LMFDB - Embedded newform 126.3.q.a.113.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(29,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.29"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			113.4
Character	$\chi$	$=$	126.113
Dual form			126.3.q.a.29.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.392589 - 2.97420i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-4.50944 - 2.60353i) q^{5} +(2.58390 + 3.36504i) q^{6} +(1.32288 + 2.29129i) q^{7} +2.82843i q^{8} +(-8.69175 + 2.33528i) q^{9} +7.36389 q^{10} +(-11.4711 + 6.62282i) q^{11} +(-5.54406 - 2.29422i) q^{12} +(-4.01343 + 6.95146i) q^{13} +(-3.24037 - 1.87083i) q^{14} +(-5.97306 + 14.4341i) q^{15} +(-2.00000 - 3.46410i) q^{16} -8.82428i q^{17} +(8.99388 - 9.00611i) q^{18} -3.48936 q^{19} +(-9.01889 + 5.20706i) q^{20} +(6.29540 - 4.83403i) q^{21} +(9.36608 - 16.2225i) q^{22} +(-32.7769 - 18.9238i) q^{23} +(8.41231 - 1.11041i) q^{24} +(1.05672 + 1.83030i) q^{25} -11.3517i q^{26} +(10.3579 + 24.9342i) q^{27} +5.29150 q^{28} +(-13.4482 + 7.76433i) q^{29} +(-2.89098 - 21.9017i) q^{30} +(11.9168 - 20.6405i) q^{31} +(4.89898 + 2.82843i) q^{32} +(24.2010 + 31.5172i) q^{33} +(6.23971 + 10.8075i) q^{34} -13.7766i q^{35} +(-4.64693 + 17.3898i) q^{36} +19.2212 q^{37} +(4.27358 - 2.46735i) q^{38} +(22.2507 + 9.20767i) q^{39} +(7.36389 - 12.7546i) q^{40} +(29.2689 + 16.8984i) q^{41} +(-4.29209 + 10.3720i) q^{42} +(-22.7888 - 39.4714i) q^{43} +26.4913i q^{44} +(45.2749 + 12.0984i) q^{45} +53.5245 q^{46} +(52.1392 - 30.1026i) q^{47} +(-9.51776 + 7.30837i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-2.58843 - 1.49443i) q^{50} +(-26.2452 + 3.46432i) q^{51} +(8.02685 + 13.9029i) q^{52} +63.7924i q^{53} +(-30.3169 - 23.2139i) q^{54} +68.9708 q^{55} +(-6.48074 + 3.74166i) q^{56} +(1.36989 + 10.3781i) q^{57} +(10.9804 - 19.0187i) q^{58} +(-94.5815 - 54.6066i) q^{59} +(19.0276 + 24.7798i) q^{60} +(-39.6043 - 68.5967i) q^{61} +33.7057i q^{62} +(-16.8489 - 16.8260i) q^{63} -8.00000 q^{64} +(36.1966 - 20.8981i) q^{65} +(-51.9261 - 21.4878i) q^{66} +(-53.3828 + 92.4617i) q^{67} +(-15.2841 - 8.82428i) q^{68} +(-43.4153 + 104.915i) q^{69} +(9.74151 + 16.8728i) q^{70} -94.1409i q^{71} +(-6.60516 - 24.5840i) q^{72} -3.40818 q^{73} +(-23.5411 + 13.5915i) q^{74} +(5.02881 - 3.86146i) q^{75} +(-3.48936 + 6.04375i) q^{76} +(-30.3496 - 17.5223i) q^{77} +(-33.7622 + 4.45655i) q^{78} +(-78.0889 - 135.254i) q^{79} +20.8282i q^{80} +(70.0930 - 40.5953i) q^{81} -47.7959 q^{82} +(130.062 - 75.0915i) q^{83} +(-2.07739 - 15.7380i) q^{84} +(-22.9743 + 39.7926i) q^{85} +(55.8210 + 32.2283i) q^{86} +(28.3723 + 36.9495i) q^{87} +(-18.7322 - 32.4450i) q^{88} +29.5689i q^{89} +(-64.0051 + 17.1967i) q^{90} -21.2371 q^{91} +(-65.5539 + 37.8476i) q^{92} +(-66.0673 - 27.3397i) q^{93} +(-42.5715 + 73.7360i) q^{94} +(15.7351 + 9.08466i) q^{95} +(6.48903 - 15.6810i) q^{96} +(40.7964 + 70.6614i) q^{97} -9.89949i q^{98} +(84.2374 - 84.3519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 36 q^{5} + 8 q^{6} - 32 q^{9} - 24 q^{12} - 44 q^{15} - 48 q^{16} + 48 q^{18} + 24 q^{19} + 72 q^{20} + 28 q^{21} + 24 q^{22} - 72 q^{23} - 16 q^{24} + 72 q^{25} - 108 q^{29} - 56 q^{30}+ \cdots - 440 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 + 36 * q^5 + 8 * q^6 - 32 * q^9 - 24 * q^12 - 44 * q^15 - 48 * q^16 + 48 * q^18 + 24 * q^19 + 72 * q^20 + 28 * q^21 + 24 * q^22 - 72 * q^23 - 16 * q^24 + 72 * q^25 - 108 * q^29 - 56 * q^30 - 60 * q^31 + 104 * q^33 - 48 * q^34 - 80 * q^36 - 168 * q^37 + 144 * q^38 + 64 * q^39 + 108 * q^41 + 60 * q^43 + 116 * q^45 - 324 * q^47 - 48 * q^48 - 84 * q^49 + 144 * q^50 - 268 * q^51 - 208 * q^54 + 264 * q^55 + 60 * q^57 - 432 * q^59 - 32 * q^60 - 192 * q^64 - 180 * q^65 - 112 * q^66 + 72 * q^67 + 72 * q^68 + 536 * q^69 + 96 * q^72 + 24 * q^73 + 288 * q^74 + 76 * q^75 + 24 * q^76 - 64 * q^78 + 12 * q^79 + 544 * q^81 - 288 * q^82 + 756 * q^83 + 112 * q^84 - 156 * q^85 + 360 * q^86 + 280 * q^87 - 48 * q^88 + 80 * q^90 - 168 * q^91 - 144 * q^92 + 436 * q^93 - 936 * q^95 - 64 * q^96 + 48 * q^97 - 440 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	−0.392589	−	2.97420i	−0.130863	−	0.991400i
$3$	−0.392589	−	2.97420i	−0.130863	−	0.991400i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	−4.50944	−	2.60353i	−0.901889	−	0.520706i	−0.0240762	−	0.999710i	$-0.507664\pi$
$5$	−4.50944	−	2.60353i	−0.901889	−	0.520706i	−0.877812	+	0.479004i	$0.840998\pi$
$6$	2.58390	+	3.36504i	0.430650	+	0.560839i
$7$	1.32288	+	2.29129i	0.188982	+	0.327327i
$7$	1.32288	+	2.29129i	0.188982	+	0.327327i
$8$			2.82843i			0.353553i
$9$	−8.69175	+	2.33528i	−0.965750	+	0.259475i
$10$	7.36389			0.736389
$11$	−11.4711	+	6.62282i	−1.04282	+	0.602074i	−0.920632	−	0.390432i	$-0.872326\pi$
$11$	−11.4711	+	6.62282i	−1.04282	+	0.602074i	−0.122191	+	0.992507i	$0.538992\pi$
$12$	−5.54406	−	2.29422i	−0.462005	−	0.191185i
$13$	−4.01343	+	6.95146i	−0.308725	+	0.534728i	−0.978084	−	0.208212i	$-0.933236\pi$
$13$	−4.01343	+	6.95146i	−0.308725	+	0.534728i	0.669359	+	0.742939i	$0.266569\pi$
$14$	−3.24037	−	1.87083i	−0.231455	−	0.133631i
$15$	−5.97306	+	14.4341i	−0.398204	+	0.962274i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	8.82428i		−	0.519075i	−0.965733	−	0.259538i	$-0.916430\pi$
$17$		−	8.82428i		−	0.519075i	0.965733	−	0.259538i	$-0.0835702\pi$
$18$	8.99388	−	9.00611i	0.499660	−	0.500340i
$19$	−3.48936			−0.183651			−0.0918253	−	0.995775i	$-0.529270\pi$
$19$	−3.48936			−0.183651			−0.0918253	+	0.995775i	$0.529270\pi$
$20$	−9.01889	+	5.20706i	−0.450944	+	0.260353i
$21$	6.29540	−	4.83403i	0.299781	−	0.230192i
$22$	9.36608	−	16.2225i	0.425731	−	0.737387i
$23$	−32.7769	−	18.9238i	−1.42508	−	0.822773i	−0.428357	−	0.903609i	$-0.640907\pi$
$23$	−32.7769	−	18.9238i	−1.42508	−	0.822773i	−0.996727	+	0.0808365i	$0.974241\pi$
$24$	8.41231	−	1.11041i	0.350513	−	0.0462671i
$25$	1.05672	+	1.83030i	0.0422689	+	0.0732118i
$26$		−	11.3517i		−	0.436603i
$27$	10.3579	+	24.9342i	0.383625	+	0.923489i
$28$	5.29150			0.188982
$29$	−13.4482	+	7.76433i	−0.463732	+	0.267736i	−0.713612	−	0.700541i	$-0.752942\pi$
$29$	−13.4482	+	7.76433i	−0.463732	+	0.267736i	0.249880	+	0.968277i	$0.419609\pi$
$30$	−2.89098	−	21.9017i	−0.0963661	−	0.730056i
$31$	11.9168	−	20.6405i	0.384412	−	0.665821i	−0.607275	−	0.794491i	$-0.707738\pi$
$31$	11.9168	−	20.6405i	0.384412	−	0.665821i	0.991687	+	0.128670i	$0.0410708\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	24.2010	+	31.5172i	0.733364	+	0.955066i
$34$	6.23971	+	10.8075i	0.183521	+	0.317867i
$35$		−	13.7766i		−	0.393617i
$36$	−4.64693	+	17.3898i	−0.129081	+	0.483051i
$37$	19.2212			0.519492			0.259746	−	0.965677i	$-0.416361\pi$
$37$	19.2212			0.519492			0.259746	+	0.965677i	$0.416361\pi$
$38$	4.27358	−	2.46735i	0.112463	−	0.0649303i
$39$	22.2507	+	9.20767i	0.570530	+	0.236094i
$40$	7.36389	−	12.7546i	0.184097	−	0.318866i
$41$	29.2689	+	16.8984i	0.713875	+	0.412156i	0.812494	−	0.582969i	$-0.198109\pi$
$41$	29.2689	+	16.8984i	0.713875	+	0.412156i	−0.0986192	+	0.995125i	$0.531443\pi$
$42$	−4.29209	+	10.3720i	−0.102193	+	0.246952i
$43$	−22.7888	−	39.4714i	−0.529973	−	0.917940i	−0.999389	−	0.0349628i	$-0.988869\pi$
$43$	−22.7888	−	39.4714i	−0.529973	−	0.917940i	0.469416	−	0.882977i	$-0.344465\pi$
$44$			26.4913i			0.602074i
$45$	45.2749	+	12.0984i	1.00611	+	0.268854i
$46$	53.5245			1.16358
$47$	52.1392	−	30.1026i	1.10935	−	0.640481i	0.170685	−	0.985326i	$-0.445402\pi$
$47$	52.1392	−	30.1026i	1.10935	−	0.640481i	0.938660	+	0.344845i	$0.112068\pi$
$48$	−9.51776	+	7.30837i	−0.198287	+	0.152258i
$49$	−3.50000	+	6.06218i	−0.0714286	+	0.123718i
$50$	−2.58843	−	1.49443i	−0.0517686	−	0.0298886i
$51$	−26.2452	+	3.46432i	−0.514612	+	0.0679278i
$52$	8.02685	+	13.9029i	0.154363	+	0.267364i
$53$			63.7924i			1.20363i	0.798636	+	0.601815i	$0.205555\pi$
$53$			63.7924i			1.20363i	−0.798636	+	0.601815i	$0.794445\pi$
$54$	−30.3169	−	23.2139i	−0.561424	−	0.429887i
$55$	68.9708			1.25401
$56$	−6.48074	+	3.74166i	−0.115728	+	0.0668153i
$57$	1.36989	+	10.3781i	0.0240331	+	0.182071i
$58$	10.9804	−	19.0187i	0.189318	−	0.327908i
$59$	−94.5815	−	54.6066i	−1.60308	−	0.925536i	−0.990867	−	0.134840i	$-0.956948\pi$
$59$	−94.5815	−	54.6066i	−1.60308	−	0.925536i	−0.612208	−	0.790697i	$-0.709719\pi$
$60$	19.0276	+	24.7798i	0.317126	+	0.412996i
$61$	−39.6043	−	68.5967i	−0.649251	−	1.12454i	−0.983302	−	0.181981i	$-0.941749\pi$
$61$	−39.6043	−	68.5967i	−0.649251	−	1.12454i	0.334051	−	0.942555i	$-0.391584\pi$
$62$			33.7057i			0.543641i
$63$	−16.8489	−	16.8260i	−0.267443	−	0.267080i
$64$	−8.00000			−0.125000
$65$	36.1966	−	20.8981i	0.556872	−	0.321510i
$66$	−51.9261	−	21.4878i	−0.786758	−	0.325573i
$67$	−53.3828	+	92.4617i	−0.796758	+	1.38003i	0.124958	+	0.992162i	$0.460120\pi$
$67$	−53.3828	+	92.4617i	−0.796758	+	1.38003i	−0.921717	+	0.387864i	$0.873213\pi$
$68$	−15.2841	−	8.82428i	−0.224766	−	0.129769i
$69$	−43.4153	+	104.915i	−0.629207	+	1.52050i
$70$	9.74151	+	16.8728i	0.139164	+	0.241040i
$71$		−	94.1409i		−	1.32593i	−0.748651	−	0.662964i	$-0.769298\pi$
$71$		−	94.1409i		−	1.32593i	0.748651	−	0.662964i	$-0.230702\pi$
$72$	−6.60516	−	24.5840i	−0.0917384	−	0.341444i
$73$	−3.40818			−0.0466874			−0.0233437	−	0.999727i	$-0.507431\pi$
$73$	−3.40818			−0.0466874			−0.0233437	+	0.999727i	$0.507431\pi$
$74$	−23.5411	+	13.5915i	−0.318123	+	0.183668i
$75$	5.02881	−	3.86146i	0.0670508	−	0.0514861i
$76$	−3.48936	+	6.04375i	−0.0459127	+	0.0795231i
$77$	−30.3496	−	17.5223i	−0.394150	−	0.227563i
$78$	−33.7622	+	4.45655i	−0.432849	+	0.0571352i
$79$	−78.0889	−	135.254i	−0.988467	−	1.71208i	−0.625381	−	0.780320i	$-0.715056\pi$
$79$	−78.0889	−	135.254i	−0.988467	−	1.71208i	−0.363087	−	0.931755i	$-0.618277\pi$
$80$			20.8282i			0.260353i
$81$	70.0930	−	40.5953i	0.865345	−	0.501176i
$82$	−47.7959			−0.582876
$83$	130.062	−	75.0915i	1.56702	−	0.904717i	0.570502	−	0.821296i	$-0.306749\pi$
$83$	130.062	−	75.0915i	1.56702	−	0.904717i	0.996514	−	0.0834211i	$-0.0265847\pi$
$84$	−2.07739	−	15.7380i	−0.0247308	−	0.187357i
$85$	−22.9743	+	39.7926i	−0.270286	+	0.468148i
$86$	55.8210	+	32.2283i	0.649082	+	0.374747i
$87$	28.3723	+	36.9495i	0.326119	+	0.424707i
$88$	−18.7322	−	32.4450i	−0.212865	−	0.368694i
$89$			29.5689i			0.332235i	0.986106	+	0.166117i	$0.0531230\pi$
$89$			29.5689i			0.332235i	−0.986106	+	0.166117i	$0.946877\pi$
$90$	−64.0051	+	17.1967i	−0.711168	+	0.191075i
$91$	−21.2371			−0.233374
$92$	−65.5539	+	37.8476i	−0.712542	+	0.411386i
$93$	−66.0673	−	27.3397i	−0.710401	−	0.293975i
$94$	−42.5715	+	73.7360i	−0.452888	+	0.784425i
$95$	15.7351	+	9.08466i	0.165632	+	0.0956280i
$96$	6.48903	−	15.6810i	0.0675940	−	0.163343i
$97$	40.7964	+	70.6614i	0.420581	+	0.728468i	0.995996	−	0.0893933i	$-0.0284928\pi$
$97$	40.7964	+	70.6614i	0.420581	+	0.728468i	−0.575415	+	0.817862i	$0.695159\pi$
$98$		−	9.89949i		−	0.101015i
$99$	84.2374	−	84.3519i	0.850883	−	0.852040i
$100$	4.22689			0.0422689
$101$	−0.619620	+	0.357738i	−0.00613485	+	0.00354196i	−0.503064	−	0.864249i	$-0.667794\pi$
$101$	−0.619620	+	0.357738i	−0.00613485	+	0.00354196i	0.496929	+	0.867791i	$0.334461\pi$
$102$	29.6940	−	22.8011i	0.291118	−	0.223540i
$103$	−89.9236	+	155.752i	−0.873044	+	1.51216i	−0.0142130	+	0.999899i	$0.504524\pi$
$103$	−89.9236	+	155.752i	−0.873044	+	1.51216i	−0.858831	+	0.512258i	$0.828809\pi$
$104$	−19.6617	−	11.3517i	−0.189055	−	0.109151i
$105$	−40.9743	+	5.40853i	−0.390232	+	0.0515099i
$106$	−45.1080	−	78.1294i	−0.425547	−	0.737070i
$107$			63.7076i			0.595398i	0.954660	+	0.297699i	$0.0962191\pi$
$107$			63.7076i			0.595398i	−0.954660	+	0.297699i	$0.903781\pi$
$108$	53.5452	+	6.99384i	0.495789	+	0.0647578i
$109$	−184.582			−1.69341			−0.846705	−	0.532063i	$-0.821417\pi$
$109$	−184.582			−1.69341			−0.846705	+	0.532063i	$0.821417\pi$
$110$	−84.4716	+	48.7697i	−0.767923	+	0.443361i
$111$	−7.54604	−	57.1678i	−0.0679824	−	0.515025i
$112$	5.29150	−	9.16515i	0.0472456	−	0.0818317i
$113$	108.448	+	62.6124i	0.959715	+	0.554092i	0.896085	−	0.443882i	$-0.146399\pi$
$113$	108.448	+	62.6124i	0.959715	+	0.554092i	0.0636298	+	0.997974i	$0.479732\pi$
$114$	−9.01616	−	11.7418i	−0.0790892	−	0.102999i
$115$	98.5372	+	170.671i	0.856845	+	1.48410i
$116$			31.0573i			0.267736i
$117$	18.6501	−	69.7928i	0.159403	−	0.596520i
$118$	154.451			1.30891
$119$	20.2190	−	11.6734i	0.169907	−	0.0980960i
$120$	−40.8258	−	16.8944i	−0.340215	−	0.140786i
$121$	27.2234	−	47.1523i	0.224987	−	0.389688i
$122$	97.0103	+	56.0090i	0.795167	+	0.459090i
$123$	38.7686	−	93.6856i	0.315192	−	0.761672i
$124$	−23.8336	−	41.2809i	−0.192206	−	0.332911i
$125$			119.172i			0.953373i
$126$	32.5334	+	8.69361i	0.258201	+	0.0689969i
$127$	186.865			1.47138			0.735688	−	0.677320i	$-0.236859\pi$
$127$	186.865			1.47138			0.735688	+	0.677320i	$0.236859\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	−108.449	+	83.2746i	−0.840692	+	0.645540i
$130$	−29.5544	+	51.1898i	−0.227342	+	0.393768i
$131$	12.5131	+	7.22447i	0.0955202	+	0.0551486i	0.546999	−	0.837133i	$-0.315770\pi$
$131$	12.5131	+	7.22447i	0.0955202	+	0.0551486i	−0.451479	+	0.892282i	$0.649103\pi$
$132$	78.7904	−	10.4002i	0.596897	−	0.0787892i
$133$	−4.61599	−	7.99514i	−0.0347067	−	0.0601138i
$134$		−	150.989i		−	1.12679i
$135$	18.2087	−	139.406i	0.134879	−	1.03264i
$136$	24.9588			0.183521
$137$	31.0324	−	17.9166i	0.226514	−	0.130778i	−0.382449	−	0.923977i	$-0.624919\pi$
$137$	31.0324	−	17.9166i	0.226514	−	0.130778i	0.608963	+	0.793199i	$0.291586\pi$
$138$	−21.0131	−	159.193i	−0.152269	−	1.15357i
$139$	−17.5299	+	30.3627i	−0.126115	+	0.218437i	−0.922168	−	0.386789i	$-0.873584\pi$
$139$	−17.5299	+	30.3627i	−0.126115	+	0.218437i	0.796053	+	0.605226i	$0.206917\pi$
$140$	−23.8617	−	13.7766i	−0.170441	−	0.0984041i
$141$	−110.000	−	143.255i	−0.780145	−	1.01599i
$142$	66.5677	+	115.299i	0.468786	+	0.811962i
$143$		−	106.321i		−	0.743502i
$144$	25.4731	+	25.4385i	0.176897	+	0.176657i
$145$	80.8586			0.557646
$146$	4.17415	−	2.40995i	0.0285901	−	0.0165065i
$147$	19.4042	+	8.02976i	0.132001	+	0.0546242i
$148$	19.2212	−	33.2921i	0.129873	−	0.224947i
$149$	145.432	+	83.9654i	0.976056	+	0.563526i	0.901077	−	0.433659i	$-0.142778\pi$
$149$	145.432	+	83.9654i	0.976056	+	0.563526i	0.0749788	+	0.997185i	$0.476111\pi$
$150$	−3.42855	+	8.28520i	−0.0228570	+	0.0552347i
$151$	−97.0005	−	168.010i	−0.642387	−	1.11265i	−0.984898	−	0.173133i	$-0.944611\pi$
$151$	−97.0005	−	168.010i	−0.642387	−	1.11265i	0.342511	−	0.939514i	$-0.388723\pi$
$152$		−	9.86941i		−	0.0649303i
$153$	20.6072	+	76.6984i	0.134687	+	0.501297i
$154$	49.5606			0.321822
$155$	−107.476	+	62.0513i	−0.693394	+	0.400331i
$156$	38.1988	−	29.3316i	0.244864	−	0.188023i
$157$	−8.25239	+	14.2936i	−0.0525630	+	0.0910417i	−0.891110	−	0.453788i	$-0.850072\pi$
$157$	−8.25239	+	14.2936i	−0.0525630	+	0.0910417i	0.838547	+	0.544830i	$0.183406\pi$
$158$	191.278	+	110.434i	1.21062	+	0.698952i
$159$	189.731	−	25.0442i	1.19328	−	0.157511i
$160$	−14.7278	−	25.5093i	−0.0920486	−	0.159433i
$161$		−	100.135i		−	0.621958i
$162$	−57.1408	+	99.2821i	−0.352721	+	0.612852i
$163$	−174.369			−1.06975			−0.534873	−	0.844933i	$-0.679641\pi$
$163$	−174.369			−1.06975			−0.534873	+	0.844933i	$0.679641\pi$
$164$	58.5377	−	33.7968i	0.356937	−	0.206078i
$165$	−27.0772	−	205.133i	−0.164104	−	1.24323i
$166$	−106.195	+	183.936i	−0.639732	+	1.10805i
$167$	−126.279	−	72.9072i	−0.756162	−	0.436570i	0.0717543	−	0.997422i	$-0.477140\pi$
$167$	−126.279	−	72.9072i	−0.756162	−	0.436570i	−0.827916	+	0.560852i	$0.810474\pi$
$168$	13.6727	+	17.8061i	0.0813852	+	0.105989i
$169$	52.2848	+	90.5599i	0.309378	+	0.535858i
$170$		−	64.9810i		−	0.382241i
$171$	30.3287	−	8.14863i	0.177361	−	0.0476528i
$172$	−91.1553			−0.529973
$173$	−50.3479	+	29.0684i	−0.291028	+	0.168025i	−0.638406	−	0.769700i	$-0.720406\pi$
$173$	−50.3479	+	29.0684i	−0.291028	+	0.168025i	0.347377	+	0.937725i	$0.387072\pi$
$174$	−60.8761	−	25.1915i	−0.349863	−	0.144779i
$175$	−2.79582	+	4.84251i	−0.0159761	+	0.0276715i
$176$	45.8842	+	26.4913i	0.260706	+	0.150519i
$177$	−125.279	+	302.742i	−0.707794	+	1.71041i
$178$	−20.9084	−	36.2143i	−0.117463	−	0.203451i
$179$			177.566i			0.991989i	0.868326	+	0.495995i	$0.165196\pi$
$179$			177.566i			0.991989i	−0.868326	+	0.495995i	$0.834804\pi$
$180$	66.2300	−	66.3200i	0.367944	−	0.368445i
$181$	42.0375			0.232251			0.116126	−	0.993235i	$-0.462952\pi$
$181$	42.0375			0.232251			0.116126	+	0.993235i	$0.462952\pi$
$182$	26.0100	−	15.0169i	0.142912	−	0.0825103i
$183$	−188.472	+	144.721i	−1.02990	+	0.790828i
$184$	53.5245	−	92.7072i	0.290894	−	0.503843i
$185$	−86.6770	−	50.0430i	−0.468524	−	0.270503i
$186$	100.248	−	13.2325i	0.538966	−	0.0711425i
$187$	58.4416	+	101.224i	0.312522	+	0.541304i
$188$		−	120.410i		−	0.640481i
$189$	−43.4293	+	56.7177i	−0.229784	+	0.300094i
$190$	−25.6953			−0.135238
$191$	−74.7660	+	43.1662i	−0.391445	+	0.226001i	−0.682786	−	0.730618i	$-0.739232\pi$
$191$	−74.7660	+	43.1662i	−0.391445	+	0.226001i	0.291341	+	0.956619i	$0.405899\pi$
$192$	3.14071	+	23.7936i	0.0163579	+	0.123925i
$193$	69.3030	−	120.036i	0.359083	−	0.621950i	−0.628725	−	0.777628i	$-0.716423\pi$
$193$	69.3030	−	120.036i	0.359083	−	0.621950i	0.987808	+	0.155678i	$0.0497562\pi$
$194$	−99.9303	−	57.6948i	−0.515105	−	0.297396i
$195$	−76.3657	−	99.4517i	−0.391619	−	0.510009i
$196$	7.00000	+	12.1244i	0.0357143	+	0.0618590i
$197$		−	39.4308i		−	0.200156i	−0.994980	−	0.100078i	$-0.968091\pi$
$197$		−	39.4308i		−	0.200156i	0.994980	−	0.100078i	$-0.0319093\pi$
$198$	−43.5235	+	162.874i	−0.219816	+	0.822598i
$199$	88.0429			0.442427			0.221213	−	0.975225i	$-0.428998\pi$
$199$	88.0429			0.442427			0.221213	+	0.975225i	$0.428998\pi$
$200$	−5.17686	+	2.98886i	−0.0258843	+	0.0149443i
$201$	295.957	+	122.472i	1.47242	+	0.609312i
$202$	0.505918	−	0.876275i	0.00250454	−	0.00433800i
$203$	−35.5806	−	20.5425i	−0.175274	−	0.101195i
$204$	−20.2448	+	48.9223i	−0.0992393	+	0.239815i
$205$	−87.9909	−	152.405i	−0.429224	−	0.743437i
$206$		−	254.342i		−	1.23467i
$207$	329.081	+	87.9374i	1.58976	+	0.424818i
$208$	32.1074			0.154363
$209$	40.0267	−	23.1094i	0.191515	−	0.110571i
$210$	46.3587	−	35.5973i	0.220756	−	0.169511i
$211$	−96.3691	+	166.916i	−0.456726	+	0.791072i	−0.998786	−	0.0492677i	$-0.984311\pi$
$211$	−96.3691	+	166.916i	−0.456726	+	0.791072i	0.542060	+	0.840340i	$0.317645\pi$
$212$	110.492	+	63.7924i	0.521187	+	0.300907i
$213$	−279.994	+	36.9587i	−1.31453	+	0.173515i
$214$	−45.0480	−	78.0255i	−0.210505	−	0.364605i
$215$			237.326i			1.10384i
$216$	−70.5246	+	29.2965i	−0.326503	+	0.135632i
$217$	63.0577			0.290588
$218$	226.065	−	130.519i	1.03700	−	0.598711i
$219$	1.33801	+	10.1366i	0.00610966	+	0.0462859i
$220$	68.9708	−	119.461i	0.313503	−	0.543004i
$221$	61.3416	+	35.4156i	0.277564	+	0.160252i
$222$	49.6657	+	64.6801i	0.223719	+	0.291352i
$223$	−89.9715	−	155.835i	−0.403459	−	0.698812i	0.590681	−	0.806905i	$-0.298859\pi$
$223$	−89.9715	−	155.835i	−0.403459	−	0.698812i	−0.994141	+	0.108093i	$0.965526\pi$
$224$			14.9666i			0.0668153i
$225$	−13.4590	−	13.4407i	−0.0598178	−	0.0597366i
$226$	−177.095			−0.783604
$227$	−82.1961	+	47.4559i	−0.362097	+	0.209057i	−0.670000	−	0.742361i	$-0.733706\pi$
$227$	−82.1961	+	47.4559i	−0.362097	+	0.209057i	0.307903	+	0.951418i	$0.400373\pi$
$228$	19.3452	+	8.00536i	0.0848475	+	0.0351112i
$229$	177.233	−	306.977i	0.773945	−	1.34051i	−0.161441	−	0.986882i	$-0.551614\pi$
$229$	177.233	−	306.977i	0.773945	−	1.34051i	0.935386	−	0.353629i	$-0.115052\pi$
$230$	−241.366	−	139.353i	−1.04942	−	0.605881i
$231$	−40.2000	+	97.1448i	−0.174026	+	0.420540i
$232$	−21.9608	−	38.0373i	−0.0946588	−	0.163954i
$233$			192.278i			0.825226i	0.910907	+	0.412613i	$0.135384\pi$
$233$			192.278i			0.825226i	−0.910907	+	0.412613i	$0.864616\pi$
$234$	26.5093	+	98.6660i	0.113288	+	0.421650i
$235$	−313.492			−1.33401
$236$	−189.163	+	109.213i	−0.801538	+	0.462768i
$237$	−371.616	+	285.351i	−1.56800	+	1.20401i
$238$	−16.5087	+	28.5939i	−0.0693644	+	0.120143i
$239$	−251.206	−	145.034i	−1.05107	−	0.606836i	−0.128122	−	0.991758i	$-0.540895\pi$
$239$	−251.206	−	145.034i	−1.05107	−	0.606836i	−0.922949	+	0.384922i	$0.874228\pi$
$240$	61.9473	−	8.17694i	0.258114	−	0.0340706i
$241$	55.9605	+	96.9265i	0.232201	+	0.402184i	0.958456	−	0.285242i	$-0.0920739\pi$
$241$	55.9605	+	96.9265i	0.232201	+	0.402184i	−0.726254	+	0.687426i	$0.758741\pi$
$242$			76.9993i			0.318179i
$243$	−148.256	−	192.533i	−0.610108	−	0.792318i
$244$	−158.417			−0.649251
$245$	31.5661	−	18.2247i	0.128841	−	0.0743865i
$246$	18.7641	+	142.155i	0.0762770	+	0.577864i
$247$	14.0043	−	24.2562i	0.0566976	−	0.0982031i
$248$	58.3800	+	33.7057i	0.235403	+	0.135910i
$249$	−274.398	−	357.352i	−1.10200	−	1.43515i
$250$	−84.2671	−	145.955i	−0.337068	−	0.583819i
$251$		−	203.517i		−	0.810826i	−0.914134	−	0.405413i	$-0.867128\pi$
$251$		−	203.517i		−	0.810826i	0.914134	−	0.405413i	$-0.132872\pi$
$252$	−45.9924	+	12.3571i	−0.182510	+	0.0490362i
$253$	501.315			1.98148
$254$	−228.862	+	132.133i	−0.901030	+	0.520210i
$255$	127.371	+	52.7080i	0.499493	+	0.206698i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	259.814	+	150.004i	1.01095	+	0.583673i	0.911470	−	0.411367i	$-0.134948\pi$
$257$	259.814	+	150.004i	1.01095	+	0.583673i	0.0994809	+	0.995039i	$0.468282\pi$
$258$	73.9387	−	178.675i	0.286584	−	0.692540i
$259$	25.4273	+	44.0413i	0.0981748	+	0.170044i
$260$		−	83.5926i		−	0.321510i
$261$	98.7566	−	98.8910i	0.378378	−	0.378893i
$262$	−20.4339			−0.0779919
$263$	−163.477	+	94.3833i	−0.621584	+	0.358872i	−0.777486	−	0.628901i	$-0.783505\pi$
$263$	−163.477	+	94.3833i	−0.621584	+	0.358872i	0.155901	+	0.987773i	$0.450172\pi$
$264$	−89.1440	+	68.4508i	−0.337667	+	0.259283i
$265$	166.085	−	287.668i	0.626737	−	1.08554i
$266$	11.3068	+	6.52800i	0.0425069	+	0.0245414i
$267$	87.9438	−	11.6084i	0.329377	−	0.0434772i
$268$	106.766	+	184.923i	0.398379	+	0.690013i
$269$		−	260.462i		−	0.968261i	−0.874996	−	0.484131i	$-0.839136\pi$
$269$		−	260.462i		−	0.968261i	0.874996	−	0.484131i	$-0.160864\pi$
$270$	76.2742	+	183.613i	0.282497	+	0.680047i
$271$	−142.144			−0.524518			−0.262259	−	0.964998i	$-0.584467\pi$
$271$	−142.144			−0.524518			−0.262259	+	0.964998i	$0.584467\pi$
$272$	−30.5682	+	17.6486i	−0.112383	+	0.0648844i
$273$	8.33744	+	63.1633i	0.0305401	+	0.231367i
$274$	−25.3378	+	43.8864i	−0.0924739	+	0.160169i
$275$	−24.2434	−	13.9969i	−0.0881579	−	0.0508980i
$276$	138.302	+	180.112i	0.501094	+	0.652579i
$277$	5.33049	+	9.23268i	0.0192436	+	0.0333310i	0.875487	−	0.483242i	$-0.160541\pi$
$277$	5.33049	+	9.23268i	0.0192436	+	0.0333310i	−0.856243	+	0.516573i	$0.827208\pi$
$278$		−	49.5822i		−	0.178353i
$279$	−55.3764	+	207.231i	−0.198482	+	0.742762i
$280$	38.9660			0.139164
$281$	−153.223	+	88.4636i	−0.545279	+	0.314817i	−0.747216	−	0.664582i	$-0.768610\pi$
$281$	−153.223	+	88.4636i	−0.545279	+	0.314817i	0.201937	+	0.979399i	$0.435276\pi$
$282$	236.019	+	97.6682i	0.836946	+	0.346341i
$283$	151.466	−	262.347i	0.535216	−	0.927022i	−0.463936	−	0.885869i	$-0.653563\pi$
$283$	151.466	−	262.347i	0.535216	−	0.927022i	0.999153	−	0.0411536i	$-0.0131033\pi$
$284$	−163.057	−	94.1409i	−0.574144	−	0.331482i
$285$	20.8422	−	50.3659i	0.0731304	−	0.176722i
$286$	75.1801	+	130.216i	0.262868	+	0.455300i
$287$			89.4179i			0.311561i
$288$	−49.1859	−	13.1435i	−0.170784	−	0.0456371i
$289$	211.132			0.730561
$290$	−99.0312	+	57.1757i	−0.341487	+	0.197158i
$291$	194.145	−	149.078i	0.667165	−	0.512294i
$292$	−3.40818	+	5.90314i	−0.0116719	+	0.0202162i
$293$	−465.106	−	268.529i	−1.58739	−	0.916481i	−0.993735	−	0.111763i	$-0.964350\pi$
$293$	−465.106	−	268.529i	−1.58739	−	0.916481i	−0.593657	−	0.804718i	$-0.702317\pi$
$294$	−29.4431	+	3.88643i	−0.100147	+	0.0132192i
$295$	284.340	+	492.491i	0.963864	+	1.66946i
$296$			54.3658i			0.183668i
$297$	−283.950	−	217.423i	−0.956062	−	0.732065i
$298$	−237.490			−0.796946
$299$	263.096	−	151.898i	0.879919	−	0.508021i
$300$	−1.65943	−	12.5716i	−0.00553143	−	0.0419054i
$301$	60.2936	−	104.432i	0.200311	−	0.346949i
$302$	237.602	+	137.179i	0.786760	+	0.454236i
$303$	1.30724	+	1.70243i	0.00431433	+	0.00561859i
$304$	6.97873	+	12.0875i	0.0229563	+	0.0397615i
$305$			412.444i			1.35227i
$306$	−79.4725	−	79.3646i	−0.259714	−	0.259361i
$307$	509.581			1.65987			0.829937	−	0.557858i	$-0.188376\pi$
$307$	509.581			1.65987			0.829937	+	0.557858i	$0.188376\pi$
$308$	−60.6991	+	35.0446i	−0.197075	+	0.113781i
$309$	498.541	+	206.304i	1.61340	+	0.667651i
$310$	87.7538	−	151.994i	0.283077	−	0.490304i
$311$	−270.660	−	156.265i	−0.870289	−	0.502461i	−0.00284453	−	0.999996i	$-0.500905\pi$
$311$	−270.660	−	156.265i	−0.870289	−	0.502461i	−0.867444	+	0.497535i	$0.834239\pi$
$312$	−26.0432	+	62.9344i	−0.0834719	+	0.201713i
$313$	−282.583	−	489.447i	−0.902820	−	1.56373i	−0.823817	−	0.566855i	$-0.808160\pi$
$313$	−282.583	−	489.447i	−0.902820	−	1.56373i	−0.0790023	−	0.996874i	$-0.525173\pi$
$314$		−	23.3413i		−	0.0743353i
$315$	32.1721	+	119.743i	0.102134	+	0.380135i
$316$	−312.356			−0.988467
$317$	118.015	−	68.1358i	0.372286	−	0.214939i	−0.302171	−	0.953254i	$-0.597711\pi$
$317$	118.015	−	68.1358i	0.372286	−	0.214939i	0.674457	+	0.738314i	$0.264378\pi$
$318$	−214.664	+	164.833i	−0.675043	+	0.518343i
$319$	102.843	−	178.130i	0.322393	−	0.558402i
$320$	36.0755	+	20.8282i	0.112736	+	0.0650882i
$321$	189.479	−	25.0109i	0.590278	−	0.0779155i
$322$	70.8063	+	122.640i	0.219895	+	0.380870i
$323$			30.7911i			0.0953286i
$324$	−0.220160	−	162.000i	−0.000679506	−	0.500000i
$325$	−16.9643			−0.0521978
$326$	213.557	−	123.297i	0.655083	−	0.378212i
$327$	72.4648	+	548.983i	0.221605	+	1.67885i
$328$	−47.7959	+	82.7849i	−0.145719	+	0.252393i
$329$	137.947	+	79.6440i	0.419293	+	0.242079i
$330$	178.214	+	232.089i	0.540041	+	0.703300i
$331$	243.423	+	421.621i	0.735416	+	1.27378i	0.954540	+	0.298081i	$0.0963467\pi$
$331$	243.423	+	421.621i	0.735416	+	1.27378i	−0.219124	+	0.975697i	$0.570320\pi$
$332$		−	300.366i		−	0.904717i
$333$	−167.066	+	44.8869i	−0.501700	+	0.134795i
$334$	206.213			0.617403
$335$	481.454	−	277.967i	1.43717	−	0.829753i
$336$	−29.3364	−	12.1399i	−0.0873107	−	0.0361305i
$337$	29.0085	−	50.2442i	0.0860786	−	0.149093i	−0.819772	−	0.572690i	$-0.805900\pi$
$337$	29.0085	−	50.2442i	0.0860786	−	0.149093i	0.905850	+	0.423598i	$0.139233\pi$
$338$	−128.071	−	73.9419i	−0.378909	−	0.218763i
$339$	143.646	−	347.127i	0.423736	−	1.02397i
$340$	45.9485	+	79.5852i	0.135143	+	0.234074i
$341$			315.690i			0.925778i
$342$	−31.3829	+	31.4256i	−0.0917629	+	0.0918877i
$343$	−18.5203			−0.0539949
$344$	111.642	−	64.4566i	0.324541	−	0.187374i
$345$	468.927	−	360.073i	1.35921	−	1.04369i
$346$	41.1089	−	71.2027i	0.118812	−	0.205788i
$347$	−216.133	−	124.784i	−0.622861	−	0.359609i	0.155121	−	0.987895i	$-0.450423\pi$
$347$	−216.133	−	124.784i	−0.622861	−	0.359609i	−0.777982	+	0.628287i	$0.783757\pi$
$348$	92.3708	−	12.1928i	0.265433	−	0.0350367i
$349$	−112.209	−	194.351i	−0.321515	−	0.556880i	0.659286	−	0.751892i	$-0.270859\pi$
$349$	−112.209	−	194.351i	−0.321515	−	0.556880i	−0.980801	+	0.195012i	$0.937525\pi$
$350$		−	7.90778i		−	0.0225937i
$351$	−214.900	−	28.0693i	−0.612250	−	0.0799694i
$352$	−74.9286			−0.212865
$353$	192.298	−	111.023i	0.544753	−	0.314513i	−0.202250	−	0.979334i	$-0.564825\pi$
$353$	192.298	−	111.023i	0.544753	−	0.314513i	0.747003	+	0.664821i	$0.231492\pi$
$354$	−60.6357	−	459.368i	−0.171287	−	1.29765i
$355$	−245.099	+	424.523i	−0.690418	+	1.19584i
$356$	51.2148	+	29.5689i	0.143862	+	0.0830586i
$357$	−42.6569	−	55.5524i	−0.119487	−	0.155609i
$358$	−125.558	−	217.473i	−0.350721	−	0.607467i
$359$		−	316.242i		−	0.880898i	−0.897778	−	0.440449i	$-0.854819\pi$
$359$		−	316.242i		−	0.880898i	0.897778	−	0.440449i	$-0.145181\pi$
$360$	−34.2195	+	128.057i	−0.0950541	+	0.355713i
$361$	−348.824			−0.966272
$362$	−51.4852	+	29.7250i	−0.142224	+	0.0821133i
$363$	−150.928	−	62.4563i	−0.415779	−	0.172056i
$364$	−21.2371	+	36.7837i	−0.0583436	+	0.101054i
$365$	15.3690	+	8.87330i	0.0421069	+	0.0243104i
$366$	128.497	−	310.517i	0.351084	−	0.848407i
$367$	232.627	+	402.922i	0.633862	+	1.09788i	0.986755	+	0.162217i	$0.0518646\pi$
$367$	232.627	+	402.922i	0.633862	+	1.09788i	−0.352893	+	0.935664i	$0.614802\pi$
$368$			151.390i			0.411386i
$369$	−293.860	−	78.5256i	−0.796369	−	0.212806i
$370$	141.543			0.382549
$371$	−146.167	+	84.3894i	−0.393980	+	0.227465i
$372$	−113.421	+	87.0922i	−0.304895	+	0.234119i
$373$	−39.8509	+	69.0237i	−0.106839	+	0.185050i	−0.914488	−	0.404613i	$-0.867406\pi$
$373$	−39.8509	+	69.0237i	−0.106839	+	0.185050i	0.807649	+	0.589663i	$0.200740\pi$
$374$	−143.152	−	82.6489i	−0.382760	−	0.220986i
$375$	354.440	−	46.7855i	0.945174	−	0.124761i
$376$	85.1430	+	147.472i	0.226444	+	0.392213i
$377$		−	124.646i		−	0.330627i
$378$	13.0843	−	100.174i	0.0346145	−	0.265010i
$379$	135.902			0.358579			0.179290	−	0.983796i	$-0.442620\pi$
$379$	135.902			0.358579			0.179290	+	0.983796i	$0.442620\pi$
$380$	31.4702	−	18.1693i	0.0828162	−	0.0478140i
$381$	−73.3611	−	555.773i	−0.192549	−	1.45872i
$382$	61.0462	−	105.735i	0.159807	−	0.276794i
$383$	345.859	+	199.682i	0.903027	+	0.521363i	0.878181	−	0.478328i	$-0.158757\pi$
$383$	345.859	+	199.682i	0.903027	+	0.521363i	0.0248460	+	0.999691i	$0.492090\pi$
$384$	−20.6712	−	26.9203i	−0.0538312	−	0.0701049i
$385$	91.2397	+	158.032i	0.236986	+	0.410472i
$386$			196.018i			0.507820i
$387$	290.252	+	289.857i	0.750004	+	0.748985i
$388$	163.186			0.420581
$389$	−382.780	+	220.998i	−0.984011	+	0.568119i	−0.903479	−	0.428633i	$-0.858995\pi$
$389$	−382.780	+	220.998i	−0.984011	+	0.568119i	−0.0805324	+	0.996752i	$0.525662\pi$
$390$	163.851	+	67.8043i	0.420132	+	0.173857i
$391$	−166.989	+	289.233i	−0.427081	+	0.739726i
$392$	−17.1464	−	9.89949i	−0.0437409	−	0.0252538i
$393$	16.5745	−	40.0529i	0.0421743	−	0.101916i
$394$	27.8818	+	48.2926i	0.0707659	+	0.122570i
$395$			813.227i			2.05880i
$396$	−61.8645	−	230.255i	−0.156223	−	0.581453i
$397$	−384.151			−0.967635			−0.483817	−	0.875169i	$-0.660750\pi$
$397$	−384.151			−0.967635			−0.483817	+	0.875169i	$0.660750\pi$
$398$	−107.830	+	62.2557i	−0.270930	+	0.156421i
$399$	−21.9670	+	16.8677i	−0.0550550	+	0.0422749i
$400$	4.22689	−	7.32118i	0.0105672	−	0.0183030i
$401$	224.637	+	129.694i	0.560193	+	0.323427i	0.753223	−	0.657765i	$-0.228498\pi$
$401$	224.637	+	129.694i	0.560193	+	0.323427i	−0.193030	+	0.981193i	$0.561832\pi$
$402$	−449.073	+	59.2768i	−1.11710	+	0.147455i
$403$	95.6542	+	165.678i	0.237355	+	0.411112i
$404$			1.43095i			0.00354196i
$405$	−421.771	+	0.573193i	−1.04141	+	0.00141529i
$406$	58.1029			0.143111
$407$	−220.488	+	127.299i	−0.541739	+	0.312773i
$408$	−9.79857	−	74.2326i	−0.0240161	−	0.181943i
$409$	47.4549	−	82.1943i	0.116027	−	0.200964i	−0.802163	−	0.597105i	$-0.796318\pi$
$409$	47.4549	−	82.1943i	0.116027	−	0.200964i	0.918190	+	0.396141i	$0.129651\pi$
$410$	215.533	+	124.438i	0.525690	+	0.303507i
$411$	−65.4704	−	85.2628i	−0.159295	−	0.207452i
$412$	179.847	+	311.504i	0.436522	+	0.756079i
$413$		−	288.951i		−	0.699640i
$414$	−465.222	+	124.995i	−1.12372	+	0.301919i
$415$	−782.012			−1.88437
$416$	−39.3234	+	22.7034i	−0.0945274	+	0.0545754i
$417$	97.1870	+	40.2175i	0.233062	+	0.0964448i
$418$	−32.6816	+	56.6063i	−0.0781857	+	0.135422i
$419$	−139.448	−	80.5105i	−0.332812	−	0.192149i	0.324277	−	0.945962i	$-0.394879\pi$
$419$	−139.448	−	80.5105i	−0.332812	−	0.192149i	−0.657089	+	0.753813i	$0.728212\pi$
$420$	−31.6065	+	76.3781i	−0.0752535	+	0.181853i
$421$	−266.914	−	462.308i	−0.634000	−	1.09812i	−0.986726	−	0.162393i	$-0.948079\pi$
$421$	−266.914	−	462.308i	−0.634000	−	1.09812i	0.352727	−	0.935726i	$-0.385255\pi$
$422$		−	272.573i		−	0.645908i
$423$	−382.883	+	383.404i	−0.905161	+	0.906392i
$424$	−180.432			−0.425547
$425$	16.1510	−	9.32481i	0.0380025	−	0.0219407i
$426$	316.788	−	243.251i	0.743633	−	0.571011i
$427$	104.783	−	181.490i	0.245394	−	0.425035i
$428$	110.345	+	63.7076i	0.257815	+	0.148849i
$429$	−316.219	+	41.7404i	−0.737108	+	0.0972969i
$430$	−167.815	−	290.663i	−0.390266	−	0.675961i
$431$			224.292i			0.520399i	0.965555	+	0.260200i	$0.0837884\pi$
$431$			224.292i			0.520399i	−0.965555	+	0.260200i	$0.916212\pi$
$432$	65.6589	−	85.7491i	0.151988	−	0.198493i
$433$	−754.086			−1.74154			−0.870770	−	0.491691i	$-0.836379\pi$
$433$	−754.086			−1.74154			−0.870770	+	0.491691i	$0.836379\pi$
$434$	−77.2295	+	44.5885i	−0.177948	+	0.102738i
$435$	−31.7442	−	240.490i	−0.0729752	−	0.552850i
$436$	−184.582	+	319.705i	−0.423353	+	0.733268i
$437$	114.371	+	66.0319i	0.261718	+	0.151103i
$438$	−8.80640	−	11.4686i	−0.0201059	−	0.0261841i
$439$	−250.978	−	434.707i	−0.571705	−	0.990222i	−0.996391	−	0.0848812i	$-0.972949\pi$
$439$	−250.978	−	434.707i	−0.571705	−	0.990222i	0.424686	−	0.905341i	$-0.360384\pi$
$440$			195.079i			0.443361i
$441$	16.2642	−	60.8644i	0.0368804	−	0.138014i
$442$	−100.170			−0.226630
$443$	−213.379	+	123.194i	−0.481668	+	0.278091i	−0.721111	−	0.692819i	$-0.756368\pi$
$443$	−213.379	+	123.194i	−0.481668	+	0.278091i	0.239443	+	0.970910i	$0.423035\pi$
$444$	−106.564	−	44.0977i	−0.240008	−	0.0993190i
$445$	76.9834	−	133.339i	0.172996	−	0.299639i
$446$	220.384	+	127.239i	0.494135	+	0.285289i
$447$	192.635	−	465.509i	0.430950	−	1.04141i
$448$	−10.5830	−	18.3303i	−0.0236228	−	0.0409159i
$449$		−	187.215i		−	0.416959i	−0.978027	−	0.208480i	$-0.933149\pi$
$449$		−	187.215i		−	0.416959i	0.978027	−	0.208480i	$-0.0668515\pi$
$450$	25.9879	+	6.94451i	0.0577508	+	0.0154322i
$451$	−447.660			−0.992594
$452$	216.896	−	125.225i	0.479858	−	0.277046i
$453$	−461.613	+	354.458i	−1.01901	+	0.782467i
$454$	67.1128	−	116.243i	0.147826	−	0.256041i
$455$	95.7673	+	55.2913i	0.210478	+	0.121519i
$456$	−29.3536	+	3.87462i	−0.0643720	+	0.00849698i
$457$	273.781	+	474.203i	0.599084	+	1.03764i	0.992957	+	0.118479i	$0.0378019\pi$
$457$	273.781	+	474.203i	0.599084	+	1.03764i	−0.393872	+	0.919165i	$0.628865\pi$
$458$			501.291i			1.09452i
$459$	220.026	−	91.4008i	0.479360	−	0.199130i
$460$	394.149			0.856845
$461$	126.424	−	72.9908i	0.274238	−	0.158332i	−0.356574	−	0.934267i	$-0.616055\pi$
$461$	126.424	−	72.9908i	0.274238	−	0.158332i	0.630812	+	0.775936i	$0.282722\pi$
$462$	−19.4570	−	147.403i	−0.0421146	−	0.319055i
$463$	−95.3446	+	165.142i	−0.205928	+	0.356677i	−0.950428	−	0.310945i	$-0.899355\pi$
$463$	−95.3446	+	165.142i	−0.205928	+	0.356677i	0.744500	+	0.667622i	$0.232688\pi$
$464$	53.7929	+	31.0573i	0.115933	+	0.0669339i
$465$	226.747	+	295.295i	0.487628	+	0.635043i
$466$	−135.961	−	235.491i	−0.291761	−	0.505345i
$467$		−	728.372i		−	1.55968i	−0.625977	−	0.779841i	$-0.715300\pi$
$467$		−	728.372i		−	1.55968i	0.625977	−	0.779841i	$-0.284700\pi$
$468$	−102.235	−	102.096i	−0.218450	−	0.218153i
$469$	−282.475			−0.602293
$470$	383.948	−	221.672i	0.816910	−	0.471643i
$471$	45.7517	+	18.9328i	0.0971374	+	0.0401970i
$472$	154.451	−	267.517i	0.327226	−	0.566773i
$473$	522.824	+	301.853i	1.10534	+	0.638166i
$474$	253.360	−	612.255i	0.534516	−	1.29168i
$475$	−3.68729	−	6.38657i	−0.00776271	−	0.0134454i
$476$		−	46.6937i		−	0.0980960i
$477$	−148.973	−	554.467i	−0.312312	−	1.16241i
$478$	410.218			0.858196
$479$	636.669	−	367.581i	1.32916	−	0.767392i	0.343992	−	0.938972i	$-0.388221\pi$
$479$	636.669	−	367.581i	1.32916	−	0.767392i	0.985170	+	0.171580i	$0.0548872\pi$
$480$	−70.0877	+	53.8180i	−0.146016	+	0.112121i
$481$	−77.1430	+	133.616i	−0.160380	+	0.277787i
$482$	−137.075	−	79.1401i	−0.284387	−	0.164191i
$483$	−297.822	+	39.3120i	−0.616609	+	0.0813913i
$484$	−54.4468	−	94.3045i	−0.112493	−	0.194844i
$485$		−	424.858i		−	0.875996i
$486$	317.718	+	130.971i	0.653740	+	0.269488i
$487$	−189.093			−0.388281			−0.194140	−	0.980974i	$-0.562192\pi$
$487$	−189.093			−0.388281			−0.194140	+	0.980974i	$0.562192\pi$
$488$	194.021	−	112.018i	0.397583	−	0.229545i
$489$	68.4552	+	518.607i	0.139990	+	1.06055i
$490$	−25.7736	+	44.6412i	−0.0525992	+	0.0911045i
$491$	−285.887	−	165.057i	−0.582254	−	0.336164i	0.179775	−	0.983708i	$-0.442463\pi$
$491$	−285.887	−	165.057i	−0.582254	−	0.336164i	−0.762029	+	0.647543i	$0.775796\pi$
$492$	−123.500	−	160.835i	−0.251016	−	0.326900i
$493$	68.5147	+	118.671i	0.138975	+	0.240712i
$494$			39.6102i			0.0801825i
$495$	−599.476	+	161.066i	−1.21106	+	0.325386i
$496$	−95.3342			−0.192206
$497$	215.704	−	124.537i	0.434012	−	0.250577i
$498$	588.754	+	243.635i	1.18224	+	0.489228i
$499$	−153.572	+	265.994i	−0.307759	+	0.533054i	−0.977872	−	0.209205i	$-0.932912\pi$
$499$	−153.572	+	265.994i	−0.307759	+	0.533054i	0.670113	+	0.742259i	$0.266246\pi$
$500$	206.411	+	119.172i	0.412823	+	0.238343i
$501$	−167.265	+	404.202i	−0.333862	+	0.806790i
$502$	143.909	+	249.257i	0.286670	+	0.496528i
$503$		−	38.9199i		−	0.0773755i	−0.999251	−	0.0386878i	$-0.987682\pi$
$503$		−	38.9199i		−	0.0773755i	0.999251	−	0.0386878i	$-0.0123178\pi$
$504$	47.5912	−	47.6559i	0.0944269	−	0.0945553i
$505$	3.72552			0.00737727
$506$	−613.983	+	354.483i	−1.21340	+	0.700559i
$507$	248.817	−	191.058i	0.490763	−	0.376841i
$508$	186.865	−	323.659i	0.367844	−	0.637125i
$509$	130.399	+	75.2856i	0.256186	+	0.147909i	0.622593	−	0.782546i	$-0.286079\pi$
$509$	130.399	+	75.2856i	0.256186	+	0.147909i	−0.366408	+	0.930454i	$0.619412\pi$
$510$	−193.267	+	25.5109i	−0.378954	+	0.0500213i
$511$	−4.50860	−	7.80912i	−0.00882309	−	0.0152820i
$512$		−	22.6274i		−	0.0441942i
$513$	−36.1424	−	87.0045i	−0.0704530	−	0.169599i
$514$	−424.275			−0.825438
$515$	811.011	−	468.237i	1.57478	−	0.909198i
$516$	35.7866	+	271.114i	0.0693539	+	0.525415i
$517$	−398.728	+	690.617i	−0.771234	+	1.33582i
$518$	−62.2839	−	35.9596i	−0.120239	−	0.0694201i
$519$	106.221	+	138.333i	0.204665	+	0.266537i
$520$	59.1089	+	102.380i	0.113671	+	0.196884i
$521$			440.225i			0.844961i	0.906372	+	0.422480i	$0.138840\pi$
$521$			440.225i			0.844961i	−0.906372	+	0.422480i	$0.861160\pi$
$522$	−51.0252	+	190.948i	−0.0977495	+	0.365800i
$523$	324.153			0.619795			0.309898	−	0.950770i	$-0.399705\pi$
$523$	324.153			0.619795			0.309898	+	0.950770i	$0.399705\pi$
$524$	25.0263	−	14.4489i	0.0477601	−	0.0275743i
$525$	15.5002	+	6.41422i	0.0295242	+	0.0122176i
$526$	133.478	−	231.191i	0.253761	−	0.439526i
$527$	−182.137	−	105.157i	−0.345611	−	0.199539i
$528$	60.7767	−	146.869i	0.115107	−	0.278161i
$529$	451.719	+	782.400i	0.853911	+	1.47902i
$530$			469.760i			0.886340i
$531$	949.600	+	253.753i	1.78832	+	0.477878i
$532$	−18.4640			−0.0347067
$533$	−234.937	+	135.641i	−0.440782	+	0.254486i
$534$	−99.5003	+	76.4030i	−0.186330	+	0.143077i
$535$	165.864	−	287.286i	0.310027	−	0.536982i
$536$	−261.521	−	150.989i	−0.487913	−	0.281697i
$537$	528.117	−	69.7105i	0.983459	−	0.129815i
$538$	184.175	+	319.000i	0.342332	+	0.592937i
$539$		−	92.7194i		−	0.172021i
$540$	−223.250	−	170.945i	−0.413426	−	0.316564i
$541$	−476.266			−0.880344			−0.440172	−	0.897914i	$-0.645083\pi$
$541$	−476.266			−0.880344			−0.440172	+	0.897914i	$0.645083\pi$
$542$	174.091	−	100.511i	0.321200	−	0.185445i
$543$	−16.5035	−	125.028i	−0.0303931	−	0.230254i
$544$	24.9588	−	43.2300i	0.0458802	−	0.0794669i
$545$	832.361	+	480.564i	1.52727	+	0.881768i
$546$	−54.8744	−	71.4635i	−0.100503	−	0.130885i
$547$	169.902	+	294.279i	0.310607	+	0.537988i	0.978494	−	0.206275i	$-0.0661343\pi$
$547$	169.902	+	294.279i	0.310607	+	0.537988i	−0.667887	+	0.744263i	$0.732801\pi$
$548$		−	71.6663i		−	0.130778i
$549$	504.423	+	503.738i	0.918803	+	0.917555i
$550$	39.5893			0.0719806
$551$	46.9257	−	27.0926i	0.0851646	−	0.0491698i
$552$	−296.743	−	122.797i	−0.537578	−	0.222458i
$553$	206.604	−	357.848i	0.373605	−	0.647104i
$554$	−13.0570	−	7.53845i	−0.0235686	−	0.0136073i
$555$	−114.809	+	277.441i	−0.206864	+	0.499894i
$556$	35.0599	+	60.7255i	0.0630573	+	0.109219i
$557$		−	507.929i		−	0.911902i	−0.890005	−	0.455951i	$-0.849299\pi$
$557$		−	507.929i		−	0.911902i	0.890005	−	0.455951i	$-0.150701\pi$
$558$	−78.7123	−	292.962i	−0.141061	−	0.525021i
$559$	365.845			0.654464
$560$	−47.7235	+	27.5532i	−0.0852205	+	0.0492021i
$561$	278.116	−	213.556i	0.495751	−	0.380671i
$562$	125.106	−	216.691i	0.222609	−	0.385570i
$563$	−393.970	−	227.459i	−0.699769	−	0.404012i	0.107492	−	0.994206i	$-0.465718\pi$
$563$	−393.970	−	227.459i	−0.699769	−	0.404012i	−0.807261	+	0.590194i	$0.799051\pi$
$564$	−358.125	+	47.2718i	−0.634973	+	0.0838152i
$565$	−326.026	−	564.694i	−0.577038	−	0.999458i
$566$			428.411i			0.756910i
$567$	185.740	+	106.901i	0.327583	+	0.188537i
$568$	266.271			0.468786
$569$	382.086	−	220.597i	0.671504	−	0.387693i	−0.125142	−	0.992139i	$-0.539939\pi$
$569$	382.086	−	220.597i	0.671504	−	0.387693i	0.796646	+	0.604446i	$0.206605\pi$
$570$	10.0877	+	76.4230i	0.0176977	+	0.134075i
$571$	133.930	−	231.973i	0.234553	−	0.406258i	−0.724590	−	0.689181i	$-0.757971\pi$
$571$	133.930	−	231.973i	0.234553	−	0.406258i	0.959143	+	0.282923i	$0.0913039\pi$
$572$	−184.153	−	106.321i	−0.321946	−	0.185875i
$573$	157.737	+	205.423i	0.275283	+	0.358504i
$574$	−63.2280	−	109.514i	−0.110153	−	0.190791i
$575$		−	79.9887i		−	0.139111i
$576$	69.5340	−	18.6822i	0.120719	−	0.0324344i
$577$	608.884			1.05526			0.527629	−	0.849475i	$-0.323081\pi$
$577$	608.884			1.05526			0.527629	+	0.849475i	$0.323081\pi$
$578$	−258.583	+	149.293i	−0.447375	+	0.258292i
$579$	−384.220	−	158.996i	−0.663592	−	0.274605i
$580$	80.8586	−	140.051i	0.139411	−	0.241468i
$581$	344.113	+	198.674i	0.592277	+	0.341951i
$582$	−132.364	+	319.863i	−0.227430	+	0.549593i
$583$	−422.485	−	731.766i	−0.724674	−	1.25517i
$584$		−	9.63979i		−	0.0165065i
$585$	−265.809	+	266.171i	−0.454375	+	0.454993i
$586$	759.515			1.29610
$587$	−407.910	+	235.507i	−0.694907	+	0.401205i	−0.805448	−	0.592667i	$-0.798075\pi$
$587$	−407.910	+	235.507i	−0.694907	+	0.401205i	0.110541	+	0.993872i	$0.464742\pi$
$588$	33.3122	−	25.5793i	0.0566533	−	0.0435022i
$589$	−41.5820	+	72.0221i	−0.0705976	+	0.122279i
$590$	−696.488	−	402.117i	−1.18049	−	0.681555i
$591$	−117.275	+	15.4801i	−0.198435	+	0.0261930i
$592$	−38.4424	−	66.5843i	−0.0649366	−	0.112473i
$593$		−	354.707i		−	0.598157i	−0.954229	−	0.299078i	$-0.903321\pi$
$593$		−	354.707i		−	0.598157i	0.954229	−	0.299078i	$-0.0966792\pi$
$594$	501.508	+	65.5049i	0.844290	+	0.110278i
$595$	−121.568			−0.204317
$596$	290.865	−	167.931i	0.488028	−	0.281763i
$597$	−34.5647	−	261.857i	−0.0578973	−	0.438622i
$598$	−214.817	+	372.074i	−0.359225	+	0.622197i
$599$	−5.34958	−	3.08858i	−0.00893085	−	0.00515623i	0.495528	−	0.868592i	$-0.334975\pi$
$599$	−5.34958	−	3.08858i	−0.00893085	−	0.00515623i	−0.504459	+	0.863436i	$0.668308\pi$
$600$	10.9218	+	14.2236i	0.0182031	+	0.0237060i
$601$	13.6355	+	23.6173i	0.0226880	+	0.0392967i	0.877146	−	0.480223i	$-0.159444\pi$
$601$	13.6355	+	23.6173i	0.0226880	+	0.0392967i	−0.854459	+	0.519520i	$0.826111\pi$
$602$			170.536i			0.283282i
$603$	248.066	−	928.318i	0.411386	−	1.53950i
$604$	−388.002			−0.642387
$605$	−245.525	+	141.754i	−0.405826	+	0.234304i
$606$	−2.80484	−	1.16069i	−0.00462844	−	0.00191532i
$607$	−109.142	+	189.040i	−0.179806	+	0.311433i	−0.941814	−	0.336135i	$-0.890880\pi$
$607$	−109.142	+	189.040i	−0.179806	+	0.311433i	0.762008	+	0.647567i	$0.224214\pi$
$608$	−17.0943	−	9.86941i	−0.0281157	−	0.0162326i
$609$	−47.1289	+	113.889i	−0.0773874	+	0.187009i
$610$	−291.642	−	505.138i	−0.478101	−	0.828096i
$611$			483.258i			0.790930i
$612$	153.453	+	41.0058i	0.250740	+	0.0670029i
$613$	691.709			1.12840			0.564200	−	0.825638i	$-0.309185\pi$
$613$	691.709			1.12840			0.564200	+	0.825638i	$0.309185\pi$
$614$	−624.107	+	360.328i	−1.01646	+	0.586854i
$615$	−418.738	+	321.535i	−0.680875	+	0.522821i
$616$	49.5606	−	85.8415i	0.0804555	−	0.139353i
$617$	−1066.69	−	615.852i	−1.72883	−	0.998139i	−0.894901	−	0.446264i	$-0.852754\pi$
$617$	−1066.69	−	615.852i	−1.72883	−	0.998139i	−0.833927	−	0.551875i	$-0.813912\pi$
$618$	−756.465	+	99.8520i	−1.22405	+	0.161573i
$619$	135.951	+	235.475i	0.219631	+	0.380411i	0.954695	−	0.297586i	$-0.0961815\pi$
$619$	135.951	+	235.475i	0.219631	+	0.380411i	−0.735064	+	0.677997i	$0.762848\pi$
$620$			248.205i			0.400331i
$621$	132.350	−	1013.28i	0.213124	−	1.63169i
$622$	441.986			0.710588
$623$	−67.7508	+	39.1159i	−0.108749	+	0.0627864i
$624$	−12.6050	−	95.4939i	−0.0202004	−	0.153035i
$625$	336.685	−	583.155i	0.538696	−	0.933048i
$626$	692.183	+	399.632i	1.10572	+	0.638390i
$627$	−84.4461	−	109.975i	−0.134683	−	0.175399i
$628$	16.5048	+	28.5871i	0.0262815	+	0.0455209i
$629$		−	169.613i		−	0.269656i
$630$	−124.073	−	123.905i	−0.196942	−	0.196674i
$631$	−793.352			−1.25729			−0.628647	−	0.777691i	$-0.716391\pi$
$631$	−793.352			−1.25729			−0.628647	+	0.777691i	$0.716391\pi$
$632$	382.556	−	220.869i	0.605310	−	0.349476i
$633$	534.276	+	221.092i	0.844038	+	0.349276i
$634$	−96.3586	+	166.898i	−0.151985	+	0.263246i
$635$	−842.656	−	486.508i	−1.32702	−	0.766154i
$636$	146.354	−	353.669i	0.230116	−	0.556083i
$637$	−28.0940	−	48.6602i	−0.0441036	−	0.0763897i
$638$			290.885i			0.455933i
$639$	219.845	+	818.249i	0.344046	+	1.28051i
$640$	−58.9111			−0.0920486
$641$	−714.591	+	412.569i	−1.11481	+	0.643634i	−0.940070	−	0.340982i	$-0.889241\pi$
$641$	−714.591	+	412.569i	−1.11481	+	0.643634i	−0.174736	+	0.984615i	$0.555907\pi$
$642$	−214.378	+	164.614i	−0.333922	+	0.256408i
$643$	485.838	−	841.496i	0.755580	−	1.30870i	−0.189506	−	0.981880i	$-0.560689\pi$
$643$	485.838	−	841.496i	0.755580	−	1.30870i	0.945086	−	0.326823i	$-0.105978\pi$
$644$	−173.439	−	100.135i	−0.269316	−	0.155489i
$645$	705.854	−	93.1714i	1.09435	−	0.144452i
$646$	−21.7726	−	37.7113i	−0.0337037	−	0.0583766i
$647$			234.968i			0.363166i	0.983376	+	0.181583i	$0.0581221\pi$
$647$			234.968i			0.363166i	−0.983376	+	0.181583i	$0.941878\pi$
$648$	114.821	+	198.253i	0.177193	+	0.305946i
$649$	1446.60			2.22897
$650$	20.7769	−	11.9956i	0.0319645	−	0.0184547i
$651$	−24.7557	−	187.546i	−0.0380273	−	0.288089i
$652$	−174.369	+	302.015i	−0.267436	+	0.463214i
$653$	177.198	+	102.305i	0.271360	+	0.156670i	0.629506	−	0.776996i	$-0.283257\pi$
$653$	177.198	+	102.305i	0.271360	+	0.156670i	−0.358145	+	0.933666i	$0.616591\pi$
$654$	−476.941	−	621.124i	−0.729267	−	0.949731i
$655$	−37.6182	−	65.1567i	−0.0574324	−	0.0994758i
$656$		−	135.187i		−	0.206078i
$657$	29.6230	−	7.95905i	0.0450884	−	0.0121142i
$658$	−225.267			−0.342351
$659$	−888.097	+	512.743i	−1.34764	+	0.778062i	−0.987915	−	0.154995i	$-0.950464\pi$
$659$	−888.097	+	512.743i	−1.34764	+	0.778062i	−0.359728	+	0.933057i	$0.617130\pi$
$660$	−382.378	−	158.234i	−0.579360	−	0.239748i
$661$	−416.193	+	720.867i	−0.629641	+	1.09057i	0.357983	+	0.933728i	$0.383465\pi$
$661$	−416.193	+	720.867i	−0.629641	+	1.09057i	−0.987624	+	0.156842i	$0.949869\pi$
$662$	−596.262	−	344.252i	−0.900697	−	0.520018i
$663$	81.2511	−	196.346i	0.122551	−	0.296148i
$664$	212.391	+	367.872i	0.319866	+	0.554024i
$665$			48.0715i			0.0722879i
$666$	172.873	−	173.108i	0.259570	−	0.259923i
$667$	587.722			0.881143
$668$	−252.558	+	145.814i	−0.378081	+	0.218285i
$669$	−428.163	+	328.772i	−0.640005	+	0.491439i
$670$	−393.105	+	680.878i	−0.586724	+	1.01624i
$671$	908.606	+	524.584i	1.35411	+	0.781794i
$672$	44.5138	−	5.87574i	0.0662407	−	0.00874365i
$673$	11.9190	+	20.6443i	0.0177102	+	0.0306750i	0.874745	−	0.484584i	$-0.161029\pi$
$673$	11.9190	+	20.6443i	0.0177102	+	0.0306750i	−0.857034	+	0.515259i	$0.827696\pi$
$674$			82.0484i			0.121734i
$675$	−34.6916	+	45.3065i	−0.0513949	+	0.0671207i
$676$	209.139			0.309378
$677$	−878.026	+	506.929i	−1.29694	+	0.748787i	−0.979874	−	0.199618i	$-0.936030\pi$
$677$	−878.026	+	506.929i	−1.29694	+	0.748787i	−0.317063	+	0.948405i	$0.602697\pi$
$678$	69.5254	+	526.715i	0.102545	+	0.776866i
$679$	−107.937	+	186.953i	−0.158965	+	0.275335i
$680$	−112.550	−	64.9810i	−0.165515	−	0.0955604i
$681$	173.413	+	225.837i	0.254644	+	0.331626i
$682$	−223.227	−	386.640i	−0.327312	−	0.566921i
$683$		−	1203.04i		−	1.76141i	−0.473666	−	0.880704i	$-0.657070\pi$
$683$		−	1203.04i		−	1.76141i	0.473666	−	0.880704i	$-0.342930\pi$
$684$	16.2148	−	60.6794i	0.0237059	−	0.0887126i
$685$	−186.585			−0.272387
$686$	22.6826	−	13.0958i	0.0330650	−	0.0190901i
$687$	−982.591	−	406.612i	−1.43026	−	0.591866i
$688$	−91.1553	+	157.886i	−0.132493	+	0.229485i
$689$	−443.450	−	256.026i	−0.643614	−	0.371591i
$690$	−319.705	+	772.579i	−0.463341	+	1.11968i
$691$	−460.688	−	797.935i	−0.666698	−	1.15475i	−0.978822	−	0.204713i	$-0.934374\pi$
$691$	−460.688	−	797.935i	−0.666698	−	1.15475i	0.312124	−	0.950041i	$-0.398960\pi$
$692$			116.273i			0.168025i
$693$	304.710	+	81.4250i	0.439697	+	0.117496i
$694$	352.943			0.508564
$695$	158.101	−	91.2794i	0.227483	−	0.131337i
$696$	−104.509	+	80.2490i	−0.150157	+	0.115300i
$697$	149.116	−	258.277i	0.213940	−	0.370555i
$698$	274.854	+	158.687i	0.393774	+	0.227345i
$699$	571.872	−	75.4861i	0.818129	−	0.107992i
$700$	5.59164	+	9.68501i	0.00798806	+	0.0138357i
$701$		−	258.234i		−	0.368379i	−0.982891	−	0.184189i	$-0.941034\pi$
$701$		−	258.234i		−	0.368379i	0.982891	−	0.184189i	$-0.0589660\pi$
$702$	283.045	−	117.579i	0.403198	−	0.167492i
$703$	−67.0698			−0.0954051
$704$	91.7684	−	52.9825i	0.130353	−	0.0752593i
$705$	123.073	+	932.388i	0.174572	+	1.32254i
$706$	−157.010	+	271.950i	−0.222394	+	0.385198i
$707$	−1.63936	−	0.946486i	−0.00231876	−	0.00133873i
$708$	399.086	+	519.733i	0.563680	+	0.734086i
$709$	−54.5101	−	94.4143i	−0.0768831	−	0.133165i	0.825021	−	0.565103i	$-0.191164\pi$
$709$	−54.5101	−	94.4143i	−0.0768831	−	0.133165i	−0.901904	+	0.431937i	$0.857830\pi$
$710$		−	693.243i		−	0.976399i
$711$	994.585	+	993.234i	1.39885	+	1.39695i
$712$	−83.6334			−0.117463
$713$	−781.191	+	451.021i	−1.09564	+	0.632568i
$714$	91.5253	+	37.8746i	0.128187	+	0.0530456i
$715$	−276.809	+	479.447i	−0.387146	+	0.670556i
$716$	307.553	+	177.566i	0.429544	+	0.247997i
$717$	−332.739	+	804.076i	−0.464071	+	1.12145i
$718$	223.617	+	387.316i	0.311444	+	0.539437i
$719$		−	736.032i		−	1.02369i	−0.859078	−	0.511844i	$-0.828962\pi$
$719$		−	736.032i		−	1.02369i	0.859078	−	0.511844i	$-0.171038\pi$
$720$	−48.6397	−	181.034i	−0.0675551	−	0.251436i
$721$	−475.831			−0.659960
$722$	427.221	−	246.656i	0.591719	−	0.341629i
$723$	266.309	−	204.490i	0.368339	−	0.282836i
$724$	42.0375	−	72.8111i	0.0580629	−	0.100568i
$725$	−28.4220	−	16.4095i	−0.0392028	−	0.0226338i
$726$	229.012	−	30.2291i	0.315443	−	0.0416379i
$727$	−216.054	−	374.217i	−0.297186	−	0.514741i	0.678305	−	0.734780i	$-0.262715\pi$
$727$	−216.054	−	374.217i	−0.297186	−	0.514741i	−0.975491	+	0.220039i	$0.929381\pi$
$728$		−	60.0675i		−	0.0825103i
$729$	−514.429	+	516.531i	−0.705664	+	0.708547i
$730$	−25.0975			−0.0343801
$731$	−348.307	+	201.095i	−0.476480	+	0.275096i
$732$	62.1929	+	471.165i	0.0849630	+	0.643668i
$733$	−267.895	+	464.008i	−0.365478	+	0.633026i	−0.988853	−	0.148897i	$-0.952428\pi$
$733$	−267.895	+	464.008i	−0.365478	+	0.633026i	0.623375	+	0.781923i	$0.285761\pi$
$734$	−569.818	−	328.985i	−0.776319	−	0.448208i
$735$	−66.5964	−	86.7291i	−0.0906074	−	0.117999i
$736$	−107.049	−	185.414i	−0.145447	−	0.251922i
$737$		−	1414.18i		−	1.91883i
$738$	415.430	−	111.617i	0.562913	−	0.151242i
$739$	895.470			1.21173			0.605866	−	0.795567i	$-0.292827\pi$
$739$	895.470			1.21173			0.605866	+	0.795567i	$0.292827\pi$
$740$	−173.354	+	100.086i	−0.234262	+	0.135251i
$741$	−77.6407	−	32.1289i	−0.104778	−	0.0433589i
$742$	119.345	−	206.711i	0.160842	−	0.278586i
$743$	1157.51	+	668.291i	1.55789	+	0.899450i	0.997458	+	0.0712503i	$0.0226989\pi$
$743$	1157.51	+	668.291i	1.55789	+	0.899450i	0.560434	+	0.828199i	$0.310634\pi$
$744$	77.3283	−	186.867i	0.103936	−	0.251165i
$745$	−437.213	−	757.274i	−0.586863	−	1.01648i
$746$		−	112.715i		−	0.151093i
$747$	−955.110	+	956.408i	−1.27859	+	1.28033i
$748$	233.766			0.312522
$749$	−145.972	+	84.2772i	−0.194890	+	0.112520i
$750$	−401.017	+	307.927i	−0.534689	+	0.410570i
$751$	570.632	−	988.364i	0.759830	−	1.31606i	−0.183107	−	0.983093i	$-0.558615\pi$
$751$	570.632	−	988.364i	0.759830	−	1.31606i	0.942937	−	0.332971i	$-0.108051\pi$
$752$	−208.557	−	120.410i	−0.277336	−	0.160120i
$753$	−605.302	+	79.8987i	−0.803854	+	0.106107i
$754$	88.1383	+	152.660i	0.116894	+	0.202467i
$755$			1010.17i			1.33798i
$756$	54.8087	+	131.939i	0.0724983	+	0.174523i
$757$	775.634			1.02462			0.512308	−	0.858802i	$-0.328791\pi$
$757$	775.634			1.02462			0.512308	+	0.858802i	$0.328791\pi$
$758$	−166.445	+	96.0969i	−0.219584	+	0.126777i
$759$	−196.811	−	1491.01i	−0.259303	−	1.96444i
$760$	−25.6953	+	44.5055i	−0.0338096	+	0.0585599i
$761$	105.553	+	60.9413i	0.138703	+	0.0800805i	0.567746	−	0.823204i	$-0.307816\pi$
$761$	105.553	+	60.9413i	0.138703	+	0.0800805i	−0.429042	+	0.903284i	$0.641149\pi$
$762$	482.840	+	628.807i	0.633648	+	0.825206i
$763$	−244.179	−	422.930i	−0.320024	−	0.554299i
$764$			172.665i			0.226001i
$765$	106.760	−	399.519i	0.139555	−	0.522246i
$766$	−564.786			−0.737319
$767$	759.192	−	438.320i	0.989820	−	0.571473i
$768$	44.3525	+	18.3537i	0.0577506	+	0.0238981i
$769$	−682.681	+	1182.44i	−0.887752	+	1.53763i	−0.0452251	+	0.998977i	$0.514401\pi$
$769$	−682.681	+	1182.44i	−0.887752	+	1.53763i	−0.842527	+	0.538655i	$0.818933\pi$
$770$	−223.491	−	129.032i	−0.290248	−	0.167575i
$771$	344.141	−	831.630i	0.446357	−	1.07864i
$772$	−138.606	−	240.073i	−0.179541	−	0.310975i
$773$		−	231.520i		−	0.299508i	−0.988723	−	0.149754i	$-0.952152\pi$
$773$		−	231.520i		−	0.299508i	0.988723	−	0.149754i	$-0.0478482\pi$
$774$	−560.444	−	149.762i	−0.724088	−	0.193492i
$775$	50.3709			0.0649947
$776$	−199.861	+	115.390i	−0.257552	+	0.148698i
$777$	121.005	−	92.9160i	0.155734	−	0.119583i
$778$	312.539	−	541.333i	0.401721	−	0.695801i
$779$	−102.130	−	58.9646i	−0.131104	−	0.0756927i
$780$	−248.621	+	32.8175i	−0.318745	+	0.0420738i
$781$	623.478	+	1079.90i	0.798307	+	1.38271i
$782$		−	472.316i		−	0.603984i
$783$	−332.892	−	254.899i	−0.425150	−	0.325541i
$784$	28.0000			0.0357143
$785$	74.4273	−	42.9706i	0.0948119	−	0.0547397i
$786$	8.02212	+	60.7745i	0.0102063	+	0.0773212i
$787$	395.226	−	684.552i	0.502193	−	0.869824i	−0.497804	−	0.867290i	$-0.665860\pi$
$787$	395.226	−	684.552i	0.502193	−	0.869824i	0.999997	−	0.00253434i	$-0.000806706\pi$
$788$	−68.2961	−	39.4308i	−0.0866702	−	0.0500390i
$789$	344.894	+	449.159i	0.437128	+	0.569276i
$790$	−575.038	−	995.995i	−0.727896	−	1.26075i
$791$			331.314i			0.418854i
$792$	238.583	+	238.259i	0.301242	+	0.300832i
$793$	635.796			0.801760
$794$	470.487	−	271.636i	0.592553	−	0.342110i
$795$	−920.786	−	381.036i	−1.15822	−	0.479290i
$796$	88.0429	−	152.495i	0.110607	−	0.191576i
$797$	−66.4876	−	38.3866i	−0.0834223	−	0.0481639i	0.457709	−	0.889102i	$-0.348670\pi$
$797$	−66.4876	−	38.3866i	−0.0834223	−	0.0481639i	−0.541131	+	0.840938i	$0.682004\pi$
$798$	14.9767	−	36.1916i	0.0187677	−	0.0453529i
$799$	−265.634	−	460.091i	−0.332458	−	0.575834i
$800$			11.9554i			0.0149443i
$801$	−69.0515	−	257.005i	−0.0862067	−	0.320855i
$802$	−366.831			−0.457395
$803$	39.0954	−	22.5718i	0.0486867	−	0.0281093i
$804$	508.085	−	390.141i	0.631946	−	0.485251i
$805$	−260.705	+	451.554i	−0.323857	+	0.560937i
$806$	−234.304	−	135.276i	−0.290700	−	0.167836i
$807$	−774.667	+	102.255i	−0.959935	+	0.126710i
$808$	−1.01184	−	1.75255i	−0.00125227	−	0.00216900i
$809$			163.583i			0.202204i	0.994876	+	0.101102i	$0.0322368\pi$
$809$			163.583i			0.202204i	−0.994876	+	0.101102i	$0.967763\pi$
$810$	516.157	−	298.939i	0.637231	−	0.369061i
$811$	24.8546			0.0306469			0.0153235	−	0.999883i	$-0.495122\pi$
$811$	24.8546			0.0306469			0.0153235	+	0.999883i	$0.495122\pi$
$812$	−71.1613	+	41.0850i	−0.0876371	+	0.0505973i
$813$	55.8043	+	422.766i	0.0686400	+	0.520007i
$814$	180.027	−	311.817i	0.221164	−	0.383067i
$815$	786.305	+	453.974i	0.964792	+	0.557023i
$816$	64.4911	+	83.9874i	0.0790332	+	0.102926i
$817$	79.5185	+	137.730i	0.0973299	+	0.168580i
$818$			134.223i			0.164087i
$819$	184.587	−	49.5944i	0.225381	−	0.0605549i
$820$	−351.964			−0.429224
$821$	−251.574	+	145.246i	−0.306424	+	0.176914i	−0.645325	−	0.763908i	$-0.723278\pi$
$821$	−251.574	+	145.246i	−0.306424	+	0.176914i	0.338901	+	0.940822i	$0.389945\pi$
$822$	140.474	+	58.1305i	0.170894	+	0.0707184i
$823$	−41.1232	+	71.2275i	−0.0499675	+	0.0865462i	−0.889927	−	0.456102i	$-0.849245\pi$
$823$	−41.1232	+	71.2275i	−0.0499675	+	0.0865462i	0.839960	+	0.542649i	$0.182578\pi$
$824$	−440.534	−	254.342i	−0.534628	−	0.308668i
$825$	−32.1120	+	77.5999i	−0.0389237	+	0.0940604i
$826$	204.319	+	353.891i	0.247360	+	0.428440i
$827$			1043.82i			1.26218i	0.775709	+	0.631090i	$0.217392\pi$
$827$			1043.82i			1.26218i	−0.775709	+	0.631090i	$0.782608\pi$
$828$	481.393	−	482.048i	0.581393	−	0.582184i
$829$	−121.734			−0.146844			−0.0734222	−	0.997301i	$-0.523392\pi$
$829$	−121.734			−0.146844			−0.0734222	+	0.997301i	$0.523392\pi$
$830$	957.765	−	552.966i	1.15393	−	0.666224i
$831$	25.3672	−	19.4786i	0.0305261	−	0.0234400i
$832$	32.1074	−	55.6117i	0.0385906	−	0.0668410i
$833$	53.4944	+	30.8850i	0.0642189	+	0.0370768i
$834$	−147.467	+	19.4654i	−0.176819	+	0.0233398i
$835$	379.632	+	657.542i	0.454649	+	0.787475i
$836$		−	92.4376i		−	0.110571i
$837$	638.086	+	83.3440i	0.762349	+	0.0995747i
$838$	227.718			0.271740
$839$	873.889	−	504.540i	1.04158	−	0.601359i	0.121303	−	0.992616i	$-0.461293\pi$
$839$	873.889	−	504.540i	1.04158	−	0.601359i	0.920282	+	0.391257i	$0.127960\pi$
$840$	−15.2976	−	115.893i	−0.0182115	−	0.137968i
$841$	−299.930	+	519.494i	−0.356635	+	0.617710i
$842$	653.803	+	377.473i	0.776488	+	0.448305i
$843$	323.262	+	420.987i	0.383467	+	0.499392i
$844$	192.738	+	333.832i	0.228363	+	0.395536i
$845$		−	544.500i		−	0.644379i
$846$	197.827	−	740.311i	0.233838	−	0.875072i
$847$	144.053			0.170074
$848$	220.983	−	127.585i	0.260593	−	0.150454i
$849$	−839.738	−	347.496i	−0.989090	−	0.409301i
$850$	−13.1873	+	22.8410i	−0.0155144	+	0.0268718i
$851$	−630.013	−	363.738i	−0.740321	−	0.427424i
$852$	−215.980	+	521.923i	−0.253497	+	0.612585i
$853$	−572.363	−	991.362i	−0.671000	−	1.16221i	−0.977621	−	0.210375i	$-0.932532\pi$
$853$	−572.363	−	991.362i	−0.671000	−	1.16221i	0.306620	−	0.951832i	$-0.400802\pi$
$854$			296.372i			0.347039i
$855$	−157.981	−	42.2157i	−0.184773	−	0.0493751i
$856$	−180.192			−0.210505
$857$	−874.127	+	504.678i	−1.01999	+	0.588889i	−0.914100	−	0.405490i	$-0.867101\pi$
$857$	−874.127	+	504.678i	−1.01999	+	0.588889i	−0.105886	+	0.994378i	$0.533768\pi$
$858$	357.773	−	274.722i	0.416985	−	0.320189i
$859$	−544.449	+	943.013i	−0.633817	+	1.09780i	0.352947	+	0.935643i	$0.385180\pi$
$859$	−544.449	+	943.013i	−0.633817	+	1.09780i	−0.986764	+	0.162160i	$0.948154\pi$
$860$	411.060	+	237.326i	0.477977	+	0.275960i
$861$	265.947	−	35.1045i	0.308881	−	0.0407718i
$862$	−158.598	−	274.701i	−0.183989	−	0.318678i
$863$			989.092i			1.14611i	0.819517	+	0.573055i	$0.194242\pi$
$863$			989.092i			1.14611i	−0.819517	+	0.573055i	$0.805758\pi$
$864$	−19.7816	+	151.449i	−0.0228953	+	0.175288i
$865$	302.721			0.349967
$866$	923.564	−	533.220i	1.06647	−	0.615727i
$867$	−82.8881	−	627.949i	−0.0956034	−	0.724278i
$868$	63.0577	−	109.219i	0.0726471	−	0.125828i
$869$	1791.52	+	1034.34i	2.06159	+	1.19026i
$870$	208.931	+	272.092i	0.240150	+	0.312750i
$871$	−428.496	−	742.177i	−0.491959	−	0.852098i
$872$		−	522.076i		−	0.598711i
$873$	−519.606	−	518.900i	−0.595196	−	0.594388i
$874$	−186.767			−0.213692
$875$	−273.056	+	157.649i	−0.312065	+	0.180171i
$876$	18.8951	+	7.81911i	0.0215698	+	0.00892592i
$877$	310.022	−	536.973i	0.353502	−	0.612284i	−0.633358	−	0.773859i	$-0.718324\pi$
$877$	310.022	−	536.973i	0.353502	−	0.612284i	0.986860	+	0.161575i	$0.0516573\pi$
$878$	614.769	+	354.937i	0.700193	+	0.404256i
$879$	−616.064	+	1488.74i	−0.700869	+	1.69367i
$880$	−137.942	−	238.922i	−0.156752	−	0.271502i
$881$			636.200i			0.722134i	0.932540	+	0.361067i	$0.117587\pi$
$881$			636.200i			0.722134i	−0.932540	+	0.361067i	$0.882413\pi$
$882$	23.1181	+	86.0439i	0.0262110	+	0.0975555i
$883$	964.280			1.09205			0.546025	−	0.837769i	$-0.316140\pi$
$883$	964.280			1.09205			0.546025	+	0.837769i	$0.316140\pi$
$884$	122.683	−	70.8312i	0.138782	−	0.0801258i
$885$	1353.14	−	1039.03i	1.52897	−	1.17405i
$886$	174.223	−	301.763i	0.196640	−	0.340591i
$887$	−443.953	−	256.316i	−0.500510	−	0.288970i	0.228414	−	0.973564i	$-0.426646\pi$
$887$	−443.953	−	256.316i	−0.500510	−	0.288970i	−0.728924	+	0.684594i	$0.759979\pi$
$888$	161.695	−	21.3434i	0.182089	−	0.0240354i
$889$	247.199	+	428.161i	0.278064	+	0.481621i
$890$			217.742i			0.244654i
$891$	−535.185	+	929.883i	−0.600656	+	1.04364i
$892$	−359.886			−0.403459
$893$	−181.933	+	105.039i	−0.203732	+	0.117625i
$894$	93.2360	+	706.343i	0.104291	+	0.790093i
$895$	462.298	−	800.724i	0.516534	−	0.894664i
$896$	25.9230	+	14.9666i	0.0289319	+	0.0167038i
$897$	−555.065	−	722.866i	−0.618802	−	0.805871i
$898$	132.381	+	229.290i	0.147417	+	0.255334i
$899$			370.103i			0.411683i
$900$	−36.7390	+	9.87095i	−0.0408211	+	0.0109677i
$901$	562.922			0.624775
$902$	548.269	−	316.543i	0.607837	−	0.350935i
$903$	−334.271	−	138.327i	−0.370178	−	0.153186i
$904$	−177.095	+	306.737i	−0.195901	+	0.339311i
$905$	−189.566	−	109.446i	−0.209465	−	0.120935i
$906$	314.719	−	760.530i	0.347372	−	0.839437i
$907$	607.985	+	1053.06i	0.670325	+	1.16104i	0.977812	+	0.209485i	$0.0671788\pi$
$907$	607.985	+	1053.06i	0.670325	+	1.16104i	−0.307486	+	0.951552i	$0.599488\pi$
$908$			189.824i			0.209057i
$909$	4.55017	−	4.55635i	0.00500568	−	0.00501249i
$910$	−156.387			−0.171854
$911$	346.092	−	199.817i	0.379904	−	0.219338i	−0.297873	−	0.954606i	$-0.596277\pi$
$911$	346.092	−	199.817i	0.379904	−	0.219338i	0.677776	+	0.735268i	$0.262944\pi$
$912$	33.2109	−	25.5016i	0.0364155	−	0.0279622i
$913$	−994.635	+	1722.76i	−1.08941	+	1.88692i
$914$	−670.625	−	387.185i	−0.733725	−	0.423616i
$915$	1226.69	−	161.921i	1.34065	−	0.176963i
$916$	−354.467	−	613.954i	−0.386972	−	0.670256i
$917$			38.2283i			0.0416884i
$918$	−204.846	+	267.525i	−0.223144	+	0.291421i
$919$	−398.263			−0.433366			−0.216683	−	0.976242i	$-0.569524\pi$
$919$	−398.263			−0.433366			−0.216683	+	0.976242i	$0.569524\pi$
$920$	−482.732	+	278.705i	−0.524708	+	0.302941i
$921$	−200.056	−	1515.60i	−0.217216	−	1.64560i
$922$	−103.225	+	178.790i	−0.111957	+	0.193916i
$923$	654.417	+	377.828i	0.709011	+	0.409347i
$924$	128.060	+	166.773i	0.138593	+	0.180491i
$925$	20.3115	+	35.1805i	0.0219584	+	0.0380330i
$926$		−	269.675i		−	0.291226i
$927$	417.868	−	1563.76i	0.450775	−	1.68690i
$928$	−87.8434			−0.0946588
$929$	1491.17	−	860.930i	1.60514	−	0.926727i	0.614702	−	0.788760i	$-0.289276\pi$
$929$	1491.17	−	860.930i	1.60514	−	0.926727i	0.990437	−	0.137968i	$-0.0440570\pi$
$930$	−486.512	−	201.326i	−0.523131	−	0.216480i
$931$	12.2128	−	21.1531i	0.0131179	−	0.0227209i
$932$	333.035	+	192.278i	0.357333	+	0.206306i
$933$	−358.507	+	866.345i	−0.384252	+	0.928558i
$934$	515.037	+	892.070i	0.551431	+	0.955107i
$935$		−	608.617i		−	0.650928i
$936$	197.404	+	52.7505i	0.210902	+	0.0563573i
$937$	−1714.27			−1.82953			−0.914765	−	0.403987i	$-0.867624\pi$
$937$	−1714.27			−1.82953			−0.914765	+	0.403987i	$0.867624\pi$
$938$	345.960	−	199.740i	0.368827	−	0.212943i
$939$	−1344.78	+	1032.61i	−1.43214	+	1.09969i
$940$	−313.492	+	542.984i	−0.333502	+	0.577642i
$941$	76.8229	+	44.3537i	0.0816396	+	0.0471347i	0.540264	−	0.841496i	$-0.318324\pi$
$941$	76.8229	+	44.3537i	0.0816396	+	0.0471347i	−0.458624	+	0.888630i	$0.651658\pi$
$942$	−69.4216	+	9.16353i	−0.0736960	+	0.00972774i
$943$	−639.563	−	1107.76i	−0.678221	−	1.17471i
$944$			436.853i			0.462768i
$945$	343.508	−	142.696i	0.363501	−	0.151001i
$946$	−853.768			−0.902503
$947$	403.626	−	233.034i	0.426215	−	0.246076i	−0.271518	−	0.962433i	$-0.587526\pi$
$947$	403.626	−	233.034i	0.426215	−	0.246076i	0.697733	+	0.716358i	$0.254192\pi$
$948$	122.627	+	929.009i	0.129354	+	0.979967i
$949$	13.6785	−	23.6918i	0.0144136	−	0.0249651i
$950$	9.03197	+	5.21461i	0.00950733	+	0.00548906i
$951$	−248.981	−	324.250i	−0.261809	−	0.340957i
$952$	33.0174	+	57.1879i	0.0346822	+	0.0600713i
$953$		−	1024.37i		−	1.07489i	−0.843299	−	0.537445i	$-0.819389\pi$
$953$		−	1024.37i		−	1.07489i	0.843299	−	0.537445i	$-0.180611\pi$
$954$	574.521	+	573.741i	0.602224	+	0.601406i
$955$	449.538			0.470720
$956$	−502.412	+	290.068i	−0.525536	+	0.303418i
$957$	−570.170	−	235.945i	−0.595789	−	0.246547i
$958$	−519.838	+	900.386i	−0.542628	+	0.939860i
$959$	82.1040	+	47.4028i	0.0856142	+	0.0494294i
$960$	47.7845	−	115.473i	0.0497755	−	0.120284i
$961$	196.481	+	340.315i	0.204455	+	0.354126i
$962$		−	218.193i		−	0.226812i
$963$	−148.775	−	553.730i	−0.154491	−	0.575005i
$964$	223.842			0.232201
$965$	−625.036	+	360.865i	−0.647706	+	0.373953i
$966$	336.959	−	258.739i	0.348818	−	0.267846i
$967$	−37.7510	+	65.3866i	−0.0390393	+	0.0676180i	−0.884885	−	0.465810i	$-0.845763\pi$
$967$	−37.7510	+	65.3866i	−0.0390393	+	0.0676180i	0.845846	+	0.533428i	$0.179096\pi$
$968$	133.367	+	76.9993i	0.137776	+	0.0795448i
$969$	91.5790	−	12.0883i	0.0945088	−	0.0124750i
$970$	300.420	+	520.343i	0.309712	+	0.536436i
$971$			1674.28i			1.72429i	0.506664	+	0.862144i	$0.330878\pi$
$971$			1674.28i			1.72429i	−0.506664	+	0.862144i	$0.669122\pi$
$972$	−481.734	+	64.2542i	−0.495611	+	0.0661051i
$973$	−92.7597			−0.0953337
$974$	231.590	−	133.709i	0.237772	−	0.137278i
$975$	6.66000	+	50.4552i	0.00683077	+	0.0517490i
$976$	−158.417	+	274.387i	−0.162313	+	0.281134i
$977$	−933.331	−	538.859i	−0.955303	−	0.551544i	−0.0605785	−	0.998163i	$-0.519295\pi$
$977$	−933.331	−	538.859i	−0.955303	−	0.551544i	−0.894724	+	0.446619i	$0.852628\pi$
$978$	−450.551	−	586.756i	−0.460686	−	0.599955i
$979$	−195.829	−	339.186i	−0.200030	−	0.346462i
$980$		−	72.8988i		−	0.0743865i
$981$	1604.34	−	431.050i	1.63541	−	0.439398i
$982$	466.851			0.475408
$983$	163.825	−	94.5846i	0.166659	−	0.0962204i	−0.414351	−	0.910117i	$-0.635991\pi$
$983$	163.825	−	94.5846i	0.166659	−	0.0962204i	0.581009	+	0.813897i	$0.302658\pi$
$984$	264.983	+	109.654i	0.269292	+	0.111437i
$985$	−102.659	+	177.811i	−0.104222	+	0.180519i
$986$	−167.826	−	96.8944i	−0.170209	−	0.0982701i
$987$	182.721	−	441.551i	0.185127	−	0.447366i
$988$	−28.0086	−	48.5123i	−0.0283488	−	0.0491016i
$989$			1725.00i			1.74419i
$990$	620.315	−	621.158i	0.626581	−	0.627433i
$991$	−1637.86			−1.65273			−0.826367	−	0.563132i	$-0.809596\pi$
$991$	−1637.86			−1.65273			−0.826367	+	0.563132i	$0.809596\pi$
$992$	116.760	−	67.4115i	0.117702	−	0.0679551i
$993$	1158.42	−	889.512i	1.16659	−	0.895782i
$994$	−176.122	+	305.051i	−0.177185	+	0.306893i
$995$	−397.025	−	229.222i	−0.399020	−	0.230374i
$996$	−893.349	+	117.920i	−0.896937	+	0.118394i
$997$	298.689	+	517.345i	0.299588	+	0.518902i	0.976042	−	0.217584i	$-0.0698174\pi$
$997$	298.689	+	517.345i	0.299588	+	0.518902i	−0.676454	+	0.736485i	$0.736484\pi$
$998$		−	434.366i		−	0.435237i
$999$	199.091	+	479.266i	0.199290	+	0.479746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.q.a.113.4	yes	24
3.2	odd	2		378.3.q.a.71.12		24
9.2	odd	6	inner	126.3.q.a.29.4	✓	24
9.4	even	3		1134.3.b.c.323.10		24
9.5	odd	6		1134.3.b.c.323.15		24
9.7	even	3		378.3.q.a.197.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.q.a.29.4	✓	24	9.2	odd	6	inner
126.3.q.a.113.4	yes	24	1.1	even	1	trivial
378.3.q.a.71.12		24	3.2	odd	2
378.3.q.a.197.12		24	9.7	even	3
1134.3.b.c.323.10		24	9.4	even	3
1134.3.b.c.323.15		24	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.392589 - 2.97420i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-4.50944 - 2.60353i) q^{5} +(2.58390 + 3.36504i) q^{6} +(1.32288 + 2.29129i) q^{7} +2.82843i q^{8} +(-8.69175 + 2.33528i) q^{9} +7.36389 q^{10} +(-11.4711 + 6.62282i) q^{11} +(-5.54406 - 2.29422i) q^{12} +(-4.01343 + 6.95146i) q^{13} +(-3.24037 - 1.87083i) q^{14} +(-5.97306 + 14.4341i) q^{15} +(-2.00000 - 3.46410i) q^{16} -8.82428i q^{17} +(8.99388 - 9.00611i) q^{18} -3.48936 q^{19} +(-9.01889 + 5.20706i) q^{20} +(6.29540 - 4.83403i) q^{21} +(9.36608 - 16.2225i) q^{22} +(-32.7769 - 18.9238i) q^{23} +(8.41231 - 1.11041i) q^{24} +(1.05672 + 1.83030i) q^{25} -11.3517i q^{26} +(10.3579 + 24.9342i) q^{27} +5.29150 q^{28} +(-13.4482 + 7.76433i) q^{29} +(-2.89098 - 21.9017i) q^{30} +(11.9168 - 20.6405i) q^{31} +(4.89898 + 2.82843i) q^{32} +(24.2010 + 31.5172i) q^{33} +(6.23971 + 10.8075i) q^{34} -13.7766i q^{35} +(-4.64693 + 17.3898i) q^{36} +19.2212 q^{37} +(4.27358 - 2.46735i) q^{38} +(22.2507 + 9.20767i) q^{39} +(7.36389 - 12.7546i) q^{40} +(29.2689 + 16.8984i) q^{41} +(-4.29209 + 10.3720i) q^{42} +(-22.7888 - 39.4714i) q^{43} +26.4913i q^{44} +(45.2749 + 12.0984i) q^{45} +53.5245 q^{46} +(52.1392 - 30.1026i) q^{47} +(-9.51776 + 7.30837i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(-2.58843 - 1.49443i) q^{50} +(-26.2452 + 3.46432i) q^{51} +(8.02685 + 13.9029i) q^{52} +63.7924i q^{53} +(-30.3169 - 23.2139i) q^{54} +68.9708 q^{55} +(-6.48074 + 3.74166i) q^{56} +(1.36989 + 10.3781i) q^{57} +(10.9804 - 19.0187i) q^{58} +(-94.5815 - 54.6066i) q^{59} +(19.0276 + 24.7798i) q^{60} +(-39.6043 - 68.5967i) q^{61} +33.7057i q^{62} +(-16.8489 - 16.8260i) q^{63} -8.00000 q^{64} +(36.1966 - 20.8981i) q^{65} +(-51.9261 - 21.4878i) q^{66} +(-53.3828 + 92.4617i) q^{67} +(-15.2841 - 8.82428i) q^{68} +(-43.4153 + 104.915i) q^{69} +(9.74151 + 16.8728i) q^{70} -94.1409i q^{71} +(-6.60516 - 24.5840i) q^{72} -3.40818 q^{73} +(-23.5411 + 13.5915i) q^{74} +(5.02881 - 3.86146i) q^{75} +(-3.48936 + 6.04375i) q^{76} +(-30.3496 - 17.5223i) q^{77} +(-33.7622 + 4.45655i) q^{78} +(-78.0889 - 135.254i) q^{79} +20.8282i q^{80} +(70.0930 - 40.5953i) q^{81} -47.7959 q^{82} +(130.062 - 75.0915i) q^{83} +(-2.07739 - 15.7380i) q^{84} +(-22.9743 + 39.7926i) q^{85} +(55.8210 + 32.2283i) q^{86} +(28.3723 + 36.9495i) q^{87} +(-18.7322 - 32.4450i) q^{88} +29.5689i q^{89} +(-64.0051 + 17.1967i) q^{90} -21.2371 q^{91} +(-65.5539 + 37.8476i) q^{92} +(-66.0673 - 27.3397i) q^{93} +(-42.5715 + 73.7360i) q^{94} +(15.7351 + 9.08466i) q^{95} +(6.48903 - 15.6810i) q^{96} +(40.7964 + 70.6614i) q^{97} -9.89949i q^{98} +(84.2374 - 84.3519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 36 q^{5} + 8 q^{6} - 32 q^{9} - 24 q^{12} - 44 q^{15} - 48 q^{16} + 48 q^{18} + 24 q^{19} + 72 q^{20} + 28 q^{21} + 24 q^{22} - 72 q^{23} - 16 q^{24} + 72 q^{25} - 108 q^{29} - 56 q^{30}+ \cdots - 440 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 + 36 * q^5 + 8 * q^6 - 32 * q^9 - 24 * q^12 - 44 * q^15 - 48 * q^16 + 48 * q^18 + 24 * q^19 + 72 * q^20 + 28 * q^21 + 24 * q^22 - 72 * q^23 - 16 * q^24 + 72 * q^25 - 108 * q^29 - 56 * q^30 - 60 * q^31 + 104 * q^33 - 48 * q^34 - 80 * q^36 - 168 * q^37 + 144 * q^38 + 64 * q^39 + 108 * q^41 + 60 * q^43 + 116 * q^45 - 324 * q^47 - 48 * q^48 - 84 * q^49 + 144 * q^50 - 268 * q^51 - 208 * q^54 + 264 * q^55 + 60 * q^57 - 432 * q^59 - 32 * q^60 - 192 * q^64 - 180 * q^65 - 112 * q^66 + 72 * q^67 + 72 * q^68 + 536 * q^69 + 96 * q^72 + 24 * q^73 + 288 * q^74 + 76 * q^75 + 24 * q^76 - 64 * q^78 + 12 * q^79 + 544 * q^81 - 288 * q^82 + 756 * q^83 + 112 * q^84 - 156 * q^85 + 360 * q^86 + 280 * q^87 - 48 * q^88 + 80 * q^90 - 168 * q^91 - 144 * q^92 + 436 * q^93 - 936 * q^95 - 64 * q^96 + 48 * q^97 - 440 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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