Properties

Label 1148.2.k.a.337.2
Level $1148$
Weight $2$
Character 1148.337
Analytic conductor $9.167$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.110166016.2
Defining polynomial: \(x^{8} + 10 x^{6} + 19 x^{4} + 10 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 337.2
Root \(-1.22833i\) of defining polynomial
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.a.729.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.868559 - 0.868559i) q^{3} -4.37966i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.49121i q^{9} +O(q^{10})\) \(q+(-0.868559 - 0.868559i) q^{3} -4.37966i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.49121i q^{9} +(1.10701 + 1.10701i) q^{11} +(0.155874 + 0.155874i) q^{13} +(-3.80399 + 3.80399i) q^{15} +(5.27265 - 5.27265i) q^{17} +(5.24822 - 5.24822i) q^{19} +1.22833i q^{21} +5.28835 q^{23} -14.1814 q^{25} +(-3.90088 + 3.90088i) q^{27} +(-4.12690 - 4.12690i) q^{29} +1.03455 q^{31} -1.92300i q^{33} +(-3.09689 + 3.09689i) q^{35} -2.58579 q^{37} -0.270771i q^{39} +(-4.93089 + 4.08489i) q^{41} +8.71688i q^{43} -6.53099 q^{45} +(-2.00789 + 2.00789i) q^{47} +1.00000i q^{49} -9.15922 q^{51} +(5.98800 + 5.98800i) q^{53} +(4.84832 - 4.84832i) q^{55} -9.11678 q^{57} +6.40829 q^{59} +12.4391i q^{61} +(-1.05444 + 1.05444i) q^{63} +(0.682674 - 0.682674i) q^{65} +(-1.54565 + 1.54565i) q^{67} +(-4.59325 - 4.59325i) q^{69} +(0.123981 + 0.123981i) q^{71} -5.51668i q^{73} +(12.3174 + 12.3174i) q^{75} -1.56555i q^{77} +(-8.20809 - 8.20809i) q^{79} +2.30266 q^{81} -12.8108 q^{83} +(-23.0924 - 23.0924i) q^{85} +7.16891i q^{87} +(11.9756 + 11.9756i) q^{89} -0.220439i q^{91} +(-0.898571 - 0.898571i) q^{93} +(-22.9854 - 22.9854i) q^{95} +(6.20844 - 6.20844i) q^{97} +(1.65078 - 1.65078i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} + O(q^{10}) \) \( 8q - 4q^{3} + 12q^{11} + 4q^{13} - 8q^{15} + 8q^{17} + 8q^{19} + 28q^{23} - 4q^{25} + 8q^{27} - 16q^{29} + 28q^{31} - 8q^{35} - 32q^{37} - 4q^{45} + 20q^{47} - 20q^{51} + 32q^{53} - 4q^{55} - 36q^{57} - 20q^{59} - 8q^{63} - 4q^{67} - 44q^{69} + 8q^{71} + 12q^{75} - 12q^{79} - 16q^{81} - 64q^{83} - 56q^{85} + 4q^{89} - 4q^{93} - 52q^{95} + 56q^{97} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −0.868559 0.868559i −0.501463 0.501463i 0.410429 0.911892i \(-0.365379\pi\)
−0.911892 + 0.410429i \(0.865379\pi\)
\(4\) 0 0
\(5\) 4.37966i 1.95864i −0.202309 0.979322i \(-0.564844\pi\)
0.202309 0.979322i \(-0.435156\pi\)
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 0 0
\(9\) 1.49121i 0.497070i
\(10\) 0 0
\(11\) 1.10701 + 1.10701i 0.333775 + 0.333775i 0.854018 0.520243i \(-0.174159\pi\)
−0.520243 + 0.854018i \(0.674159\pi\)
\(12\) 0 0
\(13\) 0.155874 + 0.155874i 0.0432316 + 0.0432316i 0.728392 0.685161i \(-0.240268\pi\)
−0.685161 + 0.728392i \(0.740268\pi\)
\(14\) 0 0
\(15\) −3.80399 + 3.80399i −0.982187 + 0.982187i
\(16\) 0 0
\(17\) 5.27265 5.27265i 1.27881 1.27881i 0.337470 0.941336i \(-0.390429\pi\)
0.941336 0.337470i \(-0.109571\pi\)
\(18\) 0 0
\(19\) 5.24822 5.24822i 1.20402 1.20402i 0.231092 0.972932i \(-0.425770\pi\)
0.972932 0.231092i \(-0.0742299\pi\)
\(20\) 0 0
\(21\) 1.22833i 0.268043i
\(22\) 0 0
\(23\) 5.28835 1.10270 0.551349 0.834275i \(-0.314113\pi\)
0.551349 + 0.834275i \(0.314113\pi\)
\(24\) 0 0
\(25\) −14.1814 −2.83628
\(26\) 0 0
\(27\) −3.90088 + 3.90088i −0.750725 + 0.750725i
\(28\) 0 0
\(29\) −4.12690 4.12690i −0.766346 0.766346i 0.211115 0.977461i \(-0.432290\pi\)
−0.977461 + 0.211115i \(0.932290\pi\)
\(30\) 0 0
\(31\) 1.03455 0.185811 0.0929056 0.995675i \(-0.470385\pi\)
0.0929056 + 0.995675i \(0.470385\pi\)
\(32\) 0 0
\(33\) 1.92300i 0.334752i
\(34\) 0 0
\(35\) −3.09689 + 3.09689i −0.523470 + 0.523470i
\(36\) 0 0
\(37\) −2.58579 −0.425101 −0.212550 0.977150i \(-0.568177\pi\)
−0.212550 + 0.977150i \(0.568177\pi\)
\(38\) 0 0
\(39\) 0.270771i 0.0433581i
\(40\) 0 0
\(41\) −4.93089 + 4.08489i −0.770076 + 0.637952i
\(42\) 0 0
\(43\) 8.71688i 1.32931i 0.747150 + 0.664656i \(0.231422\pi\)
−0.747150 + 0.664656i \(0.768578\pi\)
\(44\) 0 0
\(45\) −6.53099 −0.973583
\(46\) 0 0
\(47\) −2.00789 + 2.00789i −0.292881 + 0.292881i −0.838217 0.545336i \(-0.816402\pi\)
0.545336 + 0.838217i \(0.316402\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −9.15922 −1.28255
\(52\) 0 0
\(53\) 5.98800 + 5.98800i 0.822515 + 0.822515i 0.986468 0.163953i \(-0.0524246\pi\)
−0.163953 + 0.986468i \(0.552425\pi\)
\(54\) 0 0
\(55\) 4.84832 4.84832i 0.653747 0.653747i
\(56\) 0 0
\(57\) −9.11678 −1.20755
\(58\) 0 0
\(59\) 6.40829 0.834288 0.417144 0.908840i \(-0.363031\pi\)
0.417144 + 0.908840i \(0.363031\pi\)
\(60\) 0 0
\(61\) 12.4391i 1.59266i 0.604862 + 0.796330i \(0.293228\pi\)
−0.604862 + 0.796330i \(0.706772\pi\)
\(62\) 0 0
\(63\) −1.05444 + 1.05444i −0.132848 + 0.132848i
\(64\) 0 0
\(65\) 0.682674 0.682674i 0.0846753 0.0846753i
\(66\) 0 0
\(67\) −1.54565 + 1.54565i −0.188832 + 0.188832i −0.795191 0.606359i \(-0.792629\pi\)
0.606359 + 0.795191i \(0.292629\pi\)
\(68\) 0 0
\(69\) −4.59325 4.59325i −0.552962 0.552962i
\(70\) 0 0
\(71\) 0.123981 + 0.123981i 0.0147138 + 0.0147138i 0.714425 0.699712i \(-0.246688\pi\)
−0.699712 + 0.714425i \(0.746688\pi\)
\(72\) 0 0
\(73\) 5.51668i 0.645679i −0.946454 0.322839i \(-0.895363\pi\)
0.946454 0.322839i \(-0.104637\pi\)
\(74\) 0 0
\(75\) 12.3174 + 12.3174i 1.42229 + 1.42229i
\(76\) 0 0
\(77\) 1.56555i 0.178410i
\(78\) 0 0
\(79\) −8.20809 8.20809i −0.923482 0.923482i 0.0737917 0.997274i \(-0.476490\pi\)
−0.997274 + 0.0737917i \(0.976490\pi\)
\(80\) 0 0
\(81\) 2.30266 0.255852
\(82\) 0 0
\(83\) −12.8108 −1.40617 −0.703087 0.711104i \(-0.748195\pi\)
−0.703087 + 0.711104i \(0.748195\pi\)
\(84\) 0 0
\(85\) −23.0924 23.0924i −2.50473 2.50473i
\(86\) 0 0
\(87\) 7.16891i 0.768588i
\(88\) 0 0
\(89\) 11.9756 + 11.9756i 1.26942 + 1.26942i 0.946390 + 0.323026i \(0.104700\pi\)
0.323026 + 0.946390i \(0.395300\pi\)
\(90\) 0 0
\(91\) 0.220439i 0.0231083i
\(92\) 0 0
\(93\) −0.898571 0.898571i −0.0931775 0.0931775i
\(94\) 0 0
\(95\) −22.9854 22.9854i −2.35825 2.35825i
\(96\) 0 0
\(97\) 6.20844 6.20844i 0.630371 0.630371i −0.317790 0.948161i \(-0.602941\pi\)
0.948161 + 0.317790i \(0.102941\pi\)
\(98\) 0 0
\(99\) 1.65078 1.65078i 0.165910 0.165910i
\(100\) 0 0
\(101\) 2.82012 2.82012i 0.280613 0.280613i −0.552741 0.833353i \(-0.686418\pi\)
0.833353 + 0.552741i \(0.186418\pi\)
\(102\) 0 0
\(103\) 6.30859i 0.621604i −0.950475 0.310802i \(-0.899402\pi\)
0.950475 0.310802i \(-0.100598\pi\)
\(104\) 0 0
\(105\) 5.37966 0.525001
\(106\) 0 0
\(107\) 17.5426 1.69591 0.847956 0.530067i \(-0.177833\pi\)
0.847956 + 0.530067i \(0.177833\pi\)
\(108\) 0 0
\(109\) −10.6850 + 10.6850i −1.02344 + 1.02344i −0.0237172 + 0.999719i \(0.507550\pi\)
−0.999719 + 0.0237172i \(0.992450\pi\)
\(110\) 0 0
\(111\) 2.24591 + 2.24591i 0.213172 + 0.213172i
\(112\) 0 0
\(113\) −3.42733 −0.322416 −0.161208 0.986920i \(-0.551539\pi\)
−0.161208 + 0.986920i \(0.551539\pi\)
\(114\) 0 0
\(115\) 23.1612i 2.15979i
\(116\) 0 0
\(117\) 0.232440 0.232440i 0.0214891 0.0214891i
\(118\) 0 0
\(119\) −7.45666 −0.683551
\(120\) 0 0
\(121\) 8.54907i 0.777188i
\(122\) 0 0
\(123\) 7.83074 + 0.734808i 0.706074 + 0.0662554i
\(124\) 0 0
\(125\) 40.2115i 3.59663i
\(126\) 0 0
\(127\) 21.0195 1.86518 0.932591 0.360934i \(-0.117542\pi\)
0.932591 + 0.360934i \(0.117542\pi\)
\(128\) 0 0
\(129\) 7.57112 7.57112i 0.666600 0.666600i
\(130\) 0 0
\(131\) 4.79121i 0.418610i 0.977850 + 0.209305i \(0.0671202\pi\)
−0.977850 + 0.209305i \(0.932880\pi\)
\(132\) 0 0
\(133\) −7.42210 −0.643578
\(134\) 0 0
\(135\) 17.0845 + 17.0845i 1.47040 + 1.47040i
\(136\) 0 0
\(137\) 11.4447 11.4447i 0.977783 0.977783i −0.0219757 0.999759i \(-0.506996\pi\)
0.999759 + 0.0219757i \(0.00699563\pi\)
\(138\) 0 0
\(139\) 13.7262 1.16424 0.582122 0.813101i \(-0.302223\pi\)
0.582122 + 0.813101i \(0.302223\pi\)
\(140\) 0 0
\(141\) 3.48794 0.293738
\(142\) 0 0
\(143\) 0.345107i 0.0288593i
\(144\) 0 0
\(145\) −18.0744 + 18.0744i −1.50100 + 1.50100i
\(146\) 0 0
\(147\) 0.868559 0.868559i 0.0716376 0.0716376i
\(148\) 0 0
\(149\) −5.91658 + 5.91658i −0.484705 + 0.484705i −0.906631 0.421925i \(-0.861354\pi\)
0.421925 + 0.906631i \(0.361354\pi\)
\(150\) 0 0
\(151\) −4.68164 4.68164i −0.380986 0.380986i 0.490471 0.871457i \(-0.336825\pi\)
−0.871457 + 0.490471i \(0.836825\pi\)
\(152\) 0 0
\(153\) −7.86263 7.86263i −0.635656 0.635656i
\(154\) 0 0
\(155\) 4.53099i 0.363938i
\(156\) 0 0
\(157\) −6.83898 6.83898i −0.545810 0.545810i 0.379416 0.925226i \(-0.376125\pi\)
−0.925226 + 0.379416i \(0.876125\pi\)
\(158\) 0 0
\(159\) 10.4019i 0.824921i
\(160\) 0 0
\(161\) −3.73943 3.73943i −0.294708 0.294708i
\(162\) 0 0
\(163\) 0.0562608 0.00440669 0.00220334 0.999998i \(-0.499299\pi\)
0.00220334 + 0.999998i \(0.499299\pi\)
\(164\) 0 0
\(165\) −8.42210 −0.655660
\(166\) 0 0
\(167\) 17.3830 + 17.3830i 1.34514 + 1.34514i 0.890860 + 0.454277i \(0.150102\pi\)
0.454277 + 0.890860i \(0.349898\pi\)
\(168\) 0 0
\(169\) 12.9514i 0.996262i
\(170\) 0 0
\(171\) −7.82620 7.82620i −0.598484 0.598484i
\(172\) 0 0
\(173\) 22.1109i 1.68106i −0.541767 0.840528i \(-0.682245\pi\)
0.541767 0.840528i \(-0.317755\pi\)
\(174\) 0 0
\(175\) 10.0278 + 10.0278i 0.758029 + 0.758029i
\(176\) 0 0
\(177\) −5.56598 5.56598i −0.418364 0.418364i
\(178\) 0 0
\(179\) −8.88021 + 8.88021i −0.663738 + 0.663738i −0.956259 0.292521i \(-0.905506\pi\)
0.292521 + 0.956259i \(0.405506\pi\)
\(180\) 0 0
\(181\) 2.09192 2.09192i 0.155491 0.155491i −0.625074 0.780565i \(-0.714931\pi\)
0.780565 + 0.625074i \(0.214931\pi\)
\(182\) 0 0
\(183\) 10.8041 10.8041i 0.798660 0.798660i
\(184\) 0 0
\(185\) 11.3249i 0.832621i
\(186\) 0 0
\(187\) 11.6737 0.853668
\(188\) 0 0
\(189\) 5.51668 0.401279
\(190\) 0 0
\(191\) −7.26811 + 7.26811i −0.525902 + 0.525902i −0.919348 0.393446i \(-0.871283\pi\)
0.393446 + 0.919348i \(0.371283\pi\)
\(192\) 0 0
\(193\) −0.804344 0.804344i −0.0578979 0.0578979i 0.677565 0.735463i \(-0.263035\pi\)
−0.735463 + 0.677565i \(0.763035\pi\)
\(194\) 0 0
\(195\) −1.18589 −0.0849230
\(196\) 0 0
\(197\) 2.18212i 0.155470i −0.996974 0.0777349i \(-0.975231\pi\)
0.996974 0.0777349i \(-0.0247688\pi\)
\(198\) 0 0
\(199\) −1.70711 + 1.70711i −0.121014 + 0.121014i −0.765020 0.644006i \(-0.777271\pi\)
0.644006 + 0.765020i \(0.277271\pi\)
\(200\) 0 0
\(201\) 2.68498 0.189384
\(202\) 0 0
\(203\) 5.83632i 0.409629i
\(204\) 0 0
\(205\) 17.8904 + 21.5956i 1.24952 + 1.50830i
\(206\) 0 0
\(207\) 7.88604i 0.548118i
\(208\) 0 0
\(209\) 11.6196 0.803747
\(210\) 0 0
\(211\) −6.36627 + 6.36627i −0.438272 + 0.438272i −0.891430 0.453158i \(-0.850297\pi\)
0.453158 + 0.891430i \(0.350297\pi\)
\(212\) 0 0
\(213\) 0.215369i 0.0147569i
\(214\) 0 0
\(215\) 38.1770 2.60365
\(216\) 0 0
\(217\) −0.731540 0.731540i −0.0496602 0.0496602i
\(218\) 0 0
\(219\) −4.79156 + 4.79156i −0.323784 + 0.323784i
\(220\) 0 0
\(221\) 1.64374 0.110570
\(222\) 0 0
\(223\) 16.4795 1.10355 0.551773 0.833994i \(-0.313951\pi\)
0.551773 + 0.833994i \(0.313951\pi\)
\(224\) 0 0
\(225\) 21.1475i 1.40983i
\(226\) 0 0
\(227\) 11.2174 11.2174i 0.744523 0.744523i −0.228922 0.973445i \(-0.573520\pi\)
0.973445 + 0.228922i \(0.0735201\pi\)
\(228\) 0 0
\(229\) −8.73009 + 8.73009i −0.576900 + 0.576900i −0.934048 0.357148i \(-0.883749\pi\)
0.357148 + 0.934048i \(0.383749\pi\)
\(230\) 0 0
\(231\) −1.35977 + 1.35977i −0.0894662 + 0.0894662i
\(232\) 0 0
\(233\) 16.3305 + 16.3305i 1.06985 + 1.06985i 0.997370 + 0.0724782i \(0.0230908\pi\)
0.0724782 + 0.997370i \(0.476909\pi\)
\(234\) 0 0
\(235\) 8.79387 + 8.79387i 0.573649 + 0.573649i
\(236\) 0 0
\(237\) 14.2584i 0.926184i
\(238\) 0 0
\(239\) −4.12956 4.12956i −0.267119 0.267119i 0.560819 0.827938i \(-0.310486\pi\)
−0.827938 + 0.560819i \(0.810486\pi\)
\(240\) 0 0
\(241\) 10.2473i 0.660084i −0.943966 0.330042i \(-0.892937\pi\)
0.943966 0.330042i \(-0.107063\pi\)
\(242\) 0 0
\(243\) 9.70264 + 9.70264i 0.622425 + 0.622425i
\(244\) 0 0
\(245\) 4.37966 0.279806
\(246\) 0 0
\(247\) 1.63612 0.104104
\(248\) 0 0
\(249\) 11.1270 + 11.1270i 0.705144 + 0.705144i
\(250\) 0 0
\(251\) 14.1273i 0.891709i −0.895105 0.445855i \(-0.852900\pi\)
0.895105 0.445855i \(-0.147100\pi\)
\(252\) 0 0
\(253\) 5.85425 + 5.85425i 0.368053 + 0.368053i
\(254\) 0 0
\(255\) 40.1143i 2.51205i
\(256\) 0 0
\(257\) −7.25507 7.25507i −0.452559 0.452559i 0.443644 0.896203i \(-0.353685\pi\)
−0.896203 + 0.443644i \(0.853685\pi\)
\(258\) 0 0
\(259\) 1.82843 + 1.82843i 0.113613 + 0.113613i
\(260\) 0 0
\(261\) −6.15407 + 6.15407i −0.380928 + 0.380928i
\(262\) 0 0
\(263\) −10.4488 + 10.4488i −0.644303 + 0.644303i −0.951610 0.307307i \(-0.900572\pi\)
0.307307 + 0.951610i \(0.400572\pi\)
\(264\) 0 0
\(265\) 26.2254 26.2254i 1.61101 1.61101i
\(266\) 0 0
\(267\) 20.8031i 1.27313i
\(268\) 0 0
\(269\) −18.9583 −1.15591 −0.577955 0.816069i \(-0.696149\pi\)
−0.577955 + 0.816069i \(0.696149\pi\)
\(270\) 0 0
\(271\) 1.58116 0.0960489 0.0480245 0.998846i \(-0.484707\pi\)
0.0480245 + 0.998846i \(0.484707\pi\)
\(272\) 0 0
\(273\) −0.191464 + 0.191464i −0.0115879 + 0.0115879i
\(274\) 0 0
\(275\) −15.6989 15.6989i −0.946682 0.946682i
\(276\) 0 0
\(277\) 4.00642 0.240723 0.120361 0.992730i \(-0.461595\pi\)
0.120361 + 0.992730i \(0.461595\pi\)
\(278\) 0 0
\(279\) 1.54274i 0.0923612i
\(280\) 0 0
\(281\) −6.60198 + 6.60198i −0.393841 + 0.393841i −0.876054 0.482213i \(-0.839833\pi\)
0.482213 + 0.876054i \(0.339833\pi\)
\(282\) 0 0
\(283\) −25.4135 −1.51068 −0.755338 0.655335i \(-0.772527\pi\)
−0.755338 + 0.655335i \(0.772527\pi\)
\(284\) 0 0
\(285\) 39.9284i 2.36515i
\(286\) 0 0
\(287\) 6.37512 + 0.598218i 0.376311 + 0.0353117i
\(288\) 0 0
\(289\) 38.6017i 2.27069i
\(290\) 0 0
\(291\) −10.7848 −0.632216
\(292\) 0 0
\(293\) −1.58587 + 1.58587i −0.0926473 + 0.0926473i −0.751911 0.659264i \(-0.770868\pi\)
0.659264 + 0.751911i \(0.270868\pi\)
\(294\) 0 0
\(295\) 28.0661i 1.63407i
\(296\) 0 0
\(297\) −8.63661 −0.501147
\(298\) 0 0
\(299\) 0.824315 + 0.824315i 0.0476714 + 0.0476714i
\(300\) 0 0
\(301\) 6.16376 6.16376i 0.355273 0.355273i
\(302\) 0 0
\(303\) −4.89889 −0.281434
\(304\) 0 0
\(305\) 54.4789 3.11945
\(306\) 0 0
\(307\) 9.98715i 0.569997i 0.958528 + 0.284998i \(0.0919931\pi\)
−0.958528 + 0.284998i \(0.908007\pi\)
\(308\) 0 0
\(309\) −5.47939 + 5.47939i −0.311711 + 0.311711i
\(310\) 0 0
\(311\) −8.19335 + 8.19335i −0.464602 + 0.464602i −0.900160 0.435558i \(-0.856551\pi\)
0.435558 + 0.900160i \(0.356551\pi\)
\(312\) 0 0
\(313\) 15.8900 15.8900i 0.898156 0.898156i −0.0971172 0.995273i \(-0.530962\pi\)
0.995273 + 0.0971172i \(0.0309622\pi\)
\(314\) 0 0
\(315\) 4.61811 + 4.61811i 0.260201 + 0.260201i
\(316\) 0 0
\(317\) −6.85893 6.85893i −0.385236 0.385236i 0.487748 0.872984i \(-0.337818\pi\)
−0.872984 + 0.487748i \(0.837818\pi\)
\(318\) 0 0
\(319\) 9.13702i 0.511575i
\(320\) 0 0
\(321\) −15.2368 15.2368i −0.850437 0.850437i
\(322\) 0 0
\(323\) 55.3441i 3.07943i
\(324\) 0 0
\(325\) −2.21051 2.21051i −0.122617 0.122617i
\(326\) 0 0
\(327\) 18.5611 1.02643
\(328\) 0 0
\(329\) 2.83958 0.156551
\(330\) 0 0
\(331\) 10.1612 + 10.1612i 0.558509 + 0.558509i 0.928883 0.370374i \(-0.120770\pi\)
−0.370374 + 0.928883i \(0.620770\pi\)
\(332\) 0 0
\(333\) 3.85595i 0.211305i
\(334\) 0 0
\(335\) 6.76944 + 6.76944i 0.369854 + 0.369854i
\(336\) 0 0
\(337\) 3.07470i 0.167490i −0.996487 0.0837448i \(-0.973312\pi\)
0.996487 0.0837448i \(-0.0266881\pi\)
\(338\) 0 0
\(339\) 2.97684 + 2.97684i 0.161680 + 0.161680i
\(340\) 0 0
\(341\) 1.14526 + 1.14526i 0.0620192 + 0.0620192i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 0 0
\(345\) −20.1169 + 20.1169i −1.08306 + 1.08306i
\(346\) 0 0
\(347\) −19.7853 + 19.7853i −1.06213 + 1.06213i −0.0641922 + 0.997938i \(0.520447\pi\)
−0.997938 + 0.0641922i \(0.979553\pi\)
\(348\) 0 0
\(349\) 9.92170i 0.531096i 0.964098 + 0.265548i \(0.0855529\pi\)
−0.964098 + 0.265548i \(0.914447\pi\)
\(350\) 0 0
\(351\) −1.21609 −0.0649101
\(352\) 0 0
\(353\) 8.01578 0.426637 0.213318 0.976983i \(-0.431573\pi\)
0.213318 + 0.976983i \(0.431573\pi\)
\(354\) 0 0
\(355\) 0.542994 0.542994i 0.0288191 0.0288191i
\(356\) 0 0
\(357\) 6.47655 + 6.47655i 0.342775 + 0.342775i
\(358\) 0 0
\(359\) −15.4833 −0.817178 −0.408589 0.912718i \(-0.633979\pi\)
−0.408589 + 0.912718i \(0.633979\pi\)
\(360\) 0 0
\(361\) 36.0876i 1.89935i
\(362\) 0 0
\(363\) −7.42537 + 7.42537i −0.389731 + 0.389731i
\(364\) 0 0
\(365\) −24.1612 −1.26465
\(366\) 0 0
\(367\) 17.5727i 0.917289i 0.888620 + 0.458645i \(0.151665\pi\)
−0.888620 + 0.458645i \(0.848335\pi\)
\(368\) 0 0
\(369\) 6.09142 + 7.35300i 0.317107 + 0.382782i
\(370\) 0 0
\(371\) 8.46831i 0.439653i
\(372\) 0 0
\(373\) 11.1630 0.577997 0.288999 0.957329i \(-0.406678\pi\)
0.288999 + 0.957329i \(0.406678\pi\)
\(374\) 0 0
\(375\) 34.9261 34.9261i 1.80358 1.80358i
\(376\) 0 0
\(377\) 1.28655i 0.0662607i
\(378\) 0 0
\(379\) 25.3324 1.30124 0.650620 0.759404i \(-0.274509\pi\)
0.650620 + 0.759404i \(0.274509\pi\)
\(380\) 0 0
\(381\) −18.2567 18.2567i −0.935320 0.935320i
\(382\) 0 0
\(383\) −10.3746 + 10.3746i −0.530119 + 0.530119i −0.920608 0.390489i \(-0.872306\pi\)
0.390489 + 0.920608i \(0.372306\pi\)
\(384\) 0 0
\(385\) −6.85656 −0.349443
\(386\) 0 0
\(387\) 12.9987 0.660761
\(388\) 0 0
\(389\) 9.08901i 0.460831i 0.973092 + 0.230416i \(0.0740086\pi\)
−0.973092 + 0.230416i \(0.925991\pi\)
\(390\) 0 0
\(391\) 27.8836 27.8836i 1.41014 1.41014i
\(392\) 0 0
\(393\) 4.16145 4.16145i 0.209918 0.209918i
\(394\) 0 0
\(395\) −35.9486 + 35.9486i −1.80877 + 1.80877i
\(396\) 0 0
\(397\) −16.8991 16.8991i −0.848144 0.848144i 0.141758 0.989901i \(-0.454725\pi\)
−0.989901 + 0.141758i \(0.954725\pi\)
\(398\) 0 0
\(399\) 6.44654 + 6.44654i 0.322730 + 0.322730i
\(400\) 0 0
\(401\) 17.2355i 0.860701i 0.902662 + 0.430350i \(0.141610\pi\)
−0.902662 + 0.430350i \(0.858390\pi\)
\(402\) 0 0
\(403\) 0.161260 + 0.161260i 0.00803292 + 0.00803292i
\(404\) 0 0
\(405\) 10.0849i 0.501122i
\(406\) 0 0
\(407\) −2.86249 2.86249i −0.141888 0.141888i
\(408\) 0 0
\(409\) 6.14926 0.304061 0.152031 0.988376i \(-0.451419\pi\)
0.152031 + 0.988376i \(0.451419\pi\)
\(410\) 0 0
\(411\) −19.8807 −0.980644
\(412\) 0 0
\(413\) −4.53134 4.53134i −0.222973 0.222973i
\(414\) 0 0
\(415\) 56.1072i 2.75419i
\(416\) 0 0
\(417\) −11.9220 11.9220i −0.583825 0.583825i
\(418\) 0 0
\(419\) 18.6826i 0.912705i 0.889799 + 0.456352i \(0.150844\pi\)
−0.889799 + 0.456352i \(0.849156\pi\)
\(420\) 0 0
\(421\) −14.0459 14.0459i −0.684554 0.684554i 0.276469 0.961023i \(-0.410836\pi\)
−0.961023 + 0.276469i \(0.910836\pi\)
\(422\) 0 0
\(423\) 2.99418 + 2.99418i 0.145582 + 0.145582i
\(424\) 0 0
\(425\) −74.7737 + 74.7737i −3.62706 + 3.62706i
\(426\) 0 0
\(427\) 8.79576 8.79576i 0.425656 0.425656i
\(428\) 0 0
\(429\) 0.299746 0.299746i 0.0144719 0.0144719i
\(430\) 0 0
\(431\) 12.8378i 0.618374i −0.951001 0.309187i \(-0.899943\pi\)
0.951001 0.309187i \(-0.100057\pi\)
\(432\) 0 0
\(433\) −5.64434 −0.271250 −0.135625 0.990760i \(-0.543304\pi\)
−0.135625 + 0.990760i \(0.543304\pi\)
\(434\) 0 0
\(435\) 31.3974 1.50539
\(436\) 0 0
\(437\) 27.7544 27.7544i 1.32767 1.32767i
\(438\) 0 0
\(439\) −9.47844 9.47844i −0.452381 0.452381i 0.443763 0.896144i \(-0.353643\pi\)
−0.896144 + 0.443763i \(0.853643\pi\)
\(440\) 0 0
\(441\) 1.49121 0.0710100
\(442\) 0 0
\(443\) 9.52930i 0.452751i −0.974040 0.226375i \(-0.927312\pi\)
0.974040 0.226375i \(-0.0726876\pi\)
\(444\) 0 0
\(445\) 52.4493 52.4493i 2.48633 2.48633i
\(446\) 0 0
\(447\) 10.2778 0.486123
\(448\) 0 0
\(449\) 22.0528i 1.04074i −0.853942 0.520368i \(-0.825795\pi\)
0.853942 0.520368i \(-0.174205\pi\)
\(450\) 0 0
\(451\) −9.98054 0.936537i −0.469965 0.0440998i
\(452\) 0 0
\(453\) 8.13256i 0.382101i
\(454\) 0 0
\(455\) −0.965447 −0.0452608
\(456\) 0 0
\(457\) 18.2147 18.2147i 0.852048 0.852048i −0.138337 0.990385i \(-0.544176\pi\)
0.990385 + 0.138337i \(0.0441758\pi\)
\(458\) 0 0
\(459\) 41.1360i 1.92006i
\(460\) 0 0
\(461\) −6.79545 −0.316496 −0.158248 0.987399i \(-0.550585\pi\)
−0.158248 + 0.987399i \(0.550585\pi\)
\(462\) 0 0
\(463\) −5.57774 5.57774i −0.259220 0.259220i 0.565517 0.824737i \(-0.308677\pi\)
−0.824737 + 0.565517i \(0.808677\pi\)
\(464\) 0 0
\(465\) −3.93543 + 3.93543i −0.182501 + 0.182501i
\(466\) 0 0
\(467\) 36.3150 1.68046 0.840228 0.542234i \(-0.182421\pi\)
0.840228 + 0.542234i \(0.182421\pi\)
\(468\) 0 0
\(469\) 2.18589 0.100935
\(470\) 0 0
\(471\) 11.8801i 0.547407i
\(472\) 0 0
\(473\) −9.64965 + 9.64965i −0.443691 + 0.443691i
\(474\) 0 0
\(475\) −74.4272 + 74.4272i −3.41496 + 3.41496i
\(476\) 0 0
\(477\) 8.92936 8.92936i 0.408847 0.408847i
\(478\) 0 0
\(479\) −5.30292 5.30292i −0.242297 0.242297i 0.575503 0.817800i \(-0.304806\pi\)
−0.817800 + 0.575503i \(0.804806\pi\)
\(480\) 0 0
\(481\) −0.403056 0.403056i −0.0183778 0.0183778i
\(482\) 0 0
\(483\) 6.49583i 0.295571i
\(484\) 0 0
\(485\) −27.1908 27.1908i −1.23467 1.23467i
\(486\) 0 0
\(487\) 3.16695i 0.143508i 0.997422 + 0.0717541i \(0.0228597\pi\)
−0.997422 + 0.0717541i \(0.977140\pi\)
\(488\) 0 0
\(489\) −0.0488658 0.0488658i −0.00220979 0.00220979i
\(490\) 0 0
\(491\) −6.86591 −0.309854 −0.154927 0.987926i \(-0.549514\pi\)
−0.154927 + 0.987926i \(0.549514\pi\)
\(492\) 0 0
\(493\) −43.5194 −1.96002
\(494\) 0 0
\(495\) −7.22986 7.22986i −0.324958 0.324958i
\(496\) 0 0
\(497\) 0.175335i 0.00786487i
\(498\) 0 0
\(499\) 2.01551 + 2.01551i 0.0902265 + 0.0902265i 0.750779 0.660553i \(-0.229678\pi\)
−0.660553 + 0.750779i \(0.729678\pi\)
\(500\) 0 0
\(501\) 30.1963i 1.34907i
\(502\) 0 0
\(503\) 12.2797 + 12.2797i 0.547525 + 0.547525i 0.925724 0.378199i \(-0.123457\pi\)
−0.378199 + 0.925724i \(0.623457\pi\)
\(504\) 0 0
\(505\) −12.3512 12.3512i −0.549620 0.549620i
\(506\) 0 0
\(507\) −11.2491 + 11.2491i −0.499588 + 0.499588i
\(508\) 0 0
\(509\) −0.586823 + 0.586823i −0.0260105 + 0.0260105i −0.719992 0.693982i \(-0.755855\pi\)
0.693982 + 0.719992i \(0.255855\pi\)
\(510\) 0 0
\(511\) −3.90088 + 3.90088i −0.172565 + 0.172565i
\(512\) 0 0
\(513\) 40.9454i 1.80778i
\(514\) 0 0
\(515\) −27.6295 −1.21750
\(516\) 0 0
\(517\) −4.44550 −0.195513
\(518\) 0 0
\(519\) −19.2046 + 19.2046i −0.842988 + 0.842988i
\(520\) 0 0
\(521\) 1.58336 + 1.58336i 0.0693684 + 0.0693684i 0.740940 0.671571i \(-0.234380\pi\)
−0.671571 + 0.740940i \(0.734380\pi\)
\(522\) 0 0
\(523\) 30.4893 1.33320 0.666602 0.745414i \(-0.267748\pi\)
0.666602 + 0.745414i \(0.267748\pi\)
\(524\) 0 0
\(525\) 17.4194i 0.760247i
\(526\) 0 0
\(527\) 5.45484 5.45484i 0.237617 0.237617i
\(528\) 0 0
\(529\) 4.96666 0.215942
\(530\) 0 0
\(531\) 9.55610i 0.414699i
\(532\) 0 0
\(533\) −1.40532 0.131870i −0.0608713 0.00571194i
\(534\) 0 0
\(535\) 76.8308i 3.32169i
\(536\) 0 0
\(537\) 15.4260 0.665680
\(538\) 0 0
\(539\) −1.10701 + 1.10701i −0.0476822 + 0.0476822i
\(540\) 0 0
\(541\) 22.4848i 0.966696i 0.875428 + 0.483348i \(0.160580\pi\)
−0.875428 + 0.483348i \(0.839420\pi\)
\(542\) 0 0
\(543\) −3.63391 −0.155946
\(544\) 0 0
\(545\) 46.7966 + 46.7966i 2.00455 + 2.00455i
\(546\) 0 0
\(547\) −11.2934 + 11.2934i −0.482870 + 0.482870i −0.906047 0.423177i \(-0.860915\pi\)
0.423177 + 0.906047i \(0.360915\pi\)
\(548\) 0 0
\(549\) 18.5493 0.791664
\(550\) 0 0
\(551\) −43.3177 −1.84540
\(552\) 0 0
\(553\) 11.6080i 0.493622i
\(554\) 0 0
\(555\) 9.83632 9.83632i 0.417528 0.417528i
\(556\) 0 0
\(557\) −2.04517 + 2.04517i −0.0866566 + 0.0866566i −0.749106 0.662450i \(-0.769517\pi\)
0.662450 + 0.749106i \(0.269517\pi\)
\(558\) 0 0
\(559\) −1.35873 + 1.35873i −0.0574682 + 0.0574682i
\(560\) 0 0
\(561\) −10.1393 10.1393i −0.428083 0.428083i
\(562\) 0 0
\(563\) 5.39793 + 5.39793i 0.227496 + 0.227496i 0.811646 0.584150i \(-0.198572\pi\)
−0.584150 + 0.811646i \(0.698572\pi\)
\(564\) 0 0
\(565\) 15.0105i 0.631499i
\(566\) 0 0
\(567\) −1.62823 1.62823i −0.0683792 0.0683792i
\(568\) 0 0
\(569\) 23.2256i 0.973666i −0.873495 0.486833i \(-0.838152\pi\)
0.873495 0.486833i \(-0.161848\pi\)
\(570\) 0 0
\(571\) −26.4191 26.4191i −1.10561 1.10561i −0.993721 0.111884i \(-0.964312\pi\)
−0.111884 0.993721i \(-0.535688\pi\)
\(572\) 0 0
\(573\) 12.6256 0.527441
\(574\) 0 0
\(575\) −74.9964 −3.12756
\(576\) 0 0
\(577\) 20.0881 + 20.0881i 0.836279 + 0.836279i 0.988367 0.152088i \(-0.0485996\pi\)
−0.152088 + 0.988367i \(0.548600\pi\)
\(578\) 0 0
\(579\) 1.39724i 0.0580673i
\(580\) 0 0
\(581\) 9.05864 + 9.05864i 0.375816 + 0.375816i
\(582\) 0 0
\(583\) 13.2575i 0.549070i
\(584\) 0 0
\(585\) −1.01801 1.01801i −0.0420895 0.0420895i
\(586\) 0 0
\(587\) 24.7778 + 24.7778i 1.02269 + 1.02269i 0.999737 + 0.0229544i \(0.00730725\pi\)
0.0229544 + 0.999737i \(0.492693\pi\)
\(588\) 0 0
\(589\) 5.42956 5.42956i 0.223721 0.223721i
\(590\) 0 0
\(591\) −1.89530 + 1.89530i −0.0779623 + 0.0779623i
\(592\) 0 0
\(593\) 9.33118 9.33118i 0.383185 0.383185i −0.489063 0.872248i \(-0.662661\pi\)
0.872248 + 0.489063i \(0.162661\pi\)
\(594\) 0 0
\(595\) 32.6576i 1.33883i
\(596\) 0 0
\(597\) 2.96545 0.121368
\(598\) 0 0
\(599\) −6.48082 −0.264799 −0.132400 0.991196i \(-0.542268\pi\)
−0.132400 + 0.991196i \(0.542268\pi\)
\(600\) 0 0
\(601\) 19.0624 19.0624i 0.777572 0.777572i −0.201845 0.979417i \(-0.564694\pi\)
0.979417 + 0.201845i \(0.0646938\pi\)
\(602\) 0 0
\(603\) 2.30489 + 2.30489i 0.0938626 + 0.0938626i
\(604\) 0 0
\(605\) −37.4420 −1.52223
\(606\) 0 0
\(607\) 10.7243i 0.435285i 0.976029 + 0.217642i \(0.0698367\pi\)
−0.976029 + 0.217642i \(0.930163\pi\)
\(608\) 0 0
\(609\) 5.06919 5.06919i 0.205414 0.205414i
\(610\) 0 0
\(611\) −0.625954 −0.0253234
\(612\) 0 0
\(613\) 32.8034i 1.32492i 0.749099 + 0.662458i \(0.230487\pi\)
−0.749099 + 0.662458i \(0.769513\pi\)
\(614\) 0 0
\(615\) 3.21821 34.2960i 0.129771 1.38295i
\(616\) 0 0
\(617\) 23.6634i 0.952654i −0.879268 0.476327i \(-0.841968\pi\)
0.879268 0.476327i \(-0.158032\pi\)
\(618\) 0 0
\(619\) 8.18699 0.329063 0.164531 0.986372i \(-0.447389\pi\)
0.164531 + 0.986372i \(0.447389\pi\)
\(620\) 0 0
\(621\) −20.6292 + 20.6292i −0.827823 + 0.827823i
\(622\) 0 0
\(623\) 16.9361i 0.678531i
\(624\) 0 0
\(625\) 105.206 4.20823
\(626\) 0 0
\(627\) −10.0923 10.0923i −0.403049 0.403049i
\(628\) 0 0
\(629\) −13.6340 + 13.6340i −0.543621 + 0.543621i
\(630\) 0 0
\(631\) 25.5192 1.01590 0.507952 0.861385i \(-0.330403\pi\)
0.507952 + 0.861385i \(0.330403\pi\)
\(632\) 0 0
\(633\) 11.0590 0.439555
\(634\) 0 0
\(635\) 92.0584i 3.65323i
\(636\) 0 0
\(637\) −0.155874 + 0.155874i −0.00617594 + 0.00617594i
\(638\) 0 0
\(639\) 0.184881 0.184881i 0.00731380 0.00731380i
\(640\) 0 0
\(641\) −16.8663 + 16.8663i −0.666180 + 0.666180i −0.956830 0.290650i \(-0.906129\pi\)
0.290650 + 0.956830i \(0.406129\pi\)
\(642\) 0 0
\(643\) −31.2517 31.2517i −1.23245 1.23245i −0.963021 0.269427i \(-0.913166\pi\)
−0.269427 0.963021i \(-0.586834\pi\)
\(644\) 0 0
\(645\) −33.1590 33.1590i −1.30563 1.30563i
\(646\) 0 0
\(647\) 29.3661i 1.15450i −0.816567 0.577250i \(-0.804126\pi\)
0.816567 0.577250i \(-0.195874\pi\)
\(648\) 0 0
\(649\) 7.09402 + 7.09402i 0.278465 + 0.278465i
\(650\) 0 0
\(651\) 1.27077i 0.0498054i
\(652\) 0 0
\(653\) −22.0154 22.0154i −0.861530 0.861530i 0.129986 0.991516i \(-0.458507\pi\)
−0.991516 + 0.129986i \(0.958507\pi\)
\(654\) 0 0
\(655\) 20.9839 0.819908
\(656\) 0 0
\(657\) −8.22653 −0.320947
\(658\) 0 0
\(659\) 10.7540 + 10.7540i 0.418917 + 0.418917i 0.884830 0.465913i \(-0.154274\pi\)
−0.465913 + 0.884830i \(0.654274\pi\)
\(660\) 0 0
\(661\) 31.0314i 1.20698i −0.797369 0.603492i \(-0.793776\pi\)
0.797369 0.603492i \(-0.206224\pi\)
\(662\) 0 0
\(663\) −1.42768 1.42768i −0.0554466 0.0554466i
\(664\) 0 0
\(665\) 32.5063i 1.26054i
\(666\) 0 0
\(667\) −21.8245 21.8245i −0.845048 0.845048i
\(668\) 0 0
\(669\) −14.3134 14.3134i −0.553388 0.553388i
\(670\) 0 0
\(671\) −13.7702 + 13.7702i −0.531591 + 0.531591i
\(672\) 0 0
\(673\) −13.8292 + 13.8292i −0.533077 + 0.533077i −0.921487 0.388410i \(-0.873024\pi\)
0.388410 + 0.921487i \(0.373024\pi\)
\(674\) 0 0
\(675\) 55.3201 55.3201i 2.12927 2.12927i
\(676\) 0 0
\(677\) 41.7263i 1.60367i −0.597544 0.801836i \(-0.703857\pi\)
0.597544 0.801836i \(-0.296143\pi\)
\(678\) 0 0
\(679\) −8.78006 −0.336948
\(680\) 0 0
\(681\) −19.4859 −0.746701
\(682\) 0 0
\(683\) 0.539996 0.539996i 0.0206624 0.0206624i −0.696700 0.717362i \(-0.745349\pi\)
0.717362 + 0.696700i \(0.245349\pi\)
\(684\) 0 0
\(685\) −50.1237 50.1237i −1.91513 1.91513i
\(686\) 0 0
\(687\) 15.1652 0.578588
\(688\) 0 0
\(689\) 1.86674i 0.0711172i
\(690\) 0 0
\(691\) −26.7208 + 26.7208i −1.01651 + 1.01651i −0.0166475 + 0.999861i \(0.505299\pi\)
−0.999861 + 0.0166475i \(0.994701\pi\)
\(692\) 0 0
\(693\) −2.33456 −0.0886825
\(694\) 0 0
\(695\) 60.1162i 2.28034i
\(696\) 0 0
\(697\) −4.46070 + 47.5371i −0.168961 + 1.80059i
\(698\) 0 0
\(699\) 28.3681i 1.07298i
\(700\) 0 0
\(701\) −28.3918 −1.07234 −0.536172 0.844109i \(-0.680130\pi\)
−0.536172 + 0.844109i \(0.680130\pi\)
\(702\) 0 0
\(703\) −13.5708 + 13.5708i −0.511831 + 0.511831i
\(704\) 0 0
\(705\) 15.2760i 0.575327i
\(706\) 0 0
\(707\) −3.98826 −0.149994
\(708\) 0 0
\(709\) −7.16891 7.16891i −0.269234 0.269234i 0.559557 0.828792i \(-0.310971\pi\)
−0.828792 + 0.559557i \(0.810971\pi\)
\(710\) 0 0
\(711\) −12.2400 + 12.2400i −0.459035 + 0.459035i
\(712\) 0 0
\(713\) 5.47108 0.204894
\(714\) 0 0
\(715\) 1.51145 0.0565251
\(716\) 0 0
\(717\) 7.17353i 0.267901i
\(718\) 0 0
\(719\) −8.38409 + 8.38409i −0.312674 + 0.312674i −0.845945 0.533271i \(-0.820963\pi\)
0.533271 + 0.845945i \(0.320963\pi\)
\(720\) 0 0
\(721\) −4.46085 + 4.46085i −0.166131 + 0.166131i
\(722\) 0 0
\(723\) −8.90035 + 8.90035i −0.331008 + 0.331008i
\(724\) 0 0
\(725\) 58.5253 + 58.5253i 2.17358 + 2.17358i
\(726\) 0 0
\(727\) −26.1718 26.1718i −0.970658 0.970658i 0.0289234 0.999582i \(-0.490792\pi\)
−0.999582 + 0.0289234i \(0.990792\pi\)
\(728\) 0 0
\(729\) 23.7626i 0.880098i
\(730\) 0 0
\(731\) 45.9611 + 45.9611i 1.69993 + 1.69993i
\(732\) 0 0
\(733\) 41.1504i 1.51992i −0.649967 0.759962i \(-0.725217\pi\)
0.649967 0.759962i \(-0.274783\pi\)
\(734\) 0 0
\(735\) −3.80399 3.80399i −0.140312 0.140312i
\(736\) 0 0
\(737\) −3.42210 −0.126055
\(738\) 0 0
\(739\) 8.37977 0.308255 0.154127 0.988051i \(-0.450743\pi\)
0.154127 + 0.988051i \(0.450743\pi\)
\(740\) 0 0
\(741\) −1.42107 1.42107i −0.0522042 0.0522042i
\(742\) 0 0
\(743\) 16.7799i 0.615596i 0.951452 + 0.307798i \(0.0995922\pi\)
−0.951452 + 0.307798i \(0.900408\pi\)
\(744\) 0 0
\(745\) 25.9126 + 25.9126i 0.949365 + 0.949365i
\(746\) 0 0
\(747\) 19.1037i 0.698966i
\(748\) 0 0
\(749\) −12.4045 12.4045i −0.453251 0.453251i
\(750\) 0 0
\(751\) −12.1427 12.1427i −0.443092 0.443092i 0.449958 0.893050i \(-0.351439\pi\)
−0.893050 + 0.449958i \(0.851439\pi\)
\(752\) 0 0
\(753\) −12.2704 + 12.2704i −0.447159 + 0.447159i
\(754\) 0 0
\(755\) −20.5040 + 20.5040i −0.746216 + 0.746216i
\(756\) 0 0
\(757\) −5.89100 + 5.89100i −0.214112 + 0.214112i −0.806012 0.591900i \(-0.798378\pi\)
0.591900 + 0.806012i \(0.298378\pi\)
\(758\) 0 0
\(759\) 10.1695i 0.369130i
\(760\) 0 0
\(761\) 37.8289 1.37130 0.685648 0.727934i \(-0.259519\pi\)
0.685648 + 0.727934i \(0.259519\pi\)
\(762\) 0 0
\(763\) 15.1109 0.547050
\(764\) 0 0
\(765\) −34.4357 + 34.4357i −1.24502 + 1.24502i
\(766\) 0 0
\(767\) 0.998883 + 0.998883i 0.0360676 + 0.0360676i
\(768\) 0 0
\(769\) −21.4226 −0.772519 −0.386259 0.922390i \(-0.626233\pi\)
−0.386259 + 0.922390i \(0.626233\pi\)
\(770\) 0 0
\(771\) 12.6029i 0.453883i
\(772\) 0 0
\(773\) 18.4236 18.4236i 0.662653 0.662653i −0.293352 0.956005i \(-0.594771\pi\)
0.956005 + 0.293352i \(0.0947708\pi\)
\(774\) 0 0
\(775\) −14.6714 −0.527014
\(776\) 0 0
\(777\) 3.17619i 0.113945i
\(778\) 0 0
\(779\) −4.44003 + 47.3168i −0.159081 + 1.69530i
\(780\) 0 0
\(781\) 0.274495i 0.00982222i
\(782\) 0 0
\(783\) 32.1971 1.15063
\(784\) 0 0
\(785\) −29.9524 + 29.9524i −1.06905 + 1.06905i
\(786\) 0 0
\(787\) 1.81107i 0.0645578i 0.999479 + 0.0322789i \(0.0102765\pi\)
−0.999479 + 0.0322789i \(0.989724\pi\)
\(788\) 0 0
\(789\) 18.1509 0.646189
\(790\) 0 0
\(791\) 2.42349 + 2.42349i 0.0861694 + 0.0861694i
\(792\) 0 0
\(793\) −1.93892 + 1.93892i −0.0688532 + 0.0688532i
\(794\) 0 0
\(795\) −45.5566 −1.61573
\(796\) 0 0
\(797\) 32.9410 1.16683 0.583415 0.812174i \(-0.301716\pi\)
0.583415 + 0.812174i \(0.301716\pi\)
\(798\) 0