LMFDB - Embedded newform 177.6.d.b.176.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(176,177)]

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, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("177.176");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.d (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:	$28.3879361069$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.16
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.62331 q^{2} +(-4.57233 - 14.9028i) q^{3} +42.3615 q^{4} -15.6511i q^{5} +(39.4286 + 128.512i) q^{6} -96.1896 q^{7} -89.3504 q^{8} +(-201.188 + 136.281i) q^{9} +O(q^{10})$	\(q-8.62331 q^{2} +(-4.57233 - 14.9028i) q^{3} +42.3615 q^{4} -15.6511i q^{5} +(39.4286 + 128.512i) q^{6} -96.1896 q^{7} -89.3504 q^{8} +(-201.188 + 136.281i) q^{9} +134.964i q^{10} +350.338 q^{11} +(-193.691 - 631.305i) q^{12} -274.449i q^{13} +829.473 q^{14} +(-233.245 + 71.5620i) q^{15} -585.071 q^{16} -852.484i q^{17} +(1734.90 - 1175.20i) q^{18} +764.487 q^{19} -663.003i q^{20} +(439.811 + 1433.50i) q^{21} -3021.07 q^{22} +4626.49 q^{23} +(408.540 + 1331.57i) q^{24} +2880.04 q^{25} +2366.66i q^{26} +(2950.87 + 2375.14i) q^{27} -4074.74 q^{28} +4306.70i q^{29} +(2011.35 - 617.101i) q^{30} +2771.04i q^{31} +7904.47 q^{32} +(-1601.86 - 5221.02i) q^{33} +7351.23i q^{34} +1505.47i q^{35} +(-8522.61 + 5773.08i) q^{36} +7396.72i q^{37} -6592.41 q^{38} +(-4090.07 + 1254.87i) q^{39} +1398.43i q^{40} -20713.2i q^{41} +(-3792.63 - 12361.5i) q^{42} -14509.4i q^{43} +14840.8 q^{44} +(2132.95 + 3148.80i) q^{45} -39895.7 q^{46} +9944.21 q^{47} +(2675.14 + 8719.21i) q^{48} -7554.55 q^{49} -24835.5 q^{50} +(-12704.4 + 3897.84i) q^{51} -11626.1i q^{52} -18864.2i q^{53} +(-25446.3 - 20481.5i) q^{54} -5483.17i q^{55} +8594.58 q^{56} +(-3495.49 - 11393.0i) q^{57} -37138.0i q^{58} +(15029.3 + 22114.4i) q^{59} +(-9880.62 + 3031.47i) q^{60} -2330.64i q^{61} -23895.6i q^{62} +(19352.2 - 13108.8i) q^{63} -49440.4 q^{64} -4295.43 q^{65} +(13813.4 + 45022.5i) q^{66} +4248.82i q^{67} -36112.5i q^{68} +(-21153.9 - 68947.7i) q^{69} -12982.2i q^{70} -69744.9i q^{71} +(17976.2 - 12176.8i) q^{72} +44809.4i q^{73} -63784.2i q^{74} +(-13168.5 - 42920.7i) q^{75} +32384.8 q^{76} -33698.9 q^{77} +(35269.9 - 10821.2i) q^{78} -43275.7 q^{79} +9157.00i q^{80} +(21903.9 - 54836.2i) q^{81} +178616. i q^{82} -109985. q^{83} +(18631.1 + 60725.0i) q^{84} -13342.3 q^{85} +125119. i q^{86} +(64181.9 - 19691.7i) q^{87} -31302.8 q^{88} -83865.6 q^{89} +(-18393.1 - 27153.1i) q^{90} +26399.2i q^{91} +195985. q^{92} +(41296.3 - 12670.1i) q^{93} -85752.0 q^{94} -11965.0i q^{95} +(-36141.8 - 117799. i) q^{96} +27574.0i q^{97} +65145.3 q^{98} +(-70483.6 + 47744.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9}+O(q^{10}) $ 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9	$ 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9} - 1244 q^{12} + 1116 q^{15} + 14724 q^{16} + 1784 q^{19} + 6388 q^{21} - 8140 q^{22} - 48208 q^{25} - 6458 q^{27} - 19092 q^{28} - 20832 q^{36} - 134984 q^{45} + 51180 q^{46} + 61720 q^{48} + 174556 q^{49} + 8332 q^{51} + 236784 q^{57} + 375208 q^{60} - 429890 q^{63} + 561472 q^{64} - 11596 q^{66} + 169948 q^{75} + 111488 q^{76} + 356264 q^{78} + 180260 q^{79} + 79554 q^{81} + 269308 q^{84} + 111028 q^{85} - 318764 q^{87} - 1242976 q^{88} - 513608 q^{94}+O(q^{100}) $ 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9 - 1244 * q^12 + 1116 * q^15 + 14724 * q^16 + 1784 * q^19 + 6388 * q^21 - 8140 * q^22 - 48208 * q^25 - 6458 * q^27 - 19092 * q^28 - 20832 * q^36 - 134984 * q^45 + 51180 * q^46 + 61720 * q^48 + 174556 * q^49 + 8332 * q^51 + 236784 * q^57 + 375208 * q^60 - 429890 * q^63 + 561472 * q^64 - 11596 * q^66 + 169948 * q^75 + 111488 * q^76 + 356264 * q^78 + 180260 * q^79 + 79554 * q^81 + 269308 * q^84 + 111028 * q^85 - 318764 * q^87 - 1242976 * q^88 - 513608 * q^94

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 $

$2$	−8.62331			−1.52440			−0.762200	−	0.647341i	$-0.775881\pi$
$2$	−8.62331			−1.52440			−0.762200	+	0.647341i	$0.775881\pi$
$3$	−4.57233	−	14.9028i	−0.293315	−	0.956016i
$3$	−4.57233	−	14.9028i	−0.293315	−	0.956016i
$4$	42.3615			1.32380
$5$		−	15.6511i		−	0.279975i	−0.990153	−	0.139988i	$-0.955294\pi$
$5$		−	15.6511i		−	0.279975i	0.990153	−	0.139988i	$-0.0447063\pi$
$6$	39.4286	+	128.512i	0.447130	+	1.45735i
$7$	−96.1896			−0.741965			−0.370982	−	0.928640i	$-0.620979\pi$
$7$	−96.1896			−0.741965			−0.370982	+	0.928640i	$0.620979\pi$
$8$	−89.3504			−0.493596
$9$	−201.188	+	136.281i	−0.827932	+	0.560828i
$10$			134.964i			0.426794i
$11$	350.338			0.872982			0.436491	−	0.899709i	$-0.356221\pi$
$11$	350.338			0.872982			0.436491	+	0.899709i	$0.356221\pi$
$12$	−193.691	−	631.305i	−0.388290	−	1.26557i
$13$		−	274.449i		−	0.450406i	−0.974312	−	0.225203i	$-0.927696\pi$
$13$		−	274.449i		−	0.450406i	0.974312	−	0.225203i	$-0.0723045\pi$
$14$	829.473			1.13105
$15$	−233.245	+	71.5620i	−0.267661	+	0.0821210i
$16$	−585.071			−0.571359
$17$		−	852.484i		−	0.715424i	−0.933832	−	0.357712i	$-0.883557\pi$
$17$		−	852.484i		−	0.715424i	0.933832	−	0.357712i	$-0.116443\pi$
$18$	1734.90	−	1175.20i	1.26210	−	0.854926i
$19$	764.487			0.485832			0.242916	−	0.970047i	$-0.421896\pi$
$19$	764.487			0.485832			0.242916	+	0.970047i	$0.421896\pi$
$20$		−	663.003i		−	0.370630i
$21$	439.811	+	1433.50i	0.217630	+	0.709330i
$22$	−3021.07			−1.33077
$23$	4626.49			1.82361			0.911805	−	0.410623i	$-0.134689\pi$
$23$	4626.49			1.82361			0.911805	+	0.410623i	$0.134689\pi$
$24$	408.540	+	1331.57i	0.144779	+	0.471886i
$25$	2880.04			0.921614
$26$			2366.66i			0.686599i
$27$	2950.87	+	2375.14i	0.779006	+	0.627017i
$28$	−4074.74			−0.982210
$29$			4306.70i			0.950932i	0.879734	+	0.475466i	$0.157720\pi$
$29$			4306.70i			0.950932i	−0.879734	+	0.475466i	$0.842280\pi$
$30$	2011.35	−	617.101i	0.408022	−	0.125185i
$31$			2771.04i			0.517892i	0.965892	+	0.258946i	$0.0833751\pi$
$31$			2771.04i			0.517892i	−0.965892	+	0.258946i	$0.916625\pi$
$32$	7904.47			1.36458
$33$	−1601.86	−	5221.02i	−0.256059	−	0.834585i
$34$			7351.23i			1.09059i
$35$			1505.47i			0.207732i
$36$	−8522.61	+	5773.08i	−1.09601	+	0.742422i
$37$			7396.72i			0.888249i	0.895965	+	0.444124i	$0.146485\pi$
$37$			7396.72i			0.888249i	−0.895965	+	0.444124i	$0.853515\pi$
$38$	−6592.41			−0.740602
$39$	−4090.07	+	1254.87i	−0.430595	+	0.132111i
$40$			1398.43i			0.138195i
$41$		−	20713.2i		−	1.92436i	−0.272410	−	0.962181i	$-0.587821\pi$
$41$		−	20713.2i		−	1.92436i	0.272410	−	0.962181i	$-0.412179\pi$
$42$	−3792.63	−	12361.5i	−0.331755	−	1.08130i
$43$		−	14509.4i		−	1.19668i	−0.801241	−	0.598342i	$-0.795826\pi$
$43$		−	14509.4i		−	1.19668i	0.801241	−	0.598342i	$-0.204174\pi$
$44$	14840.8			1.15565
$45$	2132.95	+	3148.80i	0.157018	+	0.231800i
$46$	−39895.7			−2.77991
$47$	9944.21			0.656637			0.328319	−	0.944567i	$-0.393518\pi$
$47$	9944.21			0.656637			0.328319	+	0.944567i	$0.393518\pi$
$48$	2675.14	+	8719.21i	0.167588	+	0.546228i
$49$	−7554.55			−0.449489
$50$	−24835.5			−1.40491
$51$	−12704.4	+	3897.84i	−0.683957	+	0.209845i
$52$		−	11626.1i		−	0.596246i
$53$		−	18864.2i		−	0.922461i	−0.887280	−	0.461231i	$-0.847408\pi$
$53$		−	18864.2i		−	0.922461i	0.887280	−	0.461231i	$-0.152592\pi$
$54$	−25446.3	−	20481.5i	−1.18752	−	0.955825i
$55$		−	5483.17i		−	0.244413i
$56$	8594.58			0.366231
$57$	−3495.49	−	11393.0i	−0.142502	−	0.464463i
$58$		−	37138.0i		−	1.44960i
$59$	15029.3	+	22114.4i	0.562092	+	0.827074i
$59$	15029.3	+	22114.4i	0.562092	+	0.827074i
$60$	−9880.62	+	3031.47i	−0.354328	+	0.108711i
$61$		−	2330.64i		−	0.0801957i	−0.999196	−	0.0400978i	$-0.987233\pi$
$61$		−	2330.64i		−	0.0801957i	0.999196	−	0.0400978i	$-0.0127670\pi$
$62$		−	23895.6i		−	0.789475i
$63$	19352.2	−	13108.8i	0.614296	−	0.416115i
$64$	−49440.4			−1.50880
$65$	−4295.43			−0.126102
$66$	13813.4	+	45022.5i	0.390337	+	1.27224i
$67$			4248.82i			0.115633i	0.998327	+	0.0578165i	$0.0184138\pi$
$67$			4248.82i			0.115633i	−0.998327	+	0.0578165i	$0.981586\pi$
$68$		−	36112.5i		−	0.947076i
$69$	−21153.9	−	68947.7i	−0.534893	−	1.74340i
$70$		−	12982.2i		−	0.316666i
$71$		−	69744.9i		−	1.64197i	−0.570947	−	0.820987i	$-0.693424\pi$
$71$		−	69744.9i		−	1.64197i	0.570947	−	0.820987i	$-0.306576\pi$
$72$	17976.2	−	12176.8i	0.408664	−	0.276822i
$73$			44809.4i			0.984150i	0.870553	+	0.492075i	$0.163762\pi$
$73$			44809.4i			0.984150i	−0.870553	+	0.492075i	$0.836238\pi$
$74$		−	63784.2i		−	1.35405i
$75$	−13168.5	−	42920.7i	−0.270323	−	0.881077i
$76$	32384.8			0.643142
$77$	−33698.9			−0.647722
$78$	35269.9	−	10821.2i	0.656399	−	0.201390i
$79$	−43275.7			−0.780147			−0.390073	−	0.920784i	$-0.627550\pi$
$79$	−43275.7			−0.780147			−0.390073	+	0.920784i	$0.627550\pi$
$80$			9157.00i			0.159966i
$81$	21903.9	−	54836.2i	0.370944	−	0.928655i
$82$			178616.i			2.93350i
$83$	−109985.			−1.75242			−0.876211	−	0.481927i	$-0.839937\pi$
$83$	−109985.			−1.75242			−0.876211	+	0.481927i	$0.839937\pi$
$84$	18631.1	+	60725.0i	0.288097	+	0.939009i
$85$	−13342.3			−0.200301
$86$			125119.i			1.82423i
$87$	64181.9	−	19691.7i	0.909106	−	0.278923i
$88$	−31302.8			−0.430901
$89$	−83865.6			−1.12230			−0.561150	−	0.827714i	$-0.689641\pi$
$89$	−83865.6			−1.12230			−0.561150	+	0.827714i	$0.689641\pi$
$90$	−18393.1	−	27153.1i	−0.239358	−	0.353357i
$91$			26399.2i			0.334185i
$92$	195985.			2.41409
$93$	41296.3	−	12670.1i	0.495113	−	0.151906i
$94$	−85752.0			−1.00098
$95$		−	11965.0i		−	0.136021i
$96$	−36141.8	−	117799.i	−0.400251	−	1.30456i
$97$			27574.0i			0.297557i	0.988871	+	0.148778i	$0.0475341\pi$
$97$			27574.0i			0.297557i	−0.988871	+	0.148778i	$0.952466\pi$
$98$	65145.3			0.685201
$99$	−70483.6	+	47744.5i	−0.722770	+	0.489593i
$100$	122003.			1.22003
$101$	18455.7			0.180022			0.0900111	−	0.995941i	$-0.471310\pi$
$101$	18455.7			0.180022			0.0900111	+	0.995941i	$0.471310\pi$
$102$	109554.	−	33612.3i	1.04262	−	0.319888i
$103$		−	65878.4i		−	0.611857i	−0.952055	−	0.305928i	$-0.901033\pi$
$103$		−	65878.4i		−	0.611857i	0.952055	−	0.305928i	$-0.0989668\pi$
$104$			24522.2i			0.222318i
$105$	22435.8	−	6883.52i	0.198595	−	0.0609309i
$106$			162672.i			1.40620i
$107$			82467.5i			0.696344i	0.937431	+	0.348172i	$0.113197\pi$
$107$			82467.5i			0.696344i	−0.937431	+	0.348172i	$0.886803\pi$
$108$	125003.	+	100614.i	1.03125	+	0.830043i
$109$			21260.6i			0.171400i	0.996321	+	0.0856998i	$0.0273126\pi$
$109$			21260.6i			0.171400i	−0.996321	+	0.0856998i	$0.972687\pi$
$110$			47283.1i			0.372584i
$111$	110232.	−	33820.2i	0.849180	−	0.260537i
$112$	56277.8			0.423928
$113$	136138.			1.00296			0.501481	−	0.865168i	$-0.332789\pi$
$113$	136138.			1.00296			0.501481	+	0.865168i	$0.332789\pi$
$114$	30142.7	+	98245.4i	0.217230	+	0.708027i
$115$		−	72409.6i		−	0.510566i
$116$			182438.i			1.25884i
$117$	37402.3	+	55215.8i	0.252600	+	0.372905i
$118$	−129602.	−	190699.i	−0.856854	−	1.26079i
$119$			82000.1i			0.530820i
$120$	20840.6	−	6394.09i	0.132116	−	0.0405346i
$121$	−38314.3			−0.237902
$122$			20097.9i			0.122250i
$123$	−308684.	+	94707.5i	−1.83972	+	0.564445i
$124$			117386.i			0.685584i
$125$		−	93985.5i		−	0.538004i
$126$	−166880.	+	113042.i	−0.936434	+	0.634325i
$127$	116559.			0.641265			0.320632	−	0.947204i	$-0.396105\pi$
$127$	116559.			0.641265			0.320632	+	0.947204i	$0.396105\pi$
$128$	173397.			0.935441
$129$	−216231.	+	66342.0i	−1.14405	+	0.351006i
$130$	37040.8			0.192231
$131$	−145699.			−0.741783			−0.370892	−	0.928676i	$-0.620948\pi$
$131$	−145699.			−0.741783			−0.370892	+	0.928676i	$0.620948\pi$
$132$	−67857.3	−	221170.i	−0.338970	−	1.10482i
$133$	−73535.7			−0.360470
$134$		−	36638.9i		−	0.176271i
$135$	37173.5	−	46184.3i	0.175549	−	0.218102i
$136$			76169.8i			0.353131i
$137$		−	241219.i		−	1.09802i	−0.835816	−	0.549009i	$-0.815005\pi$
$137$		−	241219.i		−	1.09802i	0.835816	−	0.549009i	$-0.184995\pi$
$138$	182416.	+	594558.i	0.815391	+	2.65764i
$139$	122912.			0.539580			0.269790	−	0.962919i	$-0.413046\pi$
$139$	122912.			0.539580			0.269790	+	0.962919i	$0.413046\pi$
$140$			63774.1i			0.274994i
$141$	−45468.2	−	148197.i	−0.192602	−	0.627756i
$142$			601432.i			2.50303i
$143$		−	96150.0i		−	0.393196i
$144$	117709.	−	79734.2i	0.473046	−	0.320434i
$145$	67404.5			0.266237
$146$		−	386405.i		−	1.50024i
$147$	34541.9	+	112584.i	0.131842	+	0.429718i
$148$			313336.i			1.17586i
$149$	243124.			0.897144			0.448572	−	0.893747i	$-0.351933\pi$
$149$	243124.			0.897144			0.448572	+	0.893747i	$0.351933\pi$
$150$	113556.	+	370119.i	0.412081	+	1.34311i
$151$		−	332950.i		−	1.18833i	−0.804343	−	0.594165i	$-0.797483\pi$
$151$		−	332950.i		−	1.18833i	0.804343	−	0.594165i	$-0.202517\pi$
$152$	−68307.2			−0.239805
$153$	116177.	+	171509.i	0.401230	+	0.592323i
$154$	290596.			0.987388
$155$	43369.8			0.144997
$156$	−173261.	+	53158.3i	−0.570020	+	0.174888i
$157$		−	255785.i		−	0.828182i	−0.910236	−	0.414091i	$-0.864100\pi$
$157$		−	255785.i		−	0.828182i	0.910236	−	0.414091i	$-0.135900\pi$
$158$	373180.			1.18926
$159$	−281129.	+	86253.3i	−0.881887	+	0.270572i
$160$		−	123713.i		−	0.382047i
$161$	−445021.			−1.35305
$162$	−188884.	+	472869.i	−0.565467	+	1.41564i
$163$	−46565.4			−0.137276			−0.0686380	−	0.997642i	$-0.521865\pi$
$163$	−46565.4			−0.137276			−0.0686380	+	0.997642i	$0.521865\pi$
$164$		−	877441.i		−	2.54746i
$165$	−81714.7	+	25070.9i	−0.233663	+	0.0716902i
$166$	948436.			2.67139
$167$		−	325845.i		−	0.904106i	−0.891991	−	0.452053i	$-0.850692\pi$
$167$		−	325845.i		−	0.904106i	0.891991	−	0.452053i	$-0.149308\pi$
$168$	−39297.3	−	128083.i	−0.107421	−	0.350122i
$169$	295971.			0.797135
$170$	115055.			0.305339
$171$	−153805.	+	104185.i	−0.402236	+	0.272468i
$172$		−	614642.i		−	1.58417i
$173$	244902.			0.622125			0.311063	−	0.950389i	$-0.399315\pi$
$173$	244902.			0.622125			0.311063	+	0.950389i	$0.399315\pi$
$174$	−553461.	+	169807.i	−1.38584	+	0.425190i
$175$	−277030.			−0.683805
$176$	−204973.			−0.498786
$177$	260848.	−	325093.i	0.625826	−	0.779963i
$178$	723199.			1.71083
$179$	−514091.			−1.19924			−0.599622	−	0.800283i	$-0.704682\pi$
$179$	−514091.			−1.19924			−0.599622	+	0.800283i	$0.704682\pi$
$180$	90354.9	+	133388.i	0.207860	+	0.306857i
$181$	−38977.1			−0.0884327			−0.0442163	−	0.999022i	$-0.514079\pi$
$181$	−38977.1			−0.0884327			−0.0442163	+	0.999022i	$0.514079\pi$
$182$		−	227648.i		−	0.509432i
$183$	−34733.1	+	10656.5i	−0.0766683	+	0.0235226i
$184$	−413379.			−0.900127
$185$	115767.			0.248688
$186$	−356111.	+	109258.i	−0.754750	+	0.231565i
$187$		−	298657.i		−	0.624553i
$188$	421252.			0.869254
$189$	−283843.	−	228464.i	−0.577995	−	0.465224i
$190$			103178.i			0.207350i
$191$	411306.			0.815796			0.407898	−	0.913028i	$-0.366262\pi$
$191$	411306.			0.815796			0.407898	+	0.913028i	$0.366262\pi$
$192$	226058.	+	736801.i	0.442554	+	1.44244i
$193$	162426.			0.313879			0.156940	−	0.987608i	$-0.449837\pi$
$193$	162426.			0.313879			0.156940	+	0.987608i	$0.449837\pi$
$194$		−	237779.i		−	0.453596i
$195$	19640.1	+	64014.0i	0.0369878	+	0.120556i
$196$	−320022.			−0.595031
$197$			13331.7i			0.0244749i	0.999925	+	0.0122375i	$0.00389540\pi$
$197$			13331.7i			0.0244749i	−0.999925	+	0.0122375i	$0.996105\pi$
$198$	607802.	−	411716.i	1.10179	−	0.746336i
$199$	−997443.			−1.78548			−0.892741	−	0.450570i	$-0.851221\pi$
$199$	−997443.			−1.78548			−0.892741	+	0.450570i	$0.851221\pi$
$200$	−257333.			−0.454905
$201$	63319.4	−	19427.0i	0.110547	−	0.0339169i
$202$	−159149.			−0.274426
$203$		−	414260.i		−	0.705558i
$204$	−538177.	+	165118.i	−0.905420	+	0.277792i
$205$	−324184.			−0.538774
$206$			568090.i			0.932715i
$207$	−930792.	+	630504.i	−1.50983	+	1.02273i
$208$			160573.i			0.257343i
$209$	267829.			0.424123
$210$	−193471.	+	59358.7i	−0.302738	+	0.0928830i
$211$		−	1.26844e6i		−	1.96138i	−0.195565	−	0.980691i	$-0.562654\pi$
$211$		−	1.26844e6i		−	1.96138i	0.195565	−	0.980691i	$-0.437346\pi$
$212$		−	799115.i		−	1.22115i
$213$	−1.03939e6	+	318897.i	−1.56975	+	0.481616i
$214$		−	711143.i		−	1.06151i
$215$	−227088.			−0.335042
$216$	−263661.	−	212220.i	−0.384514	−	0.309493i
$217$		−	266546.i		−	0.384257i
$218$		−	183337.i		−	0.261282i
$219$	667785.	−	204883.i	0.940863	−	0.288666i
$220$		−	232275.i		−	0.323554i
$221$	−233964.			−0.322231
$222$	−950564.	+	291643.i	−1.29449	+	0.397163i
$223$	−38038.8			−0.0512230			−0.0256115	−	0.999672i	$-0.508153\pi$
$223$	−38038.8			−0.0512230			−0.0256115	+	0.999672i	$0.508153\pi$
$224$	−760328.			−1.01247
$225$	−579429.	+	392496.i	−0.763034	+	0.516867i
$226$	−1.17396e6			−1.52892
$227$	774403.			0.997475			0.498738	−	0.866753i	$-0.333797\pi$
$227$	774403.			0.997475			0.498738	+	0.866753i	$0.333797\pi$
$228$	−148074.	−	482624.i	−0.188643	−	0.614854i
$229$			444152.i			0.559684i	0.960046	+	0.279842i	$0.0902820\pi$
$229$			444152.i			0.559684i	−0.960046	+	0.279842i	$0.909718\pi$
$230$			624411.i			0.778307i
$231$	154082.	+	502208.i	0.189987	+	0.619233i
$232$		−	384805.i		−	0.469376i
$233$	1.08612e6			1.31066			0.655328	−	0.755345i	$-0.272530\pi$
$233$	1.08612e6			1.31066			0.655328	+	0.755345i	$0.272530\pi$
$234$	−322532.	−	476143.i	−0.385064	−	0.568457i
$235$		−	155638.i		−	0.183842i
$236$	636662.	+	936798.i	0.744096	+	1.09488i
$237$	197871.	+	644929.i	0.228829	+	0.745833i
$238$		−	707112.i		−	0.809182i
$239$			96829.0i			0.109651i	0.998496	+	0.0548253i	$0.0174602\pi$
$239$			96829.0i			0.109651i	−0.998496	+	0.0548253i	$0.982540\pi$
$240$	136465.	−	41868.9i	0.152930	−	0.0469205i
$241$	−574811.			−0.637504			−0.318752	−	0.947838i	$-0.603264\pi$
$241$	−574811.			−0.637504			−0.318752	+	0.947838i	$0.603264\pi$
$242$	330396.			0.362657
$243$	−917365.	−	75700.0i	−0.996613	−	0.0822395i
$244$		−	98729.5i		−	0.106163i
$245$			118237.i			0.125846i
$246$	2.66188e6	−	816692.i	2.80447	−	0.860440i
$247$		−	209813.i		−	0.218821i
$248$		−	247594.i		−	0.255629i
$249$	502889.	+	1.63909e6i	0.514012	+	1.67534i
$250$			810466.i			0.820134i
$251$			594217.i			0.595334i	0.954670	+	0.297667i	$0.0962085\pi$
$251$			594217.i			0.595334i	−0.954670	+	0.297667i	$0.903792\pi$
$252$	819786.	−	555310.i	0.813204	−	0.550851i
$253$	1.62084e6			1.59198
$254$	−1.00513e6			−0.977544
$255$	61005.4	+	198838.i	0.0587513	+	0.191491i
$256$	86836.7			0.0828139
$257$			1.81712e6i			1.71614i	0.513535	+	0.858069i	$0.328336\pi$
$257$			1.81712e6i			1.71614i	−0.513535	+	0.858069i	$0.671664\pi$
$258$	1.86463e6	−	572088.i	1.74399	−	0.535073i
$259$		−	711488.i		−	0.659049i
$260$	−181961.			−0.166934
$261$	−586922.	−	866454.i	−0.533309	−	0.787307i
$262$	1.25640e6			1.13077
$263$		−	166247.i		−	0.148205i	−0.997251	−	0.0741026i	$-0.976391\pi$
$263$		−	166247.i		−	0.148205i	0.997251	−	0.0741026i	$-0.0236092\pi$
$264$	143127.	+	466500.i	0.126390	+	0.411948i
$265$	−295245.			−0.258266
$266$	634121.			0.549501
$267$	383461.	+	1.24983e6i	0.329188	+	1.07294i
$268$			179986.i			0.153075i
$269$	1.12035e6			0.944003			0.472001	−	0.881598i	$-0.343532\pi$
$269$	1.12035e6			0.944003			0.472001	+	0.881598i	$0.343532\pi$
$270$	−320558.	+	398262.i	−0.267607	+	0.332475i
$271$	−434153.			−0.359103			−0.179552	−	0.983749i	$-0.557465\pi$
$271$	−434153.			−0.359103			−0.179552	+	0.983749i	$0.557465\pi$
$272$			498764.i			0.408764i
$273$	393422.	−	120706.i	0.319486	−	0.0980216i
$274$			2.08010e6i			1.67382i
$275$	1.00899e6			0.804553
$276$	−896109.	−	2.92073e6i	−0.708089	−	2.30791i
$277$	234261.			0.183442			0.0917212	−	0.995785i	$-0.470763\pi$
$277$	234261.			0.183442			0.0917212	+	0.995785i	$0.470763\pi$
$278$	−1.05990e6			−0.822536
$279$	−377641.	−	557499.i	−0.290448	−	0.428779i
$280$		−	134515.i		−	0.102536i
$281$		−	1.68698e6i		−	1.27451i	−0.770653	−	0.637256i	$-0.780070\pi$
$281$		−	1.68698e6i		−	1.27451i	0.770653	−	0.637256i	$-0.219930\pi$
$282$	392087.	+	1.27795e6i	0.293602	+	0.956951i
$283$		−	932461.i		−	0.692093i	−0.938217	−	0.346047i	$-0.887524\pi$
$283$		−	932461.i		−	0.692093i	0.938217	−	0.346047i	$-0.112476\pi$
$284$		−	2.95450e6i		−	2.17364i
$285$	−178313.	+	54708.2i	−0.130038	+	0.0398970i
$286$			829132.i			0.599389i
$287$			1.99239e6i			1.42781i
$288$	−1.59028e6	+	1.07723e6i	−1.12978	+	0.765292i
$289$	693129.			0.488168
$290$	−581250.			−0.405852
$291$	410930.	−	126077.i	0.284469	−	0.0872780i
$292$			1.89819e6i			1.30282i
$293$		−	2.30802e6i		−	1.57062i	−0.619103	−	0.785310i	$-0.712504\pi$
$293$		−	2.30802e6i		−	1.57062i	0.619103	−	0.785310i	$-0.287496\pi$
$294$	−297866.	−	970848.i	−0.200980	−	0.655063i
$295$	346114.	−	235224.i	0.231560	−	0.157372i
$296$		−	660900.i		−	0.438436i
$297$	1.03380e6	+	832101.i	0.680058	+	0.547375i
$298$	−2.09653e6			−1.36761
$299$		−	1.26974e6i		−	0.821365i
$300$	−557838.	−	1.81819e6i	−0.357853	−	1.16637i
$301$			1.39566e6i			0.887897i
$302$			2.87113e6i			1.81149i
$303$	−84385.4	−	275041.i	−0.0528032	−	0.172104i
$304$	−447279.			−0.277584
$305$	−36477.1			−0.0224528
$306$	−1.00183e6	−	1.47898e6i	−0.611635	−	0.902937i
$307$	−1.65134e6			−0.999978			−0.499989	−	0.866032i	$-0.666663\pi$
$307$	−1.65134e6			−0.999978			−0.499989	+	0.866032i	$0.666663\pi$
$308$	−1.42754e6			−0.857452
$309$	−981773.	+	301218.i	−0.584945	+	0.179467i
$310$	−373992.			−0.221033
$311$			1.37371e6i			0.805365i	0.915340	+	0.402682i	$0.131922\pi$
$311$			1.37371e6i			0.805365i	−0.915340	+	0.402682i	$0.868078\pi$
$312$	365449.	−	112123.i	0.212540	−	0.0652094i
$313$		−	2.41493e6i		−	1.39330i	−0.717413	−	0.696648i	$-0.754674\pi$
$313$		−	2.41493e6i		−	1.39330i	0.717413	−	0.696648i	$-0.245326\pi$
$314$			2.20571e6i			1.26248i
$315$	−205168.	−	302882.i	−0.116502	−	0.171988i
$316$	−1.83322e6			−1.03276
$317$		−	2.08853e6i		−	1.16733i	−0.811995	−	0.583664i	$-0.801619\pi$
$317$		−	2.08853e6i		−	1.16733i	0.811995	−	0.583664i	$-0.198381\pi$
$318$	2.42426e6	−	743789.i	1.34435	−	0.412460i
$319$			1.50880e6i			0.830147i
$320$			773796.i			0.422427i
$321$	1.22900e6	−	377069.i	0.665716	−	0.204248i
$322$	3.83755e6			2.06260
$323$		−	651712.i		−	0.347576i
$324$	927881.	−	2.32294e6i	0.491054	−	1.22935i
$325$		−	790426.i		−	0.415100i
$326$	401548.			0.209264
$327$	316843.	−	97210.7i	0.163861	−	0.0502741i
$328$			1.85073e6i			0.949857i
$329$	−956530.			−0.487202
$330$	704651.	−	216194.i	0.356196	−	0.109285i
$331$	−599565.			−0.300792			−0.150396	−	0.988626i	$-0.548055\pi$
$331$	−599565.			−0.300792			−0.150396	+	0.988626i	$0.548055\pi$
$332$	−4.65914e6			−2.31985
$333$	−1.00803e6	−	1.48813e6i	−0.498155	−	0.735410i
$334$			2.80986e6i			1.37822i
$335$	66498.7			0.0323743
$336$	−257321.	−	838698.i	−0.124345	−	0.405282i
$337$			389127.i			0.186645i	0.995636	+	0.0933227i	$0.0297488\pi$
$337$			389127.i			0.186645i	−0.995636	+	0.0933227i	$0.970251\pi$
$338$	−2.55225e6			−1.21515
$339$	−622470.	−	2.02885e6i	−0.294184	−	0.958848i
$340$	−565200.			−0.265158
$341$			970802.i			0.452111i
$342$	1.32631e6	−	898421.i	0.613168	−	0.415350i
$343$	2.34333e6			1.07547
$344$			1.29642e6i			0.590678i
$345$	−1.07911e6	+	331081.i	−0.488109	+	0.149757i
$346$	−2.11187e6			−0.948368
$347$	−1.15354e6			−0.514289			−0.257144	−	0.966373i	$-0.582782\pi$
$347$	−1.15354e6			−0.514289			−0.257144	+	0.966373i	$0.582782\pi$
$348$	2.71884e6	−	834168.i	1.20347	−	0.369237i
$349$		−	2.19216e6i		−	0.963405i	−0.876335	−	0.481703i	$-0.840019\pi$
$349$		−	2.19216e6i		−	0.963405i	0.876335	−	0.481703i	$-0.159981\pi$
$350$	2.38892e6			1.04239
$351$	651855.	−	809864.i	0.282412	−	0.350869i
$352$	2.76923e6			1.19125
$353$	1.67958e6			0.717405			0.358702	−	0.933452i	$-0.383219\pi$
$353$	1.67958e6			0.717405			0.358702	+	0.933452i	$0.383219\pi$
$354$	−2.24937e6	+	2.80337e6i	−0.954009	+	1.18898i
$355$	−1.09158e6			−0.459712
$356$	−3.55267e6			−1.48570
$357$	1.22203e6	−	374932.i	0.507472	−	0.155697i
$358$	4.43317e6			1.82813
$359$			1.36229e6i			0.557872i	0.960310	+	0.278936i	$0.0899818\pi$
$359$			1.36229e6i			0.557872i	−0.960310	+	0.278936i	$0.910018\pi$
$360$	−190580.	−	281347.i	−0.0775034	−	0.114416i
$361$	−1.89166e6			−0.763968
$362$	336111.			0.134807
$363$	175186.	+	570991.i	0.0697802	+	0.227438i
$364$			1.11831e6i			0.442393i
$365$	701315.			0.275538
$366$	299515.	−	91894.1i	0.116873	−	0.0358579i
$367$			2.94384e6i			1.14091i	0.821330	+	0.570453i	$0.193232\pi$
$367$			2.94384e6i			1.14091i	−0.821330	+	0.570453i	$0.806768\pi$
$368$	−2.70683e6			−1.04194
$369$	2.82282e6	+	4.16723e6i	1.07924	+	1.59324i
$370$	−998292.			−0.379100
$371$			1.81454e6i			0.684434i
$372$	1.74937e6	−	536726.i	0.655429	−	0.201092i
$373$	4.37376e6			1.62773			0.813866	−	0.581052i	$-0.197359\pi$
$373$	4.37376e6			1.62773			0.813866	+	0.581052i	$0.197359\pi$
$374$			2.57542e6i			0.952069i
$375$	−1.40065e6	+	429733.i	−0.514340	+	0.157805i
$376$	−888519.			−0.324114
$377$	1.18197e6			0.428305
$378$	2.44767e6	+	1.97011e6i	0.881095	+	0.709188i
$379$	1.01380e6			0.362537			0.181269	−	0.983434i	$-0.441980\pi$
$379$	1.01380e6			0.362537			0.181269	+	0.983434i	$0.441980\pi$
$380$		−	506857.i		−	0.180064i
$381$	−532947.	−	1.73706e6i	−0.188093	−	0.613059i
$382$	−3.54682e6			−1.24360
$383$		−	230361.i		−	0.0802439i	−0.999195	−	0.0401220i	$-0.987225\pi$
$383$		−	230361.i		−	0.0802439i	0.999195	−	0.0401220i	$-0.0127746\pi$
$384$	−792828.	−	2.58410e6i	−0.274379	−	0.894297i
$385$			527424.i			0.181346i
$386$	−1.40065e6			−0.478477
$387$	1.97736e6	+	2.91912e6i	0.671134	+	0.990773i
$388$			1.16807e6i			0.393905i
$389$		−	5.12823e6i		−	1.71828i	−0.511743	−	0.859138i	$-0.671000\pi$
$389$		−	5.12823e6i		−	1.71828i	0.511743	−	0.859138i	$-0.329000\pi$
$390$	−169363.	−	552013.i	−0.0563842	−	0.183775i
$391$		−	3.94401e6i		−	1.30466i
$392$	675003.			0.221866
$393$	666182.	+	2.17132e6i	0.217576	+	0.709156i
$394$		−	114964.i		−	0.0373096i
$395$			677312.i			0.218422i
$396$	−2.98579e6	+	2.02253e6i	−0.956801	+	0.648122i
$397$			4.84182e6i			1.54182i	0.636946	+	0.770908i	$0.280197\pi$
$397$			4.84182e6i			1.54182i	−0.636946	+	0.770908i	$0.719803\pi$
$398$	8.60126e6			2.72179
$399$	336230.	+	1.09589e6i	0.105731	+	0.344615i
$400$	−1.68503e6			−0.526572
$401$	433851.			0.134735			0.0673674	−	0.997728i	$-0.478540\pi$
$401$	433851.			0.134735			0.0673674	+	0.997728i	$0.478540\pi$
$402$	−546023.	+	167525.i	−0.168518	+	0.0517029i
$403$	760511.			0.233261
$404$	781809.			0.238313
$405$	−858246.	−	342819.i	−0.260000	−	0.103855i
$406$			3.57229e6i			1.07555i
$407$			2.59135e6i			0.775426i
$408$	1.13514e6	−	348273.i	0.337598	−	0.103579i
$409$			5.76995e6i			1.70555i	0.522280	+	0.852774i	$0.325081\pi$
$409$			5.76995e6i			1.70555i	−0.522280	+	0.852774i	$0.674919\pi$
$410$	2.79554e6			0.821307
$411$	−3.59484e6	+	1.10293e6i	−1.04972	+	0.322065i
$412$		−	2.79071e6i		−	0.809974i
$413$	−1.44566e6	−	2.12717e6i	−0.417053	−	0.613660i
$414$	8.02651e6	−	5.43703e6i	2.30158	−	1.55905i
$415$			1.72139e6i			0.490635i
$416$		−	2.16938e6i		−	0.614613i
$417$	−561992.	−	1.83173e6i	−0.158267	−	0.515847i
$418$	−2.30957e6			−0.646533
$419$	−3.15128e6			−0.876904			−0.438452	−	0.898755i	$-0.644473\pi$
$419$	−3.15128e6			−0.876904			−0.438452	+	0.898755i	$0.644473\pi$
$420$	950413.	−	291596.i	0.262899	−	0.0806601i
$421$		−	6.24640e6i		−	1.71761i	−0.512302	−	0.858806i	$-0.671207\pi$
$421$		−	6.24640e6i		−	1.71761i	0.512302	−	0.858806i	$-0.328793\pi$
$422$			1.09381e7i			2.98993i
$423$	−2.00065e6	+	1.35521e6i	−0.543651	+	0.368261i
$424$			1.68552e6i			0.455323i
$425$		−	2.45519e6i		−	0.659345i
$426$	8.96302e6	−	2.74995e6i	2.39293	−	0.734176i
$427$			224184.i			0.0595024i
$428$			3.49345e6i			0.921818i
$429$	−1.43291e6	+	439630.i	−0.375902	+	0.115330i
$430$	1.95825e6			0.510738
$431$	−4.95326e6			−1.28439			−0.642196	−	0.766540i	$-0.721977\pi$
$431$	−4.95326e6			−1.28439			−0.642196	+	0.766540i	$0.721977\pi$
$432$	−1.72647e6	−	1.38963e6i	−0.445092	−	0.358252i
$433$	−3.42411e6			−0.877663			−0.438832	−	0.898569i	$-0.644608\pi$
$433$	−3.42411e6			−0.877663			−0.438832	+	0.898569i	$0.644608\pi$
$434$			2.29851e6i			0.585762i
$435$	−308196.	−	1.00452e6i	−0.0780915	−	0.254527i
$436$			900632.i			0.226898i
$437$	3.53689e6			0.885968
$438$	−5.75852e6	+	1.76677e6i	−1.43425	+	0.440043i
$439$	957857.			0.237213			0.118607	−	0.992941i	$-0.462157\pi$
$439$	957857.			0.237213			0.118607	+	0.992941i	$0.462157\pi$
$440$			489924.i			0.120641i
$441$	1.51988e6	−	1.02954e6i	0.372146	−	0.252086i
$442$	2.01754e6			0.491209
$443$	−3.67193e6			−0.888967			−0.444484	−	0.895787i	$-0.646613\pi$
$443$	−3.67193e6			−0.888967			−0.444484	+	0.895787i	$0.646613\pi$
$444$	4.66959e6	−	1.43268e6i	1.12414	−	0.344898i
$445$			1.31259e6i			0.314216i
$446$	328021.			0.0780843
$447$	−1.11164e6	−	3.62323e6i	−0.263146	−	0.857684i
$448$	4.75565e6			1.11948
$449$			3.99551e6i			0.935312i	0.883911	+	0.467656i	$0.154901\pi$
$449$			3.99551e6i			0.935312i	−0.883911	+	0.467656i	$0.845099\pi$
$450$	4.99660e6	−	3.38461e6i	1.16317	−	0.787912i
$451$		−	7.25661e6i		−	1.67993i
$452$	5.76703e6			1.32772
$453$	−4.96190e6	+	1.52236e6i	−1.13606	+	0.348555i
$454$	−6.67792e6			−1.52055
$455$	413176.			0.0935635
$456$	312323.	+	1.01797e6i	0.0703383	+	0.229257i
$457$		−	2.61120e6i		−	0.584858i	−0.956287	−	0.292429i	$-0.905536\pi$
$457$		−	2.61120e6i		−	0.584858i	0.956287	−	0.292429i	$-0.0944635\pi$
$458$		−	3.83006e6i		−	0.853182i
$459$	2.02477e6	−	2.51557e6i	0.448583	−	0.557320i
$460$		−	3.06738e6i		−	0.675885i
$461$			1.79955e6i			0.394378i	0.980366	+	0.197189i	$0.0631812\pi$
$461$			1.79955e6i			0.394378i	−0.980366	+	0.197189i	$0.936819\pi$
$462$	−1.32870e6	−	4.33070e6i	−0.289616	−	0.943958i
$463$			182590.i			0.0395844i	0.999804	+	0.0197922i	$0.00630047\pi$
$463$			182590.i			0.0395844i	−0.999804	+	0.0197922i	$0.993700\pi$
$464$		−	2.51973e6i		−	0.543323i
$465$	−198301.	−	646333.i	−0.0425298	−	0.138619i
$466$	−9.36596e6			−1.99796
$467$	4.66007e6			0.988781			0.494390	−	0.869240i	$-0.335391\pi$
$467$	4.66007e6			0.988781			0.494390	+	0.869240i	$0.335391\pi$
$468$	1.58442e6	+	2.33902e6i	0.334391	+	0.493651i
$469$		−	408693.i		−	0.0857955i
$470$			1.34211e6i			0.280249i
$471$	−3.81191e6	+	1.16953e6i	−0.791755	+	0.242918i
$472$	−1.34287e6	−	1.97593e6i	−0.277447	−	0.408241i
$473$		−	5.08321e6i		−	1.04468i
$474$	−1.70630e6	−	5.56143e6i	−0.348827	−	1.13695i
$475$	2.20175e6			0.447749
$476$			3.47365e6i			0.702697i
$477$	2.57083e6	+	3.79524e6i	0.517342	+	0.763735i
$478$		−	834987.i		−	0.167151i
$479$		−	3.00565e6i		−	0.598548i	−0.954167	−	0.299274i	$-0.903256\pi$
$479$		−	3.00565e6i		−	0.598548i	0.954167	−	0.299274i	$-0.0967445\pi$
$480$	−1.84368e6	+	565659.i	−0.365243	+	0.112060i
$481$	2.03002e6			0.400072
$482$	4.95678e6			0.971811
$483$	2.03478e6	+	6.63206e6i	0.396872	+	1.29354i
$484$	−1.62305e6			−0.314933
$485$	431563.			0.0833085
$486$	7.91072e6	+	652785.i	1.51924	+	0.125366i
$487$	−3.26398e6			−0.623627			−0.311813	−	0.950143i	$-0.600936\pi$
$487$	−3.26398e6			−0.623627			−0.311813	+	0.950143i	$0.600936\pi$
$488$			208244.i			0.0395843i
$489$	212913.	+	693956.i	0.0402651	+	0.131238i
$490$		−	1.01959e6i		−	0.191839i
$491$		−	7.79526e6i		−	1.45924i	−0.683852	−	0.729620i	$-0.739697\pi$
$491$		−	7.79526e6i		−	1.45924i	0.683852	−	0.729620i	$-0.260303\pi$
$492$	−1.30763e7	+	4.01195e6i	−2.43542	+	0.747210i
$493$	3.67139e6			0.680320
$494$			1.80928e6i			0.333571i
$495$	747253.	+	1.10315e6i	0.137074	+	0.202358i
$496$		−	1.62126e6i		−	0.295902i
$497$			6.70873e6i			1.21829i
$498$	−4.33657e6	−	1.41344e7i	−0.783561	−	2.55389i
$499$	−6.33385e6			−1.13872			−0.569359	−	0.822089i	$-0.692809\pi$
$499$	−6.33385e6			−1.13872			−0.569359	+	0.822089i	$0.692809\pi$
$500$		−	3.98136e6i		−	0.712208i
$501$	−4.85600e6	+	1.48987e6i	−0.864340	+	0.265188i
$502$		−	5.12412e6i		−	0.907527i
$503$	−8.49659e6			−1.49736			−0.748678	−	0.662934i	$-0.769311\pi$
$503$	−8.49659e6			−1.49736			−0.748678	+	0.662934i	$0.769311\pi$
$504$	−1.72912e6	+	1.17128e6i	−0.303214	+	0.205392i
$505$		−	288851.i		−	0.0504017i
$506$	−1.39770e7			−2.42682
$507$	−1.35328e6	−	4.41079e6i	−0.233812	−	0.762073i
$508$	4.93762e6			0.848904
$509$	−8.30576e6			−1.42097			−0.710485	−	0.703713i	$-0.751524\pi$
$509$	−8.30576e6			−1.42097			−0.710485	+	0.703713i	$0.751524\pi$
$510$	−526069.	−	1.71464e6i	−0.0895606	−	0.291909i
$511$		−	4.31020e6i		−	0.730205i
$512$	−6.29752e6			−1.06168
$513$	2.25590e6	+	1.81576e6i	0.378466	+	0.304625i
$514$		−	1.56696e7i		−	2.61608i
$515$	−1.03107e6			−0.171305
$516$	−9.15989e6	+	2.81035e6i	−1.51449	+	0.464660i
$517$	3.48383e6			0.573233
$518$			6.13538e6i			1.00466i
$519$	−1.11977e6	−	3.64973e6i	−0.182479	−	0.594761i
$520$	383799.			0.0622436
$521$			8.67596e6i			1.40031i	0.713993	+	0.700153i	$0.246885\pi$
$521$			8.67596e6i			1.40031i	−0.713993	+	0.700153i	$0.753115\pi$
$522$	5.06121e6	+	7.47170e6i	0.812977	+	1.20017i
$523$	1.07225e6			0.171412			0.0857059	−	0.996320i	$-0.472685\pi$
$523$	1.07225e6			0.171412			0.0857059	+	0.996320i	$0.472685\pi$
$524$	−6.17201e6			−0.981970
$525$	1.26667e6	+	4.12853e6i	0.200570	+	0.653728i
$526$			1.43360e6i			0.225924i
$527$	2.36227e6			0.370512
$528$	937204.	+	3.05467e6i	0.146302	+	0.476848i
$529$	1.49681e7			2.32556
$530$	2.54599e6			0.393701
$531$	−6.03747e6	−	2.40093e6i	−0.929221	−	0.369524i
$532$	−3.11508e6			−0.477189
$533$	−5.68472e6			−0.866744
$534$	−3.30671e6	−	1.07777e7i	−0.501814	−	1.63558i
$535$	1.29071e6			0.194959
$536$		−	379634.i		−	0.0570760i
$537$	2.35060e6	+	7.66141e6i	0.351757	+	1.14650i
$538$	−9.66113e6			−1.43904
$539$	−2.64665e6			−0.392396
$540$	1.57472e6	−	1.95644e6i	0.232391	−	0.288723i
$541$			7.13930e6i			1.04873i	0.851494	+	0.524364i	$0.175697\pi$
$541$			7.13930e6i			1.04873i	−0.851494	+	0.524364i	$0.824303\pi$
$542$	3.74383e6			0.547417
$543$	178216.	+	580868.i	0.0259387	+	0.0845430i
$544$		−	6.73843e6i		−	0.976251i
$545$	332752.			0.0479876
$546$	−3.39260e6	+	1.04088e6i	−0.487025	+	0.149424i
$547$	9.15909e6			1.30883			0.654416	−	0.756134i	$-0.272914\pi$
$547$	9.15909e6			1.30883			0.654416	+	0.756134i	$0.272914\pi$
$548$		−	1.02184e7i		−	1.45355i
$549$	317623.	+	468896.i	0.0449760	+	0.0663966i
$550$	−8.70082e6			−1.22646
$551$			3.29241e6i			0.461993i
$552$	1.89011e6	+	6.16051e6i	0.264021	+	0.860536i
$553$	4.16267e6			0.578841
$554$	−2.02010e6			−0.279640
$555$	−529324.	−	1.72525e6i	−0.0729439	−	0.237749i
$556$	5.20672e6			0.714294
$557$		−	7.17374e6i		−	0.979733i	−0.871797	−	0.489867i	$-0.837046\pi$
$557$		−	7.17374e6i		−	0.979733i	0.871797	−	0.489867i	$-0.162954\pi$
$558$	3.25652e6	+	4.80749e6i	0.442759	+	0.653632i
$559$	−3.98211e6			−0.538993
$560$		−	880809.i		−	0.118689i
$561$	−4.45083e6	+	1.36556e6i	−0.597082	+	0.183191i
$562$			1.45473e7i			1.94287i
$563$	6.50423e6			0.864818			0.432409	−	0.901678i	$-0.357664\pi$
$563$	6.50423e6			0.864818			0.432409	+	0.901678i	$0.357664\pi$
$564$	−1.92610e6	−	6.27783e6i	−0.254966	−	0.831021i
$565$		−	2.13071e6i		−	0.280805i
$566$			8.04090e6i			1.05503i
$567$	−2.10693e6	+	5.27467e6i	−0.275227	+	0.689029i
$568$			6.23173e6i			0.810472i
$569$	−9.92281e6			−1.28485			−0.642427	−	0.766347i	$-0.722073\pi$
$569$	−9.92281e6			−1.28485			−0.642427	+	0.766347i	$0.722073\pi$
$570$	1.53765e6	−	471765.i	0.198230	−	0.0608190i
$571$		−	8.16059e6i		−	1.04745i	−0.851889	−	0.523723i	$-0.824543\pi$
$571$		−	8.16059e6i		−	1.04745i	0.851889	−	0.523723i	$-0.175457\pi$
$572$		−	4.07306e6i		−	0.520512i
$573$	−1.88063e6	−	6.12961e6i	−0.239285	−	0.779913i
$574$		−	1.71810e7i		−	2.17655i
$575$	1.33245e7			1.68067
$576$	9.94679e6	−	6.73780e6i	1.24919	−	0.846178i
$577$	5.41195e6			0.676729			0.338364	−	0.941015i	$-0.390126\pi$
$577$	5.41195e6			0.676729			0.338364	+	0.941015i	$0.390126\pi$
$578$	−5.97707e6			−0.744164
$579$	−742666.	−	2.42060e6i	−0.0920655	−	0.300073i
$580$	2.85536e6			0.352444
$581$	1.05794e7			1.30024
$582$	−3.54358e6	+	1.08720e6i	−0.433645	+	0.133047i
$583$		−	6.60884e6i		−	0.805292i
$584$		−	4.00373e6i		−	0.485773i
$585$	864187.	−	585387.i	0.104404	−	0.0707218i
$586$			1.99028e7i			2.39425i
$587$	9.62890e6			1.15340			0.576702	−	0.816955i	$-0.304339\pi$
$587$	9.62890e6			1.15340			0.576702	+	0.816955i	$0.304339\pi$
$588$	1.46325e6	+	4.76923e6i	0.174532	+	0.568859i
$589$			2.11843e6i			0.251608i
$590$	−2.98465e6	+	2.02841e6i	−0.352991	+	0.239898i
$591$	198680.	−	60957.2i	0.0233984	−	0.00717887i
$592$		−	4.32761e6i		−	0.507509i
$593$		−	1.49397e7i		−	1.74464i	−0.488937	−	0.872319i	$-0.662615\pi$
$593$		−	1.49397e7i		−	1.74464i	0.488937	−	0.872319i	$-0.337385\pi$
$594$	−8.91479e6	−	7.17546e6i	−1.03668	−	0.834418i
$595$	1.28339e6			0.148616
$596$	1.02991e7			1.18764
$597$	4.56064e6	+	1.48647e7i	0.523709	+	1.70695i
$598$			1.09493e7i			1.25209i
$599$		−	4.04336e6i		−	0.460442i	−0.973138	−	0.230221i	$-0.926055\pi$
$599$		−	4.04336e6i		−	0.460442i	0.973138	−	0.230221i	$-0.0739450\pi$
$600$	1.17661e6	+	3.83499e6i	0.133431	+	0.434896i
$601$		−	6.81347e6i		−	0.769453i	−0.923031	−	0.384726i	$-0.874296\pi$
$601$		−	6.81347e6i		−	0.769453i	0.923031	−	0.384726i	$-0.125704\pi$
$602$		−	1.20352e7i		−	1.35351i
$603$	−579035.	−	854810.i	−0.0648502	−	0.0957362i
$604$		−	1.41043e7i		−	1.57311i
$605$			599660.i			0.0666065i
$606$	727681.	+	2.37177e6i	0.0804933	+	0.262355i
$607$	−1.15741e7			−1.27501			−0.637506	−	0.770445i	$-0.720034\pi$
$607$	−1.15741e7			−1.27501			−0.637506	+	0.770445i	$0.720034\pi$
$608$	6.04286e6			0.662954
$609$	−6.17363e6	+	1.89413e6i	−0.674524	+	0.206951i
$610$	314553.			0.0342271
$611$		−	2.72918e6i		−	0.295753i
$612$	4.92145e6	+	7.26538e6i	0.531147	+	0.784115i
$613$			1.47599e7i			1.58647i	0.608916	+	0.793234i	$0.291604\pi$
$613$			1.47599e7i			1.58647i	−0.608916	+	0.793234i	$0.708396\pi$
$614$	1.42400e7			1.52437
$615$	1.48227e6	+	4.83125e6i	0.158031	+	0.515076i
$616$	3.01101e6			0.319713
$617$			1.65063e7i			1.74557i	0.488102	+	0.872786i	$0.337689\pi$
$617$			1.65063e7i			1.74557i	−0.488102	+	0.872786i	$0.662311\pi$
$618$	8.46613e6	−	2.59749e6i	0.891690	−	0.273579i
$619$	−2.52855e6			−0.265244			−0.132622	−	0.991167i	$-0.542340\pi$
$619$	−2.52855e6			−0.265244			−0.132622	+	0.991167i	$0.542340\pi$
$620$	1.83721e6			0.191946
$621$	1.36522e7	+	1.09886e7i	1.42060	+	1.14343i
$622$		−	1.18459e7i		−	1.22770i
$623$	8.06700e6			0.832707
$624$	2.39298e6	−	734191.i	0.246024	−	0.0754827i
$625$	7.52916e6			0.770986
$626$			2.08247e7i			2.12394i
$627$	−1.22460e6	−	3.99140e6i	−0.124402	−	0.405468i
$628$		−	1.08354e7i		−	1.09634i
$629$	6.30558e6			0.635475
$630$	1.76922e6	+	2.61185e6i	0.177595	+	0.262178i
$631$	−3.72212e6			−0.372149			−0.186074	−	0.982536i	$-0.559577\pi$
$631$	−3.72212e6			−0.372149			−0.186074	+	0.982536i	$0.559577\pi$
$632$	3.86670e6			0.385077
$633$	−1.89032e7	+	5.79971e6i	−1.87511	+	0.575303i
$634$			1.80101e7i			1.77948i
$635$		−	1.82428e6i		−	0.179538i
$636$	−1.19091e7	+	3.65382e6i	−1.16744	+	0.358182i
$637$			2.07334e6i			0.202452i
$638$		−	1.30109e7i		−	1.26548i
$639$	9.50491e6	+	1.40318e7i	0.920865	+	1.35944i
$640$		−	2.71385e6i		−	0.261900i
$641$		−	1.33112e7i		−	1.27959i	−0.768544	−	0.639796i	$-0.779019\pi$
$641$		−	1.33112e7i		−	1.27959i	0.768544	−	0.639796i	$-0.220981\pi$
$642$	−1.05980e7	+	3.25158e6i	−1.01482	+	0.311356i
$643$	−1.20938e7			−1.15355			−0.576774	−	0.816904i	$-0.695689\pi$
$643$	−1.20938e7			−1.15355			−0.576774	+	0.816904i	$0.695689\pi$
$644$	−1.88517e7			−1.79117
$645$	1.03832e6	+	3.38426e6i	0.0982729	+	0.320305i
$646$			5.61992e6i			0.529845i
$647$		−	1.85305e7i		−	1.74031i	−0.492783	−	0.870153i	$-0.664020\pi$
$647$		−	1.85305e7i		−	1.74031i	0.492783	−	0.870153i	$-0.335980\pi$
$648$	−1.95712e6	+	4.89963e6i	−0.183096	+	0.458381i
$649$	5.26532e6	+	7.74750e6i	0.490697	+	0.722021i
$650$			6.81609e6i			0.632779i
$651$	−3.97228e6	+	1.21874e6i	−0.367356	+	0.112709i
$652$	−1.97258e6			−0.181726
$653$		−	3.20324e6i		−	0.293972i	−0.989139	−	0.146986i	$-0.953043\pi$
$653$		−	3.20324e6i		−	0.293972i	0.989139	−	0.146986i	$-0.0469573\pi$
$654$	−2.73224e6	+	838278.i	−0.249789	+	0.0766379i
$655$			2.28034e6i			0.207681i
$656$			1.21187e7i			1.09950i
$657$	−6.10667e6	−	9.01508e6i	−0.551939	−	0.814810i
$658$	8.24845e6			0.742690
$659$	1.42323e7			1.27662			0.638308	−	0.769781i	$-0.279635\pi$
$659$	1.42323e7			1.27662			0.638308	+	0.769781i	$0.279635\pi$
$660$	−3.46155e6	+	1.06204e6i	−0.309322	+	0.0949032i
$661$	1.50721e7			1.34175			0.670873	−	0.741572i	$-0.265920\pi$
$661$	1.50721e7			1.34175			0.670873	+	0.741572i	$0.265920\pi$
$662$	5.17024e6			0.458528
$663$	1.06976e6	+	3.48672e6i	0.0945153	+	0.308058i
$664$	9.82722e6			0.864989
$665$			1.15091e6i			0.100923i
$666$	8.69259e6	+	1.28326e7i	0.759388	+	1.12106i
$667$			1.99249e7i			1.73413i
$668$		−	1.38033e7i		−	1.19685i
$669$	173926.	+	566885.i	0.0150245	+	0.0489700i
$670$	−573439.			−0.0493515
$671$		−	816513.i		−	0.0700094i
$672$	3.47647e6	+	1.13310e7i	0.296972	+	0.967934i
$673$			1.72295e7i			1.46634i	0.680046	+	0.733169i	$0.261960\pi$
$673$			1.72295e7i			1.46634i	−0.680046	+	0.733169i	$0.738040\pi$
$674$		−	3.35557e6i		−	0.284522i
$675$	8.49863e6	+	6.84050e6i	0.717942	+	0.577868i
$676$	1.25378e7			1.05524
$677$			6.38671e6i			0.535557i	0.963481	+	0.267778i	$0.0862895\pi$
$677$			6.38671e6i			0.535557i	−0.963481	+	0.267778i	$0.913710\pi$
$678$	5.36775e6	+	1.74954e7i	0.448455	+	1.46167i
$679$		−	2.65233e6i		−	0.220777i
$680$	1.19214e6			0.0988678
$681$	−3.54083e6	−	1.15408e7i	−0.292575	−	0.953602i
$682$		−	8.37153e6i		−	0.689197i
$683$	1.27583e7			1.04650			0.523251	−	0.852179i	$-0.324719\pi$
$683$	1.27583e7			1.04650			0.523251	+	0.852179i	$0.324719\pi$
$684$	−6.51542e6	+	4.41344e6i	−0.532478	+	0.360692i
$685$	−3.77533e6			−0.307418
$686$	−2.02073e7			−1.63945
$687$	6.61911e6	−	2.03081e6i	0.535066	−	0.164164i
$688$			8.48906e6i			0.683736i
$689$	−5.17726e6			−0.415482
$690$	9.30547e6	−	2.85501e6i	0.744073	−	0.228289i
$691$			1.67771e7i			1.33666i	0.743865	+	0.668330i	$0.232991\pi$
$691$			1.67771e7i			1.33666i	−0.743865	+	0.668330i	$0.767009\pi$
$692$	1.03744e7			0.823567
$693$	6.77980e6	−	4.59252e6i	0.536270	−	0.363261i
$694$	9.94729e6			0.783982
$695$		−	1.92370e6i		−	0.151069i
$696$	−5.73468e6	+	1.75946e6i	−0.448731	+	0.137675i
$697$	−1.76576e7			−1.37674
$698$			1.89037e7i			1.46862i
$699$	−4.96611e6	−	1.61863e7i	−0.384435	−	1.25301i
$700$	−1.17354e7			−0.905219
$701$	2.10706e7			1.61951			0.809753	−	0.586771i	$-0.199601\pi$
$701$	2.10706e7			1.61951			0.809753	+	0.586771i	$0.199601\pi$
$702$	−5.62115e6	+	6.98371e6i	−0.430509	+	0.534864i
$703$			5.65469e6i			0.431539i
$704$	−1.73208e7			−1.31716
$705$	−2.31944e6	+	711627.i	−0.175756	+	0.0539237i
$706$	−1.44836e7			−1.09361
$707$	−1.77524e6			−0.133570
$708$	1.10499e7	−	1.37714e7i	0.828466	−	1.03251i
$709$	−1.18269e6			−0.0883603			−0.0441801	−	0.999024i	$-0.514068\pi$
$709$	−1.18269e6			−0.0883603			−0.0441801	+	0.999024i	$0.514068\pi$
$710$	9.41306e6			0.700785
$711$	8.70653e6	−	5.89766e6i	0.645909	−	0.437528i
$712$	7.49343e6			0.553963
$713$			1.28202e7i			0.944433i
$714$	−1.05380e7	+	3.23315e6i	−0.773590	+	0.237345i
$715$	−1.50485e6			−0.110085
$716$	−2.17777e7			−1.58756
$717$	1.44302e6	−	442734.i	0.104828	−	0.0321622i
$718$		−	1.17475e7i		−	0.850421i
$719$	3.67116e6			0.264839			0.132419	−	0.991194i	$-0.457725\pi$
$719$	3.67116e6			0.264839			0.132419	+	0.991194i	$0.457725\pi$
$720$	−1.24793e6	−	1.84228e6i	−0.0897136	−	0.132441i
$721$			6.33682e6i			0.453976i
$722$	1.63124e7			1.16459
$723$	2.62823e6	+	8.56631e6i	0.186990	+	0.609464i
$724$	−1.65113e6			−0.117067
$725$			1.24035e7i			0.876392i
$726$	−1.51068e6	−	4.92383e6i	−0.106373	−	0.346706i
$727$	−9.23008e6			−0.647693			−0.323847	−	0.946110i	$-0.604976\pi$
$727$	−9.23008e6			−0.647693			−0.323847	+	0.946110i	$0.604976\pi$
$728$		−	2.35878e6i		−	0.164952i
$729$	3.06635e6	+	1.40174e7i	0.213699	+	0.976899i
$730$	−6.04766e6			−0.420030
$731$	−1.23691e7			−0.856137
$732$	−1.47135e6	+	451424.i	−0.101493	+	0.0311392i
$733$	8.77331e6			0.603120			0.301560	−	0.953447i	$-0.402493\pi$
$733$	8.77331e6			0.603120			0.301560	+	0.953447i	$0.402493\pi$
$734$		−	2.53857e7i		−	1.73920i
$735$	1.76206e6	−	540619.i	0.120310	−	0.0369124i
$736$	3.65699e7			2.48845
$737$			1.48852e6i			0.100946i
$738$	−2.43420e7	−	3.59353e7i	−1.64519	−	2.42874i
$739$			685603.i			0.0461808i	0.999733	+	0.0230904i	$0.00735055\pi$
$739$			685603.i			0.0461808i	−0.999733	+	0.0230904i	$0.992649\pi$
$740$	4.90405e6			0.329212
$741$	−3.12680e6	+	959334.i	−0.209197	+	0.0641836i
$742$		−	1.56473e7i		−	1.04335i
$743$		−	2.53146e7i		−	1.68228i	−0.540814	−	0.841142i	$-0.681884\pi$
$743$		−	2.53146e7i		−	1.68228i	0.540814	−	0.841142i	$-0.318116\pi$
$744$	−3.68984e6	+	1.13208e6i	−0.244386	+	0.0749800i
$745$		−	3.80515e6i		−	0.251178i
$746$	−3.77163e7			−2.48132
$747$	2.21276e7	−	1.49889e7i	1.45089	−	0.982808i
$748$		−	1.26516e7i		−	0.826781i
$749$		−	7.93252e6i		−	0.516662i
$750$	1.20782e7	−	3.70572e6i	0.784061	−	0.240558i
$751$			8.32162e6i			0.538404i	0.963084	+	0.269202i	$0.0867599\pi$
$751$			8.32162e6i			0.538404i	−0.963084	+	0.269202i	$0.913240\pi$
$752$	−5.81807e6			−0.375176
$753$	8.85550e6	−	2.71696e6i	0.569149	−	0.174620i
$754$	−1.01925e7			−0.652909
$755$	−5.21103e6			−0.332703
$756$	−1.20240e7	−	9.67806e6i	−0.765147	−	0.615863i
$757$	−2.70456e7			−1.71537			−0.857684	−	0.514176i	$-0.828098\pi$
$757$	−2.70456e7			−1.71537			−0.857684	+	0.514176i	$0.828098\pi$
$758$	−8.74228e6			−0.552652
$759$	−7.41100e6	−	2.41550e7i	−0.466952	−	1.52196i
$760$			1.06908e6i			0.0671393i
$761$			1.64090e7i			1.02712i	0.858053	+	0.513561i	$0.171674\pi$
$761$			1.64090e7i			1.02712i	−0.858053	+	0.513561i	$0.828326\pi$
$762$	4.59577e6	+	1.49792e7i	0.286729	+	0.934548i
$763$		−	2.04505e6i		−	0.127172i
$764$	1.74235e7			1.07995
$765$	2.68430e6	−	1.81830e6i	0.165836	−	0.112334i
$766$			1.98647e6i			0.122324i
$767$	6.06928e6	−	4.12477e6i	0.372519	−	0.253170i
$768$	−397046.	−	1.29411e6i	−0.0242906	−	0.0791714i
$769$			4.53309e6i			0.276426i	0.990403	+	0.138213i	$0.0441358\pi$
$769$			4.53309e6i			0.276426i	−0.990403	+	0.138213i	$0.955864\pi$
$770$		−	4.54814e6i		−	0.276444i
$771$	2.70803e7	−	8.30850e6i	1.64065	−	0.503369i
$772$	6.88061e6			0.415512
$773$	−1.52665e7			−0.918948			−0.459474	−	0.888191i	$-0.651962\pi$
$773$	−1.52665e7			−0.918948			−0.459474	+	0.888191i	$0.651962\pi$
$774$	−1.70514e7	−	2.51725e7i	−1.02308	−	1.51034i
$775$			7.98073e6i			0.477296i
$776$		−	2.46375e6i		−	0.146873i
$777$	−1.06032e7	+	3.25316e6i	−0.630061	+	0.193309i
$778$			4.42223e7i			2.61934i
$779$		−	1.58349e7i		−	0.934916i
$780$	831986.	+	2.71173e6i	0.0489643	+	0.159591i
$781$		−	2.44343e7i		−	1.43341i
$782$			3.40104e7i			1.98882i
$783$	−1.02290e7	+	1.27085e7i	−0.596250	+	0.740781i
$784$	4.41995e6			0.256819
$785$	−4.00331e6			−0.231870
$786$	−5.74470e6	−	1.87240e7i	−0.331673	−	1.08104i
$787$	−3.00627e7			−1.73018			−0.865089	−	0.501618i	$-0.832738\pi$
$787$	−3.00627e7			−1.73018			−0.865089	+	0.501618i	$0.832738\pi$
$788$			564753.i			0.0323998i
$789$	−2.47754e6	+	760135.i	−0.141687	+	0.0434709i
$790$		−	5.84067e6i		−	0.332962i
$791$	−1.30951e7			−0.744163
$792$	6.29774e6	−	4.26599e6i	0.356757	−	0.241661i
$793$	−639643.			−0.0361206
$794$		−	4.17525e7i		−	2.35035i
$795$	1.34996e6	+	4.39998e6i	0.0757534	+	0.246907i
$796$	−4.22532e7			−2.36362
$797$	1.75752e7			0.980062			0.490031	−	0.871705i	$-0.336986\pi$
$797$	1.75752e7			0.980062			0.490031	+	0.871705i	$0.336986\pi$
$798$	−2.89941e6	−	9.45019e6i	−0.161177	−	0.525331i
$799$		−	8.47727e6i		−	0.469774i
$800$	2.27652e7			1.25761
$801$	1.68727e7	−	1.14293e7i	0.929188	−	0.629417i
$802$	−3.74123e6			−0.205390
$803$			1.56984e7i			0.859146i
$804$	2.68230e6	−	822958.i	0.146342	−	0.0448991i
$805$			6.96505e6i			0.378822i
$806$	−6.55812e6			−0.355584
$807$	−5.12262e6	−	1.66964e7i	−0.276890	−	0.902482i
$808$	−1.64902e6			−0.0888582
$809$	−2.35656e7			−1.26592			−0.632961	−	0.774184i	$-0.718161\pi$
$809$	−2.35656e7			−1.26592			−0.632961	+	0.774184i	$0.718161\pi$
$810$	7.40092e6	+	2.95624e6i	0.396345	+	0.158317i
$811$			9.60273e6i			0.512676i	0.966587	+	0.256338i	$0.0825159\pi$
$811$			9.60273e6i			0.512676i	−0.966587	+	0.256338i	$0.917484\pi$
$812$		−	1.75487e7i		−	0.934015i
$813$	1.98509e6	+	6.47009e6i	0.105330	+	0.343308i
$814$		−	2.23460e7i		−	1.18206i
$815$			728800.i			0.0384339i
$816$	7.43298e6	−	2.28051e6i	0.390785	−	0.119897i
$817$		−	1.10923e7i		−	0.581387i
$818$		−	4.97561e7i		−	2.59994i
$819$	−3.59771e6	−	5.31119e6i	−0.187420	−	0.276683i
$820$	−1.37329e7			−0.713227
$821$	−7.54395e6			−0.390608			−0.195304	−	0.980743i	$-0.562569\pi$
$821$	−7.54395e6			−0.390608			−0.195304	+	0.980743i	$0.562569\pi$
$822$	3.09994e7	−	9.51092e6i	1.60020	−	0.490957i
$823$		−	2.09050e6i		−	0.107585i	−0.998552	−	0.0537924i	$-0.982869\pi$
$823$		−	2.09050e6i		−	0.107585i	0.998552	−	0.0537924i	$-0.0171309\pi$
$824$			5.88626e6i			0.302010i
$825$	−4.61343e6	−	1.50368e7i	−0.235988	−	0.769165i
$826$	1.24664e7	+	1.83433e7i	0.635755	+	0.935464i
$827$		−	1.52900e7i		−	0.777399i	−0.921365	−	0.388699i	$-0.872924\pi$
$827$		−	1.52900e7i		−	0.777399i	0.921365	−	0.388699i	$-0.127076\pi$
$828$	−3.94298e7	+	2.67091e7i	−1.99870	+	1.35389i
$829$	−1.94188e7			−0.981378			−0.490689	−	0.871335i	$-0.663255\pi$
$829$	−1.94188e7			−0.981378			−0.490689	+	0.871335i	$0.663255\pi$
$830$		−	1.48441e7i		−	0.747924i
$831$	−1.07112e6	−	3.49114e6i	−0.0538065	−	0.175374i
$832$			1.35689e7i			0.679573i
$833$			6.44013e6i			0.321575i
$834$	4.84624e6	+	1.57956e7i	0.241262	+	0.786357i
$835$	−5.09982e6			−0.253127
$836$	1.13456e7			0.561452
$837$	−6.58161e6	+	8.17699e6i	−0.324727	+	0.403441i
$838$	2.71745e7			1.33675
$839$	9.13360e6			0.447958			0.223979	−	0.974594i	$-0.428095\pi$
$839$	9.13360e6			0.447958			0.223979	+	0.974594i	$0.428095\pi$
$840$	−2.00465e6	+	615045.i	−0.0980256	+	0.0300752i
$841$	1.96351e6			0.0957287
$842$			5.38647e7i			2.61833i
$843$	−2.51407e7	+	7.71342e6i	−1.21845	+	0.373834i
$844$		−	5.37328e7i		−	2.59647i
$845$		−	4.63226e6i		−	0.223178i
$846$	1.72522e7	−	1.16864e7i	0.828742	−	0.561377i
$847$	3.68544e6			0.176515
$848$			1.10369e7i			0.527056i
$849$	−1.38963e7	+	4.26352e6i	−0.661652	+	0.203002i
$850$			2.11719e7i			1.00511i
$851$			3.42208e7i			1.61982i
$852$	−4.40303e7	+	1.35089e7i	−2.07803	+	0.637562i
$853$	2.19457e7			1.03271			0.516353	−	0.856376i	$-0.327289\pi$
$853$	2.19457e7			1.03271			0.516353	+	0.856376i	$0.327289\pi$
$854$		−	1.93321e6i		−	0.0907054i
$855$	1.63061e6	+	2.40722e6i	0.0762843	+	0.112616i
$856$		−	7.36851e6i		−	0.343712i
$857$	2.16335e6			0.100618			0.0503090	−	0.998734i	$-0.483979\pi$
$857$	2.16335e6			0.100618			0.0503090	+	0.998734i	$0.483979\pi$
$858$	1.23564e7	−	3.79107e6i	0.573025	−	0.175810i
$859$		−	3.11782e6i		−	0.144168i	−0.997399	−	0.0720839i	$-0.977035\pi$
$859$		−	3.11782e6i		−	0.144168i	0.997399	−	0.0720839i	$-0.0229650\pi$
$860$	−9.61981e6			−0.443527
$861$	2.96922e7	−	9.10988e6i	1.36501	−	0.418798i
$862$	4.27135e7			1.95793
$863$	3.99620e7			1.82650			0.913251	−	0.407398i	$-0.133564\pi$
$863$	3.99620e7			1.82650			0.913251	+	0.407398i	$0.133564\pi$
$864$	2.33250e7	+	1.87742e7i	1.06301	+	0.855612i
$865$		−	3.83299e6i		−	0.174180i
$866$	2.95272e7			1.33791
$867$	−3.16921e6	−	1.03296e7i	−0.143187	−	0.466696i
$868$		−	1.12913e7i		−	0.508679i
$869$	−1.51611e7			−0.681054
$870$	2.65767e6	+	8.66226e6i	0.119043	+	0.388001i
$871$	1.16609e6			0.0520817
$872$		−	1.89965e6i		−	0.0846022i
$873$	−3.75781e6	−	5.54754e6i	−0.166878	−	0.246357i
$874$	−3.04997e7			−1.35057
$875$			9.04043e6i			0.399180i
$876$	2.82884e7	−	8.67916e6i	1.24551	−	0.382136i
$877$	8.11082e6			0.356095			0.178047	−	0.984022i	$-0.443022\pi$
$877$	8.11082e6			0.356095			0.178047	+	0.984022i	$0.443022\pi$
$878$	−8.25990e6			−0.361608
$879$	−3.43960e7	+	1.05530e7i	−1.50154	+	0.460687i
$880$			3.20805e6i			0.139648i
$881$	3.42693e7			1.48753			0.743764	−	0.668442i	$-0.233038\pi$
$881$	3.42693e7			1.48753			0.743764	+	0.668442i	$0.233038\pi$
$882$	−1.31064e7	+	8.87808e6i	−0.567300	+	0.384280i
$883$	−4.84455e6			−0.209099			−0.104549	−	0.994520i	$-0.533340\pi$
$883$	−4.84455e6			−0.209099			−0.104549	+	0.994520i	$0.533340\pi$
$884$	−9.91105e6			−0.426569
$885$	−5.08805e6	−	4.08255e6i	−0.218370	−	0.175216i
$886$	3.16642e7			1.35514
$887$	7.55607e6			0.322468			0.161234	−	0.986916i	$-0.448453\pi$
$887$	7.55607e6			0.322468			0.161234	+	0.986916i	$0.448453\pi$
$888$	−9.84926e6	+	3.02185e6i	−0.419152	+	0.128600i
$889$	−1.12118e7			−0.475796
$890$		−	1.13189e7i		−	0.478991i
$891$	7.67376e6	−	1.92112e7i	0.323828	−	0.810700i
$892$	−1.61138e6			−0.0678088
$893$	7.60221e6			0.319015
$894$	9.58605e6	+	3.12443e7i	0.401140	+	1.30745i
$895$			8.04609e6i			0.335759i
$896$	−1.66790e7			−0.694064
$897$	−1.89227e7	+	5.80566e6i	−0.785238	+	0.240919i
$898$		−	3.44545e7i		−	1.42579i
$899$	−1.19340e7			−0.492480
$900$	−2.45455e7	+	1.66267e7i	−1.01010	+	0.684227i
$901$	−1.60814e7			−0.659951
$902$			6.25760e7i			2.56089i
$903$	2.07992e7	−	6.38141e6i	0.848844	−	0.260434i
$904$	−1.21640e7			−0.495058
$905$			610034.i			0.0247590i
$906$	4.27880e7	−	1.31278e7i	1.73181	−	0.531338i
$907$	7.50163e6			0.302787			0.151393	−	0.988474i	$-0.451624\pi$
$907$	7.50163e6			0.302787			0.151393	+	0.988474i	$0.451624\pi$
$908$	3.28049e7			1.32045
$909$	−3.71305e6	+	2.51516e6i	−0.149046	+	0.100961i
$910$	−3.56294e6			−0.142628
$911$		−	1.44987e7i		−	0.578807i	−0.957207	−	0.289403i	$-0.906543\pi$
$911$		−	1.44987e7i		−	0.578807i	0.957207	−	0.289403i	$-0.0934569\pi$
$912$	2.04511e6	+	6.66572e6i	0.0814197	+	0.265375i
$913$	−3.85320e7			−1.52983
$914$			2.25172e7i			0.891558i
$915$	166785.	+	543611.i	0.00658575	+	0.0214652i
$916$			1.88149e7i			0.740907i
$917$	1.40147e7			0.550377
$918$	−1.74602e7	+	2.16925e7i	−0.683820	+	0.849578i
$919$		−	3.02501e7i		−	1.18151i	−0.806850	−	0.590757i	$-0.798829\pi$
$919$		−	3.02501e7i		−	1.18151i	0.806850	−	0.590757i	$-0.201171\pi$
$920$			6.46983e6i			0.252013i
$921$	7.55047e6	+	2.46096e7i	0.293309	+	0.955994i
$922$		−	1.55181e7i		−	0.601190i
$923$	−1.91414e7			−0.739555
$924$	6.52717e6	+	2.12743e7i	0.251504	+	0.819738i
$925$			2.13029e7i			0.818623i
$926$		−	1.57453e6i		−	0.0603425i
$927$	8.97798e6	+	1.32539e7i	0.343146	+	0.506576i
$928$			3.40421e7i			1.29762i
$929$	9.70210e6			0.368830			0.184415	−	0.982848i	$-0.440961\pi$
$929$	9.70210e6			0.368830			0.184415	+	0.982848i	$0.440961\pi$
$930$	1.71001e6	+	5.57353e6i	0.0648324	+	0.211311i
$931$	−5.77535e6			−0.218376
$932$	4.60097e7			1.73504
$933$	2.04721e7	−	6.28104e6i	0.769941	−	0.236226i
$934$	−4.01852e7			−1.50730
$935$	−4.67431e6			−0.174859
$936$	−3.34191e6	−	4.93355e6i	−0.124682	−	0.184065i
$937$			6.56064e6i			0.244117i	0.992523	+	0.122058i	$0.0389495\pi$
$937$			6.56064e6i			0.244117i	−0.992523	+	0.122058i	$0.961050\pi$
$938$			3.52428e6i			0.130787i
$939$	−3.59892e7	+	1.10419e7i	−1.33201	+	0.408675i
$940$		−	6.59304e6i		−	0.243370i
$941$	−3.87397e7			−1.42620			−0.713102	−	0.701060i	$-0.752711\pi$
$941$	−3.87397e7			−1.42620			−0.713102	+	0.701060i	$0.752711\pi$
$942$	3.28713e7	−	1.00852e7i	1.20695	−	0.370305i
$943$		−	9.58293e7i		−	3.50929i
$944$	−8.79319e6	−	1.29385e7i	−0.321156	−	0.472556i
$945$	−3.57570e6	+	4.44245e6i	−0.130251	+	0.161824i
$946$			4.38341e7i			1.59252i
$947$		−	4.97975e7i		−	1.80440i	−0.431318	−	0.902200i	$-0.641951\pi$
$947$		−	4.97975e7i		−	1.80440i	0.431318	−	0.902200i	$-0.358049\pi$
$948$	8.38210e6	+	2.73202e7i	0.302923	+	0.987331i
$949$	1.22979e7			0.443267
$950$	−1.89864e7			−0.682549
$951$	−3.11250e7	+	9.54946e6i	−1.11598	+	0.342395i
$952$		−	7.32674e6i		−	0.262010i
$953$		−	1.33843e6i		−	0.0477378i	−0.999715	−	0.0238689i	$-0.992402\pi$
$953$		−	1.33843e6i		−	0.0477378i	0.999715	−	0.0238689i	$-0.00759842\pi$
$954$	−2.21691e7	−	3.27275e7i	−0.788636	−	1.16424i
$955$		−	6.43738e6i		−	0.228402i
$956$			4.10182e6i			0.145155i
$957$	2.24854e7	−	6.89873e6i	0.793633	−	0.243495i
$958$			2.59186e7i			0.912427i
$959$			2.32027e7i			0.814691i
$960$	1.15317e7	−	3.53805e6i	0.403847	−	0.123904i
$961$	2.09505e7			0.731788
$962$	−1.75055e7			−0.609871
$963$	−1.12388e7	−	1.65914e7i	−0.390529	−	0.576525i
$964$	−2.43499e7			−0.843926
$965$		−	2.54214e6i		−	0.0878783i
$966$	−1.75466e7	−	5.71903e7i	−0.604991	−	1.97188i
$967$			1.16624e7i			0.401072i	0.979686	+	0.200536i	$0.0642684\pi$
$967$			1.16624e7i			0.401072i	−0.979686	+	0.200536i	$0.935732\pi$
$968$	3.42340e6			0.117427
$969$	−9.71234e6	+	2.97984e6i	−0.332288	+	0.101949i
$970$	−3.72150e6			−0.126996
$971$		−	1.59736e7i		−	0.543695i	−0.962340	−	0.271847i	$-0.912365\pi$
$971$		−	1.59736e7i		−	0.543695i	0.962340	−	0.271847i	$-0.0876346\pi$
$972$	−3.88609e7	−	3.20677e6i	−1.31931	−	0.108868i
$973$	−1.18228e7			−0.400349
$974$	2.81463e7			0.950657
$975$	−1.17796e7	+	3.61409e6i	−0.396842	+	0.121755i
$976$			1.36359e6i			0.0458205i
$977$	−3.75034e6			−0.125700			−0.0628499	−	0.998023i	$-0.520019\pi$
$977$	−3.75034e6			−0.125700			−0.0628499	+	0.998023i	$0.520019\pi$
$978$	−1.83601e6	−	5.98420e6i	−0.0613802	−	0.200059i
$979$	−2.93813e7			−0.979748
$980$			5.00870e6i			0.166594i
$981$	−2.89742e6	−	4.27737e6i	−0.0961257	−	0.141907i
$982$			6.72210e7i			2.22447i
$983$	−4.76620e7			−1.57322			−0.786608	−	0.617453i	$-0.788165\pi$
$983$	−4.76620e7			−1.57322			−0.786608	+	0.617453i	$0.788165\pi$
$984$	2.75811e7	−	8.46215e6i	0.908079	−	0.278608i
$985$	208656.			0.00685237
$986$	−3.16595e7			−1.03708
$987$	4.37357e6	+	1.42550e7i	0.142904	+	0.465772i
$988$		−	8.88799e6i		−	0.289675i
$989$		−	6.71278e7i		−	2.18229i
$990$	−6.44380e6	−	9.51277e6i	−0.208955	−	0.308474i
$991$		−	2.68795e7i		−	0.869435i	−0.900567	−	0.434717i	$-0.856848\pi$
$991$		−	2.68795e7i		−	0.869435i	0.900567	−	0.434717i	$-0.143152\pi$
$992$			2.19036e7i			0.706703i
$993$	2.74141e6	+	8.93521e6i	0.0882269	+	0.287562i
$994$		−	5.78515e7i		−	1.85716i
$995$			1.56111e7i			0.499891i
$996$	2.13031e7	+	6.94342e7i	0.680448	+	2.21781i
$997$	4.60750e7			1.46801			0.734003	−	0.679146i	$-0.237650\pi$
$997$	4.60750e7			1.46801			0.734003	+	0.679146i	$0.237650\pi$
$998$	5.46188e7			1.73586
$999$	−1.75682e7	+	2.18267e7i	−0.556947	+	0.691951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.d.b.176.16	yes	92
3.2	odd	2	inner	177.6.d.b.176.77	yes	92
59.58	odd	2	inner	177.6.d.b.176.78	yes	92
177.176	even	2	inner	177.6.d.b.176.15	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.d.b.176.15	✓	92	177.176	even	2	inner
177.6.d.b.176.16	yes	92	1.1	even	1	trivial
177.6.d.b.176.77	yes	92	3.2	odd	2	inner
177.6.d.b.176.78	yes	92	59.58	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.62331 q^{2} +(-4.57233 - 14.9028i) q^{3} +42.3615 q^{4} -15.6511i q^{5} +(39.4286 + 128.512i) q^{6} -96.1896 q^{7} -89.3504 q^{8} +(-201.188 + 136.281i) q^{9} +O(q^{10})\)	\(q-8.62331 q^{2} +(-4.57233 - 14.9028i) q^{3} +42.3615 q^{4} -15.6511i q^{5} +(39.4286 + 128.512i) q^{6} -96.1896 q^{7} -89.3504 q^{8} +(-201.188 + 136.281i) q^{9} +134.964i q^{10} +350.338 q^{11} +(-193.691 - 631.305i) q^{12} -274.449i q^{13} +829.473 q^{14} +(-233.245 + 71.5620i) q^{15} -585.071 q^{16} -852.484i q^{17} +(1734.90 - 1175.20i) q^{18} +764.487 q^{19} -663.003i q^{20} +(439.811 + 1433.50i) q^{21} -3021.07 q^{22} +4626.49 q^{23} +(408.540 + 1331.57i) q^{24} +2880.04 q^{25} +2366.66i q^{26} +(2950.87 + 2375.14i) q^{27} -4074.74 q^{28} +4306.70i q^{29} +(2011.35 - 617.101i) q^{30} +2771.04i q^{31} +7904.47 q^{32} +(-1601.86 - 5221.02i) q^{33} +7351.23i q^{34} +1505.47i q^{35} +(-8522.61 + 5773.08i) q^{36} +7396.72i q^{37} -6592.41 q^{38} +(-4090.07 + 1254.87i) q^{39} +1398.43i q^{40} -20713.2i q^{41} +(-3792.63 - 12361.5i) q^{42} -14509.4i q^{43} +14840.8 q^{44} +(2132.95 + 3148.80i) q^{45} -39895.7 q^{46} +9944.21 q^{47} +(2675.14 + 8719.21i) q^{48} -7554.55 q^{49} -24835.5 q^{50} +(-12704.4 + 3897.84i) q^{51} -11626.1i q^{52} -18864.2i q^{53} +(-25446.3 - 20481.5i) q^{54} -5483.17i q^{55} +8594.58 q^{56} +(-3495.49 - 11393.0i) q^{57} -37138.0i q^{58} +(15029.3 + 22114.4i) q^{59} +(-9880.62 + 3031.47i) q^{60} -2330.64i q^{61} -23895.6i q^{62} +(19352.2 - 13108.8i) q^{63} -49440.4 q^{64} -4295.43 q^{65} +(13813.4 + 45022.5i) q^{66} +4248.82i q^{67} -36112.5i q^{68} +(-21153.9 - 68947.7i) q^{69} -12982.2i q^{70} -69744.9i q^{71} +(17976.2 - 12176.8i) q^{72} +44809.4i q^{73} -63784.2i q^{74} +(-13168.5 - 42920.7i) q^{75} +32384.8 q^{76} -33698.9 q^{77} +(35269.9 - 10821.2i) q^{78} -43275.7 q^{79} +9157.00i q^{80} +(21903.9 - 54836.2i) q^{81} +178616. i q^{82} -109985. q^{83} +(18631.1 + 60725.0i) q^{84} -13342.3 q^{85} +125119. i q^{86} +(64181.9 - 19691.7i) q^{87} -31302.8 q^{88} -83865.6 q^{89} +(-18393.1 - 27153.1i) q^{90} +26399.2i q^{91} +195985. q^{92} +(41296.3 - 12670.1i) q^{93} -85752.0 q^{94} -11965.0i q^{95} +(-36141.8 - 117799. i) q^{96} +27574.0i q^{97} +65145.3 q^{98} +(-70483.6 + 47744.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9}+O(q^{10}) \) 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9	\( 92 q + 22 q^{3} + 1724 q^{4} - 80 q^{7} + 2 q^{9} - 1244 q^{12} + 1116 q^{15} + 14724 q^{16} + 1784 q^{19} + 6388 q^{21} - 8140 q^{22} - 48208 q^{25} - 6458 q^{27} - 19092 q^{28} - 20832 q^{36} - 134984 q^{45} + 51180 q^{46} + 61720 q^{48} + 174556 q^{49} + 8332 q^{51} + 236784 q^{57} + 375208 q^{60} - 429890 q^{63} + 561472 q^{64} - 11596 q^{66} + 169948 q^{75} + 111488 q^{76} + 356264 q^{78} + 180260 q^{79} + 79554 q^{81} + 269308 q^{84} + 111028 q^{85} - 318764 q^{87} - 1242976 q^{88} - 513608 q^{94}+O(q^{100}) \) 92 * q + 22 * q^3 + 1724 * q^4 - 80 * q^7 + 2 * q^9 - 1244 * q^12 + 1116 * q^15 + 14724 * q^16 + 1784 * q^19 + 6388 * q^21 - 8140 * q^22 - 48208 * q^25 - 6458 * q^27 - 19092 * q^28 - 20832 * q^36 - 134984 * q^45 + 51180 * q^46 + 61720 * q^48 + 174556 * q^49 + 8332 * q^51 + 236784 * q^57 + 375208 * q^60 - 429890 * q^63 + 561472 * q^64 - 11596 * q^66 + 169948 * q^75 + 111488 * q^76 + 356264 * q^78 + 180260 * q^79 + 79554 * q^81 + 269308 * q^84 + 111028 * q^85 - 318764 * q^87 - 1242976 * q^88 - 513608 * q^94

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