Properties

Label 252.12.k.d.109.7
Level $252$
Weight $12$
Character 252.109
Analytic conductor $193.622$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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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 109.7
Root \(10810.2 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 252.109
Dual form 252.12.k.d.37.7

$q$-expansion

\(f(q)\) \(=\) \(q+(5539.86 + 9595.32i) q^{5} +(-32020.8 + 30854.4i) q^{7} +O(q^{10})\) \(q+(5539.86 + 9595.32i) q^{5} +(-32020.8 + 30854.4i) q^{7} +(-451860. + 782645. i) q^{11} -761355. q^{13} +(-2.39149e6 + 4.14219e6i) q^{17} +(-2.25438e6 - 3.90470e6i) q^{19} +(2.38885e7 + 4.13761e7i) q^{23} +(-3.69661e7 + 6.40271e7i) q^{25} -1.65205e8 q^{29} +(-2.95464e7 + 5.11759e7i) q^{31} +(-4.73449e8 - 1.36321e8i) q^{35} +(1.08530e8 + 1.87980e8i) q^{37} +5.52269e8 q^{41} -1.04028e9 q^{43} +(6.93035e7 + 1.20037e8i) q^{47} +(7.33368e7 - 1.97597e9i) q^{49} +(-2.34318e9 + 4.05851e9i) q^{53} -1.00130e10 q^{55} +(4.49535e9 - 7.78617e9i) q^{59} +(-1.08443e8 - 1.87828e8i) q^{61} +(-4.21780e9 - 7.30545e9i) q^{65} +(-8.64085e9 + 1.49664e10i) q^{67} +5.28267e9 q^{71} +(-5.55061e9 + 9.61394e9i) q^{73} +(-9.67912e9 - 3.90028e10i) q^{77} +(2.14340e9 + 3.71248e9i) q^{79} +4.61200e10 q^{83} -5.29942e10 q^{85} +(8.53894e9 + 1.47899e10i) q^{89} +(2.43792e10 - 2.34912e10i) q^{91} +(2.49779e10 - 4.32631e10i) q^{95} +1.57413e11 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2156 q^{5} + 50512 q^{7} + O(q^{10}) \) \( 16 q + 2156 q^{5} + 50512 q^{7} + 222796 q^{11} + 2703176 q^{13} - 5114600 q^{17} + 6910556 q^{19} + 51387712 q^{23} - 191456372 q^{25} - 118854616 q^{29} + 164659160 q^{31} - 55239344 q^{35} + 75658364 q^{37} + 1815568608 q^{41} + 10754408 q^{43} + 1034359464 q^{47} + 4123496848 q^{49} + 665159988 q^{53} - 1264543896 q^{55} - 1040514580 q^{59} - 14391208024 q^{61} + 20938150200 q^{65} - 33307097284 q^{67} - 65848902896 q^{71} + 17709749204 q^{73} - 8594484604 q^{77} - 26626784032 q^{79} + 210306955048 q^{83} - 25867402032 q^{85} + 55951560072 q^{89} + 66078280292 q^{91} - 106810047392 q^{95} - 156216030712 q^{97} + O(q^{100}) \)

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
\(5\) 5539.86 + 9595.32i 0.792801 + 1.37317i 0.924226 + 0.381845i \(0.124711\pi\)
−0.131426 + 0.991326i \(0.541956\pi\)
\(6\) 0 0
\(7\) −32020.8 + 30854.4i −0.720100 + 0.693870i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −451860. + 782645.i −0.845949 + 1.46523i 0.0388451 + 0.999245i \(0.487632\pi\)
−0.884794 + 0.465982i \(0.845701\pi\)
\(12\) 0 0
\(13\) −761355. −0.568721 −0.284360 0.958717i \(-0.591781\pi\)
−0.284360 + 0.958717i \(0.591781\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.39149e6 + 4.14219e6i −0.408508 + 0.707556i −0.994723 0.102599i \(-0.967284\pi\)
0.586215 + 0.810155i \(0.300617\pi\)
\(18\) 0 0
\(19\) −2.25438e6 3.90470e6i −0.208873 0.361779i 0.742487 0.669861i \(-0.233646\pi\)
−0.951360 + 0.308082i \(0.900313\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.38885e7 + 4.13761e7i 0.773901 + 1.34044i 0.935410 + 0.353565i \(0.115031\pi\)
−0.161509 + 0.986871i \(0.551636\pi\)
\(24\) 0 0
\(25\) −3.69661e7 + 6.40271e7i −0.757065 + 1.31128i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.65205e8 −1.49567 −0.747833 0.663887i \(-0.768905\pi\)
−0.747833 + 0.663887i \(0.768905\pi\)
\(30\) 0 0
\(31\) −2.95464e7 + 5.11759e7i −0.185360 + 0.321053i −0.943698 0.330809i \(-0.892678\pi\)
0.758338 + 0.651862i \(0.226012\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.73449e8 1.36321e8i −1.52370 0.438720i
\(36\) 0 0
\(37\) 1.08530e8 + 1.87980e8i 0.257301 + 0.445658i 0.965518 0.260337i \(-0.0838335\pi\)
−0.708217 + 0.705995i \(0.750500\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.52269e8 0.744456 0.372228 0.928141i \(-0.378594\pi\)
0.372228 + 0.928141i \(0.378594\pi\)
\(42\) 0 0
\(43\) −1.04028e9 −1.07913 −0.539563 0.841945i \(-0.681411\pi\)
−0.539563 + 0.841945i \(0.681411\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.93035e7 + 1.20037e8i 0.0440775 + 0.0763445i 0.887222 0.461342i \(-0.152632\pi\)
−0.843145 + 0.537686i \(0.819298\pi\)
\(48\) 0 0
\(49\) 7.33368e7 1.97597e9i 0.0370889 0.999312i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.34318e9 + 4.05851e9i −0.769641 + 1.33306i 0.168117 + 0.985767i \(0.446232\pi\)
−0.937758 + 0.347290i \(0.887102\pi\)
\(54\) 0 0
\(55\) −1.00130e10 −2.68268
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.49535e9 7.78617e9i 0.818610 1.41787i −0.0880959 0.996112i \(-0.528078\pi\)
0.906706 0.421763i \(-0.138588\pi\)
\(60\) 0 0
\(61\) −1.08443e8 1.87828e8i −0.0164394 0.0284739i 0.857689 0.514169i \(-0.171900\pi\)
−0.874128 + 0.485695i \(0.838566\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.21780e9 7.30545e9i −0.450882 0.780951i
\(66\) 0 0
\(67\) −8.64085e9 + 1.49664e10i −0.781889 + 1.35427i 0.148952 + 0.988844i \(0.452410\pi\)
−0.930840 + 0.365426i \(0.880923\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.28267e9 0.347482 0.173741 0.984791i \(-0.444414\pi\)
0.173741 + 0.984791i \(0.444414\pi\)
\(72\) 0 0
\(73\) −5.55061e9 + 9.61394e9i −0.313375 + 0.542782i −0.979091 0.203424i \(-0.934793\pi\)
0.665715 + 0.746206i \(0.268127\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.67912e9 3.90028e10i −0.407509 1.64209i
\(78\) 0 0
\(79\) 2.14340e9 + 3.71248e9i 0.0783709 + 0.135742i 0.902547 0.430591i \(-0.141695\pi\)
−0.824176 + 0.566333i \(0.808361\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.61200e10 1.28517 0.642584 0.766216i \(-0.277863\pi\)
0.642584 + 0.766216i \(0.277863\pi\)
\(84\) 0 0
\(85\) −5.29942e10 −1.29546
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 8.53894e9 + 1.47899e10i 0.162091 + 0.280750i 0.935618 0.353013i \(-0.114843\pi\)
−0.773527 + 0.633763i \(0.781510\pi\)
\(90\) 0 0
\(91\) 2.43792e10 2.34912e10i 0.409536 0.394618i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.49779e10 4.32631e10i 0.331190 0.573637i
\(96\) 0 0
\(97\) 1.57413e11 1.86121 0.930605 0.366026i \(-0.119282\pi\)
0.930605 + 0.366026i \(0.119282\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.77841e10 1.34726e11i 0.736416 1.27551i −0.217683 0.976019i \(-0.569850\pi\)
0.954099 0.299490i \(-0.0968166\pi\)
\(102\) 0 0
\(103\) 6.88269e10 + 1.19212e11i 0.584997 + 1.01324i 0.994876 + 0.101105i \(0.0322377\pi\)
−0.409879 + 0.912140i \(0.634429\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.51994e10 + 1.64890e11i 0.656181 + 1.13654i 0.981596 + 0.190967i \(0.0611624\pi\)
−0.325416 + 0.945571i \(0.605504\pi\)
\(108\) 0 0
\(109\) −9.45648e10 + 1.63791e11i −0.588686 + 1.01963i 0.405719 + 0.913998i \(0.367021\pi\)
−0.994405 + 0.105636i \(0.966312\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.29301e11 0.660190 0.330095 0.943948i \(-0.392919\pi\)
0.330095 + 0.943948i \(0.392919\pi\)
\(114\) 0 0
\(115\) −2.64678e11 + 4.58436e11i −1.22710 + 2.12540i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −5.12273e10 2.06424e11i −0.196785 0.792962i
\(120\) 0 0
\(121\) −2.65699e11 4.60205e11i −0.931260 1.61299i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.78146e11 −0.815206
\(126\) 0 0
\(127\) 1.94863e10 0.0523369 0.0261685 0.999658i \(-0.491669\pi\)
0.0261685 + 0.999658i \(0.491669\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.37802e10 + 2.38680e10i 0.0312078 + 0.0540535i 0.881207 0.472730i \(-0.156731\pi\)
−0.850000 + 0.526783i \(0.823398\pi\)
\(132\) 0 0
\(133\) 1.92665e11 + 5.54741e10i 0.401437 + 0.115586i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.55036e11 + 2.68531e11i −0.274454 + 0.475369i −0.969997 0.243116i \(-0.921831\pi\)
0.695543 + 0.718485i \(0.255164\pi\)
\(138\) 0 0
\(139\) 5.28928e11 0.864600 0.432300 0.901730i \(-0.357702\pi\)
0.432300 + 0.901730i \(0.357702\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.44026e11 5.95871e11i 0.481109 0.833305i
\(144\) 0 0
\(145\) −9.15213e11 1.58520e12i −1.18576 2.05380i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2.21201e11 3.83131e11i −0.246753 0.427389i 0.715870 0.698234i \(-0.246030\pi\)
−0.962623 + 0.270845i \(0.912697\pi\)
\(150\) 0 0
\(151\) 8.75046e11 1.51562e12i 0.907105 1.57115i 0.0890393 0.996028i \(-0.471620\pi\)
0.818066 0.575124i \(-0.195046\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.54733e11 −0.587814
\(156\) 0 0
\(157\) −6.97856e11 + 1.20872e12i −0.583872 + 1.01130i 0.411143 + 0.911571i \(0.365130\pi\)
−0.995015 + 0.0997250i \(0.968204\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2.04156e12 5.87830e11i −1.48738 0.428262i
\(162\) 0 0
\(163\) 6.83315e11 + 1.18354e12i 0.465146 + 0.805656i 0.999208 0.0397888i \(-0.0126685\pi\)
−0.534062 + 0.845445i \(0.679335\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.20052e11 −0.369392 −0.184696 0.982796i \(-0.559130\pi\)
−0.184696 + 0.982796i \(0.559130\pi\)
\(168\) 0 0
\(169\) −1.21250e12 −0.676557
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.99102e11 + 6.91264e11i 0.195808 + 0.339149i 0.947165 0.320747i \(-0.103934\pi\)
−0.751357 + 0.659896i \(0.770600\pi\)
\(174\) 0 0
\(175\) −7.91836e11 3.19077e12i −0.364692 1.46955i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.98673e11 + 6.90522e11i −0.162153 + 0.280857i −0.935641 0.352954i \(-0.885177\pi\)
0.773488 + 0.633811i \(0.218510\pi\)
\(180\) 0 0
\(181\) 3.89173e12 1.48906 0.744528 0.667591i \(-0.232675\pi\)
0.744528 + 0.667591i \(0.232675\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.20249e12 + 2.08277e12i −0.407977 + 0.706636i
\(186\) 0 0
\(187\) −2.16124e12 3.74338e12i −0.691153 1.19711i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.64431e12 + 2.84803e12i 0.468059 + 0.810701i 0.999334 0.0364981i \(-0.0116203\pi\)
−0.531275 + 0.847199i \(0.678287\pi\)
\(192\) 0 0
\(193\) −1.74782e12 + 3.02731e12i −0.469819 + 0.813750i −0.999404 0.0345062i \(-0.989014\pi\)
0.529586 + 0.848257i \(0.322347\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5.58940e12 −1.34215 −0.671074 0.741390i \(-0.734167\pi\)
−0.671074 + 0.741390i \(0.734167\pi\)
\(198\) 0 0
\(199\) 2.69940e12 4.67549e12i 0.613162 1.06203i −0.377542 0.925992i \(-0.623231\pi\)
0.990704 0.136035i \(-0.0434359\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.29000e12 5.09731e12i 1.07703 1.03780i
\(204\) 0 0
\(205\) 3.05949e12 + 5.29920e12i 0.590205 + 1.02227i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.07466e12 0.706785
\(210\) 0 0
\(211\) 8.02377e12 1.32076 0.660381 0.750930i \(-0.270395\pi\)
0.660381 + 0.750930i \(0.270395\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −5.76299e12 9.98179e12i −0.855532 1.48182i
\(216\) 0 0
\(217\) −6.32903e11 2.55033e12i −0.0892912 0.359806i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.82078e12 3.15368e12i 0.232327 0.402402i
\(222\) 0 0
\(223\) 2.85492e10 0.00346671 0.00173336 0.999998i \(-0.499448\pi\)
0.00173336 + 0.999998i \(0.499448\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.93582e12 1.20132e13i 0.763757 1.32287i −0.177144 0.984185i \(-0.556686\pi\)
0.940901 0.338682i \(-0.109981\pi\)
\(228\) 0 0
\(229\) −2.91500e12 5.04892e12i −0.305874 0.529790i 0.671581 0.740931i \(-0.265615\pi\)
−0.977456 + 0.211141i \(0.932282\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.68712e12 1.33145e13i −0.733341 1.27018i −0.955447 0.295161i \(-0.904627\pi\)
0.222107 0.975022i \(-0.428707\pi\)
\(234\) 0 0
\(235\) −7.67864e11 + 1.32998e12i −0.0698893 + 0.121052i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.72983e13 −1.43488 −0.717438 0.696622i \(-0.754686\pi\)
−0.717438 + 0.696622i \(0.754686\pi\)
\(240\) 0 0
\(241\) 1.79662e12 3.11184e12i 0.142352 0.246560i −0.786030 0.618188i \(-0.787867\pi\)
0.928382 + 0.371628i \(0.121200\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.93663e13 1.02429e13i 1.40163 0.741326i
\(246\) 0 0
\(247\) 1.71639e12 + 2.97287e12i 0.118791 + 0.205751i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.07857e12 0.131692 0.0658461 0.997830i \(-0.479025\pi\)
0.0658461 + 0.997830i \(0.479025\pi\)
\(252\) 0 0
\(253\) −4.31770e13 −2.61872
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4.77704e12 8.27408e12i −0.265783 0.460350i 0.701986 0.712191i \(-0.252297\pi\)
−0.967768 + 0.251842i \(0.918964\pi\)
\(258\) 0 0
\(259\) −9.27524e12 2.67063e12i −0.494511 0.142385i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.62484e13 2.81431e13i 0.796259 1.37916i −0.125777 0.992059i \(-0.540142\pi\)
0.922036 0.387103i \(-0.126524\pi\)
\(264\) 0 0
\(265\) −5.19236e13 −2.44069
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5.57863e12 + 9.66247e12i −0.241485 + 0.418264i −0.961137 0.276070i \(-0.910968\pi\)
0.719653 + 0.694334i \(0.244301\pi\)
\(270\) 0 0
\(271\) −6.81340e12 1.18012e13i −0.283161 0.490449i 0.689001 0.724761i \(-0.258050\pi\)
−0.972161 + 0.234312i \(0.924716\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.34070e13 5.78626e13i −1.28088 2.21855i
\(276\) 0 0
\(277\) 1.14769e13 1.98786e13i 0.422850 0.732397i −0.573367 0.819298i \(-0.694363\pi\)
0.996217 + 0.0869014i \(0.0276965\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.32538e13 0.451291 0.225645 0.974210i \(-0.427551\pi\)
0.225645 + 0.974210i \(0.427551\pi\)
\(282\) 0 0
\(283\) −2.36242e13 + 4.09183e13i −0.773627 + 1.33996i 0.161935 + 0.986801i \(0.448226\pi\)
−0.935563 + 0.353161i \(0.885107\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.76841e13 + 1.70399e13i −0.536083 + 0.516556i
\(288\) 0 0
\(289\) 5.69746e12 + 9.86829e12i 0.166243 + 0.287941i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.50335e13 −1.21833 −0.609164 0.793045i \(-0.708495\pi\)
−0.609164 + 0.793045i \(0.708495\pi\)
\(294\) 0 0
\(295\) 9.96144e13 2.59598
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.81876e13 3.15019e13i −0.440134 0.762334i
\(300\) 0 0
\(301\) 3.33105e13 3.20971e13i 0.777079 0.748773i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.20152e12 2.08109e12i 0.0260664 0.0451483i
\(306\) 0 0
\(307\) −8.11886e13 −1.69916 −0.849580 0.527460i \(-0.823144\pi\)
−0.849580 + 0.527460i \(0.823144\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.56233e13 7.90218e13i 0.889210 1.54016i 0.0483988 0.998828i \(-0.484588\pi\)
0.840811 0.541329i \(-0.182078\pi\)
\(312\) 0 0
\(313\) −1.75443e13 3.03876e13i −0.330097 0.571745i 0.652433 0.757846i \(-0.273748\pi\)
−0.982531 + 0.186101i \(0.940415\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.71054e13 + 6.42684e13i 0.651045 + 1.12764i 0.982870 + 0.184301i \(0.0590022\pi\)
−0.331825 + 0.943341i \(0.607664\pi\)
\(318\) 0 0
\(319\) 7.46496e13 1.29297e14i 1.26526 2.19149i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.15654e13 0.341305
\(324\) 0 0
\(325\) 2.81443e13 4.87474e13i 0.430559 0.745750i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5.92283e12 1.70537e12i −0.0847133 0.0243916i
\(330\) 0 0
\(331\) −5.12968e12 8.88487e12i −0.0709637 0.122913i 0.828360 0.560196i \(-0.189274\pi\)
−0.899324 + 0.437283i \(0.855941\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.91476e14 −2.47953
\(336\) 0 0
\(337\) 5.27820e13 0.661487 0.330743 0.943721i \(-0.392701\pi\)
0.330743 + 0.943721i \(0.392701\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.67017e13 4.62487e13i −0.313610 0.543189i
\(342\) 0 0
\(343\) 5.86190e13 + 6.55348e13i 0.666685 + 0.745340i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.11874e13 1.05980e14i 0.652905 1.13086i −0.329510 0.944152i \(-0.606884\pi\)
0.982415 0.186712i \(-0.0597831\pi\)
\(348\) 0 0
\(349\) 2.45906e13 0.254232 0.127116 0.991888i \(-0.459428\pi\)
0.127116 + 0.991888i \(0.459428\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.31490e13 + 4.00952e13i −0.224787 + 0.389343i −0.956256 0.292533i \(-0.905502\pi\)
0.731468 + 0.681875i \(0.238835\pi\)
\(354\) 0 0
\(355\) 2.92653e13 + 5.06889e13i 0.275484 + 0.477153i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.74265e13 + 1.68748e14i 0.862298 + 1.49354i 0.869705 + 0.493572i \(0.164309\pi\)
−0.00740641 + 0.999973i \(0.502358\pi\)
\(360\) 0 0
\(361\) 4.80807e13 8.32781e13i 0.412744 0.714893i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.22998e14 −0.993777
\(366\) 0 0
\(367\) −7.70186e13 + 1.33400e14i −0.603854 + 1.04591i 0.388377 + 0.921501i \(0.373036\pi\)
−0.992231 + 0.124406i \(0.960298\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.01923e13 2.02254e14i −0.370750 1.49397i
\(372\) 0 0
\(373\) −7.42105e13 1.28536e14i −0.532190 0.921780i −0.999294 0.0375776i \(-0.988036\pi\)
0.467104 0.884203i \(-0.345297\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.25780e14 0.850616
\(378\) 0 0
\(379\) −2.63905e14 −1.73353 −0.866766 0.498715i \(-0.833805\pi\)
−0.866766 + 0.498715i \(0.833805\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.31627e13 4.01190e13i −0.143614 0.248746i 0.785241 0.619190i \(-0.212539\pi\)
−0.928855 + 0.370444i \(0.879206\pi\)
\(384\) 0 0
\(385\) 3.20623e14 3.08944e14i 1.93180 1.86143i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.12486e12 5.41242e12i 0.0177872 0.0308084i −0.856995 0.515325i \(-0.827671\pi\)
0.874782 + 0.484517i \(0.161005\pi\)
\(390\) 0 0
\(391\) −2.28517e14 −1.26458
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.37483e13 + 4.11333e13i −0.124265 + 0.215233i
\(396\) 0 0
\(397\) −4.83142e13 8.36827e13i −0.245882 0.425880i 0.716497 0.697590i \(-0.245744\pi\)
−0.962379 + 0.271710i \(0.912411\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.00607e13 + 1.04028e14i 0.289265 + 0.501022i 0.973635 0.228113i \(-0.0732556\pi\)
−0.684369 + 0.729136i \(0.739922\pi\)
\(402\) 0 0
\(403\) 2.24953e13 3.89631e13i 0.105418 0.182589i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.96162e14 −0.870654
\(408\) 0 0
\(409\) −1.06240e14 + 1.84013e14i −0.458998 + 0.795007i −0.998908 0.0467150i \(-0.985125\pi\)
0.539911 + 0.841722i \(0.318458\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 9.62931e13 + 3.88021e14i 0.394339 + 1.58902i
\(414\) 0 0
\(415\) 2.55498e14 + 4.42536e14i 1.01888 + 1.76475i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7.70399e13 −0.291433 −0.145716 0.989326i \(-0.546549\pi\)
−0.145716 + 0.989326i \(0.546549\pi\)
\(420\) 0 0
\(421\) −3.49104e14 −1.28648 −0.643241 0.765664i \(-0.722411\pi\)
−0.643241 + 0.765664i \(0.722411\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.76808e14 3.06241e14i −0.618534 1.07133i
\(426\) 0 0
\(427\) 9.26776e12 + 2.66848e12i 0.0315952 + 0.00909726i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.54794e13 6.14522e13i 0.114908 0.199027i −0.802835 0.596202i \(-0.796676\pi\)
0.917743 + 0.397174i \(0.130009\pi\)
\(432\) 0 0
\(433\) −5.57341e14 −1.75969 −0.879847 0.475256i \(-0.842355\pi\)
−0.879847 + 0.475256i \(0.842355\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.07708e14 1.86555e14i 0.323295 0.559963i
\(438\) 0 0
\(439\) 1.90654e14 + 3.30223e14i 0.558074 + 0.966613i 0.997657 + 0.0684109i \(0.0217929\pi\)
−0.439583 + 0.898202i \(0.644874\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.88095e13 1.19182e14i −0.191614 0.331886i 0.754171 0.656678i \(-0.228039\pi\)
−0.945785 + 0.324792i \(0.894706\pi\)
\(444\) 0 0
\(445\) −9.46091e13 + 1.63868e14i −0.257012 + 0.445157i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.91960e14 0.496429 0.248214 0.968705i \(-0.420156\pi\)
0.248214 + 0.968705i \(0.420156\pi\)
\(450\) 0 0
\(451\) −2.49548e14 + 4.32230e14i −0.629772 + 1.09080i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.60463e14 + 1.03789e14i 0.866558 + 0.249509i
\(456\) 0 0
\(457\) 3.61232e14 + 6.25673e14i 0.847711 + 1.46828i 0.883246 + 0.468910i \(0.155353\pi\)
−0.0355355 + 0.999368i \(0.511314\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.28898e14 0.959398 0.479699 0.877433i \(-0.340746\pi\)
0.479699 + 0.877433i \(0.340746\pi\)
\(462\) 0 0
\(463\) 6.20134e14 1.35453 0.677267 0.735737i \(-0.263164\pi\)
0.677267 + 0.735737i \(0.263164\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.53364e14 + 6.12045e14i 0.736173 + 1.27509i 0.954207 + 0.299148i \(0.0967025\pi\)
−0.218033 + 0.975941i \(0.569964\pi\)
\(468\) 0 0
\(469\) −1.85092e14 7.45844e14i −0.376650 1.51774i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.70059e14 8.14167e14i 0.912886 1.58116i
\(474\) 0 0
\(475\) 3.33343e14 0.632523
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.76957e13 + 1.34573e14i −0.140783 + 0.243844i −0.927792 0.373098i \(-0.878295\pi\)
0.787008 + 0.616942i \(0.211629\pi\)
\(480\) 0 0
\(481\) −8.26301e13 1.43120e14i −0.146332 0.253455i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.72045e14 + 1.51043e15i 1.47557 + 2.55576i
\(486\) 0 0
\(487\) −1.67311e14 + 2.89791e14i −0.276767 + 0.479375i −0.970579 0.240781i \(-0.922596\pi\)
0.693812 + 0.720156i \(0.255930\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.46129e14 −0.863668 −0.431834 0.901953i \(-0.642133\pi\)
−0.431834 + 0.901953i \(0.642133\pi\)
\(492\) 0 0
\(493\) 3.95087e14 6.84311e14i 0.610991 1.05827i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.69155e14 + 1.62994e14i −0.250222 + 0.241108i
\(498\) 0 0
\(499\) 3.26652e14 + 5.65778e14i 0.472642 + 0.818640i 0.999510 0.0313069i \(-0.00996694\pi\)
−0.526868 + 0.849947i \(0.676634\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1.29756e15 1.79682 0.898409 0.439161i \(-0.144724\pi\)
0.898409 + 0.439161i \(0.144724\pi\)
\(504\) 0 0
\(505\) 1.72365e15 2.33532
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.20168e14 9.00957e14i −0.674832 1.16884i −0.976518 0.215436i \(-0.930883\pi\)
0.301686 0.953407i \(-0.402451\pi\)
\(510\) 0 0
\(511\) −1.18897e14 4.79107e14i −0.150959 0.608300i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7.62583e14 + 1.32083e15i −0.927572 + 1.60660i
\(516\) 0 0
\(517\) −1.25262e14 −0.149149
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −8.26924e14 + 1.43227e15i −0.943752 + 1.63463i −0.185522 + 0.982640i \(0.559397\pi\)
−0.758231 + 0.651986i \(0.773936\pi\)
\(522\) 0 0
\(523\) −2.37190e14 4.10824e14i −0.265055 0.459089i 0.702523 0.711661i \(-0.252057\pi\)
−0.967578 + 0.252572i \(0.918724\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.41320e14 2.44774e14i −0.151442 0.262305i
\(528\) 0 0
\(529\) −6.64915e14 + 1.15167e15i −0.697847 + 1.20871i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.20473e14 −0.423388
\(534\) 0 0
\(535\) −1.05478e15 + 1.82694e15i −1.04044 + 1.80210i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.51334e15 + 9.50257e14i 1.43284 + 0.899711i
\(540\) 0 0
\(541\) −2.57042e14 4.45210e14i −0.238462 0.413028i 0.721811 0.692090i \(-0.243310\pi\)
−0.960273 + 0.279062i \(0.909977\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.09550e15 −1.86684
\(546\) 0 0
\(547\) 4.36242e14 0.380888 0.190444 0.981698i \(-0.439007\pi\)
0.190444 + 0.981698i \(0.439007\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.72435e14 + 6.45077e14i 0.312404 + 0.541100i
\(552\) 0 0
\(553\) −1.83180e14 5.27433e13i −0.150623 0.0433689i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.08792e15 + 1.88434e15i −0.859795 + 1.48921i 0.0123289 + 0.999924i \(0.496075\pi\)
−0.872124 + 0.489285i \(0.837258\pi\)
\(558\) 0 0
\(559\) 7.92020e14 0.613721
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.45391e14 7.71439e14i 0.331852 0.574785i −0.651023 0.759058i \(-0.725660\pi\)
0.982875 + 0.184273i \(0.0589931\pi\)
\(564\) 0 0
\(565\) 7.16307e14 + 1.24068e15i 0.523399 + 0.906554i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.25020e15 + 2.16542e15i 0.878747 + 1.52203i 0.852717 + 0.522372i \(0.174953\pi\)
0.0260291 + 0.999661i \(0.491714\pi\)
\(570\) 0 0
\(571\) 1.20063e15 2.07955e15i 0.827773 1.43374i −0.0720088 0.997404i \(-0.522941\pi\)
0.899782 0.436341i \(-0.143726\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.53226e15 −2.34358
\(576\) 0 0
\(577\) −8.01843e14 + 1.38883e15i −0.521942 + 0.904031i 0.477732 + 0.878506i \(0.341459\pi\)
−0.999674 + 0.0255249i \(0.991874\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.47680e15 + 1.42301e15i −0.925449 + 0.891739i
\(582\) 0 0
\(583\) −2.11758e15 3.66775e15i −1.30215 2.25540i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.58598e15 1.53150 0.765749 0.643140i \(-0.222369\pi\)
0.765749 + 0.643140i \(0.222369\pi\)
\(588\) 0 0
\(589\) 2.66436e14 0.154867
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.43649e14 + 1.28804e15i 0.416454 + 0.721320i 0.995580 0.0939186i \(-0.0299394\pi\)
−0.579126 + 0.815238i \(0.696606\pi\)
\(594\) 0 0
\(595\) 1.69692e15 1.63510e15i 0.932861 0.898881i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.28520e14 9.15423e14i 0.280036 0.485036i −0.691357 0.722513i \(-0.742987\pi\)
0.971393 + 0.237477i \(0.0763203\pi\)
\(600\) 0 0
\(601\) −2.15911e15 −1.12322 −0.561610 0.827402i \(-0.689818\pi\)
−0.561610 + 0.827402i \(0.689818\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.94388e15 5.09894e15i 1.47661 2.55756i
\(606\) 0 0
\(607\) −9.50659e14 1.64659e15i −0.468260 0.811050i 0.531082 0.847320i \(-0.321786\pi\)
−0.999342 + 0.0362702i \(0.988452\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.27646e13 9.13909e13i −0.0250678 0.0434187i
\(612\) 0 0
\(613\) −4.85740e14 + 8.41326e14i −0.226658 + 0.392583i −0.956816 0.290696i \(-0.906113\pi\)
0.730158 + 0.683279i \(0.239447\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.39104e15 0.626282 0.313141 0.949707i \(-0.398619\pi\)
0.313141 + 0.949707i \(0.398619\pi\)
\(618\) 0 0
\(619\) −1.56881e15 + 2.71726e15i −0.693859 + 1.20180i 0.276705 + 0.960955i \(0.410758\pi\)
−0.970564 + 0.240844i \(0.922576\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.29757e14 2.10120e14i −0.311526 0.0896979i
\(624\) 0 0
\(625\) 2.64095e14 + 4.57426e14i 0.110769 + 0.191858i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.03820e15 −0.420438
\(630\) 0 0
\(631\) 4.42265e15 1.76003 0.880017 0.474942i \(-0.157531\pi\)
0.880017 + 0.474942i \(0.157531\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.07951e14 + 1.86977e14i 0.0414927 + 0.0718675i
\(636\) 0 0
\(637\) −5.58354e13 + 1.50441e15i −0.0210932 + 0.568329i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.94254e14 8.56073e14i 0.180398 0.312458i −0.761618 0.648026i \(-0.775595\pi\)
0.942016 + 0.335568i \(0.108928\pi\)
\(642\) 0 0
\(643\) 2.69033e15 0.965262 0.482631 0.875824i \(-0.339681\pi\)
0.482631 + 0.875824i \(0.339681\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.47451e15 2.55393e15i 0.511299 0.885595i −0.488616 0.872499i \(-0.662498\pi\)
0.999914 0.0130960i \(-0.00416870\pi\)
\(648\) 0 0
\(649\) 4.06254e15 + 7.03652e15i 1.38501 + 2.39890i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.17965e15 2.04321e15i −0.388803 0.673427i 0.603486 0.797374i \(-0.293778\pi\)
−0.992289 + 0.123947i \(0.960445\pi\)
\(654\) 0 0
\(655\) −1.52681e14 + 2.64451e14i −0.0494831 + 0.0857072i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.40458e14 0.138050 0.0690248 0.997615i \(-0.478011\pi\)
0.0690248 + 0.997615i \(0.478011\pi\)
\(660\) 0 0
\(661\) 7.68645e14 1.33133e15i 0.236929 0.410373i −0.722903 0.690950i \(-0.757193\pi\)
0.959831 + 0.280577i \(0.0905259\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.35043e14 + 2.15600e15i 0.159540 + 0.642879i
\(666\) 0 0
\(667\) −3.94650e15 6.83554e15i −1.15750 2.00484i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.96004e14 0.0556277
\(672\) 0 0
\(673\) −3.83410e14 −0.107048 −0.0535242 0.998567i \(-0.517045\pi\)
−0.0535242 + 0.998567i \(0.517045\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.52818e15 2.64688e15i −0.412986 0.715313i 0.582228 0.813025i \(-0.302181\pi\)
−0.995215 + 0.0977120i \(0.968848\pi\)
\(678\) 0 0
\(679\) −5.04048e15 + 4.85688e15i −1.34026 + 1.29144i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.24318e15 2.15324e15i 0.320051 0.554344i −0.660447 0.750872i \(-0.729633\pi\)
0.980498 + 0.196528i \(0.0629667\pi\)
\(684\) 0 0
\(685\) −3.43552e15 −0.870350
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.78399e15 3.08997e15i 0.437711 0.758137i
\(690\) 0 0
\(691\) 1.75214e15 + 3.03479e15i 0.423096 + 0.732823i 0.996240 0.0866310i \(-0.0276101\pi\)
−0.573145 + 0.819454i \(0.694277\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.93019e15 + 5.07523e15i 0.685455 + 1.18724i
\(696\) 0 0
\(697\) −1.32075e15 + 2.28760e15i −0.304116 + 0.526745i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −5.93387e15 −1.32400 −0.662001 0.749503i \(-0.730293\pi\)
−0.662001 + 0.749503i \(0.730293\pi\)
\(702\) 0 0
\(703\) 4.89337e14 8.47557e14i 0.107487 0.186172i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.66618e15 + 6.71402e15i 0.354745 + 1.42947i
\(708\) 0 0
\(709\) −2.66852e15 4.62202e15i −0.559393 0.968896i −0.997547 0.0699967i \(-0.977701\pi\)
0.438155 0.898900i \(-0.355632\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.82328e15 −0.573801
\(714\) 0 0
\(715\) 7.62343e15 1.52569
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.51335e15 2.62120e15i −0.293718 0.508735i 0.680968 0.732313i \(-0.261559\pi\)
−0.974686 + 0.223579i \(0.928226\pi\)
\(720\) 0 0
\(721\) −5.88210e15 1.69364e15i −1.12432 0.323726i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.10699e15 1.05776e16i 1.13232 1.96123i
\(726\) 0 0
\(727\) −1.66738e15 −0.304506 −0.152253 0.988342i \(-0.548653\pi\)
−0.152253 + 0.988342i \(0.548653\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.48781e15 4.30902e15i 0.440831 0.763542i
\(732\) 0 0
\(733\) −2.19667e15 3.80474e15i −0.383436 0.664130i 0.608115 0.793849i \(-0.291926\pi\)
−0.991551 + 0.129719i \(0.958593\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.80891e15 1.35254e16i −1.32288 2.29129i
\(738\) 0 0
\(739\) −9.77656e14 + 1.69335e15i −0.163170 + 0.282620i −0.936004 0.351989i \(-0.885505\pi\)
0.772834 + 0.634609i \(0.218839\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7.66464e15 −1.24180 −0.620902 0.783888i \(-0.713234\pi\)
−0.620902 + 0.783888i \(0.713234\pi\)
\(744\) 0 0
\(745\) 2.45085e15 4.24499e15i 0.391252 0.677668i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8.13595e15 2.34259e15i −1.26113 0.363117i
\(750\) 0 0
\(751\) −4.89846e15 8.48439e15i −0.748239 1.29599i −0.948666 0.316279i \(-0.897566\pi\)
0.200427 0.979709i \(-0.435767\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.93905e16 2.87661
\(756\) 0 0
\(757\) 1.58148e15 0.231226 0.115613 0.993294i \(-0.463117\pi\)
0.115613 + 0.993294i \(0.463117\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.93379e15 6.81352e15i −0.558722 0.967734i −0.997604 0.0691896i \(-0.977959\pi\)
0.438882 0.898545i \(-0.355375\pi\)
\(762\) 0 0
\(763\) −2.02564e15 8.16246e15i −0.283580 1.14271i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.42256e15 + 5.92804e15i −0.465561 + 0.806375i
\(768\) 0 0
\(769\) 6.27927e15 0.842005 0.421002 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.66695e15 + 2.88725e15i −0.217238 + 0.376268i −0.953963 0.299925i \(-0.903038\pi\)
0.736724 + 0.676193i \(0.236372\pi\)
\(774\) 0 0
\(775\) −2.18443e15 3.78355e15i −0.280659 0.486116i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.24503e15 2.15645e15i −0.155497 0.269329i
\(780\) 0 0
\(781\) −2.38703e15 + 4.13446e15i −0.293952 + 0.509140i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.54641e16