LMFDB - Embedded newform 177.5.b.a.119.47

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			119.47
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.69186i q^{2} +(1.47875 + 8.87768i) q^{3} +13.1376 q^{4} +14.2713i q^{5} +(-15.0198 + 2.50184i) q^{6} -21.1589 q^{7} +49.2966i q^{8} +(-76.6266 + 26.2558i) q^{9} +O(q^{10})$	\(q+1.69186i q^{2} +(1.47875 + 8.87768i) q^{3} +13.1376 q^{4} +14.2713i q^{5} +(-15.0198 + 2.50184i) q^{6} -21.1589 q^{7} +49.2966i q^{8} +(-76.6266 + 26.2558i) q^{9} -24.1450 q^{10} -47.6038i q^{11} +(19.4273 + 116.632i) q^{12} -227.817 q^{13} -35.7978i q^{14} +(-126.696 + 21.1038i) q^{15} +126.799 q^{16} +178.401i q^{17} +(-44.4210 - 129.641i) q^{18} -159.896 q^{19} +187.491i q^{20} +(-31.2888 - 187.842i) q^{21} +80.5386 q^{22} +704.184i q^{23} +(-437.640 + 72.8976i) q^{24} +421.329 q^{25} -385.433i q^{26} +(-346.403 - 641.441i) q^{27} -277.978 q^{28} -468.058i q^{29} +(-35.7045 - 214.352i) q^{30} +715.507 q^{31} +1003.27i q^{32} +(422.611 - 70.3942i) q^{33} -301.829 q^{34} -301.966i q^{35} +(-1006.69 + 344.939i) q^{36} -1780.84 q^{37} -270.521i q^{38} +(-336.885 - 2022.49i) q^{39} -703.529 q^{40} -979.879i q^{41} +(317.802 - 52.9361i) q^{42} -201.165 q^{43} -625.400i q^{44} +(-374.705 - 1093.56i) q^{45} -1191.38 q^{46} +767.510i q^{47} +(187.505 + 1125.68i) q^{48} -1953.30 q^{49} +712.828i q^{50} +(-1583.79 + 263.811i) q^{51} -2992.97 q^{52} +1473.16i q^{53} +(1085.22 - 586.063i) q^{54} +679.369 q^{55} -1043.06i q^{56} +(-236.447 - 1419.51i) q^{57} +791.887 q^{58} +453.188i q^{59} +(-1664.49 + 277.253i) q^{60} +2987.07 q^{61} +1210.53i q^{62} +(1621.33 - 555.544i) q^{63} +331.397 q^{64} -3251.25i q^{65} +(119.097 + 714.997i) q^{66} -382.598 q^{67} +2343.77i q^{68} +(-6251.52 + 1041.31i) q^{69} +510.882 q^{70} +6197.74i q^{71} +(-1294.32 - 3777.43i) q^{72} +2551.37 q^{73} -3012.93i q^{74} +(623.042 + 3740.43i) q^{75} -2100.65 q^{76} +1007.24i q^{77} +(3421.75 - 569.961i) q^{78} +10554.3 q^{79} +1809.59i q^{80} +(5182.26 - 4023.79i) q^{81} +1657.81 q^{82} +2978.40i q^{83} +(-411.061 - 2467.80i) q^{84} -2546.02 q^{85} -340.341i q^{86} +(4155.27 - 692.143i) q^{87} +2346.71 q^{88} +2740.18i q^{89} +(1850.15 - 633.947i) q^{90} +4820.36 q^{91} +9251.30i q^{92} +(1058.06 + 6352.04i) q^{93} -1298.52 q^{94} -2281.93i q^{95} +(-8906.73 + 1483.59i) q^{96} -1717.30 q^{97} -3304.70i q^{98} +(1249.88 + 3647.71i) 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 $

$2$			1.69186i			0.422964i	0.977382	+	0.211482i	$0.0678289\pi$
$2$			1.69186i			0.422964i	−0.977382	+	0.211482i	$0.932171\pi$
$3$	1.47875	+	8.87768i	0.164306	+	0.986409i
$3$	1.47875	+	8.87768i	0.164306	+	0.986409i
$4$	13.1376			0.821102
$5$			14.2713i			0.570853i	0.958401	+	0.285427i	$0.0921353\pi$
$5$			14.2713i			0.570853i	−0.958401	+	0.285427i	$0.907865\pi$
$6$	−15.0198	+	2.50184i	−0.417215	+	0.0694954i
$7$	−21.1589			−0.431814			−0.215907	−	0.976414i	$-0.569271\pi$
$7$	−21.1589			−0.431814			−0.215907	+	0.976414i	$0.569271\pi$
$8$			49.2966i			0.770260i
$9$	−76.6266	+	26.2558i	−0.946007	+	0.324146i
$10$	−24.1450			−0.241450
$11$		−	47.6038i		−	0.393419i	−0.980462	−	0.196710i	$-0.936974\pi$
$11$		−	47.6038i		−	0.393419i	0.980462	−	0.196710i	$-0.0630257\pi$
$12$	19.4273	+	116.632i	0.134912	+	0.809942i
$13$	−227.817			−1.34803			−0.674015	−	0.738718i	$-0.735432\pi$
$13$	−227.817			−1.34803			−0.674015	+	0.738718i	$0.735432\pi$
$14$		−	35.7978i		−	0.182642i
$15$	−126.696	+	21.1038i	−0.563095	+	0.0937945i
$16$	126.799			0.495310
$17$			178.401i			0.617305i	0.951175	+	0.308652i	$0.0998780\pi$
$17$			178.401i			0.617305i	−0.951175	+	0.308652i	$0.900122\pi$
$18$	−44.4210	−	129.641i	−0.137102	−	0.400127i
$19$	−159.896			−0.442925			−0.221463	−	0.975169i	$-0.571083\pi$
$19$	−159.896			−0.442925			−0.221463	+	0.975169i	$0.571083\pi$
$20$			187.491i			0.468728i
$21$	−31.2888	−	187.842i	−0.0709497	−	0.425946i
$22$	80.5386			0.166402
$23$			704.184i			1.33116i	0.746327	+	0.665580i	$0.231816\pi$
$23$			704.184i			1.33116i	−0.746327	+	0.665580i	$0.768184\pi$
$24$	−437.640	+	72.8976i	−0.759792	+	0.126558i
$25$	421.329			0.674127
$26$		−	385.433i		−	0.570167i
$27$	−346.403	−	641.441i	−0.475175	−	0.879891i
$28$	−277.978			−0.354563
$29$		−	468.058i		−	0.556550i	−0.960501	−	0.278275i	$-0.910237\pi$
$29$		−	468.058i		−	0.556550i	0.960501	−	0.278275i	$-0.0897626\pi$
$30$	−35.7045	−	214.352i	−0.0396717	−	0.238169i
$31$	715.507			0.744544			0.372272	−	0.928124i	$-0.378579\pi$
$31$	715.507			0.744544			0.372272	+	0.928124i	$0.378579\pi$
$32$			1003.27i			0.979758i
$33$	422.611	−	70.3942i	0.388073	−	0.0646411i
$34$	−301.829			−0.261098
$35$		−	301.966i		−	0.246503i
$36$	−1006.69	+	344.939i	−0.776768	+	0.266157i
$37$	−1780.84			−1.30084			−0.650418	−	0.759577i	$-0.725406\pi$
$37$	−1780.84			−1.30084			−0.650418	+	0.759577i	$0.725406\pi$
$38$		−	270.521i		−	0.187341i
$39$	−336.885	−	2022.49i	−0.221489	−	1.32971i
$40$	−703.529			−0.439705
$41$		−	979.879i		−	0.582914i	−0.956584	−	0.291457i	$-0.905860\pi$
$41$		−	979.879i		−	0.582914i	0.956584	−	0.291457i	$-0.0941401\pi$
$42$	317.802	−	52.9361i	0.180160	−	0.0300091i
$43$	−201.165			−0.108796			−0.0543982	−	0.998519i	$-0.517324\pi$
$43$	−201.165			−0.108796			−0.0543982	+	0.998519i	$0.517324\pi$
$44$		−	625.400i		−	0.323037i
$45$	−374.705	−	1093.56i	−0.185040	−	0.540031i
$46$	−1191.38			−0.563032
$47$			767.510i			0.347447i	0.984794	+	0.173723i	$0.0555799\pi$
$47$			767.510i			0.347447i	−0.984794	+	0.173723i	$0.944420\pi$
$48$	187.505	+	1125.68i	0.0813823	+	0.488578i
$49$	−1953.30			−0.813536
$50$			712.828i			0.285131i
$51$	−1583.79	+	263.811i	−0.608915	+	0.101427i
$52$	−2992.97			−1.10687
$53$			1473.16i			0.524441i	0.965008	+	0.262221i	$0.0844548\pi$
$53$			1473.16i			0.524441i	−0.965008	+	0.262221i	$0.915545\pi$
$54$	1085.22	−	586.063i	0.372162	−	0.200982i
$55$	679.369			0.224585
$56$		−	1043.06i		−	0.332609i
$57$	−236.447	−	1419.51i	−0.0727752	−	0.436905i
$58$	791.887			0.235400
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	−1664.49	+	277.253i	−0.462358	+	0.0770149i
$61$	2987.07			0.802759			0.401379	−	0.915912i	$-0.368531\pi$
$61$	2987.07			0.802759			0.401379	+	0.915912i	$0.368531\pi$
$62$			1210.53i			0.314915i
$63$	1621.33	−	555.544i	0.408499	−	0.139971i
$64$	331.397			0.0809075
$65$		−	3251.25i		−	0.769527i
$66$	119.097	+	714.997i	0.0273409	+	0.164141i
$67$	−382.598			−0.0852302			−0.0426151	−	0.999092i	$-0.513569\pi$
$67$	−382.598			−0.0852302			−0.0426151	+	0.999092i	$0.513569\pi$
$68$			2343.77i			0.506870i
$69$	−6251.52	+	1041.31i	−1.31307	+	0.218717i
$70$	510.882			0.104262
$71$			6197.74i			1.22947i	0.788735	+	0.614733i	$0.210736\pi$
$71$			6197.74i			1.22947i	−0.788735	+	0.614733i	$0.789264\pi$
$72$	−1294.32	−	3777.43i	−0.249677	−	0.728671i
$73$	2551.37			0.478771			0.239385	−	0.970925i	$-0.423054\pi$
$73$	2551.37			0.478771			0.239385	+	0.970925i	$0.423054\pi$
$74$		−	3012.93i		−	0.550206i
$75$	623.042	+	3740.43i	0.110763	+	0.664965i
$76$	−2100.65			−0.363687
$77$			1007.24i			0.169884i
$78$	3421.75	−	569.961i	0.562419	−	0.0936819i
$79$	10554.3			1.69112			0.845562	−	0.533878i	$-0.179266\pi$
$79$	10554.3			1.69112			0.845562	+	0.533878i	$0.179266\pi$
$80$			1809.59i			0.282749i
$81$	5182.26	−	4023.79i	0.789859	−	0.613288i
$82$	1657.81			0.246552
$83$			2978.40i			0.432341i	0.976356	+	0.216170i	$0.0693567\pi$
$83$			2978.40i			0.432341i	−0.976356	+	0.216170i	$0.930643\pi$
$84$	−411.061	−	2467.80i	−0.0582569	−	0.349745i
$85$	−2546.02			−0.352390
$86$		−	340.341i		−	0.0460169i
$87$	4155.27	−	692.143i	0.548986	−	0.0914444i
$88$	2346.71			0.303035
$89$			2740.18i			0.345939i	0.984927	+	0.172970i	$0.0553362\pi$
$89$			2740.18i			0.345939i	−0.984927	+	0.172970i	$0.944664\pi$
$90$	1850.15	−	633.947i	0.228414	−	0.0782651i
$91$	4820.36			0.582098
$92$			9251.30i			1.09302i
$93$	1058.06	+	6352.04i	0.122333	+	0.734425i
$94$	−1298.52			−0.146957
$95$		−	2281.93i		−	0.252845i
$96$	−8906.73	+	1483.59i	−0.966443	+	0.160980i
$97$	−1717.30			−0.182517			−0.0912583	−	0.995827i	$-0.529089\pi$
$97$	−1717.30			−0.182517			−0.0912583	+	0.995827i	$0.529089\pi$
$98$		−	3304.70i		−	0.344096i
$99$	1249.88	+	3647.71i	0.127525	+	0.372178i
$100$	5535.27			0.553527
$101$			1702.52i			0.166897i	0.996512	+	0.0834484i	$0.0265934\pi$
$101$			1702.52i			0.166897i	−0.996512	+	0.0834484i	$0.973407\pi$
$102$	−446.330	−	2679.54i	−0.0428999	−	0.257549i
$103$	−1697.10			−0.159968			−0.0799839	−	0.996796i	$-0.525487\pi$
$103$	−1697.10			−0.159968			−0.0799839	+	0.996796i	$0.525487\pi$
$104$		−	11230.6i		−	1.03833i
$105$	2680.76	−	446.533i	0.243152	−	0.0405018i
$106$	−2492.36			−0.221820
$107$			6681.95i			0.583627i	0.956475	+	0.291814i	$0.0942587\pi$
$107$			6681.95i			0.583627i	−0.956475	+	0.291814i	$0.905741\pi$
$108$	−4550.91	−	8427.01i	−0.390167	−	0.722480i
$109$	12918.4			1.08731			0.543656	−	0.839308i	$-0.317039\pi$
$109$	12918.4			1.08731			0.543656	+	0.839308i	$0.317039\pi$
$110$			1149.39i			0.0949912i
$111$	−2633.43	−	15809.8i	−0.213735	−	1.28316i
$112$	−2682.93			−0.213882
$113$			3584.48i			0.280718i	0.990101	+	0.140359i	$0.0448256\pi$
$113$			3584.48i			0.280718i	−0.990101	+	0.140359i	$0.955174\pi$
$114$	2401.60	−	400.033i	0.184795	−	0.0307813i
$115$	−10049.6			−0.759897
$116$		−	6149.18i		−	0.456984i
$117$	17456.8	−	5981.52i	1.27525	−	0.436958i
$118$	−766.728			−0.0550652
$119$		−	3774.77i		−	0.266561i
$120$	−1040.35	−	6245.70i	−0.0722462	−	0.433729i
$121$	12374.9			0.845221
$122$			5053.68i			0.339538i
$123$	8699.06	−	1449.00i	0.574992	−	0.0957763i
$124$	9400.06			0.611346
$125$			14932.5i			0.955680i
$126$	939.900	+	2743.06i	0.0592026	+	0.172780i
$127$	6413.34			0.397628			0.198814	−	0.980037i	$-0.436291\pi$
$127$	6413.34			0.397628			0.198814	+	0.980037i	$0.436291\pi$
$128$			16613.0i			1.01398i
$129$	−297.473	−	1785.88i	−0.0178759	−	0.107318i
$130$	5500.64			0.325482
$131$			9589.38i			0.558789i	0.960176	+	0.279394i	$0.0901337\pi$
$131$			9589.38i			0.558789i	−0.960176	+	0.279394i	$0.909866\pi$
$132$	5552.11	−	924.813i	0.318647	−	0.0530769i
$133$	3383.22			0.191261
$134$		−	647.301i		−	0.0360493i
$135$	9154.21	−	4943.63i	0.502289	−	0.271255i
$136$	−8794.58			−0.475485
$137$			20958.4i			1.11665i	0.829623	+	0.558324i	$0.188555\pi$
$137$			20958.4i			1.11665i	−0.829623	+	0.558324i	$0.811445\pi$
$138$	−1761.75	−	10576.7i	−0.0925095	−	0.555380i
$139$	−12761.2			−0.660481			−0.330240	−	0.943897i	$-0.607130\pi$
$139$	−12761.2			−0.660481			−0.330240	+	0.943897i	$0.607130\pi$
$140$		−	3967.11i		−	0.202404i
$141$	−6813.71	+	1134.96i	−0.342725	+	0.0570876i
$142$	−10485.7			−0.520020
$143$			10844.9i			0.530341i
$144$	−9716.19	+	3329.22i	−0.468566	+	0.160553i
$145$	6679.81			0.317708
$146$			4316.55i			0.202503i
$147$	−2888.45	−	17340.8i	−0.133669	−	0.802480i
$148$	−23396.1			−1.06812
$149$			43281.2i			1.94952i	0.223261	+	0.974759i	$0.428330\pi$
$149$			43281.2i			1.94952i	−0.223261	+	0.974759i	$0.571670\pi$
$150$	−6328.26	+	1054.10i	−0.281256	+	0.0468487i
$151$	26709.5			1.17142			0.585708	−	0.810522i	$-0.300816\pi$
$151$	26709.5			1.17142			0.585708	+	0.810522i	$0.300816\pi$
$152$		−	7882.33i		−	0.341167i
$153$	−4684.07	−	13670.3i	−0.200097	−	0.583975i
$154$	−1704.11			−0.0718548
$155$			10211.2i			0.425025i
$156$	−4425.87	−	26570.7i	−0.181865	−	1.09183i
$157$	24971.8			1.01310			0.506548	−	0.862212i	$-0.330921\pi$
$157$	24971.8			1.01310			0.506548	+	0.862212i	$0.330921\pi$
$158$			17856.3i			0.715284i
$159$	−13078.2	+	2178.43i	−0.517314	+	0.0861688i
$160$	−14318.0			−0.559298
$161$		−	14899.8i		−	0.574814i
$162$	6807.66	+	8767.64i	0.259399	+	0.334082i
$163$	−43093.5			−1.62195			−0.810973	−	0.585084i	$-0.801062\pi$
$163$	−43093.5			−1.62195			−0.810973	+	0.585084i	$0.801062\pi$
$164$		−	12873.3i		−	0.478632i
$165$	1004.62	+	6031.22i	0.0369006	+	0.221532i
$166$	−5039.02			−0.182865
$167$		−	37082.1i		−	1.32963i	−0.747008	−	0.664815i	$-0.768510\pi$
$167$		−	37082.1i		−	1.32963i	0.747008	−	0.664815i	$-0.231490\pi$
$168$	9259.98	−	1542.43i	0.328089	−	0.0546497i
$169$	23339.6			0.817183
$170$		−	4307.50i		−	0.149048i
$171$	12252.3	−	4198.20i	0.419010	−	0.143572i
$172$	−2642.82			−0.0893329
$173$			15784.1i			0.527384i	0.964607	+	0.263692i	$0.0849403\pi$
$173$			15784.1i			0.527384i	−0.964607	+	0.263692i	$0.915060\pi$
$174$	1171.01	+	7030.12i	0.0386777	+	0.232201i
$175$	−8914.86			−0.291098
$176$		−	6036.12i		−	0.194864i
$177$	−4023.26	+	670.153i	−0.128420	+	0.0213908i
$178$	−4635.99			−0.146320
$179$		−	55143.7i		−	1.72104i	−0.509420	−	0.860518i	$-0.670140\pi$
$179$		−	55143.7i		−	1.72104i	0.509420	−	0.860518i	$-0.329860\pi$
$180$	−4922.74	−	14366.8i	−0.151936	−	0.443420i
$181$	−43355.6			−1.32339			−0.661696	−	0.749772i	$-0.730163\pi$
$181$	−43355.6			−1.32339			−0.661696	+	0.749772i	$0.730163\pi$
$182$			8155.34i			0.246206i
$183$	4417.13	+	26518.2i	0.131898	+	0.791849i
$184$	−34713.9			−1.02534
$185$		−	25415.0i		−	0.742586i
$186$	−10746.7	+	1790.08i	−0.310635	+	0.0517424i
$187$	8492.56			0.242860
$188$			10083.3i			0.285289i
$189$	7329.50	+	13572.2i	0.205187	+	0.379950i
$190$	3860.69			0.106944
$191$			21518.0i			0.589841i	0.955522	+	0.294921i	$0.0952932\pi$
$191$			21518.0i			0.589841i	−0.955522	+	0.294921i	$0.904707\pi$
$192$	490.054	+	2942.04i	0.0132936	+	0.0798079i
$193$	−10394.7			−0.279061			−0.139531	−	0.990218i	$-0.544559\pi$
$193$	−10394.7			−0.279061			−0.139531	+	0.990218i	$0.544559\pi$
$194$		−	2905.42i		−	0.0771979i
$195$	28863.6	−	4807.80i	0.759068	−	0.126438i
$196$	−25661.7			−0.667996
$197$		−	69748.2i		−	1.79722i	−0.438750	−	0.898609i	$-0.644579\pi$
$197$		−	69748.2i		−	1.79722i	0.438750	−	0.898609i	$-0.355421\pi$
$198$	−6171.40	+	2114.61i	−0.157418	+	0.0539386i
$199$	−26084.5			−0.658684			−0.329342	−	0.944211i	$-0.606827\pi$
$199$	−26084.5			−0.658684			−0.329342	+	0.944211i	$0.606827\pi$
$200$			20770.1i			0.519253i
$201$	−565.769	−	3396.59i	−0.0140038	−	0.0840719i
$202$	−2880.41			−0.0705913
$203$			9903.60i			0.240326i
$204$	−20807.2	+	3465.85i	−0.499981	+	0.0832818i
$205$	13984.2			0.332759
$206$		−	2871.25i		−	0.0676606i
$207$	−18488.9	−	53959.2i	−0.431490	−	1.25929i
$208$	−28887.0			−0.667692
$209$			7611.65i			0.174255i
$210$	755.469	+	4535.45i	0.0171308	+	0.102845i
$211$	10592.7			0.237926			0.118963	−	0.992899i	$-0.462043\pi$
$211$	10592.7			0.237926			0.118963	+	0.992899i	$0.462043\pi$
$212$			19353.8i			0.430619i
$213$	−55021.6	+	9164.92i	−1.21276	+	0.202009i
$214$	−11304.9			−0.246853
$215$		−	2870.89i		−	0.0621068i
$216$	31620.9	−	17076.5i	0.677745	−	0.366008i
$217$	−15139.3			−0.321505
$218$			21856.0i			0.459894i
$219$	3772.85	+	22650.3i	0.0786649	+	0.472264i
$220$	8925.29			0.184407
$221$		−	40642.8i		−	0.832145i
$222$	26747.8	−	4455.38i	0.542728	−	0.0904021i
$223$	−49290.1			−0.991174			−0.495587	−	0.868558i	$-0.665047\pi$
$223$	−49290.1			−0.991174			−0.495587	+	0.868558i	$0.665047\pi$
$224$		−	21228.1i		−	0.423074i
$225$	−32285.0	+	11062.3i	−0.637729	+	0.218515i
$226$	−6064.43			−0.118733
$227$			22383.6i			0.434388i	0.976128	+	0.217194i	$0.0696905\pi$
$227$			22383.6i			0.434388i	−0.976128	+	0.217194i	$0.930310\pi$
$228$	−3106.35	−	18648.9i	−0.0597558	−	0.358744i
$229$	97674.3			1.86256			0.931278	−	0.364308i	$-0.118694\pi$
$229$	97674.3			1.86256			0.931278	+	0.364308i	$0.118694\pi$
$230$		−	17002.5i		−	0.321409i
$231$	−8941.99	+	1489.46i	−0.167575	+	0.0279130i
$232$	23073.7			0.428688
$233$			78886.8i			1.45309i	0.687119	+	0.726545i	$0.258875\pi$
$233$			78886.8i			1.45309i	−0.687119	+	0.726545i	$0.741125\pi$
$234$	10119.9	+	29534.4i	0.184817	+	0.539382i
$235$	−10953.4			−0.198341
$236$			5953.81i			0.106898i
$237$	15607.2	+	93697.8i	0.277862	+	1.66814i
$238$	6386.37			0.112746
$239$			15958.4i			0.279379i	0.990195	+	0.139689i	$0.0446104\pi$
$239$			15958.4i			0.279379i	−0.990195	+	0.139689i	$0.955390\pi$
$240$	−16065.0	+	2675.94i	−0.278906	+	0.0464573i
$241$	−42913.4			−0.738854			−0.369427	−	0.929260i	$-0.620446\pi$
$241$	−42913.4			−0.738854			−0.369427	+	0.929260i	$0.620446\pi$
$242$			20936.5i			0.357498i
$243$	43385.2	+	40056.3i	0.734732	+	0.678357i
$244$	39242.9			0.659146
$245$		−	27876.2i		−	0.464410i
$246$	2451.50	+	14717.5i	0.0405099	+	0.243201i
$247$	36427.0			0.597076
$248$			35272.1i			0.573493i
$249$	−26441.3	+	4404.31i	−0.426465	+	0.0710362i
$250$	−25263.6			−0.404218
$251$		−	82580.9i		−	1.31079i	−0.755288	−	0.655393i	$-0.772503\pi$
$251$		−	82580.9i		−	1.31079i	0.755288	−	0.655393i	$-0.227497\pi$
$252$	21300.5	−	7298.53i	0.335420	−	0.114930i
$253$	33521.8			0.523704
$254$			10850.4i			0.168182i
$255$	−3764.94	−	22602.8i	−0.0578998	−	0.347601i
$256$	−22804.5			−0.347969
$257$		−	10251.2i		−	0.155205i	−0.996984	−	0.0776027i	$-0.975273\pi$
$257$		−	10251.2i		−	0.155205i	0.996984	−	0.0776027i	$-0.0247266\pi$
$258$	3021.44	−	503.281i	0.0453915	−	0.00756085i
$259$	37680.7			0.561719
$260$		−	42713.7i		−	0.631860i
$261$	12289.3	+	35865.7i	0.180403	+	0.526500i
$262$	−16223.8			−0.236347
$263$		−	62792.8i		−	0.907817i	−0.891048	−	0.453909i	$-0.850029\pi$
$263$		−	62792.8i		−	0.907817i	0.891048	−	0.453909i	$-0.149971\pi$
$264$	3470.20	+	20833.3i	0.0497905	+	0.298917i
$265$	−21023.9			−0.299379
$266$			5723.92i			0.0808966i
$267$	−24326.5	+	4052.05i	−0.341237	+	0.0568398i
$268$	−5026.44			−0.0699827
$269$		−	38344.8i		−	0.529909i	−0.964261	−	0.264955i	$-0.914643\pi$
$269$		−	38344.8i		−	0.529909i	0.964261	−	0.264955i	$-0.0853570\pi$
$270$	8363.90	+	15487.6i	0.114731	+	0.212450i
$271$	84701.7			1.15333			0.576665	−	0.816981i	$-0.304354\pi$
$271$	84701.7			1.15333			0.576665	+	0.816981i	$0.304354\pi$
$272$			22621.1i			0.305757i
$273$	7128.12	+	42793.6i	0.0956422	+	0.574187i
$274$	−35458.5			−0.472301
$275$		−	20056.9i		−	0.265215i
$276$	−82130.1	+	13680.4i	−1.07816	+	0.179589i
$277$	84964.2			1.10733			0.553664	−	0.832740i	$-0.313229\pi$
$277$	84964.2			1.10733			0.553664	+	0.832740i	$0.313229\pi$
$278$		−	21590.0i		−	0.279360i
$279$	−54826.8	+	18786.2i	−0.704344	+	0.241341i
$280$	14885.9			0.189871
$281$			56178.1i			0.711467i	0.934588	+	0.355733i	$0.115769\pi$
$281$			56178.1i			0.711467i	−0.934588	+	0.355733i	$0.884231\pi$
$282$	−1920.18	−	11527.8i	−0.0241460	−	0.144960i
$283$	152883.			1.90891			0.954457	−	0.298348i	$-0.0964356\pi$
$283$	152883.			1.90891			0.954457	+	0.298348i	$0.0964356\pi$
$284$			81423.6i			1.00952i
$285$	20258.2	−	3374.41i	0.249409	−	0.0415440i
$286$	−18348.1			−0.224315
$287$			20733.2i			0.251711i
$288$	−26341.7	−	76877.3i	−0.317584	−	0.926858i
$289$	51694.0			0.618935
$290$			11301.3i			0.134379i
$291$	−2539.46	−	15245.6i	−0.0299886	−	0.180036i
$292$	33518.9			0.393119
$293$		−	146118.i		−	1.70203i	−0.525140	−	0.851016i	$-0.675987\pi$
$293$		−	146118.i		−	1.70203i	0.525140	−	0.851016i	$-0.324013\pi$
$294$	29338.1	−	4886.84i	0.339420	−	0.0565371i
$295$	−6467.59			−0.0743187
$296$		−	87789.6i		−	1.00198i
$297$	−30535.0	+	16490.1i	−0.346166	+	0.186943i
$298$	−73225.6			−0.824575
$299$		−	160425.i		−	1.79444i
$300$	8185.29	+	49140.3i	0.0909477	+	0.546004i
$301$	4256.42			0.0469798
$302$			45188.5i			0.495467i
$303$	−15114.4	+	2517.60i	−0.164629	+	0.0274221i
$304$	−20274.7			−0.219385
$305$			42629.4i			0.458257i
$306$	23128.1	−	7924.76i	0.247000	−	0.0846337i
$307$	1651.13			0.0175188			0.00875938	−	0.999962i	$-0.497212\pi$
$307$	1651.13			0.0175188			0.00875938	+	0.999962i	$0.497212\pi$
$308$			13232.8i			0.139492i
$309$	−2509.59	−	15066.3i	−0.0262837	−	0.157794i
$310$	−17275.9			−0.179770
$311$		−	75755.8i		−	0.783241i	−0.920127	−	0.391620i	$-0.871915\pi$
$311$		−	75755.8i		−	0.783241i	0.920127	−	0.391620i	$-0.128085\pi$
$312$	99701.8	−	16607.3i	1.02422	−	0.170604i
$313$	99740.0			1.01808			0.509038	−	0.860744i	$-0.330001\pi$
$313$	99740.0			1.01808			0.509038	+	0.860744i	$0.330001\pi$
$314$			42248.7i			0.428503i
$315$	7928.35	+	23138.6i	0.0799028	+	0.233193i
$316$	138658.			1.38858
$317$			81335.1i			0.809393i	0.914451	+	0.404696i	$0.132623\pi$
$317$			81335.1i			0.809393i	−0.914451	+	0.404696i	$0.867377\pi$
$318$	−3685.59	−	22126.4i	−0.0364463	−	0.218805i
$319$	−22281.3			−0.218957
$320$			4729.47i			0.0461863i
$321$	−59320.3	+	9880.96i	−0.575696	+	0.0958934i
$322$	25208.2			0.243125
$323$		−	28525.6i		−	0.273420i
$324$	68082.7	−	52863.0i	0.648555	−	0.503572i
$325$	−95985.9			−0.908742
$326$		−	72907.9i		−	0.686024i
$327$	19103.1	+	114685.i	0.178652	+	1.07254i
$328$	48304.7			0.448996
$329$		−	16239.7i		−	0.150033i
$330$	−10204.0	+	1699.67i	−0.0937002	+	0.0156076i
$331$	−130668.			−1.19265			−0.596325	−	0.802743i	$-0.703373\pi$
$331$	−130668.			−1.19265			−0.596325	+	0.802743i	$0.703373\pi$
$332$			39129.1i			0.354996i
$333$	136460.	−	46757.5i	1.23060	−	0.421660i
$334$	62737.5			0.562385
$335$		−	5460.19i		−	0.0486539i
$336$	−3967.40	−	23818.2i	−0.0351420	−	0.210975i
$337$	66179.4			0.582724			0.291362	−	0.956613i	$-0.405892\pi$
$337$	66179.4			0.582724			0.291362	+	0.956613i	$0.405892\pi$
$338$			39487.1i			0.345639i
$339$	−31821.9	+	5300.57i	−0.276903	+	0.0461236i
$340$	−33448.7			−0.289348
$341$		−	34060.8i		−	0.292918i
$342$	7102.74	+	20729.1i	0.0607259	+	0.177226i
$343$	92132.2			0.783111
$344$		−	9916.74i		−	0.0838015i
$345$	−14860.9	−	89217.5i	−0.124856	−	0.749569i
$346$	−26704.4			−0.223065
$347$		−	63185.5i		−	0.524758i	−0.964965	−	0.262379i	$-0.915493\pi$
$347$		−	63185.5i		−	0.524758i	0.964965	−	0.262379i	$-0.0845070\pi$
$348$	54590.4	−	9093.11i	0.450773	−	0.0750852i
$349$	−103099.			−0.846451			−0.423226	−	0.906024i	$-0.639102\pi$
$349$	−103099.			−0.846451			−0.423226	+	0.906024i	$0.639102\pi$
$350$		−	15082.7i		−	0.123124i
$351$	78916.4	+	146131.i	0.640550	+	1.18612i
$352$	47759.5			0.385456
$353$			165280.i			1.32639i	0.748446	+	0.663196i	$0.230800\pi$
$353$			165280.i			1.32639i	−0.748446	+	0.663196i	$0.769200\pi$
$354$	−1133.80	−	6806.77i	−0.00904754	−	0.0543168i
$355$	−88449.9			−0.701844
$356$			35999.5i			0.284051i
$357$	33511.2	−	5581.96i	0.262938	−	0.0437976i
$358$	93295.1			0.727936
$359$		−	179336.i		−	1.39149i	−0.718290	−	0.695744i	$-0.755075\pi$
$359$		−	179336.i		−	1.39149i	0.718290	−	0.695744i	$-0.244925\pi$
$360$	53909.0	−	18471.7i	0.415964	−	0.142529i
$361$	−104754.			−0.803817
$362$		−	73351.5i		−	0.559747i
$363$	18299.4	+	109860.i	0.138875	+	0.833734i
$364$	63328.0			0.477962
$365$			36411.4i			0.273308i
$366$	−44865.0	+	7473.15i	−0.334923	+	0.0557881i
$367$	−69536.7			−0.516276			−0.258138	−	0.966108i	$-0.583109\pi$
$367$	−69536.7			−0.516276			−0.258138	+	0.966108i	$0.583109\pi$
$368$			89289.9i			0.659336i
$369$	25727.5	+	75084.8i	0.188949	+	0.551441i
$370$	42998.5			0.314087
$371$		−	31170.3i		−	0.226461i
$372$	13900.4	+	83450.8i	0.100448	+	0.603038i
$373$	72192.1			0.518886			0.259443	−	0.965758i	$-0.416461\pi$
$373$	72192.1			0.518886			0.259443	+	0.965758i	$0.416461\pi$
$374$			14368.2i			0.102721i
$375$	−132566.	+	22081.5i	−0.942692	+	0.157024i
$376$	−37835.7			−0.267624
$377$			106632.i			0.750245i
$378$	−22962.2	+	12400.5i	−0.160705	+	0.0867868i
$379$	−145439.			−1.01252			−0.506258	−	0.862382i	$-0.668972\pi$
$379$	−145439.			−1.01252			−0.506258	+	0.862382i	$0.668972\pi$
$380$		−	29979.1i		−	0.207612i
$381$	9483.74	+	56935.6i	0.0653326	+	0.392224i
$382$	−36405.3			−0.249482
$383$			49167.4i			0.335181i	0.985857	+	0.167591i	$0.0535987\pi$
$383$			49167.4i			0.335181i	−0.985857	+	0.167591i	$0.946401\pi$
$384$	−147485.	+	24566.6i	−1.00020	+	0.166603i
$385$	−14374.7			−0.0969789
$386$		−	17586.4i		−	0.118033i
$387$	15414.6	−	5281.74i	0.102922	−	0.0352659i
$388$	−22561.2			−0.149865
$389$			25166.2i			0.166310i	0.996537	+	0.0831550i	$0.0264997\pi$
$389$			25166.2i			0.166310i	−0.996537	+	0.0831550i	$0.973500\pi$
$390$	8134.09	+	48833.0i	0.0534786	+	0.321058i
$391$	−125627.			−0.821732
$392$		−	96291.2i		−	0.626635i
$393$	−85131.5	+	14180.3i	−0.551195	+	0.0918123i
$394$	118004.			0.760158
$395$			150624.i			0.965383i
$396$	16420.4	+	47922.3i	0.104711	+	0.305596i
$397$	−236503.			−1.50057			−0.750283	−	0.661117i	$-0.770083\pi$
$397$	−236503.			−1.50057			−0.750283	+	0.661117i	$0.770083\pi$
$398$		−	44131.2i		−	0.278599i
$399$	5002.95	+	30035.2i	0.0314254	+	0.188662i
$400$	53424.2			0.333901
$401$		−	201196.i		−	1.25121i	−0.780139	−	0.625606i	$-0.784852\pi$
$401$		−	201196.i		−	1.25121i	0.780139	−	0.625606i	$-0.215148\pi$
$402$	5746.53	−	957.199i	0.0355594	−	0.00592311i
$403$	−163005.			−1.00367
$404$			22367.0i			0.137039i
$405$	57424.8	+	73957.8i	0.350098	+	0.450893i
$406$	−16755.5			−0.101649
$407$			84774.8i			0.511774i
$408$	−13005.0	−	78075.5i	−0.0781250	−	0.469023i
$409$	−33108.2			−0.197920			−0.0989599	−	0.995091i	$-0.531552\pi$
$409$	−33108.2			−0.197920			−0.0989599	+	0.995091i	$0.531552\pi$
$410$			23659.2i			0.140745i
$411$	−186062.	+	30992.2i	−1.10147	+	0.183472i
$412$	−22295.9			−0.131350
$413$		−	9588.95i		−	0.0562174i
$414$	91291.1	−	31280.6i	0.532633	−	0.182505i
$415$	−42505.7			−0.246803
$416$		−	228562.i		−	1.32074i
$417$	−18870.6	−	113289.i	−0.108521	−	0.651505i
$418$	−12877.8			−0.0737037
$419$		−	213554.i		−	1.21641i	−0.793781	−	0.608204i	$-0.791890\pi$
$419$		−	213554.i		−	1.21641i	0.793781	−	0.608204i	$-0.208110\pi$
$420$	35218.8	−	5866.38i	0.199653	−	0.0332561i
$421$	178795.			1.00877			0.504384	−	0.863479i	$-0.331719\pi$
$421$	178795.			1.00877			0.504384	+	0.863479i	$0.331719\pi$
$422$			17921.3i			0.100634i
$423$	−20151.6	−	58811.7i	−0.112623	−	0.328687i
$424$	−72621.6			−0.403956
$425$			75165.6i			0.416142i
$426$	−15505.7	−	93088.5i	−0.0854423	−	0.512952i
$427$	−63203.0			−0.346643
$428$			87785.0i			0.479217i
$429$	−96278.0	+	16037.0i	−0.523133	+	0.0871381i
$430$	4857.12			0.0262689
$431$			127806.i			0.688014i	0.938967	+	0.344007i	$0.111784\pi$
$431$			127806.i			0.688014i	−0.938967	+	0.344007i	$0.888216\pi$
$432$	−43923.6	−	81334.2i	−0.235359	−	0.435819i
$433$	210419.			1.12230			0.561151	−	0.827714i	$-0.310359\pi$
$433$	210419.			1.12230			0.561151	+	0.827714i	$0.310359\pi$
$434$		−	25613.6i		−	0.135985i
$435$	9877.80	+	59301.3i	0.0522013	+	0.313390i
$436$	169717.			0.892794
$437$		−	112596.i		−	0.589604i
$438$	−38320.9	+	6383.11i	−0.199751	+	0.0332724i
$439$	−347889.			−1.80514			−0.902571	−	0.430542i	$-0.858322\pi$
$439$	−347889.			−1.80514			−0.902571	+	0.430542i	$0.858322\pi$
$440$			33490.6i			0.172989i
$441$	149675.	−	51285.5i	0.769611	−	0.263704i
$442$	68761.7			0.351967
$443$			96661.8i			0.492547i	0.969200	+	0.246273i	$0.0792061\pi$
$443$			96661.8i			0.492547i	−0.969200	+	0.246273i	$0.920794\pi$
$444$	−34597.0	−	207703.i	−0.175498	−	1.05360i
$445$	−39106.0			−0.197480
$446$		−	83391.7i		−	0.419231i
$447$	−384237.	+	64002.3i	−1.92302	+	0.320317i
$448$	−7012.00			−0.0349370
$449$			266768.i			1.32325i	0.749837	+	0.661623i	$0.230132\pi$
$449$			266768.i			1.32325i	−0.749837	+	0.661623i	$0.769868\pi$
$450$	−18715.9	−	54621.6i	−0.0924241	−	0.269736i
$451$	−46645.9			−0.229330
$452$			47091.6i			0.230498i
$453$	39496.7	+	237118.i	0.192471	+	1.15550i
$454$	−37869.8			−0.183731
$455$			68792.9i			0.332293i
$456$	69976.9	−	11656.0i	0.336531	−	0.0560558i
$457$	−193204.			−0.925091			−0.462545	−	0.886596i	$-0.653064\pi$
$457$	−193204.			−0.925091			−0.462545	+	0.886596i	$0.653064\pi$
$458$			165251.i			0.787794i
$459$	114434.	−	61798.6i	0.543161	−	0.293328i
$460$	−132028.			−0.623952
$461$		−	172643.i		−	0.812357i	−0.913794	−	0.406179i	$-0.866861\pi$
$461$		−	172643.i		−	0.812357i	0.913794	−	0.406179i	$-0.133139\pi$
$462$	−2519.96	−	15128.5i	−0.0118062	−	0.0708783i
$463$	−317979.			−1.48333			−0.741663	−	0.670773i	$-0.765962\pi$
$463$	−317979.			−1.48333			−0.741663	+	0.670773i	$0.765962\pi$
$464$		−	59349.4i		−	0.275664i
$465$	−90652.1	+	15099.9i	−0.419249	+	0.0698342i
$466$	−133465.			−0.614604
$467$		−	295785.i		−	1.35626i	−0.734943	−	0.678129i	$-0.762791\pi$
$467$		−	295785.i		−	1.35626i	0.734943	−	0.678129i	$-0.237209\pi$
$468$	229341.	−	78582.9i	1.04711	−	0.358787i
$469$	8095.36			0.0368036
$470$		−	18531.5i		−	0.0838911i
$471$	36927.2	+	221692.i	0.166458	+	0.999328i
$472$	−22340.6			−0.100279
$473$			9576.19i			0.0428026i
$474$	−158523.	+	26405.1i	−0.705563	+	0.117525i
$475$	−67368.8			−0.298588
$476$		−	49591.5i		−	0.218874i
$477$	−38678.9	−	112883.i	−0.169995	−	0.496125i
$478$	−26999.3			−0.118167
$479$		−	314428.i		−	1.37041i	−0.728351	−	0.685204i	$-0.759713\pi$
$479$		−	314428.i		−	1.37041i	0.728351	−	0.685204i	$-0.240287\pi$
$480$	−21172.8	−	127111.i	−0.0918960	−	0.551697i
$481$	405706.			1.75356
$482$		−	72603.2i		−	0.312508i
$483$	132275.	−	22033.1i	0.567002	−	0.0944453i
$484$	162577.			0.694012
$485$		−	24508.1i		−	0.104190i
$486$	−67769.5	+	73401.5i	−0.286921	+	0.310765i
$487$	119465.			0.503714			0.251857	−	0.967765i	$-0.418959\pi$
$487$	119465.			0.503714			0.251857	+	0.967765i	$0.418959\pi$
$488$			147252.i			0.618333i
$489$	−63724.6	−	382570.i	−0.266495	−	1.59990i
$490$	47162.5			0.196428
$491$			57165.4i			0.237121i	0.992947	+	0.118561i	$0.0378280\pi$
$491$			57165.4i			0.237121i	−0.992947	+	0.118561i	$0.962172\pi$
$492$	114285.	−	19036.4i	0.472127	−	0.0786421i
$493$	83502.1			0.343561
$494$			61629.2i			0.252541i
$495$	−52057.7	+	17837.4i	−0.212459	+	0.0727982i
$496$	90725.7			0.368780
$497$		−	131137.i		−	0.530901i
$498$	−7451.46	−	44734.8i	−0.0300457	−	0.180379i
$499$	204091.			0.819639			0.409820	−	0.912167i	$-0.365592\pi$
$499$	204091.			0.819639			0.409820	+	0.912167i	$0.365592\pi$
$500$			196178.i			0.784711i
$501$	329203.	−	54835.2i	1.31156	−	0.218466i
$502$	139715.			0.554415
$503$		−	149966.i		−	0.592730i	−0.955075	−	0.296365i	$-0.904226\pi$
$503$		−	149966.i		−	0.592730i	0.955075	−	0.296365i	$-0.0957744\pi$
$504$	27386.5	+	79926.3i	0.107814	+	0.314651i
$505$	−24297.1			−0.0952736
$506$			56714.0i			0.221508i
$507$	34513.4	+	207201.i	0.134268	+	0.806077i
$508$	84256.0			0.326493
$509$		−	400685.i		−	1.54656i	−0.634063	−	0.773281i	$-0.718614\pi$
$509$		−	400685.i		−	1.54656i	0.634063	−	0.773281i	$-0.281386\pi$
$510$	38240.6	−	6369.73i	0.147023	−	0.0244895i
$511$	−53984.2			−0.206740
$512$			227227.i			0.866801i
$513$	55388.4	+	102564.i	0.210467	+	0.389726i
$514$	17343.5			0.0656463
$515$		−	24219.9i		−	0.0913182i
$516$	−3908.09	−	23462.2i	−0.0146779	−	0.0881188i
$517$	36536.4			0.136692
$518$			63750.3i			0.237587i
$519$	−140126.	+	23340.8i	−0.520217	+	0.0866524i
$520$	160276.			0.592736
$521$		−	114952.i		−	0.423489i	−0.977325	−	0.211744i	$-0.932086\pi$
$521$		−	114952.i		−	0.423489i	0.977325	−	0.211744i	$-0.0679144\pi$
$522$	−60679.6	+	20791.6i	−0.222690	+	0.0763040i
$523$	−182568.			−0.667456			−0.333728	−	0.942669i	$-0.608307\pi$
$523$	−182568.			−0.667456			−0.333728	+	0.942669i	$0.608307\pi$
$524$			125982.i			0.458823i
$525$	−13182.9	−	79143.4i	−0.0478291	−	0.287141i
$526$	106236.			0.383974
$527$			127647.i			0.459611i
$528$	53586.8	−	8925.93i	0.192216	−	0.0320174i
$529$	−216033.			−0.771987
$530$		−	35569.4i		−	0.126626i
$531$	−11898.8	−	34726.2i	−0.0422002	−	0.123160i
$532$	44447.5			0.157045
$533$			223233.i			0.785786i
$534$	−6855.49	−	41156.9i	−0.0240412	−	0.144331i
$535$	−95360.3			−0.333166
$536$		−	18860.8i		−	0.0656494i
$537$	489548.	−	81543.9i	1.69765	−	0.282776i
$538$	64873.8			0.224132
$539$			92984.4i			0.320061i
$540$	120265.	−	64947.5i	0.412430	−	0.222728i
$541$	293720.			1.00355			0.501775	−	0.864998i	$-0.332681\pi$
$541$	293720.			1.00355			0.501775	+	0.864998i	$0.332681\pi$
$542$			143303.i			0.487817i
$543$	−64112.3	−	384898.i	−0.217441	−	1.30541i
$544$	−178985.			−0.604809
$545$			184362.i			0.620696i
$546$	−72400.6	+	12059.7i	−0.242860	+	0.0404532i
$547$	−223879.			−0.748237			−0.374118	−	0.927381i	$-0.622055\pi$
$547$	−223879.			−0.748237			−0.374118	+	0.927381i	$0.622055\pi$
$548$			275343.i			0.916881i
$549$	−228889.	+	78427.8i	−0.759415	+	0.260211i
$550$	33933.3			0.112176
$551$			74840.6i			0.246510i
$552$	−51333.3	−	308179.i	−0.168469	−	1.01140i
$553$	−223317.			−0.730251
$554$			143747.i			0.468360i
$555$	225626.	−	37582.5i	0.732494	−	0.122011i
$556$	−167651.			−0.542322
$557$			336152.i			1.08349i	0.840542	+	0.541746i	$0.182236\pi$
$557$			336152.i			1.08349i	−0.840542	+	0.541746i	$0.817764\pi$
$558$	−31783.5	−	92759.1i	−0.102078	−	0.297912i
$559$	45828.7			0.146661
$560$		−	38289.0i		−	0.122095i
$561$	12558.4	+	75394.3i	0.0399033	+	0.239559i
$562$	−95045.2			−0.300925
$563$		−	121361.i		−	0.382881i	−0.981504	−	0.191441i	$-0.938684\pi$
$563$		−	121361.i		−	0.382881i	0.981504	−	0.191441i	$-0.0613159\pi$
$564$	−89516.0	+	14910.7i	−0.281412	+	0.0468747i
$565$	−51155.4			−0.160249
$566$			258656.i			0.807402i
$567$	−109651.	+	85138.9i	−0.341072	+	0.264827i
$568$	−305528.			−0.947008
$569$			129377.i			0.399607i	0.979836	+	0.199803i	$0.0640304\pi$
$569$			129377.i			0.399607i	−0.979836	+	0.199803i	$0.935970\pi$
$570$	5709.01	+	34274.0i	0.0175716	+	0.105491i
$571$	146231.			0.448505			0.224253	−	0.974531i	$-0.428006\pi$
$571$	146231.			0.448505			0.224253	+	0.974531i	$0.428006\pi$
$572$			142477.i			0.435464i
$573$	−191030.	+	31819.8i	−0.581825	+	0.0969144i
$574$	−35077.5			−0.106465
$575$			296693.i			0.897370i
$576$	−25393.8	+	8701.09i	−0.0765390	+	0.0262258i
$577$	138885.			0.417160			0.208580	−	0.978005i	$-0.433116\pi$
$577$	138885.			0.417160			0.208580	+	0.978005i	$0.433116\pi$
$578$			87458.8i			0.261787i
$579$	−15371.3	−	92281.3i	−0.0458514	−	0.275269i
$580$	87756.9			0.260871
$581$		−	63019.6i		−	0.186691i
$582$	25793.4	−	4296.40i	0.0761487	−	0.0126841i
$583$	70127.7			0.206325
$584$			125774.i			0.368778i
$585$	85364.2	+	249132.i	0.249439	+	0.727978i
$586$	247210.			0.719898
$587$			190172.i			0.551911i	0.961170	+	0.275956i	$0.0889943\pi$
$587$			190172.i			0.551911i	−0.961170	+	0.275956i	$0.911006\pi$
$588$	−37947.4	−	227817.i	−0.109756	−	0.658918i
$589$	−114407.			−0.329777
$590$		−	10942.2i		−	0.0314341i
$591$	619203.	−	103140.i	1.77279	−	0.295294i
$592$	−225810.			−0.644316
$593$		−	121893.i		−	0.346633i	−0.984866	−	0.173317i	$-0.944552\pi$
$593$		−	121893.i		−	0.346633i	0.984866	−	0.173317i	$-0.0554484\pi$
$594$	−27898.8	−	51660.8i	−0.0790702	−	0.146416i
$595$	53871.0			0.152167
$596$			568613.i			1.60075i
$597$	−38572.6	−	231570.i	−0.108226	−	0.649732i
$598$	271416.			0.758984
$599$			365745.i			1.01935i	0.860366	+	0.509676i	$0.170235\pi$
$599$			365745.i			1.01935i	−0.860366	+	0.509676i	$0.829765\pi$
$600$	−184391.	+	30713.9i	−0.512196	+	0.0853163i
$601$	714204.			1.97730			0.988652	−	0.150222i	$-0.0479987\pi$
$601$	714204.			1.97730			0.988652	+	0.150222i	$0.0479987\pi$
$602$			7201.25i			0.0198708i
$603$	29317.2	−	10045.4i	0.0806284	−	0.0276270i
$604$	350899.			0.961852
$605$			176606.i			0.482497i
$606$	−4259.41	−	25571.4i	−0.0115986	−	0.0696320i
$607$	−26803.5			−0.0727468			−0.0363734	−	0.999338i	$-0.511581\pi$
$607$	−26803.5			−0.0727468			−0.0363734	+	0.999338i	$0.511581\pi$
$608$		−	160419.i		−	0.433959i
$609$	−87921.0	+	14645.0i	−0.237060	+	0.0394870i
$610$	−72122.7			−0.193826
$611$		−	174852.i		−	0.468368i
$612$	−61537.5	−	179595.i	−0.164300	−	0.479503i
$613$	667129.			1.77537			0.887686	−	0.460450i	$-0.152312\pi$
$613$	667129.			1.77537			0.887686	+	0.460450i	$0.152312\pi$
$614$			2793.47i			0.00740980i
$615$	20679.1	+	124147.i	0.0546742	+	0.328236i
$616$	−49653.7			−0.130855
$617$		−	395997.i		−	1.04021i	−0.854102	−	0.520105i	$-0.825893\pi$
$617$		−	395997.i		−	1.04021i	0.854102	−	0.520105i	$-0.174107\pi$
$618$	25490.0	−	4245.86i	0.0667411	−	0.0111170i
$619$	−482074.			−1.25815			−0.629075	−	0.777344i	$-0.716566\pi$
$619$	−482074.			−1.25815			−0.629075	+	0.777344i	$0.716566\pi$
$620$			134151.i			0.348989i
$621$	451692.	−	243931.i	1.17128	−	0.632534i
$622$	128168.			0.331282
$623$		−	57979.3i		−	0.149381i
$624$	−42716.8	−	256450.i	−0.109706	−	0.658617i
$625$	50224.1			0.128574
$626$			168746.i			0.430610i
$627$	−67573.8	+	11255.7i	−0.171887	+	0.0286312i
$628$	328070.			0.831855
$629$		−	317704.i		−	0.803012i
$630$	−39147.1	+	13413.6i	−0.0986323	+	0.0337960i
$631$	−52153.0			−0.130985			−0.0654924	−	0.997853i	$-0.520862\pi$
$631$	−52153.0			−0.130985			−0.0654924	+	0.997853i	$0.520862\pi$
$632$			520292.i			1.30260i
$633$	15664.0	+	94038.6i	0.0390926	+	0.234692i
$634$	−137607.			−0.342344
$635$			91526.8i			0.226987i
$636$	−171817.	+	28619.4i	−0.424767	+	0.0707533i
$637$	444995.			1.09667
$638$		−	37696.8i		−	0.0926111i
$639$	−162727.	−	474911.i	−0.398526	−	1.16308i
$640$	−237090.			−0.578833
$641$			259391.i			0.631304i	0.948875	+	0.315652i	$0.102223\pi$
$641$			259391.i			0.631304i	−0.948875	+	0.315652i	$0.897777\pi$
$642$	−16717.1	−	100361.i	−0.0405594	−	0.243498i
$643$	104877.			0.253664			0.126832	−	0.991924i	$-0.459519\pi$
$643$	104877.			0.253664			0.126832	+	0.991924i	$0.459519\pi$
$644$		−	195747.i		−	0.471981i
$645$	25486.8	−	4245.33i	0.0612627	−	0.0102045i
$646$	48261.2			0.115647
$647$			46535.5i			0.111167i	0.998454	+	0.0555835i	$0.0177019\pi$
$647$			46535.5i			0.111167i	−0.998454	+	0.0555835i	$0.982298\pi$
$648$	198359.	+	255468.i	0.472392	+	0.608397i
$649$	21573.4			0.0512188
$650$		−	162394.i		−	0.384365i
$651$	−22387.3	−	134402.i	−0.0528251	−	0.317135i
$652$	−566146.			−1.33178
$653$		−	562488.i		−	1.31913i	−0.751648	−	0.659564i	$-0.770741\pi$
$653$		−	562488.i		−	1.31913i	0.751648	−	0.659564i	$-0.229259\pi$
$654$	−194031.	+	32319.6i	−0.453644	+	0.0755633i
$655$	−136853.			−0.318986
$656$		−	124248.i		−	0.288723i
$657$	−195503.	+	66988.3i	−0.452921	+	0.155192i
$658$	27475.2			0.0634583
$659$			427681.i			0.984802i	0.870368	+	0.492401i	$0.163881\pi$
$659$			427681.i			0.984802i	−0.870368	+	0.492401i	$0.836119\pi$
$660$	13198.3	+	79235.9i	0.0302991	+	0.181901i
$661$	655175.			1.49953			0.749763	−	0.661706i	$-0.230167\pi$
$661$	655175.			1.49953			0.749763	+	0.661706i	$0.230167\pi$
$662$		−	221071.i		−	0.504448i
$663$	360814.	−	60100.7i	0.820836	−	0.136726i
$664$	−146825.			−0.333015
$665$			48283.1i			0.109182i
$666$	79106.9	+	230870.i	0.178347	+	0.520499i
$667$	329599.			0.740857
$668$		−	487170.i		−	1.09176i
$669$	−72887.9	−	437582.i	−0.162856	−	0.977704i
$670$	9237.85			0.0205788
$671$		−	142196.i		−	0.315821i
$672$	188457.	−	31391.2i	0.417324	−	0.0695135i
$673$	190841.			0.421348			0.210674	−	0.977556i	$-0.432434\pi$
$673$	190841.			0.421348			0.210674	+	0.977556i	$0.432434\pi$
$674$			111966.i			0.246471i
$675$	−145950.	−	270258.i	−0.320328	−	0.593158i
$676$	306626.			0.670990
$677$		−	776479.i		−	1.69415i	−0.531473	−	0.847076i	$-0.678361\pi$
$677$		−	776479.i		−	1.69415i	0.531473	−	0.847076i	$-0.321639\pi$
$678$	−8967.79	−	53838.1i	−0.0195086	−	0.117120i
$679$	36336.2			0.0788133
$680$		−	125510.i		−	0.271432i
$681$	−198715.	+	33099.8i	−0.428485	+	0.0713726i
$682$	57626.0			0.123894
$683$			352252.i			0.755114i	0.925986	+	0.377557i	$0.123236\pi$
$683$			352252.i			0.755114i	−0.925986	+	0.377557i	$0.876764\pi$
$684$	160966.	−	55154.4i	0.344050	−	0.117887i
$685$	−299104.			−0.637442
$686$			155874.i			0.331228i
$687$	144436.	+	867122.i	0.306029	+	1.83724i
$688$	−25507.5			−0.0538879
$689$		−	335610.i		−	0.706962i
$690$	150943.	−	25142.5i	0.317041	−	0.0528094i
$691$	−520473.			−1.09004			−0.545019	−	0.838423i	$-0.683478\pi$
$691$	−520473.			−1.09004			−0.545019	+	0.838423i	$0.683478\pi$
$692$			207365.i			0.433036i
$693$	−26446.0	−	77181.6i	−0.0550672	−	0.160712i
$694$	106901.			0.221953
$695$		−	182119.i		−	0.377038i
$696$	34120.3	+	204841.i	0.0704360	+	0.422862i
$697$	174812.			0.359836
$698$		−	174428.i		−	0.358018i
$699$	−700332.	+	116654.i	−1.43334	+	0.238751i
$700$	−117120.			−0.239021
$701$		−	540292.i		−	1.09949i	−0.835332	−	0.549746i	$-0.814724\pi$
$701$		−	540292.i		−	1.09949i	0.835332	−	0.549746i	$-0.185276\pi$
$702$	−247233.	+	133515.i	−0.501685	+	0.270929i
$703$	284750.			0.576172
$704$		−	15775.7i		−	0.0318306i
$705$	−16197.4	−	97240.7i	−0.0325886	−	0.195646i
$706$	−279630.			−0.561015
$707$		−	36023.4i		−	0.0720685i
$708$	−52856.0	+	8804.21i	−0.105446	+	0.0175640i
$709$	166254.			0.330734			0.165367	−	0.986232i	$-0.447119\pi$
$709$	166254.			0.330734			0.165367	+	0.986232i	$0.447119\pi$
$710$		−	149644.i		−	0.296855i
$711$	−808740.	+	277112.i	−1.59981	+	0.548171i
$712$	−135082.			−0.266463
$713$			503848.i			0.991107i
$714$	9443.86	+	56696.2i	0.0185248	+	0.111213i
$715$	−154772.			−0.302747
$716$		−	724457.i		−	1.41315i
$717$	−141674.	+	23598.5i	−0.275582	+	0.0459036i
$718$	303411.			0.588549
$719$			525708.i			1.01692i	0.861086	+	0.508460i	$0.169785\pi$
$719$			525708.i			1.01692i	−0.861086	+	0.508460i	$0.830215\pi$
$720$	−47512.3	−	138663.i	−0.0916519	−	0.267483i
$721$	35908.8			0.0690764
$722$		−	177229.i		−	0.339986i
$723$	−63458.3	−	380971.i	−0.121398	−	0.728813i
$724$	−569590.			−1.08664
$725$		−	197207.i		−	0.375185i
$726$	−185868.	+	30959.9i	−0.352639	+	0.0587390i
$727$	−298839.			−0.565416			−0.282708	−	0.959206i	$-0.591233\pi$
$727$	−298839.			−0.565416			−0.282708	+	0.959206i	$0.591233\pi$
$728$			237627.i			0.448367i
$729$	−291451.	+	444393.i	−0.548417	+	0.836205i
$730$	−61602.9			−0.115599
$731$		−	35888.0i		−	0.0671606i
$732$	58030.6	+	348386.i	0.108302	+	0.650188i
$733$	−380532.			−0.708245			−0.354122	−	0.935199i	$-0.615220\pi$
$733$	−380532.			−0.708245			−0.354122	+	0.935199i	$0.615220\pi$
$734$		−	117646.i		−	0.218366i
$735$	247476.	−	41222.0i	0.458098	−	0.0763053i
$736$	−706488.			−1.30421
$737$			18213.1i			0.0335312i
$738$	−127033.	+	43527.2i	−0.233240	+	0.0799187i
$739$	−630787.			−1.15503			−0.577516	−	0.816379i	$-0.695978\pi$
$739$	−630787.			−1.15503			−0.577516	+	0.816379i	$0.695978\pi$
$740$		−	333893.i		−	0.609738i
$741$	53866.5	+	323387.i	0.0981031	+	0.588961i
$742$	52735.7			0.0957849
$743$			315515.i			0.571534i	0.958299	+	0.285767i	$0.0922484\pi$
$743$			315515.i			0.571534i	−0.958299	+	0.285767i	$0.907752\pi$
$744$	−313134.	+	52158.7i	−0.565698	+	0.0942282i
$745$	−617681.			−1.11289
$746$			122139.i			0.219470i
$747$	−78200.2	−	228224.i	−0.140142	−	0.408998i
$748$	111572.			0.199413
$749$		−	141383.i		−	0.252019i
$750$	−37358.7	−	224283.i	−0.0664154	−	0.398725i
$751$	128872.			0.228497			0.114248	−	0.993452i	$-0.463554\pi$
$751$	128872.			0.228497			0.114248	+	0.993452i	$0.463554\pi$
$752$			97319.7i			0.172094i
$753$	733127.	−	122117.i	1.29297	−	0.215370i
$754$	−180405.			−0.317327
$755$			381180.i			0.668707i
$756$	96292.2	+	178306.i	0.168480	+	0.311977i
$757$	707601.			1.23480			0.617400	−	0.786650i	$-0.288186\pi$
$757$	707601.			1.23480			0.617400	+	0.786650i	$0.288186\pi$
$758$		−	246061.i		−	0.428258i
$759$	49570.4	+	297596.i	0.0860477	+	0.516587i
$760$	112491.			0.194757
$761$			450901.i			0.778596i	0.921112	+	0.389298i	$0.127282\pi$
$761$			450901.i			0.778596i	−0.921112	+	0.389298i	$0.872718\pi$
$762$	−96326.8	+	16045.1i	−0.165896	+	0.0276333i
$763$	−273338.			−0.469517
$764$			282696.i			0.484320i
$765$	195093.	−	66847.8i	0.333364	−	0.114226i
$766$	−83184.2			−0.141770
$767$		−	103244.i		−	0.175498i
$768$	−33722.2	−	202451.i	−0.0571733	−	0.343240i
$769$	−426683.			−0.721526			−0.360763	−	0.932657i	$-0.617484\pi$
$769$	−426683.			−0.721526			−0.360763	+	0.932657i	$0.617484\pi$
$770$		−	24319.9i		−	0.0410186i
$771$	91006.6	−	15158.9i	0.153096	−	0.0255012i
$772$	−136562.			−0.229138
$773$			857972.i			1.43587i	0.696112	+	0.717933i	$0.254912\pi$
$773$			857972.i			1.43587i	−0.696112	+	0.717933i	$0.745088\pi$
$774$	8935.94	+	26079.2i	0.0149162	+	0.0435323i
$775$	301464.			0.501917
$776$		−	84657.1i		−	0.140585i
$777$	55720.4	+	334517.i	0.0922938	+	0.554085i
$778$	−42577.6			−0.0703431
$779$			156679.i			0.258187i
$780$	379199.	−	63163.0i	0.623272	−	0.103818i
$781$	295036.			0.483696
$782$		−	212543.i		−	0.347563i
$783$	−300232.	+	162137.i	−0.489703	+	0.264459i
$784$	−247677.			−0.402952
$785$			356381.i			0.578329i
$786$	−23991.0	−	144030.i	−0.0388333	−	0.233135i
$787$	−497866.			−0.803828			−0.401914	−	0.915677i	$-0.631655\pi$
$787$	−497866.			−0.803828			−0.401914	+	0.915677i	$0.631655\pi$
$788$		−	916326.i		−	1.47570i
$789$	557455.	−	92855.1i	0.895479	−	0.149160i
$790$	−254834.			−0.408322
$791$		−	75843.8i		−	0.121218i
$792$	−179820.	+	61614.6i	−0.286674	+	0.0982276i
$793$	−680504.			−1.08214
$794$		−	400128.i		−	0.634685i
$795$	−31089.1	−	186643.i	−0.0491897	−	0.295310i
$796$	−342689.			−0.540846
$797$		−	228182.i		−	0.359224i	−0.983738	−	0.179612i	$-0.942516\pi$
$797$		−	228182.i		−	0.359224i	0.983738	−	0.179612i	$-0.0574842\pi$
$798$	−50815.2	+	8464.27i	−0.0797972	+	0.0132918i
$799$	−136925.			−0.214481
$800$			422708.i			0.660481i
$801$	−71945.7	−	209971.i	−0.112135	−	0.327261i
$802$	340395.			0.529217
$803$		−	121455.i		−	0.188358i
$804$	−7432.86	−	44623.1i	−0.0114986	−	0.0690316i
$805$	212639.			0.328134
$806$		−	275780.i		−	0.424515i
$807$	340413.	−	56702.5i	0.522708	−	0.0870672i
$808$	−83928.3			−0.128554
$809$			608474.i			0.929704i	0.885388	+	0.464852i	$0.153892\pi$
$809$			608474.i			0.929704i	−0.885388	+	0.464852i	$0.846108\pi$
$810$	−125126.	+	97154.4i	−0.190712	+	0.148079i
$811$	−39666.5			−0.0603090			−0.0301545	−	0.999545i	$-0.509600\pi$
$811$	−39666.5			−0.0603090			−0.0301545	+	0.999545i	$0.509600\pi$
$812$			130110.i			0.197332i
$813$	125253.	+	751955.i	0.189499	+	1.13766i
$814$	−143427.			−0.216462
$815$		−	615001.i		−	0.925893i
$816$	−200823.	+	33451.1i	−0.301602	+	0.0502377i
$817$	32165.4			0.0481887
$818$		−	56014.3i		−	0.0837129i
$819$	−369367.	+	126562.i	−0.550669	+	0.188685i
$820$	183719.			0.273229
$821$			100567.i			0.149199i	0.997214	+	0.0745997i	$0.0237679\pi$
$821$			100567.i			0.149199i	−0.997214	+	0.0745997i	$0.976232\pi$
$822$	−52434.4	−	314789.i	−0.0776019	−	0.465883i
$823$	1.04254e6			1.53920			0.769598	−	0.638529i	$-0.220457\pi$
$823$	1.04254e6			1.53920			0.769598	+	0.638529i	$0.220457\pi$
$824$		−	83661.3i		−	0.123217i
$825$	178058.	−	29659.1i	0.261610	−	0.0435763i
$826$	16223.1			0.0237779
$827$		−	103125.i		−	0.150783i	−0.997154	−	0.0753914i	$-0.975979\pi$
$827$		−	103125.i		−	0.150783i	0.997154	−	0.0753914i	$-0.0240206\pi$
$828$	−242900.	−	708896.i	−0.354297	−	1.03400i
$829$	−1.24349e6			−1.80939			−0.904694	−	0.426061i	$-0.859901\pi$
$829$	−1.24349e6			−1.80939			−0.904694	+	0.426061i	$0.859901\pi$
$830$		−	71913.4i		−	0.104389i
$831$	125641.	+	754285.i	0.181941	+	1.09228i
$832$	−75497.8			−0.109066
$833$		−	348471.i		−	0.502200i
$834$	191669.	−	31926.3i	0.275563	−	0.0459004i
$835$	529210.			0.759024
$836$			99999.0i			0.143081i
$837$	−247853.	−	458955.i	−0.353789	−	0.655118i
$838$	361302.			0.514496
$839$		−	1.18177e6i		−	1.67884i	−0.543486	−	0.839418i	$-0.682896\pi$
$839$		−	1.18177e6i		−	1.67884i	0.543486	−	0.839418i	$-0.317104\pi$
$840$	22012.6	+	132152.i	0.0311969	+	0.187291i
$841$	488202.			0.690252
$842$			302496.i			0.426673i
$843$	−498732.	+	83073.6i	−0.701797	+	0.116898i
$844$	139163.			0.195361
$845$			333086.i			0.466491i
$846$	99500.8	−	34093.6i	0.139023	−	0.0476356i
$847$	−261839.			−0.364979
$848$			186795.i			0.259761i
$849$	226076.	+	1.35725e6i	0.313646	+	1.88297i
$850$	−127169.			−0.176013
$851$		−	1.25404e6i		−	1.73162i
$852$	−722853.	+	120405.i	−0.995797	+	0.165870i
$853$	931344.			1.28001			0.640003	−	0.768372i	$-0.278933\pi$
$853$	931344.			1.28001			0.640003	+	0.768372i	$0.278933\pi$
$854$		−	106930.i		−	0.146617i
$855$	59913.9	+	174856.i	0.0819587	+	0.239193i
$856$	−329398.			−0.449545
$857$			1.08578e6i			1.47836i	0.673510	+	0.739178i	$0.264786\pi$
$857$			1.08578e6i			1.47836i	−0.673510	+	0.739178i	$0.735214\pi$
$858$	−27132.3	−	162888.i	−0.0368563	−	0.221266i
$859$	12414.5			0.0168245			0.00841226	−	0.999965i	$-0.497322\pi$
$859$	12414.5			0.0168245			0.00841226	+	0.999965i	$0.497322\pi$
$860$		−	37716.6i		−	0.0509960i
$861$	−184063.	+	30659.2i	−0.248290	+	0.0413576i
$862$	−216229.			−0.291005
$863$		−	53565.4i		−	0.0719222i	−0.999353	−	0.0359611i	$-0.988551\pi$
$863$		−	53565.4i		−	0.0719222i	0.999353	−	0.0359611i	$-0.0114492\pi$
$864$	643540.	−	347536.i	0.862081	−	0.465557i
$865$	−225260.			−0.301059
$866$			355999.i			0.474693i
$867$	76442.7	+	458923.i	0.101695	+	0.610523i
$868$	−198895.			−0.263988
$869$		−	502424.i		−	0.665321i
$870$	−100329.	+	16711.8i	−0.132553	+	0.0220793i
$871$	87162.4			0.114893
$872$			636832.i			0.837514i
$873$	131591.	−	45089.1i	0.172662	−	0.0591620i
$874$	190496.			0.249381
$875$		−	315955.i		−	0.412677i
$876$	49566.2	+	297571.i	0.0645918	+	0.387777i
$877$	495745.			0.644554			0.322277	−	0.946645i	$-0.395552\pi$
$877$	495745.			0.644554			0.322277	+	0.946645i	$0.395552\pi$
$878$		−	588577.i		−	0.763509i
$879$	1.29719e6	−	216072.i	1.67890	−	0.279654i
$880$	86143.5			0.111239
$881$			1.26959e6i			1.63574i	0.575406	+	0.817868i	$0.304844\pi$
$881$			1.26959e6i			1.63574i	−0.575406	+	0.817868i	$0.695156\pi$
$882$	86767.6	+	253228.i	0.111537	+	0.325518i
$883$	1.41366e6			1.81310			0.906552	−	0.422095i	$-0.138705\pi$
$883$	1.41366e6			1.81310			0.906552	+	0.422095i	$0.138705\pi$
$884$		−	533950.i		−	0.683276i
$885$	−9563.97	−	57417.2i	−0.0122110	−	0.0733087i
$886$	−163538.			−0.208329
$887$		−	266375.i		−	0.338569i	−0.985567	−	0.169284i	$-0.945854\pi$
$887$		−	266375.i		−	0.338569i	0.985567	−	0.169284i	$-0.0541457\pi$
$888$	779368.	−	129819.i	0.988364	−	0.164631i
$889$	−135699.			−0.171701
$890$		−	66161.8i		−	0.0835270i
$891$	−191547.	−	246695.i	−0.241280	−	0.310746i
$892$	−647555.			−0.813855
$893$		−	122722.i		−	0.153893i
$894$	−108283.	−	650074.i	−0.135483	−	0.813369i
$895$	786974.			0.982458
$896$		−	351514.i		−	0.437851i
$897$	1.42420e6	−	237229.i	1.77005	−	0.294837i
$898$	−451332.			−0.559685
$899$		−	334899.i		−	0.414376i
$900$	−424148.	+	145333.i	−0.523640	+	0.179423i
$901$	−262813.			−0.323740
$902$		−	78918.1i		−	0.0969982i
$903$	6294.20	+	37787.2i	0.00771907	+	0.0463414i
$904$	−176703.			−0.216226
$905$		−	618743.i		−	0.755462i
$906$	−401170.	+	66822.7i	−0.488733	+	0.0814081i
$907$	−824492.			−1.00224			−0.501120	−	0.865378i	$-0.667079\pi$
$907$	−824492.			−1.00224			−0.501120	+	0.865378i	$0.667079\pi$
$908$			294067.i			0.356677i
$909$	−44700.9	−	130458.i	−0.0540989	−	0.157886i
$910$	−116388.			−0.140548
$911$			621346.i			0.748681i	0.927291	+	0.374341i	$0.122131\pi$
$911$			621346.i			0.748681i	−0.927291	+	0.374341i	$0.877869\pi$
$912$	−29981.3	−	179992.i	−0.0360463	−	0.216403i
$913$	141783.			0.170091
$914$		−	326874.i		−	0.391280i
$915$	−378450.	+	63038.3i	−0.452029	+	0.0752944i
$916$	1.28321e6			1.52935
$917$		−	202901.i		−	0.241293i
$918$	104554.	+	193605.i	0.124067	+	0.229738i
$919$	−1.18437e6			−1.40235			−0.701175	−	0.712989i	$-0.747341\pi$
$919$	−1.18437e6			−1.40235			−0.701175	+	0.712989i	$0.747341\pi$
$920$		−	495413.i		−	0.585318i
$921$	2441.61	+	14658.2i	0.00287844	+	0.0172807i
$922$	292087.			0.343598
$923$		−	1.41195e6i		−	1.65736i
$924$	−117476.	+	19568.0i	−0.137596	+	0.0229194i
$925$	−750321.			−0.876928
$926$		−	537974.i		−	0.627393i
$927$	130043.	−	44558.7i	0.151331	−	0.0518529i
$928$	469590.			0.545284
$929$			1.02460e6i			1.18720i	0.804759	+	0.593601i	$0.202294\pi$
$929$			1.02460e6i			1.18720i	−0.804759	+	0.593601i	$0.797706\pi$
$930$	−25546.8	−	153370.i	−0.0295373	−	0.177327i
$931$	312325.			0.360336
$932$			1.03639e6i			1.19313i
$933$	672536.	−	112024.i	0.772596	−	0.128691i
$934$	500425.			0.573648
$935$			121200.i			0.138637i
$936$	294869.	+	860563.i	0.336571	+	0.982270i
$937$	−559795.			−0.637602			−0.318801	−	0.947822i	$-0.603280\pi$
$937$	−559795.			−0.637602			−0.318801	+	0.947822i	$0.603280\pi$
$938$			13696.2i			0.0155666i
$939$	147491.	+	885460.i	0.167276	+	1.00424i
$940$	−143901.			−0.162858
$941$			902.323i			0.00101902i	1.00000		0.000509510i	$0.000162182\pi$
$941$			902.323i			0.00101902i	−1.00000		0.000509510i	$0.999838\pi$
$942$	−375071.	+	62475.4i	−0.422680	+	0.0704056i
$943$	690015.			0.775952
$944$			57463.8i			0.0644838i
$945$	−193693.	+	104602.i	−0.216895	+	0.117132i
$946$	−16201.5			−0.0181040
$947$			84257.4i			0.0939524i	0.998896	+	0.0469762i	$0.0149585\pi$
$947$			84257.4i			0.0939524i	−0.998896	+	0.0469762i	$0.985042\pi$
$948$	205042.	+	1.23097e6i	0.228153	+	1.36971i
$949$	−581245.			−0.645397
$950$		−	113978.i		−	0.126292i
$951$	−722067.	+	120274.i	−0.798393	+	0.132988i
$952$	186084.			0.205321
$953$		−	446342.i		−	0.491453i	−0.969339	−	0.245727i	$-0.920973\pi$
$953$		−	446342.i		−	0.491453i	0.969339	−	0.245727i	$-0.0790265\pi$
$954$	190981.	−	65439.1i	0.209843	−	0.0719019i
$955$	−307091.			−0.336713
$956$			209655.i			0.229398i
$957$	−32948.6	−	197807.i	−0.0359760	−	0.215982i
$958$	531967.			0.579633
$959$		−	443456.i		−	0.482184i
$960$	−41986.8	+	6993.72i	−0.0455586	+	0.00758868i
$961$	−411571.			−0.445654
$962$			686396.i			0.741694i
$963$	−175440.	−	512015.i	−0.189180	−	0.552116i
$964$	−563780.			−0.606674
$965$		−	148347.i		−	0.159303i
$966$	37276.7	+	223791.i	0.0399470	+	0.239821i
$967$	1.13923e6			1.21832			0.609158	−	0.793049i	$-0.291508\pi$
$967$	1.13923e6			1.21832			0.609158	+	0.793049i	$0.291508\pi$
$968$			610040.i			0.651040i
$969$	253241.	−	42182.4i	0.269704	−	0.0449245i
$970$	41464.2			0.0440687
$971$			1.77077e6i			1.87812i	0.343756	+	0.939059i	$0.388301\pi$
$971$			1.77077e6i			1.87812i	−0.343756	+	0.939059i	$0.611699\pi$
$972$	569978.	+	526245.i	0.603290	+	0.557000i
$973$	270012.			0.285205
$974$			202118.i			0.213053i
$975$	−141939.	−	852133.i	−0.149312	−	0.896392i
$976$	378758.			0.397614
$977$			21925.2i			0.0229696i	0.999934	+	0.0114848i	$0.00365581\pi$
$977$			21925.2i			0.0229696i	−0.999934	+	0.0114848i	$0.996344\pi$
$978$	647254.	−	107813.i	0.676701	−	0.112718i
$979$	130443.			0.136099
$980$		−	366227.i		−	0.381328i
$981$	−989890.	+	339182.i	−1.02861	+	0.352448i
$982$	−96715.5			−0.100294
$983$		−	753605.i		−	0.779896i	−0.920837	−	0.389948i	$-0.872493\pi$
$983$		−	753605.i		−	0.779896i	0.920837	−	0.389948i	$-0.127507\pi$
$984$	71430.8	+	428834.i	0.0737726	+	0.442894i
$985$	995400.			1.02595
$986$			141274.i			0.145314i
$987$	144171.	−	24014.5i	0.147993	−	0.0246512i
$988$	478564.			0.490260
$989$		−	141657.i		−	0.144825i
$990$	−30178.3	−	88074.1i	−0.0307910	−	0.0898623i
$991$	−39554.9			−0.0402766			−0.0201383	−	0.999797i	$-0.506411\pi$
$991$	−39554.9			−0.0402766			−0.0201383	+	0.999797i	$0.506411\pi$
$992$			717848.i			0.729473i
$993$	−193226.	−	1.16003e6i	−0.195959	−	1.17644i
$994$	221865.			0.224552
$995$		−	372261.i		−	0.376012i
$996$	−347376.	+	57862.2i	−0.350171	+	0.0583279i
$997$	891547.			0.896921			0.448460	−	0.893803i	$-0.351972\pi$
$997$	891547.			0.896921			0.448460	+	0.893803i	$0.351972\pi$
$998$			345292.i			0.346678i
$999$	616889.	+	1.14231e6i	0.618124	+	1.14459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.47	yes	78
3.2	odd	2	inner	177.5.b.a.119.32	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.32	✓	78	3.2	odd	2	inner
177.5.b.a.119.47	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)

\(f(q)\)	\(=\)	\(q+1.69186i q^{2} +(1.47875 + 8.87768i) q^{3} +13.1376 q^{4} +14.2713i q^{5} +(-15.0198 + 2.50184i) q^{6} -21.1589 q^{7} +49.2966i q^{8} +(-76.6266 + 26.2558i) q^{9} +O(q^{10})\)	\(q+1.69186i q^{2} +(1.47875 + 8.87768i) q^{3} +13.1376 q^{4} +14.2713i q^{5} +(-15.0198 + 2.50184i) q^{6} -21.1589 q^{7} +49.2966i q^{8} +(-76.6266 + 26.2558i) q^{9} -24.1450 q^{10} -47.6038i q^{11} +(19.4273 + 116.632i) q^{12} -227.817 q^{13} -35.7978i q^{14} +(-126.696 + 21.1038i) q^{15} +126.799 q^{16} +178.401i q^{17} +(-44.4210 - 129.641i) q^{18} -159.896 q^{19} +187.491i q^{20} +(-31.2888 - 187.842i) q^{21} +80.5386 q^{22} +704.184i q^{23} +(-437.640 + 72.8976i) q^{24} +421.329 q^{25} -385.433i q^{26} +(-346.403 - 641.441i) q^{27} -277.978 q^{28} -468.058i q^{29} +(-35.7045 - 214.352i) q^{30} +715.507 q^{31} +1003.27i q^{32} +(422.611 - 70.3942i) q^{33} -301.829 q^{34} -301.966i q^{35} +(-1006.69 + 344.939i) q^{36} -1780.84 q^{37} -270.521i q^{38} +(-336.885 - 2022.49i) q^{39} -703.529 q^{40} -979.879i q^{41} +(317.802 - 52.9361i) q^{42} -201.165 q^{43} -625.400i q^{44} +(-374.705 - 1093.56i) q^{45} -1191.38 q^{46} +767.510i q^{47} +(187.505 + 1125.68i) q^{48} -1953.30 q^{49} +712.828i q^{50} +(-1583.79 + 263.811i) q^{51} -2992.97 q^{52} +1473.16i q^{53} +(1085.22 - 586.063i) q^{54} +679.369 q^{55} -1043.06i q^{56} +(-236.447 - 1419.51i) q^{57} +791.887 q^{58} +453.188i q^{59} +(-1664.49 + 277.253i) q^{60} +2987.07 q^{61} +1210.53i q^{62} +(1621.33 - 555.544i) q^{63} +331.397 q^{64} -3251.25i q^{65} +(119.097 + 714.997i) q^{66} -382.598 q^{67} +2343.77i q^{68} +(-6251.52 + 1041.31i) q^{69} +510.882 q^{70} +6197.74i q^{71} +(-1294.32 - 3777.43i) q^{72} +2551.37 q^{73} -3012.93i q^{74} +(623.042 + 3740.43i) q^{75} -2100.65 q^{76} +1007.24i q^{77} +(3421.75 - 569.961i) q^{78} +10554.3 q^{79} +1809.59i q^{80} +(5182.26 - 4023.79i) q^{81} +1657.81 q^{82} +2978.40i q^{83} +(-411.061 - 2467.80i) q^{84} -2546.02 q^{85} -340.341i q^{86} +(4155.27 - 692.143i) q^{87} +2346.71 q^{88} +2740.18i q^{89} +(1850.15 - 633.947i) q^{90} +4820.36 q^{91} +9251.30i q^{92} +(1058.06 + 6352.04i) q^{93} -1298.52 q^{94} -2281.93i q^{95} +(-8906.73 + 1483.59i) q^{96} -1717.30 q^{97} -3304.70i q^{98} +(1249.88 + 3647.71i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more