Properties

Label 1792.2.m.c.1345.1
Level $1792$
Weight $2$
Character 1792.1345
Analytic conductor $14.309$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.3091920422\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
Defining polynomial: \(x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1345.1
Root \(0.500000 - 2.10607i\) of defining polynomial
Character \(\chi\) \(=\) 1792.1345
Dual form 1792.2.m.c.449.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.898966 - 0.898966i) q^{3} +(0.786578 - 0.786578i) q^{5} +1.00000i q^{7} -1.38372i q^{9} +O(q^{10})\) \(q+(-0.898966 - 0.898966i) q^{3} +(0.786578 - 0.786578i) q^{5} +1.00000i q^{7} -1.38372i q^{9} +(-2.15894 + 2.15894i) q^{11} +(-1.31318 - 1.31318i) q^{13} -1.41421 q^{15} -1.79793 q^{17} +(-0.531306 - 0.531306i) q^{19} +(0.898966 - 0.898966i) q^{21} +5.95687i q^{23} +3.76259i q^{25} +(-3.94082 + 3.94082i) q^{27} +(-5.62636 - 5.62636i) q^{29} +4.34059 q^{31} +3.88163 q^{33} +(0.786578 + 0.786578i) q^{35} +(-2.12845 + 2.12845i) q^{37} +2.36101i q^{39} +0.712611i q^{41} +(-2.96951 + 2.96951i) q^{43} +(-1.08840 - 1.08840i) q^{45} -2.20207 q^{47} -1.00000 q^{49} +(1.61628 + 1.61628i) q^{51} +(3.38372 - 3.38372i) q^{53} +3.39635i q^{55} +0.955252i q^{57} +(-2.41549 + 2.41549i) q^{59} +(-7.09505 - 7.09505i) q^{61} +1.38372 q^{63} -2.06584 q^{65} +(6.76744 + 6.76744i) q^{67} +(5.35503 - 5.35503i) q^{69} +1.96788i q^{71} +10.3633i q^{73} +(3.38244 - 3.38244i) q^{75} +(-2.15894 - 2.15894i) q^{77} -14.2449 q^{79} +2.93416 q^{81} +(-5.95217 - 5.95217i) q^{83} +(-1.41421 + 1.41421i) q^{85} +10.1158i q^{87} +16.9417i q^{89} +(1.31318 - 1.31318i) q^{91} +(-3.90205 - 3.90205i) q^{93} -0.835826 q^{95} +17.6796 q^{97} +(2.98737 + 2.98737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} - 4q^{5} + O(q^{10}) \) \( 8q + 4q^{3} - 4q^{5} - 8q^{11} + 12q^{13} + 8q^{17} + 4q^{19} - 4q^{21} - 8q^{27} - 8q^{31} - 16q^{33} - 4q^{35} - 8q^{37} - 24q^{43} + 12q^{45} - 40q^{47} - 8q^{49} + 24q^{51} + 16q^{53} - 52q^{59} - 20q^{61} - 24q^{65} + 32q^{67} + 8q^{69} - 28q^{75} - 8q^{77} + 16q^{81} - 12q^{83} - 12q^{91} - 40q^{93} - 80q^{95} + 72q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.898966 0.898966i −0.519018 0.519018i 0.398256 0.917274i \(-0.369616\pi\)
−0.917274 + 0.398256i \(0.869616\pi\)
\(4\) 0 0
\(5\) 0.786578 0.786578i 0.351768 0.351768i −0.508999 0.860767i \(-0.669984\pi\)
0.860767 + 0.508999i \(0.169984\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 1.38372i 0.461240i
\(10\) 0 0
\(11\) −2.15894 + 2.15894i −0.650945 + 0.650945i −0.953221 0.302275i \(-0.902254\pi\)
0.302275 + 0.953221i \(0.402254\pi\)
\(12\) 0 0
\(13\) −1.31318 1.31318i −0.364211 0.364211i 0.501150 0.865360i \(-0.332911\pi\)
−0.865360 + 0.501150i \(0.832911\pi\)
\(14\) 0 0
\(15\) −1.41421 −0.365148
\(16\) 0 0
\(17\) −1.79793 −0.436063 −0.218031 0.975942i \(-0.569964\pi\)
−0.218031 + 0.975942i \(0.569964\pi\)
\(18\) 0 0
\(19\) −0.531306 0.531306i −0.121890 0.121890i 0.643531 0.765420i \(-0.277469\pi\)
−0.765420 + 0.643531i \(0.777469\pi\)
\(20\) 0 0
\(21\) 0.898966 0.898966i 0.196171 0.196171i
\(22\) 0 0
\(23\) 5.95687i 1.24209i 0.783773 + 0.621047i \(0.213292\pi\)
−0.783773 + 0.621047i \(0.786708\pi\)
\(24\) 0 0
\(25\) 3.76259i 0.752518i
\(26\) 0 0
\(27\) −3.94082 + 3.94082i −0.758410 + 0.758410i
\(28\) 0 0
\(29\) −5.62636 5.62636i −1.04479 1.04479i −0.998949 0.0458400i \(-0.985404\pi\)
−0.0458400 0.998949i \(-0.514596\pi\)
\(30\) 0 0
\(31\) 4.34059 0.779594 0.389797 0.920901i \(-0.372545\pi\)
0.389797 + 0.920901i \(0.372545\pi\)
\(32\) 0 0
\(33\) 3.88163 0.675705
\(34\) 0 0
\(35\) 0.786578 + 0.786578i 0.132956 + 0.132956i
\(36\) 0 0
\(37\) −2.12845 + 2.12845i −0.349915 + 0.349915i −0.860078 0.510163i \(-0.829585\pi\)
0.510163 + 0.860078i \(0.329585\pi\)
\(38\) 0 0
\(39\) 2.36101i 0.378064i
\(40\) 0 0
\(41\) 0.712611i 0.111291i 0.998451 + 0.0556456i \(0.0177217\pi\)
−0.998451 + 0.0556456i \(0.982278\pi\)
\(42\) 0 0
\(43\) −2.96951 + 2.96951i −0.452845 + 0.452845i −0.896298 0.443453i \(-0.853753\pi\)
0.443453 + 0.896298i \(0.353753\pi\)
\(44\) 0 0
\(45\) −1.08840 1.08840i −0.162249 0.162249i
\(46\) 0 0
\(47\) −2.20207 −0.321205 −0.160602 0.987019i \(-0.551344\pi\)
−0.160602 + 0.987019i \(0.551344\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 1.61628 + 1.61628i 0.226325 + 0.226325i
\(52\) 0 0
\(53\) 3.38372 3.38372i 0.464790 0.464790i −0.435432 0.900222i \(-0.643404\pi\)
0.900222 + 0.435432i \(0.143404\pi\)
\(54\) 0 0
\(55\) 3.39635i 0.457964i
\(56\) 0 0
\(57\) 0.955252i 0.126526i
\(58\) 0 0
\(59\) −2.41549 + 2.41549i −0.314470 + 0.314470i −0.846638 0.532168i \(-0.821377\pi\)
0.532168 + 0.846638i \(0.321377\pi\)
\(60\) 0 0
\(61\) −7.09505 7.09505i −0.908429 0.908429i 0.0877169 0.996145i \(-0.472043\pi\)
−0.996145 + 0.0877169i \(0.972043\pi\)
\(62\) 0 0
\(63\) 1.38372 0.174332
\(64\) 0 0
\(65\) −2.06584 −0.256235
\(66\) 0 0
\(67\) 6.76744 + 6.76744i 0.826774 + 0.826774i 0.987069 0.160295i \(-0.0512446\pi\)
−0.160295 + 0.987069i \(0.551245\pi\)
\(68\) 0 0
\(69\) 5.35503 5.35503i 0.644670 0.644670i
\(70\) 0 0
\(71\) 1.96788i 0.233545i 0.993159 + 0.116772i \(0.0372548\pi\)
−0.993159 + 0.116772i \(0.962745\pi\)
\(72\) 0 0
\(73\) 10.3633i 1.21293i 0.795109 + 0.606466i \(0.207414\pi\)
−0.795109 + 0.606466i \(0.792586\pi\)
\(74\) 0 0
\(75\) 3.38244 3.38244i 0.390571 0.390571i
\(76\) 0 0
\(77\) −2.15894 2.15894i −0.246034 0.246034i
\(78\) 0 0
\(79\) −14.2449 −1.60268 −0.801340 0.598209i \(-0.795879\pi\)
−0.801340 + 0.598209i \(0.795879\pi\)
\(80\) 0 0
\(81\) 2.93416 0.326018
\(82\) 0 0
\(83\) −5.95217 5.95217i −0.653336 0.653336i 0.300459 0.953795i \(-0.402860\pi\)
−0.953795 + 0.300459i \(0.902860\pi\)
\(84\) 0 0
\(85\) −1.41421 + 1.41421i −0.153393 + 0.153393i
\(86\) 0 0
\(87\) 10.1158i 1.08453i
\(88\) 0 0
\(89\) 16.9417i 1.79582i 0.440184 + 0.897908i \(0.354913\pi\)
−0.440184 + 0.897908i \(0.645087\pi\)
\(90\) 0 0
\(91\) 1.31318 1.31318i 0.137659 0.137659i
\(92\) 0 0
\(93\) −3.90205 3.90205i −0.404623 0.404623i
\(94\) 0 0
\(95\) −0.835826 −0.0857540
\(96\) 0 0
\(97\) 17.6796 1.79509 0.897544 0.440925i \(-0.145350\pi\)
0.897544 + 0.440925i \(0.145350\pi\)
\(98\) 0 0
\(99\) 2.98737 + 2.98737i 0.300242 + 0.300242i
\(100\) 0 0
\(101\) 6.66156 6.66156i 0.662850 0.662850i −0.293201 0.956051i \(-0.594721\pi\)
0.956051 + 0.293201i \(0.0947205\pi\)
\(102\) 0 0
\(103\) 1.88418i 0.185654i 0.995682 + 0.0928271i \(0.0295904\pi\)
−0.995682 + 0.0928271i \(0.970410\pi\)
\(104\) 0 0
\(105\) 1.41421i 0.138013i
\(106\) 0 0
\(107\) −8.94909 + 8.94909i −0.865141 + 0.865141i −0.991930 0.126789i \(-0.959533\pi\)
0.126789 + 0.991930i \(0.459533\pi\)
\(108\) 0 0
\(109\) 4.73210 + 4.73210i 0.453253 + 0.453253i 0.896433 0.443180i \(-0.146150\pi\)
−0.443180 + 0.896433i \(0.646150\pi\)
\(110\) 0 0
\(111\) 3.82680 0.363224
\(112\) 0 0
\(113\) −7.93416 −0.746383 −0.373192 0.927754i \(-0.621737\pi\)
−0.373192 + 0.927754i \(0.621737\pi\)
\(114\) 0 0
\(115\) 4.68554 + 4.68554i 0.436929 + 0.436929i
\(116\) 0 0
\(117\) −1.81707 + 1.81707i −0.167988 + 0.167988i
\(118\) 0 0
\(119\) 1.79793i 0.164816i
\(120\) 0 0
\(121\) 1.67794i 0.152540i
\(122\) 0 0
\(123\) 0.640613 0.640613i 0.0577622 0.0577622i
\(124\) 0 0
\(125\) 6.89246 + 6.89246i 0.616480 + 0.616480i
\(126\) 0 0
\(127\) −7.93161 −0.703817 −0.351908 0.936034i \(-0.614467\pi\)
−0.351908 + 0.936034i \(0.614467\pi\)
\(128\) 0 0
\(129\) 5.33897 0.470070
\(130\) 0 0
\(131\) 5.98429 + 5.98429i 0.522850 + 0.522850i 0.918431 0.395581i \(-0.129457\pi\)
−0.395581 + 0.918431i \(0.629457\pi\)
\(132\) 0 0
\(133\) 0.531306 0.531306i 0.0460700 0.0460700i
\(134\) 0 0
\(135\) 6.19951i 0.533569i
\(136\) 0 0
\(137\) 12.3380i 1.05411i 0.849831 + 0.527055i \(0.176704\pi\)
−0.849831 + 0.527055i \(0.823296\pi\)
\(138\) 0 0
\(139\) −13.0393 + 13.0393i −1.10598 + 1.10598i −0.112305 + 0.993674i \(0.535823\pi\)
−0.993674 + 0.112305i \(0.964177\pi\)
\(140\) 0 0
\(141\) 1.97958 + 1.97958i 0.166711 + 0.166711i
\(142\) 0 0
\(143\) 5.67016 0.474162
\(144\) 0 0
\(145\) −8.85114 −0.735047
\(146\) 0 0
\(147\) 0.898966 + 0.898966i 0.0741455 + 0.0741455i
\(148\) 0 0
\(149\) −8.62798 + 8.62798i −0.706832 + 0.706832i −0.965868 0.259036i \(-0.916595\pi\)
0.259036 + 0.965868i \(0.416595\pi\)
\(150\) 0 0
\(151\) 9.55274i 0.777391i −0.921366 0.388695i \(-0.872926\pi\)
0.921366 0.388695i \(-0.127074\pi\)
\(152\) 0 0
\(153\) 2.48783i 0.201129i
\(154\) 0 0
\(155\) 3.41421 3.41421i 0.274236 0.274236i
\(156\) 0 0
\(157\) −8.25742 8.25742i −0.659014 0.659014i 0.296133 0.955147i \(-0.404303\pi\)
−0.955147 + 0.296133i \(0.904303\pi\)
\(158\) 0 0
\(159\) −6.08370 −0.482469
\(160\) 0 0
\(161\) −5.95687 −0.469467
\(162\) 0 0
\(163\) 1.01263 + 1.01263i 0.0793154 + 0.0793154i 0.745652 0.666336i \(-0.232138\pi\)
−0.666336 + 0.745652i \(0.732138\pi\)
\(164\) 0 0
\(165\) 3.05320 3.05320i 0.237692 0.237692i
\(166\) 0 0
\(167\) 5.79793i 0.448657i −0.974514 0.224329i \(-0.927981\pi\)
0.974514 0.224329i \(-0.0720189\pi\)
\(168\) 0 0
\(169\) 9.55112i 0.734701i
\(170\) 0 0
\(171\) −0.735178 + 0.735178i −0.0562205 + 0.0562205i
\(172\) 0 0
\(173\) 2.65215 + 2.65215i 0.201639 + 0.201639i 0.800702 0.599063i \(-0.204460\pi\)
−0.599063 + 0.800702i \(0.704460\pi\)
\(174\) 0 0
\(175\) −3.76259 −0.284425
\(176\) 0 0
\(177\) 4.34289 0.326431
\(178\) 0 0
\(179\) −1.55045 1.55045i −0.115886 0.115886i 0.646786 0.762672i \(-0.276113\pi\)
−0.762672 + 0.646786i \(0.776113\pi\)
\(180\) 0 0
\(181\) −11.0315 + 11.0315i −0.819966 + 0.819966i −0.986103 0.166137i \(-0.946871\pi\)
0.166137 + 0.986103i \(0.446871\pi\)
\(182\) 0 0
\(183\) 12.7564i 0.942982i
\(184\) 0 0
\(185\) 3.34838i 0.246178i
\(186\) 0 0
\(187\) 3.88163 3.88163i 0.283853 0.283853i
\(188\) 0 0
\(189\) −3.94082 3.94082i −0.286652 0.286652i
\(190\) 0 0
\(191\) −16.5664 −1.19870 −0.599352 0.800485i \(-0.704575\pi\)
−0.599352 + 0.800485i \(0.704575\pi\)
\(192\) 0 0
\(193\) 17.3795 1.25101 0.625503 0.780221i \(-0.284894\pi\)
0.625503 + 0.780221i \(0.284894\pi\)
\(194\) 0 0
\(195\) 1.85712 + 1.85712i 0.132991 + 0.132991i
\(196\) 0 0
\(197\) −1.44110 + 1.44110i −0.102674 + 0.102674i −0.756578 0.653904i \(-0.773130\pi\)
0.653904 + 0.756578i \(0.273130\pi\)
\(198\) 0 0
\(199\) 13.1438i 0.931736i −0.884854 0.465868i \(-0.845742\pi\)
0.884854 0.465868i \(-0.154258\pi\)
\(200\) 0 0
\(201\) 12.1674i 0.858222i
\(202\) 0 0
\(203\) 5.62636 5.62636i 0.394893 0.394893i
\(204\) 0 0
\(205\) 0.560524 + 0.560524i 0.0391487 + 0.0391487i
\(206\) 0 0
\(207\) 8.24264 0.572903
\(208\) 0 0
\(209\) 2.29412 0.158687
\(210\) 0 0
\(211\) −3.59587 3.59587i −0.247550 0.247550i 0.572415 0.819964i \(-0.306007\pi\)
−0.819964 + 0.572415i \(0.806007\pi\)
\(212\) 0 0
\(213\) 1.76906 1.76906i 0.121214 0.121214i
\(214\) 0 0
\(215\) 4.67149i 0.318593i
\(216\) 0 0
\(217\) 4.34059i 0.294659i
\(218\) 0 0
\(219\) 9.31626 9.31626i 0.629535 0.629535i
\(220\) 0 0
\(221\) 2.36101 + 2.36101i 0.158819 + 0.158819i
\(222\) 0 0
\(223\) 27.5132 1.84242 0.921211 0.389064i \(-0.127201\pi\)
0.921211 + 0.389064i \(0.127201\pi\)
\(224\) 0 0
\(225\) 5.20637 0.347091
\(226\) 0 0
\(227\) −11.0418 11.0418i −0.732873 0.732873i 0.238315 0.971188i \(-0.423405\pi\)
−0.971188 + 0.238315i \(0.923405\pi\)
\(228\) 0 0
\(229\) 11.9717 11.9717i 0.791109 0.791109i −0.190565 0.981675i \(-0.561032\pi\)
0.981675 + 0.190565i \(0.0610321\pi\)
\(230\) 0 0
\(231\) 3.88163i 0.255393i
\(232\) 0 0
\(233\) 28.7013i 1.88029i −0.340778 0.940144i \(-0.610690\pi\)
0.340778 0.940144i \(-0.389310\pi\)
\(234\) 0 0
\(235\) −1.73210 + 1.73210i −0.112990 + 0.112990i
\(236\) 0 0
\(237\) 12.8057 + 12.8057i 0.831821 + 0.831821i
\(238\) 0 0
\(239\) −16.6348 −1.07602 −0.538008 0.842939i \(-0.680823\pi\)
−0.538008 + 0.842939i \(0.680823\pi\)
\(240\) 0 0
\(241\) −3.77267 −0.243019 −0.121510 0.992590i \(-0.538773\pi\)
−0.121510 + 0.992590i \(0.538773\pi\)
\(242\) 0 0
\(243\) 9.18473 + 9.18473i 0.589201 + 0.589201i
\(244\) 0 0
\(245\) −0.786578 + 0.786578i −0.0502526 + 0.0502526i
\(246\) 0 0
\(247\) 1.39540i 0.0887872i
\(248\) 0 0
\(249\) 10.7016i 0.678186i
\(250\) 0 0
\(251\) −20.1264 + 20.1264i −1.27037 + 1.27037i −0.324474 + 0.945895i \(0.605187\pi\)
−0.945895 + 0.324474i \(0.894813\pi\)
\(252\) 0 0
\(253\) −12.8605 12.8605i −0.808535 0.808535i
\(254\) 0 0
\(255\) 2.54266 0.159228
\(256\) 0 0
\(257\) −25.8408 −1.61190 −0.805952 0.591980i \(-0.798346\pi\)
−0.805952 + 0.591980i \(0.798346\pi\)
\(258\) 0 0
\(259\) −2.12845 2.12845i −0.132255 0.132255i
\(260\) 0 0
\(261\) −7.78530 + 7.78530i −0.481898 + 0.481898i
\(262\) 0 0
\(263\) 2.24035i 0.138146i −0.997612 0.0690728i \(-0.977996\pi\)
0.997612 0.0690728i \(-0.0220041\pi\)
\(264\) 0 0
\(265\) 5.32312i 0.326996i
\(266\) 0 0
\(267\) 15.2300 15.2300i 0.932061 0.932061i
\(268\) 0 0
\(269\) 13.3489 + 13.3489i 0.813897 + 0.813897i 0.985216 0.171319i \(-0.0548027\pi\)
−0.171319 + 0.985216i \(0.554803\pi\)
\(270\) 0 0
\(271\) 13.5670 0.824136 0.412068 0.911153i \(-0.364807\pi\)
0.412068 + 0.911153i \(0.364807\pi\)
\(272\) 0 0
\(273\) −2.36101 −0.142895
\(274\) 0 0
\(275\) −8.12322 8.12322i −0.489848 0.489848i
\(276\) 0 0
\(277\) −8.22060 + 8.22060i −0.493928 + 0.493928i −0.909541 0.415613i \(-0.863567\pi\)
0.415613 + 0.909541i \(0.363567\pi\)
\(278\) 0 0
\(279\) 6.00616i 0.359580i
\(280\) 0 0
\(281\) 4.95365i 0.295510i −0.989024 0.147755i \(-0.952795\pi\)
0.989024 0.147755i \(-0.0472047\pi\)
\(282\) 0 0
\(283\) 15.6184 15.6184i 0.928419 0.928419i −0.0691845 0.997604i \(-0.522040\pi\)
0.997604 + 0.0691845i \(0.0220397\pi\)
\(284\) 0 0
\(285\) 0.751380 + 0.751380i 0.0445079 + 0.0445079i
\(286\) 0 0
\(287\) −0.712611 −0.0420641
\(288\) 0 0
\(289\) −13.7674 −0.809849
\(290\) 0 0
\(291\) −15.8933 15.8933i −0.931684 0.931684i
\(292\) 0 0
\(293\) 14.6749 14.6749i 0.857315 0.857315i −0.133706 0.991021i \(-0.542688\pi\)
0.991021 + 0.133706i \(0.0426879\pi\)
\(294\) 0 0
\(295\) 3.79994i 0.221241i
\(296\) 0 0
\(297\) 17.0160i 0.987367i
\(298\) 0 0
\(299\) 7.82245 7.82245i 0.452384 0.452384i
\(300\) 0 0
\(301\) −2.96951 2.96951i −0.171159 0.171159i
\(302\) 0 0
\(303\) −11.9770 −0.688063
\(304\) 0 0
\(305\) −11.1616 −0.639113
\(306\) 0 0
\(307\) −9.72484 9.72484i −0.555026 0.555026i 0.372861 0.927887i \(-0.378377\pi\)
−0.927887 + 0.372861i \(0.878377\pi\)
\(308\) 0 0
\(309\) 1.69382 1.69382i 0.0963579 0.0963579i
\(310\) 0 0
\(311\) 27.1376i 1.53883i −0.638748 0.769416i \(-0.720547\pi\)
0.638748 0.769416i \(-0.279453\pi\)
\(312\) 0 0
\(313\) 13.1116i 0.741114i −0.928810 0.370557i \(-0.879167\pi\)
0.928810 0.370557i \(-0.120833\pi\)
\(314\) 0 0
\(315\) 1.08840 1.08840i 0.0613245 0.0613245i
\(316\) 0 0
\(317\) −11.4901 11.4901i −0.645350 0.645350i 0.306516 0.951866i \(-0.400837\pi\)
−0.951866 + 0.306516i \(0.900837\pi\)
\(318\) 0 0
\(319\) 24.2940 1.36020
\(320\) 0 0
\(321\) 16.0899 0.898048
\(322\) 0 0
\(323\) 0.955252 + 0.955252i 0.0531516 + 0.0531516i
\(324\) 0 0
\(325\) 4.94096 4.94096i 0.274075 0.274075i
\(326\) 0 0
\(327\) 8.50799i 0.470493i
\(328\) 0 0
\(329\) 2.20207i 0.121404i
\(330\) 0 0
\(331\) 11.4094 11.4094i 0.627116 0.627116i −0.320226 0.947341i \(-0.603759\pi\)
0.947341 + 0.320226i \(0.103759\pi\)
\(332\) 0 0
\(333\) 2.94517 + 2.94517i 0.161394 + 0.161394i
\(334\) 0 0
\(335\) 10.6462 0.581666
\(336\) 0 0
\(337\) −30.6355 −1.66882 −0.834411 0.551142i \(-0.814192\pi\)
−0.834411 + 0.551142i \(0.814192\pi\)
\(338\) 0 0
\(339\) 7.13255 + 7.13255i 0.387387 + 0.387387i
\(340\) 0 0
\(341\) −9.37109 + 9.37109i −0.507473 + 0.507473i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 8.42429i 0.453549i
\(346\) 0 0
\(347\) −4.28321 + 4.28321i −0.229935 + 0.229935i −0.812665 0.582730i \(-0.801984\pi\)
0.582730 + 0.812665i \(0.301984\pi\)
\(348\) 0 0
\(349\) 22.9861 + 22.9861i 1.23042 + 1.23042i 0.963803 + 0.266614i \(0.0859049\pi\)
0.266614 + 0.963803i \(0.414095\pi\)
\(350\) 0 0
\(351\) 10.3500 0.552442
\(352\) 0 0
\(353\) 16.0523 0.854376 0.427188 0.904163i \(-0.359504\pi\)
0.427188 + 0.904163i \(0.359504\pi\)
\(354\) 0 0
\(355\) 1.54789 + 1.54789i 0.0821536 + 0.0821536i
\(356\) 0 0
\(357\) −1.61628 + 1.61628i −0.0855427 + 0.0855427i
\(358\) 0 0
\(359\) 15.8317i 0.835563i −0.908548 0.417781i \(-0.862808\pi\)
0.908548 0.417781i \(-0.137192\pi\)
\(360\) 0 0
\(361\) 18.4354i 0.970286i
\(362\) 0 0
\(363\) 1.50841 1.50841i 0.0791712 0.0791712i
\(364\) 0 0
\(365\) 8.15154 + 8.15154i 0.426671 + 0.426671i
\(366\) 0 0
\(367\) 37.3527 1.94979 0.974897 0.222656i \(-0.0714728\pi\)
0.974897 + 0.222656i \(0.0714728\pi\)
\(368\) 0 0
\(369\) 0.986054 0.0513319
\(370\) 0 0
\(371\) 3.38372 + 3.38372i 0.175674 + 0.175674i
\(372\) 0 0
\(373\) −12.4321 + 12.4321i −0.643709 + 0.643709i −0.951465 0.307757i \(-0.900422\pi\)
0.307757 + 0.951465i \(0.400422\pi\)
\(374\) 0 0
\(375\) 12.3922i 0.639929i
\(376\) 0 0
\(377\) 14.7768i 0.761046i
\(378\) 0 0
\(379\) −2.68374 + 2.68374i −0.137854 + 0.137854i −0.772667 0.634812i \(-0.781077\pi\)
0.634812 + 0.772667i \(0.281077\pi\)
\(380\) 0 0
\(381\) 7.13025 + 7.13025i 0.365294 + 0.365294i
\(382\) 0 0
\(383\) −10.7195 −0.547739 −0.273870 0.961767i \(-0.588304\pi\)
−0.273870 + 0.961767i \(0.588304\pi\)
\(384\) 0 0
\(385\) −3.39635 −0.173094
\(386\) 0 0
\(387\) 4.10896 + 4.10896i 0.208870 + 0.208870i
\(388\) 0 0
\(389\) 18.4499 18.4499i 0.935449 0.935449i −0.0625902 0.998039i \(-0.519936\pi\)
0.998039 + 0.0625902i \(0.0199361\pi\)
\(390\) 0 0
\(391\) 10.7101i 0.541631i
\(392\) 0 0
\(393\) 10.7593i 0.542737i
\(394\) 0 0
\(395\) −11.2047 + 11.2047i −0.563772 + 0.563772i
\(396\) 0 0
\(397\) −8.43982 8.43982i −0.423583 0.423583i 0.462853 0.886435i \(-0.346826\pi\)
−0.886435 + 0.462853i \(0.846826\pi\)
\(398\) 0 0
\(399\) −0.955252 −0.0478224
\(400\) 0 0
\(401\) −33.3744 −1.66664 −0.833320 0.552791i \(-0.813563\pi\)
−0.833320 + 0.552791i \(0.813563\pi\)
\(402\) 0 0
\(403\) −5.69998 5.69998i −0.283936 0.283936i
\(404\) 0 0
\(405\) 2.30795 2.30795i 0.114683 0.114683i
\(406\) 0 0
\(407\) 9.19039i 0.455551i
\(408\) 0 0
\(409\) 8.19011i 0.404975i 0.979285 + 0.202487i \(0.0649025\pi\)
−0.979285 + 0.202487i \(0.935097\pi\)
\(410\) 0 0
\(411\) 11.0915 11.0915i 0.547103 0.547103i
\(412\) 0 0
\(413\) −2.41549 2.41549i −0.118858 0.118858i
\(414\) 0 0
\(415\) −9.36369 −0.459645
\(416\) 0 0
\(417\) 23.4438 1.14805
\(418\) 0 0
\(419\) −21.7021 21.7021i −1.06022 1.06022i −0.998067 0.0621518i \(-0.980204\pi\)
−0.0621518 0.998067i \(-0.519796\pi\)
\(420\) 0 0
\(421\) −27.4513 + 27.4513i −1.33789 + 1.33789i −0.439798 + 0.898097i \(0.644950\pi\)
−0.898097 + 0.439798i \(0.855050\pi\)
\(422\) 0 0
\(423\) 3.04704i 0.148152i
\(424\) 0 0
\(425\) 6.76489i 0.328145i
\(426\) 0 0
\(427\) 7.09505 7.09505i 0.343354 0.343354i
\(428\) 0 0
\(429\) −5.09728 5.09728i −0.246099 0.246099i
\(430\) 0 0
\(431\) 6.85598 0.330241 0.165121 0.986273i \(-0.447199\pi\)
0.165121 + 0.986273i \(0.447199\pi\)
\(432\) 0 0
\(433\) 39.3144 1.88933 0.944665 0.328037i \(-0.106387\pi\)
0.944665 + 0.328037i \(0.106387\pi\)
\(434\) 0 0
\(435\) 7.95687 + 7.95687i 0.381503 + 0.381503i
\(436\) 0 0
\(437\) 3.16492 3.16492i 0.151399 0.151399i
\(438\) 0 0
\(439\) 1.76192i 0.0840918i −0.999116 0.0420459i \(-0.986612\pi\)
0.999116 0.0420459i \(-0.0133876\pi\)
\(440\) 0 0
\(441\) 1.38372i 0.0658914i
\(442\) 0 0
\(443\) 13.1344 13.1344i 0.624032 0.624032i −0.322528 0.946560i \(-0.604533\pi\)
0.946560 + 0.322528i \(0.104533\pi\)
\(444\) 0 0
\(445\) 13.3260 + 13.3260i 0.631711 + 0.631711i
\(446\) 0 0
\(447\) 15.5125 0.733718
\(448\) 0 0
\(449\) −19.8852 −0.938443 −0.469221 0.883081i \(-0.655465\pi\)
−0.469221 + 0.883081i \(0.655465\pi\)
\(450\) 0 0
\(451\) −1.53849 1.53849i −0.0724445 0.0724445i
\(452\) 0 0
\(453\) −8.58759 + 8.58759i −0.403480 + 0.403480i
\(454\) 0 0
\(455\) 2.06584i 0.0968479i
\(456\) 0 0
\(457\) 16.7983i 0.785792i −0.919583 0.392896i \(-0.871473\pi\)
0.919583 0.392896i \(-0.128527\pi\)
\(458\) 0 0
\(459\) 7.08532 7.08532i 0.330714 0.330714i
\(460\) 0 0
\(461\) 23.5576 + 23.5576i 1.09719 + 1.09719i 0.994738 + 0.102450i \(0.0326681\pi\)
0.102450 + 0.994738i \(0.467332\pi\)
\(462\) 0 0
\(463\) −13.6063 −0.632340 −0.316170 0.948703i \(-0.602397\pi\)
−0.316170 + 0.948703i \(0.602397\pi\)
\(464\) 0 0
\(465\) −6.13853 −0.284667
\(466\) 0 0
\(467\) −17.8703 17.8703i −0.826938 0.826938i 0.160154 0.987092i \(-0.448801\pi\)
−0.987092 + 0.160154i \(0.948801\pi\)
\(468\) 0 0
\(469\) −6.76744 + 6.76744i −0.312491 + 0.312491i
\(470\) 0 0
\(471\) 14.8463i 0.684081i
\(472\) 0 0
\(473\) 12.8220i 0.589555i
\(474\) 0 0
\(475\) 1.99909 1.99909i 0.0917244 0.0917244i
\(476\) 0 0
\(477\) −4.68212 4.68212i −0.214379 0.214379i
\(478\) 0 0
\(479\) −37.3075 −1.70463 −0.852313 0.523033i \(-0.824801\pi\)
−0.852313 + 0.523033i \(0.824801\pi\)
\(480\) 0 0
\(481\) 5.59007 0.254885
\(482\) 0 0
\(483\) 5.35503 + 5.35503i 0.243662 + 0.243662i
\(484\) 0 0
\(485\) 13.9063 13.9063i 0.631455 0.631455i
\(486\) 0 0
\(487\) 7.61373i 0.345011i 0.985009 + 0.172505i \(0.0551863\pi\)
−0.985009 + 0.172505i \(0.944814\pi\)
\(488\) 0 0
\(489\) 1.82064i 0.0823323i
\(490\) 0 0
\(491\) 25.1091 25.1091i 1.13316 1.13316i 0.143508 0.989649i \(-0.454162\pi\)
0.989649 0.143508i \(-0.0458383\pi\)
\(492\) 0 0
\(493\) 10.1158 + 10.1158i 0.455593 + 0.455593i
\(494\) 0 0
\(495\) 4.69959 0.211231
\(496\) 0 0
\(497\) −1.96788 −0.0882716
\(498\) 0 0
\(499\) 16.5674 + 16.5674i 0.741658 + 0.741658i 0.972897 0.231239i \(-0.0742780\pi\)
−0.231239 + 0.972897i \(0.574278\pi\)
\(500\) 0 0
\(501\) −5.21215 + 5.21215i −0.232862 + 0.232862i
\(502\) 0 0
\(503\) 32.9297i 1.46826i −0.679007 0.734132i \(-0.737589\pi\)
0.679007 0.734132i \(-0.262411\pi\)
\(504\) 0 0
\(505\) 10.4797i 0.466339i
\(506\) 0 0
\(507\) −8.58613 + 8.58613i −0.381324 + 0.381324i
\(508\) 0 0
\(509\) −0.330168 0.330168i −0.0146345 0.0146345i 0.699752 0.714386i \(-0.253294\pi\)
−0.714386 + 0.699752i \(0.753294\pi\)
\(510\) 0 0
\(511\) −10.3633 −0.458446
\(512\) 0 0
\(513\) 4.18756 0.184885
\(514\) 0 0
\(515\) 1.48206 + 1.48206i 0.0653072 + 0.0653072i
\(516\) 0 0
\(517\) 4.75413 4.75413i 0.209087 0.209087i
\(518\) 0 0
\(519\) 4.76839i 0.209309i
\(520\) 0 0
\(521\) 5.94331i 0.260381i 0.991489 + 0.130191i \(0.0415589\pi\)
−0.991489 + 0.130191i \(0.958441\pi\)
\(522\) 0 0
\(523\) 14.4703 14.4703i 0.632743 0.632743i −0.316012 0.948755i \(-0.602344\pi\)
0.948755 + 0.316012i \(0.102344\pi\)
\(524\) 0 0
\(525\) 3.38244 + 3.38244i 0.147622 + 0.147622i
\(526\) 0 0
\(527\) −7.80409 −0.339952
\(528\) 0 0
\(529\) −12.4844 −0.542798
\(530\) 0 0
\(531\) 3.34236 + 3.34236i 0.145046 + 0.145046i
\(532\) 0 0
\(533\) 0.935787 0.935787i 0.0405334 0.0405334i
\(534\) 0 0
\(535\) 14.0783i 0.608658i
\(536\) 0 0
\(537\) 2.78760i 0.120294i
\(538\) 0 0
\(539\) 2.15894 2.15894i 0.0929922 0.0929922i
\(540\) 0 0
\(541\) −8.23256 8.23256i −0.353945 0.353945i 0.507630 0.861575i \(-0.330522\pi\)
−0.861575 + 0.507630i \(0.830522\pi\)
\(542\) 0 0
\(543\) 19.8339 0.851155
\(544\) 0 0
\(545\) 7.44432 0.318880
\(546\) 0 0
\(547\) 16.9144 + 16.9144i 0.723208 + 0.723208i 0.969257 0.246049i \(-0.0791324\pi\)
−0.246049 + 0.969257i \(0.579132\pi\)
\(548\) 0 0
\(549\) −9.81756 + 9.81756i −0.419003 + 0.419003i
\(550\) 0 0
\(551\) 5.97863i 0.254698i
\(552\) 0 0
\(553\) 14.2449i 0.605756i
\(554\) 0 0
\(555\) 3.01008 3.01008i 0.127771 0.127771i
\(556\) 0 0
\(557\) 28.0529 + 28.0529i 1.18864 + 1.18864i 0.977443 + 0.211198i \(0.0677366\pi\)
0.211198 + 0.977443i \(0.432263\pi\)
\(558\) 0 0
\(559\) 7.79899 0.329862
\(560\) 0 0
\(561\) −6.97891 −0.294650
\(562\) 0 0
\(563\) 10.7240 + 10.7240i 0.451961 + 0.451961i 0.896005 0.444044i \(-0.146457\pi\)
−0.444044 + 0.896005i \(0.646457\pi\)
\(564\) 0 0
\(565\) −6.24084 + 6.24084i −0.262554 + 0.262554i
\(566\) 0 0
\(567\) 2.93416i 0.123223i
\(568\) 0 0
\(569\) 7.70067i 0.322829i 0.986887 + 0.161414i \(0.0516056\pi\)
−0.986887 + 0.161414i \(0.948394\pi\)
\(570\) 0 0
\(571\) −33.1892 + 33.1892i −1.38892 + 1.38892i −0.561336 + 0.827588i \(0.689712\pi\)
−0.827588 + 0.561336i \(0.810288\pi\)
\(572\) 0 0
\(573\) 14.8927 + 14.8927i 0.622150 + 0.622150i
\(574\) 0 0
\(575\) −22.4133 −0.934699
\(576\) 0 0
\(577\) 7.15827 0.298003 0.149001 0.988837i \(-0.452394\pi\)
0.149001 + 0.988837i \(0.452394\pi\)
\(578\) 0 0
\(579\) −15.6236 15.6236i −0.649296 0.649296i
\(580\) 0 0
\(581\) 5.95217 5.95217i 0.246938 0.246938i
\(582\) 0 0
\(583\) 14.6105i 0.605105i
\(584\) 0 0
\(585\) 2.85854i 0.118186i
\(586\) 0 0
\(587\) −18.8145 + 18.8145i −0.776558 + 0.776558i −0.979244 0.202686i \(-0.935033\pi\)
0.202686 + 0.979244i \(0.435033\pi\)
\(588\) 0 0
\(589\) −2.30618 2.30618i −0.0950246 0.0950246i
\(590\) 0 0
\(591\) 2.59100 0.106579
\(592\) 0 0
\(593\) −4.45182 −0.182814 −0.0914072 0.995814i \(-0.529136\pi\)
−0.0914072 + 0.995814i \(0.529136\pi\)
\(594\) 0 0
\(595\) −1.41421 1.41421i −0.0579771 0.0579771i
\(596\) 0 0
\(597\) −11.8158 + 11.8158i −0.483588 + 0.483588i
\(598\) 0 0
\(599\) 29.5201i 1.20616i −0.797682 0.603079i \(-0.793940\pi\)
0.797682 0.603079i \(-0.206060\pi\)
\(600\) 0 0
\(601\) 24.5564i 1.00168i 0.865541 + 0.500838i \(0.166975\pi\)
−0.865541 + 0.500838i \(0.833025\pi\)
\(602\) 0 0
\(603\) 9.36423 9.36423i 0.381341 0.381341i
\(604\) 0 0
\(605\) 1.31983 + 1.31983i 0.0536588 + 0.0536588i
\(606\) 0 0
\(607\) −36.1536 −1.46743 −0.733714 0.679458i \(-0.762215\pi\)
−0.733714 + 0.679458i \(0.762215\pi\)
\(608\) 0 0
\(609\) −10.1158 −0.409914
\(610\) 0 0
\(611\) 2.89171 + 2.89171i 0.116986 + 0.116986i
\(612\) 0 0
\(613\) −3.35616 + 3.35616i −0.135554 + 0.135554i −0.771628 0.636074i \(-0.780557\pi\)
0.636074 + 0.771628i \(0.280557\pi\)
\(614\) 0 0
\(615\) 1.00778i 0.0406378i
\(616\) 0 0
\(617\) 25.5502i 1.02861i 0.857607 + 0.514306i \(0.171950\pi\)
−0.857607 + 0.514306i \(0.828050\pi\)
\(618\) 0 0
\(619\) −11.1501 + 11.1501i −0.448159 + 0.448159i −0.894742 0.446583i \(-0.852641\pi\)
0.446583 + 0.894742i \(0.352641\pi\)
\(620\) 0 0
\(621\) −23.4749 23.4749i −0.942017 0.942017i
\(622\) 0 0
\(623\) −16.9417 −0.678755
\(624\) 0 0
\(625\) −7.97005 −0.318802
\(626\) 0 0
\(627\) −2.06233 2.06233i −0.0823616 0.0823616i
\(628\) 0 0
\(629\) 3.82680 3.82680i 0.152585 0.152585i
\(630\) 0 0
\(631\) 25.7069i 1.02337i −0.859172 0.511687i \(-0.829021\pi\)
0.859172 0.511687i \(-0.170979\pi\)
\(632\) 0 0
\(633\) 6.46512i 0.256966i
\(634\) 0 0
\(635\) −6.23883 + 6.23883i −0.247580 + 0.247580i
\(636\) 0 0
\(637\) 1.31318 + 1.31318i 0.0520301 + 0.0520301i
\(638\) 0 0
\(639\) 2.72300 0.107720
\(640\) 0 0
\(641\) −7.39970 −0.292271 −0.146135 0.989265i \(-0.546683\pi\)
−0.146135 + 0.989265i \(0.546683\pi\)
\(642\) 0 0
\(643\) 17.2666 + 17.2666i 0.680929 + 0.680929i 0.960210 0.279280i \(-0.0900959\pi\)
−0.279280 + 0.960210i \(0.590096\pi\)
\(644\) 0 0
\(645\) 4.19951 4.19951i 0.165356 0.165356i
\(646\) 0 0
\(647\) 7.71205i 0.303192i −0.988443 0.151596i \(-0.951559\pi\)
0.988443 0.151596i \(-0.0484412\pi\)
\(648\) 0 0
\(649\) 10.4298i 0.409406i
\(650\) 0 0
\(651\) 3.90205 3.90205i 0.152933 0.152933i
\(652\) 0 0
\(653\) −4.78463 4.78463i −0.187237 0.187237i 0.607263 0.794501i \(-0.292267\pi\)
−0.794501 + 0.607263i \(0.792267\pi\)
\(654\) 0 0
\(655\) 9.41421 0.367844
\(656\) 0 0
\(657\) 14.3399 0.559453
\(658\) 0 0
\(659\) −28.1016 28.1016i −1.09468 1.09468i −0.995022 0.0996599i \(-0.968225\pi\)
−0.0996599 0.995022i \(-0.531775\pi\)
\(660\) 0 0
\(661\) −10.0875 + 10.0875i −0.392357 + 0.392357i −0.875527 0.483170i \(-0.839485\pi\)
0.483170 + 0.875527i \(0.339485\pi\)
\(662\) 0 0
\(663\) 4.24494i 0.164860i
\(664\) 0 0
\(665\) 0.835826i 0.0324120i
\(666\) 0 0
\(667\) 33.5155 33.5155i 1.29773 1.29773i
\(668\) 0 0
\(669\) −24.7335 24.7335i −0.956251 0.956251i
\(670\) 0 0
\(671\) 30.6356 1.18267
\(672\) 0 0
\(673\) 31.2930 1.20626 0.603129 0.797644i \(-0.293920\pi\)
0.603129 + 0.797644i \(0.293920\pi\)
\(674\) 0 0
\(675\) −14.8277 14.8277i −0.570718 0.570718i
\(676\) 0 0
\(677\) 3.75969 3.75969i 0.144497 0.144497i −0.631158 0.775654i \(-0.717420\pi\)
0.775654 + 0.631158i \(0.217420\pi\)
\(678\) 0 0
\(679\) 17.6796i 0.678479i
\(680\) 0 0
\(681\) 19.8525i 0.760750i
\(682\) 0 0
\(683\) −8.31693 + 8.31693i −0.318239 + 0.318239i −0.848090 0.529852i \(-0.822248\pi\)
0.529852 + 0.848090i \(0.322248\pi\)
\(684\) 0 0
\(685\) 9.70483 + 9.70483i 0.370802 + 0.370802i
\(686\) 0 0
\(687\) −21.5242 −0.821201
\(688\) 0 0
\(689\) −8.88686 −0.338563
\(690\) 0 0
\(691\) 33.6065 + 33.6065i 1.27845 + 1.27845i 0.941535 + 0.336916i \(0.109384\pi\)
0.336916 + 0.941535i \(0.390616\pi\)
\(692\) 0 0
\(693\) −2.98737 + 2.98737i −0.113481 + 0.113481i
\(694\) 0 0
\(695\) 20.5128i 0.778096i
\(696\) 0 0
\(697\) 1.28123i 0.0485299i
\(698\) 0 0
\(699\) −25.8015 + 25.8015i −0.975904 + 0.975904i
\(700\) 0 0
\(701\) −33.3319 33.3319i −1.25893 1.25893i −0.951606 0.307322i \(-0.900567\pi\)
−0.307322 0.951606i \(-0.599433\pi\)
\(702\) 0 0
\(703\) 2.26171 0.0853021
\(704\) 0 0
\(705\) 3.11419 0.117287
\(706\) 0 0
\(707\) 6.66156 + 6.66156i 0.250534 + 0.250534i
\(708\) 0 0
\(709\) 16.4665 16.4665i 0.618412 0.618412i −0.326712 0.945124i \(-0.605941\pi\)
0.945124 + 0.326712i \(0.105941\pi\)
\(710\) 0 0
\(711\) 19.7110i 0.739220i
\(712\) 0 0
\(713\) 25.8564i 0.968329i
\(714\) 0 0
\(715\) 4.46002 4.46002i 0.166795 0.166795i
\(716\) 0 0
\(717\) 14.9541 + 14.9541i 0.558473 + 0.558473i
\(718\) 0 0
\(719\) −25.5122 −0.951443 −0.475722 0.879596i \(-0.657813\pi\)
−0.475722 + 0.879596i \(0.657813\pi\)
\(720\) 0 0
\(721\) −1.88418 −0.0701707
\(722\) 0 0
\(723\) 3.39150 + 3.39150i 0.126131 + 0.126131i
\(724\) 0 0
\(725\) 21.1697 21.1697i 0.786223 0.786223i
\(726\) 0 0
\(727\) 10.8327i 0.401764i −0.979615 0.200882i \(-0.935619\pi\)
0.979615 0.200882i \(-0.0643807\pi\)
\(728\) 0 0
\(729\) 25.3160i 0.937630i
\(730\) 0 0
\(731\) 5.33897 5.33897i 0.197469 0.197469i
\(732\) 0 0
\(733\) 3.64351 + 3.64351i 0.134576 + 0.134576i 0.771186 0.636610i \(-0.219664\pi\)
−0.636610 + 0.771186i \(0.719664\pi\)
\(734\) 0 0
\(735\) 1.41421 0.0521641
\(736\) 0 0
\(737\) −29.2210 −1.07637
\(738\) 0 0
\(739\) 1.72954 + 1.72954i 0.0636223 + 0.0636223i 0.738202 0.674580i \(-0.235675\pi\)
−0.674580 + 0.738202i \(0.735675\pi\)
\(740\) 0 0
\(741\) 1.25442 1.25442i 0.0460822 0.0460822i
\(742\) 0 0
\(743\) 38.1023i 1.39784i 0.715202 + 0.698918i \(0.246335\pi\)
−0.715202 + 0.698918i \(0.753665\pi\)
\(744\) 0 0
\(745\) 13.5732i 0.497282i
\(746\) 0 0
\(747\) −8.23613 + 8.23613i −0.301344 + 0.301344i
\(748\) 0 0
\(749\) −8.94909 8.94909i −0.326993 0.326993i
\(750\) 0 0
\(751\) 33.6119 1.22651 0.613257 0.789883i \(-0.289859\pi\)
0.613257 + 0.789883i \(0.289859\pi\)
\(752\) 0 0
\(753\) 36.1860 1.31869
\(754\) 0 0
\(755\) −7.51397 7.51397i −0.273461 0.273461i
\(756\) 0 0
\(757\) 2.39019 2.39019i 0.0868729 0.0868729i −0.662335 0.749208i \(-0.730434\pi\)
0.749208 + 0.662335i \(0.230434\pi\)
\(758\) 0 0
\(759\) 23.1224i 0.839290i
\(760\) 0 0
\(761\) 3.87733i 0.140553i 0.997528 + 0.0702765i \(0.0223882\pi\)
−0.997528 + 0.0702765i \(0.977612\pi\)
\(762\) 0 0
\(763\) −4.73210 + 4.73210i −0.171313 + 0.171313i
\(764\) 0 0
\(765\) 1.95687 + 1.95687i 0.0707509 + 0.0707509i
\(766\) 0 0
\(767\) 6.34395 0.229067
\(768\) 0 0
\(769\) 24.8126 0.894764 0.447382 0.894343i \(-0.352356\pi\)
0.447382 + 0.894343i \(0.352356\pi\)
\(770\) 0 0
\(771\) 23.2300 + 23.2300i 0.836608 + 0.836608i
\(772\) 0 0
\(773\) −8.49465 + 8.49465i −0.305531 + 0.305531i −0.843173 0.537642i \(-0.819315\pi\)
0.537642 + 0.843173i \(0.319315\pi\)
\(774\) 0 0
\(775\) 16.3319i 0.586658i
\(776\) 0 0
\(777\) 3.82680i 0.137286i
\(778\) 0 0
\(779\) 0.378614 0.378614i 0.0135653 0.0135653i
\(780\) 0 0
\(781\) −4.24854 4.24854i −0.152025 0.152025i
\(782\) 0 0
\(783\) 44.3449 1.58476
\(784\) 0 0
\(785\) −12.9902 −0.463640
\(786\) 0 0
\(787\) −1.92149 1.92149i −0.0684939 0.0684939i 0.672030 0.740524i \(-0.265423\pi\)
−0.740524 + 0.672030i \(0.765423\pi\)
\(788\) 0 0
\(789\) −2.01400 + 2.01400i −0.0717001 + 0.0717001i
\(790\) 0 0
\(791\) 7.93416i 0.282106i
\(792\) 0 0
\(793\) 18.6342i 0.661719i
\(794\) 0 0
\(795\) −4.78530 + 4.78530i −0.169717 + 0.169717i
\(796\) 0 0
\(797\) −8.95191 8.95191i −0.317093 0.317093i 0.530557 0.847650i \(-0.321983\pi\)
−0.847650 + 0.530557i \(0.821983\pi\)
\(798\) 0 0
\(799\) 3.95917