Properties

Label 690.2.i.e.323.5
Level $690$
Weight $2$
Character 690.323
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 323.5
Character \(\chi\) \(=\) 690.323
Dual form 690.2.i.e.47.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.471935 + 1.66652i) q^{3} +1.00000i q^{4} +(-1.55923 + 1.60274i) q^{5} +(0.844697 - 1.51211i) q^{6} +(-3.44975 + 3.44975i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.55455 + 1.57298i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.471935 + 1.66652i) 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} +(-1.66652 + 0.471935i) q^{12} +(0.875224 + 0.875224i) q^{13} +4.87868 q^{14} +(-3.40686 - 1.84210i) q^{15} -1.00000 q^{16} +(1.35706 + 1.35706i) q^{17} +(2.91860 + 0.694081i) 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} +(-3.82697 - 3.51487i) q^{27} +(-3.44975 - 3.44975i) q^{28} -7.78450 q^{29} +(1.10645 + 3.71157i) q^{30} +5.58131 q^{31} +(0.707107 + 0.707107i) q^{32} +(6.40791 - 1.81463i) 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} +(2.30242 + 8.13040i) q^{42} +(0.142657 + 0.142657i) q^{43} +3.84509 q^{44} +(1.46207 - 6.54693i) q^{45} -1.00000 q^{46} +(3.63185 + 3.63185i) q^{47} +(-0.471935 - 1.66652i) 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} +(6.35789 - 1.80047i) q^{57} +(5.50447 + 5.50447i) q^{58} -3.87315 q^{59} +(1.84210 - 3.40686i) q^{60} -13.5655 q^{61} +(-3.94659 - 3.94659i) q^{62} +(3.38620 - 14.2389i) 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} +(-0.694081 + 2.91860i) q^{72} +(-9.60788 - 9.60788i) q^{73} -2.64393 q^{74} +(8.26450 - 2.58806i) q^{75} +3.81508 q^{76} +(13.2646 + 13.2646i) q^{77} +(2.06274 - 0.584139i) 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} +(-3.67378 - 12.9730i) q^{87} +(-2.71889 - 2.71889i) q^{88} -12.5987 q^{89} +(-5.66322 + 3.59554i) q^{90} -6.03860 q^{91} +(0.707107 + 0.707107i) q^{92} +(2.63402 + 9.30135i) 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
\(3\) 0.471935 + 1.66652i 0.272472 + 0.962164i
\(4\) 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 \(-0.803182\pi\)
0.814852 0.579670i \(-0.196818\pi\)
\(12\) −1.66652 + 0.471935i −0.481082 + 0.136236i
\(13\) 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
\(15\) −3.40686 1.84210i −0.879647 0.475628i
\(16\) −1.00000 −0.250000
\(17\) 1.35706 + 1.35706i 0.329135 + 0.329135i 0.852258 0.523122i \(-0.175233\pi\)
−0.523122 + 0.852258i \(0.675233\pi\)
\(18\) 2.91860 + 0.694081i 0.687922 + 0.163597i
\(19\) 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
\(27\) −3.82697 3.51487i −0.736501 0.676436i
\(28\) −3.44975 3.44975i −0.651941 0.651941i
\(29\) −7.78450 −1.44554 −0.722772 0.691086i \(-0.757133\pi\)
−0.722772 + 0.691086i \(0.757133\pi\)
\(30\) 1.10645 + 3.71157i 0.202010 + 0.677637i
\(31\) 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
\(33\) 6.40791 1.81463i 1.11547 0.315887i
\(34\) 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 \(0.108934\pi\)
−0.942010 + 0.335585i \(0.891066\pi\)
\(42\) 2.30242 + 8.13040i 0.355271 + 1.25455i
\(43\) 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
\(45\) 1.46207 6.54693i 0.217953 0.975959i
\(46\) −1.00000 −0.147442
\(47\) 3.63185 + 3.63185i 0.529760 + 0.529760i 0.920501 0.390741i \(-0.127781\pi\)
−0.390741 + 0.920501i \(0.627781\pi\)
\(48\) −0.471935 1.66652i −0.0681180 0.240541i
\(49\) 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 −0.910799 0.412850i \(-0.864533\pi\)
0.412850 + 0.910799i \(0.364533\pi\)
\(54\) 0.220693 + 5.19146i 0.0300326 + 0.706469i
\(55\) 6.16270 + 5.99540i 0.830979 + 0.808420i
\(56\) 4.87868i 0.651941i
\(57\) 6.35789 1.80047i 0.842123 0.238478i
\(58\) 5.50447 + 5.50447i 0.722772 + 0.722772i
\(59\) −3.87315 −0.504241 −0.252120 0.967696i \(-0.581128\pi\)
−0.252120 + 0.967696i \(0.581128\pi\)
\(60\) 1.84210 3.40686i 0.237814 0.439823i
\(61\) −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
\(63\) 3.38620 14.2389i 0.426621 1.79394i
\(64\) 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 \(0.118944\pi\)
−0.930992 + 0.365039i \(0.881056\pi\)
\(72\) −0.694081 + 2.91860i −0.0817983 + 0.343961i
\(73\) −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
\(75\) 8.26450 2.58806i 0.954302 0.298843i
\(76\) 3.81508 0.437619
\(77\) 13.2646 + 13.2646i 1.51164 + 1.51164i
\(78\) 2.06274 0.584139i 0.233559 0.0661408i
\(79\) 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 −0.808507 0.588486i \(-0.799724\pi\)
0.588486 + 0.808507i \(0.299724\pi\)
\(84\) 4.12100 7.37712i 0.449638 0.804910i
\(85\) −4.29100 + 0.0590463i −0.465424 + 0.00640447i
\(86\) 0.201747i 0.0217549i
\(87\) −3.67378 12.9730i −0.393870 1.39085i
\(88\) −2.71889 2.71889i −0.289835 0.289835i
\(89\) −12.5987 −1.33546 −0.667728 0.744406i \(-0.732733\pi\)
−0.667728 + 0.744406i \(0.732733\pi\)
\(90\) −5.66322 + 3.59554i −0.596956 + 0.379003i
\(91\) −6.03860 −0.633018
\(92\) 0.707107 + 0.707107i 0.0737210 + 0.0737210i
\(93\) 2.63402 + 9.30135i 0.273135 + 0.964505i
\(94\) 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 \(-0.810064\pi\)
0.827194 0.561916i \(-0.189936\pi\)
\(102\) 3.19833 0.905725i 0.316682 0.0896801i
\(103\) −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
\(105\) 18.1076 5.39802i 1.76712 0.526793i
\(106\) 5.12670 0.497949
\(107\) 7.21940 + 7.21940i 0.697925 + 0.697925i 0.963963 0.266037i \(-0.0857145\pi\)
−0.266037 + 0.963963i \(0.585714\pi\)
\(108\) 3.51487 3.82697i 0.338218 0.368251i
\(109\) 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 −0.985017 0.172459i \(-0.944829\pi\)
0.172459 + 0.985017i \(0.444829\pi\)
\(114\) −5.76883 3.22258i −0.540301 0.301823i
\(115\) 0.0307665 + 2.23586i 0.00286899 + 0.208495i
\(116\) 7.78450i 0.722772i
\(117\) −3.61251 0.859102i −0.333977 0.0794240i
\(118\) 2.73873 + 2.73873i 0.252120 + 0.252120i
\(119\) −9.36303 −0.858308
\(120\) −3.71157 + 1.10645i −0.338819 + 0.101005i
\(121\) −3.78475 −0.344068
\(122\) 9.59226 + 9.59226i 0.868442 + 0.868442i
\(123\) −7.16200 + 2.02818i −0.645775 + 0.182875i
\(124\) 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 \(0.163481\pi\)
−0.870985 + 0.491309i \(0.836519\pi\)
\(132\) 1.81463 + 6.40791i 0.157944 + 0.557737i
\(133\) 13.1611 + 13.1611i 1.14121 + 1.14121i
\(134\) 3.91860 0.338515
\(135\) 11.6006 0.653162i 0.998419 0.0562152i
\(136\) 1.91917 0.164568
\(137\) −10.4263 10.4263i −0.890776 0.890776i 0.103820 0.994596i \(-0.466893\pi\)
−0.994596 + 0.103820i \(0.966893\pi\)
\(138\) −0.471935 1.66652i −0.0401738 0.141863i
\(139\) 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
\(147\) 28.0000 7.92922i 2.30940 0.653991i
\(148\) 1.86954 + 1.86954i 0.153675 + 0.153675i
\(149\) −1.21978 −0.0999285 −0.0499642 0.998751i \(-0.515911\pi\)
−0.0499642 + 0.998751i \(0.515911\pi\)
\(150\) −7.67392 4.01385i −0.626573 0.327729i
\(151\) 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
\(153\) −5.60131 1.33206i −0.452839 0.107691i
\(154\) 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
\(162\) −8.54751 + 2.81782i −0.671556 + 0.221389i
\(163\) 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
\(165\) −7.08304 + 13.0997i −0.551414 + 1.01981i
\(166\) 2.83477 0.220021
\(167\) 10.9776 + 10.9776i 0.849475 + 0.849475i 0.990068 0.140593i \(-0.0449008\pi\)
−0.140593 + 0.990068i \(0.544901\pi\)
\(168\) −8.13040 + 2.30242i −0.627274 + 0.177636i
\(169\) 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 \(-0.367894\pi\)
0.915107 0.403212i \(-0.132106\pi\)
\(174\) −6.57554 + 11.7710i −0.498490 + 0.892361i
\(175\) 17.7168 + 16.7676i 1.33927 + 1.26751i
\(176\) 3.84509i 0.289835i
\(177\) −1.82787 6.45466i −0.137391 0.485162i
\(178\) 8.90860 + 8.90860i 0.667728 + 0.667728i
\(179\) 1.47094 0.109943 0.0549715 0.998488i \(-0.482493\pi\)
0.0549715 + 0.998488i \(0.482493\pi\)
\(180\) 6.54693 + 1.46207i 0.487980 + 0.108976i
\(181\) −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
\(183\) −6.40203 22.6071i −0.473252 1.67117i
\(184\) 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 \(-0.712251\pi\)
0.618480 0.785800i \(-0.287749\pi\)
\(192\) 1.66652 0.471935i 0.120270 0.0340590i
\(193\) 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
\(195\) −1.36951 4.59401i −0.0980730 0.328984i
\(196\) 16.8015 1.20011
\(197\) 0.806128 + 0.806128i 0.0574342 + 0.0574342i 0.735241 0.677806i \(-0.237069\pi\)
−0.677806 + 0.735241i \(0.737069\pi\)
\(198\) 2.66881 11.2223i 0.189664 0.797535i
\(199\) 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
\(207\) −0.694081 + 2.91860i −0.0482420 + 0.202857i
\(208\) −0.875224 0.875224i −0.0606859 0.0606859i
\(209\) −14.6693 −1.01470
\(210\) −16.6210 8.98701i −1.14696 0.620162i
\(211\) 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
\(213\) −10.2520 + 2.90322i −0.702454 + 0.198925i
\(214\) 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
\(222\) −1.24776 4.40615i −0.0837444 0.295722i
\(223\) 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
\(225\) 8.21335 + 12.5515i 0.547557 + 0.836769i
\(226\) 12.2154 0.812557
\(227\) −4.89140 4.89140i −0.324653 0.324653i 0.525896 0.850549i \(-0.323730\pi\)
−0.850549 + 0.525896i \(0.823730\pi\)
\(228\) 1.80047 + 6.35789i 0.119239 + 0.421062i
\(229\) 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 −0.936475 0.350734i \(-0.885932\pi\)
0.350734 + 0.936475i \(0.385932\pi\)
\(234\) 1.94696 + 3.16191i 0.127276 + 0.206700i
\(235\) −11.4838 + 0.158024i −0.749123 + 0.0103083i
\(236\) 3.87315i 0.252120i
\(237\) −28.6568 + 8.11521i −1.86146 + 0.527140i
\(238\) 6.62066 + 6.62066i 0.429154 + 0.429154i
\(239\) −7.07155 −0.457420 −0.228710 0.973495i \(-0.573451\pi\)
−0.228710 + 0.973495i \(0.573451\pi\)
\(240\) 3.40686 + 1.84210i 0.219912 + 0.118907i
\(241\) −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
\(243\) 15.3050 + 2.95918i 0.981817 + 0.189832i
\(244\) 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 \(-0.996796\pi\)
0.999949 0.0100654i \(-0.00320396\pi\)
\(252\) 14.2389 + 3.38620i 0.896969 + 0.213311i
\(253\) −2.71889 2.71889i −0.170935 0.170935i
\(254\) 14.7654 0.926462
\(255\) −2.12347 7.12315i −0.132977 0.446069i
\(256\) 1.00000 0.0625000
\(257\) 9.89138 + 9.89138i 0.617007 + 0.617007i 0.944763 0.327755i \(-0.106292\pi\)
−0.327755 + 0.944763i \(0.606292\pi\)
\(258\) 0.336214 0.0952114i 0.0209318 0.00592760i
\(259\) 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 −0.872909 0.487882i \(-0.837769\pi\)
0.487882 + 0.872909i \(0.337769\pi\)
\(264\) 3.24794 5.81422i 0.199897 0.357840i
\(265\) −0.157731 11.4626i −0.00968932 0.704140i
\(266\) 18.6125i 1.14121i
\(267\) −5.94575 20.9959i −0.363874 1.28493i
\(268\) −2.77087 2.77087i −0.169258 0.169258i
\(269\) −11.4973 −0.701002 −0.350501 0.936562i \(-0.613989\pi\)
−0.350501 + 0.936562i \(0.613989\pi\)
\(270\) −8.66470 7.74099i −0.527317 0.471102i
\(271\) 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
\(273\) −2.84983 10.0634i −0.172479 0.609067i
\(274\) 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 \(0.423666\pi\)
−0.237517 + 0.971383i \(0.576334\pi\)
\(282\) 8.55959 2.42396i 0.509716 0.144345i
\(283\) −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
\(285\) −7.02775 + 12.9974i −0.416288 + 0.769901i
\(286\) −4.75928 −0.281422
\(287\) −14.8256 14.8256i −0.875127 0.875127i
\(288\) −2.91860 0.694081i −0.171980 0.0408991i
\(289\) 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 −0.933409 0.358815i \(-0.883181\pi\)
0.358815 + 0.933409i \(0.383181\pi\)
\(294\) −25.4058 14.1922i −1.48170 0.827705i
\(295\) 6.03914 6.20766i 0.351612 0.361424i
\(296\) 2.64393i 0.153675i
\(297\) −13.5150 + 14.7151i −0.784219 + 0.853855i
\(298\) 0.862517 + 0.862517i 0.0499642 + 0.0499642i
\(299\) 1.23775 0.0715811
\(300\) 2.58806 + 8.26450i 0.149422 + 0.477151i
\(301\) −0.984258 −0.0567317
\(302\) −4.89377 4.89377i −0.281605 0.281605i
\(303\) 18.8223 5.33021i 1.08131 0.306213i
\(304\) 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 \(0.0577924\pi\)
−0.983563 + 0.180564i \(0.942208\pi\)
\(312\) 0.584139 + 2.06274i 0.0330704 + 0.116779i
\(313\) −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
\(315\) 17.5415 + 27.6290i 0.988351 + 1.55672i
\(316\) −17.1956 −0.967329
\(317\) −17.8078 17.8078i −1.00018 1.00018i −1.00000 0.000184598i \(-0.999941\pi\)
−0.000184598 1.00000i \(-0.500059\pi\)
\(318\) 2.41947 + 8.54373i 0.135677 + 0.479108i
\(319\) 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
\(327\) −3.60089 + 1.01972i −0.199129 + 0.0563908i
\(328\) 3.03885 + 3.03885i 0.167793 + 0.167793i
\(329\) −25.0580 −1.38149
\(330\) 14.2713 4.25441i 0.785611 0.234198i
\(331\) −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
\(333\) −1.83510 + 7.71659i −0.100563 + 0.422866i
\(334\) 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
\(342\) 2.64797 11.1347i 0.143186 0.602096i
\(343\) 33.8128 + 33.8128i 1.82572 + 1.82572i
\(344\) 0.201747 0.0108775
\(345\) −3.71157 + 1.10645i −0.199824 + 0.0595694i
\(346\) −24.5221 −1.31832
\(347\) 6.47445 + 6.47445i 0.347567 + 0.347567i 0.859203 0.511636i \(-0.170960\pi\)
−0.511636 + 0.859203i \(0.670960\pi\)
\(348\) 12.9730 3.67378i 0.695425 0.196935i
\(349\) 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 −0.202055 0.979374i \(-0.564762\pi\)
0.979374 + 0.202055i \(0.0647621\pi\)
\(354\) −3.27163 + 5.85664i −0.173885 + 0.311277i
\(355\) −9.85967 9.59200i −0.523297 0.509091i
\(356\) 12.5987i 0.667728i
\(357\) −4.41874 15.6036i −0.233865 0.825833i
\(358\) −1.04011 1.04011i −0.0549715 0.0549715i
\(359\) 3.30519 0.174441 0.0872207 0.996189i \(-0.472201\pi\)
0.0872207 + 0.996189i \(0.472201\pi\)
\(360\) −3.59554 5.66322i −0.189502 0.298478i
\(361\) 4.44518 0.233957
\(362\) 11.0911 + 11.0911i 0.582936 + 0.582936i
\(363\) −1.78615 6.30734i −0.0937488 0.331050i
\(364\) 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
\(372\) −9.30135 + 2.63402i −0.482253 + 0.136567i
\(373\) 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
\(375\) −8.73829 + 17.2813i −0.451243 + 0.892401i
\(376\) 5.13622 0.264880
\(377\) −6.81318 6.81318i −0.350897 0.350897i
\(378\) −18.6706 17.1479i −0.960311 0.881993i
\(379\) 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 −0.319680 0.947526i \(-0.603575\pi\)
0.947526 + 0.319680i \(0.103575\pi\)
\(384\) −1.51211 0.844697i −0.0771647 0.0431057i
\(385\) −41.9424 + 0.577149i −2.13758 + 0.0294142i
\(386\) 25.2157i 1.28345i
\(387\) −0.588819 0.140029i −0.0299314 0.00711806i
\(388\) −3.36602 3.36602i −0.170884 0.170884i
\(389\) 15.4882 0.785281 0.392640 0.919692i \(-0.371562\pi\)
0.392640 + 0.919692i \(0.371562\pi\)
\(390\) −2.28006 + 4.21685i −0.115456 + 0.213529i
\(391\) 1.91917 0.0970568
\(392\) −11.8805 11.8805i −0.600054 0.600054i
\(393\) −18.7426 + 5.30765i −0.945439 + 0.267736i
\(394\) 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 \(-0.974002\pi\)
0.996667 0.0815829i \(-0.0259975\pi\)
\(402\) 1.84932 + 6.53041i 0.0922359 + 0.325707i
\(403\) 4.88490 + 4.88490i 0.243334 + 0.243334i
\(404\) 11.2944 0.561916
\(405\) 6.56322 + 19.0243i 0.326129 + 0.945325i
\(406\) −37.9781 −1.88482
\(407\) −7.18856 7.18856i −0.356324 0.356324i
\(408\) 0.905725 + 3.19833i 0.0448401 + 0.158341i
\(409\) 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
\(417\) 24.4063 6.91155i 1.19518 0.338460i
\(418\) 10.3728 + 10.3728i 0.507349 + 0.507349i
\(419\) 20.6323 1.00795 0.503977 0.863717i \(-0.331870\pi\)
0.503977 + 0.863717i \(0.331870\pi\)
\(420\) 5.39802 + 18.1076i 0.263397 + 0.883559i
\(421\) −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
\(423\) −14.9906 3.56495i −0.728867 0.173334i
\(424\) 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 \(0.0931051\pi\)
−0.957527 + 0.288345i \(0.906895\pi\)
\(432\) 3.82697 + 3.51487i 0.184125 + 0.169109i
\(433\) 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
\(435\) 26.5207 + 14.3398i 1.27157 + 0.687541i
\(436\) −2.16073 −0.103480
\(437\) −2.69767 2.69767i −0.129047 0.129047i
\(438\) −22.6439 + 6.41246i −1.08197 + 0.306399i
\(439\) 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 −0.875173 0.483811i \(-0.839252\pi\)
0.483811 + 0.875173i \(0.339252\pi\)
\(444\) −2.23332 + 3.99792i −0.105989 + 0.189733i
\(445\) 19.6443 20.1924i 0.931227 0.957213i
\(446\) 23.4675i 1.11122i
\(447\) −0.575658 2.03279i −0.0272277 0.0961476i
\(448\) 3.44975 + 3.44975i 0.162985 + 0.162985i
\(449\) 16.4715 0.777340 0.388670 0.921377i \(-0.372935\pi\)
0.388670 + 0.921377i \(0.372935\pi\)
\(450\) 3.06755 14.6830i 0.144606 0.692163i
\(451\) 16.5246 0.778114
\(452\) −8.63760 8.63760i −0.406279 0.406279i
\(453\) 3.26619 + 11.5337i 0.153459 + 0.541900i
\(454\) 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 \(0.342485\pi\)
−0.474898 + 0.880041i \(0.657515\pi\)
\(462\) 31.2622 8.85302i 1.45445 0.411880i
\(463\) −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
\(465\) −19.0147 10.2813i −0.881787 0.476785i
\(466\) 12.6444 0.585741
\(467\) 5.24131 + 5.24131i 0.242539 + 0.242539i 0.817900 0.575361i \(-0.195138\pi\)
−0.575361 + 0.817900i \(0.695138\pi\)
\(468\) 0.859102 3.61251i 0.0397120 0.166988i
\(469\) 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
\(477\) 3.55835 14.9628i 0.162926 0.685100i
\(478\) 5.00034 + 5.00034i 0.228710 + 0.228710i
\(479\) 26.6043 1.21558 0.607790 0.794098i \(-0.292056\pi\)
0.607790 + 0.794098i \(0.292056\pi\)
\(480\) −1.10645 3.71157i −0.0505024 0.169409i
\(481\) 3.27254 0.149215
\(482\) 2.98827 + 2.98827i 0.136112 + 0.136112i
\(483\) −8.13040 + 2.30242i −0.369946 + 0.104764i
\(484\) 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 \(-0.708720\pi\)
0.609724 0.792614i \(-0.291280\pi\)
\(492\) −2.02818 7.16200i −0.0914375 0.322888i
\(493\) −10.5640 10.5640i −0.475780 0.475780i
\(494\) −4.72213 −0.212459
\(495\) −25.1736 5.62180i −1.13147 0.252681i
\(496\) −5.58131 −0.250608
\(497\) −21.2219 21.2219i −0.951934 0.951934i
\(498\) 1.33783 + 4.72419i 0.0599495 + 0.211696i
\(499\) 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 −0.954664 0.297685i \(-0.903785\pi\)
0.297685 + 0.954664i \(0.403785\pi\)
\(504\) −7.67404 12.4629i −0.341829 0.555140i
\(505\) 18.1020 + 17.6106i 0.805528 + 0.783660i
\(506\) 3.84509i 0.170935i
\(507\) 19.1116 5.41214i 0.848774 0.240361i
\(508\) −10.4407 10.4407i −0.463231 0.463231i
\(509\) 29.8800 1.32441 0.662205 0.749323i \(-0.269621\pi\)
0.662205 + 0.749323i \(0.269621\pi\)
\(510\) −3.53530 + 6.53835i −0.156546 + 0.289523i
\(511\) 66.2895 2.93247
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −13.4095 + 14.6002i −0.592043 + 0.644615i
\(514\) 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 \(0.00972375\pi\)
−0.999533 + 0.0305433i \(0.990276\pi\)
\(522\) −22.7199 5.40308i −0.994422 0.236486i
\(523\) −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
\(525\) −19.5823 + 37.4386i −0.854641 + 1.63395i
\(526\) 8.83047 0.385027
\(527\) 7.57418 + 7.57418i 0.329936 + 0.329936i
\(528\) −6.40791 + 1.81463i −0.278869 + 0.0789718i
\(529\) 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
\(537\) 0.694187 + 2.45134i 0.0299564 + 0.105783i
\(538\) 8.12981 + 8.12981i 0.350501 + 0.350501i
\(539\) −64.6034 −2.78267
\(540\) 0.653162 + 11.6006i 0.0281076 + 0.499209i
\(541\) 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
\(543\) −7.40239 26.1396i −0.317667 1.12176i
\(544\) 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
\(552\) 1.66652 0.471935i 0.0709317 0.0200869i
\(553\) −59.3205 59.3205i −2.52257 2.52257i
\(554\) 30.8844 1.31215
\(555\) −9.81314 + 2.92538i −0.416545 + 0.124176i
\(556\) 14.6451 0.621092
\(557\) −18.5689 18.5689i −0.786789 0.786789i 0.194178 0.980966i \(-0.437796\pi\)
−0.980966 + 0.194178i \(0.937796\pi\)
\(558\) 16.2896 + 3.87389i 0.689596 + 0.163995i
\(559\) 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 −0.480997 0.876722i \(-0.659725\pi\)
0.876722 + 0.480997i \(0.159725\pi\)
\(564\) −7.76654 4.33854i −0.327030 0.182686i
\(565\) −0.375826 27.3119i −0.0158111 1.14902i
\(566\) 25.6768i 1.07927i
\(567\) 13.7473 + 41.7005i 0.577330 + 1.75126i
\(568\) 4.34994 + 4.34994i 0.182519 + 0.182519i
\(569\) −9.13075 −0.382781 −0.191390 0.981514i \(-0.561300\pi\)
−0.191390 + 0.981514i \(0.561300\pi\)
\(570\) 14.1599 4.22120i 0.593094 0.176807i
\(571\) 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
\(573\) 36.1967 10.2504i 1.51214 0.428217i
\(574\) 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
\(582\) 2.24654 + 7.93307i 0.0931220 + 0.328836i
\(583\) 13.9389 + 13.9389i 0.577292 + 0.577292i
\(584\) −13.5876 −0.562258
\(585\) 7.00967 4.45039i 0.289814 0.184001i
\(586\) 13.9094 0.574594
\(587\) −15.2589 15.2589i −0.629804 0.629804i 0.318215 0.948019i \(-0.396917\pi\)
−0.948019 + 0.318215i \(0.896917\pi\)
\(588\) 7.92922 + 28.0000i 0.326996 + 1.15470i
\(589\) 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 −0.999346 0.0361698i \(-0.988484\pi\)
0.0361698 + 0.999346i \(0.488484\pi\)
\(594\) 19.9617 0.848587i 0.819037 0.0348179i
\(595\) 14.5992 15.0065i 0.598507 0.615208i
\(596\) 1.21978i 0.0499642i
\(597\) 30.0795 8.51811i 1.23107 0.348623i
\(598\) −0.875224 0.875224i −0.0357906 0.0357906i
\(599\) 10.6390 0.434697 0.217349 0.976094i \(-0.430259\pi\)
0.217349 + 0.976094i \(0.430259\pi\)
\(600\) 4.01385 7.67392i 0.163865 0.313286i
\(601\) −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
\(603\) 2.71983 11.4368i 0.110760 0.465744i
\(604\) 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
\(612\) 1.33206 5.60131i 0.0538454 0.226419i
\(613\) 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
\(615\) 7.91657 14.6413i 0.319227 0.590393i
\(616\) 18.7590 0.755821
\(617\) −9.12773 9.12773i −0.367469 0.367469i 0.499085 0.866553i \(-0.333670\pi\)
−0.866553 + 0.499085i \(0.833670\pi\)
\(618\) −19.7222 + 5.58507i −0.793344 + 0.224664i
\(619\) 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
\(627\) −6.92297 24.4467i −0.276477 0.976307i
\(628\) 1.67127 + 1.67127i 0.0666909 + 0.0666909i
\(629\) 5.07416 0.202320
\(630\) 7.13298 31.9404i 0.284185 1.27254i
\(631\) −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
\(633\) 3.75588 + 13.2629i 0.149283 + 0.527154i
\(634\) 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 \(0.269102\pi\)
−0.663425 + 0.748243i \(0.730898\pi\)
\(642\) 17.0147 4.81835i 0.671518 0.190165i
\(643\) −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
\(645\) −0.223223 0.748798i −0.00878940 0.0294839i
\(646\) −7.32179 −0.288072
\(647\) 19.7436 + 19.7436i 0.776203 + 0.776203i 0.979183 0.202980i \(-0.0650626\pi\)
−0.202980 + 0.979183i \(0.565063\pi\)
\(648\) −2.81782 8.54751i −0.110695 0.335778i
\(649\) 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 −0.676041 0.736864i \(-0.736306\pi\)
0.736864 + 0.676041i \(0.236306\pi\)
\(654\) 3.26726 + 1.82516i 0.127760 + 0.0713693i
\(655\) −18.0254 17.5360i −0.704310 0.685190i
\(656\) 4.29759i 0.167793i
\(657\) 39.6568 + 9.43089i 1.54716 + 0.367934i
\(658\) 17.7187 + 17.7187i 0.690745 + 0.690745i
\(659\) −10.6771 −0.415921 −0.207960 0.978137i \(-0.566682\pi\)
−0.207960 + 0.978137i \(0.566682\pi\)
\(660\) −13.0997 7.08304i −0.509905 0.275707i
\(661\) 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
\(663\) −3.95875 + 1.12106i −0.153745 + 0.0435385i
\(664\) 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
\(672\) −2.30242 8.13040i −0.0888178 0.313637i
\(673\) −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
\(675\) −17.0412 + 19.6112i −0.655915 + 0.754835i
\(676\) 11.4680 0.441076
\(677\) 32.4421 + 32.4421i 1.24685 + 1.24685i 0.957103 + 0.289749i \(0.0935719\pi\)
0.289749 + 0.957103i \(0.406428\pi\)
\(678\) 5.76488 + 20.3572i 0.221399 + 0.781813i
\(679\) 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 \(0.565076\pi\)
−0.979175 + 0.203020i \(0.934924\pi\)
\(684\) −9.74582 + 6.00102i −0.372641 + 0.229455i
\(685\) 32.9676 0.453651i 1.25963 0.0173331i
\(686\) 47.8185i 1.82572i
\(687\) −7.32194 + 2.07348i −0.279350 + 0.0791081i
\(688\) −0.142657 0.142657i −0.00543873 0.00543873i
\(689\) −6.34559 −0.241748
\(690\) 3.40686 + 1.84210i 0.129697 + 0.0701275i
\(691\) −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
\(693\) −54.7500 13.0203i −2.07978 0.494599i
\(694\) 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 \(-0.923253\pi\)
0.971074 0.238778i \(-0.0767468\pi\)
\(702\) −4.35054 + 4.73685i −0.164200 + 0.178781i
\(703\) −7.13245 7.13245i −0.269005 0.269005i
\(704\) −3.84509 −0.144917
\(705\) −5.68298 19.0634i −0.214033 0.717971i
\(706\) −20.6539 −0.777319
\(707\) 38.9627 + 38.9627i 1.46534 + 1.46534i
\(708\) 6.45466 1.82787i 0.242581 0.0686957i
\(709\) 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
\(717\) −3.33731 11.7849i −0.124634 0.440113i
\(718\) −2.33713 2.33713i −0.0872207 0.0872207i
\(719\) −18.9895 −0.708188 −0.354094 0.935210i \(-0.615211\pi\)
−0.354094 + 0.935210i \(0.615211\pi\)
\(720\) −1.46207 + 6.54693i −0.0544882 + 0.243990i
\(721\) 57.7363 2.15021
\(722\) −3.14322 3.14322i −0.116978 0.116978i
\(723\) −1.99442 7.04278i −0.0741733 0.261924i
\(724\) 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
\(732\) 22.6071 6.40203i 0.835583 0.236626i
\(733\) 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
\(735\) −30.9500 + 57.2404i −1.14161 + 2.11134i
\(736\) 1.00000 0.0368605
\(737\) 10.6542 + 10.6542i 0.392454 + 0.392454i
\(738\) −2.98287 + 12.5430i −0.109801 + 0.461712i
\(739\) 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 −0.992130 0.125208i \(-0.960040\pi\)
0.125208 + 0.992130i \(0.460040\pi\)
\(744\) 8.43958 + 4.71452i 0.309410 + 0.172843i
\(745\) 1.90193 1.95500i 0.0696812 0.0716257i
\(746\) 5.96729i 0.218478i
\(747\) 1.96756 8.27357i 0.0719893 0.302714i
\(748\) 5.21802 + 5.21802i 0.190790 + 0.190790i
\(749\) −49.8102 −1.82002
\(750\) 18.3986 6.04080i 0.671822 0.220579i
\(751\) 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
\(753\) 0.531504 0.150515i 0.0193691 0.00548506i
\(754\) 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 \(-0.651558\pi\)
0.458345 0.888774i \(-0.348442\pi\)
\(762\) 6.96830 + 24.6067i 0.252435 + 0.891408i
\(763\) −7.45396 7.45396i −0.269851 0.269851i
\(764\) 21.7200 0.785800
\(765\) 10.8687 6.90047i 0.392959 0.249487i
\(766\) −17.3767 −0.627846
\(767\) −3.38987 3.38987i −0.122401 0.122401i
\(768\) 0.471935 + 1.66652i 0.0170295 + 0.0601352i
\(769\) 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 −0.896760 0.442517i \(-0.854086\pi\)
0.442517 + 0.896760i \(0.354086\pi\)
\(774\) 0.317343 + 0.515373i 0.0114066 + 0.0185247i
\(775\) −0.767872 27.8960i −0.0275828 1.00205i
\(776\) 4.76027i 0.170884i
\(777\) −21.4962 + 6.08744i −0.771172 + 0.218386i