LMFDB - Embedded newform 19.3.d.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,3,Mod(8,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("19.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	19.d (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:	$0.517712502285$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.3
Root			$0.0702177 - 0.121621i$ of defining polynomial
Character	$\chi$	$=$	19.8
Dual form			19.3.d.a.12.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99014 + 1.14901i) q^{2} +(-3.70079 - 2.13665i) q^{3} +(0.640435 + 1.10927i) q^{4} +(-2.91992 + 5.05745i) q^{5} +(-4.91006 - 8.50447i) q^{6} +9.38186 q^{7} -6.24860i q^{8} +(4.63057 + 8.02039i) q^{9} +O(q^{10})$	\(q+(1.99014 + 1.14901i) q^{2} +(-3.70079 - 2.13665i) q^{3} +(0.640435 + 1.10927i) q^{4} +(-2.91992 + 5.05745i) q^{5} +(-4.91006 - 8.50447i) q^{6} +9.38186 q^{7} -6.24860i q^{8} +(4.63057 + 8.02039i) q^{9} +(-11.6221 + 6.71002i) q^{10} -4.66273 q^{11} -5.47355i q^{12} +(-4.96056 + 2.86398i) q^{13} +(18.6712 + 10.7798i) q^{14} +(21.6120 - 12.4777i) q^{15} +(9.74143 - 16.8726i) q^{16} +(-9.49014 + 16.4374i) q^{17} +21.2823i q^{18} +(-3.40020 - 18.6933i) q^{19} -7.48008 q^{20} +(-34.7203 - 20.0458i) q^{21} +(-9.27949 - 5.35751i) q^{22} +(6.41006 + 11.1025i) q^{23} +(-13.3511 + 23.1248i) q^{24} +(-4.55188 - 7.88409i) q^{25} -13.1629 q^{26} -1.11597i q^{27} +(6.00848 + 10.4070i) q^{28} +(27.7677 - 16.0317i) q^{29} +57.3480 q^{30} -26.9378i q^{31} +(17.1278 - 9.88874i) q^{32} +(17.2558 + 9.96264i) q^{33} +(-37.7734 + 21.8085i) q^{34} +(-27.3943 + 47.4483i) q^{35} +(-5.93117 + 10.2731i) q^{36} -0.140762i q^{37} +(14.7118 - 41.1091i) q^{38} +24.4773 q^{39} +(31.6020 + 18.2454i) q^{40} +(10.0967 + 5.82931i) q^{41} +(-46.0655 - 79.7878i) q^{42} +(-16.3988 + 28.4036i) q^{43} +(-2.98618 - 5.17221i) q^{44} -54.0836 q^{45} +29.4608i q^{46} +(-5.37062 - 9.30218i) q^{47} +(-72.1020 + 41.6281i) q^{48} +39.0193 q^{49} -20.9206i q^{50} +(70.2421 - 40.5543i) q^{51} +(-6.35383 - 3.66839i) q^{52} +(-30.7243 + 17.7387i) q^{53} +(1.28226 - 2.22093i) q^{54} +(13.6148 - 23.5815i) q^{55} -58.6235i q^{56} +(-27.3576 + 76.4450i) q^{57} +73.6821 q^{58} +(-76.1002 - 43.9365i) q^{59} +(27.6822 + 15.9823i) q^{60} +(45.7649 + 79.2672i) q^{61} +(30.9517 - 53.6099i) q^{62} +(43.4434 + 75.2462i) q^{63} -32.4825 q^{64} -33.4504i q^{65} +(22.8943 + 39.6541i) q^{66} +(17.3404 - 10.0115i) q^{67} -24.3113 q^{68} -54.7843i q^{69} +(-109.037 + 62.9525i) q^{70} +(-15.8426 - 9.14674i) q^{71} +(50.1162 - 28.9346i) q^{72} +(28.7511 - 49.7984i) q^{73} +(0.161737 - 0.280136i) q^{74} +38.9032i q^{75} +(18.5582 - 15.7436i) q^{76} -43.7451 q^{77} +(48.7133 + 28.1246i) q^{78} +(-81.7713 - 47.2107i) q^{79} +(56.8884 + 98.5336i) q^{80} +(39.2907 - 68.0535i) q^{81} +(13.3959 + 23.2023i) q^{82} +81.9397 q^{83} -51.3521i q^{84} +(-55.4209 - 95.9918i) q^{85} +(-65.2718 + 37.6847i) q^{86} -137.017 q^{87} +29.1355i q^{88} +(17.3556 - 10.0202i) q^{89} +(-107.634 - 62.1425i) q^{90} +(-46.5392 + 26.8694i) q^{91} +(-8.21046 + 14.2209i) q^{92} +(-57.5567 + 99.6911i) q^{93} -24.6835i q^{94} +(104.469 + 37.3866i) q^{95} -84.5153 q^{96} +(117.468 + 67.8200i) q^{97} +(77.6539 + 44.8335i) q^{98} +(-21.5911 - 37.3969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9	$ 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9} - 60 q^{10} + 26 q^{11} + 30 q^{13} + 54 q^{14} - 18 q^{15} + q^{16} - 42 q^{17} + 25 q^{19} + 108 q^{20} - 102 q^{21} - 39 q^{22} + 8 q^{23} - 83 q^{24} - 17 q^{25} - 148 q^{26} + 32 q^{28} - 12 q^{29} + 304 q^{30} + 51 q^{32} + 123 q^{33} - 6 q^{34} - 38 q^{35} - 54 q^{36} - 14 q^{38} - 44 q^{39} - 96 q^{40} + 63 q^{41} - 92 q^{42} - 34 q^{43} - 69 q^{44} - 28 q^{45} + 58 q^{47} - 147 q^{48} + 18 q^{49} + 132 q^{51} + 162 q^{52} - 12 q^{53} + 29 q^{54} - 28 q^{55} - 16 q^{57} + 172 q^{58} - 147 q^{59} - 222 q^{60} + 58 q^{61} - 116 q^{62} + 86 q^{63} + 166 q^{64} + 11 q^{66} + 201 q^{67} - 84 q^{68} - 198 q^{70} - 102 q^{71} + 210 q^{72} + 7 q^{73} + 174 q^{74} - 173 q^{76} - 376 q^{77} + 450 q^{78} + 134 q^{80} + 253 q^{81} - 145 q^{82} + 146 q^{83} - 90 q^{85} - 270 q^{86} - 568 q^{87} - 72 q^{89} - 438 q^{90} - 216 q^{91} + 72 q^{92} - 160 q^{93} + 558 q^{95} + 126 q^{96} + 21 q^{97} + 411 q^{98} - 56 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9 - 60 * q^10 + 26 * q^11 + 30 * q^13 + 54 * q^14 - 18 * q^15 + q^16 - 42 * q^17 + 25 * q^19 + 108 * q^20 - 102 * q^21 - 39 * q^22 + 8 * q^23 - 83 * q^24 - 17 * q^25 - 148 * q^26 + 32 * q^28 - 12 * q^29 + 304 * q^30 + 51 * q^32 + 123 * q^33 - 6 * q^34 - 38 * q^35 - 54 * q^36 - 14 * q^38 - 44 * q^39 - 96 * q^40 + 63 * q^41 - 92 * q^42 - 34 * q^43 - 69 * q^44 - 28 * q^45 + 58 * q^47 - 147 * q^48 + 18 * q^49 + 132 * q^51 + 162 * q^52 - 12 * q^53 + 29 * q^54 - 28 * q^55 - 16 * q^57 + 172 * q^58 - 147 * q^59 - 222 * q^60 + 58 * q^61 - 116 * q^62 + 86 * q^63 + 166 * q^64 + 11 * q^66 + 201 * q^67 - 84 * q^68 - 198 * q^70 - 102 * q^71 + 210 * q^72 + 7 * q^73 + 174 * q^74 - 173 * q^76 - 376 * q^77 + 450 * q^78 + 134 * q^80 + 253 * q^81 - 145 * q^82 + 146 * q^83 - 90 * q^85 - 270 * q^86 - 568 * q^87 - 72 * q^89 - 438 * q^90 - 216 * q^91 + 72 * q^92 - 160 * q^93 + 558 * q^95 + 126 * q^96 + 21 * q^97 + 411 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.99014	+	1.14901i	0.995069	+	0.574504i	0.906786	−	0.421592i	$-0.138528\pi$
$2$	1.99014	+	1.14901i	0.995069	+	0.574504i	0.0882837	+	0.996095i	$0.471862\pi$
$3$	−3.70079	−	2.13665i	−1.23360	−	0.712218i	−0.265819	−	0.964023i	$-0.585642\pi$
$3$	−3.70079	−	2.13665i	−1.23360	−	0.712218i	−0.967778	+	0.251805i	$0.918976\pi$
$4$	0.640435	+	1.10927i	0.160109	+	0.277317i
$5$	−2.91992	+	5.05745i	−0.583984	+	1.01149i	0.411017	+	0.911628i	$0.365174\pi$
$5$	−2.91992	+	5.05745i	−0.583984	+	1.01149i	−0.995001	+	0.0998627i	$0.968160\pi$
$6$	−4.91006	−	8.50447i	−0.818343	−	1.41741i
$7$	9.38186			1.34027			0.670133	−	0.742241i	$-0.266237\pi$
$7$	9.38186			1.34027			0.670133	+	0.742241i	$0.266237\pi$
$8$		−	6.24860i		−	0.781075i
$9$	4.63057	+	8.02039i	0.514508	+	0.891154i
$10$	−11.6221	+	6.71002i	−1.16221	+	0.671002i
$11$	−4.66273			−0.423885			−0.211942	−	0.977282i	$-0.567979\pi$
$11$	−4.66273			−0.423885			−0.211942	+	0.977282i	$0.567979\pi$
$12$		−	5.47355i		−	0.456129i
$13$	−4.96056	+	2.86398i	−0.381581	+	0.220306i	−0.678506	−	0.734595i	$-0.737372\pi$
$13$	−4.96056	+	2.86398i	−0.381581	+	0.220306i	0.296925	+	0.954901i	$0.404039\pi$
$14$	18.6712	+	10.7798i	1.33366	+	0.769988i
$15$	21.6120	−	12.4777i	1.44080	−	0.831848i
$16$	9.74143	−	16.8726i	0.608839	−	1.05454i
$17$	−9.49014	+	16.4374i	−0.558243	+	0.966906i	0.439400	+	0.898292i	$0.355191\pi$
$17$	−9.49014	+	16.4374i	−0.558243	+	0.966906i	−0.997643	+	0.0686144i	$0.978142\pi$
$18$			21.2823i			1.18235i
$19$	−3.40020	−	18.6933i	−0.178958	−	0.983857i
$19$	−3.40020	−	18.6933i	−0.178958	−	0.983857i
$20$	−7.48008			−0.374004
$21$	−34.7203	−	20.0458i	−1.65335	−	0.954561i
$22$	−9.27949	−	5.35751i	−0.421795	−	0.243523i
$23$	6.41006	+	11.1025i	0.278698	+	0.482720i	0.971061	−	0.238830i	$-0.0767637\pi$
$23$	6.41006	+	11.1025i	0.278698	+	0.482720i	−0.692363	+	0.721549i	$0.743430\pi$
$24$	−13.3511	+	23.1248i	−0.556295	+	0.963532i
$25$	−4.55188	−	7.88409i	−0.182075	−	0.315364i
$26$	−13.1629			−0.506266
$27$		−	1.11597i		−	0.0413322i
$28$	6.00848	+	10.4070i	0.214588	+	0.371678i
$29$	27.7677	−	16.0317i	0.957506	−	0.552817i	0.0621017	−	0.998070i	$-0.480220\pi$
$29$	27.7677	−	16.0317i	0.957506	−	0.552817i	0.895405	+	0.445253i	$0.146886\pi$
$30$	57.3480			1.91160
$31$		−	26.9378i		−	0.868960i	−0.900681	−	0.434480i	$-0.856932\pi$
$31$		−	26.9378i		−	0.868960i	0.900681	−	0.434480i	$-0.143068\pi$
$32$	17.1278	−	9.88874i	0.535244	−	0.309023i
$33$	17.2558	+	9.96264i	0.522903	+	0.301898i
$34$	−37.7734	+	21.8085i	−1.11098	+	0.641426i
$35$	−27.3943	+	47.4483i	−0.782694	+	1.35567i
$36$	−5.93117	+	10.2731i	−0.164755	+	0.285363i
$37$		−	0.140762i		−	0.00380438i	−0.999998	−	0.00190219i	$-0.999395\pi$
$37$		−	0.140762i		−	0.00380438i	0.999998	−	0.00190219i	$-0.000605487\pi$
$38$	14.7118	−	41.1091i	0.387154	−	1.08182i
$39$	24.4773			0.627623
$40$	31.6020	+	18.2454i	0.790050	+	0.456135i
$41$	10.0967	+	5.82931i	0.246260	+	0.142178i	0.618051	−	0.786138i	$-0.287923\pi$
$41$	10.0967	+	5.82931i	0.246260	+	0.142178i	−0.371790	+	0.928317i	$0.621256\pi$
$42$	−46.0655	−	79.7878i	−1.09680	−	1.89971i
$43$	−16.3988	+	28.4036i	−0.381368	+	0.660548i	−0.991258	−	0.131938i	$-0.957880\pi$
$43$	−16.3988	+	28.4036i	−0.381368	+	0.660548i	0.609890	+	0.792486i	$0.291214\pi$
$44$	−2.98618	−	5.17221i	−0.0678677	−	0.117550i
$45$	−54.0836			−1.20186
$46$			29.4608i			0.640453i
$47$	−5.37062	−	9.30218i	−0.114268	−	0.197919i	0.803219	−	0.595684i	$-0.203119\pi$
$47$	−5.37062	−	9.30218i	−0.114268	−	0.197919i	−0.917487	+	0.397766i	$0.869786\pi$
$48$	−72.1020	+	41.6281i	−1.50212	+	0.867252i
$49$	39.0193			0.796313
$50$		−	20.9206i		−	0.418411i
$51$	70.2421	−	40.5543i	1.37730	−	0.795182i
$52$	−6.35383	−	3.66839i	−0.122189	−	0.0705459i
$53$	−30.7243	+	17.7387i	−0.579703	+	0.334692i	−0.761016	−	0.648734i	$-0.775299\pi$
$53$	−30.7243	+	17.7387i	−0.579703	+	0.334692i	0.181312	+	0.983426i	$0.441966\pi$
$54$	1.28226	−	2.22093i	0.0237455	−	0.0411284i
$55$	13.6148	−	23.5815i	0.247542	−	0.428755i
$56$		−	58.6235i		−	1.04685i
$57$	−27.3576	+	76.4450i	−0.479958	+	1.34114i
$58$	73.6821			1.27038
$59$	−76.1002	−	43.9365i	−1.28983	−	0.744686i	−0.311210	−	0.950341i	$-0.600734\pi$
$59$	−76.1002	−	43.9365i	−1.28983	−	0.744686i	−0.978625	+	0.205655i	$0.934068\pi$
$60$	27.6822	+	15.9823i	0.461371	+	0.266372i
$61$	45.7649	+	79.2672i	0.750244	+	1.29946i	0.947704	+	0.319151i	$0.103398\pi$
$61$	45.7649	+	79.2672i	0.750244	+	1.29946i	−0.197460	+	0.980311i	$0.563269\pi$
$62$	30.9517	−	53.6099i	0.499221	−	0.864676i
$63$	43.4434	+	75.2462i	0.689578	+	1.19438i
$64$	−32.4825			−0.507539
$65$		−	33.4504i		−	0.514621i
$66$	22.8943	+	39.6541i	0.346883	+	0.600820i
$67$	17.3404	−	10.0115i	0.258812	−	0.149425i	−0.364981	−	0.931015i	$-0.618924\pi$
$67$	17.3404	−	10.0115i	0.258812	−	0.149425i	0.623792	+	0.781590i	$0.285591\pi$
$68$	−24.3113			−0.357519
$69$		−	54.7843i		−	0.793975i
$70$	−109.037	+	62.9525i	−1.55767	+	0.899321i
$71$	−15.8426	−	9.14674i	−0.223135	−	0.128827i	0.384266	−	0.923222i	$-0.374455\pi$
$71$	−15.8426	−	9.14674i	−0.223135	−	0.128827i	−0.607401	+	0.794395i	$0.707788\pi$
$72$	50.1162	−	28.9346i	0.696058	−	0.401869i
$73$	28.7511	−	49.7984i	0.393851	−	0.682169i	−0.599103	−	0.800672i	$-0.704476\pi$
$73$	28.7511	−	49.7984i	0.393851	−	0.682169i	0.992954	+	0.118503i	$0.0378094\pi$
$74$	0.161737	−	0.280136i	0.00218563	−	0.00378563i
$75$			38.9032i			0.518709i
$76$	18.5582	−	15.7436i	0.244187	−	0.207152i
$77$	−43.7451			−0.568118
$78$	48.7133	+	28.1246i	0.624529	+	0.360572i
$79$	−81.7713	−	47.2107i	−1.03508	−	0.597603i	−0.116644	−	0.993174i	$-0.537214\pi$
$79$	−81.7713	−	47.2107i	−1.03508	−	0.597603i	−0.918436	+	0.395571i	$0.870547\pi$
$80$	56.8884	+	98.5336i	0.711105	+	1.23167i
$81$	39.2907	−	68.0535i	0.485071	−	0.840167i
$82$	13.3959	+	23.2023i	0.163364	+	0.282955i
$83$	81.9397			0.987226			0.493613	−	0.869682i	$-0.335676\pi$
$83$	81.9397			0.987226			0.493613	+	0.869682i	$0.335676\pi$
$84$		−	51.3521i		−	0.611335i
$85$	−55.4209	−	95.9918i	−0.652011	−	1.12932i
$86$	−65.2718	+	37.6847i	−0.758975	+	0.438194i
$87$	−137.017			−1.57490
$88$			29.1355i			0.331086i
$89$	17.3556	−	10.0202i	0.195006	−	0.112587i	−0.399318	−	0.916813i	$-0.630753\pi$
$89$	17.3556	−	10.0202i	0.195006	−	0.112587i	0.594324	+	0.804226i	$0.297420\pi$
$90$	−107.634	−	62.1425i	−1.19593	−	0.690472i
$91$	−46.5392	+	26.8694i	−0.511420	+	0.295269i
$92$	−8.21046	+	14.2209i	−0.0892441	+	0.154575i
$93$	−57.5567	+	99.6911i	−0.618889	+	1.07195i
$94$		−	24.6835i		−	0.262591i
$95$	104.469	+	37.3866i	1.09967	+	0.393543i
$96$	−84.5153			−0.880367
$97$	117.468	+	67.8200i	1.21101	+	0.699175i	0.962979	−	0.269577i	$-0.0868840\pi$
$97$	117.468	+	67.8200i	1.21101	+	0.699175i	0.248028	+	0.968753i	$0.420217\pi$
$98$	77.6539	+	44.8335i	0.792387	+	0.457485i
$99$	−21.5911	−	37.3969i	−0.218092	−	0.377747i
$100$	5.83037	−	10.0985i	0.0583037	−	0.100985i
$101$	−51.2699	−	88.8020i	−0.507622	−	0.879228i	−0.999961	−	0.00882416i	$-0.997191\pi$
$101$	−51.2699	−	88.8020i	−0.507622	−	0.879228i	0.492339	−	0.870404i	$-0.336142\pi$
$102$	186.389			1.82734
$103$		−	38.8999i		−	0.377669i	−0.982009	−	0.188835i	$-0.939529\pi$
$103$		−	38.8999i		−	0.377669i	0.982009	−	0.188835i	$-0.0604710\pi$
$104$	17.8959	+	30.9965i	0.172075	+	0.298043i
$105$	202.761	−	117.064i	1.93106	−	1.11490i
$106$	−81.5274			−0.769127
$107$			152.206i			1.42249i	0.702947	+	0.711243i	$0.251867\pi$
$107$			152.206i			1.42249i	−0.702947	+	0.711243i	$0.748133\pi$
$108$	1.23791	−	0.714706i	0.0114621	−	0.00661764i
$109$	140.866	+	81.3288i	1.29234	+	0.746136i	0.979069	−	0.203527i	$-0.0652403\pi$
$109$	140.866	+	81.3288i	1.29234	+	0.746136i	0.313275	+	0.949662i	$0.398574\pi$
$110$	54.1907	−	31.2870i	0.492643	−	0.284428i
$111$	−0.300760	+	0.520932i	−0.00270955	+	0.00469308i
$112$	91.3927	−	158.297i	0.816006	−	1.41336i
$113$		−	5.01487i		−	0.0443793i	−0.999754	−	0.0221897i	$-0.992936\pi$
$113$		−	5.01487i		−	0.0443793i	0.999754	−	0.0221897i	$-0.00706377\pi$
$114$	−142.281	+	120.702i	−1.24808	+	1.05879i
$115$	−74.8675			−0.651022
$116$	35.5668	+	20.5345i	0.306610	+	0.177022i
$117$	−45.9404	−	26.5237i	−0.392653	−	0.226699i
$118$	−100.967	−	174.879i	−0.855650	−	1.48203i
$119$	−89.0352	+	154.213i	−0.748195	+	1.29591i
$120$	−77.9683	−	135.045i	−0.649735	−	1.12537i
$121$	−99.2589			−0.820322
$122$			210.337i			1.72407i
$123$	−24.9104	−	43.1462i	−0.202524	−	0.350782i
$124$	29.8812	−	17.2519i	0.240977	−	0.139128i
$125$	−92.8315			−0.742652
$126$			199.667i			1.58466i
$127$	−145.625	+	84.0766i	−1.14665	+	0.662020i	−0.948069	−	0.318064i	$-0.896967\pi$
$127$	−145.625	+	84.0766i	−1.14665	+	0.662020i	−0.198583	+	0.980084i	$0.563634\pi$
$128$	−133.156	−	76.8776i	−1.04028	−	0.600606i
$129$	121.377	−	70.0772i	0.940909	−	0.543234i
$130$	38.4347	−	66.5709i	0.295652	−	0.512084i
$131$	108.056	−	187.159i	0.824857	−	1.42869i	−0.0771714	−	0.997018i	$-0.524589\pi$
$131$	108.056	−	187.159i	0.824857	−	1.42869i	0.902028	−	0.431677i	$-0.142078\pi$
$132$			25.5217i			0.193346i
$133$	−31.9002	−	175.378i	−0.239851	−	1.31863i
$134$	46.0131			0.343381
$135$	5.64396	+	3.25854i	0.0418071	+	0.0241373i
$136$	102.711	+	59.3001i	0.755226	+	0.436030i
$137$	6.48693	+	11.2357i	0.0473499	+	0.0820123i	0.888729	−	0.458433i	$-0.151589\pi$
$137$	6.48693	+	11.2357i	0.0473499	+	0.0820123i	−0.841379	+	0.540445i	$0.818256\pi$
$138$	62.9476	−	109.028i	0.456142	−	0.790061i
$139$	108.763	+	188.383i	0.782467	+	1.35527i	0.930500	+	0.366291i	$0.119372\pi$
$139$	108.763	+	188.383i	0.782467	+	1.35527i	−0.148033	+	0.988982i	$0.547294\pi$
$140$	−70.1771			−0.501265
$141$			45.9006i			0.325536i
$142$	−21.0193	−	36.4066i	−0.148023	−	0.256384i
$143$	23.1297	−	13.3540i	0.161746	−	0.0933844i
$144$	180.434			1.25301
$145$			187.245i			1.29134i
$146$	114.437	−	66.0704i	0.783817	−	0.452537i
$147$	−144.402	−	83.3708i	−0.982329	−	0.567148i
$148$	0.156143	−	0.0901491i	0.00105502	−	0.000609115i
$149$	5.20982	−	9.02368i	0.0349653	−	0.0605616i	−0.848013	−	0.529975i	$-0.822201\pi$
$149$	5.20982	−	9.02368i	0.0349653	−	0.0605616i	0.882978	+	0.469413i	$0.155535\pi$
$150$	−44.7000	+	77.4227i	−0.298000	+	0.516151i
$151$			143.558i			0.950718i	0.879792	+	0.475359i	$0.157682\pi$
$151$			143.558i			0.950718i	−0.879792	+	0.475359i	$0.842318\pi$
$152$	−116.807	+	21.2465i	−0.768466	+	0.139779i
$153$	−175.779			−1.14888
$154$	−87.0589	−	50.2635i	−0.565317	−	0.326386i
$155$	136.236	+	78.6562i	0.878945	+	0.507459i
$156$	15.6761	+	27.1519i	0.100488	+	0.174050i
$157$	135.429	−	234.570i	0.862604	−	1.49407i	−0.00680261	−	0.999977i	$-0.502165\pi$
$157$	135.429	−	234.570i	0.862604	−	1.49407i	0.869407	−	0.494097i	$-0.164501\pi$
$158$	−108.491	−	187.912i	−0.686650	−	1.18931i
$159$	151.606			0.953494
$160$			115.497i			0.721859i
$161$	60.1383	+	104.163i	0.373530	+	0.646973i
$162$	156.388	−	90.2907i	0.965358	−	0.557350i
$163$	56.8017			0.348476			0.174238	−	0.984704i	$-0.444254\pi$
$163$	56.8017			0.348476			0.174238	+	0.984704i	$0.444254\pi$
$164$			14.9332i			0.0910561i
$165$	−100.771	+	58.1803i	−0.610734	+	0.352608i
$166$	163.071	+	94.1493i	0.982358	+	0.567165i
$167$	−29.2718	+	16.9001i	−0.175280	+	0.101198i	−0.585073	−	0.810980i	$-0.698934\pi$
$167$	−29.2718	+	16.9001i	−0.175280	+	0.101198i	0.409793	+	0.912179i	$0.365601\pi$
$168$	−125.258	+	216.953i	−0.745584	+	1.29139i
$169$	−68.0953	+	117.944i	−0.402931	+	0.697896i
$170$		−	254.716i		−	1.49833i
$171$	134.183	−	113.832i	0.784693	−	0.665682i
$172$	−42.0095			−0.244241
$173$	−59.2823	−	34.2267i	−0.342672	−	0.197842i	0.318781	−	0.947828i	$-0.396727\pi$
$173$	−59.2823	−	34.2267i	−0.342672	−	0.197842i	−0.661453	+	0.749986i	$0.730060\pi$
$174$	−272.682	−	157.433i	−1.56714	−	0.904788i
$175$	−42.7051	−	73.9674i	−0.244029	−	0.422671i
$176$	−45.4217	+	78.6726i	−0.258078	+	0.447004i
$177$	187.754	+	325.200i	1.06076	+	1.83729i
$178$	46.0533			0.258727
$179$		−	226.861i		−	1.26738i	−0.773587	−	0.633691i	$-0.781539\pi$
$179$		−	226.861i		−	1.26738i	0.773587	−	0.633691i	$-0.218461\pi$
$180$	−34.6371	−	59.9932i	−0.192428	−	0.333295i
$181$	−184.408	+	106.468i	−1.01883	+	0.588222i	−0.913765	−	0.406243i	$-0.866839\pi$
$181$	−184.408	+	106.468i	−1.01883	+	0.588222i	−0.105066	+	0.994465i	$0.533505\pi$
$182$	−123.493			−0.678532
$183$		−	391.135i		−	2.13735i
$184$	69.3754	−	40.0539i	0.377040	−	0.217684i
$185$	0.711898	+	0.411015i	0.00384810	+	0.00222170i
$186$	−229.092	+	132.266i	−1.23167	+	0.711108i
$187$	44.2500	−	76.6432i	0.236631	−	0.409857i
$188$	6.87906	−	11.9149i	0.0365908	−	0.0633771i
$189$		−	10.4699i		−	0.0553961i
$190$	164.950	+	194.440i	0.868157	+	1.02337i
$191$	34.8860			0.182649			0.0913247	−	0.995821i	$-0.470890\pi$
$191$	34.8860			0.182649			0.0913247	+	0.995821i	$0.470890\pi$
$192$	120.211	+	69.4038i	0.626098	+	0.361478i
$193$	32.2140	+	18.5988i	0.166912	+	0.0963667i	0.581129	−	0.813811i	$-0.302611\pi$
$193$	32.2140	+	18.5988i	0.166912	+	0.0963667i	−0.414217	+	0.910178i	$0.635945\pi$
$194$	155.851	+	269.942i	0.803358	+	1.39146i
$195$	−71.4718	+	123.793i	−0.366522	+	0.634835i
$196$	24.9894	+	43.2828i	0.127497	+	0.220831i
$197$	−314.378			−1.59583			−0.797914	−	0.602772i	$-0.794063\pi$
$197$	−314.378			−1.59583			−0.797914	+	0.602772i	$0.794063\pi$
$198$		−	99.2335i		−	0.501179i
$199$	−153.223	−	265.390i	−0.769965	−	1.33362i	−0.937581	−	0.347766i	$-0.886940\pi$
$199$	−153.223	−	265.390i	−0.769965	−	1.33362i	0.167617	−	0.985852i	$-0.446393\pi$
$200$	−49.2645	+	28.4429i	−0.246323	+	0.142214i
$201$	−85.5643			−0.425693
$202$		−	235.638i		−	1.16652i
$203$	260.513	−	150.407i	1.28331	−	0.740921i
$204$	89.9710	+	51.9448i	0.441034	+	0.254631i
$205$	−58.9630	+	34.0423i	−0.287624	+	0.166060i
$206$	44.6963	−	77.4163i	0.216972	−	0.375807i
$207$	−59.3645	+	102.822i	−0.286785	+	0.496726i
$208$			111.597i			0.536524i
$209$	15.8542	+	87.1618i	0.0758575	+	0.417042i
$210$	538.031			2.56205
$211$	63.4973	+	36.6602i	0.300935	+	0.173745i	0.642863	−	0.765981i	$-0.277747\pi$
$211$	63.4973	+	36.6602i	0.300935	+	0.173745i	−0.341928	+	0.939726i	$0.611080\pi$
$212$	−39.3538	−	22.7209i	−0.185631	−	0.107174i
$213$	39.0868	+	67.7003i	0.183506	+	0.317842i
$214$	−174.886	+	302.911i	−0.817223	+	1.41547i
$215$	−95.7665	−	165.872i	−0.445426	−	0.771500i
$216$	−6.97324			−0.0322835
$217$		−	252.726i		−	1.16464i
$218$	186.895	+	323.711i	0.857315	+	1.48491i
$219$	−212.804	+	122.862i	−0.971706	+	0.561015i
$220$	34.8776			0.158535
$221$		−	108.718i		−	0.491938i
$222$	−1.19711	+	0.691151i	−0.00539238	+	0.00311329i
$223$	18.0166	+	10.4019i	0.0807918	+	0.0466452i	0.539852	−	0.841760i	$-0.318480\pi$
$223$	18.0166	+	10.4019i	0.0807918	+	0.0466452i	−0.459060	+	0.888405i	$0.651814\pi$
$224$	160.691	−	92.7748i	0.717369	−	0.414173i
$225$	42.1556	−	73.0157i	0.187358	−	0.324514i
$226$	5.76212	−	9.98028i	0.0254961	−	0.0441605i
$227$			97.0130i			0.427370i	0.976903	+	0.213685i	$0.0685466\pi$
$227$			97.0130i			0.427370i	−0.976903	+	0.213685i	$0.931453\pi$
$228$	−102.319	+	18.6112i	−0.448766	+	0.0816279i
$229$	259.958			1.13519			0.567595	−	0.823308i	$-0.307874\pi$
$229$	259.958			1.13519			0.567595	+	0.823308i	$0.307874\pi$
$230$	−148.997	−	86.0233i	−0.647812	−	0.374014i
$231$	161.892	+	93.4681i	0.700829	+	0.404624i
$232$	−100.176	−	173.509i	−0.431791	−	0.747884i
$233$	184.911	−	320.275i	0.793610	−	1.37457i	−0.130109	−	0.991500i	$-0.541533\pi$
$233$	184.911	−	320.275i	0.793610	−	1.37457i	0.923718	−	0.383072i	$-0.125134\pi$
$234$	−60.9519	−	105.572i	−0.260478	−	0.451162i
$235$	62.7271			0.266924
$236$		−	112.554i		−	0.476923i
$237$	201.746	+	349.434i	0.851247	+	1.47440i
$238$	−354.385	+	204.604i	−1.48901	+	0.859681i
$239$	311.812			1.30465			0.652327	−	0.757938i	$-0.273793\pi$
$239$	311.812			1.30465			0.652327	+	0.757938i	$0.273793\pi$
$240$		−	486.203i		−	2.02585i
$241$	−295.100	+	170.376i	−1.22448	+	0.706954i	−0.965870	−	0.259027i	$-0.916598\pi$
$241$	−295.100	+	170.376i	−1.22448	+	0.706954i	−0.258611	+	0.965982i	$0.583265\pi$
$242$	−197.539	−	114.049i	−0.816277	−	0.471278i
$243$	−299.512	+	172.923i	−1.23256	+	0.711618i
$244$	−58.6189	+	101.531i	−0.240242	+	0.416111i
$245$	−113.933	+	197.338i	−0.465034	+	0.805463i
$246$		−	114.489i		−	0.465403i
$247$	70.4040	+	82.9910i	0.285037	+	0.335996i
$248$	−168.323			−0.678723
$249$	−303.242	−	175.077i	−1.21784	−	0.703120i
$250$	−184.748	−	106.664i	−0.738991	−	0.426656i
$251$	61.1331	+	105.886i	0.243558	+	0.421855i	0.961725	−	0.274015i	$-0.0883520\pi$
$251$	61.1331	+	105.886i	0.243558	+	0.421855i	−0.718167	+	0.695871i	$0.755019\pi$
$252$	−55.6454	+	96.3806i	−0.220815	+	0.382463i
$253$	−29.8884	−	51.7682i	−0.118136	−	0.204617i
$254$	−386.418			−1.52133
$255$			473.661i			1.85749i
$256$	−111.701	−	193.471i	−0.436331	−	0.755748i
$257$	−129.449	+	74.7375i	−0.503693	+	0.290807i	−0.730237	−	0.683193i	$-0.760591\pi$
$257$	−129.449	+	74.7375i	−0.503693	+	0.290807i	0.226544	+	0.974001i	$0.427257\pi$
$258$	322.077			1.24836
$259$		−	1.32061i		−	0.00509889i
$260$	37.1054	−	21.4228i	0.142713	−	0.0823954i
$261$	257.161	+	148.472i	0.985290	+	0.568857i
$262$	430.094	−	248.315i	1.64158	−	0.947767i
$263$	36.9434	−	63.9878i	0.140469	−	0.243300i	−0.787204	−	0.616692i	$-0.788472\pi$
$263$	36.9434	−	63.9878i	0.140469	−	0.243300i	0.927673	+	0.373393i	$0.121806\pi$
$264$	62.2526	−	107.825i	0.235805	−	0.408426i
$265$		−	207.182i		−	0.781819i
$266$	138.024	−	385.680i	0.518889	−	1.44992i
$267$	−85.6392			−0.320746
$268$	22.2108	+	12.8234i	0.0828762	+	0.0478486i
$269$	−37.9102	−	21.8875i	−0.140930	−	0.0813661i	0.427877	−	0.903837i	$-0.359262\pi$
$269$	−37.9102	−	21.8875i	−0.140930	−	0.0813661i	−0.568807	+	0.822471i	$0.692595\pi$
$270$	7.48817	+	12.9699i	0.0277340	+	0.0480366i
$271$	15.8330	−	27.4235i	0.0584242	−	0.101194i	−0.835334	−	0.549743i	$-0.814726\pi$
$271$	15.8330	−	27.4235i	0.0584242	−	0.101194i	0.893758	+	0.448549i	$0.148059\pi$
$272$	184.895	+	320.248i	0.679761	+	1.17738i
$273$	229.643			0.841182
$274$			29.8141i			0.108811i
$275$	21.2242	+	36.7614i	0.0771789	+	0.133678i
$276$	60.7704	−	35.0858i	0.220183	−	0.127122i
$277$	323.770			1.16884			0.584422	−	0.811450i	$-0.301321\pi$
$277$	323.770			1.16884			0.584422	+	0.811450i	$0.301321\pi$
$278$			499.878i			1.79812i
$279$	216.051	−	124.737i	0.774378	−	0.447087i
$280$	296.485	+	171.176i	1.05888	+	0.611343i
$281$	−23.7453	+	13.7094i	−0.0845029	+	0.0487878i	−0.541656	−	0.840600i	$-0.682202\pi$
$281$	−23.7453	+	13.7094i	−0.0845029	+	0.0487878i	0.457153	+	0.889388i	$0.348869\pi$
$282$	−52.7401	+	91.3485i	−0.187022	+	0.323931i
$283$	−108.587	+	188.078i	−0.383699	+	0.664586i	−0.991588	−	0.129436i	$-0.958683\pi$
$283$	−108.587	+	188.078i	−0.383699	+	0.664586i	0.607889	+	0.794022i	$0.292017\pi$
$284$		−	23.4316i		−	0.0825055i
$285$	−306.735	−	361.573i	−1.07626	−	1.26868i
$286$	61.3752			0.214599
$287$	94.7256	+	54.6898i	0.330054	+	0.190557i
$288$	158.623	+	91.5811i	0.550775	+	0.317990i
$289$	−35.6255	−	61.7051i	−0.123272	−	0.213513i
$290$	−215.146	+	372.644i	−0.741882	+	1.28498i
$291$	−289.816	−	501.975i	−0.995930	−	1.72500i
$292$	73.6529			0.252236
$293$			51.9721i			0.177379i	0.996059	+	0.0886896i	$0.0282679\pi$
$293$			51.9721i			0.177379i	−0.996059	+	0.0886896i	$0.971732\pi$
$294$	−191.587	−	331.839i	−0.651657	−	1.12870i
$295$	444.413	−	256.582i	1.50649	−	0.869770i
$296$	−0.879566			−0.00297151
$297$			5.20346i			0.0175201i
$298$	20.7365	−	11.9723i	0.0695857	−	0.0401753i
$299$	−63.5949	−	36.7165i	−0.212692	−	0.122798i
$300$	−43.1540	+	24.9150i	−0.143847	+	0.0830499i
$301$	−153.851	+	266.478i	−0.511134	+	0.885311i
$302$	−164.950	+	285.701i	−0.546191	+	0.946031i
$303$			438.184i			1.44615i
$304$	−348.528	−	124.729i	−1.14647	−	0.410292i
$305$	−534.520			−1.75252
$306$	−349.825	−	201.972i	−1.14322	−	0.660038i
$307$	−325.035	−	187.659i	−1.05875	−	0.611268i	−0.133662	−	0.991027i	$-0.542674\pi$
$307$	−325.035	−	187.659i	−1.05875	−	0.611268i	−0.925086	+	0.379759i	$0.876007\pi$
$308$	−28.0159	−	48.5250i	−0.0909608	−	0.157549i
$309$	−83.1157	+	143.961i	−0.268983	+	0.465892i
$310$	180.753	+	313.073i	0.583074	+	1.00991i
$311$	93.0136			0.299079			0.149539	−	0.988756i	$-0.452221\pi$
$311$	93.0136			0.299079			0.149539	+	0.988756i	$0.452221\pi$
$312$		−	152.949i		−	0.490221i
$313$	213.267	+	369.390i	0.681365	+	1.18016i	0.974564	+	0.224108i	$0.0719467\pi$
$313$	213.267	+	369.390i	0.681365	+	1.18016i	−0.293199	+	0.956051i	$0.594720\pi$
$314$	539.044	−	311.217i	1.71670	−	0.991138i
$315$	−507.405			−1.61081
$316$		−	120.941i		−	0.382726i
$317$	515.861	−	297.833i	1.62732	−	0.939535i	0.642434	−	0.766341i	$-0.277925\pi$
$317$	515.861	−	297.833i	1.62732	−	0.939535i	0.984888	−	0.173194i	$-0.0554088\pi$
$318$	301.716	+	174.196i	0.948793	+	0.547786i
$319$	−129.473	+	74.7514i	−0.405872	+	0.234331i
$320$	94.8462	−	164.279i	0.296394	−	0.513370i
$321$	325.211	−	563.282i	1.01312	−	1.75477i
$322$			276.397i			0.858377i
$323$	339.537	+	121.511i	1.05120	+	0.376196i
$324$	100.653			0.310656
$325$	45.1597	+	26.0730i	0.138953	+	0.0802245i
$326$	113.043	+	65.2655i	0.346758	+	0.200201i
$327$	−347.543	−	601.962i	−1.06282	−	1.84086i
$328$	36.4250	−	63.0900i	0.111052	−	0.192348i
$329$	−50.3864	−	87.2718i	−0.153150	−	0.265264i
$330$	−267.398			−0.810298
$331$			30.9531i			0.0935138i	0.998906	+	0.0467569i	$0.0148886\pi$
$331$			30.9531i			0.0935138i	−0.998906	+	0.0467569i	$0.985111\pi$
$332$	52.4771	+	90.8930i	0.158064	+	0.273774i
$333$	1.12897	−	0.651810i	0.00339029	−	0.00195739i
$334$	−77.6734			−0.232555
$335$			116.931i			0.349048i
$336$	−676.451	+	390.549i	−2.01325	+	1.16235i
$337$	−354.724	−	204.800i	−1.05259	−	0.607716i	−0.129220	−	0.991616i	$-0.541247\pi$
$337$	−354.724	−	204.800i	−1.05259	−	0.607716i	−0.923374	+	0.383900i	$0.874581\pi$
$338$	−271.038	+	156.484i	−0.801888	+	0.462970i
$339$	−10.7150	+	18.5590i	−0.0316078	+	0.0547462i
$340$	70.9870	−	122.953i	0.208785	−	0.361627i
$341$			125.604i			0.368339i
$342$	397.835	−	72.3639i	1.16326	−	0.211590i
$343$	−93.6372			−0.272995
$344$	177.483	+	102.470i	0.515938	+	0.297877i
$345$	277.069	+	159.966i	0.803099	+	0.463669i
$346$	−78.6534	−	136.232i	−0.227322	−	0.393733i
$347$	−262.970	+	455.477i	−0.757839	+	1.31262i	0.186112	+	0.982529i	$0.440411\pi$
$347$	−262.970	+	455.477i	−0.757839	+	1.31262i	−0.943951	+	0.330087i	$0.892922\pi$
$348$	−87.7503	−	151.988i	−0.252156	−	0.436747i
$349$	287.557			0.823946			0.411973	−	0.911196i	$-0.364840\pi$
$349$	287.557			0.823946			0.411973	+	0.911196i	$0.364840\pi$
$350$		−	196.274i		−	0.560783i
$351$	3.19611	+	5.53582i	0.00910572	+	0.0157716i
$352$	−79.8624	+	46.1086i	−0.226882	+	0.130990i
$353$	−18.5432			−0.0525303			−0.0262651	−	0.999655i	$-0.508361\pi$
$353$	−18.5432			−0.0525303			−0.0262651	+	0.999655i	$0.508361\pi$
$354$			862.923i			2.43764i
$355$	92.5184	−	53.4155i	0.260615	−	0.150466i
$356$	22.2303	+	12.8346i	0.0624445	+	0.0360524i
$357$	659.001	−	380.475i	1.84594	−	1.06576i
$358$	260.665	−	451.485i	0.728115	−	1.26113i
$359$	47.7457	−	82.6979i	0.132996	−	0.230356i	−0.791834	−	0.610736i	$-0.790873\pi$
$359$	47.7457	−	82.6979i	0.132996	−	0.230356i	0.924830	+	0.380380i	$0.124207\pi$
$360$			337.947i			0.938742i
$361$	−337.877	+	127.122i	−0.935948	+	0.352138i
$362$	−489.331			−1.35174
$363$	367.337	+	212.082i	1.01195	+	0.584248i
$364$	−59.6108	−	34.4163i	−0.163766	−	0.0945502i
$365$	167.902	+	290.815i	0.460005	+	0.796752i
$366$	449.417	−	778.413i	1.22792	−	2.12681i
$367$	−249.565	−	432.259i	−0.680013	−	1.17782i	−0.974976	−	0.222309i	$-0.928641\pi$
$367$	−249.565	−	432.259i	−0.680013	−	1.17782i	0.294963	−	0.955509i	$-0.404693\pi$
$368$	249.773			0.678730
$369$			107.972i			0.292608i
$370$	0.944517	+	1.63595i	0.00255275	+	0.00442149i
$371$	−288.251	+	166.422i	−0.776957	+	0.448576i
$372$	−147.445			−0.396358
$373$		−	80.0714i		−	0.214669i	−0.994223	−	0.107334i	$-0.965768\pi$
$373$		−	80.0714i		−	0.214669i	0.994223	−	0.107334i	$-0.0342315\pi$
$374$	176.127	−	101.687i	0.470928	−	0.271891i
$375$	343.550	+	198.349i	0.916134	+	0.528930i
$376$	−58.1256	+	33.5588i	−0.154589	+	0.0892522i
$377$	−91.8288	+	159.052i	−0.243578	+	0.421889i
$378$	12.0299	−	20.8365i	0.0318253	−	0.0551230i
$379$		−	338.780i		−	0.893880i	−0.894564	−	0.446940i	$-0.852514\pi$
$379$		−	338.780i		−	0.893880i	0.894564	−	0.446940i	$-0.147486\pi$
$380$	25.4338	+	139.827i	0.0669310	+	0.367967i
$381$	718.570			1.88601
$382$	69.4281	+	40.0843i	0.181749	+	0.104933i
$383$	−95.7329	−	55.2714i	−0.249955	−	0.144312i	0.369789	−	0.929116i	$-0.379430\pi$
$383$	−95.7329	−	55.2714i	−0.249955	−	0.144312i	−0.619744	+	0.784804i	$0.712763\pi$
$384$	328.521	+	569.016i	0.855524	+	1.48181i
$385$	127.732	−	221.239i	0.331772	−	0.574646i
$386$	42.7403	+	74.0283i	0.110726	+	0.191783i
$387$	−303.744			−0.784867
$388$			173.737i			0.447777i
$389$	−310.450	−	537.715i	−0.798072	−	1.38230i	−0.920870	−	0.389869i	$-0.872520\pi$
$389$	−310.450	−	537.715i	−0.798072	−	1.38230i	0.122799	−	0.992432i	$-0.460813\pi$
$390$	−284.478	+	164.243i	−0.729430	+	0.421137i
$391$	−243.329			−0.622326
$392$		−	243.816i		−	0.621980i
$393$	−799.788	+	461.758i	−2.03508	+	1.17496i
$394$	−625.656	−	361.223i	−1.58796	−	0.916809i
$395$	477.531	−	275.703i	1.20894	−	0.697982i
$396$	27.6554	−	47.9006i	0.0698370	−	0.120961i
$397$	−235.738	+	408.309i	−0.593797	+	1.02849i	0.399918	+	0.916551i	$0.369039\pi$
$397$	−235.738	+	408.309i	−0.593797	+	1.02849i	−0.993715	+	0.111936i	$0.964295\pi$
$398$		−	704.217i		−	1.76939i
$399$	−256.665	+	717.196i	−0.643272	+	1.79748i
$400$	−177.367			−0.443418
$401$	−194.968	−	112.565i	−0.486204	−	0.280710i	0.236794	−	0.971560i	$-0.423903\pi$
$401$	−194.968	−	112.565i	−0.486204	−	0.280710i	−0.722998	+	0.690850i	$0.757237\pi$
$402$	−170.285	−	98.3140i	−0.423594	−	0.244562i
$403$	77.1492	+	133.626i	0.191437	+	0.331579i
$404$	65.6701	−	113.744i	0.162550	−	0.281544i
$405$	229.452	+	397.422i	0.566547	+	0.981289i
$406$	691.275			1.70265
$407$			0.656336i			0.00161262i
$408$	−253.407	−	438.914i	−0.621096	−	1.07577i
$409$	192.756	−	111.288i	0.471286	−	0.272097i	−0.245492	−	0.969399i	$-0.578949\pi$
$409$	192.756	−	111.288i	0.471286	−	0.272097i	0.716778	+	0.697302i	$0.245616\pi$
$410$	−156.459			−0.381608
$411$		−	55.4413i		−	0.134894i
$412$	43.1504	−	24.9129i	0.104734	−	0.0604682i
$413$	−713.962	−	412.206i	−1.72872	−	0.998078i
$414$	−236.287	+	136.421i	−0.570742	+	0.329518i
$415$	−239.258	+	414.406i	−0.576524	+	0.998569i
$416$	−56.6423	+	98.1073i	−0.136159	+	0.235835i
$417$		−	929.555i		−	2.22915i
$418$	−68.5974	+	191.681i	−0.164109	+	0.458566i
$419$	306.377			0.731209			0.365605	−	0.930770i	$-0.380862\pi$
$419$	306.377			0.731209			0.365605	+	0.930770i	$0.380862\pi$
$420$	259.711	+	149.944i	0.618359	+	0.357010i
$421$	331.533	+	191.411i	0.787490	+	0.454658i	0.839078	−	0.544011i	$-0.183095\pi$
$421$	331.533	+	191.411i	0.787490	+	0.454658i	−0.0515881	+	0.998668i	$0.516428\pi$
$422$	84.2456	+	145.918i	0.199634	+	0.345776i
$423$	49.7381	−	86.1489i	0.117584	−	0.203662i
$424$	110.842	+	191.984i	0.261419	+	0.452792i
$425$	172.792			0.406569
$426$			179.644i			0.421700i
$427$	429.360	+	743.674i	1.00553	+	1.74162i
$428$	−168.837	+	97.4781i	−0.394479	+	0.227752i
$429$	−114.131			−0.266040
$430$		−	440.146i		−	1.02359i
$431$	−232.981	+	134.512i	−0.540560	+	0.312092i	−0.745306	−	0.666723i	$-0.767697\pi$
$431$	−232.981	+	134.512i	−0.540560	+	0.312092i	0.204746	+	0.978815i	$0.434363\pi$
$432$	−18.8293	−	10.8711i	−0.0435864	−	0.0251646i
$433$	−267.809	+	154.620i	−0.618497	+	0.357089i	−0.776284	−	0.630384i	$-0.782897\pi$
$433$	−267.809	+	154.620i	−0.618497	+	0.357089i	0.157787	+	0.987473i	$0.449564\pi$
$434$	290.384	−	502.961i	0.669089	−	1.15890i
$435$	400.078	−	692.955i	0.919719	−	1.59300i
$436$			208.343i			0.477852i
$437$	185.748	−	157.576i	0.425052	−	0.360586i
$438$	−564.678			−1.28922
$439$	360.006	+	207.850i	0.820059	+	0.473462i	0.850437	−	0.526077i	$-0.176338\pi$
$439$	360.006	+	207.850i	0.820059	+	0.473462i	−0.0303775	+	0.999538i	$0.509671\pi$
$440$	−147.352	−	85.0735i	−0.334890	−	0.193349i
$441$	180.682	+	312.950i	0.409710	+	0.709638i
$442$	124.918	−	216.364i	0.282620	−	0.489512i
$443$	174.507	+	302.256i	0.393922	+	0.682292i	0.992963	−	0.118426i	$-0.0377848\pi$
$443$	174.507	+	302.256i	0.393922	+	0.682292i	−0.599041	+	0.800718i	$0.704451\pi$
$444$	−0.770469			−0.00173529
$445$			117.033i			0.262996i
$446$	23.9037	+	41.4023i	0.0535956	+	0.0928304i
$447$	−38.5610	+	22.2632i	−0.0862661	+	0.0498058i
$448$	−304.746			−0.680237
$449$			631.772i			1.40707i	0.710663	+	0.703533i	$0.248395\pi$
$449$			631.772i			1.40707i	−0.710663	+	0.703533i	$0.751605\pi$
$450$	167.791	−	96.8743i	0.372869	−	0.215276i
$451$	−47.0781	−	27.1805i	−0.104386	−	0.0602673i
$452$	5.56282	−	3.21170i	0.0123071	−	0.00710553i
$453$	306.735	−	531.280i	0.677119	−	1.17280i
$454$	−111.469	+	193.069i	−0.245526	+	0.425263i
$455$		−	313.827i		−	0.689729i
$456$	477.674	+	170.947i	1.04753	+	0.374883i
$457$	539.986			1.18159			0.590794	−	0.806822i	$-0.298815\pi$
$457$	539.986			1.18159			0.590794	+	0.806822i	$0.298815\pi$
$458$	517.353	+	298.694i	1.12959	+	0.652170i
$459$	18.3436	+	10.5907i	0.0399643	+	0.0230734i
$460$	−47.9478	−	83.0480i	−0.104234	−	0.180539i
$461$	84.8213	−	146.915i	0.183994	−	0.318687i	−0.759243	−	0.650807i	$-0.774431\pi$
$461$	84.8213	−	146.915i	0.183994	−	0.318687i	0.943237	+	0.332120i	$0.107764\pi$
$462$	214.791	+	372.029i	0.464916	+	0.805258i
$463$	−462.335			−0.998564			−0.499282	−	0.866440i	$-0.666403\pi$
$463$	−462.335			−0.998564			−0.499282	+	0.866440i	$0.666403\pi$
$464$		−	624.686i		−	1.34631i
$465$	−336.122	−	582.180i	−0.722843	−	1.25200i
$466$	735.997	−	424.928i	1.57939	−	0.911863i
$467$	2.60465			0.00557741			0.00278870	−	0.999996i	$-0.499112\pi$
$467$	2.60465			0.00557741			0.00278870	+	0.999996i	$0.499112\pi$
$468$		−	67.9469i		−	0.145186i
$469$	162.685	−	93.9264i	0.346877	−	0.200269i
$470$	124.836	+	72.0739i	0.265608	+	0.153349i
$471$	−1002.39	+	578.729i	−2.12821	+	1.22872i
$472$	−274.542	+	475.520i	−0.581656	+	1.00746i
$473$	76.4633	−	132.438i	0.161656	−	0.279996i
$474$			927.229i			1.95618i
$475$	−131.902	+	111.897i	−0.277689	+	0.235573i
$476$	−228.085			−0.479170
$477$	−284.542	−	164.280i	−0.596524	−	0.344404i
$478$	620.550	+	358.275i	1.29822	+	0.749528i
$479$	−196.128	−	339.703i	−0.409452	−	0.709192i	0.585376	−	0.810762i	$-0.300947\pi$
$479$	−196.128	−	339.703i	−0.409452	−	0.709192i	−0.994828	+	0.101570i	$0.967613\pi$
$480$	246.778	−	427.432i	0.514121	−	0.890483i
$481$	0.403140	+	0.698259i	0.000838129	+	0.00145168i
$482$	−783.053			−1.62459
$483$		−	513.979i		−	1.06414i
$484$	−63.5689	−	110.105i	−0.131341	−	0.227489i
$485$	−685.993	+	396.058i	−1.41442	+	0.816615i
$486$	−794.760			−1.63531
$487$		−	93.4189i		−	0.191825i	−0.995390	−	0.0959126i	$-0.969423\pi$
$487$		−	93.4189i		−	0.191825i	0.995390	−	0.0959126i	$-0.0305769\pi$
$488$	495.309	−	285.967i	1.01498	−	0.585997i
$489$	−210.211	−	121.365i	−0.429880	−	0.248191i
$490$	−453.487	+	261.821i	−0.925483	+	0.534328i
$491$	−218.271	+	378.057i	−0.444544	+	0.769973i	−0.998020	−	0.0628921i	$-0.979968\pi$
$491$	−218.271	+	378.057i	−0.444544	+	0.769973i	0.553476	+	0.832865i	$0.313301\pi$
$492$	31.9071	−	55.2647i	0.0648518	−	0.112327i
$493$			608.571i			1.23442i
$494$	44.7566	+	246.058i	0.0906004	+	0.498094i
$495$	252.178			0.509450
$496$	−454.511	−	262.412i	−0.916354	−	0.529057i
$497$	−148.633	−	85.8134i	−0.299061	−	0.172663i
$498$	−402.329	−	696.854i	−0.807889	−	1.39931i
$499$	35.4225	−	61.3535i	0.0709869	−	0.122953i	−0.828347	−	0.560215i	$-0.810718\pi$
$499$	35.4225	−	61.3535i	0.0709869	−	0.122953i	0.899334	+	0.437262i	$0.144052\pi$
$500$	−59.4526	−	102.975i	−0.118905	−	0.205950i
$501$	144.439			0.288301
$502$			280.970i			0.559700i
$503$	−268.299	−	464.708i	−0.533398	−	0.923872i	−0.999239	−	0.0390040i	$-0.987581\pi$
$503$	−268.299	−	464.708i	−0.533398	−	0.923872i	0.465841	−	0.884868i	$-0.345752\pi$
$504$	470.183	−	271.460i	0.932903	−	0.538612i
$505$	598.816			1.18577
$506$		−	137.368i		−	0.271478i
$507$	504.013	−	290.992i	0.994108	−	0.573949i
$508$	−186.527	−	107.691i	−0.367178	−	0.211991i
$509$	577.348	−	333.332i	1.13428	−	0.654876i	0.189271	−	0.981925i	$-0.439388\pi$
$509$	577.348	−	333.332i	1.13428	−	0.654876i	0.945007	+	0.327049i	$0.106054\pi$
$510$	−544.240	+	942.651i	−1.06714	+	1.84834i
$511$	269.739	−	467.201i	0.527865	−	0.914288i
$512$			101.640i			0.198516i
$513$	−20.8611	+	3.79451i	−0.0406649	+	0.00739671i
$514$	−343.496			−0.668280
$515$	196.735	+	113.585i	0.382009	+	0.220553i
$516$	155.469	+	89.7598i	0.301296	+	0.173953i
$517$	25.0417	+	43.3736i	0.0484366	+	0.0838947i
$518$	1.51739	−	2.62820i	0.00292933	−	0.00507375i
$519$	146.261	+	253.332i	0.281813	+	0.488115i
$520$	−209.018			−0.401957
$521$			928.678i			1.78249i	0.453521	+	0.891245i	$0.350168\pi$
$521$			928.678i			1.78249i	−0.453521	+	0.891245i	$0.649832\pi$
$522$	341.190	+	590.959i	0.653621	+	1.13211i
$523$	658.229	−	380.029i	1.25856	−	0.726632i	0.285768	−	0.958299i	$-0.407751\pi$
$523$	658.229	−	380.029i	1.25856	−	0.726632i	0.972795	+	0.231667i	$0.0744178\pi$
$524$	276.812			0.528268
$525$			364.984i			0.695208i
$526$	147.045	−	84.8964i	0.279553	−	0.161400i
$527$	442.787	+	255.643i	0.840203	+	0.485091i
$528$	336.192	−	194.101i	0.636728	−	0.367615i
$529$	182.322	−	315.791i	0.344655	−	0.596959i
$530$	238.054	−	412.321i	0.449158	−	0.777964i
$531$		−	813.805i		−	1.53259i
$532$	174.111	−	147.704i	0.327276	−	0.277639i
$533$	−66.7801			−0.125291
$534$	−170.434	−	98.4000i	−0.319165	−	0.184270i
$535$	−769.774	−	444.429i	−1.43883	−	0.830709i
$536$	−62.5577	−	108.353i	−0.116712	−	0.202151i
$537$	−484.724	+	839.566i	−0.902652	+	1.56344i
$538$	−50.2978	−	87.1183i	−0.0934903	−	0.161930i
$539$	−181.937			−0.337545
$540$			8.34754i			0.0154584i
$541$	−283.890	−	491.712i	−0.524750	−	0.908894i	−0.999585	−	0.0288191i	$-0.990825\pi$
$541$	−283.890	−	491.712i	−0.524750	−	0.908894i	0.474834	−	0.880075i	$-0.342508\pi$
$542$	63.0196	−	36.3844i	0.116272	−	0.0671299i
$543$	909.943			1.67577
$544$			375.382i			0.690041i
$545$	−822.633	+	474.947i	−1.50942	+	0.871463i
$546$	457.021	+	263.861i	0.837035	+	0.483262i
$547$	477.215	−	275.520i	0.872422	−	0.503693i	0.00426966	−	0.999991i	$-0.498641\pi$
$547$	477.215	−	275.520i	0.872422	−	0.503693i	0.868152	+	0.496298i	$0.165308\pi$
$548$	−8.30892	+	14.3915i	−0.0151623	+	0.0262618i
$549$	−423.836	+	734.105i	−0.772014	+	1.33717i
$550$			97.5470i			0.177358i
$551$	−394.100	−	464.558i	−0.715246	−	0.843118i
$552$	−342.325			−0.620154
$553$	−767.167	−	442.924i	−1.38728	−	0.800947i
$554$	644.347	+	372.014i	1.16308	+	0.671505i
$555$	−1.75639	−	3.04216i	−0.00316467	−	0.00548137i
$556$	−139.311	+	241.294i	−0.250560	+	0.433982i
$557$	66.7590	+	115.630i	0.119855	+	0.207594i	0.919710	−	0.392599i	$-0.128424\pi$
$557$	66.7590	+	115.630i	0.119855	+	0.207594i	−0.799855	+	0.600193i	$0.795091\pi$
$558$	573.296			1.02741
$559$		−	187.863i		−	0.336070i
$560$	533.719	+	924.429i	0.953070	+	1.65077i
$561$	−327.520	+	189.094i	−0.583815	+	0.337065i
$562$	−63.0087			−0.112115
$563$			939.856i			1.66937i	0.550727	+	0.834685i	$0.314350\pi$
$563$			939.856i			1.66937i	−0.550727	+	0.834685i	$0.685650\pi$
$564$	−50.9160	+	29.3964i	−0.0902766	+	0.0521212i
$565$	25.3624	+	14.6430i	0.0448893	+	0.0259168i
$566$	−432.206	+	249.534i	−0.763614	+	0.440873i
$567$	368.620	−	638.469i	0.650124	−	1.12605i
$568$	−57.1543	+	98.9941i	−0.100624	+	0.174285i
$569$		−	545.726i		−	0.959096i	−0.877516	−	0.479548i	$-0.840801\pi$
$569$		−	545.726i		−	0.959096i	0.877516	−	0.479548i	$-0.159199\pi$
$570$	−194.994	−	1072.02i	−0.342096	−	1.88074i
$571$	27.4635			0.0480973			0.0240486	−	0.999711i	$-0.492344\pi$
$571$	27.4635			0.0480973			0.0240486	+	0.999711i	$0.492344\pi$
$572$	29.6262	+	17.1047i	0.0517941	+	0.0299033i
$573$	−129.106	−	74.5394i	−0.225316	−	0.130086i
$574$	125.678	+	217.681i	0.218951	+	0.379235i
$575$	58.3557	−	101.075i	0.101488	−	0.175783i
$576$	−150.412	−	260.522i	−0.261133	−	0.452295i
$577$	−90.7976			−0.157362			−0.0786808	−	0.996900i	$-0.525071\pi$
$577$	−90.7976			−0.157362			−0.0786808	+	0.996900i	$0.525071\pi$
$578$		−	163.736i		−	0.283280i
$579$	−79.4783	−	137.660i	−0.137268	−	0.237755i
$580$	−207.705	+	119.918i	−0.358111	+	0.206756i
$581$	768.747			1.32314
$582$		−	1332.00i		−	2.28866i
$583$	143.259	−	82.7107i	0.245727	−	0.141871i
$584$	−311.170	−	179.654i	−0.532825	−	0.307627i
$585$	268.285	−	154.894i	0.458607	−	0.264777i
$586$	−59.7163	+	103.432i	−0.101905	+	0.176505i
$587$	−248.332	+	430.124i	−0.423053	+	0.732750i	−0.996236	−	0.0866775i	$-0.972375\pi$
$587$	−248.332	+	430.124i	−0.423053	+	0.732750i	0.573183	+	0.819427i	$0.305708\pi$
$588$		−	213.574i		−	0.363222i
$589$	−503.555	+	91.5938i	−0.854932	+	0.155507i
$590$	1179.26			1.99874
$591$	1163.45	+	671.717i	1.96861	+	1.13658i
$592$	−2.37503	−	1.37122i	−0.00401188	−	0.00231626i
$593$	64.8320	+	112.292i	0.109329	+	0.189363i	0.915499	−	0.402321i	$-0.131797\pi$
$593$	64.8320	+	112.292i	0.109329	+	0.189363i	−0.806170	+	0.591684i	$0.798463\pi$
$594$	−5.97881	+	10.3556i	−0.0100653	+	0.0174337i
$595$	−519.951	−	900.582i	−0.873868	−	1.51358i
$596$	13.3462			0.0223930
$597$			1309.54i			2.19353i
$598$	−84.3752	−	146.142i	−0.141096	−	0.244385i
$599$	−430.839	+	248.745i	−0.719264	+	0.415267i	−0.814482	−	0.580189i	$-0.802979\pi$
$599$	−430.839	+	248.745i	−0.719264	+	0.415267i	0.0952180	+	0.995456i	$0.469645\pi$
$600$	243.090			0.405150
$601$		−	718.473i		−	1.19546i	−0.801696	−	0.597731i	$-0.796069\pi$
$601$		−	718.473i		−	1.19546i	0.801696	−	0.597731i	$-0.203931\pi$
$602$	−612.371	+	353.553i	−1.01723	+	0.587297i
$603$	160.592	+	92.7178i	0.266322	+	0.153761i
$604$	−159.245	+	91.9399i	−0.263650	+	0.152218i
$605$	289.828	−	501.997i	0.479055	−	0.829748i
$606$	−503.476	+	872.047i	−0.830819	+	1.43902i
$607$			545.141i			0.898090i	0.893509	+	0.449045i	$0.148236\pi$
$607$			545.141i			0.898090i	−0.893509	+	0.449045i	$0.851764\pi$
$608$	−243.091	−	286.551i	−0.399821	−	0.471301i
$609$	−1285.47			−2.11079
$610$	−1063.77	−	614.167i	−1.74388	−	1.00683i
$611$	53.2825	+	30.7627i	0.0872054	+	0.0503480i
$612$	−112.575	−	194.986i	−0.183946	−	0.318605i
$613$	−103.876	+	179.918i	−0.169455	+	0.293504i	−0.938228	−	0.346017i	$-0.887534\pi$
$613$	−103.876	+	179.918i	−0.169455	+	0.293504i	0.768774	+	0.639521i	$0.220867\pi$
$614$	−431.244	−	746.936i	−0.702352	−	1.21651i
$615$	290.946			0.473083
$616$			273.346i			0.443743i
$617$	398.959	+	691.018i	0.646611	+	1.11996i	0.983927	+	0.178572i	$0.0571477\pi$
$617$	398.959	+	691.018i	0.646611	+	1.11996i	−0.337316	+	0.941392i	$0.609519\pi$
$618$	−330.823	+	191.001i	−0.535313	+	0.309063i
$619$	−753.162			−1.21674			−0.608370	−	0.793654i	$-0.708176\pi$
$619$	−753.162			−1.21674			−0.608370	+	0.793654i	$0.708176\pi$
$620$			201.497i			0.324995i
$621$	12.3901	−	7.15342i	0.0199518	−	0.0115192i
$622$	185.110	+	106.873i	0.297604	+	0.171822i
$623$	162.828	−	94.0086i	0.261361	−	0.150897i
$624$	238.444	−	412.997i	0.382122	−	0.661854i
$625$	384.858	−	666.593i	0.615772	−	1.06655i
$626$			980.183i			1.56579i
$627$	127.561	−	356.443i	0.203447	−	0.568489i
$628$	346.934			0.552442
$629$	2.31376	+	1.33585i	0.00367848	+	0.00212377i
$630$	−1009.81	−	583.012i	−1.60287	−	0.925417i
$631$	142.019	+	245.984i	0.225069	+	0.389831i	0.956340	−	0.292256i	$-0.0944059\pi$
$631$	142.019	+	245.984i	0.225069	+	0.389831i	−0.731271	+	0.682087i	$0.761073\pi$
$632$	−295.000	+	510.956i	−0.466773	+	0.808474i
$633$	−156.660	−	271.343i	−0.247488	−	0.428662i
$634$	1368.85			2.15906
$635$		−	981.988i		−	1.54644i
$636$	97.0936	+	168.171i	0.152663	+	0.264420i
$637$	−193.558	+	111.751i	−0.303858	+	0.175433i
$638$	−343.560			−0.538495
$639$		−	169.419i		−	0.265131i
$640$	777.609	−	448.953i	1.21501	−	0.701489i
$641$	1029.31	+	594.275i	1.60579	+	0.927106i	0.990297	+	0.138968i	$0.0443784\pi$
$641$	1029.31	+	594.275i	1.60579	+	0.927106i	0.615498	+	0.788138i	$0.288955\pi$
$642$	1294.43	−	747.340i	2.01625	−	1.16408i
$643$	−310.711	+	538.167i	−0.483220	+	0.836962i	−0.999814	−	0.0192683i	$-0.993866\pi$
$643$	−310.711	+	538.167i	−0.483220	+	0.836962i	0.516594	+	0.856230i	$0.327200\pi$
$644$	−77.0294	+	133.419i	−0.119611	+	0.207172i
$645$			818.479i			1.26896i
$646$	536.109	+	631.955i	0.829890	+	0.978259i
$647$	367.100			0.567388			0.283694	−	0.958915i	$-0.408440\pi$
$647$	367.100			0.567388			0.283694	+	0.958915i	$0.408440\pi$
$648$	−425.239	−	245.512i	−0.656233	−	0.378877i
$649$	354.835	+	204.864i	0.546741	+	0.315661i
$650$	59.9161	+	103.778i	0.0921786	+	0.159658i
$651$	−539.989	+	935.288i	−0.829476	+	1.43669i
$652$	36.3778	+	63.0082i	0.0557942	+	0.0966383i
$653$	−407.248			−0.623656			−0.311828	−	0.950139i	$-0.600941\pi$
$653$	−407.248			−0.623656			−0.311828	+	0.950139i	$0.600941\pi$
$654$		−	1597.32i		−	2.44238i
$655$	631.032	+	1092.98i	0.963407	+	1.66867i
$656$	196.712	−	113.572i	0.299866	−	0.173128i
$657$	532.536			0.810558
$658$		−	231.577i		−	0.351941i
$659$	−186.420	+	107.630i	−0.282884	+	0.163323i	−0.634728	−	0.772736i	$-0.718888\pi$
$659$	−186.420	+	107.630i	−0.282884	+	0.163323i	0.351845	+	0.936058i	$0.385555\pi$
$660$	−129.075	−	74.5214i	−0.195568	−	0.112911i
$661$	570.950	−	329.638i	0.863767	−	0.498696i	−0.00150486	−	0.999999i	$-0.500479\pi$
$661$	570.950	−	329.638i	0.863767	−	0.498696i	0.865272	+	0.501303i	$0.167146\pi$
$662$	−35.5653	+	61.6009i	−0.0537240	+	0.0930528i
$663$	−232.293	+	402.343i	−0.350367	+	0.606853i
$664$		−	512.008i		−	0.771097i
$665$	980.111	+	350.756i	1.47385	+	0.527452i
$666$	2.99574			0.00449810
$667$	355.985	+	205.528i	0.533711	+	0.308138i
$668$	−37.4934	−	21.6468i	−0.0561279	−	0.0324055i
$669$	−44.4504	−	76.9903i	−0.0664430	−	0.115083i
$670$	−134.355	+	232.709i	−0.200529	+	0.347327i
$671$	−213.390	−	369.602i	−0.318017	−	0.550822i
$672$	−792.910			−1.17993
$673$		−	745.165i		−	1.10723i	−0.832773	−	0.553614i	$-0.813248\pi$
$673$		−	745.165i		−	1.10723i	0.832773	−	0.553614i	$-0.186752\pi$
$674$	−470.634	−	815.161i	−0.698270	−	1.20944i
$675$	−8.79839	+	5.07975i	−0.0130347	+	0.00752556i
$676$	−174.442			−0.258051
$677$		−	1174.97i		−	1.73556i	−0.496949	−	0.867780i	$-0.665546\pi$
$677$		−	1174.97i		−	1.73556i	0.496949	−	0.867780i	$-0.334454\pi$
$678$	−42.6488	+	24.6233i	−0.0629038	+	0.0363175i
$679$	1102.07	+	636.278i	1.62307	+	0.937081i
$680$	−599.814	+	346.303i	−0.882080	+	0.509269i
$681$	207.283	−	359.025i	0.304381	−	0.527203i
$682$	−144.319	+	249.969i	−0.211612	+	0.366523i
$683$			533.368i			0.780919i	0.920620	+	0.390460i	$0.127684\pi$
$683$			533.368i			0.780919i	−0.920620	+	0.390460i	$0.872316\pi$
$684$	212.205	+	75.9424i	0.310241	+	0.111027i
$685$	−75.7653			−0.110606
$686$	−186.351	−	107.590i	−0.271649	−	0.156837i
$687$	−962.052	−	555.441i	−1.40037	−	0.808502i
$688$	319.496	+	553.383i	0.464383	+	0.804335i
$689$	101.606	−	175.987i	0.147469	−	0.255424i
$690$	367.604	+	636.709i	0.532759	+	0.922766i
$691$	−847.914			−1.22708			−0.613541	−	0.789663i	$-0.710256\pi$
$691$	−847.914			−1.22708			−0.613541	+	0.789663i	$0.710256\pi$
$692$		−	87.6799i		−	0.126705i
$693$	−202.565	−	350.853i	−0.292302	−	0.506281i
$694$	−1046.69	+	604.309i	−1.50820	+	0.870762i
$695$	−1270.32			−1.82779
$696$			856.161i			1.23012i
$697$	−191.638	+	110.642i	−0.274946	+	0.158740i
$698$	572.279	+	330.405i	0.819884	+	0.473360i
$699$	−1368.63	+	790.181i	−1.95799	+	1.13045i
$700$	54.6997	−	94.7427i	0.0781425	−	0.135347i
$701$	474.994	−	822.713i	0.677594	−	1.17363i	−0.298109	−	0.954532i	$-0.596356\pi$
$701$	474.994	−	822.713i	0.677594	−	1.17363i	0.975703	−	0.219096i	$-0.0703108\pi$
$702$			14.6894i			0.0209251i
$703$	−2.63131	+	0.478619i	−0.00374297	+	0.000680824i
$704$	151.457			0.215138
$705$	−232.140	−	134.026i	−0.329277	−	0.190108i
$706$	−36.9035	−	21.3062i	−0.0522712	−	0.0301788i
$707$	−481.007	−	833.128i	−0.680349	−	1.17840i
$708$	−240.489	+	416.539i	−0.339673	+	0.588332i
$709$	−9.83456	−	17.0340i	−0.0138710	−	0.0240253i	0.859007	−	0.511965i	$-0.171082\pi$
$709$	−9.83456	−	17.0340i	−0.0138710	−	0.0240253i	−0.872878	+	0.487939i	$0.837749\pi$
$710$	245.499			0.345774
$711$		−	874.450i		−	1.22989i
$712$	−62.6125	−	108.448i	−0.0879389	−	0.152315i
$713$	299.078	−	172.673i	0.419464	−	0.242178i
$714$	1748.67			2.44912
$715$			155.970i			0.218140i
$716$	251.650	−	145.290i	0.351466	−	0.202919i
$717$	−1153.95	−	666.235i	−1.60942	−	0.929198i
$718$	190.041	−	109.720i	0.264681	−	0.152814i
$719$	−165.944	+	287.423i	−0.230798	+	0.399754i	−0.958043	−	0.286624i	$-0.907467\pi$
$719$	−165.944	+	287.423i	−0.230798	+	0.399754i	0.727245	+	0.686378i	$0.240800\pi$
$720$	−526.852	+	912.534i	−0.731739	+	1.26741i
$721$		−	364.954i		−	0.506177i
$722$	−818.487	−	135.234i	−1.13364	−	0.187304i
$723$	1456.14			2.01402
$724$	−236.203	−	136.372i	−0.326248	−	0.188359i
$725$	−252.790	−	145.949i	−0.348676	−	0.201308i
$726$	487.367	+	844.145i	0.671305	+	1.16273i
$727$	372.720	−	645.570i	0.512682	−	0.887992i	−0.487210	−	0.873285i	$-0.661985\pi$
$727$	372.720	−	645.570i	0.512682	−	0.887992i	0.999892	−	0.0147065i	$-0.00468141\pi$
$728$	167.896	+	290.805i	0.230627	+	0.399458i
$729$	770.674			1.05717
$730$			771.682i			1.05710i
$731$	−311.254	−	539.108i	−0.425792	−	0.737494i
$732$	433.873	−	250.497i	0.592723	−	0.342209i
$733$	−753.165			−1.02751			−0.513755	−	0.857937i	$-0.671746\pi$
$733$	−753.165			−1.02751			−0.513755	+	0.857937i	$0.671746\pi$
$734$		−	1147.01i		−	1.56268i
$735$	843.287	−	486.872i	1.14733	−	0.662411i
$736$	219.581	+	126.775i	0.298343	+	0.172248i
$737$	−80.8536	+	46.6809i	−0.109706	+	0.0633390i
$738$	−124.061	+	214.880i	−0.168104	+	0.291165i
$739$	−285.102	+	493.812i	−0.385795	+	0.668216i	−0.991879	−	0.127184i	$-0.959406\pi$
$739$	−285.102	+	493.812i	−0.385795	+	0.668216i	0.606084	+	0.795400i	$0.292739\pi$
$740$			1.05291i			0.00142286i
$741$	−83.2277	−	457.561i	−0.112318	−	0.617492i
$742$	−764.879			−1.03083
$743$	−790.856	−	456.601i	−1.06441	−	0.614537i	−0.137760	−	0.990466i	$-0.543990\pi$
$743$	−790.856	−	456.601i	−1.06441	−	0.614537i	−0.926649	+	0.375929i	$0.877324\pi$
$744$	622.930	+	359.649i	0.837271	+	0.483399i
$745$	30.4246	+	52.6969i	0.0408383	+	0.0707341i
$746$	92.0027	−	159.353i	0.123328	−	0.213610i
$747$	379.428	+	657.189i	0.507936	+	0.879770i
$748$	113.357			0.151547
$749$			1427.97i			1.90651i
$750$	455.808	+	789.483i	0.607745	+	1.05264i
$751$	−340.814	+	196.769i	−0.453813	+	0.262009i	−0.709439	−	0.704767i	$-0.751052\pi$
$751$	−340.814	+	196.769i	−0.453813	+	0.262009i	0.255626	+	0.966776i	$0.417718\pi$
$752$	−209.270			−0.278284
$753$		−	522.481i		−	0.693866i
$754$	−365.504	+	211.024i	−0.484753	+	0.279872i
$755$	−726.040	−	419.179i	−0.961643	−	0.555205i
$756$	11.6139	−	6.70527i	0.0153623	−	0.00886940i
$757$	−252.335	+	437.057i	−0.333335	+	0.577354i	−0.983164	−	0.182727i	$-0.941507\pi$
$757$	−252.335	+	437.057i	−0.333335	+	0.577354i	0.649828	+	0.760081i	$0.274841\pi$
$758$	389.261	−	674.220i	0.513537	−	0.889472i
$759$			255.445i			0.336554i
$760$	233.614	−	652.783i	0.307386	−	0.858925i
$761$	−564.183			−0.741371			−0.370685	−	0.928758i	$-0.620877\pi$
$761$	−564.183			−0.741371			−0.370685	+	0.928758i	$0.620877\pi$
$762$	1430.05	+	825.642i	1.87671	+	1.08352i
$763$	1321.58	+	763.015i	1.73209	+	1.00002i
$764$	22.3423	+	38.6979i	0.0292438	+	0.0506517i
$765$	513.261	−	888.995i	0.670930	−	1.16208i
$766$	−127.014	−	219.995i	−0.165815	−	0.287200i
$767$	503.333			0.656236
$768$			954.664i			1.24305i
$769$	443.262	+	767.752i	0.576413	+	0.998377i	0.995887	+	0.0906095i	$0.0288815\pi$
$769$	443.262	+	767.752i	0.576413	+	0.998377i	−0.419473	+	0.907768i	$0.637785\pi$
$770$	508.410	−	293.531i	0.660273	−	0.381209i
$771$	638.753			0.828473
$772$			47.6453i			0.0617167i
$773$	534.516	−	308.603i	0.691482	−	0.399228i	−0.112685	−	0.993631i	$-0.535945\pi$
$773$	534.516	−	308.603i	0.691482	−	0.399228i	0.804167	+	0.594403i	$0.202612\pi$
$774$	−604.492	−	349.004i	−0.780998	−	0.450909i
$775$	−212.380	+	122.617i	−0.274038	+	0.158216i
$776$	423.780	−	734.008i	0.546108	−	0.945887i
$777$	−2.82169	+	4.88731i	−0.00363152	+	0.00628997i
$778$		−	1426.84i		−	1.83398i
$779$	74.6383	−	208.561i	0.0958130	−	0.267729i
$780$	−183.092			−0.234734
$781$	73.8699	+	42.6488i	0.0945837	+	0.0546079i
$782$	−484.259	−	279.587i	−0.619258	−	0.357529i
$783$	−17.8908	−	30.9879i	−0.0228491	−	0.0395758i
$784$	380.104	−	658.359i	0.484826	−	0.839744i
$785$	790.883	+	1369.85i	1.00749	+	1.74503i
$786$	−2122.25			−2.70007
$787$			81.5848i			0.103666i	0.998656	+	0.0518328i	$0.0165063\pi$
$787$			81.5848i			0.103666i	−0.998656	+	0.0518328i	$0.983494\pi$
$788$	−201.339	−	348.729i	−0.255506	−	0.442549i
$789$	−273.440	+	157.870i	−0.346565	+	0.200089i
$790$	1267.14			1.60397
$791$		−	47.0488i		−	0.0594801i
$792$	−233.678	+	134.914i	−0.295049	+	0.170346i
$793$	−454.039	−	262.139i	−0.572558	−	0.330567i
$794$	−938.301	+	541.728i	−1.18174	+	0.682277i
$795$	−442.676	+	766.738i	−0.556826	+	0.964450i
$796$	196.259	−	339.930i	0.246556	−	0.427048i
$797$		−	814.902i		−	1.02246i	−0.859443	−	0.511231i	$-0.829190\pi$
$797$		−	814.902i		−	1.02246i	0.859443	−	0.511231i	$-0.170810\pi$
$798$	−1334.86	+	1132.41i	−1.67276	+	1.41906i
$799$	203.872			0.255158
$800$	−155.927	−	90.0247i	−0.194909	−	0.112531i
$801$	160.733	+	92.7990i	0.200665	+	0.115854i
$802$	−258.675	−	448.039i	−0.322538	−	0.558652i
$803$	−134.059	+	232.196i	−0.166947	+	0.289161i
$804$	−54.7984	−	94.9136i	−0.0681572	−	0.118052i
$805$	−702.396			−0.872542
$806$			354.580i			0.439925i
$807$	93.5320	+	162.002i	0.115901	+	0.200746i
$808$	−554.888	+	320.365i	−0.686743	+	0.396491i
$809$	1385.45			1.71255			0.856275	−	0.516520i	$-0.172773\pi$
$809$	1385.45			1.71255			0.856275	+	0.516520i	$0.172773\pi$
$810$			1054.57i			1.30193i
$811$	−346.960	+	200.317i	−0.427817	+	0.247000i	−0.698416	−	0.715692i	$-0.746112\pi$
$811$	−346.960	+	200.317i	−0.427817	+	0.247000i	0.270599	+	0.962692i	$0.412778\pi$
$812$	333.683	+	192.652i	0.410940	+	0.237256i
$813$	−117.189	+	67.6591i	−0.144144	+	0.0832216i
$814$	−0.754135	+	1.30620i	−0.000926456	+	0.00160467i
$815$	−165.856	+	287.272i	−0.203505	+	0.352481i
$816$		−	1580.23i		−	1.93655i
$817$	586.715	+	209.970i	0.718134	+	0.257001i
$818$	511.482			0.625283
$819$	−431.007	−	248.842i	−0.526260	−	0.303836i
$820$	−75.5239	−	43.6038i	−0.0921024	−	0.0531753i
$821$	40.8741	+	70.7960i	0.0497858	+	0.0862315i	0.889844	−	0.456264i	$-0.150813\pi$
$821$	40.8741	+	70.7960i	0.0497858	+	0.0862315i	−0.840059	+	0.542496i	$0.817479\pi$
$822$	63.7024	−	110.336i	0.0774969	−	0.134229i
$823$	−152.006	−	263.282i	−0.184698	−	0.319906i	0.758777	−	0.651351i	$-0.225797\pi$
$823$	−152.006	−	263.282i	−0.184698	−	0.319906i	−0.943475	+	0.331445i	$0.892464\pi$
$824$	−243.070			−0.294988
$825$		−	181.395i		−	0.219873i
$826$	−947.256	−	1640.69i	−1.14680	−	1.98631i
$827$	802.116	−	463.102i	0.969910	−	0.559978i	0.0707015	−	0.997498i	$-0.477476\pi$
$827$	802.116	−	463.102i	0.969910	−	0.559978i	0.899209	+	0.437519i	$0.144143\pi$
$828$	−152.077			−0.183667
$829$			982.984i			1.18575i	0.805296	+	0.592873i	$0.202006\pi$
$829$			982.984i			1.18575i	−0.805296	+	0.592873i	$0.797994\pi$
$830$	−952.311	+	549.817i	−1.14736	+	0.662430i
$831$	−1198.20	−	691.784i	−1.44188	−	0.832471i
$832$	161.131	−	93.0291i	0.193667	−	0.111814i
$833$	−370.299	+	641.376i	−0.444536	+	0.769960i
$834$	1068.07	−	1849.94i	1.28065	−	2.21816i
$835$		−	197.388i		−	0.236393i
$836$	−86.5320	+	73.4080i	−0.103507	+	0.0878086i
$837$	−30.0617			−0.0359160
$838$	609.732	+	352.029i	0.727604	+	0.420082i
$839$	1255.14	+	724.657i	1.49600	+	0.863716i	0.999989	−	0.00460145i	$-0.00146469\pi$
$839$	1255.14	+	724.657i	1.49600	+	0.863716i	0.496010	+	0.868317i	$0.334798\pi$
$840$	−731.487	−	1266.97i	−0.870818	−	1.50830i
$841$	93.5295	−	161.998i	0.111212	−	0.192625i
$842$	439.865	+	761.868i	0.522405	+	0.904832i
$843$	117.169			0.138990
$844$			93.9139i			0.111272i
$845$	−397.666	−	688.777i	−0.470610	−	0.815121i
$846$	197.971	−	114.299i	0.234009	−	0.135105i
$847$	−931.234			−1.09945
$848$			691.200i			0.815094i
$849$	803.715	−	464.025i	0.946660	−	0.546555i
$850$	343.880	+	198.539i	0.404565	+	0.233575i
$851$	1.56282	−	0.902294i	0.00183645	−	0.00106028i
$852$	−50.0651	+	86.7154i	−0.0587619	+	0.101779i
$853$	−291.837	+	505.476i	−0.342130	+	0.592586i	−0.984828	−	0.173533i	$-0.944482\pi$
$853$	−291.837	+	505.476i	−0.342130	+	0.592586i	0.642698	+	0.766119i	$0.277815\pi$
$854$			1973.35i			2.31072i
$855$	183.895	+	1011.00i	0.215082	+	1.18246i
$856$	951.074			1.11107
$857$	−197.002	−	113.739i	−0.229874	−	0.132718i	0.380640	−	0.924723i	$-0.375704\pi$
$857$	−197.002	−	113.739i	−0.229874	−	0.132718i	−0.610514	+	0.792005i	$0.709037\pi$
$858$	−227.137	−	131.138i	−0.264728	−	0.152841i
$859$	−451.757	−	782.466i	−0.525910	−	0.910903i	−0.999544	−	0.0301814i	$-0.990391\pi$
$859$	−451.757	−	782.466i	−0.525910	−	0.910903i	0.473634	−	0.880722i	$-0.342942\pi$
$860$	122.664	−	212.461i	0.142633	−	0.247048i
$861$	−233.706	−	404.791i	−0.271436	−	0.470141i
$862$	−618.220			−0.717193
$863$		−	448.624i		−	0.519843i	−0.965630	−	0.259921i	$-0.916303\pi$
$863$		−	448.624i		−	0.519843i	0.965630	−	0.259921i	$-0.0836967\pi$
$864$	−11.0355	−	19.1141i	−0.0127726	−	0.0221228i
$865$	346.199	−	199.878i	0.400231	−	0.231073i
$866$	−710.636			−0.820596
$867$			304.477i			0.351185i
$868$	280.341	−	161.855i	0.322973	−	0.186469i
$869$	381.278	+	220.131i	0.438754	+	0.253315i
$870$	1592.42	−	919.384i	1.83037	−	1.05676i
$871$	−57.3453	+	99.3250i	−0.0658385	+	0.114036i
$872$	508.191	−	880.213i	0.582788	−	1.00942i
$873$			1256.18i			1.43893i
$874$	550.719	−	100.173i	0.630114	−	0.114614i
$875$	−870.933			−0.995352
$876$	−272.574	−	157.371i	−0.311157	−	0.179647i
$877$	−76.1813	−	43.9833i	−0.0868658	−	0.0501520i	0.455938	−	0.890012i	$-0.349304\pi$
$877$	−76.1813	−	43.9833i	−0.0868658	−	0.0501520i	−0.542804	+	0.839860i	$0.682637\pi$
$878$	477.641	+	827.299i	0.544011	+	0.942254i
$879$	111.046	−	192.338i	0.126333	−	0.218815i
$880$	−265.255	−	459.436i	−0.301427	−	0.522086i
$881$	1590.01			1.80478			0.902388	−	0.430925i	$-0.141813\pi$
$881$	1590.01			1.80478			0.902388	+	0.430925i	$0.141813\pi$
$882$			830.419i			0.941519i
$883$	−207.973	−	360.219i	−0.235530	−	0.407949i	0.723897	−	0.689908i	$-0.242349\pi$
$883$	−207.973	−	360.219i	−0.235530	−	0.407949i	−0.959426	+	0.281959i	$0.909016\pi$
$884$	120.597	−	69.6270i	0.136422	−	0.0787636i
$885$	−2192.91			−2.47786
$886$			802.041i			0.905238i
$887$	−483.574	+	279.192i	−0.545180	+	0.314760i	−0.747175	−	0.664627i	$-0.768591\pi$
$887$	−483.574	+	279.192i	−0.545180	+	0.314760i	0.201996	+	0.979386i	$0.435257\pi$
$888$	3.25509	+	1.87933i	0.00366564	+	0.00211636i
$889$	−1366.23	+	788.795i	−1.53682	+	0.887283i
$890$	−134.472	+	232.913i	−0.151092	+	0.261700i
$891$	−183.202	+	317.315i	−0.205614	+	0.356134i
$892$			26.6469i			0.0298732i
$893$	−155.627	+	132.024i	−0.174274	+	0.147843i
$894$	−102.322			−0.114454
$895$	1147.34	+	662.417i	1.28194	+	0.740131i
$896$	−1249.25	−	721.255i	−1.39425	−	0.804972i
$897$	156.901	+	271.761i	0.174918	+	0.302966i
$898$	−725.911	+	1257.31i	−0.808364	+	1.40013i
$899$	−431.858	−	747.999i	−0.480376	−	0.832035i
$900$	107.992			0.119991
$901$		−	673.370i		−	0.747358i
$902$	−62.4613	−	108.186i	−0.0692475	−	0.119940i
$903$	1138.74	−	657.454i	1.26107	−	0.728078i
$904$	−31.3359			−0.0346636
$905$		−	1243.52i		−	1.37405i
$906$	1220.89	−	704.881i	1.34756	−	0.778014i
$907$	−333.612	−	192.611i	−0.367819	−	0.212360i	0.304686	−	0.952453i	$-0.401448\pi$
$907$	−333.612	−	192.611i	−0.367819	−	0.212360i	−0.672505	+	0.740092i	$0.734782\pi$
$908$	−107.613	+	62.1306i	−0.118517	+	0.0684257i
$909$	474.818	−	822.409i	0.522352	−	0.904740i
$910$	360.589	−	624.559i	0.396252	−	0.686328i
$911$			275.295i			0.302190i	0.988519	+	0.151095i	$0.0482800\pi$
$911$			275.295i			0.302190i	−0.988519	+	0.151095i	$0.951720\pi$
$912$	1023.33	+	1206.28i	1.12207	+	1.32267i
$913$	−382.063			−0.418470
$914$	1074.65	+	620.448i	1.17576	+	0.678827i
$915$	1978.15	+	1142.08i	2.16191	+	1.24818i
$916$	166.487	+	288.363i	0.181754	+	0.314807i
$917$	1013.77	−	1755.90i	1.10553	−	1.91483i
$918$	24.3376	+	42.1539i	0.0265115	+	0.0459193i
$919$	52.3454			0.0569591			0.0284796	−	0.999594i	$-0.490933\pi$
$919$	52.3454			0.0569591			0.0284796	+	0.999594i	$0.490933\pi$
$920$			467.817i			0.508497i
$921$	801.926	+	1388.98i	0.870712	+	1.50812i
$922$	337.612	−	194.921i	0.366174	−	0.211411i
$923$	104.784			0.113526
$924$			239.441i			0.259136i
$925$	−1.10978	+	0.640733i	−0.00119976	+	0.000692684i
$926$	−920.111	−	531.226i	−0.993640	−	0.573678i
$927$	311.993	−	180.129i	0.336562	−	0.194314i
$928$	317.066	−	549.175i	0.341666	−	0.591783i
$929$	−637.608	+	1104.37i	−0.686338	+	1.18877i	0.286676	+	0.958027i	$0.407450\pi$
$929$	−637.608	+	1104.37i	−0.686338	+	1.18877i	−0.973014	+	0.230745i	$0.925884\pi$
$930$		−	1544.83i		−	1.66110i
$931$	−132.674	−	729.399i	−0.142506	−	0.783458i
$932$	473.694			0.508256
$933$	−344.224	−	198.738i	−0.368943	−	0.213009i
$934$	5.18361	+	2.99276i	0.00554991	+	0.00320424i
$935$	258.413	+	447.584i	0.276377	+	0.478700i
$936$	−165.736	+	287.063i	−0.177069	+	0.306692i
$937$	359.964	+	623.476i	0.384167	+	0.665396i	0.991653	−	0.128934i	$-0.0411555\pi$
$937$	359.964	+	623.476i	0.384167	+	0.665396i	−0.607487	+	0.794330i	$0.707822\pi$
$938$	431.688			0.460222
$939$		−	1822.71i		−	1.94112i
$940$	40.1727	+	69.5811i	0.0427369	+	0.0740224i
$941$	76.8289	−	44.3572i	0.0816461	−	0.0471384i	−0.458621	−	0.888632i	$-0.651656\pi$
$941$	76.8289	−	44.3572i	0.0816461	−	0.0471384i	0.540267	+	0.841494i	$0.318323\pi$
$942$	−2659.85			−2.82363
$943$			149.465i			0.158500i
$944$	−1482.65	+	856.008i	−1.57060	+	0.906788i
$945$	52.9508	+	30.5712i	0.0560326	+	0.0323504i
$946$	304.345	−	175.714i	0.321718	−	0.185744i
$947$	−172.069	+	298.033i	−0.181699	+	0.314712i	−0.942459	−	0.334321i	$-0.891493\pi$
$947$	−172.069	+	298.033i	−0.181699	+	0.314712i	0.760760	+	0.649033i	$0.224826\pi$
$948$	−258.410	+	447.579i	−0.272584	+	0.472130i
$949$			329.370i			0.347071i
$950$	−391.074	+	71.1341i	−0.411657	+	0.0748780i
$951$	−2545.46			−2.67661
$952$	963.618	+	556.345i	1.01220	+	0.584396i
$953$	−1350.11	−	779.488i	−1.41670	−	0.817931i	−0.420690	−	0.907204i	$-0.638212\pi$
$953$	−1350.11	−	779.488i	−1.41670	−	0.817931i	−0.996007	+	0.0892739i	$0.971545\pi$
$954$	−377.519	−	653.882i	−0.395722	−	0.685411i
$955$	−101.864	+	176.434i	−0.106664	+	0.184748i
$956$	199.696	+	345.883i	0.208887	+	0.361802i
$957$	638.872			0.667577
$958$		−	901.408i		−	0.940927i
$959$	60.8595	+	105.412i	0.0634614	+	0.109918i
$960$	−702.012	+	405.307i	−0.731263	+	0.422195i
$961$	235.357			0.244908
$962$			1.85284i			0.00192603i
$963$	−1220.75	+	704.801i	−1.26765	+	0.731880i
$964$	−377.985	−	218.230i	−0.392100	−	0.226379i
$965$	−188.125	+	108.614i	−0.194948	+	0.112553i
$966$	590.565	−	1022.89i	0.611351	−	1.05889i
$967$	645.250	−	1117.61i	0.667270	−	1.15574i	−0.311395	−	0.950281i	$-0.600796\pi$
$967$	645.250	−	1117.61i	0.667270	−	1.15574i	0.978665	−	0.205464i	$-0.0658704\pi$
$968$			620.229i			0.640733i
$969$	−996.929	−	1175.16i	−1.02882	−	1.21276i
$970$	−1820.29			−1.87659
$971$	−439.932	−	253.995i	−0.453071	−	0.261581i	0.256055	−	0.966662i	$-0.417577\pi$
$971$	−439.932	−	253.995i	−0.453071	−	0.261581i	−0.709126	+	0.705081i	$0.750910\pi$
$972$	−383.636	−	221.492i	−0.394687	−	0.227873i
$973$	1020.40	+	1767.38i	1.04871	+	1.81643i
$974$	107.339	−	185.917i	0.110204	−	0.190879i
$975$	−111.418	−	192.981i	−0.114275	−	0.197930i
$976$	1783.26			1.82711
$977$			743.988i			0.761503i	0.924677	+	0.380752i	$0.124335\pi$
$977$			743.988i			0.761503i	−0.924677	+	0.380752i	$0.875665\pi$
$978$	−278.900	−	483.068i	−0.285173	−	0.493935i
$979$	−80.9244	+	46.7217i	−0.0826603	+	0.0477239i
$980$	−291.868			−0.297824
$981$			1506.40i			1.53557i
$982$	−868.780	+	501.590i	−0.884704	+	0.510784i
$983$	1367.75	+	789.668i	1.39140	+	0.803325i	0.993470	−	0.114091i	$-0.0363956\pi$
$983$	1367.75	+	789.668i	1.39140	+	0.803325i	0.397929	+	0.917416i	$0.369729\pi$
$984$	−269.603	+	155.655i	−0.273987	+	0.158186i
$985$	917.959	−	1589.95i	0.931938	−	1.61416i
$986$	−699.253	+	1211.14i	−0.709182	+	1.22834i
$987$			430.633i			0.436305i
$988$	−46.9699	+	131.247i	−0.0475404	+	0.132841i
$989$	−420.470			−0.425146
$990$	501.868	+	289.754i	0.506938	+	0.292681i
$991$	−1433.20	−	827.457i	−1.44621	−	0.834971i	−0.447960	−	0.894054i	$-0.647849\pi$
$991$	−1433.20	−	827.457i	−1.44621	−	0.834971i	−0.998253	+	0.0590824i	$0.981183\pi$
$992$	−266.381	−	461.385i	−0.268529	−	0.465106i
$993$	66.1360	−	114.551i	0.0666022	−	0.115358i
$994$	−197.200	−	341.561i	−0.198391	−	0.343623i
$995$	1789.60			1.79859
$996$		−	448.501i		−	0.450303i
$997$	−579.476	−	1003.68i	−0.581220	−	1.00670i	−0.995335	−	0.0964779i	$-0.969242\pi$
$997$	−579.476	−	1003.68i	−0.581220	−	1.00670i	0.414115	−	0.910224i	$-0.364091\pi$
$998$	140.991	−	81.4013i	0.141274	−	0.0815645i
$999$	−0.157086			−0.000157243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.3.d.a.8.3	✓	6
3.2	odd	2		171.3.p.d.46.1		6
4.3	odd	2		304.3.r.b.65.3		6
19.2	odd	18		361.3.f.i.127.3		18
19.3	odd	18		361.3.f.i.262.3		18
19.4	even	9		361.3.f.i.299.3		18
19.5	even	9		361.3.f.h.333.3		18
19.6	even	9		361.3.f.i.307.3		18
19.7	even	3		361.3.d.c.69.1		6
19.8	odd	6		361.3.b.b.360.5		6
19.9	even	9		361.3.f.i.116.1		18
19.10	odd	18		361.3.f.h.116.3		18
19.11	even	3		361.3.b.b.360.2		6
19.12	odd	6	inner	19.3.d.a.12.3	yes	6
19.13	odd	18		361.3.f.h.307.1		18
19.14	odd	18		361.3.f.i.333.1		18
19.15	odd	18		361.3.f.h.299.1		18
19.16	even	9		361.3.f.h.262.1		18
19.17	even	9		361.3.f.h.127.1		18
19.18	odd	2		361.3.d.c.293.1		6
57.50	even	6		171.3.p.d.145.1		6
76.31	even	6		304.3.r.b.145.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.d.a.8.3	✓	6	1.1	even	1	trivial
19.3.d.a.12.3	yes	6	19.12	odd	6	inner
171.3.p.d.46.1		6	3.2	odd	2
171.3.p.d.145.1		6	57.50	even	6
304.3.r.b.65.3		6	4.3	odd	2
304.3.r.b.145.3		6	76.31	even	6
361.3.b.b.360.2		6	19.11	even	3
361.3.b.b.360.5		6	19.8	odd	6
361.3.d.c.69.1		6	19.7	even	3
361.3.d.c.293.1		6	19.18	odd	2
361.3.f.h.116.3		18	19.10	odd	18
361.3.f.h.127.1		18	19.17	even	9
361.3.f.h.262.1		18	19.16	even	9
361.3.f.h.299.1		18	19.15	odd	18
361.3.f.h.307.1		18	19.13	odd	18
361.3.f.h.333.3		18	19.5	even	9
361.3.f.i.116.1		18	19.9	even	9
361.3.f.i.127.3		18	19.2	odd	18
361.3.f.i.262.3		18	19.3	odd	18
361.3.f.i.299.3		18	19.4	even	9
361.3.f.i.307.3		18	19.6	even	9
361.3.f.i.333.1		18	19.14	odd	18

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	19.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99014 + 1.14901i) q^{2} +(-3.70079 - 2.13665i) q^{3} +(0.640435 + 1.10927i) q^{4} +(-2.91992 + 5.05745i) q^{5} +(-4.91006 - 8.50447i) q^{6} +9.38186 q^{7} -6.24860i q^{8} +(4.63057 + 8.02039i) q^{9} +O(q^{10})\)	\(q+(1.99014 + 1.14901i) q^{2} +(-3.70079 - 2.13665i) q^{3} +(0.640435 + 1.10927i) q^{4} +(-2.91992 + 5.05745i) q^{5} +(-4.91006 - 8.50447i) q^{6} +9.38186 q^{7} -6.24860i q^{8} +(4.63057 + 8.02039i) q^{9} +(-11.6221 + 6.71002i) q^{10} -4.66273 q^{11} -5.47355i q^{12} +(-4.96056 + 2.86398i) q^{13} +(18.6712 + 10.7798i) q^{14} +(21.6120 - 12.4777i) q^{15} +(9.74143 - 16.8726i) q^{16} +(-9.49014 + 16.4374i) q^{17} +21.2823i q^{18} +(-3.40020 - 18.6933i) q^{19} -7.48008 q^{20} +(-34.7203 - 20.0458i) q^{21} +(-9.27949 - 5.35751i) q^{22} +(6.41006 + 11.1025i) q^{23} +(-13.3511 + 23.1248i) q^{24} +(-4.55188 - 7.88409i) q^{25} -13.1629 q^{26} -1.11597i q^{27} +(6.00848 + 10.4070i) q^{28} +(27.7677 - 16.0317i) q^{29} +57.3480 q^{30} -26.9378i q^{31} +(17.1278 - 9.88874i) q^{32} +(17.2558 + 9.96264i) q^{33} +(-37.7734 + 21.8085i) q^{34} +(-27.3943 + 47.4483i) q^{35} +(-5.93117 + 10.2731i) q^{36} -0.140762i q^{37} +(14.7118 - 41.1091i) q^{38} +24.4773 q^{39} +(31.6020 + 18.2454i) q^{40} +(10.0967 + 5.82931i) q^{41} +(-46.0655 - 79.7878i) q^{42} +(-16.3988 + 28.4036i) q^{43} +(-2.98618 - 5.17221i) q^{44} -54.0836 q^{45} +29.4608i q^{46} +(-5.37062 - 9.30218i) q^{47} +(-72.1020 + 41.6281i) q^{48} +39.0193 q^{49} -20.9206i q^{50} +(70.2421 - 40.5543i) q^{51} +(-6.35383 - 3.66839i) q^{52} +(-30.7243 + 17.7387i) q^{53} +(1.28226 - 2.22093i) q^{54} +(13.6148 - 23.5815i) q^{55} -58.6235i q^{56} +(-27.3576 + 76.4450i) q^{57} +73.6821 q^{58} +(-76.1002 - 43.9365i) q^{59} +(27.6822 + 15.9823i) q^{60} +(45.7649 + 79.2672i) q^{61} +(30.9517 - 53.6099i) q^{62} +(43.4434 + 75.2462i) q^{63} -32.4825 q^{64} -33.4504i q^{65} +(22.8943 + 39.6541i) q^{66} +(17.3404 - 10.0115i) q^{67} -24.3113 q^{68} -54.7843i q^{69} +(-109.037 + 62.9525i) q^{70} +(-15.8426 - 9.14674i) q^{71} +(50.1162 - 28.9346i) q^{72} +(28.7511 - 49.7984i) q^{73} +(0.161737 - 0.280136i) q^{74} +38.9032i q^{75} +(18.5582 - 15.7436i) q^{76} -43.7451 q^{77} +(48.7133 + 28.1246i) q^{78} +(-81.7713 - 47.2107i) q^{79} +(56.8884 + 98.5336i) q^{80} +(39.2907 - 68.0535i) q^{81} +(13.3959 + 23.2023i) q^{82} +81.9397 q^{83} -51.3521i q^{84} +(-55.4209 - 95.9918i) q^{85} +(-65.2718 + 37.6847i) q^{86} -137.017 q^{87} +29.1355i q^{88} +(17.3556 - 10.0202i) q^{89} +(-107.634 - 62.1425i) q^{90} +(-46.5392 + 26.8694i) q^{91} +(-8.21046 + 14.2209i) q^{92} +(-57.5567 + 99.6911i) q^{93} -24.6835i q^{94} +(104.469 + 37.3866i) q^{95} -84.5153 q^{96} +(117.468 + 67.8200i) q^{97} +(77.6539 + 44.8335i) q^{98} +(-21.5911 - 37.3969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9	\( 6 q - 3 q^{2} - 9 q^{3} + 5 q^{4} - 2 q^{5} + q^{6} + 14 q^{9} - 60 q^{10} + 26 q^{11} + 30 q^{13} + 54 q^{14} - 18 q^{15} + q^{16} - 42 q^{17} + 25 q^{19} + 108 q^{20} - 102 q^{21} - 39 q^{22} + 8 q^{23} - 83 q^{24} - 17 q^{25} - 148 q^{26} + 32 q^{28} - 12 q^{29} + 304 q^{30} + 51 q^{32} + 123 q^{33} - 6 q^{34} - 38 q^{35} - 54 q^{36} - 14 q^{38} - 44 q^{39} - 96 q^{40} + 63 q^{41} - 92 q^{42} - 34 q^{43} - 69 q^{44} - 28 q^{45} + 58 q^{47} - 147 q^{48} + 18 q^{49} + 132 q^{51} + 162 q^{52} - 12 q^{53} + 29 q^{54} - 28 q^{55} - 16 q^{57} + 172 q^{58} - 147 q^{59} - 222 q^{60} + 58 q^{61} - 116 q^{62} + 86 q^{63} + 166 q^{64} + 11 q^{66} + 201 q^{67} - 84 q^{68} - 198 q^{70} - 102 q^{71} + 210 q^{72} + 7 q^{73} + 174 q^{74} - 173 q^{76} - 376 q^{77} + 450 q^{78} + 134 q^{80} + 253 q^{81} - 145 q^{82} + 146 q^{83} - 90 q^{85} - 270 q^{86} - 568 q^{87} - 72 q^{89} - 438 q^{90} - 216 q^{91} + 72 q^{92} - 160 q^{93} + 558 q^{95} + 126 q^{96} + 21 q^{97} + 411 q^{98} - 56 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 9 * q^3 + 5 * q^4 - 2 * q^5 + q^6 + 14 * q^9 - 60 * q^10 + 26 * q^11 + 30 * q^13 + 54 * q^14 - 18 * q^15 + q^16 - 42 * q^17 + 25 * q^19 + 108 * q^20 - 102 * q^21 - 39 * q^22 + 8 * q^23 - 83 * q^24 - 17 * q^25 - 148 * q^26 + 32 * q^28 - 12 * q^29 + 304 * q^30 + 51 * q^32 + 123 * q^33 - 6 * q^34 - 38 * q^35 - 54 * q^36 - 14 * q^38 - 44 * q^39 - 96 * q^40 + 63 * q^41 - 92 * q^42 - 34 * q^43 - 69 * q^44 - 28 * q^45 + 58 * q^47 - 147 * q^48 + 18 * q^49 + 132 * q^51 + 162 * q^52 - 12 * q^53 + 29 * q^54 - 28 * q^55 - 16 * q^57 + 172 * q^58 - 147 * q^59 - 222 * q^60 + 58 * q^61 - 116 * q^62 + 86 * q^63 + 166 * q^64 + 11 * q^66 + 201 * q^67 - 84 * q^68 - 198 * q^70 - 102 * q^71 + 210 * q^72 + 7 * q^73 + 174 * q^74 - 173 * q^76 - 376 * q^77 + 450 * q^78 + 134 * q^80 + 253 * q^81 - 145 * q^82 + 146 * q^83 - 90 * q^85 - 270 * q^86 - 568 * q^87 - 72 * q^89 - 438 * q^90 - 216 * q^91 + 72 * q^92 - 160 * q^93 + 558 * q^95 + 126 * q^96 + 21 * q^97 + 411 * q^98 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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