Properties

Label 1152.2.p.d.959.2
Level $1152$
Weight $2$
Character 1152.959
Analytic conductor $9.199$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 16 x^{14} + 178 x^{12} - 1024 x^{10} + 4267 x^{8} - 7936 x^{6} + 10594 x^{4} - 2800 x^{2} + 625\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 959.2
Root \(-2.12575 + 1.22730i\) of defining polynomial
Character \(\chi\) \(=\) 1152.959
Dual form 1152.2.p.d.191.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.65068 + 0.524648i) q^{3} +(1.01255 - 1.75379i) q^{5} +(4.09406 - 2.36371i) q^{7} +(2.44949 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-1.65068 + 0.524648i) q^{3} +(1.01255 - 1.75379i) q^{5} +(4.09406 - 2.36371i) q^{7} +(2.44949 - 1.73205i) q^{9} +(-2.93038 + 1.69185i) q^{11} +(5.51787 + 3.18575i) q^{13} +(-0.751275 + 3.42617i) q^{15} -4.87832i q^{17} +1.48393 q^{19} +(-5.51787 + 6.04967i) q^{21} +(-0.751275 + 1.30125i) q^{23} +(0.449490 + 0.778539i) q^{25} +(-3.13461 + 4.14418i) q^{27} +(-3.49278 - 6.04967i) q^{29} +(-5.93430 - 3.42617i) q^{31} +(3.94949 - 4.33013i) q^{33} -9.57348i q^{35} -2.86392i q^{37} +(-10.7796 - 2.36371i) q^{39} +(4.62372 + 2.66951i) q^{41} +(2.76363 + 4.78674i) q^{43} +(-0.557419 - 6.04967i) q^{45} +(4.09406 + 7.09113i) q^{47} +(7.67423 - 13.2922i) q^{49} +(2.55940 + 8.05254i) q^{51} +4.96046 q^{53} +6.85234i q^{55} +(-2.44949 + 0.778539i) q^{57} +(-7.88242 - 4.55092i) q^{59} +(-5.51787 + 3.18575i) q^{61} +(5.93430 - 12.8810i) q^{63} +(11.1742 - 6.45145i) q^{65} +(5.48977 - 9.50857i) q^{67} +(0.557419 - 2.54209i) q^{69} +6.68558 q^{71} +0.449490 q^{73} +(-1.15042 - 1.04930i) q^{75} +(-7.99810 + 13.8531i) q^{77} +(5.93430 - 3.42617i) q^{79} +(3.00000 - 8.48528i) q^{81} +(6.06499 - 3.50162i) q^{83} +(-8.55552 - 4.93953i) q^{85} +(8.93940 + 8.15359i) q^{87} +0.142865i q^{89} +30.1207 q^{91} +(11.5932 + 2.54209i) q^{93} +(1.50255 - 2.60249i) q^{95} +(0.724745 + 1.25529i) q^{97} +(-4.24755 + 9.21975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 32q^{25} + 24q^{33} - 24q^{41} + 64q^{49} + 120q^{65} - 32q^{73} + 48q^{81} - 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) −1.65068 + 0.524648i −0.953021 + 0.302905i
\(4\) 0 0
\(5\) 1.01255 1.75379i 0.452826 0.784317i −0.545735 0.837958i \(-0.683749\pi\)
0.998560 + 0.0536411i \(0.0170827\pi\)
\(6\) 0 0
\(7\) 4.09406 2.36371i 1.54741 0.893398i 0.549072 0.835775i \(-0.314981\pi\)
0.998338 0.0576227i \(-0.0183520\pi\)
\(8\) 0 0
\(9\) 2.44949 1.73205i 0.816497 0.577350i
\(10\) 0 0
\(11\) −2.93038 + 1.69185i −0.883542 + 0.510113i −0.871825 0.489818i \(-0.837063\pi\)
−0.0117176 + 0.999931i \(0.503730\pi\)
\(12\) 0 0
\(13\) 5.51787 + 3.18575i 1.53038 + 0.883567i 0.999344 + 0.0362198i \(0.0115316\pi\)
0.531039 + 0.847347i \(0.321802\pi\)
\(14\) 0 0
\(15\) −0.751275 + 3.42617i −0.193978 + 0.884634i
\(16\) 0 0
\(17\) 4.87832i 1.18317i −0.806244 0.591583i \(-0.798503\pi\)
0.806244 0.591583i \(-0.201497\pi\)
\(18\) 0 0
\(19\) 1.48393 0.340436 0.170218 0.985406i \(-0.445553\pi\)
0.170218 + 0.985406i \(0.445553\pi\)
\(20\) 0 0
\(21\) −5.51787 + 6.04967i −1.20410 + 1.32015i
\(22\) 0 0
\(23\) −0.751275 + 1.30125i −0.156652 + 0.271328i −0.933659 0.358163i \(-0.883403\pi\)
0.777008 + 0.629491i \(0.216737\pi\)
\(24\) 0 0
\(25\) 0.449490 + 0.778539i 0.0898979 + 0.155708i
\(26\) 0 0
\(27\) −3.13461 + 4.14418i −0.603256 + 0.797548i
\(28\) 0 0
\(29\) −3.49278 6.04967i −0.648592 1.12339i −0.983459 0.181129i \(-0.942025\pi\)
0.334867 0.942265i \(-0.391309\pi\)
\(30\) 0 0
\(31\) −5.93430 3.42617i −1.06583 0.615358i −0.138792 0.990321i \(-0.544322\pi\)
−0.927040 + 0.374963i \(0.877655\pi\)
\(32\) 0 0
\(33\) 3.94949 4.33013i 0.687518 0.753778i
\(34\) 0 0
\(35\) 9.57348i 1.61821i
\(36\) 0 0
\(37\) 2.86392i 0.470826i −0.971895 0.235413i \(-0.924356\pi\)
0.971895 0.235413i \(-0.0756442\pi\)
\(38\) 0 0
\(39\) −10.7796 2.36371i −1.72612 0.378496i
\(40\) 0 0
\(41\) 4.62372 + 2.66951i 0.722104 + 0.416907i 0.815527 0.578719i \(-0.196447\pi\)
−0.0934223 + 0.995627i \(0.529781\pi\)
\(42\) 0 0
\(43\) 2.76363 + 4.78674i 0.421449 + 0.729971i 0.996081 0.0884405i \(-0.0281883\pi\)
−0.574632 + 0.818412i \(0.694855\pi\)
\(44\) 0 0
\(45\) −0.557419 6.04967i −0.0830950 0.901831i
\(46\) 0 0
\(47\) 4.09406 + 7.09113i 0.597180 + 1.03435i 0.993235 + 0.116120i \(0.0370457\pi\)
−0.396055 + 0.918227i \(0.629621\pi\)
\(48\) 0 0
\(49\) 7.67423 13.2922i 1.09632 1.89888i
\(50\) 0 0
\(51\) 2.55940 + 8.05254i 0.358387 + 1.12758i
\(52\) 0 0
\(53\) 4.96046 0.681371 0.340686 0.940177i \(-0.389341\pi\)
0.340686 + 0.940177i \(0.389341\pi\)
\(54\) 0 0
\(55\) 6.85234i 0.923970i
\(56\) 0 0
\(57\) −2.44949 + 0.778539i −0.324443 + 0.103120i
\(58\) 0 0
\(59\) −7.88242 4.55092i −1.02620 0.592479i −0.110309 0.993897i \(-0.535184\pi\)
−0.915895 + 0.401418i \(0.868517\pi\)
\(60\) 0 0
\(61\) −5.51787 + 3.18575i −0.706491 + 0.407893i −0.809761 0.586760i \(-0.800403\pi\)
0.103269 + 0.994653i \(0.467070\pi\)
\(62\) 0 0
\(63\) 5.93430 12.8810i 0.747652 1.62285i
\(64\) 0 0
\(65\) 11.1742 6.45145i 1.38599 0.800204i
\(66\) 0 0
\(67\) 5.48977 9.50857i 0.670683 1.16166i −0.307028 0.951700i \(-0.599335\pi\)
0.977711 0.209956i \(-0.0673321\pi\)
\(68\) 0 0
\(69\) 0.557419 2.54209i 0.0671053 0.306032i
\(70\) 0 0
\(71\) 6.68558 0.793432 0.396716 0.917941i \(-0.370150\pi\)
0.396716 + 0.917941i \(0.370150\pi\)
\(72\) 0 0
\(73\) 0.449490 0.0526088 0.0263044 0.999654i \(-0.491626\pi\)
0.0263044 + 0.999654i \(0.491626\pi\)
\(74\) 0 0
\(75\) −1.15042 1.04930i −0.132839 0.121162i
\(76\) 0 0
\(77\) −7.99810 + 13.8531i −0.911468 + 1.57871i
\(78\) 0 0
\(79\) 5.93430 3.42617i 0.667661 0.385474i −0.127529 0.991835i \(-0.540704\pi\)
0.795190 + 0.606361i \(0.207371\pi\)
\(80\) 0 0
\(81\) 3.00000 8.48528i 0.333333 0.942809i
\(82\) 0 0
\(83\) 6.06499 3.50162i 0.665719 0.384353i −0.128734 0.991679i \(-0.541091\pi\)
0.794452 + 0.607326i \(0.207758\pi\)
\(84\) 0 0
\(85\) −8.55552 4.93953i −0.927977 0.535768i
\(86\) 0 0
\(87\) 8.93940 + 8.15359i 0.958404 + 0.874156i
\(88\) 0 0
\(89\) 0.142865i 0.0151436i 0.999971 + 0.00757181i \(0.00241020\pi\)
−0.999971 + 0.00757181i \(0.997590\pi\)
\(90\) 0 0
\(91\) 30.1207 3.15751
\(92\) 0 0
\(93\) 11.5932 + 2.54209i 1.20216 + 0.263603i
\(94\) 0 0
\(95\) 1.50255 2.60249i 0.154158 0.267010i
\(96\) 0 0
\(97\) 0.724745 + 1.25529i 0.0735867 + 0.127456i 0.900471 0.434916i \(-0.143222\pi\)
−0.826884 + 0.562372i \(0.809889\pi\)
\(98\) 0 0
\(99\) −4.24755 + 9.21975i −0.426895 + 0.926619i
\(100\) 0 0
\(101\) 3.03765 + 5.26136i 0.302257 + 0.523525i 0.976647 0.214851i \(-0.0689265\pi\)
−0.674390 + 0.738376i \(0.735593\pi\)
\(102\) 0 0
\(103\) −4.09406 2.36371i −0.403400 0.232903i 0.284550 0.958661i \(-0.408156\pi\)
−0.687950 + 0.725758i \(0.741489\pi\)
\(104\) 0 0
\(105\) 5.02270 + 15.8028i 0.490166 + 1.54219i
\(106\) 0 0
\(107\) 11.9079i 1.15118i −0.817739 0.575590i \(-0.804773\pi\)
0.817739 0.575590i \(-0.195227\pi\)
\(108\) 0 0
\(109\) 4.15122i 0.397615i −0.980039 0.198808i \(-0.936293\pi\)
0.980039 0.198808i \(-0.0637069\pi\)
\(110\) 0 0
\(111\) 1.50255 + 4.72742i 0.142616 + 0.448707i
\(112\) 0 0
\(113\) −6.39898 3.69445i −0.601965 0.347545i 0.167849 0.985813i \(-0.446318\pi\)
−0.769814 + 0.638268i \(0.779651\pi\)
\(114\) 0 0
\(115\) 1.52140 + 2.63515i 0.141872 + 0.245729i
\(116\) 0 0
\(117\) 19.0339 1.75379i 1.75968 0.162138i
\(118\) 0 0
\(119\) −11.5309 19.9721i −1.05704 1.83084i
\(120\) 0 0
\(121\) 0.224745 0.389270i 0.0204314 0.0353881i
\(122\) 0 0
\(123\) −9.03284 1.98068i −0.814464 0.178592i
\(124\) 0 0
\(125\) 11.9460 1.06848
\(126\) 0 0
\(127\) 9.45483i 0.838981i 0.907760 + 0.419490i \(0.137791\pi\)
−0.907760 + 0.419490i \(0.862209\pi\)
\(128\) 0 0
\(129\) −7.07321 6.45145i −0.622762 0.568018i
\(130\) 0 0
\(131\) −10.5168 6.07186i −0.918854 0.530501i −0.0355850 0.999367i \(-0.511329\pi\)
−0.883269 + 0.468866i \(0.844663\pi\)
\(132\) 0 0
\(133\) 6.07529 3.50757i 0.526795 0.304145i
\(134\) 0 0
\(135\) 4.09406 + 9.69362i 0.352361 + 0.834294i
\(136\) 0 0
\(137\) −9.27526 + 5.35507i −0.792439 + 0.457515i −0.840820 0.541314i \(-0.817927\pi\)
0.0483818 + 0.998829i \(0.484594\pi\)
\(138\) 0 0
\(139\) 3.50559 6.07186i 0.297340 0.515008i −0.678186 0.734890i \(-0.737234\pi\)
0.975527 + 0.219882i \(0.0705671\pi\)
\(140\) 0 0
\(141\) −10.4783 9.55724i −0.882435 0.804865i
\(142\) 0 0
\(143\) −21.5593 −1.80288
\(144\) 0 0
\(145\) −14.1464 −1.17480
\(146\) 0 0
\(147\) −5.69400 + 25.9674i −0.469634 + 2.14175i
\(148\) 0 0
\(149\) −3.49278 + 6.04967i −0.286139 + 0.495608i −0.972885 0.231290i \(-0.925705\pi\)
0.686745 + 0.726898i \(0.259039\pi\)
\(150\) 0 0
\(151\) −2.25382 + 1.30125i −0.183414 + 0.105894i −0.588896 0.808209i \(-0.700437\pi\)
0.405482 + 0.914103i \(0.367104\pi\)
\(152\) 0 0
\(153\) −8.44949 11.9494i −0.683101 0.966050i
\(154\) 0 0
\(155\) −12.0175 + 6.93833i −0.965272 + 0.557300i
\(156\) 0 0
\(157\) −12.9586 7.48163i −1.03421 0.597099i −0.116019 0.993247i \(-0.537013\pi\)
−0.918187 + 0.396148i \(0.870347\pi\)
\(158\) 0 0
\(159\) −8.18813 + 2.60249i −0.649361 + 0.206391i
\(160\) 0 0
\(161\) 7.10318i 0.559809i
\(162\) 0 0
\(163\) −3.63487 −0.284705 −0.142352 0.989816i \(-0.545467\pi\)
−0.142352 + 0.989816i \(0.545467\pi\)
\(164\) 0 0
\(165\) −3.59506 11.3110i −0.279875 0.880562i
\(166\) 0 0
\(167\) −2.59151 + 4.48863i −0.200537 + 0.347341i −0.948702 0.316173i \(-0.897602\pi\)
0.748164 + 0.663513i \(0.230935\pi\)
\(168\) 0 0
\(169\) 13.7980 + 23.8988i 1.06138 + 1.83837i
\(170\) 0 0
\(171\) 3.63487 2.57024i 0.277965 0.196551i
\(172\) 0 0
\(173\) 1.01255 + 1.75379i 0.0769827 + 0.133338i 0.901947 0.431847i \(-0.142138\pi\)
−0.824964 + 0.565185i \(0.808805\pi\)
\(174\) 0 0
\(175\) 3.68048 + 2.12493i 0.278218 + 0.160629i
\(176\) 0 0
\(177\) 15.3990 + 3.37662i 1.15746 + 0.253802i
\(178\) 0 0
\(179\) 16.5767i 1.23900i −0.784996 0.619501i \(-0.787335\pi\)
0.784996 0.619501i \(-0.212665\pi\)
\(180\) 0 0
\(181\) 22.6220i 1.68148i 0.541436 + 0.840742i \(0.317881\pi\)
−0.541436 + 0.840742i \(0.682119\pi\)
\(182\) 0 0
\(183\) 7.43685 8.15359i 0.549748 0.602731i
\(184\) 0 0
\(185\) −5.02270 2.89986i −0.369277 0.213202i
\(186\) 0 0
\(187\) 8.25340 + 14.2953i 0.603548 + 1.04538i
\(188\) 0 0
\(189\) −3.03765 + 24.3758i −0.220956 + 1.77308i
\(190\) 0 0
\(191\) 2.59151 + 4.48863i 0.187515 + 0.324786i 0.944421 0.328738i \(-0.106623\pi\)
−0.756906 + 0.653524i \(0.773290\pi\)
\(192\) 0 0
\(193\) −0.376276 + 0.651729i −0.0270849 + 0.0469124i −0.879250 0.476360i \(-0.841956\pi\)
0.852165 + 0.523273i \(0.175289\pi\)
\(194\) 0 0
\(195\) −15.0604 + 16.5118i −1.07849 + 1.18244i
\(196\) 0 0
\(197\) −18.0213 −1.28396 −0.641982 0.766719i \(-0.721888\pi\)
−0.641982 + 0.766719i \(0.721888\pi\)
\(198\) 0 0
\(199\) 2.12493i 0.150632i −0.997160 0.0753160i \(-0.976003\pi\)
0.997160 0.0753160i \(-0.0239965\pi\)
\(200\) 0 0
\(201\) −4.07321 + 18.5758i −0.287302 + 1.31024i
\(202\) 0 0
\(203\) −28.5993 16.5118i −2.00728 1.15890i
\(204\) 0 0
\(205\) 9.36349 5.40602i 0.653975 0.377572i
\(206\) 0 0
\(207\) 0.413584 + 4.48863i 0.0287461 + 0.311982i
\(208\) 0 0
\(209\) −4.34847 + 2.51059i −0.300790 + 0.173661i
\(210\) 0 0
\(211\) −3.33884 + 5.78304i −0.229855 + 0.398121i −0.957765 0.287552i \(-0.907159\pi\)
0.727910 + 0.685673i \(0.240492\pi\)
\(212\) 0 0
\(213\) −11.0357 + 3.50757i −0.756157 + 0.240335i
\(214\) 0 0
\(215\) 11.1932 0.763372
\(216\) 0 0
\(217\) −32.3939 −2.19904
\(218\) 0 0
\(219\) −0.741964 + 0.235824i −0.0501373 + 0.0159355i
\(220\) 0 0
\(221\) 15.5411 26.9179i 1.04541 1.81070i
\(222\) 0 0
\(223\) −15.9627 + 9.21605i −1.06894 + 0.617152i −0.927891 0.372850i \(-0.878380\pi\)
−0.141048 + 0.990003i \(0.545047\pi\)
\(224\) 0 0
\(225\) 2.44949 + 1.12848i 0.163299 + 0.0752323i
\(226\) 0 0
\(227\) 17.2862 9.98022i 1.14733 0.662410i 0.199093 0.979981i \(-0.436200\pi\)
0.948235 + 0.317570i \(0.102867\pi\)
\(228\) 0 0
\(229\) 12.9586 + 7.48163i 0.856326 + 0.494400i 0.862780 0.505579i \(-0.168721\pi\)
−0.00645448 + 0.999979i \(0.502055\pi\)
\(230\) 0 0
\(231\) 5.93430 27.0633i 0.390448 1.78063i
\(232\) 0 0
\(233\) 9.75663i 0.639178i 0.947556 + 0.319589i \(0.103545\pi\)
−0.947556 + 0.319589i \(0.896455\pi\)
\(234\) 0 0
\(235\) 16.5818 1.08167
\(236\) 0 0
\(237\) −7.99810 + 8.76893i −0.519533 + 0.569603i
\(238\) 0 0
\(239\) 12.6199 21.8583i 0.816312 1.41389i −0.0920698 0.995753i \(-0.529348\pi\)
0.908382 0.418142i \(-0.137318\pi\)
\(240\) 0 0
\(241\) 4.94949 + 8.57277i 0.318825 + 0.552221i 0.980243 0.197797i \(-0.0633786\pi\)
−0.661418 + 0.750017i \(0.730045\pi\)
\(242\) 0 0
\(243\) −0.500258 + 15.5804i −0.0320915 + 0.999485i
\(244\) 0 0
\(245\) −15.5411 26.9179i −0.992883 1.71972i
\(246\) 0 0
\(247\) 8.18813 + 4.72742i 0.520998 + 0.300798i
\(248\) 0 0
\(249\) −8.17423 + 8.96204i −0.518021 + 0.567946i
\(250\) 0 0
\(251\) 18.2037i 1.14901i 0.818503 + 0.574503i \(0.194804\pi\)
−0.818503 + 0.574503i \(0.805196\pi\)
\(252\) 0 0
\(253\) 5.08419i 0.319640i
\(254\) 0 0
\(255\) 16.7139 + 3.66495i 1.04667 + 0.229508i
\(256\) 0 0
\(257\) −5.05051 2.91591i −0.315042 0.181890i 0.334138 0.942524i \(-0.391555\pi\)
−0.649181 + 0.760634i \(0.724888\pi\)
\(258\) 0 0
\(259\) −6.76947 11.7251i −0.420635 0.728560i
\(260\) 0 0
\(261\) −19.0339 8.76893i −1.17817 0.542783i
\(262\) 0 0
\(263\) 14.1224 + 24.4608i 0.870826 + 1.50832i 0.861143 + 0.508362i \(0.169749\pi\)
0.00968287 + 0.999953i \(0.496918\pi\)
\(264\) 0 0
\(265\) 5.02270 8.69958i 0.308542 0.534411i
\(266\) 0 0
\(267\) −0.0749536 0.235824i −0.00458708 0.0144322i
\(268\) 0 0
\(269\) −0.910261 −0.0554996 −0.0277498 0.999615i \(-0.508834\pi\)
−0.0277498 + 0.999615i \(0.508834\pi\)
\(270\) 0 0
\(271\) 18.9097i 1.14868i −0.818617 0.574340i \(-0.805259\pi\)
0.818617 0.574340i \(-0.194741\pi\)
\(272\) 0 0
\(273\) −49.7196 + 15.8028i −3.00917 + 0.956426i
\(274\) 0 0
\(275\) −2.63435 1.52094i −0.158857 0.0917163i
\(276\) 0 0
\(277\) 9.11294 5.26136i 0.547543 0.316124i −0.200587 0.979676i \(-0.564285\pi\)
0.748131 + 0.663551i \(0.230952\pi\)
\(278\) 0 0
\(279\) −20.4703 + 1.88614i −1.22553 + 0.112920i
\(280\) 0 0
\(281\) −19.0732 + 11.0119i −1.13781 + 0.656916i −0.945888 0.324493i \(-0.894806\pi\)
−0.191925 + 0.981410i \(0.561473\pi\)
\(282\) 0 0
\(283\) 10.1083 17.5081i 0.600877 1.04075i −0.391812 0.920045i \(-0.628152\pi\)
0.992689 0.120704i \(-0.0385151\pi\)
\(284\) 0 0
\(285\) −1.11484 + 5.08419i −0.0660372 + 0.301161i
\(286\) 0 0
\(287\) 25.2398 1.48986
\(288\) 0 0
\(289\) −6.79796 −0.399880
\(290\) 0 0
\(291\) −1.85491 1.69185i −0.108737 0.0991783i
\(292\) 0 0
\(293\) −1.01255 + 1.75379i −0.0591537 + 0.102457i −0.894086 0.447896i \(-0.852174\pi\)
0.834932 + 0.550353i \(0.185507\pi\)
\(294\) 0 0
\(295\) −15.9627 + 9.21605i −0.929382 + 0.536579i
\(296\) 0 0
\(297\) 2.17423 17.4473i 0.126162 1.01240i
\(298\) 0 0
\(299\) −8.29088 + 4.78674i −0.479474 + 0.276824i
\(300\) 0 0
\(301\) 22.6289 + 13.0648i 1.30431 + 0.753043i
\(302\) 0 0
\(303\) −7.77454 7.09113i −0.446636 0.407374i
\(304\) 0 0
\(305\) 12.9029i 0.738818i
\(306\) 0 0
\(307\) 2.96786 0.169384 0.0846922 0.996407i \(-0.473009\pi\)
0.0846922 + 0.996407i \(0.473009\pi\)
\(308\) 0 0
\(309\) 7.99810 + 1.75379i 0.454996 + 0.0997694i
\(310\) 0 0
\(311\) −15.6250 + 27.0633i −0.886011 + 1.53462i −0.0414609 + 0.999140i \(0.513201\pi\)
−0.844550 + 0.535476i \(0.820132\pi\)
\(312\) 0 0
\(313\) −1.94949 3.37662i −0.110192 0.190858i 0.805656 0.592384i \(-0.201813\pi\)
−0.915847 + 0.401526i \(0.868480\pi\)
\(314\) 0 0
\(315\) −16.5818 23.4501i −0.934276 1.32127i
\(316\) 0 0
\(317\) 8.45323 + 14.6414i 0.474781 + 0.822345i 0.999583 0.0288797i \(-0.00919399\pi\)
−0.524802 + 0.851224i \(0.675861\pi\)
\(318\) 0 0
\(319\) 20.4703 + 11.8185i 1.14612 + 0.661711i
\(320\) 0 0
\(321\) 6.24745 + 19.6561i 0.348699 + 1.09710i
\(322\) 0 0
\(323\) 7.23907i 0.402792i
\(324\) 0 0
\(325\) 5.72784i 0.317723i
\(326\) 0 0
\(327\) 2.17793 + 6.85234i 0.120440 + 0.378935i
\(328\) 0 0
\(329\) 33.5227 + 19.3543i 1.84817 + 1.06704i
\(330\) 0 0
\(331\) 16.8778 + 29.2332i 0.927687 + 1.60680i 0.787182 + 0.616721i \(0.211539\pi\)
0.140505 + 0.990080i \(0.455127\pi\)
\(332\) 0 0
\(333\) −4.96046 7.01514i −0.271831 0.384428i
\(334\) 0 0
\(335\) −11.1173 19.2558i −0.607405 1.05206i
\(336\) 0 0
\(337\) −0.0505103 + 0.0874863i −0.00275147 + 0.00476568i −0.867398 0.497615i \(-0.834209\pi\)
0.864646 + 0.502381i \(0.167542\pi\)
\(338\) 0 0
\(339\) 12.5010 + 2.74115i 0.678959 + 0.148879i
\(340\) 0 0
\(341\) 23.1863 1.25561
\(342\) 0 0
\(343\) 39.4667i 2.13100i
\(344\) 0 0
\(345\) −3.89388 3.55159i −0.209639 0.191211i
\(346\) 0 0
\(347\) 9.60805 + 5.54721i 0.515787 + 0.297790i 0.735209 0.677840i \(-0.237084\pi\)
−0.219422 + 0.975630i \(0.570417\pi\)
\(348\) 0 0
\(349\) −17.9190 + 10.3455i −0.959183 + 0.553784i −0.895921 0.444213i \(-0.853484\pi\)
−0.0632614 + 0.997997i \(0.520150\pi\)
\(350\) 0 0
\(351\) −30.4987 + 12.8810i −1.62790 + 0.687537i
\(352\) 0 0
\(353\) −4.62372 + 2.66951i −0.246096 + 0.142084i −0.617975 0.786197i \(-0.712047\pi\)
0.371879 + 0.928281i \(0.378714\pi\)
\(354\) 0 0
\(355\) 6.76947 11.7251i 0.359286 0.622302i
\(356\) 0 0
\(357\) 29.5122 + 26.9179i 1.56195 + 1.42465i
\(358\) 0 0
\(359\) −29.7474 −1.57001 −0.785004 0.619491i \(-0.787339\pi\)
−0.785004 + 0.619491i \(0.787339\pi\)
\(360\) 0 0
\(361\) −16.7980 −0.884103
\(362\) 0 0
\(363\) −0.166753 + 0.760471i −0.00875224 + 0.0399144i
\(364\) 0 0
\(365\) 0.455130 0.788309i 0.0238226 0.0412620i
\(366\) 0 0
\(367\) 10.4419 6.02866i 0.545065 0.314694i −0.202064 0.979372i \(-0.564765\pi\)
0.747129 + 0.664679i \(0.231432\pi\)
\(368\) 0 0
\(369\) 15.9495 1.46959i 0.830297 0.0765039i
\(370\) 0 0
\(371\) 20.3084 11.7251i 1.05436 0.608735i
\(372\) 0 0
\(373\) −10.4783 6.04967i −0.542547 0.313240i 0.203563 0.979062i \(-0.434748\pi\)
−0.746111 + 0.665822i \(0.768081\pi\)
\(374\) 0 0
\(375\) −19.7190 + 6.26745i −1.01829 + 0.323649i
\(376\) 0 0
\(377\) 44.5084i 2.29230i
\(378\) 0 0
\(379\) 7.60324 0.390552 0.195276 0.980748i \(-0.437440\pi\)
0.195276 + 0.980748i \(0.437440\pi\)
\(380\) 0 0
\(381\) −4.96046 15.6069i −0.254132 0.799566i
\(382\) 0 0
\(383\) −12.2822 + 21.2734i −0.627591 + 1.08702i 0.360443 + 0.932781i \(0.382625\pi\)
−0.988034 + 0.154238i \(0.950708\pi\)
\(384\) 0 0
\(385\) 16.1969 + 28.0539i 0.825472 + 1.42976i
\(386\) 0 0
\(387\) 15.0604 + 6.93833i 0.765561 + 0.352695i
\(388\) 0 0
\(389\) 12.9586 + 22.4449i 0.657025 + 1.13800i 0.981382 + 0.192066i \(0.0615187\pi\)
−0.324357 + 0.945935i \(0.605148\pi\)
\(390\) 0 0
\(391\) 6.34789 + 3.66495i 0.321026 + 0.185345i
\(392\) 0 0
\(393\) 20.5454 + 4.50510i 1.03638 + 0.227252i
\(394\) 0 0
\(395\) 13.8767i 0.698211i
\(396\) 0 0
\(397\) 23.9094i 1.19998i −0.800009 0.599988i \(-0.795172\pi\)
0.800009 0.599988i \(-0.204828\pi\)
\(398\) 0 0
\(399\) −8.18813 + 8.97727i −0.409919 + 0.449426i
\(400\) 0 0
\(401\) −16.6237 9.59771i −0.830149 0.479287i 0.0237546 0.999718i \(-0.492438\pi\)
−0.853904 + 0.520431i \(0.825771\pi\)
\(402\) 0 0
\(403\) −21.8298 37.8104i −1.08742 1.88347i
\(404\) 0 0
\(405\) −11.8437 13.8531i −0.588519 0.688367i
\(406\) 0 0
\(407\) 4.84534 + 8.39237i 0.240174 + 0.415994i
\(408\) 0 0
\(409\) 17.3990 30.1359i 0.860324 1.49013i −0.0112920 0.999936i \(-0.503594\pi\)
0.871616 0.490189i \(-0.163072\pi\)
\(410\) 0 0
\(411\) 12.5010 13.7057i 0.616627 0.676055i
\(412\) 0 0
\(413\) −43.0282 −2.11728
\(414\) 0 0
\(415\) 14.1823i 0.696179i
\(416\) 0 0
\(417\) −2.60102 + 11.8619i −0.127373 + 0.580880i
\(418\) 0 0
\(419\) 30.8252 + 17.7969i 1.50591 + 0.869437i 0.999976 + 0.00686390i \(0.00218486\pi\)
0.505933 + 0.862573i \(0.331148\pi\)
\(420\) 0 0
\(421\) −12.7080 + 7.33697i −0.619350 + 0.357582i −0.776616 0.629974i \(-0.783065\pi\)
0.157266 + 0.987556i \(0.449732\pi\)
\(422\) 0 0
\(423\) 22.3106 + 10.2785i 1.08478 + 0.499758i
\(424\) 0 0
\(425\) 3.79796 2.19275i 0.184228 0.106364i
\(426\) 0 0
\(427\) −15.0604 + 26.0853i −0.728821 + 1.26236i
\(428\) 0 0
\(429\) 35.5875 11.3110i 1.71818 0.546101i
\(430\) 0 0
\(431\) −3.00510 −0.144750 −0.0723752 0.997377i \(-0.523058\pi\)
−0.0723752 + 0.997377i \(0.523058\pi\)
\(432\) 0 0
\(433\) −26.2474 −1.26137 −0.630686 0.776038i \(-0.717226\pi\)
−0.630686 + 0.776038i \(0.717226\pi\)
\(434\) 0 0
\(435\) 23.3512 7.42189i 1.11961 0.355852i
\(436\) 0 0
\(437\) −1.11484 + 1.93095i −0.0533299 + 0.0923701i
\(438\) 0 0
\(439\) 10.4419 6.02866i 0.498367 0.287732i −0.229672 0.973268i \(-0.573765\pi\)
0.728039 + 0.685536i \(0.240432\pi\)
\(440\) 0 0
\(441\) −4.22474 45.8512i −0.201178 2.18339i
\(442\) 0 0
\(443\) −31.7339 + 18.3216i −1.50772 + 0.870484i −0.507764 + 0.861496i \(0.669528\pi\)
−0.999960 + 0.00898805i \(0.997139\pi\)
\(444\) 0 0
\(445\) 0.250554 + 0.144657i 0.0118774 + 0.00685742i
\(446\) 0 0
\(447\) 2.59151 11.8185i 0.122574 0.558998i
\(448\) 0 0
\(449\) 37.8980i 1.78852i 0.447549 + 0.894259i \(0.352297\pi\)
−0.447549 + 0.894259i \(0.647703\pi\)
\(450\) 0 0
\(451\) −18.0657 −0.850680
\(452\) 0 0
\(453\) 3.03765 3.33040i 0.142721 0.156476i
\(454\) 0 0
\(455\) 30.4987 52.8253i 1.42980 2.47649i
\(456\) 0 0
\(457\) 12.0732 + 20.9114i 0.564761 + 0.978195i 0.997072 + 0.0764703i \(0.0243650\pi\)
−0.432311 + 0.901725i \(0.642302\pi\)
\(458\) 0 0
\(459\) 20.2166 + 15.2916i 0.943631 + 0.713751i
\(460\) 0 0
\(461\) 5.51787 + 9.55724i 0.256993 + 0.445125i 0.965435 0.260644i \(-0.0839349\pi\)
−0.708442 + 0.705769i \(0.750602\pi\)
\(462\) 0 0
\(463\) 5.93430 + 3.42617i 0.275790 + 0.159228i 0.631516 0.775363i \(-0.282433\pi\)
−0.355726 + 0.934590i \(0.615766\pi\)
\(464\) 0 0
\(465\) 16.1969 17.7579i 0.751115 0.823505i
\(466\) 0 0
\(467\) 20.7739i 0.961302i −0.876912 0.480651i \(-0.840400\pi\)
0.876912 0.480651i \(-0.159600\pi\)
\(468\) 0 0
\(469\) 51.9049i 2.39675i
\(470\) 0 0
\(471\) 25.3157 + 5.55110i 1.16648 + 0.255781i
\(472\) 0 0
\(473\) −16.1969 9.35131i −0.744736 0.429974i
\(474\) 0 0
\(475\) 0.667010 + 1.15530i 0.0306045 + 0.0530086i
\(476\) 0 0
\(477\) 12.1506 8.59176i 0.556337 0.393390i
\(478\) 0 0
\(479\) 4.43175 + 7.67602i 0.202492 + 0.350726i 0.949331 0.314279i \(-0.101763\pi\)
−0.746839 + 0.665005i \(0.768429\pi\)
\(480\) 0 0
\(481\) 9.12372 15.8028i 0.416006 0.720544i
\(482\) 0 0
\(483\) −3.72666 11.7251i −0.169569 0.533509i
\(484\) 0 0
\(485\) 2.93536 0.133288
\(486\) 0 0
\(487\) 18.9097i 0.856879i 0.903571 + 0.428439i \(0.140936\pi\)
−0.903571 + 0.428439i \(0.859064\pi\)
\(488\) 0 0
\(489\) 6.00000 1.90702i 0.271329 0.0862386i
\(490\) 0 0
\(491\) 10.1083 + 5.83604i 0.456182 + 0.263377i 0.710437 0.703760i \(-0.248497\pi\)
−0.254256 + 0.967137i \(0.581830\pi\)
\(492\) 0 0
\(493\) −29.5122 + 17.0389i −1.32916 + 0.767392i
\(494\) 0 0
\(495\) 11.8686 + 16.7847i 0.533454 + 0.754418i
\(496\) 0 0
\(497\) 27.3712 15.8028i 1.22776 0.708850i
\(498\) 0 0
\(499\) −14.0767 + 24.3815i −0.630159 + 1.09147i 0.357360 + 0.933967i \(0.383677\pi\)
−0.987519 + 0.157500i \(0.949656\pi\)
\(500\) 0 0
\(501\) 1.92281 8.76893i 0.0859048 0.391767i
\(502\) 0 0
\(503\) 33.4279 1.49048 0.745238 0.666799i \(-0.232336\pi\)
0.745238 + 0.666799i \(0.232336\pi\)
\(504\) 0 0
\(505\) 12.3031 0.547479
\(506\) 0 0
\(507\) −35.3144 32.2102i −1.56837 1.43050i
\(508\) 0 0
\(509\) −11.5932 + 20.0800i −0.513858 + 0.890028i 0.486013 + 0.873952i \(0.338451\pi\)
−0.999871 + 0.0160766i \(0.994882\pi\)
\(510\) 0 0
\(511\) 1.84024 1.06246i 0.0814074 0.0470006i
\(512\) 0 0
\(513\) −4.65153 + 6.14966i −0.205370 + 0.271514i
\(514\) 0 0
\(515\) −8.29088 + 4.78674i −0.365340 + 0.210929i
\(516\) 0 0
\(517\) −23.9943 13.8531i −1.05527 0.609260i
\(518\) 0 0
\(519\) −2.59151 2.36371i −0.113755 0.103755i
\(520\) 0 0
\(521\) 27.0771i 1.18627i −0.805103 0.593135i \(-0.797890\pi\)
0.805103 0.593135i \(-0.202110\pi\)
\(522\) 0 0
\(523\) −36.9820 −1.61711 −0.808554 0.588421i \(-0.799750\pi\)
−0.808554 + 0.588421i \(0.799750\pi\)
\(524\) 0 0
\(525\) −7.19013 1.57662i −0.313803 0.0688092i
\(526\) 0 0
\(527\) −16.7139 + 28.9494i −0.728071 + 1.26106i
\(528\) 0 0
\(529\) 10.3712 + 17.9634i 0.450921 + 0.781017i
\(530\) 0 0
\(531\) −27.1903 + 2.50533i −1.17996 + 0.108722i
\(532\) 0 0
\(533\) 17.0088 + 29.4600i 0.736731 + 1.27606i
\(534\) 0 0
\(535\) −20.8839 12.0573i −0.902890 0.521284i
\(536\) 0 0
\(537\) 8.69694 + 27.3629i 0.375301 + 1.18079i
\(538\) 0 0
\(539\) 51.9348i 2.23699i
\(540\) 0 0
\(541\) 43.9568i 1.88985i 0.327287 + 0.944925i \(0.393866\pi\)
−0.327287 + 0.944925i \(0.606134\pi\)
\(542\) 0 0
\(543\) −11.8686 37.3418i −0.509331 1.60249i
\(544\) 0 0
\(545\) −7.28036 4.20332i −0.311856 0.180050i
\(546\) 0 0
\(547\) 6.23174 + 10.7937i 0.266450 + 0.461505i 0.967942 0.251172i \(-0.0808160\pi\)
−0.701493 + 0.712677i \(0.747483\pi\)
\(548\) 0 0
\(549\) −7.99810 + 17.3607i −0.341351 + 0.740936i
\(550\) 0 0
\(551\) −5.18303 8.97727i −0.220804 0.382444i
\(552\) 0 0
\(553\) 16.1969 28.0539i 0.688764 1.19297i
\(554\) 0 0
\(555\) 9.81228 + 2.15159i 0.416508 + 0.0913299i
\(556\) 0 0
\(557\) −13.0608 −0.553406 −0.276703 0.960956i \(-0.589242\pi\)
−0.276703 + 0.960956i \(0.589242\pi\)
\(558\) 0 0
\(559\) 35.2168i 1.48951i
\(560\) 0 0
\(561\) −21.1237 19.2669i −0.891844 0.813447i
\(562\) 0 0
\(563\) 9.19959 + 5.31139i 0.387717 + 0.223848i 0.681170 0.732125i \(-0.261471\pi\)
−0.293454 + 0.955973i \(0.594805\pi\)
\(564\) 0 0
\(565\) −12.9586 + 7.48163i −0.545171 + 0.314754i
\(566\) 0 0
\(567\) −7.77454 41.8304i −0.326500 1.75671i
\(568\) 0 0
\(569\) 15.7020 9.06558i 0.658264 0.380049i −0.133351 0.991069i \(-0.542574\pi\)
0.791615 + 0.611020i \(0.209241\pi\)
\(570\) 0 0
\(571\) 8.12412 14.0714i 0.339984 0.588870i −0.644445 0.764650i \(-0.722912\pi\)
0.984429 + 0.175781i \(0.0562450\pi\)
\(572\) 0 0
\(573\) −6.63271 6.04967i −0.277085 0.252728i
\(574\) 0 0
\(575\) −1.35076 −0.0563306
\(576\) 0 0
\(577\) −6.44949 −0.268496 −0.134248 0.990948i \(-0.542862\pi\)
−0.134248 + 0.990948i \(0.542862\pi\)
\(578\) 0 0
\(579\) 0.279183 1.27321i 0.0116024 0.0529127i
\(580\) 0 0
\(581\) 16.5536 28.6717i 0.686760 1.18950i
\(582\) 0 0
\(583\) −14.5360 + 8.39237i −0.602020 + 0.347576i
\(584\) 0 0
\(585\) 16.1969 35.1571i 0.669661 1.45357i
\(586\) 0 0
\(587\) 1.20474 0.695560i 0.0497251 0.0287088i −0.474931 0.880023i \(-0.657527\pi\)
0.524656 + 0.851314i \(0.324194\pi\)
\(588\) 0 0
\(589\) −8.80607 5.08419i −0.362848 0.209490i
\(590\) 0 0
\(591\) 29.7474 9.45483i 1.22364 0.388920i
\(592\) 0 0
\(593\) 2.04989i 0.0841788i −0.999114 0.0420894i \(-0.986599\pi\)
0.999114 0.0420894i \(-0.0134014\pi\)
\(594\) 0 0
\(595\) −46.7025 −1.91461
\(596\) 0 0
\(597\) 1.11484 + 3.50757i 0.0456272 + 0.143555i
\(598\) 0 0
\(599\) −2.59151 + 4.48863i −0.105886 + 0.183401i −0.914100 0.405489i \(-0.867101\pi\)
0.808214 + 0.588889i \(0.200435\pi\)
\(600\) 0 0
\(601\) −16.7247 28.9681i −0.682217 1.18163i −0.974303 0.225242i \(-0.927683\pi\)
0.292086 0.956392i \(-0.405651\pi\)
\(602\) 0 0
\(603\) −3.02218 32.7997i −0.123073 1.33571i
\(604\) 0 0
\(605\) −0.455130 0.788309i −0.0185037 0.0320493i
\(606\) 0 0
\(607\) −32.3389 18.6709i −1.31260 0.757828i −0.330071 0.943956i \(-0.607073\pi\)
−0.982525 + 0.186128i \(0.940406\pi\)
\(608\) 0 0
\(609\) 55.8712 + 12.2512i 2.26401 + 0.496442i
\(610\) 0 0
\(611\) 52.1706i 2.11060i
\(612\) 0 0
\(613\) 1.57662i 0.0636790i 0.999493 + 0.0318395i \(0.0101365\pi\)
−0.999493 + 0.0318395i \(0.989863\pi\)
\(614\) 0 0
\(615\) −12.6199 + 13.8361i −0.508883 + 0.557927i
\(616\) 0 0
\(617\) 10.3763 + 5.99075i 0.417733 + 0.241178i 0.694107 0.719872i \(-0.255799\pi\)
−0.276374 + 0.961050i \(0.589133\pi\)
\(618\) 0 0
\(619\) −16.5443 28.6555i −0.664971 1.15176i −0.979293 0.202447i \(-0.935111\pi\)
0.314323 0.949316i \(-0.398223\pi\)
\(620\) 0 0
\(621\) −3.03765 7.19231i −0.121897 0.288618i
\(622\) 0 0
\(623\) 0.337690 + 0.584897i 0.0135293 + 0.0234334i
\(624\) 0 0
\(625\) 9.84847 17.0580i 0.393939 0.682322i
\(626\) 0 0
\(627\) 5.86076 6.42559i 0.234056 0.256614i
\(628\) 0 0
\(629\) −13.9711 −0.557065
\(630\) 0 0
\(631\) 46.3190i 1.84393i 0.387271 + 0.921966i \(0.373418\pi\)
−0.387271 + 0.921966i \(0.626582\pi\)
\(632\) 0 0
\(633\) 2.47730 11.2977i 0.0984637 0.449041i
\(634\) 0 0
\(635\) 16.5818 + 9.57348i 0.658027 + 0.379912i
\(636\) 0 0
\(637\) 84.6909 48.8963i 3.35558 1.93734i
\(638\) 0 0
\(639\) 16.3763 11.5798i 0.647835 0.458088i
\(640\) 0 0
\(641\) 29.2980 16.9152i 1.15720 0.668110i 0.206568 0.978432i \(-0.433770\pi\)
0.950631 + 0.310323i \(0.100437\pi\)
\(642\) 0 0
\(643\) −7.71567 + 13.3639i −0.304276 + 0.527022i −0.977100 0.212781i \(-0.931748\pi\)
0.672824 + 0.739803i \(0.265081\pi\)
\(644\) 0 0
\(645\) −18.4764 + 5.87250i −0.727509 + 0.231229i
\(646\) 0 0
\(647\) −49.1288 −1.93145 −0.965725 0.259566i \(-0.916420\pi\)
−0.965725 + 0.259566i \(0.916420\pi\)
\(648\) 0 0
\(649\) 30.7980 1.20893
\(650\) 0 0
\(651\) 53.4719 16.9954i 2.09573 0.666101i
\(652\) 0 0
\(653\) 14.0734 24.3758i 0.550735 0.953900i −0.447487 0.894290i \(-0.647681\pi\)
0.998222 0.0596098i \(-0.0189857\pi\)
\(654\) 0 0
\(655\) −21.2975 + 12.2961i −0.832162 + 0.480449i
\(656\) 0 0
\(657\) 1.10102 0.778539i 0.0429549 0.0303737i
\(658\) 0 0
\(659\) −2.33832 + 1.35003i −0.0910881 + 0.0525897i −0.544852 0.838532i \(-0.683414\pi\)
0.453764 + 0.891122i \(0.350081\pi\)
\(660\) 0 0
\(661\) 33.9152 + 19.5810i 1.31915 + 0.761611i 0.983592 0.180409i \(-0.0577420\pi\)
0.335557 + 0.942020i \(0.391075\pi\)
\(662\) 0 0
\(663\) −11.5309 + 52.5865i −0.447824 + 2.04229i
\(664\) 0 0
\(665\) 14.2064i 0.550899i
\(666\) 0 0
\(667\) 10.4961 0.406412
\(668\) 0 0
\(669\) 21.5141 23.5875i 0.831782 0.911946i
\(670\) 0 0
\(671\) 10.7796 18.6709i 0.416143 0.720781i
\(672\) 0 0
\(673\) 2.07321 + 3.59091i 0.0799165 + 0.138419i 0.903214 0.429191i \(-0.141201\pi\)
−0.823297 + 0.567611i \(0.807868\pi\)
\(674\) 0 0
\(675\) −4.63538 0.577648i −0.178416 0.0222337i
\(676\) 0 0
\(677\) −14.0734 24.3758i −0.540885 0.936839i −0.998854 0.0478713i \(-0.984756\pi\)
0.457969 0.888968i \(-0.348577\pi\)
\(678\) 0 0
\(679\) 5.93430 + 3.42617i 0.227738 + 0.131484i
\(680\) 0 0
\(681\) −23.2980 + 25.5433i −0.892780 + 0.978823i
\(682\) 0 0
\(683\) 3.51353i 0.134442i 0.997738 + 0.0672208i \(0.0214132\pi\)
−0.997738 + 0.0672208i \(0.978587\pi\)
\(684\) 0 0
\(685\) 21.6891i 0.828697i
\(686\) 0 0
\(687\) −25.3157 5.55110i −0.965852 0.211788i
\(688\) 0 0
\(689\) 27.3712 + 15.8028i 1.04276 + 0.602037i
\(690\) 0 0
\(691\) −6.47344 11.2123i −0.246261 0.426537i 0.716224 0.697870i \(-0.245869\pi\)
−0.962486 + 0.271333i \(0.912536\pi\)
\(692\) 0 0
\(693\) 4.40304 + 47.7862i 0.167258 + 1.81525i
\(694\) 0 0
\(695\) −7.09916 12.2961i −0.269287 0.466418i
\(696\) 0 0
\(697\) 13.0227 22.5560i 0.493270 0.854369i
\(698\) 0 0
\(699\) −5.11879 16.1051i −0.193611 0.609150i
\(700\) 0 0
\(701\) 33.3118 1.25817 0.629085 0.777336i \(-0.283430\pi\)
0.629085 + 0.777336i \(0.283430\pi\)
\(702\) 0 0
\(703\) 4.24985i 0.160286i
\(704\) 0 0
\(705\) −27.3712 + 8.69958i −1.03086 + 0.327645i
\(706\) 0 0
\(707\) 24.8726 + 14.3602i 0.935432 + 0.540072i
\(708\) 0 0
\(709\) 7.99810 4.61771i 0.300375 0.173422i −0.342236 0.939614i \(-0.611184\pi\)
0.642611 + 0.766192i \(0.277851\pi\)
\(710\) 0 0
\(711\) 8.60171 18.6709i 0.322589 0.700213i
\(712\) 0 0
\(713\) 8.91658 5.14799i 0.333929 0.192794i
\(714\) 0 0
\(715\) −21.8298 + 37.8104i −0.816389 + 1.41403i
\(716\) 0 0
\(717\) −9.36349 + 42.7020i −0.349686 + 1.59474i
\(718\) 0 0
\(719\) 32.7525 1.22146 0.610731 0.791838i \(-0.290876\pi\)
0.610731 + 0.791838i \(0.290876\pi\)
\(720\) 0 0
\(721\) −22.3485 −0.832300
\(722\) 0 0
\(723\) −12.6677 11.5542i −0.471117 0.429704i
\(724\) 0 0
\(725\) 3.13993 5.43853i 0.116614 0.201982i
\(726\) 0 0
\(727\) 25.9910 15.0059i 0.963954 0.556539i 0.0665663 0.997782i \(-0.478796\pi\)
0.897388 + 0.441243i \(0.145462\pi\)
\(728\) 0 0
\(729\) −7.34847 25.9808i −0.272166 0.962250i
\(730\) 0 0
\(731\) 23.3512 13.4818i 0.863676 0.498644i
\(732\) 0 0
\(733\) 4.40304 + 2.54209i 0.162630 + 0.0938944i 0.579106 0.815252i \(-0.303402\pi\)
−0.416476 + 0.909147i \(0.636735\pi\)
\(734\) 0 0
\(735\) 39.7758 + 36.2793i 1.46715 + 1.33818i
\(736\) 0 0
\(737\) 37.1516i 1.36850i
\(738\) 0 0
\(739\) −12.8719 −0.473502 −0.236751 0.971570i \(-0.576083\pi\)
−0.236751 + 0.971570i \(0.576083\pi\)
\(740\) 0 0
\(741\) −15.9962 3.50757i −0.587635 0.128854i
\(742\) 0 0
\(743\) 4.09406 7.09113i 0.150197 0.260148i −0.781103 0.624402i \(-0.785343\pi\)
0.931300 + 0.364254i \(0.118676\pi\)
\(744\) 0 0
\(745\) 7.07321 + 12.2512i 0.259143 + 0.448848i
\(746\) 0 0
\(747\) 8.79114 19.0820i 0.321651 0.698176i
\(748\) 0 0
\(749\) −28.1468 48.7517i −1.02846 1.78135i
\(750\) 0 0
\(751\) −11.4550 6.61356i −0.418000 0.241332i 0.276221 0.961094i \(-0.410918\pi\)
−0.694221 + 0.719762i \(0.744251\pi\)
\(752\) 0 0
\(753\) −9.55051 30.0484i −0.348040 1.09503i
\(754\) 0 0
\(755\) 5.27030i 0.191806i
\(756\) 0 0
\(757\) 48.3973i 1.75903i 0.475870 + 0.879516i \(0.342133\pi\)
−0.475870 + 0.879516i \(0.657867\pi\)
\(758\) 0 0
\(759\) 2.66741 + 8.39237i 0.0968208 + 0.304624i
\(760\) 0 0
\(761\) 20.9722 + 12.1083i 0.760241 + 0.438926i 0.829382 0.558681i \(-0.188693\pi\)
−0.0691410 + 0.997607i \(0.522026\pi\)
\(762\) 0 0
\(763\) −9.81228 16.9954i −0.355228 0.615274i
\(764\) 0 0
\(765\) −29.5122 + 2.71926i −1.06702 + 0.0983152i
\(766\) 0 0
\(767\) −28.9961 50.2228i −1.04699 1.81344i
\(768\) 0 0
\(769\) 13.3990 23.2077i 0.483180 0.836892i −0.516634 0.856206i \(-0.672815\pi\)
0.999813 + 0.0193149i \(0.00614850\pi\)
\(770\) 0 0
\(771\) 9.86660 + 2.16350i 0.355337 + 0.0779166i
\(772\) 0 0
\(773\) −0.910261 −0.0327398 −0.0163699 0.999866i \(-0.505211\pi\)
−0.0163699 + 0.999866i \(0.505211\pi\)
\(774\) 0 0
\(775\) 6.16011i 0.221278i
\(776\) 0 0
\(777\) 17.3258 + 15.8028i 0.621558 + 0.566921i
\(778\) 0 0
\(779\) 6.86127 + 3.96136i 0.245831 + 0.141930i
\(780\) 0 0
\(781\) −19.5913 + 11.3110i −0.701031 + 0.404740i
\(782\) 0 0
\(783\) 36.0194 + 4.48863i 1.28723 + 0.160411i
\(784\) 0 0
\(785\) −26.2423 + 15.1510i −0.936629 + 0.540763i
\(786\) 0 0
\(787\) −6.47344 + 11.2123i −0.230753 + 0.399677i −0.958030 0.286668i \(-0.907452\pi\)
0.727277 + 0.686344i \(0.240786\pi\)
\(788\) 0 0
\(789\) −36.1449 32.9676i −1.28679 1.17368i
\(790\) 0 0
\(791\) −34.9304 −1.24198
\(792\) 0 0
\(793\) −40.5959 −1.44160
\(794\) 0 0
\(795\) −3.72666 + 16.9954i −0.132171 + 0.602764i
\(796\) 0 0
\(797\) −12.5034 + 21.6566i