Properties

Label 1792.2.m.h.449.3
Level $1792$
Weight $2$
Character 1792.449
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 449.3
Root \(0.792206 - 1.03242i\) of defining polynomial
Character \(\chi\) \(=\) 1792.449
Dual form 1792.2.m.h.1345.3

$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

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

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 −0.960630 0.277829i \(-0.910385\pi\)
0.277829 + 0.960630i \(0.410385\pi\)
\(4\) 0 0
\(5\) 1.87820 + 1.87820i 0.839958 + 0.839958i 0.988853 0.148895i \(-0.0475715\pi\)
−0.148895 + 0.988853i \(0.547572\pi\)
\(6\) 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 0.789700 0.613493i \(-0.210236\pi\)
−0.613493 + 0.789700i \(0.710236\pi\)
\(12\) 0 0
\(13\) −3.94057 + 3.94057i −1.09292 + 1.09292i −0.0977031 + 0.995216i \(0.531150\pi\)
−0.995216 + 0.0977031i \(0.968850\pi\)
\(14\) 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 −0.999316 0.0369927i \(-0.988222\pi\)
0.0369927 + 0.999316i \(0.488222\pi\)
\(20\) 0 0
\(21\) −1.18265 1.18265i −0.258075 0.258075i
\(22\) 0 0
\(23\) 3.04150i 0.634198i −0.948393 0.317099i \(-0.897291\pi\)
0.948393 0.317099i \(-0.102709\pi\)
\(24\) 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 −0.163351 0.986568i \(-0.552230\pi\)
0.986568 + 0.163351i \(0.0522304\pi\)
\(30\) 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 0.999423 0.0339701i \(-0.0108151\pi\)
−0.0339701 + 0.999423i \(0.510815\pi\)
\(38\) 0 0
\(39\) 9.32061i 1.49249i
\(40\) 0 0
\(41\) 1.38922i 0.216960i −0.994099 0.108480i \(-0.965402\pi\)
0.994099 0.108480i \(-0.0345983\pi\)
\(42\) 0 0
\(43\) 1.73902 + 1.73902i 0.265198 + 0.265198i 0.827162 0.561964i \(-0.189954\pi\)
−0.561964 + 0.827162i \(0.689954\pi\)
\(44\) 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 0.898527 + 0.438919i \(0.144639\pi\)
0.438919 + 0.898527i \(0.355361\pi\)
\(54\) 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 0.327688 0.944786i \(-0.393731\pi\)
−0.944786 + 0.327688i \(0.893731\pi\)
\(60\) 0 0
\(61\) −3.10257 + 3.10257i −0.397243 + 0.397243i −0.877260 0.480016i \(-0.840631\pi\)
0.480016 + 0.877260i \(0.340631\pi\)
\(62\) 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 −0.937026 0.349259i \(-0.886433\pi\)
0.349259 + 0.937026i \(0.386433\pi\)
\(68\) 0 0
\(69\) 3.59702 + 3.59702i 0.433031 + 0.433031i
\(70\) 0 0
\(71\) 1.11625i 0.132475i 0.997804 + 0.0662375i \(0.0210995\pi\)
−0.997804 + 0.0662375i \(0.978900\pi\)
\(72\) 0 0
\(73\) 11.2521i 1.31696i −0.752600 0.658478i \(-0.771201\pi\)
0.752600 0.658478i \(-0.228799\pi\)
\(74\) 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 0.263176 0.964748i \(-0.415230\pi\)
0.964748 0.263176i \(-0.0847700\pi\)
\(84\) 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 \(-0.992765\pi\)
0.999742 0.0227277i \(-0.00723508\pi\)
\(90\) 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 0.421637 0.906765i \(-0.361456\pi\)
−0.906765 + 0.421637i \(0.861456\pi\)
\(102\) 0 0
\(103\) 6.09849i 0.600902i −0.953797 0.300451i \(-0.902863\pi\)
0.953797 0.300451i \(-0.0971371\pi\)
\(104\) 0 0
\(105\) 4.44250i 0.433544i
\(106\) 0 0
\(107\) −5.19989 5.19989i −0.502693 0.502693i 0.409581 0.912274i \(-0.365675\pi\)
−0.912274 + 0.409581i \(0.865675\pi\)
\(108\) 0 0
\(109\) −7.70055 + 7.70055i −0.737579 + 0.737579i −0.972109 0.234530i \(-0.924645\pi\)
0.234530 + 0.972109i \(0.424645\pi\)
\(110\) 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 −0.121828 + 0.992551i \(0.538876\pi\)
−0.992551 + 0.121828i \(0.961124\pi\)
\(132\) 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 \(0.168049\pi\)
−0.863845 + 0.503757i \(0.831951\pi\)
\(138\) 0 0
\(139\) −0.524016 0.524016i −0.0444465 0.0444465i 0.684534 0.728981i \(-0.260006\pi\)
−0.728981 + 0.684534i \(0.760006\pi\)
\(140\) 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 0.783855 0.620944i \(-0.213250\pi\)
−0.620944 + 0.783855i \(0.713250\pi\)
\(150\) 0 0
\(151\) 15.1887i 1.23604i 0.786162 + 0.618020i \(0.212065\pi\)
−0.786162 + 0.618020i \(0.787935\pi\)
\(152\) 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 −0.948516 0.316728i \(-0.897416\pi\)
0.316728 + 0.948516i \(0.397416\pi\)
\(158\) 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 −0.414771 0.909926i \(-0.636138\pi\)
0.909926 + 0.414771i \(0.136138\pi\)
\(164\) 0 0
\(165\) −2.59626 2.59626i −0.202118 0.202118i
\(166\) 0 0
\(167\) 22.5263i 1.74314i 0.490271 + 0.871570i \(0.336898\pi\)
−0.490271 + 0.871570i \(0.663102\pi\)
\(168\) 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 −0.707509 0.706704i \(-0.750181\pi\)
0.706704 + 0.707509i \(0.250181\pi\)
\(174\) 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 −0.0759779 + 0.997109i \(0.524208\pi\)
−0.997109 + 0.0759779i \(0.975792\pi\)
\(180\) 0 0
\(181\) 8.65321 + 8.65321i 0.643188 + 0.643188i 0.951338 0.308150i \(-0.0997098\pi\)
−0.308150 + 0.951338i \(0.599710\pi\)
\(182\) 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 −0.994592 0.103860i \(-0.966881\pi\)
−0.103860 0.994592i \(-0.533119\pi\)
\(198\) 0 0
\(199\) 15.3483i 1.08801i 0.839082 + 0.544005i \(0.183093\pi\)
−0.839082 + 0.544005i \(0.816907\pi\)
\(200\) 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 −0.841641 0.540038i \(-0.818410\pi\)
0.540038 + 0.841641i \(0.318410\pi\)
\(212\) 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 −0.208224 + 0.978081i \(0.566768\pi\)
−0.978081 + 0.208224i \(0.933232\pi\)
\(228\) 0 0
\(229\) −8.73248 8.73248i −0.577059 0.577059i 0.357033 0.934092i \(-0.383788\pi\)
−0.934092 + 0.357033i \(0.883788\pi\)
\(230\) 0 0
\(231\) 1.38231i 0.0909491i
\(232\) 0 0
\(233\) 26.9485i 1.76545i −0.469885 0.882727i \(-0.655705\pi\)
0.469885 0.882727i \(-0.344295\pi\)
\(234\) 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 0.950681 0.310171i \(-0.100386\pi\)
−0.310171 + 0.950681i \(0.600386\pi\)
\(252\) 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 \(-0.930640\pi\)
0.976353 0.216182i \(-0.0693604\pi\)
\(264\) 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 −0.816516 0.577323i \(-0.804098\pi\)
0.577323 + 0.816516i \(0.304098\pi\)
\(270\) 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 0.903358 0.428887i \(-0.141094\pi\)
−0.428887 + 0.903358i \(0.641094\pi\)
\(278\) 0 0
\(279\) 1.60290i 0.0959634i
\(280\) 0 0
\(281\) 33.1753i 1.97907i 0.144288 + 0.989536i \(0.453911\pi\)
−0.144288 + 0.989536i \(0.546089\pi\)
\(282\) 0 0
\(283\) −2.06245 2.06245i −0.122600 0.122600i 0.643145 0.765745i \(-0.277629\pi\)
−0.765745 + 0.643145i \(0.777629\pi\)
\(284\) 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 0.845321 0.534259i \(-0.179409\pi\)
−0.534259 + 0.845321i \(0.679409\pi\)
\(294\) 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 −0.364705 0.931123i \(-0.618830\pi\)
0.931123 + 0.364705i \(0.118830\pi\)
\(308\) 0 0
\(309\) 7.21235 + 7.21235i 0.410296 + 0.410296i
\(310\) 0 0
\(311\) 9.78126i 0.554644i −0.960777 0.277322i \(-0.910553\pi\)
0.960777 0.277322i \(-0.0894469\pi\)
\(312\) 0 0
\(313\) 5.68720i 0.321460i 0.986998 + 0.160730i \(0.0513848\pi\)
−0.986998 + 0.160730i \(0.948615\pi\)
\(314\) 0 0
\(315\) −0.380704 0.380704i −0.0214502 0.0214502i
\(316\) 0 0
\(317\) 21.8662 21.8662i 1.22813 1.22813i 0.263457 0.964671i \(-0.415137\pi\)
0.964671 0.263457i \(-0.0848625\pi\)
\(318\) 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 0.424137 0.905598i \(-0.360578\pi\)
−0.905598 + 0.424137i \(0.860578\pi\)
\(332\) 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 0.857112 0.515130i \(-0.172256\pi\)
−0.515130 + 0.857112i \(0.672256\pi\)
\(348\) 0 0
\(349\) −14.0831 + 14.0831i −0.753850 + 0.753850i −0.975195 0.221346i \(-0.928955\pi\)
0.221346 + 0.975195i \(0.428955\pi\)
\(350\) 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 \(0.346682\pi\)
−0.463252 + 0.886227i \(0.653318\pi\)
\(360\) 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 0.657697 0.753283i \(-0.271531\pi\)
−0.753283 + 0.657697i \(0.771531\pi\)
\(374\) 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 0.953146 + 0.302511i \(0.0978250\pi\)
0.302511 + 0.953146i \(0.402175\pi\)
\(380\) 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 0.509040 0.860743i \(-0.330000\pi\)
−0.860743 + 0.509040i \(0.830000\pi\)
\(390\) 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 −0.986580 0.163277i \(-0.947794\pi\)
0.163277 + 0.986580i \(0.447794\pi\)
\(398\) 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 \(0.111830\pi\)
−0.938918 + 0.344140i \(0.888170\pi\)
\(410\) 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 0.266455 0.963847i \(-0.414148\pi\)
0.963847 0.266455i \(-0.0858523\pi\)
\(420\) 0 0
\(421\) −16.0774 16.0774i −0.783566 0.783566i 0.196865 0.980431i \(-0.436924\pi\)
−0.980431 + 0.196865i \(0.936924\pi\)
\(422\) 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 \(0.0406835\pi\)
−0.991843 + 0.127463i \(0.959316\pi\)
\(440\) 0 0
\(441\) 0.202696i 0.00965217i
\(442\) 0 0
\(443\) 18.0337 + 18.0337i 0.856805 + 0.856805i 0.990960 0.134155i \(-0.0428321\pi\)
−0.134155 + 0.990960i \(0.542832\pi\)
\(444\) 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 \(0.0895309\pi\)
−0.960704 + 0.277576i \(0.910469\pi\)
\(458\) 0 0
\(459\) −6.62446 6.62446i −0.309203 0.309203i
\(460\) 0 0
\(461\) −25.1973 + 25.1973i −1.17356 + 1.17356i −0.192200 + 0.981356i \(0.561562\pi\)
−0.981356 + 0.192200i \(0.938438\pi\)
\(462\) 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 −0.810606 0.585592i \(-0.800862\pi\)
0.585592 + 0.810606i \(0.300862\pi\)
\(468\) 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 \(0.215456\pi\)
−0.779534 + 0.626360i \(0.784544\pi\)
\(488\) 0 0
\(489\) 14.9527i 0.676185i
\(490\) 0 0
\(491\) 5.28148 + 5.28148i 0.238350 + 0.238350i 0.816167 0.577817i \(-0.196095\pi\)
−0.577817 + 0.816167i \(0.696095\pi\)
\(492\) 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 −0.356741 + 0.934203i \(0.616112\pi\)
−0.934203 + 0.356741i \(0.883888\pi\)
\(500\) 0 0
\(501\) −26.6407 26.6407i −1.19022 1.19022i
\(502\) 0 0
\(503\) 16.8595i 0.751729i 0.926675 + 0.375864i \(0.122654\pi\)
−0.926675 + 0.375864i \(0.877346\pi\)
\(504\) 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 −0.0506250 0.998718i \(-0.516121\pi\)
0.998718 + 0.0506250i \(0.0161213\pi\)
\(510\) 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 \(0.227461\pi\)
−0.755363 + 0.655307i \(0.772539\pi\)
\(522\) 0 0
\(523\) −12.6212 12.6212i −0.551885 0.551885i 0.375099 0.926985i \(-0.377609\pi\)
−0.926985 + 0.375099i \(0.877609\pi\)
\(524\) 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 −0.841121 0.540847i \(-0.818104\pi\)
0.540847 + 0.841121i \(0.318104\pi\)
\(542\) 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 −0.170091 0.985428i \(-0.554406\pi\)
0.985428 + 0.170091i \(0.0544062\pi\)
\(548\) 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 −0.896506 0.443032i \(-0.853903\pi\)
0.443032 + 0.896506i \(0.353903\pi\)
\(558\) 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 −0.555905 0.831246i \(-0.687628\pi\)
0.831246 + 0.555905i \(0.187628\pi\)
\(564\) 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 \(-0.720320\pi\)
0.638199 0.769871i \(-0.279680\pi\)
\(570\) 0 0
\(571\) −23.7908 23.7908i −0.995613 0.995613i 0.00437721 0.999990i \(-0.498607\pi\)
−0.999990 + 0.00437721i \(0.998607\pi\)
\(572\) 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 0.442639 0.896700i \(-0.354042\pi\)
−0.896700 + 0.442639i \(0.854042\pi\)
\(588\) 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 \(0.370124\pi\)
−0.396791 + 0.917909i \(0.629876\pi\)
\(600\) 0 0
\(601\) 40.2092i 1.64017i 0.572244 + 0.820083i \(0.306073\pi\)
−0.572244 + 0.820083i \(0.693927\pi\)
\(602\) 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 0.588759 0.808309i \(-0.299617\pi\)
−0.808309 + 0.588759i \(0.799617\pi\)
\(614\) 0 0
\(615\) 6.17161i 0.248863i
\(616\) 0 0
\(617\) 24.8297i 0.999607i −0.866139 0.499803i \(-0.833406\pi\)
0.866139 0.499803i \(-0.166594\pi\)
\(618\) 0 0
\(619\) −13.2178 13.2178i −0.531267 0.531267i 0.389683 0.920949i \(-0.372585\pi\)
−0.920949 + 0.389683i \(0.872585\pi\)
\(620\) 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 \(-0.793022\pi\)
0.795939 0.605377i \(-0.206978\pi\)
\(632\) 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 −0.334529 0.942386i \(-0.608577\pi\)
0.942386 + 0.334529i \(0.108577\pi\)
\(644\) 0 0
\(645\) −7.72559 7.72559i −0.304195 0.304195i
\(646\) 0 0
\(647\) 8.85923i 0.348292i 0.984720 + 0.174146i \(0.0557165\pi\)
−0.984720 + 0.174146i \(0.944283\pi\)
\(648\) 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 −0.658031 0.752991i \(-0.728610\pi\)
0.752991 + 0.658031i \(0.228610\pi\)
\(654\) 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 −0.996096 0.0882806i \(-0.971863\pi\)
0.0882806 + 0.996096i \(0.471863\pi\)
\(660\) 0 0
\(661\) 23.2433 + 23.2433i 0.904059 + 0.904059i 0.995784 0.0917252i \(-0.0292381\pi\)
−0.0917252 + 0.995784i \(0.529238\pi\)
\(662\) 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 0.985210 + 0.171351i \(0.0548132\pi\)
0.171351 + 0.985210i \(0.445187\pi\)
\(678\) 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 0.999684 0.0251358i \(-0.00800181\pi\)
−0.0251358 + 0.999684i \(0.508002\pi\)
\(684\) 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 −0.346674 0.937986i \(-0.612689\pi\)
0.937986 + 0.346674i \(0.112689\pi\)
\(692\) 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 −0.804895 0.593418i \(-0.797778\pi\)
0.593418 + 0.804895i \(0.297778\pi\)
\(702\) 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 0.694111 0.719868i \(-0.255798\pi\)
−0.719868 + 0.694111i \(0.755798\pi\)
\(710\) 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 \(0.0327135\pi\)
−0.994724 + 0.102592i \(0.967286\pi\)
\(728\) 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 −0.629670 0.776863i \(-0.716810\pi\)
0.776863 + 0.629670i \(0.216810\pi\)
\(734\) 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 −0.746355 0.665548i \(-0.768198\pi\)
0.665548 + 0.746355i \(0.268198\pi\)
\(740\) 0 0
\(741\) 39.0969 + 39.0969i 1.43626 + 1.43626i
\(742\) 0 0
\(743\) 22.5404i 0.826927i −0.910521 0.413464i \(-0.864319\pi\)
0.910521 0.413464i \(-0.135681\pi\)
\(744\) 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 0.724736 0.689027i \(-0.241962\pi\)
−0.689027 + 0.724736i \(0.741962\pi\)
\(758\) 0 0
\(759\) 4.20429i 0.152606i
\(760\) 0 0
\(761\) 19.9186i 0.722049i −0.932556 0.361024i \(-0.882427\pi\)
0.932556 0.361024i \(-0.117573\pi\)
\(762\) 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 0.966220 0.257720i \(-0.0829713\pi\)
−0.257720 + 0.966220i \(0.582971\pi\)
\(774\) 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 0.108184 0.994131i \(-0.465496\pi\)
0.994131 0.108184i \(-0.0345035\pi\)
\(788\) 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 0.164919 0.986307i \(-0.447264\pi\)
0.986307 0.164919i \(-0.0527364\pi\)
\(798\) 0 0
\(799\) 3.14843