Properties

Label 320.2.j.b.143.1
Level $320$
Weight $2$
Character 320.143
Analytic conductor $2.555$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Defining polynomial: \(x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 143.1
Root \(-0.480367 - 1.33013i\) of defining polynomial
Character \(\chi\) \(=\) 320.143
Dual form 320.2.j.b.47.9

$q$-expansion

\(f(q)\) \(=\) \(q-2.85601i q^{3} +(1.43498 - 1.71489i) q^{5} +(0.458895 - 0.458895i) q^{7} -5.15678 q^{9} +O(q^{10})\) \(q-2.85601i q^{3} +(1.43498 - 1.71489i) q^{5} +(0.458895 - 0.458895i) q^{7} -5.15678 q^{9} +(0.492763 - 0.492763i) q^{11} +4.52109 q^{13} +(-4.89773 - 4.09831i) q^{15} +(-3.12823 + 3.12823i) q^{17} +(-4.04508 + 4.04508i) q^{19} +(-1.31061 - 1.31061i) q^{21} +(1.80660 + 1.80660i) q^{23} +(-0.881683 - 4.92165i) q^{25} +6.15978i q^{27} +(-3.83926 - 3.83926i) q^{29} +0.139949i q^{31} +(-1.40733 - 1.40733i) q^{33} +(-0.128450 - 1.44546i) q^{35} +5.84330 q^{37} -12.9123i q^{39} -4.55648i q^{41} +7.49928 q^{43} +(-7.39986 + 8.84330i) q^{45} +(4.14073 + 4.14073i) q^{47} +6.57883i q^{49} +(8.93426 + 8.93426i) q^{51} +2.75773i q^{53} +(-0.137930 - 1.55214i) q^{55} +(11.5528 + 11.5528i) q^{57} +(3.62521 + 3.62521i) q^{59} +(3.72781 - 3.72781i) q^{61} +(-2.36642 + 2.36642i) q^{63} +(6.48766 - 7.75317i) q^{65} -3.32677 q^{67} +(5.15965 - 5.15965i) q^{69} -1.37056 q^{71} +(-2.55028 + 2.55028i) q^{73} +(-14.0563 + 2.51809i) q^{75} -0.452252i q^{77} +3.86426 q^{79} +2.12204 q^{81} -14.4698i q^{83} +(0.875628 + 9.85351i) q^{85} +(-10.9650 + 10.9650i) q^{87} -3.35011 q^{89} +(2.07470 - 2.07470i) q^{91} +0.399696 q^{93} +(1.13226 + 12.7415i) q^{95} +(-4.95582 + 4.95582i) q^{97} +(-2.54107 + 2.54107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{5} - 2q^{7} - 10q^{9} + O(q^{10}) \) \( 18q - 4q^{5} - 2q^{7} - 10q^{9} + 2q^{11} - 20q^{15} - 6q^{17} - 2q^{19} - 16q^{21} + 2q^{23} + 6q^{25} - 14q^{29} - 8q^{33} + 6q^{35} + 8q^{37} + 44q^{43} - 4q^{45} + 38q^{47} - 8q^{51} + 6q^{55} + 24q^{57} + 10q^{59} + 14q^{61} - 6q^{63} - 12q^{67} + 32q^{69} - 24q^{71} + 14q^{73} - 64q^{75} - 16q^{79} + 2q^{81} - 10q^{85} - 24q^{87} - 12q^{89} + 16q^{93} + 34q^{95} + 18q^{97} + 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.85601i 1.64892i −0.565923 0.824458i \(-0.691480\pi\)
0.565923 0.824458i \(-0.308520\pi\)
\(4\) 0 0
\(5\) 1.43498 1.71489i 0.641741 0.766921i
\(6\) 0 0
\(7\) 0.458895 0.458895i 0.173446 0.173446i −0.615046 0.788491i \(-0.710862\pi\)
0.788491 + 0.615046i \(0.210862\pi\)
\(8\) 0 0
\(9\) −5.15678 −1.71893
\(10\) 0 0
\(11\) 0.492763 0.492763i 0.148574 0.148574i −0.628907 0.777481i \(-0.716497\pi\)
0.777481 + 0.628907i \(0.216497\pi\)
\(12\) 0 0
\(13\) 4.52109 1.25393 0.626963 0.779049i \(-0.284298\pi\)
0.626963 + 0.779049i \(0.284298\pi\)
\(14\) 0 0
\(15\) −4.89773 4.09831i −1.26459 1.05818i
\(16\) 0 0
\(17\) −3.12823 + 3.12823i −0.758708 + 0.758708i −0.976087 0.217379i \(-0.930249\pi\)
0.217379 + 0.976087i \(0.430249\pi\)
\(18\) 0 0
\(19\) −4.04508 + 4.04508i −0.928005 + 0.928005i −0.997577 0.0695721i \(-0.977837\pi\)
0.0695721 + 0.997577i \(0.477837\pi\)
\(20\) 0 0
\(21\) −1.31061 1.31061i −0.285998 0.285998i
\(22\) 0 0
\(23\) 1.80660 + 1.80660i 0.376701 + 0.376701i 0.869911 0.493209i \(-0.164176\pi\)
−0.493209 + 0.869911i \(0.664176\pi\)
\(24\) 0 0
\(25\) −0.881683 4.92165i −0.176337 0.984330i
\(26\) 0 0
\(27\) 6.15978i 1.18545i
\(28\) 0 0
\(29\) −3.83926 3.83926i −0.712932 0.712932i 0.254215 0.967148i \(-0.418183\pi\)
−0.967148 + 0.254215i \(0.918183\pi\)
\(30\) 0 0
\(31\) 0.139949i 0.0251356i 0.999921 + 0.0125678i \(0.00400057\pi\)
−0.999921 + 0.0125678i \(0.995999\pi\)
\(32\) 0 0
\(33\) −1.40733 1.40733i −0.244985 0.244985i
\(34\) 0 0
\(35\) −0.128450 1.44546i −0.0217120 0.244327i
\(36\) 0 0
\(37\) 5.84330 0.960633 0.480317 0.877095i \(-0.340522\pi\)
0.480317 + 0.877095i \(0.340522\pi\)
\(38\) 0 0
\(39\) 12.9123i 2.06762i
\(40\) 0 0
\(41\) 4.55648i 0.711602i −0.934562 0.355801i \(-0.884208\pi\)
0.934562 0.355801i \(-0.115792\pi\)
\(42\) 0 0
\(43\) 7.49928 1.14363 0.571815 0.820383i \(-0.306240\pi\)
0.571815 + 0.820383i \(0.306240\pi\)
\(44\) 0 0
\(45\) −7.39986 + 8.84330i −1.10311 + 1.31828i
\(46\) 0 0
\(47\) 4.14073 + 4.14073i 0.603987 + 0.603987i 0.941368 0.337381i \(-0.109541\pi\)
−0.337381 + 0.941368i \(0.609541\pi\)
\(48\) 0 0
\(49\) 6.57883i 0.939833i
\(50\) 0 0
\(51\) 8.93426 + 8.93426i 1.25105 + 1.25105i
\(52\) 0 0
\(53\) 2.75773i 0.378803i 0.981900 + 0.189402i \(0.0606548\pi\)
−0.981900 + 0.189402i \(0.939345\pi\)
\(54\) 0 0
\(55\) −0.137930 1.55214i −0.0185985 0.209290i
\(56\) 0 0
\(57\) 11.5528 + 11.5528i 1.53020 + 1.53020i
\(58\) 0 0
\(59\) 3.62521 + 3.62521i 0.471962 + 0.471962i 0.902549 0.430587i \(-0.141694\pi\)
−0.430587 + 0.902549i \(0.641694\pi\)
\(60\) 0 0
\(61\) 3.72781 3.72781i 0.477298 0.477298i −0.426969 0.904266i \(-0.640419\pi\)
0.904266 + 0.426969i \(0.140419\pi\)
\(62\) 0 0
\(63\) −2.36642 + 2.36642i −0.298141 + 0.298141i
\(64\) 0 0
\(65\) 6.48766 7.75317i 0.804696 0.961662i
\(66\) 0 0
\(67\) −3.32677 −0.406430 −0.203215 0.979134i \(-0.565139\pi\)
−0.203215 + 0.979134i \(0.565139\pi\)
\(68\) 0 0
\(69\) 5.15965 5.15965i 0.621149 0.621149i
\(70\) 0 0
\(71\) −1.37056 −0.162655 −0.0813275 0.996687i \(-0.525916\pi\)
−0.0813275 + 0.996687i \(0.525916\pi\)
\(72\) 0 0
\(73\) −2.55028 + 2.55028i −0.298488 + 0.298488i −0.840422 0.541933i \(-0.817693\pi\)
0.541933 + 0.840422i \(0.317693\pi\)
\(74\) 0 0
\(75\) −14.0563 + 2.51809i −1.62308 + 0.290764i
\(76\) 0 0
\(77\) 0.452252i 0.0515389i
\(78\) 0 0
\(79\) 3.86426 0.434763 0.217382 0.976087i \(-0.430248\pi\)
0.217382 + 0.976087i \(0.430248\pi\)
\(80\) 0 0
\(81\) 2.12204 0.235782
\(82\) 0 0
\(83\) 14.4698i 1.58827i −0.607744 0.794133i \(-0.707925\pi\)
0.607744 0.794133i \(-0.292075\pi\)
\(84\) 0 0
\(85\) 0.875628 + 9.85351i 0.0949752 + 1.06876i
\(86\) 0 0
\(87\) −10.9650 + 10.9650i −1.17557 + 1.17557i
\(88\) 0 0
\(89\) −3.35011 −0.355111 −0.177556 0.984111i \(-0.556819\pi\)
−0.177556 + 0.984111i \(0.556819\pi\)
\(90\) 0 0
\(91\) 2.07470 2.07470i 0.217488 0.217488i
\(92\) 0 0
\(93\) 0.399696 0.0414466
\(94\) 0 0
\(95\) 1.13226 + 12.7415i 0.116168 + 1.30725i
\(96\) 0 0
\(97\) −4.95582 + 4.95582i −0.503187 + 0.503187i −0.912427 0.409240i \(-0.865794\pi\)
0.409240 + 0.912427i \(0.365794\pi\)
\(98\) 0 0
\(99\) −2.54107 + 2.54107i −0.255387 + 0.255387i
\(100\) 0 0
\(101\) −1.84536 1.84536i −0.183621 0.183621i 0.609311 0.792931i \(-0.291446\pi\)
−0.792931 + 0.609311i \(0.791446\pi\)
\(102\) 0 0
\(103\) 11.6655 + 11.6655i 1.14944 + 1.14944i 0.986664 + 0.162773i \(0.0520437\pi\)
0.162773 + 0.986664i \(0.447956\pi\)
\(104\) 0 0
\(105\) −4.12823 + 0.366853i −0.402874 + 0.0358012i
\(106\) 0 0
\(107\) 15.3106i 1.48013i −0.672534 0.740067i \(-0.734794\pi\)
0.672534 0.740067i \(-0.265206\pi\)
\(108\) 0 0
\(109\) 12.4798 + 12.4798i 1.19535 + 1.19535i 0.975544 + 0.219803i \(0.0705416\pi\)
0.219803 + 0.975544i \(0.429458\pi\)
\(110\) 0 0
\(111\) 16.6885i 1.58400i
\(112\) 0 0
\(113\) 2.53557 + 2.53557i 0.238526 + 0.238526i 0.816240 0.577713i \(-0.196055\pi\)
−0.577713 + 0.816240i \(0.696055\pi\)
\(114\) 0 0
\(115\) 5.69053 0.505686i 0.530645 0.0471555i
\(116\) 0 0
\(117\) −23.3143 −2.15541
\(118\) 0 0
\(119\) 2.87106i 0.263189i
\(120\) 0 0
\(121\) 10.5144i 0.955852i
\(122\) 0 0
\(123\) −13.0133 −1.17337
\(124\) 0 0
\(125\) −9.70527 5.55047i −0.868066 0.496449i
\(126\) 0 0
\(127\) 0.615790 + 0.615790i 0.0546426 + 0.0546426i 0.733900 0.679257i \(-0.237698\pi\)
−0.679257 + 0.733900i \(0.737698\pi\)
\(128\) 0 0
\(129\) 21.4180i 1.88575i
\(130\) 0 0
\(131\) −9.55413 9.55413i −0.834748 0.834748i 0.153414 0.988162i \(-0.450973\pi\)
−0.988162 + 0.153414i \(0.950973\pi\)
\(132\) 0 0
\(133\) 3.71253i 0.321917i
\(134\) 0 0
\(135\) 10.5633 + 8.83914i 0.909147 + 0.760752i
\(136\) 0 0
\(137\) −3.70277 3.70277i −0.316349 0.316349i 0.531014 0.847363i \(-0.321811\pi\)
−0.847363 + 0.531014i \(0.821811\pi\)
\(138\) 0 0
\(139\) −5.46761 5.46761i −0.463756 0.463756i 0.436128 0.899885i \(-0.356349\pi\)
−0.899885 + 0.436128i \(0.856349\pi\)
\(140\) 0 0
\(141\) 11.8260 11.8260i 0.995925 0.995925i
\(142\) 0 0
\(143\) 2.22783 2.22783i 0.186300 0.186300i
\(144\) 0 0
\(145\) −12.0931 + 1.07465i −1.00428 + 0.0892450i
\(146\) 0 0
\(147\) 18.7892 1.54971
\(148\) 0 0
\(149\) 4.21561 4.21561i 0.345356 0.345356i −0.513021 0.858376i \(-0.671474\pi\)
0.858376 + 0.513021i \(0.171474\pi\)
\(150\) 0 0
\(151\) −12.4417 −1.01249 −0.506244 0.862390i \(-0.668966\pi\)
−0.506244 + 0.862390i \(0.668966\pi\)
\(152\) 0 0
\(153\) 16.1316 16.1316i 1.30416 1.30416i
\(154\) 0 0
\(155\) 0.239997 + 0.200824i 0.0192771 + 0.0161306i
\(156\) 0 0
\(157\) 7.50500i 0.598964i −0.954102 0.299482i \(-0.903186\pi\)
0.954102 0.299482i \(-0.0968138\pi\)
\(158\) 0 0
\(159\) 7.87609 0.624615
\(160\) 0 0
\(161\) 1.65807 0.130675
\(162\) 0 0
\(163\) 23.7284i 1.85855i 0.369383 + 0.929277i \(0.379569\pi\)
−0.369383 + 0.929277i \(0.620431\pi\)
\(164\) 0 0
\(165\) −4.43291 + 0.393929i −0.345102 + 0.0306673i
\(166\) 0 0
\(167\) 0.402976 0.402976i 0.0311832 0.0311832i −0.691343 0.722526i \(-0.742981\pi\)
0.722526 + 0.691343i \(0.242981\pi\)
\(168\) 0 0
\(169\) 7.44028 0.572330
\(170\) 0 0
\(171\) 20.8596 20.8596i 1.59517 1.59517i
\(172\) 0 0
\(173\) −15.4500 −1.17464 −0.587320 0.809355i \(-0.699817\pi\)
−0.587320 + 0.809355i \(0.699817\pi\)
\(174\) 0 0
\(175\) −2.66312 1.85392i −0.201313 0.140143i
\(176\) 0 0
\(177\) 10.3536 10.3536i 0.778225 0.778225i
\(178\) 0 0
\(179\) −5.20444 + 5.20444i −0.388998 + 0.388998i −0.874330 0.485332i \(-0.838699\pi\)
0.485332 + 0.874330i \(0.338699\pi\)
\(180\) 0 0
\(181\) −9.08925 9.08925i −0.675599 0.675599i 0.283402 0.959001i \(-0.408537\pi\)
−0.959001 + 0.283402i \(0.908537\pi\)
\(182\) 0 0
\(183\) −10.6467 10.6467i −0.787024 0.787024i
\(184\) 0 0
\(185\) 8.38500 10.0206i 0.616478 0.736730i
\(186\) 0 0
\(187\) 3.08295i 0.225448i
\(188\) 0 0
\(189\) 2.82669 + 2.82669i 0.205611 + 0.205611i
\(190\) 0 0
\(191\) 15.1075i 1.09314i 0.837413 + 0.546571i \(0.184067\pi\)
−0.837413 + 0.546571i \(0.815933\pi\)
\(192\) 0 0
\(193\) 4.19166 + 4.19166i 0.301722 + 0.301722i 0.841687 0.539965i \(-0.181563\pi\)
−0.539965 + 0.841687i \(0.681563\pi\)
\(194\) 0 0
\(195\) −22.1431 18.5288i −1.58570 1.32688i
\(196\) 0 0
\(197\) −4.03184 −0.287256 −0.143628 0.989632i \(-0.545877\pi\)
−0.143628 + 0.989632i \(0.545877\pi\)
\(198\) 0 0
\(199\) 5.43055i 0.384961i −0.981301 0.192481i \(-0.938347\pi\)
0.981301 0.192481i \(-0.0616533\pi\)
\(200\) 0 0
\(201\) 9.50129i 0.670169i
\(202\) 0 0
\(203\) −3.52363 −0.247310
\(204\) 0 0
\(205\) −7.81385 6.53844i −0.545743 0.456664i
\(206\) 0 0
\(207\) −9.31622 9.31622i −0.647522 0.647522i
\(208\) 0 0
\(209\) 3.98653i 0.275754i
\(210\) 0 0
\(211\) −3.23020 3.23020i −0.222376 0.222376i 0.587122 0.809498i \(-0.300261\pi\)
−0.809498 + 0.587122i \(0.800261\pi\)
\(212\) 0 0
\(213\) 3.91432i 0.268205i
\(214\) 0 0
\(215\) 10.7613 12.8604i 0.733914 0.877074i
\(216\) 0 0
\(217\) 0.0642220 + 0.0642220i 0.00435967 + 0.00435967i
\(218\) 0 0
\(219\) 7.28363 + 7.28363i 0.492182 + 0.492182i
\(220\) 0 0
\(221\) −14.1430 + 14.1430i −0.951363 + 0.951363i
\(222\) 0 0
\(223\) 8.17319 8.17319i 0.547317 0.547317i −0.378347 0.925664i \(-0.623507\pi\)
0.925664 + 0.378347i \(0.123507\pi\)
\(224\) 0 0
\(225\) 4.54664 + 25.3799i 0.303110 + 1.69199i
\(226\) 0 0
\(227\) 1.54068 0.102258 0.0511292 0.998692i \(-0.483718\pi\)
0.0511292 + 0.998692i \(0.483718\pi\)
\(228\) 0 0
\(229\) −17.5646 + 17.5646i −1.16070 + 1.16070i −0.176378 + 0.984322i \(0.556438\pi\)
−0.984322 + 0.176378i \(0.943562\pi\)
\(230\) 0 0
\(231\) −1.29164 −0.0849834
\(232\) 0 0
\(233\) 9.99018 9.99018i 0.654479 0.654479i −0.299590 0.954068i \(-0.596850\pi\)
0.954068 + 0.299590i \(0.0968498\pi\)
\(234\) 0 0
\(235\) 13.0427 1.15904i 0.850814 0.0756072i
\(236\) 0 0
\(237\) 11.0364i 0.716889i
\(238\) 0 0
\(239\) −26.2762 −1.69967 −0.849833 0.527052i \(-0.823297\pi\)
−0.849833 + 0.527052i \(0.823297\pi\)
\(240\) 0 0
\(241\) −0.113242 −0.00729456 −0.00364728 0.999993i \(-0.501161\pi\)
−0.00364728 + 0.999993i \(0.501161\pi\)
\(242\) 0 0
\(243\) 12.4188i 0.796665i
\(244\) 0 0
\(245\) 11.2820 + 9.44047i 0.720778 + 0.603130i
\(246\) 0 0
\(247\) −18.2882 + 18.2882i −1.16365 + 1.16365i
\(248\) 0 0
\(249\) −41.3258 −2.61892
\(250\) 0 0
\(251\) −19.2220 + 19.2220i −1.21328 + 1.21328i −0.243339 + 0.969941i \(0.578243\pi\)
−0.969941 + 0.243339i \(0.921757\pi\)
\(252\) 0 0
\(253\) 1.78045 0.111936
\(254\) 0 0
\(255\) 28.1417 2.50080i 1.76230 0.156606i
\(256\) 0 0
\(257\) −0.757800 + 0.757800i −0.0472703 + 0.0472703i −0.730347 0.683077i \(-0.760642\pi\)
0.683077 + 0.730347i \(0.260642\pi\)
\(258\) 0 0
\(259\) 2.68146 2.68146i 0.166618 0.166618i
\(260\) 0 0
\(261\) 19.7982 + 19.7982i 1.22548 + 1.22548i
\(262\) 0 0
\(263\) −5.73017 5.73017i −0.353338 0.353338i 0.508012 0.861350i \(-0.330380\pi\)
−0.861350 + 0.508012i \(0.830380\pi\)
\(264\) 0 0
\(265\) 4.72919 + 3.95728i 0.290512 + 0.243094i
\(266\) 0 0
\(267\) 9.56795i 0.585549i
\(268\) 0 0
\(269\) 9.78879 + 9.78879i 0.596833 + 0.596833i 0.939468 0.342635i \(-0.111320\pi\)
−0.342635 + 0.939468i \(0.611320\pi\)
\(270\) 0 0
\(271\) 4.10159i 0.249154i 0.992210 + 0.124577i \(0.0397574\pi\)
−0.992210 + 0.124577i \(0.960243\pi\)
\(272\) 0 0
\(273\) −5.92537 5.92537i −0.358620 0.358620i
\(274\) 0 0
\(275\) −2.85967 1.99075i −0.172444 0.120046i
\(276\) 0 0
\(277\) 24.6755 1.48261 0.741305 0.671169i \(-0.234207\pi\)
0.741305 + 0.671169i \(0.234207\pi\)
\(278\) 0 0
\(279\) 0.721688i 0.0432063i
\(280\) 0 0
\(281\) 23.6688i 1.41196i 0.708230 + 0.705981i \(0.249494\pi\)
−0.708230 + 0.705981i \(0.750506\pi\)
\(282\) 0 0
\(283\) −13.0492 −0.775694 −0.387847 0.921724i \(-0.626781\pi\)
−0.387847 + 0.921724i \(0.626781\pi\)
\(284\) 0 0
\(285\) 36.3897 3.23375i 2.15554 0.191551i
\(286\) 0 0
\(287\) −2.09094 2.09094i −0.123424 0.123424i
\(288\) 0 0
\(289\) 2.57168i 0.151275i
\(290\) 0 0
\(291\) 14.1539 + 14.1539i 0.829714 + 0.829714i
\(292\) 0 0
\(293\) 31.6731i 1.85036i −0.379526 0.925181i \(-0.623913\pi\)
0.379526 0.925181i \(-0.376087\pi\)
\(294\) 0 0
\(295\) 11.4189 1.01474i 0.664835 0.0590802i
\(296\) 0 0
\(297\) 3.03531 + 3.03531i 0.176127 + 0.176127i
\(298\) 0 0
\(299\) 8.16779 + 8.16779i 0.472355 + 0.472355i
\(300\) 0 0
\(301\) 3.44138 3.44138i 0.198358 0.198358i
\(302\) 0 0
\(303\) −5.27037 + 5.27037i −0.302775 + 0.302775i
\(304\) 0 0
\(305\) −1.04346 11.7421i −0.0597482 0.672351i
\(306\) 0 0
\(307\) 27.3597 1.56150 0.780751 0.624843i \(-0.214837\pi\)
0.780751 + 0.624843i \(0.214837\pi\)
\(308\) 0 0
\(309\) 33.3168 33.3168i 1.89532 1.89532i
\(310\) 0 0
\(311\) 15.8076 0.896368 0.448184 0.893941i \(-0.352071\pi\)
0.448184 + 0.893941i \(0.352071\pi\)
\(312\) 0 0
\(313\) −13.8388 + 13.8388i −0.782217 + 0.782217i −0.980205 0.197988i \(-0.936559\pi\)
0.197988 + 0.980205i \(0.436559\pi\)
\(314\) 0 0
\(315\) 0.662387 + 7.45390i 0.0373213 + 0.419980i
\(316\) 0 0
\(317\) 35.0092i 1.96631i 0.182766 + 0.983156i \(0.441495\pi\)
−0.182766 + 0.983156i \(0.558505\pi\)
\(318\) 0 0
\(319\) −3.78369 −0.211846
\(320\) 0 0
\(321\) −43.7272 −2.44062
\(322\) 0 0
\(323\) 25.3079i 1.40817i
\(324\) 0 0
\(325\) −3.98617 22.2512i −0.221113 1.23428i
\(326\) 0 0
\(327\) 35.6424 35.6424i 1.97103 1.97103i
\(328\) 0 0
\(329\) 3.80032 0.209518
\(330\) 0 0
\(331\) −16.8212 + 16.8212i −0.924578 + 0.924578i −0.997349 0.0727709i \(-0.976816\pi\)
0.0727709 + 0.997349i \(0.476816\pi\)
\(332\) 0 0
\(333\) −30.1326 −1.65126
\(334\) 0 0
\(335\) −4.77384 + 5.70504i −0.260823 + 0.311700i
\(336\) 0 0
\(337\) 14.4984 14.4984i 0.789777 0.789777i −0.191680 0.981457i \(-0.561394\pi\)
0.981457 + 0.191680i \(0.0613937\pi\)
\(338\) 0 0
\(339\) 7.24160 7.24160i 0.393310 0.393310i
\(340\) 0 0
\(341\) 0.0689618 + 0.0689618i 0.00373449 + 0.00373449i
\(342\) 0 0
\(343\) 6.23125 + 6.23125i 0.336456 + 0.336456i
\(344\) 0 0
\(345\) −1.44424 16.2522i −0.0777555 0.874989i
\(346\) 0 0
\(347\) 16.7705i 0.900286i −0.892956 0.450143i \(-0.851373\pi\)
0.892956 0.450143i \(-0.148627\pi\)
\(348\) 0 0
\(349\) 1.86337 + 1.86337i 0.0997439 + 0.0997439i 0.755218 0.655474i \(-0.227531\pi\)
−0.655474 + 0.755218i \(0.727531\pi\)
\(350\) 0 0
\(351\) 27.8489i 1.48647i
\(352\) 0 0
\(353\) 24.1362 + 24.1362i 1.28464 + 1.28464i 0.937998 + 0.346642i \(0.112678\pi\)
0.346642 + 0.937998i \(0.387322\pi\)
\(354\) 0 0
\(355\) −1.96672 + 2.35035i −0.104382 + 0.124744i
\(356\) 0 0
\(357\) 8.19976 0.433978
\(358\) 0 0
\(359\) 12.2500i 0.646532i 0.946308 + 0.323266i \(0.104781\pi\)
−0.946308 + 0.323266i \(0.895219\pi\)
\(360\) 0 0
\(361\) 13.7253i 0.722386i
\(362\) 0 0
\(363\) 30.0291 1.57612
\(364\) 0 0
\(365\) 0.713853 + 8.03305i 0.0373648 + 0.420469i
\(366\) 0 0
\(367\) −2.71307 2.71307i −0.141621 0.141621i 0.632742 0.774363i \(-0.281929\pi\)
−0.774363 + 0.632742i \(0.781929\pi\)
\(368\) 0 0
\(369\) 23.4967i 1.22319i
\(370\) 0 0
\(371\) 1.26551 + 1.26551i 0.0657018 + 0.0657018i
\(372\) 0 0
\(373\) 16.4846i 0.853541i 0.904360 + 0.426771i \(0.140349\pi\)
−0.904360 + 0.426771i \(0.859651\pi\)
\(374\) 0 0
\(375\) −15.8522 + 27.7183i −0.818603 + 1.43137i
\(376\) 0 0
\(377\) −17.3576 17.3576i −0.893964 0.893964i
\(378\) 0 0
\(379\) 13.7716 + 13.7716i 0.707401 + 0.707401i 0.965988 0.258587i \(-0.0832568\pi\)
−0.258587 + 0.965988i \(0.583257\pi\)
\(380\) 0 0
\(381\) 1.75870 1.75870i 0.0901011 0.0901011i
\(382\) 0 0
\(383\) −11.5530 + 11.5530i −0.590332 + 0.590332i −0.937721 0.347389i \(-0.887068\pi\)
0.347389 + 0.937721i \(0.387068\pi\)
\(384\) 0 0
\(385\) −0.775562 0.648972i −0.0395263 0.0330747i
\(386\) 0 0
\(387\) −38.6722 −1.96582
\(388\) 0 0
\(389\) −15.7728 + 15.7728i −0.799712 + 0.799712i −0.983050 0.183338i \(-0.941310\pi\)
0.183338 + 0.983050i \(0.441310\pi\)
\(390\) 0 0
\(391\) −11.3029 −0.571612
\(392\) 0 0
\(393\) −27.2867 + 27.2867i −1.37643 + 1.37643i
\(394\) 0 0
\(395\) 5.54512 6.62677i 0.279006 0.333429i
\(396\) 0 0
\(397\) 29.9558i 1.50344i −0.659483 0.751720i \(-0.729225\pi\)
0.659483 0.751720i \(-0.270775\pi\)
\(398\) 0 0
\(399\) 10.6030 0.530815
\(400\) 0 0
\(401\) 19.9241 0.994963 0.497481 0.867475i \(-0.334258\pi\)
0.497481 + 0.867475i \(0.334258\pi\)
\(402\) 0 0
\(403\) 0.632724i 0.0315182i
\(404\) 0 0
\(405\) 3.04508 3.63906i 0.151311 0.180826i
\(406\) 0 0
\(407\) 2.87936 2.87936i 0.142725 0.142725i
\(408\) 0 0
\(409\) 5.89856 0.291665 0.145832 0.989309i \(-0.453414\pi\)
0.145832 + 0.989309i \(0.453414\pi\)
\(410\) 0 0
\(411\) −10.5751 + 10.5751i −0.521634 + 0.521634i
\(412\) 0 0
\(413\) 3.32717 0.163720
\(414\) 0 0
\(415\) −24.8141 20.7638i −1.21808 1.01926i
\(416\) 0 0
\(417\) −15.6155 + 15.6155i −0.764696 + 0.764696i
\(418\) 0 0
\(419\) −8.24430 + 8.24430i −0.402760 + 0.402760i −0.879205 0.476444i \(-0.841925\pi\)
0.476444 + 0.879205i \(0.341925\pi\)
\(420\) 0 0
\(421\) −17.1776 17.1776i −0.837184 0.837184i 0.151304 0.988487i \(-0.451653\pi\)
−0.988487 + 0.151304i \(0.951653\pi\)
\(422\) 0 0
\(423\) −21.3528 21.3528i −1.03821 1.03821i
\(424\) 0 0
\(425\) 18.1542 + 12.6380i 0.880607 + 0.613031i
\(426\) 0 0
\(427\) 3.42135i 0.165571i
\(428\) 0 0
\(429\) −6.36269 6.36269i −0.307194 0.307194i
\(430\) 0 0
\(431\) 32.1769i 1.54990i −0.632020 0.774952i \(-0.717774\pi\)
0.632020 0.774952i \(-0.282226\pi\)
\(432\) 0 0
\(433\) −20.3383 20.3383i −0.977396 0.977396i 0.0223540 0.999750i \(-0.492884\pi\)
−0.999750 + 0.0223540i \(0.992884\pi\)
\(434\) 0 0
\(435\) 3.06921 + 34.5381i 0.147158 + 1.65598i
\(436\) 0 0
\(437\) −14.6156 −0.699161
\(438\) 0 0
\(439\) 35.4180i 1.69041i −0.534444 0.845204i \(-0.679479\pi\)
0.534444 0.845204i \(-0.320521\pi\)
\(440\) 0 0
\(441\) 33.9256i 1.61550i
\(442\) 0 0
\(443\) 3.03787 0.144333 0.0721667 0.997393i \(-0.477009\pi\)
0.0721667 + 0.997393i \(0.477009\pi\)
\(444\) 0 0
\(445\) −4.80733 + 5.74507i −0.227890 + 0.272342i
\(446\) 0 0
\(447\) −12.0398 12.0398i −0.569463 0.569463i
\(448\) 0 0
\(449\) 8.65559i 0.408483i 0.978921 + 0.204241i \(0.0654727\pi\)
−0.978921 + 0.204241i \(0.934527\pi\)
\(450\) 0 0
\(451\) −2.24526 2.24526i −0.105725 0.105725i
\(452\) 0 0
\(453\) 35.5335i 1.66951i
\(454\) 0 0
\(455\) −0.580733 6.53504i −0.0272252 0.306367i
\(456\) 0 0
\(457\) −13.5575 13.5575i −0.634193 0.634193i 0.314924 0.949117i \(-0.398021\pi\)
−0.949117 + 0.314924i \(0.898021\pi\)
\(458\) 0 0
\(459\) −19.2692 19.2692i −0.899411 0.899411i
\(460\) 0 0
\(461\) −1.19682 + 1.19682i −0.0557416 + 0.0557416i −0.734428 0.678687i \(-0.762550\pi\)
0.678687 + 0.734428i \(0.262550\pi\)
\(462\) 0 0
\(463\) 21.1815 21.1815i 0.984390 0.984390i −0.0154904 0.999880i \(-0.504931\pi\)
0.999880 + 0.0154904i \(0.00493096\pi\)
\(464\) 0 0
\(465\) 0.573555 0.685435i 0.0265980 0.0317863i
\(466\) 0 0
\(467\) −24.8448 −1.14968 −0.574840 0.818266i \(-0.694936\pi\)
−0.574840 + 0.818266i \(0.694936\pi\)
\(468\) 0 0
\(469\) −1.52664 + 1.52664i −0.0704936 + 0.0704936i
\(470\) 0 0
\(471\) −21.4343 −0.987642
\(472\) 0 0
\(473\) 3.69537 3.69537i 0.169913 0.169913i
\(474\) 0 0
\(475\) 23.4749 + 16.3420i 1.07710 + 0.749822i
\(476\) 0 0
\(477\) 14.2210i 0.651135i
\(478\) 0 0
\(479\) 23.5766 1.07724 0.538621 0.842548i \(-0.318946\pi\)
0.538621 + 0.842548i \(0.318946\pi\)
\(480\) 0 0
\(481\) 26.4181 1.20456
\(482\) 0 0
\(483\) 4.73547i 0.215471i
\(484\) 0 0
\(485\) 1.38719 + 15.6102i 0.0629891 + 0.708821i
\(486\) 0 0
\(487\) 2.63011 2.63011i 0.119182 0.119182i −0.645001 0.764182i \(-0.723143\pi\)
0.764182 + 0.645001i \(0.223143\pi\)
\(488\) 0 0
\(489\) 67.7686 3.06460
\(490\) 0 0
\(491\) 18.6899 18.6899i 0.843465 0.843465i −0.145843 0.989308i \(-0.546589\pi\)
0.989308 + 0.145843i \(0.0465894\pi\)
\(492\) 0 0
\(493\) 24.0202 1.08182
\(494\) 0 0
\(495\) 0.711274 + 8.00403i 0.0319694 + 0.359754i
\(496\) 0 0
\(497\) −0.628940 + 0.628940i −0.0282118 + 0.0282118i
\(498\) 0 0
\(499\) 9.69342 9.69342i 0.433937 0.433937i −0.456028 0.889965i \(-0.650728\pi\)
0.889965 + 0.456028i \(0.150728\pi\)
\(500\) 0 0
\(501\) −1.15090 1.15090i −0.0514185 0.0514185i
\(502\) 0 0
\(503\) 13.0434 + 13.0434i 0.581577 + 0.581577i 0.935336 0.353759i \(-0.115097\pi\)
−0.353759 + 0.935336i \(0.615097\pi\)
\(504\) 0 0
\(505\) −5.81265 + 0.516538i −0.258659 + 0.0229856i
\(506\) 0 0
\(507\) 21.2495i 0.943724i
\(508\) 0 0
\(509\) −25.8539 25.8539i −1.14595 1.14595i −0.987341 0.158611i \(-0.949298\pi\)
−0.158611 0.987341i \(-0.550702\pi\)
\(510\) 0 0
\(511\) 2.34062i 0.103543i
\(512\) 0 0
\(513\) −24.9168 24.9168i −1.10010 1.10010i
\(514\) 0 0
\(515\) 36.7448 3.26531i 1.61917 0.143887i
\(516\) 0 0
\(517\) 4.08080 0.179473
\(518\) 0 0
\(519\) 44.1252i 1.93688i
\(520\) 0 0
\(521\) 25.0528i 1.09758i −0.835959 0.548792i \(-0.815088\pi\)
0.835959 0.548792i \(-0.184912\pi\)
\(522\) 0 0
\(523\) −40.3434 −1.76410 −0.882048 0.471160i \(-0.843835\pi\)
−0.882048 + 0.471160i \(0.843835\pi\)
\(524\) 0 0
\(525\) −5.29481 + 7.60588i −0.231084 + 0.331948i
\(526\) 0 0
\(527\) −0.437794 0.437794i −0.0190706 0.0190706i
\(528\) 0 0
\(529\) 16.4724i 0.716192i
\(530\) 0 0
\(531\) −18.6944 18.6944i −0.811267 0.811267i
\(532\) 0 0
\(533\) 20.6003i 0.892296i
\(534\) 0 0
\(535\) −26.2560 21.9704i −1.13515 0.949862i
\(536\) 0 0
\(537\) 14.8639 + 14.8639i 0.641425 + 0.641425i
\(538\) 0 0
\(539\) 3.24180 + 3.24180i 0.139634 + 0.139634i
\(540\) 0 0
\(541\) −24.7446 + 24.7446i −1.06385 + 1.06385i −0.0660360 + 0.997817i \(0.521035\pi\)
−0.997817 + 0.0660360i \(0.978965\pi\)
\(542\) 0 0
\(543\) −25.9590 + 25.9590i −1.11401 + 1.11401i
\(544\) 0 0
\(545\) 39.3097 3.49324i 1.68384 0.149634i
\(546\) 0 0
\(547\) −19.0254 −0.813465 −0.406733 0.913547i \(-0.633332\pi\)
−0.406733 + 0.913547i \(0.633332\pi\)
\(548\) 0 0
\(549\) −19.2235 + 19.2235i −0.820440 + 0.820440i
\(550\) 0 0
\(551\) 31.0602 1.32321
\(552\) 0 0
\(553\) 1.77329 1.77329i 0.0754079 0.0754079i
\(554\) 0 0
\(555\) −28.6189 23.9476i −1.21481 1.01652i
\(556\) 0 0
\(557\) 30.9517i 1.31146i −0.754993 0.655732i \(-0.772360\pi\)
0.754993 0.655732i \(-0.227640\pi\)
\(558\) 0 0
\(559\) 33.9050 1.43403
\(560\) 0 0
\(561\) 8.80494 0.371745
\(562\) 0 0
\(563\) 3.50238i 0.147608i −0.997273 0.0738039i \(-0.976486\pi\)
0.997273 0.0738039i \(-0.0235139\pi\)
\(564\) 0 0
\(565\) 7.98670 0.709734i 0.336003 0.0298587i
\(566\) 0 0
\(567\) 0.973793 0.973793i 0.0408955 0.0408955i
\(568\) 0 0
\(569\) −0.525780 −0.0220418 −0.0110209 0.999939i \(-0.503508\pi\)
−0.0110209 + 0.999939i \(0.503508\pi\)
\(570\) 0 0
\(571\) 11.2487 11.2487i 0.470743 0.470743i −0.431412 0.902155i \(-0.641984\pi\)
0.902155 + 0.431412i \(0.141984\pi\)
\(572\) 0 0
\(573\) 43.1472 1.80250
\(574\) 0 0
\(575\) 7.29859 10.4843i 0.304372 0.437224i
\(576\) 0 0
\(577\) −2.92884 + 2.92884i −0.121929 + 0.121929i −0.765438 0.643509i \(-0.777478\pi\)
0.643509 + 0.765438i \(0.277478\pi\)
\(578\) 0 0
\(579\) 11.9714 11.9714i 0.497515 0.497515i
\(580\) 0 0
\(581\) −6.64011 6.64011i −0.275478 0.275478i
\(582\) 0 0
\(583\) 1.35891 + 1.35891i 0.0562801 + 0.0562801i
\(584\) 0 0
\(585\) −33.4555 + 39.9814i −1.38321 + 1.65303i
\(586\) 0 0
\(587\) 23.1574i 0.955809i 0.878412 + 0.477905i \(0.158604\pi\)
−0.878412 + 0.477905i \(0.841396\pi\)
\(588\) 0 0
\(589\) −0.566106 0.566106i −0.0233260 0.0233260i
\(590\) 0 0
\(591\) 11.5150i 0.473662i
\(592\) 0 0
\(593\) −13.9325 13.9325i −0.572141 0.572141i 0.360585 0.932726i \(-0.382577\pi\)
−0.932726 + 0.360585i \(0.882577\pi\)
\(594\) 0 0
\(595\) 4.92354 + 4.11990i 0.201846 + 0.168900i
\(596\) 0 0
\(597\) −15.5097 −0.634769
\(598\) 0 0
\(599\) 33.5311i 1.37004i 0.728523 + 0.685021i \(0.240207\pi\)
−0.728523 + 0.685021i \(0.759793\pi\)
\(600\) 0 0
\(601\) 19.4164i 0.792011i 0.918248 + 0.396005i \(0.129604\pi\)
−0.918248 + 0.396005i \(0.870396\pi\)
\(602\) 0 0
\(603\) 17.1554 0.698623
\(604\) 0 0
\(605\) 18.0310 + 15.0879i 0.733063 + 0.613409i
\(606\) 0 0
\(607\) 9.51495 + 9.51495i 0.386200 + 0.386200i 0.873330 0.487130i \(-0.161956\pi\)
−0.487130 + 0.873330i \(0.661956\pi\)
\(608\) 0 0
\(609\) 10.0635i 0.407794i
\(610\) 0 0
\(611\) 18.7206 + 18.7206i 0.757355 + 0.757355i
\(612\) 0 0
\(613\) 9.37947i 0.378833i −0.981897 0.189417i \(-0.939340\pi\)
0.981897 0.189417i \(-0.0606597\pi\)
\(614\) 0 0
\(615\) −18.6738 + 22.3164i −0.753002 + 0.899884i
\(616\) 0 0
\(617\) −3.54768 3.54768i −0.142824 0.142824i 0.632079 0.774904i \(-0.282202\pi\)
−0.774904 + 0.632079i \(0.782202\pi\)
\(618\) 0 0
\(619\) −24.6158 24.6158i −0.989392 0.989392i 0.0105527 0.999944i \(-0.496641\pi\)
−0.999944 + 0.0105527i \(0.996641\pi\)
\(620\) 0 0
\(621\) −11.1282 + 11.1282i −0.446561 + 0.446561i
\(622\) 0 0
\(623\) −1.53735 + 1.53735i −0.0615926 + 0.0615926i
\(624\) 0 0
\(625\) −23.4453 + 8.67867i −0.937811 + 0.347147i
\(626\) 0 0
\(627\) 11.3856 0.454695
\(628\) 0 0
\(629\) −18.2792 + 18.2792i −0.728840 + 0.728840i
\(630\) 0 0
\(631\) 28.8921 1.15018 0.575088 0.818092i \(-0.304968\pi\)
0.575088 + 0.818092i \(0.304968\pi\)
\(632\) 0 0
\(633\) −9.22547 + 9.22547i −0.366679 + 0.366679i
\(634\) 0 0
\(635\) 1.93966 0.172367i 0.0769729 0.00684016i
\(636\) 0 0
\(637\) 29.7435i 1.17848i
\(638\) 0 0
\(639\) 7.06765 0.279592
\(640\) 0 0
\(641\) −16.6914 −0.659271 −0.329636 0.944108i \(-0.606926\pi\)
−0.329636 + 0.944108i \(0.606926\pi\)
\(642\) 0 0
\(643\) 5.22468i 0.206041i 0.994679 + 0.103021i \(0.0328507\pi\)
−0.994679 + 0.103021i \(0.967149\pi\)
\(644\) 0 0
\(645\) −36.7295 30.7343i −1.44622 1.21016i
\(646\) 0 0
\(647\) −21.6797 + 21.6797i −0.852318 + 0.852318i −0.990418 0.138100i \(-0.955900\pi\)
0.138100 + 0.990418i \(0.455900\pi\)
\(648\) 0 0
\(649\) 3.57273 0.140242
\(650\) 0 0
\(651\) 0.183418 0.183418i 0.00718874 0.00718874i
\(652\) 0 0
\(653\) 22.7642 0.890833 0.445417 0.895323i \(-0.353056\pi\)
0.445417 + 0.895323i \(0.353056\pi\)
\(654\) 0 0
\(655\) −30.0942 + 2.67431i −1.17588 + 0.104494i
\(656\) 0 0
\(657\) 13.1513 13.1513i 0.513079 0.513079i
\(658\) 0 0
\(659\) 1.66201 1.66201i 0.0647427 0.0647427i −0.673994 0.738737i \(-0.735423\pi\)
0.738737 + 0.673994i \(0.235423\pi\)
\(660\) 0 0
\(661\) −5.62818 5.62818i −0.218911 0.218911i 0.589129 0.808039i \(-0.299471\pi\)
−0.808039 + 0.589129i \(0.799471\pi\)
\(662\) 0 0
\(663\) 40.3926 + 40.3926i 1.56872 + 1.56872i
\(664\) 0 0
\(665\) 6.36657 + 5.32739i 0.246885 + 0.206587i
\(666\) 0 0
\(667\) 13.8720i 0.537125i
\(668\) 0 0
\(669\) −23.3427 23.3427i −0.902481 0.902481i
\(670\) 0 0
\(671\) 3.67386i 0.141828i
\(672\) 0 0
\(673\) 0.278251 + 0.278251i 0.0107258 + 0.0107258i 0.712449 0.701724i \(-0.247586\pi\)
−0.701724 + 0.712449i \(0.747586\pi\)
\(674\) 0 0
\(675\) 30.3163 5.43097i 1.16687 0.209038i
\(676\) 0 0
\(677\) 26.3591 1.01306 0.506531 0.862222i \(-0.330928\pi\)
0.506531 + 0.862222i \(0.330928\pi\)
\(678\) 0 0
\(679\) 4.54840i 0.174551i
\(680\) 0 0
\(681\) 4.40019i 0.168616i
\(682\) 0 0
\(683\) 2.83023 0.108296 0.0541479 0.998533i \(-0.482756\pi\)
0.0541479 + 0.998533i \(0.482756\pi\)
\(684\) 0 0
\(685\) −11.6632 + 1.03645i −0.445629 + 0.0396006i
\(686\) 0 0
\(687\) 50.1646 + 50.1646i 1.91390 + 1.91390i
\(688\) 0 0
\(689\) 12.4679i 0.474991i
\(690\) 0 0
\(691\) −22.1815 22.1815i −0.843825 0.843825i 0.145529 0.989354i \(-0.453512\pi\)
−0.989354 + 0.145529i \(0.953512\pi\)
\(692\) 0 0
\(693\) 2.33217i 0.0885917i
\(694\) 0 0
\(695\) −17.2222 + 1.53044i −0.653276 + 0.0580531i
\(696\) 0 0
\(697\) 14.2537 + 14.2537i 0.539898 + 0.539898i
\(698\) 0 0
\(699\) −28.5320 28.5320i −1.07918 1.07918i
\(700\) 0 0
\(701\) 16.2264 16.2264i 0.612864 0.612864i −0.330828 0.943691i \(-0.607328\pi\)
0.943691 + 0.330828i \(0.107328\pi\)
\(702\) 0 0
\(703\) −23.6366 + 23.6366i −0.891472 + 0.891472i
\(704\) 0 0
\(705\) −3.31022 37.2502i −0.124670 1.40292i
\(706\) 0 0
\(707\) −1.69365 −0.0636965
\(708\) 0 0
\(709\) 25.3577 25.3577i 0.952329 0.952329i −0.0465856 0.998914i \(-0.514834\pi\)
0.998914 + 0.0465856i \(0.0148340\pi\)
\(710\) 0 0
\(711\) −19.9271 −0.747326
\(712\) 0 0
\(713\) −0.252832 + 0.252832i −0.00946863 + 0.00946863i
\(714\) 0 0
\(715\) −0.623594 7.01735i −0.0233211 0.262434i
\(716\) 0 0
\(717\) 75.0450i 2.80261i
\(718\) 0 0
\(719\) −41.3374 −1.54163 −0.770813 0.637061i \(-0.780150\pi\)
−0.770813 + 0.637061i \(0.780150\pi\)
\(720\) 0 0
\(721\) 10.7065 0.398730
\(722\) 0 0
\(723\) 0.323420i 0.0120281i
\(724\) 0 0
\(725\) −15.5105 + 22.2805i −0.576045 + 0.827477i
\(726\) 0 0
\(727\) 23.4630 23.4630i 0.870193 0.870193i −0.122300 0.992493i \(-0.539027\pi\)
0.992493 + 0.122300i \(0.0390271\pi\)
\(728\) 0 0
\(729\) 41.8342 1.54942
\(730\) 0 0
\(731\) −23.4595 + 23.4595i −0.867681 + 0.867681i
\(732\) 0 0
\(733\) −15.1628 −0.560051 −0.280025 0.959993i \(-0.590343\pi\)
−0.280025 + 0.959993i \(0.590343\pi\)
\(734\) 0 0
\(735\) 26.9621 32.2214i 0.994511 1.18850i
\(736\) 0 0
\(737\) −1.63931 + 1.63931i −0.0603848 + 0.0603848i
\(738\) 0 0
\(739\) 0.974343 0.974343i 0.0358418 0.0358418i −0.688959 0.724801i \(-0.741932\pi\)
0.724801 + 0.688959i \(0.241932\pi\)
\(740\) 0 0
\(741\) 52.2312 + 52.2312i 1.91876 + 1.91876i
\(742\) 0 0
\(743\) −29.0897 29.0897i −1.06720 1.06720i −0.997573 0.0696259i \(-0.977819\pi\)
−0.0696259 0.997573i \(-0.522181\pi\)
\(744\) 0 0
\(745\) −1.18000 13.2786i −0.0432317 0.486490i
\(746\) 0 0
\(747\) 74.6176i 2.73011i
\(748\) 0 0
\(749\) −7.02596 7.02596i −0.256723 0.256723i
\(750\) 0 0
\(751\) 7.77705i 0.283789i −0.989882 0.141894i \(-0.954681\pi\)
0.989882 0.141894i \(-0.0453193\pi\)
\(752\) 0 0
\(753\) 54.8981 + 54.8981i 2.00060 + 2.00060i
\(754\) 0 0
\(755\) −17.8535 + 21.3361i −0.649755 + 0.776498i
\(756\) 0 0
\(757\) 1.42073 0.0516372 0.0258186 0.999667i \(-0.491781\pi\)
0.0258186 + 0.999667i \(0.491781\pi\)
\(758\) 0 0
\(759\) 5.08497i 0.184573i
\(760\) 0 0
\(761\) 26.6737i 0.966921i 0.875366 + 0.483460i \(0.160620\pi\)
−0.875366 + 0.483460i \(0.839380\pi\)
\(762\) 0 0
\(763\) 11.4538 0.414656
\(764\) 0 0
\(765\) −4.51542 50.8124i −0.163255 1.83713i
\(766\) 0 0
\(767\) 16.3899 + 16.3899i 0.591805 + 0.591805i
\(768\) 0 0
\(769\) 45.8210i 1.65235i −0.563415 0.826174i \(-0.690513\pi\)
0.563415 0.826174i \(-0.309487\pi\)
\(770\) 0 0
\(771\) 2.16428 + 2.16428i 0.0779447 + 0.0779447i
\(772\) 0 0
\(773\) 18.5473i 0.667101i −0.942732 0.333550i \(-0.891753\pi\)
0.942732 0.333550i \(-0.108247\pi\)
\(774\) 0 0
\(775\) 0.688782 0.123391i 0.0247418 0.00443233i
\(776\) 0 0
\(777\) −7.65827 7.65827i −0.274739 0.274739i
\(778\) 0 0
\(779\) 18.4313 + 18.4313i 0.660370 + 0.660370i
\(780\) 0 0
\(781\) −0.675359 + 0.675359i −0.0241662 + 0.0241662i
\(782\) 0 0
\(783\) 23.6490 23.6490i 0.845146 0.845146i
\(784\) 0 0
\(785\) −12.8702 10.7695i −0.459358 0.384380i
\(786\) 0 0
\(787\) 21.3016 0.759319 0.379659 0.925126i \(-0.376041\pi\)
0.379659 + 0.925126i \(0.376041\pi\)
\(788\) 0 0
\(789\) −16.3654 + 16.3654i −0.582624 + 0.582624i
\(790\) 0 0
\(791\) 2.32712 0.0827427
\(792\) 0 0
\(793\) 16.8538 16.8538i 0.598496 0.598496i
\(794\) 0 0
\(795\) 11.3020 13.5066i 0.400841 0.479030i
\(796\) 0 0
\(797\) 2.35457i 0.0834033i 0.999130 + 0.0417016i \(0.0132779\pi\)
−0.999130 + 0.0417016i \(0.986722\pi\)