Properties

Label 637.2.h.l.165.4
Level $637$
Weight $2$
Character 637.165
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
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 165.4
Root \(-0.437442 + 0.757672i\) of defining polynomial
Character \(\chi\) \(=\) 637.165
Dual form 637.2.h.l.471.4

$q$-expansion

\(f(q)\) \(=\) \(q-0.268125 q^{2} +(-0.571504 - 0.989875i) q^{3} -1.92811 q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.153235 + 0.265410i) q^{6} +1.05323 q^{8} +(0.846765 - 1.46664i) q^{9} +O(q^{10})\) \(q-0.268125 q^{2} +(-0.571504 - 0.989875i) q^{3} -1.92811 q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.153235 + 0.265410i) q^{6} +1.05323 q^{8} +(0.846765 - 1.46664i) q^{9} +(0.343436 + 0.594848i) q^{10} +(-1.97300 - 3.41734i) q^{11} +(1.10192 + 1.90859i) q^{12} +(3.15374 - 1.74755i) q^{13} +(-1.46405 + 2.53582i) q^{15} +3.57382 q^{16} -0.785100 q^{17} +(-0.227039 + 0.393243i) q^{18} +(-3.74764 + 6.49110i) q^{19} +(2.46967 + 4.27760i) q^{20} +(0.529011 + 0.916274i) q^{22} -7.95518 q^{23} +(-0.601923 - 1.04256i) q^{24} +(-0.781294 + 1.35324i) q^{25} +(-0.845598 + 0.468561i) q^{26} -5.36475 q^{27} +(-1.17586 + 2.03666i) q^{29} +(0.392550 - 0.679916i) q^{30} +(-1.27718 + 2.21215i) q^{31} -3.06468 q^{32} +(-2.25516 + 3.90605i) q^{33} +0.210505 q^{34} +(-1.63266 + 2.82784i) q^{36} +6.75716 q^{37} +(1.00484 - 1.74043i) q^{38} +(-3.53223 - 2.12308i) q^{39} +(-1.34905 - 2.33663i) q^{40} +(-1.21874 + 2.11091i) q^{41} +(1.12473 + 1.94809i) q^{43} +(3.80416 + 6.58900i) q^{44} -4.33841 q^{45} +2.13298 q^{46} +(0.658276 + 1.14017i) q^{47} +(-2.04246 - 3.53764i) q^{48} +(0.209485 - 0.362838i) q^{50} +(0.448688 + 0.777151i) q^{51} +(-6.08076 + 3.36946i) q^{52} +(-4.63977 + 8.03632i) q^{53} +1.43842 q^{54} +(-5.05434 + 8.75438i) q^{55} +8.56716 q^{57} +(0.315279 - 0.546079i) q^{58} +8.96671 q^{59} +(2.82286 - 4.88933i) q^{60} +(4.72273 - 8.18002i) q^{61} +(0.342445 - 0.593132i) q^{62} -6.32592 q^{64} +(-7.91657 - 4.75832i) q^{65} +(0.604665 - 1.04731i) q^{66} +(0.676281 + 1.17135i) q^{67} +1.51376 q^{68} +(4.54642 + 7.87463i) q^{69} +(-6.15808 - 10.6661i) q^{71} +(0.891834 - 1.54470i) q^{72} +(0.384295 - 0.665619i) q^{73} -1.81176 q^{74} +1.78605 q^{75} +(7.22585 - 12.5155i) q^{76} +(0.947080 + 0.569251i) q^{78} +(-3.09642 - 5.36316i) q^{79} +(-4.57763 - 7.92868i) q^{80} +(0.525682 + 0.910507i) q^{81} +(0.326774 - 0.565989i) q^{82} +1.07292 q^{83} +(1.00562 + 1.74178i) q^{85} +(-0.301568 - 0.522332i) q^{86} +2.68805 q^{87} +(-2.07801 - 3.59923i) q^{88} -7.66299 q^{89} +1.16324 q^{90} +15.3384 q^{92} +2.91966 q^{93} +(-0.176501 - 0.305708i) q^{94} +19.2010 q^{95} +(1.75148 + 3.03365i) q^{96} +(-1.18601 - 2.05423i) q^{97} -6.68267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} - 5q^{12} + 2q^{13} - 2q^{15} - 16q^{16} + 10q^{17} + 3q^{18} + q^{19} + q^{20} - 5q^{22} + 2q^{23} + 11q^{24} + 7q^{25} + 16q^{26} + 8q^{27} + 3q^{29} - 5q^{30} - 16q^{31} - 16q^{32} - 16q^{33} - 32q^{34} - 21q^{36} + 26q^{37} + 17q^{38} - 20q^{39} + 5q^{40} + 8q^{41} - 11q^{43} + 21q^{44} - 14q^{45} - 32q^{46} + q^{47} - 21q^{48} + 6q^{50} - 20q^{51} - 41q^{52} - 2q^{53} - 36q^{54} - 9q^{55} + 42q^{57} - 8q^{58} + 26q^{59} + 20q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 5q^{65} - 18q^{66} - 11q^{67} + 58q^{68} - 23q^{69} + 6q^{71} + 25q^{72} + 30q^{73} + 6q^{74} - 6q^{75} + 9q^{76} + 16q^{78} + 7q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} - 7q^{86} + 32q^{87} + 8q^{89} + 16q^{90} + 54q^{92} + 14q^{93} - 45q^{94} + 12q^{95} - 19q^{96} + 35q^{97} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.268125 −0.189593 −0.0947966 0.995497i \(-0.530220\pi\)
−0.0947966 + 0.995497i \(0.530220\pi\)
\(3\) −0.571504 0.989875i −0.329958 0.571504i 0.652545 0.757750i \(-0.273701\pi\)
−0.982503 + 0.186246i \(0.940368\pi\)
\(4\) −1.92811 −0.964054
\(5\) −1.28088 2.21854i −0.572826 0.992163i −0.996274 0.0862431i \(-0.972514\pi\)
0.423448 0.905920i \(-0.360820\pi\)
\(6\) 0.153235 + 0.265410i 0.0625578 + 0.108353i
\(7\) 0 0
\(8\) 1.05323 0.372371
\(9\) 0.846765 1.46664i 0.282255 0.488880i
\(10\) 0.343436 + 0.594848i 0.108604 + 0.188107i
\(11\) −1.97300 3.41734i −0.594882 1.03037i −0.993563 0.113277i \(-0.963865\pi\)
0.398681 0.917090i \(-0.369468\pi\)
\(12\) 1.10192 + 1.90859i 0.318098 + 0.550961i
\(13\) 3.15374 1.74755i 0.874690 0.484682i
\(14\) 0 0
\(15\) −1.46405 + 2.53582i −0.378017 + 0.654745i
\(16\) 3.57382 0.893455
\(17\) −0.785100 −0.190415 −0.0952073 0.995457i \(-0.530351\pi\)
−0.0952073 + 0.995457i \(0.530351\pi\)
\(18\) −0.227039 + 0.393243i −0.0535136 + 0.0926883i
\(19\) −3.74764 + 6.49110i −0.859767 + 1.48916i 0.0123849 + 0.999923i \(0.496058\pi\)
−0.872151 + 0.489236i \(0.837276\pi\)
\(20\) 2.46967 + 4.27760i 0.552235 + 0.956500i
\(21\) 0 0
\(22\) 0.529011 + 0.916274i 0.112786 + 0.195350i
\(23\) −7.95518 −1.65877 −0.829384 0.558678i \(-0.811309\pi\)
−0.829384 + 0.558678i \(0.811309\pi\)
\(24\) −0.601923 1.04256i −0.122867 0.212812i
\(25\) −0.781294 + 1.35324i −0.156259 + 0.270648i
\(26\) −0.845598 + 0.468561i −0.165835 + 0.0918924i
\(27\) −5.36475 −1.03245
\(28\) 0 0
\(29\) −1.17586 + 2.03666i −0.218353 + 0.378198i −0.954304 0.298836i \(-0.903402\pi\)
0.735952 + 0.677034i \(0.236735\pi\)
\(30\) 0.392550 0.679916i 0.0716695 0.124135i
\(31\) −1.27718 + 2.21215i −0.229389 + 0.397313i −0.957627 0.288011i \(-0.907006\pi\)
0.728238 + 0.685324i \(0.240339\pi\)
\(32\) −3.06468 −0.541764
\(33\) −2.25516 + 3.90605i −0.392573 + 0.679956i
\(34\) 0.210505 0.0361013
\(35\) 0 0
\(36\) −1.63266 + 2.82784i −0.272109 + 0.471307i
\(37\) 6.75716 1.11087 0.555435 0.831560i \(-0.312552\pi\)
0.555435 + 0.831560i \(0.312552\pi\)
\(38\) 1.00484 1.74043i 0.163006 0.282334i
\(39\) −3.53223 2.12308i −0.565609 0.339965i
\(40\) −1.34905 2.33663i −0.213304 0.369453i
\(41\) −1.21874 + 2.11091i −0.190335 + 0.329669i −0.945361 0.326025i \(-0.894291\pi\)
0.755027 + 0.655694i \(0.227624\pi\)
\(42\) 0 0
\(43\) 1.12473 + 1.94809i 0.171520 + 0.297081i 0.938951 0.344050i \(-0.111799\pi\)
−0.767432 + 0.641131i \(0.778466\pi\)
\(44\) 3.80416 + 6.58900i 0.573499 + 0.993329i
\(45\) −4.33841 −0.646732
\(46\) 2.13298 0.314491
\(47\) 0.658276 + 1.14017i 0.0960195 + 0.166311i 0.910034 0.414534i \(-0.136056\pi\)
−0.814014 + 0.580845i \(0.802722\pi\)
\(48\) −2.04246 3.53764i −0.294803 0.510614i
\(49\) 0 0
\(50\) 0.209485 0.362838i 0.0296256 0.0513130i
\(51\) 0.448688 + 0.777151i 0.0628289 + 0.108823i
\(52\) −6.08076 + 3.36946i −0.843249 + 0.467260i
\(53\) −4.63977 + 8.03632i −0.637321 + 1.10387i 0.348697 + 0.937236i \(0.386624\pi\)
−0.986018 + 0.166637i \(0.946709\pi\)
\(54\) 1.43842 0.195745
\(55\) −5.05434 + 8.75438i −0.681528 + 1.18044i
\(56\) 0 0
\(57\) 8.56716 1.13475
\(58\) 0.315279 0.546079i 0.0413981 0.0717037i
\(59\) 8.96671 1.16737 0.583683 0.811982i \(-0.301611\pi\)
0.583683 + 0.811982i \(0.301611\pi\)
\(60\) 2.82286 4.88933i 0.364429 0.631210i
\(61\) 4.72273 8.18002i 0.604684 1.04734i −0.387417 0.921905i \(-0.626633\pi\)
0.992101 0.125439i \(-0.0400340\pi\)
\(62\) 0.342445 0.593132i 0.0434906 0.0753279i
\(63\) 0 0
\(64\) −6.32592 −0.790741
\(65\) −7.91657 4.75832i −0.981929 0.590197i
\(66\) 0.604665 1.04731i 0.0744291 0.128915i
\(67\) 0.676281 + 1.17135i 0.0826209 + 0.143104i 0.904375 0.426739i \(-0.140338\pi\)
−0.821754 + 0.569842i \(0.807004\pi\)
\(68\) 1.51376 0.183570
\(69\) 4.54642 + 7.87463i 0.547324 + 0.947994i
\(70\) 0 0
\(71\) −6.15808 10.6661i −0.730829 1.26583i −0.956529 0.291637i \(-0.905800\pi\)
0.225700 0.974197i \(-0.427533\pi\)
\(72\) 0.891834 1.54470i 0.105104 0.182045i
\(73\) 0.384295 0.665619i 0.0449783 0.0779048i −0.842660 0.538446i \(-0.819011\pi\)
0.887638 + 0.460542i \(0.152345\pi\)
\(74\) −1.81176 −0.210613
\(75\) 1.78605 0.206236
\(76\) 7.22585 12.5155i 0.828862 1.43563i
\(77\) 0 0
\(78\) 0.947080 + 0.569251i 0.107236 + 0.0644550i
\(79\) −3.09642 5.36316i −0.348375 0.603402i 0.637586 0.770379i \(-0.279933\pi\)
−0.985961 + 0.166976i \(0.946600\pi\)
\(80\) −4.57763 7.92868i −0.511794 0.886454i
\(81\) 0.525682 + 0.910507i 0.0584091 + 0.101167i
\(82\) 0.326774 0.565989i 0.0360861 0.0625030i
\(83\) 1.07292 0.117768 0.0588841 0.998265i \(-0.481246\pi\)
0.0588841 + 0.998265i \(0.481246\pi\)
\(84\) 0 0
\(85\) 1.00562 + 1.74178i 0.109074 + 0.188922i
\(86\) −0.301568 0.522332i −0.0325190 0.0563245i
\(87\) 2.68805 0.288189
\(88\) −2.07801 3.59923i −0.221517 0.383679i
\(89\) −7.66299 −0.812275 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(90\) 1.16324 0.122616
\(91\) 0 0
\(92\) 15.3384 1.59914
\(93\) 2.91966 0.302755
\(94\) −0.176501 0.305708i −0.0182046 0.0315314i
\(95\) 19.2010 1.96999
\(96\) 1.75148 + 3.03365i 0.178760 + 0.309621i
\(97\) −1.18601 2.05423i −0.120421 0.208575i 0.799513 0.600649i \(-0.205091\pi\)
−0.919934 + 0.392074i \(0.871758\pi\)
\(98\) 0 0
\(99\) −6.68267 −0.671634
\(100\) 1.50642 2.60920i 0.150642 0.260920i
\(101\) −0.398665 0.690508i −0.0396686 0.0687081i 0.845509 0.533961i \(-0.179297\pi\)
−0.885178 + 0.465252i \(0.845964\pi\)
\(102\) −0.120305 0.208374i −0.0119119 0.0206321i
\(103\) 1.08309 + 1.87597i 0.106720 + 0.184844i 0.914440 0.404722i \(-0.132632\pi\)
−0.807720 + 0.589567i \(0.799299\pi\)
\(104\) 3.32160 1.84056i 0.325710 0.180482i
\(105\) 0 0
\(106\) 1.24404 2.15474i 0.120832 0.209287i
\(107\) −11.5262 −1.11428 −0.557141 0.830418i \(-0.688102\pi\)
−0.557141 + 0.830418i \(0.688102\pi\)
\(108\) 10.3438 0.995334
\(109\) −4.03912 + 6.99595i −0.386877 + 0.670091i −0.992028 0.126020i \(-0.959780\pi\)
0.605151 + 0.796111i \(0.293113\pi\)
\(110\) 1.35520 2.34727i 0.129213 0.223803i
\(111\) −3.86174 6.68874i −0.366541 0.634867i
\(112\) 0 0
\(113\) −4.02067 6.96401i −0.378233 0.655119i 0.612572 0.790415i \(-0.290135\pi\)
−0.990805 + 0.135296i \(0.956802\pi\)
\(114\) −2.29707 −0.215141
\(115\) 10.1896 + 17.6489i 0.950186 + 1.64577i
\(116\) 2.26719 3.92690i 0.210504 0.364603i
\(117\) 0.107456 6.10517i 0.00993431 0.564423i
\(118\) −2.40420 −0.221325
\(119\) 0 0
\(120\) −1.54198 + 2.67079i −0.140763 + 0.243808i
\(121\) −2.28546 + 3.95854i −0.207769 + 0.359867i
\(122\) −1.26628 + 2.19327i −0.114644 + 0.198569i
\(123\) 2.78605 0.251210
\(124\) 2.46255 4.26526i 0.221143 0.383032i
\(125\) −8.80581 −0.787615
\(126\) 0 0
\(127\) −0.894023 + 1.54849i −0.0793317 + 0.137406i −0.902962 0.429721i \(-0.858612\pi\)
0.823630 + 0.567127i \(0.191945\pi\)
\(128\) 7.82550 0.691683
\(129\) 1.28558 2.22668i 0.113189 0.196049i
\(130\) 2.12263 + 1.27583i 0.186167 + 0.111897i
\(131\) −3.19545 5.53469i −0.279188 0.483568i 0.691995 0.721902i \(-0.256732\pi\)
−0.971183 + 0.238334i \(0.923399\pi\)
\(132\) 4.34819 7.53129i 0.378461 0.655514i
\(133\) 0 0
\(134\) −0.181328 0.314069i −0.0156644 0.0271315i
\(135\) 6.87158 + 11.9019i 0.591412 + 1.02436i
\(136\) −0.826887 −0.0709050
\(137\) 10.0365 0.857480 0.428740 0.903428i \(-0.358958\pi\)
0.428740 + 0.903428i \(0.358958\pi\)
\(138\) −1.21901 2.11139i −0.103769 0.179733i
\(139\) −2.77278 4.80260i −0.235184 0.407351i 0.724142 0.689651i \(-0.242236\pi\)
−0.959326 + 0.282300i \(0.908903\pi\)
\(140\) 0 0
\(141\) 0.752416 1.30322i 0.0633648 0.109751i
\(142\) 1.65114 + 2.85985i 0.138560 + 0.239993i
\(143\) −12.1943 7.32949i −1.01974 0.612922i
\(144\) 3.02619 5.24151i 0.252182 0.436793i
\(145\) 6.02455 0.500312
\(146\) −0.103039 + 0.178469i −0.00852759 + 0.0147702i
\(147\) 0 0
\(148\) −13.0285 −1.07094
\(149\) −9.23254 + 15.9912i −0.756359 + 1.31005i 0.188337 + 0.982104i \(0.439690\pi\)
−0.944696 + 0.327947i \(0.893643\pi\)
\(150\) −0.478886 −0.0391009
\(151\) −0.803678 + 1.39201i −0.0654024 + 0.113280i −0.896872 0.442289i \(-0.854166\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(152\) −3.94710 + 6.83658i −0.320152 + 0.554520i
\(153\) −0.664795 + 1.15146i −0.0537455 + 0.0930900i
\(154\) 0 0
\(155\) 6.54366 0.525600
\(156\) 6.81052 + 4.09353i 0.545278 + 0.327744i
\(157\) −0.822967 + 1.42542i −0.0656799 + 0.113761i −0.896995 0.442040i \(-0.854255\pi\)
0.831315 + 0.555801i \(0.187588\pi\)
\(158\) 0.830229 + 1.43800i 0.0660494 + 0.114401i
\(159\) 10.6066 0.841158
\(160\) 3.92548 + 6.79913i 0.310337 + 0.537519i
\(161\) 0 0
\(162\) −0.140949 0.244130i −0.0110740 0.0191807i
\(163\) 3.27409 5.67090i 0.256447 0.444179i −0.708841 0.705369i \(-0.750782\pi\)
0.965287 + 0.261190i \(0.0841148\pi\)
\(164\) 2.34986 4.07007i 0.183493 0.317819i
\(165\) 11.5543 0.899503
\(166\) −0.287677 −0.0223281
\(167\) 4.77440 8.26950i 0.369454 0.639913i −0.620026 0.784581i \(-0.712878\pi\)
0.989480 + 0.144668i \(0.0462114\pi\)
\(168\) 0 0
\(169\) 6.89216 11.0226i 0.530166 0.847894i
\(170\) −0.269631 0.467015i −0.0206798 0.0358184i
\(171\) 6.34673 + 10.9929i 0.485347 + 0.840646i
\(172\) −2.16860 3.75613i −0.165354 0.286402i
\(173\) 5.56582 9.64028i 0.423161 0.732937i −0.573085 0.819496i \(-0.694254\pi\)
0.996247 + 0.0865588i \(0.0275870\pi\)
\(174\) −0.720733 −0.0546386
\(175\) 0 0
\(176\) −7.05115 12.2130i −0.531501 0.920586i
\(177\) −5.12451 8.87592i −0.385182 0.667155i
\(178\) 2.05464 0.154002
\(179\) 6.32173 + 10.9496i 0.472508 + 0.818409i 0.999505 0.0314588i \(-0.0100153\pi\)
−0.526997 + 0.849867i \(0.676682\pi\)
\(180\) 8.36493 0.623485
\(181\) −14.9158 −1.10868 −0.554341 0.832289i \(-0.687030\pi\)
−0.554341 + 0.832289i \(0.687030\pi\)
\(182\) 0 0
\(183\) −10.7963 −0.798082
\(184\) −8.37859 −0.617678
\(185\) −8.65509 14.9911i −0.636335 1.10216i
\(186\) −0.782836 −0.0574003
\(187\) 1.54900 + 2.68295i 0.113274 + 0.196197i
\(188\) −1.26923 2.19837i −0.0925680 0.160332i
\(189\) 0 0
\(190\) −5.14829 −0.373496
\(191\) 7.06528 12.2374i 0.511226 0.885469i −0.488690 0.872458i \(-0.662525\pi\)
0.999915 0.0130110i \(-0.00414165\pi\)
\(192\) 3.61529 + 6.26187i 0.260911 + 0.451912i
\(193\) −1.94727 3.37277i −0.140167 0.242777i 0.787392 0.616452i \(-0.211431\pi\)
−0.927560 + 0.373675i \(0.878097\pi\)
\(194\) 0.317999 + 0.550790i 0.0228310 + 0.0395444i
\(195\) −0.185791 + 10.5558i −0.0133048 + 0.755917i
\(196\) 0 0
\(197\) 5.85445 10.1402i 0.417112 0.722459i −0.578536 0.815657i \(-0.696376\pi\)
0.995648 + 0.0931979i \(0.0297089\pi\)
\(198\) 1.79179 0.127337
\(199\) −3.49684 −0.247884 −0.123942 0.992289i \(-0.539554\pi\)
−0.123942 + 0.992289i \(0.539554\pi\)
\(200\) −0.822878 + 1.42527i −0.0581863 + 0.100782i
\(201\) 0.772995 1.33887i 0.0545229 0.0944364i
\(202\) 0.106892 + 0.185143i 0.00752090 + 0.0130266i
\(203\) 0 0
\(204\) −0.865120 1.49843i −0.0605705 0.104911i
\(205\) 6.24421 0.436114
\(206\) −0.290403 0.502994i −0.0202334 0.0350452i
\(207\) −6.73617 + 11.6674i −0.468196 + 0.810939i
\(208\) 11.2709 6.24542i 0.781497 0.433042i
\(209\) 29.5764 2.04584
\(210\) 0 0
\(211\) −9.50258 + 16.4589i −0.654184 + 1.13308i 0.327913 + 0.944708i \(0.393655\pi\)
−0.982098 + 0.188373i \(0.939679\pi\)
\(212\) 8.94598 15.4949i 0.614412 1.06419i
\(213\) −7.03874 + 12.1915i −0.482286 + 0.835345i
\(214\) 3.09047 0.211260
\(215\) 2.88128 4.99053i 0.196502 0.340351i
\(216\) −5.65029 −0.384453
\(217\) 0 0
\(218\) 1.08299 1.87579i 0.0733492 0.127045i
\(219\) −0.878506 −0.0593639
\(220\) 9.74533 16.8794i 0.657030 1.13801i
\(221\) −2.47600 + 1.37200i −0.166554 + 0.0922906i
\(222\) 1.03543 + 1.79342i 0.0694936 + 0.120366i
\(223\) −5.98311 + 10.3630i −0.400658 + 0.693961i −0.993805 0.111133i \(-0.964552\pi\)
0.593147 + 0.805094i \(0.297885\pi\)
\(224\) 0 0
\(225\) 1.32315 + 2.29175i 0.0882097 + 0.152784i
\(226\) 1.07804 + 1.86723i 0.0717104 + 0.124206i
\(227\) −15.3842 −1.02108 −0.510542 0.859853i \(-0.670555\pi\)
−0.510542 + 0.859853i \(0.670555\pi\)
\(228\) −16.5184 −1.09396
\(229\) 4.33084 + 7.50123i 0.286190 + 0.495695i 0.972897 0.231239i \(-0.0742779\pi\)
−0.686707 + 0.726934i \(0.740945\pi\)
\(230\) −2.73209 4.73212i −0.180149 0.312027i
\(231\) 0 0
\(232\) −1.23845 + 2.14506i −0.0813082 + 0.140830i
\(233\) −10.1253 17.5376i −0.663333 1.14893i −0.979734 0.200301i \(-0.935808\pi\)
0.316402 0.948625i \(-0.397525\pi\)
\(234\) −0.0288117 + 1.63695i −0.00188348 + 0.107011i
\(235\) 1.68634 2.92083i 0.110005 0.190534i
\(236\) −17.2888 −1.12540
\(237\) −3.53924 + 6.13014i −0.229898 + 0.398195i
\(238\) 0 0
\(239\) 16.5526 1.07070 0.535350 0.844630i \(-0.320180\pi\)
0.535350 + 0.844630i \(0.320180\pi\)
\(240\) −5.23227 + 9.06256i −0.337742 + 0.584985i
\(241\) 16.4008 1.05647 0.528233 0.849100i \(-0.322855\pi\)
0.528233 + 0.849100i \(0.322855\pi\)
\(242\) 0.612791 1.06138i 0.0393917 0.0682284i
\(243\) −7.44626 + 12.8973i −0.477678 + 0.827362i
\(244\) −9.10595 + 15.7720i −0.582949 + 1.00970i
\(245\) 0 0
\(246\) −0.747011 −0.0476277
\(247\) −0.475582 + 27.0204i −0.0302605 + 1.71927i
\(248\) −1.34516 + 2.32989i −0.0854178 + 0.147948i
\(249\) −0.613178 1.06206i −0.0388586 0.0673051i
\(250\) 2.36106 0.149326
\(251\) −10.2154 17.6935i −0.644788 1.11681i −0.984350 0.176222i \(-0.943612\pi\)
0.339563 0.940583i \(-0.389721\pi\)
\(252\) 0 0
\(253\) 15.6956 + 27.1855i 0.986772 + 1.70914i
\(254\) 0.239710 0.415190i 0.0150407 0.0260513i
\(255\) 1.14943 1.99087i 0.0719800 0.124673i
\(256\) 10.5536 0.659602
\(257\) −13.7779 −0.859442 −0.429721 0.902962i \(-0.641388\pi\)
−0.429721 + 0.902962i \(0.641388\pi\)
\(258\) −0.344695 + 0.597030i −0.0214598 + 0.0371695i
\(259\) 0 0
\(260\) 15.2640 + 9.17456i 0.946633 + 0.568982i
\(261\) 1.99136 + 3.44914i 0.123262 + 0.213496i
\(262\) 0.856782 + 1.48399i 0.0529321 + 0.0916812i
\(263\) −12.9587 22.4451i −0.799065 1.38402i −0.920225 0.391389i \(-0.871995\pi\)
0.121160 0.992633i \(-0.461338\pi\)
\(264\) −2.37519 + 4.11395i −0.146183 + 0.253196i
\(265\) 23.7719 1.46030
\(266\) 0 0
\(267\) 4.37943 + 7.58540i 0.268017 + 0.464219i
\(268\) −1.30394 2.25850i −0.0796510 0.137960i
\(269\) 30.0666 1.83319 0.916596 0.399814i \(-0.130925\pi\)
0.916596 + 0.399814i \(0.130925\pi\)
\(270\) −1.84245 3.19121i −0.112128 0.194211i
\(271\) −14.4505 −0.877808 −0.438904 0.898534i \(-0.644633\pi\)
−0.438904 + 0.898534i \(0.644633\pi\)
\(272\) −2.80581 −0.170127
\(273\) 0 0
\(274\) −2.69105 −0.162572
\(275\) 6.16598 0.371822
\(276\) −8.76599 15.1831i −0.527651 0.913918i
\(277\) −15.3255 −0.920819 −0.460409 0.887707i \(-0.652297\pi\)
−0.460409 + 0.887707i \(0.652297\pi\)
\(278\) 0.743453 + 1.28770i 0.0445894 + 0.0772310i
\(279\) 2.16295 + 3.74634i 0.129492 + 0.224287i
\(280\) 0 0
\(281\) 5.29279 0.315741 0.157871 0.987460i \(-0.449537\pi\)
0.157871 + 0.987460i \(0.449537\pi\)
\(282\) −0.201742 + 0.349427i −0.0120135 + 0.0208081i
\(283\) −15.3923 26.6602i −0.914975 1.58478i −0.806938 0.590636i \(-0.798877\pi\)
−0.108036 0.994147i \(-0.534456\pi\)
\(284\) 11.8734 + 20.5654i 0.704559 + 1.22033i
\(285\) −10.9735 19.0066i −0.650013 1.12586i
\(286\) 3.26960 + 1.96522i 0.193335 + 0.116206i
\(287\) 0 0
\(288\) −2.59507 + 4.49479i −0.152916 + 0.264858i
\(289\) −16.3836 −0.963742
\(290\) −1.61533 −0.0948557
\(291\) −1.35562 + 2.34800i −0.0794677 + 0.137642i
\(292\) −0.740963 + 1.28339i −0.0433616 + 0.0751044i
\(293\) −8.75864 15.1704i −0.511685 0.886265i −0.999908 0.0135461i \(-0.995688\pi\)
0.488223 0.872719i \(-0.337645\pi\)
\(294\) 0 0
\(295\) −11.4853 19.8930i −0.668697 1.15822i
\(296\) 7.11681 0.413656
\(297\) 10.5847 + 18.3332i 0.614184 + 1.06380i
\(298\) 2.47548 4.28765i 0.143400 0.248377i
\(299\) −25.0886 + 13.9020i −1.45091 + 0.803976i
\(300\) −3.44370 −0.198822
\(301\) 0 0
\(302\) 0.215486 0.373233i 0.0123998 0.0214772i
\(303\) −0.455678 + 0.789257i −0.0261780 + 0.0453416i
\(304\) −13.3934 + 23.1980i −0.768163 + 1.33050i
\(305\) −24.1970 −1.38551
\(306\) 0.178248 0.308735i 0.0101898 0.0176492i
\(307\) 8.63573 0.492867 0.246434 0.969160i \(-0.420741\pi\)
0.246434 + 0.969160i \(0.420741\pi\)
\(308\) 0 0
\(309\) 1.23798 2.14425i 0.0704262 0.121982i
\(310\) −1.75452 −0.0996501
\(311\) −8.21130 + 14.2224i −0.465620 + 0.806478i −0.999229 0.0392535i \(-0.987502\pi\)
0.533609 + 0.845731i \(0.320835\pi\)
\(312\) −3.72023 2.23608i −0.210617 0.126593i
\(313\) 5.02308 + 8.70024i 0.283921 + 0.491766i 0.972347 0.233541i \(-0.0750312\pi\)
−0.688426 + 0.725307i \(0.741698\pi\)
\(314\) 0.220658 0.382191i 0.0124525 0.0215683i
\(315\) 0 0
\(316\) 5.97024 + 10.3408i 0.335852 + 0.581713i
\(317\) −5.07249 8.78581i −0.284899 0.493460i 0.687685 0.726009i \(-0.258627\pi\)
−0.972585 + 0.232549i \(0.925294\pi\)
\(318\) −2.84390 −0.159478
\(319\) 9.27992 0.519576
\(320\) 8.10273 + 14.0343i 0.452957 + 0.784544i
\(321\) 6.58729 + 11.4095i 0.367667 + 0.636817i
\(322\) 0 0
\(323\) 2.94227 5.09616i 0.163712 0.283558i
\(324\) −1.01357 1.75556i −0.0563095 0.0975310i
\(325\) −0.0991476 + 5.63312i −0.00549972 + 0.312469i
\(326\) −0.877867 + 1.52051i −0.0486206 + 0.0842133i
\(327\) 9.23349 0.510613
\(328\) −1.28360 + 2.22327i −0.0708751 + 0.122759i
\(329\) 0 0
\(330\) −3.09801 −0.170540
\(331\) −1.15958 + 2.00845i −0.0637363 + 0.110395i −0.896133 0.443786i \(-0.853635\pi\)
0.832396 + 0.554181i \(0.186968\pi\)
\(332\) −2.06871 −0.113535
\(333\) 5.72172 9.91032i 0.313549 0.543082i
\(334\) −1.28014 + 2.21726i −0.0700460 + 0.121323i
\(335\) 1.73247 3.00072i 0.0946547 0.163947i
\(336\) 0 0
\(337\) −15.9998 −0.871565 −0.435783 0.900052i \(-0.643528\pi\)
−0.435783 + 0.900052i \(0.643528\pi\)
\(338\) −1.84796 + 2.95544i −0.100516 + 0.160755i
\(339\) −4.59567 + 7.95993i −0.249602 + 0.432324i
\(340\) −1.93894 3.35834i −0.105154 0.182132i
\(341\) 10.0795 0.545837
\(342\) −1.70172 2.94747i −0.0920185 0.159381i
\(343\) 0 0
\(344\) 1.18459 + 2.05178i 0.0638690 + 0.110624i
\(345\) 11.6468 20.1729i 0.627043 1.08607i
\(346\) −1.49234 + 2.58480i −0.0802285 + 0.138960i
\(347\) −22.8208 −1.22509 −0.612543 0.790437i \(-0.709853\pi\)
−0.612543 + 0.790437i \(0.709853\pi\)
\(348\) −5.18285 −0.277830
\(349\) −11.3511 + 19.6607i −0.607612 + 1.05241i 0.384021 + 0.923324i \(0.374539\pi\)
−0.991633 + 0.129090i \(0.958794\pi\)
\(350\) 0 0
\(351\) −16.9190 + 9.37515i −0.903071 + 0.500408i
\(352\) 6.04662 + 10.4731i 0.322286 + 0.558216i
\(353\) −13.6322 23.6116i −0.725568 1.25672i −0.958740 0.284286i \(-0.908244\pi\)
0.233171 0.972436i \(-0.425090\pi\)
\(354\) 1.37401 + 2.37986i 0.0730279 + 0.126488i
\(355\) −15.7755 + 27.3239i −0.837276 + 1.45020i
\(356\) 14.7751 0.783077
\(357\) 0 0
\(358\) −1.69502 2.93585i −0.0895844 0.155165i
\(359\) 7.21309 + 12.4934i 0.380692 + 0.659378i 0.991161 0.132662i \(-0.0423524\pi\)
−0.610469 + 0.792040i \(0.709019\pi\)
\(360\) −4.56932 −0.240824
\(361\) −18.5895 32.1980i −0.978397 1.69463i
\(362\) 3.99930 0.210199
\(363\) 5.22461 0.274221
\(364\) 0 0
\(365\) −1.96894 −0.103059
\(366\) 2.89475 0.151311
\(367\) −5.69586 9.86553i −0.297322 0.514976i 0.678201 0.734877i \(-0.262760\pi\)
−0.975522 + 0.219901i \(0.929427\pi\)
\(368\) −28.4304 −1.48204
\(369\) 2.06397 + 3.57489i 0.107446 + 0.186102i
\(370\) 2.32065 + 4.01948i 0.120645 + 0.208963i
\(371\) 0 0
\(372\) −5.62943 −0.291872
\(373\) 15.4815 26.8147i 0.801599 1.38841i −0.116964 0.993136i \(-0.537316\pi\)
0.918563 0.395274i \(-0.129351\pi\)
\(374\) −0.415327 0.719367i −0.0214760 0.0371976i
\(375\) 5.03256 + 8.71665i 0.259880 + 0.450126i
\(376\) 0.693313 + 1.20085i 0.0357549 + 0.0619293i
\(377\) −0.149219 + 8.47796i −0.00768518 + 0.436637i
\(378\) 0 0
\(379\) −5.29330 + 9.16826i −0.271898 + 0.470942i −0.969348 0.245692i \(-0.920985\pi\)
0.697450 + 0.716634i \(0.254318\pi\)
\(380\) −37.0217 −1.89917
\(381\) 2.04375 0.104705
\(382\) −1.89438 + 3.28116i −0.0969249 + 0.167879i
\(383\) 15.3758 26.6317i 0.785668 1.36082i −0.142931 0.989733i \(-0.545653\pi\)
0.928599 0.371084i \(-0.121014\pi\)
\(384\) −4.47231 7.74627i −0.228227 0.395300i
\(385\) 0 0
\(386\) 0.522112 + 0.904324i 0.0265748 + 0.0460289i
\(387\) 3.80953 0.193649
\(388\) 2.28675 + 3.96077i 0.116092 + 0.201078i
\(389\) 8.18978 14.1851i 0.415239 0.719214i −0.580215 0.814463i \(-0.697031\pi\)
0.995453 + 0.0952492i \(0.0303648\pi\)
\(390\) 0.0498153 2.83028i 0.00252249 0.143317i
\(391\) 6.24561 0.315854
\(392\) 0 0
\(393\) −3.65243 + 6.32620i −0.184241 + 0.319114i
\(394\) −1.56972 + 2.71884i −0.0790816 + 0.136973i
\(395\) −7.93227 + 13.7391i −0.399116 + 0.691289i
\(396\) 12.8849 0.647492
\(397\) −7.94133 + 13.7548i −0.398564 + 0.690333i −0.993549 0.113404i \(-0.963825\pi\)
0.594985 + 0.803737i \(0.297158\pi\)
\(398\) 0.937591 0.0469972
\(399\) 0 0
\(400\) −2.79221 + 4.83624i −0.139610 + 0.241812i
\(401\) 6.63573 0.331373 0.165686 0.986178i \(-0.447016\pi\)
0.165686 + 0.986178i \(0.447016\pi\)
\(402\) −0.207259 + 0.358984i −0.0103372 + 0.0179045i
\(403\) −0.162077 + 9.20847i −0.00807362 + 0.458707i
\(404\) 0.768670 + 1.33137i 0.0382427 + 0.0662384i
\(405\) 1.34667 2.33250i 0.0669164 0.115903i
\(406\) 0 0
\(407\) −13.3319 23.0915i −0.660836 1.14460i
\(408\) 0.472570 + 0.818515i 0.0233957 + 0.0405225i
\(409\) −5.87235 −0.290369 −0.145184 0.989405i \(-0.546378\pi\)
−0.145184 + 0.989405i \(0.546378\pi\)
\(410\) −1.67423 −0.0826843
\(411\) −5.73593 9.93492i −0.282933 0.490053i
\(412\) −2.08831 3.61707i −0.102884 0.178200i
\(413\) 0 0
\(414\) 1.80614 3.12832i 0.0887667 0.153749i
\(415\) −1.37428 2.38032i −0.0674607 0.116845i
\(416\) −9.66521 + 5.35567i −0.473876 + 0.262584i
\(417\) −3.16932 + 5.48942i −0.155202 + 0.268818i
\(418\) −7.93017 −0.387877
\(419\) −15.0712 + 26.1040i −0.736274 + 1.27526i 0.217888 + 0.975974i \(0.430083\pi\)
−0.954162 + 0.299290i \(0.903250\pi\)
\(420\) 0 0
\(421\) 40.0580 1.95231 0.976153 0.217083i \(-0.0696543\pi\)
0.976153 + 0.217083i \(0.0696543\pi\)
\(422\) 2.54788 4.41306i 0.124029 0.214824i
\(423\) 2.22962 0.108408
\(424\) −4.88672 + 8.46405i −0.237320 + 0.411051i
\(425\) 0.613394 1.06243i 0.0297540 0.0515354i
\(426\) 1.88726 3.26884i 0.0914382 0.158376i
\(427\) 0 0
\(428\) 22.2238 1.07423
\(429\) −0.286184 + 16.2597i −0.0138171 + 0.785024i
\(430\) −0.772544 + 1.33809i −0.0372554 + 0.0645282i
\(431\) 1.95793 + 3.39124i 0.0943104 + 0.163350i 0.909321 0.416096i \(-0.136602\pi\)
−0.815010 + 0.579447i \(0.803269\pi\)
\(432\) −19.1726 −0.922445
\(433\) −20.3963 35.3274i −0.980182 1.69772i −0.661650 0.749813i \(-0.730144\pi\)
−0.318532 0.947912i \(-0.603190\pi\)
\(434\) 0 0
\(435\) −3.44306 5.96355i −0.165082 0.285930i
\(436\) 7.78785 13.4890i 0.372971 0.646004i
\(437\) 29.8131 51.6378i 1.42615 2.47017i
\(438\) 0.235549 0.0112550
\(439\) 25.5623 1.22002 0.610010 0.792394i \(-0.291165\pi\)
0.610010 + 0.792394i \(0.291165\pi\)
\(440\) −5.32336 + 9.22033i −0.253781 + 0.439562i
\(441\) 0 0
\(442\) 0.663878 0.367867i 0.0315775 0.0174977i
\(443\) 13.7282 + 23.7779i 0.652247 + 1.12972i 0.982576 + 0.185859i \(0.0595067\pi\)
−0.330330 + 0.943866i \(0.607160\pi\)
\(444\) 7.44586 + 12.8966i 0.353365 + 0.612046i
\(445\) 9.81535 + 17.0007i 0.465292 + 0.805910i
\(446\) 1.60422 2.77859i 0.0759621 0.131570i
\(447\) 21.1057 0.998267
\(448\) 0 0
\(449\) 7.40181 + 12.8203i 0.349313 + 0.605028i 0.986128 0.165989i \(-0.0530816\pi\)
−0.636815 + 0.771017i \(0.719748\pi\)
\(450\) −0.354769 0.614477i −0.0167240 0.0289667i
\(451\) 9.61827 0.452907
\(452\) 7.75230 + 13.4274i 0.364637 + 0.631571i
\(453\) 1.83722 0.0863203
\(454\) 4.12489 0.193590
\(455\) 0 0
\(456\) 9.02315 0.422548
\(457\) −0.651951 −0.0304970 −0.0152485 0.999884i \(-0.504854\pi\)
−0.0152485 + 0.999884i \(0.504854\pi\)
\(458\) −1.16121 2.01127i −0.0542596 0.0939805i
\(459\) 4.21186 0.196593
\(460\) −19.6467 34.0290i −0.916031 1.58661i
\(461\) 6.24774 + 10.8214i 0.290986 + 0.504003i 0.974043 0.226362i \(-0.0726833\pi\)
−0.683057 + 0.730365i \(0.739350\pi\)
\(462\) 0 0
\(463\) −0.309503 −0.0143838 −0.00719190 0.999974i \(-0.502289\pi\)
−0.00719190 + 0.999974i \(0.502289\pi\)
\(464\) −4.20233 + 7.27865i −0.195088 + 0.337903i
\(465\) −3.73973 6.47741i −0.173426 0.300382i
\(466\) 2.71486 + 4.70227i 0.125763 + 0.217829i
\(467\) 12.2387 + 21.1980i 0.566338 + 0.980926i 0.996924 + 0.0783762i \(0.0249735\pi\)
−0.430586 + 0.902549i \(0.641693\pi\)
\(468\) −0.207187 + 11.7714i −0.00957722 + 0.544134i
\(469\) 0 0
\(470\) −0.452151 + 0.783149i −0.0208562 + 0.0361240i
\(471\) 1.88132 0.0866865
\(472\) 9.44396 0.434694
\(473\) 4.43818 7.68716i 0.204068 0.353456i
\(474\) 0.948959 1.64364i 0.0435871 0.0754951i
\(475\) −5.85601 10.1429i −0.268692 0.465389i
\(476\) 0 0
\(477\) 7.85759 + 13.6097i 0.359774 + 0.623147i
\(478\) −4.43817 −0.202997
\(479\) 4.06925 + 7.04815i 0.185929 + 0.322038i 0.943889 0.330262i \(-0.107137\pi\)
−0.757960 + 0.652301i \(0.773804\pi\)
\(480\) 4.48686 7.77147i 0.204796 0.354718i
\(481\) 21.3103 11.8084i 0.971667 0.538419i
\(482\) −4.39746 −0.200299
\(483\) 0 0
\(484\) 4.40662 7.63250i 0.200301 0.346932i
\(485\) −3.03826 + 5.26243i −0.137960 + 0.238954i
\(486\) 1.99653 3.45809i 0.0905645 0.156862i
\(487\) 4.60960 0.208881 0.104440 0.994531i \(-0.466695\pi\)
0.104440 + 0.994531i \(0.466695\pi\)
\(488\) 4.97410 8.61540i 0.225167 0.390001i
\(489\) −7.48464 −0.338467
\(490\) 0 0
\(491\) −6.50947 + 11.2747i −0.293768 + 0.508822i −0.974698 0.223527i \(-0.928243\pi\)
0.680929 + 0.732349i \(0.261576\pi\)
\(492\) −5.37181 −0.242180
\(493\) 0.923171 1.59898i 0.0415775 0.0720144i
\(494\) 0.127515 7.24485i 0.00573719 0.325961i
\(495\) 8.55969 + 14.8258i 0.384729 + 0.666371i
\(496\) −4.56443 + 7.90582i −0.204949 + 0.354982i
\(497\) 0 0
\(498\) 0.164409 + 0.284764i 0.00736733 + 0.0127606i
\(499\) 16.1603 + 27.9905i 0.723436 + 1.25303i 0.959614 + 0.281319i \(0.0907717\pi\)
−0.236178 + 0.971710i \(0.575895\pi\)
\(500\) 16.9786 0.759304
\(501\) −10.9144 −0.487618
\(502\) 2.73900 + 4.74408i 0.122247 + 0.211739i
\(503\) −15.9126 27.5615i −0.709509 1.22891i −0.965039 0.262105i \(-0.915583\pi\)
0.255531 0.966801i \(-0.417750\pi\)
\(504\) 0 0
\(505\) −1.02128 + 1.76891i −0.0454465 + 0.0787156i
\(506\) −4.20838 7.28912i −0.187085 0.324041i
\(507\) −14.8499 0.522904i −0.659508 0.0232230i
\(508\) 1.72377 2.98566i 0.0764801 0.132467i
\(509\) −2.25575 −0.0999845 −0.0499922 0.998750i \(-0.515920\pi\)
−0.0499922 + 0.998750i \(0.515920\pi\)
\(510\) −0.308191 + 0.533802i −0.0136469 + 0.0236372i
\(511\) 0 0
\(512\) −18.4807 −0.816739
\(513\) 20.1051 34.8231i 0.887663 1.53748i
\(514\) 3.69420 0.162944
\(515\) 2.77461 4.80576i 0.122264 0.211767i
\(516\) −2.47873 + 4.29329i −0.109120 + 0.189001i
\(517\) 2.59756 4.49911i 0.114241 0.197870i
\(518\) 0 0
\(519\) −12.7236 −0.558502
\(520\) −8.33793 5.01158i −0.365642 0.219773i
\(521\) 5.38562 9.32817i 0.235948 0.408675i −0.723600 0.690220i \(-0.757514\pi\)
0.959548 + 0.281546i \(0.0908471\pi\)
\(522\) −0.533934 0.924801i −0.0233697 0.0404775i
\(523\) −7.40793 −0.323926 −0.161963 0.986797i \(-0.551783\pi\)
−0.161963 + 0.986797i \(0.551783\pi\)
\(524\) 6.16118 + 10.6715i 0.269152 + 0.466186i
\(525\) 0 0
\(526\) 3.47454 + 6.01809i 0.151497 + 0.262401i
\(527\) 1.00272 1.73676i 0.0436790 0.0756543i
\(528\) −8.05953 + 13.9595i −0.350746 + 0.607510i
\(529\) 40.2848 1.75151
\(530\) −6.37385 −0.276862
\(531\) 7.59270 13.1509i 0.329495 0.570702i
\(532\) 0 0
\(533\) −0.154660 + 8.78707i −0.00669906 + 0.380610i
\(534\) −1.17424 2.03384i −0.0508142 0.0880127i
\(535\) 14.7637 + 25.5715i 0.638290 + 1.10555i
\(536\) 0.712276 + 1.23370i 0.0307656 + 0.0532876i
\(537\) 7.22580 12.5154i 0.311816 0.540081i
\(538\) −8.06161 −0.347561
\(539\) 0 0
\(540\) −13.2492 22.9482i −0.570153 0.987534i
\(541\) −16.2741 28.1875i −0.699676 1.21188i −0.968579 0.248708i \(-0.919994\pi\)
0.268902 0.963168i \(-0.413339\pi\)
\(542\) 3.87455 0.166426
\(543\) 8.52445 + 14.7648i 0.365819 + 0.633617i
\(544\) 2.40608 0.103160
\(545\) 20.6944 0.886453
\(546\) 0 0
\(547\) −13.4997 −0.577206 −0.288603 0.957449i \(-0.593191\pi\)
−0.288603 + 0.957449i \(0.593191\pi\)
\(548\) −19.3515 −0.826657
\(549\) −7.99810 13.8531i −0.341350 0.591236i
\(550\) −1.65325 −0.0704950
\(551\) −8.81342 15.2653i −0.375464 0.650323i
\(552\) 4.78840 + 8.29376i 0.203808 + 0.353006i
\(553\) 0 0
\(554\) 4.10915 0.174581
\(555\) −9.89284 + 17.1349i −0.419928 + 0.727336i
\(556\) 5.34623 + 9.25994i 0.226731 + 0.392709i
\(557\) 14.8851 + 25.7818i 0.630703 + 1.09241i 0.987408 + 0.158193i \(0.0505668\pi\)
−0.356705 + 0.934217i \(0.616100\pi\)
\(558\) −0.579941 1.00449i −0.0245509 0.0425233i
\(559\) 6.95148 + 4.17825i 0.294016 + 0.176721i
\(560\) 0 0
\(561\) 1.77052 3.06664i 0.0747516 0.129474i
\(562\) −1.41913 −0.0598624
\(563\) −14.1326 −0.595617 −0.297809 0.954626i \(-0.596256\pi\)
−0.297809 + 0.954626i \(0.596256\pi\)
\(564\) −1.45074 + 2.51275i −0.0610872 + 0.105806i
\(565\) −10.3000 + 17.8401i −0.433324 + 0.750538i
\(566\) 4.12705 + 7.14826i 0.173473 + 0.300464i
\(567\) 0 0
\(568\) −6.48584 11.2338i −0.272140 0.471360i
\(569\) −24.2540 −1.01678 −0.508391 0.861127i \(-0.669759\pi\)
−0.508391 + 0.861127i \(0.669759\pi\)
\(570\) 2.94227 + 5.09616i 0.123238 + 0.213455i
\(571\) −0.604159 + 1.04643i −0.0252832 + 0.0437919i −0.878390 0.477944i \(-0.841382\pi\)
0.853107 + 0.521736i \(0.174715\pi\)
\(572\) 23.5119 + 14.1320i 0.983083 + 0.590891i
\(573\) −16.1514 −0.674732
\(574\) 0 0
\(575\) 6.21533 10.7653i 0.259197 0.448943i
\(576\) −5.35657 + 9.27786i −0.223191 + 0.386577i
\(577\) −7.30518 + 12.6529i −0.304119 + 0.526749i −0.977065 0.212943i \(-0.931695\pi\)
0.672946 + 0.739692i \(0.265029\pi\)
\(578\) 4.39286 0.182719
\(579\) −2.22575 + 3.85510i −0.0924988 + 0.160213i
\(580\) −11.6160 −0.482328
\(581\) 0 0
\(582\) 0.363475 0.629558i 0.0150665 0.0260960i
\(583\) 36.6171 1.51652
\(584\) 0.404749 0.701046i 0.0167486 0.0290095i
\(585\) −13.6822 + 7.58157i −0.565690 + 0.313459i
\(586\) 2.34841 + 4.06757i 0.0970120 + 0.168030i
\(587\) 10.7548 18.6278i 0.443897 0.768852i −0.554078 0.832465i \(-0.686929\pi\)
0.997975 + 0.0636132i \(0.0202624\pi\)
\(588\) 0 0
\(589\) −9.57284 16.5806i −0.394442 0.683193i
\(590\) 3.07949 + 5.33383i 0.126780 + 0.219590i
\(591\) −13.3834 −0.550518
\(592\) 24.1489 0.992512
\(593\) −1.32429 2.29373i −0.0543820 0.0941923i 0.837553 0.546356i \(-0.183986\pi\)
−0.891935 + 0.452164i \(0.850652\pi\)
\(594\) −2.83801 4.91558i −0.116445 0.201689i
\(595\) 0 0
\(596\) 17.8013 30.8328i 0.729171 1.26296i
\(597\) 1.99846 + 3.46143i 0.0817915 + 0.141667i
\(598\) 6.72688 3.72749i 0.275082 0.152428i
\(599\) 20.1250 34.8576i 0.822287 1.42424i −0.0816889 0.996658i \(-0.526031\pi\)
0.903975 0.427584i \(-0.140635\pi\)
\(600\) 1.88112 0.0767962
\(601\) 19.1725 33.2077i 0.782061 1.35457i −0.148679 0.988886i \(-0.547502\pi\)
0.930739 0.365683i \(-0.119165\pi\)
\(602\) 0 0
\(603\) 2.29060 0.0932806
\(604\) 1.54958 2.68395i 0.0630515 0.109208i
\(605\) 11.7096 0.476063
\(606\) 0.122179 0.211620i 0.00496317 0.00859646i
\(607\) 21.2773 36.8534i 0.863620 1.49583i −0.00479063 0.999989i \(-0.501525\pi\)
0.868411 0.495845i \(-0.165142\pi\)
\(608\) 11.4853 19.8931i 0.465791 0.806773i
\(609\) 0 0
\(610\) 6.48782 0.262684
\(611\) 4.06853 + 2.44543i 0.164595 + 0.0989314i
\(612\) 1.28180 2.22014i 0.0518136 0.0897438i
\(613\) −7.63261 13.2201i −0.308278 0.533953i 0.669708 0.742625i \(-0.266419\pi\)
−0.977986 + 0.208672i \(0.933086\pi\)
\(614\) −2.31546 −0.0934442
\(615\) −3.56859 6.18098i −0.143899 0.249241i
\(616\) 0 0
\(617\) −6.99061 12.1081i −0.281431 0.487453i 0.690306 0.723517i \(-0.257476\pi\)
−0.971737 + 0.236064i \(0.924142\pi\)
\(618\) −0.331934 + 0.574926i −0.0133523 + 0.0231269i
\(619\) −4.25792 + 7.37494i −0.171140 + 0.296424i −0.938819 0.344411i \(-0.888079\pi\)
0.767678 + 0.640835i \(0.221412\pi\)
\(620\) −12.6169 −0.506707
\(621\) 42.6775 1.71259
\(622\) 2.20166 3.81338i 0.0882784 0.152903i
\(623\) 0 0
\(624\) −12.6236 7.58750i −0.505347 0.303743i
\(625\) 15.1856 + 26.3023i 0.607425 + 1.05209i
\(626\) −1.34682 2.33275i −0.0538296 0.0932356i
\(627\) −16.9030 29.2769i −0.675042 1.16921i
\(628\) 1.58677 2.74837i 0.0633190 0.109672i
\(629\) −5.30504 −0.211526
\(630\) 0 0
\(631\) −18.4146 31.8950i −0.733074 1.26972i −0.955563 0.294786i \(-0.904752\pi\)
0.222490 0.974935i \(-0.428582\pi\)
\(632\) −3.26123 5.64861i −0.129725 0.224690i
\(633\) 21.7231 0.863414
\(634\) 1.36006 + 2.35570i 0.0540150 + 0.0935567i
\(635\) 4.58053 0.181773
\(636\) −20.4507 −0.810922
\(637\) 0 0
\(638\) −2.48818 −0.0985081
\(639\) −20.8578 −0.825121
\(640\) −10.0235 17.3612i −0.396214 0.686263i
\(641\) 25.8747 1.02199 0.510996 0.859583i \(-0.329277\pi\)
0.510996 + 0.859583i \(0.329277\pi\)
\(642\) −1.76622 3.05918i −0.0697071 0.120736i
\(643\) 20.2626 + 35.0958i 0.799078 + 1.38404i 0.920217 + 0.391408i \(0.128012\pi\)
−0.121139 + 0.992636i \(0.538655\pi\)
\(644\) 0 0
\(645\) −6.58666 −0.259350
\(646\) −0.788896 + 1.36641i −0.0310387 + 0.0537606i
\(647\) 0.892002 + 1.54499i 0.0350682 + 0.0607399i 0.883027 0.469322i \(-0.155502\pi\)
−0.847959 + 0.530062i \(0.822168\pi\)
\(648\) 0.553661 + 0.958969i 0.0217499 + 0.0376719i
\(649\) −17.6913 30.6423i −0.694445 1.20281i
\(650\) 0.0265840 1.51038i 0.00104271 0.0592420i
\(651\) 0 0
\(652\) −6.31281 + 10.9341i −0.247229 + 0.428213i
\(653\) 12.4042 0.485414 0.242707 0.970100i \(-0.421965\pi\)
0.242707 + 0.970100i \(0.421965\pi\)
\(654\) −2.47573 −0.0968088
\(655\) −8.18597 + 14.1785i −0.319852 + 0.554000i
\(656\) −4.35554 + 7.54402i −0.170055 + 0.294545i
\(657\) −0.650815 1.12725i −0.0253907 0.0439780i
\(658\) 0 0
\(659\) 0.564336 + 0.977458i 0.0219834 + 0.0380764i 0.876808 0.480841i \(-0.159669\pi\)
−0.854824 + 0.518917i \(0.826335\pi\)
\(660\) −22.2780 −0.867170
\(661\) −14.4627 25.0502i −0.562534 0.974338i −0.997274 0.0737821i \(-0.976493\pi\)
0.434740 0.900556i \(-0.356840\pi\)
\(662\) 0.310913 0.538517i 0.0120840 0.0209301i
\(663\) 2.77315 + 1.66683i 0.107700 + 0.0647342i
\(664\) 1.13003 0.0438535
\(665\) 0 0
\(666\) −1.53414 + 2.65721i −0.0594467 + 0.102965i
\(667\) 9.35421 16.2020i 0.362196 0.627342i
\(668\) −9.20556 + 15.9445i −0.356174 + 0.616911i
\(669\) 13.6775 0.528802
\(670\) −0.464518 + 0.804568i −0.0179459 + 0.0310832i
\(671\) −37.2718 −1.43886
\(672\) 0 0
\(673\) 3.54980 6.14843i 0.136835 0.237005i −0.789462 0.613799i \(-0.789640\pi\)
0.926297 + 0.376795i \(0.122974\pi\)
\(674\) 4.28995 0.165243
\(675\) 4.19145 7.25980i 0.161329 0.279430i
\(676\) −13.2888 + 21.2528i −0.511109 + 0.817416i
\(677\) −25.2010 43.6494i −0.968552 1.67758i −0.699752 0.714386i \(-0.746706\pi\)
−0.268800 0.963196i \(-0.586627\pi\)
\(678\) 1.23221 2.13426i 0.0473229 0.0819657i
\(679\) 0 0
\(680\) 1.05914 + 1.83449i 0.0406162 + 0.0703493i
\(681\) 8.79213 + 15.2284i 0.336915 + 0.583554i
\(682\) −2.70258 −0.103487
\(683\) 27.5282 1.05334 0.526669 0.850070i \(-0.323441\pi\)
0.526669 + 0.850070i \(0.323441\pi\)
\(684\) −12.2372 21.1954i −0.467901 0.810428i
\(685\) −12.8556 22.2665i −0.491186 0.850760i
\(686\) 0 0
\(687\) 4.95019 8.57398i 0.188861 0.327118i
\(688\) 4.01958 + 6.96212i 0.153245 + 0.265428i
\(689\) −0.588795 + 33.4527i −0.0224313 + 1.27445i
\(690\) −3.12280 + 5.40885i −0.118883 + 0.205912i
\(691\) 24.3338 0.925702 0.462851 0.886436i \(-0.346826\pi\)
0.462851 + 0.886436i \(0.346826\pi\)
\(692\) −10.7315 + 18.5875i −0.407950 + 0.706591i
\(693\) 0 0
\(694\) 6.11884 0.232268
\(695\) −7.10319 + 12.3031i −0.269439 + 0.466683i
\(696\) 2.83112 0.107313
\(697\) 0.956829 1.65728i 0.0362425 0.0627738i
\(698\) 3.04352 5.27153i 0.115199 0.199531i
\(699\) −11.5733 + 20.0456i −0.437744 + 0.758195i
\(700\) 0 0
\(701\) −20.5588 −0.776495 −0.388248 0.921555i \(-0.626919\pi\)
−0.388248 + 0.921555i \(0.626919\pi\)
\(702\) 4.53642 2.51371i 0.171216 0.0948740i
\(703\) −25.3234 + 43.8613i −0.955088 + 1.65426i
\(704\) 12.4811 + 21.6178i 0.470397 + 0.814752i
\(705\) −3.85501 −0.145188
\(706\) 3.65513 + 6.33088i 0.137563 + 0.238266i
\(707\) 0 0
\(708\) 9.88062 + 17.1137i 0.371336 + 0.643174i
\(709\) −20.4544 + 35.4281i −0.768183 + 1.33053i 0.170364 + 0.985381i \(0.445506\pi\)
−0.938547 + 0.345151i \(0.887828\pi\)
\(710\) 4.22981 7.32624i 0.158742 0.274949i
\(711\) −10.4878 −0.393322
\(712\) −8.07085 −0.302468
\(713\) 10.1602 17.5980i 0.380503 0.659051i
\(714\) 0 0
\(715\) −0.641405 + 36.4418i −0.0239872 + 1.36284i
\(716\) −12.1890 21.1119i −0.455524 0.788990i
\(717\) −9.45989 16.3850i −0.353286 0.611910i
\(718\) −1.93401 3.34981i −0.0721767 0.125014i
\(719\) −0.599734 + 1.03877i −0.0223663 + 0.0387396i −0.876992 0.480505i \(-0.840453\pi\)
0.854626 + 0.519245i \(0.173787\pi\)
\(720\) −15.5047 −0.577826
\(721\) 0 0
\(722\) 4.98433 + 8.63311i 0.185497 + 0.321291i
\(723\) −9.37311 16.2347i −0.348590 0.603775i
\(724\) 28.7593 1.06883
\(725\) −1.83739 3.18246i −0.0682390 0.118193i
\(726\) −1.40085 −0.0519904
\(727\) 2.06230 0.0764865 0.0382433 0.999268i \(-0.487824\pi\)
0.0382433 + 0.999268i \(0.487824\pi\)
\(728\) 0 0
\(729\) 20.1764 0.747273
\(730\) 0.527922 0.0195393
\(731\) −0.883025 1.52944i −0.0326599 0.0565685i
\(732\) 20.8164 0.769395
\(733\) 15.0310 + 26.0345i 0.555184 + 0.961606i 0.997889 + 0.0649392i \(0.0206853\pi\)
−0.442706 + 0.896667i \(0.645981\pi\)
\(734\) 1.52720 + 2.64520i 0.0563702 + 0.0976360i
\(735\) 0 0
\(736\) 24.3801 0.898662
\(737\) 2.66861 4.62216i 0.0982993 0.170259i
\(738\) −0.553401 0.958519i −0.0203710 0.0352836i
\(739\) −22.1274 38.3257i −0.813969 1.40984i −0.910066 0.414464i \(-0.863969\pi\)
0.0960970 0.995372i \(-0.469364\pi\)
\(740\) 16.6880 + 28.9044i 0.613461 + 1.06255i
\(741\) 27.0186 14.9715i 0.992553 0.549992i
\(742\) 0 0
\(743\) 4.31326 7.47078i 0.158238 0.274076i −0.775995 0.630739i \(-0.782752\pi\)
0.934233 + 0.356662i \(0.116085\pi\)
\(744\) 3.07506 0.112737
\(745\) 47.3030 1.73305
\(746\) −4.15097 + 7.18969i −0.151978 + 0.263233i
\(747\) 0.908511 1.57359i 0.0332407 0.0575746i
\(748\) −2.98665 5.17302i −0.109203 0.189144i
\(749\) 0 0
\(750\) −1.34936 2.33715i −0.0492715 0.0853408i
\(751\) 5.72211 0.208803 0.104401 0.994535i \(-0.466707\pi\)
0.104401 + 0.994535i \(0.466707\pi\)
\(752\) 2.35256 + 4.07476i 0.0857891 + 0.148591i
\(753\) −11.6763 + 20.2239i −0.425506 + 0.736998i
\(754\) 0.0400094 2.27316i 0.00145706 0.0827835i
\(755\) 4.11765 0.149857
\(756\) 0 0
\(757\) 17.3611 30.0703i 0.631000 1.09292i −0.356347 0.934354i \(-0.615978\pi\)
0.987348 0.158571i \(-0.0506887\pi\)
\(758\) 1.41927 2.45824i 0.0515501 0.0892873i
\(759\) 17.9402 31.0733i 0.651187 1.12789i
\(760\) 20.2230 0.733566
\(761\) −26.5867 + 46.0496i −0.963768 + 1.66930i −0.250880 + 0.968018i \(0.580720\pi\)
−0.712888 + 0.701278i \(0.752613\pi\)
\(762\) −0.547981 −0.0198513
\(763\) 0 0
\(764\) −13.6226 + 23.5951i −0.492849 + 0.853640i
\(765\) 3.40609 0.123147
\(766\) −4.12265 + 7.14063i −0.148957 + 0.258002i
\(767\) 28.2787 15.6697i 1.02108 0.565801i
\(768\) −6.03145 10.4468i −0.217641 0.376966i
\(769\) 2.45578 4.25354i 0.0885578 0.153387i −0.818344 0.574729i \(-0.805108\pi\)
0.906902 + 0.421342i \(0.138441\pi\)
\(770\) 0 0
\(771\) 7.87414 + 13.6384i 0.283580 + 0.491175i
\(772\) 3.75455 + 6.50306i 0.135129 + 0.234050i
\(773\) 22.9807 0.826557 0.413279 0.910605i \(-0.364384\pi\)
0.413279 + 0.910605i \(0.364384\pi\)
\(774\) −1.02143 −0.0367146
\(775\) −1.99571 3.45667i −0.0716881 0.124167i
\(776\) −1.24913 2.16356i −0.0448413 0.0776674i
\(777\) 0 0
\(778\) −2.19589 + 3.80339i −0.0787264 + 0.136358i
\(779\) −9.13476 15.8219i −0.327287 0.566877i
\(780\) 0.358225 20.3528i 0.0128265 0.728745i
\(781\) −24.2998 + 42.0885i −0.869515 + 1.50604i
\(782\) −1.67460 −0.0598837
\(783\) 6.30821