LMFDB - Embedded newform 490.4.c.d.99.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(99,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("490.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.c (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:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.6654810844696576.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1325x^{4} + 9604 $ x^8 + 1325*x^4 + 9604
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.6
Root			$-4.26030 - 4.26030i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.d.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -1.64308i q^{3} -4.00000 q^{4} +(5.90338 - 9.49474i) q^{5} +3.28615 q^{6} -8.00000i q^{8} +24.3003 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -1.64308i q^{3} -4.00000 q^{4} +(5.90338 - 9.49474i) q^{5} +3.28615 q^{6} -8.00000i q^{8} +24.3003 q^{9} +(18.9895 + 11.8068i) q^{10} +45.9009 q^{11} +6.57231i q^{12} +18.6843i q^{13} +(-15.6006 - 9.69970i) q^{15} +16.0000 q^{16} -105.839i q^{17} +48.6006i q^{18} -141.564 q^{19} +(-23.6135 + 37.9790i) q^{20} +91.8018i q^{22} +155.003i q^{23} -13.1446 q^{24} +(-55.3003 - 112.102i) q^{25} -37.3685 q^{26} -84.2903i q^{27} +90.6997 q^{29} +(19.3994 - 31.2012i) q^{30} +82.2962 q^{31} +32.0000i q^{32} -75.4187i q^{33} +211.677 q^{34} -97.2012 q^{36} -289.802i q^{37} -283.128i q^{38} +30.6997 q^{39} +(-75.9579 - 47.2270i) q^{40} +326.224 q^{41} -78.4024i q^{43} -183.604 q^{44} +(143.454 - 230.725i) q^{45} -310.006 q^{46} -227.569i q^{47} -26.2892i q^{48} +(224.204 - 110.601i) q^{50} -173.901 q^{51} -74.7371i q^{52} -10.1982i q^{53} +168.581 q^{54} +(270.970 - 435.817i) q^{55} +232.601i q^{57} +181.399i q^{58} +829.316 q^{59} +(62.4024 + 38.7988i) q^{60} -661.061 q^{61} +164.592i q^{62} -64.0000 q^{64} +(177.402 + 110.300i) q^{65} +150.837 q^{66} -35.1952i q^{67} +423.354i q^{68} +254.682 q^{69} -138.595 q^{71} -194.402i q^{72} -380.349i q^{73} +579.604 q^{74} +(-184.192 + 90.8627i) q^{75} +566.256 q^{76} +61.3994i q^{78} +236.111 q^{79} +(94.4540 - 151.916i) q^{80} +517.612 q^{81} +652.449i q^{82} -890.909i q^{83} +(-1004.91 - 624.805i) q^{85} +156.805 q^{86} -149.027i q^{87} -367.207i q^{88} -121.028 q^{89} +(461.450 + 286.908i) q^{90} -620.012i q^{92} -135.219i q^{93} +455.137 q^{94} +(-835.706 + 1344.11i) q^{95} +52.5785 q^{96} -1459.18i q^{97} +1115.41 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 60 q^{9}+O(q^{10}) $ 8 * q - 32 * q^4 + 60 * q^9	$ 8 q - 32 q^{4} + 60 q^{9} - 36 q^{11} + 144 q^{15} + 128 q^{16} - 308 q^{25} + 860 q^{29} + 424 q^{30} - 240 q^{36} + 380 q^{39} + 144 q^{44} + 208 q^{46} - 88 q^{50} - 988 q^{51} - 576 q^{60} - 512 q^{64} + 344 q^{65} - 3528 q^{71} + 3024 q^{74} - 3084 q^{79} - 1504 q^{81} - 3604 q^{85} - 896 q^{86} - 4132 q^{95} + 6504 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 + 60 * q^9 - 36 * q^11 + 144 * q^15 + 128 * q^16 - 308 * q^25 + 860 * q^29 + 424 * q^30 - 240 * q^36 + 380 * q^39 + 144 * q^44 + 208 * q^46 - 88 * q^50 - 988 * q^51 - 576 * q^60 - 512 * q^64 + 344 * q^65 - 3528 * q^71 + 3024 * q^74 - 3084 * q^79 - 1504 * q^81 - 3604 * q^85 - 896 * q^86 - 4132 * q^95 + 6504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		−	1.64308i		−	0.316210i	−0.987422	−	0.158105i	$-0.949461\pi$
$3$		−	1.64308i		−	0.316210i	0.987422	−	0.158105i	$-0.0505385\pi$
$4$	−4.00000			−0.500000
$5$	5.90338	−	9.49474i	0.528014	−	0.849236i
$5$	5.90338	−	9.49474i	0.528014	−	0.849236i
$6$	3.28615			0.223594
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$	24.3003			0.900011
$10$	18.9895	+	11.8068i	0.600500	+	0.373362i
$11$	45.9009			1.25815			0.629075	−	0.777345i	$-0.283434\pi$
$11$	45.9009			1.25815			0.629075	+	0.777345i	$0.283434\pi$
$12$			6.57231i			0.158105i
$13$			18.6843i			0.398622i	0.979936	+	0.199311i	$0.0638704\pi$
$13$			18.6843i			0.398622i	−0.979936	+	0.199311i	$0.936130\pi$
$14$		0			0
$15$	−15.6006	−	9.69970i	−0.268537	−	0.166963i
$16$	16.0000			0.250000
$17$		−	105.839i		−	1.50998i	−0.655738	−	0.754989i	$-0.727642\pi$
$17$		−	105.839i		−	1.50998i	0.655738	−	0.754989i	$-0.272358\pi$
$18$			48.6006i			0.636404i
$19$	−141.564			−1.70932			−0.854658	−	0.519191i	$-0.826233\pi$
$19$	−141.564			−1.70932			−0.854658	+	0.519191i	$0.826233\pi$
$20$	−23.6135	+	37.9790i	−0.264007	+	0.424618i
$21$		0			0
$22$			91.8018i			0.889646i
$23$			155.003i			1.40523i	0.711569	+	0.702616i	$0.247985\pi$
$23$			155.003i			1.40523i	−0.711569	+	0.702616i	$0.752015\pi$
$24$	−13.1446			−0.111797
$25$	−55.3003	−	112.102i	−0.442402	−	0.896817i
$26$	−37.3685			−0.281868
$27$		−	84.2903i		−	0.600803i
$28$		0			0
$29$	90.6997			0.580776			0.290388	−	0.956909i	$-0.406216\pi$
$29$	90.6997			0.580776			0.290388	+	0.956909i	$0.406216\pi$
$30$	19.3994	−	31.2012i	0.118061	−	0.189884i
$31$	82.2962			0.476801			0.238401	−	0.971167i	$-0.423377\pi$
$31$	82.2962			0.476801			0.238401	+	0.971167i	$0.423377\pi$
$32$			32.0000i			0.176777i
$33$		−	75.4187i		−	0.397840i
$34$	211.677			1.06772
$35$		0			0
$36$	−97.2012			−0.450006
$37$		−	289.802i		−	1.28765i	−0.765172	−	0.643826i	$-0.777346\pi$
$37$		−	289.802i		−	1.28765i	0.765172	−	0.643826i	$-0.222654\pi$
$38$		−	283.128i		−	1.20867i
$39$	30.6997			0.126048
$40$	−75.9579	−	47.2270i	−0.300250	−	0.186681i
$41$	326.224			1.24263			0.621313	−	0.783562i	$-0.286599\pi$
$41$	326.224			1.24263			0.621313	+	0.783562i	$0.286599\pi$
$42$		0			0
$43$		−	78.4024i		−	0.278052i	−0.990289	−	0.139026i	$-0.955603\pi$
$43$		−	78.4024i		−	0.278052i	0.990289	−	0.139026i	$-0.0443972\pi$
$44$	−183.604			−0.629075
$45$	143.454	−	230.725i	0.475218	−	0.764321i
$46$	−310.006			−0.993650
$47$		−	227.569i		−	0.706262i	−0.935574	−	0.353131i	$-0.885117\pi$
$47$		−	227.569i		−	0.706262i	0.935574	−	0.353131i	$-0.114883\pi$
$48$		−	26.2892i		−	0.0790526i
$49$		0			0
$50$	224.204	−	110.601i	0.634145	−	0.312826i
$51$	−173.901			−0.477471
$52$		−	74.7371i		−	0.199311i
$53$		−	10.1982i		−	0.0264308i	−0.999913	−	0.0132154i	$-0.995793\pi$
$53$		−	10.1982i		−	0.0264308i	0.999913	−	0.0132154i	$-0.00420672\pi$
$54$	168.581			0.424832
$55$	270.970	−	435.817i	0.664320	−	1.06847i
$56$		0			0
$57$			232.601i			0.540504i
$58$			181.399i			0.410671i
$59$	829.316			1.82996			0.914981	−	0.403497i	$-0.132205\pi$
$59$	829.316			1.82996			0.914981	+	0.403497i	$0.132205\pi$
$60$	62.4024	+	38.7988i	0.134269	+	0.0834817i
$61$	−661.061			−1.38754			−0.693772	−	0.720195i	$-0.744053\pi$
$61$	−661.061			−1.38754			−0.693772	+	0.720195i	$0.744053\pi$
$62$			164.592i			0.337149i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	177.402	+	110.300i	0.338524	+	0.210478i
$66$	150.837			0.281315
$67$		−	35.1952i		−	0.0641759i	−0.999485	−	0.0320879i	$-0.989784\pi$
$67$		−	35.1952i		−	0.0641759i	0.999485	−	0.0320879i	$-0.0102157\pi$
$68$			423.354i			0.754989i
$69$	254.682			0.444349
$70$		0			0
$71$	−138.595			−0.231664			−0.115832	−	0.993269i	$-0.536953\pi$
$71$	−138.595			−0.231664			−0.115832	+	0.993269i	$0.536953\pi$
$72$		−	194.402i		−	0.318202i
$73$		−	380.349i		−	0.609816i	−0.952382	−	0.304908i	$-0.901374\pi$
$73$		−	380.349i		−	0.609816i	0.952382	−	0.304908i	$-0.0986256\pi$
$74$	579.604			0.910507
$75$	−184.192	+	90.8627i	−0.283583	+	0.139892i
$76$	566.256			0.854658
$77$		0			0
$78$			61.3994i			0.0891297i
$79$	236.111			0.336260			0.168130	−	0.985765i	$-0.446227\pi$
$79$	236.111			0.336260			0.168130	+	0.985765i	$0.446227\pi$
$80$	94.4540	−	151.916i	0.132004	−	0.212309i
$81$	517.612			0.710031
$82$			652.449i			0.878670i
$83$		−	890.909i		−	1.17819i	−0.808063	−	0.589096i	$-0.799484\pi$
$83$		−	890.909i		−	1.17819i	0.808063	−	0.589096i	$-0.200516\pi$
$84$		0			0
$85$	−1004.91	−	624.805i	−1.28233	−	0.797289i
$86$	156.805			0.196613
$87$		−	149.027i		−	0.183647i
$88$		−	367.207i		−	0.444823i
$89$	−121.028			−0.144145			−0.0720727	−	0.997399i	$-0.522961\pi$
$89$	−121.028			−0.144145			−0.0720727	+	0.997399i	$0.522961\pi$
$90$	461.450	+	286.908i	0.540457	+	0.336030i
$91$		0			0
$92$		−	620.012i		−	0.702616i
$93$		−	135.219i		−	0.150769i
$94$	455.137			0.499402
$95$	−835.706	+	1344.11i	−0.902543	+	1.45161i
$96$	52.5785			0.0558986
$97$		−	1459.18i		−	1.52740i	−0.645572	−	0.763700i	$-0.723381\pi$
$97$		−	1459.18i		−	1.52740i	0.645572	−	0.763700i	$-0.276619\pi$
$98$		0			0
$99$	1115.41			1.13235
$100$	221.201	+	448.408i	0.221201	+	0.448408i
$101$	1366.89			1.34664			0.673321	−	0.739350i	$-0.264867\pi$
$101$	1366.89			1.34664			0.673321	+	0.739350i	$0.264867\pi$
$102$		−	347.802i		−	0.337623i
$103$			386.993i			0.370209i	0.982719	+	0.185105i	$0.0592624\pi$
$103$			386.993i			0.370209i	−0.982719	+	0.185105i	$0.940738\pi$
$104$	149.474			0.140934
$105$		0			0
$106$	20.3964			0.0186894
$107$		−	105.586i		−	0.0953959i	−0.998862	−	0.0476979i	$-0.984812\pi$
$107$		−	105.586i		−	0.0953959i	0.998862	−	0.0476979i	$-0.0151885\pi$
$108$			337.161i			0.300402i
$109$	461.288			0.405352			0.202676	−	0.979246i	$-0.435036\pi$
$109$	461.288			0.405352			0.202676	+	0.979246i	$0.435036\pi$
$110$	871.634	+	541.940i	0.755519	+	0.469745i
$111$	−476.167			−0.407169
$112$		0			0
$113$			1951.01i			1.62421i	0.583509	+	0.812106i	$0.301679\pi$
$113$			1951.01i			1.62421i	−0.583509	+	0.812106i	$0.698321\pi$
$114$	−465.201			−0.382194
$115$	1471.71	+	915.041i	1.19337	+	0.741983i
$116$	−362.799			−0.290388
$117$			454.033i			0.358764i
$118$			1658.63i			1.29398i
$119$		0			0
$120$	−77.5976	+	124.805i	−0.0590305	+	0.0949422i
$121$	775.892			0.582939
$122$		−	1322.12i		−	0.981142i
$123$		−	536.012i		−	0.392931i
$124$	−329.185			−0.238401
$125$	−1390.84	−	136.719i	−0.995203	−	0.0978279i
$126$		0			0
$127$		−	1027.40i		−	0.717850i	−0.933366	−	0.358925i	$-0.883143\pi$
$127$		−	1027.40i		−	0.717850i	0.933366	−	0.358925i	$-0.116857\pi$
$128$		−	128.000i		−	0.0883883i
$129$	−128.821			−0.0879230
$130$	−220.601	+	354.805i	−0.148830	+	0.239373i
$131$	−796.119			−0.530971			−0.265486	−	0.964115i	$-0.585532\pi$
$131$	−796.119			−0.530971			−0.265486	+	0.964115i	$0.585532\pi$
$132$			301.675i			0.198920i
$133$		0			0
$134$	70.3905			0.0453792
$135$	−800.315	−	497.598i	−0.510223	−	0.317232i
$136$	−846.708			−0.533858
$137$		−	1468.02i		−	0.915487i	−0.889084	−	0.457744i	$-0.848658\pi$
$137$		−	1468.02i		−	0.915487i	0.889084	−	0.457744i	$-0.151342\pi$
$138$			509.364i			0.314202i
$139$	−4.48165			−0.00273474			−0.00136737	−	0.999999i	$-0.500435\pi$
$139$	−4.48165			−0.00273474			−0.00136737	+	0.999999i	$0.500435\pi$
$140$		0			0
$141$	−373.913			−0.223327
$142$		−	277.189i		−	0.163811i
$143$			857.625i			0.501526i
$144$	388.805			0.225003
$145$	535.434	−	861.170i	0.306658	−	0.493216i
$146$	760.699			0.431205
$147$		0			0
$148$			1159.21i			0.643826i
$149$	−2292.44			−1.26043			−0.630214	−	0.776421i	$-0.717033\pi$
$149$	−2292.44			−1.26043			−0.630214	+	0.776421i	$0.717033\pi$
$150$	−181.725	−	368.385i	−0.0989187	−	0.200523i
$151$	−2652.34			−1.42943			−0.714716	−	0.699415i	$-0.753444\pi$
$151$	−2652.34			−1.42943			−0.714716	+	0.699415i	$0.753444\pi$
$152$			1132.51i			0.604335i
$153$		−	2571.91i		−	1.35900i
$154$		0			0
$155$	485.826	−	781.382i	0.251758	−	0.404917i
$156$	−122.799			−0.0630242
$157$			2952.93i			1.50108i	0.660824	+	0.750541i	$0.270207\pi$
$157$			2952.93i			1.50108i	−0.660824	+	0.750541i	$0.729793\pi$
$158$			472.222i			0.237772i
$159$	−16.7565			−0.00835769
$160$	303.832	+	188.908i	0.150125	+	0.0933406i
$161$		0			0
$162$			1035.22i			0.502068i
$163$			3861.24i			1.85543i	0.373287	+	0.927716i	$0.378231\pi$
$163$			3861.24i			1.85543i	−0.373287	+	0.927716i	$0.621769\pi$
$164$	−1304.90			−0.621313
$165$	−716.081	−	445.225i	−0.337860	−	0.210065i
$166$	1781.82			0.833107
$167$			1644.42i			0.761970i	0.924581	+	0.380985i	$0.124415\pi$
$167$			1644.42i			0.761970i	−0.924581	+	0.380985i	$0.875585\pi$
$168$		0			0
$169$	1847.90			0.841101
$170$	1249.61	−	2009.82i	0.563769	−	0.906742i
$171$	−3440.05			−1.53840
$172$			313.610i			0.139026i
$173$		−	2617.21i		−	1.15019i	−0.818087	−	0.575094i	$-0.804965\pi$
$173$		−	2617.21i		−	1.15019i	0.818087	−	0.575094i	$-0.195035\pi$
$174$	298.053			0.129858
$175$		0			0
$176$	734.414			0.314537
$177$		−	1362.63i		−	0.578653i
$178$		−	242.056i		−	0.101926i
$179$	4640.43			1.93767			0.968833	−	0.247715i	$-0.0796797\pi$
$179$	4640.43			1.93767			0.968833	+	0.247715i	$0.0796797\pi$
$180$	−573.815	+	922.900i	−0.237609	+	0.382161i
$181$	−765.567			−0.314387			−0.157194	−	0.987568i	$-0.550245\pi$
$181$	−765.567			−0.314387			−0.157194	+	0.987568i	$0.550245\pi$
$182$		0			0
$183$			1086.17i			0.438756i
$184$	1240.02			0.496825
$185$	−2751.59	−	1710.81i	−1.09352	−	0.679898i
$186$	270.438			0.106610
$187$		−	4858.08i		−	1.89978i
$188$			910.274i			0.353131i
$189$		0			0
$190$	−2688.23	−	1671.41i	−1.02645	−	0.638194i
$191$	1843.71			0.698463			0.349232	−	0.937036i	$-0.386443\pi$
$191$	1843.71			0.698463			0.349232	+	0.937036i	$0.386443\pi$
$192$			105.157i			0.0395263i
$193$		−	822.174i		−	0.306639i	−0.988177	−	0.153320i	$-0.951004\pi$
$193$		−	822.174i		−	0.306639i	0.988177	−	0.153320i	$-0.0489964\pi$
$194$	2918.37			1.08003
$195$	181.232	−	291.486i	0.0665553	−	0.107045i
$196$		0			0
$197$		−	2111.42i		−	0.763618i	−0.924241	−	0.381809i	$-0.875301\pi$
$197$		−	2111.42i		−	0.763618i	0.924241	−	0.381809i	$-0.124699\pi$
$198$			2230.81i			0.800691i
$199$	−743.392			−0.264813			−0.132406	−	0.991196i	$-0.542270\pi$
$199$	−743.392			−0.264813			−0.132406	+	0.991196i	$0.542270\pi$
$200$	−896.817	+	442.402i	−0.317073	+	0.156413i
$201$	−57.8285			−0.0202931
$202$			2733.78i			0.952220i
$203$		0			0
$204$	695.604			0.238735
$205$	1925.83	−	3097.42i	0.656124	−	1.05528i
$206$	−773.986			−0.261777
$207$			3766.62i			1.26473i
$208$			298.948i			0.0996555i
$209$	−6497.91			−2.15057
$210$		0			0
$211$	−2569.90			−0.838480			−0.419240	−	0.907875i	$-0.637703\pi$
$211$	−2569.90			−0.838480			−0.419240	+	0.907875i	$0.637703\pi$
$212$			40.7929i			0.0132154i
$213$			227.722i			0.0732546i
$214$	211.171			0.0674551
$215$	−744.410	−	462.839i	−0.236132	−	0.146816i
$216$	−674.323			−0.212416
$217$		0			0
$218$			922.577i			0.286627i
$219$	−624.943			−0.192830
$220$	−1083.88	+	1743.27i	−0.332160	+	0.534233i
$221$	1977.52			0.601910
$222$		−	952.333i		−	0.287912i
$223$			4241.83i			1.27379i	0.770952	+	0.636893i	$0.219781\pi$
$223$			4241.83i			1.27379i	−0.770952	+	0.636893i	$0.780219\pi$
$224$		0			0
$225$	−1343.81	−	2724.11i	−0.398167	−	0.807145i
$226$	−3902.03			−1.14849
$227$			905.427i			0.264737i	0.991201	+	0.132369i	$0.0422582\pi$
$227$			905.427i			0.264737i	−0.991201	+	0.132369i	$0.957742\pi$
$228$		−	930.402i		−	0.270252i
$229$	304.050			0.0877389			0.0438694	−	0.999037i	$-0.486031\pi$
$229$	304.050			0.0877389			0.0438694	+	0.999037i	$0.486031\pi$
$230$	−1830.08	+	2943.43i	−0.524661	+	0.843843i
$231$		0			0
$232$		−	725.598i		−	0.205335i
$233$			4969.61i			1.39730i	0.715466	+	0.698648i	$0.246215\pi$
$233$			4969.61i			1.39730i	−0.715466	+	0.698648i	$0.753785\pi$
$234$	−908.067			−0.253685
$235$	−2160.71	−	1343.42i	−0.599783	−	0.372916i
$236$	−3317.26			−0.914981
$237$		−	387.949i		−	0.106329i
$238$		0			0
$239$	741.901			0.200793			0.100397	−	0.994947i	$-0.467989\pi$
$239$	741.901			0.200793			0.100397	+	0.994947i	$0.467989\pi$
$240$	−249.610	−	155.195i	−0.0671343	−	0.0417409i
$241$	−3483.88			−0.931189			−0.465594	−	0.884998i	$-0.654159\pi$
$241$	−3483.88			−0.931189			−0.465594	+	0.884998i	$0.654159\pi$
$242$			1551.78i			0.412200i
$243$		−	3126.32i		−	0.825322i
$244$	2644.24			0.693772
$245$		0			0
$246$	1072.02			0.277844
$247$		−	2645.02i		−	0.681371i
$248$		−	658.370i		−	0.168575i
$249$	−1463.83			−0.372556
$250$	273.437	−	2781.68i	0.0691748	−	0.703715i
$251$	−4081.66			−1.02642			−0.513211	−	0.858262i	$-0.671544\pi$
$251$	−4081.66			−1.02642			−0.513211	+	0.858262i	$0.671544\pi$
$252$		0			0
$253$			7114.78i			1.76799i
$254$	2054.80			0.507597
$255$	−1026.60	+	1651.14i	−0.252111	+	0.405485i
$256$	256.000			0.0625000
$257$			3209.00i			0.778880i	0.921052	+	0.389440i	$0.127331\pi$
$257$			3209.00i			0.778880i	−0.921052	+	0.389440i	$0.872669\pi$
$258$		−	257.642i		−	0.0621710i
$259$		0			0
$260$	−709.610	−	441.201i	−0.169262	−	0.105239i
$261$	2204.03			0.522705
$262$		−	1592.24i		−	0.375453i
$263$		−	5040.00i		−	1.18167i	−0.806792	−	0.590836i	$-0.798798\pi$
$263$		−	5040.00i		−	1.18167i	0.806792	−	0.590836i	$-0.201202\pi$
$264$	−603.350			−0.140658
$265$	−96.8294	−	60.2039i	−0.0224460	−	0.0139558i
$266$		0			0
$267$			198.858i			0.0455803i
$268$			140.781i			0.0320879i
$269$	−5292.27			−1.19954			−0.599768	−	0.800174i	$-0.704741\pi$
$269$	−5292.27			−1.19954			−0.599768	+	0.800174i	$0.704741\pi$
$270$	995.195	−	1600.63i	0.224317	−	0.360782i
$271$	2285.68			0.512343			0.256172	−	0.966631i	$-0.417539\pi$
$271$	2285.68			0.512343			0.256172	+	0.966631i	$0.417539\pi$
$272$		−	1693.42i		−	0.377494i
$273$		0			0
$274$	2936.05			0.647347
$275$	−2538.33	−	5145.59i	−0.556608	−	1.12833i
$276$	−1018.73			−0.222175
$277$			5738.68i			1.24478i	0.782708	+	0.622389i	$0.213838\pi$
$277$			5738.68i			1.24478i	−0.782708	+	0.622389i	$0.786162\pi$
$278$		−	8.96329i		−	0.00193375i
$279$	1999.82			0.429126
$280$		0			0
$281$	−3098.71			−0.657842			−0.328921	−	0.944357i	$-0.606685\pi$
$281$	−3098.71			−0.657842			−0.328921	+	0.944357i	$0.606685\pi$
$282$		−	747.826i		−	0.157916i
$283$			6876.02i			1.44430i	0.691736	+	0.722150i	$0.256846\pi$
$283$			6876.02i			1.44430i	−0.691736	+	0.722150i	$0.743154\pi$
$284$	554.379			0.115832
$285$	2208.48	+	1373.13i	0.459015	+	0.285393i
$286$	−1715.25			−0.354632
$287$		0			0
$288$			777.610i			0.159101i
$289$	−6288.80			−1.28003
$290$	1722.34	+	1070.87i	0.348756	+	0.216840i
$291$	−2397.55			−0.482979
$292$			1521.40i			0.304908i
$293$			540.278i			0.107725i	0.998548	+	0.0538624i	$0.0171532\pi$
$293$			540.278i			0.107725i	−0.998548	+	0.0538624i	$0.982847\pi$
$294$		0			0
$295$	4895.77	−	7874.14i	0.966246	−	1.55407i
$296$	−2318.41			−0.455254
$297$		−	3869.00i		−	0.755900i
$298$		−	4584.88i		−	0.891258i
$299$	−2896.12			−0.560157
$300$	736.769	−	363.451i	0.141791	−	0.0699461i
$301$		0			0
$302$		−	5304.68i		−	1.01076i
$303$		−	2245.91i		−	0.425822i
$304$	−2265.02			−0.427329
$305$	−3902.49	+	6276.61i	−0.732643	+	1.17835i
$306$	5143.82			0.960956
$307$			2335.65i			0.434210i	0.976148	+	0.217105i	$0.0696613\pi$
$307$			2335.65i			0.434210i	−0.976148	+	0.217105i	$0.930339\pi$
$308$		0			0
$309$	635.859			0.117064
$310$	1562.76	+	971.651i	0.286319	+	0.178020i
$311$	8461.81			1.54285			0.771424	−	0.636322i	$-0.219545\pi$
$311$	8461.81			1.54285			0.771424	+	0.636322i	$0.219545\pi$
$312$		−	245.598i		−	0.0445648i
$313$			4476.99i			0.808481i	0.914653	+	0.404240i	$0.132464\pi$
$313$			4476.99i			0.808481i	−0.914653	+	0.404240i	$0.867536\pi$
$314$	−5905.87			−1.06143
$315$		0			0
$316$	−944.444			−0.168130
$317$			5106.32i			0.904730i	0.891833	+	0.452365i	$0.149420\pi$
$317$			5106.32i			0.904730i	−0.891833	+	0.452365i	$0.850580\pi$
$318$		−	33.5129i		−	0.00590978i
$319$	4163.20			0.730703
$320$	−377.816	+	607.664i	−0.0660018	+	0.106154i
$321$	−173.485			−0.0301652
$322$		0			0
$323$			14982.9i			2.58103i
$324$	−2070.45			−0.355015
$325$	2094.55	−	1033.25i	0.357491	−	0.176351i
$326$	−7722.47			−1.31199
$327$		−	757.932i		−	0.128177i
$328$		−	2609.80i		−	0.439335i
$329$		0			0
$330$	890.450	−	1432.16i	0.148538	−	0.238903i
$331$	6438.01			1.06908			0.534539	−	0.845144i	$-0.320485\pi$
$331$	6438.01			1.06908			0.534539	+	0.845144i	$0.320485\pi$
$332$			3563.63i			0.589096i
$333$		−	7042.27i		−	1.15890i
$334$	−3288.84			−0.538794
$335$	−334.170	−	207.771i	−0.0545004	−	0.0338858i
$336$		0			0
$337$		−	4480.18i		−	0.724187i	−0.932142	−	0.362093i	$-0.882062\pi$
$337$		−	4480.18i		−	0.724187i	0.932142	−	0.362093i	$-0.117938\pi$
$338$			3695.80i			0.594748i
$339$	3205.67			0.513593
$340$	4019.64	+	2499.22i	0.641163	+	0.398645i
$341$	3777.47			0.599887
$342$		−	6880.10i		−	1.08782i
$343$		0			0
$344$	−627.219			−0.0983064
$345$	1503.48	−	2418.14i	0.234623	−	0.377357i
$346$	5234.41			0.813306
$347$		−	4781.32i		−	0.739697i	−0.929092	−	0.369848i	$-0.879410\pi$
$347$		−	4781.32i		−	0.739697i	0.929092	−	0.369848i	$-0.120590\pi$
$348$			596.106i			0.0918237i
$349$	8732.50			1.33937			0.669685	−	0.742645i	$-0.266429\pi$
$349$	8732.50			1.33937			0.669685	+	0.742645i	$0.266429\pi$
$350$		0			0
$351$	1574.90			0.239493
$352$			1468.83i			0.222411i
$353$		−	11595.1i		−	1.74828i	−0.485672	−	0.874141i	$-0.661425\pi$
$353$		−	11595.1i		−	1.74828i	0.485672	−	0.874141i	$-0.338575\pi$
$354$	2725.26			0.409169
$355$	−818.176	+	1315.92i	−0.122322	+	0.196737i
$356$	484.112			0.0720727
$357$		0			0
$358$			9280.86i			1.37014i
$359$	7406.91			1.08892			0.544459	−	0.838787i	$-0.316735\pi$
$359$	7406.91			1.08892			0.544459	+	0.838787i	$0.316735\pi$
$360$	−1845.80	−	1147.63i	−0.270228	−	0.168015i
$361$	13181.4			1.92176
$362$		−	1531.13i		−	0.222305i
$363$		−	1274.85i		−	0.184331i
$364$		0			0
$365$	−3611.32	−	2245.35i	−0.517877	−	0.321991i
$366$	−2172.35			−0.310247
$367$			11724.5i			1.66762i	0.552053	+	0.833809i	$0.313845\pi$
$367$			11724.5i			1.66762i	−0.552053	+	0.833809i	$0.686155\pi$
$368$			2480.05i			0.351308i
$369$	7927.35			1.11838
$370$	3421.62	−	5503.19i	0.480761	−	0.773235i
$371$		0			0
$372$			540.876i			0.0753847i
$373$			11243.1i			1.56071i	0.625338	+	0.780354i	$0.284961\pi$
$373$			11243.1i			1.56071i	−0.625338	+	0.780354i	$0.715039\pi$
$374$	9716.17			1.34335
$375$	−224.639	+	2285.26i	−0.0309342	+	0.314694i
$376$	−1820.55			−0.249701
$377$			1694.66i			0.231510i
$378$		0			0
$379$	−4871.25			−0.660210			−0.330105	−	0.943944i	$-0.607084\pi$
$379$	−4871.25			−0.660210			−0.330105	+	0.943944i	$0.607084\pi$
$380$	3342.82	−	5376.46i	0.451272	−	0.725806i
$381$	−1688.10			−0.226992
$382$			3687.43i			0.493888i
$383$			12604.1i			1.68157i	0.541370	+	0.840784i	$0.317906\pi$
$383$			12604.1i			1.68157i	−0.541370	+	0.840784i	$0.682094\pi$
$384$	−210.314			−0.0279493
$385$		0			0
$386$	1644.35			0.216827
$387$		−	1905.20i		−	0.250250i
$388$			5836.74i			0.763700i
$389$	−12183.2			−1.58796			−0.793978	−	0.607947i	$-0.791993\pi$
$389$	−12183.2			−1.58796			−0.793978	+	0.607947i	$0.791993\pi$
$390$	582.972	+	362.464i	0.0756921	+	0.0470617i
$391$	16405.3			2.12187
$392$		0			0
$393$			1308.09i			0.167899i
$394$	4222.85			0.539959
$395$	1393.85	−	2241.81i	0.177550	−	0.285564i
$396$	−4461.62			−0.566174
$397$			3731.14i			0.471689i	0.971791	+	0.235845i	$0.0757856\pi$
$397$			3731.14i			0.471689i	−0.971791	+	0.235845i	$0.924214\pi$
$398$		−	1486.78i		−	0.187251i
$399$		0			0
$400$	−884.805	−	1793.63i	−0.110601	−	0.224204i
$401$	−3708.81			−0.461868			−0.230934	−	0.972969i	$-0.574178\pi$
$401$	−3708.81			−0.461868			−0.230934	+	0.972969i	$0.574178\pi$
$402$		−	115.657i		−	0.0143494i
$403$			1537.65i			0.190063i
$404$	−5467.57			−0.673321
$405$	3055.66	−	4914.60i	0.374906	−	0.602984i
$406$		0			0
$407$		−	13302.2i		−	1.62006i
$408$			1391.21i			0.168811i
$409$	7170.15			0.866849			0.433424	−	0.901190i	$-0.357305\pi$
$409$	7170.15			0.866849			0.433424	+	0.901190i	$0.357305\pi$
$410$	6194.83	+	3851.65i	0.746198	+	0.463950i
$411$	−2412.08			−0.289486
$412$		−	1547.97i		−	0.185105i
$413$		0			0
$414$	−7533.24			−0.894296
$415$	−8458.95	−	5259.37i	−1.00056	−	0.622102i
$416$	−597.897			−0.0704671
$417$			7.36369i			0.000864752i
$418$		−	12995.8i		−	1.52069i
$419$	4845.95			0.565013			0.282506	−	0.959265i	$-0.408834\pi$
$419$	4845.95			0.565013			0.282506	+	0.959265i	$0.408834\pi$
$420$		0			0
$421$	9744.07			1.12802			0.564010	−	0.825768i	$-0.309258\pi$
$421$	9744.07			1.12802			0.564010	+	0.825768i	$0.309258\pi$
$422$		−	5139.80i		−	0.592895i
$423$		−	5529.99i		−	0.635643i
$424$	−81.5857			−0.00934470
$425$	−11864.7	+	5852.90i	−1.35417	+	0.668018i
$426$	−455.443			−0.0517988
$427$		0			0
$428$			422.343i			0.0476979i
$429$	1409.14			0.158588
$430$	925.678	−	1488.82i	0.103814	−	0.166971i
$431$	8295.11			0.927057			0.463529	−	0.886082i	$-0.346583\pi$
$431$	8295.11			0.927057			0.463529	+	0.886082i	$0.346583\pi$
$432$		−	1348.65i		−	0.150201i
$433$		−	7365.97i		−	0.817519i	−0.912642	−	0.408760i	$-0.865961\pi$
$433$		−	7365.97i		−	0.817519i	0.912642	−	0.408760i	$-0.134039\pi$
$434$		0			0
$435$	−1414.97	−	879.760i	−0.155960	−	0.0969684i
$436$	−1845.15			−0.202676
$437$		−	21942.8i		−	2.40199i
$438$		−	1249.89i		−	0.136351i
$439$	1950.02			0.212003			0.106002	−	0.994366i	$-0.466195\pi$
$439$	1950.02			0.212003			0.106002	+	0.994366i	$0.466195\pi$
$440$	−3486.54	−	2167.76i	−0.377759	−	0.234873i
$441$		0			0
$442$			3955.03i			0.425615i
$443$			15976.4i			1.71346i	0.515763	+	0.856731i	$0.327508\pi$
$443$			15976.4i			1.71346i	−0.515763	+	0.856731i	$0.672492\pi$
$444$	1904.67			0.203584
$445$	−714.474	+	1149.13i	−0.0761108	+	0.122413i
$446$	−8483.67			−0.900702
$447$			3766.65i			0.398561i
$448$		0			0
$449$	5292.90			0.556319			0.278159	−	0.960535i	$-0.410276\pi$
$449$	5292.90			0.556319			0.278159	+	0.960535i	$0.410276\pi$
$450$	5448.23	−	2687.63i	0.570738	−	0.281547i
$451$	14974.0			1.56341
$452$		−	7804.06i		−	0.812106i
$453$			4358.00i			0.452001i
$454$	−1810.85			−0.187197
$455$		0			0
$456$	1860.80			0.191097
$457$		−	15964.8i		−	1.63414i	−0.576540	−	0.817069i	$-0.695598\pi$
$457$		−	15964.8i		−	1.63414i	0.576540	−	0.817069i	$-0.304402\pi$
$458$			608.100i			0.0620408i
$459$	−8921.17			−0.907199
$460$	−5886.85	−	3660.16i	−0.596687	−	0.370991i
$461$	−11072.7			−1.11867			−0.559337	−	0.828940i	$-0.688944\pi$
$461$	−11072.7			−1.11867			−0.559337	+	0.828940i	$0.688944\pi$
$462$		0			0
$463$			11210.0i			1.12521i	0.826727	+	0.562604i	$0.190200\pi$
$463$			11210.0i			1.12521i	−0.826727	+	0.562604i	$0.809800\pi$
$464$	1451.20			0.145194
$465$	−1283.87	−	798.249i	−0.128039	−	0.0796084i
$466$	−9939.22			−0.988037
$467$			11211.7i			1.11096i	0.831532	+	0.555478i	$0.187465\pi$
$467$			11211.7i			1.11096i	−0.831532	+	0.555478i	$0.812535\pi$
$468$		−	1816.13i		−	0.179382i
$469$		0			0
$470$	2686.85	−	4321.41i	0.263691	−	0.424110i
$471$	4851.90			0.474658
$472$		−	6634.53i		−	0.646989i
$473$		−	3598.74i		−	0.349831i
$474$	775.897			0.0751859
$475$	7828.53	+	15869.6i	0.756206	+	1.53294i
$476$		0			0
$477$		−	247.820i		−	0.0237880i
$478$			1483.80i			0.141982i
$479$	7983.06			0.761494			0.380747	−	0.924679i	$-0.375667\pi$
$479$	7983.06			0.761494			0.380747	+	0.924679i	$0.375667\pi$
$480$	310.390	−	499.219i	0.0295153	−	0.0474711i
$481$	5414.74			0.513286
$482$		−	6967.76i		−	0.658450i
$483$		0			0
$484$	−3103.57			−0.291470
$485$	−13854.6	−	8614.11i	−1.29712	−	0.806488i
$486$	6252.63			0.583591
$487$		−	4408.56i		−	0.410208i	−0.978740	−	0.205104i	$-0.934247\pi$
$487$		−	4408.56i		−	0.410208i	0.978740	−	0.205104i	$-0.0657532\pi$
$488$			5288.49i			0.490571i
$489$	6344.31			0.586707
$490$		0			0
$491$	−12504.0			−1.14928			−0.574641	−	0.818405i	$-0.694858\pi$
$491$	−12504.0			−1.14928			−0.574641	+	0.818405i	$0.694858\pi$
$492$			2144.05i			0.196466i
$493$		−	9599.52i		−	0.876959i
$494$	5290.04			0.481802
$495$	6584.66	−	10590.5i	0.597896	−	0.961630i
$496$	1316.74			0.119200
$497$		0			0
$498$		−	2927.66i		−	0.263437i
$499$	−13774.5			−1.23573			−0.617866	−	0.786283i	$-0.712003\pi$
$499$	−13774.5			−1.23573			−0.617866	+	0.786283i	$0.712003\pi$
$500$	5563.36	+	546.875i	0.497602	+	0.0489140i
$501$	2701.91			0.240943
$502$		−	8163.32i		−	0.725791i
$503$			20969.7i			1.85883i	0.369034	+	0.929416i	$0.379689\pi$
$503$			20969.7i			1.85883i	−0.369034	+	0.929416i	$0.620311\pi$
$504$		0			0
$505$	8069.28	−	12978.3i	0.711046	−	1.14362i
$506$	−14229.6			−1.25016
$507$		−	3036.24i		−	0.265965i
$508$			4109.60i			0.358925i
$509$	−21256.9			−1.85107			−0.925537	−	0.378658i	$-0.876386\pi$
$509$	−21256.9			−1.85107			−0.925537	+	0.378658i	$0.876386\pi$
$510$	−3302.29	−	2053.20i	−0.286721	−	0.178269i
$511$		0			0
$512$			512.000i			0.0441942i
$513$			11932.5i			1.02696i
$514$	−6418.01			−0.550751
$515$	3674.40	+	2284.56i	0.314395	+	0.195476i
$516$	515.285			0.0439615
$517$		−	10445.6i		−	0.888582i
$518$		0			0
$519$	−4300.27			−0.363701
$520$	882.402	−	1419.22i	0.0744152	−	0.119686i
$521$	−11484.7			−0.965750			−0.482875	−	0.875689i	$-0.660407\pi$
$521$	−11484.7			−0.965750			−0.482875	+	0.875689i	$0.660407\pi$
$522$			4408.06i			0.369608i
$523$		−	18770.0i		−	1.56932i	−0.619928	−	0.784658i	$-0.712838\pi$
$523$		−	18770.0i		−	1.56932i	0.619928	−	0.784658i	$-0.287162\pi$
$524$	3184.48			0.265486
$525$		0			0
$526$	10080.0			0.835568
$527$		−	8710.11i		−	0.719959i
$528$		−	1206.70i		−	0.0994599i
$529$	−11858.9			−0.974679
$530$	120.408	−	193.659i	0.00986826	−	0.0158717i
$531$	20152.6			1.64699
$532$		0			0
$533$			6095.27i			0.495338i
$534$	−397.717			−0.0322301
$535$	−1002.51	−	623.312i	−0.0810136	−	0.0503703i
$536$	−281.562			−0.0226896
$537$		−	7624.59i		−	0.612710i
$538$		−	10584.5i		−	0.848200i
$539$		0			0
$540$	3201.26	+	1990.39i	0.255112	+	0.158616i
$541$	20737.9			1.64805			0.824023	−	0.566556i	$-0.191725\pi$
$541$	20737.9			1.64805			0.824023	+	0.566556i	$0.191725\pi$
$542$			4571.35i			0.362281i
$543$			1257.89i			0.0994126i
$544$	3386.83			0.266929
$545$	2723.16	−	4379.81i	0.214032	−	0.344240i
$546$		0			0
$547$			11524.2i			0.900800i	0.892827	+	0.450400i	$0.148719\pi$
$547$			11524.2i			0.900800i	−0.892827	+	0.450400i	$0.851281\pi$
$548$			5872.10i			0.457744i
$549$	−16064.0			−1.24881
$550$	10291.2	−	5076.67i	0.797849	−	0.393581i
$551$	−12839.8			−0.992730
$552$		−	2037.45i		−	0.157101i
$553$		0			0
$554$	−11477.4			−0.880192
$555$	−2810.99	+	4521.08i	−0.214991	+	0.345782i
$556$	17.9266			0.00136737
$557$			11586.7i			0.881408i	0.897652	+	0.440704i	$0.145271\pi$
$557$			11586.7i			0.881408i	−0.897652	+	0.440704i	$0.854729\pi$
$558$			3999.65i			0.303438i
$559$	1464.89			0.110838
$560$		0			0
$561$	−7982.21			−0.600729
$562$		−	6197.42i		−	0.465165i
$563$			11883.8i			0.889593i	0.895632	+	0.444797i	$0.146724\pi$
$563$			11883.8i			0.889593i	−0.895632	+	0.444797i	$0.853276\pi$
$564$	1495.65			0.111664
$565$	18524.4	+	11517.6i	1.37934	+	0.857607i
$566$	−13752.0			−1.02127
$567$		0			0
$568$			1108.76i			0.0819057i
$569$	18776.4			1.38339			0.691694	−	0.722191i	$-0.256865\pi$
$569$	18776.4			1.38339			0.691694	+	0.722191i	$0.256865\pi$
$570$	−2746.26	+	4416.97i	−0.201804	+	0.324573i
$571$	9328.82			0.683711			0.341855	−	0.939753i	$-0.388945\pi$
$571$	9328.82			0.683711			0.341855	+	0.939753i	$0.388945\pi$
$572$		−	3430.50i		−	0.250763i
$573$		−	3029.37i		−	0.220861i
$574$		0			0
$575$	17376.2	−	8571.71i	1.26024	−	0.621678i
$576$	−1555.22			−0.112501
$577$		−	1156.99i		−	0.0834767i	−0.999129	−	0.0417384i	$-0.986710\pi$
$577$		−	1156.99i		−	0.0834767i	0.999129	−	0.0417384i	$-0.0132896\pi$
$578$		−	12577.6i		−	0.905119i
$579$	−1350.90			−0.0969626
$580$	−2141.74	+	3444.68i	−0.153329	+	0.246608i
$581$		0			0
$582$		−	4795.10i		−	0.341518i
$583$		−	468.107i		−	0.0332539i
$584$	−3042.80			−0.215602
$585$	4310.93	+	2680.33i	0.304675	+	0.189432i
$586$	−1080.56			−0.0761729
$587$			22250.1i			1.56450i	0.622968	+	0.782248i	$0.285927\pi$
$587$			22250.1i			1.56450i	−0.622968	+	0.782248i	$0.714073\pi$
$588$		0			0
$589$	−11650.2			−0.815004
$590$	15748.3	+	9791.53i	1.09889	+	0.683239i
$591$	−3469.23			−0.241464
$592$		−	4636.83i		−	0.321913i
$593$			3518.99i			0.243689i	0.992549	+	0.121845i	$0.0388809\pi$
$593$			3518.99i			0.243689i	−0.992549	+	0.121845i	$0.961119\pi$
$594$	7738.00			0.534502
$595$		0			0
$596$	9169.75			0.630214
$597$			1221.45i			0.0837365i
$598$		−	5792.24i		−	0.396091i
$599$	−13879.3			−0.946730			−0.473365	−	0.880866i	$-0.656961\pi$
$599$	−13879.3			−0.946730			−0.473365	+	0.880866i	$0.656961\pi$
$600$	726.901	+	1473.54i	0.0494594	+	0.100262i
$601$	−3235.75			−0.219616			−0.109808	−	0.993953i	$-0.535024\pi$
$601$	−3235.75			−0.219616			−0.109808	+	0.993953i	$0.535024\pi$
$602$		0			0
$603$		−	855.255i		−	0.0577590i
$604$	10609.4			0.714716
$605$	4580.38	−	7366.89i	0.307800	−	0.495053i
$606$	4491.82			0.301102
$607$			2283.47i			0.152691i	0.997081	+	0.0763453i	$0.0243251\pi$
$607$			2283.47i			0.152691i	−0.997081	+	0.0763453i	$0.975675\pi$
$608$		−	4530.05i		−	0.302167i
$609$		0			0
$610$	−12553.2	−	7804.99i	−0.833221	−	0.518057i
$611$	4251.95			0.281531
$612$			10287.6i			0.679498i
$613$			336.783i			0.0221901i	0.999938	+	0.0110950i	$0.00353174\pi$
$613$			336.783i			0.0221901i	−0.999938	+	0.0110950i	$0.996468\pi$
$614$	−4671.29			−0.307033
$615$	−5089.30	−	3164.28i	−0.333691	−	0.207473i
$616$		0			0
$617$			9923.71i			0.647510i	0.946141	+	0.323755i	$0.104945\pi$
$617$			9923.71i			0.647510i	−0.946141	+	0.323755i	$0.895055\pi$
$618$			1271.72i			0.0827767i
$619$	−7070.90			−0.459133			−0.229567	−	0.973293i	$-0.573731\pi$
$619$	−7070.90			−0.459133			−0.229567	+	0.973293i	$0.573731\pi$
$620$	−1943.30	+	3125.53i	−0.125879	+	0.202458i
$621$	13065.3			0.844268
$622$			16923.6i			1.09096i
$623$		0			0
$624$	491.195			0.0315121
$625$	−9508.75	+	12398.6i	−0.608560	+	0.793508i
$626$	−8953.98			−0.571682
$627$			10676.6i			0.680034i
$628$		−	11811.7i		−	0.750541i
$629$	−30672.2			−1.94433
$630$		0			0
$631$	−1932.85			−0.121942			−0.0609711	−	0.998140i	$-0.519420\pi$
$631$	−1932.85			−0.121942			−0.0609711	+	0.998140i	$0.519420\pi$
$632$		−	1888.89i		−	0.118886i
$633$			4222.55i			0.265136i
$634$	−10212.6			−0.639741
$635$	−9754.89	−	6065.13i	−0.609624	−	0.379035i
$636$	67.0258			0.00417885
$637$		0			0
$638$			8326.39i			0.516685i
$639$	−3367.89			−0.208500
$640$	−1215.33	−	755.632i	−0.0750625	−	0.0466703i
$641$	12664.2			0.780354			0.390177	−	0.920740i	$-0.372414\pi$
$641$	12664.2			0.780354			0.390177	+	0.920740i	$0.372414\pi$
$642$		−	346.971i		−	0.0213300i
$643$		−	6058.05i		−	0.371550i	−0.982592	−	0.185775i	$-0.940521\pi$
$643$		−	6058.05i		−	0.371550i	0.982592	−	0.185775i	$-0.0594795\pi$
$644$		0			0
$645$	−760.480	+	1223.12i	−0.0464246	+	0.0746674i
$646$	−29965.9			−1.82506
$647$			23819.4i			1.44735i	0.690140	+	0.723676i	$0.257549\pi$
$647$			23819.4i			1.44735i	−0.690140	+	0.723676i	$0.742451\pi$
$648$		−	4140.90i		−	0.251034i
$649$	38066.4			2.30237
$650$	2066.49	+	4189.09i	0.124699	+	0.252784i
$651$		0			0
$652$		−	15444.9i		−	0.927716i
$653$		−	26054.5i		−	1.56140i	−0.624908	−	0.780698i	$-0.714864\pi$
$653$		−	26054.5i		−	1.56140i	0.624908	−	0.780698i	$-0.285136\pi$
$654$	1515.86			0.0906346
$655$	−4699.79	+	7558.95i	−0.280360	+	0.450920i
$656$	5219.59			0.310657
$657$		−	9242.60i		−	0.548841i
$658$		0			0
$659$	3825.76			0.226146			0.113073	−	0.993587i	$-0.463931\pi$
$659$	3825.76			0.226146			0.113073	+	0.993587i	$0.463931\pi$
$660$	2864.33	+	1780.90i	0.168930	+	0.105032i
$661$	−17551.2			−1.03277			−0.516385	−	0.856356i	$-0.672723\pi$
$661$	−17551.2			−1.03277			−0.516385	+	0.856356i	$0.672723\pi$
$662$			12876.0i			0.755952i
$663$		−	3249.21i		−	0.190330i
$664$	−7127.27			−0.416554
$665$		0			0
$666$	14084.5			0.819467
$667$			14058.7i			0.816126i
$668$		−	6577.68i		−	0.380985i
$669$	6969.66			0.402784
$670$	415.541	−	668.339i	0.0239608	−	0.0385376i
$671$	−30343.3			−1.74574
$672$		0			0
$673$			12750.8i			0.730320i	0.930945	+	0.365160i	$0.118986\pi$
$673$			12750.8i			0.730320i	−0.930945	+	0.365160i	$0.881014\pi$
$674$	8960.36			0.512077
$675$	−9449.12	+	4661.28i	−0.538810	+	0.265797i
$676$	−7391.59			−0.420550
$677$			6811.42i			0.386683i	0.981132	+	0.193341i	$0.0619325\pi$
$677$			6811.42i			0.386683i	−0.981132	+	0.193341i	$0.938068\pi$
$678$			6411.34i			0.363165i
$679$		0			0
$680$	−4998.44	+	8039.28i	−0.281884	+	0.453371i
$681$	1487.69			0.0837126
$682$			7554.94i			0.424184i
$683$		−	20480.6i		−	1.14739i	−0.819068	−	0.573696i	$-0.805509\pi$
$683$		−	20480.6i		−	1.14739i	0.819068	−	0.573696i	$-0.194491\pi$
$684$	13760.2			0.769202
$685$	−13938.5	−	8666.30i	−0.777464	−	0.483390i
$686$		0			0
$687$		−	499.578i		−	0.0277439i
$688$		−	1254.44i		−	0.0695131i
$689$	190.546			0.0105359
$690$	4836.28	+	3006.97i	0.266832	+	0.165903i
$691$	5776.59			0.318020			0.159010	−	0.987277i	$-0.449170\pi$
$691$	5776.59			0.318020			0.159010	+	0.987277i	$0.449170\pi$
$692$			10468.8i			0.575094i
$693$		0			0
$694$	9562.64			0.523044
$695$	−26.4568	+	42.5521i	−0.00144398	+	0.00232244i
$696$	−1192.21			−0.0649292
$697$		−	34527.1i		−	1.87634i
$698$			17465.0i			0.947078i
$699$	8165.45			0.441839
$700$		0			0
$701$	−11445.0			−0.616650			−0.308325	−	0.951281i	$-0.599768\pi$
$701$	−11445.0			−0.616650			−0.308325	+	0.951281i	$0.599768\pi$
$702$			3149.81i			0.169347i
$703$			41025.5i			2.20100i
$704$	−2937.66			−0.157269
$705$	−2207.35	+	3550.21i	−0.117920	+	0.189657i
$706$	23190.1			1.23622
$707$		0			0
$708$			5450.52i			0.289326i
$709$	−123.956			−0.00656597			−0.00328299	−	0.999995i	$-0.501045\pi$
$709$	−123.956			−0.00656597			−0.00328299	+	0.999995i	$0.501045\pi$
$710$	−2631.84	−	1636.35i	−0.139114	−	0.0864947i
$711$	5737.57			0.302638
$712$			968.224i			0.0509631i
$713$			12756.2i			0.670017i
$714$		0			0
$715$	8142.93	+	5062.88i	0.425914	+	0.264813i
$716$	−18561.7			−0.968833
$717$		−	1219.00i		−	0.0634929i
$718$			14813.8i			0.769981i
$719$	4351.29			0.225696			0.112848	−	0.993612i	$-0.464003\pi$
$719$	4351.29			0.225696			0.112848	+	0.993612i	$0.464003\pi$
$720$	2295.26	−	3691.60i	0.118805	−	0.191080i
$721$		0			0
$722$			26362.7i			1.35889i
$723$			5724.29i			0.294452i
$724$	3062.27			0.157194
$725$	−5015.72	−	10167.6i	−0.256937	−	0.520850i
$726$	2549.70			0.130342
$727$		−	14618.1i		−	0.745745i	−0.927883	−	0.372873i	$-0.878373\pi$
$727$		−	14618.1i		−	0.745745i	0.927883	−	0.372873i	$-0.121627\pi$
$728$		0			0
$729$	8838.76			0.449055
$730$	4490.69	−	7222.64i	0.227682	−	0.366194i
$731$	−8297.99			−0.419853
$732$		−	4344.70i		−	0.219378i
$733$			13412.0i			0.675831i	0.941176	+	0.337916i	$0.109722\pi$
$733$			13412.0i			0.675831i	−0.941176	+	0.337916i	$0.890278\pi$
$734$	−23449.1			−1.17918
$735$		0			0
$736$	−4960.10			−0.248412
$737$		−	1615.49i		−	0.0807428i
$738$			15854.7i			0.790813i
$739$	−11893.7			−0.592037			−0.296018	−	0.955182i	$-0.595659\pi$
$739$	−11893.7			−0.592037			−0.296018	+	0.955182i	$0.595659\pi$
$740$	11006.4	+	6843.24i	0.546760	+	0.339949i
$741$	−4345.97			−0.215457
$742$		0			0
$743$		−	33413.5i		−	1.64983i	−0.565259	−	0.824914i	$-0.691224\pi$
$743$		−	33413.5i		−	1.64983i	0.565259	−	0.824914i	$-0.308776\pi$
$744$	−1081.75			−0.0533051
$745$	−13533.1	+	21766.1i	−0.665524	+	1.07040i
$746$	−22486.1			−1.10359
$747$		−	21649.3i		−	1.06039i
$748$			19432.3i			0.949888i
$749$		0			0
$750$	−4570.51	−	449.279i	−0.222522	−	0.0218738i
$751$	22761.9			1.10598			0.552992	−	0.833187i	$-0.313486\pi$
$751$	22761.9			1.10598			0.552992	+	0.833187i	$0.313486\pi$
$752$		−	3641.10i		−	0.176565i
$753$			6706.48i			0.324566i
$754$	−3389.32			−0.163702
$755$	−15657.8	+	25183.3i	−0.754760	+	1.21392i
$756$		0			0
$757$		−	27222.3i		−	1.30702i	−0.756919	−	0.653509i	$-0.773296\pi$
$757$		−	27222.3i		−	1.30702i	0.756919	−	0.653509i	$-0.226704\pi$
$758$		−	9742.51i		−	0.466839i
$759$	11690.1			0.559057
$760$	10752.9	+	6685.65i	0.513223	+	0.319097i
$761$	−26825.7			−1.27783			−0.638917	−	0.769276i	$-0.720617\pi$
$761$	−26825.7			−1.27783			−0.638917	+	0.769276i	$0.720617\pi$
$762$		−	3376.19i		−	0.160507i
$763$		0			0
$764$	−7374.86			−0.349232
$765$	−24419.6	−	15182.9i	−1.15411	−	0.717569i
$766$	−25208.3			−1.18905
$767$			15495.2i			0.729463i
$768$		−	420.628i		−	0.0197631i
$769$	−18093.8			−0.848477			−0.424239	−	0.905550i	$-0.639458\pi$
$769$	−18093.8			−0.848477			−0.424239	+	0.905550i	$0.639458\pi$
$770$		0			0
$771$	5272.64			0.246290
$772$			3288.70i			0.153320i
$773$		−	16783.8i		−	0.780945i	−0.920615	−	0.390473i	$-0.872312\pi$
$773$		−	16783.8i		−	0.780945i	0.920615	−	0.390473i	$-0.127688\pi$
$774$	3810.40			0.176954
$775$	−4551.01	−	9225.58i	−0.210938	−	0.427603i
$776$	−11673.5			−0.540017
$777$		0			0
$778$		−	24366.5i		−	1.12285i
$779$	−46181.6			−2.12404
$780$	−724.928	+	1165.94i	−0.0332777	+	0.0535224i
$781$	−6361.62			−0.291468
$782$			32810.6i			1.50039i
$783$		−	7645.11i		−	0.348932i
$784$		0			0
$785$	28037.4	+	17432.3i	1.27477	+	0.792592i
$786$	−2616.17			−0.118722
$787$		−	1229.26i		−	0.0556779i	−0.999612	−	0.0278389i	$-0.991137\pi$
$787$		−	1229.26i		−	0.0556779i	0.999612	−	0.0278389i	$-0.00886255\pi$
$788$			8445.69i			0.381809i
$789$	−8281.11			−0.373657
$790$	4483.63	+	2787.70i	0.201924	+	0.125547i
$791$		0			0
$792$		−	8923.24i		−	0.400345i
$793$		−	12351.4i		−	0.553106i
$794$	−7462.28			−0.333535
$795$	−98.9196	+	159.098i	−0.00441298	+	0.00709765i
$796$	2973.57			0.132406
$797$		−	10084.7i		−	0.448204i	−0.974566	−	0.224102i	$-0.928055\pi$
$797$		−	10084.7i		−	0.448204i	0.974566	−	0.224102i	$-0.0719449\pi$
$798$		0			0
$799$	−24085.5			−1.06644
$800$	3587.27	−	1769.61i	0.158536	−	0.0782064i
$801$	−2941.02			−0.129732
$802$		−	7417.61i		−	0.326590i
$803$		−	17458.4i		−	0.767239i
$804$	231.314			0.0101465
$805$		0			0
$806$	−3075.29			−0.134395
$807$			8695.61i			0.379306i
$808$		−	10935.1i		−	0.476110i
$809$	14669.5			0.637517			0.318758	−	0.947836i	$-0.396734\pi$
$809$	14669.5			0.637517			0.318758	+	0.947836i	$0.396734\pi$
$810$	9829.20	+	6111.32i	0.426374	+	0.265099i
$811$	−7101.55			−0.307483			−0.153742	−	0.988111i	$-0.549132\pi$
$811$	−7101.55			−0.307483			−0.153742	+	0.988111i	$0.549132\pi$
$812$		0			0
$813$		−	3755.54i		−	0.162008i
$814$	26604.3			1.14555
$815$	36661.5	+	22794.3i	1.57570	+	0.979694i
$816$	−2782.41			−0.119368
$817$			11099.0i			0.475279i
$818$			14340.3i			0.612955i
$819$		0			0
$820$	−7703.30	+	12389.7i	−0.328062	+	0.527641i
$821$	28867.9			1.22716			0.613579	−	0.789633i	$-0.289729\pi$
$821$	28867.9			1.22716			0.613579	+	0.789633i	$0.289729\pi$
$822$		−	4824.15i		−	0.204698i
$823$			27561.3i			1.16735i	0.811988	+	0.583674i	$0.198385\pi$
$823$			27561.3i			1.16735i	−0.811988	+	0.583674i	$0.801615\pi$
$824$	3095.94			0.130889
$825$	−8454.59	+	4170.68i	−0.356789	+	0.176005i
$826$		0			0
$827$		−	3800.50i		−	0.159802i	−0.996803	−	0.0799011i	$-0.974540\pi$
$827$		−	3800.50i		−	0.159802i	0.996803	−	0.0799011i	$-0.0254605\pi$
$828$		−	15066.5i		−	0.632363i
$829$	−26451.1			−1.10819			−0.554093	−	0.832455i	$-0.686935\pi$
$829$	−26451.1			−1.10819			−0.554093	+	0.832455i	$0.686935\pi$
$830$	10518.7	−	16917.9i	0.439892	−	0.707505i
$831$	9429.09			0.393612
$832$		−	1195.79i		−	0.0498277i
$833$		0			0
$834$	−14.7274			−0.000611472
$835$	15613.3	+	9707.63i	0.647092	+	0.402331i
$836$	25991.7			1.07529
$837$		−	6936.78i		−	0.286464i
$838$			9691.90i			0.399524i
$839$	−5455.57			−0.224490			−0.112245	−	0.993681i	$-0.535804\pi$
$839$	−5455.57			−0.224490			−0.112245	+	0.993681i	$0.535804\pi$
$840$		0			0
$841$	−16162.6			−0.662699
$842$			19488.1i			0.797631i
$843$			5091.42i			0.208016i
$844$	10279.6			0.419240
$845$	10908.8	−	17545.3i	0.444113	−	0.714293i
$846$	11060.0			0.449468
$847$		0			0
$848$		−	163.171i		−	0.00660770i
$849$	11297.8			0.456703
$850$	−11705.8	−	23729.4i	−0.472360	−	0.957545i
$851$	44920.1			1.80945
$852$		−	910.887i		−	0.0366273i
$853$		−	28638.5i		−	1.14955i	−0.818312	−	0.574774i	$-0.805090\pi$
$853$		−	28638.5i		−	1.14955i	0.818312	−	0.574774i	$-0.194910\pi$
$854$		0			0
$855$	−20307.9	+	32662.4i	−0.812299	+	1.30647i
$856$	−844.686			−0.0337275
$857$		−	7340.27i		−	0.292577i	−0.989242	−	0.146289i	$-0.953267\pi$
$857$		−	7340.27i		−	0.292577i	0.989242	−	0.146289i	$-0.0467328\pi$
$858$			2818.29i			0.112138i
$859$	−14649.7			−0.581889			−0.290945	−	0.956740i	$-0.593970\pi$
$859$	−14649.7			−0.581889			−0.290945	+	0.956740i	$0.593970\pi$
$860$	2977.64	+	1851.36i	0.118066	+	0.0734078i
$861$		0			0
$862$			16590.2i			0.655528i
$863$			5880.01i			0.231933i	0.993253	+	0.115966i	$0.0369965\pi$
$863$			5880.01i			0.231933i	−0.993253	+	0.115966i	$0.963004\pi$
$864$	2697.29			0.106208
$865$	−24849.7	−	15450.4i	−0.976781	−	0.607316i
$866$	14731.9			0.578073
$867$			10333.0i			0.404759i
$868$		0			0
$869$	10837.7			0.423066
$870$	1759.52	−	2829.94i	0.0685670	−	0.110280i
$871$	657.597			0.0255819
$872$		−	3690.31i		−	0.143314i
$873$		−	35458.6i		−	1.37468i
$874$	43885.7			1.69846
$875$		0			0
$876$	2499.77			0.0964150
$877$			11989.8i			0.461648i	0.972995	+	0.230824i	$0.0741422\pi$
$877$			11989.8i			0.461648i	−0.972995	+	0.230824i	$0.925858\pi$
$878$			3900.04i			0.149909i
$879$	887.718			0.0340637
$880$	4335.52	−	6973.08i	0.166080	−	0.267116i
$881$	6702.96			0.256332			0.128166	−	0.991753i	$-0.459091\pi$
$881$	6702.96			0.256332			0.128166	+	0.991753i	$0.459091\pi$
$882$		0			0
$883$		−	16182.7i		−	0.616752i	−0.951265	−	0.308376i	$-0.900215\pi$
$883$		−	16182.7i		−	0.616752i	0.951265	−	0.308376i	$-0.0997854\pi$
$884$	−7910.07			−0.300955
$885$	−12937.8	−	8044.12i	−0.491413	−	0.305537i
$886$	−31952.9			−1.21160
$887$		−	35343.6i		−	1.33790i	−0.743306	−	0.668952i	$-0.766743\pi$
$887$		−	35343.6i		−	1.33790i	0.743306	−	0.668952i	$-0.233257\pi$
$888$			3809.33i			0.143956i
$889$		0			0
$890$	−2298.26	−	1428.95i	−0.0865594	−	0.0538185i
$891$	23758.9			0.893325
$892$		−	16967.3i		−	0.636893i
$893$			32215.5i			1.20722i
$894$	−7533.31			−0.281825
$895$	27394.2	−	44059.7i	1.02311	−	1.64553i
$896$		0			0
$897$			4758.55i			0.177127i
$898$			10585.8i			0.393377i
$899$	7464.24			0.276915
$900$	5375.25	+	10896.5i	0.199084	+	0.403572i
$901$	−1079.36			−0.0399099
$902$			29948.0i			1.10550i
$903$		0			0
$904$	15608.1			0.574246
$905$	−4519.43	+	7268.86i	−0.166001	+	0.266989i
$906$	−8715.99			−0.319613
$907$		−	9370.08i		−	0.343030i	−0.985181	−	0.171515i	$-0.945134\pi$
$907$		−	9370.08i		−	0.343030i	0.985181	−	0.171515i	$-0.0548662\pi$
$908$		−	3621.71i		−	0.132369i
$909$	33215.9			1.21199
$910$		0			0
$911$	13365.6			0.486085			0.243042	−	0.970016i	$-0.421855\pi$
$911$	13365.6			0.486085			0.243042	+	0.970016i	$0.421855\pi$
$912$			3721.61i			0.135126i
$913$		−	40893.5i		−	1.48234i
$914$	31929.6			1.15551
$915$	10312.9	+	6412.10i	0.372607	+	0.231669i
$916$	−1216.20			−0.0438694
$917$		0			0
$918$		−	17842.3i		−	0.641487i
$919$	−17832.3			−0.640081			−0.320041	−	0.947404i	$-0.603697\pi$
$919$	−17832.3			−0.640081			−0.320041	+	0.947404i	$0.603697\pi$
$920$	7320.33	−	11773.7i	0.262330	−	0.421921i
$921$	3837.65			0.137302
$922$		−	22145.5i		−	0.791022i
$923$		−	2589.54i		−	0.0923464i
$924$		0			0
$925$	−32487.4	+	16026.1i	−1.15479	+	0.569660i
$926$	−22419.9			−0.795642
$927$			9404.04i			0.333192i
$928$			2902.39i			0.102668i
$929$	−26456.7			−0.934355			−0.467178	−	0.884163i	$-0.654729\pi$
$929$	−26456.7			−0.934355			−0.467178	+	0.884163i	$0.654729\pi$
$930$	1596.50	−	2567.74i	0.0562916	−	0.0905371i
$931$		0			0
$932$		−	19878.4i		−	0.698648i
$933$		−	13903.4i		−	0.487864i
$934$	−22423.4			−0.785564
$935$	−46126.3	−	28679.1i	−1.61336	−	1.00311i
$936$	3632.27			0.126842
$937$		−	33299.9i		−	1.16100i	−0.814259	−	0.580502i	$-0.802856\pi$
$937$		−	33299.9i		−	1.16100i	0.814259	−	0.580502i	$-0.197144\pi$
$938$		0			0
$939$	7356.04			0.255650
$940$	8642.82	+	5373.69i	0.299891	+	0.186458i
$941$	45730.1			1.58423			0.792114	−	0.610374i	$-0.208981\pi$
$941$	45730.1			1.58423			0.792114	+	0.610374i	$0.208981\pi$
$942$			9703.80i			0.335634i
$943$			50565.8i			1.74618i
$944$	13269.1			0.457491
$945$		0			0
$946$	7197.48			0.247368
$947$			5919.39i			0.203120i	0.994829	+	0.101560i	$0.0323833\pi$
$947$			5919.39i			0.203120i	−0.994829	+	0.101560i	$0.967617\pi$
$948$			1551.79i			0.0531645i
$949$	7106.55			0.243086
$950$	−31739.2	+	15657.1i	−1.08395	+	0.534718i
$951$	8390.07			0.286085
$952$		0			0
$953$		−	54267.4i		−	1.84459i	−0.386488	−	0.922295i	$-0.626312\pi$
$953$		−	54267.4i		−	1.84459i	0.386488	−	0.922295i	$-0.373688\pi$
$954$	495.639			0.0168207
$955$	10884.1	−	17505.6i	0.368798	−	0.593160i
$956$	−2967.60			−0.100397
$957$		−	6840.45i		−	0.231056i
$958$			15966.1i			0.538457i
$959$		0			0
$960$	998.438	+	620.781i	0.0335671	+	0.0208704i
$961$	−23018.3			−0.772661
$962$			10829.5i			0.362948i
$963$		−	2565.76i		−	0.0858573i
$964$	13935.5			0.465594
$965$	−7806.33	−	4853.60i	−0.260409	−	0.161910i
$966$		0			0
$967$			41100.5i			1.36681i	0.730041	+	0.683403i	$0.239501\pi$
$967$			41100.5i			1.36681i	−0.730041	+	0.683403i	$0.760499\pi$
$968$		−	6207.14i		−	0.206100i
$969$	24618.1			0.816148
$970$	17228.2	−	27709.2i	0.570273	−	0.917204i
$971$	−43892.3			−1.45064			−0.725320	−	0.688412i	$-0.758308\pi$
$971$	−43892.3			−1.45064			−0.725320	+	0.688412i	$0.758308\pi$
$972$			12505.3i			0.412661i
$973$		0			0
$974$	8817.13			0.290061
$975$	−1697.70	−	3441.50i	−0.0557641	−	0.113042i
$976$	−10577.0			−0.346886
$977$			44555.2i			1.45900i	0.683979	+	0.729502i	$0.260248\pi$
$977$			44555.2i			1.45900i	−0.683979	+	0.729502i	$0.739752\pi$
$978$			12688.6i			0.414864i
$979$	−5555.29			−0.181356
$980$		0			0
$981$	11209.4			0.364822
$982$		−	25008.0i		−	0.812665i
$983$		−	7008.12i		−	0.227390i	−0.993516	−	0.113695i	$-0.963731\pi$
$983$		−	7008.12i		−	0.227390i	0.993516	−	0.113695i	$-0.0362686\pi$
$984$	−4288.10			−0.138922
$985$	−20047.4	−	12464.5i	−0.648491	−	0.403201i
$986$	19199.0			0.620104
$987$		0			0
$988$			10580.1i			0.340686i
$989$	12152.6			0.390728
$990$	21181.0	+	13169.3i	0.679975	+	0.422776i
$991$	−2830.10			−0.0907176			−0.0453588	−	0.998971i	$-0.514443\pi$
$991$	−2830.10			−0.0907176			−0.0453588	+	0.998971i	$0.514443\pi$
$992$			2633.48i			0.0842873i
$993$		−	10578.1i		−	0.338054i
$994$		0			0
$995$	−4388.53	+	7058.32i	−0.139825	+	0.224888i
$996$	5855.33			0.186278
$997$			4635.23i			0.147241i	0.997286	+	0.0736205i	$0.0234553\pi$
$997$			4635.23i			0.147241i	−0.997286	+	0.0736205i	$0.976545\pi$
$998$		−	27549.0i		−	0.873795i
$999$	−24427.5			−0.773625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.d.99.6	yes	8
5.2	odd	4		2450.4.a.cm.1.2		4
5.3	odd	4		2450.4.a.cs.1.3		4
5.4	even	2	inner	490.4.c.d.99.3	yes	8
7.6	odd	2	inner	490.4.c.d.99.7	yes	8
35.13	even	4		2450.4.a.cs.1.2		4
35.27	even	4		2450.4.a.cm.1.3		4
35.34	odd	2	inner	490.4.c.d.99.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.c.d.99.2	✓	8	35.34	odd	2	inner
490.4.c.d.99.3	yes	8	5.4	even	2	inner
490.4.c.d.99.6	yes	8	1.1	even	1	trivial
490.4.c.d.99.7	yes	8	7.6	odd	2	inner
2450.4.a.cm.1.2		4	5.2	odd	4
2450.4.a.cm.1.3		4	35.27	even	4
2450.4.a.cs.1.2		4	35.13	even	4
2450.4.a.cs.1.3		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -1.64308i q^{3} -4.00000 q^{4} +(5.90338 - 9.49474i) q^{5} +3.28615 q^{6} -8.00000i q^{8} +24.3003 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -1.64308i q^{3} -4.00000 q^{4} +(5.90338 - 9.49474i) q^{5} +3.28615 q^{6} -8.00000i q^{8} +24.3003 q^{9} +(18.9895 + 11.8068i) q^{10} +45.9009 q^{11} +6.57231i q^{12} +18.6843i q^{13} +(-15.6006 - 9.69970i) q^{15} +16.0000 q^{16} -105.839i q^{17} +48.6006i q^{18} -141.564 q^{19} +(-23.6135 + 37.9790i) q^{20} +91.8018i q^{22} +155.003i q^{23} -13.1446 q^{24} +(-55.3003 - 112.102i) q^{25} -37.3685 q^{26} -84.2903i q^{27} +90.6997 q^{29} +(19.3994 - 31.2012i) q^{30} +82.2962 q^{31} +32.0000i q^{32} -75.4187i q^{33} +211.677 q^{34} -97.2012 q^{36} -289.802i q^{37} -283.128i q^{38} +30.6997 q^{39} +(-75.9579 - 47.2270i) q^{40} +326.224 q^{41} -78.4024i q^{43} -183.604 q^{44} +(143.454 - 230.725i) q^{45} -310.006 q^{46} -227.569i q^{47} -26.2892i q^{48} +(224.204 - 110.601i) q^{50} -173.901 q^{51} -74.7371i q^{52} -10.1982i q^{53} +168.581 q^{54} +(270.970 - 435.817i) q^{55} +232.601i q^{57} +181.399i q^{58} +829.316 q^{59} +(62.4024 + 38.7988i) q^{60} -661.061 q^{61} +164.592i q^{62} -64.0000 q^{64} +(177.402 + 110.300i) q^{65} +150.837 q^{66} -35.1952i q^{67} +423.354i q^{68} +254.682 q^{69} -138.595 q^{71} -194.402i q^{72} -380.349i q^{73} +579.604 q^{74} +(-184.192 + 90.8627i) q^{75} +566.256 q^{76} +61.3994i q^{78} +236.111 q^{79} +(94.4540 - 151.916i) q^{80} +517.612 q^{81} +652.449i q^{82} -890.909i q^{83} +(-1004.91 - 624.805i) q^{85} +156.805 q^{86} -149.027i q^{87} -367.207i q^{88} -121.028 q^{89} +(461.450 + 286.908i) q^{90} -620.012i q^{92} -135.219i q^{93} +455.137 q^{94} +(-835.706 + 1344.11i) q^{95} +52.5785 q^{96} -1459.18i q^{97} +1115.41 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 60 q^{9}+O(q^{10}) \) 8 * q - 32 * q^4 + 60 * q^9	\( 8 q - 32 q^{4} + 60 q^{9} - 36 q^{11} + 144 q^{15} + 128 q^{16} - 308 q^{25} + 860 q^{29} + 424 q^{30} - 240 q^{36} + 380 q^{39} + 144 q^{44} + 208 q^{46} - 88 q^{50} - 988 q^{51} - 576 q^{60} - 512 q^{64} + 344 q^{65} - 3528 q^{71} + 3024 q^{74} - 3084 q^{79} - 1504 q^{81} - 3604 q^{85} - 896 q^{86} - 4132 q^{95} + 6504 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 + 60 * q^9 - 36 * q^11 + 144 * q^15 + 128 * q^16 - 308 * q^25 + 860 * q^29 + 424 * q^30 - 240 * q^36 + 380 * q^39 + 144 * q^44 + 208 * q^46 - 88 * q^50 - 988 * q^51 - 576 * q^60 - 512 * q^64 + 344 * q^65 - 3528 * q^71 + 3024 * q^74 - 3084 * q^79 - 1504 * q^81 - 3604 * q^85 - 896 * q^86 - 4132 * q^95 + 6504 * q^99

Introduction

L-functions

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