Properties

Label 196.6.e.h.177.1
Level $196$
Weight $6$
Character 196.177
Analytic conductor $31.435$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [196,6,Mod(165,196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(196, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("196.165");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 196.e (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: \(31.4352286833\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 196.177
Dual form 196.6.e.h.165.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(8.00000 + 13.8564i) q^{3} +(-8.00000 + 13.8564i) q^{5} +(-6.50000 + 11.2583i) q^{9} +O(q^{10})\) \(q+(8.00000 + 13.8564i) q^{3} +(-8.00000 + 13.8564i) q^{5} +(-6.50000 + 11.2583i) q^{9} +(38.0000 + 65.8179i) q^{11} +880.000 q^{13} -256.000 q^{15} +(528.000 + 914.523i) q^{17} +(-968.000 + 1676.63i) q^{19} +(-468.000 + 810.600i) q^{23} +(1434.50 + 2484.63i) q^{25} +3680.00 q^{27} -3982.00 q^{29} +(-784.000 - 1357.93i) q^{31} +(-608.000 + 1053.09i) q^{33} +(-2469.00 + 4276.43i) q^{37} +(7040.00 + 12193.6i) q^{39} -15840.0 q^{41} -16412.0 q^{43} +(-104.000 - 180.133i) q^{45} +(10384.0 - 17985.6i) q^{47} +(-8448.00 + 14632.4i) q^{51} +(18701.0 + 32391.1i) q^{53} -1216.00 q^{55} -30976.0 q^{57} +(-10568.0 - 18304.3i) q^{59} +(1496.00 - 2591.15i) q^{61} +(-7040.00 + 12193.6i) q^{65} +(22918.0 + 39695.1i) q^{67} -14976.0 q^{69} -49840.0 q^{71} +(28160.0 + 48774.6i) q^{73} +(-22952.0 + 39754.0i) q^{75} +(-20372.0 + 35285.3i) q^{79} +(31019.5 + 53727.4i) q^{81} +112464. q^{83} -16896.0 q^{85} +(-31856.0 - 55176.2i) q^{87} +(-32128.0 + 55647.3i) q^{89} +(12544.0 - 21726.8i) q^{93} +(-15488.0 - 26826.0i) q^{95} -2272.00 q^{97} -988.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 16 q^{3} - 16 q^{5} - 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 16 q^{3} - 16 q^{5} - 13 q^{9} + 76 q^{11} + 1760 q^{13} - 512 q^{15} + 1056 q^{17} - 1936 q^{19} - 936 q^{23} + 2869 q^{25} + 7360 q^{27} - 7964 q^{29} - 1568 q^{31} - 1216 q^{33} - 4938 q^{37} + 14080 q^{39} - 31680 q^{41} - 32824 q^{43} - 208 q^{45} + 20768 q^{47} - 16896 q^{51} + 37402 q^{53} - 2432 q^{55} - 61952 q^{57} - 21136 q^{59} + 2992 q^{61} - 14080 q^{65} + 45836 q^{67} - 29952 q^{69} - 99680 q^{71} + 56320 q^{73} - 45904 q^{75} - 40744 q^{79} + 62039 q^{81} + 224928 q^{83} - 33792 q^{85} - 63712 q^{87} - 64256 q^{89} + 25088 q^{93} - 30976 q^{95} - 4544 q^{97} - 1976 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).

\(n\) \(99\) \(101\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 8.00000 + 13.8564i 0.513200 + 0.888889i 0.999883 + 0.0153100i \(0.00487351\pi\)
−0.486683 + 0.873579i \(0.661793\pi\)
\(4\) 0 0
\(5\) −8.00000 + 13.8564i −0.143108 + 0.247871i −0.928666 0.370918i \(-0.879043\pi\)
0.785557 + 0.618789i \(0.212376\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −6.50000 + 11.2583i −0.0267490 + 0.0463306i
\(10\) 0 0
\(11\) 38.0000 + 65.8179i 0.0946895 + 0.164007i 0.909479 0.415750i \(-0.136481\pi\)
−0.814789 + 0.579757i \(0.803148\pi\)
\(12\) 0 0
\(13\) 880.000 1.44419 0.722095 0.691794i \(-0.243179\pi\)
0.722095 + 0.691794i \(0.243179\pi\)
\(14\) 0 0
\(15\) −256.000 −0.293773
\(16\) 0 0
\(17\) 528.000 + 914.523i 0.443110 + 0.767489i 0.997918 0.0644890i \(-0.0205418\pi\)
−0.554808 + 0.831978i \(0.687208\pi\)
\(18\) 0 0
\(19\) −968.000 + 1676.63i −0.615165 + 1.06550i 0.375191 + 0.926948i \(0.377577\pi\)
−0.990356 + 0.138549i \(0.955756\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −468.000 + 810.600i −0.184470 + 0.319512i −0.943398 0.331663i \(-0.892390\pi\)
0.758928 + 0.651175i \(0.225724\pi\)
\(24\) 0 0
\(25\) 1434.50 + 2484.63i 0.459040 + 0.795081i
\(26\) 0 0
\(27\) 3680.00 0.971490
\(28\) 0 0
\(29\) −3982.00 −0.879238 −0.439619 0.898184i \(-0.644886\pi\)
−0.439619 + 0.898184i \(0.644886\pi\)
\(30\) 0 0
\(31\) −784.000 1357.93i −0.146525 0.253789i 0.783416 0.621498i \(-0.213476\pi\)
−0.929941 + 0.367709i \(0.880142\pi\)
\(32\) 0 0
\(33\) −608.000 + 1053.09i −0.0971894 + 0.168337i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2469.00 + 4276.43i −0.296495 + 0.513544i −0.975331 0.220745i \(-0.929151\pi\)
0.678837 + 0.734289i \(0.262484\pi\)
\(38\) 0 0
\(39\) 7040.00 + 12193.6i 0.741159 + 1.28372i
\(40\) 0 0
\(41\) −15840.0 −1.47162 −0.735810 0.677188i \(-0.763198\pi\)
−0.735810 + 0.677188i \(0.763198\pi\)
\(42\) 0 0
\(43\) −16412.0 −1.35360 −0.676800 0.736167i \(-0.736634\pi\)
−0.676800 + 0.736167i \(0.736634\pi\)
\(44\) 0 0
\(45\) −104.000 180.133i −0.00765600 0.0132606i
\(46\) 0 0
\(47\) 10384.0 17985.6i 0.685678 1.18763i −0.287546 0.957767i \(-0.592839\pi\)
0.973223 0.229862i \(-0.0738274\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −8448.00 + 14632.4i −0.454808 + 0.787751i
\(52\) 0 0
\(53\) 18701.0 + 32391.1i 0.914482 + 1.58393i 0.807658 + 0.589651i \(0.200735\pi\)
0.106824 + 0.994278i \(0.465932\pi\)
\(54\) 0 0
\(55\) −1216.00 −0.0542034
\(56\) 0 0
\(57\) −30976.0 −1.26281
\(58\) 0 0
\(59\) −10568.0 18304.3i −0.395242 0.684579i 0.597890 0.801578i \(-0.296006\pi\)
−0.993132 + 0.116999i \(0.962673\pi\)
\(60\) 0 0
\(61\) 1496.00 2591.15i 0.0514763 0.0891595i −0.839139 0.543917i \(-0.816941\pi\)
0.890615 + 0.454757i \(0.150274\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −7040.00 + 12193.6i −0.206676 + 0.357973i
\(66\) 0 0
\(67\) 22918.0 + 39695.1i 0.623720 + 1.08031i 0.988787 + 0.149334i \(0.0477128\pi\)
−0.365067 + 0.930981i \(0.618954\pi\)
\(68\) 0 0
\(69\) −14976.0 −0.378681
\(70\) 0 0
\(71\) −49840.0 −1.17336 −0.586681 0.809818i \(-0.699566\pi\)
−0.586681 + 0.809818i \(0.699566\pi\)
\(72\) 0 0
\(73\) 28160.0 + 48774.6i 0.618480 + 1.07124i 0.989763 + 0.142719i \(0.0455845\pi\)
−0.371283 + 0.928520i \(0.621082\pi\)
\(74\) 0 0
\(75\) −22952.0 + 39754.0i −0.471159 + 0.816071i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −20372.0 + 35285.3i −0.367253 + 0.636102i −0.989135 0.147010i \(-0.953035\pi\)
0.621882 + 0.783111i \(0.286369\pi\)
\(80\) 0 0
\(81\) 31019.5 + 53727.4i 0.525318 + 0.909877i
\(82\) 0 0
\(83\) 112464. 1.79192 0.895959 0.444136i \(-0.146489\pi\)
0.895959 + 0.444136i \(0.146489\pi\)
\(84\) 0 0
\(85\) −16896.0 −0.253651
\(86\) 0 0
\(87\) −31856.0 55176.2i −0.451225 0.781545i
\(88\) 0 0
\(89\) −32128.0 + 55647.3i −0.429941 + 0.744679i −0.996868 0.0790889i \(-0.974799\pi\)
0.566927 + 0.823768i \(0.308132\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 12544.0 21726.8i 0.150393 0.260489i
\(94\) 0 0
\(95\) −15488.0 26826.0i −0.176070 0.304963i
\(96\) 0 0
\(97\) −2272.00 −0.0245177 −0.0122588 0.999925i \(-0.503902\pi\)
−0.0122588 + 0.999925i \(0.503902\pi\)
\(98\) 0 0
\(99\) −988.000 −0.0101314
\(100\) 0 0
\(101\) 55000.0 + 95262.8i 0.536487 + 0.929223i 0.999090 + 0.0426572i \(0.0135823\pi\)
−0.462603 + 0.886566i \(0.653084\pi\)
\(102\) 0 0
\(103\) 42064.0 72857.0i 0.390677 0.676672i −0.601862 0.798600i \(-0.705574\pi\)
0.992539 + 0.121928i \(0.0389077\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6974.00 + 12079.3i −0.0588874 + 0.101996i −0.893966 0.448134i \(-0.852089\pi\)
0.835079 + 0.550130i \(0.185422\pi\)
\(108\) 0 0
\(109\) −11297.0 19567.0i −0.0910745 0.157746i 0.816889 0.576795i \(-0.195697\pi\)
−0.907964 + 0.419049i \(0.862363\pi\)
\(110\) 0 0
\(111\) −79008.0 −0.608644
\(112\) 0 0
\(113\) 94786.0 0.698310 0.349155 0.937065i \(-0.386469\pi\)
0.349155 + 0.937065i \(0.386469\pi\)
\(114\) 0 0
\(115\) −7488.00 12969.6i −0.0527985 0.0914496i
\(116\) 0 0
\(117\) −5720.00 + 9907.33i −0.0386306 + 0.0669101i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 77637.5 134472.i 0.482068 0.834966i
\(122\) 0 0
\(123\) −126720. 219485.i −0.755235 1.30811i
\(124\) 0 0
\(125\) −95904.0 −0.548987
\(126\) 0 0
\(127\) 140624. 0.773660 0.386830 0.922151i \(-0.373570\pi\)
0.386830 + 0.922151i \(0.373570\pi\)
\(128\) 0 0
\(129\) −131296. 227411.i −0.694668 1.20320i
\(130\) 0 0
\(131\) 121176. 209883.i 0.616934 1.06856i −0.373108 0.927788i \(-0.621708\pi\)
0.990042 0.140772i \(-0.0449586\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −29440.0 + 50991.6i −0.139028 + 0.240804i
\(136\) 0 0
\(137\) −86443.0 149724.i −0.393485 0.681536i 0.599421 0.800434i \(-0.295397\pi\)
−0.992907 + 0.118897i \(0.962064\pi\)
\(138\) 0 0
\(139\) −167376. −0.734778 −0.367389 0.930067i \(-0.619748\pi\)
−0.367389 + 0.930067i \(0.619748\pi\)
\(140\) 0 0
\(141\) 332288. 1.40756
\(142\) 0 0
\(143\) 33440.0 + 57919.8i 0.136750 + 0.236857i
\(144\) 0 0
\(145\) 31856.0 55176.2i 0.125826 0.217937i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 202301. 350396.i 0.746504 1.29298i −0.202984 0.979182i \(-0.565064\pi\)
0.949489 0.313802i \(-0.101603\pi\)
\(150\) 0 0
\(151\) −222596. 385548.i −0.794465 1.37605i −0.923178 0.384373i \(-0.874418\pi\)
0.128713 0.991682i \(-0.458916\pi\)
\(152\) 0 0
\(153\) −13728.0 −0.0474110
\(154\) 0 0
\(155\) 25088.0 0.0838758
\(156\) 0 0
\(157\) 86248.0 + 149386.i 0.279254 + 0.483683i 0.971200 0.238267i \(-0.0765794\pi\)
−0.691945 + 0.721950i \(0.743246\pi\)
\(158\) 0 0
\(159\) −299216. + 518257.i −0.938625 + 1.62575i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −83742.0 + 145045.i −0.246873 + 0.427597i −0.962657 0.270725i \(-0.912737\pi\)
0.715783 + 0.698323i \(0.246070\pi\)
\(164\) 0 0
\(165\) −9728.00 16849.4i −0.0278172 0.0481808i
\(166\) 0 0
\(167\) 206624. 0.573310 0.286655 0.958034i \(-0.407457\pi\)
0.286655 + 0.958034i \(0.407457\pi\)
\(168\) 0 0
\(169\) 403107. 1.08568
\(170\) 0 0
\(171\) −12584.0 21796.1i −0.0329100 0.0570019i
\(172\) 0 0
\(173\) 169928. 294324.i 0.431668 0.747671i −0.565349 0.824852i \(-0.691259\pi\)
0.997017 + 0.0771810i \(0.0245919\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 169088. 292869.i 0.405676 0.702652i
\(178\) 0 0
\(179\) −259770. 449935.i −0.605977 1.04958i −0.991896 0.127051i \(-0.959449\pi\)
0.385919 0.922533i \(-0.373884\pi\)
\(180\) 0 0
\(181\) 830000. 1.88314 0.941568 0.336823i \(-0.109352\pi\)
0.941568 + 0.336823i \(0.109352\pi\)
\(182\) 0 0
\(183\) 47872.0 0.105671
\(184\) 0 0
\(185\) −39504.0 68422.9i −0.0848617 0.146985i
\(186\) 0 0
\(187\) −40128.0 + 69503.7i −0.0839158 + 0.145346i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −150804. + 261200.i −0.299109 + 0.518072i −0.975932 0.218074i \(-0.930023\pi\)
0.676823 + 0.736145i \(0.263356\pi\)
\(192\) 0 0
\(193\) 242231. + 419556.i 0.468098 + 0.810769i 0.999335 0.0364539i \(-0.0116062\pi\)
−0.531238 + 0.847223i \(0.678273\pi\)
\(194\) 0 0
\(195\) −225280. −0.424264
\(196\) 0 0
\(197\) −183018. −0.335991 −0.167996 0.985788i \(-0.553729\pi\)
−0.167996 + 0.985788i \(0.553729\pi\)
\(198\) 0 0
\(199\) 452144. + 783136.i 0.809364 + 1.40186i 0.913305 + 0.407277i \(0.133522\pi\)
−0.103940 + 0.994584i \(0.533145\pi\)
\(200\) 0 0
\(201\) −366688. + 635122.i −0.640187 + 1.10884i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 126720. 219485.i 0.210601 0.364772i
\(206\) 0 0
\(207\) −6084.00 10537.8i −0.00986878 0.0170932i
\(208\) 0 0
\(209\) −147136. −0.232999
\(210\) 0 0
\(211\) −494428. −0.764534 −0.382267 0.924052i \(-0.624857\pi\)
−0.382267 + 0.924052i \(0.624857\pi\)
\(212\) 0 0
\(213\) −398720. 690603.i −0.602170 1.04299i
\(214\) 0 0
\(215\) 131296. 227411.i 0.193711 0.335518i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −450560. + 780393.i −0.634808 + 1.09952i
\(220\) 0 0
\(221\) 464640. + 804780.i 0.639935 + 1.10840i
\(222\) 0 0
\(223\) −389824. −0.524936 −0.262468 0.964941i \(-0.584536\pi\)
−0.262468 + 0.964941i \(0.584536\pi\)
\(224\) 0 0
\(225\) −37297.0 −0.0491154
\(226\) 0 0
\(227\) 39512.0 + 68436.8i 0.0508937 + 0.0881505i 0.890350 0.455277i \(-0.150460\pi\)
−0.839456 + 0.543427i \(0.817126\pi\)
\(228\) 0 0
\(229\) 629896. 1.09101e6i 0.793743 1.37480i −0.129891 0.991528i \(-0.541463\pi\)
0.923634 0.383276i \(-0.125204\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 386309. 669107.i 0.466171 0.807431i −0.533083 0.846063i \(-0.678967\pi\)
0.999254 + 0.0386317i \(0.0122999\pi\)
\(234\) 0 0
\(235\) 166144. + 287770.i 0.196252 + 0.339919i
\(236\) 0 0
\(237\) −651904. −0.753898
\(238\) 0 0
\(239\) −1.42507e6 −1.61377 −0.806886 0.590707i \(-0.798849\pi\)
−0.806886 + 0.590707i \(0.798849\pi\)
\(240\) 0 0
\(241\) −574288. 994696.i −0.636923 1.10318i −0.986104 0.166128i \(-0.946873\pi\)
0.349181 0.937055i \(-0.386460\pi\)
\(242\) 0 0
\(243\) −49192.0 + 85203.0i −0.0534415 + 0.0925634i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −851840. + 1.47543e6i −0.888415 + 1.53878i
\(248\) 0 0
\(249\) 899712. + 1.55835e6i 0.919613 + 1.59282i
\(250\) 0 0
\(251\) −278096. −0.278619 −0.139309 0.990249i \(-0.544488\pi\)
−0.139309 + 0.990249i \(0.544488\pi\)
\(252\) 0 0
\(253\) −71136.0 −0.0698696
\(254\) 0 0
\(255\) −135168. 234118.i −0.130174 0.225468i
\(256\) 0 0
\(257\) −178816. + 309718.i −0.168878 + 0.292506i −0.938026 0.346566i \(-0.887348\pi\)
0.769148 + 0.639071i \(0.220681\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 25883.0 44830.7i 0.0235187 0.0407356i
\(262\) 0 0
\(263\) 42416.0 + 73466.7i 0.0378129 + 0.0654939i 0.884313 0.466895i \(-0.154628\pi\)
−0.846500 + 0.532389i \(0.821294\pi\)
\(264\) 0 0
\(265\) −598432. −0.523480
\(266\) 0 0
\(267\) −1.02810e6 −0.882583
\(268\) 0 0
\(269\) 1.09886e6 + 1.90327e6i 0.925891 + 1.60369i 0.790121 + 0.612951i \(0.210018\pi\)
0.135770 + 0.990740i \(0.456649\pi\)
\(270\) 0 0
\(271\) 237952. 412145.i 0.196819 0.340900i −0.750677 0.660670i \(-0.770272\pi\)
0.947495 + 0.319770i \(0.103606\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −109022. + 188832.i −0.0869325 + 0.150572i
\(276\) 0 0
\(277\) 797005. + 1.38045e6i 0.624111 + 1.08099i 0.988712 + 0.149828i \(0.0478719\pi\)
−0.364601 + 0.931164i \(0.618795\pi\)
\(278\) 0 0
\(279\) 20384.0 0.0156776
\(280\) 0 0
\(281\) −1.31558e6 −0.993919 −0.496959 0.867774i \(-0.665550\pi\)
−0.496959 + 0.867774i \(0.665550\pi\)
\(282\) 0 0
\(283\) −504328. 873522.i −0.374323 0.648347i 0.615902 0.787823i \(-0.288792\pi\)
−0.990226 + 0.139476i \(0.955458\pi\)
\(284\) 0 0
\(285\) 247808. 429216.i 0.180719 0.313014i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 152360. 263896.i 0.107307 0.185861i
\(290\) 0 0
\(291\) −18176.0 31481.8i −0.0125825 0.0217935i
\(292\) 0 0
\(293\) 2.05762e6 1.40022 0.700108 0.714037i \(-0.253135\pi\)
0.700108 + 0.714037i \(0.253135\pi\)
\(294\) 0 0
\(295\) 338176. 0.226250
\(296\) 0 0
\(297\) 139840. + 242210.i 0.0919899 + 0.159331i
\(298\) 0 0
\(299\) −411840. + 713328.i −0.266410 + 0.461436i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −880000. + 1.52420e6i −0.550651 + 0.953755i
\(304\) 0 0
\(305\) 23936.0 + 41458.4i 0.0147334 + 0.0255189i
\(306\) 0 0
\(307\) 2.07099e6 1.25410 0.627050 0.778979i \(-0.284262\pi\)
0.627050 + 0.778979i \(0.284262\pi\)
\(308\) 0 0
\(309\) 1.34605e6 0.801981
\(310\) 0 0
\(311\) −476608. 825509.i −0.279422 0.483973i 0.691819 0.722071i \(-0.256809\pi\)
−0.971241 + 0.238098i \(0.923476\pi\)
\(312\) 0 0
\(313\) −1.42920e6 + 2.47545e6i −0.824579 + 1.42821i 0.0776620 + 0.996980i \(0.475255\pi\)
−0.902241 + 0.431233i \(0.858079\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 993801. 1.72131e6i 0.555458 0.962082i −0.442410 0.896813i \(-0.645876\pi\)
0.997868 0.0652685i \(-0.0207904\pi\)
\(318\) 0 0
\(319\) −151316. 262087.i −0.0832546 0.144201i
\(320\) 0 0
\(321\) −223168. −0.120884
\(322\) 0 0
\(323\) −2.04442e6 −1.09034
\(324\) 0 0
\(325\) 1.26236e6 + 2.18647e6i 0.662941 + 1.14825i
\(326\) 0 0
\(327\) 180752. 313072.i 0.0934789 0.161910i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −197290. + 341716.i −0.0989772 + 0.171434i −0.911262 0.411828i \(-0.864890\pi\)
0.812284 + 0.583262i \(0.198224\pi\)
\(332\) 0 0
\(333\) −32097.0 55593.6i −0.0158619 0.0274735i
\(334\) 0 0
\(335\) −733376. −0.357038
\(336\) 0 0
\(337\) 2.19606e6 1.05334 0.526672 0.850069i \(-0.323440\pi\)
0.526672 + 0.850069i \(0.323440\pi\)
\(338\) 0 0
\(339\) 758288. + 1.31339e6i 0.358373 + 0.620720i
\(340\) 0 0
\(341\) 59584.0 103203.i 0.0277488 0.0480623i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 119808. 207514.i 0.0541924 0.0938639i
\(346\) 0 0
\(347\) −2.01359e6 3.48765e6i −0.897735 1.55492i −0.830383 0.557194i \(-0.811878\pi\)
−0.0673525 0.997729i \(-0.521455\pi\)
\(348\) 0 0
\(349\) −1.96469e6 −0.863436 −0.431718 0.902009i \(-0.642092\pi\)
−0.431718 + 0.902009i \(0.642092\pi\)
\(350\) 0 0
\(351\) 3.23840e6 1.40302
\(352\) 0 0
\(353\) −1.67261e6 2.89704e6i −0.714426 1.23742i −0.963180 0.268856i \(-0.913354\pi\)
0.248754 0.968567i \(-0.419979\pi\)
\(354\) 0 0
\(355\) 398720. 690603.i 0.167918 0.290842i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.14756e6 1.98764e6i 0.469938 0.813957i −0.529471 0.848328i \(-0.677610\pi\)
0.999409 + 0.0343712i \(0.0109428\pi\)
\(360\) 0 0
\(361\) −635998. 1.10158e6i −0.256855 0.444886i
\(362\) 0 0
\(363\) 2.48440e6 0.989589
\(364\) 0 0
\(365\) −901120. −0.354038
\(366\) 0 0
\(367\) −1.46934e6 2.54498e6i −0.569454 0.986323i −0.996620 0.0821495i \(-0.973821\pi\)
0.427166 0.904173i \(-0.359512\pi\)
\(368\) 0 0
\(369\) 102960. 178332.i 0.0393643 0.0681810i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 207229. 358931.i 0.0771220 0.133579i −0.824885 0.565300i \(-0.808760\pi\)
0.902007 + 0.431721i \(0.142094\pi\)
\(374\) 0 0
\(375\) −767232. 1.32888e6i −0.281740 0.487988i
\(376\) 0 0
\(377\) −3.50416e6 −1.26979
\(378\) 0 0
\(379\) 2.57111e6 0.919438 0.459719 0.888065i \(-0.347950\pi\)
0.459719 + 0.888065i \(0.347950\pi\)
\(380\) 0 0
\(381\) 1.12499e6 + 1.94854e6i 0.397042 + 0.687698i
\(382\) 0 0
\(383\) 1.28366e6 2.22337e6i 0.447151 0.774489i −0.551048 0.834474i \(-0.685772\pi\)
0.998199 + 0.0599849i \(0.0191052\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 106678. 184772.i 0.0362074 0.0627131i
\(388\) 0 0
\(389\) −1.68904e6 2.92551e6i −0.565936 0.980230i −0.996962 0.0778902i \(-0.975182\pi\)
0.431026 0.902339i \(-0.358152\pi\)
\(390\) 0 0
\(391\) −988416. −0.326962
\(392\) 0 0
\(393\) 3.87763e6 1.26644
\(394\) 0 0
\(395\) −325952. 564565.i −0.105114 0.182063i
\(396\) 0 0
\(397\) 1.09886e6 1.90327e6i 0.349917 0.606073i −0.636318 0.771427i \(-0.719543\pi\)
0.986234 + 0.165354i \(0.0528766\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.73835e6 3.01092e6i 0.539855 0.935056i −0.459056 0.888407i \(-0.651812\pi\)
0.998911 0.0466490i \(-0.0148542\pi\)
\(402\) 0 0
\(403\) −689920. 1.19498e6i −0.211610 0.366519i
\(404\) 0 0
\(405\) −992624. −0.300710
\(406\) 0 0
\(407\) −375288. −0.112300
\(408\) 0 0
\(409\) 842160. + 1.45866e6i 0.248935 + 0.431168i 0.963231 0.268676i \(-0.0865860\pi\)
−0.714295 + 0.699844i \(0.753253\pi\)
\(410\) 0 0
\(411\) 1.38309e6 2.39558e6i 0.403873 0.699529i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −899712. + 1.55835e6i −0.256439 + 0.444165i
\(416\) 0 0
\(417\) −1.33901e6 2.31923e6i −0.377088 0.653136i
\(418\) 0 0
\(419\) −4.40475e6 −1.22571 −0.612853 0.790197i \(-0.709978\pi\)
−0.612853 + 0.790197i \(0.709978\pi\)
\(420\) 0 0
\(421\) 3.06601e6 0.843078 0.421539 0.906810i \(-0.361490\pi\)
0.421539 + 0.906810i \(0.361490\pi\)
\(422\) 0 0
\(423\) 134992. + 233813.i 0.0366823 + 0.0635357i
\(424\) 0 0
\(425\) −1.51483e6 + 2.62377e6i −0.406810 + 0.704616i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −535040. + 926716.i −0.140360 + 0.243110i
\(430\) 0 0
\(431\) −660176. 1.14346e6i −0.171185 0.296502i 0.767649 0.640870i \(-0.221426\pi\)
−0.938835 + 0.344369i \(0.888093\pi\)
\(432\) 0 0
\(433\) 2.91510e6 0.747196 0.373598 0.927591i \(-0.378124\pi\)
0.373598 + 0.927591i \(0.378124\pi\)
\(434\) 0 0
\(435\) 1.01939e6 0.258296
\(436\) 0 0
\(437\) −906048. 1.56932e6i −0.226959 0.393105i
\(438\) 0 0
\(439\) −3.53126e6 + 6.11633e6i −0.874518 + 1.51471i −0.0172432 + 0.999851i \(0.505489\pi\)
−0.857275 + 0.514859i \(0.827844\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3.86906e6 6.70141e6i 0.936690 1.62239i 0.165098 0.986277i \(-0.447206\pi\)
0.771592 0.636118i \(-0.219461\pi\)
\(444\) 0 0
\(445\) −514048. 890357.i −0.123056 0.213140i
\(446\) 0 0
\(447\) 6.47363e6 1.53242
\(448\) 0 0
\(449\) −5.62457e6 −1.31666 −0.658330 0.752729i \(-0.728737\pi\)
−0.658330 + 0.752729i \(0.728737\pi\)
\(450\) 0 0
\(451\) −601920. 1.04256e6i −0.139347 0.241356i
\(452\) 0 0
\(453\) 3.56154e6 6.16876e6i 0.815440 1.41238i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −2.95758e6 + 5.12268e6i −0.662439 + 1.14738i 0.317533 + 0.948247i \(0.397145\pi\)
−0.979973 + 0.199132i \(0.936188\pi\)
\(458\) 0 0
\(459\) 1.94304e6 + 3.36544e6i 0.430477 + 0.745608i
\(460\) 0 0
\(461\) 7.21195e6 1.58052 0.790261 0.612770i \(-0.209945\pi\)
0.790261 + 0.612770i \(0.209945\pi\)
\(462\) 0 0
\(463\) 5.22092e6 1.13186 0.565932 0.824452i \(-0.308516\pi\)
0.565932 + 0.824452i \(0.308516\pi\)
\(464\) 0 0
\(465\) 200704. + 347630.i 0.0430451 + 0.0745563i
\(466\) 0 0
\(467\) −2.90769e6 + 5.03626e6i −0.616958 + 1.06860i 0.373080 + 0.927799i \(0.378302\pi\)
−0.990038 + 0.140803i \(0.955031\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.37997e6 + 2.39017e6i −0.286627 + 0.496452i
\(472\) 0 0
\(473\) −623656. 1.08020e6i −0.128172 0.222000i
\(474\) 0 0
\(475\) −5.55438e6 −1.12954
\(476\) 0 0
\(477\) −486226. −0.0978458
\(478\) 0 0
\(479\) 3.76939e6 + 6.52878e6i 0.750641 + 1.30015i 0.947512 + 0.319720i \(0.103589\pi\)
−0.196871 + 0.980429i \(0.563078\pi\)
\(480\) 0 0
\(481\) −2.17272e6 + 3.76326e6i −0.428194 + 0.741655i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 18176.0 31481.8i 0.00350868 0.00607721i
\(486\) 0 0
\(487\) 3.29830e6 + 5.71282e6i 0.630185 + 1.09151i 0.987514 + 0.157533i \(0.0503541\pi\)
−0.357329 + 0.933979i \(0.616313\pi\)
\(488\) 0 0
\(489\) −2.67974e6 −0.506782
\(490\) 0 0
\(491\) −9.96666e6 −1.86572 −0.932859 0.360242i \(-0.882694\pi\)
−0.932859 + 0.360242i \(0.882694\pi\)
\(492\) 0 0
\(493\) −2.10250e6 3.64163e6i −0.389599 0.674805i
\(494\) 0 0
\(495\) 7904.00 13690.1i 0.00144989 0.00251128i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1.47135e6 2.54845e6i 0.264524 0.458169i −0.702915 0.711274i \(-0.748119\pi\)
0.967439 + 0.253105i \(0.0814519\pi\)
\(500\) 0 0
\(501\) 1.65299e6 + 2.86307e6i 0.294223 + 0.509609i
\(502\) 0 0
\(503\) 4.35142e6 0.766852 0.383426 0.923572i \(-0.374744\pi\)
0.383426 + 0.923572i \(0.374744\pi\)
\(504\) 0 0
\(505\) −1.76000e6 −0.307103
\(506\) 0 0
\(507\) 3.22486e6 + 5.58561e6i 0.557173 + 0.965053i
\(508\) 0 0
\(509\) −2.59247e6 + 4.49029e6i −0.443527 + 0.768211i −0.997948 0.0640254i \(-0.979606\pi\)
0.554422 + 0.832236i \(0.312939\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −3.56224e6 + 6.16998e6i −0.597626 + 1.03512i
\(514\) 0 0
\(515\) 673024. + 1.16571e6i 0.111818 + 0.193675i
\(516\) 0 0
\(517\) 1.57837e6 0.259706
\(518\) 0 0
\(519\) 5.43770e6 0.886128
\(520\) 0 0
\(521\) −3.70840e6 6.42314e6i −0.598539 1.03670i −0.993037 0.117803i \(-0.962415\pi\)
0.394498 0.918897i \(-0.370918\pi\)
\(522\) 0 0
\(523\) 3.23673e6 5.60618e6i 0.517430 0.896216i −0.482365 0.875971i \(-0.660222\pi\)
0.999795 0.0202453i \(-0.00644471\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 827904. 1.43397e6i 0.129853 0.224913i
\(528\) 0 0
\(529\) 2.78012e6 + 4.81532e6i 0.431941 + 0.748145i
\(530\) 0 0
\(531\) 274768. 0.0422892
\(532\) 0 0
\(533\) −1.39392e7 −2.12530
\(534\) 0 0
\(535\) −111584. 193269.i −0.0168546 0.0291930i
\(536\) 0 0
\(537\) 4.15632e6 7.19896e6i 0.621975 1.07729i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −4.55494e6 + 7.88938e6i −0.669097 + 1.15891i 0.309060 + 0.951043i \(0.399986\pi\)
−0.978157 + 0.207867i \(0.933348\pi\)
\(542\) 0 0
\(543\) 6.64000e6 + 1.15008e7i 0.966426 + 1.67390i
\(544\) 0 0
\(545\) 361504. 0.0521341
\(546\) 0 0
\(547\) −5.63776e6 −0.805635 −0.402818 0.915280i \(-0.631969\pi\)
−0.402818 + 0.915280i \(0.631969\pi\)
\(548\) 0 0
\(549\) 19448.0 + 33684.9i 0.00275387 + 0.00476985i
\(550\) 0 0
\(551\) 3.85458e6 6.67632e6i 0.540876 0.936825i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 632064. 1.09477e6i 0.0871021 0.150865i
\(556\) 0 0
\(557\) −1.85536e6 3.21358e6i −0.253390 0.438885i 0.711067 0.703124i \(-0.248212\pi\)
−0.964457 + 0.264240i \(0.914879\pi\)
\(558\) 0 0
\(559\) −1.44426e7 −1.95486
\(560\) 0 0
\(561\) −1.28410e6 −0.172262
\(562\) 0 0
\(563\) −2.63058e6 4.55631e6i −0.349769 0.605818i 0.636439 0.771327i \(-0.280407\pi\)
−0.986208 + 0.165509i \(0.947073\pi\)
\(564\) 0 0
\(565\) −758288. + 1.31339e6i −0.0999340 + 0.173091i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.40464e6 2.43292e6i 0.181880 0.315026i −0.760640 0.649173i \(-0.775115\pi\)
0.942521 + 0.334147i \(0.108448\pi\)
\(570\) 0 0
\(571\) 4.09853e6 + 7.09887e6i 0.526064 + 0.911169i 0.999539 + 0.0303619i \(0.00966596\pi\)
−0.473475 + 0.880807i \(0.657001\pi\)
\(572\) 0 0
\(573\) −4.82573e6 −0.614011
\(574\) 0 0
\(575\) −2.68538e6 −0.338717
\(576\) 0 0
\(577\) 1.84861e6 + 3.20188e6i 0.231156 + 0.400374i 0.958149 0.286271i \(-0.0924159\pi\)
−0.726993 + 0.686645i \(0.759083\pi\)
\(578\) 0 0
\(579\) −3.87570e6 + 6.71290e6i −0.480456 + 0.832174i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.42128e6 + 2.46172e6i −0.173184 + 0.299963i
\(584\) 0 0
\(585\) −91520.0 158517.i −0.0110567 0.0191508i
\(586\) 0 0
\(587\) −8.25282e6 −0.988569 −0.494284 0.869300i \(-0.664570\pi\)
−0.494284 + 0.869300i \(0.664570\pi\)
\(588\) 0 0
\(589\) 3.03565e6 0.360548
\(590\) 0 0
\(591\) −1.46414e6 2.53597e6i −0.172431 0.298659i
\(592\) 0 0
\(593\) 3.15638e6 5.46702e6i 0.368598 0.638431i −0.620749 0.784010i \(-0.713171\pi\)
0.989347 + 0.145579i \(0.0465045\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.23430e6 + 1.25302e7i −0.830732 + 1.43887i
\(598\) 0 0
\(599\) 3.46488e6 + 6.00135e6i 0.394567 + 0.683411i 0.993046 0.117728i \(-0.0375611\pi\)
−0.598479 + 0.801139i \(0.704228\pi\)
\(600\) 0 0
\(601\) 1.10092e7 1.24328 0.621638 0.783305i \(-0.286467\pi\)
0.621638 + 0.783305i \(0.286467\pi\)
\(602\) 0 0
\(603\) −595868. −0.0667355
\(604\) 0 0
\(605\) 1.24220e6 + 2.15155e6i 0.137976 + 0.238981i
\(606\) 0 0
\(607\) 166848. 288989.i 0.0183802 0.0318354i −0.856689 0.515833i \(-0.827482\pi\)
0.875069 + 0.483998i \(0.160816\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9.13792e6 1.58273e7i 0.990249 1.71516i
\(612\) 0 0
\(613\) −879637. 1.52358e6i −0.0945480 0.163762i 0.814872 0.579641i \(-0.196807\pi\)
−0.909420 + 0.415879i \(0.863474\pi\)
\(614\) 0 0
\(615\) 4.05504e6 0.432322
\(616\) 0 0
\(617\) −1.46142e7 −1.54548 −0.772738 0.634725i \(-0.781113\pi\)
−0.772738 + 0.634725i \(0.781113\pi\)
\(618\) 0 0
\(619\) 1.15772e6 + 2.00523e6i 0.121444 + 0.210348i 0.920337 0.391125i \(-0.127914\pi\)
−0.798893 + 0.601473i \(0.794581\pi\)
\(620\) 0 0
\(621\) −1.72224e6 + 2.98301e6i −0.179211 + 0.310403i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −3.71558e6 + 6.43557e6i −0.380475 + 0.659003i
\(626\) 0 0
\(627\) −1.17709e6 2.03878e6i −0.119575 0.207110i
\(628\) 0 0
\(629\) −5.21453e6 −0.525519
\(630\) 0 0
\(631\) 1.47152e7 1.47127 0.735636 0.677377i \(-0.236883\pi\)
0.735636 + 0.677377i \(0.236883\pi\)
\(632\) 0 0
\(633\) −3.95542e6 6.85100e6i −0.392359 0.679586i
\(634\) 0 0
\(635\) −1.12499e6 + 1.94854e6i −0.110717 + 0.191768i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 323960. 561115.i 0.0313862 0.0543626i
\(640\) 0 0
\(641\) −5.37775e6 9.31454e6i −0.516958 0.895398i −0.999806 0.0196939i \(-0.993731\pi\)
0.482848 0.875704i \(-0.339602\pi\)
\(642\) 0 0
\(643\) 1.81097e7 1.72736 0.863681 0.504039i \(-0.168153\pi\)
0.863681 + 0.504039i \(0.168153\pi\)
\(644\) 0 0
\(645\) 4.20147e6 0.397651
\(646\) 0 0
\(647\) −1.93838e6 3.35738e6i −0.182045 0.315311i 0.760532 0.649301i \(-0.224938\pi\)
−0.942577 + 0.333989i \(0.891605\pi\)
\(648\) 0 0
\(649\) 803168. 1.39113e6i 0.0748505 0.129645i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.91278e6 5.04509e6i 0.267316 0.463005i −0.700852 0.713307i \(-0.747197\pi\)
0.968168 + 0.250302i \(0.0805299\pi\)
\(654\) 0 0
\(655\) 1.93882e6 + 3.35813e6i 0.176577 + 0.305840i
\(656\) 0 0
\(657\) −732160. −0.0661748
\(658\) 0 0
\(659\) −6.46989e6 −0.580341 −0.290171 0.956975i \(-0.593712\pi\)
−0.290171 + 0.956975i \(0.593712\pi\)
\(660\) 0 0
\(661\) 2.09001e6 + 3.62000e6i 0.186056 + 0.322259i 0.943932 0.330140i \(-0.107096\pi\)
−0.757876 + 0.652399i \(0.773763\pi\)
\(662\) 0 0
\(663\) −7.43424e6 + 1.28765e7i −0.656830 + 1.13766i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.86358e6 3.22781e6i 0.162193 0.280927i
\(668\) 0 0
\(669\) −3.11859e6 5.40156e6i −0.269397 0.466610i
\(670\) 0 0
\(671\) 227392. 0.0194970
\(672\) 0 0
\(673\) 1.27159e7 1.08221 0.541104 0.840956i \(-0.318007\pi\)
0.541104 + 0.840956i \(0.318007\pi\)
\(674\) 0 0
\(675\) 5.27896e6 + 9.14343e6i 0.445953 + 0.772413i
\(676\) 0 0
\(677\) −5.93551e6 + 1.02806e7i −0.497722 + 0.862079i −0.999997 0.00262884i \(-0.999163\pi\)
0.502275 + 0.864708i \(0.332497\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −632192. + 1.09499e6i −0.0522374 + 0.0904778i
\(682\) 0 0
\(683\) −6.99889e6 1.21224e7i −0.574087 0.994348i −0.996140 0.0877767i \(-0.972024\pi\)
0.422053 0.906571i \(-0.361310\pi\)
\(684\) 0 0
\(685\) 2.76618e6 0.225244
\(686\) 0 0
\(687\) 2.01567e7 1.62940
\(688\) 0 0
\(689\) 1.64569e7 + 2.85042e7i 1.32069 + 2.28749i
\(690\) 0 0
\(691\) 4.90018e6 8.48737e6i 0.390407 0.676204i −0.602096 0.798423i \(-0.705668\pi\)
0.992503 + 0.122219i \(0.0390011\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.33901e6 2.31923e6i 0.105153 0.182130i
\(696\) 0 0
\(697\) −8.36352e6 1.44860e7i −0.652089 1.12945i
\(698\) 0 0
\(699\) 1.23619e7 0.956956
\(700\) 0 0
\(701\) −1.80481e6 −0.138719 −0.0693597 0.997592i \(-0.522096\pi\)
−0.0693597 + 0.997592i \(0.522096\pi\)
\(702\) 0 0
\(703\) −4.77998e6 8.27918e6i −0.364786 0.631828i
\(704\) 0 0
\(705\) −2.65830e6 + 4.60432e6i −0.201434 + 0.348893i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 3.23702e6 5.60668e6i 0.241841 0.418881i −0.719398 0.694598i \(-0.755582\pi\)
0.961239 + 0.275718i \(0.0889155\pi\)
\(710\) 0 0
\(711\) −264836. 458709.i −0.0196473 0.0340301i
\(712\) 0 0
\(713\) 1.46765e6 0.108118
\(714\) 0 0
\(715\) −1.07008e6 −0.0782801
\(716\) 0 0
\(717\) −1.14006e7 1.97464e7i −0.828188 1.43446i
\(718\) 0 0
\(719\) 1.17032e7 2.02706e7i 0.844273 1.46232i −0.0419777 0.999119i \(-0.513366\pi\)
0.886251 0.463206i \(-0.153301\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 9.18861e6 1.59151e7i 0.653738 1.13231i
\(724\) 0 0
\(725\) −5.71218e6 9.89378e6i −0.403605 0.699065i
\(726\) 0 0
\(727\) −491936. −0.0345201 −0.0172601 0.999851i \(-0.505494\pi\)
−0.0172601 + 0.999851i \(0.505494\pi\)
\(728\) 0 0
\(729\) 1.35013e7 0.940931
\(730\) 0 0
\(731\) −8.66554e6 1.50091e7i −0.599794 1.03887i
\(732\) 0 0
\(733\) −3.93210e6 + 6.81060e6i −0.270312 + 0.468194i −0.968942 0.247289i \(-0.920460\pi\)
0.698630 + 0.715483i \(0.253793\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.74177e6 + 3.01683e6i −0.118119 + 0.204589i
\(738\) 0 0
\(739\) −3.46273e6 5.99763e6i −0.233243 0.403988i 0.725518 0.688203i \(-0.241600\pi\)
−0.958761 + 0.284215i \(0.908267\pi\)
\(740\) 0 0
\(741\) −2.72589e7 −1.82374
\(742\) 0 0
\(743\) 1.59306e7 1.05867 0.529333 0.848414i \(-0.322442\pi\)
0.529333 + 0.848414i \(0.322442\pi\)
\(744\) 0 0
\(745\) 3.23682e6 + 5.60633e6i 0.213662 + 0.370073i
\(746\) 0 0
\(747\) −731016. + 1.26616e6i −0.0479320 + 0.0830206i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −5.00762e6 + 8.67346e6i −0.323990 + 0.561167i −0.981307 0.192446i \(-0.938358\pi\)
0.657317 + 0.753614i \(0.271691\pi\)
\(752\) 0 0
\(753\) −2.22477e6 3.85341e6i −0.142987 0.247661i
\(754\) 0 0
\(755\) 7.12307e6 0.454779
\(756\) 0 0
\(757\) 3.79619e6 0.240773 0.120387 0.992727i \(-0.461587\pi\)
0.120387 + 0.992727i \(0.461587\pi\)
\(758\) 0 0
\(759\) −569088. 985689.i −0.0358571 0.0621063i
\(760\) 0 0
\(761\) 5.17422e6 8.96202e6i 0.323880 0.560976i −0.657405 0.753537i \(-0.728346\pi\)
0.981285 + 0.192561i \(0.0616794\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 109824. 190221.i 0.00678490 0.0117518i
\(766\) 0 0
\(767\) −9.29984e6 1.61078e7i −0.570804 0.988662i
\(768\) 0 0
\(769\) −1.51131e7 −0.921591 −0.460796 0.887506i \(-0.652436\pi\)
−0.460796 + 0.887506i \(0.652436\pi\)
\(770\) 0 0
\(771\) −5.72211e6 −0.346673
\(772\) 0 0
\(773\) 2.83087e6 + 4.90321e6i 0.170401 + 0.295143i 0.938560 0.345116i \(-0.112160\pi\)
−0.768159 + 0.640259i \(0.778827\pi\)
\(774\) 0 0
\(775\) 2.24930e6 3.89589e6i 0.134522 0.232998i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.53331e7 2.65577e7i 0.905288 1.56801i
\(780\) 0 0
\(781\) −1.89392e6 3.28037e6i −0.111105 0.192440i
\(782\) 0 0
\(783\) −1.46538e7 −0.854171
\(784\) 0 0
\(785\) −2.75994e6 −0.159855
\(786\) 0