Properties

Label 1792.2.m.h.1345.3
Level $1792$
Weight $2$
Character 1792.1345
Analytic conductor $14.309$
Analytic rank $0$
Dimension $16$
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: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1345.3
Root \(0.792206 + 1.03242i\) of defining polynomial
Character \(\chi\) \(=\) 1792.1345
Dual form 1792.2.m.h.449.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.18265 - 1.18265i) q^{3} +(1.87820 - 1.87820i) q^{5} -1.00000i q^{7} -0.202696i q^{9} +O(q^{10})\) \(q+(-1.18265 - 1.18265i) q^{3} +(1.87820 - 1.87820i) q^{5} -1.00000i q^{7} -0.202696i q^{9} +(0.584413 - 0.584413i) q^{11} +(-3.94057 - 3.94057i) q^{13} -4.44250 q^{15} +1.74896 q^{17} +(-4.19467 - 4.19467i) q^{19} +(-1.18265 + 1.18265i) q^{21} +3.04150i q^{23} -2.05530i q^{25} +(-3.78766 + 3.78766i) q^{27} +(4.43316 + 4.43316i) q^{29} -7.90794 q^{31} -1.38231 q^{33} +(-1.87820 - 1.87820i) q^{35} +(5.87262 - 5.87262i) q^{37} +9.32061i q^{39} +1.38922i q^{41} +(1.73902 - 1.73902i) q^{43} +(-0.380704 - 0.380704i) q^{45} +1.80017 q^{47} -1.00000 q^{49} +(-2.06840 - 2.06840i) q^{51} +(9.73675 - 9.73675i) q^{53} -2.19529i q^{55} +9.92162i q^{57} +(-4.74002 + 4.74002i) q^{59} +(-3.10257 - 3.10257i) q^{61} -0.202696 q^{63} -14.8024 q^{65} +(-4.81108 - 4.81108i) q^{67} +(3.59702 - 3.59702i) q^{69} -1.11625i q^{71} +11.2521i q^{73} +(-2.43070 + 2.43070i) q^{75} +(-0.584413 - 0.584413i) q^{77} +7.61158 q^{79} +8.35083 q^{81} +(11.1869 + 11.1869i) q^{83} +(3.28490 - 3.28490i) q^{85} -10.4857i q^{87} +0.428825i q^{89} +(-3.94057 + 3.94057i) q^{91} +(9.35230 + 9.35230i) q^{93} -15.7569 q^{95} -19.2163 q^{97} +(-0.118458 - 0.118458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{3} + 4q^{5} + O(q^{10}) \) \( 16q + 4q^{3} + 4q^{5} - 8q^{11} - 12q^{13} - 8q^{17} + 4q^{19} + 4q^{21} - 56q^{27} - 8q^{31} + 16q^{33} - 4q^{35} + 8q^{37} - 24q^{43} + 36q^{45} - 40q^{47} - 16q^{49} + 24q^{51} + 32q^{53} - 4q^{59} + 20q^{61} + 24q^{63} + 72q^{65} + 32q^{67} - 56q^{69} - 28q^{75} + 8q^{77} - 40q^{81} + 36q^{83} - 12q^{91} - 8q^{93} - 80q^{95} - 72q^{97} - 8q^{99} + O(q^{100}) \)

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
\(3\) −1.18265 1.18265i −0.682801 0.682801i 0.277829 0.960630i \(-0.410385\pi\)
−0.960630 + 0.277829i \(0.910385\pi\)
\(4\) 0 0
\(5\) 1.87820 1.87820i 0.839958 0.839958i −0.148895 0.988853i \(-0.547572\pi\)
0.988853 + 0.148895i \(0.0475715\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0.202696i 0.0675652i
\(10\) 0 0
\(11\) 0.584413 0.584413i 0.176207 0.176207i −0.613493 0.789700i \(-0.710236\pi\)
0.789700 + 0.613493i \(0.210236\pi\)
\(12\) 0 0
\(13\) −3.94057 3.94057i −1.09292 1.09292i −0.995216 0.0977031i \(-0.968850\pi\)
−0.0977031 0.995216i \(-0.531150\pi\)
\(14\) 0 0
\(15\) −4.44250 −1.14705
\(16\) 0 0
\(17\) 1.74896 0.424185 0.212093 0.977250i \(-0.431972\pi\)
0.212093 + 0.977250i \(0.431972\pi\)
\(18\) 0 0
\(19\) −4.19467 4.19467i −0.962323 0.962323i 0.0369927 0.999316i \(-0.488222\pi\)
−0.999316 + 0.0369927i \(0.988222\pi\)
\(20\) 0 0
\(21\) −1.18265 + 1.18265i −0.258075 + 0.258075i
\(22\) 0 0
\(23\) 3.04150i 0.634198i 0.948393 + 0.317099i \(0.102709\pi\)
−0.948393 + 0.317099i \(0.897291\pi\)
\(24\) 0 0
\(25\) 2.05530i 0.411060i
\(26\) 0 0
\(27\) −3.78766 + 3.78766i −0.728935 + 0.728935i
\(28\) 0 0
\(29\) 4.43316 + 4.43316i 0.823217 + 0.823217i 0.986568 0.163351i \(-0.0522304\pi\)
−0.163351 + 0.986568i \(0.552230\pi\)
\(30\) 0 0
\(31\) −7.90794 −1.42031 −0.710154 0.704046i \(-0.751375\pi\)
−0.710154 + 0.704046i \(0.751375\pi\)
\(32\) 0 0
\(33\) −1.38231 −0.240629
\(34\) 0 0
\(35\) −1.87820 1.87820i −0.317474 0.317474i
\(36\) 0 0
\(37\) 5.87262 5.87262i 0.965453 0.965453i −0.0339701 0.999423i \(-0.510815\pi\)
0.999423 + 0.0339701i \(0.0108151\pi\)
\(38\) 0 0
\(39\) 9.32061i 1.49249i
\(40\) 0 0
\(41\) 1.38922i 0.216960i 0.994099 + 0.108480i \(0.0345983\pi\)
−0.994099 + 0.108480i \(0.965402\pi\)
\(42\) 0 0
\(43\) 1.73902 1.73902i 0.265198 0.265198i −0.561964 0.827162i \(-0.689954\pi\)
0.827162 + 0.561964i \(0.189954\pi\)
\(44\) 0 0
\(45\) −0.380704 0.380704i −0.0567520 0.0567520i
\(46\) 0 0
\(47\) 1.80017 0.262582 0.131291 0.991344i \(-0.458088\pi\)
0.131291 + 0.991344i \(0.458088\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −2.06840 2.06840i −0.289634 0.289634i
\(52\) 0 0
\(53\) 9.73675 9.73675i 1.33745 1.33745i 0.438919 0.898527i \(-0.355361\pi\)
0.898527 0.438919i \(-0.144639\pi\)
\(54\) 0 0
\(55\) 2.19529i 0.296013i
\(56\) 0 0
\(57\) 9.92162i 1.31415i
\(58\) 0 0
\(59\) −4.74002 + 4.74002i −0.617098 + 0.617098i −0.944786 0.327688i \(-0.893731\pi\)
0.327688 + 0.944786i \(0.393731\pi\)
\(60\) 0 0
\(61\) −3.10257 3.10257i −0.397243 0.397243i 0.480016 0.877260i \(-0.340631\pi\)
−0.877260 + 0.480016i \(0.840631\pi\)
\(62\) 0 0
\(63\) −0.202696 −0.0255372
\(64\) 0 0
\(65\) −14.8024 −1.83601
\(66\) 0 0
\(67\) −4.81108 4.81108i −0.587767 0.587767i 0.349259 0.937026i \(-0.386433\pi\)
−0.937026 + 0.349259i \(0.886433\pi\)
\(68\) 0 0
\(69\) 3.59702 3.59702i 0.433031 0.433031i
\(70\) 0 0
\(71\) 1.11625i 0.132475i −0.997804 0.0662375i \(-0.978900\pi\)
0.997804 0.0662375i \(-0.0210995\pi\)
\(72\) 0 0
\(73\) 11.2521i 1.31696i 0.752600 + 0.658478i \(0.228799\pi\)
−0.752600 + 0.658478i \(0.771201\pi\)
\(74\) 0 0
\(75\) −2.43070 + 2.43070i −0.280673 + 0.280673i
\(76\) 0 0
\(77\) −0.584413 0.584413i −0.0666000 0.0666000i
\(78\) 0 0
\(79\) 7.61158 0.856370 0.428185 0.903691i \(-0.359153\pi\)
0.428185 + 0.903691i \(0.359153\pi\)
\(80\) 0 0
\(81\) 8.35083 0.927870
\(82\) 0 0
\(83\) 11.1869 + 11.1869i 1.22792 + 1.22792i 0.964748 + 0.263176i \(0.0847700\pi\)
0.263176 + 0.964748i \(0.415230\pi\)
\(84\) 0 0
\(85\) 3.28490 3.28490i 0.356298 0.356298i
\(86\) 0 0
\(87\) 10.4857i 1.12419i
\(88\) 0 0
\(89\) 0.428825i 0.0454554i 0.999742 + 0.0227277i \(0.00723508\pi\)
−0.999742 + 0.0227277i \(0.992765\pi\)
\(90\) 0 0
\(91\) −3.94057 + 3.94057i −0.413084 + 0.413084i
\(92\) 0 0
\(93\) 9.35230 + 9.35230i 0.969788 + 0.969788i
\(94\) 0 0
\(95\) −15.7569 −1.61662
\(96\) 0 0
\(97\) −19.2163 −1.95111 −0.975557 0.219745i \(-0.929478\pi\)
−0.975557 + 0.219745i \(0.929478\pi\)
\(98\) 0 0
\(99\) −0.118458 0.118458i −0.0119055 0.0119055i
\(100\) 0 0
\(101\) −4.87547 + 4.87547i −0.485127 + 0.485127i −0.906765 0.421637i \(-0.861456\pi\)
0.421637 + 0.906765i \(0.361456\pi\)
\(102\) 0 0
\(103\) 6.09849i 0.600902i 0.953797 + 0.300451i \(0.0971371\pi\)
−0.953797 + 0.300451i \(0.902863\pi\)
\(104\) 0 0
\(105\) 4.44250i 0.433544i
\(106\) 0 0
\(107\) −5.19989 + 5.19989i −0.502693 + 0.502693i −0.912274 0.409581i \(-0.865675\pi\)
0.409581 + 0.912274i \(0.365675\pi\)
\(108\) 0 0
\(109\) −7.70055 7.70055i −0.737579 0.737579i 0.234530 0.972109i \(-0.424645\pi\)
−0.972109 + 0.234530i \(0.924645\pi\)
\(110\) 0 0
\(111\) −13.8905 −1.31842
\(112\) 0 0
\(113\) −14.2646 −1.34190 −0.670952 0.741500i \(-0.734115\pi\)
−0.670952 + 0.741500i \(0.734115\pi\)
\(114\) 0 0
\(115\) 5.71257 + 5.71257i 0.532700 + 0.532700i
\(116\) 0 0
\(117\) −0.798737 + 0.798737i −0.0738433 + 0.0738433i
\(118\) 0 0
\(119\) 1.74896i 0.160327i
\(120\) 0 0
\(121\) 10.3169i 0.937902i
\(122\) 0 0
\(123\) 1.64296 1.64296i 0.148140 0.148140i
\(124\) 0 0
\(125\) 5.53074 + 5.53074i 0.494685 + 0.494685i
\(126\) 0 0
\(127\) 8.98310 0.797121 0.398561 0.917142i \(-0.369510\pi\)
0.398561 + 0.917142i \(0.369510\pi\)
\(128\) 0 0
\(129\) −4.11328 −0.362154
\(130\) 0 0
\(131\) −12.7547 12.7547i −1.11438 1.11438i −0.992551 0.121828i \(-0.961124\pi\)
−0.121828 0.992551i \(-0.538876\pi\)
\(132\) 0 0
\(133\) −4.19467 + 4.19467i −0.363724 + 0.363724i
\(134\) 0 0
\(135\) 14.2280i 1.22455i
\(136\) 0 0
\(137\) 11.7927i 1.00751i −0.863845 0.503757i \(-0.831951\pi\)
0.863845 0.503757i \(-0.168049\pi\)
\(138\) 0 0
\(139\) −0.524016 + 0.524016i −0.0444465 + 0.0444465i −0.728981 0.684534i \(-0.760006\pi\)
0.684534 + 0.728981i \(0.260006\pi\)
\(140\) 0 0
\(141\) −2.12896 2.12896i −0.179291 0.179291i
\(142\) 0 0
\(143\) −4.60584 −0.385160
\(144\) 0 0
\(145\) 16.6527 1.38294
\(146\) 0 0
\(147\) 1.18265 + 1.18265i 0.0975430 + 0.0975430i
\(148\) 0 0
\(149\) 1.98859 1.98859i 0.162912 0.162912i −0.620944 0.783855i \(-0.713250\pi\)
0.783855 + 0.620944i \(0.213250\pi\)
\(150\) 0 0
\(151\) 15.1887i 1.23604i −0.786162 0.618020i \(-0.787935\pi\)
0.786162 0.618020i \(-0.212065\pi\)
\(152\) 0 0
\(153\) 0.354507i 0.0286602i
\(154\) 0 0
\(155\) −14.8527 + 14.8527i −1.19300 + 1.19300i
\(156\) 0 0
\(157\) −7.91629 7.91629i −0.631789 0.631789i 0.316728 0.948516i \(-0.397416\pi\)
−0.948516 + 0.316728i \(0.897416\pi\)
\(158\) 0 0
\(159\) −23.0303 −1.82642
\(160\) 0 0
\(161\) 3.04150 0.239704
\(162\) 0 0
\(163\) 6.32172 + 6.32172i 0.495155 + 0.495155i 0.909926 0.414771i \(-0.136138\pi\)
−0.414771 + 0.909926i \(0.636138\pi\)
\(164\) 0 0
\(165\) −2.59626 + 2.59626i −0.202118 + 0.202118i
\(166\) 0 0
\(167\) 22.5263i 1.74314i −0.490271 0.871570i \(-0.663102\pi\)
0.490271 0.871570i \(-0.336898\pi\)
\(168\) 0 0
\(169\) 18.0563i 1.38894i
\(170\) 0 0
\(171\) −0.850241 + 0.850241i −0.0650195 + 0.0650195i
\(172\) 0 0
\(173\) −0.0105911 0.0105911i −0.000805223 0.000805223i 0.706704 0.707509i \(-0.250181\pi\)
−0.707509 + 0.706704i \(0.750181\pi\)
\(174\) 0 0
\(175\) −2.05530 −0.155366
\(176\) 0 0
\(177\) 11.2115 0.842710
\(178\) 0 0
\(179\) −14.3569 14.3569i −1.07309 1.07309i −0.997109 0.0759779i \(-0.975792\pi\)
−0.0759779 0.997109i \(-0.524208\pi\)
\(180\) 0 0
\(181\) 8.65321 8.65321i 0.643188 0.643188i −0.308150 0.951338i \(-0.599710\pi\)
0.951338 + 0.308150i \(0.0997098\pi\)
\(182\) 0 0
\(183\) 7.33848i 0.542476i
\(184\) 0 0
\(185\) 22.0600i 1.62188i
\(186\) 0 0
\(187\) 1.02211 1.02211i 0.0747444 0.0747444i
\(188\) 0 0
\(189\) 3.78766 + 3.78766i 0.275511 + 0.275511i
\(190\) 0 0
\(191\) 17.2085 1.24517 0.622583 0.782554i \(-0.286083\pi\)
0.622583 + 0.782554i \(0.286083\pi\)
\(192\) 0 0
\(193\) 7.00982 0.504578 0.252289 0.967652i \(-0.418817\pi\)
0.252289 + 0.967652i \(0.418817\pi\)
\(194\) 0 0
\(195\) 17.5060 + 17.5060i 1.25363 + 1.25363i
\(196\) 0 0
\(197\) −15.4175 + 15.4175i −1.09845 + 1.09845i −0.103860 + 0.994592i \(0.533119\pi\)
−0.994592 + 0.103860i \(0.966881\pi\)
\(198\) 0 0
\(199\) 15.3483i 1.08801i −0.839082 0.544005i \(-0.816907\pi\)
0.839082 0.544005i \(-0.183093\pi\)
\(200\) 0 0
\(201\) 11.3796i 0.802656i
\(202\) 0 0
\(203\) 4.43316 4.43316i 0.311147 0.311147i
\(204\) 0 0
\(205\) 2.60924 + 2.60924i 0.182237 + 0.182237i
\(206\) 0 0
\(207\) 0.616500 0.0428497
\(208\) 0 0
\(209\) −4.90283 −0.339136
\(210\) 0 0
\(211\) −4.38104 4.38104i −0.301603 0.301603i 0.540038 0.841641i \(-0.318410\pi\)
−0.841641 + 0.540038i \(0.818410\pi\)
\(212\) 0 0
\(213\) −1.32013 + 1.32013i −0.0904541 + 0.0904541i
\(214\) 0 0
\(215\) 6.53246i 0.445510i
\(216\) 0 0
\(217\) 7.90794i 0.536826i
\(218\) 0 0
\(219\) 13.3072 13.3072i 0.899219 0.899219i
\(220\) 0 0
\(221\) −6.89191 6.89191i −0.463600 0.463600i
\(222\) 0 0
\(223\) −0.528935 −0.0354201 −0.0177101 0.999843i \(-0.505638\pi\)
−0.0177101 + 0.999843i \(0.505638\pi\)
\(224\) 0 0
\(225\) −0.416601 −0.0277734
\(226\) 0 0
\(227\) −17.8735 17.8735i −1.18631 1.18631i −0.978081 0.208224i \(-0.933232\pi\)
−0.208224 0.978081i \(-0.566768\pi\)
\(228\) 0 0
\(229\) −8.73248 + 8.73248i −0.577059 + 0.577059i −0.934092 0.357033i \(-0.883788\pi\)
0.357033 + 0.934092i \(0.383788\pi\)
\(230\) 0 0
\(231\) 1.38231i 0.0909491i
\(232\) 0 0
\(233\) 26.9485i 1.76545i 0.469885 + 0.882727i \(0.344295\pi\)
−0.469885 + 0.882727i \(0.655705\pi\)
\(234\) 0 0
\(235\) 3.38109 3.38109i 0.220558 0.220558i
\(236\) 0 0
\(237\) −9.00181 9.00181i −0.584730 0.584730i
\(238\) 0 0
\(239\) 19.8050 1.28108 0.640539 0.767926i \(-0.278711\pi\)
0.640539 + 0.767926i \(0.278711\pi\)
\(240\) 0 0
\(241\) 3.73993 0.240910 0.120455 0.992719i \(-0.461565\pi\)
0.120455 + 0.992719i \(0.461565\pi\)
\(242\) 0 0
\(243\) 1.48689 + 1.48689i 0.0953842 + 0.0953842i
\(244\) 0 0
\(245\) −1.87820 + 1.87820i −0.119994 + 0.119994i
\(246\) 0 0
\(247\) 33.0588i 2.10348i
\(248\) 0 0
\(249\) 26.4603i 1.67686i
\(250\) 0 0
\(251\) 10.1476 10.1476i 0.640510 0.640510i −0.310171 0.950681i \(-0.600386\pi\)
0.950681 + 0.310171i \(0.100386\pi\)
\(252\) 0 0
\(253\) 1.77749 + 1.77749i 0.111750 + 0.111750i
\(254\) 0 0
\(255\) −7.76976 −0.486561
\(256\) 0 0
\(257\) 12.6111 0.786657 0.393328 0.919398i \(-0.371324\pi\)
0.393328 + 0.919398i \(0.371324\pi\)
\(258\) 0 0
\(259\) −5.87262 5.87262i −0.364907 0.364907i
\(260\) 0 0
\(261\) 0.898582 0.898582i 0.0556208 0.0556208i
\(262\) 0 0
\(263\) 7.01176i 0.432364i 0.976353 + 0.216182i \(0.0693604\pi\)
−0.976353 + 0.216182i \(0.930640\pi\)
\(264\) 0 0
\(265\) 36.5752i 2.24680i
\(266\) 0 0
\(267\) 0.507149 0.507149i 0.0310370 0.0310370i
\(268\) 0 0
\(269\) −3.92307 3.92307i −0.239194 0.239194i 0.577323 0.816516i \(-0.304098\pi\)
−0.816516 + 0.577323i \(0.804098\pi\)
\(270\) 0 0
\(271\) 23.5746 1.43205 0.716026 0.698073i \(-0.245959\pi\)
0.716026 + 0.698073i \(0.245959\pi\)
\(272\) 0 0
\(273\) 9.32061 0.564109
\(274\) 0 0
\(275\) −1.20114 1.20114i −0.0724318 0.0724318i
\(276\) 0 0
\(277\) 7.89677 7.89677i 0.474471 0.474471i −0.428887 0.903358i \(-0.641094\pi\)
0.903358 + 0.428887i \(0.141094\pi\)
\(278\) 0 0
\(279\) 1.60290i 0.0959634i
\(280\) 0 0
\(281\) 33.1753i 1.97907i −0.144288 0.989536i \(-0.546089\pi\)
0.144288 0.989536i \(-0.453911\pi\)
\(282\) 0 0
\(283\) −2.06245 + 2.06245i −0.122600 + 0.122600i −0.765745 0.643145i \(-0.777629\pi\)
0.643145 + 0.765745i \(0.277629\pi\)
\(284\) 0 0
\(285\) 18.6348 + 18.6348i 1.10383 + 1.10383i
\(286\) 0 0
\(287\) 1.38922 0.0820030
\(288\) 0 0
\(289\) −13.9411 −0.820067
\(290\) 0 0
\(291\) 22.7260 + 22.7260i 1.33222 + 1.33222i
\(292\) 0 0
\(293\) 5.32453 5.32453i 0.311062 0.311062i −0.534259 0.845321i \(-0.679409\pi\)
0.845321 + 0.534259i \(0.179409\pi\)
\(294\) 0 0
\(295\) 17.8054i 1.03667i
\(296\) 0 0
\(297\) 4.42711i 0.256887i
\(298\) 0 0
\(299\) 11.9853 11.9853i 0.693126 0.693126i
\(300\) 0 0
\(301\) −1.73902 1.73902i −0.100235 0.100235i
\(302\) 0 0
\(303\) 11.5319 0.662491
\(304\) 0 0
\(305\) −11.6545 −0.667336
\(306\) 0 0
\(307\) 9.92446 + 9.92446i 0.566419 + 0.566419i 0.931123 0.364705i \(-0.118830\pi\)
−0.364705 + 0.931123i \(0.618830\pi\)
\(308\) 0 0
\(309\) 7.21235 7.21235i 0.410296 0.410296i
\(310\) 0 0
\(311\) 9.78126i 0.554644i 0.960777 + 0.277322i \(0.0894469\pi\)
−0.960777 + 0.277322i \(0.910553\pi\)
\(312\) 0 0
\(313\) 5.68720i 0.321460i −0.986998 0.160730i \(-0.948615\pi\)
0.986998 0.160730i \(-0.0513848\pi\)
\(314\) 0 0
\(315\) −0.380704 + 0.380704i −0.0214502 + 0.0214502i
\(316\) 0 0
\(317\) 21.8662 + 21.8662i 1.22813 + 1.22813i 0.964671 + 0.263457i \(0.0848625\pi\)
0.263457 + 0.964671i \(0.415137\pi\)
\(318\) 0 0
\(319\) 5.18159 0.290113
\(320\) 0 0
\(321\) 12.2993 0.686478
\(322\) 0 0
\(323\) −7.33631 7.33631i −0.408203 0.408203i
\(324\) 0 0
\(325\) −8.09907 + 8.09907i −0.449256 + 0.449256i
\(326\) 0 0
\(327\) 18.2141i 1.00724i
\(328\) 0 0
\(329\) 1.80017i 0.0992466i
\(330\) 0 0
\(331\) −8.75943 + 8.75943i −0.481462 + 0.481462i −0.905598 0.424137i \(-0.860578\pi\)
0.424137 + 0.905598i \(0.360578\pi\)
\(332\) 0 0
\(333\) −1.19035 1.19035i −0.0652310 0.0652310i
\(334\) 0 0
\(335\) −18.0724 −0.987400
\(336\) 0 0
\(337\) 19.1758 1.04457 0.522286 0.852771i \(-0.325079\pi\)
0.522286 + 0.852771i \(0.325079\pi\)
\(338\) 0 0
\(339\) 16.8700 + 16.8700i 0.916254 + 0.916254i
\(340\) 0 0
\(341\) −4.62150 + 4.62150i −0.250268 + 0.250268i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 13.5119i 0.727456i
\(346\) 0 0
\(347\) 6.37041 6.37041i 0.341982 0.341982i −0.515130 0.857112i \(-0.672256\pi\)
0.857112 + 0.515130i \(0.172256\pi\)
\(348\) 0 0
\(349\) −14.0831 14.0831i −0.753850 0.753850i 0.221346 0.975195i \(-0.428955\pi\)
−0.975195 + 0.221346i \(0.928955\pi\)
\(350\) 0 0
\(351\) 29.8511 1.59333
\(352\) 0 0
\(353\) 12.8957 0.686371 0.343185 0.939268i \(-0.388494\pi\)
0.343185 + 0.939268i \(0.388494\pi\)
\(354\) 0 0
\(355\) −2.09655 2.09655i −0.111274 0.111274i
\(356\) 0 0
\(357\) −2.06840 + 2.06840i −0.109471 + 0.109471i
\(358\) 0 0
\(359\) 33.5832i 1.77245i −0.463252 0.886227i \(-0.653318\pi\)
0.463252 0.886227i \(-0.346682\pi\)
\(360\) 0 0
\(361\) 16.1905i 0.852130i
\(362\) 0 0
\(363\) 12.2013 12.2013i 0.640401 0.640401i
\(364\) 0 0
\(365\) 21.1337 + 21.1337i 1.10619 + 1.10619i
\(366\) 0 0
\(367\) 7.74580 0.404328 0.202164 0.979352i \(-0.435203\pi\)
0.202164 + 0.979352i \(0.435203\pi\)
\(368\) 0 0
\(369\) 0.281589 0.0146589
\(370\) 0 0
\(371\) −9.73675 9.73675i −0.505507 0.505507i
\(372\) 0 0
\(373\) −1.84606 + 1.84606i −0.0955855 + 0.0955855i −0.753283 0.657697i \(-0.771531\pi\)
0.657697 + 0.753283i \(0.271531\pi\)
\(374\) 0 0
\(375\) 13.0818i 0.675543i
\(376\) 0 0
\(377\) 34.9384i 1.79942i
\(378\) 0 0
\(379\) 24.4450 24.4450i 1.25566 1.25566i 0.302511 0.953146i \(-0.402175\pi\)
0.953146 0.302511i \(-0.0978250\pi\)
\(380\) 0 0
\(381\) −10.6238 10.6238i −0.544275 0.544275i
\(382\) 0 0
\(383\) 22.2480 1.13682 0.568411 0.822745i \(-0.307559\pi\)
0.568411 + 0.822745i \(0.307559\pi\)
\(384\) 0 0
\(385\) −2.19529 −0.111882
\(386\) 0 0
\(387\) −0.352491 0.352491i −0.0179181 0.0179181i
\(388\) 0 0
\(389\) −6.93666 + 6.93666i −0.351703 + 0.351703i −0.860743 0.509040i \(-0.830000\pi\)
0.509040 + 0.860743i \(0.330000\pi\)
\(390\) 0 0
\(391\) 5.31947i 0.269017i
\(392\) 0 0
\(393\) 30.1685i 1.52180i
\(394\) 0 0
\(395\) 14.2961 14.2961i 0.719315 0.719315i
\(396\) 0 0
\(397\) −16.4042 16.4042i −0.823304 0.823304i 0.163277 0.986580i \(-0.447794\pi\)
−0.986580 + 0.163277i \(0.947794\pi\)
\(398\) 0 0
\(399\) 9.92162 0.496702
\(400\) 0 0
\(401\) −22.8150 −1.13932 −0.569662 0.821879i \(-0.692926\pi\)
−0.569662 + 0.821879i \(0.692926\pi\)
\(402\) 0 0
\(403\) 31.1618 + 31.1618i 1.55228 + 1.55228i
\(404\) 0 0
\(405\) 15.6846 15.6846i 0.779372 0.779372i
\(406\) 0 0
\(407\) 6.86407i 0.340239i
\(408\) 0 0
\(409\) 13.9196i 0.688281i −0.938918 0.344140i \(-0.888170\pi\)
0.938918 0.344140i \(-0.111830\pi\)
\(410\) 0 0
\(411\) −13.9465 + 13.9465i −0.687932 + 0.687932i
\(412\) 0 0
\(413\) 4.74002 + 4.74002i 0.233241 + 0.233241i
\(414\) 0 0
\(415\) 42.0226 2.06281
\(416\) 0 0
\(417\) 1.23945 0.0606962
\(418\) 0 0
\(419\) 25.1837 + 25.1837i 1.23030 + 1.23030i 0.963847 + 0.266455i \(0.0858523\pi\)
0.266455 + 0.963847i \(0.414148\pi\)
\(420\) 0 0
\(421\) −16.0774 + 16.0774i −0.783566 + 0.783566i −0.980431 0.196865i \(-0.936924\pi\)
0.196865 + 0.980431i \(0.436924\pi\)
\(422\) 0 0
\(423\) 0.364887i 0.0177414i
\(424\) 0 0
\(425\) 3.59464i 0.174366i
\(426\) 0 0
\(427\) −3.10257 + 3.10257i −0.150144 + 0.150144i
\(428\) 0 0
\(429\) 5.44708 + 5.44708i 0.262988 + 0.262988i
\(430\) 0 0
\(431\) −0.695976 −0.0335240 −0.0167620 0.999860i \(-0.505336\pi\)
−0.0167620 + 0.999860i \(0.505336\pi\)
\(432\) 0 0
\(433\) 26.4982 1.27342 0.636711 0.771103i \(-0.280295\pi\)
0.636711 + 0.771103i \(0.280295\pi\)
\(434\) 0 0
\(435\) −19.6943 19.6943i −0.944270 0.944270i
\(436\) 0 0
\(437\) 12.7581 12.7581i 0.610303 0.610303i
\(438\) 0 0
\(439\) 5.34131i 0.254927i −0.991843 0.127463i \(-0.959316\pi\)
0.991843 0.127463i \(-0.0406835\pi\)
\(440\) 0 0
\(441\) 0.202696i 0.00965217i
\(442\) 0 0
\(443\) 18.0337 18.0337i 0.856805 0.856805i −0.134155 0.990960i \(-0.542832\pi\)
0.990960 + 0.134155i \(0.0428321\pi\)
\(444\) 0 0
\(445\) 0.805422 + 0.805422i 0.0381807 + 0.0381807i
\(446\) 0 0
\(447\) −4.70360 −0.222473
\(448\) 0 0
\(449\) 5.57561 0.263129 0.131565 0.991308i \(-0.458000\pi\)
0.131565 + 0.991308i \(0.458000\pi\)
\(450\) 0 0
\(451\) 0.811878 + 0.811878i 0.0382298 + 0.0382298i
\(452\) 0 0
\(453\) −17.9629 + 17.9629i −0.843970 + 0.843970i
\(454\) 0 0
\(455\) 14.8024i 0.693948i
\(456\) 0 0
\(457\) 11.8678i 0.555151i −0.960704 0.277576i \(-0.910469\pi\)
0.960704 0.277576i \(-0.0895309\pi\)
\(458\) 0 0
\(459\) −6.62446 + 6.62446i −0.309203 + 0.309203i
\(460\) 0 0
\(461\) −25.1973 25.1973i −1.17356 1.17356i −0.981356 0.192200i \(-0.938438\pi\)
−0.192200 0.981356i \(-0.561562\pi\)
\(462\) 0 0
\(463\) −31.1785 −1.44899 −0.724494 0.689281i \(-0.757926\pi\)
−0.724494 + 0.689281i \(0.757926\pi\)
\(464\) 0 0
\(465\) 35.1310 1.62916
\(466\) 0 0
\(467\) −4.86260 4.86260i −0.225014 0.225014i 0.585592 0.810606i \(-0.300862\pi\)
−0.810606 + 0.585592i \(0.800862\pi\)
\(468\) 0 0
\(469\) −4.81108 + 4.81108i −0.222155 + 0.222155i
\(470\) 0 0
\(471\) 18.7243i 0.862772i
\(472\) 0 0
\(473\) 2.03261i 0.0934594i
\(474\) 0 0
\(475\) −8.62131 + 8.62131i −0.395573 + 0.395573i
\(476\) 0 0
\(477\) −1.97360 1.97360i −0.0903648 0.0903648i
\(478\) 0 0
\(479\) −13.2313 −0.604555 −0.302277 0.953220i \(-0.597747\pi\)
−0.302277 + 0.953220i \(0.597747\pi\)
\(480\) 0 0
\(481\) −46.2830 −2.11032
\(482\) 0 0
\(483\) −3.59702 3.59702i −0.163670 0.163670i
\(484\) 0 0
\(485\) −36.0920 + 36.0920i −1.63886 + 1.63886i
\(486\) 0 0
\(487\) 27.6451i 1.25272i −0.779534 0.626360i \(-0.784544\pi\)
0.779534 0.626360i \(-0.215456\pi\)
\(488\) 0 0
\(489\) 14.9527i 0.676185i
\(490\) 0 0
\(491\) 5.28148 5.28148i 0.238350 0.238350i −0.577817 0.816167i \(-0.696095\pi\)
0.816167 + 0.577817i \(0.196095\pi\)
\(492\) 0 0
\(493\) 7.75342 + 7.75342i 0.349196 + 0.349196i
\(494\) 0 0
\(495\) −0.444976 −0.0200002
\(496\) 0 0
\(497\) −1.11625 −0.0500709
\(498\) 0 0
\(499\) −28.8375 28.8375i −1.29094 1.29094i −0.934203 0.356741i \(-0.883888\pi\)
−0.356741 0.934203i \(-0.616112\pi\)
\(500\) 0 0
\(501\) −26.6407 + 26.6407i −1.19022 + 1.19022i
\(502\) 0 0
\(503\) 16.8595i 0.751729i −0.926675 0.375864i \(-0.877346\pi\)
0.926675 0.375864i \(-0.122654\pi\)
\(504\) 0 0
\(505\) 18.3142i 0.814973i
\(506\) 0 0
\(507\) 21.3542 21.3542i 0.948372 0.948372i
\(508\) 0 0
\(509\) 21.3899 + 21.3899i 0.948093 + 0.948093i 0.998718 0.0506250i \(-0.0161213\pi\)
−0.0506250 + 0.998718i \(0.516121\pi\)
\(510\) 0 0
\(511\) 11.2521 0.497762
\(512\) 0 0
\(513\) 31.7759 1.40294
\(514\) 0 0
\(515\) 11.4542 + 11.4542i 0.504732 + 0.504732i
\(516\) 0 0
\(517\) 1.05204 1.05204i 0.0462688 0.0462688i
\(518\) 0 0
\(519\) 0.0250509i 0.00109961i
\(520\) 0 0
\(521\) 29.9153i 1.31061i −0.755363 0.655307i \(-0.772539\pi\)
0.755363 0.655307i \(-0.227461\pi\)
\(522\) 0 0
\(523\) −12.6212 + 12.6212i −0.551885 + 0.551885i −0.926985 0.375099i \(-0.877609\pi\)
0.375099 + 0.926985i \(0.377609\pi\)
\(524\) 0 0
\(525\) 2.43070 + 2.43070i 0.106084 + 0.106084i
\(526\) 0 0
\(527\) −13.8307 −0.602473
\(528\) 0 0
\(529\) 13.7492 0.597793
\(530\) 0 0
\(531\) 0.960781 + 0.960781i 0.0416943 + 0.0416943i
\(532\) 0 0
\(533\) 5.47432 5.47432i 0.237119 0.237119i
\(534\) 0 0
\(535\) 19.5329i 0.844482i
\(536\) 0 0
\(537\) 33.9583i 1.46541i
\(538\) 0 0
\(539\) −0.584413 + 0.584413i −0.0251724 + 0.0251724i
\(540\) 0 0
\(541\) −6.98421 6.98421i −0.300275 0.300275i 0.540847 0.841121i \(-0.318104\pi\)
−0.841121 + 0.540847i \(0.818104\pi\)
\(542\) 0 0
\(543\) −20.4674 −0.878339
\(544\) 0 0
\(545\) −28.9264 −1.23907
\(546\) 0 0
\(547\) 19.0691 + 19.0691i 0.815337 + 0.815337i 0.985428 0.170091i \(-0.0544062\pi\)
−0.170091 + 0.985428i \(0.554406\pi\)
\(548\) 0 0
\(549\) −0.628877 + 0.628877i −0.0268398 + 0.0268398i
\(550\) 0 0
\(551\) 37.1912i 1.58440i
\(552\) 0 0
\(553\) 7.61158i 0.323677i
\(554\) 0 0
\(555\) −26.0891 + 26.0891i −1.10742 + 1.10742i
\(556\) 0 0
\(557\) −10.7024 10.7024i −0.453474 0.453474i 0.443032 0.896506i \(-0.353903\pi\)
−0.896506 + 0.443032i \(0.853903\pi\)
\(558\) 0 0
\(559\) −13.7055 −0.579679
\(560\) 0 0
\(561\) −2.41760 −0.102071
\(562\) 0 0
\(563\) 6.53316 + 6.53316i 0.275340 + 0.275340i 0.831246 0.555905i \(-0.187628\pi\)
−0.555905 + 0.831246i \(0.687628\pi\)
\(564\) 0 0
\(565\) −26.7919 + 26.7919i −1.12714 + 1.12714i
\(566\) 0 0
\(567\) 8.35083i 0.350702i
\(568\) 0 0
\(569\) 36.7286i 1.53974i 0.638199 + 0.769871i \(0.279680\pi\)
−0.638199 + 0.769871i \(0.720320\pi\)
\(570\) 0 0
\(571\) −23.7908 + 23.7908i −0.995613 + 0.995613i −0.999990 0.00437721i \(-0.998607\pi\)
0.00437721 + 0.999990i \(0.498607\pi\)
\(572\) 0 0
\(573\) −20.3516 20.3516i −0.850200 0.850200i
\(574\) 0 0
\(575\) 6.25121 0.260694
\(576\) 0 0
\(577\) −5.87217 −0.244462 −0.122231 0.992502i \(-0.539005\pi\)
−0.122231 + 0.992502i \(0.539005\pi\)
\(578\) 0 0
\(579\) −8.29014 8.29014i −0.344527 0.344527i
\(580\) 0 0
\(581\) 11.1869 11.1869i 0.464112 0.464112i
\(582\) 0 0
\(583\) 11.3806i 0.471335i
\(584\) 0 0
\(585\) 3.00038i 0.124051i
\(586\) 0 0
\(587\) −11.0010 + 11.0010i −0.454060 + 0.454060i −0.896700 0.442639i \(-0.854042\pi\)
0.442639 + 0.896700i \(0.354042\pi\)
\(588\) 0 0
\(589\) 33.1712 + 33.1712i 1.36679 + 1.36679i
\(590\) 0 0
\(591\) 36.4669 1.50005
\(592\) 0 0
\(593\) 26.8167 1.10123 0.550616 0.834759i \(-0.314393\pi\)
0.550616 + 0.834759i \(0.314393\pi\)
\(594\) 0 0
\(595\) −3.28490 3.28490i −0.134668 0.134668i
\(596\) 0 0
\(597\) −18.1516 + 18.1516i −0.742894 + 0.742894i
\(598\) 0 0
\(599\) 44.9307i 1.83582i −0.396791 0.917909i \(-0.629876\pi\)
0.396791 0.917909i \(-0.370124\pi\)
\(600\) 0 0
\(601\) 40.2092i 1.64017i −0.572244 0.820083i \(-0.693927\pi\)
0.572244 0.820083i \(-0.306073\pi\)
\(602\) 0 0
\(603\) −0.975185 + 0.975185i −0.0397126 + 0.0397126i
\(604\) 0 0
\(605\) 19.3773 + 19.3773i 0.787799 + 0.787799i
\(606\) 0 0
\(607\) 20.7271 0.841286 0.420643 0.907226i \(-0.361805\pi\)
0.420643 + 0.907226i \(0.361805\pi\)
\(608\) 0 0
\(609\) −10.4857 −0.424903
\(610\) 0 0
\(611\) −7.09371 7.09371i −0.286981 0.286981i
\(612\) 0 0
\(613\) −5.43581 + 5.43581i −0.219550 + 0.219550i −0.808309 0.588759i \(-0.799617\pi\)
0.588759 + 0.808309i \(0.299617\pi\)
\(614\) 0 0
\(615\) 6.17161i 0.248863i
\(616\) 0 0
\(617\) 24.8297i 0.999607i 0.866139 + 0.499803i \(0.166594\pi\)
−0.866139 + 0.499803i \(0.833406\pi\)
\(618\) 0 0
\(619\) −13.2178 + 13.2178i −0.531267 + 0.531267i −0.920949 0.389683i \(-0.872585\pi\)
0.389683 + 0.920949i \(0.372585\pi\)
\(620\) 0 0
\(621\) −11.5202 11.5202i −0.462289 0.462289i
\(622\) 0 0
\(623\) 0.428825 0.0171805
\(624\) 0 0
\(625\) 31.0522 1.24209
\(626\) 0 0
\(627\) 5.79832 + 5.79832i 0.231563 + 0.231563i
\(628\) 0 0
\(629\) 10.2710 10.2710i 0.409531 0.409531i
\(630\) 0 0
\(631\) 30.4138i 1.21075i 0.795939 + 0.605377i \(0.206978\pi\)
−0.795939 + 0.605377i \(0.793022\pi\)
\(632\) 0 0
\(633\) 10.3624i 0.411870i
\(634\) 0 0
\(635\) 16.8721 16.8721i 0.669549 0.669549i
\(636\) 0 0
\(637\) 3.94057 + 3.94057i 0.156131 + 0.156131i
\(638\) 0 0
\(639\) −0.226260 −0.00895071
\(640\) 0 0
\(641\) −41.7486 −1.64897 −0.824485 0.565884i \(-0.808535\pi\)
−0.824485 + 0.565884i \(0.808535\pi\)
\(642\) 0 0
\(643\) 15.4137 + 15.4137i 0.607857 + 0.607857i 0.942386 0.334529i \(-0.108577\pi\)
−0.334529 + 0.942386i \(0.608577\pi\)
\(644\) 0 0
\(645\) −7.72559 + 7.72559i −0.304195 + 0.304195i
\(646\) 0 0
\(647\) 8.85923i 0.348292i −0.984720 0.174146i \(-0.944283\pi\)
0.984720 0.174146i \(-0.0557165\pi\)
\(648\) 0 0
\(649\) 5.54026i 0.217474i
\(650\) 0 0
\(651\) 9.35230 9.35230i 0.366545 0.366545i
\(652\) 0 0
\(653\) 2.42659 + 2.42659i 0.0949598 + 0.0949598i 0.752991 0.658031i \(-0.228610\pi\)
−0.658031 + 0.752991i \(0.728610\pi\)
\(654\) 0 0
\(655\) −47.9117 −1.87206
\(656\) 0 0
\(657\) 2.28075 0.0889804
\(658\) 0 0
\(659\) −23.3045 23.3045i −0.907815 0.907815i 0.0882806 0.996096i \(-0.471863\pi\)
−0.996096 + 0.0882806i \(0.971863\pi\)
\(660\) 0 0
\(661\) 23.2433 23.2433i 0.904059 0.904059i −0.0917252 0.995784i \(-0.529238\pi\)
0.995784 + 0.0917252i \(0.0292381\pi\)
\(662\) 0 0
\(663\) 16.3014i 0.633093i
\(664\) 0 0
\(665\) 15.7569i 0.611026i
\(666\) 0 0
\(667\) −13.4835 + 13.4835i −0.522082 + 0.522082i
\(668\) 0 0
\(669\) 0.625543 + 0.625543i 0.0241849 + 0.0241849i
\(670\) 0 0
\(671\) −3.62636 −0.139994
\(672\) 0 0
\(673\) 46.7430 1.80181 0.900906 0.434014i \(-0.142903\pi\)
0.900906 + 0.434014i \(0.142903\pi\)
\(674\) 0 0
\(675\) 7.78478 + 7.78478i 0.299636 + 0.299636i
\(676\) 0 0
\(677\) 30.0928 30.0928i 1.15656 1.15656i 0.171351 0.985210i \(-0.445187\pi\)
0.985210 0.171351i \(-0.0548132\pi\)
\(678\) 0 0
\(679\) 19.2163i 0.737452i
\(680\) 0 0
\(681\) 42.2760i 1.62002i
\(682\) 0 0
\(683\) 25.4691 25.4691i 0.974548 0.974548i −0.0251358 0.999684i \(-0.508002\pi\)
0.999684 + 0.0251358i \(0.00800181\pi\)
\(684\) 0 0
\(685\) −22.1490 22.1490i −0.846270 0.846270i
\(686\) 0 0
\(687\) 20.6549 0.788033
\(688\) 0 0
\(689\) −76.7368 −2.92344
\(690\) 0 0
\(691\) 15.5437 + 15.5437i 0.591311 + 0.591311i 0.937986 0.346674i \(-0.112689\pi\)
−0.346674 + 0.937986i \(0.612689\pi\)
\(692\) 0 0
\(693\) −0.118458 + 0.118458i −0.00449984 + 0.00449984i
\(694\) 0 0
\(695\) 1.96842i 0.0746664i
\(696\) 0 0
\(697\) 2.42969i 0.0920311i
\(698\) 0 0
\(699\) 31.8705 31.8705i 1.20545 1.20545i
\(700\) 0 0
\(701\) −5.59915 5.59915i −0.211477 0.211477i 0.593418 0.804895i \(-0.297778\pi\)
−0.804895 + 0.593418i \(0.797778\pi\)
\(702\) 0 0
\(703\) −49.2674 −1.85815
\(704\) 0 0
\(705\) −7.99726 −0.301194
\(706\) 0 0
\(707\) 4.87547 + 4.87547i 0.183361 + 0.183361i
\(708\) 0 0
\(709\) −0.685858 + 0.685858i −0.0257579 + 0.0257579i −0.719868 0.694111i \(-0.755798\pi\)
0.694111 + 0.719868i \(0.255798\pi\)
\(710\) 0 0
\(711\) 1.54283i 0.0578608i
\(712\) 0 0
\(713\) 24.0520i 0.900756i
\(714\) 0 0
\(715\) −8.65072 + 8.65072i −0.323518 + 0.323518i
\(716\) 0 0
\(717\) −23.4223 23.4223i −0.874721 0.874721i
\(718\) 0 0
\(719\) 10.0440 0.374579 0.187289 0.982305i \(-0.440030\pi\)
0.187289 + 0.982305i \(0.440030\pi\)
\(720\) 0 0
\(721\) 6.09849 0.227119
\(722\) 0 0
\(723\) −4.42302 4.42302i −0.164494 0.164494i
\(724\) 0 0
\(725\) 9.11148 9.11148i 0.338392 0.338392i
\(726\) 0 0
\(727\) 5.53235i 0.205184i −0.994724 0.102592i \(-0.967286\pi\)
0.994724 0.102592i \(-0.0327135\pi\)
\(728\) 0 0
\(729\) 28.5694i 1.05813i
\(730\) 0 0
\(731\) 3.04147 3.04147i 0.112493 0.112493i
\(732\) 0 0
\(733\) 3.98509 + 3.98509i 0.147193 + 0.147193i 0.776863 0.629670i \(-0.216810\pi\)
−0.629670 + 0.776863i \(0.716810\pi\)
\(734\) 0 0
\(735\) 4.44250 0.163864
\(736\) 0 0
\(737\) −5.62331 −0.207137
\(738\) 0 0
\(739\) −2.19669 2.19669i −0.0808065 0.0808065i 0.665548 0.746355i \(-0.268198\pi\)
−0.746355 + 0.665548i \(0.768198\pi\)
\(740\) 0 0
\(741\) 39.0969 39.0969i 1.43626 1.43626i
\(742\) 0 0
\(743\) 22.5404i 0.826927i 0.910521 + 0.413464i \(0.135681\pi\)
−0.910521 + 0.413464i \(0.864319\pi\)
\(744\) 0 0
\(745\) 7.46996i 0.273678i
\(746\) 0 0
\(747\) 2.26754 2.26754i 0.0829649 0.0829649i
\(748\) 0 0
\(749\) 5.19989 + 5.19989i 0.190000 + 0.190000i
\(750\) 0 0
\(751\) −14.8752 −0.542805 −0.271403 0.962466i \(-0.587487\pi\)
−0.271403 + 0.962466i \(0.587487\pi\)
\(752\) 0 0
\(753\) −24.0020 −0.874682
\(754\) 0 0
\(755\) −28.5275 28.5275i −1.03822 1.03822i
\(756\) 0 0
\(757\) 0.982488 0.982488i 0.0357091 0.0357091i −0.689027 0.724736i \(-0.741962\pi\)
0.724736 + 0.689027i \(0.241962\pi\)
\(758\) 0 0
\(759\) 4.20429i 0.152606i
\(760\) 0 0
\(761\) 19.9186i 0.722049i 0.932556 + 0.361024i \(0.117573\pi\)
−0.932556 + 0.361024i \(0.882427\pi\)
\(762\) 0 0
\(763\) −7.70055 + 7.70055i −0.278779 + 0.278779i
\(764\) 0 0
\(765\) −0.665836 0.665836i −0.0240733 0.0240733i
\(766\) 0 0
\(767\) 37.3568 1.34888
\(768\) 0 0
\(769\) −9.78665 −0.352915 −0.176458 0.984308i \(-0.556464\pi\)
−0.176458 + 0.984308i \(0.556464\pi\)
\(770\) 0 0
\(771\) −14.9144 14.9144i −0.537130 0.537130i
\(772\) 0 0
\(773\) 19.6983 19.6983i 0.708499 0.708499i −0.257720 0.966220i \(-0.582971\pi\)
0.966220 + 0.257720i \(0.0829713\pi\)
\(774\) 0 0
\(775\) 16.2532i 0.583832i
\(776\) 0 0
\(777\) 13.8905i 0.498318i
\(778\) 0 0
\(779\) 5.82731 5.82731i 0.208785 0.208785i
\(780\) 0 0
\(781\) −0.652354 0.652354i −0.0233430 0.0233430i
\(782\) 0 0
\(783\) −33.5825 −1.20014
\(784\) 0 0
\(785\) −29.7368 −1.06135
\(786\) 0 0
\(787\) 30.9238 + 30.9238i 1.10231 + 1.10231i 0.994131 + 0.108184i \(0.0345035\pi\)
0.108184 + 0.994131i \(0.465496\pi\)
\(788\) 0 0
\(789\) 8.29244 8.29244i 0.295219 0.295219i
\(790\) 0 0
\(791\) 14.2646i 0.507192i
\(792\) 0 0
\(793\) 24.4518i 0.868309i
\(794\) 0 0
\(795\) −43.2555 + 43.2555i −1.53412 + 1.53412i
\(796\) 0 0
\(797\) 32.5005 + 32.5005i 1.15123 + 1.15123i 0.986307 + 0.164919i \(0.0527364\pi\)
0.164919 + 0.986307i \(0.447264\pi\)
\(798\) 0 0
\(799\) 3.14843