Properties

Label 300.2.o.a.289.2
Level $300$
Weight $2$
Character 300.289
Analytic conductor $2.396$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 289.2
Character \(\chi\) \(=\) 300.289
Dual form 300.2.o.a.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.951057 - 0.309017i) q^{3} +(0.913250 - 2.04107i) q^{5} +4.62675i q^{7} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.951057 - 0.309017i) q^{3} +(0.913250 - 2.04107i) q^{5} +4.62675i q^{7} +(0.809017 + 0.587785i) q^{9} +(4.00366 - 2.90883i) q^{11} +(2.21170 - 3.04414i) q^{13} +(-1.49928 + 1.65897i) q^{15} +(2.55872 - 0.831378i) q^{17} +(-1.81426 - 5.58371i) q^{19} +(1.42974 - 4.40030i) q^{21} +(3.92540 + 5.40285i) q^{23} +(-3.33195 - 3.72802i) q^{25} +(-0.587785 - 0.809017i) q^{27} +(-0.370972 + 1.14173i) q^{29} +(1.02048 + 3.14072i) q^{31} +(-4.70659 + 1.52926i) q^{33} +(9.44353 + 4.22538i) q^{35} +(1.10342 - 1.51873i) q^{37} +(-3.04414 + 2.21170i) q^{39} +(2.45366 + 1.78269i) q^{41} +10.6626i q^{43} +(1.93855 - 1.11447i) q^{45} +(0.246527 + 0.0801015i) q^{47} -14.4068 q^{49} -2.69040 q^{51} +(-9.31711 - 3.02731i) q^{53} +(-2.28079 - 10.8282i) q^{55} +5.87106i q^{57} +(-7.78643 - 5.65717i) q^{59} +(-5.07552 + 3.68758i) q^{61} +(-2.71953 + 3.74312i) q^{63} +(-4.19348 - 7.29430i) q^{65} +(-2.43521 + 0.791247i) q^{67} +(-2.06370 - 6.35143i) q^{69} +(2.68143 - 8.25259i) q^{71} +(2.86534 + 3.94381i) q^{73} +(2.01685 + 4.57518i) q^{75} +(13.4584 + 18.5239i) q^{77} +(-3.85443 + 11.8627i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-8.45513 + 2.74724i) q^{83} +(0.639846 - 5.98178i) q^{85} +(0.705631 - 0.971218i) q^{87} +(11.7934 - 8.56841i) q^{89} +(14.0845 + 10.2330i) q^{91} -3.30235i q^{93} +(-13.0536 - 1.39629i) q^{95} +(-3.79176 - 1.23202i) q^{97} +4.94880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\)

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
\(3\) −0.951057 0.309017i −0.549093 0.178411i
\(4\) 0 0
\(5\) 0.913250 2.04107i 0.408418 0.912795i
\(6\) 0 0
\(7\) 4.62675i 1.74875i 0.485254 + 0.874373i \(0.338727\pi\)
−0.485254 + 0.874373i \(0.661273\pi\)
\(8\) 0 0
\(9\) 0.809017 + 0.587785i 0.269672 + 0.195928i
\(10\) 0 0
\(11\) 4.00366 2.90883i 1.20715 0.877045i 0.212180 0.977231i \(-0.431944\pi\)
0.994969 + 0.100185i \(0.0319435\pi\)
\(12\) 0 0
\(13\) 2.21170 3.04414i 0.613415 0.844294i −0.383438 0.923567i \(-0.625260\pi\)
0.996853 + 0.0792730i \(0.0252599\pi\)
\(14\) 0 0
\(15\) −1.49928 + 1.65897i −0.387112 + 0.428343i
\(16\) 0 0
\(17\) 2.55872 0.831378i 0.620580 0.201639i 0.0181824 0.999835i \(-0.494212\pi\)
0.602398 + 0.798196i \(0.294212\pi\)
\(18\) 0 0
\(19\) −1.81426 5.58371i −0.416219 1.28099i −0.911156 0.412062i \(-0.864809\pi\)
0.494937 0.868929i \(-0.335191\pi\)
\(20\) 0 0
\(21\) 1.42974 4.40030i 0.311996 0.960224i
\(22\) 0 0
\(23\) 3.92540 + 5.40285i 0.818502 + 1.12657i 0.989955 + 0.141379i \(0.0451537\pi\)
−0.171453 + 0.985192i \(0.554846\pi\)
\(24\) 0 0
\(25\) −3.33195 3.72802i −0.666390 0.745603i
\(26\) 0 0
\(27\) −0.587785 0.809017i −0.113119 0.155695i
\(28\) 0 0
\(29\) −0.370972 + 1.14173i −0.0688878 + 0.212015i −0.979574 0.201084i \(-0.935554\pi\)
0.910686 + 0.413099i \(0.135554\pi\)
\(30\) 0 0
\(31\) 1.02048 + 3.14072i 0.183284 + 0.564090i 0.999915 0.0130708i \(-0.00416068\pi\)
−0.816631 + 0.577161i \(0.804161\pi\)
\(32\) 0 0
\(33\) −4.70659 + 1.52926i −0.819311 + 0.266210i
\(34\) 0 0
\(35\) 9.44353 + 4.22538i 1.59625 + 0.714219i
\(36\) 0 0
\(37\) 1.10342 1.51873i 0.181401 0.249677i −0.708627 0.705584i \(-0.750685\pi\)
0.890028 + 0.455907i \(0.150685\pi\)
\(38\) 0 0
\(39\) −3.04414 + 2.21170i −0.487453 + 0.354156i
\(40\) 0 0
\(41\) 2.45366 + 1.78269i 0.383198 + 0.278410i 0.762663 0.646797i \(-0.223892\pi\)
−0.379464 + 0.925206i \(0.623892\pi\)
\(42\) 0 0
\(43\) 10.6626i 1.62603i 0.582244 + 0.813014i \(0.302175\pi\)
−0.582244 + 0.813014i \(0.697825\pi\)
\(44\) 0 0
\(45\) 1.93855 1.11447i 0.288981 0.166135i
\(46\) 0 0
\(47\) 0.246527 + 0.0801015i 0.0359597 + 0.0116840i 0.326942 0.945045i \(-0.393982\pi\)
−0.290982 + 0.956729i \(0.593982\pi\)
\(48\) 0 0
\(49\) −14.4068 −2.05811
\(50\) 0 0
\(51\) −2.69040 −0.376731
\(52\) 0 0
\(53\) −9.31711 3.02731i −1.27980 0.415833i −0.411292 0.911504i \(-0.634922\pi\)
−0.868511 + 0.495670i \(0.834922\pi\)
\(54\) 0 0
\(55\) −2.28079 10.8282i −0.307542 1.46008i
\(56\) 0 0
\(57\) 5.87106i 0.777641i
\(58\) 0 0
\(59\) −7.78643 5.65717i −1.01371 0.736501i −0.0487233 0.998812i \(-0.515515\pi\)
−0.964983 + 0.262311i \(0.915515\pi\)
\(60\) 0 0
\(61\) −5.07552 + 3.68758i −0.649854 + 0.472147i −0.863222 0.504825i \(-0.831557\pi\)
0.213367 + 0.976972i \(0.431557\pi\)
\(62\) 0 0
\(63\) −2.71953 + 3.74312i −0.342629 + 0.471589i
\(64\) 0 0
\(65\) −4.19348 7.29430i −0.520138 0.904747i
\(66\) 0 0
\(67\) −2.43521 + 0.791247i −0.297508 + 0.0966662i −0.453968 0.891018i \(-0.649992\pi\)
0.156460 + 0.987684i \(0.449992\pi\)
\(68\) 0 0
\(69\) −2.06370 6.35143i −0.248441 0.764622i
\(70\) 0 0
\(71\) 2.68143 8.25259i 0.318227 0.979403i −0.656178 0.754606i \(-0.727828\pi\)
0.974406 0.224797i \(-0.0721718\pi\)
\(72\) 0 0
\(73\) 2.86534 + 3.94381i 0.335363 + 0.461588i 0.943080 0.332566i \(-0.107914\pi\)
−0.607717 + 0.794154i \(0.707914\pi\)
\(74\) 0 0
\(75\) 2.01685 + 4.57518i 0.232886 + 0.528297i
\(76\) 0 0
\(77\) 13.4584 + 18.5239i 1.53373 + 2.11100i
\(78\) 0 0
\(79\) −3.85443 + 11.8627i −0.433657 + 1.33466i 0.460800 + 0.887504i \(0.347563\pi\)
−0.894457 + 0.447155i \(0.852437\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 0 0
\(83\) −8.45513 + 2.74724i −0.928071 + 0.301549i −0.733774 0.679394i \(-0.762243\pi\)
−0.194298 + 0.980943i \(0.562243\pi\)
\(84\) 0 0
\(85\) 0.639846 5.98178i 0.0694011 0.648816i
\(86\) 0 0
\(87\) 0.705631 0.971218i 0.0756516 0.104125i
\(88\) 0 0
\(89\) 11.7934 8.56841i 1.25010 0.908249i 0.251870 0.967761i \(-0.418954\pi\)
0.998228 + 0.0595118i \(0.0189544\pi\)
\(90\) 0 0
\(91\) 14.0845 + 10.2330i 1.47646 + 1.07271i
\(92\) 0 0
\(93\) 3.30235i 0.342437i
\(94\) 0 0
\(95\) −13.0536 1.39629i −1.33927 0.143256i
\(96\) 0 0
\(97\) −3.79176 1.23202i −0.384995 0.125092i 0.110123 0.993918i \(-0.464875\pi\)
−0.495119 + 0.868825i \(0.664875\pi\)
\(98\) 0 0
\(99\) 4.94880 0.497373
\(100\) 0 0
\(101\) 9.36896 0.932246 0.466123 0.884720i \(-0.345650\pi\)
0.466123 + 0.884720i \(0.345650\pi\)
\(102\) 0 0
\(103\) −9.91391 3.22123i −0.976847 0.317397i −0.223270 0.974757i \(-0.571673\pi\)
−0.753577 + 0.657360i \(0.771673\pi\)
\(104\) 0 0
\(105\) −7.67561 6.93678i −0.749063 0.676961i
\(106\) 0 0
\(107\) 0.220683i 0.0213342i −0.999943 0.0106671i \(-0.996604\pi\)
0.999943 0.0106671i \(-0.00339551\pi\)
\(108\) 0 0
\(109\) 5.40941 + 3.93017i 0.518127 + 0.376442i 0.815898 0.578196i \(-0.196243\pi\)
−0.297771 + 0.954637i \(0.596243\pi\)
\(110\) 0 0
\(111\) −1.51873 + 1.10342i −0.144151 + 0.104732i
\(112\) 0 0
\(113\) −5.64782 + 7.77355i −0.531302 + 0.731274i −0.987328 0.158692i \(-0.949272\pi\)
0.456026 + 0.889966i \(0.349272\pi\)
\(114\) 0 0
\(115\) 14.6125 3.07787i 1.36262 0.287013i
\(116\) 0 0
\(117\) 3.57861 1.16276i 0.330842 0.107497i
\(118\) 0 0
\(119\) 3.84658 + 11.8385i 0.352615 + 1.08524i
\(120\) 0 0
\(121\) 4.16882 12.8303i 0.378984 1.16639i
\(122\) 0 0
\(123\) −1.78269 2.45366i −0.160740 0.221239i
\(124\) 0 0
\(125\) −10.6521 + 3.39614i −0.952749 + 0.303760i
\(126\) 0 0
\(127\) −9.40003 12.9380i −0.834118 1.14806i −0.987143 0.159842i \(-0.948902\pi\)
0.153025 0.988222i \(-0.451098\pi\)
\(128\) 0 0
\(129\) 3.29492 10.1407i 0.290101 0.892840i
\(130\) 0 0
\(131\) −3.80795 11.7197i −0.332702 1.02395i −0.967843 0.251556i \(-0.919058\pi\)
0.635140 0.772397i \(-0.280942\pi\)
\(132\) 0 0
\(133\) 25.8344 8.39411i 2.24013 0.727862i
\(134\) 0 0
\(135\) −2.18806 + 0.460878i −0.188318 + 0.0396660i
\(136\) 0 0
\(137\) −3.34717 + 4.60698i −0.285968 + 0.393601i −0.927699 0.373329i \(-0.878216\pi\)
0.641731 + 0.766930i \(0.278216\pi\)
\(138\) 0 0
\(139\) −14.5598 + 10.5783i −1.23495 + 0.897242i −0.997251 0.0740969i \(-0.976393\pi\)
−0.237697 + 0.971339i \(0.576393\pi\)
\(140\) 0 0
\(141\) −0.209709 0.152362i −0.0176606 0.0128312i
\(142\) 0 0
\(143\) 18.6212i 1.55718i
\(144\) 0 0
\(145\) 1.99157 + 1.79987i 0.165391 + 0.149471i
\(146\) 0 0
\(147\) 13.7017 + 4.45195i 1.13010 + 0.367190i
\(148\) 0 0
\(149\) 1.09001 0.0892972 0.0446486 0.999003i \(-0.485783\pi\)
0.0446486 + 0.999003i \(0.485783\pi\)
\(150\) 0 0
\(151\) 11.3789 0.926004 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(152\) 0 0
\(153\) 2.55872 + 0.831378i 0.206860 + 0.0672129i
\(154\) 0 0
\(155\) 7.34239 + 0.785384i 0.589755 + 0.0630836i
\(156\) 0 0
\(157\) 3.98415i 0.317970i −0.987281 0.158985i \(-0.949178\pi\)
0.987281 0.158985i \(-0.0508221\pi\)
\(158\) 0 0
\(159\) 7.92560 + 5.75829i 0.628541 + 0.456662i
\(160\) 0 0
\(161\) −24.9976 + 18.1618i −1.97009 + 1.43135i
\(162\) 0 0
\(163\) −12.8322 + 17.6620i −1.00509 + 1.38339i −0.0829441 + 0.996554i \(0.526432\pi\)
−0.922148 + 0.386837i \(0.873568\pi\)
\(164\) 0 0
\(165\) −1.17695 + 11.0031i −0.0916257 + 0.856589i
\(166\) 0 0
\(167\) 14.7118 4.78015i 1.13843 0.369899i 0.321658 0.946856i \(-0.395760\pi\)
0.816775 + 0.576957i \(0.195760\pi\)
\(168\) 0 0
\(169\) −0.357976 1.10174i −0.0275366 0.0847490i
\(170\) 0 0
\(171\) 1.81426 5.58371i 0.138740 0.426997i
\(172\) 0 0
\(173\) 10.0925 + 13.8911i 0.767317 + 1.05612i 0.996570 + 0.0827547i \(0.0263718\pi\)
−0.229253 + 0.973367i \(0.573628\pi\)
\(174\) 0 0
\(175\) 17.2486 15.4161i 1.30387 1.16535i
\(176\) 0 0
\(177\) 5.65717 + 7.78643i 0.425219 + 0.585264i
\(178\) 0 0
\(179\) 4.46392 13.7385i 0.333649 1.02687i −0.633734 0.773551i \(-0.718479\pi\)
0.967384 0.253316i \(-0.0815213\pi\)
\(180\) 0 0
\(181\) 3.83071 + 11.7897i 0.284734 + 0.876322i 0.986478 + 0.163893i \(0.0524051\pi\)
−0.701744 + 0.712429i \(0.747595\pi\)
\(182\) 0 0
\(183\) 5.96664 1.93868i 0.441066 0.143311i
\(184\) 0 0
\(185\) −2.09213 3.63913i −0.153817 0.267554i
\(186\) 0 0
\(187\) 7.82590 10.7714i 0.572287 0.787685i
\(188\) 0 0
\(189\) 3.74312 2.71953i 0.272272 0.197817i
\(190\) 0 0
\(191\) 1.33930 + 0.973056i 0.0969081 + 0.0704078i 0.635184 0.772361i \(-0.280924\pi\)
−0.538276 + 0.842769i \(0.680924\pi\)
\(192\) 0 0
\(193\) 16.3253i 1.17512i −0.809181 0.587560i \(-0.800089\pi\)
0.809181 0.587560i \(-0.199911\pi\)
\(194\) 0 0
\(195\) 1.73418 + 8.23315i 0.124187 + 0.589588i
\(196\) 0 0
\(197\) −12.9652 4.21264i −0.923730 0.300138i −0.191734 0.981447i \(-0.561411\pi\)
−0.731996 + 0.681309i \(0.761411\pi\)
\(198\) 0 0
\(199\) 6.07817 0.430870 0.215435 0.976518i \(-0.430883\pi\)
0.215435 + 0.976518i \(0.430883\pi\)
\(200\) 0 0
\(201\) 2.56053 0.180606
\(202\) 0 0
\(203\) −5.28252 1.71639i −0.370760 0.120467i
\(204\) 0 0
\(205\) 5.87941 3.38006i 0.410636 0.236074i
\(206\) 0 0
\(207\) 6.67829i 0.464173i
\(208\) 0 0
\(209\) −23.5057 17.0779i −1.62593 1.18130i
\(210\) 0 0
\(211\) −13.8200 + 10.0408i −0.951409 + 0.691239i −0.951140 0.308761i \(-0.900086\pi\)
−0.000268984 1.00000i \(0.500086\pi\)
\(212\) 0 0
\(213\) −5.10038 + 7.02007i −0.349472 + 0.481008i
\(214\) 0 0
\(215\) 21.7631 + 9.73760i 1.48423 + 0.664099i
\(216\) 0 0
\(217\) −14.5313 + 4.72151i −0.986450 + 0.320517i
\(218\) 0 0
\(219\) −1.50640 4.63622i −0.101793 0.313287i
\(220\) 0 0
\(221\) 3.12828 9.62787i 0.210431 0.647640i
\(222\) 0 0
\(223\) 0.460700 + 0.634100i 0.0308508 + 0.0424624i 0.824164 0.566352i \(-0.191646\pi\)
−0.793313 + 0.608814i \(0.791646\pi\)
\(224\) 0 0
\(225\) −0.504331 4.97450i −0.0336221 0.331633i
\(226\) 0 0
\(227\) −14.0771 19.3755i −0.934331 1.28600i −0.958146 0.286280i \(-0.907581\pi\)
0.0238153 0.999716i \(-0.492419\pi\)
\(228\) 0 0
\(229\) 1.71005 5.26299i 0.113003 0.347788i −0.878522 0.477702i \(-0.841470\pi\)
0.991525 + 0.129914i \(0.0414700\pi\)
\(230\) 0 0
\(231\) −7.07551 21.7762i −0.465535 1.43277i
\(232\) 0 0
\(233\) 0.863314 0.280508i 0.0565576 0.0183767i −0.280602 0.959824i \(-0.590534\pi\)
0.337159 + 0.941448i \(0.390534\pi\)
\(234\) 0 0
\(235\) 0.388634 0.430027i 0.0253517 0.0280519i
\(236\) 0 0
\(237\) 7.33156 10.0910i 0.476236 0.655482i
\(238\) 0 0
\(239\) −9.09227 + 6.60592i −0.588130 + 0.427302i −0.841646 0.540030i \(-0.818413\pi\)
0.253516 + 0.967331i \(0.418413\pi\)
\(240\) 0 0
\(241\) 16.3840 + 11.9037i 1.05539 + 0.766783i 0.973229 0.229837i \(-0.0738193\pi\)
0.0821564 + 0.996619i \(0.473819\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −13.1570 + 29.4053i −0.840570 + 1.87864i
\(246\) 0 0
\(247\) −21.0102 6.82663i −1.33685 0.434368i
\(248\) 0 0
\(249\) 8.89025 0.563397
\(250\) 0 0
\(251\) −30.6919 −1.93725 −0.968627 0.248520i \(-0.920056\pi\)
−0.968627 + 0.248520i \(0.920056\pi\)
\(252\) 0 0
\(253\) 31.4319 + 10.2129i 1.97611 + 0.642077i
\(254\) 0 0
\(255\) −2.45700 + 5.49129i −0.153863 + 0.343878i
\(256\) 0 0
\(257\) 4.77543i 0.297883i 0.988846 + 0.148941i \(0.0475866\pi\)
−0.988846 + 0.148941i \(0.952413\pi\)
\(258\) 0 0
\(259\) 7.02676 + 5.10524i 0.436622 + 0.317224i
\(260\) 0 0
\(261\) −0.971218 + 0.705631i −0.0601169 + 0.0436775i
\(262\) 0 0
\(263\) −0.711022 + 0.978638i −0.0438435 + 0.0603454i −0.830376 0.557204i \(-0.811874\pi\)
0.786532 + 0.617549i \(0.211874\pi\)
\(264\) 0 0
\(265\) −14.6878 + 16.2522i −0.902265 + 0.998364i
\(266\) 0 0
\(267\) −13.8640 + 4.50468i −0.848461 + 0.275682i
\(268\) 0 0
\(269\) 7.88763 + 24.2756i 0.480917 + 1.48011i 0.837808 + 0.545965i \(0.183837\pi\)
−0.356891 + 0.934146i \(0.616163\pi\)
\(270\) 0 0
\(271\) −1.81499 + 5.58596i −0.110253 + 0.339323i −0.990927 0.134399i \(-0.957090\pi\)
0.880675 + 0.473722i \(0.157090\pi\)
\(272\) 0 0
\(273\) −10.2330 14.0845i −0.619328 0.852432i
\(274\) 0 0
\(275\) −24.1842 5.23364i −1.45836 0.315600i
\(276\) 0 0
\(277\) 2.88332 + 3.96855i 0.173242 + 0.238447i 0.886805 0.462144i \(-0.152920\pi\)
−0.713563 + 0.700591i \(0.752920\pi\)
\(278\) 0 0
\(279\) −1.02048 + 3.14072i −0.0610946 + 0.188030i
\(280\) 0 0
\(281\) −0.400257 1.23186i −0.0238773 0.0734868i 0.938408 0.345530i \(-0.112301\pi\)
−0.962285 + 0.272043i \(0.912301\pi\)
\(282\) 0 0
\(283\) 28.7501 9.34149i 1.70902 0.555294i 0.718849 0.695166i \(-0.244669\pi\)
0.990169 + 0.139873i \(0.0446693\pi\)
\(284\) 0 0
\(285\) 11.9833 + 5.36174i 0.709827 + 0.317602i
\(286\) 0 0
\(287\) −8.24807 + 11.3525i −0.486868 + 0.670116i
\(288\) 0 0
\(289\) −7.89744 + 5.73783i −0.464555 + 0.337519i
\(290\) 0 0
\(291\) 3.22546 + 2.34344i 0.189080 + 0.137375i
\(292\) 0 0
\(293\) 8.06831i 0.471356i −0.971831 0.235678i \(-0.924269\pi\)
0.971831 0.235678i \(-0.0757310\pi\)
\(294\) 0 0
\(295\) −18.6576 + 10.7263i −1.08629 + 0.624506i
\(296\) 0 0
\(297\) −4.70659 1.52926i −0.273104 0.0887368i
\(298\) 0 0
\(299\) 25.1289 1.45324
\(300\) 0 0
\(301\) −49.3331 −2.84351
\(302\) 0 0
\(303\) −8.91041 2.89517i −0.511890 0.166323i
\(304\) 0 0
\(305\) 2.89140 + 13.7272i 0.165561 + 0.786017i
\(306\) 0 0
\(307\) 14.7750i 0.843255i −0.906769 0.421628i \(-0.861459\pi\)
0.906769 0.421628i \(-0.138541\pi\)
\(308\) 0 0
\(309\) 8.43328 + 6.12713i 0.479752 + 0.348560i
\(310\) 0 0
\(311\) 7.40552 5.38043i 0.419929 0.305096i −0.357680 0.933844i \(-0.616432\pi\)
0.777609 + 0.628748i \(0.216432\pi\)
\(312\) 0 0
\(313\) 7.79128 10.7238i 0.440389 0.606144i −0.529909 0.848054i \(-0.677774\pi\)
0.970299 + 0.241910i \(0.0777740\pi\)
\(314\) 0 0
\(315\) 5.15636 + 8.96917i 0.290528 + 0.505355i
\(316\) 0 0
\(317\) 0.751858 0.244293i 0.0422286 0.0137209i −0.287827 0.957683i \(-0.592933\pi\)
0.330055 + 0.943962i \(0.392933\pi\)
\(318\) 0 0
\(319\) 1.83587 + 5.65021i 0.102789 + 0.316351i
\(320\) 0 0
\(321\) −0.0681947 + 0.209882i −0.00380626 + 0.0117145i
\(322\) 0 0
\(323\) −9.28434 12.7788i −0.516595 0.711032i
\(324\) 0 0
\(325\) −18.7179 + 1.89768i −1.03828 + 0.105264i
\(326\) 0 0
\(327\) −3.93017 5.40941i −0.217339 0.299141i
\(328\) 0 0
\(329\) −0.370610 + 1.14062i −0.0204324 + 0.0628844i
\(330\) 0 0
\(331\) −1.04253 3.20858i −0.0573026 0.176359i 0.918308 0.395866i \(-0.129555\pi\)
−0.975611 + 0.219506i \(0.929555\pi\)
\(332\) 0 0
\(333\) 1.78537 0.580102i 0.0978376 0.0317894i
\(334\) 0 0
\(335\) −0.608960 + 5.69304i −0.0332711 + 0.311044i
\(336\) 0 0
\(337\) −10.6189 + 14.6157i −0.578449 + 0.796166i −0.993524 0.113621i \(-0.963755\pi\)
0.415076 + 0.909787i \(0.363755\pi\)
\(338\) 0 0
\(339\) 7.77355 5.64782i 0.422201 0.306747i
\(340\) 0 0
\(341\) 13.2215 + 9.60597i 0.715983 + 0.520192i
\(342\) 0 0
\(343\) 34.2694i 1.85037i
\(344\) 0 0
\(345\) −14.8484 1.58827i −0.799411 0.0855096i
\(346\) 0 0
\(347\) −2.90284 0.943191i −0.155833 0.0506332i 0.230062 0.973176i \(-0.426107\pi\)
−0.385895 + 0.922543i \(0.626107\pi\)
\(348\) 0 0
\(349\) 0.628744 0.0336559 0.0168280 0.999858i \(-0.494643\pi\)
0.0168280 + 0.999858i \(0.494643\pi\)
\(350\) 0 0
\(351\) −3.76277 −0.200842
\(352\) 0 0
\(353\) −17.9651 5.83721i −0.956184 0.310683i −0.210958 0.977495i \(-0.567658\pi\)
−0.745226 + 0.666812i \(0.767658\pi\)
\(354\) 0 0
\(355\) −14.3953 13.0097i −0.764024 0.690482i
\(356\) 0 0
\(357\) 12.4478i 0.658807i
\(358\) 0 0
\(359\) 23.4087 + 17.0074i 1.23546 + 0.897617i 0.997287 0.0736053i \(-0.0234505\pi\)
0.238176 + 0.971222i \(0.423450\pi\)
\(360\) 0 0
\(361\) −12.5149 + 9.09264i −0.658681 + 0.478560i
\(362\) 0 0
\(363\) −7.92957 + 10.9141i −0.416195 + 0.572843i
\(364\) 0 0
\(365\) 10.6664 2.24669i 0.558303 0.117597i
\(366\) 0 0
\(367\) 5.11949 1.66342i 0.267235 0.0868299i −0.172334 0.985038i \(-0.555131\pi\)
0.439570 + 0.898209i \(0.355131\pi\)
\(368\) 0 0
\(369\) 0.937217 + 2.88446i 0.0487895 + 0.150159i
\(370\) 0 0
\(371\) 14.0066 43.1079i 0.727187 2.23805i
\(372\) 0 0
\(373\) 6.46415 + 8.89714i 0.334701 + 0.460677i 0.942884 0.333120i \(-0.108101\pi\)
−0.608183 + 0.793797i \(0.708101\pi\)
\(374\) 0 0
\(375\) 11.1802 + 0.0617436i 0.577341 + 0.00318843i
\(376\) 0 0
\(377\) 2.65513 + 3.65447i 0.136746 + 0.188215i
\(378\) 0 0
\(379\) −2.18405 + 6.72183i −0.112187 + 0.345277i −0.991350 0.131245i \(-0.958103\pi\)
0.879163 + 0.476522i \(0.158103\pi\)
\(380\) 0 0
\(381\) 4.94189 + 15.2096i 0.253181 + 0.779210i
\(382\) 0 0
\(383\) −7.70484 + 2.50346i −0.393699 + 0.127921i −0.499175 0.866501i \(-0.666363\pi\)
0.105476 + 0.994422i \(0.466363\pi\)
\(384\) 0 0
\(385\) 50.0996 10.5526i 2.55331 0.537812i
\(386\) 0 0
\(387\) −6.26731 + 8.62621i −0.318585 + 0.438495i
\(388\) 0 0
\(389\) 26.7325 19.4223i 1.35539 0.984750i 0.356669 0.934231i \(-0.383912\pi\)
0.998723 0.0505192i \(-0.0160876\pi\)
\(390\) 0 0
\(391\) 14.5358 + 10.5609i 0.735107 + 0.534086i
\(392\) 0 0
\(393\) 12.3228i 0.621603i
\(394\) 0 0
\(395\) 20.6926 + 18.7008i 1.04116 + 0.940938i
\(396\) 0 0
\(397\) 11.7615 + 3.82155i 0.590294 + 0.191798i 0.588907 0.808201i \(-0.299559\pi\)
0.00138688 + 0.999999i \(0.499559\pi\)
\(398\) 0 0
\(399\) −27.1639 −1.35990
\(400\) 0 0
\(401\) −14.7983 −0.738993 −0.369496 0.929232i \(-0.620470\pi\)
−0.369496 + 0.929232i \(0.620470\pi\)
\(402\) 0 0
\(403\) 11.8178 + 3.83984i 0.588687 + 0.191276i
\(404\) 0 0
\(405\) 2.22338 + 0.237826i 0.110481 + 0.0118177i
\(406\) 0 0
\(407\) 9.29012i 0.460494i
\(408\) 0 0
\(409\) −19.1618 13.9219i −0.947491 0.688392i 0.00272132 0.999996i \(-0.499134\pi\)
−0.950212 + 0.311604i \(0.899134\pi\)
\(410\) 0 0
\(411\) 4.60698 3.34717i 0.227246 0.165104i
\(412\) 0 0
\(413\) 26.1743 36.0258i 1.28795 1.77272i
\(414\) 0 0
\(415\) −2.11433 + 19.7664i −0.103789 + 0.970297i
\(416\) 0 0
\(417\) 17.1161 5.56136i 0.838179 0.272341i
\(418\) 0 0
\(419\) −0.477059 1.46824i −0.0233058 0.0717280i 0.938727 0.344661i \(-0.112006\pi\)
−0.962033 + 0.272933i \(0.912006\pi\)
\(420\) 0 0
\(421\) −5.43760 + 16.7352i −0.265013 + 0.815625i 0.726678 + 0.686978i \(0.241063\pi\)
−0.991691 + 0.128647i \(0.958937\pi\)
\(422\) 0 0
\(423\) 0.152362 + 0.209709i 0.00740810 + 0.0101964i
\(424\) 0 0
\(425\) −11.6249 6.76883i −0.563891 0.328337i
\(426\) 0 0
\(427\) −17.0615 23.4832i −0.825665 1.13643i
\(428\) 0 0
\(429\) −5.75426 + 17.7098i −0.277818 + 0.855037i
\(430\) 0 0
\(431\) 4.83527 + 14.8814i 0.232907 + 0.716814i 0.997392 + 0.0721724i \(0.0229932\pi\)
−0.764485 + 0.644641i \(0.777007\pi\)
\(432\) 0 0
\(433\) 0.217772 0.0707586i 0.0104655 0.00340044i −0.303780 0.952742i \(-0.598249\pi\)
0.314245 + 0.949342i \(0.398249\pi\)
\(434\) 0 0
\(435\) −1.33791 2.32721i −0.0641478 0.111581i
\(436\) 0 0
\(437\) 23.0462 31.7204i 1.10245 1.51739i
\(438\) 0 0
\(439\) 15.7111 11.4147i 0.749848 0.544796i −0.145932 0.989295i \(-0.546618\pi\)
0.895780 + 0.444498i \(0.146618\pi\)
\(440\) 0 0
\(441\) −11.6553 8.46810i −0.555016 0.403243i
\(442\) 0 0
\(443\) 12.7980i 0.608051i 0.952664 + 0.304026i \(0.0983309\pi\)
−0.952664 + 0.304026i \(0.901669\pi\)
\(444\) 0 0
\(445\) −6.71842 31.8963i −0.318483 1.51203i
\(446\) 0 0
\(447\) −1.03666 0.336832i −0.0490325 0.0159316i
\(448\) 0 0
\(449\) 21.1499 0.998124 0.499062 0.866566i \(-0.333678\pi\)
0.499062 + 0.866566i \(0.333678\pi\)
\(450\) 0 0
\(451\) 15.0092 0.706755
\(452\) 0 0
\(453\) −10.8220 3.51628i −0.508462 0.165209i
\(454\) 0 0
\(455\) 33.7489 19.4022i 1.58217 0.909589i
\(456\) 0 0
\(457\) 8.97118i 0.419654i −0.977739 0.209827i \(-0.932710\pi\)
0.977739 0.209827i \(-0.0672901\pi\)
\(458\) 0 0
\(459\) −2.17658 1.58137i −0.101594 0.0738123i
\(460\) 0 0
\(461\) −22.2764 + 16.1847i −1.03751 + 0.753797i −0.969799 0.243907i \(-0.921571\pi\)
−0.0677146 + 0.997705i \(0.521571\pi\)
\(462\) 0 0
\(463\) −17.2815 + 23.7859i −0.803140 + 1.10543i 0.189206 + 0.981937i \(0.439409\pi\)
−0.992346 + 0.123489i \(0.960591\pi\)
\(464\) 0 0
\(465\) −6.74033 3.01587i −0.312575 0.139857i
\(466\) 0 0
\(467\) −12.6119 + 4.09785i −0.583609 + 0.189626i −0.585917 0.810371i \(-0.699265\pi\)
0.00230768 + 0.999997i \(0.499265\pi\)
\(468\) 0 0
\(469\) −3.66090 11.2671i −0.169045 0.520266i
\(470\) 0 0
\(471\) −1.23117 + 3.78915i −0.0567293 + 0.174595i
\(472\) 0 0
\(473\) 31.0156 + 42.6893i 1.42610 + 1.96286i
\(474\) 0 0
\(475\) −14.7711 + 25.3682i −0.677747 + 1.16397i
\(476\) 0 0
\(477\) −5.75829 7.92560i −0.263654 0.362888i
\(478\) 0 0
\(479\) 5.58057 17.1752i 0.254983 0.784757i −0.738850 0.673870i \(-0.764631\pi\)
0.993833 0.110887i \(-0.0353692\pi\)
\(480\) 0 0
\(481\) −2.18279 6.71793i −0.0995266 0.306311i
\(482\) 0 0
\(483\) 29.3865 9.54824i 1.33713 0.434460i
\(484\) 0 0
\(485\) −5.97746 + 6.61412i −0.271423 + 0.300332i
\(486\) 0 0
\(487\) 8.26258 11.3725i 0.374413 0.515336i −0.579681 0.814844i \(-0.696823\pi\)
0.954094 + 0.299508i \(0.0968226\pi\)
\(488\) 0 0
\(489\) 17.6620 12.8322i 0.798701 0.580290i
\(490\) 0 0
\(491\) 22.0310 + 16.0065i 0.994247 + 0.722363i 0.960847 0.277079i \(-0.0893665\pi\)
0.0334000 + 0.999442i \(0.489366\pi\)
\(492\) 0 0
\(493\) 3.22980i 0.145463i
\(494\) 0 0
\(495\) 4.51949 10.1009i 0.203136 0.454000i
\(496\) 0 0
\(497\) 38.1827 + 12.4063i 1.71273 + 0.556499i
\(498\) 0 0
\(499\) 8.17654 0.366032 0.183016 0.983110i \(-0.441414\pi\)
0.183016 + 0.983110i \(0.441414\pi\)
\(500\) 0 0
\(501\) −15.4689 −0.691099
\(502\) 0 0
\(503\) −9.45805 3.07311i −0.421714 0.137023i 0.0904697 0.995899i \(-0.471163\pi\)
−0.512183 + 0.858876i \(0.671163\pi\)
\(504\) 0 0
\(505\) 8.55620 19.1227i 0.380746 0.850950i
\(506\) 0 0
\(507\) 1.15844i 0.0514479i
\(508\) 0 0
\(509\) 13.9758 + 10.1540i 0.619464 + 0.450067i 0.852734 0.522345i \(-0.174943\pi\)
−0.233270 + 0.972412i \(0.574943\pi\)
\(510\) 0 0
\(511\) −18.2470 + 13.2572i −0.807200 + 0.586465i
\(512\) 0 0
\(513\) −3.45092 + 4.74979i −0.152362 + 0.209708i
\(514\) 0 0
\(515\) −15.6286 + 17.2932i −0.688680 + 0.762031i
\(516\) 0 0
\(517\) 1.22001 0.396406i 0.0536561 0.0174339i
\(518\) 0 0
\(519\) −5.30593 16.3300i −0.232905 0.716807i
\(520\) 0 0
\(521\) −3.43786 + 10.5807i −0.150615 + 0.463547i −0.997690 0.0679269i \(-0.978362\pi\)
0.847075 + 0.531474i \(0.178362\pi\)
\(522\) 0 0
\(523\) −2.20585 3.03609i −0.0964551 0.132759i 0.758062 0.652183i \(-0.226147\pi\)
−0.854517 + 0.519424i \(0.826147\pi\)
\(524\) 0 0
\(525\) −21.1682 + 9.33147i −0.923857 + 0.407259i
\(526\) 0 0
\(527\) 5.22225 + 7.18781i 0.227485 + 0.313106i
\(528\) 0 0
\(529\) −6.67462 + 20.5424i −0.290201 + 0.893146i
\(530\) 0 0
\(531\) −2.97415 9.15350i −0.129067 0.397228i
\(532\) 0 0
\(533\) 10.8535 3.52653i 0.470119 0.152751i
\(534\) 0 0
\(535\) −0.450429 0.201538i −0.0194738 0.00871326i
\(536\) 0 0
\(537\) −8.49089 + 11.6867i −0.366409 + 0.504318i
\(538\) 0 0
\(539\) −57.6799 + 41.9069i −2.48445 + 1.80506i
\(540\) 0 0
\(541\) −15.2752 11.0981i −0.656731 0.477143i 0.208826 0.977953i \(-0.433036\pi\)
−0.865557 + 0.500810i \(0.833036\pi\)
\(542\) 0 0
\(543\) 12.3964i 0.531982i
\(544\) 0 0
\(545\) 12.9619 7.45177i 0.555226 0.319199i
\(546\) 0 0
\(547\) 0.147706 + 0.0479926i 0.00631545 + 0.00205201i 0.312173 0.950025i \(-0.398943\pi\)
−0.305858 + 0.952077i \(0.598943\pi\)
\(548\) 0 0
\(549\) −6.27369 −0.267755
\(550\) 0 0
\(551\) 7.04815 0.300261
\(552\) 0 0
\(553\) −54.8858 17.8335i −2.33398 0.758356i
\(554\) 0 0
\(555\) 0.865182 + 4.10753i 0.0367249 + 0.174355i
\(556\) 0 0
\(557\) 19.0371i 0.806626i −0.915062 0.403313i \(-0.867859\pi\)
0.915062 0.403313i \(-0.132141\pi\)
\(558\) 0 0
\(559\) 32.4584 + 23.5824i 1.37285 + 0.997430i
\(560\) 0 0
\(561\) −10.7714 + 7.82590i −0.454770 + 0.330410i
\(562\) 0 0
\(563\) 18.2630 25.1369i 0.769694 1.05939i −0.226652 0.973976i \(-0.572778\pi\)
0.996345 0.0854166i \(-0.0272221\pi\)
\(564\) 0 0
\(565\) 10.7085 + 18.6268i 0.450510 + 0.783635i
\(566\) 0 0
\(567\) −4.40030 + 1.42974i −0.184795 + 0.0600436i
\(568\) 0 0
\(569\) −12.1573 37.4162i −0.509659 1.56857i −0.792794 0.609490i \(-0.791374\pi\)
0.283135 0.959080i \(-0.408626\pi\)
\(570\) 0 0
\(571\) 8.78632 27.0415i 0.367696 1.13165i −0.580580 0.814203i \(-0.697174\pi\)
0.948276 0.317448i \(-0.102826\pi\)
\(572\) 0 0
\(573\) −0.973056 1.33930i −0.0406500 0.0559499i
\(574\) 0 0
\(575\) 7.06267 32.6360i 0.294534 1.36101i
\(576\) 0 0
\(577\) 13.2014 + 18.1701i 0.549581 + 0.756433i 0.989955 0.141381i \(-0.0451544\pi\)
−0.440375 + 0.897814i \(0.645154\pi\)
\(578\) 0 0
\(579\) −5.04479 + 15.5263i −0.209654 + 0.645250i
\(580\) 0 0
\(581\) −12.7108 39.1198i −0.527332 1.62296i
\(582\) 0 0
\(583\) −46.1085 + 14.9815i −1.90962 + 0.620472i
\(584\) 0 0
\(585\) 0.894885 8.36608i 0.0369989 0.345895i
\(586\) 0 0
\(587\) −9.45335 + 13.0114i −0.390182 + 0.537039i −0.958246 0.285945i \(-0.907692\pi\)
0.568064 + 0.822984i \(0.307692\pi\)
\(588\) 0 0
\(589\) 15.6854 11.3961i 0.646307 0.469570i
\(590\) 0 0
\(591\) 11.0288 + 8.01291i 0.453665 + 0.329607i
\(592\) 0 0
\(593\) 20.4648i 0.840389i −0.907434 0.420194i \(-0.861962\pi\)
0.907434 0.420194i \(-0.138038\pi\)
\(594\) 0 0
\(595\) 27.6762 + 2.96041i 1.13461 + 0.121365i
\(596\) 0 0
\(597\) −5.78068 1.87826i −0.236588 0.0768720i
\(598\) 0 0
\(599\) −18.5688 −0.758699 −0.379349 0.925253i \(-0.623852\pi\)
−0.379349 + 0.925253i \(0.623852\pi\)
\(600\) 0 0
\(601\) 47.2047 1.92552 0.962761 0.270355i \(-0.0871409\pi\)
0.962761 + 0.270355i \(0.0871409\pi\)
\(602\) 0 0
\(603\) −2.43521 0.791247i −0.0991693 0.0322221i
\(604\) 0 0
\(605\) −22.3804 20.2261i −0.909894 0.822310i
\(606\) 0 0
\(607\) 0.0786576i 0.00319261i 0.999999 + 0.00159631i \(0.000508121\pi\)
−0.999999 + 0.00159631i \(0.999492\pi\)
\(608\) 0 0
\(609\) 4.49358 + 3.26478i 0.182089 + 0.132295i
\(610\) 0 0
\(611\) 0.789085 0.573304i 0.0319230 0.0231934i
\(612\) 0 0
\(613\) −3.12162 + 4.29654i −0.126081 + 0.173536i −0.867391 0.497627i \(-0.834205\pi\)
0.741310 + 0.671163i \(0.234205\pi\)
\(614\) 0 0
\(615\) −6.63615 + 1.39779i −0.267595 + 0.0563645i
\(616\) 0 0
\(617\) −28.9429 + 9.40411i −1.16520 + 0.378595i −0.826848 0.562426i \(-0.809868\pi\)
−0.338349 + 0.941021i \(0.609868\pi\)
\(618\) 0 0
\(619\) 9.77918 + 30.0972i 0.393058 + 1.20971i 0.930463 + 0.366385i \(0.119405\pi\)
−0.537405 + 0.843324i \(0.680595\pi\)
\(620\) 0 0
\(621\) 2.06370 6.35143i 0.0828136 0.254874i
\(622\) 0 0
\(623\) 39.6439 + 54.5651i 1.58830 + 2.18610i
\(624\) 0 0
\(625\) −2.79622 + 24.8431i −0.111849 + 0.993725i
\(626\) 0 0
\(627\) 17.0779 + 23.5057i 0.682026 + 0.938728i
\(628\) 0 0
\(629\) 1.56070 4.80335i 0.0622293 0.191522i
\(630\) 0 0
\(631\) −10.4722 32.2301i −0.416891 1.28306i −0.910548 0.413403i \(-0.864340\pi\)
0.493657 0.869657i \(-0.335660\pi\)
\(632\) 0 0
\(633\) 16.2464 5.27877i 0.645736 0.209812i
\(634\) 0 0
\(635\) −34.9920 + 7.37048i −1.38862 + 0.292489i
\(636\) 0 0
\(637\) −31.8635 + 43.8564i −1.26248 + 1.73765i
\(638\) 0 0
\(639\) 7.02007 5.10038i 0.277710 0.201768i
\(640\) 0 0
\(641\) 39.6699 + 28.8219i 1.56687 + 1.13840i 0.930080 + 0.367358i \(0.119737\pi\)
0.636788 + 0.771039i \(0.280263\pi\)
\(642\) 0 0
\(643\) 14.2509i 0.562000i 0.959708 + 0.281000i \(0.0906660\pi\)
−0.959708 + 0.281000i \(0.909334\pi\)
\(644\) 0 0
\(645\) −17.6888 15.9862i −0.696498 0.629455i
\(646\) 0 0
\(647\) 40.2623 + 13.0820i 1.58287 + 0.514307i 0.962795 0.270233i \(-0.0871006\pi\)
0.620079 + 0.784539i \(0.287101\pi\)
\(648\) 0 0
\(649\) −47.6300 −1.86964
\(650\) 0 0
\(651\) 15.2791 0.598836
\(652\) 0 0
\(653\) −44.7274 14.5328i −1.75032 0.568713i −0.754192 0.656654i \(-0.771971\pi\)
−0.996126 + 0.0879407i \(0.971971\pi\)
\(654\) 0 0
\(655\) −27.3983 2.93068i −1.07054 0.114511i
\(656\) 0 0
\(657\) 4.87481i 0.190185i
\(658\) 0 0
\(659\) −9.05013 6.57531i −0.352543 0.256138i 0.397392 0.917649i \(-0.369915\pi\)
−0.749935 + 0.661511i \(0.769915\pi\)
\(660\) 0 0
\(661\) 37.7102 27.3981i 1.46676 1.06566i 0.485218 0.874393i \(-0.338740\pi\)
0.981538 0.191268i \(-0.0612599\pi\)
\(662\) 0 0
\(663\) −5.95035 + 8.18995i −0.231092 + 0.318071i
\(664\) 0 0
\(665\) 6.46029 60.3958i 0.250519 2.34205i
\(666\) 0 0
\(667\) −7.62483 + 2.47746i −0.295235 + 0.0959276i
\(668\) 0 0
\(669\) −0.242204 0.745429i −0.00936417 0.0288199i
\(670\) 0 0
\(671\) −9.59412 + 29.5277i −0.370377 + 1.13990i
\(672\) 0 0
\(673\) −8.07264 11.1110i −0.311178 0.428299i 0.624570 0.780968i \(-0.285274\pi\)
−0.935748 + 0.352669i \(0.885274\pi\)
\(674\) 0 0
\(675\) −1.05756 + 4.88688i −0.0407054 + 0.188096i
\(676\) 0 0
\(677\) −21.6428 29.7888i −0.831801 1.14488i −0.987585 0.157085i \(-0.949790\pi\)
0.155784 0.987791i \(-0.450210\pi\)
\(678\) 0 0
\(679\) 5.70024 17.5435i 0.218755 0.673259i
\(680\) 0 0
\(681\) 7.40078 + 22.7772i 0.283598 + 0.872826i
\(682\) 0 0
\(683\) −28.6179 + 9.29850i −1.09503 + 0.355797i −0.800189 0.599748i \(-0.795267\pi\)
−0.294843 + 0.955546i \(0.595267\pi\)
\(684\) 0 0
\(685\) 6.34638 + 11.0391i 0.242483 + 0.421784i
\(686\) 0 0
\(687\) −3.25271 + 4.47697i −0.124098 + 0.170807i
\(688\) 0 0
\(689\) −29.8222 + 21.6671i −1.13614 + 0.825451i
\(690\) 0 0
\(691\) 6.76839 + 4.91752i 0.257482 + 0.187071i 0.709036 0.705172i \(-0.249130\pi\)
−0.451554 + 0.892244i \(0.649130\pi\)
\(692\) 0 0
\(693\) 22.8968i 0.869779i
\(694\) 0 0
\(695\) 8.29438 + 39.3783i 0.314624 + 1.49370i
\(696\) 0 0
\(697\) 7.76033 + 2.52148i 0.293943 + 0.0955080i
\(698\) 0 0
\(699\) −0.907742 −0.0343340
\(700\) 0 0
\(701\) −3.42495 −0.129359 −0.0646794 0.997906i \(-0.520602\pi\)
−0.0646794 + 0.997906i \(0.520602\pi\)
\(702\) 0 0
\(703\) −10.4820 3.40581i −0.395336 0.128453i
\(704\) 0 0
\(705\) −0.502498 + 0.288886i −0.0189252 + 0.0108801i
\(706\) 0 0
\(707\) 43.3478i 1.63026i
\(708\) 0 0
\(709\) −40.0330 29.0857i −1.50347 1.09234i −0.968973 0.247168i \(-0.920500\pi\)
−0.534499 0.845169i \(-0.679500\pi\)
\(710\) 0 0
\(711\) −10.0910 + 7.33156i −0.378443 + 0.274955i
\(712\) 0 0
\(713\) −12.9630 + 17.8421i −0.485469 + 0.668191i
\(714\) 0 0
\(715\) −38.0072 17.0058i −1.42139 0.635980i
\(716\) 0 0
\(717\) 10.6886 3.47294i 0.399173 0.129699i
\(718\) 0 0
\(719\) −8.08148 24.8722i −0.301388 0.927578i −0.981000 0.194006i \(-0.937852\pi\)
0.679612 0.733572i \(-0.262148\pi\)
\(720\) 0 0
\(721\) 14.9038 45.8692i 0.555046 1.70826i
\(722\) 0 0
\(723\) −11.9037 16.3840i −0.442702 0.609327i
\(724\) 0 0
\(725\) 5.49247 2.42121i 0.203985 0.0899216i
\(726\) 0 0
\(727\) 20.3475 + 28.0059i 0.754647 + 1.03868i 0.997640 + 0.0686545i \(0.0218706\pi\)
−0.242994 + 0.970028i \(0.578129\pi\)
\(728\) 0 0
\(729\) −0.309017 + 0.951057i −0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) 8.86463 + 27.2825i 0.327870 + 1.00908i
\(732\) 0 0
\(733\) 16.6104 5.39704i 0.613518 0.199344i 0.0142577 0.999898i \(-0.495461\pi\)
0.599260 + 0.800554i \(0.295461\pi\)
\(734\) 0 0
\(735\) 21.5998 23.9004i 0.796720 0.881579i
\(736\) 0 0
\(737\) −7.44814 + 10.2515i −0.274356 + 0.377618i
\(738\) 0 0
\(739\) 16.2358 11.7960i 0.597243 0.433922i −0.247656 0.968848i \(-0.579660\pi\)
0.844899 + 0.534926i \(0.179660\pi\)
\(740\) 0 0
\(741\) 17.8724 + 12.9850i 0.656557 + 0.477017i
\(742\) 0 0
\(743\) 5.84644i 0.214485i −0.994233 0.107243i \(-0.965798\pi\)
0.994233 0.107243i \(-0.0342022\pi\)
\(744\) 0 0
\(745\) 0.995453 2.22479i 0.0364706 0.0815101i
\(746\) 0 0
\(747\) −8.45513 2.74724i −0.309357 0.100516i
\(748\) 0 0
\(749\) 1.02104 0.0373081
\(750\) 0 0
\(751\) −32.7925 −1.19662 −0.598308 0.801266i \(-0.704160\pi\)
−0.598308 + 0.801266i \(0.704160\pi\)
\(752\) 0 0
\(753\) 29.1897 + 9.48431i 1.06373 + 0.345627i
\(754\) 0 0
\(755\) 10.3918 23.2252i 0.378196 0.845252i
\(756\) 0 0
\(757\) 22.6371i 0.822759i 0.911464 + 0.411379i \(0.134953\pi\)
−0.911464 + 0.411379i \(0.865047\pi\)
\(758\) 0 0
\(759\) −26.7376 19.4260i −0.970513 0.705119i
\(760\) 0 0
\(761\) 29.3923 21.3547i 1.06547 0.774109i 0.0903767 0.995908i \(-0.471193\pi\)
0.975092 + 0.221799i \(0.0711929\pi\)
\(762\) 0 0
\(763\) −18.1839 + 25.0280i −0.658301 + 0.906073i
\(764\) 0 0
\(765\) 4.03365 4.46327i 0.145837 0.161370i
\(766\) 0 0
\(767\) −34.4425 + 11.1910i −1.24365 + 0.404085i
\(768\) 0 0
\(769\) −4.51902 13.9081i −0.162960 0.501539i 0.835920 0.548851i \(-0.184935\pi\)
−0.998880 + 0.0473119i \(0.984935\pi\)
\(770\) 0 0
\(771\) 1.47569 4.54170i 0.0531456 0.163565i
\(772\) 0 0
\(773\) 17.9422 + 24.6953i 0.645336 + 0.888229i 0.998886 0.0471864i \(-0.0150255\pi\)
−0.353550 + 0.935416i \(0.615025\pi\)
\(774\) 0 0
\(775\) 8.30846 14.2691i 0.298449 0.512561i
\(776\) 0 0
\(777\) −5.10524 7.02676i −0.183150 0.252084i
\(778\) 0 0
\(779\) 5.50245 16.9348i 0.197146 0.606752i
\(780\) 0 0
\(781\) −13.2699 40.8404i −0.474833 1.46138i
\(782\) 0 0
\(783\) 1.14173 0.370972i 0.0408023 0.0132575i
\(784\) 0 0
\(785\) −8.13194 3.63852i −0.290241 0.129865i
\(786\) 0 0
\(787\) 28.8905 39.7644i 1.02984 1.41745i 0.124766 0.992186i \(-0.460182\pi\)
0.905070 0.425262i \(-0.139818\pi\)
\(788\) 0 0
\(789\) 0.978638 0.711022i 0.0348404 0.0253130i
\(790\) 0 0
\(791\) −35.9663 26.1310i −1.27881 0.929112i
\(792\) 0 0
\(793\) 23.6065i 0.838290i
\(794\) 0 0
\(795\) 18.9911 10.9180i 0.673546 0.387221i
\(796\) 0 0
\(797\) −42.3529 13.7613i −1.50022 0.487450i