LMFDB - Embedded newform 177.3.b.a.119.30

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			119.30
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.36527i q^{2} +(2.69227 - 1.32352i) q^{3} -1.59452 q^{4} +8.24482i q^{5} +(3.13049 + 6.36794i) q^{6} -0.755379 q^{7} +5.68962i q^{8} +(5.49658 - 7.12654i) q^{9} +O(q^{10})$	\(q+2.36527i q^{2} +(2.69227 - 1.32352i) q^{3} -1.59452 q^{4} +8.24482i q^{5} +(3.13049 + 6.36794i) q^{6} -0.755379 q^{7} +5.68962i q^{8} +(5.49658 - 7.12654i) q^{9} -19.5013 q^{10} -12.7075i q^{11} +(-4.29288 + 2.11038i) q^{12} -1.31367 q^{13} -1.78668i q^{14} +(10.9122 + 22.1972i) q^{15} -19.8356 q^{16} +16.7462i q^{17} +(16.8562 + 13.0009i) q^{18} +11.8048 q^{19} -13.1465i q^{20} +(-2.03368 + 0.999760i) q^{21} +30.0566 q^{22} +13.6222i q^{23} +(7.53033 + 15.3180i) q^{24} -42.9771 q^{25} -3.10719i q^{26} +(5.36613 - 26.4614i) q^{27} +1.20447 q^{28} -36.0473i q^{29} +(-52.5026 + 25.8103i) q^{30} +8.07287 q^{31} -24.1581i q^{32} +(-16.8186 - 34.2119i) q^{33} -39.6093 q^{34} -6.22797i q^{35} +(-8.76442 + 11.3634i) q^{36} +50.0853 q^{37} +27.9216i q^{38} +(-3.53675 + 1.73867i) q^{39} -46.9099 q^{40} -47.7769i q^{41} +(-2.36471 - 4.81021i) q^{42} +24.6656 q^{43} +20.2623i q^{44} +(58.7571 + 45.3183i) q^{45} -32.2203 q^{46} +18.1017i q^{47} +(-53.4027 + 26.2528i) q^{48} -48.4294 q^{49} -101.653i q^{50} +(22.1639 + 45.0851i) q^{51} +2.09468 q^{52} -47.1050i q^{53} +(62.5884 + 12.6924i) q^{54} +104.771 q^{55} -4.29782i q^{56} +(31.7816 - 15.6239i) q^{57} +85.2616 q^{58} +7.68115i q^{59} +(-17.3997 - 35.3940i) q^{60} +41.9771 q^{61} +19.0945i q^{62} +(-4.15200 + 5.38324i) q^{63} -22.2017 q^{64} -10.8310i q^{65} +(80.9205 - 39.7806i) q^{66} +84.5251 q^{67} -26.7021i q^{68} +(18.0293 + 36.6747i) q^{69} +14.7308 q^{70} -117.846i q^{71} +(40.5473 + 31.2734i) q^{72} -106.420 q^{73} +118.466i q^{74} +(-115.706 + 56.8811i) q^{75} -18.8230 q^{76} +9.59896i q^{77} +(-4.11244 - 8.36538i) q^{78} +100.619 q^{79} -163.541i q^{80} +(-20.5752 - 78.3432i) q^{81} +113.006 q^{82} -60.9531i q^{83} +(3.24275 - 1.59414i) q^{84} -138.069 q^{85} +58.3409i q^{86} +(-47.7093 - 97.0488i) q^{87} +72.3006 q^{88} +72.2494i q^{89} +(-107.190 + 138.977i) q^{90} +0.992320 q^{91} -21.7210i q^{92} +(21.7343 - 10.6846i) q^{93} -42.8155 q^{94} +97.3284i q^{95} +(-31.9738 - 65.0401i) q^{96} -171.901 q^{97} -114.549i q^{98} +(-90.5603 - 69.8476i) 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 $

$2$			2.36527i			1.18264i	0.806438	+	0.591319i	$0.201392\pi$
$2$			2.36527i			1.18264i	−0.806438	+	0.591319i	$0.798608\pi$
$3$	2.69227	−	1.32352i	0.897422	−	0.441174i
$3$	2.69227	−	1.32352i	0.897422	−	0.441174i
$4$	−1.59452			−0.398630
$5$			8.24482i			1.64896i	0.565888	+	0.824482i	$0.308533\pi$
$5$			8.24482i			1.64896i	−0.565888	+	0.824482i	$0.691467\pi$
$6$	3.13049	+	6.36794i	0.521749	+	1.06132i
$7$	−0.755379			−0.107911			−0.0539556	−	0.998543i	$-0.517183\pi$
$7$	−0.755379			−0.107911			−0.0539556	+	0.998543i	$0.517183\pi$
$8$			5.68962i			0.711202i
$9$	5.49658	−	7.12654i	0.610731	−	0.791838i
$10$	−19.5013			−1.95013
$11$		−	12.7075i		−	1.15522i	−0.816311	−	0.577612i	$-0.803985\pi$
$11$		−	12.7075i		−	1.15522i	0.816311	−	0.577612i	$-0.196015\pi$
$12$	−4.29288	+	2.11038i	−0.357740	+	0.175865i
$13$	−1.31367			−0.101052			−0.0505258	−	0.998723i	$-0.516090\pi$
$13$	−1.31367			−0.101052			−0.0505258	+	0.998723i	$0.516090\pi$
$14$		−	1.78668i		−	0.127620i
$15$	10.9122	+	22.1972i	0.727480	+	1.47982i
$16$	−19.8356			−1.23972
$17$			16.7462i			0.985068i	0.870293	+	0.492534i	$0.163929\pi$
$17$			16.7462i			0.985068i	−0.870293	+	0.492534i	$0.836071\pi$
$18$	16.8562	+	13.0009i	0.936457	+	0.722274i
$19$	11.8048			0.621305			0.310652	−	0.950524i	$-0.399453\pi$
$19$	11.8048			0.621305			0.310652	+	0.950524i	$0.399453\pi$
$20$		−	13.1465i		−	0.657327i
$21$	−2.03368	+	0.999760i	−0.0968419	+	0.0476076i
$22$	30.0566			1.36621
$23$			13.6222i			0.592272i	0.955146	+	0.296136i	$0.0956981\pi$
$23$			13.6222i			0.592272i	−0.955146	+	0.296136i	$0.904302\pi$
$24$	7.53033	+	15.3180i	0.313764	+	0.638248i
$25$	−42.9771			−1.71908
$26$		−	3.10719i		−	0.119507i
$27$	5.36613	−	26.4614i	0.198745	−	0.980051i
$28$	1.20447			0.0430167
$29$		−	36.0473i		−	1.24301i	−0.783411	−	0.621504i	$-0.786522\pi$
$29$		−	36.0473i		−	1.24301i	0.783411	−	0.621504i	$-0.213478\pi$
$30$	−52.5026	+	25.8103i	−1.75009	+	0.860345i
$31$	8.07287			0.260415			0.130208	−	0.991487i	$-0.458436\pi$
$31$	8.07287			0.260415			0.130208	+	0.991487i	$0.458436\pi$
$32$		−	24.1581i		−	0.754942i
$33$	−16.8186	−	34.2119i	−0.509655	−	1.03672i
$34$	−39.6093			−1.16498
$35$		−	6.22797i		−	0.177942i
$36$	−8.76442	+	11.3634i	−0.243456	+	0.315651i
$37$	50.0853			1.35366			0.676829	−	0.736141i	$-0.263354\pi$
$37$	50.0853			1.35366			0.676829	+	0.736141i	$0.263354\pi$
$38$			27.9216i			0.734778i
$39$	−3.53675	+	1.73867i	−0.0906859	+	0.0445813i
$40$	−46.9099			−1.17275
$41$		−	47.7769i		−	1.16529i	−0.812726	−	0.582645i	$-0.802018\pi$
$41$		−	47.7769i		−	1.16529i	0.812726	−	0.582645i	$-0.197982\pi$
$42$	−2.36471	−	4.81021i	−0.0563026	−	0.114529i
$43$	24.6656			0.573619			0.286809	−	0.957988i	$-0.407405\pi$
$43$	24.6656			0.573619			0.286809	+	0.957988i	$0.407405\pi$
$44$			20.2623i			0.460508i
$45$	58.7571	+	45.3183i	1.30571	+	1.00707i
$46$	−32.2203			−0.700442
$47$			18.1017i			0.385143i	0.981283	+	0.192572i	$0.0616827\pi$
$47$			18.1017i			0.385143i	−0.981283	+	0.192572i	$0.938317\pi$
$48$	−53.4027	+	26.2528i	−1.11256	+	0.546934i
$49$	−48.4294			−0.988355
$50$		−	101.653i		−	2.03305i
$51$	22.1639	+	45.0851i	0.434586	+	0.884022i
$52$	2.09468			0.0402823
$53$		−	47.1050i		−	0.888774i	−0.895835	−	0.444387i	$-0.853422\pi$
$53$		−	47.1050i		−	0.888774i	0.895835	−	0.444387i	$-0.146578\pi$
$54$	62.5884	+	12.6924i	1.15904	+	0.235044i
$55$	104.771			1.90492
$56$		−	4.29782i		−	0.0767467i
$57$	31.7816	−	15.6239i	0.557572	−	0.274103i
$58$	85.2616			1.47003
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	−17.3997	−	35.3940i	−0.289996	−	0.589900i
$61$	41.9771			0.688149			0.344074	−	0.938942i	$-0.388193\pi$
$61$	41.9771			0.688149			0.344074	+	0.938942i	$0.388193\pi$
$62$			19.0945i			0.307977i
$63$	−4.15200	+	5.38324i	−0.0659048	+	0.0854482i
$64$	−22.2017			−0.346902
$65$		−	10.8310i		−	0.166631i
$66$	80.9205	−	39.7806i	1.22607	−	0.602737i
$67$	84.5251			1.26157			0.630784	−	0.775958i	$-0.282733\pi$
$67$	84.5251			1.26157			0.630784	+	0.775958i	$0.282733\pi$
$68$		−	26.7021i		−	0.392678i
$69$	18.0293	+	36.6747i	0.261295	+	0.531517i
$70$	14.7308			0.210441
$71$		−	117.846i		−	1.65980i	−0.557909	−	0.829902i	$-0.688396\pi$
$71$		−	117.846i		−	1.65980i	0.557909	−	0.829902i	$-0.311604\pi$
$72$	40.5473	+	31.2734i	0.563157	+	0.434353i
$73$	−106.420			−1.45781			−0.728905	−	0.684615i	$-0.759970\pi$
$73$	−106.420			−1.45781			−0.728905	+	0.684615i	$0.759970\pi$
$74$			118.466i			1.60089i
$75$	−115.706	+	56.8811i	−1.54274	+	0.758414i
$76$	−18.8230			−0.247671
$77$			9.59896i			0.124662i
$78$	−4.11244	−	8.36538i	−0.0527235	−	0.107249i
$79$	100.619			1.27365			0.636827	−	0.771007i	$-0.280247\pi$
$79$	100.619			1.27365			0.636827	+	0.771007i	$0.280247\pi$
$80$		−	163.541i		−	2.04426i
$81$	−20.5752	−	78.3432i	−0.254014	−	0.967200i
$82$	113.006			1.37812
$83$		−	60.9531i		−	0.734375i	−0.930147	−	0.367187i	$-0.880321\pi$
$83$		−	60.9531i		−	0.734375i	0.930147	−	0.367187i	$-0.119679\pi$
$84$	3.24275	−	1.59414i	0.0386041	−	0.0189779i
$85$	−138.069			−1.62434
$86$			58.3409i			0.678383i
$87$	−47.7093	−	97.0488i	−0.548383	−	1.11550i
$88$	72.3006			0.821598
$89$			72.2494i			0.811791i	0.913920	+	0.405895i	$0.133040\pi$
$89$			72.2494i			0.811791i	−0.913920	+	0.405895i	$0.866960\pi$
$90$	−107.190	+	138.977i	−1.19100	+	1.54418i
$91$	0.992320			0.0109046
$92$		−	21.7210i		−	0.236098i
$93$	21.7343	−	10.6846i	0.233702	−	0.114888i
$94$	−42.8155			−0.455485
$95$			97.3284i			1.02451i
$96$	−31.9738	−	65.0401i	−0.333061	−	0.677501i
$97$	−171.901			−1.77218			−0.886089	−	0.463516i	$-0.846588\pi$
$97$	−171.901			−1.77218			−0.886089	+	0.463516i	$0.846588\pi$
$98$		−	114.549i		−	1.16887i
$99$	−90.5603	−	69.8476i	−0.914751	−	0.705532i
$100$	68.5279			0.685279
$101$			15.1618i			0.150117i	0.997179	+	0.0750583i	$0.0239143\pi$
$101$			15.1618i			0.150117i	−0.997179	+	0.0750583i	$0.976086\pi$
$102$	−106.639	+	52.4237i	−1.04548	+	0.513958i
$103$	−173.109			−1.68067			−0.840335	−	0.542067i	$-0.817642\pi$
$103$	−173.109			−1.68067			−0.840335	+	0.542067i	$0.817642\pi$
$104$		−	7.47428i		−	0.0718681i
$105$	−8.24285	−	16.7673i	−0.0785033	−	0.159689i
$106$	111.416			1.05110
$107$			191.084i			1.78583i	0.450224	+	0.892916i	$0.351344\pi$
$107$			191.084i			1.78583i	−0.450224	+	0.892916i	$0.648656\pi$
$108$	−8.55641	+	42.1933i	−0.0792260	+	0.390678i
$109$	12.3513			0.113314			0.0566572	−	0.998394i	$-0.481956\pi$
$109$	12.3513			0.113314			0.0566572	+	0.998394i	$0.481956\pi$
$110$			247.812i			2.25283i
$111$	134.843	−	66.2890i	1.21480	−	0.597198i
$112$	14.9834			0.133780
$113$			140.835i			1.24632i	0.782093	+	0.623162i	$0.214152\pi$
$113$			140.835i			1.24632i	−0.782093	+	0.623162i	$0.785848\pi$
$114$	36.9548	+	75.1722i	0.324165	+	0.659406i
$115$	−112.313			−0.976635
$116$			57.4781i			0.495501i
$117$	−7.22070	+	9.36193i	−0.0617154	+	0.0800165i
$118$	−18.1680			−0.153966
$119$		−	12.6497i		−	0.106300i
$120$	−126.294	+	62.0862i	−1.05245	+	0.517385i
$121$	−40.4798			−0.334544
$122$			99.2873i			0.813831i
$123$	−63.2338	−	128.628i	−0.514096	−	1.04576i
$124$	−12.8724			−0.103809
$125$		−	148.218i		−	1.18574i
$126$	−12.7328	−	9.82063i	−0.101054	−	0.0779415i
$127$	147.769			1.16354			0.581768	−	0.813355i	$-0.302361\pi$
$127$	147.769			1.16354			0.581768	+	0.813355i	$0.302361\pi$
$128$		−	149.146i		−	1.16520i
$129$	66.4064	−	32.6455i	0.514778	−	0.253066i
$130$	25.6182			0.197063
$131$			47.5616i			0.363066i	0.983385	+	0.181533i	$0.0581059\pi$
$131$			47.5616i			0.363066i	−0.983385	+	0.181533i	$0.941894\pi$
$132$	26.8176	+	54.5516i	0.203164	+	0.413270i
$133$	−8.91709			−0.0670458
$134$			199.925i			1.49198i
$135$	218.169	+	44.2427i	1.61607	+	0.327724i
$136$	−95.2792			−0.700582
$137$		−	261.817i		−	1.91107i	−0.294874	−	0.955536i	$-0.595278\pi$
$137$		−	261.817i		−	1.91107i	0.294874	−	0.955536i	$-0.404722\pi$
$138$	−86.7457	+	42.6443i	−0.628592	+	0.309017i
$139$	−138.939			−0.999560			−0.499780	−	0.866153i	$-0.666586\pi$
$139$	−138.939			−0.999560			−0.499780	+	0.866153i	$0.666586\pi$
$140$			9.93063i			0.0709331i
$141$	23.9580	+	48.7346i	0.169915	+	0.345636i
$142$	278.738			1.96295
$143$			16.6934i			0.116737i
$144$	−109.028	+	141.359i	−0.757138	+	0.981661i
$145$	297.203			2.04968
$146$		−	251.713i		−	1.72406i
$147$	−130.385	+	64.0974i	−0.886971	+	0.436036i
$148$	−79.8622			−0.539609
$149$		−	57.3808i		−	0.385106i	−0.981287	−	0.192553i	$-0.938323\pi$
$149$		−	57.3808i		−	0.385106i	0.981287	−	0.192553i	$-0.0616767\pi$
$150$	−134.539	−	273.676i	−0.896929	−	1.82450i
$151$	45.3936			0.300620			0.150310	−	0.988639i	$-0.451973\pi$
$151$	45.3936			0.300620			0.150310	+	0.988639i	$0.451973\pi$
$152$			67.1647i			0.441873i
$153$	119.342	+	92.0466i	0.780014	+	0.601612i
$154$	−22.7042			−0.147430
$155$			66.5594i			0.429415i
$156$	5.63943	−	2.77235i	0.0361502	−	0.0177715i
$157$	−74.9347			−0.477291			−0.238645	−	0.971107i	$-0.576703\pi$
$157$	−74.9347			−0.477291			−0.238645	+	0.971107i	$0.576703\pi$
$158$			237.991i			1.50627i
$159$	−62.3445	−	126.819i	−0.392104	−	0.797605i
$160$	199.180			1.24487
$161$		−	10.2900i		−	0.0639128i
$162$	185.303	−	48.6659i	1.14385	−	0.300407i
$163$	−313.263			−1.92186			−0.960930	−	0.276791i	$-0.910729\pi$
$163$	−313.263			−1.92186			−0.960930	+	0.276791i	$0.910729\pi$
$164$			76.1814i			0.464520i
$165$	282.071	−	138.666i	1.70952	−	0.840403i
$166$	144.171			0.868499
$167$			239.568i			1.43454i	0.696795	+	0.717270i	$0.254609\pi$
$167$			239.568i			1.43454i	−0.696795	+	0.717270i	$0.745391\pi$
$168$	−5.68825	−	11.5709i	−0.0338586	−	0.0688742i
$169$	−167.274			−0.989789
$170$		−	326.571i		−	1.92101i
$171$	64.8860	−	84.1273i	0.379450	−	0.491973i
$172$	−39.3299			−0.228662
$173$			277.582i			1.60452i	0.596977	+	0.802259i	$0.296369\pi$
$173$			277.582i			1.60452i	−0.596977	+	0.802259i	$0.703631\pi$
$174$	229.547	−	112.846i	1.31924	−	0.648538i
$175$	32.4640			0.185508
$176$			252.060i			1.43216i
$177$	10.1662	+	20.6797i	0.0574359	+	0.116834i
$178$	−170.890			−0.960054
$179$		−	65.6583i		−	0.366806i	−0.983038	−	0.183403i	$-0.941289\pi$
$179$		−	65.6583i		−	0.366806i	0.983038	−	0.183403i	$-0.0587114\pi$
$180$	−93.6894	−	72.2611i	−0.520497	−	0.401450i
$181$	79.2983			0.438112			0.219056	−	0.975712i	$-0.429702\pi$
$181$	79.2983			0.438112			0.219056	+	0.975712i	$0.429702\pi$
$182$			2.34711i			0.0128962i
$183$	113.013	−	55.5576i	0.617560	−	0.303593i
$184$	−77.5053			−0.421225
$185$			412.945i			2.23213i
$186$	25.2720	+	51.4076i	0.135871	+	0.276385i
$187$	212.801			1.13797
$188$		−	28.8636i		−	0.153530i
$189$	−4.05346	+	19.9884i	−0.0214469	+	0.105759i
$190$	−230.208			−1.21162
$191$			233.915i			1.22469i	0.790592	+	0.612343i	$0.209773\pi$
$191$			233.915i			1.22469i	−0.790592	+	0.612343i	$0.790227\pi$
$192$	−59.7729	+	29.3844i	−0.311317	+	0.153044i
$193$	−64.8763			−0.336147			−0.168073	−	0.985774i	$-0.553755\pi$
$193$	−64.8763			−0.336147			−0.168073	+	0.985774i	$0.553755\pi$
$194$		−	406.593i		−	2.09584i
$195$	−14.3350	−	29.1599i	−0.0735130	−	0.149538i
$196$	77.2217			0.393989
$197$		−	197.217i		−	1.00110i	−0.865707	−	0.500551i	$-0.833131\pi$
$197$		−	197.217i		−	1.00110i	0.865707	−	0.500551i	$-0.166869\pi$
$198$	165.209	−	214.200i	0.834388	−	1.08182i
$199$	−240.503			−1.20856			−0.604280	−	0.796772i	$-0.706539\pi$
$199$	−240.503			−1.20856			−0.604280	+	0.796772i	$0.706539\pi$
$200$		−	244.523i		−	1.22262i
$201$	227.564	−	111.871i	1.13216	−	0.556571i
$202$	−35.8618			−0.177534
$203$			27.2293i			0.134135i
$204$	−35.3408	−	71.8892i	−0.173239	−	0.352398i
$205$	393.912			1.92152
$206$		−	409.450i		−	1.98762i
$207$	97.0795	+	74.8758i	0.468983	+	0.361719i
$208$	26.0574			0.125276
$209$		−	150.009i		−	0.717746i
$210$	39.6593	−	19.4966i	0.188854	−	0.0928409i
$211$	−347.814			−1.64841			−0.824205	−	0.566292i	$-0.808377\pi$
$211$	−347.814			−1.64841			−0.824205	+	0.566292i	$0.808377\pi$
$212$			75.1100i			0.354292i
$213$	−155.972	−	317.273i	−0.732262	−	1.48954i
$214$	−451.966			−2.11199
$215$			203.364i			0.945877i
$216$	150.555	+	30.5312i	0.697014	+	0.141348i
$217$	−6.09808			−0.0281017
$218$			29.2141i			0.134010i
$219$	−286.511	+	140.849i	−1.30827	+	0.643148i
$220$	−167.059			−0.759361
$221$		−	21.9989i		−	0.0995427i
$222$	156.792	+	318.941i	0.706269	+	1.43667i
$223$	297.512			1.33413			0.667066	−	0.744998i	$-0.267550\pi$
$223$	297.512			1.33413			0.667066	+	0.744998i	$0.267550\pi$
$224$			18.2486i			0.0814668i
$225$	−236.227	+	306.278i	−1.04990	+	1.36124i
$226$	−333.112			−1.47395
$227$			54.2423i			0.238953i	0.992837	+	0.119476i	$0.0381216\pi$
$227$			54.2423i			0.238953i	−0.992837	+	0.119476i	$0.961878\pi$
$228$	−50.6765	+	24.9126i	−0.222265	+	0.109266i
$229$	−225.479			−0.984624			−0.492312	−	0.870419i	$-0.663848\pi$
$229$	−225.479			−0.984624			−0.492312	+	0.870419i	$0.663848\pi$
$230$		−	265.651i		−	1.15500i
$231$	12.7044	+	25.8429i	0.0549975	+	0.111874i
$232$	205.095			0.884030
$233$			73.7226i			0.316406i	0.987407	+	0.158203i	$0.0505700\pi$
$233$			73.7226i			0.316406i	−0.987407	+	0.158203i	$0.949430\pi$
$234$	−22.1435	−	17.0789i	−0.0946305	−	0.0729869i
$235$	−149.245			−0.635087
$236$		−	12.2478i		−	0.0518973i
$237$	270.892	−	133.171i	1.14300	−	0.561903i
$238$	29.9200			0.125714
$239$			338.302i			1.41549i	0.706468	+	0.707745i	$0.250287\pi$
$239$			338.302i			1.41549i	−0.706468	+	0.707745i	$0.749713\pi$
$240$	−216.450	−	440.295i	−0.901874	−	1.83456i
$241$	238.213			0.988435			0.494218	−	0.869338i	$-0.335455\pi$
$241$	238.213			0.988435			0.494218	+	0.869338i	$0.335455\pi$
$242$		−	95.7458i		−	0.395644i
$243$	−159.083	−	183.689i	−0.654662	−	0.755922i
$244$	−66.9334			−0.274317
$245$		−	399.292i		−	1.62976i
$246$	304.241	−	149.565i	1.23675	−	0.607989i
$247$	−15.5076			−0.0627838
$248$			45.9315i			0.185208i
$249$	−80.6727	−	164.102i	−0.323987	−	0.659044i
$250$	350.576			1.40230
$251$		−	151.843i		−	0.604953i	−0.953157	−	0.302477i	$-0.902187\pi$
$251$		−	151.843i		−	0.604953i	0.953157	−	0.302477i	$-0.0978134\pi$
$252$	6.62046	−	8.58369i	0.0262717	−	0.0340623i
$253$	173.104			0.684207
$254$			349.515i			1.37604i
$255$	−371.719	+	182.737i	−1.45772	+	0.716617i
$256$	263.964			1.03111
$257$		−	370.120i		−	1.44016i	−0.693893	−	0.720078i	$-0.744106\pi$
$257$		−	370.120i		−	1.44016i	0.693893	−	0.720078i	$-0.255894\pi$
$258$	77.2155	+	157.069i	0.299285	+	0.608796i
$259$	−37.8334			−0.146075
$260$			17.2702i			0.0664240i
$261$	−256.892	−	198.137i	−0.984261	−	0.759144i
$262$	−112.496			−0.429375
$263$		−	280.769i		−	1.06756i	−0.845622	−	0.533782i	$-0.820770\pi$
$263$		−	280.769i		−	1.06756i	0.845622	−	0.533782i	$-0.179230\pi$
$264$	194.652	−	95.6914i	0.737320	−	0.362467i
$265$	388.372			1.46556
$266$		−	21.0914i		−	0.0792908i
$267$	95.6236	+	194.514i	0.358141	+	0.728518i
$268$	−134.777			−0.502900
$269$			259.946i			0.966342i	0.875526	+	0.483171i	$0.160515\pi$
$269$			259.946i			0.966342i	−0.875526	+	0.483171i	$0.839485\pi$
$270$	−104.646	+	516.030i	−0.387579	+	1.91122i
$271$	142.113			0.524402			0.262201	−	0.965013i	$-0.415552\pi$
$271$	142.113			0.524402			0.262201	+	0.965013i	$0.415552\pi$
$272$		−	332.170i		−	1.22121i
$273$	2.67159	−	1.31336i	0.00978603	−	0.00481083i
$274$	619.269			2.26011
$275$			546.130i			1.98593i
$276$	−28.7482	−	58.4786i	−0.104160	−	0.211879i
$277$	246.675			0.890523			0.445262	−	0.895400i	$-0.353111\pi$
$277$	246.675			0.890523			0.445262	+	0.895400i	$0.353111\pi$
$278$		−	328.628i		−	1.18212i
$279$	44.3732	−	57.5316i	0.159044	−	0.206207i
$280$	35.4347			0.126553
$281$			68.3398i			0.243202i	0.992579	+	0.121601i	$0.0388028\pi$
$281$			68.3398i			0.243202i	−0.992579	+	0.121601i	$0.961197\pi$
$282$	−115.271	+	56.6673i	−0.408762	+	0.200948i
$283$	−104.955			−0.370866			−0.185433	−	0.982657i	$-0.559369\pi$
$283$	−104.955			−0.370866			−0.185433	+	0.982657i	$0.559369\pi$
$284$			187.908i			0.661649i
$285$	128.816	+	262.034i	0.451987	+	0.919417i
$286$	−39.4845			−0.138058
$287$			36.0897i			0.125748i
$288$	−172.164	−	132.787i	−0.597792	−	0.461067i
$289$	8.56615			0.0296406
$290$			702.967i			2.42402i
$291$	−462.804	+	227.515i	−1.59039	+	0.781838i
$292$	169.689			0.581128
$293$			9.70650i			0.0331280i	0.999863	+	0.0165640i	$0.00527273\pi$
$293$			9.70650i			0.0331280i	−0.999863	+	0.0165640i	$0.994727\pi$
$294$	−151.608	−	308.396i	−0.515673	−	1.04897i
$295$	−63.3297			−0.214677
$296$			284.966i			0.962724i
$297$	−336.257	−	68.1899i	−1.13218	−	0.229596i
$298$	135.721			0.455441
$299$		−	17.8951i		−	0.0598500i
$300$	184.495	−	90.6981i	0.614984	−	0.302327i
$301$	−18.6319			−0.0619000
$302$			107.368i			0.355524i
$303$	20.0669	+	40.8195i	0.0662275	+	0.134718i
$304$	−234.155			−0.770246
$305$			346.094i			1.13473i
$306$	−217.716	+	282.277i	−0.711489	+	0.922474i
$307$	266.280			0.867363			0.433682	−	0.901066i	$-0.357214\pi$
$307$	266.280			0.867363			0.433682	+	0.901066i	$0.357214\pi$
$308$		−	15.3057i		−	0.0496940i
$309$	−466.056	+	229.114i	−1.50827	+	0.741468i
$310$	−157.431			−0.507842
$311$			186.416i			0.599408i	0.954032	+	0.299704i	$0.0968879\pi$
$311$			186.416i			0.599408i	−0.954032	+	0.299704i	$0.903112\pi$
$312$	−9.89237	−	20.1227i	−0.0317063	−	0.0644960i
$313$	564.581			1.80377			0.901887	−	0.431972i	$-0.142182\pi$
$313$	564.581			1.80377			0.901887	+	0.431972i	$0.142182\pi$
$314$		−	177.241i		−	0.564462i
$315$	−44.3838	−	34.2325i	−0.140901	−	0.108675i
$316$	−160.439			−0.507717
$317$		−	66.4847i		−	0.209731i	−0.994486	−	0.104866i	$-0.966559\pi$
$317$		−	66.4847i		−	0.209731i	0.994486	−	0.104866i	$-0.0334412\pi$
$318$	299.962	−	147.462i	0.943277	−	0.463716i
$319$	−458.069			−1.43595
$320$		−	183.049i		−	0.572029i
$321$	252.904	+	514.449i	0.787862	+	1.60264i
$322$	24.3386			0.0755856
$323$			197.685i			0.612027i
$324$	32.8076	+	124.920i	0.101258	+	0.385556i
$325$	56.4577			0.173716
$326$		−	740.954i		−	2.27286i
$327$	33.2529	−	16.3472i	0.101691	−	0.0499913i
$328$	271.832			0.828757
$329$		−	13.6737i		−	0.0415613i
$330$	327.984	+	667.175i	0.993891	+	2.02174i
$331$	−112.836			−0.340893			−0.170446	−	0.985367i	$-0.554521\pi$
$331$	−112.836			−0.340893			−0.170446	+	0.985367i	$0.554521\pi$
$332$			97.1911i			0.292744i
$333$	275.298	−	356.935i	0.826721	−	1.07188i
$334$	−566.645			−1.69654
$335$			696.895i			2.08028i
$336$	40.3392	−	19.8308i	0.120057	−	0.0590203i
$337$	−419.505			−1.24482			−0.622411	−	0.782690i	$-0.713847\pi$
$337$	−419.505			−1.24482			−0.622411	+	0.782690i	$0.713847\pi$
$338$		−	395.650i		−	1.17056i
$339$	186.398	+	379.164i	0.549845	+	1.11848i
$340$	220.154			0.647512
$341$		−	102.586i		−	0.300838i
$342$	198.984	+	153.473i	0.581825	+	0.448752i
$343$	73.5961			0.214566
$344$			140.338i			0.407959i
$345$	−302.376	+	148.649i	−0.876453	+	0.430866i
$346$	−656.556			−1.89756
$347$		−	399.509i		−	1.15132i	−0.817688	−	0.575662i	$-0.804744\pi$
$347$		−	399.509i		−	1.15132i	0.817688	−	0.575662i	$-0.195256\pi$
$348$	76.0736	+	154.746i	0.218602	+	0.444674i
$349$	−139.763			−0.400466			−0.200233	−	0.979748i	$-0.564170\pi$
$349$	−139.763			−0.400466			−0.200233	+	0.979748i	$0.564170\pi$
$350$			76.7862i			0.219389i
$351$	−7.04932	+	34.7615i	−0.0200835	+	0.0990358i
$352$	−306.989			−0.872127
$353$		−	257.040i		−	0.728158i	−0.931368	−	0.364079i	$-0.881384\pi$
$353$		−	257.040i		−	0.728158i	0.931368	−	0.364079i	$-0.118616\pi$
$354$	−48.9131	+	24.0458i	−0.138173	+	0.0679259i
$355$	971.620			2.73696
$356$		−	115.203i		−	0.323604i
$357$	−16.7421	−	34.0563i	−0.0468968	−	0.0953959i
$358$	155.300			0.433799
$359$		−	619.504i		−	1.72564i	−0.505514	−	0.862818i	$-0.668697\pi$
$359$		−	619.504i		−	1.72564i	0.505514	−	0.862818i	$-0.331303\pi$
$360$	−257.844	+	334.305i	−0.716233	+	0.928625i
$361$	−221.647			−0.613981
$362$			187.562i			0.518128i
$363$	−108.982	+	53.5758i	−0.300227	+	0.147592i
$364$	−1.58228			−0.00434691
$365$		−	877.415i		−	2.40388i
$366$	131.409	+	267.308i	0.359041	+	0.730349i
$367$	−102.428			−0.279095			−0.139548	−	0.990215i	$-0.544565\pi$
$367$	−102.428			−0.279095			−0.139548	+	0.990215i	$0.544565\pi$
$368$		−	270.205i		−	0.734253i
$369$	−340.484	−	262.610i	−0.922721	−	0.711680i
$370$	−976.727			−2.63980
$371$			35.5821i			0.0959087i
$372$	−34.6558	+	17.0369i	−0.0931608	+	0.0457980i
$373$	−293.963			−0.788105			−0.394052	−	0.919088i	$-0.628927\pi$
$373$	−293.963			−0.788105			−0.394052	+	0.919088i	$0.628927\pi$
$374$			503.333i			1.34581i
$375$	−196.169	−	399.042i	−0.523118	−	1.06411i
$376$	−102.992			−0.273914
$377$			47.3542i			0.125608i
$378$	−47.2780	−	9.58754i	−0.125074	−	0.0253639i
$379$	−0.946681			−0.00249784			−0.00124892	−	0.999999i	$-0.500398\pi$
$379$	−0.946681			−0.00249784			−0.00124892	+	0.999999i	$0.500398\pi$
$380$		−	155.192i		−	0.408401i
$381$	397.834	−	195.576i	1.04418	−	0.513322i
$382$	−553.273			−1.44836
$383$			136.045i			0.355210i	0.984102	+	0.177605i	$0.0568349\pi$
$383$			136.045i			0.355210i	−0.984102	+	0.177605i	$0.943165\pi$
$384$	−197.398	−	401.540i	−0.514056	−	1.04568i
$385$	−79.1417			−0.205563
$386$		−	153.450i		−	0.397539i
$387$	135.577	−	175.781i	0.350327	−	0.454213i
$388$	274.100			0.706444
$389$			152.657i			0.392433i	0.980561	+	0.196217i	$0.0628656\pi$
$389$			152.657i			0.392433i	−0.980561	+	0.196217i	$0.937134\pi$
$390$	68.9711	−	33.9063i	0.176849	−	0.0869392i
$391$	−228.120			−0.583428
$392$		−	275.545i		−	0.702920i
$393$	62.9488	+	128.049i	0.160175	+	0.325823i
$394$	466.472			1.18394
$395$			829.582i			2.10021i
$396$	144.400	+	111.374i	0.364647	+	0.281246i
$397$	350.842			0.883733			0.441867	−	0.897081i	$-0.354316\pi$
$397$	350.842			0.883733			0.441867	+	0.897081i	$0.354316\pi$
$398$		−	568.856i		−	1.42929i
$399$	−24.0072	+	11.8020i	−0.0601683	+	0.0295788i
$400$	852.476			2.13119
$401$		−	522.970i		−	1.30417i	−0.758148	−	0.652083i	$-0.773895\pi$
$401$		−	522.970i		−	1.30417i	0.758148	−	0.652083i	$-0.226105\pi$
$402$	264.605	+	538.251i	0.658222	+	1.33893i
$403$	−10.6051			−0.0263154
$404$		−	24.1758i		−	0.0598411i
$405$	645.926	−	169.639i	1.59488	−	0.418861i
$406$	−64.4049			−0.158633
$407$		−	636.458i		−	1.56378i
$408$	−256.517	+	126.104i	−0.628718	+	0.309079i
$409$	639.029			1.56242			0.781209	−	0.624270i	$-0.214603\pi$
$409$	639.029			1.56242			0.781209	+	0.624270i	$0.214603\pi$
$410$			931.710i			2.27246i
$411$	−346.520	−	704.881i	−0.843115	−	1.71504i
$412$	276.026			0.669967
$413$		−	5.80218i		−	0.0140489i
$414$	−177.102	+	229.620i	−0.427782	+	0.554637i
$415$	502.547			1.21096
$416$			31.7359i			0.0762881i
$417$	−374.060	+	183.888i	−0.897026	+	0.440979i
$418$	354.812			0.848833
$419$			378.805i			0.904069i	0.892000	+	0.452035i	$0.149302\pi$
$419$			378.805i			0.904069i	−0.892000	+	0.452035i	$0.850698\pi$
$420$	13.1434	+	26.7359i	0.0312938	+	0.0636569i
$421$	−672.352			−1.59704			−0.798518	−	0.601971i	$-0.794382\pi$
$421$	−672.352			−1.59704			−0.798518	+	0.601971i	$0.794382\pi$
$422$		−	822.676i		−	1.94947i
$423$	129.003	+	99.4976i	0.304971	+	0.235219i
$424$	268.009			0.632098
$425$		−	719.701i		−	1.69341i
$426$	750.437	−	368.916i	1.76159	−	0.866000i
$427$	−31.7086			−0.0742590
$428$		−	304.688i		−	0.711887i
$429$	22.0941	+	44.9431i	0.0515014	+	0.104763i
$430$	−481.011			−1.11863
$431$		−	152.719i		−	0.354337i	−0.984180	−	0.177169i	$-0.943306\pi$
$431$		−	152.719i		−	0.354337i	0.984180	−	0.177169i	$-0.0566938\pi$
$432$	−106.440	+	524.877i	−0.246389	+	1.21499i
$433$	−72.8581			−0.168264			−0.0841318	−	0.996455i	$-0.526812\pi$
$433$	−72.8581			−0.168264			−0.0841318	+	0.996455i	$0.526812\pi$
$434$		−	14.4236i		−	0.0332341i
$435$	800.150	−	393.355i	1.83942	−	0.904264i
$436$	−19.6944			−0.0451706
$437$			160.808i			0.367981i
$438$	−333.147	−	677.678i	−0.760610	−	1.54721i
$439$	527.988			1.20271			0.601353	−	0.798984i	$-0.294629\pi$
$439$	527.988			1.20271			0.601353	+	0.798984i	$0.294629\pi$
$440$			596.106i			1.35479i
$441$	−266.196	+	345.134i	−0.603619	+	0.782617i
$442$	52.0335			0.117723
$443$			445.420i			1.00546i	0.864443	+	0.502731i	$0.167672\pi$
$443$			445.420i			1.00546i	−0.864443	+	0.502731i	$0.832328\pi$
$444$	−215.010	+	105.699i	−0.484257	+	0.238061i
$445$	−595.683			−1.33861
$446$			703.696i			1.57779i
$447$	−75.9447	−	154.484i	−0.169899	−	0.345602i
$448$	16.7707			0.0374346
$449$		−	405.943i		−	0.904104i	−0.891992	−	0.452052i	$-0.850692\pi$
$449$		−	405.943i		−	0.904104i	0.891992	−	0.452052i	$-0.149308\pi$
$450$	−724.431	−	558.742i	−1.60985	−	1.24165i
$451$	−607.124			−1.34617
$452$		−	224.564i		−	0.496823i
$453$	122.212	−	60.0794i	0.269783	−	0.132626i
$454$	−128.298			−0.282594
$455$			8.18150i			0.0179813i
$456$	88.8939	+	180.825i	0.194943	+	0.396546i
$457$	4.27855			0.00936226			0.00468113	−	0.999989i	$-0.498510\pi$
$457$	4.27855			0.00936226			0.00468113	+	0.999989i	$0.498510\pi$
$458$		−	533.319i		−	1.16445i
$459$	443.127	+	89.8620i	0.965417	+	0.195778i
$460$	179.086			0.389316
$461$		−	87.0024i		−	0.188725i	−0.995538	−	0.0943627i	$-0.969919\pi$
$461$		−	87.0024i		−	0.188725i	0.995538	−	0.0943627i	$-0.0300813\pi$
$462$	−61.1256	+	30.0494i	−0.132307	+	0.0650421i
$463$	−144.683			−0.312491			−0.156245	−	0.987718i	$-0.549939\pi$
$463$	−144.683			−0.312491			−0.156245	+	0.987718i	$0.549939\pi$
$464$			715.018i			1.54099i
$465$	88.0927	+	179.195i	0.189447	+	0.385367i
$466$	−174.374			−0.374194
$467$			322.080i			0.689678i	0.938662	+	0.344839i	$0.112066\pi$
$467$			322.080i			0.689678i	−0.938662	+	0.344839i	$0.887934\pi$
$468$	11.5136	−	14.9278i	0.0246016	−	0.0318970i
$469$	−63.8485			−0.136138
$470$		−	353.007i		−	0.751078i
$471$	−201.744	+	99.1776i	−0.428331	+	0.210568i
$472$	−43.7028			−0.0925906
$473$		−	313.438i		−	0.662659i
$474$	314.986	+	640.734i	0.664527	+	1.35176i
$475$	−507.335			−1.06807
$476$			20.1702i			0.0423744i
$477$	−335.696	−	258.917i	−0.703765	−	0.542802i
$478$	−800.177			−1.67401
$479$			174.177i			0.363625i	0.983333	+	0.181813i	$0.0581965\pi$
$479$			174.177i			0.363625i	−0.983333	+	0.181813i	$0.941804\pi$
$480$	536.244	−	263.618i	1.11718	−	0.549205i
$481$	−65.7956			−0.136789
$482$			563.439i			1.16896i
$483$	−13.6190	−	27.7033i	−0.0281966	−	0.0573567i
$484$	64.5459			0.133359
$485$		−	1417.29i		−	2.92226i
$486$	434.475	−	376.274i	0.893981	−	0.774227i
$487$	312.915			0.642537			0.321268	−	0.946988i	$-0.395891\pi$
$487$	312.915			0.642537			0.321268	+	0.946988i	$0.395891\pi$
$488$			238.833i			0.489413i
$489$	−843.388	+	414.611i	−1.72472	+	0.847875i
$490$	944.435			1.92742
$491$			308.713i			0.628744i	0.949300	+	0.314372i	$0.101794\pi$
$491$			308.713i			0.628744i	−0.949300	+	0.314372i	$0.898206\pi$
$492$	100.828	+	205.100i	0.204934	+	0.416871i
$493$	603.653			1.22445
$494$		−	36.6797i		−	0.0742505i
$495$	575.881	−	746.653i	1.16340	−	1.50839i
$496$	−160.130			−0.322843
$497$			89.0185i			0.179112i
$498$	388.146	−	190.813i	0.779410	−	0.383159i
$499$	221.514			0.443915			0.221957	−	0.975056i	$-0.428755\pi$
$499$	221.514			0.443915			0.221957	+	0.975056i	$0.428755\pi$
$500$			236.337i			0.472673i
$501$	317.074	+	644.981i	0.632882	+	1.28739i
$502$	359.151			0.715440
$503$		−	444.545i		−	0.883786i	−0.897068	−	0.441893i	$-0.854307\pi$
$503$		−	444.545i		−	0.883786i	0.897068	−	0.441893i	$-0.145693\pi$
$504$	−30.6286	−	23.6233i	−0.0607710	−	0.0468716i
$505$	−125.006			−0.247537
$506$			409.439i			0.809168i
$507$	−450.347	+	221.391i	−0.888258	+	0.436669i
$508$	−235.621			−0.463821
$509$			675.982i			1.32806i	0.747707	+	0.664029i	$0.231155\pi$
$509$			675.982i			1.32806i	−0.747707	+	0.664029i	$0.768845\pi$
$510$	−432.224	−	879.216i	−0.847498	−	1.72395i
$511$	80.3875			0.157314
$512$			27.7635i			0.0542257i
$513$	63.3460	−	312.371i	0.123481	−	0.608910i
$514$	875.435			1.70318
$515$		−	1427.25i		−	2.77137i
$516$	−105.886	+	52.0539i	−0.205206	+	0.100880i
$517$	230.027			0.444927
$518$		−	89.4864i		−	0.172754i
$519$	367.385	+	747.323i	0.707871	+	1.43993i
$520$	61.6241			0.118508
$521$		−	600.786i		−	1.15314i	−0.817048	−	0.576570i	$-0.804391\pi$
$521$		−	600.786i		−	1.15314i	0.817048	−	0.576570i	$-0.195609\pi$
$522$	468.648	−	607.621i	0.897792	−	1.16402i
$523$	690.414			1.32010			0.660052	−	0.751220i	$-0.270534\pi$
$523$	690.414			1.32010			0.660052	+	0.751220i	$0.270534\pi$
$524$		−	75.8381i		−	0.144729i
$525$	87.4016	−	42.9668i	0.166479	−	0.0818415i
$526$	664.097			1.26254
$527$			135.190i			0.256527i
$528$	333.607	+	678.613i	0.631831	+	1.28525i
$529$	343.434			0.649214
$530$			918.607i			1.73322i
$531$	54.7400	+	42.2200i	0.103089	+	0.0795104i
$532$	14.2185			0.0267265
$533$			62.7632i			0.117755i
$534$	−460.080	+	226.176i	−0.861573	+	0.423551i
$535$	−1575.45			−2.94477
$536$			480.915i			0.897230i
$537$	−86.9002	−	176.770i	−0.161825	−	0.329180i
$538$	−614.844			−1.14283
$539$			615.415i			1.14177i
$540$	−347.876	−	70.5460i	−0.644215	−	0.130641i
$541$	2.37133			0.00438324			0.00219162	−	0.999998i	$-0.499302\pi$
$541$	2.37133			0.00438324			0.00219162	+	0.999998i	$0.499302\pi$
$542$			336.136i			0.620177i
$543$	213.492	−	104.953i	0.393172	−	0.193284i
$544$	404.556			0.743669
$545$			101.834i			0.186851i
$546$	3.10645	+	6.31904i	0.00568946	+	0.0115733i
$547$	−78.2775			−0.143103			−0.0715517	−	0.997437i	$-0.522795\pi$
$547$	−78.2775			−0.143103			−0.0715517	+	0.997437i	$0.522795\pi$
$548$			417.473i			0.761812i
$549$	230.731	−	299.151i	0.420274	−	0.544902i
$550$	−1291.75			−2.34863
$551$		−	425.530i		−	0.772287i
$552$	−208.665	+	102.580i	−0.378016	+	0.185833i
$553$	−76.0052			−0.137442
$554$			583.454i			1.05317i
$555$	546.541	+	1111.76i	0.984759	+	2.00316i
$556$	221.541			0.398455
$557$			116.140i			0.208509i	0.994551	+	0.104255i	$0.0332457\pi$
$557$			116.140i			0.208509i	−0.994551	+	0.104255i	$0.966754\pi$
$558$	136.078	+	104.955i	0.243868	+	0.188091i
$559$	−32.4025			−0.0579651
$560$			123.535i			0.220599i
$561$	572.918	−	281.647i	1.02124	−	0.502045i
$562$	−161.642			−0.287620
$563$		−	509.696i		−	0.905321i	−0.891683	−	0.452661i	$-0.850475\pi$
$563$		−	509.696i		−	0.905321i	0.891683	−	0.452661i	$-0.149525\pi$
$564$	−38.2016	−	77.7085i	−0.0677333	−	0.137781i
$565$	−1161.16			−2.05514
$566$		−	248.247i		−	0.438600i
$567$	15.5421	+	59.1788i	0.0274110	+	0.104372i
$568$	670.499			1.18046
$569$			795.747i			1.39850i	0.714877	+	0.699250i	$0.246483\pi$
$569$			795.747i			1.39850i	−0.714877	+	0.699250i	$0.753517\pi$
$570$	−619.782	+	304.686i	−1.08734	+	0.534536i
$571$	−324.633			−0.568534			−0.284267	−	0.958745i	$-0.591750\pi$
$571$	−324.633			−0.568534			−0.284267	+	0.958745i	$0.591750\pi$
$572$		−	26.6180i		−	0.0465350i
$573$	309.591	+	629.761i	0.540299	+	1.09906i
$574$	−85.3620			−0.148714
$575$		−	585.444i		−	1.01816i
$576$	−122.034	+	158.221i	−0.211864	+	0.274690i
$577$	−209.324			−0.362780			−0.181390	−	0.983411i	$-0.558060\pi$
$577$	−209.324			−0.362780			−0.181390	+	0.983411i	$0.558060\pi$
$578$			20.2613i			0.0350541i
$579$	−174.664	+	85.8652i	−0.301665	+	0.148299i
$580$	−473.897			−0.817064
$581$			46.0427i			0.0792473i
$582$	−538.135	−	1094.66i	−0.924631	−	1.88085i
$583$	−598.586			−1.02673
$584$		−	605.490i		−	1.03680i
$585$	−77.1874	−	59.5334i	−0.131944	−	0.101766i
$586$	−22.9585			−0.0391784
$587$		−	84.7067i		−	0.144304i	−0.997394	−	0.0721522i	$-0.977013\pi$
$587$		−	84.7067i		−	0.144304i	0.997394	−	0.0721522i	$-0.0229867\pi$
$588$	207.901	−	102.205i	0.353574	−	0.173817i
$589$	95.2985			0.161797
$590$		−	149.792i		−	0.253885i
$591$	−261.021	−	530.960i	−0.441660	−	0.898410i
$592$	−993.472			−1.67816
$593$			1039.81i			1.75347i	0.480971	+	0.876737i	$0.340284\pi$
$593$			1039.81i			1.75347i	−0.480971	+	0.876737i	$0.659716\pi$
$594$	161.288	−	795.340i	0.271528	−	1.33896i
$595$	104.294			0.175285
$596$			91.4949i			0.153515i
$597$	−647.499	+	318.311i	−1.08459	+	0.533185i
$598$	42.3269			0.0707808
$599$			331.588i			0.553569i	0.960932	+	0.276784i	$0.0892688\pi$
$599$			331.588i			0.553569i	−0.960932	+	0.276784i	$0.910731\pi$
$600$	−323.631	−	658.321i	−0.539386	−	1.09720i
$601$	471.745			0.784933			0.392467	−	0.919766i	$-0.371622\pi$
$601$	471.745			0.784933			0.392467	+	0.919766i	$0.371622\pi$
$602$		−	44.0695i		−	0.0732052i
$603$	464.599	−	602.372i	0.770480	−	0.998958i
$604$	−72.3811			−0.119836
$605$		−	333.749i		−	0.551650i
$606$	−96.5494	+	47.4638i	−0.159322	+	0.0783232i
$607$	631.905			1.04103			0.520515	−	0.853852i	$-0.325740\pi$
$607$	631.905			1.04103			0.520515	+	0.853852i	$0.325740\pi$
$608$		−	285.182i		−	0.469049i
$609$	36.0386	+	73.3086i	0.0591767	+	0.120375i
$610$	−818.606			−1.34198
$611$		−	23.7797i		−	0.0389193i
$612$	−190.294	−	146.770i	−0.310937	−	0.239821i
$613$	727.960			1.18754			0.593768	−	0.804636i	$-0.297640\pi$
$613$	727.960			1.18754			0.593768	+	0.804636i	$0.297640\pi$
$614$			629.826i			1.02578i
$615$	1060.52	−	521.351i	1.72442	−	0.847726i
$616$	−54.6144			−0.0886597
$617$			342.421i			0.554977i	0.960729	+	0.277489i	$0.0895021\pi$
$617$			342.421i			0.554977i	−0.960729	+	0.277489i	$0.910498\pi$
$618$	−541.916	−	1102.35i	−0.876888	−	1.78374i
$619$	−882.209			−1.42522			−0.712608	−	0.701562i	$-0.752486\pi$
$619$	−882.209			−1.42522			−0.712608	+	0.701562i	$0.752486\pi$
$620$		−	106.130i		−	0.171178i
$621$	360.463	+	73.0987i	0.580456	+	0.117711i
$622$	−440.925			−0.708882
$623$		−	54.5757i		−	0.0876014i
$624$	70.1535	−	34.4876i	0.112426	−	0.0552686i
$625$	147.602			0.236164
$626$			1335.39i			2.13321i
$627$	−198.540	−	403.864i	−0.316651	−	0.644121i
$628$	119.485			0.190263
$629$			838.737i			1.33344i
$630$	80.9693	−	104.980i	0.128523	−	0.166635i
$631$	−145.624			−0.230783			−0.115392	−	0.993320i	$-0.536812\pi$
$631$	−145.624			−0.230783			−0.115392	+	0.993320i	$0.536812\pi$
$632$			572.481i			0.905825i
$633$	−936.408	+	460.340i	−1.47932	+	0.727235i
$634$	157.255			0.248036
$635$			1218.33i			1.91863i
$636$	99.4097	+	202.216i	0.156305	+	0.317950i
$637$	63.6203			0.0998749
$638$		−	1083.46i		−	1.69821i
$639$	−839.835	−	647.751i	−1.31430	−	1.01369i
$640$	1229.68			1.92137
$641$		−	588.864i		−	0.918665i	−0.888264	−	0.459332i	$-0.848089\pi$
$641$		−	588.864i		−	0.918665i	0.888264	−	0.459332i	$-0.151911\pi$
$642$	−1216.81	+	598.187i	−1.89535	+	0.931755i
$643$	86.5512			0.134605			0.0673027	−	0.997733i	$-0.478561\pi$
$643$	86.5512			0.134605			0.0673027	+	0.997733i	$0.478561\pi$
$644$			16.4076i			0.0254776i
$645$	269.156	+	547.509i	0.417296	+	0.848851i
$646$	−467.579			−0.723806
$647$		−	607.286i		−	0.938618i	−0.883034	−	0.469309i	$-0.844503\pi$
$647$		−	607.286i		−	0.938618i	0.883034	−	0.469309i	$-0.155497\pi$
$648$	445.743	−	117.065i	0.687875	−	0.180656i
$649$	97.6079			0.150397
$650$			133.538i			0.205443i
$651$	−16.4176	+	8.07093i	−0.0252191	+	0.0123977i
$652$	499.505			0.766112
$653$			1115.22i			1.70783i	0.520410	+	0.853917i	$0.325779\pi$
$653$			1115.22i			1.70783i	−0.520410	+	0.853917i	$0.674221\pi$
$654$	38.6655	+	78.6522i	0.0591216	+	0.120263i
$655$	−392.137			−0.598683
$656$			947.683i			1.44464i
$657$	−584.947	+	758.407i	−0.890330	+	1.15435i
$658$	32.3420			0.0491519
$659$			974.698i			1.47906i	0.673126	+	0.739528i	$0.264951\pi$
$659$			974.698i			1.47906i	−0.673126	+	0.739528i	$0.735049\pi$
$660$	−449.768	+	221.107i	−0.681467	+	0.335010i
$661$	−24.7297			−0.0374126			−0.0187063	−	0.999825i	$-0.505955\pi$
$661$	−24.7297			−0.0374126			−0.0187063	+	0.999825i	$0.505955\pi$
$662$		−	266.887i		−	0.403153i
$663$	−29.1161	−	59.2270i	−0.0439156	−	0.0893318i
$664$	346.800			0.522289
$665$		−	73.5198i		−	0.110556i
$666$	844.249	+	651.156i	1.26764	+	0.977711i
$667$	491.045			0.736199
$668$		−	381.997i		−	0.571852i
$669$	800.980	−	393.763i	1.19728	−	0.588584i
$670$	−1648.35			−2.46022
$671$		−	533.423i		−	0.794967i
$672$	24.1524	+	49.1299i	0.0359410	+	0.0731100i
$673$	509.624			0.757243			0.378621	−	0.925552i	$-0.376398\pi$
$673$	509.624			0.757243			0.378621	+	0.925552i	$0.376398\pi$
$674$		−	992.245i		−	1.47217i
$675$	−230.620	+	1137.23i	−0.341660	+	1.68479i
$676$	266.723			0.394560
$677$			344.692i			0.509146i	0.967054	+	0.254573i	$0.0819349\pi$
$677$			344.692i			0.509146i	−0.967054	+	0.254573i	$0.918065\pi$
$678$	−896.827	+	440.881i	−1.32275	+	0.650268i
$679$	129.851			0.191238
$680$		−	785.560i		−	1.15524i
$681$	71.7908	+	146.035i	0.105420	+	0.214441i
$682$	242.643			0.355782
$683$		−	494.770i		−	0.724407i	−0.932099	−	0.362204i	$-0.882024\pi$
$683$		−	494.770i		−	0.724407i	0.932099	−	0.362204i	$-0.117976\pi$
$684$	−103.462	+	134.143i	−0.151260	+	0.196115i
$685$	2158.63			3.15129
$686$			174.075i			0.253754i
$687$	−607.049	+	298.426i	−0.883623	+	0.434390i
$688$	−489.257			−0.711129
$689$			61.8805i			0.0898120i
$690$	−351.595	−	715.203i	−0.509558	−	1.03653i
$691$	399.559			0.578234			0.289117	−	0.957294i	$-0.406638\pi$
$691$	399.559			0.578234			0.289117	+	0.957294i	$0.406638\pi$
$692$		−	442.610i		−	0.639610i
$693$	68.4074	+	52.7614i	0.0987119	+	0.0761348i
$694$	944.949			1.36160
$695$		−	1145.53i		−	1.64824i
$696$	552.170	−	271.448i	0.793348	−	0.390011i
$697$	800.080			1.14789
$698$		−	330.577i		−	0.473606i
$699$	97.5735	+	198.481i	0.139590	+	0.283950i
$700$	−51.7645			−0.0739493
$701$		−	372.029i		−	0.530711i	−0.964151	−	0.265356i	$-0.914511\pi$
$701$		−	372.029i		−	0.530711i	0.964151	−	0.265356i	$-0.0854893\pi$
$702$	−82.2206	−	16.6736i	−0.117123	−	0.0237515i
$703$	591.247			0.841034
$704$			282.128i			0.400749i
$705$	−401.808	+	197.530i	−0.569941	+	0.280184i
$706$	607.970			0.861147
$707$		−	11.4529i		−	0.0161993i
$708$	−16.2102	−	32.9742i	−0.0228957	−	0.0465737i
$709$	−848.826			−1.19722			−0.598608	−	0.801042i	$-0.704279\pi$
$709$	−848.826			−1.19722			−0.598608	+	0.801042i	$0.704279\pi$
$710$			2298.15i			3.23683i
$711$	553.058	−	717.063i	0.777860	−	1.00853i
$712$	−411.071			−0.577347
$713$			109.971i			0.154236i
$714$	80.5526	−	39.5998i	0.112819	−	0.0554619i
$715$	−137.634			−0.192496
$716$			104.694i			0.146220i
$717$	447.750	+	910.799i	0.624477	+	1.27029i
$718$	1465.30			2.04080
$719$			735.217i			1.02256i	0.859416	+	0.511278i	$0.170828\pi$
$719$			735.217i			1.02256i	−0.859416	+	0.511278i	$0.829172\pi$
$720$	−1165.48	−	898.916i	−1.61872	−	1.24849i
$721$	130.763			0.181363
$722$		−	524.256i		−	0.726116i
$723$	641.332	−	315.280i	0.887043	−	0.436072i
$724$	−126.443			−0.174645
$725$			1549.21i			2.13684i
$726$	−126.722	−	257.773i	−0.174548	−	0.355059i
$727$	−760.051			−1.04546			−0.522731	−	0.852497i	$-0.675087\pi$
$727$	−760.051			−1.04546			−0.522731	+	0.852497i	$0.675087\pi$
$728$			5.64592i			0.00775538i
$729$	−671.409	−	283.990i	−0.921001	−	0.389561i
$730$	2075.33			2.84291
$731$			413.054i			0.565054i
$732$	−180.202	+	88.5878i	−0.246178	+	0.121022i
$733$	183.791			0.250738			0.125369	−	0.992110i	$-0.459988\pi$
$733$	183.791			0.250738			0.125369	+	0.992110i	$0.459988\pi$
$734$		−	242.270i		−	0.330069i
$735$	−528.471	−	1075.00i	−0.719008	−	1.46258i
$736$	329.088			0.447131
$737$		−	1074.10i		−	1.45740i
$738$	621.144	−	805.339i	0.841659	−	1.09124i
$739$	413.355			0.559344			0.279672	−	0.960096i	$-0.409774\pi$
$739$	413.355			0.559344			0.279672	+	0.960096i	$0.409774\pi$
$740$		−	658.449i		−	0.889796i
$741$	−41.7506	+	20.5247i	−0.0563436	+	0.0276986i
$742$	−84.1615			−0.113425
$743$			39.2804i			0.0528673i	0.999651	+	0.0264337i	$0.00841508\pi$
$743$			39.2804i			0.0528673i	−0.999651	+	0.0264337i	$0.991585\pi$
$744$	60.7913	+	123.660i	0.0817088	+	0.166209i
$745$	473.094			0.635026
$746$		−	695.303i		−	0.932042i
$747$	−434.385	−	335.034i	−0.581506	−	0.448506i
$748$	−339.316			−0.453632
$749$		−	144.341i		−	0.192711i
$750$	943.843	−	463.994i	1.25846	−	0.618659i
$751$	471.380			0.627670			0.313835	−	0.949478i	$-0.398386\pi$
$751$	471.380			0.627670			0.313835	+	0.949478i	$0.398386\pi$
$752$		−	359.058i		−	0.477471i
$753$	−200.968	−	408.802i	−0.266890	−	0.542898i
$754$	−112.006			−0.148549
$755$			374.262i			0.495711i
$756$	6.46333	−	31.8719i	0.00854938	−	0.0421586i
$757$	−1070.90			−1.41466			−0.707331	−	0.706883i	$-0.750101\pi$
$757$	−1070.90			−1.41466			−0.707331	+	0.706883i	$0.750101\pi$
$758$		−	2.23916i		−	0.00295404i
$759$	466.043	−	229.107i	0.614022	−	0.301854i
$760$	−553.761			−0.728633
$761$		−	144.426i		−	0.189784i	−0.995488	−	0.0948922i	$-0.969749\pi$
$761$		−	144.426i		−	0.189784i	0.995488	−	0.0948922i	$-0.0302506\pi$
$762$	462.590	+	940.986i	0.607074	+	1.23489i
$763$	−9.32989			−0.0122279
$764$		−	372.983i		−	0.488197i
$765$	−758.908	+	983.955i	−0.992037	+	1.28622i
$766$	−321.784			−0.420084
$767$		−	10.0905i		−	0.0131558i
$768$	710.660	−	349.362i	0.925339	−	0.454898i
$769$	−362.767			−0.471738			−0.235869	−	0.971785i	$-0.575794\pi$
$769$	−362.767			−0.471738			−0.235869	+	0.971785i	$0.575794\pi$
$770$		−	187.192i		−	0.243106i
$771$	−489.862	−	996.461i	−0.635359	−	1.29243i
$772$	103.447			0.133998
$773$			221.150i			0.286094i	0.989716	+	0.143047i	$0.0456899\pi$
$773$			221.150i			0.286094i	−0.989716	+	0.143047i	$0.954310\pi$
$774$	415.769	+	320.676i	0.537169	+	0.414310i
$775$	−346.948			−0.447675
$776$		−	978.052i		−	1.26038i
$777$	−101.858	+	50.0733i	−0.131091	+	0.0644444i
$778$	−361.075			−0.464106
$779$		−	563.997i		−	0.724001i
$780$	22.8575	+	46.4961i	0.0293045	+	0.0596103i
$781$	−1497.53			−1.91745
$782$		−	539.567i		−	0.689983i
$783$	−953.860	−	193.434i	−1.21821	−	0.247042i
$784$	960.626			1.22529
$785$		−	617.823i		−	0.787035i
$786$	−302.870	+	148.891i	−0.385331	+	0.189429i
$787$	−96.9762			−0.123223			−0.0616113	−	0.998100i	$-0.519624\pi$
$787$	−96.9762			−0.123223			−0.0616113	+	0.998100i	$0.519624\pi$
$788$			314.467i			0.399070i
$789$	−371.604	−	755.906i	−0.470981	−	0.958055i
$790$	−1962.19			−2.48378
$791$		−	106.384i		−	0.134492i
$792$	397.406	−	515.253i	0.501776	−	0.650572i
$793$	−55.1441			−0.0695386
$794$			829.838i			1.04514i
$795$	1045.60	−	514.019i	1.31522	−	0.646565i
$796$	383.488			0.481769
$797$		−	534.006i		−	0.670020i	−0.942215	−	0.335010i	$-0.891260\pi$
$797$		−	534.006i		−	0.670020i	0.942215	−	0.335010i	$-0.108740\pi$
$798$	−27.9149	−	56.7835i	−0.0349810	−	0.0711573i
$799$	−303.134			−0.379392
$800$			1038.25i			1.29781i
$801$	514.888	+	397.125i	0.642807	+	0.495786i
$802$	1236.97			1.54235
$803$			1352.33i			1.68410i
$804$	−362.856	+	178.380i	−0.451313	+	0.221866i
$805$	84.8389			0.105390
$806$		−	25.0840i		−	0.0311215i
$807$	344.044	+	699.843i	0.426325	+	0.867216i
$808$	−86.2647			−0.106763
$809$		−	71.9476i		−	0.0889339i	−0.999011	−	0.0444670i	$-0.985841\pi$
$809$		−	71.9476i		−	0.0889339i	0.999011	−	0.0444670i	$-0.0141589\pi$
$810$	401.242	+	1527.79i	0.495360	+	1.88616i
$811$	975.090			1.20233			0.601165	−	0.799125i	$-0.294703\pi$
$811$	975.090			1.20233			0.601165	+	0.799125i	$0.294703\pi$
$812$		−	43.4178i		−	0.0534702i
$813$	382.606	−	188.089i	0.470610	−	0.231352i
$814$	1505.40			1.84938
$815$		−	2582.80i		−	3.16908i
$816$	−439.634	−	894.289i	−0.538767	−	1.09594i
$817$	291.172			0.356392
$818$			1511.48i			1.84777i
$819$	5.45437	−	7.07181i	0.00665979	−	0.00863468i
$820$	−628.102			−0.765978
$821$		−	110.647i		−	0.134771i	−0.997727	−	0.0673857i	$-0.978534\pi$
$821$		−	110.647i		−	0.134771i	0.997727	−	0.0673857i	$-0.0214658\pi$
$822$	1667.24	−	819.616i	2.02827	−	0.997099i
$823$	1191.20			1.44738			0.723692	−	0.690123i	$-0.242444\pi$
$823$	1191.20			1.44738			0.723692	+	0.690123i	$0.242444\pi$
$824$		−	984.924i		−	1.19530i
$825$	722.815	+	1470.33i	0.876139	+	1.78221i
$826$	13.7237			0.0166147
$827$		−	710.454i		−	0.859074i	−0.903049	−	0.429537i	$-0.858677\pi$
$827$		−	710.454i		−	0.859074i	0.903049	−	0.429537i	$-0.141323\pi$
$828$	−154.795	−	119.391i	−0.186951	−	0.144192i
$829$	−1189.72			−1.43512			−0.717560	−	0.696496i	$-0.754741\pi$
$829$	−1189.72			−1.43512			−0.717560	+	0.696496i	$0.754741\pi$
$830$			1188.66i			1.43212i
$831$	664.114	−	326.480i	0.799175	−	0.392876i
$832$	29.1658			0.0350550
$833$		−	811.006i		−	0.973597i
$834$	−434.947	−	884.754i	−0.521519	−	1.06086i
$835$	−1975.20			−2.36551
$836$			239.193i			0.286116i
$837$	43.3200	−	213.619i	0.0517563	−	0.255220i
$838$	−895.978			−1.06919
$839$			67.2543i			0.0801601i	0.999196	+	0.0400800i	$0.0127613\pi$
$839$			67.2543i			0.0801601i	−0.999196	+	0.0400800i	$0.987239\pi$
$840$	95.3997	−	46.8986i	0.113571	−	0.0558317i
$841$	−458.405			−0.545071
$842$		−	1590.30i		−	1.88871i
$843$	90.4491	+	183.989i	0.107294	+	0.218255i
$844$	554.598			0.657106
$845$		−	1379.15i		−	1.63213i
$846$	−235.339	+	305.127i	−0.278179	+	0.360670i
$847$	30.5776			0.0361010
$848$			934.356i			1.10183i
$849$	−282.567	+	138.910i	−0.332823	+	0.163616i
$850$	1702.29			2.00269
$851$			682.275i			0.801733i
$852$	248.701	+	505.899i	0.291902	+	0.593778i
$853$	−1198.59			−1.40514			−0.702571	−	0.711614i	$-0.747965\pi$
$853$	−1198.59			−1.40514			−0.702571	+	0.711614i	$0.747965\pi$
$854$		−	74.9996i		−	0.0878215i
$855$	693.615	+	534.973i	0.811245	+	0.625700i
$856$	−1087.19			−1.27009
$857$			390.845i			0.456061i	0.973654	+	0.228031i	$0.0732287\pi$
$857$			390.845i			0.456061i	−0.973654	+	0.228031i	$0.926771\pi$
$858$	−106.303	+	52.2586i	−0.123896	+	0.0609075i
$859$	360.795			0.420017			0.210008	−	0.977700i	$-0.432651\pi$
$859$	360.795			0.420017			0.210008	+	0.977700i	$0.432651\pi$
$860$		−	324.268i		−	0.377055i
$861$	47.7655	+	97.1630i	0.0554767	+	0.112849i
$862$	361.223			0.419053
$863$			381.837i			0.442453i	0.975222	+	0.221227i	$0.0710060\pi$
$863$			381.837i			0.442453i	−0.975222	+	0.221227i	$0.928994\pi$
$864$	−639.258	−	129.636i	−0.739882	−	0.150041i
$865$	−2288.61			−2.64579
$866$		−	172.329i		−	0.198995i
$867$	23.0623	−	11.3375i	0.0266002	−	0.0130767i
$868$	9.72352			0.0112022
$869$		−	1278.61i		−	1.47136i
$870$	930.392	+	1892.57i	1.06942	+	2.17537i
$871$	−111.038			−0.127484
$872$			70.2740i			0.0805894i
$873$	−944.869	+	1225.06i	−1.08232	+	1.40328i
$874$	−380.354			−0.435188
$875$			111.961i			0.127955i
$876$	456.848	−	224.587i	0.521516	−	0.256378i
$877$	−278.561			−0.317630			−0.158815	−	0.987308i	$-0.550767\pi$
$877$	−278.561			−0.317630			−0.158815	+	0.987308i	$0.550767\pi$
$878$			1248.84i			1.42236i
$879$	12.8468	+	26.1325i	0.0146152	+	0.0297298i
$880$	−2078.19			−2.36158
$881$		−	244.844i		−	0.277916i	−0.990298	−	0.138958i	$-0.955625\pi$
$881$		−	244.844i		−	0.277916i	0.990298	−	0.138958i	$-0.0443754\pi$
$882$	−816.337	−	629.627i	−0.925552	−	0.713863i
$883$	1198.62			1.35744			0.678722	−	0.734395i	$-0.262534\pi$
$883$	1198.62			1.35744			0.678722	+	0.734395i	$0.262534\pi$
$884$			35.0778i			0.0396808i
$885$	−170.500	+	83.8182i	−0.192656	+	0.0947098i
$886$	−1053.54			−1.18910
$887$		−	170.662i		−	0.192403i	−0.995362	−	0.0962016i	$-0.969331\pi$
$887$		−	170.662i		−	0.192403i	0.995362	−	0.0962016i	$-0.0306693\pi$
$888$	377.159	+	767.205i	0.424729	+	0.863969i
$889$	−111.622			−0.125559
$890$		−	1408.95i		−	1.58309i
$891$	−995.544	+	261.458i	−1.11733	+	0.293444i
$892$	−474.389			−0.531826
$893$			213.687i			0.239291i
$894$	365.398	−	179.630i	0.408722	−	0.200928i
$895$	541.341			0.604851
$896$			112.662i			0.125738i
$897$	−23.6846	−	48.1785i	−0.0264043	−	0.0537107i
$898$	960.166			1.06923
$899$		−	291.005i		−	0.323698i
$900$	376.669	−	488.367i	0.418521	−	0.542630i
$901$	788.828			0.875503
$902$		−	1436.01i		−	1.59203i
$903$	−50.1620	+	24.6597i	−0.0555504	+	0.0273086i
$904$	−801.295			−0.886388
$905$			653.801i			0.722432i
$906$	142.104	+	289.064i	0.156848	+	0.319055i
$907$	−1043.92			−1.15096			−0.575480	−	0.817816i	$-0.695185\pi$
$907$	−1043.92			−1.15096			−0.575480	+	0.817816i	$0.695185\pi$
$908$		−	86.4905i		−	0.0952538i
$909$	108.051	+	83.3380i	0.118868	+	0.0916810i
$910$	−19.3515			−0.0212654
$911$			1049.39i			1.15191i	0.817482	+	0.575954i	$0.195369\pi$
$911$			1049.39i			1.15191i	−0.817482	+	0.575954i	$0.804631\pi$
$912$	−630.407	+	309.909i	−0.691236	+	0.339813i
$913$	−774.560			−0.848368
$914$			10.1200i			0.0110722i
$915$	458.062	+	931.776i	0.500615	+	1.01833i
$916$	359.531			0.392501
$917$		−	35.9271i		−	0.0391789i
$918$	−212.548	+	1048.12i	−0.231534	+	1.14174i
$919$	1163.95			1.26653			0.633267	−	0.773933i	$-0.281713\pi$
$919$	1163.95			1.26653			0.633267	+	0.773933i	$0.281713\pi$
$920$		−	639.018i		−	0.694584i
$921$	716.898	−	352.428i	0.778390	−	0.382658i
$922$	205.785			0.223194
$923$			154.811i			0.167726i
$924$	−20.2575	−	41.2071i	−0.0219237	−	0.0445965i
$925$	−2152.52			−2.32705
$926$		−	342.216i		−	0.369563i
$927$	−951.508	+	1233.67i	−1.02644	+	1.33082i
$928$	−870.835			−0.938400
$929$			245.337i			0.264088i	0.991244	+	0.132044i	$0.0421540\pi$
$929$			245.337i			0.264088i	−0.991244	+	0.132044i	$0.957846\pi$
$930$	−423.846	+	208.363i	−0.455749	+	0.224047i
$931$	−571.699			−0.614070
$932$		−	117.552i		−	0.126129i
$933$	246.725	+	501.881i	0.264443	+	0.537922i
$934$	−761.807			−0.815639
$935$			1754.51i			1.87648i
$936$	−53.2658	−	41.0830i	−0.0569079	−	0.0438921i
$937$	514.852			0.549468			0.274734	−	0.961520i	$-0.411410\pi$
$937$	514.852			0.549468			0.274734	+	0.961520i	$0.411410\pi$
$938$		−	151.019i		−	0.161001i
$939$	1520.00	−	747.235i	1.61875	−	0.795778i
$940$	237.975			0.253165
$941$			169.841i			0.180490i	0.995920	+	0.0902449i	$0.0287650\pi$
$941$			169.841i			0.180490i	−0.995920	+	0.0902449i	$0.971235\pi$
$942$	−234.582	−	477.180i	−0.249026	−	0.506560i
$943$	650.829			0.690169
$944$		−	152.360i		−	0.161398i
$945$	−164.801	−	33.4200i	−0.174392	−	0.0353651i
$946$	741.366			0.783685
$947$			493.994i			0.521641i	0.965387	+	0.260821i	$0.0839931\pi$
$947$			493.994i			0.521641i	−0.965387	+	0.260821i	$0.916007\pi$
$948$	−431.943	+	212.344i	−0.455636	+	0.223991i
$949$	139.801			0.147314
$950$		−	1199.99i		−	1.26314i
$951$	−87.9940	−	178.995i	−0.0925278	−	0.188217i
$952$	71.9719			0.0756007
$953$			11.5941i			0.0121659i	0.999981	+	0.00608293i	$0.00193627\pi$
$953$			11.5941i			0.0121659i	−0.999981	+	0.00608293i	$0.998064\pi$
$954$	612.409	−	794.013i	0.641938	−	0.832298i
$955$	−1928.59			−2.01946
$956$		−	539.430i		−	0.564257i
$957$	−1233.24	+	606.265i	−1.28866	+	0.633505i
$958$	−411.975			−0.430037
$959$			197.771i			0.206226i
$960$	−242.270	−	492.817i	−0.252364	−	0.513351i
$961$	−895.829			−0.932184
$962$		−	155.625i		−	0.161772i
$963$	1361.77	+	1050.31i	1.41409	+	1.09066i
$964$	−379.836			−0.394021
$965$		−	534.893i		−	0.554294i
$966$	65.5259	−	32.2126i	0.0678322	−	0.0333464i
$967$	1884.39			1.94870			0.974348	−	0.225048i	$-0.0722537\pi$
$967$	1884.39			1.94870			0.974348	+	0.225048i	$0.0722537\pi$
$968$		−	230.314i		−	0.237928i
$969$	261.640	+	532.220i	0.270010	+	0.549247i
$970$	3352.29			3.45597
$971$		−	637.817i		−	0.656867i	−0.944527	−	0.328433i	$-0.893479\pi$
$971$		−	637.817i		−	0.656867i	0.944527	−	0.328433i	$-0.106521\pi$
$972$	253.661	+	292.896i	0.260968	+	0.301334i
$973$	104.951			0.107864
$974$			740.131i			0.759888i
$975$	151.999	−	74.7230i	0.155897	−	0.0766390i
$976$	−832.640			−0.853115
$977$			1494.45i			1.52964i	0.644246	+	0.764818i	$0.277171\pi$
$977$			1494.45i			1.52964i	−0.644246	+	0.764818i	$0.722829\pi$
$978$	−980.668	−	1994.84i	−1.00273	−	2.03972i
$979$	918.106			0.937800
$980$			636.680i			0.649673i
$981$	67.8898	−	88.0218i	0.0692046	−	0.0897266i
$982$	−730.191			−0.743575
$983$		−	1058.19i		−	1.07649i	−0.842787	−	0.538247i	$-0.819087\pi$
$983$		−	1058.19i		−	1.07649i	0.842787	−	0.538247i	$-0.180913\pi$
$984$	731.845	−	359.776i	0.743745	−	0.365626i
$985$	1626.02			1.65078
$986$			1427.81i			1.44808i
$987$	−18.0974	−	36.8131i	−0.0183358	−	0.0372980i
$988$	24.7272			0.0250276
$989$			336.001i			0.339738i
$990$	1766.04	+	1362.12i	1.78388	+	1.37588i
$991$	81.6245			0.0823658			0.0411829	−	0.999152i	$-0.486887\pi$
$991$	81.6245			0.0823658			0.0411829	+	0.999152i	$0.486887\pi$
$992$		−	195.026i		−	0.196598i
$993$	−303.783	+	149.340i	−0.305925	+	0.150393i
$994$	−210.553			−0.211824
$995$		−	1982.91i		−	1.99287i
$996$	128.634	+	261.664i	0.129151	+	0.262715i
$997$	1058.73			1.06192			0.530960	−	0.847397i	$-0.321831\pi$
$997$	1058.73			1.06192			0.530960	+	0.847397i	$0.321831\pi$
$998$			523.940i			0.524990i
$999$	268.764	−	1325.33i	0.269033	−	1.32665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.30	yes	38
3.2	odd	2	inner	177.3.b.a.119.9	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.9	✓	38	3.2	odd	2	inner
177.3.b.a.119.30	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)

\(f(q)\)	\(=\)	\(q+2.36527i q^{2} +(2.69227 - 1.32352i) q^{3} -1.59452 q^{4} +8.24482i q^{5} +(3.13049 + 6.36794i) q^{6} -0.755379 q^{7} +5.68962i q^{8} +(5.49658 - 7.12654i) q^{9} +O(q^{10})\)	\(q+2.36527i q^{2} +(2.69227 - 1.32352i) q^{3} -1.59452 q^{4} +8.24482i q^{5} +(3.13049 + 6.36794i) q^{6} -0.755379 q^{7} +5.68962i q^{8} +(5.49658 - 7.12654i) q^{9} -19.5013 q^{10} -12.7075i q^{11} +(-4.29288 + 2.11038i) q^{12} -1.31367 q^{13} -1.78668i q^{14} +(10.9122 + 22.1972i) q^{15} -19.8356 q^{16} +16.7462i q^{17} +(16.8562 + 13.0009i) q^{18} +11.8048 q^{19} -13.1465i q^{20} +(-2.03368 + 0.999760i) q^{21} +30.0566 q^{22} +13.6222i q^{23} +(7.53033 + 15.3180i) q^{24} -42.9771 q^{25} -3.10719i q^{26} +(5.36613 - 26.4614i) q^{27} +1.20447 q^{28} -36.0473i q^{29} +(-52.5026 + 25.8103i) q^{30} +8.07287 q^{31} -24.1581i q^{32} +(-16.8186 - 34.2119i) q^{33} -39.6093 q^{34} -6.22797i q^{35} +(-8.76442 + 11.3634i) q^{36} +50.0853 q^{37} +27.9216i q^{38} +(-3.53675 + 1.73867i) q^{39} -46.9099 q^{40} -47.7769i q^{41} +(-2.36471 - 4.81021i) q^{42} +24.6656 q^{43} +20.2623i q^{44} +(58.7571 + 45.3183i) q^{45} -32.2203 q^{46} +18.1017i q^{47} +(-53.4027 + 26.2528i) q^{48} -48.4294 q^{49} -101.653i q^{50} +(22.1639 + 45.0851i) q^{51} +2.09468 q^{52} -47.1050i q^{53} +(62.5884 + 12.6924i) q^{54} +104.771 q^{55} -4.29782i q^{56} +(31.7816 - 15.6239i) q^{57} +85.2616 q^{58} +7.68115i q^{59} +(-17.3997 - 35.3940i) q^{60} +41.9771 q^{61} +19.0945i q^{62} +(-4.15200 + 5.38324i) q^{63} -22.2017 q^{64} -10.8310i q^{65} +(80.9205 - 39.7806i) q^{66} +84.5251 q^{67} -26.7021i q^{68} +(18.0293 + 36.6747i) q^{69} +14.7308 q^{70} -117.846i q^{71} +(40.5473 + 31.2734i) q^{72} -106.420 q^{73} +118.466i q^{74} +(-115.706 + 56.8811i) q^{75} -18.8230 q^{76} +9.59896i q^{77} +(-4.11244 - 8.36538i) q^{78} +100.619 q^{79} -163.541i q^{80} +(-20.5752 - 78.3432i) q^{81} +113.006 q^{82} -60.9531i q^{83} +(3.24275 - 1.59414i) q^{84} -138.069 q^{85} +58.3409i q^{86} +(-47.7093 - 97.0488i) q^{87} +72.3006 q^{88} +72.2494i q^{89} +(-107.190 + 138.977i) q^{90} +0.992320 q^{91} -21.7210i q^{92} +(21.7343 - 10.6846i) q^{93} -42.8155 q^{94} +97.3284i q^{95} +(-31.9738 - 65.0401i) q^{96} -171.901 q^{97} -114.549i q^{98} +(-90.5603 - 69.8476i) 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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