Properties

Label 105.3.l.a.22.2
Level 105
Weight 3
Character 105.22
Analytic conductor 2.861
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.2
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.59930 - 1.59930i) q^{2} +(-1.22474 + 1.22474i) q^{3} +1.11554i q^{4} +(-1.35929 - 4.81169i) q^{5} +3.91747 q^{6} +(1.87083 + 1.87083i) q^{7} +(-4.61313 + 4.61313i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.59930 - 1.59930i) q^{2} +(-1.22474 + 1.22474i) q^{3} +1.11554i q^{4} +(-1.35929 - 4.81169i) q^{5} +3.91747 q^{6} +(1.87083 + 1.87083i) q^{7} +(-4.61313 + 4.61313i) q^{8} -3.00000i q^{9} +(-5.52142 + 9.86926i) q^{10} -13.7143 q^{11} +(-1.36625 - 1.36625i) q^{12} +(-16.4959 + 16.4959i) q^{13} -5.98404i q^{14} +(7.55788 + 4.22830i) q^{15} +19.2177 q^{16} +(-3.05243 - 3.05243i) q^{17} +(-4.79791 + 4.79791i) q^{18} -4.66410i q^{19} +(5.36761 - 1.51634i) q^{20} -4.58258 q^{21} +(21.9333 + 21.9333i) q^{22} +(-4.61681 + 4.61681i) q^{23} -11.2998i q^{24} +(-21.3046 + 13.0810i) q^{25} +52.7638 q^{26} +(3.67423 + 3.67423i) q^{27} +(-2.08698 + 2.08698i) q^{28} -50.3467i q^{29} +(-5.32500 - 18.8497i) q^{30} +11.0632 q^{31} +(-12.2824 - 12.2824i) q^{32} +(16.7965 - 16.7965i) q^{33} +9.76351i q^{34} +(6.45883 - 11.5448i) q^{35} +3.34661 q^{36} +(-44.4533 - 44.4533i) q^{37} +(-7.45931 + 7.45931i) q^{38} -40.4065i q^{39} +(28.4675 + 15.9263i) q^{40} -20.5922 q^{41} +(7.32892 + 7.32892i) q^{42} +(41.9068 - 41.9068i) q^{43} -15.2988i q^{44} +(-14.4351 + 4.07788i) q^{45} +14.7673 q^{46} +(20.4247 + 20.4247i) q^{47} +(-23.5368 + 23.5368i) q^{48} +7.00000i q^{49} +(54.9930 + 13.1521i) q^{50} +7.47689 q^{51} +(-18.4017 - 18.4017i) q^{52} +(-46.1212 + 46.1212i) q^{53} -11.7524i q^{54} +(18.6417 + 65.9888i) q^{55} -17.2608 q^{56} +(5.71233 + 5.71233i) q^{57} +(-80.5197 + 80.5197i) q^{58} +47.2598i q^{59} +(-4.71682 + 8.43108i) q^{60} +33.7814 q^{61} +(-17.6934 - 17.6934i) q^{62} +(5.61249 - 5.61249i) q^{63} -37.5843i q^{64} +(101.796 + 56.9502i) q^{65} -53.7253 q^{66} +(-63.1243 - 63.1243i) q^{67} +(3.40509 - 3.40509i) q^{68} -11.3088i q^{69} +(-28.7933 + 8.13407i) q^{70} -31.1884 q^{71} +(13.8394 + 13.8394i) q^{72} +(-19.0978 + 19.0978i) q^{73} +142.189i q^{74} +(10.0719 - 42.1136i) q^{75} +5.20297 q^{76} +(-25.6570 - 25.6570i) q^{77} +(-64.6221 + 64.6221i) q^{78} -53.2345i q^{79} +(-26.1225 - 92.4696i) q^{80} -9.00000 q^{81} +(32.9332 + 32.9332i) q^{82} +(97.3590 - 97.3590i) q^{83} -5.11203i q^{84} +(-10.5382 + 18.8365i) q^{85} -134.043 q^{86} +(61.6619 + 61.6619i) q^{87} +(63.2657 - 63.2657i) q^{88} +156.139i q^{89} +(29.6078 + 16.5643i) q^{90} -61.7219 q^{91} +(-5.15021 - 5.15021i) q^{92} +(-13.5496 + 13.5496i) q^{93} -65.3306i q^{94} +(-22.4422 + 6.33989i) q^{95} +30.0857 q^{96} +(-76.2395 - 76.2395i) q^{97} +(11.1951 - 11.1951i) q^{98} +41.1428i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.59930 1.59930i −0.799651 0.799651i 0.183389 0.983040i \(-0.441293\pi\)
−0.983040 + 0.183389i \(0.941293\pi\)
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 1.11554i 0.278884i
\(5\) −1.35929 4.81169i −0.271859 0.962337i
\(6\) 3.91747 0.652912
\(7\) 1.87083 + 1.87083i 0.267261 + 0.267261i
\(8\) −4.61313 + 4.61313i −0.576641 + 0.576641i
\(9\) 3.00000i 0.333333i
\(10\) −5.52142 + 9.86926i −0.552142 + 0.986926i
\(11\) −13.7143 −1.24675 −0.623376 0.781922i \(-0.714239\pi\)
−0.623376 + 0.781922i \(0.714239\pi\)
\(12\) −1.36625 1.36625i −0.113854 0.113854i
\(13\) −16.4959 + 16.4959i −1.26891 + 1.26891i −0.322263 + 0.946650i \(0.604443\pi\)
−0.946650 + 0.322263i \(0.895557\pi\)
\(14\) 5.98404i 0.427432i
\(15\) 7.55788 + 4.22830i 0.503858 + 0.281887i
\(16\) 19.2177 1.20111
\(17\) −3.05243 3.05243i −0.179555 0.179555i 0.611607 0.791162i \(-0.290523\pi\)
−0.791162 + 0.611607i \(0.790523\pi\)
\(18\) −4.79791 + 4.79791i −0.266550 + 0.266550i
\(19\) 4.66410i 0.245479i −0.992439 0.122740i \(-0.960832\pi\)
0.992439 0.122740i \(-0.0391680\pi\)
\(20\) 5.36761 1.51634i 0.268380 0.0758171i
\(21\) −4.58258 −0.218218
\(22\) 21.9333 + 21.9333i 0.996966 + 0.996966i
\(23\) −4.61681 + 4.61681i −0.200731 + 0.200731i −0.800313 0.599582i \(-0.795333\pi\)
0.599582 + 0.800313i \(0.295333\pi\)
\(24\) 11.2998i 0.470826i
\(25\) −21.3046 + 13.0810i −0.852186 + 0.523240i
\(26\) 52.7638 2.02938
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −2.08698 + 2.08698i −0.0745349 + 0.0745349i
\(29\) 50.3467i 1.73609i −0.496481 0.868047i \(-0.665375\pi\)
0.496481 0.868047i \(-0.334625\pi\)
\(30\) −5.32500 18.8497i −0.177500 0.628322i
\(31\) 11.0632 0.356877 0.178438 0.983951i \(-0.442896\pi\)
0.178438 + 0.983951i \(0.442896\pi\)
\(32\) −12.2824 12.2824i −0.383826 0.383826i
\(33\) 16.7965 16.7965i 0.508984 0.508984i
\(34\) 9.76351i 0.287162i
\(35\) 6.45883 11.5448i 0.184538 0.329853i
\(36\) 3.34661 0.0929613
\(37\) −44.4533 44.4533i −1.20144 1.20144i −0.973729 0.227712i \(-0.926876\pi\)
−0.227712 0.973729i \(-0.573124\pi\)
\(38\) −7.45931 + 7.45931i −0.196298 + 0.196298i
\(39\) 40.4065i 1.03606i
\(40\) 28.4675 + 15.9263i 0.711688 + 0.398158i
\(41\) −20.5922 −0.502249 −0.251124 0.967955i \(-0.580800\pi\)
−0.251124 + 0.967955i \(0.580800\pi\)
\(42\) 7.32892 + 7.32892i 0.174498 + 0.174498i
\(43\) 41.9068 41.9068i 0.974578 0.974578i −0.0251070 0.999685i \(-0.507993\pi\)
0.999685 + 0.0251070i \(0.00799264\pi\)
\(44\) 15.2988i 0.347699i
\(45\) −14.4351 + 4.07788i −0.320779 + 0.0906196i
\(46\) 14.7673 0.321029
\(47\) 20.4247 + 20.4247i 0.434569 + 0.434569i 0.890179 0.455610i \(-0.150579\pi\)
−0.455610 + 0.890179i \(0.650579\pi\)
\(48\) −23.5368 + 23.5368i −0.490350 + 0.490350i
\(49\) 7.00000i 0.142857i
\(50\) 54.9930 + 13.1521i 1.09986 + 0.263042i
\(51\) 7.47689 0.146606
\(52\) −18.4017 18.4017i −0.353879 0.353879i
\(53\) −46.1212 + 46.1212i −0.870212 + 0.870212i −0.992495 0.122283i \(-0.960978\pi\)
0.122283 + 0.992495i \(0.460978\pi\)
\(54\) 11.7524i 0.217637i
\(55\) 18.6417 + 65.9888i 0.338941 + 1.19980i
\(56\) −17.2608 −0.308228
\(57\) 5.71233 + 5.71233i 0.100216 + 0.100216i
\(58\) −80.5197 + 80.5197i −1.38827 + 1.38827i
\(59\) 47.2598i 0.801014i 0.916294 + 0.400507i \(0.131166\pi\)
−0.916294 + 0.400507i \(0.868834\pi\)
\(60\) −4.71682 + 8.43108i −0.0786136 + 0.140518i
\(61\) 33.7814 0.553793 0.276896 0.960900i \(-0.410694\pi\)
0.276896 + 0.960900i \(0.410694\pi\)
\(62\) −17.6934 17.6934i −0.285377 0.285377i
\(63\) 5.61249 5.61249i 0.0890871 0.0890871i
\(64\) 37.5843i 0.587254i
\(65\) 101.796 + 56.9502i 1.56609 + 0.876157i
\(66\) −53.7253 −0.814020
\(67\) −63.1243 63.1243i −0.942154 0.942154i 0.0562621 0.998416i \(-0.482082\pi\)
−0.998416 + 0.0562621i \(0.982082\pi\)
\(68\) 3.40509 3.40509i 0.0500749 0.0500749i
\(69\) 11.3088i 0.163896i
\(70\) −28.7933 + 8.13407i −0.411333 + 0.116201i
\(71\) −31.1884 −0.439273 −0.219637 0.975582i \(-0.570487\pi\)
−0.219637 + 0.975582i \(0.570487\pi\)
\(72\) 13.8394 + 13.8394i 0.192214 + 0.192214i
\(73\) −19.0978 + 19.0978i −0.261614 + 0.261614i −0.825709 0.564096i \(-0.809225\pi\)
0.564096 + 0.825709i \(0.309225\pi\)
\(74\) 142.189i 1.92147i
\(75\) 10.0719 42.1136i 0.134292 0.561515i
\(76\) 5.20297 0.0684601
\(77\) −25.6570 25.6570i −0.333208 0.333208i
\(78\) −64.6221 + 64.6221i −0.828489 + 0.828489i
\(79\) 53.2345i 0.673854i −0.941531 0.336927i \(-0.890612\pi\)
0.941531 0.336927i \(-0.109388\pi\)
\(80\) −26.1225 92.4696i −0.326532 1.15587i
\(81\) −9.00000 −0.111111
\(82\) 32.9332 + 32.9332i 0.401624 + 0.401624i
\(83\) 97.3590 97.3590i 1.17300 1.17300i 0.191510 0.981491i \(-0.438662\pi\)
0.981491 0.191510i \(-0.0613384\pi\)
\(84\) 5.11203i 0.0608575i
\(85\) −10.5382 + 18.8365i −0.123979 + 0.221606i
\(86\) −134.043 −1.55864
\(87\) 61.6619 + 61.6619i 0.708758 + 0.708758i
\(88\) 63.2657 63.2657i 0.718929 0.718929i
\(89\) 156.139i 1.75437i 0.480154 + 0.877184i \(0.340581\pi\)
−0.480154 + 0.877184i \(0.659419\pi\)
\(90\) 29.6078 + 16.5643i 0.328975 + 0.184047i
\(91\) −61.7219 −0.678263
\(92\) −5.15021 5.15021i −0.0559806 0.0559806i
\(93\) −13.5496 + 13.5496i −0.145694 + 0.145694i
\(94\) 65.3306i 0.695007i
\(95\) −22.4422 + 6.33989i −0.236234 + 0.0667356i
\(96\) 30.0857 0.313392
\(97\) −76.2395 76.2395i −0.785974 0.785974i 0.194857 0.980832i \(-0.437576\pi\)
−0.980832 + 0.194857i \(0.937576\pi\)
\(98\) 11.1951 11.1951i 0.114236 0.114236i
\(99\) 41.1428i 0.415584i
\(100\) −14.5923 23.7661i −0.145923 0.237661i
\(101\) −70.4622 −0.697646 −0.348823 0.937189i \(-0.613418\pi\)
−0.348823 + 0.937189i \(0.613418\pi\)
\(102\) −11.9578 11.9578i −0.117233 0.117233i
\(103\) 60.8151 60.8151i 0.590438 0.590438i −0.347312 0.937750i \(-0.612905\pi\)
0.937750 + 0.347312i \(0.112905\pi\)
\(104\) 152.195i 1.46342i
\(105\) 6.22907 + 22.0499i 0.0593245 + 0.209999i
\(106\) 147.524 1.39173
\(107\) −52.5369 52.5369i −0.490999 0.490999i 0.417622 0.908621i \(-0.362864\pi\)
−0.908621 + 0.417622i \(0.862864\pi\)
\(108\) −4.09874 + 4.09874i −0.0379513 + 0.0379513i
\(109\) 38.7375i 0.355390i 0.984086 + 0.177695i \(0.0568640\pi\)
−0.984086 + 0.177695i \(0.943136\pi\)
\(110\) 75.7222 135.350i 0.688384 1.23045i
\(111\) 108.888 0.980972
\(112\) 35.9531 + 35.9531i 0.321010 + 0.321010i
\(113\) −40.5307 + 40.5307i −0.358679 + 0.358679i −0.863326 0.504647i \(-0.831623\pi\)
0.504647 + 0.863326i \(0.331623\pi\)
\(114\) 18.2715i 0.160276i
\(115\) 28.4902 + 15.9390i 0.247741 + 0.138600i
\(116\) 56.1636 0.484169
\(117\) 49.4876 + 49.4876i 0.422971 + 0.422971i
\(118\) 75.5827 75.5827i 0.640532 0.640532i
\(119\) 11.4211i 0.0959760i
\(120\) −54.3712 + 15.3598i −0.453093 + 0.127998i
\(121\) 67.0812 0.554390
\(122\) −54.0266 54.0266i −0.442841 0.442841i
\(123\) 25.2202 25.2202i 0.205042 0.205042i
\(124\) 12.3414i 0.0995271i
\(125\) 91.9009 + 84.7303i 0.735207 + 0.677842i
\(126\) −17.9521 −0.142477
\(127\) −3.98961 3.98961i −0.0314143 0.0314143i 0.691225 0.722639i \(-0.257071\pi\)
−0.722639 + 0.691225i \(0.757071\pi\)
\(128\) −109.238 + 109.238i −0.853424 + 0.853424i
\(129\) 102.650i 0.795739i
\(130\) −71.7215 253.883i −0.551704 1.95294i
\(131\) −72.5637 −0.553921 −0.276961 0.960881i \(-0.589327\pi\)
−0.276961 + 0.960881i \(0.589327\pi\)
\(132\) 18.7371 + 18.7371i 0.141948 + 0.141948i
\(133\) 8.72573 8.72573i 0.0656070 0.0656070i
\(134\) 201.910i 1.50679i
\(135\) 12.6849 22.6736i 0.0939622 0.167953i
\(136\) 28.1625 0.207077
\(137\) 67.6559 + 67.6559i 0.493838 + 0.493838i 0.909513 0.415675i \(-0.136455\pi\)
−0.415675 + 0.909513i \(0.636455\pi\)
\(138\) −18.0862 + 18.0862i −0.131060 + 0.131060i
\(139\) 132.992i 0.956777i 0.878148 + 0.478388i \(0.158779\pi\)
−0.878148 + 0.478388i \(0.841221\pi\)
\(140\) 12.8787 + 7.20506i 0.0919906 + 0.0514647i
\(141\) −50.0302 −0.354824
\(142\) 49.8797 + 49.8797i 0.351265 + 0.351265i
\(143\) 226.229 226.229i 1.58202 1.58202i
\(144\) 57.6532i 0.400369i
\(145\) −242.253 + 68.4361i −1.67071 + 0.471973i
\(146\) 61.0863 0.418399
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) 49.5892 49.5892i 0.335062 0.335062i
\(149\) 46.6022i 0.312767i −0.987696 0.156383i \(-0.950016\pi\)
0.987696 0.156383i \(-0.0499835\pi\)
\(150\) −83.4604 + 51.2445i −0.556403 + 0.341630i
\(151\) 162.417 1.07561 0.537803 0.843071i \(-0.319254\pi\)
0.537803 + 0.843071i \(0.319254\pi\)
\(152\) 21.5161 + 21.5161i 0.141553 + 0.141553i
\(153\) −9.15729 + 9.15729i −0.0598515 + 0.0598515i
\(154\) 82.0667i 0.532901i
\(155\) −15.0381 53.2325i −0.0970201 0.343436i
\(156\) 45.0748 0.288941
\(157\) 108.835 + 108.835i 0.693219 + 0.693219i 0.962939 0.269720i \(-0.0869312\pi\)
−0.269720 + 0.962939i \(0.586931\pi\)
\(158\) −85.1380 + 85.1380i −0.538848 + 0.538848i
\(159\) 112.973i 0.710525i
\(160\) −42.4037 + 75.7946i −0.265023 + 0.473716i
\(161\) −17.2745 −0.107295
\(162\) 14.3937 + 14.3937i 0.0888501 + 0.0888501i
\(163\) −201.498 + 201.498i −1.23619 + 1.23619i −0.274638 + 0.961548i \(0.588558\pi\)
−0.961548 + 0.274638i \(0.911442\pi\)
\(164\) 22.9713i 0.140069i
\(165\) −103.651 57.9880i −0.628186 0.351443i
\(166\) −311.413 −1.87598
\(167\) −41.4832 41.4832i −0.248402 0.248402i 0.571912 0.820315i \(-0.306202\pi\)
−0.820315 + 0.571912i \(0.806202\pi\)
\(168\) 21.1400 21.1400i 0.125833 0.125833i
\(169\) 375.227i 2.22028i
\(170\) 46.9790 13.2715i 0.276347 0.0780676i
\(171\) −13.9923 −0.0818263
\(172\) 46.7486 + 46.7486i 0.271794 + 0.271794i
\(173\) 130.020 130.020i 0.751561 0.751561i −0.223209 0.974771i \(-0.571653\pi\)
0.974771 + 0.223209i \(0.0716534\pi\)
\(174\) 197.232i 1.13352i
\(175\) −64.3296 15.3850i −0.367598 0.0879144i
\(176\) −263.557 −1.49748
\(177\) −57.8812 57.8812i −0.327013 0.327013i
\(178\) 249.713 249.713i 1.40288 1.40288i
\(179\) 95.2857i 0.532322i 0.963929 + 0.266161i \(0.0857553\pi\)
−0.963929 + 0.266161i \(0.914245\pi\)
\(180\) −4.54902 16.1028i −0.0252724 0.0894601i
\(181\) −189.309 −1.04590 −0.522952 0.852362i \(-0.675169\pi\)
−0.522952 + 0.852362i \(0.675169\pi\)
\(182\) 98.7120 + 98.7120i 0.542373 + 0.542373i
\(183\) −41.3736 + 41.3736i −0.226085 + 0.226085i
\(184\) 42.5959i 0.231499i
\(185\) −153.470 + 274.320i −0.829569 + 1.48281i
\(186\) 43.3397 0.233009
\(187\) 41.8618 + 41.8618i 0.223860 + 0.223860i
\(188\) −22.7845 + 22.7845i −0.121194 + 0.121194i
\(189\) 13.7477i 0.0727393i
\(190\) 46.0312 + 25.7524i 0.242270 + 0.135539i
\(191\) 324.784 1.70044 0.850219 0.526430i \(-0.176470\pi\)
0.850219 + 0.526430i \(0.176470\pi\)
\(192\) 46.0311 + 46.0311i 0.239746 + 0.239746i
\(193\) −24.7283 + 24.7283i −0.128126 + 0.128126i −0.768262 0.640136i \(-0.778878\pi\)
0.640136 + 0.768262i \(0.278878\pi\)
\(194\) 243.860i 1.25701i
\(195\) −194.423 + 54.9243i −0.997042 + 0.281663i
\(196\) −7.80875 −0.0398406
\(197\) 9.08901 + 9.08901i 0.0461371 + 0.0461371i 0.729799 0.683662i \(-0.239614\pi\)
−0.683662 + 0.729799i \(0.739614\pi\)
\(198\) 65.7998 65.7998i 0.332322 0.332322i
\(199\) 119.192i 0.598953i 0.954104 + 0.299476i \(0.0968120\pi\)
−0.954104 + 0.299476i \(0.903188\pi\)
\(200\) 37.9367 158.625i 0.189684 0.793127i
\(201\) 154.622 0.769265
\(202\) 112.690 + 112.690i 0.557873 + 0.557873i
\(203\) 94.1901 94.1901i 0.463991 0.463991i
\(204\) 8.34074i 0.0408860i
\(205\) 27.9909 + 99.0832i 0.136541 + 0.483333i
\(206\) −194.524 −0.944289
\(207\) 13.8504 + 13.8504i 0.0669103 + 0.0669103i
\(208\) −317.013 + 317.013i −1.52410 + 1.52410i
\(209\) 63.9647i 0.306051i
\(210\) 25.3023 45.2266i 0.120487 0.215365i
\(211\) −35.9417 −0.170340 −0.0851699 0.996366i \(-0.527143\pi\)
−0.0851699 + 0.996366i \(0.527143\pi\)
\(212\) −51.4499 51.4499i −0.242688 0.242688i
\(213\) 38.1978 38.1978i 0.179333 0.179333i
\(214\) 168.045i 0.785256i
\(215\) −258.606 144.679i −1.20282 0.672925i
\(216\) −33.8994 −0.156942
\(217\) 20.6973 + 20.6973i 0.0953793 + 0.0953793i
\(218\) 61.9529 61.9529i 0.284188 0.284188i
\(219\) 46.7798i 0.213607i
\(220\) −73.6128 + 20.7955i −0.334604 + 0.0945251i
\(221\) 100.705 0.455678
\(222\) −174.145 174.145i −0.784435 0.784435i
\(223\) −230.412 + 230.412i −1.03324 + 1.03324i −0.0338071 + 0.999428i \(0.510763\pi\)
−0.999428 + 0.0338071i \(0.989237\pi\)
\(224\) 45.9566i 0.205164i
\(225\) 39.2430 + 63.9139i 0.174413 + 0.284062i
\(226\) 129.642 0.573636
\(227\) 99.4972 + 99.4972i 0.438314 + 0.438314i 0.891444 0.453130i \(-0.149693\pi\)
−0.453130 + 0.891444i \(0.649693\pi\)
\(228\) −6.37231 + 6.37231i −0.0279487 + 0.0279487i
\(229\) 12.3627i 0.0539854i −0.999636 0.0269927i \(-0.991407\pi\)
0.999636 0.0269927i \(-0.00859309\pi\)
\(230\) −20.0732 71.0558i −0.0872746 0.308938i
\(231\) 62.8467 0.272064
\(232\) 232.256 + 232.256i 1.00110 + 1.00110i
\(233\) 214.583 214.583i 0.920959 0.920959i −0.0761385 0.997097i \(-0.524259\pi\)
0.997097 + 0.0761385i \(0.0242591\pi\)
\(234\) 158.291i 0.676458i
\(235\) 70.5142 126.041i 0.300060 0.536343i
\(236\) −52.7200 −0.223390
\(237\) 65.1987 + 65.1987i 0.275100 + 0.275100i
\(238\) −18.2659 + 18.2659i −0.0767473 + 0.0767473i
\(239\) 10.6709i 0.0446481i −0.999751 0.0223240i \(-0.992893\pi\)
0.999751 0.0223240i \(-0.00710655\pi\)
\(240\) 145.245 + 81.2583i 0.605188 + 0.338576i
\(241\) −217.027 −0.900526 −0.450263 0.892896i \(-0.648670\pi\)
−0.450263 + 0.892896i \(0.648670\pi\)
\(242\) −107.283 107.283i −0.443318 0.443318i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 37.6843i 0.154444i
\(245\) 33.6818 9.51506i 0.137477 0.0388370i
\(246\) −80.6694 −0.327924
\(247\) 76.9384 + 76.9384i 0.311492 + 0.311492i
\(248\) −51.0359 + 51.0359i −0.205790 + 0.205790i
\(249\) 238.480i 0.957751i
\(250\) −11.4680 282.487i −0.0458719 1.12995i
\(251\) −59.6693 −0.237726 −0.118863 0.992911i \(-0.537925\pi\)
−0.118863 + 0.992911i \(0.537925\pi\)
\(252\) 6.26093 + 6.26093i 0.0248450 + 0.0248450i
\(253\) 63.3161 63.3161i 0.250261 0.250261i
\(254\) 12.7612i 0.0502409i
\(255\) −10.1633 35.9765i −0.0398561 0.141084i
\(256\) 199.073 0.777629
\(257\) −224.525 224.525i −0.873639 0.873639i 0.119228 0.992867i \(-0.461958\pi\)
−0.992867 + 0.119228i \(0.961958\pi\)
\(258\) 164.169 164.169i 0.636314 0.636314i
\(259\) 166.329i 0.642197i
\(260\) −63.5300 + 113.557i −0.244346 + 0.436757i
\(261\) −151.040 −0.578698
\(262\) 116.051 + 116.051i 0.442944 + 0.442944i
\(263\) −0.00150876 + 0.00150876i −5.73673e−6 + 5.73673e-6i −0.707110 0.707104i \(-0.750001\pi\)
0.707104 + 0.707110i \(0.250001\pi\)
\(264\) 154.969i 0.587003i
\(265\) 284.613 + 159.229i 1.07401 + 0.600862i
\(266\) −27.9102 −0.104925
\(267\) −191.230 191.230i −0.716218 0.716218i
\(268\) 70.4174 70.4174i 0.262752 0.262752i
\(269\) 10.8410i 0.0403011i 0.999797 + 0.0201506i \(0.00641456\pi\)
−0.999797 + 0.0201506i \(0.993585\pi\)
\(270\) −56.5490 + 15.9750i −0.209441 + 0.0591667i
\(271\) 423.331 1.56211 0.781054 0.624464i \(-0.214682\pi\)
0.781054 + 0.624464i \(0.214682\pi\)
\(272\) −58.6607 58.6607i −0.215664 0.215664i
\(273\) 75.5936 75.5936i 0.276900 0.276900i
\(274\) 216.404i 0.789797i
\(275\) 292.178 179.396i 1.06246 0.652350i
\(276\) 12.6154 0.0457079
\(277\) 43.6341 + 43.6341i 0.157524 + 0.157524i 0.781469 0.623945i \(-0.214471\pi\)
−0.623945 + 0.781469i \(0.714471\pi\)
\(278\) 212.694 212.694i 0.765088 0.765088i
\(279\) 33.1895i 0.118959i
\(280\) 23.4624 + 83.0533i 0.0837944 + 0.296619i
\(281\) −173.395 −0.617065 −0.308532 0.951214i \(-0.599838\pi\)
−0.308532 + 0.951214i \(0.599838\pi\)
\(282\) 80.0134 + 80.0134i 0.283735 + 0.283735i
\(283\) 205.636 205.636i 0.726630 0.726630i −0.243317 0.969947i \(-0.578235\pi\)
0.969947 + 0.243317i \(0.0782354\pi\)
\(284\) 34.7918i 0.122506i
\(285\) 19.7212 35.2507i 0.0691972 0.123687i
\(286\) −723.616 −2.53013
\(287\) −38.5245 38.5245i −0.134232 0.134232i
\(288\) −36.8473 + 36.8473i −0.127942 + 0.127942i
\(289\) 270.365i 0.935520i
\(290\) 496.885 + 277.985i 1.71340 + 0.958570i
\(291\) 186.748 0.641745
\(292\) −21.3043 21.3043i −0.0729598 0.0729598i
\(293\) −240.660 + 240.660i −0.821366 + 0.821366i −0.986304 0.164938i \(-0.947258\pi\)
0.164938 + 0.986304i \(0.447258\pi\)
\(294\) 27.4223i 0.0932732i
\(295\) 227.399 64.2400i 0.770845 0.217763i
\(296\) 410.138 1.38560
\(297\) −50.3894 50.3894i −0.169661 0.169661i
\(298\) −74.5311 + 74.5311i −0.250104 + 0.250104i
\(299\) 152.316i 0.509420i
\(300\) 46.9793 + 11.2355i 0.156598 + 0.0374517i
\(301\) 156.801 0.520934
\(302\) −259.753 259.753i −0.860110 0.860110i
\(303\) 86.2982 86.2982i 0.284813 0.284813i
\(304\) 89.6334i 0.294847i
\(305\) −45.9188 162.545i −0.150554 0.532936i
\(306\) 29.2905 0.0957207
\(307\) −334.742 334.742i −1.09037 1.09037i −0.995489 0.0948775i \(-0.969754\pi\)
−0.0948775 0.995489i \(-0.530246\pi\)
\(308\) 28.6214 28.6214i 0.0929265 0.0929265i
\(309\) 148.966i 0.482091i
\(310\) −61.0844 + 109.185i −0.197046 + 0.352211i
\(311\) −29.4564 −0.0947151 −0.0473575 0.998878i \(-0.515080\pi\)
−0.0473575 + 0.998878i \(0.515080\pi\)
\(312\) 186.400 + 186.400i 0.597437 + 0.597437i
\(313\) −375.133 + 375.133i −1.19851 + 1.19851i −0.223895 + 0.974613i \(0.571877\pi\)
−0.974613 + 0.223895i \(0.928123\pi\)
\(314\) 348.121i 1.10867i
\(315\) −34.6345 19.3765i −0.109951 0.0615127i
\(316\) 59.3850 0.187927
\(317\) −409.594 409.594i −1.29209 1.29209i −0.933489 0.358605i \(-0.883252\pi\)
−0.358605 0.933489i \(-0.616748\pi\)
\(318\) −180.679 + 180.679i −0.568172 + 0.568172i
\(319\) 690.469i 2.16448i
\(320\) −180.844 + 51.0881i −0.565136 + 0.159650i
\(321\) 128.689 0.400899
\(322\) 27.6272 + 27.6272i 0.0857987 + 0.0857987i
\(323\) −14.2368 + 14.2368i −0.0440769 + 0.0440769i
\(324\) 10.0398i 0.0309871i
\(325\) 135.656 567.221i 0.417403 1.74530i
\(326\) 644.513 1.97703
\(327\) −47.4435 47.4435i −0.145087 0.145087i
\(328\) 94.9945 94.9945i 0.289617 0.289617i
\(329\) 76.4224i 0.232287i
\(330\) 73.0285 + 258.509i 0.221298 + 0.783361i
\(331\) −71.9385 −0.217337 −0.108668 0.994078i \(-0.534659\pi\)
−0.108668 + 0.994078i \(0.534659\pi\)
\(332\) 108.607 + 108.607i 0.327131 + 0.327131i
\(333\) −133.360 + 133.360i −0.400480 + 0.400480i
\(334\) 132.688i 0.397270i
\(335\) −217.930 + 389.539i −0.650537 + 1.16280i
\(336\) −88.0667 −0.262103
\(337\) −302.137 302.137i −0.896548 0.896548i 0.0985809 0.995129i \(-0.468570\pi\)
−0.995129 + 0.0985809i \(0.968570\pi\)
\(338\) −600.102 + 600.102i −1.77545 + 1.77545i
\(339\) 99.2796i 0.292860i
\(340\) −21.0128 11.7557i −0.0618022 0.0345756i
\(341\) −151.723 −0.444937
\(342\) 22.3779 + 22.3779i 0.0654325 + 0.0654325i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 386.643i 1.12396i
\(345\) −54.4145 + 15.3720i −0.157723 + 0.0445566i
\(346\) −415.883 −1.20197
\(347\) −346.764 346.764i −0.999320 0.999320i 0.000679298 1.00000i \(-0.499784\pi\)
−1.00000 0.000679298i \(0.999784\pi\)
\(348\) −68.7861 + 68.7861i −0.197661 + 0.197661i
\(349\) 29.7025i 0.0851075i 0.999094 + 0.0425537i \(0.0135494\pi\)
−0.999094 + 0.0425537i \(0.986451\pi\)
\(350\) 78.2772 + 127.488i 0.223649 + 0.364251i
\(351\) −121.219 −0.345354
\(352\) 168.444 + 168.444i 0.478535 + 0.478535i
\(353\) −368.835 + 368.835i −1.04486 + 1.04486i −0.0459136 + 0.998945i \(0.514620\pi\)
−0.998945 + 0.0459136i \(0.985380\pi\)
\(354\) 185.139i 0.522992i
\(355\) 42.3942 + 150.069i 0.119420 + 0.422729i
\(356\) −174.178 −0.489265
\(357\) 13.9880 + 13.9880i 0.0391820 + 0.0391820i
\(358\) 152.391 152.391i 0.425672 0.425672i
\(359\) 610.662i 1.70101i 0.525969 + 0.850504i \(0.323703\pi\)
−0.525969 + 0.850504i \(0.676297\pi\)
\(360\) 47.7790 85.4026i 0.132719 0.237229i
\(361\) 339.246 0.939740
\(362\) 302.762 + 302.762i 0.836358 + 0.836358i
\(363\) −82.1573 + 82.1573i −0.226329 + 0.226329i
\(364\) 68.8530i 0.189157i
\(365\) 117.852 + 65.9331i 0.322882 + 0.180639i
\(366\) 132.338 0.361578
\(367\) 72.5232 + 72.5232i 0.197611 + 0.197611i 0.798975 0.601364i \(-0.205376\pi\)
−0.601364 + 0.798975i \(0.705376\pi\)
\(368\) −88.7245 + 88.7245i −0.241099 + 0.241099i
\(369\) 61.7766i 0.167416i
\(370\) 684.167 193.276i 1.84910 0.522368i
\(371\) −172.570 −0.465148
\(372\) −15.1150 15.1150i −0.0406318 0.0406318i
\(373\) 6.51685 6.51685i 0.0174714 0.0174714i −0.698317 0.715789i \(-0.746067\pi\)
0.715789 + 0.698317i \(0.246067\pi\)
\(374\) 133.899i 0.358020i
\(375\) −216.328 + 8.78217i −0.576875 + 0.0234191i
\(376\) −188.444 −0.501181
\(377\) 830.513 + 830.513i 2.20295 + 2.20295i
\(378\) 21.9868 21.9868i 0.0581661 0.0581661i
\(379\) 224.357i 0.591970i −0.955193 0.295985i \(-0.904352\pi\)
0.955193 0.295985i \(-0.0956479\pi\)
\(380\) −7.07237 25.0351i −0.0186115 0.0658817i
\(381\) 9.77251 0.0256496
\(382\) −519.427 519.427i −1.35976 1.35976i
\(383\) 82.5720 82.5720i 0.215593 0.215593i −0.591045 0.806638i \(-0.701285\pi\)
0.806638 + 0.591045i \(0.201285\pi\)
\(384\) 267.578i 0.696818i
\(385\) −88.5782 + 158.329i −0.230073 + 0.411244i
\(386\) 79.0961 0.204912
\(387\) −125.721 125.721i −0.324859 0.324859i
\(388\) 85.0479 85.0479i 0.219196 0.219196i
\(389\) 711.444i 1.82891i −0.404693 0.914453i \(-0.632622\pi\)
0.404693 0.914453i \(-0.367378\pi\)
\(390\) 398.782 + 223.101i 1.02252 + 0.572054i
\(391\) 28.1850 0.0720843
\(392\) −32.2919 32.2919i −0.0823773 0.0823773i
\(393\) 88.8720 88.8720i 0.226137 0.226137i
\(394\) 29.0721i 0.0737871i
\(395\) −256.148 + 72.3613i −0.648475 + 0.183193i
\(396\) −45.8963 −0.115900
\(397\) −333.858 333.858i −0.840951 0.840951i 0.148032 0.988983i \(-0.452706\pi\)
−0.988983 + 0.148032i \(0.952706\pi\)
\(398\) 190.623 190.623i 0.478953 0.478953i
\(399\) 21.3736i 0.0535679i
\(400\) −409.427 + 251.387i −1.02357 + 0.628467i
\(401\) −125.123 −0.312027 −0.156014 0.987755i \(-0.549864\pi\)
−0.156014 + 0.987755i \(0.549864\pi\)
\(402\) −247.288 247.288i −0.615144 0.615144i
\(403\) −182.497 + 182.497i −0.452845 + 0.452845i
\(404\) 78.6031i 0.194562i
\(405\) 12.2336 + 43.3052i 0.0302065 + 0.106926i
\(406\) −301.277 −0.742062
\(407\) 609.645 + 609.645i 1.49790 + 1.49790i
\(408\) −34.4919 + 34.4919i −0.0845389 + 0.0845389i
\(409\) 313.700i 0.766993i −0.923542 0.383496i \(-0.874720\pi\)
0.923542 0.383496i \(-0.125280\pi\)
\(410\) 113.698 203.230i 0.277313 0.495683i
\(411\) −165.722 −0.403217
\(412\) 67.8414 + 67.8414i 0.164664 + 0.164664i
\(413\) −88.4150 + 88.4150i −0.214080 + 0.214080i
\(414\) 44.3020i 0.107010i
\(415\) −600.801 336.121i −1.44771 0.809931i
\(416\) 405.219 0.974083
\(417\) −162.881 162.881i −0.390602 0.390602i
\(418\) 102.299 102.299i 0.244734 0.244734i
\(419\) 182.061i 0.434514i −0.976114 0.217257i \(-0.930289\pi\)
0.976114 0.217257i \(-0.0697110\pi\)
\(420\) −24.5975 + 6.94875i −0.0585654 + 0.0165446i
\(421\) 444.013 1.05466 0.527331 0.849660i \(-0.323193\pi\)
0.527331 + 0.849660i \(0.323193\pi\)
\(422\) 57.4817 + 57.4817i 0.136212 + 0.136212i
\(423\) 61.2742 61.2742i 0.144856 0.144856i
\(424\) 425.527i 1.00360i
\(425\) 104.960 + 25.1021i 0.246964 + 0.0590637i
\(426\) −122.180 −0.286807
\(427\) 63.1992 + 63.1992i 0.148007 + 0.148007i
\(428\) 58.6068 58.6068i 0.136932 0.136932i
\(429\) 554.145i 1.29171i
\(430\) 182.204 + 644.975i 0.423731 + 1.49994i
\(431\) −209.687 −0.486514 −0.243257 0.969962i \(-0.578216\pi\)
−0.243257 + 0.969962i \(0.578216\pi\)
\(432\) 70.6104 + 70.6104i 0.163450 + 0.163450i
\(433\) 593.138 593.138i 1.36983 1.36983i 0.509167 0.860668i \(-0.329954\pi\)
0.860668 0.509167i \(-0.170046\pi\)
\(434\) 66.2025i 0.152540i
\(435\) 212.881 380.514i 0.489382 0.874746i
\(436\) −43.2130 −0.0991124
\(437\) 21.5333 + 21.5333i 0.0492752 + 0.0492752i
\(438\) −74.8151 + 74.8151i −0.170811 + 0.170811i
\(439\) 91.5547i 0.208553i −0.994548 0.104276i \(-0.966747\pi\)
0.994548 0.104276i \(-0.0332527\pi\)
\(440\) −390.411 218.418i −0.887299 0.496405i
\(441\) 21.0000 0.0476190
\(442\) −161.058 161.058i −0.364384 0.364384i
\(443\) 302.352 302.352i 0.682511 0.682511i −0.278054 0.960565i \(-0.589689\pi\)
0.960565 + 0.278054i \(0.0896895\pi\)
\(444\) 121.468i 0.273577i
\(445\) 751.291 212.239i 1.68829 0.476941i
\(446\) 736.995 1.65246
\(447\) 57.0759 + 57.0759i 0.127686 + 0.127686i
\(448\) 70.3137 70.3137i 0.156950 0.156950i
\(449\) 190.141i 0.423477i −0.977326 0.211738i \(-0.932088\pi\)
0.977326 0.211738i \(-0.0679125\pi\)
\(450\) 39.4563 164.979i 0.0876806 0.366620i
\(451\) 282.407 0.626180
\(452\) −45.2135 45.2135i −0.100030 0.100030i
\(453\) −198.919 + 198.919i −0.439114 + 0.439114i
\(454\) 318.252i 0.700996i
\(455\) 83.8982 + 296.986i 0.184392 + 0.652717i
\(456\) −52.7035 −0.115578
\(457\) −83.0275 83.0275i −0.181680 0.181680i 0.610408 0.792087i \(-0.291006\pi\)
−0.792087 + 0.610408i \(0.791006\pi\)
\(458\) −19.7716 + 19.7716i −0.0431695 + 0.0431695i
\(459\) 22.4307i 0.0488686i
\(460\) −17.7806 + 31.7819i −0.0386534 + 0.0690910i
\(461\) 231.095 0.501290 0.250645 0.968079i \(-0.419357\pi\)
0.250645 + 0.968079i \(0.419357\pi\)
\(462\) −100.511 100.511i −0.217556 0.217556i
\(463\) −584.068 + 584.068i −1.26149 + 1.26149i −0.311112 + 0.950373i \(0.600701\pi\)
−0.950373 + 0.311112i \(0.899299\pi\)
\(464\) 967.550i 2.08524i
\(465\) 83.6141 + 46.7784i 0.179815 + 0.100599i
\(466\) −686.367 −1.47289
\(467\) −50.5678 50.5678i −0.108282 0.108282i 0.650890 0.759172i \(-0.274396\pi\)
−0.759172 + 0.650890i \(0.774396\pi\)
\(468\) −55.2052 + 55.2052i −0.117960 + 0.117960i
\(469\) 236.190i 0.503602i
\(470\) −314.351 + 88.8036i −0.668831 + 0.188944i
\(471\) −266.591 −0.566011
\(472\) −218.016 218.016i −0.461898 0.461898i
\(473\) −574.722 + 574.722i −1.21506 + 1.21506i
\(474\) 208.545i 0.439968i
\(475\) 61.0111 + 99.3670i 0.128444 + 0.209194i
\(476\) 12.7407 0.0267662
\(477\) 138.364 + 138.364i 0.290071 + 0.290071i
\(478\) −17.0660 + 17.0660i −0.0357029 + 0.0357029i
\(479\) 479.014i 1.00003i −0.866017 0.500015i \(-0.833328\pi\)
0.866017 0.500015i \(-0.166672\pi\)
\(480\) −40.8953 144.763i −0.0851985 0.301589i
\(481\) 1466.59 3.04905
\(482\) 347.092 + 347.092i 0.720107 + 0.720107i
\(483\) 21.1569 21.1569i 0.0438030 0.0438030i
\(484\) 74.8314i 0.154610i
\(485\) −263.209 + 470.473i −0.542698 + 0.970046i
\(486\) −35.2573 −0.0725458
\(487\) 533.369 + 533.369i 1.09521 + 1.09521i 0.994962 + 0.100250i \(0.0319644\pi\)
0.100250 + 0.994962i \(0.468036\pi\)
\(488\) −155.838 + 155.838i −0.319340 + 0.319340i
\(489\) 493.568i 1.00934i
\(490\) −69.0848 38.6499i −0.140989 0.0788774i
\(491\) −348.294 −0.709356 −0.354678 0.934989i \(-0.615409\pi\)
−0.354678 + 0.934989i \(0.615409\pi\)
\(492\) 28.1340 + 28.1340i 0.0571830 + 0.0571830i
\(493\) −153.680 + 153.680i −0.311724 + 0.311724i
\(494\) 246.096i 0.498169i
\(495\) 197.966 55.9252i 0.399932 0.112980i
\(496\) 212.609 0.428647
\(497\) −58.3481 58.3481i −0.117401 0.117401i
\(498\) 381.402 381.402i 0.765867 0.765867i
\(499\) 665.697i 1.33406i 0.745030 + 0.667031i \(0.232435\pi\)
−0.745030 + 0.667031i \(0.767565\pi\)
\(500\) −94.5197 + 102.519i −0.189039 + 0.205037i
\(501\) 101.613 0.202820
\(502\) 95.4292 + 95.4292i 0.190098 + 0.190098i
\(503\) 462.086 462.086i 0.918660 0.918660i −0.0782724 0.996932i \(-0.524940\pi\)
0.996932 + 0.0782724i \(0.0249404\pi\)
\(504\) 51.7823i 0.102743i
\(505\) 95.7789 + 339.042i 0.189661 + 0.671370i
\(506\) −202.523 −0.400244
\(507\) 459.558 + 459.558i 0.906426 + 0.906426i
\(508\) 4.45055 4.45055i 0.00876093 0.00876093i
\(509\) 75.7747i 0.148870i 0.997226 + 0.0744348i \(0.0237153\pi\)
−0.997226 + 0.0744348i \(0.976285\pi\)
\(510\) −41.2830 + 73.7914i −0.0809471 + 0.144689i
\(511\) −71.4574 −0.139838
\(512\) 118.575 + 118.575i 0.231592 + 0.231592i
\(513\) 17.1370 17.1370i 0.0334055 0.0334055i
\(514\) 718.167i 1.39721i
\(515\) −375.289 209.958i −0.728716 0.407685i
\(516\) −114.510 −0.221919
\(517\) −280.110 280.110i −0.541799 0.541799i
\(518\) −266.010 + 266.010i −0.513534 + 0.513534i
\(519\) 318.483i 0.613647i
\(520\) −732.315 + 206.878i −1.40830 + 0.397842i
\(521\) −493.508 −0.947231 −0.473616 0.880732i \(-0.657051\pi\)
−0.473616 + 0.880732i \(0.657051\pi\)
\(522\) 241.559 + 241.559i 0.462757 + 0.462757i
\(523\) 88.8615 88.8615i 0.169907 0.169907i −0.617031 0.786939i \(-0.711665\pi\)
0.786939 + 0.617031i \(0.211665\pi\)
\(524\) 80.9474i 0.154480i
\(525\) 97.6301 59.9446i 0.185962 0.114180i
\(526\) 0.00482592 9.17476e−6
\(527\) −33.7696 33.7696i −0.0640789 0.0640789i
\(528\) 322.790 322.790i 0.611345 0.611345i
\(529\) 486.370i 0.919414i
\(530\) −200.528 709.837i −0.378355 1.33932i
\(531\) 141.779 0.267005
\(532\) 9.73387 + 9.73387i 0.0182967 + 0.0182967i
\(533\) 339.686 339.686i 0.637310 0.637310i
\(534\) 611.670i 1.14545i
\(535\) −181.378 + 324.204i −0.339024 + 0.605989i
\(536\) 582.401 1.08657
\(537\) −116.701 116.701i −0.217320 0.217320i
\(538\) 17.3380 17.3380i 0.0322268 0.0322268i
\(539\) 95.9999i 0.178107i
\(540\) 25.2932 + 14.1505i 0.0468393 + 0.0262045i
\(541\) 95.0854 0.175759 0.0878793 0.996131i \(-0.471991\pi\)
0.0878793 + 0.996131i \(0.471991\pi\)
\(542\) −677.035 677.035i −1.24914 1.24914i
\(543\) 231.855 231.855i 0.426988 0.426988i
\(544\) 74.9825i 0.137835i
\(545\) 186.392 52.6556i 0.342005 0.0966158i
\(546\) −241.794 −0.442846
\(547\) 638.590 + 638.590i 1.16744 + 1.16744i 0.982807 + 0.184634i \(0.0591100\pi\)
0.184634 + 0.982807i \(0.440890\pi\)
\(548\) −75.4725 + 75.4725i −0.137724 + 0.137724i
\(549\) 101.344i 0.184598i
\(550\) −754.189 180.371i −1.37125 0.327948i
\(551\) −234.822 −0.426175
\(552\) 52.1691 + 52.1691i 0.0945092 + 0.0945092i
\(553\) 99.5926 99.5926i 0.180095 0.180095i
\(554\) 139.568i 0.251928i
\(555\) −148.011 523.934i −0.266686 0.944026i
\(556\) −148.357 −0.266830
\(557\) 368.475 + 368.475i 0.661534 + 0.661534i 0.955742 0.294207i \(-0.0950556\pi\)
−0.294207 + 0.955742i \(0.595056\pi\)
\(558\) −53.0801 + 53.0801i −0.0951256 + 0.0951256i
\(559\) 1382.58i 2.47331i
\(560\) 124.124 221.866i 0.221650 0.396189i
\(561\) −102.540 −0.182781
\(562\) 277.311 + 277.311i 0.493436 + 0.493436i
\(563\) −229.051 + 229.051i −0.406840 + 0.406840i −0.880635 0.473795i \(-0.842884\pi\)
0.473795 + 0.880635i \(0.342884\pi\)
\(564\) 55.8104i 0.0989547i
\(565\) 250.114 + 139.928i 0.442680 + 0.247660i
\(566\) −657.749 −1.16210
\(567\) −16.8375 16.8375i −0.0296957 0.0296957i
\(568\) 143.876 143.876i 0.253303 0.253303i
\(569\) 156.076i 0.274298i −0.990550 0.137149i \(-0.956206\pi\)
0.990550 0.137149i \(-0.0437940\pi\)
\(570\) −87.9167 + 24.8363i −0.154240 + 0.0435725i
\(571\) −689.495 −1.20752 −0.603761 0.797166i \(-0.706332\pi\)
−0.603761 + 0.797166i \(0.706332\pi\)
\(572\) 252.366 + 252.366i 0.441200 + 0.441200i
\(573\) −397.777 + 397.777i −0.694201 + 0.694201i
\(574\) 123.225i 0.214677i
\(575\) 37.9670 158.752i 0.0660295 0.276090i
\(576\) −112.753 −0.195751
\(577\) −613.020 613.020i −1.06243 1.06243i −0.997917 0.0645083i \(-0.979452\pi\)
−0.0645083 0.997917i \(-0.520548\pi\)
\(578\) −432.396 + 432.396i −0.748090 + 0.748090i
\(579\) 60.5718i 0.104614i
\(580\) −76.3429 270.242i −0.131626 0.465934i
\(581\) 364.284 0.626995
\(582\) −298.666 298.666i −0.513172 0.513172i
\(583\) 632.519 632.519i 1.08494 1.08494i
\(584\) 176.201i 0.301714i
\(585\) 170.851 305.387i 0.292052 0.522029i
\(586\) 769.777 1.31361
\(587\) −100.105 100.105i −0.170536 0.170536i 0.616679 0.787215i \(-0.288478\pi\)
−0.787215 + 0.616679i \(0.788478\pi\)
\(588\) 9.56373 9.56373i 0.0162648 0.0162648i
\(589\) 51.5998i 0.0876057i
\(590\) −466.420 260.941i −0.790542 0.442273i
\(591\) −22.2634 −0.0376708
\(592\) −854.291 854.291i −1.44306 1.44306i
\(593\) 436.401 436.401i 0.735920 0.735920i −0.235866 0.971786i \(-0.575793\pi\)
0.971786 + 0.235866i \(0.0757925\pi\)
\(594\) 161.176i 0.271340i
\(595\) −54.9549 + 15.5247i −0.0923613 + 0.0260919i
\(596\) 51.9865 0.0872256
\(597\) −145.979 145.979i −0.244521 0.244521i
\(598\) −243.600 + 243.600i −0.407358 + 0.407358i
\(599\) 30.2472i 0.0504962i 0.999681 + 0.0252481i \(0.00803757\pi\)
−0.999681 + 0.0252481i \(0.991962\pi\)
\(600\) 147.813 + 240.738i 0.246355 + 0.401231i
\(601\) −880.877 −1.46569 −0.732843 0.680398i \(-0.761807\pi\)
−0.732843 + 0.680398i \(0.761807\pi\)
\(602\) −250.772 250.772i −0.416565 0.416565i
\(603\) −189.373 + 189.373i −0.314051 + 0.314051i
\(604\) 181.181i 0.299969i
\(605\) −91.1831 322.773i −0.150716 0.533510i
\(606\) −276.034 −0.455501
\(607\) 313.283 + 313.283i 0.516117 + 0.516117i 0.916394 0.400277i \(-0.131086\pi\)
−0.400277 + 0.916394i \(0.631086\pi\)
\(608\) −57.2865 + 57.2865i −0.0942212 + 0.0942212i
\(609\) 230.718i 0.378847i
\(610\) −186.521 + 333.397i −0.305772 + 0.546553i
\(611\) −673.847 −1.10286
\(612\) −10.2153 10.2153i −0.0166916 0.0166916i
\(613\) −83.0520 + 83.0520i −0.135485 + 0.135485i −0.771597 0.636112i \(-0.780542\pi\)
0.636112 + 0.771597i \(0.280542\pi\)
\(614\) 1070.71i 1.74383i
\(615\) −155.633 87.0700i −0.253062 0.141577i
\(616\) 236.719 0.384283
\(617\) 238.533 + 238.533i 0.386602 + 0.386602i 0.873473 0.486872i \(-0.161862\pi\)
−0.486872 + 0.873473i \(0.661862\pi\)
\(618\) 238.242 238.242i 0.385504 0.385504i
\(619\) 26.3818i 0.0426201i −0.999773 0.0213100i \(-0.993216\pi\)
0.999773 0.0213100i \(-0.00678371\pi\)
\(620\) 59.3828 16.7756i 0.0957787 0.0270573i
\(621\) −33.9265 −0.0546320
\(622\) 47.1097 + 47.1097i 0.0757390 + 0.0757390i
\(623\) −292.109 + 292.109i −0.468875 + 0.468875i
\(624\) 776.520i 1.24442i
\(625\) 282.775 557.372i 0.452440 0.891795i
\(626\) 1199.90 1.91678
\(627\) −78.3405 78.3405i −0.124945 0.124945i
\(628\) −121.410 + 121.410i −0.193328 + 0.193328i
\(629\) 271.381i 0.431448i
\(630\) 24.4022 + 86.3800i 0.0387337 + 0.137111i
\(631\) −672.112 −1.06515 −0.532577 0.846382i \(-0.678776\pi\)
−0.532577 + 0.846382i \(0.678776\pi\)
\(632\) 245.578 + 245.578i 0.388572 + 0.388572i
\(633\) 44.0194 44.0194i 0.0695410 0.0695410i
\(634\) 1310.13i 2.06645i
\(635\) −13.7737 + 24.6198i −0.0216909 + 0.0387713i
\(636\) 126.026 0.198154
\(637\) −115.471 115.471i −0.181273 0.181273i
\(638\) 1104.27 1104.27i 1.73083 1.73083i
\(639\) 93.5652i 0.146424i
\(640\) 674.107 + 377.133i 1.05329 + 0.589271i
\(641\) 582.851 0.909284 0.454642 0.890674i \(-0.349767\pi\)
0.454642 + 0.890674i \(0.349767\pi\)
\(642\) −205.812 205.812i −0.320580 0.320580i
\(643\) 488.888 488.888i 0.760324 0.760324i −0.216057 0.976381i \(-0.569320\pi\)
0.976381 + 0.216057i \(0.0693196\pi\)
\(644\) 19.2703i 0.0299229i
\(645\) 493.921 139.532i 0.765770 0.216329i
\(646\) 45.5380 0.0704923
\(647\) 501.243 + 501.243i 0.774718 + 0.774718i 0.978927 0.204209i \(-0.0654623\pi\)
−0.204209 + 0.978927i \(0.565462\pi\)
\(648\) 41.5182 41.5182i 0.0640713 0.0640713i
\(649\) 648.134i 0.998665i
\(650\) −1124.11 + 690.202i −1.72940 + 1.06185i
\(651\) −50.6978 −0.0778769
\(652\) −224.778 224.778i −0.344752 0.344752i
\(653\) 385.795 385.795i 0.590805 0.590805i −0.347044 0.937849i \(-0.612815\pi\)
0.937849 + 0.347044i \(0.112815\pi\)
\(654\) 151.753i 0.232038i
\(655\) 98.6354 + 349.154i 0.150588 + 0.533059i
\(656\) −395.735 −0.603255
\(657\) 57.2934 + 57.2934i 0.0872045 + 0.0872045i
\(658\) 122.222 122.222i 0.185748 0.185748i
\(659\) 232.235i 0.352405i −0.984354 0.176203i \(-0.943619\pi\)
0.984354 0.176203i \(-0.0563814\pi\)
\(660\) 64.6877 115.626i 0.0980117 0.175191i
\(661\) −1126.09 −1.70361 −0.851804 0.523860i \(-0.824491\pi\)
−0.851804 + 0.523860i \(0.824491\pi\)
\(662\) 115.051 + 115.051i 0.173794 + 0.173794i
\(663\) −123.338 + 123.338i −0.186030 + 0.186030i
\(664\) 898.260i 1.35280i
\(665\) −53.8463 30.1246i −0.0809719 0.0453002i
\(666\) 426.566 0.640489
\(667\) 232.441 + 232.441i 0.348488 + 0.348488i
\(668\) 46.2760 46.2760i 0.0692754 0.0692754i
\(669\) 564.391i 0.843633i
\(670\) 971.526 274.455i 1.45004 0.409634i
\(671\) −463.287 −0.690442
\(672\) 56.2851 + 56.2851i 0.0837577 + 0.0837577i
\(673\) 146.969 146.969i 0.218379 0.218379i −0.589436 0.807815i \(-0.700650\pi\)
0.807815 + 0.589436i \(0.200650\pi\)
\(674\) 966.416i 1.43385i
\(675\) −126.341 30.2156i −0.187172 0.0447638i
\(676\) 418.580 0.619200
\(677\) 312.515 + 312.515i 0.461617 + 0.461617i 0.899185 0.437568i \(-0.144160\pi\)
−0.437568 + 0.899185i \(0.644160\pi\)
\(678\) −158.778 + 158.778i −0.234186 + 0.234186i
\(679\) 285.262i 0.420121i
\(680\) −38.2811 135.509i −0.0562958 0.199278i
\(681\) −243.717 −0.357882
\(682\) 242.652 + 242.652i 0.355794 + 0.355794i
\(683\) −660.747 + 660.747i −0.967419 + 0.967419i −0.999486 0.0320664i \(-0.989791\pi\)
0.0320664 + 0.999486i \(0.489791\pi\)
\(684\) 15.6089i 0.0228200i
\(685\) 233.575 417.503i 0.340985 0.609493i
\(686\) 41.8883 0.0610616
\(687\) 15.1411 + 15.1411i 0.0220395 + 0.0220395i
\(688\) 805.354 805.354i 1.17057 1.17057i
\(689\) 1521.62i 2.20845i
\(690\) 111.610 + 62.4407i 0.161753 + 0.0904938i
\(691\) −1000.24 −1.44752 −0.723759 0.690053i \(-0.757587\pi\)
−0.723759 + 0.690053i \(0.757587\pi\)
\(692\) 145.042 + 145.042i 0.209598 + 0.209598i
\(693\) −76.9711 + 76.9711i −0.111069 + 0.111069i
\(694\) 1109.16i 1.59822i
\(695\) 639.916 180.775i 0.920742 0.260108i
\(696\) −568.909 −0.817398
\(697\) 62.8562 + 62.8562i 0.0901811 + 0.0901811i
\(698\) 47.5033 47.5033i 0.0680563 0.0680563i
\(699\) 525.620i 0.751960i
\(700\) 17.1625 71.7620i 0.0245179 0.102517i
\(701\) 440.221 0.627989 0.313995 0.949425i \(-0.398333\pi\)
0.313995 + 0.949425i \(0.398333\pi\)
\(702\) 193.866 + 193.866i 0.276163 + 0.276163i
\(703\) −207.335 + 207.335i −0.294928 + 0.294928i
\(704\) 515.441i 0.732160i
\(705\) 68.0057 + 240.729i 0.0964620 + 0.341460i
\(706\) 1179.76 1.67105
\(707\) −131.823 131.823i −0.186454 0.186454i
\(708\) 64.5686 64.5686i 0.0911985 0.0911985i
\(709\) 63.2033i 0.0891443i −0.999006 0.0445721i \(-0.985808\pi\)
0.999006 0.0445721i \(-0.0141925\pi\)
\(710\) 172.204 307.806i 0.242541 0.433530i
\(711\) −159.703 −0.224618
\(712\) −720.289 720.289i −1.01164 1.01164i
\(713\) −51.0766 + 51.0766i −0.0716361 + 0.0716361i
\(714\) 44.7420i 0.0626639i
\(715\) −1396.05 781.030i −1.95252 1.09235i
\(716\) −106.295 −0.148456
\(717\) 13.0691 + 13.0691i 0.0182275 + 0.0182275i
\(718\) 976.633 976.633i 1.36021 1.36021i
\(719\) 934.275i 1.29941i 0.760187 + 0.649704i \(0.225107\pi\)
−0.760187 + 0.649704i \(0.774893\pi\)
\(720\) −277.409 + 78.3676i −0.385290 + 0.108844i
\(721\) 227.549 0.315602
\(722\) −542.557 542.557i −0.751464 0.751464i
\(723\) 265.802 265.802i 0.367638 0.367638i
\(724\) 211.180i 0.291686i
\(725\) 658.586 + 1072.62i 0.908394 + 1.47947i
\(726\) 262.789 0.361968
\(727\) −584.907 584.907i −0.804548 0.804548i 0.179254 0.983803i \(-0.442631\pi\)
−0.983803 + 0.179254i \(0.942631\pi\)
\(728\) 284.731 284.731i 0.391114 0.391114i
\(729\) 27.0000i 0.0370370i
\(730\) −83.0342 293.928i −0.113746 0.402641i
\(731\) −255.835 −0.349980
\(732\) −46.1537 46.1537i −0.0630515 0.0630515i
\(733\) −281.681 + 281.681i −0.384285 + 0.384285i −0.872643 0.488358i \(-0.837596\pi\)
0.488358 + 0.872643i \(0.337596\pi\)
\(734\) 231.973i 0.316040i
\(735\) −29.5981 + 52.9051i −0.0402695 + 0.0719798i
\(736\) 113.411 0.154091
\(737\) 865.704 + 865.704i 1.17463 + 1.17463i
\(738\) 98.7995 98.7995i 0.133875 0.133875i
\(739\) 892.992i 1.20838i −0.796841 0.604189i \(-0.793497\pi\)
0.796841 0.604189i \(-0.206503\pi\)
\(740\) −306.014 171.201i −0.413533 0.231353i
\(741\) −188.460 −0.254332
\(742\) 275.991 + 275.991i 0.371956 + 0.371956i
\(743\) 305.538 305.538i 0.411222 0.411222i −0.470942 0.882164i \(-0.656086\pi\)
0.882164 + 0.470942i \(0.156086\pi\)
\(744\) 125.012i 0.168027i
\(745\) −224.235 + 63.3462i −0.300987 + 0.0850284i
\(746\) −20.8448 −0.0279421
\(747\) −292.077 292.077i −0.391000 0.391000i
\(748\) −46.6984 + 46.6984i −0.0624310 + 0.0624310i
\(749\) 196.575i 0.262450i
\(750\) 360.019 + 331.929i 0.480026 + 0.442572i
\(751\) 562.121 0.748496 0.374248 0.927329i \(-0.377901\pi\)
0.374248 + 0.927329i \(0.377901\pi\)
\(752\) 392.517 + 392.517i 0.521964 + 0.521964i
\(753\) 73.0796 73.0796i 0.0970513 0.0970513i
\(754\) 2656.48i 3.52319i
\(755\) −220.772 781.497i −0.292413 1.03510i
\(756\) −15.3361 −0.0202858
\(757\) 370.109 + 370.109i 0.488915 + 0.488915i 0.907964 0.419048i \(-0.137636\pi\)
−0.419048 + 0.907964i \(0.637636\pi\)
\(758\) −358.814 + 358.814i −0.473370 + 0.473370i
\(759\) 155.092i 0.204338i
\(760\) 74.2820 132.775i 0.0977395 0.174705i
\(761\) −466.002 −0.612354 −0.306177 0.951975i \(-0.599050\pi\)
−0.306177 + 0.951975i \(0.599050\pi\)
\(762\) −15.6292 15.6292i −0.0205108 0.0205108i
\(763\) −72.4712 + 72.4712i −0.0949819 + 0.0949819i
\(764\) 362.308i 0.474225i
\(765\) 56.5094 + 31.6145i 0.0738685 + 0.0413262i
\(766\) −264.115 −0.344798
\(767\) −779.592 779.592i −1.01642 1.01642i
\(768\) −243.814 + 243.814i −0.317466 + 0.317466i
\(769\) 216.013i 0.280901i −0.990088 0.140451i \(-0.955145\pi\)
0.990088 0.140451i \(-0.0448551\pi\)
\(770\) 394.879 111.553i 0.512830 0.144874i
\(771\) 549.972 0.713323
\(772\) −27.5853 27.5853i −0.0357323 0