Properties

Label 690.2.i.e.323.16
Level $690$
Weight $2$
Character 690.323
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 323.16
Character \(\chi\) \(=\) 690.323
Dual form 690.2.i.e.47.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(1.66652 + 0.471935i) q^{3} +1.00000i q^{4} +(1.55923 - 1.60274i) q^{5} +(0.844697 + 1.51211i) q^{6} +(-3.44975 + 3.44975i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.55455 + 1.57298i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(1.66652 + 0.471935i) q^{3} +1.00000i q^{4} +(1.55923 - 1.60274i) q^{5} +(0.844697 + 1.51211i) q^{6} +(-3.44975 + 3.44975i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.55455 + 1.57298i) q^{9} +(2.23586 - 0.0307665i) q^{10} +3.84509i q^{11} +(-0.471935 + 1.66652i) q^{12} +(0.875224 + 0.875224i) q^{13} -4.87868 q^{14} +(3.35488 - 1.93514i) q^{15} -1.00000 q^{16} +(-1.35706 - 1.35706i) q^{17} +(0.694081 + 2.91860i) q^{18} -3.81508i q^{19} +(1.60274 + 1.55923i) q^{20} +(-7.37712 + 4.12100i) q^{21} +(-2.71889 + 2.71889i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(-1.51211 + 0.844697i) q^{24} +(-0.137579 - 4.99811i) q^{25} +1.23775i q^{26} +(3.51487 + 3.82697i) q^{27} +(-3.44975 - 3.44975i) q^{28} +7.78450 q^{29} +(3.74061 + 1.00391i) q^{30} +5.58131 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.81463 + 6.40791i) q^{33} -1.91917i q^{34} +(0.150100 + 10.9080i) q^{35} +(-1.57298 + 2.55455i) q^{36} +(1.86954 - 1.86954i) q^{37} +(2.69767 - 2.69767i) q^{38} +(1.04553 + 1.87162i) q^{39} +(0.0307665 + 2.23586i) q^{40} -4.29759i q^{41} +(-8.13040 - 2.30242i) q^{42} +(0.142657 + 0.142657i) q^{43} -3.84509 q^{44} +(6.50423 - 1.64166i) q^{45} -1.00000 q^{46} +(-3.63185 - 3.63185i) q^{47} +(-1.66652 - 0.471935i) q^{48} -16.8015i q^{49} +(3.43691 - 3.63148i) q^{50} +(-1.62112 - 2.90201i) q^{51} +(-0.875224 + 0.875224i) q^{52} +(3.62512 - 3.62512i) q^{53} +(-0.220693 + 5.19146i) q^{54} +(6.16270 + 5.99540i) q^{55} -4.87868i q^{56} +(1.80047 - 6.35789i) q^{57} +(5.50447 + 5.50447i) q^{58} +3.87315 q^{59} +(1.93514 + 3.35488i) q^{60} -13.5655 q^{61} +(3.94659 + 3.94659i) q^{62} +(-14.2389 + 3.38620i) q^{63} -1.00000i q^{64} +(2.76744 - 0.0380814i) q^{65} +(-5.81422 + 3.24794i) q^{66} +(-2.77087 + 2.77087i) q^{67} +(1.35706 - 1.35706i) q^{68} +(-1.51211 + 0.844697i) q^{69} +(-7.60700 + 7.81928i) q^{70} -6.15174i q^{71} +(-2.91860 + 0.694081i) q^{72} +(-9.60788 - 9.60788i) q^{73} +2.64393 q^{74} +(2.12950 - 8.39436i) q^{75} +3.81508 q^{76} +(-13.2646 - 13.2646i) q^{77} +(-0.584139 + 2.06274i) q^{78} +17.1956i q^{79} +(-1.55923 + 1.60274i) q^{80} +(4.05150 + 8.03650i) q^{81} +(3.03885 - 3.03885i) q^{82} +(2.00448 - 2.00448i) q^{83} +(-4.12100 - 7.37712i) q^{84} +(-4.29100 + 0.0590463i) q^{85} +0.201747i q^{86} +(12.9730 + 3.67378i) q^{87} +(-2.71889 - 2.71889i) q^{88} +12.5987 q^{89} +(5.76001 + 3.43835i) q^{90} -6.03860 q^{91} +(-0.707107 - 0.707107i) q^{92} +(9.30135 + 2.63402i) q^{93} -5.13622i q^{94} +(-6.11459 - 5.94860i) q^{95} +(-0.844697 - 1.51211i) q^{96} +(-3.36602 + 3.36602i) q^{97} +(11.8805 - 11.8805i) q^{98} +(-6.04824 + 9.82250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{3} - 4q^{6} - 8q^{7} + O(q^{10}) \) \( 32q + 4q^{3} - 4q^{6} - 8q^{7} - 8q^{10} - 4q^{12} - 4q^{15} - 32q^{16} + 8q^{18} - 32q^{21} - 8q^{22} + 4q^{27} - 8q^{28} + 20q^{30} - 24q^{31} + 20q^{36} - 32q^{37} - 16q^{40} + 8q^{42} + 144q^{43} + 36q^{45} - 32q^{46} - 4q^{48} + 12q^{51} - 64q^{55} + 52q^{57} + 16q^{58} + 4q^{60} - 24q^{61} - 116q^{63} + 12q^{66} - 16q^{67} - 80q^{70} - 8q^{72} + 40q^{73} + 44q^{75} + 24q^{76} - 36q^{78} - 108q^{81} - 32q^{82} - 80q^{85} + 68q^{87} - 8q^{88} + 16q^{90} + 120q^{91} + 12q^{93} + 4q^{96} - 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 1.66652 + 0.471935i 0.962164 + 0.272472i
\(4\) 1.00000i 0.500000i
\(5\) 1.55923 1.60274i 0.697311 0.716769i
\(6\) 0.844697 + 1.51211i 0.344846 + 0.617318i
\(7\) −3.44975 + 3.44975i −1.30388 + 1.30388i −0.378129 + 0.925753i \(0.623432\pi\)
−0.925753 + 0.378129i \(0.876568\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 2.55455 + 1.57298i 0.851518 + 0.524325i
\(10\) 2.23586 0.0307665i 0.707040 0.00972923i
\(11\) 3.84509i 1.15934i 0.814852 + 0.579670i \(0.196818\pi\)
−0.814852 + 0.579670i \(0.803182\pi\)
\(12\) −0.471935 + 1.66652i −0.136236 + 0.481082i
\(13\) 0.875224 + 0.875224i 0.242743 + 0.242743i 0.817984 0.575241i \(-0.195092\pi\)
−0.575241 + 0.817984i \(0.695092\pi\)
\(14\) −4.87868 −1.30388
\(15\) 3.35488 1.93514i 0.866226 0.499652i
\(16\) −1.00000 −0.250000
\(17\) −1.35706 1.35706i −0.329135 0.329135i 0.523122 0.852258i \(-0.324767\pi\)
−0.852258 + 0.523122i \(0.824767\pi\)
\(18\) 0.694081 + 2.91860i 0.163597 + 0.687922i
\(19\) 3.81508i 0.875239i −0.899160 0.437619i \(-0.855822\pi\)
0.899160 0.437619i \(-0.144178\pi\)
\(20\) 1.60274 + 1.55923i 0.358385 + 0.348655i
\(21\) −7.37712 + 4.12100i −1.60982 + 0.899277i
\(22\) −2.71889 + 2.71889i −0.579670 + 0.579670i
\(23\) −0.707107 + 0.707107i −0.147442 + 0.147442i
\(24\) −1.51211 + 0.844697i −0.308659 + 0.172423i
\(25\) −0.137579 4.99811i −0.0275158 0.999621i
\(26\) 1.23775i 0.242743i
\(27\) 3.51487 + 3.82697i 0.676436 + 0.736501i
\(28\) −3.44975 3.44975i −0.651941 0.651941i
\(29\) 7.78450 1.44554 0.722772 0.691086i \(-0.242867\pi\)
0.722772 + 0.691086i \(0.242867\pi\)
\(30\) 3.74061 + 1.00391i 0.682939 + 0.183287i
\(31\) 5.58131 1.00243 0.501217 0.865322i \(-0.332886\pi\)
0.501217 + 0.865322i \(0.332886\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −1.81463 + 6.40791i −0.315887 + 1.11547i
\(34\) 1.91917i 0.329135i
\(35\) 0.150100 + 10.9080i 0.0253715 + 1.84379i
\(36\) −1.57298 + 2.55455i −0.262163 + 0.425759i
\(37\) 1.86954 1.86954i 0.307351 0.307351i −0.536530 0.843881i \(-0.680265\pi\)
0.843881 + 0.536530i \(0.180265\pi\)
\(38\) 2.69767 2.69767i 0.437619 0.437619i
\(39\) 1.04553 + 1.87162i 0.167418 + 0.299700i
\(40\) 0.0307665 + 2.23586i 0.00486461 + 0.353520i
\(41\) 4.29759i 0.671170i −0.942010 0.335585i \(-0.891066\pi\)
0.942010 0.335585i \(-0.108934\pi\)
\(42\) −8.13040 2.30242i −1.25455 0.355271i
\(43\) 0.142657 + 0.142657i 0.0217549 + 0.0217549i 0.717901 0.696146i \(-0.245103\pi\)
−0.696146 + 0.717901i \(0.745103\pi\)
\(44\) −3.84509 −0.579670
\(45\) 6.50423 1.64166i 0.969593 0.244724i
\(46\) −1.00000 −0.147442
\(47\) −3.63185 3.63185i −0.529760 0.529760i 0.390741 0.920501i \(-0.372219\pi\)
−0.920501 + 0.390741i \(0.872219\pi\)
\(48\) −1.66652 0.471935i −0.240541 0.0681180i
\(49\) 16.8015i 2.40022i
\(50\) 3.43691 3.63148i 0.486053 0.513569i
\(51\) −1.62112 2.90201i −0.227002 0.406362i
\(52\) −0.875224 + 0.875224i −0.121372 + 0.121372i
\(53\) 3.62512 3.62512i 0.497949 0.497949i −0.412850 0.910799i \(-0.635467\pi\)
0.910799 + 0.412850i \(0.135467\pi\)
\(54\) −0.220693 + 5.19146i −0.0300326 + 0.706469i
\(55\) 6.16270 + 5.99540i 0.830979 + 0.808420i
\(56\) 4.87868i 0.651941i
\(57\) 1.80047 6.35789i 0.238478 0.842123i
\(58\) 5.50447 + 5.50447i 0.722772 + 0.722772i
\(59\) 3.87315 0.504241 0.252120 0.967696i \(-0.418872\pi\)
0.252120 + 0.967696i \(0.418872\pi\)
\(60\) 1.93514 + 3.35488i 0.249826 + 0.433113i
\(61\) −13.5655 −1.73688 −0.868442 0.495791i \(-0.834878\pi\)
−0.868442 + 0.495791i \(0.834878\pi\)
\(62\) 3.94659 + 3.94659i 0.501217 + 0.501217i
\(63\) −14.2389 + 3.38620i −1.79394 + 0.426621i
\(64\) 1.00000i 0.125000i
\(65\) 2.76744 0.0380814i 0.343259 0.00472341i
\(66\) −5.81422 + 3.24794i −0.715681 + 0.399794i
\(67\) −2.77087 + 2.77087i −0.338515 + 0.338515i −0.855808 0.517293i \(-0.826940\pi\)
0.517293 + 0.855808i \(0.326940\pi\)
\(68\) 1.35706 1.35706i 0.164568 0.164568i
\(69\) −1.51211 + 0.844697i −0.182037 + 0.101690i
\(70\) −7.60700 + 7.81928i −0.909211 + 0.934582i
\(71\) 6.15174i 0.730077i −0.930992 0.365039i \(-0.881056\pi\)
0.930992 0.365039i \(-0.118944\pi\)
\(72\) −2.91860 + 0.694081i −0.343961 + 0.0817983i
\(73\) −9.60788 9.60788i −1.12452 1.12452i −0.991054 0.133463i \(-0.957390\pi\)
−0.133463 0.991054i \(-0.542610\pi\)
\(74\) 2.64393 0.307351
\(75\) 2.12950 8.39436i 0.245894 0.969297i
\(76\) 3.81508 0.437619
\(77\) −13.2646 13.2646i −1.51164 1.51164i
\(78\) −0.584139 + 2.06274i −0.0661408 + 0.233559i
\(79\) 17.1956i 1.93466i 0.253525 + 0.967329i \(0.418410\pi\)
−0.253525 + 0.967329i \(0.581590\pi\)
\(80\) −1.55923 + 1.60274i −0.174328 + 0.179192i
\(81\) 4.05150 + 8.03650i 0.450166 + 0.892945i
\(82\) 3.03885 3.03885i 0.335585 0.335585i
\(83\) 2.00448 2.00448i 0.220021 0.220021i −0.588486 0.808507i \(-0.700276\pi\)
0.808507 + 0.588486i \(0.200276\pi\)
\(84\) −4.12100 7.37712i −0.449638 0.804910i
\(85\) −4.29100 + 0.0590463i −0.465424 + 0.00640447i
\(86\) 0.201747i 0.0217549i
\(87\) 12.9730 + 3.67378i 1.39085 + 0.393870i
\(88\) −2.71889 2.71889i −0.289835 0.289835i
\(89\) 12.5987 1.33546 0.667728 0.744406i \(-0.267267\pi\)
0.667728 + 0.744406i \(0.267267\pi\)
\(90\) 5.76001 + 3.43835i 0.607159 + 0.362434i
\(91\) −6.03860 −0.633018
\(92\) −0.707107 0.707107i −0.0737210 0.0737210i
\(93\) 9.30135 + 2.63402i 0.964505 + 0.273135i
\(94\) 5.13622i 0.529760i
\(95\) −6.11459 5.94860i −0.627344 0.610313i
\(96\) −0.844697 1.51211i −0.0862115 0.154329i
\(97\) −3.36602 + 3.36602i −0.341767 + 0.341767i −0.857032 0.515264i \(-0.827694\pi\)
0.515264 + 0.857032i \(0.327694\pi\)
\(98\) 11.8805 11.8805i 1.20011 1.20011i
\(99\) −6.04824 + 9.82250i −0.607871 + 0.987199i
\(100\) 4.99811 0.137579i 0.499811 0.0137579i
\(101\) 11.2944i 1.12383i 0.827194 + 0.561916i \(0.189936\pi\)
−0.827194 + 0.561916i \(0.810064\pi\)
\(102\) 0.905725 3.19833i 0.0896801 0.316682i
\(103\) −8.36819 8.36819i −0.824542 0.824542i 0.162214 0.986756i \(-0.448137\pi\)
−0.986756 + 0.162214i \(0.948137\pi\)
\(104\) −1.23775 −0.121372
\(105\) −4.89774 + 18.2492i −0.477970 + 1.78094i
\(106\) 5.12670 0.497949
\(107\) −7.21940 7.21940i −0.697925 0.697925i 0.266037 0.963963i \(-0.414286\pi\)
−0.963963 + 0.266037i \(0.914286\pi\)
\(108\) −3.82697 + 3.51487i −0.368251 + 0.338218i
\(109\) 2.16073i 0.206960i 0.994632 + 0.103480i \(0.0329978\pi\)
−0.994632 + 0.103480i \(0.967002\pi\)
\(110\) 0.118300 + 8.59708i 0.0112795 + 0.819699i
\(111\) 3.99792 2.23332i 0.379466 0.211977i
\(112\) 3.44975 3.44975i 0.325971 0.325971i
\(113\) 8.63760 8.63760i 0.812557 0.812557i −0.172459 0.985017i \(-0.555171\pi\)
0.985017 + 0.172459i \(0.0551713\pi\)
\(114\) 5.76883 3.22258i 0.540301 0.301823i
\(115\) 0.0307665 + 2.23586i 0.00286899 + 0.208495i
\(116\) 7.78450i 0.722772i
\(117\) 0.859102 + 3.61251i 0.0794240 + 0.333977i
\(118\) 2.73873 + 2.73873i 0.252120 + 0.252120i
\(119\) 9.36303 0.858308
\(120\) −1.00391 + 3.74061i −0.0916437 + 0.341470i
\(121\) −3.78475 −0.344068
\(122\) −9.59226 9.59226i −0.868442 0.868442i
\(123\) 2.02818 7.16200i 0.182875 0.645775i
\(124\) 5.58131i 0.501217i
\(125\) −8.22521 7.57271i −0.735685 0.677324i
\(126\) −12.4629 7.67404i −1.11028 0.683658i
\(127\) −10.4407 + 10.4407i −0.926462 + 0.926462i −0.997475 0.0710131i \(-0.977377\pi\)
0.0710131 + 0.997475i \(0.477377\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0.170415 + 0.305064i 0.0150042 + 0.0268594i
\(130\) 1.98380 + 1.92995i 0.173991 + 0.169268i
\(131\) 11.2466i 0.982617i −0.870985 0.491309i \(-0.836519\pi\)
0.870985 0.491309i \(-0.163481\pi\)
\(132\) −6.40791 1.81463i −0.557737 0.157944i
\(133\) 13.1611 + 13.1611i 1.14121 + 1.14121i
\(134\) −3.91860 −0.338515
\(135\) 11.6142 + 0.333716i 0.999587 + 0.0287217i
\(136\) 1.91917 0.164568
\(137\) 10.4263 + 10.4263i 0.890776 + 0.890776i 0.994596 0.103820i \(-0.0331066\pi\)
−0.103820 + 0.994596i \(0.533107\pi\)
\(138\) −1.66652 0.471935i −0.141863 0.0401738i
\(139\) 14.6451i 1.24218i −0.783738 0.621092i \(-0.786689\pi\)
0.783738 0.621092i \(-0.213311\pi\)
\(140\) −10.9080 + 0.150100i −0.921897 + 0.0126858i
\(141\) −4.33854 7.76654i −0.365371 0.654061i
\(142\) 4.34994 4.34994i 0.365039 0.365039i
\(143\) −3.36532 + 3.36532i −0.281422 + 0.281422i
\(144\) −2.55455 1.57298i −0.212880 0.131081i
\(145\) 12.1379 12.4766i 1.00799 1.03612i
\(146\) 13.5876i 1.12452i
\(147\) 7.92922 28.0000i 0.653991 2.30940i
\(148\) 1.86954 + 1.86954i 0.153675 + 0.153675i
\(149\) 1.21978 0.0999285 0.0499642 0.998751i \(-0.484089\pi\)
0.0499642 + 0.998751i \(0.484089\pi\)
\(150\) 7.44149 4.42992i 0.607595 0.361701i
\(151\) 6.92084 0.563210 0.281605 0.959530i \(-0.409133\pi\)
0.281605 + 0.959530i \(0.409133\pi\)
\(152\) 2.69767 + 2.69767i 0.218810 + 0.218810i
\(153\) −1.33206 5.60131i −0.107691 0.452839i
\(154\) 18.7590i 1.51164i
\(155\) 8.70257 8.94542i 0.699008 0.718513i
\(156\) −1.87162 + 1.04553i −0.149850 + 0.0837091i
\(157\) 1.67127 1.67127i 0.133382 0.133382i −0.637264 0.770646i \(-0.719934\pi\)
0.770646 + 0.637264i \(0.219934\pi\)
\(158\) −12.1591 + 12.1591i −0.967329 + 0.967329i
\(159\) 7.75215 4.33051i 0.614786 0.343431i
\(160\) −2.23586 + 0.0307665i −0.176760 + 0.00243231i
\(161\) 4.87868i 0.384494i
\(162\) −2.81782 + 8.54751i −0.221389 + 0.671556i
\(163\) 9.29670 + 9.29670i 0.728173 + 0.728173i 0.970256 0.242082i \(-0.0778304\pi\)
−0.242082 + 0.970256i \(0.577830\pi\)
\(164\) 4.29759 0.335585
\(165\) 7.44081 + 12.8998i 0.579266 + 1.00425i
\(166\) 2.83477 0.220021
\(167\) −10.9776 10.9776i −0.849475 0.849475i 0.140593 0.990068i \(-0.455099\pi\)
−0.990068 + 0.140593i \(0.955099\pi\)
\(168\) 2.30242 8.13040i 0.177636 0.627274i
\(169\) 11.4680i 0.882151i
\(170\) −3.07594 2.99244i −0.235914 0.229510i
\(171\) 6.00102 9.74582i 0.458910 0.745282i
\(172\) −0.142657 + 0.142657i −0.0108775 + 0.0108775i
\(173\) −17.3398 + 17.3398i −1.31832 + 1.31832i −0.403212 + 0.915107i \(0.632106\pi\)
−0.915107 + 0.403212i \(0.867894\pi\)
\(174\) 6.57554 + 11.7710i 0.498490 + 0.892361i
\(175\) 17.7168 + 16.7676i 1.33927 + 1.26751i
\(176\) 3.84509i 0.289835i
\(177\) 6.45466 + 1.82787i 0.485162 + 0.137391i
\(178\) 8.90860 + 8.90860i 0.667728 + 0.667728i
\(179\) −1.47094 −0.109943 −0.0549715 0.998488i \(-0.517507\pi\)
−0.0549715 + 0.998488i \(0.517507\pi\)
\(180\) 1.64166 + 6.50423i 0.122362 + 0.484796i
\(181\) −15.6852 −1.16587 −0.582936 0.812518i \(-0.698096\pi\)
−0.582936 + 0.812518i \(0.698096\pi\)
\(182\) −4.26994 4.26994i −0.316509 0.316509i
\(183\) −22.6071 6.40203i −1.67117 0.473252i
\(184\) 1.00000i 0.0737210i
\(185\) −0.0813446 5.91145i −0.00598057 0.434618i
\(186\) 4.71452 + 8.43958i 0.345685 + 0.618820i
\(187\) 5.21802 5.21802i 0.381580 0.381580i
\(188\) 3.63185 3.63185i 0.264880 0.264880i
\(189\) −25.3275 1.07669i −1.84230 0.0783179i
\(190\) −0.117377 8.52997i −0.00851540 0.618829i
\(191\) 21.7200i 1.57160i 0.618480 + 0.785800i \(0.287749\pi\)
−0.618480 + 0.785800i \(0.712251\pi\)
\(192\) 0.471935 1.66652i 0.0340590 0.120270i
\(193\) 17.8302 + 17.8302i 1.28345 + 1.28345i 0.938694 + 0.344751i \(0.112037\pi\)
0.344751 + 0.938694i \(0.387963\pi\)
\(194\) −4.76027 −0.341767
\(195\) 4.62996 + 1.24259i 0.331558 + 0.0889836i
\(196\) 16.8015 1.20011
\(197\) −0.806128 0.806128i −0.0574342 0.0574342i 0.677806 0.735241i \(-0.262931\pi\)
−0.735241 + 0.677806i \(0.762931\pi\)
\(198\) −11.2223 + 2.66881i −0.797535 + 0.189664i
\(199\) 18.0493i 1.27948i −0.768590 0.639742i \(-0.779041\pi\)
0.768590 0.639742i \(-0.220959\pi\)
\(200\) 3.63148 + 3.43691i 0.256784 + 0.243026i
\(201\) −5.92537 + 3.31003i −0.417943 + 0.233471i
\(202\) −7.98633 + 7.98633i −0.561916 + 0.561916i
\(203\) −26.8546 + 26.8546i −1.88482 + 1.88482i
\(204\) 2.90201 1.62112i 0.203181 0.113501i
\(205\) −6.88793 6.70094i −0.481074 0.468014i
\(206\) 11.8344i 0.824542i
\(207\) −2.91860 + 0.694081i −0.202857 + 0.0482420i
\(208\) −0.875224 0.875224i −0.0606859 0.0606859i
\(209\) 14.6693 1.01470
\(210\) −16.3674 + 9.44094i −1.12946 + 0.651487i
\(211\) 7.95847 0.547884 0.273942 0.961746i \(-0.411672\pi\)
0.273942 + 0.961746i \(0.411672\pi\)
\(212\) 3.62512 + 3.62512i 0.248975 + 0.248975i
\(213\) 2.90322 10.2520i 0.198925 0.702454i
\(214\) 10.2098i 0.697925i
\(215\) 0.451077 0.00620705i 0.0307632 0.000423317i
\(216\) −5.19146 0.220693i −0.353234 0.0150163i
\(217\) −19.2541 + 19.2541i −1.30706 + 1.30706i
\(218\) −1.52786 + 1.52786i −0.103480 + 0.103480i
\(219\) −11.4774 20.5460i −0.775570 1.38837i
\(220\) −5.99540 + 6.16270i −0.404210 + 0.415489i
\(221\) 2.37546i 0.159791i
\(222\) 4.40615 + 1.24776i 0.295722 + 0.0837444i
\(223\) 16.5940 + 16.5940i 1.11122 + 1.11122i 0.992986 + 0.118233i \(0.0377228\pi\)
0.118233 + 0.992986i \(0.462277\pi\)
\(224\) 4.87868 0.325971
\(225\) 7.51044 12.9843i 0.500696 0.865623i
\(226\) 12.2154 0.812557
\(227\) 4.89140 + 4.89140i 0.324653 + 0.324653i 0.850549 0.525896i \(-0.176270\pi\)
−0.525896 + 0.850549i \(0.676270\pi\)
\(228\) 6.35789 + 1.80047i 0.421062 + 0.119239i
\(229\) 4.39356i 0.290335i 0.989407 + 0.145167i \(0.0463721\pi\)
−0.989407 + 0.145167i \(0.953628\pi\)
\(230\) −1.55923 + 1.60274i −0.102813 + 0.105682i
\(231\) −15.8456 28.3657i −1.04257 1.86633i
\(232\) −5.50447 + 5.50447i −0.361386 + 0.361386i
\(233\) 8.94095 8.94095i 0.585741 0.585741i −0.350734 0.936475i \(-0.614068\pi\)
0.936475 + 0.350734i \(0.114068\pi\)
\(234\) −1.94696 + 3.16191i −0.127276 + 0.206700i
\(235\) −11.4838 + 0.158024i −0.749123 + 0.0103083i
\(236\) 3.87315i 0.252120i
\(237\) −8.11521 + 28.6568i −0.527140 + 1.86146i
\(238\) 6.62066 + 6.62066i 0.429154 + 0.429154i
\(239\) 7.07155 0.457420 0.228710 0.973495i \(-0.426549\pi\)
0.228710 + 0.973495i \(0.426549\pi\)
\(240\) −3.35488 + 1.93514i −0.216557 + 0.124913i
\(241\) −4.22605 −0.272224 −0.136112 0.990693i \(-0.543461\pi\)
−0.136112 + 0.990693i \(0.543461\pi\)
\(242\) −2.67622 2.67622i −0.172034 0.172034i
\(243\) 2.95918 + 15.3050i 0.189832 + 0.981817i
\(244\) 13.5655i 0.868442i
\(245\) −26.9285 26.1975i −1.72040 1.67370i
\(246\) 6.49844 3.63016i 0.414325 0.231450i
\(247\) 3.33905 3.33905i 0.212459 0.212459i
\(248\) −3.94659 + 3.94659i −0.250608 + 0.250608i
\(249\) 4.28649 2.39452i 0.271645 0.151747i
\(250\) −0.461381 11.1708i −0.0291803 0.706504i
\(251\) 0.318931i 0.0201307i 0.999949 + 0.0100654i \(0.00320396\pi\)
−0.999949 + 0.0100654i \(0.996796\pi\)
\(252\) −3.38620 14.2389i −0.213311 0.896969i
\(253\) −2.71889 2.71889i −0.170935 0.170935i
\(254\) −14.7654 −0.926462
\(255\) −7.17888 1.92667i −0.449559 0.120653i
\(256\) 1.00000 0.0625000
\(257\) −9.89138 9.89138i −0.617007 0.617007i 0.327755 0.944763i \(-0.393708\pi\)
−0.944763 + 0.327755i \(0.893708\pi\)
\(258\) −0.0952114 + 0.336214i −0.00592760 + 0.0209318i
\(259\) 12.8989i 0.801498i
\(260\) 0.0380814 + 2.76744i 0.00236171 + 0.171629i
\(261\) 19.8859 + 12.2448i 1.23091 + 0.757935i
\(262\) 7.95253 7.95253i 0.491309 0.491309i
\(263\) 6.24409 6.24409i 0.385027 0.385027i −0.487882 0.872909i \(-0.662231\pi\)
0.872909 + 0.487882i \(0.162231\pi\)
\(264\) −3.24794 5.81422i −0.199897 0.357840i
\(265\) −0.157731 11.4626i −0.00968932 0.704140i
\(266\) 18.6125i 1.14121i
\(267\) 20.9959 + 5.94575i 1.28493 + 0.363874i
\(268\) −2.77087 2.77087i −0.169258 0.169258i
\(269\) 11.4973 0.701002 0.350501 0.936562i \(-0.386011\pi\)
0.350501 + 0.936562i \(0.386011\pi\)
\(270\) 7.97648 + 8.44842i 0.485433 + 0.514155i
\(271\) 14.4129 0.875519 0.437760 0.899092i \(-0.355772\pi\)
0.437760 + 0.899092i \(0.355772\pi\)
\(272\) 1.35706 + 1.35706i 0.0822839 + 0.0822839i
\(273\) −10.0634 2.84983i −0.609067 0.172479i
\(274\) 14.7450i 0.890776i
\(275\) 19.2182 0.529004i 1.15890 0.0319002i
\(276\) −0.844697 1.51211i −0.0508448 0.0910185i
\(277\) −21.8386 + 21.8386i −1.31215 + 1.31215i −0.392325 + 0.919827i \(0.628329\pi\)
−0.919827 + 0.392325i \(0.871671\pi\)
\(278\) 10.3557 10.3557i 0.621092 0.621092i
\(279\) 14.2578 + 8.77927i 0.853590 + 0.525601i
\(280\) −7.81928 7.60700i −0.467291 0.454605i
\(281\) 32.5667i 1.94277i −0.237517 0.971383i \(-0.576334\pi\)
0.237517 0.971383i \(-0.423666\pi\)
\(282\) 2.42396 8.55959i 0.144345 0.509716i
\(283\) −18.1562 18.1562i −1.07927 1.07927i −0.996574 0.0827000i \(-0.973646\pi\)
−0.0827000 0.996574i \(-0.526354\pi\)
\(284\) 6.15174 0.365039
\(285\) −7.38272 12.7991i −0.437315 0.758155i
\(286\) −4.75928 −0.281422
\(287\) 14.8256 + 14.8256i 0.875127 + 0.875127i
\(288\) −0.694081 2.91860i −0.0408991 0.171980i
\(289\) 13.3168i 0.783340i
\(290\) 17.4050 0.239502i 1.02206 0.0140640i
\(291\) −7.19807 + 4.02098i −0.421958 + 0.235714i
\(292\) 9.60788 9.60788i 0.562258 0.562258i
\(293\) 9.83546 9.83546i 0.574594 0.574594i −0.358815 0.933409i \(-0.616819\pi\)
0.933409 + 0.358815i \(0.116819\pi\)
\(294\) 25.4058 14.1922i 1.48170 0.827705i
\(295\) 6.03914 6.20766i 0.351612 0.361424i
\(296\) 2.64393i 0.153675i
\(297\) −14.7151 + 13.5150i −0.853855 + 0.784219i
\(298\) 0.862517 + 0.862517i 0.0499642 + 0.0499642i
\(299\) −1.23775 −0.0715811
\(300\) 8.39436 + 2.12950i 0.484648 + 0.122947i
\(301\) −0.984258 −0.0567317
\(302\) 4.89377 + 4.89377i 0.281605 + 0.281605i
\(303\) −5.33021 + 18.8223i −0.306213 + 1.08131i
\(304\) 3.81508i 0.218810i
\(305\) −21.1518 + 21.7420i −1.21115 + 1.24494i
\(306\) 3.01881 4.90263i 0.172574 0.280265i
\(307\) −16.7681 + 16.7681i −0.957004 + 0.957004i −0.999113 0.0421088i \(-0.986592\pi\)
0.0421088 + 0.999113i \(0.486592\pi\)
\(308\) 13.2646 13.2646i 0.755821 0.755821i
\(309\) −9.99648 17.8950i −0.568680 1.01801i
\(310\) 12.4790 0.171718i 0.708760 0.00975291i
\(311\) 6.36857i 0.361128i −0.983563 0.180564i \(-0.942208\pi\)
0.983563 0.180564i \(-0.0577924\pi\)
\(312\) −2.06274 0.584139i −0.116779 0.0330704i
\(313\) −16.8425 16.8425i −0.951993 0.951993i 0.0469067 0.998899i \(-0.485064\pi\)
−0.998899 + 0.0469067i \(0.985064\pi\)
\(314\) 2.36353 0.133382
\(315\) −16.7746 + 28.1013i −0.945143 + 1.58333i
\(316\) −17.1956 −0.967329
\(317\) 17.8078 + 17.8078i 1.00018 + 1.00018i 1.00000 0.000184598i \(5.87594e-5\pi\)
0.000184598 1.00000i \(0.499941\pi\)
\(318\) 8.54373 + 2.41947i 0.479108 + 0.135677i
\(319\) 29.9321i 1.67588i
\(320\) −1.60274 1.55923i −0.0895961 0.0871638i
\(321\) −8.62416 15.4383i −0.481353 0.861683i
\(322\) 3.44975 3.44975i 0.192247 0.192247i
\(323\) −5.17729 + 5.17729i −0.288072 + 0.288072i
\(324\) −8.03650 + 4.05150i −0.446472 + 0.225083i
\(325\) 4.25405 4.49488i 0.235972 0.249331i
\(326\) 13.1475i 0.728173i
\(327\) −1.01972 + 3.60089i −0.0563908 + 0.199129i
\(328\) 3.03885 + 3.03885i 0.167793 + 0.167793i
\(329\) 25.0580 1.38149
\(330\) −3.86011 + 14.3830i −0.212492 + 0.791758i
\(331\) −5.76581 −0.316918 −0.158459 0.987366i \(-0.550653\pi\)
−0.158459 + 0.987366i \(0.550653\pi\)
\(332\) 2.00448 + 2.00448i 0.110010 + 0.110010i
\(333\) 7.71659 1.83510i 0.422866 0.100563i
\(334\) 15.5247i 0.849475i
\(335\) 0.120562 + 8.76143i 0.00658699 + 0.478688i
\(336\) 7.37712 4.12100i 0.402455 0.224819i
\(337\) −11.3239 + 11.3239i −0.616851 + 0.616851i −0.944722 0.327871i \(-0.893669\pi\)
0.327871 + 0.944722i \(0.393669\pi\)
\(338\) 8.10908 8.10908i 0.441076 0.441076i
\(339\) 18.4711 10.3183i 1.00321 0.560414i
\(340\) −0.0590463 4.29100i −0.00320223 0.232712i
\(341\) 21.4607i 1.16216i
\(342\) 11.1347 2.64797i 0.602096 0.143186i
\(343\) 33.8128 + 33.8128i 1.82572 + 1.82572i
\(344\) −0.201747 −0.0108775
\(345\) −1.00391 + 3.74061i −0.0540485 + 0.201388i
\(346\) −24.5221 −1.31832
\(347\) −6.47445 6.47445i −0.347567 0.347567i 0.511636 0.859203i \(-0.329040\pi\)
−0.859203 + 0.511636i \(0.829040\pi\)
\(348\) −3.67378 + 12.9730i −0.196935 + 0.695425i
\(349\) 11.4593i 0.613401i −0.951806 0.306701i \(-0.900775\pi\)
0.951806 0.306701i \(-0.0992251\pi\)
\(350\) 0.671204 + 24.3842i 0.0358774 + 1.30339i
\(351\) −0.273164 + 6.42575i −0.0145804 + 0.342981i
\(352\) 2.71889 2.71889i 0.144917 0.144917i
\(353\) −14.6045 + 14.6045i −0.777319 + 0.777319i −0.979374 0.202055i \(-0.935238\pi\)
0.202055 + 0.979374i \(0.435238\pi\)
\(354\) 3.27163 + 5.85664i 0.173885 + 0.311277i
\(355\) −9.85967 9.59200i −0.523297 0.509091i
\(356\) 12.5987i 0.667728i
\(357\) 15.6036 + 4.41874i 0.825833 + 0.233865i
\(358\) −1.04011 1.04011i −0.0549715 0.0549715i
\(359\) −3.30519 −0.174441 −0.0872207 0.996189i \(-0.527799\pi\)
−0.0872207 + 0.996189i \(0.527799\pi\)
\(360\) −3.43835 + 5.76001i −0.181217 + 0.303579i
\(361\) 4.44518 0.233957
\(362\) −11.0911 11.0911i −0.582936 0.582936i
\(363\) −6.30734 1.78615i −0.331050 0.0937488i
\(364\) 6.03860i 0.316509i
\(365\) −30.3799 + 0.418043i −1.59016 + 0.0218814i
\(366\) −11.4587 20.5126i −0.598957 1.07221i
\(367\) −12.2911 + 12.2911i −0.641591 + 0.641591i −0.950946 0.309355i \(-0.899887\pi\)
0.309355 + 0.950946i \(0.399887\pi\)
\(368\) 0.707107 0.707107i 0.0368605 0.0368605i
\(369\) 6.75999 10.9784i 0.351911 0.571513i
\(370\) 4.12251 4.23754i 0.214319 0.220299i
\(371\) 25.0115i 1.29853i
\(372\) −2.63402 + 9.30135i −0.136567 + 0.482253i
\(373\) 4.21951 + 4.21951i 0.218478 + 0.218478i 0.807857 0.589379i \(-0.200627\pi\)
−0.589379 + 0.807857i \(0.700627\pi\)
\(374\) 7.37940 0.381580
\(375\) −10.1336 16.5018i −0.523297 0.852150i
\(376\) 5.13622 0.264880
\(377\) 6.81318 + 6.81318i 0.350897 + 0.350897i
\(378\) −17.1479 18.6706i −0.881993 0.960311i
\(379\) 24.7674i 1.27221i 0.771601 + 0.636107i \(0.219456\pi\)
−0.771601 + 0.636107i \(0.780544\pi\)
\(380\) 5.94860 6.11459i 0.305157 0.313672i
\(381\) −22.3269 + 12.4723i −1.14384 + 0.638974i
\(382\) −15.3583 + 15.3583i −0.785800 + 0.785800i
\(383\) −12.2872 + 12.2872i −0.627846 + 0.627846i −0.947526 0.319680i \(-0.896425\pi\)
0.319680 + 0.947526i \(0.396425\pi\)
\(384\) 1.51211 0.844697i 0.0771647 0.0431057i
\(385\) −41.9424 + 0.577149i −2.13758 + 0.0294142i
\(386\) 25.2157i 1.28345i
\(387\) 0.140029 + 0.588819i 0.00711806 + 0.0299314i
\(388\) −3.36602 3.36602i −0.170884 0.170884i
\(389\) −15.4882 −0.785281 −0.392640 0.919692i \(-0.628438\pi\)
−0.392640 + 0.919692i \(0.628438\pi\)
\(390\) 2.39523 + 4.15252i 0.121287 + 0.210271i
\(391\) 1.91917 0.0970568
\(392\) 11.8805 + 11.8805i 0.600054 + 0.600054i
\(393\) 5.30765 18.7426i 0.267736 0.945439i
\(394\) 1.14004i 0.0574342i
\(395\) 27.5602 + 26.8120i 1.38670 + 1.34906i
\(396\) −9.82250 6.04824i −0.493599 0.303935i
\(397\) −14.2745 + 14.2745i −0.716415 + 0.716415i −0.967869 0.251454i \(-0.919091\pi\)
0.251454 + 0.967869i \(0.419091\pi\)
\(398\) 12.7628 12.7628i 0.639742 0.639742i
\(399\) 15.7220 + 28.1443i 0.787082 + 1.40898i
\(400\) 0.137579 + 4.99811i 0.00687895 + 0.249905i
\(401\) 3.26739i 0.163166i 0.996667 + 0.0815829i \(0.0259975\pi\)
−0.996667 + 0.0815829i \(0.974002\pi\)
\(402\) −6.53041 1.84932i −0.325707 0.0922359i
\(403\) 4.88490 + 4.88490i 0.243334 + 0.243334i
\(404\) −11.2944 −0.561916
\(405\) 19.1977 + 6.03727i 0.953941 + 0.299994i
\(406\) −37.9781 −1.88482
\(407\) 7.18856 + 7.18856i 0.356324 + 0.356324i
\(408\) 3.19833 + 0.905725i 0.158341 + 0.0448401i
\(409\) 33.7644i 1.66954i 0.550596 + 0.834772i \(0.314400\pi\)
−0.550596 + 0.834772i \(0.685600\pi\)
\(410\) −0.132222 9.60878i −0.00652997 0.474544i
\(411\) 12.4550 + 22.2961i 0.614361 + 1.09978i
\(412\) 8.36819 8.36819i 0.412271 0.412271i
\(413\) −13.3614 + 13.3614i −0.657470 + 0.657470i
\(414\) −2.55455 1.57298i −0.125550 0.0773075i
\(415\) −0.0872160 6.33814i −0.00428126 0.311127i
\(416\) 1.23775i 0.0606859i
\(417\) 6.91155 24.4063i 0.338460 1.19518i
\(418\) 10.3728 + 10.3728i 0.507349 + 0.507349i
\(419\) −20.6323 −1.00795 −0.503977 0.863717i \(-0.668130\pi\)
−0.503977 + 0.863717i \(0.668130\pi\)
\(420\) −18.2492 4.89774i −0.890472 0.238985i
\(421\) −33.8481 −1.64966 −0.824828 0.565383i \(-0.808728\pi\)
−0.824828 + 0.565383i \(0.808728\pi\)
\(422\) 5.62749 + 5.62749i 0.273942 + 0.273942i
\(423\) −3.56495 14.9906i −0.173334 0.728867i
\(424\) 5.12670i 0.248975i
\(425\) −6.59603 + 6.96944i −0.319954 + 0.338067i
\(426\) 9.30213 5.19635i 0.450690 0.251764i
\(427\) 46.7975 46.7975i 2.26469 2.26469i
\(428\) 7.21940 7.21940i 0.348963 0.348963i
\(429\) −7.19657 + 4.02015i −0.347454 + 0.194095i
\(430\) 0.323349 + 0.314570i 0.0155932 + 0.0151699i
\(431\) 11.9724i 0.576690i −0.957527 0.288345i \(-0.906895\pi\)
0.957527 0.288345i \(-0.0931051\pi\)
\(432\) −3.51487 3.82697i −0.169109 0.184125i
\(433\) 13.6433 + 13.6433i 0.655655 + 0.655655i 0.954349 0.298694i \(-0.0965511\pi\)
−0.298694 + 0.954349i \(0.596551\pi\)
\(434\) −27.2294 −1.30706
\(435\) 26.1161 15.0641i 1.25217 0.722269i
\(436\) −2.16073 −0.103480
\(437\) 2.69767 + 2.69767i 0.129047 + 0.129047i
\(438\) 6.41246 22.6439i 0.306399 1.08197i
\(439\) 12.4463i 0.594027i 0.954873 + 0.297014i \(0.0959907\pi\)
−0.954873 + 0.297014i \(0.904009\pi\)
\(440\) −8.59708 + 0.118300i −0.409850 + 0.00563974i
\(441\) 26.4284 42.9204i 1.25849 2.04383i
\(442\) 1.67971 1.67971i 0.0798955 0.0798955i
\(443\) 8.23721 8.23721i 0.391362 0.391362i −0.483811 0.875173i \(-0.660748\pi\)
0.875173 + 0.483811i \(0.160748\pi\)
\(444\) 2.23332 + 3.99792i 0.105989 + 0.189733i
\(445\) 19.6443 20.1924i 0.931227 0.957213i
\(446\) 23.4675i 1.11122i
\(447\) 2.03279 + 0.575658i 0.0961476 + 0.0272277i
\(448\) 3.44975 + 3.44975i 0.162985 + 0.162985i
\(449\) −16.4715 −0.777340 −0.388670 0.921377i \(-0.627065\pi\)
−0.388670 + 0.921377i \(0.627065\pi\)
\(450\) 14.4920 3.87063i 0.683160 0.182463i
\(451\) 16.5246 0.778114
\(452\) 8.63760 + 8.63760i 0.406279 + 0.406279i
\(453\) 11.5337 + 3.26619i 0.541900 + 0.153459i
\(454\) 6.91748i 0.324653i
\(455\) −9.41560 + 9.67834i −0.441410 + 0.453728i
\(456\) 3.22258 + 5.76883i 0.150911 + 0.270150i
\(457\) −8.60752 + 8.60752i −0.402643 + 0.402643i −0.879163 0.476520i \(-0.841898\pi\)
0.476520 + 0.879163i \(0.341898\pi\)
\(458\) −3.10672 + 3.10672i −0.145167 + 0.145167i
\(459\) 0.423549 9.96332i 0.0197696 0.465048i
\(460\) −2.23586 + 0.0307665i −0.104247 + 0.00143450i
\(461\) 37.7905i 1.76008i −0.474898 0.880041i \(-0.657515\pi\)
0.474898 0.880041i \(-0.342485\pi\)
\(462\) 8.85302 31.2622i 0.411880 1.45445i
\(463\) −7.64424 7.64424i −0.355258 0.355258i 0.506804 0.862062i \(-0.330827\pi\)
−0.862062 + 0.506804i \(0.830827\pi\)
\(464\) −7.78450 −0.361386
\(465\) 18.7246 10.8006i 0.868334 0.500868i
\(466\) 12.6444 0.585741
\(467\) −5.24131 5.24131i −0.242539 0.242539i 0.575361 0.817900i \(-0.304862\pi\)
−0.817900 + 0.575361i \(0.804862\pi\)
\(468\) −3.61251 + 0.859102i −0.166988 + 0.0397120i
\(469\) 19.1176i 0.882768i
\(470\) −8.23204 8.00856i −0.379716 0.369407i
\(471\) 3.57393 1.99647i 0.164678 0.0919923i
\(472\) −2.73873 + 2.73873i −0.126060 + 0.126060i
\(473\) −0.548528 + 0.548528i −0.0252213 + 0.0252213i
\(474\) −26.0017 + 14.5251i −1.19430 + 0.667159i
\(475\) −19.0682 + 0.524875i −0.874907 + 0.0240829i
\(476\) 9.36303i 0.429154i
\(477\) 14.9628 3.55835i 0.685100 0.162926i
\(478\) 5.00034 + 5.00034i 0.228710 + 0.228710i
\(479\) −26.6043 −1.21558 −0.607790 0.794098i \(-0.707944\pi\)
−0.607790 + 0.794098i \(0.707944\pi\)
\(480\) −3.74061 1.00391i −0.170735 0.0458218i
\(481\) 3.27254 0.149215
\(482\) −2.98827 2.98827i −0.136112 0.136112i
\(483\) 2.30242 8.13040i 0.104764 0.369946i
\(484\) 3.78475i 0.172034i
\(485\) 0.146457 + 10.6433i 0.00665027 + 0.483286i
\(486\) −8.72982 + 12.9147i −0.395993 + 0.585824i
\(487\) −5.61285 + 5.61285i −0.254342 + 0.254342i −0.822748 0.568406i \(-0.807560\pi\)
0.568406 + 0.822748i \(0.307560\pi\)
\(488\) 9.59226 9.59226i 0.434221 0.434221i
\(489\) 11.1057 + 19.8805i 0.502215 + 0.899029i
\(490\) −0.516924 37.5658i −0.0233523 1.69705i
\(491\) 35.1263i 1.58523i 0.609724 + 0.792614i \(0.291280\pi\)
−0.609724 + 0.792614i \(0.708720\pi\)
\(492\) 7.16200 + 2.02818i 0.322888 + 0.0914375i
\(493\) −10.5640 10.5640i −0.475780 0.475780i
\(494\) 4.72213 0.212459
\(495\) 6.31234 + 25.0094i 0.283719 + 1.12409i
\(496\) −5.58131 −0.250608
\(497\) 21.2219 + 21.2219i 0.951934 + 0.951934i
\(498\) 4.72419 + 1.33783i 0.211696 + 0.0599495i
\(499\) 10.0259i 0.448822i −0.974495 0.224411i \(-0.927954\pi\)
0.974495 0.224411i \(-0.0720458\pi\)
\(500\) 7.57271 8.22521i 0.338662 0.367842i
\(501\) −13.1137 23.4751i −0.585876 1.04879i
\(502\) −0.225518 + 0.225518i −0.0100654 + 0.0100654i
\(503\) 14.7345 14.7345i 0.656979 0.656979i −0.297685 0.954664i \(-0.596215\pi\)
0.954664 + 0.297685i \(0.0962145\pi\)
\(504\) 7.67404 12.4629i 0.341829 0.555140i
\(505\) 18.1020 + 17.6106i 0.805528 + 0.783660i
\(506\) 3.84509i 0.170935i
\(507\) 5.41214 19.1116i 0.240361 0.848774i
\(508\) −10.4407 10.4407i −0.463231 0.463231i
\(509\) −29.8800 −1.32441 −0.662205 0.749323i \(-0.730379\pi\)
−0.662205 + 0.749323i \(0.730379\pi\)
\(510\) −3.71387 6.43860i −0.164453 0.285106i
\(511\) 66.2895 2.93247
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 14.6002 13.4095i 0.644615 0.592043i
\(514\) 13.9885i 0.617007i
\(515\) −26.4600 + 0.364103i −1.16597 + 0.0160443i
\(516\) −0.305064 + 0.170415i −0.0134297 + 0.00750209i
\(517\) 13.9648 13.9648i 0.614172 0.614172i
\(518\) −9.12089 + 9.12089i −0.400749 + 0.400749i
\(519\) −37.0803 + 20.7138i −1.62764 + 0.909234i
\(520\) −1.92995 + 1.98380i −0.0846338 + 0.0869955i
\(521\) 1.39433i 0.0610866i −0.999533 0.0305433i \(-0.990276\pi\)
0.999533 0.0305433i \(-0.00972375\pi\)
\(522\) 5.40308 + 22.7199i 0.236486 + 0.994422i
\(523\) −25.8878 25.8878i −1.13199 1.13199i −0.989845 0.142148i \(-0.954599\pi\)
−0.142148 0.989845i \(-0.545401\pi\)
\(524\) 11.2466 0.491309
\(525\) 21.6122 + 36.3047i 0.943232 + 1.58447i
\(526\) 8.83047 0.385027
\(527\) −7.57418 7.57418i −0.329936 0.329936i
\(528\) 1.81463 6.40791i 0.0789718 0.278869i
\(529\) 1.00000i 0.0434783i
\(530\) 7.99372 8.21679i 0.347225 0.356914i
\(531\) 9.89417 + 6.09236i 0.429370 + 0.264386i
\(532\) −13.1611 + 13.1611i −0.570604 + 0.570604i
\(533\) 3.76135 3.76135i 0.162922 0.162922i
\(534\) 10.6420 + 19.0506i 0.460526 + 0.824400i
\(535\) −22.8276 + 0.314119i −0.986922 + 0.0135805i
\(536\) 3.91860i 0.169258i
\(537\) −2.45134 0.694187i −0.105783 0.0299564i
\(538\) 8.12981 + 8.12981i 0.350501 + 0.350501i
\(539\) 64.6034 2.78267
\(540\) −0.333716 + 11.6142i −0.0143608 + 0.499794i
\(541\) 18.7230 0.804966 0.402483 0.915427i \(-0.368147\pi\)
0.402483 + 0.915427i \(0.368147\pi\)
\(542\) 10.1914 + 10.1914i 0.437760 + 0.437760i
\(543\) −26.1396 7.40239i −1.12176 0.317667i
\(544\) 1.91917i 0.0822839i
\(545\) 3.46309 + 3.36908i 0.148343 + 0.144315i
\(546\) −5.10079 9.13106i −0.218294 0.390773i
\(547\) 17.9273 17.9273i 0.766517 0.766517i −0.210974 0.977492i \(-0.567664\pi\)
0.977492 + 0.210974i \(0.0676636\pi\)
\(548\) −10.4263 + 10.4263i −0.445388 + 0.445388i
\(549\) −34.6538 21.3382i −1.47899 0.910692i
\(550\) 13.9634 + 13.2152i 0.595400 + 0.563500i
\(551\) 29.6985i 1.26520i
\(552\) 0.471935 1.66652i 0.0200869 0.0709317i
\(553\) −59.3205 59.3205i −2.52257 2.52257i
\(554\) −30.8844 −1.31215
\(555\) 2.65426 9.88992i 0.112667 0.419804i
\(556\) 14.6451 0.621092
\(557\) 18.5689 + 18.5689i 0.786789 + 0.786789i 0.980966 0.194178i \(-0.0622038\pi\)
−0.194178 + 0.980966i \(0.562204\pi\)
\(558\) 3.87389 + 16.2896i 0.163995 + 0.689596i
\(559\) 0.249713i 0.0105617i
\(560\) −0.150100 10.9080i −0.00634288 0.460948i
\(561\) 11.1585 6.23336i 0.471112 0.263172i
\(562\) 23.0281 23.0281i 0.971383 0.971383i
\(563\) −9.38961 + 9.38961i −0.395725 + 0.395725i −0.876722 0.480997i \(-0.840275\pi\)
0.480997 + 0.876722i \(0.340275\pi\)
\(564\) 7.76654 4.33854i 0.327030 0.182686i
\(565\) −0.375826 27.3119i −0.0158111 1.14902i
\(566\) 25.6768i 1.07927i
\(567\) −41.7005 13.7473i −1.75126 0.577330i
\(568\) 4.34994 + 4.34994i 0.182519 + 0.182519i
\(569\) 9.13075 0.382781 0.191390 0.981514i \(-0.438700\pi\)
0.191390 + 0.981514i \(0.438700\pi\)
\(570\) 3.82998 14.2707i 0.160420 0.597735i
\(571\) 33.9459 1.42059 0.710296 0.703903i \(-0.248561\pi\)
0.710296 + 0.703903i \(0.248561\pi\)
\(572\) −3.36532 3.36532i −0.140711 0.140711i
\(573\) −10.2504 + 36.1967i −0.428217 + 1.51214i
\(574\) 20.9665i 0.875127i
\(575\) 3.63148 + 3.43691i 0.151443 + 0.143329i
\(576\) 1.57298 2.55455i 0.0655406 0.106440i
\(577\) −3.14294 + 3.14294i −0.130842 + 0.130842i −0.769495 0.638653i \(-0.779492\pi\)
0.638653 + 0.769495i \(0.279492\pi\)
\(578\) 9.41638 9.41638i 0.391670 0.391670i
\(579\) 21.2996 + 38.1290i 0.885182 + 1.58459i
\(580\) 12.4766 + 12.1379i 0.518061 + 0.503997i
\(581\) 13.8299i 0.573762i
\(582\) −7.93307 2.24654i −0.328836 0.0931220i
\(583\) 13.9389 + 13.9389i 0.577292 + 0.577292i
\(584\) 13.5876 0.562258
\(585\) 7.12948 + 4.25583i 0.294768 + 0.175957i
\(586\) 13.9094 0.574594
\(587\) 15.2589 + 15.2589i 0.629804 + 0.629804i 0.948019 0.318215i \(-0.103083\pi\)
−0.318215 + 0.948019i \(0.603083\pi\)
\(588\) 28.0000 + 7.92922i 1.15470 + 0.326996i
\(589\) 21.2931i 0.877369i
\(590\) 8.65980 0.119163i 0.356518 0.00490587i
\(591\) −0.962985 1.72387i −0.0396119 0.0709103i
\(592\) −1.86954 + 1.86954i −0.0768377 + 0.0768377i
\(593\) 23.4549 23.4549i 0.963176 0.963176i −0.0361698 0.999346i \(-0.511516\pi\)
0.999346 + 0.0361698i \(0.0115157\pi\)
\(594\) −19.9617 0.848587i −0.819037 0.0348179i
\(595\) 14.5992 15.0065i 0.598507 0.615208i
\(596\) 1.21978i 0.0499642i
\(597\) 8.51811 30.0795i 0.348623 1.23107i
\(598\) −0.875224 0.875224i −0.0357906 0.0357906i
\(599\) −10.6390 −0.434697 −0.217349 0.976094i \(-0.569741\pi\)
−0.217349 + 0.976094i \(0.569741\pi\)
\(600\) 4.42992 + 7.44149i 0.180851 + 0.303798i
\(601\) −24.4899 −0.998966 −0.499483 0.866324i \(-0.666477\pi\)
−0.499483 + 0.866324i \(0.666477\pi\)
\(602\) −0.695975 0.695975i −0.0283658 0.0283658i
\(603\) −11.4368 + 2.71983i −0.465744 + 0.110760i
\(604\) 6.92084i 0.281605i
\(605\) −5.90131 + 6.06598i −0.239922 + 0.246617i
\(606\) −17.0784 + 9.54032i −0.693761 + 0.387549i
\(607\) −20.6737 + 20.6737i −0.839120 + 0.839120i −0.988743 0.149623i \(-0.952194\pi\)
0.149623 + 0.988743i \(0.452194\pi\)
\(608\) −2.69767 + 2.69767i −0.109405 + 0.109405i
\(609\) −57.4272 + 32.0799i −2.32707 + 1.29995i
\(610\) −30.3305 + 0.417363i −1.22805 + 0.0168985i
\(611\) 6.35737i 0.257192i
\(612\) 5.60131 1.33206i 0.226419 0.0538454i
\(613\) 14.6753 + 14.6753i 0.592731 + 0.592731i 0.938368 0.345637i \(-0.112337\pi\)
−0.345637 + 0.938368i \(0.612337\pi\)
\(614\) −23.7136 −0.957004
\(615\) −8.31644 14.4179i −0.335351 0.581385i
\(616\) 18.7590 0.755821
\(617\) 9.12773 + 9.12773i 0.367469 + 0.367469i 0.866553 0.499085i \(-0.166330\pi\)
−0.499085 + 0.866553i \(0.666330\pi\)
\(618\) 5.58507 19.7222i 0.224664 0.793344i
\(619\) 14.8927i 0.598587i −0.954161 0.299294i \(-0.903249\pi\)
0.954161 0.299294i \(-0.0967510\pi\)
\(620\) 8.94542 + 8.70257i 0.359257 + 0.349504i
\(621\) −5.19146 0.220693i −0.208326 0.00885612i
\(622\) 4.50326 4.50326i 0.180564 0.180564i
\(623\) −43.4622 + 43.4622i −1.74128 + 1.74128i
\(624\) −1.04553 1.87162i −0.0418546 0.0749249i
\(625\) −24.9621 + 1.37527i −0.998486 + 0.0550108i
\(626\) 23.8188i 0.951993i
\(627\) 24.4467 + 6.92297i 0.976307 + 0.276477i
\(628\) 1.67127 + 1.67127i 0.0666909 + 0.0666909i
\(629\) −5.07416 −0.202320
\(630\) −31.7320 + 8.00914i −1.26423 + 0.319092i
\(631\) −5.19423 −0.206779 −0.103390 0.994641i \(-0.532969\pi\)
−0.103390 + 0.994641i \(0.532969\pi\)
\(632\) −12.1591 12.1591i −0.483664 0.483664i
\(633\) 13.2629 + 3.75588i 0.527154 + 0.149283i
\(634\) 25.1840i 1.00018i
\(635\) 0.454279 + 33.0133i 0.0180275 + 1.31009i
\(636\) 4.33051 + 7.75215i 0.171716 + 0.307393i
\(637\) 14.7051 14.7051i 0.582637 0.582637i
\(638\) −21.1652 + 21.1652i −0.837939 + 0.837939i
\(639\) 9.67653 15.7150i 0.382798 0.621674i
\(640\) −0.0307665 2.23586i −0.00121615 0.0883800i
\(641\) 37.8880i 1.49649i −0.663425 0.748243i \(-0.730898\pi\)
0.663425 0.748243i \(-0.269102\pi\)
\(642\) 4.81835 17.0147i 0.190165 0.671518i
\(643\) −8.06700 8.06700i −0.318131 0.318131i 0.529918 0.848049i \(-0.322223\pi\)
−0.848049 + 0.529918i \(0.822223\pi\)
\(644\) 4.87868 0.192247
\(645\) 0.754656 + 0.202535i 0.0297146 + 0.00797480i
\(646\) −7.32179 −0.288072
\(647\) −19.7436 19.7436i −0.776203 0.776203i 0.202980 0.979183i \(-0.434937\pi\)
−0.979183 + 0.202980i \(0.934937\pi\)
\(648\) −8.54751 2.81782i −0.335778 0.110695i
\(649\) 14.8926i 0.584586i
\(650\) 6.18643 0.170289i 0.242652 0.00667928i
\(651\) −41.1740 + 23.0006i −1.61374 + 0.901465i
\(652\) −9.29670 + 9.29670i −0.364087 + 0.364087i
\(653\) −1.55428 + 1.55428i −0.0608235 + 0.0608235i −0.736864 0.676041i \(-0.763694\pi\)
0.676041 + 0.736864i \(0.263694\pi\)
\(654\) −3.26726 + 1.82516i −0.127760 + 0.0713693i
\(655\) −18.0254 17.5360i −0.704310 0.685190i
\(656\) 4.29759i 0.167793i
\(657\) −9.43089 39.6568i −0.367934 1.54716i
\(658\) 17.7187 + 17.7187i 0.690745 + 0.690745i
\(659\) 10.6771 0.415921 0.207960 0.978137i \(-0.433318\pi\)
0.207960 + 0.978137i \(0.433318\pi\)
\(660\) −12.8998 + 7.44081i −0.502125 + 0.289633i
\(661\) 40.2271 1.56465 0.782326 0.622869i \(-0.214033\pi\)
0.782326 + 0.622869i \(0.214033\pi\)
\(662\) −4.07705 4.07705i −0.158459 0.158459i
\(663\) 1.12106 3.95875i 0.0435385 0.153745i
\(664\) 2.83477i 0.110010i
\(665\) 41.6150 0.572643i 1.61376 0.0222062i
\(666\) 6.75407 + 4.15884i 0.261715 + 0.161152i
\(667\) −5.50447 + 5.50447i −0.213134 + 0.213134i
\(668\) 10.9776 10.9776i 0.424738 0.424738i
\(669\) 19.8229 + 35.4855i 0.766398 + 1.37195i
\(670\) −6.11001 + 6.28051i −0.236050 + 0.242637i
\(671\) 52.1606i 2.01364i
\(672\) 8.13040 + 2.30242i 0.313637 + 0.0888178i
\(673\) −24.3131 24.3131i −0.937203 0.937203i 0.0609388 0.998142i \(-0.480591\pi\)
−0.998142 + 0.0609388i \(0.980591\pi\)
\(674\) −16.0144 −0.616851
\(675\) 18.6440 18.0942i 0.717610 0.696445i
\(676\) 11.4680 0.441076
\(677\) −32.4421 32.4421i −1.24685 1.24685i −0.957103 0.289749i \(-0.906428\pi\)
−0.289749 0.957103i \(-0.593572\pi\)
\(678\) 20.3572 + 5.76488i 0.781813 + 0.221399i
\(679\) 23.2238i 0.891249i
\(680\) 2.99244 3.07594i 0.114755 0.117957i
\(681\) 5.84317 + 10.4600i 0.223911 + 0.400829i
\(682\) −15.1750 + 15.1750i −0.581080 + 0.581080i
\(683\) 30.8958 30.8958i 1.18219 1.18219i 0.203020 0.979175i \(-0.434924\pi\)
0.979175 0.203020i \(-0.0650755\pi\)
\(684\) 9.74582 + 6.00102i 0.372641 + 0.229455i
\(685\) 32.9676 0.453651i 1.25963 0.0173331i
\(686\) 47.8185i 1.82572i
\(687\) −2.07348 + 7.32194i −0.0791081 + 0.279350i
\(688\) −0.142657 0.142657i −0.00543873 0.00543873i
\(689\) 6.34559 0.241748
\(690\) −3.35488 + 1.93514i −0.127718 + 0.0736696i
\(691\) −4.89262 −0.186124 −0.0930620 0.995660i \(-0.529665\pi\)
−0.0930620 + 0.995660i \(0.529665\pi\)
\(692\) −17.3398 17.3398i −0.659159 0.659159i
\(693\) −13.0203 54.7500i −0.494599 2.07978i
\(694\) 9.15626i 0.347567i
\(695\) −23.4724 22.8352i −0.890359 0.866188i
\(696\) −11.7710 + 6.57554i −0.446180 + 0.249245i
\(697\) −5.83208 + 5.83208i −0.220906 + 0.220906i
\(698\) 8.10294 8.10294i 0.306701 0.306701i
\(699\) 19.1198 10.6807i 0.723177 0.403981i
\(700\) −16.7676 + 17.7168i −0.633755 + 0.669633i
\(701\) 12.6440i 0.477556i 0.971074 + 0.238778i \(0.0767468\pi\)
−0.971074 + 0.238778i \(0.923253\pi\)
\(702\) −4.73685 + 4.35054i −0.178781 + 0.164200i
\(703\) −7.13245 7.13245i −0.269005 0.269005i
\(704\) 3.84509 0.144917
\(705\) −19.2126 5.15628i −0.723588 0.194197i
\(706\) −20.6539 −0.777319
\(707\) −38.9627 38.9627i −1.46534 1.46534i
\(708\) −1.82787 + 6.45466i −0.0686957 + 0.242581i
\(709\) 18.0882i 0.679317i 0.940549 + 0.339658i \(0.110311\pi\)
−0.940549 + 0.339658i \(0.889689\pi\)
\(710\) −0.189268 13.7544i −0.00710309 0.516194i
\(711\) −27.0483 + 43.9271i −1.01439 + 1.64740i
\(712\) −8.90860 + 8.90860i −0.333864 + 0.333864i
\(713\) −3.94659 + 3.94659i −0.147801 + 0.147801i
\(714\) 7.90892 + 14.1580i 0.295984 + 0.529849i
\(715\) 0.146426 + 10.6411i 0.00547604 + 0.397953i
\(716\) 1.47094i 0.0549715i
\(717\) 11.7849 + 3.33731i 0.440113 + 0.124634i
\(718\) −2.33713 2.33713i −0.0872207 0.0872207i
\(719\) 18.9895 0.708188 0.354094 0.935210i \(-0.384789\pi\)
0.354094 + 0.935210i \(0.384789\pi\)
\(720\) −6.50423 + 1.64166i −0.242398 + 0.0611811i
\(721\) 57.7363 2.15021
\(722\) 3.14322 + 3.14322i 0.116978 + 0.116978i
\(723\) −7.04278 1.99442i −0.261924 0.0741733i
\(724\) 15.6852i 0.582936i
\(725\) −1.07098 38.9078i −0.0397753 1.44500i
\(726\) −3.19696 5.72297i −0.118650 0.212399i
\(727\) −2.21531 + 2.21531i −0.0821613 + 0.0821613i −0.746993 0.664832i \(-0.768503\pi\)
0.664832 + 0.746993i \(0.268503\pi\)
\(728\) 4.26994 4.26994i 0.158254 0.158254i
\(729\) −2.29144 + 26.9026i −0.0848683 + 0.996392i
\(730\) −21.7774 21.1862i −0.806019 0.784138i
\(731\) 0.387187i 0.0143206i
\(732\) 6.40203 22.6071i 0.236626 0.835583i
\(733\) 23.0122 + 23.0122i 0.849976 + 0.849976i 0.990130 0.140154i \(-0.0447597\pi\)
−0.140154 + 0.990130i \(0.544760\pi\)
\(734\) −17.3823 −0.641591
\(735\) −32.5133 56.3671i −1.19927 2.07913i
\(736\) 1.00000 0.0368605
\(737\) −10.6542 10.6542i −0.392454 0.392454i
\(738\) 12.5430 2.98287i 0.461712 0.109801i
\(739\) 10.0080i 0.368151i 0.982912 + 0.184076i \(0.0589291\pi\)
−0.982912 + 0.184076i \(0.941071\pi\)
\(740\) 5.91145 0.0813446i 0.217309 0.00299029i
\(741\) 7.14039 3.98876i 0.262309 0.146531i
\(742\) −17.6858 + 17.6858i −0.649267 + 0.649267i
\(743\) 23.6306 23.6306i 0.866922 0.866922i −0.125208 0.992130i \(-0.539960\pi\)
0.992130 + 0.125208i \(0.0399599\pi\)
\(744\) −8.43958 + 4.71452i −0.309410 + 0.172843i
\(745\) 1.90193 1.95500i 0.0696812 0.0716257i
\(746\) 5.96729i 0.218478i
\(747\) 8.27357 1.96756i 0.302714 0.0719893i
\(748\) 5.21802 + 5.21802i 0.190790 + 0.190790i
\(749\) 49.8102 1.82002
\(750\) 4.50300 18.8341i 0.164426 0.687724i
\(751\) 17.4785 0.637798 0.318899 0.947789i \(-0.396687\pi\)
0.318899 + 0.947789i \(0.396687\pi\)
\(752\) 3.63185 + 3.63185i 0.132440 + 0.132440i
\(753\) −0.150515 + 0.531504i −0.00548506 + 0.0193691i
\(754\) 9.63529i 0.350897i
\(755\) 10.7912 11.0923i 0.392732 0.403691i
\(756\) 1.07669 25.3275i 0.0391589 0.921152i
\(757\) 7.37005 7.37005i 0.267869 0.267869i −0.560372 0.828241i \(-0.689342\pi\)
0.828241 + 0.560372i \(0.189342\pi\)
\(758\) −17.5132 + 17.5132i −0.636107 + 0.636107i
\(759\) −3.24794 5.81422i −0.117893 0.211043i
\(760\) 8.52997 0.117377i 0.309414 0.00425770i
\(761\) 49.0359i 1.77755i 0.458345 + 0.888774i \(0.348442\pi\)
−0.458345 + 0.888774i \(0.651558\pi\)
\(762\) −24.6067 6.96830i −0.891408 0.252435i
\(763\) −7.45396 7.45396i −0.269851 0.269851i
\(764\) −21.7200 −0.785800
\(765\) −11.0545 6.59879i −0.399675 0.238580i
\(766\) −17.3767 −0.627846
\(767\) 3.38987 + 3.38987i 0.122401 + 0.122401i
\(768\) 1.66652 + 0.471935i 0.0601352 + 0.0170295i
\(769\) 24.0936i 0.868838i 0.900711 + 0.434419i \(0.143046\pi\)
−0.900711 + 0.434419i \(0.856954\pi\)
\(770\) −30.0659 29.2496i −1.08350 1.05408i
\(771\) −11.8161 21.1522i −0.425545 0.761779i
\(772\) −17.8302 + 17.8302i −0.641723 + 0.641723i
\(773\) 12.6293 12.6293i 0.454243 0.454243i −0.442517 0.896760i \(-0.645914\pi\)
0.896760 + 0.442517i \(0.145914\pi\)
\(774\) −0.317343 + 0.515373i −0.0114066 + 0.0185247i
\(775\) −0.767872 27.8960i −0.0275828 1.00205i
\(776\) 4.76027i 0.170884i
\(777\) −6.08744 + 21.4962i −0.218386 + 0.771172i
\(778\)