Properties

Label 475.2.l.a.251.1
Level $475$
Weight $2$
Character 475.251
Analytic conductor $3.793$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.l (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \( x^{6} - x^{3} + 1 \) 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 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 251.1
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 475.251
Dual form 475.2.l.a.176.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.826352 + 0.300767i) q^{2} +(-0.0923963 - 0.524005i) q^{3} +(-0.939693 - 0.788496i) q^{4} +(0.0812519 - 0.460802i) q^{6} +(-0.939693 + 1.62760i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(2.55303 - 0.929228i) q^{9} +O(q^{10})\) \(q+(0.826352 + 0.300767i) q^{2} +(-0.0923963 - 0.524005i) q^{3} +(-0.939693 - 0.788496i) q^{4} +(0.0812519 - 0.460802i) q^{6} +(-0.939693 + 1.62760i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(2.55303 - 0.929228i) q^{9} +(-1.70574 - 2.95442i) q^{11} +(-0.326352 + 0.565258i) q^{12} +(0.918748 - 5.21048i) q^{13} +(-1.26604 + 1.06234i) q^{14} +(-0.00727396 - 0.0412527i) q^{16} +(1.55303 + 0.565258i) q^{17} +2.38919 q^{18} +(-2.52094 - 3.55596i) q^{19} +(0.939693 + 0.342020i) q^{21} +(-0.520945 - 2.95442i) q^{22} +(-1.34730 - 1.13052i) q^{23} +(-1.15657 + 0.970481i) q^{24} +(2.32635 - 4.02936i) q^{26} +(-1.52094 - 2.63435i) q^{27} +(2.16637 - 0.788496i) q^{28} +(3.25877 - 1.18610i) q^{29} +(-0.971782 + 1.68317i) q^{31} +(-0.979055 + 5.55250i) q^{32} +(-1.39053 + 1.16679i) q^{33} +(1.11334 + 0.934204i) q^{34} +(-3.13176 - 1.13987i) q^{36} +0.837496 q^{37} +(-1.01367 - 3.69669i) q^{38} -2.81521 q^{39} +(-0.779715 - 4.42198i) q^{41} +(0.673648 + 0.565258i) q^{42} +(-3.67752 + 3.08580i) q^{43} +(-0.726682 + 4.12122i) q^{44} +(-0.773318 - 1.33943i) q^{46} +(0.673648 - 0.245188i) q^{47} +(-0.0209445 + 0.00762319i) q^{48} +(1.73396 + 3.00330i) q^{49} +(0.152704 - 0.866025i) q^{51} +(-4.97178 + 4.17182i) q^{52} +(4.67752 + 3.92490i) q^{53} +(-0.464508 - 2.63435i) q^{54} +5.33275 q^{56} +(-1.63041 + 1.64955i) q^{57} +3.04963 q^{58} +(10.1099 + 3.67972i) q^{59} +(3.36231 + 2.82131i) q^{61} +(-1.30928 + 1.09861i) q^{62} +(-0.886659 + 5.02849i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(-1.50000 + 0.545955i) q^{66} +(13.3550 - 4.86084i) q^{67} +(-1.01367 - 1.75573i) q^{68} +(-0.467911 + 0.810446i) q^{69} +(-10.5398 + 8.84397i) q^{71} +(-5.90554 - 4.95534i) q^{72} +(1.30541 + 7.40333i) q^{73} +(0.692066 + 0.251892i) q^{74} +(-0.434945 + 5.32926i) q^{76} +6.41147 q^{77} +(-2.32635 - 0.846723i) q^{78} +(-1.20914 - 6.85738i) q^{79} +(5.00387 - 4.19875i) q^{81} +(0.685670 - 3.88863i) q^{82} +(1.25624 - 2.17588i) q^{83} +(-0.613341 - 1.06234i) q^{84} +(-3.96703 + 1.44388i) q^{86} +(-0.922618 - 1.59802i) q^{87} +(-4.84002 + 8.38316i) q^{88} +(-0.396459 + 2.24843i) q^{89} +(7.61721 + 6.39160i) q^{91} +(0.374638 + 2.12467i) q^{92} +(0.971782 + 0.353700i) q^{93} +0.630415 q^{94} +3.00000 q^{96} +(-1.71301 - 0.623485i) q^{97} +(0.529563 + 3.00330i) q^{98} +(-7.10014 - 5.95772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{13} - 3 q^{14} - 18 q^{16} - 3 q^{17} + 6 q^{18} - 12 q^{19} - 6 q^{23} + 15 q^{24} + 15 q^{26} - 6 q^{27} - 6 q^{28} - 3 q^{29} + 9 q^{31} - 9 q^{32} + 9 q^{33} - 24 q^{36} + 15 q^{38} - 24 q^{39} + 21 q^{41} + 3 q^{42} + 3 q^{43} + 9 q^{44} - 18 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 3 q^{51} - 15 q^{52} + 3 q^{53} + 30 q^{54} - 6 q^{56} - 24 q^{57} - 36 q^{58} + 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{63} - 12 q^{64} - 9 q^{66} + 30 q^{67} + 15 q^{68} - 12 q^{69} - 6 q^{71} + 12 q^{72} + 12 q^{73} + 15 q^{74} + 36 q^{76} + 18 q^{77} - 15 q^{78} - 39 q^{79} + 6 q^{81} + 54 q^{82} + 3 q^{84} + 24 q^{86} + 21 q^{87} - 9 q^{88} - 12 q^{89} + 15 q^{91} - 42 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.826352 + 0.300767i 0.584319 + 0.212675i 0.617229 0.786784i \(-0.288255\pi\)
−0.0329100 + 0.999458i \(0.510477\pi\)
\(3\) −0.0923963 0.524005i −0.0533450 0.302535i 0.946449 0.322855i \(-0.104643\pi\)
−0.999794 + 0.0203202i \(0.993531\pi\)
\(4\) −0.939693 0.788496i −0.469846 0.394248i
\(5\) 0 0
\(6\) 0.0812519 0.460802i 0.0331710 0.188122i
\(7\) −0.939693 + 1.62760i −0.355170 + 0.615173i −0.987147 0.159814i \(-0.948910\pi\)
0.631977 + 0.774987i \(0.282244\pi\)
\(8\) −1.41875 2.45734i −0.501603 0.868802i
\(9\) 2.55303 0.929228i 0.851011 0.309743i
\(10\) 0 0
\(11\) −1.70574 2.95442i −0.514299 0.890792i −0.999862 0.0165906i \(-0.994719\pi\)
0.485563 0.874202i \(-0.338615\pi\)
\(12\) −0.326352 + 0.565258i −0.0942097 + 0.163176i
\(13\) 0.918748 5.21048i 0.254815 1.44513i −0.541733 0.840551i \(-0.682231\pi\)
0.796547 0.604576i \(-0.206657\pi\)
\(14\) −1.26604 + 1.06234i −0.338365 + 0.283922i
\(15\) 0 0
\(16\) −0.00727396 0.0412527i −0.00181849 0.0103132i
\(17\) 1.55303 + 0.565258i 0.376666 + 0.137095i 0.523414 0.852079i \(-0.324658\pi\)
−0.146748 + 0.989174i \(0.546881\pi\)
\(18\) 2.38919 0.563136
\(19\) −2.52094 3.55596i −0.578344 0.815793i
\(20\) 0 0
\(21\) 0.939693 + 0.342020i 0.205058 + 0.0746349i
\(22\) −0.520945 2.95442i −0.111066 0.629885i
\(23\) −1.34730 1.13052i −0.280931 0.235729i 0.491424 0.870921i \(-0.336477\pi\)
−0.772354 + 0.635192i \(0.780921\pi\)
\(24\) −1.15657 + 0.970481i −0.236085 + 0.198099i
\(25\) 0 0
\(26\) 2.32635 4.02936i 0.456235 0.790222i
\(27\) −1.52094 2.63435i −0.292706 0.506982i
\(28\) 2.16637 0.788496i 0.409406 0.149012i
\(29\) 3.25877 1.18610i 0.605138 0.220252i −0.0212363 0.999774i \(-0.506760\pi\)
0.626375 + 0.779522i \(0.284538\pi\)
\(30\) 0 0
\(31\) −0.971782 + 1.68317i −0.174537 + 0.302307i −0.940001 0.341172i \(-0.889176\pi\)
0.765464 + 0.643479i \(0.222510\pi\)
\(32\) −0.979055 + 5.55250i −0.173074 + 0.981553i
\(33\) −1.39053 + 1.16679i −0.242060 + 0.203113i
\(34\) 1.11334 + 0.934204i 0.190936 + 0.160215i
\(35\) 0 0
\(36\) −3.13176 1.13987i −0.521960 0.189978i
\(37\) 0.837496 0.137684 0.0688418 0.997628i \(-0.478070\pi\)
0.0688418 + 0.997628i \(0.478070\pi\)
\(38\) −1.01367 3.69669i −0.164439 0.599682i
\(39\) −2.81521 −0.450794
\(40\) 0 0
\(41\) −0.779715 4.42198i −0.121771 0.690598i −0.983173 0.182675i \(-0.941524\pi\)
0.861402 0.507923i \(-0.169587\pi\)
\(42\) 0.673648 + 0.565258i 0.103946 + 0.0872212i
\(43\) −3.67752 + 3.08580i −0.560816 + 0.470581i −0.878584 0.477588i \(-0.841511\pi\)
0.317768 + 0.948169i \(0.397067\pi\)
\(44\) −0.726682 + 4.12122i −0.109551 + 0.621297i
\(45\) 0 0
\(46\) −0.773318 1.33943i −0.114020 0.197488i
\(47\) 0.673648 0.245188i 0.0982617 0.0357643i −0.292422 0.956290i \(-0.594461\pi\)
0.390683 + 0.920525i \(0.372239\pi\)
\(48\) −0.0209445 + 0.00762319i −0.00302308 + 0.00110031i
\(49\) 1.73396 + 3.00330i 0.247708 + 0.429043i
\(50\) 0 0
\(51\) 0.152704 0.866025i 0.0213828 0.121268i
\(52\) −4.97178 + 4.17182i −0.689462 + 0.578527i
\(53\) 4.67752 + 3.92490i 0.642507 + 0.539127i 0.904787 0.425865i \(-0.140030\pi\)
−0.262280 + 0.964992i \(0.584474\pi\)
\(54\) −0.464508 2.63435i −0.0632115 0.358490i
\(55\) 0 0
\(56\) 5.33275 0.712618
\(57\) −1.63041 + 1.64955i −0.215954 + 0.218488i
\(58\) 3.04963 0.400436
\(59\) 10.1099 + 3.67972i 1.31620 + 0.479058i 0.902239 0.431236i \(-0.141922\pi\)
0.413962 + 0.910294i \(0.364144\pi\)
\(60\) 0 0
\(61\) 3.36231 + 2.82131i 0.430500 + 0.361232i 0.832140 0.554565i \(-0.187115\pi\)
−0.401640 + 0.915797i \(0.631560\pi\)
\(62\) −1.30928 + 1.09861i −0.166278 + 0.139524i
\(63\) −0.886659 + 5.02849i −0.111709 + 0.633531i
\(64\) −2.52094 + 4.36640i −0.315118 + 0.545801i
\(65\) 0 0
\(66\) −1.50000 + 0.545955i −0.184637 + 0.0672025i
\(67\) 13.3550 4.86084i 1.63158 0.593846i 0.646040 0.763304i \(-0.276424\pi\)
0.985537 + 0.169458i \(0.0542017\pi\)
\(68\) −1.01367 1.75573i −0.122926 0.212913i
\(69\) −0.467911 + 0.810446i −0.0563299 + 0.0975662i
\(70\) 0 0
\(71\) −10.5398 + 8.84397i −1.25085 + 1.04959i −0.254252 + 0.967138i \(0.581829\pi\)
−0.996595 + 0.0824479i \(0.973726\pi\)
\(72\) −5.90554 4.95534i −0.695975 0.583992i
\(73\) 1.30541 + 7.40333i 0.152786 + 0.866495i 0.960782 + 0.277306i \(0.0894415\pi\)
−0.807995 + 0.589189i \(0.799447\pi\)
\(74\) 0.692066 + 0.251892i 0.0804511 + 0.0292818i
\(75\) 0 0
\(76\) −0.434945 + 5.32926i −0.0498916 + 0.611308i
\(77\) 6.41147 0.730655
\(78\) −2.32635 0.846723i −0.263407 0.0958725i
\(79\) −1.20914 6.85738i −0.136039 0.771515i −0.974131 0.225986i \(-0.927440\pi\)
0.838092 0.545529i \(-0.183671\pi\)
\(80\) 0 0
\(81\) 5.00387 4.19875i 0.555986 0.466527i
\(82\) 0.685670 3.88863i 0.0757196 0.429427i
\(83\) 1.25624 2.17588i 0.137891 0.238834i −0.788807 0.614641i \(-0.789301\pi\)
0.926698 + 0.375807i \(0.122634\pi\)
\(84\) −0.613341 1.06234i −0.0669210 0.115911i
\(85\) 0 0
\(86\) −3.96703 + 1.44388i −0.427776 + 0.155698i
\(87\) −0.922618 1.59802i −0.0989151 0.171326i
\(88\) −4.84002 + 8.38316i −0.515948 + 0.893648i
\(89\) −0.396459 + 2.24843i −0.0420246 + 0.238333i −0.998584 0.0532055i \(-0.983056\pi\)
0.956559 + 0.291539i \(0.0941673\pi\)
\(90\) 0 0
\(91\) 7.61721 + 6.39160i 0.798501 + 0.670022i
\(92\) 0.374638 + 2.12467i 0.0390587 + 0.221513i
\(93\) 0.971782 + 0.353700i 0.100769 + 0.0366769i
\(94\) 0.630415 0.0650223
\(95\) 0 0
\(96\) 3.00000 0.306186
\(97\) −1.71301 0.623485i −0.173930 0.0633053i 0.253587 0.967312i \(-0.418389\pi\)
−0.427517 + 0.904007i \(0.640612\pi\)
\(98\) 0.529563 + 3.00330i 0.0534939 + 0.303379i
\(99\) −7.10014 5.95772i −0.713591 0.598774i
\(100\) 0 0
\(101\) −1.37551 + 7.80093i −0.136869 + 0.776222i 0.836671 + 0.547705i \(0.184499\pi\)
−0.973540 + 0.228516i \(0.926613\pi\)
\(102\) 0.386659 0.669713i 0.0382850 0.0663115i
\(103\) −0.00727396 0.0125989i −0.000716725 0.00124140i 0.865667 0.500621i \(-0.166895\pi\)
−0.866384 + 0.499379i \(0.833561\pi\)
\(104\) −14.1074 + 5.13468i −1.38335 + 0.503497i
\(105\) 0 0
\(106\) 2.68479 + 4.65020i 0.260770 + 0.451667i
\(107\) −1.77719 + 3.07818i −0.171807 + 0.297579i −0.939052 0.343776i \(-0.888294\pi\)
0.767244 + 0.641355i \(0.221627\pi\)
\(108\) −0.647956 + 3.67474i −0.0623496 + 0.353602i
\(109\) 5.64543 4.73708i 0.540734 0.453730i −0.331055 0.943612i \(-0.607404\pi\)
0.871789 + 0.489882i \(0.162960\pi\)
\(110\) 0 0
\(111\) −0.0773815 0.438852i −0.00734473 0.0416540i
\(112\) 0.0739780 + 0.0269258i 0.00699026 + 0.00254425i
\(113\) −7.37733 −0.694000 −0.347000 0.937865i \(-0.612800\pi\)
−0.347000 + 0.937865i \(0.612800\pi\)
\(114\) −1.84343 + 0.872729i −0.172653 + 0.0817386i
\(115\) 0 0
\(116\) −3.99747 1.45496i −0.371156 0.135090i
\(117\) −2.49613 14.1563i −0.230767 1.30875i
\(118\) 7.24763 + 6.08148i 0.667198 + 0.559846i
\(119\) −2.37939 + 1.99654i −0.218118 + 0.183023i
\(120\) 0 0
\(121\) −0.319078 + 0.552659i −0.0290071 + 0.0502417i
\(122\) 1.92989 + 3.34267i 0.174724 + 0.302631i
\(123\) −2.24510 + 0.817150i −0.202434 + 0.0736799i
\(124\) 2.24035 0.815422i 0.201190 0.0732270i
\(125\) 0 0
\(126\) −2.24510 + 3.88863i −0.200009 + 0.346426i
\(127\) 0.0175410 0.0994798i 0.00155651 0.00882740i −0.984020 0.178060i \(-0.943018\pi\)
0.985576 + 0.169233i \(0.0541290\pi\)
\(128\) 5.24170 4.39831i 0.463305 0.388759i
\(129\) 1.95677 + 1.64192i 0.172284 + 0.144563i
\(130\) 0 0
\(131\) 2.85369 + 1.03866i 0.249328 + 0.0907481i 0.463661 0.886013i \(-0.346536\pi\)
−0.214333 + 0.976761i \(0.568758\pi\)
\(132\) 2.22668 0.193808
\(133\) 8.15657 0.761570i 0.707265 0.0660365i
\(134\) 12.4979 1.07966
\(135\) 0 0
\(136\) −0.814330 4.61830i −0.0698282 0.396016i
\(137\) −14.9684 12.5600i −1.27883 1.07307i −0.993404 0.114671i \(-0.963419\pi\)
−0.285431 0.958399i \(-0.592137\pi\)
\(138\) −0.630415 + 0.528981i −0.0536645 + 0.0450298i
\(139\) 2.67365 15.1630i 0.226776 1.28611i −0.632485 0.774573i \(-0.717965\pi\)
0.859261 0.511537i \(-0.170924\pi\)
\(140\) 0 0
\(141\) −0.190722 0.330341i −0.0160617 0.0278197i
\(142\) −11.3696 + 4.13819i −0.954114 + 0.347269i
\(143\) −16.9611 + 6.17334i −1.41836 + 0.516240i
\(144\) −0.0569038 0.0985603i −0.00474198 0.00821336i
\(145\) 0 0
\(146\) −1.14796 + 6.51038i −0.0950055 + 0.538803i
\(147\) 1.41353 1.18610i 0.116586 0.0978275i
\(148\) −0.786989 0.660362i −0.0646901 0.0542814i
\(149\) −0.654048 3.70929i −0.0535817 0.303877i 0.946226 0.323507i \(-0.104862\pi\)
−0.999807 + 0.0196306i \(0.993751\pi\)
\(150\) 0 0
\(151\) −14.5963 −1.18783 −0.593914 0.804529i \(-0.702418\pi\)
−0.593914 + 0.804529i \(0.702418\pi\)
\(152\) −5.16163 + 11.2398i −0.418663 + 0.911671i
\(153\) 4.49020 0.363011
\(154\) 5.29813 + 1.92836i 0.426936 + 0.155392i
\(155\) 0 0
\(156\) 2.64543 + 2.21978i 0.211804 + 0.177725i
\(157\) 7.94743 6.66869i 0.634274 0.532219i −0.267980 0.963425i \(-0.586356\pi\)
0.902254 + 0.431205i \(0.141912\pi\)
\(158\) 1.06330 6.03028i 0.0845916 0.479743i
\(159\) 1.62449 2.81369i 0.128830 0.223140i
\(160\) 0 0
\(161\) 3.10607 1.13052i 0.244792 0.0890971i
\(162\) 5.39780 1.96464i 0.424091 0.154357i
\(163\) −1.01114 1.75135i −0.0791989 0.137177i 0.823706 0.567018i \(-0.191903\pi\)
−0.902905 + 0.429841i \(0.858570\pi\)
\(164\) −2.75402 + 4.77011i −0.215053 + 0.372483i
\(165\) 0 0
\(166\) 1.69253 1.42020i 0.131366 0.110229i
\(167\) 17.8157 + 14.9491i 1.37862 + 1.15680i 0.969720 + 0.244218i \(0.0785312\pi\)
0.408898 + 0.912580i \(0.365913\pi\)
\(168\) −0.492726 2.79439i −0.0380146 0.215592i
\(169\) −14.0890 5.12797i −1.08377 0.394460i
\(170\) 0 0
\(171\) −9.74035 6.73595i −0.744863 0.515111i
\(172\) 5.88888 0.449023
\(173\) 0.842549 + 0.306663i 0.0640578 + 0.0233151i 0.373850 0.927489i \(-0.378037\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(174\) −0.281774 1.59802i −0.0213613 0.121146i
\(175\) 0 0
\(176\) −0.109470 + 0.0918566i −0.00825164 + 0.00692395i
\(177\) 0.994070 5.63765i 0.0747189 0.423752i
\(178\) −1.00387 + 1.73875i −0.0752433 + 0.130325i
\(179\) 10.6591 + 18.4621i 0.796699 + 1.37992i 0.921755 + 0.387773i \(0.126755\pi\)
−0.125056 + 0.992150i \(0.539911\pi\)
\(180\) 0 0
\(181\) 15.1284 5.50627i 1.12448 0.409278i 0.288196 0.957571i \(-0.406945\pi\)
0.836286 + 0.548294i \(0.184722\pi\)
\(182\) 4.37211 + 7.57272i 0.324082 + 0.561327i
\(183\) 1.16772 2.02255i 0.0863202 0.149511i
\(184\) −0.866592 + 4.91469i −0.0638860 + 0.362316i
\(185\) 0 0
\(186\) 0.696652 + 0.584561i 0.0510810 + 0.0428621i
\(187\) −0.979055 5.55250i −0.0715956 0.406039i
\(188\) −0.826352 0.300767i −0.0602679 0.0219357i
\(189\) 5.71688 0.415842
\(190\) 0 0
\(191\) 18.9486 1.37107 0.685537 0.728038i \(-0.259568\pi\)
0.685537 + 0.728038i \(0.259568\pi\)
\(192\) 2.52094 + 0.917549i 0.181934 + 0.0662184i
\(193\) −2.24035 12.7057i −0.161264 0.914574i −0.952833 0.303494i \(-0.901847\pi\)
0.791569 0.611080i \(-0.209264\pi\)
\(194\) −1.22803 1.03044i −0.0881671 0.0739810i
\(195\) 0 0
\(196\) 0.738703 4.18939i 0.0527645 0.299242i
\(197\) −11.6001 + 20.0920i −0.826476 + 1.43150i 0.0743108 + 0.997235i \(0.476324\pi\)
−0.900786 + 0.434263i \(0.857009\pi\)
\(198\) −4.07532 7.05866i −0.289621 0.501637i
\(199\) −8.66550 + 3.15398i −0.614281 + 0.223580i −0.630375 0.776291i \(-0.717099\pi\)
0.0160945 + 0.999870i \(0.494877\pi\)
\(200\) 0 0
\(201\) −3.78106 6.54899i −0.266695 0.461930i
\(202\) −3.48293 + 6.03260i −0.245058 + 0.424453i
\(203\) −1.13176 + 6.41852i −0.0794339 + 0.450492i
\(204\) −0.826352 + 0.693392i −0.0578562 + 0.0485471i
\(205\) 0 0
\(206\) −0.00222152 0.0125989i −0.000154781 0.000877805i
\(207\) −4.49020 1.63430i −0.312090 0.113592i
\(208\) −0.221629 −0.0153672
\(209\) −6.20574 + 13.5135i −0.429260 + 0.934746i
\(210\) 0 0
\(211\) −13.7417 5.00157i −0.946017 0.344322i −0.177478 0.984125i \(-0.556794\pi\)
−0.768539 + 0.639803i \(0.779016\pi\)
\(212\) −1.30066 7.37641i −0.0893297 0.506614i
\(213\) 5.60813 + 4.70578i 0.384262 + 0.322435i
\(214\) −2.39440 + 2.00914i −0.163678 + 0.137342i
\(215\) 0 0
\(216\) −4.31567 + 7.47497i −0.293644 + 0.508607i
\(217\) −1.82635 3.16333i −0.123981 0.214741i
\(218\) 6.08987 2.21653i 0.412458 0.150122i
\(219\) 3.75877 1.36808i 0.253994 0.0924463i
\(220\) 0 0
\(221\) 4.37211 7.57272i 0.294100 0.509396i
\(222\) 0.0680482 0.385920i 0.00456709 0.0259013i
\(223\) 2.30928 1.93771i 0.154641 0.129759i −0.562185 0.827012i \(-0.690039\pi\)
0.716825 + 0.697253i \(0.245595\pi\)
\(224\) −8.11721 6.81115i −0.542354 0.455089i
\(225\) 0 0
\(226\) −6.09627 2.21886i −0.405518 0.147596i
\(227\) 13.7219 0.910757 0.455378 0.890298i \(-0.349504\pi\)
0.455378 + 0.890298i \(0.349504\pi\)
\(228\) 2.83275 0.264490i 0.187603 0.0175163i
\(229\) 9.41416 0.622105 0.311053 0.950393i \(-0.399318\pi\)
0.311053 + 0.950393i \(0.399318\pi\)
\(230\) 0 0
\(231\) −0.592396 3.35965i −0.0389768 0.221048i
\(232\) −7.53802 6.32515i −0.494895 0.415266i
\(233\) 18.5273 15.5463i 1.21377 1.01847i 0.214640 0.976693i \(-0.431142\pi\)
0.999127 0.0417777i \(-0.0133021\pi\)
\(234\) 2.19506 12.4488i 0.143496 0.813804i
\(235\) 0 0
\(236\) −6.59879 11.4294i −0.429545 0.743993i
\(237\) −3.48158 + 1.26719i −0.226153 + 0.0823130i
\(238\) −2.56670 + 0.934204i −0.166375 + 0.0605554i
\(239\) 11.6630 + 20.2009i 0.754415 + 1.30668i 0.945665 + 0.325143i \(0.105413\pi\)
−0.191250 + 0.981541i \(0.561254\pi\)
\(240\) 0 0
\(241\) 0.0516892 0.293144i 0.00332960 0.0188831i −0.983098 0.183082i \(-0.941393\pi\)
0.986427 + 0.164199i \(0.0525038\pi\)
\(242\) −0.429892 + 0.360723i −0.0276345 + 0.0231881i
\(243\) −9.65317 8.09997i −0.619251 0.519613i
\(244\) −0.934945 5.30234i −0.0598537 0.339447i
\(245\) 0 0
\(246\) −2.10101 −0.133956
\(247\) −20.8444 + 9.86830i −1.32629 + 0.627905i
\(248\) 5.51485 0.350193
\(249\) −1.25624 0.457236i −0.0796112 0.0289761i
\(250\) 0 0
\(251\) −12.4081 10.4116i −0.783190 0.657175i 0.160859 0.986977i \(-0.448573\pi\)
−0.944050 + 0.329802i \(0.893018\pi\)
\(252\) 4.79813 4.02611i 0.302254 0.253621i
\(253\) −1.04189 + 5.90885i −0.0655030 + 0.371486i
\(254\) 0.0444153 0.0769295i 0.00278686 0.00482699i
\(255\) 0 0
\(256\) 15.1300 5.50687i 0.945625 0.344179i
\(257\) 14.4290 5.25173i 0.900057 0.327594i 0.149782 0.988719i \(-0.452143\pi\)
0.750276 + 0.661125i \(0.229921\pi\)
\(258\) 1.12314 + 1.94534i 0.0699237 + 0.121111i
\(259\) −0.786989 + 1.36310i −0.0489011 + 0.0846992i
\(260\) 0 0
\(261\) 7.21760 6.05628i 0.446758 0.374874i
\(262\) 2.04576 + 1.71660i 0.126387 + 0.106052i
\(263\) −1.67453 9.49671i −0.103256 0.585592i −0.991903 0.127000i \(-0.959465\pi\)
0.888647 0.458592i \(-0.151646\pi\)
\(264\) 4.84002 + 1.76162i 0.297883 + 0.108420i
\(265\) 0 0
\(266\) 6.96926 + 1.82391i 0.427312 + 0.111831i
\(267\) 1.21482 0.0743459
\(268\) −16.3824 5.96270i −1.00071 0.364230i
\(269\) −3.17412 18.0013i −0.193529 1.09756i −0.914498 0.404591i \(-0.867414\pi\)
0.720969 0.692968i \(-0.243697\pi\)
\(270\) 0 0
\(271\) 14.5273 12.1899i 0.882473 0.740483i −0.0842129 0.996448i \(-0.526838\pi\)
0.966686 + 0.255965i \(0.0823932\pi\)
\(272\) 0.0120217 0.0681784i 0.000728923 0.00413393i
\(273\) 2.64543 4.58202i 0.160109 0.277316i
\(274\) −8.59152 14.8809i −0.519033 0.898991i
\(275\) 0 0
\(276\) 1.07873 0.392624i 0.0649317 0.0236332i
\(277\) 6.88191 + 11.9198i 0.413494 + 0.716193i 0.995269 0.0971571i \(-0.0309749\pi\)
−0.581775 + 0.813350i \(0.697642\pi\)
\(278\) 6.76991 11.7258i 0.406033 0.703269i
\(279\) −0.916937 + 5.20021i −0.0548956 + 0.311328i
\(280\) 0 0
\(281\) 10.0437 + 8.42767i 0.599157 + 0.502752i 0.891175 0.453661i \(-0.149882\pi\)
−0.292018 + 0.956413i \(0.594327\pi\)
\(282\) −0.0582480 0.330341i −0.00346862 0.0196715i
\(283\) −16.3293 5.94340i −0.970679 0.353298i −0.192469 0.981303i \(-0.561650\pi\)
−0.778209 + 0.628005i \(0.783872\pi\)
\(284\) 16.8776 1.00150
\(285\) 0 0
\(286\) −15.8726 −0.938565
\(287\) 7.92989 + 2.88624i 0.468087 + 0.170370i
\(288\) 2.65998 + 15.0855i 0.156741 + 0.888921i
\(289\) −10.9304 9.17166i −0.642962 0.539509i
\(290\) 0 0
\(291\) −0.168434 + 0.955234i −0.00987375 + 0.0559968i
\(292\) 4.61081 7.98617i 0.269828 0.467355i
\(293\) 7.80200 + 13.5135i 0.455798 + 0.789465i 0.998734 0.0503091i \(-0.0160206\pi\)
−0.542936 + 0.839774i \(0.682687\pi\)
\(294\) 1.52481 0.554987i 0.0889290 0.0323675i
\(295\) 0 0
\(296\) −1.18820 2.05802i −0.0690625 0.119620i
\(297\) −5.18866 + 8.98703i −0.301077 + 0.521480i
\(298\) 0.575160 3.26189i 0.0333181 0.188956i
\(299\) −7.12836 + 5.98140i −0.412243 + 0.345913i
\(300\) 0 0
\(301\) −1.56670 8.88522i −0.0903033 0.512136i
\(302\) −12.0617 4.39008i −0.694070 0.252621i
\(303\) 4.21482 0.242135
\(304\) −0.128356 + 0.129862i −0.00736170 + 0.00744807i
\(305\) 0 0
\(306\) 3.71048 + 1.35051i 0.212114 + 0.0772033i
\(307\) −3.73695 21.1933i −0.213279 1.20956i −0.883868 0.467736i \(-0.845070\pi\)
0.670589 0.741829i \(-0.266041\pi\)
\(308\) −6.02481 5.05542i −0.343296 0.288059i
\(309\) −0.00592979 + 0.00497568i −0.000337334 + 0.000283057i
\(310\) 0 0
\(311\) −7.24763 + 12.5533i −0.410975 + 0.711830i −0.994997 0.0999083i \(-0.968145\pi\)
0.584021 + 0.811738i \(0.301478\pi\)
\(312\) 3.99407 + 6.91793i 0.226120 + 0.391651i
\(313\) 18.3414 6.67571i 1.03672 0.377334i 0.233081 0.972457i \(-0.425119\pi\)
0.803634 + 0.595124i \(0.202897\pi\)
\(314\) 8.57310 3.12035i 0.483808 0.176092i
\(315\) 0 0
\(316\) −4.27079 + 7.39723i −0.240251 + 0.416127i
\(317\) −4.92246 + 27.9166i −0.276473 + 1.56795i 0.457772 + 0.889070i \(0.348648\pi\)
−0.734245 + 0.678885i \(0.762464\pi\)
\(318\) 2.18866 1.83651i 0.122734 0.102986i
\(319\) −9.06283 7.60462i −0.507421 0.425777i
\(320\) 0 0
\(321\) 1.77719 + 0.646844i 0.0991930 + 0.0361033i
\(322\) 2.90673 0.161986
\(323\) −1.90508 6.94751i −0.106001 0.386570i
\(324\) −8.01279 −0.445155
\(325\) 0 0
\(326\) −0.308811 1.75135i −0.0171035 0.0969985i
\(327\) −3.00387 2.52055i −0.166114 0.139387i
\(328\) −9.76011 + 8.18971i −0.538912 + 0.452201i
\(329\) −0.233956 + 1.32683i −0.0128984 + 0.0731504i
\(330\) 0 0
\(331\) 0.855037 + 1.48097i 0.0469971 + 0.0814014i 0.888567 0.458747i \(-0.151702\pi\)
−0.841570 + 0.540148i \(0.818368\pi\)
\(332\) −2.89615 + 1.05411i −0.158947 + 0.0578520i
\(333\) 2.13816 0.778225i 0.117170 0.0426465i
\(334\) 10.2258 + 17.7116i 0.559531 + 0.969136i
\(335\) 0 0
\(336\) 0.00727396 0.0412527i 0.000396827 0.00225052i
\(337\) −19.4873 + 16.3518i −1.06154 + 0.890737i −0.994259 0.106997i \(-0.965876\pi\)
−0.0672796 + 0.997734i \(0.521432\pi\)
\(338\) −10.1001 8.47502i −0.549375 0.460980i
\(339\) 0.681637 + 3.86576i 0.0370215 + 0.209959i
\(340\) 0 0
\(341\) 6.63041 0.359057
\(342\) −6.02300 8.49584i −0.325687 0.459403i
\(343\) −19.6732 −1.06225
\(344\) 12.8004 + 4.65895i 0.690149 + 0.251194i
\(345\) 0 0
\(346\) 0.604007 + 0.506822i 0.0324716 + 0.0272469i
\(347\) −5.90033 + 4.95096i −0.316746 + 0.265782i −0.787274 0.616604i \(-0.788508\pi\)
0.470527 + 0.882385i \(0.344064\pi\)
\(348\) −0.393056 + 2.22913i −0.0210700 + 0.119494i
\(349\) −11.3785 + 19.7082i −0.609078 + 1.05495i 0.382315 + 0.924032i \(0.375127\pi\)
−0.991393 + 0.130921i \(0.958206\pi\)
\(350\) 0 0
\(351\) −15.1236 + 5.50454i −0.807238 + 0.293811i
\(352\) 18.0744 6.57856i 0.963371 0.350638i
\(353\) −5.72281 9.91220i −0.304595 0.527573i 0.672576 0.740028i \(-0.265188\pi\)
−0.977171 + 0.212454i \(0.931854\pi\)
\(354\) 2.51707 4.35970i 0.133781 0.231715i
\(355\) 0 0
\(356\) 2.14543 1.80023i 0.113708 0.0954120i
\(357\) 1.26604 + 1.06234i 0.0670062 + 0.0562249i
\(358\) 3.25537 + 18.4621i 0.172051 + 0.975752i
\(359\) −9.75789 3.55158i −0.515002 0.187445i 0.0714274 0.997446i \(-0.477245\pi\)
−0.586429 + 0.810000i \(0.699467\pi\)
\(360\) 0 0
\(361\) −6.28968 + 17.9287i −0.331036 + 0.943618i
\(362\) 14.1575 0.744099
\(363\) 0.319078 + 0.116135i 0.0167472 + 0.00609550i
\(364\) −2.11809 12.0123i −0.111018 0.629614i
\(365\) 0 0
\(366\) 1.57326 1.32012i 0.0822358 0.0690040i
\(367\) 5.64930 32.0388i 0.294891 1.67241i −0.372754 0.927930i \(-0.621586\pi\)
0.667645 0.744480i \(-0.267303\pi\)
\(368\) −0.0368366 + 0.0638029i −0.00192024 + 0.00332596i
\(369\) −6.09967 10.5649i −0.317536 0.549989i
\(370\) 0 0
\(371\) −10.7836 + 3.92490i −0.559856 + 0.203771i
\(372\) −0.634285 1.09861i −0.0328862 0.0569605i
\(373\) 15.2429 26.4014i 0.789246 1.36701i −0.137183 0.990546i \(-0.543805\pi\)
0.926429 0.376469i \(-0.122862\pi\)
\(374\) 0.860967 4.88279i 0.0445195 0.252483i
\(375\) 0 0
\(376\) −1.55825 1.30753i −0.0803605 0.0674305i
\(377\) −3.18614 18.0695i −0.164094 0.930626i
\(378\) 4.72416 + 1.71945i 0.242984 + 0.0884391i
\(379\) 17.8598 0.917396 0.458698 0.888592i \(-0.348316\pi\)
0.458698 + 0.888592i \(0.348316\pi\)
\(380\) 0 0
\(381\) −0.0537486 −0.00275363
\(382\) 15.6582 + 5.69913i 0.801144 + 0.291593i
\(383\) 4.07310 + 23.0997i 0.208126 + 1.18034i 0.892445 + 0.451157i \(0.148988\pi\)
−0.684319 + 0.729183i \(0.739900\pi\)
\(384\) −2.78905 2.34029i −0.142328 0.119427i
\(385\) 0 0
\(386\) 1.97013 11.1732i 0.100277 0.568700i
\(387\) −6.52141 + 11.2954i −0.331502 + 0.574178i
\(388\) 1.11809 + 1.93659i 0.0567623 + 0.0983153i
\(389\) −3.67365 + 1.33710i −0.186261 + 0.0677936i −0.433467 0.901169i \(-0.642710\pi\)
0.247206 + 0.968963i \(0.420488\pi\)
\(390\) 0 0
\(391\) −1.45336 2.51730i −0.0734997 0.127305i
\(392\) 4.92009 8.52185i 0.248502 0.430418i
\(393\) 0.280592 1.59132i 0.0141540 0.0802714i
\(394\) −15.6288 + 13.1141i −0.787369 + 0.660681i
\(395\) 0 0
\(396\) 1.97431 + 11.1969i 0.0992127 + 0.562663i
\(397\) 8.41875 + 3.06417i 0.422525 + 0.153786i 0.544527 0.838743i \(-0.316709\pi\)
−0.122002 + 0.992530i \(0.538931\pi\)
\(398\) −8.10936 −0.406486
\(399\) −1.15270 4.20372i −0.0577074 0.210449i
\(400\) 0 0
\(401\) 1.90508 + 0.693392i 0.0951350 + 0.0346263i 0.389149 0.921175i \(-0.372769\pi\)
−0.294014 + 0.955801i \(0.594991\pi\)
\(402\) −1.15476 6.54899i −0.0575943 0.326634i
\(403\) 7.87733 + 6.60986i 0.392398 + 0.329261i
\(404\) 7.44356 6.24589i 0.370331 0.310745i
\(405\) 0 0
\(406\) −2.86571 + 4.96356i −0.142223 + 0.246338i
\(407\) −1.42855 2.47432i −0.0708105 0.122647i
\(408\) −2.34477 + 0.853427i −0.116083 + 0.0422509i
\(409\) 30.2656 11.0158i 1.49654 0.544696i 0.541377 0.840780i \(-0.317903\pi\)
0.955162 + 0.296084i \(0.0956808\pi\)
\(410\) 0 0
\(411\) −5.19846 + 9.00400i −0.256421 + 0.444135i
\(412\) −0.00309887 + 0.0175745i −0.000152670 + 0.000865836i
\(413\) −15.4893 + 12.9971i −0.762180 + 0.639545i
\(414\) −3.21894 2.70101i −0.158202 0.132747i
\(415\) 0 0
\(416\) 28.0317 + 10.2027i 1.37437 + 0.500228i
\(417\) −8.19253 −0.401190
\(418\) −9.19253 + 9.30039i −0.449622 + 0.454897i
\(419\) −23.2499 −1.13583 −0.567916 0.823086i \(-0.692250\pi\)
−0.567916 + 0.823086i \(0.692250\pi\)
\(420\) 0 0
\(421\) 1.12061 + 6.35532i 0.0546154 + 0.309739i 0.999862 0.0166178i \(-0.00528986\pi\)
−0.945246 + 0.326357i \(0.894179\pi\)
\(422\) −9.85117 8.26611i −0.479547 0.402388i
\(423\) 1.49201 1.25195i 0.0725440 0.0608717i
\(424\) 3.00862 17.0627i 0.146111 0.828639i
\(425\) 0 0
\(426\) 3.21894 + 5.57537i 0.155958 + 0.270128i
\(427\) −7.75150 + 2.82131i −0.375121 + 0.136533i
\(428\) 4.09714 1.49124i 0.198043 0.0720817i
\(429\) 4.80200 + 8.31731i 0.231843 + 0.401564i
\(430\) 0 0
\(431\) −2.43061 + 13.7847i −0.117078 + 0.663984i 0.868622 + 0.495475i \(0.165006\pi\)
−0.985700 + 0.168508i \(0.946105\pi\)
\(432\) −0.0976108 + 0.0819052i −0.00469630 + 0.00394067i
\(433\) 21.9800 + 18.4434i 1.05629 + 0.886333i 0.993741 0.111709i \(-0.0356323\pi\)
0.0625499 + 0.998042i \(0.480077\pi\)
\(434\) −0.557781 3.16333i −0.0267744 0.151845i
\(435\) 0 0
\(436\) −9.04013 −0.432944
\(437\) −0.623608 + 7.64090i −0.0298312 + 0.365514i
\(438\) 3.51754 0.168075
\(439\) 12.5376 + 4.56332i 0.598387 + 0.217795i 0.623414 0.781892i \(-0.285745\pi\)
−0.0250271 + 0.999687i \(0.507967\pi\)
\(440\) 0 0
\(441\) 7.21760 + 6.05628i 0.343695 + 0.288394i
\(442\) 5.89053 4.94274i 0.280184 0.235102i
\(443\) −5.88372 + 33.3682i −0.279544 + 1.58537i 0.444603 + 0.895728i \(0.353345\pi\)
−0.724147 + 0.689646i \(0.757766\pi\)
\(444\) −0.273318 + 0.473401i −0.0129711 + 0.0224666i
\(445\) 0 0
\(446\) 2.49108 0.906678i 0.117956 0.0429324i
\(447\) −1.88326 + 0.685449i −0.0890749 + 0.0324206i
\(448\) −4.73783 8.20616i −0.223841 0.387704i
\(449\) −9.42009 + 16.3161i −0.444562 + 0.770003i −0.998022 0.0628725i \(-0.979974\pi\)
0.553460 + 0.832876i \(0.313307\pi\)
\(450\) 0 0
\(451\) −11.7344 + 9.84635i −0.552552 + 0.463646i
\(452\) 6.93242 + 5.81699i 0.326074 + 0.273608i
\(453\) 1.34864 + 7.64852i 0.0633647 + 0.359359i
\(454\) 11.3391 + 4.12711i 0.532172 + 0.193695i
\(455\) 0 0
\(456\) 6.36665 + 1.66620i 0.298146 + 0.0780270i
\(457\) −14.2790 −0.667943 −0.333972 0.942583i \(-0.608389\pi\)
−0.333972 + 0.942583i \(0.608389\pi\)
\(458\) 7.77941 + 2.83147i 0.363508 + 0.132306i
\(459\) −0.872989 4.95096i −0.0407476 0.231091i
\(460\) 0 0
\(461\) −10.6695 + 8.95280i −0.496930 + 0.416973i −0.856502 0.516144i \(-0.827367\pi\)
0.359572 + 0.933117i \(0.382923\pi\)
\(462\) 0.520945 2.95442i 0.0242365 0.137452i
\(463\) −0.881445 + 1.52671i −0.0409642 + 0.0709521i −0.885781 0.464104i \(-0.846376\pi\)
0.844816 + 0.535056i \(0.179710\pi\)
\(464\) −0.0726338 0.125805i −0.00337194 0.00584037i
\(465\) 0 0
\(466\) 19.9859 7.27428i 0.925830 0.336974i
\(467\) 11.0209 + 19.0888i 0.509988 + 0.883326i 0.999933 + 0.0115724i \(0.00368368\pi\)
−0.489945 + 0.871754i \(0.662983\pi\)
\(468\) −8.81655 + 15.2707i −0.407545 + 0.705889i
\(469\) −4.63816 + 26.3043i −0.214170 + 1.21462i
\(470\) 0 0
\(471\) −4.22874 3.54834i −0.194850 0.163499i
\(472\) −5.30113 30.0642i −0.244004 1.38382i
\(473\) 15.3897 + 5.60138i 0.707617 + 0.257552i
\(474\) −3.25814 −0.149651
\(475\) 0 0
\(476\) 3.81016 0.174638
\(477\) 15.5890 + 5.67393i 0.713771 + 0.259791i
\(478\) 3.56196 + 20.2009i 0.162920 + 0.923966i
\(479\) −19.5012 16.3634i −0.891032 0.747664i 0.0773851 0.997001i \(-0.475343\pi\)
−0.968417 + 0.249337i \(0.919787\pi\)
\(480\) 0 0
\(481\) 0.769448 4.36376i 0.0350838 0.198970i
\(482\) 0.130882 0.226694i 0.00596150 0.0103256i
\(483\) −0.879385 1.52314i −0.0400134 0.0693053i
\(484\) 0.735604 0.267738i 0.0334366 0.0121699i
\(485\) 0 0
\(486\) −5.54071 9.59679i −0.251332 0.435319i
\(487\) −11.2554 + 19.4949i −0.510029 + 0.883397i 0.489903 + 0.871777i \(0.337032\pi\)
−0.999932 + 0.0116199i \(0.996301\pi\)
\(488\) 2.16267 12.2651i 0.0978993 0.555214i
\(489\) −0.824292 + 0.691663i −0.0372758 + 0.0312781i
\(490\) 0 0
\(491\) 2.71482 + 15.3965i 0.122518 + 0.694835i 0.982751 + 0.184934i \(0.0592071\pi\)
−0.860233 + 0.509902i \(0.829682\pi\)
\(492\) 2.75402 + 1.00238i 0.124161 + 0.0451909i
\(493\) 5.73143 0.258131
\(494\) −20.1928 + 1.88538i −0.908519 + 0.0848274i
\(495\) 0 0
\(496\) 0.0765042 + 0.0278452i 0.00343514 + 0.00125029i
\(497\) −4.49020 25.4652i −0.201413 1.14227i
\(498\) −0.900578 0.755675i −0.0403559 0.0338626i
\(499\) −21.9217 + 18.3945i −0.981352 + 0.823452i −0.984293 0.176544i \(-0.943508\pi\)
0.00294090 + 0.999996i \(0.499064\pi\)
\(500\) 0 0
\(501\) 6.18732 10.7168i 0.276429 0.478789i
\(502\) −7.12196 12.3356i −0.317869 0.550565i
\(503\) −23.5351 + 8.56607i −1.04938 + 0.381942i −0.808428 0.588595i \(-0.799681\pi\)
−0.240950 + 0.970538i \(0.577459\pi\)
\(504\) 13.6147 4.95534i 0.606446 0.220728i
\(505\) 0 0
\(506\) −2.63816 + 4.56942i −0.117280 + 0.203135i
\(507\) −1.38532 + 7.85651i −0.0615240 + 0.348920i
\(508\) −0.0949225 + 0.0796494i −0.00421150 + 0.00353387i
\(509\) 25.6787 + 21.5470i 1.13819 + 0.955053i 0.999378 0.0352655i \(-0.0112277\pi\)
0.138810 + 0.990319i \(0.455672\pi\)
\(510\) 0 0
\(511\) −13.2763 4.83218i −0.587309 0.213763i
\(512\) 0.473897 0.0209435
\(513\) −5.53343 + 12.0495i −0.244307 + 0.531997i
\(514\) 13.5030 0.595591
\(515\) 0 0
\(516\) −0.544111 3.08580i −0.0239531 0.135845i
\(517\) −1.87346 1.57202i −0.0823945 0.0691372i
\(518\) −1.06031 + 0.889704i −0.0465872 + 0.0390913i
\(519\) 0.0828445 0.469834i 0.00363647 0.0206234i
\(520\) 0 0
\(521\) 13.7392 + 23.7969i 0.601924 + 1.04256i 0.992530 + 0.122005i \(0.0389323\pi\)
−0.390606 + 0.920558i \(0.627734\pi\)
\(522\) 7.78581 2.83380i 0.340776 0.124032i
\(523\) −9.73277 + 3.54244i −0.425584 + 0.154900i −0.545928 0.837832i \(-0.683823\pi\)
0.120343 + 0.992732i \(0.461600\pi\)
\(524\) −1.86262 3.22615i −0.0813687 0.140935i
\(525\) 0 0
\(526\) 1.47255 8.35126i 0.0642064 0.364132i
\(527\) −2.46064 + 2.06472i −0.107187 + 0.0899406i
\(528\) 0.0582480 + 0.0488759i 0.00253492 + 0.00212705i
\(529\) −3.45677 19.6043i −0.150294 0.852361i
\(530\) 0 0
\(531\) 29.2303 1.26849
\(532\) −8.26517 5.71578i −0.358340 0.247811i
\(533\) −23.7570 −1.02903
\(534\) 1.00387 + 0.365379i 0.0434417 + 0.0158115i
\(535\) 0 0
\(536\) −30.8922 25.9216i −1.33434 1.11964i
\(537\) 8.68938 7.29125i 0.374974 0.314641i
\(538\) 2.79127 15.8301i 0.120340 0.682483i
\(539\) 5.91534 10.2457i 0.254792 0.441313i
\(540\) 0 0
\(541\) −2.37211 + 0.863378i −0.101985 + 0.0371195i −0.392509 0.919748i \(-0.628393\pi\)
0.290524 + 0.956868i \(0.406170\pi\)
\(542\) 15.6710 5.70378i 0.673128 0.244998i
\(543\) −4.28312 7.41858i −0.183806 0.318362i
\(544\) −4.65910 + 8.06980i −0.199757 + 0.345990i
\(545\) 0 0
\(546\) 3.56418 2.99070i 0.152533 0.127990i
\(547\) −5.87939 4.93339i −0.251384 0.210937i 0.508384 0.861131i \(-0.330243\pi\)
−0.759768 + 0.650194i \(0.774688\pi\)
\(548\) 4.16220 + 23.6050i 0.177800 + 1.00836i
\(549\) 11.2057 + 4.07855i 0.478249 + 0.174068i
\(550\) 0 0
\(551\) −12.4329 8.59797i −0.529659 0.366286i
\(552\) 2.65539 0.113021
\(553\) 12.2973 + 4.47584i 0.522933 + 0.190332i
\(554\) 2.10179 + 11.9198i 0.0892963 + 0.506425i
\(555\) 0 0
\(556\) −14.4684 + 12.1404i −0.613596 + 0.514868i
\(557\) −0.565360 + 3.20631i −0.0239551 + 0.135856i −0.994440 0.105307i \(-0.966418\pi\)
0.970485 + 0.241163i \(0.0775287\pi\)
\(558\) −2.32177 + 4.02142i −0.0982882 + 0.170240i
\(559\) 12.6998 + 21.9967i 0.537145 + 0.930362i
\(560\) 0 0
\(561\) −2.81908 + 1.02606i −0.119022 + 0.0433203i
\(562\) 5.76486 + 9.98503i 0.243176 + 0.421193i
\(563\) 2.62954 4.55449i 0.110822 0.191949i −0.805280 0.592895i \(-0.797985\pi\)
0.916102 + 0.400946i \(0.131318\pi\)
\(564\) −0.0812519 + 0.460802i −0.00342132 + 0.0194033i
\(565\) 0 0
\(566\) −11.7062 9.82267i −0.492048 0.412878i
\(567\) 2.13176 + 12.0898i 0.0895255 + 0.507724i
\(568\) 36.6860 + 13.3526i 1.53931 + 0.560264i
\(569\) −29.9564 −1.25584 −0.627918 0.778280i \(-0.716093\pi\)
−0.627918 + 0.778280i \(0.716093\pi\)
\(570\) 0 0
\(571\) −16.7101 −0.699295 −0.349647 0.936881i \(-0.613699\pi\)
−0.349647 + 0.936881i \(0.613699\pi\)
\(572\) 20.8059 + 7.57272i 0.869937 + 0.316631i
\(573\) −1.75078 9.92917i −0.0731399 0.414797i
\(574\) 5.68479 + 4.77011i 0.237279 + 0.199100i
\(575\) 0 0
\(576\) −2.37867 + 13.4901i −0.0991113 + 0.562088i
\(577\) −6.84002 + 11.8473i −0.284754 + 0.493208i −0.972549 0.232696i \(-0.925245\pi\)
0.687796 + 0.725904i \(0.258579\pi\)
\(578\) −6.27379 10.8665i −0.260955 0.451987i
\(579\) −6.45084 + 2.34791i −0.268088 + 0.0975759i
\(580\) 0 0
\(581\) 2.36097 + 4.08931i 0.0979494 + 0.169653i
\(582\) −0.426489 + 0.738700i −0.0176785 + 0.0306201i
\(583\) 3.61721 20.5142i 0.149810 0.849612i
\(584\) 16.3405 13.7113i 0.676174 0.567378i
\(585\) 0 0
\(586\) 2.38279 + 13.5135i 0.0984321 + 0.558236i
\(587\) −22.5872 8.22108i −0.932275 0.339320i −0.169164 0.985588i \(-0.554107\pi\)
−0.763111 + 0.646268i \(0.776329\pi\)
\(588\) −2.26352 −0.0933459
\(589\) 8.43511 0.787576i 0.347563 0.0324515i
\(590\) 0 0
\(591\) 11.6001 + 4.22210i 0.477166 + 0.173674i
\(592\) −0.00609191 0.0345490i −0.000250376 0.00141995i
\(593\) 3.24897 + 2.72621i 0.133419 + 0.111952i 0.707055 0.707158i \(-0.250023\pi\)
−0.573636 + 0.819110i \(0.694468\pi\)
\(594\) −6.99067 + 5.86587i −0.286831 + 0.240679i
\(595\) 0 0
\(596\) −2.31016 + 4.00131i −0.0946276 + 0.163900i
\(597\) 2.45336 + 4.24935i 0.100409 + 0.173914i
\(598\) −7.68954 + 2.79876i −0.314449 + 0.114450i
\(599\) 24.6894 8.98622i 1.00878 0.367167i 0.215818 0.976434i \(-0.430758\pi\)
0.792965 + 0.609267i \(0.208536\pi\)
\(600\) 0 0
\(601\) 21.1197 36.5805i 0.861492 1.49215i −0.00899659 0.999960i \(-0.502864\pi\)
0.870489 0.492188i \(-0.163803\pi\)
\(602\) 1.37774 7.81353i 0.0561523 0.318456i
\(603\) 29.5790 24.8198i 1.20455 1.01074i
\(604\) 13.7160 + 11.5091i 0.558096 + 0.468298i
\(605\) 0 0
\(606\) 3.48293 + 1.26768i 0.141484 + 0.0514960i
\(607\) 22.0969 0.896885 0.448443 0.893812i \(-0.351979\pi\)
0.448443 + 0.893812i \(0.351979\pi\)
\(608\) 22.2126 10.5161i 0.900840 0.426483i
\(609\) 3.46791 0.140527
\(610\) 0 0
\(611\) −0.658633 3.73530i −0.0266455 0.151114i
\(612\) −4.21941 3.54050i −0.170559 0.143116i
\(613\) −5.49794 + 4.61332i −0.222060 + 0.186330i −0.747030 0.664790i \(-0.768521\pi\)
0.524970 + 0.851121i \(0.324076\pi\)
\(614\) 3.28622 18.6371i 0.132621 0.752131i
\(615\) 0 0
\(616\) −9.09627 15.7552i −0.366499 0.634795i
\(617\) −46.3953 + 16.8865i −1.86781 + 0.679826i −0.895995 + 0.444065i \(0.853536\pi\)
−0.971811 + 0.235761i \(0.924242\pi\)
\(618\) −0.00639661 + 0.00232818i −0.000257310 + 9.36530e-5i
\(619\) −13.2490 22.9479i −0.532521 0.922354i −0.999279 0.0379684i \(-0.987911\pi\)
0.466758 0.884385i \(-0.345422\pi\)
\(620\) 0 0
\(621\) −0.929015 + 5.26871i −0.0372801 + 0.211426i
\(622\) −9.76470 + 8.19356i −0.391529 + 0.328532i
\(623\) −3.28699 2.75811i −0.131690 0.110501i
\(624\) 0.0204777 + 0.116135i 0.000819764 + 0.00464911i
\(625\) 0 0
\(626\) 17.1643 0.686022
\(627\) 7.65451 + 2.00324i 0.305692 + 0.0800019i
\(628\) −12.7264 −0.507838
\(629\) 1.30066 + 0.473401i 0.0518607 + 0.0188757i
\(630\) 0 0
\(631\) 25.5253 + 21.4183i 1.01615 + 0.852647i 0.989138 0.146988i \(-0.0469579\pi\)
0.0270071 + 0.999635i \(0.491402\pi\)
\(632\) −15.1355 + 12.7002i −0.602057 + 0.505185i
\(633\) −1.35117 + 7.66285i −0.0537041 + 0.304571i
\(634\) −12.4641 + 21.5884i −0.495013 + 0.857387i
\(635\) 0 0
\(636\) −3.74510 + 1.36310i −0.148503 + 0.0540506i
\(637\) 17.2417 6.27546i 0.683141 0.248643i
\(638\) −5.20187 9.00990i −0.205944 0.356705i
\(639\) −18.6905 + 32.3729i −0.739384 + 1.28065i
\(640\) 0 0
\(641\) −0.104256 + 0.0874810i −0.00411786 + 0.00345529i −0.644844 0.764314i \(-0.723078\pi\)
0.640726 + 0.767769i \(0.278633\pi\)
\(642\) 1.27403 + 1.06904i 0.0502821 + 0.0421917i
\(643\) −8.36602 47.4461i −0.329924 1.87109i −0.472536 0.881311i \(-0.656661\pi\)
0.142613 0.989779i \(-0.454450\pi\)
\(644\) −3.81016 1.38678i −0.150141 0.0546469i
\(645\) 0 0
\(646\) 0.515319 6.31407i 0.0202750 0.248424i
\(647\) 36.9718 1.45351 0.726756 0.686895i \(-0.241027\pi\)
0.726756 + 0.686895i \(0.241027\pi\)
\(648\) −17.4170 6.33927i −0.684204 0.249030i
\(649\) −6.37346 36.1457i −0.250180 1.41884i
\(650\) 0 0
\(651\) −1.48886 + 1.24930i −0.0583529 + 0.0489639i
\(652\) −0.430770 + 2.44302i −0.0168702 + 0.0956759i
\(653\) 13.5000 23.3827i 0.528296 0.915035i −0.471160 0.882048i \(-0.656165\pi\)
0.999456 0.0329874i \(-0.0105021\pi\)
\(654\) −1.72416 2.98632i −0.0674198 0.116775i
\(655\) 0 0
\(656\) −0.176747 + 0.0643307i −0.00690081 + 0.00251169i
\(657\) 10.2121 + 17.6879i 0.398413 + 0.690072i
\(658\) −0.592396 + 1.02606i −0.0230940 + 0.0400000i
\(659\) 3.27760 18.5882i 0.127677 0.724093i −0.852005 0.523534i \(-0.824613\pi\)
0.979682 0.200559i \(-0.0642757\pi\)
\(660\) 0 0
\(661\) −23.4500 19.6769i −0.912098 0.765341i 0.0604192 0.998173i \(-0.480756\pi\)
−0.972517 + 0.232832i \(0.925201\pi\)
\(662\) 0.261135 + 1.48097i 0.0101493 + 0.0575594i
\(663\) −4.37211 1.59132i −0.169799 0.0618017i
\(664\) −7.12918 −0.276666
\(665\) 0 0
\(666\) 2.00093 0.0775346
\(667\) −5.73143 2.08607i −0.221922 0.0807729i
\(668\) −4.95394 28.0952i −0.191674 1.08703i
\(669\) −1.22874 1.03104i −0.0475059 0.0398622i
\(670\) 0 0
\(671\) 2.60014 14.7461i 0.100377 0.569267i
\(672\) −2.81908 + 4.88279i −0.108748 + 0.188358i
\(673\) 5.95471 + 10.3139i 0.229537 + 0.397570i 0.957671 0.287865i \(-0.0929454\pi\)
−0.728134 + 0.685435i \(0.759612\pi\)
\(674\) −21.0214 + 7.65117i −0.809715 + 0.294712i
\(675\) 0 0
\(676\) 9.19594 + 15.9278i 0.353690 + 0.612609i
\(677\) 2.89053 5.00654i 0.111092 0.192417i −0.805119 0.593114i \(-0.797898\pi\)
0.916211 + 0.400696i \(0.131232\pi\)
\(678\) −0.599422 + 3.39949i −0.0230207 + 0.130557i
\(679\) 2.62449 2.20220i 0.100718 0.0845129i
\(680\) 0 0
\(681\) −1.26786 7.19037i −0.0485843 0.275535i
\(682\) 5.47906 + 1.99421i 0.209804 + 0.0763624i
\(683\) −21.0496 −0.805442 −0.402721 0.915323i \(-0.631935\pi\)
−0.402721 + 0.915323i \(0.631935\pi\)
\(684\) 3.84167 + 14.0099i 0.146890 + 0.535684i
\(685\) 0 0
\(686\) −16.2570 5.91707i −0.620696 0.225915i
\(687\) −0.869833 4.93307i −0.0331862 0.188208i
\(688\) 0.154048 + 0.129261i 0.00587302 + 0.00492805i
\(689\) 24.7481 20.7661i 0.942827 0.791126i
\(690\) 0 0
\(691\) 16.4688 28.5249i 0.626504 1.08514i −0.361744 0.932278i \(-0.617818\pi\)
0.988248 0.152860i \(-0.0488483\pi\)
\(692\) −0.549935 0.952515i −0.0209054 0.0362092i
\(693\) 16.3687 5.95772i 0.621796 0.226315i
\(694\) −6.36484 + 2.31661i −0.241606 + 0.0879374i
\(695\) 0 0
\(696\) −2.61793 + 4.53438i −0.0992322 + 0.171875i
\(697\) 1.28864 7.30823i 0.0488106 0.276819i
\(698\) −15.3302 + 12.8636i −0.580257 + 0.486894i
\(699\) −9.85819 8.27201i −0.372871 0.312876i
\(700\) 0 0
\(701\) −20.0694 7.30466i −0.758010 0.275893i −0.0660380 0.997817i \(-0.521036\pi\)
−0.691973 + 0.721924i \(0.743258\pi\)
\(702\) −14.1530 −0.534171
\(703\) −2.11128 2.97810i −0.0796285 0.112321i
\(704\) 17.2003 0.648260
\(705\) 0 0
\(706\) −1.74779 9.91220i −0.0657789 0.373051i
\(707\) −11.4042 9.56926i −0.428899 0.359889i
\(708\) −5.37939 + 4.51384i −0.202170 + 0.169641i
\(709\) −2.73854 + 15.5310i −0.102848 + 0.583280i 0.889210 + 0.457499i \(0.151255\pi\)
−0.992058 + 0.125781i \(0.959856\pi\)
\(710\) 0 0
\(711\) −9.45904 16.3835i −0.354742 0.614431i
\(712\) 6.08765 2.21572i 0.228144 0.0830377i
\(713\) 3.21213 1.16912i 0.120295 0.0437839i
\(714\) 0.726682 + 1.25865i 0.0271954 + 0.0471038i
\(715\) 0 0
\(716\) 4.54101 25.7534i 0.169706 0.962448i
\(717\) 9.50774 7.97794i 0.355073 0.297942i
\(718\) −6.99525 5.86971i −0.261060 0.219056i
\(719\) −6.13470 34.7916i −0.228786 1.29751i −0.855314 0.518109i \(-0.826636\pi\)
0.626529 0.779398i \(-0.284475\pi\)
\(720\) 0 0
\(721\) 0.0273411 0.00101824
\(722\) −10.5899 + 12.9237i −0.394114 + 0.480971i
\(723\) −0.158385 −0.00589040
\(724\) −18.5577 6.75444i −0.689691 0.251027i
\(725\) 0 0
\(726\) 0.228741 + 0.191936i 0.00848937 + 0.00712343i
\(727\) −30.9647 + 25.9825i −1.14842 + 0.963637i −0.999681 0.0252396i \(-0.991965\pi\)
−0.148737 + 0.988877i \(0.547521\pi\)
\(728\) 4.89945 27.7862i 0.181586 1.02982i
\(729\) 6.44562 11.1641i 0.238727 0.413487i
\(730\) 0 0
\(731\) −7.45558 + 2.71361i −0.275755 + 0.100367i
\(732\) −2.69207 + 0.979832i −0.0995016 + 0.0362156i
\(733\) −18.1382 31.4162i −0.669948 1.16038i −0.977918 0.208988i \(-0.932983\pi\)
0.307970 0.951396i \(-0.400350\pi\)
\(734\) 14.3045 24.7762i 0.527990 0.914505i
\(735\) 0 0
\(736\) 7.59627 6.37402i 0.280002 0.234950i
\(737\) −37.1411 31.1651i −1.36811 1.14798i
\(738\) −1.86288 10.5649i −0.0685737 0.388901i
\(739\) 19.4290 + 7.07158i 0.714708 + 0.260132i 0.673677 0.739026i \(-0.264714\pi\)
0.0410304 + 0.999158i \(0.486936\pi\)
\(740\) 0 0
\(741\) 7.09698 + 10.0108i 0.260714 + 0.367754i
\(742\) −10.0915 −0.370471
\(743\) 6.29978 + 2.29293i 0.231117 + 0.0841196i 0.454982 0.890500i \(-0.349646\pi\)
−0.223866 + 0.974620i \(0.571868\pi\)
\(744\) −0.509552 2.88981i −0.0186811 0.105946i
\(745\) 0 0
\(746\) 20.5367 17.2323i 0.751901 0.630920i
\(747\) 1.18535 6.72243i 0.0433695 0.245961i
\(748\) −3.45811 + 5.98962i −0.126441 + 0.219002i
\(749\) −3.34002 5.78509i −0.122042 0.211383i
\(750\) 0 0
\(751\) −10.0617 + 3.66214i −0.367155 + 0.133633i −0.519007 0.854770i \(-0.673698\pi\)
0.151853 + 0.988403i \(0.451476\pi\)
\(752\) −0.0150147 0.0260063i −0.000547531 0.000948352i
\(753\) −4.30928 + 7.46389i −0.157039 + 0.271999i
\(754\) 2.80184 15.8900i 0.102037 0.578681i
\(755\) 0 0
\(756\) −5.37211 4.50774i −0.195382 0.163945i
\(757\) 0.705432 + 4.00071i 0.0256394 + 0.145408i 0.994940 0.100470i \(-0.0320347\pi\)
−0.969301 + 0.245878i \(0.920924\pi\)
\(758\) 14.7585 + 5.37164i 0.536052 + 0.195107i
\(759\) 3.19253 0.115882
\(760\) 0 0
\(761\) −11.0077 −0.399030 −0.199515 0.979895i \(-0.563937\pi\)
−0.199515 + 0.979895i \(0.563937\pi\)
\(762\) −0.0444153 0.0161658i −0.00160900 0.000585627i
\(763\) 2.40508 + 13.6399i 0.0870697 + 0.493797i
\(764\) −17.8059 14.9409i −0.644194 0.540543i
\(765\) 0 0
\(766\) −3.58182 + 20.3135i −0.129417 + 0.733958i
\(767\) 28.4616 49.2969i 1.02769 1.78001i
\(768\) −4.28359 7.41939i −0.154571 0.267724i
\(769\) −20.0599 + 7.30121i −0.723378 + 0.263288i −0.677359 0.735652i \(-0.736876\pi\)
−0.0460191 + 0.998941i \(0.514654\pi\)
\(770\) 0 0
\(771\) −4.08512 7.07564i −0.147122 0.254823i
\(772\) −7.91312 + 13.7059i −0.284800 + 0.493287i
\(773\) −3.11128 + 17.6450i −0.111905 + 0.634645i 0.876331 + 0.481709i \(0.159984\pi\)
−0.988236 + 0.152936i \(0.951127\pi\)
\(774\) −8.78627 + 7.37256i −0.315816 + 0.265001i
\(775\) 0 0
\(776\) 0.898214 + 5.09403i 0.0322440 + 0.182865i
\(777\) 0.786989 + 0.286441i 0.0282331 + 0.0102760i
\(778\) −3.43788 −0.123254