Properties

Label 196.6.e.f.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: no (minimal twist has level 28)
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.f.165.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{3} +(48.0000 - 83.1384i) q^{5} +(119.500 - 206.980i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{3} +(48.0000 - 83.1384i) q^{5} +(119.500 - 206.980i) q^{9} +(360.000 + 623.538i) q^{11} +572.000 q^{13} +192.000 q^{15} +(-627.000 - 1086.00i) q^{17} +(47.0000 - 81.4064i) q^{19} +(-48.0000 + 83.1384i) q^{23} +(-3045.50 - 5274.96i) q^{25} +964.000 q^{27} -4374.00 q^{29} +(3122.00 + 5407.46i) q^{31} +(-720.000 + 1247.08i) q^{33} +(5399.00 - 9351.34i) q^{37} +(572.000 + 990.733i) q^{39} +12006.0 q^{41} -9160.00 q^{43} +(-11472.0 - 19870.1i) q^{45} +(12918.0 - 22374.6i) q^{47} +(1254.00 - 2171.99i) q^{51} +(-507.000 - 878.150i) q^{53} +69120.0 q^{55} +188.000 q^{57} +(-621.000 - 1075.60i) q^{59} +(-3796.00 + 6574.86i) q^{61} +(27456.0 - 47555.2i) q^{65} +(-20566.0 - 35621.4i) q^{67} -192.000 q^{69} -37632.0 q^{71} +(6719.00 + 11637.6i) q^{73} +(6091.00 - 10549.9i) q^{75} +(-3124.00 + 5410.93i) q^{79} +(-28074.5 - 48626.5i) q^{81} -25254.0 q^{83} -120384. q^{85} +(-4374.00 - 7575.99i) q^{87} +(22563.0 - 39080.3i) q^{89} +(-6244.00 + 10814.9i) q^{93} +(-4512.00 - 7815.01i) q^{95} +107222. q^{97} +172080. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + 96 q^{5} + 239 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + 96 q^{5} + 239 q^{9} + 720 q^{11} + 1144 q^{13} + 384 q^{15} - 1254 q^{17} + 94 q^{19} - 96 q^{23} - 6091 q^{25} + 1928 q^{27} - 8748 q^{29} + 6244 q^{31} - 1440 q^{33} + 10798 q^{37} + 1144 q^{39} + 24012 q^{41} - 18320 q^{43} - 22944 q^{45} + 25836 q^{47} + 2508 q^{51} - 1014 q^{53} + 138240 q^{55} + 376 q^{57} - 1242 q^{59} - 7592 q^{61} + 54912 q^{65} - 41132 q^{67} - 384 q^{69} - 75264 q^{71} + 13438 q^{73} + 12182 q^{75} - 6248 q^{79} - 56149 q^{81} - 50508 q^{83} - 240768 q^{85} - 8748 q^{87} + 45126 q^{89} - 12488 q^{93} - 9024 q^{95} + 214444 q^{97} + 344160 q^{99}+O(q^{100}) \) 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
\(3\) 1.00000 + 1.73205i 0.0641500 + 0.111111i 0.896317 0.443415i \(-0.146233\pi\)
−0.832167 + 0.554526i \(0.812900\pi\)
\(4\) 0 0
\(5\) 48.0000 83.1384i 0.858650 1.48723i −0.0145668 0.999894i \(-0.504637\pi\)
0.873217 0.487332i \(-0.162030\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 119.500 206.980i 0.491770 0.851770i
\(10\) 0 0
\(11\) 360.000 + 623.538i 0.897059 + 1.55375i 0.831236 + 0.555920i \(0.187634\pi\)
0.0658225 + 0.997831i \(0.479033\pi\)
\(12\) 0 0
\(13\) 572.000 0.938723 0.469362 0.883006i \(-0.344484\pi\)
0.469362 + 0.883006i \(0.344484\pi\)
\(14\) 0 0
\(15\) 192.000 0.220330
\(16\) 0 0
\(17\) −627.000 1086.00i −0.526193 0.911393i −0.999534 0.0305142i \(-0.990286\pi\)
0.473341 0.880879i \(-0.343048\pi\)
\(18\) 0 0
\(19\) 47.0000 81.4064i 0.0298685 0.0517338i −0.850705 0.525644i \(-0.823824\pi\)
0.880573 + 0.473910i \(0.157158\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −48.0000 + 83.1384i −0.0189200 + 0.0327704i −0.875330 0.483525i \(-0.839356\pi\)
0.856410 + 0.516296i \(0.172689\pi\)
\(24\) 0 0
\(25\) −3045.50 5274.96i −0.974560 1.68799i
\(26\) 0 0
\(27\) 964.000 0.254488
\(28\) 0 0
\(29\) −4374.00 −0.965792 −0.482896 0.875678i \(-0.660415\pi\)
−0.482896 + 0.875678i \(0.660415\pi\)
\(30\) 0 0
\(31\) 3122.00 + 5407.46i 0.583484 + 1.01062i 0.995063 + 0.0992492i \(0.0316441\pi\)
−0.411579 + 0.911374i \(0.635023\pi\)
\(32\) 0 0
\(33\) −720.000 + 1247.08i −0.115093 + 0.199346i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5399.00 9351.34i 0.648349 1.12297i −0.335168 0.942158i \(-0.608793\pi\)
0.983517 0.180815i \(-0.0578737\pi\)
\(38\) 0 0
\(39\) 572.000 + 990.733i 0.0602191 + 0.104303i
\(40\) 0 0
\(41\) 12006.0 1.11542 0.557710 0.830036i \(-0.311680\pi\)
0.557710 + 0.830036i \(0.311680\pi\)
\(42\) 0 0
\(43\) −9160.00 −0.755482 −0.377741 0.925911i \(-0.623299\pi\)
−0.377741 + 0.925911i \(0.623299\pi\)
\(44\) 0 0
\(45\) −11472.0 19870.1i −0.844516 1.46274i
\(46\) 0 0
\(47\) 12918.0 22374.6i 0.853003 1.47744i −0.0254821 0.999675i \(-0.508112\pi\)
0.878485 0.477770i \(-0.158555\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1254.00 2171.99i 0.0675106 0.116932i
\(52\) 0 0
\(53\) −507.000 878.150i −0.0247924 0.0429417i 0.853363 0.521317i \(-0.174559\pi\)
−0.878155 + 0.478375i \(0.841226\pi\)
\(54\) 0 0
\(55\) 69120.0 3.08104
\(56\) 0 0
\(57\) 188.000 0.00766427
\(58\) 0 0
\(59\) −621.000 1075.60i −0.0232253 0.0402274i 0.854179 0.519979i \(-0.174060\pi\)
−0.877404 + 0.479751i \(0.840727\pi\)
\(60\) 0 0
\(61\) −3796.00 + 6574.86i −0.130618 + 0.226236i −0.923915 0.382598i \(-0.875029\pi\)
0.793297 + 0.608835i \(0.208363\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 27456.0 47555.2i 0.806035 1.39609i
\(66\) 0 0
\(67\) −20566.0 35621.4i −0.559710 0.969446i −0.997520 0.0703784i \(-0.977579\pi\)
0.437811 0.899067i \(-0.355754\pi\)
\(68\) 0 0
\(69\) −192.000 −0.00485488
\(70\) 0 0
\(71\) −37632.0 −0.885955 −0.442977 0.896533i \(-0.646078\pi\)
−0.442977 + 0.896533i \(0.646078\pi\)
\(72\) 0 0
\(73\) 6719.00 + 11637.6i 0.147570 + 0.255598i 0.930329 0.366727i \(-0.119522\pi\)
−0.782759 + 0.622325i \(0.786188\pi\)
\(74\) 0 0
\(75\) 6091.00 10549.9i 0.125036 0.216569i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −3124.00 + 5410.93i −0.0563175 + 0.0975448i −0.892810 0.450434i \(-0.851269\pi\)
0.836492 + 0.547979i \(0.184603\pi\)
\(80\) 0 0
\(81\) −28074.5 48626.5i −0.475444 0.823493i
\(82\) 0 0
\(83\) −25254.0 −0.402379 −0.201189 0.979552i \(-0.564481\pi\)
−0.201189 + 0.979552i \(0.564481\pi\)
\(84\) 0 0
\(85\) −120384. −1.80726
\(86\) 0 0
\(87\) −4374.00 7575.99i −0.0619556 0.107310i
\(88\) 0 0
\(89\) 22563.0 39080.3i 0.301941 0.522977i −0.674635 0.738152i \(-0.735699\pi\)
0.976576 + 0.215175i \(0.0690322\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −6244.00 + 10814.9i −0.0748610 + 0.129663i
\(94\) 0 0
\(95\) −4512.00 7815.01i −0.0512932 0.0888425i
\(96\) 0 0
\(97\) 107222. 1.15706 0.578528 0.815662i \(-0.303627\pi\)
0.578528 + 0.815662i \(0.303627\pi\)
\(98\) 0 0
\(99\) 172080. 1.76458
\(100\) 0 0
\(101\) −23568.0 40821.0i −0.229890 0.398180i 0.727886 0.685699i \(-0.240503\pi\)
−0.957775 + 0.287518i \(0.907170\pi\)
\(102\) 0 0
\(103\) −61102.0 + 105832.i −0.567495 + 0.982931i 0.429317 + 0.903154i \(0.358754\pi\)
−0.996813 + 0.0797772i \(0.974579\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 64818.0 112268.i 0.547314 0.947975i −0.451144 0.892451i \(-0.648984\pi\)
0.998457 0.0555236i \(-0.0176828\pi\)
\(108\) 0 0
\(109\) 110279. + 191009.i 0.889051 + 1.53988i 0.840999 + 0.541036i \(0.181968\pi\)
0.0480515 + 0.998845i \(0.484699\pi\)
\(110\) 0 0
\(111\) 21596.0 0.166366
\(112\) 0 0
\(113\) 170694. 1.25754 0.628770 0.777591i \(-0.283559\pi\)
0.628770 + 0.777591i \(0.283559\pi\)
\(114\) 0 0
\(115\) 4608.00 + 7981.29i 0.0324914 + 0.0562767i
\(116\) 0 0
\(117\) 68354.0 118393.i 0.461636 0.799576i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −178674. + 309473.i −1.10943 + 1.92159i
\(122\) 0 0
\(123\) 12006.0 + 20795.0i 0.0715543 + 0.123936i
\(124\) 0 0
\(125\) −284736. −1.62992
\(126\) 0 0
\(127\) −249808. −1.37435 −0.687175 0.726492i \(-0.741149\pi\)
−0.687175 + 0.726492i \(0.741149\pi\)
\(128\) 0 0
\(129\) −9160.00 15865.6i −0.0484642 0.0839425i
\(130\) 0 0
\(131\) −6105.00 + 10574.2i −0.0310819 + 0.0538354i −0.881148 0.472841i \(-0.843229\pi\)
0.850066 + 0.526676i \(0.176562\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 46272.0 80145.5i 0.218516 0.378481i
\(136\) 0 0
\(137\) 6951.00 + 12039.5i 0.0316407 + 0.0548033i 0.881412 0.472348i \(-0.156593\pi\)
−0.849771 + 0.527151i \(0.823260\pi\)
\(138\) 0 0
\(139\) −431794. −1.89557 −0.947785 0.318911i \(-0.896683\pi\)
−0.947785 + 0.318911i \(0.896683\pi\)
\(140\) 0 0
\(141\) 51672.0 0.218881
\(142\) 0 0
\(143\) 205920. + 356664.i 0.842090 + 1.45854i
\(144\) 0 0
\(145\) −209952. + 363648.i −0.829278 + 1.43635i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −163407. + 283029.i −0.602983 + 1.04440i 0.389384 + 0.921076i \(0.372688\pi\)
−0.992367 + 0.123321i \(0.960645\pi\)
\(150\) 0 0
\(151\) −86740.0 150238.i −0.309583 0.536213i 0.668688 0.743543i \(-0.266856\pi\)
−0.978271 + 0.207330i \(0.933523\pi\)
\(152\) 0 0
\(153\) −299706. −1.03506
\(154\) 0 0
\(155\) 599424. 2.00403
\(156\) 0 0
\(157\) 27266.0 + 47226.1i 0.0882820 + 0.152909i 0.906785 0.421593i \(-0.138529\pi\)
−0.818503 + 0.574502i \(0.805196\pi\)
\(158\) 0 0
\(159\) 1014.00 1756.30i 0.00318086 0.00550942i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −52480.0 + 90898.0i −0.154712 + 0.267970i −0.932954 0.359995i \(-0.882778\pi\)
0.778242 + 0.627965i \(0.216112\pi\)
\(164\) 0 0
\(165\) 69120.0 + 119719.i 0.197649 + 0.342338i
\(166\) 0 0
\(167\) 160788. 0.446131 0.223066 0.974803i \(-0.428394\pi\)
0.223066 + 0.974803i \(0.428394\pi\)
\(168\) 0 0
\(169\) −44109.0 −0.118798
\(170\) 0 0
\(171\) −11233.0 19456.1i −0.0293769 0.0508822i
\(172\) 0 0
\(173\) −180282. + 312258.i −0.457970 + 0.793227i −0.998854 0.0478701i \(-0.984757\pi\)
0.540883 + 0.841098i \(0.318090\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1242.00 2151.21i 0.00297981 0.00516118i
\(178\) 0 0
\(179\) 156366. + 270834.i 0.364762 + 0.631787i 0.988738 0.149657i \(-0.0478170\pi\)
−0.623976 + 0.781444i \(0.714484\pi\)
\(180\) 0 0
\(181\) −123820. −0.280928 −0.140464 0.990086i \(-0.544859\pi\)
−0.140464 + 0.990086i \(0.544859\pi\)
\(182\) 0 0
\(183\) −15184.0 −0.0335165
\(184\) 0 0
\(185\) −518304. 897729.i −1.11341 1.92848i
\(186\) 0 0
\(187\) 451440. 781917.i 0.944052 1.63515i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −161724. + 280114.i −0.320768 + 0.555586i −0.980647 0.195786i \(-0.937274\pi\)
0.659879 + 0.751372i \(0.270608\pi\)
\(192\) 0 0
\(193\) 309977. + 536896.i 0.599013 + 1.03752i 0.992967 + 0.118391i \(0.0377735\pi\)
−0.393954 + 0.919130i \(0.628893\pi\)
\(194\) 0 0
\(195\) 109824. 0.206829
\(196\) 0 0
\(197\) −499362. −0.916748 −0.458374 0.888759i \(-0.651568\pi\)
−0.458374 + 0.888759i \(0.651568\pi\)
\(198\) 0 0
\(199\) 392966. + 680637.i 0.703432 + 1.21838i 0.967254 + 0.253809i \(0.0816835\pi\)
−0.263822 + 0.964571i \(0.584983\pi\)
\(200\) 0 0
\(201\) 41132.0 71242.7i 0.0718108 0.124380i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 576288. 998160.i 0.957756 1.65888i
\(206\) 0 0
\(207\) 11472.0 + 19870.1i 0.0186086 + 0.0322310i
\(208\) 0 0
\(209\) 67680.0 0.107175
\(210\) 0 0
\(211\) 1.06276e6 1.64335 0.821676 0.569955i \(-0.193039\pi\)
0.821676 + 0.569955i \(0.193039\pi\)
\(212\) 0 0
\(213\) −37632.0 65180.5i −0.0568340 0.0984394i
\(214\) 0 0
\(215\) −439680. + 761548.i −0.648695 + 1.12357i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −13438.0 + 23275.3i −0.0189332 + 0.0327933i
\(220\) 0 0
\(221\) −358644. 621190.i −0.493950 0.855546i
\(222\) 0 0
\(223\) 707720. 0.953014 0.476507 0.879171i \(-0.341903\pi\)
0.476507 + 0.879171i \(0.341903\pi\)
\(224\) 0 0
\(225\) −1.45575e6 −1.91704
\(226\) 0 0
\(227\) 522183. + 904447.i 0.672602 + 1.16498i 0.977164 + 0.212488i \(0.0681567\pi\)
−0.304562 + 0.952493i \(0.598510\pi\)
\(228\) 0 0
\(229\) 269858. 467408.i 0.340053 0.588989i −0.644389 0.764698i \(-0.722888\pi\)
0.984442 + 0.175709i \(0.0562217\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −88557.0 + 153385.i −0.106864 + 0.185095i −0.914498 0.404590i \(-0.867414\pi\)
0.807634 + 0.589684i \(0.200748\pi\)
\(234\) 0 0
\(235\) −1.24013e6 2.14796e6i −1.46486 2.53722i
\(236\) 0 0
\(237\) −12496.0 −0.0144511
\(238\) 0 0
\(239\) −655464. −0.742257 −0.371128 0.928582i \(-0.621029\pi\)
−0.371128 + 0.928582i \(0.621029\pi\)
\(240\) 0 0
\(241\) −693547. 1.20126e6i −0.769189 1.33228i −0.938003 0.346627i \(-0.887327\pi\)
0.168814 0.985648i \(-0.446006\pi\)
\(242\) 0 0
\(243\) 173275. 300121.i 0.188244 0.326047i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 26884.0 46564.5i 0.0280383 0.0485637i
\(248\) 0 0
\(249\) −25254.0 43741.2i −0.0258126 0.0447087i
\(250\) 0 0
\(251\) 1.88811e6 1.89166 0.945830 0.324663i \(-0.105251\pi\)
0.945830 + 0.324663i \(0.105251\pi\)
\(252\) 0 0
\(253\) −69120.0 −0.0678895
\(254\) 0 0
\(255\) −120384. 208511.i −0.115936 0.200807i
\(256\) 0 0
\(257\) −173097. + 299813.i −0.163477 + 0.283151i −0.936113 0.351698i \(-0.885604\pi\)
0.772636 + 0.634849i \(0.218938\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −522693. + 905331.i −0.474947 + 0.822633i
\(262\) 0 0
\(263\) 464544. + 804614.i 0.414131 + 0.717296i 0.995337 0.0964609i \(-0.0307523\pi\)
−0.581206 + 0.813756i \(0.697419\pi\)
\(264\) 0 0
\(265\) −97344.0 −0.0851519
\(266\) 0 0
\(267\) 90252.0 0.0774780
\(268\) 0 0
\(269\) −191034. 330881.i −0.160964 0.278799i 0.774250 0.632879i \(-0.218127\pi\)
−0.935215 + 0.354081i \(0.884794\pi\)
\(270\) 0 0
\(271\) 790280. 1.36881e6i 0.653669 1.13219i −0.328557 0.944484i \(-0.606562\pi\)
0.982226 0.187703i \(-0.0601044\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.19276e6 3.79797e6i 1.74847 3.02845i
\(276\) 0 0
\(277\) 684557. + 1.18569e6i 0.536056 + 0.928476i 0.999111 + 0.0421469i \(0.0134198\pi\)
−0.463055 + 0.886329i \(0.653247\pi\)
\(278\) 0 0
\(279\) 1.49232e6 1.14776
\(280\) 0 0
\(281\) −394854. −0.298312 −0.149156 0.988814i \(-0.547656\pi\)
−0.149156 + 0.988814i \(0.547656\pi\)
\(282\) 0 0
\(283\) −336517. 582865.i −0.249770 0.432615i 0.713692 0.700460i \(-0.247022\pi\)
−0.963462 + 0.267845i \(0.913688\pi\)
\(284\) 0 0
\(285\) 9024.00 15630.0i 0.00658092 0.0113985i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −76329.5 + 132207.i −0.0537586 + 0.0931126i
\(290\) 0 0
\(291\) 107222. + 185714.i 0.0742252 + 0.128562i
\(292\) 0 0
\(293\) 1.83468e6 1.24851 0.624254 0.781222i \(-0.285403\pi\)
0.624254 + 0.781222i \(0.285403\pi\)
\(294\) 0 0
\(295\) −119232. −0.0797697
\(296\) 0 0
\(297\) 347040. + 601091.i 0.228291 + 0.395411i
\(298\) 0 0
\(299\) −27456.0 + 47555.2i −0.0177607 + 0.0307624i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 47136.0 81641.9i 0.0294948 0.0510866i
\(304\) 0 0
\(305\) 364416. + 631187.i 0.224310 + 0.388516i
\(306\) 0 0
\(307\) −1.51056e6 −0.914727 −0.457363 0.889280i \(-0.651206\pi\)
−0.457363 + 0.889280i \(0.651206\pi\)
\(308\) 0 0
\(309\) −244408. −0.145619
\(310\) 0 0
\(311\) 937644. + 1.62405e6i 0.549714 + 0.952133i 0.998294 + 0.0583901i \(0.0185967\pi\)
−0.448580 + 0.893743i \(0.648070\pi\)
\(312\) 0 0
\(313\) 755381. 1.30836e6i 0.435818 0.754859i −0.561544 0.827447i \(-0.689792\pi\)
0.997362 + 0.0725879i \(0.0231258\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.01355e6 + 1.75551e6i −0.566495 + 0.981197i 0.430414 + 0.902631i \(0.358367\pi\)
−0.996909 + 0.0785659i \(0.974966\pi\)
\(318\) 0 0
\(319\) −1.57464e6 2.72736e6i −0.866372 1.50060i
\(320\) 0 0
\(321\) 259272. 0.140441
\(322\) 0 0
\(323\) −117876. −0.0628665
\(324\) 0 0
\(325\) −1.74203e6 3.01728e6i −0.914842 1.58455i
\(326\) 0 0
\(327\) −220558. + 382018.i −0.114065 + 0.197567i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −770044. + 1.33376e6i −0.386319 + 0.669123i −0.991951 0.126621i \(-0.959587\pi\)
0.605633 + 0.795744i \(0.292920\pi\)
\(332\) 0 0
\(333\) −1.29036e6 2.23497e6i −0.637677 1.10449i
\(334\) 0 0
\(335\) −3.94867e6 −1.92238
\(336\) 0 0
\(337\) 1.01166e6 0.485245 0.242622 0.970121i \(-0.421992\pi\)
0.242622 + 0.970121i \(0.421992\pi\)
\(338\) 0 0
\(339\) 170694. + 295651.i 0.0806713 + 0.139727i
\(340\) 0 0
\(341\) −2.24784e6 + 3.89337e6i −1.04684 + 1.81318i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −9216.00 + 15962.6i −0.00416864 + 0.00722030i
\(346\) 0 0
\(347\) 1.07874e6 + 1.86843e6i 0.480942 + 0.833017i 0.999761 0.0218677i \(-0.00696127\pi\)
−0.518818 + 0.854884i \(0.673628\pi\)
\(348\) 0 0
\(349\) −1.15798e6 −0.508906 −0.254453 0.967085i \(-0.581895\pi\)
−0.254453 + 0.967085i \(0.581895\pi\)
\(350\) 0 0
\(351\) 551408. 0.238894
\(352\) 0 0
\(353\) 1.58783e6 + 2.75020e6i 0.678215 + 1.17470i 0.975518 + 0.219920i \(0.0705796\pi\)
−0.297303 + 0.954783i \(0.596087\pi\)
\(354\) 0 0
\(355\) −1.80634e6 + 3.12867e6i −0.760725 + 1.31761i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 37308.0 64619.4i 0.0152780 0.0264622i −0.858285 0.513173i \(-0.828470\pi\)
0.873563 + 0.486711i \(0.161803\pi\)
\(360\) 0 0
\(361\) 1.23363e6 + 2.13671e6i 0.498216 + 0.862935i
\(362\) 0 0
\(363\) −714698. −0.284679
\(364\) 0 0
\(365\) 1.29005e6 0.506843
\(366\) 0 0
\(367\) 899036. + 1.55718e6i 0.348427 + 0.603493i 0.985970 0.166921i \(-0.0533826\pi\)
−0.637543 + 0.770415i \(0.720049\pi\)
\(368\) 0 0
\(369\) 1.43472e6 2.48500e6i 0.548530 0.950082i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.10230e6 + 1.90924e6i −0.410231 + 0.710542i −0.994915 0.100720i \(-0.967885\pi\)
0.584683 + 0.811262i \(0.301219\pi\)
\(374\) 0 0
\(375\) −284736. 493177.i −0.104560 0.181103i
\(376\) 0 0
\(377\) −2.50193e6 −0.906612
\(378\) 0 0
\(379\) −177568. −0.0634990 −0.0317495 0.999496i \(-0.510108\pi\)
−0.0317495 + 0.999496i \(0.510108\pi\)
\(380\) 0 0
\(381\) −249808. 432680.i −0.0881645 0.152705i
\(382\) 0 0
\(383\) 1.43734e6 2.48955e6i 0.500683 0.867209i −0.499316 0.866420i \(-0.666415\pi\)
1.00000 0.000789287i \(-0.000251238\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.09462e6 + 1.89594e6i −0.371523 + 0.643497i
\(388\) 0 0
\(389\) 2.39982e6 + 4.15662e6i 0.804091 + 1.39273i 0.916903 + 0.399110i \(0.130681\pi\)
−0.112812 + 0.993616i \(0.535986\pi\)
\(390\) 0 0
\(391\) 120384. 0.0398223
\(392\) 0 0
\(393\) −24420.0 −0.00797562
\(394\) 0 0
\(395\) 299904. + 519449.i 0.0967140 + 0.167514i
\(396\) 0 0
\(397\) 1.40821e6 2.43910e6i 0.448428 0.776699i −0.549856 0.835259i \(-0.685318\pi\)
0.998284 + 0.0585598i \(0.0186508\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.41898e6 2.45775e6i 0.440673 0.763269i −0.557066 0.830468i \(-0.688073\pi\)
0.997740 + 0.0671994i \(0.0214064\pi\)
\(402\) 0 0
\(403\) 1.78578e6 + 3.09307e6i 0.547730 + 0.948696i
\(404\) 0 0
\(405\) −5.39030e6 −1.63296
\(406\) 0 0
\(407\) 7.77456e6 2.32643
\(408\) 0 0
\(409\) −77143.0 133616.i −0.0228028 0.0394956i 0.854399 0.519618i \(-0.173926\pi\)
−0.877202 + 0.480122i \(0.840592\pi\)
\(410\) 0 0
\(411\) −13902.0 + 24079.0i −0.00405950 + 0.00703126i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1.21219e6 + 2.09958e6i −0.345502 + 0.598428i
\(416\) 0 0
\(417\) −431794. 747889.i −0.121601 0.210619i
\(418\) 0 0
\(419\) 3.72865e6 1.03757 0.518783 0.854906i \(-0.326385\pi\)
0.518783 + 0.854906i \(0.326385\pi\)
\(420\) 0 0
\(421\) −2.32623e6 −0.639658 −0.319829 0.947475i \(-0.603626\pi\)
−0.319829 + 0.947475i \(0.603626\pi\)
\(422\) 0 0
\(423\) −3.08740e6 5.34754e6i −0.838962 1.45312i
\(424\) 0 0
\(425\) −3.81906e6 + 6.61480e6i −1.02561 + 1.77642i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −411840. + 713328.i −0.108040 + 0.187131i
\(430\) 0 0
\(431\) 1.30741e6 + 2.26450e6i 0.339015 + 0.587192i 0.984248 0.176795i \(-0.0565728\pi\)
−0.645232 + 0.763986i \(0.723239\pi\)
\(432\) 0 0
\(433\) −1.19226e6 −0.305598 −0.152799 0.988257i \(-0.548829\pi\)
−0.152799 + 0.988257i \(0.548829\pi\)
\(434\) 0 0
\(435\) −839808. −0.212793
\(436\) 0 0
\(437\) 4512.00 + 7815.01i 0.00113023 + 0.00195761i
\(438\) 0 0
\(439\) −528964. + 916193.i −0.130998 + 0.226895i −0.924062 0.382244i \(-0.875151\pi\)
0.793064 + 0.609139i \(0.208485\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.06378e6 + 3.57457e6i −0.499636 + 0.865395i −1.00000 0.000420339i \(-0.999866\pi\)
0.500364 + 0.865815i \(0.333200\pi\)
\(444\) 0 0
\(445\) −2.16605e6 3.75171e6i −0.518523 0.898108i
\(446\) 0 0
\(447\) −653628. −0.154725
\(448\) 0 0
\(449\) 3.75823e6 0.879766 0.439883 0.898055i \(-0.355020\pi\)
0.439883 + 0.898055i \(0.355020\pi\)
\(450\) 0 0
\(451\) 4.32216e6 + 7.48620e6i 1.00060 + 1.73309i
\(452\) 0 0
\(453\) 173480. 300476.i 0.0397195 0.0687962i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 225557. 390676.i 0.0505203 0.0875037i −0.839659 0.543113i \(-0.817245\pi\)
0.890180 + 0.455610i \(0.150579\pi\)
\(458\) 0 0
\(459\) −604428. 1.04690e6i −0.133910 0.231939i
\(460\) 0 0
\(461\) −1.95186e6 −0.427756 −0.213878 0.976860i \(-0.568610\pi\)
−0.213878 + 0.976860i \(0.568610\pi\)
\(462\) 0 0
\(463\) −7.20218e6 −1.56139 −0.780695 0.624913i \(-0.785135\pi\)
−0.780695 + 0.624913i \(0.785135\pi\)
\(464\) 0 0
\(465\) 599424. + 1.03823e6i 0.128559 + 0.222670i
\(466\) 0 0
\(467\) −3.58900e6 + 6.21634e6i −0.761521 + 1.31899i 0.180545 + 0.983567i \(0.442214\pi\)
−0.942066 + 0.335426i \(0.891120\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −54532.0 + 94452.2i −0.0113266 + 0.0196182i
\(472\) 0 0
\(473\) −3.29760e6 5.71161e6i −0.677712 1.17383i
\(474\) 0 0
\(475\) −572554. −0.116435
\(476\) 0 0
\(477\) −242346. −0.0487686
\(478\) 0 0
\(479\) −3.08816e6 5.34885e6i −0.614980 1.06518i −0.990388 0.138316i \(-0.955831\pi\)
0.375408 0.926859i \(-0.377502\pi\)
\(480\) 0 0
\(481\) 3.08823e6 5.34897e6i 0.608621 1.05416i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.14666e6 8.91427e6i 0.993507 1.72080i
\(486\) 0 0
\(487\) −3.79665e6 6.57599e6i −0.725401 1.25643i −0.958809 0.284052i \(-0.908321\pi\)
0.233408 0.972379i \(-0.425012\pi\)
\(488\) 0 0
\(489\) −209920. −0.0396992
\(490\) 0 0
\(491\) −1.51878e6 −0.284309 −0.142155 0.989844i \(-0.545403\pi\)
−0.142155 + 0.989844i \(0.545403\pi\)
\(492\) 0 0
\(493\) 2.74250e6 + 4.75015e6i 0.508193 + 0.880217i
\(494\) 0 0
\(495\) 8.25984e6 1.43065e7i 1.51516 2.62433i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −737878. + 1.27804e6i −0.132658 + 0.229770i −0.924700 0.380696i \(-0.875685\pi\)
0.792042 + 0.610466i \(0.209018\pi\)
\(500\) 0 0
\(501\) 160788. + 278493.i 0.0286193 + 0.0495701i
\(502\) 0 0
\(503\) −1.31309e6 −0.231406 −0.115703 0.993284i \(-0.536912\pi\)
−0.115703 + 0.993284i \(0.536912\pi\)
\(504\) 0 0
\(505\) −4.52506e6 −0.789579
\(506\) 0 0
\(507\) −44109.0 76399.0i −0.00762092 0.0131998i
\(508\) 0 0
\(509\) −2.20466e6 + 3.81858e6i −0.377178 + 0.653292i −0.990651 0.136424i \(-0.956439\pi\)
0.613472 + 0.789716i \(0.289772\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 45308.0 78475.8i 0.00760119 0.0131656i
\(514\) 0 0
\(515\) 5.86579e6 + 1.01598e7i 0.974560 + 1.68799i
\(516\) 0 0
\(517\) 1.86019e7 3.06078
\(518\) 0 0
\(519\) −721128. −0.117515
\(520\) 0 0
\(521\) −1.48815e6 2.57755e6i −0.240188 0.416018i 0.720580 0.693372i \(-0.243876\pi\)
−0.960768 + 0.277354i \(0.910542\pi\)
\(522\) 0 0
\(523\) −3.17314e6 + 5.49603e6i −0.507265 + 0.878608i 0.492700 + 0.870199i \(0.336010\pi\)
−0.999965 + 0.00840891i \(0.997323\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.91499e6 6.78096e6i 0.614050 1.06357i
\(528\) 0 0
\(529\) 3.21356e6 + 5.56606e6i 0.499284 + 0.864785i
\(530\) 0 0
\(531\) −296838. −0.0456860
\(532\) 0 0
\(533\) 6.86743e6 1.04707
\(534\) 0 0
\(535\) −6.22253e6 1.07777e7i −0.939902 1.62796i
\(536\) 0 0
\(537\) −312732. + 541668.i −0.0467990 + 0.0810583i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 683333. 1.18357e6i 0.100378 0.173860i −0.811462 0.584405i \(-0.801328\pi\)
0.911840 + 0.410545i \(0.134661\pi\)
\(542\) 0 0
\(543\) −123820. 214463.i −0.0180215 0.0312142i
\(544\) 0 0
\(545\) 2.11736e7 3.05353
\(546\) 0 0
\(547\) −9.55818e6 −1.36586 −0.682931 0.730483i \(-0.739295\pi\)
−0.682931 + 0.730483i \(0.739295\pi\)
\(548\) 0 0
\(549\) 907244. + 1.57139e6i 0.128467 + 0.222512i
\(550\) 0 0
\(551\) −205578. + 356072.i −0.0288468 + 0.0499641i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.03661e6 1.79546e6i 0.142851 0.247425i
\(556\) 0 0
\(557\) −3.47144e6 6.01270e6i −0.474101 0.821167i 0.525459 0.850819i \(-0.323894\pi\)
−0.999560 + 0.0296515i \(0.990560\pi\)
\(558\) 0 0
\(559\) −5.23952e6 −0.709189
\(560\) 0 0
\(561\) 1.80576e6 0.242244
\(562\) 0 0
\(563\) −2.62331e6 4.54371e6i −0.348802 0.604143i 0.637235 0.770670i \(-0.280078\pi\)
−0.986037 + 0.166527i \(0.946745\pi\)
\(564\) 0 0
\(565\) 8.19331e6 1.41912e7i 1.07979 1.87025i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.73276e6 + 3.00122e6i −0.224366 + 0.388613i −0.956129 0.292946i \(-0.905364\pi\)
0.731763 + 0.681559i \(0.238698\pi\)
\(570\) 0 0
\(571\) −2.45034e6 4.24412e6i −0.314512 0.544750i 0.664822 0.747002i \(-0.268507\pi\)
−0.979334 + 0.202252i \(0.935174\pi\)
\(572\) 0 0
\(573\) −646896. −0.0823091
\(574\) 0 0
\(575\) 584736. 0.0737548
\(576\) 0 0
\(577\) −1.14173e6 1.97753e6i −0.142766 0.247277i 0.785772 0.618517i \(-0.212266\pi\)
−0.928537 + 0.371240i \(0.878933\pi\)
\(578\) 0 0
\(579\) −619954. + 1.07379e6i −0.0768534 + 0.133114i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 365040. 632268.i 0.0444804 0.0770424i
\(584\) 0 0
\(585\) −6.56198e6 1.13657e7i −0.792767 1.37311i
\(586\) 0 0
\(587\) 1.03157e7 1.23568 0.617838 0.786305i \(-0.288009\pi\)
0.617838 + 0.786305i \(0.288009\pi\)
\(588\) 0 0
\(589\) 586936. 0.0697112
\(590\) 0 0
\(591\) −499362. 864920.i −0.0588094 0.101861i
\(592\) 0 0
\(593\) −1.76419e6 + 3.05566e6i −0.206020 + 0.356836i −0.950457 0.310856i \(-0.899384\pi\)
0.744438 + 0.667692i \(0.232718\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −785932. + 1.36127e6i −0.0902504 + 0.156318i
\(598\) 0 0
\(599\) −1.46130e6 2.53105e6i −0.166407 0.288226i 0.770747 0.637141i \(-0.219883\pi\)
−0.937154 + 0.348916i \(0.886550\pi\)
\(600\) 0 0
\(601\) −1.17567e7 −1.32770 −0.663849 0.747866i \(-0.731078\pi\)
−0.663849 + 0.747866i \(0.731078\pi\)
\(602\) 0 0
\(603\) −9.83055e6 −1.10099
\(604\) 0 0
\(605\) 1.71528e7 + 2.97094e7i 1.90522 + 3.29994i
\(606\) 0 0
\(607\) 2.35746e6 4.08323e6i 0.259700 0.449814i −0.706462 0.707751i \(-0.749710\pi\)
0.966161 + 0.257938i \(0.0830430\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 7.38910e6 1.27983e7i 0.800734 1.38691i
\(612\) 0 0
\(613\) −106921. 185193.i −0.0114924 0.0199055i 0.860222 0.509920i \(-0.170325\pi\)
−0.871714 + 0.490014i \(0.836992\pi\)
\(614\) 0 0
\(615\) 2.30515e6 0.245760
\(616\) 0 0
\(617\) −336666. −0.0356030 −0.0178015 0.999842i \(-0.505667\pi\)
−0.0178015 + 0.999842i \(0.505667\pi\)
\(618\) 0 0
\(619\) −7.13276e6 1.23543e7i −0.748223 1.29596i −0.948674 0.316257i \(-0.897574\pi\)
0.200450 0.979704i \(-0.435760\pi\)
\(620\) 0 0
\(621\) −46272.0 + 80145.5i −0.00481492 + 0.00833969i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −4.15014e6 + 7.18825e6i −0.424974 + 0.736077i
\(626\) 0 0
\(627\) 67680.0 + 117225.i 0.00687530 + 0.0119084i
\(628\) 0 0
\(629\) −1.35407e7 −1.36463
\(630\) 0 0
\(631\) −6.59637e6 −0.659525 −0.329763 0.944064i \(-0.606969\pi\)
−0.329763 + 0.944064i \(0.606969\pi\)
\(632\) 0 0
\(633\) 1.06276e6 + 1.84076e6i 0.105421 + 0.182595i
\(634\) 0 0
\(635\) −1.19908e7 + 2.07686e7i −1.18008 + 2.04397i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −4.49702e6 + 7.78907e6i −0.435685 + 0.754629i
\(640\) 0 0
\(641\) 5.12449e6 + 8.87588e6i 0.492613 + 0.853230i 0.999964 0.00850936i \(-0.00270865\pi\)
−0.507351 + 0.861739i \(0.669375\pi\)
\(642\) 0 0
\(643\) −4.16543e6 −0.397312 −0.198656 0.980069i \(-0.563658\pi\)
−0.198656 + 0.980069i \(0.563658\pi\)
\(644\) 0 0
\(645\) −1.75872e6 −0.166455
\(646\) 0 0
\(647\) 1.67525e6 + 2.90163e6i 0.157333 + 0.272509i 0.933906 0.357518i \(-0.116377\pi\)
−0.776573 + 0.630027i \(0.783044\pi\)
\(648\) 0 0
\(649\) 447120. 774435.i 0.0416689 0.0721727i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.52704e6 7.84106e6i 0.415462 0.719601i −0.580015 0.814606i \(-0.696953\pi\)
0.995477 + 0.0950046i \(0.0302866\pi\)
\(654\) 0 0
\(655\) 586080. + 1.01512e6i 0.0533769 + 0.0924516i
\(656\) 0 0
\(657\) 3.21168e6 0.290281
\(658\) 0 0
\(659\) 6.45382e6 0.578899 0.289450 0.957193i \(-0.406528\pi\)
0.289450 + 0.957193i \(0.406528\pi\)
\(660\) 0 0
\(661\) −7.15836e6 1.23987e7i −0.637250 1.10375i −0.986034 0.166547i \(-0.946738\pi\)
0.348783 0.937203i \(-0.386595\pi\)
\(662\) 0 0
\(663\) 717288. 1.24238e6i 0.0633738 0.109767i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 209952. 363648.i 0.0182728 0.0316494i
\(668\) 0 0
\(669\) 707720. + 1.22581e6i 0.0611359 + 0.105890i
\(670\) 0 0
\(671\) −5.46624e6 −0.468686
\(672\) 0 0
\(673\) 2.27250e7 1.93404 0.967020 0.254701i \(-0.0819771\pi\)
0.967020 + 0.254701i \(0.0819771\pi\)
\(674\) 0 0
\(675\) −2.93586e6 5.08506e6i −0.248014 0.429573i
\(676\) 0 0
\(677\) 4.26625e6 7.38935e6i 0.357746 0.619633i −0.629838 0.776726i \(-0.716879\pi\)
0.987584 + 0.157093i \(0.0502122\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.04437e6 + 1.80889e6i −0.0862949 + 0.149467i
\(682\) 0 0
\(683\) 1.12460e7 + 1.94787e7i 0.922461 + 1.59775i 0.795594 + 0.605830i \(0.207159\pi\)
0.126867 + 0.991920i \(0.459508\pi\)
\(684\) 0 0
\(685\) 1.33459e6 0.108673
\(686\) 0 0
\(687\) 1.07943e6 0.0872576
\(688\) 0 0
\(689\) −290004. 502302.i −0.0232732 0.0403103i
\(690\) 0 0
\(691\) 6.34471e6 1.09894e7i 0.505495 0.875543i −0.494485 0.869186i \(-0.664643\pi\)
0.999980 0.00635656i \(-0.00202337\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.07261e7 + 3.58987e7i −1.62763 + 2.81914i
\(696\) 0 0
\(697\) −7.52776e6 1.30385e7i −0.586927 1.01659i
\(698\) 0 0
\(699\) −354228. −0.0274214
\(700\) 0 0
\(701\) −5.13939e6 −0.395018 −0.197509 0.980301i \(-0.563285\pi\)
−0.197509 + 0.980301i \(0.563285\pi\)
\(702\) 0 0
\(703\) −507506. 879026.i −0.0387305 0.0670832i
\(704\) 0 0
\(705\) 2.48026e6 4.29593e6i 0.187942 0.325525i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 5.80325e6 1.00515e7i 0.433566 0.750959i −0.563611 0.826040i \(-0.690588\pi\)
0.997177 + 0.0750815i \(0.0239217\pi\)
\(710\) 0 0
\(711\) 746636. + 1.29321e6i 0.0553905 + 0.0959391i
\(712\) 0 0
\(713\) −599424. −0.0441581
\(714\) 0 0
\(715\) 3.95366e7 2.89224
\(716\) 0 0
\(717\) −655464. 1.13530e6i −0.0476158 0.0824730i
\(718\) 0 0
\(719\) −7.54988e6 + 1.30768e7i −0.544650 + 0.943362i 0.453979 + 0.891013i \(0.350004\pi\)
−0.998629 + 0.0523493i \(0.983329\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 1.38709e6 2.40252e6i 0.0986870 0.170931i
\(724\) 0 0
\(725\) 1.33210e7 + 2.30727e7i 0.941223 + 1.63025i
\(726\) 0 0
\(727\) −2.32536e7 −1.63175 −0.815874 0.578229i \(-0.803744\pi\)
−0.815874 + 0.578229i \(0.803744\pi\)
\(728\) 0 0
\(729\) −1.29511e7 −0.902585
\(730\) 0 0
\(731\) 5.74332e6 + 9.94772e6i 0.397530 + 0.688542i
\(732\) 0 0
\(733\) −1.18907e7 + 2.05953e7i −0.817423 + 1.41582i 0.0901518 + 0.995928i \(0.471265\pi\)
−0.907575 + 0.419890i \(0.862069\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.48075e7 2.56474e7i 1.00418 1.73930i
\(738\) 0 0
\(739\) 1.25696e6 + 2.17712e6i 0.0846663 + 0.146646i 0.905249 0.424882i \(-0.139684\pi\)
−0.820583 + 0.571528i \(0.806351\pi\)
\(740\) 0 0
\(741\) 107536. 0.00719463
\(742\) 0 0
\(743\) −2.22646e7 −1.47959 −0.739797 0.672830i \(-0.765078\pi\)
−0.739797 + 0.672830i \(0.765078\pi\)
\(744\) 0 0
\(745\) 1.56871e7 + 2.71708e7i 1.03550 + 1.79354i
\(746\) 0 0
\(747\) −3.01785e6 + 5.22707e6i −0.197878 + 0.342734i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.15054e7 + 1.99279e7i −0.744392 + 1.28932i 0.206087 + 0.978534i \(0.433927\pi\)
−0.950479 + 0.310790i \(0.899406\pi\)
\(752\) 0 0
\(753\) 1.88811e6 + 3.27030e6i 0.121350 + 0.210184i
\(754\) 0 0
\(755\) −1.66541e7 −1.06329
\(756\) 0 0
\(757\) 1.59335e7 1.01058 0.505290 0.862950i \(-0.331386\pi\)
0.505290 + 0.862950i \(0.331386\pi\)
\(758\) 0 0
\(759\) −69120.0 119719.i −0.00435511 0.00754327i
\(760\) 0 0
\(761\) −8.43143e6 + 1.46037e7i −0.527764 + 0.914114i 0.471712 + 0.881752i \(0.343636\pi\)
−0.999476 + 0.0323613i \(0.989697\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −1.43859e7 + 2.49171e7i −0.888757 + 1.53937i
\(766\) 0 0
\(767\) −355212. 615245.i −0.0218021 0.0377624i
\(768\) 0 0
\(769\) −2.75402e7 −1.67939 −0.839694 0.543060i \(-0.817265\pi\)
−0.839694 + 0.543060i \(0.817265\pi\)
\(770\) 0 0
\(771\) −692388. −0.0419482
\(772\) 0 0
\(773\) −1.13410e7 1.96432e7i −0.682658 1.18240i −0.974167 0.225831i \(-0.927490\pi\)
0.291508 0.956568i \(-0.405843\pi\)
\(774\) 0 0
\(775\) 1.90161e7 3.29369e7i 1.13728 1.96983i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 564282. 977365.i 0.0333160 0.0577050i
\(780\) 0 0
\(781\) −1.35475e7 2.34650e7i −0.794753 1.37655i
\(782\) 0 0
\(783\) −4.21654e6 −0.245783
\(784\) 0 0
\(785\) 5.23507e6 0.303213