LMFDB - Embedded newform 126.3.o.a.13.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(13,126)] 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([2, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.13"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.o (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	126.13
Dual form			126.3.o.a.97.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 1.22474i) q^{2} +(-2.47578 + 1.69425i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(2.08306 + 1.20266i) q^{5} +(3.82567 + 1.83418i) q^{6} +(-3.20945 - 6.22089i) q^{7} +2.82843 q^{8} +(3.25900 - 8.38921i) q^{9} -3.40163i q^{10} +(-6.79936 - 11.7768i) q^{11} +(-0.458753 - 5.98244i) q^{12} +(-11.7604 - 6.78989i) q^{13} +(-5.34958 + 8.32959i) q^{14} +(-7.19482 + 0.551722i) q^{15} +(-2.00000 - 3.46410i) q^{16} +19.8181i q^{17} +(-12.5791 + 1.94062i) q^{18} -34.4974i q^{19} +(-4.16613 + 2.40532i) q^{20} +(18.4857 + 9.96394i) q^{21} +(-9.61574 + 16.6550i) q^{22} +(4.33552 - 7.50935i) q^{23} +(-7.00257 + 4.79208i) q^{24} +(-9.60723 - 16.6402i) q^{25} +19.2047i q^{26} +(6.14489 + 26.2915i) q^{27} +(13.9843 + 0.661961i) q^{28} +(12.9761 + 22.4752i) q^{29} +(5.76323 + 8.42170i) q^{30} +(-21.6671 - 12.5095i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(36.7867 + 17.6370i) q^{33} +(24.2721 - 14.0135i) q^{34} +(0.796113 - 16.8184i) q^{35} +(11.2715 + 14.0340i) q^{36} +39.6839 q^{37} +(-42.2505 + 24.3933i) q^{38} +(40.6201 - 3.11488i) q^{39} +(5.89179 + 3.40163i) q^{40} +(-41.8941 - 24.1876i) q^{41} +(-0.868048 - 29.6858i) q^{42} +(13.1169 + 22.7192i) q^{43} +27.1974 q^{44} +(16.8781 - 13.5558i) q^{45} -12.2627 q^{46} +(-14.5673 + 8.41045i) q^{47} +(10.8206 + 5.18785i) q^{48} +(-28.3989 + 39.9312i) q^{49} +(-13.5867 + 23.5328i) q^{50} +(-33.5768 - 49.0652i) q^{51} +(23.5209 - 13.5798i) q^{52} +35.6774 q^{53} +(27.8552 - 26.1168i) q^{54} -32.7092i q^{55} +(-9.07769 - 17.5953i) q^{56} +(58.4473 + 85.4080i) q^{57} +(18.3509 - 31.7848i) q^{58} +(63.9153 + 36.9015i) q^{59} +(6.23921 - 13.0135i) q^{60} +(-78.5405 + 45.3454i) q^{61} +35.3823i q^{62} +(-62.6480 + 6.65086i) q^{63} +8.00000 q^{64} +(-16.3318 - 28.2875i) q^{65} +(-4.41125 - 57.5256i) q^{66} +(-10.3681 + 17.9581i) q^{67} +(-34.3259 - 19.8181i) q^{68} +(1.98893 + 25.9370i) q^{69} +(-21.1612 + 10.9174i) q^{70} -38.1972 q^{71} +(9.21785 - 23.7283i) q^{72} +12.0702i q^{73} +(-28.0607 - 48.6026i) q^{74} +(51.9782 + 24.9205i) q^{75} +(59.7512 + 34.4974i) q^{76} +(-51.4402 + 80.0951i) q^{77} +(-32.5377 - 47.5467i) q^{78} +(-65.4244 - 113.318i) q^{79} -9.62126i q^{80} +(-59.7578 - 54.6809i) q^{81} +68.4128i q^{82} +(-27.6580 + 15.9683i) q^{83} +(-35.7437 + 22.0542i) q^{84} +(-23.8343 + 41.2823i) q^{85} +(18.5501 - 32.1298i) q^{86} +(-70.2047 - 33.6590i) q^{87} +(-19.2315 - 33.3099i) q^{88} -118.790i q^{89} +(-28.5370 - 11.0859i) q^{90} +(-4.49464 + 94.9521i) q^{91} +(8.67105 + 15.0187i) q^{92} +(74.8374 - 5.73877i) q^{93} +(20.6013 + 11.8942i) q^{94} +(41.4885 - 71.8602i) q^{95} +(-1.29755 - 16.9209i) q^{96} +(99.4807 - 57.4352i) q^{97} +(68.9866 + 6.54575i) q^{98} +(-120.957 + 18.6605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Character values

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

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$	−2.47578	+	1.69425i	−0.825261	+	0.564752i
$3$	−2.47578	+	1.69425i	−0.825261	+	0.564752i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	2.08306	+	1.20266i	0.416613	+	0.240532i	0.693627	−	0.720334i	$-0.256012\pi$
$5$	2.08306	+	1.20266i	0.416613	+	0.240532i	−0.277014	+	0.960866i	$0.589345\pi$
$6$	3.82567	+	1.83418i	0.637612	+	0.305697i
$7$	−3.20945	−	6.22089i	−0.458493	−	0.888698i
$7$	−3.20945	−	6.22089i	−0.458493	−	0.888698i
$8$	2.82843			0.353553
$9$	3.25900	−	8.38921i	0.362111	−	0.932135i
$10$		−	3.40163i		−	0.340163i
$11$	−6.79936	−	11.7768i	−0.618123	−	1.07062i	−0.989828	−	0.142270i	$-0.954560\pi$
$11$	−6.79936	−	11.7768i	−0.618123	−	1.07062i	0.371705	−	0.928351i	$-0.378773\pi$
$12$	−0.458753	−	5.98244i	−0.0382294	−	0.498536i
$13$	−11.7604	−	6.78989i	−0.904648	−	0.522299i	−0.0259430	−	0.999663i	$-0.508259\pi$
$13$	−11.7604	−	6.78989i	−0.904648	−	0.522299i	−0.878705	+	0.477364i	$0.841592\pi$
$14$	−5.34958	+	8.32959i	−0.382113	+	0.594970i
$15$	−7.19482	+	0.551722i	−0.479655	+	0.0367815i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$			19.8181i			1.16577i	0.812555	+	0.582884i	$0.198076\pi$
$17$			19.8181i			1.16577i	−0.812555	+	0.582884i	$0.801924\pi$
$18$	−12.5791	+	1.94062i	−0.698839	+	0.107812i
$19$		−	34.4974i		−	1.81565i	−0.419348	−	0.907826i	$-0.637741\pi$
$19$		−	34.4974i		−	1.81565i	0.419348	−	0.907826i	$-0.362259\pi$
$20$	−4.16613	+	2.40532i	−0.208306	+	0.120266i
$21$	18.4857	+	9.96394i	0.880270	+	0.474474i
$22$	−9.61574	+	16.6550i	−0.437079	+	0.757043i
$23$	4.33552	−	7.50935i	0.188501	−	0.326493i	−0.756250	−	0.654283i	$-0.772970\pi$
$23$	4.33552	−	7.50935i	0.188501	−	0.326493i	0.944751	+	0.327790i	$0.106304\pi$
$24$	−7.00257	+	4.79208i	−0.291774	+	0.199670i
$25$	−9.60723	−	16.6402i	−0.384289	−	0.665608i
$26$			19.2047i			0.738642i
$27$	6.14489	+	26.2915i	0.227588	+	0.973757i
$28$	13.9843	+	0.661961i	0.499441	+	0.0236415i
$29$	12.9761	+	22.4752i	0.447451	+	0.775008i	0.998219	−	0.0596503i	$-0.0189985\pi$
$29$	12.9761	+	22.4752i	0.447451	+	0.775008i	−0.550768	+	0.834658i	$0.685665\pi$
$30$	5.76323	+	8.42170i	0.192108	+	0.280723i
$31$	−21.6671	−	12.5095i	−0.698939	−	0.403533i	0.108013	−	0.994149i	$-0.465551\pi$
$31$	−21.6671	−	12.5095i	−0.698939	−	0.403533i	−0.806952	+	0.590617i	$0.798885\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	36.7867	+	17.6370i	1.11475	+	0.534455i
$34$	24.2721	−	14.0135i	0.713884	−	0.412161i
$35$	0.796113	−	16.8184i	0.0227461	−	0.480525i
$36$	11.2715	+	14.0340i	0.313098	+	0.389832i
$37$	39.6839			1.07254			0.536268	−	0.844047i	$-0.319833\pi$
$37$	39.6839			1.07254			0.536268	+	0.844047i	$0.319833\pi$
$38$	−42.2505	+	24.3933i	−1.11185	+	0.641930i
$39$	40.6201	−	3.11488i	1.04154	−	0.0798687i
$40$	5.89179	+	3.40163i	0.147295	+	0.0850407i
$41$	−41.8941	−	24.1876i	−1.02181	−	0.589941i	−0.107180	−	0.994240i	$-0.534182\pi$
$41$	−41.8941	−	24.1876i	−1.02181	−	0.589941i	−0.914627	+	0.404299i	$0.867516\pi$
$42$	−0.868048	−	29.6858i	−0.0206678	−	0.706805i
$43$	13.1169	+	22.7192i	0.305045	+	0.528353i	0.977271	−	0.211992i	$-0.0679952\pi$
$43$	13.1169	+	22.7192i	0.305045	+	0.528353i	−0.672226	+	0.740346i	$0.734662\pi$
$44$	27.1974			0.618123
$45$	16.8781	−	13.5558i	0.375068	−	0.301240i
$46$	−12.2627			−0.266581
$47$	−14.5673	+	8.41045i	−0.309943	+	0.178946i	−0.646901	−	0.762574i	$-0.723935\pi$
$47$	−14.5673	+	8.41045i	−0.309943	+	0.178946i	0.336958	+	0.941520i	$0.390602\pi$
$48$	10.8206	+	5.18785i	0.225430	+	0.108080i
$49$	−28.3989	+	39.9312i	−0.579569	+	0.814923i
$50$	−13.5867	+	23.5328i	−0.271733	+	0.470656i
$51$	−33.5768	−	49.0652i	−0.658369	−	0.962063i
$52$	23.5209	−	13.5798i	0.452324	−	0.261150i
$53$	35.6774			0.673159			0.336579	−	0.941655i	$-0.390730\pi$
$53$	35.6774			0.673159			0.336579	+	0.941655i	$0.390730\pi$
$54$	27.8552	−	26.1168i	0.515838	−	0.483644i
$55$		−	32.7092i		−	0.594712i
$56$	−9.07769	−	17.5953i	−0.162102	−	0.314202i
$57$	58.4473	+	85.4080i	1.02539	+	1.49839i
$58$	18.3509	−	31.7848i	0.316396	−	0.548013i
$59$	63.9153	+	36.9015i	1.08331	+	0.625449i	0.931787	−	0.363005i	$-0.118249\pi$
$59$	63.9153	+	36.9015i	1.08331	+	0.625449i	0.151522	+	0.988454i	$0.451582\pi$
$60$	6.23921	−	13.0135i	0.103987	−	0.216892i
$61$	−78.5405	+	45.3454i	−1.28755	+	0.743367i	−0.978217	−	0.207587i	$-0.933439\pi$
$61$	−78.5405	+	45.3454i	−1.28755	+	0.743367i	−0.309332	+	0.950954i	$0.600106\pi$
$62$			35.3823i			0.570682i
$63$	−62.6480	+	6.65086i	−0.994412	+	0.105569i
$64$	8.00000			0.125000
$65$	−16.3318	−	28.2875i	−0.251259	−	0.435193i
$66$	−4.41125	−	57.5256i	−0.0668371	−	0.871599i
$67$	−10.3681	+	17.9581i	−0.154748	+	0.268031i	−0.932967	−	0.359962i	$-0.882790\pi$
$67$	−10.3681	+	17.9581i	−0.154748	+	0.268031i	0.778219	+	0.627992i	$0.216123\pi$
$68$	−34.3259	−	19.8181i	−0.504792	−	0.291442i
$69$	1.98893	+	25.9370i	0.0288251	+	0.375898i
$70$	−21.1612	+	10.9174i	−0.302302	+	0.155962i
$71$	−38.1972			−0.537989			−0.268995	−	0.963142i	$-0.586691\pi$
$71$	−38.1972			−0.537989			−0.268995	+	0.963142i	$0.586691\pi$
$72$	9.21785	−	23.7283i	0.128026	−	0.329559i
$73$			12.0702i			0.165345i	0.996577	+	0.0826726i	$0.0263456\pi$
$73$			12.0702i			0.165345i	−0.996577	+	0.0826726i	$0.973654\pi$
$74$	−28.0607	−	48.6026i	−0.379199	−	0.656792i
$75$	51.9782	+	24.9205i	0.693042	+	0.332273i
$76$	59.7512	+	34.4974i	0.786200	+	0.453913i
$77$	−51.4402	+	80.0951i	−0.668054	+	1.04020i
$78$	−32.5377	−	47.5467i	−0.417149	−	0.609573i
$79$	−65.4244	−	113.318i	−0.828157	−	1.43441i	−0.899483	−	0.436956i	$-0.856056\pi$
$79$	−65.4244	−	113.318i	−0.828157	−	1.43441i	0.0713263	−	0.997453i	$-0.477277\pi$
$80$		−	9.62126i		−	0.120266i
$81$	−59.7578	−	54.6809i	−0.737751	−	0.675073i
$82$			68.4128i			0.834302i
$83$	−27.6580	+	15.9683i	−0.333229	+	0.192390i	−0.657274	−	0.753652i	$-0.728290\pi$
$83$	−27.6580	+	15.9683i	−0.333229	+	0.192390i	0.324045	+	0.946042i	$0.394957\pi$
$84$	−35.7437	+	22.0542i	−0.425521	+	0.262550i
$85$	−23.8343	+	41.2823i	−0.280404	+	0.485674i
$86$	18.5501	−	32.1298i	0.215699	−	0.373602i
$87$	−70.2047	−	33.6590i	−0.806951	−	0.386885i
$88$	−19.2315	−	33.3099i	−0.218540	−	0.378522i
$89$		−	118.790i		−	1.33472i	−0.744737	−	0.667358i	$-0.767425\pi$
$89$		−	118.790i		−	1.33472i	0.744737	−	0.667358i	$-0.232575\pi$
$90$	−28.5370	−	11.0859i	−0.317078	−	0.123177i
$91$	−4.49464	+	94.9521i	−0.0493917	+	1.04343i
$92$	8.67105	+	15.0187i	0.0942505	+	0.163247i
$93$	74.8374	−	5.73877i	0.804703	−	0.0617072i
$94$	20.6013	+	11.8942i	0.219163	+	0.126534i
$95$	41.4885	−	71.8602i	0.436721	−	0.756423i
$96$	−1.29755	−	16.9209i	−0.0135161	−	0.176259i
$97$	99.4807	−	57.4352i	1.02557	−	0.592116i	0.109861	−	0.993947i	$-0.464960\pi$
$97$	99.4807	−	57.4352i	1.02557	−	0.592116i	0.915714	+	0.401831i	$0.131626\pi$
$98$	68.9866	+	6.54575i	0.703945	+	0.0667934i
$99$	−120.957	+	18.6605i	−1.22179	+	0.188490i
$100$	38.4289			0.384289
$101$	149.663	−	86.4081i	1.48181	−	0.855526i	0.482027	−	0.876156i	$-0.339901\pi$
$101$	149.663	−	86.4081i	1.48181	−	0.855526i	0.999787	+	0.0206305i	$0.00656734\pi$
$102$	−36.3500	+	75.8174i	−0.356372	+	0.743308i
$103$	−40.4444	−	23.3506i	−0.392664	−	0.226705i	0.290650	−	0.956830i	$-0.406129\pi$
$103$	−40.4444	−	23.3506i	−0.392664	−	0.226705i	−0.683314	+	0.730125i	$0.739462\pi$
$104$	−33.2635	−	19.2047i	−0.319842	−	0.184661i
$105$	26.5236	+	42.9875i	0.252606	+	0.409404i
$106$	−25.2277	−	43.6957i	−0.237998	−	0.412224i
$107$	−69.5084			−0.649611			−0.324806	−	0.945781i	$-0.605299\pi$
$107$	−69.5084			−0.649611			−0.324806	+	0.945781i	$0.605299\pi$
$108$	−51.6830	−	15.6482i	−0.478546	−	0.144891i
$109$	135.887			1.24667			0.623334	−	0.781956i	$-0.285778\pi$
$109$	135.887			1.24667			0.623334	+	0.781956i	$0.285778\pi$
$110$	−40.0604	+	23.1289i	−0.364186	+	0.210263i
$111$	−98.2486	+	67.2346i	−0.885123	+	0.605717i
$112$	−15.1309	+	23.5596i	−0.135097	+	0.210354i
$113$	−2.05580	+	3.56076i	−0.0181930	+	0.0315111i	−0.874979	−	0.484162i	$-0.839125\pi$
$113$	−2.05580	+	3.56076i	−0.0181930	+	0.0315111i	0.856786	+	0.515673i	$0.172458\pi$
$114$	63.2745	−	131.976i	0.555039	−	1.15768i
$115$	18.0623	−	10.4283i	0.157064	−	0.0906809i
$116$	−51.9043			−0.447451
$117$	−95.2891	+	76.5325i	−0.814437	+	0.654124i
$118$		−	104.373i		−	0.884519i
$119$	123.286	−	63.6050i	1.03602	−	0.534496i
$120$	−20.3500	+	1.56051i	−0.169584	+	0.0130042i
$121$	−31.9625	+	55.3606i	−0.264153	+	0.457526i
$122$	111.073	+	64.1280i	0.910435	+	0.525640i
$123$	144.701	−	11.0961i	1.17643	−	0.0902123i
$124$	43.3342	−	25.0190i	0.349470	−	0.201766i
$125$		−	106.350i		−	0.850798i
$126$	52.4444	+	72.0249i	0.416225	+	0.571626i
$127$	12.0291			0.0947171			0.0473585	−	0.998878i	$-0.484920\pi$
$127$	12.0291			0.0947171			0.0473585	+	0.998878i	$0.484920\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	−70.9668	−	34.0244i	−0.550130	−	0.263755i
$130$	−23.0967	+	40.0046i	−0.177667	+	0.307728i
$131$	72.6514	+	41.9453i	0.554591	+	0.320193i	0.750971	−	0.660335i	$-0.229586\pi$
$131$	72.6514	+	41.9453i	0.554591	+	0.320193i	−0.196381	+	0.980528i	$0.562919\pi$
$132$	−67.3349	+	46.0794i	−0.510113	+	0.349086i
$133$	−214.604	+	110.718i	−1.61357	+	0.832462i
$134$	29.3254			0.218846
$135$	−18.8194	+	62.1570i	−0.139403	+	0.460422i
$136$			56.0539i			0.412161i
$137$	99.9694	+	173.152i	0.729703	+	1.26388i	0.957009	+	0.290060i	$0.0936751\pi$
$137$	99.9694	+	173.152i	0.729703	+	1.26388i	−0.227305	+	0.973824i	$0.572992\pi$
$138$	30.3598	−	20.7762i	0.219999	−	0.150552i
$139$	127.666	+	73.7083i	0.918464	+	0.530275i	0.883145	−	0.469101i	$-0.155422\pi$
$139$	127.666	+	73.7083i	0.918464	+	0.530275i	0.0353192	+	0.999376i	$0.488755\pi$
$140$	28.3342	+	18.1973i	0.202387	+	0.129981i
$141$	21.8161	−	45.5032i	0.154724	−	0.322718i
$142$	27.0095	+	46.7819i	0.190208	+	0.329450i
$143$			184.667i			1.29138i
$144$	−35.5791	+	5.48892i	−0.247077	+	0.0381175i
$145$			62.4231i			0.430504i
$146$	14.7829	−	8.53492i	0.101253	−	0.0584584i
$147$	2.65581	−	146.976i	0.0180667	−	0.999837i
$148$	−39.6839	+	68.7345i	−0.268134	+	0.464422i
$149$	105.785	−	183.225i	0.709967	−	1.22970i	−0.254902	−	0.966967i	$-0.582043\pi$
$149$	105.785	−	183.225i	0.709967	−	1.22970i	0.964869	−	0.262731i	$-0.0846233\pi$
$150$	−6.23292	−	81.2814i	−0.0415528	−	0.541876i
$151$	−9.48372	−	16.4263i	−0.0628061	−	0.108783i	0.832913	−	0.553405i	$-0.186672\pi$
$151$	−9.48372	−	16.4263i	−0.0628061	−	0.108783i	−0.895719	+	0.444621i	$0.853338\pi$
$152$		−	97.5733i		−	0.641930i
$153$	166.258	+	64.5871i	1.08665	+	0.422138i
$154$	134.470	+	6.36525i	0.873181	+	0.0413328i
$155$	−30.0893	−	52.1163i	−0.194125	−	0.336234i
$156$	−35.2249	+	73.4709i	−0.225801	+	0.470967i
$157$	6.98156	+	4.03081i	0.0444685	+	0.0256739i	0.522069	−	0.852903i	$-0.325160\pi$
$157$	6.98156	+	4.03081i	0.0444685	+	0.0256739i	−0.477601	+	0.878577i	$0.658494\pi$
$158$	−92.5240	+	160.256i	−0.585595	+	1.01428i
$159$	−88.3296	+	60.4466i	−0.555532	+	0.380168i
$160$	−11.7836	+	6.80326i	−0.0736474	+	0.0425204i
$161$	−60.6294	−	2.86995i	−0.376580	−	0.0178258i
$162$	−24.7150	+	111.853i	−0.152562	+	0.690453i
$163$	49.1196			0.301347			0.150673	−	0.988584i	$-0.451856\pi$
$163$	49.1196			0.301347			0.150673	+	0.988584i	$0.451856\pi$
$164$	83.7882	−	48.3751i	0.510904	−	0.294970i
$165$	55.4177	+	80.9808i	0.335865	+	0.490793i
$166$	39.1143	+	22.5826i	0.235628	+	0.136040i
$167$	−168.024	−	97.0088i	−1.00613	−	0.580891i	−0.0960758	−	0.995374i	$-0.530629\pi$
$167$	−168.024	−	97.0088i	−1.00613	−	0.580891i	−0.910057	+	0.414483i	$0.863962\pi$
$168$	52.2854	+	28.1823i	0.311222	+	0.167752i
$169$	7.70514	+	13.3457i	0.0455926	+	0.0789686i
$170$	67.4137			0.396551
$171$	−289.406	−	112.427i	−1.69243	−	0.657468i
$172$	−52.4677			−0.305045
$173$	65.2186	−	37.6540i	0.376986	−	0.217653i	−0.299520	−	0.954090i	$-0.596827\pi$
$173$	65.2186	−	37.6540i	0.376986	−	0.217653i	0.676506	+	0.736437i	$0.263493\pi$
$174$	8.41854	+	109.783i	0.0483824	+	0.630939i
$175$	−72.6830	+	113.171i	−0.415331	+	0.646694i
$176$	−27.1974	+	47.1073i	−0.154531	+	0.267655i
$177$	−220.761	+	16.9287i	−1.24724	+	0.0956421i
$178$	−145.487	+	83.9970i	−0.817343	+	0.471893i
$179$	−97.4357			−0.544334			−0.272167	−	0.962250i	$-0.587740\pi$
$179$	−97.4357			−0.544334			−0.272167	+	0.962250i	$0.587740\pi$
$180$	6.60129	+	42.7895i	0.0366738	+	0.237719i
$181$		−	83.1541i		−	0.459415i	−0.973260	−	0.229707i	$-0.926223\pi$
$181$		−	83.1541i		−	0.459415i	0.973260	−	0.229707i	$-0.0737769\pi$
$182$	119.470	−	61.6365i	0.656430	−	0.338662i
$183$	117.623	−	245.333i	0.642746	−	1.34062i
$184$	12.2627	−	21.2396i	0.0666452	−	0.115433i
$185$	82.6640	+	47.7261i	0.446833	+	0.257979i
$186$	−59.9466	−	87.5988i	−0.322293	−	0.470961i
$187$	233.394	−	134.750i	1.24810	−	0.720588i
$188$		−	33.6418i		−	0.178946i
$189$	143.834	−	122.608i	0.761029	−	0.648718i
$190$	−117.347			−0.617617
$191$	109.890	+	190.335i	0.575341	+	0.996520i	0.996005	+	0.0893029i	$0.0284639\pi$
$191$	109.890	+	190.335i	0.575341	+	0.996520i	−0.420664	+	0.907217i	$0.638203\pi$
$192$	−19.8063	+	13.5540i	−0.103158	+	0.0705939i
$193$	57.6084	−	99.7807i	0.298489	−	0.516998i	−0.677301	−	0.735706i	$-0.736851\pi$
$193$	57.6084	−	99.7807i	0.298489	−	0.516998i	0.975790	+	0.218707i	$0.0701840\pi$
$194$	−140.687	−	81.2257i	−0.725190	−	0.418689i
$195$	88.3603	+	42.3635i	0.453130	+	0.217249i
$196$	−40.7640	−	89.1195i	−0.207980	−	0.454692i
$197$	44.1864			0.224297			0.112148	−	0.993691i	$-0.464227\pi$
$197$	44.1864			0.224297			0.112148	+	0.993691i	$0.464227\pi$
$198$	108.384	+	134.947i	0.547395	+	0.681551i
$199$			14.5566i			0.0731488i	0.999331	+	0.0365744i	$0.0116446\pi$
$199$			14.5566i			0.0731488i	−0.999331	+	0.0365744i	$0.988355\pi$
$200$	−27.1733	−	47.0656i	−0.135867	−	0.235328i
$201$	−4.75639	−	62.0265i	−0.0236636	−	0.308589i
$202$	−211.656	−	122.200i	−1.04780	−	0.604948i
$203$	98.1698	−	152.856i	0.483595	−	0.752984i
$204$	118.560	−	9.09158i	0.581178	−	0.0445666i
$205$	−58.1787	−	100.769i	−0.283799	−	0.491554i
$206$			66.0455i			0.320609i
$207$	−48.8680	−	60.8446i	−0.236077	−	0.293935i
$208$			54.3191i			0.261150i
$209$	−406.270	+	234.560i	−1.94387	+	1.12230i
$210$	33.8936	−	62.8814i	0.161398	−	0.299435i
$211$	175.108	−	303.296i	0.829896	−	1.43742i	−0.0682235	−	0.997670i	$-0.521733\pi$
$211$	175.108	−	303.296i	0.829896	−	1.43742i	0.898119	−	0.439752i	$-0.144934\pi$
$212$	−35.6774	+	61.7951i	−0.168290	+	0.291486i
$213$	94.5680	−	64.7158i	0.443981	−	0.303830i
$214$	49.1499	+	85.1300i	0.229672	+	0.397804i
$215$			63.1007i			0.293492i
$216$	17.3804	+	74.3635i	0.0804646	+	0.344275i
$217$	−8.28082	+	174.937i	−0.0381604	+	0.806163i
$218$	−96.0864	−	166.427i	−0.440763	−	0.763425i
$219$	−20.4500	−	29.8832i	−0.0933790	−	0.136453i
$220$	56.6540	+	32.7092i	0.257518	+	0.148678i
$221$	134.562	−	233.069i	0.608880	−	1.05461i
$222$	151.817	+	72.7875i	0.683863	+	0.327872i
$223$	277.642	−	160.297i	1.24503	−	0.718820i	0.274918	−	0.961468i	$-0.411349\pi$
$223$	277.642	−	160.297i	1.24503	−	0.718820i	0.970114	+	0.242648i	$0.0780161\pi$
$224$	39.5537	+	1.87231i	0.176579	+	0.00835852i
$225$	−170.908	+	26.3666i	−0.759592	+	0.117185i
$226$	5.81469			0.0257287
$227$	−242.920	+	140.250i	−1.07013	+	0.617841i	−0.928218	−	0.372037i	$-0.878659\pi$
$227$	−242.920	+	140.250i	−1.07013	+	0.617841i	−0.141915	+	0.989879i	$0.545326\pi$
$228$	−206.378	+	15.8258i	−0.905168	+	0.0694112i
$229$	31.1962	+	18.0111i	0.136228	+	0.0786512i	0.566565	−	0.824017i	$-0.308272\pi$
$229$	31.1962	+	18.0111i	0.136228	+	0.0786512i	−0.430337	+	0.902668i	$0.641605\pi$
$230$	−25.5440	−	14.7478i	−0.111061	−	0.0641211i
$231$	−8.34693	−	285.451i	−0.0361339	−	1.23572i
$232$	36.7019	+	63.5695i	0.158198	+	0.274007i
$233$	−418.773			−1.79731			−0.898654	−	0.438658i	$-0.855454\pi$
$233$	−418.773			−1.79731			−0.898654	+	0.438658i	$0.855454\pi$
$234$	161.112	+	62.5882i	0.688514	+	0.267471i
$235$	−40.4596			−0.172168
$236$	−127.831	+	73.8030i	−0.541655	+	0.312725i
$237$	353.967	+	169.706i	1.49353	+	0.716059i
$238$	−165.076	−	106.018i	−0.693598	−	0.445455i
$239$	−25.6058	+	44.3506i	−0.107137	+	0.185567i	−0.914609	−	0.404338i	$-0.867502\pi$
$239$	−25.6058	+	44.3506i	−0.107137	+	0.185567i	0.807472	+	0.589906i	$0.200835\pi$
$240$	16.3009	+	23.8202i	0.0679203	+	0.0992506i
$241$	−227.784	+	131.511i	−0.945161	+	0.545689i	−0.891574	−	0.452874i	$-0.850399\pi$
$241$	−227.784	+	131.511i	−0.945161	+	0.545689i	−0.0535868	+	0.998563i	$0.517065\pi$
$242$	90.4035			0.373568
$243$	240.591	+	34.1331i	0.990086	+	0.140465i
$244$		−	181.381i		−	0.743367i
$245$	−107.180	+	49.0252i	−0.437471	+	0.200103i
$246$	−115.909	−	169.375i	−0.471173	−	0.688517i
$247$	−234.233	+	405.704i	−0.948313	+	1.64253i
$248$	−61.2839	−	35.3823i	−0.247112	−	0.142670i
$249$	41.4207	−	86.3938i	0.166348	−	0.346963i
$250$	−130.251	+	75.2006i	−0.521005	+	0.300802i
$251$			244.001i			0.972115i	0.873927	+	0.486058i	$0.161565\pi$
$251$			244.001i			0.972115i	−0.873927	+	0.486058i	$0.838435\pi$
$252$	51.1283	−	115.160i	0.202890	−	0.456985i
$253$	−117.915			−0.466067
$254$	−8.50584	−	14.7325i	−0.0334875	−	0.0580021i
$255$	−10.9341	−	142.587i	−0.0428787	−	0.559166i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−185.090	−	106.862i	−0.720193	−	0.415804i	0.0946307	−	0.995512i	$-0.469833\pi$
$257$	−185.090	−	106.862i	−0.720193	−	0.415804i	−0.814824	+	0.579709i	$0.803166\pi$
$258$	8.50992	+	110.975i	0.0329842	+	0.430136i
$259$	−127.363	−	246.869i	−0.491750	−	0.953162i
$260$	65.3273			0.251259
$261$	230.839	−	35.6123i	0.884439	−	0.136446i
$262$		−	118.639i		−	0.452821i
$263$	77.6298	+	134.459i	0.295170	+	0.511250i	0.975025	−	0.222097i	$-0.0712902\pi$
$263$	77.6298	+	134.459i	0.295170	+	0.511250i	−0.679854	+	0.733347i	$0.737957\pi$
$264$	104.048	+	49.8851i	0.394123	+	0.188959i
$265$	74.3184	+	42.9077i	0.280447	+	0.161916i
$266$	287.349	+	184.546i	1.08026	+	0.693783i
$267$	201.260	+	294.097i	0.753783	+	1.10149i
$268$	−20.7362	−	35.9161i	−0.0773739	−	0.134015i
$269$		−	128.394i		−	0.477302i	−0.971105	−	0.238651i	$-0.923295\pi$
$269$		−	128.394i		−	0.477302i	0.971105	−	0.238651i	$-0.0767052\pi$
$270$	89.4338	−	20.9026i	0.331236	−	0.0774171i
$271$		−	520.915i		−	1.92219i	−0.276210	−	0.961097i	$-0.589079\pi$
$271$		−	520.915i		−	1.92219i	0.276210	−	0.961097i	$-0.410921\pi$
$272$	68.6518	−	39.6361i	0.252396	−	0.145721i
$273$	−149.745	−	242.696i	−0.548518	−	0.888996i
$274$	141.378	−	244.874i	0.515978	−	0.893700i
$275$	−130.646	+	226.285i	−0.475076	+	0.822856i
$276$	−46.9131	−	22.4921i	−0.169975	−	0.0814930i
$277$	191.963	+	332.489i	0.693007	+	1.20032i	0.970848	+	0.239696i	$0.0770477\pi$
$277$	191.963	+	332.489i	0.693007	+	1.20032i	−0.277841	+	0.960627i	$0.589619\pi$
$278$		−	208.478i		−	0.749923i
$279$	−175.558	+	141.002i	−0.629241	+	0.505382i
$280$	2.25175	−	47.5695i	0.00804195	−	0.169891i
$281$	−45.4795	−	78.7728i	−0.161849	−	0.280330i	0.773683	−	0.633573i	$-0.218412\pi$
$281$	−45.4795	−	78.7728i	−0.161849	−	0.280330i	−0.935532	+	0.353243i	$0.885079\pi$
$282$	−71.1561	+	5.45648i	−0.252327	+	0.0193492i
$283$	−86.2442	−	49.7931i	−0.304750	−	0.175947i	0.339825	−	0.940489i	$-0.389632\pi$
$283$	−86.2442	−	49.7931i	−0.304750	−	0.175947i	−0.644575	+	0.764541i	$0.722966\pi$
$284$	38.1972	−	66.1595i	0.134497	−	0.232956i
$285$	19.0330	+	248.202i	0.0667823	+	0.870886i
$286$	226.170	−	130.580i	0.790806	−	0.456572i
$287$	−16.0112	+	338.247i	−0.0557883	+	1.17856i
$288$	31.8807	+	39.6941i	0.110697	+	0.137827i
$289$	−103.755			−0.359015
$290$	76.4524	−	44.1398i	0.263629	−	0.152206i
$291$	−148.983	+	310.743i	−0.511968	+	1.06784i
$292$	−20.9062	−	12.0702i	−0.0715966	−	0.0413363i
$293$	−493.237	−	284.771i	−1.68340	−	0.971914i	−0.959371	−	0.282149i	$-0.908953\pi$
$293$	−493.237	−	284.771i	−1.68340	−	0.971914i	−0.724033	−	0.689765i	$-0.757714\pi$
$294$	−181.886	+	100.675i	−0.618660	+	0.342432i
$295$	88.7597	+	153.736i	0.300880	+	0.521140i
$296$	112.243			0.379199
$297$	267.849	−	251.132i	0.901847	−	0.845563i
$298$	−299.205			−1.00404
$299$	−101.975	+	58.8754i	−0.341054	+	0.196908i
$300$	−95.1417	+	65.1084i	−0.317139	+	0.217028i
$301$	99.2354	−	154.515i	0.329686	−	0.513339i
$302$	−13.4120	+	23.2303i	−0.0444106	+	0.0769215i
$303$	−224.136	+	467.495i	−0.739724	+	1.54289i
$304$	−119.502	+	68.9947i	−0.393100	+	0.226956i
$305$	−218.140			−0.715213
$306$	−38.4594	−	249.294i	−0.125684	−	0.814685i
$307$		−	235.830i		−	0.768176i	−0.923296	−	0.384088i	$-0.874516\pi$
$307$		−	235.830i		−	0.768176i	0.923296	−	0.384088i	$-0.125484\pi$
$308$	−87.2887	−	169.192i	−0.283405	−	0.549325i
$309$	139.694	−	10.7121i	0.452083	−	0.0346672i
$310$	−42.5527	+	73.7035i	−0.137267	+	0.237753i
$311$	525.110	+	303.172i	1.68846	+	0.974831i	0.955701	+	0.294339i	$0.0950996\pi$
$311$	525.110	+	303.172i	1.68846	+	0.974831i	0.732756	+	0.680492i	$0.238234\pi$
$312$	114.891	−	8.81021i	0.368240	−	0.0282378i
$313$	21.4543	−	12.3867i	0.0685442	−	0.0395740i	−0.465336	−	0.885134i	$-0.654067\pi$
$313$	21.4543	−	12.3867i	0.0685442	−	0.0395740i	0.533880	+	0.845560i	$0.320733\pi$
$314$		−	11.4008i		−	0.0363084i
$315$	−138.498	−	61.4899i	−0.439677	−	0.195206i
$316$	261.697			0.828157
$317$	219.173	+	379.619i	0.691398	+	1.19754i	0.971380	+	0.237531i	$0.0763383\pi$
$317$	219.173	+	379.619i	0.691398	+	1.19754i	−0.279982	+	0.960005i	$0.590328\pi$
$318$	136.490	+	65.4389i	0.429214	+	0.205783i
$319$	176.458	−	305.634i	0.553160	−	0.958101i
$320$	16.6645	+	9.62126i	0.0520766	+	0.0300664i
$321$	172.088	−	117.765i	0.536099	−	0.366869i
$322$	39.3565	+	76.2850i	0.122225	+	0.236910i
$323$	683.671			2.11663
$324$	154.468	−	48.8227i	0.476753	−	0.150687i
$325$			260.928i			0.802855i
$326$	−34.7328	−	60.1589i	−0.106542	−	0.184537i
$327$	−336.426	+	230.227i	−1.02883	+	0.704057i
$328$	−118.494	−	68.4128i	−0.361263	−	0.208576i
$329$	99.0736	+	63.6288i	0.301135	+	0.193401i
$330$	59.9946	−	125.135i	0.181802	−	0.379196i
$331$	301.074	+	521.476i	0.909590	+	1.57546i	0.814634	+	0.579976i	$0.196938\pi$
$331$	301.074	+	521.476i	0.909590	+	1.57546i	0.0949566	+	0.995481i	$0.469729\pi$
$332$		−	63.8733i		−	0.192390i
$333$	129.330	−	332.916i	0.388378	−	0.999749i
$334$			274.382i			0.821504i
$335$	−43.1948	+	24.9385i	−0.128940	+	0.0744434i
$336$	−2.45521	−	83.9641i	−0.00730718	−	0.249893i
$337$	−58.8515	+	101.934i	−0.174634	+	0.302474i	−0.940034	−	0.341080i	$-0.889207\pi$
$337$	−58.8515	+	101.934i	−0.174634	+	0.302474i	0.765401	+	0.643554i	$0.222541\pi$
$338$	10.8967	−	18.8737i	0.0322388	−	0.0558393i
$339$	−0.943105	−	12.2987i	−0.00278202	−	0.0362794i
$340$	−47.6687	−	82.5646i	−0.140202	−	0.242837i
$341$			340.227i			0.997732i
$342$	66.9465	+	433.946i	0.195750	+	1.26885i
$343$	339.552	+	48.5091i	0.989949	+	0.141426i
$344$	37.1003	+	64.2596i	0.107850	+	0.186801i
$345$	−27.0502	+	56.4204i	−0.0784065	+	0.163537i
$346$	−92.2331	−	53.2508i	−0.266570	−	0.153904i
$347$	−136.895	+	237.110i	−0.394511	+	0.683313i	−0.993039	−	0.117789i	$-0.962419\pi$
$347$	−136.895	+	237.110i	−0.394511	+	0.683313i	0.598528	+	0.801102i	$0.295753\pi$
$348$	128.504	−	87.9391i	0.369264	−	0.252699i
$349$	184.692	−	106.632i	0.529203	−	0.305535i	−0.211489	−	0.977380i	$-0.567831\pi$
$349$	184.692	−	106.632i	0.529203	−	0.305535i	0.740692	+	0.671845i	$0.234498\pi$
$350$	190.001	+	8.99385i	0.542859	+	0.0256967i
$351$	106.249	−	350.922i	0.302705	−	0.999777i
$352$	76.9259			0.218540
$353$	497.182	−	287.048i	1.40845	−	0.813168i	0.413210	−	0.910636i	$-0.364408\pi$
$353$	497.182	−	287.048i	1.40845	−	0.813168i	0.995239	+	0.0974679i	$0.0310743\pi$
$354$	176.835	+	258.405i	0.499533	+	0.729959i
$355$	−79.5673	−	45.9382i	−0.224133	−	0.129403i
$356$	205.750	+	118.790i	0.577949	+	0.333679i
$357$	−197.466	+	366.350i	−0.553126	+	1.02619i
$358$	68.8975	+	119.334i	0.192451	+	0.333335i
$359$	34.8283			0.0970149			0.0485074	−	0.998823i	$-0.484554\pi$
$359$	34.8283			0.0970149			0.0485074	+	0.998823i	$0.484554\pi$
$360$	47.7384	−	38.3416i	0.132607	−	0.106504i
$361$	−829.069			−2.29659
$362$	−101.843	+	58.7988i	−0.281333	+	0.162428i
$363$	−14.6629	−	191.213i	−0.0403936	−	0.526759i
$364$	−159.967	−	102.737i	−0.439470	−	0.282245i
$365$	−14.5163	+	25.1430i	−0.0397708	+	0.0688850i
$366$	−383.642	+	29.4189i	−1.04820	+	0.0803795i
$367$	−12.0980	+	6.98480i	−0.0329646	+	0.0190321i	−0.516392	−	0.856352i	$-0.672725\pi$
$367$	−12.0980	+	6.98480i	−0.0329646	+	0.0190321i	0.483427	+	0.875385i	$0.339392\pi$
$368$	−34.6842			−0.0942505
$369$	−339.448	+	272.631i	−0.919912	+	0.738838i
$370$		−	134.990i		−	0.364837i
$371$	−114.505	−	221.945i	−0.308638	−	0.598235i
$372$	−64.8976	+	135.361i	−0.174456	+	0.363874i
$373$	285.616	−	494.702i	0.765727	−	1.32628i	−0.174135	−	0.984722i	$-0.555713\pi$
$373$	285.616	−	494.702i	0.765727	−	1.32628i	0.939861	−	0.341556i	$-0.110954\pi$
$374$	−330.069	−	190.565i	−0.882537	−	0.509533i
$375$	180.184	+	263.299i	0.480489	+	0.702130i
$376$	−41.2026	+	23.7883i	−0.109581	+	0.0632669i
$377$		−	352.424i		−	0.934813i
$378$	−251.869	−	89.4638i	−0.666321	−	0.236677i
$379$	−387.493			−1.02241			−0.511205	−	0.859459i	$-0.670801\pi$
$379$	−387.493			−1.02241			−0.511205	+	0.859459i	$0.670801\pi$
$380$	82.9770	+	143.720i	0.218361	+	0.378212i
$381$	−29.7814	+	20.3803i	−0.0781663	+	0.0534916i
$382$	155.408	−	269.175i	0.406827	−	0.704646i
$383$	499.981	+	288.664i	1.30543	+	0.753693i	0.981331	−	0.192329i	$-0.0616039\pi$
$383$	499.981	+	288.664i	1.30543	+	0.753693i	0.324104	+	0.946022i	$0.394937\pi$
$384$	30.6054	+	14.6735i	0.0797015	+	0.0382122i
$385$	−203.480	+	104.978i	−0.528520	+	0.272671i
$386$	−162.941			−0.422127
$387$	233.344	−	35.9989i	0.602957	−	0.0930203i
$388$			229.741i			0.592116i
$389$	−166.634	−	288.618i	−0.428364	−	0.741948i	0.568364	−	0.822777i	$-0.307577\pi$
$389$	−166.634	−	288.618i	−0.428364	−	0.741948i	−0.996728	+	0.0808291i	$0.974243\pi$
$390$	−10.5957	−	138.174i	−0.0271684	−	0.354293i
$391$	148.821	+	85.9217i	0.380616	+	0.219748i
$392$	−80.3242	+	112.943i	−0.204909	+	0.288119i
$393$	−250.935	+	19.2425i	−0.638512	+	0.0489631i
$394$	−31.2445	−	54.1171i	−0.0793009	−	0.137353i
$395$		−	314.732i		−	0.796791i
$396$	88.6364	−	228.165i	0.223829	−	0.576174i
$397$		−	279.218i		−	0.703321i	−0.936128	−	0.351661i	$-0.885617\pi$
$397$		−	279.218i		−	0.703321i	0.936128	−	0.351661i	$-0.114383\pi$
$398$	17.8281	−	10.2931i	0.0447943	−	0.0258620i
$399$	343.730	−	637.707i	0.861478	−	1.59826i
$400$	−38.4289	+	66.5608i	−0.0960723	+	0.166402i
$401$	110.631	−	191.619i	0.275888	−	0.477852i	−0.694471	−	0.719521i	$-0.744361\pi$
$401$	110.631	−	191.619i	0.275888	−	0.477852i	0.970359	+	0.241669i	$0.0776948\pi$
$402$	−72.6033	+	49.6847i	−0.180605	+	0.123594i
$403$	169.876	+	294.235i	0.421530	+	0.730111i
$404$			345.632i			0.855526i
$405$	−58.7169	−	185.772i	−0.144980	−	0.458696i
$406$	−256.626	−	12.1476i	−0.632084	−	0.0299202i
$407$	−269.825	−	467.350i	−0.662960	−	1.14828i
$408$	−94.9696	−	138.777i	−0.232769	−	0.340141i
$409$	−261.910	−	151.214i	−0.640366	−	0.369715i	0.144390	−	0.989521i	$-0.453878\pi$
$409$	−261.910	−	151.214i	−0.640366	−	0.369715i	−0.784755	+	0.619806i	$0.787211\pi$
$410$	−82.2771	+	142.508i	−0.200676	+	0.347581i
$411$	−540.866	−	259.313i	−1.31598	−	0.630932i
$412$	80.8889	−	46.7012i	0.196332	−	0.113352i
$413$	24.4274	−	516.043i	0.0591461	−	1.24950i
$414$	−39.9642	+	102.875i	−0.0965319	+	0.248489i
$415$	−76.8178			−0.185103
$416$	66.5270	−	38.4094i	0.159921	−	0.0923303i
$417$	−440.955	+	33.8139i	−1.05745	+	0.0810884i
$418$	574.552	+	331.718i	1.37453	+	0.793583i
$419$	−437.785	−	252.755i	−1.04483	−	0.603234i	−0.123634	−	0.992328i	$-0.539455\pi$
$419$	−437.785	−	252.755i	−1.04483	−	0.603234i	−0.921198	+	0.389093i	$0.872788\pi$
$420$	−100.980	+	2.95278i	−0.240429	+	0.00703043i
$421$	22.8490	+	39.5757i	0.0542733	+	0.0940040i	0.891886	−	0.452261i	$-0.149382\pi$
$421$	22.8490	+	39.5757i	0.0542733	+	0.0940040i	−0.837612	+	0.546265i	$0.816049\pi$
$422$	−495.280			−1.17365
$423$	23.0821	+	149.618i	0.0545677	+	0.353707i
$424$	100.911			0.237998
$425$	329.777	−	190.397i	0.775945	−	0.447992i
$426$	−146.130	−	70.0607i	−0.343028	−	0.164462i
$427$	534.160	+	343.058i	1.25096	+	0.803414i
$428$	69.5084	−	120.392i	0.162403	−	0.281290i
$429$	−312.874	−	457.196i	−0.729309	−	1.06573i
$430$	77.2822	−	44.6189i	0.179726	−	0.103765i
$431$	252.544			0.585948			0.292974	−	0.956120i	$-0.405355\pi$
$431$	252.544			0.585948			0.292974	+	0.956120i	$0.405355\pi$
$432$	78.7865	−	73.8694i	0.182376	−	0.170994i
$433$			830.225i			1.91738i	0.284454	+	0.958690i	$0.408188\pi$
$433$			830.225i			1.91738i	−0.284454	+	0.958690i	$0.591812\pi$
$434$	220.109	−	113.558i	0.507164	−	0.261653i
$435$	−105.761	−	154.546i	−0.243128	−	0.355278i
$436$	−135.887	+	235.363i	−0.311667	+	0.539823i
$437$	−259.053	−	149.564i	−0.592798	−	0.342252i
$438$	−22.1390	+	46.1767i	−0.0505456	+	0.105426i
$439$	193.141	−	111.510i	0.439956	−	0.254009i	−0.263623	−	0.964626i	$-0.584917\pi$
$439$	193.141	−	111.510i	0.439956	−	0.254009i	0.703579	+	0.710617i	$0.251584\pi$
$440$		−	92.5155i		−	0.210263i
$441$	242.440	+	368.380i	0.549750	+	0.835329i
$442$	−380.600			−0.861086
$443$	−102.606	−	177.719i	−0.231616	−	0.401171i	0.726668	−	0.686989i	$-0.241068\pi$
$443$	−102.606	−	177.719i	−0.231616	−	0.401171i	−0.958284	+	0.285818i	$0.907735\pi$
$444$	−18.2051	−	237.406i	−0.0410024	−	0.534699i
$445$	142.863	−	247.447i	0.321041	−	0.556060i
$446$	−392.645	−	226.694i	−0.880371	−	0.508282i
$447$	48.5291	+	632.852i	0.108566	+	1.41578i
$448$	−25.6756	−	49.7671i	−0.0573116	−	0.111087i
$449$	−441.157			−0.982532			−0.491266	−	0.871010i	$-0.663466\pi$
$449$	−441.157			−0.982532			−0.491266	+	0.871010i	$0.663466\pi$
$450$	153.143	+	190.675i	0.340317	+	0.423722i
$451$			657.839i			1.45862i
$452$	−4.11161	−	7.12151i	−0.00909648	−	0.0157556i
$453$	51.3100	+	24.6001i	0.113267	+	0.0543048i
$454$	343.541	+	198.343i	0.756698	+	0.436880i
$455$	−123.557	+	192.386i	−0.271555	+	0.422826i
$456$	165.314	+	241.570i	0.362531	+	0.529759i
$457$	−337.214	−	584.071i	−0.737886	−	1.27806i	−0.953446	−	0.301565i	$-0.902491\pi$
$457$	−337.214	−	584.071i	−0.737886	−	1.27806i	0.215560	−	0.976491i	$-0.430842\pi$
$458$		−	50.9432i		−	0.111230i
$459$	−521.046	+	121.780i	−1.13518	+	0.265315i
$460$			41.7132i			0.0906809i
$461$	82.1484	−	47.4284i	0.178196	−	0.102882i	−0.408249	−	0.912871i	$-0.633860\pi$
$461$	82.1484	−	47.4284i	0.178196	−	0.102882i	0.586445	+	0.809989i	$0.300527\pi$
$462$	−343.702	+	212.067i	−0.743945	+	0.459020i
$463$	195.201	−	338.099i	0.421601	−	0.730235i	−0.574495	−	0.818508i	$-0.694802\pi$
$463$	195.201	−	338.099i	0.421601	−	0.730235i	0.996096	+	0.0882733i	$0.0281349\pi$
$464$	51.9043	−	89.9009i	0.111863	−	0.193752i
$465$	162.793	+	78.0495i	0.350092	+	0.167848i
$466$	296.117	+	512.890i	0.635445	+	1.10062i
$467$			135.589i			0.290341i	0.989407	+	0.145170i	$0.0463731\pi$
$467$			135.589i			0.290341i	−0.989407	+	0.145170i	$0.953627\pi$
$468$	−37.2691	−	241.578i	−0.0796349	−	0.516192i
$469$	144.991	+	6.86328i	0.309149	+	0.0146339i
$470$	28.6092	+	49.5527i	0.0608707	+	0.105431i
$471$	−24.1140	+	1.84914i	−0.0511975	+	0.00392599i
$472$	180.780	+	104.373i	0.383008	+	0.221130i
$473$	178.373	−	308.952i	0.377111	−	0.653175i
$474$	−42.4456	−	553.519i	−0.0895477	−	1.16776i
$475$	−574.043	+	331.424i	−1.20851	+	0.697735i
$476$	−13.1188	+	277.143i	−0.0275605	+	0.582232i
$477$	116.273	−	299.306i	0.243758	−	0.627475i
$478$	72.4242			0.151515
$479$	176.072	−	101.655i	0.367583	−	0.212224i	−0.304819	−	0.952410i	$-0.598596\pi$
$479$	176.072	−	101.655i	0.367583	−	0.212224i	0.672402	+	0.740186i	$0.265263\pi$
$480$	17.6472	−	36.8078i	0.0367649	−	0.0766829i
$481$	−466.699	−	269.449i	−0.970269	−	0.560185i
$482$	322.135	+	185.985i	0.668330	+	0.385860i
$483$	154.968	−	95.6163i	0.320844	−	0.197963i
$484$	−63.9249	−	110.721i	−0.132076	−	0.228763i
$485$	276.300			0.569690
$486$	−128.319	−	318.798i	−0.264031	−	0.655963i
$487$	−237.902			−0.488504			−0.244252	−	0.969712i	$-0.578542\pi$
$487$	−237.902			−0.488504			−0.244252	+	0.969712i	$0.578542\pi$
$488$	−222.146	+	128.256i	−0.455217	+	0.262820i
$489$	−121.609	+	83.2210i	−0.248690	+	0.170186i
$490$	135.831	+	96.6025i	0.277207	+	0.197148i
$491$	−283.247	+	490.597i	−0.576877	+	0.999180i	0.418958	+	0.908006i	$0.362395\pi$
$491$	−283.247	+	490.597i	−0.576877	+	0.999180i	−0.995835	+	0.0911744i	$0.970938\pi$
$492$	−125.482	+	261.725i	−0.255044	+	0.531961i
$493$	−445.415	+	257.161i	−0.903480	+	0.521624i
$494$	662.512			1.34112
$495$	−274.404	−	106.599i	−0.554352	−	0.215352i
$496$			100.076i			0.201766i
$497$	122.592	+	237.621i	0.246664	+	0.478110i
$498$	−135.099	+	10.3598i	−0.271284	+	0.0208029i
$499$	−118.082	+	204.523i	−0.236636	+	0.409866i	−0.959747	−	0.280866i	$-0.909378\pi$
$499$	−118.082	+	204.523i	−0.236636	+	0.409866i	0.723111	+	0.690732i	$0.242712\pi$
$500$	184.203	+	106.350i	0.368406	+	0.212699i
$501$	580.349	−	44.5030i	1.15838	−	0.0888284i
$502$	298.839	−	172.535i	0.595297	−	0.343695i
$503$		−	711.182i		−	1.41388i	−0.707273	−	0.706941i	$-0.750075\pi$
$503$		−	711.182i		−	1.41388i	0.707273	−	0.706941i	$-0.249925\pi$
$504$	−177.195	+	18.8115i	−0.351578	+	0.0373244i
$505$	415.677			0.823124
$506$	83.3785	+	144.416i	0.164780	+	0.285407i
$507$	−41.6873	−	19.9866i	−0.0822234	−	0.0394213i
$508$	−12.0291	+	20.8350i	−0.0236793	+	0.0410137i
$509$	454.930	+	262.654i	0.893772	+	0.516019i	0.875174	−	0.483808i	$-0.160747\pi$
$509$	454.930	+	262.654i	0.893772	+	0.516019i	0.0185973	+	0.999827i	$0.494080\pi$
$510$	−166.902	+	114.216i	−0.327258	+	0.223953i
$511$	75.0874	−	38.7387i	0.146942	−	0.0758096i
$512$	22.6274			0.0441942
$513$	906.986	−	211.982i	1.76800	−	0.413221i
$514$			302.250i			0.588035i
$515$	−56.1656	−	97.2816i	−0.109059	−	0.188896i
$516$	129.899	−	88.8937i	0.251742	−	0.172275i
$517$	198.097	+	114.371i	0.383166	+	0.221221i
$518$	−212.292	+	330.550i	−0.409830	+	0.638128i
$519$	−97.6717	+	203.720i	−0.188192	+	0.392524i
$520$	−46.1934	−	80.0092i	−0.0888334	−	0.153864i
$521$		−	58.8034i		−	0.112866i	−0.998406	−	0.0564332i	$-0.982027\pi$
$521$		−	58.8034i		−	0.112866i	0.998406	−	0.0564332i	$-0.0179728\pi$
$522$	−206.844	−	257.537i	−0.396252	−	0.493365i
$523$			49.8806i			0.0953740i	0.998862	+	0.0476870i	$0.0151850\pi$
$523$			49.8806i			0.0953740i	−0.998862	+	0.0476870i	$0.984815\pi$
$524$	−145.303	+	83.8906i	−0.277295	+	0.160097i
$525$	−11.7939	−	403.331i	−0.0224646	−	0.768250i
$526$	109.785	−	190.153i	0.208717	−	0.361509i
$527$	247.914	−	429.400i	0.470426	−	0.814801i
$528$	−12.4769	−	162.707i	−0.0236305	−	0.308157i
$529$	226.906	+	393.014i	0.428935	+	0.742937i
$530$		−	121.361i		−	0.228984i
$531$	517.874	−	415.937i	0.975282	−	0.783309i
$532$	22.8359	−	482.423i	0.0429247	−	0.906810i
$533$	328.462	+	568.912i	0.616251	+	1.06738i
$534$	217.882	−	454.450i	0.408019	−	0.851031i
$535$	−144.790	−	83.5948i	−0.270636	−	0.156252i
$536$	−29.3254	+	50.7931i	−0.0547116	+	0.0947632i
$537$	241.230	−	165.081i	0.449217	−	0.307413i
$538$	−157.250	+	90.7884i	−0.292287	+	0.168752i
$539$	663.357	+	62.9423i	1.23072	+	0.116776i
$540$	−88.8396	−	94.7532i	−0.164518	−	0.175469i
$541$	943.506			1.74400			0.872002	−	0.489503i	$-0.162822\pi$
$541$	943.506			1.74400			0.872002	+	0.489503i	$0.162822\pi$
$542$	−637.988	+	368.342i	−1.17710	+	0.679598i
$543$	140.884	+	205.871i	0.259455	+	0.379137i
$544$	−97.0883	−	56.0539i	−0.178471	−	0.103040i
$545$	283.061	+	163.425i	0.519377	+	0.299863i
$546$	−191.355	+	355.012i	−0.350466	+	0.650205i
$547$	−115.302	−	199.709i	−0.210790	−	0.365100i	0.741172	−	0.671315i	$-0.234270\pi$
$547$	−115.302	−	199.709i	−0.210790	−	0.365100i	−0.951962	+	0.306216i	$0.900937\pi$
$548$	−399.877			−0.729703
$549$	124.448	+	806.674i	0.226682	+	1.46935i
$550$	369.523			0.671859
$551$	775.336	−	447.641i	1.40714	−	0.812415i
$552$	5.62555	+	73.3609i	0.0101912	+	0.132900i
$553$	−494.964	+	770.687i	−0.895053	+	1.39365i
$554$	271.476	−	470.211i	0.490030	−	0.848756i
$555$	−285.518	+	21.8945i	−0.514448	+	0.0394495i
$556$	−255.333	+	147.417i	−0.459232	+	0.265138i
$557$	−484.872			−0.870506			−0.435253	−	0.900308i	$-0.643341\pi$
$557$	−484.872			−0.870506			−0.435253	+	0.900308i	$0.643341\pi$
$558$	296.829	+	115.311i	0.531952	+	0.206650i
$559$		−	356.250i		−	0.637298i
$560$	−59.8528	+	30.8789i	−0.106880	+	0.0551410i
$561$	−349.532	+	729.041i	−0.623051	+	1.29954i
$562$	−64.3178	+	111.402i	−0.114444	+	0.198224i
$563$	−565.382	−	326.423i	−1.00423	−	0.579793i	−0.0947335	−	0.995503i	$-0.530200\pi$
$563$	−565.382	−	326.423i	−1.00423	−	0.579793i	−0.909497	+	0.415710i	$0.863533\pi$
$564$	56.9978	+	83.2898i	0.101060	+	0.147677i
$565$	−8.56474	+	4.94486i	−0.0151588	+	0.00875196i
$566$			140.836i			0.248827i
$567$	−148.374	+	547.242i	−0.261683	+	0.965154i
$568$	−108.038			−0.190208
$569$	−203.792	−	352.977i	−0.358157	−	0.620347i	0.629496	−	0.777004i	$-0.283262\pi$
$569$	−203.792	−	352.977i	−0.358157	−	0.620347i	−0.987653	+	0.156657i	$0.949928\pi$
$570$	290.526	−	198.816i	0.509695	−	0.348800i
$571$	174.770	−	302.710i	0.306076	−	0.530140i	−0.671424	−	0.741073i	$-0.734317\pi$
$571$	174.770	−	302.710i	0.306076	−	0.530140i	0.977500	+	0.210934i	$0.0676504\pi$
$572$	−319.853	−	184.667i	−0.559184	−	0.322845i
$573$	−594.540	−	285.047i	−1.03759	−	0.497464i
$574$	425.588	−	219.567i	0.741443	−	0.382521i
$575$	−166.609			−0.289756
$576$	26.0720	−	67.1137i	0.0452639	−	0.116517i
$577$		−	695.947i		−	1.20615i	−0.797686	−	0.603073i	$-0.793943\pi$
$577$		−	695.947i		−	1.20615i	0.797686	−	0.603073i	$-0.206057\pi$
$578$	73.3662	+	127.074i	0.126931	+	0.219851i
$579$	26.4280	+	344.639i	0.0456442	+	0.595231i
$580$	−108.120	−	62.4231i	−0.186414	−	0.107626i
$581$	188.104	+	120.808i	0.323759	+	0.207930i
$582$	485.927	−	37.2625i	0.834927	−	0.0640249i
$583$	−242.583	−	420.167i	−0.416095	−	0.720698i
$584$			34.1397i			0.0584584i
$585$	−290.536	+	44.8220i	−0.496642	+	0.0766188i
$586$			805.453i			1.37449i
$587$	−45.3007	+	26.1544i	−0.0771732	+	0.0445560i	−0.538090	−	0.842887i	$-0.680854\pi$
$587$	−45.3007	+	26.1544i	−0.0771732	+	0.0445560i	0.460917	+	0.887443i	$0.347521\pi$
$588$	251.914	+	151.576i	0.428425	+	0.257782i
$589$	−431.546	+	747.459i	−0.732675	+	1.26903i
$590$	125.525	−	217.416i	0.212755	−	0.368502i
$591$	−109.396	+	74.8631i	−0.185103	+	0.126672i
$592$	−79.3677	−	137.469i	−0.134067	−	0.232211i
$593$			21.8727i			0.0368848i	0.999830	+	0.0184424i	$0.00587072\pi$
$593$			21.8727i			0.0368848i	−0.999830	+	0.0184424i	$0.994129\pi$
$594$	−496.970	−	150.469i	−0.836651	−	0.253315i
$595$	333.308	+	15.7774i	0.560181	+	0.0265166i
$596$	211.570	+	366.450i	0.354983	+	0.614849i
$597$	−24.6626	−	36.0390i	−0.0413109	−	0.0603668i
$598$	144.215	+	83.2624i	0.241162	+	0.139235i
$599$	−350.512	+	607.105i	−0.585162	+	1.01353i	0.409693	+	0.912224i	$0.365636\pi$
$599$	−350.512	+	607.105i	−0.585162	+	1.01353i	−0.994855	+	0.101307i	$0.967697\pi$
$600$	147.016	+	70.4857i	0.245027	+	0.117476i
$601$	−34.2071	+	19.7495i	−0.0569170	+	0.0328611i	−0.528188	−	0.849127i	$-0.677129\pi$
$601$	−34.2071	+	19.7495i	−0.0569170	+	0.0328611i	0.471271	+	0.881988i	$0.343795\pi$
$602$	−259.411	−	12.2795i	−0.430916	−	0.0203978i
$603$	116.864	+	145.506i	0.193805	+	0.241303i
$604$	37.9349			0.0628061
$605$	−133.160	+	76.8798i	−0.220099	+	0.127074i
$606$	731.051	−	56.0593i	1.20635	−	0.0925072i
$607$	−323.783	−	186.936i	−0.533415	−	0.307968i	0.208991	−	0.977918i	$-0.432982\pi$
$607$	−323.783	−	186.936i	−0.533415	−	0.307968i	−0.742406	+	0.669950i	$0.766315\pi$
$608$	169.002	+	97.5733i	0.277964	+	0.160482i
$609$	15.9295	+	544.762i	0.0261568	+	0.894520i
$610$	154.248	+	267.166i	0.252866	+	0.437976i
$611$	228.424			0.373853
$612$	−278.126	+	223.380i	−0.454454	+	0.365000i
$613$	−672.296			−1.09673			−0.548366	−	0.836239i	$-0.684750\pi$
$613$	−672.296			−1.09673			−0.548366	+	0.836239i	$0.684750\pi$
$614$	−288.832	+	166.757i	−0.470410	+	0.271591i
$615$	314.765	+	150.911i	0.511814	+	0.245384i
$616$	−145.495	+	226.543i	−0.236193	+	0.367765i
$617$	−231.200	+	400.450i	−0.374716	+	0.649028i	−0.990285	−	0.139056i	$-0.955593\pi$
$617$	−231.200	+	400.450i	−0.374716	+	0.649028i	0.615568	+	0.788084i	$0.288927\pi$
$618$	−111.898	−	163.514i	−0.181065	−	0.264586i
$619$	692.305	−	399.702i	1.11842	−	0.645723i	0.177426	−	0.984134i	$-0.443223\pi$
$619$	692.305	−	399.702i	1.11842	−	0.645723i	0.940998	+	0.338411i	$0.109890\pi$
$620$	120.357			0.194125
$621$	224.073	+	67.8431i	0.360826	+	0.109248i
$622$		−	857.501i		−	1.37862i
$623$	−738.977	+	381.249i	−1.18616	+	0.611957i
$624$	−92.0304	−	134.482i	−0.147485	−	0.215516i
$625$	−112.278	+	194.472i	−0.179646	+	0.311155i
$626$	−30.3410	−	17.5174i	−0.0484680	−	0.0279830i
$627$	608.431	−	1269.04i	0.970385	−	2.02399i
$628$	−13.9631	+	8.06161i	−0.0222343	+	0.0128370i
$629$			786.457i			1.25033i
$630$	22.6238	+	213.105i	0.0359107	+	0.338262i
$631$	−410.154			−0.650006			−0.325003	−	0.945713i	$-0.605365\pi$
$631$	−410.154			−0.650006			−0.325003	+	0.945713i	$0.605365\pi$
$632$	−185.048	−	320.513i	−0.292798	−	0.507140i
$633$	80.3312	+	1047.57i	0.126906	+	1.65493i
$634$	309.958	−	536.863i	0.488892	−	0.846786i
$635$	25.0573	+	14.4668i	0.0394603	+	0.0227824i
$636$	−16.3671	−	213.438i	−0.0257344	−	0.335594i
$637$	605.112	−	276.783i	0.949940	−	0.434510i
$638$	−499.098			−0.782286
$639$	−124.485	+	320.445i	−0.194812	+	0.501478i
$640$		−	27.2130i		−	0.0425204i
$641$	543.226	+	940.895i	0.847466	+	1.46785i	0.883462	+	0.468502i	$0.155206\pi$
$641$	543.226	+	940.895i	0.847466	+	1.46785i	−0.0359962	+	0.999352i	$0.511460\pi$
$642$	−265.916	−	127.491i	−0.414200	−	0.198584i
$643$	−612.173	−	353.438i	−0.952057	−	0.549671i	−0.0583379	−	0.998297i	$-0.518580\pi$
$643$	−612.173	−	353.438i	−0.952057	−	0.549671i	−0.893719	+	0.448626i	$0.851913\pi$
$644$	65.6003	−	102.143i	0.101864	−	0.158608i
$645$	−106.909	−	156.224i	−0.165750	−	0.242207i
$646$	−483.428	−	837.322i	−0.748341	−	1.29616i
$647$			422.816i			0.653502i	0.945110	+	0.326751i	$0.105954\pi$
$647$			422.816i			0.653502i	−0.945110	+	0.326751i	$0.894046\pi$
$648$	−169.021	−	154.661i	−0.260834	−	0.238674i
$649$		−	1003.63i		−	1.54642i
$650$	319.570	−	184.504i	0.491647	−	0.283852i
$651$	−275.887	−	447.137i	−0.423790	−	0.686846i
$652$	−49.1196	+	85.0776i	−0.0753367	+	0.130487i
$653$	394.425	−	683.164i	0.604019	−	1.04619i	−0.388186	−	0.921581i	$-0.626898\pi$
$653$	394.425	−	683.164i	0.604019	−	1.04619i	0.992206	−	0.124611i	$-0.0397684\pi$
$654$	519.858	+	249.241i	0.794890	+	0.381103i
$655$	100.892	+	174.749i	0.154033	+	0.266793i
$656$			193.501i			0.294970i
$657$	101.260	+	39.3368i	0.154124	+	0.0598734i
$658$	7.87348	−	166.332i	0.0119658	−	0.252784i
$659$	−548.183	−	949.480i	−0.831840	−	1.44079i	−0.896578	−	0.442887i	$-0.853954\pi$
$659$	−548.183	−	949.480i	−0.831840	−	1.44079i	0.0647375	−	0.997902i	$-0.479379\pi$
$660$	−195.681	+	15.0054i	−0.296486	+	0.0227355i
$661$	−213.700	−	123.380i	−0.323298	−	0.186656i	0.329563	−	0.944133i	$-0.393098\pi$
$661$	−213.700	−	123.380i	−0.323298	−	0.186656i	−0.652862	+	0.757477i	$0.726432\pi$
$662$	425.784	−	737.479i	0.643178	−	1.11402i
$663$	61.7308	+	805.011i	0.0931084	+	1.21419i
$664$	−78.2286	+	45.1653i	−0.117814	+	0.0680200i
$665$	−580.190	−	27.4638i	−0.872466	−	0.0412989i
$666$	−499.188	+	77.0115i	−0.749531	+	0.115633i
$667$	225.032			0.337380
$668$	336.048	−	194.018i	0.503066	−	0.290446i
$669$	−415.798	+	867.256i	−0.621522	+	1.29635i
$670$	61.0867	+	35.2684i	0.0911742	+	0.0526394i
$671$	1068.05	+	616.639i	1.59173	+	0.918985i
$672$	−101.099	+	62.3786i	−0.150444	+	0.0928253i
$673$	155.614	+	269.532i	0.231225	+	0.400493i	0.958169	−	0.286204i	$-0.0923935\pi$
$673$	155.614	+	269.532i	0.231225	+	0.400493i	−0.726944	+	0.686697i	$0.759060\pi$
$674$	166.457			0.246969
$675$	378.460	−	354.840i	0.560681	−	0.525689i
$676$	−30.8206			−0.0455926
$677$	−467.683	+	270.017i	−0.690817	+	0.398843i	−0.803918	−	0.594740i	$-0.797255\pi$
$677$	−467.683	+	270.017i	−0.690817	+	0.398843i	0.113101	+	0.993583i	$0.463922\pi$
$678$	−14.3959	+	9.85157i	−0.0212329	+	0.0145303i
$679$	−676.576	−	434.523i	−0.996430	−	0.639945i
$680$	−67.4137	+	116.764i	−0.0991378	+	0.171712i
$681$	363.798	−	758.797i	0.534212	−	1.11424i
$682$	416.691	−	240.577i	0.610984	−	0.352752i
$683$	−694.411			−1.01671			−0.508353	−	0.861149i	$-0.669746\pi$
$683$	−694.411			−1.01671			−0.508353	+	0.861149i	$0.669746\pi$
$684$	484.135	−	388.839i	0.707800	−	0.568477i
$685$			480.916i			0.702067i
$686$	−180.689	−	450.166i	−0.263394	−	0.656219i
$687$	−107.750	+	8.26265i	−0.156842	+	0.0120272i
$688$	52.4677	−	90.8767i	0.0762612	−	0.132088i
$689$	−419.582	−	242.246i	−0.608972	−	0.351590i
$690$	88.2280	−	6.76561i	0.127867	−	0.00980523i
$691$	−803.725	+	464.031i	−1.16313	+	0.671535i	−0.952053	−	0.305933i	$-0.901032\pi$
$691$	−803.725	+	464.031i	−1.16313	+	0.671535i	−0.211080	+	0.977469i	$0.567698\pi$
$692$			150.616i			0.217653i
$693$	504.292	+	692.573i	0.727694	+	0.999383i
$694$	387.198			0.557923
$695$	177.292	+	307.078i	0.255096	+	0.441839i
$696$	−198.569	−	95.2020i	−0.285300	−	0.136785i
$697$	479.351	−	830.260i	0.687734	−	1.19119i
$698$	−261.194	−	150.800i	−0.374203	−	0.216046i
$699$	1036.79	−	709.508i	1.48325	−	1.01503i
$700$	−123.336	−	239.062i	−0.176194	−	0.341517i
$701$	717.659			1.02376			0.511882	−	0.859056i	$-0.328948\pi$
$701$	717.659			1.02376			0.511882	+	0.859056i	$0.328948\pi$
$702$	−504.919	+	118.011i	−0.719259	+	0.168106i
$703$		−	1368.99i		−	1.94735i
$704$	−54.3948	−	94.2146i	−0.0772654	−	0.133828i
$705$	100.169	−	68.5488i	0.142084	−	0.0972324i
$706$	−703.122	−	405.948i	−0.995923	−	0.574997i
$707$	−1017.87	−	653.716i	−1.43971	−	0.924634i
$708$	191.440	−	399.298i	0.270395	−	0.563980i
$709$	−273.064	−	472.960i	−0.385139	−	0.667081i	0.606649	−	0.794970i	$-0.292513\pi$
$709$	−273.064	−	472.960i	−0.385139	−	0.667081i	−0.991789	+	0.127889i	$0.959180\pi$
$710$			129.933i			0.183004i
$711$	−1163.87	+	179.554i	−1.63695	+	0.252538i
$712$		−	335.988i		−	0.471893i
$713$	−187.877	+	108.471i	−0.263502	+	0.152133i
$714$	588.315	−	17.2030i	0.823970	−	0.0240939i
$715$	−222.092	+	384.674i	−0.310618	+	0.538006i
$716$	97.4357	−	168.764i	0.136083	−	0.235703i
$717$	−11.7467	−	153.185i	−0.0163832	−	0.213648i
$718$	−24.6274	−	42.6558i	−0.0342999	−	0.0594092i
$719$		−	23.4875i		−	0.0326669i	−0.999867	−	0.0163335i	$-0.994801\pi$
$719$		−	23.4875i		−	0.0326669i	0.999867	−	0.0163335i	$-0.00519934\pi$
$720$	−80.7148	−	31.3557i	−0.112104	−	0.0435496i
$721$	−15.4572	+	326.543i	−0.0214385	+	0.452903i
$722$	586.240	+	1015.40i	0.811967	+	1.40637i
$723$	341.130	−	711.517i	0.471826	−	0.984117i
$724$	144.027	+	83.1541i	0.198932	+	0.114854i
$725$	249.328	−	431.849i	0.343901	−	0.595654i
$726$	−223.820	+	153.167i	−0.308291	+	0.210973i
$727$	−656.448	+	379.000i	−0.902955	+	0.521321i	−0.878158	−	0.478371i	$-0.841227\pi$
$727$	−656.448	+	379.000i	−0.902955	+	0.521321i	−0.0247971	+	0.999693i	$0.507894\pi$
$728$	−12.7128	+	268.565i	−0.0174626	+	0.368908i
$729$	−653.481	+	323.116i	−0.896407	+	0.443232i
$730$	41.0584			0.0562443
$731$	−450.250	+	259.952i	−0.615937	+	0.355612i
$732$	307.306	+	449.061i	0.419818	+	0.613472i
$733$	436.380	+	251.944i	0.595334	+	0.343716i	0.767204	−	0.641404i	$-0.221648\pi$
$733$	436.380	+	251.944i	0.595334	+	0.343716i	−0.171870	+	0.985120i	$0.554981\pi$
$734$	17.1092	+	9.87800i	0.0233095	+	0.0134578i
$735$	182.294	−	302.966i	0.248019	−	0.412199i
$736$	24.5254	+	42.4793i	0.0333226	+	0.0577164i
$737$	281.986			0.382613
$738$	573.929	+	222.957i	0.777682	+	0.302110i
$739$	−735.218			−0.994882			−0.497441	−	0.867498i	$-0.665727\pi$
$739$	−735.218			−0.994882			−0.497441	+	0.867498i	$0.665727\pi$
$740$	−165.328	+	95.4522i	−0.223416	+	0.128989i
$741$	−107.455	−	1401.29i	−0.145014	−	1.89107i
$742$	−190.859	+	297.178i	−0.257223	+	0.400510i
$743$	121.895	−	211.129i	0.164058	−	0.284157i	−0.772262	−	0.635304i	$-0.780875\pi$
$743$	121.895	−	211.129i	0.164058	−	0.284157i	0.936320	+	0.351147i	$0.114208\pi$
$744$	211.672	−	16.2317i	0.284506	−	0.0218168i
$745$	440.714	−	254.446i	0.591562	−	0.341539i
$746$	−807.844			−1.08290
$747$	43.8244	+	284.069i	0.0586672	+	0.380280i
$748$			539.000i			0.720588i
$749$	223.084	+	432.404i	0.297842	+	0.577308i
$750$	195.065	−	406.859i	0.260086	−	0.542479i
$751$	−69.2575	+	119.958i	−0.0922204	+	0.159730i	−0.908445	−	0.418004i	$-0.862730\pi$
$751$	−69.2575	+	119.958i	−0.0922204	+	0.159730i	0.816225	+	0.577735i	$0.196063\pi$
$752$	58.2693	+	33.6418i	0.0774858	+	0.0447364i
$753$	−413.400	−	604.093i	−0.549004	−	0.802249i
$754$	−431.630	+	249.202i	−0.572454	+	0.330506i
$755$		−	45.6227i		−	0.0604274i
$756$	68.5283	+	371.736i	0.0906459	+	0.491715i
$757$	448.741			0.592788			0.296394	−	0.955066i	$-0.404216\pi$
$757$	448.741			0.592788			0.296394	+	0.955066i	$0.404216\pi$
$758$	273.999	+	474.581i	0.361477	+	0.626096i
$759$	291.932	−	199.778i	0.384627	−	0.263212i
$760$	117.347	−	203.251i	0.154404	−	0.267436i
$761$	334.945	+	193.380i	0.440137	+	0.254113i	0.703656	−	0.710541i	$-0.251550\pi$
$761$	334.945	+	193.380i	0.440137	+	0.254113i	−0.263519	+	0.964654i	$0.584883\pi$
$762$	46.0193	+	22.0635i	0.0603927	+	0.0289547i
$763$	−436.121	−	845.336i	−0.571588	−	1.10791i
$764$	−439.560			−0.575341
$765$	268.650	+	334.490i	0.351176	+	0.437242i
$766$		−	816.466i		−	1.06588i
$767$	−501.114	−	867.955i	−0.653343	−	1.13162i
$768$	−3.67002	−	47.8595i	−0.00477867	−	0.0623170i
$769$	531.659	+	306.953i	0.691364	+	0.399159i	0.804123	−	0.594463i	$-0.202635\pi$
$769$	531.659	+	306.953i	0.691364	+	0.399159i	−0.112759	+	0.993622i	$0.535969\pi$
$770$	272.454	+	174.980i	0.353836	+	0.227247i
$771$	639.292	−	49.0230i	0.829173	−	0.0635837i
$772$	115.217	+	199.561i	0.149245	+	0.258499i
$773$			244.996i			0.316942i	0.987364	+	0.158471i	$0.0506564\pi$
$773$			244.996i			0.316942i	−0.987364	+	0.158471i	$0.949344\pi$
$774$	−209.089	−	260.332i	−0.270140	−	0.336346i
$775$			480.727i			0.620293i
$776$	281.374	−	162.451i	0.362595	−	0.209344i
$777$	733.583	+	395.408i	0.944122	+	0.508890i
$778$	−235.655	+	408.167i	−0.302899	+	0.524637i
$779$	−834.407	+	1445.24i	−1.07113	+	1.85525i
$780$	−161.736	+	110.681i	−0.207354	+	0.141899i
$781$	259.717	+	449.842i	0.332544	+	0.575982i
$782$		−	243.023i		−	0.310771i
$783$	−511.170	+	479.268i	−0.652835	+	0.612092i
$784$	195.124	+	18.5142i	0.248882	+	0.0236150i
$785$	9.69536	+	16.7929i	0.0123508	+	0.0213922i
$786$	201.005	+	293.725i	0.255732	+	0.373696i
$787$	1224.89	+	707.189i	1.55640	+	0.898589i	0.997597	+	0.0692898i	$0.0220733\pi$
$787$	1224.89	+	707.189i	1.55640	+	0.898589i	0.558805	+	0.829299i	$0.311260\pi$
$788$	−44.1864	+	76.5332i	−0.0560742	+	0.0971233i
$789$	−420.002	−	201.366i	−0.532322	−	0.255217i
$790$	−385.467	+	222.549i	−0.487933	+	0.281708i
$791$	28.7491	+	1.36086i	0.0363452	+	0.00172043i
$792$	−342.119	+	52.7800i	−0.431969	+	0.0666414i
$793$	1231.56			1.55304
$794$	−341.971	+	197.437i	−0.430694	+	0.248662i
$795$	−256.693	+	19.6840i	−0.322884	+	0.0247598i
$796$	−25.2128	−	14.5566i	−0.0316743	−	0.0182872i
$797$	10.1025	+	5.83266i	0.0126756	+	0.00731827i	0.506324	−	0.862343i	$-0.331004\pi$
$797$	10.1025	+	5.83266i	0.0126756	+	0.00731827i	−0.493649	+	0.869661i	$0.664337\pi$
$798$	−1024.08	+	29.9454i	−1.28331	+	0.0375255i
$799$	−166.679	−	288.696i	−0.208609	−	0.361322i
$800$	108.693			0.135867
$801$	−996.552	−	387.136i	−1.24413	−	0.483316i
$802$	−312.912			−0.390164
$803$	142.149	−	82.0696i	0.177022	−	0.102204i
$804$	112.189	+	53.7882i	0.139539	+	0.0669007i
$805$	−122.843	−	78.8947i	−0.152601	−	0.0980059i
$806$	240.242	−	416.111i	0.298066	−	0.516266i
$807$	217.533	+	317.876i	0.269557	+	0.393899i
$808$	423.312	−	244.399i	0.523900	−	0.302474i
$809$	315.185			0.389599			0.194799	−	0.980843i	$-0.437594\pi$
$809$	315.185			0.389599			0.194799	+	0.980843i	$0.437594\pi$
$810$	−186.004	+	203.274i	−0.229635	+	0.250955i
$811$			1499.13i			1.84849i	0.381800	+	0.924245i	$0.375304\pi$
$811$			1499.13i			1.84849i	−0.381800	+	0.924245i	$0.624696\pi$
$812$	166.584	+	322.891i	0.205153	+	0.397649i
$813$	882.562	+	1289.67i	1.08556	+	1.58631i
$814$	−381.590	+	660.933i	−0.468783	+	0.811957i
$815$	102.319	+	59.0740i	0.125545	+	0.0724834i
$816$	−102.813	+	214.444i	−0.125997	+	0.262799i
$817$	783.752	−	452.500i	0.959305	−	0.553855i
$818$			427.696i			0.522856i
$819$	781.925	+	347.156i	0.954732	+	0.423877i
$820$	232.715			0.283799
$821$	−638.518	−	1105.95i	−0.777732	−	1.34707i	−0.933246	−	0.359237i	$-0.883037\pi$
$821$	−638.518	−	1105.95i	−0.777732	−	1.34707i	0.155515	−	0.987834i	$-0.450296\pi$
$822$	64.8575	+	845.785i	0.0789021	+	1.02894i
$823$	−456.846	+	791.280i	−0.555098	+	0.961458i	0.442798	+	0.896622i	$0.353986\pi$
$823$	−456.846	+	791.280i	−0.555098	+	0.961458i	−0.997896	+	0.0648368i	$0.979347\pi$
$824$	−114.394	−	66.0455i	−0.138828	−	0.0801523i
$825$	−59.9342	−	781.581i	−0.0726475	−	0.947371i
$826$	−649.294	+	334.980i	−0.786070	+	0.405545i
$827$	1239.04			1.49823			0.749116	−	0.662438i	$-0.230478\pi$
$827$	1239.04			1.49823			0.749116	+	0.662438i	$0.230478\pi$
$828$	154.254	−	23.7973i	0.186297	−	0.0287407i
$829$		−	555.123i		−	0.669629i	−0.942284	−	0.334815i	$-0.891326\pi$
$829$		−	555.123i		−	0.669629i	0.942284	−	0.334815i	$-0.108674\pi$
$830$	54.3184	+	94.0822i	0.0654438	+	0.113352i
$831$	−1038.58	−	497.938i	−1.24980	−	0.599203i
$832$	−94.0834	−	54.3191i	−0.113081	−	0.0652874i
$833$	−791.359	−	562.811i	−0.950011	−	0.675643i
$834$	353.216	+	516.147i	0.423520	+	0.618882i
$835$	−233.337	−	404.151i	−0.279445	−	0.484013i
$836$		−	938.240i		−	1.12230i
$837$	195.751	−	646.530i	0.233873	−	0.772437i
$838$			714.900i			0.853102i
$839$	955.955	−	551.921i	1.13940	−	0.657832i	0.193117	−	0.981176i	$-0.438140\pi$
$839$	955.955	−	551.921i	1.13940	−	0.657832i	0.946281	+	0.323344i	$0.104807\pi$
$840$	75.0201	+	121.587i	0.0893096	+	0.144746i
$841$	83.7427	−	145.047i	0.0995752	−	0.172469i
$842$	32.3134	−	55.9685i	0.0383770	−	0.0664709i
$843$	246.059	+	117.971i	0.291885	+	0.139941i
$844$	350.216	+	606.592i	0.414948	+	0.718711i
$845$			37.0666i			0.0438658i
$846$	166.922	−	134.066i	0.197308	−	0.158470i
$847$	446.974	+	21.1579i	0.527714	+	0.0249798i
$848$	−71.3548	−	123.590i	−0.0841449	−	0.145743i
$849$	297.884	−	22.8427i	0.350865	−	0.0269054i
$850$	−466.375	−	269.262i	−0.548676	−	0.316778i
$851$	172.050	−	298.000i	0.202174	−	0.350176i
$852$	17.5231	+	228.513i	0.0205670	+	0.268207i
$853$	38.6408	−	22.3093i	0.0452999	−	0.0261539i	−0.477179	−	0.878806i	$-0.658341\pi$
$853$	38.6408	−	22.3093i	0.0452999	−	0.0261539i	0.522479	+	0.852652i	$0.325007\pi$
$854$	42.4503	−	896.788i	0.0497076	−	1.05010i
$855$	−467.640	−	582.249i	−0.546947	−	0.680993i
$856$	−196.599			−0.229672
$857$	−680.850	+	393.089i	−0.794458	+	0.458680i	−0.841530	−	0.540211i	$-0.818344\pi$
$857$	−680.850	+	393.089i	−0.794458	+	0.458680i	0.0470717	+	0.998892i	$0.485011\pi$
$858$	−338.714	+	706.477i	−0.394771	+	0.823400i
$859$	286.832	+	165.602i	0.333914	+	0.192785i	0.657577	−	0.753387i	$-0.271581\pi$
$859$	286.832	+	165.602i	0.333914	+	0.192785i	−0.323664	+	0.946172i	$0.604915\pi$
$860$	−109.294	−	63.1007i	−0.127086	−	0.0733729i
$861$	−533.437	−	864.554i	−0.619555	−	1.00413i
$862$	−178.575	−	309.301i	−0.207164	−	0.358818i
$863$	183.153			0.212228			0.106114	−	0.994354i	$-0.466159\pi$
$863$	183.153			0.212228			0.106114	+	0.994354i	$0.466159\pi$
$864$	−146.182	−	44.2598i	−0.169192	−	0.0512266i
$865$	181.139			0.209410
$866$	1016.81	−	587.058i	1.17415	−	0.677896i
$867$	256.876	−	175.788i	0.296281	−	0.202755i
$868$	−294.720	−	189.280i	−0.339539	−	0.218065i
$869$	−889.687	+	1540.98i	−1.02381	+	1.77328i
$870$	−114.495	+	238.810i	−0.131604	+	0.274495i
$871$	243.867	−	140.796i	0.279985	−	0.161649i
$872$	384.346			0.440763
$873$	−157.629	−	1021.75i	−0.180560	−	1.17039i
$874$			423.031i			0.484018i
$875$	−661.590	+	341.324i	−0.756102	+	0.390084i
$876$	72.2092	−	5.53724i	0.0824306	−	0.00632105i
$877$	−560.581	+	970.954i	−0.639203	+	1.10713i	0.346405	+	0.938085i	$0.387402\pi$
$877$	−560.581	+	970.954i	−0.639203	+	1.10713i	−0.985608	+	0.169047i	$0.945931\pi$
$878$	−273.142	−	157.699i	−0.311096	−	0.179611i
$879$	1703.62	−	130.639i	1.93814	−	0.148623i
$880$	−113.308	+	65.4184i	−0.128759	+	0.0743391i
$881$			1389.25i			1.57690i	0.615098	+	0.788450i	$0.289116\pi$
$881$			1389.25i			1.57690i	−0.615098	+	0.788450i	$0.710884\pi$
$882$	279.741	−	557.411i	0.317167	−	0.631985i
$883$	1358.53			1.53854			0.769268	−	0.638926i	$-0.220621\pi$
$883$	1358.53			1.53854			0.769268	+	0.638926i	$0.220621\pi$
$884$	269.125	+	466.138i	0.304440	+	0.527305i
$885$	−480.218	−	230.236i	−0.542620	−	0.260154i
$886$	−145.107	+	251.332i	−0.163777	+	0.283671i
$887$	−908.326	−	524.422i	−1.02404	−	0.591231i	−0.108770	−	0.994067i	$-0.534691\pi$
$887$	−908.326	−	524.422i	−1.02404	−	0.591231i	−0.915272	+	0.402836i	$0.868025\pi$
$888$	−277.889	+	190.168i	−0.312938	+	0.214153i
$889$	−38.6067	−	74.8315i	−0.0434271	−	0.0841749i
$890$	−404.078			−0.454021
$891$	−237.653	+	1075.55i	−0.266726	+	1.20713i
$892$			641.187i			0.718820i
$893$	290.138	+	502.535i	0.324903	+	0.562749i
$894$	740.767	−	506.930i	0.828599	−	0.567036i
$895$	−202.965	−	117.182i	−0.226776	−	0.130929i
$896$	−42.7966	+	66.6367i	−0.0477641	+	0.0743713i
$897$	152.719	−	318.535i	0.170255	−	0.355111i
$898$	311.945	+	540.305i	0.347378	+	0.601676i
$899$		−	649.298i		−	0.722245i
$900$	125.240	−	322.388i	0.139155	−	0.358209i
$901$			707.057i			0.784747i
$902$	805.686	−	465.163i	0.893221	−	0.515702i
$903$	16.1024	+	550.676i	0.0178321	+	0.609829i
$904$	−5.81469	+	10.0713i	−0.00643218	+	0.0111409i
$905$	100.006	−	173.215i	0.110504	−	0.191398i
$906$	−6.15279	−	80.2365i	−0.00679116	−	0.0885613i
$907$	−325.502	−	563.785i	−0.358877	−	0.621593i	0.628896	−	0.777489i	$-0.283507\pi$
$907$	−325.502	−	563.785i	−0.358877	−	0.621593i	−0.987774	+	0.155896i	$0.950174\pi$
$908$		−	561.000i		−	0.617841i
$909$	−237.143	−	1537.16i	−0.260884	−	1.69105i
$910$	322.992	+	15.2891i	0.354936	+	0.0168012i
$911$	−371.140	−	642.834i	−0.407399	−	0.705636i	0.587198	−	0.809443i	$-0.300231\pi$
$911$	−371.140	−	642.834i	−0.407399	−	0.705636i	−0.994597	+	0.103807i	$0.966897\pi$
$912$	178.967	−	373.284i	0.196236	−	0.409302i
$913$	376.113	+	217.149i	0.411953	+	0.237841i
$914$	−476.892	+	826.002i	−0.521764	+	0.903722i
$915$	540.067	−	369.584i	0.590237	−	0.403917i
$916$	−62.3924	+	36.0223i	−0.0681140	+	0.0393256i
$917$	27.7662	−	586.577i	0.0302793	−	0.639670i
$918$	517.584	+	552.037i	0.563817	+	0.601347i
$919$	630.519			0.686093			0.343046	−	0.939319i	$-0.388541\pi$
$919$	630.519			0.686093			0.343046	+	0.939319i	$0.388541\pi$
$920$	51.0880	−	29.4957i	0.0555305	−	0.0320605i
$921$	399.556	+	583.864i	0.433829	+	0.633946i
$922$	−116.175	−	67.0739i	−0.126004	−	0.0727483i
$923$	449.216	+	259.355i	0.486691	+	0.280991i
$924$	502.762	+	270.994i	0.544115	+	0.293283i
$925$	−381.252	−	660.348i	−0.412164	−	0.713890i
$926$	−552.113			−0.596234
$927$	−327.702	+	263.197i	−0.353508	+	0.283924i
$928$	−146.808			−0.158198
$929$	−164.909	+	95.2100i	−0.177512	+	0.102487i	−0.586123	−	0.810222i	$-0.699347\pi$
$929$	−164.909	+	95.2100i	−0.177512	+	0.102487i	0.408611	+	0.912709i	$0.366013\pi$
$930$	−19.5212	−	254.569i	−0.0209905	−	0.273730i
$931$	1377.52	+	979.687i	1.47962	+	1.05230i
$932$	418.773	−	725.336i	0.449327	−	0.778257i
$933$	−1813.71	+	139.081i	−1.94395	+	0.149069i
$934$	166.062	−	95.8760i	0.177797	−	0.102651i
$935$	648.233			0.693297
$936$	−269.518	+	216.467i	−0.287947	+	0.231268i
$937$			173.230i			0.184877i	0.995718	+	0.0924384i	$0.0294661\pi$
$937$			173.230i			0.184877i	−0.995718	+	0.0924384i	$0.970534\pi$
$938$	−94.1184	−	182.430i	−0.100339	−	0.194488i
$939$	−32.1301	+	67.0158i	−0.0342173	+	0.0713693i
$940$	40.4596	−	70.0780i	0.0430421	−	0.0745511i
$941$	1132.98	+	654.124i	1.20401	+	0.695137i	0.961445	−	0.274997i	$-0.0886770\pi$
$941$	1132.98	+	654.124i	1.20401	+	0.695137i	0.242568	+	0.970134i	$0.422010\pi$
$942$	19.3159	+	28.2260i	0.0205052	+	0.0299639i
$943$	−363.266	+	209.732i	−0.385223	+	0.222409i
$944$		−	295.212i		−	0.312725i
$945$	447.071	−	82.4160i	0.473092	−	0.0872127i
$946$	−504.516			−0.533315
$947$	101.101	+	175.112i	0.106759	+	0.184912i	0.914456	−	0.404686i	$-0.132619\pi$
$947$	101.101	+	175.112i	0.106759	+	0.184912i	−0.807696	+	0.589599i	$0.799286\pi$
$948$	−647.906	+	443.382i	−0.683445	+	0.467703i
$949$	81.9553	−	141.951i	0.0863597	−	0.149579i
$950$	811.820	+	468.705i	0.854547	+	0.493373i
$951$	−1185.80	−	568.519i	−1.24689	−	0.597812i
$952$	348.705	−	179.902i	0.366287	−	0.188973i
$953$	−123.695			−0.129796			−0.0648978	−	0.997892i	$-0.520672\pi$
$953$	−123.695			−0.129796			−0.0648978	+	0.997892i	$0.520672\pi$
$954$	−448.790	+	69.2365i	−0.470430	+	0.0725749i
$955$			528.641i			0.553550i
$956$	−51.2117	−	88.7012i	−0.0535687	−	0.0927837i
$957$	80.9505	+	1055.65i	0.0845878	+	1.10308i
$958$	−249.004	−	143.762i	−0.259920	−	0.150065i
$959$	756.313	−	1177.62i	0.788647	−	1.22797i
$960$	−57.5586	+	4.41378i	−0.0599569	+	0.00459769i
$961$	−167.524	−	290.160i	−0.174322	−	0.301935i
$962$			762.117i			0.792221i
$963$	−226.528	+	583.121i	−0.235232	+	0.605525i
$964$		−	526.044i		−	0.545689i
$965$	240.004	−	138.566i	0.248709	−	0.143592i
$966$	−226.684	−	122.185i	−0.234663	−	0.126485i
$967$	640.089	−	1108.67i	0.661933	−	1.14650i	−0.318174	−	0.948032i	$-0.603070\pi$
$967$	640.089	−	1108.67i	0.661933	−	1.14650i	0.980107	−	0.198469i	$-0.0635971\pi$
$968$	−90.4035	+	156.584i	−0.0933921	+	0.161760i
$969$	−1692.62	+	1158.31i	−1.74677	+	1.19537i
$970$	−195.373	−	338.396i	−0.201416	−	0.348862i
$971$		−	1011.08i		−	1.04127i	−0.853778	−	0.520637i	$-0.825695\pi$
$971$		−	1011.08i		−	1.04127i	0.853778	−	0.520637i	$-0.174305\pi$
$972$	−299.711	+	382.582i	−0.308345	+	0.393603i
$973$	48.7920	−	1030.76i	0.0501460	−	1.05936i
$974$	168.222	+	291.369i	0.172712	+	0.299147i
$975$	−442.079	−	646.001i	−0.453414	−	0.662565i
$976$	314.162	+	181.381i	0.321887	+	0.185842i
$977$	359.962	−	623.473i	0.368436	−	0.638150i	−0.620885	−	0.783902i	$-0.713227\pi$
$977$	359.962	−	623.473i	0.368436	−	0.638150i	0.989321	+	0.145751i	$0.0465599\pi$
$978$	187.915	+	90.0943i	0.192142	+	0.0921209i
$979$	−1398.97	+	807.693i	−1.42897	+	0.825019i
$980$	22.2662	−	234.667i	0.0227206	−	0.239456i
$981$	442.855	−	1139.98i	0.451432	−	1.16206i
$982$	801.142			0.815827
$983$	−203.077	+	117.247i	−0.206589	+	0.119274i	−0.599725	−	0.800206i	$-0.704724\pi$
$983$	−203.077	+	117.247i	−0.206589	+	0.119274i	0.393136	+	0.919480i	$0.371390\pi$
$984$	409.275	−	31.3845i	0.415930	−	0.0318948i
$985$	92.0432	+	53.1412i	0.0934449	+	0.0539504i
$986$	629.913	+	363.680i	0.638857	+	0.368844i
$987$	−353.088	+	10.3247i	−0.357739	+	0.0104607i
$988$	−468.467	−	811.408i	−0.474156	−	0.821263i
$989$	227.475			0.230005
$990$	63.4763	+	411.452i	0.0641174	+	0.415608i
$991$	57.3158			0.0578363			0.0289181	−	0.999582i	$-0.490794\pi$
$991$	57.3158			0.0578363			0.0289181	+	0.999582i	$0.490794\pi$
$992$	122.568	−	70.7645i	0.123556	−	0.0713352i
$993$	−1628.91	−	780.965i	−1.64039	−	0.786470i
$994$	204.339	−	318.167i	0.205572	−	0.320088i
$995$	−17.5066	+	30.3223i	−0.0175946	+	0.0304747i
$996$	108.218	+	158.137i	0.108652	+	0.158772i
$997$	763.810	−	440.986i	0.766108	−	0.442313i	−0.0653764	−	0.997861i	$-0.520825\pi$
$997$	763.810	−	440.986i	0.766108	−	0.442313i	0.831484	+	0.555548i	$0.187491\pi$
$998$	333.985			0.334654
$999$	243.853	+	1043.35i	0.244097	+	1.04439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.o.a.13.2	✓	32
3.2	odd	2		378.3.o.a.307.11		32
7.6	odd	2	inner	126.3.o.a.13.7	yes	32
9.2	odd	6		378.3.o.a.181.14		32
9.4	even	3		1134.3.c.e.811.11		16
9.5	odd	6		1134.3.c.d.811.6		16
9.7	even	3	inner	126.3.o.a.97.7	yes	32
21.20	even	2		378.3.o.a.307.14		32
63.13	odd	6		1134.3.c.e.811.14		16
63.20	even	6		378.3.o.a.181.11		32
63.34	odd	6	inner	126.3.o.a.97.2	yes	32
63.41	even	6		1134.3.c.d.811.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.o.a.13.2	✓	32	1.1	even	1	trivial
126.3.o.a.13.7	yes	32	7.6	odd	2	inner
126.3.o.a.97.2	yes	32	63.34	odd	6	inner
126.3.o.a.97.7	yes	32	9.7	even	3	inner
378.3.o.a.181.11		32	63.20	even	6
378.3.o.a.181.14		32	9.2	odd	6
378.3.o.a.307.11		32	3.2	odd	2
378.3.o.a.307.14		32	21.20	even	2
1134.3.c.d.811.3		16	63.41	even	6
1134.3.c.d.811.6		16	9.5	odd	6
1134.3.c.e.811.11		16	9.4	even	3
1134.3.c.e.811.14		16	63.13	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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-2.47578 + 1.69425i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(2.08306 + 1.20266i) q^{5} +(3.82567 + 1.83418i) q^{6} +(-3.20945 - 6.22089i) q^{7} +2.82843 q^{8} +(3.25900 - 8.38921i) q^{9} -3.40163i q^{10} +(-6.79936 - 11.7768i) q^{11} +(-0.458753 - 5.98244i) q^{12} +(-11.7604 - 6.78989i) q^{13} +(-5.34958 + 8.32959i) q^{14} +(-7.19482 + 0.551722i) q^{15} +(-2.00000 - 3.46410i) q^{16} +19.8181i q^{17} +(-12.5791 + 1.94062i) q^{18} -34.4974i q^{19} +(-4.16613 + 2.40532i) q^{20} +(18.4857 + 9.96394i) q^{21} +(-9.61574 + 16.6550i) q^{22} +(4.33552 - 7.50935i) q^{23} +(-7.00257 + 4.79208i) q^{24} +(-9.60723 - 16.6402i) q^{25} +19.2047i q^{26} +(6.14489 + 26.2915i) q^{27} +(13.9843 + 0.661961i) q^{28} +(12.9761 + 22.4752i) q^{29} +(5.76323 + 8.42170i) q^{30} +(-21.6671 - 12.5095i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(36.7867 + 17.6370i) q^{33} +(24.2721 - 14.0135i) q^{34} +(0.796113 - 16.8184i) q^{35} +(11.2715 + 14.0340i) q^{36} +39.6839 q^{37} +(-42.2505 + 24.3933i) q^{38} +(40.6201 - 3.11488i) q^{39} +(5.89179 + 3.40163i) q^{40} +(-41.8941 - 24.1876i) q^{41} +(-0.868048 - 29.6858i) q^{42} +(13.1169 + 22.7192i) q^{43} +27.1974 q^{44} +(16.8781 - 13.5558i) q^{45} -12.2627 q^{46} +(-14.5673 + 8.41045i) q^{47} +(10.8206 + 5.18785i) q^{48} +(-28.3989 + 39.9312i) q^{49} +(-13.5867 + 23.5328i) q^{50} +(-33.5768 - 49.0652i) q^{51} +(23.5209 - 13.5798i) q^{52} +35.6774 q^{53} +(27.8552 - 26.1168i) q^{54} -32.7092i q^{55} +(-9.07769 - 17.5953i) q^{56} +(58.4473 + 85.4080i) q^{57} +(18.3509 - 31.7848i) q^{58} +(63.9153 + 36.9015i) q^{59} +(6.23921 - 13.0135i) q^{60} +(-78.5405 + 45.3454i) q^{61} +35.3823i q^{62} +(-62.6480 + 6.65086i) q^{63} +8.00000 q^{64} +(-16.3318 - 28.2875i) q^{65} +(-4.41125 - 57.5256i) q^{66} +(-10.3681 + 17.9581i) q^{67} +(-34.3259 - 19.8181i) q^{68} +(1.98893 + 25.9370i) q^{69} +(-21.1612 + 10.9174i) q^{70} -38.1972 q^{71} +(9.21785 - 23.7283i) q^{72} +12.0702i q^{73} +(-28.0607 - 48.6026i) q^{74} +(51.9782 + 24.9205i) q^{75} +(59.7512 + 34.4974i) q^{76} +(-51.4402 + 80.0951i) q^{77} +(-32.5377 - 47.5467i) q^{78} +(-65.4244 - 113.318i) q^{79} -9.62126i q^{80} +(-59.7578 - 54.6809i) q^{81} +68.4128i q^{82} +(-27.6580 + 15.9683i) q^{83} +(-35.7437 + 22.0542i) q^{84} +(-23.8343 + 41.2823i) q^{85} +(18.5501 - 32.1298i) q^{86} +(-70.2047 - 33.6590i) q^{87} +(-19.2315 - 33.3099i) q^{88} -118.790i q^{89} +(-28.5370 - 11.0859i) q^{90} +(-4.49464 + 94.9521i) q^{91} +(8.67105 + 15.0187i) q^{92} +(74.8374 - 5.73877i) q^{93} +(20.6013 + 11.8942i) q^{94} +(41.4885 - 71.8602i) q^{95} +(-1.29755 - 16.9209i) q^{96} +(99.4807 - 57.4352i) q^{97} +(68.9866 + 6.54575i) q^{98} +(-120.957 + 18.6605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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