Properties

Label 29.3.c.a.12.3
Level 29
Weight 3
Character 29.12
Analytic conductor 0.790
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 29.c (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.790192766645\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 18 x^{6} + 91 x^{4} + 126 x^{2} + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 12.3
Root \(1.35225i\) of defining polynomial
Character \(\chi\) \(=\) 29.12
Dual form 29.3.c.a.17.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.909588 + 0.909588i) q^{2} +(0.442660 + 0.442660i) q^{3} -2.34530i q^{4} +4.16447i q^{5} +0.805276i q^{6} -9.68815 q^{7} +(5.77161 - 5.77161i) q^{8} -8.60810i q^{9} +O(q^{10})\) \(q+(0.909588 + 0.909588i) q^{2} +(0.442660 + 0.442660i) q^{3} -2.34530i q^{4} +4.16447i q^{5} +0.805276i q^{6} -9.68815 q^{7} +(5.77161 - 5.77161i) q^{8} -8.60810i q^{9} +(-3.78796 + 3.78796i) q^{10} +(-0.334930 - 0.334930i) q^{11} +(1.03817 - 1.03817i) q^{12} +12.2282i q^{13} +(-8.81223 - 8.81223i) q^{14} +(-1.84345 + 1.84345i) q^{15} +1.11839 q^{16} +(6.80978 + 6.80978i) q^{17} +(7.82983 - 7.82983i) q^{18} +(14.6673 + 14.6673i) q^{19} +9.76693 q^{20} +(-4.28855 - 4.28855i) q^{21} -0.609296i q^{22} -10.0844 q^{23} +5.10972 q^{24} +7.65715 q^{25} +(-11.1226 + 11.1226i) q^{26} +(7.79440 - 7.79440i) q^{27} +22.7216i q^{28} +(28.1041 - 7.15263i) q^{29} -3.35355 q^{30} +(-37.3099 - 37.3099i) q^{31} +(-22.0692 - 22.0692i) q^{32} -0.296520i q^{33} +12.3882i q^{34} -40.3460i q^{35} -20.1886 q^{36} +(-45.0215 + 45.0215i) q^{37} +26.6824i q^{38} +(-5.41292 + 5.41292i) q^{39} +(24.0357 + 24.0357i) q^{40} +(22.8142 - 22.8142i) q^{41} -7.80164i q^{42} +(-17.5030 - 17.5030i) q^{43} +(-0.785510 + 0.785510i) q^{44} +35.8482 q^{45} +(-9.17268 - 9.17268i) q^{46} +(2.20999 - 2.20999i) q^{47} +(0.495064 + 0.495064i) q^{48} +44.8602 q^{49} +(6.96485 + 6.96485i) q^{50} +6.02883i q^{51} +28.6787 q^{52} +90.1375 q^{53} +14.1794 q^{54} +(1.39481 - 1.39481i) q^{55} +(-55.9162 + 55.9162i) q^{56} +12.9852i q^{57} +(32.0691 + 19.0572i) q^{58} -90.4223 q^{59} +(4.32343 + 4.32343i) q^{60} +(-29.4354 - 29.4354i) q^{61} -67.8734i q^{62} +83.3966i q^{63} -44.6213i q^{64} -50.9239 q^{65} +(0.269711 - 0.269711i) q^{66} -31.5543i q^{67} +(15.9710 - 15.9710i) q^{68} +(-4.46397 - 4.46397i) q^{69} +(36.6983 - 36.6983i) q^{70} +99.8673i q^{71} +(-49.6826 - 49.6826i) q^{72} +(-3.96285 + 3.96285i) q^{73} -81.9020 q^{74} +(3.38951 + 3.38951i) q^{75} +(34.3992 - 34.3992i) q^{76} +(3.24485 + 3.24485i) q^{77} -9.84706 q^{78} +(-40.3117 - 40.3117i) q^{79} +4.65749i q^{80} -70.5724 q^{81} +41.5030 q^{82} +137.714 q^{83} +(-10.0579 + 10.0579i) q^{84} +(-28.3592 + 28.3592i) q^{85} -31.8411i q^{86} +(15.6067 + 9.27437i) q^{87} -3.86616 q^{88} +(83.1506 + 83.1506i) q^{89} +(32.6071 + 32.6071i) q^{90} -118.468i q^{91} +23.6510i q^{92} -33.0312i q^{93} +4.02036 q^{94} +(-61.0816 + 61.0816i) q^{95} -19.5383i q^{96} +(-79.9850 + 79.9850i) q^{97} +(40.8043 + 40.8043i) q^{98} +(-2.88311 + 2.88311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 2q^{3} - 4q^{7} - 42q^{8} + O(q^{10}) \) \( 8q + 2q^{2} - 2q^{3} - 4q^{7} - 42q^{8} + 6q^{10} - 6q^{11} + 54q^{12} - 40q^{14} - 10q^{15} - 32q^{16} + 12q^{17} + 20q^{18} - 16q^{19} + 108q^{20} - 36q^{21} + 168q^{24} + 104q^{25} - 54q^{26} - 98q^{27} + 128q^{29} - 220q^{30} - 10q^{31} - 106q^{32} - 252q^{36} - 84q^{37} - 90q^{39} + 226q^{40} + 20q^{41} - 190q^{43} + 42q^{44} + 292q^{45} + 12q^{46} + 58q^{47} + 354q^{48} - 72q^{49} - 60q^{50} - 144q^{52} + 252q^{53} + 400q^{54} - 74q^{55} - 192q^{56} + 326q^{58} - 40q^{59} - 258q^{60} - 208q^{61} + 36q^{65} - 414q^{66} - 296q^{68} + 120q^{69} + 44q^{70} - 636q^{72} - 188q^{73} - 64q^{74} - 12q^{75} + 592q^{76} + 180q^{77} + 600q^{78} - 382q^{79} - 124q^{81} + 228q^{82} + 280q^{83} - 124q^{84} + 32q^{85} + 34q^{87} + 20q^{88} - 64q^{89} + 128q^{90} - 460q^{94} - 380q^{95} - 44q^{97} - 66q^{98} + 552q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.909588 + 0.909588i 0.454794 + 0.454794i 0.896942 0.442148i \(-0.145783\pi\)
−0.442148 + 0.896942i \(0.645783\pi\)
\(3\) 0.442660 + 0.442660i 0.147553 + 0.147553i 0.777024 0.629471i \(-0.216728\pi\)
−0.629471 + 0.777024i \(0.716728\pi\)
\(4\) 2.34530i 0.586324i
\(5\) 4.16447i 0.832895i 0.909160 + 0.416447i \(0.136725\pi\)
−0.909160 + 0.416447i \(0.863275\pi\)
\(6\) 0.805276i 0.134213i
\(7\) −9.68815 −1.38402 −0.692011 0.721887i \(-0.743275\pi\)
−0.692011 + 0.721887i \(0.743275\pi\)
\(8\) 5.77161 5.77161i 0.721451 0.721451i
\(9\) 8.60810i 0.956456i
\(10\) −3.78796 + 3.78796i −0.378796 + 0.378796i
\(11\) −0.334930 0.334930i −0.0304481 0.0304481i 0.691719 0.722167i \(-0.256854\pi\)
−0.722167 + 0.691719i \(0.756854\pi\)
\(12\) 1.03817 1.03817i 0.0865141 0.0865141i
\(13\) 12.2282i 0.940628i 0.882499 + 0.470314i \(0.155859\pi\)
−0.882499 + 0.470314i \(0.844141\pi\)
\(14\) −8.81223 8.81223i −0.629445 0.629445i
\(15\) −1.84345 + 1.84345i −0.122896 + 0.122896i
\(16\) 1.11839 0.0698991
\(17\) 6.80978 + 6.80978i 0.400575 + 0.400575i 0.878436 0.477861i \(-0.158588\pi\)
−0.477861 + 0.878436i \(0.658588\pi\)
\(18\) 7.82983 7.82983i 0.434991 0.434991i
\(19\) 14.6673 + 14.6673i 0.771963 + 0.771963i 0.978449 0.206486i \(-0.0662029\pi\)
−0.206486 + 0.978449i \(0.566203\pi\)
\(20\) 9.76693 0.488347
\(21\) −4.28855 4.28855i −0.204217 0.204217i
\(22\) 0.609296i 0.0276953i
\(23\) −10.0844 −0.438454 −0.219227 0.975674i \(-0.570353\pi\)
−0.219227 + 0.975674i \(0.570353\pi\)
\(24\) 5.10972 0.212905
\(25\) 7.65715 0.306286
\(26\) −11.1226 + 11.1226i −0.427792 + 0.427792i
\(27\) 7.79440 7.79440i 0.288681 0.288681i
\(28\) 22.7216i 0.811485i
\(29\) 28.1041 7.15263i 0.969107 0.246642i
\(30\) −3.35355 −0.111785
\(31\) −37.3099 37.3099i −1.20355 1.20355i −0.973080 0.230466i \(-0.925975\pi\)
−0.230466 0.973080i \(-0.574025\pi\)
\(32\) −22.0692 22.0692i −0.689661 0.689661i
\(33\) 0.296520i 0.00898545i
\(34\) 12.3882i 0.364359i
\(35\) 40.3460i 1.15274i
\(36\) −20.1886 −0.560794
\(37\) −45.0215 + 45.0215i −1.21680 + 1.21680i −0.248050 + 0.968747i \(0.579790\pi\)
−0.968747 + 0.248050i \(0.920210\pi\)
\(38\) 26.6824i 0.702169i
\(39\) −5.41292 + 5.41292i −0.138793 + 0.138793i
\(40\) 24.0357 + 24.0357i 0.600893 + 0.600893i
\(41\) 22.8142 22.8142i 0.556443 0.556443i −0.371850 0.928293i \(-0.621276\pi\)
0.928293 + 0.371850i \(0.121276\pi\)
\(42\) 7.80164i 0.185753i
\(43\) −17.5030 17.5030i −0.407048 0.407048i 0.473660 0.880708i \(-0.342933\pi\)
−0.880708 + 0.473660i \(0.842933\pi\)
\(44\) −0.785510 + 0.785510i −0.0178525 + 0.0178525i
\(45\) 35.8482 0.796627
\(46\) −9.17268 9.17268i −0.199406 0.199406i
\(47\) 2.20999 2.20999i 0.0470210 0.0470210i −0.683205 0.730226i \(-0.739415\pi\)
0.730226 + 0.683205i \(0.239415\pi\)
\(48\) 0.495064 + 0.495064i 0.0103138 + 0.0103138i
\(49\) 44.8602 0.915514
\(50\) 6.96485 + 6.96485i 0.139297 + 0.139297i
\(51\) 6.02883i 0.118212i
\(52\) 28.6787 0.551513
\(53\) 90.1375 1.70071 0.850354 0.526212i \(-0.176388\pi\)
0.850354 + 0.526212i \(0.176388\pi\)
\(54\) 14.1794 0.262581
\(55\) 1.39481 1.39481i 0.0253601 0.0253601i
\(56\) −55.9162 + 55.9162i −0.998504 + 0.998504i
\(57\) 12.9852i 0.227811i
\(58\) 32.0691 + 19.0572i 0.552916 + 0.328573i
\(59\) −90.4223 −1.53258 −0.766291 0.642494i \(-0.777900\pi\)
−0.766291 + 0.642494i \(0.777900\pi\)
\(60\) 4.32343 + 4.32343i 0.0720572 + 0.0720572i
\(61\) −29.4354 29.4354i −0.482548 0.482548i 0.423397 0.905944i \(-0.360838\pi\)
−0.905944 + 0.423397i \(0.860838\pi\)
\(62\) 67.8734i 1.09473i
\(63\) 83.3966i 1.32376i
\(64\) 44.6213i 0.697207i
\(65\) −50.9239 −0.783445
\(66\) 0.269711 0.269711i 0.00408653 0.00408653i
\(67\) 31.5543i 0.470960i −0.971879 0.235480i \(-0.924334\pi\)
0.971879 0.235480i \(-0.0756662\pi\)
\(68\) 15.9710 15.9710i 0.234867 0.234867i
\(69\) −4.46397 4.46397i −0.0646953 0.0646953i
\(70\) 36.6983 36.6983i 0.524261 0.524261i
\(71\) 99.8673i 1.40658i 0.710902 + 0.703291i \(0.248287\pi\)
−0.710902 + 0.703291i \(0.751713\pi\)
\(72\) −49.6826 49.6826i −0.690036 0.690036i
\(73\) −3.96285 + 3.96285i −0.0542856 + 0.0542856i −0.733728 0.679443i \(-0.762222\pi\)
0.679443 + 0.733728i \(0.262222\pi\)
\(74\) −81.9020 −1.10678
\(75\) 3.38951 + 3.38951i 0.0451935 + 0.0451935i
\(76\) 34.3992 34.3992i 0.452621 0.452621i
\(77\) 3.24485 + 3.24485i 0.0421409 + 0.0421409i
\(78\) −9.84706 −0.126244
\(79\) −40.3117 40.3117i −0.510275 0.510275i 0.404335 0.914611i \(-0.367503\pi\)
−0.914611 + 0.404335i \(0.867503\pi\)
\(80\) 4.65749i 0.0582186i
\(81\) −70.5724 −0.871264
\(82\) 41.5030 0.506134
\(83\) 137.714 1.65921 0.829604 0.558352i \(-0.188566\pi\)
0.829604 + 0.558352i \(0.188566\pi\)
\(84\) −10.0579 + 10.0579i −0.119737 + 0.119737i
\(85\) −28.3592 + 28.3592i −0.333637 + 0.333637i
\(86\) 31.8411i 0.370246i
\(87\) 15.6067 + 9.27437i 0.179388 + 0.106602i
\(88\) −3.86616 −0.0439337
\(89\) 83.1506 + 83.1506i 0.934276 + 0.934276i 0.997969 0.0636936i \(-0.0202880\pi\)
−0.0636936 + 0.997969i \(0.520288\pi\)
\(90\) 32.6071 + 32.6071i 0.362302 + 0.362302i
\(91\) 118.468i 1.30185i
\(92\) 23.6510i 0.257076i
\(93\) 33.0312i 0.355174i
\(94\) 4.02036 0.0427698
\(95\) −61.0816 + 61.0816i −0.642964 + 0.642964i
\(96\) 19.5383i 0.203524i
\(97\) −79.9850 + 79.9850i −0.824588 + 0.824588i −0.986762 0.162174i \(-0.948149\pi\)
0.162174 + 0.986762i \(0.448149\pi\)
\(98\) 40.8043 + 40.8043i 0.416371 + 0.416371i
\(99\) −2.88311 + 2.88311i −0.0291223 + 0.0291223i
\(100\) 17.9583i 0.179583i
\(101\) −52.1216 52.1216i −0.516055 0.516055i 0.400320 0.916375i \(-0.368899\pi\)
−0.916375 + 0.400320i \(0.868899\pi\)
\(102\) −5.48375 + 5.48375i −0.0537623 + 0.0537623i
\(103\) 139.377 1.35318 0.676588 0.736361i \(-0.263458\pi\)
0.676588 + 0.736361i \(0.263458\pi\)
\(104\) 70.5762 + 70.5762i 0.678617 + 0.678617i
\(105\) 17.8596 17.8596i 0.170091 0.170091i
\(106\) 81.9880 + 81.9880i 0.773472 + 0.773472i
\(107\) −14.9646 −0.139856 −0.0699282 0.997552i \(-0.522277\pi\)
−0.0699282 + 0.997552i \(0.522277\pi\)
\(108\) −18.2802 18.2802i −0.169261 0.169261i
\(109\) 38.6223i 0.354333i −0.984181 0.177167i \(-0.943307\pi\)
0.984181 0.177167i \(-0.0566931\pi\)
\(110\) 2.53740 0.0230673
\(111\) −39.8584 −0.359085
\(112\) −10.8351 −0.0967418
\(113\) −20.2695 + 20.2695i −0.179376 + 0.179376i −0.791084 0.611708i \(-0.790483\pi\)
0.611708 + 0.791084i \(0.290483\pi\)
\(114\) −11.8112 + 11.8112i −0.103607 + 0.103607i
\(115\) 41.9964i 0.365186i
\(116\) −16.7750 65.9125i −0.144612 0.568211i
\(117\) 105.261 0.899670
\(118\) −82.2471 82.2471i −0.697009 0.697009i
\(119\) −65.9741 65.9741i −0.554405 0.554405i
\(120\) 21.2793i 0.177327i
\(121\) 120.776i 0.998146i
\(122\) 53.5482i 0.438920i
\(123\) 20.1978 0.164210
\(124\) −87.5029 + 87.5029i −0.705669 + 0.705669i
\(125\) 136.000i 1.08800i
\(126\) −75.8566 + 75.8566i −0.602036 + 0.602036i
\(127\) 52.2215 + 52.2215i 0.411193 + 0.411193i 0.882154 0.470961i \(-0.156093\pi\)
−0.470961 + 0.882154i \(0.656093\pi\)
\(128\) −47.6897 + 47.6897i −0.372576 + 0.372576i
\(129\) 15.4958i 0.120122i
\(130\) −46.3198 46.3198i −0.356306 0.356306i
\(131\) 25.3821 25.3821i 0.193756 0.193756i −0.603561 0.797317i \(-0.706252\pi\)
0.797317 + 0.603561i \(0.206252\pi\)
\(132\) −0.695427 −0.00526839
\(133\) −142.099 142.099i −1.06841 1.06841i
\(134\) 28.7014 28.7014i 0.214190 0.214190i
\(135\) 32.4596 + 32.4596i 0.240441 + 0.240441i
\(136\) 78.6068 0.577991
\(137\) −117.179 117.179i −0.855320 0.855320i 0.135462 0.990782i \(-0.456748\pi\)
−0.990782 + 0.135462i \(0.956748\pi\)
\(138\) 8.12075i 0.0588460i
\(139\) 62.2884 0.448118 0.224059 0.974576i \(-0.428069\pi\)
0.224059 + 0.974576i \(0.428069\pi\)
\(140\) −94.6235 −0.675882
\(141\) 1.95655 0.0138762
\(142\) −90.8381 + 90.8381i −0.639705 + 0.639705i
\(143\) 4.09558 4.09558i 0.0286404 0.0286404i
\(144\) 9.62718i 0.0668554i
\(145\) 29.7869 + 117.039i 0.205427 + 0.807164i
\(146\) −7.20912 −0.0493776
\(147\) 19.8578 + 19.8578i 0.135087 + 0.135087i
\(148\) 105.589 + 105.589i 0.713438 + 0.713438i
\(149\) 140.996i 0.946284i −0.880986 0.473142i \(-0.843120\pi\)
0.880986 0.473142i \(-0.156880\pi\)
\(150\) 6.16612i 0.0411075i
\(151\) 269.100i 1.78212i 0.453889 + 0.891058i \(0.350036\pi\)
−0.453889 + 0.891058i \(0.649964\pi\)
\(152\) 169.308 1.11387
\(153\) 58.6193 58.6193i 0.383133 0.383133i
\(154\) 5.90295i 0.0383308i
\(155\) 155.376 155.376i 1.00243 1.00243i
\(156\) 12.6949 + 12.6949i 0.0813776 + 0.0813776i
\(157\) −82.6681 + 82.6681i −0.526549 + 0.526549i −0.919541 0.392993i \(-0.871440\pi\)
0.392993 + 0.919541i \(0.371440\pi\)
\(158\) 73.3342i 0.464140i
\(159\) 39.9002 + 39.9002i 0.250945 + 0.250945i
\(160\) 91.9065 91.9065i 0.574416 0.574416i
\(161\) 97.6995 0.606829
\(162\) −64.1918 64.1918i −0.396246 0.396246i
\(163\) 16.1649 16.1649i 0.0991711 0.0991711i −0.655780 0.754952i \(-0.727660\pi\)
0.754952 + 0.655780i \(0.227660\pi\)
\(164\) −53.5060 53.5060i −0.326256 0.326256i
\(165\) 1.23485 0.00748393
\(166\) 125.263 + 125.263i 0.754598 + 0.754598i
\(167\) 134.528i 0.805558i 0.915297 + 0.402779i \(0.131956\pi\)
−0.915297 + 0.402779i \(0.868044\pi\)
\(168\) −49.5037 −0.294665
\(169\) 19.4719 0.115218
\(170\) −51.5903 −0.303472
\(171\) 126.258 126.258i 0.738349 0.738349i
\(172\) −41.0499 + 41.0499i −0.238662 + 0.238662i
\(173\) 94.1756i 0.544368i 0.962245 + 0.272184i \(0.0877459\pi\)
−0.962245 + 0.272184i \(0.912254\pi\)
\(174\) 5.75984 + 22.6316i 0.0331025 + 0.130066i
\(175\) −74.1836 −0.423906
\(176\) −0.374580 0.374580i −0.00212830 0.00212830i
\(177\) −40.0263 40.0263i −0.226137 0.226137i
\(178\) 151.266i 0.849806i
\(179\) 55.6892i 0.311113i 0.987827 + 0.155557i \(0.0497171\pi\)
−0.987827 + 0.155557i \(0.950283\pi\)
\(180\) 84.0748i 0.467082i
\(181\) −131.878 −0.728610 −0.364305 0.931280i \(-0.618693\pi\)
−0.364305 + 0.931280i \(0.618693\pi\)
\(182\) 107.757 107.757i 0.592074 0.592074i
\(183\) 26.0598i 0.142403i
\(184\) −58.2034 + 58.2034i −0.316323 + 0.316323i
\(185\) −187.491 187.491i −1.01346 1.01346i
\(186\) 30.0448 30.0448i 0.161531 0.161531i
\(187\) 4.56159i 0.0243935i
\(188\) −5.18308 5.18308i −0.0275696 0.0275696i
\(189\) −75.5133 + 75.5133i −0.399541 + 0.399541i
\(190\) −111.118 −0.584833
\(191\) 122.543 + 122.543i 0.641588 + 0.641588i 0.950946 0.309358i \(-0.100114\pi\)
−0.309358 + 0.950946i \(0.600114\pi\)
\(192\) 19.7520 19.7520i 0.102875 0.102875i
\(193\) −175.959 175.959i −0.911702 0.911702i 0.0847039 0.996406i \(-0.473006\pi\)
−0.996406 + 0.0847039i \(0.973006\pi\)
\(194\) −145.507 −0.750036
\(195\) −22.5420 22.5420i −0.115600 0.115600i
\(196\) 105.211i 0.536789i
\(197\) 42.7699 0.217106 0.108553 0.994091i \(-0.465378\pi\)
0.108553 + 0.994091i \(0.465378\pi\)
\(198\) −5.24488 −0.0264893
\(199\) −101.732 −0.511216 −0.255608 0.966781i \(-0.582276\pi\)
−0.255608 + 0.966781i \(0.582276\pi\)
\(200\) 44.1941 44.1941i 0.220970 0.220970i
\(201\) 13.9678 13.9678i 0.0694916 0.0694916i
\(202\) 94.8184i 0.469398i
\(203\) −272.277 + 69.2957i −1.34126 + 0.341358i
\(204\) 14.1394 0.0693108
\(205\) 95.0090 + 95.0090i 0.463459 + 0.463459i
\(206\) 126.776 + 126.776i 0.615417 + 0.615417i
\(207\) 86.8078i 0.419362i
\(208\) 13.6758i 0.0657491i
\(209\) 9.82502i 0.0470097i
\(210\) 32.4897 0.154713
\(211\) 84.0454 84.0454i 0.398319 0.398319i −0.479321 0.877640i \(-0.659117\pi\)
0.877640 + 0.479321i \(0.159117\pi\)
\(212\) 211.399i 0.997166i
\(213\) −44.2072 + 44.2072i −0.207546 + 0.207546i
\(214\) −13.6117 13.6117i −0.0636058 0.0636058i
\(215\) 72.8910 72.8910i 0.339028 0.339028i
\(216\) 89.9725i 0.416539i
\(217\) 361.464 + 361.464i 1.66573 + 1.66573i
\(218\) 35.1304 35.1304i 0.161149 0.161149i
\(219\) −3.50839 −0.0160200
\(220\) −3.27123 3.27123i −0.0148692 0.0148692i
\(221\) −83.2711 + 83.2711i −0.376792 + 0.376792i
\(222\) −36.2547 36.2547i −0.163310 0.163310i
\(223\) −306.140 −1.37283 −0.686413 0.727212i \(-0.740816\pi\)
−0.686413 + 0.727212i \(0.740816\pi\)
\(224\) 213.809 + 213.809i 0.954506 + 0.954506i
\(225\) 65.9135i 0.292949i
\(226\) −36.8739 −0.163159
\(227\) 19.8257 0.0873379 0.0436689 0.999046i \(-0.486095\pi\)
0.0436689 + 0.999046i \(0.486095\pi\)
\(228\) 30.4543 0.133571
\(229\) 150.087 150.087i 0.655402 0.655402i −0.298887 0.954289i \(-0.596615\pi\)
0.954289 + 0.298887i \(0.0966153\pi\)
\(230\) 38.1994 38.1994i 0.166084 0.166084i
\(231\) 2.87273i 0.0124360i
\(232\) 120.924 203.488i 0.521223 0.877103i
\(233\) 132.431 0.568375 0.284187 0.958769i \(-0.408276\pi\)
0.284187 + 0.958769i \(0.408276\pi\)
\(234\) 95.7445 + 95.7445i 0.409165 + 0.409165i
\(235\) 9.20344 + 9.20344i 0.0391636 + 0.0391636i
\(236\) 212.067i 0.898590i
\(237\) 35.6888i 0.150586i
\(238\) 120.019i 0.504280i
\(239\) 176.690 0.739288 0.369644 0.929173i \(-0.379480\pi\)
0.369644 + 0.929173i \(0.379480\pi\)
\(240\) −2.06168 + 2.06168i −0.00859034 + 0.00859034i
\(241\) 161.010i 0.668093i 0.942557 + 0.334046i \(0.108414\pi\)
−0.942557 + 0.334046i \(0.891586\pi\)
\(242\) 109.856 109.856i 0.453951 0.453951i
\(243\) −101.389 101.389i −0.417239 0.417239i
\(244\) −69.0348 + 69.0348i −0.282930 + 0.282930i
\(245\) 186.819i 0.762527i
\(246\) 18.3717 + 18.3717i 0.0746817 + 0.0746817i
\(247\) −179.354 + 179.354i −0.726130 + 0.726130i
\(248\) −430.677 −1.73660
\(249\) 60.9606 + 60.9606i 0.244822 + 0.244822i
\(250\) −123.704 + 123.704i −0.494816 + 0.494816i
\(251\) 136.621 + 136.621i 0.544306 + 0.544306i 0.924788 0.380482i \(-0.124242\pi\)
−0.380482 + 0.924788i \(0.624242\pi\)
\(252\) 195.590 0.776150
\(253\) 3.37757 + 3.37757i 0.0133501 + 0.0133501i
\(254\) 95.0001i 0.374016i
\(255\) −25.1069 −0.0984585
\(256\) −265.241 −1.03610
\(257\) −275.616 −1.07244 −0.536218 0.844079i \(-0.680148\pi\)
−0.536218 + 0.844079i \(0.680148\pi\)
\(258\) 14.0948 14.0948i 0.0546310 0.0546310i
\(259\) 436.175 436.175i 1.68407 1.68407i
\(260\) 119.432i 0.459353i
\(261\) −61.5706 241.923i −0.235903 0.926908i
\(262\) 46.1744 0.176238
\(263\) −242.820 242.820i −0.923269 0.923269i 0.0739900 0.997259i \(-0.476427\pi\)
−0.997259 + 0.0739900i \(0.976427\pi\)
\(264\) −1.71140 1.71140i −0.00648256 0.00648256i
\(265\) 375.375i 1.41651i
\(266\) 258.503i 0.971816i
\(267\) 73.6148i 0.275711i
\(268\) −74.0042 −0.276135
\(269\) 167.754 167.754i 0.623620 0.623620i −0.322836 0.946455i \(-0.604636\pi\)
0.946455 + 0.322836i \(0.104636\pi\)
\(270\) 59.0497i 0.218703i
\(271\) 282.361 282.361i 1.04192 1.04192i 0.0428420 0.999082i \(-0.486359\pi\)
0.999082 0.0428420i \(-0.0136412\pi\)
\(272\) 7.61596 + 7.61596i 0.0279998 + 0.0279998i
\(273\) 52.4412 52.4412i 0.192092 0.192092i
\(274\) 213.169i 0.777989i
\(275\) −2.56461 2.56461i −0.00932584 0.00932584i
\(276\) −10.4693 + 10.4693i −0.0379324 + 0.0379324i
\(277\) 30.5322 0.110224 0.0551122 0.998480i \(-0.482448\pi\)
0.0551122 + 0.998480i \(0.482448\pi\)
\(278\) 56.6568 + 56.6568i 0.203802 + 0.203802i
\(279\) −321.168 + 321.168i −1.15114 + 1.15114i
\(280\) −232.862 232.862i −0.831649 0.831649i
\(281\) −2.92201 −0.0103986 −0.00519931 0.999986i \(-0.501655\pi\)
−0.00519931 + 0.999986i \(0.501655\pi\)
\(282\) 1.77965 + 1.77965i 0.00631082 + 0.00631082i
\(283\) 26.9414i 0.0951993i 0.998866 + 0.0475997i \(0.0151572\pi\)
−0.998866 + 0.0475997i \(0.984843\pi\)
\(284\) 234.219 0.824713
\(285\) −54.0767 −0.189743
\(286\) 7.45058 0.0260510
\(287\) −221.027 + 221.027i −0.770129 + 0.770129i
\(288\) −189.974 + 189.974i −0.659631 + 0.659631i
\(289\) 196.254i 0.679079i
\(290\) −79.3633 + 133.551i −0.273666 + 0.460521i
\(291\) −70.8123 −0.243341
\(292\) 9.29406 + 9.29406i 0.0318290 + 0.0318290i
\(293\) −255.770 255.770i −0.872934 0.872934i 0.119857 0.992791i \(-0.461756\pi\)
−0.992791 + 0.119857i \(0.961756\pi\)
\(294\) 36.1249i 0.122874i
\(295\) 376.561i 1.27648i
\(296\) 519.693i 1.75572i
\(297\) −5.22115 −0.0175796
\(298\) 128.249 128.249i 0.430364 0.430364i
\(299\) 123.314i 0.412422i
\(300\) 7.94942 7.94942i 0.0264981 0.0264981i
\(301\) 169.572 + 169.572i 0.563362 + 0.563362i
\(302\) −244.770 + 244.770i −0.810496 + 0.810496i
\(303\) 46.1443i 0.152291i
\(304\) 16.4037 + 16.4037i 0.0539595 + 0.0539595i
\(305\) 122.583 122.583i 0.401912 0.401912i
\(306\) 106.639 0.348493
\(307\) −9.20371 9.20371i −0.0299795 0.0299795i 0.691958 0.721938i \(-0.256748\pi\)
−0.721938 + 0.691958i \(0.756748\pi\)
\(308\) 7.61013 7.61013i 0.0247082 0.0247082i
\(309\) 61.6967 + 61.6967i 0.199666 + 0.199666i
\(310\) 282.657 0.911796
\(311\) 94.0902 + 94.0902i 0.302541 + 0.302541i 0.842007 0.539466i \(-0.181374\pi\)
−0.539466 + 0.842007i \(0.681374\pi\)
\(312\) 62.4825i 0.200264i
\(313\) 133.762 0.427356 0.213678 0.976904i \(-0.431456\pi\)
0.213678 + 0.976904i \(0.431456\pi\)
\(314\) −150.388 −0.478942
\(315\) −347.303 −1.10255
\(316\) −94.5431 + 94.5431i −0.299187 + 0.299187i
\(317\) 405.329 405.329i 1.27864 1.27864i 0.337213 0.941428i \(-0.390516\pi\)
0.941428 0.337213i \(-0.109484\pi\)
\(318\) 72.5856i 0.228257i
\(319\) −11.8085 7.01726i −0.0370173 0.0219977i
\(320\) 185.824 0.580700
\(321\) −6.62424 6.62424i −0.0206363 0.0206363i
\(322\) 88.8663 + 88.8663i 0.275982 + 0.275982i
\(323\) 199.762i 0.618458i
\(324\) 165.513i 0.510844i
\(325\) 93.6329i 0.288101i
\(326\) 29.4068 0.0902049
\(327\) 17.0965 17.0965i 0.0522830 0.0522830i
\(328\) 263.349i 0.802893i
\(329\) −21.4107 + 21.4107i −0.0650781 + 0.0650781i
\(330\) 1.12320 + 1.12320i 0.00340365 + 0.00340365i
\(331\) 185.108 185.108i 0.559238 0.559238i −0.369853 0.929090i \(-0.620592\pi\)
0.929090 + 0.369853i \(0.120592\pi\)
\(332\) 322.981i 0.972834i
\(333\) 387.550 + 387.550i 1.16381 + 1.16381i
\(334\) −122.365 + 122.365i −0.366363 + 0.366363i
\(335\) 131.407 0.392260
\(336\) −4.79626 4.79626i −0.0142746 0.0142746i
\(337\) −71.8022 + 71.8022i −0.213063 + 0.213063i −0.805567 0.592504i \(-0.798139\pi\)
0.592504 + 0.805567i \(0.298139\pi\)
\(338\) 17.7114 + 17.7114i 0.0524006 + 0.0524006i
\(339\) −17.9450 −0.0529351
\(340\) 66.5107 + 66.5107i 0.195620 + 0.195620i
\(341\) 24.9924i 0.0732915i
\(342\) 229.685 0.671593
\(343\) 40.1069 0.116930
\(344\) −202.041 −0.587330
\(345\) 18.5901 18.5901i 0.0538843 0.0538843i
\(346\) −85.6610 + 85.6610i −0.247575 + 0.247575i
\(347\) 181.565i 0.523241i 0.965171 + 0.261621i \(0.0842569\pi\)
−0.965171 + 0.261621i \(0.915743\pi\)
\(348\) 21.7512 36.6024i 0.0625033 0.105179i
\(349\) 205.399 0.588536 0.294268 0.955723i \(-0.404924\pi\)
0.294268 + 0.955723i \(0.404924\pi\)
\(350\) −67.4765 67.4765i −0.192790 0.192790i
\(351\) 95.3112 + 95.3112i 0.271542 + 0.271542i
\(352\) 14.7832i 0.0419978i
\(353\) 150.904i 0.427489i 0.976890 + 0.213745i \(0.0685660\pi\)
−0.976890 + 0.213745i \(0.931434\pi\)
\(354\) 72.8149i 0.205692i
\(355\) −415.895 −1.17153
\(356\) 195.013 195.013i 0.547789 0.547789i
\(357\) 58.4082i 0.163608i
\(358\) −50.6543 + 50.6543i −0.141492 + 0.141492i
\(359\) −366.501 366.501i −1.02089 1.02089i −0.999777 0.0211170i \(-0.993278\pi\)
−0.0211170 0.999777i \(-0.506722\pi\)
\(360\) 206.902 206.902i 0.574728 0.574728i
\(361\) 69.2592i 0.191854i
\(362\) −119.955 119.955i −0.331368 0.331368i
\(363\) 53.4625 53.4625i 0.147280 0.147280i
\(364\) −277.843 −0.763306
\(365\) −16.5032 16.5032i −0.0452142 0.0452142i
\(366\) 23.7037 23.7037i 0.0647641 0.0647641i
\(367\) −84.3213 84.3213i −0.229758 0.229758i 0.582833 0.812592i \(-0.301944\pi\)
−0.812592 + 0.582833i \(0.801944\pi\)
\(368\) −11.2783 −0.0306475
\(369\) −196.387 196.387i −0.532213 0.532213i
\(370\) 341.079i 0.921835i
\(371\) −873.265 −2.35381
\(372\) −77.4680 −0.208247
\(373\) 91.4080 0.245062 0.122531 0.992465i \(-0.460899\pi\)
0.122531 + 0.992465i \(0.460899\pi\)
\(374\) 4.14917 4.14917i 0.0110940 0.0110940i
\(375\) −60.2017 + 60.2017i −0.160538 + 0.160538i
\(376\) 25.5104i 0.0678468i
\(377\) 87.4635 + 343.662i 0.231999 + 0.911569i
\(378\) −137.372 −0.363418
\(379\) 178.021 + 178.021i 0.469713 + 0.469713i 0.901822 0.432108i \(-0.142230\pi\)
−0.432108 + 0.901822i \(0.642230\pi\)
\(380\) 143.255 + 143.255i 0.376986 + 0.376986i
\(381\) 46.2327i 0.121346i
\(382\) 222.928i 0.583581i
\(383\) 142.083i 0.370973i 0.982647 + 0.185486i \(0.0593860\pi\)
−0.982647 + 0.185486i \(0.940614\pi\)
\(384\) −42.2206 −0.109950
\(385\) −13.5131 + 13.5131i −0.0350989 + 0.0350989i
\(386\) 320.100i 0.829274i
\(387\) −150.668 + 150.668i −0.389323 + 0.389323i
\(388\) 187.589 + 187.589i 0.483476 + 0.483476i
\(389\) −339.694 + 339.694i −0.873250 + 0.873250i −0.992825 0.119575i \(-0.961847\pi\)
0.119575 + 0.992825i \(0.461847\pi\)
\(390\) 41.0078i 0.105148i
\(391\) −68.6727 68.6727i −0.175634 0.175634i
\(392\) 258.916 258.916i 0.660499 0.660499i
\(393\) 22.4712 0.0571787
\(394\) 38.9030 + 38.9030i 0.0987386 + 0.0987386i
\(395\) 167.877 167.877i 0.425006 0.425006i
\(396\) 6.76175 + 6.76175i 0.0170751 + 0.0170751i
\(397\) −657.787 −1.65689 −0.828447 0.560068i \(-0.810775\pi\)
−0.828447 + 0.560068i \(0.810775\pi\)
\(398\) −92.5342 92.5342i −0.232498 0.232498i
\(399\) 125.803i 0.315296i
\(400\) 8.56364 0.0214091
\(401\) 343.872 0.857537 0.428768 0.903414i \(-0.358948\pi\)
0.428768 + 0.903414i \(0.358948\pi\)
\(402\) 25.4099 0.0632088
\(403\) 456.232 456.232i 1.13209 1.13209i
\(404\) −122.241 + 122.241i −0.302576 + 0.302576i
\(405\) 293.897i 0.725672i
\(406\) −310.690 184.629i −0.765247 0.454751i
\(407\) 30.1581 0.0740984
\(408\) 34.7961 + 34.7961i 0.0852844 + 0.0852844i
\(409\) 219.662 + 219.662i 0.537072 + 0.537072i 0.922668 0.385596i \(-0.126004\pi\)
−0.385596 + 0.922668i \(0.626004\pi\)
\(410\) 172.838i 0.421557i
\(411\) 103.741i 0.252411i
\(412\) 326.881i 0.793401i
\(413\) 876.024 2.12112
\(414\) −78.9594 + 78.9594i −0.190723 + 0.190723i
\(415\) 573.508i 1.38195i
\(416\) 269.866 269.866i 0.648715 0.648715i
\(417\) 27.5726 + 27.5726i 0.0661213 + 0.0661213i
\(418\) 8.93673 8.93673i 0.0213797 0.0213797i
\(419\) 512.017i 1.22200i 0.791631 + 0.610999i \(0.209232\pi\)
−0.791631 + 0.610999i \(0.790768\pi\)
\(420\) −41.8860 41.8860i −0.0997286 0.0997286i
\(421\) −426.710 + 426.710i −1.01356 + 1.01356i −0.0136572 + 0.999907i \(0.504347\pi\)
−0.999907 + 0.0136572i \(0.995653\pi\)
\(422\) 152.893 0.362307
\(423\) −19.0238 19.0238i −0.0449735 0.0449735i
\(424\) 520.238 520.238i 1.22698 1.22698i
\(425\) 52.1435 + 52.1435i 0.122691 + 0.122691i
\(426\) −80.4208 −0.188781
\(427\) 285.175 + 285.175i 0.667857 + 0.667857i
\(428\) 35.0965i 0.0820012i
\(429\) 3.62589 0.00845197
\(430\) 132.602 0.308376
\(431\) 596.638 1.38431 0.692156 0.721748i \(-0.256661\pi\)
0.692156 + 0.721748i \(0.256661\pi\)
\(432\) 8.71714 8.71714i 0.0201786 0.0201786i
\(433\) −41.8737 + 41.8737i −0.0967059 + 0.0967059i −0.753805 0.657099i \(-0.771783\pi\)
0.657099 + 0.753805i \(0.271783\pi\)
\(434\) 657.567i 1.51513i
\(435\) −38.6229 + 64.9938i −0.0887882 + 0.149411i
\(436\) −90.5808 −0.207754
\(437\) −147.911 147.911i −0.338470 0.338470i
\(438\) −3.19119 3.19119i −0.00728582 0.00728582i
\(439\) 344.567i 0.784891i −0.919775 0.392445i \(-0.871629\pi\)
0.919775 0.392445i \(-0.128371\pi\)
\(440\) 16.1005i 0.0365922i
\(441\) 386.161i 0.875649i
\(442\) −151.485 −0.342726
\(443\) −124.564 + 124.564i −0.281184 + 0.281184i −0.833581 0.552397i \(-0.813713\pi\)
0.552397 + 0.833581i \(0.313713\pi\)
\(444\) 93.4798i 0.210540i
\(445\) −346.278 + 346.278i −0.778154 + 0.778154i
\(446\) −278.462 278.462i −0.624353 0.624353i
\(447\) 62.4134 62.4134i 0.139627 0.139627i
\(448\) 432.297i 0.964949i
\(449\) −562.904 562.904i −1.25368 1.25368i −0.954056 0.299628i \(-0.903137\pi\)
−0.299628 0.954056i \(-0.596863\pi\)
\(450\) 59.9542 59.9542i 0.133232 0.133232i
\(451\) −15.2823 −0.0338853
\(452\) 47.5381 + 47.5381i 0.105173 + 0.105173i
\(453\) −119.120 + 119.120i −0.262957 + 0.262957i
\(454\) 18.0332 + 18.0332i 0.0397208 + 0.0397208i
\(455\) 493.358 1.08430
\(456\) 74.9458 + 74.9458i 0.164355 + 0.164355i
\(457\) 377.138i 0.825247i 0.910902 + 0.412623i \(0.135387\pi\)
−0.910902 + 0.412623i \(0.864613\pi\)
\(458\) 273.035 0.596146
\(459\) 106.156 0.231277
\(460\) −98.4940 −0.214117
\(461\) −40.0863 + 40.0863i −0.0869552 + 0.0869552i −0.749246 0.662291i \(-0.769584\pi\)
0.662291 + 0.749246i \(0.269584\pi\)
\(462\) −2.61300 + 2.61300i −0.00565584 + 0.00565584i
\(463\) 410.934i 0.887546i −0.896139 0.443773i \(-0.853640\pi\)
0.896139 0.443773i \(-0.146360\pi\)
\(464\) 31.4312 7.99939i 0.0677397 0.0172401i
\(465\) 137.558 0.295823
\(466\) 120.458 + 120.458i 0.258494 + 0.258494i
\(467\) −427.051 427.051i −0.914455 0.914455i 0.0821634 0.996619i \(-0.473817\pi\)
−0.996619 + 0.0821634i \(0.973817\pi\)
\(468\) 246.869i 0.527498i
\(469\) 305.703i 0.651818i
\(470\) 16.7427i 0.0356227i
\(471\) −73.1877 −0.155388
\(472\) −521.882 + 521.882i −1.10568 + 1.10568i
\(473\) 11.7246i 0.0247877i
\(474\) 32.4621 32.4621i 0.0684854 0.0684854i
\(475\) 112.310 + 112.310i 0.236441 + 0.236441i
\(476\) −154.729 + 154.729i −0.325061 + 0.325061i
\(477\) 775.913i 1.62665i
\(478\) 160.715 + 160.715i 0.336224 + 0.336224i
\(479\) 223.602 223.602i 0.466811 0.466811i −0.434069 0.900880i \(-0.642923\pi\)
0.900880 + 0.434069i \(0.142923\pi\)
\(480\) 81.3666 0.169514
\(481\) −550.530 550.530i −1.14455 1.14455i
\(482\) −146.453 + 146.453i −0.303845 + 0.303845i
\(483\) 43.2476 + 43.2476i 0.0895396 + 0.0895396i
\(484\) −283.255 −0.585237
\(485\) −333.096 333.096i −0.686795 0.686795i
\(486\) 184.445i 0.379516i
\(487\) 397.009 0.815214 0.407607 0.913157i \(-0.366363\pi\)
0.407607 + 0.913157i \(0.366363\pi\)
\(488\) −339.780 −0.696270
\(489\) 14.3111 0.0292661
\(490\) −169.929 + 169.929i −0.346793 + 0.346793i
\(491\) −441.208 + 441.208i −0.898591 + 0.898591i −0.995312 0.0967208i \(-0.969165\pi\)
0.0967208 + 0.995312i \(0.469165\pi\)
\(492\) 47.3699i 0.0962803i
\(493\) 240.090 + 142.675i 0.486999 + 0.289401i
\(494\) −326.277 −0.660480
\(495\) −12.0066 12.0066i −0.0242558 0.0242558i
\(496\) −41.7269 41.7269i −0.0841268 0.0841268i
\(497\) 967.529i 1.94674i
\(498\) 110.898i 0.222687i
\(499\) 94.9470i 0.190275i 0.995464 + 0.0951373i \(0.0303290\pi\)
−0.995464 + 0.0951373i \(0.969671\pi\)
\(500\) 318.960 0.637920
\(501\) −59.5502 + 59.5502i −0.118863 + 0.118863i
\(502\) 248.537i 0.495094i
\(503\) −35.4061 + 35.4061i −0.0703899 + 0.0703899i −0.741425 0.671035i \(-0.765850\pi\)
0.671035 + 0.741425i \(0.265850\pi\)
\(504\) 481.333 + 481.333i 0.955025 + 0.955025i
\(505\) 217.059 217.059i 0.429820 0.429820i
\(506\) 6.14440i 0.0121431i
\(507\) 8.61942 + 8.61942i 0.0170008 + 0.0170008i
\(508\) 122.475 122.475i 0.241092 0.241092i
\(509\) 215.741 0.423852 0.211926 0.977286i \(-0.432026\pi\)
0.211926 + 0.977286i \(0.432026\pi\)
\(510\) −22.8370 22.8370i −0.0447783 0.0447783i
\(511\) 38.3927 38.3927i 0.0751324 0.0751324i
\(512\) −50.5014 50.5014i −0.0986355 0.0986355i
\(513\) 228.646 0.445703
\(514\) −250.697 250.697i −0.487738 0.487738i
\(515\) 580.433i 1.12705i
\(516\) −36.3422 −0.0704307
\(517\) −1.48038 −0.00286341
\(518\) 793.479 1.53181
\(519\) −41.6878 + 41.6878i −0.0803232 + 0.0803232i
\(520\) −293.913 + 293.913i −0.565217 + 0.565217i
\(521\) 279.099i 0.535700i −0.963461 0.267850i \(-0.913687\pi\)
0.963461 0.267850i \(-0.0863131\pi\)
\(522\) 164.046 276.054i 0.314265 0.528839i
\(523\) −135.622 −0.259316 −0.129658 0.991559i \(-0.541388\pi\)
−0.129658 + 0.991559i \(0.541388\pi\)
\(524\) −59.5285 59.5285i −0.113604 0.113604i
\(525\) −32.8381 32.8381i −0.0625488 0.0625488i
\(526\) 441.732i 0.839795i
\(527\) 508.145i 0.964221i
\(528\) 0.331623i 0.000628074i
\(529\) −427.304 −0.807758
\(530\) −341.437 + 341.437i −0.644221 + 0.644221i
\(531\) 778.365i 1.46585i
\(532\) −333.264 + 333.264i −0.626437 + 0.626437i
\(533\) 278.975 + 278.975i 0.523406 + 0.523406i
\(534\) −66.9592 + 66.9592i −0.125392 + 0.125392i
\(535\) 62.3198i 0.116486i
\(536\) −182.119 182.119i −0.339774 0.339774i
\(537\) −24.6514 + 24.6514i −0.0459057 + 0.0459057i
\(538\) 305.174 0.567237
\(539\) −15.0250 15.0250i −0.0278757 0.0278757i
\(540\) 76.1274 76.1274i 0.140977 0.140977i
\(541\) 381.445 + 381.445i 0.705074 + 0.705074i 0.965495 0.260421i \(-0.0838614\pi\)
−0.260421 + 0.965495i \(0.583861\pi\)
\(542\) 513.665 0.947722
\(543\) −58.3773 58.3773i −0.107509 0.107509i
\(544\) 300.572i 0.552523i
\(545\) 160.842 0.295122
\(546\) 95.3997 0.174725
\(547\) 104.335 0.190739 0.0953697 0.995442i \(-0.469597\pi\)
0.0953697 + 0.995442i \(0.469597\pi\)
\(548\) −274.819 + 274.819i −0.501495 + 0.501495i
\(549\) −253.383 + 253.383i −0.461536 + 0.461536i
\(550\) 4.66547i 0.00848268i
\(551\) 517.121 + 307.301i 0.938513 + 0.557716i
\(552\) −51.5286 −0.0933489
\(553\) 390.546 + 390.546i 0.706232 + 0.706232i
\(554\) 27.7717 + 27.7717i 0.0501295 + 0.0501295i
\(555\) 165.989i 0.299080i
\(556\) 146.085i 0.262743i
\(557\) 132.616i 0.238090i −0.992889 0.119045i \(-0.962017\pi\)
0.992889 0.119045i \(-0.0379833\pi\)
\(558\) −584.261 −1.04706
\(559\) 214.030 214.030i 0.382880 0.382880i
\(560\) 45.1224i 0.0805758i
\(561\) 2.01923 2.01923i 0.00359935 0.00359935i
\(562\) −2.65783 2.65783i −0.00472923 0.00472923i
\(563\) 253.583 253.583i 0.450413 0.450413i −0.445078 0.895492i \(-0.646824\pi\)
0.895492 + 0.445078i \(0.146824\pi\)
\(564\) 4.58868i 0.00813596i
\(565\) −84.4120 84.4120i −0.149402 0.149402i
\(566\) −24.5056 + 24.5056i −0.0432961 + 0.0432961i
\(567\) 683.716 1.20585
\(568\) 576.395 + 576.395i 1.01478 + 1.01478i
\(569\) 216.864 216.864i 0.381133 0.381133i −0.490377 0.871510i \(-0.663141\pi\)
0.871510 + 0.490377i \(0.163141\pi\)
\(570\) −49.1876 49.1876i −0.0862940 0.0862940i
\(571\) 398.256 0.697472 0.348736 0.937221i \(-0.386611\pi\)
0.348736 + 0.937221i \(0.386611\pi\)
\(572\) −9.60534 9.60534i −0.0167926 0.0167926i
\(573\) 108.490i 0.189337i
\(574\) −402.087 −0.700500
\(575\) −77.2180 −0.134292
\(576\) −384.104 −0.666848
\(577\) −504.599 + 504.599i −0.874521 + 0.874521i −0.992961 0.118440i \(-0.962211\pi\)
0.118440 + 0.992961i \(0.462211\pi\)
\(578\) 178.510 178.510i 0.308841 0.308841i
\(579\) 155.780i 0.269049i
\(580\) 274.491 69.8592i 0.473260 0.120447i
\(581\) −1334.20 −2.29638
\(582\) −64.4101 64.4101i −0.110670 0.110670i
\(583\) −30.1897 30.1897i −0.0517834 0.0517834i
\(584\) 45.7440i 0.0783288i
\(585\) 438.358i 0.749330i
\(586\) 465.290i 0.794011i
\(587\) 110.932 0.188982 0.0944911 0.995526i \(-0.469878\pi\)
0.0944911 + 0.995526i \(0.469878\pi\)
\(588\) 46.5725 46.5725i 0.0792049 0.0792049i
\(589\) 1094.47i 1.85819i
\(590\) 342.516 342.516i 0.580535 0.580535i
\(591\) 18.9325 + 18.9325i 0.0320347 + 0.0320347i
\(592\) −50.3514 + 50.3514i −0.0850530 + 0.0850530i
\(593\) 988.969i 1.66774i 0.551962 + 0.833870i \(0.313879\pi\)
−0.551962 + 0.833870i \(0.686121\pi\)
\(594\) −4.74910 4.74910i −0.00799511 0.00799511i
\(595\) 274.748 274.748i 0.461761 0.461761i
\(596\) −330.678 −0.554829
\(597\) −45.0326 45.0326i −0.0754315 0.0754315i
\(598\) 112.165 112.165i 0.187567 0.187567i
\(599\) 262.125 + 262.125i 0.437604 + 0.437604i 0.891205 0.453601i \(-0.149861\pi\)
−0.453601 + 0.891205i \(0.649861\pi\)
\(600\) 39.1259 0.0652098
\(601\) −496.848 496.848i −0.826702 0.826702i 0.160357 0.987059i \(-0.448735\pi\)
−0.987059 + 0.160357i \(0.948735\pi\)
\(602\) 308.482i 0.512428i
\(603\) −271.623 −0.450452
\(604\) 631.119 1.04490
\(605\) 502.967 0.831351
\(606\) 41.9723 41.9723i 0.0692612 0.0692612i
\(607\) −466.144 + 466.144i −0.767947 + 0.767947i −0.977745 0.209798i \(-0.932719\pi\)
0.209798 + 0.977745i \(0.432719\pi\)
\(608\) 647.390i 1.06479i
\(609\) −151.200 89.8515i −0.248276 0.147539i
\(610\) 223.000 0.365574
\(611\) 27.0241 + 27.0241i 0.0442293 + 0.0442293i
\(612\) −137.480 137.480i −0.224640 0.224640i
\(613\) 581.681i 0.948908i −0.880280 0.474454i \(-0.842645\pi\)
0.880280 0.474454i \(-0.157355\pi\)
\(614\) 16.7432i 0.0272690i
\(615\) 84.1133i 0.136770i
\(616\) 37.4560 0.0608052
\(617\) −546.898 + 546.898i −0.886383 + 0.886383i −0.994174 0.107791i \(-0.965622\pi\)
0.107791 + 0.994174i \(0.465622\pi\)
\(618\) 112.237i 0.181614i
\(619\) −650.477 + 650.477i −1.05085 + 1.05085i −0.0522157 + 0.998636i \(0.516628\pi\)
−0.998636 + 0.0522157i \(0.983372\pi\)
\(620\) −364.404 364.404i −0.587748 0.587748i
\(621\) −78.6021 + 78.6021i −0.126573 + 0.126573i
\(622\) 171.167i 0.275188i
\(623\) −805.575 805.575i −1.29306 1.29306i
\(624\) −6.05373 + 6.05373i −0.00970149 + 0.00970149i
\(625\) −374.939 −0.599903
\(626\) 121.669 + 121.669i 0.194359 + 0.194359i
\(627\) 4.34914 4.34914i 0.00693643 0.00693643i
\(628\) 193.881 + 193.881i 0.308728 + 0.308728i
\(629\) −613.173 −0.974837
\(630\) −315.903 315.903i −0.501433 0.501433i
\(631\) 1020.55i 1.61735i −0.588253 0.808677i \(-0.700184\pi\)
0.588253 0.808677i \(-0.299816\pi\)
\(632\) −465.327 −0.736277
\(633\) 74.4070 0.117547
\(634\) 737.366 1.16304
\(635\) −217.475 + 217.475i −0.342480 + 0.342480i
\(636\) 93.5780 93.5780i 0.147135 0.147135i
\(637\) 548.558i 0.861159i
\(638\) −4.35807 17.1237i −0.00683083 0.0268397i
\(639\) 859.668 1.34533
\(640\) −198.603 198.603i −0.310316 0.310316i
\(641\) 65.0163 + 65.0163i 0.101430 + 0.101430i 0.756001 0.654571i \(-0.227151\pi\)
−0.654571 + 0.756001i \(0.727151\pi\)
\(642\) 12.0507i 0.0187705i
\(643\) 590.198i 0.917882i 0.888467 + 0.458941i \(0.151771\pi\)
−0.888467 + 0.458941i \(0.848229\pi\)
\(644\) 229.134i 0.355799i
\(645\) 64.5318 0.100049
\(646\) −181.701 + 181.701i −0.281271 + 0.281271i
\(647\) 96.4448i 0.149065i 0.997219 + 0.0745323i \(0.0237464\pi\)
−0.997219 + 0.0745323i \(0.976254\pi\)
\(648\) −407.316 + 407.316i −0.628575 + 0.628575i
\(649\) 30.2851 + 30.2851i 0.0466642 + 0.0466642i
\(650\) −85.1674 + 85.1674i −0.131027 + 0.131027i
\(651\) 320.011i 0.491569i
\(652\) −37.9115 37.9115i −0.0581465 0.0581465i
\(653\) −185.978 + 185.978i −0.284806 + 0.284806i −0.835022 0.550216i \(-0.814545\pi\)
0.550216 + 0.835022i \(0.314545\pi\)
\(654\) 31.1016 0.0475560
\(655\) 105.703 + 105.703i 0.161379 + 0.161379i
\(656\) 25.5150 25.5150i 0.0388949 0.0388949i
\(657\) 34.1126 + 34.1126i 0.0519218 + 0.0519218i
\(658\) −38.9498 −0.0591943
\(659\) 811.110 + 811.110i 1.23082 + 1.23082i 0.963649 + 0.267170i \(0.0860886\pi\)
0.267170 + 0.963649i \(0.413911\pi\)
\(660\) 2.89609i 0.00438801i
\(661\) 442.227 0.669027 0.334513 0.942391i \(-0.391428\pi\)
0.334513 + 0.942391i \(0.391428\pi\)
\(662\) 336.744 0.508676
\(663\) −73.7216 −0.111194
\(664\) 794.833 794.833i 1.19704 1.19704i
\(665\) 591.767 591.767i 0.889876 0.889876i
\(666\) 705.021i 1.05859i
\(667\) −283.414 + 72.1302i −0.424908 + 0.108141i
\(668\) 315.509 0.472318
\(669\) −135.516 135.516i −0.202565 0.202565i
\(670\) 119.526 + 119.526i 0.178398 + 0.178398i
\(671\) 19.7176i 0.0293854i
\(672\) 189.290i 0.281681i
\(673\) 725.102i 1.07742i −0.842492 0.538708i \(-0.818912\pi\)
0.842492 0.538708i \(-0.181088\pi\)
\(674\) −130.621 −0.193799
\(675\) 59.6829 59.6829i 0.0884191 0.0884191i
\(676\) 45.6673i 0.0675552i
\(677\) 650.790 650.790i 0.961285 0.961285i −0.0379933 0.999278i \(-0.512097\pi\)
0.999278 + 0.0379933i \(0.0120965\pi\)
\(678\) −16.3226 16.3226i −0.0240746 0.0240746i
\(679\) 774.907 774.907i 1.14125 1.14125i
\(680\) 327.356i 0.481406i
\(681\) 8.77604 + 8.77604i 0.0128870 + 0.0128870i
\(682\) −22.7328 + 22.7328i −0.0333325 + 0.0333325i
\(683\) −791.357 −1.15865 −0.579324 0.815097i \(-0.696683\pi\)
−0.579324 + 0.815097i \(0.696683\pi\)
\(684\) −296.112 296.112i −0.432912 0.432912i
\(685\) 487.988 487.988i 0.712392 0.712392i
\(686\) 36.4808 + 36.4808i 0.0531790 + 0.0531790i
\(687\) 132.875 0.193413
\(688\) −19.5751 19.5751i −0.0284522 0.0284522i
\(689\) 1102.22i 1.59973i
\(690\) 33.8187 0.0490126
\(691\) 646.166 0.935118 0.467559 0.883962i \(-0.345134\pi\)
0.467559 + 0.883962i \(0.345134\pi\)
\(692\) 220.870 0.319176
\(693\) 27.9320 27.9320i 0.0403059 0.0403059i
\(694\) −165.149 + 165.149i −0.237967 + 0.237967i
\(695\) 259.399i 0.373235i
\(696\) 143.604 36.5479i 0.206328 0.0525114i
\(697\) 310.719 0.445795
\(698\) 186.829 + 186.829i 0.267663 + 0.267663i
\(699\) 58.6220 + 58.6220i 0.0838656 + 0.0838656i
\(700\) 173.983i 0.248547i
\(701\) 738.399i 1.05335i 0.850066 + 0.526676i \(0.176562\pi\)
−0.850066 + 0.526676i \(0.823438\pi\)
\(702\) 173.388i 0.246991i
\(703\) −1320.69 −1.87864
\(704\) −14.9450 + 14.9450i −0.0212287 + 0.0212287i
\(705\) 8.14799i 0.0115574i
\(706\) −137.260 + 137.260i −0.194420 + 0.194420i
\(707\) 504.962 + 504.962i 0.714231 + 0.714231i
\(708\) −93.8736 + 93.8736i −0.132590 + 0.132590i
\(709\) 211.506i 0.298316i −0.988813 0.149158i \(-0.952344\pi\)
0.988813 0.149158i \(-0.0476564\pi\)
\(710\) −378.293 378.293i −0.532807 0.532807i
\(711\) −347.008 + 347.008i −0.488056 + 0.488056i
\(712\) 959.825 1.34807
\(713\) 376.249 + 376.249i 0.527699 + 0.527699i
\(714\) 53.1274 53.1274i 0.0744081 0.0744081i
\(715\) 17.0559 + 17.0559i 0.0238544 + 0.0238544i
\(716\) 130.608 0.182413
\(717\) 78.2135 + 78.2135i 0.109084 + 0.109084i
\(718\) 666.730i 0.928593i
\(719\) −479.844 −0.667376 −0.333688 0.942684i \(-0.608293\pi\)
−0.333688 + 0.942684i \(0.608293\pi\)
\(720\) 40.0921 0.0556835
\(721\) −1350.31 −1.87283
\(722\) −62.9974 + 62.9974i −0.0872540 + 0.0872540i
\(723\) −71.2728 + 71.2728i −0.0985792 + 0.0985792i
\(724\) 309.294i 0.427202i
\(725\) 215.197 54.7687i 0.296824 0.0755431i
\(726\) 97.2578 0.133964
\(727\) −943.499 943.499i −1.29780 1.29780i −0.929844 0.367953i \(-0.880059\pi\)
−0.367953 0.929844i \(-0.619941\pi\)
\(728\) −683.753 683.753i −0.939221 0.939221i
\(729\) 545.390i 0.748134i
\(730\) 30.0222i 0.0411263i
\(731\) 238.384i 0.326106i
\(732\) −61.1179 −0.0834944
\(733\) 256.074 256.074i 0.349350 0.349350i −0.510517 0.859868i \(-0.670546\pi\)
0.859868 + 0.510517i \(0.170546\pi\)
\(734\) 153.395i 0.208986i
\(735\) −82.6973 + 82.6973i −0.112513 + 0.112513i
\(736\) 222.555 + 222.555i 0.302385 + 0.302385i
\(737\) −10.5685 + 10.5685i −0.0143398 + 0.0143398i
\(738\) 357.262i 0.484095i
\(739\) 9.12101 + 9.12101i 0.0123424 + 0.0123424i 0.713251 0.700909i \(-0.247222\pi\)
−0.700909 + 0.713251i \(0.747222\pi\)
\(740\) −439.722 + 439.722i −0.594219 + 0.594219i
\(741\) −158.786 −0.214286
\(742\) −794.312 794.312i −1.07050 1.07050i
\(743\) −343.894 + 343.894i −0.462845 + 0.462845i −0.899587 0.436742i \(-0.856132\pi\)
0.436742 + 0.899587i \(0.356132\pi\)
\(744\) −190.643 190.643i −0.256241 0.256241i
\(745\) 587.175 0.788155
\(746\) 83.1437 + 83.1437i 0.111453 + 0.111453i
\(747\) 1185.46i 1.58696i
\(748\) −10.6983 −0.0143025
\(749\) 144.980 0.193564
\(750\) −109.517 −0.146023
\(751\) 485.159 485.159i 0.646017 0.646017i −0.306011 0.952028i \(-0.598994\pi\)
0.952028 + 0.306011i \(0.0989945\pi\)
\(752\) 2.47162 2.47162i 0.00328673 0.00328673i
\(753\) 120.953i 0.160628i
\(754\) −233.035 + 392.146i −0.309065 + 0.520088i
\(755\) −1120.66 −1.48432
\(756\) 177.101 + 177.101i 0.234261 + 0.234261i
\(757\) −158.090 158.090i −0.208838 0.208838i 0.594936 0.803773i \(-0.297178\pi\)
−0.803773 + 0.594936i \(0.797178\pi\)
\(758\) 323.852i 0.427246i
\(759\) 2.99023i 0.00393970i
\(760\) 705.078i 0.927734i
\(761\) 1412.54 1.85617 0.928084 0.372371i \(-0.121455\pi\)
0.928084 + 0.372371i \(0.121455\pi\)
\(762\) −42.0527 + 42.0527i −0.0551873 + 0.0551873i
\(763\) 374.179i 0.490405i
\(764\) 287.400 287.400i 0.376179 0.376179i
\(765\) 244.119 + 244.119i 0.319109 + 0.319109i
\(766\) −129.237 + 129.237i −0.168716 + 0.168716i
\(767\) 1105.70i 1.44159i
\(768\) −117.412 117.412i −0.152880 0.152880i
\(769\) −137.717 + 137.717i −0.179086 + 0.179086i −0.790957 0.611871i \(-0.790417\pi\)
0.611871 + 0.790957i \(0.290417\pi\)
\(770\) −24.5827 −0.0319256
\(771\) −122.004 122.004i −0.158242 0.158242i
\(772\) −412.675 + 412.675i −0.534553 + 0.534553i
\(773\) −349.001 349.001i −0.451489 0.451489i 0.444360 0.895848i \(-0.353431\pi\)
−0.895848 + 0.444360i \(0.853431\pi\)
\(774\) −274.092 −0.354124
\(775\) −285.688 285.688i −0.368629 0.368629i
\(776\) 923.285i 1.18980i
\(777\) 386.154 0.496981
\(778\) −617.964 −0.794298
\(779\) 669.244 0.859107
\(780\) −52.8676 + 52.8676i −0.0677790 + 0.0677790i
\(781\) 33.4485 33.4485i 0.0428278 0.0428278i
\(782\) 124.928i 0.159754i
\(783\)