LMFDB - Embedded newform 38.3.f.a.15.1

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			15.1
Character	$\chi$	$=$	38.15
Dual form			38.3.f.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483690 + 1.32893i) q^{2} +(-5.23364 + 0.922832i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-1.06384 + 0.892670i) q^{5} +(1.30508 - 7.40149i) q^{6} +(-4.39759 + 7.61684i) q^{7} +(2.44949 - 1.41421i) q^{8} +(18.0821 - 6.58136i) q^{9} +O(q^{10})$	\(q+(-0.483690 + 1.32893i) q^{2} +(-5.23364 + 0.922832i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-1.06384 + 0.892670i) q^{5} +(1.30508 - 7.40149i) q^{6} +(-4.39759 + 7.61684i) q^{7} +(2.44949 - 1.41421i) q^{8} +(18.0821 - 6.58136i) q^{9} +(-0.671723 - 1.84554i) q^{10} +(6.05095 + 10.4805i) q^{11} +(9.20477 + 5.31438i) q^{12} +(-16.6164 - 2.92993i) q^{13} +(-7.99516 - 9.52826i) q^{14} +(4.74399 - 5.65366i) q^{15} +(0.694593 + 3.93923i) q^{16} +(14.9401 + 5.43774i) q^{17} +27.2132i q^{18} +(-15.3555 - 11.1896i) q^{19} +2.77750 q^{20} +(15.9863 - 43.9221i) q^{21} +(-16.8546 + 2.97193i) q^{22} +(-5.07035 - 4.25452i) q^{23} +(-11.5147 + 9.66195i) q^{24} +(-4.00630 + 22.7209i) q^{25} +(11.9309 - 20.6649i) q^{26} +(-47.1405 + 27.2166i) q^{27} +(16.5295 - 6.01625i) q^{28} +(6.87484 + 18.8885i) q^{29} +(5.21868 + 9.03902i) q^{30} +(11.7968 + 6.81091i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(-41.3403 - 49.2674i) q^{33} +(-14.4527 + 17.2241i) q^{34} +(-2.12099 - 12.0287i) q^{35} +(-36.1643 - 13.1627i) q^{36} +42.6785i q^{37} +(22.2975 - 14.9941i) q^{38} +89.6683 q^{39} +(-1.34345 + 3.69109i) q^{40} +(24.5997 - 4.33758i) q^{41} +(50.6368 + 42.4893i) q^{42} +(30.1018 - 25.2584i) q^{43} +(4.20294 - 23.8361i) q^{44} +(-13.3616 + 23.1429i) q^{45} +(8.10642 - 4.68024i) q^{46} +(17.3132 - 6.30150i) q^{47} +(-7.27050 - 19.9755i) q^{48} +(-14.1775 - 24.5562i) q^{49} +(-28.2566 - 16.3139i) q^{50} +(-83.2090 - 14.6720i) q^{51} +(21.6912 + 25.8506i) q^{52} +(13.2993 - 15.8495i) q^{53} +(-13.3674 - 75.8106i) q^{54} +(-15.7929 - 5.74815i) q^{55} +24.8765i q^{56} +(90.6915 + 44.3919i) q^{57} -28.4267 q^{58} +(-33.7515 + 92.7314i) q^{59} +(-14.5364 + 2.56316i) q^{60} +(-72.1635 - 60.5524i) q^{61} +(-14.7572 + 12.3828i) q^{62} +(-29.3886 + 166.671i) q^{63} +(4.00000 - 6.92820i) q^{64} +(20.2927 - 11.7160i) q^{65} +(85.4686 - 31.1080i) q^{66} +(-10.8546 - 29.8227i) q^{67} +(-15.8989 - 27.5377i) q^{68} +(30.4626 + 17.5876i) q^{69} +(17.0112 + 2.99953i) q^{70} +(-39.8932 - 47.5428i) q^{71} +(34.9846 - 41.6930i) q^{72} +(14.4304 + 81.8388i) q^{73} +(-56.7166 - 20.6431i) q^{74} -122.610i q^{75} +(9.14092 + 36.8842i) q^{76} -106.438 q^{77} +(-43.3716 + 119.163i) q^{78} +(42.4241 - 7.48052i) q^{79} +(-4.25537 - 3.57068i) q^{80} +(88.9337 - 74.6242i) q^{81} +(-6.13427 + 34.7892i) q^{82} +(10.9566 - 18.9774i) q^{83} +(-80.9576 + 46.7409i) q^{84} +(-20.7480 + 7.55165i) q^{85} +(19.0066 + 52.2202i) q^{86} +(-53.4113 - 92.5112i) q^{87} +(29.6435 + 17.1147i) q^{88} +(-3.51200 - 0.619260i) q^{89} +(-24.2924 - 28.9505i) q^{90} +(95.3891 - 113.680i) q^{91} +(2.29871 + 13.0366i) q^{92} +(-68.0257 - 24.7593i) q^{93} +26.0560i q^{94} +(26.3245 - 1.80341i) q^{95} +30.0627 q^{96} +(18.6693 - 51.2934i) q^{97} +(39.4909 - 6.96332i) q^{98} +(178.390 + 149.687i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.483690	+	1.32893i	−0.241845	+	0.664463i
$2$	−0.483690	+	1.32893i	−0.241845	+	0.664463i
$3$	−5.23364	+	0.922832i	−1.74455	+	0.307611i	−0.952881	−	0.303344i	$-0.901897\pi$
$3$	−5.23364	+	0.922832i	−1.74455	+	0.307611i	−0.791666	+	0.610954i	$0.790786\pi$
$4$	−1.53209	−	1.28558i	−0.383022	−	0.321394i
$5$	−1.06384	+	0.892670i	−0.212769	+	0.178534i	−0.742943	−	0.669354i	$-0.766571\pi$
$5$	−1.06384	+	0.892670i	−0.212769	+	0.178534i	0.530175	+	0.847888i	$0.322126\pi$
$6$	1.30508	−	7.40149i	0.217514	−	1.23358i
$7$	−4.39759	+	7.61684i	−0.628227	+	1.08812i	0.359681	+	0.933075i	$0.382886\pi$
$7$	−4.39759	+	7.61684i	−0.628227	+	1.08812i	−0.987907	+	0.155045i	$0.950448\pi$
$8$	2.44949	−	1.41421i	0.306186	−	0.176777i
$9$	18.0821	−	6.58136i	2.00913	−	0.731262i
$10$	−0.671723	−	1.84554i	−0.0671723	−	0.184554i
$11$	6.05095	+	10.4805i	0.550086	+	0.952777i	0.998268	+	0.0588343i	$0.0187384\pi$
$11$	6.05095	+	10.4805i	0.550086	+	0.952777i	−0.448182	+	0.893942i	$0.647928\pi$
$12$	9.20477	+	5.31438i	0.767064	+	0.442865i
$13$	−16.6164	−	2.92993i	−1.27819	−	0.225379i	−0.506978	−	0.861959i	$-0.669237\pi$
$13$	−16.6164	−	2.92993i	−1.27819	−	0.225379i	−0.771211	+	0.636580i	$0.780348\pi$
$14$	−7.99516	−	9.52826i	−0.571083	−	0.680590i
$15$	4.74399	−	5.65366i	0.316266	−	0.376911i
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	14.9401	+	5.43774i	0.878827	+	0.319867i	0.741736	−	0.670692i	$-0.234003\pi$
$17$	14.9401	+	5.43774i	0.878827	+	0.319867i	0.137091	+	0.990558i	$0.456225\pi$
$18$			27.2132i			1.51184i
$19$	−15.3555	−	11.1896i	−0.808186	−	0.588928i
$19$	−15.3555	−	11.1896i	−0.808186	−	0.588928i
$20$	2.77750			0.138875
$21$	15.9863	−	43.9221i	0.761253	−	2.09153i
$22$	−16.8546	+	2.97193i	−0.766120	+	0.135088i
$23$	−5.07035	−	4.25452i	−0.220450	−	0.184979i	0.525874	−	0.850563i	$-0.323738\pi$
$23$	−5.07035	−	4.25452i	−0.220450	−	0.184979i	−0.746324	+	0.665583i	$0.768183\pi$
$24$	−11.5147	+	9.66195i	−0.479778	+	0.402581i
$25$	−4.00630	+	22.7209i	−0.160252	+	0.908835i
$26$	11.9309	−	20.6649i	0.458879	−	0.794802i
$27$	−47.1405	+	27.2166i	−1.74594	+	1.00802i
$28$	16.5295	−	6.01625i	0.590340	−	0.214866i
$29$	6.87484	+	18.8885i	0.237064	+	0.651327i	0.999988	+	0.00483943i	$0.00154044\pi$
$29$	6.87484	+	18.8885i	0.237064	+	0.651327i	−0.762925	+	0.646487i	$0.776237\pi$
$30$	5.21868	+	9.03902i	0.173956	+	0.301301i
$31$	11.7968	+	6.81091i	0.380543	+	0.219707i	0.678055	−	0.735012i	$-0.262823\pi$
$31$	11.7968	+	6.81091i	0.380543	+	0.219707i	−0.297511	+	0.954718i	$0.596157\pi$
$32$	−5.57091	−	0.982302i	−0.174091	−	0.0306970i
$33$	−41.3403	−	49.2674i	−1.25273	−	1.49295i
$34$	−14.4527	+	17.2241i	−0.425079	+	0.506590i
$35$	−2.12099	−	12.0287i	−0.0605996	−	0.343678i
$36$	−36.1643	−	13.1627i	−1.00456	−	0.365631i
$37$			42.6785i			1.15347i	0.816930	+	0.576736i	$0.195674\pi$
$37$			42.6785i			1.15347i	−0.816930	+	0.576736i	$0.804326\pi$
$38$	22.2975	−	14.9941i	0.586776	−	0.394580i
$39$	89.6683			2.29919
$40$	−1.34345	+	3.69109i	−0.0335861	+	0.0922772i
$41$	24.5997	−	4.33758i	0.599992	−	0.105795i	0.134601	−	0.990900i	$-0.457025\pi$
$41$	24.5997	−	4.33758i	0.599992	−	0.105795i	0.465391	+	0.885105i	$0.345914\pi$
$42$	50.6368	+	42.4893i	1.20564	+	1.01165i
$43$	30.1018	−	25.2584i	0.700041	−	0.587404i	−0.221744	−	0.975105i	$-0.571175\pi$
$43$	30.1018	−	25.2584i	0.700041	−	0.587404i	0.921785	+	0.387701i	$0.126731\pi$
$44$	4.20294	−	23.8361i	0.0955214	−	0.541729i
$45$	−13.3616	+	23.1429i	−0.296924	+	0.514287i
$46$	8.10642	−	4.68024i	0.176227	−	0.101744i
$47$	17.3132	−	6.30150i	0.368367	−	0.134074i	−0.151203	−	0.988503i	$-0.548315\pi$
$47$	17.3132	−	6.30150i	0.368367	−	0.134074i	0.519569	+	0.854428i	$0.326092\pi$
$48$	−7.27050	−	19.9755i	−0.151469	−	0.416157i
$49$	−14.1775	−	24.5562i	−0.289338	−	0.501147i
$50$	−28.2566	−	16.3139i	−0.565131	−	0.326279i
$51$	−83.2090	−	14.6720i	−1.63155	−	0.287686i
$52$	21.6912	+	25.8506i	0.417139	+	0.497127i
$53$	13.2993	−	15.8495i	0.250930	−	0.299047i	−0.625845	−	0.779948i	$-0.715246\pi$
$53$	13.2993	−	15.8495i	0.250930	−	0.299047i	0.876775	+	0.480900i	$0.159690\pi$
$54$	−13.3674	−	75.8106i	−0.247545	−	1.40390i
$55$	−15.7929	−	5.74815i	−0.287144	−	0.104512i
$56$			24.8765i			0.444223i
$57$	90.6915	+	44.3919i	1.59108	+	0.778806i
$58$	−28.4267			−0.490115
$59$	−33.7515	+	92.7314i	−0.572059	+	1.57172i	0.229186	+	0.973383i	$0.426394\pi$
$59$	−33.7515	+	92.7314i	−0.572059	+	1.57172i	−0.801245	+	0.598337i	$0.795829\pi$
$60$	−14.5364	+	2.56316i	−0.242274	+	0.0427194i
$61$	−72.1635	−	60.5524i	−1.18301	−	0.992662i	−0.999954	−	0.00955959i	$-0.996957\pi$
$61$	−72.1635	−	60.5524i	−1.18301	−	0.992662i	−0.183055	−	0.983103i	$-0.558599\pi$
$62$	−14.7572	+	12.3828i	−0.238019	+	0.199722i
$63$	−29.3886	+	166.671i	−0.466486	+	2.64557i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	20.2927	−	11.7160i	0.312196	−	0.180246i
$66$	85.4686	−	31.1080i	1.29498	−	0.471334i
$67$	−10.8546	−	29.8227i	−0.162009	−	0.445115i	0.831953	−	0.554847i	$-0.187223\pi$
$67$	−10.8546	−	29.8227i	−0.162009	−	0.445115i	−0.993961	+	0.109732i	$0.965001\pi$
$68$	−15.8989	−	27.5377i	−0.233807	−	0.404966i
$69$	30.4626	+	17.5876i	0.441487	+	0.254892i
$70$	17.0112	+	2.99953i	0.243017	+	0.0428504i
$71$	−39.8932	−	47.5428i	−0.561876	−	0.669617i	0.408067	−	0.912952i	$-0.366203\pi$
$71$	−39.8932	−	47.5428i	−0.561876	−	0.669617i	−0.969942	+	0.243335i	$0.921759\pi$
$72$	34.9846	−	41.6930i	0.485897	−	0.579069i
$73$	14.4304	+	81.8388i	0.197676	+	1.12108i	0.908555	+	0.417764i	$0.137186\pi$
$73$	14.4304	+	81.8388i	0.197676	+	1.12108i	−0.710879	+	0.703314i	$0.751703\pi$
$74$	−56.7166	−	20.6431i	−0.766440	−	0.278961i
$75$		−	122.610i		−	1.63480i
$76$	9.14092	+	36.8842i	0.120275	+	0.485318i
$77$	−106.438			−1.38231
$78$	−43.3716	+	119.163i	−0.556047	+	1.52773i
$79$	42.4241	−	7.48052i	0.537014	−	0.0946901i	0.101438	−	0.994842i	$-0.467656\pi$
$79$	42.4241	−	7.48052i	0.537014	−	0.0946901i	0.435576	+	0.900152i	$0.356545\pi$
$80$	−4.25537	−	3.57068i	−0.0531921	−	0.0446335i
$81$	88.9337	−	74.6242i	1.09795	−	0.921286i
$82$	−6.13427	+	34.7892i	−0.0748082	+	0.424258i
$83$	10.9566	−	18.9774i	0.132007	−	0.228643i	−0.792443	−	0.609946i	$-0.791191\pi$
$83$	10.9566	−	18.9774i	0.132007	−	0.228643i	0.924450	+	0.381303i	$0.124524\pi$
$84$	−80.9576	+	46.7409i	−0.963781	+	0.556439i
$85$	−20.7480	+	7.55165i	−0.244094	+	0.0888429i
$86$	19.0066	+	52.2202i	0.221007	+	0.607212i
$87$	−53.4113	−	92.5112i	−0.613924	−	1.06335i
$88$	29.6435	+	17.1147i	0.336857	+	0.194485i
$89$	−3.51200	−	0.619260i	−0.0394607	−	0.00695798i	0.153883	−	0.988089i	$-0.450822\pi$
$89$	−3.51200	−	0.619260i	−0.0394607	−	0.00695798i	−0.193344	+	0.981131i	$0.561933\pi$
$90$	−24.2924	−	28.9505i	−0.269915	−	0.321673i
$91$	95.3891	−	113.680i	1.04823	−	1.24923i
$92$	2.29871	+	13.0366i	0.0249860	+	0.141702i
$93$	−68.0257	−	24.7593i	−0.731459	−	0.266229i
$94$			26.0560i			0.277191i
$95$	26.3245	−	1.80341i	0.277100	−	0.0189833i
$96$	30.0627			0.313153
$97$	18.6693	−	51.2934i	0.192467	−	0.528798i	−0.805496	−	0.592601i	$-0.798101\pi$
$97$	18.6693	−	51.2934i	0.192467	−	0.528798i	0.997962	+	0.0638037i	$0.0203232\pi$
$98$	39.4909	−	6.96332i	0.402969	−	0.0710543i
$99$	178.390	+	149.687i	1.80192	+	1.51199i
$100$	35.3474	−	29.6600i	0.353474	−	0.296600i
$101$	−19.8517	+	112.585i	−0.196552	+	1.11470i	0.713640	+	0.700513i	$0.247045\pi$
$101$	−19.8517	+	112.585i	−0.196552	+	1.11470i	−0.910192	+	0.414188i	$0.864066\pi$
$102$	59.7453	−	103.482i	0.585739	−	1.01453i
$103$	38.5436	−	22.2532i	0.374210	−	0.216050i	−0.301086	−	0.953597i	$-0.597349\pi$
$103$	38.5436	−	22.2532i	0.374210	−	0.216050i	0.675296	+	0.737547i	$0.264016\pi$
$104$	−44.8454	+	16.3224i	−0.431205	+	0.156946i
$105$	22.2010	+	60.9967i	0.211438	+	0.580921i
$106$	14.6301	+	25.3400i	0.138020	+	0.239057i
$107$	123.253	+	71.1602i	1.15190	+	0.665049i	0.949349	−	0.314223i	$-0.101744\pi$
$107$	123.253	+	71.1602i	1.15190	+	0.665049i	0.202549	+	0.979272i	$0.435077\pi$
$108$	107.212	+	18.9044i	0.992707	+	0.175041i
$109$	20.2737	+	24.1613i	0.185997	+	0.221663i	0.850983	−	0.525193i	$-0.176007\pi$
$109$	20.2737	+	24.1613i	0.185997	+	0.221663i	−0.664986	+	0.746856i	$0.731562\pi$
$110$	15.2777	−	18.2073i	0.138889	−	0.165521i
$111$	−39.3851	−	223.364i	−0.354821	−	2.01229i
$112$	−33.0590	−	12.0325i	−0.295170	−	0.107433i
$113$			17.6532i			0.156223i	0.996945	+	0.0781113i	$0.0248890\pi$
$113$			17.6532i			0.156223i	−0.996945	+	0.0781113i	$0.975111\pi$
$114$	−102.860	+	99.0503i	−0.902281	+	0.868863i
$115$	9.19194			0.0799299
$116$	13.7497	−	37.7770i	0.118532	−	0.325663i
$117$	−319.744	+	56.3795i	−2.73285	+	0.481876i
$118$	−106.908	−	89.7065i	−0.906000	−	0.760224i
$119$	−107.119	+	89.8832i	−0.900157	+	0.755321i
$120$	3.62486	−	20.5576i	0.0302072	−	0.171313i
$121$	−12.7279	+	22.0453i	−0.105189	+	0.182193i
$122$	115.374	−	66.6114i	0.945692	−	0.545995i
$123$	−124.743	+	45.4027i	−1.01417	+	0.369128i
$124$	−9.31787	−	25.6006i	−0.0751441	−	0.206457i
$125$	−33.3795	−	57.8150i	−0.267036	−	0.462520i
$126$	−207.278	−	119.672i	−1.64507	−	0.949780i
$127$	−30.3701	−	5.35507i	−0.239135	−	0.0421659i	0.0527962	−	0.998605i	$-0.483187\pi$
$127$	−30.3701	−	5.35507i	−0.239135	−	0.0421659i	−0.291931	+	0.956439i	$0.594298\pi$
$128$	7.27231	+	8.66680i	0.0568149	+	0.0677094i
$129$	−134.233	+	159.972i	−1.04056	+	1.24009i
$130$	5.75434	+	32.6345i	0.0442641	+	0.251034i
$131$	190.626	+	69.3824i	1.45516	+	0.529636i	0.944028	−	0.329864i	$-0.107003\pi$
$131$	190.626	+	69.3824i	1.45516	+	0.529636i	0.511135	+	0.859500i	$0.329225\pi$
$132$			128.628i			0.974455i
$133$	152.757	−	67.7533i	1.14855	−	0.509423i
$134$	44.8824			0.334943
$135$	25.8546	−	71.0350i	0.191516	−	0.526185i
$136$	44.2857	−	7.80876i	0.325630	−	0.0574173i
$137$	−7.06246	−	5.92611i	−0.0515508	−	0.0432563i	0.616648	−	0.787239i	$-0.288490\pi$
$137$	−7.06246	−	5.92611i	−0.0515508	−	0.0432563i	−0.668199	+	0.743983i	$0.732935\pi$
$138$	−38.1070	+	31.9756i	−0.276138	+	0.231707i
$139$	23.8850	−	135.459i	0.171835	−	0.974523i	−0.769900	−	0.638165i	$-0.779694\pi$
$139$	23.8850	−	135.459i	0.171835	−	0.974523i	0.941734	−	0.336358i	$-0.109195\pi$
$140$	−12.2143	+	21.1558i	−0.0872449	+	0.151113i
$141$	−84.7960	+	48.9570i	−0.601390	+	0.347213i
$142$	82.4768	−	30.0191i	0.580822	−	0.211402i
$143$	−69.8380	−	191.878i	−0.488377	−	1.34181i
$144$	38.4852	+	66.6584i	0.267259	+	0.462905i
$145$	−24.1749	−	13.9574i	−0.166724	−	0.0962579i
$146$	−115.737	−	20.4076i	−0.792722	−	0.139778i
$147$	96.8614	+	115.435i	0.658921	+	0.785272i
$148$	54.8664	−	65.3872i	0.370719	−	0.441806i
$149$	9.55879	+	54.2106i	0.0641530	+	0.363830i	0.999937	+	0.0112550i	$0.00358264\pi$
$149$	9.55879	+	54.2106i	0.0641530	+	0.363830i	−0.935784	+	0.352575i	$0.885306\pi$
$150$	162.940	+	59.3052i	1.08626	+	0.395368i
$151$			150.117i			0.994150i	0.867708	+	0.497075i	$0.165593\pi$
$151$			150.117i			0.994150i	−0.867708	+	0.497075i	$0.834407\pi$
$152$	−53.4377	−	5.69289i	−0.351564	−	0.0374532i
$153$	305.936			1.99958
$154$	51.4831	−	141.449i	0.334306	−	0.918497i
$155$	−18.6299	+	3.28495i	−0.120193	+	0.0211932i
$156$	−137.380	−	115.275i	−0.880640	−	0.738945i
$157$	−22.3853	+	18.7835i	−0.142582	+	0.119640i	−0.711289	−	0.702900i	$-0.751888\pi$
$157$	−22.3853	+	18.7835i	−0.142582	+	0.119640i	0.568707	+	0.822540i	$0.307444\pi$
$158$	−10.5791	+	59.9968i	−0.0669560	+	0.379726i
$159$	−54.9774	+	95.2236i	−0.345770	+	0.598891i
$160$	6.80345	−	3.92797i	0.0425216	−	0.0245498i
$161$	54.7033	−	19.9104i	0.339772	−	0.123667i
$162$	56.1538	+	154.281i	0.346628	+	0.952353i
$163$	5.40139	+	9.35548i	0.0331374	+	0.0573956i	0.882118	−	0.471028i	$-0.156117\pi$
$163$	5.40139	+	9.35548i	0.0331374	+	0.0573956i	−0.848981	+	0.528423i	$0.822783\pi$
$164$	−43.2652	−	24.9792i	−0.263812	−	0.152312i
$165$	87.9591	+	15.5096i	0.533085	+	0.0939973i
$166$	19.9200	+	23.7397i	0.120000	+	0.143010i
$167$	−183.419	+	218.591i	−1.09832	+	1.30893i	−0.151036	+	0.988528i	$0.548261\pi$
$167$	−183.419	+	218.591i	−1.09832	+	1.30893i	−0.947283	+	0.320398i	$0.896183\pi$
$168$	−22.9568	−	130.195i	−0.136648	−	0.774969i
$169$	108.714	+	39.5686i	0.643276	+	0.234133i
$170$		−	31.2252i		−	0.183678i
$171$	−351.304	−	101.272i	−2.05441	−	0.592235i
$172$	−78.5901			−0.456919
$173$	51.8267	−	142.393i	0.299577	−	0.823080i	−0.694994	−	0.719016i	$-0.744593\pi$
$173$	51.8267	−	142.393i	0.299577	−	0.823080i	0.994571	−	0.104064i	$-0.0331848\pi$
$174$	148.775	−	26.2330i	0.855029	−	0.150765i
$175$	−155.443	−	130.432i	−0.888247	−	0.745328i
$176$	−37.0823	+	31.1158i	−0.210695	+	0.176794i
$177$	91.0676	−	516.470i	0.514506	−	2.91791i
$178$	2.52167	−	4.36766i	0.0141667	−	0.0245374i
$179$	245.794	−	141.909i	1.37315	−	0.792788i	0.381826	−	0.924234i	$-0.375295\pi$
$179$	245.794	−	141.909i	1.37315	−	0.792788i	0.991323	+	0.131446i	$0.0419620\pi$
$180$	50.2231	−	18.2797i	0.279017	−	0.101554i
$181$	119.504	+	328.334i	0.660242	+	1.81400i	0.575831	+	0.817569i	$0.304678\pi$
$181$	119.504	+	328.334i	0.660242	+	1.81400i	0.0844105	+	0.996431i	$0.473099\pi$
$182$	104.934	+	181.751i	0.576560	+	0.998632i
$183$	433.558	+	250.315i	2.36917	+	1.36784i
$184$	−18.4366	−	3.25086i	−0.100199	−	0.0176677i
$185$	−38.0978	−	45.4032i	−0.205934	−	0.245423i
$186$	65.8067	−	78.4253i	0.353799	−	0.421642i
$187$	33.4110	+	189.483i	0.178669	+	1.01328i
$188$	−34.6265	−	12.6030i	−0.184183	−	0.0670372i
$189$		−	478.749i		−	2.53306i
$190$	−10.3363	+	35.8556i	−0.0544015	+	0.188714i
$191$	−284.702			−1.49058			−0.745292	−	0.666738i	$-0.767690\pi$
$191$	−284.702			−1.49058			−0.745292	+	0.666738i	$0.767690\pi$
$192$	−14.5410	+	39.9511i	−0.0757343	+	0.208078i
$193$	−206.920	+	36.4855i	−1.07212	+	0.189044i	−0.681729	−	0.731604i	$-0.738772\pi$
$193$	−206.920	+	36.4855i	−1.07212	+	0.189044i	−0.390393	+	0.920648i	$0.627661\pi$
$194$	59.1350	+	49.6201i	0.304819	+	0.255774i
$195$	−95.3930	+	80.0442i	−0.489195	+	0.410483i
$196$	−9.84762	+	55.8486i	−0.0502430	+	0.284942i
$197$	109.694	−	189.995i	0.556822	−	0.964444i	−0.440937	−	0.897538i	$-0.645354\pi$
$197$	109.694	−	189.995i	0.556822	−	0.964444i	0.997759	−	0.0669060i	$-0.0213128\pi$
$198$	−285.209	+	164.665i	−1.44045	+	0.831643i
$199$	−101.187	+	36.8290i	−0.508477	+	0.185071i	−0.583503	−	0.812111i	$-0.698318\pi$
$199$	−101.187	+	36.8290i	−0.508477	+	0.185071i	0.0750258	+	0.997182i	$0.476096\pi$
$200$	22.3188	+	61.3203i	0.111594	+	0.306602i
$201$	84.3303	+	146.064i	0.419554	+	0.726688i
$202$	−140.015	−	80.8375i	−0.693142	−	0.400186i
$203$	−174.103	−	30.6991i	−0.857652	−	0.151227i
$204$	108.622	+	129.450i	0.532459	+	0.634560i
$205$	−22.2981	+	26.5739i	−0.108771	+	0.129629i
$206$	10.9297	+	61.9853i	0.0530567	+	0.300899i
$207$	−119.683	−	43.5611i	−0.578180	−	0.210440i
$208$		−	67.4911i		−	0.324477i
$209$	24.3579	−	228.642i	0.116545	−	1.09398i
$210$	−91.7985			−0.437135
$211$	−22.6688	+	62.2819i	−0.107435	+	0.295175i	−0.981748	−	0.190188i	$-0.939090\pi$
$211$	−22.6688	+	62.2819i	−0.107435	+	0.295175i	0.874313	+	0.485363i	$0.161312\pi$
$212$	−40.7514	+	7.18558i	−0.192224	+	0.0338942i
$213$	252.661	+	212.007i	1.18620	+	0.995340i
$214$	−154.183	+	129.375i	−0.720481	+	0.604555i
$215$	−9.47614	+	53.7419i	−0.0440751	+	0.249962i
$216$	−76.9801	+	133.333i	−0.356389	+	0.617284i
$217$	−103.755	+	59.9031i	−0.478135	+	0.276051i
$218$	−41.9147	+	15.2557i	−0.192269	+	0.0699803i
$219$	−151.047	−	414.998i	−0.689712	−	1.89497i
$220$	16.8065	+	29.1097i	0.0763931	+	0.132317i
$221$	−232.319	−	134.129i	−1.05122	−	0.606919i
$222$	315.884	+	55.6989i	1.42290	+	0.250896i
$223$	−77.4222	−	92.2682i	−0.347185	−	0.413759i	0.563988	−	0.825783i	$-0.309266\pi$
$223$	−77.4222	−	92.2682i	−0.347185	−	0.413759i	−0.911173	+	0.412024i	$0.864822\pi$
$224$	31.9806	−	38.1130i	0.142771	−	0.170147i
$225$	77.0917	+	437.209i	0.342630	+	1.94315i
$226$	−23.4597	−	8.53865i	−0.103804	−	0.0377816i
$227$			209.919i			0.924754i	0.886684	+	0.462377i	$0.153003\pi$
$227$			209.919i			0.924754i	−0.886684	+	0.462377i	$0.846997\pi$
$228$	−81.8782	−	184.603i	−0.359115	−	0.809663i
$229$	−328.702			−1.43538			−0.717691	−	0.696362i	$-0.754801\pi$
$229$	−328.702			−1.43538			−0.717691	+	0.696362i	$0.754801\pi$
$230$	−4.44604	+	12.2154i	−0.0193306	+	0.0531105i
$231$	557.059	−	98.2246i	2.41151	−	0.425215i
$232$	43.5522	+	36.5446i	0.187725	+	0.157520i
$233$	202.214	−	169.677i	0.867869	−	0.728229i	−0.0957789	−	0.995403i	$-0.530534\pi$
$233$	202.214	−	169.677i	0.867869	−	0.728229i	0.963648	+	0.267174i	$0.0860897\pi$
$234$	79.7326	−	452.186i	0.340738	−	1.93242i
$235$	−12.7934	+	22.1588i	−0.0544400	+	0.0942928i
$236$	170.924	−	98.6827i	0.724252	−	0.418147i
$237$	−215.129	+	78.3007i	−0.907719	+	0.330383i
$238$	−67.6360	−	185.828i	−0.284185	−	0.780791i
$239$	173.905	+	301.212i	0.727636	+	1.26030i	0.957880	+	0.287169i	$0.0927142\pi$
$239$	173.905	+	301.212i	0.727636	+	1.26030i	−0.230244	+	0.973133i	$0.573952\pi$
$240$	25.5662	+	14.7607i	0.106526	+	0.0615028i
$241$	216.962	+	38.2563i	0.900258	+	0.158740i	0.604577	−	0.796547i	$-0.293342\pi$
$241$	216.962	+	38.2563i	0.900258	+	0.158740i	0.295681	+	0.955287i	$0.404453\pi$
$242$	−23.1403	−	27.5775i	−0.0956209	−	0.113957i
$243$	−81.6808	+	97.3434i	−0.336135	+	0.400590i
$244$	32.7163	+	185.543i	0.134083	+	0.760423i
$245$	37.0033	+	13.4681i	0.151034	+	0.0549718i
$246$		−	187.735i		−	0.763150i
$247$	222.369	+	230.922i	0.900281	+	0.934909i
$248$	38.5283			0.155356
$249$	−39.8300	+	109.432i	−0.159960	+	0.439486i
$250$	92.9772	−	16.3944i	0.371909	−	0.0655776i
$251$	−88.0561	−	73.8878i	−0.350821	−	0.294374i	0.450299	−	0.892878i	$-0.351318\pi$
$251$	−88.0561	−	73.8878i	−0.350821	−	0.294374i	−0.801120	+	0.598504i	$0.795762\pi$
$252$	259.294	−	217.573i	1.02894	−	0.863387i
$253$	13.9094	−	78.8839i	0.0549777	−	0.311794i
$254$	21.8062	−	37.7695i	0.0858512	−	0.148699i
$255$	101.619	−	58.6695i	0.398504	−	0.230077i
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	−74.4601	−	204.577i	−0.289728	−	0.796021i	−0.996104	−	0.0881845i	$-0.971893\pi$
$257$	−74.4601	−	204.577i	−0.289728	−	0.796021i	0.706376	−	0.707837i	$-0.250329\pi$
$258$	−147.664	−	255.762i	−0.572342	−	0.991325i
$259$	−325.075	−	187.682i	−1.25512	−	0.724642i
$260$	−46.1521	−	8.13786i	−0.177508	−	0.0312995i
$261$	248.624	+	296.298i	0.952581	+	1.13524i
$262$	−184.408	+	219.769i	−0.703847	+	0.838813i
$263$	−53.6309	−	304.156i	−0.203920	−	1.15649i	−0.899131	−	0.437680i	$-0.855800\pi$
$263$	−53.6309	−	304.156i	−0.203920	−	1.15649i	0.695211	−	0.718806i	$-0.255311\pi$
$264$	−170.937	−	62.2160i	−0.647489	−	0.235667i
$265$			28.7333i			0.108427i
$266$	16.1522	+	235.774i	0.0607225	+	0.886369i
$267$	18.9520			0.0709813
$268$	−21.7092	+	59.6454i	−0.0810043	+	0.222557i
$269$	375.385	−	66.1905i	1.39548	−	0.246061i	0.575197	−	0.818015i	$-0.304925\pi$
$269$	375.385	−	66.1905i	1.39548	−	0.246061i	0.820286	+	0.571954i	$0.193814\pi$
$270$	81.8947	+	68.7178i	0.303314	+	0.254510i
$271$	99.7480	−	83.6985i	0.368074	−	0.308851i	−0.439925	−	0.898034i	$-0.644995\pi$
$271$	99.7480	−	83.6985i	0.368074	−	0.308851i	0.807999	+	0.589184i	$0.200551\pi$
$272$	−11.0432	+	62.6294i	−0.0406002	+	0.230255i
$273$	−394.324	+	682.990i	−1.44441	+	2.50179i
$274$	11.2914	−	6.51909i	0.0412095	−	0.0237923i
$275$	−262.369	+	95.4945i	−0.954069	+	0.347253i
$276$	−24.0612	−	66.1077i	−0.0871783	−	0.239521i
$277$	−203.421	−	352.335i	−0.734370	−	1.27197i	−0.954999	−	0.296609i	$-0.904144\pi$
$277$	−203.421	−	352.335i	−0.734370	−	1.27197i	0.220629	−	0.975358i	$-0.429189\pi$
$278$	168.462	+	97.2613i	0.605977	+	0.349861i
$279$	258.137	+	45.5165i	0.925223	+	0.163142i
$280$	−22.2065	−	26.4647i	−0.0793090	−	0.0945168i
$281$	264.929	−	315.730i	0.942807	−	1.12359i	−0.0493729	−	0.998780i	$-0.515722\pi$
$281$	264.929	−	315.730i	0.942807	−	1.12359i	0.992180	−	0.124814i	$-0.0398333\pi$
$282$	−24.0453	−	136.368i	−0.0852670	−	0.483573i
$283$	322.592	+	117.414i	1.13990	+	0.414890i	0.841877	−	0.539669i	$-0.181451\pi$
$283$	322.592	+	117.414i	1.13990	+	0.414890i	0.298023	+	0.954559i	$0.403673\pi$
$284$			124.125i			0.437062i
$285$	−136.109	+	33.7315i	−0.477575	+	0.118356i
$286$	288.772			1.00969
$287$	−75.1405	+	206.447i	−0.261813	+	0.719327i
$288$	−107.199	+	18.9021i	−0.372219	+	0.0656322i
$289$	−27.7504	−	23.2853i	−0.0960221	−	0.0805721i
$290$	30.2415	−	25.3756i	0.104281	−	0.0875022i
$291$	−50.3730	+	285.680i	−0.173103	+	0.981717i
$292$	83.1012	−	143.936i	0.284593	−	0.492930i
$293$	89.0414	−	51.4081i	0.303896	−	0.175454i	−0.340296	−	0.940318i	$-0.610527\pi$
$293$	89.0414	−	51.4081i	0.303896	−	0.175454i	0.644192	+	0.764864i	$0.277194\pi$
$294$	−200.255	+	72.8870i	−0.681141	+	0.247915i
$295$	−46.8723	−	128.781i	−0.158889	−	0.436544i
$296$	60.3565	+	104.541i	0.203907	+	0.353177i
$297$	−570.489	−	329.372i	−1.92084	−	1.10900i
$298$	−76.6654	−	13.5182i	−0.257266	−	0.0453630i
$299$	71.7857	+	85.5508i	0.240086	+	0.286123i
$300$	−157.624	+	187.849i	−0.525415	+	0.626165i
$301$	60.0140	+	340.356i	0.199382	+	1.13075i
$302$	−199.494	−	72.6098i	−0.660576	−	0.240430i
$303$		−	607.548i		−	2.00511i
$304$	33.4127	−	68.2612i	0.109910	−	0.224543i
$305$	130.824			0.428931
$306$	−147.978	+	406.566i	−0.483588	+	1.32865i
$307$	482.848	−	85.1392i	1.57280	−	0.277326i	0.681869	−	0.731474i	$-0.261167\pi$
$307$	482.848	−	85.1392i	1.57280	−	0.277326i	0.890926	+	0.454148i	$0.150056\pi$
$308$	163.073	+	136.834i	0.529457	+	0.444267i
$309$	−181.188	+	152.034i	−0.586368	+	0.492021i
$310$	4.64562	−	26.3466i	0.0149859	−	0.0849891i
$311$	−51.0404	+	88.4046i	−0.164117	+	0.284259i	−0.936341	−	0.351091i	$-0.885811\pi$
$311$	−51.0404	+	88.4046i	−0.164117	+	0.284259i	0.772224	+	0.635350i	$0.219144\pi$
$312$	219.642	−	126.810i	0.703980	−	0.406443i
$313$	−163.671	+	59.5714i	−0.522911	+	0.190324i	−0.589970	−	0.807425i	$-0.700861\pi$
$313$	−163.671	+	59.5714i	−0.522911	+	0.190324i	0.0670592	+	0.997749i	$0.478638\pi$
$314$	−14.1344	−	38.8339i	−0.0450139	−	0.123675i
$315$	−117.517	−	203.546i	−0.373071	−	0.646178i
$316$	−74.6143	−	43.0786i	−0.236121	−	0.136325i
$317$	310.871	+	54.8149i	0.980666	+	0.172918i	0.640927	−	0.767602i	$-0.278550\pi$
$317$	310.871	+	54.8149i	0.980666	+	0.172918i	0.339739	+	0.940520i	$0.389661\pi$
$318$	−99.9532	−	119.120i	−0.314318	−	0.374590i
$319$	−156.362	+	186.345i	−0.490164	+	0.584154i
$320$	1.92923	+	10.9412i	0.00602884	+	0.0341912i
$321$	−710.732	−	258.685i	−2.21412	−	0.805873i
$322$			82.3271i			0.255674i
$323$	−168.566	−	250.673i	−0.521877	−	0.776078i
$324$	−232.189			−0.716634
$325$	133.141	−	365.802i	0.409665	−	1.12554i
$326$	−15.0453	+	2.65290i	−0.0461513	+	0.00813773i
$327$	−128.402	−	107.742i	−0.392667	−	0.329487i
$328$	54.1224	−	45.4140i	0.165007	−	0.138457i
$329$	−28.1389	+	159.584i	−0.0855285	+	0.485056i
$330$	−63.1559	+	109.389i	−0.191382	+	0.331483i
$331$	−419.076	+	241.953i	−1.26609	+	0.730977i	−0.974246	−	0.225489i	$-0.927602\pi$
$331$	−419.076	+	241.953i	−1.26609	+	0.730977i	−0.291844	+	0.956466i	$0.594269\pi$
$332$	−41.1834	+	14.9895i	−0.124046	+	0.0451492i
$333$	280.883	+	771.719i	0.843491	+	2.31747i
$334$	−201.773	−	349.481i	−0.604110	−	1.04635i
$335$	38.1694	+	22.0371i	0.113938	+	0.0657824i
$336$	184.123	+	32.4659i	0.547985	+	0.0966246i
$337$	−149.781	−	178.502i	−0.444453	−	0.529679i	0.496581	−	0.867990i	$-0.334589\pi$
$337$	−149.781	−	178.502i	−0.444453	−	0.529679i	−0.941034	+	0.338312i	$0.890144\pi$
$338$	−105.167	+	125.334i	−0.311146	+	0.370809i
$339$	−16.2909	−	92.3903i	−0.0480558	−	0.272538i
$340$	41.4960	+	15.1033i	0.122047	+	0.0444215i
$341$			164.850i			0.483430i
$342$	304.505	−	417.872i	0.890366	−	1.22185i
$343$	−181.576			−0.529375
$344$	38.0132	−	104.440i	0.110504	−	0.303606i
$345$	−48.1073	+	8.48261i	−0.139441	+	0.0245873i
$346$	164.161	+	137.748i	0.474455	+	0.398115i
$347$	−138.706	+	116.388i	−0.399730	+	0.335413i	−0.820389	−	0.571805i	$-0.806243\pi$
$347$	−138.706	+	116.388i	−0.399730	+	0.335413i	0.420659	+	0.907219i	$0.361799\pi$
$348$	−37.0991	+	210.400i	−0.106607	+	0.604597i
$349$	238.811	−	413.632i	0.684271	−	1.18519i	−0.289395	−	0.957210i	$-0.593454\pi$
$349$	238.811	−	413.632i	0.684271	−	1.18519i	0.973665	−	0.227982i	$-0.0732127\pi$
$350$	248.521	−	143.484i	0.710061	−	0.409954i
$351$	863.049	−	314.124i	2.45883	−	0.894941i
$352$	−23.4142	−	64.3301i	−0.0665177	−	0.182756i
$353$	112.439	+	194.751i	0.318525	+	0.551701i	0.980180	−	0.198107i	$-0.0634792\pi$
$353$	112.439	+	194.751i	0.318525	+	0.551701i	−0.661656	+	0.749808i	$0.730146\pi$
$354$	642.302	+	370.833i	1.81441	+	1.04755i
$355$	84.8801	+	14.9667i	0.239099	+	0.0421596i
$356$	4.58459	+	5.46370i	0.0128781	+	0.0153475i
$357$	477.673	−	569.269i	1.33802	−	1.59459i
$358$	69.6988	+	395.282i	0.194689	+	1.10414i
$359$	219.445	+	79.8714i	0.611267	+	0.222483i	0.629058	−	0.777359i	$-0.283441\pi$
$359$	219.445	+	79.8714i	0.611267	+	0.222483i	−0.0177904	+	0.999842i	$0.505663\pi$
$360$			75.5845i			0.209957i
$361$	110.584	+	343.645i	0.306328	+	0.951926i
$362$	−494.134			−1.36501
$363$	46.2690	−	127.123i	0.127463	−	0.350201i
$364$	−292.289	+	51.5384i	−0.802992	+	0.141589i
$365$	−88.4067	−	74.1820i	−0.242210	−	0.203238i
$366$	−542.357	+	455.092i	−1.48185	+	1.24342i
$367$	37.9658	−	215.315i	0.103449	−	0.586689i	−0.888379	−	0.459110i	$-0.848168\pi$
$367$	37.9658	−	215.315i	0.103449	−	0.586689i	0.991828	−	0.127579i	$-0.0407206\pi$
$368$	13.2377	−	22.9284i	0.0359721	−	0.0623055i
$369$	416.267	−	240.332i	1.12810	−	0.651306i
$370$	78.7650	−	28.6681i	0.212878	−	0.0774814i
$371$	62.2383	+	170.998i	0.167758	+	0.460912i
$372$	72.3915	+	125.386i	0.194601	+	0.337058i
$373$	420.325	+	242.675i	1.12688	+	0.650602i	0.943147	−	0.332375i	$-0.107850\pi$
$373$	420.325	+	242.675i	1.12688	+	0.650602i	0.183729	+	0.982977i	$0.441183\pi$
$374$	−267.970	−	47.2503i	−0.716497	−	0.126338i
$375$	228.050	+	271.779i	0.608133	+	0.724745i
$376$	33.4969	−	39.9201i	0.0890875	−	0.106170i
$377$	−58.8936	−	334.002i	−0.156216	−	0.885947i
$378$	636.222	+	231.566i	1.68313	+	0.612608i
$379$			41.9601i			0.110713i	0.998467	+	0.0553563i	$0.0176295\pi$
$379$			41.9601i			0.110713i	−0.998467	+	0.0553563i	$0.982371\pi$
$380$	−42.6499	−	31.0791i	−0.112237	−	0.0817872i
$381$	163.888			0.430153
$382$	137.707	−	378.347i	0.360490	−	0.990438i
$383$	−556.885	+	98.1939i	−1.45401	+	0.256381i	−0.844141	−	0.536122i	$-0.819889\pi$
$383$	−556.885	+	98.1939i	−1.45401	+	0.256381i	−0.609868	+	0.792503i	$0.708778\pi$
$384$	−46.0587	−	38.6478i	−0.119944	−	0.100645i
$385$	113.234	−	95.0142i	0.294113	−	0.246790i
$386$	51.5983	−	292.628i	0.133674	−	0.758105i
$387$	378.070	−	654.836i	0.976924	−	1.69208i
$388$	−94.5445	+	54.5853i	−0.243671	+	0.140684i
$389$	−317.858	+	115.691i	−0.817115	+	0.297406i	−0.716560	−	0.697526i	$-0.754284\pi$
$389$	−317.858	+	115.691i	−0.817115	+	0.297406i	−0.100555	+	0.994931i	$0.532062\pi$
$390$	−60.2323	−	165.487i	−0.154442	−	0.424325i
$391$	−52.6163	−	91.1341i	−0.134568	−	0.233079i
$392$	−69.4555	−	40.1001i	−0.177182	−	0.102296i
$393$	−1061.70	−	187.206i	−2.70152	−	0.476351i
$394$	199.432	+	237.674i	0.506173	+	0.603233i
$395$	−38.4550	+	45.8288i	−0.0973543	+	0.116022i
$396$	−80.8756	−	458.668i	−0.204231	−	1.15825i
$397$	179.499	+	65.3324i	0.452139	+	0.164565i	0.558044	−	0.829811i	$-0.311552\pi$
$397$	179.499	+	65.3324i	0.452139	+	0.164565i	−0.105905	+	0.994376i	$0.533774\pi$
$398$		−	152.284i		−	0.382623i
$399$	−736.950	+	495.565i	−1.84699	+	1.24202i
$400$	−92.2855			−0.230714
$401$	−213.013	+	585.248i	−0.531204	+	1.45947i	0.326435	+	0.945220i	$0.394153\pi$
$401$	−213.013	+	585.248i	−0.531204	+	1.45947i	−0.857639	+	0.514252i	$0.828070\pi$
$402$	−234.898	+	41.4189i	−0.584324	+	0.103032i
$403$	−176.066	−	147.737i	−0.436888	−	0.366593i
$404$	175.151	−	146.969i	0.433541	−	0.363785i
$405$	−27.9966	+	158.777i	−0.0691275	+	0.392042i
$406$	125.009	−	216.522i	0.307903	−	0.533304i
$407$	−447.294	+	258.245i	−1.09900	+	0.634509i
$408$	−224.569	+	81.7364i	−0.550414	+	0.200334i
$409$	57.1735	+	157.083i	0.139788	+	0.384066i	0.989756	−	0.142769i	$-0.0456007\pi$
$409$	57.1735	+	157.083i	0.139788	+	0.384066i	−0.849967	+	0.526835i	$0.823379\pi$
$410$	−24.5294	−	42.4861i	−0.0598277	−	0.103625i
$411$	42.4312	+	24.4976i	0.103239	+	0.0596050i
$412$	−87.6604	−	15.4569i	−0.212768	−	0.0375167i
$413$	−557.896	−	664.874i	−1.35084	−	1.60987i
$414$	115.779	−	137.980i	0.279660	−	0.333285i
$415$	5.28445	+	29.9696i	0.0127336	+	0.0722159i
$416$	89.6907	+	32.6447i	0.215603	+	0.0784730i
$417$			730.984i			1.75296i
$418$	292.067	+	142.962i	0.698724	+	0.342014i
$419$	742.034			1.77096			0.885482	−	0.464674i	$-0.153828\pi$
$419$	742.034			1.77096			0.885482	+	0.464674i	$0.153828\pi$
$420$	44.4019	−	121.993i	0.105719	−	0.290460i
$421$	−683.636	+	120.543i	−1.62384	+	0.286326i	−0.910194	−	0.414182i	$-0.864068\pi$
$421$	−683.636	+	120.543i	−1.62384	+	0.286326i	−0.713644	+	0.700509i	$0.752956\pi$
$422$	−71.8034	−	60.2502i	−0.170150	−	0.142773i
$423$	271.588	−	227.889i	0.642052	−	0.538745i
$424$	10.1619	−	57.6312i	0.0239668	−	0.135923i
$425$	−183.405	+	317.666i	−0.431540	+	0.747449i
$426$	−403.951	+	233.221i	−0.948243	+	0.547468i
$427$	778.564	−	283.374i	1.82333	−	0.663639i
$428$	−97.3529	−	267.475i	−0.227460	−	0.624942i
$429$	542.578	+	939.773i	1.26475	+	2.19061i
$430$	−66.8355	−	38.5875i	−0.155431	−	0.0897383i
$431$	320.537	+	56.5194i	0.743706	+	0.131135i	0.532647	−	0.846338i	$-0.321198\pi$
$431$	320.537	+	56.5194i	0.743706	+	0.131135i	0.211059	+	0.977473i	$0.432309\pi$
$432$	−139.956	−	166.793i	−0.323972	−	0.386094i
$433$	−143.875	+	171.463i	−0.332274	+	0.395988i	−0.906152	−	0.422952i	$-0.860994\pi$
$433$	−143.875	+	171.463i	−0.332274	+	0.395988i	0.573878	+	0.818941i	$0.305438\pi$
$434$	−29.4215	−	166.858i	−0.0677914	−	0.384464i
$435$	139.403	+	50.7386i	0.320467	+	0.116641i
$436$		−	63.0806i		−	0.144680i
$437$	30.2513	+	122.066i	0.0692249	+	0.279327i
$438$	624.561			1.42594
$439$	71.4645	−	196.347i	0.162789	−	0.447260i	−0.831300	−	0.555824i	$-0.812403\pi$
$439$	71.4645	−	196.347i	0.162789	−	0.447260i	0.994089	+	0.108564i	$0.0346252\pi$
$440$	−46.8137	+	8.25452i	−0.106395	+	0.0187603i
$441$	−417.974	−	350.722i	−0.947786	−	0.795287i
$442$	290.618	−	243.857i	0.657506	−	0.551713i
$443$	−37.2506	+	211.259i	−0.0840871	+	0.476882i	0.913463	+	0.406922i	$0.133398\pi$
$443$	−37.2506	+	211.259i	−0.0840871	+	0.476882i	−0.997550	+	0.0699594i	$0.977713\pi$
$444$	−226.810	+	392.846i	−0.510833	+	0.884788i
$445$	4.28901	−	2.47626i	0.00963823	−	0.00556463i
$446$	160.066	−	58.2592i	0.358892	−	0.130626i
$447$	−100.055	−	274.898i	−0.223836	−	0.614984i
$448$	35.1807	+	60.9348i	0.0785283	+	0.136015i
$449$	−269.395	−	155.535i	−0.599988	−	0.346403i	0.169049	−	0.985608i	$-0.445930\pi$
$449$	−269.395	−	155.535i	−0.599988	−	0.346403i	−0.769037	+	0.639204i	$0.779264\pi$
$450$	−618.307	−	109.024i	−1.37402	−	0.242276i
$451$	194.311	+	231.571i	0.430846	+	0.513462i
$452$	22.6945	−	27.0462i	0.0502090	−	0.0598368i
$453$	−138.532	−	785.656i	−0.305811	−	1.73434i
$454$	−278.967	−	101.536i	−0.614465	−	0.223647i
$455$			206.089i			0.452943i
$456$	284.927	−	19.5195i	0.624841	−	0.0428060i
$457$	233.317			0.510539			0.255270	−	0.966870i	$-0.417836\pi$
$457$	233.317			0.510539			0.255270	+	0.966870i	$0.417836\pi$
$458$	158.990	−	436.821i	0.347139	−	0.953758i
$459$	−852.278	+	150.280i	−1.85681	+	0.327407i
$460$	−14.0829	−	11.8169i	−0.0306149	−	0.0256890i
$461$	−526.135	+	441.480i	−1.14129	+	0.957657i	−0.999480	−	0.0322370i	$-0.989737\pi$
$461$	−526.135	+	441.480i	−1.14129	+	0.957657i	−0.141811	+	0.989894i	$0.545292\pi$
$462$	−138.911	+	787.801i	−0.300672	+	1.70520i
$463$	37.9653	−	65.7578i	0.0819985	−	0.142026i	−0.822110	−	0.569329i	$-0.807203\pi$
$463$	37.9653	−	65.7578i	0.0819985	−	0.142026i	0.904108	+	0.427303i	$0.140536\pi$
$464$	−69.6309	+	40.2014i	−0.150066	+	0.0866409i
$465$	94.4706	−	34.3845i	0.203163	−	0.0739451i
$466$	127.680	+	350.798i	0.273992	+	0.752786i
$467$	110.689	+	191.718i	0.237021	+	0.410532i	0.959858	−	0.280486i	$-0.0904957\pi$
$467$	110.689	+	191.718i	0.237021	+	0.410532i	−0.722837	+	0.691018i	$0.757162\pi$
$468$	562.356	+	324.676i	1.20162	+	0.693753i
$469$	274.889	+	48.4703i	0.586117	+	0.103348i
$470$	−23.2594	−	27.7195i	−0.0494881	−	0.0589776i
$471$	99.8228	−	118.964i	0.211938	−	0.252578i
$472$	48.4682	+	274.877i	0.102687	+	0.582366i
$473$	446.866	+	162.646i	0.944747	+	0.343860i
$474$		−	323.764i		−	0.683047i
$475$	315.757	−	304.062i	0.664752	−	0.640130i
$476$	279.667			0.587535
$477$	136.169	−	374.120i	0.285469	−	0.784320i
$478$	−484.405	+	85.4136i	−1.01340	+	0.178690i
$479$	311.400	+	261.296i	0.650105	+	0.545503i	0.907103	−	0.420909i	$-0.138289\pi$
$479$	311.400	+	261.296i	0.650105	+	0.545503i	−0.256998	+	0.966412i	$0.582733\pi$
$480$	−31.9819	+	26.8360i	−0.0666291	+	0.0559084i
$481$	125.045	−	709.165i	0.259969	−	1.47436i
$482$	−155.782	+	269.823i	−0.323199	+	0.559798i
$483$	−267.924	+	154.686i	−0.554707	+	0.320260i
$484$	47.8411	−	17.4128i	0.0988454	−	0.0359768i
$485$	25.9269	+	71.2336i	0.0534575	+	0.146873i
$486$	−89.8540	−	155.632i	−0.184885	−	0.320230i
$487$	−411.136	−	237.369i	−0.844221	−	0.487411i	0.0144757	−	0.999895i	$-0.495392\pi$
$487$	−411.136	−	237.369i	−0.844221	−	0.487411i	−0.858697	+	0.512484i	$0.828725\pi$
$488$	−262.398	−	46.2678i	−0.537701	−	0.0948111i
$489$	−36.9025	−	43.9786i	−0.0754652	−	0.0899359i
$490$	−35.7962	+	42.6603i	−0.0730535	+	0.0870617i
$491$	−113.851	−	645.682i	−0.231876	−	1.31503i	−0.849094	−	0.528242i	$-0.822851\pi$
$491$	−113.851	−	645.682i	−0.231876	−	1.31503i	0.617218	−	0.786792i	$-0.288260\pi$
$492$	249.486	+	90.8054i	0.507085	+	0.184564i
$493$			319.579i			0.648232i
$494$	−414.437	+	183.818i	−0.838941	+	0.372101i
$495$	−323.401			−0.653334
$496$	−18.6357	+	51.2013i	−0.0375721	+	0.103228i
$497$	537.560	−	94.7863i	1.08161	−	0.190717i
$498$	−126.162	−	105.862i	−0.253337	−	0.212575i
$499$	579.297	−	486.088i	1.16092	−	0.974124i	0.160999	−	0.986955i	$-0.448529\pi$
$499$	579.297	−	486.088i	1.16092	−	0.974124i	0.999918	+	0.0128303i	$0.00408412\pi$
$500$	−23.1852	+	131.490i	−0.0463703	+	0.262979i
$501$	758.228	−	1313.29i	1.51343	−	2.62134i
$502$	140.783	−	81.2812i	0.280445	−	0.161915i
$503$	−22.6508	+	8.24420i	−0.0450313	+	0.0163901i	−0.364438	−	0.931228i	$-0.618739\pi$
$503$	−22.6508	+	8.24420i	−0.0450313	+	0.0163901i	0.319406	+	0.947618i	$0.396517\pi$
$504$	163.721	+	449.821i	0.324844	+	0.892501i
$505$	−79.3819	−	137.494i	−0.157192	−	0.272264i
$506$	98.1030	+	56.6398i	0.193879	+	0.111936i
$507$	−605.484	−	106.763i	−1.19425	−	0.210578i
$508$	39.6454	+	47.2475i	0.0780421	+	0.0930069i
$509$	251.606	−	299.853i	0.494315	−	0.589102i	−0.459994	−	0.887922i	$-0.652149\pi$
$509$	251.606	−	299.853i	0.494315	−	0.589102i	0.954310	+	0.298820i	$0.0965930\pi$
$510$	28.8156	+	163.421i	0.0565012	+	0.320434i
$511$	−686.812	−	249.979i	−1.34405	−	0.489196i
$512$		−	22.6274i		−	0.0441942i
$513$	1028.41	+	109.560i	2.00470	+	0.213567i
$514$	307.884			0.598996
$515$	−21.1396	+	58.0806i	−0.0410478	+	0.112778i
$516$	411.312	−	72.5255i	0.797117	−	0.140553i
$517$	170.805	+	143.322i	0.330376	+	0.277219i
$518$	406.652	−	341.221i	0.785042	−	0.658728i
$519$	−139.838	+	793.060i	−0.269437	+	1.52805i
$520$	33.1379	−	57.3965i	0.0637268	−	0.110378i
$521$	500.919	−	289.206i	0.961457	−	0.555097i	0.0648356	−	0.997896i	$-0.479348\pi$
$521$	500.919	−	289.206i	0.961457	−	0.555097i	0.896621	+	0.442799i	$0.146014\pi$
$522$	−514.015	+	187.086i	−0.984703	+	0.358403i
$523$	219.937	+	604.273i	0.420530	+	1.15540i	0.951404	+	0.307947i	$0.0996418\pi$
$523$	219.937	+	604.273i	0.420530	+	1.15540i	−0.530873	+	0.847451i	$0.678136\pi$
$524$	−202.860	−	351.365i	−0.387138	−	0.670543i
$525$	933.901	+	539.188i	1.77886	+	1.02703i
$526$	430.141	+	75.8455i	0.817759	+	0.144193i
$527$	139.210	+	165.903i	0.264155	+	0.314807i
$528$	165.361	−	197.070i	0.313184	−	0.373238i
$529$	−84.2525	−	477.819i	−0.159267	−	0.903250i
$530$	−38.1844	−	13.8980i	−0.0720460	−	0.0262226i
$531$			1898.91i			3.57611i
$532$	−321.139	−	92.5764i	−0.603645	−	0.174016i
$533$	−421.468			−0.790746
$534$	−9.16689	+	25.1858i	−0.0171665	+	0.0471645i
$535$	−194.645	+	34.3211i	−0.363822	+	0.0641516i
$536$	−68.7638	−	57.6997i	−0.128291	−	0.107649i
$537$	−1155.44	+	969.528i	−2.15165	+	1.80545i
$538$	−93.6075	+	530.874i	−0.173992	+	0.986755i
$539$	171.575	−	297.177i	0.318321	−	0.551348i
$540$	−130.932	+	75.5939i	−0.242468	+	0.139989i
$541$	255.907	−	93.1425i	0.473026	−	0.172167i	−0.0944968	−	0.995525i	$-0.530124\pi$
$541$	255.907	−	93.1425i	0.473026	−	0.172167i	0.567522	+	0.823358i	$0.307902\pi$
$542$	62.9821	+	173.042i	0.116203	+	0.319265i
$543$	−928.437	−	1608.10i	−1.70983	−	2.96151i
$544$	−77.8883	−	44.9688i	−0.143177	−	0.0826633i
$545$	−43.1361	−	7.60606i	−0.0791488	−	0.0139561i
$546$	−716.912	−	854.383i	−1.31303	−	1.56480i
$547$	−250.243	+	298.228i	−0.457483	+	0.545207i	−0.944640	−	0.328107i	$-0.893589\pi$
$547$	−250.243	+	298.228i	−0.457483	+	0.545207i	0.487158	+	0.873314i	$0.338034\pi$
$548$	3.20186	+	18.1586i	0.00584281	+	0.0331362i
$549$	−1703.39	−	619.983i	−3.10271	−	1.12929i
$550$		−	394.859i		−	0.717925i
$551$	105.788	−	366.969i	0.191993	−	0.666006i
$552$	99.4904			0.180236
$553$	−129.586	+	356.034i	−0.234332	+	0.643823i
$554$	566.619	−	99.9102i	1.02278	−	0.180343i
$555$	241.290	+	202.466i	0.434756	+	0.364804i
$556$	−210.736	+	176.829i	−0.379022	+	0.318037i
$557$	−143.518	+	813.932i	−0.257663	+	1.46128i	0.531481	+	0.847070i	$0.321636\pi$
$557$	−143.518	+	813.932i	−0.257663	+	1.46128i	−0.789144	+	0.614208i	$0.789476\pi$
$558$	−185.346	+	321.029i	−0.332162	+	0.575321i
$559$	−574.189	+	331.508i	−1.02717	+	0.593038i
$560$	45.9107	−	16.7101i	0.0819834	−	0.0298395i
$561$	−349.723	−	960.855i	−0.623392	−	1.71275i
$562$	291.438	+	504.786i	0.518574	+	0.898196i
$563$	238.760	+	137.848i	0.424084	+	0.244845i	0.696823	−	0.717243i	$-0.254596\pi$
$563$	238.760	+	137.848i	0.424084	+	0.244845i	−0.272739	+	0.962088i	$0.587930\pi$
$564$	192.853	+	34.0052i	0.341938	+	0.0602929i
$565$	−15.7585	−	18.7802i	−0.0278911	−	0.0332393i
$566$	−312.069	+	371.909i	−0.551358	+	0.657083i
$567$	177.307	+	1005.56i	0.312711	+	1.77347i
$568$	−164.954	−	60.0382i	−0.290411	−	0.105701i
$569$		−	1054.92i		−	1.85398i	−0.375083	−	0.926991i	$-0.622386\pi$
$569$		−	1054.92i		−	1.85398i	0.375083	−	0.926991i	$-0.377614\pi$
$570$	21.0077	−	197.194i	0.0368556	−	0.345955i
$571$	−1024.27			−1.79381			−0.896905	−	0.442223i	$-0.854190\pi$
$571$	−1024.27			−1.79381			−0.896905	+	0.442223i	$0.854190\pi$
$572$	−139.676	+	383.756i	−0.244189	+	0.670903i
$573$	1490.03	−	262.732i	2.60039	−	0.458520i
$574$	−238.008	−	199.712i	−0.414648	−	0.347931i
$575$	116.980	−	98.1577i	0.203443	−	0.170709i
$576$	26.7316	−	151.602i	0.0464090	−	0.263198i
$577$	−512.692	+	888.008i	−0.888547	+	1.53901i	−0.0469539	+	0.998897i	$0.514951\pi$
$577$	−512.692	+	888.008i	−0.888547	+	1.53901i	−0.841593	+	0.540112i	$0.818382\pi$
$578$	44.3671	−	25.6153i	0.0767596	−	0.0443172i
$579$	1049.27	−	381.904i	1.81222	−	0.659592i
$580$	19.0948	+	52.4627i	0.0329222	+	0.0904529i
$581$	96.3653	+	166.910i	0.165861	+	0.287280i
$582$	−355.282	−	205.122i	−0.610451	−	0.352444i
$583$	246.585	+	43.4795i	0.422958	+	0.0745790i
$584$	151.085	+	180.056i	0.258706	+	0.308314i
$585$	289.829	−	345.405i	0.495434	−	0.590435i
$586$	25.2492	+	143.195i	0.0430873	+	0.244360i
$587$	−37.4352	−	13.6253i	−0.0637738	−	0.0232118i	0.309936	−	0.950757i	$-0.399692\pi$
$587$	−37.4352	−	13.6253i	−0.0637738	−	0.0232118i	−0.373710	+	0.927546i	$0.621914\pi$
$588$		−	301.379i		−	0.512550i
$589$	−104.935	−	236.587i	−0.178158	−	0.401676i
$590$	193.812			0.328494
$591$	−398.765	+	1095.60i	−0.674729	+	1.85380i
$592$	−168.120	+	29.6442i	−0.283987	+	0.0500746i
$593$	513.934	+	431.242i	0.866668	+	0.727221i	0.963394	−	0.268090i	$-0.0863926\pi$
$593$	513.934	+	431.242i	0.866668	+	0.727221i	−0.0967260	+	0.995311i	$0.530837\pi$
$594$	713.650	−	598.824i	1.20143	−	1.00812i
$595$	33.7213	−	191.243i	0.0566745	−	0.321417i
$596$	55.0469	−	95.3440i	0.0923606	−	0.159973i
$597$	495.589	−	286.128i	0.830132	−	0.479277i
$598$	−148.413	+	54.0178i	−0.248182	+	0.0903308i
$599$	−128.363	−	352.675i	−0.214296	−	0.588774i	0.785241	−	0.619190i	$-0.212539\pi$
$599$	−128.363	−	352.675i	−0.214296	−	0.588774i	−0.999537	+	0.0304163i	$0.990317\pi$
$600$	−173.397	−	300.332i	−0.288995	−	0.500553i
$601$	−617.904	−	356.747i	−1.02813	−	0.593589i	−0.111679	−	0.993744i	$-0.535623\pi$
$601$	−617.904	−	356.747i	−1.02813	−	0.593589i	−0.916447	+	0.400155i	$0.868956\pi$
$602$	−481.336	−	84.8726i	−0.799562	−	0.140984i
$603$	−392.548	−	467.820i	−0.650992	−	0.775822i
$604$	192.986	−	229.992i	0.319514	−	0.380781i
$605$	−6.13874	−	34.8145i	−0.0101467	−	0.0575447i
$606$	807.386	+	293.865i	1.33232	+	0.484925i
$607$			185.218i			0.305136i	0.988293	+	0.152568i	$0.0487544\pi$
$607$			185.218i			0.305136i	−0.988293	+	0.152568i	$0.951246\pi$
$608$	74.5527	+	77.4202i	0.122620	+	0.127336i
$609$	939.524			1.54273
$610$	−63.2782	+	173.855i	−0.103735	+	0.285009i
$611$	−306.147	+	53.9820i	−0.501059	+	0.0883503i
$612$	−468.721	−	393.304i	−0.765884	−	0.642653i
$613$	436.254	−	366.061i	0.711670	−	0.597162i	−0.213397	−	0.976966i	$-0.568453\pi$
$613$	436.254	−	366.061i	0.711670	−	0.597162i	0.925067	+	0.379803i	$0.124008\pi$
$614$	−120.405	+	682.851i	−0.196099	+	1.11213i
$615$	92.1772	−	159.656i	0.149882	−	0.259603i
$616$	−260.719	+	150.526i	−0.423246	+	0.244361i
$617$	270.110	−	98.3119i	0.437779	−	0.159338i	−0.113722	−	0.993513i	$-0.536277\pi$
$617$	270.110	−	98.3119i	0.437779	−	0.159338i	0.551501	+	0.834174i	$0.314055\pi$
$618$	−114.404	−	314.322i	−0.185120	−	0.508612i
$619$	−383.209	−	663.737i	−0.619077	−	1.07227i	−0.989654	−	0.143472i	$-0.954173\pi$
$619$	−383.209	−	663.737i	−0.619077	−	1.07227i	0.370577	−	0.928802i	$-0.379160\pi$
$620$	32.7657	+	18.9173i	0.0528479	+	0.0305117i
$621$	354.812	+	62.5629i	0.571356	+	0.100745i
$622$	−92.7955	−	110.589i	−0.149189	−	0.177796i
$623$	20.1611	−	24.0271i	0.0323614	−	0.0385668i
$624$	62.2830	+	353.224i	0.0998125	+	0.566065i
$625$	−454.880	−	165.563i	−0.727808	−	0.264900i
$626$		−	246.321i		−	0.393484i
$627$	83.5175	+	1219.11i	0.133202	+	1.94435i
$628$	58.4440			0.0930636
$629$	−232.074	+	637.619i	−0.368958	+	1.01370i
$630$	327.340	−	57.7188i	0.519587	−	0.0916171i
$631$	539.716	+	452.876i	0.855335	+	0.717711i	0.960958	−	0.276695i	$-0.0892392\pi$
$631$	539.716	+	452.876i	0.855335	+	0.717711i	−0.105623	+	0.994406i	$0.533684\pi$
$632$	93.3384	−	78.3202i	0.147687	−	0.123924i
$633$	61.1644	−	346.881i	0.0966262	−	0.547995i
$634$	−223.210	+	386.611i	−0.352066	+	0.609797i
$635$	37.0893	−	21.4135i	0.0584084	−	0.0337221i
$636$	206.647	−	75.2135i	0.324917	−	0.118260i
$637$	163.632	+	449.576i	0.256880	+	0.705771i
$638$	−172.008	−	297.927i	−0.269605	−	0.466970i
$639$	−1034.25	−	597.125i	−1.61855	−	0.934467i
$640$	−15.4732	−	2.72834i	−0.0241769	−	0.00426303i
$641$	75.6767	+	90.1880i	0.118060	+	0.140699i	0.821838	−	0.569722i	$-0.192949\pi$
$641$	75.6767	+	90.1880i	0.118060	+	0.140699i	−0.703777	+	0.710421i	$0.748505\pi$
$642$	687.547	−	819.386i	1.07095	−	1.27630i
$643$	142.923	+	810.557i	0.222275	+	1.26059i	0.867826	+	0.496868i	$0.165517\pi$
$643$	142.923	+	810.557i	0.222275	+	1.26059i	−0.645551	+	0.763717i	$0.723372\pi$
$644$	−109.407	−	39.8208i	−0.169886	−	0.0618335i
$645$		−	290.011i		−	0.449629i
$646$	414.660	−	102.764i	0.641888	−	0.159078i
$647$	266.671			0.412165			0.206082	−	0.978535i	$-0.433928\pi$
$647$	266.671			0.412165			0.206082	+	0.978535i	$0.433928\pi$
$648$	112.308	−	308.562i	0.173314	−	0.476177i
$649$	−1176.10	+	207.379i	−1.81218	+	0.319536i
$650$	421.725	+	353.869i	0.648807	+	0.544414i
$651$	487.737	−	409.260i	0.749212	−	0.628664i
$652$	3.75177	−	21.2773i	0.00575424	−	0.0326339i
$653$	−536.805	+	929.773i	−0.822060	+	1.42385i	0.0820863	+	0.996625i	$0.473842\pi$
$653$	−536.805	+	929.773i	−0.822060	+	1.42385i	−0.904146	+	0.427224i	$0.859492\pi$
$654$	205.288	−	118.523i	0.313896	−	0.181228i
$655$	−264.732	+	96.3546i	−0.404171	+	0.147106i
$656$	34.1735	+	93.8909i	0.0520937	+	0.143126i
$657$	799.543	+	1384.85i	1.21696	+	2.10784i
$658$	−198.464	−	114.583i	−0.301617	−	0.174139i
$659$	36.9672	+	6.51832i	0.0560959	+	0.00989122i	0.201626	−	0.979463i	$-0.435378\pi$
$659$	36.9672	+	6.51832i	0.0560959	+	0.00989122i	−0.145530	+	0.989354i	$0.546489\pi$
$660$	−114.822	−	136.840i	−0.173973	−	0.207333i
$661$	155.880	−	185.770i	0.235824	−	0.281044i	−0.635133	−	0.772402i	$-0.719055\pi$
$661$	155.880	−	185.770i	0.235824	−	0.281044i	0.870958	+	0.491358i	$0.163499\pi$
$662$	−118.836	−	673.951i	−0.179510	−	1.01805i
$663$	1339.65	+	487.593i	2.02059	+	0.735434i
$664$		−	61.9799i		−	0.0933433i
$665$	−102.028	+	208.440i	−0.153426	+	0.313444i
$666$	−1161.42			−1.74387
$667$	45.5037	−	125.020i	0.0682214	−	0.187437i
$668$	562.029	−	99.1010i	0.841361	−	0.148355i
$669$	490.348	+	411.451i	0.732957	+	0.615024i
$670$	−47.7478	+	40.0652i	−0.0712654	+	0.0597988i
$671$	197.964	−	1122.71i	0.295029	−	1.67319i
$672$	−132.203	+	228.983i	−0.196731	+	0.340748i
$673$	−290.134	+	167.509i	−0.431106	+	0.248899i	−0.699818	−	0.714322i	$-0.746735\pi$
$673$	−290.134	+	167.509i	−0.431106	+	0.248899i	0.268712	+	0.963221i	$0.413402\pi$
$674$	309.663	−	112.708i	0.459441	−	0.167223i
$675$	−429.525	−	1180.11i	−0.636333	−	1.74831i
$676$	−115.691	−	200.382i	−0.171140	−	0.296423i
$677$	493.750	+	285.067i	0.729321	+	0.421074i	0.818174	−	0.574971i	$-0.194987\pi$
$677$	493.750	+	285.067i	0.729321	+	0.421074i	−0.0888527	+	0.996045i	$0.528320\pi$
$678$	130.660	+	23.0388i	0.192713	+	0.0339806i
$679$	308.594	+	367.768i	0.454483	+	0.541632i
$680$	−40.1423	+	47.8398i	−0.0590328	+	0.0703526i
$681$	−193.720	−	1098.64i	−0.284464	−	1.61328i
$682$	−219.073	−	79.7361i	−0.321222	−	0.116915i
$683$		−	1198.89i		−	1.75532i	−0.479282	−	0.877661i	$-0.659103\pi$
$683$		−	1198.89i		−	1.75532i	0.479282	−	0.877661i	$-0.340897\pi$
$684$	408.036	+	606.785i	0.596543	+	0.887113i
$685$	12.8034			0.0186911
$686$	87.8262	−	241.301i	0.128027	−	0.351750i
$687$	1720.31	−	303.337i	2.50409	−	0.441539i
$688$	120.407	+	101.033i	0.175010	+	0.146851i
$689$	−267.425	+	224.396i	−0.388135	+	0.325684i
$690$	11.9962	−	68.0340i	0.0173858	−	0.0986000i
$691$	72.6461	−	125.827i	0.105132	−	0.182094i	−0.808660	−	0.588276i	$-0.799807\pi$
$691$	72.6461	−	125.827i	0.105132	−	0.182094i	0.913792	+	0.406182i	$0.133140\pi$
$692$	−262.460	+	151.531i	−0.379277	+	0.218976i
$693$	−1924.63	+	700.508i	−2.77725	+	1.01083i
$694$	−87.5808	−	240.626i	−0.126197	−	0.346724i
$695$	95.5100	+	165.428i	0.137424	+	0.238026i
$696$	−261.661	−	151.070i	−0.375950	−	0.217055i
$697$	391.107	+	68.9627i	0.561129	+	0.0989422i
$698$	434.176	+	517.431i	0.622029	+	0.741305i
$699$	−901.730	+	1074.64i	−1.29003	+	1.53740i
$700$	70.4723	+	399.668i	0.100675	+	0.570954i
$701$	−1314.20	−	478.330i	−1.87475	−	0.682353i	−0.961381	−	0.275220i	$-0.911249\pi$
$701$	−1314.20	−	478.330i	−1.87475	−	0.682353i	−0.913369	−	0.407134i	$-0.866528\pi$
$702$			1298.87i			1.85024i
$703$	477.556	−	655.351i	0.679312	−	0.932220i
$704$	96.8151			0.137521
$705$	46.5072	−	127.777i	0.0659676	−	0.181245i
$706$	−313.195	+	55.2247i	−0.443619	+	0.0782220i
$707$	−770.241	−	646.309i	−1.08945	−	0.914157i
$708$	−803.485	+	674.204i	−1.13487	+	0.952265i
$709$	−19.1696	+	108.716i	−0.0270376	+	0.153338i	−0.995338	−	0.0964523i	$-0.969250\pi$
$709$	−19.1696	+	108.716i	−0.0270376	+	0.153338i	0.968300	+	0.249790i	$0.0803616\pi$
$710$	−60.9452	+	105.560i	−0.0858383	+	0.148676i
$711$	717.887	−	414.472i	1.00969	−	0.582943i
$712$	−9.47837	+	3.44985i	−0.0133123	+	0.00484529i
$713$	−30.8369	−	84.7236i	−0.0432495	−	0.118827i
$714$	525.471	+	910.142i	0.735953	+	1.27471i
$715$	245.581	+	141.786i	0.343469	+	0.198302i
$716$	−559.013	−	98.5690i	−0.780744	−	0.137666i
$717$	−1188.12	−	1415.95i	−1.65708	−	1.97483i
$718$	−212.286	+	252.993i	−0.295664	+	0.352358i
$719$	180.612	+	1024.30i	0.251199	+	1.42462i	0.805644	+	0.592400i	$0.201820\pi$
$719$	180.612	+	1024.30i	0.251199	+	1.42462i	−0.554445	+	0.832221i	$0.687069\pi$
$720$	−100.446	−	36.5594i	−0.139509	−	0.0507770i
$721$			391.441i			0.542914i
$722$	−510.168	−	19.2591i	−0.706603	−	0.0266746i
$723$	−1170.81			−1.61937
$724$	239.008	−	656.668i	0.330121	−	0.907000i
$725$	−456.705	+	80.5295i	−0.629938	+	0.111075i
$726$	146.557	+	122.976i	0.201869	+	0.169389i
$727$	752.214	−	631.183i	1.03468	−	0.868202i	0.0432818	−	0.999063i	$-0.486219\pi$
$727$	752.214	−	631.183i	1.03468	−	0.868202i	0.991401	+	0.130861i	$0.0417742\pi$
$728$	72.8864	−	413.359i	0.100119	−	0.567801i
$729$	−184.770	+	320.030i	−0.253456	+	0.438999i
$730$	141.344	−	81.6049i	0.193622	−	0.111787i
$731$	587.070	−	213.676i	0.803106	−	0.292307i
$732$	−342.451	−	940.875i	−0.467829	−	1.28535i
$733$	−187.485	−	324.734i	−0.255778	−	0.443020i	0.709329	−	0.704878i	$-0.248998\pi$
$733$	−187.485	−	324.734i	−0.255778	−	0.443020i	−0.965107	+	0.261858i	$0.915665\pi$
$734$	267.774	+	154.599i	0.364815	+	0.210626i
$735$	−206.091	−	36.3393i	−0.280395	−	0.0494413i
$736$	24.0672	+	28.6822i	0.0327000	+	0.0389704i
$737$	246.878	−	294.217i	0.334977	−	0.399209i
$738$	118.039	+	669.435i	0.159945	+	0.907093i
$739$	251.648	+	91.5926i	0.340526	+	0.123941i	0.506622	−	0.862168i	$-0.330894\pi$
$739$	251.648	+	91.5926i	0.340526	+	0.123941i	−0.166096	+	0.986110i	$0.553116\pi$
$740$			118.539i			0.160188i
$741$	−1376.90	−	1003.36i	−1.85817	−	1.35406i
$742$	−257.348			−0.346830
$743$	84.5421	−	232.277i	0.113785	−	0.312621i	−0.869709	−	0.493566i	$-0.835693\pi$
$743$	84.5421	−	232.277i	0.113785	−	0.312621i	0.983493	+	0.180945i	$0.0579155\pi$
$744$	−201.643	+	35.5552i	−0.271026	+	0.0477892i
$745$	−58.5612	−	49.1387i	−0.0786057	−	0.0659580i
$746$	−525.803	+	441.201i	−0.704830	+	0.591423i
$747$	73.2218	−	415.261i	0.0980211	−	0.555905i
$748$	192.407	−	333.258i	0.257228	−	0.445532i
$749$	−1084.03	+	625.867i	−1.44731	+	0.835603i
$750$	−471.480	+	171.605i	−0.628640	+	0.228806i
$751$	299.494	+	822.852i	0.398793	+	1.09568i	0.962873	+	0.269955i	$0.0870089\pi$
$751$	299.494	+	822.852i	0.398793	+	1.09568i	−0.564080	+	0.825720i	$0.690769\pi$
$752$	36.8487	+	63.8238i	0.0490009	+	0.0848721i
$753$	529.040	+	305.441i	0.702576	+	0.405632i
$754$	472.350	+	83.2881i	0.626459	+	0.110462i
$755$	−134.005	−	159.700i	−0.177490	−	0.211524i
$756$	−615.468	+	733.486i	−0.814111	+	0.970219i
$757$	31.7929	+	180.306i	0.0419985	+	0.238185i	0.998580	−	0.0532811i	$-0.0169679\pi$
$757$	31.7929	+	180.306i	0.0419985	+	0.238185i	−0.956581	+	0.291466i	$0.905857\pi$
$758$	−55.7618	−	20.2956i	−0.0735644	−	0.0267752i
$759$			425.686i			0.560851i
$760$	61.9312	−	41.6459i	0.0814884	−	0.0547973i
$761$	1245.02			1.63603			0.818017	−	0.575193i	$-0.195073\pi$
$761$	1245.02			1.63603			0.818017	+	0.575193i	$0.195073\pi$
$762$	−79.2710	+	217.795i	−0.104030	+	0.285820i
$763$	−273.188	+	48.1704i	−0.358045	+	0.0631329i
$764$	436.188	+	366.005i	0.570927	+	0.479065i
$765$	−325.468	+	273.100i	−0.425448	+	0.356993i
$766$	138.867	−	787.555i	0.181289	−	1.02814i
$767$	832.526	−	1441.98i	1.08543	−	1.88002i
$768$	73.6382	−	42.5150i	0.0958830	−	0.0553581i
$769$	920.187	−	334.921i	1.19660	−	0.435527i	0.334565	−	0.942373i	$-0.391411\pi$
$769$	920.187	−	334.921i	1.19660	−	0.435527i	0.862037	+	0.506845i	$0.169189\pi$
$770$	71.4970	+	196.436i	0.0928532	+	0.255112i
$771$	578.488	+	1001.97i	0.750309	+	1.29957i
$772$	363.924	+	210.112i	0.471404	+	0.272165i
$773$	825.024	+	145.474i	1.06730	+	0.188194i	0.679594	−	0.733588i	$-0.262156\pi$
$773$	825.024	+	145.474i	1.06730	+	0.188194i	0.387708	+	0.921782i	$0.373267\pi$
$774$	687.360	+	819.164i	0.888062	+	1.05835i
$775$	−202.011	+	240.748i	−0.260660	+	0.310642i
$776$	−26.8096	−	152.045i	−0.0345485	−	0.195934i
$777$	1874.53	+	682.272i	2.41252	+	0.878085i
$778$		−	478.368i		−	0.614869i
$779$	−426.277	−	208.655i	−0.547210	−	0.267850i
$780$	249.053			0.319299
$781$	256.883	−	705.781i	0.328916	−	0.903689i
$782$	146.560	−	25.8425i	0.187417	−	0.0330467i
$783$	−838.163	−	703.302i	−1.07045	−	0.898214i
$784$	86.8850	−	72.9052i	0.110823	−	0.0929913i
$785$	7.04699	−	39.9654i	0.00897705	−	0.0509114i
$786$	762.316	−	1320.37i	0.969867	−	1.67986i
$787$	−289.816	+	167.325i	−0.368254	+	0.212612i	−0.672695	−	0.739920i	$-0.734864\pi$
$787$	−289.816	+	167.325i	−0.368254	+	0.212612i	0.304441	+	0.952531i	$0.401530\pi$
$788$	−412.314	+	150.070i	−0.523241	+	0.190444i
$789$	561.369	+	1542.35i	0.711495	+	1.95482i
$790$	−42.3029	−	73.2707i	−0.0535479	−	0.0927478i
$791$	−134.461	−	77.6313i	−0.169989	−	0.0981433i
$792$	648.655	+	114.375i	0.819009	+	0.144413i
$793$	1021.69	+	1217.60i	1.28838	+	1.53543i
$794$	−173.644	+	206.941i	−0.218695	+	0.260630i
$795$	−26.5160	−	150.380i	−0.0333534	−	0.189157i
$796$	202.374	+	73.6581i	0.254239	+	0.0925353i
$797$		−	603.909i		−	0.757728i	−0.925452	−	0.378864i	$-0.876315\pi$
$797$		−	603.909i		−	0.757728i	0.925452	−	0.378864i	$-0.123685\pi$
$798$	−302.115	−	1219.05i	−0.378590	−	1.52763i
$799$	292.927			0.366617
$800$	44.6375	−	122.641i	0.0557969	−	0.153301i
$801$	−67.5801	+	11.9162i	−0.0843696	+	0.0148766i
$802$	−674.719	−	566.157i	−0.841296	−	0.705931i
$803$	−770.397	+	646.440i	−0.959399	+	0.805031i
$804$	58.5752	−	332.196i	0.0728547	−	0.413180i
$805$	−40.4223	+	70.0135i	−0.0502141	+	0.0869734i
$806$	281.493	−	162.520i	0.349247	−	0.201638i
$807$	−1903.55	+	692.834i	−2.35879	+	0.858531i
$808$	110.592	+	303.850i	0.136872	+	0.376052i
$809$	−119.262	−	206.568i	−0.147419	−	0.255337i	0.782854	−	0.622206i	$-0.213763\pi$
$809$	−119.262	−	206.568i	−0.147419	−	0.255337i	−0.930273	+	0.366868i	$0.880430\pi$
$810$	−197.461	−	114.004i	−0.243779	−	0.140746i
$811$	−25.5145	−	4.49890i	−0.0314606	−	0.00554735i	0.157896	−	0.987456i	$-0.449529\pi$
$811$	−25.5145	−	4.49890i	−0.0314606	−	0.00554735i	−0.189356	+	0.981908i	$0.560640\pi$
$812$	227.276	+	270.857i	0.279896	+	0.333567i
$813$	−444.806	+	530.099i	−0.547116	+	0.652028i
$814$	−126.837	−	719.331i	−0.155820	−	0.883699i
$815$	−14.0976	−	5.13110i	−0.0172977	−	0.00629583i
$816$		−	337.971i		−	0.414180i
$817$	−744.860	+	51.0282i	−0.911701	+	0.0624580i
$818$	−236.406			−0.289005
$819$	976.668	−	2683.37i	1.19251	−	3.27640i
$820$	68.3255	−	12.0476i	0.0833237	−	0.0146922i
$821$	−212.356	−	178.188i	−0.258656	−	0.217038i	0.504233	−	0.863568i	$-0.331775\pi$
$821$	−212.356	−	178.188i	−0.258656	−	0.217038i	−0.762889	+	0.646530i	$0.776220\pi$
$822$	−53.0791	+	44.5386i	−0.0645731	+	0.0541833i
$823$	−70.6734	+	400.809i	−0.0858729	+	0.487009i	0.911292	+	0.411761i	$0.135086\pi$
$823$	−70.6734	+	400.809i	−0.0858729	+	0.487009i	−0.997165	+	0.0752485i	$0.976025\pi$
$824$	62.9415	−	109.018i	0.0763853	−	0.132303i
$825$	1285.02	−	741.907i	1.55760	−	0.899281i
$826$	1153.42	−	419.810i	1.39639	−	0.508244i
$827$	167.032	+	458.917i	0.201973	+	0.554918i	0.998783	−	0.0493125i	$-0.0157030\pi$
$827$	167.032	+	458.917i	0.201973	+	0.554918i	−0.796810	+	0.604230i	$0.793481\pi$
$828$	127.364	+	220.601i	0.153822	+	0.266427i
$829$	−496.560	−	286.689i	−0.598986	−	0.345825i	0.169656	−	0.985503i	$-0.445734\pi$
$829$	−496.560	−	286.689i	−0.598986	−	0.345825i	−0.768643	+	0.639678i	$0.779068\pi$
$830$	−42.3834	−	7.47334i	−0.0510644	−	0.00900402i
$831$	1389.78	+	1656.27i	1.67241	+	1.99311i
$832$	−86.7649	+	103.402i	−0.104285	+	0.124282i
$833$	−78.2831	−	443.965i	−0.0939773	−	0.532972i
$834$	−971.423	−	353.569i	−1.16478	−	0.423944i
$835$		−	396.279i		−	0.474586i
$836$	−331.255	+	318.986i	−0.396238	+	0.381562i
$837$	−741.478			−0.885876
$838$	−358.914	+	986.108i	−0.428298	+	1.17674i
$839$	301.226	−	53.1142i	0.359030	−	0.0633066i	0.00877592	−	0.999961i	$-0.497207\pi$
$839$	301.226	−	53.1142i	0.359030	−	0.0633066i	0.350254	+	0.936655i	$0.386095\pi$
$840$	140.643	+	118.014i	0.167433	+	0.140493i
$841$	334.732	−	280.874i	0.398017	−	0.333976i
$842$	170.474	−	966.807i	0.202463	−	1.14823i
$843$	−1095.18	+	1896.90i	−1.29914	+	2.25018i
$844$	114.799	−	66.2790i	0.136017	−	0.0785296i
$845$	−150.976	+	54.9508i	−0.178670	+	0.0650305i
$846$	171.484	+	471.148i	0.202700	+	0.556912i
$847$	−111.944	−	193.892i	−0.132165	−	0.228917i
$848$	71.6724	+	41.3801i	0.0845194	+	0.0487973i
$849$	−1796.68	−	316.804i	−2.11623	−	0.373149i
$850$	−333.444	−	397.383i	−0.392287	−	0.467509i
$851$	181.577	−	216.395i	0.213369	−	0.254283i
$852$	−114.547	−	649.628i	−0.134445	−	0.762474i
$853$	1326.08	+	482.652i	1.55460	+	0.565829i	0.969492	−	0.245124i	$-0.0788287\pi$
$853$	1326.08	+	482.652i	1.55460	+	0.565829i	0.585111	+	0.810953i	$0.301051\pi$
$854$			1171.72i			1.37204i
$855$	464.135	−	205.861i	0.542848	−	0.240773i
$856$	402.543			0.470261
$857$	6.09996	−	16.7595i	0.00711780	−	0.0195560i	−0.936083	−	0.351780i	$-0.885577\pi$
$857$	6.09996	−	16.7595i	0.00711780	−	0.0195560i	0.943201	+	0.332224i	$0.107799\pi$
$858$	−1511.33	+	266.488i	−1.76145	+	0.310592i
$859$	−1192.64	−	1000.74i	−1.38840	−	1.16501i	−0.965983	−	0.258606i	$-0.916737\pi$
$859$	−1192.64	−	1000.74i	−1.38840	−	1.16501i	−0.422419	−	0.906401i	$-0.638819\pi$
$860$	83.6075	−	70.1550i	0.0972180	−	0.0815756i
$861$	202.743	−	1149.81i	0.235473	−	1.33544i
$862$	−230.151	+	398.633i	−0.266996	+	0.462451i
$863$	−574.081	+	331.446i	−0.665215	+	0.384062i	−0.794261	−	0.607577i	$-0.792142\pi$
$863$	−574.081	+	331.446i	−0.665215	+	0.384062i	0.129046	+	0.991639i	$0.458808\pi$
$864$	289.350	−	105.315i	0.334896	−	0.121892i
$865$	71.9743	+	197.748i	0.0832073	+	0.228610i
$866$	−158.271	−	274.134i	−0.182761	−	0.316551i
$867$	166.724	+	96.2582i	0.192300	+	0.111024i
$868$	235.972	+	41.6083i	0.271857	+	0.0479358i
$869$	335.106	+	399.364i	0.385623	+	0.459567i
$870$	−134.856	+	160.715i	−0.155007	+	0.184730i
$871$	92.9861	+	527.350i	0.106758	+	0.605454i
$872$	83.8294	+	30.5114i	0.0961347	+	0.0349902i
$873$		−	1050.36i		−	1.20317i
$874$	−176.849	−	18.8402i	−0.202344	−	0.0215563i
$875$	587.157			0.671037
$876$	−302.094	+	829.996i	−0.344856	+	0.947484i
$877$	687.184	−	121.169i	0.783562	−	0.138163i	0.232465	−	0.972605i	$-0.425321\pi$
$877$	687.184	−	121.169i	0.783562	−	0.138163i	0.551096	+	0.834442i	$0.314210\pi$
$878$	226.364	+	189.942i	0.257818	+	0.216335i
$879$	−418.570	+	351.222i	−0.476189	+	0.399570i
$880$	11.6737	−	66.2046i	0.0132655	−	0.0752325i
$881$	−793.347	+	1374.12i	−0.900508	+	1.55972i	−0.0736710	+	0.997283i	$0.523471\pi$
$881$	−793.347	+	1374.12i	−0.900508	+	1.55972i	−0.826837	+	0.562442i	$0.809862\pi$
$882$	668.253	−	385.816i	0.757656	−	0.437433i
$883$	302.001	−	109.920i	0.342017	−	0.124484i	−0.165300	−	0.986243i	$-0.552859\pi$
$883$	302.001	−	109.920i	0.342017	−	0.124484i	0.507318	+	0.861759i	$0.330637\pi$
$884$	183.500	+	504.161i	0.207579	+	0.570318i
$885$	364.156	+	630.736i	0.411475	+	0.712696i
$886$	−262.729	−	151.687i	−0.296534	−	0.171204i
$887$	−192.600	−	33.9606i	−0.217136	−	0.0382870i	0.0640215	−	0.997949i	$-0.479607\pi$
$887$	−192.600	−	33.9606i	−0.217136	−	0.0382870i	−0.281158	+	0.959662i	$0.590718\pi$
$888$	−412.358	−	491.429i	−0.464367	−	0.553411i
$889$	174.344	−	207.775i	0.196112	−	0.233718i
$890$	1.21622	+	6.89752i	0.00136654	+	0.00775002i
$891$	1320.24	+	480.526i	1.48175	+	0.539311i
$892$			240.895i			0.270062i
$893$	−336.365	−	96.9658i	−0.376669	−	0.108584i
$894$	413.714			0.462767
$895$	−134.808	+	370.382i	−0.150623	+	0.413834i
$896$	−97.9943	+	17.2790i	−0.109369	+	0.0192846i
$897$	−454.649	−	381.496i	−0.506856	−	0.425302i
$898$	336.998	−	282.775i	0.375276	−	0.314894i
$899$	−47.5463	+	269.648i	−0.0528879	+	0.299942i
$900$	443.954	−	768.950i	0.493282	−	0.854389i
$901$	284.878	−	164.474i	0.316180	−	0.182546i
$902$	−401.728	+	146.217i	−0.445374	+	0.162103i
$903$	−628.183	−	1725.92i	−0.695663	−	1.91132i
$904$	24.9653	+	43.2412i	0.0276165	+	0.0478332i
$905$	−420.227	−	242.618i	−0.464339	−	0.268086i
$906$	1111.09	+	195.914i	1.22636	+	0.216241i
$907$	229.744	+	273.799i	0.253302	+	0.301873i	0.877678	−	0.479250i	$-0.159091\pi$
$907$	229.744	+	273.799i	0.253302	+	0.301873i	−0.624377	+	0.781123i	$0.714647\pi$
$908$	269.867	−	321.615i	0.297210	−	0.354201i
$909$	381.999	+	2166.42i	0.420241	+	2.38331i
$910$	−273.877	−	99.6830i	−0.300964	−	0.109542i
$911$		−	32.4608i		−	0.0356321i	−0.999841	−	0.0178161i	$-0.994329\pi$
$911$		−	32.4608i		−	0.0356321i	0.999841	−	0.0178161i	$-0.00567133\pi$
$912$	−111.876	+	388.089i	−0.122672	+	0.425536i
$913$	265.191			0.290461
$914$	−112.853	+	310.060i	−0.123471	+	0.339235i
$915$	−684.686	+	120.729i	−0.748290	+	0.131944i
$916$	503.601	+	422.572i	0.549783	+	0.461323i
$917$	−1366.77	+	1146.86i	−1.49048	+	1.25066i
$918$	212.527	−	1205.30i	0.231511	−	1.31297i
$919$	229.720	−	397.886i	0.249967	−	0.432956i	−0.713549	−	0.700605i	$-0.752914\pi$
$919$	229.720	−	397.886i	0.249967	−	0.432956i	0.963516	+	0.267649i	$0.0862469\pi$
$920$	22.5156	−	12.9994i	0.0244734	−	0.0141297i
$921$	−2448.49	+	891.176i	−2.65851	+	0.967618i
$922$	−332.208	−	912.734i	−0.360312	−	0.989950i
$923$	523.585	+	906.877i	0.567265	+	0.982532i
$924$	−979.740	−	565.653i	−1.06032	−	0.612179i
$925$	−969.693	−	170.983i	−1.04832	−	0.184846i
$926$	69.0239	+	82.2595i	0.0745398	+	0.0888331i
$927$	550.495	−	656.055i	0.593846	−	0.707718i
$928$	−19.7450	−	111.979i	−0.0212769	−	0.120667i
$929$	262.118	+	95.4030i	0.282150	+	0.102694i	0.479219	−	0.877695i	$-0.340920\pi$
$929$	262.118	+	95.4030i	0.282150	+	0.102694i	−0.197069	+	0.980390i	$0.563142\pi$
$930$			142.176i			0.152877i
$931$	−57.0714	+	535.715i	−0.0613012	+	0.575419i
$932$	−527.942			−0.566462
$933$	185.545	−	509.780i	0.198869	−	0.546388i
$934$	−308.319	+	54.3649i	−0.330106	+	0.0582065i
$935$	−204.690	−	171.756i	−0.218920	−	0.183696i
$936$	−703.477	+	590.287i	−0.751578	+	0.630648i
$937$	119.917	−	680.085i	0.127980	−	0.725811i	−0.851513	−	0.524333i	$-0.824315\pi$
$937$	119.917	−	680.085i	0.127980	−	0.725811i	0.979493	−	0.201477i	$-0.0645743\pi$
$938$	−197.374	+	341.862i	−0.210420	+	0.364459i
$939$	801.622	−	462.816i	0.853697	−	0.492882i
$940$	48.0874	−	17.5024i	0.0511568	−	0.0186196i
$941$	−423.538	−	1163.66i	−0.450094	−	1.23662i	−0.932658	−	0.360762i	$-0.882517\pi$
$941$	−423.538	−	1163.66i	−0.450094	−	1.23662i	0.482564	−	0.875861i	$-0.339706\pi$
$942$	109.811	+	190.199i	0.116573	+	0.201910i
$943$	−143.183	−	82.6668i	−0.151838	−	0.0876637i
$944$	−388.734	−	68.5443i	−0.411795	−	0.0726105i
$945$	427.365	+	509.313i	0.452238	+	0.538956i
$946$	−432.288	+	515.181i	−0.456964	+	0.544589i
$947$	−158.218	−	897.302i	−0.167073	−	0.947520i	−0.946901	−	0.321526i	$-0.895804\pi$
$947$	−158.218	−	897.302i	−0.167073	−	0.947520i	0.779827	−	0.625995i	$-0.215307\pi$
$948$	430.259	+	156.601i	0.453859	+	0.165191i
$949$		−	1402.15i		−	1.47750i
$950$	251.347	+	566.689i	0.264576	+	0.596515i
$951$	−1677.57			−1.76401
$952$	−135.272	+	371.657i	−0.142092	+	0.390396i
$953$	−594.322	+	104.795i	−0.623633	+	0.109963i	−0.476530	−	0.879158i	$-0.658106\pi$
$953$	−594.322	+	104.795i	−0.623633	+	0.109963i	−0.147102	+	0.989121i	$0.546995\pi$
$954$	431.315	+	361.916i	0.452112	+	0.379367i
$955$	302.878	−	254.145i	0.317149	−	0.266120i
$956$	120.793	−	685.052i	0.126353	−	0.716581i
$957$	646.378	−	1119.56i	0.675421	−	1.16986i
$958$	−497.864	+	287.442i	−0.519691	+	0.300044i
$959$	76.1960	−	27.7331i	0.0794536	−	0.0289187i
$960$	−20.1938	−	55.4819i	−0.0210352	−	0.0577937i
$961$	−387.723	−	671.556i	−0.403458	−	0.698810i
$962$	881.945	+	509.191i	0.916782	+	0.529305i
$963$	2697.01	+	475.556i	2.80064	+	0.493828i
$964$	−283.224	−	337.533i	−0.293801	−	0.350138i
$965$	187.560	−	223.526i	0.194363	−	0.231633i
$966$	−75.9741	−	430.871i	−0.0786482	−	0.446036i
$967$	18.4649	+	6.72068i	0.0190950	+	0.00695003i	0.351550	−	0.936169i	$-0.385655\pi$
$967$	18.4649	+	6.72068i	0.0190950	+	0.00695003i	−0.332455	+	0.943119i	$0.607877\pi$
$968$			71.9997i			0.0743799i
$969$	1113.54	+	1156.37i	1.14917	+	1.19337i
$970$	−107.205			−0.110520
$971$	−54.6251	+	150.081i	−0.0562565	+	0.154564i	−0.964638	−	0.263580i	$-0.915097\pi$
$971$	−54.6251	+	150.081i	−0.0562565	+	0.154564i	0.908381	+	0.418143i	$0.137319\pi$
$972$	250.285	−	44.1319i	0.257494	−	0.0454032i
$973$	926.731	+	777.620i	0.952447	+	0.799198i
$974$	514.308	−	431.556i	0.528037	−	0.443076i
$975$	−359.239	+	2037.34i	−0.368450	+	2.08958i
$976$	188.406	−	326.328i	0.193039	−	0.334353i
$977$	868.501	−	501.429i	0.888946	−	0.513233i	0.0153487	−	0.999882i	$-0.495114\pi$
$977$	868.501	−	501.429i	0.888946	−	0.513233i	0.873598	+	0.486649i	$0.161781\pi$
$978$	76.2937	−	27.7686i	0.0780099	−	0.0283933i
$979$	−14.7607	−	40.5548i	−0.0150774	−	0.0414247i
$980$	−39.3781	−	68.2048i	−0.0401817	−	0.0695968i
$981$	525.606	+	303.459i	0.535786	+	0.309336i
$982$	913.132	+	161.010i	0.929869	+	0.163961i
$983$	−989.296	−	1179.00i	−1.00640	−	1.19939i	−0.979849	−	0.199739i	$-0.935991\pi$
$983$	−989.296	−	1179.00i	−1.00640	−	1.19939i	−0.0265556	−	0.999647i	$-0.508454\pi$
$984$	−241.347	+	287.627i	−0.245272	+	0.292303i
$985$	52.9062	+	300.046i	0.0537118	+	0.304615i
$986$	−424.696	−	154.577i	−0.430726	−	0.156772i
$987$		−	861.171i		−	0.872513i
$988$	−43.8216	−	639.666i	−0.0443539	−	0.647436i
$989$	−260.089			−0.262981
$990$	156.425	−	429.775i	0.158006	−	0.434117i
$991$	−29.9843	+	5.28704i	−0.0302566	+	0.00533505i	−0.188756	−	0.982024i	$-0.560446\pi$
$991$	−29.9843	+	5.28704i	−0.0302566	+	0.00533505i	0.158499	+	0.987359i	$0.449334\pi$
$992$	−59.0288	−	49.5310i	−0.0595048	−	0.0499305i
$993$	1970.01	−	1653.03i	1.98390	−	1.66469i
$994$	−134.048	+	760.224i	−0.134857	+	0.764813i
$995$	74.7708	−	129.507i	0.0751466	−	0.130158i
$996$	201.706	−	116.455i	0.202516	−	0.116923i
$997$	−33.6581	+	12.2505i	−0.0337594	+	0.0122874i	−0.358845	−	0.933397i	$-0.616829\pi$
$997$	−33.6581	+	12.2505i	−0.0337594	+	0.0122874i	0.325085	+	0.945685i	$0.394607\pi$
$998$	365.775	+	1004.96i	0.366508	+	1.00697i
$999$	−1161.56	−	2011.88i	−1.16272	−	2.01390i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.3.f.a.15.1	✓	24
3.2	odd	2		342.3.z.b.91.4		24
4.3	odd	2		304.3.z.c.129.4		24
19.9	even	9		722.3.b.f.721.12		24
19.10	odd	18		722.3.b.f.721.13		24
19.14	odd	18	inner	38.3.f.a.33.1	yes	24
57.14	even	18		342.3.z.b.109.4		24
76.71	even	18		304.3.z.c.33.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.3.f.a.15.1	✓	24	1.1	even	1	trivial
38.3.f.a.33.1	yes	24	19.14	odd	18	inner
304.3.z.c.33.4		24	76.71	even	18
304.3.z.c.129.4		24	4.3	odd	2
342.3.z.b.91.4		24	3.2	odd	2
342.3.z.b.109.4		24	57.14	even	18
722.3.b.f.721.12		24	19.9	even	9
722.3.b.f.721.13		24	19.10	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)

\(f(q)\)	\(=\)	\(q+(-0.483690 + 1.32893i) q^{2} +(-5.23364 + 0.922832i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-1.06384 + 0.892670i) q^{5} +(1.30508 - 7.40149i) q^{6} +(-4.39759 + 7.61684i) q^{7} +(2.44949 - 1.41421i) q^{8} +(18.0821 - 6.58136i) q^{9} +O(q^{10})\)	\(q+(-0.483690 + 1.32893i) q^{2} +(-5.23364 + 0.922832i) q^{3} +(-1.53209 - 1.28558i) q^{4} +(-1.06384 + 0.892670i) q^{5} +(1.30508 - 7.40149i) q^{6} +(-4.39759 + 7.61684i) q^{7} +(2.44949 - 1.41421i) q^{8} +(18.0821 - 6.58136i) q^{9} +(-0.671723 - 1.84554i) q^{10} +(6.05095 + 10.4805i) q^{11} +(9.20477 + 5.31438i) q^{12} +(-16.6164 - 2.92993i) q^{13} +(-7.99516 - 9.52826i) q^{14} +(4.74399 - 5.65366i) q^{15} +(0.694593 + 3.93923i) q^{16} +(14.9401 + 5.43774i) q^{17} +27.2132i q^{18} +(-15.3555 - 11.1896i) q^{19} +2.77750 q^{20} +(15.9863 - 43.9221i) q^{21} +(-16.8546 + 2.97193i) q^{22} +(-5.07035 - 4.25452i) q^{23} +(-11.5147 + 9.66195i) q^{24} +(-4.00630 + 22.7209i) q^{25} +(11.9309 - 20.6649i) q^{26} +(-47.1405 + 27.2166i) q^{27} +(16.5295 - 6.01625i) q^{28} +(6.87484 + 18.8885i) q^{29} +(5.21868 + 9.03902i) q^{30} +(11.7968 + 6.81091i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(-41.3403 - 49.2674i) q^{33} +(-14.4527 + 17.2241i) q^{34} +(-2.12099 - 12.0287i) q^{35} +(-36.1643 - 13.1627i) q^{36} +42.6785i q^{37} +(22.2975 - 14.9941i) q^{38} +89.6683 q^{39} +(-1.34345 + 3.69109i) q^{40} +(24.5997 - 4.33758i) q^{41} +(50.6368 + 42.4893i) q^{42} +(30.1018 - 25.2584i) q^{43} +(4.20294 - 23.8361i) q^{44} +(-13.3616 + 23.1429i) q^{45} +(8.10642 - 4.68024i) q^{46} +(17.3132 - 6.30150i) q^{47} +(-7.27050 - 19.9755i) q^{48} +(-14.1775 - 24.5562i) q^{49} +(-28.2566 - 16.3139i) q^{50} +(-83.2090 - 14.6720i) q^{51} +(21.6912 + 25.8506i) q^{52} +(13.2993 - 15.8495i) q^{53} +(-13.3674 - 75.8106i) q^{54} +(-15.7929 - 5.74815i) q^{55} +24.8765i q^{56} +(90.6915 + 44.3919i) q^{57} -28.4267 q^{58} +(-33.7515 + 92.7314i) q^{59} +(-14.5364 + 2.56316i) q^{60} +(-72.1635 - 60.5524i) q^{61} +(-14.7572 + 12.3828i) q^{62} +(-29.3886 + 166.671i) q^{63} +(4.00000 - 6.92820i) q^{64} +(20.2927 - 11.7160i) q^{65} +(85.4686 - 31.1080i) q^{66} +(-10.8546 - 29.8227i) q^{67} +(-15.8989 - 27.5377i) q^{68} +(30.4626 + 17.5876i) q^{69} +(17.0112 + 2.99953i) q^{70} +(-39.8932 - 47.5428i) q^{71} +(34.9846 - 41.6930i) q^{72} +(14.4304 + 81.8388i) q^{73} +(-56.7166 - 20.6431i) q^{74} -122.610i q^{75} +(9.14092 + 36.8842i) q^{76} -106.438 q^{77} +(-43.3716 + 119.163i) q^{78} +(42.4241 - 7.48052i) q^{79} +(-4.25537 - 3.57068i) q^{80} +(88.9337 - 74.6242i) q^{81} +(-6.13427 + 34.7892i) q^{82} +(10.9566 - 18.9774i) q^{83} +(-80.9576 + 46.7409i) q^{84} +(-20.7480 + 7.55165i) q^{85} +(19.0066 + 52.2202i) q^{86} +(-53.4113 - 92.5112i) q^{87} +(29.6435 + 17.1147i) q^{88} +(-3.51200 - 0.619260i) q^{89} +(-24.2924 - 28.9505i) q^{90} +(95.3891 - 113.680i) q^{91} +(2.29871 + 13.0366i) q^{92} +(-68.0257 - 24.7593i) q^{93} +26.0560i q^{94} +(26.3245 - 1.80341i) q^{95} +30.0627 q^{96} +(18.6693 - 51.2934i) q^{97} +(39.4909 - 6.96332i) q^{98} +(178.390 + 149.687i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more