Properties

Label 845.2.e.m.191.2
Level $845$
Weight $2$
Character 845.191
Analytic conductor $6.747$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 191.2
Root \(1.40994 + 0.109843i\) of defining polynomial
Character \(\chi\) \(=\) 845.191
Dual form 845.2.e.m.146.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.609843 + 1.05628i) q^{2} +(-1.16612 + 2.01978i) q^{3} +(0.256182 + 0.443720i) q^{4} -1.00000 q^{5} +(-1.42231 - 2.46350i) q^{6} +(-1.80010 - 3.11786i) q^{7} -3.06430 q^{8} +(-1.21969 - 2.11256i) q^{9} +O(q^{10})\) \(q+(-0.609843 + 1.05628i) q^{2} +(-1.16612 + 2.01978i) q^{3} +(0.256182 + 0.443720i) q^{4} -1.00000 q^{5} +(-1.42231 - 2.46350i) q^{6} +(-1.80010 - 3.11786i) q^{7} -3.06430 q^{8} +(-1.21969 - 2.11256i) q^{9} +(0.609843 - 1.05628i) q^{10} +(-2.68591 + 4.65213i) q^{11} -1.19496 q^{12} +4.39111 q^{14} +(1.16612 - 2.01978i) q^{15} +(1.35638 - 2.34932i) q^{16} +(0.565928 + 0.980215i) q^{17} +2.97527 q^{18} +(-1.13397 - 1.96410i) q^{19} +(-0.256182 - 0.443720i) q^{20} +8.39654 q^{21} +(-3.27597 - 5.67414i) q^{22} +(1.94644 - 3.37133i) q^{23} +(3.57335 - 6.18922i) q^{24} +1.00000 q^{25} -1.30752 q^{27} +(0.922305 - 1.59748i) q^{28} +(0.0123639 - 0.0214150i) q^{29} +(1.42231 + 2.46350i) q^{30} +5.46410 q^{31} +(-1.40994 - 2.44209i) q^{32} +(-6.26420 - 10.8499i) q^{33} -1.38051 q^{34} +(1.80010 + 3.11786i) q^{35} +(0.624924 - 1.08240i) q^{36} +(4.35203 - 7.53794i) q^{37} +2.76619 q^{38} +3.06430 q^{40} +(-1.86603 + 3.23205i) q^{41} +(-5.12058 + 8.86910i) q^{42} +(0.565928 + 0.980215i) q^{43} -2.75232 q^{44} +(1.21969 + 2.11256i) q^{45} +(2.37404 + 4.11196i) q^{46} +2.58535 q^{47} +(3.16341 + 5.47918i) q^{48} +(-2.98070 + 5.16273i) q^{49} +(-0.609843 + 1.05628i) q^{50} -2.63977 q^{51} -4.43937 q^{53} +(0.797382 - 1.38111i) q^{54} +(2.68591 - 4.65213i) q^{55} +(5.51603 + 9.55405i) q^{56} +5.28942 q^{57} +(0.0150801 + 0.0261196i) q^{58} +(0.0857123 + 0.148458i) q^{59} +1.19496 q^{60} +(-1.68012 - 2.91005i) q^{61} +(-3.33225 + 5.77162i) q^{62} +(-4.39111 + 7.60563i) q^{63} +8.86488 q^{64} +15.2807 q^{66} +(-3.19990 + 5.54239i) q^{67} +(-0.289961 + 0.502227i) q^{68} +(4.53957 + 7.86276i) q^{69} -4.39111 q^{70} +(5.39866 + 9.35076i) q^{71} +(3.73748 + 6.47351i) q^{72} -4.70308 q^{73} +(5.30812 + 9.19393i) q^{74} +(-1.16612 + 2.01978i) q^{75} +(0.581008 - 1.00633i) q^{76} +19.3396 q^{77} -11.9826 q^{79} +(-1.35638 + 2.34932i) q^{80} +(5.18379 - 8.97859i) q^{81} +(-2.27597 - 3.94209i) q^{82} -12.1286 q^{83} +(2.15104 + 3.72572i) q^{84} +(-0.565928 - 0.980215i) q^{85} -1.38051 q^{86} +(0.0288357 + 0.0499450i) q^{87} +(8.23042 - 14.2555i) q^{88} +(8.07702 - 13.9898i) q^{89} -2.97527 q^{90} +1.99457 q^{92} +(-6.37182 + 11.0363i) q^{93} +(-1.57666 + 2.73086i) q^{94} +(1.13397 + 1.96410i) q^{95} +6.57666 q^{96} +(-6.08408 - 10.5379i) q^{97} +(-3.63553 - 6.29692i) q^{98} +13.1039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9} + 2 q^{10} - 20 q^{12} + 4 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{17} + 40 q^{18} - 16 q^{19} + 2 q^{20} + 8 q^{21} - 12 q^{22} + 10 q^{23} + 24 q^{24} + 8 q^{25} - 4 q^{27} - 8 q^{28} - 8 q^{29} - 4 q^{30} + 16 q^{31} - 4 q^{32} - 18 q^{33} - 8 q^{34} + 10 q^{35} - 20 q^{36} + 2 q^{37} + 16 q^{38} - 12 q^{40} - 8 q^{41} + 4 q^{42} + 2 q^{43} + 24 q^{44} + 4 q^{45} - 16 q^{46} + 16 q^{47} + 28 q^{48} - 12 q^{49} - 2 q^{50} + 8 q^{51} - 24 q^{53} + 16 q^{54} - 12 q^{56} - 28 q^{57} - 22 q^{58} - 12 q^{59} + 20 q^{60} - 28 q^{61} - 4 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} - 14 q^{68} + 16 q^{69} - 4 q^{70} - 4 q^{71} - 12 q^{72} - 16 q^{73} + 10 q^{74} + 2 q^{75} - 20 q^{76} + 36 q^{77} - 16 q^{79} + 2 q^{80} + 8 q^{81} - 4 q^{82} - 24 q^{83} + 28 q^{84} - 2 q^{85} - 8 q^{86} + 22 q^{87} + 18 q^{88} + 12 q^{89} - 40 q^{90} + 44 q^{92} - 8 q^{93} + 32 q^{94} + 16 q^{95} + 8 q^{96} - 2 q^{97} + 24 q^{98} + 48 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.609843 + 1.05628i −0.431224 + 0.746903i −0.996979 0.0776710i \(-0.975252\pi\)
0.565755 + 0.824574i \(0.308585\pi\)
\(3\) −1.16612 + 2.01978i −0.673262 + 1.16612i 0.303712 + 0.952764i \(0.401774\pi\)
−0.976974 + 0.213359i \(0.931559\pi\)
\(4\) 0.256182 + 0.443720i 0.128091 + 0.221860i
\(5\) −1.00000 −0.447214
\(6\) −1.42231 2.46350i −0.580654 1.00572i
\(7\) −1.80010 3.11786i −0.680373 1.17844i −0.974867 0.222787i \(-0.928484\pi\)
0.294494 0.955653i \(-0.404849\pi\)
\(8\) −3.06430 −1.08339
\(9\) −1.21969 2.11256i −0.406562 0.704187i
\(10\) 0.609843 1.05628i 0.192849 0.334025i
\(11\) −2.68591 + 4.65213i −0.809832 + 1.40267i 0.103149 + 0.994666i \(0.467108\pi\)
−0.912980 + 0.408004i \(0.866225\pi\)
\(12\) −1.19496 −0.344955
\(13\) 0 0
\(14\) 4.39111 1.17357
\(15\) 1.16612 2.01978i 0.301092 0.521506i
\(16\) 1.35638 2.34932i 0.339094 0.587329i
\(17\) 0.565928 + 0.980215i 0.137258 + 0.237737i 0.926458 0.376399i \(-0.122838\pi\)
−0.789200 + 0.614136i \(0.789505\pi\)
\(18\) 2.97527 0.701278
\(19\) −1.13397 1.96410i −0.260152 0.450596i 0.706130 0.708082i \(-0.250439\pi\)
−0.966282 + 0.257486i \(0.917106\pi\)
\(20\) −0.256182 0.443720i −0.0572840 0.0992188i
\(21\) 8.39654 1.83228
\(22\) −3.27597 5.67414i −0.698438 1.20973i
\(23\) 1.94644 3.37133i 0.405860 0.702970i −0.588561 0.808453i \(-0.700305\pi\)
0.994421 + 0.105483i \(0.0336387\pi\)
\(24\) 3.57335 6.18922i 0.729407 1.26337i
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.30752 −0.251632
\(28\) 0.922305 1.59748i 0.174299 0.301895i
\(29\) 0.0123639 0.0214150i 0.00229593 0.00397666i −0.864875 0.501987i \(-0.832603\pi\)
0.867171 + 0.498010i \(0.165936\pi\)
\(30\) 1.42231 + 2.46350i 0.259676 + 0.449772i
\(31\) 5.46410 0.981382 0.490691 0.871334i \(-0.336744\pi\)
0.490691 + 0.871334i \(0.336744\pi\)
\(32\) −1.40994 2.44209i −0.249245 0.431705i
\(33\) −6.26420 10.8499i −1.09046 1.88873i
\(34\) −1.38051 −0.236755
\(35\) 1.80010 + 3.11786i 0.304272 + 0.527015i
\(36\) 0.624924 1.08240i 0.104154 0.180400i
\(37\) 4.35203 7.53794i 0.715470 1.23923i −0.247309 0.968937i \(-0.579546\pi\)
0.962778 0.270293i \(-0.0871205\pi\)
\(38\) 2.76619 0.448735
\(39\) 0 0
\(40\) 3.06430 0.484508
\(41\) −1.86603 + 3.23205i −0.291424 + 0.504762i −0.974147 0.225916i \(-0.927462\pi\)
0.682723 + 0.730678i \(0.260796\pi\)
\(42\) −5.12058 + 8.86910i −0.790122 + 1.36853i
\(43\) 0.565928 + 0.980215i 0.0863031 + 0.149481i 0.905946 0.423394i \(-0.139161\pi\)
−0.819643 + 0.572875i \(0.805828\pi\)
\(44\) −2.75232 −0.414929
\(45\) 1.21969 + 2.11256i 0.181820 + 0.314922i
\(46\) 2.37404 + 4.11196i 0.350034 + 0.606276i
\(47\) 2.58535 0.377113 0.188556 0.982062i \(-0.439619\pi\)
0.188556 + 0.982062i \(0.439619\pi\)
\(48\) 3.16341 + 5.47918i 0.456598 + 0.790852i
\(49\) −2.98070 + 5.16273i −0.425815 + 0.737533i
\(50\) −0.609843 + 1.05628i −0.0862449 + 0.149381i
\(51\) −2.63977 −0.369641
\(52\) 0 0
\(53\) −4.43937 −0.609795 −0.304897 0.952385i \(-0.598622\pi\)
−0.304897 + 0.952385i \(0.598622\pi\)
\(54\) 0.797382 1.38111i 0.108510 0.187945i
\(55\) 2.68591 4.65213i 0.362168 0.627293i
\(56\) 5.51603 + 9.55405i 0.737111 + 1.27671i
\(57\) 5.28942 0.700600
\(58\) 0.0150801 + 0.0261196i 0.00198012 + 0.00342967i
\(59\) 0.0857123 + 0.148458i 0.0111588 + 0.0193276i 0.871551 0.490305i \(-0.163115\pi\)
−0.860392 + 0.509633i \(0.829781\pi\)
\(60\) 1.19496 0.154269
\(61\) −1.68012 2.91005i −0.215117 0.372594i 0.738192 0.674591i \(-0.235680\pi\)
−0.953309 + 0.301997i \(0.902347\pi\)
\(62\) −3.33225 + 5.77162i −0.423196 + 0.732997i
\(63\) −4.39111 + 7.60563i −0.553228 + 0.958219i
\(64\) 8.86488 1.10811
\(65\) 0 0
\(66\) 15.2807 1.88093
\(67\) −3.19990 + 5.54239i −0.390930 + 0.677111i −0.992572 0.121655i \(-0.961180\pi\)
0.601642 + 0.798766i \(0.294513\pi\)
\(68\) −0.289961 + 0.502227i −0.0351629 + 0.0609040i
\(69\) 4.53957 + 7.86276i 0.546500 + 0.946566i
\(70\) −4.39111 −0.524838
\(71\) 5.39866 + 9.35076i 0.640703 + 1.10973i 0.985276 + 0.170971i \(0.0546905\pi\)
−0.344573 + 0.938760i \(0.611976\pi\)
\(72\) 3.73748 + 6.47351i 0.440467 + 0.762911i
\(73\) −4.70308 −0.550454 −0.275227 0.961379i \(-0.588753\pi\)
−0.275227 + 0.961379i \(0.588753\pi\)
\(74\) 5.30812 + 9.19393i 0.617056 + 1.06877i
\(75\) −1.16612 + 2.01978i −0.134652 + 0.233225i
\(76\) 0.581008 1.00633i 0.0666462 0.115435i
\(77\) 19.3396 2.20395
\(78\) 0 0
\(79\) −11.9826 −1.34815 −0.674075 0.738663i \(-0.735457\pi\)
−0.674075 + 0.738663i \(0.735457\pi\)
\(80\) −1.35638 + 2.34932i −0.151648 + 0.262661i
\(81\) 5.18379 8.97859i 0.575976 0.997621i
\(82\) −2.27597 3.94209i −0.251338 0.435331i
\(83\) −12.1286 −1.33129 −0.665643 0.746270i \(-0.731843\pi\)
−0.665643 + 0.746270i \(0.731843\pi\)
\(84\) 2.15104 + 3.72572i 0.234698 + 0.406509i
\(85\) −0.565928 0.980215i −0.0613835 0.106319i
\(86\) −1.38051 −0.148864
\(87\) 0.0288357 + 0.0499450i 0.00309152 + 0.00535466i
\(88\) 8.23042 14.2555i 0.877366 1.51964i
\(89\) 8.07702 13.9898i 0.856162 1.48292i −0.0194001 0.999812i \(-0.506176\pi\)
0.875562 0.483105i \(-0.160491\pi\)
\(90\) −2.97527 −0.313621
\(91\) 0 0
\(92\) 1.99457 0.207948
\(93\) −6.37182 + 11.0363i −0.660727 + 1.14441i
\(94\) −1.57666 + 2.73086i −0.162620 + 0.281666i
\(95\) 1.13397 + 1.96410i 0.116343 + 0.201513i
\(96\) 6.57666 0.671228
\(97\) −6.08408 10.5379i −0.617745 1.06997i −0.989896 0.141794i \(-0.954713\pi\)
0.372151 0.928172i \(-0.378620\pi\)
\(98\) −3.63553 6.29692i −0.367244 0.636085i
\(99\) 13.1039 1.31699
\(100\) 0.256182 + 0.443720i 0.0256182 + 0.0443720i
\(101\) 2.02721 3.51122i 0.201714 0.349380i −0.747366 0.664412i \(-0.768682\pi\)
0.949081 + 0.315032i \(0.102015\pi\)
\(102\) 1.60984 2.78833i 0.159398 0.276086i
\(103\) −17.9035 −1.76408 −0.882041 0.471173i \(-0.843831\pi\)
−0.882041 + 0.471173i \(0.843831\pi\)
\(104\) 0 0
\(105\) −8.39654 −0.819419
\(106\) 2.70732 4.68922i 0.262958 0.455457i
\(107\) 4.56593 7.90842i 0.441405 0.764536i −0.556389 0.830922i \(-0.687814\pi\)
0.997794 + 0.0663862i \(0.0211469\pi\)
\(108\) −0.334963 0.580172i −0.0322318 0.0558271i
\(109\) 7.37605 0.706498 0.353249 0.935529i \(-0.385077\pi\)
0.353249 + 0.935529i \(0.385077\pi\)
\(110\) 3.27597 + 5.67414i 0.312351 + 0.541008i
\(111\) 10.1500 + 17.5803i 0.963396 + 1.66865i
\(112\) −9.76645 −0.922843
\(113\) −3.53794 6.12789i −0.332821 0.576463i 0.650243 0.759727i \(-0.274667\pi\)
−0.983064 + 0.183263i \(0.941334\pi\)
\(114\) −3.22572 + 5.58710i −0.302116 + 0.523280i
\(115\) −1.94644 + 3.37133i −0.181506 + 0.314378i
\(116\) 0.0126697 0.00117635
\(117\) 0 0
\(118\) −0.209084 −0.0192478
\(119\) 2.03745 3.52897i 0.186773 0.323500i
\(120\) −3.57335 + 6.18922i −0.326201 + 0.564996i
\(121\) −8.92820 15.4641i −0.811655 1.40583i
\(122\) 4.09843 0.371055
\(123\) −4.35203 7.53794i −0.392409 0.679673i
\(124\) 1.39980 + 2.42453i 0.125706 + 0.217729i
\(125\) −1.00000 −0.0894427
\(126\) −5.35578 9.27648i −0.477131 0.826415i
\(127\) 5.71806 9.90396i 0.507395 0.878835i −0.492568 0.870274i \(-0.663942\pi\)
0.999963 0.00856072i \(-0.00272499\pi\)
\(128\) −2.58631 + 4.47962i −0.228600 + 0.395946i
\(129\) −2.63977 −0.232418
\(130\) 0 0
\(131\) −10.5680 −0.923328 −0.461664 0.887055i \(-0.652747\pi\)
−0.461664 + 0.887055i \(0.652747\pi\)
\(132\) 3.20955 5.55910i 0.279355 0.483858i
\(133\) −4.08253 + 7.07115i −0.354000 + 0.613146i
\(134\) −3.90288 6.75998i −0.337157 0.583974i
\(135\) 1.30752 0.112533
\(136\) −1.73417 3.00367i −0.148704 0.257563i
\(137\) −1.89336 3.27940i −0.161761 0.280178i 0.773739 0.633504i \(-0.218384\pi\)
−0.935500 + 0.353326i \(0.885051\pi\)
\(138\) −11.0737 −0.942656
\(139\) −1.00693 1.74406i −0.0854068 0.147929i 0.820158 0.572138i \(-0.193886\pi\)
−0.905564 + 0.424209i \(0.860552\pi\)
\(140\) −0.922305 + 1.59748i −0.0779490 + 0.135012i
\(141\) −3.01484 + 5.22186i −0.253895 + 0.439760i
\(142\) −13.1694 −1.10515
\(143\) 0 0
\(144\) −6.61742 −0.551452
\(145\) −0.0123639 + 0.0214150i −0.00102677 + 0.00177842i
\(146\) 2.86814 4.96777i 0.237369 0.411136i
\(147\) −6.95174 12.0408i −0.573370 0.993105i
\(148\) 4.45965 0.366581
\(149\) 2.75890 + 4.77855i 0.226018 + 0.391474i 0.956624 0.291324i \(-0.0940959\pi\)
−0.730607 + 0.682799i \(0.760763\pi\)
\(150\) −1.42231 2.46350i −0.116131 0.201144i
\(151\) −4.88961 −0.397911 −0.198956 0.980009i \(-0.563755\pi\)
−0.198956 + 0.980009i \(0.563755\pi\)
\(152\) 3.47484 + 6.01859i 0.281846 + 0.488172i
\(153\) 1.38051 2.39111i 0.111608 0.193310i
\(154\) −11.7941 + 20.4280i −0.950397 + 1.64614i
\(155\) −5.46410 −0.438887
\(156\) 0 0
\(157\) 10.0405 0.801323 0.400661 0.916226i \(-0.368780\pi\)
0.400661 + 0.916226i \(0.368780\pi\)
\(158\) 7.30752 12.6570i 0.581355 1.00694i
\(159\) 5.17686 8.96658i 0.410551 0.711096i
\(160\) 1.40994 + 2.44209i 0.111466 + 0.193064i
\(161\) −14.0151 −1.10454
\(162\) 6.32260 + 10.9511i 0.496750 + 0.860397i
\(163\) −3.39062 5.87273i −0.265574 0.459988i 0.702140 0.712039i \(-0.252228\pi\)
−0.967714 + 0.252051i \(0.918895\pi\)
\(164\) −1.91217 −0.149315
\(165\) 6.26420 + 10.8499i 0.487667 + 0.844664i
\(166\) 7.39654 12.8112i 0.574083 0.994341i
\(167\) −5.24490 + 9.08444i −0.405863 + 0.702975i −0.994421 0.105479i \(-0.966362\pi\)
0.588559 + 0.808455i \(0.299696\pi\)
\(168\) −25.7295 −1.98507
\(169\) 0 0
\(170\) 1.38051 0.105880
\(171\) −2.76619 + 4.79118i −0.211536 + 0.366391i
\(172\) −0.289961 + 0.502227i −0.0221093 + 0.0382944i
\(173\) 2.22923 + 3.86113i 0.169485 + 0.293557i 0.938239 0.345988i \(-0.112456\pi\)
−0.768754 + 0.639545i \(0.779123\pi\)
\(174\) −0.0703412 −0.00533255
\(175\) −1.80010 3.11786i −0.136075 0.235688i
\(176\) 7.28621 + 12.6201i 0.549219 + 0.951275i
\(177\) −0.399804 −0.0300511
\(178\) 9.85143 + 17.0632i 0.738396 + 1.27894i
\(179\) −9.31564 + 16.1352i −0.696284 + 1.20600i 0.273462 + 0.961883i \(0.411831\pi\)
−0.969746 + 0.244116i \(0.921502\pi\)
\(180\) −0.624924 + 1.08240i −0.0465791 + 0.0806773i
\(181\) 18.0900 1.34462 0.672310 0.740270i \(-0.265302\pi\)
0.672310 + 0.740270i \(0.265302\pi\)
\(182\) 0 0
\(183\) 7.83690 0.579320
\(184\) −5.96446 + 10.3307i −0.439706 + 0.761593i
\(185\) −4.35203 + 7.53794i −0.319968 + 0.554200i
\(186\) −7.77162 13.4608i −0.569843 0.986997i
\(187\) −6.08012 −0.444622
\(188\) 0.662321 + 1.14717i 0.0483047 + 0.0836662i
\(189\) 2.35366 + 4.07666i 0.171204 + 0.296533i
\(190\) −2.76619 −0.200680
\(191\) −13.6682 23.6740i −0.988994 1.71299i −0.622632 0.782515i \(-0.713937\pi\)
−0.366361 0.930473i \(-0.619397\pi\)
\(192\) −10.3375 + 17.9052i −0.746048 + 1.29219i
\(193\) −10.8837 + 18.8511i −0.783425 + 1.35693i 0.146510 + 0.989209i \(0.453196\pi\)
−0.929935 + 0.367723i \(0.880137\pi\)
\(194\) 14.8413 1.06555
\(195\) 0 0
\(196\) −3.05441 −0.218172
\(197\) 0.848360 1.46940i 0.0604432 0.104691i −0.834220 0.551431i \(-0.814082\pi\)
0.894664 + 0.446741i \(0.147415\pi\)
\(198\) −7.99131 + 13.8413i −0.567917 + 0.983662i
\(199\) −12.6627 21.9325i −0.897637 1.55475i −0.830506 0.557009i \(-0.811949\pi\)
−0.0671309 0.997744i \(-0.521385\pi\)
\(200\) −3.06430 −0.216679
\(201\) −7.46296 12.9262i −0.526397 0.911746i
\(202\) 2.47256 + 4.28259i 0.173968 + 0.301322i
\(203\) −0.0890252 −0.00624834
\(204\) −0.676260 1.17132i −0.0473477 0.0820086i
\(205\) 1.86603 3.23205i 0.130329 0.225736i
\(206\) 10.9183 18.9111i 0.760715 1.31760i
\(207\) −9.49617 −0.660030
\(208\) 0 0
\(209\) 12.1830 0.842716
\(210\) 5.12058 8.86910i 0.353353 0.612026i
\(211\) 0.167753 0.290558i 0.0115486 0.0200028i −0.860193 0.509968i \(-0.829657\pi\)
0.871742 + 0.489965i \(0.162991\pi\)
\(212\) −1.13729 1.96984i −0.0781092 0.135289i
\(213\) −25.1820 −1.72544
\(214\) 5.56900 + 9.64579i 0.380689 + 0.659373i
\(215\) −0.565928 0.980215i −0.0385959 0.0668501i
\(216\) 4.00663 0.272616
\(217\) −9.83592 17.0363i −0.667706 1.15650i
\(218\) −4.49824 + 7.79118i −0.304659 + 0.527685i
\(219\) 5.48438 9.49922i 0.370600 0.641898i
\(220\) 2.75232 0.185562
\(221\) 0 0
\(222\) −24.7597 −1.66176
\(223\) 6.14838 10.6493i 0.411726 0.713130i −0.583353 0.812219i \(-0.698259\pi\)
0.995079 + 0.0990887i \(0.0315928\pi\)
\(224\) −5.07606 + 8.79200i −0.339159 + 0.587440i
\(225\) −1.21969 2.11256i −0.0813125 0.140837i
\(226\) 8.63036 0.574083
\(227\) 3.81613 + 6.60974i 0.253286 + 0.438704i 0.964428 0.264344i \(-0.0851554\pi\)
−0.711143 + 0.703048i \(0.751822\pi\)
\(228\) 1.35505 + 2.34702i 0.0897406 + 0.155435i
\(229\) −14.4008 −0.951631 −0.475815 0.879545i \(-0.657847\pi\)
−0.475815 + 0.879545i \(0.657847\pi\)
\(230\) −2.37404 4.11196i −0.156540 0.271135i
\(231\) −22.5523 + 39.0618i −1.48384 + 2.57008i
\(232\) −0.0378868 + 0.0656218i −0.00248739 + 0.00430828i
\(233\) 9.49617 0.622115 0.311057 0.950391i \(-0.399317\pi\)
0.311057 + 0.950391i \(0.399317\pi\)
\(234\) 0 0
\(235\) −2.58535 −0.168650
\(236\) −0.0439159 + 0.0760645i −0.00285868 + 0.00495138i
\(237\) 13.9732 24.2023i 0.907657 1.57211i
\(238\) 2.48505 + 4.30423i 0.161082 + 0.279002i
\(239\) −19.9143 −1.28815 −0.644076 0.764962i \(-0.722758\pi\)
−0.644076 + 0.764962i \(0.722758\pi\)
\(240\) −3.16341 5.47918i −0.204197 0.353680i
\(241\) −11.6332 20.1493i −0.749360 1.29793i −0.948130 0.317883i \(-0.897028\pi\)
0.198770 0.980046i \(-0.436305\pi\)
\(242\) 21.7792 1.40002
\(243\) 10.1286 + 17.5432i 0.649750 + 1.12540i
\(244\) 0.860832 1.49100i 0.0551091 0.0954518i
\(245\) 2.98070 5.16273i 0.190430 0.329835i
\(246\) 10.6162 0.676866
\(247\) 0 0
\(248\) −16.7436 −1.06322
\(249\) 14.1434 24.4972i 0.896304 1.55244i
\(250\) 0.609843 1.05628i 0.0385699 0.0668050i
\(251\) −5.92008 10.2539i −0.373672 0.647219i 0.616455 0.787390i \(-0.288568\pi\)
−0.990127 + 0.140171i \(0.955235\pi\)
\(252\) −4.49969 −0.283454
\(253\) 10.4559 + 18.1101i 0.657357 + 1.13858i
\(254\) 6.97424 + 12.0797i 0.437603 + 0.757950i
\(255\) 2.63977 0.165309
\(256\) 5.71040 + 9.89070i 0.356900 + 0.618169i
\(257\) 2.77501 4.80646i 0.173100 0.299819i −0.766402 0.642361i \(-0.777955\pi\)
0.939502 + 0.342543i \(0.111288\pi\)
\(258\) 1.60984 2.78833i 0.100224 0.173594i
\(259\) −31.3363 −1.94714
\(260\) 0 0
\(261\) −0.0603205 −0.00373375
\(262\) 6.44481 11.1627i 0.398161 0.689636i
\(263\) −3.42983 + 5.94065i −0.211493 + 0.366316i −0.952182 0.305532i \(-0.901166\pi\)
0.740689 + 0.671848i \(0.234499\pi\)
\(264\) 19.1954 + 33.2474i 1.18139 + 2.04623i
\(265\) 4.43937 0.272709
\(266\) −4.97941 8.62459i −0.305307 0.528807i
\(267\) 18.8376 + 32.6277i 1.15284 + 1.99678i
\(268\) −3.27903 −0.200299
\(269\) 0.710994 + 1.23148i 0.0433501 + 0.0750845i 0.886886 0.461988i \(-0.152864\pi\)
−0.843536 + 0.537072i \(0.819530\pi\)
\(270\) −0.797382 + 1.38111i −0.0485271 + 0.0840514i
\(271\) 4.98473 8.63381i 0.302801 0.524467i −0.673968 0.738760i \(-0.735412\pi\)
0.976769 + 0.214294i \(0.0687449\pi\)
\(272\) 3.07045 0.186173
\(273\) 0 0
\(274\) 4.61862 0.279021
\(275\) −2.68591 + 4.65213i −0.161966 + 0.280534i
\(276\) −2.32591 + 4.02860i −0.140003 + 0.242493i
\(277\) 8.76187 + 15.1760i 0.526449 + 0.911837i 0.999525 + 0.0308154i \(0.00981039\pi\)
−0.473076 + 0.881022i \(0.656856\pi\)
\(278\) 2.45628 0.147318
\(279\) −6.66449 11.5432i −0.398993 0.691076i
\(280\) −5.51603 9.55405i −0.329646 0.570964i
\(281\) 10.7352 0.640406 0.320203 0.947349i \(-0.396249\pi\)
0.320203 + 0.947349i \(0.396249\pi\)
\(282\) −3.67716 6.36903i −0.218972 0.379270i
\(283\) −0.659192 + 1.14175i −0.0391849 + 0.0678702i −0.884953 0.465681i \(-0.845809\pi\)
0.845768 + 0.533551i \(0.179143\pi\)
\(284\) −2.76608 + 4.79099i −0.164137 + 0.284293i
\(285\) −5.28942 −0.313318
\(286\) 0 0
\(287\) 13.4361 0.793109
\(288\) −3.43937 + 5.95717i −0.202667 + 0.351030i
\(289\) 7.85945 13.6130i 0.462321 0.800763i
\(290\) −0.0150801 0.0261196i −0.000885536 0.00153379i
\(291\) 28.3792 1.66362
\(292\) −1.20485 2.08685i −0.0705082 0.122124i
\(293\) −9.37133 16.2316i −0.547479 0.948261i −0.998446 0.0557207i \(-0.982254\pi\)
0.450968 0.892540i \(-0.351079\pi\)
\(294\) 16.9579 0.989004
\(295\) −0.0857123 0.148458i −0.00499036 0.00864356i
\(296\) −13.3359 + 23.0985i −0.775134 + 1.34257i
\(297\) 3.51187 6.08275i 0.203780 0.352957i
\(298\) −6.72998 −0.389857
\(299\) 0 0
\(300\) −1.19496 −0.0689910
\(301\) 2.03745 3.52897i 0.117437 0.203406i
\(302\) 2.98190 5.16480i 0.171589 0.297201i
\(303\) 4.72794 + 8.18904i 0.271613 + 0.470448i
\(304\) −6.15239 −0.352864
\(305\) 1.68012 + 2.91005i 0.0962032 + 0.166629i
\(306\) 1.68379 + 2.91641i 0.0962558 + 0.166720i
\(307\) 14.3043 0.816387 0.408194 0.912895i \(-0.366159\pi\)
0.408194 + 0.912895i \(0.366159\pi\)
\(308\) 4.95445 + 8.58137i 0.282306 + 0.488969i
\(309\) 20.8777 36.1612i 1.18769 2.05714i
\(310\) 3.33225 5.77162i 0.189259 0.327806i
\(311\) 2.76102 0.156563 0.0782815 0.996931i \(-0.475057\pi\)
0.0782815 + 0.996931i \(0.475057\pi\)
\(312\) 0 0
\(313\) −16.3858 −0.926179 −0.463090 0.886311i \(-0.653259\pi\)
−0.463090 + 0.886311i \(0.653259\pi\)
\(314\) −6.12316 + 10.6056i −0.345550 + 0.598510i
\(315\) 4.39111 7.60563i 0.247411 0.428529i
\(316\) −3.06973 5.31693i −0.172686 0.299101i
\(317\) 1.78575 0.100297 0.0501487 0.998742i \(-0.484030\pi\)
0.0501487 + 0.998742i \(0.484030\pi\)
\(318\) 6.31414 + 10.9364i 0.354080 + 0.613284i
\(319\) 0.0664168 + 0.115037i 0.00371863 + 0.00644085i
\(320\) −8.86488 −0.495562
\(321\) 10.6489 + 18.4444i 0.594362 + 1.02946i
\(322\) 8.54702 14.8039i 0.476307 0.824987i
\(323\) 1.28349 2.22308i 0.0714156 0.123695i
\(324\) 5.31197 0.295110
\(325\) 0 0
\(326\) 8.27099 0.458088
\(327\) −8.60139 + 14.8980i −0.475658 + 0.823864i
\(328\) 5.71806 9.90396i 0.315727 0.546855i
\(329\) −4.65389 8.06077i −0.256577 0.444405i
\(330\) −15.2807 −0.841176
\(331\) −3.61220 6.25652i −0.198545 0.343889i 0.749512 0.661991i \(-0.230288\pi\)
−0.948057 + 0.318101i \(0.896955\pi\)
\(332\) −3.10713 5.38170i −0.170526 0.295359i
\(333\) −21.2325 −1.16353
\(334\) −6.39714 11.0802i −0.350036 0.606280i
\(335\) 3.19990 5.54239i 0.174829 0.302813i
\(336\) 11.3889 19.7261i 0.621315 1.07615i
\(337\) −4.36219 −0.237624 −0.118812 0.992917i \(-0.537909\pi\)
−0.118812 + 0.992917i \(0.537909\pi\)
\(338\) 0 0
\(339\) 16.5027 0.896303
\(340\) 0.289961 0.502227i 0.0157253 0.0272371i
\(341\) −14.6761 + 25.4197i −0.794754 + 1.37655i
\(342\) −3.37388 5.84374i −0.182439 0.315993i
\(343\) −3.73913 −0.201894
\(344\) −1.73417 3.00367i −0.0935002 0.161947i
\(345\) −4.53957 7.86276i −0.244402 0.423317i
\(346\) −5.43792 −0.292344
\(347\) 13.3536 + 23.1291i 0.716858 + 1.24163i 0.962239 + 0.272207i \(0.0877537\pi\)
−0.245381 + 0.969427i \(0.578913\pi\)
\(348\) −0.0147744 + 0.0255900i −0.000791991 + 0.00137177i
\(349\) −11.7855 + 20.4131i −0.630865 + 1.09269i 0.356510 + 0.934292i \(0.383967\pi\)
−0.987375 + 0.158399i \(0.949367\pi\)
\(350\) 4.39111 0.234715
\(351\) 0 0
\(352\) 15.1479 0.807385
\(353\) −2.86863 + 4.96862i −0.152682 + 0.264453i −0.932213 0.361911i \(-0.882124\pi\)
0.779531 + 0.626364i \(0.215458\pi\)
\(354\) 0.243818 0.422305i 0.0129588 0.0224453i
\(355\) −5.39866 9.35076i −0.286531 0.496287i
\(356\) 8.27675 0.438667
\(357\) 4.75184 + 8.23042i 0.251494 + 0.435600i
\(358\) −11.3622 19.6799i −0.600509 1.04011i
\(359\) −24.7583 −1.30669 −0.653347 0.757059i \(-0.726636\pi\)
−0.653347 + 0.757059i \(0.726636\pi\)
\(360\) −3.73748 6.47351i −0.196983 0.341184i
\(361\) 6.92820 12.0000i 0.364642 0.631579i
\(362\) −11.0321 + 19.1081i −0.579833 + 1.00430i
\(363\) 41.6455 2.18582
\(364\) 0 0
\(365\) 4.70308 0.246171
\(366\) −4.77928 + 8.27796i −0.249817 + 0.432696i
\(367\) −13.0268 + 22.5630i −0.679992 + 1.17778i 0.294991 + 0.955500i \(0.404683\pi\)
−0.974983 + 0.222280i \(0.928650\pi\)
\(368\) −5.28021 9.14558i −0.275250 0.476747i
\(369\) 9.10387 0.473928
\(370\) −5.30812 9.19393i −0.275956 0.477969i
\(371\) 7.99131 + 13.8413i 0.414888 + 0.718607i
\(372\) −6.52938 −0.338532
\(373\) −6.60224 11.4354i −0.341851 0.592103i 0.642926 0.765929i \(-0.277720\pi\)
−0.984776 + 0.173826i \(0.944387\pi\)
\(374\) 3.70792 6.42231i 0.191732 0.332089i
\(375\) 1.16612 2.01978i 0.0602183 0.104301i
\(376\) −7.92229 −0.408561
\(377\) 0 0
\(378\) −5.74146 −0.295309
\(379\) −12.9989 + 22.5147i −0.667707 + 1.15650i 0.310837 + 0.950463i \(0.399391\pi\)
−0.978544 + 0.206039i \(0.933943\pi\)
\(380\) −0.581008 + 1.00633i −0.0298051 + 0.0516239i
\(381\) 13.3359 + 23.0985i 0.683220 + 1.18337i
\(382\) 33.3418 1.70591
\(383\) 4.80010 + 8.31401i 0.245274 + 0.424826i 0.962208 0.272314i \(-0.0877889\pi\)
−0.716935 + 0.697140i \(0.754456\pi\)
\(384\) −6.03191 10.4476i −0.307815 0.533151i
\(385\) −19.3396 −0.985637
\(386\) −13.2747 22.9924i −0.675664 1.17028i
\(387\) 1.38051 2.39111i 0.0701752 0.121547i
\(388\) 3.11726 5.39926i 0.158255 0.274106i
\(389\) 5.63129 0.285518 0.142759 0.989758i \(-0.454403\pi\)
0.142759 + 0.989758i \(0.454403\pi\)
\(390\) 0 0
\(391\) 4.40617 0.222829
\(392\) 9.13376 15.8201i 0.461325 0.799038i
\(393\) 12.3236 21.3450i 0.621641 1.07671i
\(394\) 1.03473 + 1.79221i 0.0521291 + 0.0902903i
\(395\) 11.9826 0.602911
\(396\) 3.35697 + 5.81445i 0.168694 + 0.292187i
\(397\) 8.38291 + 14.5196i 0.420726 + 0.728719i 0.996011 0.0892344i \(-0.0284420\pi\)
−0.575285 + 0.817953i \(0.695109\pi\)
\(398\) 30.8891 1.54833
\(399\) −9.52147 16.4917i −0.476670 0.825616i
\(400\) 1.35638 2.34932i 0.0678189 0.117466i
\(401\) 6.93902 12.0187i 0.346518 0.600187i −0.639110 0.769115i \(-0.720697\pi\)
0.985628 + 0.168928i \(0.0540307\pi\)
\(402\) 18.2050 0.907980
\(403\) 0 0
\(404\) 2.07733 0.103351
\(405\) −5.18379 + 8.97859i −0.257585 + 0.446149i
\(406\) 0.0542914 0.0940355i 0.00269444 0.00466690i
\(407\) 23.3783 + 40.4924i 1.15882 + 2.00713i
\(408\) 8.08903 0.400466
\(409\) −14.7125 25.4829i −0.727489 1.26005i −0.957941 0.286964i \(-0.907354\pi\)
0.230453 0.973083i \(-0.425979\pi\)
\(410\) 2.27597 + 3.94209i 0.112402 + 0.194686i
\(411\) 8.83157 0.435629
\(412\) −4.58655 7.94413i −0.225963 0.391379i
\(413\) 0.308581 0.534478i 0.0151843 0.0262999i
\(414\) 5.79118 10.0306i 0.284621 0.492978i
\(415\) 12.1286 0.595369
\(416\) 0 0
\(417\) 4.69683 0.230005
\(418\) −7.42973 + 12.8687i −0.363400 + 0.629427i
\(419\) −3.48397 + 6.03440i −0.170203 + 0.294800i −0.938491 0.345305i \(-0.887776\pi\)
0.768288 + 0.640104i \(0.221109\pi\)
\(420\) −2.15104 3.72572i −0.104960 0.181796i
\(421\) 7.12125 0.347069 0.173534 0.984828i \(-0.444481\pi\)
0.173534 + 0.984828i \(0.444481\pi\)
\(422\) 0.204607 + 0.354389i 0.00996010 + 0.0172514i
\(423\) −3.15332 5.46171i −0.153320 0.265558i
\(424\) 13.6036 0.660647
\(425\) 0.565928 + 0.980215i 0.0274515 + 0.0475474i
\(426\) 15.3571 26.5993i 0.744054 1.28874i
\(427\) −6.04875 + 10.4767i −0.292720 + 0.507005i
\(428\) 4.67883 0.226160
\(429\) 0 0
\(430\) 1.38051 0.0665740
\(431\) −15.1072 + 26.1664i −0.727687 + 1.26039i 0.230171 + 0.973150i \(0.426071\pi\)
−0.957858 + 0.287241i \(0.907262\pi\)
\(432\) −1.77349 + 3.07177i −0.0853270 + 0.147791i
\(433\) −0.600065 1.03934i −0.0288373 0.0499476i 0.851247 0.524766i \(-0.175847\pi\)
−0.880084 + 0.474818i \(0.842514\pi\)
\(434\) 23.9935 1.15172
\(435\) −0.0288357 0.0499450i −0.00138257 0.00239468i
\(436\) 1.88961 + 3.27290i 0.0904960 + 0.156744i
\(437\) −8.82884 −0.422341
\(438\) 6.68922 + 11.5861i 0.319623 + 0.553604i
\(439\) 8.27705 14.3363i 0.395042 0.684233i −0.598064 0.801448i \(-0.704063\pi\)
0.993107 + 0.117215i \(0.0373966\pi\)
\(440\) −8.23042 + 14.2555i −0.392370 + 0.679605i
\(441\) 14.5421 0.692481
\(442\) 0 0
\(443\) 4.55949 0.216628 0.108314 0.994117i \(-0.465455\pi\)
0.108314 + 0.994117i \(0.465455\pi\)
\(444\) −5.20050 + 9.00753i −0.246805 + 0.427478i
\(445\) −8.07702 + 13.9898i −0.382887 + 0.663180i
\(446\) 7.49910 + 12.9888i 0.355093 + 0.615038i
\(447\) −12.8689 −0.608676
\(448\) −15.9577 27.6395i −0.753929 1.30584i
\(449\) −6.92608 11.9963i −0.326862 0.566142i 0.655025 0.755607i \(-0.272658\pi\)
−0.981887 + 0.189465i \(0.939325\pi\)
\(450\) 2.97527 0.140256
\(451\) −10.0239 17.3620i −0.472009 0.817544i
\(452\) 1.81271 3.13971i 0.0852628 0.147680i
\(453\) 5.70189 9.87596i 0.267898 0.464013i
\(454\) −9.30897 −0.436892
\(455\) 0 0
\(456\) −16.2083 −0.759025
\(457\) −20.0573 + 34.7402i −0.938240 + 1.62508i −0.169489 + 0.985532i \(0.554212\pi\)
−0.768751 + 0.639548i \(0.779122\pi\)
\(458\) 8.78222 15.2113i 0.410366 0.710775i
\(459\) −0.739961 1.28165i −0.0345384 0.0598223i
\(460\) −1.99457 −0.0929972
\(461\) 3.76950 + 6.52897i 0.175563 + 0.304084i 0.940356 0.340192i \(-0.110492\pi\)
−0.764793 + 0.644276i \(0.777159\pi\)
\(462\) −27.5068 47.6432i −1.27973 2.21656i
\(463\) 23.3031 1.08299 0.541494 0.840705i \(-0.317859\pi\)
0.541494 + 0.840705i \(0.317859\pi\)
\(464\) −0.0335403 0.0580936i −0.00155707 0.00269693i
\(465\) 6.37182 11.0363i 0.295486 0.511797i
\(466\) −5.79118 + 10.0306i −0.268271 + 0.464659i
\(467\) −22.6297 −1.04718 −0.523589 0.851971i \(-0.675407\pi\)
−0.523589 + 0.851971i \(0.675407\pi\)
\(468\) 0 0
\(469\) 23.0405 1.06391
\(470\) 1.57666 2.73086i 0.0727260 0.125965i
\(471\) −11.7085 + 20.2797i −0.539500 + 0.934441i
\(472\) −0.262648 0.454919i −0.0120893 0.0209394i
\(473\) −6.08012 −0.279564
\(474\) 17.0429 + 29.5192i 0.782808 + 1.35586i
\(475\) −1.13397 1.96410i −0.0520303 0.0901192i
\(476\) 2.08783 0.0956956
\(477\) 5.41465 + 9.37844i 0.247920 + 0.429409i
\(478\) 12.1446 21.0351i 0.555482 0.962124i
\(479\) −10.3224 + 17.8789i −0.471643 + 0.816910i −0.999474 0.0324399i \(-0.989672\pi\)
0.527831 + 0.849350i \(0.323006\pi\)
\(480\) −6.57666 −0.300182
\(481\) 0 0
\(482\) 28.3777 1.29257
\(483\) 16.3433 28.3075i 0.743648 1.28804i
\(484\) 4.57449 7.92325i 0.207931 0.360148i
\(485\) 6.08408 + 10.5379i 0.276264 + 0.478503i
\(486\) −24.7074 −1.12075
\(487\) −1.51802 2.62929i −0.0687882 0.119145i 0.829580 0.558388i \(-0.188580\pi\)
−0.898368 + 0.439243i \(0.855247\pi\)
\(488\) 5.14838 + 8.91725i 0.233056 + 0.403665i
\(489\) 15.8155 0.715203
\(490\) 3.63553 + 6.29692i 0.164236 + 0.284466i
\(491\) −5.33401 + 9.23877i −0.240720 + 0.416940i −0.960920 0.276827i \(-0.910717\pi\)
0.720199 + 0.693767i \(0.244050\pi\)
\(492\) 2.22982 3.86217i 0.100528 0.174120i
\(493\) 0.0279884 0.00126053
\(494\) 0 0
\(495\) −13.1039 −0.588975
\(496\) 7.41139 12.8369i 0.332781 0.576394i
\(497\) 19.4362 33.6646i 0.871835 1.51006i
\(498\) 17.2506 + 29.8789i 0.773016 + 1.33890i
\(499\) 33.9143 1.51821 0.759107 0.650966i \(-0.225636\pi\)
0.759107 + 0.650966i \(0.225636\pi\)
\(500\) −0.256182 0.443720i −0.0114568 0.0198438i
\(501\) −12.2324 21.1872i −0.546504 0.946572i
\(502\) 14.4413 0.644546
\(503\) 6.31380 + 10.9358i 0.281518 + 0.487604i 0.971759 0.235976i \(-0.0758286\pi\)
−0.690241 + 0.723580i \(0.742495\pi\)
\(504\) 13.4557 23.3059i 0.599363 1.03813i
\(505\) −2.02721 + 3.51122i −0.0902095 + 0.156247i
\(506\) −25.5058 −1.13387
\(507\) 0 0
\(508\) 5.85945 0.259971
\(509\) 12.0763 20.9168i 0.535273 0.927120i −0.463877 0.885899i \(-0.653542\pi\)
0.999150 0.0412201i \(-0.0131245\pi\)
\(510\) −1.60984 + 2.78833i −0.0712851 + 0.123469i
\(511\) 8.46601 + 14.6636i 0.374514 + 0.648678i
\(512\) −24.2750 −1.07281
\(513\) 1.48269 + 2.56810i 0.0654625 + 0.113384i
\(514\) 3.38465 + 5.86238i 0.149290 + 0.258578i
\(515\) 17.9035 0.788921
\(516\) −0.676260 1.17132i −0.0297707 0.0515644i
\(517\) −6.94402 + 12.0274i −0.305398 + 0.528964i
\(518\) 19.1103 33.0999i 0.839656 1.45433i
\(519\) −10.3982 −0.456431
\(520\) 0 0
\(521\) −24.7521 −1.08441 −0.542205 0.840246i \(-0.682410\pi\)
−0.542205 + 0.840246i \(0.682410\pi\)
\(522\) 0.0367861 0.0637154i 0.00161008 0.00278875i
\(523\) −18.5163 + 32.0712i −0.809662 + 1.40238i 0.103436 + 0.994636i \(0.467016\pi\)
−0.913098 + 0.407739i \(0.866317\pi\)
\(524\) −2.70732 4.68922i −0.118270 0.204850i
\(525\) 8.39654 0.366455
\(526\) −4.18332 7.24573i −0.182402 0.315929i
\(527\) 3.09229 + 5.35600i 0.134702 + 0.233311i
\(528\) −33.9865 −1.47907
\(529\) 3.92277 + 6.79444i 0.170555 + 0.295410i
\(530\) −2.70732 + 4.68922i −0.117599 + 0.203687i
\(531\) 0.209084 0.362145i 0.00907348 0.0157157i
\(532\) −4.18348 −0.181377
\(533\) 0 0
\(534\) −45.9519 −1.98854
\(535\) −4.56593 + 7.90842i −0.197402 + 0.341911i
\(536\) 9.80545 16.9835i 0.423531 0.733577i
\(537\) −21.7264 37.6312i −0.937562 1.62391i
\(538\) −1.73438 −0.0747744
\(539\) −16.0118 27.7332i −0.689677 1.19456i
\(540\) 0.334963 + 0.580172i 0.0144145 + 0.0249666i
\(541\) −8.38144 −0.360346 −0.180173 0.983635i \(-0.557666\pi\)
−0.180173 + 0.983635i \(0.557666\pi\)
\(542\) 6.07981 + 10.5305i 0.261150 + 0.452326i
\(543\) −21.0952 + 36.5379i −0.905281 + 1.56799i
\(544\) 1.59585 2.76409i 0.0684215 0.118509i
\(545\) −7.37605 −0.315955
\(546\) 0 0
\(547\) −22.7842 −0.974181 −0.487091 0.873351i \(-0.661942\pi\)
−0.487091 + 0.873351i \(0.661942\pi\)
\(548\) 0.970090 1.68025i 0.0414402 0.0717765i
\(549\) −4.09843 + 7.09870i −0.174917 + 0.302965i
\(550\) −3.27597 5.67414i −0.139688 0.241946i
\(551\) −0.0560816 −0.00238915
\(552\) −13.9106 24.0938i −0.592074 1.02550i
\(553\) 21.5699 + 37.3601i 0.917245 + 1.58871i
\(554\) −21.3735 −0.908071
\(555\) −10.1500 17.5803i −0.430844 0.746244i
\(556\) 0.515915 0.893592i 0.0218797 0.0378967i
\(557\) 14.0764 24.3810i 0.596435 1.03306i −0.396908 0.917858i \(-0.629917\pi\)
0.993343 0.115197i \(-0.0367499\pi\)
\(558\) 16.2572 0.688222
\(559\) 0 0
\(560\) 9.76645 0.412708
\(561\) 7.09017 12.2805i 0.299347 0.518484i
\(562\) −6.54676 + 11.3393i −0.276159 + 0.478321i
\(563\) 9.06514 + 15.7013i 0.382050 + 0.661731i 0.991355 0.131206i \(-0.0418848\pi\)
−0.609305 + 0.792936i \(0.708551\pi\)
\(564\) −3.08939 −0.130087
\(565\) 3.53794 + 6.12789i 0.148842 + 0.257802i
\(566\) −0.804007 1.39258i −0.0337950 0.0585346i
\(567\) −37.3253 −1.56752
\(568\) −16.5431 28.6535i −0.694133 1.20227i
\(569\) −20.2992 + 35.1593i −0.850988 + 1.47395i 0.0293292 + 0.999570i \(0.490663\pi\)
−0.880317 + 0.474385i \(0.842670\pi\)
\(570\) 3.22572 5.58710i 0.135110 0.234018i
\(571\) 24.7159 1.03433 0.517164 0.855886i \(-0.326988\pi\)
0.517164 + 0.855886i \(0.326988\pi\)
\(572\) 0 0
\(573\) 63.7551 2.66341
\(574\) −8.19393 + 14.1923i −0.342008 + 0.592375i
\(575\) 1.94644 3.37133i 0.0811720 0.140594i
\(576\) −10.8124 18.7276i −0.450516 0.780317i
\(577\) 23.0691 0.960379 0.480189 0.877165i \(-0.340568\pi\)
0.480189 + 0.877165i \(0.340568\pi\)
\(578\) 9.58607 + 16.6036i 0.398728 + 0.690617i
\(579\) −25.3834 43.9654i −1.05490 1.82714i
\(580\) −0.0126697 −0.000526079
\(581\) 21.8327 + 37.8153i 0.905771 + 1.56884i
\(582\) −17.3068 + 29.9763i −0.717392 + 1.24256i
\(583\) 11.9237 20.6525i 0.493831 0.855341i
\(584\) 14.4116 0.596358
\(585\) 0 0
\(586\) 22.8602 0.944345
\(587\) 10.1762 17.6256i 0.420015 0.727487i −0.575926 0.817502i \(-0.695358\pi\)
0.995940 + 0.0900152i \(0.0286916\pi\)
\(588\) 3.56182 6.16925i 0.146887 0.254416i
\(589\) −6.19615 10.7321i −0.255308 0.442206i
\(590\) 0.209084 0.00860786
\(591\) 1.97859 + 3.42701i 0.0813881 + 0.140968i
\(592\) −11.8060 20.4486i −0.485223 0.840432i
\(593\) 10.3834 0.426395 0.213198 0.977009i \(-0.431612\pi\)
0.213198 + 0.977009i \(0.431612\pi\)
\(594\) 4.28339 + 7.41904i 0.175750 + 0.304407i
\(595\) −2.03745 + 3.52897i −0.0835273 + 0.144674i
\(596\) −1.41356 + 2.44836i −0.0579017 + 0.100289i
\(597\) 59.0652 2.41738
\(598\) 0 0
\(599\) −31.5965 −1.29100 −0.645499 0.763761i \(-0.723351\pi\)
−0.645499 + 0.763761i \(0.723351\pi\)
\(600\) 3.57335 6.18922i 0.145881 0.252674i
\(601\) 21.9423 38.0051i 0.895044 1.55026i 0.0612928 0.998120i \(-0.480478\pi\)
0.833751 0.552141i \(-0.186189\pi\)
\(602\) 2.48505 + 4.30423i 0.101283 + 0.175428i
\(603\) 15.6115 0.635750
\(604\) −1.25263 2.16962i −0.0509688 0.0882806i
\(605\) 8.92820 + 15.4641i 0.362983 + 0.628705i
\(606\) −11.5332 −0.468505
\(607\) −1.08770 1.88395i −0.0441484 0.0764673i 0.843107 0.537746i \(-0.180724\pi\)
−0.887255 + 0.461279i \(0.847391\pi\)
\(608\) −3.19768 + 5.53854i −0.129683 + 0.224617i
\(609\) 0.103814 0.179812i 0.00420677 0.00728634i
\(610\) −4.09843 −0.165941
\(611\) 0 0
\(612\) 1.41465 0.0571837
\(613\) 7.38100 12.7843i 0.298116 0.516352i −0.677589 0.735441i \(-0.736975\pi\)
0.975705 + 0.219089i \(0.0703085\pi\)
\(614\) −8.72336 + 15.1093i −0.352046 + 0.609762i
\(615\) 4.35203 + 7.53794i 0.175491 + 0.303959i
\(616\) −59.2622 −2.38774
\(617\) 10.1486 + 17.5779i 0.408567 + 0.707659i 0.994729 0.102535i \(-0.0326953\pi\)
−0.586162 + 0.810194i \(0.699362\pi\)
\(618\) 25.4642 + 44.1053i 1.02432 + 1.77418i
\(619\) 9.94207 0.399605 0.199803 0.979836i \(-0.435970\pi\)
0.199803 + 0.979836i \(0.435970\pi\)
\(620\) −1.39980 2.42453i −0.0562175 0.0973716i
\(621\) −2.54500 + 4.40807i −0.102127 + 0.176890i
\(622\) −1.68379 + 2.91641i −0.0675138 + 0.116937i
\(623\) −58.1577 −2.33004
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 9.99276 17.3080i 0.399391 0.691766i
\(627\) −14.2069 + 24.6070i −0.567368 + 0.982711i
\(628\) 2.57221 + 4.45519i 0.102642 + 0.177782i
\(629\) 9.85174 0.392815
\(630\) 5.35578 + 9.27648i 0.213379 + 0.369584i
\(631\) −0.486710 0.843006i −0.0193756 0.0335596i 0.856175 0.516686i \(-0.172835\pi\)
−0.875551 + 0.483126i \(0.839501\pi\)
\(632\) 36.7183 1.46058
\(633\) 0.391243 + 0.677652i 0.0155505 + 0.0269342i
\(634\) −1.08903 + 1.88625i −0.0432507 + 0.0749124i
\(635\) −5.71806 + 9.90396i −0.226914 + 0.393027i
\(636\) 5.30487 0.210352
\(637\) 0 0
\(638\) −0.162015 −0.00641425
\(639\) 13.1694 22.8100i 0.520972 0.902350i
\(640\) 2.58631 4.47962i 0.102233 0.177072i
\(641\) 6.31047 + 10.9301i 0.249249 + 0.431711i 0.963318 0.268364i \(-0.0864830\pi\)
−0.714069 + 0.700075i \(0.753150\pi\)
\(642\) −25.9766 −1.02521
\(643\) −4.98022 8.62599i −0.196401 0.340176i 0.750958 0.660350i \(-0.229592\pi\)
−0.947359 + 0.320174i \(0.896259\pi\)
\(644\) −3.59042 6.21878i −0.141482 0.245054i
\(645\) 2.63977 0.103941
\(646\) 1.56546 + 2.71146i 0.0615923 + 0.106681i
\(647\) 18.1381 31.4162i 0.713084 1.23510i −0.250610 0.968088i \(-0.580631\pi\)
0.963694 0.267009i \(-0.0860354\pi\)
\(648\) −15.8847 + 27.5131i −0.624009 + 1.08081i
\(649\) −0.920861 −0.0361470
\(650\) 0 0
\(651\) 45.8796 1.79816
\(652\) 1.73723 3.00898i 0.0680353 0.117841i
\(653\) −6.87769 + 11.9125i −0.269145 + 0.466172i −0.968641 0.248464i \(-0.920074\pi\)
0.699497 + 0.714636i \(0.253408\pi\)
\(654\) −10.4910 18.1709i −0.410231 0.710540i
\(655\) 10.5680 0.412925
\(656\) 5.06207 + 8.76776i 0.197641 + 0.342324i
\(657\) 5.73629 + 9.93555i 0.223794 + 0.387623i
\(658\) 11.3526 0.442570
\(659\) 1.29092 + 2.23593i 0.0502869 + 0.0870995i 0.890073 0.455818i \(-0.150653\pi\)
−0.839786 + 0.542917i \(0.817320\pi\)
\(660\) −3.20955 + 5.55910i −0.124932 + 0.216388i
\(661\) −12.4382 + 21.5437i −0.483791 + 0.837951i −0.999827 0.0186163i \(-0.994074\pi\)
0.516036 + 0.856567i \(0.327407\pi\)
\(662\) 8.81151 0.342469
\(663\) 0 0
\(664\) 37.1656 1.44231
\(665\) 4.08253 7.07115i 0.158314 0.274207i
\(666\) 12.9485 22.4274i 0.501743 0.869045i
\(667\) −0.0481312 0.0833657i −0.00186365 0.00322793i
\(668\) −5.37460 −0.207949
\(669\) 14.3395 + 24.8368i 0.554398 + 0.960246i
\(670\) 3.90288 + 6.75998i 0.150781 + 0.261161i
\(671\) 18.0506 0.696834
\(672\) −11.8386 20.5051i −0.456685 0.791002i
\(673\) −21.6611 + 37.5181i −0.834974 + 1.44622i 0.0590774 + 0.998253i \(0.481184\pi\)
−0.894052 + 0.447964i \(0.852149\pi\)
\(674\) 2.66025 4.60770i 0.102469 0.177482i
\(675\) −1.30752 −0.0503264
\(676\) 0 0
\(677\) −41.3625 −1.58969 −0.794845 0.606813i \(-0.792448\pi\)
−0.794845 + 0.606813i \(0.792448\pi\)
\(678\) −10.0641 + 17.4315i −0.386508 + 0.669451i
\(679\) −21.9039 + 37.9386i −0.840594 + 1.45595i
\(680\) 1.73417 + 3.00367i 0.0665024 + 0.115186i
\(681\) −17.8003 −0.682110
\(682\) −17.9002 31.0041i −0.685435 1.18721i
\(683\) −1.31344 2.27495i −0.0502574 0.0870484i 0.839802 0.542892i \(-0.182671\pi\)
−0.890060 + 0.455844i \(0.849338\pi\)
\(684\) −2.83459 −0.108383
\(685\) 1.89336 + 3.27940i 0.0723416 + 0.125299i
\(686\) 2.28028 3.94957i 0.0870617 0.150795i
\(687\) 16.7931 29.0865i 0.640696 1.10972i
\(688\) 3.07045 0.117060
\(689\) 0 0
\(690\) 11.0737 0.421569
\(691\) 7.63765 13.2288i 0.290550 0.503247i −0.683390 0.730053i \(-0.739495\pi\)
0.973940 + 0.226806i \(0.0728285\pi\)
\(692\) −1.14218 + 1.97831i −0.0434190 + 0.0752039i
\(693\) −23.5882 40.8560i −0.896043 1.55199i
\(694\) −32.5744 −1.23651
\(695\) 1.00693 + 1.74406i 0.0381951 + 0.0661558i
\(696\) −0.0883613 0.153046i −0.00334933 0.00580120i
\(697\) −4.22414 −0.160001
\(698\) −14.3747 24.8976i −0.544089 0.942390i
\(699\) −11.0737 + 19.1802i −0.418846 + 0.725463i
\(700\) 0.922305 1.59748i 0.0348599 0.0603790i
\(701\) −48.1947 −1.82029 −0.910144 0.414292i \(-0.864029\pi\)
−0.910144 + 0.414292i \(0.864029\pi\)
\(702\) 0 0
\(703\) −19.7404 −0.744522
\(704\) −23.8103 + 41.2406i −0.897383 + 1.55431i
\(705\) 3.01484 5.22186i 0.113546 0.196667i
\(706\) −3.49884 6.06016i −0.131680 0.228077i
\(707\) −14.5967 −0.548964
\(708\) −0.102423 0.177401i −0.00384928 0.00666715i
\(709\) 19.4350 + 33.6624i 0.729896 + 1.26422i 0.956927 + 0.290329i \(0.0937647\pi\)
−0.227031 + 0.973887i \(0.572902\pi\)
\(710\) 13.1694 0.494237
\(711\) 14.6150 + 25.3140i 0.548107 + 0.949349i
\(712\) −24.7504 + 42.8689i −0.927560 + 1.60658i
\(713\) 10.6355 18.4213i 0.398304 0.689882i
\(714\) −11.5915 −0.433801
\(715\) 0 0
\(716\) −9.54600 −0.356751
\(717\) 23.2226 40.2227i 0.867263 1.50214i
\(718\) 15.0987 26.1517i 0.563478 0.975973i
\(719\) −3.30830 5.73015i −0.123379 0.213698i 0.797719 0.603029i \(-0.206040\pi\)
−0.921098 + 0.389331i \(0.872706\pi\)
\(720\) 6.61742 0.246617
\(721\) 32.2280 + 55.8205i 1.20023 + 2.07887i
\(722\) 8.45024 + 14.6362i 0.314485 + 0.544705i
\(723\) 54.2629 2.01806
\(724\) 4.63433 + 8.02690i 0.172234 + 0.298317i
\(725\) 0.0123639 0.0214150i 0.000459185 0.000795332i
\(726\) −25.3973 + 43.9893i −0.942581 + 1.63260i
\(727\) −18.3735 −0.681435 −0.340717 0.940166i \(-0.610670\pi\)
−0.340717 + 0.940166i \(0.610670\pi\)
\(728\) 0 0
\(729\) −16.1420 −0.597853
\(730\) −2.86814 + 4.96777i −0.106155 + 0.183866i
\(731\) −0.640548 + 1.10946i −0.0236915 + 0.0410349i
\(732\) 2.00767 + 3.47739i 0.0742057 + 0.128528i
\(733\) 0.791131 0.0292211 0.0146105 0.999893i \(-0.495349\pi\)
0.0146105 + 0.999893i \(0.495349\pi\)
\(734\) −15.8886 27.5198i −0.586458 1.01578i
\(735\) 6.95174 + 12.0408i 0.256419 + 0.444130i
\(736\) −10.9774 −0.404634
\(737\) −17.1893 29.7727i −0.633175 1.09669i
\(738\) −5.55193 + 9.61623i −0.204369 + 0.353978i
\(739\) −15.5926 + 27.0073i −0.573585 + 0.993478i 0.422609 + 0.906312i \(0.361114\pi\)
−0.996194 + 0.0871658i \(0.972219\pi\)
\(740\) −4.45965 −0.163940
\(741\) 0 0
\(742\) −19.4938 −0.715639
\(743\) −2.78152 + 4.81773i −0.102044 + 0.176745i −0.912527 0.409017i \(-0.865872\pi\)
0.810483 + 0.585763i \(0.199205\pi\)
\(744\) 19.5251 33.8185i 0.715826 1.23985i
\(745\) −2.75890 4.77855i −0.101078 0.175073i
\(746\) 16.1053 0.589658
\(747\) 14.7931 + 25.6224i 0.541251 + 0.937474i
\(748\) −1.55762 2.69787i −0.0569521 0.0986439i
\(749\) −32.8765 −1.20128
\(750\) 1.42231 + 2.46350i 0.0519352 + 0.0899545i
\(751\) 17.6048 30.4925i 0.642410 1.11269i −0.342483 0.939524i \(-0.611268\pi\)
0.984893 0.173163i \(-0.0553987\pi\)
\(752\) 3.50672 6.07381i 0.127877 0.221489i
\(753\) 27.6142 1.00632
\(754\) 0 0
\(755\) 4.88961 0.177951
\(756\) −1.20593 + 2.08873i −0.0438593 + 0.0759665i
\(757\) −25.0223 + 43.3399i −0.909451 + 1.57522i −0.0946237 + 0.995513i \(0.530165\pi\)
−0.814828 + 0.579703i \(0.803169\pi\)
\(758\) −15.8545 27.4609i −0.575863 0.997424i
\(759\) −48.7715 −1.77029
\(760\) −3.47484 6.01859i −0.126046 0.218317i
\(761\) −22.4105 38.8161i −0.812379 1.40708i −0.911195 0.411975i \(-0.864839\pi\)
0.0988165 0.995106i \(-0.468494\pi\)
\(762\) −32.5313 −1.17848
\(763\) −13.2776 22.9975i −0.480682 0.832566i
\(764\) 7.00307 12.1297i 0.253362 0.438836i
\(765\) −1.38051 + 2.39111i −0.0499124 + 0.0864508i
\(766\) −11.7092 −0.423072
\(767\) 0 0
\(768\) −26.6361 −0.961148
\(769\) 19.6817 34.0897i 0.709739 1.22930i −0.255215 0.966884i \(-0.582146\pi\)
0.964954 0.262420i \(-0.0845205\pi\)
\(770\) 11.7941 20.4280i 0.425031 0.736175i
\(771\) 6.47201 + 11.2099i 0.233084 + 0.403713i
\(772\) −11.1528 −0.401399
\(773\) −24.3902 42.2452i −0.877256 1.51945i −0.854340 0.519715i \(-0.826038\pi\)
−0.0229167 0.999737i \(-0.507295\pi\)
\(774\) 1.68379 + 2.91641i 0.0605225 + 0.104828i
\(775\) 5.46410 0.196276
\(776\) 18.6434 + 32.2914i 0.669260 + 1.15919i
\(777\) 36.5420 63.2926i 1.31094 2.27061i
\(778\) −3.43420 + 5.94822i −0.123122 + 0.213254i
\(779\) 8.46410 0.303258
\(780\) 0 0