LMFDB - Embedded newform 210.3.o.b.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(31,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("210.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.o (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 $ x^16 + 92x^14 - 112x^13 + 5846x^12 - 7728x^11 + 197216x^10 - 298200x^9 + 4836403x^8 - 6808704x^7 + 64376800x^6 - 91953512x^5 + 595763862x^4 - 630430976x^3 + 1087013404x^2 + 294123256x + 101626561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.5
Root			$-2.10711 - 3.64962i$ of defining polynomial
Character	$\chi$	$=$	210.31
Dual form			210.3.o.b.61.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(-5.26304 - 4.61524i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(-5.26304 - 4.61524i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(5.41099 - 9.37211i) q^{11} +(3.00000 - 1.73205i) q^{12} -19.2715i q^{13} +(1.93096 - 9.70935i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-8.89730 - 5.13686i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-18.0756 + 10.4359i) q^{19} -4.47214i q^{20} +(3.89764 + 11.4808i) q^{21} +15.3046 q^{22} +(-10.5373 - 18.2511i) q^{23} +(4.24264 + 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(23.6026 - 13.6270i) q^{26} -5.19615i q^{27} +(13.2569 - 4.50061i) q^{28} +19.0888 q^{29} +(2.73861 + 4.74342i) q^{30} +(-34.6556 - 20.0084i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-16.2330 + 9.37211i) q^{33} -14.5292i q^{34} +(15.3518 + 3.05312i) q^{35} -6.00000 q^{36} +(25.1827 + 43.6177i) q^{37} +(-25.5627 - 14.7586i) q^{38} +(-16.6896 + 28.9072i) q^{39} +(5.47723 - 3.16228i) q^{40} +22.7706i q^{41} +(-11.3050 + 12.8918i) q^{42} -48.4307 q^{43} +(10.8220 + 18.7442i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(14.9020 - 25.8110i) q^{46} +(57.6236 - 33.2690i) q^{47} +6.92820i q^{48} +(6.39913 + 48.5804i) q^{49} +7.07107 q^{50} +(8.89730 + 15.4106i) q^{51} +(33.3792 + 19.2715i) q^{52} +(-2.47531 + 4.28736i) q^{53} +(6.36396 - 3.67423i) q^{54} +24.1987i q^{55} +(14.8861 + 13.0539i) q^{56} +36.1511 q^{57} +(13.4978 + 23.3789i) q^{58} +(-24.4105 - 14.0934i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(-60.6988 + 35.0445i) q^{61} -56.5924i q^{62} +(4.09619 - 20.5966i) q^{63} +8.00000 q^{64} +(21.5462 + 37.3191i) q^{65} +(-22.9569 - 13.2542i) q^{66} +(-9.65287 + 16.7193i) q^{67} +(17.7946 - 10.2737i) q^{68} +36.5023i q^{69} +(7.11609 + 20.9609i) q^{70} +49.4968 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-115.159 - 66.4872i) q^{73} +(-35.6137 + 61.6848i) q^{74} +(-7.50000 + 4.33013i) q^{75} -41.7437i q^{76} +(-71.7328 + 24.3527i) q^{77} -47.2053 q^{78} +(45.0404 + 78.0122i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-27.8882 + 16.1013i) q^{82} -101.045i q^{83} +(-23.7829 - 4.72987i) q^{84} +22.9727 q^{85} +(-34.2456 - 59.3152i) q^{86} +(-28.6332 - 16.5314i) q^{87} +(-15.3046 + 26.5083i) q^{88} +(34.3077 - 19.8075i) q^{89} -9.48683i q^{90} +(-88.9425 + 101.427i) q^{91} +42.1492 q^{92} +(34.6556 + 60.0253i) q^{93} +(81.4920 + 47.0495i) q^{94} +(23.3355 - 40.4182i) q^{95} +(-8.48528 + 4.89898i) q^{96} +68.6944i q^{97} +(-54.9737 + 42.1888i) q^{98} +32.4659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9	$ 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} + 48 q^{12} + 8 q^{14} - 32 q^{16} + 12 q^{17} - 72 q^{19} - 24 q^{21} - 48 q^{22} - 12 q^{23} + 40 q^{25} + 32 q^{28} + 72 q^{29} + 120 q^{31} + 12 q^{33} - 20 q^{35} - 96 q^{36} + 44 q^{37} - 72 q^{38} + 36 q^{39} - 24 q^{42} - 56 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} - 40 q^{49} - 12 q^{51} - 72 q^{52} + 32 q^{53} + 16 q^{56} + 144 q^{57} - 88 q^{58} + 132 q^{59} + 96 q^{61} + 60 q^{63} + 128 q^{64} + 20 q^{65} + 72 q^{66} - 164 q^{67} - 24 q^{68} - 136 q^{71} - 348 q^{73} - 112 q^{74} - 120 q^{75} + 96 q^{77} + 280 q^{79} - 72 q^{81} + 264 q^{82} - 24 q^{84} + 120 q^{85} - 88 q^{86} - 108 q^{87} + 48 q^{88} - 300 q^{89} - 272 q^{91} + 48 q^{92} - 120 q^{93} + 200 q^{95} + 384 q^{98} - 24 q^{99}+O(q^{100}) $ 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 + 48 * q^12 + 8 * q^14 - 32 * q^16 + 12 * q^17 - 72 * q^19 - 24 * q^21 - 48 * q^22 - 12 * q^23 + 40 * q^25 + 32 * q^28 + 72 * q^29 + 120 * q^31 + 12 * q^33 - 20 * q^35 - 96 * q^36 + 44 * q^37 - 72 * q^38 + 36 * q^39 - 24 * q^42 - 56 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 - 40 * q^49 - 12 * q^51 - 72 * q^52 + 32 * q^53 + 16 * q^56 + 144 * q^57 - 88 * q^58 + 132 * q^59 + 96 * q^61 + 60 * q^63 + 128 * q^64 + 20 * q^65 + 72 * q^66 - 164 * q^67 - 24 * q^68 - 136 * q^71 - 348 * q^73 - 112 * q^74 - 120 * q^75 + 96 * q^77 + 280 * q^79 - 72 * q^81 + 264 * q^82 - 24 * q^84 + 120 * q^85 - 88 * q^86 - 108 * q^87 + 48 * q^88 - 300 * q^89 - 272 * q^91 + 48 * q^92 - 120 * q^93 + 200 * q^95 + 384 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		−	2.44949i		−	0.408248i
$7$	−5.26304	−	4.61524i	−0.751863	−	0.659320i
$7$	−5.26304	−	4.61524i	−0.751863	−	0.659320i
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−2.73861	−	1.58114i	−0.273861	−	0.158114i
$11$	5.41099	−	9.37211i	0.491908	−	0.852010i	−0.508049	−	0.861328i	$-0.669633\pi$
$11$	5.41099	−	9.37211i	0.491908	−	0.852010i	0.999957	+	0.00931868i	$0.00296627\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$		−	19.2715i		−	1.48242i	−0.671273	−	0.741211i	$-0.734252\pi$
$13$		−	19.2715i		−	1.48242i	0.671273	−	0.741211i	$-0.265748\pi$
$14$	1.93096	−	9.70935i	0.137926	−	0.693525i
$15$	3.87298			0.258199
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−8.89730	−	5.13686i	−0.523371	−	0.302168i	0.214942	−	0.976627i	$-0.431044\pi$
$17$	−8.89730	−	5.13686i	−0.523371	−	0.302168i	−0.738313	+	0.674459i	$0.764377\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	−18.0756	+	10.4359i	−0.951346	+	0.549260i	−0.893499	−	0.449066i	$-0.851757\pi$
$19$	−18.0756	+	10.4359i	−0.951346	+	0.549260i	−0.0578471	+	0.998325i	$0.518424\pi$
$20$		−	4.47214i		−	0.223607i
$21$	3.89764	+	11.4808i	0.185602	+	0.546704i
$22$	15.3046			0.695663
$23$	−10.5373	−	18.2511i	−0.458143	−	0.793527i	0.540720	−	0.841203i	$-0.318152\pi$
$23$	−10.5373	−	18.2511i	−0.458143	−	0.793527i	−0.998863	+	0.0476755i	$0.984819\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	23.6026	−	13.6270i	0.907794	−	0.524115i
$27$		−	5.19615i		−	0.192450i
$28$	13.2569	−	4.50061i	0.473460	−	0.160736i
$29$	19.0888			0.658235			0.329118	−	0.944289i	$-0.393249\pi$
$29$	19.0888			0.658235			0.329118	+	0.944289i	$0.393249\pi$
$30$	2.73861	+	4.74342i	0.0912871	+	0.158114i
$31$	−34.6556	−	20.0084i	−1.11792	−	0.645434i	−0.177054	−	0.984201i	$-0.556657\pi$
$31$	−34.6556	−	20.0084i	−1.11792	−	0.645434i	−0.940870	+	0.338768i	$0.889990\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	−16.2330	+	9.37211i	−0.491908	+	0.284003i
$34$		−	14.5292i		−	0.427330i
$35$	15.3518	+	3.05312i	0.438624	+	0.0872319i
$36$	−6.00000			−0.166667
$37$	25.1827	+	43.6177i	0.680614	+	1.17886i	0.974794	+	0.223107i	$0.0716201\pi$
$37$	25.1827	+	43.6177i	0.680614	+	1.17886i	−0.294180	+	0.955750i	$0.595047\pi$
$38$	−25.5627	−	14.7586i	−0.672703	−	0.388385i
$39$	−16.6896	+	28.9072i	−0.427938	+	0.741211i
$40$	5.47723	−	3.16228i	0.136931	−	0.0790569i
$41$			22.7706i			0.555382i	0.960671	+	0.277691i	$0.0895691\pi$
$41$			22.7706i			0.555382i	−0.960671	+	0.277691i	$0.910431\pi$
$42$	−11.3050	+	12.8918i	−0.269166	+	0.306947i
$43$	−48.4307			−1.12629			−0.563147	−	0.826357i	$-0.690410\pi$
$43$	−48.4307			−1.12629			−0.563147	+	0.826357i	$0.690410\pi$
$44$	10.8220	+	18.7442i	0.245954	+	0.426005i
$45$	−5.80948	−	3.35410i	−0.129099	−	0.0745356i
$46$	14.9020	−	25.8110i	0.323956	−	0.561109i
$47$	57.6236	−	33.2690i	1.22603	−	0.707851i	0.259836	−	0.965653i	$-0.416332\pi$
$47$	57.6236	−	33.2690i	1.22603	−	0.707851i	0.966198	+	0.257802i	$0.0829982\pi$
$48$			6.92820i			0.144338i
$49$	6.39913	+	48.5804i	0.130595	+	0.991436i
$50$	7.07107			0.141421
$51$	8.89730	+	15.4106i	0.174457	+	0.302168i
$52$	33.3792	+	19.2715i	0.641907	+	0.370605i
$53$	−2.47531	+	4.28736i	−0.0467040	+	0.0808937i	−0.888432	−	0.459008i	$-0.848205\pi$
$53$	−2.47531	+	4.28736i	−0.0467040	+	0.0808937i	0.841728	+	0.539901i	$0.181538\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$			24.1987i			0.439976i
$56$	14.8861	+	13.0539i	0.265824	+	0.233105i
$57$	36.1511			0.634231
$58$	13.4978	+	23.3789i	0.232721	+	0.403085i
$59$	−24.4105	−	14.0934i	−0.413737	−	0.238871i	0.278657	−	0.960391i	$-0.410111\pi$
$59$	−24.4105	−	14.0934i	−0.413737	−	0.238871i	−0.692394	+	0.721520i	$0.743444\pi$
$60$	−3.87298	+	6.70820i	−0.0645497	+	0.111803i
$61$	−60.6988	+	35.0445i	−0.995062	+	0.574499i	−0.906784	−	0.421596i	$-0.861470\pi$
$61$	−60.6988	+	35.0445i	−0.995062	+	0.574499i	−0.0882785	+	0.996096i	$0.528137\pi$
$62$		−	56.5924i		−	0.912781i
$63$	4.09619	−	20.5966i	0.0650188	−	0.326931i
$64$	8.00000			0.125000
$65$	21.5462	+	37.3191i	0.331479	+	0.574139i
$66$	−22.9569	−	13.2542i	−0.347832	−	0.200821i
$67$	−9.65287	+	16.7193i	−0.144073	+	0.249541i	−0.929027	−	0.370013i	$-0.879353\pi$
$67$	−9.65287	+	16.7193i	−0.144073	+	0.249541i	0.784954	+	0.619554i	$0.212687\pi$
$68$	17.7946	−	10.2737i	0.261685	−	0.151084i
$69$			36.5023i			0.529018i
$70$	7.11609	+	20.9609i	0.101658	+	0.299442i
$71$	49.4968			0.697138			0.348569	−	0.937283i	$-0.386668\pi$
$71$	49.4968			0.697138			0.348569	+	0.937283i	$0.386668\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	−115.159	−	66.4872i	−1.57752	−	0.910783i	−0.995204	−	0.0978221i	$-0.968812\pi$
$73$	−115.159	−	66.4872i	−1.57752	−	0.910783i	−0.582318	−	0.812961i	$-0.697854\pi$
$74$	−35.6137	+	61.6848i	−0.481266	+	0.833578i
$75$	−7.50000	+	4.33013i	−0.100000	+	0.0577350i
$76$		−	41.7437i		−	0.549260i
$77$	−71.7328	+	24.3527i	−0.931594	+	0.316269i
$78$	−47.2053			−0.605196
$79$	45.0404	+	78.0122i	0.570132	+	0.987497i	0.996552	+	0.0829717i	$0.0264411\pi$
$79$	45.0404	+	78.0122i	0.570132	+	0.987497i	−0.426420	+	0.904525i	$0.640226\pi$
$80$	7.74597	+	4.47214i	0.0968246	+	0.0559017i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−27.8882	+	16.1013i	−0.340100	+	0.196357i
$83$		−	101.045i		−	1.21741i	−0.793396	−	0.608706i	$-0.791689\pi$
$83$		−	101.045i		−	1.21741i	0.793396	−	0.608706i	$-0.208311\pi$
$84$	−23.7829	−	4.72987i	−0.283130	−	0.0563080i
$85$	22.9727			0.270267
$86$	−34.2456	−	59.3152i	−0.398205	−	0.689712i
$87$	−28.6332	−	16.5314i	−0.329118	−	0.190016i
$88$	−15.3046	+	26.5083i	−0.173916	+	0.301231i
$89$	34.3077	−	19.8075i	0.385479	−	0.222557i	−0.294720	−	0.955584i	$-0.595226\pi$
$89$	34.3077	−	19.8075i	0.385479	−	0.222557i	0.680200	+	0.733027i	$0.261893\pi$
$90$		−	9.48683i		−	0.105409i
$91$	−88.9425	+	101.427i	−0.977390	+	1.11458i
$92$	42.1492			0.458143
$93$	34.6556	+	60.0253i	0.372641	+	0.645434i
$94$	81.4920	+	47.0495i	0.866937	+	0.500526i
$95$	23.3355	−	40.4182i	0.245636	−	0.425455i
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$			68.6944i			0.708190i	0.935210	+	0.354095i	$0.115211\pi$
$97$			68.6944i			0.708190i	−0.935210	+	0.354095i	$0.884789\pi$
$98$	−54.9737	+	42.1888i	−0.560956	+	0.430498i
$99$	32.4659			0.327939
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−6.96199	−	4.01951i	−0.0689306	−	0.0397971i	0.465139	−	0.885238i	$-0.346004\pi$
$101$	−6.96199	−	4.01951i	−0.0689306	−	0.0397971i	−0.534069	+	0.845441i	$0.679338\pi$
$102$	−12.5827	+	21.7939i	−0.123360	+	0.213665i
$103$	177.158	−	102.282i	1.71998	−	0.993033i	0.801072	−	0.598568i	$-0.204263\pi$
$103$	177.158	−	102.282i	1.71998	−	0.993033i	0.918911	−	0.394465i	$-0.129070\pi$
$104$			54.5080i			0.524115i
$105$	−20.3837	−	17.8747i	−0.194130	−	0.170236i
$106$	−7.00124			−0.0660494
$107$	−82.2769	−	142.508i	−0.768943	−	1.33185i	−0.938136	−	0.346266i	$-0.887449\pi$
$107$	−82.2769	−	142.508i	−0.768943	−	1.33185i	0.169193	−	0.985583i	$-0.445884\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	39.5050	−	68.4247i	0.362432	−	0.627750i	−0.625929	−	0.779880i	$-0.715280\pi$
$109$	39.5050	−	68.4247i	0.362432	−	0.627750i	0.988360	+	0.152130i	$0.0486133\pi$
$110$	−29.6372	+	17.1110i	−0.269429	+	0.155555i
$111$		−	87.2354i		−	0.785905i
$112$	−5.46158	+	27.4622i	−0.0487641	+	0.245198i
$113$	84.5690			0.748398			0.374199	−	0.927348i	$-0.377918\pi$
$113$	84.5690			0.748398			0.374199	+	0.927348i	$0.377918\pi$
$114$	25.5627	+	44.2759i	0.224234	+	0.388385i
$115$	40.8108	+	23.5621i	0.354876	+	0.204888i
$116$	−19.0888	+	33.0628i	−0.164559	+	0.285024i
$117$	50.0688	−	28.9072i	0.427938	−	0.247070i
$118$		−	39.8621i		−	0.337815i
$119$	23.1190	+	68.0987i	0.194277	+	0.572258i
$120$	−10.9545			−0.0912871
$121$	1.94240	+	3.36434i	0.0160529	+	0.0278044i
$122$	−85.8410	−	49.5603i	−0.703615	−	0.406232i
$123$	19.7200	−	34.1560i	0.160325	−	0.277691i
$124$	69.3113	−	40.0169i	0.558962	−	0.322717i
$125$			11.1803i			0.0894427i
$126$	28.1221	−	9.54723i	0.223191	−	0.0757717i
$127$	−101.777			−0.801393			−0.400697	−	0.916211i	$-0.631232\pi$
$127$	−101.777			−0.801393			−0.400697	+	0.916211i	$0.631232\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	72.6460	+	41.9422i	0.563147	+	0.325133i
$130$	−30.4709	+	52.7771i	−0.234391	+	0.405978i
$131$	61.2264	−	35.3491i	0.467377	−	0.269840i	−0.247764	−	0.968820i	$-0.579696\pi$
$131$	61.2264	−	35.3491i	0.467377	−	0.269840i	0.715141	+	0.698980i	$0.246362\pi$
$132$		−	37.4884i		−	0.284003i
$133$	143.297	+	28.4984i	1.07742	+	0.214273i
$134$	−27.3024			−0.203750
$135$	5.80948	+	10.0623i	0.0430331	+	0.0745356i
$136$	25.1654	+	14.5292i	0.185039	+	0.106833i
$137$	58.9138	−	102.042i	0.430027	−	0.744829i	−0.566848	−	0.823823i	$-0.691837\pi$
$137$	58.9138	−	102.042i	0.430027	−	0.744829i	0.996875	+	0.0789932i	$0.0251705\pi$
$138$	−44.7060	+	25.8110i	−0.323956	+	0.187036i
$139$		−	158.507i		−	1.14034i	−0.821528	−	0.570168i	$-0.806878\pi$
$139$		−	158.507i		−	1.14034i	0.821528	−	0.570168i	$-0.193122\pi$
$140$	−20.6400	+	23.5370i	−0.147428	+	0.168122i
$141$	−115.247			−0.817356
$142$	34.9995	+	60.6209i	0.246475	+	0.426908i
$143$	−180.614	−	104.278i	−1.26304	−	0.729215i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$	−36.9653	+	21.3419i	−0.254933	+	0.147186i
$146$		−	188.054i		−	1.28804i
$147$	32.4731	−	78.4123i	0.220906	−	0.533417i
$148$	−100.731			−0.680614
$149$	147.948	+	256.254i	0.992940	+	1.71982i	0.599193	+	0.800604i	$0.295488\pi$
$149$	147.948	+	256.254i	0.992940	+	1.71982i	0.393747	+	0.919219i	$0.371179\pi$
$150$	−10.6066	−	6.12372i	−0.0707107	−	0.0408248i
$151$	62.6478	−	108.509i	0.414886	−	0.718604i	−0.580530	−	0.814239i	$-0.697155\pi$
$151$	62.6478	−	108.509i	0.414886	−	0.718604i	0.995417	+	0.0956344i	$0.0304880\pi$
$152$	51.1254	−	29.5173i	0.336352	−	0.194193i
$153$		−	30.8212i		−	0.201445i
$154$	−80.5486	−	70.6343i	−0.523043	−	0.458665i
$155$	89.4805			0.577293
$156$	−33.3792	−	57.8144i	−0.213969	−	0.370605i
$157$	4.61909	+	2.66684i	0.0294210	+	0.0169862i	0.514638	−	0.857407i	$-0.327926\pi$
$157$	4.61909	+	2.66684i	0.0294210	+	0.0169862i	−0.485217	+	0.874394i	$0.661260\pi$
$158$	−63.6967	+	110.326i	−0.403144	+	0.698266i
$159$	7.42593	−	4.28736i	0.0467040	−	0.0269646i
$160$			12.6491i			0.0790569i
$161$	−28.7752	+	144.689i	−0.178728	+	0.898686i
$162$	−12.7279			−0.0785674
$163$	−119.623	−	207.193i	−0.733883	−	1.27112i	−0.955212	−	0.295923i	$-0.904373\pi$
$163$	−119.623	−	207.193i	−0.733883	−	1.27112i	0.221329	−	0.975199i	$-0.428961\pi$
$164$	−39.4399	−	22.7706i	−0.240487	−	0.138845i
$165$	20.9567	−	36.2980i	0.127010	−	0.219988i
$166$	123.754	−	71.4497i	0.745509	−	0.430420i
$167$			310.440i			1.85892i	0.368918	+	0.929462i	$0.379728\pi$
$167$			310.440i			1.85892i	−0.368918	+	0.929462i	$0.620272\pi$
$168$	−11.0242	−	32.4726i	−0.0656202	−	0.193289i
$169$	−202.390			−1.19757
$170$	16.2442	+	28.1357i	0.0955540	+	0.165504i
$171$	−54.2267	−	31.3078i	−0.317115	−	0.183087i
$172$	48.4307	−	83.8844i	0.281574	−	0.487700i
$173$	78.7285	−	45.4539i	0.455078	−	0.262739i	−0.254894	−	0.966969i	$-0.582041\pi$
$173$	78.7285	−	45.4539i	0.455078	−	0.262739i	0.709972	+	0.704230i	$0.248707\pi$
$174$		−	46.7579i		−	0.268723i
$175$	−33.1422	+	11.2515i	−0.189384	+	0.0642944i
$176$	−43.2879			−0.245954
$177$	24.4105	+	42.2802i	0.137912	+	0.238871i
$178$	48.5184	+	28.0121i	0.272575	+	0.157371i
$179$	121.577	−	210.577i	0.679200	−	1.17641i	−0.296022	−	0.955181i	$-0.595660\pi$
$179$	121.577	−	210.577i	0.679200	−	1.17641i	0.975222	−	0.221228i	$-0.0710066\pi$
$180$	11.6190	−	6.70820i	0.0645497	−	0.0372678i
$181$		−	245.993i		−	1.35907i	−0.733641	−	0.679537i	$-0.762181\pi$
$181$		−	245.993i		−	1.35907i	0.733641	−	0.679537i	$-0.237819\pi$
$182$	−187.113	−	37.2125i	−1.02810	−	0.204464i
$183$	121.398			0.663375
$184$	29.8040	+	51.6220i	0.161978	+	0.280554i
$185$	−97.5322	−	56.3102i	−0.527201	−	0.304380i
$186$	−49.0105	+	84.8886i	−0.263497	+	0.456390i
$187$	−96.2864	+	55.5910i	−0.514901	+	0.297278i
$188$			133.076i			0.707851i
$189$	−23.9815	+	27.3475i	−0.126886	+	0.144696i
$190$	66.0027			0.347382
$191$	20.6108	+	35.6989i	0.107910	+	0.186905i	0.914923	−	0.403628i	$-0.132251\pi$
$191$	20.6108	+	35.6989i	0.107910	+	0.186905i	−0.807014	+	0.590533i	$0.798918\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	94.8727	−	164.324i	0.491568	−	0.851422i	−0.508384	−	0.861130i	$-0.669757\pi$
$193$	94.8727	−	164.324i	0.491568	−	0.851422i	0.999953	+	0.00970872i	$0.00309043\pi$
$194$	−84.1331	+	48.5743i	−0.433676	+	0.250383i
$195$		−	74.6381i		−	0.382760i
$196$	−90.5428	−	37.4967i	−0.461953	−	0.191310i
$197$	−362.318			−1.83918			−0.919589	−	0.392882i	$-0.871478\pi$
$197$	−362.318			−1.83918			−0.919589	+	0.392882i	$0.871478\pi$
$198$	22.9569	+	39.7625i	0.115944	+	0.200821i
$199$	−33.4433	−	19.3085i	−0.168057	−	0.0970278i	0.413612	−	0.910453i	$-0.364267\pi$
$199$	−33.4433	−	19.3085i	−0.168057	−	0.0970278i	−0.581669	+	0.813425i	$0.697600\pi$
$200$	−7.07107	+	12.2474i	−0.0353553	+	0.0612372i
$201$	28.9586	−	16.7193i	0.144073	−	0.0831804i
$202$		−	11.3689i		−	0.0562816i
$203$	−100.465	−	88.0995i	−0.494902	−	0.433987i
$204$	−35.5892			−0.174457
$205$	−25.4584	−	44.0952i	−0.124187	−	0.215098i
$206$	250.540	+	144.649i	1.21621	+	0.702180i
$207$	31.6119	−	54.7534i	0.152714	−	0.264509i
$208$	−66.7584	+	38.5430i	−0.320954	+	0.185303i
$209$			225.875i			1.08074i
$210$	7.47858	−	37.6041i	0.0356123	−	0.179067i
$211$	−136.551			−0.647163			−0.323581	−	0.946200i	$-0.604887\pi$
$211$	−136.551			−0.647163			−0.323581	+	0.946200i	$0.604887\pi$
$212$	−4.95062	−	8.57473i	−0.0233520	−	0.0404468i
$213$	−74.2452	−	42.8655i	−0.348569	−	0.201246i
$214$	116.357	−	201.537i	0.543725	−	0.941760i
$215$	93.7856	−	54.1471i	0.436212	−	0.251847i
$216$			14.6969i			0.0680414i
$217$	90.0502	+	265.249i	0.414978	+	1.22235i
$218$	111.737			0.512556
$219$	115.159	+	199.461i	0.525841	+	0.910783i
$220$	−41.9133	−	24.1987i	−0.190515	−	0.109994i
$221$	−98.9949	+	171.464i	−0.447941	+	0.775856i
$222$	106.841	−	61.6848i	0.481266	−	0.277859i
$223$			154.949i			0.694839i	0.937710	+	0.347419i	$0.112942\pi$
$223$			154.949i			0.694839i	−0.937710	+	0.347419i	$0.887058\pi$
$224$	−37.4961	+	12.7296i	−0.167393	+	0.0568288i
$225$	15.0000			0.0666667
$226$	59.7993	+	103.575i	0.264599	+	0.458299i
$227$	19.3590	+	11.1769i	0.0852818	+	0.0492375i	0.542034	−	0.840356i	$-0.317654\pi$
$227$	19.3590	+	11.1769i	0.0852818	+	0.0492375i	−0.456753	+	0.889594i	$0.650988\pi$
$228$	−36.1511	+	62.6156i	−0.158558	+	0.274630i
$229$	25.9105	−	14.9594i	0.113146	−	0.0653250i	−0.442359	−	0.896838i	$-0.645858\pi$
$229$	25.9105	−	14.9594i	0.113146	−	0.0653250i	0.555505	+	0.831513i	$0.312525\pi$
$230$			66.6437i			0.289755i
$231$	128.689	+	25.5933i	0.557096	+	0.110793i
$232$	−53.9913			−0.232721
$233$	126.541	+	219.176i	0.543095	+	0.940669i	0.998724	+	0.0504987i	$0.0160811\pi$
$233$	126.541	+	219.176i	0.543095	+	0.940669i	−0.455629	+	0.890170i	$0.650586\pi$
$234$	70.8079	+	40.8810i	0.302598	+	0.174705i
$235$	−74.3917	+	128.850i	−0.316561	+	0.548299i
$236$	48.8209	−	28.1868i	0.206868	−	0.119436i
$237$		−	156.024i		−	0.658331i
$238$	−67.0559	+	76.4679i	−0.281747	+	0.321294i
$239$	121.009			0.506315			0.253158	−	0.967425i	$-0.418531\pi$
$239$	121.009			0.506315			0.253158	+	0.967425i	$0.418531\pi$
$240$	−7.74597	−	13.4164i	−0.0322749	−	0.0559017i
$241$	249.755	+	144.196i	1.03633	+	0.598323i	0.918791	−	0.394745i	$-0.129167\pi$
$241$	249.755	+	144.196i	1.03633	+	0.598323i	0.117536	+	0.993069i	$0.462501\pi$
$242$	−2.74697	+	4.75789i	−0.0113511	+	0.0196607i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		−	140.178i		−	0.574499i
$245$	−66.7064	−	86.9210i	−0.272271	−	0.354780i
$246$	55.7765			0.226734
$247$	201.116	+	348.343i	0.814234	+	1.41030i
$248$	98.0209	+	56.5924i	0.395246	+	0.228195i
$249$	−87.5076	+	151.568i	−0.351436	+	0.608706i
$250$	−13.6931	+	7.90569i	−0.0547723	+	0.0316228i
$251$			422.260i			1.68231i	0.540795	+	0.841155i	$0.318124\pi$
$251$			422.260i			1.68231i	−0.540795	+	0.841155i	$0.681876\pi$
$252$	31.5782	+	27.6914i	0.125310	+	0.109887i
$253$	−228.069			−0.901457
$254$	−71.9672	−	124.651i	−0.283335	−	0.490751i
$255$	−34.4591	−	19.8950i	−0.135134	−	0.0780195i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	64.5077	−	37.2435i	0.251003	−	0.144916i	−0.369221	−	0.929342i	$-0.620375\pi$
$257$	64.5077	−	37.2435i	0.251003	−	0.144916i	0.620223	+	0.784425i	$0.287042\pi$
$258$			118.630i			0.459808i
$259$	68.7687	−	345.786i	0.265516	−	1.33508i
$260$	−86.1847			−0.331479
$261$	28.6332	+	49.5942i	0.109706	+	0.190016i
$262$	86.5872	+	49.9911i	0.330486	+	0.190806i
$263$	−156.637	+	271.304i	−0.595579	+	1.03157i	0.397885	+	0.917435i	$0.369744\pi$
$263$	−156.637	+	271.304i	−0.595579	+	1.03157i	−0.993465	+	0.114139i	$0.963589\pi$
$264$	45.9138	−	26.5083i	0.173916	−	0.100410i
$265$		−	11.0699i		−	0.0417733i
$266$	66.4229	+	195.653i	0.249710	+	0.735539i
$267$	−68.6153			−0.256986
$268$	−19.3057	−	33.4385i	−0.0720363	−	0.124771i
$269$	−138.011	−	79.6809i	−0.513053	−	0.296211i	0.221035	−	0.975266i	$-0.429057\pi$
$269$	−138.011	−	79.6809i	−0.513053	−	0.296211i	−0.734088	+	0.679055i	$0.762390\pi$
$270$	−8.21584	+	14.2302i	−0.0304290	+	0.0527046i
$271$	−163.041	+	94.1320i	−0.601629	+	0.347350i	−0.769682	−	0.638427i	$-0.779585\pi$
$271$	−163.041	+	94.1320i	−0.601629	+	0.347350i	0.168053	+	0.985778i	$0.446252\pi$
$272$			41.0949i			0.151084i
$273$	221.252	−	75.1133i	0.810446	−	0.275140i
$274$	166.633			0.608151
$275$	−27.0549	−	46.8605i	−0.0983816	−	0.170402i
$276$	−63.2238	−	36.5023i	−0.229072	−	0.132255i
$277$	−3.52372	+	6.10326i	−0.0127210	+	0.0220334i	−0.872316	−	0.488943i	$-0.837383\pi$
$277$	−3.52372	+	6.10326i	−0.0127210	+	0.0220334i	0.859595	+	0.510976i	$0.170716\pi$
$278$	194.130	−	112.081i	0.698311	−	0.403170i
$279$		−	120.051i		−	0.430289i
$280$	−43.4215	−	8.63552i	−0.155077	−	0.0308411i
$281$	198.386			0.705998			0.352999	−	0.935624i	$-0.385162\pi$
$281$	198.386			0.705998			0.352999	+	0.935624i	$0.385162\pi$
$282$	−81.4920	−	141.148i	−0.288979	−	0.500526i
$283$	−163.790	−	94.5641i	−0.578763	−	0.334149i	0.181879	−	0.983321i	$-0.441782\pi$
$283$	−163.790	−	94.5641i	−0.578763	−	0.334149i	−0.760641	+	0.649172i	$0.775115\pi$
$284$	−49.4968	+	85.7309i	−0.174284	+	0.301869i
$285$	−70.0064	+	40.4182i	−0.245636	+	0.141818i
$286$		−	294.942i		−	1.03127i
$287$	105.092	−	119.843i	0.366174	−	0.417571i
$288$	16.9706			0.0589256
$289$	−91.7253	−	158.873i	−0.317389	−	0.549733i
$290$	−52.2769	−	30.1821i	−0.180265	−	0.104076i
$291$	59.4911	−	103.042i	0.204437	−	0.354095i
$292$	230.318	−	132.974i	0.788761	−	0.455391i
$293$			486.090i			1.65901i	0.558499	+	0.829505i	$0.311378\pi$
$293$			486.090i			1.65901i	−0.558499	+	0.829505i	$0.688622\pi$
$294$	118.997	−	15.6746i	0.404752	−	0.0533150i
$295$	63.0276			0.213653
$296$	−71.2274	−	123.370i	−0.240633	−	0.416789i
$297$	−48.6989	−	28.1163i	−0.163969	−	0.0946678i
$298$	−209.230	+	362.397i	−0.702115	+	1.21610i
$299$	−351.726	+	203.069i	−1.17634	+	0.679161i
$300$		−	17.3205i		−	0.0577350i
$301$	254.892	+	223.519i	0.846818	+	0.742588i
$302$	177.195			0.586738
$303$	6.96199	+	12.0585i	0.0229769	+	0.0397971i
$304$	72.3023	+	41.7437i	0.237836	+	0.137315i
$305$	78.3618	−	135.727i	0.256924	−	0.445005i
$306$	37.7481	−	21.7939i	0.123360	−	0.0712217i
$307$			427.589i			1.39280i	0.717655	+	0.696399i	$0.245216\pi$
$307$			427.589i			1.39280i	−0.717655	+	0.696399i	$0.754784\pi$
$308$	29.5526	−	148.598i	0.0959499	−	0.482460i
$309$	−354.317			−1.14666
$310$	63.2723	+	109.591i	0.204104	+	0.353519i
$311$	−311.852	−	180.048i	−1.00274	−	0.578931i	−0.0936811	−	0.995602i	$-0.529863\pi$
$311$	−311.852	−	180.048i	−1.00274	−	0.578931i	−0.909057	+	0.416671i	$0.863197\pi$
$312$	47.2053	−	81.7620i	0.151299	−	0.262058i
$313$	505.696	−	291.964i	1.61564	−	0.932792i	0.627614	−	0.778525i	$-0.284032\pi$
$313$	505.696	−	291.964i	1.61564	−	0.932792i	0.988029	−	0.154267i	$-0.0493016\pi$
$314$			7.54295i			0.0240221i
$315$	15.0955	+	44.4649i	0.0479222	+	0.141158i
$316$	−180.162			−0.570132
$317$	−180.700	−	312.982i	−0.570032	−	0.987324i	−0.996562	−	0.0828508i	$-0.973597\pi$
$317$	−180.700	−	312.982i	−0.570032	−	0.987324i	0.426530	−	0.904473i	$-0.359736\pi$
$318$	10.5019	+	6.06325i	0.0330247	+	0.0190668i
$319$	103.289	−	178.902i	0.323791	−	0.560823i
$320$	−15.4919	+	8.94427i	−0.0484123	+	0.0279508i
$321$			285.016i			0.887899i
$322$	−197.554	+	67.0680i	−0.613521	+	0.208286i
$323$	214.432			0.663875
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$	−83.4479	−	48.1787i	−0.256763	−	0.148242i
$326$	169.172	−	293.015i	0.518934	−	0.898819i
$327$	−118.515	+	68.4247i	−0.362432	+	0.209250i
$328$		−	64.4051i		−	0.196357i
$329$	−456.819	−	90.8507i	−1.38851	−	0.276142i
$330$	59.2744			0.179619
$331$	−147.993	−	256.331i	−0.447108	−	0.774415i	0.551088	−	0.834447i	$-0.314213\pi$
$331$	−147.993	−	256.331i	−0.447108	−	0.774415i	−0.998196	+	0.0600326i	$0.980880\pi$
$332$	175.015	+	101.045i	0.527154	+	0.304353i
$333$	−75.5481	+	130.853i	−0.226871	+	0.392952i
$334$	−380.210	+	219.514i	−1.13835	+	0.657229i
$335$		−	43.1689i		−	0.128863i
$336$	31.9753	−	36.4634i	0.0951646	−	0.108522i
$337$	−22.0162			−0.0653300			−0.0326650	−	0.999466i	$-0.510399\pi$
$337$	−22.0162			−0.0653300			−0.0326650	+	0.999466i	$0.510399\pi$
$338$	−143.111	−	247.876i	−0.423406	−	0.733361i
$339$	−126.854	−	73.2389i	−0.374199	−	0.216044i
$340$	−22.9727	+	39.7899i	−0.0675669	+	0.117029i
$341$	−375.043	+	216.531i	−1.09983	+	0.634988i
$342$		−	88.5519i		−	0.258924i
$343$	190.531	−	285.214i	0.555484	−	0.831527i
$344$	136.983			0.398205
$345$	−40.8108	−	70.6863i	−0.118292	−	0.204888i
$346$	111.339	+	64.2815i	0.321789	+	0.185785i
$347$	141.953	−	245.870i	0.409086	−	0.708559i	−0.585701	−	0.810527i	$-0.699181\pi$
$347$	141.953	−	245.870i	0.409086	−	0.708559i	0.994788	+	0.101969i	$0.0325141\pi$
$348$	57.2665	−	33.0628i	0.164559	−	0.0950080i
$349$		−	317.175i		−	0.908811i	−0.890795	−	0.454406i	$-0.849852\pi$
$349$		−	317.175i		−	0.908811i	0.890795	−	0.454406i	$-0.150148\pi$
$350$	−37.2153	−	32.6347i	−0.106329	−	0.0932419i
$351$	−100.138			−0.285292
$352$	−30.6092	−	53.0166i	−0.0869579	−	0.150615i
$353$	−101.275	−	58.4712i	−0.286898	−	0.165641i	0.349644	−	0.936883i	$-0.386303\pi$
$353$	−101.275	−	58.4712i	−0.286898	−	0.165641i	−0.636542	+	0.771242i	$0.719636\pi$
$354$	−34.5216	+	59.7932i	−0.0975187	+	0.168907i
$355$	−95.8501	+	55.3391i	−0.270000	+	0.155885i
$356$			79.2302i			0.222557i
$357$	24.2967	−	122.170i	0.0680579	−	0.342212i
$358$	343.871			0.960534
$359$	−116.793	−	202.291i	−0.325329	−	0.563486i	0.656250	−	0.754543i	$-0.272142\pi$
$359$	−116.793	−	202.291i	−0.325329	−	0.563486i	−0.981579	+	0.191058i	$0.938808\pi$
$360$	16.4317	+	9.48683i	0.0456435	+	0.0263523i
$361$	37.3175	−	64.6359i	0.103373	−	0.179047i
$362$	301.278	−	173.943i	0.832260	−	0.480505i
$363$		−	6.72867i		−	0.0185363i
$364$	−86.7334	−	255.479i	−0.238279	−	0.701866i
$365$	297.340			0.814629
$366$	85.8410	+	148.681i	0.234538	+	0.406232i
$367$	443.469	+	256.037i	1.20836	+	0.697648i	0.962401	−	0.271632i	$-0.0875634\pi$
$367$	443.469	+	256.037i	1.20836	+	0.697648i	0.245960	+	0.969280i	$0.420897\pi$
$368$	−42.1492	+	73.0045i	−0.114536	+	0.198382i
$369$	−59.1599	+	34.1560i	−0.160325	+	0.0925636i
$370$		−	159.269i		−	0.430458i
$371$	32.8149	−	11.1404i	0.0884498	−	0.0300280i
$372$	−138.623			−0.372641
$373$	278.204	+	481.863i	0.745854	+	1.29186i	0.949795	+	0.312874i	$0.101292\pi$
$373$	278.204	+	481.863i	0.745854	+	1.29186i	−0.203941	+	0.978983i	$0.565375\pi$
$374$	−136.170	−	78.6175i	−0.364090	−	0.210207i
$375$	9.68246	−	16.7705i	0.0258199	−	0.0447214i
$376$	−162.984	+	94.0989i	−0.433468	+	0.250263i
$377$		−	367.870i		−	0.975782i
$378$	−50.4512	−	10.0336i	−0.133469	−	0.0265438i
$379$	−536.301			−1.41504			−0.707521	−	0.706692i	$-0.750187\pi$
$379$	−536.301			−1.41504			−0.707521	+	0.706692i	$0.750187\pi$
$380$	46.6709	+	80.8364i	0.122818	+	0.212727i
$381$	152.665	+	88.1414i	0.400697	+	0.231342i
$382$	−29.1480	+	50.4859i	−0.0763038	+	0.132162i
$383$	25.4184	−	14.6753i	0.0663666	−	0.0383168i	−0.466450	−	0.884548i	$-0.654467\pi$
$383$	25.4184	−	14.6753i	0.0663666	−	0.0383168i	0.532816	+	0.846231i	$0.321134\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	111.683	−	127.359i	0.290085	−	0.330801i
$386$	268.341			0.695183
$387$	−72.6460	−	125.827i	−0.187716	−	0.325133i
$388$	−118.982	−	68.6944i	−0.306655	−	0.177047i
$389$	349.242	−	604.905i	0.897795	−	1.55503i	0.0674875	−	0.997720i	$-0.478502\pi$
$389$	349.242	−	604.905i	0.897795	−	1.55503i	0.830307	−	0.557306i	$-0.188165\pi$
$390$	91.4126	−	52.7771i	0.234391	−	0.135326i
$391$			216.514i			0.553745i
$392$	−18.0995	−	137.406i	−0.0461721	−	0.350526i
$393$	−122.453			−0.311585
$394$	−256.198	−	443.747i	−0.650248	−	1.12626i
$395$	−174.441	−	100.713i	−0.441622	−	0.254971i
$396$	−32.4659	+	56.2326i	−0.0819847	+	0.142002i
$397$	−177.270	+	102.347i	−0.446525	+	0.257801i	−0.706361	−	0.707851i	$-0.749665\pi$
$397$	−177.270	+	102.347i	−0.446525	+	0.257801i	0.259837	+	0.965653i	$0.416331\pi$
$398$		−	54.6127i		−	0.137218i
$399$	−190.265	−	166.846i	−0.476854	−	0.418161i
$400$	−20.0000			−0.0500000
$401$	−214.984	−	372.363i	−0.536119	−	0.928585i	−0.999108	−	0.0422215i	$-0.986556\pi$
$401$	−214.984	−	372.363i	−0.536119	−	0.928585i	0.462989	−	0.886364i	$-0.346777\pi$
$402$	40.9537	+	23.6446i	0.101875	+	0.0588174i
$403$	−385.592	+	667.865i	−0.956805	+	1.65723i
$404$	13.9240	−	8.03902i	0.0344653	−	0.0198986i
$405$		−	20.1246i		−	0.0496904i
$406$	36.8598	−	185.340i	0.0907876	−	0.456502i
$407$	545.053			1.33920
$408$	−25.1654	−	43.5877i	−0.0616798	−	0.106833i
$409$	15.3567	+	8.86618i	0.0375469	+	0.0216777i	0.518656	−	0.854983i	$-0.326433\pi$
$409$	15.3567	+	8.86618i	0.0375469	+	0.0216777i	−0.481109	+	0.876661i	$0.659766\pi$
$410$	36.0035	−	62.3600i	0.0878135	−	0.152097i
$411$	−176.741	+	102.042i	−0.430027	+	0.248276i
$412$			409.129i			0.993033i
$413$	63.4289	+	186.834i	0.153581	+	0.452383i
$414$	89.4119			0.215971
$415$	112.972	+	195.673i	0.272221	+	0.471501i
$416$	−94.4106	−	54.5080i	−0.226948	−	0.131029i
$417$	−137.271	+	237.760i	−0.329187	+	0.570168i
$418$	−276.639	+	159.718i	−0.661816	+	0.382100i
$419$		−	440.768i		−	1.05195i	−0.850499	−	0.525977i	$-0.823700\pi$
$419$		−	440.768i		−	1.05195i	0.850499	−	0.525977i	$-0.176300\pi$
$420$	51.3436	−	17.4308i	0.122247	−	0.0415019i
$421$	−143.012			−0.339696			−0.169848	−	0.985470i	$-0.554328\pi$
$421$	−143.012			−0.339696			−0.169848	+	0.985470i	$0.554328\pi$
$422$	−96.5564	−	167.241i	−0.228807	−	0.396305i
$423$	172.871	+	99.8070i	0.408678	+	0.235950i
$424$	7.00124	−	12.1265i	0.0165123	−	0.0286002i
$425$	−44.4865	+	25.6843i	−0.104674	+	0.0604336i
$426$		−	121.242i		−	0.284605i
$427$	481.199	+	95.6991i	1.12693	+	0.224120i
$428$	329.108			0.768943
$429$	180.614	+	312.833i	0.421012	+	0.729215i
$430$	132.633	+	76.5756i	0.308448	+	0.178083i
$431$	391.608	−	678.285i	0.908604	−	1.57375i	0.0925988	−	0.995704i	$-0.470483\pi$
$431$	391.608	−	678.285i	0.908604	−	1.57375i	0.816005	−	0.578045i	$-0.196184\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$		−	286.669i		−	0.662053i	−0.943622	−	0.331026i	$-0.892605\pi$
$433$		−	286.669i		−	0.662053i	0.943622	−	0.331026i	$-0.107395\pi$
$434$	−261.188	+	297.848i	−0.601815	+	0.686286i
$435$	73.9307			0.169956
$436$	79.0101	+	136.849i	0.181216	+	0.313875i
$437$	380.935	+	219.933i	0.871705	+	0.503279i
$438$	−162.860	+	282.081i	−0.371826	+	0.644021i
$439$	−295.016	+	170.328i	−0.672018	+	0.387990i	−0.796841	−	0.604189i	$-0.793497\pi$
$439$	−295.016	+	170.328i	−0.672018	+	0.387990i	0.124823	+	0.992179i	$0.460164\pi$
$440$		−	68.4442i		−	0.155555i
$441$	−116.617	+	89.4960i	−0.264437	+	0.202939i
$442$	−280.000			−0.633484
$443$	−197.629	−	342.304i	−0.446116	−	0.772696i	0.552013	−	0.833835i	$-0.313860\pi$
$443$	−197.629	−	342.304i	−0.446116	−	0.772696i	−0.998129	+	0.0611396i	$0.980527\pi$
$444$	151.096	+	87.2354i	0.340307	+	0.196476i
$445$	−44.2910	+	76.7143i	−0.0995304	+	0.172392i
$446$	−189.773	+	109.566i	−0.425500	+	0.245663i
$447$		−	512.507i		−	1.14655i
$448$	−42.1043	−	36.9219i	−0.0939828	−	0.0824150i
$449$	665.078			1.48124			0.740621	−	0.671923i	$-0.234531\pi$
$449$	665.078			1.48124			0.740621	+	0.671923i	$0.234531\pi$
$450$	10.6066	+	18.3712i	0.0235702	+	0.0408248i
$451$	213.409	+	123.212i	0.473190	+	0.273197i
$452$	−84.5690	+	146.478i	−0.187100	+	0.324066i
$453$	−187.944	+	108.509i	−0.414886	+	0.239535i
$454$			31.6131i			0.0696323i
$455$	58.8381	−	295.852i	0.129314	−	0.650225i
$456$	−102.251			−0.224234
$457$	−255.468	−	442.484i	−0.559012	−	0.968236i	−0.997579	−	0.0695382i	$-0.977847\pi$
$457$	−255.468	−	442.484i	−0.559012	−	0.968236i	0.438568	−	0.898698i	$-0.355486\pi$
$458$	36.6429	+	21.1558i	0.0800064	+	0.0461917i
$459$	−26.6919	+	46.2317i	−0.0581523	+	0.100723i
$460$	−81.6215	+	47.1242i	−0.177438	+	0.102444i
$461$			174.303i			0.378097i	0.981968	+	0.189049i	$0.0605404\pi$
$461$			174.303i			0.378097i	−0.981968	+	0.189049i	$0.939460\pi$
$462$	59.6518	+	175.709i	0.129116	+	0.380322i
$463$	755.187			1.63107			0.815537	−	0.578705i	$-0.196442\pi$
$463$	755.187			1.63107			0.815537	+	0.578705i	$0.196442\pi$
$464$	−38.1776	−	66.1256i	−0.0822794	−	0.142512i
$465$	−134.221	−	77.4924i	−0.288647	−	0.166650i
$466$	−178.956	+	309.961i	−0.384026	+	0.665153i
$467$	−490.666	+	283.286i	−1.05068	+	0.606609i	−0.922839	−	0.385186i	$-0.874137\pi$
$467$	−490.666	+	283.286i	−1.05068	+	0.606609i	−0.127839	+	0.991795i	$0.540804\pi$
$468$			115.629i			0.247070i
$469$	127.967	−	43.4438i	0.272850	−	0.0926307i
$470$	−210.412			−0.447684
$471$	−4.61909	−	8.00051i	−0.00980699	−	0.0169862i
$472$	69.0432	+	39.8621i	0.146278	+	0.0844537i
$473$	−262.058	+	453.897i	−0.554033	+	0.959614i
$474$	191.090	−	110.326i	0.403144	−	0.232755i
$475$			104.359i			0.219704i
$476$	−141.069	−	28.0554i	−0.296364	−	0.0589399i
$477$	−14.8519			−0.0311360
$478$	85.5665	+	148.206i	0.179009	+	0.310053i
$479$	445.286	+	257.086i	0.929615	+	0.536714i	0.886690	−	0.462365i	$-0.152999\pi$
$479$	445.286	+	257.086i	0.929615	+	0.536714i	0.0429255	+	0.999078i	$0.486332\pi$
$480$	10.9545	−	18.9737i	0.0228218	−	0.0395285i
$481$	840.578	−	485.308i	1.74756	−	1.00896i
$482$			407.848i			0.846157i
$483$	168.467	−	192.113i	0.348792	−	0.397749i
$484$	−7.76960			−0.0160529
$485$	−76.8027	−	133.026i	−0.158356	−	0.274281i
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	−163.663	+	283.473i	−0.336064	+	0.582081i	−0.983689	−	0.179879i	$-0.942429\pi$
$487$	−163.663	+	283.473i	−0.336064	+	0.582081i	0.647624	+	0.761960i	$0.275763\pi$
$488$	171.682	−	99.1207i	0.351808	−	0.203116i
$489$			414.386i			0.847415i
$490$	59.2875	−	143.161i	0.120995	−	0.292165i
$491$	−41.8889			−0.0853134			−0.0426567	−	0.999090i	$-0.513582\pi$
$491$	−41.8889			−0.0853134			−0.0426567	+	0.999090i	$0.513582\pi$
$492$	39.4399	+	68.3119i	0.0801624	+	0.138845i
$493$	−169.839	−	98.0566i	−0.344501	−	0.198898i
$494$	−284.421	+	492.631i	−0.575751	+	0.997229i
$495$	−62.8700	+	36.2980i	−0.127010	+	0.0733293i
$496$			160.068i			0.322717i
$497$	−260.503	−	228.439i	−0.524152	−	0.459637i
$498$	−247.509			−0.497006
$499$	−207.685	−	359.721i	−0.416203	−	0.720885i	0.579351	−	0.815078i	$-0.303306\pi$
$499$	−207.685	−	359.721i	−0.416203	−	0.720885i	−0.995554	+	0.0941936i	$0.969973\pi$
$500$	−19.3649	−	11.1803i	−0.0387298	−	0.0223607i
$501$	268.849	−	465.660i	0.536625	−	0.929462i
$502$	−517.160	+	298.583i	−1.03020	+	0.594786i
$503$			51.7604i			0.102903i	0.998675	+	0.0514517i	$0.0163848\pi$
$503$			51.7604i			0.102903i	−0.998675	+	0.0514517i	$0.983615\pi$
$504$	−11.5858	+	58.2561i	−0.0229876	+	0.115587i
$505$	17.9758			0.0355956
$506$	−161.269	−	279.326i	−0.318713	−	0.552028i
$507$	303.585	+	175.275i	0.598786	+	0.345709i
$508$	101.777	−	176.283i	0.200348	−	0.347014i
$509$	136.916	−	79.0486i	0.268991	−	0.155302i	−0.359438	−	0.933169i	$-0.617032\pi$
$509$	136.916	−	79.0486i	0.268991	−	0.155302i	0.628429	+	0.777867i	$0.283698\pi$
$510$		−	56.2715i		−	0.110336i
$511$	299.233	+	881.411i	0.585583	+	1.72488i
$512$	−22.6274			−0.0441942
$513$	54.2267	+	93.9234i	0.105705	+	0.183087i
$514$	91.2276	+	52.6703i	0.177486	+	0.102471i
$515$	−228.710	+	396.138i	−0.444098	+	0.769200i
$516$	−145.292	+	83.8844i	−0.281574	+	0.162567i
$517$		−	720.073i		−	1.39279i
$518$	472.126	−	160.283i	0.911441	−	0.309428i
$519$	−157.457			−0.303385
$520$	−60.9418	−	105.554i	−0.117196	−	0.202989i
$521$	306.214	+	176.793i	0.587744	+	0.339334i	0.764205	−	0.644974i	$-0.223132\pi$
$521$	306.214	+	176.793i	0.587744	+	0.339334i	−0.176461	+	0.984308i	$0.556465\pi$
$522$	−40.4935	+	70.1368i	−0.0775737	+	0.134362i
$523$	−103.534	+	59.7756i	−0.197962	+	0.114294i	−0.595705	−	0.803204i	$-0.703127\pi$
$523$	−103.534	+	59.7756i	−0.197962	+	0.114294i	0.397742	+	0.917497i	$0.369794\pi$
$524$			141.396i			0.269840i
$525$	59.4574	+	11.8247i	0.113252	+	0.0225232i
$526$	−443.037			−0.842277
$527$	205.561	+	356.042i	0.390059	+	0.675602i
$528$	64.9319	+	37.4884i	0.122977	+	0.0710008i
$529$	42.4308	−	73.4924i	0.0802095	−	0.138927i
$530$	13.5578	−	7.82762i	0.0255808	−	0.0147691i
$531$		−	84.5604i		−	0.159247i
$532$	−192.657	+	219.699i	−0.362138	+	0.412968i
$533$	438.824			0.823309
$534$	−48.5184	−	84.0363i	−0.0908584	−	0.157371i
$535$	318.657	+	183.977i	0.595621	+	0.343882i
$536$	27.3024	−	47.2892i	0.0509374	−	0.0882261i
$537$	−364.731	+	210.577i	−0.679200	+	0.392136i
$538$		−	225.372i		−	0.418906i
$539$	489.926	+	202.894i	0.908954	+	0.376427i
$540$	−23.2379			−0.0430331
$541$	−272.691	−	472.315i	−0.504051	−	0.873041i	−0.999989	−	0.00468349i	$-0.998509\pi$
$541$	−272.691	−	472.315i	−0.504051	−	0.873041i	0.495938	−	0.868358i	$-0.334824\pi$
$542$	−230.575	−	133.123i	−0.425416	−	0.245614i
$543$	−213.036	+	368.989i	−0.392331	+	0.679537i
$544$	−50.3307	+	29.0585i	−0.0925197	+	0.0534163i
$545$			176.672i			0.324169i
$546$	248.443	+	217.864i	0.455024	+	0.399018i
$547$	−117.783			−0.215325			−0.107663	−	0.994188i	$-0.534337\pi$
$547$	−117.783			−0.215325			−0.107663	+	0.994188i	$0.534337\pi$
$548$	117.828	+	204.083i	0.215014	+	0.372415i
$549$	−182.096	−	105.133i	−0.331687	−	0.191500i
$550$	38.2615	−	66.2708i	0.0695663	−	0.120492i
$551$	−345.041	+	199.210i	−0.626209	+	0.361542i
$552$		−	103.244i		−	0.187036i
$553$	122.996	−	618.454i	0.222416	−	1.11836i
$554$	−9.96659			−0.0179902
$555$	97.5322	+	168.931i	0.175734	+	0.304380i
$556$	274.542	+	158.507i	0.493780	+	0.285084i
$557$	307.744	−	533.028i	0.552503	−	0.956963i	−0.445590	−	0.895237i	$-0.647006\pi$
$557$	307.744	−	533.028i	0.552503	−	0.956963i	0.998093	−	0.0617258i	$-0.0196604\pi$
$558$	147.031	−	84.8886i	0.263497	−	0.152130i
$559$			933.330i			1.66964i
$560$	−20.1273	−	59.2865i	−0.0359417	−	0.105869i
$561$	192.573			0.343267
$562$	140.280	+	242.972i	0.249608	+	0.432334i
$563$	−415.047	−	239.628i	−0.737207	−	0.425626i	0.0838462	−	0.996479i	$-0.473280\pi$
$563$	−415.047	−	239.628i	−0.737207	−	0.425626i	−0.821053	+	0.570852i	$0.806613\pi$
$564$	115.247	−	199.614i	0.204339	−	0.353925i
$565$	−163.767	+	94.5510i	−0.289853	+	0.167347i
$566$		−	267.468i		−	0.472558i
$567$	59.6559	−	20.2527i	0.105213	−	0.0357191i
$568$	−139.998			−0.246475
$569$	228.674	+	396.074i	0.401887	+	0.696088i	0.993954	−	0.109800i	$-0.0350212\pi$
$569$	228.674	+	396.074i	0.401887	+	0.696088i	−0.592067	+	0.805889i	$0.701688\pi$
$570$	−99.0040	−	57.1600i	−0.173691	−	0.100281i
$571$	−186.601	+	323.203i	−0.326797	+	0.566029i	−0.981874	−	0.189532i	$-0.939303\pi$
$571$	−186.601	+	323.203i	−0.326797	+	0.566029i	0.655077	+	0.755562i	$0.272636\pi$
$572$	361.229	−	208.555i	0.631519	−	0.364607i
$573$		−	71.3978i		−	0.124604i
$574$	221.088	+	43.9692i	0.385171	+	0.0766014i
$575$	−105.373			−0.183257
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−772.108	−	445.777i	−1.33814	−	0.772577i	−0.351611	−	0.936146i	$-0.614366\pi$
$577$	−772.108	−	445.777i	−1.33814	−	0.772577i	−0.986532	+	0.163569i	$0.947699\pi$
$578$	129.719	−	224.680i	0.224428	−	0.388720i
$579$	−284.618	+	164.324i	−0.491568	+	0.283807i
$580$		−	85.3678i		−	0.147186i
$581$	−466.347	+	531.804i	−0.802663	+	0.915326i
$582$	168.266			0.289117
$583$	26.7878	+	46.3978i	0.0459481	+	0.0795845i
$584$	325.719	+	188.054i	0.557738	+	0.322010i
$585$	−64.6385	+	111.957i	−0.110493	+	0.191380i
$586$	−595.336	+	343.718i	−1.01593	+	0.586549i
$587$			786.758i			1.34030i	0.742224	+	0.670151i	$0.233771\pi$
$587$			786.758i			1.34030i	−0.742224	+	0.670151i	$0.766229\pi$
$588$	103.341	+	134.657i	0.175750	+	0.229009i
$589$	835.227			1.41804
$590$	44.5672	+	77.1927i	0.0755377	+	0.130835i
$591$	543.477	+	313.777i	0.919589	+	0.530925i
$592$	100.731	−	174.471i	0.170153	−	0.294714i
$593$	−541.571	+	312.676i	−0.913273	+	0.527278i	−0.881483	−	0.472216i	$-0.843454\pi$
$593$	−541.571	+	312.676i	−0.913273	+	0.527278i	−0.0317903	+	0.999495i	$0.510121\pi$
$594$		−	79.5250i		−	0.133880i
$595$	−120.906	−	106.025i	−0.203204	−	0.178193i
$596$	−591.792			−0.992940
$597$	33.4433	+	57.9256i	0.0560190	+	0.0970278i
$598$	−497.416	−	287.183i	−0.831799	−	0.480240i
$599$	−75.2476	+	130.333i	−0.125622	+	0.217584i	−0.921976	−	0.387247i	$-0.873426\pi$
$599$	−75.2476	+	130.333i	−0.125622	+	0.217584i	0.796354	+	0.604831i	$0.206759\pi$
$600$	21.2132	−	12.2474i	0.0353553	−	0.0204124i
$601$		−	521.601i		−	0.867888i	−0.900940	−	0.433944i	$-0.857122\pi$
$601$		−	521.601i		−	0.867888i	0.900940	−	0.433944i	$-0.142878\pi$
$602$	−93.5177	+	470.230i	−0.155345	+	0.781113i
$603$	−57.9172			−0.0960485
$604$	125.296	+	217.019i	0.207443	+	0.359302i
$605$	−7.52288	−	4.34334i	−0.0124345	−	0.00717907i
$606$	−9.84575	+	17.0533i	−0.0162471	+	0.0281408i
$607$	−603.404	+	348.375i	−0.994075	+	0.573930i	−0.906490	−	0.422228i	$-0.861248\pi$
$607$	−603.404	+	348.375i	−0.994075	+	0.573930i	−0.0875852	+	0.996157i	$0.527915\pi$
$608$			118.069i			0.194193i
$609$	74.4014	+	219.155i	0.122170	+	0.359860i
$610$	221.641			0.363345
$611$	−641.143	−	1110.49i	−1.04933	−	1.81750i
$612$	53.3838	+	30.8212i	0.0872285	+	0.0503614i
$613$	−27.1244	+	46.9809i	−0.0442487	+	0.0766410i	−0.887302	−	0.461190i	$-0.847423\pi$
$613$	−27.1244	+	46.9809i	−0.0442487	+	0.0766410i	0.843053	+	0.537831i	$0.180756\pi$
$614$	−523.687	+	302.351i	−0.852911	+	0.492428i
$615$			88.1903i			0.143399i
$616$	202.891	−	68.8800i	0.329368	−	0.111818i
$617$	−969.852			−1.57188			−0.785941	−	0.618301i	$-0.787821\pi$
$617$	−969.852			−1.57188			−0.785941	+	0.618301i	$0.787821\pi$
$618$	−250.540	−	433.947i	−0.405404	−	0.702180i
$619$	−111.240	−	64.2247i	−0.179710	−	0.103756i	0.407446	−	0.913229i	$-0.366419\pi$
$619$	−111.240	−	64.2247i	−0.179710	−	0.103756i	−0.587156	+	0.809474i	$0.699753\pi$
$620$	−89.4805	+	154.985i	−0.144323	+	0.249975i
$621$	−94.8357	+	54.7534i	−0.152714	+	0.0881697i
$622$		−	509.252i		−	0.818733i
$623$	−271.979	−	54.0903i	−0.436564	−	0.0868223i
$624$	133.517			0.213969
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	715.163	+	412.899i	1.14243	+	0.659584i
$627$	195.613	−	338.812i	0.311983	−	0.540371i
$628$	−9.23819	+	5.33367i	−0.0147105	+	0.00849311i
$629$		−	517.440i		−	0.822639i
$630$	−43.7840	+	49.9296i	−0.0694984	+	0.0792533i
$631$	115.457			0.182975			0.0914877	−	0.995806i	$-0.470838\pi$
$631$	115.457			0.182975			0.0914877	+	0.995806i	$0.470838\pi$
$632$	−127.393	−	220.652i	−0.201572	−	0.349133i
$633$	204.827	+	118.257i	0.323581	+	0.186820i
$634$	255.549	−	442.623i	0.403073	−	0.698144i
$635$	197.090	−	113.790i	0.310378	−	0.179197i
$636$			17.1495i			0.0269646i
$637$	936.215	−	123.321i	1.46973	−	0.193596i
$638$	292.146			0.457910
$639$	74.2452	+	128.596i	0.116190	+	0.201246i
$640$	−21.9089	−	12.6491i	−0.0342327	−	0.0197642i
$641$	476.249	−	824.887i	0.742978	−	1.28688i	−0.208156	−	0.978096i	$-0.566746\pi$
$641$	476.249	−	824.887i	0.742978	−	1.28688i	0.951134	−	0.308780i	$-0.0999206\pi$
$642$	−349.072	+	201.537i	−0.543725	+	0.313920i
$643$			253.254i			0.393863i	0.980417	+	0.196931i	$0.0630976\pi$
$643$			253.254i			0.393863i	−0.980417	+	0.196931i	$0.936902\pi$
$644$	−221.833	−	194.529i	−0.344461	−	0.302063i
$645$	−187.571			−0.290808
$646$	151.626	+	262.624i	0.234715	+	0.406539i
$647$	870.161	+	502.388i	1.34492	+	0.776488i	0.987524	−	0.157466i	$-0.0503324\pi$
$647$	870.161	+	502.388i	1.34492	+	0.776488i	0.357393	+	0.933954i	$0.383666\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	−264.170	+	152.518i	−0.407041	+	0.235005i
$650$		−	136.270i		−	0.209646i
$651$	94.6373	−	475.860i	0.145372	−	0.730967i
$652$	478.492			0.733883
$653$	−532.797	−	922.831i	−0.815922	−	1.41322i	−0.908664	−	0.417528i	$-0.862897\pi$
$653$	−532.797	−	922.831i	−0.815922	−	1.41322i	0.0927422	−	0.995690i	$-0.470437\pi$
$654$	−167.606	−	96.7672i	−0.256278	−	0.147962i
$655$	−79.0429	+	136.906i	−0.120676	+	0.209017i
$656$	78.8798	−	45.5413i	0.120244	−	0.0694227i
$657$		−	398.923i		−	0.607189i
$658$	−211.751	−	623.728i	−0.321810	−	0.947915i
$659$	432.265			0.655941			0.327970	−	0.944688i	$-0.393635\pi$
$659$	432.265			0.655941			0.327970	+	0.944688i	$0.393635\pi$
$660$	41.9133	+	72.5960i	0.0635051	+	0.109994i
$661$	327.626	+	189.155i	0.495652	+	0.286165i	0.726916	−	0.686726i	$-0.240953\pi$
$661$	327.626	+	189.155i	0.495652	+	0.286165i	−0.231264	+	0.972891i	$0.574286\pi$
$662$	209.294	−	362.507i	0.316153	−	0.547594i
$663$	296.985	−	171.464i	0.447941	−	0.258619i
$664$			285.799i			0.430420i
$665$	−309.355	+	105.024i	−0.465196	+	0.157931i
$666$	−213.682			−0.320844
$667$	−201.144	−	348.392i	−0.301566	−	0.522328i
$668$	−537.698	−	310.440i	−0.804937	−	0.464731i
$669$	134.190	−	232.424i	0.200583	−	0.347419i
$670$	52.8709	−	30.5251i	0.0789119	−	0.0455598i
$671$			758.501i			1.13040i
$672$	67.2683	+	13.3781i	0.100102	+	0.0199079i
$673$	−689.666			−1.02476			−0.512382	−	0.858758i	$-0.671237\pi$
$673$	−689.666			−1.02476			−0.512382	+	0.858758i	$0.671237\pi$
$674$	−15.5678	−	26.9642i	−0.0230976	−	0.0400063i
$675$	−22.5000	−	12.9904i	−0.0333333	−	0.0192450i
$676$	202.390	−	350.549i	0.299393	−	0.518564i
$677$	328.663	−	189.754i	0.485470	−	0.280286i	−0.237223	−	0.971455i	$-0.576237\pi$
$677$	328.663	−	189.754i	0.485470	−	0.280286i	0.722693	+	0.691169i	$0.242904\pi$
$678$		−	207.151i		−	0.305532i
$679$	317.041	−	361.541i	0.466924	−	0.532461i
$680$	−64.9767			−0.0955540
$681$	−19.3590	−	33.5307i	−0.0284273	−	0.0492375i
$682$	−530.390	−	306.221i	−0.777698	−	0.449004i
$683$	−373.753	+	647.360i	−0.547223	+	0.947818i	0.451240	+	0.892403i	$0.350982\pi$
$683$	−373.753	+	647.360i	−0.547223	+	0.947818i	−0.998463	+	0.0554159i	$0.982352\pi$
$684$	108.453	−	62.6156i	0.158558	−	0.0915433i
$685$			263.470i			0.384628i
$686$	484.040	+	31.6754i	0.705598	+	0.0461740i
$687$	−51.8209			−0.0754308
$688$	96.8613	+	167.769i	0.140787	+	0.243850i
$689$	82.6238	+	47.7029i	0.119918	+	0.0692350i
$690$	57.7151	−	99.9656i	0.0836451	−	0.144878i
$691$	771.026	−	445.152i	1.11581	−	0.644214i	0.175483	−	0.984482i	$-0.443851\pi$
$691$	771.026	−	445.152i	1.11581	−	0.644214i	0.940328	+	0.340268i	$0.110518\pi$
$692$			181.816i			0.262739i
$693$	−170.869	−	149.838i	−0.246565	−	0.216217i
$694$	401.504			0.578536
$695$	177.216	+	306.947i	0.254987	+	0.441650i
$696$	80.9870	+	46.7579i	0.116361	+	0.0671808i
$697$	116.970	−	202.597i	0.167819	−	0.290670i
$698$	388.459	−	224.277i	0.556531	−	0.321313i
$699$		−	438.352i		−	0.627112i
$700$	13.6540	−	68.6554i	0.0195057	−	0.0980792i
$701$	−650.703			−0.928250			−0.464125	−	0.885770i	$-0.653631\pi$
$701$	−650.703			−0.928250			−0.464125	+	0.885770i	$0.653631\pi$
$702$	−70.8079	−	122.643i	−0.100866	−	0.174705i
$703$	−910.384	−	525.610i	−1.29500	−	0.747667i
$704$	43.2879	−	74.9769i	0.0614885	−	0.106501i
$705$	223.175	−	128.850i	0.316561	−	0.182766i
$706$		−	165.382i		−	0.234251i
$707$	18.0902	+	53.2861i	0.0255873	+	0.0753693i
$708$	−97.6419			−0.137912
$709$	196.427	+	340.222i	0.277048	+	0.479862i	0.970650	−	0.240497i	$-0.0773105\pi$
$709$	196.427	+	340.222i	0.277048	+	0.479862i	−0.693602	+	0.720359i	$0.743977\pi$
$710$	−135.553	−	78.2613i	−0.190919	−	0.110227i
$711$	−135.121	+	234.037i	−0.190044	+	0.329166i
$712$	−97.0368	+	56.0242i	−0.136288	+	0.0786857i
$713$			843.339i			1.18280i
$714$	166.807	−	56.6298i	0.233623	−	0.0793134i
$715$	466.344			0.652230
$716$	243.154	+	421.155i	0.339600	+	0.588205i
$717$	−181.514	−	104.797i	−0.253158	−	0.146161i
$718$	165.170	−	286.083i	0.230042	−	0.398444i
$719$	899.919	−	519.569i	1.25163	−	0.722627i	0.280194	−	0.959943i	$-0.409601\pi$
$719$	899.919	−	519.569i	1.25163	−	0.722627i	0.971432	+	0.237317i	$0.0762679\pi$
$720$			26.8328i			0.0372678i
$721$	−1404.45	−	279.312i	−1.94792	−	0.387395i
$722$	105.550			0.146191
$723$	−249.755	−	432.588i	−0.345442	−	0.598323i
$724$	426.072	+	245.993i	0.588497	+	0.339769i
$725$	47.7220	−	82.6570i	0.0658235	−	0.114010i
$726$	8.24091	−	4.75789i	0.0113511	−	0.00655357i
$727$		−	610.568i		−	0.839846i	−0.907560	−	0.419923i	$-0.862057\pi$
$727$		−	610.568i		−	0.839846i	0.907560	−	0.419923i	$-0.137943\pi$
$728$	251.567	−	286.877i	0.345559	−	0.394062i
$729$	−27.0000			−0.0370370
$730$	210.251	+	364.165i	0.288015	+	0.498856i
$731$	430.902	+	248.781i	0.589469	+	0.340330i
$732$	−121.398	+	210.267i	−0.165844	+	0.287250i
$733$	934.574	−	539.576i	1.27500	−	0.736121i	0.299074	−	0.954230i	$-0.403322\pi$
$733$	934.574	−	539.576i	1.27500	−	0.736121i	0.975924	+	0.218109i	$0.0699889\pi$
$734$			724.181i			0.986623i
$735$	24.7837	+	188.151i	0.0337194	+	0.255988i
$736$	−119.216			−0.161978
$737$	104.463	+	180.935i	0.141741	+	0.245503i
$738$	−83.6647	−	48.3038i	−0.113367	−	0.0654523i
$739$	−378.082	+	654.857i	−0.511613	+	0.886139i	0.488297	+	0.872678i	$0.337618\pi$
$739$	−378.082	+	654.857i	−0.511613	+	0.886139i	−0.999909	+	0.0134615i	$0.995715\pi$
$740$	195.064	−	112.620i	0.263601	−	0.152190i
$741$		−	696.686i		−	0.940197i
$742$	36.8478	+	32.3124i	0.0496601	+	0.0435477i
$743$	963.993			1.29743			0.648717	−	0.761030i	$-0.275306\pi$
$743$	963.993			1.29743			0.648717	+	0.761030i	$0.275306\pi$
$744$	−98.0209	−	169.777i	−0.131749	−	0.228195i
$745$	−573.001	−	330.822i	−0.769128	−	0.444056i
$746$	−393.439	+	681.457i	−0.527398	+	0.913481i
$747$	262.523	−	151.568i	0.351436	−	0.202902i
$748$		−	222.364i		−	0.297278i
$749$	−224.681	+	1129.75i	−0.299975	+	1.50835i
$750$	27.3861			0.0365148
$751$	−416.806	−	721.929i	−0.555001	−	0.961290i	−0.997903	−	0.0647203i	$-0.979384\pi$
$751$	−416.806	−	721.929i	−0.555001	−	0.961290i	0.442902	−	0.896570i	$-0.353949\pi$
$752$	−230.494	−	133.076i	−0.306508	−	0.176963i
$753$	365.688	−	633.389i	0.485641	−	0.841155i
$754$	450.547	−	260.123i	0.597542	−	0.344991i
$755$			280.170i			0.371086i
$756$	−23.3859	−	68.8847i	−0.0309337	−	0.0911173i
$757$	−744.966			−0.984103			−0.492051	−	0.870566i	$-0.663753\pi$
$757$	−744.966			−0.984103			−0.492051	+	0.870566i	$0.663753\pi$
$758$	−379.222	−	656.832i	−0.500293	−	0.866533i
$759$	342.103	+	197.513i	0.450729	+	0.260228i
$760$	−66.0027	+	114.320i	−0.0868456	+	0.150421i
$761$	−64.1518	+	37.0381i	−0.0842993	+	0.0486702i	−0.541557	−	0.840664i	$-0.682165\pi$
$761$	−64.1518	+	37.0381i	−0.0842993	+	0.0486702i	0.457258	+	0.889334i	$0.348832\pi$
$762$			249.302i			0.327167i
$763$	−523.713	+	177.797i	−0.686387	+	0.233023i
$764$	−82.4431			−0.107910
$765$	34.4591	+	59.6849i	0.0450446	+	0.0780195i
$766$	35.9471	+	20.7540i	0.0469283	+	0.0270941i
$767$	−271.601	+	470.426i	−0.354108	+	0.613332i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$			961.553i			1.25039i	0.780467	+	0.625197i	$0.214981\pi$
$769$			961.553i			1.25039i	−0.780467	+	0.625197i	$0.785019\pi$
$770$	234.953	+	46.7267i	0.305134	+	0.0606840i
$771$	−129.015			−0.167335
$772$	189.745	+	328.649i	0.245784	+	0.425711i
$773$	−1191.17	−	687.723i	−1.54097	−	0.889680i	−0.998778	−	0.0494271i	$-0.984260\pi$
$773$	−1191.17	−	687.723i	−1.54097	−	0.889680i	−0.542194	−	0.840253i	$-0.682406\pi$
$774$	102.737	−	177.946i	0.132735	−	0.229904i
$775$	−173.278	+	100.042i	−0.223585	+	0.129087i
$776$		−	194.297i		−	0.250383i
$777$	−402.612	+	459.123i	−0.518163	+	0.590892i
$778$	987.806			1.26967
$779$	−237.633	−	411.592i	−0.305049	−	0.528360i
$780$	129.277	+	74.6381i	0.165740	+	0.0956899i
$781$	267.826	−	463.889i	0.342928	−	0.593968i
$782$	−265.175	+	153.099i	−0.339098	+	0.195779i
$783$		−	99.1884i		−	0.126677i
$784$	155.489	−	119.328i	0.198328	−	0.152204i
$785$	−11.9264			−0.0151929
$786$	−86.5872	−	149.973i	−0.110162	−	0.190806i
$787$	329.679	+	190.340i	0.418906	+	0.241856i	0.694609	−	0.719387i	$-0.255577\pi$
$787$	329.679	+	190.340i	0.418906	+	0.241856i	−0.275703	+	0.961243i	$0.588911\pi$
$788$	362.318	−	627.553i	0.459795	−	0.796387i
$789$	469.912	−	271.304i	0.595579	−	0.343858i
$790$		−	284.860i		−	0.360583i
$791$	−445.090	−	390.306i	−0.562693	−	0.493434i
$792$	−91.8275			−0.115944
$793$	675.358	+	1169.76i	0.851650	+	1.47510i
$794$	−250.698	−	144.741i	−0.315741	−	0.182293i
$795$	−9.58684	+	16.6049i	−0.0120589	+	0.0208867i
$796$	66.8867	−	38.6170i	0.0840285	−	0.0485139i
$797$		−	511.440i		−	0.641706i	−0.947129	−	0.320853i	$-0.896030\pi$
$797$		−	511.440i		−	0.641706i	0.947129	−	0.320853i	$-0.103970\pi$
$798$	69.8064	−	351.004i	0.0874768	−	0.439855i
$799$	−683.593			−0.855560
$800$	−14.1421	−	24.4949i	−0.0176777	−	0.0306186i
$801$	102.923	+	59.4226i	0.128493	+	0.0741856i
$802$	304.033	−	526.600i	0.379093	−	0.656609i
$803$	−1246.25	+	719.522i	−1.55199	+	0.896043i
$804$			66.8770i			0.0831804i
$805$	−106.044	−	312.360i	−0.131731	−	0.388024i
$806$	−1090.62			−1.35313
$807$	138.011	+	239.043i	0.171018	+	0.296211i
$808$	19.6915	+	11.3689i	0.0243707	+	0.0140704i
$809$	−579.187	+	1003.18i	−0.715930	+	1.24003i	0.246670	+	0.969099i	$0.420664\pi$
$809$	−579.187	+	1003.18i	−0.715930	+	1.24003i	−0.962600	+	0.270927i	$0.912670\pi$
$810$	24.6475	−	14.2302i	0.0304290	−	0.0175682i
$811$			92.0692i			0.113526i	0.998388	+	0.0567628i	$0.0180779\pi$
$811$			92.0692i			0.113526i	−0.998388	+	0.0567628i	$0.981922\pi$
$812$	253.058	−	85.9113i	0.311648	−	0.105802i
$813$	326.083			0.401086
$814$	385.411	+	667.551i	0.473478	+	0.820088i
$815$	463.298	+	267.485i	0.568463	+	0.328202i
$816$	35.5892	−	61.6423i	0.0436142	−	0.0755421i
$817$	875.412	−	505.419i	1.07150	−	0.618628i
$818$			25.0774i			0.0306569i
$819$	−396.928	−	78.9396i	−0.484649	−	0.0963853i
$820$	101.833			0.124187
$821$	493.467	+	854.711i	0.601057	+	1.04106i	0.992661	+	0.120927i	$0.0385867\pi$
$821$	493.467	+	854.711i	0.601057	+	1.04106i	−0.391605	+	0.920134i	$0.628080\pi$
$822$	−249.950	−	144.309i	−0.304075	−	0.175558i
$823$	−277.748	+	481.074i	−0.337483	+	0.584537i	−0.983959	−	0.178397i	$-0.942909\pi$
$823$	−277.748	+	481.074i	−0.337483	+	0.584537i	0.646476	+	0.762935i	$0.276242\pi$
$824$	−501.079	+	289.298i	−0.608106	+	0.351090i
$825$			93.7211i			0.113601i
$826$	−183.973	+	209.796i	−0.222728	+	0.253990i
$827$	−1323.46			−1.60032			−0.800160	−	0.599787i	$-0.795252\pi$
$827$	−1323.46			−1.60032			−0.800160	+	0.599787i	$0.795252\pi$
$828$	63.2238	+	109.507i	0.0763572	+	0.132255i
$829$	911.903	+	526.488i	1.10000	+	0.635088i	0.936222	−	0.351409i	$-0.114297\pi$
$829$	911.903	+	526.488i	1.10000	+	0.635088i	0.163782	+	0.986497i	$0.447631\pi$
$830$	−159.766	+	276.723i	−0.192490	+	0.333402i
$831$	10.5712	−	6.10326i	0.0127210	−	0.00734448i
$832$		−	154.172i		−	0.185303i
$833$	192.615	−	465.106i	0.231231	−	0.558350i
$834$	−388.261			−0.465540
$835$	−347.083	−	601.165i	−0.415668	−	0.719958i
$836$	−391.227	−	225.875i	−0.467975	−	0.270185i
$837$	−103.967	+	180.076i	−0.124214	+	0.215145i
$838$	539.829	−	311.670i	0.644187	−	0.371922i
$839$		−	1254.98i		−	1.49580i	−0.663810	−	0.747901i	$-0.731062\pi$
$839$		−	1254.98i		−	1.49580i	0.663810	−	0.747901i	$-0.268938\pi$
$840$	57.6537	+	50.5574i	0.0686353	+	0.0601874i
$841$	−476.617			−0.566727
$842$	−101.125	−	175.153i	−0.120101	−	0.208020i
$843$	−297.578	−	171.807i	−0.352999	−	0.203804i
$844$	136.551	−	236.514i	0.161791	−	0.280230i
$845$	391.926	−	226.279i	0.463818	−	0.267785i
$846$			282.297i			0.333684i
$847$	5.30429	−	26.6713i	0.00626244	−	0.0314891i
$848$	19.8025			0.0233520
$849$	163.790	+	283.692i	0.192921	+	0.334149i
$850$	−62.9134	−	36.3231i	−0.0740158	−	0.0427330i
$851$	530.715	−	919.226i	0.623637	−	1.08017i
$852$	148.490	−	85.7309i	0.174284	−	0.100623i
$853$			454.825i			0.533207i	0.963806	+	0.266603i	$0.0859014\pi$
$853$			454.825i			0.533207i	−0.963806	+	0.266603i	$0.914099\pi$
$854$	223.052	+	657.015i	0.261185	+	0.769338i
$855$	140.013			0.163758
$856$	232.714	+	403.073i	0.271863	+	0.470880i
$857$	−146.132	−	84.3691i	−0.170515	−	0.0984470i	0.412314	−	0.911042i	$-0.364721\pi$
$857$	−146.132	−	84.3691i	−0.170515	−	0.0984470i	−0.582829	+	0.812595i	$0.698054\pi$
$858$	−255.427	+	442.413i	−0.297701	+	0.515633i
$859$	−707.715	+	408.599i	−0.823882	+	0.475669i	−0.851753	−	0.523943i	$-0.824461\pi$
$859$	−707.715	+	408.599i	−0.823882	+	0.475669i	0.0278711	+	0.999612i	$0.491127\pi$
$860$			216.588i			0.251847i
$861$	−261.425	+	88.7518i	−0.303629	+	0.103080i
$862$	1107.64			1.28496
$863$	616.950	+	1068.59i	0.714890	+	1.23823i	0.963002	+	0.269495i	$0.0868567\pi$
$863$	616.950	+	1068.59i	0.714890	+	1.23823i	−0.248112	+	0.968731i	$0.579810\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$	−101.638	+	176.042i	−0.117501	+	0.203517i
$866$	351.096	−	202.705i	0.405423	−	0.234071i
$867$			317.746i			0.366489i
$868$	−549.475	−	109.278i	−0.633036	−	0.125896i
$869$	974.852			1.12181
$870$	52.2769	+	90.5462i	0.0600884	+	0.104076i
$871$	322.205	+	186.025i	0.369925	+	0.213576i
$872$	−111.737	+	193.534i	−0.128139	+	0.221943i
$873$	−178.473	+	103.042i	−0.204437	+	0.118032i
$874$			622.065i			0.711744i
$875$	51.5999	−	58.8426i	0.0589714	−	0.0672486i
$876$	−460.637			−0.525841
$877$	−37.4779	−	64.9136i	−0.0427342	−	0.0740177i	0.843867	−	0.536552i	$-0.180274\pi$
$877$	−37.4779	−	64.9136i	−0.0427342	−	0.0740177i	−0.886601	+	0.462534i	$0.846940\pi$
$878$	−417.216	−	240.880i	−0.475189	−	0.274350i
$879$	420.966	−	729.135i	0.478915	−	0.829505i
$880$	83.8267	−	48.3974i	0.0952576	−	0.0549970i
$881$		−	461.343i		−	0.523658i	−0.965114	−	0.261829i	$-0.915674\pi$
$881$		−	461.343i		−	0.523658i	0.965114	−	0.261829i	$-0.0843257\pi$
$882$	−192.070	−	79.5426i	−0.217767	−	0.0901843i
$883$	237.840			0.269354			0.134677	−	0.990890i	$-0.457000\pi$
$883$	237.840			0.269354			0.134677	+	0.990890i	$0.457000\pi$
$884$	−197.990	−	342.928i	−0.223970	−	0.387928i
$885$	−94.5414	−	54.5835i	−0.106826	−	0.0616762i
$886$	279.490	−	484.091i	0.315452	−	0.546379i
$887$	7.89260	−	4.55679i	0.00889808	−	0.00513731i	−0.495544	−	0.868583i	$-0.665031\pi$
$887$	7.89260	−	4.55679i	0.00889808	−	0.00513731i	0.504442	+	0.863445i	$0.331698\pi$
$888$			246.739i			0.277859i
$889$	535.656	+	469.725i	0.602538	+	0.528375i
$890$	−125.274			−0.140757
$891$	48.6989	+	84.3490i	0.0546565	+	0.0946678i
$892$	−268.380	−	154.949i	−0.300874	−	0.173710i
$893$	−694.386	+	1202.71i	−0.777588	+	1.34682i
$894$	627.691	−	362.397i	0.702115	−	0.405366i
$895$			543.708i			0.607495i
$896$	15.4477	−	77.6748i	0.0172407	−	0.0866906i
$897$	703.452			0.784228
$898$	470.281	+	814.551i	0.523698	+	0.907072i
$899$	−661.535	−	381.938i	−0.735857	−	0.424847i
$900$	−15.0000	+	25.9808i	−0.0166667	+	0.0288675i
$901$	44.0472	−	25.4306i	0.0488870	−	0.0282249i
$902$			348.495i			0.386358i
$903$	−188.765	−	556.022i	−0.209042	−	0.615750i
$904$	−239.197			−0.264599
$905$	275.028	+	476.362i	0.303898	+	0.526367i
$906$	−265.792	−	153.455i	−0.293369	−	0.169377i
$907$	−420.352	+	728.070i	−0.463453	+	0.802723i	−0.999130	−	0.0416991i	$-0.986723\pi$
$907$	−420.352	+	728.070i	−0.463453	+	0.802723i	0.535678	+	0.844423i	$0.320056\pi$
$908$	−38.7179	+	22.3538i	−0.0426409	+	0.0246187i
$909$		−	24.1171i		−	0.0265314i
$910$	403.948	−	137.138i	0.443899	−	0.150701i
$911$	−35.4735			−0.0389390			−0.0194695	−	0.999810i	$-0.506198\pi$
$911$	−35.4735			−0.0389390			−0.0194695	+	0.999810i	$0.506198\pi$
$912$	−72.3023	−	125.231i	−0.0792788	−	0.137315i
$913$	−947.006	−	546.754i	−1.03725	−	0.598854i
$914$	361.287	−	625.767i	0.395281	−	0.684646i
$915$	−235.085	+	135.727i	−0.256924	+	0.148335i
$916$			59.8377i			0.0653250i
$917$	−485.381	−	96.5310i	−0.529314	−	0.105268i
$918$	−75.4961			−0.0822398
$919$	−215.680	−	373.569i	−0.234690	−	0.406495i	0.724493	−	0.689282i	$-0.242074\pi$
$919$	−215.680	−	373.569i	−0.234690	−	0.406495i	−0.959182	+	0.282788i	$0.908741\pi$
$920$	−115.430	−	66.6437i	−0.125468	−	0.0724388i
$921$	370.303	−	641.384i	0.402066	−	0.696399i
$922$	−213.477	+	123.251i	−0.231536	+	0.133678i
$923$		−	953.876i		−	1.03345i
$924$	−173.018	+	197.303i	−0.187249	+	0.213531i
$925$	251.827			0.272245
$926$	533.998	+	924.911i	0.576671	+	0.998824i
$927$	531.475	+	306.847i	0.573328	+	0.331011i
$928$	53.9913	−	93.5157i	0.0581803	−	0.100771i
$929$	531.053	−	306.603i	0.571639	−	0.330036i	−0.186165	−	0.982519i	$-0.559606\pi$
$929$	531.053	−	306.603i	0.571639	−	0.330036i	0.757804	+	0.652483i	$0.226272\pi$
$930$		−	219.182i		−	0.235679i
$931$	−622.649	−	811.337i	−0.668796	−	0.871468i
$932$	−506.165			−0.543095
$933$	311.852	+	540.143i	0.334246	+	0.578931i
$934$	−693.907	−	400.627i	−0.742941	−	0.428937i
$935$	124.305	−	215.303i	0.132947	−	0.230271i
$936$	−141.616	+	81.7620i	−0.151299	+	0.0873525i
$937$		−	1360.68i		−	1.45216i	−0.687609	−	0.726081i	$-0.741340\pi$
$937$		−	1360.68i		−	1.45216i	0.687609	−	0.726081i	$-0.258660\pi$
$938$	143.694	+	126.007i	0.153192	+	0.134336i
$939$	−1011.39			−1.07710
$940$	−148.783	−	257.700i	−0.158280	−	0.274149i
$941$	−146.671	−	84.6806i	−0.155867	−	0.0899900i	0.420038	−	0.907507i	$-0.362017\pi$
$941$	−146.671	−	84.6806i	−0.155867	−	0.0899900i	−0.575905	+	0.817517i	$0.695350\pi$
$942$	6.53239	−	11.3144i	0.00693459	−	0.0120111i
$943$	415.590	−	239.941i	0.440710	−	0.254444i
$944$			112.747i			0.119436i
$945$	15.8645	−	79.7704i	0.0167878	−	0.0844131i
$946$	−741.211			−0.783521
$947$	639.583	+	1107.79i	0.675378	+	1.16979i	0.976358	+	0.216158i	$0.0693527\pi$
$947$	639.583	+	1107.79i	0.675378	+	1.16979i	−0.300981	+	0.953630i	$0.597314\pi$
$948$	270.242	+	156.024i	0.285066	+	0.164583i
$949$	−1281.31	+	2219.29i	−1.35016	+	2.33855i
$950$	−127.814	+	73.7932i	−0.134541	+	0.0776771i
$951$			625.964i			0.658216i
$952$	−65.3904	−	192.612i	−0.0686874	−	0.202324i
$953$	−1.43779			−0.00150870			−0.000754349	−	1.00000i	$-0.500240\pi$
$953$	−1.43779			−0.00150870			−0.000754349		1.00000i	$0.500240\pi$
$954$	−10.5019	−	18.1897i	−0.0110082	−	0.0190668i
$955$	−79.8252	−	46.0871i	−0.0835866	−	0.0482587i
$956$	−121.009	+	209.594i	−0.126579	+	0.219241i
$957$	−309.868	+	178.902i	−0.323791	+	0.186941i
$958$			727.149i			0.759028i
$959$	−781.012	+	265.148i	−0.814402	+	0.276484i
$960$	30.9839			0.0322749
$961$	320.176	+	554.560i	0.333169	+	0.577066i
$962$	1188.76	+	686.329i	1.23571	+	0.713440i
$963$	246.831	−	427.524i	0.256314	−	0.443950i
$964$	−499.509	+	288.392i	−0.518163	+	0.299162i
$965$			424.284i			0.439672i
$966$	354.413	+	70.4844i	0.366887	+	0.0729653i
$967$	486.815			0.503428			0.251714	−	0.967802i	$-0.419006\pi$
$967$	486.815			0.503428			0.251714	+	0.967802i	$0.419006\pi$
$968$	−5.49394	−	9.51578i	−0.00567556	−	0.00983035i
$969$	−321.648	−	185.703i	−0.331938	−	0.191644i
$970$	108.615	−	188.127i	0.111975	−	0.193946i
$971$	378.215	−	218.362i	0.389511	−	0.224884i	−0.292437	−	0.956285i	$-0.594466\pi$
$971$	378.215	−	218.362i	0.389511	−	0.224884i	0.681948	+	0.731401i	$0.261133\pi$
$972$			31.1769i			0.0320750i
$973$	−731.547	+	834.227i	−0.751847	+	0.857376i
$974$	−462.910			−0.475267
$975$	83.4479	+	144.536i	0.0855876	+	0.148242i
$976$	242.795	+	140.178i	0.248766	+	0.143625i
$977$	−127.517	+	220.866i	−0.130519	+	0.226066i	−0.923877	−	0.382690i	$-0.874998\pi$
$977$	−127.517	+	220.866i	−0.130519	+	0.226066i	0.793358	+	0.608756i	$0.208331\pi$
$978$	−507.517	+	293.015i	−0.518934	+	0.299606i
$979$		−	428.714i		−	0.437910i
$980$	217.258	−	28.6178i	0.221692	−	0.0292018i
$981$	237.030			0.241621
$982$	−29.6199	−	51.3032i	−0.0301628	−	0.0522436i
$983$	1195.88	+	690.443i	1.21656	+	0.702383i	0.964181	−	0.265244i	$-0.0854525\pi$
$983$	1195.88	+	690.443i	1.21656	+	0.702383i	0.252383	+	0.967628i	$0.418786\pi$
$984$	−55.7765	+	96.6077i	−0.0566834	+	0.0981785i
$985$	701.626	−	405.084i	0.712311	−	0.411253i
$986$		−	277.346i		−	0.281284i
$987$	606.550	+	531.893i	0.614539	+	0.538899i
$988$	−804.464			−0.814234
$989$	510.328	+	883.914i	0.516004	+	0.893745i
$990$	−88.9116	−	51.3331i	−0.0898097	−	0.0518517i
$991$	311.554	−	539.628i	0.314384	−	0.544528i	−0.664923	−	0.746912i	$-0.731535\pi$
$991$	311.554	−	539.628i	0.314384	−	0.544528i	0.979306	+	0.202384i	$0.0648688\pi$
$992$	−196.042	+	113.185i	−0.197623	+	0.114098i
$993$			512.662i			0.516276i
$994$	95.5763	−	480.581i	0.0961533	−	0.483482i
$995$	86.3503			0.0867843
$996$	−175.015	−	303.135i	−0.175718	−	0.304353i
$997$	485.248	+	280.158i	0.486708	+	0.281001i	0.723208	−	0.690630i	$-0.242667\pi$
$997$	485.248	+	280.158i	0.486708	+	0.281001i	−0.236499	+	0.971632i	$0.576000\pi$
$998$	293.711	−	508.723i	0.294300	−	0.509742i
$999$	226.644	−	130.853i	0.226871	−	0.130984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.o.b.31.5	✓	16
3.2	odd	2		630.3.v.c.451.3		16
5.2	odd	4		1050.3.q.e.199.7		32
5.3	odd	4		1050.3.q.e.199.16		32
5.4	even	2		1050.3.p.i.451.3		16
7.3	odd	6		1470.3.f.d.391.3		16
7.4	even	3		1470.3.f.d.391.5		16
7.5	odd	6	inner	210.3.o.b.61.5	yes	16
21.5	even	6		630.3.v.c.271.3		16
35.12	even	12		1050.3.q.e.649.16		32
35.19	odd	6		1050.3.p.i.901.3		16
35.33	even	12		1050.3.q.e.649.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.5	✓	16	1.1	even	1	trivial
210.3.o.b.61.5	yes	16	7.5	odd	6	inner
630.3.v.c.271.3		16	21.5	even	6
630.3.v.c.451.3		16	3.2	odd	2
1050.3.p.i.451.3		16	5.4	even	2
1050.3.p.i.901.3		16	35.19	odd	6
1050.3.q.e.199.7		32	5.2	odd	4
1050.3.q.e.199.16		32	5.3	odd	4
1050.3.q.e.649.7		32	35.33	even	12
1050.3.q.e.649.16		32	35.12	even	12
1470.3.f.d.391.3		16	7.3	odd	6
1470.3.f.d.391.5		16	7.4	even	3

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(-5.26304 - 4.61524i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(-5.26304 - 4.61524i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(5.41099 - 9.37211i) q^{11} +(3.00000 - 1.73205i) q^{12} -19.2715i q^{13} +(1.93096 - 9.70935i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-8.89730 - 5.13686i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-18.0756 + 10.4359i) q^{19} -4.47214i q^{20} +(3.89764 + 11.4808i) q^{21} +15.3046 q^{22} +(-10.5373 - 18.2511i) q^{23} +(4.24264 + 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(23.6026 - 13.6270i) q^{26} -5.19615i q^{27} +(13.2569 - 4.50061i) q^{28} +19.0888 q^{29} +(2.73861 + 4.74342i) q^{30} +(-34.6556 - 20.0084i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-16.2330 + 9.37211i) q^{33} -14.5292i q^{34} +(15.3518 + 3.05312i) q^{35} -6.00000 q^{36} +(25.1827 + 43.6177i) q^{37} +(-25.5627 - 14.7586i) q^{38} +(-16.6896 + 28.9072i) q^{39} +(5.47723 - 3.16228i) q^{40} +22.7706i q^{41} +(-11.3050 + 12.8918i) q^{42} -48.4307 q^{43} +(10.8220 + 18.7442i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(14.9020 - 25.8110i) q^{46} +(57.6236 - 33.2690i) q^{47} +6.92820i q^{48} +(6.39913 + 48.5804i) q^{49} +7.07107 q^{50} +(8.89730 + 15.4106i) q^{51} +(33.3792 + 19.2715i) q^{52} +(-2.47531 + 4.28736i) q^{53} +(6.36396 - 3.67423i) q^{54} +24.1987i q^{55} +(14.8861 + 13.0539i) q^{56} +36.1511 q^{57} +(13.4978 + 23.3789i) q^{58} +(-24.4105 - 14.0934i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(-60.6988 + 35.0445i) q^{61} -56.5924i q^{62} +(4.09619 - 20.5966i) q^{63} +8.00000 q^{64} +(21.5462 + 37.3191i) q^{65} +(-22.9569 - 13.2542i) q^{66} +(-9.65287 + 16.7193i) q^{67} +(17.7946 - 10.2737i) q^{68} +36.5023i q^{69} +(7.11609 + 20.9609i) q^{70} +49.4968 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-115.159 - 66.4872i) q^{73} +(-35.6137 + 61.6848i) q^{74} +(-7.50000 + 4.33013i) q^{75} -41.7437i q^{76} +(-71.7328 + 24.3527i) q^{77} -47.2053 q^{78} +(45.0404 + 78.0122i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-27.8882 + 16.1013i) q^{82} -101.045i q^{83} +(-23.7829 - 4.72987i) q^{84} +22.9727 q^{85} +(-34.2456 - 59.3152i) q^{86} +(-28.6332 - 16.5314i) q^{87} +(-15.3046 + 26.5083i) q^{88} +(34.3077 - 19.8075i) q^{89} -9.48683i q^{90} +(-88.9425 + 101.427i) q^{91} +42.1492 q^{92} +(34.6556 + 60.0253i) q^{93} +(81.4920 + 47.0495i) q^{94} +(23.3355 - 40.4182i) q^{95} +(-8.48528 + 4.89898i) q^{96} +68.6944i q^{97} +(-54.9737 + 42.1888i) q^{98} +32.4659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9	\( 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} + 48 q^{12} + 8 q^{14} - 32 q^{16} + 12 q^{17} - 72 q^{19} - 24 q^{21} - 48 q^{22} - 12 q^{23} + 40 q^{25} + 32 q^{28} + 72 q^{29} + 120 q^{31} + 12 q^{33} - 20 q^{35} - 96 q^{36} + 44 q^{37} - 72 q^{38} + 36 q^{39} - 24 q^{42} - 56 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} - 40 q^{49} - 12 q^{51} - 72 q^{52} + 32 q^{53} + 16 q^{56} + 144 q^{57} - 88 q^{58} + 132 q^{59} + 96 q^{61} + 60 q^{63} + 128 q^{64} + 20 q^{65} + 72 q^{66} - 164 q^{67} - 24 q^{68} - 136 q^{71} - 348 q^{73} - 112 q^{74} - 120 q^{75} + 96 q^{77} + 280 q^{79} - 72 q^{81} + 264 q^{82} - 24 q^{84} + 120 q^{85} - 88 q^{86} - 108 q^{87} + 48 q^{88} - 300 q^{89} - 272 q^{91} + 48 q^{92} - 120 q^{93} + 200 q^{95} + 384 q^{98} - 24 q^{99}+O(q^{100}) \) 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 + 48 * q^12 + 8 * q^14 - 32 * q^16 + 12 * q^17 - 72 * q^19 - 24 * q^21 - 48 * q^22 - 12 * q^23 + 40 * q^25 + 32 * q^28 + 72 * q^29 + 120 * q^31 + 12 * q^33 - 20 * q^35 - 96 * q^36 + 44 * q^37 - 72 * q^38 + 36 * q^39 - 24 * q^42 - 56 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 - 40 * q^49 - 12 * q^51 - 72 * q^52 + 32 * q^53 + 16 * q^56 + 144 * q^57 - 88 * q^58 + 132 * q^59 + 96 * q^61 + 60 * q^63 + 128 * q^64 + 20 * q^65 + 72 * q^66 - 164 * q^67 - 24 * q^68 - 136 * q^71 - 348 * q^73 - 112 * q^74 - 120 * q^75 + 96 * q^77 + 280 * q^79 - 72 * q^81 + 264 * q^82 - 24 * q^84 + 120 * q^85 - 88 * q^86 - 108 * q^87 + 48 * q^88 - 300 * q^89 - 272 * q^91 + 48 * q^92 - 120 * q^93 + 200 * q^95 + 384 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more