i
$961$	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
$966$	12.1568	+	4.30204i	0.391138	+	0.138416i
$967$			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
$969$	−39.2154	−	35.1259i	−1.25978	−	1.12841i
$970$	−32.6928	+	13.4506i	−1.04970	+	0.431873i
$971$	−4.39573	+	7.61362i	−0.141066	+	0.244333i	−0.927898	−	0.372834i	$-0.878386\pi$
$971$	−4.39573	+	7.61362i	−0.141066	+	0.244333i	0.786833	+	0.617167i	$0.211720\pi$
$972$	−30.0473	+	8.31610i	−0.963769	+	0.266739i
$973$	−5.57596	−	9.65784i	−0.178757	−	0.309616i
$974$	4.06654	−	1.67307i	0.130300	−	0.0536088i
$975$	2.50599	+	6.23659i	0.0802560	+	0.199731i
$976$	0.0981393	−	10.2947i	0.00314136	−	0.329526i
$977$	−27.1638	+	15.6830i	−0.869047	+	0.501745i	−0.867032	−	0.498253i	$-0.833975\pi$
$977$	−27.1638	+	15.6830i	−0.869047	+	0.501745i	−0.00201588	+	0.999998i	$0.500642\pi$
$978$	29.6785	−	25.3587i	0.949012	−	0.810881i
$979$	−11.3114	−	6.53062i	−0.361513	−	0.208719i
$980$	2.34711	+	2.36959i	0.0749757	+	0.0756938i
$981$	−22.9122	+	16.8291i	−0.731530	+	0.537310i
$982$	−6.30578	−	0.845465i	−0.201226	−	0.0269799i
$983$	25.0538			0.799092			0.399546	−	0.916713i	$-0.369168\pi$
$983$	25.0538			0.799092			0.399546	+	0.916713i	$0.369168\pi$
$984$	−18.4853	+	8.71393i	−0.589291	+	0.277790i
$985$	−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
$990$	16.2532	+	29.7354i	0.516562	+	0.945054i
$991$	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
$996$	25.5949	+	39.6007i	0.811007	+	1.25480i
$997$	−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
$999$	−27.0520	−	2.63053i	−0.855887	−	0.0832262i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.p.b.35.1	✓	40	13.9	even	3	inner
156.2.p.b.35.7	yes	40	52.35	odd	6	inner
156.2.p.b.35.14	yes	40	156.35	even	6	inner
156.2.p.b.35.20	yes	40	39.35	odd	6	inner
156.2.p.b.107.1	yes	40	12.11	even	2	inner
156.2.p.b.107.7	yes	40	3.2	odd	2	inner
156.2.p.b.107.14	yes	40	1.1	even	1	trivial
156.2.p.b.107.20	yes	40	4.3	odd	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	156.2.p.b.107.14

Level	$156$
Weight	$2$
Character	156.107
Analytic conductor	$1.246$
Analytic rank	$0$
Dimension	$40$
Inner twists	$8$