LMFDB - Embedded newform 177.3.b.a.119.26

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			119.26
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.50450i q^{2} +(2.07476 + 2.16688i) q^{3} +1.73647 q^{4} -9.35091i q^{5} +(-3.26008 + 3.12148i) q^{6} +7.09053 q^{7} +8.63054i q^{8} +(-0.390753 + 8.99151i) q^{9} +O(q^{10})$	\(q+1.50450i q^{2} +(2.07476 + 2.16688i) q^{3} +1.73647 q^{4} -9.35091i q^{5} +(-3.26008 + 3.12148i) q^{6} +7.09053 q^{7} +8.63054i q^{8} +(-0.390753 + 8.99151i) q^{9} +14.0685 q^{10} -19.6440i q^{11} +(3.60276 + 3.76273i) q^{12} +5.28870 q^{13} +10.6677i q^{14} +(20.2623 - 19.4009i) q^{15} -6.03878 q^{16} +18.6801i q^{17} +(-13.5278 - 0.587888i) q^{18} -28.5841 q^{19} -16.2376i q^{20} +(14.7111 + 15.3643i) q^{21} +29.5544 q^{22} +22.2573i q^{23} +(-18.7014 + 17.9063i) q^{24} -62.4396 q^{25} +7.95686i q^{26} +(-20.2943 + 17.8085i) q^{27} +12.3125 q^{28} +17.6355i q^{29} +(29.1887 + 30.4847i) q^{30} -8.65134 q^{31} +25.4368i q^{32} +(42.5662 - 40.7565i) q^{33} -28.1042 q^{34} -66.3029i q^{35} +(-0.678531 + 15.6135i) q^{36} -2.64085 q^{37} -43.0049i q^{38} +(10.9728 + 11.4600i) q^{39} +80.7034 q^{40} -43.6618i q^{41} +(-23.1157 + 22.1329i) q^{42} +14.7841 q^{43} -34.1112i q^{44} +(84.0789 + 3.65389i) q^{45} -33.4861 q^{46} +43.3598i q^{47} +(-12.5290 - 13.0853i) q^{48} +1.27559 q^{49} -93.9405i q^{50} +(-40.4775 + 38.7567i) q^{51} +9.18367 q^{52} -30.3805i q^{53} +(-26.7929 - 30.5328i) q^{54} -183.689 q^{55} +61.1951i q^{56} +(-59.3051 - 61.9384i) q^{57} -26.5327 q^{58} +7.68115i q^{59} +(35.1849 - 33.6891i) q^{60} +67.1584 q^{61} -13.0160i q^{62} +(-2.77064 + 63.7546i) q^{63} -62.4248 q^{64} -49.4541i q^{65} +(61.3183 + 64.0409i) q^{66} +33.3864 q^{67} +32.4374i q^{68} +(-48.2289 + 46.1785i) q^{69} +99.7529 q^{70} -61.7198i q^{71} +(-77.6016 - 3.37240i) q^{72} +41.7753 q^{73} -3.97316i q^{74} +(-129.547 - 135.299i) q^{75} -49.6355 q^{76} -139.286i q^{77} +(-17.2416 + 16.5086i) q^{78} -16.0603 q^{79} +56.4681i q^{80} +(-80.6946 - 7.02691i) q^{81} +65.6893 q^{82} +50.6679i q^{83} +(25.5455 + 26.6797i) q^{84} +174.676 q^{85} +22.2427i q^{86} +(-38.2141 + 36.5894i) q^{87} +169.538 q^{88} -119.246i q^{89} +(-5.49729 + 126.497i) q^{90} +37.4996 q^{91} +38.6491i q^{92} +(-17.9494 - 18.7464i) q^{93} -65.2349 q^{94} +267.287i q^{95} +(-55.1185 + 52.7752i) q^{96} +58.4958 q^{97} +1.91912i q^{98} +(176.629 + 7.67594i) 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 $

$2$			1.50450i			0.752251i	0.926569	+	0.376126i	$0.122744\pi$
$2$			1.50450i			0.752251i	−0.926569	+	0.376126i	$0.877256\pi$
$3$	2.07476	+	2.16688i	0.691586	+	0.722294i
$3$	2.07476	+	2.16688i	0.691586	+	0.722294i
$4$	1.73647			0.434118
$5$		−	9.35091i		−	1.87018i	−0.354407	−	0.935091i	$-0.615317\pi$
$5$		−	9.35091i		−	1.87018i	0.354407	−	0.935091i	$-0.384683\pi$
$6$	−3.26008	+	3.12148i	−0.543347	+	0.520247i
$7$	7.09053			1.01293			0.506466	−	0.862260i	$-0.330951\pi$
$7$	7.09053			1.01293			0.506466	+	0.862260i	$0.330951\pi$
$8$			8.63054i			1.07882i
$9$	−0.390753	+	8.99151i	−0.0434170	+	0.999057i
$10$	14.0685			1.40685
$11$		−	19.6440i		−	1.78582i	−0.450239	−	0.892908i	$-0.648661\pi$
$11$		−	19.6440i		−	1.78582i	0.450239	−	0.892908i	$-0.351339\pi$
$12$	3.60276	+	3.76273i	0.300230	+	0.313561i
$13$	5.28870			0.406823			0.203411	−	0.979093i	$-0.434797\pi$
$13$	5.28870			0.406823			0.203411	+	0.979093i	$0.434797\pi$
$14$			10.6677i			0.761980i
$15$	20.2623	−	19.4009i	1.35082	−	1.29339i
$16$	−6.03878			−0.377424
$17$			18.6801i			1.09883i	0.835550	+	0.549414i	$0.185149\pi$
$17$			18.6801i			1.09883i	−0.835550	+	0.549414i	$0.814851\pi$
$18$	−13.5278	−	0.587888i	−0.751542	−	0.0326605i
$19$	−28.5841			−1.50443			−0.752213	−	0.658920i	$-0.771014\pi$
$19$	−28.5841			−1.50443			−0.752213	+	0.658920i	$0.771014\pi$
$20$		−	16.2376i		−	0.811880i
$21$	14.7111	+	15.3643i	0.700530	+	0.731635i
$22$	29.5544			1.34338
$23$			22.2573i			0.967708i	0.875149	+	0.483854i	$0.160763\pi$
$23$			22.2573i			0.967708i	−0.875149	+	0.483854i	$0.839237\pi$
$24$	−18.7014	+	17.9063i	−0.779223	+	0.746095i
$25$	−62.4396			−2.49758
$26$			7.95686i			0.306033i
$27$	−20.2943	+	17.8085i	−0.751639	+	0.659574i
$28$	12.3125			0.439732
$29$			17.6355i			0.608121i	0.952653	+	0.304061i	$0.0983426\pi$
$29$			17.6355i			0.608121i	−0.952653	+	0.304061i	$0.901657\pi$
$30$	29.1887	+	30.4847i	0.972956	+	1.01616i
$31$	−8.65134			−0.279075			−0.139538	−	0.990217i	$-0.544562\pi$
$31$	−8.65134			−0.279075			−0.139538	+	0.990217i	$0.544562\pi$
$32$			25.4368i			0.794900i
$33$	42.5662	−	40.7565i	1.28988	−	1.23505i
$34$	−28.1042			−0.826595
$35$		−	66.3029i		−	1.89437i
$36$	−0.678531	+	15.6135i	−0.0188481	+	0.433708i
$37$	−2.64085			−0.0713742			−0.0356871	−	0.999363i	$-0.511362\pi$
$37$	−2.64085			−0.0713742			−0.0356871	+	0.999363i	$0.511362\pi$
$38$		−	43.0049i		−	1.13171i
$39$	10.9728	+	11.4600i	0.281353	+	0.293846i
$40$	80.7034			2.01758
$41$		−	43.6618i		−	1.06492i	−0.846454	−	0.532461i	$-0.821267\pi$
$41$		−	43.6618i		−	1.06492i	0.846454	−	0.532461i	$-0.178733\pi$
$42$	−23.1157	+	22.1329i	−0.550373	+	0.526975i
$43$	14.7841			0.343817			0.171908	−	0.985113i	$-0.445007\pi$
$43$	14.7841			0.343817			0.171908	+	0.985113i	$0.445007\pi$
$44$		−	34.1112i		−	0.775255i
$45$	84.0789	+	3.65389i	1.86842	+	0.0811976i
$46$	−33.4861			−0.727959
$47$			43.3598i			0.922549i	0.887258	+	0.461274i	$0.152608\pi$
$47$			43.3598i			0.922549i	−0.887258	+	0.461274i	$0.847392\pi$
$48$	−12.5290	−	13.0853i	−0.261021	−	0.272611i
$49$	1.27559			0.0260324
$50$		−	93.9405i		−	1.87881i
$51$	−40.4775	+	38.7567i	−0.793677	+	0.759935i
$52$	9.18367			0.176609
$53$		−	30.3805i		−	0.573217i	−0.958048	−	0.286608i	$-0.907472\pi$
$53$		−	30.3805i		−	0.573217i	0.958048	−	0.286608i	$-0.0925279\pi$
$54$	−26.7929	−	30.5328i	−0.496166	−	0.565422i
$55$	−183.689			−3.33980
$56$			61.1951i			1.09277i
$57$	−59.3051	−	61.9384i	−1.04044	−	1.08664i
$58$	−26.5327			−0.457460
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	35.1849	−	33.6891i	0.586416	−	0.561485i
$61$	67.1584			1.10096			0.550479	−	0.834849i	$-0.314445\pi$
$61$	67.1584			1.10096			0.550479	+	0.834849i	$0.314445\pi$
$62$		−	13.0160i		−	0.209935i
$63$	−2.77064	+	63.7546i	−0.0439784	+	1.01198i
$64$	−62.4248			−0.975388
$65$		−	49.4541i		−	0.760833i
$66$	61.3183	+	64.0409i	0.929065	+	0.970317i
$67$	33.3864			0.498304			0.249152	−	0.968464i	$-0.419848\pi$
$67$	33.3864			0.498304			0.249152	+	0.968464i	$0.419848\pi$
$68$			32.4374i			0.477021i
$69$	−48.2289	+	46.1785i	−0.698969	+	0.669253i
$70$	99.7529			1.42504
$71$		−	61.7198i		−	0.869293i	−0.900601	−	0.434647i	$-0.856873\pi$
$71$		−	61.7198i		−	0.869293i	0.900601	−	0.434647i	$-0.143127\pi$
$72$	−77.6016	−	3.37240i	−1.07780	−	0.0468390i
$73$	41.7753			0.572264			0.286132	−	0.958190i	$-0.407630\pi$
$73$	41.7753			0.572264			0.286132	+	0.958190i	$0.407630\pi$
$74$		−	3.97316i		−	0.0536914i
$75$	−129.547	−	135.299i	−1.72729	−	1.80399i
$76$	−49.6355			−0.653098
$77$		−	139.286i		−	1.80891i
$78$	−17.2416	+	16.5086i	−0.221046	+	0.211648i
$79$	−16.0603			−0.203294			−0.101647	−	0.994821i	$-0.532411\pi$
$79$	−16.0603			−0.203294			−0.101647	+	0.994821i	$0.532411\pi$
$80$			56.4681i			0.705852i
$81$	−80.6946	−	7.02691i	−0.996230	−	0.0867520i
$82$	65.6893			0.801089
$83$			50.6679i			0.610456i	0.952279	+	0.305228i	$0.0987327\pi$
$83$			50.6679i			0.610456i	−0.952279	+	0.305228i	$0.901267\pi$
$84$	25.5455	+	26.6797i	0.304113	+	0.317616i
$85$	174.676			2.05501
$86$			22.2427i			0.258637i
$87$	−38.2141	+	36.5894i	−0.439242	+	0.420568i
$88$	169.538			1.92657
$89$		−	119.246i		−	1.33984i	−0.742434	−	0.669919i	$-0.766329\pi$
$89$		−	119.246i		−	1.33984i	0.742434	−	0.669919i	$-0.233671\pi$
$90$	−5.49729	+	126.497i	−0.0610810	+	1.40552i
$91$	37.4996			0.412084
$92$			38.6491i			0.420099i
$93$	−17.9494	−	18.7464i	−0.193005	−	0.201574i
$94$	−65.2349			−0.693989
$95$			267.287i			2.81355i
$96$	−55.1185	+	52.7752i	−0.574151	+	0.549742i
$97$	58.4958			0.603050			0.301525	−	0.953458i	$-0.402504\pi$
$97$	58.4958			0.603050			0.301525	+	0.953458i	$0.402504\pi$
$98$			1.91912i			0.0195829i
$99$	176.629	+	7.67594i	1.78413	+	0.0775347i
$100$	−108.425			−1.08425
$101$		−	65.7293i		−	0.650785i	−0.945579	−	0.325393i	$-0.894504\pi$
$101$		−	65.7293i		−	0.650785i	0.945579	−	0.325393i	$-0.105496\pi$
$102$	−58.3095	−	60.8986i	−0.571662	−	0.597045i
$103$	−107.070			−1.03951			−0.519756	−	0.854315i	$-0.673977\pi$
$103$	−107.070			−1.03951			−0.519756	+	0.854315i	$0.673977\pi$
$104$			45.6443i			0.438887i
$105$	143.671	−	137.563i	1.36829	−	1.31012i
$106$	45.7075			0.431203
$107$		−	24.7229i		−	0.231055i	−0.993304	−	0.115528i	$-0.963144\pi$
$107$		−	24.7229i		−	0.231055i	0.993304	−	0.115528i	$-0.0368559\pi$
$108$	−35.2404	+	30.9240i	−0.326300	+	0.286333i
$109$	−54.3272			−0.498414			−0.249207	−	0.968450i	$-0.580170\pi$
$109$	−54.3272			−0.498414			−0.249207	+	0.968450i	$0.580170\pi$
$110$		−	276.361i		−	2.51237i
$111$	−5.47912	−	5.72240i	−0.0493614	−	0.0515532i
$112$	−42.8182			−0.382305
$113$			89.2190i			0.789549i	0.918778	+	0.394774i	$0.129177\pi$
$113$			89.2190i			0.789549i	−0.918778	+	0.394774i	$0.870823\pi$
$114$	93.1864	−	89.2247i	0.817425	−	0.782673i
$115$	208.126			1.80979
$116$			30.6236i			0.263996i
$117$	−2.06657	+	47.5534i	−0.0176630	+	0.406439i
$118$	−11.5563			−0.0979348
$119$			132.452i			1.11304i
$120$	167.440	+	174.875i	1.39533	+	1.45729i
$121$	−264.886			−2.18914
$122$			101.040i			0.828197i
$123$	94.6100	−	90.5877i	0.769187	−	0.736486i
$124$	−15.0228			−0.121152
$125$			350.094i			2.80075i
$126$	−95.9189	−	4.16844i	−0.761261	−	0.0330828i
$127$	−185.143			−1.45782			−0.728908	−	0.684612i	$-0.759972\pi$
$127$	−185.143			−1.45782			−0.728908	+	0.684612i	$0.759972\pi$
$128$			7.82879i			0.0611624i
$129$	30.6735	+	32.0354i	0.237779	+	0.248337i
$130$	74.4039			0.572338
$131$		−	23.1778i		−	0.176929i	−0.996079	−	0.0884647i	$-0.971804\pi$
$131$		−	23.1778i		−	0.176929i	0.996079	−	0.0884647i	$-0.0281960\pi$
$132$	73.9150	−	70.7725i	0.559962	−	0.536156i
$133$	−202.676			−1.52388
$134$			50.2299i			0.374850i
$135$	166.526	+	189.770i	1.23352	+	1.40570i
$136$	−161.219			−1.18543
$137$			152.484i			1.11302i	0.830840	+	0.556512i	$0.187861\pi$
$137$			152.484i			1.11302i	−0.830840	+	0.556512i	$0.812139\pi$
$138$	−69.4756	−	72.5605i	−0.503447	−	0.525801i
$139$	147.205			1.05903			0.529513	−	0.848302i	$-0.322375\pi$
$139$	147.205			1.05903			0.529513	+	0.848302i	$0.322375\pi$
$140$		−	115.133i		−	0.822379i
$141$	−93.9555	+	89.9611i	−0.666351	+	0.638022i
$142$	92.8576			0.653927
$143$		−	103.891i		−	0.726511i
$144$	2.35967	−	54.2978i	0.0163866	−	0.377068i
$145$	164.908			1.13730
$146$			62.8510i			0.430486i
$147$	2.64653	+	2.76405i	0.0180036	+	0.0188030i
$148$	−4.58576			−0.0309848
$149$		−	32.7895i		−	0.220064i	−0.993928	−	0.110032i	$-0.964905\pi$
$149$		−	32.7895i		−	0.220064i	0.993928	−	0.110032i	$-0.0350953\pi$
$150$	203.558	−	194.904i	1.35705	−	1.29936i
$151$	122.450			0.810928			0.405464	−	0.914111i	$-0.367110\pi$
$151$	122.450			0.810928			0.405464	+	0.914111i	$0.367110\pi$
$152$		−	246.696i		−	1.62300i
$153$	−167.962	−	7.29929i	−1.09779	−	0.0477078i
$154$	209.556			1.36076
$155$			80.8979i			0.521922i
$156$	19.0539	+	19.8999i	0.122140	+	0.127564i
$157$	154.489			0.984006			0.492003	−	0.870594i	$-0.336265\pi$
$157$	154.489			0.984006			0.492003	+	0.870594i	$0.336265\pi$
$158$		−	24.1627i		−	0.152928i
$159$	65.8309	−	63.0322i	0.414031	−	0.396429i
$160$	237.857			1.48661
$161$			157.816i			0.980223i
$162$	10.5720	−	121.405i	0.0652593	−	0.749415i
$163$	−90.2530			−0.553700			−0.276850	−	0.960913i	$-0.589290\pi$
$163$	−90.2530			−0.553700			−0.276850	+	0.960913i	$0.589290\pi$
$164$		−	75.8175i		−	0.462302i
$165$	−381.111	−	398.033i	−2.30976	−	2.41232i
$166$	−76.2300			−0.459217
$167$		−	256.147i		−	1.53381i	−0.641758	−	0.766907i	$-0.721795\pi$
$167$		−	256.147i		−	1.53381i	0.641758	−	0.766907i	$-0.278205\pi$
$168$	−132.602	+	126.965i	−0.789300	+	0.755744i
$169$	−141.030			−0.834495
$170$			262.800i			1.54588i
$171$	11.1693	−	257.014i	0.0653176	−	1.50301i
$172$	25.6722			0.149257
$173$		−	231.773i		−	1.33973i	−0.742484	−	0.669864i	$-0.766353\pi$
$173$		−	231.773i		−	1.33973i	0.742484	−	0.669864i	$-0.233647\pi$
$174$	−55.0489	−	57.4932i	−0.316373	−	0.330421i
$175$	−442.729			−2.52988
$176$			118.626i			0.674010i
$177$	−16.6441	+	15.9365i	−0.0940347	+	0.0900369i
$178$	179.405			1.00790
$179$			269.568i			1.50597i	0.658039	+	0.752984i	$0.271386\pi$
$179$			269.568i			1.50597i	−0.658039	+	0.752984i	$0.728614\pi$
$180$	146.001	+	6.34488i	0.811114	+	0.0352493i
$181$	−36.1729			−0.199850			−0.0999251	−	0.994995i	$-0.531860\pi$
$181$	−36.1729			−0.199850			−0.0999251	+	0.994995i	$0.531860\pi$
$182$			56.4183i			0.309991i
$183$	139.338	+	145.524i	0.761407	+	0.795215i
$184$	−192.092			−1.04398
$185$			24.6943i			0.133483i
$186$	28.2041	−	27.0050i	0.151635	−	0.145188i
$187$	366.951			1.96231
$188$			75.2930i			0.400495i
$189$	−143.897	+	126.272i	−0.761360	+	0.668104i
$190$	−402.135			−2.11650
$191$		−	29.5445i		−	0.154683i	−0.997005	−	0.0773417i	$-0.975357\pi$
$191$		−	29.5445i		−	0.154683i	0.997005	−	0.0773417i	$-0.0246432\pi$
$192$	−129.516	−	135.267i	−0.674565	−	0.704517i
$193$	142.657			0.739156			0.369578	−	0.929200i	$-0.379502\pi$
$193$	142.657			0.739156			0.369578	+	0.929200i	$0.379502\pi$
$194$			88.0072i			0.453645i
$195$	107.161	−	102.605i	0.549545	−	0.526182i
$196$	2.21502			0.0113011
$197$		−	8.10839i		−	0.0411593i	−0.999788	−	0.0205797i	$-0.993449\pi$
$197$		−	8.10839i		−	0.0411593i	0.999788	−	0.0205797i	$-0.00655118\pi$
$198$	−11.5485	+	265.739i	−0.0583256	+	1.34212i
$199$	192.191			0.965786			0.482893	−	0.875679i	$-0.339586\pi$
$199$	192.191			0.965786			0.482893	+	0.875679i	$0.339586\pi$
$200$		−	538.887i		−	2.69443i
$201$	69.2687	+	72.3443i	0.344620	+	0.359922i
$202$	98.8899			0.489554
$203$			125.045i			0.615986i
$204$	−70.2881	+	67.2998i	−0.344549	+	0.329901i
$205$	−408.278			−1.99160
$206$		−	161.087i		−	0.781975i
$207$	−200.127	−	8.69709i	−0.966795	−	0.0420149i
$208$	−31.9373			−0.153545
$209$			561.506i			2.68663i
$210$	206.963	+	216.153i	0.985539	+	1.02930i
$211$	124.794			0.591439			0.295720	−	0.955275i	$-0.404441\pi$
$211$	124.794			0.591439			0.295720	+	0.955275i	$0.404441\pi$
$212$		−	52.7548i		−	0.248844i
$213$	133.740	−	128.054i	0.627885	−	0.601191i
$214$	37.1957			0.173812
$215$		−	138.245i		−	0.643000i
$216$	−153.697	−	175.150i	−0.711560	−	0.810881i
$217$	−61.3426			−0.282685
$218$		−	81.7354i		−	0.374933i
$219$	86.6736	+	90.5220i	0.395770	+	0.413343i
$220$	−318.971			−1.44987
$221$			98.7933i			0.447028i
$222$	8.60937	−	8.24335i	0.0387810	−	0.0371322i
$223$	−265.562			−1.19086			−0.595430	−	0.803407i	$-0.703018\pi$
$223$	−265.562			−1.19086			−0.595430	+	0.803407i	$0.703018\pi$
$224$			180.360i			0.805180i
$225$	24.3984	−	561.426i	0.108437	−	2.49523i
$226$	−134.230			−0.593939
$227$		−	22.3352i		−	0.0983931i	−0.998789	−	0.0491966i	$-0.984334\pi$
$227$		−	22.3352i		−	0.0983931i	0.998789	−	0.0491966i	$-0.0156661\pi$
$228$	−102.982	−	107.554i	−0.451674	−	0.471729i
$229$	189.051			0.825551			0.412775	−	0.910833i	$-0.364559\pi$
$229$	189.051			0.825551			0.412775	+	0.910833i	$0.364559\pi$
$230$			313.126i			1.36142i
$231$	301.817	−	288.985i	1.30657	−	1.25102i
$232$	−152.204			−0.656052
$233$		−	222.374i		−	0.954396i	−0.878796	−	0.477198i	$-0.841652\pi$
$233$		−	222.374i		−	0.954396i	0.878796	−	0.477198i	$-0.158348\pi$
$234$	−71.5442	−	3.10916i	−0.305744	−	0.0132870i
$235$	405.454			1.72533
$236$			13.3381i			0.0565173i
$237$	−33.3212	−	34.8007i	−0.140596	−	0.146838i
$238$	−199.274			−0.837285
$239$			195.861i			0.819501i	0.912198	+	0.409751i	$0.134384\pi$
$239$			195.861i			0.819501i	−0.912198	+	0.409751i	$0.865616\pi$
$240$	−122.360	+	117.158i	−0.509832	+	0.488157i
$241$	26.5673			0.110238			0.0551189	−	0.998480i	$-0.482446\pi$
$241$	26.5673			0.110238			0.0551189	+	0.998480i	$0.482446\pi$
$242$		−	398.522i		−	1.64678i
$243$	−152.195	−	189.435i	−0.626318	−	0.779567i
$244$	116.619			0.477945
$245$		−	11.9279i		−	0.0486853i
$246$	136.290	+	142.341i	0.554022	+	0.578622i
$247$	−151.173			−0.612035
$248$		−	74.6657i		−	0.301071i
$249$	−109.791	+	105.124i	−0.440929	+	0.422183i
$250$	−526.717			−2.10687
$251$		−	358.916i		−	1.42994i	−0.699154	−	0.714971i	$-0.746440\pi$
$251$		−	358.916i		−	1.42994i	0.699154	−	0.714971i	$-0.253560\pi$
$252$	−4.81114	+	110.708i	−0.0190918	+	0.439317i
$253$	437.221			1.72815
$254$		−	278.548i		−	1.09664i
$255$	362.410	+	378.502i	1.42122	+	1.48432i
$256$	−261.478			−1.02140
$257$		−	18.4478i		−	0.0717814i	−0.999356	−	0.0358907i	$-0.988573\pi$
$257$		−	18.4478i		−	0.0717814i	0.999356	−	0.0358907i	$-0.0114268\pi$
$258$	−48.1974	+	46.1483i	−0.186812	+	0.178870i
$259$	−18.7250			−0.0722973
$260$		−	85.8757i		−	0.330291i
$261$	−158.570	−	6.89112i	−0.607548	−	0.0264028i
$262$	34.8710			0.133095
$263$			170.772i			0.649322i	0.945831	+	0.324661i	$0.105250\pi$
$263$			170.772i			0.649322i	−0.945831	+	0.324661i	$0.894750\pi$
$264$	351.751	+	367.369i	1.33239	+	1.39155i
$265$	−284.085			−1.07202
$266$		−	304.927i		−	1.14634i
$267$	258.391	−	247.406i	0.967757	−	0.926614i
$268$	57.9745			0.216323
$269$			113.815i			0.423105i	0.977367	+	0.211552i	$0.0678519\pi$
$269$			113.815i			0.423105i	−0.977367	+	0.211552i	$0.932148\pi$
$270$	−285.509	+	250.539i	−1.05744	+	0.927920i
$271$	285.172			1.05230			0.526148	−	0.850393i	$-0.323636\pi$
$271$	285.172			1.05230			0.526148	+	0.850393i	$0.323636\pi$
$272$		−	112.805i		−	0.414724i
$273$	77.8027	+	81.2573i	0.284992	+	0.297646i
$274$	−229.413			−0.837274
$275$			1226.56i			4.46022i
$276$	−83.7481	+	80.1876i	−0.303435	+	0.290535i
$277$	14.4234			0.0520702			0.0260351	−	0.999661i	$-0.491712\pi$
$277$	14.4234			0.0520702			0.0260351	+	0.999661i	$0.491712\pi$
$278$			221.470i			0.796654i
$279$	3.38053	−	77.7886i	0.0121166	−	0.278812i
$280$	572.230			2.04368
$281$		−	378.218i		−	1.34597i	−0.739655	−	0.672987i	$-0.765011\pi$
$281$		−	378.218i		−	1.34597i	0.739655	−	0.672987i	$-0.234989\pi$
$282$	−135.347	−	141.356i	−0.479953	−	0.501264i
$283$	190.998			0.674903			0.337452	−	0.941343i	$-0.390435\pi$
$283$	190.998			0.674903			0.337452	+	0.941343i	$0.390435\pi$
$284$		−	107.175i		−	0.377376i
$285$	−579.180	+	554.557i	−2.03221	+	1.94581i
$286$	156.304			0.546519
$287$		−	309.585i		−	1.07869i
$288$	−228.715	−	9.93949i	−0.794150	−	0.0345121i
$289$	−59.9455			−0.207424
$290$			248.105i			0.855534i
$291$	121.365	+	126.754i	0.417061	+	0.435579i
$292$	72.5415			0.248430
$293$		−	450.672i		−	1.53813i	−0.639171	−	0.769065i	$-0.720722\pi$
$293$		−	450.672i		−	1.53813i	0.639171	−	0.769065i	$-0.279278\pi$
$294$	−4.15851	+	3.98172i	−0.0141446	+	0.0135433i
$295$	71.8257			0.243477
$296$		−	22.7919i		−	0.0769998i
$297$	349.830	+	398.660i	1.17788	+	1.34229i
$298$	49.3320			0.165543
$299$			117.712i			0.393686i
$300$	−224.955	−	234.943i	−0.749849	−	0.783144i
$301$	104.827			0.348263
$302$			184.227i			0.610022i
$303$	142.428	−	136.372i	0.470058	−	0.450074i
$304$	172.613			0.567806
$305$		−	627.993i		−	2.05899i
$306$	10.9818	−	252.700i	0.0358882	−	0.825816i
$307$	−165.062			−0.537662			−0.268831	−	0.963187i	$-0.586637\pi$
$307$	−165.062			−0.537662			−0.268831	+	0.963187i	$0.586637\pi$
$308$		−	241.866i		−	0.785281i
$309$	−222.144	−	232.007i	−0.718912	−	0.750833i
$310$	−121.711			−0.392617
$311$			591.518i			1.90199i	0.309212	+	0.950993i	$0.399935\pi$
$311$			591.518i			1.90199i	−0.309212	+	0.950993i	$0.600065\pi$
$312$	−98.9058	+	94.7009i	−0.317006	+	0.303528i
$313$	350.121			1.11860			0.559298	−	0.828966i	$-0.311071\pi$
$313$	350.121			1.11860			0.559298	+	0.828966i	$0.311071\pi$
$314$			232.429i			0.740220i
$315$	596.163	+	25.9080i	1.89258	+	0.0822477i
$316$	−27.8882			−0.0882537
$317$			2.33568i			0.00736808i	0.999993	+	0.00368404i	$0.00117267\pi$
$317$			2.33568i			0.00736808i	−0.999993	+	0.00368404i	$0.998827\pi$
$318$	94.8321	+	99.0428i	0.298214	+	0.311455i
$319$	346.432			1.08599
$320$			583.729i			1.82415i
$321$	53.5717	−	51.2941i	0.166890	−	0.159795i
$322$	−237.434			−0.737374
$323$		−	533.953i		−	1.65311i
$324$	−140.124	−	12.2020i	−0.432481	−	0.0376606i
$325$	−330.224			−1.01607
$326$		−	135.786i		−	0.416521i
$327$	−112.716	−	117.721i	−0.344696	−	0.360002i
$328$	376.825			1.14886
$329$			307.444i			0.934480i
$330$	598.841	−	573.382i	1.81467	−	1.73752i
$331$	−37.9525			−0.114660			−0.0573301	−	0.998355i	$-0.518259\pi$
$331$	−37.9525			−0.114660			−0.0573301	+	0.998355i	$0.518259\pi$
$332$			87.9833i			0.265010i
$333$	1.03192	−	23.7452i	0.00309885	−	0.0713069i
$334$	385.374			1.15381
$335$		−	312.193i		−	0.931919i
$336$	−88.8373	−	92.7819i	−0.264397	−	0.276137i
$337$	340.605			1.01070			0.505349	−	0.862915i	$-0.331364\pi$
$337$	340.605			1.01070			0.505349	+	0.862915i	$0.331364\pi$
$338$		−	212.180i		−	0.627750i
$339$	−193.327	+	185.108i	−0.570286	+	0.546041i
$340$	303.320			0.892116
$341$			169.947i			0.498377i
$342$	386.679	+	16.8043i	1.13064	+	0.0491353i
$343$	−338.391			−0.986564
$344$			127.595i			0.370915i
$345$	431.811	+	450.984i	1.25163	+	1.30720i
$346$	348.703			1.00781
$347$			647.225i			1.86520i	0.360911	+	0.932600i	$0.382466\pi$
$347$			647.225i			1.86520i	−0.360911	+	0.932600i	$0.617534\pi$
$348$	−66.3577	+	63.5365i	−0.190683	+	0.182576i
$349$	384.765			1.10248			0.551239	−	0.834348i	$-0.314155\pi$
$349$	384.765			1.10248			0.551239	+	0.834348i	$0.314155\pi$
$350$		−	666.088i		−	1.90311i
$351$	−107.330	+	94.1838i	−0.305784	+	0.268330i
$352$	499.680			1.41954
$353$		−	537.674i		−	1.52316i	−0.648074	−	0.761578i	$-0.724425\pi$
$353$		−	537.674i		−	1.52316i	0.648074	−	0.761578i	$-0.275575\pi$
$354$	−23.9765	−	25.0411i	−0.0677304	−	0.0707377i
$355$	−577.137			−1.62574
$356$		−	207.067i		−	0.581648i
$357$	−287.007	+	274.805i	−0.803941	+	0.769763i
$358$	−405.566			−1.13287
$359$			61.1053i			0.170210i	0.996372	+	0.0851048i	$0.0271225\pi$
$359$			61.1053i			0.170210i	−0.996372	+	0.0851048i	$0.972877\pi$
$360$	−31.5351	+	725.646i	−0.0875974	+	2.01568i
$361$	456.051			1.26330
$362$		−	54.4222i		−	0.150338i
$363$	−549.575	−	573.977i	−1.51398	−	1.58120i
$364$	65.1171			0.178893
$365$		−	390.637i		−	1.07024i
$366$	−218.942	+	209.634i	−0.598202	+	0.572770i
$367$	444.355			1.21078			0.605388	−	0.795931i	$-0.293018\pi$
$367$	444.355			1.21078			0.605388	+	0.795931i	$0.293018\pi$
$368$		−	134.407i		−	0.365236i
$369$	392.586	+	17.0610i	1.06392	+	0.0462357i
$370$	−37.1527			−0.100413
$371$		−	215.414i		−	0.580630i
$372$	−31.1687	−	32.5526i	−0.0837868	−	0.0875071i
$373$	−8.79441			−0.0235775			−0.0117888	−	0.999931i	$-0.503753\pi$
$373$	−8.79441			−0.0235775			−0.0117888	+	0.999931i	$0.503753\pi$
$374$			552.079i			1.47615i
$375$	−758.612	+	726.361i	−2.02297	+	1.93696i
$376$	−374.218			−0.995261
$377$			93.2689i			0.247398i
$378$	−189.976	−	216.493i	−0.502582	−	0.572734i
$379$	−133.349			−0.351844			−0.175922	−	0.984404i	$-0.556291\pi$
$379$	−133.349			−0.351844			−0.175922	+	0.984404i	$0.556291\pi$
$380$			464.137i			1.22141i
$381$	−384.126	−	401.182i	−1.00821	−	1.05297i
$382$	44.4498			0.116361
$383$			612.768i			1.59992i	0.600056	+	0.799958i	$0.295145\pi$
$383$			612.768i			1.59992i	−0.600056	+	0.799958i	$0.704855\pi$
$384$	−16.9641	+	16.2428i	−0.0441772	+	0.0422991i
$385$	−1302.45			−3.38299
$386$			214.628i			0.556031i
$387$	−5.77693	+	132.932i	−0.0149275	+	0.343493i
$388$	101.576			0.261795
$389$			225.199i			0.578918i	0.957190	+	0.289459i	$0.0934754\pi$
$389$			225.199i			0.578918i	−0.957190	+	0.289459i	$0.906525\pi$
$390$	154.370	+	161.224i	0.395821	+	0.413396i
$391$	−415.768			−1.06334
$392$			11.0090i			0.0280842i
$393$	50.2234	−	48.0882i	0.127795	−	0.122362i
$394$	12.1991			0.0309622
$395$			150.178i			0.380198i
$396$	306.711	+	13.3290i	0.774524	+	0.0336592i
$397$	−455.986			−1.14858			−0.574289	−	0.818652i	$-0.694722\pi$
$397$	−455.986			−1.14858			−0.574289	+	0.818652i	$0.694722\pi$
$398$			289.153i			0.726514i
$399$	−420.505	−	439.176i	−1.05390	−	1.10069i
$400$	377.059			0.942647
$401$		−	398.057i		−	0.992661i	−0.868134	−	0.496331i	$-0.834680\pi$
$401$		−	398.057i		−	0.992661i	0.868134	−	0.496331i	$-0.165320\pi$
$402$	−108.842	+	104.215i	−0.270752	+	0.259241i
$403$	−45.7543			−0.113534
$404$		−	114.137i		−	0.282518i
$405$	−65.7081	+	754.568i	−0.162242	+	1.86313i
$406$	−188.131			−0.463376
$407$			51.8767i			0.127461i
$408$	−334.491	−	349.343i	−0.819831	−	0.856232i
$409$	786.441			1.92284			0.961419	−	0.275089i	$-0.0887073\pi$
$409$	786.441			1.92284			0.961419	+	0.275089i	$0.0887073\pi$
$410$		−	614.255i		−	1.49818i
$411$	−330.415	+	316.368i	−0.803930	+	0.769752i
$412$	−185.924			−0.451271
$413$			54.4634i			0.131873i
$414$	13.0848	−	301.091i	0.0316058	−	0.727273i
$415$	473.791			1.14166
$416$			134.527i			0.323383i
$417$	305.414	+	318.975i	0.732408	+	0.764929i
$418$	−844.787			−2.02102
$419$		−	152.439i		−	0.363817i	−0.983315	−	0.181908i	$-0.941773\pi$
$419$		−	152.439i		−	0.363817i	0.983315	−	0.181908i	$-0.0582275\pi$
$420$	249.480	−	238.873i	0.594000	−	0.568746i
$421$	−442.750			−1.05166			−0.525832	−	0.850589i	$-0.676246\pi$
$421$	−442.750			−1.05166			−0.525832	+	0.850589i	$0.676246\pi$
$422$			187.753i			0.444911i
$423$	−389.870	−	16.9429i	−0.921679	−	0.0400543i
$424$	262.200			0.618396
$425$		−	1166.38i		−	2.74441i
$426$	192.657	+	201.212i	0.452247	+	0.472327i
$427$	476.189			1.11520
$428$		−	42.9307i		−	0.100305i
$429$	225.120	−	215.549i	0.524754	−	0.502445i
$430$	207.990			0.483698
$431$		−	38.8281i		−	0.0900885i	−0.998985	−	0.0450442i	$-0.985657\pi$
$431$		−	38.8281i		−	0.0900885i	0.998985	−	0.0450442i	$-0.0143429\pi$
$432$	122.553	−	107.542i	0.283687	−	0.248939i
$433$	−491.902			−1.13603			−0.568016	−	0.823018i	$-0.692289\pi$
$433$	−491.902			−1.13603			−0.568016	+	0.823018i	$0.692289\pi$
$434$		−	92.2900i		−	0.212650i
$435$	342.145	+	357.337i	0.786540	+	0.821463i
$436$	−94.3375			−0.216371
$437$		−	636.204i		−	1.45584i
$438$	−136.191	+	130.401i	−0.310938	+	0.297718i
$439$	164.965			0.375775			0.187887	−	0.982191i	$-0.439836\pi$
$439$	164.965			0.375775			0.187887	+	0.982191i	$0.439836\pi$
$440$		−	1585.34i		−	3.60304i
$441$	−0.498439	+	11.4695i	−0.00113025	+	0.0260078i
$442$	−148.635			−0.336278
$443$		−	243.990i		−	0.550768i	−0.961334	−	0.275384i	$-0.911195\pi$
$443$		−	243.990i		−	0.550768i	0.961334	−	0.275384i	$-0.0888050\pi$
$444$	−9.51434	−	9.93679i	−0.0214287	−	0.0223802i
$445$	−1115.06			−2.50574
$446$		−	399.538i		−	0.895826i
$447$	71.0511	−	68.0304i	0.158951	−	0.152193i
$448$	−442.625			−0.988002
$449$		−	484.609i		−	1.07931i	−0.841887	−	0.539654i	$-0.818555\pi$
$449$		−	484.609i		−	1.07931i	0.841887	−	0.539654i	$-0.181445\pi$
$450$	844.667	+	36.7075i	1.87704	+	0.0815722i
$451$	−857.692			−1.90176
$452$			154.926i			0.342757i
$453$	254.054	+	265.335i	0.560827	+	0.585728i
$454$	33.6034			0.0740163
$455$		−	350.656i		−	0.770672i
$456$	534.561	−	511.835i	1.17228	−	1.12245i
$457$	−744.037			−1.62809			−0.814045	−	0.580802i	$-0.802739\pi$
$457$	−744.037			−1.62809			−0.814045	+	0.580802i	$0.802739\pi$
$458$			284.428i			0.621022i
$459$	−332.664	−	379.099i	−0.724759	−	0.825923i
$460$	361.405			0.785662
$461$			185.525i			0.402441i	0.979546	+	0.201220i	$0.0644907\pi$
$461$			185.525i			0.402441i	−0.979546	+	0.201220i	$0.935509\pi$
$462$	434.779	+	454.084i	0.941080	+	0.982866i
$463$	141.705			0.306058			0.153029	−	0.988222i	$-0.451097\pi$
$463$	141.705			0.306058			0.153029	+	0.988222i	$0.451097\pi$
$464$		−	106.497i		−	0.229520i
$465$	−175.296	+	167.844i	−0.376981	+	0.360954i
$466$	334.563			0.717946
$467$			205.961i			0.441031i	0.975383	+	0.220515i	$0.0707739\pi$
$467$			205.961i			0.441031i	−0.975383	+	0.220515i	$0.929226\pi$
$468$	−3.58854	+	82.5751i	−0.00766783	+	0.176442i
$469$	236.727			0.504748
$470$			610.006i			1.29789i
$471$	320.527	+	334.759i	0.680525	+	0.710741i
$472$	−66.2924			−0.140450
$473$		−	290.419i		−	0.613994i
$474$	52.3577	−	50.1318i	0.110459	−	0.105763i
$475$	1784.78			3.75743
$476$			229.998i			0.483190i
$477$	273.167	+	11.8713i	0.572676	+	0.0248873i
$478$	−294.673			−0.616471
$479$			285.339i			0.595697i	0.954613	+	0.297849i	$0.0962691\pi$
$479$			285.339i			0.595697i	−0.954613	+	0.297849i	$0.903731\pi$
$480$	493.496	+	515.408i	1.02812	+	1.07377i
$481$	−13.9666			−0.0290367
$482$			39.9706i			0.0829266i
$483$	−341.968	+	327.430i	−0.708009	+	0.677908i
$484$	−459.967			−0.950345
$485$		−	546.990i		−	1.12781i
$486$	285.005	−	228.978i	0.586431	−	0.471149i
$487$	−507.398			−1.04188			−0.520942	−	0.853592i	$-0.674419\pi$
$487$	−507.398			−1.04188			−0.520942	+	0.853592i	$0.674419\pi$
$488$			579.613i			1.18773i
$489$	−187.253	−	195.568i	−0.382931	−	0.399934i
$490$	17.9456			0.0366236
$491$			158.306i			0.322416i	0.986920	+	0.161208i	$0.0515390\pi$
$491$			158.306i			0.322416i	−0.986920	+	0.161208i	$0.948461\pi$
$492$	164.288	−	157.303i	0.333918	−	0.319722i
$493$	−329.433			−0.668221
$494$		−	227.440i		−	0.460404i
$495$	71.7770	−	1651.64i	0.145004	−	3.33665i
$496$	52.2435			0.105330
$497$		−	437.626i		−	0.880535i
$498$	−158.159	−	165.181i	−0.317588	−	0.331689i
$499$	703.877			1.41058			0.705288	−	0.708921i	$-0.250818\pi$
$499$	703.877			1.41058			0.705288	+	0.708921i	$0.250818\pi$
$500$			607.928i			1.21586i
$501$	555.040	−	531.443i	1.10786	−	1.06076i
$502$	539.989			1.07568
$503$			785.933i			1.56249i	0.624224	+	0.781245i	$0.285415\pi$
$503$			785.933i			1.56249i	−0.624224	+	0.781245i	$0.714585\pi$
$504$	−550.236	−	23.9121i	−1.09174	−	0.0474447i
$505$	−614.629			−1.21709
$506$			657.801i			1.30000i
$507$	−292.603	−	305.595i	−0.577125	−	0.602751i
$508$	−321.495			−0.632864
$509$			705.767i			1.38658i	0.720661	+	0.693288i	$0.243839\pi$
$509$			705.767i			1.38658i	−0.720661	+	0.693288i	$0.756161\pi$
$510$	−569.457	+	545.247i	−1.11658	+	1.06911i
$511$	296.209			0.579665
$512$		−	362.079i		−	0.707185i
$513$	580.093	−	509.040i	1.13079	−	0.992281i
$514$	27.7548			0.0539977
$515$			1001.20i			1.94408i
$516$	53.2636	+	55.6286i	0.103224	+	0.107807i
$517$	851.759			1.64750
$518$		−	28.1718i		−	0.0543857i
$519$	502.224	−	480.873i	0.967677	−	0.926537i
$520$	426.816			0.820800
$521$			8.30979i			0.0159497i	0.999968	+	0.00797485i	$0.00253850\pi$
$521$			8.30979i			0.0159497i	−0.999968	+	0.00797485i	$0.997462\pi$
$522$	10.3677	−	238.569i	0.0198615	−	0.457029i
$523$	535.808			1.02449			0.512245	−	0.858840i	$-0.328814\pi$
$523$	535.808			1.02449			0.512245	+	0.858840i	$0.328814\pi$
$524$		−	40.2475i		−	0.0768082i
$525$	−918.557	−	959.342i	−1.74963	−	1.82732i
$526$	−256.926			−0.488453
$527$		−	161.608i		−	0.306656i
$528$	−257.048	+	246.120i	−0.486833	+	0.466136i
$529$	33.6137			0.0635420
$530$		−	427.407i		−	0.806429i
$531$	−69.0651	−	3.00143i	−0.130066	−	0.00565241i
$532$	−351.942			−0.661545
$533$		−	230.914i		−	0.433235i
$534$	372.223	+	388.750i	0.697047	+	0.727997i
$535$	−231.182			−0.432116
$536$			288.142i			0.537579i
$537$	−584.123	+	559.289i	−1.08775	+	1.04151i
$538$	−171.235			−0.318281
$539$		−	25.0576i		−	0.0464891i
$540$	289.167	+	329.530i	0.535495	+	0.610241i
$541$	−957.545			−1.76995			−0.884977	−	0.465635i	$-0.845826\pi$
$541$	−957.545			−1.76995			−0.884977	+	0.465635i	$0.845826\pi$
$542$			429.042i			0.791591i
$543$	−75.0500	−	78.3823i	−0.138214	−	0.144351i
$544$	−475.161			−0.873458
$545$			508.008i			0.932126i
$546$	−122.252	+	117.054i	−0.223904	+	0.214385i
$547$	−106.032			−0.193843			−0.0969214	−	0.995292i	$-0.530900\pi$
$547$	−106.032			−0.193843			−0.0969214	+	0.995292i	$0.530900\pi$
$548$			264.785i			0.483184i
$549$	−26.2423	+	603.856i	−0.0478002	+	1.09992i
$550$	−1845.37			−3.35521
$551$		−	504.095i		−	0.914874i
$552$	−398.545	−	416.241i	−0.722002	−	0.754060i
$553$	−113.876			−0.205924
$554$			21.7001i			0.0391699i
$555$	−53.5097	+	51.2348i	−0.0964139	+	0.0923149i
$556$	255.617			0.459742
$557$		−	2.19030i		−	0.00393232i	−0.999998	−	0.00196616i	$-0.999374\pi$
$557$		−	2.19030i		−	0.00393232i	0.999998	−	0.00196616i	$-0.000625849\pi$
$558$	117.033	+	5.08602i	0.209737	+	0.00911473i
$559$	78.1887			0.139872
$560$			400.389i			0.714980i
$561$	761.335	+	795.140i	1.35710	+	1.41736i
$562$	569.031			1.01251
$563$			488.602i			0.867855i	0.900948	+	0.433927i	$0.142873\pi$
$563$			488.602i			0.867855i	−0.900948	+	0.433927i	$0.857127\pi$
$564$	−163.151	+	156.215i	−0.289275	+	0.276977i
$565$	834.279			1.47660
$566$			287.356i			0.507697i
$567$	−572.167	−	49.8245i	−1.00911	−	0.0878740i
$568$	532.675			0.937808
$569$		−	389.337i		−	0.684248i	−0.939655	−	0.342124i	$-0.888854\pi$
$569$		−	389.337i		−	0.684248i	0.939655	−	0.342124i	$-0.111146\pi$
$570$	−834.332	−	871.378i	−1.46374	−	1.52873i
$571$	−522.297			−0.914706			−0.457353	−	0.889285i	$-0.651202\pi$
$571$	−522.297			−0.914706			−0.457353	+	0.889285i	$0.651202\pi$
$572$		−	180.404i		−	0.315391i
$573$	64.0195	−	61.2978i	0.111727	−	0.106977i
$574$	465.772			0.811450
$575$		−	1389.73i		−	2.41693i
$576$	24.3927	−	561.294i	0.0423484	−	0.974468i
$577$	867.206			1.50296			0.751478	−	0.659758i	$-0.229341\pi$
$577$	867.206			1.50296			0.751478	+	0.659758i	$0.229341\pi$
$578$		−	90.1882i		−	0.156035i
$579$	295.979	+	309.121i	0.511190	+	0.533888i
$580$	286.358			0.493721
$581$			359.262i			0.618351i
$582$	−190.701	+	182.594i	−0.327665	+	0.313735i
$583$	−596.794			−1.02366
$584$			360.543i			0.617368i
$585$	444.668	+	19.3243i	0.760115	+	0.0330330i
$586$	678.037			1.15706
$587$		−	698.172i		−	1.18939i	−0.803951	−	0.594695i	$-0.797273\pi$
$587$		−	698.172i		−	1.18939i	0.803951	−	0.594695i	$-0.202727\pi$
$588$	4.59563	+	4.79969i	0.00781570	+	0.00816273i
$589$	247.291			0.419848
$590$			108.062i			0.183156i
$591$	17.5699	−	16.8230i	0.0297291	−	0.0284652i
$592$	15.9475			0.0269383
$593$			227.806i			0.384158i	0.981379	+	0.192079i	$0.0615230\pi$
$593$			227.806i			0.384158i	−0.981379	+	0.192079i	$0.938477\pi$
$594$	−599.785	+	526.320i	−1.00974	+	0.886061i
$595$	1238.54			2.08159
$596$		−	56.9381i		−	0.0955337i
$597$	398.751	+	416.456i	0.667924	+	0.697582i
$598$	−177.098			−0.296150
$599$		−	304.030i		−	0.507562i	−0.967262	−	0.253781i	$-0.918326\pi$
$599$		−	304.030i		−	0.507562i	0.967262	−	0.253781i	$-0.0816742\pi$
$600$	1167.70	−	1118.06i	1.94617	−	1.86343i
$601$	−939.805			−1.56374			−0.781868	−	0.623445i	$-0.785733\pi$
$601$	−939.805			−1.56374			−0.781868	+	0.623445i	$0.785733\pi$
$602$			157.713i			0.261981i
$603$	−13.0458	+	300.194i	−0.0216348	+	0.497834i
$604$	212.631			0.352038
$605$			2476.93i			4.09409i
$606$	205.173	+	214.283i	0.338569	+	0.353602i
$607$	−918.465			−1.51312			−0.756561	−	0.653923i	$-0.773122\pi$
$607$	−918.465			−1.51312			−0.756561	+	0.653923i	$0.773122\pi$
$608$		−	727.088i		−	1.19587i
$609$	−270.958	+	259.438i	−0.444923	+	0.426007i
$610$	944.817			1.54888
$611$			229.317i			0.375314i
$612$	−291.662	−	12.6750i	−0.476571	−	0.0207108i
$613$	−328.504			−0.535895			−0.267947	−	0.963434i	$-0.586345\pi$
$613$	−328.504			−0.535895			−0.267947	+	0.963434i	$0.586345\pi$
$614$		−	248.337i		−	0.404457i
$615$	−847.078	−	884.690i	−1.37736	−	1.43852i
$616$	1202.11			1.95148
$617$			968.760i			1.57011i	0.619424	+	0.785057i	$0.287366\pi$
$617$			968.760i			1.57011i	−0.619424	+	0.785057i	$0.712634\pi$
$618$	349.056	−	334.216i	0.564815	−	0.540803i
$619$	812.768			1.31303			0.656517	−	0.754311i	$-0.272029\pi$
$619$	812.768			1.31303			0.656517	+	0.754311i	$0.272029\pi$
$620$			140.477i			0.226576i
$621$	−396.369	−	451.695i	−0.638275	−	0.727367i
$622$	−889.940			−1.43077
$623$		−	845.514i		−	1.35717i
$624$	−66.2622	−	69.2043i	−0.106189	−	0.110904i
$625$	1712.71			2.74034
$626$			526.758i			0.841466i
$627$	−1216.72	+	1164.99i	−1.94054	+	1.85804i
$628$	268.265			0.427174
$629$		−	49.3312i		−	0.0784281i
$630$	−38.9787	+	896.930i	−0.0618710	+	1.42370i
$631$	−22.1005			−0.0350246			−0.0175123	−	0.999847i	$-0.505575\pi$
$631$	−22.1005			−0.0350246			−0.0175123	+	0.999847i	$0.505575\pi$
$632$		−	138.609i		−	0.219317i
$633$	258.917	+	270.413i	0.409031	+	0.427193i
$634$	−3.51404			−0.00554265
$635$			1731.25i			2.72638i
$636$	114.314	−	109.454i	0.179738	−	0.172097i
$637$	6.74619			0.0105906
$638$			521.208i			0.816940i
$639$	554.955	+	24.1172i	0.868473	+	0.0377421i
$640$	73.2063			0.114385
$641$			482.527i			0.752772i	0.926463	+	0.376386i	$0.122833\pi$
$641$			482.527i			0.752772i	−0.926463	+	0.376386i	$0.877167\pi$
$642$	77.1722	+	80.5987i	0.120206	+	0.125543i
$643$	−1172.14			−1.82292			−0.911462	−	0.411384i	$-0.865045\pi$
$643$	−1172.14			−1.82292			−0.911462	+	0.411384i	$0.865045\pi$
$644$			274.043i			0.425532i
$645$	299.561	−	286.825i	0.464435	−	0.444690i
$646$	803.334			1.24355
$647$		−	212.268i		−	0.328080i	−0.986454	−	0.164040i	$-0.947547\pi$
$647$		−	212.268i		−	0.328080i	0.986454	−	0.164040i	$-0.0524526\pi$
$648$	60.6460	−	696.438i	0.0935896	−	1.07475i
$649$	150.888			0.232493
$650$		−	496.823i		−	0.764343i
$651$	−127.271	−	132.922i	−0.195501	−	0.204181i
$652$	−156.722			−0.240371
$653$		−	370.397i		−	0.567224i	−0.958939	−	0.283612i	$-0.908467\pi$
$653$		−	370.397i		−	0.567224i	0.958939	−	0.283612i	$-0.0915327\pi$
$654$	177.111	−	169.581i	0.270812	−	0.259298i
$655$	−216.733			−0.330890
$656$			263.664i			0.401927i
$657$	−16.3238	+	375.623i	−0.0248460	+	0.571724i
$658$	−462.550			−0.702964
$659$		−	1206.27i		−	1.83046i	−0.402931	−	0.915230i	$-0.632009\pi$
$659$		−	1206.27i		−	1.83046i	0.402931	−	0.915230i	$-0.367991\pi$
$660$	−661.788	−	691.172i	−1.00271	−	1.04723i
$661$	279.734			0.423198			0.211599	−	0.977357i	$-0.432133\pi$
$661$	279.734			0.423198			0.211599	+	0.977357i	$0.432133\pi$
$662$		−	57.0996i		−	0.0862532i
$663$	−214.073	+	204.972i	−0.322886	+	0.309159i
$664$	−437.291			−0.658571
$665$			1895.21i			2.84994i
$666$	35.7247	+	1.55252i	0.0536407	+	0.00233112i
$667$	−392.519			−0.588484
$668$		−	444.792i		−	0.665856i
$669$	−550.976	−	575.441i	−0.823582	−	0.860151i
$670$	469.695			0.701038
$671$		−	1319.26i		−	1.96611i
$672$	−390.819	+	374.204i	−0.581576	+	0.556851i
$673$	−72.6008			−0.107876			−0.0539382	−	0.998544i	$-0.517177\pi$
$673$	−72.6008			−0.107876			−0.0539382	+	0.998544i	$0.517177\pi$
$674$			512.441i			0.760299i
$675$	1267.16	−	1111.96i	1.87728	−	1.64734i
$676$	−244.894			−0.362269
$677$		−	1191.38i		−	1.75979i	−0.475172	−	0.879893i	$-0.657614\pi$
$677$		−	1191.38i		−	1.75979i	0.475172	−	0.879893i	$-0.342386\pi$
$678$	−278.495	−	290.861i	−0.410760	−	0.428999i
$679$	414.766			0.610849
$680$			1507.55i			2.21698i
$681$	48.3978	−	46.3402i	0.0710687	−	0.0680473i
$682$	−255.685			−0.374905
$683$			1224.58i			1.79295i	0.443094	+	0.896475i	$0.353881\pi$
$683$			1224.58i			1.79295i	−0.443094	+	0.896475i	$0.646119\pi$
$684$	19.3952	−	446.298i	0.0283555	−	0.652482i
$685$	1425.87			2.08156
$686$		−	509.111i		−	0.742144i
$687$	392.235	+	409.651i	0.570939	+	0.596290i
$688$	−89.2781			−0.129765
$689$		−	160.673i		−	0.233198i
$690$	−678.507	+	649.661i	−0.983343	+	0.941537i
$691$	−1352.87			−1.95785			−0.978923	−	0.204229i	$-0.934531\pi$
$691$	−1352.87			−1.95785			−0.978923	+	0.204229i	$0.934531\pi$
$692$		−	402.467i		−	0.581600i
$693$	1252.39	+	54.4264i	1.80721	+	0.0785374i
$694$	−973.751			−1.40310
$695$		−	1376.50i		−	1.98057i
$696$	−315.787	−	329.808i	−0.453716	−	0.473862i
$697$	815.606			1.17017
$698$			578.879i			0.829340i
$699$	481.859	−	461.373i	0.689355	−	0.660047i
$700$	−768.787			−1.09827
$701$		−	799.448i		−	1.14044i	−0.821492	−	0.570220i	$-0.806858\pi$
$701$		−	799.448i		−	1.14044i	0.821492	−	0.570220i	$-0.193142\pi$
$702$	−141.700	−	161.479i	−0.201852	−	0.230026i
$703$	75.4862			0.107377
$704$			1226.27i			1.74186i
$705$	841.218	+	878.570i	1.19322	+	1.24620i
$706$	808.932			1.14580
$707$		−	466.056i		−	0.659202i
$708$	−28.9021	+	27.6733i	−0.0408221	+	0.0390866i
$709$	437.816			0.617512			0.308756	−	0.951141i	$-0.400087\pi$
$709$	437.816			0.617512			0.308756	+	0.951141i	$0.400087\pi$
$710$		−	868.304i		−	1.22296i
$711$	6.27559	−	144.406i	0.00882642	−	0.203103i
$712$	1029.15			1.44544
$713$		−	192.555i		−	0.270063i
$714$	−413.445	−	431.803i	−0.579055	−	0.604766i
$715$	−971.476			−1.35871
$716$			468.098i			0.653768i
$717$	−424.407	+	406.364i	−0.591921	+	0.566756i
$718$	−91.9330			−0.128040
$719$			995.948i			1.38519i	0.721329	+	0.692593i	$0.243532\pi$
$719$			995.948i			1.38519i	−0.721329	+	0.692593i	$0.756468\pi$
$720$	−507.734	−	22.0651i	−0.705186	−	0.0306459i
$721$	−759.181			−1.05296
$722$			686.130i			0.950318i
$723$	55.1208	+	57.5682i	0.0762390	+	0.0796241i
$724$	−62.8132			−0.0867585
$725$		−	1101.15i		−	1.51883i
$726$	863.549	−	826.836i	1.18946	−	1.13889i
$727$	810.654			1.11507			0.557533	−	0.830155i	$-0.311748\pi$
$727$	810.654			1.11507			0.557533	+	0.830155i	$0.311748\pi$
$728$			323.642i			0.444563i
$729$	94.7142	−	722.821i	0.129923	−	0.991524i
$730$	587.714			0.805088
$731$			276.169i			0.377796i
$732$	241.956	+	252.699i	0.330541	+	0.345217i
$733$	−753.454			−1.02790			−0.513952	−	0.857819i	$-0.671819\pi$
$733$	−753.454			−1.02790			−0.513952	+	0.857819i	$0.671819\pi$
$734$			668.533i			0.910807i
$735$	25.8463	−	24.7475i	0.0351651	−	0.0336701i
$736$	−566.153			−0.769230
$737$		−	655.841i		−	0.889879i
$738$	−25.6683	+	590.646i	−0.0347809	+	0.800334i
$739$	536.212			0.725592			0.362796	−	0.931869i	$-0.381822\pi$
$739$	536.212			0.725592			0.362796	+	0.931869i	$0.381822\pi$
$740$			42.8810i			0.0579473i
$741$	−313.647	−	327.573i	−0.423275	−	0.442069i
$742$	324.091			0.436780
$743$		−	329.135i		−	0.442981i	−0.975163	−	0.221490i	$-0.928908\pi$
$743$		−	329.135i		−	0.442981i	0.975163	−	0.221490i	$-0.0710922\pi$
$744$	161.792	−	154.913i	0.217462	−	0.208217i
$745$	−306.612			−0.411560
$746$		−	13.2312i		−	0.0177362i
$747$	−455.581	−	19.7986i	−0.609881	−	0.0265042i
$748$	637.200			0.851872
$749$		−	175.299i		−	0.234044i
$750$	−1092.81	−	1141.33i	−1.45708	−	1.52178i
$751$	152.366			0.202884			0.101442	−	0.994841i	$-0.467654\pi$
$751$	152.366			0.202884			0.101442	+	0.994841i	$0.467654\pi$
$752$		−	261.840i		−	0.348192i
$753$	777.728	−	744.663i	1.03284	−	0.988929i
$754$	−140.323			−0.186105
$755$		−	1145.02i		−	1.51658i
$756$	−249.873	+	219.267i	−0.330520	+	0.290036i
$757$	−1062.25			−1.40324			−0.701618	−	0.712554i	$-0.747539\pi$
$757$	−1062.25			−1.40324			−0.701618	+	0.712554i	$0.747539\pi$
$758$		−	200.624i		−	0.264675i
$759$	907.129	+	947.407i	1.19516	+	1.24823i
$760$	−2306.83			−3.03531
$761$			347.069i			0.456069i	0.973653	+	0.228035i	$0.0732299\pi$
$761$			347.069i			0.456069i	−0.973653	+	0.228035i	$0.926770\pi$
$762$	603.580	−	577.919i	0.792099	−	0.758424i
$763$	−385.208			−0.504860
$764$		−	51.3032i		−	0.0671508i
$765$	−68.2550	+	1570.60i	−0.0892223	+	2.05307i
$766$	−921.911			−1.20354
$767$			40.6232i			0.0529638i
$768$	−542.503	−	566.591i	−0.706385	−	0.737749i
$769$	−599.875			−0.780071			−0.390036	−	0.920800i	$-0.627537\pi$
$769$	−599.875			−0.780071			−0.390036	+	0.920800i	$0.627537\pi$
$770$		−	1959.54i		−	2.54486i
$771$	39.9742	−	38.2748i	0.0518473	−	0.0496430i
$772$	247.720			0.320881
$773$		−	915.795i		−	1.18473i	−0.805670	−	0.592364i	$-0.798195\pi$
$773$		−	915.795i		−	1.18473i	0.805670	−	0.592364i	$-0.201805\pi$
$774$	−199.996	−	8.69141i	−0.258393	−	0.0112292i
$775$	540.186			0.697014
$776$			504.851i			0.650581i
$777$	−38.8499	−	40.5749i	−0.0499998	−	0.0522199i
$778$	−338.813			−0.435492
$779$			1248.03i			1.60210i
$780$	186.082	−	178.171i	0.238567	−	0.228425i
$781$	−1212.42			−1.55240
$782$		−	625.524i		−	0.799902i
$783$	−314.062	−	357.900i	−0.401101	−	0.457088i
$784$	−7.70299			−0.00982524
$785$		−	1444.61i		−	1.84027i
$786$	72.3489	+	75.5613i	0.0920469	+	0.0961340i
$787$	−393.797			−0.500377			−0.250188	−	0.968197i	$-0.580493\pi$
$787$	−393.797			−0.500377			−0.250188	+	0.968197i	$0.580493\pi$
$788$		−	14.0800i		−	0.0178680i
$789$	−370.042	+	354.310i	−0.469001	+	0.449062i
$790$	−225.943			−0.286004
$791$			632.610i			0.799760i
$792$	−66.2475	+	1524.40i	−0.0836458	+	1.92475i
$793$	355.181			0.447895
$794$		−	686.032i		−	0.864020i
$795$	−589.408	−	615.579i	−0.741394	−	0.774313i
$796$	333.735			0.419265
$797$			448.991i			0.563352i	0.959510	+	0.281676i	$0.0908903\pi$
$797$			448.991i			0.563352i	−0.959510	+	0.281676i	$0.909110\pi$
$798$	660.741	−	632.650i	0.827996	−	0.792795i
$799$	−809.964			−1.01372
$800$		−	1588.26i		−	1.98533i
$801$	1072.20	+	46.5955i	1.33858	+	0.0581717i
$802$	598.878			0.746731
$803$		−	820.632i		−	1.02196i
$804$	120.283	+	125.624i	0.149606	+	0.156249i
$805$	1475.72			1.83320
$806$		−	68.8375i		−	0.0854063i
$807$	−246.624	+	236.139i	−0.305606	+	0.292613i
$808$	567.279			0.702078
$809$			6.16325i			0.00761835i	0.999993	+	0.00380918i	$0.00121250\pi$
$809$			6.16325i			0.00761835i	−0.999993	+	0.00380918i	$0.998787\pi$
$810$	−1135.25	−	98.8580i	−1.40154	−	0.122047i
$811$	1002.77			1.23647			0.618233	−	0.785995i	$-0.287849\pi$
$811$	1002.77			1.23647			0.618233	+	0.785995i	$0.287849\pi$
$812$			217.137i			0.267410i
$813$	591.663	+	617.934i	0.727753	+	0.760066i
$814$	−78.0487			−0.0958829
$815$			843.948i			1.03552i
$816$	244.435	−	234.043i	0.299553	−	0.286817i
$817$	−422.591			−0.517247
$818$			1183.20i			1.44646i
$819$	−14.6531	+	337.179i	−0.0178914	+	0.411695i
$820$	−708.963			−0.864589
$821$			67.3901i			0.0820829i	0.999157	+	0.0410415i	$0.0130676\pi$
$821$			67.3901i			0.0820829i	−0.999157	+	0.0410415i	$0.986932\pi$
$822$	−475.977	−	497.111i	−0.579047	−	0.604758i
$823$	−77.1659			−0.0937617			−0.0468808	−	0.998900i	$-0.514928\pi$
$823$	−77.1659			−0.0937617			−0.0468808	+	0.998900i	$0.514928\pi$
$824$		−	924.070i		−	1.12144i
$825$	−2657.81	+	2544.82i	−3.22159	+	3.08463i
$826$	−81.9403			−0.0992013
$827$		−	1.39503i		−	0.00168686i	−1.00000		0.000843428i	$-0.999732\pi$
$827$		−	1.39503i		−	0.00168686i	1.00000		0.000843428i	$-0.000268471\pi$
$828$	−347.514	−	15.1022i	−0.419703	−	0.0182394i
$829$	939.784			1.13364			0.566818	−	0.823843i	$-0.308174\pi$
$829$	939.784			1.13364			0.566818	+	0.823843i	$0.308174\pi$
$830$			712.820i			0.858819i
$831$	29.9251	+	31.2539i	0.0360110	+	0.0376100i
$832$	−330.146			−0.396810
$833$			23.8281i			0.0286051i
$834$	−479.899	+	459.497i	−0.575419	+	0.550955i
$835$	−2395.21			−2.86851
$836$			975.038i			1.16631i
$837$	175.573	−	154.067i	0.209764	−	0.184071i
$838$	229.345			0.273682
$839$			856.708i			1.02111i	0.859846	+	0.510553i	$0.170559\pi$
$839$			856.708i			1.02111i	−0.859846	+	0.510553i	$0.829441\pi$
$840$	1187.24	+	1239.95i	1.41338	+	1.47614i
$841$	529.988			0.630188
$842$		−	666.119i		−	0.791115i
$843$	819.555	−	784.712i	0.972188	−	0.930857i
$844$	216.701			0.256754
$845$			1318.76i			1.56066i
$846$	25.4907	−	586.561i	0.0301309	−	0.693334i
$847$	−1878.18			−2.21745
$848$			183.461i			0.216346i
$849$	396.274	+	413.869i	0.466754	+	0.487478i
$850$	1754.82			2.06449
$851$		−	58.7781i		−	0.0690694i
$852$	232.235	−	222.362i	0.272576	−	0.260988i
$853$	1318.09			1.54524			0.772619	−	0.634870i	$-0.218946\pi$
$853$	1318.09			1.54524			0.772619	+	0.634870i	$0.218946\pi$
$854$			716.427i			0.838908i
$855$	−2403.32	−	104.443i	−2.81090	−	0.122156i
$856$	213.372			0.249267
$857$		−	393.329i		−	0.458960i	−0.973313	−	0.229480i	$-0.926297\pi$
$857$		−	393.329i		−	0.458960i	0.973313	−	0.229480i	$-0.0737026\pi$
$858$	324.294	+	338.693i	0.377965	+	0.394747i
$859$	635.290			0.739569			0.369785	−	0.929118i	$-0.379432\pi$
$859$	635.290			0.739569			0.369785	+	0.929118i	$0.379432\pi$
$860$		−	240.058i		−	0.279138i
$861$	670.835	−	642.315i	0.779135	−	0.746010i
$862$	58.4170			0.0677692
$863$		−	612.527i		−	0.709764i	−0.934911	−	0.354882i	$-0.884521\pi$
$863$		−	612.527i		−	0.709764i	0.934911	−	0.354882i	$-0.115479\pi$
$864$	−452.991	−	516.221i	−0.524295	−	0.597478i
$865$	−2167.29			−2.50553
$866$		−	740.067i		−	0.854581i
$867$	−124.372	−	129.895i	−0.143452	−	0.149821i
$868$	−106.520			−0.122718
$869$			315.487i			0.363046i
$870$	−537.614	+	514.758i	−0.617947	+	0.591675i
$871$	176.570			0.202721
$872$		−	468.873i		−	0.537698i
$873$	−22.8574	+	525.966i	−0.0261826	+	0.602481i
$874$	957.171			1.09516
$875$			2482.35i			2.83697i
$876$	150.506	+	157.189i	0.171811	+	0.179439i
$877$	−333.916			−0.380748			−0.190374	−	0.981712i	$-0.560970\pi$
$877$	−333.916			−0.380748			−0.190374	+	0.981712i	$0.560970\pi$
$878$			248.190i			0.282677i
$879$	976.553	−	935.036i	1.11098	−	1.06375i
$880$	1109.26			1.26052
$881$		−	72.8170i		−	0.0826526i	−0.999146	−	0.0413263i	$-0.986842\pi$
$881$		−	72.8170i		−	0.0826526i	0.999146	−	0.0413263i	$-0.0131583\pi$
$882$	−17.2558	−	0.749903i	−0.0195644	−	0.000850230i
$883$	−94.4807			−0.107000			−0.0534998	−	0.998568i	$-0.517038\pi$
$883$	−94.4807			−0.107000			−0.0534998	+	0.998568i	$0.517038\pi$
$884$			171.552i			0.194063i
$885$	149.021	+	155.638i	0.168385	+	0.175862i
$886$	367.084			0.414316
$887$			128.565i			0.144944i	0.997370	+	0.0724721i	$0.0230888\pi$
$887$			128.565i			0.144944i	−0.997370	+	0.0724721i	$0.976911\pi$
$888$	49.3874	−	47.2878i	0.0556165	−	0.0532520i
$889$	−1312.76			−1.47667
$890$		−	1677.60i		−	1.88495i
$891$	−138.037	+	1585.16i	−0.154923	+	1.77908i
$892$	−461.140			−0.516973
$893$		−	1239.40i		−	1.38791i
$894$	102.352	+	106.897i	0.114488	+	0.119571i
$895$	2520.71			2.81644
$896$			55.5102i			0.0619534i
$897$	−255.068	+	244.224i	−0.284357	+	0.272267i
$898$	729.095			0.811910
$899$		−	152.571i		−	0.169712i
$900$	42.3672	−	974.900i	0.0470746	−	1.08322i
$901$	567.510			0.629867
$902$		−	1290.40i		−	1.43060i
$903$	217.491	+	227.148i	0.240854	+	0.251548i
$904$	−770.008			−0.851779
$905$			338.249i			0.373756i
$906$	−399.197	+	382.226i	−0.440615	+	0.421883i
$907$	829.839			0.914927			0.457464	−	0.889228i	$-0.348758\pi$
$907$	829.839			0.914927			0.457464	+	0.889228i	$0.348758\pi$
$908$		−	38.7845i		−	0.0427142i
$909$	591.006	+	25.6839i	0.650172	+	0.0282551i
$910$	527.563			0.579739
$911$		−	952.043i		−	1.04505i	−0.852623	−	0.522526i	$-0.824990\pi$
$911$		−	952.043i		−	1.04505i	0.852623	−	0.522526i	$-0.175010\pi$
$912$	358.131	+	374.032i	0.392687	+	0.410123i
$913$	995.319			1.09016
$914$		−	1119.41i		−	1.22473i
$915$	1360.79	−	1302.93i	1.48720	−	1.42397i
$916$	328.282			0.358386
$917$		−	164.343i		−	0.179218i
$918$	570.355	−	500.494i	0.621302	−	0.545201i
$919$	−909.562			−0.989730			−0.494865	−	0.868970i	$-0.664782\pi$
$919$	−909.562			−0.989730			−0.494865	+	0.868970i	$0.664782\pi$
$920$			1796.24i			1.95243i
$921$	−342.464	−	357.670i	−0.371840	−	0.388350i
$922$	−279.123			−0.302736
$923$		−	326.417i		−	0.353648i
$924$	524.096	−	501.815i	0.567204	−	0.543089i
$925$	164.893			0.178263
$926$			213.195i			0.230232i
$927$	41.8378	−	962.719i	0.0451325	−	1.03853i
$928$	−448.591			−0.483395
$929$		−	466.979i		−	0.502669i	−0.967900	−	0.251334i	$-0.919131\pi$
$929$		−	466.979i		−	0.502669i	0.967900	−	0.251334i	$-0.0808694\pi$
$930$	−252.521	−	263.734i	−0.271528	−	0.283585i
$931$	−36.4615			−0.0391638
$932$		−	386.147i		−	0.414320i
$933$	−1281.75	+	1227.26i	−1.37379	+	1.31539i
$934$	−309.870			−0.331766
$935$		−	3431.33i		−	3.66987i
$936$	−410.411	−	17.8356i	−0.438474	−	0.0190552i
$937$	1117.18			1.19229			0.596145	−	0.802877i	$-0.296698\pi$
$937$	1117.18			1.19229			0.596145	+	0.802877i	$0.296698\pi$
$938$			356.156i			0.379698i
$939$	726.416	+	758.670i	0.773606	+	0.807956i
$940$	704.059			0.748998
$941$			1024.26i			1.08848i	0.838930	+	0.544240i	$0.183182\pi$
$941$			1024.26i			1.08848i	−0.838930	+	0.544240i	$0.816818\pi$
$942$	−503.646	+	482.234i	−0.534656	+	0.511926i
$943$	971.793			1.03053
$944$		−	46.3848i		−	0.0491364i
$945$	1180.76	+	1345.57i	1.24948	+	1.42388i
$946$	436.936			0.461878
$947$			1630.09i			1.72132i	0.509177	+	0.860662i	$0.329950\pi$
$947$			1630.09i			1.72132i	−0.509177	+	0.860662i	$0.670050\pi$
$948$	−57.8612	−	60.4304i	−0.0610351	−	0.0637451i
$949$	220.937			0.232810
$950$			2685.20i			2.82653i
$951$	−5.06114	+	4.84597i	−0.00532192	+	0.00509566i
$952$	−1143.13			−1.20077
$953$			1428.36i			1.49880i	0.662117	+	0.749401i	$0.269658\pi$
$953$			1428.36i			1.49880i	−0.662117	+	0.749401i	$0.730342\pi$
$954$	−17.8603	+	410.980i	−0.0187215	+	0.430797i
$955$	−276.268			−0.289286
$956$			340.107i			0.355760i
$957$	718.762	+	750.677i	0.751058	+	0.784406i
$958$	−429.293			−0.448114
$959$			1081.19i			1.12742i
$960$	−1264.87	+	1211.10i	−1.31758	+	1.26156i
$961$	−886.154			−0.922117
$962$		−	21.0128i		−	0.0218429i
$963$	222.297	+	9.66055i	0.230838	+	0.0100317i
$964$	46.1334			0.0478562
$965$		−	1333.97i		−	1.38236i
$966$	−492.619	−	514.492i	−0.509958	−	0.532601i
$967$	−1274.51			−1.31800			−0.659002	−	0.752141i	$-0.729021\pi$
$967$	−1274.51			−1.31800			−0.659002	+	0.752141i	$0.729021\pi$
$968$		−	2286.11i		−	2.36168i
$969$	1157.01	−	1107.82i	1.19403	−	1.14327i
$970$	822.947			0.848399
$971$			870.609i			0.896611i	0.893881	+	0.448305i	$0.147972\pi$
$971$			870.609i			0.896611i	−0.893881	+	0.448305i	$0.852028\pi$
$972$	−264.283	−	328.948i	−0.271896	−	0.338424i
$973$	1043.76			1.07272
$974$		−	763.381i		−	0.783759i
$975$	−685.135	−	715.556i	−0.702702	−	0.733904i
$976$	−405.555			−0.415528
$977$			546.656i			0.559525i	0.960069	+	0.279763i	$0.0902558\pi$
$977$			546.656i			0.559525i	−0.960069	+	0.279763i	$0.909744\pi$
$978$	294.232	−	281.723i	0.300851	−	0.288060i
$979$	−2342.46			−2.39271
$980$		−	20.7125i		−	0.0211352i
$981$	21.2285	−	488.483i	0.0216396	−	0.497944i
$982$	−238.172			−0.242538
$983$			1542.54i			1.56921i	0.619994	+	0.784607i	$0.287135\pi$
$983$			1542.54i			1.56921i	−0.619994	+	0.784607i	$0.712865\pi$
$984$	781.821	+	816.535i	0.794533	+	0.829812i
$985$	−75.8209			−0.0769755
$986$		−	495.633i		−	0.502670i
$987$	−666.194	+	637.872i	−0.674969	+	0.646273i
$988$	−262.507			−0.265695
$989$			329.054i			0.332714i
$990$	2484.90	+	107.989i	2.51000	+	0.109080i
$991$	−234.842			−0.236975			−0.118487	−	0.992956i	$-0.537805\pi$
$991$	−234.842			−0.236975			−0.118487	+	0.992956i	$0.537805\pi$
$992$		−	220.062i		−	0.221837i
$993$	−78.7423	−	82.2386i	−0.0792974	−	0.0828183i
$994$	658.410			0.662384
$995$		−	1797.17i		−	1.80620i
$996$	−190.649	+	182.544i	−0.191415	+	0.183277i
$997$	71.0515			0.0712653			0.0356326	−	0.999365i	$-0.488655\pi$
$997$	71.0515			0.0712653			0.0356326	+	0.999365i	$0.488655\pi$
$998$			1058.98i			1.06111i
$999$	53.5940	−	47.0295i	0.0536477	−	0.0470766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.26	yes	38
3.2	odd	2	inner	177.3.b.a.119.13	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.13	✓	38	3.2	odd	2	inner
177.3.b.a.119.26	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)

\(f(q)\)	\(=\)	\(q+1.50450i q^{2} +(2.07476 + 2.16688i) q^{3} +1.73647 q^{4} -9.35091i q^{5} +(-3.26008 + 3.12148i) q^{6} +7.09053 q^{7} +8.63054i q^{8} +(-0.390753 + 8.99151i) q^{9} +O(q^{10})\)	\(q+1.50450i q^{2} +(2.07476 + 2.16688i) q^{3} +1.73647 q^{4} -9.35091i q^{5} +(-3.26008 + 3.12148i) q^{6} +7.09053 q^{7} +8.63054i q^{8} +(-0.390753 + 8.99151i) q^{9} +14.0685 q^{10} -19.6440i q^{11} +(3.60276 + 3.76273i) q^{12} +5.28870 q^{13} +10.6677i q^{14} +(20.2623 - 19.4009i) q^{15} -6.03878 q^{16} +18.6801i q^{17} +(-13.5278 - 0.587888i) q^{18} -28.5841 q^{19} -16.2376i q^{20} +(14.7111 + 15.3643i) q^{21} +29.5544 q^{22} +22.2573i q^{23} +(-18.7014 + 17.9063i) q^{24} -62.4396 q^{25} +7.95686i q^{26} +(-20.2943 + 17.8085i) q^{27} +12.3125 q^{28} +17.6355i q^{29} +(29.1887 + 30.4847i) q^{30} -8.65134 q^{31} +25.4368i q^{32} +(42.5662 - 40.7565i) q^{33} -28.1042 q^{34} -66.3029i q^{35} +(-0.678531 + 15.6135i) q^{36} -2.64085 q^{37} -43.0049i q^{38} +(10.9728 + 11.4600i) q^{39} +80.7034 q^{40} -43.6618i q^{41} +(-23.1157 + 22.1329i) q^{42} +14.7841 q^{43} -34.1112i q^{44} +(84.0789 + 3.65389i) q^{45} -33.4861 q^{46} +43.3598i q^{47} +(-12.5290 - 13.0853i) q^{48} +1.27559 q^{49} -93.9405i q^{50} +(-40.4775 + 38.7567i) q^{51} +9.18367 q^{52} -30.3805i q^{53} +(-26.7929 - 30.5328i) q^{54} -183.689 q^{55} +61.1951i q^{56} +(-59.3051 - 61.9384i) q^{57} -26.5327 q^{58} +7.68115i q^{59} +(35.1849 - 33.6891i) q^{60} +67.1584 q^{61} -13.0160i q^{62} +(-2.77064 + 63.7546i) q^{63} -62.4248 q^{64} -49.4541i q^{65} +(61.3183 + 64.0409i) q^{66} +33.3864 q^{67} +32.4374i q^{68} +(-48.2289 + 46.1785i) q^{69} +99.7529 q^{70} -61.7198i q^{71} +(-77.6016 - 3.37240i) q^{72} +41.7753 q^{73} -3.97316i q^{74} +(-129.547 - 135.299i) q^{75} -49.6355 q^{76} -139.286i q^{77} +(-17.2416 + 16.5086i) q^{78} -16.0603 q^{79} +56.4681i q^{80} +(-80.6946 - 7.02691i) q^{81} +65.6893 q^{82} +50.6679i q^{83} +(25.5455 + 26.6797i) q^{84} +174.676 q^{85} +22.2427i q^{86} +(-38.2141 + 36.5894i) q^{87} +169.538 q^{88} -119.246i q^{89} +(-5.49729 + 126.497i) q^{90} +37.4996 q^{91} +38.6491i q^{92} +(-17.9494 - 18.7464i) q^{93} -65.2349 q^{94} +267.287i q^{95} +(-55.1185 + 52.7752i) q^{96} +58.4958 q^{97} +1.91912i q^{98} +(176.629 + 7.67594i) 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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