Properties

Label 1183.2.e.g.508.1
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.1
Root \(-0.181721 + 0.314749i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.g.170.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19402 - 2.06810i) q^{2} +(1.37574 - 2.38285i) q^{3} +(-1.85136 + 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} -6.57063 q^{6} +(1.69505 + 2.03145i) q^{7} +4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +O(q^{10})\) \(q+(-1.19402 - 2.06810i) q^{2} +(1.37574 - 2.38285i) q^{3} +(-1.85136 + 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} -6.57063 q^{6} +(1.69505 + 2.03145i) q^{7} +4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +(1.17286 - 2.03145i) q^{10} +(-0.293901 + 0.509052i) q^{11} +(5.09398 + 8.82303i) q^{12} +(2.17733 - 5.93113i) q^{14} +2.70272 q^{15} +(-1.15235 - 1.99593i) q^{16} +(3.22710 - 5.58950i) q^{17} +(-5.45742 + 9.45253i) q^{18} +(-1.91345 - 3.31419i) q^{19} -3.63711 q^{20} +(7.17260 - 1.24430i) q^{21} +1.40369 q^{22} +(-4.13001 - 7.15338i) q^{23} +(5.59398 - 9.68906i) q^{24} +(2.01756 - 3.49452i) q^{25} -4.32156 q^{27} +(-9.65231 + 1.67448i) q^{28} -3.96018 q^{29} +(-3.22710 - 5.58950i) q^{30} +(-1.49436 + 2.58831i) q^{31} +(1.31430 - 2.27644i) q^{32} +(0.808663 + 1.40065i) q^{33} -15.4129 q^{34} +(-0.895609 + 2.43967i) q^{35} +16.9238 q^{36} +(0.877941 + 1.52064i) q^{37} +(-4.56938 + 7.91440i) q^{38} +(1.99705 + 3.45900i) q^{40} -3.67169 q^{41} +(-11.1376 - 13.3479i) q^{42} +6.38085 q^{43} +(-1.08823 - 1.88488i) q^{44} +(2.24482 - 3.88814i) q^{45} +(-9.86261 + 17.0825i) q^{46} +(-2.17030 - 3.75906i) q^{47} -6.34134 q^{48} +(-1.25361 + 6.88683i) q^{49} -9.63603 q^{50} +(-8.87930 - 15.3794i) q^{51} +(-0.212770 + 0.368529i) q^{53} +(5.16002 + 8.93742i) q^{54} -0.577387 q^{55} +(6.89235 + 8.26022i) q^{56} -10.5296 q^{57} +(4.72853 + 8.19006i) q^{58} +(3.00431 - 5.20362i) q^{59} +(-5.00371 + 8.66669i) q^{60} +(-1.10337 - 1.91109i) q^{61} +7.13717 q^{62} +(4.16735 - 11.3520i) q^{63} -10.8866 q^{64} +(1.93112 - 3.34479i) q^{66} +(3.50651 - 6.07346i) q^{67} +(11.9491 + 20.6964i) q^{68} -22.7272 q^{69} +(6.11486 - 1.06080i) q^{70} -3.60253 q^{71} +(-9.29247 - 16.0950i) q^{72} +(2.46714 - 4.27321i) q^{73} +(2.09656 - 3.63134i) q^{74} +(-5.55128 - 9.61510i) q^{75} +14.1699 q^{76} +(-1.53229 + 0.265822i) q^{77} +(-1.39270 - 2.41223i) q^{79} +(1.13193 - 1.96056i) q^{80} +(0.910609 - 1.57722i) q^{81} +(4.38406 + 7.59342i) q^{82} +2.86819 q^{83} +(-9.28903 + 25.3037i) q^{84} +6.33983 q^{85} +(-7.61885 - 13.1962i) q^{86} +(-5.44818 + 9.43652i) q^{87} +(-1.19505 + 2.06989i) q^{88} +(-1.04656 - 1.81269i) q^{89} -10.7214 q^{90} +30.5845 q^{92} +(4.11170 + 7.12167i) q^{93} +(-5.18275 + 8.97679i) q^{94} +(1.87954 - 3.25546i) q^{95} +(-3.61628 - 6.26357i) q^{96} -7.69704 q^{97} +(15.7395 - 5.63041i) q^{98} +2.68663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} + q^{3} - 4q^{4} - q^{5} - 18q^{6} + 6q^{7} + 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q - 2q^{2} + q^{3} - 4q^{4} - q^{5} - 18q^{6} + 6q^{7} + 6q^{8} + 3q^{9} + 4q^{10} - 4q^{11} + 5q^{12} - 2q^{14} - 4q^{15} + 8q^{16} + 5q^{17} - 3q^{18} + q^{19} - 2q^{20} + 9q^{21} + 10q^{22} - q^{23} + 11q^{24} + 7q^{25} - 8q^{27} - 8q^{28} - 6q^{29} - 5q^{30} - 16q^{31} - 8q^{32} - 16q^{33} - 32q^{34} - 28q^{35} + 42q^{36} + 13q^{37} - 17q^{38} - 5q^{40} - 16q^{41} - 52q^{42} + 22q^{43} - 21q^{44} + 7q^{45} - 16q^{46} + q^{47} - 42q^{48} + 6q^{49} + 12q^{50} - 20q^{51} - 2q^{53} + 18q^{54} - 18q^{55} + 9q^{56} - 42q^{57} + 8q^{58} - 13q^{59} - 20q^{60} - 5q^{61} - 10q^{62} - 8q^{63} - 30q^{64} + 18q^{66} + 11q^{67} + 29q^{68} - 46q^{69} + 39q^{70} + 12q^{71} - 25q^{72} + 30q^{73} - 3q^{74} - 3q^{75} - 18q^{76} + 11q^{77} + 7q^{79} + 7q^{80} - 6q^{81} + q^{82} + 54q^{83} - 41q^{84} - 2q^{85} + 7q^{86} + 16q^{87} - 4q^{89} - 16q^{90} + 54q^{92} + 7q^{93} + 45q^{94} - 6q^{95} - 19q^{96} - 70q^{97} + 82q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19402 2.06810i −0.844299 1.46237i −0.886229 0.463248i \(-0.846684\pi\)
0.0419302 0.999121i \(-0.486649\pi\)
\(3\) 1.37574 2.38285i 0.794283 1.37574i −0.129010 0.991643i \(-0.541180\pi\)
0.923293 0.384096i \(-0.125487\pi\)
\(4\) −1.85136 + 3.20665i −0.925680 + 1.60333i
\(5\) 0.491140 + 0.850679i 0.219644 + 0.380435i 0.954699 0.297572i \(-0.0961769\pi\)
−0.735055 + 0.678008i \(0.762844\pi\)
\(6\) −6.57063 −2.68245
\(7\) 1.69505 + 2.03145i 0.640669 + 0.767817i
\(8\) 4.06616 1.43761
\(9\) −2.28532 3.95828i −0.761772 1.31943i
\(10\) 1.17286 2.03145i 0.370891 0.642402i
\(11\) −0.293901 + 0.509052i −0.0886146 + 0.153485i −0.906926 0.421291i \(-0.861577\pi\)
0.818311 + 0.574775i \(0.194911\pi\)
\(12\) 5.09398 + 8.82303i 1.47051 + 2.54699i
\(13\) 0 0
\(14\) 2.17733 5.93113i 0.581916 1.58516i
\(15\) 2.70272 0.697840
\(16\) −1.15235 1.99593i −0.288088 0.498983i
\(17\) 3.22710 5.58950i 0.782687 1.35565i −0.147685 0.989035i \(-0.547182\pi\)
0.930371 0.366619i \(-0.119485\pi\)
\(18\) −5.45742 + 9.45253i −1.28633 + 2.22798i
\(19\) −1.91345 3.31419i −0.438975 0.760327i 0.558636 0.829413i \(-0.311325\pi\)
−0.997611 + 0.0690863i \(0.977992\pi\)
\(20\) −3.63711 −0.813282
\(21\) 7.17260 1.24430i 1.56519 0.271528i
\(22\) 1.40369 0.299269
\(23\) −4.13001 7.15338i −0.861166 1.49158i −0.870805 0.491629i \(-0.836402\pi\)
0.00963902 0.999954i \(-0.496932\pi\)
\(24\) 5.59398 9.68906i 1.14187 1.97777i
\(25\) 2.01756 3.49452i 0.403513 0.698904i
\(26\) 0 0
\(27\) −4.32156 −0.831685
\(28\) −9.65231 + 1.67448i −1.82412 + 0.316447i
\(29\) −3.96018 −0.735387 −0.367694 0.929947i \(-0.619853\pi\)
−0.367694 + 0.929947i \(0.619853\pi\)
\(30\) −3.22710 5.58950i −0.589185 1.02050i
\(31\) −1.49436 + 2.58831i −0.268395 + 0.464874i −0.968448 0.249218i \(-0.919827\pi\)
0.700053 + 0.714091i \(0.253160\pi\)
\(32\) 1.31430 2.27644i 0.232338 0.402421i
\(33\) 0.808663 + 1.40065i 0.140770 + 0.243821i
\(34\) −15.4129 −2.64329
\(35\) −0.895609 + 2.43967i −0.151386 + 0.412380i
\(36\) 16.9238 2.82063
\(37\) 0.877941 + 1.52064i 0.144333 + 0.249991i 0.929124 0.369769i \(-0.120563\pi\)
−0.784791 + 0.619760i \(0.787230\pi\)
\(38\) −4.56938 + 7.91440i −0.741252 + 1.28389i
\(39\) 0 0
\(40\) 1.99705 + 3.45900i 0.315762 + 0.546916i
\(41\) −3.67169 −0.573421 −0.286710 0.958017i \(-0.592562\pi\)
−0.286710 + 0.958017i \(0.592562\pi\)
\(42\) −11.1376 13.3479i −1.71856 2.05963i
\(43\) 6.38085 0.973070 0.486535 0.873661i \(-0.338261\pi\)
0.486535 + 0.873661i \(0.338261\pi\)
\(44\) −1.08823 1.88488i −0.164058 0.284156i
\(45\) 2.24482 3.88814i 0.334638 0.579610i
\(46\) −9.86261 + 17.0825i −1.45416 + 2.51868i
\(47\) −2.17030 3.75906i −0.316570 0.548316i 0.663200 0.748442i \(-0.269198\pi\)
−0.979770 + 0.200127i \(0.935865\pi\)
\(48\) −6.34134 −0.915294
\(49\) −1.25361 + 6.88683i −0.179087 + 0.983833i
\(50\) −9.63603 −1.36274
\(51\) −8.87930 15.3794i −1.24335 2.15355i
\(52\) 0 0
\(53\) −0.212770 + 0.368529i −0.0292263 + 0.0506214i −0.880269 0.474476i \(-0.842638\pi\)
0.851042 + 0.525097i \(0.175971\pi\)
\(54\) 5.16002 + 8.93742i 0.702190 + 1.21623i
\(55\) −0.577387 −0.0778548
\(56\) 6.89235 + 8.26022i 0.921029 + 1.10382i
\(57\) −10.5296 −1.39468
\(58\) 4.72853 + 8.19006i 0.620887 + 1.07541i
\(59\) 3.00431 5.20362i 0.391128 0.677454i −0.601470 0.798895i \(-0.705418\pi\)
0.992599 + 0.121441i \(0.0387516\pi\)
\(60\) −5.00371 + 8.66669i −0.645977 + 1.11886i
\(61\) −1.10337 1.91109i −0.141272 0.244691i 0.786704 0.617331i \(-0.211786\pi\)
−0.927976 + 0.372640i \(0.878453\pi\)
\(62\) 7.13717 0.906422
\(63\) 4.16735 11.3520i 0.525036 1.43022i
\(64\) −10.8866 −1.36083
\(65\) 0 0
\(66\) 1.93112 3.34479i 0.237704 0.411716i
\(67\) 3.50651 6.07346i 0.428389 0.741991i −0.568341 0.822793i \(-0.692415\pi\)
0.996730 + 0.0808015i \(0.0257480\pi\)
\(68\) 11.9491 + 20.6964i 1.44904 + 2.50980i
\(69\) −22.7272 −2.73604
\(70\) 6.11486 1.06080i 0.730866 0.126790i
\(71\) −3.60253 −0.427542 −0.213771 0.976884i \(-0.568575\pi\)
−0.213771 + 0.976884i \(0.568575\pi\)
\(72\) −9.29247 16.0950i −1.09513 1.89682i
\(73\) 2.46714 4.27321i 0.288756 0.500141i −0.684757 0.728772i \(-0.740092\pi\)
0.973513 + 0.228631i \(0.0734249\pi\)
\(74\) 2.09656 3.63134i 0.243720 0.422135i
\(75\) −5.55128 9.61510i −0.641007 1.11026i
\(76\) 14.1699 1.62540
\(77\) −1.53229 + 0.265822i −0.174621 + 0.0302932i
\(78\) 0 0
\(79\) −1.39270 2.41223i −0.156691 0.271397i 0.776982 0.629522i \(-0.216749\pi\)
−0.933674 + 0.358125i \(0.883416\pi\)
\(80\) 1.13193 1.96056i 0.126554 0.219198i
\(81\) 0.910609 1.57722i 0.101179 0.175247i
\(82\) 4.38406 + 7.59342i 0.484138 + 0.838552i
\(83\) 2.86819 0.314825 0.157412 0.987533i \(-0.449685\pi\)
0.157412 + 0.987533i \(0.449685\pi\)
\(84\) −9.28903 + 25.3037i −1.01352 + 2.76086i
\(85\) 6.33983 0.687651
\(86\) −7.61885 13.1962i −0.821562 1.42299i
\(87\) −5.44818 + 9.43652i −0.584106 + 1.01170i
\(88\) −1.19505 + 2.06989i −0.127393 + 0.220651i
\(89\) −1.04656 1.81269i −0.110935 0.192145i 0.805213 0.592986i \(-0.202051\pi\)
−0.916147 + 0.400842i \(0.868718\pi\)
\(90\) −10.7214 −1.13014
\(91\) 0 0
\(92\) 30.5845 3.18866
\(93\) 4.11170 + 7.12167i 0.426363 + 0.738483i
\(94\) −5.18275 + 8.97679i −0.534560 + 0.925885i
\(95\) 1.87954 3.25546i 0.192837 0.334003i
\(96\) −3.61628 6.26357i −0.369085 0.639273i
\(97\) −7.69704 −0.781516 −0.390758 0.920493i \(-0.627787\pi\)
−0.390758 + 0.920493i \(0.627787\pi\)
\(98\) 15.7395 5.63041i 1.58993 0.568758i
\(99\) 2.68663 0.270016
\(100\) 7.47047 + 12.9392i 0.747047 + 1.29392i
\(101\) 1.31866 2.28399i 0.131212 0.227265i −0.792932 0.609310i \(-0.791447\pi\)
0.924144 + 0.382045i \(0.124780\pi\)
\(102\) −21.2041 + 36.7266i −2.09952 + 3.63647i
\(103\) 5.43095 + 9.40669i 0.535128 + 0.926868i 0.999157 + 0.0410486i \(0.0130699\pi\)
−0.464029 + 0.885820i \(0.653597\pi\)
\(104\) 0 0
\(105\) 4.58125 + 5.49045i 0.447084 + 0.535813i
\(106\) 1.01621 0.0987027
\(107\) 7.99024 + 13.8395i 0.772446 + 1.33792i 0.936219 + 0.351418i \(0.114300\pi\)
−0.163773 + 0.986498i \(0.552366\pi\)
\(108\) 8.00077 13.8577i 0.769874 1.33346i
\(109\) 4.61738 7.99754i 0.442265 0.766026i −0.555592 0.831455i \(-0.687508\pi\)
0.997857 + 0.0654294i \(0.0208417\pi\)
\(110\) 0.689410 + 1.19409i 0.0657327 + 0.113852i
\(111\) 4.83127 0.458564
\(112\) 2.10135 5.72416i 0.198559 0.540882i
\(113\) 10.1802 0.957677 0.478838 0.877903i \(-0.341058\pi\)
0.478838 + 0.877903i \(0.341058\pi\)
\(114\) 12.5726 + 21.7763i 1.17753 + 2.03954i
\(115\) 4.05682 7.02662i 0.378301 0.655236i
\(116\) 7.33173 12.6989i 0.680734 1.17907i
\(117\) 0 0
\(118\) −14.3488 −1.32092
\(119\) 16.8249 2.91878i 1.54234 0.267564i
\(120\) 10.9897 1.00322
\(121\) 5.32724 + 9.22706i 0.484295 + 0.838823i
\(122\) −2.63489 + 4.56376i −0.238552 + 0.413184i
\(123\) −5.05128 + 8.74908i −0.455459 + 0.788878i
\(124\) −5.53320 9.58378i −0.496896 0.860649i
\(125\) 8.87502 0.793806
\(126\) −28.4530 + 4.93601i −2.53479 + 0.439735i
\(127\) 4.25026 0.377149 0.188575 0.982059i \(-0.439613\pi\)
0.188575 + 0.982059i \(0.439613\pi\)
\(128\) 10.3702 + 17.9617i 0.916606 + 1.58761i
\(129\) 8.77838 15.2046i 0.772893 1.33869i
\(130\) 0 0
\(131\) 1.08478 + 1.87890i 0.0947779 + 0.164160i 0.909516 0.415669i \(-0.136453\pi\)
−0.814738 + 0.579829i \(0.803119\pi\)
\(132\) −5.98851 −0.521233
\(133\) 3.48923 9.50479i 0.302555 0.824170i
\(134\) −16.7474 −1.44675
\(135\) −2.12249 3.67626i −0.182675 0.316402i
\(136\) 13.1219 22.7278i 1.12519 1.94889i
\(137\) 4.18158 7.24271i 0.357257 0.618787i −0.630245 0.776396i \(-0.717045\pi\)
0.987501 + 0.157610i \(0.0503788\pi\)
\(138\) 27.1367 + 47.0022i 2.31003 + 4.00110i
\(139\) −0.576914 −0.0489332 −0.0244666 0.999701i \(-0.507789\pi\)
−0.0244666 + 0.999701i \(0.507789\pi\)
\(140\) −6.16508 7.38862i −0.521045 0.624452i
\(141\) −11.9430 −1.00579
\(142\) 4.30149 + 7.45040i 0.360973 + 0.625224i
\(143\) 0 0
\(144\) −5.26698 + 9.12267i −0.438915 + 0.760223i
\(145\) −1.94500 3.36885i −0.161524 0.279767i
\(146\) −11.7832 −0.975187
\(147\) 14.6856 + 12.4616i 1.21125 + 1.02782i
\(148\) −6.50154 −0.534423
\(149\) 1.40331 + 2.43061i 0.114964 + 0.199123i 0.917765 0.397123i \(-0.129991\pi\)
−0.802801 + 0.596246i \(0.796658\pi\)
\(150\) −13.2567 + 22.9612i −1.08240 + 1.87478i
\(151\) −11.5054 + 19.9280i −0.936300 + 1.62172i −0.164000 + 0.986460i \(0.552440\pi\)
−0.772300 + 0.635258i \(0.780894\pi\)
\(152\) −7.78039 13.4760i −0.631073 1.09305i
\(153\) −29.4998 −2.38492
\(154\) 2.37933 + 2.85154i 0.191732 + 0.229784i
\(155\) −2.93576 −0.235806
\(156\) 0 0
\(157\) −11.2880 + 19.5513i −0.900879 + 1.56037i −0.0745227 + 0.997219i \(0.523743\pi\)
−0.826356 + 0.563148i \(0.809590\pi\)
\(158\) −3.32583 + 5.76050i −0.264588 + 0.458281i
\(159\) 0.585433 + 1.01400i 0.0464278 + 0.0804154i
\(160\) 2.58203 0.204127
\(161\) 7.53119 20.5153i 0.593541 1.61683i
\(162\) −4.34913 −0.341700
\(163\) 4.08857 + 7.08161i 0.320242 + 0.554675i 0.980538 0.196331i \(-0.0629026\pi\)
−0.660296 + 0.751005i \(0.729569\pi\)
\(164\) 6.79761 11.7738i 0.530804 0.919380i
\(165\) −0.794333 + 1.37583i −0.0618388 + 0.107108i
\(166\) −3.42467 5.93170i −0.265806 0.460389i
\(167\) 2.32771 0.180124 0.0900619 0.995936i \(-0.471293\pi\)
0.0900619 + 0.995936i \(0.471293\pi\)
\(168\) 29.1649 5.05953i 2.25012 0.390351i
\(169\) 0 0
\(170\) −7.56988 13.1114i −0.580583 1.00560i
\(171\) −8.74566 + 15.1479i −0.668798 + 1.15839i
\(172\) −11.8133 + 20.4611i −0.900752 + 1.56015i
\(173\) 4.06686 + 7.04401i 0.309198 + 0.535546i 0.978187 0.207726i \(-0.0666061\pi\)
−0.668989 + 0.743272i \(0.733273\pi\)
\(174\) 26.0209 1.97264
\(175\) 10.5188 1.82480i 0.795149 0.137942i
\(176\) 1.35471 0.102115
\(177\) −8.26630 14.3177i −0.621333 1.07618i
\(178\) −2.49922 + 4.32877i −0.187324 + 0.324455i
\(179\) 10.4963 18.1801i 0.784528 1.35884i −0.144752 0.989468i \(-0.546239\pi\)
0.929281 0.369375i \(-0.120428\pi\)
\(180\) 8.31194 + 14.3967i 0.619536 + 1.07307i
\(181\) −1.60807 −0.119527 −0.0597635 0.998213i \(-0.519035\pi\)
−0.0597635 + 0.998213i \(0.519035\pi\)
\(182\) 0 0
\(183\) −6.07180 −0.448841
\(184\) −16.7933 29.0868i −1.23802 2.14431i
\(185\) −0.862384 + 1.49369i −0.0634037 + 0.109818i
\(186\) 9.81889 17.0068i 0.719956 1.24700i
\(187\) 1.89690 + 3.28552i 0.138715 + 0.240261i
\(188\) 16.0720 1.17217
\(189\) −7.32526 8.77905i −0.532834 0.638582i
\(190\) −8.97683 −0.651247
\(191\) 5.78111 + 10.0132i 0.418307 + 0.724529i 0.995769 0.0918886i \(-0.0292904\pi\)
−0.577463 + 0.816417i \(0.695957\pi\)
\(192\) −14.9771 + 25.9412i −1.08088 + 1.87214i
\(193\) 11.7894 20.4199i 0.848621 1.46985i −0.0338178 0.999428i \(-0.510767\pi\)
0.882439 0.470427i \(-0.155900\pi\)
\(194\) 9.19041 + 15.9183i 0.659833 + 1.14286i
\(195\) 0 0
\(196\) −19.7628 16.7699i −1.41163 1.19785i
\(197\) 1.47094 0.104800 0.0524002 0.998626i \(-0.483313\pi\)
0.0524002 + 0.998626i \(0.483313\pi\)
\(198\) −3.20788 5.55622i −0.227974 0.394863i
\(199\) −4.69700 + 8.13543i −0.332961 + 0.576706i −0.983091 0.183117i \(-0.941381\pi\)
0.650130 + 0.759823i \(0.274714\pi\)
\(200\) 8.20374 14.2093i 0.580092 1.00475i
\(201\) −9.64810 16.7110i −0.680524 1.17870i
\(202\) −6.29802 −0.443127
\(203\) −6.71271 8.04493i −0.471140 0.564643i
\(204\) 65.7551 4.60378
\(205\) −1.80331 3.12343i −0.125949 0.218150i
\(206\) 12.9693 22.4635i 0.903615 1.56511i
\(207\) −18.8767 + 32.6955i −1.31202 + 2.27249i
\(208\) 0 0
\(209\) 2.24946 0.155598
\(210\) 5.88472 16.0302i 0.406084 1.10619i
\(211\) −8.94219 −0.615605 −0.307803 0.951450i \(-0.599594\pi\)
−0.307803 + 0.951450i \(0.599594\pi\)
\(212\) −0.787829 1.36456i −0.0541083 0.0937184i
\(213\) −4.95615 + 8.58430i −0.339589 + 0.588186i
\(214\) 19.0810 33.0493i 1.30435 2.25920i
\(215\) 3.13389 + 5.42805i 0.213729 + 0.370190i
\(216\) −17.5722 −1.19563
\(217\) −7.79104 + 1.35159i −0.528890 + 0.0917518i
\(218\) −22.0530 −1.49362
\(219\) −6.78827 11.7576i −0.458709 0.794507i
\(220\) 1.06895 1.85148i 0.0720686 0.124827i
\(221\) 0 0
\(222\) −5.76863 9.99156i −0.387165 0.670589i
\(223\) −21.8196 −1.46115 −0.730574 0.682833i \(-0.760748\pi\)
−0.730574 + 0.682833i \(0.760748\pi\)
\(224\) 6.85229 1.18873i 0.457838 0.0794256i
\(225\) −18.4431 −1.22954
\(226\) −12.1554 21.0538i −0.808565 1.40048i
\(227\) −9.27627 + 16.0670i −0.615687 + 1.06640i 0.374576 + 0.927196i \(0.377788\pi\)
−0.990263 + 0.139206i \(0.955545\pi\)
\(228\) 19.4941 33.7648i 1.29103 2.23613i
\(229\) 9.67525 + 16.7580i 0.639359 + 1.10740i 0.985574 + 0.169247i \(0.0541334\pi\)
−0.346215 + 0.938155i \(0.612533\pi\)
\(230\) −19.3757 −1.27759
\(231\) −1.47462 + 4.01692i −0.0970230 + 0.264294i
\(232\) −16.1027 −1.05720
\(233\) −8.08170 13.9979i −0.529450 0.917034i −0.999410 0.0343462i \(-0.989065\pi\)
0.469960 0.882688i \(-0.344268\pi\)
\(234\) 0 0
\(235\) 2.13184 3.69245i 0.139066 0.240869i
\(236\) 11.1241 + 19.2676i 0.724119 + 1.25421i
\(237\) −7.66398 −0.497829
\(238\) −26.1256 31.3105i −1.69347 2.02956i
\(239\) −16.1037 −1.04166 −0.520831 0.853660i \(-0.674378\pi\)
−0.520831 + 0.853660i \(0.674378\pi\)
\(240\) −3.11449 5.39445i −0.201039 0.348210i
\(241\) −2.00300 + 3.46930i −0.129025 + 0.223477i −0.923299 0.384082i \(-0.874518\pi\)
0.794274 + 0.607559i \(0.207851\pi\)
\(242\) 12.7217 22.0346i 0.817779 1.41643i
\(243\) −8.98786 15.5674i −0.576572 0.998651i
\(244\) 8.17095 0.523092
\(245\) −6.47418 + 2.31598i −0.413620 + 0.147962i
\(246\) 24.1253 1.53817
\(247\) 0 0
\(248\) −6.07631 + 10.5245i −0.385846 + 0.668305i
\(249\) 3.94588 6.83446i 0.250060 0.433116i
\(250\) −10.5969 18.3544i −0.670209 1.16084i
\(251\) 3.24688 0.204941 0.102471 0.994736i \(-0.467325\pi\)
0.102471 + 0.994736i \(0.467325\pi\)
\(252\) 28.6867 + 34.3799i 1.80709 + 2.16573i
\(253\) 4.85525 0.305247
\(254\) −5.07489 8.78996i −0.318427 0.551531i
\(255\) 8.72195 15.1069i 0.546190 0.946029i
\(256\) 13.8778 24.0371i 0.867365 1.50232i
\(257\) 13.4462 + 23.2895i 0.838751 + 1.45276i 0.890940 + 0.454122i \(0.150047\pi\)
−0.0521891 + 0.998637i \(0.516620\pi\)
\(258\) −41.9262 −2.61021
\(259\) −1.60095 + 4.36106i −0.0994784 + 0.270983i
\(260\) 0 0
\(261\) 9.05027 + 15.6755i 0.560198 + 0.970291i
\(262\) 2.59050 4.48688i 0.160042 0.277200i
\(263\) 1.90353 3.29701i 0.117377 0.203302i −0.801351 0.598195i \(-0.795885\pi\)
0.918727 + 0.394893i \(0.129218\pi\)
\(264\) 3.28815 + 5.69525i 0.202372 + 0.350518i
\(265\) −0.418000 −0.0256775
\(266\) −23.8231 + 4.13282i −1.46069 + 0.253399i
\(267\) −5.75915 −0.352455
\(268\) 12.9836 + 22.4883i 0.793102 + 1.37369i
\(269\) 11.9190 20.6444i 0.726716 1.25871i −0.231548 0.972824i \(-0.574379\pi\)
0.958264 0.285886i \(-0.0922878\pi\)
\(270\) −5.06859 + 8.77905i −0.308464 + 0.534276i
\(271\) 4.95068 + 8.57482i 0.300732 + 0.520883i 0.976302 0.216413i \(-0.0694357\pi\)
−0.675570 + 0.737296i \(0.736102\pi\)
\(272\) −14.8750 −0.901931
\(273\) 0 0
\(274\) −19.9715 −1.20653
\(275\) 1.18593 + 2.05409i 0.0715142 + 0.123866i
\(276\) 42.0763 72.8783i 2.53270 4.38676i
\(277\) −5.89289 + 10.2068i −0.354069 + 0.613266i −0.986958 0.160977i \(-0.948536\pi\)
0.632889 + 0.774243i \(0.281869\pi\)
\(278\) 0.688846 + 1.19312i 0.0413142 + 0.0715584i
\(279\) 13.6603 0.817823
\(280\) −3.64169 + 9.92010i −0.217633 + 0.592840i
\(281\) −12.9976 −0.775372 −0.387686 0.921791i \(-0.626726\pi\)
−0.387686 + 0.921791i \(0.626726\pi\)
\(282\) 14.2602 + 24.6994i 0.849184 + 1.47083i
\(283\) 8.40249 14.5535i 0.499476 0.865118i −0.500524 0.865723i \(-0.666859\pi\)
1.00000 0.000604910i \(0.000192549\pi\)
\(284\) 6.66959 11.5521i 0.395767 0.685489i
\(285\) −5.17151 8.95733i −0.306334 0.530586i
\(286\) 0 0
\(287\) −6.22369 7.45886i −0.367373 0.440283i
\(288\) −12.0144 −0.707955
\(289\) −12.3283 21.3533i −0.725197 1.25608i
\(290\) −4.64474 + 8.04493i −0.272749 + 0.472414i
\(291\) −10.5891 + 18.3409i −0.620746 + 1.07516i
\(292\) 9.13512 + 15.8225i 0.534592 + 0.925941i
\(293\) 14.0956 0.823476 0.411738 0.911302i \(-0.364922\pi\)
0.411738 + 0.911302i \(0.364922\pi\)
\(294\) 8.23701 45.2508i 0.480392 2.63908i
\(295\) 5.90215 0.343637
\(296\) 3.56985 + 6.18316i 0.207493 + 0.359389i
\(297\) 1.27011 2.19990i 0.0736994 0.127651i
\(298\) 3.35116 5.80438i 0.194128 0.336239i
\(299\) 0 0
\(300\) 41.1097 2.37347
\(301\) 10.8159 + 12.9624i 0.623416 + 0.747140i
\(302\) 54.9508 3.16207
\(303\) −3.62827 6.28434i −0.208439 0.361026i
\(304\) −4.40993 + 7.63822i −0.252927 + 0.438082i
\(305\) 1.08382 1.87723i 0.0620593 0.107490i
\(306\) 35.2233 + 61.0085i 2.01358 + 3.48762i
\(307\) −15.8786 −0.906240 −0.453120 0.891450i \(-0.649689\pi\)
−0.453120 + 0.891450i \(0.649689\pi\)
\(308\) 1.98443 5.40566i 0.113073 0.308016i
\(309\) 29.8863 1.70017
\(310\) 3.50535 + 6.07145i 0.199091 + 0.344835i
\(311\) 14.3017 24.7713i 0.810975 1.40465i −0.101208 0.994865i \(-0.532271\pi\)
0.912183 0.409784i \(-0.134396\pi\)
\(312\) 0 0
\(313\) 9.28962 + 16.0901i 0.525080 + 0.909465i 0.999573 + 0.0292063i \(0.00929798\pi\)
−0.474493 + 0.880259i \(0.657369\pi\)
\(314\) 53.9122 3.04244
\(315\) 11.7037 2.03035i 0.659427 0.114397i
\(316\) 10.3136 0.580184
\(317\) 15.3223 + 26.5389i 0.860584 + 1.49057i 0.871366 + 0.490633i \(0.163234\pi\)
−0.0107826 + 0.999942i \(0.503432\pi\)
\(318\) 1.39804 2.42147i 0.0783979 0.135789i
\(319\) 1.16390 2.01594i 0.0651660 0.112871i
\(320\) −5.34685 9.26102i −0.298898 0.517707i
\(321\) 43.9700 2.45416
\(322\) −51.4200 + 8.92033i −2.86552 + 0.497110i
\(323\) −24.6995 −1.37432
\(324\) 3.37173 + 5.84001i 0.187318 + 0.324445i
\(325\) 0 0
\(326\) 9.76366 16.9112i 0.540759 0.936622i
\(327\) −12.7046 22.0051i −0.702568 1.21688i
\(328\) −14.9297 −0.824353
\(329\) 3.95760 10.7807i 0.218190 0.594357i
\(330\) 3.79379 0.208842
\(331\) 13.6138 + 23.5799i 0.748284 + 1.29607i 0.948644 + 0.316344i \(0.102455\pi\)
−0.200360 + 0.979722i \(0.564211\pi\)
\(332\) −5.31005 + 9.19728i −0.291427 + 0.504766i
\(333\) 4.01275 6.95028i 0.219897 0.380873i
\(334\) −2.77933 4.81395i −0.152078 0.263407i
\(335\) 6.88876 0.376373
\(336\) −10.7489 12.8821i −0.586400 0.702779i
\(337\) −12.3160 −0.670898 −0.335449 0.942058i \(-0.608888\pi\)
−0.335449 + 0.942058i \(0.608888\pi\)
\(338\) 0 0
\(339\) 14.0054 24.2580i 0.760666 1.31751i
\(340\) −11.7373 + 20.3296i −0.636545 + 1.10253i
\(341\) −0.878389 1.52141i −0.0475674 0.0823892i
\(342\) 41.7699 2.25866
\(343\) −16.1152 + 9.12688i −0.870140 + 0.492805i
\(344\) 25.9456 1.39889
\(345\) −11.1623 19.3336i −0.600956 1.04089i
\(346\) 9.71182 16.8214i 0.522111 0.904322i
\(347\) −3.07253 + 5.32177i −0.164942 + 0.285688i −0.936635 0.350308i \(-0.886077\pi\)
0.771693 + 0.635996i \(0.219410\pi\)
\(348\) −20.1731 34.9408i −1.08139 1.87302i
\(349\) −13.0313 −0.697547 −0.348774 0.937207i \(-0.613402\pi\)
−0.348774 + 0.937207i \(0.613402\pi\)
\(350\) −16.3336 19.5752i −0.873065 1.04634i
\(351\) 0 0
\(352\) 0.772550 + 1.33810i 0.0411771 + 0.0713208i
\(353\) 15.8332 27.4240i 0.842718 1.45963i −0.0448710 0.998993i \(-0.514288\pi\)
0.887589 0.460637i \(-0.152379\pi\)
\(354\) −19.7402 + 34.1911i −1.04918 + 1.81724i
\(355\) −1.76935 3.06460i −0.0939072 0.162652i
\(356\) 7.75021 0.410761
\(357\) 16.1917 44.1067i 0.856954 2.33438i
\(358\) −50.1310 −2.64950
\(359\) 9.96610 + 17.2618i 0.525991 + 0.911043i 0.999542 + 0.0302764i \(0.00963874\pi\)
−0.473551 + 0.880767i \(0.657028\pi\)
\(360\) 9.12780 15.8098i 0.481077 0.833251i
\(361\) 2.17744 3.77144i 0.114602 0.198497i
\(362\) 1.92007 + 3.32566i 0.100917 + 0.174793i
\(363\) 29.3156 1.53867
\(364\) 0 0
\(365\) 4.84684 0.253695
\(366\) 7.24984 + 12.5571i 0.378955 + 0.656370i
\(367\) −9.85950 + 17.0772i −0.514662 + 0.891420i 0.485194 + 0.874407i \(0.338749\pi\)
−0.999855 + 0.0170133i \(0.994584\pi\)
\(368\) −9.51844 + 16.4864i −0.496183 + 0.859414i
\(369\) 8.39096 + 14.5336i 0.436816 + 0.756588i
\(370\) 4.11881 0.214127
\(371\) −1.10931 + 0.192442i −0.0575923 + 0.00999109i
\(372\) −30.4490 −1.57870
\(373\) −8.77345 15.1961i −0.454272 0.786823i 0.544374 0.838843i \(-0.316767\pi\)
−0.998646 + 0.0520202i \(0.983434\pi\)
\(374\) 4.52986 7.84595i 0.234234 0.405704i
\(375\) 12.2097 21.1478i 0.630507 1.09207i
\(376\) −8.82478 15.2850i −0.455103 0.788262i
\(377\) 0 0
\(378\) −9.40946 + 25.6317i −0.483971 + 1.31835i
\(379\) 11.7014 0.601058 0.300529 0.953773i \(-0.402837\pi\)
0.300529 + 0.953773i \(0.402837\pi\)
\(380\) 6.95942 + 12.0541i 0.357010 + 0.618360i
\(381\) 5.84725 10.1277i 0.299563 0.518859i
\(382\) 13.8055 23.9119i 0.706352 1.22344i
\(383\) −10.7644 18.6445i −0.550036 0.952690i −0.998271 0.0587748i \(-0.981281\pi\)
0.448235 0.893916i \(-0.352053\pi\)
\(384\) 57.0669 2.91218
\(385\) −0.978699 1.17293i −0.0498791 0.0597783i
\(386\) −56.3072 −2.86596
\(387\) −14.5823 25.2572i −0.741258 1.28390i
\(388\) 14.2500 24.6817i 0.723435 1.25303i
\(389\) −13.2455 + 22.9419i −0.671574 + 1.16320i 0.305884 + 0.952069i \(0.401048\pi\)
−0.977458 + 0.211131i \(0.932285\pi\)
\(390\) 0 0
\(391\) −53.3118 −2.69609
\(392\) −5.09738 + 28.0030i −0.257457 + 1.41436i
\(393\) 5.96951 0.301122
\(394\) −1.75633 3.04206i −0.0884828 0.153257i
\(395\) 1.36802 2.36949i 0.0688327 0.119222i
\(396\) −4.97392 + 8.61508i −0.249949 + 0.432924i
\(397\) −16.8995 29.2707i −0.848160 1.46906i −0.882849 0.469658i \(-0.844377\pi\)
0.0346887 0.999398i \(-0.488956\pi\)
\(398\) 22.4332 1.12447
\(399\) −17.8482 21.3904i −0.893529 1.07086i
\(400\) −9.29977 −0.464989
\(401\) 10.8059 + 18.7164i 0.539623 + 0.934655i 0.998924 + 0.0463741i \(0.0147666\pi\)
−0.459301 + 0.888281i \(0.651900\pi\)
\(402\) −23.0400 + 39.9065i −1.14913 + 1.99035i
\(403\) 0 0
\(404\) 4.88264 + 8.45697i 0.242920 + 0.420750i
\(405\) 1.78895 0.0888934
\(406\) −8.62262 + 23.4884i −0.427934 + 1.16571i
\(407\) −1.03211 −0.0511599
\(408\) −36.1047 62.5351i −1.78745 3.09595i
\(409\) 3.87109 6.70492i 0.191413 0.331537i −0.754306 0.656523i \(-0.772026\pi\)
0.945719 + 0.324986i \(0.105360\pi\)
\(410\) −4.30637 + 7.45886i −0.212677 + 0.368367i
\(411\) −11.5055 19.9282i −0.567526 0.982984i
\(412\) −40.2186 −1.98143
\(413\) 15.6634 2.71728i 0.770744 0.133709i
\(414\) 90.1567 4.43096
\(415\) 1.40868 + 2.43991i 0.0691495 + 0.119770i
\(416\) 0 0
\(417\) −0.793683 + 1.37470i −0.0388668 + 0.0673193i
\(418\) −2.68589 4.65211i −0.131371 0.227542i
\(419\) −8.10194 −0.395806 −0.197903 0.980222i \(-0.563413\pi\)
−0.197903 + 0.980222i \(0.563413\pi\)
\(420\) −26.0875 + 4.52565i −1.27294 + 0.220829i
\(421\) 32.1124 1.56506 0.782530 0.622612i \(-0.213929\pi\)
0.782530 + 0.622612i \(0.213929\pi\)
\(422\) 10.6771 + 18.4933i 0.519755 + 0.900242i
\(423\) −9.91963 + 17.1813i −0.482309 + 0.835384i
\(424\) −0.865159 + 1.49850i −0.0420158 + 0.0727735i
\(425\) −13.0218 22.5543i −0.631648 1.09405i
\(426\) 23.6709 1.14686
\(427\) 2.01203 5.48085i 0.0973690 0.265237i
\(428\) −59.1713 −2.86015
\(429\) 0 0
\(430\) 7.48384 12.9624i 0.360903 0.625102i
\(431\) −14.7640 + 25.5721i −0.711159 + 1.23176i 0.253263 + 0.967397i \(0.418496\pi\)
−0.964422 + 0.264366i \(0.914837\pi\)
\(432\) 4.97996 + 8.62554i 0.239598 + 0.414997i
\(433\) 22.0910 1.06163 0.530813 0.847489i \(-0.321887\pi\)
0.530813 + 0.847489i \(0.321887\pi\)
\(434\) 12.0979 + 14.4988i 0.580716 + 0.695967i
\(435\) −10.7033 −0.513183
\(436\) 17.0969 + 29.6127i 0.818792 + 1.41819i
\(437\) −15.8051 + 27.3752i −0.756060 + 1.30953i
\(438\) −16.2106 + 28.0777i −0.774575 + 1.34160i
\(439\) 3.17790 + 5.50428i 0.151673 + 0.262705i 0.931843 0.362863i \(-0.118201\pi\)
−0.780170 + 0.625568i \(0.784867\pi\)
\(440\) −2.34775 −0.111924
\(441\) 30.1249 10.7764i 1.43452 0.513164i
\(442\) 0 0
\(443\) 6.78135 + 11.7456i 0.322192 + 0.558052i 0.980940 0.194311i \(-0.0622472\pi\)
−0.658748 + 0.752363i \(0.728914\pi\)
\(444\) −8.94443 + 15.4922i −0.424484 + 0.735227i
\(445\) 1.02801 1.78057i 0.0487324 0.0844070i
\(446\) 26.0530 + 45.1251i 1.23365 + 2.13674i
\(447\) 7.72237 0.365255
\(448\) −18.4534 22.1157i −0.871839 1.04487i
\(449\) −21.9118 −1.03408 −0.517041 0.855961i \(-0.672966\pi\)
−0.517041 + 0.855961i \(0.672966\pi\)
\(450\) 22.0214 + 38.1421i 1.03810 + 1.79804i
\(451\) 1.07911 1.86908i 0.0508134 0.0880115i
\(452\) −18.8473 + 32.6445i −0.886502 + 1.53547i
\(453\) 31.6570 + 54.8315i 1.48737 + 2.57621i
\(454\) 44.3041 2.07930
\(455\) 0 0
\(456\) −42.8151 −2.00500
\(457\) 7.60732 + 13.1763i 0.355855 + 0.616359i 0.987264 0.159091i \(-0.0508563\pi\)
−0.631409 + 0.775450i \(0.717523\pi\)
\(458\) 23.1049 40.0188i 1.07962 1.86996i
\(459\) −13.9461 + 24.1554i −0.650949 + 1.12748i
\(460\) 15.0213 + 26.0176i 0.700371 + 1.21308i
\(461\) 16.2163 0.755267 0.377633 0.925955i \(-0.376738\pi\)
0.377633 + 0.925955i \(0.376738\pi\)
\(462\) 10.0681 1.74662i 0.468412 0.0812600i
\(463\) 1.44769 0.0672799 0.0336400 0.999434i \(-0.489290\pi\)
0.0336400 + 0.999434i \(0.489290\pi\)
\(464\) 4.56353 + 7.90426i 0.211856 + 0.366946i
\(465\) −4.03884 + 6.99547i −0.187297 + 0.324407i
\(466\) −19.2994 + 33.4275i −0.894027 + 1.54850i
\(467\) −7.00337 12.1302i −0.324078 0.561319i 0.657248 0.753675i \(-0.271721\pi\)
−0.981325 + 0.192356i \(0.938387\pi\)
\(468\) 0 0
\(469\) 18.2817 3.17150i 0.844169 0.146446i
\(470\) −10.1818 −0.469652
\(471\) 31.0586 + 53.7951i 1.43111 + 2.47875i
\(472\) 12.2160 21.1588i 0.562288 0.973912i
\(473\) −1.87534 + 3.24818i −0.0862282 + 0.149352i
\(474\) 9.15094 + 15.8499i 0.420316 + 0.728009i
\(475\) −15.4420 −0.708528
\(476\) −21.7895 + 59.3553i −0.998719 + 2.72055i
\(477\) 1.94499 0.0890550
\(478\) 19.2281 + 33.3041i 0.879474 + 1.52329i
\(479\) −15.0122 + 26.0018i −0.685923 + 1.18805i 0.287223 + 0.957864i \(0.407268\pi\)
−0.973146 + 0.230189i \(0.926065\pi\)
\(480\) 3.55219 6.15258i 0.162135 0.280826i
\(481\) 0 0
\(482\) 9.56649 0.435742
\(483\) −38.5238 46.1693i −1.75289 2.10078i
\(484\) −39.4506 −1.79321
\(485\) −3.78033 6.54772i −0.171656 0.297317i
\(486\) −21.4633 + 37.1756i −0.973597 + 1.68632i
\(487\) −14.2452 + 24.6733i −0.645510 + 1.11806i 0.338674 + 0.940904i \(0.390022\pi\)
−0.984184 + 0.177152i \(0.943312\pi\)
\(488\) −4.48649 7.77082i −0.203094 0.351769i
\(489\) 22.4992 1.01745
\(490\) 12.5200 + 10.6239i 0.565595 + 0.479941i
\(491\) −28.4677 −1.28473 −0.642365 0.766399i \(-0.722047\pi\)
−0.642365 + 0.766399i \(0.722047\pi\)
\(492\) −18.7035 32.3954i −0.843218 1.46050i
\(493\) −12.7799 + 22.1354i −0.575578 + 0.996930i
\(494\) 0 0
\(495\) 1.31951 + 2.28546i 0.0593076 + 0.102724i
\(496\) 6.88812 0.309286
\(497\) −6.10647 7.31838i −0.273913 0.328274i
\(498\) −18.8458 −0.844501
\(499\) −13.1164 22.7183i −0.587172 1.01701i −0.994601 0.103775i \(-0.966908\pi\)
0.407429 0.913237i \(-0.366425\pi\)
\(500\) −16.4309 + 28.4591i −0.734811 + 1.27273i
\(501\) 3.20233 5.54659i 0.143069 0.247803i
\(502\) −3.87684 6.71488i −0.173032 0.299700i
\(503\) 8.53175 0.380412 0.190206 0.981744i \(-0.439084\pi\)
0.190206 + 0.981744i \(0.439084\pi\)
\(504\) 16.9451 46.1591i 0.754795 2.05609i
\(505\) 2.59059 0.115280
\(506\) −5.79726 10.0412i −0.257720 0.446384i
\(507\) 0 0
\(508\) −7.86876 + 13.6291i −0.349120 + 0.604693i
\(509\) −6.51298 11.2808i −0.288683 0.500014i 0.684813 0.728719i \(-0.259884\pi\)
−0.973496 + 0.228706i \(0.926551\pi\)
\(510\) −41.6567 −1.84459
\(511\) 12.8627 2.23142i 0.569014 0.0987124i
\(512\) −24.8008 −1.09605
\(513\) 8.26908 + 14.3225i 0.365089 + 0.632352i
\(514\) 32.1100 55.6162i 1.41631 2.45312i
\(515\) −5.33472 + 9.24000i −0.235076 + 0.407163i
\(516\) 32.5039 + 56.2984i 1.43090 + 2.47840i
\(517\) 2.55141 0.112211
\(518\) 10.9307 1.89625i 0.480266 0.0833164i
\(519\) 22.3798 0.982363
\(520\) 0 0
\(521\) −2.23285 + 3.86741i −0.0978230 + 0.169434i −0.910783 0.412885i \(-0.864521\pi\)
0.812960 + 0.582319i \(0.197855\pi\)
\(522\) 21.6124 37.4337i 0.945948 1.63843i
\(523\) 1.45406 + 2.51850i 0.0635815 + 0.110126i 0.896064 0.443925i \(-0.146414\pi\)
−0.832482 + 0.554051i \(0.813081\pi\)
\(524\) −8.03330 −0.350936
\(525\) 10.1229 27.5752i 0.441801 1.20348i
\(526\) −9.09140 −0.396404
\(527\) 9.64490 + 16.7055i 0.420138 + 0.727701i
\(528\) 1.86373 3.22807i 0.0811084 0.140484i
\(529\) −22.6139 + 39.1684i −0.983213 + 1.70297i
\(530\) 0.499100 + 0.864466i 0.0216795 + 0.0375500i
\(531\) −27.4632 −1.19180
\(532\) 24.0187 + 28.7855i 1.04134 + 1.24801i
\(533\) 0 0
\(534\) 6.87654 + 11.9105i 0.297577 + 0.515418i
\(535\) −7.84866 + 13.5943i −0.339327 + 0.587732i
\(536\) 14.2581 24.6957i 0.615854 1.06669i
\(537\) −28.8803 50.0221i −1.24628 2.15861i
\(538\) −56.9262 −2.45426
\(539\) −3.13732 2.66220i −0.135134 0.114669i
\(540\) 15.7180 0.676394
\(541\) −9.23193 15.9902i −0.396912 0.687471i 0.596431 0.802664i \(-0.296585\pi\)
−0.993343 + 0.115193i \(0.963251\pi\)
\(542\) 11.8224 20.4770i 0.507815 0.879562i
\(543\) −2.21229 + 3.83180i −0.0949384 + 0.164438i
\(544\) −8.48277 14.6926i −0.363696 0.629940i
\(545\) 9.07112 0.388564
\(546\) 0 0
\(547\) 34.9817 1.49571 0.747856 0.663861i \(-0.231083\pi\)
0.747856 + 0.663861i \(0.231083\pi\)
\(548\) 15.4832 + 26.8177i 0.661411 + 1.14560i
\(549\) −5.04310 + 8.73491i −0.215234 + 0.372797i
\(550\) 2.83204 4.90524i 0.120759 0.209160i
\(551\) 7.57760 + 13.1248i 0.322817 + 0.559135i
\(552\) −92.4127 −3.93334
\(553\) 2.53964 6.91806i 0.107996 0.294186i
\(554\) 28.1449 1.19576
\(555\) 2.37283 + 4.10986i 0.100721 + 0.174454i
\(556\) 1.06808 1.84996i 0.0452965 0.0784559i
\(557\) 0.0265706 0.0460217i 0.00112583 0.00195000i −0.865462 0.500975i \(-0.832975\pi\)
0.866588 + 0.499025i \(0.166308\pi\)
\(558\) −16.3107 28.2510i −0.690487 1.19596i
\(559\) 0 0
\(560\) 5.90148 1.02379i 0.249383 0.0432629i
\(561\) 10.4385 0.440716
\(562\) 15.5194 + 26.8804i 0.654646 + 1.13388i
\(563\) −3.99253 + 6.91527i −0.168265 + 0.291444i −0.937810 0.347149i \(-0.887150\pi\)
0.769545 + 0.638593i \(0.220483\pi\)
\(564\) 22.1109 38.2972i 0.931037 1.61260i
\(565\) 4.99992 + 8.66012i 0.210348 + 0.364334i
\(566\) −40.1309 −1.68683
\(567\) 4.74758 0.823608i 0.199380 0.0345883i
\(568\) −14.6485 −0.614637
\(569\) 13.3621 + 23.1438i 0.560167 + 0.970237i 0.997481 + 0.0709285i \(0.0225962\pi\)
−0.437315 + 0.899308i \(0.644070\pi\)
\(570\) −12.3498 + 21.3904i −0.517275 + 0.895946i
\(571\) −6.74647 + 11.6852i −0.282331 + 0.489012i −0.971958 0.235153i \(-0.924441\pi\)
0.689627 + 0.724164i \(0.257774\pi\)
\(572\) 0 0
\(573\) 31.8132 1.32902
\(574\) −7.99447 + 21.7772i −0.333683 + 0.908964i
\(575\) −33.3302 −1.38996
\(576\) 24.8794 + 43.0923i 1.03664 + 1.79551i
\(577\) 6.00662 10.4038i 0.250059 0.433115i −0.713483 0.700673i \(-0.752883\pi\)
0.963542 + 0.267558i \(0.0862167\pi\)
\(578\) −29.4406 + 50.9925i −1.22457 + 2.12101i
\(579\) −32.4383 56.1848i −1.34809 2.33496i
\(580\) 14.4036 0.598078
\(581\) 4.86172 + 5.82659i 0.201698 + 0.241728i
\(582\) 50.5745 2.09638
\(583\) −0.125067 0.216622i −0.00517974 0.00897158i
\(584\) 10.0318 17.3756i 0.415118 0.719005i
\(585\) 0 0
\(586\) −16.8305 29.1512i −0.695260 1.20422i
\(587\) −10.4235 −0.430225 −0.215113 0.976589i \(-0.569012\pi\)
−0.215113 + 0.976589i \(0.569012\pi\)
\(588\) −67.1486 + 24.0207i −2.76916 + 0.990599i
\(589\) 11.4375 0.471275
\(590\) −7.04728 12.2062i −0.290132 0.502523i
\(591\) 2.02364 3.50504i 0.0832412 0.144178i
\(592\) 2.02339 3.50462i 0.0831610 0.144039i
\(593\) −11.1751 19.3558i −0.458905 0.794847i 0.539998 0.841666i \(-0.318425\pi\)
−0.998903 + 0.0468194i \(0.985091\pi\)
\(594\) −6.06615 −0.248897
\(595\) 10.7463 + 12.8791i 0.440557 + 0.527991i
\(596\) −10.3921 −0.425679
\(597\) 12.9237 + 22.3845i 0.528931 + 0.916135i
\(598\) 0 0
\(599\) −0.579463 + 1.00366i −0.0236762 + 0.0410084i −0.877621 0.479356i \(-0.840870\pi\)
0.853945 + 0.520364i \(0.174204\pi\)
\(600\) −22.5724 39.0966i −0.921515 1.59611i
\(601\) 42.1813 1.72061 0.860306 0.509778i \(-0.170272\pi\)
0.860306 + 0.509778i \(0.170272\pi\)
\(602\) 13.8932 37.8456i 0.566245 1.54247i
\(603\) −32.0540 −1.30534
\(604\) −42.6014 73.7879i −1.73343 3.00239i
\(605\) −5.23284 + 9.06355i −0.212745 + 0.368486i
\(606\) −8.66444 + 15.0072i −0.351969 + 0.609628i
\(607\) 9.07844 + 15.7243i 0.368482 + 0.638230i 0.989328 0.145702i \(-0.0465441\pi\)
−0.620846 + 0.783932i \(0.713211\pi\)
\(608\) −10.0594 −0.407962
\(609\) −28.4048 + 4.92765i −1.15102 + 0.199679i
\(610\) −5.17640 −0.209586
\(611\) 0 0
\(612\) 54.6147 94.5955i 2.20767 3.82380i
\(613\) −0.451323 + 0.781714i −0.0182288 + 0.0315731i −0.874996 0.484130i \(-0.839136\pi\)
0.856767 + 0.515703i \(0.172469\pi\)
\(614\) 18.9594 + 32.8386i 0.765137 + 1.32526i
\(615\) −9.92354 −0.400156
\(616\) −6.23055 + 1.08087i −0.251036 + 0.0435497i
\(617\) 26.0436 1.04848 0.524238 0.851572i \(-0.324350\pi\)
0.524238 + 0.851572i \(0.324350\pi\)
\(618\) −35.6848 61.8079i −1.43545 2.48628i
\(619\) 13.4171 23.2390i 0.539277 0.934056i −0.459666 0.888092i \(-0.652031\pi\)
0.998943 0.0459638i \(-0.0146359\pi\)
\(620\) 5.43515 9.41396i 0.218281 0.378074i
\(621\) 17.8481 + 30.9138i 0.716218 + 1.24053i
\(622\) −68.3060 −2.73882
\(623\) 1.90843 5.19863i 0.0764596 0.208279i
\(624\) 0 0
\(625\) −5.72894 9.92281i −0.229158 0.396912i
\(626\) 22.1839 38.4237i 0.886649 1.53572i
\(627\) 3.09467 5.36012i 0.123589 0.214063i
\(628\) −41.7962 72.3932i −1.66785 2.88880i
\(629\) 11.3328 0.451869
\(630\) −18.1734 21.7801i −0.724044 0.867739i
\(631\) 33.6121 1.33808 0.669039 0.743228i \(-0.266706\pi\)
0.669039 + 0.743228i \(0.266706\pi\)
\(632\) −5.66296 9.80853i −0.225260 0.390162i
\(633\) −12.3021 + 21.3079i −0.488965 + 0.846913i
\(634\) 36.5901 63.3760i 1.45318 2.51698i
\(635\) 2.08747 + 3.61561i 0.0828388 + 0.143481i
\(636\) −4.33539 −0.171909
\(637\) 0 0
\(638\) −5.55889 −0.220078
\(639\) 8.23293 + 14.2598i 0.325690 + 0.564111i
\(640\) −10.1865 + 17.6435i −0.402655 + 0.697419i
\(641\) −10.5921 + 18.3460i −0.418361 + 0.724622i −0.995775 0.0918294i \(-0.970729\pi\)
0.577414 + 0.816452i \(0.304062\pi\)
\(642\) −52.5010 90.9343i −2.07205 3.58889i
\(643\) −0.661539 −0.0260886 −0.0130443 0.999915i \(-0.504152\pi\)
−0.0130443 + 0.999915i \(0.504152\pi\)
\(644\) 51.8423 + 62.1310i 2.04287 + 2.44831i
\(645\) 17.2457 0.679047
\(646\) 29.4917 + 51.0811i 1.16034 + 2.00976i
\(647\) 20.0162 34.6690i 0.786916 1.36298i −0.140931 0.990019i \(-0.545010\pi\)
0.927848 0.372960i \(-0.121657\pi\)
\(648\) 3.70268 6.41323i 0.145455 0.251936i
\(649\) 1.76594 + 3.05870i 0.0693193 + 0.120065i
\(650\) 0 0
\(651\) −7.49781 + 20.4243i −0.293862 + 0.800492i
\(652\) −30.2777 −1.18577
\(653\) −6.35602 11.0089i −0.248730 0.430813i 0.714444 0.699693i \(-0.246680\pi\)
−0.963174 + 0.268880i \(0.913347\pi\)
\(654\) −30.3391 + 52.5489i −1.18635 + 2.05482i
\(655\) −1.06556 + 1.84560i −0.0416349 + 0.0721138i
\(656\) 4.23107 + 7.32844i 0.165196 + 0.286127i
\(657\) −22.5527 −0.879867
\(658\) −27.0209 + 4.68759i −1.05339 + 0.182741i
\(659\) −14.1904 −0.552781 −0.276391 0.961045i \(-0.589138\pi\)
−0.276391 + 0.961045i \(0.589138\pi\)
\(660\) −2.94119 5.09430i −0.114486 0.198295i
\(661\) 25.0890 43.4554i 0.975848 1.69022i 0.298742 0.954334i \(-0.403433\pi\)
0.677106 0.735885i \(-0.263234\pi\)
\(662\) 32.5104 56.3096i 1.26355 2.18853i
\(663\) 0 0
\(664\) 11.6625 0.452594
\(665\) 9.79923 1.69997i 0.379998 0.0659219i
\(666\) −19.1652 −0.742635
\(667\) 16.3556 + 28.3287i 0.633290 + 1.09689i
\(668\) −4.30944 + 7.46417i −0.166737 + 0.288797i
\(669\) −30.0181 + 51.9928i −1.16057 + 2.01016i
\(670\) −8.22530 14.2466i −0.317771 0.550396i
\(671\) 1.29713 0.0500751
\(672\) 6.59439 17.9634i 0.254384 0.692952i
\(673\) −1.87427 −0.0722479 −0.0361240 0.999347i \(-0.511501\pi\)
−0.0361240 + 0.999347i \(0.511501\pi\)
\(674\) 14.7056 + 25.4708i 0.566438 + 0.981100i
\(675\) −8.71902 + 15.1018i −0.335595 + 0.581268i
\(676\) 0 0
\(677\) 1.00439 + 1.73966i 0.0386020 + 0.0668607i 0.884681 0.466197i \(-0.154376\pi\)
−0.846079 + 0.533058i \(0.821043\pi\)
\(678\) −66.8906 −2.56892
\(679\) −13.0469 15.6362i −0.500693 0.600062i
\(680\) 25.7788 0.988571
\(681\) 25.5234 + 44.2079i 0.978061 + 1.69405i
\(682\) −2.09762 + 3.63319i −0.0803222 + 0.139122i
\(683\) −7.05061 + 12.2120i −0.269784 + 0.467280i −0.968806 0.247820i \(-0.920286\pi\)
0.699022 + 0.715100i \(0.253619\pi\)
\(684\) −32.3828 56.0886i −1.23819 2.14460i
\(685\) 8.21497 0.313878
\(686\) 38.1172 + 22.4302i 1.45532 + 0.856390i
\(687\) 53.2425 2.03133
\(688\) −7.35298 12.7357i −0.280330 0.485546i
\(689\) 0 0
\(690\) −26.6559 + 46.1693i −1.01477 + 1.75764i
\(691\) −17.8460 30.9102i −0.678895 1.17588i −0.975314 0.220822i \(-0.929126\pi\)
0.296419 0.955058i \(-0.404207\pi\)
\(692\) −30.1169 −1.14487
\(693\) 4.55397 + 5.45776i 0.172991 + 0.207323i
\(694\) 14.6746 0.557041
\(695\) −0.283346 0.490769i −0.0107479 0.0186159i
\(696\) −22.1532 + 38.3704i −0.839714 + 1.45443i
\(697\) −11.8489 + 20.5229i −0.448809 + 0.777360i
\(698\) 15.5596 + 26.9500i 0.588938 + 1.02007i
\(699\) −44.4732 −1.68213
\(700\) −13.6226 + 37.1086i −0.514888 + 1.40257i
\(701\) −6.15865 −0.232609 −0.116305 0.993214i \(-0.537105\pi\)
−0.116305 + 0.993214i \(0.537105\pi\)
\(702\) 0 0
\(703\) 3.35979 5.81932i 0.126717 0.219480i
\(704\) 3.19959 5.54185i 0.120589 0.208866i
\(705\) −5.86571 10.1597i −0.220915 0.382637i
\(706\) −75.6207 −2.84602
\(707\) 6.87501 1.19268i 0.258561 0.0448552i
\(708\) 61.2156 2.30062
\(709\) 17.0185 + 29.4770i 0.639144 + 1.10703i 0.985621 + 0.168972i \(0.0540447\pi\)
−0.346477 + 0.938059i \(0.612622\pi\)
\(710\) −4.22527 + 7.31838i −0.158571 + 0.274654i
\(711\) −6.36553 + 11.0254i −0.238726 + 0.413486i
\(712\) −4.25547 7.37069i −0.159480 0.276228i
\(713\) 24.6869 0.924530
\(714\) −110.550 + 19.1782i −4.13724 + 0.717727i
\(715\) 0 0
\(716\) 38.8648 + 67.3158i 1.45244 + 2.51571i
\(717\) −22.1545 + 38.3727i −0.827375 + 1.43306i
\(718\) 23.7994 41.2218i 0.888187 1.53838i
\(719\) 11.4824 + 19.8881i 0.428222 + 0.741702i 0.996715 0.0809859i \(-0.0258069\pi\)
−0.568493 + 0.822688i \(0.692474\pi\)
\(720\) −10.3473 −0.385621
\(721\) −9.90351 + 26.9775i −0.368826 + 1.00470i
\(722\) −10.3996 −0.387034
\(723\) 5.51122 + 9.54571i 0.204964 + 0.355009i
\(724\) 2.97712 5.15653i 0.110644 0.191641i
\(725\) −7.98992 + 13.8389i −0.296738 + 0.513966i
\(726\) −35.0034 60.6276i −1.29910 2.25010i
\(727\) 1.06558 0.0395203 0.0197601 0.999805i \(-0.493710\pi\)
0.0197601 + 0.999805i \(0.493710\pi\)
\(728\) 0 0
\(729\) −43.9962 −1.62949
\(730\) −5.78721 10.0237i −0.214194 0.370996i
\(731\) 20.5916 35.6658i 0.761609 1.31915i
\(732\) 11.2411 19.4702i 0.415483 0.719637i
\(733\) −13.1689 22.8092i −0.486404 0.842476i 0.513474 0.858105i \(-0.328358\pi\)
−0.999878 + 0.0156289i \(0.995025\pi\)
\(734\) 47.0897 1.73811
\(735\) −3.38816 + 18.6132i −0.124974 + 0.686558i
\(736\) −21.7123 −0.800326
\(737\) 2.06114 + 3.57000i 0.0759230 + 0.131502i
\(738\) 20.0379 34.7067i 0.737606 1.27757i
\(739\) 17.1075 29.6310i 0.629308 1.08999i −0.358383 0.933575i \(-0.616672\pi\)
0.987691 0.156419i \(-0.0499950\pi\)
\(740\) −3.19317 5.53073i −0.117383 0.203314i
\(741\) 0 0
\(742\) 1.72252 + 2.06438i 0.0632358 + 0.0757857i
\(743\) −22.4782 −0.824644 −0.412322 0.911038i \(-0.635282\pi\)
−0.412322 + 0.911038i \(0.635282\pi\)
\(744\) 16.7188 + 28.9579i 0.612942 + 1.06165i
\(745\) −1.37845 + 2.38754i −0.0505023 + 0.0874726i
\(746\) −20.9513 + 36.2888i −0.767083 + 1.32863i
\(747\) −6.55472 11.3531i −0.239825 0.415388i
\(748\) −14.0474 −0.513623
\(749\) −14.5705 + 39.6905i −0.532393 + 1.45026i
\(750\) −58.3145 −2.12934
\(751\) 21.2712 + 36.8428i 0.776197 + 1.34441i 0.934119 + 0.356961i \(0.116187\pi\)
−0.157923 + 0.987451i \(0.550480\pi\)
\(752\) −5.00189 + 8.66353i −0.182400 + 0.315927i
\(753\) 4.46686 7.73683i 0.162781 0.281946i
\(754\) 0 0
\(755\) −22.6031 −0.822612
\(756\) 41.7131 7.23637i 1.51709 0.263184i
\(757\) −11.2380 −0.408454 −0.204227 0.978924i \(-0.565468\pi\)
−0.204227 + 0.978924i \(0.565468\pi\)
\(758\) −13.9716 24.1996i −0.507473 0.878969i
\(759\) 6.67956 11.5693i 0.242453 0.419941i
\(760\) 7.64252 13.2372i 0.277223 0.480165i
\(761\) 6.40422 + 11.0924i 0.232153 + 0.402101i 0.958441 0.285289i \(-0.0920897\pi\)
−0.726289 + 0.687390i \(0.758756\pi\)
\(762\) −27.9269 −1.01168
\(763\) 24.0733 4.17623i 0.871513 0.151190i
\(764\) −42.8117 −1.54887
\(765\) −14.4885 25.0948i −0.523833 0.907306i
\(766\) −25.7058 + 44.5238i −0.928789 + 1.60871i
\(767\) 0 0
\(768\) −38.1846 66.1377i −1.37787 2.38654i
\(769\) 51.3517 1.85179 0.925895 0.377781i \(-0.123313\pi\)
0.925895 + 0.377781i \(0.123313\pi\)
\(770\) −1.25716 + 3.42455i −0.0453049 + 0.123412i
\(771\) 73.9938 2.66482
\(772\) 43.6529 + 75.6091i 1.57110 + 2.72123i
\(773\) 10.0023 17.3245i 0.359759 0.623120i −0.628162 0.778083i \(-0.716192\pi\)
0.987920 + 0.154963i \(0.0495257\pi\)
\(774\) −34.8230 + 60.3151i −1.25169 + 2.16798i
\(775\) 6.02993 + 10.4441i 0.216602 + 0.375165i
\(776\) −31.2974 −1.12351
\(777\) 8.18925 + 9.81450i 0.293788 + 0.352093i
\(778\) 63.2615 2.26804
\(779\) 7.02558 + 12.1687i 0.251717 + 0.435987i
\(780\) 0