Properties

Label 384.2.k.b.287.3
Level $384$
Weight $2$
Character 384.287
Analytic conductor $3.066$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.k (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.163368480538624.2
Defining polynomial: \(x^{12} - 2 x^{10} - 2 x^{8} + 16 x^{6} - 8 x^{4} - 32 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 287.3
Root \(-1.27715 + 0.607364i\) of defining polynomial
Character \(\chi\) \(=\) 384.287
Dual form 384.2.k.b.95.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0835731 - 1.73003i) q^{3} +(-0.431733 + 0.431733i) q^{5} -3.10278 q^{7} +(-2.98603 + 0.289169i) q^{9} +O(q^{10})\) \(q+(-0.0835731 - 1.73003i) q^{3} +(-0.431733 + 0.431733i) q^{5} -3.10278 q^{7} +(-2.98603 + 0.289169i) q^{9} +(-2.98603 - 2.98603i) q^{11} +(-2.10278 + 2.10278i) q^{13} +(0.782994 + 0.710831i) q^{15} -2.42945i q^{17} +(0.710831 + 0.710831i) q^{19} +(0.259309 + 5.36790i) q^{21} -5.97206i q^{23} +4.62721i q^{25} +(0.749823 + 5.14177i) q^{27} +(-2.86119 - 2.86119i) q^{29} -0.524438i q^{31} +(-4.91638 + 5.41549i) q^{33} +(1.33957 - 1.33957i) q^{35} +(-1.52444 - 1.52444i) q^{37} +(3.81361 + 3.46214i) q^{39} +1.81568 q^{41} +(-0.710831 + 0.710831i) q^{43} +(1.16432 - 1.41401i) q^{45} -7.53805 q^{47} +2.62721 q^{49} +(-4.20304 + 0.203037i) q^{51} +(8.83325 - 8.83325i) q^{53} +2.57834 q^{55} +(1.17036 - 1.28917i) q^{57} +(0.0804722 + 0.0804722i) q^{59} +(5.72999 - 5.72999i) q^{61} +(9.26498 - 0.897225i) q^{63} -1.81568i q^{65} +(0.391944 + 0.391944i) q^{67} +(-10.3319 + 0.499104i) q^{69} +5.01985i q^{71} -13.4600i q^{73} +(8.00523 - 0.386711i) q^{75} +(9.26498 + 9.26498i) q^{77} -3.47556i q^{79} +(8.83276 - 1.72693i) q^{81} +(-4.55202 + 4.55202i) q^{83} +(1.04888 + 1.04888i) q^{85} +(-4.71083 + 5.18907i) q^{87} +12.5579 q^{89} +(6.52444 - 6.52444i) q^{91} +(-0.907295 + 0.0438289i) q^{93} -0.613779 q^{95} -8.67609 q^{97} +(9.77985 + 8.05292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{3} - 8 q^{7} + O(q^{10}) \) \( 12 q + 2 q^{3} - 8 q^{7} + 4 q^{13} + 12 q^{19} + 8 q^{21} - 10 q^{27} - 4 q^{33} + 4 q^{37} + 20 q^{39} - 12 q^{43} + 12 q^{45} - 20 q^{49} - 24 q^{51} + 24 q^{55} - 12 q^{61} - 28 q^{67} - 4 q^{69} + 34 q^{75} - 4 q^{81} - 32 q^{85} - 60 q^{87} + 56 q^{91} - 28 q^{93} - 8 q^{97} + 52 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.0835731 1.73003i −0.0482510 0.998835i
\(4\) 0 0
\(5\) −0.431733 + 0.431733i −0.193077 + 0.193077i −0.797024 0.603947i \(-0.793594\pi\)
0.603947 + 0.797024i \(0.293594\pi\)
\(6\) 0 0
\(7\) −3.10278 −1.17274 −0.586369 0.810044i \(-0.699443\pi\)
−0.586369 + 0.810044i \(0.699443\pi\)
\(8\) 0 0
\(9\) −2.98603 + 0.289169i −0.995344 + 0.0963895i
\(10\) 0 0
\(11\) −2.98603 2.98603i −0.900322 0.900322i 0.0951415 0.995464i \(-0.469670\pi\)
−0.995464 + 0.0951415i \(0.969670\pi\)
\(12\) 0 0
\(13\) −2.10278 + 2.10278i −0.583205 + 0.583205i −0.935783 0.352578i \(-0.885305\pi\)
0.352578 + 0.935783i \(0.385305\pi\)
\(14\) 0 0
\(15\) 0.782994 + 0.710831i 0.202168 + 0.183536i
\(16\) 0 0
\(17\) 2.42945i 0.589229i −0.955616 0.294615i \(-0.904809\pi\)
0.955616 0.294615i \(-0.0951913\pi\)
\(18\) 0 0
\(19\) 0.710831 + 0.710831i 0.163076 + 0.163076i 0.783928 0.620852i \(-0.213213\pi\)
−0.620852 + 0.783928i \(0.713213\pi\)
\(20\) 0 0
\(21\) 0.259309 + 5.36790i 0.0565858 + 1.17137i
\(22\) 0 0
\(23\) 5.97206i 1.24526i −0.782516 0.622631i \(-0.786064\pi\)
0.782516 0.622631i \(-0.213936\pi\)
\(24\) 0 0
\(25\) 4.62721i 0.925443i
\(26\) 0 0
\(27\) 0.749823 + 5.14177i 0.144304 + 0.989533i
\(28\) 0 0
\(29\) −2.86119 2.86119i −0.531309 0.531309i 0.389653 0.920962i \(-0.372595\pi\)
−0.920962 + 0.389653i \(0.872595\pi\)
\(30\) 0 0
\(31\) 0.524438i 0.0941918i −0.998890 0.0470959i \(-0.985003\pi\)
0.998890 0.0470959i \(-0.0149966\pi\)
\(32\) 0 0
\(33\) −4.91638 + 5.41549i −0.855832 + 0.942715i
\(34\) 0 0
\(35\) 1.33957 1.33957i 0.226429 0.226429i
\(36\) 0 0
\(37\) −1.52444 1.52444i −0.250616 0.250616i 0.570607 0.821223i \(-0.306708\pi\)
−0.821223 + 0.570607i \(0.806708\pi\)
\(38\) 0 0
\(39\) 3.81361 + 3.46214i 0.610666 + 0.554385i
\(40\) 0 0
\(41\) 1.81568 0.283561 0.141780 0.989898i \(-0.454717\pi\)
0.141780 + 0.989898i \(0.454717\pi\)
\(42\) 0 0
\(43\) −0.710831 + 0.710831i −0.108401 + 0.108401i −0.759227 0.650826i \(-0.774423\pi\)
0.650826 + 0.759227i \(0.274423\pi\)
\(44\) 0 0
\(45\) 1.16432 1.41401i 0.173567 0.210788i
\(46\) 0 0
\(47\) −7.53805 −1.09954 −0.549769 0.835317i \(-0.685284\pi\)
−0.549769 + 0.835317i \(0.685284\pi\)
\(48\) 0 0
\(49\) 2.62721 0.375316
\(50\) 0 0
\(51\) −4.20304 + 0.203037i −0.588543 + 0.0284309i
\(52\) 0 0
\(53\) 8.83325 8.83325i 1.21334 1.21334i 0.243419 0.969921i \(-0.421731\pi\)
0.969921 0.243419i \(-0.0782690\pi\)
\(54\) 0 0
\(55\) 2.57834 0.347663
\(56\) 0 0
\(57\) 1.17036 1.28917i 0.155017 0.170755i
\(58\) 0 0
\(59\) 0.0804722 + 0.0804722i 0.0104766 + 0.0104766i 0.712326 0.701849i \(-0.247642\pi\)
−0.701849 + 0.712326i \(0.747642\pi\)
\(60\) 0 0
\(61\) 5.72999 5.72999i 0.733650 0.733650i −0.237691 0.971341i \(-0.576391\pi\)
0.971341 + 0.237691i \(0.0763906\pi\)
\(62\) 0 0
\(63\) 9.26498 0.897225i 1.16728 0.113040i
\(64\) 0 0
\(65\) 1.81568i 0.225207i
\(66\) 0 0
\(67\) 0.391944 + 0.391944i 0.0478835 + 0.0478835i 0.730643 0.682760i \(-0.239220\pi\)
−0.682760 + 0.730643i \(0.739220\pi\)
\(68\) 0 0
\(69\) −10.3319 + 0.499104i −1.24381 + 0.0600850i
\(70\) 0 0
\(71\) 5.01985i 0.595747i 0.954605 + 0.297873i \(0.0962774\pi\)
−0.954605 + 0.297873i \(0.903723\pi\)
\(72\) 0 0
\(73\) 13.4600i 1.57537i −0.616078 0.787686i \(-0.711279\pi\)
0.616078 0.787686i \(-0.288721\pi\)
\(74\) 0 0
\(75\) 8.00523 0.386711i 0.924365 0.0446535i
\(76\) 0 0
\(77\) 9.26498 + 9.26498i 1.05584 + 1.05584i
\(78\) 0 0
\(79\) 3.47556i 0.391031i −0.980701 0.195516i \(-0.937362\pi\)
0.980701 0.195516i \(-0.0626380\pi\)
\(80\) 0 0
\(81\) 8.83276 1.72693i 0.981418 0.191881i
\(82\) 0 0
\(83\) −4.55202 + 4.55202i −0.499649 + 0.499649i −0.911329 0.411680i \(-0.864942\pi\)
0.411680 + 0.911329i \(0.364942\pi\)
\(84\) 0 0
\(85\) 1.04888 + 1.04888i 0.113767 + 0.113767i
\(86\) 0 0
\(87\) −4.71083 + 5.18907i −0.505054 + 0.556326i
\(88\) 0 0
\(89\) 12.5579 1.33114 0.665568 0.746338i \(-0.268190\pi\)
0.665568 + 0.746338i \(0.268190\pi\)
\(90\) 0 0
\(91\) 6.52444 6.52444i 0.683947 0.683947i
\(92\) 0 0
\(93\) −0.907295 + 0.0438289i −0.0940821 + 0.00454485i
\(94\) 0 0
\(95\) −0.613779 −0.0629724
\(96\) 0 0
\(97\) −8.67609 −0.880923 −0.440462 0.897771i \(-0.645185\pi\)
−0.440462 + 0.897771i \(0.645185\pi\)
\(98\) 0 0
\(99\) 9.77985 + 8.05292i 0.982912 + 0.809348i
\(100\) 0 0
\(101\) −0.182046 + 0.182046i −0.0181142 + 0.0181142i −0.716106 0.697992i \(-0.754077\pi\)
0.697992 + 0.716106i \(0.254077\pi\)
\(102\) 0 0
\(103\) 6.35720 0.626394 0.313197 0.949688i \(-0.398600\pi\)
0.313197 + 0.949688i \(0.398600\pi\)
\(104\) 0 0
\(105\) −2.42945 2.20555i −0.237090 0.215240i
\(106\) 0 0
\(107\) −1.64646 1.64646i −0.159169 0.159169i 0.623029 0.782199i \(-0.285902\pi\)
−0.782199 + 0.623029i \(0.785902\pi\)
\(108\) 0 0
\(109\) −6.57331 + 6.57331i −0.629609 + 0.629609i −0.947970 0.318360i \(-0.896868\pi\)
0.318360 + 0.947970i \(0.396868\pi\)
\(110\) 0 0
\(111\) −2.50993 + 2.76473i −0.238232 + 0.262417i
\(112\) 0 0
\(113\) 8.31277i 0.782000i −0.920391 0.391000i \(-0.872129\pi\)
0.920391 0.391000i \(-0.127871\pi\)
\(114\) 0 0
\(115\) 2.57834 + 2.57834i 0.240431 + 0.240431i
\(116\) 0 0
\(117\) 5.67090 6.88701i 0.524274 0.636704i
\(118\) 0 0
\(119\) 7.53805i 0.691012i
\(120\) 0 0
\(121\) 6.83276i 0.621160i
\(122\) 0 0
\(123\) −0.151742 3.14118i −0.0136821 0.283231i
\(124\) 0 0
\(125\) −4.15639 4.15639i −0.371759 0.371759i
\(126\) 0 0
\(127\) 15.7789i 1.40015i 0.714070 + 0.700074i \(0.246850\pi\)
−0.714070 + 0.700074i \(0.753150\pi\)
\(128\) 0 0
\(129\) 1.28917 + 1.17036i 0.113505 + 0.103044i
\(130\) 0 0
\(131\) −0.0804722 + 0.0804722i −0.00703089 + 0.00703089i −0.710613 0.703583i \(-0.751583\pi\)
0.703583 + 0.710613i \(0.251583\pi\)
\(132\) 0 0
\(133\) −2.20555 2.20555i −0.191245 0.191245i
\(134\) 0 0
\(135\) −2.54359 1.89615i −0.218918 0.163194i
\(136\) 0 0
\(137\) −13.2604 −1.13291 −0.566457 0.824091i \(-0.691686\pi\)
−0.566457 + 0.824091i \(0.691686\pi\)
\(138\) 0 0
\(139\) −8.39194 + 8.39194i −0.711795 + 0.711795i −0.966911 0.255115i \(-0.917887\pi\)
0.255115 + 0.966911i \(0.417887\pi\)
\(140\) 0 0
\(141\) 0.629978 + 13.0411i 0.0530537 + 1.09826i
\(142\) 0 0
\(143\) 12.5579 1.05014
\(144\) 0 0
\(145\) 2.47054 0.205167
\(146\) 0 0
\(147\) −0.219564 4.54517i −0.0181094 0.374879i
\(148\) 0 0
\(149\) −5.79002 + 5.79002i −0.474337 + 0.474337i −0.903315 0.428978i \(-0.858874\pi\)
0.428978 + 0.903315i \(0.358874\pi\)
\(150\) 0 0
\(151\) 9.94610 0.809402 0.404701 0.914449i \(-0.367376\pi\)
0.404701 + 0.914449i \(0.367376\pi\)
\(152\) 0 0
\(153\) 0.702522 + 7.25443i 0.0567955 + 0.586486i
\(154\) 0 0
\(155\) 0.226417 + 0.226417i 0.0181863 + 0.0181863i
\(156\) 0 0
\(157\) 9.15165 9.15165i 0.730381 0.730381i −0.240314 0.970695i \(-0.577250\pi\)
0.970695 + 0.240314i \(0.0772504\pi\)
\(158\) 0 0
\(159\) −16.0200 14.5436i −1.27047 1.15338i
\(160\) 0 0
\(161\) 18.5300i 1.46037i
\(162\) 0 0
\(163\) −15.7003 15.7003i −1.22974 1.22974i −0.964062 0.265678i \(-0.914404\pi\)
−0.265678 0.964062i \(-0.585596\pi\)
\(164\) 0 0
\(165\) −0.215480 4.46061i −0.0167751 0.347258i
\(166\) 0 0
\(167\) 19.1437i 1.48139i −0.671843 0.740694i \(-0.734497\pi\)
0.671843 0.740694i \(-0.265503\pi\)
\(168\) 0 0
\(169\) 4.15667i 0.319744i
\(170\) 0 0
\(171\) −2.32811 1.91701i −0.178035 0.146598i
\(172\) 0 0
\(173\) −13.3281 13.3281i −1.01331 1.01331i −0.999910 0.0134040i \(-0.995733\pi\)
−0.0134040 0.999910i \(-0.504267\pi\)
\(174\) 0 0
\(175\) 14.3572i 1.08530i
\(176\) 0 0
\(177\) 0.132494 0.145945i 0.00995889 0.0109699i
\(178\) 0 0
\(179\) 9.18451 9.18451i 0.686483 0.686483i −0.274970 0.961453i \(-0.588668\pi\)
0.961453 + 0.274970i \(0.0886680\pi\)
\(180\) 0 0
\(181\) 16.5139 + 16.5139i 1.22747 + 1.22747i 0.964919 + 0.262548i \(0.0845627\pi\)
0.262548 + 0.964919i \(0.415437\pi\)
\(182\) 0 0
\(183\) −10.3919 9.43420i −0.768195 0.697396i
\(184\) 0 0
\(185\) 1.31630 0.0967764
\(186\) 0 0
\(187\) −7.25443 + 7.25443i −0.530496 + 0.530496i
\(188\) 0 0
\(189\) −2.32653 15.9537i −0.169230 1.16046i
\(190\) 0 0
\(191\) −3.17852 −0.229989 −0.114995 0.993366i \(-0.536685\pi\)
−0.114995 + 0.993366i \(0.536685\pi\)
\(192\) 0 0
\(193\) −11.4600 −0.824907 −0.412454 0.910979i \(-0.635328\pi\)
−0.412454 + 0.910979i \(0.635328\pi\)
\(194\) 0 0
\(195\) −3.14118 + 0.151742i −0.224944 + 0.0108664i
\(196\) 0 0
\(197\) −14.8053 + 14.8053i −1.05483 + 1.05483i −0.0564281 + 0.998407i \(0.517971\pi\)
−0.998407 + 0.0564281i \(0.982029\pi\)
\(198\) 0 0
\(199\) −24.4550 −1.73357 −0.866783 0.498686i \(-0.833816\pi\)
−0.866783 + 0.498686i \(0.833816\pi\)
\(200\) 0 0
\(201\) 0.645320 0.710831i 0.0455173 0.0501382i
\(202\) 0 0
\(203\) 8.87762 + 8.87762i 0.623087 + 0.623087i
\(204\) 0 0
\(205\) −0.783887 + 0.783887i −0.0547491 + 0.0547491i
\(206\) 0 0
\(207\) 1.72693 + 17.8328i 0.120030 + 1.23946i
\(208\) 0 0
\(209\) 4.24513i 0.293642i
\(210\) 0 0
\(211\) 6.18639 + 6.18639i 0.425889 + 0.425889i 0.887225 0.461336i \(-0.152630\pi\)
−0.461336 + 0.887225i \(0.652630\pi\)
\(212\) 0 0
\(213\) 8.68451 0.419525i 0.595053 0.0287454i
\(214\) 0 0
\(215\) 0.613779i 0.0418594i
\(216\) 0 0
\(217\) 1.62721i 0.110462i
\(218\) 0 0
\(219\) −23.2862 + 1.12489i −1.57354 + 0.0760132i
\(220\) 0 0
\(221\) 5.10860 + 5.10860i 0.343641 + 0.343641i
\(222\) 0 0
\(223\) 8.18996i 0.548441i −0.961667 0.274220i \(-0.911580\pi\)
0.961667 0.274220i \(-0.0884197\pi\)
\(224\) 0 0
\(225\) −1.33804 13.8170i −0.0892030 0.921133i
\(226\) 0 0
\(227\) −9.91030 + 9.91030i −0.657770 + 0.657770i −0.954852 0.297082i \(-0.903986\pi\)
0.297082 + 0.954852i \(0.403986\pi\)
\(228\) 0 0
\(229\) −7.15165 7.15165i −0.472594 0.472594i 0.430159 0.902753i \(-0.358458\pi\)
−0.902753 + 0.430159i \(0.858458\pi\)
\(230\) 0 0
\(231\) 15.2544 16.8030i 1.00367 1.10556i
\(232\) 0 0
\(233\) −19.6431 −1.28686 −0.643432 0.765503i \(-0.722490\pi\)
−0.643432 + 0.765503i \(0.722490\pi\)
\(234\) 0 0
\(235\) 3.25443 3.25443i 0.212295 0.212295i
\(236\) 0 0
\(237\) −6.01284 + 0.290464i −0.390576 + 0.0188676i
\(238\) 0 0
\(239\) 9.44247 0.610782 0.305391 0.952227i \(-0.401213\pi\)
0.305391 + 0.952227i \(0.401213\pi\)
\(240\) 0 0
\(241\) 16.6167 1.07037 0.535186 0.844734i \(-0.320241\pi\)
0.535186 + 0.844734i \(0.320241\pi\)
\(242\) 0 0
\(243\) −3.72583 15.1366i −0.239012 0.971017i
\(244\) 0 0
\(245\) −1.13425 + 1.13425i −0.0724649 + 0.0724649i
\(246\) 0 0
\(247\) −2.98944 −0.190213
\(248\) 0 0
\(249\) 8.25557 + 7.49472i 0.523176 + 0.474958i
\(250\) 0 0
\(251\) −2.03382 2.03382i −0.128374 0.128374i 0.640001 0.768374i \(-0.278934\pi\)
−0.768374 + 0.640001i \(0.778934\pi\)
\(252\) 0 0
\(253\) −17.8328 + 17.8328i −1.12114 + 1.12114i
\(254\) 0 0
\(255\) 1.72693 1.90225i 0.108145 0.119123i
\(256\) 0 0
\(257\) 15.0761i 0.940421i 0.882554 + 0.470211i \(0.155822\pi\)
−0.882554 + 0.470211i \(0.844178\pi\)
\(258\) 0 0
\(259\) 4.72999 + 4.72999i 0.293907 + 0.293907i
\(260\) 0 0
\(261\) 9.37096 + 7.71623i 0.580048 + 0.477623i
\(262\) 0 0
\(263\) 29.8138i 1.83840i 0.393796 + 0.919198i \(0.371162\pi\)
−0.393796 + 0.919198i \(0.628838\pi\)
\(264\) 0 0
\(265\) 7.62721i 0.468536i
\(266\) 0 0
\(267\) −1.04950 21.7256i −0.0642285 1.32958i
\(268\) 0 0
\(269\) 16.3713 + 16.3713i 0.998176 + 0.998176i 0.999998 0.00182258i \(-0.000580145\pi\)
−0.00182258 + 0.999998i \(0.500580\pi\)
\(270\) 0 0
\(271\) 13.3466i 0.810751i 0.914150 + 0.405375i \(0.132859\pi\)
−0.914150 + 0.405375i \(0.867141\pi\)
\(272\) 0 0
\(273\) −11.8328 10.7422i −0.716151 0.650149i
\(274\) 0 0
\(275\) 13.8170 13.8170i 0.833197 0.833197i
\(276\) 0 0
\(277\) −10.6811 10.6811i −0.641766 0.641766i 0.309224 0.950989i \(-0.399931\pi\)
−0.950989 + 0.309224i \(0.899931\pi\)
\(278\) 0 0
\(279\) 0.151651 + 1.56599i 0.00907911 + 0.0937533i
\(280\) 0 0
\(281\) −17.5943 −1.04959 −0.524794 0.851229i \(-0.675858\pi\)
−0.524794 + 0.851229i \(0.675858\pi\)
\(282\) 0 0
\(283\) 17.1758 17.1758i 1.02100 1.02100i 0.0212224 0.999775i \(-0.493244\pi\)
0.999775 0.0212224i \(-0.00675580\pi\)
\(284\) 0 0
\(285\) 0.0512954 + 1.06186i 0.00303848 + 0.0628990i
\(286\) 0 0
\(287\) −5.63363 −0.332543
\(288\) 0 0
\(289\) 11.0978 0.652809
\(290\) 0 0
\(291\) 0.725088 + 15.0099i 0.0425054 + 0.879897i
\(292\) 0 0
\(293\) 3.72465 3.72465i 0.217597 0.217597i −0.589888 0.807485i \(-0.700828\pi\)
0.807485 + 0.589888i \(0.200828\pi\)
\(294\) 0 0
\(295\) −0.0694851 −0.00404558
\(296\) 0 0
\(297\) 13.1145 17.5925i 0.760979 1.02082i
\(298\) 0 0
\(299\) 12.5579 + 12.5579i 0.726242 + 0.726242i
\(300\) 0 0
\(301\) 2.20555 2.20555i 0.127126 0.127126i
\(302\) 0 0
\(303\) 0.330160 + 0.299731i 0.0189672 + 0.0172191i
\(304\) 0 0
\(305\) 4.94765i 0.283302i
\(306\) 0 0
\(307\) 13.4408 + 13.4408i 0.767108 + 0.767108i 0.977596 0.210488i \(-0.0675054\pi\)
−0.210488 + 0.977596i \(0.567505\pi\)
\(308\) 0 0
\(309\) −0.531291 10.9982i −0.0302241 0.625664i
\(310\) 0 0
\(311\) 13.8320i 0.784341i 0.919893 + 0.392170i \(0.128276\pi\)
−0.919893 + 0.392170i \(0.871724\pi\)
\(312\) 0 0
\(313\) 3.94056i 0.222734i −0.993779 0.111367i \(-0.964477\pi\)
0.993779 0.111367i \(-0.0355229\pi\)
\(314\) 0 0
\(315\) −3.61264 + 4.38736i −0.203549 + 0.247200i
\(316\) 0 0
\(317\) −8.92199 8.92199i −0.501109 0.501109i 0.410673 0.911782i \(-0.365294\pi\)
−0.911782 + 0.410673i \(0.865294\pi\)
\(318\) 0 0
\(319\) 17.0872i 0.956699i
\(320\) 0 0
\(321\) −2.71083 + 2.98603i −0.151304 + 0.166664i
\(322\) 0 0
\(323\) 1.72693 1.72693i 0.0960891 0.0960891i
\(324\) 0 0
\(325\) −9.72999 9.72999i −0.539723 0.539723i
\(326\) 0 0
\(327\) 11.9214 + 10.8227i 0.659255 + 0.598497i
\(328\) 0 0
\(329\) 23.3889 1.28947
\(330\) 0 0
\(331\) −9.44082 + 9.44082i −0.518914 + 0.518914i −0.917243 0.398328i \(-0.869590\pi\)
0.398328 + 0.917243i \(0.369590\pi\)
\(332\) 0 0
\(333\) 4.99284 + 4.11120i 0.273606 + 0.225292i
\(334\) 0 0
\(335\) −0.338430 −0.0184904
\(336\) 0 0
\(337\) 5.94056 0.323603 0.161801 0.986823i \(-0.448270\pi\)
0.161801 + 0.986823i \(0.448270\pi\)
\(338\) 0 0
\(339\) −14.3814 + 0.694724i −0.781089 + 0.0377322i
\(340\) 0 0
\(341\) −1.56599 + 1.56599i −0.0848030 + 0.0848030i
\(342\) 0 0
\(343\) 13.5678 0.732591
\(344\) 0 0
\(345\) 4.24513 4.67609i 0.228550 0.251752i
\(346\) 0 0
\(347\) 4.09918 + 4.09918i 0.220056 + 0.220056i 0.808522 0.588466i \(-0.200268\pi\)
−0.588466 + 0.808522i \(0.700268\pi\)
\(348\) 0 0
\(349\) 8.10278 8.10278i 0.433732 0.433732i −0.456164 0.889896i \(-0.650777\pi\)
0.889896 + 0.456164i \(0.150777\pi\)
\(350\) 0 0
\(351\) −12.3887 9.23527i −0.661259 0.492942i
\(352\) 0 0
\(353\) 29.2465i 1.55664i −0.627870 0.778318i \(-0.716073\pi\)
0.627870 0.778318i \(-0.283927\pi\)
\(354\) 0 0
\(355\) −2.16724 2.16724i −0.115025 0.115025i
\(356\) 0 0
\(357\) 13.0411 0.629978i 0.690207 0.0333420i
\(358\) 0 0
\(359\) 21.3235i 1.12541i −0.826657 0.562706i \(-0.809760\pi\)
0.826657 0.562706i \(-0.190240\pi\)
\(360\) 0 0
\(361\) 17.9894i 0.946812i
\(362\) 0 0
\(363\) 11.8209 0.571035i 0.620437 0.0299716i
\(364\) 0 0
\(365\) 5.81112 + 5.81112i 0.304168 + 0.304168i
\(366\) 0 0
\(367\) 32.8277i 1.71359i −0.515654 0.856797i \(-0.672451\pi\)
0.515654 0.856797i \(-0.327549\pi\)
\(368\) 0 0
\(369\) −5.42166 + 0.525036i −0.282240 + 0.0273323i
\(370\) 0 0
\(371\) −27.4076 + 27.4076i −1.42293 + 1.42293i
\(372\) 0 0
\(373\) −1.35720 1.35720i −0.0702732 0.0702732i 0.671097 0.741370i \(-0.265824\pi\)
−0.741370 + 0.671097i \(0.765824\pi\)
\(374\) 0 0
\(375\) −6.84333 + 7.53805i −0.353388 + 0.389263i
\(376\) 0 0
\(377\) 12.0329 0.619724
\(378\) 0 0
\(379\) 17.3869 17.3869i 0.893106 0.893106i −0.101708 0.994814i \(-0.532431\pi\)
0.994814 + 0.101708i \(0.0324308\pi\)
\(380\) 0 0
\(381\) 27.2980 1.31869i 1.39852 0.0675585i
\(382\) 0 0
\(383\) 32.9757 1.68498 0.842491 0.538711i \(-0.181088\pi\)
0.842491 + 0.538711i \(0.181088\pi\)
\(384\) 0 0
\(385\) −8.00000 −0.407718
\(386\) 0 0
\(387\) 1.91701 2.32811i 0.0974473 0.118345i
\(388\) 0 0
\(389\) 3.97434 3.97434i 0.201507 0.201507i −0.599138 0.800645i \(-0.704490\pi\)
0.800645 + 0.599138i \(0.204490\pi\)
\(390\) 0 0
\(391\) −14.5089 −0.733744
\(392\) 0 0
\(393\) 0.145945 + 0.132494i 0.00736195 + 0.00668346i
\(394\) 0 0
\(395\) 1.50052 + 1.50052i 0.0754991 + 0.0754991i
\(396\) 0 0
\(397\) 15.9355 15.9355i 0.799782 0.799782i −0.183279 0.983061i \(-0.558671\pi\)
0.983061 + 0.183279i \(0.0586712\pi\)
\(398\) 0 0
\(399\) −3.63135 + 4.00000i −0.181795 + 0.200250i
\(400\) 0 0
\(401\) 29.7716i 1.48672i 0.668891 + 0.743361i \(0.266769\pi\)
−0.668891 + 0.743361i \(0.733231\pi\)
\(402\) 0 0
\(403\) 1.10278 + 1.10278i 0.0549331 + 0.0549331i
\(404\) 0 0
\(405\) −3.06782 + 4.55897i −0.152441 + 0.226537i
\(406\) 0 0
\(407\) 9.10404i 0.451270i
\(408\) 0 0
\(409\) 15.6655i 0.774610i −0.921952 0.387305i \(-0.873406\pi\)
0.921952 0.387305i \(-0.126594\pi\)
\(410\) 0 0
\(411\) 1.10821 + 22.9410i 0.0546642 + 1.13159i
\(412\) 0 0
\(413\) −0.249687 0.249687i −0.0122863 0.0122863i
\(414\) 0 0
\(415\) 3.93051i 0.192941i
\(416\) 0 0
\(417\) 15.2197 + 13.8170i 0.745311 + 0.676621i
\(418\) 0 0
\(419\) 14.1554 14.1554i 0.691538 0.691538i −0.271032 0.962570i \(-0.587365\pi\)
0.962570 + 0.271032i \(0.0873650\pi\)
\(420\) 0 0
\(421\) 7.35720 + 7.35720i 0.358568 + 0.358568i 0.863285 0.504717i \(-0.168403\pi\)
−0.504717 + 0.863285i \(0.668403\pi\)
\(422\) 0 0
\(423\) 22.5089 2.17977i 1.09442 0.105984i
\(424\) 0 0
\(425\) 11.2416 0.545298
\(426\) 0 0
\(427\) −17.7789 + 17.7789i −0.860380 + 0.860380i
\(428\) 0 0
\(429\) −1.04950 21.7256i −0.0506705 1.04892i
\(430\) 0 0
\(431\) −20.7097 −0.997553 −0.498776 0.866731i \(-0.666217\pi\)
−0.498776 + 0.866731i \(0.666217\pi\)
\(432\) 0 0
\(433\) −23.4005 −1.12456 −0.562279 0.826948i \(-0.690075\pi\)
−0.562279 + 0.826948i \(0.690075\pi\)
\(434\) 0 0
\(435\) −0.206471 4.27411i −0.00989951 0.204928i
\(436\) 0 0
\(437\) 4.24513 4.24513i 0.203072 0.203072i
\(438\) 0 0
\(439\) 20.2594 0.966931 0.483465 0.875363i \(-0.339378\pi\)
0.483465 + 0.875363i \(0.339378\pi\)
\(440\) 0 0
\(441\) −7.84494 + 0.759707i −0.373569 + 0.0361765i
\(442\) 0 0
\(443\) 4.05264 + 4.05264i 0.192547 + 0.192547i 0.796796 0.604249i \(-0.206527\pi\)
−0.604249 + 0.796796i \(0.706527\pi\)
\(444\) 0 0
\(445\) −5.42166 + 5.42166i −0.257011 + 0.257011i
\(446\) 0 0
\(447\) 10.5008 + 9.53303i 0.496671 + 0.450897i
\(448\) 0 0
\(449\) 5.38394i 0.254084i −0.991897 0.127042i \(-0.959452\pi\)
0.991897 0.127042i \(-0.0405483\pi\)
\(450\) 0 0
\(451\) −5.42166 5.42166i −0.255296 0.255296i
\(452\) 0 0
\(453\) −0.831227 17.2071i −0.0390544 0.808459i
\(454\) 0 0
\(455\) 5.63363i 0.264109i
\(456\) 0 0
\(457\) 28.0766i 1.31337i 0.754165 + 0.656685i \(0.228042\pi\)
−0.754165 + 0.656685i \(0.771958\pi\)
\(458\) 0 0
\(459\) 12.4917 1.82166i 0.583062 0.0850279i
\(460\) 0 0
\(461\) −22.7962 22.7962i −1.06172 1.06172i −0.997965 0.0637594i \(-0.979691\pi\)
−0.0637594 0.997965i \(-0.520309\pi\)
\(462\) 0 0
\(463\) 0.740035i 0.0343923i −0.999852 0.0171962i \(-0.994526\pi\)
0.999852 0.0171962i \(-0.00547398\pi\)
\(464\) 0 0
\(465\) 0.372787 0.410632i 0.0172876 0.0190426i
\(466\) 0 0
\(467\) −9.73282 + 9.73282i −0.450381 + 0.450381i −0.895481 0.445100i \(-0.853168\pi\)
0.445100 + 0.895481i \(0.353168\pi\)
\(468\) 0 0
\(469\) −1.21611 1.21611i −0.0561549 0.0561549i
\(470\) 0 0
\(471\) −16.5975 15.0678i −0.764772 0.694289i
\(472\) 0 0
\(473\) 4.24513 0.195191
\(474\) 0 0
\(475\) −3.28917 + 3.28917i −0.150917 + 0.150917i
\(476\) 0 0
\(477\) −23.8221 + 28.9307i −1.09074 + 1.32464i
\(478\) 0 0
\(479\) −28.2478 −1.29067 −0.645337 0.763898i \(-0.723283\pi\)
−0.645337 + 0.763898i \(0.723283\pi\)
\(480\) 0 0
\(481\) 6.41110 0.292321
\(482\) 0 0
\(483\) 32.0575 1.54861i 1.45866 0.0704641i
\(484\) 0 0
\(485\) 3.74576 3.74576i 0.170086 0.170086i
\(486\) 0 0
\(487\) 19.7094 0.893117 0.446559 0.894754i \(-0.352649\pi\)
0.446559 + 0.894754i \(0.352649\pi\)
\(488\) 0 0
\(489\) −25.8499 + 28.4741i −1.16897 + 1.28764i
\(490\) 0 0
\(491\) −29.4414 29.4414i −1.32867 1.32867i −0.906529 0.422143i \(-0.861278\pi\)
−0.422143 0.906529i \(-0.638722\pi\)
\(492\) 0 0
\(493\) −6.95112 + 6.95112i −0.313063 + 0.313063i
\(494\) 0 0
\(495\) −7.69899 + 0.745574i −0.346044 + 0.0335111i
\(496\) 0 0
\(497\) 15.5755i 0.698656i
\(498\) 0 0
\(499\) −4.43026 4.43026i −0.198326 0.198326i 0.600956 0.799282i \(-0.294787\pi\)
−0.799282 + 0.600956i \(0.794787\pi\)
\(500\) 0 0
\(501\) −33.1193 + 1.59990i −1.47966 + 0.0714784i
\(502\) 0 0
\(503\) 27.6805i 1.23421i −0.786879 0.617107i \(-0.788304\pi\)
0.786879 0.617107i \(-0.211696\pi\)
\(504\) 0 0
\(505\) 0.157190i 0.00699488i
\(506\) 0 0
\(507\) 7.19119 0.347386i 0.319372 0.0154280i
\(508\) 0 0
\(509\) 17.3235 + 17.3235i 0.767851 + 0.767851i 0.977728 0.209877i \(-0.0673063\pi\)
−0.209877 + 0.977728i \(0.567306\pi\)
\(510\) 0 0
\(511\) 41.7633i 1.84750i
\(512\) 0 0
\(513\) −3.12193 + 4.18793i −0.137837 + 0.184902i
\(514\) 0 0
\(515\) −2.74461 + 2.74461i −0.120942 + 0.120942i
\(516\) 0 0
\(517\) 22.5089 + 22.5089i 0.989938 + 0.989938i
\(518\) 0 0
\(519\) −21.9441 + 24.1719i −0.963240 + 1.06103i
\(520\) 0 0
\(521\) 10.1284 0.443735 0.221868 0.975077i \(-0.428785\pi\)
0.221868 + 0.975077i \(0.428785\pi\)
\(522\) 0 0
\(523\) −1.45641 + 1.45641i −0.0636842 + 0.0636842i −0.738232 0.674547i \(-0.764339\pi\)
0.674547 + 0.738232i \(0.264339\pi\)
\(524\) 0 0
\(525\) −24.8384 + 1.19988i −1.08404 + 0.0523669i
\(526\) 0 0
\(527\) −1.27410 −0.0555006
\(528\) 0 0
\(529\) −12.6655 −0.550675
\(530\) 0 0
\(531\) −0.263563 0.217023i −0.0114376 0.00941798i
\(532\) 0 0
\(533\) −3.81796 + 3.81796i −0.165374 + 0.165374i
\(534\) 0 0
\(535\) 1.42166 0.0614638
\(536\) 0 0
\(537\) −16.6571 15.1219i −0.718806 0.652560i
\(538\) 0 0
\(539\) −7.84494 7.84494i −0.337905 0.337905i
\(540\) 0 0
\(541\) −5.18996 + 5.18996i −0.223134 + 0.223134i −0.809817 0.586683i \(-0.800434\pi\)
0.586683 + 0.809817i \(0.300434\pi\)
\(542\) 0 0
\(543\) 27.1894 29.9497i 1.16681 1.28526i
\(544\) 0 0
\(545\) 5.67583i 0.243126i
\(546\) 0 0
\(547\) −12.6413 12.6413i −0.540505 0.540505i 0.383172 0.923677i \(-0.374832\pi\)
−0.923677 + 0.383172i \(0.874832\pi\)
\(548\) 0 0
\(549\) −15.4530 + 18.7669i −0.659518 + 0.800950i
\(550\) 0 0
\(551\) 4.06764i 0.173287i
\(552\) 0 0
\(553\) 10.7839i 0.458578i
\(554\) 0 0
\(555\) −0.110007 2.27724i −0.00466955 0.0966636i
\(556\) 0 0
\(557\) 6.90317 + 6.90317i 0.292497 + 0.292497i 0.838066 0.545569i \(-0.183686\pi\)
−0.545569 + 0.838066i \(0.683686\pi\)
\(558\) 0 0
\(559\) 2.98944i 0.126440i
\(560\) 0 0
\(561\) 13.1567 + 11.9441i 0.555475 + 0.504281i
\(562\) 0 0
\(563\) 18.3840 18.3840i 0.774794 0.774794i −0.204146 0.978940i \(-0.565442\pi\)
0.978940 + 0.204146i \(0.0654418\pi\)
\(564\) 0 0
\(565\) 3.58890 + 3.58890i 0.150986 + 0.150986i
\(566\) 0 0
\(567\) −27.4061 + 5.35828i −1.15095 + 0.225027i
\(568\) 0 0
\(569\) −43.5570 −1.82601 −0.913003 0.407953i \(-0.866243\pi\)
−0.913003 + 0.407953i \(0.866243\pi\)
\(570\) 0 0
\(571\) −7.00859 + 7.00859i −0.293301 + 0.293301i −0.838383 0.545082i \(-0.816498\pi\)
0.545082 + 0.838383i \(0.316498\pi\)
\(572\) 0 0
\(573\) 0.265638 + 5.49894i 0.0110972 + 0.229721i
\(574\) 0 0
\(575\) 27.6340 1.15242
\(576\) 0 0
\(577\) 28.4494 1.18436 0.592182 0.805804i \(-0.298267\pi\)
0.592182 + 0.805804i \(0.298267\pi\)
\(578\) 0 0
\(579\) 0.957746 + 19.8261i 0.0398026 + 0.823946i
\(580\) 0 0
\(581\) 14.1239 14.1239i 0.585958 0.585958i
\(582\) 0 0
\(583\) −52.7527 −2.18479
\(584\) 0 0
\(585\) 0.525036 + 5.42166i 0.0217076 + 0.224158i
\(586\) 0 0
\(587\) −19.9011 19.9011i −0.821405 0.821405i 0.164904 0.986310i \(-0.447268\pi\)
−0.986310 + 0.164904i \(0.947268\pi\)
\(588\) 0 0
\(589\) 0.372787 0.372787i 0.0153604 0.0153604i
\(590\) 0 0
\(591\) 26.8510 + 24.3764i 1.10450 + 1.00271i
\(592\) 0 0
\(593\) 20.4344i 0.839140i −0.907723 0.419570i \(-0.862181\pi\)
0.907723 0.419570i \(-0.137819\pi\)
\(594\) 0 0
\(595\) −3.25443 3.25443i −0.133418 0.133418i
\(596\) 0 0
\(597\) 2.04378 + 42.3079i 0.0836462 + 1.73155i
\(598\) 0 0
\(599\) 32.6704i 1.33488i −0.744665 0.667438i \(-0.767391\pi\)
0.744665 0.667438i \(-0.232609\pi\)
\(600\) 0 0
\(601\) 6.73553i 0.274748i −0.990519 0.137374i \(-0.956134\pi\)
0.990519 0.137374i \(-0.0438662\pi\)
\(602\) 0 0
\(603\) −1.28369 1.05702i −0.0522760 0.0430451i
\(604\) 0 0
\(605\) −2.94993 2.94993i −0.119932 0.119932i
\(606\) 0 0
\(607\) 21.2388i 0.862058i −0.902338 0.431029i \(-0.858151\pi\)
0.902338 0.431029i \(-0.141849\pi\)
\(608\) 0 0
\(609\) 14.6167 16.1005i 0.592297 0.652426i
\(610\) 0 0
\(611\) 15.8508 15.8508i 0.641256 0.641256i
\(612\) 0 0
\(613\) 9.62219 + 9.62219i 0.388637 + 0.388637i 0.874201 0.485564i \(-0.161386\pi\)
−0.485564 + 0.874201i \(0.661386\pi\)
\(614\) 0 0
\(615\) 1.42166 + 1.29064i 0.0573270 + 0.0520436i
\(616\) 0 0
\(617\) 3.74576 0.150798 0.0753992 0.997153i \(-0.475977\pi\)
0.0753992 + 0.997153i \(0.475977\pi\)
\(618\) 0 0
\(619\) 13.0680 13.0680i 0.525249 0.525249i −0.393903 0.919152i \(-0.628876\pi\)
0.919152 + 0.393903i \(0.128876\pi\)
\(620\) 0 0
\(621\) 30.7070 4.47799i 1.23223 0.179696i
\(622\) 0 0
\(623\) −38.9643 −1.56107
\(624\) 0 0
\(625\) −19.5472 −0.781887
\(626\) 0 0
\(627\) −7.34422 + 0.354779i −0.293300 + 0.0141685i
\(628\) 0 0
\(629\) −3.70355 + 3.70355i −0.147670 + 0.147670i
\(630\) 0 0
\(631\) −7.51388 −0.299123 −0.149561 0.988752i \(-0.547786\pi\)
−0.149561 + 0.988752i \(0.547786\pi\)
\(632\) 0 0
\(633\) 10.1857 11.2197i 0.404843 0.445942i
\(634\) 0 0
\(635\) −6.81226 6.81226i −0.270336 0.270336i
\(636\) 0 0
\(637\) −5.52444 + 5.52444i −0.218886 + 0.218886i
\(638\) 0 0
\(639\) −1.45158 14.9894i −0.0574238 0.592973i
\(640\) 0 0
\(641\) 27.7227i 1.09498i −0.836811 0.547491i \(-0.815583\pi\)
0.836811 0.547491i \(-0.184417\pi\)
\(642\) 0 0
\(643\) −19.7003 19.7003i −0.776903 0.776903i 0.202400 0.979303i \(-0.435126\pi\)
−0.979303 + 0.202400i \(0.935126\pi\)
\(644\) 0 0
\(645\) −1.06186 + 0.0512954i −0.0418106 + 0.00201976i
\(646\) 0 0
\(647\) 5.29520i 0.208176i 0.994568 + 0.104088i \(0.0331923\pi\)
−0.994568 + 0.104088i \(0.966808\pi\)
\(648\) 0 0
\(649\) 0.480585i 0.0188646i
\(650\) 0 0
\(651\) 2.81513 0.135991i 0.110334 0.00532992i
\(652\) 0 0
\(653\) −29.7039 29.7039i −1.16240 1.16240i −0.983948 0.178457i \(-0.942890\pi\)
−0.178457 0.983948i \(-0.557110\pi\)
\(654\) 0 0
\(655\) 0.0694851i 0.00271501i
\(656\) 0 0
\(657\) 3.89220 + 40.1919i 0.151849 + 1.56804i
\(658\) 0 0
\(659\) −1.03268 + 1.03268i −0.0402276 + 0.0402276i −0.726934 0.686707i \(-0.759056\pi\)
0.686707 + 0.726934i \(0.259056\pi\)
\(660\) 0 0
\(661\) −29.8277 29.8277i −1.16016 1.16016i −0.984439 0.175725i \(-0.943773\pi\)
−0.175725 0.984439i \(-0.556227\pi\)
\(662\) 0 0
\(663\) 8.41110 9.26498i 0.326660 0.359822i
\(664\) 0 0
\(665\) 1.90442 0.0738502
\(666\) 0 0
\(667\) −17.0872 + 17.0872i −0.661619 + 0.661619i
\(668\) 0 0
\(669\) −14.1689 + 0.684461i −0.547802 + 0.0264628i
\(670\) 0 0
\(671\) −34.2198 −1.32104
\(672\) 0 0
\(673\) −0.891685 −0.0343719 −0.0171860 0.999852i \(-0.505471\pi\)
−0.0171860 + 0.999852i \(0.505471\pi\)
\(674\) 0 0
\(675\) −23.7920 + 3.46959i −0.915756 + 0.133545i
\(676\) 0 0
\(677\) 8.13073 8.13073i 0.312489 0.312489i −0.533384 0.845873i \(-0.679080\pi\)
0.845873 + 0.533384i \(0.179080\pi\)
\(678\) 0 0
\(679\) 26.9200 1.03309
\(680\) 0 0
\(681\) 17.9734 + 16.3169i 0.688742 + 0.625266i
\(682\) 0 0
\(683\) 14.5917 + 14.5917i 0.558337 + 0.558337i 0.928834 0.370497i \(-0.120813\pi\)
−0.370497 + 0.928834i \(0.620813\pi\)
\(684\) 0 0
\(685\) 5.72496 5.72496i 0.218740 0.218740i
\(686\) 0 0
\(687\) −11.7749 + 12.9703i −0.449241 + 0.494847i
\(688\) 0 0
\(689\) 37.1487i 1.41525i
\(690\) 0 0
\(691\) 11.2197 + 11.2197i 0.426817 + 0.426817i 0.887543 0.460726i \(-0.152411\pi\)
−0.460726 + 0.887543i \(0.652411\pi\)
\(692\) 0 0
\(693\) −30.3447 24.9864i −1.15270 0.949154i
\(694\) 0 0
\(695\) 7.24616i 0.274863i
\(696\) 0 0
\(697\) 4.41110i 0.167082i
\(698\) 0 0
\(699\) 1.64164 + 33.9833i 0.0620924 + 1.28536i
\(700\) 0 0
\(701\) 14.7166 + 14.7166i 0.555837 + 0.555837i 0.928120 0.372282i \(-0.121425\pi\)
−0.372282 + 0.928120i \(0.621425\pi\)
\(702\) 0 0
\(703\) 2.16724i 0.0817389i
\(704\) 0 0
\(705\) −5.90225 5.35828i −0.222292 0.201805i
\(706\) 0 0
\(707\) 0.564847 0.564847i 0.0212433 0.0212433i
\(708\) 0 0
\(709\) 23.2978 + 23.2978i 0.874966 + 0.874966i 0.993009 0.118043i \(-0.0376620\pi\)
−0.118043 + 0.993009i \(0.537662\pi\)
\(710\) 0 0
\(711\) 1.00502 + 10.3781i 0.0376913 + 0.389211i
\(712\) 0 0
\(713\) −3.13198 −0.117293
\(714\) 0 0
\(715\) −5.42166 + 5.42166i −0.202759 + 0.202759i
\(716\) 0 0
\(717\) −0.789136 16.3358i −0.0294708 0.610071i
\(718\) 0 0
\(719\) 27.3421 1.01969 0.509844 0.860267i \(-0.329703\pi\)
0.509844 + 0.860267i \(0.329703\pi\)
\(720\) 0 0
\(721\) −19.7250 −0.734596
\(722\) 0 0
\(723\) −1.38871 28.7474i −0.0516465 1.06913i
\(724\) 0 0
\(725\) 13.2393 13.2393i 0.491696 0.491696i
\(726\) 0 0
\(727\) 24.1517 0.895735 0.447868 0.894100i \(-0.352184\pi\)
0.447868 + 0.894100i \(0.352184\pi\)
\(728\) 0 0
\(729\) −25.8755 + 7.71083i −0.958353 + 0.285586i
\(730\) 0 0
\(731\) 1.72693 + 1.72693i 0.0638729 + 0.0638729i
\(732\) 0 0
\(733\) 6.00502 6.00502i 0.221801 0.221801i −0.587456 0.809256i \(-0.699870\pi\)
0.809256 + 0.587456i \(0.199870\pi\)
\(734\) 0 0
\(735\) 2.05709 + 1.86751i 0.0758770 + 0.0688840i
\(736\) 0 0
\(737\) 2.34071i 0.0862212i
\(738\) 0 0
\(739\) 10.9008 + 10.9008i 0.400992 + 0.400992i 0.878583 0.477590i \(-0.158490\pi\)
−0.477590 + 0.878583i \(0.658490\pi\)
\(740\) 0 0
\(741\) 0.249837 + 5.17183i 0.00917798 + 0.189992i
\(742\) 0 0
\(743\) 1.29064i 0.0473490i 0.999720 + 0.0236745i \(0.00753652\pi\)
−0.999720 + 0.0236745i \(0.992463\pi\)
\(744\) 0 0
\(745\) 4.99948i 0.183167i
\(746\) 0 0
\(747\) 12.2762 14.9088i 0.449162 0.545483i
\(748\) 0 0
\(749\) 5.10860 + 5.10860i 0.186664 + 0.186664i
\(750\) 0 0
\(751\) 1.46552i 0.0534774i −0.999642 0.0267387i \(-0.991488\pi\)
0.999642 0.0267387i \(-0.00851221\pi\)
\(752\) 0 0
\(753\) −3.34861 + 3.68855i −0.122030 + 0.134418i
\(754\) 0 0
\(755\) −4.29406 + 4.29406i −0.156277 + 0.156277i
\(756\) 0 0
\(757\) −4.71943 4.71943i −0.171530 0.171530i 0.616121 0.787651i \(-0.288703\pi\)
−0.787651 + 0.616121i \(0.788703\pi\)
\(758\) 0 0
\(759\) 32.3416 + 29.3609i 1.17393 + 1.06573i
\(760\) 0 0
\(761\) 29.1578 1.05697 0.528485 0.848943i \(-0.322760\pi\)
0.528485 + 0.848943i \(0.322760\pi\)
\(762\) 0 0
\(763\) 20.3955 20.3955i 0.738367 0.738367i
\(764\) 0 0
\(765\) −3.43528 2.82867i −0.124203 0.102271i
\(766\) 0 0
\(767\) −0.338430 −0.0122200
\(768\) 0 0
\(769\) 20.8122 0.750505 0.375253 0.926923i \(-0.377556\pi\)
0.375253 + 0.926923i \(0.377556\pi\)
\(770\) 0 0
\(771\) 26.0822 1.25996i 0.939326 0.0453762i
\(772\) 0 0
\(773\) 26.6607 26.6607i 0.958918 0.958918i −0.0402703 0.999189i \(-0.512822\pi\)
0.999189 + 0.0402703i \(0.0128219\pi\)
\(774\) 0 0
\(775\) 2.42669 0.0871691
\(776\) 0 0
\(777\) 7.78774 8.57834i 0.279384 0.307746i
\(778\) 0 0
\(779\) 1.29064 + 1.29064i 0.0462419 + 0.0462419i
\(780\) 0 0
\(781\) 14.9894 14.9894i 0.536364 0.536364i
\(782\) 0 0
\(783\) 12.5662 16.8569i 0.449078 0.602418i
\(784\) 0 0
\(785\) 7.90214i 0.282040i
\(786\) 0 0
\(787\) 32.7875 + 32.7875i 1.16875 + 1.16875i 0.982504 + 0.186243i \(0.0596311\pi\)
0.186243 + 0.982504i \(0.440369\pi\)
\(788\) 0 0
\(789\) 51.5788 2.49163i 1.83625 0.0887044i
\(790\) 0 0
\(791\) 25.7927i 0.917082i
\(792\) 0 0
\(793\) 24.0978i 0.855736i
\(794\) 0 0
\(795\) 13.1953 0.637430i 0.467990 0.0226073i
\(796\) 0 0
\(797\) 11.2627 + 11.2627i 0.398945 + 0.398945i