LMFDB - Embedded newform 77.5.d.a.34.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,5,Mod(34,77)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, 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("77.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	77.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:	$7.95948715746$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.23
Character	$\chi$	$=$	77.34
Dual form			77.5.d.a.34.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.07641 q^{2} -0.250162i q^{3} +20.9227 q^{4} -37.5950i q^{5} -1.52009i q^{6} +(40.7077 + 27.2742i) q^{7} +29.9126 q^{8} +80.9374 q^{9} +O(q^{10})$	\(q+6.07641 q^{2} -0.250162i q^{3} +20.9227 q^{4} -37.5950i q^{5} -1.52009i q^{6} +(40.7077 + 27.2742i) q^{7} +29.9126 q^{8} +80.9374 q^{9} -228.443i q^{10} -36.4829 q^{11} -5.23408i q^{12} -190.226i q^{13} +(247.357 + 165.729i) q^{14} -9.40484 q^{15} -153.003 q^{16} +358.442i q^{17} +491.809 q^{18} +439.873i q^{19} -786.591i q^{20} +(6.82297 - 10.1835i) q^{21} -221.685 q^{22} +397.747 q^{23} -7.48301i q^{24} -788.383 q^{25} -1155.89i q^{26} -40.5106i q^{27} +(851.717 + 570.651i) q^{28} -1575.87 q^{29} -57.1477 q^{30} +1029.39i q^{31} -1408.31 q^{32} +9.12663i q^{33} +2178.04i q^{34} +(1025.37 - 1530.41i) q^{35} +1693.43 q^{36} +593.518 q^{37} +2672.85i q^{38} -47.5873 q^{39} -1124.57i q^{40} -2745.19i q^{41} +(41.4592 - 61.8793i) q^{42} -1483.16 q^{43} -763.322 q^{44} -3042.84i q^{45} +2416.87 q^{46} +2680.99i q^{47} +38.2755i q^{48} +(913.236 + 2220.54i) q^{49} -4790.54 q^{50} +89.6686 q^{51} -3980.05i q^{52} +3346.70 q^{53} -246.159i q^{54} +1371.57i q^{55} +(1217.67 + 815.843i) q^{56} +110.040 q^{57} -9575.64 q^{58} +198.065i q^{59} -196.775 q^{60} +2197.82i q^{61} +6254.97i q^{62} +(3294.78 + 2207.50i) q^{63} -6109.42 q^{64} -7151.54 q^{65} +55.4572i q^{66} +1959.36 q^{67} +7499.59i q^{68} -99.5012i q^{69} +(6230.59 - 9299.37i) q^{70} +814.881 q^{71} +2421.05 q^{72} -7896.48i q^{73} +3606.46 q^{74} +197.224i q^{75} +9203.35i q^{76} +(-1485.13 - 995.041i) q^{77} -289.160 q^{78} +2232.99 q^{79} +5752.13i q^{80} +6545.80 q^{81} -16680.9i q^{82} -11747.7i q^{83} +(142.755 - 213.067i) q^{84} +13475.6 q^{85} -9012.30 q^{86} +394.223i q^{87} -1091.30 q^{88} -4890.05i q^{89} -18489.5i q^{90} +(5188.26 - 7743.66i) q^{91} +8321.96 q^{92} +257.513 q^{93} +16290.8i q^{94} +16537.0 q^{95} +352.305i q^{96} +15616.1i q^{97} +(5549.19 + 13492.9i) q^{98} -2952.83 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9}+O(q^{10}) $ 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9	$ 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9} + 360 q^{14} - 68 q^{15} + 2008 q^{16} - 1740 q^{18} + 1238 q^{21} + 300 q^{23} - 4008 q^{25} + 24 q^{28} - 2052 q^{29} + 1604 q^{30} - 780 q^{32} + 294 q^{35} - 2712 q^{36} + 1884 q^{37} + 7696 q^{39} + 7488 q^{42} + 1748 q^{43} - 2904 q^{44} - 9628 q^{46} - 9140 q^{49} + 8220 q^{50} + 15640 q^{51} - 4392 q^{53} + 5736 q^{56} - 11860 q^{57} - 9056 q^{58} + 19408 q^{60} - 14412 q^{63} + 8560 q^{64} - 7104 q^{65} - 9524 q^{67} - 22744 q^{70} - 8748 q^{71} - 67764 q^{72} + 13980 q^{74} - 726 q^{77} + 13880 q^{78} + 41624 q^{79} + 51188 q^{81} + 56956 q^{84} + 29584 q^{85} + 24 q^{86} - 7260 q^{88} + 9104 q^{91} - 32928 q^{92} + 18252 q^{93} - 56412 q^{95} - 15372 q^{98}+O(q^{100}) $ 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9 + 360 * q^14 - 68 * q^15 + 2008 * q^16 - 1740 * q^18 + 1238 * q^21 + 300 * q^23 - 4008 * q^25 + 24 * q^28 - 2052 * q^29 + 1604 * q^30 - 780 * q^32 + 294 * q^35 - 2712 * q^36 + 1884 * q^37 + 7696 * q^39 + 7488 * q^42 + 1748 * q^43 - 2904 * q^44 - 9628 * q^46 - 9140 * q^49 + 8220 * q^50 + 15640 * q^51 - 4392 * q^53 + 5736 * q^56 - 11860 * q^57 - 9056 * q^58 + 19408 * q^60 - 14412 * q^63 + 8560 * q^64 - 7104 * q^65 - 9524 * q^67 - 22744 * q^70 - 8748 * q^71 - 67764 * q^72 + 13980 * q^74 - 726 * q^77 + 13880 * q^78 + 41624 * q^79 + 51188 * q^81 + 56956 * q^84 + 29584 * q^85 + 24 * q^86 - 7260 * q^88 + 9104 * q^91 - 32928 * q^92 + 18252 * q^93 - 56412 * q^95 - 15372 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$-1$	$1$

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 $

$2$	6.07641			1.51910			0.759551	−	0.650448i	$-0.225419\pi$
$2$	6.07641			1.51910			0.759551	+	0.650448i	$0.225419\pi$
$3$		−	0.250162i		−	0.0277958i	−0.999903	−	0.0138979i	$-0.995576\pi$
$3$		−	0.250162i		−	0.0277958i	0.999903	−	0.0138979i	$-0.00442398\pi$
$4$	20.9227			1.30767
$5$		−	37.5950i		−	1.50380i	−0.659277	−	0.751900i	$-0.729138\pi$
$5$		−	37.5950i		−	1.50380i	0.659277	−	0.751900i	$-0.270862\pi$
$6$		−	1.52009i		−	0.0422247i
$7$	40.7077	+	27.2742i	0.830770	+	0.556616i
$7$	40.7077	+	27.2742i	0.830770	+	0.556616i
$8$	29.9126			0.467385
$9$	80.9374			0.999227
$10$		−	228.443i		−	2.28443i
$11$	−36.4829			−0.301511
$11$	−36.4829			−0.301511
$12$		−	5.23408i		−	0.0363478i
$13$		−	190.226i		−	1.12560i	−0.826594	−	0.562799i	$-0.809725\pi$
$13$		−	190.226i		−	1.12560i	0.826594	−	0.562799i	$-0.190275\pi$
$14$	247.357	+	165.729i	1.26202	+	0.845557i
$15$	−9.40484			−0.0417993
$16$	−153.003			−0.597666
$17$			358.442i			1.24028i	0.784490	+	0.620142i	$0.212925\pi$
$17$			358.442i			1.24028i	−0.784490	+	0.620142i	$0.787075\pi$
$18$	491.809			1.51793
$19$			439.873i			1.21848i	0.792984	+	0.609242i	$0.208526\pi$
$19$			439.873i			1.21848i	−0.792984	+	0.609242i	$0.791474\pi$
$20$		−	786.591i		−	1.96648i
$21$	6.82297	−	10.1835i	0.0154716	−	0.0230919i
$22$	−221.685			−0.458027
$23$	397.747			0.751884			0.375942	−	0.926643i	$-0.377319\pi$
$23$	397.747			0.751884			0.375942	+	0.926643i	$0.377319\pi$
$24$		−	7.48301i		−	0.0129913i
$25$	−788.383			−1.26141
$26$		−	1155.89i		−	1.70990i
$27$		−	40.5106i		−	0.0555701i
$28$	851.717	+	570.651i	1.08637	+	0.727872i
$29$	−1575.87			−1.87381			−0.936903	−	0.349590i	$-0.886321\pi$
$29$	−1575.87			−1.87381			−0.936903	+	0.349590i	$0.886321\pi$
$30$	−57.1477			−0.0634974
$31$			1029.39i			1.07116i	0.844484	+	0.535581i	$0.179907\pi$
$31$			1029.39i			1.07116i	−0.844484	+	0.535581i	$0.820093\pi$
$32$	−1408.31			−1.37530
$33$			9.12663i			0.00838075i
$34$			2178.04i			1.88412i
$35$	1025.37	−	1530.41i	0.837040	−	1.24931i
$36$	1693.43			1.30666
$37$	593.518			0.433541			0.216771	−	0.976223i	$-0.430448\pi$
$37$	593.518			0.433541			0.216771	+	0.976223i	$0.430448\pi$
$38$			2672.85i			1.85100i
$39$	−47.5873			−0.0312869
$40$		−	1124.57i		−	0.702853i
$41$		−	2745.19i		−	1.63307i	−0.577296	−	0.816535i	$-0.695892\pi$
$41$		−	2745.19i		−	1.63307i	0.577296	−	0.816535i	$-0.304108\pi$
$42$	41.4592	−	61.8793i	0.0235029	−	0.0350790i
$43$	−1483.16			−0.802142			−0.401071	−	0.916047i	$-0.631362\pi$
$43$	−1483.16			−0.802142			−0.401071	+	0.916047i	$0.631362\pi$
$44$	−763.322			−0.394278
$45$		−	3042.84i		−	1.50264i
$46$	2416.87			1.14219
$47$			2680.99i			1.21367i	0.794829	+	0.606834i	$0.207561\pi$
$47$			2680.99i			1.21367i	−0.794829	+	0.606834i	$0.792439\pi$
$48$			38.2755i			0.0166126i
$49$	913.236	+	2220.54i	0.380356	+	0.924840i
$50$	−4790.54			−1.91622
$51$	89.6686			0.0344747
$52$		−	3980.05i		−	1.47191i
$53$	3346.70			1.19142			0.595710	−	0.803200i	$-0.296871\pi$
$53$	3346.70			1.19142			0.595710	+	0.803200i	$0.296871\pi$
$54$		−	246.159i		−	0.0844167i
$55$			1371.57i			0.453413i
$56$	1217.67	+	815.843i	0.388289	+	0.260154i
$57$	110.040			0.0338687
$58$	−9575.64			−2.84650
$59$			198.065i			0.0568990i	0.999595	+	0.0284495i	$0.00905698\pi$
$59$			198.065i			0.0568990i	−0.999595	+	0.0284495i	$0.990943\pi$
$60$	−196.775			−0.0546598
$61$			2197.82i			0.590652i	0.955397	+	0.295326i	$0.0954283\pi$
$61$			2197.82i			0.590652i	−0.955397	+	0.295326i	$0.904572\pi$
$62$			6254.97i			1.62720i
$63$	3294.78	+	2207.50i	0.830128	+	0.556186i
$64$	−6109.42			−1.49156
$65$	−7151.54			−1.69267
$66$			55.4572i			0.0127312i
$67$	1959.36			0.436480			0.218240	−	0.975895i	$-0.429968\pi$
$67$	1959.36			0.436480			0.218240	+	0.975895i	$0.429968\pi$
$68$			7499.59i			1.62188i
$69$		−	99.5012i		−	0.0208992i
$70$	6230.59	−	9299.37i	1.27155	−	1.89783i
$71$	814.881			0.161651			0.0808253	−	0.996728i	$-0.474244\pi$
$71$	814.881			0.161651			0.0808253	+	0.996728i	$0.474244\pi$
$72$	2421.05			0.467024
$73$		−	7896.48i		−	1.48179i	−0.671618	−	0.740897i	$-0.734401\pi$
$73$		−	7896.48i		−	1.48179i	0.671618	−	0.740897i	$-0.265599\pi$
$74$	3606.46			0.658594
$75$			197.224i			0.0350620i
$76$			9203.35i			1.59338i
$77$	−1485.13	−	995.041i	−0.250486	−	0.167826i
$78$	−289.160			−0.0475280
$79$	2232.99			0.357794			0.178897	−	0.983868i	$-0.442747\pi$
$79$	2232.99			0.357794			0.178897	+	0.983868i	$0.442747\pi$
$80$			5752.13i			0.898770i
$81$	6545.80			0.997683
$82$		−	16680.9i		−	2.48080i
$83$		−	11747.7i		−	1.70529i	−0.522492	−	0.852644i	$-0.674998\pi$
$83$		−	11747.7i		−	1.70529i	0.522492	−	0.852644i	$-0.325002\pi$
$84$	142.755	−	213.067i	0.0202318	−	0.0301966i
$85$	13475.6			1.86514
$86$	−9012.30			−1.21854
$87$			394.223i			0.0520839i
$88$	−1091.30			−0.140922
$89$		−	4890.05i		−	0.617353i	−0.951167	−	0.308676i	$-0.900114\pi$
$89$		−	4890.05i		−	0.617353i	0.951167	−	0.308676i	$-0.0998860\pi$
$90$		−	18489.5i		−	2.28266i
$91$	5188.26	−	7743.66i	0.626526	−	0.935112i
$92$	8321.96			0.983218
$93$	257.513			0.0297738
$94$			16290.8i			1.84369i
$95$	16537.0			1.83236
$96$			352.305i			0.0382276i
$97$			15616.1i			1.65970i	0.557987	+	0.829849i	$0.311574\pi$
$97$			15616.1i			1.65970i	−0.557987	+	0.829849i	$0.688426\pi$
$98$	5549.19	+	13492.9i	0.577800	+	1.40493i
$99$	−2952.83			−0.301278
$100$	−16495.1			−1.64951
$101$		−	3793.81i		−	0.371905i	−0.982559	−	0.185953i	$-0.940463\pi$
$101$		−	3793.81i		−	0.371905i	0.982559	−	0.185953i	$-0.0595371\pi$
$102$	544.863			0.0523705
$103$			446.252i			0.0420635i	0.999779	+	0.0210317i	$0.00669511\pi$
$103$			446.252i			0.0420635i	−0.999779	+	0.0210317i	$0.993305\pi$
$104$		−	5690.16i		−	0.526087i
$105$	−382.850	−	256.510i	−0.0347256	−	0.0232662i
$106$	20335.9			1.80989
$107$	−3204.64			−0.279905			−0.139953	−	0.990158i	$-0.544695\pi$
$107$	−3204.64			−0.279905			−0.139953	+	0.990158i	$0.544695\pi$
$108$		−	847.593i		−	0.0726675i
$109$	−4137.46			−0.348242			−0.174121	−	0.984724i	$-0.555708\pi$
$109$	−4137.46			−0.348242			−0.174121	+	0.984724i	$0.555708\pi$
$110$			8334.24i			0.688780i
$111$		−	148.476i		−	0.0120506i
$112$	−6228.38	−	4173.02i	−0.496523	−	0.332671i
$113$	−12605.8			−0.987222			−0.493611	−	0.869683i	$-0.664323\pi$
$113$	−12605.8			−0.987222			−0.493611	+	0.869683i	$0.664323\pi$
$114$	668.645			0.0514501
$115$		−	14953.3i		−	1.13068i
$116$	−32971.5			−2.45032
$117$		−	15396.4i		−	1.12473i
$118$			1203.53i			0.0864354i
$119$	−9776.22	+	14591.3i	−0.690362	+	1.03039i
$120$	−281.324			−0.0195364
$121$	1331.00			0.0909091
$122$			13354.8i			0.897261i
$123$	−686.743			−0.0453925
$124$			21537.6i			1.40073i
$125$			6142.39i			0.393113i
$126$	20020.4	+	13413.7i	1.26105	+	0.844904i
$127$	4359.50			0.270290			0.135145	−	0.990826i	$-0.456850\pi$
$127$	4359.50			0.270290			0.135145	+	0.990826i	$0.456850\pi$
$128$	−14590.4			−0.890526
$129$			371.031i			0.0222962i
$130$	−43455.7			−2.57134
$131$		−	11242.2i		−	0.655101i	−0.944834	−	0.327551i	$-0.893777\pi$
$131$		−	11242.2i		−	0.655101i	0.944834	−	0.327551i	$-0.106223\pi$
$132$			190.954i			0.0109593i
$133$	−11997.2	+	17906.2i	−0.678228	+	1.01228i
$134$	11905.9			0.663057
$135$	−1523.00			−0.0835663
$136$			10721.9i			0.579690i
$137$	−2923.50			−0.155762			−0.0778812	−	0.996963i	$-0.524815\pi$
$137$	−2923.50			−0.155762			−0.0778812	+	0.996963i	$0.524815\pi$
$138$		−	604.610i		−	0.0317481i
$139$		−	20170.9i		−	1.04399i	−0.852949	−	0.521994i	$-0.825188\pi$
$139$		−	20170.9i		−	1.04399i	0.852949	−	0.521994i	$-0.174812\pi$
$140$	21453.6	−	32020.3i	1.09457	−	1.63369i
$141$	670.683			0.0337349
$142$	4951.55			0.245564
$143$			6939.99i			0.339380i
$144$	−12383.6			−0.597205
$145$			59244.8i			2.81783i
$146$		−	47982.3i		−	2.25100i
$147$	555.495	−	228.457i	0.0257067	−	0.0105723i
$148$	12418.0			0.566930
$149$	−32999.6			−1.48640			−0.743201	−	0.669069i	$-0.766693\pi$
$149$	−32999.6			−1.48640			−0.743201	+	0.669069i	$0.766693\pi$
$150$			1198.41i			0.0532627i
$151$	−22922.7			−1.00534			−0.502668	−	0.864480i	$-0.667648\pi$
$151$	−22922.7			−1.00534			−0.502668	+	0.864480i	$0.667648\pi$
$152$			13157.8i			0.569501i
$153$			29011.4i			1.23932i
$154$	−9024.28	−	6046.28i	−0.380515	−	0.254945i
$155$	38699.7			1.61081
$156$	−995.658			−0.0409130
$157$			3246.88i			0.131725i	0.997829	+	0.0658623i	$0.0209798\pi$
$157$			3246.88i			0.131725i	−0.997829	+	0.0658623i	$0.979020\pi$
$158$	13568.6			0.543525
$159$		−	837.217i		−	0.0331164i
$160$			52945.3i			2.06818i
$161$	16191.4	+	10848.2i	0.624643	+	0.418511i
$162$	39774.9			1.51558
$163$	−17010.5			−0.640237			−0.320118	−	0.947378i	$-0.603723\pi$
$163$	−17010.5			−0.640237			−0.320118	+	0.947378i	$0.603723\pi$
$164$		−	57436.9i		−	2.13552i
$165$	343.116			0.0126030
$166$		−	71384.0i		−	2.59051i
$167$		−	16830.5i		−	0.603482i	−0.953390	−	0.301741i	$-0.902432\pi$
$167$		−	16830.5i		−	0.603482i	0.953390	−	0.301741i	$-0.0975678\pi$
$168$	204.093	−	304.616i	0.00723119	−	0.0107928i
$169$	−7624.90			−0.266969
$170$	81883.4			2.83333
$171$			35602.2i			1.21754i
$172$	−31031.8			−1.04894
$173$		−	28148.0i		−	0.940492i	−0.882535	−	0.470246i	$-0.844165\pi$
$173$		−	28148.0i		−	0.940492i	0.882535	−	0.470246i	$-0.155835\pi$
$174$			2395.46i			0.0791208i
$175$	−32093.3	−	21502.5i	−1.04794	−	0.702123i
$176$	5581.97			0.180203
$177$	49.5485			0.00158155
$178$		−	29713.9i		−	0.937822i
$179$	27246.8			0.850373			0.425187	−	0.905106i	$-0.360208\pi$
$179$	27246.8			0.850373			0.425187	+	0.905106i	$0.360208\pi$
$180$		−	63664.6i		−	1.96496i
$181$			21526.5i			0.657078i	0.944490	+	0.328539i	$0.106556\pi$
$181$			21526.5i			0.657078i	−0.944490	+	0.328539i	$0.893444\pi$
$182$	31526.0	−	47053.7i	0.951757	−	1.42053i
$183$	549.811			0.0164176
$184$	11897.7			0.351419
$185$		−	22313.3i		−	0.651959i
$186$	1564.76			0.0452294
$187$		−	13077.0i		−	0.373959i
$188$			56093.7i			1.58708i
$189$	1104.89	−	1649.09i	0.0309312	−	0.0461660i
$190$	100486.			2.78354
$191$	2236.49			0.0613057			0.0306528	−	0.999530i	$-0.490241\pi$
$191$	2236.49			0.0613057			0.0306528	+	0.999530i	$0.490241\pi$
$192$			1528.34i			0.0414590i
$193$	−40101.5			−1.07658			−0.538289	−	0.842760i	$-0.680929\pi$
$193$	−40101.5			−1.07658			−0.538289	+	0.842760i	$0.680929\pi$
$194$			94889.9i			2.52125i
$195$			1789.05i			0.0470492i
$196$	19107.4	+	46459.8i	0.497381	+	1.20939i
$197$	30449.6			0.784601			0.392300	−	0.919837i	$-0.371679\pi$
$197$	30449.6			0.784601			0.392300	+	0.919837i	$0.371679\pi$
$198$	−17942.6			−0.457673
$199$			33116.5i			0.836255i	0.908388	+	0.418127i	$0.137313\pi$
$199$			33116.5i			0.836255i	−0.908388	+	0.418127i	$0.862687\pi$
$200$	−23582.6			−0.589566
$201$		−	490.157i		−	0.0121323i
$202$		−	23052.7i		−	0.564962i
$203$	−64150.1	−	42980.6i	−1.55670	−	1.04299i
$204$	1876.11			0.0450815
$205$	−103205.			−2.45581
$206$			2711.61i			0.0638988i
$207$	32192.6			0.751303
$208$			29105.1i			0.672731i
$209$		−	16047.8i		−	0.367387i
$210$	−2326.35	−	1558.66i	−0.0527517	−	0.0353437i
$211$	−48364.7			−1.08634			−0.543168	−	0.839624i	$-0.682775\pi$
$211$	−48364.7			−1.08634			−0.543168	+	0.839624i	$0.682775\pi$
$212$	70022.1			1.55799
$213$		−	203.852i		−	0.00449321i
$214$	−19472.7			−0.425205
$215$			55759.4i			1.20626i
$216$		−	1211.78i		−	0.0259726i
$217$	−28075.7	+	41903.9i	−0.596226	+	0.889888i
$218$	−25140.9			−0.529015
$219$	−1975.40			−0.0411877
$220$			28697.1i			0.592915i
$221$	68184.9			1.39606
$222$		−	902.200i		−	0.0183061i
$223$			1116.54i			0.0224526i	0.999937	+	0.0112263i	$0.00357351\pi$
$223$			1116.54i			0.0224526i	−0.999937	+	0.0112263i	$0.996426\pi$
$224$	−57329.0	−	38410.5i	−1.14256	−	0.765515i
$225$	−63809.7			−1.26044
$226$	−76598.2			−1.49969
$227$		−	12815.8i		−	0.248711i	−0.992238	−	0.124355i	$-0.960314\pi$
$227$		−	12815.8i		−	0.248711i	0.992238	−	0.124355i	$-0.0396863\pi$
$228$	2302.33			0.0442892
$229$		−	35948.7i		−	0.685507i	−0.939425	−	0.342753i	$-0.888640\pi$
$229$		−	35948.7i		−	0.685507i	0.939425	−	0.342753i	$-0.111360\pi$
$230$		−	90862.3i		−	1.71762i
$231$	−248.922	+	371.524i	−0.00466486	+	0.00696247i
$232$	−47138.4			−0.875789
$233$	39870.1			0.734405			0.367202	−	0.930141i	$-0.380316\pi$
$233$	39870.1			0.734405			0.367202	+	0.930141i	$0.380316\pi$
$234$		−	93554.8i		−	1.70858i
$235$	100792.			1.82511
$236$			4144.07i			0.0744052i
$237$		−	558.609i		−	0.00994516i
$238$	−59404.3	+	88663.0i	−1.04873	+	1.56527i
$239$	30335.9			0.531081			0.265541	−	0.964100i	$-0.414450\pi$
$239$	30335.9			0.531081			0.265541	+	0.964100i	$0.414450\pi$
$240$	1438.97			0.0249820
$241$			27373.3i			0.471294i	0.971839	+	0.235647i	$0.0757210\pi$
$241$			27373.3i			0.471294i	−0.971839	+	0.235647i	$0.924279\pi$
$242$	8087.70			0.138100
$243$		−	4918.87i		−	0.0833015i
$244$			45984.4i			0.772379i
$245$	83481.2	−	34333.1i	1.39077	−	0.571980i
$246$	−4172.93			−0.0689558
$247$	83675.2			1.37152
$248$			30791.6i			0.500645i
$249$	−2938.84			−0.0473998
$250$			37323.7i			0.597179i
$251$			9405.92i			0.149298i	0.997210	+	0.0746490i	$0.0237836\pi$
$251$			9405.92i			0.149298i	−0.997210	+	0.0746490i	$0.976216\pi$
$252$	68935.8	+	46187.0i	1.08553	+	0.727309i
$253$	−14510.9			−0.226702
$254$	26490.1			0.410598
$255$		−	3371.09i		−	0.0518430i
$256$	9093.53			0.138756
$257$		−	17509.7i		−	0.265102i	−0.991176	−	0.132551i	$-0.957683\pi$
$257$		−	17509.7i		−	0.265102i	0.991176	−	0.132551i	$-0.0423168\pi$
$258$			2254.54i			0.0338702i
$259$	24160.8	+	16187.7i	0.360173	+	0.241316i
$260$	−149630.			−2.21346
$261$	−127547.			−1.87236
$262$		−	68312.2i		−	0.995166i
$263$	123204.			1.78120			0.890602	−	0.454783i	$-0.150283\pi$
$263$	123204.			1.78120			0.890602	+	0.454783i	$0.150283\pi$
$264$			273.002i			0.00391704i
$265$		−	125819.i		−	1.79166i
$266$	−72899.8	+	108805.i	−1.03030	+	1.53776i
$267$	−1223.31			−0.0171598
$268$	40995.1			0.570772
$269$			66432.0i			0.918063i	0.888420	+	0.459031i	$0.151803\pi$
$269$			66432.0i			0.918063i	−0.888420	+	0.459031i	$0.848197\pi$
$270$	−9254.35			−0.126946
$271$			33632.5i			0.457953i	0.973432	+	0.228977i	$0.0735379\pi$
$271$			33632.5i			0.457953i	−0.973432	+	0.228977i	$0.926462\pi$
$272$		−	54842.5i		−	0.741275i
$273$	−1937.17	−	1297.91i	−0.0259922	−	0.0174148i
$274$	−17764.4			−0.236619
$275$	28762.5			0.380330
$276$		−	2081.84i		−	0.0273293i
$277$	23534.7			0.306724			0.153362	−	0.988170i	$-0.450990\pi$
$277$	23534.7			0.306724			0.153362	+	0.988170i	$0.450990\pi$
$278$		−	122567.i		−	1.58593i
$279$			83315.8i			1.07033i
$280$	30671.6	−	45778.5i	0.391220	−	0.583909i
$281$	−129682.			−1.64236			−0.821179	−	0.570671i	$-0.806683\pi$
$281$	−129682.			−1.64236			−0.821179	+	0.570671i	$0.806683\pi$
$282$	4075.34			0.0512467
$283$			20003.7i			0.249768i	0.992171	+	0.124884i	$0.0398559\pi$
$283$			20003.7i			0.249768i	−0.992171	+	0.124884i	$0.960144\pi$
$284$	17049.5			0.211386
$285$		−	4136.93i		−	0.0509318i
$286$			42170.2i			0.515553i
$287$	74872.9	−	111750.i	0.908993	−	1.35670i
$288$	−113985.			−1.37424
$289$	−44959.5			−0.538302
$290$			359996.i			4.28057i
$291$	3906.56			0.0461327
$292$		−	165216.i		−	1.93770i
$293$			109175.i			1.27171i	0.771811	+	0.635853i	$0.219351\pi$
$293$			109175.i			1.27171i	−0.771811	+	0.635853i	$0.780649\pi$
$294$	3375.42	−	1388.20i	0.0390511	−	0.0160604i
$295$	7446.27			0.0855647
$296$	17753.7			0.202631
$297$			1477.94i			0.0167550i
$298$	−200519.			−2.25800
$299$		−	75661.8i		−	0.846319i
$300$			4126.46i			0.0458496i
$301$	−60376.1	−	40452.0i	−0.666396	−	0.446486i
$302$	−139287.			−1.52721
$303$	−949.067			−0.0103374
$304$		−	67301.6i		−	0.728247i
$305$	82626.9			0.888222
$306$			176285.i			1.88266i
$307$		−	128395.i		−	1.36229i	−0.732147	−	0.681147i	$-0.761482\pi$
$307$		−	128395.i		−	1.36229i	0.732147	−	0.681147i	$-0.238518\pi$
$308$	−31073.1	−	20819.0i	−0.327554	−	0.219462i
$309$	111.635			0.00116919
$310$	235155.			2.44699
$311$		−	122777.i		−	1.26939i	−0.772762	−	0.634696i	$-0.781125\pi$
$311$		−	122777.i		−	1.26939i	0.772762	−	0.634696i	$-0.218875\pi$
$312$	−1423.46			−0.0146230
$313$			7145.53i			0.0729366i	0.999335	+	0.0364683i	$0.0116108\pi$
$313$			7145.53i			0.0729366i	−0.999335	+	0.0364683i	$0.988389\pi$
$314$			19729.4i			0.200103i
$315$	82991.1	−	123867.i	0.836393	−	1.24835i
$316$	46720.3			0.467876
$317$	56042.8			0.557701			0.278850	−	0.960335i	$-0.410047\pi$
$317$	56042.8			0.557701			0.278850	+	0.960335i	$0.410047\pi$
$318$		−	5087.27i		−	0.0503073i
$319$	57492.3			0.564974
$320$			229683.i			2.24300i
$321$			801.679i			0.00778020i
$322$	98385.3	+	65918.3i	0.948896	+	0.635761i
$323$	−157669.			−1.51126
$324$	136956.			1.30464
$325$			149971.i			1.41984i
$326$	−103362.			−0.972585
$327$			1035.04i			0.00967966i
$328$		−	82115.9i		−	0.763272i
$329$	−73121.9	+	109137.i	−0.675547	+	1.00828i
$330$	2084.91			0.0191452
$331$	90147.1			0.822803			0.411401	−	0.911454i	$-0.365039\pi$
$331$	90147.1			0.822803			0.411401	+	0.911454i	$0.365039\pi$
$332$		−	245795.i		−	2.22996i
$333$	48037.8			0.433206
$334$		−	102269.i		−	0.916751i
$335$		−	73662.0i		−	0.656378i
$336$	−1043.93	+	1558.11i	−0.00924685	+	0.0138013i
$337$	183461.			1.61541			0.807705	−	0.589586i	$-0.200709\pi$
$337$	183461.			1.61541			0.807705	+	0.589586i	$0.200709\pi$
$338$	−46332.0			−0.405553
$339$			3153.50i			0.0274406i
$340$	281947.			2.43899
$341$		−	37554.9i		−	0.322967i
$342$			216333.i			1.84957i
$343$	−23387.7	+	115301.i	−0.198793	+	0.980042i
$344$	−44365.3			−0.374909
$345$	−3740.75			−0.0314282
$346$		−	171039.i		−	1.42870i
$347$	−68521.2			−0.569070			−0.284535	−	0.958666i	$-0.591839\pi$
$347$	−68521.2			−0.569070			−0.284535	+	0.958666i	$0.591839\pi$
$348$			8248.23i			0.0681087i
$349$			86985.3i			0.714159i	0.934074	+	0.357080i	$0.116228\pi$
$349$			86985.3i			0.714159i	−0.934074	+	0.357080i	$0.883772\pi$
$350$	−195012.	−	130658.i	−1.59193	−	1.06660i
$351$	−7706.17			−0.0625496
$352$	51379.1			0.414669
$353$		−	91139.6i		−	0.731405i	−0.930732	−	0.365702i	$-0.880829\pi$
$353$		−	91139.6i		−	0.731405i	0.930732	−	0.365702i	$-0.119171\pi$
$354$	301.077			0.00240254
$355$		−	30635.4i		−	0.243090i
$356$		−	102313.i		−	0.807295i
$357$	3650.20	+	2445.64i	0.0286405	+	0.0191892i
$358$	165563.			1.29180
$359$	125132.			0.970911			0.485456	−	0.874261i	$-0.338654\pi$
$359$	125132.			0.970911			0.485456	+	0.874261i	$0.338654\pi$
$360$		−	91019.4i		−	0.702310i
$361$	−63167.0			−0.484703
$362$			130804.i			0.998168i
$363$		−	332.966i		−	0.00252689i
$364$	108553.	−	162019.i	0.819290	−	1.22282i
$365$	−296868.			−2.22832
$366$	3340.87			0.0249401
$367$		−	203357.i		−	1.50982i	−0.655826	−	0.754912i	$-0.727680\pi$
$367$		−	203357.i		−	1.50982i	0.655826	−	0.754912i	$-0.272320\pi$
$368$	−60856.3			−0.449376
$369$		−	222189.i		−	1.63181i
$370$		−	135585.i		−	0.990393i
$371$	136236.	+	91278.5i	0.989795	+	0.663163i
$372$	5387.89			0.0389343
$373$	−198032.			−1.42337			−0.711685	−	0.702499i	$-0.752068\pi$
$373$	−198032.			−1.42337			−0.711685	+	0.702499i	$0.752068\pi$
$374$		−	79461.1i		−	0.568083i
$375$	1536.59			0.0109269
$376$			80195.5i			0.567250i
$377$			299771.i			2.10915i
$378$	6713.79	−	10020.6i	0.0469877	−	0.0701308i
$379$	−5240.22			−0.0364814			−0.0182407	−	0.999834i	$-0.505807\pi$
$379$	−5240.22			−0.0364814			−0.0182407	+	0.999834i	$0.505807\pi$
$380$	346000.			2.39612
$381$		−	1090.58i		−	0.00751292i
$382$	13589.8			0.0931296
$383$			225049.i			1.53419i	0.641531	+	0.767097i	$0.278300\pi$
$383$			225049.i			1.53419i	−0.641531	+	0.767097i	$0.721700\pi$
$384$			3649.96i			0.0247529i
$385$	−37408.6	+	55833.6i	−0.252377	+	0.376681i
$386$	−243673.			−1.63543
$387$	−120043.			−0.801523
$388$			326732.i			2.17034i
$389$	118444.			0.782732			0.391366	−	0.920235i	$-0.372003\pi$
$389$	118444.			0.782732			0.391366	+	0.920235i	$0.372003\pi$
$390$			10871.0i			0.0714725i
$391$			142569.i			0.932549i
$392$	27317.3	+	66422.2i	0.177773	+	0.432256i
$393$	−2812.37			−0.0182091
$394$	185024.			1.19189
$395$		−	83949.2i		−	0.538050i
$396$	−61781.3			−0.393973
$397$			57509.2i			0.364885i	0.983217	+	0.182443i	$0.0584004\pi$
$397$			57509.2i			0.364885i	−0.983217	+	0.182443i	$0.941600\pi$
$398$			201230.i			1.27036i
$399$	4479.46	+	3001.24i	0.0281371	+	0.0188519i
$400$	120625.			0.753904
$401$	288456.			1.79387			0.896935	−	0.442163i	$-0.145789\pi$
$401$	288456.			1.79387			0.896935	+	0.442163i	$0.145789\pi$
$402$		−	2978.40i		−	0.0184302i
$403$	195816.			1.20570
$404$		−	79376.9i		−	0.486330i
$405$		−	246089.i		−	1.50031i
$406$	−389802.	−	261168.i	−2.36479	−	1.58441i
$407$	−21653.2			−0.130718
$408$	2682.22			0.0161129
$409$		−	11546.5i		−	0.0690248i	−0.999404	−	0.0345124i	$-0.989012\pi$
$409$		−	11546.5i		−	0.0690248i	0.999404	−	0.0345124i	$-0.0109878\pi$
$410$	−627118.			−3.73063
$411$			731.350i			0.00432954i
$412$			9336.81i			0.0550052i
$413$	−5402.08	+	8062.79i	−0.0316709	+	0.0472700i
$414$	195615.			1.14131
$415$	−441656.			−2.56441
$416$			267897.i			1.54804i
$417$	−5046.00			−0.0290185
$418$		−	97513.1i		−	0.558098i
$419$		−	324130.i		−	1.84625i	−0.384497	−	0.923126i	$-0.625625\pi$
$419$		−	324130.i		−	1.84625i	0.384497	−	0.923126i	$-0.374375\pi$
$420$	−8010.27	−	5366.89i	−0.0454097	−	0.0304245i
$421$	−2558.97			−0.0144378			−0.00721891	−	0.999974i	$-0.502298\pi$
$421$	−2558.97			−0.0144378			−0.00721891	+	0.999974i	$0.502298\pi$
$422$	−293884.			−1.65025
$423$			216993.i			1.21273i
$424$	100109.			0.556851
$425$		−	282590.i		−	1.56451i
$426$		−	1238.69i		−	0.00682564i
$427$	−59943.7	+	89468.1i	−0.328767	+	0.490696i
$428$	−67049.8			−0.366024
$429$	1736.12			0.00943335
$430$			338817.i			1.83243i
$431$	246232.			1.32553			0.662765	−	0.748827i	$-0.269383\pi$
$431$	246232.			1.32553			0.662765	+	0.748827i	$0.269383\pi$
$432$			6198.23i			0.0332124i
$433$			135735.i			0.723960i	0.932186	+	0.361980i	$0.117899\pi$
$433$			135735.i			0.723960i	−0.932186	+	0.361980i	$0.882101\pi$
$434$	−170599.	+	254625.i	−0.905728	+	1.35183i
$435$	14820.8			0.0783238
$436$	−86567.0			−0.455386
$437$			174958.i			0.916159i
$438$	−12003.3			−0.0625683
$439$			148695.i			0.771558i	0.922591	+	0.385779i	$0.126067\pi$
$439$			148695.i			0.771558i	−0.922591	+	0.385779i	$0.873933\pi$
$440$			41027.4i			0.211918i
$441$	73914.9	+	179725.i	0.380063	+	0.924125i
$442$	414320.			2.12076
$443$	−109684.			−0.558901			−0.279451	−	0.960160i	$-0.590152\pi$
$443$	−109684.			−0.558901			−0.279451	+	0.960160i	$0.590152\pi$
$444$		−	3106.52i		−	0.0157583i
$445$	−183841.			−0.928375
$446$			6784.57i			0.0341077i
$447$			8255.25i			0.0413157i
$448$	−248700.	−	166629.i	−1.23914	−	0.830225i
$449$	50925.7			0.252606			0.126303	−	0.991992i	$-0.459689\pi$
$449$	50925.7			0.252606			0.126303	+	0.991992i	$0.459689\pi$
$450$	−387734.			−1.91474
$451$			100152.i			0.492389i
$452$	−263749.			−1.29096
$453$			5734.38i			0.0279441i
$454$		−	77874.2i		−	0.377817i
$455$	−291123.	−	195053.i	−1.40622	−	0.942169i
$456$	3291.57			0.0158297
$457$	−295485.			−1.41483			−0.707413	−	0.706800i	$-0.750138\pi$
$457$	−295485.			−1.41483			−0.707413	+	0.706800i	$0.750138\pi$
$458$		−	218439.i		−	1.04135i
$459$	14520.7			0.0689227
$460$		−	312864.i		−	1.47856i
$461$			268853.i			1.26507i	0.774533	+	0.632534i	$0.217985\pi$
$461$			268853.i			1.26507i	−0.774533	+	0.632534i	$0.782015\pi$
$462$	−1512.55	+	2257.53i	−0.00708640	+	0.0105767i
$463$	46731.0			0.217993			0.108997	−	0.994042i	$-0.465236\pi$
$463$	46731.0			0.217993			0.108997	+	0.994042i	$0.465236\pi$
$464$	241112.			1.11991
$465$		−	9681.21i		−	0.0447738i
$466$	242267.			1.11564
$467$			331514.i			1.52009i	0.649873	+	0.760043i	$0.274822\pi$
$467$			331514.i			1.52009i	−0.649873	+	0.760043i	$0.725178\pi$
$468$		−	322135.i		−	1.47077i
$469$	79761.0	+	53439.9i	0.362614	+	0.242952i
$470$	612453.			2.77253
$471$	812.246			0.00366139
$472$			5924.66i			0.0265937i
$473$	54110.0			0.241855
$474$		−	3394.34i		−	0.0151077i
$475$		−	346788.i		−	1.53701i
$476$	−204545.	+	305291.i	−0.902767	+	1.34741i
$477$	270873.			1.19050
$478$	184333.			0.806767
$479$		−	250794.i		−	1.09307i	−0.837437	−	0.546533i	$-0.815947\pi$
$479$		−	250794.i		−	1.09307i	0.837437	−	0.546533i	$-0.184053\pi$
$480$	13244.9			0.0574866
$481$		−	112903.i		−	0.487993i
$482$			166331.i			0.715944i
$483$	2713.82	−	4050.47i	0.0116328	−	0.0173624i
$484$	27848.2			0.118879
$485$	587087.			2.49585
$486$		−	29889.1i		−	0.126544i
$487$	−432364.			−1.82302			−0.911510	−	0.411277i	$-0.865083\pi$
$487$	−432364.			−1.82302			−0.911510	+	0.411277i	$0.865083\pi$
$488$			65742.5i			0.276062i
$489$			4255.37i			0.0177959i
$490$	507266.	−	208622.i	2.11273	−	0.868896i
$491$	167601.			0.695206			0.347603	−	0.937642i	$-0.386996\pi$
$491$	167601.			0.695206			0.347603	+	0.937642i	$0.386996\pi$
$492$	−14368.5			−0.0593584
$493$		−	564858.i		−	2.32405i
$494$	508445.			2.08348
$495$			111012.i			0.453062i
$496$		−	157499.i		−	0.640197i
$497$	33171.9	+	22225.2i	0.134294	+	0.0899774i
$498$	−17857.6			−0.0720052
$499$	308225.			1.23785			0.618923	−	0.785452i	$-0.287569\pi$
$499$	308225.			1.23785			0.618923	+	0.785452i	$0.287569\pi$
$500$			128516.i			0.514063i
$501$	−4210.36			−0.0167743
$502$			57154.2i			0.226799i
$503$		−	322662.i		−	1.27530i	−0.770326	−	0.637650i	$-0.779907\pi$
$503$		−	322662.i		−	1.27530i	0.770326	−	0.637650i	$-0.220093\pi$
$504$	98555.5	+	66032.3i	0.387989	+	0.259953i
$505$	−142628.			−0.559271
$506$	−88174.4			−0.344383
$507$			1907.46i			0.00742062i
$508$	91212.8			0.353450
$509$			187685.i			0.724428i	0.932095	+	0.362214i	$0.117979\pi$
$509$			187685.i			0.724428i	−0.932095	+	0.362214i	$0.882021\pi$
$510$		−	20484.1i		−	0.0787548i
$511$	215370.	−	321448.i	0.824791	−	1.23103i
$512$	288702.			1.10131
$513$	17819.5			0.0677113
$514$		−	106396.i		−	0.402716i
$515$	16776.8			0.0632551
$516$			7762.99i			0.0291561i
$517$		−	97810.3i		−	0.365935i
$518$	146811.	+	98363.3i	0.547140	+	0.366584i
$519$	−7041.56			−0.0261417
$520$	−213921.			−0.791130
$521$		−	142211.i		−	0.523912i	−0.965080	−	0.261956i	$-0.915632\pi$
$521$		−	142211.i		−	0.523912i	0.965080	−	0.261956i	$-0.0843676\pi$
$522$	−775027.			−2.84430
$523$			460169.i			1.68234i	0.540772	+	0.841170i	$0.318132\pi$
$523$			460169.i			1.68234i	−0.540772	+	0.841170i	$0.681868\pi$
$524$		−	235218.i		−	0.856657i
$525$	−5379.12	+	8028.52i	−0.0195161	+	0.0291284i
$526$	748639.			2.70583
$527$	−368975.			−1.32854
$528$		−	1396.40i		−	0.00500889i
$529$	−121639.			−0.434670
$530$		−	764528.i		−	2.72171i
$531$			16030.9i			0.0568551i
$532$	−251014.	+	374647.i	−0.886900	+	1.32373i
$533$	−522206.			−1.83818
$534$	−7433.31			−0.0260675
$535$			120478.i			0.420922i
$536$	58609.5			0.204004
$537$		−	6816.12i		−	0.0236368i
$538$			403668.i			1.39463i
$539$	−33317.5	−	81011.7i	−0.114682	−	0.278850i
$540$	−31865.3			−0.109277
$541$	79647.9			0.272132			0.136066	−	0.990700i	$-0.456554\pi$
$541$	79647.9			0.272132			0.136066	+	0.990700i	$0.456554\pi$
$542$			204365.i			0.695678i
$543$	5385.12			0.0182640
$544$		−	504797.i		−	1.70576i
$545$			155548.i			0.523686i
$546$	−11771.0	−	7886.61i	−0.0394848	−	0.0264548i
$547$	−258425.			−0.863693			−0.431846	−	0.901947i	$-0.642138\pi$
$547$	−258425.			−0.863693			−0.431846	+	0.901947i	$0.642138\pi$
$548$	−61167.7			−0.203686
$549$			177886.i			0.590196i
$550$	174773.			0.577761
$551$		−	693182.i		−	2.28320i
$552$		−	2976.34i		−	0.00976798i
$553$	90899.9	+	60903.0i	0.297244	+	0.199154i
$554$	143006.			0.465946
$555$	−5581.95			−0.0181217
$556$		−	422031.i		−	1.36519i
$557$	−131825.			−0.424902			−0.212451	−	0.977172i	$-0.568145\pi$
$557$	−131825.			−0.424902			−0.212451	+	0.977172i	$0.568145\pi$
$558$			506261.i			1.62595i
$559$			282136.i			0.902889i
$560$	−156885.	+	234156.i	−0.500270	+	0.746671i
$561$	−3271.37			−0.0103945
$562$	−788002.			−2.49491
$563$			546092.i			1.72285i	0.507881	+	0.861427i	$0.330429\pi$
$563$			546092.i			1.72285i	−0.507881	+	0.861427i	$0.669571\pi$
$564$	14032.5			0.0441141
$565$			473916.i			1.48458i
$566$			121550.i			0.379423i
$567$	266464.	+	178531.i	0.828845	+	0.555327i
$568$	24375.2			0.0755531
$569$	491940.			1.51945			0.759727	−	0.650242i	$-0.225333\pi$
$569$	491940.			1.51945			0.759727	+	0.650242i	$0.225333\pi$
$570$		−	25137.7i		−	0.0773706i
$571$	521474.			1.59941			0.799707	−	0.600391i	$-0.204988\pi$
$571$	521474.			1.59941			0.799707	+	0.600391i	$0.204988\pi$
$572$			145204.i			0.443798i
$573$		−	559.486i		−	0.00170404i
$574$	454958.	−	679041.i	1.38085	−	2.06097i
$575$	−313577.			−0.948437
$576$	−494480.			−1.49040
$577$		−	69552.8i		−	0.208912i	−0.994530	−	0.104456i	$-0.966690\pi$
$577$		−	69552.8i		−	0.208912i	0.994530	−	0.104456i	$-0.0333101\pi$
$578$	−273193.			−0.817736
$579$			10031.9i			0.0299243i
$580$			1.23956e6i			3.68479i
$581$	320410.	−	478223.i	0.949191	−	1.41670i
$582$	23737.9			0.0700802
$583$	−122097.			−0.359226
$584$		−	236205.i		−	0.692568i
$585$	−578827.			−1.69136
$586$			663390.i			1.93185i
$587$			210986.i			0.612319i	0.951980	+	0.306159i	$0.0990440\pi$
$587$			210986.i			0.612319i	−0.951980	+	0.306159i	$0.900956\pi$
$588$	11622.5	−	4779.95i	0.0336159	−	0.0138251i
$589$	−452799.			−1.30519
$590$	45246.6			0.129982
$591$		−	7617.33i		−	0.0218086i
$592$	−90809.8			−0.259113
$593$		−	323075.i		−	0.918744i	−0.888244	−	0.459372i	$-0.848074\pi$
$593$		−	323075.i		−	0.918744i	0.888244	−	0.459372i	$-0.151926\pi$
$594$			8980.59i			0.0254526i
$595$	548562.	+	367537.i	1.54950	+	1.03817i
$596$	−690442.			−1.94373
$597$	8284.50			0.0232444
$598$		−	459752.i		−	1.28564i
$599$	−576246.			−1.60603			−0.803016	−	0.595957i	$-0.796773\pi$
$599$	−576246.			−1.60603			−0.803016	+	0.595957i	$0.796773\pi$
$600$			5899.48i			0.0163874i
$601$		−	7585.78i		−	0.0210015i	−0.999945	−	0.0105008i	$-0.996657\pi$
$601$		−	7585.78i		−	0.0210015i	0.999945	−	0.0105008i	$-0.00334256\pi$
$602$	−366870.	−	245803.i	−1.01232	−	0.678257i
$603$	158585.			0.436142
$604$	−479605.			−1.31465
$605$		−	50038.9i		−	0.136709i
$606$	−5766.92			−0.0157036
$607$			639599.i			1.73592i	0.496632	+	0.867961i	$0.334570\pi$
$607$			639599.i			1.73592i	−0.496632	+	0.867961i	$0.665430\pi$
$608$		−	619476.i		−	1.67578i
$609$	−10752.1	+	16047.9i	−0.0289908	+	0.0432697i
$610$	502075.			1.34930
$611$	509994.			1.36610
$612$			606997.i			1.62063i
$613$	54317.9			0.144551			0.0722756	−	0.997385i	$-0.476974\pi$
$613$	54317.9			0.144551			0.0722756	+	0.997385i	$0.476974\pi$
$614$		−	780179.i		−	2.06946i
$615$			25818.1i			0.0682612i
$616$	−44424.3	−	29764.3i	−0.117074	−	0.0784394i
$617$	−181969.			−0.477999			−0.239000	−	0.971020i	$-0.576819\pi$
$617$	−181969.			−0.477999			−0.239000	+	0.971020i	$0.576819\pi$
$618$	678.342			0.00177612
$619$		−	217644.i		−	0.568022i	−0.958821	−	0.284011i	$-0.908335\pi$
$619$		−	217644.i		−	0.568022i	0.958821	−	0.284011i	$-0.0916653\pi$
$620$	809705.			2.10641
$621$		−	16113.0i		−	0.0417823i
$622$		−	746042.i		−	1.92834i
$623$	133372.	−	199063.i	0.343629	−	0.512878i
$624$	7280.98			0.0186991
$625$	−261816.			−0.670250
$626$			43419.2i			0.110798i
$627$	−4014.56			−0.0102118
$628$			67933.6i			0.172252i
$629$			212742.i			0.537714i
$630$	504288.	−	752667.i	1.27057	−	1.89636i
$631$	−615688.			−1.54633			−0.773165	−	0.634205i	$-0.781328\pi$
$631$	−615688.			−1.54633			−0.773165	+	0.634205i	$0.781328\pi$
$632$	66794.6			0.167227
$633$			12099.0i			0.0301956i
$634$	340539.			0.847205
$635$		−	163895.i		−	0.406462i
$636$		−	17516.9i		−	0.0433054i
$637$	422404.	−	173721.i	1.04100	−	0.428128i
$638$	349347.			0.858253
$639$	65954.4			0.161526
$640$			548525.i			1.33917i
$641$	−266585.			−0.648814			−0.324407	−	0.945918i	$-0.605165\pi$
$641$	−266585.			−0.648814			−0.324407	+	0.945918i	$0.605165\pi$
$642$			4871.33i			0.0118189i
$643$		−	6841.46i		−	0.0165473i	−0.999966	−	0.00827365i	$-0.997366\pi$
$643$		−	6841.46i		−	0.0165473i	0.999966	−	0.00827365i	$-0.00263361\pi$
$644$	338768.	+	226975.i	0.816828	+	0.547275i
$645$	13948.9			0.0335290
$646$	−958060.			−2.29577
$647$			605602.i			1.44670i	0.690481	+	0.723350i	$0.257399\pi$
$647$			605602.i			1.44670i	−0.690481	+	0.723350i	$0.742601\pi$
$648$	195802.			0.466302
$649$		−	7226.00i		−	0.0171557i
$650$			911285.i			2.15689i
$651$	10482.8	+	7023.47i	0.0247351	+	0.0165726i
$652$	−355905.			−0.837220
$653$	−610422.			−1.43154			−0.715771	−	0.698336i	$-0.753924\pi$
$653$	−610422.			−1.43154			−0.715771	+	0.698336i	$0.753924\pi$
$654$			6289.30i			0.0147044i
$655$	−422650.			−0.985141
$656$			420021.i			0.976030i
$657$		−	639121.i		−	1.48065i
$658$	−444319.	+	663161.i	−1.02623	+	1.53168i
$659$	338376.			0.779163			0.389582	−	0.920992i	$-0.372620\pi$
$659$	338376.			0.779163			0.389582	+	0.920992i	$0.372620\pi$
$660$	7178.92			0.0164805
$661$		−	250770.i		−	0.573948i	−0.957938	−	0.286974i	$-0.907351\pi$
$661$		−	250770.i		−	0.573948i	0.957938	−	0.286974i	$-0.0926494\pi$
$662$	547771.			1.24992
$663$		−	17057.3i		−	0.0388046i
$664$		−	351406.i		−	0.797026i
$665$	673184.	+	451034.i	1.52227	+	1.01992i
$666$	291898.			0.658085
$667$	−626798.			−1.40889
$668$		−	352141.i		−	0.789156i
$669$	279.317			0.000624087
$670$		−	447601.i		−	0.997105i
$671$		−	80182.7i		−	0.178088i
$672$	−9608.85	+	14341.6i	−0.0212781	+	0.0317583i
$673$	−43429.9			−0.0958868			−0.0479434	−	0.998850i	$-0.515267\pi$
$673$	−43429.9			−0.0958868			−0.0479434	+	0.998850i	$0.515267\pi$
$674$	1.11478e6			2.45397
$675$			31937.9i			0.0700969i
$676$	−159534.			−0.349108
$677$		−	545737.i		−	1.19071i	−0.803462	−	0.595355i	$-0.797011\pi$
$677$		−	545737.i		−	1.19071i	0.803462	−	0.595355i	$-0.202989\pi$
$678$			19162.0i			0.0416851i
$679$	−425917.	+	635696.i	−0.923816	+	1.37883i
$680$	403091.			0.871737
$681$	−3206.03			−0.00691312
$682$		−	228199.i		−	0.490620i
$683$	−55413.2			−0.118788			−0.0593939	−	0.998235i	$-0.518917\pi$
$683$	−55413.2			−0.118788			−0.0593939	+	0.998235i	$0.518917\pi$
$684$			744895.i			1.59215i
$685$			109909.i			0.234235i
$686$	−142114.	+	700616.i	−0.301986	+	1.48878i
$687$	−8992.99			−0.0190542
$688$	226927.			0.479413
$689$		−	636628.i		−	1.34106i
$690$	−22730.3			−0.0477427
$691$		−	328455.i		−	0.687891i	−0.938990	−	0.343945i	$-0.888236\pi$
$691$		−	328455.i		−	0.687891i	0.938990	−	0.343945i	$-0.111764\pi$
$692$		−	588933.i		−	1.22985i
$693$	−120203.	−	80536.1i	−0.250293	−	0.167696i
$694$	−416363.			−0.864476
$695$	−758325.			−1.56995
$696$			11792.3i			0.0243432i
$697$	983991.			2.02547
$698$			528558.i			1.08488i
$699$		−	9973.99i		−	0.0204134i
$700$	−671480.	−	449892.i	−1.37037	−	0.918147i
$701$	−298887.			−0.608234			−0.304117	−	0.952635i	$-0.598361\pi$
$701$	−298887.			−0.608234			−0.304117	+	0.952635i	$0.598361\pi$
$702$	−46825.8			−0.0950192
$703$			261072.i			0.528263i
$704$	222889.			0.449721
$705$		−	25214.3i		−	0.0507305i
$706$		−	553802.i		−	1.11108i
$707$	103473.	−	154437.i	0.207009	−	0.308968i
$708$	1036.69			0.00206815
$709$	482931.			0.960711			0.480356	−	0.877074i	$-0.340508\pi$
$709$	482931.			0.960711			0.480356	+	0.877074i	$0.340508\pi$
$710$		−	186153.i		−	0.369279i
$711$	180732.			0.357517
$712$		−	146274.i		−	0.288541i
$713$			409435.i			0.805389i
$714$	22180.1	+	14860.7i	0.0435078	+	0.0291503i
$715$	260909.			0.510360
$716$	570078.			1.11201
$717$		−	7588.89i		−	0.0147618i
$718$	760353.			1.47491
$719$		−	138301.i		−	0.267527i	−0.991013	−	0.133764i	$-0.957294\pi$
$719$		−	138301.i		−	0.267527i	0.991013	−	0.133764i	$-0.0427063\pi$
$720$			465563.i			0.898076i
$721$	−12171.2	+	18165.9i	−0.0234132	+	0.0349451i
$722$	−383828.			−0.736313
$723$	6847.75			0.0131000
$724$			450394.i			0.859242i
$725$	1.24239e6			2.36364
$726$		−	2023.24i		−	0.00383861i
$727$			380948.i			0.720771i	0.932804	+	0.360385i	$0.117355\pi$
$727$			380948.i			0.720771i	−0.932804	+	0.360385i	$0.882645\pi$
$728$	155195.	−	231633.i	0.292829	−	0.437057i
$729$	528979.			0.995367
$730$	−1.80389e6			−3.38505
$731$		−	531627.i		−	0.994884i
$732$	11503.5			0.0214689
$733$		−	492587.i		−	0.916801i	−0.888746	−	0.458401i	$-0.848422\pi$
$733$		−	492587.i		−	0.916801i	0.888746	−	0.458401i	$-0.151578\pi$
$734$		−	1.23568e6i		−	2.29358i
$735$	−8588.84	−	20883.8i	−0.0158986	−	0.0386577i
$736$	−560150.			−1.03407
$737$	−71483.0			−0.131604
$738$		−	1.35011e6i		−	2.47888i
$739$	−455198.			−0.833511			−0.416756	−	0.909019i	$-0.636833\pi$
$739$	−455198.			−0.833511			−0.416756	+	0.909019i	$0.636833\pi$
$740$		−	466856.i		−	0.852549i
$741$		−	20932.4i		−	0.0381225i
$742$	827828.	+	554645.i	1.50360	+	1.00741i
$743$	−793766.			−1.43785			−0.718927	−	0.695086i	$-0.755366\pi$
$743$	−793766.			−1.43785			−0.718927	+	0.695086i	$0.755366\pi$
$744$	7702.90			0.0139158
$745$			1.24062e6i			2.23525i
$746$	−1.20332e6			−2.16224
$747$		−	950831.i		−	1.70397i
$748$		−	273607.i		−	0.489016i
$749$	−130453.	−	87403.9i	−0.232537	−	0.155800i
$750$	9336.97			0.0165991
$751$	174541.			0.309469			0.154735	−	0.987956i	$-0.450548\pi$
$751$	174541.			0.309469			0.154735	+	0.987956i	$0.450548\pi$
$752$		−	410199.i		−	0.725368i
$753$	2353.00			0.00414985
$754$			1.82153e6i			3.20402i
$755$			861777.i			1.51182i
$756$	23117.4	−	34503.6i	0.0404479	−	0.0603699i
$757$	78989.3			0.137840			0.0689202	−	0.997622i	$-0.478045\pi$
$757$	78989.3			0.137840			0.0689202	+	0.997622i	$0.478045\pi$
$758$	−31841.7			−0.0554189
$759$			3630.09i			0.00630135i
$760$	494666.			0.856415
$761$			510720.i			0.881888i	0.897535	+	0.440944i	$0.145356\pi$
$761$			510720.i			0.881888i	−0.897535	+	0.440944i	$0.854644\pi$
$762$		−	6626.83i		−	0.0114129i
$763$	−168427.	−	112846.i	−0.289309	−	0.193837i
$764$	46793.6			0.0801677
$765$	1.09068e6			1.86370
$766$			1.36749e6i			2.33060i
$767$	37677.2			0.0640454
$768$		−	2274.86i		−	0.00385684i
$769$		−	1.02228e6i		−	1.72869i	−0.502903	−	0.864343i	$-0.667735\pi$
$769$		−	1.02228e6i		−	1.72869i	0.502903	−	0.864343i	$-0.332265\pi$
$770$	−227310.	+	339268.i	−0.383386	+	0.572218i
$771$	−4380.26			−0.00736871
$772$	−839033.			−1.40781
$773$			785803.i			1.31509i	0.753417	+	0.657544i	$0.228404\pi$
$773$			785803.i			1.31509i	−0.753417	+	0.657544i	$0.771596\pi$
$774$	−729432.			−1.21759
$775$		−	811550.i		−	1.35118i
$776$			467119.i			0.775718i
$777$	4049.56	−	6044.11i	0.00670758	−	0.0100113i
$778$	719713.			1.18905
$779$	1.20753e6			1.98987
$780$			37431.7i			0.0615249i
$781$	−29729.2			−0.0487395
$782$			866308.i			1.41664i
$783$			63839.5i			0.104128i
$784$	−139727.	−	339748.i	−0.227326	−	0.552746i
$785$	122066.			0.198087
$786$	−17089.1			−0.0276614
$787$			141844.i			0.229013i	0.993422	+	0.114507i	$0.0365287\pi$
$787$			141844.i			0.229013i	−0.993422	+	0.114507i	$0.963471\pi$
$788$	637089.			1.02600
$789$		−	30821.0i		−	0.0495100i
$790$		−	510110.i		−	0.817353i
$791$	−513155.	−	343814.i	−0.820154	−	0.549504i
$792$	−88326.9			−0.140813
$793$	418082.			0.664836
$794$			349449.i			0.554298i
$795$	−31475.2			−0.0498005
$796$			692889.i			1.09355i
$797$		−	995434.i		−	1.56710i	−0.621331	−	0.783548i	$-0.713408\pi$
$797$		−	995434.i		−	1.56710i	0.621331	−	0.783548i	$-0.286592\pi$
$798$	27219.0	+	18236.8i	0.0427432	+	0.0286380i
$799$	−960980.			−1.50529
$800$	1.11029e6			1.73482
$801$		−	395788.i		−	0.616876i
$802$	1.75278e6			2.72507
$803$			288086.i			0.446778i
$804$		−	10255.4i		−	0.0158651i
$805$	407839.	−	608714.i	0.629357	−	0.939337i
$806$	1.18986e6			1.83158
$807$	16618.8			0.0255183
$808$		−	113483.i		−	0.173823i
$809$	−417110.			−0.637315			−0.318657	−	0.947870i	$-0.603232\pi$
$809$	−417110.			−0.637315			−0.318657	+	0.947870i	$0.603232\pi$
$810$		−	1.49534e6i		−	2.27913i
$811$			410552.i			0.624204i	0.950049	+	0.312102i	$0.101033\pi$
$811$			410552.i			0.624204i	−0.950049	+	0.312102i	$0.898967\pi$
$812$	−1.34220e6	−	899273.i	−2.03565	−	1.36389i
$813$	8413.59			0.0127292
$814$	−131574.			−0.198573
$815$			639508.i			0.962788i
$816$	−13719.5			−0.0206043
$817$		−	652402.i		−	0.977398i
$818$		−	70161.5i		−	0.104856i
$819$	419924.	−	626752.i	0.626042	−	0.934390i
$820$	−2.15934e6			−3.21139
$821$	262574.			0.389551			0.194776	−	0.980848i	$-0.437602\pi$
$821$	262574.			0.389551			0.194776	+	0.980848i	$0.437602\pi$
$822$			4443.98i			0.00657701i
$823$	919163.			1.35704			0.678520	−	0.734582i	$-0.262622\pi$
$823$	919163.			1.35704			0.678520	+	0.734582i	$0.262622\pi$
$824$			13348.6i			0.0196598i
$825$		−	7195.29i		−	0.0105716i
$826$	−32825.2	+	48992.8i	−0.0481114	+	0.0718079i
$827$	603776.			0.882804			0.441402	−	0.897309i	$-0.354481\pi$
$827$	603776.			0.882804			0.441402	+	0.897309i	$0.354481\pi$
$828$	673558.			0.982458
$829$		−	229295.i		−	0.333646i	−0.985987	−	0.166823i	$-0.946649\pi$
$829$		−	229295.i		−	0.333646i	0.985987	−	0.166823i	$-0.0533509\pi$
$830$	−2.68368e6			−3.89560
$831$		−	5887.48i		−	0.00852565i
$832$			1.16217e6i			1.67889i
$833$	−795935.	+	327342.i	−1.14706	+	0.471750i
$834$	−30661.5			−0.0440821
$835$	−632743.			−0.907516
$836$		−	335764.i		−	0.480421i
$837$	41701.1			0.0595245
$838$		−	1.96955e6i		−	2.80465i
$839$			700620.i			0.995311i	0.867375	+	0.497655i	$0.165806\pi$
$839$			700620.i			0.995311i	−0.867375	+	0.497655i	$0.834194\pi$
$840$	−11452.0	−	7672.88i	−0.0162302	−	0.0108743i
$841$	1.77609e6			2.51115
$842$	−15549.4			−0.0219325
$843$			32441.6i			0.0456506i
$844$	−1.01192e6			−1.42057
$845$			286658.i			0.401468i
$846$			1.31854e6i			1.84226i
$847$	54182.0	+	36302.0i	0.0755245	+	0.0506015i
$848$	−512053.			−0.712071
$849$	5004.16			0.00694250
$850$		−	1.71713e6i		−	2.37665i
$851$	236070.			0.325973
$852$		−	4265.15i		−	0.00587564i
$853$			258333.i			0.355044i	0.984117	+	0.177522i	$0.0568081\pi$
$853$			258333.i			0.355044i	−0.984117	+	0.177522i	$0.943192\pi$
$854$	−364242.	+	543645.i	−0.499430	+	0.745417i
$855$	1.33846e6			1.83094
$856$	−95859.2			−0.130824
$857$		−	551246.i		−	0.750557i	−0.926912	−	0.375279i	$-0.877547\pi$
$857$		−	551246.i		−	0.750557i	0.926912	−	0.375279i	$-0.122453\pi$
$858$	10549.4			0.0143302
$859$			110670.i			0.149983i	0.997184	+	0.0749915i	$0.0238930\pi$
$859$			110670.i			0.149983i	−0.997184	+	0.0749915i	$0.976107\pi$
$860$			1.16664e6i			1.57739i
$861$	−27955.7	−	18730.4i	−0.0377107	−	0.0252662i
$862$	1.49621e6			2.01362
$863$	−932078.			−1.25150			−0.625750	−	0.780024i	$-0.715207\pi$
$863$	−932078.			−1.25150			−0.625750	+	0.780024i	$0.715207\pi$
$864$			57051.4i			0.0764256i
$865$	−1.05822e6			−1.41431
$866$			824779.i			1.09977i
$867$			11247.2i			0.0149625i
$868$	−587420.	+	876746.i	−0.779668	+	1.16368i
$869$	−81465.9			−0.107879
$870$	90057.4			0.118982
$871$		−	372721.i		−	0.491300i
$872$	−123762.			−0.162763
$873$			1.26393e6i			1.65842i
$874$			1.06312e6i			1.39174i
$875$	−167529.	+	250043.i	−0.218813	+	0.326586i
$876$	−41330.8			−0.0538599
$877$	906788.			1.17898			0.589490	−	0.807775i	$-0.299329\pi$
$877$	906788.			1.17898			0.589490	+	0.807775i	$0.299329\pi$
$878$			903534.i			1.17208i
$879$	27311.4			0.0353481
$880$		−	209854.i		−	0.270989i
$881$		−	772826.i		−	0.995704i	−0.867262	−	0.497852i	$-0.834122\pi$
$881$		−	772826.i		−	0.995704i	0.867262	−	0.497852i	$-0.165878\pi$
$882$	449137.	+	1.09208e6i	0.577354	+	1.40384i
$883$	−1.33655e6			−1.71421			−0.857107	−	0.515139i	$-0.827740\pi$
$883$	−1.33655e6			−1.71421			−0.857107	+	0.515139i	$0.827740\pi$
$884$	1.42662e6			1.82559
$885$		−	1862.78i		−	0.00237834i
$886$	−666484.			−0.849028
$887$			1.04339e6i			1.32616i	0.748546	+	0.663082i	$0.230752\pi$
$887$			1.04339e6i			1.32616i	−0.748546	+	0.663082i	$0.769248\pi$
$888$		−	4441.30i		−	0.00563228i
$889$	177465.	+	118902.i	0.224549	+	0.150448i
$890$	−1.11710e6			−1.41030
$891$	−238809.			−0.300813
$892$			23361.2i			0.0293606i
$893$	−1.17930e6			−1.47883
$894$			50162.3i			0.0627628i
$895$		−	1.02434e6i		−	1.27879i
$896$	−593941.	−	397941.i	−0.739822	−	0.495682i
$897$	−18927.7			−0.0235241
$898$	309445.			0.383735
$899$		−	1.62218e6i		−	2.00715i
$900$	−1.33507e6			−1.64824
$901$			1.19960e6i			1.47770i
$902$			608567.i			0.747989i
$903$	−10119.6	+	15103.8i	−0.0124104	+	0.0185230i
$904$	−377074.			−0.461413
$905$	809289.			0.988113
$906$			34844.5i			0.0424500i
$907$	−479690.			−0.583104			−0.291552	−	0.956555i	$-0.594172\pi$
$907$	−479690.			−0.583104			−0.291552	+	0.956555i	$0.594172\pi$
$908$		−	268142.i		−	0.325232i
$909$		−	307061.i		−	0.371618i
$910$	−1.76898e6	−	1.18522e6i	−2.13619	−	1.43125i
$911$	21199.8			0.0255444			0.0127722	−	0.999918i	$-0.495934\pi$
$911$	21199.8			0.0255444			0.0127722	+	0.999918i	$0.495934\pi$
$912$	−16836.3			−0.0202422
$913$			428591.i			0.514164i
$914$	−1.79549e6			−2.14927
$915$		−	20670.1i		−	0.0246888i
$916$		−	752145.i		−	0.896418i
$917$	306622.	−	457644.i	0.364640	−	0.544238i
$918$	88233.7			0.104701
$919$	405640.			0.480297			0.240148	−	0.970736i	$-0.422804\pi$
$919$	405640.			0.480297			0.240148	+	0.970736i	$0.422804\pi$
$920$		−	447292.i		−	0.528464i
$921$	−32119.5			−0.0378660
$922$			1.63366e6i			1.92177i
$923$		−	155011.i		−	0.181954i
$924$	−5208.13	+	7773.31i	−0.00610011	+	0.00910463i
$925$	−467920.			−0.546875
$926$	283957.			0.331154
$927$			36118.5i			0.0420310i
$928$	2.21931e6			2.57705
$929$			1.61598e6i			1.87242i	0.351439	+	0.936211i	$0.385692\pi$
$929$			1.61598e6i			1.87242i	−0.351439	+	0.936211i	$0.614308\pi$
$930$		−	58827.0i		−	0.0680160i
$931$	−976755.	+	401707.i	−1.12690	+	0.463458i
$932$	834192.			0.960360
$933$	−30714.1			−0.0352837
$934$			2.01441e6i			2.30917i
$935$	−491629.			−0.562360
$936$		−	460547.i		−	0.525681i
$937$		−	150657.i		−	0.171597i	−0.996313	−	0.0857984i	$-0.972656\pi$
$937$		−	150657.i		−	0.171597i	0.996313	−	0.0857984i	$-0.0273441\pi$
$938$	484660.	+	324723.i	0.550848	+	0.369069i
$939$	1787.54			0.00202733
$940$	2.10884e6			2.38665
$941$		−	1.31184e6i		−	1.48150i	−0.671783	−	0.740748i	$-0.734471\pi$
$941$		−	1.31184e6i		−	1.48150i	0.671783	−	0.740748i	$-0.265529\pi$
$942$	4935.54			0.00556202
$943$		−	1.09189e6i		−	1.22788i
$944$		−	30304.5i		−	0.0340066i
$945$	−61997.7	−	41538.5i	−0.0694244	−	0.0465144i
$946$	328794.			0.367403
$947$	−162513.			−0.181213			−0.0906063	−	0.995887i	$-0.528880\pi$
$947$	−162513.			−0.181213			−0.0906063	+	0.995887i	$0.528880\pi$
$948$		−	11687.6i		−	0.0130050i
$949$	−1.50212e6			−1.66790
$950$		−	2.10723e6i		−	2.33488i
$951$		−	14019.8i		−	0.0155017i
$952$	−292432.	+	436466.i	−0.322665	+	0.481589i
$953$	277435.			0.305475			0.152737	−	0.988267i	$-0.451191\pi$
$953$	277435.			0.305475			0.152737	+	0.988267i	$0.451191\pi$
$954$	1.64593e6			1.80849
$955$		−	84080.9i		−	0.0921915i
$956$	634710.			0.694480
$957$		−	14382.4i		−	0.0157039i
$958$		−	1.52393e6i		−	1.66048i
$959$	−119009.	−	79736.2i	−0.129403	−	0.0866999i
$960$	57458.1			0.0623460
$961$	−136114.			−0.147386
$962$		−	686042.i		−	0.741311i
$963$	−259375.			−0.279689
$964$			572724.i			0.616298i
$965$			1.50761e6i			1.61896i
$966$	16490.3	−	24612.3i	0.0176715	−	0.0263753i
$967$	868738.			0.929043			0.464521	−	0.885562i	$-0.346226\pi$
$967$	868738.			0.929043			0.464521	+	0.885562i	$0.346226\pi$
$968$	39813.7			0.0424895
$969$			39442.8i			0.0420068i
$970$	3.56738e6			3.79146
$971$		−	817246.i		−	0.866791i	−0.901204	−	0.433395i	$-0.857315\pi$
$971$		−	817246.i		−	0.866791i	0.901204	−	0.433395i	$-0.142685\pi$
$972$		−	102916.i		−	0.108931i
$973$	550145.	−	821111.i	0.581101	−	0.867314i
$974$	−2.62722e6			−2.76935
$975$	37517.1			0.0394657
$976$		−	336272.i		−	0.353013i
$977$	−710102.			−0.743929			−0.371965	−	0.928247i	$-0.621316\pi$
$977$	−710102.			−0.743929			−0.371965	+	0.928247i	$0.621316\pi$
$978$			25857.4i			0.0270338i
$979$			178403.i			0.186139i
$980$	1.74666e6	−	718342.i	1.81868	−	0.747962i
$981$	−334875.			−0.347973
$982$	1.01841e6			1.05609
$983$			939175.i			0.971940i	0.873975	+	0.485970i	$0.161534\pi$
$983$			939175.i			0.971940i	−0.873975	+	0.485970i	$0.838466\pi$
$984$	−20542.3			−0.0212158
$985$		−	1.14475e6i		−	1.17988i
$986$		−	3.43231e6i		−	3.53047i
$987$	27302.0	+	18292.3i	0.0280259	+	0.0187774i
$988$	1.75071e6			1.79350
$989$	−589923.			−0.603118
$990$			674552.i			0.688248i
$991$	1.26729e6			1.29041			0.645207	−	0.764007i	$-0.276771\pi$
$991$	1.26729e6			1.29041			0.645207	+	0.764007i	$0.276771\pi$
$992$		−	1.44969e6i		−	1.47317i
$993$		−	22551.4i		−	0.0228705i
$994$	201566.	+	135050.i	0.204007	+	0.136685i
$995$	1.24502e6			1.25756
$996$	−61488.6			−0.0619834
$997$			199421.i			0.200623i	0.994956	+	0.100312i	$0.0319839\pi$
$997$			199421.i			0.200623i	−0.994956	+	0.100312i	$0.968016\pi$
$998$	1.87290e6			1.88041
$999$		−	24043.8i		−	0.0240919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.5.d.a.34.23	✓	28
7.6	odd	2	inner	77.5.d.a.34.24	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.5.d.a.34.23	✓	28	1.1	even	1	trivial
77.5.d.a.34.24	yes	28	7.6	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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	77.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.07641 q^{2} -0.250162i q^{3} +20.9227 q^{4} -37.5950i q^{5} -1.52009i q^{6} +(40.7077 + 27.2742i) q^{7} +29.9126 q^{8} +80.9374 q^{9} +O(q^{10})\)	\(q+6.07641 q^{2} -0.250162i q^{3} +20.9227 q^{4} -37.5950i q^{5} -1.52009i q^{6} +(40.7077 + 27.2742i) q^{7} +29.9126 q^{8} +80.9374 q^{9} -228.443i q^{10} -36.4829 q^{11} -5.23408i q^{12} -190.226i q^{13} +(247.357 + 165.729i) q^{14} -9.40484 q^{15} -153.003 q^{16} +358.442i q^{17} +491.809 q^{18} +439.873i q^{19} -786.591i q^{20} +(6.82297 - 10.1835i) q^{21} -221.685 q^{22} +397.747 q^{23} -7.48301i q^{24} -788.383 q^{25} -1155.89i q^{26} -40.5106i q^{27} +(851.717 + 570.651i) q^{28} -1575.87 q^{29} -57.1477 q^{30} +1029.39i q^{31} -1408.31 q^{32} +9.12663i q^{33} +2178.04i q^{34} +(1025.37 - 1530.41i) q^{35} +1693.43 q^{36} +593.518 q^{37} +2672.85i q^{38} -47.5873 q^{39} -1124.57i q^{40} -2745.19i q^{41} +(41.4592 - 61.8793i) q^{42} -1483.16 q^{43} -763.322 q^{44} -3042.84i q^{45} +2416.87 q^{46} +2680.99i q^{47} +38.2755i q^{48} +(913.236 + 2220.54i) q^{49} -4790.54 q^{50} +89.6686 q^{51} -3980.05i q^{52} +3346.70 q^{53} -246.159i q^{54} +1371.57i q^{55} +(1217.67 + 815.843i) q^{56} +110.040 q^{57} -9575.64 q^{58} +198.065i q^{59} -196.775 q^{60} +2197.82i q^{61} +6254.97i q^{62} +(3294.78 + 2207.50i) q^{63} -6109.42 q^{64} -7151.54 q^{65} +55.4572i q^{66} +1959.36 q^{67} +7499.59i q^{68} -99.5012i q^{69} +(6230.59 - 9299.37i) q^{70} +814.881 q^{71} +2421.05 q^{72} -7896.48i q^{73} +3606.46 q^{74} +197.224i q^{75} +9203.35i q^{76} +(-1485.13 - 995.041i) q^{77} -289.160 q^{78} +2232.99 q^{79} +5752.13i q^{80} +6545.80 q^{81} -16680.9i q^{82} -11747.7i q^{83} +(142.755 - 213.067i) q^{84} +13475.6 q^{85} -9012.30 q^{86} +394.223i q^{87} -1091.30 q^{88} -4890.05i q^{89} -18489.5i q^{90} +(5188.26 - 7743.66i) q^{91} +8321.96 q^{92} +257.513 q^{93} +16290.8i q^{94} +16537.0 q^{95} +352.305i q^{96} +15616.1i q^{97} +(5549.19 + 13492.9i) q^{98} -2952.83 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9}+O(q^{10}) \) 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9	\( 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9} + 360 q^{14} - 68 q^{15} + 2008 q^{16} - 1740 q^{18} + 1238 q^{21} + 300 q^{23} - 4008 q^{25} + 24 q^{28} - 2052 q^{29} + 1604 q^{30} - 780 q^{32} + 294 q^{35} - 2712 q^{36} + 1884 q^{37} + 7696 q^{39} + 7488 q^{42} + 1748 q^{43} - 2904 q^{44} - 9628 q^{46} - 9140 q^{49} + 8220 q^{50} + 15640 q^{51} - 4392 q^{53} + 5736 q^{56} - 11860 q^{57} - 9056 q^{58} + 19408 q^{60} - 14412 q^{63} + 8560 q^{64} - 7104 q^{65} - 9524 q^{67} - 22744 q^{70} - 8748 q^{71} - 67764 q^{72} + 13980 q^{74} - 726 q^{77} + 13880 q^{78} + 41624 q^{79} + 51188 q^{81} + 56956 q^{84} + 29584 q^{85} + 24 q^{86} - 7260 q^{88} + 9104 q^{91} - 32928 q^{92} + 18252 q^{93} - 56412 q^{95} - 15372 q^{98}+O(q^{100}) \) 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9 + 360 * q^14 - 68 * q^15 + 2008 * q^16 - 1740 * q^18 + 1238 * q^21 + 300 * q^23 - 4008 * q^25 + 24 * q^28 - 2052 * q^29 + 1604 * q^30 - 780 * q^32 + 294 * q^35 - 2712 * q^36 + 1884 * q^37 + 7696 * q^39 + 7488 * q^42 + 1748 * q^43 - 2904 * q^44 - 9628 * q^46 - 9140 * q^49 + 8220 * q^50 + 15640 * q^51 - 4392 * q^53 + 5736 * q^56 - 11860 * q^57 - 9056 * q^58 + 19408 * q^60 - 14412 * q^63 + 8560 * q^64 - 7104 * q^65 - 9524 * q^67 - 22744 * q^70 - 8748 * q^71 - 67764 * q^72 + 13980 * q^74 - 726 * q^77 + 13880 * q^78 + 41624 * q^79 + 51188 * q^81 + 56956 * q^84 + 29584 * q^85 + 24 * q^86 - 7260 * q^88 + 9104 * q^91 - 32928 * q^92 + 18252 * q^93 - 56412 * q^95 - 15372 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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