Properties

Label 403.2.h.b.118.4
Level 403
Weight 2
Character 403.118
Analytic conductor 3.218
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 118.4
Character \(\chi\) \(=\) 403.118
Dual form 403.2.h.b.222.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.72349 q^{2} +(-1.49143 - 2.58324i) q^{3} +0.970414 q^{4} +(-1.96711 + 3.40713i) q^{5} +(2.57047 + 4.45218i) q^{6} +(0.142448 + 0.246727i) q^{7} +1.77448 q^{8} +(-2.94874 + 5.10737i) q^{9} +O(q^{10})\) \(q-1.72349 q^{2} +(-1.49143 - 2.58324i) q^{3} +0.970414 q^{4} +(-1.96711 + 3.40713i) q^{5} +(2.57047 + 4.45218i) q^{6} +(0.142448 + 0.246727i) q^{7} +1.77448 q^{8} +(-2.94874 + 5.10737i) q^{9} +(3.39029 - 5.87216i) q^{10} +(2.19472 - 3.80137i) q^{11} +(-1.44731 - 2.50681i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.245507 - 0.425231i) q^{14} +11.7352 q^{15} -4.99912 q^{16} +(2.72208 + 4.71478i) q^{17} +(5.08212 - 8.80250i) q^{18} +(-0.983819 - 1.70403i) q^{19} +(-1.90891 + 3.30633i) q^{20} +(0.424902 - 0.735952i) q^{21} +(-3.78258 + 6.55162i) q^{22} +0.503278 q^{23} +(-2.64652 - 4.58390i) q^{24} +(-5.23904 - 9.07428i) q^{25} +(0.861744 - 1.49259i) q^{26} +8.64280 q^{27} +(0.138233 + 0.239427i) q^{28} -1.05528 q^{29} -20.2256 q^{30} +(-3.07690 - 4.64033i) q^{31} +5.06698 q^{32} -13.0931 q^{33} +(-4.69148 - 8.12587i) q^{34} -1.12084 q^{35} +(-2.86150 + 4.95626i) q^{36} +(-2.36478 - 4.09593i) q^{37} +(1.69560 + 2.93687i) q^{38} +2.98286 q^{39} +(-3.49060 + 6.04589i) q^{40} +(2.42267 - 4.19619i) q^{41} +(-0.732314 + 1.26841i) q^{42} +(-2.52626 - 4.37561i) q^{43} +(2.12979 - 3.68890i) q^{44} +(-11.6010 - 20.0935i) q^{45} -0.867394 q^{46} +13.5233 q^{47} +(7.45586 + 12.9139i) q^{48} +(3.45942 - 5.99189i) q^{49} +(9.02942 + 15.6394i) q^{50} +(8.11960 - 14.0636i) q^{51} +(-0.485207 + 0.840403i) q^{52} +(-5.72403 + 9.91431i) q^{53} -14.8958 q^{54} +(8.63451 + 14.9554i) q^{55} +(0.252771 + 0.437812i) q^{56} +(-2.93460 + 5.08288i) q^{57} +1.81877 q^{58} +(-3.96529 - 6.86809i) q^{59} +11.3880 q^{60} +11.2007 q^{61} +(5.30301 + 7.99756i) q^{62} -1.68017 q^{63} +1.26537 q^{64} +(-1.96711 - 3.40713i) q^{65} +22.5658 q^{66} +(0.707197 - 1.22490i) q^{67} +(2.64154 + 4.57529i) q^{68} +(-0.750605 - 1.30009i) q^{69} +1.93176 q^{70} +(5.19624 - 9.00016i) q^{71} +(-5.23248 + 9.06293i) q^{72} +(4.53442 - 7.85385i) q^{73} +(4.07568 + 7.05928i) q^{74} +(-15.6273 + 27.0673i) q^{75} +(-0.954712 - 1.65361i) q^{76} +1.25053 q^{77} -5.14093 q^{78} +(-4.01900 - 6.96112i) q^{79} +(9.83382 - 17.0327i) q^{80} +(-4.04393 - 7.00429i) q^{81} +(-4.17544 + 7.23208i) q^{82} +(-0.505524 + 0.875594i) q^{83} +(0.412331 - 0.714178i) q^{84} -21.4185 q^{85} +(4.35398 + 7.54131i) q^{86} +(1.57388 + 2.72604i) q^{87} +(3.89449 - 6.74546i) q^{88} +14.0470 q^{89} +(19.9942 + 34.6309i) q^{90} -0.284895 q^{91} +0.488388 q^{92} +(-7.39808 + 14.8691i) q^{93} -23.3073 q^{94} +7.74112 q^{95} +(-7.55705 - 13.0892i) q^{96} -1.31688 q^{97} +(-5.96227 + 10.3269i) q^{98} +(12.9433 + 22.4185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} + O(q^{10}) \) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} - 7q^{10} - 5q^{11} - 28q^{12} - 17q^{13} - 7q^{14} + 8q^{15} + 18q^{16} - 8q^{17} + 6q^{18} + 3q^{19} - 8q^{20} + 13q^{21} + 12q^{22} - 14q^{23} - 6q^{24} - 26q^{25} - 3q^{26} + 28q^{27} - 7q^{28} - 18q^{29} - 60q^{30} - 9q^{31} + 58q^{32} - 14q^{33} - 15q^{34} + 50q^{35} - 49q^{36} - 6q^{37} + 2q^{38} + 4q^{39} - 29q^{40} - 5q^{41} + 8q^{42} - q^{43} - 22q^{44} + 13q^{45} + 34q^{46} + 16q^{47} - 49q^{48} + 3q^{49} - 35q^{51} - 17q^{52} + 30q^{53} - 2q^{54} + 21q^{55} - 7q^{56} + 34q^{58} - 9q^{59} - 38q^{60} - 28q^{61} - 62q^{62} + 88q^{63} + 56q^{64} - 5q^{65} + 140q^{66} - 31q^{67} - 39q^{68} + 5q^{69} + 56q^{70} + q^{71} - 32q^{72} - 10q^{73} - 39q^{74} - 2q^{75} - 16q^{76} + 76q^{77} - 23q^{79} - 22q^{80} - 29q^{81} - 10q^{82} + 3q^{83} + 52q^{84} - 32q^{85} + 4q^{86} + 18q^{87} - 10q^{88} + 26q^{89} + 35q^{90} + 4q^{91} - 94q^{92} - 41q^{93} + 70q^{94} + 28q^{95} - 23q^{96} + 32q^{97} - 38q^{98} - 70q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.72349 −1.21869 −0.609345 0.792905i \(-0.708568\pi\)
−0.609345 + 0.792905i \(0.708568\pi\)
\(3\) −1.49143 2.58324i −0.861079 1.49143i −0.870889 0.491481i \(-0.836456\pi\)
0.00980961 0.999952i \(-0.496877\pi\)
\(4\) 0.970414 0.485207
\(5\) −1.96711 + 3.40713i −0.879718 + 1.52372i −0.0280673 + 0.999606i \(0.508935\pi\)
−0.851651 + 0.524110i \(0.824398\pi\)
\(6\) 2.57047 + 4.45218i 1.04939 + 1.81759i
\(7\) 0.142448 + 0.246727i 0.0538402 + 0.0932539i 0.891689 0.452648i \(-0.149521\pi\)
−0.837849 + 0.545902i \(0.816187\pi\)
\(8\) 1.77448 0.627374
\(9\) −2.94874 + 5.10737i −0.982914 + 1.70246i
\(10\) 3.39029 5.87216i 1.07210 1.85694i
\(11\) 2.19472 3.80137i 0.661734 1.14616i −0.318426 0.947948i \(-0.603154\pi\)
0.980160 0.198209i \(-0.0635123\pi\)
\(12\) −1.44731 2.50681i −0.417801 0.723653i
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i
\(14\) −0.245507 0.425231i −0.0656145 0.113648i
\(15\) 11.7352 3.03003
\(16\) −4.99912 −1.24978
\(17\) 2.72208 + 4.71478i 0.660201 + 1.14350i 0.980563 + 0.196207i \(0.0628624\pi\)
−0.320361 + 0.947296i \(0.603804\pi\)
\(18\) 5.08212 8.80250i 1.19787 2.07477i
\(19\) −0.983819 1.70403i −0.225704 0.390930i 0.730827 0.682563i \(-0.239135\pi\)
−0.956530 + 0.291633i \(0.905801\pi\)
\(20\) −1.90891 + 3.30633i −0.426845 + 0.739318i
\(21\) 0.424902 0.735952i 0.0927213 0.160598i
\(22\) −3.78258 + 6.55162i −0.806449 + 1.39681i
\(23\) 0.503278 0.104941 0.0524704 0.998622i \(-0.483290\pi\)
0.0524704 + 0.998622i \(0.483290\pi\)
\(24\) −2.64652 4.58390i −0.540218 0.935685i
\(25\) −5.23904 9.07428i −1.04781 1.81486i
\(26\) 0.861744 1.49259i 0.169002 0.292720i
\(27\) 8.64280 1.66331
\(28\) 0.138233 + 0.239427i 0.0261236 + 0.0452474i
\(29\) −1.05528 −0.195961 −0.0979804 0.995188i \(-0.531238\pi\)
−0.0979804 + 0.995188i \(0.531238\pi\)
\(30\) −20.2256 −3.69266
\(31\) −3.07690 4.64033i −0.552628 0.833428i
\(32\) 5.06698 0.895723
\(33\) −13.0931 −2.27922
\(34\) −4.69148 8.12587i −0.804581 1.39358i
\(35\) −1.12084 −0.189457
\(36\) −2.86150 + 4.95626i −0.476917 + 0.826044i
\(37\) −2.36478 4.09593i −0.388768 0.673366i 0.603516 0.797351i \(-0.293766\pi\)
−0.992284 + 0.123985i \(0.960433\pi\)
\(38\) 1.69560 + 2.93687i 0.275063 + 0.476423i
\(39\) 2.98286 0.477641
\(40\) −3.49060 + 6.04589i −0.551912 + 0.955939i
\(41\) 2.42267 4.19619i 0.378357 0.655334i −0.612466 0.790497i \(-0.709822\pi\)
0.990823 + 0.135163i \(0.0431557\pi\)
\(42\) −0.732314 + 1.26841i −0.112999 + 0.195719i
\(43\) −2.52626 4.37561i −0.385251 0.667274i 0.606553 0.795043i \(-0.292552\pi\)
−0.991804 + 0.127769i \(0.959218\pi\)
\(44\) 2.12979 3.68890i 0.321078 0.556123i
\(45\) −11.6010 20.0935i −1.72937 2.99536i
\(46\) −0.867394 −0.127890
\(47\) 13.5233 1.97258 0.986289 0.165027i \(-0.0527712\pi\)
0.986289 + 0.165027i \(0.0527712\pi\)
\(48\) 7.45586 + 12.9139i 1.07616 + 1.86396i
\(49\) 3.45942 5.99189i 0.494202 0.855984i
\(50\) 9.02942 + 15.6394i 1.27695 + 2.21175i
\(51\) 8.11960 14.0636i 1.13697 1.96929i
\(52\) −0.485207 + 0.840403i −0.0672861 + 0.116543i
\(53\) −5.72403 + 9.91431i −0.786256 + 1.36184i 0.141990 + 0.989868i \(0.454650\pi\)
−0.928246 + 0.371967i \(0.878683\pi\)
\(54\) −14.8958 −2.02706
\(55\) 8.63451 + 14.9554i 1.16428 + 2.01659i
\(56\) 0.252771 + 0.437812i 0.0337779 + 0.0585050i
\(57\) −2.93460 + 5.08288i −0.388697 + 0.673244i
\(58\) 1.81877 0.238816
\(59\) −3.96529 6.86809i −0.516237 0.894149i −0.999822 0.0188519i \(-0.993999\pi\)
0.483585 0.875297i \(-0.339334\pi\)
\(60\) 11.3880 1.47019
\(61\) 11.2007 1.43410 0.717049 0.697023i \(-0.245492\pi\)
0.717049 + 0.697023i \(0.245492\pi\)
\(62\) 5.30301 + 7.99756i 0.673483 + 1.01569i
\(63\) −1.68017 −0.211681
\(64\) 1.26537 0.158172
\(65\) −1.96711 3.40713i −0.243990 0.422603i
\(66\) 22.5658 2.77766
\(67\) 0.707197 1.22490i 0.0863979 0.149646i −0.819588 0.572953i \(-0.805798\pi\)
0.905986 + 0.423308i \(0.139131\pi\)
\(68\) 2.64154 + 4.57529i 0.320334 + 0.554835i
\(69\) −0.750605 1.30009i −0.0903623 0.156512i
\(70\) 1.93176 0.230889
\(71\) 5.19624 9.00016i 0.616681 1.06812i −0.373406 0.927668i \(-0.621810\pi\)
0.990087 0.140454i \(-0.0448564\pi\)
\(72\) −5.23248 + 9.06293i −0.616654 + 1.06808i
\(73\) 4.53442 7.85385i 0.530714 0.919224i −0.468644 0.883387i \(-0.655257\pi\)
0.999358 0.0358363i \(-0.0114095\pi\)
\(74\) 4.07568 + 7.05928i 0.473788 + 0.820625i
\(75\) −15.6273 + 27.0673i −1.80449 + 3.12547i
\(76\) −0.954712 1.65361i −0.109513 0.189682i
\(77\) 1.25053 0.142511
\(78\) −5.14093 −0.582096
\(79\) −4.01900 6.96112i −0.452173 0.783187i 0.546347 0.837559i \(-0.316018\pi\)
−0.998521 + 0.0543715i \(0.982684\pi\)
\(80\) 9.83382 17.0327i 1.09945 1.90431i
\(81\) −4.04393 7.00429i −0.449325 0.778254i
\(82\) −4.17544 + 7.23208i −0.461101 + 0.798650i
\(83\) −0.505524 + 0.875594i −0.0554885 + 0.0961089i −0.892435 0.451175i \(-0.851005\pi\)
0.836947 + 0.547284i \(0.184338\pi\)
\(84\) 0.412331 0.714178i 0.0449890 0.0779232i
\(85\) −21.4185 −2.32316
\(86\) 4.35398 + 7.54131i 0.469501 + 0.813200i
\(87\) 1.57388 + 2.72604i 0.168738 + 0.292262i
\(88\) 3.89449 6.74546i 0.415154 0.719068i
\(89\) 14.0470 1.48898 0.744488 0.667636i \(-0.232694\pi\)
0.744488 + 0.667636i \(0.232694\pi\)
\(90\) 19.9942 + 34.6309i 2.10757 + 3.65042i
\(91\) −0.284895 −0.0298652
\(92\) 0.488388 0.0509180
\(93\) −7.39808 + 14.8691i −0.767145 + 1.54185i
\(94\) −23.3073 −2.40396
\(95\) 7.74112 0.794222
\(96\) −7.55705 13.0892i −0.771288 1.33591i
\(97\) −1.31688 −0.133709 −0.0668545 0.997763i \(-0.521296\pi\)
−0.0668545 + 0.997763i \(0.521296\pi\)
\(98\) −5.96227 + 10.3269i −0.602280 + 1.04318i
\(99\) 12.9433 + 22.4185i 1.30085 + 2.25315i
\(100\) −5.08403 8.80580i −0.508403 0.880580i
\(101\) 1.92367 0.191412 0.0957062 0.995410i \(-0.469489\pi\)
0.0957062 + 0.995410i \(0.469489\pi\)
\(102\) −13.9940 + 24.2384i −1.38562 + 2.39996i
\(103\) −2.01665 + 3.49294i −0.198706 + 0.344169i −0.948109 0.317945i \(-0.897007\pi\)
0.749403 + 0.662114i \(0.230341\pi\)
\(104\) −0.887240 + 1.53675i −0.0870011 + 0.150690i
\(105\) 1.67166 + 2.89540i 0.163137 + 0.282562i
\(106\) 9.86530 17.0872i 0.958203 1.65966i
\(107\) −7.57237 13.1157i −0.732049 1.26795i −0.956006 0.293347i \(-0.905231\pi\)
0.223957 0.974599i \(-0.428102\pi\)
\(108\) 8.38709 0.807048
\(109\) 5.43050 0.520147 0.260074 0.965589i \(-0.416253\pi\)
0.260074 + 0.965589i \(0.416253\pi\)
\(110\) −14.8815 25.7755i −1.41889 2.45760i
\(111\) −7.05383 + 12.2176i −0.669520 + 1.15964i
\(112\) −0.712114 1.23342i −0.0672884 0.116547i
\(113\) −0.281428 + 0.487448i −0.0264745 + 0.0458552i −0.878959 0.476897i \(-0.841761\pi\)
0.852485 + 0.522752i \(0.175095\pi\)
\(114\) 5.05775 8.76028i 0.473702 0.820476i
\(115\) −0.990003 + 1.71474i −0.0923182 + 0.159900i
\(116\) −1.02406 −0.0950815
\(117\) −2.94874 5.10737i −0.272611 0.472177i
\(118\) 6.83414 + 11.8371i 0.629134 + 1.08969i
\(119\) −0.775508 + 1.34322i −0.0710907 + 0.123133i
\(120\) 20.8240 1.90096
\(121\) −4.13361 7.15962i −0.375783 0.650875i
\(122\) −19.3042 −1.74772
\(123\) −14.4530 −1.30318
\(124\) −2.98587 4.50304i −0.268139 0.404385i
\(125\) 21.5519 1.92766
\(126\) 2.89575 0.257974
\(127\) 7.52902 + 13.0406i 0.668093 + 1.15717i 0.978437 + 0.206546i \(0.0662223\pi\)
−0.310344 + 0.950624i \(0.600444\pi\)
\(128\) −12.3148 −1.08849
\(129\) −7.53549 + 13.0518i −0.663463 + 1.14915i
\(130\) 3.39029 + 5.87216i 0.297348 + 0.515022i
\(131\) −1.80816 3.13182i −0.157979 0.273628i 0.776161 0.630535i \(-0.217165\pi\)
−0.934140 + 0.356907i \(0.883831\pi\)
\(132\) −12.7057 −1.10589
\(133\) 0.280286 0.485469i 0.0243039 0.0420955i
\(134\) −1.21885 + 2.11110i −0.105292 + 0.182372i
\(135\) −17.0013 + 29.4472i −1.46324 + 2.53441i
\(136\) 4.83028 + 8.36629i 0.414193 + 0.717403i
\(137\) 3.84892 6.66653i 0.328836 0.569560i −0.653446 0.756974i \(-0.726677\pi\)
0.982281 + 0.187414i \(0.0600105\pi\)
\(138\) 1.29366 + 2.24068i 0.110124 + 0.190740i
\(139\) −16.2622 −1.37935 −0.689673 0.724121i \(-0.742246\pi\)
−0.689673 + 0.724121i \(0.742246\pi\)
\(140\) −1.08768 −0.0919257
\(141\) −20.1691 34.9339i −1.69855 2.94197i
\(142\) −8.95567 + 15.5117i −0.751543 + 1.30171i
\(143\) 2.19472 + 3.80137i 0.183532 + 0.317887i
\(144\) 14.7411 25.5324i 1.22843 2.12770i
\(145\) 2.07585 3.59548i 0.172390 0.298589i
\(146\) −7.81503 + 13.5360i −0.646776 + 1.12025i
\(147\) −20.6379 −1.70219
\(148\) −2.29482 3.97474i −0.188633 0.326722i
\(149\) 0.882419 + 1.52839i 0.0722906 + 0.125211i 0.899905 0.436086i \(-0.143636\pi\)
−0.827614 + 0.561297i \(0.810302\pi\)
\(150\) 26.9335 46.6503i 2.19911 3.80898i
\(151\) −14.4398 −1.17509 −0.587546 0.809191i \(-0.699906\pi\)
−0.587546 + 0.809191i \(0.699906\pi\)
\(152\) −1.74577 3.02376i −0.141601 0.245259i
\(153\) −32.1068 −2.59568
\(154\) −2.15528 −0.173677
\(155\) 21.8628 1.35538i 1.75606 0.108867i
\(156\) 2.89461 0.231755
\(157\) 13.7892 1.10050 0.550249 0.835001i \(-0.314533\pi\)
0.550249 + 0.835001i \(0.314533\pi\)
\(158\) 6.92671 + 11.9974i 0.551059 + 0.954463i
\(159\) 34.1480 2.70811
\(160\) −9.96729 + 17.2639i −0.787984 + 1.36483i
\(161\) 0.0716908 + 0.124172i 0.00565003 + 0.00978614i
\(162\) 6.96967 + 12.0718i 0.547589 + 0.948451i
\(163\) 20.6972 1.62113 0.810564 0.585649i \(-0.199160\pi\)
0.810564 + 0.585649i \(0.199160\pi\)
\(164\) 2.35099 4.07204i 0.183582 0.317973i
\(165\) 25.7556 44.6100i 2.00507 3.47288i
\(166\) 0.871266 1.50908i 0.0676233 0.117127i
\(167\) 5.31886 + 9.21254i 0.411586 + 0.712888i 0.995063 0.0992417i \(-0.0316417\pi\)
−0.583478 + 0.812129i \(0.698308\pi\)
\(168\) 0.753981 1.30593i 0.0581709 0.100755i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 36.9146 2.83122
\(171\) 11.6041 0.887389
\(172\) −2.45152 4.24615i −0.186926 0.323766i
\(173\) 6.17766 10.7000i 0.469679 0.813507i −0.529720 0.848172i \(-0.677703\pi\)
0.999399 + 0.0346651i \(0.0110365\pi\)
\(174\) −2.71257 4.69830i −0.205639 0.356177i
\(175\) 1.49258 2.58522i 0.112828 0.195424i
\(176\) −10.9717 + 19.0035i −0.827022 + 1.43244i
\(177\) −11.8279 + 20.4866i −0.889042 + 1.53987i
\(178\) −24.2098 −1.81460
\(179\) −9.17272 15.8876i −0.685601 1.18750i −0.973248 0.229759i \(-0.926206\pi\)
0.287647 0.957737i \(-0.407127\pi\)
\(180\) −11.2578 19.4990i −0.839104 1.45337i
\(181\) 8.45399 14.6427i 0.628380 1.08839i −0.359497 0.933146i \(-0.617052\pi\)
0.987877 0.155240i \(-0.0496150\pi\)
\(182\) 0.491014 0.0363964
\(183\) −16.7050 28.9340i −1.23487 2.13886i
\(184\) 0.893057 0.0658370
\(185\) 18.6072 1.36802
\(186\) 12.7505 25.6267i 0.934913 1.87904i
\(187\) 23.8968 1.74751
\(188\) 13.1232 0.957109
\(189\) 1.23115 + 2.13241i 0.0895528 + 0.155110i
\(190\) −13.3417 −0.967911
\(191\) −8.99331 + 15.5769i −0.650733 + 1.12710i 0.332212 + 0.943205i \(0.392205\pi\)
−0.982945 + 0.183898i \(0.941128\pi\)
\(192\) −1.88722 3.26876i −0.136198 0.235903i
\(193\) 6.36595 + 11.0262i 0.458231 + 0.793680i 0.998868 0.0475766i \(-0.0151498\pi\)
−0.540636 + 0.841256i \(0.681816\pi\)
\(194\) 2.26963 0.162950
\(195\) −5.86762 + 10.1630i −0.420189 + 0.727789i
\(196\) 3.35707 5.81461i 0.239790 0.415329i
\(197\) −5.22317 + 9.04679i −0.372135 + 0.644557i −0.989894 0.141811i \(-0.954708\pi\)
0.617759 + 0.786368i \(0.288041\pi\)
\(198\) −22.3077 38.6381i −1.58534 2.74589i
\(199\) 1.64202 2.84406i 0.116400 0.201610i −0.801939 0.597406i \(-0.796198\pi\)
0.918338 + 0.395796i \(0.129531\pi\)
\(200\) −9.29656 16.1021i −0.657366 1.13859i
\(201\) −4.21895 −0.297582
\(202\) −3.31543 −0.233273
\(203\) −0.150322 0.260366i −0.0105506 0.0182741i
\(204\) 7.87937 13.6475i 0.551666 0.955514i
\(205\) 9.53131 + 16.5087i 0.665695 + 1.15302i
\(206\) 3.47567 6.02004i 0.242161 0.419436i
\(207\) −1.48404 + 2.57043i −0.103148 + 0.178657i
\(208\) 2.49956 4.32937i 0.173313 0.300188i
\(209\) −8.63684 −0.597423
\(210\) −2.88108 4.99018i −0.198814 0.344355i
\(211\) −9.03055 15.6414i −0.621689 1.07680i −0.989171 0.146766i \(-0.953113\pi\)
0.367482 0.930031i \(-0.380220\pi\)
\(212\) −5.55468 + 9.62098i −0.381497 + 0.660772i
\(213\) −30.9994 −2.12404
\(214\) 13.0509 + 22.6048i 0.892141 + 1.54523i
\(215\) 19.8777 1.35565
\(216\) 15.3365 1.04352
\(217\) 0.706596 1.42016i 0.0479668 0.0964066i
\(218\) −9.35940 −0.633899
\(219\) −27.0511 −1.82795
\(220\) 8.37905 + 14.5129i 0.564916 + 0.978463i
\(221\) −5.44416 −0.366214
\(222\) 12.1572 21.0569i 0.815938 1.41325i
\(223\) −1.83304 3.17492i −0.122749 0.212608i 0.798102 0.602523i \(-0.205838\pi\)
−0.920851 + 0.389915i \(0.872504\pi\)
\(224\) 0.721779 + 1.25016i 0.0482259 + 0.0835297i
\(225\) 61.7942 4.11962
\(226\) 0.485038 0.840111i 0.0322643 0.0558833i
\(227\) −2.13470 + 3.69741i −0.141685 + 0.245405i −0.928131 0.372253i \(-0.878585\pi\)
0.786446 + 0.617659i \(0.211919\pi\)
\(228\) −2.84778 + 4.93249i −0.188599 + 0.326662i
\(229\) −10.8694 18.8264i −0.718272 1.24408i −0.961684 0.274161i \(-0.911600\pi\)
0.243412 0.969923i \(-0.421733\pi\)
\(230\) 1.70626 2.95533i 0.112507 0.194869i
\(231\) −1.86508 3.23042i −0.122714 0.212546i
\(232\) −1.87258 −0.122941
\(233\) −17.3895 −1.13923 −0.569613 0.821913i \(-0.692907\pi\)
−0.569613 + 0.821913i \(0.692907\pi\)
\(234\) 5.08212 + 8.80250i 0.332229 + 0.575437i
\(235\) −26.6018 + 46.0757i −1.73531 + 3.00565i
\(236\) −3.84798 6.66489i −0.250482 0.433847i
\(237\) −11.9881 + 20.7641i −0.778714 + 1.34877i
\(238\) 1.33658 2.31502i 0.0866376 0.150061i
\(239\) −5.05622 + 8.75763i −0.327060 + 0.566484i −0.981927 0.189260i \(-0.939391\pi\)
0.654867 + 0.755744i \(0.272724\pi\)
\(240\) −58.6659 −3.78687
\(241\) 5.39697 + 9.34783i 0.347650 + 0.602147i 0.985831 0.167739i \(-0.0536465\pi\)
−0.638182 + 0.769886i \(0.720313\pi\)
\(242\) 7.12423 + 12.3395i 0.457963 + 0.793215i
\(243\) 0.901708 1.56180i 0.0578446 0.100190i
\(244\) 10.8693 0.695834
\(245\) 13.6101 + 23.5734i 0.869517 + 1.50605i
\(246\) 24.9096 1.58818
\(247\) 1.96764 0.125198
\(248\) −5.45990 8.23418i −0.346704 0.522871i
\(249\) 3.01582 0.191120
\(250\) −37.1445 −2.34922
\(251\) 11.7025 + 20.2693i 0.738655 + 1.27939i 0.953101 + 0.302651i \(0.0978718\pi\)
−0.214447 + 0.976736i \(0.568795\pi\)
\(252\) −1.63046 −0.102709
\(253\) 1.10456 1.91315i 0.0694428 0.120278i
\(254\) −12.9762 22.4754i −0.814198 1.41023i
\(255\) 31.9443 + 55.3291i 2.00043 + 3.46484i
\(256\) 18.6937 1.16836
\(257\) −2.05783 + 3.56426i −0.128364 + 0.222333i −0.923043 0.384697i \(-0.874306\pi\)
0.794679 + 0.607030i \(0.207639\pi\)
\(258\) 12.9873 22.4947i 0.808556 1.40046i
\(259\) 0.673716 1.16691i 0.0418627 0.0725083i
\(260\) −1.90891 3.30633i −0.118386 0.205050i
\(261\) 3.11175 5.38971i 0.192613 0.333615i
\(262\) 3.11634 + 5.39766i 0.192528 + 0.333468i
\(263\) −8.74231 −0.539074 −0.269537 0.962990i \(-0.586871\pi\)
−0.269537 + 0.962990i \(0.586871\pi\)
\(264\) −23.2335 −1.42992
\(265\) −22.5196 39.0051i −1.38337 2.39606i
\(266\) −0.483069 + 0.836700i −0.0296189 + 0.0513014i
\(267\) −20.9501 36.2866i −1.28213 2.22071i
\(268\) 0.686274 1.18866i 0.0419209 0.0726090i
\(269\) −6.60006 + 11.4316i −0.402413 + 0.696999i −0.994017 0.109230i \(-0.965162\pi\)
0.591604 + 0.806229i \(0.298495\pi\)
\(270\) 29.3016 50.7519i 1.78324 3.08866i
\(271\) 10.2575 0.623100 0.311550 0.950230i \(-0.399152\pi\)
0.311550 + 0.950230i \(0.399152\pi\)
\(272\) −13.6080 23.5698i −0.825107 1.42913i
\(273\) 0.424902 + 0.735952i 0.0257163 + 0.0445419i
\(274\) −6.63357 + 11.4897i −0.400749 + 0.694117i
\(275\) −45.9929 −2.77348
\(276\) −0.728398 1.26162i −0.0438444 0.0759407i
\(277\) 22.4898 1.35128 0.675642 0.737230i \(-0.263867\pi\)
0.675642 + 0.737230i \(0.263867\pi\)
\(278\) 28.0278 1.68100
\(279\) 32.7729 2.03174i 1.96206 0.121637i
\(280\) −1.98891 −0.118860
\(281\) 10.3314 0.616318 0.308159 0.951335i \(-0.400287\pi\)
0.308159 + 0.951335i \(0.400287\pi\)
\(282\) 34.7612 + 60.2082i 2.07000 + 3.58535i
\(283\) −16.6331 −0.988737 −0.494368 0.869252i \(-0.664601\pi\)
−0.494368 + 0.869252i \(0.664601\pi\)
\(284\) 5.04251 8.73388i 0.299218 0.518260i
\(285\) −11.5454 19.9971i −0.683888 1.18453i
\(286\) −3.78258 6.55162i −0.223669 0.387405i
\(287\) 1.38041 0.0814833
\(288\) −14.9412 + 25.8789i −0.880419 + 1.52493i
\(289\) −6.31944 + 10.9456i −0.371732 + 0.643859i
\(290\) −3.57771 + 6.19678i −0.210090 + 0.363887i
\(291\) 1.96404 + 3.40182i 0.115134 + 0.199418i
\(292\) 4.40027 7.62148i 0.257506 0.446014i
\(293\) −6.40046 11.0859i −0.373919 0.647647i 0.616246 0.787554i \(-0.288653\pi\)
−0.990165 + 0.139907i \(0.955319\pi\)
\(294\) 35.5693 2.07444
\(295\) 31.2007 1.81657
\(296\) −4.19626 7.26814i −0.243903 0.422452i
\(297\) 18.9685 32.8545i 1.10067 1.90641i
\(298\) −1.52084 2.63417i −0.0880999 0.152593i
\(299\) −0.251639 + 0.435852i −0.0145527 + 0.0252060i
\(300\) −15.1650 + 26.2665i −0.875551 + 1.51650i
\(301\) 0.719719 1.24659i 0.0414839 0.0718523i
\(302\) 24.8868 1.43207
\(303\) −2.86903 4.96930i −0.164821 0.285479i
\(304\) 4.91824 + 8.51863i 0.282080 + 0.488577i
\(305\) −22.0329 + 38.1621i −1.26160 + 2.18516i
\(306\) 55.3358 3.16334
\(307\) −13.9160 24.1032i −0.794229 1.37564i −0.923328 0.384013i \(-0.874542\pi\)
0.129099 0.991632i \(-0.458792\pi\)
\(308\) 1.21353 0.0691475
\(309\) 12.0308 0.684407
\(310\) −37.6803 + 2.33598i −2.14010 + 0.132675i
\(311\) 12.4177 0.704142 0.352071 0.935973i \(-0.385478\pi\)
0.352071 + 0.935973i \(0.385478\pi\)
\(312\) 5.29304 0.299659
\(313\) 3.24239 + 5.61599i 0.183271 + 0.317435i 0.942993 0.332814i \(-0.107998\pi\)
−0.759722 + 0.650249i \(0.774665\pi\)
\(314\) −23.7655 −1.34117
\(315\) 3.30507 5.72455i 0.186220 0.322542i
\(316\) −3.90010 6.75517i −0.219398 0.380008i
\(317\) −14.1705 24.5439i −0.795892 1.37852i −0.922271 0.386543i \(-0.873669\pi\)
0.126380 0.991982i \(-0.459664\pi\)
\(318\) −58.8537 −3.30035
\(319\) −2.31605 + 4.01151i −0.129674 + 0.224602i
\(320\) −2.48913 + 4.31130i −0.139147 + 0.241009i
\(321\) −22.5874 + 39.1225i −1.26070 + 2.18360i
\(322\) −0.123558 0.214009i −0.00688564 0.0119263i
\(323\) 5.35607 9.27699i 0.298020 0.516185i
\(324\) −3.92428 6.79706i −0.218016 0.377614i
\(325\) 10.4781 0.581219
\(326\) −35.6714 −1.97565
\(327\) −8.09922 14.0283i −0.447888 0.775764i
\(328\) 4.29898 7.44605i 0.237371 0.411139i
\(329\) 1.92637 + 3.33656i 0.106204 + 0.183951i
\(330\) −44.3895 + 76.8848i −2.44356 + 4.23237i
\(331\) 2.59869 4.50106i 0.142837 0.247401i −0.785727 0.618573i \(-0.787711\pi\)
0.928564 + 0.371173i \(0.121044\pi\)
\(332\) −0.490568 + 0.849688i −0.0269234 + 0.0466327i
\(333\) 27.8925 1.52850
\(334\) −9.16700 15.8777i −0.501596 0.868789i
\(335\) 2.78227 + 4.81903i 0.152012 + 0.263292i
\(336\) −2.12414 + 3.67912i −0.115881 + 0.200712i
\(337\) −11.5640 −0.629930 −0.314965 0.949103i \(-0.601993\pi\)
−0.314965 + 0.949103i \(0.601993\pi\)
\(338\) 0.861744 + 1.49259i 0.0468727 + 0.0811859i
\(339\) 1.67892 0.0911866
\(340\) −20.7848 −1.12722
\(341\) −24.3926 + 1.51221i −1.32093 + 0.0818907i
\(342\) −19.9996 −1.08145
\(343\) 3.96541 0.214112
\(344\) −4.48280 7.76443i −0.241696 0.418630i
\(345\) 5.90609 0.317973
\(346\) −10.6471 + 18.4414i −0.572393 + 0.991414i
\(347\) 16.3466 + 28.3131i 0.877530 + 1.51993i 0.854043 + 0.520202i \(0.174144\pi\)
0.0234871 + 0.999724i \(0.492523\pi\)
\(348\) 1.52732 + 2.64539i 0.0818727 + 0.141808i
\(349\) 19.2350 1.02963 0.514813 0.857302i \(-0.327861\pi\)
0.514813 + 0.857302i \(0.327861\pi\)
\(350\) −2.57244 + 4.45560i −0.137503 + 0.238162i
\(351\) −4.32140 + 7.48488i −0.230659 + 0.399514i
\(352\) 11.1206 19.2614i 0.592730 1.02664i
\(353\) 11.8708 + 20.5608i 0.631819 + 1.09434i 0.987180 + 0.159614i \(0.0510248\pi\)
−0.355360 + 0.934729i \(0.615642\pi\)
\(354\) 20.3853 35.3084i 1.08347 1.87662i
\(355\) 20.4432 + 35.4086i 1.08501 + 1.87929i
\(356\) 13.6314 0.722461
\(357\) 4.62647 0.244859
\(358\) 15.8091 + 27.3821i 0.835535 + 1.44719i
\(359\) 11.1881 19.3783i 0.590484 1.02275i −0.403683 0.914899i \(-0.632270\pi\)
0.994167 0.107849i \(-0.0343964\pi\)
\(360\) −20.5857 35.6555i −1.08496 1.87921i
\(361\) 7.56420 13.1016i 0.398116 0.689557i
\(362\) −14.5704 + 25.2366i −0.765801 + 1.32641i
\(363\) −12.3300 + 21.3562i −0.647157 + 1.12091i
\(364\) −0.276466 −0.0144908
\(365\) 17.8394 + 30.8988i 0.933757 + 1.61731i
\(366\) 28.7909 + 49.8674i 1.50493 + 2.60661i
\(367\) 2.13405 3.69628i 0.111397 0.192944i −0.804937 0.593360i \(-0.797801\pi\)
0.916334 + 0.400416i \(0.131134\pi\)
\(368\) −2.51595 −0.131153
\(369\) 14.2877 + 24.7469i 0.743785 + 1.28827i
\(370\) −32.0692 −1.66720
\(371\) −3.26150 −0.169329
\(372\) −7.17920 + 14.4292i −0.372224 + 0.748119i
\(373\) 10.5071 0.544035 0.272017 0.962292i \(-0.412309\pi\)
0.272017 + 0.962292i \(0.412309\pi\)
\(374\) −41.1859 −2.12967
\(375\) −32.1432 55.6737i −1.65987 2.87498i
\(376\) 23.9969 1.23754
\(377\) 0.527641 0.913900i 0.0271749 0.0470683i
\(378\) −2.12187 3.67518i −0.109137 0.189031i
\(379\) 5.11343 + 8.85671i 0.262659 + 0.454939i 0.966948 0.254975i \(-0.0820672\pi\)
−0.704289 + 0.709914i \(0.748734\pi\)
\(380\) 7.51209 0.385362
\(381\) 22.4581 38.8985i 1.15056 1.99283i
\(382\) 15.4999 26.8466i 0.793042 1.37359i
\(383\) 1.86447 3.22936i 0.0952700 0.165012i −0.814451 0.580232i \(-0.802962\pi\)
0.909721 + 0.415219i \(0.136295\pi\)
\(384\) 18.3667 + 31.8121i 0.937272 + 1.62340i
\(385\) −2.45993 + 4.26073i −0.125370 + 0.217147i
\(386\) −10.9716 19.0035i −0.558442 0.967250i
\(387\) 29.7971 1.51467
\(388\) −1.27792 −0.0648766
\(389\) 1.14376 + 1.98105i 0.0579909 + 0.100443i 0.893563 0.448937i \(-0.148197\pi\)
−0.835573 + 0.549380i \(0.814864\pi\)
\(390\) 10.1128 17.5158i 0.512080 0.886949i
\(391\) 1.36996 + 2.37285i 0.0692820 + 0.120000i
\(392\) 6.13867 10.6325i 0.310050 0.537022i
\(393\) −5.39349 + 9.34179i −0.272065 + 0.471231i
\(394\) 9.00207 15.5920i 0.453518 0.785515i
\(395\) 31.6233 1.59114
\(396\) 12.5604 + 21.7552i 0.631183 + 1.09324i
\(397\) −10.2554 17.7629i −0.514704 0.891494i −0.999854 0.0170631i \(-0.994568\pi\)
0.485150 0.874431i \(-0.338765\pi\)
\(398\) −2.83000 + 4.90170i −0.141855 + 0.245700i
\(399\) −1.67211 −0.0837101
\(400\) 26.1906 + 45.3634i 1.30953 + 2.26817i
\(401\) 1.49557 0.0746850 0.0373425 0.999303i \(-0.488111\pi\)
0.0373425 + 0.999303i \(0.488111\pi\)
\(402\) 7.27131 0.362660
\(403\) 5.55710 0.344510i 0.276819 0.0171613i
\(404\) 1.86676 0.0928747
\(405\) 31.8194 1.58112
\(406\) 0.259079 + 0.448738i 0.0128579 + 0.0222705i
\(407\) −20.7602 −1.02904
\(408\) 14.4081 24.9555i 0.713306 1.23548i
\(409\) −9.99000 17.3032i −0.493974 0.855587i 0.506002 0.862532i \(-0.331123\pi\)
−0.999976 + 0.00694470i \(0.997789\pi\)
\(410\) −16.4271 28.4526i −0.811277 1.40517i
\(411\) −22.9616 −1.13261
\(412\) −1.95698 + 3.38959i −0.0964137 + 0.166993i
\(413\) 1.12969 1.95669i 0.0555886 0.0962823i
\(414\) 2.55772 4.43010i 0.125705 0.217728i
\(415\) −1.98884 3.44478i −0.0976285 0.169097i
\(416\) −2.53349 + 4.38813i −0.124214 + 0.215146i
\(417\) 24.2540 + 42.0092i 1.18773 + 2.05720i
\(418\) 14.8855 0.728074
\(419\) −11.2655 −0.550358 −0.275179 0.961393i \(-0.588737\pi\)
−0.275179 + 0.961393i \(0.588737\pi\)
\(420\) 1.62220 + 2.80973i 0.0791553 + 0.137101i
\(421\) 10.7086 18.5479i 0.521907 0.903969i −0.477769 0.878486i \(-0.658554\pi\)
0.999675 0.0254832i \(-0.00811243\pi\)
\(422\) 15.5641 + 26.9577i 0.757647 + 1.31228i
\(423\) −39.8768 + 69.0686i −1.93887 + 3.35823i
\(424\) −10.1572 + 17.5927i −0.493276 + 0.854379i
\(425\) 28.5221 49.4018i 1.38353 2.39634i
\(426\) 53.4271 2.58855
\(427\) 1.59551 + 2.76350i 0.0772121 + 0.133735i
\(428\) −7.34833 12.7277i −0.355195 0.615216i
\(429\) 6.54656 11.3390i 0.316071 0.547451i
\(430\) −34.2590 −1.65212
\(431\) −17.3927 30.1251i −0.837779 1.45108i −0.891747 0.452534i \(-0.850520\pi\)
0.0539682 0.998543i \(-0.482813\pi\)
\(432\) −43.2064 −2.07877
\(433\) 0.0954850 0.00458872 0.00229436 0.999997i \(-0.499270\pi\)
0.00229436 + 0.999997i \(0.499270\pi\)
\(434\) −1.21781 + 2.44763i −0.0584567 + 0.117490i
\(435\) −12.3840 −0.593766
\(436\) 5.26983 0.252379
\(437\) −0.495135 0.857599i −0.0236855 0.0410245i
\(438\) 46.6223 2.22770
\(439\) −9.99694 + 17.3152i −0.477128 + 0.826410i −0.999656 0.0262118i \(-0.991656\pi\)
0.522528 + 0.852622i \(0.324989\pi\)
\(440\) 15.3218 + 26.5381i 0.730437 + 1.26515i
\(441\) 20.4019 + 35.3370i 0.971517 + 1.68272i
\(442\) 9.38295 0.446301
\(443\) 1.19664 2.07264i 0.0568539 0.0984739i −0.836198 0.548428i \(-0.815226\pi\)
0.893052 + 0.449954i \(0.148560\pi\)
\(444\) −6.84513 + 11.8561i −0.324856 + 0.562667i
\(445\) −27.6319 + 47.8599i −1.30988 + 2.26878i
\(446\) 3.15922 + 5.47194i 0.149594 + 0.259104i
\(447\) 2.63214 4.55899i 0.124496 0.215633i
\(448\) 0.180250 + 0.312202i 0.00851600 + 0.0147501i
\(449\) −7.00619 −0.330643 −0.165321 0.986240i \(-0.552866\pi\)
−0.165321 + 0.986240i \(0.552866\pi\)
\(450\) −106.502 −5.02054
\(451\) −10.6342 18.4189i −0.500744 0.867313i
\(452\) −0.273102 + 0.473026i −0.0128456 + 0.0222493i
\(453\) 21.5359 + 37.3014i 1.01185 + 1.75257i
\(454\) 3.67913 6.37244i 0.172670 0.299073i
\(455\) 0.560420 0.970677i 0.0262729 0.0455060i
\(456\) −5.20739 + 9.01947i −0.243858 + 0.422375i
\(457\) −33.2893 −1.55721 −0.778603 0.627516i \(-0.784072\pi\)
−0.778603 + 0.627516i \(0.784072\pi\)
\(458\) 18.7333 + 32.4471i 0.875352 + 1.51615i
\(459\) 23.5264 + 40.7489i 1.09812 + 1.90200i
\(460\) −0.960713 + 1.66400i −0.0447935 + 0.0775845i
\(461\) 27.5968 1.28531 0.642655 0.766156i \(-0.277833\pi\)
0.642655 + 0.766156i \(0.277833\pi\)
\(462\) 3.21445 + 5.56760i 0.149550 + 0.259028i
\(463\) 21.9218 1.01879 0.509396 0.860532i \(-0.329869\pi\)
0.509396 + 0.860532i \(0.329869\pi\)
\(464\) 5.27548 0.244908
\(465\) −36.1082 54.4554i −1.67448 2.52531i
\(466\) 29.9706 1.38836
\(467\) −29.3072 −1.35617 −0.678087 0.734982i \(-0.737191\pi\)
−0.678087 + 0.734982i \(0.737191\pi\)
\(468\) −2.86150 4.95626i −0.132273 0.229103i
\(469\) 0.402954 0.0186067
\(470\) 45.8480 79.4110i 2.11481 3.66296i
\(471\) −20.5657 35.6208i −0.947615 1.64132i
\(472\) −7.03634 12.1873i −0.323874 0.560966i
\(473\) −22.1777 −1.01973
\(474\) 20.6614 35.7867i 0.949011 1.64374i
\(475\) −10.3085 + 17.8549i −0.472988 + 0.819239i
\(476\) −0.752564 + 1.30348i −0.0344937 + 0.0597449i
\(477\) −33.7574 58.4695i −1.54564 2.67713i
\(478\) 8.71434 15.0937i 0.398585 0.690369i
\(479\) 5.65436 + 9.79363i 0.258354 + 0.447482i 0.965801 0.259284i \(-0.0834865\pi\)
−0.707447 + 0.706766i \(0.750153\pi\)
\(480\) 59.4622 2.71406
\(481\) 4.72957 0.215650
\(482\) −9.30162 16.1109i −0.423677 0.733831i
\(483\) 0.213844 0.370389i 0.00973024 0.0168533i
\(484\) −4.01131 6.94780i −0.182332 0.315809i
\(485\) 2.59045 4.48679i 0.117626 0.203735i
\(486\) −1.55408 + 2.69175i −0.0704947 + 0.122100i
\(487\) −5.74161 + 9.94476i −0.260177 + 0.450640i −0.966289 0.257460i \(-0.917114\pi\)
0.706112 + 0.708100i \(0.250448\pi\)
\(488\) 19.8754 0.899715
\(489\) −30.8685 53.4657i −1.39592 2.41780i
\(490\) −23.4569 40.6285i −1.05967 1.83541i
\(491\) −7.35221 + 12.7344i −0.331801 + 0.574695i −0.982865 0.184327i \(-0.940989\pi\)
0.651064 + 0.759022i \(0.274323\pi\)
\(492\) −14.0254 −0.632313
\(493\) −2.87256 4.97542i −0.129374 0.224082i
\(494\) −3.39120 −0.152577
\(495\) −101.844 −4.57754
\(496\) 15.3818 + 23.1976i 0.690664 + 1.04160i
\(497\) 2.96077 0.132809
\(498\) −5.19774 −0.232916
\(499\) 11.3715 + 19.6960i 0.509057 + 0.881712i 0.999945 + 0.0104898i \(0.00333906\pi\)
−0.490888 + 0.871223i \(0.663328\pi\)
\(500\) 20.9143 0.935315
\(501\) 15.8654 27.4798i 0.708816 1.22770i
\(502\) −20.1691 34.9339i −0.900191 1.55918i
\(503\) 0.814567 + 1.41087i 0.0363197 + 0.0629076i 0.883614 0.468216i \(-0.155103\pi\)
−0.847294 + 0.531124i \(0.821770\pi\)
\(504\) −2.98142 −0.132803
\(505\) −3.78407 + 6.55420i −0.168389 + 0.291658i
\(506\) −1.90369 + 3.29729i −0.0846293 + 0.146582i
\(507\) −1.49143 + 2.58324i −0.0662368 + 0.114726i
\(508\) 7.30627 + 12.6548i 0.324163 + 0.561467i
\(509\) −7.65500 + 13.2589i −0.339302 + 0.587688i −0.984302 0.176495i \(-0.943524\pi\)
0.645000 + 0.764183i \(0.276858\pi\)
\(510\) −55.0556 95.3591i −2.43790 4.22257i
\(511\) 2.58367 0.114295
\(512\) −7.58874 −0.335378
\(513\) −8.50296 14.7276i −0.375415 0.650237i
\(514\) 3.54664 6.14297i 0.156436 0.270955i
\(515\) −7.93393 13.7420i −0.349611 0.605544i
\(516\) −7.31254 + 12.6657i −0.321917 + 0.557576i
\(517\) 29.6799 51.4071i 1.30532 2.26088i
\(518\) −1.16114 + 2.01116i −0.0510177 + 0.0883652i
\(519\) −36.8542 −1.61772
\(520\) −3.49060 6.04589i −0.153073 0.265130i
\(521\) 9.46953 + 16.4017i 0.414868 + 0.718572i 0.995415 0.0956551i \(-0.0304946\pi\)
−0.580547 + 0.814227i \(0.697161\pi\)
\(522\) −5.36307 + 9.28911i −0.234735 + 0.406573i
\(523\) 29.5628 1.29269 0.646346 0.763044i \(-0.276296\pi\)
0.646346 + 0.763044i \(0.276296\pi\)
\(524\) −1.75466 3.03916i −0.0766527 0.132766i
\(525\) −8.90431 −0.388616
\(526\) 15.0673 0.656964
\(527\) 13.5026 27.1383i 0.588181 1.18216i
\(528\) 65.4541 2.84853
\(529\) −22.7467 −0.988987
\(530\) 38.8122 + 67.2248i 1.68590 + 2.92006i
\(531\) 46.7705 2.02967
\(532\) 0.271993 0.471106i 0.0117924 0.0204250i
\(533\) 2.42267 + 4.19619i 0.104937 + 0.181757i
\(534\) 36.1073 + 62.5396i 1.56251 + 2.70635i
\(535\) 59.5827 2.57599
\(536\) 1.25491 2.17356i 0.0542037 0.0938836i
\(537\) −27.3610 + 47.3906i −1.18071 + 2.04505i
\(538\) 11.3751 19.7023i 0.490416 0.849426i
\(539\) −15.1849 26.3011i −0.654061 1.13287i
\(540\) −16.4983 + 28.5759i −0.709975 + 1.22971i
\(541\) −9.19666 15.9291i −0.395395 0.684844i 0.597756 0.801678i \(-0.296059\pi\)
−0.993152 + 0.116833i \(0.962726\pi\)
\(542\) −17.6787 −0.759366
\(543\) −50.4342 −2.16434
\(544\) 13.7927 + 23.8897i 0.591358 + 1.02426i
\(545\) −10.6824 + 18.5024i −0.457583 + 0.792557i
\(546\) −0.732314 1.26841i −0.0313402 0.0542828i
\(547\) 12.0781 20.9198i 0.516421 0.894467i −0.483397 0.875401i \(-0.660597\pi\)
0.999818 0.0190660i \(-0.00606927\pi\)
\(548\) 3.73505 6.46929i 0.159553 0.276354i
\(549\) −33.0279 + 57.2059i −1.40959 + 2.44149i
\(550\) 79.2683 3.38001
\(551\) 1.03821 + 1.79823i 0.0442291 + 0.0766070i
\(552\) −1.33193 2.30698i −0.0566909 0.0981915i
\(553\) 1.14500 1.98319i 0.0486902 0.0843339i
\(554\) −38.7610 −1.64680
\(555\) −27.7513 48.0667i −1.17798 2.04032i
\(556\) −15.7811 −0.669268
\(557\) −34.7425 −1.47209 −0.736043 0.676935i \(-0.763308\pi\)
−0.736043 + 0.676935i \(0.763308\pi\)
\(558\) −56.4837 + 3.50169i −2.39115 + 0.148238i
\(559\) 5.05252 0.213699
\(560\) 5.60322 0.236779
\(561\) −35.6405 61.7312i −1.50474 2.60629i
\(562\) −17.8060 −0.751101
\(563\) 5.75857 9.97414i 0.242695 0.420360i −0.718786 0.695231i \(-0.755302\pi\)
0.961481 + 0.274871i \(0.0886353\pi\)
\(564\) −19.5724 33.9004i −0.824146 1.42746i
\(565\) −1.10720 1.91773i −0.0465802 0.0806793i
\(566\) 28.6670 1.20496
\(567\) 1.15210 1.99549i 0.0483835 0.0838027i
\(568\) 9.22063 15.9706i 0.386889 0.670112i
\(569\) −12.8090 + 22.1859i −0.536982 + 0.930079i 0.462083 + 0.886837i \(0.347102\pi\)
−0.999065 + 0.0432427i \(0.986231\pi\)
\(570\) 19.8983 + 34.4649i 0.833448 + 1.44357i
\(571\) −13.8809 + 24.0424i −0.580896 + 1.00614i 0.414477 + 0.910060i \(0.363964\pi\)
−0.995373 + 0.0960819i \(0.969369\pi\)
\(572\) 2.12979 + 3.68890i 0.0890509 + 0.154241i
\(573\) 53.6517 2.24133
\(574\) −2.37913 −0.0993029
\(575\) −2.63669 4.56688i −0.109958 0.190452i
\(576\) −3.73126 + 6.46274i −0.155469 + 0.269281i
\(577\) −9.97895 17.2840i −0.415429 0.719544i 0.580044 0.814585i \(-0.303035\pi\)
−0.995473 + 0.0950406i \(0.969702\pi\)
\(578\) 10.8915 18.8646i 0.453026 0.784664i
\(579\) 18.9888 32.8895i 0.789147 1.36684i
\(580\) 2.01444 3.48911i 0.0836449 0.144877i
\(581\) −0.288043 −0.0119500
\(582\) −3.38500 5.86299i −0.140313 0.243029i
\(583\) 25.1253 + 43.5183i 1.04058 + 1.80234i
\(584\) 8.04624 13.9365i 0.332956 0.576697i
\(585\) 23.2020 0.959284
\(586\) 11.0311 + 19.1065i 0.455691 + 0.789281i
\(587\) 16.8075 0.693719 0.346859 0.937917i \(-0.387248\pi\)
0.346859 + 0.937917i \(0.387248\pi\)
\(588\) −20.0274 −0.825914
\(589\) −4.88012 + 9.80837i −0.201082 + 0.404147i
\(590\) −53.7740 −2.21384
\(591\) 31.1600 1.28175
\(592\) 11.8218 + 20.4760i 0.485875 + 0.841560i
\(593\) 35.3173 1.45031 0.725154 0.688586i \(-0.241768\pi\)
0.725154 + 0.688586i \(0.241768\pi\)
\(594\) −32.6921 + 56.6243i −1.34137 + 2.32332i
\(595\) −3.05102 5.28452i −0.125080 0.216644i
\(596\) 0.856312 + 1.48318i 0.0350759 + 0.0607532i
\(597\) −9.79583 −0.400917
\(598\) 0.433697 0.751185i 0.0177352 0.0307183i
\(599\) 3.45578 5.98559i 0.141200 0.244565i −0.786749 0.617273i \(-0.788237\pi\)
0.927949 + 0.372708i \(0.121571\pi\)
\(600\) −27.7304 + 48.0305i −1.13209 + 1.96084i
\(601\) 14.3145 + 24.7935i 0.583901 + 1.01135i 0.995011 + 0.0997610i \(0.0318078\pi\)
−0.411110 + 0.911586i \(0.634859\pi\)
\(602\) −1.24043 + 2.14848i −0.0505561 + 0.0875657i
\(603\) 4.17068 + 7.22384i 0.169843 + 0.294177i
\(604\) −14.0126 −0.570163
\(605\) 32.5250 1.32233
\(606\) 4.94474 + 8.56453i 0.200866 + 0.347910i
\(607\) −9.12245 + 15.8006i −0.370269 + 0.641325i −0.989607 0.143800i \(-0.954068\pi\)
0.619338 + 0.785125i \(0.287401\pi\)
\(608\) −4.98499 8.63425i −0.202168 0.350165i
\(609\) −0.448391 + 0.776637i −0.0181697 + 0.0314709i
\(610\) 37.9735 65.7720i 1.53750 2.66303i
\(611\) −6.76166 + 11.7115i −0.273547 + 0.473798i
\(612\) −31.1569 −1.25944
\(613\) 20.7489 + 35.9382i 0.838042 + 1.45153i 0.891529 + 0.452963i \(0.149633\pi\)
−0.0534876 + 0.998569i \(0.517034\pi\)
\(614\) 23.9841 + 41.5417i 0.967919 + 1.67649i
\(615\) 28.4306 49.2433i 1.14643 1.98568i
\(616\) 2.21905 0.0894079
\(617\) −2.29891 3.98183i −0.0925506 0.160302i 0.816033 0.578005i \(-0.196169\pi\)
−0.908584 + 0.417703i \(0.862835\pi\)
\(618\) −20.7349 −0.834081
\(619\) −34.4649 −1.38526 −0.692630 0.721293i \(-0.743548\pi\)
−0.692630 + 0.721293i \(0.743548\pi\)
\(620\) 21.2160 1.31528i 0.852055 0.0528229i
\(621\) 4.34973 0.174549
\(622\) −21.4017 −0.858131
\(623\) 2.00096 + 3.46576i 0.0801667 + 0.138853i
\(624\) −14.9117 −0.596946
\(625\) −16.1998 + 28.0589i −0.647992 + 1.12236i
\(626\) −5.58823 9.67910i −0.223351 0.386855i
\(627\) 12.8813 + 22.3110i 0.514428 + 0.891016i
\(628\) 13.3812 0.533969
\(629\) 12.8743 22.2989i 0.513330 0.889114i
\(630\) −5.69625 + 9.86620i −0.226944 + 0.393079i
\(631\) −1.75803 + 3.04501i −0.0699863 + 0.121220i −0.898895 0.438164i \(-0.855629\pi\)
0.828909 + 0.559384i \(0.188962\pi\)
\(632\) −7.13164 12.3524i −0.283682 0.491351i
\(633\) −26.9369 + 46.6561i −1.07065 + 1.85441i
\(634\) 24.4226 + 42.3012i 0.969946 + 1.68000i
\(635\) −59.2416 −2.35093
\(636\) 33.1377 1.31400
\(637\) 3.45942 + 5.99189i 0.137067 + 0.237407i
\(638\) 3.99168 6.91380i 0.158032 0.273720i
\(639\) 30.6448 + 53.0783i 1.21229 + 2.09974i
\(640\) 24.2246 41.9582i 0.957560 1.65854i
\(641\) −5.51565 + 9.55339i −0.217855 + 0.377336i −0.954152 0.299322i \(-0.903239\pi\)
0.736297 + 0.676659i \(0.236573\pi\)
\(642\) 38.9291 67.4271i 1.53641 2.66114i
\(643\) −27.8612 −1.09874 −0.549369 0.835580i \(-0.685132\pi\)
−0.549369 + 0.835580i \(0.685132\pi\)
\(644\) 0.0695698 + 0.120498i 0.00274143 + 0.00474830i
\(645\) −29.6462 51.3488i −1.16732 2.02186i
\(646\) −9.23113 + 15.9888i −0.363194 + 0.629070i
\(647\) 11.1755 0.439354 0.219677 0.975573i \(-0.429500\pi\)
0.219677 + 0.975573i \(0.429500\pi\)
\(648\) −7.17587 12.4290i −0.281895 0.488256i
\(649\) −34.8109 −1.36645
\(650\) −18.0588 −0.708326
\(651\) −4.72245 + 0.292767i −0.185087 + 0.0114744i
\(652\) 20.0848 0.786583
\(653\) 9.43311 0.369146 0.184573 0.982819i \(-0.440910\pi\)
0.184573 + 0.982819i \(0.440910\pi\)
\(654\) 13.9589 + 24.1775i 0.545837 + 0.945417i
\(655\) 14.2274 0.555909
\(656\) −12.1112 + 20.9773i −0.472864 + 0.819024i
\(657\) 26.7417 + 46.3179i 1.04329 + 1.80704i
\(658\) −3.32007 5.75053i −0.129430 0.224179i
\(659\) −8.42384 −0.328146 −0.164073 0.986448i \(-0.552463\pi\)
−0.164073 + 0.986448i \(0.552463\pi\)
\(660\) 24.9936 43.2902i 0.972874 1.68507i
\(661\) −16.5657 + 28.6926i −0.644330 + 1.11601i 0.340126 + 0.940380i \(0.389530\pi\)
−0.984456 + 0.175633i \(0.943803\pi\)
\(662\) −4.47881 + 7.75753i −0.174074 + 0.301505i
\(663\) 8.11960 + 14.0636i 0.315339 + 0.546183i
\(664\) −0.897043 + 1.55372i −0.0348120 + 0.0602962i
\(665\) 1.10270 + 1.90994i 0.0427611 + 0.0740643i
\(666\) −48.0725 −1.86277
\(667\) −0.531100 −0.0205643
\(668\) 5.16150 + 8.93997i 0.199704 + 0.345898i
\(669\) −5.46771 + 9.47036i −0.211394 + 0.366145i
\(670\) −4.79521 8.30554i −0.185255 0.320871i
\(671\) 24.5823 42.5779i 0.948991 1.64370i
\(672\) 2.15297 3.72905i 0.0830526 0.143851i
\(673\) 3.76690 6.52447i 0.145203 0.251500i −0.784245 0.620451i \(-0.786950\pi\)
0.929449 + 0.368951i \(0.120283\pi\)
\(674\) 19.9304 0.767690
\(675\) −45.2799 78.4271i −1.74283 3.01866i
\(676\) −0.485207 0.840403i −0.0186618 0.0323232i
\(677\) 13.5846 23.5293i 0.522100 0.904303i −0.477570 0.878594i \(-0.658482\pi\)
0.999669 0.0257096i \(-0.00818451\pi\)
\(678\) −2.89361 −0.111128
\(679\) −0.187587 0.324910i −0.00719892 0.0124689i
\(680\) −38.0067 −1.45749
\(681\) 12.7350 0.488008
\(682\) 42.0403 2.60628i 1.60981 0.0997995i
\(683\) −27.6752 −1.05896 −0.529481 0.848322i \(-0.677613\pi\)
−0.529481 + 0.848322i \(0.677613\pi\)
\(684\) 11.2608 0.430567
\(685\) 15.1425 + 26.2276i 0.578565 + 1.00210i
\(686\) −6.83434 −0.260936
\(687\) −32.4220 + 56.1566i −1.23698 + 2.14251i
\(688\) 12.6291 + 21.8742i 0.481479 + 0.833946i
\(689\) −5.72403 9.91431i −0.218068 0.377705i
\(690\) −10.1791 −0.387511
\(691\) 17.3549 30.0596i 0.660213 1.14352i −0.320346 0.947301i \(-0.603799\pi\)
0.980559 0.196222i \(-0.0628674\pi\)
\(692\) 5.99488 10.3834i 0.227891 0.394719i
\(693\) −3.68750 + 6.38693i −0.140076 + 0.242620i
\(694\) −28.1731 48.7973i −1.06944 1.85232i
\(695\) 31.9896 55.4076i 1.21343 2.10173i
\(696\) 2.79282 + 4.83731i 0.105862 + 0.183358i
\(697\) 26.3788 0.999168
\(698\) −33.1513 −1.25480
\(699\) 25.9353 + 44.9212i 0.980963 + 1.69908i
\(700\) 1.44842 2.50873i 0.0547450 0.0948212i
\(701\) 14.9666 + 25.9228i 0.565279 + 0.979092i 0.997024 + 0.0770964i \(0.0245649\pi\)
−0.431744 + 0.901996i \(0.642102\pi\)
\(702\) 7.44789 12.9001i 0.281102 0.486883i
\(703\) −4.65304 + 8.05930i −0.175493 + 0.303962i
\(704\) 2.77715 4.81016i 0.104668 0.181290i
\(705\) 158.699 5.97696
\(706\) −20.4592 35.4364i −0.769992 1.33367i
\(707\) 0.274023 + 0.474621i 0.0103057 + 0.0178500i
\(708\) −11.4780 + 19.8805i −0.431369 + 0.747154i
\(709\) −23.2378 −0.872715 −0.436357 0.899773i \(-0.643732\pi\)
−0.436357 + 0.899773i \(0.643732\pi\)
\(710\) −35.2336 61.0263i −1.32229 2.29028i
\(711\) 47.4040 1.77779
\(712\) 24.9261 0.934144
\(713\) −1.54854 2.33538i −0.0579932 0.0874606i
\(714\) −7.97367 −0.298407
\(715\) −17.2690 −0.645825
\(716\) −8.90133 15.4176i −0.332658 0.576181i
\(717\) 30.1640 1.12650
\(718\) −19.2825 + 33.3983i −0.719617 + 1.24641i
\(719\) −24.6681 42.7265i −0.919966 1.59343i −0.799463 0.600715i \(-0.794882\pi\)
−0.120503 0.992713i \(-0.538451\pi\)
\(720\) 57.9948 + 100.450i 2.16134 + 3.74355i
\(721\) −1.14907 −0.0427935
\(722\) −13.0368 + 22.5804i −0.485180 + 0.840356i
\(723\) 16.0984 27.8833i 0.598708 1.03699i
\(724\) 8.20387 14.2095i 0.304894 0.528092i
\(725\) 5.52866 + 9.57591i 0.205329 + 0.355640i
\(726\) 21.2506 36.8071i 0.788684 1.36604i
\(727\) −2.15207 3.72749i −0.0798157 0.138245i 0.823355 0.567527i \(-0.192100\pi\)
−0.903170 + 0.429282i \(0.858767\pi\)
\(728\) −0.505541 −0.0187366
\(729\) −29.6429 −1.09789
\(730\) −30.7460 53.2537i −1.13796 1.97101i
\(731\) 13.7534 23.8215i 0.508686 0.881070i
\(732\) −16.2108 28.0779i −0.599168 1.03779i
\(733\) −19.3357 + 33.4904i −0.714179 + 1.23699i 0.249096 + 0.968479i \(0.419866\pi\)
−0.963275 + 0.268516i \(0.913467\pi\)
\(734\) −3.67801 + 6.37051i −0.135758 + 0.235140i
\(735\) 40.5971 70.3162i 1.49745 2.59365i
\(736\) 2.55010 0.0939979
\(737\) −3.10420 5.37664i −0.114345 0.198051i
\(738\) −24.6246 42.6511i −0.906444 1.57001i
\(739\) 21.8031 37.7642i 0.802042 1.38918i −0.116228 0.993223i \(-0.537080\pi\)
0.918270 0.395955i \(-0.129586\pi\)
\(740\) 18.0566 0.663775
\(741\) −2.93460 5.08288i −0.107805 0.186724i
\(742\) 5.62116 0.206359
\(743\) 16.5682 0.607830 0.303915 0.952699i \(-0.401706\pi\)
0.303915 + 0.952699i \(0.401706\pi\)
\(744\) −13.1277 + 26.3849i −0.481287 + 0.967319i
\(745\) −6.94326 −0.254381
\(746\) −18.1088 −0.663010
\(747\) −2.98132 5.16380i −0.109081 0.188934i
\(748\) 23.1898 0.847904
\(749\) 2.15733 3.73661i 0.0788273 0.136533i
\(750\) 55.3985 + 95.9530i 2.02287 + 3.50371i
\(751\) −2.00080 3.46548i −0.0730101 0.126457i 0.827209 0.561894i \(-0.189927\pi\)
−0.900219 + 0.435437i \(0.856594\pi\)
\(752\) −67.6047 −2.46529
\(753\) 34.9069 60.4606i 1.27208 2.20331i
\(754\) −0.909383 + 1.57510i −0.0331178 + 0.0573617i
\(755\) 28.4046 49.1982i 1.03375 1.79051i
\(756\) 1.19472 + 2.06932i 0.0434516 + 0.0752604i
\(757\) 10.4037 18.0198i 0.378129 0.654939i −0.612661 0.790346i \(-0.709901\pi\)
0.990790 + 0.135407i \(0.0432341\pi\)
\(758\) −8.81293 15.2644i −0.320100 0.554430i
\(759\) −6.58948 −0.239183
\(760\) 13.7365 0.498274
\(761\) −3.57006 6.18352i −0.129415 0.224153i 0.794035 0.607872i \(-0.207976\pi\)
−0.923450 + 0.383719i \(0.874643\pi\)
\(762\) −38.7062 + 67.0411i −1.40218 + 2.42864i
\(763\) 0.773562 + 1.33985i 0.0280048 + 0.0485058i
\(764\) −8.72723 + 15.1160i −0.315740 + 0.546878i
\(765\) 63.1577 109.392i 2.28347 3.95509i
\(766\) −3.21339 + 5.56576i −0.116105 + 0.201099i
\(767\) 7.93059 0.286357
\(768\) −27.8804 48.2902i −1.00605 1.74252i
\(769\) −10.9620 18.9867i −0.395299 0.684677i 0.597841 0.801615i \(-0.296026\pi\)
−0.993139 + 0.116938i \(0.962692\pi\)
\(770\) 4.23967 7.34332i 0.152787 0.264635i
\(771\) 12.2764 0.442126