Properties

Label 14.3.d.a.3.1
Level $14$
Weight $3$
Character 14.3
Analytic conductor $0.381$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 14.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.381472370104\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 3.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 14.3
Dual form 14.3.d.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(0.621320 + 0.358719i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-5.74264 + 3.31552i) q^{5} -1.01461i q^{6} +(6.24264 - 3.16693i) q^{7} +2.82843 q^{8} +(-4.24264 - 7.34847i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(0.621320 + 0.358719i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-5.74264 + 3.31552i) q^{5} -1.01461i q^{6} +(6.24264 - 3.16693i) q^{7} +2.82843 q^{8} +(-4.24264 - 7.34847i) q^{9} +(8.12132 + 4.68885i) q^{10} +(2.37868 - 4.11999i) q^{11} +(-1.24264 + 0.717439i) q^{12} +15.2913i q^{13} +(-8.29289 - 5.40629i) q^{14} -4.75736 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-3.25736 - 1.88064i) q^{17} +(-6.00000 + 10.3923i) q^{18} +(3.62132 - 2.09077i) q^{19} -13.2621i q^{20} +(5.01472 + 0.271680i) q^{21} -6.72792 q^{22} +(13.8640 + 24.0131i) q^{23} +(1.75736 + 1.01461i) q^{24} +(9.48528 - 16.4290i) q^{25} +(18.7279 - 10.8126i) q^{26} -12.5446i q^{27} +(-0.757359 + 13.9795i) q^{28} +3.51472 q^{29} +(3.36396 + 5.82655i) q^{30} +(-42.3198 - 24.4334i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(2.95584 - 1.70656i) q^{33} +5.31925i q^{34} +(-25.3492 + 38.8841i) q^{35} +16.9706 q^{36} +(1.47056 + 2.54709i) q^{37} +(-5.12132 - 2.95680i) q^{38} +(-5.48528 + 9.50079i) q^{39} +(-16.2426 + 9.37769i) q^{40} -27.9590i q^{41} +(-3.21320 - 6.33386i) q^{42} -10.4853 q^{43} +(4.75736 + 8.23999i) q^{44} +(48.7279 + 28.1331i) q^{45} +(19.6066 - 33.9596i) q^{46} +(45.6213 - 26.3395i) q^{47} -2.86976i q^{48} +(28.9411 - 39.5400i) q^{49} -26.8284 q^{50} +(-1.34924 - 2.33696i) q^{51} +(-26.4853 - 15.2913i) q^{52} +(-27.9853 + 48.4719i) q^{53} +(-15.3640 + 8.87039i) q^{54} +31.5462i q^{55} +(17.6569 - 8.95743i) q^{56} +3.00000 q^{57} +(-2.48528 - 4.30463i) q^{58} +(33.5330 + 19.3603i) q^{59} +(4.75736 - 8.23999i) q^{60} +(-78.3823 + 45.2540i) q^{61} +69.1080i q^{62} +(-49.7574 - 32.4377i) q^{63} +8.00000 q^{64} +(-50.6985 - 87.8124i) q^{65} +(-4.18019 - 2.41344i) q^{66} +(17.3198 - 29.9988i) q^{67} +(6.51472 - 3.76127i) q^{68} +19.8931i q^{69} +(65.5477 + 3.55114i) q^{70} +36.4264 q^{71} +(-12.0000 - 20.7846i) q^{72} +(45.5589 + 26.3034i) q^{73} +(2.07969 - 3.60213i) q^{74} +(11.7868 - 6.80511i) q^{75} +8.36308i q^{76} +(1.80152 - 33.2528i) q^{77} +15.5147 q^{78} +(16.8934 + 29.2602i) q^{79} +(22.9706 + 13.2621i) q^{80} +(-33.6838 + 58.3420i) q^{81} +(-34.2426 + 19.7700i) q^{82} -127.577i q^{83} +(-5.48528 + 8.41407i) q^{84} +24.9411 q^{85} +(7.41421 + 12.8418i) q^{86} +(2.18377 + 1.26080i) q^{87} +(6.72792 - 11.6531i) q^{88} +(-43.5883 + 25.1657i) q^{89} -79.5724i q^{90} +(48.4264 + 95.4580i) q^{91} -55.4558 q^{92} +(-17.5294 - 30.3619i) q^{93} +(-64.5183 - 37.2497i) q^{94} +(-13.8640 + 24.0131i) q^{95} +(-3.51472 + 2.02922i) q^{96} +101.792i q^{97} +(-68.8909 - 7.48650i) q^{98} -40.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{7} + 24 q^{10} + 18 q^{11} + 12 q^{12} - 36 q^{14} - 36 q^{15} - 8 q^{16} - 30 q^{17} - 24 q^{18} + 6 q^{19} + 54 q^{21} + 24 q^{22} + 30 q^{23} + 24 q^{24} + 4 q^{25} + 24 q^{26} - 20 q^{28} + 48 q^{29} - 12 q^{30} - 42 q^{31} - 90 q^{33} - 42 q^{35} - 62 q^{37} - 12 q^{38} + 12 q^{39} - 48 q^{40} + 72 q^{42} - 8 q^{43} + 36 q^{44} + 144 q^{45} + 36 q^{46} + 174 q^{47} - 20 q^{49} - 96 q^{50} + 54 q^{51} - 72 q^{52} - 78 q^{53} - 36 q^{54} + 48 q^{56} + 12 q^{57} + 24 q^{58} - 78 q^{59} + 36 q^{60} - 42 q^{61} - 216 q^{63} + 32 q^{64} - 84 q^{65} - 144 q^{66} - 58 q^{67} + 60 q^{68} + 84 q^{70} - 24 q^{71} - 48 q^{72} + 318 q^{73} + 96 q^{74} + 132 q^{75} + 126 q^{77} + 96 q^{78} + 110 q^{79} + 24 q^{80} + 18 q^{81} - 120 q^{82} + 12 q^{84} - 36 q^{85} + 24 q^{86} - 144 q^{87} - 24 q^{88} - 378 q^{89} + 24 q^{91} - 120 q^{92} - 138 q^{93} - 12 q^{94} - 30 q^{95} - 48 q^{96} - 120 q^{98} + 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.353553 0.612372i
\(3\) 0.621320 + 0.358719i 0.207107 + 0.119573i 0.599966 0.800025i \(-0.295181\pi\)
−0.392859 + 0.919599i \(0.628514\pi\)
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) −5.74264 + 3.31552i −1.14853 + 0.663103i −0.948528 0.316693i \(-0.897428\pi\)
−0.200000 + 0.979796i \(0.564094\pi\)
\(6\) 1.01461i 0.169102i
\(7\) 6.24264 3.16693i 0.891806 0.452418i
\(8\) 2.82843 0.353553
\(9\) −4.24264 7.34847i −0.471405 0.816497i
\(10\) 8.12132 + 4.68885i 0.812132 + 0.468885i
\(11\) 2.37868 4.11999i 0.216244 0.374545i −0.737413 0.675442i \(-0.763953\pi\)
0.953657 + 0.300897i \(0.0972861\pi\)
\(12\) −1.24264 + 0.717439i −0.103553 + 0.0597866i
\(13\) 15.2913i 1.17625i 0.808769 + 0.588126i \(0.200134\pi\)
−0.808769 + 0.588126i \(0.799866\pi\)
\(14\) −8.29289 5.40629i −0.592350 0.386163i
\(15\) −4.75736 −0.317157
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −3.25736 1.88064i −0.191609 0.110626i 0.401126 0.916023i \(-0.368619\pi\)
−0.592736 + 0.805397i \(0.701952\pi\)
\(18\) −6.00000 + 10.3923i −0.333333 + 0.577350i
\(19\) 3.62132 2.09077i 0.190596 0.110041i −0.401666 0.915786i \(-0.631569\pi\)
0.592261 + 0.805746i \(0.298235\pi\)
\(20\) 13.2621i 0.663103i
\(21\) 5.01472 + 0.271680i 0.238796 + 0.0129371i
\(22\) −6.72792 −0.305815
\(23\) 13.8640 + 24.0131i 0.602781 + 1.04405i 0.992398 + 0.123070i \(0.0392740\pi\)
−0.389617 + 0.920977i \(0.627393\pi\)
\(24\) 1.75736 + 1.01461i 0.0732233 + 0.0422755i
\(25\) 9.48528 16.4290i 0.379411 0.657160i
\(26\) 18.7279 10.8126i 0.720305 0.415868i
\(27\) 12.5446i 0.464616i
\(28\) −0.757359 + 13.9795i −0.0270485 + 0.499268i
\(29\) 3.51472 0.121197 0.0605986 0.998162i \(-0.480699\pi\)
0.0605986 + 0.998162i \(0.480699\pi\)
\(30\) 3.36396 + 5.82655i 0.112132 + 0.194218i
\(31\) −42.3198 24.4334i −1.36516 0.788173i −0.374850 0.927085i \(-0.622306\pi\)
−0.990305 + 0.138913i \(0.955639\pi\)
\(32\) −2.82843 + 4.89898i −0.0883883 + 0.153093i
\(33\) 2.95584 1.70656i 0.0895710 0.0517139i
\(34\) 5.31925i 0.156448i
\(35\) −25.3492 + 38.8841i −0.724264 + 1.11097i
\(36\) 16.9706 0.471405
\(37\) 1.47056 + 2.54709i 0.0397449 + 0.0688403i 0.885214 0.465185i \(-0.154012\pi\)
−0.845469 + 0.534025i \(0.820679\pi\)
\(38\) −5.12132 2.95680i −0.134772 0.0778104i
\(39\) −5.48528 + 9.50079i −0.140648 + 0.243610i
\(40\) −16.2426 + 9.37769i −0.406066 + 0.234442i
\(41\) 27.9590i 0.681927i −0.940077 0.340963i \(-0.889247\pi\)
0.940077 0.340963i \(-0.110753\pi\)
\(42\) −3.21320 6.33386i −0.0765048 0.150806i
\(43\) −10.4853 −0.243844 −0.121922 0.992540i \(-0.538906\pi\)
−0.121922 + 0.992540i \(0.538906\pi\)
\(44\) 4.75736 + 8.23999i 0.108122 + 0.187272i
\(45\) 48.7279 + 28.1331i 1.08284 + 0.625180i
\(46\) 19.6066 33.9596i 0.426230 0.738253i
\(47\) 45.6213 26.3395i 0.970666 0.560415i 0.0712271 0.997460i \(-0.477309\pi\)
0.899439 + 0.437046i \(0.143975\pi\)
\(48\) 2.86976i 0.0597866i
\(49\) 28.9411 39.5400i 0.590635 0.806939i
\(50\) −26.8284 −0.536569
\(51\) −1.34924 2.33696i −0.0264557 0.0458227i
\(52\) −26.4853 15.2913i −0.509332 0.294063i
\(53\) −27.9853 + 48.4719i −0.528024 + 0.914565i 0.471442 + 0.881897i \(0.343734\pi\)
−0.999466 + 0.0326677i \(0.989600\pi\)
\(54\) −15.3640 + 8.87039i −0.284518 + 0.164266i
\(55\) 31.5462i 0.573567i
\(56\) 17.6569 8.95743i 0.315301 0.159954i
\(57\) 3.00000 0.0526316
\(58\) −2.48528 4.30463i −0.0428497 0.0742178i
\(59\) 33.5330 + 19.3603i 0.568356 + 0.328141i 0.756492 0.654002i \(-0.226911\pi\)
−0.188136 + 0.982143i \(0.560245\pi\)
\(60\) 4.75736 8.23999i 0.0792893 0.137333i
\(61\) −78.3823 + 45.2540i −1.28495 + 0.741869i −0.977750 0.209774i \(-0.932727\pi\)
−0.307205 + 0.951643i \(0.599394\pi\)
\(62\) 69.1080i 1.11464i
\(63\) −49.7574 32.4377i −0.789799 0.514884i
\(64\) 8.00000 0.125000
\(65\) −50.6985 87.8124i −0.779977 1.35096i
\(66\) −4.18019 2.41344i −0.0633363 0.0365672i
\(67\) 17.3198 29.9988i 0.258505 0.447743i −0.707337 0.706877i \(-0.750104\pi\)
0.965842 + 0.259134i \(0.0834370\pi\)
\(68\) 6.51472 3.76127i 0.0958047 0.0553129i
\(69\) 19.8931i 0.288306i
\(70\) 65.5477 + 3.55114i 0.936396 + 0.0507306i
\(71\) 36.4264 0.513048 0.256524 0.966538i \(-0.417423\pi\)
0.256524 + 0.966538i \(0.417423\pi\)
\(72\) −12.0000 20.7846i −0.166667 0.288675i
\(73\) 45.5589 + 26.3034i 0.624094 + 0.360321i 0.778461 0.627693i \(-0.216001\pi\)
−0.154367 + 0.988014i \(0.549334\pi\)
\(74\) 2.07969 3.60213i 0.0281039 0.0486774i
\(75\) 11.7868 6.80511i 0.157157 0.0907348i
\(76\) 8.36308i 0.110041i
\(77\) 1.80152 33.2528i 0.0233963 0.431854i
\(78\) 15.5147 0.198907
\(79\) 16.8934 + 29.2602i 0.213840 + 0.370383i 0.952913 0.303243i \(-0.0980694\pi\)
−0.739073 + 0.673626i \(0.764736\pi\)
\(80\) 22.9706 + 13.2621i 0.287132 + 0.165776i
\(81\) −33.6838 + 58.3420i −0.415849 + 0.720272i
\(82\) −34.2426 + 19.7700i −0.417593 + 0.241098i
\(83\) 127.577i 1.53708i −0.639803 0.768539i \(-0.720984\pi\)
0.639803 0.768539i \(-0.279016\pi\)
\(84\) −5.48528 + 8.41407i −0.0653010 + 0.100167i
\(85\) 24.9411 0.293425
\(86\) 7.41421 + 12.8418i 0.0862118 + 0.149323i
\(87\) 2.18377 + 1.26080i 0.0251008 + 0.0144919i
\(88\) 6.72792 11.6531i 0.0764537 0.132422i
\(89\) −43.5883 + 25.1657i −0.489756 + 0.282761i −0.724473 0.689303i \(-0.757917\pi\)
0.234717 + 0.972064i \(0.424584\pi\)
\(90\) 79.5724i 0.884137i
\(91\) 48.4264 + 95.4580i 0.532158 + 1.04899i
\(92\) −55.4558 −0.602781
\(93\) −17.5294 30.3619i −0.188489 0.326472i
\(94\) −64.5183 37.2497i −0.686365 0.396273i
\(95\) −13.8640 + 24.0131i −0.145936 + 0.252769i
\(96\) −3.51472 + 2.02922i −0.0366117 + 0.0211377i
\(97\) 101.792i 1.04940i 0.851287 + 0.524700i \(0.175823\pi\)
−0.851287 + 0.524700i \(0.824177\pi\)
\(98\) −68.8909 7.48650i −0.702968 0.0763928i
\(99\) −40.3675 −0.407753
\(100\) 18.9706 + 32.8580i 0.189706 + 0.328580i
\(101\) −51.6838 29.8396i −0.511720 0.295442i 0.221820 0.975088i \(-0.428800\pi\)
−0.733541 + 0.679646i \(0.762134\pi\)
\(102\) −1.90812 + 3.30496i −0.0187070 + 0.0324015i
\(103\) 104.077 60.0890i 1.01046 0.583388i 0.0991322 0.995074i \(-0.468393\pi\)
0.911326 + 0.411686i \(0.135060\pi\)
\(104\) 43.2503i 0.415868i
\(105\) −29.6985 + 15.0662i −0.282843 + 0.143488i
\(106\) 79.1543 0.746739
\(107\) 56.8051 + 98.3893i 0.530889 + 0.919526i 0.999350 + 0.0360423i \(0.0114751\pi\)
−0.468462 + 0.883484i \(0.655192\pi\)
\(108\) 21.7279 + 12.5446i 0.201184 + 0.116154i
\(109\) 72.6543 125.841i 0.666553 1.15450i −0.312308 0.949981i \(-0.601102\pi\)
0.978862 0.204524i \(-0.0655645\pi\)
\(110\) 38.6360 22.3065i 0.351237 0.202787i
\(111\) 2.11008i 0.0190097i
\(112\) −23.4558 15.2913i −0.209427 0.136529i
\(113\) 34.5442 0.305700 0.152850 0.988249i \(-0.451155\pi\)
0.152850 + 0.988249i \(0.451155\pi\)
\(114\) −2.12132 3.67423i −0.0186081 0.0322301i
\(115\) −159.231 91.9323i −1.38462 0.799412i
\(116\) −3.51472 + 6.08767i −0.0302993 + 0.0524799i
\(117\) 112.368 64.8754i 0.960406 0.554491i
\(118\) 54.7592i 0.464061i
\(119\) −26.2904 1.42432i −0.220927 0.0119691i
\(120\) −13.4558 −0.112132
\(121\) 49.1838 + 85.1888i 0.406477 + 0.704040i
\(122\) 110.849 + 63.9988i 0.908600 + 0.524581i
\(123\) 10.0294 17.3715i 0.0815401 0.141232i
\(124\) 84.6396 48.8667i 0.682578 0.394086i
\(125\) 39.9814i 0.319851i
\(126\) −4.54416 + 83.8770i −0.0360647 + 0.665690i
\(127\) −247.338 −1.94754 −0.973772 0.227526i \(-0.926936\pi\)
−0.973772 + 0.227526i \(0.926936\pi\)
\(128\) −5.65685 9.79796i −0.0441942 0.0765466i
\(129\) −6.51472 3.76127i −0.0505017 0.0291572i
\(130\) −71.6985 + 124.185i −0.551527 + 0.955272i
\(131\) −127.864 + 73.8223i −0.976061 + 0.563529i −0.901079 0.433656i \(-0.857223\pi\)
−0.0749822 + 0.997185i \(0.523890\pi\)
\(132\) 6.82623i 0.0517139i
\(133\) 15.9853 24.5204i 0.120190 0.184364i
\(134\) −48.9878 −0.365581
\(135\) 41.5919 + 72.0393i 0.308088 + 0.533624i
\(136\) −9.21320 5.31925i −0.0677441 0.0391121i
\(137\) 16.2868 28.2096i 0.118882 0.205909i −0.800443 0.599409i \(-0.795402\pi\)
0.919325 + 0.393500i \(0.128736\pi\)
\(138\) 24.3640 14.0665i 0.176550 0.101931i
\(139\) 68.5857i 0.493422i 0.969089 + 0.246711i \(0.0793499\pi\)
−0.969089 + 0.246711i \(0.920650\pi\)
\(140\) −42.0000 82.7903i −0.300000 0.591359i
\(141\) 37.7939 0.268042
\(142\) −25.7574 44.6131i −0.181390 0.314176i
\(143\) 63.0000 + 36.3731i 0.440559 + 0.254357i
\(144\) −16.9706 + 29.3939i −0.117851 + 0.204124i
\(145\) −20.1838 + 11.6531i −0.139198 + 0.0803662i
\(146\) 74.3973i 0.509571i
\(147\) 32.1655 14.1853i 0.218813 0.0964984i
\(148\) −5.88225 −0.0397449
\(149\) −46.1985 80.0181i −0.310057 0.537034i 0.668317 0.743876i \(-0.267015\pi\)
−0.978374 + 0.206842i \(0.933681\pi\)
\(150\) −16.6690 9.62388i −0.111127 0.0641592i
\(151\) 45.8934 79.4897i 0.303930 0.526422i −0.673093 0.739558i \(-0.735035\pi\)
0.977022 + 0.213136i \(0.0683678\pi\)
\(152\) 10.2426 5.91359i 0.0673858 0.0389052i
\(153\) 31.9155i 0.208598i
\(154\) −42.0000 + 21.3068i −0.272727 + 0.138356i
\(155\) 324.037 2.09056
\(156\) −10.9706 19.0016i −0.0703241 0.121805i
\(157\) 7.32338 + 4.22815i 0.0466457 + 0.0269309i 0.523142 0.852246i \(-0.324760\pi\)
−0.476496 + 0.879177i \(0.658093\pi\)
\(158\) 23.8909 41.3802i 0.151208 0.261900i
\(159\) −34.7756 + 20.0777i −0.218715 + 0.126275i
\(160\) 37.5108i 0.234442i
\(161\) 162.595 + 105.999i 1.00991 + 0.658378i
\(162\) 95.2721 0.588099
\(163\) −110.989 192.238i −0.680913 1.17938i −0.974703 0.223506i \(-0.928250\pi\)
0.293789 0.955870i \(-0.405084\pi\)
\(164\) 48.4264 + 27.9590i 0.295283 + 0.170482i
\(165\) −11.3162 + 19.6003i −0.0685832 + 0.118790i
\(166\) −156.250 + 90.2109i −0.941264 + 0.543439i
\(167\) 168.841i 1.01102i 0.862820 + 0.505511i \(0.168696\pi\)
−0.862820 + 0.505511i \(0.831304\pi\)
\(168\) 14.1838 + 0.768426i 0.0844272 + 0.00457396i
\(169\) −64.8234 −0.383570
\(170\) −17.6360 30.5465i −0.103741 0.179685i
\(171\) −30.7279 17.7408i −0.179695 0.103747i
\(172\) 10.4853 18.1610i 0.0609609 0.105587i
\(173\) −142.323 + 82.1704i −0.822678 + 0.474974i −0.851339 0.524616i \(-0.824209\pi\)
0.0286608 + 0.999589i \(0.490876\pi\)
\(174\) 3.56608i 0.0204947i
\(175\) 7.18377 132.599i 0.0410501 0.757711i
\(176\) −19.0294 −0.108122
\(177\) 13.8898 + 24.0579i 0.0784736 + 0.135920i
\(178\) 61.6432 + 35.5897i 0.346310 + 0.199942i
\(179\) −92.5919 + 160.374i −0.517273 + 0.895943i 0.482526 + 0.875882i \(0.339720\pi\)
−0.999799 + 0.0200614i \(0.993614\pi\)
\(180\) −97.4558 + 56.2662i −0.541421 + 0.312590i
\(181\) 155.086i 0.856830i −0.903582 0.428415i \(-0.859072\pi\)
0.903582 0.428415i \(-0.140928\pi\)
\(182\) 82.6690 126.809i 0.454226 0.696753i
\(183\) −64.9340 −0.354831
\(184\) 39.2132 + 67.9193i 0.213115 + 0.369126i
\(185\) −16.8898 9.75135i −0.0912964 0.0527100i
\(186\) −24.7904 + 42.9382i −0.133282 + 0.230850i
\(187\) −15.4964 + 8.94687i −0.0828686 + 0.0478442i
\(188\) 105.358i 0.560415i
\(189\) −39.7279 78.3116i −0.210201 0.414347i
\(190\) 39.2132 0.206385
\(191\) −124.048 214.857i −0.649465 1.12491i −0.983251 0.182257i \(-0.941660\pi\)
0.333786 0.942649i \(-0.391674\pi\)
\(192\) 4.97056 + 2.86976i 0.0258883 + 0.0149466i
\(193\) −77.1690 + 133.661i −0.399840 + 0.692543i −0.993706 0.112021i \(-0.964268\pi\)
0.593866 + 0.804564i \(0.297601\pi\)
\(194\) 124.669 71.9777i 0.642624 0.371019i
\(195\) 72.7461i 0.373057i
\(196\) 39.5442 + 89.6675i 0.201756 + 0.457487i
\(197\) −181.103 −0.919303 −0.459651 0.888099i \(-0.652026\pi\)
−0.459651 + 0.888099i \(0.652026\pi\)
\(198\) 28.5442 + 49.4399i 0.144162 + 0.249697i
\(199\) 301.989 + 174.353i 1.51753 + 0.876147i 0.999788 + 0.0206121i \(0.00656150\pi\)
0.517744 + 0.855535i \(0.326772\pi\)
\(200\) 26.8284 46.4682i 0.134142 0.232341i
\(201\) 21.5223 12.4259i 0.107076 0.0618204i
\(202\) 84.3992i 0.417818i
\(203\) 21.9411 11.1309i 0.108084 0.0548318i
\(204\) 5.39697 0.0264557
\(205\) 92.6985 + 160.558i 0.452188 + 0.783212i
\(206\) −147.187 84.9786i −0.714502 0.412518i
\(207\) 117.640 203.758i 0.568307 0.984337i
\(208\) 52.9706 30.5826i 0.254666 0.147032i
\(209\) 19.8931i 0.0951823i
\(210\) 39.4523 + 25.7196i 0.187868 + 0.122474i
\(211\) 364.073 1.72547 0.862733 0.505660i \(-0.168751\pi\)
0.862733 + 0.505660i \(0.168751\pi\)
\(212\) −55.9706 96.9439i −0.264012 0.457282i
\(213\) 22.6325 + 13.0669i 0.106256 + 0.0613468i
\(214\) 80.3345 139.143i 0.375395 0.650203i
\(215\) 60.2132 34.7641i 0.280061 0.161694i
\(216\) 35.4815i 0.164266i
\(217\) −341.566 18.5048i −1.57404 0.0852757i
\(218\) −205.497 −0.942649
\(219\) 18.8711 + 32.6857i 0.0861694 + 0.149250i
\(220\) −54.6396 31.5462i −0.248362 0.143392i
\(221\) 28.7574 49.8092i 0.130124 0.225381i
\(222\) 2.58431 1.49205i 0.0116410 0.00672095i
\(223\) 123.231i 0.552603i 0.961071 + 0.276302i \(0.0891089\pi\)
−0.961071 + 0.276302i \(0.910891\pi\)
\(224\) −2.14214 + 39.5400i −0.00956311 + 0.176518i
\(225\) −160.971 −0.715425
\(226\) −24.4264 42.3078i −0.108081 0.187203i
\(227\) −66.1432 38.1878i −0.291380 0.168228i 0.347184 0.937797i \(-0.387138\pi\)
−0.638564 + 0.769569i \(0.720471\pi\)
\(228\) −3.00000 + 5.19615i −0.0131579 + 0.0227901i
\(229\) 309.419 178.643i 1.35117 0.780101i 0.362760 0.931883i \(-0.381834\pi\)
0.988414 + 0.151782i \(0.0485012\pi\)
\(230\) 260.024i 1.13054i
\(231\) 13.0477 20.0144i 0.0564837 0.0866423i
\(232\) 9.94113 0.0428497
\(233\) 136.537 + 236.488i 0.585994 + 1.01497i 0.994751 + 0.102328i \(0.0326291\pi\)
−0.408757 + 0.912643i \(0.634038\pi\)
\(234\) −158.912 91.7477i −0.679110 0.392084i
\(235\) −174.658 + 302.516i −0.743225 + 1.28730i
\(236\) −67.0660 + 38.7206i −0.284178 + 0.164070i
\(237\) 24.2400i 0.102278i
\(238\) 16.8457 + 33.2061i 0.0707801 + 0.139522i
\(239\) −265.103 −1.10922 −0.554608 0.832112i \(-0.687132\pi\)
−0.554608 + 0.832112i \(0.687132\pi\)
\(240\) 9.51472 + 16.4800i 0.0396447 + 0.0686666i
\(241\) −75.8970 43.8191i −0.314925 0.181822i 0.334203 0.942501i \(-0.391533\pi\)
−0.649128 + 0.760679i \(0.724866\pi\)
\(242\) 69.5563 120.475i 0.287423 0.497831i
\(243\) −139.632 + 80.6168i −0.574619 + 0.331757i
\(244\) 181.016i 0.741869i
\(245\) −35.1030 + 323.019i −0.143278 + 1.31844i
\(246\) −28.3675 −0.115315
\(247\) 31.9706 + 55.3746i 0.129435 + 0.224189i
\(248\) −119.698 69.1080i −0.482655 0.278661i
\(249\) 45.7645 79.2664i 0.183793 0.318339i
\(250\) −48.9670 + 28.2711i −0.195868 + 0.113084i
\(251\) 495.655i 1.97472i −0.158491 0.987360i \(-0.550663\pi\)
0.158491 0.987360i \(-0.449337\pi\)
\(252\) 105.941 53.7446i 0.420401 0.213272i
\(253\) 131.912 0.521390
\(254\) 174.894 + 302.926i 0.688561 + 1.19262i
\(255\) 15.4964 + 8.94687i 0.0607703 + 0.0350858i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 346.875 200.268i 1.34971 0.779254i 0.361499 0.932372i \(-0.382265\pi\)
0.988208 + 0.153119i \(0.0489317\pi\)
\(258\) 10.6385i 0.0412345i
\(259\) 17.2466 + 11.2434i 0.0665894 + 0.0434108i
\(260\) 202.794 0.779977
\(261\) −14.9117 25.8278i −0.0571329 0.0989571i
\(262\) 180.827 + 104.400i 0.690179 + 0.398475i
\(263\) 16.1726 28.0118i 0.0614928 0.106509i −0.833640 0.552308i \(-0.813747\pi\)
0.895133 + 0.445799i \(0.147081\pi\)
\(264\) 8.36039 4.82687i 0.0316681 0.0182836i
\(265\) 371.142i 1.40054i
\(266\) −41.3345 2.23936i −0.155393 0.00841863i
\(267\) −36.1097 −0.135242
\(268\) 34.6396 + 59.9976i 0.129252 + 0.223872i
\(269\) −265.838 153.482i −0.988246 0.570564i −0.0834963 0.996508i \(-0.526609\pi\)
−0.904749 + 0.425944i \(0.859942\pi\)
\(270\) 58.8198 101.879i 0.217851 0.377329i
\(271\) −65.8051 + 37.9926i −0.242823 + 0.140194i −0.616474 0.787376i \(-0.711439\pi\)
0.373650 + 0.927570i \(0.378106\pi\)
\(272\) 15.0451i 0.0553129i
\(273\) −4.15433 + 76.6815i −0.0152173 + 0.280885i
\(274\) −46.0660 −0.168124
\(275\) −45.1249 78.1586i −0.164091 0.284213i
\(276\) −34.4558 19.8931i −0.124840 0.0720764i
\(277\) −139.206 + 241.111i −0.502547 + 0.870438i 0.497448 + 0.867494i \(0.334270\pi\)
−0.999996 + 0.00294398i \(0.999063\pi\)
\(278\) 84.0000 48.4974i 0.302158 0.174451i
\(279\) 414.648i 1.48619i
\(280\) −71.6985 + 109.981i −0.256066 + 0.392789i
\(281\) 394.690 1.40459 0.702296 0.711885i \(-0.252158\pi\)
0.702296 + 0.711885i \(0.252158\pi\)
\(282\) −26.7244 46.2879i −0.0947672 0.164142i
\(283\) 126.783 + 73.1981i 0.447996 + 0.258650i 0.706983 0.707230i \(-0.250056\pi\)
−0.258988 + 0.965881i \(0.583389\pi\)
\(284\) −36.4264 + 63.0924i −0.128262 + 0.222156i
\(285\) −17.2279 + 9.94655i −0.0604488 + 0.0349002i
\(286\) 102.879i 0.359715i
\(287\) −88.5442 174.538i −0.308516 0.608146i
\(288\) 48.0000 0.166667
\(289\) −137.426 238.030i −0.475524 0.823632i
\(290\) 28.5442 + 16.4800i 0.0984281 + 0.0568275i
\(291\) −36.5147 + 63.2453i −0.125480 + 0.217338i
\(292\) −91.1177 + 52.6069i −0.312047 + 0.180160i
\(293\) 299.678i 1.02279i 0.859345 + 0.511396i \(0.170872\pi\)
−0.859345 + 0.511396i \(0.829128\pi\)
\(294\) −40.1177 29.3640i −0.136455 0.0998776i
\(295\) −256.757 −0.870364
\(296\) 4.15938 + 7.20426i 0.0140520 + 0.0243387i
\(297\) −51.6838 29.8396i −0.174019 0.100470i
\(298\) −65.3345 + 113.163i −0.219243 + 0.379741i
\(299\) −367.191 + 211.998i −1.22806 + 0.709023i
\(300\) 27.2204i 0.0907348i
\(301\) −65.4558 + 33.2061i −0.217461 + 0.110319i
\(302\) −129.806 −0.429822
\(303\) −21.4081 37.0799i −0.0706539 0.122376i
\(304\) −14.4853 8.36308i −0.0476490 0.0275101i
\(305\) 300.081 519.755i 0.983871 1.70412i
\(306\) 39.0883 22.5676i 0.127740 0.0737505i
\(307\) 20.9886i 0.0683666i −0.999416 0.0341833i \(-0.989117\pi\)
0.999416 0.0341833i \(-0.0108830\pi\)
\(308\) 55.7939 + 36.3731i 0.181149 + 0.118094i
\(309\) 86.2203 0.279030
\(310\) −229.128 396.862i −0.739124 1.28020i
\(311\) 157.651 + 91.0197i 0.506916 + 0.292668i 0.731565 0.681772i \(-0.238790\pi\)
−0.224649 + 0.974440i \(0.572124\pi\)
\(312\) −15.5147 + 26.8723i −0.0497267 + 0.0861291i
\(313\) −84.8087 + 48.9643i −0.270954 + 0.156435i −0.629321 0.777145i \(-0.716667\pi\)
0.358367 + 0.933581i \(0.383334\pi\)
\(314\) 11.9590i 0.0380861i
\(315\) 393.286 + 21.3068i 1.24853 + 0.0676408i
\(316\) −67.5736 −0.213840
\(317\) 240.985 + 417.399i 0.760206 + 1.31672i 0.942744 + 0.333517i \(0.108235\pi\)
−0.182538 + 0.983199i \(0.558431\pi\)
\(318\) 49.1802 + 28.3942i 0.154655 + 0.0892899i
\(319\) 8.36039 14.4806i 0.0262081 0.0453938i
\(320\) −45.9411 + 26.5241i −0.143566 + 0.0828879i
\(321\) 81.5084i 0.253920i
\(322\) 14.8492 274.090i 0.0461157 0.851213i
\(323\) −15.7279 −0.0486933
\(324\) −67.3675 116.684i −0.207924 0.360136i
\(325\) 251.220 + 145.042i 0.772986 + 0.446283i
\(326\) −156.962 + 271.866i −0.481478 + 0.833945i
\(327\) 90.2832 52.1250i 0.276095 0.159404i
\(328\) 79.0800i 0.241098i
\(329\) 201.382 308.907i 0.612104 0.938928i
\(330\) 32.0071 0.0969913
\(331\) −112.504 194.862i −0.339890 0.588707i 0.644522 0.764586i \(-0.277056\pi\)
−0.984412 + 0.175879i \(0.943723\pi\)
\(332\) 220.971 + 127.577i 0.665574 + 0.384269i
\(333\) 12.4781 21.6128i 0.0374719 0.0649032i
\(334\) 206.787 119.388i 0.619122 0.357450i
\(335\) 229.696i 0.685661i
\(336\) −9.08831 17.9149i −0.0270485 0.0533180i
\(337\) −264.368 −0.784473 −0.392237 0.919864i \(-0.628299\pi\)
−0.392237 + 0.919864i \(0.628299\pi\)
\(338\) 45.8370 + 79.3921i 0.135613 + 0.234888i
\(339\) 21.4630 + 12.3917i 0.0633126 + 0.0365536i
\(340\) −24.9411 + 43.1993i −0.0733563 + 0.127057i
\(341\) −201.331 + 116.238i −0.590412 + 0.340875i
\(342\) 50.1785i 0.146721i
\(343\) 55.4487 338.488i 0.161658 0.986847i
\(344\) −29.6569 −0.0862118
\(345\) −65.9558 114.239i −0.191176 0.331127i
\(346\) 201.276 + 116.207i 0.581722 + 0.335857i
\(347\) 95.6285 165.633i 0.275586 0.477330i −0.694697 0.719303i \(-0.744461\pi\)
0.970283 + 0.241973i \(0.0777947\pi\)
\(348\) −4.36753 + 2.52160i −0.0125504 + 0.00724597i
\(349\) 135.448i 0.388104i 0.980991 + 0.194052i \(0.0621630\pi\)
−0.980991 + 0.194052i \(0.937837\pi\)
\(350\) −167.480 + 84.9637i −0.478515 + 0.242753i
\(351\) 191.823 0.546505
\(352\) 13.4558 + 23.3062i 0.0382268 + 0.0662108i
\(353\) −301.802 174.245i −0.854962 0.493612i 0.00736010 0.999973i \(-0.497657\pi\)
−0.862322 + 0.506360i \(0.830991\pi\)
\(354\) 19.6432 34.0230i 0.0554892 0.0961101i
\(355\) −209.184 + 120.772i −0.589250 + 0.340204i
\(356\) 100.663i 0.282761i
\(357\) −15.8238 10.3158i −0.0443244 0.0288959i
\(358\) 261.889 0.731535
\(359\) −152.415 263.991i −0.424555 0.735351i 0.571824 0.820377i \(-0.306236\pi\)
−0.996379 + 0.0850256i \(0.972903\pi\)
\(360\) 137.823 + 79.5724i 0.382843 + 0.221034i
\(361\) −171.757 + 297.492i −0.475782 + 0.824079i
\(362\) −189.941 + 109.663i −0.524699 + 0.302935i
\(363\) 70.5727i 0.194415i
\(364\) −213.765 11.5810i −0.587265 0.0318159i
\(365\) −348.838 −0.955720
\(366\) 45.9153 + 79.5276i 0.125452 + 0.217288i
\(367\) −82.2761 47.5021i −0.224186 0.129434i 0.383701 0.923457i \(-0.374649\pi\)
−0.607887 + 0.794024i \(0.707983\pi\)
\(368\) 55.4558 96.0523i 0.150695 0.261012i
\(369\) −205.456 + 118.620i −0.556791 + 0.321463i
\(370\) 27.5810i 0.0745432i
\(371\) −21.1949 + 391.220i −0.0571291 + 1.05450i
\(372\) 70.1177 0.188489
\(373\) −126.779 219.588i −0.339891 0.588708i 0.644521 0.764586i \(-0.277057\pi\)
−0.984412 + 0.175879i \(0.943723\pi\)
\(374\) 21.9153 + 12.6528i 0.0585970 + 0.0338310i
\(375\) 14.3421 24.8412i 0.0382456 0.0662433i
\(376\) 129.037 74.4993i 0.343182 0.198136i
\(377\) 53.7446i 0.142559i
\(378\) −67.8198 + 104.031i −0.179417 + 0.275215i
\(379\) 508.250 1.34103 0.670514 0.741897i \(-0.266074\pi\)
0.670514 + 0.741897i \(0.266074\pi\)
\(380\) −27.7279 48.0262i −0.0729682 0.126385i
\(381\) −153.676 88.7250i −0.403350 0.232874i
\(382\) −175.430 + 303.854i −0.459241 + 0.795428i
\(383\) 413.753 238.881i 1.08030 0.623709i 0.149320 0.988789i \(-0.452292\pi\)
0.930976 + 0.365080i \(0.118958\pi\)
\(384\) 8.11689i 0.0211377i
\(385\) 99.9045 + 196.932i 0.259492 + 0.511511i
\(386\) 218.267 0.565459
\(387\) 44.4853 + 77.0508i 0.114949 + 0.199098i
\(388\) −176.309 101.792i −0.454404 0.262350i
\(389\) −85.1102 + 147.415i −0.218792 + 0.378959i −0.954439 0.298406i \(-0.903545\pi\)
0.735647 + 0.677365i \(0.236878\pi\)
\(390\) −89.0955 + 51.4393i −0.228450 + 0.131896i
\(391\) 104.292i 0.266732i
\(392\) 81.8579 111.836i 0.208821 0.285296i
\(393\) −105.926 −0.269532
\(394\) 128.059 + 221.804i 0.325023 + 0.562956i
\(395\) −194.025 112.021i −0.491204 0.283597i
\(396\) 40.3675 69.9186i 0.101938 0.176562i
\(397\) 211.786 122.275i 0.533467 0.307997i −0.208960 0.977924i \(-0.567008\pi\)
0.742427 + 0.669927i \(0.233675\pi\)
\(398\) 493.146i 1.23906i
\(399\) 18.7279 9.50079i 0.0469371 0.0238115i
\(400\) −75.8823 −0.189706
\(401\) 208.786 + 361.629i 0.520664 + 0.901817i 0.999711 + 0.0240277i \(0.00764899\pi\)
−0.479047 + 0.877789i \(0.659018\pi\)
\(402\) −30.4371 17.5729i −0.0757142 0.0437136i
\(403\) 373.617 647.124i 0.927090 1.60577i
\(404\) 103.368 59.6793i 0.255860 0.147721i
\(405\) 446.716i 1.10300i
\(406\) −29.1472 19.0016i −0.0717911 0.0468019i
\(407\) 13.9920 0.0343784
\(408\) −3.81623 6.60991i −0.00935351 0.0162008i
\(409\) 266.919 + 154.106i 0.652614 + 0.376787i 0.789457 0.613806i \(-0.210362\pi\)
−0.136843 + 0.990593i \(0.543696\pi\)
\(410\) 131.095 227.064i 0.319745 0.553815i
\(411\) 20.2386 11.6848i 0.0492424 0.0284301i
\(412\) 240.356i 0.583388i
\(413\) 270.647 + 14.6627i 0.655320 + 0.0355029i
\(414\) −332.735 −0.803708
\(415\) 422.985 + 732.631i 1.01924 + 1.76538i
\(416\) −74.9117 43.2503i −0.180076 0.103967i
\(417\) −24.6030 + 42.6137i −0.0590001 + 0.102191i
\(418\) −24.3640 + 14.0665i −0.0582870 + 0.0336520i
\(419\) 103.142i 0.246163i −0.992397 0.123081i \(-0.960722\pi\)
0.992397 0.123081i \(-0.0392776\pi\)
\(420\) 3.60303 66.5055i 0.00857864 0.158346i
\(421\) −165.220 −0.392447 −0.196224 0.980559i \(-0.562868\pi\)
−0.196224 + 0.980559i \(0.562868\pi\)
\(422\) −257.439 445.897i −0.610044 1.05663i
\(423\) −387.110 223.498i −0.915153 0.528364i
\(424\) −79.1543 + 137.099i −0.186685 + 0.323347i
\(425\) −61.7939 + 35.6767i −0.145398 + 0.0839453i
\(426\) 36.9587i 0.0867574i
\(427\) −345.996 + 530.736i −0.810295 + 1.24294i
\(428\) −227.220 −0.530889
\(429\) 26.0955 + 45.1987i 0.0608286 + 0.105358i
\(430\) −85.1543 49.1639i −0.198033 0.114335i
\(431\) −297.268 + 514.883i −0.689717 + 1.19463i 0.282212 + 0.959352i \(0.408932\pi\)
−0.971929 + 0.235273i \(0.924402\pi\)
\(432\) −43.4558 + 25.0892i −0.100592 + 0.0580770i
\(433\) 40.6267i 0.0938261i −0.998899 0.0469131i \(-0.985062\pi\)
0.998899 0.0469131i \(-0.0149384\pi\)
\(434\) 218.860 + 431.416i 0.504286 + 0.994046i
\(435\) −16.7208 −0.0384386
\(436\) 145.309 + 251.682i 0.333277 + 0.577252i
\(437\) 100.412 + 57.9727i 0.229775 + 0.132661i
\(438\) 26.6878 46.2246i 0.0609310 0.105536i
\(439\) 126.959 73.3001i 0.289201 0.166971i −0.348380 0.937353i \(-0.613268\pi\)
0.637582 + 0.770383i \(0.279935\pi\)
\(440\) 89.2261i 0.202787i
\(441\) −413.345 44.9190i −0.937291 0.101857i
\(442\) −81.3381 −0.184023
\(443\) −53.6802 92.9768i −0.121174 0.209880i 0.799057 0.601256i \(-0.205333\pi\)
−0.920231 + 0.391376i \(0.871999\pi\)
\(444\) −3.65476 2.11008i −0.00823145 0.00475243i
\(445\) 166.875 289.035i 0.374999 0.649518i
\(446\) 150.926 87.1372i 0.338399 0.195375i
\(447\) 66.2892i 0.148298i
\(448\) 49.9411 25.3354i 0.111476 0.0565523i
\(449\) 135.161 0.301028 0.150514 0.988608i \(-0.451907\pi\)
0.150514 + 0.988608i \(0.451907\pi\)
\(450\) 113.823 + 197.148i 0.252941 + 0.438106i
\(451\) −115.191 66.5055i −0.255412 0.147462i
\(452\) −34.5442 + 59.8322i −0.0764251 + 0.132372i
\(453\) 57.0290 32.9257i 0.125892 0.0726837i
\(454\) 108.011i 0.237910i
\(455\) −594.588 387.622i −1.30679 0.851918i
\(456\) 8.48528 0.0186081
\(457\) −79.8675 138.335i −0.174765 0.302702i 0.765315 0.643656i \(-0.222583\pi\)
−0.940080 + 0.340954i \(0.889250\pi\)
\(458\) −437.584 252.639i −0.955424 0.551614i
\(459\) −23.5919 + 40.8623i −0.0513984 + 0.0890247i
\(460\) 318.463 183.865i 0.692311 0.399706i
\(461\) 310.250i 0.672993i 0.941685 + 0.336497i \(0.109242\pi\)
−0.941685 + 0.336497i \(0.890758\pi\)
\(462\) −33.7386 1.82784i −0.0730274 0.00395636i
\(463\) −326.014 −0.704135 −0.352067 0.935975i \(-0.614521\pi\)
−0.352067 + 0.935975i \(0.614521\pi\)
\(464\) −7.02944 12.1753i −0.0151496 0.0262400i
\(465\) 201.331 + 116.238i 0.432969 + 0.249975i
\(466\) 193.092 334.445i 0.414360 0.717693i
\(467\) 515.769 297.779i 1.10443 0.637643i 0.167048 0.985949i \(-0.446576\pi\)
0.937381 + 0.348306i \(0.113243\pi\)
\(468\) 259.502i 0.554491i
\(469\) 13.1173 242.122i 0.0279687 0.516252i
\(470\) 494.007 1.05108
\(471\) 3.03344 + 5.25408i 0.00644043 + 0.0111551i
\(472\) 94.8457 + 54.7592i 0.200944 + 0.116015i
\(473\) −24.9411 + 43.1993i −0.0527297 + 0.0913304i
\(474\) 29.6878 17.1402i 0.0626324 0.0361608i
\(475\) 79.3262i 0.167002i
\(476\) 28.7574 44.1119i 0.0604146 0.0926721i
\(477\) 474.926 0.995652
\(478\) 187.456 + 324.683i 0.392167 + 0.679253i
\(479\) 438.798 + 253.340i 0.916071 + 0.528894i 0.882379 0.470539i \(-0.155940\pi\)
0.0336914 + 0.999432i \(0.489274\pi\)
\(480\) 13.4558 23.3062i 0.0280330 0.0485546i
\(481\) −38.9483 + 22.4868i −0.0809735 + 0.0467501i
\(482\) 123.939i 0.257135i
\(483\) 63.0000 + 124.185i 0.130435 + 0.257113i
\(484\) −196.735 −0.406477
\(485\) −337.492 584.554i −0.695861 1.20527i
\(486\) 197.470 + 114.009i 0.406317 + 0.234587i
\(487\) −105.651 + 182.992i −0.216942 + 0.375755i −0.953872 0.300215i \(-0.902942\pi\)
0.736930 + 0.675970i \(0.236275\pi\)
\(488\) −221.698 + 127.998i −0.454300 + 0.262290i
\(489\) 159.255i 0.325676i
\(490\) 420.437 185.416i 0.858035 0.378401i
\(491\) −784.161 −1.59707 −0.798534 0.601949i \(-0.794391\pi\)
−0.798534 + 0.601949i \(0.794391\pi\)
\(492\) 20.0589 + 34.7430i 0.0407701 + 0.0706158i
\(493\) −11.4487 6.60991i −0.0232225 0.0134075i
\(494\) 45.2132 78.3116i 0.0915247 0.158525i
\(495\) 231.816 133.839i 0.468316 0.270382i
\(496\) 195.467i 0.394086i
\(497\) 227.397 115.360i 0.457539 0.232112i
\(498\) −129.442 −0.259923
\(499\) 85.7462 + 148.517i 0.171836 + 0.297629i 0.939062 0.343748i \(-0.111697\pi\)
−0.767226 + 0.641377i \(0.778363\pi\)
\(500\) 69.2498 + 39.9814i 0.138500 + 0.0799628i
\(501\) −60.5665 + 104.904i −0.120891 + 0.209390i
\(502\) −607.051 + 350.481i −1.20926 + 0.698169i
\(503\) 20.0883i 0.0399370i −0.999801 0.0199685i \(-0.993643\pi\)
0.999801 0.0199685i \(-0.00635659\pi\)
\(504\) −140.735 91.7477i −0.279236 0.182039i
\(505\) 395.735 0.783634
\(506\) −93.2756 161.558i −0.184339 0.319285i
\(507\) −40.2761 23.2534i −0.0794400 0.0458647i
\(508\) 247.338 428.402i 0.486886 0.843311i
\(509\) −412.890 + 238.382i −0.811178 + 0.468334i −0.847365 0.531011i \(-0.821812\pi\)
0.0361865 + 0.999345i \(0.488479\pi\)
\(510\) 25.3056i 0.0496187i
\(511\) 367.709 + 19.9211i 0.719587 + 0.0389846i
\(512\) 22.6274 0.0441942
\(513\) −26.2279 45.4281i −0.0511266 0.0885538i
\(514\) −490.555 283.222i −0.954387 0.551016i
\(515\) −398.452 + 690.139i −0.773693 + 1.34008i
\(516\) 13.0294 7.52255i 0.0252508 0.0145786i
\(517\) 250.613i 0.484744i
\(518\) 1.57507 29.0730i 0.00304068 0.0561255i
\(519\) −117.905 −0.227176
\(520\) −143.397 248.371i −0.275763 0.477636i
\(521\) 739.823 + 427.137i 1.42001 + 0.819841i 0.996299 0.0859587i \(-0.0273953\pi\)
0.423707 + 0.905799i \(0.360729\pi\)
\(522\) −21.0883 + 36.5260i −0.0403991 + 0.0699732i
\(523\) −513.554 + 296.501i −0.981940 + 0.566923i −0.902855 0.429945i \(-0.858533\pi\)
−0.0790845 + 0.996868i \(0.525200\pi\)
\(524\) 295.289i 0.563529i
\(525\) 52.0294 79.8098i 0.0991037 0.152019i
\(526\) −45.7431 −0.0869640
\(527\) 91.9005 + 159.176i 0.174384 + 0.302043i
\(528\) −11.8234 6.82623i −0.0223928 0.0129285i
\(529\) −119.919 + 207.706i −0.226690 + 0.392638i
\(530\) −454.555 + 262.437i −0.857651 + 0.495165i
\(531\) 328.555i 0.618748i
\(532\) 26.4853 + 52.2077i 0.0497844 + 0.0981348i
\(533\) 427.529 0.802118
\(534\) 25.5334 + 44.2252i 0.0478154 + 0.0828188i
\(535\) −652.422 376.676i −1.21948 0.704068i
\(536\) 48.9878 84.8494i 0.0913952 0.158301i
\(537\) −115.058 + 66.4290i −0.214262 + 0.123704i
\(538\) 434.112i 0.806899i
\(539\) −94.0629 213.290i −0.174514 0.395715i
\(540\) −166.368 −0.308088
\(541\) −427.595 740.617i −0.790380 1.36898i −0.925732 0.378180i \(-0.876550\pi\)
0.135352 0.990798i \(-0.456783\pi\)
\(542\) 93.0624 + 53.7296i 0.171702 + 0.0991322i
\(543\) 55.6325 96.3583i 0.102454 0.177455i
\(544\) 18.4264 10.6385i 0.0338721 0.0195560i
\(545\) 963.546i 1.76797i
\(546\) 96.8528 49.1340i 0.177386 0.0899890i
\(547\) 415.897 0.760323 0.380161 0.924920i \(-0.375868\pi\)
0.380161 + 0.924920i \(0.375868\pi\)
\(548\) 32.5736 + 56.4191i 0.0594409 + 0.102955i
\(549\) 665.095 + 383.993i 1.21147 + 0.699441i
\(550\) −63.8162 + 110.533i −0.116030 + 0.200969i
\(551\) 12.7279 7.34847i 0.0230997 0.0133366i
\(552\) 56.2662i 0.101931i
\(553\) 198.124 + 129.161i 0.358272 + 0.233564i
\(554\) 393.733 0.710709
\(555\) −6.99600 12.1174i −0.0126054 0.0218332i
\(556\) −118.794 68.5857i −0.213658 0.123356i
\(557\) 292.110 505.950i 0.524435 0.908348i −0.475160 0.879899i \(-0.657610\pi\)
0.999595 0.0284485i \(-0.00905667\pi\)
\(558\) 507.838 293.200i 0.910103 0.525448i
\(559\) 160.333i 0.286822i
\(560\) 185.397 + 10.0441i 0.331066 + 0.0179360i
\(561\) −12.8377 −0.0228835
\(562\) −279.088 483.395i −0.496598 0.860134i
\(563\) 789.076 + 455.573i 1.40156 + 0.809189i 0.994552 0.104237i \(-0.0332402\pi\)
0.407004 + 0.913426i \(0.366573\pi\)
\(564\) −37.7939 + 65.4610i −0.0670105 + 0.116066i
\(565\) −198.375 + 114.532i −0.351106 + 0.202711i
\(566\) 207.035i 0.365787i
\(567\) −25.5107 + 470.882i −0.0449924 + 0.830480i
\(568\) 103.029 0.181390
\(569\) −350.000 606.217i −0.615113 1.06541i −0.990365 0.138485i \(-0.955777\pi\)
0.375251 0.926923i \(-0.377556\pi\)
\(570\) 24.3640 + 14.0665i 0.0427438 + 0.0246781i
\(571\) 281.231 487.107i 0.492525 0.853077i −0.507438 0.861688i \(-0.669408\pi\)
0.999963 + 0.00861055i \(0.00274086\pi\)
\(572\) −126.000 + 72.7461i −0.220280 + 0.127179i
\(573\) 177.993i 0.310634i
\(574\) −151.154 + 231.861i −0.263335 + 0.403939i
\(575\) 526.014 0.914807
\(576\) −33.9411 58.7878i −0.0589256 0.102062i
\(577\) −573.014 330.830i −0.993092 0.573362i −0.0868946 0.996218i \(-0.527694\pi\)
−0.906197 + 0.422856i \(0.861028\pi\)
\(578\) −194.350 + 336.625i −0.336246 + 0.582395i
\(579\) −95.8934 + 55.3641i −0.165619 + 0.0956202i
\(580\) 46.6124i 0.0803662i
\(581\) −404.029 796.420i −0.695402 1.37077i
\(582\) 103.279 0.177456
\(583\) 133.136 + 230.598i 0.228364 + 0.395538i
\(584\) 128.860 + 74.3973i 0.220651 + 0.127393i
\(585\) −430.191 + 745.113i −0.735369 + 1.27370i
\(586\) 367.029 211.905i 0.626330 0.361612i
\(587\) 823.029i 1.40209i −0.713116 0.701046i \(-0.752717\pi\)
0.713116 0.701046i \(-0.247283\pi\)
\(588\) −7.59589 + 69.8975i −0.0129182 + 0.118873i
\(589\) −204.338 −0.346924
\(590\) 181.555 + 314.462i 0.307720 + 0.532987i
\(591\) −112.523 64.9650i −0.190394 0.109924i
\(592\) 5.88225 10.1884i 0.00993623 0.0172101i
\(593\) −538.890 + 311.128i −0.908752 + 0.524668i −0.880029 0.474919i \(-0.842477\pi\)
−0.0287225 + 0.999587i \(0.509144\pi\)
\(594\) 84.3992i 0.142086i
\(595\) 155.698 78.9868i 0.261678 0.132751i
\(596\) 184.794 0.310057
\(597\) 125.088 + 216.659i 0.209527 + 0.362912i
\(598\) 519.286 + 299.810i 0.868372 + 0.501355i
\(599\) 256.422 444.137i 0.428084 0.741463i −0.568619 0.822601i \(-0.692522\pi\)
0.996703 + 0.0811377i \(0.0258554\pi\)
\(600\) 33.3381 19.2478i 0.0555635 0.0320796i
\(601\) 680.160i 1.13171i 0.824504 + 0.565857i \(0.191454\pi\)
−0.824504 + 0.565857i \(0.808546\pi\)
\(602\) 86.9533 + 56.6864i 0.144441 + 0.0941635i
\(603\) −293.927 −0.487441
\(604\) 91.7868 + 158.979i 0.151965 + 0.263211i
\(605\) −564.889 326.139i −0.933701 0.539073i
\(606\) −30.2756 + 52.4390i −0.0499598 + 0.0865329i
\(607\) 33.5482 19.3690i 0.0552688 0.0319095i −0.472111 0.881539i \(-0.656508\pi\)
0.527380 + 0.849630i \(0.323175\pi\)
\(608\) 23.6544i 0.0389052i
\(609\) 17.6253 + 0.954877i 0.0289414 + 0.00156794i
\(610\) −848.756 −1.39140
\(611\) 402.765 + 697.609i 0.659189 + 1.14175i
\(612\) −55.2792 31.9155i −0.0903255 0.0521495i
\(613\) −200.552 + 347.366i −0.327164 + 0.566665i −0.981948 0.189151i \(-0.939426\pi\)
0.654784 + 0.755816i \(0.272760\pi\)
\(614\) −25.7056 + 14.8412i −0.0418658 + 0.0241713i
\(615\) 133.011i 0.216278i
\(616\) 5.09545 94.0530i 0.00827184 0.152683i
\(617\) −959.044 −1.55437 −0.777183 0.629275i \(-0.783352\pi\)
−0.777183 + 0.629275i \(0.783352\pi\)
\(618\) −60.9670 105.598i −0.0986521 0.170870i
\(619\) −869.951 502.267i −1.40541 0.811416i −0.410473 0.911873i \(-0.634636\pi\)
−0.994941 + 0.100457i \(0.967970\pi\)
\(620\) −324.037 + 561.248i −0.522640 + 0.905238i
\(621\) 301.235 173.918i 0.485081 0.280061i
\(622\) 257.443i 0.413895i
\(623\) −192.408 + 295.142i −0.308841 + 0.473743i
\(624\) 43.8823 0.0703241
\(625\) 369.691 + 640.323i 0.591505 + 1.02452i
\(626\) 119.938 + 69.2460i 0.191594 + 0.110617i
\(627\) 7.13604 12.3600i 0.0113812 0.0197129i
\(628\) −14.6468 + 8.45631i −0.0233229 + 0.0134655i
\(629\) 11.0624i 0.0175873i
\(630\) −252.000 496.742i −0.400000 0.788479i
\(631\) −386.514 −0.612542 −0.306271 0.951944i \(-0.599081\pi\)
−0.306271 + 0.951944i \(0.599081\pi\)
\(632\) 47.7817 + 82.7604i 0.0756040 + 0.130950i
\(633\) 226.206 + 130.600i 0.357356 + 0.206319i
\(634\) 340.805 590.291i 0.537547 0.931058i
\(635\) 1420.37 820.053i 2.23681 1.29142i
\(636\) 80.3109i 0.126275i
\(637\) 604.617 + 442.547i 0.949164 + 0.694736i
\(638\) −23.6468 −0.0370639
\(639\) −154.544 267.678i −0.241853 0.418902i
\(640\) 64.9706 + 37.5108i 0.101517 + 0.0586106i
\(641\) 496.074 859.225i 0.773906 1.34044i −0.161502 0.986872i \(-0.551634\pi\)
0.935407 0.353572i \(-0.115033\pi\)
\(642\) 99.8269 57.6351i 0.155494 0.0897743i
\(643\) 944.986i 1.46965i 0.678256 + 0.734826i \(0.262736\pi\)
−0.678256 + 0.734826i \(0.737264\pi\)
\(644\) −346.191 + 175.625i −0.537564 + 0.272709i
\(645\) 49.8823 0.0773368
\(646\) 11.1213 + 19.2627i 0.0172157 + 0.0298184i
\(647\) 2.50357 + 1.44544i 0.00386951 + 0.00223406i 0.501934 0.864906i \(-0.332622\pi\)
−0.498064 + 0.867140i \(0.665956\pi\)
\(648\) −95.2721 + 165.016i −0.147025 + 0.254654i
\(649\) 159.529 92.1039i 0.245807 0.141917i
\(650\) 410.241i 0.631140i
\(651\) −205.584 134.024i −0.315797 0.205874i
\(652\) 443.955 0.680913
\(653\) 161.529 + 279.777i 0.247365 + 0.428449i 0.962794 0.270237i \(-0.0871019\pi\)
−0.715429 + 0.698686i \(0.753769\pi\)
\(654\) −127.680 73.7159i −0.195229 0.112716i
\(655\) 489.518 847.870i 0.747356 1.29446i
\(656\) −96.8528 + 55.9180i −0.147641 + 0.0852409i
\(657\) 446.384i 0.679428i
\(658\) −520.731 28.2114i −0.791385 0.0428744i
\(659\) 295.955 0.449098 0.224549 0.974463i \(-0.427909\pi\)
0.224549 + 0.974463i \(0.427909\pi\)
\(660\) −22.6325 39.2006i −0.0342916 0.0593948i
\(661\) 17.9710 + 10.3756i 0.0271876 + 0.0156968i 0.513532 0.858070i \(-0.328337\pi\)
−0.486345 + 0.873767i \(0.661670\pi\)
\(662\) −159.104 + 275.576i −0.240338 + 0.416278i
\(663\) 35.7351 20.6316i 0.0538990 0.0311186i
\(664\) 360.843i 0.543439i
\(665\) −10.5000 + 193.811i −0.0157895 + 0.291445i
\(666\) −35.2935 −0.0529933
\(667\) 48.7279 + 84.3992i 0.0730554 + 0.126536i
\(668\) −292.441 168.841i −0.437785 0.252756i
\(669\) −44.2052 + 76.5656i −0.0660765 + 0.114448i
\(670\) 281.319 162.420i 0.419880 0.242418i
\(671\) 430.579i 0.641698i
\(672\) −15.5147 + 23.7986i −0.0230874 + 0.0354146i
\(673\) 627.044 0.931714 0.465857 0.884860i \(-0.345746\pi\)
0.465857 + 0.884860i \(0.345746\pi\)
\(674\) 186.936 + 323.783i 0.277353 + 0.480390i
\(675\) −206.095 118.989i −0.305327 0.176280i
\(676\) 64.8234 112.277i 0.0958926 0.166091i
\(677\) −94.6097 + 54.6230i −0.139749 + 0.0806838i −0.568244 0.822860i \(-0.692377\pi\)
0.428496 + 0.903544i \(0.359044\pi\)
\(678\) 35.0489i 0.0516946i
\(679\) 322.368 + 635.450i 0.474768 + 0.935861i
\(680\) 70.5442 0.103741
\(681\) −27.3974 47.4537i −0.0402311 0.0696824i
\(682\) 284.724 + 164.386i 0.417484 + 0.241035i
\(683\) −396.783 + 687.248i −0.580941 + 1.00622i 0.414427 + 0.910083i \(0.363982\pi\)
−0.995368 + 0.0961370i \(0.969351\pi\)
\(684\) 61.4558 35.4815i 0.0898477 0.0518736i
\(685\) 215.996i 0.315323i
\(686\) −453.770 + 171.437i −0.661473 + 0.249908i
\(687\) 256.331 0.373116
\(688\) 20.9706 + 36.3221i 0.0304805 + 0.0527937i
\(689\) −741.198 427.931i −1.07576 0.621090i
\(690\) −93.2756 + 161.558i −0.135182 + 0.234142i
\(691\) 159.253 91.9447i 0.230467 0.133060i −0.380320 0.924855i \(-0.624186\pi\)
0.610788 + 0.791794i \(0.290853\pi\)
\(692\) 328.682i 0.474974i
\(693\) −252.000 + 127.841i −0.363636 + 0.184475i
\(694\) −270.478 −0.389738
\(695\) −227.397 393.863i −0.327190 0.566710i
\(696\) 6.17662 + 3.56608i 0.00887446 + 0.00512367i
\(697\) −52.5807 + 91.0725i −0.0754386 + 0.130664i
\(698\) 165.889 95.7763i 0.237664 0.137215i
\(699\) 195.913i 0.280277i
\(700\) 222.485 + 145.042i 0.317836 + 0.207203i
\(701\) −1043.82 −1.48905 −0.744525 0.667595i \(-0.767324\pi\)
−0.744525 + 0.667595i \(0.767324\pi\)
\(702\) −135.640 234.935i −0.193219 0.334665i
\(703\) 10.6508 + 6.14922i 0.0151504 + 0.00874711i
\(704\) 19.0294 32.9600i 0.0270305 0.0468181i
\(705\) −217.037 + 125.306i −0.307854 + 0.177740i
\(706\) 492.840i 0.698073i
\(707\) −417.143 22.5993i −0.590019 0.0319651i
\(708\) −55.5593 −0.0784736
\(709\) 490.279 + 849.188i 0.691507 + 1.19773i 0.971344 + 0.237678i \(0.0763864\pi\)
−0.279836 + 0.960048i \(0.590280\pi\)
\(710\) 295.831 + 170.798i 0.416663 + 0.240560i
\(711\) 143.345 248.281i 0.201611 0.349200i
\(712\) −123.286 + 71.1794i −0.173155 + 0.0999711i
\(713\) 1354.97i 1.90038i
\(714\) −1.44513 + 26.6745i −0.00202399 + 0.0373593i
\(715\) −482.382 −0.674660
\(716\) −185.184 320.748i −0.258637 0.447972i
\(717\) −164.714 95.0975i −0.229726 0.132632i
\(718\) −215.548 + 373.340i −0.300206 + 0.519972i
\(719\) −674.187 + 389.242i −0.937673 + 0.541366i −0.889230 0.457460i \(-0.848759\pi\)
−0.0484429 + 0.998826i \(0.515426\pi\)
\(720\) 225.065i 0.312590i
\(721\) 459.419 704.719i 0.637197 0.977419i
\(722\) 485.803 0.672858
\(723\) −31.4376 54.4514i −0.0434821 0.0753132i
\(724\) 268.617 + 155.086i 0.371018 + 0.214208i
\(725\) 33.3381 57.7433i 0.0459836 0.0796459i
\(726\) 86.4335 49.9024i 0.119054 0.0687361i
\(727\) 735.255i 1.01135i −0.862723 0.505677i \(-0.831243\pi\)
0.862723 0.505677i \(-0.168757\pi\)
\(728\) 136.971 + 269.996i 0.188146 + 0.370874i
\(729\) 490.632 0.673021
\(730\) 246.665 + 427.237i 0.337898 + 0.585256i
\(731\) 34.1543 + 19.7190i 0.0467227 + 0.0269754i
\(732\) 64.9340 112.469i 0.0887076 0.153646i
\(733\) −414.705 + 239.430i −0.565764 + 0.326644i −0.755456 0.655200i \(-0.772585\pi\)
0.189692 + 0.981844i \(0.439251\pi\)
\(734\) 134.356i 0.183047i
\(735\) −137.683 + 188.106i −0.187324 + 0.255926i
\(736\) −156.853 −0.213115
\(737\) −82.3965 142.715i −0.111800 0.193643i
\(738\) 290.558 + 167.754i 0.393711 + 0.227309i
\(739\) 9.95227 17.2378i 0.0134672 0.0233259i −0.859213 0.511618i \(-0.829046\pi\)
0.872680 + 0.488292i \(0.162380\pi\)
\(740\) 33.7797 19.5027i 0.0456482 0.0263550i
\(741\) 45.8739i 0.0619080i
\(742\) 494.132 250.676i 0.665946 0.337838i
\(743\) 43.3095 0.0582901 0.0291450 0.999575i \(-0.490722\pi\)
0.0291450 + 0.999575i \(0.490722\pi\)
\(744\) −49.5807 85.8764i −0.0666408 0.115425i
\(745\) 530.603 + 306.344i 0.712218 + 0.411199i
\(746\) −179.293 + 310.544i −0.240339 + 0.416279i
\(747\) −937.499 + 541.265i −1.25502 + 0.724585i
\(748\) 35.7875i 0.0478442i
\(749\) 666.206 + 434.311i 0.889460 + 0.579855i
\(750\) −40.5656 −0.0540874
\(751\) −112.665 195.142i −0.150020 0.259842i 0.781215 0.624263i \(-0.214600\pi\)
−0.931235 + 0.364420i \(0.881267\pi\)
\(752\) −182.485 105.358i −0.242667 0.140104i
\(753\) 177.801 307.961i 0.236124 0.408978i
\(754\) 65.8234 38.0031i 0.0872989 0.0504020i
\(755\) 608.641i 0.806147i
\(756\) 175.368 + 9.50079i 0.231968 + 0.0125672i
\(757\) 935.779 1.23617 0.618084 0.786112i \(-0.287909\pi\)
0.618084 + 0.786112i \(0.287909\pi\)
\(758\) −359.387 622.476i −0.474125 0.821209i
\(759\) 81.9594 + 47.3193i 0.107983 + 0.0623443i
\(760\) −39.2132 + 67.9193i −0.0515963 + 0.0893674i
\(761\) 1214.79 701.357i 1.59630 0.921625i 0.604110 0.796901i \(-0.293529\pi\)
0.992191 0.124724i \(-0.0398046\pi\)
\(762\) 250.952i 0.329334i
\(763\) 55.0254 1015.67i 0.0721172 1.33115i
\(764\) 496.191 0.649465
\(765\) −105.816 183.279i −0.138322 0.239581i
\(766\) −585.136 337.828i −0.763885 0.441029i
\(767\) −296.044 + 512.763i −0.385976 + 0.668530i
\(768\) −9.94113 + 5.73951i −0.0129442 + 0.00747332i
\(769\) 1.72330i 0.00224097i 0.999999 + 0.00112048i \(0.000356661\pi\)
−0.999999 + 0.00112048i \(0.999643\pi\)
\(770\) 170.548 261.609i 0.221491 0.339752i
\(771\)