Properties

Label 349.2.e.a.123.6
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.6
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.71754 + 0.991624i) q^{2} +(-1.29117 + 2.23637i) q^{3} +(0.966636 - 1.67426i) q^{4} +(-0.796466 + 1.37952i) q^{5} -5.12141i q^{6} +(-1.81826 + 1.04977i) q^{7} -0.132337i q^{8} +(-1.83422 - 3.17696i) q^{9} +O(q^{10})\) \(q+(-1.71754 + 0.991624i) q^{2} +(-1.29117 + 2.23637i) q^{3} +(0.966636 - 1.67426i) q^{4} +(-0.796466 + 1.37952i) q^{5} -5.12141i q^{6} +(-1.81826 + 1.04977i) q^{7} -0.132337i q^{8} +(-1.83422 - 3.17696i) q^{9} -3.15918i q^{10} -2.83760i q^{11} +(2.49618 + 4.32350i) q^{12} +(-3.23077 + 1.86529i) q^{13} +(2.08196 - 3.60606i) q^{14} +(-2.05674 - 3.56238i) q^{15} +(2.06450 + 3.57582i) q^{16} -1.69939 q^{17} +(6.30071 + 3.63771i) q^{18} +(0.686145 - 1.18844i) q^{19} +(1.53979 + 2.66699i) q^{20} -5.42173i q^{21} +(2.81384 + 4.87371i) q^{22} +(0.0635168 + 0.110014i) q^{23} +(0.295953 + 0.170869i) q^{24} +(1.23128 + 2.13265i) q^{25} +(3.69933 - 6.40742i) q^{26} +1.72614 q^{27} +4.05899i q^{28} +(0.829833 - 1.43731i) q^{29} +(7.06508 + 4.07903i) q^{30} +1.80717 q^{31} +(-6.86253 - 3.96208i) q^{32} +(6.34592 + 3.66382i) q^{33} +(2.91877 - 1.68516i) q^{34} -3.34443i q^{35} -7.09210 q^{36} +4.87375 q^{37} +2.72159i q^{38} -9.63358i q^{39} +(0.182561 + 0.105402i) q^{40} -0.265830 q^{41} +(5.37631 + 9.31205i) q^{42} +(5.78504 + 3.34000i) q^{43} +(-4.75089 - 2.74293i) q^{44} +5.84358 q^{45} +(-0.218186 - 0.125970i) q^{46} -7.15836i q^{47} -10.6625 q^{48} +(-1.29595 + 2.24466i) q^{49} +(-4.22956 - 2.44194i) q^{50} +(2.19419 - 3.80046i) q^{51} +7.21222i q^{52} -3.20421i q^{53} +(-2.96472 + 1.71168i) q^{54} +(3.91453 + 2.26005i) q^{55} +(0.138923 + 0.240622i) q^{56} +(1.77185 + 3.06894i) q^{57} +3.29153i q^{58} +(-9.87848 - 5.70335i) q^{59} -7.95248 q^{60} -6.52140i q^{61} +(-3.10389 + 1.79203i) q^{62} +(6.67018 + 3.85103i) q^{63} +7.45757 q^{64} -5.94255i q^{65} -14.5325 q^{66} -12.8875 q^{67} +(-1.64269 + 2.84522i) q^{68} -0.328043 q^{69} +(3.31642 + 5.74421i) q^{70} +(-6.82502 + 3.94043i) q^{71} +(-0.420428 + 0.242734i) q^{72} +(-7.79947 + 13.5091i) q^{73} +(-8.37087 + 4.83293i) q^{74} -6.35917 q^{75} +(-1.32651 - 2.29757i) q^{76} +(2.97884 + 5.15950i) q^{77} +(9.55289 + 16.5461i) q^{78} -13.1287i q^{79} -6.57722 q^{80} +(3.27393 - 5.67061i) q^{81} +(0.456574 - 0.263603i) q^{82} +(-7.22933 - 12.5216i) q^{83} +(-9.07740 - 5.24084i) q^{84} +(1.35351 - 2.34434i) q^{85} -13.2481 q^{86} +(2.14291 + 3.71162i) q^{87} -0.375519 q^{88} +(5.33906 + 3.08251i) q^{89} +(-10.0366 + 5.79463i) q^{90} +(3.91625 - 6.78315i) q^{91} +0.245591 q^{92} +(-2.33335 + 4.04149i) q^{93} +(7.09840 + 12.2948i) q^{94} +(1.09298 + 1.89310i) q^{95} +(17.7213 - 10.2314i) q^{96} +(-4.25334 + 2.45566i) q^{97} -5.14040i q^{98} +(-9.01496 + 5.20479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.71754 + 0.991624i −1.21449 + 0.701184i −0.963733 0.266867i \(-0.914012\pi\)
−0.250753 + 0.968051i \(0.580678\pi\)
\(3\) −1.29117 + 2.23637i −0.745455 + 1.29117i 0.204527 + 0.978861i \(0.434435\pi\)
−0.949982 + 0.312305i \(0.898899\pi\)
\(4\) 0.966636 1.67426i 0.483318 0.837132i
\(5\) −0.796466 + 1.37952i −0.356190 + 0.616940i −0.987321 0.158737i \(-0.949258\pi\)
0.631130 + 0.775677i \(0.282591\pi\)
\(6\) 5.12141i 2.09081i
\(7\) −1.81826 + 1.04977i −0.687238 + 0.396777i −0.802576 0.596549i \(-0.796538\pi\)
0.115339 + 0.993326i \(0.463205\pi\)
\(8\) 0.132337i 0.0467880i
\(9\) −1.83422 3.17696i −0.611407 1.05899i
\(10\) 3.15918i 0.999020i
\(11\) 2.83760i 0.855569i −0.903881 0.427785i \(-0.859294\pi\)
0.903881 0.427785i \(-0.140706\pi\)
\(12\) 2.49618 + 4.32350i 0.720584 + 1.24809i
\(13\) −3.23077 + 1.86529i −0.896055 + 0.517337i −0.875918 0.482460i \(-0.839743\pi\)
−0.0201366 + 0.999797i \(0.506410\pi\)
\(14\) 2.08196 3.60606i 0.556427 0.963760i
\(15\) −2.05674 3.56238i −0.531048 0.919802i
\(16\) 2.06450 + 3.57582i 0.516125 + 0.893955i
\(17\) −1.69939 −0.412162 −0.206081 0.978535i \(-0.566071\pi\)
−0.206081 + 0.978535i \(0.566071\pi\)
\(18\) 6.30071 + 3.63771i 1.48509 + 0.857418i
\(19\) 0.686145 1.18844i 0.157412 0.272646i −0.776522 0.630090i \(-0.783018\pi\)
0.933935 + 0.357443i \(0.116351\pi\)
\(20\) 1.53979 + 2.66699i 0.344307 + 0.596357i
\(21\) 5.42173i 1.18312i
\(22\) 2.81384 + 4.87371i 0.599912 + 1.03908i
\(23\) 0.0635168 + 0.110014i 0.0132442 + 0.0229396i 0.872572 0.488486i \(-0.162451\pi\)
−0.859327 + 0.511426i \(0.829117\pi\)
\(24\) 0.295953 + 0.170869i 0.0604111 + 0.0348784i
\(25\) 1.23128 + 2.13265i 0.246257 + 0.426529i
\(26\) 3.69933 6.40742i 0.725498 1.25660i
\(27\) 1.72614 0.332195
\(28\) 4.05899i 0.767078i
\(29\) 0.829833 1.43731i 0.154096 0.266902i −0.778633 0.627479i \(-0.784087\pi\)
0.932730 + 0.360577i \(0.117420\pi\)
\(30\) 7.06508 + 4.07903i 1.28990 + 0.744725i
\(31\) 1.80717 0.324577 0.162288 0.986743i \(-0.448113\pi\)
0.162288 + 0.986743i \(0.448113\pi\)
\(32\) −6.86253 3.96208i −1.21313 0.700404i
\(33\) 6.34592 + 3.66382i 1.10468 + 0.637789i
\(34\) 2.91877 1.68516i 0.500566 0.289002i
\(35\) 3.34443i 0.565313i
\(36\) −7.09210 −1.18202
\(37\) 4.87375 0.801239 0.400620 0.916244i \(-0.368795\pi\)
0.400620 + 0.916244i \(0.368795\pi\)
\(38\) 2.72159i 0.441500i
\(39\) 9.63358i 1.54261i
\(40\) 0.182561 + 0.105402i 0.0288654 + 0.0166655i
\(41\) −0.265830 −0.0415157 −0.0207578 0.999785i \(-0.506608\pi\)
−0.0207578 + 0.999785i \(0.506608\pi\)
\(42\) 5.37631 + 9.31205i 0.829583 + 1.43688i
\(43\) 5.78504 + 3.34000i 0.882211 + 0.509345i 0.871387 0.490597i \(-0.163221\pi\)
0.0108241 + 0.999941i \(0.496555\pi\)
\(44\) −4.75089 2.74293i −0.716224 0.413512i
\(45\) 5.84358 0.871109
\(46\) −0.218186 0.125970i −0.0321698 0.0185732i
\(47\) 7.15836i 1.04415i −0.852898 0.522077i \(-0.825157\pi\)
0.852898 0.522077i \(-0.174843\pi\)
\(48\) −10.6625 −1.53899
\(49\) −1.29595 + 2.24466i −0.185136 + 0.320665i
\(50\) −4.22956 2.44194i −0.598151 0.345342i
\(51\) 2.19419 3.80046i 0.307249 0.532170i
\(52\) 7.21222i 1.00015i
\(53\) 3.20421i 0.440132i −0.975485 0.220066i \(-0.929373\pi\)
0.975485 0.220066i \(-0.0706273\pi\)
\(54\) −2.96472 + 1.71168i −0.403447 + 0.232930i
\(55\) 3.91453 + 2.26005i 0.527835 + 0.304746i
\(56\) 0.138923 + 0.240622i 0.0185644 + 0.0321545i
\(57\) 1.77185 + 3.06894i 0.234688 + 0.406491i
\(58\) 3.29153i 0.432199i
\(59\) −9.87848 5.70335i −1.28607 0.742512i −0.308118 0.951348i \(-0.599699\pi\)
−0.977951 + 0.208836i \(0.933033\pi\)
\(60\) −7.95248 −1.02666
\(61\) 6.52140i 0.834980i −0.908682 0.417490i \(-0.862910\pi\)
0.908682 0.417490i \(-0.137090\pi\)
\(62\) −3.10389 + 1.79203i −0.394194 + 0.227588i
\(63\) 6.67018 + 3.85103i 0.840364 + 0.485184i
\(64\) 7.45757 0.932197
\(65\) 5.94255i 0.737083i
\(66\) −14.5325 −1.78883
\(67\) −12.8875 −1.57446 −0.787228 0.616662i \(-0.788485\pi\)
−0.787228 + 0.616662i \(0.788485\pi\)
\(68\) −1.64269 + 2.84522i −0.199206 + 0.345034i
\(69\) −0.328043 −0.0394918
\(70\) 3.31642 + 5.74421i 0.396388 + 0.686564i
\(71\) −6.82502 + 3.94043i −0.809981 + 0.467643i −0.846949 0.531674i \(-0.821563\pi\)
0.0369681 + 0.999316i \(0.488230\pi\)
\(72\) −0.420428 + 0.242734i −0.0495480 + 0.0286065i
\(73\) −7.79947 + 13.5091i −0.912859 + 1.58112i −0.102852 + 0.994697i \(0.532797\pi\)
−0.810006 + 0.586421i \(0.800536\pi\)
\(74\) −8.37087 + 4.83293i −0.973094 + 0.561816i
\(75\) −6.35917 −0.734293
\(76\) −1.32651 2.29757i −0.152161 0.263550i
\(77\) 2.97884 + 5.15950i 0.339470 + 0.587980i
\(78\) 9.55289 + 16.5461i 1.08165 + 1.87348i
\(79\) 13.1287i 1.47710i −0.674200 0.738548i \(-0.735512\pi\)
0.674200 0.738548i \(-0.264488\pi\)
\(80\) −6.57722 −0.735356
\(81\) 3.27393 5.67061i 0.363770 0.630068i
\(82\) 0.456574 0.263603i 0.0504202 0.0291101i
\(83\) −7.22933 12.5216i −0.793522 1.37442i −0.923774 0.382939i \(-0.874912\pi\)
0.130252 0.991481i \(-0.458421\pi\)
\(84\) −9.07740 5.24084i −0.990425 0.571822i
\(85\) 1.35351 2.34434i 0.146808 0.254279i
\(86\) −13.2481 −1.42858
\(87\) 2.14291 + 3.71162i 0.229744 + 0.397928i
\(88\) −0.375519 −0.0400304
\(89\) 5.33906 + 3.08251i 0.565939 + 0.326745i 0.755526 0.655119i \(-0.227381\pi\)
−0.189587 + 0.981864i \(0.560715\pi\)
\(90\) −10.0366 + 5.79463i −1.05795 + 0.610808i
\(91\) 3.91625 6.78315i 0.410535 0.711068i
\(92\) 0.245591 0.0256046
\(93\) −2.33335 + 4.04149i −0.241957 + 0.419083i
\(94\) 7.09840 + 12.2948i 0.732144 + 1.26811i
\(95\) 1.09298 + 1.89310i 0.112138 + 0.194228i
\(96\) 17.7213 10.2314i 1.80867 1.04424i
\(97\) −4.25334 + 2.45566i −0.431861 + 0.249335i −0.700139 0.714007i \(-0.746879\pi\)
0.268278 + 0.963341i \(0.413545\pi\)
\(98\) 5.14040i 0.519258i
\(99\) −9.01496 + 5.20479i −0.906038 + 0.523101i
\(100\) 4.76081 0.476081
\(101\) 8.68981i 0.864669i 0.901713 + 0.432334i \(0.142310\pi\)
−0.901713 + 0.432334i \(0.857690\pi\)
\(102\) 8.70326i 0.861751i
\(103\) 1.95356i 0.192490i 0.995358 + 0.0962451i \(0.0306833\pi\)
−0.995358 + 0.0962451i \(0.969317\pi\)
\(104\) 0.246846 + 0.427549i 0.0242052 + 0.0419246i
\(105\) 7.47938 + 4.31822i 0.729913 + 0.421415i
\(106\) 3.17737 + 5.50337i 0.308614 + 0.534534i
\(107\) −0.711024 + 0.410510i −0.0687373 + 0.0396855i −0.533975 0.845500i \(-0.679302\pi\)
0.465237 + 0.885186i \(0.345969\pi\)
\(108\) 1.66855 2.89001i 0.160556 0.278091i
\(109\) 3.25582 5.63924i 0.311851 0.540141i −0.666912 0.745136i \(-0.732384\pi\)
0.978763 + 0.204995i \(0.0657178\pi\)
\(110\) −8.96450 −0.854731
\(111\) −6.29282 + 10.8995i −0.597288 + 1.03453i
\(112\) −7.50760 4.33451i −0.709401 0.409573i
\(113\) 9.36684 5.40795i 0.881158 0.508737i 0.0101178 0.999949i \(-0.496779\pi\)
0.871040 + 0.491212i \(0.163446\pi\)
\(114\) −6.08647 3.51403i −0.570050 0.329119i
\(115\) −0.202356 −0.0188698
\(116\) −1.60429 2.77872i −0.148955 0.257998i
\(117\) 11.8519 + 6.84270i 1.09571 + 0.632607i
\(118\) 22.6223 2.08255
\(119\) 3.08993 1.78397i 0.283254 0.163537i
\(120\) −0.471433 + 0.272182i −0.0430357 + 0.0248467i
\(121\) 2.94801 0.268001
\(122\) 6.46678 + 11.2008i 0.585475 + 1.01407i
\(123\) 0.343231 0.594493i 0.0309481 0.0536036i
\(124\) 1.74687 3.02567i 0.156874 0.271713i
\(125\) −11.8874 −1.06324
\(126\) −15.2751 −1.36081
\(127\) 15.3326i 1.36054i −0.732960 0.680272i \(-0.761862\pi\)
0.732960 0.680272i \(-0.238138\pi\)
\(128\) 0.916344 0.529052i 0.0809942 0.0467620i
\(129\) −14.9389 + 8.62498i −1.31530 + 0.759387i
\(130\) 5.89278 + 10.2066i 0.516831 + 0.895177i
\(131\) 9.61607i 0.840160i −0.907487 0.420080i \(-0.862002\pi\)
0.907487 0.420080i \(-0.137998\pi\)
\(132\) 12.2684 7.08316i 1.06783 0.616510i
\(133\) 2.88119i 0.249830i
\(134\) 22.1348 12.7795i 1.91216 1.10398i
\(135\) −1.37481 + 2.38124i −0.118325 + 0.204945i
\(136\) 0.224891i 0.0192843i
\(137\) −5.74633 3.31765i −0.490942 0.283446i 0.234023 0.972231i \(-0.424811\pi\)
−0.724965 + 0.688785i \(0.758144\pi\)
\(138\) 0.563428 0.325296i 0.0479622 0.0276910i
\(139\) −18.8913 −1.60234 −0.801169 0.598438i \(-0.795788\pi\)
−0.801169 + 0.598438i \(0.795788\pi\)
\(140\) −5.59946 3.23285i −0.473241 0.273226i
\(141\) 16.0087 + 9.24263i 1.34818 + 0.778370i
\(142\) 7.81485 13.5357i 0.655807 1.13589i
\(143\) 5.29294 + 9.16765i 0.442618 + 0.766637i
\(144\) 7.57350 13.1177i 0.631125 1.09314i
\(145\) 1.32187 + 2.28954i 0.109775 + 0.190136i
\(146\) 30.9366i 2.56033i
\(147\) −3.34658 5.79645i −0.276022 0.478083i
\(148\) 4.71114 8.15994i 0.387253 0.670743i
\(149\) −10.9286 + 6.30963i −0.895306 + 0.516905i −0.875674 0.482902i \(-0.839583\pi\)
−0.0196315 + 0.999807i \(0.506249\pi\)
\(150\) 10.9221 6.30590i 0.891789 0.514875i
\(151\) 9.07924 15.7257i 0.738858 1.27974i −0.214152 0.976800i \(-0.568699\pi\)
0.953010 0.302939i \(-0.0979679\pi\)
\(152\) −0.157274 0.0908021i −0.0127566 0.00736502i
\(153\) 3.11705 + 5.39890i 0.251999 + 0.436475i
\(154\) −10.2326 5.90778i −0.824564 0.476062i
\(155\) −1.43935 + 2.49302i −0.115611 + 0.200244i
\(156\) −16.1292 9.31217i −1.29137 0.745570i
\(157\) −3.49618 + 6.05556i −0.279025 + 0.483286i −0.971143 0.238499i \(-0.923345\pi\)
0.692117 + 0.721785i \(0.256678\pi\)
\(158\) 13.0188 + 22.5492i 1.03572 + 1.79391i
\(159\) 7.16578 + 4.13717i 0.568284 + 0.328099i
\(160\) 10.9315 6.31133i 0.864214 0.498954i
\(161\) −0.230980 0.133357i −0.0182038 0.0105100i
\(162\) 12.9860i 1.02028i
\(163\) 8.62960i 0.675922i −0.941160 0.337961i \(-0.890263\pi\)
0.941160 0.337961i \(-0.109737\pi\)
\(164\) −0.256961 + 0.445069i −0.0200653 + 0.0347541i
\(165\) −10.1086 + 5.83621i −0.786955 + 0.454349i
\(166\) 24.8334 + 14.3375i 1.92744 + 1.11281i
\(167\) 14.5408i 1.12520i 0.826729 + 0.562601i \(0.190199\pi\)
−0.826729 + 0.562601i \(0.809801\pi\)
\(168\) −0.717493 −0.0553557
\(169\) 0.458589 0.794300i 0.0352761 0.0611000i
\(170\) 5.36868i 0.411759i
\(171\) −5.03416 −0.384972
\(172\) 11.1841 6.45712i 0.852777 0.492351i
\(173\) 17.4213 10.0582i 1.32452 0.764710i 0.340071 0.940400i \(-0.389549\pi\)
0.984446 + 0.175689i \(0.0562154\pi\)
\(174\) −7.36107 4.24991i −0.558041 0.322185i
\(175\) −4.47759 2.58514i −0.338474 0.195418i
\(176\) 10.1468 5.85823i 0.764841 0.441581i
\(177\) 25.5095 14.7279i 1.91741 1.10702i
\(178\) −12.2268 −0.916434
\(179\) 21.9761i 1.64257i 0.570517 + 0.821286i \(0.306743\pi\)
−0.570517 + 0.821286i \(0.693257\pi\)
\(180\) 5.64862 9.78369i 0.421023 0.729233i
\(181\) −2.72681 −0.202682 −0.101341 0.994852i \(-0.532313\pi\)
−0.101341 + 0.994852i \(0.532313\pi\)
\(182\) 15.5338i 1.15144i
\(183\) 14.5842 + 8.42021i 1.07810 + 0.622440i
\(184\) 0.0145589 0.00840560i 0.00107330 0.000619669i
\(185\) −3.88177 + 6.72343i −0.285394 + 0.494317i
\(186\) 9.25523i 0.678627i
\(187\) 4.82219i 0.352634i
\(188\) −11.9850 6.91953i −0.874094 0.504659i
\(189\) −3.13857 + 1.81205i −0.228297 + 0.131807i
\(190\) −3.75449 2.16766i −0.272379 0.157258i
\(191\) −1.18052 2.04473i −0.0854196 0.147951i 0.820150 0.572148i \(-0.193890\pi\)
−0.905570 + 0.424197i \(0.860556\pi\)
\(192\) −9.62897 + 16.6779i −0.694911 + 1.20362i
\(193\) 9.09429 + 5.25059i 0.654621 + 0.377946i 0.790224 0.612817i \(-0.209964\pi\)
−0.135603 + 0.990763i \(0.543297\pi\)
\(194\) 4.87019 8.43542i 0.349659 0.605628i
\(195\) 13.2897 + 7.67282i 0.951696 + 0.549462i
\(196\) 2.50543 + 4.33954i 0.178959 + 0.309967i
\(197\) −17.8632 10.3133i −1.27270 0.734793i −0.297204 0.954814i \(-0.596054\pi\)
−0.975495 + 0.220021i \(0.929387\pi\)
\(198\) 10.3224 17.8789i 0.733580 1.27060i
\(199\) −18.4820 + 10.6706i −1.31015 + 0.756416i −0.982121 0.188251i \(-0.939718\pi\)
−0.328030 + 0.944667i \(0.606385\pi\)
\(200\) 0.282227 0.162944i 0.0199565 0.0115219i
\(201\) 16.6399 28.8211i 1.17369 2.03289i
\(202\) −8.61703 14.9251i −0.606292 1.05013i
\(203\) 3.48455i 0.244567i
\(204\) −4.24198 7.34732i −0.296998 0.514415i
\(205\) 0.211725 0.366718i 0.0147875 0.0256127i
\(206\) −1.93720 3.35533i −0.134971 0.233777i
\(207\) 0.233008 0.403581i 0.0161952 0.0280508i
\(208\) −13.3399 7.70177i −0.924953 0.534022i
\(209\) −3.37231 1.94701i −0.233268 0.134677i
\(210\) −17.1282 −1.18196
\(211\) −10.6421 + 6.14424i −0.732634 + 0.422987i −0.819385 0.573243i \(-0.805685\pi\)
0.0867507 + 0.996230i \(0.472352\pi\)
\(212\) −5.36469 3.09731i −0.368449 0.212724i
\(213\) 20.3510i 1.39443i
\(214\) 0.814143 1.41014i 0.0556536 0.0963949i
\(215\) −9.21518 + 5.32039i −0.628470 + 0.362847i
\(216\) 0.228431i 0.0155428i
\(217\) −3.28590 + 1.89711i −0.223061 + 0.128785i
\(218\) 12.9142i 0.874659i
\(219\) −20.1408 34.8849i −1.36099 2.35730i
\(220\) 7.56785 4.36930i 0.510225 0.294578i
\(221\) 5.49034 3.16985i 0.369320 0.213227i
\(222\) 24.9604i 1.67524i
\(223\) 18.5530 1.24240 0.621201 0.783651i \(-0.286645\pi\)
0.621201 + 0.783651i \(0.286645\pi\)
\(224\) 16.6371 1.11162
\(225\) 4.51689 7.82348i 0.301126 0.521566i
\(226\) −10.7253 + 18.5768i −0.713436 + 1.23571i
\(227\) −9.38540 16.2560i −0.622931 1.07895i −0.988937 0.148335i \(-0.952609\pi\)
0.366007 0.930612i \(-0.380725\pi\)
\(228\) 6.85096 0.453716
\(229\) −14.1485 + 8.16866i −0.934961 + 0.539800i −0.888377 0.459114i \(-0.848167\pi\)
−0.0465841 + 0.998914i \(0.514834\pi\)
\(230\) 0.347555 0.200661i 0.0229171 0.0132312i
\(231\) −15.3847 −1.01224
\(232\) −0.190209 0.109817i −0.0124878 0.00720986i
\(233\) 9.56812 + 16.5725i 0.626829 + 1.08570i 0.988184 + 0.153271i \(0.0489807\pi\)
−0.361356 + 0.932428i \(0.617686\pi\)
\(234\) −27.1415 −1.77430
\(235\) 9.87510 + 5.70139i 0.644180 + 0.371918i
\(236\) −19.0978 + 11.0261i −1.24316 + 0.717739i
\(237\) 29.3606 + 16.9514i 1.90718 + 1.10111i
\(238\) −3.53806 + 6.12810i −0.229338 + 0.397226i
\(239\) 17.4585 1.12929 0.564647 0.825333i \(-0.309012\pi\)
0.564647 + 0.825333i \(0.309012\pi\)
\(240\) 8.49229 14.7091i 0.548175 0.949466i
\(241\) −11.9932 + 20.7728i −0.772549 + 1.33809i 0.163612 + 0.986525i \(0.447685\pi\)
−0.936162 + 0.351570i \(0.885648\pi\)
\(242\) −5.06334 + 2.92332i −0.325484 + 0.187918i
\(243\) 11.0436 + 19.1281i 0.708446 + 1.22707i
\(244\) −10.9185 6.30382i −0.698988 0.403561i
\(245\) −2.06437 3.57559i −0.131888 0.228436i
\(246\) 1.36142i 0.0868012i
\(247\) 5.11943i 0.325741i
\(248\) 0.239154i 0.0151863i
\(249\) 37.3371 2.36614
\(250\) 20.4171 11.7878i 1.29129 0.745526i
\(251\) 16.7712i 1.05859i 0.848438 + 0.529294i \(0.177543\pi\)
−0.848438 + 0.529294i \(0.822457\pi\)
\(252\) 12.8953 7.44509i 0.812326 0.468997i
\(253\) 0.312177 0.180236i 0.0196264 0.0113313i
\(254\) 15.2041 + 26.3343i 0.953992 + 1.65236i
\(255\) 3.49520 + 6.05387i 0.218878 + 0.379108i
\(256\) −8.50682 + 14.7342i −0.531676 + 0.920890i
\(257\) −9.73589 −0.607308 −0.303654 0.952782i \(-0.598207\pi\)
−0.303654 + 0.952782i \(0.598207\pi\)
\(258\) 17.1055 29.6276i 1.06494 1.84453i
\(259\) −8.86174 + 5.11633i −0.550642 + 0.317913i
\(260\) −9.94940 5.74429i −0.617035 0.356246i
\(261\) −6.08839 −0.376862
\(262\) 9.53553 + 16.5160i 0.589107 + 1.02036i
\(263\) −22.2328 −1.37093 −0.685466 0.728105i \(-0.740401\pi\)
−0.685466 + 0.728105i \(0.740401\pi\)
\(264\) 0.484857 0.839797i 0.0298409 0.0516859i
\(265\) 4.42027 + 2.55204i 0.271535 + 0.156771i
\(266\) −2.85705 4.94856i −0.175177 0.303416i
\(267\) −13.7872 + 7.96006i −0.843765 + 0.487148i
\(268\) −12.4575 + 21.5770i −0.760964 + 1.31803i
\(269\) −10.0212 −0.611001 −0.305500 0.952192i \(-0.598824\pi\)
−0.305500 + 0.952192i \(0.598824\pi\)
\(270\) 5.45318i 0.331870i
\(271\) 6.40471 + 11.0933i 0.389059 + 0.673869i 0.992323 0.123672i \(-0.0394670\pi\)
−0.603264 + 0.797541i \(0.706134\pi\)
\(272\) −3.50839 6.07671i −0.212727 0.368455i
\(273\) 10.1131 + 17.5164i 0.612071 + 1.06014i
\(274\) 13.1594 0.794991
\(275\) 6.05160 3.49389i 0.364925 0.210690i
\(276\) −0.317099 + 0.549231i −0.0190871 + 0.0330598i
\(277\) 3.90437 2.25419i 0.234591 0.135441i −0.378097 0.925766i \(-0.623421\pi\)
0.612688 + 0.790325i \(0.290088\pi\)
\(278\) 32.4466 18.7330i 1.94602 1.12353i
\(279\) −3.31474 5.74130i −0.198448 0.343723i
\(280\) −0.442591 −0.0264499
\(281\) −9.47211 + 16.4062i −0.565059 + 0.978710i 0.431985 + 0.901881i \(0.357813\pi\)
−0.997044 + 0.0768299i \(0.975520\pi\)
\(282\) −36.6609 −2.18312
\(283\) 9.12245 0.542273 0.271137 0.962541i \(-0.412600\pi\)
0.271137 + 0.962541i \(0.412600\pi\)
\(284\) 15.2358i 0.904081i
\(285\) −5.64489 −0.334374
\(286\) −18.1817 10.4972i −1.07511 0.620714i
\(287\) 0.483348 0.279061i 0.0285311 0.0164725i
\(288\) 29.0693i 1.71293i
\(289\) −14.1121 −0.830122
\(290\) −4.54073 2.62159i −0.266641 0.153945i
\(291\) 12.6827i 0.743472i
\(292\) 15.0785 + 26.1167i 0.882403 + 1.52837i
\(293\) 0.670536 + 1.16140i 0.0391731 + 0.0678498i 0.884947 0.465691i \(-0.154194\pi\)
−0.845774 + 0.533541i \(0.820861\pi\)
\(294\) 11.4958 + 6.63711i 0.670449 + 0.387084i
\(295\) 15.7358 9.08504i 0.916171 0.528952i
\(296\) 0.644975i 0.0374884i
\(297\) 4.89809i 0.284216i
\(298\) 12.5136 21.6741i 0.724891 1.25555i
\(299\) −0.410417 0.236954i −0.0237350 0.0137034i
\(300\) −6.14700 + 10.6469i −0.354897 + 0.614700i
\(301\) −14.0250 −0.808385
\(302\) 36.0128i 2.07230i
\(303\) −19.4336 11.2200i −1.11643 0.644572i
\(304\) 5.66619 0.324978
\(305\) 8.99640 + 5.19408i 0.515133 + 0.297412i
\(306\) −10.7074 6.18189i −0.612099 0.353395i
\(307\) −5.14287 8.90770i −0.293519 0.508390i 0.681120 0.732171i \(-0.261493\pi\)
−0.974639 + 0.223782i \(0.928160\pi\)
\(308\) 11.5178 0.656288
\(309\) −4.36888 2.52237i −0.248537 0.143493i
\(310\) 5.70916i 0.324259i
\(311\) 14.2376i 0.807342i 0.914904 + 0.403671i \(0.132266\pi\)
−0.914904 + 0.403671i \(0.867734\pi\)
\(312\) −1.27488 −0.0721756
\(313\) −9.07245 −0.512805 −0.256403 0.966570i \(-0.582537\pi\)
−0.256403 + 0.966570i \(0.582537\pi\)
\(314\) 13.8676i 0.782592i
\(315\) −10.6251 + 6.13443i −0.598659 + 0.345636i
\(316\) −21.9809 12.6907i −1.23652 0.713908i
\(317\) −5.27477 3.04539i −0.296260 0.171046i 0.344501 0.938786i \(-0.388048\pi\)
−0.640762 + 0.767740i \(0.721381\pi\)
\(318\) −16.4101 −0.920230
\(319\) −4.07852 2.35474i −0.228354 0.131840i
\(320\) −5.93971 + 10.2879i −0.332040 + 0.575110i
\(321\) 2.12015i 0.118335i
\(322\) 0.528958 0.0294777
\(323\) −1.16603 + 2.01962i −0.0648795 + 0.112375i
\(324\) −6.32940 10.9628i −0.351633 0.609047i
\(325\) −7.95599 4.59339i −0.441319 0.254796i
\(326\) 8.55731 + 14.8217i 0.473946 + 0.820898i
\(327\) 8.40760 + 14.5624i 0.464941 + 0.805302i
\(328\) 0.0351790i 0.00194244i
\(329\) 7.51465 + 13.0158i 0.414296 + 0.717582i
\(330\) 11.5747 20.0479i 0.637164 1.10360i
\(331\) 1.22880 + 0.709450i 0.0675411 + 0.0389949i 0.533390 0.845869i \(-0.320918\pi\)
−0.465849 + 0.884864i \(0.654251\pi\)
\(332\) −27.9525 −1.53409
\(333\) −8.93953 15.4837i −0.489883 0.848503i
\(334\) −14.4190 24.9745i −0.788974 1.36654i
\(335\) 10.2644 17.7785i 0.560806 0.971345i
\(336\) 19.3871 11.1932i 1.05765 0.610637i
\(337\) −10.5081 18.2006i −0.572412 0.991447i −0.996317 0.0857407i \(-0.972674\pi\)
0.423905 0.905707i \(-0.360659\pi\)
\(338\) 1.81899i 0.0989402i
\(339\) 27.9302i 1.51696i
\(340\) −2.61670 4.53225i −0.141910 0.245796i
\(341\) 5.12802i 0.277698i
\(342\) 8.64639 4.99200i 0.467543 0.269936i
\(343\) 20.1386i 1.08738i
\(344\) 0.442004 0.765573i 0.0238312 0.0412769i
\(345\) 0.261275 0.452542i 0.0140666 0.0243641i
\(346\) −19.9479 + 34.5508i −1.07241 + 1.85746i
\(347\) −26.4755 + 15.2856i −1.42128 + 0.820575i −0.996408 0.0846800i \(-0.973013\pi\)
−0.424869 + 0.905255i \(0.639680\pi\)
\(348\) 8.28564 0.444157
\(349\) 17.0986 7.52572i 0.915269 0.402842i
\(350\) 10.2539 0.548096
\(351\) −5.57676 + 3.21974i −0.297665 + 0.171857i
\(352\) −11.2428 + 19.4731i −0.599244 + 1.03792i
\(353\) −1.73413 + 3.00360i −0.0922983 + 0.159865i −0.908478 0.417933i \(-0.862755\pi\)
0.816180 + 0.577798i \(0.196088\pi\)
\(354\) −29.2091 + 50.5917i −1.55245 + 2.68892i
\(355\) 12.5537i 0.666280i
\(356\) 10.3219 5.95933i 0.547058 0.315844i
\(357\) 9.21362i 0.487637i
\(358\) −21.7920 37.7449i −1.15174 1.99488i
\(359\) 25.3651i 1.33872i −0.742940 0.669358i \(-0.766569\pi\)
0.742940 0.669358i \(-0.233431\pi\)
\(360\) 0.773319i 0.0407575i
\(361\) 8.55841 + 14.8236i 0.450443 + 0.780190i
\(362\) 4.68342 2.70397i 0.246155 0.142118i
\(363\) −3.80637 + 6.59283i −0.199783 + 0.346034i
\(364\) −7.57119 13.1137i −0.396838 0.687344i
\(365\) −12.4240 21.5190i −0.650303 1.12636i
\(366\) −33.3987 −1.74578
\(367\) 13.4743 + 7.77937i 0.703351 + 0.406080i 0.808594 0.588367i \(-0.200229\pi\)
−0.105243 + 0.994446i \(0.533562\pi\)
\(368\) −0.262261 + 0.454250i −0.0136713 + 0.0236794i
\(369\) 0.487591 + 0.844532i 0.0253830 + 0.0439646i
\(370\) 15.3970i 0.800454i
\(371\) 3.36369 + 5.82609i 0.174634 + 0.302475i
\(372\) 4.51101 + 7.81329i 0.233885 + 0.405100i
\(373\) −3.23051 1.86513i −0.167269 0.0965729i 0.414028 0.910264i \(-0.364121\pi\)
−0.581298 + 0.813691i \(0.697455\pi\)
\(374\) −4.78180 8.28232i −0.247261 0.428269i
\(375\) 15.3486 26.5845i 0.792596 1.37282i
\(376\) −0.947312 −0.0488539
\(377\) 6.19151i 0.318879i
\(378\) 3.59375 6.22456i 0.184843 0.320157i
\(379\) −15.3303 8.85097i −0.787466 0.454644i 0.0516035 0.998668i \(-0.483567\pi\)
−0.839070 + 0.544024i \(0.816900\pi\)
\(380\) 4.22607 0.216793
\(381\) 34.2892 + 19.7969i 1.75669 + 1.01422i
\(382\) 4.05520 + 2.34127i 0.207482 + 0.119790i
\(383\) −7.37928 + 4.26043i −0.377064 + 0.217698i −0.676540 0.736406i \(-0.736521\pi\)
0.299476 + 0.954104i \(0.403188\pi\)
\(384\) 2.73237i 0.139436i
\(385\) −9.49018 −0.483664
\(386\) −20.8264 −1.06004
\(387\) 24.5052i 1.24567i
\(388\) 9.49494i 0.482032i
\(389\) −7.59992 4.38782i −0.385331 0.222471i 0.294804 0.955558i \(-0.404746\pi\)
−0.680135 + 0.733087i \(0.738079\pi\)
\(390\) −30.4342 −1.54110
\(391\) −0.107940 0.186957i −0.00545875 0.00945484i
\(392\) 0.297050 + 0.171502i 0.0150033 + 0.00866216i
\(393\) 21.5051 + 12.4159i 1.08479 + 0.626302i
\(394\) 40.9077 2.06090
\(395\) 18.1113 + 10.4566i 0.911280 + 0.526128i
\(396\) 20.1246i 1.01130i
\(397\) −34.1004 −1.71145 −0.855725 0.517430i \(-0.826889\pi\)
−0.855725 + 0.517430i \(0.826889\pi\)
\(398\) 21.1624 36.6543i 1.06077 1.83731i
\(399\) −6.44338 3.72009i −0.322573 0.186237i
\(400\) −5.08397 + 8.80570i −0.254199 + 0.440285i
\(401\) 1.59167i 0.0794840i 0.999210 + 0.0397420i \(0.0126536\pi\)
−0.999210 + 0.0397420i \(0.987346\pi\)
\(402\) 66.0020i 3.29188i
\(403\) −5.83854 + 3.37088i −0.290839 + 0.167916i
\(404\) 14.5490 + 8.39989i 0.723841 + 0.417910i
\(405\) 5.21515 + 9.03291i 0.259143 + 0.448849i
\(406\) −3.45536 5.98486i −0.171487 0.297024i
\(407\) 13.8298i 0.685516i
\(408\) −0.502939 0.290372i −0.0248992 0.0143756i
\(409\) 9.00611 0.445324 0.222662 0.974896i \(-0.428525\pi\)
0.222662 + 0.974896i \(0.428525\pi\)
\(410\) 0.839804i 0.0414750i
\(411\) 14.8389 8.56727i 0.731951 0.422592i
\(412\) 3.27078 + 1.88838i 0.161140 + 0.0930340i
\(413\) 23.9489 1.17845
\(414\) 0.924225i 0.0454232i
\(415\) 23.0317 1.13058
\(416\) 29.5617 1.44938
\(417\) 24.3918 42.2478i 1.19447 2.06888i
\(418\) 7.72279 0.377734
\(419\) 1.18039 + 2.04450i 0.0576660 + 0.0998805i 0.893417 0.449228i \(-0.148301\pi\)
−0.835751 + 0.549108i \(0.814967\pi\)
\(420\) 14.4597 8.34830i 0.705560 0.407355i
\(421\) 5.83834 3.37077i 0.284543 0.164281i −0.350935 0.936400i \(-0.614136\pi\)
0.635478 + 0.772119i \(0.280803\pi\)
\(422\) 12.1855 21.1060i 0.593183 1.02742i
\(423\) −22.7418 + 13.1300i −1.10575 + 0.638403i
\(424\) −0.424034 −0.0205929
\(425\) −2.09243 3.62419i −0.101498 0.175799i
\(426\) 20.1805 + 34.9537i 0.977750 + 1.69351i
\(427\) 6.84599 + 11.8576i 0.331301 + 0.573830i
\(428\) 1.58725i 0.0767228i
\(429\) −27.3363 −1.31981
\(430\) 10.5516 18.2760i 0.508846 0.881347i
\(431\) 23.1360 13.3576i 1.11442 0.643412i 0.174452 0.984666i \(-0.444185\pi\)
0.939971 + 0.341253i \(0.110851\pi\)
\(432\) 3.56361 + 6.17236i 0.171454 + 0.296968i
\(433\) 28.6127 + 16.5195i 1.37504 + 0.793878i 0.991557 0.129671i \(-0.0413921\pi\)
0.383480 + 0.923549i \(0.374725\pi\)
\(434\) 3.76245 6.51675i 0.180603 0.312814i
\(435\) −6.82701 −0.327330
\(436\) −6.29438 10.9022i −0.301446 0.522120i
\(437\) 0.174327 0.00833919
\(438\) 69.1855 + 39.9442i 3.30581 + 1.90861i
\(439\) −8.55008 + 4.93639i −0.408073 + 0.235601i −0.689961 0.723846i \(-0.742373\pi\)
0.281888 + 0.959447i \(0.409039\pi\)
\(440\) 0.299088 0.518035i 0.0142585 0.0246964i
\(441\) 9.50826 0.452774
\(442\) −6.28659 + 10.8887i −0.299023 + 0.517923i
\(443\) 18.3943 + 31.8599i 0.873940 + 1.51371i 0.857887 + 0.513838i \(0.171777\pi\)
0.0160528 + 0.999871i \(0.494890\pi\)
\(444\) 12.1657 + 21.0717i 0.577360 + 1.00002i
\(445\) −8.50476 + 4.91023i −0.403164 + 0.232767i
\(446\) −31.8656 + 18.3976i −1.50888 + 0.871153i
\(447\) 32.5871i 1.54132i
\(448\) −13.5598 + 7.82876i −0.640641 + 0.369874i
\(449\) 8.42248 0.397481 0.198741 0.980052i \(-0.436315\pi\)
0.198741 + 0.980052i \(0.436315\pi\)
\(450\) 17.9162i 0.844579i
\(451\) 0.754320i 0.0355195i
\(452\) 20.9101i 0.983527i
\(453\) 23.4456 + 40.6090i 1.10157 + 1.90798i
\(454\) 32.2396 + 18.6136i 1.51308 + 0.873578i
\(455\) 6.23833 + 10.8051i 0.292457 + 0.506551i
\(456\) 0.406133 0.234481i 0.0190189 0.0109806i
\(457\) 15.4714 26.7972i 0.723719 1.25352i −0.235780 0.971807i \(-0.575764\pi\)
0.959499 0.281712i \(-0.0909023\pi\)
\(458\) 16.2005 28.0601i 0.756999 1.31116i
\(459\) −2.93338 −0.136918
\(460\) −0.195605 + 0.338797i −0.00912012 + 0.0157965i
\(461\) −12.7772 7.37695i −0.595096 0.343579i 0.172014 0.985094i \(-0.444973\pi\)
−0.767110 + 0.641516i \(0.778306\pi\)
\(462\) 26.4239 15.2558i 1.22935 0.709766i
\(463\) 19.8564 + 11.4641i 0.922807 + 0.532783i 0.884530 0.466484i \(-0.154479\pi\)
0.0382778 + 0.999267i \(0.487813\pi\)
\(464\) 6.85277 0.318132
\(465\) −3.71687 6.43781i −0.172366 0.298546i
\(466\) −32.8673 18.9760i −1.52255 0.879045i
\(467\) 21.2858 0.984989 0.492494 0.870316i \(-0.336085\pi\)
0.492494 + 0.870316i \(0.336085\pi\)
\(468\) 22.9129 13.2288i 1.05915 0.611501i
\(469\) 23.4328 13.5289i 1.08203 0.624708i
\(470\) −22.6145 −1.04313
\(471\) −9.02829 15.6375i −0.416002 0.720536i
\(472\) −0.754761 + 1.30728i −0.0347407 + 0.0601727i
\(473\) 9.47758 16.4157i 0.435780 0.754793i
\(474\) −67.2375 −3.08832
\(475\) 3.37935 0.155055
\(476\) 6.89781i 0.316161i
\(477\) −10.1797 + 5.87723i −0.466095 + 0.269100i
\(478\) −29.9856 + 17.3122i −1.37151 + 0.791843i
\(479\) 0.777547 + 1.34675i 0.0355270 + 0.0615346i 0.883242 0.468917i \(-0.155356\pi\)
−0.847715 + 0.530452i \(0.822022\pi\)
\(480\) 32.5959i 1.48779i
\(481\) −15.7460 + 9.09094i −0.717954 + 0.414511i
\(482\) 47.5709i 2.16680i
\(483\) 0.596468 0.344371i 0.0271402 0.0156694i
\(484\) 2.84965 4.93575i 0.129530 0.224352i
\(485\) 7.82341i 0.355243i
\(486\) −37.9357 21.9022i −1.72080 0.993503i
\(487\) −24.2008 + 13.9723i −1.09664 + 0.633148i −0.935337 0.353757i \(-0.884904\pi\)
−0.161306 + 0.986904i \(0.551571\pi\)
\(488\) −0.863020 −0.0390671
\(489\) 19.2989 + 11.1422i 0.872728 + 0.503870i
\(490\) 7.09128 + 4.09415i 0.320351 + 0.184955i
\(491\) −18.0422 + 31.2501i −0.814235 + 1.41030i 0.0956409 + 0.995416i \(0.469510\pi\)
−0.909876 + 0.414880i \(0.863823\pi\)
\(492\) −0.663558 1.14932i −0.0299155 0.0518152i
\(493\) −1.41021 + 2.44255i −0.0635126 + 0.110007i
\(494\) −5.07655 8.79284i −0.228405 0.395608i
\(495\) 16.5818i 0.745294i
\(496\) 3.73090 + 6.46210i 0.167522 + 0.290157i
\(497\) 8.27311 14.3294i 0.371100 0.642764i
\(498\) −64.1280 + 37.0243i −2.87364 + 1.65910i
\(499\) 30.3454 17.5199i 1.35845 0.784299i 0.369031 0.929417i \(-0.379690\pi\)
0.989414 + 0.145118i \(0.0463563\pi\)
\(500\) −11.4908 + 19.9026i −0.513882 + 0.890070i
\(501\) −32.5186 18.7746i −1.45282 0.838788i
\(502\) −16.6307 28.8053i −0.742266 1.28564i
\(503\) −27.5339 15.8967i −1.22768 0.708799i −0.261133 0.965303i \(-0.584096\pi\)
−0.966543 + 0.256504i \(0.917429\pi\)
\(504\) 0.509632 0.882709i 0.0227008 0.0393190i
\(505\) −11.9878 6.92114i −0.533449 0.307987i
\(506\) −0.357452 + 0.619125i −0.0158907 + 0.0275235i
\(507\) 1.18423 + 2.05115i 0.0525935 + 0.0910946i
\(508\) −25.6707 14.8210i −1.13895 0.657576i
\(509\) 17.3765 10.0323i 0.770198 0.444674i −0.0627475 0.998029i \(-0.519986\pi\)
0.832945 + 0.553356i \(0.186653\pi\)
\(510\) −12.0063 6.93185i −0.531649 0.306948i
\(511\) 32.7507i 1.44880i
\(512\) 31.6260i 1.39769i
\(513\) 1.18438 2.05141i 0.0522917 0.0905719i
\(514\) 16.7218 9.65434i 0.737568 0.425835i
\(515\) −2.69498 1.55595i −0.118755 0.0685632i
\(516\) 33.3489i 1.46810i
\(517\) −20.3126 −0.893346
\(518\) 10.1469 17.5750i 0.445831 0.772202i
\(519\) 51.9472i 2.28023i
\(520\) −0.786417 −0.0344867
\(521\) 27.3734 15.8040i 1.19925 0.692387i 0.238862 0.971053i \(-0.423226\pi\)
0.960388 + 0.278666i \(0.0898922\pi\)
\(522\) 10.4571 6.03739i 0.457694 0.264250i
\(523\) −34.7800 20.0802i −1.52082 0.878048i −0.999698 0.0245672i \(-0.992179\pi\)
−0.521125 0.853480i \(-0.674487\pi\)
\(524\) −16.0998 9.29525i −0.703325 0.406065i
\(525\) 11.5626 6.67568i 0.504634 0.291351i
\(526\) 38.1857 22.0465i 1.66498 0.961275i
\(527\) −3.07108 −0.133778
\(528\) 30.2558i 1.31672i
\(529\) 11.4919 19.9046i 0.499649 0.865418i
\(530\) −10.1227 −0.439701
\(531\) 41.8448i 1.81591i
\(532\) 4.82386 + 2.78506i 0.209141 + 0.120748i
\(533\) 0.858836 0.495849i 0.0372003 0.0214776i
\(534\) 15.7868 27.3435i 0.683161 1.18327i
\(535\) 1.30783i 0.0565424i
\(536\) 1.70549i 0.0736657i
\(537\) −49.1466 28.3748i −2.12083 1.22446i
\(538\) 17.2118 9.93722i 0.742052 0.428424i
\(539\) 6.36945 + 3.67740i 0.274352 + 0.158397i
\(540\) 2.65788 + 4.60359i 0.114377 + 0.198107i
\(541\) 4.64194 8.04007i 0.199572 0.345670i −0.748817 0.662776i \(-0.769378\pi\)
0.948390 + 0.317107i \(0.102711\pi\)
\(542\) −22.0007 12.7021i −0.945013 0.545604i
\(543\) 3.52077 6.09815i 0.151091 0.261697i
\(544\) 11.6621 + 6.73312i 0.500008 + 0.288680i
\(545\) 5.18629 + 8.98293i 0.222156 + 0.384786i
\(546\) −34.7393 20.0567i −1.48670 0.858349i
\(547\) −18.8260 + 32.6076i −0.804941 + 1.39420i 0.111390 + 0.993777i \(0.464470\pi\)
−0.916331 + 0.400422i \(0.868864\pi\)
\(548\) −11.1092 + 6.41392i −0.474563 + 0.273989i
\(549\) −20.7183 + 11.9617i −0.884234 + 0.510513i
\(550\) −6.92926 + 12.0018i −0.295464 + 0.511759i
\(551\) −1.13877 1.97241i −0.0485133 0.0840275i
\(552\) 0.0434121i 0.00184774i
\(553\) 13.7822 + 23.8714i 0.586078 + 1.01512i
\(554\) −4.47062 + 7.74334i −0.189938 + 0.328983i
\(555\) −10.0240 17.3621i −0.425497 0.736982i
\(556\) −18.2610 + 31.6290i −0.774439 + 1.34137i
\(557\) −24.3827 14.0774i −1.03313 0.596478i −0.115250 0.993336i \(-0.536767\pi\)
−0.917880 + 0.396859i \(0.870100\pi\)
\(558\) 11.3864 + 6.57396i 0.482026 + 0.278298i
\(559\) −24.9202 −1.05401
\(560\) 11.9591 6.90459i 0.505364 0.291772i
\(561\) −10.7842 6.22625i −0.455309 0.262873i
\(562\) 37.5711i 1.58484i
\(563\) −7.27796 + 12.6058i −0.306730 + 0.531271i −0.977645 0.210263i \(-0.932568\pi\)
0.670915 + 0.741534i \(0.265901\pi\)
\(564\) 30.9492 17.8685i 1.30320 0.752401i
\(565\) 17.2290i 0.724829i
\(566\) −15.6682 + 9.04604i −0.658584 + 0.380233i
\(567\) 13.7475i 0.577342i
\(568\) 0.521463 + 0.903200i 0.0218801 + 0.0378974i
\(569\) 29.2876 16.9092i 1.22780 0.708872i 0.261232 0.965276i \(-0.415871\pi\)
0.966570 + 0.256404i \(0.0825378\pi\)
\(570\) 9.69534 5.59761i 0.406093 0.234458i
\(571\) 2.38897i 0.0999752i −0.998750 0.0499876i \(-0.984082\pi\)
0.998750 0.0499876i \(-0.0159182\pi\)
\(572\) 20.4654 0.855702
\(573\) 6.09700 0.254706
\(574\) −0.553447 + 0.958599i −0.0231004 + 0.0400111i
\(575\) −0.156414 + 0.270918i −0.00652293 + 0.0112981i
\(576\) −13.6788 23.6924i −0.569952 0.987185i
\(577\) −21.6354 −0.900694 −0.450347 0.892854i \(-0.648700\pi\)
−0.450347 + 0.892854i \(0.648700\pi\)
\(578\) 24.2381 13.9939i 1.00817 0.582068i
\(579\) −23.4845 + 13.5588i −0.975982 + 0.563483i
\(580\) 5.11106 0.212225
\(581\) 26.2896 + 15.1783i 1.09068 + 0.629702i
\(582\) 12.5765 + 21.7831i 0.521311 + 0.902937i
\(583\) −9.09227 −0.376564
\(584\) 1.78774 + 1.03215i 0.0739774 + 0.0427109i
\(585\) −18.8793 + 10.9000i −0.780562 + 0.450657i
\(586\) −2.30335 1.32984i −0.0951505 0.0549351i
\(587\) −10.6810 + 18.5001i −0.440853 + 0.763579i −0.997753 0.0670002i \(-0.978657\pi\)
0.556900 + 0.830579i \(0.311991\pi\)
\(588\) −12.9397 −0.533625
\(589\) 1.23998 2.14771i 0.0510924 0.0884947i
\(590\) −18.0179 + 31.2079i −0.741785 + 1.28481i
\(591\) 46.1287 26.6324i 1.89748 1.09551i
\(592\) 10.0619 + 17.4276i 0.413540 + 0.716272i
\(593\) 10.0895 + 5.82517i 0.414326 + 0.239211i 0.692647 0.721277i \(-0.256445\pi\)
−0.278321 + 0.960488i \(0.589778\pi\)
\(594\) 4.85707 + 8.41269i 0.199288 + 0.345177i
\(595\) 5.68350i 0.233001i
\(596\) 24.3965i 0.999318i
\(597\) 55.1099i 2.25550i
\(598\) 0.939878 0.0384345
\(599\) −11.9805 + 6.91697i −0.489511 + 0.282620i −0.724372 0.689410i \(-0.757870\pi\)
0.234860 + 0.972029i \(0.424537\pi\)
\(600\) 0.841550i 0.0343561i
\(601\) −8.16060 + 4.71152i −0.332878 + 0.192187i −0.657118 0.753788i \(-0.728225\pi\)
0.324240 + 0.945975i \(0.394891\pi\)
\(602\) 24.0885 13.9075i 0.981772 0.566826i
\(603\) 23.6385 + 40.9431i 0.962634 + 1.66733i
\(604\) −17.5526 30.4021i −0.714207 1.23704i
\(605\) −2.34799 + 4.06684i −0.0954594 + 0.165341i
\(606\) 44.5041 1.80785
\(607\) 24.0905 41.7260i 0.977804 1.69361i 0.307452 0.951564i \(-0.400524\pi\)
0.670352 0.742043i \(-0.266143\pi\)
\(608\) −9.41737 + 5.43712i −0.381925 + 0.220504i
\(609\) −7.79272 4.49913i −0.315777 0.182314i
\(610\) −20.6023 −0.834162
\(611\) 13.3524 + 23.1270i 0.540180 + 0.935619i
\(612\) 12.0522 0.487183
\(613\) 2.12324 3.67756i 0.0857568 0.148535i −0.819957 0.572426i \(-0.806003\pi\)
0.905713 + 0.423890i \(0.139336\pi\)
\(614\) 17.6662 + 10.1996i 0.712949 + 0.411621i
\(615\) 0.546743 + 0.946987i 0.0220468 + 0.0381862i
\(616\) 0.682790 0.394209i 0.0275104 0.0158831i
\(617\) −23.0338 + 39.8956i −0.927304 + 1.60614i −0.139491 + 0.990223i \(0.544547\pi\)
−0.787813 + 0.615914i \(0.788787\pi\)
\(618\) 10.0050 0.402460
\(619\) 19.6979i 0.791726i −0.918309 0.395863i \(-0.870445\pi\)
0.918309 0.395863i \(-0.129555\pi\)
\(620\) 2.78265 + 4.81969i 0.111754 + 0.193564i
\(621\) 0.109639 + 0.189900i 0.00439966 + 0.00762043i
\(622\) −14.1184 24.4537i −0.566095 0.980506i
\(623\) −12.9437 −0.518580
\(624\) 34.4480 19.8885i 1.37902 0.796179i
\(625\) 3.31147 5.73563i 0.132459 0.229425i
\(626\) 15.5823 8.99646i 0.622795 0.359571i
\(627\) 8.70844 5.02782i 0.347781 0.200792i
\(628\) 6.75906 + 11.7070i 0.269716 + 0.467162i
\(629\) −8.28239 −0.330241
\(630\) 12.1661 21.0723i 0.484709 0.839540i
\(631\) 14.5856 0.580645 0.290323 0.956929i \(-0.406237\pi\)
0.290323 + 0.956929i \(0.406237\pi\)
\(632\) −1.73741 −0.0691105
\(633\) 31.7329i 1.26127i
\(634\) 12.0795 0.479739
\(635\) 21.1516 + 12.2119i 0.839374 + 0.484613i
\(636\) 13.8534 7.99827i 0.549324 0.317152i
\(637\) 9.66930i 0.383112i
\(638\) 9.34006 0.369776
\(639\) 25.0372 + 14.4552i 0.990456 + 0.571840i
\(640\) 1.68549i 0.0666247i
\(641\) −4.84571 8.39302i −0.191394 0.331504i 0.754318 0.656509i \(-0.227968\pi\)
−0.945712 + 0.325005i \(0.894634\pi\)
\(642\) 2.10239 + 3.64144i 0.0829746 + 0.143716i
\(643\) 8.70993 + 5.02868i 0.343486 + 0.198312i 0.661813 0.749669i \(-0.269787\pi\)
−0.318326 + 0.947981i \(0.603121\pi\)
\(644\) −0.446548 + 0.257815i −0.0175965 + 0.0101593i
\(645\) 27.4780i 1.08195i
\(646\) 4.62504i 0.181970i
\(647\) −18.1211 + 31.3867i −0.712416 + 1.23394i 0.251532 + 0.967849i \(0.419066\pi\)
−0.963948 + 0.266091i \(0.914268\pi\)
\(648\) −0.750430 0.433261i −0.0294797 0.0170201i
\(649\) −16.1838 + 28.0312i −0.635271 + 1.10032i
\(650\) 18.2197 0.714634
\(651\) 9.79796i 0.384012i
\(652\) −14.4482 8.34168i −0.565836 0.326685i
\(653\) −6.42247 −0.251331 −0.125665 0.992073i \(-0.540107\pi\)
−0.125665 + 0.992073i \(0.540107\pi\)
\(654\) −28.8808 16.6744i −1.12933 0.652019i
\(655\) 13.2656 + 7.65888i 0.518328 + 0.299257i
\(656\) −0.548806 0.950560i −0.0214273 0.0371131i
\(657\) 57.2238 2.23251
\(658\) −25.8135 14.9034i −1.00631 0.580996i
\(659\) 27.4198i 1.06813i 0.845445 + 0.534063i \(0.179335\pi\)
−0.845445 + 0.534063i \(0.820665\pi\)
\(660\) 22.5660i 0.878380i
\(661\) −30.6464 −1.19201 −0.596003 0.802982i \(-0.703245\pi\)
−0.596003 + 0.802982i \(0.703245\pi\)
\(662\) −2.81403 −0.109370
\(663\) 16.3712i 0.635805i
\(664\) −1.65706 + 0.956704i −0.0643064 + 0.0371273i
\(665\) −3.97465 2.29477i −0.154130 0.0889872i
\(666\) 30.7081 + 17.7293i 1.18991 + 0.686997i
\(667\) 0.210834 0.00816351
\(668\) 24.3451 + 14.0557i 0.941942 + 0.543831i
\(669\) −23.9550 + 41.4914i −0.926155 + 1.60415i
\(670\) 40.7139i 1.57291i
\(671\) −18.5051 −0.714383
\(672\) −21.4813 + 37.2067i −0.828660 + 1.43528i
\(673\) 2.33030 + 4.03620i 0.0898266 + 0.155584i 0.907438 0.420187i \(-0.138035\pi\)
−0.817611 + 0.575771i \(0.804702\pi\)
\(674\) 36.0962 + 20.8402i 1.39037 + 0.802733i
\(675\) 2.12536 + 3.68124i 0.0818053 + 0.141691i
\(676\) −0.886578 1.53560i −0.0340992 0.0590615i
\(677\) 32.6959i 1.25661i −0.777968 0.628303i \(-0.783750\pi\)
0.777968 0.628303i \(-0.216250\pi\)
\(678\) −27.6963 47.9714i −1.06367 1.84233i
\(679\) 5.15578 8.93007i 0.197861 0.342705i
\(680\) −0.310242 0.179118i −0.0118972 0.00686887i
\(681\) 48.4724 1.85747
\(682\) 5.08507 + 8.80760i 0.194717 + 0.337260i
\(683\) 2.04473 + 3.54158i 0.0782396 + 0.135515i 0.902490 0.430710i \(-0.141737\pi\)
−0.824251 + 0.566225i \(0.808403\pi\)
\(684\) −4.86621 + 8.42852i −0.186064 + 0.322272i
\(685\) 9.15352 5.28479i 0.349738 0.201921i
\(686\) 19.9700 + 34.5890i 0.762457 + 1.32061i
\(687\) 42.1884i 1.60959i
\(688\) 27.5817i 1.05154i
\(689\) 5.97677 + 10.3521i 0.227697 + 0.394382i
\(690\) 1.03635i 0.0394531i
\(691\) 21.7228 12.5417i 0.826374 0.477107i −0.0262356 0.999656i \(-0.508352\pi\)
0.852610 + 0.522549i \(0.175019\pi\)
\(692\) 38.8905i 1.47839i
\(693\) 10.9277 18.9273i 0.415109 0.718989i
\(694\) 30.3152 52.5074i 1.15075 1.99315i
\(695\) 15.0463 26.0609i 0.570737 0.988546i
\(696\) 0.491183 0.283585i 0.0186183 0.0107493i
\(697\) 0.451748 0.0171112
\(698\) −21.9050 + 29.8812i −0.829116 + 1.13102i
\(699\) −49.4162 −1.86909
\(700\) −8.65640 + 4.99777i −0.327181 + 0.188898i
\(701\) −1.93949 + 3.35929i −0.0732534 + 0.126879i −0.900325 0.435217i \(-0.856672\pi\)
0.827072 + 0.562096i \(0.190005\pi\)
\(702\) 6.38555 11.0601i 0.241007 0.417436i
\(703\) 3.34410 5.79215i 0.126125 0.218455i
\(704\) 21.1616i 0.797559i
\(705\) −25.5008 + 14.7229i −0.960415 + 0.554496i
\(706\) 6.87841i 0.258872i
\(707\) −9.12233 15.8003i −0.343080 0.594233i
\(708\) 56.9462i 2.14017i
\(709\) 5.18048i 0.194557i 0.995257 + 0.0972786i \(0.0310138\pi\)
−0.995257 + 0.0972786i \(0.968986\pi\)
\(710\) 12.4485 + 21.5615i 0.467185 + 0.809188i
\(711\) −41.7095 + 24.0810i −1.56423 + 0.903107i
\(712\) 0.407929 0.706553i 0.0152878 0.0264792i
\(713\) 0.114786 + 0.198814i 0.00429875 + 0.00744566i
\(714\) −9.13645 15.8248i −0.341923 0.592228i
\(715\) −16.8626 −0.630625
\(716\) 36.7938 + 21.2429i 1.37505 + 0.793884i
\(717\) −22.5418 + 39.0435i −0.841838 + 1.45811i
\(718\) 25.1526 + 43.5656i 0.938687 + 1.62585i
\(719\) 12.6463i 0.471626i 0.971798 + 0.235813i \(0.0757752\pi\)
−0.971798 + 0.235813i \(0.924225\pi\)
\(720\) 12.0641 + 20.8956i 0.449601 + 0.778733i
\(721\) −2.05080 3.55208i −0.0763757 0.132287i
\(722\) −29.3989 16.9735i −1.09411 0.631686i
\(723\) −30.9704 53.6423i −1.15180 1.99498i
\(724\) −2.63584 + 4.56540i −0.0979601 + 0.169672i
\(725\) 4.08704 0.151789
\(726\) 15.0980i 0.560338i
\(727\) 7.93722 13.7477i 0.294375 0.509873i −0.680464 0.732781i \(-0.738222\pi\)
0.974839 + 0.222908i \(0.0715551\pi\)
\(728\) −0.897659 0.518264i −0.0332695 0.0192081i
\(729\) −37.3928 −1.38492
\(730\) 42.6776 + 24.6399i 1.57957 + 0.911965i
\(731\) −9.83104 5.67595i −0.363614 0.209933i
\(732\) 28.1953 16.2786i 1.04213 0.601673i
\(733\) 17.9921i 0.664554i 0.943182 + 0.332277i \(0.107817\pi\)
−0.943182 + 0.332277i \(0.892183\pi\)
\(734\) −30.8568 −1.13895
\(735\) 10.6618 0.393265
\(736\) 1.00664i 0.0371051i
\(737\) 36.5696i 1.34706i
\(738\) −1.67492 0.967013i −0.0616545 0.0355963i
\(739\) −14.4008 −0.529743 −0.264871 0.964284i \(-0.585330\pi\)
−0.264871 + 0.964284i \(0.585330\pi\)
\(740\) 7.50453 + 12.9982i 0.275872 + 0.477824i
\(741\) −11.4489 6.61003i −0.420586 0.242826i
\(742\) −11.5546 6.67104i −0.424182 0.244901i
\(743\) −30.5028 −1.11904 −0.559520 0.828817i \(-0.689015\pi\)
−0.559520 + 0.828817i \(0.689015\pi\)
\(744\) 0.534836 + 0.308788i 0.0196081 + 0.0113207i
\(745\) 20.1016i 0.736467i
\(746\) 7.39804 0.270862
\(747\) −26.5204 + 45.9346i −0.970329 + 1.68066i
\(748\) 8.07362 + 4.66131i 0.295201 + 0.170434i
\(749\) 0.861884 1.49283i 0.0314926 0.0545467i
\(750\) 60.8800i 2.22302i
\(751\) 31.0882i 1.13442i 0.823572 + 0.567212i \(0.191978\pi\)
−0.823572 + 0.567212i \(0.808022\pi\)
\(752\) 25.5970 14.7784i 0.933427 0.538914i
\(753\) −37.5065 21.6544i −1.36681 0.789131i
\(754\) −6.13965 10.6342i −0.223593 0.387274i
\(755\) 14.4626 + 25.0500i 0.526348 + 0.911662i
\(756\) 7.00639i 0.254820i
\(757\) −20.8957 12.0642i −0.759469 0.438480i 0.0696362 0.997572i \(-0.477816\pi\)
−0.829105 + 0.559093i \(0.811149\pi\)
\(758\) 35.1073 1.27516
\(759\) 0.930856i 0.0337879i
\(760\) 0.250526 0.144642i 0.00908755 0.00524670i
\(761\) −1.58149 0.913073i −0.0573289 0.0330989i 0.471062 0.882100i \(-0.343871\pi\)
−0.528391 + 0.849001i \(0.677204\pi\)
\(762\) −78.5242 −2.84463
\(763\) 13.6715i 0.494940i
\(764\) −4.56455 −0.165139
\(765\) −9.93051 −0.359039
\(766\) 8.44949 14.6349i 0.305293 0.528782i