LMFDB - Embedded newform 42.3.h.b.23.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,3,Mod(11,42)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("42.11"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	42.h (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.14441711031$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.4857532416.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 7x^{6} - 2x^{5} + 98x^{4} - 98x^{3} + 67x^{2} - 30x + 9 $ x^8 - 2x^7 - 7x^6 - 2x^5 + 98x^4 - 98x^3 + 67x^2 - 30*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Root			$0.461396 - 0.310963i$ of defining polynomial
Character	$\chi$	$=$	42.23
Dual form			42.3.h.b.11.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(2.97112 + 0.415287i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.422792 + 0.244099i) q^{5} +(-3.34521 - 2.60952i) q^{6} +(4.69042 - 5.19615i) q^{7} -2.82843i q^{8} +(8.65507 + 2.46773i) q^{9} +(-0.345208 - 0.597918i) q^{10} +(-13.1367 + 7.58446i) q^{11} +(2.25182 + 5.56141i) q^{12} -17.3808 q^{13} +(-9.41880 + 3.04734i) q^{14} +(1.15479 + 0.900826i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(0.422792 - 0.244099i) q^{17} +(-8.85530 - 9.14241i) q^{18} +(-6.53562 + 11.3200i) q^{19} +0.976395i q^{20} +(16.0937 - 13.4905i) q^{21} +21.4521 q^{22} +(5.78819 + 3.34181i) q^{23} +(1.17461 - 8.40359i) q^{24} +(-12.3808 - 21.4442i) q^{25} +(21.2871 + 12.2901i) q^{26} +(24.6904 + 10.9263i) q^{27} +(13.6904 + 2.92789i) q^{28} -47.3084i q^{29} +(-0.777345 - 1.91984i) q^{30} +(14.2260 + 24.6402i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-42.1803 + 17.0788i) q^{33} -0.690416 q^{34} +(3.25144 - 1.05196i) q^{35} +(4.38083 + 17.4588i) q^{36} +(0.500000 - 0.866025i) q^{37} +(16.0089 - 9.24277i) q^{38} +(-51.6405 - 7.21804i) q^{39} +(0.690416 - 1.19584i) q^{40} +28.3850i q^{41} +(-29.2499 + 5.14249i) q^{42} -2.14249 q^{43} +(-26.2733 - 15.1689i) q^{44} +(3.05692 + 3.15603i) q^{45} +(-4.72604 - 8.18574i) q^{46} +(63.7304 + 36.7947i) q^{47} +(-7.38083 + 9.46168i) q^{48} +(-5.00000 - 48.7442i) q^{49} +35.0183i q^{50} +(1.35753 - 0.549666i) q^{51} +(-17.3808 - 30.1045i) q^{52} +(52.7077 - 30.4308i) q^{53} +(-22.5134 - 30.8407i) q^{54} -7.40543 q^{55} +(-14.6969 - 13.2665i) q^{56} +(-24.1192 + 30.9190i) q^{57} +(-33.4521 + 57.9407i) q^{58} +(-87.4669 + 50.4991i) q^{59} +(-0.405485 + 2.90098i) q^{60} +(17.1192 - 29.6513i) q^{61} -40.2373i q^{62} +(53.4186 - 33.3984i) q^{63} -8.00000 q^{64} +(-7.34847 - 4.24264i) q^{65} +(63.7366 + 8.90878i) q^{66} +(49.9877 + 86.5812i) q^{67} +(0.845583 + 0.488198i) q^{68} +(15.8096 + 12.3327i) q^{69} +(-4.72604 - 1.01073i) q^{70} -82.9000i q^{71} +(6.97981 - 24.4802i) q^{72} +(25.8808 + 44.8269i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(-27.8794 - 68.8549i) q^{75} -26.1425 q^{76} +(-22.2064 + 103.834i) q^{77} +(58.1425 + 45.3556i) q^{78} +(33.3685 - 57.7960i) q^{79} +(-1.69117 + 0.976395i) q^{80} +(68.8206 + 42.7168i) q^{81} +(20.0712 - 34.7644i) q^{82} -88.7584i q^{83} +(39.4599 + 14.3845i) q^{84} +0.238337 q^{85} +(2.62401 + 1.51497i) q^{86} +(19.6466 - 140.559i) q^{87} +(21.4521 + 37.1561i) q^{88} +(-50.6945 - 29.2685i) q^{89} +(-1.51230 - 6.02690i) q^{90} +(-81.5233 + 90.3134i) q^{91} +13.3673i q^{92} +(32.0345 + 79.1169i) q^{93} +(-52.0356 - 90.1283i) q^{94} +(-5.52641 + 3.19068i) q^{95} +(15.7301 - 6.36910i) q^{96} +25.0958 q^{97} +(-28.3437 + 63.2348i) q^{98} +(-132.415 + 33.2262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 8 q^{4} - 8 q^{6} - 10 q^{9} + 16 q^{10} + 4 q^{12} - 64 q^{13} + 28 q^{15} - 16 q^{16} - 40 q^{18} + 4 q^{19} + 26 q^{21} - 16 q^{22} - 8 q^{24} - 24 q^{25} + 160 q^{27} + 72 q^{28} + 52 q^{30}+ \cdots - 140 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 8 * q^4 - 8 * q^6 - 10 * q^9 + 16 * q^10 + 4 * q^12 - 64 * q^13 + 28 * q^15 - 16 * q^16 - 40 * q^18 + 4 * q^19 + 26 * q^21 - 16 * q^22 - 8 * q^24 - 24 * q^25 + 160 * q^27 + 72 * q^28 + 52 * q^30 + 20 * q^31 - 106 * q^33 + 32 * q^34 - 40 * q^36 + 4 * q^37 - 72 * q^39 - 32 * q^40 - 88 * q^42 + 208 * q^43 - 58 * q^45 + 56 * q^46 + 16 * q^48 - 40 * q^49 + 14 * q^51 - 64 * q^52 - 32 * q^54 - 472 * q^55 - 268 * q^57 - 80 * q^58 + 28 * q^60 + 212 * q^61 + 178 * q^63 - 64 * q^64 + 224 * q^66 + 156 * q^67 + 164 * q^69 + 56 * q^70 + 80 * q^72 + 132 * q^73 + 164 * q^75 + 16 * q^76 + 240 * q^78 - 52 * q^79 + 98 * q^81 + 48 * q^82 - 124 * q^84 + 152 * q^85 - 260 * q^87 - 16 * q^88 - 256 * q^90 - 352 * q^91 - 210 * q^93 - 360 * q^94 + 16 * q^96 + 576 * q^97 - 140 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	2.97112	+	0.415287i	0.990372	+	0.138429i
$3$	2.97112	+	0.415287i	0.990372	+	0.138429i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	0.422792	+	0.244099i	0.0845583	+	0.0488198i	0.541683	−	0.840583i	$-0.317787\pi$
$5$	0.422792	+	0.244099i	0.0845583	+	0.0488198i	−0.457125	+	0.889403i	$0.651121\pi$
$6$	−3.34521	−	2.60952i	−0.557535	−	0.434920i
$7$	4.69042	−	5.19615i	0.670059	−	0.742307i
$7$	4.69042	−	5.19615i	0.670059	−	0.742307i
$8$		−	2.82843i		−	0.353553i
$9$	8.65507	+	2.46773i	0.961675	+	0.274193i
$10$	−0.345208	−	0.597918i	−0.0345208	−	0.0597918i
$11$	−13.1367	+	7.58446i	−1.19424	+	0.689496i	−0.959266	−	0.282505i	$-0.908835\pi$
$11$	−13.1367	+	7.58446i	−1.19424	+	0.689496i	−0.234976	+	0.972001i	$0.575501\pi$
$12$	2.25182	+	5.56141i	0.187652	+	0.463451i
$13$	−17.3808			−1.33699			−0.668494	−	0.743718i	$-0.733061\pi$
$13$	−17.3808			−1.33699			−0.668494	+	0.743718i	$0.733061\pi$
$14$	−9.41880	+	3.04734i	−0.672771	+	0.217667i
$15$	1.15479	+	0.900826i	0.0769861	+	0.0600551i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	0.422792	−	0.244099i	0.0248701	−	0.0143588i	−0.487513	−	0.873116i	$-0.662096\pi$
$17$	0.422792	−	0.244099i	0.0248701	−	0.0143588i	0.512384	+	0.858757i	$0.328763\pi$
$18$	−8.85530	−	9.14241i	−0.491961	−	0.507911i
$19$	−6.53562	+	11.3200i	−0.343980	+	0.595791i	−0.985168	−	0.171593i	$-0.945109\pi$
$19$	−6.53562	+	11.3200i	−0.343980	+	0.595791i	0.641188	+	0.767384i	$0.278442\pi$
$20$			0.976395i			0.0488198i
$21$	16.0937	−	13.4905i	0.766365	−	0.642405i
$22$	21.4521			0.975094
$23$	5.78819	+	3.34181i	0.251661	+	0.145296i	0.620524	−	0.784187i	$-0.286920\pi$
$23$	5.78819	+	3.34181i	0.251661	+	0.145296i	−0.368864	+	0.929483i	$0.620253\pi$
$24$	1.17461	−	8.40359i	0.0489421	−	0.350150i
$25$	−12.3808	−	21.4442i	−0.495233	−	0.857769i
$26$	21.2871	+	12.2901i	0.818734	+	0.472696i
$27$	24.6904	+	10.9263i	0.914460	+	0.404677i
$28$	13.6904	+	2.92789i	0.488943	+	0.104567i
$29$		−	47.3084i		−	1.63132i	−0.578529	−	0.815662i	$-0.696373\pi$
$29$		−	47.3084i		−	1.63132i	0.578529	−	0.815662i	$-0.303627\pi$
$30$	−0.777345	−	1.91984i	−0.0259115	−	0.0639948i
$31$	14.2260	+	24.6402i	0.458904	+	0.794846i	0.998903	−	0.0468198i	$-0.0149087\pi$
$31$	14.2260	+	24.6402i	0.458904	+	0.794846i	−0.539999	+	0.841666i	$0.681575\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	−42.1803	+	17.0788i	−1.27819	+	0.517540i
$34$	−0.690416			−0.0203063
$35$	3.25144	−	1.05196i	0.0928984	−	0.0300561i
$36$	4.38083	+	17.4588i	0.121690	+	0.484966i
$37$	0.500000	−	0.866025i	0.0135135	−	0.0234061i	−0.859190	−	0.511657i	$-0.829032\pi$
$37$	0.500000	−	0.866025i	0.0135135	−	0.0234061i	0.872703	+	0.488251i	$0.162365\pi$
$38$	16.0089	−	9.24277i	0.421288	−	0.243231i
$39$	−51.6405	−	7.21804i	−1.32411	−	0.185078i
$40$	0.690416	−	1.19584i	0.0172604	−	0.0298959i
$41$			28.3850i			0.692318i	0.938176	+	0.346159i	$0.112514\pi$
$41$			28.3850i			0.692318i	−0.938176	+	0.346159i	$0.887486\pi$
$42$	−29.2499	+	5.14249i	−0.696425	+	0.122440i
$43$	−2.14249			−0.0498255			−0.0249127	−	0.999690i	$-0.507931\pi$
$43$	−2.14249			−0.0498255			−0.0249127	+	0.999690i	$0.507931\pi$
$44$	−26.2733	−	15.1689i	−0.597121	−	0.344748i
$45$	3.05692	+	3.15603i	0.0679316	+	0.0701340i
$46$	−4.72604	−	8.18574i	−0.102740	−	0.177951i
$47$	63.7304	+	36.7947i	1.35597	+	0.782867i	0.989077	−	0.147398i	$-0.0470899\pi$
$47$	63.7304	+	36.7947i	1.35597	+	0.782867i	0.366888	+	0.930265i	$0.380423\pi$
$48$	−7.38083	+	9.46168i	−0.153767	+	0.197118i
$49$	−5.00000	−	48.7442i	−0.102041	−	0.994780i
$50$			35.0183i			0.700366i
$51$	1.35753	−	0.549666i	0.0266183	−	0.0107778i
$52$	−17.3808	−	30.1045i	−0.334247	−	0.578932i
$53$	52.7077	−	30.4308i	0.994484	−	0.574166i	0.0878725	−	0.996132i	$-0.471993\pi$
$53$	52.7077	−	30.4308i	0.994484	−	0.574166i	0.906612	+	0.421966i	$0.138660\pi$
$54$	−22.5134	−	30.8407i	−0.416915	−	0.571123i
$55$	−7.40543			−0.134644
$56$	−14.6969	−	13.2665i	−0.262445	−	0.236902i
$57$	−24.1192	+	30.9190i	−0.423143	+	0.542438i
$58$	−33.4521	+	57.9407i	−0.576760	+	0.998978i
$59$	−87.4669	+	50.4991i	−1.48249	+	0.855916i	−0.999802	−	0.0198761i	$-0.993673\pi$
$59$	−87.4669	+	50.4991i	−1.48249	+	0.855916i	−0.482688	+	0.875792i	$0.660339\pi$
$60$	−0.405485	+	2.90098i	−0.00675808	+	0.0483497i
$61$	17.1192	−	29.6513i	0.280642	−	0.486086i	−0.690901	−	0.722949i	$-0.742786\pi$
$61$	17.1192	−	29.6513i	0.280642	−	0.486086i	0.971543	+	0.236863i	$0.0761193\pi$
$62$		−	40.2373i		−	0.648989i
$63$	53.4186	−	33.3984i	0.847915	−	0.530133i
$64$	−8.00000			−0.125000
$65$	−7.34847	−	4.24264i	−0.113053	−	0.0652714i
$66$	63.7366	+	8.90878i	0.965707	+	0.134981i
$67$	49.9877	+	86.5812i	0.746085	+	1.29226i	0.949686	+	0.313203i	$0.101402\pi$
$67$	49.9877	+	86.5812i	0.746085	+	1.29226i	−0.203601	+	0.979054i	$0.565265\pi$
$68$	0.845583	+	0.488198i	0.0124350	+	0.00717938i
$69$	15.8096	+	12.3327i	0.229124	+	0.178735i
$70$	−4.72604	−	1.01073i	−0.0675148	−	0.0144390i
$71$		−	82.9000i		−	1.16761i	−0.811895	−	0.583803i	$-0.801564\pi$
$71$		−	82.9000i		−	1.16761i	0.811895	−	0.583803i	$-0.198436\pi$
$72$	6.97981	−	24.4802i	0.0969418	−	0.340003i
$73$	25.8808	+	44.8269i	0.354532	+	0.614067i	0.987038	−	0.160488i	$-0.0513069\pi$
$73$	25.8808	+	44.8269i	0.354532	+	0.614067i	−0.632506	+	0.774556i	$0.717974\pi$
$74$	−1.22474	+	0.707107i	−0.0165506	+	0.00955550i
$75$	−27.8794	−	68.8549i	−0.371725	−	0.918066i
$76$	−26.1425			−0.343980
$77$	−22.2064	+	103.834i	−0.288395	+	1.34850i
$78$	58.1425	+	45.3556i	0.745417	+	0.581482i
$79$	33.3685	−	57.7960i	0.422387	−	0.731595i	−0.573786	−	0.819005i	$-0.694526\pi$
$79$	33.3685	−	57.7960i	0.422387	−	0.731595i	0.996172	+	0.0874105i	$0.0278592\pi$
$80$	−1.69117	+	0.976395i	−0.0211396	+	0.0122049i
$81$	68.8206	+	42.7168i	0.849637	+	0.527368i
$82$	20.0712	−	34.7644i	0.244771	−	0.423956i
$83$		−	88.7584i		−	1.06938i	−0.845049	−	0.534689i	$-0.820429\pi$
$83$		−	88.7584i		−	1.06938i	0.845049	−	0.534689i	$-0.179571\pi$
$84$	39.4599	+	14.3845i	0.469761	+	0.171245i
$85$	0.238337			0.00280396
$86$	2.62401	+	1.51497i	0.0305117	+	0.0176160i
$87$	19.6466	−	140.559i	0.225823	−	1.61562i
$88$	21.4521	+	37.1561i	0.243774	+	0.422228i
$89$	−50.6945	−	29.2685i	−0.569601	−	0.328859i	0.187389	−	0.982286i	$-0.439997\pi$
$89$	−50.6945	−	29.2685i	−0.569601	−	0.328859i	−0.756990	+	0.653427i	$0.773331\pi$
$90$	−1.51230	−	6.02690i	−0.0168033	−	0.0669656i
$91$	−81.5233	+	90.3134i	−0.895861	+	0.992455i
$92$			13.3673i			0.145296i
$93$	32.0345	+	79.1169i	0.344457	+	0.850719i
$94$	−52.0356	−	90.1283i	−0.553570	−	0.958812i
$95$	−5.52641	+	3.19068i	−0.0581728	+	0.0335861i
$96$	15.7301	−	6.36910i	0.163855	−	0.0663448i
$97$	25.0958			0.258720			0.129360	−	0.991598i	$-0.458708\pi$
$97$	25.0958			0.258720			0.129360	+	0.991598i	$0.458708\pi$
$98$	−28.3437	+	63.2348i	−0.289221	+	0.645253i
$99$	−132.415	+	33.2262i	−1.33753	+	0.335618i
$100$	24.7617	−	42.8885i	0.247617	−	0.428885i
$101$	−81.5177	+	47.0643i	−0.807106	+	0.465983i	−0.845950	−	0.533262i	$-0.820966\pi$
$101$	−81.5177	+	47.0643i	−0.807106	+	0.465983i	0.0388437	+	0.999245i	$0.487633\pi$
$102$	−2.05131	−	0.286721i	−0.0201108	−	0.00281099i
$103$	4.74937	−	8.22614i	0.0461103	−	0.0798655i	−0.842049	−	0.539401i	$-0.818651\pi$
$103$	4.74937	−	8.22614i	0.0461103	−	0.0798655i	0.888159	+	0.459535i	$0.151984\pi$
$104$			49.1604i			0.472696i
$105$	10.0973	−	1.77523i	0.0961646	−	0.0169069i
$106$	−86.0712			−0.811993
$107$	−29.5248	−	17.0461i	−0.275932	−	0.159310i	0.355648	−	0.934620i	$-0.384260\pi$
$107$	−29.5248	−	17.0461i	−0.275932	−	0.159310i	−0.631581	+	0.775310i	$0.717593\pi$
$108$	5.76556	+	53.6913i	0.0533848	+	0.497142i
$109$	−33.1904	−	57.4875i	−0.304499	−	0.527408i	0.672650	−	0.739960i	$-0.265156\pi$
$109$	−33.1904	−	57.4875i	−0.304499	−	0.527408i	−0.977150	+	0.212552i	$0.931822\pi$
$110$	9.06976	+	5.23643i	0.0824523	+	0.0476039i
$111$	1.84521	−	2.36542i	0.0166235	−	0.0213101i
$112$	8.61917	+	26.6404i	0.0769569	+	0.237861i
$113$			72.0901i			0.637966i	0.947761	+	0.318983i	$0.103341\pi$
$113$			72.0901i			0.637966i	−0.947761	+	0.318983i	$0.896659\pi$
$114$	51.4028	−	20.8130i	0.450902	−	0.182570i
$115$	1.63147	+	2.82578i	0.0141867	+	0.0245720i
$116$	81.9405	−	47.3084i	0.706384	−	0.407831i
$117$	−150.432	−	42.8913i	−1.28575	−	0.366592i
$118$	142.833			1.21045
$119$	0.714694	−	3.34181i	0.00600583	−	0.0280825i
$120$	2.54792	−	3.26625i	0.0212327	−	0.0272187i
$121$	54.5479	−	94.4798i	0.450809	−	0.780825i
$122$	−41.9332	+	24.2102i	−0.343715	+	0.198444i
$123$	−11.7879	+	84.3352i	−0.0958369	+	0.685652i
$124$	−28.4521	+	49.2804i	−0.229452	+	0.397423i
$125$		−	24.2935i		−	0.194348i
$126$	−89.0404	+	3.13183i	−0.706670	+	0.0248558i
$127$	−59.3808			−0.467566			−0.233783	−	0.972289i	$-0.575110\pi$
$127$	−59.3808			−0.467566			−0.233783	+	0.972289i	$0.575110\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	−6.36560	−	0.889751i	−0.0493458	−	0.00689729i
$130$	6.00000	+	10.3923i	0.0461538	+	0.0799408i
$131$	87.7287	+	50.6502i	0.669685	+	0.386643i	0.795957	−	0.605353i	$-0.206968\pi$
$131$	87.7287	+	50.6502i	0.669685	+	0.386643i	−0.126272	+	0.991996i	$0.540301\pi$
$132$	−71.7617	−	55.9796i	−0.543649	−	0.424088i
$133$	28.1658	+	87.0558i	0.211773	+	0.654555i
$134$		−	141.387i		−	1.05512i
$135$	7.77181	+	10.6464i	0.0575690	+	0.0788625i
$136$	−0.690416	−	1.19584i	−0.00507659	−	0.00879291i
$137$	115.140	−	66.4758i	0.840434	−	0.485225i	−0.0169774	−	0.999856i	$-0.505404\pi$
$137$	115.140	−	66.4758i	0.840434	−	0.485225i	0.857412	+	0.514631i	$0.172071\pi$
$138$	−10.6422	−	26.2835i	−0.0771173	−	0.190460i
$139$	71.6658			0.515581			0.257791	−	0.966201i	$-0.417005\pi$
$139$	71.6658			0.515581			0.257791	+	0.966201i	$0.417005\pi$
$140$	5.07350	+	4.57970i	0.0362393	+	0.0327121i
$141$	174.070	+	135.788i	1.23454	+	0.963035i
$142$	−58.6192	+	101.531i	−0.412811	+	0.715010i
$143$	228.326	−	131.824i	1.59669	−	0.921847i
$144$	−25.8586	+	25.0466i	−0.179574	+	0.173935i
$145$	11.5479	−	20.0016i	0.0796408	−	0.137942i
$146$		−	73.2020i		−	0.501384i
$147$	5.38728	−	146.901i	0.0366481	−	0.999328i
$148$	2.00000			0.0135135
$149$	−15.9653	−	9.21758i	−0.107150	−	0.0618629i	0.445467	−	0.895298i	$-0.353038\pi$
$149$	−15.9653	−	9.21758i	−0.107150	−	0.0618629i	−0.552617	+	0.833435i	$0.686371\pi$
$150$	−14.5426	+	104.043i	−0.0969510	+	0.693623i
$151$	−25.0123	−	43.3226i	−0.165644	−	0.286904i	0.771240	−	0.636545i	$-0.219637\pi$
$151$	−25.0123	−	43.3226i	−0.165644	−	0.286904i	−0.936884	+	0.349641i	$0.886304\pi$
$152$	32.0179	+	18.4855i	0.210644	+	0.121615i
$153$	4.26166	−	1.06936i	0.0278540	−	0.00698925i
$154$	100.619	−	111.468i	0.653371	−	0.723820i
$155$			13.8902i			0.0896144i
$156$	−39.1385	−	96.6620i	−0.250888	−	0.619628i
$157$	0.500000	+	0.866025i	0.00318471	+	0.00551609i	0.867613	−	0.497239i	$-0.165653\pi$
$157$	0.500000	+	0.866025i	0.00318471	+	0.00551609i	−0.864429	+	0.502756i	$0.832320\pi$
$158$	−81.7359	+	47.1902i	−0.517316	+	0.298672i
$159$	169.238	−	68.5246i	1.06439	−	0.430972i
$160$	2.76166			0.0172604
$161$	44.5136	−	14.4018i	0.276482	−	0.0894524i
$162$	−54.0823	−	100.981i	−0.333841	−	0.623338i
$163$	−57.9631	+	100.395i	−0.355602	+	0.615921i	−0.987221	−	0.159358i	$-0.949057\pi$
$163$	−57.9631	+	100.395i	−0.355602	+	0.615921i	0.631619	+	0.775279i	$0.282391\pi$
$164$	−49.1643	+	28.3850i	−0.299782	+	0.173079i
$165$	−22.0024	−	3.07538i	−0.133348	−	0.0186387i
$166$	−62.7617	+	108.706i	−0.378082	+	0.654858i
$167$			199.369i			1.19383i	0.802305	+	0.596914i	$0.203607\pi$
$167$			199.369i			1.19383i	−0.802305	+	0.596914i	$0.796393\pi$
$168$	−38.1569	−	45.5198i	−0.227124	−	0.270951i
$169$	133.093			0.787534
$170$	−0.291902	−	0.168530i	−0.00171707	−	0.000991351i
$171$	−84.5011	+	81.8475i	−0.494159	+	0.478640i
$172$	−2.14249	−	3.71091i	−0.0124564	−	0.0215751i
$173$	30.0784	+	17.3658i	0.173864	+	0.100380i	0.584406	−	0.811461i	$-0.301327\pi$
$173$	30.0784	+	17.3658i	0.173864	+	0.100380i	−0.410543	+	0.911841i	$0.634661\pi$
$174$	−123.452	+	158.256i	−0.709495	+	0.909519i
$175$	−169.499	−	36.2497i	−0.968564	−	0.207141i
$176$		−	60.6756i		−	0.344748i
$177$	−280.846	+	113.715i	−1.58670	+	0.642456i
$178$	41.3919	+	71.6928i	0.232539	+	0.402769i
$179$	−187.165	+	108.060i	−1.04561	+	0.603685i	−0.921418	−	0.388573i	$-0.872968\pi$
$179$	−187.165	+	108.060i	−1.04561	+	0.603685i	−0.124195	+	0.992258i	$0.539635\pi$
$180$	−2.40948	+	8.45077i	−0.0133860	+	0.0469487i
$181$	−320.093			−1.76847			−0.884236	−	0.467041i	$-0.845320\pi$
$181$	−320.093			−1.76847			−0.884236	+	0.467041i	$0.845320\pi$
$182$	163.707	−	52.9652i	0.899486	−	0.291018i
$183$	63.1768	−	80.9880i	0.345229	−	0.442557i
$184$	9.45208	−	16.3715i	0.0513700	−	0.0889754i
$185$	0.422792	−	0.244099i	0.00228536	−	0.00131945i
$186$	16.7100	−	119.550i	0.0898390	−	0.642741i
$187$	−3.70271	+	6.41329i	−0.0198006	+	0.0342957i
$188$			147.179i			0.782867i
$189$	172.583	−	77.0464i	0.913137	−	0.407653i
$190$	9.02460			0.0474979
$191$	−34.5983	−	19.9753i	−0.181143	−	0.104583i	0.406687	−	0.913568i	$-0.366684\pi$
$191$	−34.5983	−	19.9753i	−0.181143	−	0.104583i	−0.587829	+	0.808985i	$0.700017\pi$
$192$	−23.7689	−	3.32230i	−0.123797	−	0.0173036i
$193$	−173.426	−	300.383i	−0.898581	−	1.55639i	−0.829309	−	0.558791i	$-0.811265\pi$
$193$	−173.426	−	300.383i	−0.898581	−	1.55639i	−0.0692729	−	0.997598i	$-0.522068\pi$
$194$	−30.7360	−	17.7454i	−0.158433	−	0.0914713i
$195$	−20.0712	−	15.6571i	−0.102929	−	0.0802929i
$196$	79.4275	−	57.4045i	0.405242	−	0.292880i
$197$			92.3617i			0.468841i	0.972135	+	0.234421i	$0.0753193\pi$
$197$			92.3617i			0.468841i	−0.972135	+	0.234421i	$0.924681\pi$
$198$	185.669	+	52.9380i	0.937724	+	0.267364i
$199$	21.6069	+	37.4242i	0.108577	+	0.188061i	0.915194	−	0.403013i	$-0.132037\pi$
$199$	21.6069	+	37.4242i	0.108577	+	0.188061i	−0.806617	+	0.591075i	$0.798704\pi$
$200$	−60.6534	+	35.0183i	−0.303267	+	0.175091i
$201$	112.563	+	278.002i	0.560016	+	1.38310i
$202$	133.118			0.659000
$203$	−245.822	−	221.896i	−1.21094	−	1.09308i
$204$	2.30958	+	1.80165i	0.0113215	+	0.00883163i
$205$	−6.92875	+	12.0010i	−0.0337988	+	0.0585412i
$206$	−11.6335	+	6.71662i	−0.0564734	+	0.0326049i
$207$	41.8505	+	43.2074i	0.202176	+	0.208731i
$208$	34.7617	−	60.2090i	0.167123	−	0.289466i
$209$		−	198.277i		−	0.948692i
$210$	−13.6219	−	4.96566i	−0.0648661	−	0.0236460i
$211$	306.142			1.45091			0.725456	−	0.688268i	$-0.241629\pi$
$211$	306.142			1.45091			0.725456	+	0.688268i	$0.241629\pi$
$212$	105.415	+	60.8616i	0.497242	+	0.287083i
$213$	34.4273	−	246.306i	0.161631	−	1.15636i
$214$	24.1069	+	41.7543i	0.112649	+	0.195114i
$215$	−0.905829	−	0.522980i	−0.00421316	−	0.00243247i
$216$	30.9042	−	69.8350i	0.143075	−	0.323310i
$217$	194.760	+	41.6522i	0.897513	+	0.191946i
$218$			93.8767i			0.430627i
$219$	58.2789	+	143.934i	0.266114	+	0.657233i
$220$	−7.40543	−	12.8266i	−0.0336610	−	0.0583026i
$221$	−7.34847	+	4.24264i	−0.0332510	+	0.0191975i
$222$	−3.93251	+	1.59228i	−0.0177140	+	0.00717241i
$223$	1.57252			0.00705164			0.00352582	−	0.999994i	$-0.498878\pi$
$223$	1.57252			0.00705164			0.00352582	+	0.999994i	$0.498878\pi$
$224$	8.28131	−	38.7223i	0.0369701	−	0.172868i
$225$	−54.2383	−	216.154i	−0.241059	−	0.960684i
$226$	50.9754	−	88.2920i	0.225555	−	0.390673i
$227$	−4.15727	+	2.40020i	−0.0183140	+	0.0105736i	−0.509129	−	0.860690i	$-0.670032\pi$
$227$	−4.15727	+	2.40020i	−0.0183140	+	0.0105736i	0.490815	+	0.871264i	$0.336699\pi$
$228$	−77.6724	−	10.8566i	−0.340668	−	0.0476169i
$229$	−155.903	+	270.032i	−0.680799	+	1.17918i	0.293939	+	0.955824i	$0.405034\pi$
$229$	−155.903	+	270.032i	−0.680799	+	1.17918i	−0.974737	+	0.223354i	$0.928300\pi$
$230$		−	4.61448i		−	0.0200630i
$231$	−109.099	+	299.282i	−0.472290	+	1.29559i
$232$	−133.808			−0.576760
$233$	−105.315	−	60.8034i	−0.451994	−	0.260959i	0.256678	−	0.966497i	$-0.417372\pi$
$233$	−105.315	−	60.8034i	−0.451994	−	0.260959i	−0.708672	+	0.705538i	$0.750705\pi$
$234$	153.913	+	158.903i	0.657746	+	0.679071i
$235$	17.9631	+	31.1130i	0.0764388	+	0.132396i
$236$	−174.934	−	100.998i	−0.741245	−	0.427958i
$237$	123.144	−	157.861i	0.519594	−	0.666081i
$238$	−3.23834	+	3.58751i	−0.0136065	+	0.0150736i
$239$		−	59.6992i		−	0.249788i	−0.992170	−	0.124894i	$-0.960141\pi$
$239$		−	59.6992i		−	0.249788i	0.992170	−	0.124894i	$-0.0398590\pi$
$240$	−5.43014	+	2.19866i	−0.0226256	+	0.00916110i
$241$	98.3575	+	170.360i	0.408122	+	0.706889i	0.994679	−	0.103019i	$-0.0328503\pi$
$241$	98.3575	+	170.360i	0.408122	+	0.706889i	−0.586557	+	0.809908i	$0.699517\pi$
$242$	−133.615	+	77.1424i	−0.552126	+	0.318770i
$243$	186.734	+	155.497i	0.768454	+	0.639906i
$244$	68.4767			0.280642
$245$	9.78445	−	21.8291i	0.0399365	−	0.0890985i
$246$	74.0712	−	94.9538i	0.301103	−	0.385991i
$247$	113.595	−	196.752i	0.459897	−	0.796565i
$248$	69.6931	−	40.2373i	0.281020	−	0.162247i
$249$	36.8602	−	263.712i	0.148033	−	1.05908i
$250$	−17.1781	+	29.7534i	−0.0687125	+	0.119013i
$251$			269.204i			1.07253i	0.844051	+	0.536264i	$0.180165\pi$
$251$			269.204i			1.07253i	−0.844051	+	0.536264i	$0.819835\pi$
$252$	111.266	+	59.1254i	0.441533	+	0.234625i
$253$	−101.383			−0.400725
$254$	72.7264	+	41.9886i	0.286324	+	0.165309i
$255$	0.708127	+	0.0989783i	0.00277697	+	0.000388150i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−163.458	−	94.3727i	−0.636024	−	0.367209i	0.147057	−	0.989128i	$-0.453020\pi$
$257$	−163.458	−	94.3727i	−0.636024	−	0.367209i	−0.783081	+	0.621919i	$0.786353\pi$
$258$	7.16709	+	5.59088i	0.0277794	+	0.0216701i
$259$	−2.15479	−	6.66010i	−0.00831966	−	0.0257147i
$260$		−	16.9706i		−	0.0652714i
$261$	116.745	−	409.458i	0.447297	−	1.56880i
$262$	−71.6302	−	124.067i	−0.273398	−	0.473539i
$263$	−179.554	+	103.666i	−0.682717	+	0.394167i	−0.800878	−	0.598828i	$-0.795633\pi$
$263$	−179.554	+	103.666i	−0.682717	+	0.394167i	0.118161	+	0.992994i	$0.462300\pi$
$264$	48.3062	+	119.304i	0.182978	+	0.451909i
$265$	29.7125			0.112123
$266$	27.0618	−	126.537i	0.101736	−	0.475704i
$267$	−138.464	−	108.013i	−0.518593	−	0.404542i
$268$	−99.9754	+	173.162i	−0.373043	+	0.646129i
$269$	158.445	−	91.4783i	0.589015	−	0.340068i	−0.175693	−	0.984445i	$-0.556217\pi$
$269$	158.445	−	91.4783i	0.589015	−	0.340068i	0.764708	+	0.644377i	$0.222883\pi$
$270$	−1.99032	−	18.5347i	−0.00737155	−	0.0686469i
$271$	97.5110	−	168.894i	0.359819	−	0.623225i	−0.628111	−	0.778124i	$-0.716172\pi$
$271$	97.5110	−	168.894i	0.359819	−	0.623225i	0.987930	+	0.154898i	$0.0495050\pi$
$272$			1.95279i			0.00717938i
$273$	−279.721	+	234.476i	−1.02462	+	0.858887i
$274$	−188.022			−0.686212
$275$	325.286	+	187.804i	1.18286	+	0.682923i
$276$	−5.55125	+	39.7157i	−0.0201132	+	0.143897i
$277$	52.6425	+	91.1795i	0.190045	+	0.329168i	0.945265	−	0.326304i	$-0.105803\pi$
$277$	52.6425	+	91.1795i	0.190045	+	0.329168i	−0.755220	+	0.655472i	$0.772470\pi$
$278$	−87.7723	−	50.6754i	−0.315728	−	0.182286i
$279$	62.3219	+	248.369i	0.223376	+	0.890212i
$280$	−2.97540	−	9.19647i	−0.0106264	−	0.0328445i
$281$			472.177i			1.68035i	0.542319	+	0.840173i	$0.317546\pi$
$281$			472.177i			1.68035i	−0.542319	+	0.840173i	$0.682454\pi$
$282$	−117.175	−	289.392i	−0.415513	−	1.02621i
$283$	−159.725	−	276.651i	−0.564398	−	0.977567i	−0.997105	−	0.0760322i	$-0.975775\pi$
$283$	−159.725	−	276.651i	−0.564398	−	0.977567i	0.432707	−	0.901535i	$-0.357559\pi$
$284$	143.587	−	82.9000i	0.505588	−	0.291901i
$285$	−17.7447	+	7.18482i	−0.0622620	+	0.0252099i
$286$	−372.855			−1.30369
$287$	147.493	+	133.138i	0.513913	+	0.463894i
$288$	49.3808	−	12.3909i	0.171461	−	0.0430238i
$289$	−144.381	+	250.075i	−0.499588	+	0.865311i
$290$	−28.2865	+	16.3312i	−0.0975397	+	0.0563146i
$291$	74.5627	+	10.4220i	0.256229	+	0.0358144i
$292$	−51.7617	+	89.6538i	−0.177266	+	0.307034i
$293$		−	477.594i		−	1.63001i	−0.579451	−	0.815007i	$-0.696733\pi$
$293$		−	477.594i		−	1.63001i	0.579451	−	0.815007i	$-0.303267\pi$
$294$	−110.473	+	176.107i	−0.375758	+	0.599004i
$295$	−49.3070			−0.167143
$296$	−2.44949	−	1.41421i	−0.00827530	−	0.00477775i
$297$	−407.219	+	43.7286i	−1.37111	+	0.147234i
$298$	13.0356	+	22.5784i	0.0437437	+	0.0757663i
$299$	−100.604	−	58.0835i	−0.336467	−	0.194259i
$300$	91.3808	−	117.143i	0.304603	−	0.390478i
$301$	−10.0492	+	11.1327i	−0.0333860	+	0.0369858i
$302$			70.7455i			0.234256i
$303$	−261.744	+	105.980i	−0.863841	+	0.349770i
$304$	−26.1425	−	45.2801i	−0.0859950	−	0.148948i
$305$	14.4757	−	8.35754i	0.0474612	−	0.0274018i
$306$	−5.97560	−	1.70376i	−0.0195281	−	0.00556785i
$307$	−104.619			−0.340779			−0.170390	−	0.985377i	$-0.554503\pi$
$307$	−104.619			−0.340779			−0.170390	+	0.985377i	$0.554503\pi$
$308$	−202.053	+	65.3717i	−0.656016	+	0.212246i
$309$	17.5271	−	22.4685i	0.0567221	−	0.0727135i
$310$	9.82188	−	17.0120i	0.0316835	−	0.0548774i
$311$	166.931	−	96.3776i	0.536755	−	0.309896i	−0.207007	−	0.978339i	$-0.566372\pi$
$311$	166.931	−	96.3776i	0.536755	−	0.309896i	0.743763	+	0.668443i	$0.233039\pi$
$312$	−20.4157	+	146.061i	−0.0654349	+	0.468145i
$313$	270.451	−	468.435i	0.864060	−	1.49660i	−0.00391733	−	0.999992i	$-0.501247\pi$
$313$	270.451	−	468.435i	0.864060	−	1.49660i	0.867977	−	0.496604i	$-0.165420\pi$
$314$		−	1.41421i		−	0.00450386i
$315$	30.7374	−	1.08113i	0.0975792	−	0.00343216i
$316$	133.474			0.422387
$317$	268.088	+	154.781i	0.845704	+	0.488268i	0.859199	−	0.511641i	$-0.170962\pi$
$317$	268.088	+	154.781i	0.845704	+	0.488268i	−0.0134949	+	0.999909i	$0.504296\pi$
$318$	−255.728	−	35.7443i	−0.804175	−	0.112403i
$319$	358.808	+	621.474i	1.12479	+	1.94820i
$320$	−3.38233	−	1.95279i	−0.0105698	−	0.00610247i
$321$	−80.6425	−	62.9073i	−0.251223	−	0.195973i
$322$	−64.7014	−	13.8373i	−0.200936	−	0.0429730i
$323$			6.38135i			0.0197565i
$324$	−5.16717	+	161.918i	−0.0159480	+	0.499746i
$325$	215.189	+	372.719i	0.662120	+	1.14683i
$326$	141.980	−	81.9722i	0.435522	−	0.251449i
$327$	−74.7388	−	184.586i	−0.228559	−	0.564482i
$328$	80.2850			0.244771
$329$	490.113	−	158.570i	1.48971	−	0.481976i
$330$	24.7727	+	19.3246i	0.0750688	+	0.0585594i
$331$	166.749	−	288.818i	0.503775	−	0.872563i	−0.496216	−	0.868199i	$-0.665278\pi$
$331$	166.749	−	288.818i	0.503775	−	0.872563i	0.999990	−	0.00436394i	$-0.00138909\pi$
$332$	153.734	−	88.7584i	0.463054	−	0.267345i
$333$	6.46466	−	6.26165i	0.0194134	−	0.0188037i
$334$	140.975	−	244.177i	0.422082	−	0.731068i
$335$			48.8078i			0.145695i
$336$	14.5451	+	82.7311i	0.0432891	+	0.246224i
$337$	138.619			0.411333			0.205666	−	0.978622i	$-0.434064\pi$
$337$	138.619			0.411333			0.205666	+	0.978622i	$0.434064\pi$
$338$	−163.005	−	94.1112i	−0.482264	−	0.278435i
$339$	−29.9381	+	214.188i	−0.0883130	+	0.631823i
$340$	0.238337	+	0.412812i	0.000700991	+	0.00121415i
$341$	−373.765	−	215.794i	−1.09609	−	0.632826i
$342$	161.367	−	40.4910i	0.471834	−	0.118395i
$343$	−276.735	−	202.650i	−0.806806	−	0.590816i
$344$			6.05989i			0.0176160i
$345$	3.67377	+	9.07326i	0.0106486	+	0.0262993i
$346$	−24.5589	−	42.5373i	−0.0709796	−	0.122940i
$347$	371.400	−	214.428i	1.07032	−	0.617948i	0.142049	−	0.989860i	$-0.454631\pi$
$347$	371.400	−	214.428i	1.07032	−	0.617948i	0.928268	+	0.371912i	$0.121298\pi$
$348$	263.101	−	106.530i	0.756039	−	0.306120i
$349$	166.236			0.476320			0.238160	−	0.971226i	$-0.423456\pi$
$349$	166.236			0.476320			0.238160	+	0.971226i	$0.423456\pi$
$350$	181.960	+	164.250i	0.519887	+	0.469287i
$351$	−429.140	−	189.908i	−1.22262	−	0.541047i
$352$	−42.9042	+	74.3122i	−0.121887	+	0.211114i
$353$	−246.566	+	142.355i	−0.698488	+	0.403272i	−0.806784	−	0.590846i	$-0.798794\pi$
$353$	−246.566	+	142.355i	−0.698488	+	0.403272i	0.108296	+	0.994119i	$0.465461\pi$
$354$	424.373	+	59.3167i	1.19879	+	0.167561i
$355$	20.2358	−	35.0494i	0.0570023	−	0.0987308i
$356$		−	117.074i		−	0.328859i
$357$	3.51125	−	9.63212i	0.00983544	−	0.0269807i
$358$	305.639			0.853739
$359$	−365.863	−	211.231i	−1.01912	−	0.588388i	−0.105269	−	0.994444i	$-0.533570\pi$
$359$	−365.863	−	211.231i	−1.01912	−	0.588388i	−0.913848	+	0.406056i	$0.866904\pi$
$360$	8.92660	−	8.64628i	0.0247961	−	0.0240174i
$361$	95.0712	+	164.668i	0.263355	+	0.456145i
$362$	392.033	+	226.340i	1.08296	+	0.625249i
$363$	201.305	−	258.057i	0.554558	−	0.710902i
$364$	−237.951	−	50.8891i	−0.653711	−	0.139805i
$365$			25.2699i			0.0692327i
$366$	−134.643	+	54.5169i	−0.367876	+	0.148953i
$367$	−85.2506	−	147.658i	−0.232291	−	0.402339i	0.726191	−	0.687493i	$-0.241289\pi$
$367$	−85.2506	−	147.658i	−0.232291	−	0.402339i	−0.958482	+	0.285154i	$0.907955\pi$
$368$	−23.1528	+	13.3673i	−0.0629151	+	0.0363241i
$369$	−70.0467	+	245.675i	−0.189828	+	0.665785i
$370$	−0.690416			−0.00186599
$371$	89.0979	−	416.610i	0.240156	−	1.12294i
$372$	−105.000	+	134.602i	−0.282258	+	0.361834i
$373$	−152.262	+	263.725i	−0.408208	+	0.707037i	−0.994689	−	0.102926i	$-0.967180\pi$
$373$	−152.262	+	263.725i	−0.408208	+	0.707037i	0.586481	+	0.809963i	$0.300513\pi$
$374$	9.06976	−	5.23643i	0.0242507	−	0.0140011i
$375$	10.0888	−	72.1789i	0.0269035	−	0.192477i
$376$	104.071	−	180.257i	0.276785	−	0.479406i
$377$			822.259i			2.18106i
$378$	−265.850	−	27.6723i	−0.703307	−	0.0732072i
$379$	−512.899			−1.35330			−0.676648	−	0.736307i	$-0.736568\pi$
$379$	−512.899			−1.35330			−0.676648	+	0.736307i	$0.736568\pi$
$380$	−11.0528	−	6.38135i	−0.0290864	−	0.0167930i
$381$	−176.427	−	24.6601i	−0.463064	−	0.0647247i
$382$	28.2494	+	48.9293i	0.0739512	+	0.128087i
$383$	−371.340	−	214.393i	−0.969555	−	0.559773i	−0.0704548	−	0.997515i	$-0.522445\pi$
$383$	−371.340	−	214.393i	−0.969555	−	0.559773i	−0.899101	+	0.437742i	$0.855778\pi$
$384$	26.7617	+	20.8761i	0.0696918	+	0.0543650i
$385$	−34.7345	+	38.4797i	−0.0902196	+	0.0999473i
$386$			490.523i			1.27079i
$387$	−18.5434	−	5.28711i	−0.0479159	−	0.0136618i
$388$	25.0958	+	43.4673i	0.0646800	+	0.112029i
$389$	−61.2237	+	35.3475i	−0.157387	+	0.0908677i	−0.576625	−	0.817009i	$-0.695631\pi$
$389$	−61.2237	+	35.3475i	−0.157387	+	0.0908677i	0.419238	+	0.907876i	$0.362297\pi$
$390$	13.5109	+	33.3685i	0.0346434	+	0.0855602i
$391$	3.26293			0.00834509
$392$	−137.870	+	14.1421i	−0.351708	+	0.0360769i
$393$	239.618	+	186.920i	0.609715	+	0.475624i
$394$	65.3096	−	113.120i	0.165760	−	0.287105i
$395$	28.2159	−	16.2904i	0.0714326	−	0.0412416i
$396$	−189.965	−	196.124i	−0.479709	−	0.495262i
$397$	−26.6646	+	46.1844i	−0.0671651	+	0.116333i	−0.897652	−	0.440704i	$-0.854729\pi$
$397$	−26.6646	+	46.1844i	−0.0671651	+	0.116333i	0.830487	+	0.557038i	$0.188062\pi$
$398$		−	61.1135i		−	0.153551i
$399$	47.5308	+	270.350i	0.119125	+	0.677568i
$400$	99.0467			0.247617
$401$	−253.211	−	146.191i	−0.631448	−	0.364567i	0.149865	−	0.988707i	$-0.452116\pi$
$401$	−253.211	−	146.191i	−0.631448	−	0.364567i	−0.781313	+	0.624140i	$0.785449\pi$
$402$	58.7160	−	420.076i	0.146060	−	1.04497i
$403$	−247.260	−	428.268i	−0.613549	−	1.06270i
$404$	−163.035	−	94.1286i	−0.403553	−	0.232992i
$405$	18.6696	+	34.8593i	0.0460978	+	0.0860725i
$406$	144.165	+	445.588i	0.355085	+	1.09751i
$407$			15.1689i			0.0372701i
$408$	−1.55469	−	3.83969i	−0.00381052	−	0.00941100i
$409$	2.28372	+	3.95552i	0.00558367	+	0.00967120i	0.868804	−	0.495157i	$-0.164889\pi$
$409$	2.28372	+	3.95552i	0.00558367	+	0.00967120i	−0.863220	+	0.504828i	$0.831556\pi$
$410$	16.9719	−	9.79874i	0.0413949	−	0.0238994i
$411$	369.700	−	149.692i	0.899512	−	0.364213i
$412$	18.9975			0.0461103
$413$	−147.855	+	691.353i	−0.358004	+	1.67398i
$414$	−20.7040	−	82.5108i	−0.0500096	−	0.199301i
$415$	21.6658	−	37.5263i	0.0522068	−	0.0904248i
$416$	−85.1483	+	49.1604i	−0.204684	+	0.118174i
$417$	212.928	+	29.7619i	0.510618	+	0.0713715i
$418$	−140.203	+	242.838i	−0.335413	+	0.580953i
$419$		−	378.002i		−	0.902152i	−0.892486	−	0.451076i	$-0.851040\pi$
$419$		−	378.002i		−	0.902152i	0.892486	−	0.451076i	$-0.148960\pi$
$420$	13.1721	+	15.7138i	0.0313621	+	0.0374138i
$421$	−742.806			−1.76438			−0.882192	−	0.470890i	$-0.843933\pi$
$421$	−742.806			−1.76438			−0.882192	+	0.470890i	$0.843933\pi$
$422$	−374.946	−	216.475i	−0.888499	−	0.512975i
$423$	460.791	+	475.731i	1.08934	+	1.12466i
$424$	−86.0712	−	149.080i	−0.202998	−	0.351603i
$425$	−10.4690	−	6.04429i	−0.0246330	−	0.0142219i
$426$	−216.329	+	277.318i	−0.507815	+	0.650981i
$427$	−73.7765	−	228.031i	−0.172779	−	0.534029i
$428$		−	68.1845i		−	0.159310i
$429$	733.128	−	296.844i	1.70892	−	0.691944i
$430$	0.739606	+	1.28104i	0.00172001	+	0.00297915i
$431$	−328.013	+	189.379i	−0.761052	+	0.439394i	−0.829673	−	0.558249i	$-0.811473\pi$
$431$	−328.013	+	189.379i	−0.761052	+	0.439394i	0.0686212	+	0.997643i	$0.478140\pi$
$432$	−87.2305	+	63.6776i	−0.201923	+	0.147402i
$433$	521.567			1.20454			0.602272	−	0.798291i	$-0.294262\pi$
$433$	521.567			1.20454			0.602272	+	0.798291i	$0.294262\pi$
$434$	−209.079	−	188.730i	−0.481749	−	0.434861i
$435$	42.6166	−	54.6313i	0.0979693	−	0.125589i
$436$	66.3808	−	114.975i	0.152250	−	0.263704i
$437$	−75.6589	+	43.6817i	−0.173132	+	0.0999581i
$438$	30.3999	−	217.492i	0.0694061	−	0.496557i
$439$	−365.056	+	632.296i	−0.831564	+	1.44031i	0.0652343	+	0.997870i	$0.479221\pi$
$439$	−365.056	+	632.296i	−0.831564	+	1.44031i	−0.896798	+	0.442440i	$0.854113\pi$
$440$			20.9457i			0.0476039i
$441$	77.0125	−	434.224i	0.174631	−	0.984634i
$442$	12.0000			0.0271493
$443$	559.279	+	322.900i	1.26248	+	0.728894i	0.973554	−	0.228457i	$-0.0733680\pi$
$443$	559.279	+	322.900i	1.26248	+	0.728894i	0.288928	+	0.957351i	$0.406701\pi$
$444$	5.94223	+	0.830575i	0.0133834	+	0.00187066i
$445$	−14.2888	−	24.7489i	−0.0321097	−	0.0556156i
$446$	−1.92593	−	1.11194i	−0.00431823	−	0.00249313i
$447$	−43.6069	−	34.0167i	−0.0975545	−	0.0761000i
$448$	−37.5233	+	41.5692i	−0.0837574	+	0.0927884i
$449$		−	681.682i		−	1.51822i	−0.650961	−	0.759112i	$-0.725634\pi$
$449$		−	681.682i		−	1.51822i	0.650961	−	0.759112i	$-0.274366\pi$
$450$	−86.4158	+	303.086i	−0.192035	+	0.673524i
$451$	−215.285	−	372.885i	−0.477350	−	0.826795i
$452$	−124.864	+	72.0901i	−0.276247	+	0.159491i
$453$	−56.3231	−	139.104i	−0.124334	−	0.307072i
$454$	6.78880			0.0149533
$455$	−56.5128	+	18.2840i	−0.124204	+	0.0401847i
$456$	87.4521	+	68.2193i	0.191781	+	0.149604i
$457$	31.4533	−	54.4788i	0.0688257	−	0.119210i	−0.829559	−	0.558419i	$-0.811408\pi$
$457$	31.4533	−	54.4788i	0.0688257	−	0.119210i	0.898385	+	0.439210i	$0.144741\pi$
$458$	381.883	−	220.480i	0.833805	−	0.481397i
$459$	13.1060	−	1.40737i	0.0285534	−	0.00306616i
$460$	−3.26293	+	5.65156i	−0.00709333	+	0.0122860i
$461$			113.099i			0.245333i	0.992448	+	0.122667i	$0.0391446\pi$
$461$			113.099i			0.245333i	−0.992448	+	0.122667i	$0.960855\pi$
$462$	345.243	−	289.399i	0.747279	−	0.626406i
$463$	595.951			1.28715			0.643575	−	0.765383i	$-0.277450\pi$
$463$	595.951			1.28715			0.643575	+	0.765383i	$0.277450\pi$
$464$	163.881	+	94.6168i	0.353192	+	0.203915i
$465$	−5.76844	+	41.2695i	−0.0124052	+	0.0887517i
$466$	85.9890	+	148.937i	0.184526	+	0.319608i
$467$	452.173	+	261.062i	0.968250	+	0.559020i	0.898702	−	0.438559i	$-0.144511\pi$
$467$	452.173	+	261.062i	0.968250	+	0.559020i	0.0695480	+	0.997579i	$0.477844\pi$
$468$	−76.1425	−	303.448i	−0.162698	−	0.648393i
$469$	684.352	+	146.358i	1.45917	+	0.312065i
$470$		−	50.8073i		−	0.108101i
$471$	1.12591	+	2.78071i	0.00239047	+	0.00590384i
$472$	142.833	+	247.394i	0.302612	+	0.524140i
$473$	28.1452	−	16.2497i	0.0595036	−	0.0343544i
$474$	−262.444	+	106.264i	−0.553680	+	0.224185i
$475$	323.666			0.681402
$476$	6.50289	−	2.10393i	0.0136615	−	0.00442002i
$477$	531.284	−	133.312i	1.11380	−	0.279480i
$478$	−42.2137	+	73.1163i	−0.0883133	+	0.152963i
$479$	−614.222	+	354.621i	−1.28230	+	0.740336i	−0.977268	−	0.212006i	$-0.932000\pi$
$479$	−614.222	+	354.621i	−1.28230	+	0.740336i	−0.305031	+	0.952342i	$0.598667\pi$
$480$	8.20522	+	1.14688i	0.0170942	+	0.00238934i
$481$	−8.69042	+	15.0522i	−0.0180674	+	0.0312936i
$482$		−	278.197i		−	0.577172i
$483$	138.236	−	24.3036i	0.286203	−	0.0503180i
$484$	218.192			0.450809
$485$	10.6103	+	6.12587i	0.0218769	+	0.0126307i
$486$	−118.749	−	322.485i	−0.244339	−	0.663550i
$487$	−202.391	−	350.551i	−0.415586	−	0.719817i	0.579903	−	0.814685i	$-0.303090\pi$
$487$	−202.391	−	350.551i	−0.415586	−	0.719817i	−0.995490	+	0.0948684i	$0.969757\pi$
$488$	−83.8665	−	48.4203i	−0.171857	−	0.0992220i
$489$	−213.908	+	274.214i	−0.437440	+	0.560765i
$490$	−27.4190	+	19.8165i	−0.0559571	+	0.0404418i
$491$		−	202.531i		−	0.412487i	−0.978501	−	0.206244i	$-0.933876\pi$
$491$		−	202.531i		−	0.412487i	0.978501	−	0.206244i	$-0.0661239\pi$
$492$	−157.861	+	63.9179i	−0.320855	+	0.129914i
$493$	−11.5479	−	20.0016i	−0.0234238	−	0.0405712i
$494$	−278.249	+	160.647i	−0.563257	+	0.325196i
$495$	−64.0945	−	18.2746i	−0.129484	−	0.0369184i
$496$	−113.808			−0.229452
$497$	−430.761	−	388.836i	−0.866723	−	0.782365i
$498$	−231.617	+	296.915i	−0.465094	+	0.596215i
$499$	−9.58481	+	16.6014i	−0.0192080	+	0.0332693i	−0.875470	−	0.483273i	$-0.839448\pi$
$499$	−9.58481	+	16.6014i	−0.0192080	+	0.0332693i	0.856262	+	0.516542i	$0.172781\pi$
$500$	42.0776	−	24.2935i	0.0841552	−	0.0485871i
$501$	−82.7956	+	592.350i	−0.165261	+	1.18233i
$502$	190.356	−	329.707i	0.379196	−	0.656786i
$503$		−	234.752i		−	0.466704i	−0.972392	−	0.233352i	$-0.925031\pi$
$503$		−	234.752i		−	0.466704i	0.972392	−	0.233352i	$-0.0749695\pi$
$504$	−94.4649	−	151.091i	−0.187430	−	0.299783i
$505$	−45.9533			−0.0909967
$506$	124.169	+	71.6889i	0.245393	+	0.141678i
$507$	395.436	+	55.2720i	0.779952	+	0.109018i
$508$	−59.3808	−	102.851i	−0.116891	−	0.202462i
$509$	621.600	+	358.881i	1.22122	+	0.705071i	0.965178	−	0.261595i	$-0.0842486\pi$
$509$	621.600	+	358.881i	1.22122	+	0.705071i	0.256041	+	0.966666i	$0.417582\pi$
$510$	−0.797287	−	0.621945i	−0.00156331	−	0.00121950i
$511$	354.319	+	75.7761i	0.693384	+	0.148290i
$512$			22.6274i			0.0441942i
$513$	−285.053	+	208.086i	−0.555659	+	0.405626i
$514$	133.463	+	231.165i	0.259656	+	0.449737i
$515$	4.01598	−	2.31863i	0.00779803	−	0.00450219i
$516$	−4.82451	−	11.9153i	−0.00934982	−	0.0230917i
$517$	−1116.27			−2.15913
$518$	−2.07033	+	9.68059i	−0.00399677	+	0.0186884i
$519$	82.1548	+	64.0870i	0.158294	+	0.123482i
$520$	−12.0000	+	20.7846i	−0.0230769	+	0.0399704i
$521$	529.130	−	305.494i	1.01561	−	0.586360i	0.102777	−	0.994704i	$-0.467227\pi$
$521$	529.130	−	305.494i	1.01561	−	0.586360i	0.912828	+	0.408344i	$0.133894\pi$
$522$	−432.512	+	418.930i	−0.828568	+	0.802548i
$523$	−213.676	+	370.097i	−0.408558	+	0.707642i	−0.994728	−	0.102545i	$-0.967301\pi$
$523$	−213.676	+	370.097i	−0.408558	+	0.707642i	0.586171	+	0.810187i	$0.300635\pi$
$524$			202.601i			0.386643i
$525$	−488.547	−	178.093i	−0.930565	−	0.339224i
$526$	293.211			0.557436
$527$	12.0293	+	6.94512i	0.0228260	+	0.0131786i
$528$	25.1978	−	180.274i	0.0477232	−	0.341429i
$529$	−242.165	−	419.441i	−0.457778	−	0.792895i
$530$	−36.3902	−	21.0099i	−0.0686608	−	0.0396413i
$531$	−881.651	+	221.228i	−1.66036	+	0.416625i
$532$	−122.619	+	135.840i	−0.230487	+	0.255339i
$533$		−	493.355i		−	0.925620i
$534$	93.2069	+	230.197i	0.174545	+	0.431081i
$535$	−8.32188	−	14.4139i	−0.0155549	−	0.0269419i
$536$	244.889	−	141.387i	0.456882	−	0.263781i
$537$	−600.964	+	243.331i	−1.11911	+	0.453130i
$538$	−258.740			−0.480929
$539$	435.382	+	602.414i	0.807758	+	1.11765i
$540$	−10.6684	+	24.1076i	−0.0197562	+	0.0446437i
$541$	163.758	−	283.637i	0.302695	−	0.524283i	−0.674051	−	0.738685i	$-0.735447\pi$
$541$	163.758	−	283.637i	0.302695	−	0.524283i	0.976745	+	0.214402i	$0.0687804\pi$
$542$	−238.852	+	137.901i	−0.440687	+	0.254431i
$543$	−951.035	−	132.931i	−1.75145	−	0.244808i
$544$	1.38083	−	2.39167i	0.00253829	−	0.00439645i
$545$		−	32.4070i		−	0.0594623i
$546$	508.387	−	89.3807i	0.931112	−	0.163701i
$547$	313.754			0.573591			0.286795	−	0.957992i	$-0.407410\pi$
$547$	313.754			0.573591			0.286795	+	0.957992i	$0.407410\pi$
$548$	230.279	+	132.952i	0.420217	+	0.242613i
$549$	221.339	−	214.388i	0.403168	−	0.390507i
$550$	−265.595	−	460.023i	−0.482899	−	0.836406i
$551$	535.532	+	309.190i	0.971928	+	0.561143i
$552$	34.8821	−	44.7163i	0.0631922	−	0.0810077i
$553$	−143.805	−	444.475i	−0.260044	−	0.803753i
$554$		−	148.895i		−	0.268764i
$555$	1.35753	−	0.549666i	0.00244601	−	0.000990390i
$556$	71.6658	+	124.129i	0.128895	+	0.223253i
$557$	−156.050	+	90.0952i	−0.280161	+	0.161751i	−0.633496	−	0.773746i	$-0.718381\pi$
$557$	−156.050	+	90.0952i	−0.280161	+	0.161751i	0.353335	+	0.935497i	$0.385047\pi$
$558$	99.2950	−	348.257i	0.177948	−	0.624116i
$559$	37.2383			0.0666160
$560$	−2.85877	+	13.3673i	−0.00510495	+	0.0238701i
$561$	−13.6646	+	17.5169i	−0.0243575	+	0.0312245i
$562$	333.880	−	578.296i	0.594092	−	1.02900i
$563$	−348.106	+	200.979i	−0.618305	+	0.356979i	−0.776209	−	0.630476i	$-0.782860\pi$
$563$	−348.106	+	200.979i	−0.618305	+	0.356979i	0.157904	+	0.987455i	$0.449526\pi$
$564$	−61.1216	+	437.286i	−0.108372	+	0.775330i
$565$	−17.5971	+	30.4791i	−0.0311453	+	0.0539453i
$566$			451.770i			0.798180i
$567$	544.760	−	157.242i	0.960777	−	0.277324i
$568$	−234.477			−0.412811
$569$	−37.0446	−	21.3877i	−0.0651048	−	0.0375883i	0.467094	−	0.884208i	$-0.345301\pi$
$569$	−37.0446	−	21.3877i	−0.0651048	−	0.0375883i	−0.532199	+	0.846619i	$0.678634\pi$
$570$	26.8131	+	3.74780i	0.0470406	+	0.00657509i
$571$	256.084	+	443.550i	0.448483	+	0.776795i	0.998287	−	0.0584985i	$-0.0186313\pi$
$571$	256.084	+	443.550i	0.448483	+	0.776795i	−0.549805	+	0.835293i	$0.685298\pi$
$572$	456.652	+	263.648i	0.798343	+	0.460924i
$573$	−94.5000	−	73.7172i	−0.164921	−	0.128651i
$574$	−86.4987	−	267.353i	−0.150695	−	0.465772i
$575$		−	165.498i		−	0.287822i
$576$	−69.2406	−	19.7419i	−0.120209	−	0.0342741i
$577$	34.7409	+	60.1730i	0.0602095	+	0.104286i	0.894559	−	0.446950i	$-0.147490\pi$
$577$	34.7409	+	60.1730i	0.0602095	+	0.104286i	−0.834349	+	0.551236i	$0.814156\pi$
$578$	353.659	−	204.185i	0.611867	−	0.353262i
$579$	−390.524	−	964.495i	−0.674481	−	1.66579i
$580$	46.1917			0.0796408
$581$	−461.202	−	416.314i	−0.793807	−	0.716547i
$582$	−83.9508	−	65.4881i	−0.144245	−	0.112522i
$583$	−461.602	+	799.518i	−0.791770	+	1.37139i
$584$	126.790	−	73.2020i	0.217106	−	0.125346i
$585$	−53.1318	−	54.8544i	−0.0908236	−	0.0937683i
$586$	−337.710	+	584.931i	−0.576297	+	0.998175i
$587$		−	462.715i		−	0.788271i	−0.919052	−	0.394136i	$-0.871044\pi$
$587$		−	462.715i		−	0.788271i	0.919052	−	0.394136i	$-0.128956\pi$
$588$	259.828	−	137.570i	0.441884	−	0.233963i
$589$	−371.904			−0.631416
$590$	60.3886	+	34.8653i	0.102353	+	0.0590938i
$591$	−38.3566	+	274.417i	−0.0649013	+	0.464327i
$592$	2.00000	+	3.46410i	0.00337838	+	0.00585152i
$593$	470.604	+	271.704i	0.793599	+	0.458185i	0.841228	−	0.540680i	$-0.181833\pi$
$593$	470.604	+	271.704i	0.793599	+	0.458185i	−0.0476289	+	0.998865i	$0.515166\pi$
$594$	529.661	+	234.391i	0.891685	+	0.394598i
$595$	1.11790	−	1.23844i	0.00187882	−	0.00208140i
$596$		−	36.8703i		−	0.0618629i
$597$	48.6547	+	120.165i	0.0814987	+	0.201281i
$598$	82.1425	+	142.275i	0.137362	+	0.237918i
$599$	117.002	−	67.5512i	0.195329	−	0.112773i	−0.399146	−	0.916887i	$-0.630693\pi$
$599$	117.002	−	67.5512i	0.195329	−	0.112773i	0.594475	+	0.804114i	$0.297360\pi$
$600$	−194.751	+	78.8548i	−0.324585	+	0.131425i
$601$	846.422			1.40836			0.704178	−	0.710023i	$-0.251316\pi$
$601$	846.422			1.40836			0.704178	+	0.710023i	$0.251316\pi$
$602$	20.1797	−	6.52890i	0.0335211	−	0.0108454i
$603$	218.988	+	872.723i	0.363164	+	1.44730i
$604$	50.0246	−	86.6451i	0.0828222	−	0.143452i
$605$	46.1248	−	26.6302i	0.0762393	−	0.0440168i
$606$	395.509	+	55.2822i	0.652655	+	0.0912247i
$607$	−211.916	+	367.050i	−0.349121	+	0.604695i	−0.986094	−	0.166191i	$-0.946853\pi$
$607$	−211.916	+	367.050i	−0.349121	+	0.604695i	0.636973	+	0.770886i	$0.280186\pi$
$608$			73.9421i			0.121615i
$609$	−638.214	−	761.366i	−1.04797	−	1.25019i
$610$	−23.6387			−0.0387519
$611$	−1107.69	−	639.523i	−1.81291	−	1.04668i
$612$	6.11384	+	6.31206i	0.00998994	+	0.0103138i
$613$	42.4754	+	73.5696i	0.0692910	+	0.120016i	0.898589	−	0.438790i	$-0.144593\pi$
$613$	42.4754	+	73.5696i	0.0692910	+	0.120016i	−0.829298	+	0.558806i	$0.811260\pi$
$614$	128.132	+	73.9769i	0.208684	+	0.120484i
$615$	−25.5700	+	32.7788i	−0.0415772	+	0.0532989i
$616$	293.688	+	62.8092i	0.476766	+	0.101963i
$617$			241.052i			0.390684i	0.980735	+	0.195342i	$0.0625817\pi$
$617$			241.052i			0.390684i	−0.980735	+	0.195342i	$0.937418\pi$
$618$	−37.3539	+	15.1246i	−0.0604432	+	0.0244735i
$619$	−0.872341	−	1.51094i	−0.00140927	−	0.00244094i	0.865320	−	0.501220i	$-0.167115\pi$
$619$	−0.872341	−	1.51094i	−0.00140927	−	0.00244094i	−0.866729	+	0.498779i	$0.833782\pi$
$620$	−24.0586	+	13.8902i	−0.0388042	+	0.0224036i
$621$	106.399	+	145.754i	0.171335	+	0.234709i
$622$	−272.597			−0.438259
$623$	−389.862	+	126.135i	−0.625781	+	0.202464i
$624$	128.285	−	164.452i	0.205585	−	0.263545i
$625$	−303.591	+	525.835i	−0.485745	+	0.841335i
$626$	−662.466	+	382.475i	−1.05825	+	0.610983i
$627$	82.3417	−	589.103i	0.131327	−	0.939558i
$628$	−1.00000	+	1.73205i	−0.00159236	+	0.00275804i
$629$		−	0.488198i		−	0.000776149i
$630$	−38.4100	−	20.4105i	−0.0609683	−	0.0323977i
$631$	655.852			1.03939			0.519693	−	0.854353i	$-0.326046\pi$
$631$	655.852			1.03939			0.519693	+	0.854353i	$0.326046\pi$
$632$	−163.472	−	94.3805i	−0.258658	−	0.149336i
$633$	909.585	+	127.137i	1.43694	+	0.200848i
$634$	−218.893	−	379.134i	−0.345257	−	0.598003i
$635$	−25.1057	−	14.4948i	−0.0395366	−	0.0228264i
$636$	287.926	+	224.604i	0.452714	+	0.353152i
$637$	86.9042	+	847.215i	0.136427	+	1.33001i
$638$		−	1014.86i		−	1.59069i
$639$	204.575	−	717.506i	0.320149	−	1.12286i
$640$	2.76166	+	4.78334i	0.00431510	+	0.00747397i
$641$	830.357	−	479.407i	1.29541	−	0.747905i	0.315802	−	0.948825i	$-0.397727\pi$
$641$	830.357	−	479.407i	1.29541	−	0.747905i	0.979608	+	0.200920i	$0.0643933\pi$
$642$	54.2843	+	134.068i	0.0845550	+	0.208829i
$643$	1189.28			1.84958			0.924788	−	0.380483i	$-0.124242\pi$
$643$	1189.28			1.84958			0.924788	+	0.380483i	$0.124242\pi$
$644$	69.4583	+	62.6980i	0.107855	+	0.0973571i
$645$	−2.47414	−	1.93002i	−0.00383587	−	0.00299227i
$646$	4.51230	−	7.81553i	0.00698498	−	0.0120983i
$647$	383.479	−	221.402i	0.592703	−	0.342198i	−0.173462	−	0.984841i	$-0.555495\pi$
$647$	383.479	−	221.402i	0.592703	−	0.342198i	0.766166	+	0.642643i	$0.222162\pi$
$648$	120.821	−	194.654i	0.186453	−	0.300392i
$649$	766.016	−	1326.78i	1.18030	−	2.04434i
$650$		−	608.647i		−	0.936380i
$651$	561.358	+	204.635i	0.862302	+	0.314340i
$652$	−231.852			−0.355602
$653$	752.726	+	434.586i	1.15272	+	0.665523i	0.949548	−	0.313620i	$-0.101542\pi$
$653$	752.726	+	434.586i	1.15272	+	0.665523i	0.203171	+	0.979143i	$0.434875\pi$
$654$	−38.9858	+	278.919i	−0.0596113	+	0.426481i
$655$	24.7273	+	42.8290i	0.0377516	+	0.0653877i
$656$	−98.3286	−	56.7701i	−0.149891	−	0.0865397i
$657$	113.380	+	451.847i	0.172572	+	0.687743i
$658$	−712.389	−	152.354i	−1.08266	−	0.231542i
$659$			892.094i			1.35371i	0.736117	+	0.676854i	$0.236657\pi$
$659$			892.094i			1.35371i	−0.736117	+	0.676854i	$0.763343\pi$
$660$	−16.6757	−	41.1846i	−0.0252662	−	0.0624010i
$661$	−610.399	−	1057.24i	−0.923448	−	1.59946i	−0.794038	−	0.607867i	$-0.792025\pi$
$661$	−610.399	−	1057.24i	−0.923448	−	1.59946i	−0.129409	−	0.991591i	$-0.541308\pi$
$662$	−408.451	+	235.819i	−0.616995	+	0.356222i
$663$	−23.5951	+	9.55366i	−0.0355884	+	0.0144097i
$664$	−251.047			−0.378082
$665$	−9.34194	+	43.6817i	−0.0140480	+	0.0656867i
$666$	−12.3452	+	3.09772i	−0.0185363	+	0.00465122i
$667$	158.096	−	273.830i	0.237025	−	0.410540i
$668$	−345.318	+	199.369i	−0.516943	+	0.298457i
$669$	4.67213	+	0.653046i	0.00698375	+	0.000976153i
$670$	34.5123	−	59.7771i	0.0515109	−	0.0892195i
$671$			519.358i			0.774006i
$672$	40.6856	−	111.609i	0.0605441	−	0.166086i
$673$	−476.142			−0.707493			−0.353746	−	0.935341i	$-0.615092\pi$
$673$	−476.142			−0.707493			−0.353746	+	0.935341i	$0.615092\pi$
$674$	−169.773	−	98.0186i	−0.251889	−	0.145428i
$675$	−71.3824	−	664.743i	−0.105752	−	0.984805i
$676$	133.093	+	230.524i	0.196884	+	0.341012i
$677$	−592.287	−	341.957i	−0.874870	−	0.505107i	−0.00590674	−	0.999983i	$-0.501880\pi$
$677$	−592.287	−	341.957i	−0.874870	−	0.505107i	−0.868964	+	0.494876i	$0.835214\pi$
$678$	188.120	−	241.156i	0.277464	−	0.355688i
$679$	117.710	−	130.402i	0.173358	−	0.192050i
$680$		−	0.674119i		−	0.000991351i
$681$	−13.3485	+	5.40482i	−0.0196013	+	0.00793659i
$682$	305.178	+	528.584i	0.447475	+	0.775050i
$683$	182.353	−	105.282i	0.266988	−	0.154146i	−0.360530	−	0.932748i	$-0.617404\pi$
$683$	182.353	−	105.282i	0.266988	−	0.154146i	0.627518	+	0.778602i	$0.284071\pi$
$684$	−226.265	−	64.5127i	−0.330797	−	0.0943169i
$685$	64.9067			0.0947543
$686$	195.634	+	443.875i	0.285181	+	0.647049i
$687$	−575.346	+	737.551i	−0.837477	+	1.07358i
$688$	4.28499	−	7.42182i	0.00622818	−	0.0107875i
$689$	−916.103	+	528.912i	−1.32961	+	0.767652i
$690$	1.91634	−	13.7102i	0.00277730	−	0.0198698i
$691$	−465.536	+	806.331i	−0.673713	+	1.16690i	0.303130	+	0.952949i	$0.401968\pi$
$691$	−465.536	+	806.331i	−0.673713	+	1.16690i	−0.976843	+	0.213956i	$0.931365\pi$
$692$			69.4632i			0.100380i
$693$	−448.434	+	843.894i	−0.647091	+	1.21774i
$694$	−606.494			−0.873910
$695$	30.2997	+	17.4935i	0.0435967	+	0.0251706i
$696$	−397.560	−	55.5689i	−0.571207	−	0.0798404i
$697$	6.92875	+	12.0010i	0.00994082	+	0.0172180i
$698$	−203.596	−	117.546i	−0.291685	−	0.168405i
$699$	−287.651	−	224.390i	−0.411518	−	0.321015i
$700$	−106.712	−	329.830i	−0.152446	−	0.471186i
$701$		−	459.553i		−	0.655568i	−0.944753	−	0.327784i	$-0.893698\pi$
$701$		−	459.553i		−	0.655568i	0.944753	−	0.327784i	$-0.106302\pi$
$702$	391.302	+	536.036i	0.557410	+	0.763584i
$703$	6.53562	+	11.3200i	0.00929676	+	0.0161025i
$704$	105.093	−	60.6756i	0.149280	−	0.0861870i
$705$	40.4497	+	99.9003i	0.0573754	+	0.141702i
$706$	402.641			0.570313
$707$	−137.799	+	644.330i	−0.194906	+	0.911357i
$708$	−477.806	−	372.725i	−0.674867	−	0.526448i
$709$	81.6400	−	141.405i	0.115148	−	0.199442i	−0.802691	−	0.596395i	$-0.796599\pi$
$709$	81.6400	−	141.405i	0.115148	−	0.199442i	0.917839	+	0.396953i	$0.129932\pi$
$710$	−49.5674	+	28.6177i	−0.0698132	+	0.0403067i
$711$	431.432	−	417.884i	0.606796	−	0.587741i
$712$	−82.7837	+	143.386i	−0.116269	+	0.201384i
$713$			190.163i			0.266708i
$714$	−11.1113	+	9.31406i	−0.0155621	+	0.0130449i
$715$	128.712			0.180017
$716$	−374.329	−	216.119i	−0.522806	−	0.301842i
$717$	24.7923	−	177.373i	0.0345779	−	0.247383i
$718$	298.726	+	517.409i	0.416053	+	0.720625i
$719$	−535.422	−	309.126i	−0.744676	−	0.429939i	0.0790907	−	0.996867i	$-0.474798\pi$
$719$	−535.422	−	309.126i	−0.744676	−	0.429939i	−0.823767	+	0.566928i	$0.808132\pi$
$720$	−17.0467	+	4.27742i	−0.0236759	+	0.00594087i
$721$	−20.4678	−	63.2625i	−0.0283881	−	0.0877427i
$722$		−	268.902i		−	0.372441i
$723$	221.483	+	547.007i	0.306339	+	0.756579i
$724$	−320.093	−	554.418i	−0.442118	−	0.765771i
$725$	−1014.49	+	585.717i	−1.39930	+	0.807886i
$726$	−429.021	+	173.711i	−0.590938	+	0.239271i
$727$	−870.614			−1.19754			−0.598772	−	0.800920i	$-0.704344\pi$
$727$	−870.614			−1.19754			−0.598772	+	0.800920i	$0.704344\pi$
$728$	255.445	+	230.583i	0.350886	+	0.316735i
$729$	490.233	+	539.548i	0.672474	+	0.740121i
$730$	17.8685	−	30.9492i	0.0244774	−	0.0423962i
$731$	−0.905829	+	0.522980i	−0.00123916	+	0.000715431i
$732$	203.452	+	28.4375i	0.277940	+	0.0388490i
$733$	578.834	−	1002.57i	0.789678	−	1.36776i	−0.136486	−	0.990642i	$-0.543581\pi$
$733$	578.834	−	1002.57i	0.789678	−	1.36776i	0.926164	−	0.377121i	$-0.123086\pi$
$734$			241.125i			0.328508i
$735$	38.1361	−	60.7936i	0.0518859	−	0.0827124i
$736$	37.8083			0.0513700
$737$	−1313.34	−	758.259i	−1.78201	−	1.02885i
$738$	259.507	−	251.358i	0.351636	−	0.340594i
$739$	233.941	+	405.198i	0.316564	+	0.548306i	0.979769	−	0.200133i	$-0.0641373\pi$
$739$	233.941	+	405.198i	0.316564	+	0.548306i	−0.663204	+	0.748438i	$0.730804\pi$
$740$	0.845583	+	0.488198i	0.00114268	+	0.000659727i
$741$	419.211	−	537.398i	0.565737	−	0.725233i
$742$	−403.710	+	447.239i	−0.544083	+	0.602748i
$743$			659.621i			0.887780i	0.896081	+	0.443890i	$0.146402\pi$
$743$			659.621i			0.887780i	−0.896081	+	0.443890i	$0.853598\pi$
$744$	223.776	−	90.6071i	0.300775	−	0.121784i
$745$	−4.50000	−	7.79423i	−0.00604027	−	0.0104621i
$746$	372.963	−	215.331i	0.499951	−	0.288647i
$747$	219.032	−	768.210i	0.293216	−	1.02839i
$748$	−14.8109			−0.0198006
$749$	−227.058	+	73.4617i	−0.303148	+	0.0980798i
$750$	−63.3944	+	81.2669i	−0.0845259	+	0.108356i
$751$	−76.3490	+	132.240i	−0.101663	+	0.176086i	−0.912370	−	0.409367i	$-0.865750\pi$
$751$	−76.3490	+	132.240i	−0.101663	+	0.176086i	0.810707	+	0.585452i	$0.199083\pi$
$752$	−254.921	+	147.179i	−0.338991	+	0.195717i
$753$	−111.797	+	799.838i	−0.148469	+	1.06220i
$754$	581.425	−	1007.06i	0.771121	−	1.33562i
$755$		−	24.4219i		−	0.0323469i
$756$	306.031	+	221.876i	0.404803	+	0.293487i
$757$	304.909			0.402786			0.201393	−	0.979510i	$-0.435453\pi$
$757$	304.909			0.402786			0.201393	+	0.979510i	$0.435453\pi$
$758$	628.171	+	362.674i	0.828721	+	0.478462i
$759$	−301.222	−	42.1032i	−0.396867	−	0.0554720i
$760$	9.02460	+	15.6311i	0.0118745	+	0.0205672i
$761$	1011.81	+	584.172i	1.32959	+	0.767637i	0.985236	−	0.171204i	$-0.0547659\pi$
$761$	1011.81	+	584.172i	1.32959	+	0.767637i	0.344350	+	0.938841i	$0.388099\pi$
$762$	198.641	+	154.955i	0.260684	+	0.203353i
$763$	−454.391	−	97.1778i	−0.595532	−	0.127363i
$764$		−	79.9013i		−	0.104583i
$765$	2.06282	+	0.588152i	0.00269650	+	0.000768827i
$766$	303.198	+	525.154i	0.395819	+	0.685579i
$767$	1520.25	−	877.716i	1.98207	−	1.14435i
$768$	−18.0145	−	44.4913i	−0.0234564	−	0.0579314i
$769$	−684.909			−0.890649			−0.445325	−	0.895369i	$-0.646912\pi$
$769$	−684.909			−0.890649			−0.445325	+	0.895369i	$0.646912\pi$
$770$	69.7502	−	22.5668i	0.0905847	−	0.0293076i
$771$	−446.462	−	348.274i	−0.579069	−	0.451718i
$772$	346.852	−	600.766i	0.449291	−	0.778194i
$773$	1300.52	−	750.854i	1.68243	−	0.971351i	0.722390	−	0.691485i	$-0.243043\pi$
$773$	1300.52	−	750.854i	1.68243	−	0.971351i	0.960039	−	0.279866i	$-0.0902899\pi$
$774$	18.9724	+	19.5876i	0.0245122	+	0.0253069i
$775$	352.260	−	610.133i	0.454530	−	0.787268i
$776$		−	70.9818i		−	0.0914713i
$777$	−3.63629	−	20.6828i	−0.00467991	−	0.0266188i
$778$	99.9779			0.128506
$779$	−321.319	−	185.514i	−0.412477	−	0.238144i
$780$	7.04766	−	50.4215i	0.00903546	−	0.0646430i
$781$	628.752	+	1089.03i	0.805060	+	1.39440i
$782$	−3.99626	−	2.30724i	−0.00511031	−	0.00295044i
$783$	516.904	−	1168.06i	0.660159	−	1.49178i
$784$	178.855	+	80.1680i	0.228131	+	0.102255i
$785$			0.488198i			0.000621908i
$786$	−161.298	−	398.365i	−0.205214	−	0.506826i
$787$	394.224	+	682.815i	0.500919	+	0.867618i	0.999999	+	0.00106186i	$0.000338000\pi$
$787$	394.224	+	682.815i	0.500919	+	0.867618i	−0.499080	+	0.866556i	$0.666329\pi$
$788$	−159.975	+	92.3617i	−0.203014	+	0.117210i
$789$	−576.528	+	233.437i	−0.730708	+	0.295864i
$790$	−46.0763			−0.0583245
$791$	374.591	+	338.133i	0.473567	+	0.427475i
$792$	93.9779	+	374.527i	0.118659	+	0.472887i
$793$	−297.545	+	515.364i	−0.375215	+	0.649891i
$794$	65.3145	−	37.7094i	0.0822601	−	0.0474929i
$795$	88.2792	+	12.3392i	0.111043	+	0.0155210i
$796$	−43.2137	+	74.8484i	−0.0542886	+	0.0940306i
$797$		−	1050.25i		−	1.31775i	−0.752253	−	0.658875i	$-0.771033\pi$
$797$		−	1050.25i		−	1.31775i	0.752253	−	0.658875i	$-0.228967\pi$
$798$	132.953	−	364.719i	0.166608	−	0.457041i
$799$	35.9262			0.0449640
$800$	−121.307	−	70.0366i	−0.151634	−	0.0875457i
$801$	−366.538	−	378.421i	−0.457600	−	0.472436i
$802$	206.746	+	358.094i	0.257787	+	0.446501i
$803$	−679.975	−	392.584i	−0.846794	−	0.488897i
$804$	−368.951	+	472.967i	−0.458894	+	0.588268i
$805$	22.3354	+	4.77675i	0.0277459	+	0.00593385i
$806$			699.358i			0.867690i
$807$	508.748	−	205.992i	0.630419	−	0.255257i
$808$	133.118	+	230.567i	0.164750	+	0.285355i
$809$	−255.525	+	147.527i	−0.315853	+	0.182358i	−0.649543	−	0.760325i	$-0.725040\pi$
$809$	−255.525	+	147.527i	−0.315853	+	0.182358i	0.333690	+	0.942683i	$0.391706\pi$
$810$	1.78375	−	55.8952i	0.00220216	−	0.0690064i
$811$	−1122.32			−1.38387			−0.691935	−	0.721960i	$-0.743242\pi$
$811$	−1122.32			−1.38387			−0.691935	+	0.721960i	$0.743242\pi$
$812$	138.514	−	647.671i	0.170583	−	0.797625i
$813$	359.856	−	461.309i	0.442628	−	0.567416i
$814$	10.7260	−	18.5780i	0.0131770	−	0.0228232i
$815$	−49.0126	+	28.2975i	−0.0601382	+	0.0347208i
$816$	−0.810969	+	5.80197i	−0.000993835	+	0.00711026i
$817$	14.0025	−	24.2531i	0.0171390	−	0.0296856i
$818$		−	6.45934i		−	0.00789650i
$819$	−928.460	+	580.492i	−1.13365	+	0.708781i
$820$	−27.7150			−0.0337988
$821$	1020.75	+	589.332i	1.24330	+	0.717822i	0.969765	−	0.244039i	$-0.0784725\pi$
$821$	1020.75	+	589.332i	1.24330	+	0.717822i	0.273539	+	0.961861i	$0.411806\pi$
$822$	−558.636	−	78.0832i	−0.679605	−	0.0949917i
$823$	182.990	+	316.948i	0.222345	+	0.385113i	0.955520	−	0.294927i	$-0.0952954\pi$
$823$	182.990	+	316.948i	0.222345	+	0.385113i	−0.733174	+	0.680041i	$0.761962\pi$
$824$	−23.2670	−	13.4332i	−0.0282367	−	0.0163025i
$825$	888.469	+	693.074i	1.07693	+	0.840089i
$826$	669.946	−	742.182i	0.811072	−	0.898525i
$827$		−	791.154i		−	0.956655i	−0.878182	−	0.478327i	$-0.841243\pi$
$827$		−	791.154i		−	0.956655i	0.878182	−	0.478327i	$-0.158757\pi$
$828$	−32.9868	+	115.695i	−0.0398392	+	0.139728i
$829$	−206.615	−	357.868i	−0.249234	−	0.431687i	0.714079	−	0.700065i	$-0.246846\pi$
$829$	−206.615	−	357.868i	−0.249234	−	0.431687i	−0.963314	+	0.268378i	$0.913512\pi$
$830$	−53.0702	+	30.6401i	−0.0639400	+	0.0369158i
$831$	118.541	+	292.767i	0.142649	+	0.352306i
$832$	139.047			0.167123
$833$	−14.0124	−	19.3882i	−0.0168216	−	0.0232751i
$834$	−239.737	−	187.013i	−0.287455	−	0.224237i
$835$	−48.6658	+	84.2917i	−0.0582824	+	0.100948i
$836$	343.425	−	198.277i	0.410796	−	0.237173i
$837$	82.0211	+	763.815i	0.0979942	+	0.912563i
$838$	−267.288	+	462.956i	−0.318959	+	0.552453i
$839$		−	1406.19i		−	1.67603i	−0.545650	−	0.838013i	$-0.683717\pi$
$839$		−	1406.19i		−	1.67603i	0.545650	−	0.838013i	$-0.316283\pi$
$840$	−5.02110	−	28.5594i	−0.00597750	−	0.0339993i
$841$	−1397.08			−1.66122
$842$	909.748	+	525.243i	1.08046	+	0.623804i
$843$	−196.089	+	1402.89i	−0.232609	+	1.66417i
$844$	306.142	+	530.254i	0.362728	+	0.628263i
$845$	56.2707	+	32.4879i	0.0665926	+	0.0384472i
$846$	−227.959	−	908.477i	−0.269455	−	1.07385i
$847$	−235.079	−	726.589i	−0.277543	−	0.857838i
$848$			243.446i			0.287083i
$849$	−359.671	−	888.295i	−0.423641	−	1.04628i
$850$	8.54792	+	14.8054i	0.0100564	+	0.0174182i
$851$	5.78819	−	3.34181i	0.00680164	−	0.00392693i
$852$	461.041	−	186.676i	0.541128	−	0.219103i
$853$	451.573			0.529393			0.264697	−	0.964332i	$-0.414728\pi$
$853$	451.573			0.529393			0.264697	+	0.964332i	$0.414728\pi$
$854$	−70.8846	+	331.447i	−0.0830030	+	0.388111i
$855$	−55.7053	+	13.9778i	−0.0651523	+	0.0163483i
$856$	−48.2137	+	83.5087i	−0.0563245	+	0.0975568i
$857$	−981.314	+	566.562i	−1.14506	+	0.661099i	−0.947678	−	0.319228i	$-0.896576\pi$
$857$	−981.314	+	566.562i	−1.14506	+	0.661099i	−0.197379	+	0.980327i	$0.563243\pi$
$858$	−1107.80	−	154.842i	−1.29114	−	0.180468i
$859$	−544.103	+	942.414i	−0.633415	+	1.09711i	0.353434	+	0.935459i	$0.385014\pi$
$859$	−544.103	+	942.414i	−0.633415	+	1.09711i	−0.986849	+	0.161647i	$0.948319\pi$
$860$		−	2.09192i		−	0.00243247i
$861$	382.928	+	456.819i	0.444748	+	0.530568i
$862$	535.644			0.621396
$863$	789.679	+	455.921i	0.915039	+	0.528298i	0.882049	−	0.471157i	$-0.156164\pi$
$863$	789.679	+	455.921i	0.915039	+	0.528298i	0.0329902	+	0.999456i	$0.489497\pi$
$864$	151.862	−	16.3075i	0.175766	−	0.0188744i
$865$	8.47794	+	14.6842i	0.00980109	+	0.0169760i
$866$	−638.787	−	368.804i	−0.737629	−	0.425871i
$867$	−532.825	+	683.042i	−0.614562	+	0.787823i
$868$	122.617	+	378.987i	0.141263	+	0.436621i
$869$			1012.33i			1.16494i
$870$	−90.8247	+	36.7750i	−0.104396	+	0.0422701i
$871$	−868.828	−	1504.85i	−0.997506	−	1.72773i
$872$	−162.599	+	93.8767i	−0.186467	+	0.107657i
$873$	217.206	+	61.9299i	0.248805	+	0.0709391i
$874$	123.550			0.141362
$875$	−126.233	−	113.947i	−0.144266	−	0.130225i
$876$	−191.022	+	244.876i	−0.218062	+	0.279539i
$877$	496.092	−	859.257i	0.565669	−	0.979768i	−0.431318	−	0.902200i	$-0.641951\pi$
$877$	496.092	−	859.257i	0.565669	−	0.979768i	0.996987	−	0.0775680i	$-0.0247155\pi$
$878$	894.202	−	516.268i	1.01845	−	0.588004i
$879$	198.339	−	1418.99i	0.225641	−	1.61432i
$880$	14.8109	−	25.6532i	0.0168305	−	0.0291513i
$881$			1072.77i			1.21768i	0.793294	+	0.608838i	$0.208364\pi$
$881$			1072.77i			1.21768i	−0.793294	+	0.608838i	$0.791636\pi$
$882$	−401.363	+	477.357i	−0.455060	+	0.541221i
$883$	615.282			0.696809			0.348405	−	0.937344i	$-0.386724\pi$
$883$	615.282			0.696809			0.348405	+	0.937344i	$0.386724\pi$
$884$	−14.6969	−	8.48528i	−0.0166255	−	0.00959873i
$885$	−146.497	−	20.4766i	−0.165533	−	0.0231374i
$886$	−456.650	−	790.941i	−0.515406	−	0.892709i
$887$	−145.006	−	83.7193i	−0.163479	−	0.0943848i	0.416028	−	0.909352i	$-0.363422\pi$
$887$	−145.006	−	83.7193i	−0.163479	−	0.0943848i	−0.579507	+	0.814967i	$0.696755\pi$
$888$	−6.69042	−	5.21904i	−0.00753425	−	0.00587729i
$889$	−278.521	+	308.552i	−0.313297	+	0.347077i
$890$			40.4148i			0.0454099i
$891$	−1228.06	−	39.1902i	−1.37829	−	0.0439845i
$892$	1.57252	+	2.72368i	0.00176291	+	0.00305345i
$893$	−833.035	+	480.953i	−0.932850	+	0.538581i
$894$	29.3539	+	72.4965i	0.0328343	+	0.0810923i
$895$	−105.509			−0.117887
$896$	75.3504	−	24.3787i	0.0840964	−	0.0272084i
$897$	−274.784	−	214.352i	−0.306336	−	0.238966i
$898$	−482.022	+	834.887i	−0.536773	+	0.929718i
$899$	1165.69	−	673.011i	1.29665	−	0.748622i
$900$	320.151	−	310.098i	0.355724	−	0.344553i
$901$	14.8562	−	25.7318i	0.0164886	−	0.0285591i
$902$			608.918i			0.675075i
$903$	−34.4806	+	28.9033i	−0.0381845	+	0.0320081i
$904$	203.902			0.225555
$905$	−135.333	−	78.1344i	−0.149539	−	0.0863364i
$906$	−29.3797	+	210.193i	−0.0324279	+	0.232001i
$907$	−791.771	−	1371.39i	−0.872956	−	1.51200i	−0.858924	−	0.512103i	$-0.828867\pi$
$907$	−791.771	−	1371.39i	−0.872956	−	1.51200i	−0.0140325	−	0.999902i	$-0.504467\pi$
$908$	−8.31454	−	4.80040i	−0.00915699	−	0.00528679i
$909$	−821.684	+	206.181i	−0.903943	+	0.226821i
$910$	82.1425	+	17.5673i	0.0902665	+	0.0193047i
$911$		−	375.771i		−	0.412481i	−0.978501	−	0.206241i	$-0.933877\pi$
$911$		−	375.771i		−	0.412481i	0.978501	−	0.206241i	$-0.0661230\pi$
$912$	−58.8681	−	145.389i	−0.0645484	−	0.159418i
$913$	673.184	+	1165.99i	0.737332	+	1.27710i
$914$	−77.0447	+	44.4818i	−0.0842939	+	0.0486671i
$915$	46.4797	−	18.8197i	0.0507975	−	0.0205679i
$916$	−623.612			−0.680799
$917$	674.670	−	218.281i	0.735736	−	0.238038i
$918$	−17.0467	−	7.54367i	−0.0185693	−	0.00821750i
$919$	−90.8647	+	157.382i	−0.0988735	+	0.171254i	−0.911219	−	0.411923i	$-0.864857\pi$
$919$	−90.8647	+	157.382i	−0.0988735	+	0.171254i	0.812345	+	0.583177i	$0.198191\pi$
$920$	7.99252	−	4.61448i	0.00868752	−	0.00501574i
$921$	−310.836	−	43.4470i	−0.337498	−	0.0471737i
$922$	79.9729	−	138.517i	0.0867385	−	0.150235i
$923$			1440.87i			1.56107i
$924$	−627.470	+	110.317i	−0.679081	+	0.119391i
$925$	−24.7617			−0.0267694
$926$	−729.888	−	421.401i	−0.788216	−	0.455077i
$927$	61.4060	−	59.4777i	0.0662417	−	0.0641615i
$928$	−133.808	−	231.763i	−0.144190	−	0.249744i
$929$	1400.44	+	808.543i	1.50747	+	0.870337i	0.999962	+	0.00868915i	$0.00276588\pi$
$929$	1400.44	+	808.543i	1.50747	+	0.870337i	0.507506	+	0.861648i	$0.330567\pi$
$930$	36.2468	−	46.4657i	0.0389751	−	0.0499632i
$931$	584.464	+	261.974i	0.627781	+	0.281390i
$932$		−	243.214i		−	0.260959i
$933$	535.996	−	217.025i	0.574486	−	0.232610i
$934$	−369.198	−	639.469i	−0.395287	−	0.684656i
$935$	−3.13095	+	1.80766i	−0.00334861	+	0.00193332i
$936$	−121.315	+	425.487i	−0.129610	+	0.454580i
$937$	911.700			0.972999			0.486499	−	0.873681i	$-0.338274\pi$
$937$	911.700			0.972999			0.486499	+	0.873681i	$0.338274\pi$
$938$	−734.666	−	663.162i	−0.783226	−	0.706996i
$939$	998.076	−	1279.46i	1.06291	−	1.36258i
$940$	−35.9262	+	62.2260i	−0.0382194	+	0.0661979i
$941$	−306.260	+	176.819i	−0.325462	+	0.187906i	−0.653825	−	0.756646i	$-0.726837\pi$
$941$	−306.260	+	176.819i	−0.325462	+	0.187906i	0.328362	+	0.944552i	$0.393503\pi$
$942$	0.587305	−	4.20179i	0.000623466	−	0.00446050i
$943$	−94.8575	+	164.298i	−0.100591	+	0.174229i
$944$		−	403.992i		−	0.427958i
$945$	91.7735	+	9.55270i	0.0971148	+	0.0101087i
$946$	−45.9610			−0.0485845
$947$	−61.3349	−	35.4117i	−0.0647676	−	0.0373936i	0.467267	−	0.884117i	$-0.345239\pi$
$947$	−61.3349	−	35.4117i	−0.0647676	−	0.0373936i	−0.532034	+	0.846723i	$0.678572\pi$
$948$	396.567	+	55.4301i	0.418320	+	0.0584706i
$949$	−449.830	−	779.129i	−0.474005	−	0.821000i
$950$	−396.408	−	228.866i	−0.417272	−	0.240912i
$951$	732.243	+	571.206i	0.769972	+	0.600637i
$952$	−9.45208	−	2.02146i	−0.00992865	−	0.00212338i
$953$		−	302.798i		−	0.317731i	−0.987300	−	0.158866i	$-0.949216\pi$
$953$		−	302.798i		−	0.317731i	0.987300	−	0.158866i	$-0.0507836\pi$
$954$	−744.953	−	212.401i	−0.780873	−	0.222643i
$955$	−9.75190	−	16.8908i	−0.0102114	−	0.0176867i
$956$	103.402	−	59.6992i	0.108161	−	0.0624469i
$957$	807.971	+	1995.48i	0.844275	+	2.08514i
$958$	1003.02			1.04699
$959$	194.634	−	910.082i	0.202955	−	0.948990i
$960$	−9.23834	−	7.20661i	−0.00962327	−	0.00750688i
$961$	75.7396	−	131.185i	0.0788133	−	0.136509i
$962$	21.2871	−	12.2901i	0.0221279	−	0.0127756i
$963$	−213.474	−	220.395i	−0.221676	−	0.228863i
$964$	−196.715	+	340.720i	−0.204061	+	0.353444i
$965$		−	169.333i		−	0.175474i
$966$	−186.489	−	67.9819i	−0.193053	−	0.0703747i
$967$	693.562			0.717231			0.358615	−	0.933485i	$-0.383249\pi$
$967$	693.562			0.717231			0.358615	+	0.933485i	$0.383249\pi$
$968$	−267.229	−	154.285i	−0.276063	−	0.159385i
$969$	−2.65009	+	18.9597i	−0.00273488	+	0.0195663i
$970$	−8.66328	−	15.0052i	−0.00893122	−	0.0154693i
$971$	−1154.63	−	666.624i	−1.18911	−	0.686533i	−0.231006	−	0.972952i	$-0.574202\pi$
$971$	−1154.63	−	666.624i	−1.18911	−	0.686533i	−0.958104	+	0.286419i	$0.907535\pi$
$972$	−82.5946	+	478.930i	−0.0849738	+	0.492727i
$973$	336.142	−	372.387i	0.345470	−	0.382720i
$974$			572.447i			0.587728i
$975$	484.567	+	1196.76i	0.496992	+	1.22744i
$976$	68.4767	+	118.605i	0.0701605	+	0.121522i
$977$	−149.808	+	86.4919i	−0.153335	+	0.0885281i	−0.574704	−	0.818361i	$-0.694883\pi$
$977$	−149.808	+	86.4919i	−0.153335	+	0.0885281i	0.421369	+	0.906889i	$0.361550\pi$
$978$	455.881	−	184.587i	0.466136	−	0.188739i
$979$	887.941			0.906988
$980$	47.5936	−	4.88198i	0.0485649	−	0.00498161i
$981$	−145.402	−	579.464i	−0.148218	−	0.590687i
$982$	−143.211	+	248.049i	−0.145836	+	0.252596i
$983$	−931.635	+	537.880i	−0.947747	+	0.547182i	−0.892380	−	0.451284i	$-0.850966\pi$
$983$	−931.635	+	537.880i	−0.947747	+	0.547182i	−0.0553665	+	0.998466i	$0.517633\pi$
$984$	238.536	+	33.3413i	0.242415	+	0.0338835i
$985$	−22.5454	+	39.0497i	−0.0228887	+	0.0396444i
$986$			32.6625i			0.0331262i
$987$	1522.04	−	267.592i	1.54208	−	0.271117i
$988$	454.378			0.459897
$989$	−12.4012	−	7.15982i	−0.0125391	−	0.00723945i
$990$	65.5773	+	67.7034i	0.0662397	+	0.0683873i
$991$	84.6069	+	146.543i	0.0853752	+	0.147874i	0.905551	−	0.424237i	$-0.139458\pi$
$991$	84.6069	+	146.543i	0.0853752	+	0.147874i	−0.820176	+	0.572112i	$0.806124\pi$
$992$	139.386	+	80.4746i	0.140510	+	0.0811236i
$993$	615.374	−	788.864i	0.619712	−	0.794425i
$994$	252.624	+	780.819i	0.254149	+	0.785532i
$995$			21.0968i			0.0212029i
$996$	493.622	−	199.868i	0.495605	−	0.200670i
$997$	793.355	+	1374.13i	0.795742	+	1.37827i	0.922367	+	0.386315i	$0.126252\pi$
$997$	793.355	+	1374.13i	0.795742	+	1.37827i	−0.126625	+	0.991951i	$0.540414\pi$
$998$	23.4779	−	13.5550i	0.0235250	−	0.0135821i
$999$	21.8076	−	15.9194i	0.0218295	−	0.0159353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.3.h.b.23.2	yes	8
3.2	odd	2	inner	42.3.h.b.23.3	yes	8
4.3	odd	2		336.3.bn.g.65.1		8
7.2	even	3		294.3.b.i.197.3		4
7.3	odd	6		294.3.h.h.263.4		8
7.4	even	3	inner	42.3.h.b.11.3	yes	8
7.5	odd	6		294.3.b.e.197.4		4
7.6	odd	2		294.3.h.h.275.1		8
12.11	even	2		336.3.bn.g.65.3		8
21.2	odd	6		294.3.b.i.197.1		4
21.5	even	6		294.3.b.e.197.2		4
21.11	odd	6	inner	42.3.h.b.11.2	✓	8
21.17	even	6		294.3.h.h.263.1		8
21.20	even	2		294.3.h.h.275.4		8
28.11	odd	6		336.3.bn.g.305.3		8
84.11	even	6		336.3.bn.g.305.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.h.b.11.2	✓	8	21.11	odd	6	inner
42.3.h.b.11.3	yes	8	7.4	even	3	inner
42.3.h.b.23.2	yes	8	1.1	even	1	trivial
42.3.h.b.23.3	yes	8	3.2	odd	2	inner
294.3.b.e.197.2		4	21.5	even	6
294.3.b.e.197.4		4	7.5	odd	6
294.3.b.i.197.1		4	21.2	odd	6
294.3.b.i.197.3		4	7.2	even	3
294.3.h.h.263.1		8	21.17	even	6
294.3.h.h.263.4		8	7.3	odd	6
294.3.h.h.275.1		8	7.6	odd	2
294.3.h.h.275.4		8	21.20	even	2
336.3.bn.g.65.1		8	4.3	odd	2
336.3.bn.g.65.3		8	12.11	even	2
336.3.bn.g.305.1		8	84.11	even	6
336.3.bn.g.305.3		8	28.11	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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	42.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(2.97112 + 0.415287i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.422792 + 0.244099i) q^{5} +(-3.34521 - 2.60952i) q^{6} +(4.69042 - 5.19615i) q^{7} -2.82843i q^{8} +(8.65507 + 2.46773i) q^{9} +(-0.345208 - 0.597918i) q^{10} +(-13.1367 + 7.58446i) q^{11} +(2.25182 + 5.56141i) q^{12} -17.3808 q^{13} +(-9.41880 + 3.04734i) q^{14} +(1.15479 + 0.900826i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(0.422792 - 0.244099i) q^{17} +(-8.85530 - 9.14241i) q^{18} +(-6.53562 + 11.3200i) q^{19} +0.976395i q^{20} +(16.0937 - 13.4905i) q^{21} +21.4521 q^{22} +(5.78819 + 3.34181i) q^{23} +(1.17461 - 8.40359i) q^{24} +(-12.3808 - 21.4442i) q^{25} +(21.2871 + 12.2901i) q^{26} +(24.6904 + 10.9263i) q^{27} +(13.6904 + 2.92789i) q^{28} -47.3084i q^{29} +(-0.777345 - 1.91984i) q^{30} +(14.2260 + 24.6402i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-42.1803 + 17.0788i) q^{33} -0.690416 q^{34} +(3.25144 - 1.05196i) q^{35} +(4.38083 + 17.4588i) q^{36} +(0.500000 - 0.866025i) q^{37} +(16.0089 - 9.24277i) q^{38} +(-51.6405 - 7.21804i) q^{39} +(0.690416 - 1.19584i) q^{40} +28.3850i q^{41} +(-29.2499 + 5.14249i) q^{42} -2.14249 q^{43} +(-26.2733 - 15.1689i) q^{44} +(3.05692 + 3.15603i) q^{45} +(-4.72604 - 8.18574i) q^{46} +(63.7304 + 36.7947i) q^{47} +(-7.38083 + 9.46168i) q^{48} +(-5.00000 - 48.7442i) q^{49} +35.0183i q^{50} +(1.35753 - 0.549666i) q^{51} +(-17.3808 - 30.1045i) q^{52} +(52.7077 - 30.4308i) q^{53} +(-22.5134 - 30.8407i) q^{54} -7.40543 q^{55} +(-14.6969 - 13.2665i) q^{56} +(-24.1192 + 30.9190i) q^{57} +(-33.4521 + 57.9407i) q^{58} +(-87.4669 + 50.4991i) q^{59} +(-0.405485 + 2.90098i) q^{60} +(17.1192 - 29.6513i) q^{61} -40.2373i q^{62} +(53.4186 - 33.3984i) q^{63} -8.00000 q^{64} +(-7.34847 - 4.24264i) q^{65} +(63.7366 + 8.90878i) q^{66} +(49.9877 + 86.5812i) q^{67} +(0.845583 + 0.488198i) q^{68} +(15.8096 + 12.3327i) q^{69} +(-4.72604 - 1.01073i) q^{70} -82.9000i q^{71} +(6.97981 - 24.4802i) q^{72} +(25.8808 + 44.8269i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(-27.8794 - 68.8549i) q^{75} -26.1425 q^{76} +(-22.2064 + 103.834i) q^{77} +(58.1425 + 45.3556i) q^{78} +(33.3685 - 57.7960i) q^{79} +(-1.69117 + 0.976395i) q^{80} +(68.8206 + 42.7168i) q^{81} +(20.0712 - 34.7644i) q^{82} -88.7584i q^{83} +(39.4599 + 14.3845i) q^{84} +0.238337 q^{85} +(2.62401 + 1.51497i) q^{86} +(19.6466 - 140.559i) q^{87} +(21.4521 + 37.1561i) q^{88} +(-50.6945 - 29.2685i) q^{89} +(-1.51230 - 6.02690i) q^{90} +(-81.5233 + 90.3134i) q^{91} +13.3673i q^{92} +(32.0345 + 79.1169i) q^{93} +(-52.0356 - 90.1283i) q^{94} +(-5.52641 + 3.19068i) q^{95} +(15.7301 - 6.36910i) q^{96} +25.0958 q^{97} +(-28.3437 + 63.2348i) q^{98} +(-132.415 + 33.2262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 8 q^{4} - 8 q^{6} - 10 q^{9} + 16 q^{10} + 4 q^{12} - 64 q^{13} + 28 q^{15} - 16 q^{16} - 40 q^{18} + 4 q^{19} + 26 q^{21} - 16 q^{22} - 8 q^{24} - 24 q^{25} + 160 q^{27} + 72 q^{28} + 52 q^{30}+ \cdots - 140 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 8 * q^4 - 8 * q^6 - 10 * q^9 + 16 * q^10 + 4 * q^12 - 64 * q^13 + 28 * q^15 - 16 * q^16 - 40 * q^18 + 4 * q^19 + 26 * q^21 - 16 * q^22 - 8 * q^24 - 24 * q^25 + 160 * q^27 + 72 * q^28 + 52 * q^30 + 20 * q^31 - 106 * q^33 + 32 * q^34 - 40 * q^36 + 4 * q^37 - 72 * q^39 - 32 * q^40 - 88 * q^42 + 208 * q^43 - 58 * q^45 + 56 * q^46 + 16 * q^48 - 40 * q^49 + 14 * q^51 - 64 * q^52 - 32 * q^54 - 472 * q^55 - 268 * q^57 - 80 * q^58 + 28 * q^60 + 212 * q^61 + 178 * q^63 - 64 * q^64 + 224 * q^66 + 156 * q^67 + 164 * q^69 + 56 * q^70 + 80 * q^72 + 132 * q^73 + 164 * q^75 + 16 * q^76 + 240 * q^78 - 52 * q^79 + 98 * q^81 + 48 * q^82 - 124 * q^84 + 152 * q^85 - 260 * q^87 - 16 * q^88 - 256 * q^90 - 352 * q^91 - 210 * q^93 - 360 * q^94 + 16 * q^96 + 576 * q^97 - 140 * q^99

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