Properties

Label 336.6.q.e.289.2
Level $336$
Weight $6$
Character 336.289
Analytic conductor $53.889$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,6,Mod(193,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.193");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not 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: \(53.8889634572\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-83})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 20x^{2} - 21x + 441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.2
Root \(4.19493 - 1.84460i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.6.q.e.193.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.50000 - 7.79423i) q^{3} +(35.8645 - 62.1192i) q^{5} +(87.5000 - 95.6596i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(-4.50000 - 7.79423i) q^{3} +(35.8645 - 62.1192i) q^{5} +(87.5000 - 95.6596i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-280.305 - 485.503i) q^{11} +533.509 q^{13} -645.562 q^{15} +(-502.850 - 870.962i) q^{17} +(684.263 - 1185.18i) q^{19} +(-1139.34 - 251.527i) q^{21} +(1614.04 - 2795.60i) q^{23} +(-1010.03 - 1749.42i) q^{25} +729.000 q^{27} -753.456 q^{29} +(4103.21 + 7106.97i) q^{31} +(-2522.75 + 4369.52i) q^{33} +(-2804.15 - 8866.21i) q^{35} +(1404.33 - 2432.37i) q^{37} +(-2400.79 - 4158.29i) q^{39} +245.827 q^{41} +17504.5 q^{43} +(2905.03 + 5031.65i) q^{45} +(-8172.74 + 14155.6i) q^{47} +(-1494.50 - 16740.4i) q^{49} +(-4525.65 + 7838.66i) q^{51} +(14820.8 + 25670.4i) q^{53} -40212.0 q^{55} -12316.7 q^{57} +(-5178.05 - 8968.65i) q^{59} +(-477.089 + 826.343i) q^{61} +(3166.58 + 10012.2i) q^{63} +(19134.0 - 33141.1i) q^{65} +(-9907.60 - 17160.5i) q^{67} -29052.7 q^{69} -62125.4 q^{71} +(-13554.8 - 23477.6i) q^{73} +(-9090.27 + 15744.8i) q^{75} +(-70969.7 - 15667.6i) q^{77} +(22343.7 - 38700.4i) q^{79} +(-3280.50 - 5681.99i) q^{81} -15606.6 q^{83} -72137.9 q^{85} +(3390.55 + 5872.61i) q^{87} +(-6817.66 + 11808.5i) q^{89} +(46682.0 - 51035.2i) q^{91} +(36928.9 - 63962.7i) q^{93} +(-49081.6 - 85011.8i) q^{95} -12919.5 q^{97} +45409.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{3} + 33 q^{5} + 350 q^{7} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{3} + 33 q^{5} + 350 q^{7} - 162 q^{9} - 1137 q^{11} + 1850 q^{13} - 594 q^{15} + 324 q^{17} + 2311 q^{19} - 1575 q^{21} + 1596 q^{23} - 395 q^{25} + 2916 q^{27} - 4434 q^{29} + 4294 q^{31} - 10233 q^{33} - 15414 q^{35} + 19109 q^{37} - 8325 q^{39} - 25716 q^{41} + 5542 q^{43} + 2673 q^{45} - 23160 q^{47} - 5978 q^{49} + 2916 q^{51} + 31653 q^{53} - 35778 q^{55} - 41598 q^{57} + 41097 q^{59} - 42052 q^{61} - 14175 q^{63} + 23106 q^{65} + 30763 q^{67} - 28728 q^{69} - 204192 q^{71} + 28577 q^{73} - 3555 q^{75} - 96873 q^{77} - 18464 q^{79} - 13122 q^{81} - 122358 q^{83} - 247272 q^{85} + 19953 q^{87} - 29322 q^{89} + 161875 q^{91} + 38646 q^{93} - 61662 q^{95} - 19582 q^{97} + 184194 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −4.50000 7.79423i −0.288675 0.500000i
\(4\) 0 0
\(5\) 35.8645 62.1192i 0.641564 1.11122i −0.343519 0.939146i \(-0.611619\pi\)
0.985084 0.172076i \(-0.0550476\pi\)
\(6\) 0 0
\(7\) 87.5000 95.6596i 0.674937 0.737876i
\(8\) 0 0
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −280.305 485.503i −0.698472 1.20979i −0.968996 0.247076i \(-0.920530\pi\)
0.270524 0.962713i \(-0.412803\pi\)
\(12\) 0 0
\(13\) 533.509 0.875555 0.437777 0.899083i \(-0.355766\pi\)
0.437777 + 0.899083i \(0.355766\pi\)
\(14\) 0 0
\(15\) −645.562 −0.740815
\(16\) 0 0
\(17\) −502.850 870.962i −0.422004 0.730932i 0.574132 0.818763i \(-0.305340\pi\)
−0.996135 + 0.0878311i \(0.972006\pi\)
\(18\) 0 0
\(19\) 684.263 1185.18i 0.434850 0.753182i −0.562434 0.826842i \(-0.690135\pi\)
0.997283 + 0.0736606i \(0.0234682\pi\)
\(20\) 0 0
\(21\) −1139.34 251.527i −0.563775 0.124462i
\(22\) 0 0
\(23\) 1614.04 2795.60i 0.636201 1.10193i −0.350058 0.936728i \(-0.613838\pi\)
0.986259 0.165205i \(-0.0528286\pi\)
\(24\) 0 0
\(25\) −1010.03 1749.42i −0.323209 0.559815i
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −753.456 −0.166365 −0.0831827 0.996534i \(-0.526508\pi\)
−0.0831827 + 0.996534i \(0.526508\pi\)
\(30\) 0 0
\(31\) 4103.21 + 7106.97i 0.766866 + 1.32825i 0.939254 + 0.343222i \(0.111518\pi\)
−0.172389 + 0.985029i \(0.555148\pi\)
\(32\) 0 0
\(33\) −2522.75 + 4369.52i −0.403263 + 0.698472i
\(34\) 0 0
\(35\) −2804.15 8866.21i −0.386929 1.22340i
\(36\) 0 0
\(37\) 1404.33 2432.37i 0.168642 0.292096i −0.769301 0.638887i \(-0.779395\pi\)
0.937943 + 0.346791i \(0.112729\pi\)
\(38\) 0 0
\(39\) −2400.79 4158.29i −0.252751 0.437777i
\(40\) 0 0
\(41\) 245.827 0.0228387 0.0114193 0.999935i \(-0.496365\pi\)
0.0114193 + 0.999935i \(0.496365\pi\)
\(42\) 0 0
\(43\) 17504.5 1.44371 0.721853 0.692047i \(-0.243291\pi\)
0.721853 + 0.692047i \(0.243291\pi\)
\(44\) 0 0
\(45\) 2905.03 + 5031.65i 0.213855 + 0.370407i
\(46\) 0 0
\(47\) −8172.74 + 14155.6i −0.539663 + 0.934725i 0.459258 + 0.888303i \(0.348115\pi\)
−0.998922 + 0.0464219i \(0.985218\pi\)
\(48\) 0 0
\(49\) −1494.50 16740.4i −0.0889213 0.996039i
\(50\) 0 0
\(51\) −4525.65 + 7838.66i −0.243644 + 0.422004i
\(52\) 0 0
\(53\) 14820.8 + 25670.4i 0.724741 + 1.25529i 0.959081 + 0.283133i \(0.0913739\pi\)
−0.234340 + 0.972155i \(0.575293\pi\)
\(54\) 0 0
\(55\) −40212.0 −1.79246
\(56\) 0 0
\(57\) −12316.7 −0.502121
\(58\) 0 0
\(59\) −5178.05 8968.65i −0.193659 0.335426i 0.752801 0.658248i \(-0.228702\pi\)
−0.946460 + 0.322821i \(0.895369\pi\)
\(60\) 0 0
\(61\) −477.089 + 826.343i −0.0164163 + 0.0284339i −0.874117 0.485716i \(-0.838559\pi\)
0.857701 + 0.514150i \(0.171892\pi\)
\(62\) 0 0
\(63\) 3166.58 + 10012.2i 0.100517 + 0.317817i
\(64\) 0 0
\(65\) 19134.0 33141.1i 0.561725 0.972935i
\(66\) 0 0
\(67\) −9907.60 17160.5i −0.269638 0.467027i 0.699130 0.714994i \(-0.253571\pi\)
−0.968768 + 0.247967i \(0.920237\pi\)
\(68\) 0 0
\(69\) −29052.7 −0.734622
\(70\) 0 0
\(71\) −62125.4 −1.46259 −0.731296 0.682060i \(-0.761084\pi\)
−0.731296 + 0.682060i \(0.761084\pi\)
\(72\) 0 0
\(73\) −13554.8 23477.6i −0.297705 0.515641i 0.677905 0.735149i \(-0.262888\pi\)
−0.975611 + 0.219509i \(0.929555\pi\)
\(74\) 0 0
\(75\) −9090.27 + 15744.8i −0.186605 + 0.323209i
\(76\) 0 0
\(77\) −70969.7 15667.6i −1.36410 0.301145i
\(78\) 0 0
\(79\) 22343.7 38700.4i 0.402798 0.697666i −0.591265 0.806477i \(-0.701371\pi\)
0.994062 + 0.108812i \(0.0347045\pi\)
\(80\) 0 0
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −15606.6 −0.248665 −0.124332 0.992241i \(-0.539679\pi\)
−0.124332 + 0.992241i \(0.539679\pi\)
\(84\) 0 0
\(85\) −72137.9 −1.08297
\(86\) 0 0
\(87\) 3390.55 + 5872.61i 0.0480255 + 0.0831827i
\(88\) 0 0
\(89\) −6817.66 + 11808.5i −0.0912347 + 0.158023i −0.908031 0.418903i \(-0.862415\pi\)
0.816796 + 0.576926i \(0.195748\pi\)
\(90\) 0 0
\(91\) 46682.0 51035.2i 0.590944 0.646050i
\(92\) 0 0
\(93\) 36928.9 63962.7i 0.442750 0.766866i
\(94\) 0 0
\(95\) −49081.6 85011.8i −0.557968 0.966429i
\(96\) 0 0
\(97\) −12919.5 −0.139417 −0.0697086 0.997567i \(-0.522207\pi\)
−0.0697086 + 0.997567i \(0.522207\pi\)
\(98\) 0 0
\(99\) 45409.4 0.465648
\(100\) 0 0
\(101\) −12571.5 21774.4i −0.122626 0.212394i 0.798177 0.602424i \(-0.205798\pi\)
−0.920802 + 0.390029i \(0.872465\pi\)
\(102\) 0 0
\(103\) −80376.6 + 139216.i −0.746511 + 1.29300i 0.202974 + 0.979184i \(0.434939\pi\)
−0.949485 + 0.313811i \(0.898394\pi\)
\(104\) 0 0
\(105\) −56486.6 + 61754.1i −0.500003 + 0.546629i
\(106\) 0 0
\(107\) −47187.8 + 81731.6i −0.398446 + 0.690129i −0.993534 0.113531i \(-0.963784\pi\)
0.595088 + 0.803661i \(0.297117\pi\)
\(108\) 0 0
\(109\) 41696.7 + 72220.9i 0.336152 + 0.582233i 0.983705 0.179788i \(-0.0575410\pi\)
−0.647553 + 0.762020i \(0.724208\pi\)
\(110\) 0 0
\(111\) −25278.0 −0.194731
\(112\) 0 0
\(113\) −179254. −1.32060 −0.660301 0.751001i \(-0.729571\pi\)
−0.660301 + 0.751001i \(0.729571\pi\)
\(114\) 0 0
\(115\) −115774. 200526.i −0.816328 1.41392i
\(116\) 0 0
\(117\) −21607.1 + 37424.6i −0.145926 + 0.252751i
\(118\) 0 0
\(119\) −127315. 28106.8i −0.824163 0.181946i
\(120\) 0 0
\(121\) −76616.4 + 132703.i −0.475727 + 0.823984i
\(122\) 0 0
\(123\) −1106.22 1916.04i −0.00659295 0.0114193i
\(124\) 0 0
\(125\) 79256.4 0.453690
\(126\) 0 0
\(127\) 143674. 0.790440 0.395220 0.918586i \(-0.370668\pi\)
0.395220 + 0.918586i \(0.370668\pi\)
\(128\) 0 0
\(129\) −78770.2 136434.i −0.416762 0.721853i
\(130\) 0 0
\(131\) 26144.9 45284.3i 0.133110 0.230553i −0.791764 0.610827i \(-0.790837\pi\)
0.924874 + 0.380274i \(0.124170\pi\)
\(132\) 0 0
\(133\) −53500.6 169159.i −0.262259 0.829215i
\(134\) 0 0
\(135\) 26145.2 45284.9i 0.123469 0.213855i
\(136\) 0 0
\(137\) −4705.05 8149.39i −0.0214172 0.0370957i 0.855118 0.518433i \(-0.173484\pi\)
−0.876535 + 0.481337i \(0.840151\pi\)
\(138\) 0 0
\(139\) −183094. −0.803781 −0.401890 0.915688i \(-0.631647\pi\)
−0.401890 + 0.915688i \(0.631647\pi\)
\(140\) 0 0
\(141\) 147109. 0.623150
\(142\) 0 0
\(143\) −149545. 259020.i −0.611551 1.05924i
\(144\) 0 0
\(145\) −27022.3 + 46804.1i −0.106734 + 0.184869i
\(146\) 0 0
\(147\) −123753. + 86980.4i −0.472350 + 0.331992i
\(148\) 0 0
\(149\) 83500.8 144628.i 0.308123 0.533685i −0.669828 0.742516i \(-0.733632\pi\)
0.977952 + 0.208830i \(0.0669657\pi\)
\(150\) 0 0
\(151\) 188132. + 325855.i 0.671461 + 1.16300i 0.977490 + 0.210982i \(0.0676662\pi\)
−0.306029 + 0.952022i \(0.599000\pi\)
\(152\) 0 0
\(153\) 81461.7 0.281336
\(154\) 0 0
\(155\) 588639. 1.96797
\(156\) 0 0
\(157\) −19537.5 33840.0i −0.0632587 0.109567i 0.832662 0.553782i \(-0.186816\pi\)
−0.895920 + 0.444215i \(0.853483\pi\)
\(158\) 0 0
\(159\) 133387. 231034.i 0.418429 0.724741i
\(160\) 0 0
\(161\) −126197. 399013.i −0.383694 1.21317i
\(162\) 0 0
\(163\) −238959. + 413890.i −0.704458 + 1.22016i 0.262428 + 0.964951i \(0.415477\pi\)
−0.966887 + 0.255206i \(0.917857\pi\)
\(164\) 0 0
\(165\) 180954. + 313422.i 0.517439 + 0.896230i
\(166\) 0 0
\(167\) −39793.4 −0.110413 −0.0552064 0.998475i \(-0.517582\pi\)
−0.0552064 + 0.998475i \(0.517582\pi\)
\(168\) 0 0
\(169\) −86661.4 −0.233404
\(170\) 0 0
\(171\) 55425.3 + 95999.5i 0.144950 + 0.251061i
\(172\) 0 0
\(173\) −24169.1 + 41862.1i −0.0613968 + 0.106342i −0.895090 0.445886i \(-0.852889\pi\)
0.833693 + 0.552228i \(0.186222\pi\)
\(174\) 0 0
\(175\) −255727. 56455.5i −0.631220 0.139351i
\(176\) 0 0
\(177\) −46602.5 + 80717.9i −0.111809 + 0.193659i
\(178\) 0 0
\(179\) −71455.3 123764.i −0.166687 0.288711i 0.770566 0.637360i \(-0.219974\pi\)
−0.937253 + 0.348650i \(0.886640\pi\)
\(180\) 0 0
\(181\) −77245.3 −0.175257 −0.0876285 0.996153i \(-0.527929\pi\)
−0.0876285 + 0.996153i \(0.527929\pi\)
\(182\) 0 0
\(183\) 8587.61 0.0189559
\(184\) 0 0
\(185\) −100731. 174472.i −0.216389 0.374797i
\(186\) 0 0
\(187\) −281903. + 488270.i −0.589516 + 1.02107i
\(188\) 0 0
\(189\) 63787.5 69735.8i 0.129892 0.142004i
\(190\) 0 0
\(191\) 136027. 235606.i 0.269800 0.467307i −0.699010 0.715112i \(-0.746376\pi\)
0.968810 + 0.247805i \(0.0797092\pi\)
\(192\) 0 0
\(193\) 8016.89 + 13885.7i 0.0154922 + 0.0268333i 0.873668 0.486523i \(-0.161735\pi\)
−0.858175 + 0.513357i \(0.828402\pi\)
\(194\) 0 0
\(195\) −344413. −0.648624
\(196\) 0 0
\(197\) 1.03228e6 1.89510 0.947552 0.319603i \(-0.103549\pi\)
0.947552 + 0.319603i \(0.103549\pi\)
\(198\) 0 0
\(199\) −440868. 763606.i −0.789180 1.36690i −0.926470 0.376369i \(-0.877173\pi\)
0.137290 0.990531i \(-0.456161\pi\)
\(200\) 0 0
\(201\) −89168.4 + 154444.i −0.155676 + 0.269638i
\(202\) 0 0
\(203\) −65927.4 + 72075.3i −0.112286 + 0.122757i
\(204\) 0 0
\(205\) 8816.49 15270.6i 0.0146525 0.0253788i
\(206\) 0 0
\(207\) 130737. + 226443.i 0.212067 + 0.367311i
\(208\) 0 0
\(209\) −767210. −1.21492
\(210\) 0 0
\(211\) 372813. 0.576480 0.288240 0.957558i \(-0.406930\pi\)
0.288240 + 0.957558i \(0.406930\pi\)
\(212\) 0 0
\(213\) 279564. + 484219.i 0.422214 + 0.731296i
\(214\) 0 0
\(215\) 627791. 1.08737e6i 0.926230 1.60428i
\(216\) 0 0
\(217\) 1.03888e6 + 229348.i 1.49767 + 0.330633i
\(218\) 0 0
\(219\) −121993. + 211299.i −0.171880 + 0.297705i
\(220\) 0 0
\(221\) −268275. 464666.i −0.369487 0.639971i
\(222\) 0 0
\(223\) 1.08205e6 1.45708 0.728541 0.685002i \(-0.240199\pi\)
0.728541 + 0.685002i \(0.240199\pi\)
\(224\) 0 0
\(225\) 163625. 0.215473
\(226\) 0 0
\(227\) 276524. + 478954.i 0.356179 + 0.616921i 0.987319 0.158748i \(-0.0507459\pi\)
−0.631140 + 0.775669i \(0.717413\pi\)
\(228\) 0 0
\(229\) −261512. + 452952.i −0.329536 + 0.570773i −0.982420 0.186685i \(-0.940226\pi\)
0.652884 + 0.757458i \(0.273559\pi\)
\(230\) 0 0
\(231\) 197246. + 623658.i 0.243209 + 0.768983i
\(232\) 0 0
\(233\) 182090. 315390.i 0.219734 0.380590i −0.734993 0.678075i \(-0.762814\pi\)
0.954727 + 0.297485i \(0.0961477\pi\)
\(234\) 0 0
\(235\) 586223. + 1.01537e6i 0.692458 + 1.19937i
\(236\) 0 0
\(237\) −402186. −0.465111
\(238\) 0 0
\(239\) −371841. −0.421078 −0.210539 0.977585i \(-0.567522\pi\)
−0.210539 + 0.977585i \(0.567522\pi\)
\(240\) 0 0
\(241\) 855737. + 1.48218e6i 0.949069 + 1.64384i 0.747391 + 0.664384i \(0.231306\pi\)
0.201678 + 0.979452i \(0.435360\pi\)
\(242\) 0 0
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −1.09350e6 507550.i −1.16387 0.540212i
\(246\) 0 0
\(247\) 365060. 632303.i 0.380735 0.659452i
\(248\) 0 0
\(249\) 70229.9 + 121642.i 0.0717833 + 0.124332i
\(250\) 0 0
\(251\) −58134.1 −0.0582434 −0.0291217 0.999576i \(-0.509271\pi\)
−0.0291217 + 0.999576i \(0.509271\pi\)
\(252\) 0 0
\(253\) −1.80969e6 −1.77748
\(254\) 0 0
\(255\) 324621. + 562260.i 0.312627 + 0.541485i
\(256\) 0 0
\(257\) 155920. 270061.i 0.147254 0.255052i −0.782957 0.622075i \(-0.786290\pi\)
0.930212 + 0.367023i \(0.119623\pi\)
\(258\) 0 0
\(259\) −109801. 347171.i −0.101708 0.321583i
\(260\) 0 0
\(261\) 30515.0 52853.5i 0.0277276 0.0480255i
\(262\) 0 0
\(263\) 431983. + 748216.i 0.385103 + 0.667018i 0.991783 0.127928i \(-0.0408326\pi\)
−0.606681 + 0.794946i \(0.707499\pi\)
\(264\) 0 0
\(265\) 2.12617e6 1.85987
\(266\) 0 0
\(267\) 122718. 0.105349
\(268\) 0 0
\(269\) 560346. + 970548.i 0.472145 + 0.817779i 0.999492 0.0318707i \(-0.0101465\pi\)
−0.527347 + 0.849650i \(0.676813\pi\)
\(270\) 0 0
\(271\) 570058. 987369.i 0.471515 0.816688i −0.527954 0.849273i \(-0.677041\pi\)
0.999469 + 0.0325848i \(0.0103739\pi\)
\(272\) 0 0
\(273\) −607849. 134192.i −0.493616 0.108973i
\(274\) 0 0
\(275\) −566233. + 980744.i −0.451506 + 0.782031i
\(276\) 0 0
\(277\) 994005. + 1.72167e6i 0.778375 + 1.34819i 0.932878 + 0.360193i \(0.117289\pi\)
−0.154502 + 0.987992i \(0.549377\pi\)
\(278\) 0 0
\(279\) −664720. −0.511244
\(280\) 0 0
\(281\) 532321. 0.402168 0.201084 0.979574i \(-0.435554\pi\)
0.201084 + 0.979574i \(0.435554\pi\)
\(282\) 0 0
\(283\) 1.31237e6 + 2.27308e6i 0.974067 + 1.68713i 0.682980 + 0.730437i \(0.260684\pi\)
0.291087 + 0.956697i \(0.405983\pi\)
\(284\) 0 0
\(285\) −441734. + 765106.i −0.322143 + 0.557968i
\(286\) 0 0
\(287\) 21509.9 23515.7i 0.0154146 0.0168521i
\(288\) 0 0
\(289\) 204212. 353705.i 0.143826 0.249113i
\(290\) 0 0
\(291\) 58137.7 + 100697.i 0.0402463 + 0.0697086i
\(292\) 0 0
\(293\) 609962. 0.415082 0.207541 0.978226i \(-0.433454\pi\)
0.207541 + 0.978226i \(0.433454\pi\)
\(294\) 0 0
\(295\) −742834. −0.496978
\(296\) 0 0
\(297\) −204342. 353931.i −0.134421 0.232824i
\(298\) 0 0
\(299\) 861104. 1.49148e6i 0.557029 0.964802i
\(300\) 0 0
\(301\) 1.53164e6 1.67447e6i 0.974409 1.06528i
\(302\) 0 0
\(303\) −113143. + 195970.i −0.0707981 + 0.122626i
\(304\) 0 0
\(305\) 34221.2 + 59272.8i 0.0210642 + 0.0364843i
\(306\) 0 0
\(307\) 1.34843e6 0.816551 0.408275 0.912859i \(-0.366130\pi\)
0.408275 + 0.912859i \(0.366130\pi\)
\(308\) 0 0
\(309\) 1.44678e6 0.861997
\(310\) 0 0
\(311\) −1.66530e6 2.88439e6i −0.976320 1.69104i −0.675507 0.737353i \(-0.736075\pi\)
−0.300813 0.953683i \(-0.597258\pi\)
\(312\) 0 0
\(313\) 1.41835e6 2.45666e6i 0.818320 1.41737i −0.0885991 0.996067i \(-0.528239\pi\)
0.906919 0.421305i \(-0.138428\pi\)
\(314\) 0 0
\(315\) 735516. + 162376.i 0.417653 + 0.0922032i
\(316\) 0 0
\(317\) 544195. 942574.i 0.304163 0.526826i −0.672912 0.739723i \(-0.734957\pi\)
0.977075 + 0.212897i \(0.0682899\pi\)
\(318\) 0 0
\(319\) 211198. + 365805.i 0.116202 + 0.201267i
\(320\) 0 0
\(321\) 849380. 0.460086
\(322\) 0 0
\(323\) −1.37633e6 −0.734033
\(324\) 0 0
\(325\) −538860. 933332.i −0.282988 0.490149i
\(326\) 0 0
\(327\) 375271. 649988.i 0.194078 0.336152i
\(328\) 0 0
\(329\) 639004. + 2.02042e6i 0.325472 + 1.02908i
\(330\) 0 0
\(331\) 652773. 1.13064e6i 0.327485 0.567221i −0.654527 0.756039i \(-0.727132\pi\)
0.982012 + 0.188817i \(0.0604654\pi\)
\(332\) 0 0
\(333\) 113751. + 197022.i 0.0562140 + 0.0973654i
\(334\) 0 0
\(335\) −1.42133e6 −0.691961
\(336\) 0 0
\(337\) −3.17016e6 −1.52057 −0.760285 0.649590i \(-0.774941\pi\)
−0.760285 + 0.649590i \(0.774941\pi\)
\(338\) 0 0
\(339\) 806641. + 1.39714e6i 0.381225 + 0.660301i
\(340\) 0 0
\(341\) 2.30030e6 3.98424e6i 1.07127 1.85549i
\(342\) 0 0
\(343\) −1.73215e6 1.32182e6i −0.794969 0.606650i
\(344\) 0 0
\(345\) −1.04196e6 + 1.80473e6i −0.471307 + 0.816328i
\(346\) 0 0
\(347\) −857958. 1.48603e6i −0.382510 0.662526i 0.608911 0.793239i \(-0.291607\pi\)
−0.991420 + 0.130713i \(0.958273\pi\)
\(348\) 0 0
\(349\) −2.95822e6 −1.30007 −0.650034 0.759905i \(-0.725245\pi\)
−0.650034 + 0.759905i \(0.725245\pi\)
\(350\) 0 0
\(351\) 388928. 0.168501
\(352\) 0 0
\(353\) −1.88490e6 3.26474e6i −0.805103 1.39448i −0.916222 0.400672i \(-0.868777\pi\)
0.111119 0.993807i \(-0.464557\pi\)
\(354\) 0 0
\(355\) −2.22810e6 + 3.85918e6i −0.938347 + 1.62526i
\(356\) 0 0
\(357\) 353848. + 1.11880e6i 0.146942 + 0.464605i
\(358\) 0 0
\(359\) 964935. 1.67132e6i 0.395150 0.684420i −0.597970 0.801518i \(-0.704026\pi\)
0.993120 + 0.117099i \(0.0373593\pi\)
\(360\) 0 0
\(361\) 301617. + 522416.i 0.121811 + 0.210984i
\(362\) 0 0
\(363\) 1.37909e6 0.549323
\(364\) 0 0
\(365\) −1.94455e6 −0.763988
\(366\) 0 0
\(367\) 1.18371e6 + 2.05025e6i 0.458754 + 0.794586i 0.998895 0.0469885i \(-0.0149624\pi\)
−0.540141 + 0.841575i \(0.681629\pi\)
\(368\) 0 0
\(369\) −9956.01 + 17244.3i −0.00380644 + 0.00659295i
\(370\) 0 0
\(371\) 3.75244e6 + 828409.i 1.41540 + 0.312471i
\(372\) 0 0
\(373\) −1.76914e6 + 3.06425e6i −0.658402 + 1.14039i 0.322627 + 0.946526i \(0.395434\pi\)
−0.981029 + 0.193860i \(0.937899\pi\)
\(374\) 0 0
\(375\) −356654. 617742.i −0.130969 0.226845i
\(376\) 0 0
\(377\) −401975. −0.145662
\(378\) 0 0
\(379\) −1.79847e6 −0.643139 −0.321569 0.946886i \(-0.604210\pi\)
−0.321569 + 0.946886i \(0.604210\pi\)
\(380\) 0 0
\(381\) −646533. 1.11983e6i −0.228180 0.395220i
\(382\) 0 0
\(383\) 1.30407e6 2.25872e6i 0.454261 0.786802i −0.544385 0.838836i \(-0.683237\pi\)
0.998645 + 0.0520333i \(0.0165702\pi\)
\(384\) 0 0
\(385\) −3.51855e6 + 3.84667e6i −1.20980 + 1.32261i
\(386\) 0 0
\(387\) −708932. + 1.22791e6i −0.240618 + 0.416762i
\(388\) 0 0
\(389\) 1.41498e6 + 2.45081e6i 0.474106 + 0.821175i 0.999560 0.0296466i \(-0.00943818\pi\)
−0.525455 + 0.850821i \(0.676105\pi\)
\(390\) 0 0
\(391\) −3.24648e6 −1.07392
\(392\) 0 0
\(393\) −470609. −0.153702
\(394\) 0 0
\(395\) −1.60269e6 2.77594e6i −0.516841 0.895195i
\(396\) 0 0
\(397\) 1.21531e6 2.10498e6i 0.387000 0.670303i −0.605045 0.796191i \(-0.706845\pi\)
0.992044 + 0.125888i \(0.0401781\pi\)
\(398\) 0 0
\(399\) −1.07771e6 + 1.17821e6i −0.338900 + 0.370503i
\(400\) 0 0
\(401\) 1.21592e6 2.10604e6i 0.377611 0.654041i −0.613103 0.790003i \(-0.710079\pi\)
0.990714 + 0.135962i \(0.0434124\pi\)
\(402\) 0 0
\(403\) 2.18910e6 + 3.79163e6i 0.671433 + 1.16296i
\(404\) 0 0
\(405\) −470614. −0.142570
\(406\) 0 0
\(407\) −1.57457e6 −0.471167
\(408\) 0 0
\(409\) 2.38733e6 + 4.13497e6i 0.705674 + 1.22226i 0.966448 + 0.256863i \(0.0826889\pi\)
−0.260774 + 0.965400i \(0.583978\pi\)
\(410\) 0 0
\(411\) −42345.5 + 73344.5i −0.0123652 + 0.0214172i
\(412\) 0 0
\(413\) −1.31102e6 289427.i −0.378210 0.0834956i
\(414\) 0 0
\(415\) −559725. + 969472.i −0.159534 + 0.276322i
\(416\) 0 0
\(417\) 823924. + 1.42708e6i 0.232032 + 0.401890i
\(418\) 0 0
\(419\) 457181. 0.127219 0.0636097 0.997975i \(-0.479739\pi\)
0.0636097 + 0.997975i \(0.479739\pi\)
\(420\) 0 0
\(421\) −1.82396e6 −0.501545 −0.250773 0.968046i \(-0.580685\pi\)
−0.250773 + 0.968046i \(0.580685\pi\)
\(422\) 0 0
\(423\) −661992. 1.14660e6i −0.179888 0.311575i
\(424\) 0 0
\(425\) −1.01579e6 + 1.75939e6i −0.272791 + 0.472488i
\(426\) 0 0
\(427\) 37302.3 + 117943.i 0.00990069 + 0.0313042i
\(428\) 0 0
\(429\) −1.34591e6 + 2.33118e6i −0.353079 + 0.611551i
\(430\) 0 0
\(431\) −1.69124e6 2.92932e6i −0.438544 0.759580i 0.559034 0.829145i \(-0.311172\pi\)
−0.997577 + 0.0695651i \(0.977839\pi\)
\(432\) 0 0
\(433\) −285266. −0.0731190 −0.0365595 0.999331i \(-0.511640\pi\)
−0.0365595 + 0.999331i \(0.511640\pi\)
\(434\) 0 0
\(435\) 486402. 0.123246
\(436\) 0 0
\(437\) −2.20886e6 3.82585e6i −0.553304 0.958351i
\(438\) 0 0
\(439\) 2.17610e6 3.76911e6i 0.538911 0.933421i −0.460052 0.887892i \(-0.652169\pi\)
0.998963 0.0455294i \(-0.0144975\pi\)
\(440\) 0 0
\(441\) 1.23484e6 + 573151.i 0.302352 + 0.140337i
\(442\) 0 0
\(443\) −2.55280e6 + 4.42158e6i −0.618027 + 1.07045i 0.371819 + 0.928305i \(0.378734\pi\)
−0.989845 + 0.142148i \(0.954599\pi\)
\(444\) 0 0
\(445\) 489024. + 847015.i 0.117066 + 0.202764i
\(446\) 0 0
\(447\) −1.50301e6 −0.355790
\(448\) 0 0
\(449\) 3.04163e6 0.712016 0.356008 0.934483i \(-0.384138\pi\)
0.356008 + 0.934483i \(0.384138\pi\)
\(450\) 0 0
\(451\) −68906.7 119350.i −0.0159522 0.0276300i
\(452\) 0 0
\(453\) 1.69319e6 2.93269e6i 0.387668 0.671461i
\(454\) 0 0
\(455\) −1.49604e6 4.73020e6i −0.338777 1.07115i
\(456\) 0 0
\(457\) 872162. 1.51063e6i 0.195347 0.338351i −0.751667 0.659542i \(-0.770750\pi\)
0.947014 + 0.321192i \(0.104083\pi\)
\(458\) 0 0
\(459\) −366578. 634931.i −0.0812147 0.140668i
\(460\) 0 0
\(461\) −6.85701e6 −1.50273 −0.751367 0.659884i \(-0.770605\pi\)
−0.751367 + 0.659884i \(0.770605\pi\)
\(462\) 0 0
\(463\) −5.13844e6 −1.11398 −0.556992 0.830518i \(-0.688045\pi\)
−0.556992 + 0.830518i \(0.688045\pi\)
\(464\) 0 0
\(465\) −2.64887e6 4.58798e6i −0.568105 0.983987i
\(466\) 0 0
\(467\) −2.29085e6 + 3.96788e6i −0.486077 + 0.841910i −0.999872 0.0160029i \(-0.994906\pi\)
0.513795 + 0.857913i \(0.328239\pi\)
\(468\) 0 0
\(469\) −2.50848e6 553784.i −0.526597 0.116254i
\(470\) 0 0
\(471\) −175838. + 304560.i −0.0365224 + 0.0632587i
\(472\) 0 0
\(473\) −4.90660e6 8.49848e6i −1.00839 1.74658i
\(474\) 0 0
\(475\) −2.76450e6 −0.562190
\(476\) 0 0
\(477\) −2.40097e6 −0.483161
\(478\) 0 0
\(479\) −144261. 249868.i −0.0287284 0.0497590i 0.851304 0.524673i \(-0.175812\pi\)
−0.880032 + 0.474914i \(0.842479\pi\)
\(480\) 0 0
\(481\) 749223. 1.29769e6i 0.147655 0.255746i
\(482\) 0 0
\(483\) −2.54211e6 + 2.77917e6i −0.495823 + 0.542060i
\(484\) 0 0
\(485\) −463352. + 802549.i −0.0894451 + 0.154923i
\(486\) 0 0
\(487\) −3.90842e6 6.76959e6i −0.746757 1.29342i −0.949369 0.314162i \(-0.898277\pi\)
0.202613 0.979259i \(-0.435057\pi\)
\(488\) 0 0
\(489\) 4.30127e6 0.813438
\(490\) 0 0
\(491\) −3.14467e6 −0.588669 −0.294335 0.955702i \(-0.595098\pi\)
−0.294335 + 0.955702i \(0.595098\pi\)
\(492\) 0 0
\(493\) 378875. + 656232.i 0.0702068 + 0.121602i
\(494\) 0 0
\(495\) 1.62859e6 2.82080e6i 0.298743 0.517439i
\(496\) 0 0
\(497\) −5.43597e6 + 5.94289e6i −0.987157 + 1.07921i
\(498\) 0 0
\(499\) 3.36281e6 5.82456e6i 0.604577 1.04716i −0.387541 0.921852i \(-0.626676\pi\)
0.992118 0.125305i \(-0.0399911\pi\)
\(500\) 0 0
\(501\) 179070. + 310159.i 0.0318734 + 0.0552064i
\(502\) 0 0
\(503\) 9.45056e6 1.66547 0.832737 0.553669i \(-0.186773\pi\)
0.832737 + 0.553669i \(0.186773\pi\)
\(504\) 0 0
\(505\) −1.80348e6 −0.314690
\(506\) 0 0
\(507\) 389976. + 675458.i 0.0673780 + 0.116702i
\(508\) 0 0
\(509\) 4.41851e6 7.65308e6i 0.755930 1.30931i −0.188981 0.981981i \(-0.560519\pi\)
0.944911 0.327328i \(-0.106148\pi\)
\(510\) 0 0
\(511\) −3.43191e6 757645.i −0.581411 0.128355i
\(512\) 0 0
\(513\) 498828. 863995.i 0.0836869 0.144950i
\(514\) 0 0
\(515\) 5.76534e6 + 9.98585e6i 0.957870 + 1.65908i
\(516\) 0 0
\(517\) 9.16344e6 1.50776
\(518\) 0 0
\(519\) 435044. 0.0708949
\(520\) 0 0
\(521\) −347492. 601874.i −0.0560855 0.0971430i 0.836619 0.547784i \(-0.184529\pi\)
−0.892705 + 0.450641i \(0.851195\pi\)
\(522\) 0 0
\(523\) 1.79105e6 3.10219e6i 0.286321 0.495923i −0.686607 0.727028i \(-0.740901\pi\)
0.972929 + 0.231105i \(0.0742342\pi\)
\(524\) 0 0
\(525\) 710743. + 2.24724e6i 0.112542 + 0.355837i
\(526\) 0 0
\(527\) 4.12660e6 7.14748e6i 0.647240 1.12105i
\(528\) 0 0
\(529\) −1.99208e6 3.45038e6i −0.309504 0.536077i
\(530\) 0 0
\(531\) 838845. 0.129106
\(532\) 0 0
\(533\) 131151. 0.0199965
\(534\) 0 0
\(535\) 3.38473e6 + 5.86253e6i 0.511258 + 0.885525i
\(536\) 0 0
\(537\) −643098. + 1.11388e6i −0.0962368 + 0.166687i
\(538\) 0 0
\(539\) −7.70860e6 + 5.41801e6i −1.14289 + 0.803282i
\(540\) 0 0
\(541\) 2.58423e6 4.47602e6i 0.379610 0.657504i −0.611395 0.791325i \(-0.709391\pi\)
0.991005 + 0.133821i \(0.0427248\pi\)
\(542\) 0 0
\(543\) 347604. + 602068.i 0.0505924 + 0.0876285i
\(544\) 0 0
\(545\) 5.98174e6 0.862653
\(546\) 0 0
\(547\) −8.47489e6 −1.21106 −0.605530 0.795822i \(-0.707039\pi\)
−0.605530 + 0.795822i \(0.707039\pi\)
\(548\) 0 0
\(549\) −38644.2 66933.8i −0.00547210 0.00947795i
\(550\) 0 0
\(551\) −515562. + 892980.i −0.0723439 + 0.125303i
\(552\) 0 0
\(553\) −1.74699e6 5.52367e6i −0.242928 0.768095i
\(554\) 0 0
\(555\) −906583. + 1.57025e6i −0.124932 + 0.216389i
\(556\) 0 0
\(557\) 5.21063e6 + 9.02508e6i 0.711627 + 1.23257i 0.964246 + 0.265009i \(0.0853748\pi\)
−0.252619 + 0.967566i \(0.581292\pi\)
\(558\) 0 0
\(559\) 9.33880e6 1.26404
\(560\) 0 0
\(561\) 5.07425e6 0.680714
\(562\) 0 0
\(563\) −3.62039e6 6.27069e6i −0.481375 0.833767i 0.518396 0.855141i \(-0.326529\pi\)
−0.999772 + 0.0213739i \(0.993196\pi\)
\(564\) 0 0
\(565\) −6.42885e6 + 1.11351e7i −0.847251 + 1.46748i
\(566\) 0 0
\(567\) −830581. 183363.i −0.108499 0.0239527i
\(568\) 0 0
\(569\) −458268. + 793743.i −0.0593388 + 0.102778i −0.894169 0.447730i \(-0.852233\pi\)
0.834830 + 0.550508i \(0.185566\pi\)
\(570\) 0 0
\(571\) 5.03538e6 + 8.72154e6i 0.646312 + 1.11944i 0.983997 + 0.178186i \(0.0570228\pi\)
−0.337685 + 0.941259i \(0.609644\pi\)
\(572\) 0 0
\(573\) −2.44849e6 −0.311538
\(574\) 0 0
\(575\) −6.52091e6 −0.822505
\(576\) 0 0
\(577\) −5.84987e6 1.01323e7i −0.731488 1.26697i −0.956247 0.292560i \(-0.905493\pi\)
0.224760 0.974414i \(-0.427840\pi\)
\(578\) 0 0
\(579\) 72152.0 124971.i 0.00894442 0.0154922i
\(580\) 0 0
\(581\) −1.36558e6 + 1.49292e6i −0.167833 + 0.183484i
\(582\) 0 0
\(583\) 8.30871e6 1.43911e7i 1.01242 1.75357i
\(584\) 0 0
\(585\) 1.54986e6 + 2.68443e6i 0.187242 + 0.324312i
\(586\) 0 0
\(587\) 6.92367e6 0.829357 0.414678 0.909968i \(-0.363894\pi\)
0.414678 + 0.909968i \(0.363894\pi\)
\(588\) 0 0
\(589\) 1.12307e7 1.33389
\(590\) 0 0
\(591\) −4.64527e6 8.04584e6i −0.547069 0.947552i
\(592\) 0 0
\(593\) −7.88850e6 + 1.36633e7i −0.921208 + 1.59558i −0.123660 + 0.992325i \(0.539463\pi\)
−0.797548 + 0.603255i \(0.793870\pi\)
\(594\) 0 0
\(595\) −6.31207e6 + 6.90068e6i −0.730936 + 0.799097i
\(596\) 0 0
\(597\) −3.96781e6 + 6.87245e6i −0.455633 + 0.789180i
\(598\) 0 0
\(599\) 7.13541e6 + 1.23589e7i 0.812553 + 1.40738i 0.911072 + 0.412248i \(0.135256\pi\)
−0.0985183 + 0.995135i \(0.531410\pi\)
\(600\) 0 0
\(601\) 7.63222e6 0.861916 0.430958 0.902372i \(-0.358176\pi\)
0.430958 + 0.902372i \(0.358176\pi\)
\(602\) 0 0
\(603\) 1.60503e6 0.179759
\(604\) 0 0
\(605\) 5.49562e6 + 9.51869e6i 0.610419 + 1.05728i
\(606\) 0 0
\(607\) −1.78017e6 + 3.08335e6i −0.196106 + 0.339665i −0.947262 0.320459i \(-0.896163\pi\)
0.751157 + 0.660124i \(0.229496\pi\)
\(608\) 0 0
\(609\) 858444. + 189515.i 0.0937927 + 0.0207061i
\(610\) 0 0
\(611\) −4.36023e6 + 7.55214e6i −0.472505 + 0.818402i
\(612\) 0 0
\(613\) 6.86420e6 + 1.18891e7i 0.737800 + 1.27791i 0.953484 + 0.301445i \(0.0974688\pi\)
−0.215683 + 0.976463i \(0.569198\pi\)
\(614\) 0 0
\(615\) −158697. −0.0169192
\(616\) 0 0
\(617\) −6.51173e6 −0.688626 −0.344313 0.938855i \(-0.611888\pi\)
−0.344313 + 0.938855i \(0.611888\pi\)
\(618\) 0 0
\(619\) 4.42555e6 + 7.66527e6i 0.464238 + 0.804083i 0.999167 0.0408136i \(-0.0129950\pi\)
−0.534929 + 0.844897i \(0.679662\pi\)
\(620\) 0 0
\(621\) 1.17663e6 2.03799e6i 0.122437 0.212067i
\(622\) 0 0
\(623\) 533054. + 1.68542e6i 0.0550238 + 0.173976i
\(624\) 0 0
\(625\) 5.99884e6 1.03903e7i 0.614281 1.06397i
\(626\) 0 0
\(627\) 3.45244e6 + 5.97981e6i 0.350718 + 0.607461i
\(628\) 0 0
\(629\) −2.82467e6 −0.284670
\(630\) 0 0
\(631\) 6.89663e6 0.689546 0.344773 0.938686i \(-0.387956\pi\)
0.344773 + 0.938686i \(0.387956\pi\)
\(632\) 0 0
\(633\) −1.67766e6 2.90579e6i −0.166416 0.288240i
\(634\) 0 0
\(635\) 5.15280e6 8.92492e6i 0.507118 0.878355i
\(636\) 0 0
\(637\) −797329. 8.93116e6i −0.0778554 0.872086i
\(638\) 0 0
\(639\) 2.51608e6 4.35797e6i 0.243765 0.422214i
\(640\) 0 0
\(641\) 8.33473e6 + 1.44362e7i 0.801210 + 1.38774i 0.918820 + 0.394677i \(0.129144\pi\)
−0.117610 + 0.993060i \(0.537523\pi\)
\(642\) 0 0
\(643\) 1.28697e7 1.22756 0.613779 0.789478i \(-0.289649\pi\)
0.613779 + 0.789478i \(0.289649\pi\)
\(644\) 0 0
\(645\) −1.13002e7 −1.06952
\(646\) 0 0
\(647\) −5.73656e6 9.93601e6i −0.538754 0.933150i −0.998971 0.0453435i \(-0.985562\pi\)
0.460217 0.887806i \(-0.347772\pi\)
\(648\) 0 0
\(649\) −2.90287e6 + 5.02792e6i −0.270530 + 0.468572i
\(650\) 0 0
\(651\) −2.88737e6 9.12934e6i −0.267023 0.844280i
\(652\) 0 0
\(653\) 6.59005e6 1.14143e7i 0.604791 1.04753i −0.387293 0.921957i \(-0.626590\pi\)
0.992084 0.125573i \(-0.0400768\pi\)
\(654\) 0 0
\(655\) −1.87535e6 3.24820e6i −0.170797 0.295829i
\(656\) 0 0
\(657\) 2.19588e6 0.198470
\(658\) 0 0
\(659\) 1.13068e7 1.01421 0.507104 0.861885i \(-0.330716\pi\)
0.507104 + 0.861885i \(0.330716\pi\)
\(660\) 0 0
\(661\) −1.10160e6 1.90802e6i −0.0980661 0.169856i 0.812818 0.582518i \(-0.197932\pi\)
−0.910884 + 0.412662i \(0.864599\pi\)
\(662\) 0 0
\(663\) −2.41447e6 + 4.18199e6i −0.213324 + 0.369487i
\(664\) 0 0
\(665\) −1.24268e7 2.74341e6i −1.08970 0.240567i
\(666\) 0 0
\(667\) −1.21611e6 + 2.10636e6i −0.105842 + 0.183323i
\(668\) 0 0
\(669\) −4.86921e6 8.43372e6i −0.420623 0.728541i
\(670\) 0 0
\(671\) 534922. 0.0458653
\(672\) 0 0
\(673\) −1.89787e7 −1.61521 −0.807606 0.589723i \(-0.799237\pi\)
−0.807606 + 0.589723i \(0.799237\pi\)
\(674\) 0 0
\(675\) −736312. 1.27533e6i −0.0622017 0.107736i
\(676\) 0 0
\(677\) 9.82377e6 1.70153e7i 0.823771 1.42681i −0.0790842 0.996868i \(-0.525200\pi\)
0.902855 0.429945i \(-0.141467\pi\)
\(678\) 0 0
\(679\) −1.13046e6 + 1.23587e6i −0.0940977 + 0.102873i
\(680\) 0 0
\(681\) 2.48872e6 4.31059e6i 0.205640 0.356179i
\(682\) 0 0
\(683\) 8.13523e6 + 1.40906e7i 0.667295 + 1.15579i 0.978658 + 0.205498i \(0.0658813\pi\)
−0.311363 + 0.950291i \(0.600785\pi\)
\(684\) 0 0
\(685\) −674978. −0.0549621
\(686\) 0 0
\(687\) 4.70722e6 0.380515
\(688\) 0 0
\(689\) 7.90704e6 + 1.36954e7i 0.634550 + 1.09907i
\(690\) 0 0
\(691\) 9.72335e6 1.68413e7i 0.774677 1.34178i −0.160299 0.987069i \(-0.551246\pi\)
0.934976 0.354712i \(-0.115421\pi\)
\(692\) 0 0
\(693\) 3.97332e6 4.34384e6i 0.314283 0.343591i
\(694\) 0 0
\(695\) −6.56659e6 + 1.13737e7i −0.515677 + 0.893179i
\(696\) 0 0
\(697\) −123614. 214106.i −0.00963800 0.0166935i
\(698\) 0 0
\(699\) −3.27763e6 −0.253727
\(700\) 0 0
\(701\) 1.49625e7 1.15003 0.575014 0.818144i \(-0.304997\pi\)
0.575014 + 0.818144i \(0.304997\pi\)
\(702\) 0 0
\(703\) −1.92187e6 3.32877e6i −0.146668 0.254036i
\(704\) 0 0
\(705\) 5.27601e6 9.13831e6i 0.399791 0.692458i
\(706\) 0 0
\(707\) −3.18293e6 702680.i −0.239485 0.0528700i
\(708\) 0 0
\(709\) −793193. + 1.37385e6i −0.0592603 + 0.102642i −0.894134 0.447800i \(-0.852208\pi\)
0.834873 + 0.550442i \(0.185541\pi\)
\(710\) 0 0
\(711\) 1.80984e6 + 3.13473e6i 0.134266 + 0.232555i
\(712\) 0 0
\(713\) 2.64910e7 1.95152
\(714\) 0 0
\(715\) −2.14535e7 −1.56940
\(716\) 0 0
\(717\) 1.67329e6 + 2.89822e6i 0.121555 + 0.210539i
\(718\) 0 0
\(719\) −9.08376e6 + 1.57335e7i −0.655305 + 1.13502i 0.326512 + 0.945193i \(0.394127\pi\)
−0.981817 + 0.189829i \(0.939207\pi\)
\(720\) 0 0
\(721\) 6.28442e6 + 1.98702e7i 0.450222 + 1.42352i
\(722\) 0 0
\(723\) 7.70164e6 1.33396e7i 0.547945 0.949069i
\(724\) 0 0
\(725\) 761013. + 1.31811e6i 0.0537709 + 0.0931339i
\(726\) 0 0
\(727\) −1.26903e7 −0.890506 −0.445253 0.895405i \(-0.646886\pi\)
−0.445253 + 0.895405i \(0.646886\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) −8.80214e6 1.52458e7i −0.609249 1.05525i
\(732\) 0 0
\(733\) 1.55701e6 2.69681e6i 0.107036 0.185392i −0.807532 0.589824i \(-0.799197\pi\)
0.914568 + 0.404432i \(0.132531\pi\)
\(734\) 0 0
\(735\) 964792. + 1.08070e7i 0.0658742 + 0.737880i
\(736\) 0 0
\(737\) −5.55430e6 + 9.62033e6i −0.376670 + 0.652411i
\(738\) 0 0
\(739\) 4.54950e6 + 7.87996e6i 0.306445 + 0.530778i 0.977582 0.210555i \(-0.0675272\pi\)
−0.671137 + 0.741333i \(0.734194\pi\)
\(740\) 0 0
\(741\) −6.57109e6 −0.439634
\(742\) 0 0
\(743\) 8.79218e6 0.584285 0.292142 0.956375i \(-0.405632\pi\)
0.292142 + 0.956375i \(0.405632\pi\)
\(744\) 0 0
\(745\) −5.98943e6 1.03740e7i −0.395362 0.684787i
\(746\) 0 0
\(747\) 632069. 1.09478e6i 0.0414441 0.0717833i
\(748\) 0 0
\(749\) 3.68948e6 + 1.16655e7i 0.240304 + 0.759798i
\(750\) 0 0
\(751\) −1.40459e7 + 2.43282e7i −0.908759 + 1.57402i −0.0929698 + 0.995669i \(0.529636\pi\)
−0.815790 + 0.578349i \(0.803697\pi\)
\(752\) 0 0
\(753\) 261603. + 453110.i 0.0168134 + 0.0291217i
\(754\) 0 0
\(755\) 2.69891e7 1.72314
\(756\) 0 0
\(757\) −4.18815e6 −0.265634 −0.132817 0.991141i \(-0.542402\pi\)
−0.132817 + 0.991141i \(0.542402\pi\)
\(758\) 0 0
\(759\) 8.14362e6 + 1.41052e7i 0.513113 + 0.888738i
\(760\) 0 0
\(761\) 196591. 340506.i 0.0123056 0.0213139i −0.859807 0.510619i \(-0.829416\pi\)
0.872113 + 0.489305i \(0.162750\pi\)
\(762\) 0 0
\(763\) 1.05571e7 + 2.33063e6i 0.656497 + 0.144932i
\(764\) 0 0
\(765\) 2.92159e6 5.06034e6i 0.180495 0.312627i
\(766\) 0 0
\(767\) −2.76254e6 4.78486e6i −0.169559 0.293684i
\(768\) 0 0
\(769\) 1.57517e7 0.960530 0.480265 0.877124i \(-0.340541\pi\)
0.480265 + 0.877124i \(0.340541\pi\)
\(770\) 0 0
\(771\) −2.80655e6 −0.170035
\(772\) 0 0
\(773\) −1.44236e6 2.49824e6i −0.0868210 0.150378i 0.819345 0.573301i \(-0.194337\pi\)
−0.906166 + 0.422923i \(0.861004\pi\)
\(774\) 0 0
\(775\) 8.28873e6 1.43565e7i 0.495717 0.858606i
\(776\) 0 0
\(777\) −2.21182e6 + 2.41808e6i −0.131431 + 0.143687i
\(778\) 0 0
\(779\) 168211. 291349.i 0.00993139 0.0172017i
\(780\) 0 0
\(781\) 1.74141e7 + 3.01620e7i 1.02158 + 1.76943i