Properties

Label 252.12.k.d.109.5
Level $252$
Weight $12$
Character 252.109
Analytic conductor $193.622$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(193.622481501\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 581500324 x^{14} - 481772282104 x^{13} + 132272376701859942 x^{12} + \)\(18\!\cdots\!08\)\( x^{11} - \)\(14\!\cdots\!08\)\( x^{10} - \)\(25\!\cdots\!56\)\( x^{9} + \)\(80\!\cdots\!79\)\( x^{8} + \)\(11\!\cdots\!68\)\( x^{7} - \)\(19\!\cdots\!68\)\( x^{6} + \)\(59\!\cdots\!08\)\( x^{5} + \)\(21\!\cdots\!06\)\( x^{4} - \)\(37\!\cdots\!04\)\( x^{3} - \)\(31\!\cdots\!28\)\( x^{2} + \)\(25\!\cdots\!24\)\( x + \)\(79\!\cdots\!77\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{42}\cdot 3^{15}\cdot 7^{9} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.5
Root \(2396.04 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 252.109
Dual form 252.12.k.d.37.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1332.77 + 2308.42i) q^{5} +(43648.5 + 8493.30i) q^{7} +O(q^{10})\) \(q+(1332.77 + 2308.42i) q^{5} +(43648.5 + 8493.30i) q^{7} +(-262991. + 455515. i) q^{11} -1.10180e6 q^{13} +(222021. - 384552. i) q^{17} +(-1.58519e6 - 2.74562e6i) q^{19} +(-2.38816e7 - 4.13641e7i) q^{23} +(2.08615e7 - 3.61332e7i) q^{25} +1.65232e8 q^{29} +(-8.05562e7 + 1.39527e8i) q^{31} +(3.85672e7 + 1.12079e8i) q^{35} +(-1.73311e8 - 3.00184e8i) q^{37} +1.07369e9 q^{41} +1.10803e9 q^{43} +(4.49033e7 + 7.77748e7i) q^{47} +(1.83305e9 + 7.41439e8i) q^{49} +(-1.97953e8 + 3.42864e8i) q^{53} -1.40203e9 q^{55} +(-3.65401e9 + 6.32894e9i) q^{59} +(-6.05057e9 - 1.04799e10i) q^{61} +(-1.46844e9 - 2.54341e9i) q^{65} +(8.63592e9 - 1.49578e10i) q^{67} +1.31065e10 q^{71} +(-7.39348e9 + 1.28059e10i) q^{73} +(-1.53480e10 + 1.76489e10i) q^{77} +(-1.45406e10 - 2.51850e10i) q^{79} -2.43778e9 q^{83} +1.18361e9 q^{85} +(4.46315e10 + 7.73040e10i) q^{89} +(-4.80917e10 - 9.35787e9i) q^{91} +(4.22537e9 - 7.31856e9i) q^{95} +6.63296e10 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 2156q^{5} + 50512q^{7} + O(q^{10}) \) \( 16q + 2156q^{5} + 50512q^{7} + 222796q^{11} + 2703176q^{13} - 5114600q^{17} + 6910556q^{19} + 51387712q^{23} - 191456372q^{25} - 118854616q^{29} + 164659160q^{31} - 55239344q^{35} + 75658364q^{37} + 1815568608q^{41} + 10754408q^{43} + 1034359464q^{47} + 4123496848q^{49} + 665159988q^{53} - 1264543896q^{55} - 1040514580q^{59} - 14391208024q^{61} + 20938150200q^{65} - 33307097284q^{67} - 65848902896q^{71} + 17709749204q^{73} - 8594484604q^{77} - 26626784032q^{79} + 210306955048q^{83} - 25867402032q^{85} + 55951560072q^{89} + 66078280292q^{91} - 106810047392q^{95} - 156216030712q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1332.77 + 2308.42i 0.190730 + 0.330355i 0.945492 0.325644i \(-0.105581\pi\)
−0.754762 + 0.655999i \(0.772248\pi\)
\(6\) 0 0
\(7\) 43648.5 + 8493.30i 0.981590 + 0.191002i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −262991. + 455515.i −0.492359 + 0.852791i −0.999961 0.00880080i \(-0.997199\pi\)
0.507602 + 0.861591i \(0.330532\pi\)
\(12\) 0 0
\(13\) −1.10180e6 −0.823024 −0.411512 0.911404i \(-0.634999\pi\)
−0.411512 + 0.911404i \(0.634999\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 222021. 384552.i 0.0379250 0.0656880i −0.846440 0.532484i \(-0.821259\pi\)
0.884365 + 0.466796i \(0.154592\pi\)
\(18\) 0 0
\(19\) −1.58519e6 2.74562e6i −0.146871 0.254388i 0.783199 0.621772i \(-0.213587\pi\)
−0.930069 + 0.367384i \(0.880253\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.38816e7 4.13641e7i −0.773677 1.34005i −0.935535 0.353234i \(-0.885082\pi\)
0.161857 0.986814i \(-0.448252\pi\)
\(24\) 0 0
\(25\) 2.08615e7 3.61332e7i 0.427244 0.740008i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.65232e8 1.49591 0.747954 0.663750i \(-0.231036\pi\)
0.747954 + 0.663750i \(0.231036\pi\)
\(30\) 0 0
\(31\) −8.05562e7 + 1.39527e8i −0.505370 + 0.875327i 0.494611 + 0.869115i \(0.335311\pi\)
−0.999981 + 0.00621203i \(0.998023\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.85672e7 + 1.12079e8i 0.124121 + 0.360703i
\(36\) 0 0
\(37\) −1.73311e8 3.00184e8i −0.410882 0.711669i 0.584104 0.811679i \(-0.301446\pi\)
−0.994986 + 0.100010i \(0.968113\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.07369e9 1.44734 0.723668 0.690148i \(-0.242455\pi\)
0.723668 + 0.690148i \(0.242455\pi\)
\(42\) 0 0
\(43\) 1.10803e9 1.14941 0.574706 0.818360i \(-0.305117\pi\)
0.574706 + 0.818360i \(0.305117\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.49033e7 + 7.77748e7i 0.0285588 + 0.0494653i 0.879952 0.475063i \(-0.157575\pi\)
−0.851393 + 0.524529i \(0.824242\pi\)
\(48\) 0 0
\(49\) 1.83305e9 + 7.41439e8i 0.927037 + 0.374970i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.97953e8 + 3.42864e8i −0.0650196 + 0.112617i −0.896703 0.442633i \(-0.854044\pi\)
0.831683 + 0.555251i \(0.187378\pi\)
\(54\) 0 0
\(55\) −1.40203e9 −0.375631
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.65401e9 + 6.32894e9i −0.665402 + 1.15251i 0.313774 + 0.949498i \(0.398407\pi\)
−0.979176 + 0.203012i \(0.934927\pi\)
\(60\) 0 0
\(61\) −6.05057e9 1.04799e10i −0.917238 1.58870i −0.803591 0.595182i \(-0.797080\pi\)
−0.113647 0.993521i \(-0.536253\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.46844e9 2.54341e9i −0.156976 0.271890i
\(66\) 0 0
\(67\) 8.63592e9 1.49578e10i 0.781442 1.35350i −0.149659 0.988738i \(-0.547818\pi\)
0.931101 0.364760i \(-0.118849\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.31065e10 0.862113 0.431056 0.902325i \(-0.358141\pi\)
0.431056 + 0.902325i \(0.358141\pi\)
\(72\) 0 0
\(73\) −7.39348e9 + 1.28059e10i −0.417420 + 0.722993i −0.995679 0.0928606i \(-0.970399\pi\)
0.578259 + 0.815853i \(0.303732\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.53480e10 + 1.76489e10i −0.646179 + 0.743049i
\(78\) 0 0
\(79\) −1.45406e10 2.51850e10i −0.531658 0.920859i −0.999317 0.0369500i \(-0.988236\pi\)
0.467659 0.883909i \(-0.345098\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −2.43778e9 −0.0679305 −0.0339652 0.999423i \(-0.510814\pi\)
−0.0339652 + 0.999423i \(0.510814\pi\)
\(84\) 0 0
\(85\) 1.18361e9 0.0289338
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.46315e10 + 7.73040e10i 0.847220 + 1.46743i 0.883679 + 0.468094i \(0.155059\pi\)
−0.0364584 + 0.999335i \(0.511608\pi\)
\(90\) 0 0
\(91\) −4.80917e10 9.35787e9i −0.807872 0.157199i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.22537e9 7.31856e9i 0.0560254 0.0970389i
\(96\) 0 0
\(97\) 6.63296e10 0.784265 0.392132 0.919909i \(-0.371738\pi\)
0.392132 + 0.919909i \(0.371738\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.40959e10 + 2.44149e10i −0.133452 + 0.231146i −0.925005 0.379954i \(-0.875940\pi\)
0.791553 + 0.611101i \(0.209273\pi\)
\(102\) 0 0
\(103\) −7.47509e10 1.29472e11i −0.635348 1.10045i −0.986441 0.164114i \(-0.947523\pi\)
0.351093 0.936340i \(-0.385810\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.31786e11 + 2.28259e11i 0.908358 + 1.57332i 0.816345 + 0.577564i \(0.195997\pi\)
0.0920128 + 0.995758i \(0.470670\pi\)
\(108\) 0 0
\(109\) 2.35713e10 4.08266e10i 0.146736 0.254155i −0.783283 0.621665i \(-0.786456\pi\)
0.930019 + 0.367511i \(0.119790\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.07560e10 −0.361270 −0.180635 0.983550i \(-0.557815\pi\)
−0.180635 + 0.983550i \(0.557815\pi\)
\(114\) 0 0
\(115\) 6.36572e10 1.10258e11i 0.295128 0.511176i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.29570e10 1.48994e10i 0.0497733 0.0572350i
\(120\) 0 0
\(121\) 4.32686e9 + 7.49434e9i 0.0151654 + 0.0262672i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2.41368e11 0.707414
\(126\) 0 0
\(127\) −9.35541e10 −0.251271 −0.125635 0.992076i \(-0.540097\pi\)
−0.125635 + 0.992076i \(0.540097\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.03929e10 5.26420e10i −0.0688303 0.119218i 0.829556 0.558423i \(-0.188593\pi\)
−0.898387 + 0.439205i \(0.855260\pi\)
\(132\) 0 0
\(133\) −4.58716e10 1.33306e11i −0.0955784 0.277757i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.72230e11 + 2.98311e11i −0.304891 + 0.528087i −0.977237 0.212150i \(-0.931954\pi\)
0.672346 + 0.740237i \(0.265287\pi\)
\(138\) 0 0
\(139\) 3.54339e11 0.579211 0.289606 0.957146i \(-0.406476\pi\)
0.289606 + 0.957146i \(0.406476\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.89763e11 5.01884e11i 0.405223 0.701867i
\(144\) 0 0
\(145\) 2.20216e11 + 3.81425e11i 0.285315 + 0.494180i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.87394e11 3.24576e11i −0.209041 0.362069i 0.742372 0.669988i \(-0.233701\pi\)
−0.951413 + 0.307919i \(0.900368\pi\)
\(150\) 0 0
\(151\) −2.29692e11 + 3.97838e11i −0.238107 + 0.412413i −0.960171 0.279413i \(-0.909860\pi\)
0.722064 + 0.691826i \(0.243194\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.29451e11 −0.385558
\(156\) 0 0
\(157\) −6.37048e11 + 1.10340e12i −0.532996 + 0.923176i 0.466261 + 0.884647i \(0.345601\pi\)
−0.999257 + 0.0385292i \(0.987733\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.91077e11 2.00831e12i −0.503482 1.46315i
\(162\) 0 0
\(163\) 8.84049e11 + 1.53122e12i 0.601790 + 1.04233i 0.992550 + 0.121838i \(0.0388787\pi\)
−0.390761 + 0.920492i \(0.627788\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.36833e12 0.815174 0.407587 0.913166i \(-0.366370\pi\)
0.407587 + 0.913166i \(0.366370\pi\)
\(168\) 0 0
\(169\) −5.78208e11 −0.322632
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.14381e12 + 1.98114e12i 0.561179 + 0.971990i 0.997394 + 0.0721478i \(0.0229853\pi\)
−0.436215 + 0.899842i \(0.643681\pi\)
\(174\) 0 0
\(175\) 1.21746e12 1.39998e12i 0.560721 0.644780i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.28321e12 2.22258e12i 0.521922 0.903995i −0.477753 0.878494i \(-0.658549\pi\)
0.999675 0.0255010i \(-0.00811811\pi\)
\(180\) 0 0
\(181\) 4.37998e12 1.67587 0.837934 0.545771i \(-0.183763\pi\)
0.837934 + 0.545771i \(0.183763\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.61968e11 8.00152e11i 0.156735 0.271474i
\(186\) 0 0
\(187\) 1.16779e11 + 2.02268e11i 0.0373454 + 0.0646842i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.48818e10 + 1.47020e11i 0.0241619 + 0.0418496i 0.877854 0.478929i \(-0.158975\pi\)
−0.853692 + 0.520779i \(0.825642\pi\)
\(192\) 0 0
\(193\) −1.61580e11 + 2.79865e11i −0.0434333 + 0.0752286i −0.886925 0.461914i \(-0.847163\pi\)
0.843492 + 0.537142i \(0.180496\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.26787e11 −0.198531 −0.0992657 0.995061i \(-0.531649\pi\)
−0.0992657 + 0.995061i \(0.531649\pi\)
\(198\) 0 0
\(199\) −2.12706e12 + 3.68418e12i −0.483157 + 0.836853i −0.999813 0.0193401i \(-0.993843\pi\)
0.516656 + 0.856193i \(0.327177\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 7.21213e12 + 1.40336e12i 1.46837 + 0.285721i
\(204\) 0 0
\(205\) 1.43099e12 + 2.47854e12i 0.276051 + 0.478134i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.66756e12 0.289253
\(210\) 0 0
\(211\) 6.58675e12 1.08422 0.542110 0.840307i \(-0.317626\pi\)
0.542110 + 0.840307i \(0.317626\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.47675e12 + 2.55780e12i 0.219228 + 0.379713i
\(216\) 0 0
\(217\) −4.70120e12 + 5.40597e12i −0.663255 + 0.762685i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.44622e11 + 4.23698e11i −0.0312132 + 0.0540628i
\(222\) 0 0
\(223\) −7.33282e11 −0.0890419 −0.0445209 0.999008i \(-0.514176\pi\)
−0.0445209 + 0.999008i \(0.514176\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.85905e11 + 1.01482e12i −0.0645186 + 0.111749i −0.896480 0.443084i \(-0.853885\pi\)
0.831962 + 0.554833i \(0.187218\pi\)
\(228\) 0 0
\(229\) −7.12391e12 1.23390e13i −0.747521 1.29474i −0.949008 0.315253i \(-0.897911\pi\)
0.201487 0.979491i \(-0.435423\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.16183e12 + 1.24047e13i 0.683229 + 1.18339i 0.973990 + 0.226592i \(0.0727584\pi\)
−0.290760 + 0.956796i \(0.593908\pi\)
\(234\) 0 0
\(235\) −1.19692e11 + 2.07312e11i −0.0108941 + 0.0188691i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.00149e13 0.830728 0.415364 0.909655i \(-0.363654\pi\)
0.415364 + 0.909655i \(0.363654\pi\)
\(240\) 0 0
\(241\) 6.58907e12 1.14126e13i 0.522072 0.904255i −0.477598 0.878578i \(-0.658493\pi\)
0.999670 0.0256770i \(-0.00817415\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 7.31483e11 + 5.21963e12i 0.0529408 + 0.377769i
\(246\) 0 0
\(247\) 1.74655e12 + 3.02511e12i 0.120878 + 0.209367i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.25032e13 1.42574 0.712868 0.701298i \(-0.247396\pi\)
0.712868 + 0.701298i \(0.247396\pi\)
\(252\) 0 0
\(253\) 2.51226e13 1.52371
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.53000e12 + 1.13103e13i 0.363313 + 0.629276i 0.988504 0.151195i \(-0.0483123\pi\)
−0.625191 + 0.780472i \(0.714979\pi\)
\(258\) 0 0
\(259\) −5.01523e12 1.45746e13i −0.267388 0.777046i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.14385e13 + 1.98121e13i −0.560547 + 0.970897i 0.436901 + 0.899509i \(0.356076\pi\)
−0.997449 + 0.0713872i \(0.977257\pi\)
\(264\) 0 0
\(265\) −1.05530e12 −0.0496048
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.89726e12 1.19464e13i 0.298565 0.517130i −0.677243 0.735760i \(-0.736825\pi\)
0.975808 + 0.218630i \(0.0701586\pi\)
\(270\) 0 0
\(271\) −5.69926e11 9.87141e11i −0.0236858 0.0410250i 0.853940 0.520372i \(-0.174207\pi\)
−0.877625 + 0.479347i \(0.840873\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.09728e13 + 1.90054e13i 0.420715 + 0.728699i
\(276\) 0 0
\(277\) 2.28587e13 3.95924e13i 0.842195 1.45873i −0.0458392 0.998949i \(-0.514596\pi\)
0.888035 0.459777i \(-0.152070\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.91820e13 1.33414 0.667072 0.744994i \(-0.267548\pi\)
0.667072 + 0.744994i \(0.267548\pi\)
\(282\) 0 0
\(283\) −1.93169e12 + 3.34578e12i −0.0632574 + 0.109565i −0.895920 0.444216i \(-0.853482\pi\)
0.832662 + 0.553781i \(0.186816\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.68651e13 + 9.11921e12i 1.42069 + 0.276444i
\(288\) 0 0
\(289\) 1.70374e13 + 2.95096e13i 0.497123 + 0.861043i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 9.78633e12 0.264757 0.132379 0.991199i \(-0.457739\pi\)
0.132379 + 0.991199i \(0.457739\pi\)
\(294\) 0 0
\(295\) −1.94798e13 −0.507649
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.63126e13 + 4.55748e13i 0.636755 + 1.10289i
\(300\) 0 0
\(301\) 4.83639e13 + 9.41084e12i 1.12825 + 0.219539i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.61280e13 2.79346e13i 0.349890 0.606028i
\(306\) 0 0
\(307\) 9.68832e12 0.202762 0.101381 0.994848i \(-0.467674\pi\)
0.101381 + 0.994848i \(0.467674\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.64052e13 2.84146e13i 0.319741 0.553808i −0.660693 0.750656i \(-0.729737\pi\)
0.980434 + 0.196849i \(0.0630707\pi\)
\(312\) 0 0
\(313\) 4.65288e13 + 8.05902e13i 0.875443 + 1.51631i 0.856290 + 0.516496i \(0.172764\pi\)
0.0191533 + 0.999817i \(0.493903\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.88239e13 3.26039e13i −0.330281 0.572063i 0.652286 0.757973i \(-0.273810\pi\)
−0.982567 + 0.185910i \(0.940477\pi\)
\(318\) 0 0
\(319\) −4.34546e13 + 7.52656e13i −0.736524 + 1.27570i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.40778e12 −0.0222803
\(324\) 0 0
\(325\) −2.29851e13 + 3.98114e13i −0.351632 + 0.609044i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.29940e12 + 3.77613e12i 0.0185851 + 0.0540094i
\(330\) 0 0
\(331\) −5.00419e13 8.66751e13i −0.692276 1.19906i −0.971090 0.238713i \(-0.923275\pi\)
0.278814 0.960345i \(-0.410059\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4.60387e13 0.596179
\(336\) 0 0
\(337\) 8.73473e13 1.09467 0.547337 0.836912i \(-0.315642\pi\)
0.547337 + 0.836912i \(0.315642\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.23712e13 7.33890e13i −0.497647 0.861950i
\(342\) 0 0
\(343\) 7.37128e13 + 4.79314e13i 0.838350 + 0.545133i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.55238e13 6.15290e13i 0.379059 0.656550i −0.611866 0.790961i \(-0.709581\pi\)
0.990926 + 0.134411i \(0.0429142\pi\)
\(348\) 0 0
\(349\) −7.50390e13 −0.775796 −0.387898 0.921702i \(-0.626799\pi\)
−0.387898 + 0.921702i \(0.626799\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6.79326e12 1.17663e13i 0.0659655 0.114256i −0.831156 0.556039i \(-0.812321\pi\)
0.897122 + 0.441783i \(0.145654\pi\)
\(354\) 0 0
\(355\) 1.74679e13 + 3.02552e13i 0.164431 + 0.284803i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7.02740e13 + 1.21718e14i 0.621978 + 1.07730i 0.989117 + 0.147131i \(0.0470040\pi\)
−0.367139 + 0.930166i \(0.619663\pi\)
\(360\) 0 0
\(361\) 5.32195e13 9.21789e13i 0.456858 0.791301i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.94152e13 −0.318459
\(366\) 0 0
\(367\) −1.75641e13 + 3.04219e13i −0.137709 + 0.238519i −0.926629 0.375977i \(-0.877307\pi\)
0.788920 + 0.614496i \(0.210641\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.15524e13 + 1.32842e13i −0.0853326 + 0.0981251i
\(372\) 0 0
\(373\) 8.94455e13 + 1.54924e14i 0.641446 + 1.11102i 0.985110 + 0.171924i \(0.0549985\pi\)
−0.343664 + 0.939093i \(0.611668\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.82052e14 −1.23117
\(378\) 0 0
\(379\) −3.33296e13 −0.218935 −0.109467 0.993990i \(-0.534915\pi\)
−0.109467 + 0.993990i \(0.534915\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.37824e13 2.38718e13i −0.0854539 0.148010i 0.820131 0.572176i \(-0.193901\pi\)
−0.905585 + 0.424166i \(0.860567\pi\)
\(384\) 0 0
\(385\) −6.11964e13 1.19078e13i −0.368716 0.0717462i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.16390e14 2.01594e14i 0.662513 1.14751i −0.317440 0.948278i \(-0.602823\pi\)
0.979953 0.199228i \(-0.0638436\pi\)
\(390\) 0 0
\(391\) −2.12089e13 −0.117367
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.87584e13 6.71316e13i 0.202807 0.351272i
\(396\) 0 0
\(397\) 7.15857e13 + 1.23990e14i 0.364316 + 0.631014i 0.988666 0.150131i \(-0.0479694\pi\)
−0.624350 + 0.781145i \(0.714636\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.44586e14 + 2.50431e14i 0.696359 + 1.20613i 0.969721 + 0.244217i \(0.0785310\pi\)
−0.273362 + 0.961911i \(0.588136\pi\)
\(402\) 0 0
\(403\) 8.87564e13 1.53731e14i 0.415932 0.720415i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.82318e14 0.809206
\(408\) 0 0
\(409\) 4.66276e13 8.07613e13i 0.201449 0.348919i −0.747547 0.664209i \(-0.768768\pi\)
0.948995 + 0.315290i \(0.102102\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.13246e14 + 2.45214e14i −0.873283 + 1.00420i
\(414\) 0 0
\(415\) −3.24900e12 5.62742e12i −0.0129564 0.0224412i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.50519e14 1.70426 0.852130 0.523330i \(-0.175311\pi\)
0.852130 + 0.523330i \(0.175311\pi\)
\(420\) 0 0
\(421\) 1.82722e14 0.673347 0.336673 0.941621i \(-0.390698\pi\)
0.336673 + 0.941621i \(0.390698\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −9.26341e12 1.60447e13i −0.0324065 0.0561296i
\(426\) 0 0
\(427\) −1.75089e14 5.08821e14i −0.596907 1.73465i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7.13121e13 + 1.23516e14i −0.230961 + 0.400036i −0.958091 0.286463i \(-0.907520\pi\)
0.727130 + 0.686500i \(0.240854\pi\)
\(432\) 0 0
\(433\) −1.67830e14 −0.529892 −0.264946 0.964263i \(-0.585354\pi\)
−0.264946 + 0.964263i \(0.585354\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.57135e13 + 1.31140e14i −0.227261 + 0.393628i
\(438\) 0 0
\(439\) −2.55296e14 4.42186e14i −0.747291 1.29435i −0.949117 0.314925i \(-0.898021\pi\)
0.201826 0.979421i \(-0.435313\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.38404e14 2.39723e14i −0.385415 0.667559i 0.606411 0.795151i \(-0.292609\pi\)
−0.991827 + 0.127592i \(0.959275\pi\)
\(444\) 0 0
\(445\) −1.18967e14 + 2.06057e14i −0.323181 + 0.559766i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −7.18277e14 −1.85754 −0.928768 0.370661i \(-0.879131\pi\)
−0.928768 + 0.370661i \(0.879131\pi\)
\(450\) 0 0
\(451\) −2.82372e14 + 4.89083e14i −0.712609 + 1.23428i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4.24932e13 1.23488e14i −0.102154 0.296867i
\(456\) 0 0
\(457\) −2.69134e14 4.66153e14i −0.631581 1.09393i −0.987229 0.159310i \(-0.949073\pi\)
0.355648 0.934620i \(-0.384260\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3.08940e14 −0.691065 −0.345532 0.938407i \(-0.612302\pi\)
−0.345532 + 0.938407i \(0.612302\pi\)
\(462\) 0 0
\(463\) −3.55334e14 −0.776142 −0.388071 0.921630i \(-0.626858\pi\)
−0.388071 + 0.921630i \(0.626858\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.09007e14 1.88806e14i −0.227097 0.393344i 0.729849 0.683608i \(-0.239590\pi\)
−0.956947 + 0.290264i \(0.906257\pi\)
\(468\) 0 0
\(469\) 5.03986e14 5.79540e14i 1.02558 1.17932i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.91403e14 + 5.04724e14i −0.565923 + 0.980207i
\(474\) 0 0
\(475\) −1.32278e14 −0.250999
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3.15790e14 + 5.46965e14i −0.572207 + 0.991092i 0.424132 + 0.905601i \(0.360579\pi\)
−0.996339 + 0.0854915i \(0.972754\pi\)
\(480\) 0 0
\(481\) 1.90954e14 + 3.30741e14i 0.338166 + 0.585721i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.84020e13 + 1.53117e14i 0.149583 + 0.259085i
\(486\) 0 0
\(487\) −1.36327e14 + 2.36125e14i −0.225513 + 0.390600i −0.956473 0.291820i \(-0.905739\pi\)
0.730960 + 0.682420i \(0.239072\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.03331e15 −1.63411 −0.817055 0.576560i \(-0.804395\pi\)
−0.817055 + 0.576560i \(0.804395\pi\)
\(492\) 0 0
\(493\) 3.66850e13 6.35403e13i 0.0567324 0.0982633i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.72077e14 + 1.11317e14i 0.846241 + 0.164665i
\(498\) 0 0
\(499\) −1.89945e14 3.28995e14i −0.274837 0.476031i 0.695257 0.718761i \(-0.255291\pi\)
−0.970094 + 0.242730i \(0.921957\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.88084e14 −0.398928 −0.199464 0.979905i \(-0.563920\pi\)
−0.199464 + 0.979905i \(0.563920\pi\)
\(504\) 0 0
\(505\) −7.51465e13 −0.101814
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −7.02577e14 1.21690e15i −0.911478 1.57873i −0.811977 0.583690i \(-0.801608\pi\)
−0.0995016 0.995037i \(-0.531725\pi\)
\(510\) 0 0
\(511\) −4.31478e14 + 4.96162e14i −0.547828 + 0.629954i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.99251e14 3.45113e14i 0.242360 0.419780i
\(516\) 0 0
\(517\) −4.72368e13 −0.0562448
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8.31749e14 1.44063e15i 0.949259 1.64417i 0.202269 0.979330i \(-0.435168\pi\)
0.746990 0.664835i \(-0.231498\pi\)
\(522\) 0 0
\(523\) 5.23224e13 + 9.06250e13i 0.0584693 + 0.101272i 0.893778 0.448509i \(-0.148045\pi\)
−0.835309 + 0.549781i \(0.814711\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.57704e13 + 6.19561e13i 0.0383323 + 0.0663936i
\(528\) 0 0
\(529\) −6.64255e14 + 1.15052e15i −0.697154 + 1.20751i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.18299e15 −1.19119
\(534\) 0 0
\(535\) −3.51279e14 + 6.08434e14i −0.346503 + 0.600161i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −8.19814e14 + 6.39991e14i −0.776206 + 0.605948i
\(540\) 0 0
\(541\) 9.40174e13 + 1.62843e14i 0.0872215 + 0.151072i 0.906336 0.422558i \(-0.138868\pi\)
−0.819114 + 0.573630i \(0.805535\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.25660e14 0.111948
\(546\) 0 0
\(547\) 2.21322e15 1.93238 0.966192 0.257824i \(-0.0830056\pi\)
0.966192 + 0.257824i \(0.0830056\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.61923e14 4.53665e14i −0.219705 0.380541i
\(552\) 0 0
\(553\) −4.20770e14 1.22279e15i −0.345985 1.00545i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.08922e14 7.08274e14i 0.323174 0.559755i −0.657967 0.753047i \(-0.728583\pi\)
0.981141 + 0.193292i \(0.0619166\pi\)
\(558\) 0 0
\(559\) −1.22082e15 −0.945993
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.06151e15 1.83858e15i 0.790909 1.36989i −0.134495 0.990914i \(-0.542941\pi\)
0.925405 0.378981i \(-0.123725\pi\)
\(564\) 0 0
\(565\) −9.43014e13 1.63335e14i −0.0689051 0.119347i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.39692e14 7.61570e14i −0.309052 0.535294i 0.669103 0.743169i \(-0.266678\pi\)
−0.978155 + 0.207876i \(0.933345\pi\)
\(570\) 0 0
\(571\) 3.97661e14 6.88769e14i 0.274166 0.474870i −0.695758 0.718276i \(-0.744931\pi\)
0.969924 + 0.243406i \(0.0782648\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.99282e15 −1.32220
\(576\) 0 0
\(577\) −8.87379e14 + 1.53699e15i −0.577620 + 1.00047i 0.418132 + 0.908386i \(0.362685\pi\)
−0.995752 + 0.0920805i \(0.970648\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.06405e14 2.07048e13i −0.0666799 0.0129748i
\(582\) 0 0
\(583\) −1.04120e14 1.80341e14i −0.0640260 0.110896i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.91619e15 −1.13482 −0.567412 0.823434i \(-0.692055\pi\)
−0.567412 + 0.823434i \(0.692055\pi\)
\(588\) 0 0
\(589\) 5.10786e14 0.296896
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.37770e14 4.11829e14i −0.133154 0.230630i 0.791736 0.610863i \(-0.209177\pi\)
−0.924891 + 0.380233i \(0.875844\pi\)
\(594\) 0 0
\(595\) 5.16629e13 + 1.00528e13i 0.0284011 + 0.00552640i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.06635e15 + 1.84697e15i −0.565006 + 0.978618i 0.432044 + 0.901853i \(0.357793\pi\)
−0.997049 + 0.0767657i \(0.975541\pi\)
\(600\) 0 0
\(601\) 3.19165e12 0.00166037 0.000830187 1.00000i \(-0.499736\pi\)
0.000830187 1.00000i \(0.499736\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.15334e13 + 1.99765e13i −0.00578500 + 0.0100199i
\(606\) 0 0
\(607\) 6.33721e14 + 1.09764e15i 0.312148 + 0.540656i 0.978827 0.204689i \(-0.0656183\pi\)
−0.666679 + 0.745345i \(0.732285\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.94743e13 8.56919e13i −0.0235046 0.0407111i
\(612\) 0 0
\(613\) 5.75304e14 9.96455e14i 0.268451 0.464970i −0.700011 0.714132i \(-0.746822\pi\)
0.968462 + 0.249162i \(0.0801550\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.65065e14 0.0743169 0.0371584 0.999309i \(-0.488169\pi\)
0.0371584 + 0.999309i \(0.488169\pi\)
\(618\) 0 0
\(619\) −1.48618e15 + 2.57414e15i −0.657313 + 1.13850i 0.323995 + 0.946059i \(0.394974\pi\)
−0.981308 + 0.192441i \(0.938360\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.29153e15 + 3.75327e15i 0.551342 + 1.60223i
\(624\) 0 0
\(625\) −6.96942e14 1.20714e15i −0.292319 0.506310i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.53915e14 −0.0623309
\(630\) 0 0
\(631\) 4.28671e15 1.70594 0.852968 0.521964i \(-0.174800\pi\)
0.852968 + 0.521964i \(0.174800\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.24686e14 2.15962e14i −0.0479250 0.0830085i
\(636\) 0 0
\(637\) −2.01965e15 8.16914e14i −0.762973 0.308610i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.32146e15 2.28884e15i 0.482321 0.835404i −0.517473 0.855699i \(-0.673127\pi\)
0.999794 + 0.0202954i \(0.00646067\pi\)
\(642\) 0 0
\(643\) −2.07428e15 −0.744228 −0.372114 0.928187i \(-0.621367\pi\)
−0.372114 + 0.928187i \(0.621367\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.01990e15 1.76651e15i 0.353657 0.612552i −0.633230 0.773964i \(-0.718271\pi\)
0.986887 + 0.161412i \(0.0516047\pi\)
\(648\) 0 0
\(649\) −1.92195e15 3.32891e15i −0.655233 1.13490i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.93480e15 + 5.08322e15i 0.967289 + 1.67539i 0.703336 + 0.710858i \(0.251693\pi\)
0.263953 + 0.964536i \(0.414974\pi\)
\(654\) 0 0
\(655\) 8.10133e13 1.40319e14i 0.0262561 0.0454768i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.41751e15 −1.38455 −0.692274 0.721634i \(-0.743391\pi\)
−0.692274 + 0.721634i \(0.743391\pi\)
\(660\) 0 0
\(661\) −5.04436e13 + 8.73709e13i −0.0155488 + 0.0269314i −0.873695 0.486474i \(-0.838283\pi\)
0.858146 + 0.513405i \(0.171616\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.46590e14 2.83557e14i 0.0735286 0.0845514i
\(666\) 0 0
\(667\) −3.94600e15 6.83467e15i −1.15735 2.00459i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.36499e15 1.80644
\(672\) 0 0
\(673\) 2.37415e15 0.662866 0.331433 0.943479i \(-0.392468\pi\)
0.331433 + 0.943479i \(0.392468\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.65318e15 + 2.86340e15i 0.446769 + 0.773827i 0.998174 0.0604114i \(-0.0192412\pi\)
−0.551405 + 0.834238i \(0.685908\pi\)
\(678\) 0 0
\(679\) 2.89519e15 + 5.63357e14i 0.769826 + 0.149796i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.56905e15 + 2.71767e15i −0.403946 + 0.699654i −0.994198 0.107564i \(-0.965695\pi\)
0.590253 + 0.807219i \(0.299028\pi\)
\(684\) 0 0
\(685\) −9.18170e14 −0.232608
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.18103e14 3.77766e14i 0.0535127 0.0926867i
\(690\) 0 0
\(691\) 3.74263e15 + 6.48243e15i 0.903749 + 1.56534i 0.822588 + 0.568638i \(0.192529\pi\)
0.0811608 + 0.996701i \(0.474137\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.72251e14 + 8.17963e14i 0.110473 + 0.191345i
\(696\) 0 0
\(697\) 2.38383e14 4.12892e14i 0.0548903 0.0950727i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4.02232e15 0.897487 0.448743 0.893661i \(-0.351872\pi\)
0.448743 + 0.893661i \(0.351872\pi\)
\(702\) 0 0
\(703\) −5.49461e14 + 9.51695e14i −0.120693 + 0.209047i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.22630e14 + 9.45952e14i −0.175145 + 0.201401i
\(708\) 0 0
\(709\) −6.43811e14 1.11511e15i −0.134960 0.233757i 0.790622 0.612304i \(-0.209757\pi\)
−0.925582 + 0.378547i \(0.876424\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7.69524e15 1.56397
\(714\) 0 0
\(715\) 1.54475e15 0.309153
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 9.68896e14 + 1.67818e15i 0.188048 + 0.325708i 0.944599 0.328226i \(-0.106451\pi\)
−0.756552 + 0.653934i \(0.773117\pi\)
\(720\) 0 0
\(721\) −2.16312e15 6.28615e15i −0.413462 1.20155i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.44699e15 5.97036e15i 0.639118 1.10698i
\(726\) 0 0
\(727\) 8.16531e15 1.49119 0.745596 0.666398i \(-0.232165\pi\)
0.745596 + 0.666398i \(0.232165\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.46007e14 4.26096e14i 0.0435914 0.0755026i
\(732\) 0 0
\(733\) 4.09691e15 + 7.09605e15i 0.715129 + 1.23864i 0.962910 + 0.269824i \(0.0869655\pi\)
−0.247781 + 0.968816i \(0.579701\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.54234e15 + 7.86757e15i 0.769500 + 1.33281i
\(738\) 0 0
\(739\) −2.53817e14 + 4.39624e14i −0.0423620 + 0.0733731i −0.886429 0.462865i \(-0.846822\pi\)
0.844067 + 0.536238i \(0.180155\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7.56283e15 −1.22531 −0.612655 0.790350i \(-0.709899\pi\)
−0.612655 + 0.790350i \(0.709899\pi\)
\(744\) 0 0
\(745\) 4.99506e14 8.65169e14i 0.0797409 0.138115i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.81357e15 + 1.10825e16i 0.591128 + 1.71785i
\(750\) 0 0
\(751\) −1.98511e15 3.43832e15i −0.303226 0.525202i 0.673639 0.739061i \(-0.264730\pi\)
−0.976865 + 0.213858i \(0.931397\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.22450e15 −0.181657
\(756\) 0 0
\(757\) 5.28767e15 0.773103 0.386551 0.922268i \(-0.373666\pi\)
0.386551 + 0.922268i \(0.373666\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −7.14612e14 1.23774e15i −0.101497 0.175798i 0.810804 0.585317i \(-0.199030\pi\)
−0.912302 + 0.409519i \(0.865697\pi\)
\(762\) 0 0
\(763\) 1.37560e15 1.58182e15i 0.192579 0.221449i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.02597e15 6.97319e15i 0.547642 0.948543i
\(768\) 0 0
\(769\) −5.17246e15 −0.693589 −0.346795 0.937941i \(-0.612730\pi\)
−0.346795 + 0.937941i \(0.612730\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6.71899e15 1.16376e16i 0.875622 1.51662i 0.0195238 0.999809i \(-0.493785\pi\)
0.856098 0.516813i \(-0.172882\pi\)
\(774\) 0 0
\(775\) 3.36105e15 + 5.82151e15i 0.431833 + 0.747956i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.70201e15 2.94796e15i −0.212571 0.368185i
\(780\) 0 0
\(781\) −3.44688e15 + 5.97018e15i −0.424469 + 0.735202i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.39615e15 −0.406634