LMFDB - Embedded newform 42.3.h.b.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,3,Mod(11,42)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.14441711031$
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			11.2
Root			$0.461396 + 0.310963i$ of defining polynomial
Character	$\chi$	$=$	42.11
Dual form			42.3.h.b.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(2.97112 - 0.415287i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.422792 - 0.244099i) q^{5} +(-3.34521 + 2.60952i) q^{6} +(4.69042 + 5.19615i) q^{7} +2.82843i q^{8} +(8.65507 - 2.46773i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 8 * q - 2 * q^3 + 8 * q^4 - 8 * q^6 - 10 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	−0.457125	−	0.889403i	$-0.651121\pi$
$5$	0.422792	−	0.244099i	0.0845583	−	0.0488198i	0.541683	+	0.840583i	$0.317787\pi$
$6$	−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	−0.234976	−	0.972001i	$-0.575501\pi$
$11$	−13.1367	−	7.58446i	−1.19424	−	0.689496i	−0.959266	+	0.282505i	$0.908835\pi$
$12$	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	0.512384	−	0.858757i	$-0.328763\pi$
$17$	0.422792	+	0.244099i	0.0248701	+	0.0143588i	−0.487513	+	0.873116i	$0.662096\pi$
$18$	−8.85530	+	9.14241i	−0.491961	+	0.507911i
$19$	−6.53562	−	11.3200i	−0.343980	−	0.595791i	0.641188	−	0.767384i	$-0.278442\pi$
$19$	−6.53562	−	11.3200i	−0.343980	−	0.595791i	−0.985168	+	0.171593i	$0.945109\pi$
$20$		−	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	−0.368864	−	0.929483i	$-0.620253\pi$
$23$	5.78819	−	3.34181i	0.251661	−	0.145296i	0.620524	+	0.784187i	$0.286920\pi$
$24$	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	$0.303627\pi$
$29$			47.3084i			1.63132i	−0.578529	+	0.815662i	$0.696373\pi$
$30$	−0.777345	+	1.91984i	−0.0259115	+	0.0639948i
$31$	14.2260	−	24.6402i	0.458904	−	0.794846i	−0.539999	−	0.841666i	$-0.681575\pi$
$31$	14.2260	−	24.6402i	0.458904	−	0.794846i	0.998903	+	0.0468198i	$0.0149087\pi$
$32$	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	0.872703	−	0.488251i	$-0.162365\pi$
$37$	0.500000	+	0.866025i	0.0135135	+	0.0234061i	−0.859190	+	0.511657i	$0.829032\pi$
$38$	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	$-0.887486\pi$
$41$		−	28.3850i		−	0.692318i	0.938176	−	0.346159i	$-0.112514\pi$
$42$	−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	0.366888	−	0.930265i	$-0.380423\pi$
$47$	63.7304	−	36.7947i	1.35597	−	0.782867i	0.989077	+	0.147398i	$0.0470899\pi$
$48$	−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	0.906612	−	0.421966i	$-0.138660\pi$
$53$	52.7077	+	30.4308i	0.994484	+	0.574166i	0.0878725	+	0.996132i	$0.471993\pi$
$54$	−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	−0.482688	−	0.875792i	$-0.660339\pi$
$59$	−87.4669	−	50.4991i	−1.48249	−	0.855916i	−0.999802	+	0.0198761i	$0.993673\pi$
$60$	−0.405485	−	2.90098i	−0.00675808	−	0.0483497i
$61$	17.1192	+	29.6513i	0.280642	+	0.486086i	0.971543	−	0.236863i	$-0.0761193\pi$
$61$	17.1192	+	29.6513i	0.280642	+	0.486086i	−0.690901	+	0.722949i	$0.742786\pi$
$62$			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	−0.203601	−	0.979054i	$-0.565265\pi$
$67$	49.9877	−	86.5812i	0.746085	−	1.29226i	0.949686	−	0.313203i	$-0.101402\pi$
$68$	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	$0.198436\pi$
$71$			82.9000i			1.16761i	−0.811895	+	0.583803i	$0.801564\pi$
$72$	6.97981	+	24.4802i	0.0969418	+	0.340003i
$73$	25.8808	−	44.8269i	0.354532	−	0.614067i	−0.632506	−	0.774556i	$-0.717974\pi$
$73$	25.8808	−	44.8269i	0.354532	−	0.614067i	0.987038	+	0.160488i	$0.0513069\pi$
$74$	−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	0.996172	−	0.0874105i	$-0.0278592\pi$
$79$	33.3685	+	57.7960i	0.422387	+	0.731595i	−0.573786	+	0.819005i	$0.694526\pi$
$80$	−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	$0.179571\pi$
$83$			88.7584i			1.06938i	−0.845049	+	0.534689i	$0.820429\pi$
$84$	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	−0.756990	−	0.653427i	$-0.773331\pi$
$89$	−50.6945	+	29.2685i	−0.569601	+	0.328859i	0.187389	+	0.982286i	$0.439997\pi$
$90$	−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	0.0388437	−	0.999245i	$-0.487633\pi$
$101$	−81.5177	−	47.0643i	−0.807106	−	0.465983i	−0.845950	+	0.533262i	$0.820966\pi$
$102$	−2.05131	+	0.286721i	−0.0201108	+	0.00281099i
$103$	4.74937	+	8.22614i	0.0461103	+	0.0798655i	0.888159	−	0.459535i	$-0.151984\pi$
$103$	4.74937	+	8.22614i	0.0461103	+	0.0798655i	−0.842049	+	0.539401i	$0.818651\pi$
$104$		−	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	−0.631581	−	0.775310i	$-0.717593\pi$
$107$	−29.5248	+	17.0461i	−0.275932	+	0.159310i	0.355648	+	0.934620i	$0.384260\pi$
$108$	5.76556	−	53.6913i	0.0533848	−	0.497142i
$109$	−33.1904	+	57.4875i	−0.304499	+	0.527408i	−0.977150	−	0.212552i	$-0.931822\pi$
$109$	−33.1904	+	57.4875i	−0.304499	+	0.527408i	0.672650	+	0.739960i	$0.265156\pi$
$110$	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	$-0.896659\pi$
$113$		−	72.0901i		−	0.637966i	0.947761	−	0.318983i	$-0.103341\pi$
$114$	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	−0.126272	−	0.991996i	$-0.540301\pi$
$131$	87.7287	−	50.6502i	0.669685	−	0.386643i	0.795957	+	0.605353i	$0.206968\pi$
$132$	−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	0.857412	−	0.514631i	$-0.172071\pi$
$137$	115.140	+	66.4758i	0.840434	+	0.485225i	−0.0169774	+	0.999856i	$0.505404\pi$
$138$	−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	−0.552617	−	0.833435i	$-0.686371\pi$
$149$	−15.9653	+	9.21758i	−0.107150	+	0.0618629i	0.445467	+	0.895298i	$0.353038\pi$
$150$	−14.5426	−	104.043i	−0.0969510	−	0.693623i
$151$	−25.0123	+	43.3226i	−0.165644	+	0.286904i	−0.936884	−	0.349641i	$-0.886304\pi$
$151$	−25.0123	+	43.3226i	−0.165644	+	0.286904i	0.771240	+	0.636545i	$0.219637\pi$
$152$	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	−0.864429	−	0.502756i	$-0.832320\pi$
$157$	0.500000	−	0.866025i	0.00318471	−	0.00551609i	0.867613	+	0.497239i	$0.165653\pi$
$158$	−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	0.631619	−	0.775279i	$-0.282391\pi$
$163$	−57.9631	−	100.395i	−0.355602	−	0.615921i	−0.987221	+	0.159358i	$0.949057\pi$
$164$	−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	$-0.796393\pi$
$167$		−	199.369i		−	1.19383i	0.802305	−	0.596914i	$-0.203607\pi$
$168$	−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	−0.410543	−	0.911841i	$-0.634661\pi$
$173$	30.0784	−	17.3658i	0.173864	−	0.100380i	0.584406	+	0.811461i	$0.301327\pi$
$174$	−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	−0.124195	−	0.992258i	$-0.539635\pi$
$179$	−187.165	−	108.060i	−1.04561	−	0.603685i	−0.921418	+	0.388573i	$0.872968\pi$
$180$	−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	−0.587829	−	0.808985i	$-0.700017\pi$
$191$	−34.5983	+	19.9753i	−0.181143	+	0.104583i	0.406687	+	0.913568i	$0.366684\pi$
$192$	−23.7689	+	3.32230i	−0.123797	+	0.0173036i
$193$	−173.426	+	300.383i	−0.898581	+	1.55639i	−0.0692729	+	0.997598i	$0.522068\pi$
$193$	−173.426	+	300.383i	−0.898581	+	1.55639i	−0.829309	+	0.558791i	$0.811265\pi$
$194$	−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	$-0.924681\pi$
$197$		−	92.3617i		−	0.468841i	0.972135	−	0.234421i	$-0.0753193\pi$
$198$	185.669	−	52.9380i	0.937724	−	0.267364i
$199$	21.6069	−	37.4242i	0.108577	−	0.188061i	−0.806617	−	0.591075i	$-0.798704\pi$
$199$	21.6069	−	37.4242i	0.108577	−	0.188061i	0.915194	+	0.403013i	$0.132037\pi$
$200$	−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	0.490815	−	0.871264i	$-0.336699\pi$
$227$	−4.15727	−	2.40020i	−0.0183140	−	0.0105736i	−0.509129	+	0.860690i	$0.670032\pi$
$228$	−77.6724	+	10.8566i	−0.340668	+	0.0476169i
$229$	−155.903	−	270.032i	−0.680799	−	1.17918i	−0.974737	−	0.223354i	$-0.928300\pi$
$229$	−155.903	−	270.032i	−0.680799	−	1.17918i	0.293939	−	0.955824i	$-0.405034\pi$
$230$			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	−0.708672	−	0.705538i	$-0.750705\pi$
$233$	−105.315	+	60.8034i	−0.451994	+	0.260959i	0.256678	+	0.966497i	$0.417372\pi$
$234$	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	$0.0398590\pi$
$239$			59.6992i			0.249788i	−0.992170	+	0.124894i	$0.960141\pi$
$240$	−5.43014	−	2.19866i	−0.0226256	−	0.00916110i
$241$	98.3575	−	170.360i	0.408122	−	0.706889i	−0.586557	−	0.809908i	$-0.699517\pi$
$241$	98.3575	−	170.360i	0.408122	−	0.706889i	0.994679	+	0.103019i	$0.0328503\pi$
$242$	−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	$-0.819835\pi$
$251$		−	269.204i		−	1.07253i	0.844051	−	0.536264i	$-0.180165\pi$
$252$	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	−0.783081	−	0.621919i	$-0.786353\pi$
$257$	−163.458	+	94.3727i	−0.636024	+	0.367209i	0.147057	+	0.989128i	$0.453020\pi$
$258$	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	0.118161	−	0.992994i	$-0.462300\pi$
$263$	−179.554	−	103.666i	−0.682717	−	0.394167i	−0.800878	+	0.598828i	$0.795633\pi$
$264$	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	0.764708	−	0.644377i	$-0.222883\pi$
$269$	158.445	+	91.4783i	0.589015	+	0.340068i	−0.175693	+	0.984445i	$0.556217\pi$
$270$	−1.99032	+	18.5347i	−0.00737155	+	0.0686469i
$271$	97.5110	+	168.894i	0.359819	+	0.623225i	0.987930	−	0.154898i	$-0.0495050\pi$
$271$	97.5110	+	168.894i	0.359819	+	0.623225i	−0.628111	+	0.778124i	$0.716172\pi$
$272$		−	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	−0.755220	−	0.655472i	$-0.772470\pi$
$277$	52.6425	−	91.1795i	0.190045	−	0.329168i	0.945265	+	0.326304i	$0.105803\pi$
$278$	−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	$-0.682454\pi$
$281$		−	472.177i		−	1.68035i	0.542319	−	0.840173i	$-0.317546\pi$
$282$	−117.175	+	289.392i	−0.415513	+	1.02621i
$283$	−159.725	+	276.651i	−0.564398	+	0.977567i	0.432707	+	0.901535i	$0.357559\pi$
$283$	−159.725	+	276.651i	−0.564398	+	0.977567i	−0.997105	+	0.0760322i	$0.975775\pi$
$284$	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	$0.303267\pi$
$293$			477.594i			1.63001i	−0.579451	+	0.815007i	$0.696733\pi$
$294$	−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	0.743763	−	0.668443i	$-0.233039\pi$
$311$	166.931	+	96.3776i	0.536755	+	0.309896i	−0.207007	+	0.978339i	$0.566372\pi$
$312$	−20.4157	−	146.061i	−0.0654349	−	0.468145i
$313$	270.451	+	468.435i	0.864060	+	1.49660i	0.867977	+	0.496604i	$0.165420\pi$
$313$	270.451	+	468.435i	0.864060	+	1.49660i	−0.00391733	+	0.999992i	$0.501247\pi$
$314$			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	−0.0134949	−	0.999909i	$-0.504296\pi$
$317$	268.088	−	154.781i	0.845704	−	0.488268i	0.859199	+	0.511641i	$0.170962\pi$
$318$	−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	0.999990	+	0.00436394i	$0.00138909\pi$
$331$	166.749	+	288.818i	0.503775	+	0.872563i	−0.496216	+	0.868199i	$0.665278\pi$
$332$	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	0.928268	−	0.371912i	$-0.121298\pi$
$347$	371.400	+	214.428i	1.07032	+	0.617948i	0.142049	+	0.989860i	$0.454631\pi$
$348$	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	0.108296	−	0.994119i	$-0.465461\pi$
$353$	−246.566	−	142.355i	−0.698488	−	0.403272i	−0.806784	+	0.590846i	$0.798794\pi$
$354$	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	−0.913848	−	0.406056i	$-0.866904\pi$
$359$	−365.863	+	211.231i	−1.01912	+	0.588388i	−0.105269	+	0.994444i	$0.533570\pi$
$360$	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	−0.958482	−	0.285154i	$-0.907955\pi$
$367$	−85.2506	+	147.658i	−0.232291	+	0.402339i	0.726191	+	0.687493i	$0.241289\pi$
$368$	−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	0.586481	−	0.809963i	$-0.300513\pi$
$373$	−152.262	−	263.725i	−0.408208	−	0.707037i	−0.994689	+	0.102926i	$0.967180\pi$
$374$	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	−0.899101	−	0.437742i	$-0.855778\pi$
$383$	−371.340	+	214.393i	−0.969555	+	0.559773i	−0.0704548	+	0.997515i	$0.522445\pi$
$384$	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	0.419238	−	0.907876i	$-0.362297\pi$
$389$	−61.2237	−	35.3475i	−0.157387	−	0.0908677i	−0.576625	+	0.817009i	$0.695631\pi$
$390$	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	0.830487	−	0.557038i	$-0.188062\pi$
$397$	−26.6646	−	46.1844i	−0.0671651	−	0.116333i	−0.897652	+	0.440704i	$0.854729\pi$
$398$			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	−0.781313	−	0.624140i	$-0.785449\pi$
$401$	−253.211	+	146.191i	−0.631448	+	0.364567i	0.149865	+	0.988707i	$0.452116\pi$
$402$	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	−0.863220	−	0.504828i	$-0.831556\pi$
$409$	2.28372	−	3.95552i	0.00558367	−	0.00967120i	0.868804	+	0.495157i	$0.164889\pi$
$410$	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	$0.148960\pi$
$419$			378.002i			0.902152i	−0.892486	+	0.451076i	$0.851040\pi$
$420$	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	0.0686212	−	0.997643i	$-0.478140\pi$
$431$	−328.013	−	189.379i	−0.761052	−	0.439394i	−0.829673	+	0.558249i	$0.811473\pi$
$432$	−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	−0.896798	−	0.442440i	$-0.854113\pi$
$439$	−365.056	−	632.296i	−0.831564	−	1.44031i	0.0652343	−	0.997870i	$-0.479221\pi$
$440$		−	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	0.288928	−	0.957351i	$-0.406701\pi$
$443$	559.279	−	322.900i	1.26248	−	0.728894i	0.973554	+	0.228457i	$0.0733680\pi$
$444$	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	$0.274366\pi$
$449$			681.682i			1.51822i	−0.650961	+	0.759112i	$0.725634\pi$
$450$	−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	0.898385	−	0.439210i	$-0.144741\pi$
$457$	31.4533	+	54.4788i	0.0688257	+	0.119210i	−0.829559	+	0.558419i	$0.811408\pi$
$458$	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	$-0.960855\pi$
$461$		−	113.099i		−	0.245333i	0.992448	−	0.122667i	$-0.0391446\pi$
$462$	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	0.0695480	−	0.997579i	$-0.477844\pi$
$467$	452.173	−	261.062i	0.968250	−	0.559020i	0.898702	+	0.438559i	$0.144511\pi$
$468$	−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	−0.305031	−	0.952342i	$-0.598667\pi$
$479$	−614.222	−	354.621i	−1.28230	−	0.740336i	−0.977268	+	0.212006i	$0.932000\pi$
$480$	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	−0.995490	−	0.0948684i	$-0.969757\pi$
$487$	−202.391	+	350.551i	−0.415586	+	0.719817i	0.579903	+	0.814685i	$0.303090\pi$
$488$	−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	$0.0661239\pi$
$491$			202.531i			0.412487i	−0.978501	+	0.206244i	$0.933876\pi$
$492$	−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	0.856262	−	0.516542i	$-0.172781\pi$
$499$	−9.58481	−	16.6014i	−0.0192080	−	0.0332693i	−0.875470	+	0.483273i	$0.839448\pi$
$500$	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	$0.0749695\pi$
$503$			234.752i			0.466704i	−0.972392	+	0.233352i	$0.925031\pi$
$504$	−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	0.256041	−	0.966666i	$-0.417582\pi$
$509$	621.600	−	358.881i	1.22122	−	0.705071i	0.965178	+	0.261595i	$0.0842486\pi$
$510$	−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	0.912828	−	0.408344i	$-0.133894\pi$
$521$	529.130	+	305.494i	1.01561	+	0.586360i	0.102777	+	0.994704i	$0.467227\pi$
$522$	−432.512	−	418.930i	−0.828568	−	0.802548i
$523$	−213.676	−	370.097i	−0.408558	−	0.707642i	0.586171	−	0.810187i	$-0.300635\pi$
$523$	−213.676	−	370.097i	−0.408558	−	0.707642i	−0.994728	+	0.102545i	$0.967301\pi$
$524$		−	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	0.976745	−	0.214402i	$-0.0687804\pi$
$541$	163.758	+	283.637i	0.302695	+	0.524283i	−0.674051	+	0.738685i	$0.735447\pi$
$542$	−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	0.353335	−	0.935497i	$-0.385047\pi$
$557$	−156.050	−	90.0952i	−0.280161	−	0.161751i	−0.633496	+	0.773746i	$0.718381\pi$
$558$	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	0.157904	−	0.987455i	$-0.449526\pi$
$563$	−348.106	−	200.979i	−0.618305	−	0.356979i	−0.776209	+	0.630476i	$0.782860\pi$
$564$	−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	−0.532199	−	0.846619i	$-0.678634\pi$
$569$	−37.0446	+	21.3877i	−0.0651048	+	0.0375883i	0.467094	+	0.884208i	$0.345301\pi$
$570$	26.8131	−	3.74780i	0.0470406	−	0.00657509i
$571$	256.084	−	443.550i	0.448483	−	0.776795i	−0.549805	−	0.835293i	$-0.685298\pi$
$571$	256.084	−	443.550i	0.448483	−	0.776795i	0.998287	+	0.0584985i	$0.0186313\pi$
$572$	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	−0.834349	−	0.551236i	$-0.814156\pi$
$577$	34.7409	−	60.1730i	0.0602095	−	0.104286i	0.894559	+	0.446950i	$0.147490\pi$
$578$	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	$0.128956\pi$
$587$			462.715i			0.788271i	−0.919052	+	0.394136i	$0.871044\pi$
$588$	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	−0.0476289	−	0.998865i	$-0.515166\pi$
$593$	470.604	−	271.704i	0.793599	−	0.458185i	0.841228	+	0.540680i	$0.181833\pi$
$594$	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	0.594475	−	0.804114i	$-0.297360\pi$
$599$	117.002	+	67.5512i	0.195329	+	0.112773i	−0.399146	+	0.916887i	$0.630693\pi$
$600$	−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	0.636973	−	0.770886i	$-0.280186\pi$
$607$	−211.916	−	367.050i	−0.349121	−	0.604695i	−0.986094	+	0.166191i	$0.946853\pi$
$608$		−	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	−0.829298	−	0.558806i	$-0.811260\pi$
$613$	42.4754	−	73.5696i	0.0692910	−	0.120016i	0.898589	+	0.438790i	$0.144593\pi$
$614$	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	$-0.937418\pi$
$617$		−	241.052i		−	0.390684i	0.980735	−	0.195342i	$-0.0625817\pi$
$618$	−37.3539	−	15.1246i	−0.0604432	−	0.0244735i
$619$	−0.872341	+	1.51094i	−0.00140927	+	0.00244094i	−0.866729	−	0.498779i	$-0.833782\pi$
$619$	−0.872341	+	1.51094i	−0.00140927	+	0.00244094i	0.865320	+	0.501220i	$0.167115\pi$
$620$	−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	0.979608	−	0.200920i	$-0.0643933\pi$
$641$	830.357	+	479.407i	1.29541	+	0.747905i	0.315802	+	0.948825i	$0.397727\pi$
$642$	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	0.766166	−	0.642643i	$-0.222162\pi$
$647$	383.479	+	221.402i	0.592703	+	0.342198i	−0.173462	+	0.984841i	$0.555495\pi$
$648$	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	0.203171	−	0.979143i	$-0.434875\pi$
$653$	752.726	−	434.586i	1.15272	−	0.665523i	0.949548	+	0.313620i	$0.101542\pi$
$654$	−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	$-0.763343\pi$
$659$		−	892.094i		−	1.35371i	0.736117	−	0.676854i	$-0.236657\pi$
$660$	−16.6757	+	41.1846i	−0.0252662	+	0.0624010i
$661$	−610.399	+	1057.24i	−0.923448	+	1.59946i	−0.129409	+	0.991591i	$0.541308\pi$
$661$	−610.399	+	1057.24i	−0.923448	+	1.59946i	−0.794038	+	0.607867i	$0.792025\pi$
$662$	−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	−0.868964	−	0.494876i	$-0.835214\pi$
$677$	−592.287	+	341.957i	−0.874870	+	0.505107i	−0.00590674	+	0.999983i	$0.501880\pi$
$678$	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	0.627518	−	0.778602i	$-0.284071\pi$
$683$	182.353	+	105.282i	0.266988	+	0.154146i	−0.360530	+	0.932748i	$0.617404\pi$
$684$	−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	−0.976843	−	0.213956i	$-0.931365\pi$
$691$	−465.536	−	806.331i	−0.673713	−	1.16690i	0.303130	−	0.952949i	$-0.401968\pi$
$692$		−	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	$0.106302\pi$
$701$			459.553i			0.655568i	−0.944753	+	0.327784i	$0.893698\pi$
$702$	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	0.917839	−	0.396953i	$-0.129932\pi$
$709$	81.6400	+	141.405i	0.115148	+	0.199442i	−0.802691	+	0.596395i	$0.796599\pi$
$710$	−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	−0.823767	−	0.566928i	$-0.808132\pi$
$719$	−535.422	+	309.126i	−0.744676	+	0.429939i	0.0790907	+	0.996867i	$0.474798\pi$
$720$	−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	0.926164	+	0.377121i	$0.123086\pi$
$733$	578.834	+	1002.57i	0.789678	+	1.36776i	−0.136486	+	0.990642i	$0.543581\pi$
$734$		−	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	−0.663204	−	0.748438i	$-0.730804\pi$
$739$	233.941	−	405.198i	0.316564	−	0.548306i	0.979769	+	0.200133i	$0.0641373\pi$
$740$	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	$-0.853598\pi$
$743$		−	659.621i		−	0.887780i	0.896081	−	0.443890i	$-0.146402\pi$
$744$	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	0.810707	−	0.585452i	$-0.199083\pi$
$751$	−76.3490	−	132.240i	−0.101663	−	0.176086i	−0.912370	+	0.409367i	$0.865750\pi$
$752$	−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	0.344350	−	0.938841i	$-0.388099\pi$
$761$	1011.81	−	584.172i	1.32959	−	0.767637i	0.985236	+	0.171204i	$0.0547659\pi$
$762$	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	0.960039	+	0.279866i	$0.0902899\pi$
$773$	1300.52	+	750.854i	1.68243	+	0.971351i	0.722390	+	0.691485i	$0.243043\pi$
$774$	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	−0.499080	−	0.866556i	$-0.666329\pi$
$787$	394.224	−	682.815i	0.500919	−	0.867618i	0.999999	−	0.00106186i	$-0.000338000\pi$
$788$	−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	$0.228967\pi$
$797$			1050.25i			1.31775i	−0.752253	+	0.658875i	$0.771033\pi$
$798$	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	0.333690	−	0.942683i	$-0.391706\pi$
$809$	−255.525	−	147.527i	−0.315853	−	0.182358i	−0.649543	+	0.760325i	$0.725040\pi$
$810$	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	0.273539	−	0.961861i	$-0.411806\pi$
$821$	1020.75	−	589.332i	1.24330	−	0.717822i	0.969765	+	0.244039i	$0.0784725\pi$
$822$	−558.636	+	78.0832i	−0.679605	+	0.0949917i
$823$	182.990	−	316.948i	0.222345	−	0.385113i	−0.733174	−	0.680041i	$-0.761962\pi$
$823$	182.990	−	316.948i	0.222345	−	0.385113i	0.955520	+	0.294927i	$0.0952954\pi$
$824$	−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	$0.158757\pi$
$827$			791.154i			0.956655i	−0.878182	+	0.478327i	$0.841243\pi$
$828$	−32.9868	−	115.695i	−0.0398392	−	0.139728i
$829$	−206.615	+	357.868i	−0.249234	+	0.431687i	−0.963314	−	0.268378i	$-0.913512\pi$
$829$	−206.615	+	357.868i	−0.249234	+	0.431687i	0.714079	+	0.700065i	$0.246846\pi$
$830$	−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	$0.316283\pi$
$839$			1406.19i			1.67603i	−0.545650	+	0.838013i	$0.683717\pi$
$840$	−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	−0.197379	−	0.980327i	$-0.563243\pi$
$857$	−981.314	−	566.562i	−1.14506	−	0.661099i	−0.947678	+	0.319228i	$0.896576\pi$
$858$	−1107.80	+	154.842i	−1.29114	+	0.180468i
$859$	−544.103	−	942.414i	−0.633415	−	1.09711i	−0.986849	−	0.161647i	$-0.948319\pi$
$859$	−544.103	−	942.414i	−0.633415	−	1.09711i	0.353434	−	0.935459i	$-0.385014\pi$
$860$			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	0.0329902	−	0.999456i	$-0.489497\pi$
$863$	789.679	−	455.921i	0.915039	−	0.528298i	0.882049	+	0.471157i	$0.156164\pi$
$864$	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	0.996987	+	0.0775680i	$0.0247155\pi$
$877$	496.092	+	859.257i	0.565669	+	0.979768i	−0.431318	+	0.902200i	$0.641951\pi$
$878$	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	$-0.791636\pi$
$881$		−	1072.77i		−	1.21768i	0.793294	−	0.608838i	$-0.208364\pi$
$882$	−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	−0.579507	−	0.814967i	$-0.696755\pi$
$887$	−145.006	+	83.7193i	−0.163479	+	0.0943848i	0.416028	+	0.909352i	$0.363422\pi$
$888$	−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	−0.0140325	+	0.999902i	$0.504467\pi$
$907$	−791.771	+	1371.39i	−0.872956	+	1.51200i	−0.858924	+	0.512103i	$0.828867\pi$
$908$	−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	$0.0661230\pi$
$911$			375.771i			0.412481i	−0.978501	+	0.206241i	$0.933877\pi$
$912$	−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	0.812345	−	0.583177i	$-0.198191\pi$
$919$	−90.8647	−	157.382i	−0.0988735	−	0.171254i	−0.911219	+	0.411923i	$0.864857\pi$
$920$	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	0.507506	−	0.861648i	$-0.330567\pi$
$929$	1400.44	−	808.543i	1.50747	−	0.870337i	0.999962	−	0.00868915i	$-0.00276588\pi$
$930$	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	0.328362	−	0.944552i	$-0.393503\pi$
$941$	−306.260	−	176.819i	−0.325462	−	0.187906i	−0.653825	+	0.756646i	$0.726837\pi$
$942$	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	−0.532034	−	0.846723i	$-0.678572\pi$
$947$	−61.3349	+	35.4117i	−0.0647676	+	0.0373936i	0.467267	+	0.884117i	$0.345239\pi$
$948$	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	$0.0507836\pi$
$953$			302.798i			0.317731i	−0.987300	+	0.158866i	$0.949216\pi$
$954$	−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	−0.958104	−	0.286419i	$-0.907535\pi$
$971$	−1154.63	+	666.624i	−1.18911	+	0.686533i	−0.231006	+	0.972952i	$0.574202\pi$
$972$	−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	0.421369	−	0.906889i	$-0.361550\pi$
$977$	−149.808	−	86.4919i	−0.153335	−	0.0885281i	−0.574704	+	0.818361i	$0.694883\pi$
$978$	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	−0.0553665	−	0.998466i	$-0.517633\pi$
$983$	−931.635	−	537.880i	−0.947747	−	0.547182i	−0.892380	+	0.451284i	$0.850966\pi$
$984$	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	−0.820176	−	0.572112i	$-0.806124\pi$
$991$	84.6069	−	146.543i	0.0853752	−	0.147874i	0.905551	+	0.424237i	$0.139458\pi$
$992$	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	−0.126625	−	0.991951i	$-0.540414\pi$
$997$	793.355	−	1374.13i	0.795742	−	1.37827i	0.922367	−	0.386315i	$-0.126252\pi$
$998$	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.11.2	✓	8
3.2	odd	2	inner	42.3.h.b.11.3	yes	8
4.3	odd	2		336.3.bn.g.305.1		8
7.2	even	3	inner	42.3.h.b.23.3	yes	8
7.3	odd	6		294.3.b.e.197.2		4
7.4	even	3		294.3.b.i.197.1		4
7.5	odd	6		294.3.h.h.275.4		8
7.6	odd	2		294.3.h.h.263.1		8
12.11	even	2		336.3.bn.g.305.3		8
21.2	odd	6	inner	42.3.h.b.23.2	yes	8
21.5	even	6		294.3.h.h.275.1		8
21.11	odd	6		294.3.b.i.197.3		4
21.17	even	6		294.3.b.e.197.4		4
21.20	even	2		294.3.h.h.263.4		8
28.23	odd	6		336.3.bn.g.65.3		8
84.23	even	6		336.3.bn.g.65.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.h.b.11.2	✓	8	1.1	even	1	trivial
42.3.h.b.11.3	yes	8	3.2	odd	2	inner
42.3.h.b.23.2	yes	8	21.2	odd	6	inner
42.3.h.b.23.3	yes	8	7.2	even	3	inner
294.3.b.e.197.2		4	7.3	odd	6
294.3.b.e.197.4		4	21.17	even	6
294.3.b.i.197.1		4	7.4	even	3
294.3.b.i.197.3		4	21.11	odd	6
294.3.h.h.263.1		8	7.6	odd	2
294.3.h.h.263.4		8	21.20	even	2
294.3.h.h.275.1		8	21.5	even	6
294.3.h.h.275.4		8	7.5	odd	6
336.3.bn.g.65.1		8	84.23	even	6
336.3.bn.g.65.3		8	28.23	odd	6
336.3.bn.g.305.1		8	4.3	odd	2
336.3.bn.g.305.3		8	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(2.97112 - 0.415287i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.422792 - 0.244099i) q^{5} +(-3.34521 + 2.60952i) q^{6} +(4.69042 + 5.19615i) q^{7} +2.82843i q^{8} +(8.65507 - 2.46773i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 8 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 8 * q^4 - 8 * q^6 - 10 * q^9	\( 8 q - 2 q^{3} + 8 q^{4} - 8 q^{6} - 10 q^{9} + 16 q^{10} + 4 q^{12} - 64 q^{13} + 28 q^{15} - 16 q^{16} - 40 q^{18} + 4 q^{19} + 26 q^{21} - 16 q^{22} - 8 q^{24} - 24 q^{25} + 160 q^{27} + 72 q^{28} + 52 q^{30} + 20 q^{31} - 106 q^{33} + 32 q^{34} - 40 q^{36} + 4 q^{37} - 72 q^{39} - 32 q^{40} - 88 q^{42} + 208 q^{43} - 58 q^{45} + 56 q^{46} + 16 q^{48} - 40 q^{49} + 14 q^{51} - 64 q^{52} - 32 q^{54} - 472 q^{55} - 268 q^{57} - 80 q^{58} + 28 q^{60} + 212 q^{61} + 178 q^{63} - 64 q^{64} + 224 q^{66} + 156 q^{67} + 164 q^{69} + 56 q^{70} + 80 q^{72} + 132 q^{73} + 164 q^{75} + 16 q^{76} + 240 q^{78} - 52 q^{79} + 98 q^{81} + 48 q^{82} - 124 q^{84} + 152 q^{85} - 260 q^{87} - 16 q^{88} - 256 q^{90} - 352 q^{91} - 210 q^{93} - 360 q^{94} + 16 q^{96} + 576 q^{97} - 140 q^{99}+O(q^{100}) \) 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

Introduction

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