Properties

Label 165.6.f.a.131.37
Level $165$
Weight $6$
Character 165.131
Analytic conductor $26.463$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [165,6,Mod(131,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.131");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 165.f (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: \(26.4633302691\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 131.37
Character \(\chi\) \(=\) 165.131
Dual form 165.6.f.a.131.38

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.39738 q^{2} +(-15.5493 + 1.10386i) q^{3} -30.0473 q^{4} +25.0000i q^{5} +(21.7283 - 1.54251i) q^{6} -138.835i q^{7} +86.7037 q^{8} +(240.563 - 34.3284i) q^{9} +O(q^{10})\) \(q-1.39738 q^{2} +(-15.5493 + 1.10386i) q^{3} -30.0473 q^{4} +25.0000i q^{5} +(21.7283 - 1.54251i) q^{6} -138.835i q^{7} +86.7037 q^{8} +(240.563 - 34.3284i) q^{9} -34.9345i q^{10} +(-275.850 + 291.475i) q^{11} +(467.216 - 33.1679i) q^{12} -840.588i q^{13} +194.006i q^{14} +(-27.5964 - 388.733i) q^{15} +840.357 q^{16} +1960.61 q^{17} +(-336.158 + 47.9698i) q^{18} -523.450i q^{19} -751.183i q^{20} +(153.254 + 2158.80i) q^{21} +(385.467 - 407.301i) q^{22} -1436.21i q^{23} +(-1348.18 + 95.7084i) q^{24} -625.000 q^{25} +1174.62i q^{26} +(-3702.70 + 799.331i) q^{27} +4171.63i q^{28} -2962.47 q^{29} +(38.5626 + 543.208i) q^{30} -5097.69 q^{31} -3948.81 q^{32} +(3967.54 - 4836.74i) q^{33} -2739.72 q^{34} +3470.88 q^{35} +(-7228.28 + 1031.48i) q^{36} -7043.39 q^{37} +731.458i q^{38} +(927.888 + 13070.6i) q^{39} +2167.59i q^{40} +434.057 q^{41} +(-214.154 - 3016.66i) q^{42} +16663.2i q^{43} +(8288.56 - 8758.05i) q^{44} +(858.211 + 6014.08i) q^{45} +2006.93i q^{46} +22378.6i q^{47} +(-13067.0 + 927.633i) q^{48} -2468.25 q^{49} +873.362 q^{50} +(-30486.2 + 2164.23i) q^{51} +25257.4i q^{52} -27604.6i q^{53} +(5174.08 - 1116.97i) q^{54} +(-7286.88 - 6896.25i) q^{55} -12037.5i q^{56} +(577.813 + 8139.29i) q^{57} +4139.70 q^{58} +19119.9i q^{59} +(829.198 + 11680.4i) q^{60} -22975.3i q^{61} +7123.41 q^{62} +(-4766.00 - 33398.6i) q^{63} -21373.4 q^{64} +21014.7 q^{65} +(-5544.16 + 6758.76i) q^{66} -4684.91 q^{67} -58911.1 q^{68} +(1585.37 + 22332.1i) q^{69} -4850.14 q^{70} -40174.4i q^{71} +(20857.7 - 2976.40i) q^{72} +17831.2i q^{73} +9842.29 q^{74} +(9718.33 - 689.910i) q^{75} +15728.3i q^{76} +(40467.0 + 38297.8i) q^{77} +(-1296.61 - 18264.6i) q^{78} +50592.8i q^{79} +21008.9i q^{80} +(56692.1 - 16516.3i) q^{81} -606.542 q^{82} -74818.7 q^{83} +(-4604.88 - 64866.1i) q^{84} +49015.3i q^{85} -23284.8i q^{86} +(46064.5 - 3270.14i) q^{87} +(-23917.2 + 25272.0i) q^{88} -18693.0i q^{89} +(-1199.25 - 8403.95i) q^{90} -116703. q^{91} +43154.3i q^{92} +(79265.6 - 5627.11i) q^{93} -31271.4i q^{94} +13086.2 q^{95} +(61401.4 - 4358.92i) q^{96} -46491.6 q^{97} +3449.08 q^{98} +(-56353.5 + 79587.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 44 q^{3} + 1280 q^{4} - 352 q^{9} + 2112 q^{12} + 1100 q^{15} + 13792 q^{16} - 9892 q^{22} - 50000 q^{25} - 10780 q^{27} + 2112 q^{31} + 6316 q^{33} + 69560 q^{34} - 17268 q^{36} - 7456 q^{37} - 100712 q^{42} + 61352 q^{48} - 233408 q^{49} - 15800 q^{55} - 93728 q^{58} + 62700 q^{60} + 212400 q^{64} + 203724 q^{66} + 182072 q^{67} - 122584 q^{69} + 6600 q^{70} - 27500 q^{75} - 489128 q^{78} + 194872 q^{81} - 237544 q^{82} - 641716 q^{88} + 168272 q^{91} + 433336 q^{93} + 949008 q^{97} + 328952 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39738 −0.247024 −0.123512 0.992343i \(-0.539416\pi\)
−0.123512 + 0.992343i \(0.539416\pi\)
\(3\) −15.5493 + 1.10386i −0.997490 + 0.0708124i
\(4\) −30.0473 −0.938979
\(5\) 25.0000i 0.447214i
\(6\) 21.7283 1.54251i 0.246404 0.0174924i
\(7\) 138.835i 1.07091i −0.844562 0.535457i \(-0.820139\pi\)
0.844562 0.535457i \(-0.179861\pi\)
\(8\) 86.7037 0.478975
\(9\) 240.563 34.3284i 0.989971 0.141269i
\(10\) 34.9345i 0.110473i
\(11\) −275.850 + 291.475i −0.687372 + 0.726306i
\(12\) 467.216 33.1679i 0.936622 0.0664914i
\(13\) 840.588i 1.37951i −0.724043 0.689755i \(-0.757718\pi\)
0.724043 0.689755i \(-0.242282\pi\)
\(14\) 194.006i 0.264542i
\(15\) −27.5964 388.733i −0.0316683 0.446091i
\(16\) 840.357 0.820661
\(17\) 1960.61 1.64539 0.822696 0.568482i \(-0.192469\pi\)
0.822696 + 0.568482i \(0.192469\pi\)
\(18\) −336.158 + 47.9698i −0.244547 + 0.0348969i
\(19\) 523.450i 0.332653i −0.986071 0.166326i \(-0.946810\pi\)
0.986071 0.166326i \(-0.0531905\pi\)
\(20\) 751.183i 0.419924i
\(21\) 153.254 + 2158.80i 0.0758340 + 1.06823i
\(22\) 385.467 407.301i 0.169797 0.179415i
\(23\) 1436.21i 0.566107i −0.959104 0.283053i \(-0.908653\pi\)
0.959104 0.283053i \(-0.0913473\pi\)
\(24\) −1348.18 + 95.7084i −0.477772 + 0.0339173i
\(25\) −625.000 −0.200000
\(26\) 1174.62i 0.340772i
\(27\) −3702.70 + 799.331i −0.977482 + 0.211017i
\(28\) 4171.63i 1.00557i
\(29\) −2962.47 −0.654123 −0.327061 0.945003i \(-0.606058\pi\)
−0.327061 + 0.945003i \(0.606058\pi\)
\(30\) 38.5626 + 543.208i 0.00782283 + 0.110195i
\(31\) −5097.69 −0.952728 −0.476364 0.879248i \(-0.658046\pi\)
−0.476364 + 0.879248i \(0.658046\pi\)
\(32\) −3948.81 −0.681698
\(33\) 3967.54 4836.74i 0.634215 0.773157i
\(34\) −2739.72 −0.406451
\(35\) 3470.88 0.478928
\(36\) −7228.28 + 1031.48i −0.929562 + 0.132649i
\(37\) −7043.39 −0.845819 −0.422910 0.906172i \(-0.638991\pi\)
−0.422910 + 0.906172i \(0.638991\pi\)
\(38\) 731.458i 0.0821732i
\(39\) 927.888 + 13070.6i 0.0976864 + 1.37605i
\(40\) 2167.59i 0.214204i
\(41\) 434.057 0.0403262 0.0201631 0.999797i \(-0.493581\pi\)
0.0201631 + 0.999797i \(0.493581\pi\)
\(42\) −214.154 3016.66i −0.0187328 0.263878i
\(43\) 16663.2i 1.37432i 0.726507 + 0.687159i \(0.241142\pi\)
−0.726507 + 0.687159i \(0.758858\pi\)
\(44\) 8288.56 8758.05i 0.645427 0.681986i
\(45\) 858.211 + 6014.08i 0.0631775 + 0.442729i
\(46\) 2006.93i 0.139842i
\(47\) 22378.6i 1.47771i 0.673866 + 0.738854i \(0.264633\pi\)
−0.673866 + 0.738854i \(0.735367\pi\)
\(48\) −13067.0 + 927.633i −0.818601 + 0.0581130i
\(49\) −2468.25 −0.146859
\(50\) 873.362 0.0494048
\(51\) −30486.2 + 2164.23i −1.64126 + 0.116514i
\(52\) 25257.4i 1.29533i
\(53\) 27604.6i 1.34987i −0.737878 0.674934i \(-0.764172\pi\)
0.737878 0.674934i \(-0.235828\pi\)
\(54\) 5174.08 1116.97i 0.241462 0.0521263i
\(55\) −7286.88 6896.25i −0.324814 0.307402i
\(56\) 12037.5i 0.512941i
\(57\) 577.813 + 8139.29i 0.0235559 + 0.331817i
\(58\) 4139.70 0.161584
\(59\) 19119.9i 0.715082i 0.933897 + 0.357541i \(0.116385\pi\)
−0.933897 + 0.357541i \(0.883615\pi\)
\(60\) 829.198 + 11680.4i 0.0297358 + 0.418870i
\(61\) 22975.3i 0.790562i −0.918560 0.395281i \(-0.870647\pi\)
0.918560 0.395281i \(-0.129353\pi\)
\(62\) 7123.41 0.235347
\(63\) −4766.00 33398.6i −0.151287 1.06017i
\(64\) −21373.4 −0.652265
\(65\) 21014.7 0.616936
\(66\) −5544.16 + 6758.76i −0.156666 + 0.190988i
\(67\) −4684.91 −0.127501 −0.0637506 0.997966i \(-0.520306\pi\)
−0.0637506 + 0.997966i \(0.520306\pi\)
\(68\) −58911.1 −1.54499
\(69\) 1585.37 + 22332.1i 0.0400874 + 0.564685i
\(70\) −4850.14 −0.118307
\(71\) 40174.4i 0.945809i −0.881114 0.472905i \(-0.843205\pi\)
0.881114 0.472905i \(-0.156795\pi\)
\(72\) 20857.7 2976.40i 0.474171 0.0676644i
\(73\) 17831.2i 0.391628i 0.980641 + 0.195814i \(0.0627348\pi\)
−0.980641 + 0.195814i \(0.937265\pi\)
\(74\) 9842.29 0.208938
\(75\) 9718.33 689.910i 0.199498 0.0141625i
\(76\) 15728.3i 0.312354i
\(77\) 40467.0 + 38297.8i 0.777812 + 0.736116i
\(78\) −1296.61 18264.6i −0.0241309 0.339917i
\(79\) 50592.8i 0.912055i 0.889966 + 0.456027i \(0.150728\pi\)
−0.889966 + 0.456027i \(0.849272\pi\)
\(80\) 21008.9i 0.367011i
\(81\) 56692.1 16516.3i 0.960086 0.279705i
\(82\) −606.542 −0.00996153
\(83\) −74818.7 −1.19211 −0.596053 0.802945i \(-0.703265\pi\)
−0.596053 + 0.802945i \(0.703265\pi\)
\(84\) −4604.88 64866.1i −0.0712066 1.00304i
\(85\) 49015.3i 0.735841i
\(86\) 23284.8i 0.339490i
\(87\) 46064.5 3270.14i 0.652481 0.0463200i
\(88\) −23917.2 + 25272.0i −0.329234 + 0.347882i
\(89\) 18693.0i 0.250152i −0.992147 0.125076i \(-0.960082\pi\)
0.992147 0.125076i \(-0.0399175\pi\)
\(90\) −1199.25 8403.95i −0.0156064 0.109365i
\(91\) −116703. −1.47734
\(92\) 43154.3i 0.531562i
\(93\) 79265.6 5627.11i 0.950337 0.0674650i
\(94\) 31271.4i 0.365030i
\(95\) 13086.2 0.148767
\(96\) 61401.4 4358.92i 0.679986 0.0482726i
\(97\) −46491.6 −0.501702 −0.250851 0.968026i \(-0.580710\pi\)
−0.250851 + 0.968026i \(0.580710\pi\)
\(98\) 3449.08 0.0362776
\(99\) −56353.5 + 79587.6i −0.577873 + 0.816126i
\(100\) 18779.6 0.187796
\(101\) −69872.9 −0.681562 −0.340781 0.940143i \(-0.610691\pi\)
−0.340781 + 0.940143i \(0.610691\pi\)
\(102\) 42600.8 3024.25i 0.405431 0.0287818i
\(103\) −35346.8 −0.328289 −0.164145 0.986436i \(-0.552486\pi\)
−0.164145 + 0.986436i \(0.552486\pi\)
\(104\) 72882.1i 0.660750i
\(105\) −53969.9 + 3831.36i −0.477725 + 0.0339140i
\(106\) 38574.1i 0.333450i
\(107\) 196873. 1.66236 0.831181 0.556001i \(-0.187665\pi\)
0.831181 + 0.556001i \(0.187665\pi\)
\(108\) 111256. 24017.8i 0.917836 0.198140i
\(109\) 30375.0i 0.244878i −0.992476 0.122439i \(-0.960928\pi\)
0.992476 0.122439i \(-0.0390716\pi\)
\(110\) 10182.5 + 9636.68i 0.0802369 + 0.0759357i
\(111\) 109520. 7774.89i 0.843696 0.0598945i
\(112\) 116671.i 0.878858i
\(113\) 76118.7i 0.560783i 0.959886 + 0.280392i \(0.0904643\pi\)
−0.959886 + 0.280392i \(0.909536\pi\)
\(114\) −807.424 11373.7i −0.00581888 0.0819669i
\(115\) 35905.2 0.253171
\(116\) 89014.4 0.614208
\(117\) −28856.1 202214.i −0.194882 1.36568i
\(118\) 26717.8i 0.176643i
\(119\) 272202.i 1.76207i
\(120\) −2392.71 33704.6i −0.0151683 0.213666i
\(121\) −8864.36 160807.i −0.0550407 0.998484i
\(122\) 32105.2i 0.195288i
\(123\) −6749.29 + 479.136i −0.0402249 + 0.00285559i
\(124\) 153172. 0.894592
\(125\) 15625.0i 0.0894427i
\(126\) 6659.91 + 46670.6i 0.0373716 + 0.261889i
\(127\) 215773.i 1.18710i 0.804797 + 0.593551i \(0.202274\pi\)
−0.804797 + 0.593551i \(0.797726\pi\)
\(128\) 156229. 0.842823
\(129\) −18393.8 259101.i −0.0973187 1.37087i
\(130\) −29365.5 −0.152398
\(131\) −337322. −1.71738 −0.858690 0.512496i \(-0.828721\pi\)
−0.858690 + 0.512496i \(0.828721\pi\)
\(132\) −119214. + 145331.i −0.595514 + 0.725978i
\(133\) −72673.3 −0.356243
\(134\) 6546.59 0.0314959
\(135\) −19983.3 92567.5i −0.0943696 0.437143i
\(136\) 169992. 0.788101
\(137\) 352292.i 1.60362i 0.597578 + 0.801811i \(0.296130\pi\)
−0.597578 + 0.801811i \(0.703870\pi\)
\(138\) −2215.36 31206.4i −0.00990255 0.139491i
\(139\) 287525.i 1.26223i 0.775690 + 0.631115i \(0.217402\pi\)
−0.775690 + 0.631115i \(0.782598\pi\)
\(140\) −104291. −0.449703
\(141\) −24702.8 347972.i −0.104640 1.47400i
\(142\) 56138.9i 0.233638i
\(143\) 245010. + 231876.i 1.00195 + 0.948236i
\(144\) 202159. 28848.1i 0.812431 0.115934i
\(145\) 74061.8i 0.292533i
\(146\) 24916.9i 0.0967415i
\(147\) 38379.6 2724.59i 0.146490 0.0103994i
\(148\) 211635. 0.794207
\(149\) −73103.7 −0.269758 −0.134879 0.990862i \(-0.543065\pi\)
−0.134879 + 0.990862i \(0.543065\pi\)
\(150\) −13580.2 + 964.066i −0.0492808 + 0.00349847i
\(151\) 74060.0i 0.264327i 0.991228 + 0.132163i \(0.0421924\pi\)
−0.991228 + 0.132163i \(0.957808\pi\)
\(152\) 45385.0i 0.159332i
\(153\) 471651. 67304.7i 1.62889 0.232443i
\(154\) −56547.8 53516.5i −0.192138 0.181839i
\(155\) 127442.i 0.426073i
\(156\) −27880.6 392736.i −0.0917255 1.29208i
\(157\) 72104.8 0.233461 0.116731 0.993164i \(-0.462759\pi\)
0.116731 + 0.993164i \(0.462759\pi\)
\(158\) 70697.3i 0.225300i
\(159\) 30471.5 + 429232.i 0.0955874 + 1.34648i
\(160\) 98720.4i 0.304864i
\(161\) −199397. −0.606252
\(162\) −79220.4 + 23079.5i −0.237164 + 0.0690939i
\(163\) 18749.8 0.0552748 0.0276374 0.999618i \(-0.491202\pi\)
0.0276374 + 0.999618i \(0.491202\pi\)
\(164\) −13042.2 −0.0378654
\(165\) 120918. + 99188.4i 0.345766 + 0.283629i
\(166\) 104550. 0.294479
\(167\) 550753. 1.52815 0.764075 0.645128i \(-0.223196\pi\)
0.764075 + 0.645128i \(0.223196\pi\)
\(168\) 13287.7 + 187176.i 0.0363226 + 0.511653i
\(169\) −335295. −0.903048
\(170\) 68493.0i 0.181771i
\(171\) −17969.2 125923.i −0.0469936 0.329316i
\(172\) 500685.i 1.29046i
\(173\) −603362. −1.53272 −0.766360 0.642412i \(-0.777934\pi\)
−0.766360 + 0.642412i \(0.777934\pi\)
\(174\) −64369.5 + 4569.63i −0.161179 + 0.0114422i
\(175\) 86772.1i 0.214183i
\(176\) −231813. + 244943.i −0.564099 + 0.596051i
\(177\) −21105.6 297302.i −0.0506367 0.713287i
\(178\) 26121.2i 0.0617936i
\(179\) 402941.i 0.939959i 0.882677 + 0.469979i \(0.155739\pi\)
−0.882677 + 0.469979i \(0.844261\pi\)
\(180\) −25786.9 180707.i −0.0593224 0.415713i
\(181\) −806318. −1.82941 −0.914703 0.404127i \(-0.867575\pi\)
−0.914703 + 0.404127i \(0.867575\pi\)
\(182\) 163079. 0.364938
\(183\) 25361.4 + 357250.i 0.0559816 + 0.788577i
\(184\) 124525.i 0.271151i
\(185\) 176085.i 0.378262i
\(186\) −110764. + 7863.21i −0.234756 + 0.0166655i
\(187\) −540835. + 571469.i −1.13100 + 1.19506i
\(188\) 672418.i 1.38754i
\(189\) 110975. + 514065.i 0.225981 + 1.04680i
\(190\) −18286.4 −0.0367490
\(191\) 220023.i 0.436400i −0.975904 0.218200i \(-0.929982\pi\)
0.975904 0.218200i \(-0.0700185\pi\)
\(192\) 332342. 23593.2i 0.650628 0.0461884i
\(193\) 697297.i 1.34749i 0.738965 + 0.673744i \(0.235315\pi\)
−0.738965 + 0.673744i \(0.764685\pi\)
\(194\) 64966.5 0.123932
\(195\) −326764. + 23197.2i −0.615387 + 0.0436867i
\(196\) 74164.4 0.137897
\(197\) −389876. −0.715749 −0.357874 0.933770i \(-0.616498\pi\)
−0.357874 + 0.933770i \(0.616498\pi\)
\(198\) 78747.2 111214.i 0.142749 0.201603i
\(199\) −161225. −0.288602 −0.144301 0.989534i \(-0.546093\pi\)
−0.144301 + 0.989534i \(0.546093\pi\)
\(200\) −54189.8 −0.0957949
\(201\) 72847.2 5171.46i 0.127181 0.00902866i
\(202\) 97638.9 0.168362
\(203\) 411296.i 0.700510i
\(204\) 916029. 65029.4i 1.54111 0.109404i
\(205\) 10851.4i 0.0180344i
\(206\) 49392.8 0.0810954
\(207\) −49302.8 345499.i −0.0799735 0.560429i
\(208\) 706394.i 1.13211i
\(209\) 152572. + 144394.i 0.241608 + 0.228656i
\(210\) 75416.4 5353.86i 0.118010 0.00837758i
\(211\) 1.26540e6i 1.95669i 0.206984 + 0.978344i \(0.433635\pi\)
−0.206984 + 0.978344i \(0.566365\pi\)
\(212\) 829444.i 1.26750i
\(213\) 44346.8 + 624685.i 0.0669750 + 0.943435i
\(214\) −275106. −0.410644
\(215\) −416580. −0.614614
\(216\) −321038. + 69304.9i −0.468189 + 0.101072i
\(217\) 707739.i 1.02029i
\(218\) 42445.4i 0.0604908i
\(219\) −19683.1 277263.i −0.0277321 0.390644i
\(220\) 218951. + 207214.i 0.304993 + 0.288644i
\(221\) 1.64807e6i 2.26983i
\(222\) −153041. + 10864.5i −0.208413 + 0.0147954i
\(223\) −1.46934e6 −1.97861 −0.989305 0.145860i \(-0.953405\pi\)
−0.989305 + 0.145860i \(0.953405\pi\)
\(224\) 548235.i 0.730040i
\(225\) −150352. + 21455.3i −0.197994 + 0.0282538i
\(226\) 106367.i 0.138527i
\(227\) 477669. 0.615265 0.307633 0.951505i \(-0.400463\pi\)
0.307633 + 0.951505i \(0.400463\pi\)
\(228\) −17361.7 244564.i −0.0221185 0.311570i
\(229\) −354213. −0.446351 −0.223175 0.974778i \(-0.571642\pi\)
−0.223175 + 0.974778i \(0.571642\pi\)
\(230\) −50173.2 −0.0625392
\(231\) −671510. 550834.i −0.827985 0.679190i
\(232\) −256857. −0.313308
\(233\) 677802. 0.817924 0.408962 0.912551i \(-0.365891\pi\)
0.408962 + 0.912551i \(0.365891\pi\)
\(234\) 40322.9 + 282570.i 0.0481406 + 0.337355i
\(235\) −559465. −0.660851
\(236\) 574502.i 0.671447i
\(237\) −55847.1 786684.i −0.0645848 0.909765i
\(238\) 380370.i 0.435275i
\(239\) 514240. 0.582332 0.291166 0.956672i \(-0.405957\pi\)
0.291166 + 0.956672i \(0.405957\pi\)
\(240\) −23190.8 326674.i −0.0259889 0.366089i
\(241\) 417830.i 0.463401i 0.972787 + 0.231700i \(0.0744289\pi\)
−0.972787 + 0.231700i \(0.925571\pi\)
\(242\) 12386.9 + 224708.i 0.0135964 + 0.246650i
\(243\) −863293. + 319397.i −0.937869 + 0.346989i
\(244\) 690345.i 0.742321i
\(245\) 61706.3i 0.0656771i
\(246\) 9431.32 669.535i 0.00993653 0.000705400i
\(247\) −440005. −0.458898
\(248\) −441988. −0.456333
\(249\) 1.16338e6 82589.0i 1.18911 0.0844158i
\(250\) 21834.1i 0.0220945i
\(251\) 549499.i 0.550532i −0.961368 0.275266i \(-0.911234\pi\)
0.961368 0.275266i \(-0.0887660\pi\)
\(252\) 143206. + 1.00354e6i 0.142056 + 0.995482i
\(253\) 418619. + 396179.i 0.411167 + 0.389126i
\(254\) 301517.i 0.293243i
\(255\) −54105.8 762155.i −0.0521067 0.733994i
\(256\) 465638. 0.444067
\(257\) 836092.i 0.789625i 0.918762 + 0.394813i \(0.129191\pi\)
−0.918762 + 0.394813i \(0.870809\pi\)
\(258\) 25703.1 + 362063.i 0.0240401 + 0.338637i
\(259\) 977872.i 0.905801i
\(260\) −631436. −0.579290
\(261\) −712661. + 101697.i −0.647563 + 0.0924075i
\(262\) 471367. 0.424234
\(263\) 94258.7 0.0840295 0.0420148 0.999117i \(-0.486622\pi\)
0.0420148 + 0.999117i \(0.486622\pi\)
\(264\) 344000. 419363.i 0.303773 0.370323i
\(265\) 690114. 0.603679
\(266\) 101552. 0.0880005
\(267\) 20634.4 + 290664.i 0.0177139 + 0.249524i
\(268\) 140769. 0.119721
\(269\) 877258.i 0.739174i 0.929196 + 0.369587i \(0.120501\pi\)
−0.929196 + 0.369587i \(0.879499\pi\)
\(270\) 27924.2 + 129352.i 0.0233116 + 0.107985i
\(271\) 1.92473e6i 1.59201i −0.605287 0.796007i \(-0.706942\pi\)
0.605287 0.796007i \(-0.293058\pi\)
\(272\) 1.64761e6 1.35031
\(273\) 1.81466e6 128824.i 1.47363 0.104614i
\(274\) 492286.i 0.396133i
\(275\) 172406. 182172.i 0.137474 0.145261i
\(276\) −47636.1 671020.i −0.0376412 0.530228i
\(277\) 1.65035e6i 1.29234i −0.763194 0.646170i \(-0.776370\pi\)
0.763194 0.646170i \(-0.223630\pi\)
\(278\) 401781.i 0.311801i
\(279\) −1.22632e6 + 174996.i −0.943174 + 0.134591i
\(280\) 300938. 0.229394
\(281\) −1.85767e6 −1.40347 −0.701735 0.712438i \(-0.747591\pi\)
−0.701735 + 0.712438i \(0.747591\pi\)
\(282\) 34519.1 + 486250.i 0.0258486 + 0.364113i
\(283\) 954831.i 0.708697i −0.935113 0.354349i \(-0.884703\pi\)
0.935113 0.354349i \(-0.115297\pi\)
\(284\) 1.20713e6i 0.888095i
\(285\) −203482. + 14445.3i −0.148393 + 0.0105345i
\(286\) −342373. 324019.i −0.247505 0.234237i
\(287\) 60262.4i 0.0431859i
\(288\) −949939. + 135557.i −0.674861 + 0.0963029i
\(289\) 2.42414e6 1.70731
\(290\) 103492.i 0.0722626i
\(291\) 722913. 51320.1i 0.500442 0.0355267i
\(292\) 535780.i 0.367730i
\(293\) 234905. 0.159854 0.0799268 0.996801i \(-0.474531\pi\)
0.0799268 + 0.996801i \(0.474531\pi\)
\(294\) −53630.9 + 3807.29i −0.0361865 + 0.00256890i
\(295\) −477998. −0.319794
\(296\) −610688. −0.405126
\(297\) 788405. 1.29974e6i 0.518631 0.854998i
\(298\) 102154. 0.0666366
\(299\) −1.20726e6 −0.780950
\(300\) −292010. + 20730.0i −0.187324 + 0.0132983i
\(301\) 2.31344e6 1.47178
\(302\) 103490.i 0.0652951i
\(303\) 1.08648e6 77129.6i 0.679851 0.0482630i
\(304\) 439884.i 0.272995i
\(305\) 574382. 0.353550
\(306\) −659075. + 94050.2i −0.402375 + 0.0574191i
\(307\) 1.40308e6i 0.849641i 0.905278 + 0.424820i \(0.139663\pi\)
−0.905278 + 0.424820i \(0.860337\pi\)
\(308\) −1.21593e6 1.15075e6i −0.730349 0.691198i
\(309\) 549618. 39017.7i 0.327465 0.0232469i
\(310\) 178085.i 0.105250i
\(311\) 436429.i 0.255866i −0.991783 0.127933i \(-0.959166\pi\)
0.991783 0.127933i \(-0.0408342\pi\)
\(312\) 80451.3 + 1.13327e6i 0.0467893 + 0.659092i
\(313\) 513930. 0.296513 0.148256 0.988949i \(-0.452634\pi\)
0.148256 + 0.988949i \(0.452634\pi\)
\(314\) −100758. −0.0576706
\(315\) 834966. 119150.i 0.474125 0.0676578i
\(316\) 1.52018e6i 0.856400i
\(317\) 3.22326e6i 1.80155i 0.434282 + 0.900777i \(0.357002\pi\)
−0.434282 + 0.900777i \(0.642998\pi\)
\(318\) −42580.2 599801.i −0.0236124 0.332613i
\(319\) 817199. 863487.i 0.449626 0.475093i
\(320\) 534336.i 0.291702i
\(321\) −3.06124e6 + 217319.i −1.65819 + 0.117716i
\(322\) 278633. 0.149759
\(323\) 1.02628e6i 0.547344i
\(324\) −1.70345e6 + 496271.i −0.901501 + 0.262637i
\(325\) 525368.i 0.275902i
\(326\) −26200.5 −0.0136542
\(327\) 33529.6 + 472311.i 0.0173404 + 0.244263i
\(328\) 37634.3 0.0193152
\(329\) 3.10694e6 1.58250
\(330\) −168969. 138604.i −0.0854126 0.0700633i
\(331\) −1.55711e6 −0.781178 −0.390589 0.920565i \(-0.627729\pi\)
−0.390589 + 0.920565i \(0.627729\pi\)
\(332\) 2.24810e6 1.11936
\(333\) −1.69438e6 + 241789.i −0.837337 + 0.119488i
\(334\) −769611. −0.377490
\(335\) 117123.i 0.0570202i
\(336\) 128788. + 1.81416e6i 0.0622340 + 0.876652i
\(337\) 1.46323e6i 0.701839i −0.936406 0.350919i \(-0.885869\pi\)
0.936406 0.350919i \(-0.114131\pi\)
\(338\) 468535. 0.223075
\(339\) −84024.0 1.18359e6i −0.0397104 0.559375i
\(340\) 1.47278e6i 0.690940i
\(341\) 1.40620e6 1.48585e6i 0.654878 0.691972i
\(342\) 25109.8 + 175962.i 0.0116085 + 0.0813491i
\(343\) 1.99072e6i 0.913642i
\(344\) 1.44476e6i 0.658263i
\(345\) −558302. + 39634.2i −0.252535 + 0.0179276i
\(346\) 843126. 0.378619
\(347\) 293544. 0.130873 0.0654364 0.997857i \(-0.479156\pi\)
0.0654364 + 0.997857i \(0.479156\pi\)
\(348\) −1.38411e6 + 98259.1i −0.612666 + 0.0434935i
\(349\) 455937.i 0.200374i −0.994969 0.100187i \(-0.968056\pi\)
0.994969 0.100187i \(-0.0319441\pi\)
\(350\) 121254.i 0.0529084i
\(351\) 671908. + 3.11244e6i 0.291100 + 1.34845i
\(352\) 1.08928e6 1.15098e6i 0.468580 0.495121i
\(353\) 3.10592e6i 1.32664i −0.748334 0.663322i \(-0.769146\pi\)
0.748334 0.663322i \(-0.230854\pi\)
\(354\) 29492.6 + 415443.i 0.0125085 + 0.176199i
\(355\) 1.00436e6 0.422979
\(356\) 561675.i 0.234888i
\(357\) 300472. + 4.23256e6i 0.124777 + 1.75765i
\(358\) 563062.i 0.232193i
\(359\) −3.80076e6 −1.55645 −0.778224 0.627987i \(-0.783879\pi\)
−0.778224 + 0.627987i \(0.783879\pi\)
\(360\) 74410.0 + 521442.i 0.0302604 + 0.212056i
\(361\) 2.20210e6 0.889342
\(362\) 1.12673e6 0.451907
\(363\) 315342. + 2.49065e6i 0.125608 + 0.992080i
\(364\) 3.50662e6 1.38719
\(365\) −445780. −0.175141
\(366\) −35439.5 499214.i −0.0138288 0.194798i
\(367\) 1.87699e6 0.727438 0.363719 0.931509i \(-0.381507\pi\)
0.363719 + 0.931509i \(0.381507\pi\)
\(368\) 1.20693e6i 0.464581i
\(369\) 104418. 14900.5i 0.0399217 0.00569685i
\(370\) 246057.i 0.0934398i
\(371\) −3.83249e6 −1.44559
\(372\) −2.38172e6 + 169080.i −0.892346 + 0.0633482i
\(373\) 4.12896e6i 1.53663i −0.640073 0.768314i \(-0.721096\pi\)
0.640073 0.768314i \(-0.278904\pi\)
\(374\) 755752. 798560.i 0.279383 0.295208i
\(375\) 17247.7 + 242958.i 0.00633365 + 0.0892182i
\(376\) 1.94031e6i 0.707785i
\(377\) 2.49022e6i 0.902369i
\(378\) −155075. 718344.i −0.0558228 0.258585i
\(379\) −2.43886e6 −0.872147 −0.436073 0.899911i \(-0.643631\pi\)
−0.436073 + 0.899911i \(0.643631\pi\)
\(380\) −393207. −0.139689
\(381\) −238182. 3.35512e6i −0.0840615 1.18412i
\(382\) 307456.i 0.107801i
\(383\) 4.81751e6i 1.67813i 0.544032 + 0.839065i \(0.316897\pi\)
−0.544032 + 0.839065i \(0.683103\pi\)
\(384\) −2.42925e6 + 172454.i −0.840707 + 0.0596823i
\(385\) −957444. + 1.01168e6i −0.329201 + 0.347848i
\(386\) 974389.i 0.332862i
\(387\) 572021. + 4.00855e6i 0.194149 + 1.36054i
\(388\) 1.39695e6 0.471087
\(389\) 5.52977e6i 1.85282i −0.376518 0.926409i \(-0.622879\pi\)
0.376518 0.926409i \(-0.377121\pi\)
\(390\) 456614. 32415.3i 0.152015 0.0107917i
\(391\) 2.81585e6i 0.931467i
\(392\) −214006. −0.0703415
\(393\) 5.24513e6 372355.i 1.71307 0.121612i
\(394\) 544804. 0.176807
\(395\) −1.26482e6 −0.407883
\(396\) 1.69327e6 2.39140e6i 0.542611 0.766326i
\(397\) 2.45580e6 0.782018 0.391009 0.920387i \(-0.372126\pi\)
0.391009 + 0.920387i \(0.372126\pi\)
\(398\) 225292. 0.0712916
\(399\) 1.13002e6 80220.9i 0.355348 0.0252264i
\(400\) −525223. −0.164132
\(401\) 3.23210e6i 1.00375i 0.864942 + 0.501873i \(0.167355\pi\)
−0.864942 + 0.501873i \(0.832645\pi\)
\(402\) −101795. + 7226.50i −0.0314168 + 0.00223030i
\(403\) 4.28506e6i 1.31430i
\(404\) 2.09949e6 0.639972
\(405\) 412907. + 1.41730e6i 0.125088 + 0.429364i
\(406\) 574737.i 0.173043i
\(407\) 1.94292e6 2.05297e6i 0.581392 0.614324i
\(408\) −2.64326e6 + 187647.i −0.786122 + 0.0558073i
\(409\) 4.07843e6i 1.20555i −0.797912 0.602774i \(-0.794062\pi\)
0.797912 0.602774i \(-0.205938\pi\)
\(410\) 15163.5i 0.00445493i
\(411\) −388880. 5.47791e6i −0.113556 1.59960i
\(412\) 1.06208e6 0.308257
\(413\) 2.65452e6 0.765792
\(414\) 68894.7 + 482793.i 0.0197554 + 0.138440i
\(415\) 1.87047e6i 0.533126i
\(416\) 3.31933e6i 0.940409i
\(417\) −317386. 4.47081e6i −0.0893815 1.25906i
\(418\) −213202. 201773.i −0.0596829 0.0564835i
\(419\) 4.08003e6i 1.13535i −0.823254 0.567673i \(-0.807844\pi\)
0.823254 0.567673i \(-0.192156\pi\)
\(420\) 1.62165e6 115122.i 0.448574 0.0318445i
\(421\) −2.92970e6 −0.805598 −0.402799 0.915288i \(-0.631963\pi\)
−0.402799 + 0.915288i \(0.631963\pi\)
\(422\) 1.76824e6i 0.483349i
\(423\) 768223. + 5.38347e6i 0.208755 + 1.46289i
\(424\) 2.39342e6i 0.646552i
\(425\) −1.22538e6 −0.329078
\(426\) −61969.3 872922.i −0.0165444 0.233051i
\(427\) −3.18978e6 −0.846625
\(428\) −5.91550e6 −1.56092
\(429\) −4.06570e6 3.33506e6i −1.06658 0.874905i
\(430\) 582120. 0.151824
\(431\) 1.75639e6 0.455437 0.227718 0.973727i \(-0.426873\pi\)
0.227718 + 0.973727i \(0.426873\pi\)
\(432\) −3.11159e6 + 671723.i −0.802181 + 0.173173i
\(433\) 5.00535e6 1.28297 0.641483 0.767137i \(-0.278320\pi\)
0.641483 + 0.767137i \(0.278320\pi\)
\(434\) 988981.i 0.252037i
\(435\) 81753.6 + 1.15161e6i 0.0207149 + 0.291798i
\(436\) 912687.i 0.229935i
\(437\) −751783. −0.188317
\(438\) 27504.7 + 387442.i 0.00685049 + 0.0964986i
\(439\) 7.01591e6i 1.73749i 0.495257 + 0.868746i \(0.335074\pi\)
−0.495257 + 0.868746i \(0.664926\pi\)
\(440\) −631799. 597931.i −0.155578 0.147238i
\(441\) −593770. + 84731.2i −0.145386 + 0.0207466i
\(442\) 2.30297e6i 0.560704i
\(443\) 6.53003e6i 1.58091i 0.612523 + 0.790453i \(0.290155\pi\)
−0.612523 + 0.790453i \(0.709845\pi\)
\(444\) −3.29078e6 + 233615.i −0.792213 + 0.0562397i
\(445\) 467325. 0.111871
\(446\) 2.05323e6 0.488765
\(447\) 1.13671e6 80696.0i 0.269080 0.0191022i
\(448\) 2.96739e6i 0.698520i
\(449\) 6.61450e6i 1.54839i 0.632945 + 0.774197i \(0.281846\pi\)
−0.632945 + 0.774197i \(0.718154\pi\)
\(450\) 210099. 29981.2i 0.0489094 0.00697938i
\(451\) −119735. + 126517.i −0.0277190 + 0.0292891i
\(452\) 2.28716e6i 0.526564i
\(453\) −81751.5 1.15158e6i −0.0187176 0.263663i
\(454\) −667485. −0.151985
\(455\) 2.91758e6i 0.660685i
\(456\) 50098.5 + 705706.i 0.0112827 + 0.158932i
\(457\) 5.03908e6i 1.12865i 0.825551 + 0.564327i \(0.190864\pi\)
−0.825551 + 0.564327i \(0.809136\pi\)
\(458\) 494970. 0.110259
\(459\) −7.25955e6 + 1.56718e6i −1.60834 + 0.347205i
\(460\) −1.07886e6 −0.237722
\(461\) 6.76448e6 1.48246 0.741229 0.671252i \(-0.234243\pi\)
0.741229 + 0.671252i \(0.234243\pi\)
\(462\) 938355. + 769725.i 0.204532 + 0.167776i
\(463\) −6.63151e6 −1.43767 −0.718837 0.695179i \(-0.755325\pi\)
−0.718837 + 0.695179i \(0.755325\pi\)
\(464\) −2.48953e6 −0.536813
\(465\) 140678. + 1.98164e6i 0.0301713 + 0.425004i
\(466\) −947146. −0.202047
\(467\) 1.23427e6i 0.261890i −0.991390 0.130945i \(-0.958199\pi\)
0.991390 0.130945i \(-0.0418012\pi\)
\(468\) 867048. + 6.07600e6i 0.182990 + 1.28234i
\(469\) 650431.i 0.136543i
\(470\) 781786. 0.163246
\(471\) −1.12118e6 + 79593.3i −0.232875 + 0.0165320i
\(472\) 1.65777e6i 0.342506i
\(473\) −4.85691e6 4.59655e6i −0.998175 0.944667i
\(474\) 78039.7 + 1.09930e6i 0.0159540 + 0.224734i
\(475\) 327156.i 0.0665305i
\(476\) 8.17895e6i 1.65455i
\(477\) −947621. 6.64064e6i −0.190695 1.33633i
\(478\) −718588. −0.143850
\(479\) 1.55344e6 0.309354 0.154677 0.987965i \(-0.450566\pi\)
0.154677 + 0.987965i \(0.450566\pi\)
\(480\) 108973. + 1.53504e6i 0.0215882 + 0.304099i
\(481\) 5.92059e6i 1.16682i
\(482\) 583867.i 0.114471i
\(483\) 3.10048e6 220105.i 0.604730 0.0429301i
\(484\) 266350. + 4.83182e6i 0.0516821 + 0.937556i
\(485\) 1.16229e6i 0.224368i
\(486\) 1.20635e6 446319.i 0.231676 0.0857146i
\(487\) −6.15081e6 −1.17519 −0.587597 0.809153i \(-0.699926\pi\)
−0.587597 + 0.809153i \(0.699926\pi\)
\(488\) 1.99204e6i 0.378659i
\(489\) −291546. + 20697.0i −0.0551360 + 0.00391414i
\(490\) 86227.1i 0.0162238i
\(491\) 7.02276e6 1.31463 0.657316 0.753615i \(-0.271692\pi\)
0.657316 + 0.753615i \(0.271692\pi\)
\(492\) 202798. 14396.8i 0.0377704 0.00268134i
\(493\) −5.80826e6 −1.07629
\(494\) 614855. 0.113359
\(495\) −1.98969e6 1.40884e6i −0.364983 0.258433i
\(496\) −4.28388e6 −0.781867
\(497\) −5.57763e6 −1.01288
\(498\) −1.62568e6 + 115408.i −0.293740 + 0.0208527i
\(499\) −4.29161e6 −0.771559 −0.385780 0.922591i \(-0.626067\pi\)
−0.385780 + 0.922591i \(0.626067\pi\)
\(500\) 469490.i 0.0839848i
\(501\) −8.56384e6 + 607952.i −1.52431 + 0.108212i
\(502\) 767859.i 0.135995i
\(503\) −5.99556e6 −1.05660 −0.528299 0.849058i \(-0.677170\pi\)
−0.528299 + 0.849058i \(0.677170\pi\)
\(504\) −413230. 2.89579e6i −0.0724628 0.507797i
\(505\) 1.74682e6i 0.304804i
\(506\) −584970. 553612.i −0.101568 0.0961234i
\(507\) 5.21362e6 370118.i 0.900781 0.0639470i
\(508\) 6.48340e6i 1.11466i
\(509\) 6.95131e6i 1.18925i 0.804004 + 0.594624i \(0.202699\pi\)
−0.804004 + 0.594624i \(0.797301\pi\)
\(510\) 75606.4 + 1.06502e6i 0.0128716 + 0.181314i
\(511\) 2.47560e6 0.419400
\(512\) −5.65000e6 −0.952518
\(513\) 418409. + 1.93818e6i 0.0701953 + 0.325162i
\(514\) 1.16834e6i 0.195057i
\(515\) 883669.i 0.146815i
\(516\) 552684. + 7.78531e6i 0.0913803 + 1.28722i
\(517\) −6.52281e6 6.17315e6i −1.07327 1.01573i
\(518\) 1.36646e6i 0.223755i
\(519\) 9.38187e6 666025.i 1.52887 0.108536i
\(520\) 1.82205e6 0.295497
\(521\) 204305.i 0.0329750i 0.999864 + 0.0164875i \(0.00524837\pi\)
−0.999864 + 0.0164875i \(0.994752\pi\)
\(522\) 995858. 142109.i 0.159964 0.0228269i
\(523\) 2.38745e6i 0.381662i 0.981623 + 0.190831i \(0.0611183\pi\)
−0.981623 + 0.190831i \(0.938882\pi\)
\(524\) 1.01356e7 1.61258
\(525\) −95783.9 1.34925e6i −0.0151668 0.213645i
\(526\) −131715. −0.0207573
\(527\) −9.99459e6 −1.56761
\(528\) 3.33415e6 4.06459e6i 0.520475 0.634500i
\(529\) 4.37365e6 0.679523
\(530\) −964351. −0.149123
\(531\) 656357. + 4.59954e6i 0.101019 + 0.707911i
\(532\) 2.18364e6 0.334504
\(533\) 364863.i 0.0556303i
\(534\) −28834.1 406168.i −0.00437575 0.0616385i
\(535\) 4.92181e6i 0.743431i
\(536\) −406199. −0.0610698
\(537\) −444789. 6.26546e6i −0.0665607 0.937599i
\(538\) 1.22586e6i 0.182594i
\(539\) 680868. 719434.i 0.100946 0.106664i
\(540\) 600444. + 2.78141e6i 0.0886111 + 0.410469i
\(541\) 2.50628e6i 0.368159i 0.982911 + 0.184080i \(0.0589304\pi\)
−0.982911 + 0.184080i \(0.941070\pi\)
\(542\) 2.68958e6i 0.393266i
\(543\) 1.25377e7 890059.i 1.82481 0.129545i
\(544\) −7.74209e6 −1.12166
\(545\) 759375. 0.109513
\(546\) −2.53577e6 + 180016.i −0.364022 + 0.0258421i
\(547\) 1.27903e7i 1.82773i −0.406020 0.913864i \(-0.633084\pi\)
0.406020 0.913864i \(-0.366916\pi\)
\(548\) 1.05854e7i 1.50577i
\(549\) −788705. 5.52700e6i −0.111682 0.782634i
\(550\) −240917. + 254563.i −0.0339595 + 0.0358830i
\(551\) 1.55071e6i 0.217596i
\(552\) 137457. + 1.93627e6i 0.0192008 + 0.270470i
\(553\) 7.02407e6 0.976733
\(554\) 2.30617e6i 0.319239i
\(555\) 194372. + 2.73800e6i 0.0267856 + 0.377312i
\(556\) 8.63935e6i 1.18521i
\(557\) 741557. 0.101276 0.0506380 0.998717i \(-0.483875\pi\)
0.0506380 + 0.998717i \(0.483875\pi\)
\(558\) 1.71363e6 244535.i 0.232987 0.0332473i
\(559\) 1.40069e7 1.89589
\(560\) 2.91678e6 0.393037
\(561\) 7.77880e6 9.48297e6i 1.04353 1.27215i
\(562\) 2.59587e6 0.346691
\(563\) 4.67593e6 0.621723 0.310861 0.950455i \(-0.399382\pi\)
0.310861 + 0.950455i \(0.399382\pi\)
\(564\) 742252. + 1.04556e7i 0.0982548 + 1.38405i
\(565\) −1.90297e6 −0.250790
\(566\) 1.33426e6i 0.175065i
\(567\) −2.29305e6 7.87087e6i −0.299540 1.02817i
\(568\) 3.48327e6i 0.453019i
\(569\) 6.02363e6 0.779970 0.389985 0.920821i \(-0.372480\pi\)
0.389985 + 0.920821i \(0.372480\pi\)
\(570\) 284342. 20185.6i 0.0366567 0.00260228i
\(571\) 4.58256e6i 0.588190i −0.955776 0.294095i \(-0.904982\pi\)
0.955776 0.294095i \(-0.0950183\pi\)
\(572\) −7.36191e6 6.96727e6i −0.940807 0.890374i
\(573\) 242874. + 3.42121e6i 0.0309025 + 0.435304i
\(574\) 84209.5i 0.0106680i
\(575\) 897631.i 0.113221i
\(576\) −5.14165e6 + 733716.i −0.645724 + 0.0921450i
\(577\) 1.48538e7 1.85737 0.928684 0.370871i \(-0.120941\pi\)
0.928684 + 0.370871i \(0.120941\pi\)
\(578\) −3.38745e6 −0.421748
\(579\) −769716. 1.08425e7i −0.0954188 1.34410i
\(580\) 2.22536e6i 0.274682i
\(581\) 1.03875e7i 1.27664i
\(582\) −1.01018e6 + 71713.6i −0.123621 + 0.00877595i
\(583\) 8.04604e6 + 7.61472e6i 0.980417 + 0.927861i
\(584\) 1.54603e6i 0.187580i
\(585\) 5.05536e6 721402.i 0.610749 0.0871540i
\(586\) −328251. −0.0394877
\(587\) 1.13235e7i 1.35639i −0.734880 0.678197i \(-0.762762\pi\)
0.734880 0.678197i \(-0.237238\pi\)
\(588\) −1.15321e6 + 81866.8i −0.137551 + 0.00976482i
\(589\) 2.66838e6i 0.316928i
\(590\) 667944. 0.0789969
\(591\) 6.06230e6 430367.i 0.713952 0.0506839i
\(592\) −5.91896e6 −0.694131
\(593\) 2.42922e6 0.283681 0.141840 0.989890i \(-0.454698\pi\)
0.141840 + 0.989890i \(0.454698\pi\)
\(594\) −1.10170e6 + 1.81623e6i −0.128114 + 0.211205i
\(595\) 6.80505e6 0.788024
\(596\) 2.19657e6 0.253297
\(597\) 2.50694e6 177969.i 0.287877 0.0204366i
\(598\) 1.68700e6 0.192913
\(599\) 3.45814e6i 0.393799i 0.980424 + 0.196900i \(0.0630873\pi\)
−0.980424 + 0.196900i \(0.936913\pi\)
\(600\) 842615. 59817.7i 0.0955544 0.00678347i
\(601\) 423984.i 0.0478810i −0.999713 0.0239405i \(-0.992379\pi\)
0.999713 0.0239405i \(-0.00762123\pi\)
\(602\) −3.23275e6 −0.363565
\(603\) −1.12702e6 + 160826.i −0.126222 + 0.0180120i
\(604\) 2.22530e6i 0.248197i
\(605\) 4.02017e6 221609.i 0.446536 0.0246150i
\(606\) −1.51822e6 + 107779.i −0.167940 + 0.0119221i
\(607\) 6.40194e6i 0.705245i 0.935766 + 0.352622i \(0.114710\pi\)
−0.935766 + 0.352622i \(0.885290\pi\)
\(608\) 2.06701e6i 0.226768i
\(609\) −454011. 6.39537e6i −0.0496048 0.698751i
\(610\) −802629. −0.0873354
\(611\) 1.88112e7 2.03851
\(612\) −1.41718e7 + 2.02233e6i −1.52949 + 0.218259i
\(613\) 675340.i 0.0725891i 0.999341 + 0.0362946i \(0.0115555\pi\)
−0.999341 + 0.0362946i \(0.988445\pi\)
\(614\) 1.96063e6i 0.209882i
\(615\) −11978.4 168732.i −0.00127706 0.0179891i
\(616\) 3.50864e6 + 3.32056e6i 0.372552 + 0.352581i
\(617\) 1.23886e7i 1.31011i −0.755580 0.655057i \(-0.772645\pi\)
0.755580 0.655057i \(-0.227355\pi\)
\(618\) −768025. + 54522.6i −0.0808918 + 0.00574256i
\(619\) −2.48834e6 −0.261026 −0.130513 0.991447i \(-0.541662\pi\)
−0.130513 + 0.991447i \(0.541662\pi\)
\(620\) 3.82930e6i 0.400074i
\(621\) 1.14801e6 + 5.31785e6i 0.119458 + 0.553359i
\(622\) 609857.i 0.0632050i
\(623\) −2.59525e6 −0.267892
\(624\) 779757. + 1.09839e7i 0.0801674 + 1.12927i
\(625\) 390625. 0.0400000
\(626\) −718155. −0.0732458
\(627\) −2.53179e6 2.07681e6i −0.257193 0.210973i
\(628\) −2.16656e6 −0.219215
\(629\) −1.38094e7 −1.39170
\(630\) −1.16676e6 + 166498.i −0.117120 + 0.0167131i
\(631\) −3.88805e6 −0.388739 −0.194369 0.980928i \(-0.562266\pi\)
−0.194369 + 0.980928i \(0.562266\pi\)
\(632\) 4.38658e6i 0.436851i
\(633\) −1.39682e6 1.96761e7i −0.138558 1.95178i
\(634\) 4.50412e6i 0.445027i
\(635\) −5.39432e6 −0.530888
\(636\) −915586. 1.28973e7i −0.0897545 1.26432i
\(637\) 2.07478e6i 0.202593i
\(638\) −1.14194e6 + 1.20662e6i −0.111068 + 0.117360i
\(639\) −1.37912e6 9.66448e6i −0.133614 0.936324i
\(640\) 3.90572e6i 0.376922i
\(641\) 1.83757e7i 1.76644i 0.468963 + 0.883218i \(0.344628\pi\)
−0.468963 + 0.883218i \(0.655372\pi\)
\(642\) 4.27771e6 303677.i 0.409613 0.0290787i
\(643\) −1.32875e7 −1.26740 −0.633702 0.773577i \(-0.718466\pi\)
−0.633702 + 0.773577i \(0.718466\pi\)
\(644\) 5.99134e6 0.569258
\(645\) 6.47754e6 459844.i 0.613071 0.0435223i
\(646\) 1.43410e6i 0.135207i
\(647\) 94897.1i 0.00891235i −0.999990 0.00445618i \(-0.998582\pi\)
0.999990 0.00445618i \(-0.00141845\pi\)
\(648\) 4.91541e6 1.43202e6i 0.459857 0.133972i
\(649\) −5.57298e6 5.27423e6i −0.519368 0.491527i
\(650\) 734138.i 0.0681545i
\(651\) −781242. 1.10049e7i −0.0722492 1.01773i
\(652\) −563380. −0.0519018
\(653\) 1.28910e7i 1.18305i −0.806285 0.591527i \(-0.798525\pi\)
0.806285 0.591527i \(-0.201475\pi\)
\(654\) −46853.6 659997.i −0.00428350 0.0603389i
\(655\) 8.43305e6i 0.768035i
\(656\) 364762. 0.0330941
\(657\) 612117. + 4.28953e6i 0.0553249 + 0.387700i
\(658\) −4.34158e6 −0.390916
\(659\) −8.08015e6 −0.724780 −0.362390 0.932027i \(-0.618039\pi\)
−0.362390 + 0.932027i \(0.618039\pi\)
\(660\) −3.63328e6 2.98035e6i −0.324667 0.266322i
\(661\) −1.49581e6 −0.133160 −0.0665799 0.997781i \(-0.521209\pi\)
−0.0665799 + 0.997781i \(0.521209\pi\)
\(662\) 2.17588e6 0.192970
\(663\) 1.81923e6 + 2.56263e7i 0.160732 + 2.26414i
\(664\) −6.48705e6 −0.570988
\(665\) 1.81683e6i 0.159317i
\(666\) 2.36769e6 337870.i 0.206842 0.0295165i
\(667\) 4.25473e6i 0.370303i
\(668\) −1.65487e7 −1.43490
\(669\) 2.28473e7 1.62194e6i 1.97364 0.140110i
\(670\) 163665.i 0.0140854i
\(671\) 6.69672e6 + 6.33773e6i 0.574190 + 0.543410i
\(672\) −605172. 8.52468e6i −0.0516959 0.728207i
\(673\) 5.41721e6i 0.461040i 0.973068 + 0.230520i \(0.0740427\pi\)
−0.973068 + 0.230520i \(0.925957\pi\)
\(674\) 2.04468e6i 0.173371i
\(675\) 2.31419e6 499582.i 0.195496 0.0422034i
\(676\) 1.00747e7 0.847943
\(677\) 1.02950e7 0.863283 0.431642 0.902045i \(-0.357935\pi\)
0.431642 + 0.902045i \(0.357935\pi\)
\(678\) 117413. + 1.65393e6i 0.00980943 + 0.138179i
\(679\) 6.45468e6i 0.537280i
\(680\) 4.24981e6i 0.352449i
\(681\) −7.42743e6 + 527278.i −0.613721 + 0.0435684i
\(682\) −1.96499e6 + 2.07630e6i −0.161771 + 0.170934i
\(683\) 2.35514e7i 1.93182i −0.258887 0.965908i \(-0.583356\pi\)
0.258887 0.965908i \(-0.416644\pi\)
\(684\) 539927. + 3.78364e6i 0.0441260 + 0.309221i
\(685\) −8.80731e6 −0.717161
\(686\) 2.78180e6i 0.225692i
\(687\) 5.50778e6 391000.i 0.445230 0.0316071i
\(688\) 1.40030e7i 1.12785i
\(689\) −2.32041e7 −1.86216
\(690\) 780160. 55384.0i 0.0623822 0.00442855i
\(691\) −8.87036e6 −0.706718 −0.353359 0.935488i \(-0.614961\pi\)
−0.353359 + 0.935488i \(0.614961\pi\)
\(692\) 1.81294e7 1.43919
\(693\) 1.10496e7 + 7.82385e6i 0.874002 + 0.618853i
\(694\) −410192. −0.0323287
\(695\) −7.18812e6 −0.564486
\(696\) 3.99396e6 283533.i 0.312522 0.0221861i
\(697\) 851017. 0.0663523
\(698\) 637117.i 0.0494972i
\(699\) −1.05394e7 + 748195.i −0.815871 + 0.0579191i
\(700\) 2.60727e6i 0.201113i
\(701\) 2.46502e7 1.89463 0.947317 0.320297i \(-0.103783\pi\)
0.947317 + 0.320297i \(0.103783\pi\)
\(702\) −938910. 4.34927e6i −0.0719087 0.333099i
\(703\) 3.68686e6i 0.281364i
\(704\) 5.89586e6 6.22982e6i 0.448348 0.473744i
\(705\) 8.69931e6 617569.i 0.659192 0.0467964i
\(706\) 4.34016e6i 0.327713i
\(707\) 9.70082e6i 0.729895i
\(708\) 634168. + 8.93312e6i 0.0475468 + 0.669762i
\(709\) −2.60825e7 −1.94865 −0.974326 0.225141i \(-0.927716\pi\)
−0.974326 + 0.225141i \(0.927716\pi\)
\(710\) −1.40347e6 −0.104486
\(711\) 1.73677e6 + 1.21708e7i 0.128845 + 0.902908i
\(712\) 1.62075e6i 0.119817i
\(713\) 7.32135e6i 0.539346i
\(714\) −419873. 5.91449e6i −0.0308229 0.434182i
\(715\) −5.79691e6 + 6.12526e6i −0.424064 + 0.448084i
\(716\) 1.21073e7i 0.882602i
\(717\) −7.99608e6 + 567647.i −0.580871 + 0.0412364i
\(718\) 5.31111e6 0.384480
\(719\) 1.34835e7i 0.972700i −0.873764 0.486350i \(-0.838328\pi\)
0.873764 0.486350i \(-0.161672\pi\)
\(720\) 721203. + 5.05397e6i 0.0518473 + 0.363330i
\(721\) 4.90738e6i 0.351570i
\(722\) −3.07717e6 −0.219689
\(723\) −461224. 6.49697e6i −0.0328145 0.462238i
\(724\) 2.42277e7 1.71777
\(725\) 1.85155e6 0.130825
\(726\) −440653. 3.48039e6i −0.0310281 0.245068i
\(727\) −1.07470e7 −0.754135 −0.377068 0.926186i \(-0.623068\pi\)
−0.377068 + 0.926186i \(0.623068\pi\)
\(728\) −1.01186e7 −0.707607
\(729\) 1.30710e7 5.91936e6i 0.910944 0.412531i
\(730\) 622924. 0.0432641
\(731\) 3.26701e7i 2.26129i
\(732\) −762042. 1.07344e7i −0.0525655 0.740458i
\(733\) 1.57510e6i 0.108280i 0.998533 + 0.0541399i \(0.0172417\pi\)
−0.998533 + 0.0541399i \(0.982758\pi\)
\(734\) −2.62286e6 −0.179695
\(735\) 68114.9 + 959491.i 0.00465076 + 0.0655123i
\(736\) 5.67133e6i 0.385914i
\(737\) 1.29233e6 1.36553e6i 0.0876407 0.0926048i
\(738\) −145912. + 20821.6i −0.00986163 + 0.00140726i
\(739\) 9.91755e6i 0.668026i −0.942568 0.334013i \(-0.891597\pi\)
0.942568 0.334013i \(-0.108403\pi\)
\(740\) 5.29088e6i 0.355180i
\(741\) 6.84179e6 485703.i 0.457746 0.0324956i
\(742\) 5.35544e6 0.357096
\(743\) −1.35817e7 −0.902571 −0.451286 0.892380i \(-0.649034\pi\)
−0.451286 + 0.892380i \(0.649034\pi\)
\(744\) 6.87262e6 487891.i 0.455187 0.0323140i
\(745\) 1.82759e6i 0.120639i
\(746\) 5.76973e6i 0.379584i
\(747\) −1.79986e7 + 2.56841e6i −1.18015 + 0.168408i
\(748\) 1.62507e7 1.71711e7i 1.06198 1.12213i
\(749\) 2.73329e7i 1.78025i
\(750\) −24101.7 339505.i −0.00156457 0.0220390i
\(751\) −2.10798e7 −1.36385 −0.681924 0.731423i \(-0.738856\pi\)
−0.681924 + 0.731423i \(0.738856\pi\)
\(752\) 1.88060e7i 1.21270i
\(753\) 606568. + 8.54434e6i 0.0389845 + 0.549150i
\(754\) 3.47978e6i 0.222907i
\(755\) −1.85150e6 −0.118211
\(756\) −3.33451e6 1.54463e7i −0.212191 0.982924i
\(757\) −1.95414e7 −1.23941 −0.619706 0.784834i \(-0.712748\pi\)
−0.619706 + 0.784834i \(0.712748\pi\)
\(758\) 3.40802e6 0.215441
\(759\) −6.94657e6 5.69822e6i −0.437689 0.359033i
\(760\) 1.13463e6 0.0712555
\(761\) 1.73938e7 1.08876 0.544380 0.838839i \(-0.316765\pi\)
0.544380 + 0.838839i \(0.316765\pi\)
\(762\) 332831. + 4.68838e6i 0.0207652 + 0.292506i
\(763\) −4.21712e6 −0.262244
\(764\) 6.61110e6i 0.409770i
\(765\) 1.68262e6 + 1.17913e7i 0.103952 + 0.728462i
\(766\) 6.73189e6i 0.414538i
\(767\) 1.60720e7 0.986463
\(768\) −7.24036e6 + 513998.i −0.442953 + 0.0314455i
\(769\) 7.80032e6i 0.475660i 0.971307 + 0.237830i \(0.0764361\pi\)
−0.971307 + 0.237830i \(0.923564\pi\)
\(770\) 1.33791e6 1.41370e6i 0.0813207 0.0859269i
\(771\) −922925. 1.30007e7i −0.0559153 0.787643i
\(772\) 2.09519e7i 1.26526i
\(773\) 2.80638e7i 1.68927i −0.535346 0.844633i \(-0.679819\pi\)
0.535346 0.844633i \(-0.320181\pi\)
\(774\) −799331. 5.60146e6i −0.0479595 0.336085i
\(775\) 3.18606e6 0.190546
\(776\) −4.03099e6 −0.240302
\(777\) −1.07943e6 1.52052e7i −0.0641419 0.903527i
\(778\) 7.72719e6i 0.457691i
\(779\) 227207.i 0.0134146i
\(780\) 9.81840e6 697014.i 0.577835 0.0410209i
\(781\) 1.17098e7 + 1.10821e7i 0.686947 + 0.650122i
\(782\) 3.93481e6i 0.230095i
\(783\) 1.09691e7 2.36800e6i 0.639394 0.138031i
\(784\) −2.07421e6 −0.120521
\(785\) 1.80262e6i 0.104407i
\(786\) −7.32943e6 + 520321.i −0.423169 + 0.0300410i
\(787\) 2.41883e7i 1.39209i 0.717996 + 0.696047i \(0.245059\pi\)
−0.717996 + 0.696047i \(0.754941\pi\)
\(788\) 1.17147e7 0.672073
\(789\) −1.46566e6 + 104048.i −0.0838186 + 0.00595033i
\(790\) 1.76743e6 0.100757
\(791\) 1.05680e7 0.600551
\(792\) −4.88605e6 + 6.90054e6i −0.276787 + 0.390904i
\(793\) −1.93127e7 −1.09059
\(794\) −3.43169e6 −0.193177
\(795\) −1.07308e7 + 761787.i −0.602164 + 0.0427480i
\(796\) 4.84437e6 0.270991
\(797\) 3.01945e7i 1.68377i 0.539659 + 0.841884i \(0.318553\pi\)
−0.539659 + 0.841884i \(0.681447\pi\)
\(798\) −1.57907e6 + 112099.i −0.0877796 + 0.00623153i
\(799\) 4.38758e7i 2.43141i
\(800\) 2.46801e6 0.136340
\(801\) −641702. 4.49685e6i −0.0353388 0.247643i
\(802\) 4.51647e6i 0.247949i
\(803\) −5.19735e6 4.91874e6i −0.284441 0.269194i
\(804\) −2.18886e6 + 155389.i −0.119420 + 0.00847772i
\(805\) 4.98492e6i 0.271124i
\(806\) 5.98785e6i 0.324663i
\(807\) −968366. 1.36408e7i −0.0523427 0.737318i
\(808\) −6.05823e6 −0.326451
\(809\) −2.41414e7 −1.29685 −0.648427 0.761277i \(-0.724573\pi\)
−0.648427 + 0.761277i \(0.724573\pi\)
\(810\) −576988. 1.98051e6i −0.0308997 0.106063i
\(811\) 2.59455e7i 1.38519i 0.721326 + 0.692596i \(0.243533\pi\)
−0.721326 + 0.692596i \(0.756467\pi\)
\(812\) 1.23583e7i 0.657764i
\(813\) 2.12463e6 + 2.99283e7i 0.112734 + 1.58802i
\(814\) −2.71500e6 + 2.86878e6i −0.143618 + 0.151753i
\(815\) 468744.i 0.0247196i
\(816\) −2.56193e7 + 1.81873e6i −1.34692 + 0.0956186i
\(817\) 8.72234e6 0.457170
\(818\) 5.69911e6i 0.297799i
\(819\) −2.80745e7 + 4.00624e6i −1.46252 + 0.208702i
\(820\) 326056.i 0.0169339i
\(821\) −1.80459e7 −0.934375 −0.467188 0.884158i \(-0.654733\pi\)
−0.467188 + 0.884158i \(0.654733\pi\)
\(822\) 543413. + 7.65472e6i 0.0280511 + 0.395139i
\(823\) −1.21944e7 −0.627568 −0.313784 0.949494i \(-0.601597\pi\)
−0.313784 + 0.949494i \(0.601597\pi\)
\(824\) −3.06469e6 −0.157242
\(825\) −2.47971e6 + 3.02296e6i −0.126843 + 0.154631i
\(826\) −3.70937e6 −0.189169
\(827\) −1.17300e7 −0.596396 −0.298198 0.954504i \(-0.596386\pi\)
−0.298198 + 0.954504i \(0.596386\pi\)
\(828\) 1.48142e6 + 1.03813e7i 0.0750934 + 0.526231i
\(829\) −1.10261e7 −0.557231 −0.278616 0.960403i \(-0.589876\pi\)
−0.278616 + 0.960403i \(0.589876\pi\)
\(830\) 2.61375e6i 0.131695i
\(831\) 1.82175e6 + 2.56618e7i 0.0915137 + 1.28910i
\(832\) 1.79662e7i 0.899806i
\(833\) −4.83928e6 −0.241640
\(834\) 443508. + 6.24743e6i 0.0220794 + 0.311018i
\(835\) 1.37688e7i 0.683409i
\(836\) −4.58440e6 4.33864e6i −0.226864 0.214703i
\(837\) 1.88752e7 4.07474e6i 0.931275 0.201042i
\(838\) 5.70135e6i 0.280458i
\(839\) 1.88733e7i 0.925641i −0.886452 0.462821i \(-0.846837\pi\)
0.886452 0.462821i \(-0.153163\pi\)
\(840\) −4.67939e6 + 332193.i −0.228818 + 0.0162440i
\(841\) −1.17349e7 −0.572123
\(842\) 4.09391e6 0.199002
\(843\) 2.88855e7 2.05060e6i 1.39995 0.0993831i
\(844\) 3.80219e7i 1.83729i
\(845\) 8.38238e6i 0.403855i
\(846\) −1.07350e6 7.52275e6i −0.0515675 0.361369i
\(847\) −2.23257e7 + 1.23069e6i −1.06929 + 0.0589439i
\(848\) 2.31977e7i 1.10778i
\(849\) 1.05400e6 + 1.48470e7i 0.0501845 + 0.706918i
\(850\) 1.71232e6 0.0812903
\(851\) 1.01158e7i 0.478824i
\(852\) −1.33250e6 1.87701e7i −0.0628881 0.885866i
\(853\) 1.21410e7i 0.571324i −0.958330 0.285662i \(-0.907786\pi\)
0.958330 0.285662i \(-0.0922135\pi\)
\(854\) 4.45733e6 0.209137
\(855\) 3.14807e6 449230.i 0.147275 0.0210162i
\(856\) 1.70696e7 0.796230
\(857\) 1.39003e7 0.646504 0.323252 0.946313i \(-0.395224\pi\)
0.323252 + 0.946313i \(0.395224\pi\)
\(858\) 5.68133e6 + 4.66035e6i 0.263470 + 0.216123i
\(859\) 3.57507e6 0.165311 0.0826555 0.996578i \(-0.473660\pi\)
0.0826555 + 0.996578i \(0.473660\pi\)
\(860\) 1.25171e7 0.577109
\(861\) 66521.0 + 937040.i 0.00305809 + 0.0430775i
\(862\) −2.45435e6 −0.112504
\(863\) 1.01838e7i 0.465458i 0.972542 + 0.232729i \(0.0747656\pi\)
−0.972542 + 0.232729i \(0.925234\pi\)
\(864\) 1.46213e7 3.15641e6i 0.666347 0.143850i
\(865\) 1.50840e7i 0.685453i
\(866\) −6.99438e6 −0.316923
\(867\) −3.76938e7 + 2.67590e6i −1.70303 + 0.120899i
\(868\) 2.12657e7i 0.958032i
\(869\) −1.47465e7 1.39560e7i −0.662431 0.626920i
\(870\) −114241. 1.60924e6i −0.00511709 0.0720812i
\(871\) 3.93808e6i 0.175889i
\(872\) 2.63362e6i 0.117290i
\(873\) −1.11842e7 + 1.59598e6i −0.496670 + 0.0708750i
\(874\) 1.05053e6 0.0465188
\(875\) −2.16930e6 −0.0957855
\(876\) 591424. + 8.33101e6i 0.0260398 + 0.366807i
\(877\) 3.85273e7i 1.69149i 0.533585 + 0.845746i \(0.320844\pi\)
−0.533585 + 0.845746i \(0.679156\pi\)
\(878\) 9.80389e6i 0.429203i
\(879\) −3.65261e6 + 259301.i −0.159452 + 0.0113196i
\(880\) −6.12357e6 5.79531e6i −0.266562 0.252273i
\(881\) 9.15303e6i 0.397306i 0.980070 + 0.198653i \(0.0636567\pi\)
−0.980070 + 0.198653i \(0.936343\pi\)
\(882\) 829722. 118402.i 0.0359138 0.00512491i
\(883\) 4.56227e6 0.196915 0.0984575 0.995141i \(-0.468609\pi\)
0.0984575 + 0.995141i \(0.468609\pi\)
\(884\) 4.95200e7i 2.13133i
\(885\) 7.43254e6 527641.i 0.318992 0.0226454i
\(886\) 9.12493e6i 0.390522i
\(887\) 2.66298e7 1.13647 0.568236 0.822866i \(-0.307626\pi\)
0.568236 + 0.822866i \(0.307626\pi\)
\(888\) 9.49579e6 674112.i 0.404109 0.0286879i
\(889\) 2.99569e7 1.27128
\(890\) −653031. −0.0276350
\(891\) −1.08244e7 + 2.10804e7i −0.456784 + 0.889577i
\(892\) 4.41498e7 1.85787
\(893\) 1.17141e7 0.491563
\(894\) −1.58842e6 + 112763.i −0.0664694 + 0.00471870i
\(895\) −1.00735e7 −0.420362
\(896\) 2.16901e7i 0.902591i
\(897\) 1.87721e7 1.33264e6i 0.778989 0.0553009i
\(898\) 9.24297e6i 0.382490i
\(899\) 1.51018e7 0.623202
\(900\) 4.51767e6 644674.i 0.185912 0.0265298i
\(901\) 5.41218e7i 2.22106i
\(902\) 167315. 176792.i 0.00684727 0.00723512i
\(903\) −3.59724e7 + 2.55371e6i −1.46808 + 0.104220i
\(904\) 6.59977e6i 0.268601i
\(905\) 2.01580e7i 0.818135i
\(906\) 114238. + 1.60920e6i 0.00462370 + 0.0651312i
\(907\) 4.08806e7 1.65006 0.825029 0.565091i \(-0.191159\pi\)
0.825029 + 0.565091i \(0.191159\pi\)
\(908\) −1.43527e7 −0.577721
\(909\) −1.68088e7 + 2.39863e6i −0.674726 + 0.0962837i
\(910\) 4.07697e6i 0.163205i
\(911\) 1.44844e7i 0.578237i 0.957293 + 0.289118i \(0.0933621\pi\)
−0.957293 + 0.289118i \(0.906638\pi\)
\(912\) 485569. + 6.83990e6i 0.0193314 + 0.272310i
\(913\) 2.06387e7 2.18078e7i 0.819419 0.865833i
\(914\) 7.04151e6i 0.278805i
\(915\) −8.93125e6 + 634035.i −0.352663 + 0.0250357i
\(916\) 1.06432e7 0.419114
\(917\) 4.68322e7i 1.83917i
\(918\) 1.01444e7 2.18994e6i 0.397299 0.0857681i
\(919\) 2.32892e7i 0.909634i −0.890585 0.454817i \(-0.849705\pi\)
0.890585 0.454817i \(-0.150295\pi\)
\(920\) 3.11312e6 0.121262
\(921\) −1.54879e6 2.18169e7i −0.0601651 0.847508i
\(922\) −9.45255e6 −0.366203
\(923\) −3.37701e7 −1.30475
\(924\) 2.01771e7 + 1.65511e7i 0.777461 + 0.637745i
\(925\) 4.40212e6 0.169164
\(926\) 9.26674e6 0.355140
\(927\) −8.50312e6 + 1.21340e6i −0.324997 + 0.0463772i
\(928\) 1.16983e7 0.445914
\(929\) 3.26942e6i 0.124289i 0.998067 + 0.0621443i \(0.0197939\pi\)
−0.998067 + 0.0621443i \(0.980206\pi\)
\(930\) −196580. 2.76910e6i −0.00745303 0.104986i
\(931\) 1.29201e6i 0.0488529i
\(932\) −2.03661e7 −0.768013
\(933\) 481754. + 6.78617e6i 0.0181185 + 0.255224i
\(934\) 1.72475e6i 0.0646933i
\(935\) −1.42867e7 1.35209e7i −0.534446 0.505797i
\(936\) −2.50193e6 1.75327e7i −0.0933437 0.654124i
\(937\) 4.66482e7i 1.73574i −0.496787 0.867872i \(-0.665487\pi\)
0.496787 0.867872i \(-0.334513\pi\)
\(938\) 908899.i 0.0337294i
\(939\) −7.99127e6 + 567305.i −0.295768 + 0.0209968i
\(940\) 1.68104e7 0.620525
\(941\) −5.01997e6 −0.184811 −0.0924054 0.995721i \(-0.529456\pi\)
−0.0924054 + 0.995721i \(0.529456\pi\)
\(942\) 1.56672e6 111222.i 0.0575258 0.00408379i
\(943\) 623396.i 0.0228289i
\(944\) 1.60675e7i 0.586840i
\(945\) −1.28516e7 + 2.77438e6i −0.468143 + 0.101062i
\(946\) 6.78694e6 + 6.42312e6i 0.246573 + 0.233356i
\(947\) 1.94472e6i 0.0704663i −0.999379 0.0352332i \(-0.988783\pi\)
0.999379 0.0352332i \(-0.0112174\pi\)
\(948\) 1.67806e6 + 2.36377e7i 0.0606438 + 0.854250i
\(949\) 1.49887e7 0.540254
\(950\) 457161.i 0.0164346i
\(951\) −3.55801e6 5.01195e7i −0.127572 1.79703i
\(952\) 2.36009e7i 0.843989i
\(953\) −3.60789e7 −1.28683 −0.643415 0.765517i \(-0.722483\pi\)
−0.643415 + 0.765517i \(0.722483\pi\)
\(954\) 1.32419e6 + 9.27949e6i 0.0471062 + 0.330106i
\(955\) 5.50057e6 0.195164
\(956\) −1.54515e7 −0.546798
\(957\) −1.17537e7 + 1.43287e7i −0.414854 + 0.505740i
\(958\) −2.17075e6 −0.0764180
\(959\) 4.89106e7 1.71734
\(960\) 589829. + 8.30856e6i 0.0206561 + 0.290970i
\(961\) −2.64271e6 −0.0923085
\(962\) 8.27331e6i 0.288232i
\(963\) 4.73603e7 6.75833e6i 1.64569 0.234841i
\(964\) 1.25547e7i 0.435124i
\(965\) −1.74324e7 −0.602615
\(966\) −4.33255e6 + 307570.i −0.149383 + 0.0106048i
\(967\) 2.09471e7i 0.720372i −0.932880 0.360186i \(-0.882713\pi\)
0.932880 0.360186i \(-0.117287\pi\)
\(968\) −768573. 1.39425e7i −0.0263631 0.478249i
\(969\) 1.13287e6 + 1.59580e7i 0.0387587 + 0.545970i
\(970\) 1.62416e6i 0.0554243i
\(971\) 2.80807e7i 0.955785i −0.878418 0.477893i \(-0.841401\pi\)
0.878418 0.477893i \(-0.158599\pi\)
\(972\) 2.59396e7 9.59703e6i 0.880640 0.325815i
\(973\) 3.99186e7 1.35174
\(974\) 8.59502e6 0.290301
\(975\) −579930. 8.16911e6i −0.0195373 0.275209i
\(976\) 1.93074e7i 0.648783i
\(977\) 4.09204e7i 1.37153i 0.727825 + 0.685763i \(0.240531\pi\)
−0.727825 + 0.685763i \(0.759469\pi\)
\(978\) 407401. 28921.6i 0.0136199 0.000966887i
\(979\) 5.44855e6 + 5.15647e6i 0.181687 + 0.171948i
\(980\) 1.85411e6i 0.0616695i
\(981\) −1.04273e6 7.30710e6i −0.0345937 0.242422i
\(982\) −9.81346e6 −0.324746
\(983\) 1.12318e7i 0.370736i 0.982669 + 0.185368i \(0.0593478\pi\)
−0.982669 + 0.185368i \(0.940652\pi\)
\(984\) −585188. + 41542.8i −0.0192667 + 0.00136776i
\(985\) 9.74689e6i 0.320093i
\(986\) 8.11634e6 0.265869
\(987\) −4.83109e7 + 3.42962e6i −1.57853 + 0.112061i
\(988\) 1.32210e7 0.430895
\(989\) 2.39318e7 0.778011
\(990\) 2.78035e6 + 1.96868e6i 0.0901596 + 0.0638391i
\(991\) 2.65187e7 0.857764 0.428882 0.903360i \(-0.358908\pi\)
0.428882 + 0.903360i \(0.358908\pi\)
\(992\) 2.01298e7 0.649473
\(993\) 2.42120e7 1.71883e6i 0.779217 0.0553171i
\(994\) 7.79406e6 0.250206
\(995\) 4.03062e6i 0.129067i
\(996\) −3.49564e7 + 2.48158e6i −1.11655 + 0.0792647i
\(997\) 8.63647e6i 0.275168i −0.990490 0.137584i \(-0.956066\pi\)
0.990490 0.137584i \(-0.0439338\pi\)
\(998\) 5.99701e6 0.190594
\(999\) 2.60796e7 5.63000e6i 0.826774 0.178482i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 165.6.f.a.131.37 80
3.2 odd 2 inner 165.6.f.a.131.43 yes 80
11.10 odd 2 inner 165.6.f.a.131.44 yes 80
33.32 even 2 inner 165.6.f.a.131.38 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.f.a.131.37 80 1.1 even 1 trivial
165.6.f.a.131.38 yes 80 33.32 even 2 inner
165.6.f.a.131.43 yes 80 3.2 odd 2 inner
165.6.f.a.131.44 yes 80 11.10 odd 2 inner