LMFDB - Embedded newform 105.3.n.b.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(31,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, 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("105.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.n (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 456 x^{8} - 1050 x^{7} + 1999 x^{6} - 2844 x^{5} + 2949 x^{4} + \cdots + 36 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 456x^8 - 1050x^7 + 1999x^6 - 2844x^5 + 2949x^4 - 2136x^3 + 1020x^2 - 288*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.5
Root			$0.500000 + 2.38770i$ of defining polynomial
Character	$\chi$	$=$	105.31
Dual form			105.3.n.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)

$f(q)$	$=$	$q+(1.46731 + 2.54146i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-2.30602 + 3.99415i) q^{4} +(1.93649 - 1.11803i) q^{5} +5.08293i q^{6} +(-5.41652 + 4.43411i) q^{7} -1.79613 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.46731 + 2.54146i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-2.30602 + 3.99415i) q^{4} +(1.93649 - 1.11803i) q^{5} +5.08293i q^{6} +(-5.41652 + 4.43411i) q^{7} -1.79613 q^{8} +(1.50000 + 2.59808i) q^{9} +(5.68288 + 3.28101i) q^{10} +(0.802146 - 1.38936i) q^{11} +(-6.91807 + 3.99415i) q^{12} -14.1348i q^{13} +(-19.2169 - 7.25965i) q^{14} +3.87298 q^{15} +(6.58860 + 11.4118i) q^{16} +(-14.5477 - 8.39913i) q^{17} +(-4.40194 + 7.62439i) q^{18} +(20.5611 - 11.8710i) q^{19} +10.3129i q^{20} +(-11.9648 + 1.96032i) q^{21} +4.70800 q^{22} +(-9.88325 - 17.1183i) q^{23} +(-2.69420 - 1.55550i) q^{24} +(2.50000 - 4.33013i) q^{25} +(35.9231 - 20.7402i) q^{26} +5.19615i q^{27} +(-5.21987 - 31.8596i) q^{28} -22.0642 q^{29} +(5.68288 + 9.84304i) q^{30} +(49.7493 + 28.7228i) q^{31} +(-22.9274 + 39.7114i) q^{32} +(2.40644 - 1.38936i) q^{33} -49.2966i q^{34} +(-5.53156 + 14.6425i) q^{35} -13.8361 q^{36} +(7.24712 + 12.5524i) q^{37} +(60.3392 + 34.8369i) q^{38} +(12.2411 - 21.2022i) q^{39} +(-3.47819 + 2.00814i) q^{40} -25.0310i q^{41} +(-22.5382 - 27.5318i) q^{42} -55.2263 q^{43} +(3.69954 + 6.40778i) q^{44} +(5.80948 + 3.35410i) q^{45} +(29.0037 - 50.2358i) q^{46} +(25.8922 - 14.9489i) q^{47} +22.8236i q^{48} +(9.67736 - 48.0349i) q^{49} +14.6731 q^{50} +(-14.5477 - 25.1974i) q^{51} +(56.4565 + 32.5952i) q^{52} +(-28.3940 + 49.1799i) q^{53} +(-13.2058 + 7.62439i) q^{54} -3.58731i q^{55} +(9.72878 - 7.96424i) q^{56} +41.1222 q^{57} +(-32.3751 - 56.0753i) q^{58} +(-41.1857 - 23.7786i) q^{59} +(-8.93119 + 15.4693i) q^{60} +(-76.2082 + 43.9988i) q^{61} +168.581i q^{62} +(-19.6449 - 7.42137i) q^{63} -81.8578 q^{64} +(-15.8032 - 27.3719i) q^{65} +(7.06200 + 4.07725i) q^{66} +(-1.62251 + 2.81028i) q^{67} +(67.0948 - 38.7372i) q^{68} -34.2366i q^{69} +(-45.3298 + 7.42685i) q^{70} -93.9438 q^{71} +(-2.69420 - 4.66649i) q^{72} +(-38.7392 - 22.3661i) q^{73} +(-21.2676 + 36.8366i) q^{74} +(7.50000 - 4.33013i) q^{75} +109.499i q^{76} +(1.81572 + 11.0823i) q^{77} +71.8461 q^{78} +(66.8061 + 115.712i) q^{79} +(25.5176 + 14.7326i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(63.6154 - 36.7284i) q^{82} +21.8666i q^{83} +(19.7614 - 52.3099i) q^{84} -37.5620 q^{85} +(-81.0344 - 140.356i) q^{86} +(-33.0963 - 19.1081i) q^{87} +(-1.44076 + 2.49547i) q^{88} +(85.1781 - 49.1776i) q^{89} +19.6861i q^{90} +(62.6752 + 76.5614i) q^{91} +91.1640 q^{92} +(49.7493 + 86.1684i) q^{93} +(75.9840 + 43.8694i) q^{94} +(26.5443 - 45.9760i) q^{95} +(-68.7821 + 39.7114i) q^{96} +155.791i q^{97} +(136.279 - 45.8876i) q^{98} +4.81288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9	$ 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9} + 20 q^{11} - 66 q^{12} + 32 q^{14} - 82 q^{16} - 78 q^{17} - 6 q^{18} - 6 q^{19} + 36 q^{21} + 56 q^{22} + 2 q^{23} + 60 q^{24} + 30 q^{25} + 36 q^{26} - 128 q^{28} - 100 q^{29} + 108 q^{31} - 108 q^{32} + 60 q^{33} - 60 q^{35} - 132 q^{36} - 34 q^{37} + 126 q^{38} - 42 q^{39} - 90 q^{40} + 114 q^{42} - 124 q^{43} + 234 q^{44} + 278 q^{46} + 96 q^{47} - 60 q^{49} + 20 q^{50} - 78 q^{51} - 444 q^{52} - 76 q^{53} - 18 q^{54} + 112 q^{56} - 12 q^{57} - 52 q^{58} - 270 q^{59} + 60 q^{60} - 60 q^{61} + 42 q^{63} + 700 q^{64} - 60 q^{65} + 84 q^{66} - 18 q^{67} + 108 q^{68} - 300 q^{70} - 628 q^{71} + 60 q^{72} + 234 q^{73} + 244 q^{74} + 90 q^{75} - 196 q^{77} + 72 q^{78} + 108 q^{79} + 480 q^{80} - 54 q^{81} + 480 q^{82} - 192 q^{84} - 60 q^{85} + 130 q^{86} - 150 q^{87} - 668 q^{88} - 186 q^{89} + 444 q^{91} + 456 q^{92} + 108 q^{93} + 30 q^{94} - 324 q^{96} + 416 q^{98} + 120 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9 + 20 * q^11 - 66 * q^12 + 32 * q^14 - 82 * q^16 - 78 * q^17 - 6 * q^18 - 6 * q^19 + 36 * q^21 + 56 * q^22 + 2 * q^23 + 60 * q^24 + 30 * q^25 + 36 * q^26 - 128 * q^28 - 100 * q^29 + 108 * q^31 - 108 * q^32 + 60 * q^33 - 60 * q^35 - 132 * q^36 - 34 * q^37 + 126 * q^38 - 42 * q^39 - 90 * q^40 + 114 * q^42 - 124 * q^43 + 234 * q^44 + 278 * q^46 + 96 * q^47 - 60 * q^49 + 20 * q^50 - 78 * q^51 - 444 * q^52 - 76 * q^53 - 18 * q^54 + 112 * q^56 - 12 * q^57 - 52 * q^58 - 270 * q^59 + 60 * q^60 - 60 * q^61 + 42 * q^63 + 700 * q^64 - 60 * q^65 + 84 * q^66 - 18 * q^67 + 108 * q^68 - 300 * q^70 - 628 * q^71 + 60 * q^72 + 234 * q^73 + 244 * q^74 + 90 * q^75 - 196 * q^77 + 72 * q^78 + 108 * q^79 + 480 * q^80 - 54 * q^81 + 480 * q^82 - 192 * q^84 - 60 * q^85 + 130 * q^86 - 150 * q^87 - 668 * q^88 - 186 * q^89 + 444 * q^91 + 456 * q^92 + 108 * q^93 + 30 * q^94 - 324 * q^96 + 416 * q^98 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.46731	+	2.54146i	0.733657	+	1.27073i	0.955310	+	0.295606i	$0.0955215\pi$
$2$	1.46731	+	2.54146i	0.733657	+	1.27073i	−0.221653	+	0.975126i	$0.571145\pi$
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	−2.30602	+	3.99415i	−0.576506	+	0.998538i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$			5.08293i			0.847154i
$7$	−5.41652	+	4.43411i	−0.773788	+	0.633444i
$7$	−5.41652	+	4.43411i	−0.773788	+	0.633444i
$8$	−1.79613			−0.224516
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	5.68288	+	3.28101i	0.568288	+	0.328101i
$11$	0.802146	−	1.38936i	0.0729224	−	0.126305i	−0.827259	−	0.561821i	$-0.810101\pi$
$11$	0.802146	−	1.38936i	0.0729224	−	0.126305i	0.900181	+	0.435516i	$0.143434\pi$
$12$	−6.91807	+	3.99415i	−0.576506	+	0.332846i
$13$		−	14.1348i		−	1.08729i	−0.839315	−	0.543646i	$-0.817043\pi$
$13$		−	14.1348i		−	1.08729i	0.839315	−	0.543646i	$-0.182957\pi$
$14$	−19.2169	−	7.25965i	−1.37263	−	0.518547i
$15$	3.87298			0.258199
$16$	6.58860	+	11.4118i	0.411788	+	0.713237i
$17$	−14.5477	−	8.39913i	−0.855748	−	0.494066i	0.00683814	−	0.999977i	$-0.497823\pi$
$17$	−14.5477	−	8.39913i	−0.855748	−	0.494066i	−0.862586	+	0.505910i	$0.831157\pi$
$18$	−4.40194	+	7.62439i	−0.244552	+	0.423577i
$19$	20.5611	−	11.8710i	1.08216	−	0.624787i	0.150684	−	0.988582i	$-0.451852\pi$
$19$	20.5611	−	11.8710i	1.08216	−	0.624787i	0.931479	+	0.363795i	$0.118519\pi$
$20$			10.3129i			0.515643i
$21$	−11.9648	+	1.96032i	−0.569754	+	0.0933486i
$22$	4.70800			0.214000
$23$	−9.88325	−	17.1183i	−0.429706	−	0.744273i	0.567141	−	0.823621i	$-0.308050\pi$
$23$	−9.88325	−	17.1183i	−0.429706	−	0.744273i	−0.996847	+	0.0793476i	$0.974716\pi$
$24$	−2.69420	−	1.55550i	−0.112258	−	0.0648123i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	35.9231	−	20.7402i	1.38166	−	0.797700i
$27$			5.19615i			0.192450i
$28$	−5.21987	−	31.8596i	−0.186424	−	1.13784i
$29$	−22.0642			−0.760834			−0.380417	−	0.924815i	$-0.624219\pi$
$29$	−22.0642			−0.760834			−0.380417	+	0.924815i	$0.624219\pi$
$30$	5.68288	+	9.84304i	0.189429	+	0.328101i
$31$	49.7493	+	28.7228i	1.60482	+	0.926542i	0.990505	+	0.137479i	$0.0438999\pi$
$31$	49.7493	+	28.7228i	1.60482	+	0.926542i	0.614312	+	0.789063i	$0.289433\pi$
$32$	−22.9274	+	39.7114i	−0.716480	+	1.24098i
$33$	2.40644	−	1.38936i	0.0729224	−	0.0421017i
$34$		−	49.2966i		−	1.44990i
$35$	−5.53156	+	14.6425i	−0.158045	+	0.418356i
$36$	−13.8361			−0.384337
$37$	7.24712	+	12.5524i	0.195868	+	0.339254i	0.947185	−	0.320688i	$-0.103914\pi$
$37$	7.24712	+	12.5524i	0.195868	+	0.339254i	−0.751317	+	0.659942i	$0.770581\pi$
$38$	60.3392	+	34.8369i	1.58787	+	0.916760i
$39$	12.2411	−	21.2022i	0.313874	−	0.543646i
$40$	−3.47819	+	2.00814i	−0.0869549	+	0.0502034i
$41$		−	25.0310i		−	0.610513i	−0.952270	−	0.305256i	$-0.901258\pi$
$41$		−	25.0310i		−	0.610513i	0.952270	−	0.305256i	$-0.0987422\pi$
$42$	−22.5382	−	27.5318i	−0.536625	−	0.655518i
$43$	−55.2263			−1.28433			−0.642167	−	0.766565i	$-0.721964\pi$
$43$	−55.2263			−1.28433			−0.642167	+	0.766565i	$0.721964\pi$
$44$	3.69954	+	6.40778i	0.0840804	+	0.145631i
$45$	5.80948	+	3.35410i	0.129099	+	0.0745356i
$46$	29.0037	−	50.2358i	0.630515	−	1.09208i
$47$	25.8922	−	14.9489i	0.550898	−	0.318061i	−0.198586	−	0.980083i	$-0.563635\pi$
$47$	25.8922	−	14.9489i	0.550898	−	0.318061i	0.749484	+	0.662023i	$0.230302\pi$
$48$			22.8236i			0.475492i
$49$	9.67736	−	48.0349i	0.197497	−	0.980303i
$50$	14.6731			0.293463
$51$	−14.5477	−	25.1974i	−0.285249	−	0.494066i
$52$	56.4565	+	32.5952i	1.08570	+	0.626830i
$53$	−28.3940	+	49.1799i	−0.535736	+	0.927923i	0.463391	+	0.886154i	$0.346633\pi$
$53$	−28.3940	+	49.1799i	−0.535736	+	0.927923i	−0.999127	+	0.0417687i	$0.986701\pi$
$54$	−13.2058	+	7.62439i	−0.244552	+	0.141192i
$55$		−	3.58731i		−	0.0652237i
$56$	9.72878	−	7.96424i	0.173728	−	0.142219i
$57$	41.1222			0.721442
$58$	−32.3751	−	56.0753i	−0.558191	−	0.966815i
$59$	−41.1857	−	23.7786i	−0.698062	−	0.403026i	0.108563	−	0.994090i	$-0.465375\pi$
$59$	−41.1857	−	23.7786i	−0.698062	−	0.403026i	−0.806625	+	0.591063i	$0.798708\pi$
$60$	−8.93119	+	15.4693i	−0.148853	+	0.257821i
$61$	−76.2082	+	43.9988i	−1.24932	+	0.721292i	−0.970973	−	0.239189i	$-0.923118\pi$
$61$	−76.2082	+	43.9988i	−1.24932	+	0.721292i	−0.278342	+	0.960482i	$0.589785\pi$
$62$			168.581i			2.71906i
$63$	−19.6449	−	7.42137i	−0.311824	−	0.117799i
$64$	−81.8578			−1.27903
$65$	−15.8032	−	27.3719i	−0.243126	−	0.421106i
$66$	7.06200	+	4.07725i	0.107000	+	0.0617765i
$67$	−1.62251	+	2.81028i	−0.0242166	+	0.0419444i	−0.877880	−	0.478881i	$-0.841042\pi$
$67$	−1.62251	+	2.81028i	−0.0242166	+	0.0419444i	0.853663	+	0.520826i	$0.174376\pi$
$68$	67.0948	−	38.7372i	0.986688	−	0.569664i
$69$		−	34.2366i		−	0.496182i
$70$	−45.3298	+	7.42685i	−0.647569	+	0.106098i
$71$	−93.9438			−1.32315			−0.661576	−	0.749878i	$-0.730112\pi$
$71$	−93.9438			−1.32315			−0.661576	+	0.749878i	$0.730112\pi$
$72$	−2.69420	−	4.66649i	−0.0374194	−	0.0648123i
$73$	−38.7392	−	22.3661i	−0.530674	−	0.306385i	0.210617	−	0.977569i	$-0.432453\pi$
$73$	−38.7392	−	22.3661i	−0.530674	−	0.306385i	−0.741291	+	0.671184i	$0.765786\pi$
$74$	−21.2676	+	36.8366i	−0.287400	+	0.497792i
$75$	7.50000	−	4.33013i	0.100000	−	0.0577350i
$76$			109.499i			1.44077i
$77$	1.81572	+	11.0823i	0.0235808	+	0.143926i
$78$	71.8461			0.921104
$79$	66.8061	+	115.712i	0.845647	+	1.46470i	0.885058	+	0.465480i	$0.154118\pi$
$79$	66.8061	+	115.712i	0.845647	+	1.46470i	−0.0394112	+	0.999223i	$0.512548\pi$
$80$	25.5176	+	14.7326i	0.318969	+	0.184157i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	63.6154	−	36.7284i	0.775798	−	0.447907i
$83$			21.8666i			0.263454i	0.991286	+	0.131727i	$0.0420522\pi$
$83$			21.8666i			0.263454i	−0.991286	+	0.131727i	$0.957948\pi$
$84$	19.7614	−	52.3099i	0.235254	−	0.622737i
$85$	−37.5620			−0.441906
$86$	−81.0344	−	140.356i	−0.942261	−	1.63204i
$87$	−33.0963	−	19.1081i	−0.380417	−	0.219634i
$88$	−1.44076	+	2.49547i	−0.0163723	+	0.0283576i
$89$	85.1781	−	49.1776i	0.957057	−	0.552557i	0.0617912	−	0.998089i	$-0.480319\pi$
$89$	85.1781	−	49.1776i	0.957057	−	0.552557i	0.895266	+	0.445532i	$0.146985\pi$
$90$			19.6861i			0.218734i
$91$	62.6752	+	76.5614i	0.688739	+	0.841334i
$92$	91.1640			0.990913
$93$	49.7493	+	86.1684i	0.534939	+	0.926542i
$94$	75.9840	+	43.8694i	0.808340	+	0.466695i
$95$	26.5443	−	45.9760i	0.279413	−	0.483958i
$96$	−68.7821	+	39.7114i	−0.716480	+	0.413660i
$97$			155.791i			1.60609i	0.595917	+	0.803046i	$0.296789\pi$
$97$			155.791i			1.60609i	−0.595917	+	0.803046i	$0.703211\pi$
$98$	136.279	−	45.8876i	1.39060	−	0.468241i
$99$	4.81288			0.0486149
$100$	11.5301	+	19.9708i	0.115301	+	0.199708i
$101$	−85.9738	−	49.6370i	−0.851226	−	0.491456i	0.00983838	−	0.999952i	$-0.496868\pi$
$101$	−85.9738	−	49.6370i	−0.851226	−	0.491456i	−0.861064	+	0.508496i	$0.830202\pi$
$102$	42.6921	−	73.9450i	0.418550	−	0.724951i
$103$	22.1188	−	12.7703i	0.214745	−	0.123983i	−0.388769	−	0.921335i	$-0.627100\pi$
$103$	22.1188	−	12.7703i	0.214745	−	0.123983i	0.603515	+	0.797352i	$0.293766\pi$
$104$			25.3880i			0.244115i
$105$	−20.9781	+	17.1732i	−0.199791	+	0.163555i
$106$	−166.652			−1.57219
$107$	−3.07073	−	5.31865i	−0.0286984	−	0.0497070i	0.851320	−	0.524648i	$-0.175803\pi$
$107$	−3.07073	−	5.31865i	−0.0286984	−	0.0497070i	−0.880018	+	0.474941i	$0.842470\pi$
$108$	−20.7542	−	11.9825i	−0.192169	−	0.110949i
$109$	59.6625	−	103.338i	0.547362	−	0.948059i	−0.451092	−	0.892478i	$-0.648965\pi$
$109$	59.6625	−	103.338i	0.547362	−	0.948059i	0.998454	−	0.0555818i	$-0.0177014\pi$
$110$	9.11701	−	5.26371i	0.0828819	−	0.0478519i
$111$			25.1048i			0.226169i
$112$	−86.2885	−	32.5976i	−0.770433	−	0.291050i
$113$	−175.224			−1.55065			−0.775326	−	0.631561i	$-0.782414\pi$
$113$	−175.224			−1.55065			−0.775326	+	0.631561i	$0.782414\pi$
$114$	60.3392	+	104.511i	0.529291	+	0.916760i
$115$	−38.2777	−	22.0996i	−0.332849	−	0.192171i
$116$	50.8805	−	88.1276i	0.438625	−	0.759721i
$117$	36.7233	−	21.2022i	0.313874	−	0.181215i
$118$		−	139.563i		−	1.18273i
$119$	116.041	−	19.0121i	0.975131	−	0.159766i
$120$	−6.95639			−0.0579699
$121$	59.2131	+	102.560i	0.489365	+	0.847604i
$122$	−223.643	−	129.120i	−1.83314	−	1.05836i
$123$	21.6775	−	37.5465i	0.176240	−	0.305256i
$124$	−229.446	+	132.471i	−1.85037	+	1.06831i
$125$		−	11.1803i		−	0.0894427i
$126$	−9.96416	−	60.8163i	−0.0790807	−	0.482669i
$127$	172.288			1.35660			0.678299	−	0.734786i	$-0.262718\pi$
$127$	172.288			1.35660			0.678299	+	0.734786i	$0.262718\pi$
$128$	−28.4017	−	49.1932i	−0.221888	−	0.384322i
$129$	−82.8395	−	47.8274i	−0.642167	−	0.370755i
$130$	46.3765	−	80.3264i	0.356742	−	0.617895i
$131$	214.084	−	123.602i	1.63423	−	0.943525i	0.651465	−	0.758678i	$-0.274155\pi$
$131$	214.084	−	123.602i	1.63423	−	0.943525i	0.982767	−	0.184846i	$-0.0591787\pi$
$132$			12.8156i			0.0970876i
$133$	−58.7325	+	155.469i	−0.441598	+	1.16894i
$134$	−9.52295			−0.0710668
$135$	5.80948	+	10.0623i	0.0430331	+	0.0745356i
$136$	26.1296	+	15.0859i	0.192130	+	0.110926i
$137$	34.4467	−	59.6634i	0.251436	−	0.435499i	−0.712486	−	0.701687i	$-0.752431\pi$
$137$	34.4467	−	59.6634i	0.251436	−	0.435499i	0.963921	+	0.266187i	$0.0857640\pi$
$138$	87.0110	−	50.2358i	0.630515	−	0.364028i
$139$		−	95.2969i		−	0.685589i	−0.939410	−	0.342795i	$-0.888627\pi$
$139$		−	95.2969i		−	0.685589i	0.939410	−	0.342795i	$-0.111373\pi$
$140$	−45.7283	−	55.8598i	−0.326631	−	0.398998i
$141$	51.7844			0.367265
$142$	−137.845	−	238.755i	−0.970740	−	1.68137i
$143$	−19.6383	−	11.3382i	−0.137331	−	0.0792879i
$144$	−19.7658	+	34.2354i	−0.137263	+	0.237746i
$145$	−42.7271	+	24.6685i	−0.294670	+	0.170128i
$146$		−	131.272i		−	0.899126i
$147$	56.1155	−	63.6715i	0.381738	−	0.433139i
$148$	−66.8482			−0.451677
$149$	121.776	+	210.922i	0.817290	+	1.41559i	0.907672	+	0.419680i	$0.137858\pi$
$149$	121.776	+	210.922i	0.817290	+	1.41559i	−0.0903825	+	0.995907i	$0.528809\pi$
$150$	22.0097	+	12.7073i	0.146731	+	0.0847154i
$151$	87.5637	−	151.665i	0.579892	−	1.00440i	−0.415599	−	0.909548i	$-0.636428\pi$
$151$	87.5637	−	151.665i	0.579892	−	1.00440i	0.995491	−	0.0948546i	$-0.0302386\pi$
$152$	−36.9305	+	21.3218i	−0.242964	+	0.140275i
$153$		−	50.3948i		−	0.329378i
$154$	−25.5010	+	20.8758i	−0.165591	+	0.135557i
$155$	128.452			0.828724
$156$	56.4565	+	97.7855i	0.361901	+	0.626830i
$157$	−151.777	−	87.6283i	−0.966731	−	0.558142i	−0.0684927	−	0.997652i	$-0.521819\pi$
$157$	−151.777	−	87.6283i	−0.966731	−	0.558142i	−0.898238	+	0.439509i	$0.855152\pi$
$158$	−196.051	+	339.571i	−1.24083	+	2.14918i
$159$	−85.1821	+	49.1799i	−0.535736	+	0.309308i
$160$			102.534i			0.640840i
$161$	129.437	+	48.8981i	0.803958	+	0.303715i
$162$	−26.4117			−0.163035
$163$	48.5314	+	84.0588i	0.297739	+	0.515698i	0.975618	−	0.219475i	$-0.0704343\pi$
$163$	48.5314	+	84.0588i	0.297739	+	0.515698i	−0.677880	+	0.735173i	$0.737101\pi$
$164$	99.9777	+	57.7221i	0.609620	+	0.351964i
$165$	3.10670	−	5.38096i	0.0188285	−	0.0326119i
$166$	−55.5733	+	32.0853i	−0.334779	+	0.193285i
$167$			85.8560i			0.514108i	0.966397	+	0.257054i	$0.0827518\pi$
$167$			85.8560i			0.514108i	−0.966397	+	0.257054i	$0.917248\pi$
$168$	21.4904	−	3.52099i	0.127919	−	0.0209583i
$169$	−30.7925			−0.182204
$170$	−55.1153	−	95.4625i	−0.324208	−	0.561544i
$171$	61.6833	+	35.6129i	0.360721	+	0.208262i
$172$	127.353	−	220.582i	0.740426	−	1.28246i
$173$	−122.735	+	70.8613i	−0.709453	+	0.409603i	−0.810858	−	0.585242i	$-0.800999\pi$
$173$	−122.735	+	70.8613i	−0.709453	+	0.409603i	0.101406	+	0.994845i	$0.467666\pi$
$174$		−	112.151i		−	0.644544i
$175$	5.65896	+	34.5395i	0.0323369	+	0.197369i
$176$	21.1401			0.120114
$177$	−41.1857	−	71.3357i	−0.232687	−	0.403026i
$178$	249.966	+	144.318i	1.40430	+	0.810775i
$179$	−59.3441	+	102.787i	−0.331531	+	0.574229i	−0.982812	−	0.184608i	$-0.940899\pi$
$179$	−59.3441	+	102.787i	−0.331531	+	0.574229i	0.651281	+	0.758837i	$0.274232\pi$
$180$	−26.7936	+	15.4693i	−0.148853	+	0.0859404i
$181$			127.263i			0.703108i	0.936168	+	0.351554i	$0.114347\pi$
$181$			127.263i			0.703108i	−0.936168	+	0.351554i	$0.885653\pi$
$182$	−102.614	+	271.626i	−0.563812	+	1.49245i
$183$	−152.416			−0.832877
$184$	17.7516	+	30.7467i	0.0964762	+	0.167102i
$185$	28.0680	+	16.2051i	0.151719	+	0.0875949i
$186$	−145.996	+	252.872i	−0.784924	+	1.35953i
$187$	−23.3388	+	13.4747i	−0.124806	+	0.0720570i
$188$			137.890i			0.733456i
$189$	−23.0403	−	28.1451i	−0.121906	−	0.148916i
$190$	155.795			0.819975
$191$	155.253	+	268.907i	0.812845	+	1.40789i	0.910865	+	0.412705i	$0.135416\pi$
$191$	155.253	+	268.907i	0.812845	+	1.40789i	−0.0980198	+	0.995184i	$0.531251\pi$
$192$	−122.787	−	70.8910i	−0.639514	−	0.369224i
$193$	33.3276	−	57.7251i	0.172682	−	0.299094i	−0.766675	−	0.642036i	$-0.778090\pi$
$193$	33.3276	−	57.7251i	0.172682	−	0.299094i	0.939357	+	0.342942i	$0.111423\pi$
$194$	−395.937	+	228.594i	−2.04091	+	1.17832i
$195$		−	54.7438i		−	0.280738i
$196$	169.542	+	149.422i	0.865012	+	0.762359i
$197$	71.9016			0.364983			0.182491	−	0.983207i	$-0.441584\pi$
$197$	71.9016			0.364983			0.182491	+	0.983207i	$0.441584\pi$
$198$	7.06200	+	12.2317i	0.0356667	+	0.0617765i
$199$	218.030	+	125.880i	1.09563	+	0.632562i	0.935069	−	0.354465i	$-0.115337\pi$
$199$	218.030	+	125.880i	1.09563	+	0.632562i	0.160559	+	0.987026i	$0.448670\pi$
$200$	−4.49033	+	7.77748i	−0.0224516	+	0.0388874i
$201$	−4.86754	+	2.81028i	−0.0242166	+	0.0139815i
$202$		−	291.332i		−	1.44224i
$203$	119.511	−	97.8349i	0.588724	−	0.481946i
$204$	134.190			0.657792
$205$	−27.9855	−	48.4724i	−0.136515	−	0.236451i
$206$	64.9104	+	37.4760i	0.315099	+	0.181923i
$207$	29.6497	−	51.3549i	0.143235	−	0.248091i
$208$	161.303	−	93.1286i	0.775497	−	0.447734i
$209$		−	38.0890i		−	0.182244i
$210$	−74.4266	−	28.1165i	−0.354412	−	0.133888i
$211$	221.716			1.05079			0.525394	−	0.850859i	$-0.323918\pi$
$211$	221.716			1.05079			0.525394	+	0.850859i	$0.323918\pi$
$212$	−130.955	−	226.820i	−0.617710	−	1.06991i
$213$	−140.916	−	81.3577i	−0.661576	−	0.381961i
$214$	9.01144	−	15.6083i	0.0421095	−	0.0729359i
$215$	−106.945	+	61.7449i	−0.497420	+	0.287186i
$216$		−	9.33297i		−	0.0432082i
$217$	−396.828	+	65.0164i	−1.82870	+	0.299615i
$218$	350.175			1.60631
$219$	−38.7392	−	67.0983i	−0.176891	−	0.306385i
$220$	14.3282	+	8.27241i	0.0651284	+	0.0376019i
$221$	−118.720	+	205.629i	−0.537194	+	0.930448i
$222$	−63.8029	+	36.8366i	−0.287400	+	0.165931i
$223$		−	40.4387i		−	0.181339i	−0.995881	−	0.0906697i	$-0.971099\pi$
$223$		−	40.4387i		−	0.181339i	0.995881	−	0.0906697i	$-0.0289007\pi$
$224$	−51.8980	−	316.760i	−0.231688	−	1.41411i
$225$	15.0000			0.0666667
$226$	−257.108	−	445.324i	−1.13765	−	1.97046i
$227$	32.5124	+	18.7711i	0.143227	+	0.0826919i	0.569901	−	0.821713i	$-0.306982\pi$
$227$	32.5124	+	18.7711i	0.143227	+	0.0826919i	−0.426674	+	0.904405i	$0.640315\pi$
$228$	−94.8288	+	164.248i	−0.415916	+	0.720387i
$229$	−20.5984	+	11.8925i	−0.0899495	+	0.0519324i	−0.544300	−	0.838891i	$-0.683205\pi$
$229$	−20.5984	+	11.8925i	−0.0899495	+	0.0519324i	0.454351	+	0.890823i	$0.349871\pi$
$230$		−	129.708i		−	0.563949i
$231$	−6.87396	+	18.1959i	−0.0297574	+	0.0787701i
$232$	39.6302			0.170820
$233$	−189.553	−	328.315i	−0.813531	−	1.40908i	−0.910378	−	0.413778i	$-0.864209\pi$
$233$	−189.553	−	328.315i	−0.813531	−	1.40908i	0.0968469	−	0.995299i	$-0.469124\pi$
$234$	107.769	+	62.2206i	0.460552	+	0.265900i
$235$	33.4267	−	57.8967i	0.142241	−	0.246369i
$236$	189.950	−	109.668i	0.804874	−	0.464694i
$237$			231.423i			0.976469i
$238$	218.587	+	267.016i	0.918431	+	1.12192i
$239$	−289.970			−1.21326			−0.606632	−	0.794983i	$-0.707480\pi$
$239$	−289.970			−1.21326			−0.606632	+	0.794983i	$0.707480\pi$
$240$	25.5176	+	44.1977i	0.106323	+	0.184157i
$241$	−365.640	−	211.102i	−1.51718	−	0.875944i	−0.999796	−	0.0201895i	$-0.993573\pi$
$241$	−365.640	−	211.102i	−1.51718	−	0.875944i	−0.517383	−	0.855754i	$-0.673094\pi$
$242$	−173.769	+	300.976i	−0.718052	+	1.24370i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		−	405.849i		−	1.66332i
$245$	−34.9645	−	103.839i	−0.142712	−	0.423832i
$246$	127.231			0.517199
$247$	−167.794	−	290.627i	−0.679326	−	1.17663i
$248$	−89.3564	−	51.5899i	−0.360308	−	0.208024i
$249$	−18.9371	+	32.8000i	−0.0760525	+	0.131727i
$250$	28.4144	−	16.4051i	0.113658	−	0.0656203i
$251$		−	380.518i		−	1.51601i	−0.652251	−	0.758003i	$-0.726175\pi$
$251$		−	380.518i		−	1.51601i	0.652251	−	0.758003i	$-0.273825\pi$
$252$	74.9437	−	61.3510i	0.297396	−	0.243456i
$253$	−31.7112			−0.125341
$254$	252.801	+	437.863i	0.995278	+	1.72387i
$255$	−56.3431	−	32.5297i	−0.220953	−	0.127567i
$256$	−80.3672	+	139.200i	−0.313935	+	0.543751i
$257$	33.2435	−	19.1932i	0.129352	−	0.0746816i	−0.433928	−	0.900948i	$-0.642873\pi$
$257$	33.2435	−	19.1932i	0.129352	−	0.0746816i	0.563280	+	0.826266i	$0.309539\pi$
$258$		−	280.711i		−	1.08803i
$259$	−94.9128	−	35.8557i	−0.366459	−	0.138439i
$260$	145.770			0.560654
$261$	−33.0963	−	57.3244i	−0.126806	−	0.219634i
$262$	628.259	+	362.725i	2.39793	+	1.38445i
$263$	118.700	−	205.595i	0.451332	−	0.781729i	−0.547137	−	0.837043i	$-0.684282\pi$
$263$	118.700	−	205.595i	0.451332	−	0.781729i	0.998469	+	0.0553134i	$0.0176158\pi$
$264$	−4.32228	+	2.49547i	−0.0163723	+	0.00945254i
$265$			126.982i			0.479177i
$266$	−481.299	+	78.8561i	−1.80939	+	0.296452i
$267$	170.356			0.638038
$268$	−7.48311	−	12.9611i	−0.0279221	−	0.0483624i
$269$	2.08569	+	1.20417i	0.00775349	+	0.00447648i	0.503872	−	0.863778i	$-0.331908\pi$
$269$	2.08569	+	1.20417i	0.00775349	+	0.00447648i	−0.496118	+	0.868255i	$0.665242\pi$
$270$	−17.0487	+	29.5291i	−0.0631432	+	0.109367i
$271$	−131.384	+	75.8546i	−0.484812	+	0.279906i	−0.722420	−	0.691455i	$-0.756970\pi$
$271$	−131.384	+	75.8546i	−0.484812	+	0.279906i	0.237608	+	0.971361i	$0.423637\pi$
$272$		−	221.354i		−	0.813802i
$273$	27.7087	+	169.120i	0.101497	+	0.619489i
$274$	202.176			0.737870
$275$	−4.01073	−	6.94679i	−0.0145845	−	0.0252610i
$276$	136.746	+	78.9504i	0.495457	+	0.286052i
$277$	−13.6515	+	23.6450i	−0.0492833	+	0.0853612i	−0.889615	−	0.456712i	$-0.849027\pi$
$277$	−13.6515	+	23.6450i	−0.0492833	+	0.0853612i	0.840331	+	0.542073i	$0.182360\pi$
$278$	242.193	−	139.830i	0.871200	−	0.502987i
$279$			172.337i			0.617694i
$280$	9.93541	−	26.2998i	0.0354836	−	0.0939279i
$281$	320.774			1.14155			0.570773	−	0.821108i	$-0.306644\pi$
$281$	320.774			1.14155			0.570773	+	0.821108i	$0.306644\pi$
$282$	75.9840	+	131.608i	0.269447	+	0.466695i
$283$	27.8601	+	16.0851i	0.0984457	+	0.0568377i	0.548415	−	0.836207i	$-0.315232\pi$
$283$	27.8601	+	16.0851i	0.0984457	+	0.0568377i	−0.449969	+	0.893044i	$0.648565\pi$
$284$	216.637	−	375.226i	0.762805	−	1.32122i
$285$	79.6328	−	45.9760i	0.279413	−	0.161319i
$286$		−	66.5466i		−	0.232681i
$287$	110.990	+	135.581i	0.386726	+	0.472408i
$288$	−137.564			−0.477654
$289$	−3.40932	−	5.90512i	−0.0117970	−	0.0204329i
$290$	−125.388	−	72.3929i	−0.432373	−	0.249631i
$291$	−134.919	+	233.686i	−0.463639	+	0.803046i
$292$	178.667	−	103.153i	0.611873	−	0.353265i
$293$		−	187.120i		−	0.638636i	−0.947648	−	0.319318i	$-0.896546\pi$
$293$		−	187.120i		−	0.638636i	0.947648	−	0.319318i	$-0.103454\pi$
$294$	244.158	+	49.1893i	0.830468	+	0.167311i
$295$	−106.341			−0.360478
$296$	−13.0168	−	22.5457i	−0.0439756	−	0.0761681i
$297$	7.21931	+	4.16807i	0.0243075	+	0.0140339i
$298$	−357.368	+	618.979i	−1.19922	+	2.07711i
$299$	−241.964	+	139.698i	−0.809243	+	0.467216i
$300$			39.9415i			0.133138i
$301$	299.135	−	244.880i	0.993803	−	0.813554i
$302$	513.934			1.70177
$303$	−85.9738	−	148.911i	−0.283742	−	0.491456i
$304$	270.938	+	156.426i	0.891243	+	0.514560i
$305$	−98.3844	+	170.407i	−0.322572	+	0.558711i
$306$	128.076	−	73.9450i	0.418550	−	0.241650i
$307$			12.3135i			0.0401090i	0.999799	+	0.0200545i	$0.00638397\pi$
$307$			12.3135i			0.0401090i	−0.999799	+	0.0200545i	$0.993616\pi$
$308$	−48.4514	−	18.3037i	−0.157310	−	0.0594277i
$309$	44.2376			0.143164
$310$	188.480	+	326.457i	0.607999	+	1.05309i
$311$	−302.282	−	174.523i	−0.971968	−	0.561166i	−0.0721324	−	0.997395i	$-0.522980\pi$
$311$	−302.282	−	174.523i	−0.971968	−	0.561166i	−0.899836	+	0.436229i	$0.856314\pi$
$312$	−21.9866	+	38.0819i	−0.0704699	+	0.122057i
$313$	315.978	−	182.430i	1.00951	−	0.582843i	0.0984640	−	0.995141i	$-0.468607\pi$
$313$	315.978	−	182.430i	1.00951	−	0.582843i	0.911049	+	0.412298i	$0.135274\pi$
$314$		−	514.313i		−	1.63794i
$315$	−46.3396	+	7.59229i	−0.147110	+	0.0241025i
$316$	−616.226			−1.95008
$317$	222.951	+	386.162i	0.703314	+	1.21818i	0.967297	+	0.253648i	$0.0816305\pi$
$317$	222.951	+	386.162i	0.703314	+	1.21818i	−0.263983	+	0.964527i	$0.585036\pi$
$318$	−249.978	−	144.325i	−0.786094	−	0.453851i
$319$	−17.6987	+	30.6550i	−0.0554818	+	0.0960973i
$320$	−158.517	+	91.5198i	−0.495366	+	0.285999i
$321$		−	10.6373i		−	0.0331380i
$322$	65.6522	+	400.709i	0.203889	+	1.24444i
$323$	−398.823			−1.23475
$324$	−20.7542	−	35.9474i	−0.0640562	−	0.110949i
$325$	−61.2055	−	35.3370i	−0.188324	−	0.108729i
$326$	−142.422	+	246.681i	−0.436876	+	0.756692i
$327$	178.987	−	103.338i	0.547362	−	0.316020i
$328$			44.9590i			0.137070i
$329$	−73.9607	+	195.780i	−0.224804	+	0.595075i
$330$	18.2340			0.0552546
$331$	−30.4929	−	52.8152i	−0.0921235	−	0.159563i	0.816281	−	0.577655i	$-0.196032\pi$
$331$	−30.4929	−	52.8152i	−0.0921235	−	0.159563i	−0.908404	+	0.418092i	$0.862699\pi$
$332$	−87.3387	−	50.4250i	−0.263068	−	0.151883i
$333$	−21.7414	+	37.6572i	−0.0652894	+	0.113085i
$334$	−218.200	+	125.978i	−0.653293	+	0.377179i
$335$			7.25610i			0.0216600i
$336$	−101.202	−	123.624i	−0.301197	−	0.367930i
$337$	−422.369			−1.25332			−0.626660	−	0.779293i	$-0.715578\pi$
$337$	−422.369			−1.25332			−0.626660	+	0.779293i	$0.715578\pi$
$338$	−45.1822	−	78.2579i	−0.133675	−	0.231532i
$339$	−262.835	−	151.748i	−0.775326	−	0.447635i
$340$	86.6190	−	150.028i	0.254762	−	0.441260i
$341$	79.8125	−	46.0797i	0.234054	−	0.135131i
$342$			209.021i			0.611173i
$343$	160.574	+	303.092i	0.468146	+	0.883651i
$344$	99.1938			0.288354
$345$	−38.2777	−	66.2988i	−0.110950	−	0.192171i
$346$	−360.183	−	207.952i	−1.04099	−	0.601016i
$347$	339.215	−	587.538i	0.977566	−	1.69319i	0.306371	−	0.951912i	$-0.400885\pi$
$347$	339.215	−	587.538i	0.977566	−	1.69319i	0.671195	−	0.741281i	$-0.265781\pi$
$348$	152.642	−	88.1276i	0.438625	−	0.253240i
$349$		−	386.656i		−	1.10790i	−0.832551	−	0.553949i	$-0.813120\pi$
$349$		−	386.656i		−	1.10790i	0.832551	−	0.553949i	$-0.186880\pi$
$350$	−79.4774	+	65.0623i	−0.227078	+	0.185892i
$351$	73.4466			0.209249
$352$	36.7822	+	63.7086i	0.104495	+	0.180990i
$353$	205.212	+	118.479i	0.581337	+	0.335635i	0.761664	−	0.647972i	$-0.224382\pi$
$353$	205.212	+	118.479i	0.581337	+	0.335635i	−0.180328	+	0.983607i	$0.557716\pi$
$354$	120.865	−	209.344i	0.341426	−	0.591367i
$355$	−181.921	+	105.032i	−0.512455	+	0.295866i
$356$			453.619i			1.27421i
$357$	190.526	+	71.9759i	0.533686	+	0.201613i
$358$	−348.306			−0.972921
$359$	98.9067	+	171.311i	0.275506	+	0.477191i	0.970263	−	0.242054i	$-0.0778212\pi$
$359$	98.9067	+	171.311i	0.275506	+	0.477191i	−0.694757	+	0.719245i	$0.744488\pi$
$360$	−10.4346	−	6.02441i	−0.0289850	−	0.0167345i
$361$	101.339	−	175.525i	0.280719	−	0.486219i
$362$	−323.433	+	186.734i	−0.893462	+	0.515840i
$363$			205.120i			0.565070i
$364$	−450.328	+	73.7819i	−1.23717	+	0.202697i
$365$	−100.024			−0.274039
$366$	−223.643	−	387.361i	−0.611046	−	1.05836i
$367$	492.379	+	284.275i	1.34163	+	0.774592i	0.987047	−	0.160431i	$-0.0512884\pi$
$367$	492.379	+	284.275i	1.34163	+	0.774592i	0.354586	+	0.935023i	$0.384622\pi$
$368$	130.234	−	225.571i	0.353896	−	0.612965i
$369$	65.0325	−	37.5465i	0.176240	−	0.101752i
$370$			95.1117i			0.257059i
$371$	−64.2722	−	392.286i	−0.173241	−	1.05737i
$372$	−458.893			−1.23358
$373$	−53.5591	−	92.7670i	−0.143590	−	0.248705i	0.785256	−	0.619171i	$-0.212531\pi$
$373$	−53.5591	−	92.7670i	−0.143590	−	0.248705i	−0.928846	+	0.370466i	$0.879198\pi$
$374$	−68.4907	−	39.5431i	−0.183130	−	0.105730i
$375$	9.68246	−	16.7705i	0.0258199	−	0.0447214i
$376$	−46.5058	+	26.8501i	−0.123686	+	0.0714099i
$377$			311.873i			0.827248i
$378$	37.7223	−	99.8537i	0.0997943	−	0.264163i
$379$	295.227			0.778962			0.389481	−	0.921034i	$-0.372654\pi$
$379$	295.227			0.778962			0.389481	+	0.921034i	$0.372654\pi$
$380$	122.423	+	212.044i	0.322167	+	0.558010i
$381$	258.432	+	149.206i	0.678299	+	0.391616i
$382$	−455.611	+	789.142i	−1.19270	+	2.06582i
$383$	−461.928	+	266.694i	−1.20608	+	0.696330i	−0.961900	−	0.273400i	$-0.911852\pi$
$383$	−461.928	+	266.694i	−1.20608	+	0.696330i	−0.244179	+	0.969730i	$0.578518\pi$
$384$		−	98.3863i		−	0.256214i
$385$	15.9065	+	19.4307i	0.0413156	+	0.0504694i
$386$	195.608			0.506757
$387$	−82.8395	−	143.482i	−0.214056	−	0.370755i
$388$	−622.252	−	359.257i	−1.60374	−	0.925921i
$389$	310.439	−	537.697i	0.798044	−	1.38225i	−0.122844	−	0.992426i	$-0.539201\pi$
$389$	310.439	−	537.697i	0.798044	−	1.38225i	0.920888	−	0.389827i	$-0.127465\pi$
$390$	139.129	−	80.3264i	0.356742	−	0.205965i
$391$			332.043i			0.849214i
$392$	−17.3818	+	86.2770i	−0.0443414	+	0.220094i
$393$	428.169			1.08949
$394$	105.502	+	182.735i	0.267772	+	0.463795i
$395$	258.739	+	149.383i	0.655035	+	0.378185i
$396$	−11.0986	+	19.2234i	−0.0280268	+	0.0485438i
$397$	−182.330	+	105.268i	−0.459269	+	0.265159i	−0.711737	−	0.702446i	$-0.752091\pi$
$397$	−182.330	+	105.268i	−0.459269	+	0.265159i	0.252468	+	0.967605i	$0.418758\pi$
$398$			738.821i			1.85633i
$399$	−222.739	+	182.340i	−0.558244	+	0.456993i
$400$	65.8860			0.164715
$401$	89.4626	+	154.954i	0.223099	+	0.386418i	0.955747	−	0.294189i	$-0.0950495\pi$
$401$	89.4626	+	154.954i	0.223099	+	0.386418i	−0.732649	+	0.680607i	$0.761716\pi$
$402$	−14.2844	−	8.24712i	−0.0355334	−	0.0205152i
$403$	405.991	−	703.197i	1.00742	−	1.74490i
$404$	396.515	−	228.928i	0.981474	−	0.566654i
$405$			20.1246i			0.0496904i
$406$	424.004	+	160.178i	1.04435	+	0.394528i
$407$	23.2530			0.0571327
$408$	26.1296	+	45.2578i	0.0640432	+	0.110926i
$409$	−382.695	−	220.949i	−0.935685	−	0.540218i	−0.0470800	−	0.998891i	$-0.514992\pi$
$409$	−382.695	−	220.949i	−0.935685	−	0.540218i	−0.888605	+	0.458673i	$0.848325\pi$
$410$	82.1272	−	142.248i	0.200310	−	0.346947i
$411$	103.340	−	59.6634i	0.251436	−	0.145166i
$412$			117.794i			0.285909i
$413$	328.520	−	53.8247i	0.795447	−	0.130326i
$414$	174.022			0.420343
$415$	24.4477	+	42.3446i	0.0589100	+	0.102035i
$416$	561.312	+	324.074i	1.34931	+	0.779023i
$417$	82.5295	−	142.945i	0.197912	−	0.342795i
$418$	96.8017	−	55.8885i	0.231583	−	0.133705i
$419$			708.526i			1.69099i	0.533980	+	0.845497i	$0.320696\pi$
$419$			708.526i			1.69099i	−0.533980	+	0.845497i	$0.679304\pi$
$420$	−20.2165	−	123.392i	−0.0481345	−	0.293789i
$421$	88.2687			0.209664			0.104832	−	0.994490i	$-0.466569\pi$
$421$	88.2687			0.209664			0.104832	+	0.994490i	$0.466569\pi$
$422$	325.328	+	563.484i	0.770919	+	1.33527i
$423$	77.6766	+	44.8466i	0.183633	+	0.106020i
$424$	50.9994	−	88.3336i	0.120282	−	0.208334i
$425$	−72.7386	+	41.9956i	−0.171150	+	0.0988133i
$426$		−	477.509i		−	1.12091i
$427$	217.688	−	576.236i	0.509807	−	1.34950i
$428$	28.3247			0.0661791
$429$	−19.6383	−	34.0145i	−0.0457769	−	0.0792879i
$430$	−313.845	−	181.198i	−0.729872	−	0.421392i
$431$	−358.982	+	621.776i	−0.832906	+	1.44264i	0.0628182	+	0.998025i	$0.479991\pi$
$431$	−358.982	+	621.776i	−0.832906	+	1.44264i	−0.895724	+	0.444610i	$0.853342\pi$
$432$	−59.2974	+	34.2354i	−0.137263	+	0.0792486i
$433$			269.982i			0.623516i	0.950162	+	0.311758i	$0.100918\pi$
$433$			269.982i			0.623516i	−0.950162	+	0.311758i	$0.899082\pi$
$434$	−747.509	−	913.125i	−1.72237	−	2.10397i
$435$	−85.4542			−0.196446
$436$	275.166	+	476.602i	0.631115	+	1.09312i
$437$	−406.421	−	234.647i	−0.930025	−	0.536950i
$438$	113.685	−	196.909i	0.259555	−	0.449563i
$439$	−380.277	+	219.553i	−0.866235	+	0.500121i	−0.866095	−	0.499879i	$-0.833378\pi$
$439$	−380.277	+	219.553i	−0.866235	+	0.500121i	−0.000139457		1.00000i	$0.500044\pi$
$440$			6.44327i			0.0146438i
$441$	139.314	−	46.9098i	0.315905	−	0.106371i
$442$	−696.798			−1.57647
$443$	−222.566	−	385.496i	−0.502407	−	0.870195i	−0.999996	−	0.00278185i	$-0.999115\pi$
$443$	−222.566	−	385.496i	−0.502407	−	0.870195i	0.497589	−	0.867413i	$-0.334219\pi$
$444$	−100.272	−	57.8922i	−0.225838	−	0.130388i
$445$	109.964	−	190.464i	0.247111	−	0.428009i
$446$	102.773	−	59.3363i	0.230434	−	0.133041i
$447$			421.845i			0.943725i
$448$	443.385	−	362.967i	0.989698	−	0.810193i
$449$	180.242			0.401431			0.200715	−	0.979650i	$-0.435673\pi$
$449$	180.242			0.401431			0.200715	+	0.979650i	$0.435673\pi$
$450$	22.0097	+	38.1219i	0.0489105	+	0.0847154i
$451$	−34.7771	−	20.0785i	−0.0771110	−	0.0445200i
$452$	404.070	−	699.870i	0.893960	−	1.54838i
$453$	262.691	−	151.665i	0.579892	−	0.334801i
$454$			110.172i			0.242670i
$455$	206.968	+	78.1875i	0.454875	+	0.171841i
$456$	−73.8609			−0.161976
$457$	−42.3220	−	73.3038i	−0.0926083	−	0.160402i	0.816000	−	0.578052i	$-0.196187\pi$
$457$	−42.3220	−	73.3038i	−0.0926083	−	0.160402i	−0.908608	+	0.417650i	$0.862854\pi$
$458$	−60.4488	−	34.9001i	−0.131984	−	0.0762011i
$459$	43.6431	−	75.5921i	0.0950831	−	0.164689i
$460$	176.538	−	101.924i	0.383779	−	0.221575i
$461$		−	107.442i		−	0.233062i	−0.993187	−	0.116531i	$-0.962822\pi$
$461$		−	107.442i		−	0.233062i	0.993187	−	0.116531i	$-0.0371775\pi$
$462$	−56.3304	+	9.22919i	−0.121927	+	0.0199766i
$463$	149.680			0.323282			0.161641	−	0.986850i	$-0.448321\pi$
$463$	149.680			0.323282			0.161641	+	0.986850i	$0.448321\pi$
$464$	−145.372	−	251.792i	−0.313302	−	0.542655i
$465$	192.678	+	111.243i	0.414362	+	0.239232i
$466$	556.267	−	963.483i	1.19371	−	2.06756i
$467$	−479.199	+	276.666i	−1.02612	+	0.592432i	−0.915872	−	0.401471i	$-0.868499\pi$
$467$	−479.199	+	276.666i	−1.02612	+	0.592432i	−0.110251	+	0.993904i	$0.535166\pi$
$468$			195.571i			0.417887i
$469$	−3.67269	−	22.4163i	−0.00783090	−	0.0477960i
$470$	196.190			0.417425
$471$	−151.777	−	262.885i	−0.322244	−	0.558142i
$472$	73.9749	+	42.7094i	0.156726	+	0.0904861i
$473$	−44.2996	+	76.7291i	−0.0936566	+	0.162218i
$474$	−588.153	+	339.571i	−1.24083	+	0.716394i
$475$		−	118.710i		−	0.249915i
$476$	−191.655	+	507.326i	−0.402637	+	1.06581i
$477$	−170.364			−0.357158
$478$	−425.477	−	736.948i	−0.890120	−	1.54173i
$479$	29.1066	+	16.8047i	0.0607654	+	0.0350829i	0.530075	−	0.847951i	$-0.322164\pi$
$479$	29.1066	+	16.8047i	0.0607654	+	0.0350829i	−0.469310	+	0.883034i	$0.655497\pi$
$480$	−88.7973	+	153.801i	−0.184994	+	0.320420i
$481$	177.425	−	102.437i	0.368868	−	0.212966i
$482$		−	1239.01i		−	2.57057i
$483$	151.809	+	185.443i	0.314304	+	0.383940i
$484$	−546.187			−1.12849
$485$	174.180	+	301.688i	0.359133	+	0.622037i
$486$	−39.6175	−	22.8732i	−0.0815175	−	0.0470641i
$487$	−462.447	+	800.981i	−0.949582	+	1.64472i	−0.203277	+	0.979121i	$0.565159\pi$
$487$	−462.447	+	800.981i	−0.949582	+	1.64472i	−0.746305	+	0.665604i	$0.768174\pi$
$488$	136.880	−	79.0277i	0.280492	−	0.161942i
$489$			168.118i			0.343799i
$490$	212.598	−	241.225i	0.433874	−	0.492296i
$491$	−488.514			−0.994937			−0.497469	−	0.867482i	$-0.665737\pi$
$491$	−488.514			−0.994937			−0.497469	+	0.867482i	$0.665737\pi$
$492$	99.9777	+	173.166i	0.203207	+	0.351964i
$493$	320.983	+	185.320i	0.651082	+	0.375902i
$494$	492.412	−	852.883i	0.996785	−	1.72648i
$495$	9.32009	−	5.38096i	0.0188285	−	0.0108706i
$496$			756.972i			1.52615i
$497$	508.848	−	416.557i	1.02384	−	0.838143i
$498$	−111.147			−0.223186
$499$	−161.538	−	279.792i	−0.323723	−	0.560704i	0.657530	−	0.753428i	$-0.271601\pi$
$499$	−161.538	−	279.792i	−0.323723	−	0.560704i	−0.981253	+	0.192724i	$0.938268\pi$
$500$	44.6560	+	25.7821i	0.0893119	+	0.0515643i
$501$	−74.3535	+	128.784i	−0.148410	+	0.257054i
$502$	967.072	−	558.339i	1.92644	−	1.11223i
$503$			78.1922i			0.155452i	0.996975	+	0.0777259i	$0.0247659\pi$
$503$			78.1922i			0.155452i	−0.996975	+	0.0777259i	$0.975234\pi$
$504$	35.2849	+	13.3298i	0.0700097	+	0.0264479i
$505$	−221.983			−0.439571
$506$	−46.5304	−	80.5929i	−0.0919572	−	0.159275i
$507$	−46.1887	−	26.6671i	−0.0911020	−	0.0525977i
$508$	−397.300	+	688.144i	−0.782087	+	1.35461i
$509$	266.782	−	154.027i	0.524131	−	0.302607i	−0.214492	−	0.976726i	$-0.568810\pi$
$509$	266.782	−	154.027i	0.524131	−	0.302607i	0.738623	+	0.674119i	$0.235476\pi$
$510$		−	190.925i		−	0.374363i
$511$	309.005	−	50.6275i	0.604707	−	0.0990753i
$512$	−698.910			−1.36506
$513$	61.6833	+	106.839i	0.120240	+	0.208262i
$514$	97.5574	+	56.3248i	0.189800	+	0.109581i
$515$	28.5552	−	49.4591i	0.0554470	−	0.0960371i
$516$	382.060	−	220.582i	0.740426	−	0.427485i
$517$		−	47.9647i		−	0.0927750i
$518$	−48.1410	−	293.829i	−0.0929363	−	0.567238i
$519$	−245.471			−0.472969
$520$	28.3846	+	49.1636i	0.0545858	+	0.0945453i
$521$	12.6590	+	7.30866i	0.0242974	+	0.0140281i	0.512100	−	0.858926i	$-0.328868\pi$
$521$	12.6590	+	7.30866i	0.0242974	+	0.0140281i	−0.487802	+	0.872954i	$0.662201\pi$
$522$	97.1252	−	168.226i	0.186064	−	0.322272i
$523$	−362.441	+	209.255i	−0.693004	+	0.400106i	−0.804736	−	0.593632i	$-0.797693\pi$
$523$	−362.441	+	209.255i	−0.693004	+	0.400106i	0.111732	+	0.993738i	$0.464360\pi$
$524$			1140.11i			2.17579i
$525$	−21.4236	+	56.7100i	−0.0408069	+	0.108019i
$526$	696.682			1.32449
$527$	−482.493	−	835.702i	−0.915546	−	1.58577i
$528$	31.7101	+	18.3079i	0.0600571	+	0.0346740i
$529$	69.1428	−	119.759i	0.130705	−	0.226387i
$530$	−322.720	+	186.322i	−0.608906	+	0.351552i
$531$		−	142.671i		−	0.268684i
$532$	−485.530	−	593.103i	−0.912650	−	1.11485i
$533$	−353.808			−0.663806
$534$	249.966	+	432.954i	0.468101	+	0.810775i
$535$	−11.8929	−	6.86635i	−0.0222297	−	0.0128343i
$536$	2.91425	−	5.04763i	0.00543703	−	0.00941722i
$537$	−178.032	+	102.787i	−0.331531	+	0.191410i
$538$			7.06760i			0.0131368i
$539$	−58.9750	−	51.9763i	−0.109416	−	0.0964310i
$540$	−53.5871			−0.0992355
$541$	198.442	+	343.712i	0.366806	+	0.635327i	0.989064	−	0.147485i	$-0.0471178\pi$
$541$	198.442	+	343.712i	0.366806	+	0.635327i	−0.622258	+	0.782812i	$0.713784\pi$
$542$	−385.563	−	222.605i	−0.711372	−	0.410711i
$543$	−110.213	+	190.894i	−0.202970	+	0.351554i
$544$	667.082	−	385.140i	1.22625	−	0.707978i
$545$		−	266.819i		−	0.489576i
$546$	−389.156	+	318.574i	−0.712740	+	0.583468i
$547$	608.832			1.11304			0.556519	−	0.830835i	$-0.312137\pi$
$547$	608.832			1.11304			0.556519	+	0.830835i	$0.312137\pi$
$548$	158.870	+	275.170i	0.289908	+	0.502136i
$549$	−228.625	−	131.997i	−0.416438	−	0.240431i
$550$	11.7700	−	20.3862i	0.0214000	−	0.0370659i
$551$	−453.664	+	261.923i	−0.823346	+	0.475359i
$552$			61.4934i			0.111401i
$553$	−874.934	−	330.528i	−1.58216	−	0.597701i
$554$	−80.1240			−0.144628
$555$	28.0680	+	48.6152i	0.0505730	+	0.0875949i
$556$	380.630	+	219.757i	0.684586	+	0.395246i
$557$	−499.110	+	864.484i	−0.896068	+	1.55204i	−0.0635915	+	0.997976i	$0.520255\pi$
$557$	−499.110	+	864.484i	−0.896068	+	1.55204i	−0.832477	+	0.554060i	$0.813078\pi$
$558$	−437.988	+	252.872i	−0.784924	+	0.453176i
$559$			780.613i			1.39645i
$560$	−203.542	+	33.3484i	−0.363468	+	0.0595507i
$561$	−46.6776			−0.0832042
$562$	470.677	+	815.237i	0.837504	+	1.45060i
$563$	347.219	+	200.467i	0.616729	+	0.356069i	0.775595	−	0.631231i	$-0.217450\pi$
$563$	347.219	+	200.467i	0.616729	+	0.356069i	−0.158865	+	0.987300i	$0.550783\pi$
$564$	−119.416	+	206.835i	−0.211730	+	0.366728i
$565$	−339.319	+	195.906i	−0.600565	+	0.346736i
$566$			94.4074i			0.166797i
$567$	−10.1861	−	62.1711i	−0.0179649	−	0.109649i
$568$	168.735			0.297069
$569$	263.756	+	456.838i	0.463543	+	0.802879i	0.999134	−	0.0415977i	$-0.0132448\pi$
$569$	263.756	+	456.838i	0.463543	+	0.802879i	−0.535592	+	0.844477i	$0.679911\pi$
$570$	233.693	+	134.923i	0.409987	+	0.236706i
$571$	56.0721	−	97.1198i	0.0981999	−	0.170087i	−0.812740	−	0.582627i	$-0.802025\pi$
$571$	56.0721	−	97.1198i	0.0981999	−	0.170087i	0.910940	+	0.412540i	$0.135358\pi$
$572$	90.5727	−	52.2922i	0.158344	−	0.0914199i
$573$			537.814i			0.938593i
$574$	−181.717	+	481.018i	−0.316579	+	0.838010i
$575$	−98.8325			−0.171883
$576$	−122.787	−	212.673i	−0.213171	−	0.369224i
$577$	161.212	+	93.0756i	0.279396	+	0.161309i	0.633150	−	0.774029i	$-0.281762\pi$
$577$	161.212	+	93.0756i	0.279396	+	0.161309i	−0.353754	+	0.935339i	$0.615095\pi$
$578$	10.0051	−	17.3293i	0.0173099	−	0.0299816i
$579$	99.9828	−	57.7251i	0.172682	−	0.0996979i
$580$		−	227.545i		−	0.392318i
$581$	−96.9591	−	118.441i	−0.166883	−	0.203857i
$582$	−791.874			−1.36061
$583$	45.5523	+	78.8989i	0.0781343	+	0.135333i
$584$	69.5807	+	40.1724i	0.119145	+	0.0687884i
$585$	47.4095	−	82.1157i	0.0810420	−	0.140369i
$586$	475.560	−	274.564i	0.811535	−	0.468540i
$587$		−	887.350i		−	1.51167i	−0.654763	−	0.755835i	$-0.727231\pi$
$587$		−	887.350i		−	1.51167i	0.654763	−	0.755835i	$-0.272769\pi$
$588$	124.910	+	370.961i	0.212432	+	0.630887i
$589$	1363.87			2.31557
$590$	−156.036	−	270.262i	−0.264467	−	0.458071i
$591$	107.852	+	62.2686i	0.182491	+	0.105361i
$592$	−95.4969	+	165.405i	−0.161312	+	0.279401i
$593$	886.844	−	512.020i	1.49552	−	0.863440i	0.495535	−	0.868588i	$-0.334972\pi$
$593$	886.844	−	512.020i	1.49552	−	0.863440i	0.999987	+	0.00514842i	$0.00163880\pi$
$594$			24.4635i			0.0411843i
$595$	203.456	−	166.554i	0.341942	−	0.279923i
$596$	−1123.27			−1.88469
$597$	218.030	+	377.639i	0.365210	+	0.632562i
$598$	−710.073	−	409.961i	−1.18741	−	0.685553i
$599$	−355.717	+	616.120i	−0.593851	+	1.02858i	0.399857	+	0.916578i	$0.369060\pi$
$599$	−355.717	+	616.120i	−0.593851	+	1.02858i	−0.993708	+	0.112003i	$0.964273\pi$
$600$	−13.4710	+	7.77748i	−0.0224516	+	0.0129625i
$601$			3.30599i			0.00550082i	0.999996	+	0.00275041i	$0.000875484\pi$
$601$			3.30599i			0.00550082i	−0.999996	+	0.00275041i	$0.999125\pi$
$602$	1061.28	+	400.924i	1.76292	+	0.665987i
$603$	−9.73508			−0.0161444
$604$	403.848	+	699.485i	0.668622	+	1.15809i
$605$	229.331	+	132.405i	0.379060	+	0.218851i
$606$	252.301	−	436.999i	0.416339	−	0.721120i
$607$	470.370	−	271.568i	0.774910	−	0.447395i	−0.0597133	−	0.998216i	$-0.519019\pi$
$607$	470.370	−	271.568i	0.774910	−	0.447395i	0.834623	+	0.550821i	$0.185685\pi$
$608$			1088.68i			1.79059i
$609$	263.994	−	43.2528i	0.433488	−	0.0710227i
$610$	−577.443			−0.946629
$611$	−211.299	−	365.981i	−0.345825	−	0.598987i
$612$	201.284	+	116.212i	0.328896	+	0.189888i
$613$	210.450	−	364.510i	0.343311	−	0.594632i	−0.641734	−	0.766927i	$-0.721785\pi$
$613$	210.450	−	364.510i	0.343311	−	0.594632i	0.985045	+	0.172295i	$0.0551181\pi$
$614$	−31.2942	+	18.0677i	−0.0509678	+	0.0294262i
$615$		−	96.9448i		−	0.157634i
$616$	−3.26128	−	19.9052i	−0.00529428	−	0.0323137i
$617$	305.401			0.494978			0.247489	−	0.968891i	$-0.420395\pi$
$617$	305.401			0.494978			0.247489	+	0.968891i	$0.420395\pi$
$618$	64.9104	+	112.428i	0.105033	+	0.181923i
$619$	185.129	+	106.885i	0.299078	+	0.172673i	0.642029	−	0.766681i	$-0.278093\pi$
$619$	185.129	+	106.885i	0.299078	+	0.172673i	−0.342950	+	0.939353i	$0.611426\pi$
$620$	−296.214	+	513.057i	−0.477764	+	0.827512i
$621$	88.9492	−	51.3549i	0.143235	−	0.0826970i
$622$		−	1024.32i		−	1.64681i
$623$	−243.310	+	644.060i	−0.390546	+	1.03380i
$624$	322.607			0.516998
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	927.277	+	535.364i	1.48127	+	0.855213i
$627$	32.9860	−	57.1335i	0.0526093	−	0.0911220i
$628$	700.001	−	404.146i	1.11465	−	0.643545i
$629$		−	243.478i		−	0.387088i
$630$	−87.2903	−	106.630i	−0.138556	−	0.169254i
$631$	−574.361			−0.910239			−0.455120	−	0.890430i	$-0.650403\pi$
$631$	−574.361			−0.910239			−0.455120	+	0.890430i	$0.650403\pi$
$632$	−119.993	−	207.833i	−0.189862	−	0.328850i
$633$	332.575	+	192.012i	0.525394	+	0.303337i
$634$	−654.277	+	1133.24i	−1.03198	+	1.78745i
$635$	333.634	−	192.624i	0.525408	−	0.303344i
$636$		−	453.640i		−	0.713271i
$637$	−678.963	−	136.787i	−1.06588	−	0.214737i
$638$	−103.878			−0.162818
$639$	−140.916	−	244.073i	−0.220525	−	0.381961i
$640$	−109.999	−	63.5081i	−0.171874	−	0.0992314i
$641$	−118.236	+	204.791i	−0.184455	+	0.319486i	−0.943393	−	0.331677i	$-0.892385\pi$
$641$	−118.236	+	204.791i	−0.184455	+	0.319486i	0.758937	+	0.651163i	$0.225719\pi$
$642$	27.0343	−	15.6083i	0.0421095	−	0.0243120i
$643$			36.7218i			0.0571101i	0.999592	+	0.0285551i	$0.00909060\pi$
$643$			36.7218i			0.0571101i	−0.999592	+	0.0285551i	$0.990909\pi$
$644$	−493.792	+	404.231i	−0.766757	+	0.627688i
$645$	−213.891			−0.331614
$646$	−585.199	−	1013.59i	−0.905880	−	1.56903i
$647$	−24.4070	−	14.0914i	−0.0377233	−	0.0217796i	0.481020	−	0.876710i	$-0.340267\pi$
$647$	−24.4070	−	14.0914i	−0.0377233	−	0.0217796i	−0.518743	+	0.854930i	$0.673600\pi$
$648$	8.08259	−	13.9995i	0.0124731	−	0.0216041i
$649$	−66.0739	+	38.1478i	−0.101809	+	0.0587793i
$650$		−	207.402i		−	0.319080i
$651$	−651.548	−	246.139i	−1.00084	−	0.378093i
$652$	−447.658			−0.686592
$653$	266.689	+	461.919i	0.408406	+	0.707380i	0.994711	−	0.102710i	$-0.0327515\pi$
$653$	266.689	+	461.919i	0.408406	+	0.707380i	−0.586305	+	0.810090i	$0.699418\pi$
$654$	525.262	+	303.260i	0.803153	+	0.463700i
$655$	276.382	−	478.707i	0.421957	−	0.730851i
$656$	285.649	−	164.920i	0.435441	−	0.251402i
$657$		−	134.197i		−	0.204257i
$658$	−606.090	+	99.3019i	−0.921110	+	0.150915i
$659$	300.839			0.456509			0.228255	−	0.973601i	$-0.426698\pi$
$659$	300.839			0.456509			0.228255	+	0.973601i	$0.426698\pi$
$660$	14.3282	+	24.8172i	0.0217095	+	0.0376019i
$661$	−1065.65	−	615.252i	−1.61217	−	0.930790i	−0.988865	−	0.148815i	$-0.952454\pi$
$661$	−1065.65	−	615.252i	−1.61217	−	0.930790i	−0.623310	−	0.781975i	$-0.714212\pi$
$662$	89.4853	−	154.993i	0.135174	−	0.234129i
$663$	−356.160	+	205.629i	−0.537194	+	0.310149i
$664$		−	39.2754i		−	0.0591497i
$665$	60.0852	+	366.730i	0.0903536	+	0.551474i
$666$	−127.606			−0.191600
$667$	218.066	+	377.701i	0.326935	+	0.566268i
$668$	−342.922	−	197.986i	−0.513356	−	0.296386i
$669$	35.0209	−	60.6580i	0.0523482	−	0.0906697i
$670$	−18.4411	+	10.6470i	−0.0275241	+	0.0158910i
$671$			141.174i			0.210393i
$672$	196.475	−	520.085i	0.292374	−	0.773936i
$673$	194.527			0.289044			0.144522	−	0.989502i	$-0.453836\pi$
$673$	194.527			0.289044			0.144522	+	0.989502i	$0.453836\pi$
$674$	−619.748	−	1073.43i	−0.919507	−	1.59263i
$675$	22.5000	+	12.9904i	0.0333333	+	0.0192450i
$676$	71.0081	−	122.990i	0.105042	−	0.181937i
$677$	341.492	−	197.161i	0.504420	−	0.291227i	−0.226117	−	0.974100i	$-0.572603\pi$
$677$	341.492	−	197.161i	0.504420	−	0.291227i	0.730537	+	0.682873i	$0.239270\pi$
$678$		−	890.649i		−	1.31364i
$679$	−690.794	−	843.844i	−1.01737	−	1.24278i
$680$	67.4664			0.0992153
$681$	32.5124	+	56.3132i	0.0477422	+	0.0826919i
$682$	234.220	+	135.227i	0.343431	+	0.198280i
$683$	−41.5965	+	72.0473i	−0.0609026	+	0.105486i	−0.894869	−	0.446329i	$-0.852731\pi$
$683$	−41.5965	+	72.0473i	−0.0609026	+	0.105486i	0.833966	+	0.551815i	$0.186065\pi$
$684$	−284.486	+	164.248i	−0.415916	+	0.240129i
$685$		−	154.050i		−	0.224891i
$686$	−534.685	+	852.825i	−0.779424	+	1.24319i
$687$	−41.1969			−0.0599663
$688$	−363.865	−	630.232i	−0.528873	−	0.916035i
$689$	695.148	+	401.344i	1.00892	+	0.582502i
$690$	112.331	−	194.563i	0.162798	−	0.281975i
$691$	−582.709	+	336.427i	−0.843284	+	0.486870i	−0.858379	−	0.513016i	$-0.828528\pi$
$691$	−582.709	+	336.427i	−0.843284	+	0.486870i	0.0150952	+	0.999886i	$0.495195\pi$
$692$		−	653.631i		−	0.944554i
$693$	−26.0690	+	21.3408i	−0.0376177	+	0.0307948i
$694$	1990.94			2.86879
$695$	−106.545	−	184.542i	−0.153302	−	0.265527i
$696$	59.4452	+	34.3207i	0.0854098	+	0.0493114i
$697$	−210.239	+	364.144i	−0.301634	+	0.522445i
$698$	982.673	−	567.346i	1.40784	−	0.812817i
$699$		−	656.630i		−	0.939385i
$700$	−151.006	−	57.0462i	−0.215722	−	0.0814945i
$701$	−1004.17			−1.43248			−0.716242	−	0.697852i	$-0.754139\pi$
$701$	−1004.17			−1.43248			−0.716242	+	0.697852i	$0.754139\pi$
$702$	107.769	+	186.662i	0.153517	+	0.265900i
$703$	298.018	+	172.061i	0.423923	+	0.244752i
$704$	−65.6619	+	113.730i	−0.0932698	+	0.161548i
$705$	100.280	−	57.8967i	0.142241	−	0.0821230i
$706$			695.385i			0.984964i
$707$	685.775	−	112.357i	0.969978	−	0.158921i
$708$	379.901			0.536583
$709$	−516.313	−	894.280i	−0.728227	−	1.26133i	−0.957632	−	0.287995i	$-0.907011\pi$
$709$	−516.313	−	894.280i	−0.728227	−	1.26133i	0.229405	−	0.973331i	$-0.426322\pi$
$710$	−533.872	−	308.231i	−0.751932	−	0.434128i
$711$	−200.418	+	347.135i	−0.281882	+	0.488235i
$712$	−152.991	+	88.3294i	−0.214875	+	0.124058i
$713$		−	1135.50i		−	1.59256i
$714$	96.6372	+	589.826i	0.135346	+	0.826087i
$715$	−50.7058			−0.0709173
$716$	−273.698	−	474.058i	−0.382259	−	0.662093i
$717$	−434.955	−	251.121i	−0.606632	−	0.350239i
$718$	−290.254	+	502.735i	−0.404254	+	0.700189i
$719$	504.385	−	291.207i	0.701509	−	0.405017i	−0.106400	−	0.994323i	$-0.533932\pi$
$719$	504.385	−	291.207i	0.701509	−	0.405017i	0.807909	+	0.589307i	$0.200599\pi$
$720$			88.3954i			0.122771i
$721$	−63.1820	+	167.248i	−0.0876310	+	0.231966i
$722$	594.787			0.823805
$723$	−365.640	−	633.307i	−0.505726	−	0.875944i
$724$	−508.306	−	293.470i	−0.702080	−	0.405346i
$725$	−55.1604	+	95.5407i	−0.0760834	+	0.131780i
$726$	−521.306	+	300.976i	−0.718052	+	0.414567i
$727$		−	480.491i		−	0.660924i	−0.943819	−	0.330462i	$-0.892796\pi$
$727$		−	480.491i		−	0.660924i	0.943819	−	0.330462i	$-0.107204\pi$
$728$	−112.573	−	137.514i	−0.154633	−	0.188893i
$729$	−27.0000			−0.0370370
$730$	−146.767	−	254.208i	−0.201051	−	0.348230i
$731$	803.417	+	463.853i	1.09907	+	0.634546i
$732$	351.476	−	608.774i	0.480158	−	0.831659i
$733$	22.7350	−	13.1260i	0.0310163	−	0.0179073i	−0.484412	−	0.874840i	$-0.660966\pi$
$733$	22.7350	−	13.1260i	0.0310163	−	0.0179073i	0.515428	+	0.856933i	$0.327633\pi$
$734$			1668.49i			2.27314i
$735$	37.4803	−	186.038i	0.0509935	−	0.253113i
$736$	906.388			1.23151
$737$	2.60299	+	4.50850i	0.00353187	+	0.00611737i
$738$	190.846	+	110.185i	0.258599	+	0.149302i
$739$	120.242	−	208.266i	0.162710	−	0.281821i	−0.773130	−	0.634248i	$-0.781310\pi$
$739$	120.242	−	208.266i	0.162710	−	0.281821i	0.935840	+	0.352426i	$0.114643\pi$
$740$	−129.451	+	74.7385i	−0.174934	+	0.100998i
$741$		−	581.254i		−	0.784418i
$742$	902.673	−	738.953i	1.21654	−	0.995893i
$743$	282.401			0.380082			0.190041	−	0.981776i	$-0.439138\pi$
$743$	282.401			0.380082			0.190041	+	0.981776i	$0.439138\pi$
$744$	−89.3564	−	154.770i	−0.120103	−	0.208024i
$745$	471.637	+	272.300i	0.633070	+	0.365503i
$746$	157.176	−	272.237i	0.210692	−	0.364929i
$747$	−56.8112	+	32.8000i	−0.0760525	+	0.0439089i
$748$		−	124.291i		−	0.166165i
$749$	40.2161	+	15.1927i	0.0536931	+	0.0202839i
$750$	56.8288			0.0757718
$751$	579.282	+	1003.35i	0.771347	+	1.33601i	0.936825	+	0.349799i	$0.113750\pi$
$751$	579.282	+	1003.35i	0.771347	+	1.33601i	−0.165477	+	0.986214i	$0.552916\pi$
$752$	341.187	+	196.984i	0.453706	+	0.261947i
$753$	329.538	−	570.777i	0.437634	−	0.758003i
$754$	−792.613	+	457.615i	−1.05121	+	0.606917i
$755$		−	391.597i		−	0.518671i
$756$	165.547	−	27.1233i	0.218978	−	0.0358773i
$757$	525.023			0.693558			0.346779	−	0.937947i	$-0.387275\pi$
$757$	525.023			0.693558			0.346779	+	0.937947i	$0.387275\pi$
$758$	433.190	+	750.308i	0.571491	+	0.989852i
$759$	−47.5669	−	27.4627i	−0.0626704	−	0.0361828i
$760$	−47.6770	+	82.5790i	−0.0627329	+	0.108657i
$761$	36.2141	−	20.9082i	0.0475875	−	0.0274746i	−0.476018	−	0.879436i	$-0.657920\pi$
$761$	36.2141	−	20.9082i	0.0475875	−	0.0274746i	0.523605	+	0.851961i	$0.324587\pi$
$762$			875.727i			1.14925i
$763$	135.051	+	824.285i	0.177000	+	1.08032i
$764$	−1432.07			−1.87444
$765$	−56.3431	−	97.5890i	−0.0736511	−	0.127567i
$766$	−1355.59	−	782.649i	−1.76970	−	1.02174i
$767$	−336.105	+	582.151i	−0.438207	+	0.758998i
$768$	−241.102	+	139.200i	−0.313935	+	0.181250i
$769$		−	223.564i		−	0.290720i	−0.989379	−	0.145360i	$-0.953566\pi$
$769$		−	223.564i		−	0.290720i	0.989379	−	0.145360i	$-0.0464341\pi$
$770$	−26.0426	+	68.9368i	−0.0338216	+	0.0895283i
$771$	66.4871			0.0862348
$772$	153.708	+	266.231i	0.199104	+	0.344859i
$773$	198.633	+	114.681i	0.256963	+	0.148358i	0.622948	−	0.782263i	$-0.285935\pi$
$773$	198.633	+	114.681i	0.256963	+	0.148358i	−0.365985	+	0.930621i	$0.619268\pi$
$774$	243.103	−	421.067i	0.314087	−	0.544014i
$775$	248.747	−	143.614i	0.320963	−	0.185308i
$776$		−	279.821i		−	0.360594i
$777$	−111.317	−	135.981i	−0.143266	−	0.175007i
$778$	1822.05			2.34196
$779$	−297.142	−	514.666i	−0.381441	−	0.660675i
$780$	218.655	+	126.241i	0.280327	+	0.161847i
$781$	−75.3567	+	130.522i	−0.0964874	+	0.167121i
$782$	−843.874	+	487.211i	−1.07912	+	0.623032i
$783$		−	114.649i		−	0.146422i
$784$	611.925	−	206.047i	0.780516	−	0.262815i
$785$	−391.886			−0.499218
$786$	628.259	+	1088.18i	0.799311	+	1.38445i
$787$	−439.545	−	253.771i	−0.558507	−	0.322454i	0.194039	−	0.980994i	$-0.437841\pi$
$787$	−439.545	−	253.771i	−0.558507	−	0.322454i	−0.752546	+	0.658540i	$0.771174\pi$
$788$	−165.807	+	287.186i	−0.210415	+	0.364449i
$789$	356.101	−	205.595i	0.451332	−	0.260576i
$790$			876.767i			1.10983i
$791$	949.102	−	776.961i	1.19988	−	0.982251i
$792$	−8.64456			−0.0109148
$793$	621.915	+	1077.19i	0.784256	+	1.35837i
$794$	−535.070	−	308.923i	−0.673892	−	0.389072i
$795$	−109.970	+	190.473i	−0.138327	+	0.239589i
$796$	−1005.57	+	580.563i	−1.26327	+	0.729351i
$797$		−	188.007i		−	0.235893i	−0.993020	−	0.117946i	$-0.962369\pi$
$797$		−	188.007i		−	0.235893i	0.993020	−	0.117946i	$-0.0376311\pi$
$798$	−790.240	−	298.533i	−0.990276	−	0.374101i
$799$	−502.230			−0.628573
$800$	114.637	+	198.557i	0.143296	+	0.248196i
$801$	255.534	+	147.533i	0.319019	+	0.184186i
$802$	−262.539	+	454.732i	−0.327356	+	0.566997i
$803$	−62.1490	+	35.8817i	−0.0773960	+	0.0446846i
$804$		−	25.9223i		−	0.0322416i
$805$	305.324	−	50.0243i	0.379284	−	0.0621420i
$806$	2382.86			2.95641
$807$	2.08569	+	3.61252i	0.00258450	+	0.00447648i
$808$	154.420	+	89.1546i	0.191114	+	0.110340i
$809$	357.632	−	619.436i	0.442066	−	0.765681i	−0.555776	−	0.831332i	$-0.687579\pi$
$809$	357.632	−	619.436i	0.442066	−	0.765681i	0.997843	+	0.0656506i	$0.0209123\pi$
$810$	−51.1460	+	29.5291i	−0.0631432	+	0.0364557i
$811$		−	466.873i		−	0.575676i	−0.957679	−	0.287838i	$-0.907063\pi$
$811$		−	466.873i		−	0.575676i	0.957679	−	0.287838i	$-0.0929365\pi$
$812$	115.172	+	702.955i	0.141838	+	0.865708i
$813$	−262.768			−0.323208
$814$	34.1195	+	59.0967i	0.0419158	+	0.0726003i
$815$	187.961	+	108.519i	0.230627	+	0.133153i
$816$	191.698	−	332.031i	0.234924	−	0.406901i
$817$	−1135.51	+	655.590i	−1.38986	+	0.802435i
$818$		−	1296.81i		−	1.58534i
$819$	−104.900	+	277.677i	−0.128082	+	0.339044i
$820$	258.141			0.314806
$821$	−472.000	−	817.527i	−0.574908	−	0.995770i	−0.996052	−	0.0887760i	$-0.971704\pi$
$821$	−472.000	−	817.527i	−0.574908	−	0.995770i	0.421144	−	0.906994i	$-0.361629\pi$
$822$	303.265	+	175.090i	0.368935	+	0.213005i
$823$	−668.349	+	1157.61i	−0.812089	+	1.40658i	0.0993107	+	0.995056i	$0.468336\pi$
$823$	−668.349	+	1157.61i	−0.812089	+	1.40658i	−0.911400	+	0.411523i	$0.864997\pi$
$824$	−39.7282	+	22.9371i	−0.0482139	+	0.0278363i
$825$		−	13.8936i		−	0.0168407i
$826$	618.835	+	755.943i	0.749195	+	0.915185i
$827$	−429.075			−0.518833			−0.259417	−	0.965766i	$-0.583530\pi$
$827$	−429.075			−0.518833			−0.259417	+	0.965766i	$0.583530\pi$
$828$	136.746	+	236.851i	0.165152	+	0.286052i
$829$	191.041	+	110.298i	0.230447	+	0.133049i	0.610778	−	0.791802i	$-0.290857\pi$
$829$	191.041	+	110.298i	0.230447	+	0.133049i	−0.380331	+	0.924850i	$0.624190\pi$
$830$	−71.7448	+	124.266i	−0.0864395	+	0.149718i
$831$	−40.9544	+	23.6450i	−0.0492833	+	0.0284537i
$832$			1157.04i			1.39068i
$833$	−544.234	+	617.516i	−0.653343	+	0.741316i
$834$	484.387			0.580800
$835$	95.9900	+	166.259i	0.114958	+	0.199113i
$836$	152.133	+	87.8341i	0.181977	+	0.105065i
$837$	−149.248	+	258.505i	−0.178313	+	0.308847i
$838$	−1800.69	+	1039.63i	−2.14880	+	1.24061i
$839$			630.841i			0.751896i	0.926641	+	0.375948i	$0.122683\pi$
$839$			630.841i			0.751896i	−0.926641	+	0.375948i	$0.877317\pi$
$840$	37.6794	−	30.8454i	0.0448564	−	0.0367207i
$841$	−354.172			−0.421132
$842$	129.518	+	224.332i	0.153822	+	0.266427i
$843$	481.162	+	277.799i	0.570773	+	0.329536i
$844$	−511.283	+	885.569i	−0.605786	+	1.04925i
$845$	−59.6293	+	34.4270i	−0.0705673	+	0.0407420i
$846$			263.216i			0.311130i
$847$	−775.492	−	292.962i	−0.915575	−	0.345881i
$848$	−748.308			−0.882439
$849$	27.8601	+	48.2552i	0.0328152	+	0.0568377i
$850$	−213.461	−	123.242i	−0.251130	−	0.144990i
$851$	143.250	−	248.117i	0.168332	−	0.291559i
$852$	649.910	−	375.226i	0.762805	−	0.440406i
$853$		−	149.967i		−	0.175812i	−0.996129	−	0.0879059i	$-0.971983\pi$
$853$		−	149.967i		−	0.175812i	0.996129	−	0.0879059i	$-0.0280175\pi$
$854$	1783.90	−	292.274i	2.08887	−	0.342242i
$855$	159.266			0.186276
$856$	5.51543	+	9.55300i	0.00644326	+	0.0111600i
$857$	−927.899	−	535.723i	−1.08273	−	0.625114i	−0.151098	−	0.988519i	$-0.548281\pi$
$857$	−927.899	−	535.723i	−1.08273	−	0.625114i	−0.931632	+	0.363404i	$0.881614\pi$
$858$	57.6311	−	99.8200i	0.0671691	−	0.116340i
$859$	−563.339	+	325.244i	−0.655808	+	0.378631i	−0.790678	−	0.612232i	$-0.790272\pi$
$859$	−563.339	+	325.244i	−0.655808	+	0.378631i	0.134870	+	0.990863i	$0.456938\pi$
$860$		−	569.541i		−	0.662257i
$861$	49.0688	+	299.492i	0.0569905	+	0.347842i
$862$	−2106.96			−2.44427
$863$	−482.709	−	836.077i	−0.559339	−	0.968803i	−0.997552	−	0.0699320i	$-0.977722\pi$
$863$	−482.709	−	836.077i	−0.559339	−	0.968803i	0.438213	−	0.898871i	$-0.355612\pi$
$864$	−206.346	−	119.134i	−0.238827	−	0.137887i
$865$	−158.451	+	274.445i	−0.183180	+	0.317277i
$866$	−686.150	+	396.149i	−0.792321	+	0.457447i
$867$		−	11.8102i		−	0.0136220i
$868$	655.410	−	1734.92i	0.755081	−	1.99876i
$869$	214.353			0.246666
$870$	−125.388	−	217.179i	−0.144124	−	0.249631i
$871$	39.7227	+	22.9339i	0.0456058	+	0.0263305i
$872$	−107.162	+	185.610i	−0.122892	+	0.212855i
$873$	−404.757	+	233.686i	−0.463639	+	0.267682i
$874$		−	1377.21i		−	1.57575i
$875$	49.5748	+	60.5585i	0.0566570	+	0.0692097i
$876$	357.334			0.407916
$877$	264.508	+	458.141i	0.301605	+	0.522396i	0.976500	−	0.215518i	$-0.0691441\pi$
$877$	264.508	+	458.141i	0.301605	+	0.522396i	−0.674894	+	0.737914i	$0.735811\pi$
$878$	−1115.97	−	644.307i	−1.27104	−	0.733834i
$879$	162.051	−	280.681i	0.184358	−	0.319318i
$880$	40.9376	−	23.6353i	0.0465200	−	0.0268583i
$881$		−	135.937i		−	0.154299i	−0.997020	−	0.0771494i	$-0.975418\pi$
$881$		−	135.937i		−	0.154299i	0.997020	−	0.0771494i	$-0.0245819\pi$
$882$	323.637	+	285.231i	0.366936	+	0.323391i
$883$	−322.267			−0.364968			−0.182484	−	0.983209i	$-0.558414\pi$
$883$	−322.267			−0.364968			−0.182484	+	0.983209i	$0.558414\pi$
$884$	−547.542	−	948.371i	−0.619391	−	1.07282i
$885$	−159.511	−	92.0940i	−0.180239	−	0.104061i
$886$	653.150	−	1131.29i	0.737189	−	1.27685i
$887$	−423.336	+	244.413i	−0.477267	+	0.275550i	−0.719277	−	0.694724i	$-0.755527\pi$
$887$	−423.336	+	244.413i	−0.477267	+	0.275550i	0.242010	+	0.970274i	$0.422193\pi$
$888$		−	45.0915i		−	0.0507787i
$889$	−933.201	+	763.943i	−1.04972	+	0.859329i
$890$	645.410			0.725180
$891$	7.21931	+	12.5042i	0.00810249	+	0.0140339i
$892$	161.518	+	93.2525i	0.181074	+	0.104543i
$893$	354.915	−	614.730i	0.397441	−	0.688388i
$894$	−1072.10	+	618.979i	−1.19922	+	0.692371i
$895$			265.395i			0.296531i
$896$	371.966	+	140.520i	0.415141	+	0.156830i
$897$	−483.927			−0.539495
$898$	264.472	+	458.079i	0.294512	+	0.510111i
$899$	−1097.68	−	633.745i	−1.22100	−	0.704944i
$900$	−34.5904	+	59.9123i	−0.0384337	+	0.0665692i
$901$	826.136	−	476.970i	0.916911	−	0.529379i
$902$		−	117.846i		−	0.130650i
$903$	660.774	−	108.261i	0.731754	−	0.119891i
$904$	314.725			0.348147
$905$	142.284	+	246.443i	0.157220	+	0.272313i
$906$	770.901	+	445.080i	0.850884	+	0.491258i
$907$	733.851	−	1271.07i	0.809097	−	1.40140i	−0.104393	−	0.994536i	$-0.533290\pi$
$907$	733.851	−	1271.07i	0.809097	−	1.40140i	0.913490	−	0.406861i	$-0.133377\pi$
$908$	−149.949	+	86.5731i	−0.165142	+	0.0953448i
$909$		−	297.822i		−	0.327637i
$910$	104.977	+	640.728i	0.115359	+	0.704097i
$911$	1059.21			1.16269			0.581347	−	0.813656i	$-0.302526\pi$
$911$	1059.21			1.16269			0.581347	+	0.813656i	$0.302526\pi$
$912$	270.938	+	469.278i	0.297081	+	0.514560i
$913$	30.3806	+	17.5402i	0.0332756	+	0.0192117i
$914$	124.199	−	215.119i	0.135885	−	0.235360i
$915$	−295.153	+	170.407i	−0.322572	+	0.186237i
$916$		−	109.698i		−	0.119757i
$917$	−611.529	+	1618.77i	−0.666880	+	1.76528i
$918$	256.153			0.279034
$919$	−108.411	−	187.773i	−0.117966	−	0.204323i	0.800996	−	0.598670i	$-0.204304\pi$
$919$	−108.411	−	187.773i	−0.117966	−	0.204323i	−0.918961	+	0.394347i	$0.870971\pi$
$920$	68.7517	+	39.6938i	0.0747301	+	0.0431455i
$921$	−10.6638	+	18.4702i	−0.0115785	+	0.0200545i
$922$	273.059	−	157.651i	0.296160	−	0.170988i
$923$			1327.88i			1.43865i
$924$	−56.8256	−	69.4158i	−0.0614996	−	0.0751253i
$925$	72.4712			0.0783473
$926$	219.627	+	380.405i	0.237178	+	0.410805i
$927$	66.3563	+	38.3109i	0.0715818	+	0.0413278i
$928$	505.874	−	876.199i	0.545122	−	0.944180i
$929$	1591.30	−	918.738i	1.71292	−	0.988954i	0.782347	−	0.622843i	$-0.214023\pi$
$929$	1591.30	−	918.738i	1.71292	−	0.988954i	0.930571	−	0.366111i	$-0.119311\pi$
$930$			652.913i			0.702057i
$931$	−371.243	−	1102.53i	−0.398757	−	1.18424i
$932$	1748.45			1.87602
$933$	−302.282	−	523.568i	−0.323989	−	0.561166i
$934$	−1406.27	−	811.912i	−1.50564	−	0.869284i
$935$	−30.1302	+	52.1871i	−0.0322249	+	0.0558151i
$936$	−65.9598	+	38.0819i	−0.0704699	+	0.0406858i
$937$		−	111.843i		−	0.119363i	−0.998217	−	0.0596815i	$-0.980992\pi$
$937$		−	111.843i		−	0.119363i	0.998217	−	0.0596815i	$-0.0190085\pi$
$938$	51.5813	−	42.2258i	0.0549907	−	0.0450169i
$939$	631.955			0.673009
$940$	154.165	+	267.022i	0.164006	+	0.284066i
$941$	−1026.44	−	592.613i	−1.09079	−	0.629769i	−0.157005	−	0.987598i	$-0.550184\pi$
$941$	−1026.44	−	592.613i	−1.09079	−	0.629769i	−0.933787	+	0.357829i	$0.883517\pi$
$942$	445.408	−	771.470i	0.472833	−	0.818970i
$943$	−428.488	+	247.388i	−0.454389	+	0.262341i
$944$		−	626.670i		−	0.663845i
$945$	−76.0845	−	28.7428i	−0.0805127	−	0.0304157i
$946$	−260.006			−0.274848
$947$	−286.259	−	495.815i	−0.302280	−	0.523564i	0.674372	−	0.738392i	$-0.264414\pi$
$947$	−286.259	−	495.815i	−0.302280	−	0.523564i	−0.976652	+	0.214828i	$0.931081\pi$
$948$	−924.339	−	533.667i	−0.975041	−	0.562940i
$949$	−316.140	+	547.571i	−0.333130	+	0.576998i
$950$	301.696	−	174.184i	0.317575	−	0.183352i
$951$			772.323i			0.812117i
$952$	−208.424	+	34.1483i	−0.218933	+	0.0358700i
$953$	−1238.36			−1.29943			−0.649714	−	0.760178i	$-0.725112\pi$
$953$	−1238.36			−1.29943			−0.649714	+	0.760178i	$0.725112\pi$
$954$	−249.978	−	432.974i	−0.262031	−	0.453851i
$955$	601.294	+	347.157i	0.629627	+	0.363515i
$956$	668.678	−	1158.18i	0.699454	−	1.21149i
$957$	−53.0961	+	30.6550i	−0.0554818	+	0.0320324i
$958$			98.6312i			0.102955i
$959$	77.9729	+	475.908i	0.0813064	+	0.496255i
$960$	−317.034			−0.330244
$961$	1169.50	+	2025.63i	1.21696	+	2.10783i
$962$	520.678	+	300.614i	0.541245	+	0.312488i
$963$	9.21218	−	15.9560i	0.00956612	−	0.0165690i
$964$	1686.35	−	973.614i	1.74933	−	1.00997i
$965$		−	149.046i		−	0.154451i
$966$	−248.546	+	657.920i	−0.257294	+	0.681076i
$967$	1623.86			1.67927			0.839637	−	0.543148i	$-0.182768\pi$
$967$	1623.86			1.67927			0.839637	+	0.543148i	$0.182768\pi$
$968$	−106.355	−	184.212i	−0.109870	−	0.190301i
$969$	−598.234	−	345.391i	−0.617373	−	0.356440i
$970$	−511.152	+	885.342i	−0.526961	+	0.912723i
$971$	156.256	−	90.2143i	0.160922	−	0.0929086i	−0.417376	−	0.908734i	$-0.637050\pi$
$971$	156.256	−	90.2143i	0.160922	−	0.0929086i	0.578299	+	0.815825i	$0.303717\pi$
$972$		−	71.8947i		−	0.0739657i
$973$	422.557	+	516.177i	0.434282	+	0.530501i
$974$	−2714.22			−2.78667
$975$	−61.2055	−	106.011i	−0.0627748	−	0.108729i
$976$	−1004.21	−	579.782i	−1.02891	−	0.594039i
$977$	31.2859	−	54.1888i	0.0320225	−	0.0554645i	−0.849570	−	0.527476i	$-0.823139\pi$
$977$	31.2859	−	54.1888i	0.0320225	−	0.0554645i	0.881592	+	0.472011i	$0.156472\pi$
$978$	−427.265	+	246.681i	−0.436876	+	0.252231i
$979$		−	157.790i		−	0.161175i
$980$	495.376	+	99.8012i	0.505486	+	0.101838i
$981$	357.975			0.364908
$982$	−716.804	−	1241.54i	−0.729943	−	1.26430i
$983$	−382.880	−	221.056i	−0.389502	−	0.224879i	0.292442	−	0.956283i	$-0.405532\pi$
$983$	−382.880	−	221.056i	−0.389502	−	0.224879i	−0.681944	+	0.731404i	$0.738865\pi$
$984$	−38.9357	+	67.4385i	−0.0395688	+	0.0685351i
$985$	139.237	−	80.3884i	0.141357	−	0.0816126i
$986$			1087.69i			1.10313i
$987$	−280.491	+	229.618i	−0.284185	+	0.232642i
$988$	1547.74			1.56654
$989$	545.816	+	945.381i	0.551886	+	0.955895i
$990$	27.3510	+	15.7911i	0.0276273	+	0.0159506i
$991$	−491.223	+	850.824i	−0.495684	+	0.858551i	−0.999988	−	0.00497599i	$-0.998416\pi$
$991$	−491.223	+	850.824i	−0.495684	+	0.858551i	0.504303	+	0.863527i	$0.331749\pi$
$992$	−2281.24	+	1317.08i	−2.29964	+	1.32770i
$993$		−	105.630i		−	0.106375i
$994$	1805.31	+	681.999i	1.81620	+	0.686116i
$995$	562.951			0.565780
$996$	−87.3387	−	151.275i	−0.0876894	−	0.151883i
$997$	138.793	+	80.1322i	0.139211	+	0.0803733i	0.567988	−	0.823037i	$-0.307722\pi$
$997$	138.793	+	80.1322i	0.139211	+	0.0803733i	−0.428777	+	0.903410i	$0.641055\pi$
$998$	474.053	−	821.084i	0.475003	−	0.822730i
$999$	−65.2241	+	37.6572i	−0.0652894	+	0.0376949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.n.b.31.5	✓	12
3.2	odd	2		315.3.w.b.136.2		12
5.2	odd	4		525.3.s.j.199.3		24
5.3	odd	4		525.3.s.j.199.10		24
5.4	even	2		525.3.o.m.451.2		12
7.3	odd	6		735.3.h.b.391.4		12
7.4	even	3		735.3.h.b.391.3		12
7.5	odd	6	inner	105.3.n.b.61.5	yes	12
21.5	even	6		315.3.w.b.271.2		12
35.12	even	12		525.3.s.j.124.10		24
35.19	odd	6		525.3.o.m.376.2		12
35.33	even	12		525.3.s.j.124.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.b.31.5	✓	12	1.1	even	1	trivial
105.3.n.b.61.5	yes	12	7.5	odd	6	inner
315.3.w.b.136.2		12	3.2	odd	2
315.3.w.b.271.2		12	21.5	even	6
525.3.o.m.376.2		12	35.19	odd	6
525.3.o.m.451.2		12	5.4	even	2
525.3.s.j.124.3		24	35.33	even	12
525.3.s.j.124.10		24	35.12	even	12
525.3.s.j.199.3		24	5.2	odd	4
525.3.s.j.199.10		24	5.3	odd	4
735.3.h.b.391.3		12	7.4	even	3
735.3.h.b.391.4		12	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46731 + 2.54146i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-2.30602 + 3.99415i) q^{4} +(1.93649 - 1.11803i) q^{5} +5.08293i q^{6} +(-5.41652 + 4.43411i) q^{7} -1.79613 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.46731 + 2.54146i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-2.30602 + 3.99415i) q^{4} +(1.93649 - 1.11803i) q^{5} +5.08293i q^{6} +(-5.41652 + 4.43411i) q^{7} -1.79613 q^{8} +(1.50000 + 2.59808i) q^{9} +(5.68288 + 3.28101i) q^{10} +(0.802146 - 1.38936i) q^{11} +(-6.91807 + 3.99415i) q^{12} -14.1348i q^{13} +(-19.2169 - 7.25965i) q^{14} +3.87298 q^{15} +(6.58860 + 11.4118i) q^{16} +(-14.5477 - 8.39913i) q^{17} +(-4.40194 + 7.62439i) q^{18} +(20.5611 - 11.8710i) q^{19} +10.3129i q^{20} +(-11.9648 + 1.96032i) q^{21} +4.70800 q^{22} +(-9.88325 - 17.1183i) q^{23} +(-2.69420 - 1.55550i) q^{24} +(2.50000 - 4.33013i) q^{25} +(35.9231 - 20.7402i) q^{26} +5.19615i q^{27} +(-5.21987 - 31.8596i) q^{28} -22.0642 q^{29} +(5.68288 + 9.84304i) q^{30} +(49.7493 + 28.7228i) q^{31} +(-22.9274 + 39.7114i) q^{32} +(2.40644 - 1.38936i) q^{33} -49.2966i q^{34} +(-5.53156 + 14.6425i) q^{35} -13.8361 q^{36} +(7.24712 + 12.5524i) q^{37} +(60.3392 + 34.8369i) q^{38} +(12.2411 - 21.2022i) q^{39} +(-3.47819 + 2.00814i) q^{40} -25.0310i q^{41} +(-22.5382 - 27.5318i) q^{42} -55.2263 q^{43} +(3.69954 + 6.40778i) q^{44} +(5.80948 + 3.35410i) q^{45} +(29.0037 - 50.2358i) q^{46} +(25.8922 - 14.9489i) q^{47} +22.8236i q^{48} +(9.67736 - 48.0349i) q^{49} +14.6731 q^{50} +(-14.5477 - 25.1974i) q^{51} +(56.4565 + 32.5952i) q^{52} +(-28.3940 + 49.1799i) q^{53} +(-13.2058 + 7.62439i) q^{54} -3.58731i q^{55} +(9.72878 - 7.96424i) q^{56} +41.1222 q^{57} +(-32.3751 - 56.0753i) q^{58} +(-41.1857 - 23.7786i) q^{59} +(-8.93119 + 15.4693i) q^{60} +(-76.2082 + 43.9988i) q^{61} +168.581i q^{62} +(-19.6449 - 7.42137i) q^{63} -81.8578 q^{64} +(-15.8032 - 27.3719i) q^{65} +(7.06200 + 4.07725i) q^{66} +(-1.62251 + 2.81028i) q^{67} +(67.0948 - 38.7372i) q^{68} -34.2366i q^{69} +(-45.3298 + 7.42685i) q^{70} -93.9438 q^{71} +(-2.69420 - 4.66649i) q^{72} +(-38.7392 - 22.3661i) q^{73} +(-21.2676 + 36.8366i) q^{74} +(7.50000 - 4.33013i) q^{75} +109.499i q^{76} +(1.81572 + 11.0823i) q^{77} +71.8461 q^{78} +(66.8061 + 115.712i) q^{79} +(25.5176 + 14.7326i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(63.6154 - 36.7284i) q^{82} +21.8666i q^{83} +(19.7614 - 52.3099i) q^{84} -37.5620 q^{85} +(-81.0344 - 140.356i) q^{86} +(-33.0963 - 19.1081i) q^{87} +(-1.44076 + 2.49547i) q^{88} +(85.1781 - 49.1776i) q^{89} +19.6861i q^{90} +(62.6752 + 76.5614i) q^{91} +91.1640 q^{92} +(49.7493 + 86.1684i) q^{93} +(75.9840 + 43.8694i) q^{94} +(26.5443 - 45.9760i) q^{95} +(-68.7821 + 39.7114i) q^{96} +155.791i q^{97} +(136.279 - 45.8876i) q^{98} +4.81288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9	\( 12 q + 2 q^{2} + 18 q^{3} - 22 q^{4} + 22 q^{7} + 40 q^{8} + 18 q^{9} + 20 q^{11} - 66 q^{12} + 32 q^{14} - 82 q^{16} - 78 q^{17} - 6 q^{18} - 6 q^{19} + 36 q^{21} + 56 q^{22} + 2 q^{23} + 60 q^{24} + 30 q^{25} + 36 q^{26} - 128 q^{28} - 100 q^{29} + 108 q^{31} - 108 q^{32} + 60 q^{33} - 60 q^{35} - 132 q^{36} - 34 q^{37} + 126 q^{38} - 42 q^{39} - 90 q^{40} + 114 q^{42} - 124 q^{43} + 234 q^{44} + 278 q^{46} + 96 q^{47} - 60 q^{49} + 20 q^{50} - 78 q^{51} - 444 q^{52} - 76 q^{53} - 18 q^{54} + 112 q^{56} - 12 q^{57} - 52 q^{58} - 270 q^{59} + 60 q^{60} - 60 q^{61} + 42 q^{63} + 700 q^{64} - 60 q^{65} + 84 q^{66} - 18 q^{67} + 108 q^{68} - 300 q^{70} - 628 q^{71} + 60 q^{72} + 234 q^{73} + 244 q^{74} + 90 q^{75} - 196 q^{77} + 72 q^{78} + 108 q^{79} + 480 q^{80} - 54 q^{81} + 480 q^{82} - 192 q^{84} - 60 q^{85} + 130 q^{86} - 150 q^{87} - 668 q^{88} - 186 q^{89} + 444 q^{91} + 456 q^{92} + 108 q^{93} + 30 q^{94} - 324 q^{96} + 416 q^{98} + 120 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 18 * q^3 - 22 * q^4 + 22 * q^7 + 40 * q^8 + 18 * q^9 + 20 * q^11 - 66 * q^12 + 32 * q^14 - 82 * q^16 - 78 * q^17 - 6 * q^18 - 6 * q^19 + 36 * q^21 + 56 * q^22 + 2 * q^23 + 60 * q^24 + 30 * q^25 + 36 * q^26 - 128 * q^28 - 100 * q^29 + 108 * q^31 - 108 * q^32 + 60 * q^33 - 60 * q^35 - 132 * q^36 - 34 * q^37 + 126 * q^38 - 42 * q^39 - 90 * q^40 + 114 * q^42 - 124 * q^43 + 234 * q^44 + 278 * q^46 + 96 * q^47 - 60 * q^49 + 20 * q^50 - 78 * q^51 - 444 * q^52 - 76 * q^53 - 18 * q^54 + 112 * q^56 - 12 * q^57 - 52 * q^58 - 270 * q^59 + 60 * q^60 - 60 * q^61 + 42 * q^63 + 700 * q^64 - 60 * q^65 + 84 * q^66 - 18 * q^67 + 108 * q^68 - 300 * q^70 - 628 * q^71 + 60 * q^72 + 234 * q^73 + 244 * q^74 + 90 * q^75 - 196 * q^77 + 72 * q^78 + 108 * q^79 + 480 * q^80 - 54 * q^81 + 480 * q^82 - 192 * q^84 - 60 * q^85 + 130 * q^86 - 150 * q^87 - 668 * q^88 - 186 * q^89 + 444 * q^91 + 456 * q^92 + 108 * q^93 + 30 * q^94 - 324 * q^96 + 416 * q^98 + 120 * q^99

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