Properties

Label 845.2.m.g.361.2
Level $845$
Weight $2$
Character 845.361
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.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(1.40994 + 0.109843i\) of defining polynomial
Character \(\chi\) \(=\) 845.361
Dual form 845.2.m.g.316.2

$q$-expansion

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

Character values

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

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.05628 + 0.609843i −0.746903 + 0.431224i −0.824574 0.565755i \(-0.808585\pi\)
0.0776710 + 0.996979i \(0.475252\pi\)
\(3\) −1.16612 2.01978i −0.673262 1.16612i −0.976974 0.213359i \(-0.931559\pi\)
0.303712 0.952764i \(-0.401774\pi\)
\(4\) −0.256182 + 0.443720i −0.128091 + 0.221860i
\(5\) 1.00000i 0.447214i
\(6\) 2.46350 + 1.42231i 1.00572 + 0.580654i
\(7\) −3.11786 1.80010i −1.17844 0.680373i −0.222787 0.974867i \(-0.571516\pi\)
−0.955653 + 0.294494i \(0.904849\pi\)
\(8\) 3.06430i 1.08339i
\(9\) −1.21969 + 2.11256i −0.406562 + 0.704187i
\(10\) −0.609843 1.05628i −0.192849 0.334025i
\(11\) 4.65213 2.68591i 1.40267 0.809832i 0.408004 0.912980i \(-0.366225\pi\)
0.994666 + 0.103149i \(0.0328917\pi\)
\(12\) 1.19496 0.344955
\(13\) 0 0
\(14\) 4.39111 1.17357
\(15\) 2.01978 1.16612i 0.521506 0.301092i
\(16\) 1.35638 + 2.34932i 0.339094 + 0.587329i
\(17\) −0.565928 + 0.980215i −0.137258 + 0.237737i −0.926458 0.376399i \(-0.877162\pi\)
0.789200 + 0.614136i \(0.210495\pi\)
\(18\) 2.97527i 0.701278i
\(19\) 1.96410 + 1.13397i 0.450596 + 0.260152i 0.708082 0.706130i \(-0.249561\pi\)
−0.257486 + 0.966282i \(0.582894\pi\)
\(20\) −0.443720 0.256182i −0.0992188 0.0572840i
\(21\) 8.39654i 1.83228i
\(22\) −3.27597 + 5.67414i −0.698438 + 1.20973i
\(23\) −1.94644 3.37133i −0.405860 0.702970i 0.588561 0.808453i \(-0.299695\pi\)
−0.994421 + 0.105483i \(0.966361\pi\)
\(24\) −6.18922 + 3.57335i −1.26337 + 0.729407i
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −1.30752 −0.251632
\(28\) 1.59748 0.922305i 0.301895 0.174299i
\(29\) 0.0123639 + 0.0214150i 0.00229593 + 0.00397666i 0.867171 0.498010i \(-0.165936\pi\)
−0.864875 + 0.501987i \(0.832603\pi\)
\(30\) −1.42231 + 2.46350i −0.259676 + 0.449772i
\(31\) 5.46410i 0.981382i −0.871334 0.490691i \(-0.836744\pi\)
0.871334 0.490691i \(-0.163256\pi\)
\(32\) 2.44209 + 1.40994i 0.431705 + 0.249245i
\(33\) −10.8499 6.26420i −1.88873 1.09046i
\(34\) 1.38051i 0.236755i
\(35\) 1.80010 3.11786i 0.304272 0.527015i
\(36\) −0.624924 1.08240i −0.104154 0.180400i
\(37\) −7.53794 + 4.35203i −1.23923 + 0.715470i −0.968937 0.247309i \(-0.920454\pi\)
−0.270293 + 0.962778i \(0.587121\pi\)
\(38\) −2.76619 −0.448735
\(39\) 0 0
\(40\) 3.06430 0.484508
\(41\) −3.23205 + 1.86603i −0.504762 + 0.291424i −0.730678 0.682723i \(-0.760796\pi\)
0.225916 + 0.974147i \(0.427462\pi\)
\(42\) −5.12058 8.86910i −0.790122 1.36853i
\(43\) −0.565928 + 0.980215i −0.0863031 + 0.149481i −0.905946 0.423394i \(-0.860839\pi\)
0.819643 + 0.572875i \(0.194172\pi\)
\(44\) 2.75232i 0.414929i
\(45\) −2.11256 1.21969i −0.314922 0.181820i
\(46\) 4.11196 + 2.37404i 0.606276 + 0.350034i
\(47\) 2.58535i 0.377113i 0.982062 + 0.188556i \(0.0603808\pi\)
−0.982062 + 0.188556i \(0.939619\pi\)
\(48\) 3.16341 5.47918i 0.456598 0.790852i
\(49\) 2.98070 + 5.16273i 0.425815 + 0.737533i
\(50\) 1.05628 0.609843i 0.149381 0.0862449i
\(51\) 2.63977 0.369641
\(52\) 0 0
\(53\) −4.43937 −0.609795 −0.304897 0.952385i \(-0.598622\pi\)
−0.304897 + 0.952385i \(0.598622\pi\)
\(54\) 1.38111 0.797382i 0.187945 0.108510i
\(55\) 2.68591 + 4.65213i 0.362168 + 0.627293i
\(56\) −5.51603 + 9.55405i −0.737111 + 1.27671i
\(57\) 5.28942i 0.700600i
\(58\) −0.0261196 0.0150801i −0.00342967 0.00198012i
\(59\) 0.148458 + 0.0857123i 0.0193276 + 0.0111588i 0.509633 0.860392i \(-0.329781\pi\)
−0.490305 + 0.871551i \(0.663115\pi\)
\(60\) 1.19496i 0.154269i
\(61\) −1.68012 + 2.91005i −0.215117 + 0.372594i −0.953309 0.301997i \(-0.902347\pi\)
0.738192 + 0.674591i \(0.235680\pi\)
\(62\) 3.33225 + 5.77162i 0.423196 + 0.732997i
\(63\) 7.60563 4.39111i 0.958219 0.553228i
\(64\) −8.86488 −1.10811
\(65\) 0 0
\(66\) 15.2807 1.88093
\(67\) −5.54239 + 3.19990i −0.677111 + 0.390930i −0.798766 0.601642i \(-0.794513\pi\)
0.121655 + 0.992572i \(0.461180\pi\)
\(68\) −0.289961 0.502227i −0.0351629 0.0609040i
\(69\) −4.53957 + 7.86276i −0.546500 + 0.946566i
\(70\) 4.39111i 0.524838i
\(71\) −9.35076 5.39866i −1.10973 0.640703i −0.170971 0.985276i \(-0.554691\pi\)
−0.938760 + 0.344573i \(0.888024\pi\)
\(72\) 6.47351 + 3.73748i 0.762911 + 0.440467i
\(73\) 4.70308i 0.550454i −0.961379 0.275227i \(-0.911247\pi\)
0.961379 0.275227i \(-0.0887531\pi\)
\(74\) 5.30812 9.19393i 0.617056 1.06877i
\(75\) 1.16612 + 2.01978i 0.134652 + 0.233225i
\(76\) −1.00633 + 0.581008i −0.115435 + 0.0666462i
\(77\) −19.3396 −2.20395
\(78\) 0 0
\(79\) −11.9826 −1.34815 −0.674075 0.738663i \(-0.735457\pi\)
−0.674075 + 0.738663i \(0.735457\pi\)
\(80\) −2.34932 + 1.35638i −0.262661 + 0.151648i
\(81\) 5.18379 + 8.97859i 0.575976 + 0.997621i
\(82\) 2.27597 3.94209i 0.251338 0.435331i
\(83\) 12.1286i 1.33129i 0.746270 + 0.665643i \(0.231843\pi\)
−0.746270 + 0.665643i \(0.768157\pi\)
\(84\) −3.72572 2.15104i −0.406509 0.234698i
\(85\) −0.980215 0.565928i −0.106319 0.0613835i
\(86\) 1.38051i 0.148864i
\(87\) 0.0288357 0.0499450i 0.00309152 0.00535466i
\(88\) −8.23042 14.2555i −0.877366 1.51964i
\(89\) −13.9898 + 8.07702i −1.48292 + 0.856162i −0.999812 0.0194001i \(-0.993824\pi\)
−0.483105 + 0.875562i \(0.660491\pi\)
\(90\) 2.97527 0.313621
\(91\) 0 0
\(92\) 1.99457 0.207948
\(93\) −11.0363 + 6.37182i −1.14441 + 0.660727i
\(94\) −1.57666 2.73086i −0.162620 0.281666i
\(95\) −1.13397 + 1.96410i −0.116343 + 0.201513i
\(96\) 6.57666i 0.671228i
\(97\) 10.5379 + 6.08408i 1.06997 + 0.617745i 0.928172 0.372151i \(-0.121380\pi\)
0.141794 + 0.989896i \(0.454713\pi\)
\(98\) −6.29692 3.63553i −0.636085 0.367244i
\(99\) 13.1039i 1.31699i
\(100\) 0.256182 0.443720i 0.0256182 0.0443720i
\(101\) −2.02721 3.51122i −0.201714 0.349380i 0.747366 0.664412i \(-0.231318\pi\)
−0.949081 + 0.315032i \(0.897985\pi\)
\(102\) −2.78833 + 1.60984i −0.276086 + 0.159398i
\(103\) 17.9035 1.76408 0.882041 0.471173i \(-0.156169\pi\)
0.882041 + 0.471173i \(0.156169\pi\)
\(104\) 0 0
\(105\) −8.39654 −0.819419
\(106\) 4.68922 2.70732i 0.455457 0.262958i
\(107\) 4.56593 + 7.90842i 0.441405 + 0.764536i 0.997794 0.0663862i \(-0.0211469\pi\)
−0.556389 + 0.830922i \(0.687814\pi\)
\(108\) 0.334963 0.580172i 0.0322318 0.0558271i
\(109\) 7.37605i 0.706498i −0.935529 0.353249i \(-0.885077\pi\)
0.935529 0.353249i \(-0.114923\pi\)
\(110\) −5.67414 3.27597i −0.541008 0.312351i
\(111\) 17.5803 + 10.1500i 1.66865 + 0.963396i
\(112\) 9.76645i 0.922843i
\(113\) −3.53794 + 6.12789i −0.332821 + 0.576463i −0.983064 0.183263i \(-0.941334\pi\)
0.650243 + 0.759727i \(0.274667\pi\)
\(114\) 3.22572 + 5.58710i 0.302116 + 0.523280i
\(115\) 3.37133 1.94644i 0.314378 0.181506i
\(116\) −0.0126697 −0.00117635
\(117\) 0 0
\(118\) −0.209084 −0.0192478
\(119\) 3.52897 2.03745i 0.323500 0.186773i
\(120\) −3.57335 6.18922i −0.326201 0.564996i
\(121\) 8.92820 15.4641i 0.811655 1.40583i
\(122\) 4.09843i 0.371055i
\(123\) 7.53794 + 4.35203i 0.679673 + 0.392409i
\(124\) 2.42453 + 1.39980i 0.217729 + 0.125706i
\(125\) 1.00000i 0.0894427i
\(126\) −5.35578 + 9.27648i −0.477131 + 0.826415i
\(127\) −5.71806 9.90396i −0.507395 0.878835i −0.999963 0.00856072i \(-0.997275\pi\)
0.492568 0.870274i \(-0.336058\pi\)
\(128\) 4.47962 2.58631i 0.395946 0.228600i
\(129\) 2.63977 0.232418
\(130\) 0 0
\(131\) −10.5680 −0.923328 −0.461664 0.887055i \(-0.652747\pi\)
−0.461664 + 0.887055i \(0.652747\pi\)
\(132\) 5.55910 3.20955i 0.483858 0.279355i
\(133\) −4.08253 7.07115i −0.354000 0.613146i
\(134\) 3.90288 6.75998i 0.337157 0.583974i
\(135\) 1.30752i 0.112533i
\(136\) 3.00367 + 1.73417i 0.257563 + 0.148704i
\(137\) −3.27940 1.89336i −0.280178 0.161761i 0.353326 0.935500i \(-0.385051\pi\)
−0.633504 + 0.773739i \(0.718384\pi\)
\(138\) 11.0737i 0.942656i
\(139\) −1.00693 + 1.74406i −0.0854068 + 0.147929i −0.905564 0.424209i \(-0.860552\pi\)
0.820158 + 0.572138i \(0.193886\pi\)
\(140\) 0.922305 + 1.59748i 0.0779490 + 0.135012i
\(141\) 5.22186 3.01484i 0.439760 0.253895i
\(142\) 13.1694 1.10515
\(143\) 0 0
\(144\) −6.61742 −0.551452
\(145\) −0.0214150 + 0.0123639i −0.00177842 + 0.00102677i
\(146\) 2.86814 + 4.96777i 0.237369 + 0.411136i
\(147\) 6.95174 12.0408i 0.573370 0.993105i
\(148\) 4.45965i 0.366581i
\(149\) −4.77855 2.75890i −0.391474 0.226018i 0.291324 0.956624i \(-0.405904\pi\)
−0.682799 + 0.730607i \(0.739237\pi\)
\(150\) −2.46350 1.42231i −0.201144 0.116131i
\(151\) 4.88961i 0.397911i −0.980009 0.198956i \(-0.936245\pi\)
0.980009 0.198956i \(-0.0637549\pi\)
\(152\) 3.47484 6.01859i 0.281846 0.488172i
\(153\) −1.38051 2.39111i −0.111608 0.193310i
\(154\) 20.4280 11.7941i 1.64614 0.950397i
\(155\) 5.46410 0.438887
\(156\) 0 0
\(157\) 10.0405 0.801323 0.400661 0.916226i \(-0.368780\pi\)
0.400661 + 0.916226i \(0.368780\pi\)
\(158\) 12.6570 7.30752i 1.00694 0.581355i
\(159\) 5.17686 + 8.96658i 0.410551 + 0.711096i
\(160\) −1.40994 + 2.44209i −0.111466 + 0.193064i
\(161\) 14.0151i 1.10454i
\(162\) −10.9511 6.32260i −0.860397 0.496750i
\(163\) −5.87273 3.39062i −0.459988 0.265574i 0.252051 0.967714i \(-0.418895\pi\)
−0.712039 + 0.702140i \(0.752228\pi\)
\(164\) 1.91217i 0.149315i
\(165\) 6.26420 10.8499i 0.487667 0.844664i
\(166\) −7.39654 12.8112i −0.574083 0.994341i
\(167\) 9.08444 5.24490i 0.702975 0.405863i −0.105479 0.994421i \(-0.533638\pi\)
0.808455 + 0.588559i \(0.200304\pi\)
\(168\) 25.7295 1.98507
\(169\) 0 0
\(170\) 1.38051 0.105880
\(171\) −4.79118 + 2.76619i −0.366391 + 0.211536i
\(172\) −0.289961 0.502227i −0.0221093 0.0382944i
\(173\) −2.22923 + 3.86113i −0.169485 + 0.293557i −0.938239 0.345988i \(-0.887544\pi\)
0.768754 + 0.639545i \(0.220877\pi\)
\(174\) 0.0703412i 0.00533255i
\(175\) 3.11786 + 1.80010i 0.235688 + 0.136075i
\(176\) 12.6201 + 7.28621i 0.951275 + 0.549219i
\(177\) 0.399804i 0.0300511i
\(178\) 9.85143 17.0632i 0.738396 1.27894i
\(179\) 9.31564 + 16.1352i 0.696284 + 1.20600i 0.969746 + 0.244116i \(0.0784979\pi\)
−0.273462 + 0.961883i \(0.588169\pi\)
\(180\) 1.08240 0.624924i 0.0806773 0.0465791i
\(181\) −18.0900 −1.34462 −0.672310 0.740270i \(-0.734698\pi\)
−0.672310 + 0.740270i \(0.734698\pi\)
\(182\) 0 0
\(183\) 7.83690 0.579320
\(184\) −10.3307 + 5.96446i −0.761593 + 0.439706i
\(185\) −4.35203 7.53794i −0.319968 0.554200i
\(186\) 7.77162 13.4608i 0.569843 0.986997i
\(187\) 6.08012i 0.444622i
\(188\) −1.14717 0.662321i −0.0836662 0.0483047i
\(189\) 4.07666 + 2.35366i 0.296533 + 0.171204i
\(190\) 2.76619i 0.200680i
\(191\) −13.6682 + 23.6740i −0.988994 + 1.71299i −0.366361 + 0.930473i \(0.619397\pi\)
−0.622632 + 0.782515i \(0.713937\pi\)
\(192\) 10.3375 + 17.9052i 0.746048 + 1.29219i
\(193\) 18.8511 10.8837i 1.35693 0.783425i 0.367723 0.929935i \(-0.380137\pi\)
0.989209 + 0.146510i \(0.0468041\pi\)
\(194\) −14.8413 −1.06555
\(195\) 0 0
\(196\) −3.05441 −0.218172
\(197\) 1.46940 0.848360i 0.104691 0.0604432i −0.446741 0.894664i \(-0.647415\pi\)
0.551431 + 0.834220i \(0.314082\pi\)
\(198\) −7.99131 13.8413i −0.567917 0.983662i
\(199\) 12.6627 21.9325i 0.897637 1.55475i 0.0671309 0.997744i \(-0.478615\pi\)
0.830506 0.557009i \(-0.188051\pi\)
\(200\) 3.06430i 0.216679i
\(201\) 12.9262 + 7.46296i 0.911746 + 0.526397i
\(202\) 4.28259 + 2.47256i 0.301322 + 0.173968i
\(203\) 0.0890252i 0.00624834i
\(204\) −0.676260 + 1.17132i −0.0473477 + 0.0820086i
\(205\) −1.86603 3.23205i −0.130329 0.225736i
\(206\) −18.9111 + 10.9183i −1.31760 + 0.760715i
\(207\) 9.49617 0.660030
\(208\) 0 0
\(209\) 12.1830 0.842716
\(210\) 8.86910 5.12058i 0.612026 0.353353i
\(211\) 0.167753 + 0.290558i 0.0115486 + 0.0200028i 0.871742 0.489965i \(-0.162991\pi\)
−0.860193 + 0.509968i \(0.829657\pi\)
\(212\) 1.13729 1.96984i 0.0781092 0.135289i
\(213\) 25.1820i 1.72544i
\(214\) −9.64579 5.56900i −0.659373 0.380689i
\(215\) −0.980215 0.565928i −0.0668501 0.0385959i
\(216\) 4.00663i 0.272616i
\(217\) −9.83592 + 17.0363i −0.667706 + 1.15650i
\(218\) 4.49824 + 7.79118i 0.304659 + 0.527685i
\(219\) −9.49922 + 5.48438i −0.641898 + 0.370600i
\(220\) −2.75232 −0.185562
\(221\) 0 0
\(222\) −24.7597 −1.66176
\(223\) 10.6493 6.14838i 0.713130 0.411726i −0.0990887 0.995079i \(-0.531593\pi\)
0.812219 + 0.583353i \(0.198259\pi\)
\(224\) −5.07606 8.79200i −0.339159 0.587440i
\(225\) 1.21969 2.11256i 0.0813125 0.140837i
\(226\) 8.63036i 0.574083i
\(227\) −6.60974 3.81613i −0.438704 0.253286i 0.264344 0.964428i \(-0.414845\pi\)
−0.703048 + 0.711143i \(0.748178\pi\)
\(228\) 2.34702 + 1.35505i 0.155435 + 0.0897406i
\(229\) 14.4008i 0.951631i −0.879545 0.475815i \(-0.842153\pi\)
0.879545 0.475815i \(-0.157847\pi\)
\(230\) −2.37404 + 4.11196i −0.156540 + 0.271135i
\(231\) 22.5523 + 39.0618i 1.48384 + 2.57008i
\(232\) 0.0656218 0.0378868i 0.00430828 0.00248739i
\(233\) −9.49617 −0.622115 −0.311057 0.950391i \(-0.600683\pi\)
−0.311057 + 0.950391i \(0.600683\pi\)
\(234\) 0 0
\(235\) −2.58535 −0.168650
\(236\) −0.0760645 + 0.0439159i −0.00495138 + 0.00285868i
\(237\) 13.9732 + 24.2023i 0.907657 + 1.57211i
\(238\) −2.48505 + 4.30423i −0.161082 + 0.279002i
\(239\) 19.9143i 1.28815i 0.764962 + 0.644076i \(0.222758\pi\)
−0.764962 + 0.644076i \(0.777242\pi\)
\(240\) 5.47918 + 3.16341i 0.353680 + 0.204197i
\(241\) −20.1493 11.6332i −1.29793 0.749360i −0.317883 0.948130i \(-0.602972\pi\)
−0.980046 + 0.198770i \(0.936305\pi\)
\(242\) 21.7792i 1.40002i
\(243\) 10.1286 17.5432i 0.649750 1.12540i
\(244\) −0.860832 1.49100i −0.0551091 0.0954518i
\(245\) −5.16273 + 2.98070i −0.329835 + 0.190430i
\(246\) −10.6162 −0.676866
\(247\) 0 0
\(248\) −16.7436 −1.06322
\(249\) 24.4972 14.1434i 1.55244 0.896304i
\(250\) 0.609843 + 1.05628i 0.0385699 + 0.0668050i
\(251\) 5.92008 10.2539i 0.373672 0.647219i −0.616455 0.787390i \(-0.711432\pi\)
0.990127 + 0.140171i \(0.0447652\pi\)
\(252\) 4.49969i 0.283454i
\(253\) −18.1101 10.4559i −1.13858 0.657357i
\(254\) 12.0797 + 6.97424i 0.757950 + 0.437603i
\(255\) 2.63977i 0.165309i
\(256\) 5.71040 9.89070i 0.356900 0.618169i
\(257\) −2.77501 4.80646i −0.173100 0.299819i 0.766402 0.642361i \(-0.222045\pi\)
−0.939502 + 0.342543i \(0.888712\pi\)
\(258\) −2.78833 + 1.60984i −0.173594 + 0.100224i
\(259\) 31.3363 1.94714
\(260\) 0 0
\(261\) −0.0603205 −0.00373375
\(262\) 11.1627 6.44481i 0.689636 0.398161i
\(263\) −3.42983 5.94065i −0.211493 0.366316i 0.740689 0.671848i \(-0.234499\pi\)
−0.952182 + 0.305532i \(0.901166\pi\)
\(264\) −19.1954 + 33.2474i −1.18139 + 2.04623i
\(265\) 4.43937i 0.272709i
\(266\) 8.62459 + 4.97941i 0.528807 + 0.305307i
\(267\) 32.6277 + 18.8376i 1.99678 + 1.15284i
\(268\) 3.27903i 0.200299i
\(269\) 0.710994 1.23148i 0.0433501 0.0750845i −0.843536 0.537072i \(-0.819530\pi\)
0.886886 + 0.461988i \(0.152864\pi\)
\(270\) 0.797382 + 1.38111i 0.0485271 + 0.0840514i
\(271\) −8.63381 + 4.98473i −0.524467 + 0.302801i −0.738760 0.673968i \(-0.764588\pi\)
0.214294 + 0.976769i \(0.431255\pi\)
\(272\) −3.07045 −0.186173
\(273\) 0 0
\(274\) 4.61862 0.279021
\(275\) −4.65213 + 2.68591i −0.280534 + 0.161966i
\(276\) −2.32591 4.02860i −0.140003 0.242493i
\(277\) −8.76187 + 15.1760i −0.526449 + 0.911837i 0.473076 + 0.881022i \(0.343144\pi\)
−0.999525 + 0.0308154i \(0.990190\pi\)
\(278\) 2.45628i 0.147318i
\(279\) 11.5432 + 6.66449i 0.691076 + 0.398993i
\(280\) −9.55405 5.51603i −0.570964 0.329646i
\(281\) 10.7352i 0.640406i 0.947349 + 0.320203i \(0.103751\pi\)
−0.947349 + 0.320203i \(0.896249\pi\)
\(282\) −3.67716 + 6.36903i −0.218972 + 0.379270i
\(283\) 0.659192 + 1.14175i 0.0391849 + 0.0678702i 0.884953 0.465681i \(-0.154191\pi\)
−0.845768 + 0.533551i \(0.820857\pi\)
\(284\) 4.79099 2.76608i 0.284293 0.164137i
\(285\) 5.28942 0.313318
\(286\) 0 0
\(287\) 13.4361 0.793109
\(288\) −5.95717 + 3.43937i −0.351030 + 0.202667i
\(289\) 7.85945 + 13.6130i 0.462321 + 0.800763i
\(290\) 0.0150801 0.0261196i 0.000885536 0.00153379i
\(291\) 28.3792i 1.66362i
\(292\) 2.08685 + 1.20485i 0.122124 + 0.0705082i
\(293\) −16.2316 9.37133i −0.948261 0.547479i −0.0557207 0.998446i \(-0.517746\pi\)
−0.892540 + 0.450968i \(0.851079\pi\)
\(294\) 16.9579i 0.989004i
\(295\) −0.0857123 + 0.148458i −0.00499036 + 0.00864356i
\(296\) 13.3359 + 23.0985i 0.775134 + 1.34257i
\(297\) −6.08275 + 3.51187i −0.352957 + 0.203780i
\(298\) 6.72998 0.389857
\(299\) 0 0
\(300\) −1.19496 −0.0689910
\(301\) 3.52897 2.03745i 0.203406 0.117437i
\(302\) 2.98190 + 5.16480i 0.171589 + 0.297201i
\(303\) −4.72794 + 8.18904i −0.271613 + 0.470448i
\(304\) 6.15239i 0.352864i
\(305\) −2.91005 1.68012i −0.166629 0.0962032i
\(306\) 2.91641 + 1.68379i 0.166720 + 0.0962558i
\(307\) 14.3043i 0.816387i 0.912895 + 0.408194i \(0.133841\pi\)
−0.912895 + 0.408194i \(0.866159\pi\)
\(308\) 4.95445 8.58137i 0.282306 0.488969i
\(309\) −20.8777 36.1612i −1.18769 2.05714i
\(310\) −5.77162 + 3.33225i −0.327806 + 0.189259i
\(311\) −2.76102 −0.156563 −0.0782815 0.996931i \(-0.524943\pi\)
−0.0782815 + 0.996931i \(0.524943\pi\)
\(312\) 0 0
\(313\) −16.3858 −0.926179 −0.463090 0.886311i \(-0.653259\pi\)
−0.463090 + 0.886311i \(0.653259\pi\)
\(314\) −10.6056 + 6.12316i −0.598510 + 0.345550i
\(315\) 4.39111 + 7.60563i 0.247411 + 0.428529i
\(316\) 3.06973 5.31693i 0.172686 0.299101i
\(317\) 1.78575i 0.100297i −0.998742 0.0501487i \(-0.984030\pi\)
0.998742 0.0501487i \(-0.0159695\pi\)
\(318\) −10.9364 6.31414i −0.613284 0.354080i
\(319\) 0.115037 + 0.0664168i 0.00644085 + 0.00371863i
\(320\) 8.86488i 0.495562i
\(321\) 10.6489 18.4444i 0.594362 1.02946i
\(322\) −8.54702 14.8039i −0.476307 0.824987i
\(323\) −2.22308 + 1.28349i −0.123695 + 0.0714156i
\(324\) −5.31197 −0.295110
\(325\) 0 0
\(326\) 8.27099 0.458088
\(327\) −14.8980 + 8.60139i −0.823864 + 0.475658i
\(328\) 5.71806 + 9.90396i 0.315727 + 0.546855i
\(329\) 4.65389 8.06077i 0.256577 0.444405i
\(330\) 15.2807i 0.841176i
\(331\) 6.25652 + 3.61220i 0.343889 + 0.198545i 0.661991 0.749512i \(-0.269712\pi\)
−0.318101 + 0.948057i \(0.603045\pi\)
\(332\) −5.38170 3.10713i −0.295359 0.170526i
\(333\) 21.2325i 1.16353i
\(334\) −6.39714 + 11.0802i −0.350036 + 0.606280i
\(335\) −3.19990 5.54239i −0.174829 0.302813i
\(336\) −19.7261 + 11.3889i −1.07615 + 0.621315i
\(337\) 4.36219 0.237624 0.118812 0.992917i \(-0.462091\pi\)
0.118812 + 0.992917i \(0.462091\pi\)
\(338\) 0 0
\(339\) 16.5027 0.896303
\(340\) 0.502227 0.289961i 0.0272371 0.0157253i
\(341\) −14.6761 25.4197i −0.794754 1.37655i
\(342\) 3.37388 5.84374i 0.182439 0.315993i
\(343\) 3.73913i 0.201894i
\(344\) 3.00367 + 1.73417i 0.161947 + 0.0935002i
\(345\) −7.86276 4.53957i −0.423317 0.244402i
\(346\) 5.43792i 0.292344i
\(347\) 13.3536 23.1291i 0.716858 1.24163i −0.245381 0.969427i \(-0.578913\pi\)
0.962239 0.272207i \(-0.0877537\pi\)
\(348\) 0.0147744 + 0.0255900i 0.000791991 + 0.00137177i
\(349\) 20.4131 11.7855i 1.09269 0.630865i 0.158399 0.987375i \(-0.449367\pi\)
0.934292 + 0.356510i \(0.116033\pi\)
\(350\) −4.39111 −0.234715
\(351\) 0 0
\(352\) 15.1479 0.807385
\(353\) −4.96862 + 2.86863i −0.264453 + 0.152682i −0.626364 0.779531i \(-0.715458\pi\)
0.361911 + 0.932213i \(0.382124\pi\)
\(354\) 0.243818 + 0.422305i 0.0129588 + 0.0224453i
\(355\) 5.39866 9.35076i 0.286531 0.496287i
\(356\) 8.27675i 0.438667i
\(357\) −8.23042 4.75184i −0.435600 0.251494i
\(358\) −19.6799 11.3622i −1.04011 0.600509i
\(359\) 24.7583i 1.30669i −0.757059 0.653347i \(-0.773364\pi\)
0.757059 0.653347i \(-0.226636\pi\)
\(360\) −3.73748 + 6.47351i −0.196983 + 0.341184i
\(361\) −6.92820 12.0000i −0.364642 0.631579i
\(362\) 19.1081 11.0321i 1.00430 0.579833i
\(363\) −41.6455 −2.18582
\(364\) 0 0
\(365\) 4.70308 0.246171
\(366\) −8.27796 + 4.77928i −0.432696 + 0.249817i
\(367\) −13.0268 22.5630i −0.679992 1.17778i −0.974983 0.222280i \(-0.928650\pi\)
0.294991 0.955500i \(-0.404683\pi\)
\(368\) 5.28021 9.14558i 0.275250 0.476747i
\(369\) 9.10387i 0.473928i
\(370\) 9.19393 + 5.30812i 0.477969 + 0.275956i
\(371\) 13.8413 + 7.99131i 0.718607 + 0.414888i
\(372\) 6.52938i 0.338532i
\(373\) −6.60224 + 11.4354i −0.341851 + 0.592103i −0.984776 0.173826i \(-0.944387\pi\)
0.642926 + 0.765929i \(0.277720\pi\)
\(374\) −3.70792 6.42231i −0.191732 0.332089i
\(375\) −2.01978 + 1.16612i −0.104301 + 0.0602183i
\(376\) 7.92229 0.408561
\(377\) 0 0
\(378\) −5.74146 −0.295309
\(379\) −22.5147 + 12.9989i −1.15650 + 0.667707i −0.950463 0.310837i \(-0.899391\pi\)
−0.206039 + 0.978544i \(0.566057\pi\)
\(380\) −0.581008 1.00633i −0.0298051 0.0516239i
\(381\) −13.3359 + 23.0985i −0.683220 + 1.18337i
\(382\) 33.3418i 1.70591i
\(383\) −8.31401 4.80010i −0.424826 0.245274i 0.272314 0.962208i \(-0.412211\pi\)
−0.697140 + 0.716935i \(0.745544\pi\)
\(384\) −10.4476 6.03191i −0.533151 0.307815i
\(385\) 19.3396i 0.985637i
\(386\) −13.2747 + 22.9924i −0.675664 + 1.17028i
\(387\) −1.38051 2.39111i −0.0701752 0.121547i
\(388\) −5.39926 + 3.11726i −0.274106 + 0.158255i
\(389\) −5.63129 −0.285518 −0.142759 0.989758i \(-0.545597\pi\)
−0.142759 + 0.989758i \(0.545597\pi\)
\(390\) 0 0
\(391\) 4.40617 0.222829
\(392\) 15.8201 9.13376i 0.799038 0.461325i
\(393\) 12.3236 + 21.3450i 0.621641 + 1.07671i
\(394\) −1.03473 + 1.79221i −0.0521291 + 0.0902903i
\(395\) 11.9826i 0.602911i
\(396\) −5.81445 3.35697i −0.292187 0.168694i
\(397\) 14.5196 + 8.38291i 0.728719 + 0.420726i 0.817953 0.575285i \(-0.195109\pi\)
−0.0892344 + 0.996011i \(0.528442\pi\)
\(398\) 30.8891i 1.54833i
\(399\) −9.52147 + 16.4917i −0.476670 + 0.825616i
\(400\) −1.35638 2.34932i −0.0678189 0.117466i
\(401\) −12.0187 + 6.93902i −0.600187 + 0.346518i −0.769115 0.639110i \(-0.779303\pi\)
0.168928 + 0.985628i \(0.445969\pi\)
\(402\) −18.2050 −0.907980
\(403\) 0 0
\(404\) 2.07733 0.103351
\(405\) −8.97859 + 5.18379i −0.446149 + 0.257585i
\(406\) 0.0542914 + 0.0940355i 0.00269444 + 0.00466690i
\(407\) −23.3783 + 40.4924i −1.15882 + 2.00713i
\(408\) 8.08903i 0.400466i
\(409\) 25.4829 + 14.7125i 1.26005 + 0.727489i 0.973083 0.230453i \(-0.0740208\pi\)
0.286964 + 0.957941i \(0.407354\pi\)
\(410\) 3.94209 + 2.27597i 0.194686 + 0.112402i
\(411\) 8.83157i 0.435629i
\(412\) −4.58655 + 7.94413i −0.225963 + 0.391379i
\(413\) −0.308581 0.534478i −0.0151843 0.0262999i
\(414\) −10.0306 + 5.79118i −0.492978 + 0.284621i
\(415\) −12.1286 −0.595369
\(416\) 0 0
\(417\) 4.69683 0.230005
\(418\) −12.8687 + 7.42973i −0.629427 + 0.363400i
\(419\) −3.48397 6.03440i −0.170203 0.294800i 0.768288 0.640104i \(-0.221109\pi\)
−0.938491 + 0.345305i \(0.887776\pi\)
\(420\) 2.15104 3.72572i 0.104960 0.181796i
\(421\) 7.12125i 0.347069i −0.984828 0.173534i \(-0.944481\pi\)
0.984828 0.173534i \(-0.0555188\pi\)
\(422\) −0.354389 0.204607i −0.0172514 0.00996010i
\(423\) −5.46171 3.15332i −0.265558 0.153320i
\(424\) 13.6036i 0.660647i
\(425\) 0.565928 0.980215i 0.0274515 0.0475474i
\(426\) −15.3571 26.5993i −0.744054 1.28874i
\(427\) 10.4767 6.04875i 0.507005 0.292720i
\(428\) −4.67883 −0.226160
\(429\) 0 0
\(430\) 1.38051 0.0665740
\(431\) −26.1664 + 15.1072i −1.26039 + 0.727687i −0.973150 0.230171i \(-0.926071\pi\)
−0.287241 + 0.957858i \(0.592738\pi\)
\(432\) −1.77349 3.07177i −0.0853270 0.147791i
\(433\) 0.600065 1.03934i 0.0288373 0.0499476i −0.851247 0.524766i \(-0.824153\pi\)
0.880084 + 0.474818i \(0.157486\pi\)
\(434\) 23.9935i 1.15172i
\(435\) 0.0499450 + 0.0288357i 0.00239468 + 0.00138257i
\(436\) 3.27290 + 1.88961i 0.156744 + 0.0904960i
\(437\) 8.82884i 0.422341i
\(438\) 6.68922 11.5861i 0.319623 0.553604i
\(439\) −8.27705 14.3363i −0.395042 0.684233i 0.598064 0.801448i \(-0.295937\pi\)
−0.993107 + 0.117215i \(0.962603\pi\)
\(440\) 14.2555 8.23042i 0.679605 0.392370i
\(441\) −14.5421 −0.692481
\(442\) 0 0
\(443\) 4.55949 0.216628 0.108314 0.994117i \(-0.465455\pi\)
0.108314 + 0.994117i \(0.465455\pi\)
\(444\) −9.00753 + 5.20050i −0.427478 + 0.246805i
\(445\) −8.07702 13.9898i −0.382887 0.663180i
\(446\) −7.49910 + 12.9888i −0.355093 + 0.615038i
\(447\) 12.8689i 0.608676i
\(448\) 27.6395 + 15.9577i 1.30584 + 0.753929i
\(449\) −11.9963 6.92608i −0.566142 0.326862i 0.189465 0.981887i \(-0.439325\pi\)
−0.755607 + 0.655025i \(0.772658\pi\)
\(450\) 2.97527i 0.140256i
\(451\) −10.0239 + 17.3620i −0.472009 + 0.817544i
\(452\) −1.81271 3.13971i −0.0852628 0.147680i
\(453\) −9.87596 + 5.70189i −0.464013 + 0.267898i
\(454\) 9.30897 0.436892
\(455\) 0 0
\(456\) −16.2083 −0.759025
\(457\) −34.7402 + 20.0573i −1.62508 + 0.938240i −0.639548 + 0.768751i \(0.720878\pi\)
−0.985532 + 0.169489i \(0.945788\pi\)
\(458\) 8.78222 + 15.2113i 0.410366 + 0.710775i
\(459\) 0.739961 1.28165i 0.0345384 0.0598223i
\(460\) 1.99457i 0.0929972i
\(461\) −6.52897 3.76950i −0.304084 0.175563i 0.340192 0.940356i \(-0.389508\pi\)
−0.644276 + 0.764793i \(0.722841\pi\)
\(462\) −47.6432 27.5068i −2.21656 1.27973i
\(463\) 23.3031i 1.08299i 0.840705 + 0.541494i \(0.182141\pi\)
−0.840705 + 0.541494i \(0.817859\pi\)
\(464\) −0.0335403 + 0.0580936i −0.00155707 + 0.00269693i
\(465\) −6.37182 11.0363i −0.295486 0.511797i
\(466\) 10.0306 5.79118i 0.464659 0.268271i
\(467\) 22.6297 1.04718 0.523589 0.851971i \(-0.324593\pi\)
0.523589 + 0.851971i \(0.324593\pi\)
\(468\) 0 0
\(469\) 23.0405 1.06391
\(470\) 2.73086 1.57666i 0.125965 0.0727260i
\(471\) −11.7085 20.2797i −0.539500 0.934441i
\(472\) 0.262648 0.454919i 0.0120893 0.0209394i
\(473\) 6.08012i 0.279564i
\(474\) −29.5192 17.0429i −1.35586 0.782808i
\(475\) −1.96410 1.13397i −0.0901192 0.0520303i
\(476\) 2.08783i 0.0956956i
\(477\) 5.41465 9.37844i 0.247920 0.429409i
\(478\) −12.1446 21.0351i −0.555482 0.962124i
\(479\) 17.8789 10.3224i 0.816910 0.471643i −0.0324399 0.999474i \(-0.510328\pi\)
0.849350 + 0.527831i \(0.176994\pi\)
\(480\) 6.57666 0.300182
\(481\) 0 0
\(482\) 28.3777 1.29257
\(483\) 28.3075 16.3433i 1.28804 0.743648i
\(484\) 4.57449 + 7.92325i 0.207931 + 0.360148i
\(485\) −6.08408 + 10.5379i −0.276264 + 0.478503i
\(486\) 24.7074i 1.12075i
\(487\) 2.62929 + 1.51802i 0.119145 + 0.0687882i 0.558388 0.829580i \(-0.311420\pi\)
−0.439243 + 0.898368i \(0.644753\pi\)
\(488\) 8.91725 + 5.14838i 0.403665 + 0.233056i
\(489\) 15.8155i 0.715203i
\(490\) 3.63553 6.29692i 0.164236 0.284466i
\(491\) 5.33401 + 9.23877i 0.240720 + 0.416940i 0.960920 0.276827i \(-0.0892830\pi\)
−0.720199 + 0.693767i \(0.755950\pi\)
\(492\) −3.86217 + 2.22982i −0.174120 + 0.100528i
\(493\) −0.0279884 −0.00126053
\(494\) 0 0
\(495\) −13.1039 −0.588975
\(496\) 12.8369 7.41139i 0.576394 0.332781i
\(497\) 19.4362 + 33.6646i 0.871835 + 1.51006i
\(498\) −17.2506 + 29.8789i −0.773016 + 1.33890i
\(499\) 33.9143i 1.51821i −0.650966 0.759107i \(-0.725636\pi\)
0.650966 0.759107i \(-0.274364\pi\)
\(500\) 0.443720 + 0.256182i 0.0198438 + 0.0114568i
\(501\) −21.1872 12.2324i −0.946572 0.546504i
\(502\) 14.4413i 0.644546i
\(503\) 6.31380 10.9358i 0.281518 0.487604i −0.690241 0.723580i \(-0.742495\pi\)
0.971759 + 0.235976i \(0.0758286\pi\)
\(504\) −13.4557 23.3059i −0.599363 1.03813i
\(505\) 3.51122 2.02721i 0.156247 0.0902095i
\(506\) 25.5058 1.13387
\(507\) 0 0
\(508\) 5.85945 0.259971
\(509\) 20.9168 12.0763i 0.927120 0.535273i 0.0412201 0.999150i \(-0.486876\pi\)
0.885899 + 0.463877i \(0.153542\pi\)
\(510\) −1.60984 2.78833i −0.0712851 0.123469i
\(511\) −8.46601 + 14.6636i −0.374514 + 0.648678i
\(512\) 24.2750i 1.07281i
\(513\) −2.56810 1.48269i −0.113384 0.0654625i
\(514\) 5.86238 + 3.38465i 0.258578 + 0.149290i
\(515\) 17.9035i 0.788921i
\(516\) −0.676260 + 1.17132i −0.0297707 + 0.0515644i
\(517\) 6.94402 + 12.0274i 0.305398 + 0.528964i
\(518\) −33.0999 + 19.1103i −1.45433 + 0.839656i
\(519\) 10.3982 0.456431
\(520\) 0 0
\(521\) −24.7521 −1.08441 −0.542205 0.840246i \(-0.682410\pi\)
−0.542205 + 0.840246i \(0.682410\pi\)
\(522\) 0.0637154 0.0367861i 0.00278875 0.00161008i
\(523\) −18.5163 32.0712i −0.809662 1.40238i −0.913098 0.407739i \(-0.866317\pi\)
0.103436 0.994636i \(-0.467016\pi\)
\(524\) 2.70732 4.68922i 0.118270 0.204850i
\(525\) 8.39654i 0.366455i
\(526\) 7.24573 + 4.18332i 0.315929 + 0.182402i
\(527\) 5.35600 + 3.09229i 0.233311 + 0.134702i
\(528\) 33.9865i 1.47907i
\(529\) 3.92277 6.79444i 0.170555 0.295410i
\(530\) 2.70732 + 4.68922i 0.117599 + 0.203687i
\(531\) −0.362145 + 0.209084i −0.0157157 + 0.00907348i
\(532\) 4.18348 0.181377
\(533\) 0 0
\(534\) −45.9519 −1.98854
\(535\) −7.90842 + 4.56593i −0.341911 + 0.197402i
\(536\) 9.80545 + 16.9835i 0.423531 + 0.733577i
\(537\) 21.7264 37.6312i 0.937562 1.62391i
\(538\) 1.73438i 0.0747744i
\(539\) 27.7332 + 16.0118i 1.19456 + 0.689677i
\(540\) 0.580172 + 0.334963i 0.0249666 + 0.0144145i
\(541\) 8.38144i 0.360346i −0.983635 0.180173i \(-0.942334\pi\)
0.983635 0.180173i \(-0.0576658\pi\)
\(542\) 6.07981 10.5305i 0.261150 0.452326i
\(543\) 21.0952 + 36.5379i 0.905281 + 1.56799i
\(544\) −2.76409 + 1.59585i −0.118509 + 0.0684215i
\(545\) 7.37605 0.315955
\(546\) 0 0
\(547\) −22.7842 −0.974181 −0.487091 0.873351i \(-0.661942\pi\)
−0.487091 + 0.873351i \(0.661942\pi\)
\(548\) 1.68025 0.970090i 0.0717765 0.0414402i
\(549\) −4.09843 7.09870i −0.174917 0.302965i
\(550\) 3.27597 5.67414i 0.139688 0.241946i
\(551\) 0.0560816i 0.00238915i
\(552\) 24.0938 + 13.9106i 1.02550 + 0.592074i
\(553\) 37.3601 + 21.5699i 1.58871 + 0.917245i
\(554\) 21.3735i 0.908071i
\(555\) −10.1500 + 17.5803i −0.430844 + 0.746244i
\(556\) −0.515915 0.893592i −0.0218797 0.0378967i
\(557\) −24.3810 + 14.0764i −1.03306 + 0.596435i −0.917858 0.396908i \(-0.870083\pi\)
−0.115197 + 0.993343i \(0.536750\pi\)
\(558\) −16.2572 −0.688222
\(559\) 0 0
\(560\) 9.76645 0.412708
\(561\) 12.2805 7.09017i 0.518484 0.299347i
\(562\) −6.54676 11.3393i −0.276159 0.478321i
\(563\) −9.06514 + 15.7013i −0.382050 + 0.661731i −0.991355 0.131206i \(-0.958115\pi\)
0.609305 + 0.792936i \(0.291449\pi\)
\(564\) 3.08939i 0.130087i
\(565\) −6.12789 3.53794i −0.257802 0.148842i
\(566\) −1.39258 0.804007i −0.0585346 0.0337950i
\(567\) 37.3253i 1.56752i
\(568\) −16.5431 + 28.6535i −0.694133 + 1.20227i
\(569\) 20.2992 + 35.1593i 0.850988 + 1.47395i 0.880317 + 0.474385i \(0.157330\pi\)
−0.0293292 + 0.999570i \(0.509337\pi\)
\(570\) −5.58710 + 3.22572i −0.234018 + 0.135110i
\(571\) −24.7159 −1.03433 −0.517164 0.855886i \(-0.673012\pi\)
−0.517164 + 0.855886i \(0.673012\pi\)
\(572\) 0 0
\(573\) 63.7551 2.66341
\(574\) −14.1923 + 8.19393i −0.592375 + 0.342008i
\(575\) 1.94644 + 3.37133i 0.0811720 + 0.140594i
\(576\) 10.8124 18.7276i 0.450516 0.780317i
\(577\) 23.0691i 0.960379i −0.877165 0.480189i \(-0.840568\pi\)
0.877165 0.480189i \(-0.159432\pi\)
\(578\) −16.6036 9.58607i −0.690617 0.398728i
\(579\) −43.9654 25.3834i −1.82714 1.05490i
\(580\) 0.0126697i 0.000526079i
\(581\) 21.8327 37.8153i 0.905771 1.56884i
\(582\) 17.3068 + 29.9763i 0.717392 + 1.24256i
\(583\) −20.6525 + 11.9237i −0.855341 + 0.493831i
\(584\) −14.4116 −0.596358
\(585\) 0 0
\(586\) 22.8602 0.944345
\(587\) 17.6256 10.1762i 0.727487 0.420015i −0.0900152 0.995940i \(-0.528692\pi\)
0.817502 + 0.575926i \(0.195358\pi\)
\(588\) 3.56182 + 6.16925i 0.146887 + 0.254416i
\(589\) 6.19615 10.7321i 0.255308 0.442206i
\(590\) 0.209084i 0.00860786i
\(591\) −3.42701 1.97859i −0.140968 0.0813881i
\(592\) −20.4486 11.8060i −0.840432 0.485223i
\(593\) 10.3834i 0.426395i 0.977009 + 0.213198i \(0.0683878\pi\)
−0.977009 + 0.213198i \(0.931612\pi\)
\(594\) 4.28339 7.41904i 0.175750 0.304407i
\(595\) 2.03745 + 3.52897i 0.0835273 + 0.144674i
\(596\) 2.44836 1.41356i 0.100289 0.0579017i
\(597\) −59.0652 −2.41738
\(598\) 0 0
\(599\) −31.5965 −1.29100 −0.645499 0.763761i \(-0.723351\pi\)
−0.645499 + 0.763761i \(0.723351\pi\)
\(600\) 6.18922 3.57335i 0.252674 0.145881i
\(601\) 21.9423 + 38.0051i 0.895044 + 1.55026i 0.833751 + 0.552141i \(0.186189\pi\)
0.0612928 + 0.998120i \(0.480478\pi\)
\(602\) −2.48505 + 4.30423i −0.101283 + 0.175428i
\(603\) 15.6115i 0.635750i
\(604\) 2.16962 + 1.25263i 0.0882806 + 0.0509688i
\(605\) 15.4641 + 8.92820i 0.628705 + 0.362983i
\(606\) 11.5332i 0.468505i
\(607\) −1.08770 + 1.88395i −0.0441484 + 0.0764673i −0.887255 0.461279i \(-0.847391\pi\)
0.843107 + 0.537746i \(0.180724\pi\)
\(608\) 3.19768 + 5.53854i 0.129683 + 0.224617i
\(609\) −0.179812 + 0.103814i −0.00728634 + 0.00420677i
\(610\) 4.09843 0.165941
\(611\) 0 0
\(612\) 1.41465 0.0571837
\(613\) 12.7843 7.38100i 0.516352 0.298116i −0.219089 0.975705i \(-0.570309\pi\)
0.735441 + 0.677589i \(0.236975\pi\)
\(614\) −8.72336 15.1093i −0.352046 0.609762i
\(615\) −4.35203 + 7.53794i −0.175491 + 0.303959i
\(616\) 59.2622i 2.38774i
\(617\) −17.5779 10.1486i −0.707659 0.408567i 0.102535 0.994729i \(-0.467305\pi\)
−0.810194 + 0.586162i \(0.800638\pi\)
\(618\) 44.1053 + 25.4642i 1.77418 + 1.02432i
\(619\) 9.94207i 0.399605i 0.979836 + 0.199803i \(0.0640301\pi\)
−0.979836 + 0.199803i \(0.935970\pi\)
\(620\) −1.39980 + 2.42453i −0.0562175 + 0.0973716i
\(621\) 2.54500 + 4.40807i 0.102127 + 0.176890i
\(622\) 2.91641 1.68379i 0.116937 0.0675138i
\(623\) 58.1577 2.33004
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 17.3080 9.99276i 0.691766 0.399391i
\(627\) −14.2069 24.6070i −0.567368 0.982711i
\(628\) −2.57221 + 4.45519i −0.102642 + 0.177782i
\(629\) 9.85174i 0.392815i
\(630\) −9.27648 5.35578i −0.369584 0.213379i
\(631\) −0.843006 0.486710i −0.0335596 0.0193756i 0.483126 0.875551i \(-0.339501\pi\)
−0.516686 + 0.856175i \(0.672835\pi\)
\(632\) 36.7183i 1.46058i
\(633\) 0.391243 0.677652i 0.0155505 0.0269342i
\(634\) 1.08903 + 1.88625i 0.0432507 + 0.0749124i
\(635\) 9.90396 5.71806i 0.393027 0.226914i
\(636\) −5.30487 −0.210352
\(637\) 0 0
\(638\) −0.162015 −0.00641425
\(639\) 22.8100 13.1694i 0.902350 0.520972i
\(640\) 2.58631 + 4.47962i 0.102233 + 0.177072i
\(641\) −6.31047 + 10.9301i −0.249249 + 0.431711i −0.963318 0.268364i \(-0.913517\pi\)
0.714069 + 0.700075i \(0.246850\pi\)
\(642\) 25.9766i 1.02521i
\(643\) 8.62599 + 4.98022i 0.340176 + 0.196401i 0.660350 0.750958i \(-0.270408\pi\)
−0.320174 + 0.947359i \(0.603741\pi\)
\(644\) −6.21878 3.59042i −0.245054 0.141482i
\(645\) 2.63977i 0.103941i
\(646\) 1.56546 2.71146i 0.0615923 0.106681i
\(647\) −18.1381 31.4162i −0.713084 1.23510i −0.963694 0.267009i \(-0.913965\pi\)
0.250610 0.968088i \(-0.419369\pi\)
\(648\) 27.5131 15.8847i 1.08081 0.624009i
\(649\) 0.920861 0.0361470
\(650\) 0 0
\(651\) 45.8796 1.79816
\(652\) 3.00898 1.73723i 0.117841 0.0680353i
\(653\) −6.87769 11.9125i −0.269145 0.466172i 0.699497 0.714636i \(-0.253408\pi\)
−0.968641 + 0.248464i \(0.920074\pi\)
\(654\) 10.4910 18.1709i 0.410231 0.710540i
\(655\) 10.5680i 0.412925i
\(656\) −8.76776 5.06207i −0.342324 0.197641i
\(657\) 9.93555 + 5.73629i 0.387623 + 0.223794i
\(658\) 11.3526i 0.442570i
\(659\) 1.29092 2.23593i 0.0502869 0.0870995i −0.839786 0.542917i \(-0.817320\pi\)
0.890073 + 0.455818i \(0.150653\pi\)
\(660\) 3.20955 + 5.55910i 0.124932 + 0.216388i
\(661\) 21.5437 12.4382i 0.837951 0.483791i −0.0186163 0.999827i \(-0.505926\pi\)
0.856567 + 0.516036i \(0.172593\pi\)
\(662\) −8.81151 −0.342469
\(663\) 0 0
\(664\) 37.1656 1.44231
\(665\) 7.07115 4.08253i 0.274207 0.158314i
\(666\) 12.9485 + 22.4274i 0.501743 + 0.869045i
\(667\) 0.0481312 0.0833657i 0.00186365 0.00322793i
\(668\) 5.37460i 0.207949i
\(669\) −24.8368 14.3395i −0.960246 0.554398i
\(670\) 6.75998 + 3.90288i 0.261161 + 0.150781i
\(671\) 18.0506i 0.696834i
\(672\) −11.8386 + 20.5051i −0.456685 + 0.791002i
\(673\) 21.6611 + 37.5181i 0.834974 + 1.44622i 0.894052 + 0.447964i \(0.147851\pi\)
−0.0590774 + 0.998253i \(0.518816\pi\)
\(674\) −4.60770 + 2.66025i −0.177482 + 0.102469i
\(675\) 1.30752 0.0503264
\(676\) 0 0
\(677\) −41.3625 −1.58969 −0.794845 0.606813i \(-0.792448\pi\)
−0.794845 + 0.606813i \(0.792448\pi\)
\(678\) −17.4315 + 10.0641i −0.669451 + 0.386508i
\(679\) −21.9039 37.9386i −0.840594 1.45595i
\(680\) −1.73417 + 3.00367i −0.0665024 + 0.115186i
\(681\) 17.8003i 0.682110i
\(682\) 31.0041 + 17.9002i 1.18721 + 0.685435i
\(683\) −2.27495 1.31344i −0.0870484 0.0502574i 0.455844 0.890060i \(-0.349338\pi\)
−0.542892 + 0.839802i \(0.682671\pi\)
\(684\) 2.83459i 0.108383i
\(685\) 1.89336 3.27940i 0.0723416 0.125299i
\(686\) −2.28028 3.94957i −0.0870617 0.150795i
\(687\) −29.0865 + 16.7931i −1.10972 + 0.640696i
\(688\) −3.07045 −0.117060
\(689\) 0 0
\(690\) 11.0737 0.421569
\(691\) 13.2288 7.63765i 0.503247 0.290550i −0.226806 0.973940i \(-0.572828\pi\)
0.730053 + 0.683390i \(0.239495\pi\)
\(692\) −1.14218 1.97831i −0.0434190 0.0752039i
\(693\) 23.5882 40.8560i 0.896043 1.55199i
\(694\) 32.5744i 1.23651i
\(695\) −1.74406 1.00693i −0.0661558 0.0381951i
\(696\) −0.153046 0.0883613i −0.00580120 0.00334933i
\(697\) 4.22414i 0.160001i
\(698\) −14.3747 + 24.8976i −0.544089 + 0.942390i
\(699\) 11.0737 + 19.1802i 0.418846 + 0.725463i
\(700\) −1.59748 + 0.922305i −0.0603790 + 0.0348599i
\(701\) 48.1947 1.82029 0.910144 0.414292i \(-0.135971\pi\)
0.910144 + 0.414292i \(0.135971\pi\)
\(702\) 0 0
\(703\) −19.7404 −0.744522
\(704\) −41.2406 + 23.8103i −1.55431 + 0.897383i
\(705\) 3.01484 + 5.22186i 0.113546 + 0.196667i
\(706\) 3.49884 6.06016i 0.131680 0.228077i
\(707\) 14.5967i 0.548964i
\(708\) 0.177401 + 0.102423i 0.00666715 + 0.00384928i
\(709\) 33.6624 + 19.4350i 1.26422 + 0.729896i 0.973887 0.227031i \(-0.0729019\pi\)
0.290329 + 0.956927i \(0.406235\pi\)
\(710\) 13.1694i 0.494237i
\(711\) 14.6150 25.3140i 0.548107 0.949349i
\(712\) 24.7504 + 42.8689i 0.927560 + 1.60658i
\(713\) −18.4213 + 10.6355i −0.689882 + 0.398304i
\(714\) 11.5915 0.433801
\(715\) 0 0
\(716\) −9.54600 −0.356751
\(717\) 40.2227 23.2226i 1.50214 0.867263i
\(718\) 15.0987 + 26.1517i 0.563478 + 0.975973i
\(719\) 3.30830 5.73015i 0.123379 0.213698i −0.797719 0.603029i \(-0.793960\pi\)
0.921098 + 0.389331i \(0.127294\pi\)
\(720\) 6.61742i 0.246617i
\(721\) −55.8205 32.2280i −2.07887 1.20023i
\(722\) 14.6362 + 8.45024i 0.544705 + 0.314485i
\(723\) 54.2629i 2.01806i
\(724\) 4.63433 8.02690i 0.172234 0.298317i
\(725\) −0.0123639 0.0214150i −0.000459185 0.000795332i
\(726\) 43.9893 25.3973i 1.63260 0.942581i
\(727\) 18.3735 0.681435 0.340717 0.940166i \(-0.389330\pi\)
0.340717 + 0.940166i \(0.389330\pi\)
\(728\) 0 0
\(729\) −16.1420 −0.597853
\(730\) −4.96777 + 2.86814i −0.183866 + 0.106155i
\(731\) −0.640548 1.10946i −0.0236915 0.0410349i
\(732\) −2.00767 + 3.47739i −0.0742057 + 0.128528i
\(733\) 0.791131i 0.0292211i −0.999893 0.0146105i \(-0.995349\pi\)
0.999893 0.0146105i \(-0.00465084\pi\)
\(734\) 27.5198 + 15.8886i 1.01578 + 0.586458i
\(735\) 12.0408 + 6.95174i 0.444130 + 0.256419i
\(736\) 10.9774i 0.404634i
\(737\) −17.1893 + 29.7727i −0.633175 + 1.09669i
\(738\) 5.55193 + 9.61623i 0.204369 + 0.353978i
\(739\) 27.0073 15.5926i 0.993478 0.573585i 0.0871658 0.996194i \(-0.472219\pi\)
0.906312 + 0.422609i \(0.138886\pi\)
\(740\) 4.45965 0.163940
\(741\) 0 0
\(742\) −19.4938 −0.715639
\(743\) −4.81773 + 2.78152i −0.176745 + 0.102044i −0.585763 0.810483i \(-0.699205\pi\)
0.409017 + 0.912527i \(0.365872\pi\)
\(744\) 19.5251 + 33.8185i 0.715826 + 1.23985i
\(745\) 2.75890 4.77855i 0.101078 0.175073i
\(746\) 16.1053i 0.589658i
\(747\) −25.6224 14.7931i −0.937474 0.541251i
\(748\) −2.69787 1.55762i −0.0986439 0.0569521i
\(749\) 32.8765i 1.20128i
\(750\) 1.42231 2.46350i 0.0519352 0.0899545i
\(751\) −17.6048 30.4925i −0.642410 1.11269i −0.984893 0.173163i \(-0.944601\pi\)
0.342483 0.939524i \(-0.388732\pi\)
\(752\) −6.07381 + 3.50672i −0.221489 + 0.127877i
\(753\) −27.6142 −1.00632
\(754\) 0 0
\(755\) 4.88961 0.177951
\(756\) −2.08873 + 1.20593i −0.0759665 + 0.0438593i
\(757\) −25.0223 43.3399i −0.909451 1.57522i −0.814828 0.579703i \(-0.803169\pi\)
−0.0946237 0.995513i \(-0.530165\pi\)
\(758\) 15.8545 27.4609i 0.575863 0.997424i
\(759\) 48.7715i 1.77029i
\(760\) 6.01859 + 3.47484i 0.218317 + 0.126046i
\(761\) −38.8161 22.4105i −1.40708 0.812379i −0.411975 0.911195i \(-0.635161\pi\)
−0.995106 + 0.0988165i \(0.968494\pi\)
\(762\) 32.5313i 1.17848i
\(763\) −13.2776 + 22.9975i −0.480682 + 0.832566i
\(764\) −7.00307 12.1297i −0.253362 0.438836i
\(765\) 2.39111 1.38051i 0.0864508 0.0499124i
\(766\) 11.7092 0.423072
\(767\) 0 0
\(768\) −26.6361 −0.961148
\(769\) 34.0897 19.6817i 1.22930 0.709739i 0.262420 0.964954i \(-0.415479\pi\)
0.966884 + 0.255215i \(0.0821461\pi\)
\(770\) 11.7941 + 20.4280i 0.425031 + 0.736175i
\(771\) −6.47201 + 11.2099i −0.233084 + 0.403713i
\(772\) 11.1528i 0.401399i
\(773\) 42.2452 + 24.3902i 1.51945 + 0.877256i 0.999737 + 0.0229167i \(0.00729525\pi\)
0.519715 + 0.854340i \(0.326038\pi\)
\(774\) 2.91641 + 1.68379i 0.104828 + 0.0605225i
\(775\) 5.46410i 0.196276i
\(776\) 18.6434 32.2914i 0.669260 1.15919i
\(777\) −36.5420 63.2926i −1.31094 2.27061i
\(778\) 5.94822