Properties

Label 1815.2.c.d.364.4
Level $1815$
Weight $2$
Character 1815.364
Analytic conductor $14.493$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.4928479669\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 364.4
Root \(1.45161 - 1.45161i\) of defining polynomial
Character \(\chi\) \(=\) 1815.364
Dual form 1815.2.c.d.364.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.21432i q^{2} +1.00000i q^{3} +0.525428 q^{4} +(0.311108 + 2.21432i) q^{5} -1.21432 q^{6} -4.90321i q^{7} +3.06668i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.21432i q^{2} +1.00000i q^{3} +0.525428 q^{4} +(0.311108 + 2.21432i) q^{5} -1.21432 q^{6} -4.90321i q^{7} +3.06668i q^{8} -1.00000 q^{9} +(-2.68889 + 0.377784i) q^{10} +0.525428i q^{12} +4.14764i q^{13} +5.95407 q^{14} +(-2.21432 + 0.311108i) q^{15} -2.67307 q^{16} +5.33185i q^{17} -1.21432i q^{18} -5.18421 q^{19} +(0.163465 + 1.16346i) q^{20} +4.90321 q^{21} -4.00000i q^{23} -3.06668 q^{24} +(-4.80642 + 1.37778i) q^{25} -5.03657 q^{26} -1.00000i q^{27} -2.57628i q^{28} +1.80642 q^{29} +(-0.377784 - 2.68889i) q^{30} +2.62222 q^{31} +2.88739i q^{32} -6.47457 q^{34} +(10.8573 - 1.52543i) q^{35} -0.525428 q^{36} +5.80642i q^{37} -6.29529i q^{38} -4.14764 q^{39} +(-6.79060 + 0.954067i) q^{40} -1.80642 q^{41} +5.95407i q^{42} +4.90321i q^{43} +(-0.311108 - 2.21432i) q^{45} +4.85728 q^{46} +7.05086i q^{47} -2.67307i q^{48} -17.0415 q^{49} +(-1.67307 - 5.83654i) q^{50} -5.33185 q^{51} +2.17929i q^{52} +7.18421i q^{53} +1.21432 q^{54} +15.0366 q^{56} -5.18421i q^{57} +2.19358i q^{58} -1.67307 q^{59} +(-1.16346 + 0.163465i) q^{60} -0.755569 q^{61} +3.18421i q^{62} +4.90321i q^{63} -8.85236 q^{64} +(-9.18421 + 1.29036i) q^{65} -4.85728i q^{67} +2.80150i q^{68} +4.00000 q^{69} +(1.85236 + 13.1842i) q^{70} +0.428639 q^{71} -3.06668i q^{72} +12.7096i q^{73} -7.05086 q^{74} +(-1.37778 - 4.80642i) q^{75} -2.72393 q^{76} -5.03657i q^{78} -6.42864 q^{79} +(-0.831613 - 5.91903i) q^{80} +1.00000 q^{81} -2.19358i q^{82} -2.90321i q^{83} +2.57628 q^{84} +(-11.8064 + 1.65878i) q^{85} -5.95407 q^{86} +1.80642i q^{87} -0.622216 q^{89} +(2.68889 - 0.377784i) q^{90} +20.3368 q^{91} -2.10171i q^{92} +2.62222i q^{93} -8.56199 q^{94} +(-1.61285 - 11.4795i) q^{95} -2.88739 q^{96} -2.75557i q^{97} -20.6938i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 10 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 10 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9} - 16 q^{10} - 4 q^{14} + 10 q^{16} - 4 q^{19} + 14 q^{20} + 16 q^{21} - 18 q^{24} - 2 q^{25} - 16 q^{26} - 16 q^{29} - 2 q^{30} + 16 q^{31} - 52 q^{34} + 12 q^{35} + 10 q^{36} - 12 q^{39} + 12 q^{40} + 16 q^{41} - 2 q^{45} - 24 q^{46} - 22 q^{49} + 16 q^{50} + 8 q^{51} - 6 q^{54} + 76 q^{56} + 16 q^{59} - 20 q^{60} - 4 q^{61} - 66 q^{64} - 28 q^{65} + 24 q^{69} + 24 q^{70} - 24 q^{71} - 16 q^{74} - 8 q^{75} + 36 q^{76} - 12 q^{79} - 58 q^{80} + 6 q^{81} - 24 q^{84} - 44 q^{85} + 4 q^{86} - 4 q^{89} + 16 q^{90} + 16 q^{91} - 24 q^{94} + 44 q^{95} + 22 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).

\(n\) \(727\) \(1211\) \(1696\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.21432i 0.858654i 0.903149 + 0.429327i \(0.141249\pi\)
−0.903149 + 0.429327i \(0.858751\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 0.525428 0.262714
\(5\) 0.311108 + 2.21432i 0.139132 + 0.990274i
\(6\) −1.21432 −0.495744
\(7\) 4.90321i 1.85324i −0.375999 0.926620i \(-0.622700\pi\)
0.375999 0.926620i \(-0.377300\pi\)
\(8\) 3.06668i 1.08423i
\(9\) −1.00000 −0.333333
\(10\) −2.68889 + 0.377784i −0.850302 + 0.119466i
\(11\) 0 0
\(12\) 0.525428i 0.151678i
\(13\) 4.14764i 1.15035i 0.818031 + 0.575175i \(0.195066\pi\)
−0.818031 + 0.575175i \(0.804934\pi\)
\(14\) 5.95407 1.59129
\(15\) −2.21432 + 0.311108i −0.571735 + 0.0803277i
\(16\) −2.67307 −0.668268
\(17\) 5.33185i 1.29316i 0.762845 + 0.646582i \(0.223802\pi\)
−0.762845 + 0.646582i \(0.776198\pi\)
\(18\) 1.21432i 0.286218i
\(19\) −5.18421 −1.18934 −0.594669 0.803970i \(-0.702717\pi\)
−0.594669 + 0.803970i \(0.702717\pi\)
\(20\) 0.163465 + 1.16346i 0.0365518 + 0.260159i
\(21\) 4.90321 1.06997
\(22\) 0 0
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) −3.06668 −0.625983
\(25\) −4.80642 + 1.37778i −0.961285 + 0.275557i
\(26\) −5.03657 −0.987752
\(27\) 1.00000i 0.192450i
\(28\) 2.57628i 0.486872i
\(29\) 1.80642 0.335444 0.167722 0.985834i \(-0.446359\pi\)
0.167722 + 0.985834i \(0.446359\pi\)
\(30\) −0.377784 2.68889i −0.0689737 0.490922i
\(31\) 2.62222 0.470964 0.235482 0.971879i \(-0.424333\pi\)
0.235482 + 0.971879i \(0.424333\pi\)
\(32\) 2.88739i 0.510423i
\(33\) 0 0
\(34\) −6.47457 −1.11038
\(35\) 10.8573 1.52543i 1.83522 0.257844i
\(36\) −0.525428 −0.0875713
\(37\) 5.80642i 0.954570i 0.878749 + 0.477285i \(0.158379\pi\)
−0.878749 + 0.477285i \(0.841621\pi\)
\(38\) 6.29529i 1.02123i
\(39\) −4.14764 −0.664154
\(40\) −6.79060 + 0.954067i −1.07369 + 0.150851i
\(41\) −1.80642 −0.282116 −0.141058 0.990001i \(-0.545050\pi\)
−0.141058 + 0.990001i \(0.545050\pi\)
\(42\) 5.95407i 0.918732i
\(43\) 4.90321i 0.747733i 0.927483 + 0.373866i \(0.121968\pi\)
−0.927483 + 0.373866i \(0.878032\pi\)
\(44\) 0 0
\(45\) −0.311108 2.21432i −0.0463772 0.330091i
\(46\) 4.85728 0.716167
\(47\) 7.05086i 1.02847i 0.857648 + 0.514236i \(0.171925\pi\)
−0.857648 + 0.514236i \(0.828075\pi\)
\(48\) 2.67307i 0.385825i
\(49\) −17.0415 −2.43450
\(50\) −1.67307 5.83654i −0.236608 0.825411i
\(51\) −5.33185 −0.746609
\(52\) 2.17929i 0.302213i
\(53\) 7.18421i 0.986827i 0.869795 + 0.493413i \(0.164251\pi\)
−0.869795 + 0.493413i \(0.835749\pi\)
\(54\) 1.21432 0.165248
\(55\) 0 0
\(56\) 15.0366 2.00935
\(57\) 5.18421i 0.686665i
\(58\) 2.19358i 0.288031i
\(59\) −1.67307 −0.217815 −0.108908 0.994052i \(-0.534735\pi\)
−0.108908 + 0.994052i \(0.534735\pi\)
\(60\) −1.16346 + 0.163465i −0.150203 + 0.0211032i
\(61\) −0.755569 −0.0967407 −0.0483703 0.998829i \(-0.515403\pi\)
−0.0483703 + 0.998829i \(0.515403\pi\)
\(62\) 3.18421i 0.404395i
\(63\) 4.90321i 0.617747i
\(64\) −8.85236 −1.10654
\(65\) −9.18421 + 1.29036i −1.13916 + 0.160050i
\(66\) 0 0
\(67\) 4.85728i 0.593411i −0.954969 0.296706i \(-0.904112\pi\)
0.954969 0.296706i \(-0.0958880\pi\)
\(68\) 2.80150i 0.339732i
\(69\) 4.00000 0.481543
\(70\) 1.85236 + 13.1842i 0.221399 + 1.57581i
\(71\) 0.428639 0.0508701 0.0254351 0.999676i \(-0.491903\pi\)
0.0254351 + 0.999676i \(0.491903\pi\)
\(72\) 3.06668i 0.361411i
\(73\) 12.7096i 1.48755i 0.668430 + 0.743775i \(0.266967\pi\)
−0.668430 + 0.743775i \(0.733033\pi\)
\(74\) −7.05086 −0.819645
\(75\) −1.37778 4.80642i −0.159093 0.554998i
\(76\) −2.72393 −0.312456
\(77\) 0 0
\(78\) 5.03657i 0.570279i
\(79\) −6.42864 −0.723278 −0.361639 0.932318i \(-0.617783\pi\)
−0.361639 + 0.932318i \(0.617783\pi\)
\(80\) −0.831613 5.91903i −0.0929772 0.661768i
\(81\) 1.00000 0.111111
\(82\) 2.19358i 0.242240i
\(83\) 2.90321i 0.318669i −0.987225 0.159334i \(-0.949065\pi\)
0.987225 0.159334i \(-0.0509348\pi\)
\(84\) 2.57628 0.281095
\(85\) −11.8064 + 1.65878i −1.28059 + 0.179920i
\(86\) −5.95407 −0.642044
\(87\) 1.80642i 0.193669i
\(88\) 0 0
\(89\) −0.622216 −0.0659547 −0.0329774 0.999456i \(-0.510499\pi\)
−0.0329774 + 0.999456i \(0.510499\pi\)
\(90\) 2.68889 0.377784i 0.283434 0.0398220i
\(91\) 20.3368 2.13187
\(92\) 2.10171i 0.219118i
\(93\) 2.62222i 0.271911i
\(94\) −8.56199 −0.883102
\(95\) −1.61285 11.4795i −0.165475 1.17777i
\(96\) −2.88739 −0.294693
\(97\) 2.75557i 0.279786i −0.990167 0.139893i \(-0.955324\pi\)
0.990167 0.139893i \(-0.0446758\pi\)
\(98\) 20.6938i 2.09039i
\(99\) 0 0
\(100\) −2.52543 + 0.723926i −0.252543 + 0.0723926i
\(101\) 17.8064 1.77181 0.885903 0.463871i \(-0.153540\pi\)
0.885903 + 0.463871i \(0.153540\pi\)
\(102\) 6.47457i 0.641078i
\(103\) 4.94914i 0.487654i −0.969819 0.243827i \(-0.921597\pi\)
0.969819 0.243827i \(-0.0784029\pi\)
\(104\) −12.7195 −1.24725
\(105\) 1.52543 + 10.8573i 0.148866 + 1.05956i
\(106\) −8.72393 −0.847343
\(107\) 11.1985i 1.08260i −0.840830 0.541300i \(-0.817932\pi\)
0.840830 0.541300i \(-0.182068\pi\)
\(108\) 0.525428i 0.0505593i
\(109\) 15.7146 1.50518 0.752591 0.658488i \(-0.228804\pi\)
0.752591 + 0.658488i \(0.228804\pi\)
\(110\) 0 0
\(111\) −5.80642 −0.551121
\(112\) 13.1066i 1.23846i
\(113\) 1.76494i 0.166031i 0.996548 + 0.0830156i \(0.0264551\pi\)
−0.996548 + 0.0830156i \(0.973545\pi\)
\(114\) 6.29529 0.589608
\(115\) 8.85728 1.24443i 0.825946 0.116044i
\(116\) 0.949145 0.0881259
\(117\) 4.14764i 0.383450i
\(118\) 2.03164i 0.187028i
\(119\) 26.1432 2.39654
\(120\) −0.954067 6.79060i −0.0870940 0.619894i
\(121\) 0 0
\(122\) 0.917502i 0.0830667i
\(123\) 1.80642i 0.162880i
\(124\) 1.37778 0.123729
\(125\) −4.54617 10.2143i −0.406622 0.913597i
\(126\) −5.95407 −0.530430
\(127\) 18.7096i 1.66021i −0.557606 0.830106i \(-0.688280\pi\)
0.557606 0.830106i \(-0.311720\pi\)
\(128\) 4.97481i 0.439715i
\(129\) −4.90321 −0.431704
\(130\) −1.56691 11.1526i −0.137428 0.978145i
\(131\) 1.24443 0.108726 0.0543632 0.998521i \(-0.482687\pi\)
0.0543632 + 0.998521i \(0.482687\pi\)
\(132\) 0 0
\(133\) 25.4193i 2.20413i
\(134\) 5.89829 0.509535
\(135\) 2.21432 0.311108i 0.190578 0.0267759i
\(136\) −16.3511 −1.40209
\(137\) 18.7971i 1.60594i 0.596019 + 0.802970i \(0.296748\pi\)
−0.596019 + 0.802970i \(0.703252\pi\)
\(138\) 4.85728i 0.413479i
\(139\) 14.0415 1.19098 0.595492 0.803361i \(-0.296957\pi\)
0.595492 + 0.803361i \(0.296957\pi\)
\(140\) 5.70471 0.801502i 0.482136 0.0677393i
\(141\) −7.05086 −0.593789
\(142\) 0.520505i 0.0436798i
\(143\) 0 0
\(144\) 2.67307 0.222756
\(145\) 0.561993 + 4.00000i 0.0466709 + 0.332182i
\(146\) −15.4336 −1.27729
\(147\) 17.0415i 1.40556i
\(148\) 3.05086i 0.250779i
\(149\) −3.05086 −0.249936 −0.124968 0.992161i \(-0.539883\pi\)
−0.124968 + 0.992161i \(0.539883\pi\)
\(150\) 5.83654 1.67307i 0.476551 0.136606i
\(151\) 0.326929 0.0266051 0.0133026 0.999912i \(-0.495766\pi\)
0.0133026 + 0.999912i \(0.495766\pi\)
\(152\) 15.8983i 1.28952i
\(153\) 5.33185i 0.431055i
\(154\) 0 0
\(155\) 0.815792 + 5.80642i 0.0655260 + 0.466383i
\(156\) −2.17929 −0.174483
\(157\) 19.9081i 1.58884i −0.607367 0.794421i \(-0.707774\pi\)
0.607367 0.794421i \(-0.292226\pi\)
\(158\) 7.80642i 0.621046i
\(159\) −7.18421 −0.569745
\(160\) −6.39361 + 0.898290i −0.505459 + 0.0710160i
\(161\) −19.6128 −1.54571
\(162\) 1.21432i 0.0954060i
\(163\) 12.1748i 0.953607i −0.879010 0.476804i \(-0.841795\pi\)
0.879010 0.476804i \(-0.158205\pi\)
\(164\) −0.949145 −0.0741158
\(165\) 0 0
\(166\) 3.52543 0.273626
\(167\) 13.0049i 1.00635i −0.864184 0.503176i \(-0.832165\pi\)
0.864184 0.503176i \(-0.167835\pi\)
\(168\) 15.0366i 1.16010i
\(169\) −4.20294 −0.323303
\(170\) −2.01429 14.3368i −0.154489 1.09958i
\(171\) 5.18421 0.396446
\(172\) 2.57628i 0.196440i
\(173\) 13.8938i 1.05633i 0.849142 + 0.528165i \(0.177120\pi\)
−0.849142 + 0.528165i \(0.822880\pi\)
\(174\) −2.19358 −0.166295
\(175\) 6.75557 + 23.5669i 0.510673 + 1.78149i
\(176\) 0 0
\(177\) 1.67307i 0.125756i
\(178\) 0.755569i 0.0566323i
\(179\) −12.8573 −0.960998 −0.480499 0.876995i \(-0.659544\pi\)
−0.480499 + 0.876995i \(0.659544\pi\)
\(180\) −0.163465 1.16346i −0.0121839 0.0867195i
\(181\) 0.917502 0.0681974 0.0340987 0.999418i \(-0.489144\pi\)
0.0340987 + 0.999418i \(0.489144\pi\)
\(182\) 24.6953i 1.83054i
\(183\) 0.755569i 0.0558532i
\(184\) 12.2667 0.904314
\(185\) −12.8573 + 1.80642i −0.945286 + 0.132811i
\(186\) −3.18421 −0.233477
\(187\) 0 0
\(188\) 3.70471i 0.270194i
\(189\) −4.90321 −0.356656
\(190\) 13.9398 1.95851i 1.01130 0.142085i
\(191\) 14.3684 1.03966 0.519831 0.854269i \(-0.325995\pi\)
0.519831 + 0.854269i \(0.325995\pi\)
\(192\) 8.85236i 0.638864i
\(193\) 11.7605i 0.846539i −0.906004 0.423269i \(-0.860882\pi\)
0.906004 0.423269i \(-0.139118\pi\)
\(194\) 3.34614 0.240239
\(195\) −1.29036 9.18421i −0.0924049 0.657695i
\(196\) −8.95407 −0.639576
\(197\) 3.82071i 0.272215i 0.990694 + 0.136107i \(0.0434592\pi\)
−0.990694 + 0.136107i \(0.956541\pi\)
\(198\) 0 0
\(199\) 13.7146 0.972199 0.486100 0.873903i \(-0.338419\pi\)
0.486100 + 0.873903i \(0.338419\pi\)
\(200\) −4.22522 14.7397i −0.298768 1.04226i
\(201\) 4.85728 0.342606
\(202\) 21.6227i 1.52137i
\(203\) 8.85728i 0.621659i
\(204\) −2.80150 −0.196144
\(205\) −0.561993 4.00000i −0.0392513 0.279372i
\(206\) 6.00984 0.418726
\(207\) 4.00000i 0.278019i
\(208\) 11.0869i 0.768741i
\(209\) 0 0
\(210\) −13.1842 + 1.85236i −0.909797 + 0.127825i
\(211\) −1.95851 −0.134830 −0.0674148 0.997725i \(-0.521475\pi\)
−0.0674148 + 0.997725i \(0.521475\pi\)
\(212\) 3.77478i 0.259253i
\(213\) 0.428639i 0.0293699i
\(214\) 13.5986 0.929578
\(215\) −10.8573 + 1.52543i −0.740460 + 0.104033i
\(216\) 3.06668 0.208661
\(217\) 12.8573i 0.872809i
\(218\) 19.0825i 1.29243i
\(219\) −12.7096 −0.858838
\(220\) 0 0
\(221\) −22.1146 −1.48759
\(222\) 7.05086i 0.473222i
\(223\) 26.0098i 1.74175i 0.491506 + 0.870874i \(0.336446\pi\)
−0.491506 + 0.870874i \(0.663554\pi\)
\(224\) 14.1575 0.945937
\(225\) 4.80642 1.37778i 0.320428 0.0918523i
\(226\) −2.14320 −0.142563
\(227\) 6.34122i 0.420882i 0.977607 + 0.210441i \(0.0674899\pi\)
−0.977607 + 0.210441i \(0.932510\pi\)
\(228\) 2.72393i 0.180396i
\(229\) 23.3274 1.54152 0.770759 0.637127i \(-0.219877\pi\)
0.770759 + 0.637127i \(0.219877\pi\)
\(230\) 1.51114 + 10.7556i 0.0996415 + 0.709201i
\(231\) 0 0
\(232\) 5.53972i 0.363700i
\(233\) 1.42372i 0.0932708i −0.998912 0.0466354i \(-0.985150\pi\)
0.998912 0.0466354i \(-0.0148499\pi\)
\(234\) 5.03657 0.329251
\(235\) −15.6128 + 2.19358i −1.01847 + 0.143093i
\(236\) −0.879077 −0.0572231
\(237\) 6.42864i 0.417585i
\(238\) 31.7462i 2.05780i
\(239\) −18.9590 −1.22636 −0.613178 0.789945i \(-0.710109\pi\)
−0.613178 + 0.789945i \(0.710109\pi\)
\(240\) 5.91903 0.831613i 0.382072 0.0536804i
\(241\) 1.34614 0.0867126 0.0433563 0.999060i \(-0.486195\pi\)
0.0433563 + 0.999060i \(0.486195\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) −0.396997 −0.0254151
\(245\) −5.30174 37.7353i −0.338716 2.41082i
\(246\) 2.19358 0.139857
\(247\) 21.5022i 1.36816i
\(248\) 8.04149i 0.510635i
\(249\) 2.90321 0.183984
\(250\) 12.4035 5.52051i 0.784463 0.349147i
\(251\) 1.08250 0.0683267 0.0341633 0.999416i \(-0.489123\pi\)
0.0341633 + 0.999416i \(0.489123\pi\)
\(252\) 2.57628i 0.162291i
\(253\) 0 0
\(254\) 22.7195 1.42555
\(255\) −1.65878 11.8064i −0.103877 0.739347i
\(256\) −11.6637 −0.728981
\(257\) 0.133353i 0.00831834i −0.999991 0.00415917i \(-0.998676\pi\)
0.999991 0.00415917i \(-0.00132391\pi\)
\(258\) 5.95407i 0.370684i
\(259\) 28.4701 1.76905
\(260\) −4.82564 + 0.677993i −0.299273 + 0.0420473i
\(261\) −1.80642 −0.111815
\(262\) 1.51114i 0.0933584i
\(263\) 0.147643i 0.00910407i −0.999990 0.00455203i \(-0.998551\pi\)
0.999990 0.00455203i \(-0.00144896\pi\)
\(264\) 0 0
\(265\) −15.9081 + 2.23506i −0.977229 + 0.137299i
\(266\) −30.8671 −1.89258
\(267\) 0.622216i 0.0380790i
\(268\) 2.55215i 0.155897i
\(269\) 26.8573 1.63752 0.818759 0.574138i \(-0.194663\pi\)
0.818759 + 0.574138i \(0.194663\pi\)
\(270\) 0.377784 + 2.68889i 0.0229912 + 0.163641i
\(271\) −3.08250 −0.187248 −0.0936242 0.995608i \(-0.529845\pi\)
−0.0936242 + 0.995608i \(0.529845\pi\)
\(272\) 14.2524i 0.864180i
\(273\) 20.3368i 1.23084i
\(274\) −22.8256 −1.37895
\(275\) 0 0
\(276\) 2.10171 0.126508
\(277\) 8.70964i 0.523311i 0.965161 + 0.261656i \(0.0842685\pi\)
−0.965161 + 0.261656i \(0.915732\pi\)
\(278\) 17.0509i 1.02264i
\(279\) −2.62222 −0.156988
\(280\) 4.67799 + 33.2958i 0.279564 + 1.98980i
\(281\) 20.3783 1.21567 0.607833 0.794065i \(-0.292039\pi\)
0.607833 + 0.794065i \(0.292039\pi\)
\(282\) 8.56199i 0.509859i
\(283\) 6.32248i 0.375833i −0.982185 0.187916i \(-0.939827\pi\)
0.982185 0.187916i \(-0.0601734\pi\)
\(284\) 0.225219 0.0133643
\(285\) 11.4795 1.61285i 0.679987 0.0955369i
\(286\) 0 0
\(287\) 8.85728i 0.522829i
\(288\) 2.88739i 0.170141i
\(289\) −11.4286 −0.672273
\(290\) −4.85728 + 0.682439i −0.285229 + 0.0400742i
\(291\) 2.75557 0.161534
\(292\) 6.67799i 0.390800i
\(293\) 16.6780i 0.974339i 0.873308 + 0.487169i \(0.161971\pi\)
−0.873308 + 0.487169i \(0.838029\pi\)
\(294\) 20.6938 1.20689
\(295\) −0.520505 3.70471i −0.0303050 0.215697i
\(296\) −17.8064 −1.03498
\(297\) 0 0
\(298\) 3.70471i 0.214608i
\(299\) 16.5906 0.959458
\(300\) −0.723926 2.52543i −0.0417959 0.145806i
\(301\) 24.0415 1.38573
\(302\) 0.396997i 0.0228446i
\(303\) 17.8064i 1.02295i
\(304\) 13.8578 0.794797
\(305\) −0.235063 1.67307i −0.0134597 0.0957998i
\(306\) 6.47457 0.370127
\(307\) 9.58565i 0.547082i 0.961860 + 0.273541i \(0.0881949\pi\)
−0.961860 + 0.273541i \(0.911805\pi\)
\(308\) 0 0
\(309\) 4.94914 0.281547
\(310\) −7.05086 + 0.990632i −0.400462 + 0.0562641i
\(311\) 14.5303 0.823941 0.411970 0.911197i \(-0.364841\pi\)
0.411970 + 0.911197i \(0.364841\pi\)
\(312\) 12.7195i 0.720099i
\(313\) 21.0321i 1.18881i 0.804167 + 0.594403i \(0.202612\pi\)
−0.804167 + 0.594403i \(0.797388\pi\)
\(314\) 24.1748 1.36427
\(315\) −10.8573 + 1.52543i −0.611738 + 0.0859481i
\(316\) −3.37778 −0.190015
\(317\) 0.990632i 0.0556394i −0.999613 0.0278197i \(-0.991144\pi\)
0.999613 0.0278197i \(-0.00885643\pi\)
\(318\) 8.72393i 0.489213i
\(319\) 0 0
\(320\) −2.75404 19.6019i −0.153955 1.09578i
\(321\) 11.1985 0.625039
\(322\) 23.8163i 1.32723i
\(323\) 27.6414i 1.53801i
\(324\) 0.525428 0.0291904
\(325\) −5.71456 19.9353i −0.316987 1.10581i
\(326\) 14.7841 0.818818
\(327\) 15.7146i 0.869017i
\(328\) 5.53972i 0.305880i
\(329\) 34.5718 1.90601
\(330\) 0 0
\(331\) −17.5812 −0.966350 −0.483175 0.875524i \(-0.660517\pi\)
−0.483175 + 0.875524i \(0.660517\pi\)
\(332\) 1.52543i 0.0837187i
\(333\) 5.80642i 0.318190i
\(334\) 15.7921 0.864107
\(335\) 10.7556 1.51114i 0.587639 0.0825623i
\(336\) −13.1066 −0.715025
\(337\) 3.16992i 0.172676i 0.996266 + 0.0863382i \(0.0275166\pi\)
−0.996266 + 0.0863382i \(0.972483\pi\)
\(338\) 5.10372i 0.277606i
\(339\) −1.76494 −0.0958582
\(340\) −6.20342 + 0.871569i −0.336428 + 0.0472675i
\(341\) 0 0
\(342\) 6.29529i 0.340410i
\(343\) 49.2355i 2.65847i
\(344\) −15.0366 −0.810717
\(345\) 1.24443 + 8.85728i 0.0669979 + 0.476860i
\(346\) −16.8716 −0.907021
\(347\) 4.97634i 0.267144i −0.991039 0.133572i \(-0.957355\pi\)
0.991039 0.133572i \(-0.0426447\pi\)
\(348\) 0.949145i 0.0508795i
\(349\) 18.2034 0.974407 0.487203 0.873289i \(-0.338017\pi\)
0.487203 + 0.873289i \(0.338017\pi\)
\(350\) −28.6178 + 8.20342i −1.52968 + 0.438491i
\(351\) 4.14764 0.221385
\(352\) 0 0
\(353\) 22.4099i 1.19276i −0.802703 0.596379i \(-0.796605\pi\)
0.802703 0.596379i \(-0.203395\pi\)
\(354\) 2.03164 0.107981
\(355\) 0.133353 + 0.949145i 0.00707765 + 0.0503754i
\(356\) −0.326929 −0.0173272
\(357\) 26.1432i 1.38364i
\(358\) 15.6128i 0.825165i
\(359\) 21.3274 1.12562 0.562809 0.826587i \(-0.309721\pi\)
0.562809 + 0.826587i \(0.309721\pi\)
\(360\) 6.79060 0.954067i 0.357896 0.0502837i
\(361\) 7.87601 0.414527
\(362\) 1.11414i 0.0585579i
\(363\) 0 0
\(364\) 10.6855 0.560072
\(365\) −28.1432 + 3.95407i −1.47308 + 0.206965i
\(366\) 0.917502 0.0479586
\(367\) 35.1338i 1.83397i 0.398921 + 0.916985i \(0.369385\pi\)
−0.398921 + 0.916985i \(0.630615\pi\)
\(368\) 10.6923i 0.557374i
\(369\) 1.80642 0.0940387
\(370\) −2.19358 15.6128i −0.114039 0.811673i
\(371\) 35.2257 1.82883
\(372\) 1.37778i 0.0714348i
\(373\) 17.0049i 0.880481i −0.897880 0.440241i \(-0.854893\pi\)
0.897880 0.440241i \(-0.145107\pi\)
\(374\) 0 0
\(375\) 10.2143 4.54617i 0.527465 0.234763i
\(376\) −21.6227 −1.11511
\(377\) 7.49240i 0.385878i
\(378\) 5.95407i 0.306244i
\(379\) −2.36842 −0.121657 −0.0608287 0.998148i \(-0.519374\pi\)
−0.0608287 + 0.998148i \(0.519374\pi\)
\(380\) −0.847435 6.03164i −0.0434725 0.309417i
\(381\) 18.7096 0.958524
\(382\) 17.4479i 0.892710i
\(383\) 1.21585i 0.0621271i −0.999517 0.0310635i \(-0.990111\pi\)
0.999517 0.0310635i \(-0.00988942\pi\)
\(384\) 4.97481 0.253870
\(385\) 0 0
\(386\) 14.2810 0.726884
\(387\) 4.90321i 0.249244i
\(388\) 1.44785i 0.0735035i
\(389\) −2.26671 −0.114927 −0.0574633 0.998348i \(-0.518301\pi\)
−0.0574633 + 0.998348i \(0.518301\pi\)
\(390\) 11.1526 1.56691i 0.564732 0.0793438i
\(391\) 21.3274 1.07857
\(392\) 52.2607i 2.63957i
\(393\) 1.24443i 0.0627733i
\(394\) −4.63957 −0.233738
\(395\) −2.00000 14.2351i −0.100631 0.716244i
\(396\) 0 0
\(397\) 18.4889i 0.927929i −0.885854 0.463965i \(-0.846426\pi\)
0.885854 0.463965i \(-0.153574\pi\)
\(398\) 16.6539i 0.834782i
\(399\) −25.4193 −1.27256
\(400\) 12.8479 3.68292i 0.642396 0.184146i
\(401\) 17.5625 0.877028 0.438514 0.898724i \(-0.355505\pi\)
0.438514 + 0.898724i \(0.355505\pi\)
\(402\) 5.89829i 0.294180i
\(403\) 10.8760i 0.541773i
\(404\) 9.35599 0.465478
\(405\) 0.311108 + 2.21432i 0.0154591 + 0.110030i
\(406\) 10.7556 0.533790
\(407\) 0 0
\(408\) 16.3511i 0.809498i
\(409\) −21.3461 −1.05550 −0.527749 0.849400i \(-0.676964\pi\)
−0.527749 + 0.849400i \(0.676964\pi\)
\(410\) 4.85728 0.682439i 0.239884 0.0337032i
\(411\) −18.7971 −0.927190
\(412\) 2.60042i 0.128113i
\(413\) 8.20342i 0.403664i
\(414\) −4.85728 −0.238722
\(415\) 6.42864 0.903212i 0.315570 0.0443369i
\(416\) −11.9759 −0.587165
\(417\) 14.0415i 0.687615i
\(418\) 0 0
\(419\) −28.8573 −1.40977 −0.704885 0.709321i \(-0.749001\pi\)
−0.704885 + 0.709321i \(0.749001\pi\)
\(420\) 0.801502 + 5.70471i 0.0391093 + 0.278362i
\(421\) −35.4893 −1.72964 −0.864822 0.502078i \(-0.832569\pi\)
−0.864822 + 0.502078i \(0.832569\pi\)
\(422\) 2.37826i 0.115772i
\(423\) 7.05086i 0.342824i
\(424\) −22.0316 −1.06995
\(425\) −7.34614 25.6271i −0.356340 1.24310i
\(426\) −0.520505 −0.0252186
\(427\) 3.70471i 0.179284i
\(428\) 5.88400i 0.284414i
\(429\) 0 0
\(430\) −1.85236 13.1842i −0.0893286 0.635799i
\(431\) −9.24443 −0.445289 −0.222644 0.974900i \(-0.571469\pi\)
−0.222644 + 0.974900i \(0.571469\pi\)
\(432\) 2.67307i 0.128608i
\(433\) 6.28544i 0.302059i 0.988529 + 0.151030i \(0.0482589\pi\)
−0.988529 + 0.151030i \(0.951741\pi\)
\(434\) 15.6128 0.749441
\(435\) −4.00000 + 0.561993i −0.191785 + 0.0269455i
\(436\) 8.25686 0.395432
\(437\) 20.7368i 0.991977i
\(438\) 15.4336i 0.737444i
\(439\) −36.5303 −1.74350 −0.871749 0.489952i \(-0.837014\pi\)
−0.871749 + 0.489952i \(0.837014\pi\)
\(440\) 0 0
\(441\) 17.0415 0.811499
\(442\) 26.8542i 1.27732i
\(443\) 38.2766i 1.81857i 0.416170 + 0.909287i \(0.363372\pi\)
−0.416170 + 0.909287i \(0.636628\pi\)
\(444\) −3.05086 −0.144787
\(445\) −0.193576 1.37778i −0.00917639 0.0653132i
\(446\) −31.5843 −1.49556
\(447\) 3.05086i 0.144300i
\(448\) 43.4050i 2.05069i
\(449\) 31.8479 1.50300 0.751498 0.659735i \(-0.229332\pi\)
0.751498 + 0.659735i \(0.229332\pi\)
\(450\) 1.67307 + 5.83654i 0.0788693 + 0.275137i
\(451\) 0 0
\(452\) 0.927346i 0.0436187i
\(453\) 0.326929i 0.0153605i
\(454\) −7.70027 −0.361391
\(455\) 6.32693 + 45.0321i 0.296611 + 2.11114i
\(456\) 15.8983 0.744506
\(457\) 1.39207i 0.0651185i −0.999470 0.0325592i \(-0.989634\pi\)
0.999470 0.0325592i \(-0.0103658\pi\)
\(458\) 28.3269i 1.32363i
\(459\) 5.33185 0.248870
\(460\) 4.65386 0.653858i 0.216987 0.0304863i
\(461\) 7.70471 0.358844 0.179422 0.983772i \(-0.442577\pi\)
0.179422 + 0.983772i \(0.442577\pi\)
\(462\) 0 0
\(463\) 4.68244i 0.217611i −0.994063 0.108806i \(-0.965297\pi\)
0.994063 0.108806i \(-0.0347026\pi\)
\(464\) −4.82870 −0.224167
\(465\) −5.80642 + 0.815792i −0.269266 + 0.0378314i
\(466\) 1.72885 0.0800873
\(467\) 12.8573i 0.594964i 0.954727 + 0.297482i \(0.0961468\pi\)
−0.954727 + 0.297482i \(0.903853\pi\)
\(468\) 2.17929i 0.100738i
\(469\) −23.8163 −1.09973
\(470\) −2.66370 18.9590i −0.122867 0.874513i
\(471\) 19.9081 0.917318
\(472\) 5.13077i 0.236163i
\(473\) 0 0
\(474\) 7.80642 0.358561
\(475\) 24.9175 7.14272i 1.14329 0.327731i
\(476\) 13.7364 0.629605
\(477\) 7.18421i 0.328942i
\(478\) 23.0223i 1.05301i
\(479\) 8.38715 0.383219 0.191609 0.981471i \(-0.438629\pi\)
0.191609 + 0.981471i \(0.438629\pi\)
\(480\) −0.898290 6.39361i −0.0410011 0.291827i
\(481\) −24.0830 −1.09809
\(482\) 1.63465i 0.0744561i
\(483\) 19.6128i 0.892415i
\(484\) 0 0
\(485\) 6.10171 0.857279i 0.277064 0.0389270i
\(486\) −1.21432 −0.0550827
\(487\) 9.83500i 0.445667i 0.974857 + 0.222833i \(0.0715306\pi\)
−0.974857 + 0.222833i \(0.928469\pi\)
\(488\) 2.31708i 0.104890i
\(489\) 12.1748 0.550565
\(490\) 45.8227 6.43801i 2.07006 0.290840i
\(491\) 32.9403 1.48657 0.743286 0.668973i \(-0.233266\pi\)
0.743286 + 0.668973i \(0.233266\pi\)
\(492\) 0.949145i 0.0427908i
\(493\) 9.63158i 0.433785i
\(494\) 26.1106 1.17477
\(495\) 0 0
\(496\) −7.00937 −0.314730
\(497\) 2.10171i 0.0942746i
\(498\) 3.52543i 0.157978i
\(499\) 1.63158 0.0730397 0.0365199 0.999333i \(-0.488373\pi\)
0.0365199 + 0.999333i \(0.488373\pi\)
\(500\) −2.38868 5.36689i −0.106825 0.240014i
\(501\) 13.0049 0.581017
\(502\) 1.31450i 0.0586689i
\(503\) 41.8622i 1.86654i 0.359171 + 0.933272i \(0.383059\pi\)
−0.359171 + 0.933272i \(0.616941\pi\)
\(504\) −15.0366 −0.669782
\(505\) 5.53972 + 39.4291i 0.246514 + 1.75457i
\(506\) 0 0
\(507\) 4.20294i 0.186659i
\(508\) 9.83056i 0.436160i
\(509\) 38.8573 1.72232 0.861159 0.508335i \(-0.169739\pi\)
0.861159 + 0.508335i \(0.169739\pi\)
\(510\) 14.3368 2.01429i 0.634843 0.0891943i
\(511\) 62.3180 2.75679
\(512\) 24.1131i 1.06566i
\(513\) 5.18421i 0.228888i
\(514\) 0.161933 0.00714257
\(515\) 10.9590 1.53972i 0.482911 0.0678481i
\(516\) −2.57628 −0.113415
\(517\) 0 0
\(518\) 34.5718i 1.51900i
\(519\) −13.8938 −0.609872
\(520\) −3.95713 28.1650i −0.173532 1.23512i
\(521\) 11.1111 0.486785 0.243393 0.969928i \(-0.421740\pi\)
0.243393 + 0.969928i \(0.421740\pi\)
\(522\) 2.19358i 0.0960102i
\(523\) 27.3002i 1.19375i 0.802332 + 0.596877i \(0.203592\pi\)
−0.802332 + 0.596877i \(0.796408\pi\)
\(524\) 0.653858 0.0285639
\(525\) −23.5669 + 6.75557i −1.02854 + 0.294837i
\(526\) 0.179286 0.00781724
\(527\) 13.9813i 0.609033i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) −2.71408 19.3176i −0.117892 0.839101i
\(531\) 1.67307 0.0726051
\(532\) 13.3560i 0.579055i
\(533\) 7.49240i 0.324532i
\(534\) 0.755569 0.0326967
\(535\) 24.7971 3.48394i 1.07207 0.150624i
\(536\) 14.8957 0.643396
\(537\) 12.8573i 0.554833i
\(538\) 32.6133i 1.40606i
\(539\) 0 0
\(540\) 1.16346 0.163465i 0.0500675 0.00703440i
\(541\) 16.1017 0.692267 0.346133 0.938185i \(-0.387494\pi\)
0.346133 + 0.938185i \(0.387494\pi\)
\(542\) 3.74314i 0.160782i
\(543\) 0.917502i 0.0393738i
\(544\) −15.3951 −0.660061
\(545\) 4.88892 + 34.7971i 0.209418 + 1.49054i
\(546\) −24.6953 −1.05686
\(547\) 40.0370i 1.71186i −0.517091 0.855930i \(-0.672985\pi\)
0.517091 0.855930i \(-0.327015\pi\)
\(548\) 9.87649i 0.421903i
\(549\) 0.755569 0.0322469
\(550\) 0 0
\(551\) −9.36488 −0.398957
\(552\) 12.2667i 0.522106i
\(553\) 31.5210i 1.34041i
\(554\) −10.5763 −0.449343
\(555\) −1.80642 12.8573i −0.0766784 0.545761i
\(556\) 7.37778 0.312888
\(557\) 28.2908i 1.19872i 0.800479 + 0.599361i \(0.204578\pi\)
−0.800479 + 0.599361i \(0.795422\pi\)
\(558\) 3.18421i 0.134798i
\(559\) −20.3368 −0.860154
\(560\) −29.0223 + 4.07758i −1.22641 + 0.172309i
\(561\) 0 0
\(562\) 24.7457i 1.04384i
\(563\) 32.7926i 1.38204i −0.722834 0.691022i \(-0.757161\pi\)
0.722834 0.691022i \(-0.242839\pi\)
\(564\) −3.70471 −0.155997
\(565\) −3.90813 + 0.549086i −0.164416 + 0.0231002i
\(566\) 7.67752 0.322710
\(567\) 4.90321i 0.205916i
\(568\) 1.31450i 0.0551551i
\(569\) −8.88586 −0.372515 −0.186257 0.982501i \(-0.559636\pi\)
−0.186257 + 0.982501i \(0.559636\pi\)
\(570\) 1.95851 + 13.9398i 0.0820331 + 0.583873i
\(571\) 10.6953 0.447586 0.223793 0.974637i \(-0.428156\pi\)
0.223793 + 0.974637i \(0.428156\pi\)
\(572\) 0 0
\(573\) 14.3684i 0.600249i
\(574\) −10.7556 −0.448929
\(575\) 5.51114 + 19.2257i 0.229830 + 0.801767i
\(576\) 8.85236 0.368848
\(577\) 27.1338i 1.12960i −0.825229 0.564798i \(-0.808954\pi\)
0.825229 0.564798i \(-0.191046\pi\)
\(578\) 13.8780i 0.577250i
\(579\) 11.7605 0.488749
\(580\) 0.295286 + 2.10171i 0.0122611 + 0.0872688i
\(581\) −14.2351 −0.590570
\(582\) 3.34614i 0.138702i
\(583\) 0 0
\(584\) −38.9763 −1.61285
\(585\) 9.18421 1.29036i 0.379720 0.0533500i
\(586\) −20.2524 −0.836620
\(587\) 10.9590i 0.452326i −0.974089 0.226163i \(-0.927382\pi\)
0.974089 0.226163i \(-0.0726182\pi\)
\(588\) 8.95407i 0.369260i
\(589\) −13.5941 −0.560136
\(590\) 4.49871 0.632060i 0.185209 0.0260215i
\(591\) −3.82071 −0.157163
\(592\) 15.5210i 0.637908i
\(593\) 23.7003i 0.973253i −0.873610 0.486627i \(-0.838227\pi\)
0.873610 0.486627i \(-0.161773\pi\)
\(594\) 0 0
\(595\) 8.13335 + 57.8894i 0.333435 + 2.37323i
\(596\) −1.60300 −0.0656616
\(597\) 13.7146i 0.561299i
\(598\) 20.1463i 0.823842i
\(599\) −41.7146 −1.70441 −0.852205 0.523208i \(-0.824735\pi\)
−0.852205 + 0.523208i \(0.824735\pi\)
\(600\) 14.7397 4.22522i 0.601748 0.172494i
\(601\) −14.5906 −0.595162 −0.297581 0.954697i \(-0.596180\pi\)
−0.297581 + 0.954697i \(0.596180\pi\)
\(602\) 29.1941i 1.18986i
\(603\) 4.85728i 0.197804i
\(604\) 0.171778 0.00698953
\(605\) 0 0
\(606\) −21.6227 −0.878362
\(607\) 19.9826i 0.811071i 0.914079 + 0.405535i \(0.132915\pi\)
−0.914079 + 0.405535i \(0.867085\pi\)
\(608\) 14.9688i 0.607066i
\(609\) 8.85728 0.358915
\(610\) 2.03164 0.285442i 0.0822588 0.0115572i
\(611\) −29.2444 −1.18310
\(612\) 2.80150i 0.113244i
\(613\) 19.0781i 0.770555i 0.922801 + 0.385278i \(0.125894\pi\)
−0.922801 + 0.385278i \(0.874106\pi\)
\(614\) −11.6400 −0.469754
\(615\) 4.00000 0.561993i 0.161296 0.0226617i
\(616\) 0 0
\(617\) 39.3590i 1.58454i −0.610174 0.792268i \(-0.708900\pi\)
0.610174 0.792268i \(-0.291100\pi\)
\(618\) 6.00984i 0.241751i
\(619\) 23.0923 0.928160 0.464080 0.885793i \(-0.346385\pi\)
0.464080 + 0.885793i \(0.346385\pi\)
\(620\) 0.428639 + 3.05086i 0.0172146 + 0.122525i
\(621\) −4.00000 −0.160514
\(622\) 17.6445i 0.707480i
\(623\) 3.05086i 0.122230i
\(624\) 11.0869 0.443833
\(625\) 21.2034 13.2444i 0.848137 0.529777i
\(626\) −25.5397 −1.02077
\(627\) 0 0
\(628\) 10.4603i 0.417411i
\(629\) −30.9590 −1.23442
\(630\) −1.85236 13.1842i −0.0737997 0.525271i
\(631\) −25.5111 −1.01558 −0.507791 0.861480i \(-0.669538\pi\)
−0.507791 + 0.861480i \(0.669538\pi\)
\(632\) 19.7146i 0.784203i
\(633\) 1.95851i 0.0778439i
\(634\) 1.20294 0.0477750
\(635\) 41.4291 5.82071i 1.64406 0.230988i
\(636\) −3.77478 −0.149680
\(637\) 70.6820i 2.80052i
\(638\) 0 0
\(639\) −0.428639 −0.0169567
\(640\) 11.0158 1.54770i 0.435439 0.0611783i
\(641\) −6.25380 −0.247010 −0.123505 0.992344i \(-0.539414\pi\)
−0.123505 + 0.992344i \(0.539414\pi\)
\(642\) 13.5986i 0.536692i
\(643\) 6.84743i 0.270036i −0.990843 0.135018i \(-0.956891\pi\)
0.990843 0.135018i \(-0.0431093\pi\)
\(644\) −10.3051 −0.406079
\(645\) −1.52543 10.8573i −0.0600637 0.427505i
\(646\) 33.5655 1.32062
\(647\) 20.2953i 0.797890i 0.916975 + 0.398945i \(0.130624\pi\)
−0.916975 + 0.398945i \(0.869376\pi\)
\(648\) 3.06668i 0.120470i
\(649\) 0 0
\(650\) 24.2079 6.93930i 0.949511 0.272182i
\(651\) 12.8573 0.503916
\(652\) 6.39700i 0.250526i
\(653\) 10.6222i 0.415679i 0.978163 + 0.207840i \(0.0666432\pi\)
−0.978163 + 0.207840i \(0.933357\pi\)
\(654\) −19.0825 −0.746185
\(655\) 0.387152 + 2.75557i 0.0151273 + 0.107669i
\(656\) 4.82870 0.188529
\(657\) 12.7096i 0.495850i
\(658\) 41.9813i 1.63660i
\(659\) 10.1017 0.393507 0.196753 0.980453i \(-0.436960\pi\)
0.196753 + 0.980453i \(0.436960\pi\)
\(660\) 0 0
\(661\) 21.6128 0.840642 0.420321 0.907375i \(-0.361917\pi\)
0.420321 + 0.907375i \(0.361917\pi\)
\(662\) 21.3492i 0.829760i
\(663\) 22.1146i 0.858861i
\(664\) 8.90321 0.345512
\(665\) −56.2864 + 7.90813i −2.18269 + 0.306664i
\(666\) 7.05086 0.273215
\(667\) 7.22570i 0.279780i
\(668\) 6.83314i 0.264382i
\(669\) −26.0098 −1.00560
\(670\) 1.83500 + 13.0607i 0.0708924 + 0.504579i
\(671\) 0 0
\(672\) 14.1575i 0.546137i
\(673\) 10.2208i 0.393982i 0.980405 + 0.196991i \(0.0631170\pi\)
−0.980405 + 0.196991i \(0.936883\pi\)
\(674\) −3.84929 −0.148269
\(675\) 1.37778 + 4.80642i 0.0530309 + 0.184999i
\(676\) −2.20834 −0.0849363
\(677\) 13.9224i 0.535082i −0.963546 0.267541i \(-0.913789\pi\)
0.963546 0.267541i \(-0.0862111\pi\)
\(678\) 2.14320i 0.0823090i
\(679\) −13.5111 −0.518510
\(680\) −5.08694 36.2065i −0.195075 1.38846i
\(681\) −6.34122 −0.242996
\(682\) 0 0
\(683\) 10.3970i 0.397830i 0.980017 + 0.198915i \(0.0637418\pi\)
−0.980017 + 0.198915i \(0.936258\pi\)
\(684\) 2.72393 0.104152
\(685\) −41.6227 + 5.84791i −1.59032 + 0.223437i
\(686\) −59.7877 −2.28270
\(687\) 23.3274i 0.889996i
\(688\) 13.1066i 0.499686i
\(689\) −29.7975 −1.13520
\(690\) −10.7556 + 1.51114i −0.409458 + 0.0575280i
\(691\) −0.977725 −0.0371944 −0.0185972 0.999827i \(-0.505920\pi\)
−0.0185972 + 0.999827i \(0.505920\pi\)
\(692\) 7.30021i 0.277512i
\(693\) 0 0
\(694\) 6.04287 0.229384
\(695\) 4.36842 + 31.0923i 0.165703 + 1.17940i
\(696\) −5.53972 −0.209982
\(697\) 9.63158i 0.364822i
\(698\) 22.1048i 0.836678i
\(699\) 1.42372 0.0538499
\(700\) 3.54956 + 12.3827i 0.134161 + 0.468022i
\(701\) −48.9688 −1.84953 −0.924764 0.380542i \(-0.875737\pi\)
−0.924764 + 0.380542i \(0.875737\pi\)
\(702\) 5.03657i 0.190093i
\(703\) 30.1017i 1.13531i
\(704\) 0 0
\(705\) −2.19358 15.6128i −0.0826149 0.588014i
\(706\) 27.2128 1.02417
\(707\) 87.3087i 3.28358i
\(708\) 0.879077i 0.0330378i
\(709\) 37.2672 1.39960 0.699799 0.714340i \(-0.253273\pi\)
0.699799 + 0.714340i \(0.253273\pi\)
\(710\) −1.15257 + 0.161933i −0.0432550 + 0.00607725i
\(711\) 6.42864 0.241093
\(712\) 1.90813i 0.0715103i
\(713\) 10.4889i 0.392811i
\(714\) −31.7462 −1.18807
\(715\) 0 0
\(716\) −6.75557 −0.252467
\(717\) 18.9590i 0.708036i
\(718\) 25.8983i 0.966516i
\(719\) −5.83500 −0.217609 −0.108804 0.994063i \(-0.534702\pi\)
−0.108804 + 0.994063i \(0.534702\pi\)
\(720\) 0.831613 + 5.91903i 0.0309924 + 0.220589i
\(721\) −24.2667 −0.903739
\(722\) 9.56400i 0.355935i
\(723\) 1.34614i 0.0500635i
\(724\) 0.482081 0.0179164
\(725\) −8.68244 + 2.48886i −0.322458 + 0.0924340i
\(726\) 0 0
\(727\) 46.8385i 1.73715i −0.495562 0.868573i \(-0.665038\pi\)
0.495562 0.868573i \(-0.334962\pi\)
\(728\) 62.3663i 2.31145i
\(729\) −1.00000 −0.0370370
\(730\) −4.80150 34.1748i −0.177712 1.26487i
\(731\) −26.1432 −0.966941
\(732\) 0.396997i 0.0146734i
\(733\) 45.2083i 1.66981i −0.550395 0.834904i \(-0.685523\pi\)
0.550395 0.834904i \(-0.314477\pi\)
\(734\) −42.6637 −1.57475
\(735\) 37.7353 5.30174i 1.39189 0.195558i
\(736\) 11.5496 0.425723
\(737\) 0 0
\(738\) 2.19358i 0.0807467i
\(739\) 5.65433 0.207998 0.103999 0.994577i \(-0.466836\pi\)
0.103999 + 0.994577i \(0.466836\pi\)
\(740\) −6.75557 + 0.949145i −0.248340 + 0.0348913i
\(741\) 21.5022 0.789905
\(742\) 42.7753i 1.57033i
\(743\) 4.50622i 0.165317i 0.996578 + 0.0826585i \(0.0263411\pi\)
−0.996578 + 0.0826585i \(0.973659\pi\)
\(744\) −8.04149 −0.294815
\(745\) −0.949145 6.75557i −0.0347740 0.247505i
\(746\) 20.6494 0.756029
\(747\) 2.90321i 0.106223i
\(748\) 0 0
\(749\) −54.9086 −2.00632
\(750\) 5.52051 + 12.4035i 0.201580 + 0.452910i
\(751\) 47.5121 1.73374 0.866870 0.498534i \(-0.166128\pi\)
0.866870 + 0.498534i \(0.166128\pi\)
\(752\) 18.8474i 0.687295i
\(753\) 1.08250i 0.0394484i
\(754\) −9.09817 −0.331336
\(755\) 0.101710 + 0.723926i 0.00370161 + 0.0263464i
\(756\) −2.57628 −0.0936985
\(757\) 46.6637i 1.69602i −0.529979 0.848011i \(-0.677800\pi\)
0.529979 0.848011i \(-0.322200\pi\)
\(758\) 2.87601i 0.104462i
\(759\) 0 0
\(760\) 35.2039 4.94608i 1.27698 0.179413i
\(761\) −14.9304 −0.541227 −0.270613 0.962688i \(-0.587227\pi\)
−0.270613 + 0.962688i \(0.587227\pi\)
\(762\) 22.7195i 0.823040i
\(763\) 77.0518i 2.78946i
\(764\) 7.54956 0.273134
\(765\) 11.8064 1.65878i 0.426862 0.0599733i
\(766\) 1.47643 0.0533457
\(767\) 6.93930i 0.250564i
\(768\) 11.6637i 0.420878i
\(769\) 38.8573 1.40123 0.700615 0.713540i \(-0.252909\pi\)
0.700615 + 0.713540i \(0.252909\pi\)
\(770\) 0 0
\(771\) 0.133353 0.00480259
\(772\) 6.17929i 0.222397i
\(773\) 36.3368i 1.30694i 0.756951 + 0.653471i \(0.226688\pi\)
−0.756951 + 0.653471i \(0.773312\pi\)
\(774\) 5.95407 0.214015
\(775\) −12.6035 + 3.61285i −0.452730 + 0.129777i
\(776\) 8.45044 0.303353
\(777\) 28.4701i 1.02136i
\(778\) 2.75251i 0.0986821i
\(779\) 9.36488 0.335532
\(780\) −0.677993 4.82564i −0.0242760 0.172785i
\(781\) 0 0
\(782\) 25.8983i 0.926121i
\(783\) 1.80642i 0.0645563i
\(784\) 45.5531 1.62690
\(785\) 44.0830 6.19358i 1.57339 0.221058i
\(786\) −1.51114 −0.0539005
\(787\) 33.5482i 1.19586i 0.801547 + 0.597932i \(0.204011\pi\)
−0.801547 + 0.597932i \(0.795989\pi\)