LMFDB - Embedded newform 177.5.b.a.119.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,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, 5, names="a")

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

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
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:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.52
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.69145i q^{2} +(-5.71505 - 6.95257i) q^{3} +8.75607 q^{4} +3.65373i q^{5} +(18.7125 - 15.3818i) q^{6} +22.3529 q^{7} +66.6298i q^{8} +(-15.6765 + 79.4685i) q^{9} +O(q^{10})$	\(q+2.69145i q^{2} +(-5.71505 - 6.95257i) q^{3} +8.75607 q^{4} +3.65373i q^{5} +(18.7125 - 15.3818i) q^{6} +22.3529 q^{7} +66.6298i q^{8} +(-15.6765 + 79.4685i) q^{9} -9.83386 q^{10} -122.947i q^{11} +(-50.0414 - 60.8772i) q^{12} -0.917855 q^{13} +60.1618i q^{14} +(25.4028 - 20.8813i) q^{15} -39.2340 q^{16} +352.419i q^{17} +(-213.886 - 42.1925i) q^{18} +133.579 q^{19} +31.9924i q^{20} +(-127.748 - 155.410i) q^{21} +330.905 q^{22} -754.157i q^{23} +(463.249 - 380.793i) q^{24} +611.650 q^{25} -2.47036i q^{26} +(642.102 - 345.175i) q^{27} +195.724 q^{28} +1370.31i q^{29} +(56.2009 + 68.3706i) q^{30} +1455.10 q^{31} +960.481i q^{32} +(-854.795 + 702.646i) q^{33} -948.519 q^{34} +81.6716i q^{35} +(-137.264 + 695.832i) q^{36} +1869.95 q^{37} +359.523i q^{38} +(5.24558 + 6.38145i) q^{39} -243.448 q^{40} +1118.01i q^{41} +(418.280 - 343.828i) q^{42} +1275.10 q^{43} -1076.53i q^{44} +(-290.357 - 57.2777i) q^{45} +2029.78 q^{46} +1079.01i q^{47} +(224.224 + 272.777i) q^{48} -1901.35 q^{49} +1646.23i q^{50} +(2450.22 - 2014.09i) q^{51} -8.03681 q^{52} -990.574i q^{53} +(929.022 + 1728.19i) q^{54} +449.214 q^{55} +1489.37i q^{56} +(-763.413 - 928.720i) q^{57} -3688.12 q^{58} +453.188i q^{59} +(222.429 - 182.838i) q^{60} +3408.91 q^{61} +3916.32i q^{62} +(-350.415 + 1776.35i) q^{63} -3212.83 q^{64} -3.35360i q^{65} +(-1891.14 - 2300.64i) q^{66} -5369.84 q^{67} +3085.81i q^{68} +(-5243.33 + 4310.04i) q^{69} -219.815 q^{70} -104.981i q^{71} +(-5294.98 - 1044.52i) q^{72} +10170.8 q^{73} +5032.89i q^{74} +(-3495.61 - 4252.54i) q^{75} +1169.63 q^{76} -2748.22i q^{77} +(-17.1754 + 14.1183i) q^{78} +4028.36 q^{79} -143.350i q^{80} +(-6069.50 - 2491.57i) q^{81} -3009.07 q^{82} -13445.0i q^{83} +(-1118.57 - 1360.78i) q^{84} -1287.64 q^{85} +3431.88i q^{86} +(9527.17 - 7831.38i) q^{87} +8191.92 q^{88} +1161.48i q^{89} +(154.160 - 781.482i) q^{90} -20.5167 q^{91} -6603.45i q^{92} +(-8315.94 - 10116.7i) q^{93} -2904.11 q^{94} +488.064i q^{95} +(6677.81 - 5489.19i) q^{96} -3664.47 q^{97} -5117.39i q^{98} +(9770.39 + 1927.37i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * 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 $

$2$			2.69145i			0.672864i	0.941708	+	0.336432i	$0.109220\pi$
$2$			2.69145i			0.672864i	−0.941708	+	0.336432i	$0.890780\pi$
$3$	−5.71505	−	6.95257i	−0.635005	−	0.772508i
$3$	−5.71505	−	6.95257i	−0.635005	−	0.772508i
$4$	8.75607			0.547255
$5$			3.65373i			0.146149i	0.997326	+	0.0730747i	$0.0232811\pi$
$5$			3.65373i			0.146149i	−0.997326	+	0.0730747i	$0.976719\pi$
$6$	18.7125	−	15.3818i	0.519792	−	0.427272i
$7$	22.3529			0.456182			0.228091	−	0.973640i	$-0.426752\pi$
$7$	22.3529			0.456182			0.228091	+	0.973640i	$0.426752\pi$
$8$			66.6298i			1.04109i
$9$	−15.6765	+	79.4685i	−0.193537	+	0.981093i
$10$	−9.83386			−0.0983386
$11$		−	122.947i		−	1.01609i	−0.861331	−	0.508044i	$-0.830369\pi$
$11$		−	122.947i		−	1.01609i	0.861331	−	0.508044i	$-0.169631\pi$
$12$	−50.0414	−	60.8772i	−0.347510	−	0.422759i
$13$	−0.917855			−0.00543109			−0.00271555	−	0.999996i	$-0.500864\pi$
$13$	−0.917855			−0.00543109			−0.00271555	+	0.999996i	$0.500864\pi$
$14$			60.1618i			0.306948i
$15$	25.4028	−	20.8813i	0.112902	−	0.0928056i
$16$	−39.2340			−0.153258
$17$			352.419i			1.21944i	0.792616	+	0.609721i	$0.208719\pi$
$17$			352.419i			1.21944i	−0.792616	+	0.609721i	$0.791281\pi$
$18$	−213.886	−	42.1925i	−0.660142	−	0.130224i
$19$	133.579			0.370026			0.185013	−	0.982736i	$-0.440767\pi$
$19$	133.579			0.370026			0.185013	+	0.982736i	$0.440767\pi$
$20$			31.9924i			0.0799809i
$21$	−127.748	−	155.410i	−0.289678	−	0.352404i
$22$	330.905			0.683689
$23$		−	754.157i		−	1.42563i	−0.701354	−	0.712813i	$-0.747421\pi$
$23$		−	754.157i		−	1.42563i	0.701354	−	0.712813i	$-0.252579\pi$
$24$	463.249	−	380.793i	0.804251	−	0.661098i
$25$	611.650			0.978640
$26$		−	2.47036i		−	0.00365439i
$27$	642.102	−	345.175i	0.880799	−	0.473490i
$28$	195.724			0.249648
$29$			1370.31i			1.62938i	0.579896	+	0.814690i	$0.303093\pi$
$29$			1370.31i			1.62938i	−0.579896	+	0.814690i	$0.696907\pi$
$30$	56.2009	+	68.3706i	0.0624455	+	0.0759673i
$31$	1455.10			1.51415			0.757074	−	0.653330i	$-0.226628\pi$
$31$	1455.10			1.51415			0.757074	+	0.653330i	$0.226628\pi$
$32$			960.481i			0.937970i
$33$	−854.795	+	702.646i	−0.784936	+	0.645221i
$34$	−948.519			−0.820518
$35$			81.6716i			0.0666707i
$36$	−137.264	+	695.832i	−0.105914	+	0.536908i
$37$	1869.95			1.36593			0.682963	−	0.730453i	$-0.260691\pi$
$37$	1869.95			1.36593			0.682963	+	0.730453i	$0.260691\pi$
$38$			359.523i			0.248977i
$39$	5.24558	+	6.38145i	0.00344877	+	0.00419556i
$40$	−243.448			−0.152155
$41$			1118.01i			0.665085i	0.943088	+	0.332543i	$0.107907\pi$
$41$			1118.01i			0.665085i	−0.943088	+	0.332543i	$0.892093\pi$
$42$	418.280	−	343.828i	0.237120	−	0.194914i
$43$	1275.10			0.689618			0.344809	−	0.938673i	$-0.387944\pi$
$43$	1275.10			0.689618			0.344809	+	0.938673i	$0.387944\pi$
$44$		−	1076.53i		−	0.556059i
$45$	−290.357	−	57.2777i	−0.143386	−	0.0282853i
$46$	2029.78			0.959252
$47$			1079.01i			0.488461i	0.969717	+	0.244231i	$0.0785354\pi$
$47$			1079.01i			0.488461i	−0.969717	+	0.244231i	$0.921465\pi$
$48$	224.224	+	272.777i	0.0973194	+	0.118393i
$49$	−1901.35			−0.791898
$50$			1646.23i			0.658491i
$51$	2450.22	−	2014.09i	0.942029	−	0.774352i
$52$	−8.03681			−0.00297219
$53$		−	990.574i		−	0.352643i	−0.984333	−	0.176322i	$-0.943580\pi$
$53$		−	990.574i		−	0.352643i	0.984333	−	0.176322i	$-0.0564198\pi$
$54$	929.022	+	1728.19i	0.318594	+	0.592657i
$55$	449.214			0.148501
$56$			1489.37i			0.474927i
$57$	−763.413	−	928.720i	−0.234969	−	0.285848i
$58$	−3688.12			−1.09635
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	222.429	−	182.838i	0.0617859	−	0.0507883i
$61$	3408.91			0.916127			0.458064	−	0.888919i	$-0.348543\pi$
$61$	3408.91			0.916127			0.458064	+	0.888919i	$0.348543\pi$
$62$			3916.32i			1.01881i
$63$	−350.415	+	1776.35i	−0.0882880	+	0.447557i
$64$	−3212.83			−0.784383
$65$		−	3.35360i		−	0.000793751i
$66$	−1891.14	−	2300.64i	−0.434146	−	0.528155i
$67$	−5369.84			−1.19622			−0.598111	−	0.801413i	$-0.704082\pi$
$67$	−5369.84			−1.19622			−0.598111	+	0.801413i	$0.704082\pi$
$68$			3085.81i			0.667345i
$69$	−5243.33	+	4310.04i	−1.10131	+	0.905281i
$70$	−219.815			−0.0448603
$71$		−	104.981i		−	0.0208255i	−0.999946	−	0.0104128i	$-0.996685\pi$
$71$		−	104.981i		−	0.0208255i	0.999946	−	0.0104128i	$-0.00331454\pi$
$72$	−5294.98	−	1044.52i	−1.02141	−	0.201489i
$73$	10170.8			1.90858			0.954292	−	0.298875i	$-0.0966113\pi$
$73$	10170.8			1.90858			0.954292	+	0.298875i	$0.0966113\pi$
$74$			5032.89i			0.919082i
$75$	−3495.61	−	4252.54i	−0.621442	−	0.756007i
$76$	1169.63			0.202499
$77$		−	2748.22i		−	0.463521i
$78$	−17.1754	+	14.1183i	−0.00282304	+	0.00232055i
$79$	4028.36			0.645467			0.322733	−	0.946490i	$-0.395398\pi$
$79$	4028.36			0.645467			0.322733	+	0.946490i	$0.395398\pi$
$80$		−	143.350i		−	0.0223985i
$81$	−6069.50	−	2491.57i	−0.925087	−	0.379755i
$82$	−3009.07			−0.447512
$83$		−	13445.0i		−	1.95167i	−0.218514	−	0.975834i	$-0.570121\pi$
$83$		−	13445.0i		−	1.95167i	0.218514	−	0.975834i	$-0.429879\pi$
$84$	−1118.57	−	1360.78i	−0.158528	−	0.192855i
$85$	−1287.64			−0.178221
$86$			3431.88i			0.464019i
$87$	9527.17	−	7831.38i	1.25871	−	1.03467i
$88$	8191.92			1.05784
$89$			1161.48i			0.146633i	0.997309	+	0.0733167i	$0.0233584\pi$
$89$			1161.48i			0.146633i	−0.997309	+	0.0733167i	$0.976642\pi$
$90$	154.160	−	781.482i	0.0190321	−	0.0964793i
$91$	−20.5167			−0.00247757
$92$		−	6603.45i		−	0.780181i
$93$	−8315.94	−	10116.7i	−0.961491	−	1.16969i
$94$	−2904.11			−0.328668
$95$			488.064i			0.0540791i
$96$	6677.81	−	5489.19i	0.724589	−	0.595616i
$97$	−3664.47			−0.389464			−0.194732	−	0.980856i	$-0.562384\pi$
$97$	−3664.47			−0.389464			−0.194732	+	0.980856i	$0.562384\pi$
$98$		−	5117.39i		−	0.532839i
$99$	9770.39	+	1927.37i	0.996877	+	0.196650i
$100$	5355.66			0.535566
$101$			1262.42i			0.123755i	0.998084	+	0.0618774i	$0.0197088\pi$
$101$			1262.42i			0.123755i	−0.998084	+	0.0618774i	$0.980291\pi$
$102$	5420.83	+	6594.65i	0.521033	+	0.633857i
$103$	−13300.7			−1.25372			−0.626861	−	0.779131i	$-0.715661\pi$
$103$	−13300.7			−1.25372			−0.626861	+	0.779131i	$0.715661\pi$
$104$		−	61.1565i		−	0.00565427i
$105$	567.827	−	466.757i	0.0515036	−	0.0423362i
$106$	2666.09			0.237281
$107$			8733.96i			0.762858i	0.924398	+	0.381429i	$0.124568\pi$
$107$			8733.96i			0.762858i	−0.924398	+	0.381429i	$0.875432\pi$
$108$	5622.30	−	3022.37i	0.482021	−	0.259120i
$109$	−14560.4			−1.22552			−0.612760	−	0.790269i	$-0.709941\pi$
$109$	−14560.4			−1.22552			−0.612760	+	0.790269i	$0.709941\pi$
$110$			1209.04i			0.0999206i
$111$	−10686.9	−	13001.0i	−0.867370	−	1.05519i
$112$	−876.993			−0.0699134
$113$		−	4033.56i		−	0.315887i	−0.987448	−	0.157943i	$-0.949514\pi$
$113$		−	4033.56i		−	0.315887i	0.987448	−	0.157943i	$-0.0504864\pi$
$114$	2499.61	−	2054.69i	0.192337	−	0.158102i
$115$	2755.49			0.208354
$116$			11998.5i			0.891686i
$117$	14.3887	−	72.9406i	0.00105112	−	0.00532841i
$118$	−1219.73			−0.0875994
$119$			7877.59i			0.556288i
$120$	1391.31	+	1692.59i	0.0966191	+	0.117541i
$121$	−474.886			−0.0324353
$122$			9174.92i			0.616429i
$123$	7773.03	−	6389.47i	0.513784	−	0.422333i
$124$	12740.9			0.828624
$125$			4518.39i			0.289177i
$126$	−4780.97	−	943.126i	−0.301145	−	0.0594058i
$127$	−21140.6			−1.31072			−0.655361	−	0.755316i	$-0.727484\pi$
$127$	−21140.6			−1.31072			−0.655361	+	0.755316i	$0.727484\pi$
$128$			6720.50i			0.410187i
$129$	−7287.27	−	8865.25i	−0.437911	−	0.532735i
$130$	9.02605			0.000534086
$131$		−	23279.6i		−	1.35654i	−0.734812	−	0.678271i	$-0.762730\pi$
$131$		−	23279.6i		−	1.35654i	0.734812	−	0.678271i	$-0.237270\pi$
$132$	−7484.65	+	6152.42i	−0.429560	+	0.353100i
$133$	2985.89			0.168799
$134$		−	14452.7i		−	0.804894i
$135$	1261.18	+	2346.07i	0.0692003	+	0.128728i
$136$	−23481.6			−1.26955
$137$			119.342i			0.00635845i	0.999995	+	0.00317922i	$0.00101198\pi$
$137$			119.342i			0.00635845i	−0.999995	+	0.00317922i	$0.998988\pi$
$138$	−11600.3	−	14112.2i	−0.609130	−	0.741030i
$139$	−14867.4			−0.769494			−0.384747	−	0.923022i	$-0.625711\pi$
$139$	−14867.4			−0.769494			−0.384747	+	0.923022i	$0.625711\pi$
$140$			715.123i			0.0364858i
$141$	7501.90	−	6166.60i	0.377340	−	0.310175i
$142$	282.553			0.0140127
$143$			112.847i			0.00551847i
$144$	615.050	−	3117.87i	0.0296610	−	0.150360i
$145$	−5006.74			−0.238133
$146$			27374.4i			1.28422i
$147$	10866.3	+	13219.3i	0.502859	+	0.611747i
$148$	16373.4			0.747509
$149$			29931.1i			1.34819i	0.738646	+	0.674093i	$0.235465\pi$
$149$			29931.1i			1.34819i	−0.738646	+	0.674093i	$0.764535\pi$
$150$	11445.5	−	9408.27i	0.508690	−	0.418145i
$151$	−17252.7			−0.756665			−0.378333	−	0.925670i	$-0.623502\pi$
$151$	−17252.7			−0.756665			−0.378333	+	0.925670i	$0.623502\pi$
$152$			8900.38i			0.385231i
$153$	−28006.2	−	5524.69i	−1.19639	−	0.236007i
$154$	7396.70			0.311886
$155$			5316.53i			0.221292i
$156$	45.9307	+	55.8765i	0.00188736	+	0.00229604i
$157$	−34157.1			−1.38574			−0.692870	−	0.721063i	$-0.743654\pi$
$157$	−34157.1			−1.38574			−0.692870	+	0.721063i	$0.743654\pi$
$158$			10842.1i			0.434311i
$159$	−6887.04	+	5661.18i	−0.272420	+	0.223930i
$160$	−3509.34			−0.137084
$161$		−	16857.6i		−	0.650345i
$162$	6705.96	−	16335.8i	0.255523	−	0.622457i
$163$	20800.0			0.782866			0.391433	−	0.920207i	$-0.371980\pi$
$163$	20800.0			0.782866			0.391433	+	0.920207i	$0.371980\pi$
$164$			9789.37i			0.363971i
$165$	−2567.28	−	3123.19i	−0.0942987	−	0.114718i
$166$	36186.7			1.31321
$167$			28532.1i			1.02306i	0.859265	+	0.511530i	$0.170921\pi$
$167$			28532.1i			1.02306i	−0.859265	+	0.511530i	$0.829079\pi$
$168$	10355.0	−	8511.83i	0.366885	−	0.301581i
$169$	−28560.2			−0.999971
$170$		−	3465.64i		−	0.119918i
$171$	−2094.06	+	10615.4i	−0.0716137	+	0.363030i
$172$	11164.9			0.377397
$173$		−	18222.1i		−	0.608843i	−0.952537	−	0.304422i	$-0.901537\pi$
$173$		−	18222.1i		−	0.608843i	0.952537	−	0.304422i	$-0.0984632\pi$
$174$	21077.8	+	25641.9i	0.696189	+	0.846940i
$175$	13672.2			0.446438
$176$			4823.69i			0.155723i
$177$	3150.82	−	2589.99i	0.100572	−	0.0826706i
$178$	−3126.08			−0.0986643
$179$			38805.8i			1.21113i	0.795796	+	0.605565i	$0.207053\pi$
$179$			38805.8i			1.21113i	−0.795796	+	0.605565i	$0.792947\pi$
$180$	−2542.39	−	501.528i	−0.0784687	−	0.0154792i
$181$	47165.8			1.43969			0.719847	−	0.694132i	$-0.244212\pi$
$181$	47165.8			1.43969			0.719847	+	0.694132i	$0.244212\pi$
$182$		−	55.2199i		−	0.00166706i
$183$	−19482.1	−	23700.7i	−0.581745	−	0.707715i
$184$	50249.3			1.48421
$185$			6832.31i			0.199629i
$186$	27228.5	−	22382.0i	0.787042	−	0.646953i
$187$	43328.7			1.23906
$188$			9447.90i			0.267313i
$189$	14352.9	−	7715.66i	0.401805	−	0.215998i
$190$	−1313.60			−0.0363878
$191$			21370.2i			0.585790i	0.956145	+	0.292895i	$0.0946187\pi$
$191$			21370.2i			0.585790i	−0.956145	+	0.292895i	$0.905381\pi$
$192$	18361.5	+	22337.5i	0.498087	+	0.605942i
$193$	−65341.8			−1.75419			−0.877094	−	0.480318i	$-0.840521\pi$
$193$	−65341.8			−1.75419			−0.877094	+	0.480318i	$0.840521\pi$
$194$		−	9862.75i		−	0.262056i
$195$	−23.3161	+	19.1660i	−0.000613179	+	0.000504036i
$196$	−16648.3			−0.433370
$197$		−	39380.4i		−	1.01472i	−0.861733	−	0.507362i	$-0.830621\pi$
$197$		−	39380.4i		−	1.01472i	0.861733	−	0.507362i	$-0.169379\pi$
$198$	−5187.43	+	26296.6i	−0.132319	+	0.670762i
$199$	8277.96			0.209034			0.104517	−	0.994523i	$-0.466670\pi$
$199$	8277.96			0.209034			0.104517	+	0.994523i	$0.466670\pi$
$200$			40754.2i			1.01885i
$201$	30688.9	+	37334.2i	0.759607	+	0.924091i
$202$	−3397.75			−0.0832701
$203$			30630.4i			0.743294i
$204$	21454.3	−	17635.5i	0.515530	−	0.423768i
$205$	−4084.90			−0.0972018
$206$		−	35798.3i		−	0.843584i
$207$	59931.7	+	11822.5i	1.39867	+	0.275911i
$208$	36.0111			0.000832357
$209$		−	16423.1i		−	0.375979i
$210$	1256.25	+	1528.28i	0.0284865	+	0.0346549i
$211$	67639.6			1.51927			0.759637	−	0.650347i	$-0.225377\pi$
$211$	67639.6			1.51927			0.759637	+	0.650347i	$0.225377\pi$
$212$		−	8673.54i		−	0.192986i
$213$	−729.891	+	599.974i	−0.0160879	+	0.0132243i
$214$	−23507.1			−0.513299
$215$			4658.89i			0.100787i
$216$	22998.9	+	42783.2i	0.492947	+	0.916992i
$217$	32525.6			0.690727
$218$		−	39188.6i		−	0.824607i
$219$	−58126.9	−	70713.5i	−1.21196	−	1.47440i
$220$	3933.35			0.0812677
$221$		−	323.469i		−	0.00662291i
$222$	34991.5	−	28763.2i	0.709998	−	0.583622i
$223$	−15502.3			−0.311737			−0.155868	−	0.987778i	$-0.549818\pi$
$223$	−15502.3			−0.311737			−0.155868	+	0.987778i	$0.549818\pi$
$224$			21469.6i			0.427885i
$225$	−9588.52	+	48606.9i	−0.189403	+	0.960137i
$226$	10856.1			0.212549
$227$		−	90194.1i		−	1.75036i	−0.483802	−	0.875178i	$-0.660744\pi$
$227$		−	90194.1i		−	1.75036i	0.483802	−	0.875178i	$-0.339256\pi$
$228$	−6684.50	−	8131.95i	−0.128588	−	0.156432i
$229$	44735.6			0.853066			0.426533	−	0.904472i	$-0.359735\pi$
$229$	44735.6			0.853066			0.426533	+	0.904472i	$0.359735\pi$
$230$			7416.27i			0.140194i
$231$	−19107.2	+	15706.2i	−0.358074	+	0.294338i
$232$	−91303.5			−1.69633
$233$			9980.66i			0.183843i	0.995766	+	0.0919216i	$0.0293009\pi$
$233$			9980.66i			0.183843i	−0.995766	+	0.0919216i	$0.970699\pi$
$234$	196.316	+	38.7266i	0.00358529	+	0.000707258i
$235$	−3942.42			−0.0713883
$236$			3968.14i			0.0712465i
$237$	−23022.3	−	28007.5i	−0.409875	−	0.498628i
$238$	−21202.2			−0.374306
$239$		−	36063.8i		−	0.631357i	−0.948866	−	0.315679i	$-0.897768\pi$
$239$		−	36063.8i		−	0.631357i	0.948866	−	0.315679i	$-0.102232\pi$
$240$	−996.654	+	819.254i	−0.0173030	+	0.0142232i
$241$	16694.2			0.287430			0.143715	−	0.989619i	$-0.454095\pi$
$241$	16694.2			0.287430			0.143715	+	0.989619i	$0.454095\pi$
$242$		−	1278.13i		−	0.0218246i
$243$	17364.6	+	56438.1i	0.294071	+	0.955784i
$244$	29848.7			0.501355
$245$		−	6947.02i		−	0.115735i
$246$	17197.0	+	20920.8i	0.284172	+	0.345706i
$247$	−122.607			−0.00200965
$248$			96952.8i			1.57637i
$249$	−93477.6	+	76839.0i	−1.50768	+	1.23932i
$250$	−12161.0			−0.194577
$251$		−	75734.9i		−	1.20212i	−0.799203	−	0.601061i	$-0.794745\pi$
$251$		−	75734.9i		−	1.20212i	0.799203	−	0.601061i	$-0.205255\pi$
$252$	−3068.26	+	15553.9i	−0.0483160	+	0.244928i
$253$	−92721.1			−1.44856
$254$		−	56899.1i		−	0.881937i
$255$	7358.95	+	8952.44i	0.113171	+	0.137677i
$256$	−69493.3			−1.06038
$257$		−	124405.i		−	1.88353i	−0.336269	−	0.941766i	$-0.609165\pi$
$257$		−	124405.i		−	1.88353i	0.336269	−	0.941766i	$-0.390835\pi$
$258$	23860.4	−	19613.4i	0.358458	−	0.294654i
$259$	41798.9			0.623111
$260$		−	29.3643i		−	0.000434384i
$261$	−108896.	−	21481.6i	−1.59857	−	0.315345i
$262$	62656.0			0.912767
$263$			86024.0i			1.24368i	0.783145	+	0.621839i	$0.213614\pi$
$263$			86024.0i			1.24368i	−0.783145	+	0.621839i	$0.786386\pi$
$264$	−46817.2	−	56954.9i	−0.671734	−	0.817190i
$265$	3619.29			0.0515385
$266$			8036.38i			0.113579i
$267$	8075.29	−	6637.93i	0.113275	−	0.0931130i
$268$	−47018.7			−0.654638
$269$		−	13233.4i		−	0.182880i	−0.995811	−	0.0914402i	$-0.970853\pi$
$269$		−	13233.4i		−	0.182880i	0.995811	−	0.0914402i	$-0.0291470\pi$
$270$	−6314.34	+	3394.40i	−0.0866165	+	0.0465624i
$271$	73836.8			1.00539			0.502695	−	0.864464i	$-0.332342\pi$
$271$	73836.8			1.00539			0.502695	+	0.864464i	$0.332342\pi$
$272$		−	13826.8i		−	0.186889i
$273$	117.254	+	142.644i	0.00157327	+	0.00191394i
$274$	−321.203			−0.00427837
$275$		−	75200.4i		−	0.994385i
$276$	−45911.0	+	37739.0i	−0.602696	+	0.495419i
$277$	8134.35			0.106014			0.0530070	−	0.998594i	$-0.483119\pi$
$277$	8134.35			0.106014			0.0530070	+	0.998594i	$0.483119\pi$
$278$		−	40014.9i		−	0.517764i
$279$	−22810.8	+	115634.i	−0.293043	+	1.48552i
$280$	−5441.76			−0.0694103
$281$			121574.i			1.53967i	0.638242	+	0.769835i	$0.279662\pi$
$281$			121574.i			1.53967i	−0.638242	+	0.769835i	$0.720338\pi$
$282$	16597.1	+	20191.0i	0.208706	+	0.253898i
$283$	−7329.56			−0.0915177			−0.0457588	−	0.998953i	$-0.514571\pi$
$283$	−7329.56			−0.0915177			−0.0457588	+	0.998953i	$0.514571\pi$
$284$		−	919.225i		−	0.0113969i
$285$	3393.30	−	2789.31i	0.0417765	−	0.0343405i
$286$	−303.723			−0.00371318
$287$			24990.8i			0.303400i
$288$	−76328.0	−	15057.0i	−0.920236	−	0.181532i
$289$	−40678.0			−0.487039
$290$		−	13475.4i		−	0.160231i
$291$	20942.6	+	25477.5i	0.247312	+	0.300864i
$292$	89056.7			1.04448
$293$		−	85397.0i		−	0.994735i	−0.867540	−	0.497368i	$-0.834300\pi$
$293$		−	85397.0i		−	0.994735i	0.867540	−	0.497368i	$-0.165700\pi$
$294$	−35579.0	+	29246.1i	−0.411623	+	0.338356i
$295$	−1655.83			−0.0190270
$296$			124595.i			1.42205i
$297$	−42438.1	−	78944.4i	−0.481108	−	0.894969i
$298$	−80558.1			−0.907145
$299$			692.207i			0.00774272i
$300$	−30607.8	−	37235.6i	−0.340087	−	0.413729i
$301$	28502.3			0.314591
$302$		−	46434.9i		−	0.509132i
$303$	8777.08	−	7214.80i	0.0956015	−	0.0785849i
$304$	−5240.85			−0.0567093
$305$			12455.2i			0.133891i
$306$	14869.4	−	75377.4i	0.158800	−	0.805005i
$307$	22581.6			0.239595			0.119797	−	0.992798i	$-0.461776\pi$
$307$	22581.6			0.239595			0.119797	+	0.992798i	$0.461776\pi$
$308$		−	24063.6i		−	0.253664i
$309$	76014.4	+	92474.4i	0.796120	+	0.968511i
$310$	−14309.2			−0.148899
$311$		−	63130.8i		−	0.652710i	−0.945247	−	0.326355i	$-0.894179\pi$
$311$		−	63130.8i		−	0.652710i	0.945247	−	0.326355i	$-0.105821\pi$
$312$	−425.195	+	349.512i	−0.00436796	+	0.00359049i
$313$	−177713.			−1.81397			−0.906985	−	0.421163i	$-0.861622\pi$
$313$	−177713.			−1.81397			−0.906985	+	0.421163i	$0.861622\pi$
$314$		−	91932.2i		−	0.932413i
$315$	−6490.32	−	1280.32i	−0.0654101	−	0.0129032i
$316$	35272.6			0.353235
$317$		−	68993.3i		−	0.686576i	−0.939230	−	0.343288i	$-0.888459\pi$
$317$		−	68993.3i		−	0.686576i	0.939230	−	0.343288i	$-0.111541\pi$
$318$	−15236.8	−	18536.1i	−0.150674	−	0.183301i
$319$	168475.			1.65559
$320$		−	11738.8i		−	0.114637i
$321$	60723.5	−	49915.0i	0.589314	−	0.484419i
$322$	45371.5			0.437594
$323$			47075.9i			0.451225i
$324$	−53145.0	−	21816.4i	−0.506258	−	0.207823i
$325$	−561.406			−0.00531509
$326$			55982.1i			0.526762i
$327$	83213.3	+	101232.i	0.778211	+	0.946723i
$328$	−74492.7			−0.692415
$329$			24119.0i			0.222827i
$330$	8405.93	−	6909.72i	0.0771895	−	0.0634501i
$331$	58531.4			0.534236			0.267118	−	0.963664i	$-0.413929\pi$
$331$	58531.4			0.534236			0.267118	+	0.963664i	$0.413929\pi$
$332$		−	117726.i		−	1.06806i
$333$	−29314.3	+	148602.i	−0.264357	+	1.34010i
$334$	−76792.9			−0.688380
$335$		−	19620.0i		−	0.174827i
$336$	5012.06	+	6097.36i	0.0443954	+	0.0540086i
$337$	−169918.			−1.49616			−0.748081	−	0.663608i	$-0.769024\pi$
$337$	−169918.			−1.49616			−0.748081	+	0.663608i	$0.769024\pi$
$338$		−	76868.4i		−	0.672844i
$339$	−28043.6	+	23052.0i	−0.244025	+	0.200590i
$340$	−11274.7			−0.0975321
$341$		−	178899.i		−	1.53851i
$342$	−28570.8	−	5636.05i	−0.244270	−	0.0481862i
$343$	−96170.0			−0.817432
$344$			84959.9i			0.717955i
$345$	−15747.7	−	19157.7i	−0.132306	−	0.160955i
$346$	49043.9			0.409668
$347$		−	61581.2i		−	0.511434i	−0.966752	−	0.255717i	$-0.917688\pi$
$347$		−	61581.2i		−	0.511434i	0.966752	−	0.255717i	$-0.0823115\pi$
$348$	83420.6	−	68572.2i	0.688835	−	0.566225i
$349$	215132.			1.76626			0.883128	−	0.469132i	$-0.155433\pi$
$349$	215132.			1.76626			0.883128	+	0.469132i	$0.155433\pi$
$350$			36798.0i			0.300392i
$351$	−589.357	+	316.820i	−0.00478370	+	0.00257157i
$352$	118088.			0.953060
$353$		−	47015.6i		−	0.377305i	−0.982044	−	0.188653i	$-0.939588\pi$
$353$		−	47015.6i		−	0.377305i	0.982044	−	0.188653i	$-0.0604120\pi$
$354$	6970.83	+	8480.28i	0.0556261	+	0.0676712i
$355$	383.574			0.00304364
$356$			10170.0i			0.0802458i
$357$	54769.5	−	45020.8i	0.429736	−	0.353245i
$358$	−104444.			−0.814926
$359$		−	36472.1i		−	0.282990i	−0.989939	−	0.141495i	$-0.954809\pi$
$359$		−	36472.1i		−	0.282990i	0.989939	−	0.141495i	$-0.0451910\pi$
$360$	3816.40	−	19346.4i	0.0294475	−	0.149278i
$361$	−112478.			−0.863081
$362$			126945.i			0.968718i
$363$	2713.99	+	3301.68i	0.0205966	+	0.0250565i
$364$	−179.646			−0.00135586
$365$			37161.6i			0.278938i
$366$	63789.3	−	52435.1i	0.476196	−	0.391435i
$367$	−97416.3			−0.723269			−0.361634	−	0.932320i	$-0.617781\pi$
$367$	−97416.3			−0.723269			−0.361634	+	0.932320i	$0.617781\pi$
$368$			29588.6i			0.218488i
$369$	−88846.5	−	17526.4i	−0.652511	−	0.128718i
$370$	−18388.8			−0.134323
$371$		−	22142.2i		−	0.160869i
$372$	−72815.0	−	88582.2i	−0.526181	−	0.640119i
$373$	124860.			0.897440			0.448720	−	0.893672i	$-0.351880\pi$
$373$	124860.			0.897440			0.448720	+	0.893672i	$0.351880\pi$
$374$			116617.i			0.833719i
$375$	31414.4	−	25822.8i	0.223391	−	0.183629i
$376$	−71894.3			−0.508533
$377$		−	1257.75i		−	0.00884932i
$378$	20766.3	+	38630.1i	0.145337	+	0.270360i
$379$	−133641.			−0.930381			−0.465191	−	0.885211i	$-0.654014\pi$
$379$	−133641.			−0.930381			−0.465191	+	0.885211i	$0.654014\pi$
$380$			4273.52i			0.0295950i
$381$	120820.	+	146982.i	0.832315	+	1.01254i
$382$	−57516.9			−0.394157
$383$		−	22401.1i		−	0.152711i	−0.997081	−	0.0763557i	$-0.975672\pi$
$383$		−	22401.1i		−	0.152711i	0.997081	−	0.0763557i	$-0.0243285\pi$
$384$	46724.8	−	38408.0i	0.316873	−	0.260471i
$385$	10041.3			0.0677433
$386$		−	175864.i		−	1.18033i
$387$	−19989.1	+	101331.i	−0.133466	+	0.676579i
$388$	−32086.4			−0.213136
$389$			128505.i			0.849218i	0.905377	+	0.424609i	$0.139588\pi$
$389$			128505.i			0.849218i	−0.905377	+	0.424609i	$0.860412\pi$
$390$	−51.5843	−	62.7543i	−0.000339147	−	0.000412586i
$391$	265779.			1.73847
$392$		−	126686.i		−	0.824438i
$393$	−161853.	+	133044.i	−1.04794	+	0.861411i
$394$	105991.			0.682771
$395$			14718.5i			0.0943346i
$396$	85550.3	+	16876.2i	0.545546	+	0.107618i
$397$	109933.			0.697501			0.348751	−	0.937216i	$-0.386606\pi$
$397$	109933.			0.697501			0.348751	+	0.937216i	$0.386606\pi$
$398$			22279.7i			0.140651i
$399$	−17064.5	−	20759.6i	−0.107188	−	0.130399i
$400$	−23997.5			−0.149984
$401$		−	196757.i		−	1.22361i	−0.791010	−	0.611803i	$-0.790445\pi$
$401$		−	196757.i		−	1.22361i	0.791010	−	0.611803i	$-0.209555\pi$
$402$	−100483.	+	82597.8i	−0.621787	+	0.511112i
$403$	−1335.57			−0.00822348
$404$			11053.9i			0.0677254i
$405$	9103.55	−	22176.3i	0.0555010	−	0.135201i
$406$	−82440.3			−0.500135
$407$		−	229904.i		−	1.38790i
$408$	134198.	+	163258.i	0.806171	+	0.980738i
$409$	269066.			1.60847			0.804233	−	0.594315i	$-0.202577\pi$
$409$	269066.			1.60847			0.804233	+	0.594315i	$0.202577\pi$
$410$		−	10994.3i		−	0.0654035i
$411$	829.732	−	682.044i	0.00491195	−	0.00403765i
$412$	−116462.			−0.686106
$413$			10130.1i			0.0593898i
$414$	−31819.8	+	161303.i	−0.185651	+	0.941116i
$415$	49124.6			0.285235
$416$		−	881.582i		−	0.00509420i
$417$	84967.8	+	103367.i	0.488633	+	0.594440i
$418$	44202.1			0.252983
$419$			209827.i			1.19518i	0.801802	+	0.597590i	$0.203875\pi$
$419$			209827.i			1.19518i	−0.801802	+	0.597590i	$0.796125\pi$
$420$	4971.94	−	4086.96i	0.0281856	−	0.0231687i
$421$	−117308.			−0.661854			−0.330927	−	0.943656i	$-0.607361\pi$
$421$	−117308.			−0.661854			−0.330927	+	0.943656i	$0.607361\pi$
$422$			182049.i			1.02226i
$423$	−85747.4	−	16915.1i	−0.479226	−	0.0945352i
$424$	66001.8			0.367134
$425$			215557.i			1.19340i
$426$	−1614.80	−	1964.47i	−0.00889816	−	0.0108249i
$427$	76199.1			0.417921
$428$			76475.2i			0.417478i
$429$	784.578	−	644.927i	0.00426306	−	0.00350426i
$430$	−12539.2			−0.0678160
$431$			160861.i			0.865959i	0.901404	+	0.432979i	$0.142538\pi$
$431$			160861.i			0.865959i	−0.901404	+	0.432979i	$0.857462\pi$
$432$	−25192.2	+	13542.6i	−0.134989	+	0.0725660i
$433$	83767.1			0.446784			0.223392	−	0.974729i	$-0.428287\pi$
$433$	83767.1			0.446784			0.223392	+	0.974729i	$0.428287\pi$
$434$			87541.2i			0.464765i
$435$	28613.8	+	34809.7i	0.151216	+	0.183960i
$436$	−127492.			−0.670671
$437$		−	100740.i		−	0.527519i
$438$	190322.	−	156446.i	0.992068	−	0.815484i
$439$	−100136.			−0.519589			−0.259794	−	0.965664i	$-0.583655\pi$
$439$	−100136.			−0.519589			−0.259794	+	0.965664i	$0.583655\pi$
$440$			29931.1i			0.154603i
$441$	29806.4	−	151097.i	0.153261	−	0.776926i
$442$	870.603			0.00445631
$443$		−	27661.8i		−	0.140953i	−0.997513	−	0.0704764i	$-0.977548\pi$
$443$		−	27661.8i		−	0.140953i	0.997513	−	0.0704764i	$-0.0224519\pi$
$444$	−93575.0	−	113838.i	−0.474672	−	0.577457i
$445$	−4243.75			−0.0214304
$446$		−	41723.9i		−	0.209756i
$447$	208098.	−	171058.i	1.04148	−	0.856105i
$448$	−71816.2			−0.357822
$449$		−	215392.i		−	1.06840i	−0.845357	−	0.534202i	$-0.820612\pi$
$449$		−	215392.i		−	1.06840i	0.845357	−	0.534202i	$-0.179388\pi$
$450$	−130823.	−	25807.1i	−0.646041	−	0.127442i
$451$	137455.			0.675785
$452$		−	35318.1i		−	0.172871i
$453$	98600.1	+	119951.i	0.480486	+	0.584530i
$454$	242753.			1.17775
$455$		−	74.9627i		−	0.000362095i
$456$	61880.5	−	50866.1i	0.297594	−	0.244624i
$457$	47885.4			0.229282			0.114641	−	0.993407i	$-0.463428\pi$
$457$	47885.4			0.229282			0.114641	+	0.993407i	$0.463428\pi$
$458$			120404.i			0.573997i
$459$	121646.	+	226289.i	0.577394	+	1.07408i
$460$	24127.3			0.114023
$461$			61515.5i			0.289456i	0.989471	+	0.144728i	$0.0462308\pi$
$461$			61515.5i			0.289456i	−0.989471	+	0.144728i	$0.953769\pi$
$462$	−42272.5	−	51426.1i	−0.198050	−	0.240935i
$463$	104362.			0.486833			0.243416	−	0.969922i	$-0.421732\pi$
$463$	104362.			0.486833			0.243416	+	0.969922i	$0.421732\pi$
$464$		−	53762.7i		−	0.249715i
$465$	36963.6	−	30384.2i	0.170950	−	0.140521i
$466$	−26862.5			−0.123701
$467$			262028.i			1.20147i	0.799447	+	0.600737i	$0.205126\pi$
$467$			262028.i			1.20147i	−0.799447	+	0.600737i	$0.794874\pi$
$468$	125.989	−	638.673i	0.000575228	−	0.00291600i
$469$	−120032.			−0.545695
$470$		−	10610.8i		−	0.0480346i
$471$	195209.	+	237480.i	0.879952	+	1.07049i
$472$	−30195.8			−0.135539
$473$		−	156770.i		−	0.700712i
$474$	75380.8	−	61963.4i	0.335509	−	0.275790i
$475$	81703.9			0.362122
$476$			68976.7i			0.304431i
$477$	78719.5	+	15528.7i	0.345976	+	0.0682494i
$478$	97064.0			0.424817
$479$		−	191629.i		−	0.835198i	−0.908631	−	0.417599i	$-0.862872\pi$
$479$		−	191629.i		−	0.835198i	0.908631	−	0.417599i	$-0.137128\pi$
$480$	20056.0	+	24398.9i	0.0870488	+	0.105898i
$481$	−1716.35			−0.00741847
$482$			44931.7i			0.193401i
$483$	−117204.	+	96342.0i	−0.502397	+	0.412973i
$484$	−4158.13			−0.0177504
$485$		−	13389.0i		−	0.0569199i
$486$	−151900.	+	46736.1i	−0.643112	+	0.197870i
$487$	−244922.			−1.03269			−0.516344	−	0.856381i	$-0.672708\pi$
$487$	−244922.			−1.03269			−0.516344	+	0.856381i	$0.672708\pi$
$488$			227135.i			0.953772i
$489$	−118873.	−	144613.i	−0.497124	−	0.604770i
$490$	18697.6			0.0778741
$491$			276138.i			1.14542i	0.819760	+	0.572708i	$0.194107\pi$
$491$			276138.i			1.14542i	−0.819760	+	0.572708i	$0.805893\pi$
$492$	68061.3	−	55946.7i	0.281171	−	0.231124i
$493$	−482923.			−1.98694
$494$		−	329.990i		−	0.00135222i
$495$	−7042.10	+	35698.4i	−0.0287403	+	0.145693i
$496$	−57089.2			−0.232055
$497$		−	2346.64i		−	0.00950022i
$498$	−206809.	−	251591.i	−0.833893	−	1.01446i
$499$	−205373.			−0.824786			−0.412393	−	0.911006i	$-0.635307\pi$
$499$	−205373.			−0.824786			−0.412393	+	0.911006i	$0.635307\pi$
$500$			39563.4i			0.158253i
$501$	198372.	−	163062.i	0.790322	−	0.649649i
$502$	203837.			0.808864
$503$			226075.i			0.893544i	0.894648	+	0.446772i	$0.147427\pi$
$503$			226075.i			0.893544i	−0.894648	+	0.446772i	$0.852573\pi$
$504$	−118358.	−	23348.1i	−0.465948	−	0.0919159i
$505$	−4612.55			−0.0180867
$506$		−	249554.i		−	0.974685i
$507$	163223.	+	198567.i	0.634986	+	0.772485i
$508$	−185109.			−0.717299
$509$		−	91546.0i		−	0.353349i	−0.984269	−	0.176674i	$-0.943466\pi$
$509$		−	91546.0i		−	0.353349i	0.984269	−	0.176674i	$-0.0565340\pi$
$510$	−24095.1	+	19806.3i	−0.0926377	+	0.0761487i
$511$	227348.			0.870662
$512$		−	79509.9i		−	0.303306i
$513$	85771.7	−	46108.2i	0.325919	−	0.175204i
$514$	334831.			1.26736
$515$		−	48597.4i		−	0.183231i
$516$	−63807.9	−	77624.7i	−0.239649	−	0.291542i
$517$	132661.			0.496320
$518$			112500.i			0.419268i
$519$	−126690.	+	104140.i	−0.470336	+	0.386619i
$520$	223.450			0.000826367
$521$			422512.i			1.55655i	0.627923	+	0.778276i	$0.283905\pi$
$521$			422512.i			1.55655i	−0.627923	+	0.778276i	$0.716095\pi$
$522$	57816.8	−	293090.i	0.212184	−	1.07562i
$523$	−68616.0			−0.250855			−0.125427	−	0.992103i	$-0.540030\pi$
$523$	−68616.0			−0.250855			−0.125427	+	0.992103i	$0.540030\pi$
$524$		−	203838.i		−	0.742373i
$525$	−78137.1	−	95056.7i	−0.283491	−	0.344877i
$526$	−231530.			−0.836826
$527$			512803.i			1.84642i
$528$	33537.0	−	27567.6i	0.120297	−	0.0988851i
$529$	−288911.			−1.03241
$530$			9741.16i			0.0346784i
$531$	−36014.2	−	7104.39i	−0.127727	−	0.0251963i
$532$	26144.7			0.0923762
$533$		−	1026.17i		−	0.00361214i
$534$	17865.7	+	21734.3i	0.0626523	+	0.0762189i
$535$	−31911.6			−0.111491
$536$		−	357792.i		−	1.24538i
$537$	269800.	−	221777.i	0.935608	−	0.769074i
$538$	35617.1			0.123053
$539$			233764.i			0.804638i
$540$	11042.9	+	20542.4i	0.0378702	+	0.0704471i
$541$	−12212.0			−0.0417245			−0.0208623	−	0.999782i	$-0.506641\pi$
$541$	−12212.0			−0.0417245			−0.0208623	+	0.999782i	$0.506641\pi$
$542$			198728.i			0.676490i
$543$	−269555.	−	327924.i	−0.914214	−	1.11218i
$544$	−338492.			−1.14380
$545$		−	53199.8i		−	0.179109i
$546$	−383.920	+	315.584i	−0.00128782	+	0.00105859i
$547$	249969.			0.835434			0.417717	−	0.908577i	$-0.362830\pi$
$547$	249969.			0.835434			0.417717	+	0.908577i	$0.362830\pi$
$548$			1044.97i			0.00347969i
$549$	−53439.7	+	270901.i	−0.177304	+	0.898806i
$550$	202398.			0.669085
$551$			183045.i			0.602913i
$552$	−287177.	−	349362.i	−0.942480	−	1.14656i
$553$	90045.6			0.294450
$554$			21893.2i			0.0713330i
$555$	47502.1	−	39047.0i	0.154215	−	0.126766i
$556$	−130180.			−0.421109
$557$		−	291658.i		−	0.940076i	−0.882646	−	0.470038i	$-0.844240\pi$
$557$		−	291658.i		−	0.940076i	0.882646	−	0.470038i	$-0.155760\pi$
$558$	−311224.	−	61394.2i	−0.999552	−	0.197178i
$559$	−1170.36			−0.00374538
$560$		−	3204.30i		−	0.0102178i
$561$	−247626.	−	301246.i	−0.786810	−	0.957184i
$562$	−327211.			−1.03599
$563$		−	564661.i		−	1.78144i	−0.454553	−	0.890720i	$-0.650201\pi$
$563$		−	564661.i		−	1.78144i	0.454553	−	0.890720i	$-0.349799\pi$
$564$	65687.2	−	53995.2i	0.206501	−	0.169745i
$565$	14737.5			0.0461666
$566$		−	19727.2i		−	0.0615789i
$567$	−135671.	−	55693.9i	−0.422008	−	0.173237i
$568$	6994.90			0.0216813
$569$			426831.i			1.31835i	0.751989	+	0.659175i	$0.229095\pi$
$569$			426831.i			1.31835i	−0.751989	+	0.659175i	$0.770905\pi$
$570$	7507.29	+	9132.90i	0.0231065	+	0.0281099i
$571$	−410430.			−1.25883			−0.629414	−	0.777070i	$-0.716705\pi$
$571$	−410430.			−1.25883			−0.629414	+	0.777070i	$0.716705\pi$
$572$			988.099i			0.00302001i
$573$	148578.	−	122132.i	0.452528	−	0.371980i
$574$	−67261.5			−0.204147
$575$		−	461280.i		−	1.39518i
$576$	50365.9	−	255319.i	0.151807	−	0.769553i
$577$	−7045.07			−0.0211609			−0.0105804	−	0.999944i	$-0.503368\pi$
$577$	−7045.07			−0.0211609			−0.0105804	+	0.999944i	$0.503368\pi$
$578$		−	109483.i		−	0.327711i
$579$	373431.	+	454293.i	1.11392	+	1.35512i
$580$	−43839.4			−0.130319
$581$		−	300536.i		−	0.890315i
$582$	−68571.5	+	56366.1i	−0.202441	+	0.166407i
$583$	−121788.			−0.358316
$584$			677682.i			1.98701i
$585$	266.505	+	52.5726i	0.000778743	+	0.000153620i
$586$	229842.			0.669321
$587$		−	93808.0i		−	0.272247i	−0.990692	−	0.136124i	$-0.956536\pi$
$587$		−	93808.0i		−	0.272247i	0.990692	−	0.136124i	$-0.0434645\pi$
$588$	95146.0	+	115749.i	0.275192	+	0.334782i
$589$	194371.			0.560274
$590$		−	4456.58i		−	0.0128026i
$591$	−273795.	+	225061.i	−0.783883	+	0.644355i
$592$	−73365.6			−0.209339
$593$		−	364567.i		−	1.03674i	−0.855158	−	0.518368i	$-0.826540\pi$
$593$		−	364567.i		−	1.03674i	0.855158	−	0.518368i	$-0.173460\pi$
$594$	212475.	−	114220.i	0.602192	−	0.323720i
$595$	−28782.6			−0.0813010
$596$			262079.i			0.737801i
$597$	−47308.9	−	57553.1i	−0.132738	−	0.161480i
$598$	−1863.04			−0.00520979
$599$		−	100121.i		−	0.279043i	−0.990219	−	0.139521i	$-0.955444\pi$
$599$		−	100121.i		−	0.279043i	0.990219	−	0.139521i	$-0.0445564\pi$
$600$	283346.	−	232912.i	0.787073	−	0.646978i
$601$	−148652.			−0.411549			−0.205774	−	0.978599i	$-0.565971\pi$
$601$	−148652.			−0.411549			−0.205774	+	0.978599i	$0.565971\pi$
$602$			76712.6i			0.211677i
$603$	84180.2	−	426733.i	0.231513	−	1.17361i
$604$	−151066.			−0.414089
$605$		−	1735.11i		−	0.00474040i
$606$	19418.3	+	23623.1i	0.0528769	+	0.0643268i
$607$	222267.			0.603251			0.301626	−	0.953426i	$-0.402471\pi$
$607$	222267.			0.603251			0.301626	+	0.953426i	$0.402471\pi$
$608$			128301.i			0.347073i
$609$	212960.	−	175054.i	0.574201	−	0.471996i
$610$	−33522.7			−0.0900906
$611$		−	990.375i		−	0.00265288i
$612$	−245224.	−	48374.6i	−0.654728	−	0.129156i
$613$	164165.			0.436877			0.218439	−	0.975851i	$-0.429904\pi$
$613$	164165.			0.436877			0.218439	+	0.975851i	$0.429904\pi$
$614$			60777.2i			0.161215i
$615$	23345.4	+	28400.6i	0.0617236	+	0.0750891i
$616$	183113.			0.482568
$617$		−	382686.i		−	1.00524i	−0.864506	−	0.502622i	$-0.832369\pi$
$617$		−	382686.i		−	1.00524i	0.864506	−	0.502622i	$-0.167631\pi$
$618$	−248891.	+	204589.i	−0.651675	+	0.535680i
$619$	−329349.			−0.859557			−0.429779	−	0.902934i	$-0.641408\pi$
$619$	−329349.			−0.859557			−0.429779	+	0.902934i	$0.641408\pi$
$620$			46551.9i			0.121103i
$621$	−260316.	−	484246.i	−0.675021	−	1.25569i
$622$	169914.			0.439185
$623$			25962.5i			0.0668915i
$624$	−205.805	−	250.370i	−0.000528551	−	0.000643002i
$625$	365772.			0.936377
$626$		−	478306.i		−	1.22055i
$627$	−114183.	+	93859.1i	−0.290447	+	0.238749i
$628$	−299082.			−0.758352
$629$			659006.i			1.66567i
$630$	3445.93	−	17468.4i	0.00868211	−	0.0440121i
$631$	−208873.			−0.524594			−0.262297	−	0.964987i	$-0.584480\pi$
$631$	−208873.			−0.524594			−0.262297	+	0.964987i	$0.584480\pi$
$632$			268409.i			0.671990i
$633$	−386563.	−	470269.i	−0.964747	−	1.17365i
$634$	185692.			0.461972
$635$		−	77242.3i		−	0.191561i
$636$	−60303.4	+	49569.7i	−0.149083	+	0.122547i
$637$	1745.16			0.00430087
$638$			453443.i			1.11399i
$639$	8342.72	+	1645.74i	0.0204318	+	0.00403050i
$640$	−24554.9			−0.0599485
$641$			232155.i			0.565017i	0.959265	+	0.282509i	$0.0911665\pi$
$641$			232155.i			0.565017i	−0.959265	+	0.282509i	$0.908833\pi$
$642$	134344.	+	163434.i	0.325948	+	0.396528i
$643$	209174.			0.505924			0.252962	−	0.967476i	$-0.418595\pi$
$643$	209174.			0.505924			0.252962	+	0.967476i	$0.418595\pi$
$644$		−	147606.i		−	0.355905i
$645$	32391.2	−	26625.8i	0.0778589	−	0.0640004i
$646$	−126703.			−0.303613
$647$		−	81749.3i		−	0.195288i	−0.995221	−	0.0976440i	$-0.968869\pi$
$647$		−	81749.3i		−	0.195288i	0.995221	−	0.0976440i	$-0.0311307\pi$
$648$	166013.	−	404410.i	0.395360	−	0.963100i
$649$	55717.9			0.132283
$650$		−	1511.00i		−	0.00357633i
$651$	−185885.	−	226137.i	−0.438615	−	0.533592i
$652$	182126.			0.428427
$653$		−	356530.i		−	0.836122i	−0.908419	−	0.418061i	$-0.862710\pi$
$653$		−	356530.i		−	0.836122i	0.908419	−	0.418061i	$-0.137290\pi$
$654$	−272462.	+	223965.i	−0.637015	+	0.523630i
$655$	85057.5			0.198258
$656$		−	43863.9i		−	0.101929i
$657$	−159443.	+	808262.i	−0.369381	+	1.87250i
$658$	−64915.3			−0.149932
$659$			455548.i			1.04897i	0.851420	+	0.524485i	$0.175742\pi$
$659$			455548.i			1.04897i	−0.851420	+	0.524485i	$0.824258\pi$
$660$	−22479.3	−	27346.9i	−0.0516054	−	0.0627799i
$661$	−361402.			−0.827156			−0.413578	−	0.910469i	$-0.635721\pi$
$661$	−361402.			−0.827156			−0.413578	+	0.910469i	$0.635721\pi$
$662$			157535.i			0.359468i
$663$	−2248.94	+	1848.64i	−0.00511625	+	0.00420558i
$664$	895841.			2.03186
$665$			10909.6i			0.0246699i
$666$	−399956.	−	78898.0i	−0.901705	−	0.177876i
$667$	1.03343e6			2.32289
$668$			249829.i			0.559874i
$669$	88596.6	+	107781.i	0.197954	+	0.240819i
$670$	52806.2			0.117635
$671$		−	419114.i		−	0.930866i
$672$	149269.	−	122699.i	0.330544	−	0.271709i
$673$	−116443.			−0.257089			−0.128544	−	0.991704i	$-0.541030\pi$
$673$	−116443.			−0.257089			−0.128544	+	0.991704i	$0.541030\pi$
$674$		−	457325.i		−	1.00671i
$675$	392742.	−	211126.i	0.861985	−	0.463377i
$676$	−250075.			−0.547239
$677$		−	476770.i		−	1.04024i	−0.854094	−	0.520118i	$-0.825888\pi$
$677$		−	476770.i		−	1.04024i	0.854094	−	0.520118i	$-0.174112\pi$
$678$	−62043.3	−	75478.1i	−0.134970	−	0.164196i
$679$	−81911.6			−0.177667
$680$		−	85795.5i		−	0.185544i
$681$	−627081.	+	515463.i	−1.35216	+	1.11148i
$682$	481499.			1.03521
$683$			526531.i			1.12871i	0.825532	+	0.564356i	$0.190875\pi$
$683$			526531.i			1.12871i	−0.825532	+	0.564356i	$0.809125\pi$
$684$	−18335.7	+	92948.9i	−0.0391909	+	0.198670i
$685$	−436.043			−0.000929283
$686$		−	258837.i		−	0.550020i
$687$	−255666.	−	311028.i	−0.541701	−	0.659000i
$688$	−50027.4			−0.105689
$689$			909.204i			0.00191524i
$690$	51562.1	−	42384.3i	0.108301	−	0.0890240i
$691$	155810.			0.326316			0.163158	−	0.986600i	$-0.447832\pi$
$691$	155810.			0.326316			0.163158	+	0.986600i	$0.447832\pi$
$692$		−	159554.i		−	0.333192i
$693$	218397.	+	43082.4i	0.454757	+	0.0897084i
$694$	165743.			0.344125
$695$		−	54321.5i		−	0.112461i
$696$	521804.	+	634794.i	1.07718	+	1.31043i
$697$	−394007.			−0.811033
$698$			579017.i			1.18845i
$699$	69391.2	−	57039.9i	0.142020	−	0.116741i
$700$	119715.			0.244315
$701$			229962.i			0.467972i	0.972240	+	0.233986i	$0.0751770\pi$
$701$			229962.i			0.467972i	−0.972240	+	0.233986i	$0.924823\pi$
$702$	−852.707	−	1586.23i	−0.00173032	−	0.00321878i
$703$	249787.			0.505428
$704$			395007.i			0.797003i
$705$	22531.1	+	27409.9i	0.0453319	+	0.0551480i
$706$	126540.			0.253875
$707$			28218.8i			0.0564547i
$708$	27588.8	−	22678.1i	0.0550385	−	0.0452419i
$709$	−947919.			−1.88573			−0.942864	−	0.333178i	$-0.891879\pi$
$709$	−947919.			−1.88573			−0.942864	+	0.333178i	$0.891879\pi$
$710$			1032.37i			0.00204795i
$711$	−63150.5	+	320128.i	−0.124922	+	0.633263i
$712$	−77389.4			−0.152659
$713$		−	1.09737e6i		−	2.15861i
$714$	121171.	+	147410.i	0.237686	+	0.289154i
$715$	−412.314			−0.000806521
$716$			339787.i			0.662797i
$717$	−250736.	+	206106.i	−0.487728	+	0.400915i
$718$	98162.9			0.190414
$719$			37919.1i			0.0733500i	0.999327	+	0.0366750i	$0.0116766\pi$
$719$			37919.1i			0.0733500i	−0.999327	+	0.0366750i	$0.988323\pi$
$720$	11391.8	+	2247.23i	0.0219750	+	0.00433493i
$721$	−297310.			−0.571926
$722$		−	302728.i		−	0.580736i
$723$	−95408.2	−	116068.i	−0.182519	−	0.222042i
$724$	412988.			0.787880
$725$			838150.i			1.59458i
$726$	−8886.31	+	7304.59i	−0.0168596	+	0.0138587i
$727$	−632730.			−1.19715			−0.598577	−	0.801065i	$-0.704267\pi$
$727$	−632730.			−1.19715			−0.598577	+	0.801065i	$0.704267\pi$
$728$		−	1367.03i		−	0.00257937i
$729$	293150.	−	443275.i	0.551614	−	0.834100i
$730$	−100019.			−0.187687
$731$			449370.i			0.840949i
$732$	−170586.	−	207525.i	−0.318363	−	0.387301i
$733$	−473944.			−0.882103			−0.441051	−	0.897482i	$-0.645394\pi$
$733$	−473944.			−0.882103			−0.441051	+	0.897482i	$0.645394\pi$
$734$		−	262192.i		−	0.486661i
$735$	−48299.6	+	39702.5i	−0.0894065	+	0.0734926i
$736$	724353.			1.33719
$737$			660204.i			1.21547i
$738$	47171.6	−	239126.i	0.0866100	−	0.439051i
$739$	−490032.			−0.897295			−0.448647	−	0.893709i	$-0.648094\pi$
$739$	−490032.			−0.897295			−0.448647	+	0.893709i	$0.648094\pi$
$740$			59824.2i			0.109248i
$741$	700.702	+	852.431i	0.00127614	+	0.00155247i
$742$	59594.8			0.108243
$743$			429957.i			0.778838i	0.921061	+	0.389419i	$0.127324\pi$
$743$			429957.i			0.778838i	−0.921061	+	0.389419i	$0.872676\pi$
$744$	674071.	−	554090.i	1.21775	−	1.00100i
$745$	−109360.			−0.197036
$746$			336055.i			0.603855i
$747$	1.06846e6	+	210771.i	1.91477	+	0.377719i
$748$	379390.			0.678082
$749$			195230.i			0.348002i
$750$	69500.9	+	84550.5i	0.123557	+	0.150312i
$751$	259444.			0.460007			0.230003	−	0.973190i	$-0.426126\pi$
$751$	259444.			0.460007			0.230003	+	0.973190i	$0.426126\pi$
$752$		−	42333.9i		−	0.0748604i
$753$	−526552.	+	432829.i	−0.928649	+	0.763354i
$754$	3385.16			0.00595439
$755$		−	63036.9i		−	0.110586i
$756$	125675.	−	67558.9i	0.219889	−	0.118206i
$757$	103286.			0.180240			0.0901200	−	0.995931i	$-0.471275\pi$
$757$	103286.			0.180240			0.0901200	+	0.995931i	$0.471275\pi$
$758$		−	359688.i		−	0.626019i
$759$	529905.	+	644650.i	0.919845	+	1.11903i
$760$	−32519.6			−0.0563012
$761$		−	815782.i		−	1.40866i	−0.709875	−	0.704328i	$-0.751249\pi$
$761$		−	815782.i		−	1.40866i	0.709875	−	0.704328i	$-0.248751\pi$
$762$	−395595.	+	325181.i	−0.681303	+	0.560035i
$763$	−325467.			−0.559060
$764$			187119.i			0.320576i
$765$	20185.7	−	102327.i	0.0344923	−	0.174851i
$766$	60291.5			0.102754
$767$		−	415.961i		−	0.000707068i
$768$	397157.	+	483157.i	0.673349	+	0.819154i
$769$	188165.			0.318190			0.159095	−	0.987263i	$-0.449142\pi$
$769$	188165.			0.318190			0.159095	+	0.987263i	$0.449142\pi$
$770$			27025.6i			0.0455820i
$771$	−864937.	+	710983.i	−1.45504	+	1.19605i
$772$	−572137.			−0.959988
$773$			706818.i			1.18290i	0.806341	+	0.591451i	$0.201445\pi$
$773$			706818.i			1.18290i	−0.806341	+	0.591451i	$0.798555\pi$
$774$	−272727.	−	53799.8i	−0.455245	−	0.0898047i
$775$	890010.			1.48181
$776$		−	244163.i		−	0.405468i
$777$	−238883.	−	290610.i	−0.395679	−	0.481358i
$778$	−345864.			−0.571408
$779$			149343.i			0.246099i
$780$	−204.158	+	167.819i	−0.000335565	+	0.000275836i
$781$	−12907.1			−0.0211606
$782$			715332.i			1.16975i
$783$	472996.	+	879879.i	0.771496	+	1.43516i
$784$	74597.4			0.121364
$785$		−	124801.i		−	0.202525i
$786$	−358082.	−	435620.i	−0.579612	−	0.705120i
$787$	−29122.5			−0.0470196			−0.0235098	−	0.999724i	$-0.507484\pi$
$787$	−29122.5			−0.0470196			−0.0235098	+	0.999724i	$0.507484\pi$
$788$		−	344818.i		−	0.555313i
$789$	598088.	−	491631.i	0.960751	−	0.789742i
$790$	−39614.3			−0.0634743
$791$		−	90161.8i		−	0.144102i
$792$	−128420.	+	651000.i	−0.204731	+	1.03784i
$793$	−3128.88			−0.00497557
$794$			295878.i			0.469323i
$795$	−20684.4	−	25163.4i	−0.0327272	−	0.0398139i
$796$	72482.4			0.114395
$797$		−	456766.i		−	0.719079i	−0.933130	−	0.359540i	$-0.882934\pi$
$797$		−	456766.i		−	0.719079i	0.933130	−	0.359540i	$-0.117066\pi$
$798$	55873.5	−	45928.3i	0.0877406	−	0.0721232i
$799$	−380264.			−0.595650
$800$			587478.i			0.917935i
$801$	−92301.4	−	18208.0i	−0.143861	−	0.0283790i
$802$	529563.			0.823320
$803$		−	1.25047e6i		−	1.93929i
$804$	268714.	+	326901.i	0.415699	+	0.505713i
$805$	61593.2			0.0950475
$806$		−	3594.62i		−	0.00553328i
$807$	−92006.2	+	75629.5i	−0.141276	+	0.116130i
$808$	−84115.0			−0.128840
$809$		−	153327.i		−	0.234272i	−0.993116	−	0.117136i	$-0.962629\pi$
$809$		−	153327.i		−	0.234272i	0.993116	−	0.117136i	$-0.0373713\pi$
$810$	59686.5	+	24501.8i	0.0909717	+	0.0373446i
$811$	−127155.			−0.193327			−0.0966635	−	0.995317i	$-0.530817\pi$
$811$	−127155.			−0.193327			−0.0966635	+	0.995317i	$0.530817\pi$
$812$			268202.i			0.406771i
$813$	−421981.	−	513356.i	−0.638428	−	0.776671i
$814$	618777.			0.933868
$815$			75997.5i			0.114415i
$816$	−96131.7	+	79020.7i	−0.144373	+	0.118675i
$817$	170328.			0.255177
$818$			724178.i			1.08228i
$819$	321.630	−	1630.43i	0.000479500	−	0.00243072i
$820$	−35767.7			−0.0531941
$821$		−	319929.i		−	0.474643i	−0.971431	−	0.237321i	$-0.923731\pi$
$821$		−	319929.i		−	0.474643i	0.971431	−	0.237321i	$-0.0762694\pi$
$822$	1835.69	+	2233.19i	0.00271679	+	0.00330507i
$823$	1.24453e6			1.83741			0.918706	−	0.394942i	$-0.129235\pi$
$823$	1.24453e6			1.83741			0.918706	+	0.394942i	$0.129235\pi$
$824$		−	886226.i		−	1.30524i
$825$	−522836.	+	429774.i	−0.768170	+	0.631440i
$826$	−27264.6			−0.0399613
$827$		−	735008.i		−	1.07469i	−0.843364	−	0.537343i	$-0.819428\pi$
$827$		−	735008.i		−	1.07469i	0.843364	−	0.537343i	$-0.180572\pi$
$828$	524767.	+	103519.i	0.765430	+	0.150994i
$829$	462547.			0.673049			0.336525	−	0.941675i	$-0.390748\pi$
$829$	462547.			0.673049			0.336525	+	0.941675i	$0.390748\pi$
$830$			132217.i			0.191924i
$831$	−46488.2	−	56554.6i	−0.0673195	−	0.0818967i
$832$	2948.92			0.00426006
$833$		−	670070.i		−	0.965674i
$834$	−278206.	+	228687.i	−0.399977	+	0.328783i
$835$	−104249.			−0.149520
$836$		−	143802.i		−	0.205756i
$837$	934320.	−	502262.i	1.33366	−	0.716934i
$838$	−564739.			−0.804193
$839$		−	113693.i		−	0.161514i	−0.996734	−	0.0807568i	$-0.974266\pi$
$839$		−	113693.i		−	0.161514i	0.996734	−	0.0807568i	$-0.0257337\pi$
$840$	31099.9	+	37834.3i	0.0440759	+	0.0536200i
$841$	−1.17047e6			−1.65488
$842$		−	315728.i		−	0.445337i
$843$	845252.	−	694801.i	1.18941	−	0.977699i
$844$	592257.			0.831430
$845$		−	104351.i		−	0.146145i
$846$	45526.2	−	230785.i	0.0636093	−	0.322454i
$847$	−10615.1			−0.0147964
$848$			38864.2i			0.0540452i
$849$	41888.8	+	50959.3i	0.0581142	+	0.0706981i
$850$	−580162.			−0.802992
$851$		−	1.41024e6i		−	1.94730i
$852$	−6390.98	+	5253.42i	−0.00880416	+	0.00723707i
$853$	−26560.1			−0.0365032			−0.0182516	−	0.999833i	$-0.505810\pi$
$853$	−26560.1			−0.0365032			−0.0182516	+	0.999833i	$0.505810\pi$
$854$			205086.i			0.281204i
$855$	−38785.7	−	7651.12i	−0.0530566	−	0.0104663i
$856$	−581942.			−0.794205
$857$			500794.i			0.681864i	0.940088	+	0.340932i	$0.110743\pi$
$857$			500794.i			0.681864i	−0.940088	+	0.340932i	$0.889257\pi$
$858$	1735.79	+	2111.66i	0.00235789	+	0.00286846i
$859$	374009.			0.506869			0.253434	−	0.967353i	$-0.418440\pi$
$859$	374009.			0.506869			0.253434	+	0.967353i	$0.418440\pi$
$860$			40793.6i			0.0551562i
$861$	173750.	−	142823.i	0.234379	−	0.192661i
$862$	−432951.			−0.582672
$863$		−	622632.i		−	0.836007i	−0.908445	−	0.418004i	$-0.862730\pi$
$863$		−	622632.i		−	0.836007i	0.908445	−	0.418004i	$-0.137270\pi$
$864$	331534.	+	616727.i	0.444120	+	0.826163i
$865$	66578.6			0.0889820
$866$			225455.i			0.300625i
$867$	232477.	+	282817.i	0.309273	+	0.376242i
$868$	284797.			0.378003
$869$		−	495273.i		−	0.655851i
$870$	−93688.8	+	77012.7i	−0.123780	+	0.101747i
$871$	4928.74			0.00649680
$872$		−	970157.i		−	1.27588i
$873$	57446.0	−	291210.i	0.0753757	−	0.382101i
$874$	271137.			0.354948
$875$			100999.i			0.131917i
$876$	−508963.	−	619173.i	−0.663251	−	0.806870i
$877$	1.47961e6			1.92375			0.961873	−	0.273497i	$-0.0881804\pi$
$877$	1.47961e6			1.92375			0.961873	+	0.273497i	$0.0881804\pi$
$878$		−	269511.i		−	0.349612i
$879$	−593729.	+	488048.i	−0.768441	+	0.631662i
$880$	−17624.5			−0.0227589
$881$			868848.i			1.11942i	0.828689	+	0.559709i	$0.189087\pi$
$881$			868848.i			1.11942i	−0.828689	+	0.559709i	$0.810913\pi$
$882$	406671.	+	80222.6i	0.522765	+	0.103124i
$883$	−1.11196e6			−1.42616			−0.713080	−	0.701083i	$-0.752700\pi$
$883$	−1.11196e6			−1.42616			−0.713080	+	0.701083i	$0.752700\pi$
$884$		−	2832.32i		−	0.00362442i
$885$	9463.13	+	11512.3i	0.0120823	+	0.0146985i
$886$	74450.5			0.0948419
$887$		−	1.31641e6i		−	1.67319i	−0.547822	−	0.836595i	$-0.684543\pi$
$887$		−	1.31641e6i		−	1.67319i	0.547822	−	0.836595i	$-0.315457\pi$
$888$	866253.	−	712064.i	1.09855	−	0.903011i
$889$	−472555.			−0.597928
$890$		−	11421.9i		−	0.0144197i
$891$	−306331.	+	746224.i	−0.385865	+	0.939970i
$892$	−135740.			−0.170599
$893$			144134.i			0.180743i
$894$	460393.	+	560086.i	0.576042	+	0.700777i
$895$	−141786.			−0.177006
$896$			150223.i			0.187120i
$897$	4812.61	−	3955.99i	0.00598131	−	0.00491666i
$898$	579716.			0.718891
$899$			1.99393e6i			2.46712i
$900$	−83957.8	+	425606.i	−0.103652	+	0.525440i
$901$	349097.			0.430028
$902$			369955.i			0.454711i
$903$	−162892.	−	198164.i	−0.199767	−	0.243024i
$904$	268755.			0.328867
$905$			172331.i			0.210410i
$906$	−322842.	+	265378.i	−0.393309	+	0.323302i
$907$	−1.15372e6			−1.40244			−0.701221	−	0.712944i	$-0.747361\pi$
$907$	−1.15372e6			−1.40244			−0.701221	+	0.712944i	$0.747361\pi$
$908$		−	789746.i		−	0.957890i
$909$	−100323.	−	19790.3i	−0.121415	−	0.0239511i
$910$	201.759			0.000243640
$911$		−	827151.i		−	0.996662i	−0.866987	−	0.498331i	$-0.833946\pi$
$911$		−	827151.i		−	0.996662i	0.866987	−	0.498331i	$-0.166054\pi$
$912$	29951.7	+	36437.4i	0.0360107	+	0.0438084i
$913$	−1.65302e6			−1.98307
$914$			128881.i			0.154276i
$915$	86596.0	−	71182.3i	0.103432	−	0.0850217i
$916$	391709.			0.466844
$917$		−	520367.i		−	0.618830i
$918$	−609046.	+	327405.i	−0.722712	+	0.388508i
$919$	614145.			0.727176			0.363588	−	0.931560i	$-0.381552\pi$
$919$	614145.			0.727176			0.363588	+	0.931560i	$0.381552\pi$
$920$			183598.i			0.216916i
$921$	−129055.	−	157000.i	−0.152144	−	0.185089i
$922$	−165566.			−0.194765
$923$			96.3577i			0.000113105i
$924$	−167304.	+	137525.i	−0.195958	+	0.161078i
$925$	1.14376e6			1.33675
$926$			280885.i			0.327572i
$927$	208509.	−	1.05699e6i	0.242641	−	1.23002i
$928$	−1.31616e6			−1.52831
$929$			141985.i			0.164517i	0.996611	+	0.0822584i	$0.0262133\pi$
$929$			141985.i			0.164517i	−0.996611	+	0.0822584i	$0.973787\pi$
$930$	81777.7	+	99485.7i	0.0945517	+	0.115026i
$931$	−253981.			−0.293023
$932$			87391.4i			0.100609i
$933$	−438921.	+	360795.i	−0.504224	+	0.414474i
$934$	−705237.			−0.808428
$935$			158312.i			0.181088i
$936$	4860.02	+	958.719i	0.00554736	+	0.00109431i
$937$	−884504.			−1.00744			−0.503722	−	0.863866i	$-0.668036\pi$
$937$	−884504.			−1.00744			−0.503722	+	0.863866i	$0.668036\pi$
$938$		−	323060.i		−	0.367178i
$939$	1.01564e6	+	1.23556e6i	1.15188	+	1.40131i
$940$	−34520.1			−0.0390676
$941$			736405.i			0.831644i	0.909446	+	0.415822i	$0.136506\pi$
$941$			736405.i			0.831644i	−0.909446	+	0.415822i	$0.863494\pi$
$942$	−639165.	+	525397.i	−0.720297	+	0.592087i
$943$	843154.			0.948164
$944$		−	17780.3i		−	0.0199524i
$945$	28191.0	+	52441.5i	0.0315679	+	0.0587235i
$946$	421938.			0.471484
$947$			23491.8i			0.0261948i	0.999914	+	0.0130974i	$0.00416916\pi$
$947$			23491.8i			0.0261948i	−0.999914	+	0.0130974i	$0.995831\pi$
$948$	−201585.	−	245235.i	−0.224306	−	0.272877i
$949$	−9335.36			−0.0103657
$950$			219902.i			0.243659i
$951$	−479681.	+	394300.i	−0.530385	+	0.435979i
$952$	−524882.			−0.579146
$953$		−	266400.i		−	0.293324i	−0.989187	−	0.146662i	$-0.953147\pi$
$953$		−	266400.i		−	0.293324i	0.989187	−	0.146662i	$-0.0468530\pi$
$954$	−41794.8	+	211870.i	−0.0459225	+	0.232794i
$955$	−78081.0			−0.0856128
$956$		−	315777.i		−	0.345513i
$957$	−962842.	−	1.17133e6i	−1.05131	−	1.27896i
$958$	515760.			0.561974
$959$			2667.64i			0.00290061i
$960$	−81615.1	+	67088.0i	−0.0885581	+	0.0727951i
$961$	1.19378e6			1.29264
$962$		−	4619.46i		−	0.00499162i
$963$	−694075.	−	136918.i	−0.748435	−	0.147641i
$964$	146176.			0.157297
$965$		−	238741.i		−	0.256373i
$966$	−259300.	−	315448.i	−0.277874	−	0.338045i
$967$	−900514.			−0.963025			−0.481513	−	0.876439i	$-0.659912\pi$
$967$	−900514.			−0.963025			−0.481513	+	0.876439i	$0.659912\pi$
$968$		−	31641.6i		−	0.0337681i
$969$	327299.	−	269041.i	0.348575	−	0.286531i
$970$	36035.9			0.0382994
$971$		−	282724.i		−	0.299864i	−0.988696	−	0.149932i	$-0.952094\pi$
$971$		−	282724.i		−	0.299864i	0.988696	−	0.149932i	$-0.0479055\pi$
$972$	152046.	+	494176.i	0.160932	+	0.523057i
$973$	−332329.			−0.351029
$974$		−	659196.i		−	0.694859i
$975$	3208.46	+	3903.22i	0.00337511	+	0.00410595i
$976$	−133745.			−0.140404
$977$		−	522927.i		−	0.547837i	−0.961753	−	0.273919i	$-0.911680\pi$
$977$		−	522927.i		−	0.547837i	0.961753	−	0.273919i	$-0.0883199\pi$
$978$	389220.	−	319941.i	0.406928	−	0.334496i
$979$	142800.			0.148992
$980$		−	60828.6i		−	0.0633367i
$981$	228256.	−	1.15709e6i	0.237183	−	1.20235i
$982$	−743212.			−0.770708
$983$			784774.i			0.812152i	0.913839	+	0.406076i	$0.133103\pi$
$983$			784774.i			0.812152i	−0.913839	+	0.406076i	$0.866897\pi$
$984$	425729.	+	517916.i	0.439687	+	0.534896i
$985$	143886.			0.148301
$986$		−	1.29976e6i		−	1.33694i
$987$	167689.	−	137841.i	0.172136	−	0.141496i
$988$	−1073.55			−0.00109979
$989$		−	961628.i		−	0.983138i
$990$	−96080.6	−	18953.5i	−0.0980314	−	0.0193383i
$991$	−1.39542e6			−1.42088			−0.710439	−	0.703758i	$-0.751504\pi$
$991$	−1.39542e6			−1.42088			−0.710439	+	0.703758i	$0.751504\pi$
$992$			1.39759e6i			1.42022i
$993$	−334510.	−	406944.i	−0.339243	−	0.412702i
$994$	6315.88			0.00639235
$995$			30245.4i			0.0305502i
$996$	−818497.	+	672808.i	−0.825084	+	0.678223i
$997$	−1.73135e6			−1.74179			−0.870893	−	0.491472i	$-0.836459\pi$
$997$	−1.73135e6			−1.74179			−0.870893	+	0.491472i	$0.836459\pi$
$998$		−	552751.i		−	0.554969i
$999$	1.20070e6	−	645460.i	1.20311	−	0.646753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.52	yes	78
3.2	odd	2	inner	177.5.b.a.119.27	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.27	✓	78	3.2	odd	2	inner
177.5.b.a.119.52	yes	78	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.69145i q^{2} +(-5.71505 - 6.95257i) q^{3} +8.75607 q^{4} +3.65373i q^{5} +(18.7125 - 15.3818i) q^{6} +22.3529 q^{7} +66.6298i q^{8} +(-15.6765 + 79.4685i) q^{9} +O(q^{10})\)	\(q+2.69145i q^{2} +(-5.71505 - 6.95257i) q^{3} +8.75607 q^{4} +3.65373i q^{5} +(18.7125 - 15.3818i) q^{6} +22.3529 q^{7} +66.6298i q^{8} +(-15.6765 + 79.4685i) q^{9} -9.83386 q^{10} -122.947i q^{11} +(-50.0414 - 60.8772i) q^{12} -0.917855 q^{13} +60.1618i q^{14} +(25.4028 - 20.8813i) q^{15} -39.2340 q^{16} +352.419i q^{17} +(-213.886 - 42.1925i) q^{18} +133.579 q^{19} +31.9924i q^{20} +(-127.748 - 155.410i) q^{21} +330.905 q^{22} -754.157i q^{23} +(463.249 - 380.793i) q^{24} +611.650 q^{25} -2.47036i q^{26} +(642.102 - 345.175i) q^{27} +195.724 q^{28} +1370.31i q^{29} +(56.2009 + 68.3706i) q^{30} +1455.10 q^{31} +960.481i q^{32} +(-854.795 + 702.646i) q^{33} -948.519 q^{34} +81.6716i q^{35} +(-137.264 + 695.832i) q^{36} +1869.95 q^{37} +359.523i q^{38} +(5.24558 + 6.38145i) q^{39} -243.448 q^{40} +1118.01i q^{41} +(418.280 - 343.828i) q^{42} +1275.10 q^{43} -1076.53i q^{44} +(-290.357 - 57.2777i) q^{45} +2029.78 q^{46} +1079.01i q^{47} +(224.224 + 272.777i) q^{48} -1901.35 q^{49} +1646.23i q^{50} +(2450.22 - 2014.09i) q^{51} -8.03681 q^{52} -990.574i q^{53} +(929.022 + 1728.19i) q^{54} +449.214 q^{55} +1489.37i q^{56} +(-763.413 - 928.720i) q^{57} -3688.12 q^{58} +453.188i q^{59} +(222.429 - 182.838i) q^{60} +3408.91 q^{61} +3916.32i q^{62} +(-350.415 + 1776.35i) q^{63} -3212.83 q^{64} -3.35360i q^{65} +(-1891.14 - 2300.64i) q^{66} -5369.84 q^{67} +3085.81i q^{68} +(-5243.33 + 4310.04i) q^{69} -219.815 q^{70} -104.981i q^{71} +(-5294.98 - 1044.52i) q^{72} +10170.8 q^{73} +5032.89i q^{74} +(-3495.61 - 4252.54i) q^{75} +1169.63 q^{76} -2748.22i q^{77} +(-17.1754 + 14.1183i) q^{78} +4028.36 q^{79} -143.350i q^{80} +(-6069.50 - 2491.57i) q^{81} -3009.07 q^{82} -13445.0i q^{83} +(-1118.57 - 1360.78i) q^{84} -1287.64 q^{85} +3431.88i q^{86} +(9527.17 - 7831.38i) q^{87} +8191.92 q^{88} +1161.48i q^{89} +(154.160 - 781.482i) q^{90} -20.5167 q^{91} -6603.45i q^{92} +(-8315.94 - 10116.7i) q^{93} -2904.11 q^{94} +488.064i q^{95} +(6677.81 - 5489.19i) q^{96} -3664.47 q^{97} -5117.39i q^{98} +(9770.39 + 1927.37i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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