LMFDB - Embedded newform 38.3.f.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,3,Mod(3,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("38.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.03542500457$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.3
Character	$\chi$	$=$	38.3
Dual form			38.3.f.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.909039 - 1.08335i) q^{2} +(-0.830875 - 2.28281i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(0.0233547 - 0.132451i) q^{5} +(-3.22838 - 1.17503i) q^{6} +(4.79341 + 8.30244i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(2.37354 - 1.99163i) q^{9} +O(q^{10})$	\(q+(0.909039 - 1.08335i) q^{2} +(-0.830875 - 2.28281i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(0.0233547 - 0.132451i) q^{5} +(-3.22838 - 1.17503i) q^{6} +(4.79341 + 8.30244i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(2.37354 - 1.99163i) q^{9} +(-0.122261 - 0.145705i) q^{10} +(-7.19093 + 12.4551i) q^{11} +(-4.20770 + 2.42931i) q^{12} +(1.30073 - 3.57374i) q^{13} +(13.3518 + 2.35429i) q^{14} +(-0.321766 + 0.0567360i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-3.78497 - 3.17596i) q^{17} -4.38184i q^{18} +(-17.3463 + 7.75273i) q^{19} -0.268989 q^{20} +(14.9702 - 17.8407i) q^{21} +(6.95635 + 19.1124i) q^{22} +(-3.30421 - 18.7391i) q^{23} +(-1.19316 + 6.76675i) q^{24} +(23.4753 + 8.54432i) q^{25} +(-2.68919 - 4.65782i) q^{26} +(-25.4533 - 14.6954i) q^{27} +(14.6879 - 12.3246i) q^{28} +(-23.8175 - 28.3846i) q^{29} +(-0.231033 + 0.400160i) q^{30} +(26.2409 - 15.1502i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(34.4073 + 6.06693i) q^{33} +(-6.88136 + 1.21337i) q^{34} +(1.21162 - 0.440993i) q^{35} +(-4.74707 - 3.98327i) q^{36} +48.8558i q^{37} +(-7.36956 + 25.8397i) q^{38} -9.23891 q^{39} +(-0.244522 + 0.291410i) q^{40} +(-9.73690 - 26.7519i) q^{41} +(-5.71931 - 32.4358i) q^{42} +(-10.5466 + 59.8126i) q^{43} +(27.0291 + 9.83777i) q^{44} +(-0.208361 - 0.360892i) q^{45} +(-23.3046 - 13.4549i) q^{46} +(-48.6668 + 40.8363i) q^{47} +(6.24613 + 7.44385i) q^{48} +(-21.4536 + 37.1588i) q^{49} +(30.5965 - 17.6649i) q^{50} +(-4.10529 + 11.2792i) q^{51} +(-7.49063 - 1.32080i) q^{52} +(31.2537 - 5.51088i) q^{53} +(-39.0583 + 14.2161i) q^{54} +(1.48175 + 1.24333i) q^{55} -27.1156i q^{56} +(32.1106 + 33.1568i) q^{57} -52.4016 q^{58} +(54.6471 - 65.1259i) q^{59} +(0.223496 + 0.614051i) q^{60} +(-20.0147 - 113.509i) q^{61} +(7.44103 - 42.2002i) q^{62} +(27.9127 + 10.1594i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-0.442968 - 0.255748i) q^{65} +(37.8502 - 31.7601i) q^{66} +(42.6779 + 50.8615i) q^{67} +(-4.94092 + 8.55793i) q^{68} +(-40.0324 + 23.1127i) q^{69} +(0.623658 - 1.71349i) q^{70} +(56.2117 + 9.91164i) q^{71} +(-8.63054 + 1.52180i) q^{72} +(75.4032 - 27.4445i) q^{73} +(52.9279 + 44.4118i) q^{74} -60.6889i q^{75} +(21.2942 + 31.4731i) q^{76} -137.876 q^{77} +(-8.39853 + 10.0090i) q^{78} +(-35.2967 - 96.9769i) q^{79} +(0.0934190 + 0.529805i) q^{80} +(-7.55610 + 42.8528i) q^{81} +(-37.8329 - 13.7701i) q^{82} +(-40.5635 - 70.2580i) q^{83} +(-40.3385 - 23.2894i) q^{84} +(-0.509057 + 0.427150i) q^{85} +(55.2107 + 65.7976i) q^{86} +(-45.0073 + 77.9550i) q^{87} +(35.2282 - 20.3390i) q^{88} +(-42.3645 + 116.395i) q^{89} +(-0.580381 - 0.102337i) q^{90} +(35.9057 - 6.33114i) q^{91} +(-35.7612 + 13.0160i) q^{92} +(-56.3878 - 47.3150i) q^{93} +89.8450i q^{94} +(0.621741 + 2.47861i) q^{95} +13.7423 q^{96} +(6.38795 - 7.61286i) q^{97} +(20.7538 + 57.0206i) q^{98} +(7.73797 + 43.8842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9	$ 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25} + 48 q^{26} + 126 q^{27} + 72 q^{28} - 210 q^{29} - 108 q^{31} - 132 q^{33} - 24 q^{34} - 66 q^{35} - 12 q^{36} + 84 q^{38} + 120 q^{39} + 54 q^{41} + 72 q^{42} + 90 q^{43} - 48 q^{44} - 144 q^{45} - 360 q^{46} - 246 q^{47} - 48 q^{48} + 54 q^{49} - 432 q^{50} - 342 q^{51} + 36 q^{52} - 174 q^{53} - 42 q^{55} - 12 q^{57} + 48 q^{58} + 228 q^{59} + 132 q^{60} + 12 q^{61} + 204 q^{62} + 174 q^{63} + 96 q^{64} + 630 q^{65} + 696 q^{66} + 72 q^{67} - 48 q^{68} + 702 q^{69} + 528 q^{70} + 432 q^{71} + 96 q^{72} - 144 q^{74} + 72 q^{76} - 144 q^{77} - 708 q^{78} - 246 q^{79} - 642 q^{81} - 384 q^{82} - 126 q^{83} - 540 q^{84} - 684 q^{85} - 12 q^{86} - 324 q^{87} - 12 q^{89} - 336 q^{90} + 372 q^{91} - 132 q^{92} - 168 q^{93} - 570 q^{95} + 72 q^{97} + 384 q^{98} - 204 q^{99}+O(q^{100}) $ 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9 + 30 * q^11 - 36 * q^12 - 90 * q^13 - 48 * q^14 - 114 * q^15 + 18 * q^17 - 12 * q^19 + 24 * q^20 + 90 * q^21 + 84 * q^22 + 120 * q^23 - 24 * q^24 + 252 * q^25 + 48 * q^26 + 126 * q^27 + 72 * q^28 - 210 * q^29 - 108 * q^31 - 132 * q^33 - 24 * q^34 - 66 * q^35 - 12 * q^36 + 84 * q^38 + 120 * q^39 + 54 * q^41 + 72 * q^42 + 90 * q^43 - 48 * q^44 - 144 * q^45 - 360 * q^46 - 246 * q^47 - 48 * q^48 + 54 * q^49 - 432 * q^50 - 342 * q^51 + 36 * q^52 - 174 * q^53 - 42 * q^55 - 12 * q^57 + 48 * q^58 + 228 * q^59 + 132 * q^60 + 12 * q^61 + 204 * q^62 + 174 * q^63 + 96 * q^64 + 630 * q^65 + 696 * q^66 + 72 * q^67 - 48 * q^68 + 702 * q^69 + 528 * q^70 + 432 * q^71 + 96 * q^72 - 144 * q^74 + 72 * q^76 - 144 * q^77 - 708 * q^78 - 246 * q^79 - 642 * q^81 - 384 * q^82 - 126 * q^83 - 540 * q^84 - 684 * q^85 - 12 * q^86 - 324 * q^87 - 12 * q^89 - 336 * q^90 + 372 * q^91 - 132 * q^92 - 168 * q^93 - 570 * q^95 + 72 * q^97 + 384 * q^98 - 204 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.909039	−	1.08335i	0.454519	−	0.541675i
$2$	0.909039	−	1.08335i	0.454519	−	0.541675i
$3$	−0.830875	−	2.28281i	−0.276958	−	0.760936i	−0.997703	−	0.0677361i	$-0.978422\pi$
$3$	−0.830875	−	2.28281i	−0.276958	−	0.760936i	0.720745	−	0.693200i	$-0.243800\pi$
$4$	−0.347296	−	1.96962i	−0.0868241	−	0.492404i
$5$	0.0233547	−	0.132451i	0.00467095	−	0.0264903i	−0.982383	−	0.186878i	$-0.940163\pi$
$5$	0.0233547	−	0.132451i	0.00467095	−	0.0264903i	0.987054	+	0.160387i	$0.0512743\pi$
$6$	−3.22838	−	1.17503i	−0.538063	−	0.195839i
$7$	4.79341	+	8.30244i	0.684774	+	1.18606i	0.973508	+	0.228653i	$0.0734322\pi$
$7$	4.79341	+	8.30244i	0.684774	+	1.18606i	−0.288734	+	0.957409i	$0.593234\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$	2.37354	−	1.99163i	0.263726	−	0.221293i
$10$	−0.122261	−	0.145705i	−0.0122261	−	0.0145705i
$11$	−7.19093	+	12.4551i	−0.653721	+	1.13228i	0.328492	+	0.944507i	$0.393460\pi$
$11$	−7.19093	+	12.4551i	−0.653721	+	1.13228i	−0.982213	+	0.187771i	$0.939874\pi$
$12$	−4.20770	+	2.42931i	−0.350641	+	0.202443i
$13$	1.30073	−	3.57374i	0.100056	−	0.274903i	−0.879557	−	0.475793i	$-0.842161\pi$
$13$	1.30073	−	3.57374i	0.100056	−	0.274903i	0.979614	+	0.200890i	$0.0643834\pi$
$14$	13.3518	+	2.35429i	0.953704	+	0.168164i
$15$	−0.321766	+	0.0567360i	−0.0214511	+	0.00378240i
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	−3.78497	−	3.17596i	−0.222645	−	0.186821i	0.524642	−	0.851323i	$-0.324199\pi$
$17$	−3.78497	−	3.17596i	−0.222645	−	0.186821i	−0.747287	+	0.664502i	$0.768644\pi$
$18$		−	4.38184i		−	0.243436i
$19$	−17.3463	+	7.75273i	−0.912965	+	0.408039i
$19$	−17.3463	+	7.75273i	−0.912965	+	0.408039i
$20$	−0.268989			−0.0134495
$21$	14.9702	−	17.8407i	0.712864	−	0.849559i
$22$	6.95635	+	19.1124i	0.316198	+	0.868747i
$23$	−3.30421	−	18.7391i	−0.143661	−	0.814743i	−0.968432	−	0.249276i	$-0.919807\pi$
$23$	−3.30421	−	18.7391i	−0.143661	−	0.814743i	0.824771	−	0.565466i	$-0.191304\pi$
$24$	−1.19316	+	6.76675i	−0.0497150	+	0.281948i
$25$	23.4753	+	8.54432i	0.939013	+	0.341773i
$26$	−2.68919	−	4.65782i	−0.103430	−	0.179147i
$27$	−25.4533	−	14.6954i	−0.942713	−	0.544276i
$28$	14.6879	−	12.3246i	0.524567	−	0.440164i
$29$	−23.8175	−	28.3846i	−0.821295	−	0.978781i	0.178692	−	0.983905i	$-0.442813\pi$
$29$	−23.8175	−	28.3846i	−0.821295	−	0.978781i	−0.999987	+	0.00512403i	$0.998369\pi$
$30$	−0.231033	+	0.400160i	−0.00770109	+	0.0133387i
$31$	26.2409	−	15.1502i	0.846480	−	0.488715i	−0.0129817	−	0.999916i	$-0.504132\pi$
$31$	26.2409	−	15.1502i	0.846480	−	0.488715i	0.859462	+	0.511200i	$0.170799\pi$
$32$	−1.93476	+	5.31570i	−0.0604612	+	0.166116i
$33$	34.4073	+	6.06693i	1.04264	+	0.183846i
$34$	−6.88136	+	1.21337i	−0.202393	+	0.0356873i
$35$	1.21162	−	0.440993i	0.0346176	−	0.0125998i
$36$	−4.74707	−	3.98327i	−0.131863	−	0.110646i
$37$			48.8558i			1.32043i	0.751078	+	0.660213i	$0.229534\pi$
$37$			48.8558i			1.32043i	−0.751078	+	0.660213i	$0.770466\pi$
$38$	−7.36956	+	25.8397i	−0.193936	+	0.679992i
$39$	−9.23891			−0.236895
$40$	−0.244522	+	0.291410i	−0.00611304	+	0.00728524i
$41$	−9.73690	−	26.7519i	−0.237485	−	0.652485i	−0.999985	−	0.00549680i	$-0.998250\pi$
$41$	−9.73690	−	26.7519i	−0.237485	−	0.652485i	0.762500	−	0.646989i	$-0.223972\pi$
$42$	−5.71931	−	32.4358i	−0.136174	−	0.772282i
$43$	−10.5466	+	59.8126i	−0.245269	+	1.39099i	0.574598	+	0.818436i	$0.305159\pi$
$43$	−10.5466	+	59.8126i	−0.245269	+	1.39099i	−0.819867	+	0.572554i	$0.805953\pi$
$44$	27.0291	+	9.83777i	0.614297	+	0.223586i
$45$	−0.208361	−	0.360892i	−0.00463025	−	0.00801982i
$46$	−23.3046	−	13.4549i	−0.506623	−	0.292499i
$47$	−48.6668	+	40.8363i	−1.03546	+	0.868857i	−0.991491	−	0.130175i	$-0.958446\pi$
$47$	−48.6668	+	40.8363i	−1.03546	+	0.868857i	−0.0439729	+	0.999033i	$0.514002\pi$
$48$	6.24613	+	7.44385i	0.130128	+	0.155080i
$49$	−21.4536	+	37.1588i	−0.437830	+	0.758343i
$50$	30.5965	−	17.6649i	0.611929	−	0.353298i
$51$	−4.10529	+	11.2792i	−0.0804958	+	0.221160i
$52$	−7.49063	−	1.32080i	−0.144051	−	0.0254000i
$53$	31.2537	−	5.51088i	0.589693	−	0.103979i	0.129164	−	0.991623i	$-0.458771\pi$
$53$	31.2537	−	5.51088i	0.589693	−	0.103979i	0.460529	+	0.887644i	$0.347660\pi$
$54$	−39.0583	+	14.2161i	−0.723302	+	0.263261i
$55$	1.48175	+	1.24333i	0.0269408	+	0.0226060i
$56$		−	27.1156i		−	0.484208i
$57$	32.1106	+	33.1568i	0.563344	+	0.581698i
$58$	−52.4016			−0.903476
$59$	54.6471	−	65.1259i	0.926223	−	1.10383i	−0.0681272	−	0.997677i	$-0.521702\pi$
$59$	54.6471	−	65.1259i	0.926223	−	1.10383i	0.994350	−	0.106153i	$-0.0338532\pi$
$60$	0.223496	+	0.614051i	0.00372494	+	0.0102342i
$61$	−20.0147	−	113.509i	−0.328110	−	1.86080i	−0.486856	−	0.873482i	$-0.661856\pi$
$61$	−20.0147	−	113.509i	−0.328110	−	1.86080i	0.158746	−	0.987319i	$-0.449255\pi$
$62$	7.44103	−	42.2002i	0.120017	−	0.680648i
$63$	27.9127	+	10.1594i	0.443059	+	0.161260i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−0.442968	−	0.255748i	−0.00681489	−	0.00393458i
$66$	37.8502	−	31.7601i	0.573487	−	0.481213i
$67$	42.6779	+	50.8615i	0.636984	+	0.759127i	0.983891	−	0.178772i	$-0.0572125\pi$
$67$	42.6779	+	50.8615i	0.636984	+	0.759127i	−0.346907	+	0.937900i	$0.612768\pi$
$68$	−4.94092	+	8.55793i	−0.0726606	+	0.125852i
$69$	−40.0324	+	23.1127i	−0.580179	+	0.334967i
$70$	0.623658	−	1.71349i	0.00890940	−	0.0244784i
$71$	56.2117	+	9.91164i	0.791714	+	0.139601i	0.554859	−	0.831945i	$-0.312772\pi$
$71$	56.2117	+	9.91164i	0.791714	+	0.139601i	0.236855	+	0.971545i	$0.423883\pi$
$72$	−8.63054	+	1.52180i	−0.119869	+	0.0211361i
$73$	75.4032	−	27.4445i	1.03292	−	0.375952i	0.230728	−	0.973018i	$-0.425889\pi$
$73$	75.4032	−	27.4445i	1.03292	−	0.375952i	0.802192	+	0.597066i	$0.203667\pi$
$74$	52.9279	+	44.4118i	0.715243	+	0.600160i
$75$		−	60.6889i		−	0.809186i
$76$	21.2942	+	31.4731i	0.280187	+	0.414120i
$77$	−137.876			−1.79060
$78$	−8.39853	+	10.0090i	−0.107673	+	0.128320i
$79$	−35.2967	−	96.9769i	−0.446794	−	1.22756i	−0.934944	−	0.354796i	$-0.884550\pi$
$79$	−35.2967	−	96.9769i	−0.446794	−	1.22756i	0.488150	−	0.872760i	$-0.337672\pi$
$80$	0.0934190	+	0.529805i	0.00116774	+	0.00662256i
$81$	−7.55610	+	42.8528i	−0.0932852	+	0.529047i
$82$	−37.8329	−	13.7701i	−0.461377	−	0.167927i
$83$	−40.5635	−	70.2580i	−0.488717	−	0.846482i	0.511199	−	0.859462i	$-0.329202\pi$
$83$	−40.5635	−	70.2580i	−0.488717	−	0.846482i	−0.999916	+	0.0129800i	$0.995868\pi$
$84$	−40.3385	−	23.2894i	−0.480220	−	0.277255i
$85$	−0.509057	+	0.427150i	−0.00598891	+	0.00502529i
$86$	55.2107	+	65.7976i	0.641985	+	0.765088i
$87$	−45.0073	+	77.9550i	−0.517326	+	0.896034i
$88$	35.2282	−	20.3390i	0.400321	−	0.231125i
$89$	−42.3645	+	116.395i	−0.476005	+	1.30781i	0.436852	+	0.899534i	$0.356093\pi$
$89$	−42.3645	+	116.395i	−0.476005	+	1.30781i	−0.912857	+	0.408280i	$0.866129\pi$
$90$	−0.580381	−	0.102337i	−0.00644867	−	0.00113708i
$91$	35.9057	−	6.33114i	0.394568	−	0.0695730i
$92$	−35.7612	+	13.0160i	−0.388709	+	0.141479i
$93$	−56.3878	−	47.3150i	−0.606321	−	0.508764i
$94$			89.8450i			0.955798i
$95$	0.621741	+	2.47861i	0.00654464	+	0.0260906i
$96$	13.7423			0.143149
$97$	6.38795	−	7.61286i	0.0658551	−	0.0784831i	−0.732111	−	0.681185i	$-0.761465\pi$
$97$	6.38795	−	7.61286i	0.0658551	−	0.0784831i	0.797966	+	0.602702i	$0.205909\pi$
$98$	20.7538	+	57.0206i	0.211774	+	0.581843i
$99$	7.73797	+	43.8842i	0.0781613	+	0.443275i
$100$	8.67613	−	49.2048i	0.0867613	−	0.492048i
$101$	41.7514	+	15.1963i	0.413380	+	0.150458i	0.540334	−	0.841450i	$-0.318298\pi$
$101$	41.7514	+	15.1963i	0.413380	+	0.150458i	−0.126954	+	0.991909i	$0.540520\pi$
$102$	8.48744	+	14.7007i	0.0832102	+	0.144124i
$103$	3.02385	+	1.74582i	0.0293578	+	0.0169497i	0.514607	−	0.857426i	$-0.327938\pi$
$103$	3.02385	+	1.74582i	0.0293578	+	0.0169497i	−0.485249	+	0.874376i	$0.661271\pi$
$104$	−8.24016	+	6.91432i	−0.0792323	+	0.0664838i
$105$	−2.01340	−	2.39948i	−0.0191753	−	0.0228522i
$106$	22.4407	−	38.8684i	0.211704	−	0.366683i
$107$	76.1518	−	43.9663i	0.711699	−	0.410900i	−0.0999905	−	0.994988i	$-0.531881\pi$
$107$	76.1518	−	43.9663i	0.711699	−	0.410900i	0.811690	+	0.584089i	$0.198548\pi$
$108$	−20.1046	+	55.2368i	−0.186153	+	0.511452i
$109$	−46.7484	−	8.24300i	−0.428884	−	0.0756239i	−0.0449607	−	0.998989i	$-0.514316\pi$
$109$	−46.7484	−	8.24300i	−0.428884	−	0.0756239i	−0.383923	+	0.923365i	$0.625427\pi$
$110$	2.69393	−	0.475012i	0.0244903	−	0.00431830i
$111$	111.528	−	40.5930i	1.00476	−	0.365703i
$112$	−29.3757	−	24.6492i	−0.262283	−	0.220082i
$113$			131.681i			1.16532i	0.812718	+	0.582658i	$0.197987\pi$
$113$			131.681i			1.16532i	−0.812718	+	0.582658i	$0.802013\pi$
$114$	65.1103	−	4.64624i	0.571143	−	0.0407565i
$115$	−2.55918			−0.0222538
$116$	−47.6351	+	56.7693i	−0.410647	+	0.489391i
$117$	−4.03023	−	11.0730i	−0.0344464	−	0.0946408i
$118$	−20.8778	−	118.404i	−0.176931	−	1.00342i
$119$	8.22533	−	46.6481i	0.0691204	−	0.392001i
$120$	0.868399	+	0.316071i	0.00723666	+	0.00263393i
$121$	−42.9189	−	74.3378i	−0.354702	−	0.614362i
$122$	−141.164	−	81.5011i	−1.15708	−	0.668042i
$123$	−52.9794	+	44.4550i	−0.430726	+	0.361422i
$124$	−38.9534	−	46.4228i	−0.314140	−	0.374378i
$125$	3.36115	−	5.82168i	0.0268892	−	0.0465734i
$126$	36.3800	−	21.0040i	0.288730	−	0.166698i
$127$	25.8542	−	71.0338i	0.203576	−	0.559321i	−0.795325	−	0.606183i	$-0.792700\pi$
$127$	25.8542	−	71.0338i	0.203576	−	0.559321i	0.998901	+	0.0468619i	$0.0149221\pi$
$128$	11.1418	+	1.96460i	0.0870455	+	0.0153485i
$129$	145.304	−	25.6209i	1.12638	−	0.198612i
$130$	−0.679739	+	0.247405i	−0.00522876	+	0.00190311i
$131$	−64.0748	−	53.7651i	−0.489120	−	0.410421i	0.364591	−	0.931168i	$-0.381209\pi$
$131$	−64.0748	−	53.7651i	−0.489120	−	0.410421i	−0.853711	+	0.520747i	$0.825653\pi$
$132$		−	69.8761i		−	0.529365i
$133$	−147.515	−	106.855i	−1.10913	−	0.803419i
$134$	93.8967			0.700722
$135$	−2.54089	+	3.02811i	−0.0188214	+	0.0224304i
$136$	4.77974	+	13.1322i	0.0351452	+	0.0965606i
$137$	41.9319	+	237.807i	0.306072	+	1.73582i	0.618416	+	0.785851i	$0.287775\pi$
$137$	41.9319	+	237.807i	0.306072	+	1.73582i	−0.312344	+	0.949969i	$0.601114\pi$
$138$	−11.3518	+	64.3794i	−0.0822596	+	0.466518i
$139$	9.82739	+	3.57688i	0.0707006	+	0.0257329i	0.377128	−	0.926161i	$-0.376912\pi$
$139$	9.82739	+	3.57688i	0.0707006	+	0.0257329i	−0.306428	+	0.951894i	$0.599134\pi$
$140$	−1.28938	−	2.23327i	−0.00920983	−	0.0159519i
$141$	133.657	+	77.1672i	0.947925	+	0.547285i
$142$	61.8364	−	51.8869i	0.435468	−	0.365401i
$143$	35.1576	+	41.8992i	0.245857	+	0.293001i
$144$	−6.19686	+	10.7333i	−0.0430338	+	0.0745367i
$145$	−4.31584	+	2.49175i	−0.0297644	+	0.0171845i
$146$	38.8124	−	106.636i	0.265838	−	0.730385i
$147$	102.652	+	18.1003i	0.698311	+	0.123131i
$148$	96.2271	−	16.9674i	0.650183	−	0.114645i
$149$	−132.450	+	48.2077i	−0.888923	+	0.323542i	−0.745805	−	0.666164i	$-0.767935\pi$
$149$	−132.450	+	48.2077i	−0.888923	+	0.323542i	−0.143118	+	0.989706i	$0.545713\pi$
$150$	−65.7474	−	55.1686i	−0.438316	−	0.367791i
$151$		−	13.1372i		−	0.0870011i	−0.999053	−	0.0435005i	$-0.986149\pi$
$151$		−	13.1372i		−	0.0870011i	0.999053	−	0.0435005i	$-0.0138510\pi$
$152$	53.4537	+	5.54117i	0.351669	+	0.0364551i
$153$	−15.3091			−0.100059
$154$	−125.335	+	149.368i	−0.813864	+	0.969925i
$155$	−1.39381	−	3.82947i	−0.00899233	−	0.0247062i
$156$	3.20864	+	18.1971i	0.0205682	+	0.116648i
$157$	−6.46656	+	36.6737i	−0.0411883	+	0.233590i	−0.998452	−	0.0556275i	$-0.982284\pi$
$157$	−6.46656	+	36.6737i	−0.0411883	+	0.233590i	0.957263	+	0.289218i	$0.0933952\pi$
$158$	−137.146	−	49.9171i	−0.868013	−	0.315931i
$159$	−38.5482	−	66.7675i	−0.242442	−	0.419921i
$160$	0.658886	+	0.380408i	0.00411804	+	0.00237755i
$161$	139.742	−	117.257i	0.867960	−	0.728305i
$162$	39.5558	+	47.1408i	0.244172	+	0.290992i
$163$	−43.4716	+	75.2951i	−0.266697	+	0.461933i	−0.968007	−	0.250924i	$-0.919266\pi$
$163$	−43.4716	+	75.2951i	−0.266697	+	0.461933i	0.701310	+	0.712857i	$0.252599\pi$
$164$	−49.3094	+	28.4688i	−0.300667	+	0.173590i
$165$	1.60715	−	4.41560i	0.00974028	−	0.0267612i
$166$	−112.988	−	19.9228i	−0.680650	−	0.120017i
$167$	−221.559	+	39.0668i	−1.32670	+	0.233933i	−0.791696	−	0.610916i	$-0.790801\pi$
$167$	−221.559	+	39.0668i	−1.32670	+	0.233933i	−0.535005	+	0.844849i	$0.679690\pi$
$168$	−61.8998	+	22.5297i	−0.368451	+	0.134105i
$169$	118.382	+	99.3341i	0.700484	+	0.587776i
$170$			0.939783i			0.00552814i
$171$	−25.7315	+	52.9489i	−0.150477	+	0.309643i
$172$	121.471			0.706224
$173$	100.248	−	119.471i	0.579467	−	0.690582i	−0.394078	−	0.919077i	$-0.628936\pi$
$173$	100.248	−	119.471i	0.579467	−	0.690582i	0.973545	+	0.228495i	$0.0733805\pi$
$174$	43.5392	+	119.623i	0.250225	+	0.687488i
$175$	41.5883	+	235.859i	0.237647	+	1.34776i
$176$	9.98953	−	56.6535i	0.0567587	−	0.321895i
$177$	−194.075	−	70.6375i	−1.09647	−	0.399082i
$178$	87.5861	+	151.704i	0.492057	+	0.852267i
$179$	98.1132	+	56.6457i	0.548119	+	0.316456i	0.748363	−	0.663290i	$-0.230840\pi$
$179$	98.1132	+	56.6457i	0.548119	+	0.316456i	−0.200244	+	0.979746i	$0.564174\pi$
$180$	−0.638455	+	0.535728i	−0.00354697	+	0.00297626i
$181$	−123.719	−	147.443i	−0.683530	−	0.814600i	0.307027	−	0.951701i	$-0.400666\pi$
$181$	−123.719	−	147.443i	−0.683530	−	0.814600i	−0.990557	+	0.137101i	$0.956221\pi$
$182$	25.7808	−	44.6537i	0.141653	−	0.245350i
$183$	−242.489	+	140.001i	−1.32508	+	0.765035i
$184$	−18.4074	+	50.5740i	−0.100040	+	0.274859i
$185$	6.47101	+	1.14101i	0.0349784	+	0.00616764i
$186$	−102.517	+	18.0766i	−0.551169	+	0.0971860i
$187$	66.7742	−	24.3038i	0.357081	−	0.129967i
$188$	97.3336	+	81.6726i	0.517732	+	0.434429i
$189$		−	281.765i		−	1.49082i
$190$	3.25039	+	1.57959i	0.0171073	+	0.00831362i
$191$	28.7434			0.150489			0.0752444	−	0.997165i	$-0.476026\pi$
$191$	28.7434			0.150489			0.0752444	+	0.997165i	$0.476026\pi$
$192$	12.4923	−	14.8877i	0.0650639	−	0.0775401i
$193$	−57.6520	−	158.397i	−0.298715	−	0.820712i	−0.994715	−	0.102671i	$-0.967261\pi$
$193$	−57.6520	−	158.397i	−0.298715	−	0.820712i	0.696000	−	0.718041i	$-0.254961\pi$
$194$	−2.44050	−	13.8408i	−0.0125799	−	0.0713442i
$195$	−0.215772	+	1.22371i	−0.00110652	+	0.00627541i
$196$	80.6393	+	29.3503i	0.411425	+	0.149747i
$197$	137.145	+	237.541i	0.696165	+	1.20579i	0.969786	+	0.243956i	$0.0784452\pi$
$197$	137.145	+	237.541i	0.696165	+	1.20579i	−0.273621	+	0.961838i	$0.588221\pi$
$198$	54.5761	+	31.5095i	0.275637	+	0.159139i
$199$	−20.8845	+	17.5242i	−0.104947	+	0.0880612i	−0.693751	−	0.720215i	$-0.744043\pi$
$199$	−20.8845	+	17.5242i	−0.104947	+	0.0880612i	0.588804	+	0.808276i	$0.299599\pi$
$200$	−45.4191	−	54.1283i	−0.227095	−	0.270642i
$201$	80.6472	−	139.685i	0.401230	−	0.694950i
$202$	54.4166	−	31.4174i	0.269389	−	0.155532i
$203$	121.494	−	333.803i	0.598495	−	1.64435i
$204$	23.6414	+	4.16862i	0.115889	+	0.0204344i
$205$	−3.77073	+	0.664881i	−0.0183938	+	0.00324332i
$206$	4.64013	−	1.68887i	0.0225249	−	0.00819840i
$207$	−45.1640	−	37.8971i	−0.218184	−	0.183078i
$208$			15.2124i			0.0731364i
$209$	28.1755	−	271.799i	0.134811	−	1.30047i
$210$	−4.42974			−0.0210940
$211$	−128.748	+	153.436i	−0.610180	+	0.727184i	−0.979349	−	0.202178i	$-0.935198\pi$
$211$	−128.748	+	153.436i	−0.610180	+	0.727184i	0.369169	+	0.929362i	$0.379642\pi$
$212$	−21.7086	−	59.6440i	−0.102399	−	0.281339i
$213$	−24.0785	−	136.556i	−0.113045	−	0.641107i
$214$	21.5941	−	122.466i	0.100907	−	0.572272i
$215$	7.67594	+	2.79381i	0.0357021	+	0.0129945i
$216$	41.5650	+	71.9927i	0.192431	+	0.333300i
$217$	251.567	+	145.242i	1.15929	+	0.669319i
$218$	−51.4262	+	43.1517i	−0.235900	+	0.197943i
$219$	−125.301	−	149.328i	−0.572151	−	0.681863i
$220$	1.93428	−	3.35027i	0.00879219	−	0.0152285i
$221$	−16.2733	+	9.39539i	−0.0736348	+	0.0425131i
$222$	57.4072	−	157.725i	0.258591	−	0.710473i
$223$	−228.354	−	40.2649i	−1.02401	−	0.180560i	−0.363669	−	0.931528i	$-0.618476\pi$
$223$	−228.354	−	40.2649i	−1.02401	−	0.180560i	−0.660339	+	0.750968i	$0.729587\pi$
$224$	−53.4074	+	9.41717i	−0.238426	+	0.0420409i
$225$	72.7366	−	26.4740i	0.323274	−	0.117662i
$226$	142.656	+	119.703i	0.631223	+	0.529659i
$227$			3.92632i			0.0172966i	0.999963	+	0.00864828i	$0.00275287\pi$
$227$			3.92632i			0.0172966i	−0.999963	+	0.00864828i	$0.997247\pi$
$228$	54.1543	−	74.7608i	0.237519	−	0.327898i
$229$	314.593			1.37377			0.686885	−	0.726766i	$-0.258978\pi$
$229$	314.593			1.37377			0.686885	+	0.726766i	$0.258978\pi$
$230$	−2.32640	+	2.77249i	−0.0101148	+	0.0120543i
$231$	114.558	+	314.746i	0.495922	+	1.36253i
$232$	18.1989	+	103.211i	0.0784435	+	0.444875i
$233$	−17.9777	+	101.956i	−0.0771574	+	0.437581i	0.921618	+	0.388099i	$0.126868\pi$
$233$	−17.9777	+	101.956i	−0.0771574	+	0.437581i	−0.998775	+	0.0494821i	$0.984243\pi$
$234$	−15.6596	−	5.69961i	−0.0669212	−	0.0243573i
$235$	4.27222	+	7.39970i	0.0181797	+	0.0314881i
$236$	−147.252	−	85.0159i	−0.623948	−	0.360237i
$237$	−192.053	+	161.151i	−0.810348	+	0.679963i
$238$	−43.0591	−	51.3159i	−0.180921	−	0.215613i
$239$	187.040	−	323.964i	0.782596	−	1.35550i	−0.147829	−	0.989013i	$-0.547228\pi$
$239$	187.040	−	323.964i	0.782596	−	1.35550i	0.930425	−	0.366483i	$-0.119438\pi$
$240$	1.13182	−	0.653459i	0.00471594	−	0.00272275i
$241$	−121.209	+	333.019i	−0.502941	+	1.38182i	0.385448	+	0.922729i	$0.374047\pi$
$241$	−121.209	+	333.019i	−0.502941	+	1.38182i	−0.888390	+	0.459090i	$0.848175\pi$
$242$	−119.549	−	21.0797i	−0.494004	−	0.0871062i
$243$	−156.397	+	27.5769i	−0.643607	+	0.113485i
$244$	−216.618	+	78.8425i	−0.887778	+	0.323125i
$245$	4.42069	+	3.70940i	0.0180436	+	0.0151404i
$246$			97.8065i			0.397587i
$247$	5.14327	+	72.0755i	0.0208230	+	0.291803i
$248$	−85.7023			−0.345574
$249$	−126.683	+	150.974i	−0.508765	+	0.606323i
$250$	−3.25150	−	8.93343i	−0.0130060	−	0.0357337i
$251$	28.5340	+	161.824i	0.113681	+	0.644718i	0.987395	+	0.158277i	$0.0505939\pi$
$251$	28.5340	+	161.824i	0.113681	+	0.644718i	−0.873714	+	0.486441i	$0.838295\pi$
$252$	10.3161	−	58.5057i	0.0409370	−	0.232165i
$253$	257.157	+	93.5974i	1.01643	+	0.369950i
$254$	−53.4520	−	92.5816i	−0.210441	−	0.364495i
$255$	1.39806	+	0.807173i	0.00548260	+	0.00316538i
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	25.2860	+	30.1347i	0.0983891	+	0.117256i	0.812992	−	0.582275i	$-0.197837\pi$
$257$	25.2860	+	30.1347i	0.0983891	+	0.117256i	−0.714603	+	0.699530i	$0.753393\pi$
$258$	104.330	−	180.705i	0.404380	−	0.700408i
$259$	−405.622	+	234.186i	−1.56611	+	0.904193i
$260$	−0.349883	+	0.961297i	−0.00134571	+	0.00369729i
$261$	−113.064	−	19.9362i	−0.433194	−	0.0763838i
$262$	−116.493	+	20.5408i	−0.444629	+	0.0784002i
$263$	141.620	−	51.5455i	0.538480	−	0.195991i	−0.0584410	−	0.998291i	$-0.518613\pi$
$263$	141.620	−	51.5455i	0.538480	−	0.195991i	0.596921	+	0.802300i	$0.296391\pi$
$264$	−75.7003	−	63.5201i	−0.286744	−	0.240607i
$265$		−	4.26830i		−	0.0161068i
$266$	−249.858	+	62.6750i	−0.939315	+	0.235620i
$267$	300.908			1.12700
$268$	85.3558	−	101.723i	0.318492	−	0.379564i
$269$	74.2330	+	203.953i	0.275959	+	0.758191i	0.997810	+	0.0661428i	$0.0210693\pi$
$269$	74.2330	+	203.953i	0.275959	+	0.758191i	−0.721851	+	0.692048i	$0.756708\pi$
$270$	0.970740	+	5.50534i	0.00359533	+	0.0203901i
$271$	28.7438	−	163.014i	0.106066	−	0.601529i	−0.884723	−	0.466116i	$-0.845653\pi$
$271$	28.7438	−	163.014i	0.106066	−	0.601529i	0.990789	−	0.135413i	$-0.0432361\pi$
$272$	18.5718	+	6.75958i	0.0682786	+	0.0248514i
$273$	−44.2859	−	76.7054i	−0.162219	−	0.280972i
$274$	295.746	+	170.749i	1.07937	+	0.623173i
$275$	−275.229	+	230.945i	−1.00083	+	0.839799i
$276$	59.4262	+	70.8214i	0.215312	+	0.256599i
$277$	130.985	−	226.872i	0.472869	−	0.819033i	−0.526649	−	0.850083i	$-0.676552\pi$
$277$	130.985	−	226.872i	0.472869	−	0.819033i	0.999518	+	0.0310501i	$0.00988513\pi$
$278$	12.8085	−	7.39498i	0.0460737	−	0.0266007i
$279$	32.1101	−	88.2217i	0.115090	−	0.316207i
$280$	−3.59150	−	0.633279i	−0.0128268	−	0.00226171i
$281$	−356.267	+	62.8195i	−1.26785	+	0.223557i	−0.766815	−	0.641868i	$-0.778160\pi$
$281$	−356.267	+	62.8195i	−1.26785	+	0.223557i	−0.501039	+	0.865425i	$0.667049\pi$
$282$	205.099	−	74.6499i	0.727301	−	0.264716i
$283$	183.794	+	154.222i	0.649449	+	0.544953i	0.906904	−	0.421338i	$-0.138439\pi$
$283$	183.794	+	154.222i	0.649449	+	0.544953i	−0.257454	+	0.966290i	$0.582884\pi$
$284$		−	114.158i		−	0.401964i
$285$	5.14160	−	3.47873i	0.0180407	−	0.0122061i
$286$	77.3512			0.270459
$287$	175.433	−	209.073i	0.611265	−	0.728477i
$288$	5.99471	+	16.4703i	0.0208150	+	0.0571887i
$289$	−45.9451	−	260.568i	−0.158980	−	0.901618i
$290$	−1.22383	+	6.94066i	−0.00422009	+	0.0239333i
$291$	−22.6863	−	8.25713i	−0.0779597	−	0.0283750i
$292$	−80.2424	−	138.984i	−0.274803	−	0.475972i
$293$	247.800	+	143.067i	0.845734	+	0.488285i	0.859209	−	0.511624i	$-0.170956\pi$
$293$	247.800	+	143.067i	0.845734	+	0.488285i	−0.0134750	+	0.999909i	$0.504289\pi$
$294$	112.923	−	94.7540i	0.384093	−	0.322292i
$295$	−7.34974	−	8.75908i	−0.0249144	−	0.0296918i
$296$	69.0925	−	119.672i	0.233421	−	0.404297i
$297$	366.065	−	211.348i	1.23254	−	0.711609i
$298$	−68.1760	+	187.312i	−0.228778	+	0.628564i
$299$	−71.2664	−	12.5662i	−0.238349	−	0.0420274i
$300$	−119.534	+	21.0770i	−0.398446	+	0.0702568i
$301$	−547.144	+	199.144i	−1.81776	+	0.661609i
$302$	−14.2322	−	11.9422i	−0.0471263	−	0.0395437i
$303$		−	107.937i		−	0.356227i
$304$	54.5945	−	52.8719i	0.179587	−	0.173921i
$305$	−15.5018			−0.0508257
$306$	−13.9166	+	16.5851i	−0.0454790	+	0.0541997i
$307$	−55.0330	−	151.202i	−0.179261	−	0.492514i	0.817221	−	0.576324i	$-0.195513\pi$
$307$	−55.0330	−	151.202i	−0.179261	−	0.492514i	−0.996482	+	0.0838098i	$0.973291\pi$
$308$	47.8840	+	271.564i	0.155467	+	0.881700i
$309$	1.47294	−	8.35343i	0.00476678	−	0.0270338i
$310$	−5.41568	−	1.97115i	−0.0174699	−	0.00635854i
$311$	−19.8317	−	34.3495i	−0.0637676	−	0.110449i	0.832379	−	0.554207i	$-0.186978\pi$
$311$	−19.8317	−	34.3495i	−0.0637676	−	0.110449i	−0.896147	+	0.443758i	$0.853645\pi$
$312$	22.6306	+	13.0658i	0.0725340	+	0.0418775i
$313$	277.958	−	233.235i	0.888046	−	0.745159i	−0.0797714	−	0.996813i	$-0.525419\pi$
$313$	277.958	−	233.235i	0.888046	−	0.745159i	0.967817	+	0.251654i	$0.0809746\pi$
$314$	33.8521	+	40.3433i	0.107809	+	0.128482i
$315$	1.99752	−	3.45981i	0.00634134	−	0.0109835i
$316$	−178.749	+	103.201i	−0.565660	+	0.326584i
$317$	55.1222	−	151.447i	0.173887	−	0.477751i	−0.821880	−	0.569660i	$-0.807075\pi$
$317$	55.1222	−	151.447i	0.173887	−	0.477751i	0.995767	+	0.0919094i	$0.0292970\pi$
$318$	−107.374	−	18.9330i	−0.337655	−	0.0595378i
$319$	524.803	−	92.5369i	1.64515	−	0.290084i
$320$	1.01107	−	0.367999i	0.00315959	−	0.00115000i
$321$	−163.639	−	137.310i	−0.509780	−	0.427756i
$322$		−	257.980i		−	0.801182i
$323$	90.2776	+	25.7475i	0.279497	+	0.0797135i
$324$	87.0277			0.268604
$325$	61.0703	−	72.7807i	0.187909	−	0.223941i
$326$	42.0535	+	115.541i	0.128999	+	0.354421i
$327$	20.0248	+	113.567i	0.0612380	+	0.347298i
$328$	−13.9825	+	79.2986i	−0.0426295	+	0.241764i
$329$	−572.321	−	208.308i	−1.73958	−	0.633154i
$330$	−3.32268	−	5.75505i	−0.0100687	−	0.0174395i
$331$	−483.559	−	279.183i	−1.46090	−	0.843452i	−0.461849	−	0.886958i	$-0.652814\pi$
$331$	−483.559	−	279.183i	−1.46090	−	0.843452i	−0.999053	+	0.0435059i	$0.986147\pi$
$332$	−124.294	+	104.295i	−0.374379	+	0.314141i
$333$	97.3028	+	115.961i	0.292201	+	0.348231i
$334$	−159.083	+	275.539i	−0.476296	+	0.824968i
$335$	7.73341	−	4.46488i	0.0230848	−	0.0133280i
$336$	−31.8618	+	87.5396i	−0.0948268	+	0.260535i
$337$	−476.416	−	84.0050i	−1.41370	−	0.249273i	−0.585938	−	0.810356i	$-0.699274\pi$
$337$	−476.416	−	84.0050i	−1.41370	−	0.249273i	−0.827759	+	0.561083i	$0.810385\pi$
$338$	215.227	−	37.9504i	0.636767	−	0.112279i
$339$	300.602	−	109.410i	0.886731	−	0.322744i
$340$	1.01811	+	0.854300i	0.00299445	+	0.00251265i
$341$			435.775i			1.27793i
$342$	33.9713	+	76.0089i	0.0993311	+	0.222248i
$343$	58.4097			0.170291
$344$	110.421	−	131.595i	0.320993	−	0.382544i
$345$	2.12636	+	5.84213i	0.00616337	+	0.0169337i
$346$	−38.2995	−	217.207i	−0.110692	−	0.627766i
$347$	73.2119	−	415.205i	0.210985	−	1.19656i	−0.676754	−	0.736210i	$-0.736614\pi$
$347$	73.2119	−	415.205i	0.210985	−	1.19656i	0.887739	−	0.460347i	$-0.152275\pi$
$348$	169.172	+	61.5737i	0.486127	+	0.176936i
$349$	214.757	+	371.970i	0.615350	+	1.06582i	0.990323	+	0.138782i	$0.0443186\pi$
$349$	214.757	+	371.970i	0.615350	+	1.06582i	−0.374973	+	0.927036i	$0.622348\pi$
$350$	293.323	+	169.350i	0.838066	+	0.483858i
$351$	−85.6256	+	71.8484i	−0.243948	+	0.204696i
$352$	−52.2947	−	62.3224i	−0.148564	−	0.177052i
$353$	−253.397	+	438.896i	−0.717837	+	1.24333i	0.244018	+	0.969771i	$0.421535\pi$
$353$	−253.397	+	438.896i	−0.717837	+	1.24333i	−0.961855	+	0.273560i	$0.911799\pi$
$354$	−252.947	+	146.039i	−0.714539	+	0.412539i
$355$	2.62562	−	7.21383i	0.00739611	−	0.0203206i
$356$	243.967	+	43.0180i	0.685301	+	0.120837i
$357$	−113.323	+	19.9819i	−0.317431	+	0.0559717i
$358$	150.556	−	54.7979i	0.420547	−	0.153067i
$359$	233.736	+	196.127i	0.651074	+	0.546316i	0.907397	−	0.420275i	$-0.138067\pi$
$359$	233.736	+	196.127i	0.651074	+	0.546316i	−0.256323	+	0.966591i	$0.582511\pi$
$360$			1.17867i			0.00327408i
$361$	240.790	−	268.963i	0.667009	−	0.745050i
$362$	−272.197			−0.751926
$363$	−134.039	+	159.741i	−0.369253	+	0.440058i
$364$	−24.9398	−	68.5216i	−0.0685160	−	0.188246i
$365$	−1.87404	−	10.6282i	−0.00513435	−	0.0291184i
$366$	−68.7618	+	389.968i	−0.187874	+	1.06549i
$367$	194.088	+	70.6422i	0.528850	+	0.192486i	0.592625	−	0.805479i	$-0.298092\pi$
$367$	194.088	+	70.6422i	0.528850	+	0.192486i	−0.0637749	+	0.997964i	$0.520314\pi$
$368$	38.0563	+	65.9155i	0.103414	+	0.179118i
$369$	−76.3908	−	44.1043i	−0.207021	−	0.119524i
$370$	7.11852	−	5.97315i	0.0192392	−	0.0161436i
$371$	195.566	+	233.066i	0.527132	+	0.628211i
$372$	−73.6091	+	127.495i	−0.197874	+	0.342728i
$373$	−47.3868	+	27.3588i	−0.127042	+	0.0733479i	−0.562174	−	0.827019i	$-0.690035\pi$
$373$	−47.3868	+	27.3588i	−0.127042	+	0.0733479i	0.435132	+	0.900367i	$0.356702\pi$
$374$	34.3708	−	94.4330i	0.0919005	−	0.252495i
$375$	−16.0825	−	2.83577i	−0.0428866	−	0.00756206i
$376$	176.960	−	31.2028i	0.470638	−	0.0829863i
$377$	−132.420	+	48.1968i	−0.351246	+	0.127843i
$378$	−305.251	−	256.136i	−0.807542	−	0.677608i
$379$			27.3708i			0.0722186i	0.999348	+	0.0361093i	$0.0114964\pi$
$379$			27.3708i			0.0722186i	−0.999348	+	0.0361093i	$0.988504\pi$
$380$	4.66597	−	2.08540i	0.0122789	−	0.00548790i
$381$	−183.638			−0.481990
$382$	26.1288	−	31.1391i	0.0684001	−	0.0815160i
$383$	−98.6738	−	271.104i	−0.257634	−	0.707844i	−0.999312	−	0.0370876i	$-0.988192\pi$
$383$	−98.6738	−	271.104i	−0.257634	−	0.707844i	0.741678	−	0.670756i	$-0.234030\pi$
$384$	−4.77264	−	27.0670i	−0.0124288	−	0.0704870i
$385$	−3.22007	+	18.2619i	−0.00836381	+	0.0474335i
$386$	−224.008	−	81.5322i	−0.580331	−	0.211223i
$387$	94.0920	+	162.972i	0.243132	+	0.421117i
$388$	−17.2129	−	9.93788i	−0.0443632	−	0.0256131i
$389$	30.8250	−	25.8652i	0.0792416	−	0.0664916i	−0.602306	−	0.798265i	$-0.705751\pi$
$389$	30.8250	−	25.8652i	0.0792416	−	0.0664916i	0.681548	+	0.731773i	$0.261307\pi$
$390$	1.12956	+	1.34615i	0.00289630	+	0.00345167i
$391$	−47.0083	+	81.4208i	−0.120226	+	0.208237i
$392$	105.101	−	60.6801i	0.268115	−	0.154796i
$393$	−69.4974	+	190.942i	−0.176838	+	0.485859i
$394$	382.010	+	67.3587i	0.969569	+	0.170961i
$395$	−13.6691	+	2.41022i	−0.0346052	+	0.00610183i
$396$	83.7476	−	30.4816i	0.211484	−	0.0769739i
$397$	−78.8492	−	66.1624i	−0.198613	−	0.166656i	0.538057	−	0.842908i	$-0.319158\pi$
$397$	−78.8492	−	66.1624i	−0.198613	−	0.166656i	−0.736670	+	0.676252i	$0.763603\pi$
$398$			38.5554i			0.0968728i
$399$	−121.363	+	425.531i	−0.304167	+	1.06649i
$400$	−99.9276			−0.249819
$401$	−179.295	+	213.676i	−0.447120	+	0.532857i	−0.941780	−	0.336229i	$-0.890848\pi$
$401$	−179.295	+	213.676i	−0.447120	+	0.532857i	0.494660	+	0.869087i	$0.335293\pi$
$402$	−78.0164	−	214.348i	−0.194071	−	0.533205i
$403$	−20.0104	−	113.484i	−0.0496535	−	0.281599i
$404$	15.4307	−	87.5118i	0.0381948	−	0.216613i
$405$	5.49944	+	2.00163i	0.0135789	+	0.00494230i
$406$	−251.183	−	435.061i	−0.618676	−	1.07158i
$407$	−608.502	−	351.319i	−1.49509	−	0.863191i
$408$	26.0070	−	21.8225i	0.0637427	−	0.0534865i
$409$	−179.753	−	214.222i	−0.439495	−	0.523769i	0.500142	−	0.865943i	$-0.333281\pi$
$409$	−179.753	−	214.222i	−0.439495	−	0.523769i	−0.939637	+	0.342174i	$0.888837\pi$
$410$	−2.70744	+	4.68942i	−0.00660351	+	0.0114376i
$411$	508.029	−	293.311i	1.23608	−	0.713651i
$412$	2.38842	−	6.56214i	0.00579715	−	0.0159275i
$413$	802.650	+	141.529i	1.94346	+	0.342685i
$414$	−82.1117	+	14.4785i	−0.198337	+	0.0349722i
$415$	−10.2531	+	3.73183i	−0.0247063	+	0.00899236i
$416$	16.4803	+	13.8286i	0.0396162	+	0.0332419i
$417$		−	25.4060i		−	0.0609256i
$418$	−268.841	−	277.600i	−0.643160	−	0.664114i
$419$	−75.9603			−0.181290			−0.0906448	−	0.995883i	$-0.528893\pi$
$419$	−75.9603			−0.181290			−0.0906448	+	0.995883i	$0.528893\pi$
$420$	−4.02681	+	4.79896i	−0.00958764	+	0.0114261i
$421$	2.28360	+	6.27414i	0.00542423	+	0.0149030i	0.942375	−	0.334558i	$-0.108587\pi$
$421$	2.28360	+	6.27414i	0.00542423	+	0.0149030i	−0.936951	+	0.349461i	$0.886365\pi$
$422$	49.1879	+	278.958i	0.116559	+	0.661039i
$423$	−34.1815	+	193.853i	−0.0808073	+	0.458281i
$424$	−84.3493	−	30.7006i	−0.198937	−	0.0724072i
$425$	−61.7168	−	106.897i	−0.145216	−	0.251522i
$426$	−169.826	−	98.0492i	−0.398653	−	0.230162i
$427$	846.462	−	710.266i	1.98235	−	1.66339i
$428$	−113.044	−	134.721i	−0.264121	−	0.314768i
$429$	66.4363	−	115.071i	0.154863	−	0.268231i
$430$	10.0044	−	5.77605i	0.0232661	−	0.0134327i
$431$	93.0522	−	255.659i	0.215898	−	0.593176i	−0.783711	−	0.621126i	$-0.786676\pi$
$431$	93.0522	−	255.659i	0.215898	−	0.593176i	0.999609	+	0.0279498i	$0.00889787\pi$
$432$	115.778	+	20.4147i	0.268004	+	0.0472563i
$433$	368.702	−	65.0121i	0.851505	−	0.150143i	0.269171	−	0.963092i	$-0.413250\pi$
$433$	368.702	−	65.0121i	0.851505	−	0.150143i	0.582335	+	0.812949i	$0.302139\pi$
$434$	386.032	−	140.504i	0.889475	−	0.323742i
$435$	9.27411	+	7.78190i	0.0213198	+	0.0178894i
$436$			94.9391i			0.217750i
$437$	202.595	+	299.438i	0.463604	+	0.685212i
$438$	−275.678			−0.629402
$439$	−530.569	+	632.308i	−1.20859	+	1.44034i	−0.343176	+	0.939271i	$0.611503\pi$
$439$	−530.569	+	632.308i	−1.20859	+	1.44034i	−0.865409	+	0.501066i	$0.832942\pi$
$440$	−1.87118	−	5.14104i	−0.00425269	−	0.0116842i
$441$	23.0857	+	130.926i	0.0523485	+	0.296883i
$442$	−4.61456	+	26.1704i	−0.0104402	+	0.0592092i
$443$	266.381	+	96.9546i	0.601311	+	0.218859i	0.624697	−	0.780867i	$-0.285223\pi$
$443$	266.381	+	96.9546i	0.601311	+	0.218859i	−0.0233863	+	0.999727i	$0.507445\pi$
$444$	−118.686	−	205.570i	−0.267311	−	0.462996i
$445$	14.4273	+	8.32961i	0.0324209	+	0.0187182i
$446$	−251.204	+	210.785i	−0.563237	+	0.472612i
$447$	220.098	+	262.302i	0.492389	+	0.586806i
$448$	−38.3473	+	66.4195i	−0.0855967	+	0.148258i
$449$	640.492	−	369.788i	1.42649	−	0.823582i	0.429645	−	0.902998i	$-0.358639\pi$
$449$	640.492	−	369.788i	1.42649	−	0.823582i	0.996842	+	0.0794158i	$0.0253055\pi$
$450$	37.4398	−	102.865i	0.0831997	−	0.228589i
$451$	403.214	+	71.0975i	0.894044	+	0.157644i
$452$	259.360	−	45.7322i	0.573806	−	0.101177i
$453$	−29.9896	+	10.9153i	−0.0662023	+	0.0240957i
$454$	4.25358	+	3.56918i	0.00936912	+	0.00786162i
$455$		−	4.90362i		−	0.0107772i
$456$	−31.7639	−	126.629i	−0.0696576	−	0.277694i
$457$	−816.550			−1.78676			−0.893380	−	0.449301i	$-0.851673\pi$
$457$	−816.550			−1.78676			−0.893380	+	0.449301i	$0.851673\pi$
$458$	285.977	−	340.815i	0.624405	−	0.744137i
$459$	49.6675	+	136.460i	0.108208	+	0.297299i
$460$	0.888795	+	5.04061i	0.00193216	+	0.0109578i
$461$	−4.53069	+	25.6948i	−0.00982796	+	0.0557371i	−0.989327	−	0.145710i	$-0.953453\pi$
$461$	−4.53069	+	25.6948i	−0.00982796	+	0.0557371i	0.979499	+	0.201447i	$0.0645644\pi$
$462$	445.117	+	162.009i	0.963458	+	0.350670i
$463$	−428.391	−	741.995i	−0.925250	−	1.60258i	−0.791158	−	0.611611i	$-0.790522\pi$
$463$	−428.391	−	741.995i	−0.925250	−	1.60258i	−0.134092	−	0.990969i	$-0.542812\pi$
$464$	128.357	+	74.1071i	0.276632	+	0.159713i
$465$	−7.58386	+	6.36361i	−0.0163094	+	0.0136852i
$466$	94.1122	+	112.159i	0.201957	+	0.240683i
$467$	−279.089	+	483.396i	−0.597620	+	1.03511i	0.395551	+	0.918444i	$0.370554\pi$
$467$	−279.089	+	483.396i	−0.597620	+	1.03511i	−0.993171	+	0.116665i	$0.962780\pi$
$468$	−20.4098	+	11.7836i	−0.0436107	+	0.0251787i
$469$	−217.702	+	598.131i	−0.464183	+	1.27533i
$470$	11.9001	+	2.09831i	0.0253193	+	0.00446448i
$471$	89.0919	−	15.7093i	0.189155	−	0.0333531i
$472$	−225.960	+	82.2426i	−0.478728	+	0.174243i
$473$	−669.129	−	561.466i	−1.41465	−	1.18703i
$474$			354.553i			0.748002i
$475$	−473.452	+	33.7853i	−0.996742	+	0.0711270i
$476$	−94.7355			−0.199024
$477$	63.2062	−	75.3263i	0.132508	−	0.157917i
$478$	−180.939	−	497.126i	−0.378533	−	1.04001i
$479$	−123.861	−	702.449i	−0.258582	−	1.46649i	−0.786708	−	0.617325i	$-0.788216\pi$
$479$	−123.861	−	702.449i	−0.258582	−	1.46649i	0.528126	−	0.849166i	$-0.322895\pi$
$480$	0.320947	−	1.82018i	0.000668640	−	0.00379205i
$481$	174.598	+	63.5484i	0.362989	+	0.132117i
$482$	250.592	+	434.039i	0.519901	+	0.900495i
$483$	−383.783	−	221.577i	−0.794583	−	0.458753i
$484$	−131.511	+	110.351i	−0.271718	+	0.227998i
$485$	−0.859144	−	1.02389i	−0.00177143	−	0.00211111i
$486$	−112.295	+	194.501i	−0.231060	+	0.400207i
$487$	−208.405	+	120.323i	−0.427937	+	0.247069i	−0.698467	−	0.715642i	$-0.746134\pi$
$487$	−208.405	+	120.323i	−0.427937	+	0.247069i	0.270530	+	0.962711i	$0.412801\pi$
$488$	−111.500	+	306.344i	−0.228484	+	0.627754i
$489$	208.004	+	36.6767i	0.425366	+	0.0750034i
$490$	8.03715	−	1.41717i	0.0164024	−	0.00289218i
$491$	−427.599	+	155.633i	−0.870874	+	0.316972i	−0.738521	−	0.674231i	$-0.764475\pi$
$491$	−427.599	+	155.633i	−0.870874	+	0.316972i	−0.132353	+	0.991203i	$0.542253\pi$
$492$	105.959	+	88.9099i	0.215363	+	0.180711i
$493$			183.079i			0.371356i
$494$	82.7584	+	59.9474i	0.167527	+	0.121351i
$495$	5.99324			0.0121076
$496$	−77.9068	+	92.8457i	−0.157070	+	0.187189i
$497$	187.155	+	514.205i	0.376570	+	1.03462i
$498$	48.3988	+	274.483i	0.0971863	+	0.551171i
$499$	−95.4908	+	541.555i	−0.191364	+	1.08528i	0.726138	+	0.687549i	$0.241313\pi$
$499$	−95.4908	+	541.555i	−0.191364	+	1.08528i	−0.917502	+	0.397731i	$0.869798\pi$
$500$	−12.6338	−	4.59832i	−0.0252676	−	0.00919664i
$501$	273.270	+	473.317i	0.545449	+	0.944745i
$502$	201.251	+	116.192i	0.400898	+	0.231459i
$503$	−362.224	+	303.942i	−0.720127	+	0.604258i	−0.927420	−	0.374021i	$-0.877979\pi$
$503$	−362.224	+	303.942i	−0.720127	+	0.604258i	0.207294	+	0.978279i	$0.433534\pi$
$504$	−54.0044	−	64.3599i	−0.107152	−	0.127698i
$505$	2.98786	−	5.17512i	0.00591655	−	0.0102478i
$506$	335.164	−	193.507i	0.662380	−	0.382425i
$507$	128.400	−	352.777i	0.253255	−	0.695813i
$508$	−148.888	−	26.2530i	−0.293087	−	0.0516792i
$509$	50.3545	−	8.87886i	0.0989283	−	0.0174437i	−0.123965	−	0.992287i	$-0.539561\pi$
$509$	50.3545	−	8.87886i	0.0989283	−	0.0174437i	0.222893	+	0.974843i	$0.428450\pi$
$510$	2.14535	−	0.780842i	0.00420656	−	0.00153106i
$511$	589.295	+	494.477i	1.15322	+	0.967666i
$512$		−	22.6274i		−	0.0441942i
$513$	555.451	+	57.5797i	1.08275	+	0.112241i
$514$	55.6324			0.108234
$515$	0.301857	−	0.359740i	0.000586131	−	0.000698524i
$516$	−100.927	−	277.294i	−0.195595	−	0.537392i
$517$	−158.659	−	899.799i	−0.306884	−	1.74042i
$518$	−115.021	+	652.315i	−0.222048	+	1.25930i
$519$	−356.022	−	129.581i	−0.685977	−	0.249675i
$520$	0.723363	+	1.25290i	0.00139108	+	0.00240943i
$521$	−664.541	−	383.673i	−1.27551	−	0.736416i	−0.299491	−	0.954099i	$-0.596817\pi$
$521$	−664.541	−	383.673i	−1.27551	−	0.736416i	−0.976020	+	0.217683i	$0.930150\pi$
$522$	−124.377	+	104.365i	−0.238270	+	0.199932i
$523$	212.240	+	252.938i	0.405813	+	0.483629i	0.929783	−	0.368108i	$-0.119994\pi$
$523$	212.240	+	252.938i	0.405813	+	0.483629i	−0.523970	+	0.851736i	$0.675550\pi$
$524$	−83.6437	+	144.875i	−0.159625	+	0.276479i
$525$	503.866	−	290.907i	0.959745	−	0.554109i
$526$	72.8964	−	200.281i	0.138586	−	0.380763i
$527$	−147.437	−	25.9972i	−0.279767	−	0.0493305i
$528$	−137.629	+	24.2677i	−0.260661	+	0.0459616i
$529$	156.862	−	57.0931i	0.296525	−	0.107926i
$530$	−4.62407	−	3.88006i	−0.00872466	−	0.00732086i
$531$		−	263.416i		−	0.496075i
$532$	−159.231	+	327.658i	−0.299307	+	0.615898i
$533$	−108.269			−0.203132
$534$	273.537	−	325.989i	0.512242	−	0.610466i
$535$	−4.04489	−	11.1132i	−0.00756053	−	0.0207724i
$536$	−32.6100	−	184.940i	−0.0608395	−	0.345038i
$537$	47.7915	−	271.039i	0.0889973	−	0.504729i
$538$	288.434	+	104.981i	0.536122	+	0.195133i
$539$	−308.543	−	534.413i	−0.572437	−	0.991489i
$540$	6.84665	+	3.95292i	0.0126790	+	0.00732021i
$541$	552.127	−	463.289i	1.02057	−	0.856357i	0.0308680	−	0.999523i	$-0.490173\pi$
$541$	552.127	−	463.289i	1.02057	−	0.856357i	0.989699	+	0.143166i	$0.0457284\pi$
$542$	−150.472	−	179.326i	−0.277624	−	0.330860i
$543$	−233.788	+	404.933i	−0.430549	+	0.745733i
$544$	24.2055	−	13.9750i	0.0444954	−	0.0256894i
$545$	−2.18359	+	5.99937i	−0.00400659	+	0.0110080i
$546$	−123.356	−	21.7511i	−0.225928	−	0.0398371i
$547$	328.022	−	57.8391i	0.599674	−	0.105739i	0.134433	−	0.990923i	$-0.457079\pi$
$547$	328.022	−	57.8391i	0.599674	−	0.105739i	0.465241	+	0.885184i	$0.345968\pi$
$548$	453.826	−	165.179i	0.828150	−	0.301422i
$549$	−273.574	−	229.556i	−0.498313	−	0.418134i
$550$			508.108i			0.923832i
$551$	633.206	+	307.718i	1.14919	+	0.558473i
$552$	130.745			0.236857
$553$	635.953	−	757.899i	1.15000	−	1.37052i
$554$	−126.712	−	348.138i	−0.228722	−	0.628408i
$555$	−2.77188	−	15.7201i	−0.00499438	−	0.0283246i
$556$	3.63206	−	20.5984i	0.00653247	−	0.0370475i
$557$	−201.081	−	73.1876i	−0.361008	−	0.131396i	0.155147	−	0.987891i	$-0.450415\pi$
$557$	−201.081	−	73.1876i	−0.361008	−	0.131396i	−0.516155	+	0.856495i	$0.672637\pi$
$558$	−66.3857	−	114.983i	−0.118971	−	0.206063i
$559$	200.036	+	115.491i	0.357846	+	0.206603i
$560$	−3.95088	+	3.31518i	−0.00705514	+	0.00591997i
$561$	−110.962	−	132.239i	−0.197793	−	0.235721i
$562$	−255.805	+	443.067i	−0.455169	+	0.788376i
$563$	−775.038	+	447.469i	−1.37662	+	0.794793i	−0.991751	−	0.128177i	$-0.959087\pi$
$563$	−775.038	+	447.469i	−1.37662	+	0.794793i	−0.384871	+	0.922970i	$0.625754\pi$
$564$	105.571	−	290.054i	0.187182	−	0.514280i
$565$	17.4413	+	3.07537i	0.0308695	+	0.00544313i
$566$	334.152	−	58.9200i	0.590375	−	0.104099i
$567$	−392.002	+	142.677i	−0.691362	+	0.251635i
$568$	−123.673	−	103.774i	−0.217734	−	0.182700i
$569$		−	341.934i		−	0.600938i	−0.953792	−	0.300469i	$-0.902857\pi$
$569$		−	341.934i		−	0.600938i	0.953792	−	0.300469i	$-0.0971433\pi$
$570$	0.905233	−	8.73245i	0.00158813	−	0.0153201i
$571$	233.859			0.409561			0.204780	−	0.978808i	$-0.434352\pi$
$571$	233.859			0.409561			0.204780	+	0.978808i	$0.434352\pi$
$572$	70.3152	−	83.7984i	0.122929	−	0.146501i
$573$	−23.8821	−	65.6156i	−0.0416791	−	0.114512i
$574$	−67.0238	−	380.111i	−0.116766	−	0.662214i
$575$	82.5454	−	468.138i	0.143557	−	0.814153i
$576$	23.2926	+	8.47780i	0.0404385	+	0.0147184i
$577$	204.402	+	354.035i	0.354250	+	0.613579i	0.986989	−	0.160786i	$-0.0514029\pi$
$577$	204.402	+	354.035i	0.354250	+	0.613579i	−0.632739	+	0.774365i	$0.718070\pi$
$578$	−324.052	−	187.091i	−0.560643	−	0.323688i
$579$	−313.690	+	263.217i	−0.541778	+	0.454606i
$580$	6.40666	+	7.63516i	0.0110460	+	0.0131641i
$581$	388.875	−	673.552i	0.669321	−	1.15930i
$582$	−29.5681	+	17.0711i	−0.0508043	+	0.0293319i
$583$	−156.105	+	428.896i	−0.267762	+	0.735670i
$584$	−223.512	−	39.4111i	−0.382725	−	0.0674848i
$585$	−1.56076	+	0.275203i	−0.00266796	+	0.000470433i
$586$	380.252	−	138.400i	0.648894	−	0.236178i
$587$	334.409	+	280.603i	0.569692	+	0.478028i	0.881544	−	0.472102i	$-0.156505\pi$
$587$	334.409	+	280.603i	0.569692	+	0.478028i	−0.311852	+	0.950131i	$0.600949\pi$
$588$		−	208.471i		−	0.354542i
$589$	−337.728	+	466.238i	−0.573391	+	0.791576i
$590$	−16.1704			−0.0274074
$591$	428.312	−	510.442i	0.724723	−	0.863692i
$592$	−66.8387	−	183.638i	−0.112903	−	0.310199i
$593$	43.1107	+	244.493i	0.0726993	+	0.412298i	0.999339	+	0.0363480i	$0.0115725\pi$
$593$	43.1107	+	244.493i	0.0726993	+	0.412298i	−0.926640	+	0.375950i	$0.877316\pi$
$594$	103.804	−	588.700i	0.174754	−	0.991078i
$595$	−5.98651	−	2.17891i	−0.0100614	−	0.00366203i
$596$	140.950	+	244.132i	0.236493	+	0.409618i
$597$	57.3567	+	33.1149i	0.0960749	+	0.0554689i
$598$	−78.3976	+	65.7834i	−0.131100	+	0.110006i
$599$	528.918	+	630.340i	0.883002	+	1.05232i	0.998259	+	0.0589851i	$0.0187864\pi$
$599$	528.918	+	630.340i	0.883002	+	1.05232i	−0.115257	+	0.993336i	$0.536769\pi$
$600$	−85.8271	+	148.657i	−0.143045	+	0.247761i
$601$	−256.283	+	147.965i	−0.426428	+	0.246198i	−0.697824	−	0.716270i	$-0.745848\pi$
$601$	−256.283	+	147.965i	−0.426428	+	0.246198i	0.271396	+	0.962468i	$0.412515\pi$
$602$	−281.632	+	773.779i	−0.467828	+	1.28535i
$603$	202.595	+	35.7230i	0.335978	+	0.0592421i
$604$	−25.8752	+	4.56249i	−0.0428397	+	0.00755379i
$605$	−10.8485	+	3.94853i	−0.0179314	+	0.00652650i
$606$	−116.933	−	98.1187i	−0.192959	−	0.161912i
$607$			395.597i			0.651725i	0.945417	+	0.325862i	$0.105655\pi$
$607$			395.597i			0.651725i	−0.945417	+	0.325862i	$0.894345\pi$
$608$	−7.65028	−	107.208i	−0.0125827	−	0.176328i
$609$	−862.955			−1.41700
$610$	−14.0918	+	16.7939i	−0.0231013	+	0.0275310i
$611$	82.6356	+	227.040i	0.135247	+	0.371587i
$612$	5.31679	+	30.1530i	0.00868757	+	0.0492697i
$613$	−74.0927	+	420.201i	−0.120869	+	0.685482i	0.862807	+	0.505533i	$0.168704\pi$
$613$	−74.0927	+	420.201i	−0.120869	+	0.685482i	−0.983676	+	0.179949i	$0.942407\pi$
$614$	−213.832	−	77.8284i	−0.348260	−	0.126756i
$615$	4.65080	+	8.05542i	0.00756227	+	0.0130982i
$616$	337.727	+	194.987i	0.548258	+	0.316537i
$617$	144.881	−	121.570i	0.234816	−	0.197034i	−0.517785	−	0.855511i	$-0.673243\pi$
$617$	144.881	−	121.570i	0.234816	−	0.197034i	0.752601	+	0.658477i	$0.228799\pi$
$618$	−7.71074	−	9.18930i	−0.0124769	−	0.0148694i
$619$	−66.7756	+	115.659i	−0.107876	+	0.186848i	−0.914910	−	0.403658i	$-0.867738\pi$
$619$	−66.7756	+	115.659i	−0.107876	+	0.186848i	0.807033	+	0.590506i	$0.201072\pi$
$620$	−7.05851	+	4.07523i	−0.0113847	+	0.00657296i
$621$	−191.276	+	525.528i	−0.308013	+	0.846260i
$622$	−55.2404	−	9.74037i	−0.0888109	−	0.0156598i
$623$	−1169.44	+	206.203i	−1.87710	+	0.330984i
$624$	34.7269	−	12.6396i	0.0556521	−	0.0202557i
$625$	477.739	+	400.870i	0.764382	+	0.641393i
$626$		−	513.146i		−	0.819722i
$627$	−643.875	+	161.511i	−1.02691	+	0.257594i
$628$	74.4789			0.118597
$629$	155.164	−	184.917i	0.246684	−	0.293986i
$630$	−1.93236	−	5.30912i	−0.00306724	−	0.00842717i
$631$	−190.004	−	1077.57i	−0.301116	−	1.70771i	−0.641248	−	0.767334i	$-0.721583\pi$
$631$	−190.004	−	1077.57i	−0.301116	−	1.70771i	0.340132	−	0.940378i	$-0.389528\pi$
$632$	−50.6871	+	287.461i	−0.0802011	+	0.454843i
$633$	457.238	+	166.421i	0.722335	+	0.262908i
$634$	−113.962	−	197.388i	−0.179751	−	0.311337i
$635$	−8.80470	−	5.08340i	−0.0138657	−	0.00800535i
$636$	−118.119	+	99.1133i	−0.185721	+	0.155839i
$637$	104.890	+	125.003i	0.164663	+	0.196238i
$638$	376.816	−	652.665i	0.590621	−	1.02299i
$639$	153.161	−	88.4274i	0.239688	−	0.138384i
$640$	0.520429	−	1.42987i	0.000813170	−	0.00223417i
$641$	−259.969	−	45.8396i	−0.405568	−	0.0715126i	−0.0328571	−	0.999460i	$-0.510461\pi$
$641$	−259.969	−	45.8396i	−0.405568	−	0.0715126i	−0.372711	+	0.927947i	$0.621572\pi$
$642$	−297.509	+	52.4589i	−0.463410	+	0.0817116i
$643$	−200.292	+	72.9004i	−0.311496	+	0.113375i	−0.493038	−	0.870008i	$-0.664114\pi$
$643$	−200.292	+	72.9004i	−0.311496	+	0.113375i	0.181541	+	0.983383i	$0.441891\pi$
$644$	−279.483	−	234.514i	−0.433980	−	0.364153i
$645$		−	19.8440i		−	0.0307659i
$646$	109.959	−	74.3969i	0.170216	−	0.115165i
$647$	473.328			0.731573			0.365787	−	0.930699i	$-0.380800\pi$
$647$	473.328			0.731573			0.365787	+	0.930699i	$0.380800\pi$
$648$	79.1116	−	94.2815i	0.122086	−	0.145496i
$649$	418.183	+	1148.95i	0.644350	+	1.77034i
$650$	−23.3318	−	132.321i	−0.0358950	−	0.203571i
$651$	122.540	−	694.957i	0.188233	−	1.06752i
$652$	163.400	+	59.4727i	0.250613	+	0.0912158i
$653$	153.973	+	266.690i	0.235794	+	0.408407i	0.959503	−	0.281698i	$-0.0908977\pi$
$653$	153.973	+	266.690i	0.235794	+	0.408407i	−0.723709	+	0.690105i	$0.757564\pi$
$654$	141.236	+	81.5425i	0.215957	+	0.124683i
$655$	−8.61771	+	7.23111i	−0.0131568	+	0.0110399i
$656$	73.1975	+	87.2334i	0.111582	+	0.132978i
$657$	124.313	−	215.316i	0.189213	−	0.327726i
$658$	−745.932	+	430.664i	−1.13364	+	0.654505i
$659$	142.359	−	391.127i	0.216022	−	0.593516i	−0.783593	−	0.621275i	$-0.786615\pi$
$659$	142.359	−	391.127i	0.216022	−	0.593516i	0.999615	+	0.0277593i	$0.00883719\pi$
$660$	−9.25518	−	1.63194i	−0.0140230	−	0.00247263i
$661$	−116.034	+	20.4600i	−0.175544	+	0.0309531i	−0.260729	−	0.965412i	$-0.583963\pi$
$661$	−116.034	+	20.4600i	−0.175544	+	0.0309531i	0.0851852	+	0.996365i	$0.472852\pi$
$662$	−742.027	+	270.076i	−1.12089	+	0.407969i
$663$	34.9689	+	29.3424i	0.0527435	+	0.0442570i
$664$			229.462i			0.345575i
$665$	−17.5982	+	17.0430i	−0.0264635	+	0.0256285i
$666$	214.078			0.321439
$667$	−453.204	+	540.108i	−0.679467	+	0.809757i
$668$	153.893	+	422.818i	0.230379	+	0.632962i
$669$	97.8162	+	554.743i	0.146213	+	0.829212i
$670$	2.19293	−	12.4367i	0.00327304	−	0.0185623i
$671$	1557.68	+	566.951i	2.32144	+	0.844934i
$672$	65.8724	+	114.094i	0.0980245	+	0.169783i
$673$	341.118	+	196.945i	0.506862	+	0.292637i	0.731543	−	0.681796i	$-0.238801\pi$
$673$	341.118	+	196.945i	0.506862	+	0.292637i	−0.224681	+	0.974432i	$0.572134\pi$
$674$	−524.087	+	439.762i	−0.777578	+	0.652465i
$675$	−471.961	−	562.461i	−0.699201	−	0.833276i
$676$	154.536	−	267.665i	0.228604	−	0.395954i
$677$	416.207	−	240.297i	0.614781	−	0.354944i	−0.160053	−	0.987108i	$-0.551167\pi$
$677$	416.207	−	240.297i	0.614781	−	0.354944i	0.774834	+	0.632165i	$0.217833\pi$
$678$	154.729	−	425.115i	0.228214	−	0.627013i
$679$	93.8253	+	16.5439i	0.138182	+	0.0243652i
$680$	1.85101	−	0.326383i	0.00272208	−	0.000479975i
$681$	8.96304	−	3.26228i	0.0131616	−	0.00479042i
$682$	472.097	+	396.137i	0.692225	+	0.580846i
$683$		−	50.6796i		−	0.0742014i	−0.999312	−	0.0371007i	$-0.988188\pi$
$683$		−	50.6796i		−	0.0742014i	0.999312	−	0.0371007i	$-0.0118122\pi$
$684$	113.225	+	32.2923i	0.165534	+	0.0472109i
$685$	32.4772			0.0474120
$686$	53.0967	−	63.2782i	0.0774005	−	0.0922423i
$687$	−261.387	−	718.156i	−0.380477	−	1.04535i
$688$	−42.1863	−	239.250i	−0.0613173	−	0.347748i
$689$	20.9584	−	118.861i	0.0304185	−	0.172512i
$690$	8.26202	+	3.00713i	0.0119739	+	0.00435816i
$691$	−169.082	−	292.858i	−0.244692	−	0.423818i	0.717353	−	0.696710i	$-0.245353\pi$
$691$	−169.082	−	292.858i	−0.244692	−	0.423818i	−0.962045	+	0.272891i	$0.912020\pi$
$692$	−270.127	−	155.958i	−0.390357	−	0.225373i
$693$	−327.255	+	274.599i	−0.472229	+	0.396247i
$694$	−383.260	−	456.752i	−0.552248	−	0.658144i
$695$	0.703278	−	1.21811i	0.00101191	−	0.00175268i
$696$	220.490	−	127.300i	0.316796	−	0.182902i
$697$	−48.1092	+	132.179i	−0.0690233	+	0.189640i
$698$	598.197	+	105.478i	0.857015	+	0.151115i
$699$	247.684	−	43.6734i	0.354341	−	0.0624799i
$700$	450.108	−	163.826i	0.643011	−	0.234037i
$701$	−1036.93	−	870.091i	−1.47922	−	1.24121i	−0.907011	−	0.421107i	$-0.861642\pi$
$701$	−1036.93	−	870.091i	−1.47922	−	1.24121i	−0.572210	−	0.820107i	$-0.693914\pi$
$702$			158.076i			0.225179i
$703$	−378.766	−	847.469i	−0.538785	−	1.20550i
$704$	−115.055			−0.163430
$705$	13.3424	−	15.9009i	0.0189254	−	0.0225544i
$706$	245.131	+	673.491i	0.347210	+	0.953953i
$707$	73.9657	+	419.481i	0.104619	+	0.593325i
$708$	−71.7272	+	406.785i	−0.101310	+	0.574555i
$709$	−1134.30	−	412.852i	−1.59986	−	0.582301i	−0.620461	−	0.784237i	$-0.713054\pi$
$709$	−1134.30	−	412.852i	−1.59986	−	0.582301i	−0.979399	+	0.201936i	$0.935277\pi$
$710$	−5.42831	−	9.40211i	−0.00764551	−	0.0132424i
$711$	−276.920	−	159.880i	−0.389480	−	0.224866i
$712$	268.379	−	225.197i	0.376937	−	0.316288i
$713$	−370.606	−	441.671i	−0.519784	−	0.619454i
$714$	−81.3676	+	140.933i	−0.113960	+	0.197385i
$715$	6.37070	−	3.67813i	0.00891007	−	0.00514423i
$716$	77.4959	−	212.918i	0.108234	−	0.297372i
$717$	−894.954	−	157.805i	−1.24819	−	0.220090i
$718$	424.949	−	74.9300i	0.591852	−	0.104359i
$719$	822.828	−	299.485i	1.14441	−	0.416530i	0.300903	−	0.953655i	$-0.402712\pi$
$719$	822.828	−	299.485i	1.14441	−	0.416530i	0.843503	+	0.537125i	$0.180490\pi$
$720$	1.27691	+	1.07146i	0.00177349	+	0.00148813i
$721$			33.4738i			0.0464269i
$722$	−72.4933	−	505.358i	−0.100406	−	0.699942i
$723$	860.927			1.19077
$724$	−247.438	+	294.885i	−0.341765	+	0.407300i
$725$	−316.597	−	869.843i	−0.436686	−	1.19978i
$726$	51.2092	+	290.422i	0.0705361	+	0.400030i
$727$	10.6960	−	60.6598i	0.0147125	−	0.0834386i	−0.976567	−	0.215212i	$-0.930956\pi$
$727$	10.6960	−	60.6598i	0.0147125	−	0.0834386i	0.991280	+	0.131773i	$0.0420670\pi$
$728$	−96.9042	−	35.2702i	−0.133110	−	0.0484481i
$729$	388.711	+	673.267i	0.533211	+	0.923549i
$730$	−13.2176	−	7.63121i	−0.0181064	−	0.0104537i
$731$	229.881	−	192.893i	0.314475	−	0.263876i
$732$	359.965	+	428.989i	0.491755	+	0.586051i
$733$	465.280	−	805.889i	0.634761	−	1.09944i	−0.351804	−	0.936074i	$-0.614432\pi$
$733$	465.280	−	805.889i	0.634761	−	1.09944i	0.986566	−	0.163365i	$-0.0522349\pi$
$734$	252.964	−	146.049i	0.344637	−	0.198976i
$735$	4.79481	−	13.1736i	0.00652355	−	0.0179233i
$736$	106.004	+	18.6914i	0.144028	+	0.0253959i
$737$	−940.377	+	165.814i	−1.27595	+	0.224985i
$738$	−117.223	+	42.6655i	−0.158838	+	0.0578124i
$739$	383.325	+	321.648i	0.518708	+	0.435247i	0.864181	−	0.503181i	$-0.167837\pi$
$739$	383.325	+	321.648i	0.518708	+	0.435247i	−0.345473	+	0.938429i	$0.612282\pi$
$740$		−	13.1417i		−	0.0177590i
$741$	160.261	−	71.6268i	0.216277	−	0.0966623i
$742$	430.270			0.579878
$743$	−190.681	+	227.245i	−0.256637	+	0.305848i	−0.878944	−	0.476926i	$-0.841751\pi$
$743$	−190.681	+	227.245i	−0.256637	+	0.305848i	0.622307	+	0.782773i	$0.286196\pi$
$744$	71.2079	+	195.642i	0.0957095	+	0.262960i
$745$	3.29185	+	18.6690i	0.00441859	+	0.0250590i
$746$	−13.4373	+	76.2067i	−0.0180125	+	0.102154i
$747$	−236.207	−	85.9724i	−0.316208	−	0.115090i
$748$	−71.0596	−	123.079i	−0.0949995	−	0.164544i
$749$	730.055	+	421.497i	0.974706	+	0.562747i
$750$	−17.6917	+	14.8451i	−0.0235890	+	0.0197935i
$751$	−169.108	−	201.535i	−0.225178	−	0.268356i	0.641613	−	0.767029i	$-0.278266\pi$
$751$	−169.108	−	201.535i	−0.225178	−	0.268356i	−0.866791	+	0.498672i	$0.833821\pi$
$752$	127.060	−	220.074i	0.168963	−	0.292652i
$753$	345.706	−	199.593i	0.459104	−	0.265064i
$754$	−68.1605	+	187.270i	−0.0903986	+	0.248368i
$755$	−1.74003	−	0.306815i	−0.00230468	−	0.000406378i
$756$	−554.970	+	97.8561i	−0.734087	+	0.129439i
$757$	−545.605	+	198.584i	−0.720747	+	0.262330i	−0.676243	−	0.736679i	$-0.736393\pi$
$757$	−545.605	+	198.584i	−0.720747	+	0.262330i	−0.0445039	+	0.999009i	$0.514171\pi$
$758$	29.6522	+	24.8812i	0.0391190	+	0.0328247i
$759$		−	664.807i		−	0.875899i
$760$	1.98233	−	6.95060i	0.00260833	−	0.00914552i
$761$	906.742			1.19151			0.595757	−	0.803165i	$-0.296852\pi$
$761$	906.742			1.19151			0.595757	+	0.803165i	$0.296852\pi$
$762$	−166.934	+	198.945i	−0.219074	+	0.261082i
$763$	−155.647	−	427.638i	−0.203994	−	0.560469i
$764$	−9.98246	−	56.6133i	−0.0130660	−	0.0741012i
$765$	−0.357540	+	2.02771i	−0.000467373	+	0.00265060i
$766$	−383.399	−	139.546i	−0.500521	−	0.182175i
$767$	−161.662	−	280.006i	−0.210771	−	0.365066i
$768$	−33.6616	−	19.4345i	−0.0438302	−	0.0253054i
$769$	−673.472	+	565.110i	−0.875777	+	0.734864i	−0.965306	−	0.261120i	$-0.915908\pi$
$769$	−673.472	+	565.110i	−0.875777	+	0.734864i	0.0895296	+	0.995984i	$0.471464\pi$
$770$	16.8569	+	20.0893i	0.0218921	+	0.0260899i
$771$	47.7822	−	82.7613i	0.0619744	−	0.107343i
$772$	−291.960	+	168.563i	−0.378186	+	0.218346i
$773$	300.271	−	824.988i	0.388449	−	1.06726i	−0.579251	−	0.815150i	$-0.696655\pi$
$773$	300.271	−	824.988i	0.388449	−	1.06726i	0.967700	−	0.252106i	$-0.0811231\pi$
$774$	262.089	+	46.2134i	0.338617	+	0.0597073i
$775$	745.461	−	131.445i	0.961885	−	0.169606i
$776$	−26.4134	+	9.61370i	−0.0340379	+	0.0123888i
$777$	871.623	+	731.379i	1.12178	+	0.941285i
$778$		−	56.9068i		−	0.0731449i
$779$	376.300	+	388.560i	0.483055	+	0.498793i
$780$	2.48517			0.00318611
$781$	−527.664	+	628.846i	−0.675626	+	0.805180i
$782$	45.4749	+	124.941i	0.0581520	+	0.159771i
$783$	189.109	+	1072.49i	0.241519	+	1.36972i
$784$	29.8031	−	169.022i	0.0380141	−	0.215589i
$785$	4.70645	+	1.71301i	0.00599548	+	0.00218218i
$786$	143.682	+	248.864i	0.182801	+	0.316621i
$787$	228.280	+	131.797i	0.290063	+	0.167468i	0.637970	−	0.770061i	$-0.279774\pi$
$787$	228.280	+	131.797i	0.290063	+	0.167468i	−0.347907	+	0.937529i	$0.613108\pi$
$788$	420.235	−	352.619i	0.533293	−	0.447486i
$789$	−235.337	−	280.464i	−0.298273	−	0.355468i
$790$	−9.81459	+	16.9994i	−0.0124235	+	0.0215182i
$791$	−1093.27	+	631.200i	−1.38214	+	0.797977i
$792$	43.1076	−	118.437i	0.0544287	−	0.149542i
$793$	−431.685	−	76.1177i	−0.544369	−	0.0959870i
$794$	−143.354	+	25.2772i	−0.180547	+	0.0318352i
$795$	−9.74372	+	3.54643i	−0.0122563	+	0.00446091i
$796$	41.7690	+	35.0483i	0.0524736	+	0.0440306i
$797$			304.514i			0.382076i	0.981583	+	0.191038i	$0.0611853\pi$
$797$			304.514i			0.382076i	−0.981583	+	0.191038i	$0.938815\pi$
$798$	350.676	+	518.303i	0.439443	+	0.649502i
$799$	313.897			0.392862
$800$	−90.8381	+	108.257i	−0.113548	+	0.135321i
$801$	131.263	+	360.643i	0.163874	+	0.450241i
$802$	68.4994	+	388.479i	0.0854107	+	0.484388i
$803$	−200.396	+	1136.50i	−0.249559	+	1.41532i
$804$	−303.134	−	110.332i	−0.377033	−	0.137229i
$805$	−12.2672	−	21.2475i	−0.0152388	−	0.0263944i
$806$	−141.133	−	81.4835i	−0.175104	−	0.101096i
$807$	403.908	−	338.919i	0.500506	−	0.419975i
$808$	−80.7789	−	96.2685i	−0.0999739	−	0.119144i
$809$	−677.053	+	1172.69i	−0.836901	+	1.44955i	0.0555729	+	0.998455i	$0.482301\pi$
$809$	−677.053	+	1172.69i	−0.836901	+	1.44955i	−0.892474	+	0.451100i	$0.851032\pi$
$810$	7.16767	−	4.13826i	0.00884897	−	0.00510896i
$811$	385.220	−	1058.38i	0.474994	−	1.30504i	−0.438700	−	0.898634i	$-0.644561\pi$
$811$	385.220	−	1058.38i	0.474994	−	1.30504i	0.913694	−	0.406402i	$-0.133217\pi$
$812$	−699.658	−	123.369i	−0.861648	−	0.151932i
$813$	−396.013	+	69.8278i	−0.487101	+	0.0858891i
$814$	−933.753	+	339.858i	−1.14712	+	0.417516i
$815$	8.95766	+	7.51637i	0.0109910	+	0.00922254i
$816$		−	48.0122i		−	0.0588385i
$817$	−280.767	−	1119.29i	−0.343656	−	1.37000i
$818$	−395.480			−0.483472
$819$	72.6141	−	86.5381i	0.0886619	−	0.105663i
$820$	2.61912	+	7.19597i	0.00319405	+	0.00877558i
$821$	228.903	+	1298.17i	0.278810	+	1.58121i	0.726594	+	0.687068i	$0.241102\pi$
$821$	228.903	+	1298.17i	0.278810	+	1.58121i	−0.447784	+	0.894142i	$0.647787\pi$
$822$	144.060	−	817.004i	0.175255	−	0.993922i
$823$	−728.159	−	265.028i	−0.884761	−	0.322027i	−0.140632	−	0.990062i	$-0.544913\pi$
$823$	−728.159	−	265.028i	−0.884761	−	0.322027i	−0.744130	+	0.668035i	$0.767136\pi$
$824$	−4.93793	−	8.55274i	−0.00599263	−	0.0103795i
$825$	755.884	+	436.410i	0.916223	+	0.528982i
$826$	882.966	−	740.896i	1.06897	−	0.896969i
$827$	−479.689	−	571.672i	−0.580036	−	0.691259i	0.393623	−	0.919272i	$-0.371222\pi$
$827$	−479.689	−	571.672i	−0.580036	−	0.691259i	−0.973658	+	0.228013i	$0.926777\pi$
$828$	−58.9574	+	102.117i	−0.0712046	+	0.123330i
$829$	−350.952	+	202.622i	−0.423344	+	0.244418i	−0.696507	−	0.717550i	$-0.745264\pi$
$829$	−350.952	+	202.622i	−0.423344	+	0.244418i	0.273163	+	0.961968i	$0.411930\pi$
$830$	−5.27760	+	14.5001i	−0.00635856	+	0.0174700i
$831$	−626.737	−	110.511i	−0.754197	−	0.132985i
$832$	29.9625	−	5.28320i	0.0360126	−	0.00635000i
$833$	199.216	−	72.5088i	0.239155	−	0.0870454i
$834$	−27.5236	−	23.0950i	−0.0330019	−	0.0276919i
$835$			30.2582i			0.0362373i
$836$	−545.124	+	38.8998i	−0.652063	+	0.0465309i
$837$	−890.554			−1.06398
$838$	−69.0509	+	82.2916i	−0.0823996	+	0.0982001i
$839$	334.380	+	918.701i	0.398546	+	1.09500i	0.962993	+	0.269526i	$0.0868671\pi$
$839$	334.380	+	918.701i	0.398546	+	1.09500i	−0.564447	+	0.825469i	$0.690911\pi$
$840$	1.53843	+	8.72489i	0.00183147	+	0.0103868i
$841$	−92.3746	+	523.882i	−0.109839	+	0.622928i
$842$	8.87298	+	3.22950i	0.0105380	+	0.00383551i
$843$	439.418	+	761.095i	0.521255	+	0.902841i
$844$	346.923	+	200.296i	0.411047	+	0.237318i
$845$	15.9217	−	13.3599i	0.0188423	−	0.0158105i
$846$	178.938	+	213.250i	0.211511	+	0.252069i
$847$	411.457	−	712.664i	0.485781	−	0.841398i
$848$	−109.936	+	63.4718i	−0.129642	+	0.0748488i
$849$	199.349	−	547.706i	0.234804	−	0.645119i
$850$	−171.910	−	30.3123i	−0.202247	−	0.0356615i
$851$	915.513	−	161.430i	1.07581	−	0.189694i
$852$	−260.600	+	94.8507i	−0.305869	+	0.111327i
$853$	−567.678	−	476.338i	−0.665507	−	0.558427i	0.246225	−	0.969213i	$-0.420810\pi$
$853$	−567.678	−	476.338i	−0.665507	−	0.558427i	−0.911732	+	0.410786i	$0.865254\pi$
$854$		−	1562.67i		−	1.82983i
$855$	6.41220	+	4.64478i	0.00749965	+	0.00543249i
$856$	−248.711			−0.290550
$857$	−14.0229	+	16.7118i	−0.0163628	+	0.0195004i	−0.774164	−	0.632985i	$-0.781829\pi$
$857$	−14.0229	+	16.7118i	−0.0163628	+	0.0195004i	0.757801	+	0.652486i	$0.226274\pi$
$858$	−64.2691	−	176.578i	−0.0749057	−	0.205802i
$859$	136.313	+	773.068i	0.158688	+	0.899962i	0.955337	+	0.295520i	$0.0954929\pi$
$859$	136.313	+	773.068i	0.158688	+	0.899962i	−0.796649	+	0.604442i	$0.793396\pi$
$860$	2.83691	−	16.0889i	0.00329874	−	0.0187081i
$861$	−623.036	−	226.767i	−0.723620	−	0.263376i
$862$	−192.380	−	333.212i	−0.223179	−	0.386557i
$863$	933.691	+	539.067i	1.08191	+	0.624643i	0.931412	−	0.363967i	$-0.118578\pi$
$863$	933.691	+	539.067i	1.08191	+	0.624643i	0.150501	+	0.988610i	$0.451911\pi$
$864$	127.363	−	106.870i	0.147410	−	0.123692i
$865$	−13.4828	−	16.0682i	−0.0155870	−	0.0185759i
$866$	264.733	−	458.532i	0.305697	−	0.529482i
$867$	−556.652	+	321.383i	−0.642043	+	0.370684i
$868$	198.703	−	545.932i	0.228920	−	0.628954i
$869$	1461.67	+	257.732i	1.68201	+	0.296584i
$870$	16.8610	−	2.97306i	0.0193805	−	0.00341731i
$871$	237.278	−	86.3623i	0.272421	−	0.0991530i
$872$	102.852	+	86.3033i	0.117950	+	0.0989717i
$873$		−	30.7918i		−	0.0352713i
$874$	508.563	+	52.7192i	0.581879	+	0.0603194i
$875$	64.4455			0.0736520
$876$	−250.602	+	298.656i	−0.286076	+	0.340932i
$877$	−435.177	−	1195.64i	−0.496211	−	1.36333i	−0.894910	−	0.446246i	$-0.852761\pi$
$877$	−435.177	−	1195.64i	−0.496211	−	1.36333i	0.398699	−	0.917082i	$-0.369462\pi$
$878$	202.703	+	1149.58i	0.230869	+	1.30932i
$879$	120.705	−	684.551i	0.137321	−	0.778784i
$880$	−7.27052	−	2.64625i	−0.00826196	−	0.00300711i
$881$	37.3983	+	64.7758i	0.0424499	+	0.0735253i	0.886470	−	0.462787i	$-0.153150\pi$
$881$	37.3983	+	64.7758i	0.0424499	+	0.0735253i	−0.844020	+	0.536312i	$0.819817\pi$
$882$	162.824	+	94.0065i	0.184608	+	0.106583i
$883$	182.146	−	152.839i	0.206281	−	0.173090i	−0.533794	−	0.845614i	$-0.679234\pi$
$883$	182.146	−	152.839i	0.206281	−	0.173090i	0.740075	+	0.672524i	$0.234790\pi$
$884$	24.1570	+	28.7891i	0.0273269	+	0.0325669i
$885$	−13.8886	+	24.0558i	−0.0156933	+	0.0271816i
$886$	347.186	−	200.448i	0.391858	−	0.226239i
$887$	−23.3425	+	64.1329i	−0.0263162	+	0.0723031i	−0.952155	−	0.305615i	$-0.901138\pi$
$887$	−23.3425	+	64.1329i	−0.0263162	+	0.0723031i	0.925839	+	0.377918i	$0.123360\pi$
$888$	−330.595	−	58.2928i	−0.372292	−	0.0656451i
$889$	713.684	−	125.842i	0.802794	−	0.141554i
$890$	22.1389	−	8.05789i	0.0248751	−	0.00905381i
$891$	−479.398	−	402.263i	−0.538045	−	0.451474i
$892$			463.753i			0.519902i
$893$	527.597	−	1085.66i	0.590815	−	1.21575i
$894$	484.243			0.541659
$895$	9.79421	−	11.6723i	0.0109432	−	0.0130417i
$896$	37.0964	+	101.921i	0.0414022	+	0.113752i
$897$	30.5272	+	173.129i	0.0340326	+	0.193008i
$898$	181.622	−	1030.03i	0.202252	−	1.14703i
$899$	−1055.03	−	383.998i	−1.17355	−	0.427139i
$900$	−77.4047	−	134.069i	−0.0860052	−	0.148965i
$901$	−135.797	−	78.4023i	−0.150718	−	0.0870169i
$902$	443.561	−	372.191i	0.491752	−	0.412629i
$903$	909.217	+	1083.56i	1.00688	+	1.19996i
$904$	186.225	−	322.550i	0.206001	−	0.356804i
$905$	−22.4184	+	12.9433i	−0.0247717	+	0.0143019i
$906$	−15.4366	+	42.4118i	−0.0170382	+	0.0468121i
$907$	−112.934	−	19.9132i	−0.124513	−	0.0219551i	0.111044	−	0.993815i	$-0.464580\pi$
$907$	−112.934	−	19.9132i	−0.124513	−	0.0219551i	−0.235557	+	0.971860i	$0.575692\pi$
$908$	7.73334	−	1.36360i	0.00851689	−	0.00150176i
$909$	129.364	−	47.0846i	0.142314	−	0.0517982i
$910$	−5.31234	−	4.45758i	−0.00583773	−	0.00489844i
$911$			173.800i			0.190779i	0.995440	+	0.0953896i	$0.0304097\pi$
$911$			173.800i			0.190779i	−0.995440	+	0.0953896i	$0.969590\pi$
$912$	−166.058	−	80.6989i	−0.182081	−	0.0884856i
$913$	1166.76			1.27794
$914$	−742.275	+	884.609i	−0.812118	+	0.967844i
$915$	12.8801	+	35.3877i	0.0140766	+	0.0386751i
$916$	−109.257	−	619.628i	−0.119276	−	0.676449i
$917$	139.245	−	789.695i	0.151848	−	0.861172i
$918$	192.984	+	70.2405i	0.210222	+	0.0765147i
$919$	−252.031	−	436.530i	−0.274244	−	0.475005i	0.695700	−	0.718333i	$-0.255094\pi$
$919$	−252.031	−	436.530i	−0.274244	−	0.475005i	−0.969944	+	0.243327i	$0.921761\pi$
$920$	6.26870	+	3.61923i	0.00681380	+	0.00393395i
$921$	−299.440	+	251.260i	−0.325124	+	0.272812i
$922$	23.7179	+	28.2659i	0.0257244	+	0.0306572i
$923$	108.538	−	187.993i	0.117593	−	0.203676i
$924$	580.142	−	334.945i	0.627859	−	0.362495i
$925$	−417.439	+	1146.91i	−0.451286	+	1.23990i
$926$	−1193.26	−	210.405i	−1.28862	−	0.227219i
$927$	10.6543	−	1.87863i	0.0114933	−	0.00202657i
$928$	196.966	−	71.6896i	0.212247	−	0.0772517i
$929$	−729.312	−	611.966i	−0.785051	−	0.658736i	0.159464	−	0.987204i	$-0.449023\pi$
$929$	−729.312	−	611.966i	−0.785051	−	0.658736i	−0.944515	+	0.328468i	$0.893468\pi$
$930$			14.0007i			0.0150546i
$931$	84.0597	−	810.893i	0.0902897	−	0.870992i
$932$	207.059			0.222166
$933$	−61.9358	+	73.8122i	−0.0663834	+	0.0791127i
$934$	269.985	+	741.777i	0.289063	+	0.794193i
$935$	−1.65958	−	9.41194i	−0.00177495	−	0.0100662i
$936$	−5.78754	+	32.8228i	−0.00618327	+	0.0350670i
$937$	898.672	+	327.090i	0.959095	+	0.349082i	0.773679	−	0.633578i	$-0.218414\pi$
$937$	898.672	+	327.090i	0.959095	+	0.349082i	0.185416	+	0.982660i	$0.440637\pi$
$938$	450.086	+	779.572i	0.479836	+	0.831100i
$939$	−763.379	−	440.737i	−0.812970	−	0.469368i
$940$	13.0908	−	10.9845i	0.0139264	−	0.0116857i
$941$	229.351	+	273.330i	0.243731	+	0.290468i	0.874017	−	0.485896i	$-0.161507\pi$
$941$	229.351	+	273.330i	0.243731	+	0.290468i	−0.630285	+	0.776364i	$0.717062\pi$
$942$	63.9693	−	110.798i	0.0679080	−	0.117620i
$943$	−469.133	+	270.854i	−0.497490	+	0.287226i
$944$	−116.309	+	319.555i	−0.123208	+	0.338512i
$945$	−37.3202	−	6.58056i	−0.0394923	−	0.00696355i
$946$	−1216.53	+	214.507i	−1.28597	+	0.226752i
$947$	1332.95	−	485.155i	1.40755	−	0.512307i	0.477142	−	0.878826i	$-0.341673\pi$
$947$	1332.95	−	485.155i	1.40755	−	0.512307i	0.930411	+	0.366519i	$0.119450\pi$
$948$	384.105	+	322.302i	0.405174	+	0.339981i
$949$		−	305.169i		−	0.321569i
$950$	−393.785	+	543.627i	−0.414511	+	0.572239i
$951$	−391.524			−0.411697
$952$	−86.1183	+	102.632i	−0.0904604	+	0.107806i
$953$	−20.9340	−	57.5157i	−0.0219664	−	0.0603523i	0.928225	−	0.372020i	$-0.121335\pi$
$953$	−20.9340	−	57.5157i	−0.0219664	−	0.0603523i	−0.950191	+	0.311668i	$0.899112\pi$
$954$	−24.1478	−	136.949i	−0.0253122	−	0.143552i
$955$	0.671293	−	3.80709i	0.000702925	−	0.00398649i
$956$	−703.042	−	255.886i	−0.735400	−	0.267664i
$957$	−647.289	−	1121.14i	−0.676373	−	1.17151i
$958$	−873.593	−	504.369i	−0.911892	−	0.526481i
$959$	−1773.38	+	1488.05i	−1.84920	+	1.55166i
$960$	−1.68014	−	2.00232i	−0.00175015	−	0.00208575i
$961$	−21.4443	+	37.1426i	−0.0223146	+	0.0386500i
$962$	227.561	−	131.383i	0.236550	−	0.136572i
$963$	93.1844	−	256.022i	0.0967647	−	0.265859i
$964$	698.014	+	123.079i	0.724081	+	0.127675i
$965$	−22.3264	+	3.93675i	−0.0231362	+	0.00407953i
$966$	−588.920	+	214.349i	−0.609648	+	0.221894i
$967$	674.727	+	566.163i	0.697752	+	0.585484i	0.921133	−	0.389247i	$-0.127265\pi$
$967$	674.727	+	566.163i	0.697752	+	0.585484i	−0.223381	+	0.974731i	$0.571709\pi$
$968$			242.786i			0.250812i
$969$	−16.2328	−	227.480i	−0.0167521	−	0.234757i
$970$	−1.89022			−0.00194869
$971$	−821.640	+	979.193i	−0.846180	+	1.00844i	0.153614	+	0.988131i	$0.450909\pi$
$971$	−821.640	+	979.193i	−0.846180	+	1.00844i	−0.999794	+	0.0203066i	$0.993536\pi$
$972$	108.632	+	298.464i	0.111761	+	0.307061i
$973$	17.4099	+	98.7367i	0.0178931	+	0.101477i
$974$	−59.0967	+	335.154i	−0.0606742	+	0.344101i
$975$	−216.886	−	78.9401i	−0.222447	−	0.0809642i
$976$	230.520	+	399.272i	0.236188	+	0.409090i
$977$	1206.76	+	696.722i	1.23517	+	0.713123i	0.968102	−	0.250555i	$-0.0806132\pi$
$977$	1206.76	+	696.722i	1.23517	+	0.713123i	0.267064	+	0.963679i	$0.413947\pi$
$978$	228.817	−	192.000i	0.233964	−	0.196319i
$979$	−1145.07	−	1364.64i	−1.16963	−	1.39392i
$980$	5.77080	−	9.99532i	0.00588857	−	0.0101993i
$981$	−127.376	+	73.5405i	−0.129843	+	0.0749649i
$982$	−220.099	+	604.716i	−0.224133	+	0.615801i
$983$	−1533.07	−	270.322i	−1.55958	−	0.274997i	−0.673736	−	0.738972i	$-0.735311\pi$
$983$	−1533.07	−	270.322i	−1.55958	−	0.274997i	−0.885848	+	0.463976i	$0.846423\pi$
$984$	192.641	−	33.9678i	0.195774	−	0.0345202i
$985$	34.6656	−	12.6173i	0.0351935	−	0.0128094i
$986$	198.338	+	166.426i	0.201154	+	0.168789i
$987$			1479.58i			1.49906i
$988$	140.175	−	35.1618i	0.141877	−	0.0355889i
$989$	1155.68			1.16853
$990$	5.44809	−	6.49278i	0.00550312	−	0.00655836i
$991$	−279.137	−	766.924i	−0.281673	−	0.773889i	−0.997163	−	0.0752669i	$-0.976019\pi$
$991$	−279.137	−	766.924i	−0.281673	−	0.773889i	0.715491	−	0.698622i	$-0.246203\pi$
$992$	29.7641	+	168.801i	0.0300041	+	0.170162i
$993$	−235.544	+	1335.84i	−0.237205	+	1.34525i
$994$	727.195	+	264.677i	0.731585	+	0.266275i
$995$	1.83335	+	3.17545i	0.00184256	+	0.00319141i
$996$	341.358	+	197.083i	0.342729	+	0.197875i
$997$	−278.681	+	233.841i	−0.279520	+	0.234545i	−0.771759	−	0.635915i	$-0.780623\pi$
$997$	−278.681	+	233.841i	−0.279520	+	0.234545i	0.492239	+	0.870460i	$0.336179\pi$
$998$	499.889	+	595.745i	0.500891	+	0.596938i
$999$	717.958	−	1243.54i	0.718676	−	1.24478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.3.f.a.3.3	✓	24
3.2	odd	2		342.3.z.b.307.1		24
4.3	odd	2		304.3.z.c.193.3		24
19.5	even	9		722.3.b.f.721.8		24
19.13	odd	18	inner	38.3.f.a.13.3	yes	24
19.14	odd	18		722.3.b.f.721.17		24
57.32	even	18		342.3.z.b.127.1		24
76.51	even	18		304.3.z.c.241.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.3.f.a.3.3	✓	24	1.1	even	1	trivial
38.3.f.a.13.3	yes	24	19.13	odd	18	inner
304.3.z.c.193.3		24	4.3	odd	2
304.3.z.c.241.3		24	76.51	even	18
342.3.z.b.127.1		24	57.32	even	18
342.3.z.b.307.1		24	3.2	odd	2
722.3.b.f.721.8		24	19.5	even	9
722.3.b.f.721.17		24	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.909039 - 1.08335i) q^{2} +(-0.830875 - 2.28281i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(0.0233547 - 0.132451i) q^{5} +(-3.22838 - 1.17503i) q^{6} +(4.79341 + 8.30244i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(2.37354 - 1.99163i) q^{9} +O(q^{10})\)	\(q+(0.909039 - 1.08335i) q^{2} +(-0.830875 - 2.28281i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(0.0233547 - 0.132451i) q^{5} +(-3.22838 - 1.17503i) q^{6} +(4.79341 + 8.30244i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(2.37354 - 1.99163i) q^{9} +(-0.122261 - 0.145705i) q^{10} +(-7.19093 + 12.4551i) q^{11} +(-4.20770 + 2.42931i) q^{12} +(1.30073 - 3.57374i) q^{13} +(13.3518 + 2.35429i) q^{14} +(-0.321766 + 0.0567360i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-3.78497 - 3.17596i) q^{17} -4.38184i q^{18} +(-17.3463 + 7.75273i) q^{19} -0.268989 q^{20} +(14.9702 - 17.8407i) q^{21} +(6.95635 + 19.1124i) q^{22} +(-3.30421 - 18.7391i) q^{23} +(-1.19316 + 6.76675i) q^{24} +(23.4753 + 8.54432i) q^{25} +(-2.68919 - 4.65782i) q^{26} +(-25.4533 - 14.6954i) q^{27} +(14.6879 - 12.3246i) q^{28} +(-23.8175 - 28.3846i) q^{29} +(-0.231033 + 0.400160i) q^{30} +(26.2409 - 15.1502i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(34.4073 + 6.06693i) q^{33} +(-6.88136 + 1.21337i) q^{34} +(1.21162 - 0.440993i) q^{35} +(-4.74707 - 3.98327i) q^{36} +48.8558i q^{37} +(-7.36956 + 25.8397i) q^{38} -9.23891 q^{39} +(-0.244522 + 0.291410i) q^{40} +(-9.73690 - 26.7519i) q^{41} +(-5.71931 - 32.4358i) q^{42} +(-10.5466 + 59.8126i) q^{43} +(27.0291 + 9.83777i) q^{44} +(-0.208361 - 0.360892i) q^{45} +(-23.3046 - 13.4549i) q^{46} +(-48.6668 + 40.8363i) q^{47} +(6.24613 + 7.44385i) q^{48} +(-21.4536 + 37.1588i) q^{49} +(30.5965 - 17.6649i) q^{50} +(-4.10529 + 11.2792i) q^{51} +(-7.49063 - 1.32080i) q^{52} +(31.2537 - 5.51088i) q^{53} +(-39.0583 + 14.2161i) q^{54} +(1.48175 + 1.24333i) q^{55} -27.1156i q^{56} +(32.1106 + 33.1568i) q^{57} -52.4016 q^{58} +(54.6471 - 65.1259i) q^{59} +(0.223496 + 0.614051i) q^{60} +(-20.0147 - 113.509i) q^{61} +(7.44103 - 42.2002i) q^{62} +(27.9127 + 10.1594i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-0.442968 - 0.255748i) q^{65} +(37.8502 - 31.7601i) q^{66} +(42.6779 + 50.8615i) q^{67} +(-4.94092 + 8.55793i) q^{68} +(-40.0324 + 23.1127i) q^{69} +(0.623658 - 1.71349i) q^{70} +(56.2117 + 9.91164i) q^{71} +(-8.63054 + 1.52180i) q^{72} +(75.4032 - 27.4445i) q^{73} +(52.9279 + 44.4118i) q^{74} -60.6889i q^{75} +(21.2942 + 31.4731i) q^{76} -137.876 q^{77} +(-8.39853 + 10.0090i) q^{78} +(-35.2967 - 96.9769i) q^{79} +(0.0934190 + 0.529805i) q^{80} +(-7.55610 + 42.8528i) q^{81} +(-37.8329 - 13.7701i) q^{82} +(-40.5635 - 70.2580i) q^{83} +(-40.3385 - 23.2894i) q^{84} +(-0.509057 + 0.427150i) q^{85} +(55.2107 + 65.7976i) q^{86} +(-45.0073 + 77.9550i) q^{87} +(35.2282 - 20.3390i) q^{88} +(-42.3645 + 116.395i) q^{89} +(-0.580381 - 0.102337i) q^{90} +(35.9057 - 6.33114i) q^{91} +(-35.7612 + 13.0160i) q^{92} +(-56.3878 - 47.3150i) q^{93} +89.8450i q^{94} +(0.621741 + 2.47861i) q^{95} +13.7423 q^{96} +(6.38795 - 7.61286i) q^{97} +(20.7538 + 57.0206i) q^{98} +(7.73797 + 43.8842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9	\( 24 q - 6 q^{3} + 12 q^{6} - 18 q^{7} + 6 q^{9} + 30 q^{11} - 36 q^{12} - 90 q^{13} - 48 q^{14} - 114 q^{15} + 18 q^{17} - 12 q^{19} + 24 q^{20} + 90 q^{21} + 84 q^{22} + 120 q^{23} - 24 q^{24} + 252 q^{25} + 48 q^{26} + 126 q^{27} + 72 q^{28} - 210 q^{29} - 108 q^{31} - 132 q^{33} - 24 q^{34} - 66 q^{35} - 12 q^{36} + 84 q^{38} + 120 q^{39} + 54 q^{41} + 72 q^{42} + 90 q^{43} - 48 q^{44} - 144 q^{45} - 360 q^{46} - 246 q^{47} - 48 q^{48} + 54 q^{49} - 432 q^{50} - 342 q^{51} + 36 q^{52} - 174 q^{53} - 42 q^{55} - 12 q^{57} + 48 q^{58} + 228 q^{59} + 132 q^{60} + 12 q^{61} + 204 q^{62} + 174 q^{63} + 96 q^{64} + 630 q^{65} + 696 q^{66} + 72 q^{67} - 48 q^{68} + 702 q^{69} + 528 q^{70} + 432 q^{71} + 96 q^{72} - 144 q^{74} + 72 q^{76} - 144 q^{77} - 708 q^{78} - 246 q^{79} - 642 q^{81} - 384 q^{82} - 126 q^{83} - 540 q^{84} - 684 q^{85} - 12 q^{86} - 324 q^{87} - 12 q^{89} - 336 q^{90} + 372 q^{91} - 132 q^{92} - 168 q^{93} - 570 q^{95} + 72 q^{97} + 384 q^{98} - 204 q^{99}+O(q^{100}) \) 24 * q - 6 * q^3 + 12 * q^6 - 18 * q^7 + 6 * q^9 + 30 * q^11 - 36 * q^12 - 90 * q^13 - 48 * q^14 - 114 * q^15 + 18 * q^17 - 12 * q^19 + 24 * q^20 + 90 * q^21 + 84 * q^22 + 120 * q^23 - 24 * q^24 + 252 * q^25 + 48 * q^26 + 126 * q^27 + 72 * q^28 - 210 * q^29 - 108 * q^31 - 132 * q^33 - 24 * q^34 - 66 * q^35 - 12 * q^36 + 84 * q^38 + 120 * q^39 + 54 * q^41 + 72 * q^42 + 90 * q^43 - 48 * q^44 - 144 * q^45 - 360 * q^46 - 246 * q^47 - 48 * q^48 + 54 * q^49 - 432 * q^50 - 342 * q^51 + 36 * q^52 - 174 * q^53 - 42 * q^55 - 12 * q^57 + 48 * q^58 + 228 * q^59 + 132 * q^60 + 12 * q^61 + 204 * q^62 + 174 * q^63 + 96 * q^64 + 630 * q^65 + 696 * q^66 + 72 * q^67 - 48 * q^68 + 702 * q^69 + 528 * q^70 + 432 * q^71 + 96 * q^72 - 144 * q^74 + 72 * q^76 - 144 * q^77 - 708 * q^78 - 246 * q^79 - 642 * q^81 - 384 * q^82 - 126 * q^83 - 540 * q^84 - 684 * q^85 - 12 * q^86 - 324 * q^87 - 12 * q^89 - 336 * q^90 + 372 * q^91 - 132 * q^92 - 168 * q^93 - 570 * q^95 + 72 * q^97 + 384 * q^98 - 204 * q^99

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