LMFDB - Embedded newform 177.3.b.a.119.15

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

$q$-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	$-0.894031\pi$
$2$		−	1.30718i		−	0.653590i	0.945095	−	0.326795i	$-0.105969\pi$
$3$	−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	$-0.875636\pi$
$5$		−	3.80837i		−	0.761674i	0.924642	−	0.380837i	$-0.124364\pi$
$6$	−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	$-0.982735\pi$
$11$		−	1.19271i		−	0.108429i	0.998529	−	0.0542143i	$-0.0172654\pi$
$12$	−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	$-0.762763\pi$
$17$		−	23.0586i		−	1.35639i	0.734882	−	0.678195i	$-0.237237\pi$
$18$	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	$0.0687065\pi$
$23$			9.85208i			0.428351i	−0.976795	+	0.214176i	$0.931294\pi$
$24$	−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	$0.292183\pi$
$29$			46.0717i			1.58868i	−0.607475	+	0.794339i	$0.707817\pi$
$30$	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	$-0.887248\pi$
$41$		−	28.4426i		−	0.693722i	0.937917	−	0.346861i	$-0.112752\pi$
$42$	−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	$0.150887\pi$
$47$			42.9083i			0.912943i	−0.889738	+	0.456472i	$0.849113\pi$
$48$	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	$0.147977\pi$
$53$			47.5216i			0.896635i	−0.893874	+	0.448317i	$0.852023\pi$
$54$	−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	$-0.809871\pi$
$71$		−	79.8633i		−	1.12484i	0.826853	−	0.562418i	$-0.190129\pi$
$72$	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	$-0.995905\pi$
$83$		−	2.13566i		−	0.0257309i	0.999917	−	0.0128654i	$-0.00409531\pi$
$84$	−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	$0.361186\pi$
$89$			161.341i			1.81281i	−0.422404	+	0.906407i	$0.638814\pi$
$90$	−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	$0.137330\pi$
$101$			84.4713i			0.836349i	−0.908367	+	0.418175i	$0.862670\pi$
$102$	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	$-0.715016\pi$
$107$		−	167.005i		−	1.56080i	0.625281	−	0.780399i	$-0.284984\pi$
$108$	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	$0.323746\pi$
$113$			192.230i			1.70115i	−0.525854	+	0.850575i	$0.676254\pi$
$114$	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	$-0.921846\pi$
$131$		−	63.6841i		−	0.486138i	0.970009	−	0.243069i	$-0.0781541\pi$
$132$	−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	$0.0389299\pi$
$137$			33.4272i			0.243994i	−0.992530	+	0.121997i	$0.961070\pi$
$138$	−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	$0.161148\pi$
$149$			144.503i			0.969822i	−0.874564	+	0.484911i	$0.838852\pi$
$150$	−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	$0.203271\pi$
$167$			199.086i			1.19213i	−0.802935	+	0.596066i	$0.796729\pi$
$168$	−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	$-0.991203\pi$
$173$		−	9.56148i		−	0.0552687i	0.999618	−	0.0276343i	$-0.00879741\pi$
$174$	−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	$0.142390\pi$
$179$			154.856i			0.865119i	−0.901605	+	0.432560i	$0.857610\pi$
$180$	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	$-0.825007\pi$
$191$		−	199.587i		−	1.04496i	0.852652	−	0.522480i	$-0.174993\pi$
$192$	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	$0.0322575\pi$
$197$			39.8596i			0.202333i	−0.994870	+	0.101166i	$0.967743\pi$
$198$	−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	$0.224239\pi$
$227$			294.024i			1.29526i	−0.761956	+	0.647629i	$0.775761\pi$
$228$	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	$0.0432174\pi$
$233$			63.0754i			0.270710i	−0.990797	+	0.135355i	$0.956783\pi$
$234$	−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	$0.186280\pi$
$239$			264.038i			1.10476i	−0.833593	+	0.552380i	$0.813720\pi$
$240$	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	$-0.923007\pi$
$251$		−	120.243i		−	0.479055i	0.970890	−	0.239528i	$-0.0769926\pi$
$252$	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	$-0.838679\pi$
$257$		−	249.489i		−	0.970773i	0.874300	−	0.485387i	$-0.161321\pi$
$258$	−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	$-0.873956\pi$
$263$		−	202.885i		−	0.771424i	0.922619	−	0.385712i	$-0.126044\pi$
$264$	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	$-0.656374\pi$
$269$		−	474.375i		−	1.76347i	0.471741	−	0.881737i	$-0.343626\pi$
$270$	−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	$-0.778645\pi$
$281$		−	360.072i		−	1.28140i	0.767793	−	0.640698i	$-0.221355\pi$
$282$	−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	$-0.924596\pi$
$293$		−	137.522i		−	0.469359i	0.972073	−	0.234679i	$-0.0754040\pi$
$294$	−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	$0.0170720\pi$
$311$			33.3440i			0.107215i	−0.998562	+	0.0536077i	$0.982928\pi$
$312$	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	$0.222932\pi$
$317$			408.609i			1.28899i	−0.764609	+	0.644494i	$0.777068\pi$
$318$	−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	$-0.809738\pi$
$347$		−	390.559i		−	1.12553i	0.826617	−	0.562765i	$-0.190262\pi$
$348$	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	$-0.912151\pi$
$353$		−	192.382i		−	0.544991i	0.962157	−	0.272496i	$-0.0878490\pi$
$354$	−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	$-0.689831\pi$
$359$		−	594.058i		−	1.65476i	0.561644	−	0.827379i	$-0.310169\pi$
$360$	−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	$0.152659\pi$
$383$			353.447i			0.922838i	−0.887182	+	0.461419i	$0.847341\pi$
$384$	−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	$0.0458842\pi$
$389$			111.760i			0.287302i	−0.989628	+	0.143651i	$0.954116\pi$
$390$	−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	$0.170697\pi$
$401$			409.763i			1.02185i	−0.859625	+	0.510926i	$0.829303\pi$
$402$	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	$-0.862564\pi$
$419$		−	350.684i		−	0.836955i	0.908227	−	0.418478i	$-0.137436\pi$
$420$	−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	$0.121705\pi$
$431$			321.611i			0.746196i	−0.927792	+	0.373098i	$0.878295\pi$
$432$	−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	$-0.733521\pi$
$443$		−	658.077i		−	1.48550i	0.669568	−	0.742751i	$-0.266479\pi$
$444$	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	$0.221554\pi$
$449$			575.777i			1.28235i	−0.767393	+	0.641177i	$0.778446\pi$
$450$	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	$0.212536\pi$
$461$			570.888i			1.23837i	−0.785246	+	0.619184i	$0.787464\pi$
$462$	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	$-0.858175\pi$
$467$		−	402.518i		−	0.861923i	0.902370	−	0.430961i	$-0.141825\pi$
$468$	−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	$0.227939\pi$
$479$			628.870i			1.31288i	−0.754378	+	0.656440i	$0.772061\pi$
$480$	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	$0.271542\pi$
$491$			739.745i			1.50661i	−0.657671	+	0.753305i	$0.728458\pi$
$492$	−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	$-0.878111\pi$
$503$		−	375.876i		−	0.747269i	0.927576	−	0.373635i	$-0.121889\pi$
$504$	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	$0.177775\pi$
$509$			539.451i			1.05982i	−0.848052	+	0.529912i	$0.822225\pi$
$510$	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	$0.0438403\pi$
$521$			143.060i			0.274587i	−0.990530	+	0.137293i	$0.956160\pi$
$522$	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	$0.103526\pi$
$557$			355.959i			0.639064i	−0.947575	+	0.319532i	$0.896474\pi$
$558$	−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	$-0.934365\pi$
$563$		−	230.539i		−	0.409483i	0.978816	−	0.204741i	$-0.0656353\pi$
$564$	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	$-0.835351\pi$
$569$		−	562.742i		−	0.989002i	0.869177	−	0.494501i	$-0.164649\pi$
$570$	−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	$0.156844\pi$
$587$			555.352i			0.946085i	−0.881040	+	0.473042i	$0.843156\pi$
$588$	−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	$-0.938397\pi$
$593$		−	228.099i		−	0.384653i	0.981331	−	0.192327i	$-0.0616033\pi$
$594$	−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	$0.00572327\pi$
$599$			21.5391i			0.0359584i	−0.999838	+	0.0179792i	$0.994277\pi$
$600$	−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	$-0.928660\pi$
$617$		−	274.258i		−	0.444502i	0.974990	−	0.222251i	$-0.0713404\pi$
$618$	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	$-0.715036\pi$
$641$		−	1000.42i		−	1.56072i	0.625330	−	0.780360i	$-0.284964\pi$
$642$	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	$-0.869050\pi$
$647$		−	517.452i		−	0.799772i	0.916565	−	0.399886i	$-0.130950\pi$
$648$	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	$-0.925785\pi$
$653$		−	301.747i		−	0.462094i	0.972943	−	0.231047i	$-0.0742151\pi$
$654$	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	$0.181300\pi$
$659$			710.758i			1.07854i	−0.842133	+	0.539270i	$0.818700\pi$
$660$	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	$-0.833027\pi$
$677$		−	678.127i		−	1.00167i	0.865544	−	0.500833i	$-0.166973\pi$
$678$	−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	$-0.807732\pi$
$683$		−	775.837i		−	1.13592i	0.823055	−	0.567962i	$-0.192268\pi$
$684$	−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	$0.0586426\pi$
$701$			256.833i			0.366381i	−0.983077	+	0.183191i	$0.941357\pi$
$702$	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	$0.0712649\pi$
$719$			319.264i			0.444039i	−0.975042	+	0.222020i	$0.928735\pi$
$720$	−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	$0.0743415\pi$
$743$			343.910i			0.462867i	−0.972851	+	0.231433i	$0.925658\pi$
$744$	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	$-0.984232\pi$
$761$		−	75.3637i		−	0.0990325i	0.998773	−	0.0495162i	$-0.0157680\pi$
$762$	−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	$-0.856108\pi$
$773$		−	675.310i		−	0.873622i	0.899553	−	0.436811i	$-0.143892\pi$
$774$	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	$-0.983591\pi$
$797$		−	82.1332i		−	0.103053i	0.998672	−	0.0515265i	$-0.0164087\pi$
$798$	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	$0.210553\pi$
$809$			993.904i			1.22856i	−0.789089	+	0.614279i	$0.789447\pi$
$810$	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	$0.210829\pi$
$821$			1009.77i			1.22993i	−0.788556	+	0.614964i	$0.789171\pi$
$822$	−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	$-0.999543\pi$
$827$		−	2.37348i		−	0.00286998i	0.999999	−	0.00143499i	$-0.000456772\pi$
$828$	−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	$-0.764408\pi$
$839$		−	1131.62i		−	1.34877i	0.738378	−	0.674387i	$-0.235592\pi$
$840$	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	$-0.800079\pi$
$857$		−	1007.12i		−	1.17517i	0.809162	−	0.587585i	$-0.199921\pi$
$858$	−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	$-0.731496\pi$
$863$		−	1289.31i		−	1.49399i	0.664829	−	0.746995i	$-0.268504\pi$
$864$	−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	$0.215801\pi$
$881$			1105.13i			1.25441i	−0.778855	+	0.627204i	$0.784199\pi$
$882$	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	$0.00488534\pi$
$887$			27.2258i			0.0306943i	−0.999882	+	0.0153471i	$0.995115\pi$
$888$	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	$-0.966938\pi$
$911$		−	188.903i		−	0.207358i	0.994611	−	0.103679i	$-0.0330615\pi$
$912$	−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	$0.278172\pi$
$929$			1424.79i			1.53368i	−0.641838	+	0.766841i	$0.721828\pi$
$930$	−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	$0.00572193\pi$
$941$			33.8290i			0.0359500i	−0.999838	+	0.0179750i	$0.994278\pi$
$942$	−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	$-0.898264\pi$
$947$		−	595.096i		−	0.628401i	0.949357	−	0.314201i	$-0.101736\pi$
$948$	−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	$0.0770213\pi$
$953$			456.707i			0.479231i	−0.970868	+	0.239615i	$0.922979\pi$
$954$	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	$0.0240812\pi$
$971$			146.778i			0.151162i	−0.997140	+	0.0755810i	$0.975919\pi$
$972$	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	$-0.875491\pi$
$977$		−	744.977i		−	0.762515i	0.924469	−	0.381257i	$-0.124509\pi$
$978$	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	$0.00330915\pi$
$983$			20.4382i			0.0207916i	−0.999946	+	0.0103958i	$0.996691\pi$
$984$	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.119.15	✓	38
3.2	odd	2	inner	177.3.b.a.119.24	yes	38

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

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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