LMFDB - Embedded newform 42.3.g.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,3,Mod(19,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("42.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$42 = 2 \cdot 3 \cdot 7$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	42.g (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14441711031$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} + 2x^{2} + 4$ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	42.19
Dual form			42.3.g.a.31.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(7.24264 + 4.18154i) q^{5} +2.44949i q^{6} +(-6.74264 + 1.88064i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-10.2426 + 5.91359i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-3.00000 - 1.73205i) q^{12} -17.8639i q^{13} +(2.46447 - 9.58783i) q^{14} +14.4853 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-16.2426 + 9.37769i) q^{17} +(2.12132 + 3.67423i) q^{18} +(-14.7426 - 8.51167i) q^{19} -16.7262i q^{20} +(-8.48528 + 8.66025i) q^{21} +8.48528 q^{22} +(-6.72792 + 11.6531i) q^{23} +(4.24264 - 2.44949i) q^{24} +(22.4706 + 38.9202i) q^{25} +(21.8787 + 12.6317i) q^{26} -5.19615i q^{27} +(10.0000 + 9.79796i) q^{28} +33.9411 q^{29} +(-10.2426 + 17.7408i) q^{30} +(12.7721 - 7.37396i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-9.00000 - 5.19615i) q^{33} -26.5241i q^{34} +(-56.6985 - 14.5738i) q^{35} -6.00000 q^{36} +(-2.98528 + 5.17066i) q^{37} +(20.8492 - 12.0373i) q^{38} +(-15.4706 - 26.7958i) q^{39} +(20.4853 + 11.8272i) q^{40} +35.2354i q^{41} +(-4.60660 - 16.5160i) q^{42} +15.4853 q^{43} +(-6.00000 + 10.3923i) q^{44} +(21.7279 - 12.5446i) q^{45} +(-9.51472 - 16.4800i) q^{46} +(-28.7574 - 16.6031i) q^{47} +6.92820i q^{48} +(41.9264 - 25.3609i) q^{49} -63.5563 q^{50} +(-16.2426 + 28.1331i) q^{51} +(-30.9411 + 17.8639i) q^{52} +(17.2721 + 29.9161i) q^{53} +(6.36396 + 3.67423i) q^{54} -50.1785i q^{55} +(-19.0711 + 5.31925i) q^{56} -29.4853 q^{57} +(-24.0000 + 41.5692i) q^{58} +(23.6985 - 13.6823i) q^{59} +(-14.4853 - 25.0892i) q^{60} +(-34.9706 - 20.1903i) q^{61} +20.8567i q^{62} +(-5.22792 + 20.3389i) q^{63} +8.00000 q^{64} +(74.6985 - 129.382i) q^{65} +(12.7279 - 7.34847i) q^{66} +(57.1985 + 99.0707i) q^{67} +(32.4853 + 18.7554i) q^{68} +23.3062i q^{69} +(57.9411 - 59.1359i) q^{70} +18.6030 q^{71} +(4.24264 - 7.34847i) q^{72} +(-101.353 + 58.5161i) q^{73} +(-4.22183 - 7.31242i) q^{74} +(67.4117 + 38.9202i) q^{75} +34.0467i q^{76} +(30.0000 + 29.3939i) q^{77} +43.7574 q^{78} +(44.1690 - 76.5030i) q^{79} +(-28.9706 + 16.7262i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-43.1543 - 24.9152i) q^{82} +75.7601i q^{83} +(23.4853 + 6.03668i) q^{84} -156.853 q^{85} +(-10.9497 + 18.9655i) q^{86} +(50.9117 - 29.3939i) q^{87} +(-8.48528 - 14.6969i) q^{88} +(-18.0000 - 10.3923i) q^{89} +35.4815i q^{90} +(33.5955 + 120.450i) q^{91} +26.9117 q^{92} +(12.7721 - 22.1219i) q^{93} +(40.6690 - 23.4803i) q^{94} +(-71.1838 - 123.294i) q^{95} +(-8.48528 - 4.89898i) q^{96} +30.5826i q^{97} +(1.41421 + 69.2820i) q^{98} -18.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 6 q^{3} - 4 q^{4} + 12 q^{5} - 10 q^{7} + 6 q^{9} - 24 q^{10} - 12 q^{11} - 12 q^{12} + 24 q^{14} + 24 q^{15} - 8 q^{16} - 48 q^{17} - 42 q^{19} + 24 q^{23} + 22 q^{25} + 96 q^{26} + 40 q^{28} - 24 q^{30}+ \cdots - 72 q^{99}+O(q^{100})$ 4 * q + 6 * q^3 - 4 * q^4 + 12 * q^5 - 10 * q^7 + 6 * q^9 - 24 * q^10 - 12 * q^11 - 12 * q^12 + 24 * q^14 + 24 * q^15 - 8 * q^16 - 48 * q^17 - 42 * q^19 + 24 * q^23 + 22 * q^25 + 96 * q^26 + 40 * q^28 - 24 * q^30 + 102 * q^31 - 36 * q^33 - 108 * q^35 - 24 * q^36 + 22 * q^37 + 24 * q^38 + 6 * q^39 + 48 * q^40 + 24 * q^42 + 28 * q^43 - 24 * q^44 + 36 * q^45 - 72 * q^46 - 132 * q^47 - 2 * q^49 - 192 * q^50 - 48 * q^51 + 12 * q^52 + 120 * q^53 - 48 * q^56 - 84 * q^57 - 96 * q^58 - 24 * q^59 - 24 * q^60 - 72 * q^61 + 30 * q^63 + 32 * q^64 + 180 * q^65 + 110 * q^67 + 96 * q^68 + 96 * q^70 + 312 * q^71 - 66 * q^73 - 48 * q^74 + 66 * q^75 + 120 * q^77 + 192 * q^78 - 10 * q^79 - 48 * q^80 - 18 * q^81 + 48 * q^82 + 60 * q^84 - 288 * q^85 - 24 * q^86 - 72 * q^89 - 222 * q^91 - 96 * q^92 + 102 * q^93 - 24 * q^94 - 132 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$ .

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	7.24264	+	4.18154i	1.44853	+	0.836308i	0.998394	−	0.0566528i	$-0.0180428\pi$
$5$	7.24264	+	4.18154i	1.44853	+	0.836308i	0.450134	+	0.892961i	$0.351376\pi$
$6$			2.44949i			0.408248i
$7$	−6.74264	+	1.88064i	−0.963234	+	0.268662i
$7$	−6.74264	+	1.88064i	−0.963234	+	0.268662i
$8$	2.82843			0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	−10.2426	+	5.91359i	−1.02426	+	0.591359i
$11$	−3.00000	−	5.19615i	−0.272727	−	0.472377i	0.696832	−	0.717234i	$-0.254592\pi$
$11$	−3.00000	−	5.19615i	−0.272727	−	0.472377i	−0.969559	+	0.244857i	$0.921259\pi$
$12$	−3.00000	−	1.73205i	−0.250000	−	0.144338i
$13$		−	17.8639i		−	1.37414i	−0.726590	−	0.687072i	$-0.758896\pi$
$13$		−	17.8639i		−	1.37414i	0.726590	−	0.687072i	$-0.241104\pi$
$14$	2.46447	−	9.58783i	0.176033	−	0.684845i
$15$	14.4853			0.965685
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−16.2426	+	9.37769i	−0.955449	+	0.551629i	−0.894770	−	0.446528i	$-0.852660\pi$
$17$	−16.2426	+	9.37769i	−0.955449	+	0.551629i	−0.0606799	+	0.998157i	$0.519327\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	−14.7426	−	8.51167i	−0.775928	−	0.447983i	0.0590569	−	0.998255i	$-0.481191\pi$
$19$	−14.7426	−	8.51167i	−0.775928	−	0.447983i	−0.834985	+	0.550272i	$0.814524\pi$
$20$		−	16.7262i		−	0.836308i
$21$	−8.48528	+	8.66025i	−0.404061	+	0.412393i
$22$	8.48528			0.385695
$23$	−6.72792	+	11.6531i	−0.292518	+	0.506657i	−0.974405	−	0.224802i	$-0.927827\pi$
$23$	−6.72792	+	11.6531i	−0.292518	+	0.506657i	0.681886	+	0.731458i	$0.261160\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$	22.4706	+	38.9202i	0.898823	+	1.55681i
$26$	21.8787	+	12.6317i	0.841488	+	0.485833i
$27$		−	5.19615i		−	0.192450i
$28$	10.0000	+	9.79796i	0.357143	+	0.349927i
$29$	33.9411			1.17038			0.585192	−	0.810895i	$-0.301019\pi$
$29$	33.9411			1.17038			0.585192	+	0.810895i	$0.301019\pi$
$30$	−10.2426	+	17.7408i	−0.341421	+	0.591359i
$31$	12.7721	−	7.37396i	0.412003	−	0.237870i	−0.279647	−	0.960103i	$-0.590218\pi$
$31$	12.7721	−	7.37396i	0.412003	−	0.237870i	0.691650	+	0.722233i	$0.256884\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	−9.00000	−	5.19615i	−0.272727	−	0.157459i
$34$		−	26.5241i		−	0.780121i
$35$	−56.6985	−	14.5738i	−1.61996	−	0.416396i
$36$	−6.00000			−0.166667
$37$	−2.98528	+	5.17066i	−0.0806833	+	0.139748i	−0.903544	−	0.428496i	$-0.859044\pi$
$37$	−2.98528	+	5.17066i	−0.0806833	+	0.139748i	0.822860	+	0.568244i	$0.192377\pi$
$38$	20.8492	−	12.0373i	0.548664	−	0.316771i
$39$	−15.4706	−	26.7958i	−0.396681	−	0.687072i
$40$	20.4853	+	11.8272i	0.512132	+	0.295680i
$41$			35.2354i			0.859399i	0.902972	+	0.429700i	$0.141381\pi$
$41$			35.2354i			0.859399i	−0.902972	+	0.429700i	$0.858619\pi$
$42$	−4.60660	−	16.5160i	−0.109681	−	0.393239i
$43$	15.4853			0.360123			0.180061	−	0.983655i	$-0.442370\pi$
$43$	15.4853			0.360123			0.180061	+	0.983655i	$0.442370\pi$
$44$	−6.00000	+	10.3923i	−0.136364	+	0.236189i
$45$	21.7279	−	12.5446i	0.482843	−	0.278769i
$46$	−9.51472	−	16.4800i	−0.206842	−	0.358260i
$47$	−28.7574	−	16.6031i	−0.611859	−	0.353257i	0.161834	−	0.986818i	$-0.448259\pi$
$47$	−28.7574	−	16.6031i	−0.611859	−	0.353257i	−0.773693	+	0.633561i	$0.781592\pi$
$48$			6.92820i			0.144338i
$49$	41.9264	−	25.3609i	0.855641	−	0.517570i
$50$	−63.5563			−1.27113
$51$	−16.2426	+	28.1331i	−0.318483	+	0.551629i
$52$	−30.9411	+	17.8639i	−0.595022	+	0.343536i
$53$	17.2721	+	29.9161i	0.325888	+	0.564455i	0.981692	−	0.190477i	$-0.0610033\pi$
$53$	17.2721	+	29.9161i	0.325888	+	0.564455i	−0.655803	+	0.754932i	$0.727670\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		−	50.1785i		−	0.912336i
$56$	−19.0711	+	5.31925i	−0.340555	+	0.0949865i
$57$	−29.4853			−0.517286
$58$	−24.0000	+	41.5692i	−0.413793	+	0.716711i
$59$	23.6985	−	13.6823i	0.401669	−	0.231904i	−0.285535	−	0.958368i	$-0.592171\pi$
$59$	23.6985	−	13.6823i	0.401669	−	0.231904i	0.687204	+	0.726465i	$0.258838\pi$
$60$	−14.4853	−	25.0892i	−0.241421	−	0.418154i
$61$	−34.9706	−	20.1903i	−0.573288	−	0.330988i	0.185174	−	0.982706i	$-0.440715\pi$
$61$	−34.9706	−	20.1903i	−0.573288	−	0.330988i	−0.758461	+	0.651718i	$0.774049\pi$
$62$			20.8567i			0.336399i
$63$	−5.22792	+	20.3389i	−0.0829829	+	0.322839i
$64$	8.00000			0.125000
$65$	74.6985	−	129.382i	1.14921	−	1.99049i
$66$	12.7279	−	7.34847i	0.192847	−	0.111340i
$67$	57.1985	+	99.0707i	0.853709	+	1.47867i	0.877838	+	0.478958i	$0.158985\pi$
$67$	57.1985	+	99.0707i	0.853709	+	1.47867i	−0.0241291	+	0.999709i	$0.507681\pi$
$68$	32.4853	+	18.7554i	0.477725	+	0.275814i
$69$			23.3062i			0.337771i
$70$	57.9411	−	59.1359i	0.827730	−	0.844799i
$71$	18.6030			0.262015			0.131007	−	0.991381i	$-0.458179\pi$
$71$	18.6030			0.262015			0.131007	+	0.991381i	$0.458179\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	−101.353	+	58.5161i	−1.38839	+	0.801590i	−0.993134	−	0.116979i	$-0.962679\pi$
$73$	−101.353	+	58.5161i	−1.38839	+	0.801590i	−0.395260	+	0.918569i	$0.629346\pi$
$74$	−4.22183	−	7.31242i	−0.0570517	−	0.0988164i
$75$	67.4117	+	38.9202i	0.898823	+	0.518935i
$76$			34.0467i			0.447983i
$77$	30.0000	+	29.3939i	0.389610	+	0.381739i
$78$	43.7574			0.560992
$79$	44.1690	−	76.5030i	0.559102	−	0.968393i	−0.438470	−	0.898746i	$-0.644479\pi$
$79$	44.1690	−	76.5030i	0.559102	−	0.968393i	0.997572	−	0.0696469i	$-0.0221873\pi$
$80$	−28.9706	+	16.7262i	−0.362132	+	0.209077i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−43.1543	−	24.9152i	−0.526272	−	0.303843i
$83$			75.7601i			0.912772i	0.889782	+	0.456386i	$0.150856\pi$
$83$			75.7601i			0.912772i	−0.889782	+	0.456386i	$0.849144\pi$
$84$	23.4853	+	6.03668i	0.279587	+	0.0718653i
$85$	−156.853			−1.84533
$86$	−10.9497	+	18.9655i	−0.127323	+	0.220529i
$87$	50.9117	−	29.3939i	0.585192	−	0.337861i
$88$	−8.48528	−	14.6969i	−0.0964237	−	0.167011i
$89$	−18.0000	−	10.3923i	−0.202247	−	0.116767i	0.395456	−	0.918485i	$-0.370587\pi$
$89$	−18.0000	−	10.3923i	−0.202247	−	0.116767i	−0.597703	+	0.801717i	$0.703920\pi$
$90$			35.4815i			0.394239i
$91$	33.5955	+	120.450i	0.369181	+	1.32362i
$92$	26.9117			0.292518
$93$	12.7721	−	22.1219i	0.137334	−	0.237870i
$94$	40.6690	−	23.4803i	0.432649	−	0.249790i
$95$	−71.1838	−	123.294i	−0.749303	−	1.29783i
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$			30.5826i			0.315284i	0.987496	+	0.157642i	$0.0503892\pi$
$97$			30.5826i			0.315284i	−0.987496	+	0.157642i	$0.949611\pi$
$98$	1.41421	+	69.2820i	0.0144308	+	0.706960i
$99$	−18.0000			−0.181818
$100$	44.9411	−	77.8403i	0.449411	−	0.778403i
$101$	110.823	−	63.9839i	1.09726	−	0.633504i	0.161761	−	0.986830i	$-0.448283\pi$
$101$	110.823	−	63.9839i	1.09726	−	0.633504i	0.935500	+	0.353326i	$0.114949\pi$
$102$	−22.9706	−	39.7862i	−0.225202	−	0.390061i
$103$	−70.1102	−	40.4781i	−0.680681	−	0.392992i	0.119430	−	0.992843i	$-0.461893\pi$
$103$	−70.1102	−	40.4781i	−0.680681	−	0.392992i	−0.800112	+	0.599851i	$0.795226\pi$
$104$		−	50.5266i		−	0.485833i
$105$	−97.6690	+	27.2416i	−0.930181	+	0.259443i
$106$	−48.8528			−0.460876
$107$	−84.7279	+	146.753i	−0.791850	+	1.37152i	0.132971	+	0.991120i	$0.457548\pi$
$107$	−84.7279	+	146.753i	−0.791850	+	1.37152i	−0.924820	+	0.380404i	$0.875785\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	−89.4706	−	154.968i	−0.820831	−	1.42172i	−0.905064	−	0.425275i	$-0.860177\pi$
$109$	−89.4706	−	154.968i	−0.820831	−	1.42172i	0.0842335	−	0.996446i	$-0.473156\pi$
$110$	61.4558	+	35.4815i	0.558689	+	0.322560i
$111$			10.3413i			0.0931650i
$112$	6.97056	−	27.1185i	0.0622372	−	0.242129i
$113$	−17.3970			−0.153955			−0.0769777	−	0.997033i	$-0.524527\pi$
$113$	−17.3970			−0.153955			−0.0769777	+	0.997033i	$0.524527\pi$
$114$	20.8492	−	36.1119i	0.182888	−	0.316771i
$115$	−97.4558	+	56.2662i	−0.847442	+	0.489271i
$116$	−33.9411	−	58.7878i	−0.292596	−	0.506791i
$117$	−46.4117	−	26.7958i	−0.396681	−	0.229024i
$118$			38.6995i			0.327962i
$119$	91.8823	−	93.7769i	0.772120	−	0.788041i
$120$	40.9706			0.341421
$121$	42.5000	−	73.6122i	0.351240	−	0.608365i
$122$	49.4558	−	28.5533i	0.405376	−	0.234044i
$123$	30.5147	+	52.8530i	0.248087	+	0.429700i
$124$	−25.5442	−	14.7479i	−0.206001	−	0.118935i
$125$			166.769i			1.33415i
$126$	−21.2132	−	20.7846i	−0.168359	−	0.164957i
$127$	167.426			1.31832			0.659159	−	0.752004i	$-0.270912\pi$
$127$	167.426			1.31832			0.659159	+	0.752004i	$0.270912\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	23.2279	−	13.4106i	0.180061	−	0.103959i
$130$	105.640	+	182.973i	0.812612	+	1.40749i
$131$	−1.54416	−	0.891519i	−0.0117874	−	0.00680549i	0.494095	−	0.869408i	$-0.335500\pi$
$131$	−1.54416	−	0.891519i	−0.0117874	−	0.00680549i	−0.505882	+	0.862603i	$0.668833\pi$
$132$			20.7846i			0.157459i
$133$	115.412	+	29.6656i	0.867757	+	0.223049i
$134$	−161.782			−1.20733
$135$	21.7279	−	37.6339i	0.160948	−	0.278769i
$136$	−45.9411	+	26.5241i	−0.337802	+	0.195030i
$137$	−50.4853	−	87.4431i	−0.368506	−	0.638271i	0.620826	−	0.783948i	$-0.286797\pi$
$137$	−50.4853	−	87.4431i	−0.368506	−	0.638271i	−0.989332	+	0.145677i	$0.953464\pi$
$138$	−28.5442	−	16.4800i	−0.206842	−	0.119420i
$139$		−	140.542i		−	1.01110i	−0.862799	−	0.505548i	$-0.831290\pi$
$139$		−	140.542i		−	1.01110i	0.862799	−	0.505548i	$-0.168710\pi$
$140$	31.4558	+	112.779i	0.224685	+	0.805561i
$141$	−57.5147			−0.407906
$142$	−13.1543	+	22.7840i	−0.0926361	+	0.160450i
$143$	−92.8234	+	53.5916i	−0.649115	+	0.374766i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$	245.823	+	141.926i	1.69533	+	0.978801i
$146$		−	165.508i		−	1.13362i
$147$	40.9264	−	74.3507i	0.278411	−	0.505787i
$148$	11.9411			0.0806833
$149$	−91.4558	+	158.406i	−0.613798	+	1.06313i	0.376797	+	0.926296i	$0.377026\pi$
$149$	−91.4558	+	158.406i	−0.613798	+	1.06313i	−0.990594	+	0.136833i	$0.956308\pi$
$150$	−95.3345	+	55.0414i	−0.635563	+	0.366943i
$151$	144.397	+	250.103i	0.956271	+	1.65631i	0.731432	+	0.681915i	$0.238852\pi$
$151$	144.397	+	250.103i	0.956271	+	1.65631i	0.224840	+	0.974396i	$0.427814\pi$
$152$	−41.6985	−	24.0746i	−0.274332	−	0.158386i
$153$			56.2662i			0.367753i
$154$	−57.2132	+	15.9577i	−0.371514	+	0.103622i
$155$	123.338			0.795730
$156$	−30.9411	+	53.5916i	−0.198341	+	0.343536i
$157$	162.000	−	93.5307i	1.03185	−	0.595737i	0.114334	−	0.993442i	$-0.463527\pi$
$157$	162.000	−	93.5307i	1.03185	−	0.595737i	0.917513	+	0.397705i	$0.130193\pi$
$158$	62.4645	+	108.192i	0.395345	+	0.684757i
$159$	51.8162	+	29.9161i	0.325888	+	0.188152i
$160$		−	47.3087i		−	0.295680i
$161$	23.4487	−	91.2255i	0.145644	−	0.566618i
$162$	12.7279			0.0785674
$163$	−8.02944	+	13.9074i	−0.0492604	+	0.0853214i	−0.889604	−	0.456732i	$-0.849020\pi$
$163$	−8.02944	+	13.9074i	−0.0492604	+	0.0853214i	0.840344	+	0.542054i	$0.182353\pi$
$164$	61.0294	−	35.2354i	0.372131	−	0.214850i
$165$	−43.4558	−	75.2677i	−0.263369	−	0.456168i
$166$	−92.7868	−	53.5705i	−0.558957	−	0.322714i
$167$		−	176.117i		−	1.05459i	−0.849681	−	0.527297i	$-0.823206\pi$
$167$		−	176.117i		−	1.05459i	0.849681	−	0.527297i	$-0.176794\pi$
$168$	−24.0000	+	24.4949i	−0.142857	+	0.145803i
$169$	−150.118			−0.888271
$170$	110.912	−	192.105i	0.652422	−	1.13003i
$171$	−44.2279	+	25.5350i	−0.258643	+	0.149328i
$172$	−15.4853	−	26.8213i	−0.0900307	−	0.155938i
$173$	−200.184	−	115.576i	−1.15713	−	0.668070i	−0.206517	−	0.978443i	$-0.566213\pi$
$173$	−200.184	−	115.576i	−1.15713	−	0.668070i	−0.950615	+	0.310373i	$0.899546\pi$
$174$			83.1384i			0.477807i
$175$	−224.706	−	220.166i	−1.28403	−	1.25809i
$176$	24.0000			0.136364
$177$	23.6985	−	41.0470i	0.133890	−	0.231904i
$178$	25.4558	−	14.6969i	0.143010	−	0.0825671i
$179$	42.6396	+	73.8540i	0.238210	+	0.412592i	0.960201	−	0.279311i	$-0.0901060\pi$
$179$	42.6396	+	73.8540i	0.238210	+	0.412592i	−0.721991	+	0.691903i	$0.756773\pi$
$180$	−43.4558	−	25.0892i	−0.241421	−	0.139385i
$181$		−	5.58655i		−	0.0308649i	−0.999881	−	0.0154325i	$-0.995087\pi$
$181$		−	5.58655i		−	0.0308649i	0.999881	−	0.0154325i	$-0.00491250\pi$
$182$	−171.276	−	44.0249i	−0.941075	−	0.241895i
$183$	−69.9411			−0.382192
$184$	−19.0294	+	32.9600i	−0.103421	+	0.179130i
$185$	−43.2426	+	24.9662i	−0.233744	+	0.134952i
$186$	18.0624	+	31.2851i	0.0971099	+	0.168199i
$187$	97.4558	+	56.2662i	0.521154	+	0.300889i
$188$			66.4123i			0.353257i
$189$	9.77208	+	35.0358i	0.0517041	+	0.185375i
$190$	201.338			1.05967
$191$	−92.6985	+	160.558i	−0.485332	+	0.840620i	−0.999858	−	0.0168547i	$-0.994635\pi$
$191$	−92.6985	+	160.558i	−0.485332	+	0.840620i	0.514526	+	0.857475i	$0.327968\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	−113.897	−	197.275i	−0.590140	−	1.02215i	−0.994213	−	0.107425i	$-0.965739\pi$
$193$	−113.897	−	197.275i	−0.590140	−	1.02215i	0.404073	−	0.914727i	$-0.367594\pi$
$194$	−37.4558	−	21.6251i	−0.193071	−	0.111470i
$195$		−	258.763i		−	1.32699i
$196$	−85.8528	−	47.2577i	−0.438025	−	0.241111i
$197$	123.161			0.625185			0.312593	−	0.949887i	$-0.398803\pi$
$197$	123.161			0.625185			0.312593	+	0.949887i	$0.398803\pi$
$198$	12.7279	−	22.0454i	0.0642824	−	0.111340i
$199$	5.39697	−	3.11594i	0.0271205	−	0.0156580i	−0.486378	−	0.873748i	$-0.661682\pi$
$199$	5.39697	−	3.11594i	0.0271205	−	0.0156580i	0.513499	+	0.858090i	$0.328349\pi$
$200$	63.5563	+	110.083i	0.317782	+	0.550414i
$201$	171.595	+	99.0707i	0.853709	+	0.492889i
$202$			180.974i			0.895910i
$203$	−228.853	+	63.8309i	−1.12735	+	0.314438i
$204$	64.9706			0.318483
$205$	−147.338	+	255.197i	−0.718722	+	1.24486i
$206$	99.1508	−	57.2447i	0.481314	−	0.277887i
$207$	20.1838	+	34.9593i	0.0975061	+	0.168886i
$208$	61.8823	+	35.7277i	0.297511	+	0.171768i
$209$			102.140i			0.488708i
$210$	35.6985	−	138.882i	0.169993	−	0.661345i
$211$	−124.912			−0.591999			−0.295999	−	0.955188i	$-0.595653\pi$
$211$	−124.912			−0.591999			−0.295999	+	0.955188i	$0.595653\pi$
$212$	34.5442	−	59.8322i	0.162944	−	0.282228i
$213$	27.9045	−	16.1107i	0.131007	−	0.0756371i
$214$	−119.823	−	207.540i	−0.559922	−	0.969814i
$215$	112.154	+	64.7523i	0.521648	+	0.301174i
$216$		−	14.6969i		−	0.0680414i
$217$	−72.2498	+	73.7396i	−0.332948	+	0.339814i
$218$	253.061			1.16083
$219$	−101.353	+	175.548i	−0.462798	+	0.801590i
$220$	−86.9117	+	50.1785i	−0.395053	+	0.228084i
$221$	167.522	+	290.156i	0.758017	+	1.31292i
$222$	−12.6655	−	7.31242i	−0.0570517	−	0.0329388i
$223$		−	228.631i		−	1.02525i	−0.858613	−	0.512625i	$-0.828673\pi$
$223$		−	228.631i		−	1.02525i	0.858613	−	0.512625i	$-0.171327\pi$
$224$	28.2843	+	27.7128i	0.126269	+	0.123718i
$225$	134.823			0.599215
$226$	12.3015	−	21.3068i	0.0544315	−	0.0942781i
$227$	−146.823	+	84.7685i	−0.646799	+	0.373430i	−0.787229	−	0.616661i	$-0.788485\pi$
$227$	−146.823	+	84.7685i	−0.646799	+	0.373430i	0.140430	+	0.990091i	$0.455152\pi$
$228$	29.4853	+	51.0700i	0.129321	+	0.223991i
$229$	30.0442	+	17.3460i	0.131197	+	0.0757467i	0.564162	−	0.825664i	$-0.309199\pi$
$229$	30.0442	+	17.3460i	0.131197	+	0.0757467i	−0.432965	+	0.901411i	$0.642533\pi$
$230$		−	159.145i		−	0.691934i
$231$	70.4558	+	18.1101i	0.305004	+	0.0783985i
$232$	96.0000			0.413793
$233$	127.243	−	220.391i	0.546106	−	0.945883i	−0.452431	−	0.891800i	$-0.649443\pi$
$233$	127.243	−	220.391i	0.546106	−	0.945883i	0.998536	−	0.0540833i	$-0.0172237\pi$
$234$	65.6360	−	37.8950i	0.280496	−	0.161944i
$235$	−138.853	−	240.500i	−0.590863	−	1.02340i
$236$	−47.3970	−	27.3647i	−0.200835	−	0.115952i
$237$		−	153.006i		−	0.645595i
$238$	49.8823	+	178.843i	0.209589	+	0.751440i
$239$	197.147			0.824884			0.412442	−	0.910984i	$-0.364676\pi$
$239$	197.147			0.824884			0.412442	+	0.910984i	$0.364676\pi$
$240$	−28.9706	+	50.1785i	−0.120711	+	0.209077i
$241$	76.6173	−	44.2350i	0.317914	−	0.183548i	−0.332548	−	0.943086i	$-0.607908\pi$
$241$	76.6173	−	44.2350i	0.317914	−	0.183548i	0.650462	+	0.759538i	$0.274575\pi$
$242$	60.1041	+	104.103i	0.248364	+	0.430179i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$			80.7611i			0.330988i
$245$	409.706	−	8.36308i	1.67227	−	0.0341350i
$246$	−86.3087			−0.350848
$247$	−152.051	+	263.361i	−0.615592	+	1.06624i
$248$	36.1249	−	20.8567i	0.145665	−	0.0840997i
$249$	65.6102	+	113.640i	0.263495	+	0.456386i
$250$	−204.250	−	117.924i	−0.816999	−	0.471695i
$251$		−	215.903i		−	0.860172i	−0.902788	−	0.430086i	$-0.858483\pi$
$251$		−	215.903i		−	0.860172i	0.902788	−	0.430086i	$-0.141517\pi$
$252$	40.4558	−	11.2838i	0.160539	−	0.0447771i
$253$	80.7351			0.319111
$254$	−118.388	+	205.055i	−0.466096	+	0.807302i
$255$	−235.279	+	135.839i	−0.922664	+	0.532700i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−3.72792	−	2.15232i	−0.0145055	−	0.00837477i	0.492730	−	0.870182i	$-0.335999\pi$
$257$	−3.72792	−	2.15232i	−0.0145055	−	0.00837477i	−0.507235	+	0.861808i	$0.669332\pi$
$258$			37.9310i			0.147020i
$259$	10.4045	−	40.4781i	0.0401720	−	0.156286i
$260$	−298.794			−1.14921
$261$	50.9117	−	88.1816i	0.195064	−	0.337861i
$262$	2.18377	−	1.26080i	0.00833499	−	0.00481221i
$263$	−141.338	−	244.805i	−0.537407	−	0.930817i	−0.999043	−	0.0437468i	$-0.986071\pi$
$263$	−141.338	−	244.805i	−0.537407	−	0.930817i	0.461635	−	0.887070i	$-0.347263\pi$
$264$	−25.4558	−	14.6969i	−0.0964237	−	0.0556702i
$265$			288.896i			1.09017i
$266$	−117.941	+	120.373i	−0.443388	+	0.452531i
$267$	−36.0000			−0.134831
$268$	114.397	−	198.141i	0.426854	−	0.739333i
$269$	−330.765	+	190.967i	−1.22961	+	0.709914i	−0.966948	−	0.254974i	$-0.917933\pi$
$269$	−330.765	+	190.967i	−1.22961	+	0.709914i	−0.262660	+	0.964888i	$0.584600\pi$
$270$	30.7279	+	53.2223i	0.113807	+	0.197120i
$271$	−73.0294	−	42.1636i	−0.269481	−	0.155585i	0.359171	−	0.933272i	$-0.383060\pi$
$271$	−73.0294	−	42.1636i	−0.269481	−	0.155585i	−0.628652	+	0.777687i	$0.716393\pi$
$272$		−	75.0215i		−	0.275814i
$273$	154.706	+	151.580i	0.566687	+	0.555238i
$274$	142.794			0.521146
$275$	134.823	−	233.521i	0.490267	−	0.849167i
$276$	40.3675	−	23.3062i	0.146259	−	0.0844428i
$277$	68.5589	+	118.747i	0.247505	+	0.428691i	0.962833	−	0.270098i	$-0.0870560\pi$
$277$	68.5589	+	118.747i	0.247505	+	0.428691i	−0.715328	+	0.698789i	$0.753723\pi$
$278$	172.128	+	99.3784i	0.619167	+	0.357476i
$279$		−	44.2438i		−	0.158580i
$280$	−160.368	−	41.2211i	−0.572741	−	0.147218i
$281$	−325.103			−1.15695			−0.578474	−	0.815701i	$-0.696352\pi$
$281$	−325.103			−1.15695			−0.578474	+	0.815701i	$0.696352\pi$
$282$	40.6690	−	70.4409i	0.144216	−	0.249790i
$283$	168.507	−	97.2876i	0.595432	−	0.343773i	−0.171811	−	0.985130i	$-0.554962\pi$
$283$	168.507	−	97.2876i	0.595432	−	0.343773i	0.767242	+	0.641357i	$0.221628\pi$
$284$	−18.6030	−	32.2214i	−0.0655036	−	0.113456i
$285$	−213.551	−	123.294i	−0.749303	−	0.432610i
$286$		−	151.580i		−	0.530000i
$287$	−66.2649	−	237.579i	−0.230888	−	0.827803i
$288$	−16.9706			−0.0589256
$289$	31.3823	−	54.3557i	0.108589	−	0.188082i
$290$	−347.647	+	200.714i	−1.19878	+	0.692117i
$291$	26.4853	+	45.8739i	0.0910147	+	0.157642i
$292$	202.706	+	117.032i	0.694197	+	0.400795i
$293$		−	239.702i		−	0.818095i	−0.912513	−	0.409048i	$-0.865861\pi$
$293$		−	239.702i		−	0.818095i	0.912513	−	0.409048i	$-0.134139\pi$
$294$	62.1213	+	102.698i	0.211297	+	0.349314i
$295$	228.853			0.775772
$296$	−8.44365	+	14.6248i	−0.0285258	+	0.0494082i
$297$	−27.0000	+	15.5885i	−0.0909091	+	0.0524864i
$298$	−129.338	−	224.020i	−0.434020	−	0.751745i
$299$	208.169	+	120.187i	0.696219	+	0.401962i
$300$		−	155.681i		−	0.518935i
$301$	−104.412	+	29.1222i	−0.346883	+	0.0967515i
$302$	−408.416			−1.35237
$303$	110.823	−	191.952i	0.365754	−	0.633504i
$304$	58.9706	−	34.0467i	0.193982	−	0.111996i
$305$	−168.853	−	292.462i	−0.553616	−	0.958891i
$306$	−68.9117	−	39.7862i	−0.225202	−	0.130020i
$307$			540.272i			1.75984i	0.475120	+	0.879921i	$0.342405\pi$
$307$			540.272i			1.75984i	−0.475120	+	0.879921i	$0.657595\pi$
$308$	20.9117	−	81.3554i	0.0678951	−	0.264141i
$309$	−140.220			−0.453788
$310$	−87.2132	+	151.058i	−0.281333	+	0.487283i
$311$	350.044	−	202.098i	1.12554	−	0.649832i	0.182732	−	0.983163i	$-0.441506\pi$
$311$	350.044	−	202.098i	1.12554	−	0.649832i	0.942810	+	0.333330i	$0.108172\pi$
$312$	−43.7574	−	75.7900i	−0.140248	−	0.242917i
$313$	−113.706	−	65.6482i	−0.363278	−	0.209739i	0.307240	−	0.951632i	$-0.400595\pi$
$313$	−113.706	−	65.6482i	−0.363278	−	0.209739i	−0.670518	+	0.741893i	$0.733928\pi$
$314$			264.545i			0.842500i
$315$	−122.912	+	125.446i	−0.390196	+	0.398242i
$316$	−176.676			−0.559102
$317$	46.9706	−	81.3554i	0.148172	−	0.256642i	−0.782380	−	0.622802i	$-0.785994\pi$
$317$	46.9706	−	81.3554i	0.148172	−	0.256642i	0.930552	+	0.366160i	$0.119328\pi$
$318$	−73.2792	+	42.3078i	−0.230438	+	0.133043i
$319$	−101.823	−	176.363i	−0.319196	−	0.552863i
$320$	57.9411	+	33.4523i	0.181066	+	0.104539i
$321$			293.506i			0.914349i
$322$	95.1472	+	93.2248i	0.295488	+	0.289518i
$323$	319.279			0.988481
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$	695.265	−	401.411i	2.13928	−	1.23511i
$326$	−11.3553	−	19.6680i	−0.0348323	−	0.0603314i
$327$	−268.412	−	154.968i	−0.820831	−	0.473907i
$328$			99.6607i			0.303843i
$329$	225.125	+	57.8664i	0.684270	+	0.175886i
$330$	122.912			0.372460
$331$	130.684	−	226.351i	0.394815	−	0.683840i	−0.598263	−	0.801300i	$-0.704142\pi$
$331$	130.684	−	226.351i	0.394815	−	0.683840i	0.993078	+	0.117460i	$0.0374754\pi$
$332$	131.220	−	75.7601i	0.395242	−	0.228193i
$333$	8.95584	+	15.5120i	0.0268944	+	0.0465825i
$334$	215.698	+	124.534i	0.645804	+	0.372855i
$335$			956.711i			2.85585i
$336$	−13.0294	−	46.7144i	−0.0387781	−	0.139031i
$337$	136.265			0.404347			0.202173	−	0.979350i	$-0.435200\pi$
$337$	136.265			0.404347			0.202173	+	0.979350i	$0.435200\pi$
$338$	106.149	−	183.856i	0.314051	−	0.543952i
$339$	−26.0955	+	15.0662i	−0.0769777	+	0.0444431i
$340$	156.853	+	271.677i	0.461332	+	0.799050i
$341$	−76.6325	−	44.2438i	−0.224729	−	0.129747i
$342$		−	72.2239i		−	0.211181i
$343$	−235.000	+	249.848i	−0.685131	+	0.728420i
$344$	43.7990			0.127323
$345$	−97.4558	+	168.798i	−0.282481	+	0.489271i
$346$	283.103	−	163.449i	0.818216	−	0.472397i
$347$	161.095	+	279.026i	0.464252	+	0.804108i	0.999167	−	0.0407975i	$-0.0129899\pi$
$347$	161.095	+	279.026i	0.464252	+	0.804108i	−0.534915	+	0.844906i	$0.679657\pi$
$348$	−101.823	−	58.7878i	−0.292596	−	0.168930i
$349$			346.495i			0.992821i	0.868088	+	0.496411i	$0.165349\pi$
$349$			346.495i			0.992821i	−0.868088	+	0.496411i	$0.834651\pi$
$350$	428.538	−	119.526i	1.22439	−	0.341504i
$351$	−92.8234			−0.264454
$352$	−16.9706	+	29.3939i	−0.0482118	+	0.0835053i
$353$	−537.448	+	310.296i	−1.52252	+	0.879025i	−0.522869	+	0.852413i	$0.675138\pi$
$353$	−537.448	+	310.296i	−1.52252	+	0.879025i	−0.999646	+	0.0266116i	$0.991528\pi$
$354$	33.5147	+	58.0492i	0.0946743	+	0.163981i
$355$	134.735	+	77.7893i	0.379535	+	0.219125i
$356$			41.5692i			0.116767i
$357$	56.6102	−	220.238i	0.158572	−	0.616912i
$358$	−120.603			−0.336880
$359$	−10.1177	+	17.5245i	−0.0281831	+	0.0488146i	−0.879773	−	0.475394i	$-0.842305\pi$
$359$	−10.1177	+	17.5245i	−0.0281831	+	0.0488146i	0.851590	+	0.524209i	$0.175639\pi$
$360$	61.4558	−	35.4815i	0.170711	−	0.0985599i
$361$	−35.6030	−	61.6663i	−0.0986234	−	0.170821i
$362$	6.84210	+	3.95029i	0.0189008	+	0.0109124i
$363$		−	147.224i		−	0.405577i
$364$	175.029	−	178.639i	0.480850	−	0.490766i
$365$	−978.749			−2.68151
$366$	49.4558	−	85.6600i	0.135125	−	0.234044i
$367$	−269.831	+	155.787i	−0.735234	+	0.424488i	−0.820334	−	0.571885i	$-0.806212\pi$
$367$	−269.831	+	155.787i	−0.735234	+	0.424488i	0.0850998	+	0.996372i	$0.472879\pi$
$368$	−26.9117	−	46.6124i	−0.0731296	−	0.126664i
$369$	91.5442	+	52.8530i	0.248087	+	0.143233i
$370$		−	70.6149i		−	0.190851i
$371$	−172.721	−	169.231i	−0.465555	−	0.456149i
$372$	−51.0883			−0.137334
$373$	340.691	−	590.094i	0.913380	−	1.58202i	0.104125	−	0.994564i	$-0.466796\pi$
$373$	340.691	−	590.094i	0.913380	−	1.58202i	0.809255	−	0.587457i	$-0.199871\pi$
$374$	−137.823	+	79.5724i	−0.368512	+	0.212760i
$375$	144.426	+	250.154i	0.385137	+	0.667077i
$376$	−81.3381	−	46.9606i	−0.216325	−	0.124895i
$377$		−	606.320i		−	1.60828i
$378$	−49.8198	−	12.8057i	−0.131798	−	0.0338776i
$379$	−624.779			−1.64849			−0.824246	−	0.566231i	$-0.808401\pi$
$379$	−624.779			−1.64849			−0.824246	+	0.566231i	$0.808401\pi$
$380$	−142.368	+	246.588i	−0.374651	+	0.648915i
$381$	251.140	−	144.996i	0.659159	−	0.380566i
$382$	−131.095	−	227.064i	−0.343182	−	0.594408i
$383$	119.772	+	69.1502i	0.312720	+	0.180549i	0.648143	−	0.761519i	$-0.275546\pi$
$383$	119.772	+	69.1502i	0.312720	+	0.180549i	−0.335423	+	0.942068i	$0.608879\pi$
$384$			19.5959i			0.0510310i
$385$	94.3675	+	338.336i	0.245110	+	0.878794i
$386$	322.149			0.834584
$387$	23.2279	−	40.2319i	0.0600205	−	0.103959i
$388$	52.9706	−	30.5826i	0.136522	−	0.0788211i
$389$	281.787	+	488.069i	0.724388	+	1.25468i	0.959226	+	0.282642i	$0.0912107\pi$
$389$	281.787	+	488.069i	0.724388	+	1.25468i	−0.234838	+	0.972035i	$0.575456\pi$
$390$	316.919	+	182.973i	0.812612	+	0.469162i
$391$		−	252.370i		−	0.645446i
$392$	118.586	−	71.7315i	0.302515	−	0.182989i
$393$	−3.08831			−0.00785830
$394$	−87.0883	+	150.841i	−0.221036	+	0.382846i
$395$	639.801	−	369.389i	1.61975	−	0.935163i
$396$	18.0000	+	31.1769i	0.0454545	+	0.0787296i
$397$	−392.603	−	226.669i	−0.988923	−	0.570955i	−0.0839711	−	0.996468i	$-0.526760\pi$
$397$	−392.603	−	226.669i	−0.988923	−	0.570955i	−0.904952	+	0.425513i	$0.860094\pi$
$398$			8.81321i			0.0221438i
$399$	198.809	−	55.4511i	0.498267	−	0.138975i
$400$	−179.765			−0.449411
$401$	137.875	−	238.807i	0.343828	−	0.595528i	−0.641312	−	0.767280i	$-0.721610\pi$
$401$	137.875	−	238.807i	0.343828	−	0.595528i	0.985140	+	0.171752i	$0.0549429\pi$
$402$	−242.673	+	140.107i	−0.603663	+	0.348525i
$403$	−131.727	−	228.159i	−0.326867	−	0.566151i
$404$	−221.647	−	127.968i	−0.548631	−	0.316752i
$405$		−	75.2677i		−	0.185846i
$406$	83.6468	−	325.422i	0.206026	−	0.801531i
$407$	35.8234			0.0880181
$408$	−45.9411	+	79.5724i	−0.112601	+	0.195030i
$409$	−377.441	+	217.916i	−0.922839	+	0.532801i	−0.884540	−	0.466465i	$-0.845527\pi$
$409$	−377.441	+	217.916i	−0.922839	+	0.532801i	−0.0382993	+	0.999266i	$0.512194\pi$
$410$	−208.368	−	360.903i	−0.508213	−	0.880252i
$411$	−151.456	−	87.4431i	−0.368506	−	0.212757i
$412$			161.913i			0.392992i
$413$	−134.059	+	136.823i	−0.324598	+	0.331291i
$414$	−57.0883			−0.137894
$415$	−316.794	+	548.703i	−0.763359	+	1.32218i
$416$	−87.5147	+	50.5266i	−0.210372	+	0.121458i
$417$	−121.713	−	210.813i	−0.291878	−	0.505548i
$418$	−125.095	−	72.2239i	−0.299271	−	0.172784i
$419$		−	301.257i		−	0.718991i	−0.933147	−	0.359496i	$-0.882949\pi$
$419$		−	301.257i		−	0.718991i	0.933147	−	0.359496i	$-0.117051\pi$
$420$	144.853	+	141.926i	0.344888	+	0.337920i
$421$	−203.794			−0.484071			−0.242036	−	0.970267i	$-0.577815\pi$
$421$	−203.794			−0.484071			−0.242036	+	0.970267i	$0.577815\pi$
$422$	88.3259	−	152.985i	0.209303	−	0.362524i
$423$	−86.2721	+	49.8092i	−0.203953	+	0.117752i
$424$	48.8528	+	84.6156i	0.115219	+	0.199565i
$425$	−729.963	−	421.444i	−1.71756	−	0.991633i
$426$			45.5679i			0.106967i
$427$	273.765	+	70.3688i	0.641135	+	0.164798i
$428$	338.912			0.791850
$429$	−92.8234	+	160.775i	−0.216372	+	0.374766i
$430$	−158.610	+	91.5736i	−0.368861	+	0.212962i
$431$	197.860	+	342.703i	0.459072	+	0.795136i	0.998912	−	0.0466317i	$-0.0148487\pi$
$431$	197.860	+	342.703i	0.459072	+	0.795136i	−0.539840	+	0.841767i	$0.681515\pi$
$432$	18.0000	+	10.3923i	0.0416667	+	0.0240563i
$433$		−	44.2685i		−	0.102237i	−0.998693	−	0.0511184i	$-0.983721\pi$
$433$		−	44.2685i		−	0.102237i	0.998693	−	0.0511184i	$-0.0162786\pi$
$434$	−39.2239	−	140.629i	−0.0903777	−	0.324031i
$435$	491.647			1.13022
$436$	−178.941	+	309.935i	−0.410415	+	0.710860i
$437$	198.375	−	114.532i	0.453947	−	0.262086i
$438$	−143.335	−	248.263i	−0.327248	−	0.566810i
$439$	344.558	+	198.931i	0.784871	+	0.453146i	0.838154	−	0.545434i	$-0.183635\pi$
$439$	344.558	+	198.931i	0.784871	+	0.453146i	−0.0532827	+	0.998579i	$0.516968\pi$
$440$		−	141.926i		−	0.322560i
$441$	−3.00000	−	146.969i	−0.00680272	−	0.333264i
$442$	−473.823			−1.07200
$443$	59.2721	−	102.662i	0.133797	−	0.231743i	−0.791340	−	0.611376i	$-0.790616\pi$
$443$	59.2721	−	102.662i	0.133797	−	0.231743i	0.925137	+	0.379633i	$0.123950\pi$
$444$	17.9117	−	10.3413i	0.0403416	−	0.0232913i
$445$	−86.9117	−	150.535i	−0.195307	−	0.338282i
$446$	280.014	+	161.666i	0.627835	+	0.362481i
$447$			316.812i			0.708752i
$448$	−53.9411	+	15.0451i	−0.120404	+	0.0335828i
$449$	713.897			1.58997			0.794985	−	0.606629i	$-0.207479\pi$
$449$	713.897			1.58997			0.794985	+	0.606629i	$0.207479\pi$
$450$	−95.3345	+	165.124i	−0.211854	+	0.366943i
$451$	183.088	−	105.706i	0.405961	−	0.234382i
$452$	17.3970	+	30.1324i	0.0384889	+	0.0666647i
$453$	433.191	+	250.103i	0.956271	+	0.552104i
$454$		−	239.762i		−	0.528109i
$455$	−260.345	+	1012.85i	−0.572187	+	2.22605i
$456$	−83.3970			−0.182888
$457$	62.5883	−	108.406i	0.136955	−	0.237213i	−0.789388	−	0.613895i	$-0.789602\pi$
$457$	62.5883	−	108.406i	0.136955	−	0.237213i	0.926342	+	0.376682i	$0.122935\pi$
$458$	−42.4889	+	24.5310i	−0.0927704	+	0.0535610i
$459$	48.7279	+	84.3992i	0.106161	+	0.183876i
$460$	194.912	+	112.532i	0.423721	+	0.244635i
$461$			655.767i			1.42249i	0.702945	+	0.711244i	$0.251868\pi$
$461$			655.767i			1.42249i	−0.702945	+	0.711244i	$0.748132\pi$
$462$	−72.0000	+	73.4847i	−0.155844	+	0.159058i
$463$	869.396			1.87775			0.938873	−	0.344265i	$-0.111872\pi$
$463$	869.396			1.87775			0.938873	+	0.344265i	$0.111872\pi$
$464$	−67.8823	+	117.576i	−0.146298	+	0.253395i
$465$	185.007	−	106.814i	0.397865	−	0.229707i
$466$	179.948	+	311.680i	0.386155	+	0.668840i
$467$	−231.551	−	133.686i	−0.495827	−	0.286266i	0.231162	−	0.972915i	$-0.425747\pi$
$467$	−231.551	−	133.686i	−0.495827	−	0.286266i	−0.726989	+	0.686649i	$0.759081\pi$
$468$			107.183i			0.229024i
$469$	−571.985	−	560.428i	−1.21958	−	1.19494i
$470$	392.735			0.835607
$471$	162.000	−	280.592i	0.343949	−	0.595737i
$472$	67.0294	−	38.6995i	0.142012	−	0.0819904i
$473$	−46.4558	−	80.4639i	−0.0982153	−	0.170114i
$474$	187.393	+	108.192i	0.395345	+	0.228252i
$475$		−	765.048i		−	1.61063i
$476$	−254.309	−	65.3678i	−0.534262	−	0.137327i
$477$	103.632			0.217259
$478$	−139.404	+	241.455i	−0.291640	+	0.505136i
$479$	235.331	−	135.868i	0.491296	−	0.283650i	−0.233816	−	0.972281i	$-0.575121\pi$
$479$	235.331	−	135.868i	0.491296	−	0.283650i	0.725112	+	0.688631i	$0.241788\pi$
$480$	−40.9706	−	70.9631i	−0.0853553	−	0.147840i
$481$	92.3680	+	53.3287i	0.192033	+	0.110870i
$482$			125.116i			0.259576i
$483$	−43.8305	−	157.145i	−0.0907464	−	0.325353i
$484$	−170.000			−0.351240
$485$	−127.882	+	221.499i	−0.263675	+	0.456698i
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	280.757	+	486.285i	0.576503	+	0.998532i	0.995877	+	0.0907186i	$0.0289164\pi$
$487$	280.757	+	486.285i	0.576503	+	0.998532i	−0.419374	+	0.907814i	$0.637750\pi$
$488$	−98.9117	−	57.1067i	−0.202688	−	0.117022i
$489$			27.8148i			0.0568810i
$490$	−279.463	+	507.698i	−0.570333	+	1.03612i
$491$	−406.441			−0.827781			−0.413891	−	0.910327i	$-0.635830\pi$
$491$	−406.441			−0.827781			−0.413891	+	0.910327i	$0.635830\pi$
$492$	61.0294	−	105.706i	0.124044	−	0.214850i
$493$	−551.294	+	318.289i	−1.11824	+	0.645618i
$494$	−215.033	−	372.448i	−0.435289	−	0.753944i
$495$	−130.368	−	75.2677i	−0.263369	−	0.152056i
$496$			58.9917i			0.118935i
$497$	−125.434	+	34.9856i	−0.252381	+	0.0703935i
$498$	−185.574			−0.372638
$499$	185.713	−	321.665i	0.372171	−	0.644619i	−0.617728	−	0.786391i	$-0.711947\pi$
$499$	185.713	−	321.665i	0.372171	−	0.644619i	0.989899	+	0.141773i	$0.0452802\pi$
$500$	288.853	−	166.769i	0.577706	−	0.333538i
$501$	−152.522	−	264.176i	−0.304435	−	0.527297i
$502$	264.426	+	152.667i	0.526746	+	0.304117i
$503$			64.6292i			0.128488i	0.997934	+	0.0642438i	$0.0204635\pi$
$503$			64.6292i			0.128488i	−0.997934	+	0.0642438i	$0.979536\pi$
$504$	−14.7868	+	57.5270i	−0.0293389	+	0.114141i
$505$	1070.21			2.11922
$506$	−57.0883	+	98.8799i	−0.112823	+	0.195415i
$507$	−225.177	+	130.006i	−0.444135	+	0.256422i
$508$	−167.426	−	289.991i	−0.329580	−	0.570849i
$509$	871.889	+	503.385i	1.71294	+	0.988969i	0.930534	+	0.366205i	$0.119343\pi$
$509$	871.889	+	503.385i	1.71294	+	0.988969i	0.782410	+	0.622764i	$0.213990\pi$
$510$		−	384.209i		−	0.753352i
$511$	573.338	−	585.161i	1.12199	−	1.14513i
$512$	22.6274			0.0441942
$513$	−44.2279	+	76.6050i	−0.0862143	+	0.149328i
$514$	5.27208	−	3.04384i	0.0102570	−	0.00592186i
$515$	−338.522	−	586.337i	−0.657324	−	1.13852i
$516$	−46.4558	−	26.8213i	−0.0900307	−	0.0519793i
$517$			199.237i			0.385371i
$518$	42.2183	+	41.3653i	0.0815024	+	0.0798557i
$519$	−400.368			−0.771421
$520$	211.279	−	365.946i	0.406306	−	0.703743i
$521$	−322.294	+	186.077i	−0.618607	+	0.357153i	−0.776327	−	0.630331i	$-0.782919\pi$
$521$	−322.294	+	186.077i	−0.618607	+	0.357153i	0.157719	+	0.987484i	$0.449586\pi$
$522$	72.0000	+	124.708i	0.137931	+	0.238904i
$523$	−551.904	−	318.642i	−1.05527	−	0.609258i	−0.131147	−	0.991363i	$-0.541866\pi$
$523$	−551.904	−	318.642i	−1.05527	−	0.609258i	−0.924119	+	0.382105i	$0.875199\pi$
$524$			3.56608i			0.00680549i
$525$	−527.727	−	135.648i	−1.00520	−	0.258377i
$526$	399.765			0.760009
$527$	−138.302	+	239.545i	−0.262432	+	0.454545i
$528$	36.0000	−	20.7846i	0.0681818	−	0.0393648i
$529$	173.970	+	301.325i	0.328866	+	0.569613i
$530$	−353.823	−	204.280i	−0.667591	−	0.385434i
$531$		−	82.0940i		−	0.154603i
$532$	−64.0294	−	229.564i	−0.120356	−	0.431512i
$533$	629.440			1.18094
$534$	25.4558	−	44.0908i	0.0476701	−	0.0825671i
$535$	−1227.31	+	708.586i	−2.29403	+	1.32446i
$536$	161.782	+	280.214i	0.301832	+	0.522788i
$537$	127.919	+	73.8540i	0.238210	+	0.137531i
$538$		−	540.136i		−	1.00397i
$539$	−257.558	−	141.773i	−0.477845	−	0.263030i
$540$	−86.9117			−0.160948
$541$	−110.412	+	191.239i	−0.204088	+	0.353491i	−0.949842	−	0.312731i	$-0.898756\pi$
$541$	−110.412	+	191.239i	−0.204088	+	0.353491i	0.745754	+	0.666222i	$0.232090\pi$
$542$	103.279	−	59.6283i	0.190552	−	0.110015i
$543$	−4.83810	−	8.37983i	−0.00890994	−	0.0154325i
$544$	91.8823	+	53.0482i	0.168901	+	0.0975152i
$545$		−	1496.50i		−	2.74587i
$546$	−295.040	+	82.2917i	−0.540367	+	0.150717i
$547$	−160.676			−0.293741			−0.146870	−	0.989156i	$-0.546920\pi$
$547$	−160.676			−0.293741			−0.146870	+	0.989156i	$0.546920\pi$
$548$	−100.971	+	174.886i	−0.184253	+	0.319135i
$549$	−104.912	+	60.5708i	−0.191096	+	0.110329i
$550$	190.669	+	330.248i	0.346671	+	0.600452i
$551$	−500.382	−	288.896i	−0.908134	−	0.524311i
$552$			65.9199i			0.119420i
$553$	−153.942	+	598.898i	−0.278375	+	1.08300i
$554$	−193.914			−0.350025
$555$	−43.2426	+	74.8985i	−0.0779147	+	0.134952i
$556$	−243.426	+	140.542i	−0.437817	+	0.252774i
$557$	237.177	+	410.802i	0.425811	+	0.737526i	0.996496	−	0.0836431i	$-0.0266556\pi$
$557$	237.177	+	410.802i	0.425811	+	0.737526i	−0.570685	+	0.821169i	$0.693322\pi$
$558$	54.1873	+	31.2851i	0.0971099	+	0.0560664i
$559$		−	276.627i		−	0.494860i
$560$	163.882	−	167.262i	0.292647	−	0.298681i
$561$	194.912			0.347436
$562$	229.882	−	398.168i	0.409043	−	0.708484i
$563$	−430.301	+	248.434i	−0.764300	+	0.441269i	−0.830837	−	0.556515i	$-0.812138\pi$
$563$	−430.301	+	248.434i	−0.764300	+	0.441269i	0.0665378	+	0.997784i	$0.478805\pi$
$564$	57.5147	+	99.6184i	0.101976	+	0.176628i
$565$	−126.000	−	72.7461i	−0.223009	−	0.128754i
$566$			275.171i			0.486168i
$567$	45.0000	+	44.0908i	0.0793651	+	0.0777616i
$568$	52.6173			0.0926361
$569$	−392.647	+	680.084i	−0.690065	+	1.19523i	0.281752	+	0.959487i	$0.409085\pi$
$569$	−392.647	+	680.084i	−0.690065	+	1.19523i	−0.971816	+	0.235740i	$0.924249\pi$
$570$	302.007	−	174.364i	0.529837	−	0.305902i
$571$	357.521	+	619.245i	0.626132	+	1.08449i	0.988321	+	0.152388i	$0.0486963\pi$
$571$	357.521	+	619.245i	0.626132	+	1.08449i	−0.362189	+	0.932105i	$0.617970\pi$
$572$	185.647	+	107.183i	0.324557	+	0.187383i
$573$			321.117i			0.560414i
$574$	337.831	+	86.8364i	0.588555	+	0.151283i
$575$	−604.721			−1.05169
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	669.117	−	386.315i	1.15965	−	0.669524i	0.208429	−	0.978038i	$-0.433165\pi$
$577$	669.117	−	386.315i	1.15965	−	0.669524i	0.951220	+	0.308514i	$0.0998317\pi$
$578$	44.3812	+	76.8705i	0.0767841	+	0.132994i
$579$	−341.691	−	197.275i	−0.590140	−	0.340717i
$580$		−	567.705i		−	0.978801i
$581$	−142.477	−	510.823i	−0.245228	−	0.879214i
$582$	−74.9117			−0.128714
$583$	103.632	−	179.497i	0.177757	−	0.307885i
$584$	−286.669	+	165.508i	−0.490872	+	0.283405i
$585$	−224.095	−	388.145i	−0.383069	−	0.663495i
$586$	293.574	+	169.495i	0.500979	+	0.289240i
$587$		−	436.477i		−	0.743572i	−0.928318	−	0.371786i	$-0.878746\pi$
$587$		−	436.477i		−	0.743572i	0.928318	−	0.371786i	$-0.121254\pi$
$588$	−169.706	+	3.46410i	−0.288615	+	0.00589133i
$589$	−251.059			−0.426246
$590$	−161.823	+	280.286i	−0.274277	+	0.475062i
$591$	184.742	−	106.661i	0.312593	−	0.180475i
$592$	−11.9411	−	20.6826i	−0.0201708	−	0.0349369i
$593$	722.397	+	417.076i	1.21821	+	0.703332i	0.964534	−	0.263958i	$-0.0850279\pi$
$593$	722.397	+	417.076i	1.21821	+	0.703332i	0.253673	+	0.967290i	$0.418361\pi$
$594$		−	44.0908i		−	0.0742270i
$595$	1057.60	−	294.983i	1.77748	−	0.495770i
$596$	365.823			0.613798
$597$	5.39697	−	9.34783i	0.00904015	−	0.0156580i
$598$	−294.396	+	169.970i	−0.492301	+	0.284230i
$599$	−436.794	−	756.549i	−0.729205	−	1.26302i	−0.957220	−	0.289363i	$-0.906557\pi$
$599$	−436.794	−	756.549i	−0.729205	−	1.26302i	0.228014	−	0.973658i	$-0.426777\pi$
$600$	190.669	+	110.083i	0.317782	+	0.183471i
$601$			198.982i			0.331085i	0.986203	+	0.165542i	$0.0529375\pi$
$601$			198.982i			0.331085i	−0.986203	+	0.165542i	$0.947063\pi$
$602$	38.1630	−	148.470i	0.0633936	−	0.246628i
$603$	343.191			0.569139
$604$	288.794	−	500.206i	0.478136	−	0.828155i
$605$	615.624	−	355.431i	1.01756	−	0.587489i
$606$	156.728	+	271.461i	0.258627	+	0.447955i
$607$	137.654	+	79.4748i	0.226778	+	0.130930i	0.609085	−	0.793105i	$-0.291537\pi$
$607$	137.654	+	79.4748i	0.226778	+	0.130930i	−0.382307	+	0.924035i	$0.624870\pi$
$608$			96.2985i			0.158386i
$609$	−288.000	+	293.939i	−0.472906	+	0.482658i
$610$	477.588			0.782931
$611$	−296.595	+	513.718i	−0.485426	+	0.840782i
$612$	97.4558	−	56.2662i	0.159242	−	0.0919382i
$613$	357.368	+	618.979i	0.582981	+	1.00975i	0.995124	+	0.0986338i	$0.0314473\pi$
$613$	357.368	+	618.979i	0.582981	+	1.00975i	−0.412143	+	0.911119i	$0.635219\pi$
$614$	−661.695	−	382.030i	−1.07768	−	0.622198i
$615$			510.394i			0.829909i
$616$	84.8528	+	83.1384i	0.137748	+	0.134965i
$617$	−639.381			−1.03627			−0.518137	−	0.855298i	$-0.673374\pi$
$617$	−639.381			−1.03627			−0.518137	+	0.855298i	$0.673374\pi$
$618$	99.1508	−	171.734i	0.160438	−	0.277887i
$619$	148.978	−	86.0126i	0.240676	−	0.138954i	−0.374812	−	0.927101i	$-0.622293\pi$
$619$	148.978	−	86.0126i	0.240676	−	0.138954i	0.615487	+	0.788147i	$0.288959\pi$
$620$	−123.338	−	213.628i	−0.198932	−	0.344561i
$621$	60.5513	+	34.9593i	0.0975061	+	0.0562952i
$622$			571.619i			0.919002i
$623$	140.912	+	36.2201i	0.226182	+	0.0581382i
$624$	123.765			0.198341
$625$	−135.588	+	234.846i	−0.216941	+	0.375753i
$626$	160.805	−	92.8406i	0.256876	−	0.148308i
$627$	88.4558	+	153.210i	0.141078	+	0.244354i
$628$	−324.000	−	187.061i	−0.515924	−	0.297869i
$629$		−	111.980i		−	0.178029i
$630$	−66.7279	−	239.239i	−0.105917	−	0.379745i
$631$	−1141.06			−1.80833			−0.904166	−	0.427180i	$-0.859507\pi$
$631$	−1141.06			−1.80833			−0.904166	+	0.427180i	$0.859507\pi$
$632$	124.929	−	216.383i	0.197672	−	0.342379i
$633$	−187.368	+	108.177i	−0.295999	+	0.170895i
$634$	66.4264	+	115.054i	0.104774	+	0.181473i
$635$	1212.61	+	700.100i	1.90962	+	1.10252i
$636$		−	119.664i		−	0.188152i
$637$	−453.044	−	748.968i	−0.711215	−	1.17577i
$638$	288.000			0.451411
$639$	27.9045	−	48.3321i	0.0436691	−	0.0756371i
$640$	−81.9411	+	47.3087i	−0.128033	+	0.0739199i
$641$	−114.551	−	198.409i	−0.178707	−	0.309530i	0.762731	−	0.646716i	$-0.223858\pi$
$641$	−114.551	−	198.409i	−0.178707	−	0.309530i	−0.941438	+	0.337186i	$0.890525\pi$
$642$	−359.470	−	207.540i	−0.559922	−	0.323271i
$643$			707.670i			1.10058i	0.834975	+	0.550288i	$0.185482\pi$
$643$			707.670i			1.10058i	−0.834975	+	0.550288i	$0.814518\pi$
$644$	−181.456	+	50.6111i	−0.281764	+	0.0785887i
$645$	224.309			0.347765
$646$	−225.765	+	391.036i	−0.349481	+	0.605318i
$647$	1021.37	−	589.687i	1.57862	−	0.911417i	0.583568	−	0.812064i	$-0.301656\pi$
$647$	1021.37	−	589.687i	1.57862	−	0.911417i	0.995052	−	0.0993530i	$-0.0316773\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	−142.191	−	82.0940i	−0.219092	−	0.126493i
$650$			1135.36i			1.74671i
$651$	−44.5143	+	173.180i	−0.0683783	+	0.266021i
$652$	32.1177			0.0492604
$653$	77.3818	−	134.029i	0.118502	−	0.205252i	−0.800672	−	0.599103i	$-0.795524\pi$
$653$	77.3818	−	134.029i	0.118502	−	0.205252i	0.919174	+	0.393851i	$0.128857\pi$
$654$	379.591	−	219.157i	0.580415	−	0.335103i
$655$	−7.45584	−	12.9139i	−0.0113830	−	0.0197159i
$656$	−122.059	−	70.4707i	−0.186065	−	0.107425i
$657$			351.096i			0.534393i
$658$	−230.059	+	234.803i	−0.349634	+	0.356843i
$659$	591.308			0.897280			0.448640	−	0.893712i	$-0.351908\pi$
$659$	591.308			0.897280			0.448640	+	0.893712i	$0.351908\pi$
$660$	−86.9117	+	150.535i	−0.131684	+	0.228084i
$661$	140.441	−	81.0837i	0.212468	−	0.122668i	−0.389990	−	0.920819i	$-0.627522\pi$
$661$	140.441	−	81.0837i	0.212468	−	0.122668i	0.602458	+	0.798151i	$0.294188\pi$
$662$	184.815	+	320.109i	0.279176	+	0.483548i
$663$	502.566	+	290.156i	0.758017	+	0.437642i
$664$			214.282i			0.322714i
$665$	711.838	+	697.456i	1.07043	+	1.04881i
$666$	−25.3310			−0.0380345
$667$	−228.353	+	395.519i	−0.342359	+	0.592983i
$668$	−305.044	+	176.117i	−0.456652	+	0.263648i
$669$	−198.000	−	342.946i	−0.295964	−	0.512625i
$670$	−1171.73	−	676.497i	−1.74885	−	1.00970i
$671$			242.283i			0.361078i
$672$	66.4264	+	17.0743i	0.0988488	+	0.0254082i
$673$	42.3238			0.0628883			0.0314441	−	0.999506i	$-0.489989\pi$
$673$	42.3238			0.0628883			0.0314441	+	0.999506i	$0.489989\pi$
$674$	−96.3539	+	166.890i	−0.142958	+	0.247611i
$675$	202.235	−	116.760i	0.299608	−	0.172978i
$676$	150.118	+	260.012i	0.222068	+	0.384632i
$677$	430.721	+	248.677i	0.636220	+	0.367322i	0.783157	−	0.621824i	$-0.213608\pi$
$677$	430.721	+	248.677i	0.636220	+	0.367322i	−0.146937	+	0.989146i	$0.546941\pi$
$678$		−	42.6137i		−	0.0628521i
$679$	−57.5147	−	206.207i	−0.0847050	−	0.303693i
$680$	−443.647			−0.652422
$681$	−146.823	+	254.306i	−0.215600	+	0.373430i
$682$	108.375	−	62.5701i	0.158907	−	0.0917451i
$683$	−608.080	−	1053.23i	−0.890308	−	1.54206i	−0.839506	−	0.543350i	$-0.817156\pi$
$683$	−608.080	−	1053.23i	−0.890308	−	1.54206i	−0.0508015	−	0.998709i	$-0.516178\pi$
$684$	88.4558	+	51.0700i	0.129321	+	0.0746638i
$685$		−	844.425i		−	1.23274i
$686$	−139.830	−	464.484i	−0.203834	−	0.677091i
$687$	60.0883			0.0874648
$688$	−30.9706	+	53.6426i	−0.0450154	+	0.0779689i
$689$	534.418	−	308.546i	0.775642	−	0.447817i
$690$	−137.823	−	238.717i	−0.199744	−	0.345967i
$691$	−932.182	−	538.196i	−1.34903	−	0.778865i	−0.360921	−	0.932596i	$-0.617538\pi$
$691$	−932.182	−	538.196i	−1.34903	−	0.778865i	−0.988113	+	0.153731i	$0.950871\pi$
$692$			462.305i			0.668070i
$693$	121.368	−	33.8515i	0.175134	−	0.0488477i
$694$	−455.647			−0.656552
$695$	587.683	−	1017.90i	0.845588	−	1.46460i
$696$	144.000	−	83.1384i	0.206897	−	0.119452i
$697$	−330.426	−	572.315i	−0.474069	−	0.821112i
$698$	−424.368	−	245.009i	−0.607976	−	0.351015i
$699$		−	440.781i		−	0.630589i
$700$	−156.632	+	609.367i	−0.223761	+	0.870525i
$701$	−695.897			−0.992720			−0.496360	−	0.868117i	$-0.665330\pi$
$701$	−695.897			−0.992720			−0.496360	+	0.868117i	$0.665330\pi$
$702$	65.6360	−	113.685i	0.0934986	−	0.161944i
$703$	88.0219	−	50.8194i	0.125209	−	0.0722894i
$704$	−24.0000	−	41.5692i	−0.0340909	−	0.0590472i
$705$	−416.558	−	240.500i	−0.590863	−	0.341135i
$706$		−	877.649i		−	1.24313i
$707$	−626.912	+	639.839i	−0.886721	+	0.905006i
$708$	−94.7939			−0.133890
$709$	−127.412	+	220.684i	−0.179707	+	0.311261i	−0.941780	−	0.336229i	$-0.890848\pi$
$709$	−127.412	+	220.684i	−0.179707	+	0.311261i	0.762073	+	0.647491i	$0.224182\pi$
$710$	−190.544	+	110.011i	−0.268372	+	0.154945i
$711$	−132.507	−	229.509i	−0.186367	−	0.322798i
$712$	−50.9117	−	29.3939i	−0.0715052	−	0.0412835i
$713$			198.446i			0.278325i
$714$	229.706	+	225.065i	0.321717	+	0.315217i
$715$	−896.382			−1.25368
$716$	85.2792	−	147.708i	0.119105	−	0.206296i
$717$	295.721	−	170.734i	0.412442	−	0.238123i
$718$	−14.3087	−	24.7833i	−0.0199285	−	0.0345172i
$719$	−964.925	−	557.100i	−1.34204	−	0.774826i	−0.354931	−	0.934892i	$-0.615496\pi$
$719$	−964.925	−	557.100i	−1.34204	−	0.774826i	−0.987106	+	0.160066i	$0.948829\pi$
$720$			100.357i			0.139385i
$721$	548.852	+	141.078i	0.761238	+	0.195669i
$722$	100.701			0.139474
$723$	76.6173	−	132.705i	0.105971	−	0.183548i
$724$	−9.67619	+	5.58655i	−0.0133649	+	0.00771623i
$725$	762.676	+	1320.99i	1.05197	+	1.82206i
$726$	180.312	+	104.103i	0.248364	+	0.143393i
$727$		−	398.345i		−	0.547930i	−0.961740	−	0.273965i	$-0.911665\pi$
$727$		−	398.345i		−	0.547930i	0.961740	−	0.273965i	$-0.0883353\pi$
$728$	95.0223	+	340.683i	0.130525	+	0.467971i
$729$	−27.0000			−0.0370370
$730$	692.080	−	1198.72i	0.948055	−	1.64208i
$731$	−251.522	+	145.216i	−0.344079	+	0.198654i
$732$	69.9411	+	121.142i	0.0955480	+	0.165494i
$733$	818.514	+	472.569i	1.11666	+	0.644706i	0.940547	−	0.339663i	$-0.110313\pi$
$733$	818.514	+	472.569i	1.11666	+	0.644706i	0.176116	+	0.984369i	$0.443646\pi$
$734$		−	440.632i		−	0.600316i
$735$	607.316	−	367.360i	0.826280	−	0.499810i
$736$	76.1177			0.103421
$737$	343.191	−	594.424i	0.465659	−	0.806546i
$738$	−129.463	+	74.7455i	−0.175424	+	0.101281i
$739$	−96.3162	−	166.825i	−0.130333	−	0.225744i	0.793472	−	0.608607i	$-0.208271\pi$
$739$	−96.3162	−	166.825i	−0.130333	−	0.225744i	−0.923805	+	0.382863i	$0.874938\pi$
$740$	86.4853	+	49.9323i	0.116872	+	0.0674761i
$741$			526.721i			0.710825i
$742$	329.397	−	91.8744i	0.443931	−	0.123820i
$743$	−911.616			−1.22694			−0.613470	−	0.789718i	$-0.710227\pi$
$743$	−911.616			−1.22694			−0.613470	+	0.789718i	$0.710227\pi$
$744$	36.1249	−	62.5701i	0.0485550	−	0.0840997i
$745$	−1324.76	+	764.853i	−1.77821	+	1.02665i
$746$	481.810	+	834.519i	0.645858	+	1.11866i
$747$	196.831	+	113.640i	0.263495	+	0.152129i
$748$		−	225.065i		−	0.300889i
$749$	295.301	−	1148.85i	0.394260	−	1.53384i
$750$	−408.500			−0.544666
$751$	195.831	−	339.189i	0.260760	−	0.451650i	−0.705684	−	0.708527i	$-0.749360\pi$
$751$	195.831	−	339.189i	0.260760	−	0.451650i	0.966444	+	0.256877i	$0.0826935\pi$
$752$	115.029	−	66.4123i	0.152965	−	0.0883142i
$753$	−186.978	−	323.855i	−0.248310	−	0.430086i
$754$	742.587	+	428.733i	0.984863	+	0.568611i
$755$			2415.21i			3.19895i
$756$	50.9117	−	51.9615i	0.0673435	−	0.0687322i
$757$	−152.823			−0.201879			−0.100940	−	0.994893i	$-0.532185\pi$
$757$	−152.823			−0.201879			−0.100940	+	0.994893i	$0.532185\pi$
$758$	441.785	−	765.195i	0.582830	−	1.00949i
$759$	121.103	−	69.9186i	0.159555	−	0.0921194i
$760$	−201.338	−	348.728i	−0.264919	−	0.458852i
$761$	−109.331	−	63.1223i	−0.143667	−	0.0829465i	0.426443	−	0.904514i	$-0.359766\pi$
$761$	−109.331	−	63.1223i	−0.143667	−	0.0829465i	−0.570111	+	0.821568i	$0.693100\pi$
$762$			410.109i			0.538201i
$763$	894.706	+	876.629i	1.17262	+	1.14892i
$764$	370.794			0.485332
$765$	−235.279	+	407.516i	−0.307555	+	0.532700i
$766$	−169.383	+	97.7931i	−0.221126	+	0.127667i
$767$	−244.419	−	423.347i	−0.318669	−	0.551951i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$		−	369.148i		−	0.480037i	−0.970768	−	0.240018i	$-0.922847\pi$
$769$		−	369.148i		−	0.480037i	0.970768	−	0.240018i	$-0.0771535\pi$
$770$	−481.103	−	123.663i	−0.624809	−	0.160602i
$771$	−7.45584			−0.00967036
$772$	−227.794	+	394.551i	−0.295070	+	0.511076i
$773$	−1215.65	+	701.853i	−1.57263	+	0.907961i	−0.576789	+	0.816893i	$0.695695\pi$
$773$	−1215.65	+	701.853i	−1.57263	+	0.907961i	−0.995845	+	0.0910674i	$0.970972\pi$
$774$	32.8492	+	56.8966i	0.0424409	+	0.0735098i
$775$	573.992	+	331.394i	0.740634	+	0.427605i
$776$			86.5006i			0.111470i
$777$	−19.4483	−	69.7278i	−0.0250299	−	0.0897398i
$778$	−797.013			−1.02444
$779$	299.912	−	519.462i	0.384996	−	0.666832i
$780$	−448.191	+	258.763i	−0.574604	+	0.331748i
$781$	−55.8091	−	96.6642i	−0.0714585	−	0.123770i
$782$	309.088	+	178.452i	0.395254	+	0.228200i
$783$		−	176.363i		−	0.225240i
$784$	4.00000	+	195.959i	0.00510204	+	0.249948i
$785$	1564.41			1.99288
$786$	2.18377	−	3.78239i	0.00277833	−	0.00481221i
$787$	196.161	−	113.253i	0.249251	−	0.143905i	−0.370170	−	0.928964i	$-0.620701\pi$
$787$	196.161	−	113.253i	0.249251	−	0.143905i	0.619421	+	0.785059i	$0.287367\pi$
$788$	−123.161	−	213.322i	−0.156296	−	0.270713i
$789$	−424.014	−	244.805i	−0.537407	−	0.310272i
$790$			1044.79i			1.32252i
$791$	117.302	−	32.7174i	0.148295	−	0.0413621i
$792$	−50.9117			−0.0642824
$793$	−360.676	+	624.709i	−0.454825	+	0.787780i
$794$	555.224	−	320.559i	0.699274	−	0.403726i
$795$	250.191	+	433.343i	0.314706	+	0.545086i
$796$	−10.7939	−	6.23188i	−0.0135602	−	0.00782900i
$797$		−	688.414i		−	0.863756i	−0.901932	−	0.431878i	$-0.857851\pi$
$797$		−	688.414i		−	0.863756i	0.901932	−	0.431878i	$-0.142149\pi$
$798$	−72.6655	+	282.700i	−0.0910595	+	0.354260i
$799$	622.794			0.779467
$800$	127.113	−	220.166i	0.158891	−	0.275207i
$801$	−54.0000	+	31.1769i	−0.0674157	+	0.0389225i
$802$	194.985	+	337.724i	0.243123	+	0.421102i
$803$	608.117	+	351.096i	0.757306	+	0.437231i
$804$		−	396.283i		−	0.492889i
$805$	551.294	−	562.662i	0.684837	−	0.698958i
$806$	372.582			0.462260
$807$	−330.765	+	572.901i	−0.409869	+	0.709914i
$808$	313.456	−	180.974i	0.387940	−	0.223977i
$809$	−12.6396	−	21.8924i	−0.0156237	−	0.0270611i	0.858108	−	0.513470i	$-0.171640\pi$
$809$	−12.6396	−	21.8924i	−0.0156237	−	0.0270611i	−0.873732	+	0.486408i	$0.838307\pi$
$810$	92.1838	+	53.2223i	0.113807	+	0.0657066i
$811$			1527.62i			1.88362i	0.336145	+	0.941810i	$0.390877\pi$
$811$			1527.62i			1.88362i	−0.336145	+	0.941810i	$0.609123\pi$
$812$	339.411	+	332.554i	0.417994	+	0.409549i
$813$	−146.059			−0.179654
$814$	−25.3310	+	43.8745i	−0.0311191	+	0.0538999i
$815$	−116.309	+	67.1508i	−0.142710	+	0.0823937i
$816$	−64.9706	−	112.532i	−0.0796208	−	0.137907i
$817$	−228.294	−	131.806i	−0.279430	−	0.161329i
$818$		−	616.359i		−	0.753495i
$819$	363.331	+	93.3909i	0.443627	+	0.114030i
$820$	589.352			0.718722
$821$	58.3310	−	101.032i	0.0710487	−	0.123060i	−0.828312	−	0.560266i	$-0.810699\pi$
$821$	58.3310	−	101.032i	0.0710487	−	0.123060i	0.899361	+	0.437206i	$0.144032\pi$
$822$	214.191	−	123.663i	0.260573	−	0.150442i
$823$	−62.9554	−	109.042i	−0.0764950	−	0.132493i	0.825240	−	0.564782i	$-0.191040\pi$
$823$	−62.9554	−	109.042i	−0.0764950	−	0.132493i	−0.901735	+	0.432288i	$0.857706\pi$
$824$	−198.302	−	114.489i	−0.240657	−	0.138943i
$825$		−	467.042i		−	0.566111i
$826$	−72.7797	−	260.937i	−0.0881110	−	0.315904i
$827$	−1434.40			−1.73446			−0.867229	−	0.497910i	$-0.834101\pi$
$827$	−1434.40			−1.73446			−0.867229	+	0.497910i	$0.834101\pi$
$828$	40.3675	−	69.9186i	0.0487531	−	0.0844428i
$829$	−32.3225	+	18.6614i	−0.0389898	+	0.0225107i	−0.519368	−	0.854551i	$-0.673833\pi$
$829$	−32.3225	+	18.6614i	−0.0389898	+	0.0225107i	0.480378	+	0.877061i	$0.340499\pi$
$830$	−448.014	−	775.984i	−0.539776	−	0.934920i
$831$	205.677	+	118.747i	0.247505	+	0.142897i
$832$		−	142.911i		−	0.171768i
$833$	−443.169	+	805.101i	−0.532015	+	0.966508i
$834$	344.257			0.412778
$835$	736.441	−	1275.55i	0.881965	−	1.52761i
$836$	176.912	−	102.140i	0.211617	−	0.122177i
$837$	−38.3162	−	66.3657i	−0.0457781	−	0.0792899i
$838$	368.963	+	213.021i	0.440290	+	0.254202i
$839$			3.07370i			0.00366353i	0.999998	+	0.00183177i	$0.000583069\pi$
$839$			3.07370i			0.00366353i	−0.999998	+	0.00183177i	$0.999417\pi$
$840$	−276.250	+	77.0508i	−0.328869	+	0.0917271i
$841$	311.000			0.369798
$842$	144.104	−	249.596i	0.171145	−	0.296432i
$843$	−487.654	+	281.547i	−0.578474	+	0.333982i
$844$	124.912	+	216.353i	0.148000	+	0.256343i
$845$	−1087.25	−	627.723i	−1.28669	−	0.742868i
$846$		−	140.882i		−	0.166527i
$847$	−148.124	+	576.267i	−0.174881	+	0.680363i
$848$	−138.177			−0.162944
$849$	168.507	−	291.863i	0.198477	−	0.343773i
$850$	1032.32	−	596.012i	1.21450	−	0.701191i
$851$	−40.1695	−	69.5756i	−0.0472027	−	0.0817574i
$852$	−55.8091	−	32.2214i	−0.0655036	−	0.0378185i
$853$		−	155.257i		−	0.182013i	−0.995850	−	0.0910063i	$-0.970992\pi$
$853$		−	155.257i		−	0.182013i	0.995850	−	0.0910063i	$-0.0290083\pi$
$854$	−279.765	+	285.533i	−0.327593	+	0.334348i
$855$	−427.103			−0.499535
$856$	−239.647	+	415.080i	−0.279961	+	0.484907i
$857$	−1388.98	+	801.931i	−1.62075	+	0.935742i	−0.634033	+	0.773306i	$0.718602\pi$
$857$	−1388.98	+	801.931i	−1.62075	+	0.935742i	−0.986719	+	0.162436i	$0.948065\pi$
$858$	−131.272	−	227.370i	−0.152998	−	0.265000i
$859$	545.367	+	314.868i	0.634886	+	0.366551i	0.782642	−	0.622472i	$-0.213872\pi$
$859$	545.367	+	314.868i	0.634886	+	0.366551i	−0.147756	+	0.989024i	$0.547205\pi$
$860$		−	259.009i		−	0.301174i
$861$	−305.147	−	298.982i	−0.354410	−	0.347250i
$862$	−559.632			−0.649226
$863$	−514.706	+	891.496i	−0.596414	+	1.03302i	0.396931	+	0.917848i	$0.370075\pi$
$863$	−514.706	+	891.496i	−0.596414	+	1.03302i	−0.993346	+	0.115172i	$0.963258\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$	−966.573	−	1674.15i	−1.11743	−	1.93544i
$866$	54.2176	+	31.3026i	0.0626070	+	0.0361462i
$867$		−	108.711i		−	0.125388i
$868$	199.971	+	51.4007i	0.230381	+	0.0592174i
$869$	−530.029			−0.609929
$870$	−347.647	+	602.142i	−0.399594	+	0.692117i
$871$	1769.79	−	1021.79i	2.03190	−	1.17312i
$872$	−253.061	−	438.314i	−0.290208	−	0.502654i
$873$	79.4558	+	45.8739i	0.0910147	+	0.0525474i
$874$			323.944i			0.370646i
$875$	−313.632	−	1124.47i	−0.358437	−	1.28510i
$876$	405.411			0.462798
$877$	−324.220	+	561.566i	−0.369693	+	0.640326i	−0.989517	−	0.144414i	$-0.953870\pi$
$877$	−324.220	+	561.566i	−0.369693	+	0.640326i	0.619825	+	0.784740i	$0.287204\pi$
$878$	−487.279	+	281.331i	−0.554988	+	0.320422i
$879$	−207.588	−	359.553i	−0.236164	−	0.409048i
$880$	173.823	+	100.357i	0.197527	+	0.114042i
$881$		−	363.857i		−	0.413005i	−0.978446	−	0.206502i	$-0.933792\pi$
$881$		−	363.857i		−	0.413005i	0.978446	−	0.206502i	$-0.0662082\pi$
$882$	182.121	+	100.249i	0.206487	+	0.113661i
$883$	1536.16			1.73971			0.869853	−	0.493312i	$-0.164214\pi$
$883$	1536.16			1.73971			0.869853	+	0.493312i	$0.164214\pi$
$884$	335.044	−	580.313i	0.379009	−	0.656462i
$885$	343.279	−	198.192i	0.387886	−	0.223946i
$886$	83.8234	+	145.186i	0.0946088	+	0.163867i
$887$	974.720	+	562.755i	1.09890	+	0.634447i	0.935931	−	0.352185i	$-0.114561\pi$
$887$	974.720	+	562.755i	1.09890	+	0.634447i	0.162964	+	0.986632i	$0.447894\pi$
$888$			29.2497i			0.0329388i
$889$	−1128.90	+	314.868i	−1.26985	+	0.354183i
$890$	245.823			0.276206
$891$	−27.0000	+	46.7654i	−0.0303030	+	0.0524864i
$892$	−396.000	+	228.631i	−0.443946	+	0.256312i
$893$	282.640	+	489.546i	0.316506	+	0.548204i
$894$	−388.014	−	224.020i	−0.434020	−	0.250582i
$895$			713.197i			0.796868i
$896$	19.7157	−	76.7026i	0.0220042	−	0.0856056i
$897$	416.339			0.464146
$898$	−504.801	+	874.341i	−0.562139	+	0.973654i
$899$	433.499	−	250.281i	0.482201	−	0.278399i
$900$	−134.823	−	233.521i	−0.149804	−	0.259468i
$901$	−561.088	−	323.944i	−0.622740	−	0.359539i
$902$			298.982i			0.331466i
$903$	−131.397	+	134.106i	−0.145512	+	0.148512i
$904$	−49.2061			−0.0544315
$905$	23.3604	−	40.4614i	0.0258126	−	0.0447087i
$906$	−612.624	+	353.699i	−0.676186	+	0.390396i
$907$	−117.448	−	203.426i	−0.129491	−	0.224285i	0.793989	−	0.607933i	$-0.208001\pi$
$907$	−117.448	−	203.426i	−0.129491	−	0.224285i	−0.923479	+	0.383648i	$0.874668\pi$
$908$	293.647	+	169.537i	0.323400	+	0.186715i
$909$		−	383.903i		−	0.422336i
$910$	−1056.40	−	1035.05i	−1.16087	−	1.13742i
$911$	224.278			0.246189			0.123095	−	0.992395i	$-0.460718\pi$
$911$	224.278			0.246189			0.123095	+	0.992395i	$0.460718\pi$
$912$	58.9706	−	102.140i	0.0646607	−	0.111996i
$913$	393.661	−	227.280i	0.431173	−	0.248938i
$914$	88.5132	+	153.309i	0.0968416	+	0.167735i
$915$	−506.558	−	292.462i	−0.553616	−	0.319630i
$916$		−	69.3840i		−	0.0757467i
$917$	12.0883	+	3.10719i	0.0131825	+	0.00338843i
$918$	−137.823			−0.150134
$919$	466.081	−	807.276i	0.507161	−	0.878428i	−0.492805	−	0.870140i	$-0.664028\pi$
$919$	466.081	−	807.276i	0.507161	−	0.878428i	0.999966	−	0.00828836i	$-0.00263830\pi$
$920$	−275.647	+	159.145i	−0.299616	+	0.172983i
$921$	467.889	+	810.407i	0.508023	+	0.879921i
$922$	−803.147	−	463.697i	−0.871092	−	0.502925i
$923$		−	332.322i		−	0.360046i
$924$	−39.0883	−	140.143i	−0.0423034	−	0.151670i
$925$	−268.324			−0.290080
$926$	−614.756	+	1064.79i	−0.663883	+	1.14988i
$927$	−210.331	+	121.434i	−0.226894	+	0.130997i
$928$	−96.0000	−	166.277i	−0.103448	−	0.179178i
$929$	−618.390	−	357.028i	−0.665651	−	0.384314i	0.128776	−	0.991674i	$-0.458895\pi$
$929$	−618.390	−	357.028i	−0.665651	−	0.384314i	−0.794427	+	0.607360i	$0.792229\pi$
$930$			302.115i			0.324855i
$931$	−833.970	+	17.0233i	−0.895778	+	0.0182850i
$932$	−508.971			−0.546106
$933$	350.044	−	606.294i	0.375181	−	0.649832i
$934$	327.463	−	189.061i	0.350603	−	0.202421i
$935$	470.558	+	815.031i	0.503271	+	0.871691i
$936$	−131.272	−	75.7900i	−0.140248	−	0.0809722i
$937$		−	1723.25i		−	1.83912i	−0.392952	−	0.919559i	$-0.628546\pi$
$937$		−	1723.25i		−	1.83912i	0.392952	−	0.919559i	$-0.371454\pi$
$938$	1090.84	−	304.253i	1.16294	−	0.324363i
$939$	−227.412			−0.242185
$940$	−277.706	+	481.000i	−0.295432	+	0.511702i
$941$	835.508	−	482.381i	0.887893	−	0.512625i	0.0146405	−	0.999893i	$-0.495340\pi$
$941$	835.508	−	482.381i	0.887893	−	0.512625i	0.873253	+	0.487267i	$0.162006\pi$
$942$	229.103	+	396.817i	0.243209	+	0.421250i
$943$	−410.601	−	237.061i	−0.435420	−	0.251390i
$944$			109.459i			0.115952i
$945$	−75.7279	+	294.614i	−0.0801354	+	0.311761i
$946$	131.397			0.138897
$947$	−725.881	+	1257.26i	−0.766506	+	1.32763i	0.172940	+	0.984932i	$0.444673\pi$
$947$	−725.881	+	1257.26i	−0.766506	+	1.32763i	−0.939447	+	0.342695i	$0.888660\pi$
$948$	−265.014	+	153.006i	−0.279551	+	0.161399i
$949$	1045.32	+	1810.55i	1.10150	+	1.90785i
$950$	936.988	+	540.971i	0.986304	+	0.569443i
$951$		−	162.711i		−	0.171094i
$952$	259.882	−	265.241i	0.272986	−	0.278615i
$953$	1147.43			1.20401			0.602007	−	0.798491i	$-0.294368\pi$
$953$	1147.43			1.20401			0.602007	+	0.798491i	$0.294368\pi$
$954$	−73.2792	+	126.923i	−0.0768126	+	0.133043i
$955$	−1342.76	+	775.245i	−1.40604	+	0.811775i
$956$	−197.147	−	341.469i	−0.206221	−	0.357185i
$957$	−305.470	−	176.363i	−0.319196	−	0.184288i
$958$			384.294i			0.401142i
$959$	504.853	+	494.653i	0.526437	+	0.515801i
$960$	115.882			0.120711
$961$	−371.749	+	643.889i	−0.386836	+	0.670020i
$962$	−130.628	+	75.4181i	−0.135788	+	0.0783972i
$963$	254.184	+	440.259i	0.263950	+	0.457175i
$964$	−153.235	−	88.4701i	−0.158957	−	0.0917739i
$965$		−	1905.06i		−	1.97415i
$966$	223.456	+	57.4374i	0.231321	+	0.0594590i
$967$	412.190			0.426257			0.213128	−	0.977024i	$-0.431635\pi$
$967$	412.190			0.426257			0.213128	+	0.977024i	$0.431635\pi$
$968$	120.208	−	208.207i	0.124182	−	0.215089i
$969$	478.919	−	276.504i	0.494240	−	0.285350i
$970$	−180.853	−	313.246i	−0.186446	−	0.322934i
$971$	869.595	+	502.061i	0.895566	+	0.517056i	0.875759	−	0.482748i	$-0.160361\pi$
$971$	869.595	+	502.061i	0.895566	+	0.517056i	0.0198073	+	0.999804i	$0.493695\pi$
$972$			31.1769i			0.0320750i
$973$	264.309	+	947.626i	0.271643	+	0.973922i
$974$	−794.101			−0.815298
$975$	695.265	−	1204.23i	0.713092	−	1.23511i
$976$	139.882	−	80.7611i	0.143322	−	0.0827470i
$977$	794.117	+	1375.45i	0.812812	+	1.40783i	0.910889	+	0.412652i	$0.135397\pi$
$977$	794.117	+	1375.45i	0.812812	+	1.40783i	−0.0980772	+	0.995179i	$0.531269\pi$
$978$	−34.0660	−	19.6680i	−0.0348323	−	0.0201105i
$979$			124.708i			0.127383i
$980$	−424.191	−	701.268i	−0.432848	−	0.715579i
$981$	−536.823			−0.547221
$982$	287.397	−	497.786i	0.292665	−	0.506911i
$983$	721.861	−	416.767i	0.734345	−	0.423974i	−0.0856648	−	0.996324i	$-0.527301\pi$
$983$	721.861	−	416.767i	0.734345	−	0.423974i	0.820009	+	0.572350i	$0.193968\pi$
$984$	86.3087	+	149.491i	0.0877121	+	0.151922i
$985$	892.014	+	515.005i	0.905598	+	0.522847i
$986$		−	900.259i		−	0.913041i
$987$	387.801	−	108.164i	0.392909	−	0.109589i
$988$	608.205			0.615592
$989$	−104.184	+	180.452i	−0.105343	+	0.182459i
$990$	184.368	−	106.445i	0.186230	−	0.107520i
$991$	−33.4483	−	57.9341i	−0.0337520	−	0.0584602i	0.848656	−	0.528945i	$-0.177412\pi$
$991$	−33.4483	−	57.9341i	−0.0337520	−	0.0584602i	−0.882408	+	0.470485i	$0.844079\pi$
$992$	−72.2498	−	41.7134i	−0.0728324	−	0.0420498i
$993$		−	452.702i		−	0.455893i
$994$	45.8465	−	178.363i	0.0461233	−	0.179439i
$995$	52.1177			0.0523796
$996$	131.220	−	227.280i	0.131747	−	0.228193i
$997$	1268.65	−	732.453i	1.27246	−	0.734657i	0.297012	−	0.954874i	$-0.404010\pi$
$997$	1268.65	−	732.453i	1.27246	−	0.734657i	0.975451	+	0.220217i	$0.0706765\pi$
$998$	262.638	+	454.903i	0.263164	+	0.455814i
$999$	26.8675	+	15.5120i	0.0268944	+	0.0155275i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.3.g.a.19.1	✓	4
3.2	odd	2		126.3.n.a.19.2		4
4.3	odd	2		336.3.bh.e.145.2		4
5.2	odd	4		1050.3.q.a.649.1		8
5.3	odd	4		1050.3.q.a.649.4		8
5.4	even	2		1050.3.p.a.901.2		4
7.2	even	3		294.3.c.a.97.4		4
7.3	odd	6	inner	42.3.g.a.31.1	yes	4
7.4	even	3		294.3.g.a.31.1		4
7.5	odd	6		294.3.c.a.97.3		4
7.6	odd	2		294.3.g.a.19.1		4
12.11	even	2		1008.3.cg.h.145.1		4
21.2	odd	6		882.3.c.b.685.2		4
21.5	even	6		882.3.c.b.685.1		4
21.11	odd	6		882.3.n.e.325.2		4
21.17	even	6		126.3.n.a.73.2		4
21.20	even	2		882.3.n.e.19.2		4
28.3	even	6		336.3.bh.e.241.2		4
28.19	even	6		2352.3.f.e.97.4		4
28.23	odd	6		2352.3.f.e.97.1		4
35.3	even	12		1050.3.q.a.199.1		8
35.17	even	12		1050.3.q.a.199.4		8
35.24	odd	6		1050.3.p.a.451.2		4
84.59	odd	6		1008.3.cg.h.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.g.a.19.1	✓	4	1.1	even	1	trivial
42.3.g.a.31.1	yes	4	7.3	odd	6	inner
126.3.n.a.19.2		4	3.2	odd	2
126.3.n.a.73.2		4	21.17	even	6
294.3.c.a.97.3		4	7.5	odd	6
294.3.c.a.97.4		4	7.2	even	3
294.3.g.a.19.1		4	7.6	odd	2
294.3.g.a.31.1		4	7.4	even	3
336.3.bh.e.145.2		4	4.3	odd	2
336.3.bh.e.241.2		4	28.3	even	6
882.3.c.b.685.1		4	21.5	even	6
882.3.c.b.685.2		4	21.2	odd	6
882.3.n.e.19.2		4	21.20	even	2
882.3.n.e.325.2		4	21.11	odd	6
1008.3.cg.h.145.1		4	12.11	even	2
1008.3.cg.h.577.1		4	84.59	odd	6
1050.3.p.a.451.2		4	35.24	odd	6
1050.3.p.a.901.2		4	5.4	even	2
1050.3.q.a.199.1		8	35.3	even	12
1050.3.q.a.199.4		8	35.17	even	12
1050.3.q.a.649.1		8	5.2	odd	4
1050.3.q.a.649.4		8	5.3	odd	4
2352.3.f.e.97.1		4	28.23	odd	6
2352.3.f.e.97.4		4	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	42.3.g.a.19.1

Level	$42$
Weight	$3$
Character	42.19
Analytic conductor	$1.144$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$