Properties

Label 1900.2.i.c.501.1
Level $1900$
Weight $2$
Character 1900.501
Analytic conductor $15.172$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1783323.2
Defining polynomial: \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 501.1
Root \(0.356769 - 0.617942i\) of defining polynomial
Character \(\chi\) \(=\) 1900.501
Dual form 1900.2.i.c.201.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.60220 - 2.77509i) q^{3} +2.20440 q^{7} +(-3.63409 + 6.29444i) q^{9} +O(q^{10})\) \(q+(-1.60220 - 2.77509i) q^{3} +2.20440 q^{7} +(-3.63409 + 6.29444i) q^{9} -1.20440 q^{11} +(-0.500000 + 0.866025i) q^{13} +(-1.07031 - 1.85383i) q^{17} +(4.30660 - 0.673184i) q^{19} +(-3.53189 - 6.11742i) q^{21} +(-4.63409 + 8.02649i) q^{23} +13.6770 q^{27} +(-4.16599 + 7.21570i) q^{29} +8.26819 q^{31} +(1.92969 + 3.34233i) q^{33} +2.20440 q^{37} +3.20440 q^{39} +(3.30660 + 5.72720i) q^{41} +(1.17251 + 2.03084i) q^{43} +(-4.16599 + 7.21570i) q^{47} -2.14061 q^{49} +(-3.42969 + 5.94040i) q^{51} +(0.134095 - 0.232259i) q^{53} +(-8.76819 - 10.8726i) q^{57} +(4.16599 + 7.21570i) q^{59} +(1.70440 - 2.95211i) q^{61} +(-8.01100 + 13.8755i) q^{63} +(-1.06379 + 1.84253i) q^{67} +29.6990 q^{69} +(5.23630 + 9.06953i) q^{71} +(-2.42969 - 4.20835i) q^{73} -2.65498 q^{77} +(-8.20440 - 14.2104i) q^{79} +(-11.0110 - 19.0716i) q^{81} +5.73181 q^{83} +26.6990 q^{87} +(5.40880 - 9.36832i) q^{89} +(-1.10220 + 1.90907i) q^{91} +(-13.2473 - 22.9450i) q^{93} +(7.87039 + 13.6319i) q^{97} +(4.37691 - 7.58103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{3} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{3} - 4 q^{7} - 8 q^{9} + 10 q^{11} - 3 q^{13} - 3 q^{17} - 16 q^{21} - 14 q^{23} + 20 q^{27} - 6 q^{29} + 22 q^{31} + 15 q^{33} - 4 q^{37} + 2 q^{39} - 6 q^{41} - 5 q^{43} - 6 q^{47} - 6 q^{49} - 24 q^{51} - 13 q^{53} - 25 q^{57} + 6 q^{59} - 7 q^{61} - 5 q^{63} + 4 q^{67} + 30 q^{69} + 9 q^{71} - 18 q^{73} - 40 q^{77} - 32 q^{79} - 23 q^{81} + 62 q^{83} + 12 q^{87} - 2 q^{89} + 2 q^{91} - 14 q^{93} + 11 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −1.60220 2.77509i −0.925031 1.60220i −0.791511 0.611155i \(-0.790705\pi\)
−0.133520 0.991046i \(-0.542628\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.20440 0.833185 0.416593 0.909093i \(-0.363224\pi\)
0.416593 + 0.909093i \(0.363224\pi\)
\(8\) 0 0
\(9\) −3.63409 + 6.29444i −1.21136 + 2.09815i
\(10\) 0 0
\(11\) −1.20440 −0.363141 −0.181570 0.983378i \(-0.558118\pi\)
−0.181570 + 0.983378i \(0.558118\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.07031 1.85383i −0.259588 0.449619i 0.706544 0.707669i \(-0.250253\pi\)
−0.966131 + 0.258050i \(0.916920\pi\)
\(18\) 0 0
\(19\) 4.30660 0.673184i 0.988002 0.154439i
\(20\) 0 0
\(21\) −3.53189 6.11742i −0.770722 1.33493i
\(22\) 0 0
\(23\) −4.63409 + 8.02649i −0.966276 + 1.67364i −0.260127 + 0.965574i \(0.583765\pi\)
−0.706148 + 0.708064i \(0.749569\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 13.6770 2.63214
\(28\) 0 0
\(29\) −4.16599 + 7.21570i −0.773605 + 1.33992i 0.161971 + 0.986796i \(0.448215\pi\)
−0.935575 + 0.353127i \(0.885118\pi\)
\(30\) 0 0
\(31\) 8.26819 1.48501 0.742505 0.669840i \(-0.233637\pi\)
0.742505 + 0.669840i \(0.233637\pi\)
\(32\) 0 0
\(33\) 1.92969 + 3.34233i 0.335916 + 0.581824i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.20440 0.362401 0.181201 0.983446i \(-0.442002\pi\)
0.181201 + 0.983446i \(0.442002\pi\)
\(38\) 0 0
\(39\) 3.20440 0.513115
\(40\) 0 0
\(41\) 3.30660 + 5.72720i 0.516405 + 0.894439i 0.999819 + 0.0190471i \(0.00606323\pi\)
−0.483414 + 0.875392i \(0.660603\pi\)
\(42\) 0 0
\(43\) 1.17251 + 2.03084i 0.178806 + 0.309701i 0.941472 0.337092i \(-0.109443\pi\)
−0.762666 + 0.646793i \(0.776110\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.16599 + 7.21570i −0.607672 + 1.05252i 0.383951 + 0.923353i \(0.374563\pi\)
−0.991623 + 0.129165i \(0.958770\pi\)
\(48\) 0 0
\(49\) −2.14061 −0.305802
\(50\) 0 0
\(51\) −3.42969 + 5.94040i −0.480253 + 0.831823i
\(52\) 0 0
\(53\) 0.134095 0.232259i 0.0184193 0.0319032i −0.856669 0.515867i \(-0.827470\pi\)
0.875088 + 0.483964i \(0.160803\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −8.76819 10.8726i −1.16138 1.44012i
\(58\) 0 0
\(59\) 4.16599 + 7.21570i 0.542366 + 0.939405i 0.998768 + 0.0496310i \(0.0158045\pi\)
−0.456402 + 0.889774i \(0.650862\pi\)
\(60\) 0 0
\(61\) 1.70440 2.95211i 0.218226 0.377979i −0.736040 0.676939i \(-0.763306\pi\)
0.954266 + 0.298960i \(0.0966396\pi\)
\(62\) 0 0
\(63\) −8.01100 + 13.8755i −1.00929 + 1.74814i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.06379 + 1.84253i −0.129962 + 0.225101i −0.923662 0.383209i \(-0.874819\pi\)
0.793699 + 0.608310i \(0.208152\pi\)
\(68\) 0 0
\(69\) 29.6990 3.57534
\(70\) 0 0
\(71\) 5.23630 + 9.06953i 0.621434 + 1.07636i 0.989219 + 0.146444i \(0.0467829\pi\)
−0.367785 + 0.929911i \(0.619884\pi\)
\(72\) 0 0
\(73\) −2.42969 4.20835i −0.284374 0.492550i 0.688083 0.725632i \(-0.258452\pi\)
−0.972457 + 0.233082i \(0.925119\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.65498 −0.302564
\(78\) 0 0
\(79\) −8.20440 14.2104i −0.923067 1.59880i −0.794640 0.607080i \(-0.792341\pi\)
−0.128427 0.991719i \(-0.540993\pi\)
\(80\) 0 0
\(81\) −11.0110 19.0716i −1.22344 2.11907i
\(82\) 0 0
\(83\) 5.73181 0.629148 0.314574 0.949233i \(-0.398138\pi\)
0.314574 + 0.949233i \(0.398138\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 26.6990 2.86243
\(88\) 0 0
\(89\) 5.40880 9.36832i 0.573332 0.993040i −0.422889 0.906182i \(-0.638984\pi\)
0.996221 0.0868585i \(-0.0276828\pi\)
\(90\) 0 0
\(91\) −1.10220 + 1.90907i −0.115542 + 0.200125i
\(92\) 0 0
\(93\) −13.2473 22.9450i −1.37368 2.37929i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.87039 + 13.6319i 0.799117 + 1.38411i 0.920192 + 0.391468i \(0.128033\pi\)
−0.121075 + 0.992643i \(0.538634\pi\)
\(98\) 0 0
\(99\) 4.37691 7.58103i 0.439896 0.761922i
\(100\) 0 0
\(101\) 5.27471 9.13606i 0.524853 0.909072i −0.474728 0.880133i \(-0.657454\pi\)
0.999581 0.0289397i \(-0.00921308\pi\)
\(102\) 0 0
\(103\) 0.731811 0.0721075 0.0360537 0.999350i \(-0.488521\pi\)
0.0360537 + 0.999350i \(0.488521\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.3958 1.29502 0.647509 0.762058i \(-0.275811\pi\)
0.647509 + 0.762058i \(0.275811\pi\)
\(108\) 0 0
\(109\) −2.96811 5.14091i −0.284293 0.492410i 0.688144 0.725574i \(-0.258426\pi\)
−0.972437 + 0.233164i \(0.925092\pi\)
\(110\) 0 0
\(111\) −3.53189 6.11742i −0.335233 0.580640i
\(112\) 0 0
\(113\) −15.6132 −1.46877 −0.734383 0.678735i \(-0.762529\pi\)
−0.734383 + 0.678735i \(0.762529\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −3.63409 6.29444i −0.335972 0.581921i
\(118\) 0 0
\(119\) −2.35939 4.08658i −0.216285 0.374616i
\(120\) 0 0
\(121\) −9.54942 −0.868129
\(122\) 0 0
\(123\) 10.5957 18.3523i 0.955380 1.65477i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −7.67699 + 13.2969i −0.681223 + 1.17991i 0.293385 + 0.955994i \(0.405218\pi\)
−0.974608 + 0.223918i \(0.928115\pi\)
\(128\) 0 0
\(129\) 3.75719 6.50764i 0.330802 0.572965i
\(130\) 0 0
\(131\) 3.89780 + 6.75119i 0.340552 + 0.589854i 0.984535 0.175186i \(-0.0560526\pi\)
−0.643983 + 0.765040i \(0.722719\pi\)
\(132\) 0 0
\(133\) 9.49348 1.48397i 0.823189 0.128676i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.23630 14.2657i 0.703674 1.21880i −0.263494 0.964661i \(-0.584875\pi\)
0.967168 0.254138i \(-0.0817919\pi\)
\(138\) 0 0
\(139\) 9.76819 16.9190i 0.828527 1.43505i −0.0706667 0.997500i \(-0.522513\pi\)
0.899194 0.437551i \(-0.144154\pi\)
\(140\) 0 0
\(141\) 26.6990 2.24846
\(142\) 0 0
\(143\) 0.602201 1.04304i 0.0503586 0.0872236i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 3.42969 + 5.94040i 0.282876 + 0.489956i
\(148\) 0 0
\(149\) 2.83850 + 4.91642i 0.232539 + 0.402769i 0.958555 0.284909i \(-0.0919634\pi\)
−0.726016 + 0.687678i \(0.758630\pi\)
\(150\) 0 0
\(151\) −14.2264 −1.15773 −0.578864 0.815424i \(-0.696504\pi\)
−0.578864 + 0.815424i \(0.696504\pi\)
\(152\) 0 0
\(153\) 15.5584 1.25782
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.327492 0.567233i −0.0261367 0.0452701i 0.852661 0.522464i \(-0.174987\pi\)
−0.878798 + 0.477194i \(0.841654\pi\)
\(158\) 0 0
\(159\) −0.859386 −0.0681538
\(160\) 0 0
\(161\) −10.2154 + 17.6936i −0.805087 + 1.39445i
\(162\) 0 0
\(163\) 12.6770 0.992939 0.496469 0.868054i \(-0.334630\pi\)
0.496469 + 0.868054i \(0.334630\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.89780 + 6.75119i −0.301621 + 0.522422i −0.976503 0.215503i \(-0.930861\pi\)
0.674882 + 0.737925i \(0.264194\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) −11.4133 + 29.5540i −0.872796 + 2.26005i
\(172\) 0 0
\(173\) −5.37039 9.30179i −0.408303 0.707202i 0.586397 0.810024i \(-0.300546\pi\)
−0.994700 + 0.102822i \(0.967213\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 13.3495 23.1220i 1.00341 1.73796i
\(178\) 0 0
\(179\) −1.54942 −0.115809 −0.0579044 0.998322i \(-0.518442\pi\)
−0.0579044 + 0.998322i \(0.518442\pi\)
\(180\) 0 0
\(181\) 4.11320 7.12428i 0.305732 0.529544i −0.671692 0.740831i \(-0.734432\pi\)
0.977424 + 0.211287i \(0.0677655\pi\)
\(182\) 0 0
\(183\) −10.9232 −0.807464
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.28908 + 2.23275i 0.0942668 + 0.163275i
\(188\) 0 0
\(189\) 30.1496 2.19306
\(190\) 0 0
\(191\) 16.2812 1.17807 0.589034 0.808108i \(-0.299508\pi\)
0.589034 + 0.808108i \(0.299508\pi\)
\(192\) 0 0
\(193\) 8.60669 + 14.9072i 0.619523 + 1.07304i 0.989573 + 0.144033i \(0.0460072\pi\)
−0.370050 + 0.929012i \(0.620659\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.2044 0.727034 0.363517 0.931588i \(-0.381576\pi\)
0.363517 + 0.931588i \(0.381576\pi\)
\(198\) 0 0
\(199\) −5.03189 + 8.71550i −0.356701 + 0.617825i −0.987408 0.158197i \(-0.949432\pi\)
0.630706 + 0.776022i \(0.282765\pi\)
\(200\) 0 0
\(201\) 6.81761 0.480877
\(202\) 0 0
\(203\) −9.18351 + 15.9063i −0.644556 + 1.11640i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −33.6815 58.3380i −2.34102 4.05477i
\(208\) 0 0
\(209\) −5.18688 + 0.810784i −0.358784 + 0.0560831i
\(210\) 0 0
\(211\) 6.12758 + 10.6133i 0.421840 + 0.730648i 0.996119 0.0880113i \(-0.0280512\pi\)
−0.574280 + 0.818659i \(0.694718\pi\)
\(212\) 0 0
\(213\) 16.7792 29.0624i 1.14969 1.99132i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 18.2264 1.23729
\(218\) 0 0
\(219\) −7.78571 + 13.4852i −0.526110 + 0.911249i
\(220\) 0 0
\(221\) 2.14061 0.143993
\(222\) 0 0
\(223\) −10.0748 17.4501i −0.674658 1.16854i −0.976569 0.215206i \(-0.930958\pi\)
0.301911 0.953336i \(-0.402376\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.25515 0.547914 0.273957 0.961742i \(-0.411667\pi\)
0.273957 + 0.961742i \(0.411667\pi\)
\(228\) 0 0
\(229\) −26.6860 −1.76346 −0.881729 0.471756i \(-0.843620\pi\)
−0.881729 + 0.471756i \(0.843620\pi\)
\(230\) 0 0
\(231\) 4.25382 + 7.36783i 0.279881 + 0.484768i
\(232\) 0 0
\(233\) 7.00448 + 12.1321i 0.458879 + 0.794802i 0.998902 0.0468485i \(-0.0149178\pi\)
−0.540023 + 0.841650i \(0.681584\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −26.2902 + 45.5360i −1.70773 + 2.95788i
\(238\) 0 0
\(239\) −12.2682 −0.793563 −0.396782 0.917913i \(-0.629873\pi\)
−0.396782 + 0.917913i \(0.629873\pi\)
\(240\) 0 0
\(241\) −4.93621 + 8.54977i −0.317969 + 0.550739i −0.980064 0.198681i \(-0.936334\pi\)
0.662095 + 0.749420i \(0.269668\pi\)
\(242\) 0 0
\(243\) −14.7682 + 25.5793i −0.947380 + 1.64091i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −1.57031 + 4.06622i −0.0999162 + 0.258727i
\(248\) 0 0
\(249\) −9.18351 15.9063i −0.581981 1.00802i
\(250\) 0 0
\(251\) −14.4198 + 24.9758i −0.910170 + 1.57646i −0.0963474 + 0.995348i \(0.530716\pi\)
−0.813823 + 0.581113i \(0.802617\pi\)
\(252\) 0 0
\(253\) 5.58131 9.66711i 0.350894 0.607766i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.39780 + 4.15311i −0.149571 + 0.259064i −0.931069 0.364844i \(-0.881122\pi\)
0.781498 + 0.623907i \(0.214456\pi\)
\(258\) 0 0
\(259\) 4.85939 0.301948
\(260\) 0 0
\(261\) −30.2792 52.4451i −1.87424 3.24627i
\(262\) 0 0
\(263\) 10.2044 + 17.6745i 0.629230 + 1.08986i 0.987706 + 0.156320i \(0.0499631\pi\)
−0.358476 + 0.933539i \(0.616704\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −34.6640 −2.12140
\(268\) 0 0
\(269\) −0.563788 0.976509i −0.0343747 0.0595388i 0.848326 0.529474i \(-0.177611\pi\)
−0.882701 + 0.469935i \(0.844277\pi\)
\(270\) 0 0
\(271\) −9.83850 17.0408i −0.597646 1.03515i −0.993168 0.116697i \(-0.962769\pi\)
0.395522 0.918457i \(-0.370564\pi\)
\(272\) 0 0
\(273\) 7.06379 0.427520
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −7.35398 −0.441858 −0.220929 0.975290i \(-0.570909\pi\)
−0.220929 + 0.975290i \(0.570909\pi\)
\(278\) 0 0
\(279\) −30.0474 + 52.0436i −1.79889 + 3.11577i
\(280\) 0 0
\(281\) −6.73630 + 11.6676i −0.401854 + 0.696031i −0.993950 0.109836i \(-0.964967\pi\)
0.592096 + 0.805867i \(0.298301\pi\)
\(282\) 0 0
\(283\) 10.6595 + 18.4627i 0.633640 + 1.09750i 0.986802 + 0.161934i \(0.0517731\pi\)
−0.353162 + 0.935562i \(0.614894\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7.28908 + 12.6251i 0.430261 + 0.745233i
\(288\) 0 0
\(289\) 6.20889 10.7541i 0.365229 0.632594i
\(290\) 0 0
\(291\) 25.2199 43.6821i 1.47842 2.56069i
\(292\) 0 0
\(293\) −8.08580 −0.472377 −0.236189 0.971707i \(-0.575898\pi\)
−0.236189 + 0.971707i \(0.575898\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −16.4726 −0.955837
\(298\) 0 0
\(299\) −4.63409 8.02649i −0.267997 0.464184i
\(300\) 0 0
\(301\) 2.58468 + 4.47679i 0.148978 + 0.258038i
\(302\) 0 0
\(303\) −33.8046 −1.94202
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 14.2922 + 24.7549i 0.815701 + 1.41284i 0.908824 + 0.417180i \(0.136982\pi\)
−0.0931229 + 0.995655i \(0.529685\pi\)
\(308\) 0 0
\(309\) −1.17251 2.03084i −0.0667016 0.115531i
\(310\) 0 0
\(311\) −10.7408 −0.609054 −0.304527 0.952504i \(-0.598498\pi\)
−0.304527 + 0.952504i \(0.598498\pi\)
\(312\) 0 0
\(313\) 5.71092 9.89160i 0.322800 0.559107i −0.658264 0.752787i \(-0.728709\pi\)
0.981065 + 0.193680i \(0.0620424\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.62309 2.81128i 0.0911619 0.157897i −0.816838 0.576867i \(-0.804275\pi\)
0.908000 + 0.418970i \(0.137609\pi\)
\(318\) 0 0
\(319\) 5.01752 8.69060i 0.280927 0.486580i
\(320\) 0 0
\(321\) −21.4627 37.1745i −1.19793 2.07488i
\(322\) 0 0
\(323\) −5.85735 7.26318i −0.325912 0.404134i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −9.51100 + 16.4735i −0.525960 + 0.910989i
\(328\) 0 0
\(329\) −9.18351 + 15.9063i −0.506303 + 0.876943i
\(330\) 0 0
\(331\) 35.1208 1.93042 0.965208 0.261483i \(-0.0842116\pi\)
0.965208 + 0.261483i \(0.0842116\pi\)
\(332\) 0 0
\(333\) −8.01100 + 13.8755i −0.439000 + 0.760371i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 7.93621 + 13.7459i 0.432313 + 0.748788i 0.997072 0.0764677i \(-0.0243642\pi\)
−0.564759 + 0.825256i \(0.691031\pi\)
\(338\) 0 0
\(339\) 25.0155 + 43.3281i 1.35865 + 2.35326i
\(340\) 0 0
\(341\) −9.95822 −0.539268
\(342\) 0 0
\(343\) −20.1496 −1.08798
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −16.3221 28.2707i −0.876216 1.51765i −0.855462 0.517866i \(-0.826727\pi\)
−0.0207537 0.999785i \(-0.506607\pi\)
\(348\) 0 0
\(349\) −21.7538 −1.16446 −0.582228 0.813026i \(-0.697819\pi\)
−0.582228 + 0.813026i \(0.697819\pi\)
\(350\) 0 0
\(351\) −6.83850 + 11.8446i −0.365012 + 0.632219i
\(352\) 0 0
\(353\) −8.67699 −0.461830 −0.230915 0.972974i \(-0.574172\pi\)
−0.230915 + 0.972974i \(0.574172\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −7.56042 + 13.0950i −0.400140 + 0.693063i
\(358\) 0 0
\(359\) −5.81109 10.0651i −0.306697 0.531216i 0.670940 0.741511i \(-0.265891\pi\)
−0.977638 + 0.210296i \(0.932557\pi\)
\(360\) 0 0
\(361\) 18.0936 5.79827i 0.952297 0.305172i
\(362\) 0 0
\(363\) 15.3001 + 26.5005i 0.803046 + 1.39092i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 15.3046 26.5083i 0.798892 1.38372i −0.121446 0.992598i \(-0.538753\pi\)
0.920338 0.391123i \(-0.127913\pi\)
\(368\) 0 0
\(369\) −48.0660 −2.50222
\(370\) 0 0
\(371\) 0.295598 0.511992i 0.0153467 0.0265813i
\(372\) 0 0
\(373\) −4.70980 −0.243864 −0.121932 0.992538i \(-0.538909\pi\)
−0.121932 + 0.992538i \(0.538909\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.16599 7.21570i −0.214559 0.371628i
\(378\) 0 0
\(379\) 10.0638 0.516942 0.258471 0.966019i \(-0.416781\pi\)
0.258471 + 0.966019i \(0.416781\pi\)
\(380\) 0 0
\(381\) 49.2003 2.52061
\(382\) 0 0
\(383\) 13.7219 + 23.7671i 0.701158 + 1.21444i 0.968060 + 0.250717i \(0.0806664\pi\)
−0.266903 + 0.963723i \(0.586000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −17.0440 −0.866396
\(388\) 0 0
\(389\) −0.257185 + 0.445458i −0.0130398 + 0.0225856i −0.872472 0.488665i \(-0.837484\pi\)
0.859432 + 0.511250i \(0.170817\pi\)
\(390\) 0 0
\(391\) 19.8396 1.00333
\(392\) 0 0
\(393\) 12.4901 21.6335i 0.630043 1.09127i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.55278 + 2.68950i 0.0779320 + 0.134982i 0.902358 0.430988i \(-0.141835\pi\)
−0.824426 + 0.565970i \(0.808502\pi\)
\(398\) 0 0
\(399\) −19.3286 23.9677i −0.967641 1.19988i
\(400\) 0 0
\(401\) 6.51752 + 11.2887i 0.325470 + 0.563730i 0.981607 0.190911i \(-0.0611443\pi\)
−0.656138 + 0.754641i \(0.727811\pi\)
\(402\) 0 0
\(403\) −4.13409 + 7.16046i −0.205934 + 0.356688i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.65498 −0.131603
\(408\) 0 0
\(409\) −13.7747 + 23.8585i −0.681115 + 1.17973i 0.293525 + 0.955951i \(0.405172\pi\)
−0.974641 + 0.223775i \(0.928162\pi\)
\(410\) 0 0
\(411\) −52.7848 −2.60368
\(412\) 0 0
\(413\) 9.18351 + 15.9063i 0.451891 + 0.782698i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −62.6024 −3.06565
\(418\) 0 0
\(419\) 16.5494 0.808492 0.404246 0.914650i \(-0.367534\pi\)
0.404246 + 0.914650i \(0.367534\pi\)
\(420\) 0 0
\(421\) 7.93418 + 13.7424i 0.386688 + 0.669764i 0.992002 0.126223i \(-0.0402856\pi\)
−0.605314 + 0.795987i \(0.706952\pi\)
\(422\) 0 0
\(423\) −30.2792 52.4451i −1.47222 2.54997i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3.75719 6.50764i 0.181823 0.314927i
\(428\) 0 0
\(429\) −3.85939 −0.186333
\(430\) 0 0
\(431\) −11.4472 + 19.8272i −0.551393 + 0.955041i 0.446781 + 0.894643i \(0.352570\pi\)
−0.998174 + 0.0603975i \(0.980763\pi\)
\(432\) 0 0
\(433\) −10.6660 + 18.4740i −0.512575 + 0.887805i 0.487319 + 0.873224i \(0.337975\pi\)
−0.999894 + 0.0145814i \(0.995358\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −14.5539 + 37.6865i −0.696208 + 1.80279i
\(438\) 0 0
\(439\) 5.08783 + 8.81238i 0.242829 + 0.420592i 0.961519 0.274739i \(-0.0885913\pi\)
−0.718690 + 0.695331i \(0.755258\pi\)
\(440\) 0 0
\(441\) 7.77919 13.4740i 0.370438 0.641617i
\(442\) 0 0
\(443\) −3.30660 + 5.72720i −0.157101 + 0.272108i −0.933822 0.357737i \(-0.883548\pi\)
0.776721 + 0.629845i \(0.216882\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 9.09568 15.7542i 0.430211 0.745147i
\(448\) 0 0
\(449\) 10.9870 0.518507 0.259253 0.965809i \(-0.416524\pi\)
0.259253 + 0.965809i \(0.416524\pi\)
\(450\) 0 0
\(451\) −3.98248 6.89785i −0.187528 0.324807i
\(452\) 0 0
\(453\) 22.7936 + 39.4796i 1.07094 + 1.85491i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −12.5494 −0.587037 −0.293518 0.955953i \(-0.594826\pi\)
−0.293518 + 0.955953i \(0.594826\pi\)
\(458\) 0 0
\(459\) −14.6386 25.3548i −0.683270 1.18346i
\(460\) 0 0
\(461\) 11.6386 + 20.1586i 0.542063 + 0.938880i 0.998785 + 0.0492710i \(0.0156898\pi\)
−0.456723 + 0.889609i \(0.650977\pi\)
\(462\) 0 0
\(463\) 23.3958 1.08729 0.543647 0.839314i \(-0.317043\pi\)
0.543647 + 0.839314i \(0.317043\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.6352 0.584688 0.292344 0.956313i \(-0.405565\pi\)
0.292344 + 0.956313i \(0.405565\pi\)
\(468\) 0 0
\(469\) −2.34502 + 4.06169i −0.108283 + 0.187551i
\(470\) 0 0
\(471\) −1.04942 + 1.81764i −0.0483546 + 0.0837526i
\(472\) 0 0
\(473\) −1.41217 2.44595i −0.0649316 0.112465i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.974625 + 1.68810i 0.0446250 + 0.0772928i
\(478\) 0 0
\(479\) −2.01752 + 3.49445i −0.0921830 + 0.159666i −0.908429 0.418038i \(-0.862718\pi\)
0.816246 + 0.577704i \(0.196051\pi\)
\(480\) 0 0
\(481\) −1.10220 + 1.90907i −0.0502560 + 0.0870460i
\(482\) 0 0
\(483\) 65.4685 2.97892
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −6.54942 −0.296782 −0.148391 0.988929i \(-0.547409\pi\)
−0.148391 + 0.988929i \(0.547409\pi\)
\(488\) 0 0
\(489\) −20.3111 35.1798i −0.918499 1.59089i
\(490\) 0 0
\(491\) −1.04290 1.80635i −0.0470653 0.0815195i 0.841533 0.540206i \(-0.181654\pi\)
−0.888598 + 0.458686i \(0.848320\pi\)
\(492\) 0 0
\(493\) 17.8355 0.803273
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 11.5429 + 19.9929i 0.517770 + 0.896803i
\(498\) 0 0
\(499\) 12.0539 + 20.8780i 0.539607 + 0.934626i 0.998925 + 0.0463546i \(0.0147604\pi\)
−0.459318 + 0.888272i \(0.651906\pi\)
\(500\) 0 0
\(501\) 24.9802 1.11603
\(502\) 0 0
\(503\) −4.13858 + 7.16823i −0.184530 + 0.319616i −0.943418 0.331606i \(-0.892410\pi\)
0.758888 + 0.651221i \(0.225743\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 19.2264 33.3011i 0.853875 1.47895i
\(508\) 0 0
\(509\) 2.86591 4.96389i 0.127029 0.220021i −0.795495 0.605960i \(-0.792789\pi\)
0.922524 + 0.385939i \(0.126123\pi\)
\(510\) 0 0
\(511\) −5.35602 9.27690i −0.236936 0.410386i
\(512\) 0 0
\(513\) 58.9014 9.20713i 2.60056 0.406505i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 5.01752 8.69060i 0.220670 0.382212i
\(518\) 0 0
\(519\) −17.2089 + 29.8067i −0.755386 + 1.30837i
\(520\) 0 0
\(521\) 14.8086 0.648778 0.324389 0.945924i \(-0.394841\pi\)
0.324389 + 0.945924i \(0.394841\pi\)
\(522\) 0 0
\(523\) 7.79356 13.4988i 0.340789 0.590263i −0.643791 0.765202i \(-0.722639\pi\)
0.984579 + 0.174938i \(0.0559726\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.84950 15.3278i −0.385490 0.667689i
\(528\) 0 0
\(529\) −31.4497 54.4724i −1.36738 2.36837i
\(530\) 0 0
\(531\) −60.5584 −2.62801
\(532\) 0 0
\(533\) −6.61320 −0.286450
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.48248 + 4.29978i 0.107127 + 0.185549i
\(538\) 0 0
\(539\) 2.57816 0.111049
\(540\) 0 0
\(541\) −14.0539 + 24.3421i −0.604224 + 1.04655i 0.387949 + 0.921681i \(0.373184\pi\)
−0.992174 + 0.124867i \(0.960150\pi\)
\(542\) 0 0
\(543\) −26.3607 −1.13125
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −21.6835 + 37.5569i −0.927120 + 1.60582i −0.139004 + 0.990292i \(0.544390\pi\)
−0.788116 + 0.615527i \(0.788943\pi\)
\(548\) 0 0
\(549\) 12.3879 + 21.4565i 0.528703 + 0.915741i
\(550\) 0 0
\(551\) −13.0838 + 33.8796i −0.557387 + 1.44332i
\(552\) 0 0
\(553\) −18.0858 31.3255i −0.769086 1.33210i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.65814 14.9963i 0.366857 0.635415i −0.622215 0.782846i \(-0.713767\pi\)
0.989072 + 0.147431i \(0.0471005\pi\)
\(558\) 0 0
\(559\) −2.34502 −0.0991836
\(560\) 0 0
\(561\) 4.13073 7.15463i 0.174399 0.302069i
\(562\) 0 0
\(563\) −8.35398 −0.352078 −0.176039 0.984383i \(-0.556329\pi\)
−0.176039 + 0.984383i \(0.556329\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −24.2727 42.0415i −1.01936 1.76558i
\(568\) 0 0
\(569\) −10.6640 −0.447056 −0.223528 0.974697i \(-0.571757\pi\)
−0.223528 + 0.974697i \(0.571757\pi\)
\(570\) 0 0
\(571\) −2.56512 −0.107347 −0.0536735 0.998559i \(-0.517093\pi\)
−0.0536735 + 0.998559i \(0.517093\pi\)
\(572\) 0 0
\(573\) −26.0858 45.1819i −1.08975 1.88750i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −20.4218 −0.850172 −0.425086 0.905153i \(-0.639756\pi\)
−0.425086 + 0.905153i \(0.639756\pi\)
\(578\) 0 0
\(579\) 27.5793 47.7687i 1.14616 1.98520i
\(580\) 0 0
\(581\) 12.6352 0.524197
\(582\) 0 0
\(583\) −0.161504 + 0.279733i −0.00668880 + 0.0115853i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4.40432 7.62850i −0.181786 0.314862i 0.760703 0.649100i \(-0.224854\pi\)
−0.942489 + 0.334238i \(0.891521\pi\)
\(588\) 0 0
\(589\) 35.6078 5.56601i 1.46719 0.229343i
\(590\) 0 0
\(591\) −16.3495 28.3182i −0.672529 1.16485i
\(592\) 0 0
\(593\) 16.4726 28.5314i 0.676448 1.17164i −0.299595 0.954066i \(-0.596852\pi\)
0.976043 0.217576i \(-0.0698151\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 32.2484 1.31984
\(598\) 0 0
\(599\) 9.56379 16.5650i 0.390766 0.676826i −0.601785 0.798658i \(-0.705544\pi\)
0.992551 + 0.121832i \(0.0388769\pi\)
\(600\) 0 0
\(601\) 19.3100 0.787670 0.393835 0.919181i \(-0.371148\pi\)
0.393835 + 0.919181i \(0.371148\pi\)
\(602\) 0 0
\(603\) −7.73181 13.3919i −0.314864 0.545360i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −36.8773 −1.49680 −0.748402 0.663245i \(-0.769179\pi\)
−0.748402 + 0.663245i \(0.769179\pi\)
\(608\) 0 0
\(609\) 58.8553 2.38494
\(610\) 0 0
\(611\) −4.16599 7.21570i −0.168538 0.291916i
\(612\) 0 0
\(613\) −14.2603 24.6996i −0.575970 0.997609i −0.995936 0.0900688i \(-0.971291\pi\)
0.419966 0.907540i \(-0.362042\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.64713 + 9.78112i −0.227345 + 0.393773i −0.957020 0.290021i \(-0.906338\pi\)
0.729675 + 0.683794i \(0.239671\pi\)
\(618\) 0 0
\(619\) 27.2044 1.09344 0.546719 0.837316i \(-0.315877\pi\)
0.546719 + 0.837316i \(0.315877\pi\)
\(620\) 0 0
\(621\) −63.3805 + 109.778i −2.54337 + 4.40525i
\(622\) 0 0
\(623\) 11.9232 20.6515i 0.477692 0.827387i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 10.5604 + 13.0950i 0.421743 + 0.522965i
\(628\) 0 0
\(629\) −2.35939 4.08658i −0.0940749 0.162942i
\(630\) 0 0
\(631\) −4.19136 + 7.25965i −0.166856 + 0.289002i −0.937313 0.348490i \(-0.886695\pi\)
0.770457 + 0.637492i \(0.220028\pi\)
\(632\) 0 0
\(633\) 19.6352 34.0092i 0.780430 1.35174i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.07031 1.85383i 0.0424071 0.0734513i
\(638\) 0 0
\(639\) −76.1168 −3.01113
\(640\) 0 0
\(641\) −9.55594 16.5514i −0.377437 0.653740i 0.613252 0.789888i \(-0.289861\pi\)
−0.990689 + 0.136148i \(0.956528\pi\)
\(642\) 0 0
\(643\) −24.1112 41.7618i −0.950852 1.64692i −0.743588 0.668638i \(-0.766877\pi\)
−0.207264 0.978285i \(-0.566456\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 30.0817 1.18263 0.591317 0.806439i \(-0.298608\pi\)
0.591317 + 0.806439i \(0.298608\pi\)
\(648\) 0 0
\(649\) −5.01752 8.69060i −0.196955 0.341136i
\(650\) 0 0
\(651\) −29.2024 50.5800i −1.14453 1.98239i
\(652\) 0 0
\(653\) −41.9124 −1.64016 −0.820079 0.572250i \(-0.806071\pi\)
−0.820079 + 0.572250i \(0.806071\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 35.3189 1.37792
\(658\) 0 0
\(659\) 20.0936 34.8032i 0.782737 1.35574i −0.147604 0.989047i \(-0.547156\pi\)
0.930341 0.366694i \(-0.119511\pi\)
\(660\) 0 0
\(661\) 0.757185 1.31148i 0.0294511 0.0510108i −0.850924 0.525289i \(-0.823957\pi\)
0.880375 + 0.474278i \(0.157291\pi\)
\(662\) 0 0
\(663\) −3.42969 5.94040i −0.133198 0.230706i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −38.6112 66.8765i −1.49503 2.58947i
\(668\) 0 0
\(669\) −32.2837 + 55.9170i −1.24816 + 2.16187i
\(670\) 0 0
\(671\) −2.05278 + 3.55553i −0.0792468 + 0.137260i
\(672\) 0 0
\(673\) 7.76686 0.299390 0.149695 0.988732i \(-0.452171\pi\)
0.149695 + 0.988732i \(0.452171\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.19136 −0.237953 −0.118977 0.992897i \(-0.537961\pi\)
−0.118977 + 0.992897i \(0.537961\pi\)
\(678\) 0 0
\(679\) 17.3495 + 30.0502i 0.665813 + 1.15322i
\(680\) 0 0
\(681\) −13.2264 22.9088i −0.506837 0.877868i
\(682\) 0 0
\(683\) −2.92317 −0.111852 −0.0559261 0.998435i \(-0.517811\pi\)
−0.0559261 + 0.998435i \(0.517811\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 42.7563 + 74.0560i 1.63125 + 2.82541i
\(688\) 0 0
\(689\) 0.134095 + 0.232259i 0.00510860 + 0.00884835i
\(690\) 0 0
\(691\) −2.35805 −0.0897046 −0.0448523 0.998994i \(-0.514282\pi\)
−0.0448523 + 0.998994i \(0.514282\pi\)
\(692\) 0 0
\(693\) 9.64847 16.7116i 0.366515 0.634822i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 7.07816 12.2597i 0.268104 0.464370i
\(698\) 0 0
\(699\) 22.4452 38.8762i 0.848955 1.47043i
\(700\) 0 0
\(701\) −12.2792 21.2682i −0.463779 0.803288i 0.535367 0.844620i \(-0.320173\pi\)
−0.999145 + 0.0413314i \(0.986840\pi\)
\(702\) 0 0
\(703\) 9.49348 1.48397i 0.358053 0.0559689i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 11.6276 20.1396i 0.437300 0.757426i
\(708\) 0 0
\(709\) −3.63858 + 6.30220i −0.136650 + 0.236684i −0.926226 0.376968i \(-0.876967\pi\)
0.789577 + 0.613652i \(0.210300\pi\)
\(710\) 0 0
\(711\) 119.262 4.47269
\(712\) 0 0
\(713\) −38.3156 + 66.3645i −1.43493 + 2.48537i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 19.6561 + 34.0454i 0.734071 + 1.27145i
\(718\) 0 0
\(719\) −16.4452 28.4839i −0.613302 1.06227i −0.990680 0.136211i \(-0.956508\pi\)
0.377378 0.926059i \(-0.376826\pi\)
\(720\) 0 0
\(721\) 1.61320 0.0600789
\(722\) 0 0
\(723\) 31.6352 1.17653
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 13.9551 + 24.1709i 0.517565 + 0.896449i 0.999792 + 0.0204023i \(0.00649470\pi\)
−0.482227 + 0.876046i \(0.660172\pi\)
\(728\) 0 0
\(729\) 28.5804 1.05853
\(730\) 0 0
\(731\) 2.50989 4.34725i 0.0928315 0.160789i
\(732\) 0 0
\(733\) 4.89710 0.180878 0.0904392 0.995902i \(-0.471173\pi\)
0.0904392 + 0.995902i \(0.471173\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.28123 2.21915i 0.0471946 0.0817435i
\(738\) 0 0
\(739\) 11.5936 + 20.0808i 0.426479 + 0.738684i 0.996557 0.0829069i \(-0.0264204\pi\)
−0.570078 + 0.821591i \(0.693087\pi\)
\(740\) 0 0
\(741\) 13.8001 2.15715i 0.506959 0.0792449i
\(742\) 0 0
\(743\) 19.9901 + 34.6239i 0.733366 + 1.27023i 0.955436 + 0.295197i \(0.0953852\pi\)
−0.222070 + 0.975031i \(0.571281\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −20.8299 + 36.0785i −0.762128 + 1.32004i
\(748\) 0 0
\(749\) 29.5296 1.07899
\(750\) 0 0
\(751\) 10.2936 17.8290i 0.375617 0.650589i −0.614802 0.788682i \(-0.710764\pi\)
0.990419 + 0.138093i \(0.0440973\pi\)
\(752\) 0 0
\(753\) 92.4137 3.36774
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −17.3176 29.9950i −0.629419 1.09019i −0.987668 0.156560i \(-0.949960\pi\)
0.358249 0.933626i \(-0.383374\pi\)
\(758\) 0 0
\(759\) −35.7695 −1.29835
\(760\) 0 0
\(761\) 24.3890 0.884102 0.442051 0.896990i \(-0.354251\pi\)
0.442051 + 0.896990i \(0.354251\pi\)
\(762\) 0 0
\(763\) −6.54290 11.3326i −0.236869 0.410269i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.33198 −0.300850
\(768\) 0 0
\(769\) −3.27471 + 5.67196i −0.118089 + 0.204536i −0.919010 0.394233i \(-0.871010\pi\)
0.800921 + 0.598770i \(0.204343\pi\)
\(770\) 0 0
\(771\) 15.3670 0.553430
\(772\) 0 0
\(773\) −18.7363 + 32.4522i −0.673898 + 1.16723i 0.302892 + 0.953025i \(0.402048\pi\)
−0.976790 + 0.214200i \(0.931286\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −7.78571 13.4852i −0.279311 0.483781i
\(778\) 0 0
\(779\) 18.0957 + 22.4388i 0.648345 + 0.803955i
\(780\) 0 0
\(781\) −6.30660 10.9234i −0.225668 0.390868i
\(782\) 0 0
\(783\) −56.9782 + 98.6891i −2.03623 + 3.52686i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 12.8306 0.457363 0.228682 0.973501i \(-0.426559\pi\)
0.228682 + 0.973501i \(0.426559\pi\)
\(788\) 0 0
\(789\) 32.6990 56.6363i 1.16412 2.01631i
\(790\) 0 0
\(791\) −34.4178 −1.22376
\(792\) 0 0
\(793\) 1.70440 + 2.95211i 0.0605251 + 0.104833i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 28.3032 1.00255 0.501276 0.865287i \(-0.332864\pi\)
0.501276 + 0.865287i \(0.332864\pi\)
\(798\) 0 0