Properties

Label 750.2.l.b.143.3
Level $750$
Weight $2$
Character 750.143
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 143.3
Character \(\chi\) \(=\) 750.143
Dual form 750.2.l.b.257.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.453990 + 0.891007i) q^{2} +(-0.522656 - 1.65131i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(-0.712495 + 0.712495i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.45366 + 1.72614i) q^{9} +O(q^{10})\) \(q+(-0.453990 + 0.891007i) q^{2} +(-0.522656 - 1.65131i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.70861 + 0.283990i) q^{6} +(-0.712495 + 0.712495i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.45366 + 1.72614i) q^{9} +(0.348148 - 0.113120i) q^{11} +(-1.02873 + 1.39345i) q^{12} +(-2.33563 + 1.19006i) q^{13} +(-0.311372 - 0.958303i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.919013 + 5.80242i) q^{17} +(-0.424059 - 2.96988i) q^{18} +(0.341785 - 0.470426i) q^{19} +(1.54894 + 0.804162i) q^{21} +(-0.0572652 + 0.361558i) q^{22} +(6.05243 + 3.08387i) q^{23} +(-0.774543 - 1.54922i) q^{24} -2.62134i q^{26} +(4.13281 + 3.14959i) q^{27} +(0.995214 + 0.157626i) q^{28} +(-0.368253 + 0.267552i) q^{29} +(-2.36811 - 1.72054i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.368759 - 0.515779i) q^{33} +(-5.58722 - 1.81540i) q^{34} +(2.83870 + 0.970457i) q^{36} +(-4.35053 - 8.53839i) q^{37} +(0.263986 + 0.518102i) q^{38} +(3.18589 + 3.23486i) q^{39} +(10.0917 + 3.27898i) q^{41} +(-1.41972 + 1.01503i) q^{42} +(7.18512 + 7.18512i) q^{43} +(-0.296153 - 0.215168i) q^{44} +(-5.49549 + 3.99271i) q^{46} +(8.16222 + 1.29277i) q^{47} +(1.73200 + 0.0132082i) q^{48} +5.98470i q^{49} +(9.10128 - 4.55025i) q^{51} +(2.33563 + 1.19006i) q^{52} +(-1.38217 + 8.72670i) q^{53} +(-4.68256 + 2.25248i) q^{54} +(-0.592264 + 0.815182i) q^{56} +(-0.955457 - 0.318522i) q^{57} +(-0.0712068 - 0.449582i) q^{58} +(-2.91096 + 8.95903i) q^{59} +(-0.335312 - 1.03198i) q^{61} +(2.60811 - 1.32890i) q^{62} +(0.518359 - 2.97808i) q^{63} +(0.951057 - 0.309017i) q^{64} +(0.626975 - 0.0944078i) q^{66} +(-13.0896 + 2.07319i) q^{67} +(4.15407 - 4.15407i) q^{68} +(1.92909 - 11.6062i) q^{69} +(-0.755873 - 1.04037i) q^{71} +(-2.15343 + 2.08872i) q^{72} +(-4.33350 + 8.50497i) q^{73} +9.58285 q^{74} -0.581479 q^{76} +(-0.167456 + 0.328652i) q^{77} +(-4.32864 + 1.37006i) q^{78} +(7.17322 + 9.87309i) q^{79} +(3.04091 - 8.47071i) q^{81} +(-7.50310 + 7.50310i) q^{82} +(-0.937190 + 0.148436i) q^{83} +(-0.259864 - 1.72579i) q^{84} +(-9.66396 + 3.14001i) q^{86} +(0.634281 + 0.468264i) q^{87} +(0.326166 - 0.166190i) q^{88} +(-0.626378 - 1.92779i) q^{89} +(0.816210 - 2.51204i) q^{91} +(-1.06263 - 6.70917i) q^{92} +(-1.60343 + 4.80974i) q^{93} +(-4.85743 + 6.68568i) q^{94} +(-0.798080 + 1.53723i) q^{96} +(2.81727 - 17.7876i) q^{97} +(-5.33241 - 2.71700i) q^{98} +(-0.658978 + 0.878510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{3} - 4q^{7} + O(q^{10}) \) \( 80q - 4q^{3} - 4q^{7} + 4q^{12} + 20q^{16} + 8q^{18} - 40q^{19} + 36q^{22} - 4q^{27} + 16q^{28} - 4q^{33} - 40q^{34} + 24q^{37} - 40q^{39} + 4q^{42} + 24q^{43} + 4q^{48} + 64q^{57} - 20q^{58} - 64q^{63} - 96q^{67} + 140q^{69} - 8q^{72} - 100q^{73} - 100q^{78} + 80q^{79} - 40q^{81} - 96q^{82} + 60q^{84} - 80q^{87} - 4q^{88} - 12q^{93} + 32q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.453990 + 0.891007i −0.321020 + 0.630037i
\(3\) −0.522656 1.65131i −0.301755 0.953385i
\(4\) −0.587785 0.809017i −0.293893 0.404508i
\(5\) 0 0
\(6\) 1.70861 + 0.283990i 0.697537 + 0.115939i
\(7\) −0.712495 + 0.712495i −0.269298 + 0.269298i −0.828817 0.559519i \(-0.810986\pi\)
0.559519 + 0.828817i \(0.310986\pi\)
\(8\) 0.987688 0.156434i 0.349201 0.0553079i
\(9\) −2.45366 + 1.72614i −0.817887 + 0.575378i
\(10\) 0 0
\(11\) 0.348148 0.113120i 0.104971 0.0341070i −0.256061 0.966661i \(-0.582425\pi\)
0.361031 + 0.932554i \(0.382425\pi\)
\(12\) −1.02873 + 1.39345i −0.296969 + 0.402256i
\(13\) −2.33563 + 1.19006i −0.647787 + 0.330064i −0.746826 0.665020i \(-0.768423\pi\)
0.0990392 + 0.995084i \(0.468423\pi\)
\(14\) −0.311372 0.958303i −0.0832176 0.256117i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 0.919013 + 5.80242i 0.222893 + 1.40729i 0.804562 + 0.593868i \(0.202400\pi\)
−0.581669 + 0.813426i \(0.697600\pi\)
\(18\) −0.424059 2.96988i −0.0999516 0.700007i
\(19\) 0.341785 0.470426i 0.0784108 0.107923i −0.768010 0.640438i \(-0.778753\pi\)
0.846421 + 0.532515i \(0.178753\pi\)
\(20\) 0 0
\(21\) 1.54894 + 0.804162i 0.338007 + 0.175482i
\(22\) −0.0572652 + 0.361558i −0.0122090 + 0.0770844i
\(23\) 6.05243 + 3.08387i 1.26202 + 0.643031i 0.951533 0.307548i \(-0.0995083\pi\)
0.310486 + 0.950578i \(0.399508\pi\)
\(24\) −0.774543 1.54922i −0.158103 0.316233i
\(25\) 0 0
\(26\) 2.62134i 0.514086i
\(27\) 4.13281 + 3.14959i 0.795359 + 0.606138i
\(28\) 0.995214 + 0.157626i 0.188078 + 0.0297886i
\(29\) −0.368253 + 0.267552i −0.0683830 + 0.0496831i −0.621452 0.783453i \(-0.713457\pi\)
0.553069 + 0.833136i \(0.313457\pi\)
\(30\) 0 0
\(31\) −2.36811 1.72054i −0.425326 0.309017i 0.354451 0.935074i \(-0.384668\pi\)
−0.779777 + 0.626057i \(0.784668\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −0.368759 0.515779i −0.0641926 0.0897855i
\(34\) −5.58722 1.81540i −0.958200 0.311338i
\(35\) 0 0
\(36\) 2.83870 + 0.970457i 0.473117 + 0.161743i
\(37\) −4.35053 8.53839i −0.715222 1.40370i −0.906517 0.422169i \(-0.861269\pi\)
0.191295 0.981533i \(-0.438731\pi\)
\(38\) 0.263986 + 0.518102i 0.0428242 + 0.0840472i
\(39\) 3.18589 + 3.23486i 0.510151 + 0.517992i
\(40\) 0 0
\(41\) 10.0917 + 3.27898i 1.57605 + 0.512090i 0.961036 0.276425i \(-0.0891497\pi\)
0.615016 + 0.788515i \(0.289150\pi\)
\(42\) −1.41972 + 1.01503i −0.219067 + 0.156623i
\(43\) 7.18512 + 7.18512i 1.09572 + 1.09572i 0.994905 + 0.100815i \(0.0321451\pi\)
0.100815 + 0.994905i \(0.467855\pi\)
\(44\) −0.296153 0.215168i −0.0446467 0.0324377i
\(45\) 0 0
\(46\) −5.49549 + 3.99271i −0.810266 + 0.588693i
\(47\) 8.16222 + 1.29277i 1.19058 + 0.188570i 0.720119 0.693850i \(-0.244087\pi\)
0.470463 + 0.882420i \(0.344087\pi\)
\(48\) 1.73200 + 0.0132082i 0.249993 + 0.00190644i
\(49\) 5.98470i 0.854957i
\(50\) 0 0
\(51\) 9.10128 4.55025i 1.27443 0.637162i
\(52\) 2.33563 + 1.19006i 0.323893 + 0.165032i
\(53\) −1.38217 + 8.72670i −0.189856 + 1.19870i 0.690123 + 0.723692i \(0.257556\pi\)
−0.879979 + 0.475012i \(0.842444\pi\)
\(54\) −4.68256 + 2.25248i −0.637215 + 0.306523i
\(55\) 0 0
\(56\) −0.592264 + 0.815182i −0.0791446 + 0.108933i
\(57\) −0.955457 0.318522i −0.126553 0.0421893i
\(58\) −0.0712068 0.449582i −0.00934992 0.0590330i
\(59\) −2.91096 + 8.95903i −0.378975 + 1.16637i 0.561782 + 0.827285i \(0.310116\pi\)
−0.940757 + 0.339081i \(0.889884\pi\)
\(60\) 0 0
\(61\) −0.335312 1.03198i −0.0429323 0.132132i 0.927293 0.374337i \(-0.122130\pi\)
−0.970225 + 0.242205i \(0.922130\pi\)
\(62\) 2.60811 1.32890i 0.331230 0.168770i
\(63\) 0.518359 2.97808i 0.0653071 0.375203i
\(64\) 0.951057 0.309017i 0.118882 0.0386271i
\(65\) 0 0
\(66\) 0.626975 0.0944078i 0.0771753 0.0116208i
\(67\) −13.0896 + 2.07319i −1.59915 + 0.253280i −0.891411 0.453196i \(-0.850284\pi\)
−0.707737 + 0.706476i \(0.750284\pi\)
\(68\) 4.15407 4.15407i 0.503756 0.503756i
\(69\) 1.92909 11.6062i 0.232235 1.39723i
\(70\) 0 0
\(71\) −0.755873 1.04037i −0.0897056 0.123469i 0.761805 0.647806i \(-0.224313\pi\)
−0.851511 + 0.524337i \(0.824313\pi\)
\(72\) −2.15343 + 2.08872i −0.253784 + 0.246158i
\(73\) −4.33350 + 8.50497i −0.507198 + 0.995432i 0.485435 + 0.874273i \(0.338661\pi\)
−0.992633 + 0.121159i \(0.961339\pi\)
\(74\) 9.58285 1.11398
\(75\) 0 0
\(76\) −0.581479 −0.0667002
\(77\) −0.167456 + 0.328652i −0.0190834 + 0.0374533i
\(78\) −4.32864 + 1.37006i −0.490122 + 0.155128i
\(79\) 7.17322 + 9.87309i 0.807050 + 1.11081i 0.991772 + 0.128018i \(0.0408616\pi\)
−0.184722 + 0.982791i \(0.559138\pi\)
\(80\) 0 0
\(81\) 3.04091 8.47071i 0.337879 0.941189i
\(82\) −7.50310 + 7.50310i −0.828579 + 0.828579i
\(83\) −0.937190 + 0.148436i −0.102870 + 0.0162930i −0.207657 0.978202i \(-0.566584\pi\)
0.104787 + 0.994495i \(0.466584\pi\)
\(84\) −0.259864 1.72579i −0.0283535 0.188300i
\(85\) 0 0
\(86\) −9.66396 + 3.14001i −1.04209 + 0.338596i
\(87\) 0.634281 + 0.468264i 0.0680021 + 0.0502032i
\(88\) 0.326166 0.166190i 0.0347694 0.0177159i
\(89\) −0.626378 1.92779i −0.0663960 0.204346i 0.912354 0.409401i \(-0.134262\pi\)
−0.978750 + 0.205056i \(0.934262\pi\)
\(90\) 0 0
\(91\) 0.816210 2.51204i 0.0855620 0.263333i
\(92\) −1.06263 6.70917i −0.110787 0.699479i
\(93\) −1.60343 + 4.80974i −0.166268 + 0.498747i
\(94\) −4.85743 + 6.68568i −0.501006 + 0.689576i
\(95\) 0 0
\(96\) −0.798080 + 1.53723i −0.0814537 + 0.156893i
\(97\) 2.81727 17.7876i 0.286051 1.80605i −0.257065 0.966394i \(-0.582755\pi\)
0.543115 0.839658i \(-0.317245\pi\)
\(98\) −5.33241 2.71700i −0.538655 0.274458i
\(99\) −0.658978 + 0.878510i −0.0662297 + 0.0882936i
\(100\) 0 0
\(101\) 0.362340i 0.0360542i 0.999837 + 0.0180271i \(0.00573851\pi\)
−0.999837 + 0.0180271i \(0.994261\pi\)
\(102\) −0.0775950 + 10.1751i −0.00768305 + 1.00748i
\(103\) 7.83651 + 1.24118i 0.772154 + 0.122297i 0.530065 0.847957i \(-0.322167\pi\)
0.242089 + 0.970254i \(0.422167\pi\)
\(104\) −2.12071 + 1.54078i −0.207952 + 0.151086i
\(105\) 0 0
\(106\) −7.14805 5.19336i −0.694280 0.504424i
\(107\) −9.06892 9.06892i −0.876725 0.876725i 0.116469 0.993194i \(-0.462842\pi\)
−0.993194 + 0.116469i \(0.962842\pi\)
\(108\) 0.118865 5.19479i 0.0114378 0.499869i
\(109\) −4.33696 1.40916i −0.415405 0.134973i 0.0938551 0.995586i \(-0.470081\pi\)
−0.509260 + 0.860613i \(0.670081\pi\)
\(110\) 0 0
\(111\) −11.8257 + 11.6467i −1.12245 + 1.10546i
\(112\) −0.457450 0.897796i −0.0432249 0.0848337i
\(113\) −6.17652 12.1221i −0.581038 1.14035i −0.975203 0.221311i \(-0.928966\pi\)
0.394166 0.919039i \(-0.371034\pi\)
\(114\) 0.717574 0.706712i 0.0672069 0.0661896i
\(115\) 0 0
\(116\) 0.432908 + 0.140660i 0.0401945 + 0.0130600i
\(117\) 3.67663 6.95162i 0.339905 0.642677i
\(118\) −6.66100 6.66100i −0.613195 0.613195i
\(119\) −4.78899 3.47940i −0.439006 0.318956i
\(120\) 0 0
\(121\) −8.79078 + 6.38687i −0.799161 + 0.580625i
\(122\) 1.07173 + 0.169746i 0.0970301 + 0.0153681i
\(123\) 0.140152 18.3782i 0.0126371 1.65711i
\(124\) 2.92715i 0.262866i
\(125\) 0 0
\(126\) 2.41816 + 1.81388i 0.215427 + 0.161594i
\(127\) 17.5736 + 8.95420i 1.55941 + 0.794557i 0.999424 0.0339477i \(-0.0108080\pi\)
0.559982 + 0.828505i \(0.310808\pi\)
\(128\) −0.156434 + 0.987688i −0.0138270 + 0.0873001i
\(129\) 8.10953 15.6202i 0.714004 1.37528i
\(130\) 0 0
\(131\) −6.37019 + 8.76782i −0.556566 + 0.766048i −0.990885 0.134711i \(-0.956989\pi\)
0.434318 + 0.900759i \(0.356989\pi\)
\(132\) −0.200523 + 0.601499i −0.0174533 + 0.0523538i
\(133\) 0.0916565 + 0.578696i 0.00794763 + 0.0501793i
\(134\) 4.09532 12.6041i 0.353782 1.08883i
\(135\) 0 0
\(136\) 1.81540 + 5.58722i 0.155669 + 0.479100i
\(137\) −7.75294 + 3.95032i −0.662378 + 0.337498i −0.752652 0.658419i \(-0.771226\pi\)
0.0902740 + 0.995917i \(0.471226\pi\)
\(138\) 9.46545 + 6.98796i 0.805753 + 0.594854i
\(139\) −2.91069 + 0.945741i −0.246882 + 0.0802167i −0.429844 0.902903i \(-0.641431\pi\)
0.182962 + 0.983120i \(0.441431\pi\)
\(140\) 0 0
\(141\) −2.13127 14.1540i −0.179485 1.19199i
\(142\) 1.27013 0.201170i 0.106587 0.0168818i
\(143\) −0.678525 + 0.678525i −0.0567411 + 0.0567411i
\(144\) −0.883429 2.86698i −0.0736191 0.238915i
\(145\) 0 0
\(146\) −5.61062 7.72236i −0.464338 0.639107i
\(147\) 9.88261 3.12794i 0.815104 0.257988i
\(148\) −4.35053 + 8.53839i −0.357611 + 0.701851i
\(149\) −5.85789 −0.479897 −0.239948 0.970786i \(-0.577131\pi\)
−0.239948 + 0.970786i \(0.577131\pi\)
\(150\) 0 0
\(151\) 3.64976 0.297013 0.148507 0.988911i \(-0.452553\pi\)
0.148507 + 0.988911i \(0.452553\pi\)
\(152\) 0.263986 0.518102i 0.0214121 0.0420236i
\(153\) −12.2707 12.6508i −0.992028 1.02276i
\(154\) −0.216807 0.298409i −0.0174708 0.0240465i
\(155\) 0 0
\(156\) 0.744434 4.47884i 0.0596024 0.358594i
\(157\) −2.27502 + 2.27502i −0.181567 + 0.181567i −0.792038 0.610472i \(-0.790980\pi\)
0.610472 + 0.792038i \(0.290980\pi\)
\(158\) −12.0536 + 1.90910i −0.958930 + 0.151880i
\(159\) 15.1329 2.27866i 1.20012 0.180709i
\(160\) 0 0
\(161\) −6.50956 + 2.11508i −0.513025 + 0.166692i
\(162\) 6.16691 + 6.55509i 0.484518 + 0.515017i
\(163\) 3.29567 1.67923i 0.258137 0.131527i −0.320134 0.947372i \(-0.603728\pi\)
0.578270 + 0.815845i \(0.303728\pi\)
\(164\) −3.27898 10.0917i −0.256045 0.788026i
\(165\) 0 0
\(166\) 0.293218 0.902431i 0.0227581 0.0700422i
\(167\) −1.42932 9.02439i −0.110604 0.698328i −0.979214 0.202831i \(-0.934986\pi\)
0.868610 0.495497i \(-0.165014\pi\)
\(168\) 1.65567 + 0.551953i 0.127738 + 0.0425841i
\(169\) −3.60230 + 4.95814i −0.277100 + 0.381395i
\(170\) 0 0
\(171\) −0.0266046 + 1.74423i −0.00203450 + 0.133385i
\(172\) 1.58958 10.0362i 0.121204 0.765252i
\(173\) 8.21156 + 4.18400i 0.624313 + 0.318104i 0.737374 0.675485i \(-0.236065\pi\)
−0.113061 + 0.993588i \(0.536065\pi\)
\(174\) −0.705184 + 0.352561i −0.0534598 + 0.0267276i
\(175\) 0 0
\(176\) 0.366065i 0.0275932i
\(177\) 16.3156 + 0.124423i 1.22635 + 0.00935217i
\(178\) 2.00205 + 0.317093i 0.150060 + 0.0237671i
\(179\) 10.9316 7.94230i 0.817069 0.593635i −0.0988026 0.995107i \(-0.531501\pi\)
0.915871 + 0.401472i \(0.131501\pi\)
\(180\) 0 0
\(181\) −13.0973 9.51573i −0.973514 0.707299i −0.0172639 0.999851i \(-0.505496\pi\)
−0.956250 + 0.292552i \(0.905496\pi\)
\(182\) 1.86769 + 1.86769i 0.138442 + 0.138442i
\(183\) −1.52887 + 1.09308i −0.113018 + 0.0808026i
\(184\) 6.46034 + 2.09909i 0.476262 + 0.154747i
\(185\) 0 0
\(186\) −3.55757 3.61225i −0.260854 0.264863i
\(187\) 0.976324 + 1.91614i 0.0713959 + 0.140122i
\(188\) −3.75176 7.36324i −0.273625 0.537020i
\(189\) −5.18867 + 0.700541i −0.377420 + 0.0509568i
\(190\) 0 0
\(191\) 14.6868 + 4.77202i 1.06270 + 0.345291i 0.787639 0.616136i \(-0.211303\pi\)
0.275058 + 0.961428i \(0.411303\pi\)
\(192\) −1.00736 1.40898i −0.0726998 0.101684i
\(193\) −6.05387 6.05387i −0.435767 0.435767i 0.454817 0.890585i \(-0.349704\pi\)
−0.890585 + 0.454817i \(0.849704\pi\)
\(194\) 14.5698 + 10.5856i 1.04605 + 0.760001i
\(195\) 0 0
\(196\) 4.84173 3.51772i 0.345838 0.251266i
\(197\) 6.25646 + 0.990925i 0.445754 + 0.0706005i 0.375277 0.926913i \(-0.377548\pi\)
0.0704774 + 0.997513i \(0.477548\pi\)
\(198\) −0.483589 0.985989i −0.0343672 0.0700712i
\(199\) 10.3976i 0.737069i −0.929614 0.368535i \(-0.879860\pi\)
0.929614 0.368535i \(-0.120140\pi\)
\(200\) 0 0
\(201\) 10.2648 + 20.5314i 0.724025 + 1.44817i
\(202\) −0.322847 0.164499i −0.0227155 0.0115741i
\(203\) 0.0717494 0.453008i 0.00503582 0.0317949i
\(204\) −9.03082 4.68852i −0.632284 0.328262i
\(205\) 0 0
\(206\) −4.66360 + 6.41889i −0.324928 + 0.447225i
\(207\) −20.1738 + 2.88055i −1.40217 + 0.200212i
\(208\) −0.410067 2.58906i −0.0284331 0.179519i
\(209\) 0.0657771 0.202441i 0.00454990 0.0140031i
\(210\) 0 0
\(211\) 1.12958 + 3.47648i 0.0777632 + 0.239331i 0.982380 0.186896i \(-0.0598427\pi\)
−0.904617 + 0.426226i \(0.859843\pi\)
\(212\) 7.87247 4.01122i 0.540683 0.275492i
\(213\) −1.32291 + 1.79194i −0.0906445 + 0.122781i
\(214\) 12.1977 3.96326i 0.833815 0.270923i
\(215\) 0 0
\(216\) 4.57463 + 2.46430i 0.311264 + 0.167674i
\(217\) 2.91314 0.461396i 0.197757 0.0313216i
\(218\) 3.22451 3.22451i 0.218391 0.218391i
\(219\) 16.3093 + 2.71079i 1.10208 + 0.183178i
\(220\) 0 0
\(221\) −9.05171 12.4586i −0.608884 0.838057i
\(222\) −5.00853 15.8243i −0.336151 1.06206i
\(223\) 0.959975 1.88406i 0.0642847 0.126166i −0.856628 0.515934i \(-0.827445\pi\)
0.920913 + 0.389768i \(0.127445\pi\)
\(224\) 1.00762 0.0673244
\(225\) 0 0
\(226\) 13.6049 0.904987
\(227\) −7.03137 + 13.7998i −0.466689 + 0.915928i 0.530960 + 0.847397i \(0.321831\pi\)
−0.997649 + 0.0685314i \(0.978169\pi\)
\(228\) 0.303913 + 0.960203i 0.0201272 + 0.0635910i
\(229\) −0.971347 1.33694i −0.0641884 0.0883477i 0.775716 0.631082i \(-0.217389\pi\)
−0.839904 + 0.542735i \(0.817389\pi\)
\(230\) 0 0
\(231\) 0.630228 + 0.104751i 0.0414660 + 0.00689211i
\(232\) −0.321865 + 0.321865i −0.0211315 + 0.0211315i
\(233\) −17.2497 + 2.73209i −1.13007 + 0.178985i −0.693342 0.720609i \(-0.743862\pi\)
−0.436726 + 0.899594i \(0.643862\pi\)
\(234\) 4.52478 + 6.43187i 0.295794 + 0.420465i
\(235\) 0 0
\(236\) 8.95903 2.91096i 0.583183 0.189488i
\(237\) 12.5544 17.0054i 0.815497 1.10462i
\(238\) 5.27432 2.68740i 0.341884 0.174198i
\(239\) 1.97435 + 6.07643i 0.127710 + 0.393052i 0.994385 0.105822i \(-0.0337472\pi\)
−0.866675 + 0.498873i \(0.833747\pi\)
\(240\) 0 0
\(241\) 5.94510 18.2971i 0.382958 1.17862i −0.554993 0.831855i \(-0.687279\pi\)
0.937951 0.346768i \(-0.112721\pi\)
\(242\) −1.69982 10.7322i −0.109268 0.689893i
\(243\) −15.5771 0.594232i −0.999273 0.0381200i
\(244\) −0.637801 + 0.877858i −0.0408310 + 0.0561991i
\(245\) 0 0
\(246\) 16.3115 + 8.46842i 1.03998 + 0.539927i
\(247\) −0.238446 + 1.50549i −0.0151719 + 0.0957918i
\(248\) −2.60811 1.32890i −0.165615 0.0843851i
\(249\) 0.734942 + 1.47001i 0.0465751 + 0.0931582i
\(250\) 0 0
\(251\) 10.1849i 0.642864i −0.946933 0.321432i \(-0.895836\pi\)
0.946933 0.321432i \(-0.104164\pi\)
\(252\) −2.71400 + 1.33111i −0.170966 + 0.0838522i
\(253\) 2.45599 + 0.388991i 0.154407 + 0.0244556i
\(254\) −15.9565 + 11.5931i −1.00120 + 0.727414i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −1.62811 1.62811i −0.101558 0.101558i 0.654502 0.756060i \(-0.272878\pi\)
−0.756060 + 0.654502i \(0.772878\pi\)
\(258\) 10.2361 + 14.3171i 0.637270 + 0.891342i
\(259\) 9.18328 + 2.98383i 0.570621 + 0.185406i
\(260\) 0 0
\(261\) 0.441739 1.29214i 0.0273429 0.0799813i
\(262\) −4.92018 9.65639i −0.303970 0.596574i
\(263\) 7.63791 + 14.9902i 0.470973 + 0.924338i 0.997256 + 0.0740278i \(0.0235854\pi\)
−0.526283 + 0.850310i \(0.676415\pi\)
\(264\) −0.444904 0.451742i −0.0273820 0.0278028i
\(265\) 0 0
\(266\) −0.557233 0.181056i −0.0341662 0.0111013i
\(267\) −2.85601 + 2.04192i −0.174785 + 0.124963i
\(268\) 9.37111 + 9.37111i 0.572432 + 0.572432i
\(269\) −4.85348 3.52626i −0.295922 0.215000i 0.429910 0.902872i \(-0.358545\pi\)
−0.725832 + 0.687872i \(0.758545\pi\)
\(270\) 0 0
\(271\) −10.0235 + 7.28250i −0.608885 + 0.442380i −0.849021 0.528359i \(-0.822808\pi\)
0.240137 + 0.970739i \(0.422808\pi\)
\(272\) −5.80242 0.919013i −0.351823 0.0557234i
\(273\) −4.57475 0.0348870i −0.276876 0.00211146i
\(274\) 8.70132i 0.525666i
\(275\) 0 0
\(276\) −10.5235 + 5.26132i −0.633443 + 0.316694i
\(277\) −5.49796 2.80135i −0.330340 0.168317i 0.280952 0.959722i \(-0.409350\pi\)
−0.611292 + 0.791405i \(0.709350\pi\)
\(278\) 0.478765 3.02280i 0.0287144 0.181296i
\(279\) 8.78043 + 0.133927i 0.525671 + 0.00801799i
\(280\) 0 0
\(281\) 5.28744 7.27753i 0.315422 0.434141i −0.621640 0.783303i \(-0.713533\pi\)
0.937063 + 0.349161i \(0.113533\pi\)
\(282\) 13.5789 + 4.52683i 0.808613 + 0.269569i
\(283\) −2.05054 12.9466i −0.121892 0.769594i −0.970594 0.240723i \(-0.922615\pi\)
0.848702 0.528871i \(-0.177385\pi\)
\(284\) −0.397386 + 1.22303i −0.0235805 + 0.0725733i
\(285\) 0 0
\(286\) −0.296526 0.912614i −0.0175340 0.0539640i
\(287\) −9.52650 + 4.85400i −0.562332 + 0.286522i
\(288\) 2.95556 + 0.514439i 0.174158 + 0.0303136i
\(289\) −16.6555 + 5.41171i −0.979737 + 0.318336i
\(290\) 0 0
\(291\) −30.8453 + 4.64457i −1.80818 + 0.272270i
\(292\) 9.42784 1.49322i 0.551722 0.0873842i
\(293\) 9.52977 9.52977i 0.556735 0.556735i −0.371641 0.928376i \(-0.621205\pi\)
0.928376 + 0.371641i \(0.121205\pi\)
\(294\) −1.69960 + 10.2255i −0.0991225 + 0.596365i
\(295\) 0 0
\(296\) −5.63266 7.75269i −0.327392 0.450616i
\(297\) 1.79511 + 0.629019i 0.104163 + 0.0364994i
\(298\) 2.65942 5.21941i 0.154056 0.302353i
\(299\) −17.8062 −1.02976
\(300\) 0 0
\(301\) −10.2387 −0.590150
\(302\) −1.65696 + 3.25196i −0.0953472 + 0.187129i
\(303\) 0.598336 0.189379i 0.0343735 0.0108795i
\(304\) 0.341785 + 0.470426i 0.0196027 + 0.0269808i
\(305\) 0 0
\(306\) 16.8428 5.18992i 0.962837 0.296688i
\(307\) −13.4223 + 13.4223i −0.766053 + 0.766053i −0.977409 0.211356i \(-0.932212\pi\)
0.211356 + 0.977409i \(0.432212\pi\)
\(308\) 0.364313 0.0577015i 0.0207587 0.00328785i
\(309\) −2.04622 13.5892i −0.116405 0.773064i
\(310\) 0 0
\(311\) 20.3576 6.61457i 1.15437 0.375078i 0.331583 0.943426i \(-0.392417\pi\)
0.822788 + 0.568348i \(0.192417\pi\)
\(312\) 3.65271 + 2.69665i 0.206794 + 0.152668i
\(313\) −11.3795 + 5.79816i −0.643210 + 0.327732i −0.744990 0.667075i \(-0.767546\pi\)
0.101781 + 0.994807i \(0.467546\pi\)
\(314\) −0.994222 3.05990i −0.0561072 0.172680i
\(315\) 0 0
\(316\) 3.77118 11.6065i 0.212146 0.652917i
\(317\) 4.33787 + 27.3883i 0.243639 + 1.53828i 0.741460 + 0.670997i \(0.234134\pi\)
−0.497821 + 0.867280i \(0.665866\pi\)
\(318\) −4.83989 + 14.5180i −0.271408 + 0.814129i
\(319\) −0.0979413 + 0.134805i −0.00548366 + 0.00754761i
\(320\) 0 0
\(321\) −10.2357 + 19.7155i −0.571300 + 1.10041i
\(322\) 1.07072 6.76029i 0.0596692 0.376736i
\(323\) 3.04372 + 1.55085i 0.169357 + 0.0862917i
\(324\) −8.64035 + 2.51881i −0.480019 + 0.139934i
\(325\) 0 0
\(326\) 3.69881i 0.204858i
\(327\) −0.0602315 + 7.89818i −0.00333081 + 0.436770i
\(328\) 10.4804 + 1.65992i 0.578681 + 0.0916540i
\(329\) −6.73663 + 4.89445i −0.371402 + 0.269840i
\(330\) 0 0
\(331\) 15.0534 + 10.9369i 0.827410 + 0.601149i 0.918826 0.394664i \(-0.129139\pi\)
−0.0914151 + 0.995813i \(0.529139\pi\)
\(332\) 0.670954 + 0.670954i 0.0368234 + 0.0368234i
\(333\) 25.4131 + 13.4407i 1.39263 + 0.736547i
\(334\) 8.68968 + 2.82345i 0.475478 + 0.154492i
\(335\) 0 0
\(336\) −1.24345 + 1.22463i −0.0678359 + 0.0668091i
\(337\) 9.42193 + 18.4916i 0.513245 + 1.00730i 0.991625 + 0.129148i \(0.0412242\pi\)
−0.478380 + 0.878153i \(0.658776\pi\)
\(338\) −2.78232 5.46062i −0.151339 0.297019i
\(339\) −16.7892 + 16.5350i −0.911862 + 0.898060i
\(340\) 0 0
\(341\) −1.01908 0.331120i −0.0551864 0.0179312i
\(342\) −1.54205 0.815571i −0.0833843 0.0441010i
\(343\) −9.25153 9.25153i −0.499536 0.499536i
\(344\) 8.22066 + 5.97266i 0.443228 + 0.322024i
\(345\) 0 0
\(346\) −7.45594 + 5.41706i −0.400834 + 0.291223i
\(347\) −7.36133 1.16592i −0.395177 0.0625898i −0.0443161 0.999018i \(-0.514111\pi\)
−0.350861 + 0.936428i \(0.614111\pi\)
\(348\) 0.00601220 0.788383i 0.000322288 0.0422618i
\(349\) 16.1042i 0.862040i −0.902342 0.431020i \(-0.858154\pi\)
0.902342 0.431020i \(-0.141846\pi\)
\(350\) 0 0
\(351\) −13.4009 2.43796i −0.715287 0.130129i
\(352\) −0.326166 0.166190i −0.0173847 0.00885796i
\(353\) 0.0677049 0.427472i 0.00360357 0.0227520i −0.985821 0.167800i \(-0.946334\pi\)
0.989425 + 0.145048i \(0.0463337\pi\)
\(354\) −7.51798 + 14.4808i −0.399576 + 0.769646i
\(355\) 0 0
\(356\) −1.19144 + 1.63988i −0.0631463 + 0.0869135i
\(357\) −3.24259 + 9.72664i −0.171616 + 0.514788i
\(358\) 2.11378 + 13.3459i 0.111717 + 0.705352i
\(359\) −0.0683480 + 0.210354i −0.00360727 + 0.0111020i −0.952844 0.303461i \(-0.901858\pi\)
0.949237 + 0.314563i \(0.101858\pi\)
\(360\) 0 0
\(361\) 5.76684 + 17.7485i 0.303518 + 0.934132i
\(362\) 14.4246 7.34971i 0.758141 0.386292i
\(363\) 15.1413 + 11.1782i 0.794710 + 0.586702i
\(364\) −2.51204 + 0.816210i −0.131666 + 0.0427810i
\(365\) 0 0
\(366\) −0.279844 1.85848i −0.0146277 0.0971445i
\(367\) −16.4940 + 2.61239i −0.860980 + 0.136366i −0.571284 0.820753i \(-0.693554\pi\)
−0.289697 + 0.957119i \(0.593554\pi\)
\(368\) −4.80323 + 4.80323i −0.250386 + 0.250386i
\(369\) −30.4215 + 9.37406i −1.58368 + 0.487994i
\(370\) 0 0
\(371\) −5.23293 7.20252i −0.271680 0.373936i
\(372\) 4.83364 1.52989i 0.250612 0.0793212i
\(373\) −0.0479661 + 0.0941389i −0.00248359 + 0.00487433i −0.892245 0.451552i \(-0.850871\pi\)
0.889761 + 0.456426i \(0.150871\pi\)
\(374\) −2.15054 −0.111202
\(375\) 0 0
\(376\) 8.26396 0.426181
\(377\) 0.541700 1.06315i 0.0278990 0.0547548i
\(378\) 1.73142 4.94118i 0.0890546 0.254147i
\(379\) −5.78536 7.96287i −0.297174 0.409025i 0.634154 0.773207i \(-0.281349\pi\)
−0.931328 + 0.364182i \(0.881349\pi\)
\(380\) 0 0
\(381\) 5.60123 33.6995i 0.286960 1.72648i
\(382\) −10.9196 + 10.9196i −0.558693 + 0.558693i
\(383\) 32.8669 5.20561i 1.67942 0.265994i 0.757349 0.653010i \(-0.226494\pi\)
0.922073 + 0.387016i \(0.126494\pi\)
\(384\) 1.71274 0.257899i 0.0874030 0.0131609i
\(385\) 0 0
\(386\) 8.14244 2.64564i 0.414439 0.134659i
\(387\) −30.0323 5.22736i −1.52663 0.265722i
\(388\) −16.0464 + 8.17604i −0.814632 + 0.415076i
\(389\) 10.3312 + 31.7962i 0.523814 + 1.61213i 0.766650 + 0.642066i \(0.221922\pi\)
−0.242836 + 0.970067i \(0.578078\pi\)
\(390\) 0 0
\(391\) −12.3316 + 37.9528i −0.623637 + 1.91936i
\(392\) 0.936214 + 5.91102i 0.0472859 + 0.298552i
\(393\) 17.8078 + 5.93662i 0.898286 + 0.299463i
\(394\) −3.72329 + 5.12467i −0.187577 + 0.258177i
\(395\) 0 0
\(396\) 1.09807 + 0.0167487i 0.0551799 + 0.000841653i
\(397\) −2.14742 + 13.5583i −0.107776 + 0.680471i 0.873349 + 0.487096i \(0.161944\pi\)
−0.981125 + 0.193376i \(0.938056\pi\)
\(398\) 9.26436 + 4.72043i 0.464381 + 0.236614i
\(399\) 0.907703 0.453812i 0.0454420 0.0227190i
\(400\) 0 0
\(401\) 8.63025i 0.430974i 0.976507 + 0.215487i \(0.0691339\pi\)
−0.976507 + 0.215487i \(0.930866\pi\)
\(402\) −22.9538 0.175045i −1.14483 0.00873046i
\(403\) 7.57858 + 1.20033i 0.377516 + 0.0597926i
\(404\) 0.293139 0.212978i 0.0145842 0.0105961i
\(405\) 0 0
\(406\) 0.371060 + 0.269591i 0.0184154 + 0.0133796i
\(407\) −2.48049 2.48049i −0.122953 0.122953i
\(408\) 8.27741 5.91798i 0.409793 0.292984i
\(409\) −25.9908 8.44492i −1.28516 0.417574i −0.414767 0.909928i \(-0.636137\pi\)
−0.870395 + 0.492353i \(0.836137\pi\)
\(410\) 0 0
\(411\) 10.5753 + 10.7379i 0.521642 + 0.529660i
\(412\) −3.60205 7.06941i −0.177460 0.348285i
\(413\) −4.30921 8.45731i −0.212043 0.416157i
\(414\) 6.59212 19.2827i 0.323985 0.947694i
\(415\) 0 0
\(416\) 2.49304 + 0.810037i 0.122231 + 0.0397154i
\(417\) 3.08300 + 4.31216i 0.150975 + 0.211167i
\(418\) 0.150514 + 0.150514i 0.00736189 + 0.00736189i
\(419\) −20.8362 15.1384i −1.01791 0.739557i −0.0520594 0.998644i \(-0.516579\pi\)
−0.965854 + 0.259087i \(0.916579\pi\)
\(420\) 0 0
\(421\) 28.5994 20.7787i 1.39385 1.01269i 0.398419 0.917203i \(-0.369559\pi\)
0.995431 0.0954876i \(-0.0304410\pi\)
\(422\) −3.61038 0.571828i −0.175751 0.0278362i
\(423\) −22.2588 + 10.9171i −1.08226 + 0.530806i
\(424\) 8.83548i 0.429089i
\(425\) 0 0
\(426\) −0.996037 1.99225i −0.0482582 0.0965246i
\(427\) 0.974191 + 0.496375i 0.0471444 + 0.0240213i
\(428\) −2.00633 + 12.6675i −0.0969797 + 0.612306i
\(429\) 1.47509 + 0.765821i 0.0712181 + 0.0369742i
\(430\) 0 0
\(431\) −19.9752 + 27.4935i −0.962171 + 1.32432i −0.0162678 + 0.999868i \(0.505178\pi\)
−0.945904 + 0.324448i \(0.894822\pi\)
\(432\) −4.27254 + 2.95726i −0.205563 + 0.142281i
\(433\) −2.98384 18.8393i −0.143394 0.905357i −0.949541 0.313641i \(-0.898451\pi\)
0.806147 0.591715i \(-0.201549\pi\)
\(434\) −0.911432 + 2.80510i −0.0437501 + 0.134649i
\(435\) 0 0
\(436\) 1.40916 + 4.33696i 0.0674867 + 0.207703i
\(437\) 3.51936 1.79320i 0.168354 0.0857806i
\(438\) −9.81959 + 13.3010i −0.469198 + 0.635547i
\(439\) 33.6517 10.9341i 1.60611 0.521856i 0.637499 0.770451i \(-0.279969\pi\)
0.968607 + 0.248596i \(0.0799691\pi\)
\(440\) 0 0
\(441\) −10.3304 14.6844i −0.491924 0.699259i
\(442\) 15.2101 2.40904i 0.723470 0.114586i
\(443\) 10.2497 10.2497i 0.486977 0.486977i −0.420374 0.907351i \(-0.638101\pi\)
0.907351 + 0.420374i \(0.138101\pi\)
\(444\) 16.3734 + 2.72144i 0.777046 + 0.129154i
\(445\) 0 0
\(446\) 1.24289 + 1.71069i 0.0588524 + 0.0810034i
\(447\) 3.06166 + 9.67320i 0.144811 + 0.457526i
\(448\) −0.457450 + 0.897796i −0.0216125 + 0.0424169i
\(449\) 9.47944 0.447362 0.223681 0.974662i \(-0.428193\pi\)
0.223681 + 0.974662i \(0.428193\pi\)
\(450\) 0 0
\(451\) 3.88431 0.182905
\(452\) −6.17652 + 12.1221i −0.290519 + 0.570175i
\(453\) −1.90757 6.02689i −0.0896254 0.283168i
\(454\) −9.10358 12.5300i −0.427252 0.588062i
\(455\) 0 0
\(456\) −0.993521 0.165134i −0.0465259 0.00773312i
\(457\) 25.4852 25.4852i 1.19215 1.19215i 0.215682 0.976464i \(-0.430803\pi\)
0.976464 0.215682i \(-0.0691974\pi\)
\(458\) 1.63221 0.258516i 0.0762681 0.0120797i
\(459\) −14.4771 + 26.8748i −0.675734 + 1.25441i
\(460\) 0 0
\(461\) 21.4340 6.96431i 0.998279 0.324360i 0.236101 0.971728i \(-0.424130\pi\)
0.762178 + 0.647368i \(0.224130\pi\)
\(462\) −0.379451 + 0.513982i −0.0176537 + 0.0239126i
\(463\) −5.05300 + 2.57463i −0.234833 + 0.119653i −0.567448 0.823409i \(-0.692069\pi\)
0.332615 + 0.943063i \(0.392069\pi\)
\(464\) −0.140660 0.432908i −0.00652999 0.0200972i
\(465\) 0 0
\(466\) 5.39691 16.6100i 0.250007 0.769442i
\(467\) −1.81829 11.4802i −0.0841404 0.531242i −0.993371 0.114950i \(-0.963329\pi\)
0.909231 0.416292i \(-0.136671\pi\)
\(468\) −7.78505 + 1.11160i −0.359864 + 0.0513838i
\(469\) 7.84913 10.8034i 0.362439 0.498854i
\(470\) 0 0
\(471\) 4.94583 + 2.56772i 0.227892 + 0.118314i
\(472\) −1.47363 + 9.30410i −0.0678291 + 0.428256i
\(473\) 3.31427 + 1.68871i 0.152390 + 0.0776467i
\(474\) 9.45238 + 18.9064i 0.434162 + 0.868399i
\(475\) 0 0
\(476\) 5.91951i 0.271320i
\(477\) −11.6721 23.7982i −0.534428 1.08964i
\(478\) −6.31048 0.999482i −0.288635 0.0457152i
\(479\) −2.20406 + 1.60135i −0.100706 + 0.0731673i −0.636999 0.770865i \(-0.719824\pi\)
0.536293 + 0.844032i \(0.319824\pi\)
\(480\) 0 0
\(481\) 20.3224 + 14.7651i 0.926622 + 0.673230i
\(482\) 13.6039 + 13.6039i 0.619639 + 0.619639i
\(483\) 6.89493 + 9.64386i 0.313730 + 0.438811i
\(484\) 10.3342 + 3.35778i 0.469735 + 0.152626i
\(485\) 0 0
\(486\) 7.60133 13.6095i 0.344803 0.617342i
\(487\) 12.3082 + 24.1563i 0.557739 + 1.09462i 0.981964 + 0.189068i \(0.0605466\pi\)
−0.424225 + 0.905557i \(0.639453\pi\)
\(488\) −0.492622 0.966824i −0.0222999 0.0437661i
\(489\) −4.49543 4.56452i −0.203290 0.206415i
\(490\) 0 0
\(491\) 37.5268 + 12.1932i 1.69356 + 0.550271i 0.987464 0.157846i \(-0.0504550\pi\)
0.706095 + 0.708117i \(0.250455\pi\)
\(492\) −14.9507 + 10.6891i −0.674029 + 0.481901i
\(493\) −1.89088 1.89088i −0.0851609 0.0851609i
\(494\) −1.23315 0.895933i −0.0554819 0.0403099i
\(495\) 0 0
\(496\) 2.36811 1.72054i 0.106331 0.0772543i
\(497\) 1.27981 + 0.202702i 0.0574075 + 0.00909245i
\(498\) −1.64345 0.0125329i −0.0736446 0.000561613i
\(499\) 11.3155i 0.506552i −0.967394 0.253276i \(-0.918492\pi\)
0.967394 0.253276i \(-0.0815081\pi\)
\(500\) 0 0
\(501\) −14.1550 + 7.07690i −0.632400 + 0.316173i
\(502\) 9.07480 + 4.62384i 0.405028 + 0.206372i
\(503\) −1.34669 + 8.50269i −0.0600461 + 0.379116i 0.939305 + 0.343084i \(0.111472\pi\)
−0.999351 + 0.0360317i \(0.988528\pi\)
\(504\) 0.0461019 3.02251i 0.00205354 0.134633i
\(505\) 0 0
\(506\) −1.46159 + 2.01171i −0.0649756 + 0.0894312i
\(507\) 10.0702 + 3.35712i 0.447233 + 0.149095i
\(508\) −3.08541 19.4805i −0.136893 0.864307i
\(509\) −0.697725 + 2.14738i −0.0309261 + 0.0951808i −0.965328 0.261039i \(-0.915935\pi\)
0.934402 + 0.356220i \(0.115935\pi\)
\(510\) 0 0
\(511\) −2.97215 9.14735i −0.131480 0.404655i
\(512\) 0.891007 0.453990i 0.0393773 0.0200637i
\(513\) 2.89418 0.867702i 0.127781 0.0383100i
\(514\) 2.18980 0.711508i 0.0965878 0.0313833i
\(515\) 0 0
\(516\) −17.4037 + 2.62059i −0.766154 + 0.115365i
\(517\) 2.98790 0.473237i 0.131408 0.0208129i
\(518\) −6.82773 + 6.82773i −0.299993 + 0.299993i
\(519\) 2.61727 15.7466i 0.114885 0.691201i
\(520\) 0 0
\(521\) −13.0319 17.9369i −0.570938 0.785829i 0.421727 0.906723i \(-0.361424\pi\)
−0.992665 + 0.120894i \(0.961424\pi\)
\(522\) 0.950757 + 0.980210i 0.0416135 + 0.0429026i
\(523\) 5.09249 9.99457i 0.222679 0.437032i −0.752456 0.658642i \(-0.771131\pi\)
0.975135 + 0.221610i \(0.0711312\pi\)
\(524\) 10.8376 0.473444
\(525\) 0 0
\(526\) −16.8239 −0.733558
\(527\) 7.80694 15.3220i 0.340076 0.667436i
\(528\) 0.604487 0.191326i 0.0263069 0.00832639i
\(529\) 13.6026 + 18.7224i 0.591417 + 0.814016i
\(530\) 0 0
\(531\) −8.32197 27.0071i −0.361143 1.17201i
\(532\) 0.414301 0.414301i 0.0179622 0.0179622i
\(533\) −27.4725 + 4.35122i −1.18997 + 0.188472i
\(534\) −0.522762 3.47174i −0.0226221 0.150237i
\(535\) 0 0
\(536\) −12.6041 + 4.09532i −0.544415 + 0.176891i
\(537\) −18.8287 13.9005i −0.812518 0.599849i
\(538\) 5.34536 2.72359i 0.230455 0.117423i
\(539\) 0.676991 + 2.08356i 0.0291601 + 0.0897455i
\(540\) 0 0
\(541\) 3.02125 9.29846i 0.129894 0.399772i −0.864867 0.502001i \(-0.832597\pi\)
0.994761 + 0.102229i \(0.0325974\pi\)
\(542\) −1.93818 12.2372i −0.0832520 0.525632i
\(543\) −8.86807 + 26.6012i −0.380565 + 1.14156i
\(544\) 3.45309 4.75277i 0.148050 0.203773i
\(545\) 0 0
\(546\) 2.10798 4.06029i 0.0902131 0.173765i
\(547\) 1.65483 10.4482i 0.0707555 0.446732i −0.926722 0.375748i \(-0.877386\pi\)
0.997477 0.0709846i \(-0.0226141\pi\)
\(548\) 7.75294 + 3.95032i 0.331189 + 0.168749i
\(549\) 2.60409 + 1.95335i 0.111140 + 0.0833668i
\(550\) 0 0
\(551\) 0.264681i 0.0112758i
\(552\) 0.0897208 11.7651i 0.00381877 0.500757i
\(553\) −12.1454 1.92364i −0.516475 0.0818016i
\(554\) 4.99204 3.62693i 0.212092 0.154094i
\(555\) 0 0
\(556\) 2.47598 + 1.79891i 0.105005 + 0.0762906i
\(557\) 2.23937 + 2.23937i 0.0948850 + 0.0948850i 0.752956 0.658071i \(-0.228627\pi\)
−0.658071 + 0.752956i \(0.728627\pi\)
\(558\) −4.10556 + 7.76262i −0.173802 + 0.328618i
\(559\) −25.3325 8.23103i −1.07145 0.348135i
\(560\) 0 0
\(561\) 2.65387 2.61370i 0.112047 0.110351i
\(562\) 4.08388 + 8.01507i 0.172268 + 0.338095i
\(563\) 4.61877 + 9.06485i 0.194658 + 0.382038i 0.967619 0.252416i \(-0.0812251\pi\)
−0.772961 + 0.634454i \(0.781225\pi\)
\(564\) −10.1981 + 10.0438i −0.429419 + 0.422919i
\(565\) 0 0
\(566\) 12.4664 + 4.05058i 0.524002 + 0.170259i
\(567\) 3.86870 + 8.20197i 0.162470 + 0.344450i
\(568\) −0.909316 0.909316i −0.0381541 0.0381541i
\(569\) 10.0063 + 7.26997i 0.419484 + 0.304773i 0.777430 0.628969i \(-0.216523\pi\)
−0.357946 + 0.933742i \(0.616523\pi\)
\(570\) 0 0
\(571\) 22.7821 16.5522i 0.953402 0.692687i 0.00179324 0.999998i \(-0.499429\pi\)
0.951609 + 0.307311i \(0.0994292\pi\)
\(572\) 0.947765 + 0.150111i 0.0396281 + 0.00627647i
\(573\) 0.203969 26.7466i 0.00852093 1.11735i
\(574\) 10.6918i 0.446269i
\(575\) 0 0
\(576\) −1.80017 + 2.39988i −0.0750069 + 0.0999948i
\(577\) 9.96640 + 5.07813i 0.414907 + 0.211405i 0.648967 0.760817i \(-0.275201\pi\)
−0.234060 + 0.972222i \(0.575201\pi\)
\(578\) 2.73958 17.2971i 0.113952 0.719463i
\(579\) −6.83274 + 13.1609i −0.283959 + 0.546949i
\(580\) 0 0
\(581\) 0.561983 0.773503i 0.0233150 0.0320903i
\(582\) 9.86511 29.5919i 0.408922 1.22662i
\(583\) 0.505965 + 3.19454i 0.0209549 + 0.132304i
\(584\) −2.94968 + 9.07817i −0.122059 + 0.375657i
\(585\) 0 0
\(586\) 4.16466 + 12.8175i 0.172041 + 0.529487i
\(587\) −0.534451 + 0.272317i −0.0220592 + 0.0112397i −0.464985 0.885318i \(-0.653940\pi\)
0.442926 + 0.896558i \(0.353940\pi\)
\(588\) −8.33941 6.15664i −0.343911 0.253896i
\(589\) −1.61877 + 0.525971i −0.0667003 + 0.0216722i
\(590\) 0 0
\(591\) −1.63365 10.8493i −0.0671992 0.446279i
\(592\) 9.46487 1.49909i 0.389004 0.0616122i
\(593\) 1.69633 1.69633i 0.0696598 0.0696598i −0.671419 0.741078i \(-0.734315\pi\)
0.741078 + 0.671419i \(0.234315\pi\)
\(594\) −1.37542 + 1.31389i −0.0564343 + 0.0539095i
\(595\) 0 0
\(596\) 3.44318 + 4.73913i 0.141038 + 0.194122i
\(597\) −17.1697 + 5.43439i −0.702711 + 0.222415i
\(598\) 8.08385 15.8654i 0.330573 0.648786i
\(599\) 12.0681 0.493088 0.246544 0.969132i \(-0.420705\pi\)
0.246544 + 0.969132i \(0.420705\pi\)
\(600\) 0 0
\(601\) 8.03062 0.327576 0.163788 0.986496i \(-0.447629\pi\)
0.163788 + 0.986496i \(0.447629\pi\)
\(602\) 4.64828 9.12277i 0.189450 0.371816i
\(603\) 28.5388 27.6813i 1.16219 1.12727i
\(604\) −2.14528 2.95272i −0.0872900 0.120144i
\(605\) 0 0
\(606\) −0.102901 + 0.619098i −0.00418007 + 0.0251491i
\(607\) 27.1756 27.1756i 1.10302 1.10302i 0.108980 0.994044i \(-0.465242\pi\)
0.994044 0.108980i \(-0.0347584\pi\)
\(608\) −0.574320 + 0.0909634i −0.0232918 + 0.00368905i
\(609\) −0.785558 + 0.118287i −0.0318324 + 0.00479321i
\(610\) 0 0
\(611\) −20.6024 + 6.69412i −0.833483 + 0.270815i
\(612\) −3.02220 + 17.3632i −0.122165 + 0.701865i
\(613\) 25.9627 13.2287i 1.04862 0.534300i 0.157245 0.987560i \(-0.449739\pi\)
0.891379 + 0.453259i \(0.149739\pi\)
\(614\) −5.86577 18.0530i −0.236723 0.728560i
\(615\) 0 0
\(616\) −0.113982 + 0.350801i −0.00459248 + 0.0141342i
\(617\) 3.00048 + 18.9443i 0.120795 + 0.762667i 0.971503 + 0.237029i \(0.0761736\pi\)
−0.850708 + 0.525639i \(0.823826\pi\)
\(618\) 13.0371 + 4.34618i 0.524427 + 0.174829i
\(619\) 11.4117 15.7069i 0.458676 0.631314i −0.515557 0.856855i \(-0.672415\pi\)
0.974234 + 0.225541i \(0.0724151\pi\)
\(620\) 0 0
\(621\) 15.3006 + 31.8077i 0.613993 + 1.27640i
\(622\) −3.34851 + 21.1417i −0.134263 + 0.847704i
\(623\) 1.81984 + 0.927252i 0.0729102 + 0.0371496i
\(624\) −4.06103 + 2.03034i −0.162571 + 0.0812786i
\(625\) 0 0
\(626\) 12.7716i 0.510454i
\(627\) −0.368672 0.00281149i −0.0147233 0.000112280i
\(628\) 3.17776 + 0.503308i 0.126806 + 0.0200842i
\(629\) 45.5451 33.0905i 1.81600 1.31940i
\(630\) 0 0
\(631\) 8.91070 + 6.47400i 0.354729 + 0.257726i 0.750850 0.660472i \(-0.229644\pi\)
−0.396121 + 0.918198i \(0.629644\pi\)
\(632\) 8.62939 + 8.62939i 0.343259 + 0.343259i
\(633\) 5.15037 3.68228i 0.204709 0.146358i
\(634\) −26.3725 8.56893i −1.04738 0.340316i
\(635\) 0 0
\(636\) −10.7384 10.9034i −0.425804 0.432348i
\(637\) −7.12216 13.9780i −0.282190 0.553830i
\(638\) −0.0756474 0.148466i −0.00299491 0.00587784i
\(639\) 3.65047 + 1.24798i 0.144411 + 0.0493692i
\(640\) 0 0
\(641\) −41.8679 13.6037i −1.65368 0.537314i −0.674148 0.738596i \(-0.735489\pi\)
−0.979533 + 0.201283i \(0.935489\pi\)
\(642\) −12.9198 18.0707i −0.509902 0.713195i
\(643\) −21.0709 21.0709i −0.830957 0.830957i 0.156691 0.987648i \(-0.449917\pi\)
−0.987648 + 0.156691i \(0.949917\pi\)
\(644\) 5.53736 + 4.02313i 0.218203 + 0.158534i
\(645\) 0 0
\(646\) −2.76364 + 2.00790i −0.108734 + 0.0789998i
\(647\) 32.0404 + 5.07470i 1.25964 + 0.199507i 0.750322 0.661073i \(-0.229899\pi\)
0.509316 + 0.860580i \(0.329899\pi\)
\(648\) 1.67836 8.84212i 0.0659324 0.347351i
\(649\) 3.44836i 0.135360i
\(650\) 0 0
\(651\) −2.28448 4.56935i −0.0895358 0.179087i
\(652\) −3.29567 1.67923i −0.129068 0.0657636i
\(653\) −4.84433 + 30.5859i −0.189573 + 1.19692i 0.690945 + 0.722907i \(0.257195\pi\)
−0.880518 + 0.474012i \(0.842805\pi\)
\(654\) −7.00998 3.63936i −0.274112 0.142310i
\(655\) 0 0
\(656\) −6.23698 + 8.58447i −0.243513 + 0.335167i
\(657\) −4.04779 28.3485i −0.157919 1.10598i
\(658\) −1.30262 8.22441i −0.0507814 0.320621i
\(659\) 6.85074 21.0844i 0.266867 0.821332i −0.724390 0.689390i \(-0.757879\pi\)
0.991257 0.131942i \(-0.0421213\pi\)
\(660\) 0 0
\(661\) −9.91334 30.5101i −0.385584 1.18671i −0.936056 0.351852i \(-0.885552\pi\)
0.550471 0.834854i \(-0.314448\pi\)
\(662\) −16.5790 + 8.44742i −0.644361 + 0.328318i
\(663\) −15.8421 + 21.4588i −0.615257 + 0.833389i
\(664\) −0.902431 + 0.293218i −0.0350211 + 0.0113790i
\(665\) 0 0
\(666\) −23.5131 + 16.5413i −0.911114 + 0.640963i
\(667\) −3.05392 + 0.483694i −0.118248 + 0.0187287i
\(668\) −6.46075 + 6.46075i −0.249974 + 0.249974i
\(669\) −3.61290 0.600505i −0.139683 0.0232169i
\(670\) 0 0
\(671\) −0.233477 0.321353i −0.00901327 0.0124057i
\(672\) −0.526638 1.66389i −0.0203155 0.0641861i
\(673\) −17.0242 + 33.4118i −0.656234 + 1.28793i 0.287676 + 0.957728i \(0.407117\pi\)
−0.943910 + 0.330204i \(0.892883\pi\)
\(674\) −20.7536 −0.799398
\(675\) 0 0
\(676\) 6.12860 0.235715
\(677\) 13.6443 26.7784i 0.524391 1.02918i −0.465192 0.885210i \(-0.654015\pi\)
0.989583 0.143966i \(-0.0459855\pi\)
\(678\) −7.11070 22.4660i −0.273085 0.862802i
\(679\) 10.6662 + 14.6808i 0.409333 + 0.563399i
\(680\) 0 0
\(681\) 26.4628 + 4.39842i 1.01406 + 0.168548i
\(682\) 0.757684 0.757684i 0.0290132 0.0290132i
\(683\) −32.9389 + 5.21701i −1.26037 + 0.199623i −0.750640 0.660711i \(-0.770255\pi\)
−0.509731 + 0.860334i \(0.670255\pi\)
\(684\) 1.42675 1.00371i 0.0545533 0.0383779i
\(685\) 0 0
\(686\) 12.4433 4.04307i 0.475087 0.154365i
\(687\) −1.70003 + 2.30276i −0.0648602 + 0.0878557i
\(688\) −9.05378 + 4.61313i −0.345172 + 0.175874i
\(689\) −7.15707 22.0272i −0.272663 0.839169i
\(690\) 0 0
\(691\) 0.495555 1.52516i 0.0188518 0.0580199i −0.941188 0.337883i \(-0.890289\pi\)
0.960040 + 0.279863i \(0.0902891\pi\)
\(692\) −1.44171 9.10259i −0.0548055 0.346028i
\(693\) −0.156416 1.09545i −0.00594175 0.0416128i
\(694\) 4.38081 6.02967i 0.166293 0.228883i
\(695\) 0 0
\(696\) 0.699725 + 0.363275i 0.0265230 + 0.0137699i
\(697\) −9.75164 + 61.5694i −0.369370 + 2.33211i
\(698\) 14.3490 + 7.31117i 0.543117 + 0.276732i
\(699\) 13.5272 + 27.0568i 0.511646 + 1.02338i
\(700\) 0 0
\(701\) 17.1529i 0.647855i 0.946082 + 0.323928i \(0.105003\pi\)
−0.946082 + 0.323928i \(0.894997\pi\)
\(702\) 8.25612 10.8335i 0.311607 0.408883i
\(703\) −5.50363 0.871689i −0.207573 0.0328764i
\(704\) 0.296153 0.215168i 0.0111617 0.00810943i
\(705\) 0 0
\(706\) 0.350143 + 0.254394i 0.0131778 + 0.00957423i
\(707\) −0.258165 0.258165i −0.00970931 0.00970931i
\(708\) −9.48940 13.2727i −0.356633 0.498819i
\(709\) 43.3999 + 14.1015i 1.62992 + 0.529592i 0.974252 0.225460i \(-0.0723886\pi\)
0.655664 + 0.755052i \(0.272389\pi\)
\(710\) 0 0
\(711\) −34.6429 11.8433i −1.29921 0.444157i
\(712\) −0.920240 1.80607i −0.0344875 0.0676855i
\(713\) −9.02694 17.7164i −0.338062 0.663483i
\(714\) −7.19440 7.30497i −0.269244 0.273382i
\(715\) 0 0
\(716\) −12.8509 4.17551i −0.480261 0.156046i
\(717\) 9.00218 6.43616i 0.336193 0.240363i
\(718\) −0.156397 0.156397i −0.00583669 0.00583669i
\(719\) −18.8277 13.6791i −0.702155 0.510145i 0.178478 0.983944i \(-0.442883\pi\)
−0.880633 + 0.473798i \(0.842883\pi\)
\(720\) 0 0
\(721\) −6.46780 + 4.69913i −0.240874 + 0.175005i
\(722\) −18.4321 2.91936i −0.685973 0.108647i
\(723\) −33.3215 0.254110i −1.23924 0.00945044i
\(724\) 16.1891i 0.601664i
\(725\) 0 0
\(726\) −16.8338 + 8.41618i −0.624762 + 0.312354i
\(727\) −24.2957 12.3793i −0.901077 0.459122i −0.0588635 0.998266i \(-0.518748\pi\)
−0.842213 + 0.539144i \(0.818748\pi\)
\(728\) 0.413192 2.60879i 0.0153139 0.0966882i
\(729\) 7.16021 + 26.0333i 0.265193 + 0.964195i
\(730\) 0 0
\(731\) −35.0879 + 48.2943i −1.29777 + 1.78623i
\(732\) 1.78297 + 0.594391i 0.0659004 + 0.0219693i
\(733\) 0.915975 + 5.78324i 0.0338323 + 0.213609i 0.998813 0.0487128i \(-0.0155119\pi\)
−0.964981 + 0.262322i \(0.915512\pi\)
\(734\) 5.16046 15.8823i 0.190476 0.586225i
\(735\) 0 0
\(736\) −2.09909 6.46034i −0.0773735 0.238131i
\(737\) −4.32260 + 2.20247i −0.159225 + 0.0811292i
\(738\) 5.45871 31.3615i 0.200938 1.15443i
\(739\) 10.9906 3.57105i 0.404295 0.131363i −0.0998086 0.995007i \(-0.531823\pi\)
0.504103 + 0.863643i \(0.331823\pi\)
\(740\) 0 0
\(741\) 2.61065 0.393103i 0.0959047 0.0144410i
\(742\) 8.79319 1.39270i 0.322808 0.0511278i
\(743\) 5.09866 5.09866i 0.187052 0.187052i −0.607369 0.794420i \(-0.707775\pi\)
0.794420 + 0.607369i \(0.207775\pi\)
\(744\) −0.831282 + 5.00136i −0.0304763 + 0.183359i
\(745\) 0 0
\(746\) −0.0621022 0.0854763i −0.00227372 0.00312951i
\(747\) 2.04333 1.98193i 0.0747614 0.0725150i
\(748\) 0.976324 1.91614i 0.0356980 0.0700612i
\(749\) 12.9231 0.472200
\(750\) 0 0
\(751\) −19.8804 −0.725445 −0.362723 0.931897i \(-0.618153\pi\)
−0.362723 + 0.931897i \(0.618153\pi\)
\(752\) −3.75176 + 7.36324i −0.136813 + 0.268510i
\(753\) −16.8184 + 5.32319i −0.612897 + 0.193988i
\(754\) 0.701343 + 0.965316i 0.0255414 + 0.0351547i
\(755\) 0 0
\(756\) 3.61657 + 3.78595i 0.131533 + 0.137694i
\(757\) 16.4335 16.4335i 0.597285 0.597285i −0.342304 0.939589i \(-0.611207\pi\)
0.939589 + 0.342304i \(0.111207\pi\)
\(758\) 9.72147 1.53973i 0.353100 0.0559255i
\(759\) −0.641293 4.25892i −0.0232775 0.154589i
\(760\) 0 0
\(761\) −4.02479 + 1.30773i −0.145898 + 0.0474052i −0.381056 0.924552i \(-0.624439\pi\)
0.235157 + 0.971957i \(0.424439\pi\)
\(762\) 27.4835 + 20.2900i 0.995624 + 0.735028i
\(763\) 4.09408 2.08604i 0.148216 0.0755197i
\(764\) −4.77202 14.6868i −0.172646 0.531349i
\(765\) 0 0
\(766\) −10.2830 + 31.6480i −0.371542 + 1.14349i
\(767\) −3.86287 24.3892i −0.139480 0.880642i
\(768\) −0.547779 + 1.64315i −0.0197663 + 0.0592920i
\(769\) 4.46592 6.14681i 0.161045 0.221660i −0.720867 0.693073i \(-0.756256\pi\)
0.881912 + 0.471414i \(0.156256\pi\)
\(770\) 0 0
\(771\) −1.83757 + 3.53945i −0.0661785 + 0.127470i
\(772\) −1.33931 + 8.45606i −0.0482028 + 0.304340i
\(773\) −12.3217 6.27822i −0.443181 0.225812i 0.218136 0.975918i \(-0.430002\pi\)
−0.661317 + 0.750106i \(0.730002\pi\)
\(774\) 18.2920 24.3858i 0.657493 0.876531i
\(775\) 0 0
\(776\) 18.0093i 0.646495i
\(777\) 0.127537 16.7240i 0.00457536 0.599969i
\(778\) −33.0209 5.23000i −1.18386 0.187505i
\(779\) 4.99169 3.62668i 0.178846 0.129939i
\(780\) 0 0
\(781\) −0.380843 0.276698i −0.0136276 0.00990105i
\(782\) −28.2178 28.2178i −1.00907 1.00907i