Properties

Label 625.2.e.a.124.2
Level $625$
Weight $2$
Character 625.124
Analytic conductor $4.991$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.e (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.99065012633\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 124.2
Root \(-0.357358 + 1.86824i\) of defining polynomial
Character \(\chi\) \(=\) 625.124
Dual form 625.2.e.a.499.2

$q$-expansion

\(f(q)\) \(=\) \(q+(2.19625 + 0.713605i) q^{2} +(-0.279141 + 0.384204i) q^{3} +(2.69625 + 1.95894i) q^{4} +(-0.887234 + 0.644613i) q^{6} +3.03582i q^{7} +(1.80902 + 2.48990i) q^{8} +(0.857358 + 2.63868i) q^{9} +O(q^{10})\) \(q+(2.19625 + 0.713605i) q^{2} +(-0.279141 + 0.384204i) q^{3} +(2.69625 + 1.95894i) q^{4} +(-0.887234 + 0.644613i) q^{6} +3.03582i q^{7} +(1.80902 + 2.48990i) q^{8} +(0.857358 + 2.63868i) q^{9} +(0.618034 - 1.90211i) q^{11} +(-1.50527 + 0.489091i) q^{12} +(-1.35736 + 0.441032i) q^{13} +(-2.16637 + 6.66742i) q^{14} +(0.136498 + 0.420099i) q^{16} +(-1.09343 - 1.50497i) q^{17} +6.40701i q^{18} +(0.730800 - 0.530958i) q^{19} +(-1.16637 - 0.847421i) q^{21} +(2.71472 - 3.73648i) q^{22} +(3.16637 + 1.02882i) q^{23} -1.46160 q^{24} -3.29582 q^{26} +(-2.60809 - 0.847421i) q^{27} +(-5.94699 + 8.18532i) q^{28} +(3.20619 + 2.32943i) q^{29} +(5.21004 - 3.78532i) q^{31} -5.13532i q^{32} +(0.558282 + 0.768409i) q^{33} +(-1.32748 - 4.08557i) q^{34} +(-2.85736 + 8.79404i) q^{36} +(-3.63324 + 1.18051i) q^{37} +(1.98391 - 0.644613i) q^{38} +(0.209447 - 0.644613i) q^{39} +(-0.566805 - 1.74445i) q^{41} +(-1.95693 - 2.69348i) q^{42} +3.59445i q^{43} +(5.39250 - 3.91788i) q^{44} +(6.21998 + 4.51908i) q^{46} +(-2.82134 + 3.88324i) q^{47} +(-0.199506 - 0.0648235i) q^{48} -2.21619 q^{49} +0.883436 q^{51} +(-4.52373 - 1.46985i) q^{52} +(5.58674 - 7.68949i) q^{53} +(-5.12330 - 3.72230i) q^{54} +(-7.55888 + 5.49184i) q^{56} +0.428989i q^{57} +(5.37930 + 7.40398i) q^{58} +(-3.28968 - 10.1246i) q^{59} +(4.41097 - 13.5756i) q^{61} +(14.1438 - 4.59559i) q^{62} +(-8.01054 + 2.60278i) q^{63} +(3.93759 - 12.1186i) q^{64} +(0.677786 + 2.08601i) q^{66} +(6.28353 + 8.64854i) q^{67} -6.19974i q^{68} +(-1.27914 + 0.929350i) q^{69} +(-10.0802 - 7.32371i) q^{71} +(-5.01906 + 6.90814i) q^{72} +(-0.254532 - 0.0827026i) q^{73} -8.82193 q^{74} +3.01054 q^{76} +(5.77447 + 1.87624i) q^{77} +(0.919998 - 1.26627i) q^{78} +(-6.93470 - 5.03835i) q^{79} +(-5.68017 + 4.12688i) q^{81} -4.23572i q^{82} +(-7.41677 - 10.2083i) q^{83} +(-1.48479 - 4.56972i) q^{84} +(-2.56502 + 7.89432i) q^{86} +(-1.78996 + 0.581593i) q^{87} +(5.85410 - 1.90211i) q^{88} +(1.47338 - 4.53460i) q^{89} +(-1.33889 - 4.12069i) q^{91} +(6.52195 + 8.97669i) q^{92} +3.05836i q^{93} +(-8.96746 + 6.51524i) q^{94} +(1.97301 + 1.43348i) q^{96} +(-5.85319 + 8.05623i) q^{97} +(-4.86730 - 1.58148i) q^{98} +5.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.19625 + 0.713605i 1.55298 + 0.504595i 0.954922 0.296855i \(-0.0959379\pi\)
0.598061 + 0.801450i \(0.295938\pi\)
\(3\) −0.279141 + 0.384204i −0.161162 + 0.221821i −0.881959 0.471325i \(-0.843776\pi\)
0.720797 + 0.693146i \(0.243776\pi\)
\(4\) 2.69625 + 1.95894i 1.34813 + 0.979470i
\(5\) 0 0
\(6\) −0.887234 + 0.644613i −0.362212 + 0.263162i
\(7\) 3.03582i 1.14743i 0.819055 + 0.573716i \(0.194498\pi\)
−0.819055 + 0.573716i \(0.805502\pi\)
\(8\) 1.80902 + 2.48990i 0.639584 + 0.880312i
\(9\) 0.857358 + 2.63868i 0.285786 + 0.879558i
\(10\) 0 0
\(11\) 0.618034 1.90211i 0.186344 0.573509i −0.813625 0.581390i \(-0.802509\pi\)
0.999969 + 0.00788181i \(0.00250889\pi\)
\(12\) −1.50527 + 0.489091i −0.434533 + 0.141188i
\(13\) −1.35736 + 0.441032i −0.376463 + 0.122320i −0.491136 0.871083i \(-0.663418\pi\)
0.114673 + 0.993403i \(0.463418\pi\)
\(14\) −2.16637 + 6.66742i −0.578988 + 1.78194i
\(15\) 0 0
\(16\) 0.136498 + 0.420099i 0.0341246 + 0.105025i
\(17\) −1.09343 1.50497i −0.265195 0.365009i 0.655565 0.755138i \(-0.272430\pi\)
−0.920760 + 0.390129i \(0.872430\pi\)
\(18\) 6.40701i 1.51015i
\(19\) 0.730800 0.530958i 0.167657 0.121810i −0.500793 0.865567i \(-0.666958\pi\)
0.668450 + 0.743757i \(0.266958\pi\)
\(20\) 0 0
\(21\) −1.16637 0.847421i −0.254524 0.184922i
\(22\) 2.71472 3.73648i 0.578779 0.796621i
\(23\) 3.16637 + 1.02882i 0.660235 + 0.214523i 0.619922 0.784664i \(-0.287164\pi\)
0.0403132 + 0.999187i \(0.487164\pi\)
\(24\) −1.46160 −0.298348
\(25\) 0 0
\(26\) −3.29582 −0.646364
\(27\) −2.60809 0.847421i −0.501928 0.163086i
\(28\) −5.94699 + 8.18532i −1.12387 + 1.54688i
\(29\) 3.20619 + 2.32943i 0.595375 + 0.432565i 0.844234 0.535974i \(-0.180056\pi\)
−0.248859 + 0.968540i \(0.580056\pi\)
\(30\) 0 0
\(31\) 5.21004 3.78532i 0.935751 0.679863i −0.0116431 0.999932i \(-0.503706\pi\)
0.947394 + 0.320069i \(0.103706\pi\)
\(32\) 5.13532i 0.907805i
\(33\) 0.558282 + 0.768409i 0.0971844 + 0.133763i
\(34\) −1.32748 4.08557i −0.227661 0.700669i
\(35\) 0 0
\(36\) −2.85736 + 8.79404i −0.476226 + 1.46567i
\(37\) −3.63324 + 1.18051i −0.597301 + 0.194075i −0.592037 0.805911i \(-0.701676\pi\)
−0.00526493 + 0.999986i \(0.501676\pi\)
\(38\) 1.98391 0.644613i 0.321833 0.104570i
\(39\) 0.209447 0.644613i 0.0335384 0.103221i
\(40\) 0 0
\(41\) −0.566805 1.74445i −0.0885201 0.272437i 0.896991 0.442049i \(-0.145748\pi\)
−0.985511 + 0.169613i \(0.945748\pi\)
\(42\) −1.95693 2.69348i −0.301960 0.415613i
\(43\) 3.59445i 0.548149i 0.961708 + 0.274074i \(0.0883715\pi\)
−0.961708 + 0.274074i \(0.911629\pi\)
\(44\) 5.39250 3.91788i 0.812950 0.590643i
\(45\) 0 0
\(46\) 6.21998 + 4.51908i 0.917086 + 0.666302i
\(47\) −2.82134 + 3.88324i −0.411534 + 0.566428i −0.963592 0.267378i \(-0.913843\pi\)
0.552057 + 0.833806i \(0.313843\pi\)
\(48\) −0.199506 0.0648235i −0.0287962 0.00935647i
\(49\) −2.21619 −0.316598
\(50\) 0 0
\(51\) 0.883436 0.123706
\(52\) −4.52373 1.46985i −0.627329 0.203831i
\(53\) 5.58674 7.68949i 0.767398 1.05623i −0.229165 0.973388i \(-0.573599\pi\)
0.996562 0.0828447i \(-0.0264005\pi\)
\(54\) −5.12330 3.72230i −0.697193 0.506540i
\(55\) 0 0
\(56\) −7.55888 + 5.49184i −1.01010 + 0.733879i
\(57\) 0.428989i 0.0568209i
\(58\) 5.37930 + 7.40398i 0.706337 + 0.972190i
\(59\) −3.28968 10.1246i −0.428279 1.31811i −0.899819 0.436263i \(-0.856302\pi\)
0.471540 0.881845i \(-0.343698\pi\)
\(60\) 0 0
\(61\) 4.41097 13.5756i 0.564766 1.73817i −0.103879 0.994590i \(-0.533125\pi\)
0.668645 0.743582i \(-0.266875\pi\)
\(62\) 14.1438 4.59559i 1.79626 0.583641i
\(63\) −8.01054 + 2.60278i −1.00923 + 0.327920i
\(64\) 3.93759 12.1186i 0.492198 1.51483i
\(65\) 0 0
\(66\) 0.677786 + 2.08601i 0.0834297 + 0.256770i
\(67\) 6.28353 + 8.64854i 0.767656 + 1.05659i 0.996538 + 0.0831333i \(0.0264927\pi\)
−0.228883 + 0.973454i \(0.573507\pi\)
\(68\) 6.19974i 0.751828i
\(69\) −1.27914 + 0.929350i −0.153990 + 0.111881i
\(70\) 0 0
\(71\) −10.0802 7.32371i −1.19630 0.869165i −0.202387 0.979306i \(-0.564870\pi\)
−0.993916 + 0.110141i \(0.964870\pi\)
\(72\) −5.01906 + 6.90814i −0.591502 + 0.814132i
\(73\) −0.254532 0.0827026i −0.0297908 0.00967961i 0.294084 0.955780i \(-0.404986\pi\)
−0.323874 + 0.946100i \(0.604986\pi\)
\(74\) −8.82193 −1.02553
\(75\) 0 0
\(76\) 3.01054 0.345332
\(77\) 5.77447 + 1.87624i 0.658062 + 0.213817i
\(78\) 0.919998 1.26627i 0.104169 0.143377i
\(79\) −6.93470 5.03835i −0.780214 0.566859i 0.124829 0.992178i \(-0.460162\pi\)
−0.905043 + 0.425319i \(0.860162\pi\)
\(80\) 0 0
\(81\) −5.68017 + 4.12688i −0.631129 + 0.458542i
\(82\) 4.23572i 0.467757i
\(83\) −7.41677 10.2083i −0.814097 1.12051i −0.990678 0.136222i \(-0.956504\pi\)
0.176582 0.984286i \(-0.443496\pi\)
\(84\) −1.48479 4.56972i −0.162004 0.498597i
\(85\) 0 0
\(86\) −2.56502 + 7.89432i −0.276593 + 0.851266i
\(87\) −1.78996 + 0.581593i −0.191904 + 0.0623533i
\(88\) 5.85410 1.90211i 0.624049 0.202766i
\(89\) 1.47338 4.53460i 0.156178 0.480666i −0.842100 0.539321i \(-0.818681\pi\)
0.998278 + 0.0586546i \(0.0186810\pi\)
\(90\) 0 0
\(91\) −1.33889 4.12069i −0.140354 0.431966i
\(92\) 6.52195 + 8.97669i 0.679960 + 0.935885i
\(93\) 3.05836i 0.317137i
\(94\) −8.96746 + 6.51524i −0.924923 + 0.671996i
\(95\) 0 0
\(96\) 1.97301 + 1.43348i 0.201370 + 0.146304i
\(97\) −5.85319 + 8.05623i −0.594302 + 0.817986i −0.995172 0.0981488i \(-0.968708\pi\)
0.400870 + 0.916135i \(0.368708\pi\)
\(98\) −4.86730 1.58148i −0.491671 0.159754i
\(99\) 5.54893 0.557689
\(100\) 0 0
\(101\) 9.34612 0.929974 0.464987 0.885318i \(-0.346059\pi\)
0.464987 + 0.885318i \(0.346059\pi\)
\(102\) 1.94025 + 0.630425i 0.192113 + 0.0624213i
\(103\) −5.33949 + 7.34917i −0.526115 + 0.724136i −0.986532 0.163567i \(-0.947700\pi\)
0.460417 + 0.887703i \(0.347700\pi\)
\(104\) −3.55361 2.58185i −0.348460 0.253171i
\(105\) 0 0
\(106\) 17.7571 12.9013i 1.72473 1.25309i
\(107\) 5.62871i 0.544148i 0.962276 + 0.272074i \(0.0877096\pi\)
−0.962276 + 0.272074i \(0.912290\pi\)
\(108\) −5.37202 7.39396i −0.516923 0.711484i
\(109\) 3.12509 + 9.61803i 0.299329 + 0.921240i 0.981733 + 0.190265i \(0.0609346\pi\)
−0.682404 + 0.730975i \(0.739065\pi\)
\(110\) 0 0
\(111\) 0.560629 1.72544i 0.0532125 0.163771i
\(112\) −1.27534 + 0.414384i −0.120509 + 0.0391556i
\(113\) 10.1877 3.31019i 0.958381 0.311397i 0.212264 0.977212i \(-0.431916\pi\)
0.746116 + 0.665815i \(0.231916\pi\)
\(114\) −0.306129 + 0.942167i −0.0286716 + 0.0882420i
\(115\) 0 0
\(116\) 4.08147 + 12.5615i 0.378955 + 1.16630i
\(117\) −2.32748 3.20350i −0.215176 0.296164i
\(118\) 24.5836i 2.26311i
\(119\) 4.56882 3.31944i 0.418823 0.304293i
\(120\) 0 0
\(121\) 5.66312 + 4.11450i 0.514829 + 0.374045i
\(122\) 19.3752 26.6676i 1.75415 2.41437i
\(123\) 0.828443 + 0.269177i 0.0746982 + 0.0242709i
\(124\) 21.4628 1.92742
\(125\) 0 0
\(126\) −19.4505 −1.73279
\(127\) −10.8049 3.51072i −0.958779 0.311526i −0.212501 0.977161i \(-0.568161\pi\)
−0.746278 + 0.665635i \(0.768161\pi\)
\(128\) 11.2589 15.4966i 0.995158 1.36972i
\(129\) −1.38100 1.00336i −0.121591 0.0883408i
\(130\) 0 0
\(131\) −6.46219 + 4.69506i −0.564605 + 0.410209i −0.833141 0.553060i \(-0.813460\pi\)
0.268537 + 0.963269i \(0.413460\pi\)
\(132\) 3.16546i 0.275518i
\(133\) 1.61189 + 2.21858i 0.139769 + 0.192375i
\(134\) 7.62857 + 23.4783i 0.659008 + 2.02822i
\(135\) 0 0
\(136\) 1.76920 5.44504i 0.151708 0.466908i
\(137\) −8.88027 + 2.88537i −0.758692 + 0.246514i −0.662717 0.748870i \(-0.730597\pi\)
−0.0959750 + 0.995384i \(0.530597\pi\)
\(138\) −3.47250 + 1.12828i −0.295599 + 0.0960460i
\(139\) −5.53605 + 17.0382i −0.469562 + 1.44516i 0.383592 + 0.923503i \(0.374687\pi\)
−0.853154 + 0.521660i \(0.825313\pi\)
\(140\) 0 0
\(141\) −0.704407 2.16794i −0.0593217 0.182574i
\(142\) −16.9125 23.2780i −1.41926 1.95345i
\(143\) 2.85442i 0.238699i
\(144\) −0.991477 + 0.720350i −0.0826231 + 0.0600292i
\(145\) 0 0
\(146\) −0.500000 0.363271i −0.0413803 0.0300645i
\(147\) 0.618628 0.851468i 0.0510236 0.0702279i
\(148\) −12.1087 3.93435i −0.995328 0.323402i
\(149\) 6.31395 0.517259 0.258629 0.965977i \(-0.416729\pi\)
0.258629 + 0.965977i \(0.416729\pi\)
\(150\) 0 0
\(151\) 4.71947 0.384065 0.192033 0.981389i \(-0.438492\pi\)
0.192033 + 0.981389i \(0.438492\pi\)
\(152\) 2.64406 + 0.859107i 0.214462 + 0.0696828i
\(153\) 3.03367 4.17549i 0.245258 0.337569i
\(154\) 11.3433 + 8.24138i 0.914068 + 0.664109i
\(155\) 0 0
\(156\) 1.82748 1.32774i 0.146316 0.106305i
\(157\) 1.46908i 0.117245i 0.998280 + 0.0586225i \(0.0186708\pi\)
−0.998280 + 0.0586225i \(0.981329\pi\)
\(158\) −11.6349 16.0141i −0.925626 1.27402i
\(159\) 1.39485 + 4.29290i 0.110619 + 0.340449i
\(160\) 0 0
\(161\) −3.12330 + 9.61253i −0.246151 + 0.757574i
\(162\) −15.4200 + 5.01027i −1.21151 + 0.393644i
\(163\) 4.24142 1.37812i 0.332214 0.107943i −0.138160 0.990410i \(-0.544119\pi\)
0.470374 + 0.882467i \(0.344119\pi\)
\(164\) 1.88902 5.81380i 0.147508 0.453982i
\(165\) 0 0
\(166\) −9.00439 27.7127i −0.698876 2.15092i
\(167\) −6.13275 8.44101i −0.474567 0.653185i 0.502883 0.864355i \(-0.332273\pi\)
−0.977449 + 0.211170i \(0.932273\pi\)
\(168\) 4.43715i 0.342334i
\(169\) −8.86931 + 6.44393i −0.682255 + 0.495687i
\(170\) 0 0
\(171\) 2.02758 + 1.47312i 0.155053 + 0.112653i
\(172\) −7.04132 + 9.69155i −0.536896 + 0.738973i
\(173\) 7.30049 + 2.37207i 0.555046 + 0.180345i 0.573091 0.819492i \(-0.305744\pi\)
−0.0180448 + 0.999837i \(0.505744\pi\)
\(174\) −4.34623 −0.329486
\(175\) 0 0
\(176\) 0.883436 0.0665915
\(177\) 4.80819 + 1.56228i 0.361406 + 0.117428i
\(178\) 6.47182 8.90770i 0.485084 0.667660i
\(179\) 12.5533 + 9.12053i 0.938280 + 0.681700i 0.948006 0.318253i \(-0.103096\pi\)
−0.00972631 + 0.999953i \(0.503096\pi\)
\(180\) 0 0
\(181\) 1.28679 0.934906i 0.0956462 0.0694910i −0.538934 0.842348i \(-0.681173\pi\)
0.634580 + 0.772857i \(0.281173\pi\)
\(182\) 10.0055i 0.741658i
\(183\) 3.98451 + 5.48421i 0.294543 + 0.405404i
\(184\) 3.16637 + 9.74510i 0.233428 + 0.718418i
\(185\) 0 0
\(186\) −2.18246 + 6.71692i −0.160026 + 0.492509i
\(187\) −3.53840 + 1.14970i −0.258753 + 0.0840741i
\(188\) −15.2141 + 4.94335i −1.10960 + 0.360531i
\(189\) 2.57261 7.91769i 0.187130 0.575927i
\(190\) 0 0
\(191\) 6.07788 + 18.7058i 0.439780 + 1.35350i 0.888108 + 0.459635i \(0.152020\pi\)
−0.448328 + 0.893869i \(0.647980\pi\)
\(192\) 3.55690 + 4.89565i 0.256697 + 0.353313i
\(193\) 13.1100i 0.943680i −0.881684 0.471840i \(-0.843590\pi\)
0.881684 0.471840i \(-0.156410\pi\)
\(194\) −18.6040 + 13.5166i −1.33569 + 0.970437i
\(195\) 0 0
\(196\) −5.97539 4.34138i −0.426814 0.310098i
\(197\) −2.01580 + 2.77451i −0.143620 + 0.197676i −0.874767 0.484544i \(-0.838985\pi\)
0.731147 + 0.682220i \(0.238985\pi\)
\(198\) 12.1869 + 3.95975i 0.866082 + 0.281407i
\(199\) −17.6959 −1.25443 −0.627215 0.778846i \(-0.715805\pi\)
−0.627215 + 0.778846i \(0.715805\pi\)
\(200\) 0 0
\(201\) −5.07680 −0.358090
\(202\) 20.5264 + 6.66944i 1.44423 + 0.469260i
\(203\) −7.07174 + 9.73341i −0.496339 + 0.683152i
\(204\) 2.38197 + 1.73060i 0.166771 + 0.121166i
\(205\) 0 0
\(206\) −16.9713 + 12.3303i −1.18244 + 0.859096i
\(207\) 9.23710i 0.642023i
\(208\) −0.370554 0.510024i −0.0256933 0.0353638i
\(209\) −0.558282 1.71821i −0.0386172 0.118851i
\(210\) 0 0
\(211\) −1.00235 + 3.08491i −0.0690044 + 0.212374i −0.979612 0.200898i \(-0.935614\pi\)
0.910608 + 0.413272i \(0.135614\pi\)
\(212\) 30.1265 9.78869i 2.06910 0.672290i
\(213\) 5.62761 1.82852i 0.385597 0.125288i
\(214\) −4.01668 + 12.3621i −0.274575 + 0.845054i
\(215\) 0 0
\(216\) −2.60809 8.02688i −0.177458 0.546160i
\(217\) 11.4915 + 15.8167i 0.780096 + 1.07371i
\(218\) 23.3537i 1.58171i
\(219\) 0.102825 0.0747068i 0.00694828 0.00504822i
\(220\) 0 0
\(221\) 2.14791 + 1.56055i 0.144484 + 0.104974i
\(222\) 2.46256 3.38943i 0.165276 0.227483i
\(223\) −27.3094 8.87335i −1.82877 0.594203i −0.999368 0.0355515i \(-0.988681\pi\)
−0.829402 0.558652i \(-0.811319\pi\)
\(224\) 15.5899 1.04164
\(225\) 0 0
\(226\) 24.7370 1.64548
\(227\) 11.1470 + 3.62187i 0.739851 + 0.240392i 0.654609 0.755968i \(-0.272833\pi\)
0.0852426 + 0.996360i \(0.472833\pi\)
\(228\) −0.840364 + 1.15666i −0.0556544 + 0.0766018i
\(229\) −13.2689 9.64043i −0.876835 0.637058i 0.0555774 0.998454i \(-0.482300\pi\)
−0.932412 + 0.361397i \(0.882300\pi\)
\(230\) 0 0
\(231\) −2.33275 + 1.69484i −0.153484 + 0.111512i
\(232\) 12.1971i 0.800777i
\(233\) 13.2337 + 18.2147i 0.866971 + 1.19328i 0.979862 + 0.199676i \(0.0639890\pi\)
−0.112891 + 0.993607i \(0.536011\pi\)
\(234\) −2.82570 8.69660i −0.184722 0.568514i
\(235\) 0 0
\(236\) 10.9637 33.7427i 0.713674 2.19646i
\(237\) 3.87152 1.25793i 0.251482 0.0817114i
\(238\) 12.4030 4.02999i 0.803969 0.261226i
\(239\) 2.04981 6.30867i 0.132591 0.408074i −0.862616 0.505859i \(-0.831176\pi\)
0.995208 + 0.0977848i \(0.0311757\pi\)
\(240\) 0 0
\(241\) 8.10430 + 24.9425i 0.522044 + 1.60668i 0.770089 + 0.637936i \(0.220212\pi\)
−0.248045 + 0.968748i \(0.579788\pi\)
\(242\) 9.50150 + 13.0777i 0.610780 + 0.840666i
\(243\) 11.5613i 0.741655i
\(244\) 38.4868 27.9623i 2.46386 1.79010i
\(245\) 0 0
\(246\) 1.62738 + 1.18236i 0.103758 + 0.0753846i
\(247\) −0.757788 + 1.04301i −0.0482169 + 0.0663649i
\(248\) 18.8501 + 6.12477i 1.19698 + 0.388923i
\(249\) 5.99241 0.379753
\(250\) 0 0
\(251\) −10.9121 −0.688766 −0.344383 0.938829i \(-0.611912\pi\)
−0.344383 + 0.938829i \(0.611912\pi\)
\(252\) −26.6971 8.67441i −1.68176 0.546437i
\(253\) 3.91385 5.38696i 0.246062 0.338675i
\(254\) −21.2250 15.4208i −1.33177 0.967590i
\(255\) 0 0
\(256\) 15.1684 11.0205i 0.948024 0.688780i
\(257\) 6.58051i 0.410481i 0.978712 + 0.205240i \(0.0657976\pi\)
−0.978712 + 0.205240i \(0.934202\pi\)
\(258\) −2.31703 3.18912i −0.144252 0.198546i
\(259\) −3.58382 11.0299i −0.222688 0.685362i
\(260\) 0 0
\(261\) −3.39777 + 10.4573i −0.210317 + 0.647288i
\(262\) −17.5430 + 5.70007i −1.08381 + 0.352152i
\(263\) −25.7805 + 8.37660i −1.58970 + 0.516524i −0.964531 0.263969i \(-0.914968\pi\)
−0.625165 + 0.780493i \(0.714968\pi\)
\(264\) −0.903319 + 2.78013i −0.0555954 + 0.171105i
\(265\) 0 0
\(266\) 1.95693 + 6.02280i 0.119987 + 0.369282i
\(267\) 1.33093 + 1.83187i 0.0814517 + 0.112109i
\(268\) 35.6277i 2.17631i
\(269\) 0.816664 0.593341i 0.0497929 0.0361766i −0.562610 0.826722i \(-0.690203\pi\)
0.612403 + 0.790546i \(0.290203\pi\)
\(270\) 0 0
\(271\) −5.05800 3.67485i −0.307252 0.223231i 0.423465 0.905913i \(-0.360814\pi\)
−0.730716 + 0.682681i \(0.760814\pi\)
\(272\) 0.482986 0.664773i 0.0292853 0.0403078i
\(273\) 1.95693 + 0.635844i 0.118439 + 0.0384830i
\(274\) −21.5623 −1.30263
\(275\) 0 0
\(276\) −5.26943 −0.317182
\(277\) −23.4629 7.62355i −1.40975 0.458055i −0.497418 0.867511i \(-0.665718\pi\)
−0.912330 + 0.409456i \(0.865718\pi\)
\(278\) −24.3171 + 33.4696i −1.45844 + 2.00738i
\(279\) 14.4551 + 10.5022i 0.865404 + 0.628753i
\(280\) 0 0
\(281\) −1.48771 + 1.08089i −0.0887495 + 0.0644803i −0.631275 0.775559i \(-0.717468\pi\)
0.542526 + 0.840039i \(0.317468\pi\)
\(282\) 5.26401i 0.313467i
\(283\) −5.07915 6.99084i −0.301924 0.415563i 0.630918 0.775850i \(-0.282679\pi\)
−0.932841 + 0.360287i \(0.882679\pi\)
\(284\) −12.8321 39.4931i −0.761445 2.34349i
\(285\) 0 0
\(286\) −2.03693 + 6.26902i −0.120446 + 0.370695i
\(287\) 5.29582 1.72072i 0.312602 0.101571i
\(288\) 13.5504 4.40280i 0.798467 0.259438i
\(289\) 4.18393 12.8768i 0.246114 0.757460i
\(290\) 0 0
\(291\) −1.46137 4.49765i −0.0856672 0.263657i
\(292\) −0.524274 0.721601i −0.0306808 0.0422285i
\(293\) 6.29156i 0.367557i −0.982968 0.183779i \(-0.941167\pi\)
0.982968 0.183779i \(-0.0588329\pi\)
\(294\) 1.96627 1.42858i 0.114675 0.0833166i
\(295\) 0 0
\(296\) −9.51195 6.91084i −0.552871 0.401684i
\(297\) −3.22378 + 4.43715i −0.187063 + 0.257470i
\(298\) 13.8670 + 4.50567i 0.803295 + 0.261006i
\(299\) −4.75164 −0.274795
\(300\) 0 0
\(301\) −10.9121 −0.628963
\(302\) 10.3651 + 3.36784i 0.596447 + 0.193797i
\(303\) −2.60888 + 3.59082i −0.149876 + 0.206287i
\(304\) 0.322808 + 0.234534i 0.0185143 + 0.0134514i
\(305\) 0 0
\(306\) 9.64236 7.00558i 0.551217 0.400483i
\(307\) 28.6661i 1.63606i −0.575175 0.818030i \(-0.695066\pi\)
0.575175 0.818030i \(-0.304934\pi\)
\(308\) 11.8940 + 16.3706i 0.677722 + 0.932804i
\(309\) −1.33312 4.10291i −0.0758383 0.233406i
\(310\) 0 0
\(311\) −2.42161 + 7.45295i −0.137317 + 0.422618i −0.995943 0.0899842i \(-0.971318\pi\)
0.858626 + 0.512602i \(0.171318\pi\)
\(312\) 1.98391 0.644613i 0.112317 0.0364940i
\(313\) 20.3614 6.61582i 1.15090 0.373949i 0.329415 0.944185i \(-0.393149\pi\)
0.821480 + 0.570237i \(0.193149\pi\)
\(314\) −1.04834 + 3.22646i −0.0591613 + 0.182080i
\(315\) 0 0
\(316\) −8.82785 27.1693i −0.496605 1.52839i
\(317\) −2.36280 3.25211i −0.132708 0.182657i 0.737491 0.675356i \(-0.236010\pi\)
−0.870200 + 0.492699i \(0.836010\pi\)
\(318\) 10.4237i 0.584530i
\(319\) 6.41238 4.65887i 0.359025 0.260847i
\(320\) 0 0
\(321\) −2.16258 1.57120i −0.120703 0.0876961i
\(322\) −13.7191 + 18.8827i −0.764536 + 1.05229i
\(323\) −1.59815 0.519271i −0.0889235 0.0288930i
\(324\) −23.3995 −1.29997
\(325\) 0 0
\(326\) 10.2987 0.570390
\(327\) −4.56763 1.48411i −0.252590 0.0820716i
\(328\) 3.31813 4.56702i 0.183213 0.252171i
\(329\) −11.7888 8.56506i −0.649938 0.472207i
\(330\) 0 0
\(331\) −9.42008 + 6.84409i −0.517775 + 0.376185i −0.815765 0.578384i \(-0.803684\pi\)
0.297990 + 0.954569i \(0.403684\pi\)
\(332\) 42.0532i 2.30797i
\(333\) −6.22998 8.57483i −0.341401 0.469898i
\(334\) −7.44552 22.9149i −0.407400 1.25385i
\(335\) 0 0
\(336\) 0.196792 0.605664i 0.0107359 0.0330417i
\(337\) 20.4808 6.65461i 1.11566 0.362500i 0.307550 0.951532i \(-0.400491\pi\)
0.808110 + 0.589032i \(0.200491\pi\)
\(338\) −24.0777 + 7.82330i −1.30965 + 0.425532i
\(339\) −1.57202 + 4.83818i −0.0853804 + 0.262774i
\(340\) 0 0
\(341\) −3.98012 12.2495i −0.215535 0.663350i
\(342\) 3.40185 + 4.68224i 0.183951 + 0.253187i
\(343\) 14.5228i 0.784157i
\(344\) −8.94982 + 6.50243i −0.482542 + 0.350587i
\(345\) 0 0
\(346\) 14.3410 + 10.4193i 0.770976 + 0.560147i
\(347\) 9.16782 12.6184i 0.492155 0.677393i −0.488629 0.872492i \(-0.662503\pi\)
0.980784 + 0.195099i \(0.0625028\pi\)
\(348\) −5.96548 1.93830i −0.319783 0.103904i
\(349\) −5.56598 −0.297940 −0.148970 0.988842i \(-0.547596\pi\)
−0.148970 + 0.988842i \(0.547596\pi\)
\(350\) 0 0
\(351\) 3.91385 0.208906
\(352\) −9.76796 3.17380i −0.520634 0.169164i
\(353\) −4.71531 + 6.49007i −0.250971 + 0.345431i −0.915851 0.401519i \(-0.868483\pi\)
0.664880 + 0.746950i \(0.268483\pi\)
\(354\) 9.44515 + 6.86230i 0.502004 + 0.364727i
\(355\) 0 0
\(356\) 12.8556 9.34014i 0.681346 0.495027i
\(357\) 2.68195i 0.141944i
\(358\) 21.0618 + 28.9891i 1.11315 + 1.53212i
\(359\) 3.81411 + 11.7386i 0.201301 + 0.619541i 0.999845 + 0.0176044i \(0.00560395\pi\)
−0.798544 + 0.601936i \(0.794396\pi\)
\(360\) 0 0
\(361\) −5.61917 + 17.2940i −0.295746 + 0.910212i
\(362\) 3.49326 1.13503i 0.183602 0.0596558i
\(363\) −3.16162 + 1.02727i −0.165942 + 0.0539178i
\(364\) 4.46219 13.7332i 0.233883 0.719816i
\(365\) 0 0
\(366\) 4.83742 + 14.8881i 0.252856 + 0.778211i
\(367\) −15.7967 21.7423i −0.824581 1.13494i −0.988908 0.148532i \(-0.952545\pi\)
0.164327 0.986406i \(-0.447455\pi\)
\(368\) 1.47062i 0.0766615i
\(369\) 4.11707 2.99123i 0.214326 0.155717i
\(370\) 0 0
\(371\) 23.3439 + 16.9603i 1.21195 + 0.880536i
\(372\) −5.99114 + 8.24610i −0.310626 + 0.427540i
\(373\) 26.2862 + 8.54089i 1.36105 + 0.442231i 0.896392 0.443262i \(-0.146179\pi\)
0.464654 + 0.885492i \(0.346179\pi\)
\(374\) −8.59164 −0.444263
\(375\) 0 0
\(376\) −14.7727 −0.761845
\(377\) −5.37930 1.74784i −0.277048 0.0900184i
\(378\) 11.3002 15.5534i 0.581220 0.799981i
\(379\) −2.81103 2.04233i −0.144393 0.104908i 0.513244 0.858243i \(-0.328444\pi\)
−0.657637 + 0.753335i \(0.728444\pi\)
\(380\) 0 0
\(381\) 4.36492 3.17130i 0.223622 0.162471i
\(382\) 45.4198i 2.32388i
\(383\) 16.0888 + 22.1443i 0.822098 + 1.13152i 0.989343 + 0.145606i \(0.0465132\pi\)
−0.167244 + 0.985916i \(0.553487\pi\)
\(384\) 2.81103 + 8.65146i 0.143450 + 0.441493i
\(385\) 0 0
\(386\) 9.35538 28.7929i 0.476176 1.46552i
\(387\) −9.48459 + 3.08173i −0.482129 + 0.156653i
\(388\) −31.5634 + 10.2556i −1.60239 + 0.520647i
\(389\) −3.36350 + 10.3518i −0.170536 + 0.524857i −0.999402 0.0345916i \(-0.988987\pi\)
0.828865 + 0.559448i \(0.188987\pi\)
\(390\) 0 0
\(391\) −1.91385 5.89024i −0.0967878 0.297882i
\(392\) −4.00912 5.51808i −0.202491 0.278705i
\(393\) 3.79339i 0.191351i
\(394\) −6.40712 + 4.65504i −0.322786 + 0.234518i
\(395\) 0 0
\(396\) 14.9613 + 10.8700i 0.751835 + 0.546240i
\(397\) 9.53460 13.1233i 0.478528 0.658637i −0.499693 0.866202i \(-0.666554\pi\)
0.978221 + 0.207565i \(0.0665539\pi\)
\(398\) −38.8647 12.6279i −1.94811 0.632979i
\(399\) −1.30233 −0.0651981
\(400\) 0 0
\(401\) 3.78686 0.189107 0.0945534 0.995520i \(-0.469858\pi\)
0.0945534 + 0.995520i \(0.469858\pi\)
\(402\) −11.1499 3.62283i −0.556108 0.180690i
\(403\) −5.40244 + 7.43582i −0.269115 + 0.370405i
\(404\) 25.1995 + 18.3085i 1.25372 + 0.910882i
\(405\) 0 0
\(406\) −22.4771 + 16.3306i −1.11552 + 0.810473i
\(407\) 7.64044i 0.378722i
\(408\) 1.59815 + 2.19967i 0.0791203 + 0.108900i
\(409\) −0.573491 1.76502i −0.0283573 0.0872748i 0.935876 0.352329i \(-0.114610\pi\)
−0.964234 + 0.265054i \(0.914610\pi\)
\(410\) 0 0
\(411\) 1.37027 4.21726i 0.0675905 0.208022i
\(412\) −28.7932 + 9.35547i −1.41854 + 0.460911i
\(413\) 30.7364 9.98686i 1.51244 0.491421i
\(414\) −6.59164 + 20.2870i −0.323961 + 0.997051i
\(415\) 0 0
\(416\) 2.26484 + 6.97046i 0.111043 + 0.341755i
\(417\) −5.00082 6.88304i −0.244891 0.337064i
\(418\) 4.17202i 0.204060i
\(419\) 11.6071 8.43307i 0.567045 0.411983i −0.266985 0.963701i \(-0.586028\pi\)
0.834031 + 0.551718i \(0.186028\pi\)
\(420\) 0 0
\(421\) −12.5030 9.08394i −0.609358 0.442724i 0.239830 0.970815i \(-0.422908\pi\)
−0.849188 + 0.528091i \(0.822908\pi\)
\(422\) −4.40281 + 6.05995i −0.214325 + 0.294994i
\(423\) −12.6655 4.11527i −0.615818 0.200091i
\(424\) 29.2525 1.42063
\(425\) 0 0
\(426\) 13.6645 0.662046
\(427\) 41.2129 + 13.3909i 1.99443 + 0.648030i
\(428\) −11.0263 + 15.1764i −0.532977 + 0.733580i
\(429\) −1.09668 0.796785i −0.0529483 0.0384692i
\(430\) 0 0
\(431\) −10.1162 + 7.34985i −0.487280 + 0.354030i −0.804137 0.594444i \(-0.797372\pi\)
0.316857 + 0.948473i \(0.397372\pi\)
\(432\) 1.21133i 0.0582801i
\(433\) −13.2223 18.1989i −0.635424 0.874586i 0.362937 0.931813i \(-0.381774\pi\)
−0.998361 + 0.0572279i \(0.981774\pi\)
\(434\) 13.9514 + 42.9379i 0.669688 + 2.06109i
\(435\) 0 0
\(436\) −10.4151 + 32.0545i −0.498794 + 1.53513i
\(437\) 2.86025 0.929350i 0.136824 0.0444569i
\(438\) 0.279141 0.0906984i 0.0133379 0.00433374i
\(439\) −3.76308 + 11.5816i −0.179602 + 0.552758i −0.999814 0.0193023i \(-0.993855\pi\)
0.820212 + 0.572060i \(0.193855\pi\)
\(440\) 0 0
\(441\) −1.90006 5.84779i −0.0904792 0.278466i
\(442\) 3.60373 + 4.96011i 0.171412 + 0.235929i
\(443\) 20.7101i 0.983968i 0.870604 + 0.491984i \(0.163728\pi\)
−0.870604 + 0.491984i \(0.836272\pi\)
\(444\) 4.89162 3.55397i 0.232146 0.168664i
\(445\) 0 0
\(446\) −53.6461 38.9762i −2.54022 1.84558i
\(447\) −1.76248 + 2.42585i −0.0833625 + 0.114739i
\(448\) 36.7900 + 11.9538i 1.73816 + 0.564764i
\(449\) 25.9539 1.22484 0.612420 0.790533i \(-0.290196\pi\)
0.612420 + 0.790533i \(0.290196\pi\)
\(450\) 0 0
\(451\) −3.66844 −0.172740
\(452\) 33.9531 + 11.0320i 1.59702 + 0.518904i
\(453\) −1.31740 + 1.81324i −0.0618968 + 0.0851936i
\(454\) 21.8970 + 15.9091i 1.02768 + 0.746650i
\(455\) 0 0
\(456\) −1.06814 + 0.776048i −0.0500202 + 0.0363418i
\(457\) 8.50150i 0.397684i −0.980032 0.198842i \(-0.936282\pi\)
0.980032 0.198842i \(-0.0637180\pi\)
\(458\) −22.2624 30.6416i −1.04025 1.43179i
\(459\) 1.57641 + 4.85170i 0.0735806 + 0.226458i
\(460\) 0 0
\(461\) 4.56884 14.0614i 0.212792 0.654906i −0.786511 0.617576i \(-0.788115\pi\)
0.999303 0.0373301i \(-0.0118853\pi\)
\(462\) −6.33275 + 2.05763i −0.294626 + 0.0957298i
\(463\) −21.1060 + 6.85774i −0.980877 + 0.318706i −0.755199 0.655496i \(-0.772460\pi\)
−0.225678 + 0.974202i \(0.572460\pi\)
\(464\) −0.540953 + 1.66488i −0.0251131 + 0.0772902i
\(465\) 0 0
\(466\) 16.0665 + 49.4477i 0.744267 + 2.29062i
\(467\) 16.7527 + 23.0581i 0.775222 + 1.06700i 0.995793 + 0.0916308i \(0.0292080\pi\)
−0.220571 + 0.975371i \(0.570792\pi\)
\(468\) 13.1968i 0.610024i
\(469\) −26.2554 + 19.0757i −1.21236 + 0.880832i
\(470\) 0 0
\(471\) −0.564426 0.410079i −0.0260074 0.0188955i
\(472\) 19.2581 26.5065i 0.886426 1.22006i
\(473\) 6.83706 + 2.22149i 0.314368 + 0.102144i
\(474\) 9.40048 0.431779
\(475\) 0 0
\(476\) 18.8213 0.862671
\(477\) 25.0799 + 8.14895i 1.14833 + 0.373115i
\(478\) 9.00380 12.3927i 0.411824 0.566827i
\(479\) 20.2715 + 14.7281i 0.926227 + 0.672943i 0.945066 0.326879i \(-0.105997\pi\)
−0.0188390 + 0.999823i \(0.505997\pi\)
\(480\) 0 0
\(481\) 4.41097 3.20475i 0.201123 0.146124i
\(482\) 60.5632i 2.75858i
\(483\) −2.82134 3.88324i −0.128375 0.176693i
\(484\) 7.20913 + 22.1874i 0.327688 + 1.00852i
\(485\) 0 0
\(486\) 8.25017 25.3914i 0.374235 1.15178i
\(487\) 1.39310 0.452644i 0.0631272 0.0205113i −0.277283 0.960788i \(-0.589434\pi\)
0.340410 + 0.940277i \(0.389434\pi\)
\(488\) 41.7813 13.5756i 1.89135 0.614537i
\(489\) −0.654474 + 2.01426i −0.0295963 + 0.0910881i
\(490\) 0 0
\(491\) −6.20155 19.0864i −0.279872 0.861358i −0.987889 0.155162i \(-0.950410\pi\)
0.708017 0.706195i \(-0.249590\pi\)
\(492\) 1.70639 + 2.34864i 0.0769298 + 0.105885i
\(493\) 7.37229i 0.332031i
\(494\) −2.40859 + 1.74994i −0.108367 + 0.0787335i
\(495\) 0 0
\(496\) 2.30137 + 1.67204i 0.103335 + 0.0750770i
\(497\) 22.2335 30.6017i 0.997307 1.37268i
\(498\) 13.1608 + 4.27621i 0.589751 + 0.191622i
\(499\) −0.624999 −0.0279788 −0.0139894 0.999902i \(-0.504453\pi\)
−0.0139894 + 0.999902i \(0.504453\pi\)
\(500\) 0 0
\(501\) 4.95498 0.221372
\(502\) −23.9657 7.78693i −1.06964 0.347548i
\(503\) 11.3473 15.6182i 0.505951 0.696382i −0.477279 0.878752i \(-0.658377\pi\)
0.983230 + 0.182370i \(0.0583767\pi\)
\(504\) −20.9719 15.2369i −0.934161 0.678707i
\(505\) 0 0
\(506\) 12.4400 9.03816i 0.553024 0.401795i
\(507\) 5.20639i 0.231224i
\(508\) −22.2554 30.6319i −0.987423 1.35907i
\(509\) 3.25091 + 10.0053i 0.144094 + 0.443476i 0.996893 0.0787629i \(-0.0250970\pi\)
−0.852799 + 0.522239i \(0.825097\pi\)
\(510\) 0 0
\(511\) 0.251070 0.772714i 0.0111067 0.0341828i
\(512\) 4.74321 1.54116i 0.209622 0.0681103i
\(513\) −2.35594 + 0.765491i −0.104017 + 0.0337973i
\(514\) −4.69588 + 14.4524i −0.207127 + 0.637470i
\(515\) 0 0
\(516\) −1.75801 5.41061i −0.0773923 0.238189i
\(517\) 5.64267 + 7.76648i 0.248165 + 0.341569i
\(518\) 26.7818i 1.17672i
\(519\) −2.94923 + 2.14274i −0.129457 + 0.0940558i
\(520\) 0 0
\(521\) 8.09580 + 5.88195i 0.354684 + 0.257693i 0.750831 0.660494i \(-0.229653\pi\)
−0.396148 + 0.918187i \(0.629653\pi\)
\(522\) −14.9247 + 20.5421i −0.653237 + 0.899103i
\(523\) −21.6680 7.04035i −0.947474 0.307853i −0.205785 0.978597i \(-0.565975\pi\)
−0.741689 + 0.670744i \(0.765975\pi\)
\(524\) −26.6210 −1.16295
\(525\) 0 0
\(526\) −62.5981 −2.72941
\(527\) −11.3936 3.70200i −0.496312 0.161262i
\(528\) −0.246603 + 0.339420i −0.0107320 + 0.0147714i
\(529\) −9.63993 7.00382i −0.419127 0.304514i
\(530\) 0 0
\(531\) 23.8951 17.3608i 1.03696 0.753393i
\(532\) 9.13943i 0.396245i
\(533\) 1.53871 + 2.11786i 0.0666491 + 0.0917346i
\(534\) 1.61583 + 4.97301i 0.0699237 + 0.215203i
\(535\) 0 0
\(536\) −10.1670 + 31.2907i −0.439146 + 1.35155i
\(537\) −7.00829 + 2.27713i −0.302430 + 0.0982655i
\(538\) 2.21701 0.720350i 0.0955821 0.0310565i
\(539\) −1.36968 + 4.21544i −0.0589962 + 0.181572i
\(540\) 0 0
\(541\) 1.00709 + 3.09949i 0.0432980 + 0.133257i 0.970369 0.241629i \(-0.0776817\pi\)
−0.927071 + 0.374886i \(0.877682\pi\)
\(542\) −8.48624 11.6803i −0.364515 0.501712i
\(543\) 0.755360i 0.0324156i
\(544\) −7.72851 + 5.61509i −0.331357 + 0.240745i
\(545\) 0 0
\(546\) 3.84416 + 2.79295i 0.164515 + 0.119527i
\(547\) −7.98700 + 10.9932i −0.341499 + 0.470033i −0.944879 0.327421i \(-0.893821\pi\)
0.603379 + 0.797454i \(0.293821\pi\)
\(548\) −29.5957 9.61622i −1.26427 0.410785i
\(549\) 39.6033 1.69023
\(550\) 0 0
\(551\) 3.57992 0.152510
\(552\) −4.62798 1.50372i −0.196980 0.0640026i
\(553\) 15.2955 21.0525i 0.650432 0.895242i
\(554\) −46.0901 33.4865i −1.95818 1.42270i
\(555\) 0 0
\(556\) −48.3034 + 35.0945i −2.04852 + 1.48834i
\(557\) 27.6399i 1.17114i −0.810621 0.585571i \(-0.800870\pi\)
0.810621 0.585571i \(-0.199130\pi\)
\(558\) 24.2525 + 33.3808i 1.02669 + 1.41312i
\(559\) −1.58527 4.87896i −0.0670498 0.206358i
\(560\) 0 0
\(561\) 0.545994 1.68040i 0.0230519 0.0709464i
\(562\) −4.03871 + 1.31226i −0.170363 + 0.0553543i
\(563\) −1.57804 + 0.512737i −0.0665065 + 0.0216093i −0.342081 0.939670i \(-0.611132\pi\)
0.275575 + 0.961280i \(0.411132\pi\)
\(564\) 2.34761 7.22520i 0.0988522 0.304236i
\(565\) 0 0
\(566\) −6.16637 18.9781i −0.259192 0.797711i
\(567\) −12.5285 17.2439i −0.526146 0.724178i
\(568\) 38.3475i 1.60902i
\(569\) 14.4675 10.5113i 0.606509 0.440655i −0.241674 0.970357i \(-0.577697\pi\)
0.848183 + 0.529703i \(0.177697\pi\)
\(570\) 0 0
\(571\) 29.8303 + 21.6730i 1.24836 + 0.906987i 0.998126 0.0611975i \(-0.0194920\pi\)
0.250235 + 0.968185i \(0.419492\pi\)
\(572\) −5.59164 + 7.69623i −0.233798 + 0.321796i
\(573\) −8.88344 2.88640i −0.371111 0.120581i
\(574\) 12.8589 0.536718
\(575\) 0 0
\(576\) 35.3531 1.47305
\(577\) −21.6971 7.04982i −0.903262 0.293488i −0.179679 0.983725i \(-0.557506\pi\)
−0.723583 + 0.690238i \(0.757506\pi\)
\(578\) 18.3779 25.2950i 0.764421 1.05213i
\(579\) 5.03693 + 3.65954i 0.209328 + 0.152085i
\(580\) 0 0
\(581\) 30.9906 22.5160i 1.28571 0.934120i
\(582\) 10.9208i 0.452682i
\(583\) −11.1735 15.3790i −0.462758 0.636932i
\(584\) −0.254532 0.783370i −0.0105326 0.0324161i
\(585\) 0 0
\(586\) 4.48969 13.8179i 0.185467 0.570810i
\(587\) 10.5429 3.42560i 0.435153 0.141390i −0.0832455 0.996529i \(-0.526529\pi\)
0.518398 + 0.855139i \(0.326529\pi\)
\(588\) 3.33595 1.08392i 0.137572 0.0447000i
\(589\) 1.79766 5.53262i 0.0740712 0.227968i
\(590\) 0 0
\(591\) −0.503288 1.54896i −0.0207025 0.0637157i
\(592\) −0.991864 1.36518i −0.0407654 0.0561087i
\(593\) 11.1321i 0.457139i −0.973528 0.228570i \(-0.926595\pi\)
0.973528 0.228570i \(-0.0734049\pi\)
\(594\) −10.2466 + 7.44459i −0.420423 + 0.305455i
\(595\) 0 0
\(596\) 17.0240 + 12.3687i 0.697330 + 0.506640i
\(597\) 4.93965 6.79885i 0.202167 0.278258i
\(598\) −10.4358 3.39080i −0.426752 0.138660i
\(599\) −36.2736 −1.48210 −0.741049 0.671451i \(-0.765671\pi\)
−0.741049 + 0.671451i \(0.765671\pi\)
\(600\) 0 0
\(601\) −15.1051 −0.616150 −0.308075 0.951362i \(-0.599685\pi\)
−0.308075 + 0.951362i \(0.599685\pi\)
\(602\) −23.9657 7.78693i −0.976769 0.317372i
\(603\) −17.4335 + 23.9951i −0.709945 + 0.977156i
\(604\) 12.7249 + 9.24517i 0.517768 + 0.376181i
\(605\) 0 0
\(606\) −8.29219 + 6.02463i −0.336847 + 0.244734i
\(607\) 33.5066i 1.35999i −0.733216 0.679996i \(-0.761982\pi\)
0.733216 0.679996i \(-0.238018\pi\)
\(608\) −2.72664 3.75289i −0.110580 0.152200i
\(609\) −1.76561 5.43399i −0.0715461 0.220196i
\(610\) 0 0
\(611\) 2.11693 6.51524i 0.0856418 0.263579i
\(612\) 16.3591 5.31539i 0.661277 0.214862i
\(613\) −26.6571 + 8.66140i −1.07667 + 0.349831i −0.793081 0.609116i \(-0.791524\pi\)
−0.283587 + 0.958947i \(0.591524\pi\)
\(614\) 20.4563 62.9579i 0.825548 2.54078i
\(615\) 0 0
\(616\) 5.77447 + 17.7720i 0.232660 + 0.716054i
\(617\) −17.9406 24.6931i −0.722260 0.994105i −0.999446 0.0332890i \(-0.989402\pi\)
0.277186 0.960816i \(-0.410598\pi\)
\(618\) 9.96234i 0.400744i
\(619\) −17.5533 + 12.7532i −0.705528 + 0.512596i −0.881728 0.471758i \(-0.843619\pi\)
0.176200 + 0.984354i \(0.443619\pi\)
\(620\) 0 0
\(621\) −7.38636 5.36650i −0.296404 0.215350i
\(622\) −10.6369 + 14.6405i −0.426502 + 0.587029i
\(623\) 13.7662 + 4.47291i 0.551531 + 0.179203i
\(624\) 0.299391 0.0119852
\(625\) 0 0
\(626\) 49.4399 1.97601
\(627\) 0.815985 + 0.265130i 0.0325873 + 0.0105883i
\(628\) −2.87783 + 3.96100i −0.114838 + 0.158061i
\(629\) 5.74932 + 4.17712i 0.229240 + 0.166553i
\(630\) 0 0
\(631\) 13.1285 9.53840i 0.522637 0.379718i −0.294960 0.955510i \(-0.595306\pi\)
0.817596 + 0.575792i \(0.195306\pi\)
\(632\) 26.3812i 1.04939i
\(633\) −0.905439 1.24623i −0.0359880 0.0495332i
\(634\) −2.86857 8.82857i −0.113926 0.350627i
\(635\) 0 0
\(636\) −4.64868 + 14.3072i −0.184332 + 0.567316i
\(637\) 3.00816 0.977409i 0.119187 0.0387264i
\(638\) 17.4078 5.65614i 0.689181 0.223929i
\(639\) 10.6825 32.8775i 0.422595 1.30061i
\(640\) 0 0
\(641\) −6.85321 21.0920i −0.270685 0.833084i −0.990329 0.138740i \(-0.955695\pi\)
0.719643 0.694344i \(-0.244305\pi\)
\(642\) −3.62834 4.99398i −0.143199 0.197097i
\(643\) 13.2767i 0.523583i 0.965124 + 0.261792i \(0.0843133\pi\)
−0.965124 + 0.261792i \(0.915687\pi\)
\(644\) −27.2516 + 19.7994i −1.07386 + 0.780207i
\(645\) 0 0
\(646\) −3.13939 2.28090i −0.123518 0.0897407i
\(647\) −6.63333 + 9.12999i −0.260783 + 0.358937i −0.919251 0.393672i \(-0.871205\pi\)
0.658468 + 0.752609i \(0.271205\pi\)
\(648\) −20.5510 6.67743i −0.807321 0.262314i
\(649\) −21.2912 −0.835754
\(650\) 0 0
\(651\) −9.28462 −0.363893
\(652\) 14.1356 + 4.59293i 0.553592 + 0.179873i
\(653\) 21.0506 28.9736i 0.823773 1.13383i −0.165277 0.986247i \(-0.552852\pi\)
0.989050 0.147579i \(-0.0471480\pi\)
\(654\) −8.97259 6.51897i −0.350856 0.254912i
\(655\) 0 0
\(656\) 0.655472 0.476228i 0.0255919 0.0185936i
\(657\) 0.742534i 0.0289690i
\(658\) −19.7791 27.2236i −0.771069 1.06129i
\(659\) −12.2882 37.8193i −0.478681 1.47323i −0.840928 0.541147i \(-0.817990\pi\)
0.362247 0.932082i \(-0.382010\pi\)
\(660\) 0 0
\(661\) −1.93053 + 5.94157i −0.0750890 + 0.231100i −0.981555 0.191178i \(-0.938769\pi\)
0.906466 + 0.422278i \(0.138769\pi\)
\(662\) −25.5728 + 8.30912i −0.993917 + 0.322943i
\(663\) −1.19914 + 0.389624i −0.0465707 + 0.0151317i
\(664\) 12.0006 36.9340i 0.465713 1.43332i
\(665\) 0 0
\(666\) −7.56355 23.2782i −0.293082 0.902012i
\(667\) 7.75544 + 10.6744i 0.300292 + 0.413316i
\(668\) 34.7728i 1.34540i
\(669\) 11.0323 8.01546i 0.426535 0.309896i
\(670\) 0 0
\(671\) −23.0961 16.7803i −0.891616 0.647797i
\(672\) −4.35178 + 5.98970i −0.167873 + 0.231058i
\(673\) 39.4334 + 12.8127i 1.52005 + 0.493893i 0.945789 0.324782i \(-0.105291\pi\)
0.574257 + 0.818675i \(0.305291\pi\)
\(674\) 49.7297 1.91552
\(675\) 0 0
\(676\) −36.5372 −1.40528
\(677\) −1.36872 0.444723i −0.0526041 0.0170921i 0.282597 0.959239i \(-0.408804\pi\)
−0.335201 + 0.942147i \(0.608804\pi\)
\(678\) −6.90510 + 9.50406i −0.265189 + 0.365001i
\(679\) −24.4572 17.7692i −0.938583 0.681920i
\(680\) 0 0
\(681\) −4.50312 + 3.27171i −0.172560 + 0.125372i
\(682\) 29.7433i 1.13893i
\(683\) −4.98808 6.86550i −0.190864 0.262701i 0.702851 0.711337i \(-0.251910\pi\)
−0.893715 + 0.448636i \(0.851910\pi\)
\(684\) 2.58111 + 7.94382i 0.0986910 + 0.303740i
\(685\) 0 0
\(686\) −10.3635 + 31.8957i −0.395682 + 1.21778i
\(687\) 7.40779 2.40694i 0.282625 0.0918304i
\(688\) −1.51003 + 0.490637i −0.0575692 + 0.0187054i
\(689\) −4.19189 + 12.9013i −0.159698 + 0.491501i
\(690\) 0 0
\(691\) −13.5287 41.6370i −0.514655 1.58395i −0.783908 0.620877i \(-0.786777\pi\)
0.269253 0.963070i \(-0.413223\pi\)
\(692\) 15.0372 + 20.6969i 0.571629 + 0.786780i
\(693\) 16.8456i 0.639910i
\(694\) 29.1394 21.1710i 1.10612 0.803641i
\(695\) 0 0
\(696\) −4.68617 3.40470i −0.177629 0.129055i
\(697\) −2.00558 + 2.76045i −0.0759668 + 0.104559i
\(698\) −12.2243 3.97191i −0.462696 0.150339i
\(699\) −10.6922 −0.404418
\(700\) 0 0
\(701\) 0.840795 0.0317564 0.0158782 0.999874i \(-0.494946\pi\)
0.0158782 + 0.999874i \(0.494946\pi\)
\(702\) 8.59580 + 2.79295i 0.324428 + 0.105413i
\(703\) −2.02837 + 2.79182i −0.0765015 + 0.105295i
\(704\) −20.6175 14.9795i −0.777050 0.564560i
\(705\) 0 0
\(706\) −14.9873 + 10.8889i −0.564056 + 0.409811i
\(707\) 28.3731i 1.06708i
\(708\) 9.90369 + 13.6313i 0.372203 + 0.512294i
\(709\) 4.13503 + 12.7263i 0.155294 + 0.477947i 0.998191 0.0601294i \(-0.0191513\pi\)
−0.842896 + 0.538076i \(0.819151\pi\)
\(710\) 0 0
\(711\) 7.34906 22.6181i 0.275611 0.848244i
\(712\) 13.9561 4.53460i 0.523025 0.169941i
\(713\) 20.3913 6.62555i 0.763662 0.248129i
\(714\) −1.91385 + 5.89024i −0.0716242 + 0.220437i
\(715\) 0 0
\(716\) 15.9803 + 49.1824i 0.597214 + 1.83803i
\(717\) 1.85163 + 2.54855i 0.0691505 + 0.0951775i
\(718\) 28.5027i 1.06371i
\(719\) 35.1233 25.5186i 1.30988 0.951683i 0.309880 0.950776i \(-0.399711\pi\)
1.00000 0.000907154i \(-0.000288756\pi\)
\(720\) 0 0
\(721\) −22.3107 16.2097i −0.830896 0.603681i
\(722\) −24.6822 + 33.9721i −0.918577 + 1.26431i
\(723\) −11.8452 3.84875i −0.440529 0.143137i
\(724\) 5.30093 0.197007
\(725\) 0 0
\(726\) −7.67677 −0.284912
\(727\) −30.4795 9.90338i −1.13042 0.367296i −0.316685 0.948531i \(-0.602570\pi\)
−0.813736 + 0.581235i \(0.802570\pi\)
\(728\) 7.83802 10.7881i 0.290496 0.399834i
\(729\) −12.5986 9.15342i −0.466615 0.339016i
\(730\) 0 0
\(731\) 5.40955 3.93027i 0.200079 0.145366i
\(732\) 22.5922i 0.835032i
\(733\) 4.78415 + 6.58481i 0.176706 + 0.243216i 0.888178 0.459499i \(-0.151971\pi\)
−0.711472 + 0.702715i \(0.751971\pi\)
\(734\) −19.1781 59.0241i −0.707877 2.17862i
\(735\) 0 0
\(736\) 5.28331 16.2603i 0.194745 0.599364i
\(737\) 20.3339 6.60690i 0.749010 0.243368i
\(738\) 11.1767 3.63152i 0.411419 0.133678i
\(739\) 2.20241 6.77831i 0.0810169 0.249344i −0.902341 0.431023i \(-0.858153\pi\)
0.983358 + 0.181678i \(0.0581529\pi\)
\(740\) 0 0
\(741\) −0.189198 0.582291i −0.00695036 0.0213910i
\(742\) 39.1660 + 53.9074i 1.43783 + 1.97900i
\(743\) 21.9040i 0.803578i −0.915732 0.401789i \(-0.868388\pi\)
0.915732 0.401789i \(-0.131612\pi\)
\(744\) −7.61500 + 5.53262i −0.279179 + 0.202836i
\(745\) 0 0
\(746\) 51.6362 + 37.5159i 1.89054 + 1.37355i
\(747\) 20.5776 28.3226i 0.752895 1.03627i
\(748\) −11.7926 3.83165i −0.431180 0.140099i
\(749\) −17.0877 −0.624373
\(750\) 0 0
\(751\) 9.21909 0.336409 0.168205 0.985752i \(-0.446203\pi\)
0.168205 + 0.985752i \(0.446203\pi\)
\(752\) −2.01645 0.655185i −0.0735325 0.0238921i
\(753\) 3.04601 4.19248i 0.111003 0.152782i
\(754\) −10.5670 7.67740i −0.384829 0.279594i
\(755\) 0 0
\(756\) 22.4467 16.3085i 0.816379 0.593134i
\(757\) 45.6524i 1.65926i 0.558311 + 0.829632i \(0.311450\pi\)
−0.558311 + 0.829632i \(0.688550\pi\)
\(758\) −4.71631 6.49144i −0.171304 0.235780i
\(759\) 0.977177 + 3.00744i 0.0354693 + 0.109163i
\(760\) 0 0
\(761\) 12.3316 37.9526i 0.447019 1.37578i −0.433236 0.901280i \(-0.642628\pi\)
0.880255 0.474501i \(-0.157372\pi\)
\(762\) 11.8495 3.85014i 0.429263 0.139476i
\(763\) −29.1986 + 9.48719i −1.05706 + 0.343459i
\(764\) −20.2561 + 62.3417i −0.732838 + 2.25544i
\(765\) 0 0
\(766\) 19.5327 + 60.1155i 0.705745 + 2.17206i
\(767\) 8.93053 + 12.2918i 0.322463 + 0.443832i
\(768\) 8.90403i 0.321296i
\(769\) −35.8734 + 26.0636i −1.29363 + 0.939876i −0.999872 0.0160040i \(-0.994906\pi\)
−0.293757 + 0.955880i \(0.594906\pi\)
\(770\) 0 0
\(771\) −2.52826 1.83689i −0.0910531 0.0661539i
\(772\) 25.6818 35.3479i 0.924307 1.27220i
\(773\) 36.6103 + 11.8954i 1.31678 + 0.427848i 0.881389 0.472392i \(-0.156609\pi\)
0.435393 + 0.900240i \(0.356609\pi\)
\(774\) −23.0297 −0.827785
\(775\) 0 0
\(776\) −30.6477 −1.10019
\(777\) 5.23811 + 1.70197i 0.187916 + 0.0610577i
\(778\) −14.7742 + 20.3349i −0.529680 + 0.729042i