LMFDB - Embedded newform 177.3.b.a.119.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,3,Mod(119,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.b (of order $2$, degree $1$, 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:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.24
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.30718i q^{2} +(-2.48886 + 1.67498i) q^{3} +2.29128 q^{4} +3.80837i q^{5} +(-2.18951 - 3.25339i) q^{6} +12.3524 q^{7} +8.22384i q^{8} +(3.38885 - 8.33761i) q^{9} +O(q^{10})$	\(q+1.30718i q^{2} +(-2.48886 + 1.67498i) q^{3} +2.29128 q^{4} +3.80837i q^{5} +(-2.18951 - 3.25339i) q^{6} +12.3524 q^{7} +8.22384i q^{8} +(3.38885 - 8.33761i) q^{9} -4.97823 q^{10} +1.19271i q^{11} +(-5.70267 + 3.83786i) q^{12} -14.6743 q^{13} +16.1468i q^{14} +(-6.37896 - 9.47850i) q^{15} -1.58493 q^{16} +23.0586i q^{17} +(10.8988 + 4.42984i) q^{18} -14.4644 q^{19} +8.72603i q^{20} +(-30.7433 + 20.6900i) q^{21} -1.55909 q^{22} -9.85208i q^{23} +(-13.7748 - 20.4680i) q^{24} +10.4963 q^{25} -19.1820i q^{26} +(5.53098 + 26.4274i) q^{27} +28.3027 q^{28} -46.0717i q^{29} +(12.3901 - 8.33845i) q^{30} -19.2515 q^{31} +30.8236i q^{32} +(-1.99778 - 2.96850i) q^{33} -30.1418 q^{34} +47.0423i q^{35} +(7.76481 - 19.1038i) q^{36} -3.90320 q^{37} -18.9076i q^{38} +(36.5224 - 24.5793i) q^{39} -31.3194 q^{40} +28.4426i q^{41} +(-27.0456 - 40.1870i) q^{42} +57.0037 q^{43} +2.73284i q^{44} +(31.7527 + 12.9060i) q^{45} +12.8784 q^{46} -42.9083i q^{47} +(3.94467 - 2.65473i) q^{48} +103.581 q^{49} +13.7206i q^{50} +(-38.6228 - 57.3897i) q^{51} -33.6230 q^{52} -47.5216i q^{53} +(-34.5454 + 7.22999i) q^{54} -4.54230 q^{55} +101.584i q^{56} +(35.9999 - 24.2277i) q^{57} +60.2240 q^{58} -7.68115i q^{59} +(-14.6160 - 21.7179i) q^{60} +39.9643 q^{61} -25.1652i q^{62} +(41.8603 - 102.989i) q^{63} -46.6317 q^{64} -55.8853i q^{65} +(3.88037 - 2.61146i) q^{66} -54.3907 q^{67} +52.8337i q^{68} +(16.5021 + 24.5205i) q^{69} -61.4928 q^{70} +79.8633i q^{71} +(68.5671 + 27.8694i) q^{72} +123.963 q^{73} -5.10218i q^{74} +(-26.1239 + 17.5812i) q^{75} -33.1420 q^{76} +14.7328i q^{77} +(32.1296 + 47.7414i) q^{78} +28.8678 q^{79} -6.03599i q^{80} +(-58.0314 - 56.5098i) q^{81} -37.1796 q^{82} +2.13566i q^{83} +(-70.4415 + 47.4066i) q^{84} -87.8157 q^{85} +74.5141i q^{86} +(77.1693 + 114.666i) q^{87} -9.80869 q^{88} -161.341i q^{89} +(-16.8705 + 41.5065i) q^{90} -181.263 q^{91} -22.5739i q^{92} +(47.9143 - 32.2460i) q^{93} +56.0889 q^{94} -55.0859i q^{95} +(-51.6290 - 76.7156i) q^{96} +0.232853 q^{97} +135.399i q^{98} +(9.94438 + 4.04193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) $ 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9	$ 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) $ 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9 + 36 * q^10 - 4 * q^13 - 17 * q^15 + 100 * q^16 - 2 * q^18 - 28 * q^19 - 11 * q^21 + 84 * q^22 - 6 * q^24 - 166 * q^25 + 3 * q^27 + 12 * q^28 + 102 * q^30 - 40 * q^31 - 46 * q^33 - 148 * q^34 - 96 * q^36 + 112 * q^37 + 62 * q^39 - 56 * q^40 + 14 * q^42 + 164 * q^43 + 55 * q^45 - 4 * q^46 - 124 * q^48 + 242 * q^49 + 52 * q^51 + 8 * q^52 + 18 * q^54 - 228 * q^55 - 147 * q^57 - 80 * q^58 + 128 * q^60 + 12 * q^61 + 86 * q^63 + 48 * q^64 - 24 * q^66 + 124 * q^67 - 240 * q^69 + 148 * q^70 + 166 * q^72 - 192 * q^73 - 78 * q^75 - 304 * q^76 + 244 * q^78 + 64 * q^79 - 156 * q^81 - 180 * q^82 + 300 * q^84 - 52 * q^85 - 83 * q^87 - 96 * q^88 - 376 * q^90 - 332 * q^91 + 454 * q^93 + 768 * q^94 - 722 * q^96 + 416 * q^97 + 494 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$			1.30718i			0.653590i	0.945095	+	0.326795i	$0.105969\pi$
$2$			1.30718i			0.653590i	−0.945095	+	0.326795i	$0.894031\pi$
$3$	−2.48886	+	1.67498i	−0.829620	+	0.558328i
$3$	−2.48886	+	1.67498i	−0.829620	+	0.558328i
$4$	2.29128			0.572820
$5$			3.80837i			0.761674i	0.924642	+	0.380837i	$0.124364\pi$
$5$			3.80837i			0.761674i	−0.924642	+	0.380837i	$0.875636\pi$
$6$	−2.18951	−	3.25339i	−0.364918	−	0.542232i
$7$	12.3524			1.76462			0.882311	−	0.470666i	$-0.155986\pi$
$7$	12.3524			1.76462			0.882311	+	0.470666i	$0.155986\pi$
$8$			8.22384i			1.02798i
$9$	3.38885	−	8.33761i	0.376539	−	0.926401i
$10$	−4.97823			−0.497823
$11$			1.19271i			0.108429i	0.998529	+	0.0542143i	$0.0172654\pi$
$11$			1.19271i			0.108429i	−0.998529	+	0.0542143i	$0.982735\pi$
$12$	−5.70267	+	3.83786i	−0.475223	+	0.319821i
$13$	−14.6743			−1.12880			−0.564398	−	0.825503i	$-0.690892\pi$
$13$	−14.6743			−1.12880			−0.564398	+	0.825503i	$0.690892\pi$
$14$			16.1468i			1.15334i
$15$	−6.37896	−	9.47850i	−0.425264	−	0.631900i
$16$	−1.58493			−0.0990581
$17$			23.0586i			1.35639i	0.734882	+	0.678195i	$0.237237\pi$
$17$			23.0586i			1.35639i	−0.734882	+	0.678195i	$0.762763\pi$
$18$	10.8988	+	4.42984i	0.605487	+	0.246102i
$19$	−14.4644			−0.761285			−0.380643	−	0.924722i	$-0.624297\pi$
$19$	−14.4644			−0.761285			−0.380643	+	0.924722i	$0.624297\pi$
$20$			8.72603i			0.436302i
$21$	−30.7433	+	20.6900i	−1.46397	+	0.985239i
$22$	−1.55909			−0.0708679
$23$		−	9.85208i		−	0.428351i	−0.976795	−	0.214176i	$-0.931294\pi$
$23$		−	9.85208i		−	0.428351i	0.976795	−	0.214176i	$-0.0687065\pi$
$24$	−13.7748	−	20.4680i	−0.573950	−	0.852833i
$25$	10.4963			0.419853
$26$		−	19.1820i		−	0.737770i
$27$	5.53098	+	26.4274i	0.204851	+	0.978793i
$28$	28.3027			1.01081
$29$		−	46.0717i		−	1.58868i	−0.607475	−	0.794339i	$-0.707817\pi$
$29$		−	46.0717i		−	1.58868i	0.607475	−	0.794339i	$-0.292183\pi$
$30$	12.3901	−	8.33845i	0.413004	−	0.277948i
$31$	−19.2515			−0.621017			−0.310508	−	0.950571i	$-0.600499\pi$
$31$	−19.2515			−0.621017			−0.310508	+	0.950571i	$0.600499\pi$
$32$			30.8236i			0.963236i
$33$	−1.99778	−	2.96850i	−0.0605387	−	0.0899545i
$34$	−30.1418			−0.886523
$35$			47.0423i			1.34407i
$36$	7.76481	−	19.1038i	0.215689	−	0.530660i
$37$	−3.90320			−0.105492			−0.0527459	−	0.998608i	$-0.516797\pi$
$37$	−3.90320			−0.105492			−0.0527459	+	0.998608i	$0.516797\pi$
$38$		−	18.9076i		−	0.497569i
$39$	36.5224	−	24.5793i	0.936472	−	0.630239i
$40$	−31.3194			−0.782985
$41$			28.4426i			0.693722i	0.937917	+	0.346861i	$0.112752\pi$
$41$			28.4426i			0.693722i	−0.937917	+	0.346861i	$0.887248\pi$
$42$	−27.0456	−	40.1870i	−0.643942	−	0.956834i
$43$	57.0037			1.32567			0.662834	−	0.748767i	$-0.269354\pi$
$43$	57.0037			1.32567			0.662834	+	0.748767i	$0.269354\pi$
$44$			2.73284i			0.0621100i
$45$	31.7527	+	12.9060i	0.705615	+	0.286800i
$46$	12.8784			0.279966
$47$		−	42.9083i		−	0.912943i	−0.889738	−	0.456472i	$-0.849113\pi$
$47$		−	42.9083i		−	0.912943i	0.889738	−	0.456472i	$-0.150887\pi$
$48$	3.94467	−	2.65473i	0.0821806	−	0.0553069i
$49$	103.581			2.11389
$50$			13.7206i			0.274412i
$51$	−38.6228	−	57.3897i	−0.757310	−	1.12529i
$52$	−33.6230			−0.646596
$53$		−	47.5216i		−	0.896635i	−0.893874	−	0.448317i	$-0.852023\pi$
$53$		−	47.5216i		−	0.896635i	0.893874	−	0.448317i	$-0.147977\pi$
$54$	−34.5454	+	7.22999i	−0.639730	+	0.133889i
$55$	−4.54230			−0.0825872
$56$			101.584i			1.81400i
$57$	35.9999	−	24.2277i	0.631578	−	0.425047i
$58$	60.2240			1.03834
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	−14.6160	−	21.7179i	−0.243600	−	0.361965i
$61$	39.9643			0.655152			0.327576	−	0.944825i	$-0.393768\pi$
$61$	39.9643			0.655152			0.327576	+	0.944825i	$0.393768\pi$
$62$		−	25.1652i		−	0.405890i
$63$	41.8603	−	102.989i	0.664450	−	1.63475i
$64$	−46.6317			−0.728620
$65$		−	55.8853i		−	0.859774i
$66$	3.88037	−	2.61146i	0.0587934	−	0.0395675i
$67$	−54.3907			−0.811802			−0.405901	−	0.913917i	$-0.633042\pi$
$67$	−54.3907			−0.811802			−0.405901	+	0.913917i	$0.633042\pi$
$68$			52.8337i			0.776966i
$69$	16.5021	+	24.5205i	0.239161	+	0.355369i
$70$	−61.4928			−0.878469
$71$			79.8633i			1.12484i	0.826853	+	0.562418i	$0.190129\pi$
$71$			79.8633i			1.12484i	−0.826853	+	0.562418i	$0.809871\pi$
$72$	68.5671	+	27.8694i	0.952321	+	0.387075i
$73$	123.963			1.69813			0.849065	−	0.528289i	$-0.177166\pi$
$73$	123.963			1.69813			0.849065	+	0.528289i	$0.177166\pi$
$74$		−	5.10218i		−	0.0689484i
$75$	−26.1239	+	17.5812i	−0.348319	+	0.234416i
$76$	−33.1420			−0.436079
$77$			14.7328i			0.191336i
$78$	32.1296	+	47.7414i	0.411918	+	0.612069i
$79$	28.8678			0.365415			0.182707	−	0.983167i	$-0.441514\pi$
$79$	28.8678			0.365415			0.182707	+	0.983167i	$0.441514\pi$
$80$		−	6.03599i		−	0.0754499i
$81$	−58.0314	−	56.5098i	−0.716436	−	0.697652i
$82$	−37.1796			−0.453410
$83$			2.13566i			0.0257309i	0.999917	+	0.0128654i	$0.00409531\pi$
$83$			2.13566i			0.0257309i	−0.999917	+	0.0128654i	$0.995905\pi$
$84$	−70.4415	+	47.4066i	−0.838589	+	0.564364i
$85$	−87.8157			−1.03313
$86$			74.5141i			0.866443i
$87$	77.1693	+	114.666i	0.887004	+	1.31800i
$88$	−9.80869			−0.111462
$89$		−	161.341i		−	1.81281i	−0.422404	−	0.906407i	$-0.638814\pi$
$89$		−	161.341i		−	1.81281i	0.422404	−	0.906407i	$-0.361186\pi$
$90$	−16.8705	+	41.5065i	−0.187450	+	0.461183i
$91$	−181.263			−1.99190
$92$		−	22.5739i		−	0.245368i
$93$	47.9143	−	32.2460i	0.515208	−	0.346731i
$94$	56.0889			0.596691
$95$		−	55.0859i		−	0.579851i
$96$	−51.6290	−	76.7156i	−0.537802	−	0.799120i
$97$	0.232853			0.00240055			0.00120028	−	0.999999i	$-0.499618\pi$
$97$	0.232853			0.00240055			0.00120028	+	0.999999i	$0.499618\pi$
$98$			135.399i			1.38162i
$99$	9.94438	+	4.04193i	0.100448	+	0.0408276i
$100$	24.0500			0.240500
$101$		−	84.4713i		−	0.836349i	−0.908367	−	0.418175i	$-0.862670\pi$
$101$		−	84.4713i		−	0.836349i	0.908367	−	0.418175i	$-0.137330\pi$
$102$	75.0187	−	50.4870i	0.735477	−	0.494971i
$103$	−29.5611			−0.287001			−0.143501	−	0.989650i	$-0.545836\pi$
$103$	−29.5611			−0.287001			−0.143501	+	0.989650i	$0.545836\pi$
$104$		−	120.679i		−	1.16038i
$105$	−78.7952	−	117.082i	−0.750430	−	1.11506i
$106$	62.1194			0.586032
$107$			167.005i			1.56080i	0.625281	+	0.780399i	$0.284984\pi$
$107$			167.005i			1.56080i	−0.625281	+	0.780399i	$0.715016\pi$
$108$	12.6730	+	60.5526i	0.117343	+	0.560672i
$109$	−84.6922			−0.776993			−0.388496	−	0.921450i	$-0.627005\pi$
$109$	−84.6922			−0.776993			−0.388496	+	0.921450i	$0.627005\pi$
$110$		−	5.93760i		−	0.0539782i
$111$	9.71451	−	6.53779i	0.0875181	−	0.0588990i
$112$	−19.5776			−0.174800
$113$		−	192.230i		−	1.70115i	−0.525854	−	0.850575i	$-0.676254\pi$
$113$		−	192.230i		−	1.70115i	0.525854	−	0.850575i	$-0.323746\pi$
$114$	31.6700	+	47.0584i	0.277807	+	0.412793i
$115$	37.5204			0.326264
$116$		−	105.563i		−	0.910026i
$117$	−49.7292	+	122.349i	−0.425036	+	1.04572i
$118$	10.0406			0.0850902
$119$			284.828i			2.39352i
$120$	77.9496	−	52.4595i	0.649580	−	0.437163i
$121$	119.577			0.988243
$122$			52.2405i			0.428201i
$123$	−47.6409	−	70.7896i	−0.387324	−	0.575525i
$124$	−44.1106			−0.355730
$125$			135.183i			1.08146i
$126$	134.625	+	54.7190i	1.06846	+	0.434278i
$127$	160.912			1.26702			0.633511	−	0.773734i	$-0.281613\pi$
$127$	160.912			1.26702			0.633511	+	0.773734i	$0.281613\pi$
$128$			62.3382i			0.487017i
$129$	−141.874	+	95.4803i	−1.09980	+	0.740158i
$130$	73.0522			0.561940
$131$			63.6841i			0.486138i	0.970009	+	0.243069i	$0.0781541\pi$
$131$			63.6841i			0.486138i	−0.970009	+	0.243069i	$0.921846\pi$
$132$	−4.57747	−	6.80166i	−0.0346778	−	0.0515277i
$133$	−178.670			−1.34338
$134$		−	71.0985i		−	0.530586i
$135$	−100.645	+	21.0640i	−0.745521	+	0.156030i
$136$	−189.630			−1.39434
$137$		−	33.4272i		−	0.243994i	−0.992530	−	0.121997i	$-0.961070\pi$
$137$		−	33.4272i		−	0.243994i	0.992530	−	0.121997i	$-0.0389299\pi$
$138$	−32.0527	+	21.5712i	−0.232266	+	0.156313i
$139$	−91.5357			−0.658530			−0.329265	−	0.944237i	$-0.606801\pi$
$139$	−91.5357			−0.658530			−0.329265	+	0.944237i	$0.606801\pi$
$140$			107.787i			0.769908i
$141$	71.8708	+	106.793i	0.509722	+	0.757396i
$142$	−104.396			−0.735182
$143$		−	17.5023i		−	0.122394i
$144$	−5.37109	+	13.2145i	−0.0372992	+	0.0917675i
$145$	175.458			1.21005
$146$			162.043i			1.10988i
$147$	−257.798	+	173.496i	−1.75373	+	1.18025i
$148$	−8.94331			−0.0604278
$149$		−	144.503i		−	0.969822i	−0.874564	−	0.484911i	$-0.838852\pi$
$149$		−	144.503i		−	0.969822i	0.874564	−	0.484911i	$-0.161148\pi$
$150$	−22.9818	−	34.1486i	−0.153212	−	0.227658i
$151$	−253.295			−1.67745			−0.838726	−	0.544554i	$-0.816699\pi$
$151$	−253.295			−1.67745			−0.838726	+	0.544554i	$0.816699\pi$
$152$		−	118.953i		−	0.782586i
$153$	192.254	+	78.1423i	1.25656	+	0.510734i
$154$	−19.2585			−0.125055
$155$		−	73.3169i		−	0.473012i
$156$	83.6830	−	56.3180i	0.536429	−	0.361013i
$157$	179.184			1.14130			0.570651	−	0.821193i	$-0.306691\pi$
$157$	179.184			1.14130			0.570651	+	0.821193i	$0.306691\pi$
$158$			37.7354i			0.238832i
$159$	79.5980	+	118.275i	0.500617	+	0.743866i
$160$	−117.388			−0.733672
$161$		−	121.696i		−	0.755878i
$162$	73.8686	−	75.8575i	0.455979	−	0.468256i
$163$	−103.948			−0.637715			−0.318858	−	0.947803i	$-0.603299\pi$
$163$	−103.948			−0.637715			−0.318858	+	0.947803i	$0.603299\pi$
$164$			65.1699i			0.397377i
$165$	11.3051	−	7.60828i	0.0685160	−	0.0461108i
$166$	−2.79170			−0.0168175
$167$		−	199.086i		−	1.19213i	−0.802935	−	0.596066i	$-0.796729\pi$
$167$		−	199.086i		−	1.19213i	0.802935	−	0.596066i	$-0.203271\pi$
$168$	−170.151	−	252.828i	−1.01281	−	1.50493i
$169$	46.3364			0.274180
$170$		−	114.791i		−	0.675241i
$171$	−49.0178	+	120.599i	−0.286654	+	0.705255i
$172$	130.611			0.759368
$173$			9.56148i			0.0552687i	0.999618	+	0.0276343i	$0.00879741\pi$
$173$			9.56148i			0.0552687i	−0.999618	+	0.0276343i	$0.991203\pi$
$174$	−149.889	+	100.874i	−0.861432	+	0.579737i
$175$	129.654			0.740882
$176$		−	1.89037i		−	0.0107407i
$177$	12.8658	+	19.1173i	0.0726881	+	0.108007i
$178$	210.901			1.18484
$179$		−	154.856i		−	0.865119i	−0.901605	−	0.432560i	$-0.857610\pi$
$179$		−	154.856i		−	0.865119i	0.901605	−	0.432560i	$-0.142390\pi$
$180$	72.7542	+	29.5712i	0.404190	+	0.164285i
$181$	244.908			1.35308			0.676542	−	0.736404i	$-0.263478\pi$
$181$	244.908			1.35308			0.676542	+	0.736404i	$0.263478\pi$
$182$		−	236.943i		−	1.30189i
$183$	−99.4654	+	66.9395i	−0.543527	+	0.365790i
$184$	81.0219			0.440336
$185$		−	14.8648i		−	0.0803503i
$186$	42.1513	+	62.6327i	0.226620	+	0.336735i
$187$	−27.5023			−0.147071
$188$		−	98.3149i		−	0.522952i
$189$	68.3206	+	326.441i	0.361485	+	1.72720i
$190$	72.0072			0.378985
$191$			199.587i			1.04496i	0.852652	+	0.522480i	$0.174993\pi$
$191$			199.587i			1.04496i	−0.852652	+	0.522480i	$0.825007\pi$
$192$	116.060	−	78.1074i	0.604478	−	0.406809i
$193$	305.794			1.58442			0.792212	−	0.610245i	$-0.208929\pi$
$193$	305.794			1.58442			0.792212	+	0.610245i	$0.208929\pi$
$194$			0.304381i			0.00156898i
$195$	93.6071	+	139.091i	0.480036	+	0.713286i
$196$	237.332			1.21088
$197$		−	39.8596i		−	0.202333i	−0.994870	−	0.101166i	$-0.967743\pi$
$197$		−	39.8596i		−	0.202333i	0.994870	−	0.101166i	$-0.0322575\pi$
$198$	−5.28354	+	12.9991i	−0.0266845	+	0.0656521i
$199$	−181.977			−0.914456			−0.457228	−	0.889350i	$-0.651158\pi$
$199$	−181.977			−0.914456			−0.457228	+	0.889350i	$0.651158\pi$
$200$			86.3201i			0.431600i
$201$	135.371	−	91.1036i	0.673487	−	0.453252i
$202$	110.419			0.546630
$203$		−	569.094i		−	2.80342i
$204$	−88.4957	−	131.496i	−0.433802	−	0.644587i
$205$	−108.320			−0.528390
$206$		−	38.6417i		−	0.187581i
$207$	−82.1428	−	33.3873i	−0.396825	−	0.161291i
$208$	23.2578			0.111816
$209$		−	17.2519i		−	0.0825451i
$210$	153.047	−	103.000i	0.728796	−	0.490474i
$211$	10.4581			0.0495646			0.0247823	−	0.999693i	$-0.492111\pi$
$211$	10.4581			0.0495646			0.0247823	+	0.999693i	$0.492111\pi$
$212$		−	108.885i		−	0.513610i
$213$	−133.770	−	198.769i	−0.628027	−	0.933186i
$214$	−218.306			−1.02012
$215$			217.091i			1.00973i
$216$	−217.335	+	45.4859i	−1.00618	+	0.210583i
$217$	−237.802			−1.09586
$218$		−	110.708i		−	0.507835i
$219$	−308.528	+	207.637i	−1.40880	+	0.948114i
$220$	−10.4077			−0.0473076
$221$		−	338.370i		−	1.53109i
$222$	8.54608	+	12.6986i	0.0384958	+	0.0572010i
$223$	83.7996			0.375783			0.187891	−	0.982190i	$-0.439835\pi$
$223$	83.7996			0.375783			0.187891	+	0.982190i	$0.439835\pi$
$224$			380.744i			1.69975i
$225$	35.5705	−	87.5142i	0.158091	−	0.388952i
$226$	251.279			1.11186
$227$		−	294.024i		−	1.29526i	−0.761956	−	0.647629i	$-0.775761\pi$
$227$		−	294.024i		−	1.29526i	0.761956	−	0.647629i	$-0.224239\pi$
$228$	82.4859	−	55.5124i	0.361780	−	0.243475i
$229$	−329.219			−1.43764			−0.718818	−	0.695198i	$-0.755317\pi$
$229$	−329.219			−1.43764			−0.718818	+	0.695198i	$0.755317\pi$
$230$			49.0459i			0.213243i
$231$	−24.6773	−	36.6680i	−0.106828	−	0.158736i
$232$	378.886			1.63313
$233$		−	63.0754i		−	0.270710i	−0.990797	−	0.135355i	$-0.956783\pi$
$233$		−	63.0754i		−	0.270710i	0.990797	−	0.135355i	$-0.0432174\pi$
$234$	−159.932	−	65.0051i	−0.683471	−	0.277799i
$235$	163.411			0.695365
$236$		−	17.5996i		−	0.0745748i
$237$	−71.8478	+	48.3531i	−0.303155	+	0.204021i
$238$	−372.322			−1.56438
$239$		−	264.038i		−	1.10476i	−0.833593	−	0.552380i	$-0.813720\pi$
$239$		−	264.038i		−	1.10476i	0.833593	−	0.552380i	$-0.186280\pi$
$240$	10.1102	+	15.0227i	0.0421258	+	0.0625948i
$241$	−38.4617			−0.159592			−0.0797961	−	0.996811i	$-0.525427\pi$
$241$	−38.4617			−0.159592			−0.0797961	+	0.996811i	$0.525427\pi$
$242$			156.309i			0.645906i
$243$	239.085	+	43.4435i	0.983889	+	0.178780i
$244$	91.5692			0.375284
$245$			394.474i			1.61010i
$246$	92.5348	−	62.2753i	0.376158	−	0.253151i
$247$	212.256			0.859336
$248$		−	158.321i		−	0.638392i
$249$	−3.57720	−	5.31537i	−0.0143663	−	0.0213469i
$250$	−176.709			−0.706835
$251$			120.243i			0.479055i	0.970890	+	0.239528i	$0.0769926\pi$
$251$			120.243i			0.479055i	−0.970890	+	0.239528i	$0.923007\pi$
$252$	95.9137	−	235.977i	0.380610	−	0.936415i
$253$	11.7507			0.0464455
$254$			210.341i			0.828113i
$255$	218.561	−	147.090i	0.857102	−	0.576824i
$256$	−268.014			−1.04693
$257$			249.489i			0.970773i	0.874300	+	0.485387i	$0.161321\pi$
$257$			249.489i			0.970773i	−0.874300	+	0.485387i	$0.838679\pi$
$258$	−124.810	−	185.455i	−0.483760	−	0.718819i
$259$	−48.2137			−0.186153
$260$		−	128.049i		−	0.492496i
$261$	−384.127	−	156.130i	−1.47175	−	0.598199i
$262$	−83.2466			−0.317735
$263$			202.885i			0.771424i	0.922619	+	0.385712i	$0.126044\pi$
$263$			202.885i			0.771424i	−0.922619	+	0.385712i	$0.873956\pi$
$264$	24.4125	−	16.4294i	0.0924714	−	0.0622326i
$265$	180.980			0.682943
$266$		−	233.554i		−	0.878021i
$267$	270.243	+	401.554i	1.01215	+	1.50395i
$268$	−124.624			−0.465016
$269$			474.375i			1.76347i	0.471741	+	0.881737i	$0.343626\pi$
$269$			474.375i			1.76347i	−0.471741	+	0.881737i	$0.656374\pi$
$270$	−27.5345	−	131.562i	−0.101980	−	0.487265i
$271$	−184.439			−0.680585			−0.340293	−	0.940320i	$-0.610526\pi$
$271$	−184.439			−0.680585			−0.340293	+	0.940320i	$0.610526\pi$
$272$		−	36.5463i		−	0.134361i
$273$	451.138	−	303.612i	1.65252	−	1.11213i
$274$	43.6954			0.159472
$275$			12.5191i			0.0455241i
$276$	37.8109	+	56.1832i	0.136996	+	0.203562i
$277$	−376.578			−1.35949			−0.679744	−	0.733450i	$-0.737909\pi$
$277$	−376.578			−1.35949			−0.679744	+	0.733450i	$0.737909\pi$
$278$		−	119.654i		−	0.430409i
$279$	−65.2406	+	160.512i	−0.233837	+	0.575310i
$280$	−386.869			−1.38167
$281$			360.072i			1.28140i	0.767793	+	0.640698i	$0.221355\pi$
$281$			360.072i			1.28140i	−0.767793	+	0.640698i	$0.778645\pi$
$282$	−139.598	+	93.9481i	−0.495027	+	0.333149i
$283$	−342.882			−1.21160			−0.605799	−	0.795618i	$-0.707146\pi$
$283$	−342.882			−1.21160			−0.605799	+	0.795618i	$0.707146\pi$
$284$			182.989i			0.644328i
$285$	92.2680	+	137.101i	0.323747	+	0.481056i
$286$	22.8787			0.0799954
$287$			351.333i			1.22416i
$288$	256.995	+	104.457i	0.892343	+	0.362696i
$289$	−242.700			−0.839792
$290$			229.355i			0.790880i
$291$	−0.579540	+	0.390026i	−0.00199155	+	0.00134030i
$292$	284.035			0.972722
$293$			137.522i			0.469359i	0.972073	+	0.234679i	$0.0754040\pi$
$293$			137.522i			0.469359i	−0.972073	+	0.234679i	$0.924596\pi$
$294$	−226.791	−	336.989i	−0.771397	−	1.14622i
$295$	29.2526			0.0991615
$296$		−	32.0992i		−	0.108443i
$297$	−31.5204	+	6.59688i	−0.106129	+	0.0222117i
$298$	188.892			0.633866
$299$			144.573i			0.483521i
$300$	−59.8571	+	40.2834i	−0.199524	+	0.134278i
$301$	704.130			2.33930
$302$		−	331.103i		−	1.09637i
$303$	141.488	+	210.237i	0.466957	+	0.693852i
$304$	22.9251			0.0754115
$305$			152.199i			0.499012i
$306$	−102.146	+	251.310i	−0.333811	+	0.821276i
$307$	−71.9236			−0.234279			−0.117139	−	0.993115i	$-0.537372\pi$
$307$	−71.9236			−0.234279			−0.117139	+	0.993115i	$0.537372\pi$
$308$			33.7570i			0.109601i
$309$	73.5735	−	49.5144i	0.238102	−	0.160241i
$310$	95.8384			0.309156
$311$		−	33.3440i		−	0.107215i	−0.998562	−	0.0536077i	$-0.982928\pi$
$311$		−	33.3440i		−	0.107215i	0.998562	−	0.0536077i	$-0.0170720\pi$
$312$	202.136	+	300.354i	0.647872	+	0.962674i
$313$	−163.093			−0.521065			−0.260532	−	0.965465i	$-0.583898\pi$
$313$	−163.093			−0.521065			−0.260532	+	0.965465i	$0.583898\pi$
$314$			234.226i			0.745944i
$315$	392.220	+	159.420i	1.24514	+	0.506094i
$316$	66.1441			0.209317
$317$		−	408.609i		−	1.28899i	−0.764609	−	0.644494i	$-0.777068\pi$
$317$		−	408.609i		−	1.28899i	0.764609	−	0.644494i	$-0.222932\pi$
$318$	−154.606	+	104.049i	−0.486184	+	0.327198i
$319$	54.9503			0.172258
$320$		−	177.591i		−	0.554971i
$321$	−279.732	−	415.653i	−0.871438	−	1.29487i
$322$	159.079			0.494035
$323$		−	333.530i		−	1.03260i
$324$	−132.966	−	129.480i	−0.410389	−	0.399629i
$325$	−154.027			−0.473928
$326$		−	135.878i		−	0.416805i
$327$	210.787	−	141.858i	0.644609	−	0.433817i
$328$	−233.907			−0.713132
$329$		−	530.019i		−	1.61100i
$330$	9.94539	+	14.7779i	0.0301376	+	0.0447814i
$331$	−593.300			−1.79245			−0.896224	−	0.443603i	$-0.853700\pi$
$331$	−593.300			−1.79245			−0.896224	+	0.443603i	$0.853700\pi$
$332$			4.89340i			0.0147392i
$333$	−13.2274	+	32.5433i	−0.0397218	+	0.0977276i
$334$	260.242			0.779167
$335$		−	207.140i		−	0.618328i
$336$	48.7259	−	32.7922i	0.145018	−	0.0975958i
$337$	324.138			0.961833			0.480917	−	0.876766i	$-0.340304\pi$
$337$	324.138			0.961833			0.480917	+	0.876766i	$0.340304\pi$
$338$			60.5701i			0.179201i
$339$	321.982	+	478.434i	0.949800	+	1.41131i
$340$	−201.210			−0.591795
$341$		−	22.9616i		−	0.0673360i
$342$	−157.644	−	64.0751i	−0.460948	−	0.187354i
$343$	674.201			1.96560
$344$			468.789i			1.36276i
$345$	−93.3829	+	62.8460i	−0.270675	+	0.182162i
$346$	−12.4986			−0.0361231
$347$			390.559i			1.12553i	0.826617	+	0.562765i	$0.190262\pi$
$347$			390.559i			1.12553i	−0.826617	+	0.562765i	$0.809738\pi$
$348$	176.816	+	262.732i	0.508093	+	0.754976i
$349$	42.3900			0.121461			0.0607306	−	0.998154i	$-0.480657\pi$
$349$	42.3900			0.121461			0.0607306	+	0.998154i	$0.480657\pi$
$350$			169.482i			0.484233i
$351$	−81.1635	−	387.805i	−0.231235	−	1.10486i
$352$	−36.7637			−0.104442
$353$			192.382i			0.544991i	0.962157	+	0.272496i	$0.0878490\pi$
$353$			192.382i			0.544991i	−0.962157	+	0.272496i	$0.912151\pi$
$354$	−24.9898	+	16.8179i	−0.0705926	+	0.0475083i
$355$	−304.149			−0.856758
$356$		−	369.676i		−	1.03842i
$357$	−477.083	−	708.898i	−1.33637	−	1.98571i
$358$	202.425			0.565434
$359$			594.058i			1.65476i	0.561644	+	0.827379i	$0.310169\pi$
$359$			594.058i			1.65476i	−0.561644	+	0.827379i	$0.689831\pi$
$360$	−106.137	+	261.129i	−0.294825	+	0.725358i
$361$	−151.780			−0.420445
$362$			320.139i			0.884362i
$363$	−297.612	+	200.290i	−0.819867	+	0.551764i
$364$	−415.323			−1.14100
$365$			472.099i			1.29342i
$366$	−87.5020	−	130.019i	−0.239077	−	0.355244i
$367$	−575.716			−1.56871			−0.784354	−	0.620313i	$-0.787006\pi$
$367$	−575.716			−1.56871			−0.784354	+	0.620313i	$0.787006\pi$
$368$			15.6148i			0.0424316i
$369$	237.143	+	96.3877i	0.642664	+	0.261213i
$370$	19.4310			0.0525162
$371$		−	587.004i		−	1.58222i
$372$	109.785	−	73.8845i	0.295121	−	0.198614i
$373$	−411.683			−1.10371			−0.551853	−	0.833941i	$-0.686079\pi$
$373$	−411.683			−1.10371			−0.551853	+	0.833941i	$0.686079\pi$
$374$		−	35.9505i		−	0.0961244i
$375$	−226.430	−	336.452i	−0.603812	−	0.897205i
$376$	352.871			0.938487
$377$			676.071i			1.79329i
$378$	−426.717	+	89.3074i	−1.12888	+	0.236263i
$379$	485.114			1.27998			0.639991	−	0.768382i	$-0.278938\pi$
$379$	485.114			1.27998			0.639991	+	0.768382i	$0.278938\pi$
$380$		−	126.217i		−	0.332150i
$381$	−400.487	+	269.525i	−1.05115	+	0.707414i
$382$	−260.897			−0.682975
$383$		−	353.447i		−	0.922838i	−0.887182	−	0.461419i	$-0.847341\pi$
$383$		−	353.447i		−	0.922838i	0.887182	−	0.461419i	$-0.152659\pi$
$384$	−104.416	−	155.151i	−0.271915	−	0.404039i
$385$	−56.1081			−0.145735
$386$			399.728i			1.03556i
$387$	193.177	−	475.274i	0.499166	−	1.22810i
$388$	0.533532			0.00137508
$389$		−	111.760i		−	0.287302i	−0.989628	−	0.143651i	$-0.954116\pi$
$389$		−	111.760i		−	0.287302i	0.989628	−	0.143651i	$-0.0458842\pi$
$390$	−181.817	+	122.361i	−0.466197	+	0.313747i
$391$	227.175			0.581011
$392$			851.831i			2.17304i
$393$	−106.670	−	158.501i	−0.271424	−	0.403310i
$394$	52.1037			0.132243
$395$			109.939i			0.278327i
$396$	22.7854	+	9.26120i	0.0575388	+	0.0233869i
$397$	−612.174			−1.54200			−0.771001	−	0.636834i	$-0.780243\pi$
$397$	−612.174			−1.54200			−0.771001	+	0.636834i	$0.780243\pi$
$398$		−	237.876i		−	0.597679i
$399$	444.684	−	299.269i	1.11450	−	0.750048i
$400$	−16.6359			−0.0415898
$401$		−	409.763i		−	1.02185i	−0.859625	−	0.510926i	$-0.829303\pi$
$401$		−	409.763i		−	1.02185i	0.859625	−	0.510926i	$-0.170697\pi$
$402$	119.089	+	176.954i	0.296241	+	0.440185i
$403$	282.503			0.701001
$404$		−	193.547i		−	0.479077i
$405$	215.210	−	221.005i	0.531384	−	0.545691i
$406$	743.908			1.83229
$407$		−	4.65540i		−	0.0114383i
$408$	471.964	−	317.628i	1.15677	−	0.778500i
$409$	−572.552			−1.39988			−0.699941	−	0.714201i	$-0.746790\pi$
$409$	−572.552			−1.39988			−0.699941	+	0.714201i	$0.746790\pi$
$410$		−	141.594i		−	0.345350i
$411$	55.9901	+	83.1957i	0.136229	+	0.202423i
$412$	−67.7327			−0.164400
$413$		−	94.8803i		−	0.229734i
$414$	43.6432	−	107.375i	0.105418	−	0.259361i
$415$	−8.13340			−0.0195985
$416$		−	452.316i		−	1.08730i
$417$	227.820	−	153.321i	0.546330	−	0.367676i
$418$	22.5514			0.0539507
$419$			350.684i			0.836955i	0.908227	+	0.418478i	$0.137436\pi$
$419$			350.684i			0.836955i	−0.908227	+	0.418478i	$0.862564\pi$
$420$	−180.542	−	268.267i	−0.429861	−	0.638731i
$421$	566.440			1.34546			0.672732	−	0.739886i	$-0.265121\pi$
$421$	566.440			1.34546			0.672732	+	0.739886i	$0.265121\pi$
$422$			13.6707i			0.0323949i
$423$	−357.753	−	145.410i	−0.845751	−	0.343759i
$424$	390.810			0.921722
$425$			242.031i			0.569484i
$426$	259.827	−	174.861i	0.609922	−	0.410473i
$427$	493.653			1.15610
$428$			382.656i			0.894056i
$429$	29.3161	+	43.5608i	0.0683359	+	0.101540i
$430$	−283.777			−0.659947
$431$		−	321.611i		−	0.746196i	−0.927792	−	0.373098i	$-0.878295\pi$
$431$		−	321.611i		−	0.746196i	0.927792	−	0.373098i	$-0.121705\pi$
$432$	−8.76621	−	41.8856i	−0.0202922	−	0.0969573i
$433$	288.242			0.665685			0.332843	−	0.942982i	$-0.391992\pi$
$433$	288.242			0.665685			0.332843	+	0.942982i	$0.391992\pi$
$434$		−	310.850i		−	0.716243i
$435$	−436.690	+	293.889i	−1.00389	+	0.675607i
$436$	−194.053			−0.445077
$437$			142.505i			0.326098i
$438$	−271.419	−	403.301i	−0.619678	−	0.920780i
$439$	−207.559			−0.472801			−0.236400	−	0.971656i	$-0.575968\pi$
$439$	−207.559			−0.472801			−0.236400	+	0.971656i	$0.575968\pi$
$440$		−	37.3551i		−	0.0848980i
$441$	351.020	−	863.615i	0.795964	−	1.95831i
$442$	442.311			1.00070
$443$			658.077i			1.48550i	0.669568	+	0.742751i	$0.266479\pi$
$443$			658.077i			1.48550i	−0.669568	+	0.742751i	$0.733521\pi$
$444$	22.2586	−	14.9799i	0.0501321	−	0.0337385i
$445$	614.444			1.38077
$446$			109.541i			0.245608i
$447$	242.041	+	359.649i	0.541479	+	0.804584i
$448$	−576.011			−1.28574
$449$		−	575.777i		−	1.28235i	−0.767393	−	0.641177i	$-0.778446\pi$
$449$		−	575.777i		−	1.28235i	0.767393	−	0.641177i	$-0.221554\pi$
$450$	114.397	+	46.4971i	0.254215	+	0.103327i
$451$	−33.9239			−0.0752192
$452$		−	440.452i		−	0.974452i
$453$	630.417	−	424.266i	1.39165	−	0.936569i
$454$	384.342			0.846568
$455$		−	690.316i		−	1.51718i
$456$	199.245	+	296.058i	0.436940	+	0.649249i
$457$	−716.921			−1.56876			−0.784378	−	0.620284i	$-0.787017\pi$
$457$	−716.921			−1.56876			−0.784378	+	0.620284i	$0.787017\pi$
$458$		−	430.348i		−	0.939625i
$459$	−609.380	+	127.537i	−1.32762	+	0.277858i
$460$	85.9696			0.186890
$461$		−	570.888i		−	1.23837i	−0.785246	−	0.619184i	$-0.787464\pi$
$461$		−	570.888i		−	1.23837i	0.785246	−	0.619184i	$-0.212536\pi$
$462$	47.9317	−	32.2577i	0.103748	−	0.0698218i
$463$	−297.331			−0.642183			−0.321091	−	0.947048i	$-0.604050\pi$
$463$	−297.331			−0.642183			−0.321091	+	0.947048i	$0.604050\pi$
$464$			73.0203i			0.157371i
$465$	122.805	+	182.475i	0.264096	+	0.392420i
$466$	82.4509			0.176933
$467$			402.518i			0.861923i	0.902370	+	0.430961i	$0.141825\pi$
$467$			402.518i			0.861923i	−0.902370	+	0.430961i	$0.858175\pi$
$468$	−113.943	+	280.335i	−0.243469	+	0.599007i
$469$	−671.854			−1.43252
$470$			213.607i			0.454484i
$471$	−445.965	+	300.131i	−0.946847	+	0.637221i
$472$	63.1685			0.133832
$473$			67.9891i			0.143740i
$474$	−63.2062	−	93.9181i	−0.133346	−	0.198140i
$475$	−151.823			−0.319628
$476$			652.621i			1.37105i
$477$	−396.217	−	161.044i	−0.830643	−	0.337618i
$478$	345.145			0.722060
$479$		−	628.870i		−	1.31288i	−0.754378	−	0.656440i	$-0.772061\pi$
$479$		−	628.870i		−	1.31288i	0.754378	−	0.656440i	$-0.227939\pi$
$480$	292.161	−	196.622i	0.608669	−	0.409630i
$481$	57.2768			0.119079
$482$		−	50.2764i		−	0.104308i
$483$	203.840	+	302.885i	0.422028	+	0.627092i
$484$	273.985			0.566085
$485$			0.886792i			0.00182844i
$486$	−56.7885	+	312.527i	−0.116849	+	0.643060i
$487$	481.364			0.988428			0.494214	−	0.869340i	$-0.335456\pi$
$487$	481.364			0.988428			0.494214	+	0.869340i	$0.335456\pi$
$488$			328.660i			0.673483i
$489$	258.711	−	174.111i	0.529062	−	0.356055i
$490$	−515.648			−1.05234
$491$		−	739.745i		−	1.50661i	−0.657671	−	0.753305i	$-0.728458\pi$
$491$		−	739.745i		−	1.50661i	0.657671	−	0.753305i	$-0.271542\pi$
$492$	−109.159	−	162.199i	−0.221867	−	0.329672i
$493$	1062.35			2.15487
$494$			277.457i			0.561654i
$495$	−15.3932	+	37.8719i	−0.0310973	+	0.0765089i
$496$	30.5123			0.0615167
$497$			986.500i			1.98491i
$498$	6.94815	−	4.67605i	0.0139521	−	0.00938966i
$499$	−630.412			−1.26335			−0.631675	−	0.775233i	$-0.717632\pi$
$499$	−630.412			−1.26335			−0.631675	+	0.775233i	$0.717632\pi$
$500$			309.742i			0.619484i
$501$	333.466	+	495.498i	0.665601	+	0.989017i
$502$	−157.179			−0.313106
$503$			375.876i			0.747269i	0.927576	+	0.373635i	$0.121889\pi$
$503$			375.876i			0.747269i	−0.927576	+	0.373635i	$0.878111\pi$
$504$	846.966	+	344.253i	1.68049	+	0.683041i
$505$	321.698			0.637025
$506$			15.3603i			0.0303564i
$507$	−115.325	+	77.6128i	−0.227465	+	0.153082i
$508$	368.694			0.725775
$509$		−	539.451i		−	1.05982i	−0.848052	−	0.529912i	$-0.822225\pi$
$509$		−	539.451i		−	1.05982i	0.848052	−	0.529912i	$-0.177775\pi$
$510$	192.273	+	285.699i	0.377006	+	0.560194i
$511$	1531.24			2.99656
$512$		−	100.990i		−	0.197246i
$513$	−80.0024	−	382.257i	−0.155950	−	0.745141i
$514$	−326.127			−0.634488
$515$		−	112.580i		−	0.218601i
$516$	−325.073	+	218.772i	−0.629987	+	0.423977i
$517$	51.1774			0.0989891
$518$		−	63.0240i		−	0.121668i
$519$	−16.0153	−	23.7972i	−0.0308581	−	0.0458520i
$520$	459.592			0.883830
$521$		−	143.060i		−	0.274587i	−0.990530	−	0.137293i	$-0.956160\pi$
$521$		−	143.060i		−	0.274587i	0.990530	−	0.137293i	$-0.0438403\pi$
$522$	204.090	−	502.124i	0.390977	−	0.961923i
$523$	447.990			0.856578			0.428289	−	0.903642i	$-0.359117\pi$
$523$	447.990			0.856578			0.428289	+	0.903642i	$0.359117\pi$
$524$			145.918i			0.278469i
$525$	−322.692	+	217.169i	−0.614651	+	0.413655i
$526$	−265.207			−0.504195
$527$		−	443.913i		−	0.842340i
$528$	3.16634	+	4.70486i	0.00599685	+	0.00891072i
$529$	431.937			0.816515
$530$			236.574i			0.446365i
$531$	−64.0424	−	26.0303i	−0.120607	−	0.0490212i
$532$	−409.382			−0.769515
$533$		−	417.376i		−	0.783070i
$534$	−524.904	+	353.256i	−0.982966	+	0.661529i
$535$	−636.019			−1.18882
$536$		−	447.300i		−	0.834516i
$537$	259.382	+	385.416i	0.483021	+	0.717720i
$538$	−620.094			−1.15259
$539$			123.542i			0.229206i
$540$	−230.607	+	48.2635i	−0.427049	+	0.0893769i
$541$	−165.991			−0.306823			−0.153412	−	0.988162i	$-0.549026\pi$
$541$	−165.991			−0.306823			−0.153412	+	0.988162i	$0.549026\pi$
$542$		−	241.095i		−	0.444824i
$543$	−609.542	+	410.217i	−1.12255	+	0.755465i
$544$	−710.749			−1.30652
$545$		−	322.539i		−	0.591815i
$546$	396.876	+	589.719i	0.726880	+	1.08007i
$547$	472.010			0.862907			0.431453	−	0.902135i	$-0.358001\pi$
$547$	472.010			0.862907			0.431453	+	0.902135i	$0.358001\pi$
$548$		−	76.5911i		−	0.139765i
$549$	135.433	−	333.206i	0.246690	−	0.606933i
$550$	−16.3648			−0.0297541
$551$			666.400i			1.20944i
$552$	−201.652	+	135.710i	−0.365312	+	0.245852i
$553$	356.585			0.644819
$554$		−	492.255i		−	0.888548i
$555$	24.8983	+	36.9964i	0.0448618	+	0.0666602i
$556$	−209.734			−0.377219
$557$		−	355.959i		−	0.639064i	−0.947575	−	0.319532i	$-0.896474\pi$
$557$		−	355.959i		−	0.639064i	0.947575	−	0.319532i	$-0.103526\pi$
$558$	−209.818	−	85.2812i	−0.376017	−	0.152834i
$559$	−836.492			−1.49641
$560$		−	74.5588i		−	0.133141i
$561$	68.4495	−	46.0660i	0.122013	−	0.0821141i
$562$	−470.680			−0.837508
$563$			230.539i			0.409483i	0.978816	+	0.204741i	$0.0656353\pi$
$563$			230.539i			0.409483i	−0.978816	+	0.204741i	$0.934365\pi$
$564$	164.676	+	244.692i	0.291979	+	0.433851i
$565$	732.083			1.29572
$566$		−	448.209i		−	0.791888i
$567$	−716.824	−	698.030i	−1.26424	−	1.23109i
$568$	−656.783			−1.15631
$569$			562.742i			0.989002i	0.869177	+	0.494501i	$0.164649\pi$
$569$			562.742i			0.989002i	−0.869177	+	0.494501i	$0.835351\pi$
$570$	−179.216	+	120.611i	−0.314414	+	0.211598i
$571$	674.756			1.18171			0.590854	−	0.806778i	$-0.298791\pi$
$571$	674.756			1.18171			0.590854	+	0.806778i	$0.298791\pi$
$572$		−	40.1027i		−	0.0701095i
$573$	−334.306	−	496.745i	−0.583430	−	0.866919i
$574$	−459.256			−0.800097
$575$		−	103.411i		−	0.179845i
$576$	−158.028	+	388.797i	−0.274354	+	0.674994i
$577$	−379.150			−0.657105			−0.328553	−	0.944486i	$-0.606561\pi$
$577$	−379.150			−0.657105			−0.328553	+	0.944486i	$0.606561\pi$
$578$		−	317.253i		−	0.548880i
$579$	−761.079	+	512.200i	−1.31447	+	0.884629i
$580$	402.023			0.693143
$581$			26.3805i			0.0454053i
$582$	−0.509834	−	0.757563i	−0.000876004	−	0.00130165i
$583$	56.6798			0.0972208
$584$			1019.46i			1.74564i
$585$	−465.950	−	189.387i	−0.796495	−	0.323739i
$586$	−179.766			−0.306768
$587$		−	555.352i		−	0.946085i	−0.881040	−	0.473042i	$-0.843156\pi$
$587$		−	555.352i		−	0.946085i	0.881040	−	0.473042i	$-0.156844\pi$
$588$	−590.687	+	397.528i	−1.00457	+	0.676068i
$589$	278.462			0.472771
$590$			38.2385i			0.0648110i
$591$	66.7642	+	99.2049i	0.112968	+	0.167859i
$592$	6.18629			0.0104498
$593$			228.099i			0.384653i	0.981331	+	0.192327i	$0.0616033\pi$
$593$			228.099i			0.384653i	−0.981331	+	0.192327i	$0.938397\pi$
$594$	−8.62331	−	41.2028i	−0.0145174	−	0.0693650i
$595$	−1084.73			−1.82308
$596$		−	331.098i		−	0.555533i
$597$	452.915	−	304.808i	0.758651	−	0.510566i
$598$	−188.983			−0.316025
$599$		−	21.5391i		−	0.0359584i	−0.999838	−	0.0179792i	$-0.994277\pi$
$599$		−	21.5391i		−	0.0359584i	0.999838	−	0.0179792i	$-0.00572327\pi$
$600$	−144.585	−	214.839i	−0.240975	−	0.358064i
$601$	602.048			1.00174			0.500872	−	0.865521i	$-0.333013\pi$
$601$	602.048			1.00174			0.500872	+	0.865521i	$0.333013\pi$
$602$			920.425i			1.52895i
$603$	−184.322	+	453.488i	−0.305675	+	0.752054i
$604$	−580.370			−0.960878
$605$			455.395i			0.752719i
$606$	−274.818	+	184.950i	−0.453495	+	0.305199i
$607$	−113.664			−0.187256			−0.0936281	−	0.995607i	$-0.529846\pi$
$607$	−113.664			−0.187256			−0.0936281	+	0.995607i	$0.529846\pi$
$608$		−	445.845i		−	0.733298i
$609$	953.223	+	1416.39i	1.56523	+	2.32577i
$610$	−198.951			−0.326149
$611$			629.652i			1.03053i
$612$	440.507	+	179.046i	0.719782	+	0.292558i
$613$	−160.198			−0.261335			−0.130667	−	0.991426i	$-0.541712\pi$
$613$	−160.198			−0.261335			−0.130667	+	0.991426i	$0.541712\pi$
$614$		−	94.0172i		−	0.153122i
$615$	269.593	−	181.434i	0.438363	−	0.295015i
$616$	−121.160			−0.196689
$617$			274.258i			0.444502i	0.974990	+	0.222251i	$0.0713404\pi$
$617$			274.258i			0.444502i	−0.974990	+	0.222251i	$0.928660\pi$
$618$	64.7243	+	96.1738i	0.104732	+	0.155621i
$619$	270.664			0.437261			0.218630	−	0.975808i	$-0.429841\pi$
$619$	270.664			0.437261			0.218630	+	0.975808i	$0.429841\pi$
$620$		−	167.989i		−	0.270951i
$621$	260.365	−	54.4917i	0.419267	−	0.0877482i
$622$	43.5866			0.0700749
$623$		−	1992.94i		−	3.19893i
$624$	−57.8854	+	38.9564i	−0.0927651	+	0.0624302i
$625$	−252.419			−0.403870
$626$		−	213.192i		−	0.340563i
$627$	28.8967	+	42.9376i	0.0460873	+	0.0684811i
$628$	410.562			0.653760
$629$		−	90.0023i		−	0.143088i
$630$	−208.390	+	512.703i	−0.330778	+	0.813814i
$631$	−927.683			−1.47018			−0.735090	−	0.677970i	$-0.762860\pi$
$631$	−927.683			−1.47018			−0.735090	+	0.677970i	$0.762860\pi$
$632$			237.404i			0.375639i
$633$	−26.0288	+	17.5172i	−0.0411198	+	0.0276733i
$634$	534.126			0.842470
$635$			612.811i			0.965057i
$636$	182.381	+	271.000i	0.286763	+	0.426101i
$637$	−1519.98			−2.38615
$638$			71.8300i			0.112586i
$639$	665.869	+	270.645i	1.04205	+	0.423545i
$640$	−237.407			−0.370948
$641$			1000.42i			1.56072i	0.625330	+	0.780360i	$0.284964\pi$
$641$			1000.42i			1.56072i	−0.625330	+	0.780360i	$0.715036\pi$
$642$	543.334	−	365.660i	0.846315	−	0.569564i
$643$	932.909			1.45087			0.725434	−	0.688291i	$-0.241639\pi$
$643$	932.909			1.45087			0.725434	+	0.688291i	$0.241639\pi$
$644$		−	278.840i		−	0.432982i
$645$	−363.624	−	540.310i	−0.563759	−	0.837689i
$646$	435.984			0.674897
$647$			517.452i			0.799772i	0.916565	+	0.399886i	$0.130950\pi$
$647$			517.452i			0.799772i	−0.916565	+	0.399886i	$0.869050\pi$
$648$	464.728	−	477.240i	0.717173	−	0.736482i
$649$	9.16141			0.0141162
$650$		−	201.341i		−	0.309755i
$651$	591.855	−	398.314i	0.909147	−	0.611849i
$652$	−238.173			−0.365296
$653$			301.747i			0.462094i	0.972943	+	0.231047i	$0.0742151\pi$
$653$			301.747i			0.462094i	−0.972943	+	0.231047i	$0.925785\pi$
$654$	185.434	+	275.537i	0.283539	+	0.421310i
$655$	−242.532			−0.370278
$656$		−	45.0795i		−	0.0687187i
$657$	420.094	−	1033.56i	0.639412	−	1.57315i
$658$	692.831			1.05293
$659$		−	710.758i		−	1.07854i	−0.842133	−	0.539270i	$-0.818700\pi$
$659$		−	710.758i		−	1.07854i	0.842133	−	0.539270i	$-0.181300\pi$
$660$	25.9032	−	17.4327i	0.0392473	−	0.0264132i
$661$	824.370			1.24716			0.623578	−	0.781761i	$-0.285678\pi$
$661$	824.370			1.24716			0.623578	+	0.781761i	$0.285678\pi$
$662$		−	775.550i		−	1.17153i
$663$	566.765	+	842.156i	0.854849	+	1.27022i
$664$	−17.5634			−0.0264508
$665$		−	680.440i		−	1.02322i
$666$	−42.5400	−	17.2905i	−0.0638738	−	0.0259618i
$667$	−453.902			−0.680512
$668$		−	456.162i		−	0.682877i
$669$	−208.565	+	140.363i	−0.311757	+	0.209810i
$670$	270.769			0.404133
$671$			47.6659i			0.0710372i
$672$	−637.740	−	947.618i	−0.949018	−	1.41015i
$673$	−866.939			−1.28817			−0.644085	−	0.764954i	$-0.722762\pi$
$673$	−866.939			−1.28817			−0.644085	+	0.764954i	$0.722762\pi$
$674$			423.707i			0.628645i
$675$	58.0550	+	277.391i	0.0860073	+	0.410949i
$676$	106.170			0.157056
$677$			678.127i			1.00167i	0.865544	+	0.500833i	$0.166973\pi$
$677$			678.127i			1.00167i	−0.865544	+	0.500833i	$0.833027\pi$
$678$	−625.399	+	420.889i	−0.922418	+	0.620780i
$679$	2.87629			0.00423607
$680$		−	722.182i		−	1.06203i
$681$	492.485	+	731.784i	0.723179	+	1.07457i
$682$	30.0149			0.0440101
$683$			775.837i			1.13592i	0.823055	+	0.567962i	$0.192268\pi$
$683$			775.837i			1.13592i	−0.823055	+	0.567962i	$0.807732\pi$
$684$	−112.313	+	276.325i	−0.164201	+	0.403984i
$685$	127.303			0.185844
$686$			881.303i			1.28470i
$687$	819.380	−	551.436i	1.19269	−	0.802673i
$688$	−90.3468			−0.131318
$689$			697.349i			1.01212i
$690$	−82.1511	−	122.068i	−0.119060	−	0.176911i
$691$	−12.5020			−0.0180926			−0.00904632	−	0.999959i	$-0.502880\pi$
$691$	−12.5020			−0.0180926			−0.00904632	+	0.999959i	$0.502880\pi$
$692$			21.9080i			0.0316590i
$693$	122.837	+	49.9274i	0.177253	+	0.0720453i
$694$	−510.531			−0.735635
$695$		−	348.602i		−	0.501585i
$696$	−942.994	+	634.628i	−1.35488	+	0.911822i
$697$	−655.847			−0.940957
$698$			55.4114i			0.0793859i
$699$	105.650	+	156.986i	0.151145	+	0.224586i
$700$	297.074			0.424392
$701$		−	256.833i		−	0.366381i	−0.983077	−	0.183191i	$-0.941357\pi$
$701$		−	256.833i		−	0.366381i	0.983077	−	0.183191i	$-0.0586426\pi$
$702$	506.931	−	106.095i	0.722124	−	0.151133i
$703$	56.4575			0.0803093
$704$		−	55.6183i		−	0.0790032i
$705$	−406.707	+	273.710i	−0.576889	+	0.388242i
$706$	−251.478			−0.356201
$707$		−	1043.42i		−	1.47584i
$708$	29.4791	+	43.8031i	0.0416372	+	0.0618687i
$709$	738.720			1.04192			0.520959	−	0.853582i	$-0.325574\pi$
$709$	738.720			1.04192			0.520959	+	0.853582i	$0.325574\pi$
$710$		−	397.578i		−	0.559969i
$711$	97.8286	−	240.688i	0.137593	−	0.338521i
$712$	1326.84			1.86354
$713$			189.667i			0.266013i
$714$	926.658	−	623.634i	1.29784	−	0.873437i
$715$	66.6552			0.0932241
$716$		−	354.819i		−	0.495557i
$717$	442.259	+	657.153i	0.616818	+	0.916531i
$718$	−776.541			−1.08153
$719$		−	319.264i		−	0.444039i	−0.975042	−	0.222020i	$-0.928735\pi$
$719$		−	319.264i		−	0.444039i	0.975042	−	0.222020i	$-0.0712649\pi$
$720$	−50.3257	−	20.4551i	−0.0698969	−	0.0284099i
$721$	−365.149			−0.506448
$722$		−	198.405i		−	0.274798i
$723$	95.7259	−	64.4228i	0.132401	−	0.0891048i
$724$	561.153			0.775073
$725$		−	483.583i		−	0.667011i
$726$	−261.816	−	389.032i	−0.360628	−	0.535857i
$727$	548.565			0.754559			0.377280	−	0.926099i	$-0.376860\pi$
$727$	548.565			0.754559			0.377280	+	0.926099i	$0.376860\pi$
$728$		−	1490.68i		−	2.04763i
$729$	−667.817	+	292.339i	−0.916072	+	0.401014i
$730$	−617.118			−0.845367
$731$			1314.43i			1.79812i
$732$	−227.903	+	153.377i	−0.311343	+	0.209531i
$733$	45.2936			0.0617921			0.0308960	−	0.999523i	$-0.490164\pi$
$733$	45.2936			0.0617921			0.0308960	+	0.999523i	$0.490164\pi$
$734$		−	752.565i		−	1.02529i
$735$	−660.737	−	981.790i	−0.898962	−	1.33577i
$736$	303.676			0.412604
$737$		−	64.8726i		−	0.0880225i
$738$	−125.996	+	309.989i	−0.170727	+	0.420039i
$739$	549.302			0.743304			0.371652	−	0.928372i	$-0.378791\pi$
$739$	549.302			0.743304			0.371652	+	0.928372i	$0.378791\pi$
$740$		−	34.0594i		−	0.0460262i
$741$	−528.275	+	355.525i	−0.712922	+	0.479791i
$742$	767.321			1.03413
$743$		−	343.910i		−	0.462867i	−0.972851	−	0.231433i	$-0.925658\pi$
$743$		−	343.910i		−	0.462867i	0.972851	−	0.231433i	$-0.0743415\pi$
$744$	265.186	+	394.040i	0.356433	+	0.529623i
$745$	550.322			0.738688
$746$		−	538.144i		−	0.721372i
$747$	17.8063	+	7.23745i	0.0238371	+	0.00968869i
$748$	−63.0155			−0.0842454
$749$			2062.91i			2.75422i
$750$	439.803	−	295.984i	0.586405	−	0.394646i
$751$	354.918			0.472594			0.236297	−	0.971681i	$-0.424066\pi$
$751$	354.918			0.472594			0.236297	+	0.971681i	$0.424066\pi$
$752$			68.0066i			0.0904344i
$753$	−201.405	−	299.268i	−0.267470	−	0.397434i
$754$	−883.747			−1.17208
$755$		−	964.642i		−	1.27767i
$756$	156.542	+	747.967i	0.207066	+	0.989374i
$757$	−235.656			−0.311303			−0.155651	−	0.987812i	$-0.549748\pi$
$757$	−235.656			−0.311303			−0.155651	+	0.987812i	$0.549748\pi$
$758$			634.131i			0.836585i
$759$	−29.2459	+	19.6823i	−0.0385321	+	0.0259318i
$760$	453.017			0.596075
$761$			75.3637i			0.0990325i	0.998773	+	0.0495162i	$0.0157680\pi$
$761$			75.3637i			0.0990325i	−0.998773	+	0.0495162i	$0.984232\pi$
$762$	−352.317	−	523.509i	−0.462359	−	0.687019i
$763$	−1046.15			−1.37110
$764$			457.310i			0.598573i
$765$	−297.595	+	732.173i	−0.389013	+	0.957089i
$766$	462.019			0.603158
$767$			112.716i			0.146957i
$768$	667.050	−	448.919i	0.868554	−	0.584530i
$769$	−324.938			−0.422546			−0.211273	−	0.977427i	$-0.567761\pi$
$769$	−324.938			−0.422546			−0.211273	+	0.977427i	$0.567761\pi$
$770$		−	73.3434i		−	0.0952512i
$771$	−417.890	−	620.943i	−0.542010	−	0.805373i
$772$	700.659			0.907590
$773$			675.310i			0.873622i	0.899553	+	0.436811i	$0.143892\pi$
$773$			675.310i			0.873622i	−0.899553	+	0.436811i	$0.856108\pi$
$774$	621.270	+	252.517i	0.802674	+	0.326250i
$775$	−202.070			−0.260736
$776$			1.91495i			0.00246772i
$777$	119.997	−	80.7571i	0.154436	−	0.103935i
$778$	146.091			0.187778
$779$		−	411.406i		−	0.528120i
$780$	214.480	+	318.696i	0.274974	+	0.408584i
$781$	−95.2541			−0.121964
$782$			296.959i			0.379743i
$783$	1217.55	−	254.821i	1.55499	−	0.325442i
$784$	−164.168			−0.209398
$785$			682.401i			0.869300i
$786$	207.189	−	139.437i	0.263599	−	0.177400i
$787$	−791.979			−1.00633			−0.503164	−	0.864191i	$-0.667831\pi$
$787$	−791.979			−1.00633			−0.503164	+	0.864191i	$0.667831\pi$
$788$		−	91.3294i		−	0.115900i
$789$	−339.828	−	504.951i	−0.430708	−	0.639989i
$790$	−143.710			−0.181912
$791$		−	2374.49i		−	3.00189i
$792$	−33.2402	+	81.7810i	−0.0419700	+	0.103259i
$793$	−586.449			−0.739532
$794$		−	800.223i		−	1.00784i
$795$	−450.434	+	303.139i	−0.566583	+	0.381306i
$796$	−416.959			−0.523818
$797$			82.1332i			0.103053i	0.998672	+	0.0515265i	$0.0164087\pi$
$797$			82.1332i			0.103053i	−0.998672	+	0.0515265i	$0.983591\pi$
$798$	391.199	+	581.282i	0.490224	+	0.728424i
$799$	989.407			1.23831
$800$			323.534i			0.404418i
$801$	−1345.19	−	546.759i	−1.67939	−	0.682596i
$802$	535.634			0.667873
$803$			147.853i			0.184126i
$804$	310.172	−	208.744i	0.385787	−	0.259632i
$805$	463.465			0.575733
$806$			369.283i			0.458167i
$807$	−794.570	−	1180.65i	−0.984598	−	1.46301i
$808$	694.678			0.859750
$809$		−	993.904i		−	1.22856i	−0.789089	−	0.614279i	$-0.789447\pi$
$809$		−	993.904i		−	1.22856i	0.789089	−	0.614279i	$-0.210553\pi$
$810$	288.893	+	281.319i	0.356658	+	0.347307i
$811$	−402.328			−0.496089			−0.248045	−	0.968749i	$-0.579788\pi$
$811$	−402.328			−0.496089			−0.248045	+	0.968749i	$0.579788\pi$
$812$		−	1303.95i		−	1.60585i
$813$	459.042	−	308.932i	0.564627	−	0.379990i
$814$	6.08545			0.00747598
$815$		−	395.871i		−	0.485731i
$816$	61.2144	+	90.9586i	0.0750177	+	0.111469i
$817$	−824.526			−1.00921
$818$		−	748.429i		−	0.914949i
$819$	−614.273	+	1511.30i	−0.750028	+	1.84530i
$820$	−248.191			−0.302672
$821$		−	1009.77i		−	1.22993i	−0.788556	−	0.614964i	$-0.789171\pi$
$821$		−	1009.77i		−	1.22993i	0.788556	−	0.614964i	$-0.210829\pi$
$822$	−108.752	+	73.1892i	−0.132302	+	0.0890379i
$823$	39.4522			0.0479371			0.0239686	−	0.999713i	$-0.492370\pi$
$823$	39.4522			0.0479371			0.0239686	+	0.999713i	$0.492370\pi$
$824$		−	243.106i		−	0.295031i
$825$	−20.9693	−	31.1583i	−0.0254174	−	0.0377677i
$826$	124.026			0.150152
$827$			2.37348i			0.00286998i	0.999999	+	0.00143499i	$0.000456772\pi$
$827$			2.37348i			0.00286998i	−0.999999	+	0.00143499i	$0.999543\pi$
$828$	−188.212	−	76.4995i	−0.227309	−	0.0923907i
$829$	246.190			0.296973			0.148486	−	0.988914i	$-0.452560\pi$
$829$	246.190			0.296973			0.148486	+	0.988914i	$0.452560\pi$
$830$		−	10.6318i		−	0.0128094i
$831$	937.250	−	630.762i	1.12786	−	0.759040i
$832$	684.289			0.822463
$833$			2388.43i			2.86726i
$834$	200.418	+	297.801i	0.240310	+	0.357076i
$835$	758.194			0.908016
$836$		−	39.5290i		−	0.0472835i
$837$	−106.480	−	508.768i	−0.127216	−	0.607847i
$838$	−458.408			−0.547026
$839$			1131.62i			1.34877i	0.738378	+	0.674387i	$0.235592\pi$
$839$			1131.62i			1.34877i	−0.738378	+	0.674387i	$0.764408\pi$
$840$	962.862	−	647.999i	1.14626	−	0.771427i
$841$	−1281.60			−1.52390
$842$			740.440i			0.879382i
$843$	−603.116	−	896.170i	−0.715440	−	1.06307i
$844$	23.9625			0.0283916
$845$			176.466i			0.208836i
$846$	190.077	−	467.647i	0.224678	−	0.552775i
$847$	1477.06			1.74388
$848$			75.3184i			0.0888189i
$849$	853.386	−	574.322i	1.00517	−	0.676469i
$850$	−316.378			−0.372209
$851$			38.4546i			0.0451875i
$852$	−306.504	−	455.434i	−0.359746	−	0.534547i
$853$	172.218			0.201897			0.100949	−	0.994892i	$-0.467812\pi$
$853$	172.218			0.201897			0.100949	+	0.994892i	$0.467812\pi$
$854$			645.293i			0.755613i
$855$	−459.284	−	186.678i	−0.537175	−	0.218337i
$856$	−1373.43			−1.60447
$857$			1007.12i			1.17517i	0.809162	+	0.587585i	$0.199921\pi$
$857$			1007.12i			1.17517i	−0.809162	+	0.587585i	$0.800079\pi$
$858$	−56.9418	+	38.3214i	−0.0663658	+	0.0446637i
$859$	−725.208			−0.844246			−0.422123	−	0.906539i	$-0.638715\pi$
$859$	−725.208			−0.844246			−0.422123	+	0.906539i	$0.638715\pi$
$860$			497.416i			0.578391i
$861$	−588.477	−	874.419i	−0.683481	−	1.01559i
$862$	420.403			0.487707
$863$			1289.31i			1.49399i	0.664829	+	0.746995i	$0.268504\pi$
$863$			1289.31i			1.49399i	−0.664829	+	0.746995i	$0.731496\pi$
$864$	−814.587	+	170.485i	−0.942809	+	0.197320i
$865$	−36.4137			−0.0420967
$866$			376.784i			0.435086i
$867$	604.046	−	406.519i	0.696709	−	0.468880i
$868$	−544.870			−0.627730
$869$			34.4310i			0.0396214i
$870$	−384.166	−	570.833i	−0.441571	−	0.656130i
$871$	798.148			0.916358
$872$		−	696.495i		−	0.798733i
$873$	0.789106	−	1.94144i	0.000903901	−	0.00222387i
$874$	−186.279			−0.213134
$875$			1669.83i			1.90838i
$876$	−706.923	+	475.754i	−0.806990	+	0.543098i
$877$	−641.084			−0.730997			−0.365498	−	0.930812i	$-0.619101\pi$
$877$	−641.084			−0.730997			−0.365498	+	0.930812i	$0.619101\pi$
$878$		−	271.318i		−	0.309018i
$879$	−230.347	−	342.273i	−0.262056	−	0.389389i
$880$	7.19922			0.00818093
$881$		−	1105.13i		−	1.25441i	−0.778855	−	0.627204i	$-0.784199\pi$
$881$		−	1105.13i		−	1.25441i	0.778855	−	0.627204i	$-0.215801\pi$
$882$	1128.90	+	458.847i	1.27993	+	0.520234i
$883$	476.587			0.539737			0.269868	−	0.962897i	$-0.413020\pi$
$883$	476.587			0.539737			0.269868	+	0.962897i	$0.413020\pi$
$884$		−	775.300i		−	0.877037i
$885$	−72.8057	+	48.9977i	−0.0822664	+	0.0553647i
$886$	−860.226			−0.970909
$887$		−	27.2258i		−	0.0306943i	−0.999882	−	0.0153471i	$-0.995115\pi$
$887$		−	27.2258i		−	0.0306943i	0.999882	−	0.0153471i	$-0.00488534\pi$
$888$	53.7657	+	79.8905i	0.0605470	+	0.0899668i
$889$	1987.64			2.23581
$890$			803.190i			0.902460i
$891$	67.4001	−	69.2148i	0.0756455	−	0.0776822i
$892$	192.008			0.215256
$893$			620.644i			0.695010i
$894$	−470.126	+	316.391i	−0.525868	+	0.353905i
$895$	589.750			0.658939
$896$			770.024i			0.859402i
$897$	−242.157	−	359.822i	−0.269964	−	0.401139i
$898$	752.645			0.838135
$899$			886.949i			0.986595i
$900$	81.5019	−	200.519i	0.0905577	−	0.222799i
$901$	1095.78			1.21619
$902$		−	44.3446i		−	0.0491626i
$903$	−1752.48	+	1179.41i	−1.94073	+	1.30610i
$904$	1580.87			1.74875
$905$			932.700i			1.03061i
$906$	554.592	+	824.068i	0.612132	+	0.909568i
$907$	−1033.62			−1.13960			−0.569801	−	0.821783i	$-0.692980\pi$
$907$	−1033.62			−1.13960			−0.569801	+	0.821783i	$0.692980\pi$
$908$		−	673.690i		−	0.741949i
$909$	−704.288	−	286.261i	−0.774794	−	0.314918i
$910$	902.367			0.991612
$911$			188.903i			0.207358i	0.994611	+	0.103679i	$0.0330615\pi$
$911$			188.903i			0.207358i	−0.994611	+	0.103679i	$0.966938\pi$
$912$	−57.0573	+	38.3992i	−0.0625629	+	0.0421043i
$913$	−2.54724			−0.00278996
$914$		−	937.145i		−	1.02532i
$915$	−254.930	−	378.801i	−0.278612	−	0.413990i
$916$	−754.332			−0.823506
$917$			786.648i			0.857850i
$918$	−166.714	−	796.569i	−0.181605	−	0.867723i
$919$	−241.237			−0.262500			−0.131250	−	0.991349i	$-0.541899\pi$
$919$	−241.237			−0.262500			−0.131250	+	0.991349i	$0.541899\pi$
$920$			308.561i			0.335393i
$921$	179.008	−	120.471i	0.194362	−	0.130804i
$922$	746.253			0.809385
$923$		−	1171.94i		−	1.26971i
$924$	−56.5425	−	84.0165i	−0.0611932	−	0.0909270i
$925$	−40.9692			−0.0442910
$926$		−	388.665i		−	0.419724i
$927$	−100.178	+	246.469i	−0.108067	+	0.265878i
$928$	1420.09			1.53027
$929$		−	1424.79i		−	1.53368i	−0.641838	−	0.766841i	$-0.721828\pi$
$929$		−	1424.79i		−	1.53368i	0.641838	−	0.766841i	$-0.278172\pi$
$930$	−238.528	+	160.528i	−0.256482	+	0.172611i
$931$	−1498.24			−1.60928
$932$		−	144.523i		−	0.155068i
$933$	55.8507	+	82.9885i	0.0598614	+	0.0889480i
$934$	−526.164			−0.563344
$935$		−	104.739i		−	0.112020i
$936$	−1006.18	−	408.965i	−1.07498	−	0.436928i
$937$	669.227			0.714223			0.357111	−	0.934062i	$-0.383762\pi$
$937$	669.227			0.714223			0.357111	+	0.934062i	$0.383762\pi$
$938$		−	878.234i		−	0.936284i
$939$	405.917	−	273.179i	0.432286	−	0.290925i
$940$	374.420			0.398319
$941$		−	33.8290i		−	0.0359500i	−0.999838	−	0.0179750i	$-0.994278\pi$
$941$		−	33.8290i		−	0.0359500i	0.999838	−	0.0179750i	$-0.00572193\pi$
$942$	−392.326	−	582.957i	−0.416482	−	0.618850i
$943$	280.219			0.297157
$944$			12.1741i			0.0128963i
$945$	−1243.21	+	260.190i	−1.31556	+	0.275334i
$946$	−88.8741			−0.0939472
$947$			595.096i			0.628401i	0.949357	+	0.314201i	$0.101736\pi$
$947$			595.096i			0.628401i	−0.949357	+	0.314201i	$0.898264\pi$
$948$	−164.623	+	110.790i	−0.173653	+	0.116867i
$949$	−1819.08			−1.91684
$950$		−	198.460i		−	0.208906i
$951$	684.414	+	1016.97i	0.719678	+	1.06937i
$952$	−2342.38			−2.46049
$953$		−	456.707i		−	0.479231i	−0.970868	−	0.239615i	$-0.922979\pi$
$953$		−	456.707i		−	0.479231i	0.970868	−	0.239615i	$-0.0770213\pi$
$954$	210.513	−	517.927i	0.220664	−	0.542900i
$955$	−760.102			−0.795918
$956$		−	604.984i		−	0.632828i
$957$	−136.764	+	92.0410i	−0.142909	+	0.0961765i
$958$	822.046			0.858086
$959$		−	412.905i		−	0.430558i
$960$	297.462	+	441.998i	0.309856	+	0.460415i
$961$	−590.379			−0.614338
$962$			74.8712i			0.0778287i
$963$	1392.43	+	565.957i	1.44593	+	0.587702i
$964$	−88.1265			−0.0914175
$965$			1164.58i			1.20682i
$966$	−395.926	+	266.455i	−0.409861	+	0.275834i
$967$	−109.483			−0.113220			−0.0566098	−	0.998396i	$-0.518029\pi$
$967$	−109.483			−0.113220			−0.0566098	+	0.998396i	$0.518029\pi$
$968$			983.385i			1.01589i
$969$	558.657	+	830.109i	0.576529	+	0.856665i
$970$	−1.15920			−0.00119505
$971$		−	146.778i		−	0.151162i	−0.997140	−	0.0755810i	$-0.975919\pi$
$971$		−	146.778i		−	0.151162i	0.997140	−	0.0755810i	$-0.0240812\pi$
$972$	547.810	+	99.5412i	0.563591	+	0.102409i
$973$	−1130.68			−1.16206
$974$			629.230i			0.646027i
$975$	383.351	−	257.992i	0.393180	−	0.264608i
$976$	−63.3405			−0.0648980
$977$			744.977i			0.762515i	0.924469	+	0.381257i	$0.124509\pi$
$977$			744.977i			0.762515i	−0.924469	+	0.381257i	$0.875491\pi$
$978$	227.594	+	338.182i	0.232714	+	0.345790i
$979$	192.433			0.196561
$980$			903.849i			0.922295i
$981$	−287.009	+	706.130i	−0.292568	+	0.719807i
$982$	966.981			0.984706
$983$		−	20.4382i		−	0.0207916i	−0.999946	−	0.0103958i	$-0.996691\pi$
$983$		−	20.4382i		−	0.0207916i	0.999946	−	0.0103958i	$-0.00330915\pi$
$984$	582.162	−	391.791i	0.591628	−	0.398162i
$985$	151.800			0.154112
$986$			1388.68i			1.40840i
$987$	887.774	+	1319.14i	0.899467	+	1.33652i
$988$	486.337			0.492244
$989$		−	561.605i		−	0.567851i
$990$	−49.5054	−	20.1217i	−0.0500054	−	0.0203249i
$991$	−53.8739			−0.0543631			−0.0271816	−	0.999631i	$-0.508653\pi$
$991$	−53.8739			−0.0543631			−0.0271816	+	0.999631i	$0.508653\pi$
$992$		−	593.400i		−	0.598186i
$993$	1476.64	−	993.768i	1.48705	−	1.00077i
$994$	−1289.53			−1.29732
$995$		−	693.034i		−	0.696517i
$996$	−8.19637	−	12.1790i	−0.00822929	−	0.0122279i
$997$	−694.578			−0.696668			−0.348334	−	0.937370i	$-0.613253\pi$
$997$	−694.578			−0.696668			−0.348334	+	0.937370i	$0.613253\pi$
$998$		−	824.062i		−	0.825713i
$999$	−21.5885	−	103.151i	−0.0216101	−	0.103255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.24	yes	38
3.2	odd	2	inner	177.3.b.a.119.15	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.15	✓	38	3.2	odd	2	inner
177.3.b.a.119.24	yes	38	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.30718i q^{2} +(-2.48886 + 1.67498i) q^{3} +2.29128 q^{4} +3.80837i q^{5} +(-2.18951 - 3.25339i) q^{6} +12.3524 q^{7} +8.22384i q^{8} +(3.38885 - 8.33761i) q^{9} +O(q^{10})\)	\(q+1.30718i q^{2} +(-2.48886 + 1.67498i) q^{3} +2.29128 q^{4} +3.80837i q^{5} +(-2.18951 - 3.25339i) q^{6} +12.3524 q^{7} +8.22384i q^{8} +(3.38885 - 8.33761i) q^{9} -4.97823 q^{10} +1.19271i q^{11} +(-5.70267 + 3.83786i) q^{12} -14.6743 q^{13} +16.1468i q^{14} +(-6.37896 - 9.47850i) q^{15} -1.58493 q^{16} +23.0586i q^{17} +(10.8988 + 4.42984i) q^{18} -14.4644 q^{19} +8.72603i q^{20} +(-30.7433 + 20.6900i) q^{21} -1.55909 q^{22} -9.85208i q^{23} +(-13.7748 - 20.4680i) q^{24} +10.4963 q^{25} -19.1820i q^{26} +(5.53098 + 26.4274i) q^{27} +28.3027 q^{28} -46.0717i q^{29} +(12.3901 - 8.33845i) q^{30} -19.2515 q^{31} +30.8236i q^{32} +(-1.99778 - 2.96850i) q^{33} -30.1418 q^{34} +47.0423i q^{35} +(7.76481 - 19.1038i) q^{36} -3.90320 q^{37} -18.9076i q^{38} +(36.5224 - 24.5793i) q^{39} -31.3194 q^{40} +28.4426i q^{41} +(-27.0456 - 40.1870i) q^{42} +57.0037 q^{43} +2.73284i q^{44} +(31.7527 + 12.9060i) q^{45} +12.8784 q^{46} -42.9083i q^{47} +(3.94467 - 2.65473i) q^{48} +103.581 q^{49} +13.7206i q^{50} +(-38.6228 - 57.3897i) q^{51} -33.6230 q^{52} -47.5216i q^{53} +(-34.5454 + 7.22999i) q^{54} -4.54230 q^{55} +101.584i q^{56} +(35.9999 - 24.2277i) q^{57} +60.2240 q^{58} -7.68115i q^{59} +(-14.6160 - 21.7179i) q^{60} +39.9643 q^{61} -25.1652i q^{62} +(41.8603 - 102.989i) q^{63} -46.6317 q^{64} -55.8853i q^{65} +(3.88037 - 2.61146i) q^{66} -54.3907 q^{67} +52.8337i q^{68} +(16.5021 + 24.5205i) q^{69} -61.4928 q^{70} +79.8633i q^{71} +(68.5671 + 27.8694i) q^{72} +123.963 q^{73} -5.10218i q^{74} +(-26.1239 + 17.5812i) q^{75} -33.1420 q^{76} +14.7328i q^{77} +(32.1296 + 47.7414i) q^{78} +28.8678 q^{79} -6.03599i q^{80} +(-58.0314 - 56.5098i) q^{81} -37.1796 q^{82} +2.13566i q^{83} +(-70.4415 + 47.4066i) q^{84} -87.8157 q^{85} +74.5141i q^{86} +(77.1693 + 114.666i) q^{87} -9.80869 q^{88} -161.341i q^{89} +(-16.8705 + 41.5065i) q^{90} -181.263 q^{91} -22.5739i q^{92} +(47.9143 - 32.2460i) q^{93} +56.0889 q^{94} -55.0859i q^{95} +(-51.6290 - 76.7156i) q^{96} +0.232853 q^{97} +135.399i q^{98} +(9.94438 + 4.04193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) \) 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9	\( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) \) 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9 + 36 * q^10 - 4 * q^13 - 17 * q^15 + 100 * q^16 - 2 * q^18 - 28 * q^19 - 11 * q^21 + 84 * q^22 - 6 * q^24 - 166 * q^25 + 3 * q^27 + 12 * q^28 + 102 * q^30 - 40 * q^31 - 46 * q^33 - 148 * q^34 - 96 * q^36 + 112 * q^37 + 62 * q^39 - 56 * q^40 + 14 * q^42 + 164 * q^43 + 55 * q^45 - 4 * q^46 - 124 * q^48 + 242 * q^49 + 52 * q^51 + 8 * q^52 + 18 * q^54 - 228 * q^55 - 147 * q^57 - 80 * q^58 + 128 * q^60 + 12 * q^61 + 86 * q^63 + 48 * q^64 - 24 * q^66 + 124 * q^67 - 240 * q^69 + 148 * q^70 + 166 * q^72 - 192 * q^73 - 78 * q^75 - 304 * q^76 + 244 * q^78 + 64 * q^79 - 156 * q^81 - 180 * q^82 + 300 * q^84 - 52 * q^85 - 83 * q^87 - 96 * q^88 - 376 * q^90 - 332 * q^91 + 454 * q^93 + 768 * q^94 - 722 * q^96 + 416 * q^97 + 494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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