Properties

Label 300.2.o.a.109.2
Level $300$
Weight $2$
Character 300.109
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 109.2
Character \(\chi\) \(=\) 300.109
Dual form 300.2.o.a.289.2

$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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 \(-0.661273\pi\)
0.485254 0.874373i \(-0.338727\pi\)
\(8\) 0 0
\(9\) 0.809017 0.587785i 0.269672 0.195928i
\(10\) 0 0
\(11\) 4.00366 + 2.90883i 1.20715 + 0.877045i 0.994969 0.100185i \(-0.0319435\pi\)
0.212180 + 0.977231i \(0.431944\pi\)
\(12\) 0 0
\(13\) 2.21170 + 3.04414i 0.613415 + 0.844294i 0.996853 0.0792730i \(-0.0252599\pi\)
−0.383438 + 0.923567i \(0.625260\pi\)
\(14\) 0 0
\(15\) −1.49928 1.65897i −0.387112 0.428343i
\(16\) 0 0
\(17\) 2.55872 + 0.831378i 0.620580 + 0.201639i 0.602398 0.798196i \(-0.294212\pi\)
0.0181824 + 0.999835i \(0.494212\pi\)
\(18\) 0 0
\(19\) −1.81426 + 5.58371i −0.416219 + 1.28099i 0.494937 + 0.868929i \(0.335191\pi\)
−0.911156 + 0.412062i \(0.864809\pi\)
\(20\) 0 0
\(21\) 1.42974 + 4.40030i 0.311996 + 0.960224i
\(22\) 0 0
\(23\) 3.92540 5.40285i 0.818502 1.12657i −0.171453 0.985192i \(-0.554846\pi\)
0.989955 0.141379i \(-0.0451537\pi\)
\(24\) 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 0.910686 0.413099i \(-0.135554\pi\)
−0.979574 + 0.201084i \(0.935554\pi\)
\(30\) 0 0
\(31\) 1.02048 3.14072i 0.183284 0.564090i −0.816631 0.577161i \(-0.804161\pi\)
0.999915 + 0.0130708i \(0.00416068\pi\)
\(32\) 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 0.890028 0.455907i \(-0.150685\pi\)
−0.708627 + 0.705584i \(0.750685\pi\)
\(38\) 0 0
\(39\) −3.04414 2.21170i −0.487453 0.354156i
\(40\) 0 0
\(41\) 2.45366 1.78269i 0.383198 0.278410i −0.379464 0.925206i \(-0.623892\pi\)
0.762663 + 0.646797i \(0.223892\pi\)
\(42\) 0 0
\(43\) 10.6626i 1.62603i −0.582244 0.813014i \(-0.697825\pi\)
0.582244 0.813014i \(-0.302175\pi\)
\(44\) 0 0
\(45\) 1.93855 + 1.11447i 0.288981 + 0.166135i
\(46\) 0 0
\(47\) 0.246527 0.0801015i 0.0359597 0.0116840i −0.290982 0.956729i \(-0.593982\pi\)
0.326942 + 0.945045i \(0.393982\pi\)
\(48\) 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 −0.868511 0.495670i \(-0.834922\pi\)
−0.411292 + 0.911504i \(0.634922\pi\)
\(54\) 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 −0.964983 0.262311i \(-0.915515\pi\)
−0.0487233 + 0.998812i \(0.515515\pi\)
\(60\) 0 0
\(61\) −5.07552 3.68758i −0.649854 0.472147i 0.213367 0.976972i \(-0.431557\pi\)
−0.863222 + 0.504825i \(0.831557\pi\)
\(62\) 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 0.156460 0.987684i \(-0.449992\pi\)
−0.453968 + 0.891018i \(0.649992\pi\)
\(68\) 0 0
\(69\) −2.06370 + 6.35143i −0.248441 + 0.764622i
\(70\) 0 0
\(71\) 2.68143 + 8.25259i 0.318227 + 0.979403i 0.974406 + 0.224797i \(0.0721718\pi\)
−0.656178 + 0.754606i \(0.727828\pi\)
\(72\) 0 0
\(73\) 2.86534 3.94381i 0.335363 0.461588i −0.607717 0.794154i \(-0.707914\pi\)
0.943080 + 0.332566i \(0.107914\pi\)
\(74\) 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 −0.894457 0.447155i \(-0.852437\pi\)
0.460800 0.887504i \(-0.347563\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 0 0
\(83\) −8.45513 2.74724i −0.928071 0.301549i −0.194298 0.980943i \(-0.562243\pi\)
−0.733774 + 0.679394i \(0.762243\pi\)
\(84\) 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 0.998228 0.0595118i \(-0.0189544\pi\)
0.251870 + 0.967761i \(0.418954\pi\)
\(90\) 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 −0.495119 0.868825i \(-0.664875\pi\)
0.110123 + 0.993918i \(0.464875\pi\)
\(98\) 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 −0.753577 0.657360i \(-0.771673\pi\)
−0.223270 + 0.974757i \(0.571673\pi\)
\(104\) 0 0
\(105\) −7.67561 + 6.93678i −0.749063 + 0.676961i
\(106\) 0 0
\(107\) 0.220683i 0.0213342i 0.999943 + 0.0106671i \(0.00339551\pi\)
−0.999943 + 0.0106671i \(0.996604\pi\)
\(108\) 0 0
\(109\) 5.40941 3.93017i 0.518127 0.376442i −0.297771 0.954637i \(-0.596243\pi\)
0.815898 + 0.578196i \(0.196243\pi\)
\(110\) 0 0
\(111\) −1.51873 1.10342i −0.144151 0.104732i
\(112\) 0 0
\(113\) −5.64782 7.77355i −0.531302 0.731274i 0.456026 0.889966i \(-0.349272\pi\)
−0.987328 + 0.158692i \(0.949272\pi\)
\(114\) 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 0.153025 + 0.988222i \(0.451098\pi\)
−0.987143 + 0.159842i \(0.948902\pi\)
\(128\) 0 0
\(129\) 3.29492 + 10.1407i 0.290101 + 0.892840i
\(130\) 0 0
\(131\) −3.80795 + 11.7197i −0.332702 + 1.02395i 0.635140 + 0.772397i \(0.280942\pi\)
−0.967843 + 0.251556i \(0.919058\pi\)
\(132\) 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 0.641731 0.766930i \(-0.278216\pi\)
−0.927699 + 0.373329i \(0.878216\pi\)
\(138\) 0 0
\(139\) −14.5598 10.5783i −1.23495 0.897242i −0.237697 0.971339i \(-0.576393\pi\)
−0.997251 + 0.0740969i \(0.976393\pi\)
\(140\) 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 \(0.0508221\pi\)
−0.987281 + 0.158985i \(0.949178\pi\)
\(158\) 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 −0.922148 0.386837i \(-0.873568\pi\)
−0.0829441 0.996554i \(-0.526432\pi\)
\(164\) 0 0
\(165\) −1.17695 11.0031i −0.0916257 0.856589i
\(166\) 0 0
\(167\) 14.7118 + 4.78015i 1.13843 + 0.369899i 0.816775 0.576957i \(-0.195760\pi\)
0.321658 + 0.946856i \(0.395760\pi\)
\(168\) 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 −0.229253 0.973367i \(-0.573628\pi\)
0.996570 0.0827547i \(-0.0263718\pi\)
\(174\) 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 0.967384 + 0.253316i \(0.0815213\pi\)
−0.633734 + 0.773551i \(0.718479\pi\)
\(180\) 0 0
\(181\) 3.83071 11.7897i 0.284734 0.876322i −0.701744 0.712429i \(-0.747595\pi\)
0.986478 0.163893i \(-0.0524051\pi\)
\(182\) 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 −0.538276 0.842769i \(-0.680924\pi\)
0.635184 + 0.772361i \(0.280924\pi\)
\(192\) 0 0
\(193\) 16.3253i 1.17512i 0.809181 + 0.587560i \(0.199911\pi\)
−0.809181 + 0.587560i \(0.800089\pi\)
\(194\) 0 0
\(195\) 1.73418 8.23315i 0.124187 0.589588i
\(196\) 0 0
\(197\) −12.9652 + 4.21264i −0.923730 + 0.300138i −0.731996 0.681309i \(-0.761411\pi\)
−0.191734 + 0.981447i \(0.561411\pi\)
\(198\) 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 −0.000268984 1.00000i \(-0.500086\pi\)
−0.951140 + 0.308761i \(0.900086\pi\)
\(212\) 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 −0.793313 0.608814i \(-0.791646\pi\)
0.824164 + 0.566352i \(0.191646\pi\)
\(224\) 0 0
\(225\) −0.504331 + 4.97450i −0.0336221 + 0.331633i
\(226\) 0 0
\(227\) −14.0771 + 19.3755i −0.934331 + 1.28600i 0.0238153 + 0.999716i \(0.492419\pi\)
−0.958146 + 0.286280i \(0.907581\pi\)
\(228\) 0 0
\(229\) 1.71005 + 5.26299i 0.113003 + 0.347788i 0.991525 0.129914i \(-0.0414700\pi\)
−0.878522 + 0.477702i \(0.841470\pi\)
\(230\) 0 0
\(231\) −7.07551 + 21.7762i −0.465535 + 1.43277i
\(232\) 0 0
\(233\) 0.863314 + 0.280508i 0.0565576 + 0.0183767i 0.337159 0.941448i \(-0.390534\pi\)
−0.280602 + 0.959824i \(0.590534\pi\)
\(234\) 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 0.253516 0.967331i \(-0.418413\pi\)
−0.841646 + 0.540030i \(0.818413\pi\)
\(240\) 0 0
\(241\) 16.3840 11.9037i 1.05539 0.766783i 0.0821564 0.996619i \(-0.473819\pi\)
0.973229 + 0.229837i \(0.0738193\pi\)
\(242\) 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 \(-0.952413\pi\)
0.988846 0.148941i \(-0.0475866\pi\)
\(258\) 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 0.786532 0.617549i \(-0.211874\pi\)
−0.830376 + 0.557204i \(0.811874\pi\)
\(264\) 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 −0.356891 0.934146i \(-0.616163\pi\)
0.837808 0.545965i \(-0.183837\pi\)
\(270\) 0 0
\(271\) −1.81499 5.58596i −0.110253 0.339323i 0.880675 0.473722i \(-0.157090\pi\)
−0.990927 + 0.134399i \(0.957090\pi\)
\(272\) 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 −0.713563 0.700591i \(-0.752920\pi\)
0.886805 + 0.462144i \(0.152920\pi\)
\(278\) 0 0
\(279\) −1.02048 3.14072i −0.0610946 0.188030i
\(280\) 0 0
\(281\) −0.400257 + 1.23186i −0.0238773 + 0.0734868i −0.962285 0.272043i \(-0.912301\pi\)
0.938408 + 0.345530i \(0.112301\pi\)
\(282\) 0 0
\(283\) 28.7501 + 9.34149i 1.70902 + 0.555294i 0.990169 0.139873i \(-0.0446693\pi\)
0.718849 + 0.695166i \(0.244669\pi\)
\(284\) 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 \(0.0757310\pi\)
−0.971831 + 0.235678i \(0.924269\pi\)
\(294\) 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 \(0.138541\pi\)
−0.906769 + 0.421628i \(0.861459\pi\)
\(308\) 0 0
\(309\) 8.43328 6.12713i 0.479752 0.348560i
\(310\) 0 0
\(311\) 7.40552 + 5.38043i 0.419929 + 0.305096i 0.777609 0.628748i \(-0.216432\pi\)
−0.357680 + 0.933844i \(0.616432\pi\)
\(312\) 0 0
\(313\) 7.79128 + 10.7238i 0.440389 + 0.606144i 0.970299 0.241910i \(-0.0777740\pi\)
−0.529909 + 0.848054i \(0.677774\pi\)
\(314\) 0 0
\(315\) 5.15636 8.96917i 0.290528 0.505355i
\(316\) 0 0
\(317\) 0.751858 + 0.244293i 0.0422286 + 0.0137209i 0.330055 0.943962i \(-0.392933\pi\)
−0.287827 + 0.957683i \(0.592933\pi\)
\(318\) 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 −0.975611 0.219506i \(-0.929555\pi\)
0.918308 + 0.395866i \(0.129555\pi\)
\(332\) 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 0.415076 0.909787i \(-0.363755\pi\)
−0.993524 + 0.113621i \(0.963755\pi\)
\(338\) 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 −0.385895 0.922543i \(-0.626107\pi\)
0.230062 + 0.973176i \(0.426107\pi\)
\(348\) 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 −0.745226 0.666812i \(-0.767658\pi\)
−0.210958 + 0.977495i \(0.567658\pi\)
\(354\) 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 0.238176 0.971222i \(-0.423450\pi\)
0.997287 + 0.0736053i \(0.0234505\pi\)
\(360\) 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 0.439570 0.898209i \(-0.355131\pi\)
−0.172334 + 0.985038i \(0.555131\pi\)
\(368\) 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 −0.608183 0.793797i \(-0.708101\pi\)
0.942884 + 0.333120i \(0.108101\pi\)
\(374\) 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 0.879163 0.476522i \(-0.158103\pi\)
−0.991350 + 0.131245i \(0.958103\pi\)
\(380\) 0 0
\(381\) 4.94189 15.2096i 0.253181 0.779210i
\(382\) 0 0
\(383\) −7.70484 2.50346i −0.393699 0.127921i 0.105476 0.994422i \(-0.466363\pi\)
−0.499175 + 0.866501i \(0.666363\pi\)
\(384\) 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 0.998723 + 0.0505192i \(0.0160876\pi\)
0.356669 + 0.934231i \(0.383912\pi\)
\(390\) 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 0.00138688 0.999999i \(-0.499559\pi\)
0.588907 + 0.808201i \(0.299559\pi\)
\(398\) 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 −0.950212 0.311604i \(-0.899134\pi\)
0.00272132 + 0.999996i \(0.499134\pi\)
\(410\) 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 −0.962033 0.272933i \(-0.912006\pi\)
0.938727 + 0.344661i \(0.112006\pi\)
\(420\) 0 0
\(421\) −5.43760 16.7352i −0.265013 0.815625i −0.991691 0.128647i \(-0.958937\pi\)
0.726678 0.686978i \(-0.241063\pi\)
\(422\) 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 −0.764485 0.644641i \(-0.777007\pi\)
0.997392 0.0721724i \(-0.0229932\pi\)
\(432\) 0 0
\(433\) 0.217772 + 0.0707586i 0.0104655 + 0.00340044i 0.314245 0.949342i \(-0.398249\pi\)
−0.303780 + 0.952742i \(0.598249\pi\)
\(434\) 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 0.895780 0.444498i \(-0.146618\pi\)
−0.145932 + 0.989295i \(0.546618\pi\)
\(440\) 0 0
\(441\) −11.6553 + 8.46810i −0.555016 + 0.403243i
\(442\) 0 0
\(443\) 12.7980i 0.608051i −0.952664 0.304026i \(-0.901669\pi\)
0.952664 0.304026i \(-0.0983309\pi\)
\(444\) 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 \(0.0672901\pi\)
−0.977739 + 0.209827i \(0.932710\pi\)
\(458\) 0 0
\(459\) −2.17658 + 1.58137i −0.101594 + 0.0738123i
\(460\) 0 0
\(461\) −22.2764 16.1847i −1.03751 0.753797i −0.0677146 0.997705i \(-0.521571\pi\)
−0.969799 + 0.243907i \(0.921571\pi\)
\(462\) 0 0
\(463\) −17.2815 23.7859i −0.803140 1.10543i −0.992346 0.123489i \(-0.960591\pi\)
0.189206 0.981937i \(-0.439409\pi\)
\(464\) 0 0
\(465\) −6.74033 + 3.01587i −0.312575 + 0.139857i
\(466\) 0 0
\(467\) −12.6119 4.09785i −0.583609 0.189626i 0.00230768 0.999997i \(-0.499265\pi\)
−0.585917 + 0.810371i \(0.699265\pi\)
\(468\) 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 0.993833 + 0.110887i \(0.0353692\pi\)
−0.738850 + 0.673870i \(0.764631\pi\)
\(480\) 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 0.954094 0.299508i \(-0.0968226\pi\)
−0.579681 + 0.814844i \(0.696823\pi\)
\(488\) 0 0
\(489\) 17.6620 + 12.8322i 0.798701 + 0.580290i
\(490\) 0 0
\(491\) 22.0310 16.0065i 0.994247 0.722363i 0.0334000 0.999442i \(-0.489366\pi\)
0.960847 + 0.277079i \(0.0893665\pi\)
\(492\) 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 −0.512183 0.858876i \(-0.671163\pi\)
0.0904697 + 0.995899i \(0.471163\pi\)
\(504\) 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 −0.233270 0.972412i \(-0.574943\pi\)
0.852734 + 0.522345i \(0.174943\pi\)
\(510\) 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 0.847075 0.531474i \(-0.178362\pi\)
−0.997690 + 0.0679269i \(0.978362\pi\)
\(522\) 0 0
\(523\) −2.20585 + 3.03609i −0.0964551 + 0.132759i −0.854517 0.519424i \(-0.826147\pi\)
0.758062 + 0.652183i \(0.226147\pi\)
\(524\) 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 −0.865557 0.500810i \(-0.833036\pi\)
0.208826 + 0.977953i \(0.433036\pi\)
\(542\) 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 −0.305858 0.952077i \(-0.598943\pi\)
0.312173 + 0.950025i \(0.398943\pi\)
\(548\) 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 \(0.132141\pi\)
−0.915062 + 0.403313i \(0.867859\pi\)
\(558\) 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 0.996345 + 0.0854166i \(0.0272221\pi\)
−0.226652 + 0.973976i \(0.572778\pi\)
\(564\) 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 0.283135 + 0.959080i \(0.408626\pi\)
−0.792794 + 0.609490i \(0.791374\pi\)
\(570\) 0 0
\(571\) 8.78632 + 27.0415i 0.367696 + 1.13165i 0.948276 + 0.317448i \(0.102826\pi\)
−0.580580 + 0.814203i \(0.697174\pi\)
\(572\) 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 −0.440375 0.897814i \(-0.645154\pi\)
0.989955 + 0.141381i \(0.0451544\pi\)
\(578\) 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 0.568064 0.822984i \(-0.307692\pi\)
−0.958246 + 0.285945i \(0.907692\pi\)
\(588\) 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 \(0.138038\pi\)
−0.907434 + 0.420194i \(0.861962\pi\)
\(594\) 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 \(-0.999492\pi\)
0.999999 0.00159631i \(-0.000508121\pi\)
\(608\) 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 0.741310 0.671163i \(-0.234205\pi\)
−0.867391 + 0.497627i \(0.834205\pi\)
\(614\) 0 0
\(615\) −6.63615 1.39779i −0.267595 0.0563645i
\(616\) 0 0
\(617\) −28.9429 9.40411i −1.16520 0.378595i −0.338349 0.941021i \(-0.609868\pi\)
−0.826848 + 0.562426i \(0.809868\pi\)
\(618\) 0 0
\(619\) 9.77918 30.0972i 0.393058 1.20971i −0.537405 0.843324i \(-0.680595\pi\)
0.930463 0.366385i \(-0.119405\pi\)
\(620\) 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 0.493657 + 0.869657i \(0.335660\pi\)
−0.910548 + 0.413403i \(0.864340\pi\)
\(632\) 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 0.636788 0.771039i \(-0.280263\pi\)
0.930080 0.367358i \(-0.119737\pi\)
\(642\) 0 0
\(643\) 14.2509i 0.562000i −0.959708 0.281000i \(-0.909334\pi\)
0.959708 0.281000i \(-0.0906660\pi\)
\(644\) 0 0
\(645\) −17.6888 + 15.9862i −0.696498 + 0.629455i
\(646\) 0 0
\(647\) 40.2623 13.0820i 1.58287 0.514307i 0.620079 0.784539i \(-0.287101\pi\)
0.962795 + 0.270233i \(0.0871006\pi\)
\(648\) 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 −0.996126 0.0879407i \(-0.971971\pi\)
−0.754192 + 0.656654i \(0.771971\pi\)
\(654\) 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 −0.749935 0.661511i \(-0.769915\pi\)
0.397392 + 0.917649i \(0.369915\pi\)
\(660\) 0 0
\(661\) 37.7102 + 27.3981i 1.46676 + 1.06566i 0.981538 + 0.191268i \(0.0612599\pi\)
0.485218 + 0.874393i \(0.338740\pi\)
\(662\) 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 −0.935748 0.352669i \(-0.885274\pi\)
0.624570 + 0.780968i \(0.285274\pi\)
\(674\) 0 0
\(675\) −1.05756 4.88688i −0.0407054 0.188096i
\(676\) 0 0
\(677\) −21.6428 + 29.7888i −0.831801 + 1.14488i 0.155784 + 0.987791i \(0.450210\pi\)
−0.987585 + 0.157085i \(0.949790\pi\)
\(678\) 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 −0.294843 0.955546i \(-0.595267\pi\)
−0.800189 + 0.599748i \(0.795267\pi\)
\(684\) 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 −0.451554 0.892244i \(-0.649130\pi\)
0.709036 + 0.705172i \(0.249130\pi\)
\(692\) 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 −0.534499 + 0.845169i \(0.679500\pi\)
−0.968973 + 0.247168i \(0.920500\pi\)
\(710\) 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 0.679612 + 0.733572i \(0.262148\pi\)
−0.981000 + 0.194006i \(0.937852\pi\)
\(720\) 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 −0.242994 0.970028i \(-0.578129\pi\)
0.997640 0.0686545i \(-0.0218706\pi\)
\(728\) 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 0.599260 0.800554i \(-0.295461\pi\)
0.0142577 + 0.999898i \(0.495461\pi\)
\(734\) 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 0.844899 0.534926i \(-0.179660\pi\)
−0.247656 + 0.968848i \(0.579660\pi\)
\(740\) 0 0
\(741\) 17.8724 12.9850i 0.656557 0.477017i
\(742\) 0 0
\(743\) 5.84644i 0.214485i 0.994233 + 0.107243i \(0.0342022\pi\)
−0.994233 + 0.107243i \(0.965798\pi\)
\(744\) 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 \(-0.865047\pi\)
0.911464 0.411379i \(-0.134953\pi\)
\(758\) 0 0
\(759\) −26.7376 + 19.4260i −0.970513 + 0.705119i
\(760\) 0 0
\(761\) 29.3923 + 21.3547i 1.06547 + 0.774109i 0.975092 0.221799i \(-0.0711929\pi\)
0.0903767 + 0.995908i \(0.471193\pi\)
\(762\) 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 −0.998880 0.0473119i \(-0.984935\pi\)
0.835920 + 0.548851i \(0.184935\pi\)
\(770\) 0 0
\(771\) 1.47569 + 4.54170i 0.0531456 + 0.163565i
\(772\) 0 0
\(773\) 17.9422 24.6953i 0.645336 0.888229i −0.353550 0.935416i \(-0.615025\pi\)
0.998886 + 0.0471864i \(0.0150255\pi\)
\(774\) 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 0.905070 + 0.425262i \(0.139818\pi\)
0.124766 + 0.992186i \(0.460182\pi\)
\(788\) 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 −0.940081 0.340951i \(-0.889251\pi\)