LMFDB - Embedded newform 177.3.b.a.119.1

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			119.1
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.77988i q^{2} +(2.45428 - 1.72526i) q^{3} -10.2875 q^{4} -1.62741i q^{5} +(-6.52128 - 9.27688i) q^{6} -7.78423 q^{7} +23.7661i q^{8} +(3.04695 - 8.46854i) q^{9} +O(q^{10})$	\(q-3.77988i q^{2} +(2.45428 - 1.72526i) q^{3} -10.2875 q^{4} -1.62741i q^{5} +(-6.52128 - 9.27688i) q^{6} -7.78423 q^{7} +23.7661i q^{8} +(3.04695 - 8.46854i) q^{9} -6.15142 q^{10} +2.72883i q^{11} +(-25.2484 + 17.7486i) q^{12} +9.61474 q^{13} +29.4235i q^{14} +(-2.80771 - 3.99412i) q^{15} +48.6829 q^{16} -27.3790i q^{17} +(-32.0101 - 11.5171i) q^{18} -27.7110 q^{19} +16.7420i q^{20} +(-19.1047 + 13.4298i) q^{21} +10.3146 q^{22} -3.53027i q^{23} +(41.0027 + 58.3285i) q^{24} +22.3515 q^{25} -36.3426i q^{26} +(-7.13238 - 26.0409i) q^{27} +80.0804 q^{28} -6.30381i q^{29} +(-15.0973 + 10.6128i) q^{30} +39.9365 q^{31} -88.9515i q^{32} +(4.70794 + 6.69729i) q^{33} -103.489 q^{34} +12.6681i q^{35} +(-31.3455 + 87.1202i) q^{36} +44.2391 q^{37} +104.744i q^{38} +(23.5972 - 16.5879i) q^{39} +38.6772 q^{40} -50.1258i q^{41} +(50.7632 + 72.2134i) q^{42} -53.9729 q^{43} -28.0728i q^{44} +(-13.7818 - 4.95864i) q^{45} -13.3440 q^{46} +47.0156i q^{47} +(119.481 - 83.9907i) q^{48} +11.5943 q^{49} -84.4862i q^{50} +(-47.2359 - 67.1957i) q^{51} -98.9118 q^{52} -9.97840i q^{53} +(-98.4316 + 26.9595i) q^{54} +4.44092 q^{55} -185.001i q^{56} +(-68.0104 + 47.8086i) q^{57} -23.8277 q^{58} +7.68115i q^{59} +(28.8843 + 41.0895i) q^{60} -71.5942 q^{61} -150.955i q^{62} +(-23.7182 + 65.9211i) q^{63} -141.494 q^{64} -15.6471i q^{65} +(25.3150 - 17.7955i) q^{66} +86.8469 q^{67} +281.662i q^{68} +(-6.09063 - 8.66425i) q^{69} +47.8841 q^{70} -119.483i q^{71} +(201.264 + 72.4140i) q^{72} +16.4375 q^{73} -167.219i q^{74} +(54.8569 - 38.5622i) q^{75} +285.077 q^{76} -21.2418i q^{77} +(-62.7005 - 89.1948i) q^{78} +127.483 q^{79} -79.2271i q^{80} +(-62.4322 - 51.6064i) q^{81} -189.470 q^{82} +125.458i q^{83} +(196.540 - 138.160i) q^{84} -44.5569 q^{85} +204.011i q^{86} +(-10.8757 - 15.4713i) q^{87} -64.8535 q^{88} +137.168i q^{89} +(-18.7431 + 52.0935i) q^{90} -74.8434 q^{91} +36.3177i q^{92} +(98.0153 - 68.9009i) q^{93} +177.714 q^{94} +45.0971i q^{95} +(-153.464 - 218.312i) q^{96} +0.0640655 q^{97} -43.8251i q^{98} +(23.1092 + 8.31459i) 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 $

$2$		−	3.77988i		−	1.88994i	−0.327155	−	0.944971i	$-0.606090\pi$
$2$		−	3.77988i		−	1.88994i	0.327155	−	0.944971i	$-0.393910\pi$
$3$	2.45428	−	1.72526i	0.818092	−	0.575087i
$3$	2.45428	−	1.72526i	0.818092	−	0.575087i
$4$	−10.2875			−2.57188
$5$		−	1.62741i		−	0.325482i	−0.986669	−	0.162741i	$-0.947966\pi$
$5$		−	1.62741i		−	0.325482i	0.986669	−	0.162741i	$-0.0520335\pi$
$6$	−6.52128	−	9.27688i	−1.08688	−	1.54615i
$7$	−7.78423			−1.11203			−0.556017	−	0.831171i	$-0.687671\pi$
$7$	−7.78423			−1.11203			−0.556017	+	0.831171i	$0.687671\pi$
$8$			23.7661i			2.97076i
$9$	3.04695	−	8.46854i	0.338550	−	0.940948i
$10$	−6.15142			−0.615142
$11$			2.72883i			0.248075i	0.992278	+	0.124038i	$0.0395843\pi$
$11$			2.72883i			0.248075i	−0.992278	+	0.124038i	$0.960416\pi$
$12$	−25.2484	+	17.7486i	−2.10403	+	1.47905i
$13$	9.61474			0.739595			0.369798	−	0.929112i	$-0.379427\pi$
$13$	9.61474			0.739595			0.369798	+	0.929112i	$0.379427\pi$
$14$			29.4235i			2.10168i
$15$	−2.80771	−	3.99412i	−0.187181	−	0.266274i
$16$	48.6829			3.04268
$17$		−	27.3790i		−	1.61053i	−0.592915	−	0.805265i	$-0.702023\pi$
$17$		−	27.3790i		−	1.61053i	0.592915	−	0.805265i	$-0.297977\pi$
$18$	−32.0101	−	11.5171i	−1.77834	−	0.639840i
$19$	−27.7110			−1.45847			−0.729236	−	0.684262i	$-0.760124\pi$
$19$	−27.7110			−1.45847			−0.729236	+	0.684262i	$0.760124\pi$
$20$			16.7420i			0.837101i
$21$	−19.1047	+	13.4298i	−0.909746	+	0.639516i
$22$	10.3146			0.468847
$23$		−	3.53027i		−	0.153490i	−0.997051	−	0.0767449i	$-0.975547\pi$
$23$		−	3.53027i		−	0.153490i	0.997051	−	0.0767449i	$-0.0244527\pi$
$24$	41.0027	+	58.3285i	1.70845	+	2.43036i
$25$	22.3515			0.894061
$26$		−	36.3426i		−	1.39779i
$27$	−7.13238	−	26.0409i	−0.264162	−	0.964478i
$28$	80.0804			2.86002
$29$		−	6.30381i		−	0.217373i	−0.994076	−	0.108686i	$-0.965336\pi$
$29$		−	6.30381i		−	0.217373i	0.994076	−	0.108686i	$-0.0346644\pi$
$30$	−15.0973	+	10.6128i	−0.503243	+	0.353760i
$31$	39.9365			1.28828			0.644138	−	0.764910i	$-0.277216\pi$
$31$	39.9365			1.28828			0.644138	+	0.764910i	$0.277216\pi$
$32$		−	88.9515i		−	2.77973i
$33$	4.70794	+	6.69729i	0.142665	+	0.202948i
$34$	−103.489			−3.04381
$35$			12.6681i			0.361947i
$36$	−31.3455	+	87.1202i	−0.870710	+	2.42001i
$37$	44.2391			1.19565			0.597825	−	0.801626i	$-0.296032\pi$
$37$	44.2391			1.19565			0.597825	+	0.801626i	$0.296032\pi$
$38$			104.744i			2.75643i
$39$	23.5972	−	16.5879i	0.605057	−	0.425332i
$40$	38.6772			0.966929
$41$		−	50.1258i		−	1.22258i	−0.791406	−	0.611290i	$-0.790651\pi$
$41$		−	50.1258i		−	1.22258i	0.791406	−	0.611290i	$-0.209349\pi$
$42$	50.7632	+	72.2134i	1.20865	+	1.71937i
$43$	−53.9729			−1.25518			−0.627591	−	0.778543i	$-0.715959\pi$
$43$	−53.9729			−1.25518			−0.627591	+	0.778543i	$0.715959\pi$
$44$		−	28.0728i		−	0.638019i
$45$	−13.7818	−	4.95864i	−0.306262	−	0.110192i
$46$	−13.3440			−0.290087
$47$			47.0156i			1.00033i	0.865929	+	0.500166i	$0.166728\pi$
$47$			47.0156i			1.00033i	−0.865929	+	0.500166i	$0.833272\pi$
$48$	119.481	−	83.9907i	2.48920	−	1.74981i
$49$	11.5943			0.236618
$50$		−	84.4862i		−	1.68972i
$51$	−47.2359	−	67.1957i	−0.926195	−	1.31756i
$52$	−98.9118			−1.90215
$53$		−	9.97840i		−	0.188272i	−0.995559	−	0.0941358i	$-0.969991\pi$
$53$		−	9.97840i		−	0.188272i	0.995559	−	0.0941358i	$-0.0300088\pi$
$54$	−98.4316	+	26.9595i	−1.82281	+	0.499251i
$55$	4.44092			0.0807440
$56$		−	185.001i		−	3.30358i
$57$	−68.0104	+	47.8086i	−1.19316	+	0.838748i
$58$	−23.8277			−0.410822
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	28.8843	+	41.0895i	0.481406	+	0.684826i
$61$	−71.5942			−1.17368			−0.586838	−	0.809705i	$-0.699627\pi$
$61$	−71.5942			−1.17368			−0.586838	+	0.809705i	$0.699627\pi$
$62$		−	150.955i		−	2.43477i
$63$	−23.7182	+	65.9211i	−0.376479	+	1.04637i
$64$	−141.494			−2.21085
$65$		−	15.6471i		−	0.240725i
$66$	25.3150	−	17.7955i	0.383560	−	0.269628i
$67$	86.8469			1.29622			0.648111	−	0.761546i	$-0.275559\pi$
$67$	86.8469			1.29622			0.648111	+	0.761546i	$0.275559\pi$
$68$			281.662i			4.14209i
$69$	−6.09063	−	8.66425i	−0.0882700	−	0.125569i
$70$	47.8841			0.684059
$71$		−	119.483i		−	1.68285i	−0.540372	−	0.841426i	$-0.681717\pi$
$71$		−	119.483i		−	1.68285i	0.540372	−	0.841426i	$-0.318283\pi$
$72$	201.264	+	72.4140i	2.79533	+	1.00575i
$73$	16.4375			0.225172			0.112586	−	0.993642i	$-0.464087\pi$
$73$	16.4375			0.225172			0.112586	+	0.993642i	$0.464087\pi$
$74$		−	167.219i		−	2.25971i
$75$	54.8569	−	38.5622i	0.731425	−	0.514163i
$76$	285.077			3.75101
$77$		−	21.2418i		−	0.275868i
$78$	−62.7005	−	89.1948i	−0.803852	−	1.14352i
$79$	127.483			1.61371			0.806854	−	0.590751i	$-0.201169\pi$
$79$	127.483			1.61371			0.806854	+	0.590751i	$0.201169\pi$
$80$		−	79.2271i		−	0.990339i
$81$	−62.4322	−	51.6064i	−0.770768	−	0.637116i
$82$	−189.470			−2.31061
$83$			125.458i			1.51155i	0.654833	+	0.755774i	$0.272739\pi$
$83$			125.458i			1.51155i	−0.654833	+	0.755774i	$0.727261\pi$
$84$	196.540	−	138.160i	2.33976	−	1.64476i
$85$	−44.5569			−0.524199
$86$			204.011i			2.37222i
$87$	−10.8757	−	15.4713i	−0.125008	−	0.177831i
$88$	−64.8535			−0.736971
$89$			137.168i			1.54121i	0.637313	+	0.770605i	$0.280046\pi$
$89$			137.168i			1.54121i	−0.637313	+	0.770605i	$0.719954\pi$
$90$	−18.7431	+	52.0935i	−0.208256	+	0.578817i
$91$	−74.8434			−0.822455
$92$			36.3177i			0.394757i
$93$	98.0153	−	68.9009i	1.05393	−	0.740870i
$94$	177.714			1.89057
$95$			45.0971i			0.474707i
$96$	−153.464	−	218.312i	−1.59859	−	2.27408i
$97$	0.0640655			0.000660469			0.000330234	−	1.00000i	$-0.499895\pi$
$97$	0.0640655			0.000660469			0.000330234		1.00000i	$0.499895\pi$
$98$		−	43.8251i		−	0.447195i
$99$	23.1092	+	8.31459i	0.233426	+	0.0839858i
$100$	−229.942			−2.29942
$101$		−	131.783i		−	1.30478i	−0.757881	−	0.652392i	$-0.773765\pi$
$101$		−	131.783i		−	1.30478i	0.757881	−	0.652392i	$-0.226235\pi$
$102$	−253.992	+	178.546i	−2.49012	+	1.75045i
$103$	55.5732			0.539546			0.269773	−	0.962924i	$-0.413051\pi$
$103$	55.5732			0.539546			0.269773	+	0.962924i	$0.413051\pi$
$104$			228.505i			2.19716i
$105$	21.8559	+	31.0911i	0.208151	+	0.296106i
$106$	−37.7172			−0.355822
$107$		−	9.15117i		−	0.0855250i	−0.999085	−	0.0427625i	$-0.986384\pi$
$107$		−	9.15117i		−	0.0855250i	0.999085	−	0.0427625i	$-0.0136159\pi$
$108$	73.3744	+	267.896i	0.679393	+	2.48052i
$109$	40.4952			0.371516			0.185758	−	0.982596i	$-0.440526\pi$
$109$	40.4952			0.371516			0.185758	+	0.982596i	$0.440526\pi$
$110$		−	16.7862i		−	0.152601i
$111$	108.575	−	76.3240i	0.978153	−	0.687603i
$112$	−378.959			−3.38356
$113$			116.150i			1.02787i	0.857828	+	0.513937i	$0.171813\pi$
$113$			116.150i			1.02787i	−0.857828	+	0.513937i	$0.828187\pi$
$114$	180.711	+	257.071i	1.58518	+	2.25501i
$115$	−5.74519			−0.0499582
$116$			64.8505i			0.559056i
$117$	29.2956	−	81.4228i	0.250390	−	0.695921i
$118$	29.0338			0.246049
$119$			213.125i			1.79096i
$120$	94.9245	−	66.7282i	0.791037	−	0.556068i
$121$	113.554			0.938459
$122$			270.618i			2.21818i
$123$	−86.4801	−	123.023i	−0.703090	−	1.00018i
$124$	−410.848			−3.31329
$125$		−	77.0604i		−	0.616483i
$126$	249.174	+	89.6519i	1.97757	+	0.711523i
$127$	−66.5716			−0.524186			−0.262093	−	0.965043i	$-0.584413\pi$
$127$	−66.5716			−0.524186			−0.262093	+	0.965043i	$0.584413\pi$
$128$			179.027i			1.39864i
$129$	−132.464	+	93.1173i	−1.02686	+	0.721839i
$130$	−59.1443			−0.454956
$131$			66.2829i			0.505976i	0.967469	+	0.252988i	$0.0814133\pi$
$131$			66.2829i			0.505976i	−0.967469	+	0.252988i	$0.918587\pi$
$132$	−48.4330	−	68.8985i	−0.366916	−	0.521959i
$133$	215.709			1.62187
$134$		−	328.271i		−	2.44978i
$135$	−42.3793	+	11.6073i	−0.313921	+	0.0859800i
$136$	650.692			4.78450
$137$			49.1043i			0.358425i	0.983810	+	0.179213i	$0.0573550\pi$
$137$			49.1043i			0.358425i	−0.983810	+	0.179213i	$0.942645\pi$
$138$	−32.7498	+	23.0219i	−0.237318	+	0.166825i
$139$	227.787			1.63875			0.819377	−	0.573254i	$-0.194319\pi$
$139$	227.787			1.63875			0.819377	+	0.573254i	$0.194319\pi$
$140$		−	130.324i		−	0.930884i
$141$	81.1142	+	115.389i	0.575278	+	0.818364i
$142$	−451.630			−3.18049
$143$			26.2370i			0.183475i
$144$	148.334	−	412.273i	1.03010	−	2.86301i
$145$	−10.2589			−0.0707509
$146$		−	62.1319i		−	0.425561i
$147$	28.4556	−	20.0032i	0.193576	−	0.136076i
$148$	−455.110			−3.07507
$149$			23.3606i			0.156783i	0.996923	+	0.0783914i	$0.0249784\pi$
$149$			23.3606i			0.156783i	−0.996923	+	0.0783914i	$0.975022\pi$
$150$	−145.761	−	207.352i	−0.971738	−	1.38235i
$151$	133.696			0.885406			0.442703	−	0.896668i	$-0.354020\pi$
$151$	133.696			0.885406			0.442703	+	0.896668i	$0.354020\pi$
$152$		−	658.581i		−	4.33277i
$153$	−231.860	−	83.4225i	−1.51543	−	0.545245i
$154$	−80.2916			−0.521374
$155$		−	64.9932i		−	0.419311i
$156$	−242.757	+	170.649i	−1.55613	+	1.09390i
$157$	194.685			1.24003			0.620016	−	0.784589i	$-0.287126\pi$
$157$	194.685			1.24003			0.620016	+	0.784589i	$0.287126\pi$
$158$		−	481.870i		−	3.04981i
$159$	−17.2153	−	24.4897i	−0.108273	−	0.154024i
$160$	−144.761			−0.904754
$161$			27.4804i			0.170686i
$162$	−195.066	+	235.986i	−1.20411	+	1.45671i
$163$	27.5035			0.168733			0.0843665	−	0.996435i	$-0.473113\pi$
$163$	27.5035			0.168733			0.0843665	+	0.996435i	$0.473113\pi$
$164$			515.670i			3.14433i
$165$	10.8992	−	7.66175i	0.0660561	−	0.0464348i
$166$	474.218			2.85674
$167$		−	83.9120i		−	0.502467i	−0.967927	−	0.251233i	$-0.919164\pi$
$167$		−	83.9120i		−	0.502467i	0.967927	−	0.251233i	$-0.0808362\pi$
$168$	−319.174	−	454.043i	−1.89985	−	2.70264i
$169$	−76.5567			−0.452999
$170$			168.420i			0.990705i
$171$	−84.4339	+	234.671i	−0.493766	+	1.37235i
$172$	555.247			3.22818
$173$		−	237.213i		−	1.37118i	−0.727990	−	0.685588i	$-0.759545\pi$
$173$		−	237.213i		−	1.37118i	0.727990	−	0.685588i	$-0.240455\pi$
$174$	−58.4797	+	41.1089i	−0.336090	+	0.236258i
$175$	−173.990			−0.994226
$176$			132.847i			0.754814i
$177$	13.2520	+	18.8517i	0.0748699	+	0.106507i
$178$	518.478			2.91280
$179$			226.853i			1.26733i	0.773606	+	0.633667i	$0.218451\pi$
$179$			226.853i			1.26733i	−0.773606	+	0.633667i	$0.781549\pi$
$180$	141.780	+	51.0121i	0.787669	+	0.283400i
$181$	−108.540			−0.599666			−0.299833	−	0.953992i	$-0.596931\pi$
$181$	−108.540			−0.599666			−0.299833	+	0.953992i	$0.596931\pi$
$182$			282.899i			1.55439i
$183$	−175.712	+	123.519i	−0.960175	+	0.674966i
$184$	83.9005			0.455981
$185$		−	71.9952i		−	0.389163i
$186$	−260.438	−	370.486i	−1.40020	−	1.99186i
$187$	74.7126			0.399532
$188$		−	483.674i		−	2.57273i
$189$	55.5201	+	202.709i	0.293757	+	1.07253i
$190$	170.462			0.897168
$191$			0.101903i			0.000533522i	1.00000		0.000266761i	$8.49127e-5\pi$
$191$			0.101903i			0.000533522i	−1.00000		0.000266761i	$0.999915\pi$
$192$	−347.266	+	244.115i	−1.80868	+	1.27143i
$193$	−162.720			−0.843108			−0.421554	−	0.906803i	$-0.638515\pi$
$193$	−162.720			−0.843108			−0.421554	+	0.906803i	$0.638515\pi$
$194$		−	0.242160i		−	0.00124825i
$195$	−26.9954	−	38.4024i	−0.138438	−	0.196935i
$196$	−119.276			−0.608553
$197$			208.516i			1.05846i	0.848479	+	0.529230i	$0.177519\pi$
$197$			208.516i			1.05846i	−0.848479	+	0.529230i	$0.822481\pi$
$198$	31.4282	−	87.3499i	0.158728	−	0.441161i
$199$	−43.8940			−0.220573			−0.110286	−	0.993900i	$-0.535177\pi$
$199$	−43.8940			−0.220573			−0.110286	+	0.993900i	$0.535177\pi$
$200$			531.208i			2.65604i
$201$	213.146	−	149.834i	1.06043	−	0.745441i
$202$	−498.125			−2.46597
$203$			49.0703i			0.241726i
$204$	485.941	+	691.277i	2.38206	+	3.38861i
$205$	−81.5753			−0.397928
$206$		−	210.060i		−	1.01971i
$207$	−29.8962	−	10.7565i	−0.144426	−	0.0519640i
$208$	468.074			2.25035
$209$		−	75.6184i		−	0.361811i
$210$	117.521	−	82.6126i	0.559623	−	0.393393i
$211$	−297.742			−1.41110			−0.705550	−	0.708660i	$-0.749300\pi$
$211$	−297.742			−1.41110			−0.705550	+	0.708660i	$0.749300\pi$
$212$			102.653i			0.484212i
$213$	−206.139	−	293.243i	−0.967786	−	1.37673i
$214$	−34.5904			−0.161637
$215$			87.8360i			0.408540i
$216$	618.890	−	169.509i	2.86523	−	0.784762i
$217$	−310.875			−1.43261
$218$		−	153.067i		−	0.702143i
$219$	40.3422	−	28.3590i	0.184211	−	0.129493i
$220$	−45.6860			−0.207664
$221$		−	263.242i		−	1.19114i
$222$	−288.496	−	410.401i	−1.29953	−	1.84865i
$223$	−297.595			−1.33451			−0.667254	−	0.744830i	$-0.732530\pi$
$223$	−297.595			−1.33451			−0.667254	+	0.744830i	$0.732530\pi$
$224$			692.419i			3.09116i
$225$	68.1040	−	189.285i	0.302684	−	0.841266i
$226$	439.032			1.94262
$227$			66.8134i			0.294332i	0.989112	+	0.147166i	$0.0470152\pi$
$227$			66.8134i			0.294332i	−0.989112	+	0.147166i	$0.952985\pi$
$228$	699.658	−	491.832i	3.06867	−	2.15716i
$229$	92.6270			0.404485			0.202242	−	0.979336i	$-0.435177\pi$
$229$	92.6270			0.404485			0.202242	+	0.979336i	$0.435177\pi$
$230$			21.7162i			0.0944181i
$231$	−36.6477	−	52.1333i	−0.158648	−	0.225685i
$232$	149.817			0.645762
$233$			31.5019i			0.135201i	0.997712	+	0.0676007i	$0.0215344\pi$
$233$			31.5019i			0.135201i	−0.997712	+	0.0676007i	$0.978466\pi$
$234$	−307.769	−	110.734i	−1.31525	−	0.473222i
$235$	76.5138			0.325590
$236$		−	79.0199i		−	0.334830i
$237$	312.878	−	219.941i	1.32016	−	0.928022i
$238$	805.586			3.38482
$239$		−	208.641i		−	0.872973i	−0.899711	−	0.436487i	$-0.856223\pi$
$239$		−	208.641i		−	0.872973i	0.899711	−	0.436487i	$-0.143777\pi$
$240$	−136.687	−	194.445i	−0.569531	−	0.810189i
$241$	368.093			1.52736			0.763679	−	0.645596i	$-0.223391\pi$
$241$	368.093			1.52736			0.763679	+	0.645596i	$0.223391\pi$
$242$		−	429.219i		−	1.77363i
$243$	−242.260	−	18.9446i	−0.996956	−	0.0779612i
$244$	736.527			3.01855
$245$		−	18.8687i		−	0.0770150i
$246$	−465.011	+	326.885i	−1.89029	+	1.32880i
$247$	−266.434			−1.07868
$248$			949.135i			3.82716i
$249$	216.449	+	307.910i	0.869272	+	1.23659i
$250$	−291.279			−1.16512
$251$			262.798i			1.04701i	0.852024	+	0.523503i	$0.175375\pi$
$251$			262.798i			1.04701i	−0.852024	+	0.523503i	$0.824625\pi$
$252$	244.001	−	678.164i	0.968258	−	2.69113i
$253$	9.63348			0.0380770
$254$			251.633i			0.990680i
$255$	−109.355	+	76.8723i	−0.428843	+	0.301460i
$256$	110.722			0.432506
$257$			86.3269i			0.335902i	0.985795	+	0.167951i	$0.0537151\pi$
$257$			86.3269i			0.335902i	−0.985795	+	0.167951i	$0.946285\pi$
$258$	351.972	+	500.700i	1.36423	+	1.94070i
$259$	−344.367			−1.32960
$260$			160.970i			0.619116i
$261$	−53.3840	−	19.2074i	−0.204536	−	0.0735915i
$262$	250.541			0.956265
$263$			198.233i			0.753737i	0.926267	+	0.376868i	$0.122999\pi$
$263$			198.233i			0.753737i	−0.926267	+	0.376868i	$0.877001\pi$
$264$	−159.168	+	111.889i	−0.602911	+	0.423823i
$265$	−16.2390			−0.0612791
$266$		−	815.353i		−	3.06524i
$267$	236.650	+	336.647i	0.886330	+	1.26085i
$268$	−893.439			−3.33373
$269$		−	265.983i		−	0.988784i	−0.869239	−	0.494392i	$-0.835391\pi$
$269$		−	265.983i		−	0.988784i	0.869239	−	0.494392i	$-0.164609\pi$
$270$	43.8743	+	160.189i	0.162497	+	0.593291i
$271$	−55.0011			−0.202956			−0.101478	−	0.994838i	$-0.532357\pi$
$271$	−55.0011			−0.202956			−0.101478	+	0.994838i	$0.532357\pi$
$272$		−	1332.89i		−	4.90033i
$273$	−183.686	+	129.124i	−0.672844	+	0.472983i
$274$	185.608			0.677403
$275$			60.9934i			0.221794i
$276$	62.6574	+	89.1336i	0.227020	+	0.322948i
$277$	57.8384			0.208803			0.104401	−	0.994535i	$-0.466707\pi$
$277$	57.8384			0.208803			0.104401	+	0.994535i	$0.466707\pi$
$278$		−	861.008i		−	3.09715i
$279$	121.685	−	338.204i	0.436146	−	1.21220i
$280$	−301.072			−1.07526
$281$		−	204.730i		−	0.728578i	−0.931286	−	0.364289i	$-0.881312\pi$
$281$		−	204.730i		−	0.728578i	0.931286	−	0.364289i	$-0.118688\pi$
$282$	436.158	−	306.602i	1.54666	−	1.08724i
$283$	−245.355			−0.866980			−0.433490	−	0.901158i	$-0.642718\pi$
$283$	−245.355			−0.866980			−0.433490	+	0.901158i	$0.642718\pi$
$284$			1229.18i			4.32809i
$285$	77.8043	+	110.681i	0.272998	+	0.388354i
$286$	99.1726			0.346757
$287$			390.191i			1.35955i
$288$	−753.289	−	271.031i	−2.61559	−	0.941078i
$289$	−460.611			−1.59381
$290$			38.7774i			0.133715i
$291$	0.157234	−	0.110530i	0.000540324	−	0.000379827i
$292$	−169.101			−0.579114
$293$			444.473i			1.51697i	0.651690	+	0.758486i	$0.274060\pi$
$293$			444.473i			1.51697i	−0.651690	+	0.758486i	$0.725940\pi$
$294$	−75.6097	−	107.559i	−0.257176	−	0.365846i
$295$	12.5004			0.0423742
$296$			1051.39i			3.55199i
$297$	71.0611	−	19.4630i	0.239263	−	0.0655320i
$298$	88.3005			0.296310
$299$		−	33.9426i		−	0.113520i
$300$	−564.341	+	396.710i	−1.88114	+	1.32237i
$301$	420.137			1.39581
$302$		−	505.356i		−	1.67337i
$303$	−227.361	−	323.433i	−0.750365	−	1.06743i
$304$	−1349.05			−4.43767
$305$			116.513i			0.382010i
$306$	−315.327	+	876.404i	−1.03048	+	2.86407i
$307$	−383.922			−1.25056			−0.625281	−	0.780400i	$-0.715015\pi$
$307$	−383.922			−1.25056			−0.625281	+	0.780400i	$0.715015\pi$
$308$			218.526i			0.709499i
$309$	136.392	−	95.8783i	0.441398	−	0.310286i
$310$	−245.667			−0.792473
$311$			99.6589i			0.320447i	0.987081	+	0.160223i	$0.0512214\pi$
$311$			99.6589i			0.320447i	−0.987081	+	0.160223i	$0.948779\pi$
$312$	394.230	+	560.814i	1.26356	+	1.79748i
$313$	−230.288			−0.735743			−0.367872	−	0.929877i	$-0.619913\pi$
$313$	−230.288			−0.735743			−0.367872	+	0.929877i	$0.619913\pi$
$314$		−	735.887i		−	2.34359i
$315$	107.281	+	38.5992i	0.340574	+	0.122537i
$316$	−1311.48			−4.15026
$317$		−	455.975i		−	1.43841i	−0.694799	−	0.719204i	$-0.744507\pi$
$317$		−	455.975i		−	1.43841i	0.694799	−	0.719204i	$-0.255493\pi$
$318$	−92.5684	+	65.0720i	−0.291096	+	0.204629i
$319$	17.2020			0.0539247
$320$			230.270i			0.719592i
$321$	−15.7882	−	22.4595i	−0.0491843	−	0.0699673i
$322$	103.873			0.322586
$323$			758.699i			2.34891i
$324$	642.272	+	530.902i	1.98232	+	1.63859i
$325$	214.904			0.661244
$326$		−	103.960i		−	0.318895i
$327$	99.3864	−	69.8648i	0.303934	−	0.213654i
$328$	1191.29			3.63199
$329$		−	365.981i		−	1.11240i
$330$	−28.9605	−	41.1979i	−0.0877591	−	0.124842i
$331$	−578.942			−1.74907			−0.874535	−	0.484963i	$-0.838833\pi$
$331$	−578.942			−1.74907			−0.874535	+	0.484963i	$0.838833\pi$
$332$		−	1290.66i		−	3.88752i
$333$	134.794	−	374.640i	0.404788	−	1.12505i
$334$	−317.177			−0.949633
$335$		−	141.336i		−	0.421897i
$336$	−930.071	+	653.804i	−2.76807	+	1.94584i
$337$	161.282			0.478581			0.239291	−	0.970948i	$-0.423085\pi$
$337$	161.282			0.478581			0.239291	+	0.970948i	$0.423085\pi$
$338$			289.376i			0.856141i
$339$	200.389	+	285.064i	0.591117	+	0.840895i
$340$	458.380			1.34818
$341$			108.980i			0.319589i
$342$	887.030	+	319.150i	2.59366	+	0.933188i
$343$	291.175			0.848906
$344$		−	1282.72i		−	3.72885i
$345$	−14.1003	+	9.91196i	−0.0408704	+	0.0287303i
$346$	−896.639			−2.59144
$347$			332.681i			0.958735i	0.877614	+	0.479367i	$0.159134\pi$
$347$			332.681i			0.958735i	−0.877614	+	0.479367i	$0.840866\pi$
$348$	111.884	+	159.161i	0.321506	+	0.457360i
$349$	135.069			0.387018			0.193509	−	0.981099i	$-0.438013\pi$
$349$	135.069			0.387018			0.193509	+	0.981099i	$0.438013\pi$
$350$			657.660i			1.87903i
$351$	−68.5760	−	250.377i	−0.195373	−	0.713324i
$352$	242.733			0.689583
$353$		−	286.915i		−	0.812789i	−0.913698	−	0.406395i	$-0.866786\pi$
$353$		−	286.915i		−	0.812789i	0.913698	−	0.406395i	$-0.133214\pi$
$354$	71.2571	−	50.0909i	0.201291	−	0.141500i
$355$	−194.447			−0.547738
$356$		−	1411.11i		−	3.96380i
$357$	367.696	+	523.067i	1.02996	+	1.46517i
$358$	857.478			2.39519
$359$		−	376.147i		−	1.04776i	−0.851791	−	0.523881i	$-0.824483\pi$
$359$		−	376.147i		−	1.04776i	0.851791	−	0.523881i	$-0.175517\pi$
$360$	117.847	−	327.539i	0.327354	−	0.909831i
$361$	406.897			1.12714
$362$			410.267i			1.13333i
$363$	278.692	−	195.909i	0.767746	−	0.539695i
$364$	769.953			2.11525
$365$		−	26.7506i		−	0.0732893i
$366$	466.886	+	664.171i	1.27565	+	1.81467i
$367$	−226.341			−0.616732			−0.308366	−	0.951268i	$-0.599782\pi$
$367$	−226.341			−0.616732			−0.308366	+	0.951268i	$0.599782\pi$
$368$		−	171.864i		−	0.467021i
$369$	−424.492	−	152.731i	−1.15039	−	0.413905i
$370$	−272.133			−0.735495
$371$			77.6742i			0.209364i
$372$	−1008.33	+	708.820i	−2.71058	+	1.90543i
$373$	5.23611			0.0140378			0.00701891	−	0.999975i	$-0.497766\pi$
$373$	5.23611			0.0140378			0.00701891	+	0.999975i	$0.497766\pi$
$374$		−	282.405i		−	0.755093i
$375$	−132.949	−	189.128i	−0.354531	−	0.504340i
$376$	−1117.38			−2.97175
$377$		−	60.6095i		−	0.160768i
$378$	766.215	−	209.859i	2.02702	−	0.555184i
$379$	99.8976			0.263582			0.131791	−	0.991278i	$-0.457927\pi$
$379$	99.8976			0.263582			0.131791	+	0.991278i	$0.457927\pi$
$380$		−	463.937i		−	1.22089i
$381$	−163.385	+	114.853i	−0.428832	+	0.301452i
$382$	0.385180			0.00100833
$383$			526.256i			1.37404i	0.726641	+	0.687018i	$0.241081\pi$
$383$			526.256i			1.37404i	−0.726641	+	0.687018i	$0.758919\pi$
$384$	308.867	+	439.381i	0.804342	+	1.14422i
$385$	−34.5692			−0.0897900
$386$			615.062i			1.59342i
$387$	−164.453	+	457.071i	−0.424942	+	1.18106i
$388$	−0.659074			−0.00169865
$389$		−	12.8702i		−	0.0330854i	−0.999863	−	0.0165427i	$-0.994734\pi$
$389$		−	12.8702i		−	0.0330854i	0.999863	−	0.0165427i	$-0.00526595\pi$
$390$	−145.157	+	102.039i	−0.372196	+	0.261640i
$391$	−96.6552			−0.247200
$392$			275.551i			0.702936i
$393$	114.355	+	162.676i	0.290980	+	0.413935i
$394$	788.168			2.00043
$395$		−	207.467i		−	0.525233i
$396$	−237.736	−	85.5365i	−0.600343	−	0.216001i
$397$	−197.743			−0.498092			−0.249046	−	0.968492i	$-0.580117\pi$
$397$	−197.743			−0.498092			−0.249046	+	0.968492i	$0.580117\pi$
$398$			165.914i			0.416870i
$399$	529.409	−	372.154i	1.32684	−	0.932716i
$400$	1088.14			2.72035
$401$			37.8334i			0.0943475i	0.998887	+	0.0471738i	$0.0150214\pi$
$401$			37.8334i			0.0943475i	−0.998887	+	0.0471738i	$0.984979\pi$
$402$	−566.353	−	805.668i	−1.40884	−	2.00415i
$403$	383.979			0.952803
$404$			1355.72i			3.35575i
$405$	−83.9848	+	101.603i	−0.207370	+	0.250871i
$406$	185.480			0.456847
$407$			120.721i			0.296611i
$408$	1596.98	−	1122.61i	3.91416	−	2.75150i
$409$	201.720			0.493203			0.246601	−	0.969117i	$-0.420686\pi$
$409$	201.720			0.493203			0.246601	+	0.969117i	$0.420686\pi$
$410$			308.345i			0.752061i
$411$	84.7177	+	120.515i	0.206126	+	0.293225i
$412$	−571.711			−1.38765
$413$		−	59.7918i		−	0.144774i
$414$	−40.6585	+	113.004i	−0.0982088	+	0.272957i
$415$	204.172			0.491982
$416$		−	855.245i		−	2.05588i
$417$	559.052	−	392.992i	1.34065	−	0.942427i
$418$	−285.829			−0.683801
$419$		−	362.156i		−	0.864335i	−0.901793	−	0.432168i	$-0.857749\pi$
$419$		−	362.156i		−	0.864335i	0.901793	−	0.432168i	$-0.142251\pi$
$420$	−224.842	−	319.851i	−0.535339	−	0.761549i
$421$	459.569			1.09161			0.545806	−	0.837911i	$-0.316223\pi$
$421$	459.569			1.09161			0.545806	+	0.837911i	$0.316223\pi$
$422$			1125.43i			2.66690i
$423$	398.154	+	143.254i	0.941262	+	0.338663i
$424$	237.147			0.559310
$425$		−	611.963i		−	1.43991i
$426$	−1108.42	+	779.179i	−2.60194	+	1.82906i
$427$	557.306			1.30517
$428$			94.1428i			0.219960i
$429$	45.2656	+	64.3928i	0.105514	+	0.150100i
$430$	332.010			0.772116
$431$			290.802i			0.674714i	0.941377	+	0.337357i	$0.109533\pi$
$431$			290.802i			0.674714i	−0.941377	+	0.337357i	$0.890467\pi$
$432$	−347.225	−	1267.75i	−0.803761	−	2.93460i
$433$	−687.774			−1.58839			−0.794196	−	0.607662i	$-0.792108\pi$
$433$	−687.774			−1.58839			−0.794196	+	0.607662i	$0.792108\pi$
$434$			1175.07i			2.70754i
$435$	−25.1781	+	17.6993i	−0.0578808	+	0.0406879i
$436$	−416.595			−0.955493
$437$			97.8270i			0.223861i
$438$	−107.194	−	152.489i	−0.244735	−	0.348148i
$439$	335.293			0.763765			0.381882	−	0.924211i	$-0.375276\pi$
$439$	335.293			0.763765			0.381882	+	0.924211i	$0.375276\pi$
$440$			105.543i			0.239871i
$441$	35.3272	−	98.1867i	0.0801071	−	0.222646i
$442$	−995.025			−2.25119
$443$		−	303.866i		−	0.685928i	−0.939348	−	0.342964i	$-0.888569\pi$
$443$		−	303.866i		−	0.685928i	0.939348	−	0.342964i	$-0.111431\pi$
$444$	−1116.97	+	785.184i	−2.51569	+	1.76843i
$445$	223.228			0.501636
$446$			1124.87i			2.52214i
$447$	40.3032	+	57.3335i	0.0901637	+	0.128263i
$448$	1101.43			2.45854
$449$			144.114i			0.320967i	0.987039	+	0.160483i	$0.0513053\pi$
$449$			144.114i			0.320967i	−0.987039	+	0.160483i	$0.948695\pi$
$450$	−715.474	−	257.425i	−1.58994	−	0.572056i
$451$	136.785			0.303292
$452$		−	1194.89i		−	2.64357i
$453$	328.128	−	230.661i	0.724344	−	0.509185i
$454$	252.547			0.556271
$455$			121.801i			0.267694i
$456$	−1136.22	−	1616.34i	−2.49172	−	3.54460i
$457$	463.300			1.01379			0.506893	−	0.862009i	$-0.330794\pi$
$457$	463.300			1.01379			0.506893	+	0.862009i	$0.330794\pi$
$458$		−	350.119i		−	0.764452i
$459$	−712.975	+	195.277i	−1.55332	+	0.425441i
$460$	59.1038			0.128486
$461$			390.113i			0.846232i	0.906076	+	0.423116i	$0.139064\pi$
$461$			390.113i			0.846232i	−0.906076	+	0.423116i	$0.860936\pi$
$462$	−197.058	+	138.524i	−0.426532	+	0.299835i
$463$	335.403			0.724413			0.362207	−	0.932098i	$-0.382023\pi$
$463$	335.403			0.724413			0.362207	+	0.932098i	$0.382023\pi$
$464$		−	306.888i		−	0.661396i
$465$	−112.130	−	159.511i	−0.241140	−	0.343035i
$466$	119.074			0.255523
$467$		−	434.067i		−	0.929481i	−0.885447	−	0.464740i	$-0.846148\pi$
$467$		−	434.067i		−	0.929481i	0.885447	−	0.464740i	$-0.153852\pi$
$468$	−301.379	+	837.638i	−0.643973	+	1.78983i
$469$	−676.037			−1.44144
$470$		−	289.213i		−	0.615347i
$471$	477.811	−	335.883i	1.01446	−	0.713126i
$472$	−182.551			−0.386760
$473$		−	147.283i		−	0.311380i
$474$	−831.352	−	1182.64i	−1.75391	−	2.49503i
$475$	−619.383			−1.30396
$476$		−	2192.52i		−	4.60614i
$477$	−84.5024	−	30.4037i	−0.177154	−	0.0637394i
$478$	−788.637			−1.64987
$479$			627.445i			1.30991i	0.755669	+	0.654953i	$0.227312\pi$
$479$			627.445i			1.30991i	−0.755669	+	0.654953i	$0.772688\pi$
$480$	−355.283	+	249.750i	−0.740172	+	0.520312i
$481$	425.347			0.884298
$482$		−	1391.35i		−	2.88662i
$483$	47.4109	+	67.4445i	0.0981592	+	0.139637i
$484$	−1168.18			−2.41360
$485$		−	0.104261i		−	0.000214971i
$486$	−71.6083	+	915.716i	−0.147342	+	1.88419i
$487$	199.609			0.409875			0.204938	−	0.978775i	$-0.434301\pi$
$487$	199.609			0.409875			0.204938	+	0.978775i	$0.434301\pi$
$488$		−	1701.51i		−	3.48671i
$489$	67.5011	−	47.4507i	0.138039	−	0.0970361i
$490$	−71.3214			−0.145554
$491$		−	681.187i		−	1.38735i	−0.720290	−	0.693674i	$-0.755991\pi$
$491$		−	681.187i		−	1.38735i	0.720290	−	0.693674i	$-0.244009\pi$
$492$	889.665	+	1265.60i	1.80826	+	2.57235i
$493$	−172.592			−0.350085
$494$			1007.09i			2.03864i
$495$	13.5313	−	37.6081i	0.0273359	−	0.0759760i
$496$	1944.23			3.91981
$497$			930.080i			1.87139i
$498$	1163.86	−	818.150i	2.33707	−	1.64287i
$499$	844.498			1.69238			0.846190	−	0.532881i	$-0.178891\pi$
$499$	844.498			1.69238			0.846190	+	0.532881i	$0.178891\pi$
$500$			792.760i			1.58552i
$501$	−144.770	−	205.943i	−0.288962	−	0.411064i
$502$	993.347			1.97878
$503$		−	306.629i		−	0.609600i	−0.952416	−	0.304800i	$-0.901410\pi$
$503$		−	306.629i		−	0.609600i	0.952416	−	0.304800i	$-0.0985896\pi$
$504$	−1566.68	−	563.688i	−3.10850	−	1.11843i
$505$	−214.466			−0.424684
$506$		−	36.4134i		−	0.0719633i
$507$	−187.891	+	132.080i	−0.370595	+	0.260514i
$508$	684.856			1.34814
$509$			509.953i			1.00187i	0.865484	+	0.500936i	$0.167011\pi$
$509$			509.953i			1.00187i	−0.865484	+	0.500936i	$0.832989\pi$
$510$	290.568	+	413.349i	0.569742	+	0.810488i
$511$	−127.954			−0.250398
$512$			297.591i			0.581233i
$513$	197.645	+	721.619i	0.385273	+	1.40666i
$514$	326.306			0.634836
$515$		−	90.4405i		−	0.175613i
$516$	1362.73	−	957.945i	2.64095	−	1.85648i
$517$	−128.297			−0.248158
$518$			1301.67i			2.51287i
$519$	−409.255	−	582.187i	−0.788545	−	1.12175i
$520$	371.871			0.715137
$521$			55.1618i			0.105877i	0.998598	+	0.0529384i	$0.0168587\pi$
$521$			55.1618i			0.105877i	−0.998598	+	0.0529384i	$0.983141\pi$
$522$	−72.6017	+	201.785i	−0.139084	+	0.386562i
$523$	−855.419			−1.63560			−0.817801	−	0.575502i	$-0.804807\pi$
$523$	−855.419			−1.63560			−0.817801	+	0.575502i	$0.804807\pi$
$524$		−	681.886i		−	1.30131i
$525$	−427.019	+	300.177i	−0.813369	+	0.571766i
$526$	749.297			1.42452
$527$		−	1093.42i		−	2.07481i
$528$	229.196	+	326.044i	0.434084	+	0.617507i
$529$	516.537			0.976441
$530$			61.3813i			0.115814i
$531$	65.0481	+	23.4041i	0.122501	+	0.0440754i
$532$	−2219.11			−4.17125
$533$		−	481.947i		−	0.904215i
$534$	1272.49	−	894.509i	2.38294	−	1.67511i
$535$	−14.8927			−0.0278369
$536$			2064.01i			3.85077i
$537$	391.381	+	556.760i	0.728828	+	1.03680i
$538$	−1005.38			−1.86874
$539$			31.6388i			0.0586991i
$540$	435.977	−	119.410i	0.807366	−	0.221130i
$541$	436.832			0.807452			0.403726	−	0.914880i	$-0.367715\pi$
$541$	436.832			0.807452			0.403726	+	0.914880i	$0.367715\pi$
$542$			207.898i			0.383575i
$543$	−266.386	+	187.259i	−0.490582	+	0.344860i
$544$	−2435.40			−4.47684
$545$		−	65.9023i		−	0.120922i
$546$	488.075	+	694.313i	0.893910	+	1.27164i
$547$	515.478			0.942372			0.471186	−	0.882034i	$-0.343826\pi$
$547$	515.478			0.942372			0.471186	+	0.882034i	$0.343826\pi$
$548$		−	505.161i		−	0.921826i
$549$	−218.144	+	606.298i	−0.397348	+	1.10437i
$550$	230.548			0.419178
$551$			174.685i			0.317032i
$552$	205.915	−	144.750i	0.373035	−	0.262229i
$553$	−992.357			−1.79450
$554$		−	218.622i		−	0.394625i
$555$	−124.210	−	176.696i	−0.223803	−	0.318371i
$556$	−2343.36			−4.21468
$557$			79.9557i			0.143547i	0.997421	+	0.0717735i	$0.0228659\pi$
$557$			79.9557i			0.143547i	−0.997421	+	0.0717735i	$0.977134\pi$
$558$	−1278.37	−	459.954i	−2.29099	−	0.824290i
$559$	−518.935			−0.928328
$560$			616.722i			1.10129i
$561$	183.365	−	128.899i	0.326854	−	0.229766i
$562$	−773.857			−1.37697
$563$		−	83.9743i		−	0.149155i	−0.997215	−	0.0745775i	$-0.976239\pi$
$563$		−	83.9743i		−	0.149155i	0.997215	−	0.0745775i	$-0.0237608\pi$
$564$	−834.464	−	1187.07i	−1.47955	−	2.10473i
$565$	189.023			0.334555
$566$			927.415i			1.63854i
$567$	485.987	+	401.716i	0.857120	+	0.708494i
$568$	2839.63			4.99935
$569$		−	269.476i		−	0.473596i	−0.971559	−	0.236798i	$-0.923902\pi$
$569$		−	269.476i		−	0.473596i	0.971559	−	0.236798i	$-0.0760980\pi$
$570$	418.361	−	294.091i	0.733966	−	0.515949i
$571$	−301.627			−0.528243			−0.264122	−	0.964489i	$-0.585082\pi$
$571$	−301.627			−0.528243			−0.264122	+	0.964489i	$0.585082\pi$
$572$		−	269.913i		−	0.471876i
$573$	0.175809	+	0.250098i	0.000306822	+	0.000436470i
$574$	1474.88			2.56947
$575$		−	78.9068i		−	0.137229i
$576$	−431.126	+	1198.25i	−0.748483	+	2.08030i
$577$	−31.1811			−0.0540400			−0.0270200	−	0.999635i	$-0.508602\pi$
$577$	−31.1811			−0.0540400			−0.0270200	+	0.999635i	$0.508602\pi$
$578$			1741.05i			3.01220i
$579$	−399.359	+	280.734i	−0.689740	+	0.484860i
$580$	105.538			0.181963
$581$		−	976.598i		−	1.68089i
$582$	−0.417789	−	0.594327i	−0.000717851	−	0.00102118i
$583$	27.2293			0.0467055
$584$			390.656i			0.668931i
$585$	−132.508	−	47.6760i	−0.226510	−	0.0814975i
$586$	1680.05			2.86699
$587$		−	250.764i		−	0.427196i	−0.976922	−	0.213598i	$-0.931482\pi$
$587$		−	250.764i		−	0.427196i	0.976922	−	0.213598i	$-0.0685183\pi$
$588$	−292.737	+	205.783i	−0.497853	+	0.349971i
$589$	−1106.68			−1.87891
$590$		−	47.2500i		−	0.0800847i
$591$	359.745	+	511.757i	0.608706	+	0.865917i
$592$	2153.69			3.63799
$593$		−	517.385i		−	0.872488i	−0.899828	−	0.436244i	$-0.856308\pi$
$593$		−	517.385i		−	0.872488i	0.899828	−	0.436244i	$-0.143692\pi$
$594$	−73.5679	−	268.603i	−0.123852	−	0.452193i
$595$	346.841			0.582927
$596$		−	240.323i		−	0.403226i
$597$	−107.728	+	75.7286i	−0.180449	+	0.126849i
$598$	−128.299			−0.214547
$599$			716.875i			1.19679i	0.801202	+	0.598393i	$0.204194\pi$
$599$			716.875i			1.19679i	−0.801202	+	0.598393i	$0.795806\pi$
$600$	916.473	+	1303.73i	1.52745	+	2.17289i
$601$	−459.122			−0.763931			−0.381965	−	0.924177i	$-0.624753\pi$
$601$	−459.122			−0.763931			−0.381965	+	0.924177i	$0.624753\pi$
$602$		−	1588.07i		−	2.63799i
$603$	264.618	−	735.466i	0.438836	−	1.21968i
$604$	−1375.40			−2.27716
$605$		−	184.798i		−	0.305452i
$606$	−1222.54	+	859.396i	−2.01739	+	1.41815i
$607$	−226.409			−0.372996			−0.186498	−	0.982455i	$-0.559714\pi$
$607$	−226.409			−0.372996			−0.186498	+	0.982455i	$0.559714\pi$
$608$			2464.93i			4.05416i
$609$	84.6591	+	120.432i	0.139013	+	0.197754i
$610$	440.406			0.721977
$611$			452.043i			0.739842i
$612$	2385.27	+	858.210i	3.89749	+	1.40230i
$613$	397.612			0.648634			0.324317	−	0.945949i	$-0.394866\pi$
$613$	397.612			0.648634			0.324317	+	0.945949i	$0.394866\pi$
$614$			1451.18i			2.36349i
$615$	−200.208	+	140.739i	−0.325542	+	0.228843i
$616$	504.835			0.819537
$617$		−	872.102i		−	1.41346i	−0.707486	−	0.706728i	$-0.750171\pi$
$617$		−	872.102i		−	1.41346i	0.707486	−	0.706728i	$-0.249829\pi$
$618$	−362.409	−	515.546i	−0.586422	−	0.834217i
$619$	784.482			1.26734			0.633669	−	0.773605i	$-0.281548\pi$
$619$	784.482			1.26734			0.633669	+	0.773605i	$0.281548\pi$
$620$			668.618i			1.07842i
$621$	−91.9313	+	25.1792i	−0.148038	+	0.0405462i
$622$	376.699			0.605625
$623$		−	1067.75i		−	1.71388i
$624$	1148.78	−	807.549i	1.84100	−	1.29415i
$625$	433.379			0.693407
$626$			870.460i			1.39051i
$627$	−130.461	−	185.588i	−0.208073	−	0.295994i
$628$	−2002.83			−3.18921
$629$		−	1211.22i		−	1.92563i
$630$	145.900	−	405.508i	0.231588	−	0.643664i
$631$	969.299			1.53613			0.768066	−	0.640371i	$-0.221219\pi$
$631$	969.299			1.53613			0.768066	+	0.640371i	$0.221219\pi$
$632$			3029.77i			4.79394i
$633$	−730.742	+	513.683i	−1.15441	+	0.811506i
$634$	−1723.53			−2.71851
$635$			108.339i			0.170613i
$636$	177.103	+	251.939i	0.278464	+	0.396130i
$637$	111.476			0.175002
$638$		−	65.0215i		−	0.101915i
$639$	−1011.84	−	364.057i	−1.58348	−	0.569730i
$640$	291.350			0.455234
$641$			690.806i			1.07770i	0.842402	+	0.538850i	$0.181141\pi$
$641$			690.806i			1.07770i	−0.842402	+	0.538850i	$0.818859\pi$
$642$	−84.8943	+	59.6774i	−0.132234	+	0.0929555i
$643$	−237.937			−0.370043			−0.185021	−	0.982735i	$-0.559235\pi$
$643$	−237.937			−0.370043			−0.185021	+	0.982735i	$0.559235\pi$
$644$		−	282.705i		−	0.438983i
$645$	151.540	+	215.574i	0.234946	+	0.334223i
$646$	2867.79			4.43931
$647$		−	509.640i		−	0.787698i	−0.919175	−	0.393849i	$-0.871143\pi$
$647$		−	509.640i		−	0.787698i	0.919175	−	0.393849i	$-0.128857\pi$
$648$	1226.48	−	1483.77i	1.89272	−	2.28977i
$649$	−20.9605			−0.0322966
$650$		−	812.313i		−	1.24971i
$651$	−762.974	+	536.341i	−1.17200	+	0.823873i
$652$	−282.942			−0.433961
$653$			529.277i			0.810531i	0.914199	+	0.405265i	$0.132821\pi$
$653$			529.277i			0.810531i	−0.914199	+	0.405265i	$0.867179\pi$
$654$	−264.081	−	375.669i	−0.403793	−	0.574418i
$655$	107.869			0.164686
$656$		−	2440.27i		−	3.71992i
$657$	50.0843	−	139.202i	0.0762318	−	0.211875i
$658$	−1383.36			−2.10238
$659$		−	132.453i		−	0.200991i	−0.994938	−	0.100495i	$-0.967957\pi$
$659$		−	132.453i		−	0.200991i	0.994938	−	0.100495i	$-0.0320427\pi$
$660$	−112.126	+	78.8204i	−0.169888	+	0.119425i
$661$	310.745			0.470114			0.235057	−	0.971982i	$-0.424472\pi$
$661$	310.745			0.470114			0.235057	+	0.971982i	$0.424472\pi$
$662$			2188.33i			3.30564i
$663$	−454.161	−	646.069i	−0.685010	−	0.974463i
$664$	−2981.66			−4.49045
$665$		−	351.047i		−	0.527890i
$666$	−1416.10	−	509.506i	−2.12627	−	0.765025i
$667$	−22.2541			−0.0333645
$668$			863.246i			1.29228i
$669$	−730.381	+	513.429i	−1.09175	+	0.767458i
$670$	−534.232			−0.797361
$671$		−	195.368i		−	0.291160i
$672$	1194.60	+	1699.39i	1.77768	+	2.52885i
$673$	−722.988			−1.07428			−0.537138	−	0.843494i	$-0.680495\pi$
$673$	−722.988			−1.07428			−0.537138	+	0.843494i	$0.680495\pi$
$674$		−	609.627i		−	0.904491i
$675$	−159.420	−	582.054i	−0.236177	−	0.862303i
$676$	787.579			1.16506
$677$		−	619.452i		−	0.914995i	−0.889211	−	0.457498i	$-0.848746\pi$
$677$		−	619.452i		−	0.914995i	0.889211	−	0.457498i	$-0.151254\pi$
$678$	1077.51	−	757.445i	1.58924	−	1.11718i
$679$	−0.498700			−0.000734463
$680$		−	1058.94i		−	1.55727i
$681$	115.271	+	163.979i	0.169267	+	0.240791i
$682$	411.931			0.604005
$683$		−	329.882i		−	0.482989i	−0.970402	−	0.241495i	$-0.922362\pi$
$683$		−	329.882i		−	0.482989i	0.970402	−	0.241495i	$-0.0776376\pi$
$684$	868.615	−	2414.18i	1.26991	−	3.52951i
$685$	79.9128			0.116661
$686$		−	1100.61i		−	1.60438i
$687$	227.332	−	159.806i	0.330906	−	0.232614i
$688$	−2627.56			−3.81912
$689$		−	95.9397i		−	0.139245i
$690$	37.4660	+	53.2975i	0.0542986	+	0.0772427i
$691$	1065.98			1.54266			0.771331	−	0.636435i	$-0.219591\pi$
$691$	1065.98			1.54266			0.771331	+	0.636435i	$0.219591\pi$
$692$			2440.34i			3.52650i
$693$	−179.887	−	64.7227i	−0.259577	−	0.0933950i
$694$	1257.50			1.81195
$695$		−	370.703i		−	0.533386i
$696$	367.692	−	258.473i	0.528293	−	0.371369i
$697$	−1372.40			−1.96900
$698$		−	510.546i		−	0.731441i
$699$	54.3490	+	77.3144i	0.0777525	+	0.110607i
$700$	1789.92			2.55703
$701$			716.616i			1.02228i	0.859498	+	0.511138i	$0.170776\pi$
$701$			716.616i			1.02228i	−0.859498	+	0.511138i	$0.829224\pi$
$702$	−946.394	+	259.209i	−1.34814	+	0.369244i
$703$	−1225.91			−1.74382
$704$		−	386.114i		−	0.548457i
$705$	187.786	−	132.006i	0.266363	−	0.187243i
$706$	−1084.50			−1.53612
$707$			1025.83i			1.45096i
$708$	−136.330	−	193.937i	−0.192556	−	0.273922i
$709$	−271.634			−0.383123			−0.191561	−	0.981481i	$-0.561355\pi$
$709$	−271.634			−0.383123			−0.191561	+	0.981481i	$0.561355\pi$
$710$			734.987i			1.03519i
$711$	388.434	−	1079.59i	0.546321	−	1.51842i
$712$	−3259.94			−4.57856
$713$		−	140.987i		−	0.197737i
$714$	1977.13	−	1389.85i	2.76909	−	1.94656i
$715$	42.6983			0.0597179
$716$		−	2333.75i		−	3.25943i
$717$	−359.959	−	512.062i	−0.502035	−	0.714172i
$718$	−1421.79			−1.98021
$719$			810.340i			1.12704i	0.826103	+	0.563519i	$0.190553\pi$
$719$			810.340i			1.12704i	−0.826103	+	0.563519i	$0.809447\pi$
$720$	−670.938	−	241.401i	−0.931858	−	0.335279i
$721$	−432.595			−0.599993
$722$		−	1538.02i		−	2.13023i
$723$	903.403	−	635.057i	1.24952	−	0.878364i
$724$	1116.60			1.54227
$725$		−	140.900i		−	0.194345i
$726$	−740.515	−	1053.42i	−1.01999	−	1.45099i
$727$	1389.13			1.91078			0.955388	−	0.295354i	$-0.0954375\pi$
$727$	1389.13			1.91078			0.955388	+	0.295354i	$0.0954375\pi$
$728$		−	1778.73i		−	2.44332i
$729$	−627.258	+	371.467i	−0.860437	+	0.509557i
$730$	−101.114			−0.138513
$731$			1477.72i			2.02151i
$732$	1807.64	−	1270.70i	2.46945	−	1.73593i
$733$	426.964			0.582489			0.291244	−	0.956649i	$-0.405931\pi$
$733$	426.964			0.582489			0.291244	+	0.956649i	$0.405931\pi$
$734$			855.541i			1.16559i
$735$	−32.5534	−	46.3090i	−0.0442903	−	0.0630054i
$736$	−314.022			−0.426661
$737$			236.990i			0.321560i
$738$	−577.305	+	1604.53i	−0.782255	+	2.17416i
$739$	−637.653			−0.862859			−0.431430	−	0.902147i	$-0.641991\pi$
$739$	−637.653			−0.862859			−0.431430	+	0.902147i	$0.641991\pi$
$740$			740.651i			1.00088i
$741$	−653.902	+	459.668i	−0.882459	+	0.620334i
$742$	293.599			0.395686
$743$			824.103i			1.10916i	0.832132	+	0.554578i	$0.187120\pi$
$743$			824.103i			1.10916i	−0.832132	+	0.554578i	$0.812880\pi$
$744$	1637.51	+	2329.44i	2.20095	+	3.13097i
$745$	38.0174			0.0510300
$746$		−	19.7919i		−	0.0265307i
$747$	1062.45	+	382.266i	1.42229	+	0.511734i
$748$	−768.607			−1.02755
$749$			71.2349i			0.0951066i
$750$	−714.880	+	502.533i	−0.953173	+	0.670044i
$751$	313.749			0.417775			0.208888	−	0.977940i	$-0.433016\pi$
$751$	313.749			0.417775			0.208888	+	0.977940i	$0.433016\pi$
$752$			2288.86i			3.04370i
$753$	453.396	+	644.980i	0.602119	+	0.856547i
$754$	−229.097			−0.303842
$755$		−	217.579i		−	0.288184i
$756$	−571.164	−	2085.37i	−0.755508	−	2.75842i
$757$	−681.004			−0.899608			−0.449804	−	0.893127i	$-0.648506\pi$
$757$	−681.004			−0.899608			−0.449804	+	0.893127i	$0.648506\pi$
$758$		−	377.601i		−	0.498155i
$759$	23.6432	−	16.6203i	0.0311505	−	0.0218976i
$760$	−1071.78			−1.41024
$761$		−	1057.16i		−	1.38918i	−0.719408	−	0.694588i	$-0.755587\pi$
$761$		−	1057.16i		−	1.38918i	0.719408	−	0.694588i	$-0.244413\pi$
$762$	434.132	+	617.576i	0.569727	+	0.810468i
$763$	−315.224			−0.413138
$764$		−	1.04833i		−	0.00137215i
$765$	−135.763	+	377.332i	−0.177468	+	0.493244i
$766$	1989.18			2.59685
$767$			73.8522i			0.0962871i
$768$	271.742	−	191.024i	0.353830	−	0.248729i
$769$	−50.4233			−0.0655700			−0.0327850	−	0.999462i	$-0.510438\pi$
$769$	−50.4233			−0.0655700			−0.0327850	+	0.999462i	$0.510438\pi$
$770$			130.667i			0.169698i
$771$	148.936	+	211.870i	0.193173	+	0.274799i
$772$	1673.98			2.16837
$773$			750.635i			0.971068i	0.874218	+	0.485534i	$0.161375\pi$
$773$			750.635i			0.971068i	−0.874218	+	0.485534i	$0.838625\pi$
$774$	1727.68	+	621.612i	2.23214	+	0.803116i
$775$	892.643			1.15180
$776$			1.52258i			0.00196209i
$777$	−845.173	+	594.123i	−1.08774	+	0.764638i
$778$	−48.6480			−0.0625295
$779$			1389.03i			1.78310i
$780$	277.716	+	395.065i	0.356046	+	0.506494i
$781$	326.047			0.417474
$782$			365.345i			0.467193i
$783$	−164.157	+	44.9611i	−0.209651	+	0.0574216i
$784$	564.444			0.719954
$785$		−	316.833i		−	0.403608i
$786$	614.898	−	432.249i	0.782313	−	0.549936i
$787$	41.9123			0.0532558			0.0266279	−	0.999645i	$-0.491523\pi$
$787$	41.9123			0.0532558			0.0266279	+	0.999645i	$0.491523\pi$
$788$		−	2145.12i		−	2.72223i
$789$	342.003	+	486.518i	0.433464	+	0.616626i
$790$	−784.201			−0.992660
$791$		−	904.136i		−	1.14303i
$792$	−197.605	+	549.214i	−0.249502	+	0.693452i
$793$	−688.360			−0.868045
$794$			747.444i			0.941365i
$795$	−39.8549	+	28.0164i	−0.0501319	+	0.0352408i
$796$	451.560			0.567287
$797$			1412.00i			1.77164i	0.464026	+	0.885822i	$0.346405\pi$
$797$			1412.00i			1.77164i	−0.464026	+	0.885822i	$0.653595\pi$
$798$	−1406.70	−	2001.10i	−1.76278	−	2.50765i
$799$	1287.24			1.61107
$800$		−	1988.20i		−	2.48525i
$801$	1161.61	+	417.943i	1.45020	+	0.521776i
$802$	143.006			0.178311
$803$			44.8552i			0.0558595i
$804$	−2192.75	+	1541.42i	−2.72730	+	1.91718i
$805$	44.7219			0.0555552
$806$		−	1451.40i		−	1.80074i
$807$	−458.890	−	652.796i	−0.568637	−	0.808917i
$808$	3131.97			3.87620
$809$		−	1581.01i		−	1.95427i	−0.212617	−	0.977136i	$-0.568199\pi$
$809$		−	1581.01i		−	1.95427i	0.212617	−	0.977136i	$-0.431801\pi$
$810$	384.047	+	317.453i	0.474132	+	0.391917i
$811$	−1101.66			−1.35840			−0.679198	−	0.733955i	$-0.737672\pi$
$811$	−1101.66			−1.35840			−0.679198	+	0.733955i	$0.737672\pi$
$812$		−	504.812i		−	0.621689i
$813$	−134.988	+	94.8913i	−0.166037	+	0.116717i
$814$	456.310			0.560578
$815$		−	44.7594i		−	0.0549196i
$816$	−2299.58	−	3271.28i	−2.81812	−	4.00892i
$817$	1495.64			1.83065
$818$		−	762.478i		−	0.932124i
$819$	−228.044	+	633.814i	−0.278442	+	0.773888i
$820$	839.207			1.02342
$821$			304.663i			0.371088i	0.982636	+	0.185544i	$0.0594048\pi$
$821$			304.663i			0.371088i	−0.982636	+	0.185544i	$0.940595\pi$
$822$	455.534	−	320.223i	0.554178	−	0.389566i
$823$	1418.02			1.72299			0.861497	−	0.507763i	$-0.169528\pi$
$823$	1418.02			1.72299			0.861497	+	0.507763i	$0.169528\pi$
$824$			1320.76i			1.60286i
$825$	105.230	+	149.695i	0.127551	+	0.181448i
$826$	−226.006			−0.273615
$827$			573.645i			0.693645i	0.937931	+	0.346823i	$0.112739\pi$
$827$			573.645i			0.693645i	−0.937931	+	0.346823i	$0.887261\pi$
$828$	307.557	+	110.658i	0.371446	+	0.133645i
$829$	−63.8873			−0.0770655			−0.0385327	−	0.999257i	$-0.512268\pi$
$829$	−63.8873			−0.0770655			−0.0385327	+	0.999257i	$0.512268\pi$
$830$		−	771.748i		−	0.929817i
$831$	141.951	−	99.7863i	0.170820	−	0.120080i
$832$	−1360.43			−1.63513
$833$		−	317.440i		−	0.381081i
$834$	−1485.46	−	2113.15i	−1.78113	−	2.53376i
$835$	−136.559			−0.163544
$836$			777.925i			0.930533i
$837$	−284.842	−	1039.98i	−0.340314	−	1.24251i
$838$	−1368.91			−1.63354
$839$		−	1441.99i		−	1.71869i	−0.511392	−	0.859347i	$-0.670870\pi$
$839$		−	1441.99i		−	1.71869i	0.511392	−	0.859347i	$-0.329130\pi$
$840$	−738.914	+	519.428i	−0.879660	+	0.618367i
$841$	801.262			0.952749
$842$		−	1737.12i		−	2.06308i
$843$	−353.213	−	502.465i	−0.418996	−	0.596044i
$844$	3063.03			3.62918
$845$			124.589i			0.147443i
$846$	541.484	−	1504.97i	0.640053	−	1.77893i
$847$	−883.927			−1.04360
$848$		−	485.778i		−	0.572851i
$849$	−602.170	+	423.302i	−0.709270	+	0.498589i
$850$	−2313.15			−2.72135
$851$		−	156.176i		−	0.183520i
$852$	2120.65	+	3016.74i	2.48903	+	3.54078i
$853$	45.5840			0.0534397			0.0267198	−	0.999643i	$-0.491494\pi$
$853$	45.5840			0.0534397			0.0267198	+	0.999643i	$0.491494\pi$
$854$		−	2106.55i		−	2.46669i
$855$	381.907	+	137.409i	0.446674	+	0.160712i
$856$	217.487			0.254074
$857$			1490.87i			1.73964i	0.493368	+	0.869821i	$0.335766\pi$
$857$			1490.87i			1.73964i	−0.493368	+	0.869821i	$0.664234\pi$
$858$	243.397	−	171.099i	0.283680	−	0.199416i
$859$	−575.769			−0.670278			−0.335139	−	0.942169i	$-0.608783\pi$
$859$	−575.769			−0.670278			−0.335139	+	0.942169i	$0.608783\pi$
$860$		−	903.615i		−	1.05071i
$861$	673.181	+	957.637i	0.781860	+	1.11224i
$862$	1099.20			1.27517
$863$			817.599i			0.947392i	0.880688	+	0.473696i	$0.157080\pi$
$863$			817.599i			0.947392i	−0.880688	+	0.473696i	$0.842920\pi$
$864$	−2316.38	+	634.435i	−2.68099	+	0.734300i
$865$	−386.044			−0.446293
$866$			2599.70i			3.00197i
$867$	−1130.47	+	794.673i	−1.30388	+	0.916578i
$868$	3198.14			3.68449
$869$			347.879i			0.400321i
$870$	66.9011	+	95.1704i	0.0768978	+	0.109391i
$871$	835.011			0.958680
$872$			962.412i			1.10368i
$873$	0.195204	−	0.542541i	0.000223602	−	0.000621467i
$874$	369.775			0.423083
$875$			599.856i			0.685550i
$876$	−415.021	+	291.744i	−0.473769	+	0.333041i
$877$	1332.73			1.51965			0.759825	−	0.650127i	$-0.225284\pi$
$877$	1332.73			1.51965			0.759825	+	0.650127i	$0.225284\pi$
$878$		−	1267.37i		−	1.44347i
$879$	766.831	+	1090.86i	0.872391	+	1.24102i
$880$	216.197			0.245678
$881$			1008.40i			1.14460i	0.820043	+	0.572302i	$0.193950\pi$
$881$			1008.40i			1.14460i	−0.820043	+	0.572302i	$0.806050\pi$
$882$	−371.134	−	133.533i	−0.420787	−	0.151398i
$883$	−408.779			−0.462943			−0.231472	−	0.972842i	$-0.574354\pi$
$883$	−408.779			−0.462943			−0.231472	+	0.972842i	$0.574354\pi$
$884$			2708.11i			3.06347i
$885$	30.6794	−	21.5664i	0.0346660	−	0.0243688i
$886$	−1148.58			−1.29636
$887$			736.680i			0.830530i	0.909701	+	0.415265i	$0.136311\pi$
$887$			736.680i			0.830530i	−0.909701	+	0.415265i	$0.863689\pi$
$888$	1813.92	+	2580.40i	2.04270	+	2.90586i
$889$	518.209			0.582912
$890$		−	843.776i		−	0.948063i
$891$	140.825	−	170.367i	0.158053	−	0.191208i
$892$	3061.52			3.43219
$893$		−	1302.85i		−	1.45896i
$894$	216.714	−	152.341i	0.242409	−	0.170404i
$895$	369.183			0.412495
$896$		−	1393.58i		−	1.55534i
$897$	−58.5598	−	83.3045i	−0.0652841	−	0.0928701i
$898$	544.734			0.606608
$899$		−	251.752i		−	0.280036i
$900$	−700.621	+	1947.27i	−0.778468	+	2.16363i
$901$	−273.199			−0.303217
$902$		−	517.030i		−	0.573204i
$903$	1031.13	−	724.847i	1.14190	−	0.802709i
$904$	−2760.42			−3.05357
$905$			176.639i			0.195181i
$906$	−871.872	−	1240.28i	−0.962331	−	1.36897i
$907$	−631.452			−0.696199			−0.348099	−	0.937458i	$-0.613173\pi$
$907$	−631.452			−0.696199			−0.348099	+	0.937458i	$0.613173\pi$
$908$		−	687.344i		−	0.756987i
$909$	−1116.01	−	401.537i	−1.22774	−	0.441735i
$910$	460.393			0.505927
$911$		−	15.0589i		−	0.0165301i	−0.999966	−	0.00826503i	$-0.997369\pi$
$911$		−	15.0589i		−	0.0165301i	0.999966	−	0.00826503i	$-0.00263087\pi$
$912$	−3310.94	+	2327.46i	−3.63042	+	2.55204i
$913$	−342.354			−0.374977
$914$		−	1751.22i		−	1.91599i
$915$	201.016	+	285.956i	0.219689	+	0.312520i
$916$	−952.901			−1.04029
$917$		−	515.961i		−	0.562662i
$918$	738.126	+	2694.96i	0.804059	+	2.93569i
$919$	788.939			0.858476			0.429238	−	0.903192i	$-0.358782\pi$
$919$	788.939			0.858476			0.429238	+	0.903192i	$0.358782\pi$
$920$		−	136.541i		−	0.148414i
$921$	−942.252	+	662.366i	−1.02307	+	0.719181i
$922$	1474.58			1.59933
$923$		−	1148.79i		−	1.24463i
$924$	377.014	+	536.322i	0.408023	+	0.580435i
$925$	988.811			1.06899
$926$		−	1267.79i		−	1.36910i
$927$	169.329	−	470.624i	0.182663	−	0.507685i
$928$	−560.733			−0.604238
$929$			922.437i			0.992935i	0.868055	+	0.496468i	$0.165370\pi$
$929$			922.437i			0.992935i	−0.868055	+	0.496468i	$0.834630\pi$
$930$	−602.934	+	423.839i	−0.648316	+	0.455741i
$931$	−321.289			−0.345101
$932$		−	324.076i		−	0.347721i
$933$	171.938	+	244.591i	0.184285	+	0.262155i
$934$	−1640.72			−1.75666
$935$		−	121.588i		−	0.130041i
$936$	1935.10	+	696.242i	2.06741	+	0.743849i
$937$	148.574			0.158563			0.0792817	−	0.996852i	$-0.474737\pi$
$937$	148.574			0.158563			0.0792817	+	0.996852i	$0.474737\pi$
$938$			2555.34i			2.72424i
$939$	−565.190	+	397.306i	−0.601906	+	0.423116i
$940$	−787.137			−0.837379
$941$			304.574i			0.323671i	0.986818	+	0.161835i	$0.0517414\pi$
$941$			304.574i			0.323671i	−0.986818	+	0.161835i	$0.948259\pi$
$942$	−1269.60	−	1806.07i	−1.34777	−	1.91727i
$943$	−176.957			−0.187654
$944$			373.941i			0.396124i
$945$	329.890	−	90.3540i	0.349090	−	0.0956127i
$946$	−556.711			−0.588489
$947$		−	399.833i		−	0.422210i	−0.977463	−	0.211105i	$-0.932294\pi$
$947$		−	399.833i		−	0.422210i	0.977463	−	0.211105i	$-0.0677062\pi$
$948$	−3218.74	+	2262.65i	−3.39530	+	2.38676i
$949$	158.043			0.166536
$950$			2341.19i			2.46441i
$951$	−786.676	−	1119.09i	−0.827209	−	1.17675i
$952$	−5065.14			−5.32052
$953$		−	986.817i		−	1.03548i	−0.855537	−	0.517742i	$-0.826773\pi$
$953$		−	986.817i		−	1.03548i	0.855537	−	0.517742i	$-0.173227\pi$
$954$	−114.922	+	319.409i	−0.120464	+	0.334810i
$955$	0.165838			0.000173652
$956$			2146.39i			2.24518i
$957$	42.2185	−	29.6779i	0.0441154	−	0.0310114i
$958$	2371.67			2.47565
$959$		−	382.239i		−	0.398581i
$960$	397.275	+	565.145i	0.413828	+	0.588693i
$961$	633.927			0.659654
$962$		−	1607.76i		−	1.67127i
$963$	−77.4970	−	27.8832i	−0.0804746	−	0.0289545i
$964$	−3786.77			−3.92818
$965$			264.812i			0.274417i
$966$	254.932	−	179.208i	0.263905	−	0.185515i
$967$	−410.782			−0.424801			−0.212400	−	0.977183i	$-0.568128\pi$
$967$	−410.782			−0.424801			−0.212400	+	0.977183i	$0.568128\pi$
$968$			2698.72i			2.78794i
$969$	1308.95	+	1862.06i	1.35083	+	1.92163i
$970$	−0.394094			−0.000406282
$971$		−	99.6561i		−	0.102632i	−0.998682	−	0.0513162i	$-0.983658\pi$
$971$		−	99.6561i		−	0.102632i	0.998682	−	0.0513162i	$-0.0163416\pi$
$972$	2492.26	+	194.893i	2.56405	+	0.200507i
$973$	−1773.15			−1.82235
$974$		−	754.500i		−	0.774640i
$975$	527.434	−	370.766i	0.540958	−	0.380273i
$976$	−3485.42			−3.57112
$977$			477.901i			0.489152i	0.969630	+	0.244576i	$0.0786487\pi$
$977$			477.901i			0.489152i	−0.969630	+	0.244576i	$0.921351\pi$
$978$	−179.358	−	255.146i	−0.183393	−	0.260886i
$979$	−374.307			−0.382336
$980$			194.112i			0.198073i
$981$	123.387	−	342.935i	0.125777	−	0.349577i
$982$	−2574.81			−2.62200
$983$		−	1880.18i		−	1.91269i	−0.292237	−	0.956346i	$-0.594400\pi$
$983$		−	1880.18i		−	1.91269i	0.292237	−	0.956346i	$-0.405600\pi$
$984$	2923.76	−	2055.29i	2.97131	−	2.08871i
$985$	339.342			0.344510
$986$			652.378i			0.661641i
$987$	−631.412	−	898.218i	−0.639729	−	0.910049i
$988$	2740.94			2.77423
$989$			190.539i			0.192658i
$990$	−142.154	−	51.1466i	−0.143590	−	0.0516632i
$991$	−292.800			−0.295459			−0.147730	−	0.989028i	$-0.547197\pi$
$991$	−292.800			−0.295459			−0.147730	+	0.989028i	$0.547197\pi$
$992$		−	3552.41i		−	3.58106i
$993$	−1420.88	+	998.826i	−1.43090	+	1.00587i
$994$	3515.59			3.53681
$995$			71.4336i			0.0717926i
$996$	−2226.72	−	3167.63i	−2.23566	−	3.18035i
$997$	−941.929			−0.944763			−0.472381	−	0.881394i	$-0.656606\pi$
$997$	−941.929			−0.944763			−0.472381	+	0.881394i	$0.656606\pi$
$998$		−	3192.10i		−	3.19850i
$999$	−315.530	−	1152.03i	−0.315846	−	1.15318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.1	✓	38
3.2	odd	2	inner	177.3.b.a.119.38	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.1	✓	38	1.1	even	1	trivial
177.3.b.a.119.38	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)

\(f(q)\)	\(=\)	\(q-3.77988i q^{2} +(2.45428 - 1.72526i) q^{3} -10.2875 q^{4} -1.62741i q^{5} +(-6.52128 - 9.27688i) q^{6} -7.78423 q^{7} +23.7661i q^{8} +(3.04695 - 8.46854i) q^{9} +O(q^{10})\)	\(q-3.77988i q^{2} +(2.45428 - 1.72526i) q^{3} -10.2875 q^{4} -1.62741i q^{5} +(-6.52128 - 9.27688i) q^{6} -7.78423 q^{7} +23.7661i q^{8} +(3.04695 - 8.46854i) q^{9} -6.15142 q^{10} +2.72883i q^{11} +(-25.2484 + 17.7486i) q^{12} +9.61474 q^{13} +29.4235i q^{14} +(-2.80771 - 3.99412i) q^{15} +48.6829 q^{16} -27.3790i q^{17} +(-32.0101 - 11.5171i) q^{18} -27.7110 q^{19} +16.7420i q^{20} +(-19.1047 + 13.4298i) q^{21} +10.3146 q^{22} -3.53027i q^{23} +(41.0027 + 58.3285i) q^{24} +22.3515 q^{25} -36.3426i q^{26} +(-7.13238 - 26.0409i) q^{27} +80.0804 q^{28} -6.30381i q^{29} +(-15.0973 + 10.6128i) q^{30} +39.9365 q^{31} -88.9515i q^{32} +(4.70794 + 6.69729i) q^{33} -103.489 q^{34} +12.6681i q^{35} +(-31.3455 + 87.1202i) q^{36} +44.2391 q^{37} +104.744i q^{38} +(23.5972 - 16.5879i) q^{39} +38.6772 q^{40} -50.1258i q^{41} +(50.7632 + 72.2134i) q^{42} -53.9729 q^{43} -28.0728i q^{44} +(-13.7818 - 4.95864i) q^{45} -13.3440 q^{46} +47.0156i q^{47} +(119.481 - 83.9907i) q^{48} +11.5943 q^{49} -84.4862i q^{50} +(-47.2359 - 67.1957i) q^{51} -98.9118 q^{52} -9.97840i q^{53} +(-98.4316 + 26.9595i) q^{54} +4.44092 q^{55} -185.001i q^{56} +(-68.0104 + 47.8086i) q^{57} -23.8277 q^{58} +7.68115i q^{59} +(28.8843 + 41.0895i) q^{60} -71.5942 q^{61} -150.955i q^{62} +(-23.7182 + 65.9211i) q^{63} -141.494 q^{64} -15.6471i q^{65} +(25.3150 - 17.7955i) q^{66} +86.8469 q^{67} +281.662i q^{68} +(-6.09063 - 8.66425i) q^{69} +47.8841 q^{70} -119.483i q^{71} +(201.264 + 72.4140i) q^{72} +16.4375 q^{73} -167.219i q^{74} +(54.8569 - 38.5622i) q^{75} +285.077 q^{76} -21.2418i q^{77} +(-62.7005 - 89.1948i) q^{78} +127.483 q^{79} -79.2271i q^{80} +(-62.4322 - 51.6064i) q^{81} -189.470 q^{82} +125.458i q^{83} +(196.540 - 138.160i) q^{84} -44.5569 q^{85} +204.011i q^{86} +(-10.8757 - 15.4713i) q^{87} -64.8535 q^{88} +137.168i q^{89} +(-18.7431 + 52.0935i) q^{90} -74.8434 q^{91} +36.3177i q^{92} +(98.0153 - 68.9009i) q^{93} +177.714 q^{94} +45.0971i q^{95} +(-153.464 - 218.312i) q^{96} +0.0640655 q^{97} -43.8251i q^{98} +(23.1092 + 8.31459i) 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

Related objects

Downloads

Learn more