Properties

Label 336.6.q.e.193.2
Level $336$
Weight $6$
Character 336.193
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 193.2
Root \(4.19493 + 1.84460i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.6.q.e.289.2

$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.985084 + 0.172076i \(0.0550476\pi\)
−0.343519 + 0.939146i \(0.611619\pi\)
\(6\) 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 0.270524 + 0.962713i \(0.412803\pi\)
−0.968996 + 0.247076i \(0.920530\pi\)
\(12\) 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 −0.996135 0.0878311i \(-0.972006\pi\)
0.574132 + 0.818763i \(0.305340\pi\)
\(18\) 0 0
\(19\) 684.263 + 1185.18i 0.434850 + 0.753182i 0.997283 0.0736606i \(-0.0234682\pi\)
−0.562434 + 0.826842i \(0.690135\pi\)
\(20\) 0 0
\(21\) −1139.34 + 251.527i −0.563775 + 0.124462i
\(22\) 0 0
\(23\) 1614.04 + 2795.60i 0.636201 + 1.10193i 0.986259 + 0.165205i \(0.0528286\pi\)
−0.350058 + 0.936728i \(0.613838\pi\)
\(24\) 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 −0.172389 0.985029i \(-0.555148\pi\)
0.939254 0.343222i \(-0.111518\pi\)
\(32\) 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 0.937943 0.346791i \(-0.112729\pi\)
−0.769301 + 0.638887i \(0.779395\pi\)
\(38\) 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 −0.998922 0.0464219i \(-0.985218\pi\)
0.459258 0.888303i \(-0.348115\pi\)
\(48\) 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 −0.234340 0.972155i \(-0.575293\pi\)
0.959081 0.283133i \(-0.0913739\pi\)
\(54\) 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 −0.946460 0.322821i \(-0.895369\pi\)
0.752801 + 0.658248i \(0.228702\pi\)
\(60\) 0 0
\(61\) −477.089 826.343i −0.0164163 0.0284339i 0.857701 0.514150i \(-0.171892\pi\)
−0.874117 + 0.485716i \(0.838559\pi\)
\(62\) 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 −0.968768 0.247967i \(-0.920237\pi\)
0.699130 + 0.714994i \(0.253571\pi\)
\(68\) 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 −0.975611 0.219509i \(-0.929555\pi\)
0.677905 + 0.735149i \(0.262888\pi\)
\(74\) 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 0.994062 0.108812i \(-0.0347045\pi\)
−0.591265 + 0.806477i \(0.701371\pi\)
\(80\) 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 0.816796 0.576926i \(-0.195748\pi\)
−0.908031 + 0.418903i \(0.862415\pi\)
\(90\) 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 −0.920802 0.390029i \(-0.872465\pi\)
0.798177 + 0.602424i \(0.205798\pi\)
\(102\) 0 0
\(103\) −80376.6 139216.i −0.746511 1.29300i −0.949485 0.313811i \(-0.898394\pi\)
0.202974 0.979184i \(-0.434939\pi\)
\(104\) 0 0
\(105\) −56486.6 61754.1i −0.500003 0.546629i
\(106\) 0 0
\(107\) −47187.8 81731.6i −0.398446 0.690129i 0.595088 0.803661i \(-0.297117\pi\)
−0.993534 + 0.113531i \(0.963784\pi\)
\(108\) 0 0
\(109\) 41696.7 72220.9i 0.336152 0.582233i −0.647553 0.762020i \(-0.724208\pi\)
0.983705 + 0.179788i \(0.0575410\pi\)
\(110\) 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 0.924874 0.380274i \(-0.124170\pi\)
−0.791764 + 0.610827i \(0.790837\pi\)
\(132\) 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 −0.876535 0.481337i \(-0.840151\pi\)
0.855118 + 0.518433i \(0.173484\pi\)
\(138\) 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 0.977952 0.208830i \(-0.0669657\pi\)
−0.669828 + 0.742516i \(0.733632\pi\)
\(150\) 0 0
\(151\) 188132. 325855.i 0.671461 1.16300i −0.306029 0.952022i \(-0.599000\pi\)
0.977490 0.210982i \(-0.0676662\pi\)
\(152\) 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 −0.895920 0.444215i \(-0.853483\pi\)
0.832662 + 0.553782i \(0.186816\pi\)
\(158\) 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 −0.966887 0.255206i \(-0.917857\pi\)
0.262428 0.964951i \(-0.415477\pi\)
\(164\) 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 0.833693 0.552228i \(-0.186222\pi\)
−0.895090 + 0.445886i \(0.852889\pi\)
\(174\) 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 −0.937253 0.348650i \(-0.886640\pi\)
0.770566 + 0.637360i \(0.219974\pi\)
\(180\) 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 0.968810 0.247805i \(-0.0797092\pi\)
−0.699010 + 0.715112i \(0.746376\pi\)
\(192\) 0 0
\(193\) 8016.89 13885.7i 0.0154922 0.0268333i −0.858175 0.513357i \(-0.828402\pi\)
0.873668 + 0.486523i \(0.161735\pi\)
\(194\) 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 0.137290 + 0.990531i \(0.456161\pi\)
−0.926470 + 0.376369i \(0.877173\pi\)
\(200\) 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 −0.631140 0.775669i \(-0.717413\pi\)
0.987319 + 0.158748i \(0.0507459\pi\)
\(228\) 0 0
\(229\) −261512. 452952.i −0.329536 0.570773i 0.652884 0.757458i \(-0.273559\pi\)
−0.982420 + 0.186685i \(0.940226\pi\)
\(230\) 0 0
\(231\) 197246. 623658.i 0.243209 0.768983i
\(232\) 0 0
\(233\) 182090. + 315390.i 0.219734 + 0.380590i 0.954727 0.297485i \(-0.0961477\pi\)
−0.734993 + 0.678075i \(0.762814\pi\)
\(234\) 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 0.201678 0.979452i \(-0.435360\pi\)
0.747391 0.664384i \(-0.231306\pi\)
\(242\) 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 0.930212 0.367023i \(-0.119623\pi\)
−0.782957 + 0.622075i \(0.786290\pi\)
\(258\) 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 −0.606681 0.794946i \(-0.707499\pi\)
0.991783 + 0.127928i \(0.0408326\pi\)
\(264\) 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 −0.527347 0.849650i \(-0.676813\pi\)
0.999492 + 0.0318707i \(0.0101465\pi\)
\(270\) 0 0
\(271\) 570058. + 987369.i 0.471515 + 0.816688i 0.999469 0.0325848i \(-0.0103739\pi\)
−0.527954 + 0.849273i \(0.677041\pi\)
\(272\) 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 −0.154502 0.987992i \(-0.549377\pi\)
0.932878 0.360193i \(-0.117289\pi\)
\(278\) 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 0.291087 0.956697i \(-0.405983\pi\)
0.682980 0.730437i \(-0.260684\pi\)
\(284\) 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 −0.300813 + 0.953683i \(0.597258\pi\)
−0.675507 + 0.737353i \(0.736075\pi\)
\(312\) 0 0
\(313\) 1.41835e6 + 2.45666e6i 0.818320 + 1.41737i 0.906919 + 0.421305i \(0.138428\pi\)
−0.0885991 + 0.996067i \(0.528239\pi\)
\(314\) 0 0
\(315\) 735516. 162376.i 0.417653 0.0922032i
\(316\) 0 0
\(317\) 544195. + 942574.i 0.304163 + 0.526826i 0.977075 0.212897i \(-0.0682899\pi\)
−0.672912 + 0.739723i \(0.734957\pi\)
\(318\) 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 0.982012 0.188817i \(-0.0604654\pi\)
−0.654527 + 0.756039i \(0.727132\pi\)
\(332\) 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 −0.991420 0.130713i \(-0.958273\pi\)
0.608911 + 0.793239i \(0.291607\pi\)
\(348\) 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 0.111119 + 0.993807i \(0.464557\pi\)
−0.916222 + 0.400672i \(0.868777\pi\)
\(354\) 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 0.993120 0.117099i \(-0.0373593\pi\)
−0.597970 + 0.801518i \(0.704026\pi\)
\(360\) 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 −0.540141 0.841575i \(-0.681629\pi\)
0.998895 + 0.0469885i \(0.0149624\pi\)
\(368\) 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 −0.981029 0.193860i \(-0.937899\pi\)
0.322627 0.946526i \(-0.395434\pi\)
\(374\) 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 0.998645 0.0520333i \(-0.0165702\pi\)
−0.544385 + 0.838836i \(0.683237\pi\)
\(384\) 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 −0.525455 0.850821i \(-0.676105\pi\)
0.999560 + 0.0296466i \(0.00943818\pi\)
\(390\) 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 0.992044 0.125888i \(-0.0401781\pi\)
−0.605045 + 0.796191i \(0.706845\pi\)
\(398\) 0 0
\(399\) −1.07771e6 1.17821e6i −0.338900 0.370503i
\(400\) 0 0
\(401\) 1.21592e6 + 2.10604e6i 0.377611 + 0.654041i 0.990714 0.135962i \(-0.0434124\pi\)
−0.613103 + 0.790003i \(0.710079\pi\)
\(402\) 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 −0.260774 0.965400i \(-0.583978\pi\)
0.966448 0.256863i \(-0.0826889\pi\)
\(410\) 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 −0.997577 0.0695651i \(-0.977839\pi\)
0.559034 + 0.829145i \(0.311172\pi\)
\(432\) 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 0.998963 + 0.0455294i \(0.0144975\pi\)
−0.460052 + 0.887892i \(0.652169\pi\)
\(440\) 0 0
\(441\) 1.23484e6 573151.i 0.302352 0.140337i
\(442\) 0 0
\(443\) −2.55280e6 4.42158e6i −0.618027 1.07045i −0.989845 0.142148i \(-0.954599\pi\)
0.371819 0.928305i \(-0.378734\pi\)
\(444\) 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 0.947014 0.321192i \(-0.104083\pi\)
−0.751667 + 0.659542i \(0.770750\pi\)
\(458\) 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 0.513795 0.857913i \(-0.328239\pi\)
−0.999872 + 0.0160029i \(0.994906\pi\)
\(468\) 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 −0.880032 0.474914i \(-0.842479\pi\)
0.851304 + 0.524673i \(0.175812\pi\)
\(480\) 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 0.202613 + 0.979259i \(0.435057\pi\)
−0.949369 + 0.314162i \(0.898277\pi\)
\(488\) 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 0.992118 + 0.125305i \(0.0399911\pi\)
−0.387541 + 0.921852i \(0.626676\pi\)
\(500\) 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 0.944911 + 0.327328i \(0.106148\pi\)
−0.188981 + 0.981981i \(0.560519\pi\)
\(510\) 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 −0.892705 0.450641i \(-0.851195\pi\)
0.836619 + 0.547784i \(0.184529\pi\)
\(522\) 0 0
\(523\) 1.79105e6 + 3.10219e6i 0.286321 + 0.495923i 0.972929 0.231105i \(-0.0742342\pi\)
−0.686607 + 0.727028i \(0.740901\pi\)
\(524\) 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 0.991005 0.133821i \(-0.0427248\pi\)
−0.611395 + 0.791325i \(0.709391\pi\)
\(542\) 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 −0.252619 0.967566i \(-0.581292\pi\)
0.964246 0.265009i \(-0.0853748\pi\)
\(558\) 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 −0.999772 0.0213739i \(-0.993196\pi\)
0.518396 + 0.855141i \(0.326529\pi\)
\(564\) 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 0.834830 0.550508i \(-0.185566\pi\)
−0.894169 + 0.447730i \(0.852233\pi\)
\(570\) 0 0
\(571\) 5.03538e6 8.72154e6i 0.646312 1.11944i −0.337685 0.941259i \(-0.609644\pi\)
0.983997 0.178186i \(-0.0570228\pi\)
\(572\) 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 0.224760 + 0.974414i \(0.427840\pi\)
−0.956247 + 0.292560i \(0.905493\pi\)
\(578\) 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 −0.797548 0.603255i \(-0.793870\pi\)
−0.123660 0.992325i \(-0.539463\pi\)
\(594\) 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 −0.0985183 0.995135i \(-0.531410\pi\)
0.911072 0.412248i \(-0.135256\pi\)
\(600\) 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 0.751157 0.660124i \(-0.229496\pi\)
−0.947262 + 0.320459i \(0.896163\pi\)
\(608\) 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 −0.215683 0.976463i \(-0.569198\pi\)
0.953484 0.301445i \(-0.0974688\pi\)
\(614\) 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 −0.534929 0.844897i \(-0.679662\pi\)
0.999167 + 0.0408136i \(0.0129950\pi\)
\(620\) 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 −0.117610 0.993060i \(-0.537523\pi\)
0.918820 0.394677i \(-0.129144\pi\)
\(642\) 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 0.460217 + 0.887806i \(0.347772\pi\)
−0.998971 + 0.0453435i \(0.985562\pi\)
\(648\) 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 0.992084 + 0.125573i \(0.0400768\pi\)
−0.387293 + 0.921957i \(0.626590\pi\)
\(654\) 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 −0.910884 0.412662i \(-0.864599\pi\)
0.812818 + 0.582518i \(0.197932\pi\)
\(662\) 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 0.902855 + 0.429945i \(0.141467\pi\)
−0.0790842 + 0.996868i \(0.525200\pi\)
\(678\) 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 −0.311363 0.950291i \(-0.600785\pi\)
0.978658 0.205498i \(-0.0658813\pi\)
\(684\) 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 0.934976 + 0.354712i \(0.115421\pi\)
−0.160299 + 0.987069i \(0.551246\pi\)
\(692\) 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 0.834873 0.550442i \(-0.185541\pi\)
−0.894134 + 0.447800i \(0.852208\pi\)
\(710\) 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 −0.981817 0.189829i \(-0.939207\pi\)
0.326512 0.945193i \(-0.394127\pi\)
\(720\) 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 0.914568 0.404432i \(-0.132531\pi\)
−0.807532 + 0.589824i \(0.799197\pi\)
\(734\) 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 −0.671137 0.741333i \(-0.734194\pi\)
0.977582 + 0.210555i \(0.0675272\pi\)
\(740\) 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 −0.815790 0.578349i \(-0.803697\pi\)
−0.0929698 0.995669i \(-0.529636\pi\)
\(752\) 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 0.872113 0.489305i \(-0.162750\pi\)
−0.859807 + 0.510619i \(0.829416\pi\)
\(762\) 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 −0.906166 0.422923i \(-0.861004\pi\)
0.819345 + 0.573301i \(0.194337\pi\)
\(774\) 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