LMFDB - Embedded newform 177.5.b.a.119.20

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			119.20
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.59

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.27932i q^{2} +(-6.98370 - 5.67697i) q^{3} -2.31259 q^{4} -6.15778i q^{5} +(-24.2936 + 29.8855i) q^{6} -22.1503 q^{7} -58.5728i q^{8} +(16.5440 + 79.2925i) q^{9} +O(q^{10})$	\(q-4.27932i q^{2} +(-6.98370 - 5.67697i) q^{3} -2.31259 q^{4} -6.15778i q^{5} +(-24.2936 + 29.8855i) q^{6} -22.1503 q^{7} -58.5728i q^{8} +(16.5440 + 79.2925i) q^{9} -26.3511 q^{10} -60.0378i q^{11} +(16.1504 + 13.1285i) q^{12} -252.105 q^{13} +94.7883i q^{14} +(-34.9575 + 43.0040i) q^{15} -287.653 q^{16} +475.495i q^{17} +(339.318 - 70.7971i) q^{18} -114.066 q^{19} +14.2404i q^{20} +(154.691 + 125.747i) q^{21} -256.921 q^{22} +529.132i q^{23} +(-332.516 + 409.055i) q^{24} +587.082 q^{25} +1078.84i q^{26} +(334.603 - 647.674i) q^{27} +51.2246 q^{28} -1258.45i q^{29} +(184.028 + 149.594i) q^{30} +14.1344 q^{31} +293.796i q^{32} +(-340.833 + 419.286i) q^{33} +2034.79 q^{34} +136.397i q^{35} +(-38.2595 - 183.371i) q^{36} -682.331 q^{37} +488.125i q^{38} +(1760.62 + 1431.19i) q^{39} -360.678 q^{40} +1784.12i q^{41} +(538.110 - 661.972i) q^{42} +1895.39 q^{43} +138.843i q^{44} +(488.265 - 101.874i) q^{45} +2264.33 q^{46} +742.817i q^{47} +(2008.88 + 1633.00i) q^{48} -1910.36 q^{49} -2512.31i q^{50} +(2699.37 - 3320.71i) q^{51} +583.016 q^{52} +3076.72i q^{53} +(-2771.61 - 1431.87i) q^{54} -369.699 q^{55} +1297.41i q^{56} +(796.602 + 647.549i) q^{57} -5385.33 q^{58} +453.188i q^{59} +(80.8424 - 99.4507i) q^{60} +1439.20 q^{61} -60.4856i q^{62} +(-366.455 - 1756.35i) q^{63} -3345.21 q^{64} +1552.41i q^{65} +(1794.26 + 1458.53i) q^{66} +3224.97 q^{67} -1099.62i q^{68} +(3003.87 - 3695.30i) q^{69} +583.685 q^{70} -5483.87i q^{71} +(4644.38 - 969.029i) q^{72} -8856.56 q^{73} +2919.91i q^{74} +(-4100.00 - 3332.85i) q^{75} +263.788 q^{76} +1329.86i q^{77} +(6124.53 - 7534.28i) q^{78} -9349.35 q^{79} +1771.31i q^{80} +(-6013.59 + 2623.63i) q^{81} +7634.84 q^{82} +7555.94i q^{83} +(-357.737 - 290.801i) q^{84} +2927.99 q^{85} -8110.97i q^{86} +(-7144.21 + 8788.66i) q^{87} -3516.58 q^{88} +4863.80i q^{89} +(-435.953 - 2089.44i) q^{90} +5584.20 q^{91} -1223.67i q^{92} +(-98.7102 - 80.2405i) q^{93} +3178.75 q^{94} +702.393i q^{95} +(1667.87 - 2051.78i) q^{96} -12596.8 q^{97} +8175.06i q^{98} +(4760.54 - 993.265i) 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 $

$2$		−	4.27932i		−	1.06983i	−0.844906	−	0.534915i	$-0.820344\pi$
$2$		−	4.27932i		−	1.06983i	0.844906	−	0.534915i	$-0.179656\pi$
$3$	−6.98370	−	5.67697i	−0.775966	−	0.630775i
$3$	−6.98370	−	5.67697i	−0.775966	−	0.630775i
$4$	−2.31259			−0.144537
$5$		−	6.15778i		−	0.246311i	−0.992387	−	0.123156i	$-0.960699\pi$
$5$		−	6.15778i		−	0.246311i	0.992387	−	0.123156i	$-0.0393014\pi$
$6$	−24.2936	+	29.8855i	−0.674822	+	0.830152i
$7$	−22.1503			−0.452047			−0.226024	−	0.974122i	$-0.572573\pi$
$7$	−22.1503			−0.452047			−0.226024	+	0.974122i	$0.572573\pi$
$8$		−	58.5728i		−	0.915200i
$9$	16.5440	+	79.2925i	0.204247	+	0.978919i
$10$	−26.3511			−0.263511
$11$		−	60.0378i		−	0.496180i	−0.968737	−	0.248090i	$-0.920197\pi$
$11$		−	60.0378i		−	0.496180i	0.968737	−	0.248090i	$-0.0798029\pi$
$12$	16.1504	+	13.1285i	0.112156	+	0.0911702i
$13$	−252.105			−1.49175			−0.745873	−	0.666089i	$-0.767967\pi$
$13$	−252.105			−1.49175			−0.745873	+	0.666089i	$0.767967\pi$
$14$			94.7883i			0.483614i
$15$	−34.9575	+	43.0040i	−0.155367	+	0.191129i
$16$	−287.653			−1.12365
$17$			475.495i			1.64531i	0.568541	+	0.822655i	$0.307508\pi$
$17$			475.495i			1.64531i	−0.568541	+	0.822655i	$0.692492\pi$
$18$	339.318	−	70.7971i	1.04728	−	0.218510i
$19$	−114.066			−0.315972			−0.157986	−	0.987441i	$-0.550500\pi$
$19$	−114.066			−0.315972			−0.157986	+	0.987441i	$0.550500\pi$
$20$			14.2404i			0.0356010i
$21$	154.691	+	125.747i	0.350773	+	0.285140i
$22$	−256.921			−0.530828
$23$			529.132i			1.00025i	0.865953	+	0.500125i	$0.166713\pi$
$23$			529.132i			1.00025i	−0.865953	+	0.500125i	$0.833287\pi$
$24$	−332.516	+	409.055i	−0.577285	+	0.710164i
$25$	587.082			0.939331
$26$			1078.84i			1.59591i
$27$	334.603	−	647.674i	0.458989	−	0.888442i
$28$	51.2246			0.0653375
$29$		−	1258.45i		−	1.49638i	−0.663485	−	0.748189i	$-0.730923\pi$
$29$		−	1258.45i		−	1.49638i	0.663485	−	0.748189i	$-0.269077\pi$
$30$	184.028	+	149.594i	0.204476	+	0.166216i
$31$	14.1344			0.0147080			0.00735400	−	0.999973i	$-0.497659\pi$
$31$	14.1344			0.0147080			0.00735400	+	0.999973i	$0.497659\pi$
$32$			293.796i			0.286910i
$33$	−340.833	+	419.286i	−0.312978	+	0.385019i
$34$	2034.79			1.76020
$35$			136.397i			0.111344i
$36$	−38.2595	−	183.371i	−0.0295212	−	0.141490i
$37$	−682.331			−0.498416			−0.249208	−	0.968450i	$-0.580170\pi$
$37$	−682.331			−0.498416			−0.249208	+	0.968450i	$0.580170\pi$
$38$			488.125i			0.338037i
$39$	1760.62	+	1431.19i	1.15754	+	0.940955i
$40$	−360.678			−0.225424
$41$			1784.12i			1.06135i	0.847577	+	0.530673i	$0.178061\pi$
$41$			1784.12i			1.06135i	−0.847577	+	0.530673i	$0.821939\pi$
$42$	538.110	−	661.972i	0.305051	−	0.375268i
$43$	1895.39			1.02509			0.512544	−	0.858661i	$-0.328703\pi$
$43$	1895.39			1.02509			0.512544	+	0.858661i	$0.328703\pi$
$44$			138.843i			0.0717163i
$45$	488.265	−	101.874i	0.241119	−	0.0503083i
$46$	2264.33			1.07010
$47$			742.817i			0.336269i	0.985764	+	0.168134i	$0.0537742\pi$
$47$			742.817i			0.336269i	−0.985764	+	0.168134i	$0.946226\pi$
$48$	2008.88	+	1633.00i	0.871911	+	0.708767i
$49$	−1910.36			−0.795653
$50$		−	2512.31i		−	1.00492i
$51$	2699.37	−	3320.71i	1.03782	−	1.27670i
$52$	583.016			0.215612
$53$			3076.72i			1.09531i	0.836705	+	0.547654i	$0.184479\pi$
$53$			3076.72i			1.09531i	−0.836705	+	0.547654i	$0.815521\pi$
$54$	−2771.61	−	1431.87i	−0.950482	−	0.491040i
$55$	−369.699			−0.122215
$56$			1297.41i			0.413714i
$57$	796.602	+	647.549i	0.245184	+	0.199307i
$58$	−5385.33			−1.60087
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	80.8424	−	99.4507i	0.0224562	−	0.0276252i
$61$	1439.20			0.386779			0.193389	−	0.981122i	$-0.438052\pi$
$61$	1439.20			0.386779			0.193389	+	0.981122i	$0.438052\pi$
$62$		−	60.4856i		−	0.0157351i
$63$	−366.455	−	1756.35i	−0.0923292	−	0.442518i
$64$	−3345.21			−0.816701
$65$			1552.41i			0.367433i
$66$	1794.26	+	1458.53i	0.411905	+	0.334833i
$67$	3224.97			0.718417			0.359209	−	0.933257i	$-0.383047\pi$
$67$	3224.97			0.718417			0.359209	+	0.933257i	$0.383047\pi$
$68$		−	1099.62i		−	0.237808i
$69$	3003.87	−	3695.30i	0.630932	−	0.776160i
$70$	583.685			0.119119
$71$		−	5483.87i		−	1.08785i	−0.839133	−	0.543927i	$-0.816937\pi$
$71$		−	5483.87i		−	1.08785i	0.839133	−	0.543927i	$-0.183063\pi$
$72$	4644.38	−	969.029i	0.895907	−	0.186927i
$73$	−8856.56			−1.66195			−0.830977	−	0.556306i	$-0.812218\pi$
$73$	−8856.56			−1.66195			−0.830977	+	0.556306i	$0.812218\pi$
$74$			2919.91i			0.533220i
$75$	−4100.00	−	3332.85i	−0.728889	−	0.592506i
$76$	263.788			0.0456697
$77$			1329.86i			0.224297i
$78$	6124.53	−	7534.28i	1.00666	−	1.23838i
$79$	−9349.35			−1.49805			−0.749027	−	0.662540i	$-0.769479\pi$
$79$	−9349.35			−1.49805			−0.749027	+	0.662540i	$0.769479\pi$
$80$			1771.31i			0.276766i
$81$	−6013.59	+	2623.63i	−0.916566	+	0.399882i
$82$	7634.84			1.13546
$83$			7555.94i			1.09681i	0.836212	+	0.548406i	$0.184765\pi$
$83$			7555.94i			1.09681i	−0.836212	+	0.548406i	$0.815235\pi$
$84$	−357.737	−	290.801i	−0.0506997	−	0.0412132i
$85$	2927.99			0.405258
$86$		−	8110.97i		−	1.09667i
$87$	−7144.21	+	8788.66i	−0.943878	+	1.16114i
$88$	−3516.58			−0.454104
$89$			4863.80i			0.614038i	0.951703	+	0.307019i	$0.0993316\pi$
$89$			4863.80i			0.614038i	−0.951703	+	0.307019i	$0.900668\pi$
$90$	−435.953	−	2089.44i	−0.0538213	−	0.257956i
$91$	5584.20			0.674339
$92$		−	1223.67i		−	0.144573i
$93$	−98.7102	−	80.2405i	−0.0114129	−	0.00927743i
$94$	3178.75			0.359750
$95$			702.393i			0.0778274i
$96$	1667.87	−	2051.78i	0.180976	−	0.222633i
$97$	−12596.8			−1.33880			−0.669400	−	0.742902i	$-0.733449\pi$
$97$	−12596.8			−1.33880			−0.669400	+	0.742902i	$0.733449\pi$
$98$			8175.06i			0.851214i
$99$	4760.54	−	993.265i	0.485720	−	0.101343i
$100$	−1357.68			−0.135768
$101$		−	7786.36i		−	0.763293i	−0.924308	−	0.381647i	$-0.875357\pi$
$101$		−	7786.36i		−	0.763293i	0.924308	−	0.381647i	$-0.124643\pi$
$102$	−14210.4	−	11551.5i	−1.36586	−	1.11029i
$103$	−18936.3			−1.78493			−0.892464	−	0.451118i	$-0.851025\pi$
$103$	−18936.3			−1.78493			−0.892464	+	0.451118i	$0.851025\pi$
$104$			14766.5i			1.36525i
$105$	774.320	−	952.552i	0.0702331	−	0.0863993i
$106$	13166.3			1.17179
$107$			11612.8i			1.01431i	0.861856	+	0.507153i	$0.169302\pi$
$107$			11612.8i			1.01431i	−0.861856	+	0.507153i	$0.830698\pi$
$108$	−773.800	+	1497.81i	−0.0663408	+	0.128413i
$109$	−20455.6			−1.72171			−0.860854	−	0.508852i	$-0.830070\pi$
$109$	−20455.6			−1.72171			−0.860854	+	0.508852i	$0.830070\pi$
$110$			1582.06i			0.130749i
$111$	4765.19	+	3873.57i	0.386754	+	0.314388i
$112$	6371.61			0.507941
$113$		−	16856.6i		−	1.32012i	−0.751215	−	0.660058i	$-0.770532\pi$
$113$		−	16856.6i		−	1.32012i	0.751215	−	0.660058i	$-0.229468\pi$
$114$	2771.07	−	3408.92i	0.213225	−	0.262305i
$115$	3258.28			0.246373
$116$			2910.29i			0.216282i
$117$	−4170.82	−	19990.0i	−0.304684	−	1.46030i
$118$	1939.34			0.139280
$119$		−	10532.4i		−	0.743758i
$120$	2518.87	+	2047.56i	0.174921	+	0.142192i
$121$	11036.5			0.753805
$122$		−	6158.82i		−	0.413788i
$123$	10128.4	−	12459.8i	0.669470	−	0.823569i
$124$	−32.6871			−0.00212585
$125$		−	7463.73i		−	0.477679i
$126$	−7516.00	+	1568.18i	−0.473419	+	0.0987766i
$127$	−13357.8			−0.828186			−0.414093	−	0.910235i	$-0.635901\pi$
$127$	−13357.8			−0.828186			−0.414093	+	0.910235i	$0.635901\pi$
$128$			19015.9i			1.16064i
$129$	−13236.8	−	10760.1i	−0.795433	−	0.646599i
$130$	6643.24			0.393091
$131$		−	2111.19i		−	0.123022i	−0.998106	−	0.0615112i	$-0.980408\pi$
$131$		−	2111.19i		−	0.123022i	0.998106	−	0.0615112i	$-0.0195920\pi$
$132$	788.207	−	969.636i	0.0452368	−	0.0556495i
$133$	2526.60			0.142834
$134$		−	13800.7i		−	0.768584i
$135$	−3988.23	−	2060.41i	−0.218833	−	0.113054i
$136$	27851.1			1.50579
$137$		−	8167.28i		−	0.435148i	−0.976044	−	0.217574i	$-0.930186\pi$
$137$		−	8167.28i		−	0.435148i	0.976044	−	0.217574i	$-0.0698143\pi$
$138$	−15813.4	−	12854.5i	−0.830360	−	0.674991i
$139$	29247.4			1.51376			0.756880	−	0.653554i	$-0.226723\pi$
$139$	29247.4			1.51376			0.756880	+	0.653554i	$0.226723\pi$
$140$		−	315.430i		−	0.0160933i
$141$	4216.95	−	5187.61i	0.212110	−	0.260933i
$142$	−23467.2			−1.16382
$143$			15135.8i			0.740174i
$144$	−4758.94	−	22808.7i	−0.229501	−	1.09996i
$145$	−7749.28			−0.368575
$146$			37900.0i			1.77801i
$147$	13341.4	+	10845.1i	0.617400	+	0.501878i
$148$	1577.95			0.0720395
$149$		−	7551.99i		−	0.340164i	−0.985430	−	0.170082i	$-0.945597\pi$
$149$		−	7551.99i		−	0.340164i	0.985430	−	0.170082i	$-0.0544033\pi$
$150$	−14262.3	+	17545.2i	−0.633881	+	0.779788i
$151$	855.883			0.0375371			0.0187685	−	0.999824i	$-0.494025\pi$
$151$	855.883			0.0375371			0.0187685	+	0.999824i	$0.494025\pi$
$152$			6681.16i			0.289178i
$153$	−37703.1	+	7866.58i	−1.61063	+	0.336049i
$154$	5690.88			0.239959
$155$		−	87.0364i		−	0.00362274i
$156$	−4071.60	−	3309.76i	−0.167308	−	0.136003i
$157$	−283.730			−0.0115108			−0.00575540	−	0.999983i	$-0.501832\pi$
$157$	−283.730			−0.0115108			−0.00575540	+	0.999983i	$0.501832\pi$
$158$			40008.9i			1.60266i
$159$	17466.4	−	21486.9i	0.690892	−	0.849921i
$160$	1809.13			0.0706692
$161$		−	11720.4i		−	0.452160i
$162$	11227.4	+	25734.1i	0.427806	+	0.980571i
$163$	−24701.2			−0.929699			−0.464850	−	0.885390i	$-0.653892\pi$
$163$	−24701.2			−0.929699			−0.464850	+	0.885390i	$0.653892\pi$
$164$		−	4125.95i		−	0.153404i
$165$	2581.87	+	2098.77i	0.0948344	+	0.0770899i
$166$	32334.3			1.17340
$167$			18044.7i			0.647019i	0.946225	+	0.323509i	$0.104863\pi$
$167$			18044.7i			0.647019i	−0.946225	+	0.323509i	$0.895137\pi$
$168$	7365.34	−	9060.69i	0.260960	−	0.321028i
$169$	34995.9			1.22530
$170$		−	12529.8i		−	0.433557i
$171$	−1887.11	−	9044.57i	−0.0645363	−	0.309311i
$172$	−4383.26			−0.148163
$173$		−	34014.6i		−	1.13651i	−0.822853	−	0.568254i	$-0.807619\pi$
$173$		−	34014.6i		−	1.13651i	0.822853	−	0.568254i	$-0.192381\pi$
$174$	37609.5	+	30572.4i	1.24222	+	1.00979i
$175$	−13004.0			−0.424622
$176$			17270.1i			0.557531i
$177$	2572.73	−	3164.92i	0.0821199	−	0.101022i
$178$	20813.8			0.656917
$179$		−	43081.0i		−	1.34456i	−0.740298	−	0.672279i	$-0.765316\pi$
$179$		−	43081.0i		−	1.34456i	0.740298	−	0.672279i	$-0.234684\pi$
$180$	−1129.16	+	235.593i	−0.0348506	+	0.00727140i
$181$	−13197.5			−0.402840			−0.201420	−	0.979505i	$-0.564556\pi$
$181$	−13197.5			−0.402840			−0.201420	+	0.979505i	$0.564556\pi$
$182$		−	23896.6i		−	0.721428i
$183$	−10051.0	−	8170.32i	−0.300127	−	0.243970i
$184$	30992.8			0.915429
$185$			4201.64i			0.122765i
$186$	−343.375	+	422.413i	−0.00992528	+	0.0122099i
$187$	28547.6			0.816370
$188$		−	1717.83i		−	0.0486032i
$189$	−7411.55	+	14346.2i	−0.207485	+	0.401618i
$190$	3005.76			0.0832621
$191$			31696.9i			0.868860i	0.900706	+	0.434430i	$0.143050\pi$
$191$			31696.9i			0.868860i	−0.900706	+	0.434430i	$0.856950\pi$
$192$	23361.9	+	18990.6i	0.633732	+	0.515154i
$193$	9475.70			0.254388			0.127194	−	0.991878i	$-0.459403\pi$
$193$	9475.70			0.254388			0.127194	+	0.991878i	$0.459403\pi$
$194$			53905.7i			1.43229i
$195$	8812.96	−	10841.5i	0.231768	−	0.285116i
$196$	4417.89			0.115001
$197$			60627.6i			1.56221i	0.624402	+	0.781103i	$0.285343\pi$
$197$			60627.6i			1.56221i	−0.624402	+	0.781103i	$0.714657\pi$
$198$	−4250.50	−	20371.9i	−0.108420	−	0.519638i
$199$	48045.0			1.21323			0.606614	−	0.794996i	$-0.292527\pi$
$199$	48045.0			1.21323			0.606614	+	0.794996i	$0.292527\pi$
$200$		−	34387.0i		−	0.859676i
$201$	−22522.2	−	18308.1i	−0.557467	−	0.453159i
$202$	−33320.3			−0.816594
$203$			27875.2i			0.676434i
$204$	−6242.54	+	7679.44i	−0.150003	+	0.184531i
$205$	10986.2			0.261421
$206$			81034.5i			1.90957i
$207$	−41956.2	+	8753.97i	−0.979164	+	0.204298i
$208$	72518.8			1.67619
$209$			6848.27i			0.156779i
$210$	−4076.28	−	3313.56i	−0.0924326	−	0.0751375i
$211$	−44652.8			−1.00296			−0.501480	−	0.865169i	$-0.667211\pi$
$211$	−44652.8			−1.00296			−0.501480	+	0.865169i	$0.667211\pi$
$212$		−	7115.19i		−	0.158312i
$213$	−31131.8	+	38297.7i	−0.686191	+	0.844138i
$214$	49694.8			1.08514
$215$		−	11671.4i		−	0.252490i
$216$	−37936.1	−	19598.6i	−0.813102	−	0.420067i
$217$	−313.081			−0.00664871
$218$			87536.2i			1.84194i
$219$	61851.5	+	50278.4i	1.28962	+	1.04832i
$220$	854.963			0.0176645
$221$		−	119875.i		−	2.45438i
$222$	16576.3	−	20391.8i	0.336342	−	0.413761i
$223$	−21774.9			−0.437872			−0.218936	−	0.975739i	$-0.570259\pi$
$223$	−21774.9			−0.437872			−0.218936	+	0.975739i	$0.570259\pi$
$224$		−	6507.67i		−	0.129697i
$225$	9712.68	+	46551.2i	0.191855	+	0.919529i
$226$	−72134.6			−1.41230
$227$			37951.3i			0.736504i	0.929726	+	0.368252i	$0.120044\pi$
$227$			37951.3i			0.736504i	−0.929726	+	0.368252i	$0.879956\pi$
$228$	−1842.21	−	1497.52i	−0.0354381	−	0.0288073i
$229$	−67237.0			−1.28215			−0.641073	−	0.767480i	$-0.721510\pi$
$229$	−67237.0			−1.28215			−0.641073	+	0.767480i	$0.721510\pi$
$230$		−	13943.2i		−	0.263577i
$231$	7549.55	−	9287.30i	0.141481	−	0.174047i
$232$	−73711.2			−1.36949
$233$			20931.8i			0.385562i	0.981242	+	0.192781i	$0.0617507\pi$
$233$			20931.8i			0.385562i	−0.981242	+	0.192781i	$0.938249\pi$
$234$	−85543.7	+	17848.3i	−1.56227	+	0.325960i
$235$	4574.10			0.0828267
$236$		−	1048.04i		−	0.0188171i
$237$	65293.0	+	53076.0i	1.16244	+	0.944934i
$238$	−45071.3			−0.795694
$239$		−	98619.7i		−	1.72651i	−0.504772	−	0.863253i	$-0.668423\pi$
$239$		−	98619.7i		−	1.72651i	0.504772	−	0.863253i	$-0.331577\pi$
$240$	10055.6	−	12370.3i	0.174577	−	0.214761i
$241$	−12396.0			−0.213426			−0.106713	−	0.994290i	$-0.534033\pi$
$241$	−12396.0			−0.213426			−0.106713	+	0.994290i	$0.534033\pi$
$242$		−	47228.6i		−	0.806444i
$243$	56891.4	+	15816.4i	0.963460	+	0.267852i
$244$	−3328.29			−0.0559039
$245$			11763.6i			0.195978i
$246$	−53319.4	−	43342.8i	−0.881079	−	0.716220i
$247$	28756.6			0.471350
$248$		−	827.891i		−	0.0134608i
$249$	42894.8	−	52768.3i	0.691841	−	0.851089i
$250$	−31939.7			−0.511035
$251$			14187.1i			0.225189i	0.993641	+	0.112594i	$0.0359160\pi$
$251$			14187.1i			0.225189i	−0.993641	+	0.112594i	$0.964084\pi$
$252$	847.460	+	4061.73i	0.0133450	+	0.0639601i
$253$	31767.9			0.496304
$254$			57162.3i			0.886018i
$255$	−20448.2	−	16622.1i	−0.314466	−	0.255626i
$256$	27852.1			0.424989
$257$			80227.0i			1.21466i	0.794450	+	0.607330i	$0.207759\pi$
$257$			80227.0i			1.21466i	−0.794450	+	0.607330i	$0.792241\pi$
$258$	−46045.8	+	56644.6i	−0.691752	+	0.850979i
$259$	15113.8			0.225307
$260$		−	3590.08i		−	0.0531077i
$261$	99786.0	−	20819.9i	1.46483	−	0.305631i
$262$	−9034.45			−0.131613
$263$			9763.42i			0.141153i	0.997506	+	0.0705766i	$0.0224839\pi$
$263$			9763.42i			0.141153i	−0.997506	+	0.0705766i	$0.977516\pi$
$264$	24558.7	+	19963.5i	0.352369	+	0.286437i
$265$	18945.7			0.269786
$266$		−	10812.1i		−	0.152808i
$267$	27611.6	−	33967.3i	0.387320	−	0.476473i
$268$	−7458.05			−0.103838
$269$		−	80885.6i		−	1.11781i	−0.829233	−	0.558903i	$-0.811222\pi$
$269$		−	80885.6i		−	1.11781i	0.829233	−	0.558903i	$-0.188778\pi$
$270$	−8817.15	+	17066.9i	−0.120949	+	0.234114i
$271$	6394.26			0.0870667			0.0435333	−	0.999052i	$-0.486139\pi$
$271$	6394.26			0.0870667			0.0435333	+	0.999052i	$0.486139\pi$
$272$		−	136778.i		−	1.84875i
$273$	−38998.4	−	31701.3i	−0.523264	−	0.425356i
$274$	−34950.4			−0.465534
$275$		−	35247.1i		−	0.466077i
$276$	−6946.72	+	8545.72i	−0.0911931	+	0.112184i
$277$	−106955.			−1.39393			−0.696966	−	0.717104i	$-0.745467\pi$
$277$	−106955.			−1.39393			−0.696966	+	0.717104i	$0.745467\pi$
$278$		−	125159.i		−	1.61947i
$279$	233.839	+	1120.75i	0.00300406	+	0.0143979i
$280$	7989.13			0.101902
$281$		−	63996.3i		−	0.810480i	−0.914210	−	0.405240i	$-0.867188\pi$
$281$		−	63996.3i		−	0.810480i	0.914210	−	0.405240i	$-0.132812\pi$
$282$	−22199.5	−	18045.7i	−0.279154	−	0.226921i
$283$	−73114.9			−0.912921			−0.456461	−	0.889744i	$-0.650883\pi$
$283$	−73114.9			−0.912921			−0.456461	+	0.889744i	$0.650883\pi$
$284$			12682.0i			0.157235i
$285$	3987.46	−	4905.30i	0.0490916	−	0.0603915i
$286$	64771.0			0.791861
$287$		−	39518.9i		−	0.479779i
$288$	−23295.8	+	4860.56i	−0.280862	+	0.0586005i
$289$	−142574.			−1.70704
$290$			33161.7i			0.394312i
$291$	87972.1	+	71511.5i	1.03886	+	0.844482i
$292$	20481.6			0.240214
$293$		−	135587.i		−	1.57937i	−0.613511	−	0.789686i	$-0.710244\pi$
$293$		−	135587.i		−	1.57937i	0.613511	−	0.789686i	$-0.289756\pi$
$294$	46409.6	−	57092.1i	0.536924	−	0.660513i
$295$	2790.63			0.0320670
$296$			39966.1i			0.456150i
$297$	−38884.9	−	20088.8i	−0.440827	−	0.227741i
$298$	−32317.4			−0.363918
$299$		−	133397.i		−	1.49212i
$300$	9481.62	+	7707.51i	0.105351	+	0.0856390i
$301$	−41983.4			−0.463388
$302$		−	3662.60i		−	0.0401583i
$303$	−44202.9	+	54377.5i	−0.481466	+	0.592290i
$304$	32811.5			0.355041
$305$		−	8862.30i		−	0.0952679i
$306$	33663.6	+	161344.i	0.359516	+	1.72310i
$307$	76474.3			0.811407			0.405703	−	0.914005i	$-0.367027\pi$
$307$	76474.3			0.811407			0.405703	+	0.914005i	$0.367027\pi$
$308$		−	3075.41i		−	0.0324192i
$309$	132245.	+	107501.i	1.38504	+	1.12589i
$310$	−372.457			−0.00387572
$311$		−	2253.38i		−	0.0232977i	−0.999932	−	0.0116489i	$-0.996292\pi$
$311$		−	2253.38i		−	0.0232977i	0.999932	−	0.0116489i	$-0.00370803\pi$
$312$	83829.0	−	103125.i	0.861162	−	1.05938i
$313$	108428.			1.10676			0.553380	−	0.832929i	$-0.313338\pi$
$313$	108428.			1.10676			0.553380	+	0.832929i	$0.313338\pi$
$314$			1214.17i			0.0123146i
$315$	−10815.2	+	2256.55i	−0.108997	+	0.0227417i
$316$	21621.2			0.216524
$317$		−	25903.9i		−	0.257778i	−0.991659	−	0.128889i	$-0.958859\pi$
$317$		−	25903.9i		−	0.257778i	0.991659	−	0.128889i	$-0.0411412\pi$
$318$	−91949.2	−	74744.5i	−0.909271	−	0.739137i
$319$	−75554.8			−0.742473
$320$			20599.0i			0.201162i
$321$	65925.5	−	81100.2i	0.639798	−	0.787067i
$322$	−50155.6			−0.483735
$323$		−	54237.7i		−	0.519872i
$324$	13907.0	−	6067.38i	0.132478	−	0.0577978i
$325$	−148006.			−1.40124
$326$			105704.i			0.994621i
$327$	142856.	+	116126.i	1.33599	+	1.08601i
$328$	104501.			0.971345
$329$		−	16453.6i		−	0.152009i
$330$	8981.32	−	11048.6i	0.0824731	−	0.101457i
$331$	197638.			1.80391			0.901956	−	0.431828i	$-0.142131\pi$
$331$	197638.			1.80391			0.901956	+	0.431828i	$0.142131\pi$
$332$		−	17473.8i		−	0.158530i
$333$	−11288.5	−	54103.7i	−0.101800	−	0.487909i
$334$	77219.1			0.692200
$335$		−	19858.7i		−	0.176954i
$336$	−44497.4	−	36171.4i	−0.394145	−	0.320396i
$337$	−104229.			−0.917756			−0.458878	−	0.888499i	$-0.651749\pi$
$337$	−104229.			−0.917756			−0.458878	+	0.888499i	$0.651749\pi$
$338$		−	149759.i		−	1.31087i
$339$	−95694.2	+	117721.i	−0.832695	+	1.02436i
$340$	−6771.24			−0.0585748
$341$		−	848.597i		−	0.00729781i
$342$	−38704.6	+	8075.54i	−0.330911	+	0.0690429i
$343$	95498.0			0.811720
$344$		−	111018.i		−	0.938161i
$345$	−22754.8	−	18497.2i	−0.191177	−	0.155406i
$346$	−145559.			−1.21587
$347$			14398.4i			0.119579i	0.998211	+	0.0597895i	$0.0190429\pi$
$347$			14398.4i			0.119579i	−0.998211	+	0.0597895i	$0.980957\pi$
$348$	16521.6	−	20324.6i	0.136425	−	0.167828i
$349$	−97324.6			−0.799046			−0.399523	−	0.916723i	$-0.630824\pi$
$349$	−97324.6			−0.799046			−0.399523	+	0.916723i	$0.630824\pi$
$350$			55648.5i			0.454273i
$351$	−84355.0	+	163282.i	−0.684694	+	1.32533i
$352$	17638.9			0.142359
$353$			72467.5i			0.581559i	0.956790	+	0.290780i	$0.0939146\pi$
$353$			72467.5i			0.581559i	−0.956790	+	0.290780i	$0.906085\pi$
$354$	−13543.7	−	11009.6i	−0.108077	−	0.0878543i
$355$	−33768.5			−0.267950
$356$		−	11248.0i		−	0.0887512i
$357$	−59791.8	+	73554.7i	−0.469143	+	0.577131i
$358$	−184357.			−1.43845
$359$			160864.i			1.24816i	0.781361	+	0.624080i	$0.214526\pi$
$359$			160864.i			1.24816i	−0.781361	+	0.624080i	$0.785474\pi$
$360$	−5967.06	−	28599.1i	−0.0460421	−	0.220672i
$361$	−117310.			−0.900162
$362$			56476.2i			0.430971i
$363$	−77075.3	−	62653.7i	−0.584927	−	0.475481i
$364$	−12914.0			−0.0974669
$365$			54536.7i			0.409358i
$366$	−34963.4	+	43011.3i	−0.261007	+	0.321085i
$367$	243423.			1.80729			0.903647	−	0.428277i	$-0.140879\pi$
$367$	243423.			1.80729			0.903647	+	0.428277i	$0.140879\pi$
$368$		−	152207.i		−	1.12393i
$369$	−141468.	+	29516.5i	−1.03897	+	0.216777i
$370$	17980.2			0.131338
$371$		−	68150.2i		−	0.495130i
$372$	228.276	+	185.563i	0.00164959	+	0.00134093i
$373$	−167437.			−1.20346			−0.601732	−	0.798698i	$-0.705523\pi$
$373$	−167437.			−1.20346			−0.601732	+	0.798698i	$0.705523\pi$
$374$		−	122165.i		−	0.873377i
$375$	−42371.4	+	52124.4i	−0.301308	+	0.370662i
$376$	43508.9			0.307753
$377$			317263.i			2.23222i
$378$	61391.9	+	31716.4i	0.429663	+	0.221973i
$379$	184407.			1.28380			0.641902	−	0.766786i	$-0.278145\pi$
$379$	184407.			1.28380			0.641902	+	0.766786i	$0.278145\pi$
$380$		−	1624.35i		−	0.0112489i
$381$	93286.9	+	75831.9i	0.642644	+	0.522398i
$382$	135641.			0.929532
$383$		−	83917.5i		−	0.572077i	−0.958218	−	0.286039i	$-0.907661\pi$
$383$		−	83917.5i		−	0.572077i	0.958218	−	0.286039i	$-0.0923386\pi$
$384$	107953.	−	132802.i	0.732103	−	0.900618i
$385$	8188.95			0.0552468
$386$		−	40549.5i		−	0.272152i
$387$	31357.3	+	150290.i	0.209371	+	1.00348i
$388$	29131.2			0.193506
$389$			110053.i			0.727280i	0.931540	+	0.363640i	$0.118466\pi$
$389$			110053.i			0.727280i	−0.931540	+	0.363640i	$0.881534\pi$
$390$	−46394.4	−	37713.5i	−0.305026	−	0.247952i
$391$	−251600.			−1.64572
$392$			111895.i			0.728182i
$393$	−11985.1	+	14743.9i	−0.0775994	+	0.0954612i
$394$	259445.			1.67130
$395$			57571.2i			0.368987i
$396$	−11009.2	+	2297.02i	−0.0702045	+	0.0146478i
$397$	−136778.			−0.867831			−0.433916	−	0.900953i	$-0.642868\pi$
$397$	−136778.			−0.867831			−0.433916	+	0.900953i	$0.642868\pi$
$398$		−	205600.i		−	1.29795i
$399$	−17645.0	−	14343.4i	−0.110835	−	0.0900962i
$400$	−168876.			−1.05548
$401$		−	294178.i		−	1.82945i	−0.404075	−	0.914726i	$-0.632406\pi$
$401$		−	294178.i		−	1.82945i	0.404075	−	0.914726i	$-0.367594\pi$
$402$	−78346.2	+	96379.9i	−0.484803	+	0.596395i
$403$	−3563.35			−0.0219406
$404$			18006.7i			0.110324i
$405$	16155.7	+	37030.4i	0.0984955	+	0.225760i
$406$	119287.			0.723669
$407$			40965.6i			0.247304i
$408$	−194503.	−	158110.i	−1.16844	−	0.949813i
$409$	−25699.3			−0.153629			−0.0768146	−	0.997045i	$-0.524475\pi$
$409$	−25699.3			−0.153629			−0.0768146	+	0.997045i	$0.524475\pi$
$410$		−	47013.6i		−	0.279676i
$411$	−46365.4	+	57037.8i	−0.274480	+	0.337660i
$412$	43791.9			0.257988
$413$		−	10038.2i		−	0.0588515i
$414$	37461.0	+	179544.i	0.218564	+	1.04754i
$415$	46527.8			0.270157
$416$		−	74067.4i		−	0.427997i
$417$	−204255.	−	166036.i	−1.17463	−	0.954841i
$418$	29305.9			0.167727
$419$			285438.i			1.62586i	0.582362	+	0.812930i	$0.302129\pi$
$419$			285438.i			1.62586i	−0.582362	+	0.812930i	$0.697871\pi$
$420$	−1790.68	+	2202.86i	−0.0101513	+	0.0124879i
$421$	232861.			1.31381			0.656906	−	0.753973i	$-0.271865\pi$
$421$	232861.			1.31381			0.656906	+	0.753973i	$0.271865\pi$
$422$			191084.i			1.07300i
$423$	−58899.8	+	12289.2i	−0.329180	+	0.0686818i
$424$	180212.			1.00243
$425$			279154.i			1.54549i
$426$	163888.	+	133223.i	0.903084	+	0.734108i
$427$	−31878.8			−0.174842
$428$		−	26855.6i		−	0.146605i
$429$	85925.6	−	105704.i	0.466883	−	0.574350i
$430$	−49945.5			−0.270122
$431$			173860.i			0.935934i	0.883746	+	0.467967i	$0.155013\pi$
$431$			173860.i			0.935934i	−0.883746	+	0.467967i	$0.844987\pi$
$432$	−96249.6	+	186306.i	−0.515741	+	0.998294i
$433$	41757.2			0.222718			0.111359	−	0.993780i	$-0.464480\pi$
$433$	41757.2			0.222718			0.111359	+	0.993780i	$0.464480\pi$
$434$			1339.77i			0.00711299i
$435$	54118.6	+	43992.4i	0.286001	+	0.232487i
$436$	47305.5			0.248850
$437$		−	60356.0i		−	0.316051i
$438$	215157.	−	264682.i	1.12152	−	1.37968i
$439$	130301.			0.676112			0.338056	−	0.941126i	$-0.390231\pi$
$439$	130301.			0.676112			0.338056	+	0.941126i	$0.390231\pi$
$440$			21654.3i			0.111851i
$441$	−31605.1	−	151477.i	−0.162510	−	0.778881i
$442$	−512982.			−2.62577
$443$		−	141019.i		−	0.718571i	−0.933228	−	0.359286i	$-0.883020\pi$
$443$		−	141019.i		−	0.718571i	0.933228	−	0.359286i	$-0.116980\pi$
$444$	−11019.9	−	8957.99i	−0.0559002	−	0.0454407i
$445$	29950.2			0.151244
$446$			93181.9i			0.468449i
$447$	−42872.4	+	52740.8i	−0.214567	+	0.263956i
$448$	74097.3			0.369187
$449$		−	147657.i		−	0.732422i	−0.930532	−	0.366211i	$-0.880655\pi$
$449$		−	147657.i		−	0.732422i	0.930532	−	0.366211i	$-0.119345\pi$
$450$	199207.	−	41563.7i	0.983740	−	0.205253i
$451$	107115.			0.526619
$452$			38982.3i			0.190805i
$453$	−5977.23	−	4858.82i	−0.0291275	−	0.0236774i
$454$	162406.			0.787934
$455$		−	34386.3i		−	0.166097i
$456$	37928.8	−	46659.2i	0.182406	−	0.224392i
$457$	321911.			1.54136			0.770679	−	0.637224i	$-0.219917\pi$
$457$	321911.			1.54136			0.770679	+	0.637224i	$0.219917\pi$
$458$			287729.i			1.37168i
$459$	307966.	+	159102.i	1.46176	+	0.755179i
$460$	−7535.07			−0.0356100
$461$			11046.7i			0.0519794i	0.999662	+	0.0259897i	$0.00827372\pi$
$461$			11046.7i			0.0519794i	−0.999662	+	0.0259897i	$0.991726\pi$
$462$	−39743.4	−	32306.9i	−0.186200	−	0.151360i
$463$	26678.1			0.124450			0.0622248	−	0.998062i	$-0.480180\pi$
$463$	26678.1			0.124450			0.0622248	+	0.998062i	$0.480180\pi$
$464$			361999.i			1.68140i
$465$	−494.103	+	607.836i	−0.00228513	+	0.00281112i
$466$	89573.8			0.412486
$467$			115761.i			0.530796i	0.964139	+	0.265398i	$0.0855034\pi$
$467$			115761.i			0.530796i	−0.964139	+	0.265398i	$0.914497\pi$
$468$	9645.41	+	46228.7i	0.0440381	+	0.211067i
$469$	−71434.2			−0.324758
$470$		−	19574.1i		−	0.0886105i
$471$	1981.48	+	1610.72i	0.00893199	+	0.00726072i
$472$	26544.5			0.119149
$473$		−	113795.i		−	0.508628i
$474$	227129.	−	279410.i	1.01092	−	1.24361i
$475$	−66966.0			−0.296802
$476$			24357.0i			0.107500i
$477$	−243961.	+	50901.2i	−1.07222	+	0.223713i
$478$	−422025.			−1.84707
$479$		−	65690.2i		−	0.286306i	−0.989701	−	0.143153i	$-0.954276\pi$
$479$		−	65690.2i		−	0.286306i	0.989701	−	0.143153i	$-0.0457240\pi$
$480$	−12634.4	−	10270.4i	−0.0548369	−	0.0445763i
$481$	172019.			0.743509
$482$			53046.4i			0.228330i
$483$	−66536.6	+	81852.0i	−0.285211	+	0.350861i
$484$	−25522.8			−0.108953
$485$			77568.1i			0.329761i
$486$	67683.3	−	243456.i	0.286556	−	1.03074i
$487$	228454.			0.963255			0.481628	−	0.876376i	$-0.340046\pi$
$487$	228454.			0.963255			0.481628	+	0.876376i	$0.340046\pi$
$488$		−	84298.3i		−	0.353980i
$489$	172506.	+	140228.i	0.721415	+	0.586431i
$490$	50340.2			0.209663
$491$		−	257752.i		−	1.06915i	−0.845121	−	0.534575i	$-0.820472\pi$
$491$		−	257752.i		−	1.06915i	0.845121	−	0.534575i	$-0.179528\pi$
$492$	−23422.9	+	28814.4i	−0.0967632	+	0.119036i
$493$	598388.			2.46201
$494$		−	123059.i		−	0.504264i
$495$	−6116.30	−	29314.4i	−0.0249620	−	0.119638i
$496$	−4065.80			−0.0165266
$497$			121469.i			0.491761i
$498$	−225813.	−	183561.i	−0.910520	−	0.740152i
$499$	89231.0			0.358356			0.179178	−	0.983817i	$-0.442656\pi$
$499$	89231.0			0.358356			0.179178	+	0.983817i	$0.442656\pi$
$500$			17260.6i			0.0690422i
$501$	102439.	−	126019.i	0.408123	−	0.502065i
$502$	60711.2			0.240914
$503$		−	83970.8i		−	0.331889i	−0.986135	−	0.165944i	$-0.946933\pi$
$503$		−	83970.8i		−	0.331889i	0.986135	−	0.165944i	$-0.0530672\pi$
$504$	−102875.	+	21464.3i	−0.404992	+	0.0844997i
$505$	−47946.6			−0.188008
$506$		−	135945.i		−	0.530961i
$507$	−244401.	−	198671.i	−0.950794	−	0.772890i
$508$	30891.1			0.119703
$509$		−	181429.i		−	0.700279i	−0.936697	−	0.350140i	$-0.886134\pi$
$509$		−	181429.i		−	0.700279i	0.936697	−	0.350140i	$-0.113866\pi$
$510$	−71131.3	+	87504.3i	−0.273477	+	0.336426i
$511$	196175.			0.751282
$512$			185067.i			0.705976i
$513$	−38166.8	+	73877.6i	−0.145028	+	0.280723i
$514$	343317.			1.29948
$515$			116606.i			0.439648i
$516$	30611.3	+	24883.6i	0.114970	+	0.0934575i
$517$	44597.1			0.166850
$518$		−	64677.0i		−	0.241041i
$519$	−193100.	+	237547.i	−0.716881	+	0.881892i
$520$	90928.8			0.336275
$521$		−	196948.i		−	0.725565i	−0.931874	−	0.362782i	$-0.881827\pi$
$521$		−	196948.i		−	0.725565i	0.931874	−	0.362782i	$-0.118173\pi$
$522$	−89094.9	−	427016.i	−0.326973	−	1.56712i
$523$	−254761.			−0.931386			−0.465693	−	0.884946i	$-0.654195\pi$
$523$	−254761.			−0.931386			−0.465693	+	0.884946i	$0.654195\pi$
$524$			4882.31i			0.0177813i
$525$	90816.3	+	73823.6i	0.329492	+	0.267841i
$526$	41780.8			0.151010
$527$			6720.82i			0.0241992i
$528$	98041.7	−	120609.i	0.351676	−	0.432625i
$529$	−140.123			−0.000500723
$530$		−	81074.9i		−	0.288625i
$531$	−35934.4	+	7497.53i	−0.127444	+	0.0265907i
$532$	−5842.98			−0.0206448
$533$		−	449786.i		−	1.58326i
$534$	−145357.	−	118159.i	−0.509745	−	0.414366i
$535$	71508.9			0.249835
$536$		−	188896.i		−	0.657496i
$537$	−244569.	+	300864.i	−0.848113	+	1.04333i
$538$	−346136.			−1.19586
$539$			114694.i			0.394787i
$540$	9223.15	+	4764.88i	0.0316295	+	0.0163405i
$541$	262863.			0.898123			0.449061	−	0.893501i	$-0.351758\pi$
$541$	262863.			0.898123			0.449061	+	0.893501i	$0.351758\pi$
$542$		−	27363.1i		−	0.0931466i
$543$	92167.0	+	74921.6i	0.312591	+	0.254102i
$544$	−139698.			−0.472056
$545$			125961.i			0.424076i
$546$	−135660.	+	166887.i	−0.455059	+	0.559804i
$547$	−578584.			−1.93371			−0.966856	−	0.255324i	$-0.917818\pi$
$547$	−578584.			−1.93371			−0.966856	+	0.255324i	$0.917818\pi$
$548$			18887.6i			0.0628949i
$549$	23810.2	+	114118.i	0.0789984	+	0.378625i
$550$	−150834.			−0.498623
$551$			143547.i			0.472814i
$552$	−216444.	−	175945.i	−0.710342	−	0.577430i
$553$	207091.			0.677191
$554$			457695.i			1.49127i
$555$	23852.6	−	29343.0i	0.0774372	−	0.0952617i
$556$	−67637.2			−0.218794
$557$		−	306771.i		−	0.988789i	−0.869238	−	0.494395i	$-0.835390\pi$
$557$		−	306771.i		−	0.988789i	0.869238	−	0.494395i	$-0.164610\pi$
$558$	4796.05	−	1000.67i	0.0154034	−	0.00321384i
$559$	−477836.			−1.52917
$560$		−	39234.9i		−	0.125111i
$561$	−199368.	−	162064.i	−0.633475	−	0.514945i
$562$	−273861.			−0.867076
$563$			140141.i			0.442127i	0.975259	+	0.221063i	$0.0709528\pi$
$563$			140141.i			0.442127i	−0.975259	+	0.221063i	$0.929047\pi$
$564$	−9752.09	+	11996.8i	−0.0306577	+	0.0377145i
$565$	−103799.			−0.325159
$566$			312882.i			0.976671i
$567$	133203.	−	58114.2i	0.414331	−	0.180766i
$568$	−321206.			−0.995604
$569$			138389.i			0.427440i	0.976895	+	0.213720i	$0.0685581\pi$
$569$			138389.i			0.427440i	−0.976895	+	0.213720i	$0.931442\pi$
$570$	−20991.3	−	17063.6i	−0.0646086	−	0.0525196i
$571$	−456870.			−1.40127			−0.700633	−	0.713522i	$-0.747099\pi$
$571$	−456870.			−1.40127			−0.700633	+	0.713522i	$0.747099\pi$
$572$		−	35003.0i		−	0.106982i
$573$	179942.	−	221361.i	0.548055	−	0.674206i
$574$	−169114.			−0.513282
$575$			310644.i			0.939566i
$576$	−55343.1	−	265250.i	−0.166809	−	0.799484i
$577$	−78115.9			−0.234632			−0.117316	−	0.993095i	$-0.537429\pi$
$577$	−78115.9			−0.234632			−0.117316	+	0.993095i	$0.537429\pi$
$578$			610120.i			1.82625i
$579$	−66175.4	−	53793.2i	−0.197396	−	0.160461i
$580$	17920.9			0.0532726
$581$		−	167366.i		−	0.495810i
$582$	306021.	−	376461.i	0.903452	−	1.11141i
$583$	184719.			0.543469
$584$			518753.i			1.52102i
$585$	−123094.	+	25683.0i	−0.359688	+	0.0750471i
$586$	−580222.			−1.68966
$587$		−	72130.4i		−	0.209335i	−0.994507	−	0.104668i	$-0.966622\pi$
$587$		−	72130.4i		−	0.209335i	0.994507	−	0.104668i	$-0.0333778\pi$
$588$	−30853.2	−	25080.2i	−0.0892371	−	0.0725399i
$589$	−1612.25			−0.00464732
$590$		−	11942.0i		−	0.0343062i
$591$	344181.	−	423405.i	0.985400	−	1.21222i
$592$	196275.			0.560043
$593$		−	553039.i		−	1.57270i	−0.617781	−	0.786350i	$-0.711968\pi$
$593$		−	553039.i		−	1.57270i	0.617781	−	0.786350i	$-0.288032\pi$
$594$	−85966.5	+	166401.i	−0.243644	+	0.471610i
$595$	−64855.9			−0.183196
$596$			17464.7i			0.0491663i
$597$	−335532.	−	272750.i	−0.941424	−	0.765273i
$598$	−570848.			−1.59631
$599$			119830.i			0.333973i	0.985959	+	0.166987i	$0.0534037\pi$
$599$			119830.i			0.333973i	−0.985959	+	0.166987i	$0.946596\pi$
$600$	−195214.	+	240149.i	−0.542262	+	0.667079i
$601$	−502379.			−1.39086			−0.695428	−	0.718595i	$-0.744785\pi$
$601$	−502379.			−1.39086			−0.695428	+	0.718595i	$0.744785\pi$
$602$			179661.i			0.495746i
$603$	53354.0	+	255716.i	0.146734	+	0.703272i
$604$	−1979.31			−0.00542550
$605$		−	67960.1i		−	0.185671i
$606$	232699.	+	189158.i	0.633650	+	0.515087i
$607$	−58904.7			−0.159872			−0.0799361	−	0.996800i	$-0.525472\pi$
$607$	−58904.7			−0.159872			−0.0799361	+	0.996800i	$0.525472\pi$
$608$		−	33512.1i		−	0.0906557i
$609$	158246.	−	194672.i	0.426677	−	0.524890i
$610$	−37924.6			−0.101921
$611$		−	187268.i		−	0.501627i
$612$	87191.9	−	18192.2i	0.232795	−	0.0485716i
$613$	105673.			0.281219			0.140609	−	0.990065i	$-0.455094\pi$
$613$	105673.			0.281219			0.140609	+	0.990065i	$0.455094\pi$
$614$		−	327258.i		−	0.868067i
$615$	−76724.5	−	62368.5i	−0.202854	−	0.164898i
$616$	77893.4			0.205276
$617$		−	98537.6i		−	0.258840i	−0.991590	−	0.129420i	$-0.958688\pi$
$617$		−	98537.6i		−	0.258840i	0.991590	−	0.129420i	$-0.0413116\pi$
$618$	460031.	−	565920.i	1.20451	−	1.48176i
$619$	544530.			1.42115			0.710576	−	0.703620i	$-0.248434\pi$
$619$	544530.			1.42115			0.710576	+	0.703620i	$0.248434\pi$
$620$			201.280i			0.000523620i
$621$	342705.	+	177049.i	0.888664	+	0.459104i
$622$	−9642.94			−0.0249246
$623$		−	107735.i		−	0.277574i
$624$	−506449.	−	411687.i	−1.30067	−	1.05730i
$625$	320966.			0.821673
$626$		−	463999.i		−	1.18405i
$627$	38877.4	−	47826.2i	0.0988922	−	0.121655i
$628$	656.151			0.00166374
$629$		−	324445.i		−	0.820048i
$630$	9656.48	+	46281.8i	0.0243298	+	0.116608i
$631$	−174511.			−0.438293			−0.219146	−	0.975692i	$-0.570327\pi$
$631$	−174511.			−0.438293			−0.219146	+	0.975692i	$0.570327\pi$
$632$			547618.i			1.37102i
$633$	311842.	+	253493.i	0.778263	+	0.632642i
$634$	−110851.			−0.275779
$635$			82254.4i			0.203991i
$636$	−40392.7	+	49690.3i	−0.0998594	+	0.122845i
$637$	481612.			1.18691
$638$			323323.i			0.794320i
$639$	434830.	−	90725.2i	1.06492	−	0.222191i
$640$	117096.			0.285879
$641$			336179.i			0.818192i	0.912491	+	0.409096i	$0.134156\pi$
$641$			336179.i			0.818192i	−0.912491	+	0.409096i	$0.865844\pi$
$642$	−347054.	−	282116.i	−0.842028	−	0.684476i
$643$	148628.			0.359484			0.179742	−	0.983714i	$-0.442474\pi$
$643$	148628.			0.359484			0.179742	+	0.983714i	$0.442474\pi$
$644$			27104.6i			0.0653539i
$645$	−66258.0	+	81509.3i	−0.159265	+	0.195924i
$646$	−232101.			−0.556175
$647$		−	222352.i		−	0.531168i	−0.964088	−	0.265584i	$-0.914435\pi$
$647$		−	222352.i		−	0.531168i	0.964088	−	0.265584i	$-0.0855648\pi$
$648$	153673.	+	352233.i	0.365973	+	0.838842i
$649$	27208.4			0.0645971
$650$			633366.i			1.49909i
$651$	2186.46	+	1777.35i	0.00515917	+	0.00419383i
$652$	57123.7			0.134376
$653$			712522.i			1.67098i	0.549504	+	0.835491i	$0.314817\pi$
$653$			712522.i			1.67098i	−0.549504	+	0.835491i	$0.685183\pi$
$654$	496940.	−	611326.i	1.16185	−	1.42928i
$655$	−13000.2			−0.0303018
$656$		−	513209.i		−	1.19258i
$657$	−146523.	−	702258.i	−0.339449	−	1.62692i
$658$	−70410.4			−0.162624
$659$			294531.i			0.678205i	0.940749	+	0.339102i	$0.110123\pi$
$659$			294531.i			0.678205i	−0.940749	+	0.339102i	$0.889877\pi$
$660$	−5970.80	−	4853.60i	−0.0137071	−	0.0111423i
$661$	−217428.			−0.497638			−0.248819	−	0.968550i	$-0.580042\pi$
$661$	−217428.			−0.497638			−0.248819	+	0.968550i	$0.580042\pi$
$662$		−	845758.i		−	1.92988i
$663$	−680524.	+	837167.i	−1.54816	+	1.90452i
$664$	442572.			1.00380
$665$		−	15558.2i		−	0.0351817i
$666$	−231527.	+	48307.0i	−0.521980	+	0.108909i
$667$	665889.			1.49675
$668$		−	41730.0i		−	0.0935181i
$669$	152069.	+	123616.i	0.339774	+	0.276198i
$670$	−84981.6			−0.189311
$671$		−	86406.6i		−	0.191912i
$672$	−36943.9	+	45447.6i	−0.0818095	+	0.100640i
$673$	−793047.			−1.75093			−0.875465	−	0.483282i	$-0.839445\pi$
$673$	−793047.			−1.75093			−0.875465	+	0.483282i	$0.839445\pi$
$674$			446028.i			0.981844i
$675$	196439.	−	380238.i	0.431142	−	0.834541i
$676$	−80931.2			−0.177102
$677$			866103.i			1.88970i	0.327509	+	0.944848i	$0.393791\pi$
$677$			866103.i			1.88970i	−0.327509	+	0.944848i	$0.606209\pi$
$678$	503766.	+	409506.i	1.09590	+	0.890842i
$679$	279022.			0.605201
$680$		−	171501.i		−	0.370892i
$681$	215449.	−	265040.i	0.464568	−	0.571502i
$682$	−3631.42			−0.00780742
$683$		−	837102.i		−	1.79447i	−0.441551	−	0.897236i	$-0.645571\pi$
$683$		−	837102.i		−	1.79447i	0.441551	−	0.897236i	$-0.354429\pi$
$684$	4364.11	+	20916.4i	0.00932788	+	0.0447069i
$685$	−50292.3			−0.107182
$686$		−	408667.i		−	0.868403i
$687$	469563.	+	381702.i	0.994901	+	0.808745i
$688$	−545215.			−1.15184
$689$		−	775656.i		−	1.63392i
$690$	−79155.3	+	97375.2i	−0.166258	+	0.204527i
$691$	−354204.			−0.741817			−0.370909	−	0.928669i	$-0.620954\pi$
$691$	−354204.			−0.741817			−0.370909	+	0.928669i	$0.620954\pi$
$692$			78661.8i			0.164268i
$693$	−105448.	+	22001.1i	−0.219568	+	0.0458119i
$694$	61615.3			0.127929
$695$		−	180099.i		−	0.372856i
$696$	514777.	+	418457.i	1.06267	+	0.863837i
$697$	−848341.			−1.74624
$698$			416483.i			0.854843i
$699$	118829.	−	146181.i	0.243203	−	0.299183i
$700$	30073.0			0.0613735
$701$			95502.1i			0.194347i	0.995267	+	0.0971733i	$0.0309801\pi$
$701$			95502.1i			0.194347i	−0.995267	+	0.0971733i	$0.969020\pi$
$702$	698736.	+	360982.i	1.41788	+	0.732507i
$703$	77830.7			0.157485
$704$			200839.i			0.405231i
$705$	−31944.1	−	25967.0i	−0.0642707	−	0.0522450i
$706$	310112.			0.622170
$707$			172470.i			0.345045i
$708$	−5949.68	+	7319.18i	−0.0118694	+	0.0146014i
$709$	512215.			1.01897			0.509483	−	0.860481i	$-0.329837\pi$
$709$	512215.			1.01897			0.509483	+	0.860481i	$0.329837\pi$
$710$			144506.i			0.286661i
$711$	−154676.	−	741333.i	−0.305973	−	1.46647i
$712$	284886.			0.561968
$713$			7478.96i			0.0147117i
$714$	314764.	+	255869.i	0.617432	+	0.501904i
$715$	93203.0			0.182313
$716$			99628.7i			0.194338i
$717$	−559861.	+	688730.i	−1.08904	+	1.33971i
$718$	688389.			1.33532
$719$			684555.i			1.32419i	0.749420	+	0.662095i	$0.230333\pi$
$719$			684555.i			1.32419i	−0.749420	+	0.662095i	$0.769667\pi$
$720$	−140451.	+	29304.5i	−0.270932	+	0.0565287i
$721$	419445.			0.806872
$722$			502007.i			0.963020i
$723$	86569.8	+	70371.7i	0.165611	+	0.134624i
$724$	30520.3			0.0582253
$725$		−	738816.i		−	1.40559i
$726$	−268115.	+	329830.i	−0.508684	+	0.625773i
$727$	327581.			0.619798			0.309899	−	0.950769i	$-0.399705\pi$
$727$	327581.			0.619798			0.309899	+	0.950769i	$0.399705\pi$
$728$		−	327082.i		−	0.617155i
$729$	−307523.	−	433427.i	−0.578659	−	0.815570i
$730$	233380.			0.437943
$731$			901246.i			1.68659i
$732$	23243.8	+	18894.6i	0.0433795	+	0.0352627i
$733$	47153.8			0.0877624			0.0438812	−	0.999037i	$-0.486028\pi$
$733$	47153.8			0.0877624			0.0438812	+	0.999037i	$0.486028\pi$
$734$		−	1.04168e6i		−	1.93350i
$735$	66781.6	−	82153.4i	0.123618	−	0.152072i
$736$	−155457.			−0.286982
$737$		−	193620.i		−	0.356464i
$738$	126311.	+	605385.i	0.231914	+	1.11152i
$739$	−61.3175			−0.000112278			−5.61392e−5	−	1.00000i	$-0.500018\pi$
$739$	−61.3175			−0.000112278			−5.61392e−5		1.00000i	$0.500018\pi$
$740$		−	9716.68i		−	0.0177441i
$741$	−200827.	−	163250.i	−0.365752	−	0.297316i
$742$	−291637.			−0.529705
$743$		−	272594.i		−	0.493785i	−0.969043	−	0.246893i	$-0.920591\pi$
$743$		−	272594.i		−	0.493785i	0.969043	−	0.246893i	$-0.0794095\pi$
$744$	−4699.91	+	5781.74i	−0.00849071	+	0.0104451i
$745$	−46503.4			−0.0837862
$746$			716516.i			1.28750i
$747$	−599129.	+	125005.i	−1.07369	+	0.224020i
$748$	−66019.0			−0.117996
$749$		−	257227.i		−	0.458514i
$750$	223057.	+	181321.i	0.396546	+	0.322348i
$751$	576871.			1.02282			0.511409	−	0.859337i	$-0.329124\pi$
$751$	576871.			1.02282			0.511409	+	0.859337i	$0.329124\pi$
$752$		−	213674.i		−	0.377847i
$753$	80539.8	−	99078.4i	0.142043	−	0.174739i
$754$	1.35767e6			2.38809
$755$		−	5270.34i		−	0.00924580i
$756$	17139.9	−	33176.9i	0.0299892	−	0.0580486i
$757$	−959951.			−1.67516			−0.837582	−	0.546311i	$-0.816032\pi$
$757$	−959951.			−1.67516			−0.837582	+	0.546311i	$0.816032\pi$
$758$		−	789137.i		−	1.37345i
$759$	−221858.	−	180346.i	−0.385115	−	0.313056i
$760$	41141.1			0.0712277
$761$			7881.85i			0.0136100i	0.999977	+	0.00680502i	$0.00216612\pi$
$761$			7881.85i			0.0136100i	−0.999977	+	0.00680502i	$0.997834\pi$
$762$	324509.	−	399204.i	0.558878	−	0.687520i
$763$	453098.			0.778293
$764$		−	73301.9i		−	0.125582i
$765$	48440.6	+	232167.i	0.0827727	+	0.396715i
$766$	−359110.			−0.612026
$767$		−	114251.i		−	0.194209i
$768$	−194510.	−	158115.i	−0.329777	−	0.268072i
$769$	−561017.			−0.948688			−0.474344	−	0.880339i	$-0.657315\pi$
$769$	−561017.			−0.948688			−0.474344	+	0.880339i	$0.657315\pi$
$770$		−	35043.1i		−	0.0591047i
$771$	455447.	−	560281.i	0.766176	−	0.942535i
$772$	−21913.4			−0.0367685
$773$		−	168175.i		−	0.281450i	−0.990049	−	0.140725i	$-0.955057\pi$
$773$		−	168175.i		−	0.281450i	0.990049	−	0.140725i	$-0.0449434\pi$
$774$	643139.	−	134188.i	1.07355	−	0.223991i
$775$	8298.04			0.0138157
$776$			737829.i			1.22527i
$777$	−105550.	−	85800.8i	−0.174831	−	0.142118i
$778$	470951.			0.778066
$779$		−	203508.i		−	0.335356i
$780$	−20380.8	+	25072.0i	−0.0334990	+	0.0412098i
$781$	−329239.			−0.539771
$782$			1.07668e6i			1.76064i
$783$	−815069.	−	421082.i	−1.32945	−	0.686821i
$784$	549523.			0.894033
$785$			1747.14i			0.00283524i
$786$	63093.8	+	51288.3i	0.102127	+	0.0830182i
$787$	−257334.			−0.415477			−0.207739	−	0.978184i	$-0.566610\pi$
$787$	−257334.			−0.415477			−0.207739	+	0.978184i	$0.566610\pi$
$788$		−	140207.i		−	0.225796i
$789$	55426.7	−	68184.8i	0.0890358	−	0.109530i
$790$	246366.			0.394754
$791$			373378.i			0.596754i
$792$	−58178.3	−	278838.i	−0.0927493	−	0.444531i
$793$	−362831.			−0.576976
$794$			585317.i			0.928432i
$795$	−132311.	−	107554.i	−0.209345	−	0.170174i
$796$	−111109.			−0.175356
$797$		−	51060.9i		−	0.0803844i	−0.999192	−	0.0401922i	$-0.987203\pi$
$797$		−	51060.9i		−	0.0803844i	0.999192	−	0.0401922i	$-0.0127970\pi$
$798$	−61380.1	+	75508.5i	−0.0963877	+	0.118574i
$799$	−353206.			−0.553266
$800$			172482.i			0.269504i
$801$	−385663.	+	80466.7i	−0.601094	+	0.125415i
$802$	−1.25888e6			−1.95720
$803$			531728.i			0.824629i
$804$	52084.7	+	42339.1i	0.0805746	+	0.0654983i
$805$	−72171.9			−0.111372
$806$			15248.7i			0.0234727i
$807$	−459185.	+	564880.i	−0.705084	+	0.867380i
$808$	−456069.			−0.698566
$809$			213692.i			0.326506i	0.986584	+	0.163253i	$0.0521987\pi$
$809$			213692.i			0.326506i	−0.986584	+	0.163253i	$0.947801\pi$
$810$	158465.	−	69135.5i	0.241525	−	0.105373i
$811$	371451.			0.564754			0.282377	−	0.959303i	$-0.408877\pi$
$811$	371451.			0.564754			0.282377	+	0.959303i	$0.408877\pi$
$812$		−	64463.8i		−	0.0977696i
$813$	−44655.6	−	36300.0i	−0.0675608	−	0.0549194i
$814$	175305.			0.264573
$815$			152104.i			0.228995i
$816$	−776483.	+	955213.i	−1.16614	+	1.43456i
$817$	−216199.			−0.323899
$818$			109975.i			0.164357i
$819$	92385.0	+	442785.i	0.137732	+	0.660123i
$820$	−25406.7			−0.0377850
$821$		−	413384.i		−	0.613293i	−0.951824	−	0.306646i	$-0.900793\pi$
$821$		−	413384.i		−	0.613293i	0.951824	−	0.306646i	$-0.0992069\pi$
$822$	244083.	+	198413.i	0.361239	+	0.293647i
$823$	−173022.			−0.255448			−0.127724	−	0.991810i	$-0.540767\pi$
$823$	−173022.			−0.255448			−0.127724	+	0.991810i	$0.540767\pi$
$824$			1.10915e6i			1.63357i
$825$	−200097.	+	246155.i	−0.293990	+	0.361660i
$826$	−42956.9			−0.0629611
$827$			408937.i			0.597923i	0.954265	+	0.298961i	$0.0966402\pi$
$827$			408937.i			0.597923i	−0.954265	+	0.298961i	$0.903360\pi$
$828$	97027.6	−	20244.3i	0.141525	−	0.0295286i
$829$	256066.			0.372600			0.186300	−	0.982493i	$-0.440350\pi$
$829$	256066.			0.372600			0.186300	+	0.982493i	$0.440350\pi$
$830$		−	199107.i		−	0.289022i
$831$	746941.	+	607181.i	1.08164	+	0.879257i
$832$	843343.			1.21831
$833$		−	908368.i		−	1.30910i
$834$	−710523.	+	874071.i	−1.02152	+	1.25665i
$835$	111115.			0.159368
$836$		−	15837.2i		−	0.0226604i
$837$	4729.40	−	9154.48i	0.00675081	−	0.0130672i
$838$	1.22148e6			1.73939
$839$			491521.i			0.698261i	0.937074	+	0.349131i	$0.113523\pi$
$839$			491521.i			0.698261i	−0.937074	+	0.349131i	$0.886477\pi$
$840$	−55793.7	−	45354.1i	−0.0790727	−	0.0642773i
$841$	−876427.			−1.23915
$842$		−	996488.i		−	1.40556i
$843$	−363305.	+	446931.i	−0.511230	+	0.628905i
$844$	103264.			0.144965
$845$		−	215497.i		−	0.301806i
$846$	52589.3	+	252051.i	0.0734779	+	0.352167i
$847$	−244461.			−0.340756
$848$		−	885028.i		−	1.23074i
$849$	510612.	+	415071.i	0.708396	+	0.575847i
$850$	1.19459e6			1.65341
$851$		−	361043.i		−	0.498540i
$852$	71995.1	−	88566.9i	0.0991799	−	0.122009i
$853$	792382.			1.08902			0.544511	−	0.838754i	$-0.316715\pi$
$853$	792382.			1.08902			0.544511	+	0.838754i	$0.316715\pi$
$854$			136420.i			0.187052i
$855$	−55694.4	+	11620.4i	−0.0761868	+	0.0158960i
$856$	680194.			0.928293
$857$		−	343873.i		−	0.468205i	−0.972212	−	0.234103i	$-0.924785\pi$
$857$		−	343873.i		−	0.468205i	0.972212	−	0.234103i	$-0.0752152\pi$
$858$	−452341.	−	367703.i	−0.614457	−	0.499486i
$859$	31963.6			0.0433181			0.0216591	−	0.999765i	$-0.493105\pi$
$859$	31963.6			0.0433181			0.0216591	+	0.999765i	$0.493105\pi$
$860$			26991.1i			0.0364942i
$861$	−224348.	+	275988.i	−0.302632	+	0.372292i
$862$	744003.			1.00129
$863$		−	1.04370e6i		−	1.40138i	−0.713467	−	0.700689i	$-0.752876\pi$
$863$		−	1.04370e6i		−	1.40138i	0.713467	−	0.700689i	$-0.247124\pi$
$864$	190284.	+	98305.0i	0.254903	+	0.131689i
$865$	−209454.			−0.279935
$866$		−	178692.i		−	0.238270i
$867$	995694.	+	809389.i	1.32461	+	1.07676i
$868$	724.028			0.000960984
$869$			561314.i			0.743304i
$870$	188258.	−	231591.i	0.248722	−	0.305973i
$871$	−813032.			−1.07170
$872$			1.19814e6i			1.57571i
$873$	−208401.	−	998830.i	−0.273446	−	1.31058i
$874$	−258283.			−0.338121
$875$			165324.i			0.215933i
$876$	−143037.	−	116273.i	−0.186398	−	0.151521i
$877$	482594.			0.627455			0.313727	−	0.949513i	$-0.398422\pi$
$877$	482594.			0.627455			0.313727	+	0.949513i	$0.398422\pi$
$878$		−	557600.i		−	0.723325i
$879$	−769726.	+	946902.i	−0.996227	+	1.22554i
$880$	106345.			0.137326
$881$		−	88682.2i		−	0.114258i	−0.998367	−	0.0571288i	$-0.981805\pi$
$881$		−	88682.2i		−	0.114258i	0.998367	−	0.0571288i	$-0.0181946\pi$
$882$	−648221.	+	135248.i	−0.833270	+	0.173858i
$883$	719406.			0.922683			0.461341	−	0.887223i	$-0.347368\pi$
$883$	719406.			0.922683			0.461341	+	0.887223i	$0.347368\pi$
$884$			277221.i			0.354749i
$885$	−19488.9	−	15842.3i	−0.0248829	−	0.0202270i
$886$	−603465.			−0.768749
$887$		−	1.29701e6i		−	1.64853i	−0.566208	−	0.824263i	$-0.691590\pi$
$887$		−	1.29701e6i		−	1.64853i	0.566208	−	0.824263i	$-0.308410\pi$
$888$	226886.	−	279111.i	0.287728	−	0.353957i
$889$	295880.			0.374379
$890$		−	128166.i		−	0.161806i
$891$	157517.	+	361043.i	0.198414	+	0.454782i
$892$	50356.5			0.0632887
$893$		−	84730.2i		−	0.106252i
$894$	225695.	+	183465.i	0.282388	+	0.229550i
$895$	−265283.			−0.331179
$896$		−	421209.i		−	0.524665i
$897$	−757290.	+	931603.i	−0.941190	+	1.15783i
$898$	−631872.			−0.783567
$899$		−	17787.5i		−	0.0220087i
$900$	−22461.5	−	107654.i	−0.0277302	−	0.132906i
$901$	−1.46296e6			−1.80212
$902$		−	458379.i		−	0.563393i
$903$	293199.	+	238339.i	0.359573	+	0.292293i
$904$	−987336.			−1.20817
$905$			81267.0i			0.0992241i
$906$	−20792.5	+	25578.5i	−0.0253308	+	0.0311615i
$907$	−1.08905e6			−1.32383			−0.661917	−	0.749577i	$-0.730257\pi$
$907$	−1.08905e6			−1.32383			−0.661917	+	0.749577i	$0.730257\pi$
$908$		−	87765.9i		−	0.106452i
$909$	617399.	−	128817.i	0.747203	−	0.155900i
$910$	−147150.			−0.177696
$911$		−	1.03194e6i		−	1.24342i	−0.783249	−	0.621708i	$-0.786439\pi$
$911$		−	1.03194e6i		−	1.24342i	0.783249	−	0.621708i	$-0.213561\pi$
$912$	−229145.	−	186270.i	−0.275500	−	0.223951i
$913$	453642.			0.544216
$914$		−	1.37756e6i		−	1.64899i
$915$	−50311.0	+	61891.6i	−0.0600926	+	0.0739247i
$916$	155492.			0.185317
$917$			46763.4i			0.0556119i
$918$	680848.	−	1.31788e6i	0.807913	−	1.56384i
$919$	636063.			0.753128			0.376564	−	0.926391i	$-0.377105\pi$
$919$	636063.			0.753128			0.376564	+	0.926391i	$0.377105\pi$
$920$		−	190847.i		−	0.225480i
$921$	−534073.	−	434142.i	−0.629624	−	0.511815i
$922$	47272.5			0.0556092
$923$			1.38251e6i			1.62280i
$924$	−17459.0	+	21477.7i	−0.0204492	+	0.0251562i
$925$	−400584.			−0.468177
$926$		−	114164.i		−	0.133140i
$927$	−313282.	−	1.50151e6i	−0.364566	−	1.74730i
$928$	369729.			0.429326
$929$		−	699770.i		−	0.810819i	−0.914135	−	0.405410i	$-0.867129\pi$
$929$		−	699770.i		−	0.810819i	0.914135	−	0.405410i	$-0.132871\pi$
$930$	2601.12	+	2114.43i	0.00300743	+	0.00244471i
$931$	217907.			0.251404
$932$		−	48406.6i		−	0.0557280i
$933$	−12792.4	+	15736.9i	−0.0146956	+	0.0180783i
$934$	495378.			0.567862
$935$		−	175790.i		−	0.201081i
$936$	−1.17087e6	+	244297.i	−1.33647	+	0.278847i
$937$	618984.			0.705018			0.352509	−	0.935808i	$-0.385329\pi$
$937$	618984.			0.705018			0.352509	+	0.935808i	$0.385329\pi$
$938$			305690.i			0.347436i
$939$	−757230.	−	615544.i	−0.858809	−	0.698116i
$940$	−10578.0			−0.0119715
$941$		−	355317.i		−	0.401270i	−0.979666	−	0.200635i	$-0.935699\pi$
$941$		−	355317.i		−	0.401270i	0.979666	−	0.200635i	$-0.0643006\pi$
$942$	6892.81	−	8479.39i	0.00776773	−	0.00955571i
$943$	−944038.			−1.06161
$944$		−	130361.i		−	0.146286i
$945$	88340.6	+	45638.7i	0.0989229	+	0.0511057i
$946$	−486965.			−0.544146
$947$		−	1.41857e6i		−	1.58179i	−0.611949	−	0.790897i	$-0.709614\pi$
$947$		−	1.41857e6i		−	1.58179i	0.611949	−	0.790897i	$-0.290386\pi$
$948$	−150996.	−	122743.i	−0.168015	−	0.136578i
$949$	2.23278e6			2.47921
$950$			286569.i			0.317528i
$951$	−147056.	+	180905.i	−0.162600	+	0.200027i
$952$	−616909.			−0.680687
$953$			1.61591e6i			1.77922i	0.456717	+	0.889612i	$0.349025\pi$
$953$			1.61591e6i			1.77922i	−0.456717	+	0.889612i	$0.650975\pi$
$954$	217823.	+	1.04399e6i	0.239335	+	1.14709i
$955$	195182.			0.214010
$956$			228067.i			0.249544i
$957$	527652.	+	428922.i	0.576134	+	0.468333i
$958$	−281110.			−0.306298
$959$			180908.i			0.196707i
$960$	116940.	−	143857.i	0.126888	−	0.156095i
$961$	−923321.			−0.999784
$962$		−	736125.i		−	0.795429i
$963$	−920807.	+	192122.i	−0.992924	+	0.207169i
$964$	28666.9			0.0308479
$965$		−	58349.2i		−	0.0626586i
$966$	350271.	+	284732.i	0.375362	+	0.305128i
$967$	1.00655e6			1.07642			0.538211	−	0.842810i	$-0.319100\pi$
$967$	1.00655e6			1.07642			0.538211	+	0.842810i	$0.319100\pi$
$968$		−	646437.i		−	0.689883i
$969$	−307906.	+	378780.i	−0.327922	+	0.403403i
$970$	331939.			0.352789
$971$			1.24879e6i			1.32449i	0.749286	+	0.662247i	$0.230397\pi$
$971$			1.24879e6i			1.32449i	−0.749286	+	0.662247i	$0.769603\pi$
$972$	−131566.	−	36576.8i	−0.139256	−	0.0387144i
$973$	−647838.			−0.684291
$974$		−	977629.i		−	1.03052i
$975$	1.03363e6	+	840227.i	1.08732	+	0.883868i
$976$	−413992.			−0.434603
$977$		−	190012.i		−	0.199063i	−0.995034	−	0.0995316i	$-0.968266\pi$
$977$		−	190012.i		−	0.199063i	0.995034	−	0.0995316i	$-0.0317344\pi$
$978$	600080.	−	738207.i	0.627381	−	0.771792i
$979$	292012.			0.304674
$980$		−	27204.4i		−	0.0283261i
$981$	−338418.	−	1.62198e6i	−0.351654	−	1.68541i
$982$	−1.10300e6			−1.14381
$983$		−	648718.i		−	0.671350i	−0.941978	−	0.335675i	$-0.891036\pi$
$983$		−	648718.i		−	0.671350i	0.941978	−	0.335675i	$-0.108964\pi$
$984$	−729804.	−	593250.i	−0.753731	−	0.612699i
$985$	373331.			0.384789
$986$		−	2.56070e6i		−	2.63393i
$987$	−93406.8	+	114907.i	−0.0958836	+	0.117954i
$988$	−66502.2			−0.0681275
$989$			1.00291e6i			1.02534i
$990$	−125446.	+	26173.6i	−0.127993	+	0.0267051i
$991$	1.28425e6			1.30769			0.653844	−	0.756630i	$-0.273155\pi$
$991$	1.28425e6			1.30769			0.653844	+	0.756630i	$0.273155\pi$
$992$			4152.63i			0.00421988i
$993$	−1.38025e6	−	1.12199e6i	−1.39977	−	1.13786i
$994$	519807.			0.526101
$995$		−	295851.i		−	0.298831i
$996$	−99198.2	+	122032.i	−0.0999966	+	0.123014i
$997$	1.27034e6			1.27800			0.639000	−	0.769207i	$-0.279348\pi$
$997$	1.27034e6			1.27800			0.639000	+	0.769207i	$0.279348\pi$
$998$		−	381848.i		−	0.383380i
$999$	−228310.	+	441928.i	−0.228767	+	0.442813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.20	✓	78
3.2	odd	2	inner	177.5.b.a.119.59	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.20	✓	78	1.1	even	1	trivial
177.5.b.a.119.59	yes	78	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.27932i q^{2} +(-6.98370 - 5.67697i) q^{3} -2.31259 q^{4} -6.15778i q^{5} +(-24.2936 + 29.8855i) q^{6} -22.1503 q^{7} -58.5728i q^{8} +(16.5440 + 79.2925i) q^{9} +O(q^{10})\)	\(q-4.27932i q^{2} +(-6.98370 - 5.67697i) q^{3} -2.31259 q^{4} -6.15778i q^{5} +(-24.2936 + 29.8855i) q^{6} -22.1503 q^{7} -58.5728i q^{8} +(16.5440 + 79.2925i) q^{9} -26.3511 q^{10} -60.0378i q^{11} +(16.1504 + 13.1285i) q^{12} -252.105 q^{13} +94.7883i q^{14} +(-34.9575 + 43.0040i) q^{15} -287.653 q^{16} +475.495i q^{17} +(339.318 - 70.7971i) q^{18} -114.066 q^{19} +14.2404i q^{20} +(154.691 + 125.747i) q^{21} -256.921 q^{22} +529.132i q^{23} +(-332.516 + 409.055i) q^{24} +587.082 q^{25} +1078.84i q^{26} +(334.603 - 647.674i) q^{27} +51.2246 q^{28} -1258.45i q^{29} +(184.028 + 149.594i) q^{30} +14.1344 q^{31} +293.796i q^{32} +(-340.833 + 419.286i) q^{33} +2034.79 q^{34} +136.397i q^{35} +(-38.2595 - 183.371i) q^{36} -682.331 q^{37} +488.125i q^{38} +(1760.62 + 1431.19i) q^{39} -360.678 q^{40} +1784.12i q^{41} +(538.110 - 661.972i) q^{42} +1895.39 q^{43} +138.843i q^{44} +(488.265 - 101.874i) q^{45} +2264.33 q^{46} +742.817i q^{47} +(2008.88 + 1633.00i) q^{48} -1910.36 q^{49} -2512.31i q^{50} +(2699.37 - 3320.71i) q^{51} +583.016 q^{52} +3076.72i q^{53} +(-2771.61 - 1431.87i) q^{54} -369.699 q^{55} +1297.41i q^{56} +(796.602 + 647.549i) q^{57} -5385.33 q^{58} +453.188i q^{59} +(80.8424 - 99.4507i) q^{60} +1439.20 q^{61} -60.4856i q^{62} +(-366.455 - 1756.35i) q^{63} -3345.21 q^{64} +1552.41i q^{65} +(1794.26 + 1458.53i) q^{66} +3224.97 q^{67} -1099.62i q^{68} +(3003.87 - 3695.30i) q^{69} +583.685 q^{70} -5483.87i q^{71} +(4644.38 - 969.029i) q^{72} -8856.56 q^{73} +2919.91i q^{74} +(-4100.00 - 3332.85i) q^{75} +263.788 q^{76} +1329.86i q^{77} +(6124.53 - 7534.28i) q^{78} -9349.35 q^{79} +1771.31i q^{80} +(-6013.59 + 2623.63i) q^{81} +7634.84 q^{82} +7555.94i q^{83} +(-357.737 - 290.801i) q^{84} +2927.99 q^{85} -8110.97i q^{86} +(-7144.21 + 8788.66i) q^{87} -3516.58 q^{88} +4863.80i q^{89} +(-435.953 - 2089.44i) q^{90} +5584.20 q^{91} -1223.67i q^{92} +(-98.7102 - 80.2405i) q^{93} +3178.75 q^{94} +702.393i q^{95} +(1667.87 - 2051.78i) q^{96} -12596.8 q^{97} +8175.06i q^{98} +(4760.54 - 993.265i) 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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