LMFDB - Embedded newform 14.3.d.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,3,Mod(3,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, 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("14.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	14.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:	$0.381472370104$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	14.5
Dual form			14.3.d.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(0.621320 - 0.358719i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-5.74264 - 3.31552i) q^{5} +1.01461i q^{6} +(6.24264 + 3.16693i) q^{7} +2.82843 q^{8} +(-4.24264 + 7.34847i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(0.621320 - 0.358719i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-5.74264 - 3.31552i) q^{5} +1.01461i q^{6} +(6.24264 + 3.16693i) q^{7} +2.82843 q^{8} +(-4.24264 + 7.34847i) q^{9} +(8.12132 - 4.68885i) q^{10} +(2.37868 + 4.11999i) q^{11} +(-1.24264 - 0.717439i) q^{12} -15.2913i q^{13} +(-8.29289 + 5.40629i) q^{14} -4.75736 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-3.25736 + 1.88064i) q^{17} +(-6.00000 - 10.3923i) q^{18} +(3.62132 + 2.09077i) q^{19} +13.2621i q^{20} +(5.01472 - 0.271680i) q^{21} -6.72792 q^{22} +(13.8640 - 24.0131i) q^{23} +(1.75736 - 1.01461i) q^{24} +(9.48528 + 16.4290i) q^{25} +(18.7279 + 10.8126i) q^{26} +12.5446i q^{27} +(-0.757359 - 13.9795i) q^{28} +3.51472 q^{29} +(3.36396 - 5.82655i) q^{30} +(-42.3198 + 24.4334i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(2.95584 + 1.70656i) q^{33} -5.31925i q^{34} +(-25.3492 - 38.8841i) q^{35} +16.9706 q^{36} +(1.47056 - 2.54709i) q^{37} +(-5.12132 + 2.95680i) q^{38} +(-5.48528 - 9.50079i) q^{39} +(-16.2426 - 9.37769i) q^{40} +27.9590i q^{41} +(-3.21320 + 6.33386i) q^{42} -10.4853 q^{43} +(4.75736 - 8.23999i) q^{44} +(48.7279 - 28.1331i) q^{45} +(19.6066 + 33.9596i) q^{46} +(45.6213 + 26.3395i) q^{47} +2.86976i q^{48} +(28.9411 + 39.5400i) q^{49} -26.8284 q^{50} +(-1.34924 + 2.33696i) q^{51} +(-26.4853 + 15.2913i) q^{52} +(-27.9853 - 48.4719i) q^{53} +(-15.3640 - 8.87039i) q^{54} -31.5462i q^{55} +(17.6569 + 8.95743i) q^{56} +3.00000 q^{57} +(-2.48528 + 4.30463i) q^{58} +(33.5330 - 19.3603i) q^{59} +(4.75736 + 8.23999i) q^{60} +(-78.3823 - 45.2540i) q^{61} -69.1080i q^{62} +(-49.7574 + 32.4377i) q^{63} +8.00000 q^{64} +(-50.6985 + 87.8124i) q^{65} +(-4.18019 + 2.41344i) q^{66} +(17.3198 + 29.9988i) q^{67} +(6.51472 + 3.76127i) q^{68} -19.8931i q^{69} +(65.5477 - 3.55114i) q^{70} +36.4264 q^{71} +(-12.0000 + 20.7846i) q^{72} +(45.5589 - 26.3034i) q^{73} +(2.07969 + 3.60213i) q^{74} +(11.7868 + 6.80511i) q^{75} -8.36308i q^{76} +(1.80152 + 33.2528i) q^{77} +15.5147 q^{78} +(16.8934 - 29.2602i) q^{79} +(22.9706 - 13.2621i) q^{80} +(-33.6838 - 58.3420i) q^{81} +(-34.2426 - 19.7700i) q^{82} +127.577i q^{83} +(-5.48528 - 8.41407i) q^{84} +24.9411 q^{85} +(7.41421 - 12.8418i) q^{86} +(2.18377 - 1.26080i) q^{87} +(6.72792 + 11.6531i) q^{88} +(-43.5883 - 25.1657i) q^{89} +79.5724i q^{90} +(48.4264 - 95.4580i) q^{91} -55.4558 q^{92} +(-17.5294 + 30.3619i) q^{93} +(-64.5183 + 37.2497i) q^{94} +(-13.8640 - 24.0131i) q^{95} +(-3.51472 - 2.02922i) q^{96} -101.792i q^{97} +(-68.8909 + 7.48650i) q^{98} -40.3675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7}+O(q^{10}) $ 4 * q - 6 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^7	$ 4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7} + 24 q^{10} + 18 q^{11} + 12 q^{12} - 36 q^{14} - 36 q^{15} - 8 q^{16} - 30 q^{17} - 24 q^{18} + 6 q^{19} + 54 q^{21} + 24 q^{22} + 30 q^{23} + 24 q^{24} + 4 q^{25} + 24 q^{26} - 20 q^{28} + 48 q^{29} - 12 q^{30} - 42 q^{31} - 90 q^{33} - 42 q^{35} - 62 q^{37} - 12 q^{38} + 12 q^{39} - 48 q^{40} + 72 q^{42} - 8 q^{43} + 36 q^{44} + 144 q^{45} + 36 q^{46} + 174 q^{47} - 20 q^{49} - 96 q^{50} + 54 q^{51} - 72 q^{52} - 78 q^{53} - 36 q^{54} + 48 q^{56} + 12 q^{57} + 24 q^{58} - 78 q^{59} + 36 q^{60} - 42 q^{61} - 216 q^{63} + 32 q^{64} - 84 q^{65} - 144 q^{66} - 58 q^{67} + 60 q^{68} + 84 q^{70} - 24 q^{71} - 48 q^{72} + 318 q^{73} + 96 q^{74} + 132 q^{75} + 126 q^{77} + 96 q^{78} + 110 q^{79} + 24 q^{80} + 18 q^{81} - 120 q^{82} + 12 q^{84} - 36 q^{85} + 24 q^{86} - 144 q^{87} - 24 q^{88} - 378 q^{89} + 24 q^{91} - 120 q^{92} - 138 q^{93} - 12 q^{94} - 30 q^{95} - 48 q^{96} - 120 q^{98} + 144 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^7 + 24 * q^10 + 18 * q^11 + 12 * q^12 - 36 * q^14 - 36 * q^15 - 8 * q^16 - 30 * q^17 - 24 * q^18 + 6 * q^19 + 54 * q^21 + 24 * q^22 + 30 * q^23 + 24 * q^24 + 4 * q^25 + 24 * q^26 - 20 * q^28 + 48 * q^29 - 12 * q^30 - 42 * q^31 - 90 * q^33 - 42 * q^35 - 62 * q^37 - 12 * q^38 + 12 * q^39 - 48 * q^40 + 72 * q^42 - 8 * q^43 + 36 * q^44 + 144 * q^45 + 36 * q^46 + 174 * q^47 - 20 * q^49 - 96 * q^50 + 54 * q^51 - 72 * q^52 - 78 * q^53 - 36 * q^54 + 48 * q^56 + 12 * q^57 + 24 * q^58 - 78 * q^59 + 36 * q^60 - 42 * q^61 - 216 * q^63 + 32 * q^64 - 84 * q^65 - 144 * q^66 - 58 * q^67 + 60 * q^68 + 84 * q^70 - 24 * q^71 - 48 * q^72 + 318 * q^73 + 96 * q^74 + 132 * q^75 + 126 * q^77 + 96 * q^78 + 110 * q^79 + 24 * q^80 + 18 * q^81 - 120 * q^82 + 12 * q^84 - 36 * q^85 + 24 * q^86 - 144 * q^87 - 24 * q^88 - 378 * q^89 + 24 * q^91 - 120 * q^92 - 138 * q^93 - 12 * q^94 - 30 * q^95 - 48 * q^96 - 120 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	0.621320	−	0.358719i	0.207107	−	0.119573i	−0.392859	−	0.919599i	$-0.628514\pi$
$3$	0.621320	−	0.358719i	0.207107	−	0.119573i	0.599966	+	0.800025i	$0.295181\pi$
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−5.74264	−	3.31552i	−1.14853	−	0.663103i	−0.200000	−	0.979796i	$-0.564094\pi$
$5$	−5.74264	−	3.31552i	−1.14853	−	0.663103i	−0.948528	+	0.316693i	$0.897428\pi$
$6$			1.01461i			0.169102i
$7$	6.24264	+	3.16693i	0.891806	+	0.452418i
$7$	6.24264	+	3.16693i	0.891806	+	0.452418i
$8$	2.82843			0.353553
$9$	−4.24264	+	7.34847i	−0.471405	+	0.816497i
$10$	8.12132	−	4.68885i	0.812132	−	0.468885i
$11$	2.37868	+	4.11999i	0.216244	+	0.374545i	0.953657	−	0.300897i	$-0.0972861\pi$
$11$	2.37868	+	4.11999i	0.216244	+	0.374545i	−0.737413	+	0.675442i	$0.763953\pi$
$12$	−1.24264	−	0.717439i	−0.103553	−	0.0597866i
$13$		−	15.2913i		−	1.17625i	−0.808769	−	0.588126i	$-0.799866\pi$
$13$		−	15.2913i		−	1.17625i	0.808769	−	0.588126i	$-0.200134\pi$
$14$	−8.29289	+	5.40629i	−0.592350	+	0.386163i
$15$	−4.75736			−0.317157
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−3.25736	+	1.88064i	−0.191609	+	0.110626i	−0.592736	−	0.805397i	$-0.701952\pi$
$17$	−3.25736	+	1.88064i	−0.191609	+	0.110626i	0.401126	+	0.916023i	$0.368619\pi$
$18$	−6.00000	−	10.3923i	−0.333333	−	0.577350i
$19$	3.62132	+	2.09077i	0.190596	+	0.110041i	0.592261	−	0.805746i	$-0.298235\pi$
$19$	3.62132	+	2.09077i	0.190596	+	0.110041i	−0.401666	+	0.915786i	$0.631569\pi$
$20$			13.2621i			0.663103i
$21$	5.01472	−	0.271680i	0.238796	−	0.0129371i
$22$	−6.72792			−0.305815
$23$	13.8640	−	24.0131i	0.602781	−	1.04405i	−0.389617	−	0.920977i	$-0.627393\pi$
$23$	13.8640	−	24.0131i	0.602781	−	1.04405i	0.992398	−	0.123070i	$-0.0392740\pi$
$24$	1.75736	−	1.01461i	0.0732233	−	0.0422755i
$25$	9.48528	+	16.4290i	0.379411	+	0.657160i
$26$	18.7279	+	10.8126i	0.720305	+	0.415868i
$27$			12.5446i			0.464616i
$28$	−0.757359	−	13.9795i	−0.0270485	−	0.499268i
$29$	3.51472			0.121197			0.0605986	−	0.998162i	$-0.480699\pi$
$29$	3.51472			0.121197			0.0605986	+	0.998162i	$0.480699\pi$
$30$	3.36396	−	5.82655i	0.112132	−	0.194218i
$31$	−42.3198	+	24.4334i	−1.36516	+	0.788173i	−0.990305	−	0.138913i	$-0.955639\pi$
$31$	−42.3198	+	24.4334i	−1.36516	+	0.788173i	−0.374850	+	0.927085i	$0.622306\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	2.95584	+	1.70656i	0.0895710	+	0.0517139i
$34$		−	5.31925i		−	0.156448i
$35$	−25.3492	−	38.8841i	−0.724264	−	1.11097i
$36$	16.9706			0.471405
$37$	1.47056	−	2.54709i	0.0397449	−	0.0688403i	−0.845469	−	0.534025i	$-0.820679\pi$
$37$	1.47056	−	2.54709i	0.0397449	−	0.0688403i	0.885214	+	0.465185i	$0.154012\pi$
$38$	−5.12132	+	2.95680i	−0.134772	+	0.0778104i
$39$	−5.48528	−	9.50079i	−0.140648	−	0.243610i
$40$	−16.2426	−	9.37769i	−0.406066	−	0.234442i
$41$			27.9590i			0.681927i	0.940077	+	0.340963i	$0.110753\pi$
$41$			27.9590i			0.681927i	−0.940077	+	0.340963i	$0.889247\pi$
$42$	−3.21320	+	6.33386i	−0.0765048	+	0.150806i
$43$	−10.4853			−0.243844			−0.121922	−	0.992540i	$-0.538906\pi$
$43$	−10.4853			−0.243844			−0.121922	+	0.992540i	$0.538906\pi$
$44$	4.75736	−	8.23999i	0.108122	−	0.187272i
$45$	48.7279	−	28.1331i	1.08284	−	0.625180i
$46$	19.6066	+	33.9596i	0.426230	+	0.738253i
$47$	45.6213	+	26.3395i	0.970666	+	0.560415i	0.899439	−	0.437046i	$-0.143975\pi$
$47$	45.6213	+	26.3395i	0.970666	+	0.560415i	0.0712271	+	0.997460i	$0.477309\pi$
$48$			2.86976i			0.0597866i
$49$	28.9411	+	39.5400i	0.590635	+	0.806939i
$50$	−26.8284			−0.536569
$51$	−1.34924	+	2.33696i	−0.0264557	+	0.0458227i
$52$	−26.4853	+	15.2913i	−0.509332	+	0.294063i
$53$	−27.9853	−	48.4719i	−0.528024	−	0.914565i	−0.999466	−	0.0326677i	$-0.989600\pi$
$53$	−27.9853	−	48.4719i	−0.528024	−	0.914565i	0.471442	−	0.881897i	$-0.343734\pi$
$54$	−15.3640	−	8.87039i	−0.284518	−	0.164266i
$55$		−	31.5462i		−	0.573567i
$56$	17.6569	+	8.95743i	0.315301	+	0.159954i
$57$	3.00000			0.0526316
$58$	−2.48528	+	4.30463i	−0.0428497	+	0.0742178i
$59$	33.5330	−	19.3603i	0.568356	−	0.328141i	−0.188136	−	0.982143i	$-0.560245\pi$
$59$	33.5330	−	19.3603i	0.568356	−	0.328141i	0.756492	+	0.654002i	$0.226911\pi$
$60$	4.75736	+	8.23999i	0.0792893	+	0.137333i
$61$	−78.3823	−	45.2540i	−1.28495	−	0.741869i	−0.307205	−	0.951643i	$-0.599394\pi$
$61$	−78.3823	−	45.2540i	−1.28495	−	0.741869i	−0.977750	+	0.209774i	$0.932727\pi$
$62$		−	69.1080i		−	1.11464i
$63$	−49.7574	+	32.4377i	−0.789799	+	0.514884i
$64$	8.00000			0.125000
$65$	−50.6985	+	87.8124i	−0.779977	+	1.35096i
$66$	−4.18019	+	2.41344i	−0.0633363	+	0.0365672i
$67$	17.3198	+	29.9988i	0.258505	+	0.447743i	0.965842	−	0.259134i	$-0.0834370\pi$
$67$	17.3198	+	29.9988i	0.258505	+	0.447743i	−0.707337	+	0.706877i	$0.750104\pi$
$68$	6.51472	+	3.76127i	0.0958047	+	0.0553129i
$69$		−	19.8931i		−	0.288306i
$70$	65.5477	−	3.55114i	0.936396	−	0.0507306i
$71$	36.4264			0.513048			0.256524	−	0.966538i	$-0.417423\pi$
$71$	36.4264			0.513048			0.256524	+	0.966538i	$0.417423\pi$
$72$	−12.0000	+	20.7846i	−0.166667	+	0.288675i
$73$	45.5589	−	26.3034i	0.624094	−	0.360321i	−0.154367	−	0.988014i	$-0.549334\pi$
$73$	45.5589	−	26.3034i	0.624094	−	0.360321i	0.778461	+	0.627693i	$0.216001\pi$
$74$	2.07969	+	3.60213i	0.0281039	+	0.0486774i
$75$	11.7868	+	6.80511i	0.157157	+	0.0907348i
$76$		−	8.36308i		−	0.110041i
$77$	1.80152	+	33.2528i	0.0233963	+	0.431854i
$78$	15.5147			0.198907
$79$	16.8934	−	29.2602i	0.213840	−	0.370383i	−0.739073	−	0.673626i	$-0.764736\pi$
$79$	16.8934	−	29.2602i	0.213840	−	0.370383i	0.952913	+	0.303243i	$0.0980694\pi$
$80$	22.9706	−	13.2621i	0.287132	−	0.165776i
$81$	−33.6838	−	58.3420i	−0.415849	−	0.720272i
$82$	−34.2426	−	19.7700i	−0.417593	−	0.241098i
$83$			127.577i			1.53708i	0.639803	+	0.768539i	$0.279016\pi$
$83$			127.577i			1.53708i	−0.639803	+	0.768539i	$0.720984\pi$
$84$	−5.48528	−	8.41407i	−0.0653010	−	0.100167i
$85$	24.9411			0.293425
$86$	7.41421	−	12.8418i	0.0862118	−	0.149323i
$87$	2.18377	−	1.26080i	0.0251008	−	0.0144919i
$88$	6.72792	+	11.6531i	0.0764537	+	0.132422i
$89$	−43.5883	−	25.1657i	−0.489756	−	0.282761i	0.234717	−	0.972064i	$-0.424584\pi$
$89$	−43.5883	−	25.1657i	−0.489756	−	0.282761i	−0.724473	+	0.689303i	$0.757917\pi$
$90$			79.5724i			0.884137i
$91$	48.4264	−	95.4580i	0.532158	−	1.04899i
$92$	−55.4558			−0.602781
$93$	−17.5294	+	30.3619i	−0.188489	+	0.326472i
$94$	−64.5183	+	37.2497i	−0.686365	+	0.396273i
$95$	−13.8640	−	24.0131i	−0.145936	−	0.252769i
$96$	−3.51472	−	2.02922i	−0.0366117	−	0.0211377i
$97$		−	101.792i		−	1.04940i	−0.851287	−	0.524700i	$-0.824177\pi$
$97$		−	101.792i		−	1.04940i	0.851287	−	0.524700i	$-0.175823\pi$
$98$	−68.8909	+	7.48650i	−0.702968	+	0.0763928i
$99$	−40.3675			−0.407753
$100$	18.9706	−	32.8580i	0.189706	−	0.328580i
$101$	−51.6838	+	29.8396i	−0.511720	+	0.295442i	−0.733541	−	0.679646i	$-0.762134\pi$
$101$	−51.6838	+	29.8396i	−0.511720	+	0.295442i	0.221820	+	0.975088i	$0.428800\pi$
$102$	−1.90812	−	3.30496i	−0.0187070	−	0.0324015i
$103$	104.077	+	60.0890i	1.01046	+	0.583388i	0.911326	−	0.411686i	$-0.135060\pi$
$103$	104.077	+	60.0890i	1.01046	+	0.583388i	0.0991322	+	0.995074i	$0.468393\pi$
$104$		−	43.2503i		−	0.415868i
$105$	−29.6985	−	15.0662i	−0.282843	−	0.143488i
$106$	79.1543			0.746739
$107$	56.8051	−	98.3893i	0.530889	−	0.919526i	−0.468462	−	0.883484i	$-0.655192\pi$
$107$	56.8051	−	98.3893i	0.530889	−	0.919526i	0.999350	−	0.0360423i	$-0.0114751\pi$
$108$	21.7279	−	12.5446i	0.201184	−	0.116154i
$109$	72.6543	+	125.841i	0.666553	+	1.15450i	0.978862	+	0.204524i	$0.0655645\pi$
$109$	72.6543	+	125.841i	0.666553	+	1.15450i	−0.312308	+	0.949981i	$0.601102\pi$
$110$	38.6360	+	22.3065i	0.351237	+	0.202787i
$111$		−	2.11008i		−	0.0190097i
$112$	−23.4558	+	15.2913i	−0.209427	+	0.136529i
$113$	34.5442			0.305700			0.152850	−	0.988249i	$-0.451155\pi$
$113$	34.5442			0.305700			0.152850	+	0.988249i	$0.451155\pi$
$114$	−2.12132	+	3.67423i	−0.0186081	+	0.0322301i
$115$	−159.231	+	91.9323i	−1.38462	+	0.799412i
$116$	−3.51472	−	6.08767i	−0.0302993	−	0.0524799i
$117$	112.368	+	64.8754i	0.960406	+	0.554491i
$118$			54.7592i			0.464061i
$119$	−26.2904	+	1.42432i	−0.220927	+	0.0119691i
$120$	−13.4558			−0.112132
$121$	49.1838	−	85.1888i	0.406477	−	0.704040i
$122$	110.849	−	63.9988i	0.908600	−	0.524581i
$123$	10.0294	+	17.3715i	0.0815401	+	0.141232i
$124$	84.6396	+	48.8667i	0.682578	+	0.394086i
$125$			39.9814i			0.319851i
$126$	−4.54416	−	83.8770i	−0.0360647	−	0.665690i
$127$	−247.338			−1.94754			−0.973772	−	0.227526i	$-0.926936\pi$
$127$	−247.338			−1.94754			−0.973772	+	0.227526i	$0.926936\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	−6.51472	+	3.76127i	−0.0505017	+	0.0291572i
$130$	−71.6985	−	124.185i	−0.551527	−	0.955272i
$131$	−127.864	−	73.8223i	−0.976061	−	0.563529i	−0.0749822	−	0.997185i	$-0.523890\pi$
$131$	−127.864	−	73.8223i	−0.976061	−	0.563529i	−0.901079	+	0.433656i	$0.857223\pi$
$132$		−	6.82623i		−	0.0517139i
$133$	15.9853	+	24.5204i	0.120190	+	0.184364i
$134$	−48.9878			−0.365581
$135$	41.5919	−	72.0393i	0.308088	−	0.533624i
$136$	−9.21320	+	5.31925i	−0.0677441	+	0.0391121i
$137$	16.2868	+	28.2096i	0.118882	+	0.205909i	0.919325	−	0.393500i	$-0.128736\pi$
$137$	16.2868	+	28.2096i	0.118882	+	0.205909i	−0.800443	+	0.599409i	$0.795402\pi$
$138$	24.3640	+	14.0665i	0.176550	+	0.101931i
$139$		−	68.5857i		−	0.493422i	−0.969089	−	0.246711i	$-0.920650\pi$
$139$		−	68.5857i		−	0.493422i	0.969089	−	0.246711i	$-0.0793499\pi$
$140$	−42.0000	+	82.7903i	−0.300000	+	0.591359i
$141$	37.7939			0.268042
$142$	−25.7574	+	44.6131i	−0.181390	+	0.314176i
$143$	63.0000	−	36.3731i	0.440559	−	0.254357i
$144$	−16.9706	−	29.3939i	−0.117851	−	0.204124i
$145$	−20.1838	−	11.6531i	−0.139198	−	0.0803662i
$146$			74.3973i			0.509571i
$147$	32.1655	+	14.1853i	0.218813	+	0.0964984i
$148$	−5.88225			−0.0397449
$149$	−46.1985	+	80.0181i	−0.310057	+	0.537034i	−0.978374	−	0.206842i	$-0.933681\pi$
$149$	−46.1985	+	80.0181i	−0.310057	+	0.537034i	0.668317	+	0.743876i	$0.267015\pi$
$150$	−16.6690	+	9.62388i	−0.111127	+	0.0641592i
$151$	45.8934	+	79.4897i	0.303930	+	0.526422i	0.977022	−	0.213136i	$-0.0683678\pi$
$151$	45.8934	+	79.4897i	0.303930	+	0.526422i	−0.673093	+	0.739558i	$0.735035\pi$
$152$	10.2426	+	5.91359i	0.0673858	+	0.0389052i
$153$		−	31.9155i		−	0.208598i
$154$	−42.0000	−	21.3068i	−0.272727	−	0.138356i
$155$	324.037			2.09056
$156$	−10.9706	+	19.0016i	−0.0703241	+	0.121805i
$157$	7.32338	−	4.22815i	0.0466457	−	0.0269309i	−0.476496	−	0.879177i	$-0.658093\pi$
$157$	7.32338	−	4.22815i	0.0466457	−	0.0269309i	0.523142	+	0.852246i	$0.324760\pi$
$158$	23.8909	+	41.3802i	0.151208	+	0.261900i
$159$	−34.7756	−	20.0777i	−0.218715	−	0.126275i
$160$			37.5108i			0.234442i
$161$	162.595	−	105.999i	1.00991	−	0.658378i
$162$	95.2721			0.588099
$163$	−110.989	+	192.238i	−0.680913	+	1.17938i	0.293789	+	0.955870i	$0.405084\pi$
$163$	−110.989	+	192.238i	−0.680913	+	1.17938i	−0.974703	+	0.223506i	$0.928250\pi$
$164$	48.4264	−	27.9590i	0.295283	−	0.170482i
$165$	−11.3162	−	19.6003i	−0.0685832	−	0.118790i
$166$	−156.250	−	90.2109i	−0.941264	−	0.543439i
$167$		−	168.841i		−	1.01102i	−0.862820	−	0.505511i	$-0.831304\pi$
$167$		−	168.841i		−	1.01102i	0.862820	−	0.505511i	$-0.168696\pi$
$168$	14.1838	−	0.768426i	0.0844272	−	0.00457396i
$169$	−64.8234			−0.383570
$170$	−17.6360	+	30.5465i	−0.103741	+	0.179685i
$171$	−30.7279	+	17.7408i	−0.179695	+	0.103747i
$172$	10.4853	+	18.1610i	0.0609609	+	0.105587i
$173$	−142.323	−	82.1704i	−0.822678	−	0.474974i	0.0286608	−	0.999589i	$-0.490876\pi$
$173$	−142.323	−	82.1704i	−0.822678	−	0.474974i	−0.851339	+	0.524616i	$0.824209\pi$
$174$			3.56608i			0.0204947i
$175$	7.18377	+	132.599i	0.0410501	+	0.757711i
$176$	−19.0294			−0.108122
$177$	13.8898	−	24.0579i	0.0784736	−	0.135920i
$178$	61.6432	−	35.5897i	0.346310	−	0.199942i
$179$	−92.5919	−	160.374i	−0.517273	−	0.895943i	−0.999799	−	0.0200614i	$-0.993614\pi$
$179$	−92.5919	−	160.374i	−0.517273	−	0.895943i	0.482526	−	0.875882i	$-0.339720\pi$
$180$	−97.4558	−	56.2662i	−0.541421	−	0.312590i
$181$			155.086i			0.856830i	0.903582	+	0.428415i	$0.140928\pi$
$181$			155.086i			0.856830i	−0.903582	+	0.428415i	$0.859072\pi$
$182$	82.6690	+	126.809i	0.454226	+	0.696753i
$183$	−64.9340			−0.354831
$184$	39.2132	−	67.9193i	0.213115	−	0.369126i
$185$	−16.8898	+	9.75135i	−0.0912964	+	0.0527100i
$186$	−24.7904	−	42.9382i	−0.133282	−	0.230850i
$187$	−15.4964	−	8.94687i	−0.0828686	−	0.0478442i
$188$		−	105.358i		−	0.560415i
$189$	−39.7279	+	78.3116i	−0.210201	+	0.414347i
$190$	39.2132			0.206385
$191$	−124.048	+	214.857i	−0.649465	+	1.12491i	0.333786	+	0.942649i	$0.391674\pi$
$191$	−124.048	+	214.857i	−0.649465	+	1.12491i	−0.983251	+	0.182257i	$0.941660\pi$
$192$	4.97056	−	2.86976i	0.0258883	−	0.0149466i
$193$	−77.1690	−	133.661i	−0.399840	−	0.692543i	0.593866	−	0.804564i	$-0.297601\pi$
$193$	−77.1690	−	133.661i	−0.399840	−	0.692543i	−0.993706	+	0.112021i	$0.964268\pi$
$194$	124.669	+	71.9777i	0.642624	+	0.371019i
$195$			72.7461i			0.373057i
$196$	39.5442	−	89.6675i	0.201756	−	0.457487i
$197$	−181.103			−0.919303			−0.459651	−	0.888099i	$-0.652026\pi$
$197$	−181.103			−0.919303			−0.459651	+	0.888099i	$0.652026\pi$
$198$	28.5442	−	49.4399i	0.144162	−	0.249697i
$199$	301.989	−	174.353i	1.51753	−	0.876147i	0.517744	−	0.855535i	$-0.326772\pi$
$199$	301.989	−	174.353i	1.51753	−	0.876147i	0.999788	−	0.0206121i	$-0.00656150\pi$
$200$	26.8284	+	46.4682i	0.134142	+	0.232341i
$201$	21.5223	+	12.4259i	0.107076	+	0.0618204i
$202$		−	84.3992i		−	0.417818i
$203$	21.9411	+	11.1309i	0.108084	+	0.0548318i
$204$	5.39697			0.0264557
$205$	92.6985	−	160.558i	0.452188	−	0.783212i
$206$	−147.187	+	84.9786i	−0.714502	+	0.412518i
$207$	117.640	+	203.758i	0.568307	+	0.984337i
$208$	52.9706	+	30.5826i	0.254666	+	0.147032i
$209$			19.8931i			0.0951823i
$210$	39.4523	−	25.7196i	0.187868	−	0.122474i
$211$	364.073			1.72547			0.862733	−	0.505660i	$-0.168751\pi$
$211$	364.073			1.72547			0.862733	+	0.505660i	$0.168751\pi$
$212$	−55.9706	+	96.9439i	−0.264012	+	0.457282i
$213$	22.6325	−	13.0669i	0.106256	−	0.0613468i
$214$	80.3345	+	139.143i	0.375395	+	0.650203i
$215$	60.2132	+	34.7641i	0.280061	+	0.161694i
$216$			35.4815i			0.164266i
$217$	−341.566	+	18.5048i	−1.57404	+	0.0852757i
$218$	−205.497			−0.942649
$219$	18.8711	−	32.6857i	0.0861694	−	0.149250i
$220$	−54.6396	+	31.5462i	−0.248362	+	0.143392i
$221$	28.7574	+	49.8092i	0.130124	+	0.225381i
$222$	2.58431	+	1.49205i	0.0116410	+	0.00672095i
$223$		−	123.231i		−	0.552603i	−0.961071	−	0.276302i	$-0.910891\pi$
$223$		−	123.231i		−	0.552603i	0.961071	−	0.276302i	$-0.0891089\pi$
$224$	−2.14214	−	39.5400i	−0.00956311	−	0.176518i
$225$	−160.971			−0.715425
$226$	−24.4264	+	42.3078i	−0.108081	+	0.187203i
$227$	−66.1432	+	38.1878i	−0.291380	+	0.168228i	−0.638564	−	0.769569i	$-0.720471\pi$
$227$	−66.1432	+	38.1878i	−0.291380	+	0.168228i	0.347184	+	0.937797i	$0.387138\pi$
$228$	−3.00000	−	5.19615i	−0.0131579	−	0.0227901i
$229$	309.419	+	178.643i	1.35117	+	0.780101i	0.988414	−	0.151782i	$-0.0485012\pi$
$229$	309.419	+	178.643i	1.35117	+	0.780101i	0.362760	+	0.931883i	$0.381834\pi$
$230$		−	260.024i		−	1.13054i
$231$	13.0477	+	20.0144i	0.0564837	+	0.0866423i
$232$	9.94113			0.0428497
$233$	136.537	−	236.488i	0.585994	−	1.01497i	−0.408757	−	0.912643i	$-0.634038\pi$
$233$	136.537	−	236.488i	0.585994	−	1.01497i	0.994751	−	0.102328i	$-0.0326291\pi$
$234$	−158.912	+	91.7477i	−0.679110	+	0.392084i
$235$	−174.658	−	302.516i	−0.743225	−	1.28730i
$236$	−67.0660	−	38.7206i	−0.284178	−	0.164070i
$237$		−	24.2400i		−	0.102278i
$238$	16.8457	−	33.2061i	0.0707801	−	0.139522i
$239$	−265.103			−1.10922			−0.554608	−	0.832112i	$-0.687132\pi$
$239$	−265.103			−1.10922			−0.554608	+	0.832112i	$0.687132\pi$
$240$	9.51472	−	16.4800i	0.0396447	−	0.0686666i
$241$	−75.8970	+	43.8191i	−0.314925	+	0.181822i	−0.649128	−	0.760679i	$-0.724866\pi$
$241$	−75.8970	+	43.8191i	−0.314925	+	0.181822i	0.334203	+	0.942501i	$0.391533\pi$
$242$	69.5563	+	120.475i	0.287423	+	0.497831i
$243$	−139.632	−	80.6168i	−0.574619	−	0.331757i
$244$			181.016i			0.741869i
$245$	−35.1030	−	323.019i	−0.143278	−	1.31844i
$246$	−28.3675			−0.115315
$247$	31.9706	−	55.3746i	0.129435	−	0.224189i
$248$	−119.698	+	69.1080i	−0.482655	+	0.278661i
$249$	45.7645	+	79.2664i	0.183793	+	0.318339i
$250$	−48.9670	−	28.2711i	−0.195868	−	0.113084i
$251$			495.655i			1.97472i	0.158491	+	0.987360i	$0.449337\pi$
$251$			495.655i			1.97472i	−0.158491	+	0.987360i	$0.550663\pi$
$252$	105.941	+	53.7446i	0.420401	+	0.213272i
$253$	131.912			0.521390
$254$	174.894	−	302.926i	0.688561	−	1.19262i
$255$	15.4964	−	8.94687i	0.0607703	−	0.0350858i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	346.875	+	200.268i	1.34971	+	0.779254i	0.988208	−	0.153119i	$-0.0489317\pi$
$257$	346.875	+	200.268i	1.34971	+	0.779254i	0.361499	+	0.932372i	$0.382265\pi$
$258$		−	10.6385i		−	0.0412345i
$259$	17.2466	−	11.2434i	0.0665894	−	0.0434108i
$260$	202.794			0.779977
$261$	−14.9117	+	25.8278i	−0.0571329	+	0.0989571i
$262$	180.827	−	104.400i	0.690179	−	0.398475i
$263$	16.1726	+	28.0118i	0.0614928	+	0.106509i	0.895133	−	0.445799i	$-0.147081\pi$
$263$	16.1726	+	28.0118i	0.0614928	+	0.106509i	−0.833640	+	0.552308i	$0.813747\pi$
$264$	8.36039	+	4.82687i	0.0316681	+	0.0182836i
$265$			371.142i			1.40054i
$266$	−41.3345	+	2.23936i	−0.155393	+	0.00841863i
$267$	−36.1097			−0.135242
$268$	34.6396	−	59.9976i	0.129252	−	0.223872i
$269$	−265.838	+	153.482i	−0.988246	+	0.570564i	−0.904749	−	0.425944i	$-0.859942\pi$
$269$	−265.838	+	153.482i	−0.988246	+	0.570564i	−0.0834963	+	0.996508i	$0.526609\pi$
$270$	58.8198	+	101.879i	0.217851	+	0.377329i
$271$	−65.8051	−	37.9926i	−0.242823	−	0.140194i	0.373650	−	0.927570i	$-0.378106\pi$
$271$	−65.8051	−	37.9926i	−0.242823	−	0.140194i	−0.616474	+	0.787376i	$0.711439\pi$
$272$		−	15.0451i		−	0.0553129i
$273$	−4.15433	−	76.6815i	−0.0152173	−	0.280885i
$274$	−46.0660			−0.168124
$275$	−45.1249	+	78.1586i	−0.164091	+	0.284213i
$276$	−34.4558	+	19.8931i	−0.124840	+	0.0720764i
$277$	−139.206	−	241.111i	−0.502547	−	0.870438i	−0.999996	−	0.00294398i	$-0.999063\pi$
$277$	−139.206	−	241.111i	−0.502547	−	0.870438i	0.497448	−	0.867494i	$-0.334270\pi$
$278$	84.0000	+	48.4974i	0.302158	+	0.174451i
$279$		−	414.648i		−	1.48619i
$280$	−71.6985	−	109.981i	−0.256066	−	0.392789i
$281$	394.690			1.40459			0.702296	−	0.711885i	$-0.252158\pi$
$281$	394.690			1.40459			0.702296	+	0.711885i	$0.252158\pi$
$282$	−26.7244	+	46.2879i	−0.0947672	+	0.164142i
$283$	126.783	−	73.1981i	0.447996	−	0.258650i	−0.258988	−	0.965881i	$-0.583389\pi$
$283$	126.783	−	73.1981i	0.447996	−	0.258650i	0.706983	+	0.707230i	$0.250056\pi$
$284$	−36.4264	−	63.0924i	−0.128262	−	0.222156i
$285$	−17.2279	−	9.94655i	−0.0604488	−	0.0349002i
$286$			102.879i			0.359715i
$287$	−88.5442	+	174.538i	−0.308516	+	0.608146i
$288$	48.0000			0.166667
$289$	−137.426	+	238.030i	−0.475524	+	0.823632i
$290$	28.5442	−	16.4800i	0.0984281	−	0.0568275i
$291$	−36.5147	−	63.2453i	−0.125480	−	0.217338i
$292$	−91.1177	−	52.6069i	−0.312047	−	0.180160i
$293$		−	299.678i		−	1.02279i	−0.859345	−	0.511396i	$-0.829128\pi$
$293$		−	299.678i		−	1.02279i	0.859345	−	0.511396i	$-0.170872\pi$
$294$	−40.1177	+	29.3640i	−0.136455	+	0.0998776i
$295$	−256.757			−0.870364
$296$	4.15938	−	7.20426i	0.0140520	−	0.0243387i
$297$	−51.6838	+	29.8396i	−0.174019	+	0.100470i
$298$	−65.3345	−	113.163i	−0.219243	−	0.379741i
$299$	−367.191	−	211.998i	−1.22806	−	0.709023i
$300$		−	27.2204i		−	0.0907348i
$301$	−65.4558	−	33.2061i	−0.217461	−	0.110319i
$302$	−129.806			−0.429822
$303$	−21.4081	+	37.0799i	−0.0706539	+	0.122376i
$304$	−14.4853	+	8.36308i	−0.0476490	+	0.0275101i
$305$	300.081	+	519.755i	0.983871	+	1.70412i
$306$	39.0883	+	22.5676i	0.127740	+	0.0737505i
$307$			20.9886i			0.0683666i	0.999416	+	0.0341833i	$0.0108830\pi$
$307$			20.9886i			0.0683666i	−0.999416	+	0.0341833i	$0.989117\pi$
$308$	55.7939	−	36.3731i	0.181149	−	0.118094i
$309$	86.2203			0.279030
$310$	−229.128	+	396.862i	−0.739124	+	1.28020i
$311$	157.651	−	91.0197i	0.506916	−	0.292668i	−0.224649	−	0.974440i	$-0.572124\pi$
$311$	157.651	−	91.0197i	0.506916	−	0.292668i	0.731565	+	0.681772i	$0.238790\pi$
$312$	−15.5147	−	26.8723i	−0.0497267	−	0.0861291i
$313$	−84.8087	−	48.9643i	−0.270954	−	0.156435i	0.358367	−	0.933581i	$-0.383334\pi$
$313$	−84.8087	−	48.9643i	−0.270954	−	0.156435i	−0.629321	+	0.777145i	$0.716667\pi$
$314$			11.9590i			0.0380861i
$315$	393.286	−	21.3068i	1.24853	−	0.0676408i
$316$	−67.5736			−0.213840
$317$	240.985	−	417.399i	0.760206	−	1.31672i	−0.182538	−	0.983199i	$-0.558431\pi$
$317$	240.985	−	417.399i	0.760206	−	1.31672i	0.942744	−	0.333517i	$-0.108235\pi$
$318$	49.1802	−	28.3942i	0.154655	−	0.0892899i
$319$	8.36039	+	14.4806i	0.0262081	+	0.0453938i
$320$	−45.9411	−	26.5241i	−0.143566	−	0.0828879i
$321$		−	81.5084i		−	0.253920i
$322$	14.8492	+	274.090i	0.0461157	+	0.851213i
$323$	−15.7279			−0.0486933
$324$	−67.3675	+	116.684i	−0.207924	+	0.360136i
$325$	251.220	−	145.042i	0.772986	−	0.446283i
$326$	−156.962	−	271.866i	−0.481478	−	0.833945i
$327$	90.2832	+	52.1250i	0.276095	+	0.159404i
$328$			79.0800i			0.241098i
$329$	201.382	+	308.907i	0.612104	+	0.938928i
$330$	32.0071			0.0969913
$331$	−112.504	+	194.862i	−0.339890	+	0.588707i	−0.984412	−	0.175879i	$-0.943723\pi$
$331$	−112.504	+	194.862i	−0.339890	+	0.588707i	0.644522	+	0.764586i	$0.277056\pi$
$332$	220.971	−	127.577i	0.665574	−	0.384269i
$333$	12.4781	+	21.6128i	0.0374719	+	0.0649032i
$334$	206.787	+	119.388i	0.619122	+	0.357450i
$335$		−	229.696i		−	0.685661i
$336$	−9.08831	+	17.9149i	−0.0270485	+	0.0533180i
$337$	−264.368			−0.784473			−0.392237	−	0.919864i	$-0.628299\pi$
$337$	−264.368			−0.784473			−0.392237	+	0.919864i	$0.628299\pi$
$338$	45.8370	−	79.3921i	0.135613	−	0.234888i
$339$	21.4630	−	12.3917i	0.0633126	−	0.0365536i
$340$	−24.9411	−	43.1993i	−0.0733563	−	0.127057i
$341$	−201.331	−	116.238i	−0.590412	−	0.340875i
$342$		−	50.1785i		−	0.146721i
$343$	55.4487	+	338.488i	0.161658	+	0.986847i
$344$	−29.6569			−0.0862118
$345$	−65.9558	+	114.239i	−0.191176	+	0.331127i
$346$	201.276	−	116.207i	0.581722	−	0.335857i
$347$	95.6285	+	165.633i	0.275586	+	0.477330i	0.970283	−	0.241973i	$-0.0777947\pi$
$347$	95.6285	+	165.633i	0.275586	+	0.477330i	−0.694697	+	0.719303i	$0.744461\pi$
$348$	−4.36753	−	2.52160i	−0.0125504	−	0.00724597i
$349$		−	135.448i		−	0.388104i	−0.980991	−	0.194052i	$-0.937837\pi$
$349$		−	135.448i		−	0.388104i	0.980991	−	0.194052i	$-0.0621630\pi$
$350$	−167.480	−	84.9637i	−0.478515	−	0.242753i
$351$	191.823			0.546505
$352$	13.4558	−	23.3062i	0.0382268	−	0.0662108i
$353$	−301.802	+	174.245i	−0.854962	+	0.493612i	−0.862322	−	0.506360i	$-0.830991\pi$
$353$	−301.802	+	174.245i	−0.854962	+	0.493612i	0.00736010	+	0.999973i	$0.497657\pi$
$354$	19.6432	+	34.0230i	0.0554892	+	0.0961101i
$355$	−209.184	−	120.772i	−0.589250	−	0.340204i
$356$			100.663i			0.282761i
$357$	−15.8238	+	10.3158i	−0.0443244	+	0.0288959i
$358$	261.889			0.731535
$359$	−152.415	+	263.991i	−0.424555	+	0.735351i	−0.996379	−	0.0850256i	$-0.972903\pi$
$359$	−152.415	+	263.991i	−0.424555	+	0.735351i	0.571824	+	0.820377i	$0.306236\pi$
$360$	137.823	−	79.5724i	0.382843	−	0.221034i
$361$	−171.757	−	297.492i	−0.475782	−	0.824079i
$362$	−189.941	−	109.663i	−0.524699	−	0.302935i
$363$		−	70.5727i		−	0.194415i
$364$	−213.765	+	11.5810i	−0.587265	+	0.0318159i
$365$	−348.838			−0.955720
$366$	45.9153	−	79.5276i	0.125452	−	0.217288i
$367$	−82.2761	+	47.5021i	−0.224186	+	0.129434i	−0.607887	−	0.794024i	$-0.707983\pi$
$367$	−82.2761	+	47.5021i	−0.224186	+	0.129434i	0.383701	+	0.923457i	$0.374649\pi$
$368$	55.4558	+	96.0523i	0.150695	+	0.261012i
$369$	−205.456	−	118.620i	−0.556791	−	0.321463i
$370$		−	27.5810i		−	0.0745432i
$371$	−21.1949	−	391.220i	−0.0571291	−	1.05450i
$372$	70.1177			0.188489
$373$	−126.779	+	219.588i	−0.339891	+	0.588708i	−0.984412	−	0.175879i	$-0.943723\pi$
$373$	−126.779	+	219.588i	−0.339891	+	0.588708i	0.644521	+	0.764586i	$0.277057\pi$
$374$	21.9153	−	12.6528i	0.0585970	−	0.0338310i
$375$	14.3421	+	24.8412i	0.0382456	+	0.0662433i
$376$	129.037	+	74.4993i	0.343182	+	0.198136i
$377$		−	53.7446i		−	0.142559i
$378$	−67.8198	−	104.031i	−0.179417	−	0.275215i
$379$	508.250			1.34103			0.670514	−	0.741897i	$-0.266074\pi$
$379$	508.250			1.34103			0.670514	+	0.741897i	$0.266074\pi$
$380$	−27.7279	+	48.0262i	−0.0729682	+	0.126385i
$381$	−153.676	+	88.7250i	−0.403350	+	0.232874i
$382$	−175.430	−	303.854i	−0.459241	−	0.795428i
$383$	413.753	+	238.881i	1.08030	+	0.623709i	0.930976	−	0.365080i	$-0.118958\pi$
$383$	413.753	+	238.881i	1.08030	+	0.623709i	0.149320	+	0.988789i	$0.452292\pi$
$384$			8.11689i			0.0211377i
$385$	99.9045	−	196.932i	0.259492	−	0.511511i
$386$	218.267			0.565459
$387$	44.4853	−	77.0508i	0.114949	−	0.199098i
$388$	−176.309	+	101.792i	−0.454404	+	0.262350i
$389$	−85.1102	−	147.415i	−0.218792	−	0.378959i	0.735647	−	0.677365i	$-0.236878\pi$
$389$	−85.1102	−	147.415i	−0.218792	−	0.378959i	−0.954439	+	0.298406i	$0.903545\pi$
$390$	−89.0955	−	51.4393i	−0.228450	−	0.131896i
$391$			104.292i			0.266732i
$392$	81.8579	+	111.836i	0.208821	+	0.285296i
$393$	−105.926			−0.269532
$394$	128.059	−	221.804i	0.325023	−	0.562956i
$395$	−194.025	+	112.021i	−0.491204	+	0.283597i
$396$	40.3675	+	69.9186i	0.101938	+	0.176562i
$397$	211.786	+	122.275i	0.533467	+	0.307997i	0.742427	−	0.669927i	$-0.233675\pi$
$397$	211.786	+	122.275i	0.533467	+	0.307997i	−0.208960	+	0.977924i	$0.567008\pi$
$398$			493.146i			1.23906i
$399$	18.7279	+	9.50079i	0.0469371	+	0.0238115i
$400$	−75.8823			−0.189706
$401$	208.786	−	361.629i	0.520664	−	0.901817i	−0.479047	−	0.877789i	$-0.659018\pi$
$401$	208.786	−	361.629i	0.520664	−	0.901817i	0.999711	−	0.0240277i	$-0.00764899\pi$
$402$	−30.4371	+	17.5729i	−0.0757142	+	0.0437136i
$403$	373.617	+	647.124i	0.927090	+	1.60577i
$404$	103.368	+	59.6793i	0.255860	+	0.147721i
$405$			446.716i			1.10300i
$406$	−29.1472	+	19.0016i	−0.0717911	+	0.0468019i
$407$	13.9920			0.0343784
$408$	−3.81623	+	6.60991i	−0.00935351	+	0.0162008i
$409$	266.919	−	154.106i	0.652614	−	0.376787i	−0.136843	−	0.990593i	$-0.543696\pi$
$409$	266.919	−	154.106i	0.652614	−	0.376787i	0.789457	+	0.613806i	$0.210362\pi$
$410$	131.095	+	227.064i	0.319745	+	0.553815i
$411$	20.2386	+	11.6848i	0.0492424	+	0.0284301i
$412$		−	240.356i		−	0.583388i
$413$	270.647	−	14.6627i	0.655320	−	0.0355029i
$414$	−332.735			−0.803708
$415$	422.985	−	732.631i	1.01924	−	1.76538i
$416$	−74.9117	+	43.2503i	−0.180076	+	0.103967i
$417$	−24.6030	−	42.6137i	−0.0590001	−	0.102191i
$418$	−24.3640	−	14.0665i	−0.0582870	−	0.0336520i
$419$			103.142i			0.246163i	0.992397	+	0.123081i	$0.0392776\pi$
$419$			103.142i			0.246163i	−0.992397	+	0.123081i	$0.960722\pi$
$420$	3.60303	+	66.5055i	0.00857864	+	0.158346i
$421$	−165.220			−0.392447			−0.196224	−	0.980559i	$-0.562868\pi$
$421$	−165.220			−0.392447			−0.196224	+	0.980559i	$0.562868\pi$
$422$	−257.439	+	445.897i	−0.610044	+	1.05663i
$423$	−387.110	+	223.498i	−0.915153	+	0.528364i
$424$	−79.1543	−	137.099i	−0.186685	−	0.323347i
$425$	−61.7939	−	35.6767i	−0.145398	−	0.0839453i
$426$			36.9587i			0.0867574i
$427$	−345.996	−	530.736i	−0.810295	−	1.24294i
$428$	−227.220			−0.530889
$429$	26.0955	−	45.1987i	0.0608286	−	0.105358i
$430$	−85.1543	+	49.1639i	−0.198033	+	0.114335i
$431$	−297.268	−	514.883i	−0.689717	−	1.19463i	−0.971929	−	0.235273i	$-0.924402\pi$
$431$	−297.268	−	514.883i	−0.689717	−	1.19463i	0.282212	−	0.959352i	$-0.408932\pi$
$432$	−43.4558	−	25.0892i	−0.100592	−	0.0580770i
$433$			40.6267i			0.0938261i	0.998899	+	0.0469131i	$0.0149384\pi$
$433$			40.6267i			0.0938261i	−0.998899	+	0.0469131i	$0.985062\pi$
$434$	218.860	−	431.416i	0.504286	−	0.994046i
$435$	−16.7208			−0.0384386
$436$	145.309	−	251.682i	0.333277	−	0.577252i
$437$	100.412	−	57.9727i	0.229775	−	0.132661i
$438$	26.6878	+	46.2246i	0.0609310	+	0.105536i
$439$	126.959	+	73.3001i	0.289201	+	0.166971i	0.637582	−	0.770383i	$-0.279935\pi$
$439$	126.959	+	73.3001i	0.289201	+	0.166971i	−0.348380	+	0.937353i	$0.613268\pi$
$440$		−	89.2261i		−	0.202787i
$441$	−413.345	+	44.9190i	−0.937291	+	0.101857i
$442$	−81.3381			−0.184023
$443$	−53.6802	+	92.9768i	−0.121174	+	0.209880i	−0.920231	−	0.391376i	$-0.871999\pi$
$443$	−53.6802	+	92.9768i	−0.121174	+	0.209880i	0.799057	+	0.601256i	$0.205333\pi$
$444$	−3.65476	+	2.11008i	−0.00823145	+	0.00475243i
$445$	166.875	+	289.035i	0.374999	+	0.649518i
$446$	150.926	+	87.1372i	0.338399	+	0.195375i
$447$			66.2892i			0.148298i
$448$	49.9411	+	25.3354i	0.111476	+	0.0565523i
$449$	135.161			0.301028			0.150514	−	0.988608i	$-0.451907\pi$
$449$	135.161			0.301028			0.150514	+	0.988608i	$0.451907\pi$
$450$	113.823	−	197.148i	0.252941	−	0.438106i
$451$	−115.191	+	66.5055i	−0.255412	+	0.147462i
$452$	−34.5442	−	59.8322i	−0.0764251	−	0.132372i
$453$	57.0290	+	32.9257i	0.125892	+	0.0726837i
$454$		−	108.011i		−	0.237910i
$455$	−594.588	+	387.622i	−1.30679	+	0.851918i
$456$	8.48528			0.0186081
$457$	−79.8675	+	138.335i	−0.174765	+	0.302702i	−0.940080	−	0.340954i	$-0.889250\pi$
$457$	−79.8675	+	138.335i	−0.174765	+	0.302702i	0.765315	+	0.643656i	$0.222583\pi$
$458$	−437.584	+	252.639i	−0.955424	+	0.551614i
$459$	−23.5919	−	40.8623i	−0.0513984	−	0.0890247i
$460$	318.463	+	183.865i	0.692311	+	0.399706i
$461$		−	310.250i		−	0.672993i	−0.941685	−	0.336497i	$-0.890758\pi$
$461$		−	310.250i		−	0.672993i	0.941685	−	0.336497i	$-0.109242\pi$
$462$	−33.7386	+	1.82784i	−0.0730274	+	0.00395636i
$463$	−326.014			−0.704135			−0.352067	−	0.935975i	$-0.614521\pi$
$463$	−326.014			−0.704135			−0.352067	+	0.935975i	$0.614521\pi$
$464$	−7.02944	+	12.1753i	−0.0151496	+	0.0262400i
$465$	201.331	−	116.238i	0.432969	−	0.249975i
$466$	193.092	+	334.445i	0.414360	+	0.717693i
$467$	515.769	+	297.779i	1.10443	+	0.637643i	0.937381	−	0.348306i	$-0.113243\pi$
$467$	515.769	+	297.779i	1.10443	+	0.637643i	0.167048	+	0.985949i	$0.446576\pi$
$468$		−	259.502i		−	0.554491i
$469$	13.1173	+	242.122i	0.0279687	+	0.516252i
$470$	494.007			1.05108
$471$	3.03344	−	5.25408i	0.00644043	−	0.0111551i
$472$	94.8457	−	54.7592i	0.200944	−	0.116015i
$473$	−24.9411	−	43.1993i	−0.0527297	−	0.0913304i
$474$	29.6878	+	17.1402i	0.0626324	+	0.0361608i
$475$			79.3262i			0.167002i
$476$	28.7574	+	44.1119i	0.0604146	+	0.0926721i
$477$	474.926			0.995652
$478$	187.456	−	324.683i	0.392167	−	0.679253i
$479$	438.798	−	253.340i	0.916071	−	0.528894i	0.0336914	−	0.999432i	$-0.489274\pi$
$479$	438.798	−	253.340i	0.916071	−	0.528894i	0.882379	+	0.470539i	$0.155940\pi$
$480$	13.4558	+	23.3062i	0.0280330	+	0.0485546i
$481$	−38.9483	−	22.4868i	−0.0809735	−	0.0467501i
$482$		−	123.939i		−	0.257135i
$483$	63.0000	−	124.185i	0.130435	−	0.257113i
$484$	−196.735			−0.406477
$485$	−337.492	+	584.554i	−0.695861	+	1.20527i
$486$	197.470	−	114.009i	0.406317	−	0.234587i
$487$	−105.651	−	182.992i	−0.216942	−	0.375755i	0.736930	−	0.675970i	$-0.236275\pi$
$487$	−105.651	−	182.992i	−0.216942	−	0.375755i	−0.953872	+	0.300215i	$0.902942\pi$
$488$	−221.698	−	127.998i	−0.454300	−	0.262290i
$489$			159.255i			0.325676i
$490$	420.437	+	185.416i	0.858035	+	0.378401i
$491$	−784.161			−1.59707			−0.798534	−	0.601949i	$-0.794391\pi$
$491$	−784.161			−1.59707			−0.798534	+	0.601949i	$0.794391\pi$
$492$	20.0589	−	34.7430i	0.0407701	−	0.0706158i
$493$	−11.4487	+	6.60991i	−0.0232225	+	0.0134075i
$494$	45.2132	+	78.3116i	0.0915247	+	0.158525i
$495$	231.816	+	133.839i	0.468316	+	0.270382i
$496$		−	195.467i		−	0.394086i
$497$	227.397	+	115.360i	0.457539	+	0.232112i
$498$	−129.442			−0.259923
$499$	85.7462	−	148.517i	0.171836	−	0.297629i	−0.767226	−	0.641377i	$-0.778363\pi$
$499$	85.7462	−	148.517i	0.171836	−	0.297629i	0.939062	+	0.343748i	$0.111697\pi$
$500$	69.2498	−	39.9814i	0.138500	−	0.0799628i
$501$	−60.5665	−	104.904i	−0.120891	−	0.209390i
$502$	−607.051	−	350.481i	−1.20926	−	0.698169i
$503$			20.0883i			0.0399370i	0.999801	+	0.0199685i	$0.00635659\pi$
$503$			20.0883i			0.0399370i	−0.999801	+	0.0199685i	$0.993643\pi$
$504$	−140.735	+	91.7477i	−0.279236	+	0.182039i
$505$	395.735			0.783634
$506$	−93.2756	+	161.558i	−0.184339	+	0.319285i
$507$	−40.2761	+	23.2534i	−0.0794400	+	0.0458647i
$508$	247.338	+	428.402i	0.486886	+	0.843311i
$509$	−412.890	−	238.382i	−0.811178	−	0.468334i	0.0361865	−	0.999345i	$-0.488479\pi$
$509$	−412.890	−	238.382i	−0.811178	−	0.468334i	−0.847365	+	0.531011i	$0.821812\pi$
$510$			25.3056i			0.0496187i
$511$	367.709	−	19.9211i	0.719587	−	0.0389846i
$512$	22.6274			0.0441942
$513$	−26.2279	+	45.4281i	−0.0511266	+	0.0885538i
$514$	−490.555	+	283.222i	−0.954387	+	0.551016i
$515$	−398.452	−	690.139i	−0.773693	−	1.34008i
$516$	13.0294	+	7.52255i	0.0252508	+	0.0145786i
$517$			250.613i			0.484744i
$518$	1.57507	+	29.0730i	0.00304068	+	0.0561255i
$519$	−117.905			−0.227176
$520$	−143.397	+	248.371i	−0.275763	+	0.477636i
$521$	739.823	−	427.137i	1.42001	−	0.819841i	0.423707	−	0.905799i	$-0.360729\pi$
$521$	739.823	−	427.137i	1.42001	−	0.819841i	0.996299	+	0.0859587i	$0.0273953\pi$
$522$	−21.0883	−	36.5260i	−0.0403991	−	0.0699732i
$523$	−513.554	−	296.501i	−0.981940	−	0.566923i	−0.0790845	−	0.996868i	$-0.525200\pi$
$523$	−513.554	−	296.501i	−0.981940	−	0.566923i	−0.902855	+	0.429945i	$0.858533\pi$
$524$			295.289i			0.563529i
$525$	52.0294	+	79.8098i	0.0991037	+	0.152019i
$526$	−45.7431			−0.0869640
$527$	91.9005	−	159.176i	0.174384	−	0.302043i
$528$	−11.8234	+	6.82623i	−0.0223928	+	0.0129285i
$529$	−119.919	−	207.706i	−0.226690	−	0.392638i
$530$	−454.555	−	262.437i	−0.857651	−	0.495165i
$531$			328.555i			0.618748i
$532$	26.4853	−	52.2077i	0.0497844	−	0.0981348i
$533$	427.529			0.802118
$534$	25.5334	−	44.2252i	0.0478154	−	0.0828188i
$535$	−652.422	+	376.676i	−1.21948	+	0.704068i
$536$	48.9878	+	84.8494i	0.0913952	+	0.158301i
$537$	−115.058	−	66.4290i	−0.214262	−	0.123704i
$538$		−	434.112i		−	0.806899i
$539$	−94.0629	+	213.290i	−0.174514	+	0.395715i
$540$	−166.368			−0.308088
$541$	−427.595	+	740.617i	−0.790380	+	1.36898i	0.135352	+	0.990798i	$0.456783\pi$
$541$	−427.595	+	740.617i	−0.790380	+	1.36898i	−0.925732	+	0.378180i	$0.876550\pi$
$542$	93.0624	−	53.7296i	0.171702	−	0.0991322i
$543$	55.6325	+	96.3583i	0.102454	+	0.177455i
$544$	18.4264	+	10.6385i	0.0338721	+	0.0195560i
$545$		−	963.546i		−	1.76797i
$546$	96.8528	+	49.1340i	0.177386	+	0.0899890i
$547$	415.897			0.760323			0.380161	−	0.924920i	$-0.375868\pi$
$547$	415.897			0.760323			0.380161	+	0.924920i	$0.375868\pi$
$548$	32.5736	−	56.4191i	0.0594409	−	0.102955i
$549$	665.095	−	383.993i	1.21147	−	0.699441i
$550$	−63.8162	−	110.533i	−0.116030	−	0.200969i
$551$	12.7279	+	7.34847i	0.0230997	+	0.0133366i
$552$		−	56.2662i		−	0.101931i
$553$	198.124	−	129.161i	0.358272	−	0.233564i
$554$	393.733			0.710709
$555$	−6.99600	+	12.1174i	−0.0126054	+	0.0218332i
$556$	−118.794	+	68.5857i	−0.213658	+	0.123356i
$557$	292.110	+	505.950i	0.524435	+	0.908348i	0.999595	+	0.0284485i	$0.00905667\pi$
$557$	292.110	+	505.950i	0.524435	+	0.908348i	−0.475160	+	0.879899i	$0.657610\pi$
$558$	507.838	+	293.200i	0.910103	+	0.525448i
$559$			160.333i			0.286822i
$560$	185.397	−	10.0441i	0.331066	−	0.0179360i
$561$	−12.8377			−0.0228835
$562$	−279.088	+	483.395i	−0.496598	+	0.860134i
$563$	789.076	−	455.573i	1.40156	−	0.809189i	0.407004	−	0.913426i	$-0.366573\pi$
$563$	789.076	−	455.573i	1.40156	−	0.809189i	0.994552	+	0.104237i	$0.0332402\pi$
$564$	−37.7939	−	65.4610i	−0.0670105	−	0.116066i
$565$	−198.375	−	114.532i	−0.351106	−	0.202711i
$566$			207.035i			0.365787i
$567$	−25.5107	−	470.882i	−0.0449924	−	0.830480i
$568$	103.029			0.181390
$569$	−350.000	+	606.217i	−0.615113	+	1.06541i	0.375251	+	0.926923i	$0.377556\pi$
$569$	−350.000	+	606.217i	−0.615113	+	1.06541i	−0.990365	+	0.138485i	$0.955777\pi$
$570$	24.3640	−	14.0665i	0.0427438	−	0.0246781i
$571$	281.231	+	487.107i	0.492525	+	0.853077i	0.999963	−	0.00861055i	$-0.00274086\pi$
$571$	281.231	+	487.107i	0.492525	+	0.853077i	−0.507438	+	0.861688i	$0.669408\pi$
$572$	−126.000	−	72.7461i	−0.220280	−	0.127179i
$573$			177.993i			0.310634i
$574$	−151.154	−	231.861i	−0.263335	−	0.403939i
$575$	526.014			0.914807
$576$	−33.9411	+	58.7878i	−0.0589256	+	0.102062i
$577$	−573.014	+	330.830i	−0.993092	+	0.573362i	−0.906197	−	0.422856i	$-0.861028\pi$
$577$	−573.014	+	330.830i	−0.993092	+	0.573362i	−0.0868946	+	0.996218i	$0.527694\pi$
$578$	−194.350	−	336.625i	−0.336246	−	0.582395i
$579$	−95.8934	−	55.3641i	−0.165619	−	0.0956202i
$580$			46.6124i			0.0803662i
$581$	−404.029	+	796.420i	−0.695402	+	1.37077i
$582$	103.279			0.177456
$583$	133.136	−	230.598i	0.228364	−	0.395538i
$584$	128.860	−	74.3973i	0.220651	−	0.127393i
$585$	−430.191	−	745.113i	−0.735369	−	1.27370i
$586$	367.029	+	211.905i	0.626330	+	0.361612i
$587$			823.029i			1.40209i	0.713116	+	0.701046i	$0.247283\pi$
$587$			823.029i			1.40209i	−0.713116	+	0.701046i	$0.752717\pi$
$588$	−7.59589	−	69.8975i	−0.0129182	−	0.118873i
$589$	−204.338			−0.346924
$590$	181.555	−	314.462i	0.307720	−	0.532987i
$591$	−112.523	+	64.9650i	−0.190394	+	0.109924i
$592$	5.88225	+	10.1884i	0.00993623	+	0.0172101i
$593$	−538.890	−	311.128i	−0.908752	−	0.524668i	−0.0287225	−	0.999587i	$-0.509144\pi$
$593$	−538.890	−	311.128i	−0.908752	−	0.524668i	−0.880029	+	0.474919i	$0.842477\pi$
$594$		−	84.3992i		−	0.142086i
$595$	155.698	+	78.9868i	0.261678	+	0.132751i
$596$	184.794			0.310057
$597$	125.088	−	216.659i	0.209527	−	0.362912i
$598$	519.286	−	299.810i	0.868372	−	0.501355i
$599$	256.422	+	444.137i	0.428084	+	0.741463i	0.996703	−	0.0811377i	$-0.0258554\pi$
$599$	256.422	+	444.137i	0.428084	+	0.741463i	−0.568619	+	0.822601i	$0.692522\pi$
$600$	33.3381	+	19.2478i	0.0555635	+	0.0320796i
$601$		−	680.160i		−	1.13171i	−0.824504	−	0.565857i	$-0.808546\pi$
$601$		−	680.160i		−	1.13171i	0.824504	−	0.565857i	$-0.191454\pi$
$602$	86.9533	−	56.6864i	0.144441	−	0.0941635i
$603$	−293.927			−0.487441
$604$	91.7868	−	158.979i	0.151965	−	0.263211i
$605$	−564.889	+	326.139i	−0.933701	+	0.539073i
$606$	−30.2756	−	52.4390i	−0.0499598	−	0.0865329i
$607$	33.5482	+	19.3690i	0.0552688	+	0.0319095i	0.527380	−	0.849630i	$-0.323175\pi$
$607$	33.5482	+	19.3690i	0.0552688	+	0.0319095i	−0.472111	+	0.881539i	$0.656508\pi$
$608$		−	23.6544i		−	0.0389052i
$609$	17.6253	−	0.954877i	0.0289414	−	0.00156794i
$610$	−848.756			−1.39140
$611$	402.765	−	697.609i	0.659189	−	1.14175i
$612$	−55.2792	+	31.9155i	−0.0903255	+	0.0521495i
$613$	−200.552	−	347.366i	−0.327164	−	0.566665i	0.654784	−	0.755816i	$-0.272760\pi$
$613$	−200.552	−	347.366i	−0.327164	−	0.566665i	−0.981948	+	0.189151i	$0.939426\pi$
$614$	−25.7056	−	14.8412i	−0.0418658	−	0.0241713i
$615$		−	133.011i		−	0.216278i
$616$	5.09545	+	94.0530i	0.00827184	+	0.152683i
$617$	−959.044			−1.55437			−0.777183	−	0.629275i	$-0.783352\pi$
$617$	−959.044			−1.55437			−0.777183	+	0.629275i	$0.783352\pi$
$618$	−60.9670	+	105.598i	−0.0986521	+	0.170870i
$619$	−869.951	+	502.267i	−1.40541	+	0.811416i	−0.994941	−	0.100457i	$-0.967970\pi$
$619$	−869.951	+	502.267i	−1.40541	+	0.811416i	−0.410473	+	0.911873i	$0.634636\pi$
$620$	−324.037	−	561.248i	−0.522640	−	0.905238i
$621$	301.235	+	173.918i	0.485081	+	0.280061i
$622$			257.443i			0.413895i
$623$	−192.408	−	295.142i	−0.308841	−	0.473743i
$624$	43.8823			0.0703241
$625$	369.691	−	640.323i	0.591505	−	1.02452i
$626$	119.938	−	69.2460i	0.191594	−	0.110617i
$627$	7.13604	+	12.3600i	0.0113812	+	0.0197129i
$628$	−14.6468	−	8.45631i	−0.0233229	−	0.0134655i
$629$			11.0624i			0.0175873i
$630$	−252.000	+	496.742i	−0.400000	+	0.788479i
$631$	−386.514			−0.612542			−0.306271	−	0.951944i	$-0.599081\pi$
$631$	−386.514			−0.612542			−0.306271	+	0.951944i	$0.599081\pi$
$632$	47.7817	−	82.7604i	0.0756040	−	0.130950i
$633$	226.206	−	130.600i	0.357356	−	0.206319i
$634$	340.805	+	590.291i	0.537547	+	0.931058i
$635$	1420.37	+	820.053i	2.23681	+	1.29142i
$636$			80.3109i			0.126275i
$637$	604.617	−	442.547i	0.949164	−	0.694736i
$638$	−23.6468			−0.0370639
$639$	−154.544	+	267.678i	−0.241853	+	0.418902i
$640$	64.9706	−	37.5108i	0.101517	−	0.0586106i
$641$	496.074	+	859.225i	0.773906	+	1.34044i	0.935407	+	0.353572i	$0.115033\pi$
$641$	496.074	+	859.225i	0.773906	+	1.34044i	−0.161502	+	0.986872i	$0.551634\pi$
$642$	99.8269	+	57.6351i	0.155494	+	0.0897743i
$643$		−	944.986i		−	1.46965i	−0.678256	−	0.734826i	$-0.737264\pi$
$643$		−	944.986i		−	1.46965i	0.678256	−	0.734826i	$-0.262736\pi$
$644$	−346.191	−	175.625i	−0.537564	−	0.272709i
$645$	49.8823			0.0773368
$646$	11.1213	−	19.2627i	0.0172157	−	0.0298184i
$647$	2.50357	−	1.44544i	0.00386951	−	0.00223406i	−0.498064	−	0.867140i	$-0.665956\pi$
$647$	2.50357	−	1.44544i	0.00386951	−	0.00223406i	0.501934	+	0.864906i	$0.332622\pi$
$648$	−95.2721	−	165.016i	−0.147025	−	0.254654i
$649$	159.529	+	92.1039i	0.245807	+	0.141917i
$650$			410.241i			0.631140i
$651$	−205.584	+	134.024i	−0.315797	+	0.205874i
$652$	443.955			0.680913
$653$	161.529	−	279.777i	0.247365	−	0.428449i	−0.715429	−	0.698686i	$-0.753769\pi$
$653$	161.529	−	279.777i	0.247365	−	0.428449i	0.962794	+	0.270237i	$0.0871019\pi$
$654$	−127.680	+	73.7159i	−0.195229	+	0.112716i
$655$	489.518	+	847.870i	0.747356	+	1.29446i
$656$	−96.8528	−	55.9180i	−0.147641	−	0.0852409i
$657$			446.384i			0.679428i
$658$	−520.731	+	28.2114i	−0.791385	+	0.0428744i
$659$	295.955			0.449098			0.224549	−	0.974463i	$-0.427909\pi$
$659$	295.955			0.449098			0.224549	+	0.974463i	$0.427909\pi$
$660$	−22.6325	+	39.2006i	−0.0342916	+	0.0593948i
$661$	17.9710	−	10.3756i	0.0271876	−	0.0156968i	−0.486345	−	0.873767i	$-0.661670\pi$
$661$	17.9710	−	10.3756i	0.0271876	−	0.0156968i	0.513532	+	0.858070i	$0.328337\pi$
$662$	−159.104	−	275.576i	−0.240338	−	0.416278i
$663$	35.7351	+	20.6316i	0.0538990	+	0.0311186i
$664$			360.843i			0.543439i
$665$	−10.5000	−	193.811i	−0.0157895	−	0.291445i
$666$	−35.2935			−0.0529933
$667$	48.7279	−	84.3992i	0.0730554	−	0.126536i
$668$	−292.441	+	168.841i	−0.437785	+	0.252756i
$669$	−44.2052	−	76.5656i	−0.0660765	−	0.114448i
$670$	281.319	+	162.420i	0.419880	+	0.242418i
$671$		−	430.579i		−	0.641698i
$672$	−15.5147	−	23.7986i	−0.0230874	−	0.0354146i
$673$	627.044			0.931714			0.465857	−	0.884860i	$-0.345746\pi$
$673$	627.044			0.931714			0.465857	+	0.884860i	$0.345746\pi$
$674$	186.936	−	323.783i	0.277353	−	0.480390i
$675$	−206.095	+	118.989i	−0.305327	+	0.176280i
$676$	64.8234	+	112.277i	0.0958926	+	0.166091i
$677$	−94.6097	−	54.6230i	−0.139749	−	0.0806838i	0.428496	−	0.903544i	$-0.359044\pi$
$677$	−94.6097	−	54.6230i	−0.139749	−	0.0806838i	−0.568244	+	0.822860i	$0.692377\pi$
$678$			35.0489i			0.0516946i
$679$	322.368	−	635.450i	0.474768	−	0.935861i
$680$	70.5442			0.103741
$681$	−27.3974	+	47.4537i	−0.0402311	+	0.0696824i
$682$	284.724	−	164.386i	0.417484	−	0.241035i
$683$	−396.783	−	687.248i	−0.580941	−	1.00622i	−0.995368	−	0.0961370i	$-0.969351\pi$
$683$	−396.783	−	687.248i	−0.580941	−	1.00622i	0.414427	−	0.910083i	$-0.363982\pi$
$684$	61.4558	+	35.4815i	0.0898477	+	0.0518736i
$685$		−	215.996i		−	0.315323i
$686$	−453.770	−	171.437i	−0.661473	−	0.249908i
$687$	256.331			0.373116
$688$	20.9706	−	36.3221i	0.0304805	−	0.0527937i
$689$	−741.198	+	427.931i	−1.07576	+	0.621090i
$690$	−93.2756	−	161.558i	−0.135182	−	0.234142i
$691$	159.253	+	91.9447i	0.230467	+	0.133060i	0.610788	−	0.791794i	$-0.290853\pi$
$691$	159.253	+	91.9447i	0.230467	+	0.133060i	−0.380320	+	0.924855i	$0.624186\pi$
$692$			328.682i			0.474974i
$693$	−252.000	−	127.841i	−0.363636	−	0.184475i
$694$	−270.478			−0.389738
$695$	−227.397	+	393.863i	−0.327190	+	0.566710i
$696$	6.17662	−	3.56608i	0.00887446	−	0.00512367i
$697$	−52.5807	−	91.0725i	−0.0754386	−	0.130664i
$698$	165.889	+	95.7763i	0.237664	+	0.137215i
$699$		−	195.913i		−	0.280277i
$700$	222.485	−	145.042i	0.317836	−	0.207203i
$701$	−1043.82			−1.48905			−0.744525	−	0.667595i	$-0.767324\pi$
$701$	−1043.82			−1.48905			−0.744525	+	0.667595i	$0.767324\pi$
$702$	−135.640	+	234.935i	−0.193219	+	0.334665i
$703$	10.6508	−	6.14922i	0.0151504	−	0.00874711i
$704$	19.0294	+	32.9600i	0.0270305	+	0.0468181i
$705$	−217.037	−	125.306i	−0.307854	−	0.177740i
$706$		−	492.840i		−	0.698073i
$707$	−417.143	+	22.5993i	−0.590019	+	0.0319651i
$708$	−55.5593			−0.0784736
$709$	490.279	−	849.188i	0.691507	−	1.19773i	−0.279836	−	0.960048i	$-0.590280\pi$
$709$	490.279	−	849.188i	0.691507	−	1.19773i	0.971344	−	0.237678i	$-0.0763864\pi$
$710$	295.831	−	170.798i	0.416663	−	0.240560i
$711$	143.345	+	248.281i	0.201611	+	0.349200i
$712$	−123.286	−	71.1794i	−0.173155	−	0.0999711i
$713$			1354.97i			1.90038i
$714$	−1.44513	−	26.6745i	−0.00202399	−	0.0373593i
$715$	−482.382			−0.674660
$716$	−185.184	+	320.748i	−0.258637	+	0.447972i
$717$	−164.714	+	95.0975i	−0.229726	+	0.132632i
$718$	−215.548	−	373.340i	−0.300206	−	0.519972i
$719$	−674.187	−	389.242i	−0.937673	−	0.541366i	−0.0484429	−	0.998826i	$-0.515426\pi$
$719$	−674.187	−	389.242i	−0.937673	−	0.541366i	−0.889230	+	0.457460i	$0.848759\pi$
$720$			225.065i			0.312590i
$721$	459.419	+	704.719i	0.637197	+	0.977419i
$722$	485.803			0.672858
$723$	−31.4376	+	54.4514i	−0.0434821	+	0.0753132i
$724$	268.617	−	155.086i	0.371018	−	0.214208i
$725$	33.3381	+	57.7433i	0.0459836	+	0.0796459i
$726$	86.4335	+	49.9024i	0.119054	+	0.0687361i
$727$			735.255i			1.01135i	0.862723	+	0.505677i	$0.168757\pi$
$727$			735.255i			1.01135i	−0.862723	+	0.505677i	$0.831243\pi$
$728$	136.971	−	269.996i	0.188146	−	0.370874i
$729$	490.632			0.673021
$730$	246.665	−	427.237i	0.337898	−	0.585256i
$731$	34.1543	−	19.7190i	0.0467227	−	0.0269754i
$732$	64.9340	+	112.469i	0.0887076	+	0.153646i
$733$	−414.705	−	239.430i	−0.565764	−	0.326644i	0.189692	−	0.981844i	$-0.439251\pi$
$733$	−414.705	−	239.430i	−0.565764	−	0.326644i	−0.755456	+	0.655200i	$0.772585\pi$
$734$		−	134.356i		−	0.183047i
$735$	−137.683	−	188.106i	−0.187324	−	0.255926i
$736$	−156.853			−0.213115
$737$	−82.3965	+	142.715i	−0.111800	+	0.193643i
$738$	290.558	−	167.754i	0.393711	−	0.227309i
$739$	9.95227	+	17.2378i	0.0134672	+	0.0233259i	0.872680	−	0.488292i	$-0.162380\pi$
$739$	9.95227	+	17.2378i	0.0134672	+	0.0233259i	−0.859213	+	0.511618i	$0.829046\pi$
$740$	33.7797	+	19.5027i	0.0456482	+	0.0263550i
$741$		−	45.8739i		−	0.0619080i
$742$	494.132	+	250.676i	0.665946	+	0.337838i
$743$	43.3095			0.0582901			0.0291450	−	0.999575i	$-0.490722\pi$
$743$	43.3095			0.0582901			0.0291450	+	0.999575i	$0.490722\pi$
$744$	−49.5807	+	85.8764i	−0.0666408	+	0.115425i
$745$	530.603	−	306.344i	0.712218	−	0.411199i
$746$	−179.293	−	310.544i	−0.240339	−	0.416279i
$747$	−937.499	−	541.265i	−1.25502	−	0.724585i
$748$			35.7875i			0.0478442i
$749$	666.206	−	434.311i	0.889460	−	0.579855i
$750$	−40.5656			−0.0540874
$751$	−112.665	+	195.142i	−0.150020	+	0.259842i	−0.931235	−	0.364420i	$-0.881267\pi$
$751$	−112.665	+	195.142i	−0.150020	+	0.259842i	0.781215	+	0.624263i	$0.214600\pi$
$752$	−182.485	+	105.358i	−0.242667	+	0.140104i
$753$	177.801	+	307.961i	0.236124	+	0.408978i
$754$	65.8234	+	38.0031i	0.0872989	+	0.0504020i
$755$		−	608.641i		−	0.806147i
$756$	175.368	−	9.50079i	0.231968	−	0.0125672i
$757$	935.779			1.23617			0.618084	−	0.786112i	$-0.287909\pi$
$757$	935.779			1.23617			0.618084	+	0.786112i	$0.287909\pi$
$758$	−359.387	+	622.476i	−0.474125	+	0.821209i
$759$	81.9594	−	47.3193i	0.107983	−	0.0623443i
$760$	−39.2132	−	67.9193i	−0.0515963	−	0.0893674i
$761$	1214.79	+	701.357i	1.59630	+	0.921625i	0.992191	+	0.124724i	$0.0398046\pi$
$761$	1214.79	+	701.357i	1.59630	+	0.921625i	0.604110	+	0.796901i	$0.293529\pi$
$762$		−	250.952i		−	0.329334i
$763$	55.0254	+	1015.67i	0.0721172	+	1.33115i
$764$	496.191			0.649465
$765$	−105.816	+	183.279i	−0.138322	+	0.239581i
$766$	−585.136	+	337.828i	−0.763885	+	0.441029i
$767$	−296.044	−	512.763i	−0.385976	−	0.668530i
$768$	−9.94113	−	5.73951i	−0.0129442	−	0.00747332i
$769$		−	1.72330i		−	0.00224097i	−0.999999	−	0.00112048i	$-0.999643\pi$
$769$		−	1.72330i		−	0.00224097i	0.999999	−	0.00112048i	$-0.000356661\pi$
$770$	170.548	+	261.609i	0.221491	+	0.339752i
$771$	287.360			0.372711
$772$	−154.338	+	267.321i	−0.199920	+	0.346271i
$773$	194.213	−	112.129i	0.251245	−	0.145057i	−0.369089	−	0.929394i	$-0.620330\pi$
$773$	194.213	−	112.129i	0.251245	−	0.145057i	0.620334	+	0.784337i	$0.286997\pi$
$774$	62.9117	+	108.966i	0.0812813	+	0.140783i
$775$	−802.831	−	463.514i	−1.03591	−	0.598083i
$776$		−	287.911i		−	0.371019i
$777$	6.68247	−	13.1725i	0.00860034	−	0.0169530i
$778$	240.728			0.309419
$779$	−58.4558	+	101.248i	−0.0750396	+	0.129972i
$780$	126.000	−	72.7461i	0.161538	−	0.0932643i
$781$	86.6468	+	150.077i	0.110943	+	0.192160i
$782$	−127.731	−	73.7458i	−0.163340	−	0.0943041i
$783$			44.0908i			0.0563101i
$784$	−194.853	+	21.1750i	−0.248537	+	0.0270089i
$785$	−56.0740			−0.0714319
$786$	74.9010	−	129.732i	0.0952939	−	0.165054i
$787$	60.7979	−	35.1017i	0.0772528	−	0.0446019i	−0.460876	−	0.887465i	$-0.652465\pi$
$787$	60.7979	−	35.1017i	0.0772528	−	0.0446019i	0.538129	+	0.842863i	$0.319131\pi$
$788$	181.103	+	313.679i	0.229826	+	0.398070i
$789$	20.0968	+	11.6029i	0.0254712	+	0.0147058i
$790$		−	316.842i		−	0.401066i
$791$	215.647	+	109.399i	0.272625	+	0.138305i
$792$	−114.177			−0.144162
$793$	−691.992	+	1198.57i	−0.872625	+	1.51143i
$794$	−299.511	+	172.923i	−0.377218	+	0.217787i
$795$	133.136	+	230.598i	0.167467	+	0.290061i
$796$	−603.978	−	348.707i	−0.758766	−	0.438074i
$797$		−	1305.38i		−	1.63787i	−0.573889	−	0.818933i	$-0.694566\pi$
$797$		−	1305.38i		−	1.63787i	0.573889	−	0.818933i	$-0.305434\pi$
$798$	−24.8787	+	16.2189i	−0.0311763	+	0.0203244i
$799$	−198.140			−0.247985
$800$	53.6569	−	92.9364i	0.0670711	−	0.116170i
$801$	369.859	−	213.538i	0.461747	−	0.266590i
$802$	295.269	+	511.420i	0.368165	+	0.637681i
$803$	216.740	+	125.135i	0.269913	+	0.155834i
$804$		−	49.7036i		−	0.0618204i
$805$	−1285.17	+	69.6258i	−1.59648	+	0.0864917i
$806$	−1056.75			−1.31110
$807$	−110.114	+	190.723i	−0.136448	+	0.236335i
$808$	−146.184	+	84.3992i	−0.180921	+	0.104455i
$809$	−381.382	−	660.573i	−0.471424	−	0.816531i	0.528041	−	0.849219i	$-0.322927\pi$
$809$	−381.382	−	660.573i	−0.471424	−	0.816531i	−0.999466	+	0.0326879i	$0.989593\pi$
$810$	−547.113	−	315.876i	−0.675449	−	0.389970i
$811$		−	1214.98i		−	1.49813i	−0.662498	−	0.749064i	$-0.730504\pi$
$811$		−	1214.98i		−	1.49813i	0.662498	−	0.749064i	$-0.269496\pi$
$812$	−2.66190	−	49.1340i	−0.00327821	−	0.0605099i
$813$	−54.5147			−0.0670538
$814$	−9.89383	+	17.1366i	−0.0121546	+	0.0210524i
$815$	1274.74	−	735.970i	1.56410	−	0.903031i
$816$	−5.39697	−	9.34783i	−0.00661393	−	0.0114557i
$817$	−37.9706	−	21.9223i	−0.0464756	−	0.0268327i
$818$			435.877i			0.532857i
$819$	496.014	+	760.854i	0.605634	+	0.929004i
$820$	−370.794			−0.452188
$821$	291.684	−	505.211i	0.355279	−	0.615361i	−0.631887	−	0.775061i	$-0.717719\pi$
$821$	291.684	−	505.211i	0.355279	−	0.615361i	0.987166	+	0.159700i	$0.0510527\pi$
$822$	−28.6218	+	16.5248i	−0.0348197	+	0.0201031i
$823$	−515.371	−	892.648i	−0.626210	−	1.08463i	−0.988306	−	0.152486i	$-0.951272\pi$
$823$	−515.371	−	892.648i	−0.626210	−	1.08463i	0.362096	−	0.932141i	$-0.382061\pi$
$824$	294.375	+	169.957i	0.357251	+	0.206259i
$825$			64.7487i			0.0784833i
$826$	−173.418	+	341.842i	−0.209950	+	0.413852i
$827$	152.102			0.183920			0.0919599	−	0.995763i	$-0.470687\pi$
$827$	152.102			0.183920			0.0919599	+	0.995763i	$0.470687\pi$
$828$	235.279	−	407.516i	0.284154	−	0.492169i
$829$	532.095	−	307.205i	0.641852	−	0.370573i	−0.143476	−	0.989654i	$-0.545828\pi$
$829$	532.095	−	307.205i	0.641852	−	0.370573i	0.785327	+	0.619081i	$0.212495\pi$
$830$	598.191	+	1036.10i	0.720712	+	1.24831i
$831$	−172.983	−	99.8715i	−0.208162	−	0.120182i
$832$		−	122.330i		−	0.147032i
$833$	−168.632	−	74.3682i	−0.202439	−	0.0892776i
$834$	69.5879			0.0834387
$835$	−559.794	+	969.592i	−0.670412	+	1.16119i
$836$	34.4558	−	19.8931i	0.0412151	−	0.0237956i
$837$	−306.507	−	530.886i	−0.366197	−	0.634272i
$838$	−126.323	−	72.9326i	−0.150743	−	0.0870317i
$839$			1546.14i			1.84284i	0.388568	+	0.921420i	$0.372970\pi$
$839$			1546.14i			1.84284i	−0.388568	+	0.921420i	$0.627030\pi$
$840$	−84.0000	−	42.6137i	−0.100000	−	0.0507306i
$841$	−828.647			−0.985311
$842$	116.828	−	202.353i	0.138751	−	0.240324i
$843$	245.229	−	141.583i	0.290901	−	0.167952i
$844$	−364.073	−	630.593i	−0.431366	−	0.747148i
$845$	372.257	+	214.923i	0.440541	+	0.254347i
$846$		−	632.148i		−	0.747219i
$847$	576.823	−	376.041i	0.681019	−	0.443969i
$848$	223.882			0.264012
$849$	52.5152	−	90.9589i	0.0618553	−	0.107137i
$850$	87.3898	−	50.4545i	0.102812	−	0.0593583i
$851$	−40.7756	−	70.6255i	−0.0479150	−	0.0829912i
$852$	−45.2649	−	26.1337i	−0.0531279	−	0.0306734i
$853$			1235.15i			1.44800i	0.689798	+	0.724002i	$0.257699\pi$
$853$			1235.15i			1.44800i	−0.689798	+	0.724002i	$0.742301\pi$
$854$	894.672	−	48.4701i	1.04763	−	0.0567566i
$855$	235.279			0.275180
$856$	160.669	−	278.287i	0.187697	−	0.325102i
$857$	−953.219	+	550.341i	−1.11227	+	0.642172i	−0.939417	−	0.342775i	$-0.888633\pi$
$857$	−953.219	+	550.341i	−1.11227	+	0.642172i	−0.172857	+	0.984947i	$0.555300\pi$
$858$	36.9045	+	63.9205i	0.0430123	+	0.0744995i
$859$	512.488	+	295.885i	0.596610	+	0.344453i	0.767707	−	0.640801i	$-0.221398\pi$
$859$	512.488	+	295.885i	0.596610	+	0.344453i	−0.171096	+	0.985254i	$0.554731\pi$
$860$		−	139.056i		−	0.161694i
$861$	7.59589	+	140.207i	0.00882217	+	0.162841i
$862$	840.801			0.975407
$863$	32.3635	−	56.0553i	0.0375012	−	0.0649540i	−0.846666	−	0.532125i	$-0.821394\pi$
$863$	32.3635	−	56.0553i	0.0375012	−	0.0649540i	0.884167	+	0.467171i	$0.154727\pi$
$864$	61.4558	−	35.4815i	0.0711294	−	0.0410666i
$865$	544.875	+	943.751i	0.629913	+	1.09104i
$866$	−49.7574	−	28.7274i	−0.0574565	−	0.0331725i
$867$			197.190i			0.227440i
$868$	373.617	+	573.105i	0.430435	+	0.660259i
$869$	160.736			0.184967
$870$	11.8234	−	20.4787i	0.0135901	−	0.0235387i
$871$	458.720	−	264.842i	0.526659	−	0.304067i
$872$	205.497	+	355.932i	0.235662	+	0.408179i
$873$	748.014	+	431.866i	0.856832	+	0.494692i
$874$			163.972i			0.187611i
$875$	−126.618	+	249.589i	−0.144706	+	0.285245i
$876$	−75.4844			−0.0861694
$877$	152.096	−	263.438i	0.173427	−	0.300385i	−0.766188	−	0.642616i	$-0.777849\pi$
$877$	152.096	−	263.438i	0.173427	−	0.300385i	0.939616	+	0.342231i	$0.111182\pi$
$878$	−179.548	+	103.662i	−0.204496	+	0.118066i
$879$	−107.500	−	186.196i	−0.122299	−	0.211827i
$880$	109.279	+	63.0924i	0.124181	+	0.0716959i
$881$		−	863.732i		−	0.980400i	−0.871610	−	0.490200i	$-0.836924\pi$
$881$		−	863.732i		−	0.980400i	0.871610	−	0.490200i	$-0.163076\pi$
$882$	237.265	−	538.005i	0.269008	−	0.609983i
$883$	−567.456			−0.642645			−0.321323	−	0.946970i	$-0.604127\pi$
$883$	−567.456			−0.642645			−0.321323	+	0.946970i	$0.604127\pi$
$884$	57.5147	−	99.6184i	0.0650619	−	0.112691i
$885$	−159.529	+	92.1039i	−0.180258	+	0.104072i
$886$	−75.9153	−	131.489i	−0.0856831	−	0.148408i
$887$	−770.555	−	444.880i	−0.868721	−	0.501556i	−0.00179783	−	0.999998i	$-0.500572\pi$
$887$	−770.555	−	444.880i	−0.868721	−	0.501556i	−0.866923	+	0.498442i	$0.833906\pi$
$888$		−	5.96820i		−	0.00672095i
$889$	−1544.04	−	783.302i	−1.73683	−	0.881105i
$890$	−471.993			−0.530329
$891$	160.246	−	277.554i	0.179849	−	0.311508i
$892$	−213.442	+	123.231i	−0.239284	+	0.138151i
$893$	110.140	+	190.767i	0.123337	+	0.213625i
$894$	−81.1873	−	46.8735i	−0.0908136	−	0.0524312i
$895$			1227.96i			1.37202i
$896$	−66.3431	+	43.2503i	−0.0740437	+	0.0482704i
$897$	−304.191			−0.339120
$898$	−95.5736	+	165.538i	−0.106429	+	0.184341i
$899$	−148.742	+	85.8764i	−0.165453	+	0.0955243i
$900$	160.971	+	278.809i	0.178856	+	0.309788i
$901$	182.316	+	105.260i	0.202349	+	0.116826i
$902$		−	188.106i		−	0.208543i
$903$	−52.5807	+	2.84864i	−0.0582289	+	0.00315464i
$904$	97.7056			0.108081
$905$	514.191	−	890.605i	0.568167	−	0.984094i
$906$	−80.6512	+	46.5640i	−0.0890190	+	0.0513951i
$907$	−186.989	−	323.874i	−0.206162	−	0.357083i	0.744340	−	0.667800i	$-0.232764\pi$
$907$	−186.989	−	323.874i	−0.206162	−	0.357083i	−0.950502	+	0.310717i	$0.899431\pi$
$908$	132.286	+	76.3756i	0.145690	+	0.0841141i
$909$		−	506.395i		−	0.557091i
$910$	−54.3015	−	1002.31i	−0.0596720	−	1.10144i
$911$	1133.75			1.24451			0.622256	−	0.782814i	$-0.286216\pi$
$911$	1133.75			1.24451			0.622256	+	0.782814i	$0.286216\pi$
$912$	−6.00000	+	10.3923i	−0.00657895	+	0.0113951i
$913$	−525.618	+	303.466i	−0.575704	+	0.332383i
$914$	−112.950	−	195.635i	−0.123577	−	0.214042i
$915$	372.893	+	215.290i	0.407533	+	0.235289i
$916$		−	714.572i		−	0.780101i
$917$	−564.419	−	865.782i	−0.615506	−	0.944146i
$918$	66.7279			0.0726884
$919$	−228.151	+	395.169i	−0.248260	+	0.429999i	−0.963043	−	0.269347i	$-0.913192\pi$
$919$	−228.151	+	395.169i	−0.248260	+	0.429999i	0.714783	+	0.699346i	$0.246525\pi$
$920$	−450.375	+	260.024i	−0.489538	+	0.282635i
$921$	7.52900	+	13.0406i	0.00817481	+	0.0141592i
$922$	379.977	+	219.380i	0.412122	+	0.237939i
$923$		−	557.007i		−	0.603474i
$924$	21.6182	−	42.6137i	0.0233963	−	0.0461187i
$925$	55.7948			0.0603187
$926$	230.527	−	399.284i	0.248949	−	0.431193i
$927$	−883.124	+	509.872i	−0.952669	+	0.550024i
$928$	−9.94113	−	17.2185i	−0.0107124	−	0.0185545i
$929$	−824.058	−	475.770i	−0.887037	−	0.512131i	−0.0140650	−	0.999901i	$-0.504477\pi$
$929$	−824.058	−	475.770i	−0.887037	−	0.512131i	−0.872972	+	0.487770i	$0.837811\pi$
$930$			328.771i			0.353518i
$931$	22.1360	+	203.696i	0.0237766	+	0.218793i
$932$	−546.146			−0.585994
$933$	65.3011	−	113.105i	0.0699904	−	0.121227i
$934$	−729.407	+	421.123i	−0.780949	+	0.450881i
$935$	59.3269	+	102.757i	0.0634513	+	0.109901i
$936$	317.823	+	183.495i	0.339555	+	0.196042i
$937$			1295.71i			1.38283i	0.722460	+	0.691413i	$0.243011\pi$
$937$			1295.71i			1.38283i	−0.722460	+	0.691413i	$0.756989\pi$
$938$	−305.813	−	155.141i	−0.326027	−	0.165395i
$939$	−70.2578			−0.0748219
$940$	−349.316	+	605.033i	−0.371613	+	0.643652i
$941$	−1175.10	+	678.446i	−1.24878	+	0.720984i	−0.970866	−	0.239622i	$-0.922977\pi$
$941$	−1175.10	+	678.446i	−1.24878	+	0.720984i	−0.277915	+	0.960606i	$0.589643\pi$
$942$	4.28993	+	7.43038i	0.00455407	+	0.00788788i
$943$	671.382	+	387.622i	0.711964	+	0.411052i
$944$			154.882i			0.164070i
$945$	487.786	−	317.997i	0.516176	−	0.336504i
$946$	70.5442			0.0745710
$947$	354.731	−	614.412i	0.374584	−	0.648799i	−0.615681	−	0.787996i	$-0.711119\pi$
$947$	354.731	−	614.412i	0.374584	−	0.648799i	0.990265	+	0.139197i	$0.0444522\pi$
$948$	−41.9848	+	24.2400i	−0.0442878	+	0.0255696i
$949$	−402.213	−	696.654i	−0.423828	−	0.734092i
$950$	−97.1543	−	56.0921i	−0.102268	−	0.0590443i
$951$		−	345.784i		−	0.363601i
$952$	−74.3604	+	4.02858i	−0.0781097	+	0.00423170i
$953$	936.603			0.982794			0.491397	−	0.870936i	$-0.336486\pi$
$953$	936.603			0.982794			0.491397	+	0.870936i	$0.336486\pi$
$954$	−335.823	+	581.663i	−0.352016	+	0.609710i
$955$	1424.72	−	822.564i	1.49186	−	0.861324i
$956$	265.103	+	459.171i	0.277304	+	0.480305i
$957$	10.3890	+	5.99807i	0.0108558	+	0.00626757i
$958$			716.554i			0.747969i
$959$	12.3350	+	227.681i	0.0128623	+	0.237415i
$960$	−38.0589			−0.0396447
$961$	713.477	−	1235.78i	0.742432	−	1.28593i
$962$	55.0812	−	31.8011i	0.0572569	−	0.0330573i
$963$	482.007	+	834.861i	0.500527	+	0.866938i
$964$	151.794	+	87.6383i	0.157463	+	0.0909111i
$965$			1023.42i			1.06054i
$966$	107.548	+	164.971i	0.111333	+	0.170778i
$967$	1374.37			1.42127			0.710635	−	0.703561i	$-0.248408\pi$
$967$	1374.37			1.42127			0.710635	+	0.703561i	$0.248408\pi$
$968$	139.113	−	240.950i	0.143711	−	0.248916i
$969$	−9.77208	+	5.64191i	−0.0100847	+	0.00582241i
$970$	−477.286	−	826.684i	−0.492048	−	0.852252i
$971$	−27.2466	−	15.7309i	−0.0280604	−	0.0162007i	0.485904	−	0.874012i	$-0.338490\pi$
$971$	−27.2466	−	15.7309i	−0.0280604	−	0.0162007i	−0.513965	+	0.857811i	$0.671824\pi$
$972$			322.467i			0.331757i
$973$	217.206	−	428.156i	0.223233	−	0.440037i
$974$	298.825			0.306802
$975$	104.059	−	180.235i	0.106727	−	0.184857i
$976$	313.529	−	181.016i	0.321239	−	0.185467i
$977$	270.949	+	469.297i	0.277327	+	0.480345i	0.970720	−	0.240215i	$-0.0772181\pi$
$977$	270.949	+	469.297i	0.277327	+	0.480345i	−0.693392	+	0.720560i	$0.743885\pi$
$978$	−195.047	−	112.611i	−0.199435	−	0.115144i
$979$		−	239.445i		−	0.244581i
$980$	−524.382	+	383.819i	−0.535083	+	0.391652i
$981$	−1232.98			−1.25687
$982$	554.485	−	960.397i	0.564649	−	0.978001i
$983$	19.4161	−	11.2099i	0.0197519	−	0.0114038i	−0.490092	−	0.871671i	$-0.663037\pi$
$983$	19.4161	−	11.2099i	0.0197519	−	0.0114038i	0.509843	+	0.860267i	$0.329703\pi$
$984$	28.3675	+	49.1340i	0.0288288	+	0.0499329i
$985$	1040.01	+	600.448i	1.05584	+	0.609592i
$986$		−	18.6957i		−	0.0189611i
$987$	235.934	+	119.691i	0.239042	+	0.121267i
$988$	−127.882			−0.129435
$989$	−145.368	+	251.784i	−0.146984	+	0.254584i
$990$	−327.838	+	189.277i	−0.331149	+	0.191189i
$991$	−339.017	−	587.195i	−0.342096	−	0.592528i	0.642726	−	0.766097i	$-0.277804\pi$
$991$	−339.017	−	587.195i	−0.342096	−	0.592528i	−0.984822	+	0.173568i	$0.944470\pi$
$992$	239.397	+	138.216i	0.241328	+	0.139331i
$993$			161.429i			0.162567i
$994$	−302.080	+	196.932i	−0.303904	+	0.198120i
$995$	−2312.28			−2.32390
$996$	91.5290	−	158.533i	0.0918966	−	0.159170i
$997$	758.779	−	438.081i	0.761062	−	0.439400i	−0.0686147	−	0.997643i	$-0.521858\pi$
$997$	758.779	−	438.081i	0.761062	−	0.439400i	0.829677	+	0.558244i	$0.188525\pi$
$998$	121.263	+	210.034i	0.121506	+	0.210455i
$999$	31.9523	+	18.4477i	0.0319843	+	0.0184661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.3.d.a.5.1	yes	4
3.2	odd	2		126.3.n.c.19.2		4
4.3	odd	2		112.3.s.b.33.1		4
5.2	odd	4		350.3.i.a.299.2		8
5.3	odd	4		350.3.i.a.299.3		8
5.4	even	2		350.3.k.a.201.2		4
7.2	even	3		98.3.b.b.97.4		4
7.3	odd	6	inner	14.3.d.a.3.1	✓	4
7.4	even	3		98.3.d.a.31.1		4
7.5	odd	6		98.3.b.b.97.3		4
7.6	odd	2		98.3.d.a.19.1		4
8.3	odd	2		448.3.s.c.257.2		4
8.5	even	2		448.3.s.d.257.1		4
12.11	even	2		1008.3.cg.l.145.2		4
21.2	odd	6		882.3.c.f.685.1		4
21.5	even	6		882.3.c.f.685.2		4
21.11	odd	6		882.3.n.b.325.2		4
21.17	even	6		126.3.n.c.73.2		4
21.20	even	2		882.3.n.b.19.2		4
28.3	even	6		112.3.s.b.17.1		4
28.11	odd	6		784.3.s.c.129.2		4
28.19	even	6		784.3.c.e.97.3		4
28.23	odd	6		784.3.c.e.97.2		4
28.27	even	2		784.3.s.c.705.2		4
35.3	even	12		350.3.i.a.199.2		8
35.17	even	12		350.3.i.a.199.3		8
35.24	odd	6		350.3.k.a.101.2		4
56.3	even	6		448.3.s.c.129.2		4
56.45	odd	6		448.3.s.d.129.1		4
84.59	odd	6		1008.3.cg.l.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.3.d.a.3.1	✓	4	7.3	odd	6	inner
14.3.d.a.5.1	yes	4	1.1	even	1	trivial
98.3.b.b.97.3		4	7.5	odd	6
98.3.b.b.97.4		4	7.2	even	3
98.3.d.a.19.1		4	7.6	odd	2
98.3.d.a.31.1		4	7.4	even	3
112.3.s.b.17.1		4	28.3	even	6
112.3.s.b.33.1		4	4.3	odd	2
126.3.n.c.19.2		4	3.2	odd	2
126.3.n.c.73.2		4	21.17	even	6
350.3.i.a.199.2		8	35.3	even	12
350.3.i.a.199.3		8	35.17	even	12
350.3.i.a.299.2		8	5.2	odd	4
350.3.i.a.299.3		8	5.3	odd	4
350.3.k.a.101.2		4	35.24	odd	6
350.3.k.a.201.2		4	5.4	even	2
448.3.s.c.129.2		4	56.3	even	6
448.3.s.c.257.2		4	8.3	odd	2
448.3.s.d.129.1		4	56.45	odd	6
448.3.s.d.257.1		4	8.5	even	2
784.3.c.e.97.2		4	28.23	odd	6
784.3.c.e.97.3		4	28.19	even	6
784.3.s.c.129.2		4	28.11	odd	6
784.3.s.c.705.2		4	28.27	even	2
882.3.c.f.685.1		4	21.2	odd	6
882.3.c.f.685.2		4	21.5	even	6
882.3.n.b.19.2		4	21.20	even	2
882.3.n.b.325.2		4	21.11	odd	6
1008.3.cg.l.145.2		4	12.11	even	2
1008.3.cg.l.577.2		4	84.59	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(0.621320 - 0.358719i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-5.74264 - 3.31552i) q^{5} +1.01461i q^{6} +(6.24264 + 3.16693i) q^{7} +2.82843 q^{8} +(-4.24264 + 7.34847i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(0.621320 - 0.358719i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-5.74264 - 3.31552i) q^{5} +1.01461i q^{6} +(6.24264 + 3.16693i) q^{7} +2.82843 q^{8} +(-4.24264 + 7.34847i) q^{9} +(8.12132 - 4.68885i) q^{10} +(2.37868 + 4.11999i) q^{11} +(-1.24264 - 0.717439i) q^{12} -15.2913i q^{13} +(-8.29289 + 5.40629i) q^{14} -4.75736 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-3.25736 + 1.88064i) q^{17} +(-6.00000 - 10.3923i) q^{18} +(3.62132 + 2.09077i) q^{19} +13.2621i q^{20} +(5.01472 - 0.271680i) q^{21} -6.72792 q^{22} +(13.8640 - 24.0131i) q^{23} +(1.75736 - 1.01461i) q^{24} +(9.48528 + 16.4290i) q^{25} +(18.7279 + 10.8126i) q^{26} +12.5446i q^{27} +(-0.757359 - 13.9795i) q^{28} +3.51472 q^{29} +(3.36396 - 5.82655i) q^{30} +(-42.3198 + 24.4334i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(2.95584 + 1.70656i) q^{33} -5.31925i q^{34} +(-25.3492 - 38.8841i) q^{35} +16.9706 q^{36} +(1.47056 - 2.54709i) q^{37} +(-5.12132 + 2.95680i) q^{38} +(-5.48528 - 9.50079i) q^{39} +(-16.2426 - 9.37769i) q^{40} +27.9590i q^{41} +(-3.21320 + 6.33386i) q^{42} -10.4853 q^{43} +(4.75736 - 8.23999i) q^{44} +(48.7279 - 28.1331i) q^{45} +(19.6066 + 33.9596i) q^{46} +(45.6213 + 26.3395i) q^{47} +2.86976i q^{48} +(28.9411 + 39.5400i) q^{49} -26.8284 q^{50} +(-1.34924 + 2.33696i) q^{51} +(-26.4853 + 15.2913i) q^{52} +(-27.9853 - 48.4719i) q^{53} +(-15.3640 - 8.87039i) q^{54} -31.5462i q^{55} +(17.6569 + 8.95743i) q^{56} +3.00000 q^{57} +(-2.48528 + 4.30463i) q^{58} +(33.5330 - 19.3603i) q^{59} +(4.75736 + 8.23999i) q^{60} +(-78.3823 - 45.2540i) q^{61} -69.1080i q^{62} +(-49.7574 + 32.4377i) q^{63} +8.00000 q^{64} +(-50.6985 + 87.8124i) q^{65} +(-4.18019 + 2.41344i) q^{66} +(17.3198 + 29.9988i) q^{67} +(6.51472 + 3.76127i) q^{68} -19.8931i q^{69} +(65.5477 - 3.55114i) q^{70} +36.4264 q^{71} +(-12.0000 + 20.7846i) q^{72} +(45.5589 - 26.3034i) q^{73} +(2.07969 + 3.60213i) q^{74} +(11.7868 + 6.80511i) q^{75} -8.36308i q^{76} +(1.80152 + 33.2528i) q^{77} +15.5147 q^{78} +(16.8934 - 29.2602i) q^{79} +(22.9706 - 13.2621i) q^{80} +(-33.6838 - 58.3420i) q^{81} +(-34.2426 - 19.7700i) q^{82} +127.577i q^{83} +(-5.48528 - 8.41407i) q^{84} +24.9411 q^{85} +(7.41421 - 12.8418i) q^{86} +(2.18377 - 1.26080i) q^{87} +(6.72792 + 11.6531i) q^{88} +(-43.5883 - 25.1657i) q^{89} +79.5724i q^{90} +(48.4264 - 95.4580i) q^{91} -55.4558 q^{92} +(-17.5294 + 30.3619i) q^{93} +(-64.5183 + 37.2497i) q^{94} +(-13.8640 - 24.0131i) q^{95} +(-3.51472 - 2.02922i) q^{96} -101.792i q^{97} +(-68.8909 + 7.48650i) q^{98} -40.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7}+O(q^{10}) \) 4 * q - 6 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^7	\( 4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7} + 24 q^{10} + 18 q^{11} + 12 q^{12} - 36 q^{14} - 36 q^{15} - 8 q^{16} - 30 q^{17} - 24 q^{18} + 6 q^{19} + 54 q^{21} + 24 q^{22} + 30 q^{23} + 24 q^{24} + 4 q^{25} + 24 q^{26} - 20 q^{28} + 48 q^{29} - 12 q^{30} - 42 q^{31} - 90 q^{33} - 42 q^{35} - 62 q^{37} - 12 q^{38} + 12 q^{39} - 48 q^{40} + 72 q^{42} - 8 q^{43} + 36 q^{44} + 144 q^{45} + 36 q^{46} + 174 q^{47} - 20 q^{49} - 96 q^{50} + 54 q^{51} - 72 q^{52} - 78 q^{53} - 36 q^{54} + 48 q^{56} + 12 q^{57} + 24 q^{58} - 78 q^{59} + 36 q^{60} - 42 q^{61} - 216 q^{63} + 32 q^{64} - 84 q^{65} - 144 q^{66} - 58 q^{67} + 60 q^{68} + 84 q^{70} - 24 q^{71} - 48 q^{72} + 318 q^{73} + 96 q^{74} + 132 q^{75} + 126 q^{77} + 96 q^{78} + 110 q^{79} + 24 q^{80} + 18 q^{81} - 120 q^{82} + 12 q^{84} - 36 q^{85} + 24 q^{86} - 144 q^{87} - 24 q^{88} - 378 q^{89} + 24 q^{91} - 120 q^{92} - 138 q^{93} - 12 q^{94} - 30 q^{95} - 48 q^{96} - 120 q^{98} + 144 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^7 + 24 * q^10 + 18 * q^11 + 12 * q^12 - 36 * q^14 - 36 * q^15 - 8 * q^16 - 30 * q^17 - 24 * q^18 + 6 * q^19 + 54 * q^21 + 24 * q^22 + 30 * q^23 + 24 * q^24 + 4 * q^25 + 24 * q^26 - 20 * q^28 + 48 * q^29 - 12 * q^30 - 42 * q^31 - 90 * q^33 - 42 * q^35 - 62 * q^37 - 12 * q^38 + 12 * q^39 - 48 * q^40 + 72 * q^42 - 8 * q^43 + 36 * q^44 + 144 * q^45 + 36 * q^46 + 174 * q^47 - 20 * q^49 - 96 * q^50 + 54 * q^51 - 72 * q^52 - 78 * q^53 - 36 * q^54 + 48 * q^56 + 12 * q^57 + 24 * q^58 - 78 * q^59 + 36 * q^60 - 42 * q^61 - 216 * q^63 + 32 * q^64 - 84 * q^65 - 144 * q^66 - 58 * q^67 + 60 * q^68 + 84 * q^70 - 24 * q^71 - 48 * q^72 + 318 * q^73 + 96 * q^74 + 132 * q^75 + 126 * q^77 + 96 * q^78 + 110 * q^79 + 24 * q^80 + 18 * q^81 - 120 * q^82 + 12 * q^84 - 36 * q^85 + 24 * q^86 - 144 * q^87 - 24 * q^88 - 378 * q^89 + 24 * q^91 - 120 * q^92 - 138 * q^93 - 12 * q^94 - 30 * q^95 - 48 * q^96 - 120 * q^98 + 144 * q^99

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