Properties

Label 75.3.f.c.43.1
Level $75$
Weight $3$
Character 75.43
Analytic conductor $2.044$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.04360198270\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.1
Root \(-1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 75.43
Dual form 75.3.f.c.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.224745 + 0.224745i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.89898i q^{4} -0.550510 q^{6} +(-3.44949 + 3.44949i) q^{7} +(-1.77526 - 1.77526i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-0.224745 + 0.224745i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.89898i q^{4} -0.550510 q^{6} +(-3.44949 + 3.44949i) q^{7} +(-1.77526 - 1.77526i) q^{8} +3.00000i q^{9} +11.3485 q^{11} +(-4.77526 + 4.77526i) q^{12} +(5.55051 + 5.55051i) q^{13} -1.55051i q^{14} -14.7980 q^{16} +(17.3485 - 17.3485i) q^{17} +(-0.674235 - 0.674235i) q^{18} -8.69694i q^{19} -8.44949 q^{21} +(-2.55051 + 2.55051i) q^{22} +(-11.5505 - 11.5505i) q^{23} -4.34847i q^{24} -2.49490 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-13.4495 - 13.4495i) q^{28} -35.1464i q^{29} +10.6969 q^{31} +(10.4268 - 10.4268i) q^{32} +(13.8990 + 13.8990i) q^{33} +7.79796i q^{34} -11.6969 q^{36} +(6.04541 - 6.04541i) q^{37} +(1.95459 + 1.95459i) q^{38} +13.5959i q^{39} +0.696938 q^{41} +(1.89898 - 1.89898i) q^{42} +(26.4949 + 26.4949i) q^{43} +44.2474i q^{44} +5.19184 q^{46} +(-44.2474 + 44.2474i) q^{47} +(-18.1237 - 18.1237i) q^{48} +25.2020i q^{49} +42.4949 q^{51} +(-21.6413 + 21.6413i) q^{52} +(0.696938 + 0.696938i) q^{53} -1.65153i q^{54} +12.2474 q^{56} +(10.6515 - 10.6515i) q^{57} +(7.89898 + 7.89898i) q^{58} +39.9342i q^{59} +5.90918 q^{61} +(-2.40408 + 2.40408i) q^{62} +(-10.3485 - 10.3485i) q^{63} -54.5051i q^{64} -6.24745 q^{66} +(45.1010 - 45.1010i) q^{67} +(67.6413 + 67.6413i) q^{68} -28.2929i q^{69} -68.0000 q^{71} +(5.32577 - 5.32577i) q^{72} +(-77.7878 - 77.7878i) q^{73} +2.71735i q^{74} +33.9092 q^{76} +(-39.1464 + 39.1464i) q^{77} +(-3.05561 - 3.05561i) q^{78} +24.4949i q^{79} -9.00000 q^{81} +(-0.156633 + 0.156633i) q^{82} +(-13.1464 - 13.1464i) q^{83} -32.9444i q^{84} -11.9092 q^{86} +(43.0454 - 43.0454i) q^{87} +(-20.1464 - 20.1464i) q^{88} -82.1816i q^{89} -38.2929 q^{91} +(45.0352 - 45.0352i) q^{92} +(13.1010 + 13.1010i) q^{93} -19.8888i q^{94} +25.5403 q^{96} +(24.5959 - 24.5959i) q^{97} +(-5.66403 - 5.66403i) q^{98} +34.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 12q^{6} - 4q^{7} - 12q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 12q^{6} - 4q^{7} - 12q^{8} + 16q^{11} - 24q^{12} + 32q^{13} - 20q^{16} + 40q^{17} + 12q^{18} - 24q^{21} - 20q^{22} - 56q^{23} + 88q^{26} - 44q^{28} - 16q^{31} + 76q^{32} + 36q^{33} + 12q^{36} - 64q^{37} + 96q^{38} - 56q^{41} - 12q^{42} + 8q^{43} - 136q^{46} - 128q^{47} - 48q^{48} + 72q^{51} + 80q^{52} - 56q^{53} + 72q^{57} + 12q^{58} + 200q^{61} - 88q^{62} - 12q^{63} + 24q^{66} + 200q^{67} + 104q^{68} - 272q^{71} + 36q^{72} - 76q^{73} + 312q^{76} - 88q^{77} - 120q^{78} - 36q^{81} - 128q^{82} + 16q^{83} - 224q^{86} + 84q^{87} - 12q^{88} - 16q^{91} - 104q^{92} + 72q^{93} - 84q^{96} + 20q^{97} + 188q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.224745 + 0.224745i −0.112372 + 0.112372i −0.761057 0.648685i \(-0.775319\pi\)
0.648685 + 0.761057i \(0.275319\pi\)
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 3.89898i 0.974745i
\(5\) 0 0
\(6\) −0.550510 −0.0917517
\(7\) −3.44949 + 3.44949i −0.492784 + 0.492784i −0.909182 0.416398i \(-0.863292\pi\)
0.416398 + 0.909182i \(0.363292\pi\)
\(8\) −1.77526 1.77526i −0.221907 0.221907i
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) 11.3485 1.03168 0.515840 0.856685i \(-0.327480\pi\)
0.515840 + 0.856685i \(0.327480\pi\)
\(12\) −4.77526 + 4.77526i −0.397938 + 0.397938i
\(13\) 5.55051 + 5.55051i 0.426962 + 0.426962i 0.887592 0.460630i \(-0.152376\pi\)
−0.460630 + 0.887592i \(0.652376\pi\)
\(14\) 1.55051i 0.110751i
\(15\) 0 0
\(16\) −14.7980 −0.924872
\(17\) 17.3485 17.3485i 1.02050 1.02050i 0.0207127 0.999785i \(-0.493406\pi\)
0.999785 0.0207127i \(-0.00659354\pi\)
\(18\) −0.674235 0.674235i −0.0374575 0.0374575i
\(19\) 8.69694i 0.457734i −0.973458 0.228867i \(-0.926498\pi\)
0.973458 0.228867i \(-0.0735020\pi\)
\(20\) 0 0
\(21\) −8.44949 −0.402357
\(22\) −2.55051 + 2.55051i −0.115932 + 0.115932i
\(23\) −11.5505 11.5505i −0.502196 0.502196i 0.409924 0.912120i \(-0.365555\pi\)
−0.912120 + 0.409924i \(0.865555\pi\)
\(24\) 4.34847i 0.181186i
\(25\) 0 0
\(26\) −2.49490 −0.0959576
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) −13.4495 13.4495i −0.480339 0.480339i
\(29\) 35.1464i 1.21195i −0.795485 0.605973i \(-0.792784\pi\)
0.795485 0.605973i \(-0.207216\pi\)
\(30\) 0 0
\(31\) 10.6969 0.345063 0.172531 0.985004i \(-0.444805\pi\)
0.172531 + 0.985004i \(0.444805\pi\)
\(32\) 10.4268 10.4268i 0.325837 0.325837i
\(33\) 13.8990 + 13.8990i 0.421181 + 0.421181i
\(34\) 7.79796i 0.229352i
\(35\) 0 0
\(36\) −11.6969 −0.324915
\(37\) 6.04541 6.04541i 0.163389 0.163389i −0.620677 0.784066i \(-0.713142\pi\)
0.784066 + 0.620677i \(0.213142\pi\)
\(38\) 1.95459 + 1.95459i 0.0514366 + 0.0514366i
\(39\) 13.5959i 0.348613i
\(40\) 0 0
\(41\) 0.696938 0.0169985 0.00849925 0.999964i \(-0.497295\pi\)
0.00849925 + 0.999964i \(0.497295\pi\)
\(42\) 1.89898 1.89898i 0.0452138 0.0452138i
\(43\) 26.4949 + 26.4949i 0.616160 + 0.616160i 0.944544 0.328384i \(-0.106504\pi\)
−0.328384 + 0.944544i \(0.606504\pi\)
\(44\) 44.2474i 1.00562i
\(45\) 0 0
\(46\) 5.19184 0.112866
\(47\) −44.2474 + 44.2474i −0.941435 + 0.941435i −0.998377 0.0569424i \(-0.981865\pi\)
0.0569424 + 0.998377i \(0.481865\pi\)
\(48\) −18.1237 18.1237i −0.377578 0.377578i
\(49\) 25.2020i 0.514327i
\(50\) 0 0
\(51\) 42.4949 0.833233
\(52\) −21.6413 + 21.6413i −0.416179 + 0.416179i
\(53\) 0.696938 + 0.696938i 0.0131498 + 0.0131498i 0.713651 0.700501i \(-0.247040\pi\)
−0.700501 + 0.713651i \(0.747040\pi\)
\(54\) 1.65153i 0.0305839i
\(55\) 0 0
\(56\) 12.2474 0.218704
\(57\) 10.6515 10.6515i 0.186869 0.186869i
\(58\) 7.89898 + 7.89898i 0.136189 + 0.136189i
\(59\) 39.9342i 0.676851i 0.940993 + 0.338425i \(0.109894\pi\)
−0.940993 + 0.338425i \(0.890106\pi\)
\(60\) 0 0
\(61\) 5.90918 0.0968719 0.0484359 0.998826i \(-0.484576\pi\)
0.0484359 + 0.998826i \(0.484576\pi\)
\(62\) −2.40408 + 2.40408i −0.0387755 + 0.0387755i
\(63\) −10.3485 10.3485i −0.164261 0.164261i
\(64\) 54.5051i 0.851642i
\(65\) 0 0
\(66\) −6.24745 −0.0946583
\(67\) 45.1010 45.1010i 0.673150 0.673150i −0.285291 0.958441i \(-0.592090\pi\)
0.958441 + 0.285291i \(0.0920903\pi\)
\(68\) 67.6413 + 67.6413i 0.994725 + 0.994725i
\(69\) 28.2929i 0.410041i
\(70\) 0 0
\(71\) −68.0000 −0.957746 −0.478873 0.877884i \(-0.658955\pi\)
−0.478873 + 0.877884i \(0.658955\pi\)
\(72\) 5.32577 5.32577i 0.0739690 0.0739690i
\(73\) −77.7878 77.7878i −1.06559 1.06559i −0.997693 0.0678931i \(-0.978372\pi\)
−0.0678931 0.997693i \(-0.521628\pi\)
\(74\) 2.71735i 0.0367209i
\(75\) 0 0
\(76\) 33.9092 0.446173
\(77\) −39.1464 + 39.1464i −0.508395 + 0.508395i
\(78\) −3.05561 3.05561i −0.0391745 0.0391745i
\(79\) 24.4949i 0.310062i 0.987910 + 0.155031i \(0.0495477\pi\)
−0.987910 + 0.155031i \(0.950452\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) −0.156633 + 0.156633i −0.00191016 + 0.00191016i
\(83\) −13.1464 13.1464i −0.158391 0.158391i 0.623463 0.781853i \(-0.285725\pi\)
−0.781853 + 0.623463i \(0.785725\pi\)
\(84\) 32.9444i 0.392195i
\(85\) 0 0
\(86\) −11.9092 −0.138479
\(87\) 43.0454 43.0454i 0.494775 0.494775i
\(88\) −20.1464 20.1464i −0.228937 0.228937i
\(89\) 82.1816i 0.923389i −0.887039 0.461695i \(-0.847242\pi\)
0.887039 0.461695i \(-0.152758\pi\)
\(90\) 0 0
\(91\) −38.2929 −0.420801
\(92\) 45.0352 45.0352i 0.489513 0.489513i
\(93\) 13.1010 + 13.1010i 0.140871 + 0.140871i
\(94\) 19.8888i 0.211583i
\(95\) 0 0
\(96\) 25.5403 0.266045
\(97\) 24.5959 24.5959i 0.253566 0.253566i −0.568865 0.822431i \(-0.692617\pi\)
0.822431 + 0.568865i \(0.192617\pi\)
\(98\) −5.66403 5.66403i −0.0577962 0.0577962i
\(99\) 34.0454i 0.343893i
\(100\) 0 0
\(101\) −105.621 −1.04575 −0.522876 0.852409i \(-0.675141\pi\)
−0.522876 + 0.852409i \(0.675141\pi\)
\(102\) −9.55051 + 9.55051i −0.0936325 + 0.0936325i
\(103\) 89.2474 + 89.2474i 0.866480 + 0.866480i 0.992081 0.125601i \(-0.0400858\pi\)
−0.125601 + 0.992081i \(0.540086\pi\)
\(104\) 19.7071i 0.189492i
\(105\) 0 0
\(106\) −0.313267 −0.00295535
\(107\) −68.7423 + 68.7423i −0.642452 + 0.642452i −0.951158 0.308706i \(-0.900104\pi\)
0.308706 + 0.951158i \(0.400104\pi\)
\(108\) −14.3258 14.3258i −0.132646 0.132646i
\(109\) 68.6969i 0.630247i −0.949051 0.315124i \(-0.897954\pi\)
0.949051 0.315124i \(-0.102046\pi\)
\(110\) 0 0
\(111\) 14.8082 0.133407
\(112\) 51.0454 51.0454i 0.455763 0.455763i
\(113\) −97.6413 97.6413i −0.864083 0.864083i 0.127727 0.991809i \(-0.459232\pi\)
−0.991809 + 0.127727i \(0.959232\pi\)
\(114\) 4.78775i 0.0419978i
\(115\) 0 0
\(116\) 137.035 1.18134
\(117\) −16.6515 + 16.6515i −0.142321 + 0.142321i
\(118\) −8.97500 8.97500i −0.0760593 0.0760593i
\(119\) 119.687i 1.00577i
\(120\) 0 0
\(121\) 7.78775 0.0643616
\(122\) −1.32806 + 1.32806i −0.0108857 + 0.0108857i
\(123\) 0.853572 + 0.853572i 0.00693961 + 0.00693961i
\(124\) 41.7071i 0.336348i
\(125\) 0 0
\(126\) 4.65153 0.0369169
\(127\) −164.621 + 164.621i −1.29623 + 1.29623i −0.365362 + 0.930865i \(0.619055\pi\)
−0.930865 + 0.365362i \(0.880945\pi\)
\(128\) 53.9569 + 53.9569i 0.421538 + 0.421538i
\(129\) 64.8990i 0.503093i
\(130\) 0 0
\(131\) 106.136 0.810200 0.405100 0.914272i \(-0.367237\pi\)
0.405100 + 0.914272i \(0.367237\pi\)
\(132\) −54.1918 + 54.1918i −0.410544 + 0.410544i
\(133\) 30.0000 + 30.0000i 0.225564 + 0.225564i
\(134\) 20.2724i 0.151287i
\(135\) 0 0
\(136\) −61.5959 −0.452911
\(137\) 166.631 166.631i 1.21629 1.21629i 0.247363 0.968923i \(-0.420436\pi\)
0.968923 0.247363i \(-0.0795639\pi\)
\(138\) 6.35867 + 6.35867i 0.0460774 + 0.0460774i
\(139\) 191.171i 1.37533i 0.726026 + 0.687667i \(0.241365\pi\)
−0.726026 + 0.687667i \(0.758635\pi\)
\(140\) 0 0
\(141\) −108.384 −0.768679
\(142\) 15.2827 15.2827i 0.107624 0.107624i
\(143\) 62.9898 + 62.9898i 0.440488 + 0.440488i
\(144\) 44.3939i 0.308291i
\(145\) 0 0
\(146\) 34.9648 0.239485
\(147\) −30.8661 + 30.8661i −0.209973 + 0.209973i
\(148\) 23.5709 + 23.5709i 0.159263 + 0.159263i
\(149\) 84.8536i 0.569487i −0.958604 0.284744i \(-0.908092\pi\)
0.958604 0.284744i \(-0.0919084\pi\)
\(150\) 0 0
\(151\) 148.969 0.986552 0.493276 0.869873i \(-0.335799\pi\)
0.493276 + 0.869873i \(0.335799\pi\)
\(152\) −15.4393 + 15.4393i −0.101574 + 0.101574i
\(153\) 52.0454 + 52.0454i 0.340166 + 0.340166i
\(154\) 17.5959i 0.114259i
\(155\) 0 0
\(156\) −53.0102 −0.339809
\(157\) −16.8536 + 16.8536i −0.107348 + 0.107348i −0.758741 0.651393i \(-0.774185\pi\)
0.651393 + 0.758741i \(0.274185\pi\)
\(158\) −5.50510 5.50510i −0.0348424 0.0348424i
\(159\) 1.70714i 0.0107368i
\(160\) 0 0
\(161\) 79.6867 0.494949
\(162\) 2.02270 2.02270i 0.0124858 0.0124858i
\(163\) −130.606 130.606i −0.801265 0.801265i 0.182029 0.983293i \(-0.441734\pi\)
−0.983293 + 0.182029i \(0.941734\pi\)
\(164\) 2.71735i 0.0165692i
\(165\) 0 0
\(166\) 5.90918 0.0355975
\(167\) 45.0352 45.0352i 0.269672 0.269672i −0.559296 0.828968i \(-0.688929\pi\)
0.828968 + 0.559296i \(0.188929\pi\)
\(168\) 15.0000 + 15.0000i 0.0892857 + 0.0892857i
\(169\) 107.384i 0.635406i
\(170\) 0 0
\(171\) 26.0908 0.152578
\(172\) −103.303 + 103.303i −0.600599 + 0.600599i
\(173\) −146.631 146.631i −0.847579 0.847579i 0.142252 0.989831i \(-0.454566\pi\)
−0.989831 + 0.142252i \(0.954566\pi\)
\(174\) 19.3485i 0.111198i
\(175\) 0 0
\(176\) −167.934 −0.954171
\(177\) −48.9092 + 48.9092i −0.276323 + 0.276323i
\(178\) 18.4699 + 18.4699i 0.103763 + 0.103763i
\(179\) 183.712i 1.02632i −0.858292 0.513161i \(-0.828474\pi\)
0.858292 0.513161i \(-0.171526\pi\)
\(180\) 0 0
\(181\) −286.272 −1.58162 −0.790808 0.612064i \(-0.790339\pi\)
−0.790808 + 0.612064i \(0.790339\pi\)
\(182\) 8.60612 8.60612i 0.0472864 0.0472864i
\(183\) 7.23724 + 7.23724i 0.0395478 + 0.0395478i
\(184\) 41.0102i 0.222882i
\(185\) 0 0
\(186\) −5.88877 −0.0316601
\(187\) 196.879 196.879i 1.05283 1.05283i
\(188\) −172.520 172.520i −0.917659 0.917659i
\(189\) 25.3485i 0.134119i
\(190\) 0 0
\(191\) 48.0908 0.251784 0.125892 0.992044i \(-0.459821\pi\)
0.125892 + 0.992044i \(0.459821\pi\)
\(192\) 66.7548 66.7548i 0.347681 0.347681i
\(193\) 255.565 + 255.565i 1.32417 + 1.32417i 0.910364 + 0.413809i \(0.135802\pi\)
0.413809 + 0.910364i \(0.364198\pi\)
\(194\) 11.0556i 0.0569877i
\(195\) 0 0
\(196\) −98.2622 −0.501338
\(197\) 96.6969 96.6969i 0.490847 0.490847i −0.417726 0.908573i \(-0.637173\pi\)
0.908573 + 0.417726i \(0.137173\pi\)
\(198\) −7.65153 7.65153i −0.0386441 0.0386441i
\(199\) 192.606i 0.967870i −0.875104 0.483935i \(-0.839207\pi\)
0.875104 0.483935i \(-0.160793\pi\)
\(200\) 0 0
\(201\) 110.474 0.549624
\(202\) 23.7378 23.7378i 0.117514 0.117514i
\(203\) 121.237 + 121.237i 0.597228 + 0.597228i
\(204\) 165.687i 0.812190i
\(205\) 0 0
\(206\) −40.1158 −0.194737
\(207\) 34.6515 34.6515i 0.167399 0.167399i
\(208\) −82.1362 82.1362i −0.394886 0.394886i
\(209\) 98.6969i 0.472234i
\(210\) 0 0
\(211\) 147.212 0.697688 0.348844 0.937181i \(-0.386574\pi\)
0.348844 + 0.937181i \(0.386574\pi\)
\(212\) −2.71735 + 2.71735i −0.0128177 + 0.0128177i
\(213\) −83.2827 83.2827i −0.390998 0.390998i
\(214\) 30.8990i 0.144388i
\(215\) 0 0
\(216\) 13.0454 0.0603954
\(217\) −36.8990 + 36.8990i −0.170041 + 0.170041i
\(218\) 15.4393 + 15.4393i 0.0708224 + 0.0708224i
\(219\) 190.540i 0.870047i
\(220\) 0 0
\(221\) 192.586 0.871429
\(222\) −3.32806 + 3.32806i −0.0149913 + 0.0149913i
\(223\) −167.429 167.429i −0.750803 0.750803i 0.223826 0.974629i \(-0.428145\pi\)
−0.974629 + 0.223826i \(0.928145\pi\)
\(224\) 71.9342i 0.321135i
\(225\) 0 0
\(226\) 43.8888 0.194198
\(227\) −253.171 + 253.171i −1.11529 + 1.11529i −0.122870 + 0.992423i \(0.539210\pi\)
−0.992423 + 0.122870i \(0.960790\pi\)
\(228\) 41.5301 + 41.5301i 0.182150 + 0.182150i
\(229\) 224.202i 0.979048i 0.871990 + 0.489524i \(0.162829\pi\)
−0.871990 + 0.489524i \(0.837171\pi\)
\(230\) 0 0
\(231\) −95.8888 −0.415103
\(232\) −62.3939 + 62.3939i −0.268939 + 0.268939i
\(233\) 205.712 + 205.712i 0.882883 + 0.882883i 0.993827 0.110944i \(-0.0353873\pi\)
−0.110944 + 0.993827i \(0.535387\pi\)
\(234\) 7.48469i 0.0319859i
\(235\) 0 0
\(236\) −155.703 −0.659757
\(237\) −30.0000 + 30.0000i −0.126582 + 0.126582i
\(238\) −26.8990 26.8990i −0.113021 0.113021i
\(239\) 345.798i 1.44685i 0.690401 + 0.723427i \(0.257434\pi\)
−0.690401 + 0.723427i \(0.742566\pi\)
\(240\) 0 0
\(241\) 101.576 0.421475 0.210738 0.977543i \(-0.432413\pi\)
0.210738 + 0.977543i \(0.432413\pi\)
\(242\) −1.75026 + 1.75026i −0.00723247 + 0.00723247i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 23.0398i 0.0944254i
\(245\) 0 0
\(246\) −0.383672 −0.00155964
\(247\) 48.2724 48.2724i 0.195435 0.195435i
\(248\) −18.9898 18.9898i −0.0765718 0.0765718i
\(249\) 32.2020i 0.129325i
\(250\) 0 0
\(251\) −331.258 −1.31975 −0.659876 0.751375i \(-0.729391\pi\)
−0.659876 + 0.751375i \(0.729391\pi\)
\(252\) 40.3485 40.3485i 0.160113 0.160113i
\(253\) −131.081 131.081i −0.518105 0.518105i
\(254\) 73.9954i 0.291321i
\(255\) 0 0
\(256\) 193.767 0.756904
\(257\) −33.2372 + 33.2372i −0.129328 + 0.129328i −0.768808 0.639480i \(-0.779150\pi\)
0.639480 + 0.768808i \(0.279150\pi\)
\(258\) −14.5857 14.5857i −0.0565338 0.0565338i
\(259\) 41.7071i 0.161031i
\(260\) 0 0
\(261\) 105.439 0.403982
\(262\) −23.8536 + 23.8536i −0.0910442 + 0.0910442i
\(263\) 278.157 + 278.157i 1.05763 + 1.05763i 0.998235 + 0.0593952i \(0.0189172\pi\)
0.0593952 + 0.998235i \(0.481083\pi\)
\(264\) 49.3485i 0.186926i
\(265\) 0 0
\(266\) −13.4847 −0.0506943
\(267\) 100.652 100.652i 0.376972 0.376972i
\(268\) 175.848 + 175.848i 0.656149 + 0.656149i
\(269\) 488.499i 1.81598i 0.418988 + 0.907992i \(0.362385\pi\)
−0.418988 + 0.907992i \(0.637615\pi\)
\(270\) 0 0
\(271\) 131.576 0.485518 0.242759 0.970087i \(-0.421947\pi\)
0.242759 + 0.970087i \(0.421947\pi\)
\(272\) −256.722 + 256.722i −0.943831 + 0.943831i
\(273\) −46.8990 46.8990i −0.171791 0.171791i
\(274\) 74.8990i 0.273354i
\(275\) 0 0
\(276\) 110.313 0.399686
\(277\) −101.510 + 101.510i −0.366461 + 0.366461i −0.866185 0.499724i \(-0.833435\pi\)
0.499724 + 0.866185i \(0.333435\pi\)
\(278\) −42.9648 42.9648i −0.154550 0.154550i
\(279\) 32.0908i 0.115021i
\(280\) 0 0
\(281\) 343.303 1.22172 0.610860 0.791739i \(-0.290824\pi\)
0.610860 + 0.791739i \(0.290824\pi\)
\(282\) 24.3587 24.3587i 0.0863783 0.0863783i
\(283\) −1.19184 1.19184i −0.00421143 0.00421143i 0.704998 0.709209i \(-0.250948\pi\)
−0.709209 + 0.704998i \(0.750948\pi\)
\(284\) 265.131i 0.933558i
\(285\) 0 0
\(286\) −28.3133 −0.0989974
\(287\) −2.40408 + 2.40408i −0.00837659 + 0.00837659i
\(288\) 31.2804 + 31.2804i 0.108612 + 0.108612i
\(289\) 312.939i 1.08283i
\(290\) 0 0
\(291\) 60.2474 0.207036
\(292\) 303.293 303.293i 1.03867 1.03867i
\(293\) −96.5653 96.5653i −0.329574 0.329574i 0.522850 0.852425i \(-0.324869\pi\)
−0.852425 + 0.522850i \(0.824869\pi\)
\(294\) 13.8740i 0.0471904i
\(295\) 0 0
\(296\) −21.4643 −0.0725145
\(297\) −41.6969 + 41.6969i −0.140394 + 0.140394i
\(298\) 19.0704 + 19.0704i 0.0639946 + 0.0639946i
\(299\) 128.222i 0.428838i
\(300\) 0 0
\(301\) −182.788 −0.607268
\(302\) −33.4801 + 33.4801i −0.110861 + 0.110861i
\(303\) −129.359 129.359i −0.426926 0.426926i
\(304\) 128.697i 0.423345i
\(305\) 0 0
\(306\) −23.3939 −0.0764506
\(307\) 124.969 124.969i 0.407066 0.407066i −0.473648 0.880714i \(-0.657063\pi\)
0.880714 + 0.473648i \(0.157063\pi\)
\(308\) −152.631 152.631i −0.495556 0.495556i
\(309\) 218.611i 0.707478i
\(310\) 0 0
\(311\) −586.302 −1.88522 −0.942608 0.333902i \(-0.891635\pi\)
−0.942608 + 0.333902i \(0.891635\pi\)
\(312\) 24.1362 24.1362i 0.0773597 0.0773597i
\(313\) 102.373 + 102.373i 0.327072 + 0.327072i 0.851472 0.524400i \(-0.175710\pi\)
−0.524400 + 0.851472i \(0.675710\pi\)
\(314\) 7.57551i 0.0241258i
\(315\) 0 0
\(316\) −95.5051 −0.302231
\(317\) 108.783 108.783i 0.343165 0.343165i −0.514391 0.857556i \(-0.671982\pi\)
0.857556 + 0.514391i \(0.171982\pi\)
\(318\) −0.383672 0.383672i −0.00120651 0.00120651i
\(319\) 398.858i 1.25034i
\(320\) 0 0
\(321\) −168.384 −0.524560
\(322\) −17.9092 + 17.9092i −0.0556186 + 0.0556186i
\(323\) −150.879 150.879i −0.467116 0.467116i
\(324\) 35.0908i 0.108305i
\(325\) 0 0
\(326\) 58.7061 0.180080
\(327\) 84.1362 84.1362i 0.257297 0.257297i
\(328\) −1.23724 1.23724i −0.00377208 0.00377208i
\(329\) 305.262i 0.927849i
\(330\) 0 0
\(331\) −245.423 −0.741461 −0.370730 0.928741i \(-0.620893\pi\)
−0.370730 + 0.928741i \(0.620893\pi\)
\(332\) 51.2577 51.2577i 0.154391 0.154391i
\(333\) 18.1362 + 18.1362i 0.0544631 + 0.0544631i
\(334\) 20.2429i 0.0606074i
\(335\) 0 0
\(336\) 125.035 0.372129
\(337\) −213.808 + 213.808i −0.634446 + 0.634446i −0.949180 0.314734i \(-0.898085\pi\)
0.314734 + 0.949180i \(0.398085\pi\)
\(338\) 24.1339 + 24.1339i 0.0714022 + 0.0714022i
\(339\) 239.171i 0.705520i
\(340\) 0 0
\(341\) 121.394 0.355994
\(342\) −5.86378 + 5.86378i −0.0171455 + 0.0171455i
\(343\) −255.959 255.959i −0.746237 0.746237i
\(344\) 94.0704i 0.273460i
\(345\) 0 0
\(346\) 65.9092 0.190489
\(347\) 160.050 160.050i 0.461239 0.461239i −0.437822 0.899062i \(-0.644250\pi\)
0.899062 + 0.437822i \(0.144250\pi\)
\(348\) 167.833 + 167.833i 0.482279 + 0.482279i
\(349\) 298.009i 0.853894i 0.904277 + 0.426947i \(0.140411\pi\)
−0.904277 + 0.426947i \(0.859589\pi\)
\(350\) 0 0
\(351\) −40.7878 −0.116204
\(352\) 118.328 118.328i 0.336159 0.336159i
\(353\) 22.5199 + 22.5199i 0.0637957 + 0.0637957i 0.738285 0.674489i \(-0.235636\pi\)
−0.674489 + 0.738285i \(0.735636\pi\)
\(354\) 21.9842i 0.0621022i
\(355\) 0 0
\(356\) 320.424 0.900069
\(357\) −146.586 + 146.586i −0.410604 + 0.410604i
\(358\) 41.2883 + 41.2883i 0.115330 + 0.115330i
\(359\) 48.2724i 0.134464i −0.997737 0.0672318i \(-0.978583\pi\)
0.997737 0.0672318i \(-0.0214167\pi\)
\(360\) 0 0
\(361\) 285.363 0.790480
\(362\) 64.3383 64.3383i 0.177730 0.177730i
\(363\) 9.53801 + 9.53801i 0.0262755 + 0.0262755i
\(364\) 149.303i 0.410173i
\(365\) 0 0
\(366\) −3.25307 −0.00888816
\(367\) −146.510 + 146.510i −0.399209 + 0.399209i −0.877954 0.478745i \(-0.841092\pi\)
0.478745 + 0.877954i \(0.341092\pi\)
\(368\) 170.924 + 170.924i 0.464467 + 0.464467i
\(369\) 2.09082i 0.00566617i
\(370\) 0 0
\(371\) −4.80816 −0.0129600
\(372\) −51.0806 + 51.0806i −0.137313 + 0.137313i
\(373\) −86.2066 86.2066i −0.231117 0.231117i 0.582042 0.813159i \(-0.302254\pi\)
−0.813159 + 0.582042i \(0.802254\pi\)
\(374\) 88.4949i 0.236617i
\(375\) 0 0
\(376\) 157.101 0.417822
\(377\) 195.081 195.081i 0.517455 0.517455i
\(378\) 5.69694 + 5.69694i 0.0150713 + 0.0150713i
\(379\) 210.000i 0.554090i 0.960857 + 0.277045i \(0.0893551\pi\)
−0.960857 + 0.277045i \(0.910645\pi\)
\(380\) 0 0
\(381\) −403.237 −1.05837
\(382\) −10.8082 + 10.8082i −0.0282936 + 0.0282936i
\(383\) 10.6311 + 10.6311i 0.0277575 + 0.0277575i 0.720849 0.693092i \(-0.243752\pi\)
−0.693092 + 0.720849i \(0.743752\pi\)
\(384\) 132.167i 0.344184i
\(385\) 0 0
\(386\) −114.874 −0.297601
\(387\) −79.4847 + 79.4847i −0.205387 + 0.205387i
\(388\) 95.8990 + 95.8990i 0.247162 + 0.247162i
\(389\) 535.337i 1.37619i 0.725621 + 0.688094i \(0.241552\pi\)
−0.725621 + 0.688094i \(0.758448\pi\)
\(390\) 0 0
\(391\) −400.767 −1.02498
\(392\) 44.7401 44.7401i 0.114133 0.114133i
\(393\) 129.990 + 129.990i 0.330763 + 0.330763i
\(394\) 43.4643i 0.110315i
\(395\) 0 0
\(396\) −132.742 −0.335208
\(397\) −118.742 + 118.742i −0.299099 + 0.299099i −0.840661 0.541562i \(-0.817833\pi\)
0.541562 + 0.840661i \(0.317833\pi\)
\(398\) 43.2872 + 43.2872i 0.108762 + 0.108762i
\(399\) 73.4847i 0.184172i
\(400\) 0 0
\(401\) 420.302 1.04813 0.524067 0.851677i \(-0.324414\pi\)
0.524067 + 0.851677i \(0.324414\pi\)
\(402\) −24.8286 + 24.8286i −0.0617626 + 0.0617626i
\(403\) 59.3735 + 59.3735i 0.147329 + 0.147329i
\(404\) 411.814i 1.01934i
\(405\) 0 0
\(406\) −54.4949 −0.134224
\(407\) 68.6061 68.6061i 0.168565 0.168565i
\(408\) −75.4393 75.4393i −0.184900 0.184900i
\(409\) 515.110i 1.25944i 0.776823 + 0.629719i \(0.216830\pi\)
−0.776823 + 0.629719i \(0.783170\pi\)
\(410\) 0 0
\(411\) 408.161 0.993093
\(412\) −347.974 + 347.974i −0.844597 + 0.844597i
\(413\) −137.753 137.753i −0.333541 0.333541i
\(414\) 15.5755i 0.0376220i
\(415\) 0 0
\(416\) 115.748 0.278240
\(417\) −234.136 + 234.136i −0.561478 + 0.561478i
\(418\) 22.1816 + 22.1816i 0.0530661 + 0.0530661i
\(419\) 88.6015i 0.211460i 0.994395 + 0.105730i \(0.0337178\pi\)
−0.994395 + 0.105730i \(0.966282\pi\)
\(420\) 0 0
\(421\) −257.151 −0.610810 −0.305405 0.952223i \(-0.598792\pi\)
−0.305405 + 0.952223i \(0.598792\pi\)
\(422\) −33.0852 + 33.0852i −0.0784009 + 0.0784009i
\(423\) −132.742 132.742i −0.313812 0.313812i
\(424\) 2.47449i 0.00583605i
\(425\) 0 0
\(426\) 37.4347 0.0878749
\(427\) −20.3837 + 20.3837i −0.0477369 + 0.0477369i
\(428\) −268.025 268.025i −0.626227 0.626227i
\(429\) 154.293i 0.359657i
\(430\) 0 0
\(431\) 804.636 1.86690 0.933452 0.358702i \(-0.116781\pi\)
0.933452 + 0.358702i \(0.116781\pi\)
\(432\) 54.3712 54.3712i 0.125859 0.125859i
\(433\) 344.848 + 344.848i 0.796416 + 0.796416i 0.982528 0.186113i \(-0.0595890\pi\)
−0.186113 + 0.982528i \(0.559589\pi\)
\(434\) 16.5857i 0.0382159i
\(435\) 0 0
\(436\) 267.848 0.614330
\(437\) −100.454 + 100.454i −0.229872 + 0.229872i
\(438\) 42.8230 + 42.8230i 0.0977693 + 0.0977693i
\(439\) 432.929i 0.986170i −0.869981 0.493085i \(-0.835869\pi\)
0.869981 0.493085i \(-0.164131\pi\)
\(440\) 0 0
\(441\) −75.6061 −0.171442
\(442\) −43.2827 + 43.2827i −0.0979246 + 0.0979246i
\(443\) −245.131 245.131i −0.553342 0.553342i 0.374062 0.927404i \(-0.377965\pi\)
−0.927404 + 0.374062i \(0.877965\pi\)
\(444\) 57.7367i 0.130038i
\(445\) 0 0
\(446\) 75.2577 0.168739
\(447\) 103.924 103.924i 0.232492 0.232492i
\(448\) 188.015 + 188.015i 0.419676 + 0.419676i
\(449\) 386.091i 0.859890i −0.902855 0.429945i \(-0.858533\pi\)
0.902855 0.429945i \(-0.141467\pi\)
\(450\) 0 0
\(451\) 7.90918 0.0175370
\(452\) 380.702 380.702i 0.842260 0.842260i
\(453\) 182.449 + 182.449i 0.402758 + 0.402758i
\(454\) 113.798i 0.250656i
\(455\) 0 0
\(456\) −37.8184 −0.0829350
\(457\) 223.747 223.747i 0.489599 0.489599i −0.418580 0.908180i \(-0.637472\pi\)
0.908180 + 0.418580i \(0.137472\pi\)
\(458\) −50.3883 50.3883i −0.110018 0.110018i
\(459\) 127.485i 0.277744i
\(460\) 0 0
\(461\) −722.620 −1.56751 −0.783753 0.621073i \(-0.786697\pi\)
−0.783753 + 0.621073i \(0.786697\pi\)
\(462\) 21.5505 21.5505i 0.0466461 0.0466461i
\(463\) 129.702 + 129.702i 0.280133 + 0.280133i 0.833162 0.553029i \(-0.186528\pi\)
−0.553029 + 0.833162i \(0.686528\pi\)
\(464\) 520.095i 1.12090i
\(465\) 0 0
\(466\) −92.4653 −0.198423
\(467\) −415.258 + 415.258i −0.889203 + 0.889203i −0.994446 0.105244i \(-0.966438\pi\)
0.105244 + 0.994446i \(0.466438\pi\)
\(468\) −64.9240 64.9240i −0.138726 0.138726i
\(469\) 311.151i 0.663435i
\(470\) 0 0
\(471\) −41.2827 −0.0876489
\(472\) 70.8934 70.8934i 0.150198 0.150198i
\(473\) 300.677 + 300.677i 0.635680 + 0.635680i
\(474\) 13.4847i 0.0284487i
\(475\) 0 0
\(476\) −466.656 −0.980370
\(477\) −2.09082 + 2.09082i −0.00438326 + 0.00438326i
\(478\) −77.7163 77.7163i −0.162586 0.162586i
\(479\) 304.949i 0.636637i −0.947984 0.318318i \(-0.896882\pi\)
0.947984 0.318318i \(-0.103118\pi\)
\(480\) 0 0
\(481\) 67.1102 0.139522
\(482\) −22.8286 + 22.8286i −0.0473622 + 0.0473622i
\(483\) 97.5959 + 97.5959i 0.202062 + 0.202062i
\(484\) 30.3643i 0.0627361i
\(485\) 0 0
\(486\) 4.95459 0.0101946
\(487\) 429.318 429.318i 0.881556 0.881556i −0.112137 0.993693i \(-0.535769\pi\)
0.993693 + 0.112137i \(0.0357694\pi\)
\(488\) −10.4903 10.4903i −0.0214965 0.0214965i
\(489\) 319.918i 0.654230i
\(490\) 0 0
\(491\) −414.318 −0.843825 −0.421912 0.906637i \(-0.638641\pi\)
−0.421912 + 0.906637i \(0.638641\pi\)
\(492\) −3.32806 + 3.32806i −0.00676435 + 0.00676435i
\(493\) −609.737 609.737i −1.23679 1.23679i
\(494\) 21.6980i 0.0439230i
\(495\) 0 0
\(496\) −158.293 −0.319139
\(497\) 234.565 234.565i 0.471962 0.471962i
\(498\) 7.23724 + 7.23724i 0.0145326 + 0.0145326i
\(499\) 367.585i 0.736643i −0.929699 0.368321i \(-0.879933\pi\)
0.929699 0.368321i \(-0.120067\pi\)
\(500\) 0 0
\(501\) 110.313 0.220186
\(502\) 74.4485 74.4485i 0.148304 0.148304i
\(503\) 9.59133 + 9.59133i 0.0190683 + 0.0190683i 0.716577 0.697508i \(-0.245708\pi\)
−0.697508 + 0.716577i \(0.745708\pi\)
\(504\) 36.7423i 0.0729015i
\(505\) 0 0
\(506\) 58.9194 0.116441
\(507\) 131.518 131.518i 0.259404 0.259404i
\(508\) −641.854 641.854i −1.26349 1.26349i
\(509\) 777.489i 1.52748i −0.645522 0.763742i \(-0.723360\pi\)
0.645522 0.763742i \(-0.276640\pi\)
\(510\) 0 0
\(511\) 536.656 1.05021
\(512\) −259.376 + 259.376i −0.506593 + 0.506593i
\(513\) 31.9546 + 31.9546i 0.0622897 + 0.0622897i
\(514\) 14.9398i 0.0290658i
\(515\) 0 0
\(516\) −253.040 −0.490387
\(517\) −502.141 + 502.141i −0.971259 + 0.971259i
\(518\) −9.37347 9.37347i −0.0180955 0.0180955i
\(519\) 359.171i 0.692045i
\(520\) 0 0
\(521\) 321.605 0.617284 0.308642 0.951178i \(-0.400125\pi\)
0.308642 + 0.951178i \(0.400125\pi\)
\(522\) −23.6969 + 23.6969i −0.0453964 + 0.0453964i
\(523\) 582.454 + 582.454i 1.11368 + 1.11368i 0.992649 + 0.121030i \(0.0386198\pi\)
0.121030 + 0.992649i \(0.461380\pi\)
\(524\) 413.823i 0.789738i
\(525\) 0 0
\(526\) −125.029 −0.237697
\(527\) 185.576 185.576i 0.352136 0.352136i
\(528\) −205.677 205.677i −0.389539 0.389539i
\(529\) 262.171i 0.495598i
\(530\) 0 0
\(531\) −119.803 −0.225617
\(532\) −116.969 + 116.969i −0.219867 + 0.219867i
\(533\) 3.86836 + 3.86836i 0.00725772 + 0.00725772i
\(534\) 45.2418i 0.0847225i
\(535\) 0 0
\(536\) −160.132 −0.298753
\(537\) 225.000 225.000i 0.418994 0.418994i
\(538\) −109.788 109.788i −0.204066 0.204066i
\(539\) 286.005i 0.530621i
\(540\) 0 0
\(541\) 460.697 0.851566 0.425783 0.904825i \(-0.359999\pi\)
0.425783 + 0.904825i \(0.359999\pi\)
\(542\) −29.5709 + 29.5709i −0.0545589 + 0.0545589i
\(543\) −350.611 350.611i −0.645692 0.645692i
\(544\) 361.778i 0.665032i
\(545\) 0 0
\(546\) 21.0806 0.0386092
\(547\) 661.778 661.778i 1.20983 1.20983i 0.238750 0.971081i \(-0.423262\pi\)
0.971081 0.238750i \(-0.0767376\pi\)
\(548\) 649.691 + 649.691i 1.18557 + 1.18557i
\(549\) 17.7276i 0.0322906i
\(550\) 0 0
\(551\) −305.666 −0.554748
\(552\) −50.2270 + 50.2270i −0.0909910 + 0.0909910i
\(553\) −84.4949 84.4949i −0.152794 0.152794i
\(554\) 45.6276i 0.0823602i
\(555\) 0 0
\(556\) −745.373 −1.34060
\(557\) −125.909 + 125.909i −0.226049 + 0.226049i −0.811040 0.584991i \(-0.801098\pi\)
0.584991 + 0.811040i \(0.301098\pi\)
\(558\) −7.21225 7.21225i −0.0129252 0.0129252i
\(559\) 294.120i 0.526155i
\(560\) 0 0
\(561\) 482.252 0.859629
\(562\) −77.1556 + 77.1556i −0.137288 + 0.137288i
\(563\) 200.009 + 200.009i 0.355256 + 0.355256i 0.862061 0.506805i \(-0.169174\pi\)
−0.506805 + 0.862061i \(0.669174\pi\)
\(564\) 422.586i 0.749265i
\(565\) 0 0
\(566\) 0.535718 0.000946498
\(567\) 31.0454 31.0454i 0.0547538 0.0547538i
\(568\) 120.717 + 120.717i 0.212531 + 0.212531i
\(569\) 599.839i 1.05420i 0.849804 + 0.527099i \(0.176720\pi\)
−0.849804 + 0.527099i \(0.823280\pi\)
\(570\) 0 0
\(571\) −247.970 −0.434274 −0.217137 0.976141i \(-0.569672\pi\)
−0.217137 + 0.976141i \(0.569672\pi\)
\(572\) −245.596 + 245.596i −0.429363 + 0.429363i
\(573\) 58.8990 + 58.8990i 0.102791 + 0.102791i
\(574\) 1.08061i 0.00188260i
\(575\) 0 0
\(576\) 163.515 0.283881
\(577\) 292.121 292.121i 0.506276 0.506276i −0.407105 0.913381i \(-0.633462\pi\)
0.913381 + 0.407105i \(0.133462\pi\)
\(578\) 70.3314 + 70.3314i 0.121681 + 0.121681i
\(579\) 626.005i 1.08118i
\(580\) 0 0
\(581\) 90.6969 0.156105
\(582\) −13.5403 + 13.5403i −0.0232651 + 0.0232651i
\(583\) 7.90918 + 7.90918i 0.0135664 + 0.0135664i
\(584\) 276.186i 0.472922i
\(585\) 0 0
\(586\) 43.4051 0.0740702
\(587\) −611.217 + 611.217i −1.04126 + 1.04126i −0.0421437 + 0.999112i \(0.513419\pi\)
−0.999112 + 0.0421437i \(0.986581\pi\)
\(588\) −120.346 120.346i −0.204670 0.204670i
\(589\) 93.0306i 0.157947i
\(590\) 0 0
\(591\) 236.858 0.400775
\(592\) −89.4597 + 89.4597i −0.151114 + 0.151114i
\(593\) −524.742 524.742i −0.884894 0.884894i 0.109133 0.994027i \(-0.465193\pi\)
−0.994027 + 0.109133i \(0.965193\pi\)
\(594\) 18.7423i 0.0315528i
\(595\) 0 0
\(596\) 330.842 0.555105
\(597\) 235.893 235.893i 0.395131 0.395131i
\(598\) 28.8173 + 28.8173i 0.0481895 + 0.0481895i
\(599\) 368.858i 0.615790i 0.951420 + 0.307895i \(0.0996245\pi\)
−0.951420 + 0.307895i \(0.900375\pi\)
\(600\) 0 0
\(601\) 932.484 1.55155 0.775777 0.631007i \(-0.217358\pi\)
0.775777 + 0.631007i \(0.217358\pi\)
\(602\) 41.0806 41.0806i 0.0682402 0.0682402i
\(603\) 135.303 + 135.303i 0.224383 + 0.224383i
\(604\) 580.829i 0.961637i
\(605\) 0 0
\(606\) 58.1454 0.0959495
\(607\) −513.611 + 513.611i −0.846146 + 0.846146i −0.989650 0.143504i \(-0.954163\pi\)
0.143504 + 0.989650i \(0.454163\pi\)
\(608\) −90.6811 90.6811i −0.149147 0.149147i
\(609\) 296.969i 0.487634i
\(610\) 0 0
\(611\) −491.192 −0.803915
\(612\) −202.924 + 202.924i −0.331575 + 0.331575i
\(613\) 615.287 + 615.287i 1.00373 + 1.00373i 0.999993 + 0.00373821i \(0.00118991\pi\)
0.00373821 + 0.999993i \(0.498810\pi\)
\(614\) 56.1725i 0.0914861i
\(615\) 0 0
\(616\) 138.990 0.225633
\(617\) −546.752 + 546.752i −0.886145 + 0.886145i −0.994150 0.108005i \(-0.965554\pi\)
0.108005 + 0.994150i \(0.465554\pi\)
\(618\) −49.1316 49.1316i −0.0795010 0.0795010i
\(619\) 152.869i 0.246962i −0.992347 0.123481i \(-0.960594\pi\)
0.992347 0.123481i \(-0.0394058\pi\)
\(620\) 0 0
\(621\) 84.8786 0.136680
\(622\) 131.768 131.768i 0.211846 0.211846i
\(623\) 283.485 + 283.485i 0.455032 + 0.455032i
\(624\) 201.192i 0.322423i
\(625\) 0 0
\(626\) −46.0158 −0.0735077
\(627\) 120.879 120.879i 0.192789 0.192789i
\(628\) −65.7117 65.7117i −0.104637 0.104637i
\(629\) 209.757i 0.333477i
\(630\) 0 0
\(631\) −41.4847 −0.0657444 −0.0328722 0.999460i \(-0.510465\pi\)
−0.0328722 + 0.999460i \(0.510465\pi\)
\(632\) 43.4847 43.4847i 0.0688049 0.0688049i
\(633\) 180.297 + 180.297i 0.284830 + 0.284830i
\(634\) 48.8969i 0.0771245i
\(635\) 0 0
\(636\) −6.65612 −0.0104656
\(637\) −139.884 + 139.884i −0.219598 + 0.219598i
\(638\) 89.6413 + 89.6413i 0.140504 + 0.140504i
\(639\) 204.000i 0.319249i
\(640\) 0 0
\(641\) 47.2122 0.0736541 0.0368270 0.999322i \(-0.488275\pi\)
0.0368270 + 0.999322i \(0.488275\pi\)
\(642\) 37.8434 37.8434i 0.0589461 0.0589461i
\(643\) −460.372 460.372i −0.715976 0.715976i 0.251803 0.967779i \(-0.418977\pi\)
−0.967779 + 0.251803i \(0.918977\pi\)
\(644\) 310.697i 0.482449i
\(645\) 0 0
\(646\) 67.8184 0.104982
\(647\) 281.287 281.287i 0.434756 0.434756i −0.455487 0.890243i \(-0.650535\pi\)
0.890243 + 0.455487i \(0.150535\pi\)
\(648\) 15.9773 + 15.9773i 0.0246563 + 0.0246563i
\(649\) 453.192i 0.698293i
\(650\) 0 0
\(651\) −90.3837 −0.138838
\(652\) 509.231 509.231i 0.781029 0.781029i
\(653\) −89.8230 89.8230i −0.137554 0.137554i 0.634977 0.772531i \(-0.281010\pi\)
−0.772531 + 0.634977i \(0.781010\pi\)
\(654\) 37.8184i 0.0578263i
\(655\) 0 0
\(656\) −10.3133 −0.0157214
\(657\) 233.363 233.363i 0.355195 0.355195i
\(658\) 68.6061 + 68.6061i 0.104265 + 0.104265i
\(659\) 1081.24i 1.64072i −0.571844 0.820362i \(-0.693772\pi\)
0.571844 0.820362i \(-0.306228\pi\)
\(660\) 0 0
\(661\) −632.393 −0.956721 −0.478361 0.878163i \(-0.658769\pi\)
−0.478361 + 0.878163i \(0.658769\pi\)
\(662\) 55.1577 55.1577i 0.0833197 0.0833197i
\(663\) 235.868 + 235.868i 0.355759 + 0.355759i
\(664\) 46.6765i 0.0702960i
\(665\) 0 0
\(666\) −8.15205 −0.0122403
\(667\) −405.959 + 405.959i −0.608634 + 0.608634i
\(668\) 175.591 + 175.591i 0.262861 + 0.262861i
\(669\) 410.116i 0.613028i
\(670\) 0 0
\(671\) 67.0602 0.0999407
\(672\) −88.1010 + 88.1010i −0.131103 + 0.131103i
\(673\) −233.293 233.293i −0.346646 0.346646i 0.512213 0.858859i \(-0.328826\pi\)
−0.858859 + 0.512213i \(0.828826\pi\)
\(674\) 96.1046i 0.142588i
\(675\) 0 0
\(676\) 418.687 0.619359
\(677\) 48.3883 48.3883i 0.0714745 0.0714745i −0.670466 0.741940i \(-0.733906\pi\)
0.741940 + 0.670466i \(0.233906\pi\)
\(678\) 53.7526 + 53.7526i 0.0792810 + 0.0792810i
\(679\) 169.687i 0.249907i
\(680\) 0 0
\(681\) −620.141 −0.910633
\(682\) −27.2827 + 27.2827i −0.0400039 + 0.0400039i
\(683\) −213.410 213.410i −0.312459 0.312459i 0.533402 0.845862i \(-0.320913\pi\)
−0.845862 + 0.533402i \(0.820913\pi\)
\(684\) 101.728i 0.148724i
\(685\) 0 0
\(686\) 115.051 0.167713
\(687\) −274.590 + 274.590i −0.399695 + 0.399695i
\(688\) −392.070 392.070i −0.569870 0.569870i
\(689\) 7.73673i 0.0112289i
\(690\) 0 0
\(691\) 151.121 0.218700 0.109350 0.994003i \(-0.465123\pi\)
0.109350 + 0.994003i \(0.465123\pi\)
\(692\) 571.712 571.712i 0.826173 0.826173i
\(693\) −117.439 117.439i −0.169465 0.169465i
\(694\) 71.9408i 0.103661i
\(695\) 0 0
\(696\) −152.833 −0.219588
\(697\) 12.0908 12.0908i 0.0173469 0.0173469i
\(698\) −66.9760 66.9760i −0.0959542 0.0959542i
\(699\) 503.889i 0.720871i
\(700\) 0 0
\(701\) −745.680 −1.06374 −0.531869 0.846827i \(-0.678510\pi\)
−0.531869 + 0.846827i \(0.678510\pi\)
\(702\) 9.16684 9.16684i 0.0130582 0.0130582i
\(703\) −52.5765 52.5765i −0.0747888 0.0747888i
\(704\) 618.549i 0.878621i
\(705\) 0 0
\(706\) −10.1225 −0.0143378
\(707\) 364.338 364.338i 0.515330 0.515330i
\(708\) −190.696 190.696i −0.269345 0.269345i
\(709\) 719.049i 1.01417i −0.861895 0.507087i \(-0.830722\pi\)
0.861895 0.507087i \(-0.169278\pi\)
\(710\) 0 0
\(711\) −73.4847 −0.103354
\(712\) −145.893 + 145.893i −0.204906 + 0.204906i
\(713\) −123.555 123.555i −0.173289 0.173289i
\(714\) 65.8888i 0.0922812i
\(715\) 0 0
\(716\) 716.288 1.00040
\(717\) −423.514 + 423.514i −0.590675 + 0.590675i
\(718\) 10.8490 + 10.8490i 0.0151100 + 0.0151100i
\(719\) 605.271i 0.841824i 0.907101 + 0.420912i \(0.138290\pi\)
−0.907101 + 0.420912i \(0.861710\pi\)
\(720\) 0 0
\(721\) −615.716 −0.853975
\(722\) −64.1339 + 64.1339i −0.0888282 + 0.0888282i
\(723\) 124.404 + 124.404i 0.172067 + 0.172067i
\(724\) 1116.17i 1.54167i
\(725\) 0 0
\(726\) −4.28724 −0.00590529
\(727\) 246.126 246.126i 0.338550 0.338550i −0.517271 0.855821i \(-0.673052\pi\)
0.855821 + 0.517271i \(0.173052\pi\)
\(728\) 67.9796 + 67.9796i 0.0933786 + 0.0933786i
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 919.292 1.25758
\(732\) −28.2179 + 28.2179i −0.0385490 + 0.0385490i
\(733\) 270.763 + 270.763i 0.369390 + 0.369390i 0.867255 0.497865i \(-0.165882\pi\)
−0.497865 + 0.867255i \(0.665882\pi\)
\(734\) 65.8546i 0.0897202i
\(735\) 0 0
\(736\) −240.869 −0.327268
\(737\) 511.828 511.828i 0.694474 0.694474i
\(738\) −0.469900 0.469900i −0.000636721 0.000636721i
\(739\) 515.666i 0.697789i 0.937162 + 0.348895i \(0.113443\pi\)
−0.937162 + 0.348895i \(0.886557\pi\)
\(740\) 0 0
\(741\) 118.243 0.159572
\(742\) 1.08061 1.08061i 0.00145635 0.00145635i
\(743\) −420.702 420.702i −0.566220 0.566220i 0.364847 0.931067i \(-0.381121\pi\)
−0.931067 + 0.364847i \(0.881121\pi\)
\(744\) 46.5153i 0.0625206i
\(745\) 0 0
\(746\) 38.7490 0.0519424
\(747\) 39.4393 39.4393i 0.0527969 0.0527969i
\(748\) 767.626 + 767.626i 1.02624 + 1.02624i
\(749\) 474.252i 0.633180i
\(750\) 0 0
\(751\) −859.787 −1.14486 −0.572428 0.819955i \(-0.693998\pi\)
−0.572428 + 0.819955i \(0.693998\pi\)
\(752\) 654.772 654.772i 0.870707 0.870707i
\(753\) −405.706 405.706i −0.538786 0.538786i
\(754\) 87.6867i 0.116295i
\(755\) 0 0
\(756\) 98.8332 0.130732
\(757\) 956.075 956.075i 1.26298 1.26298i 0.313337 0.949642i \(-0.398553\pi\)
0.949642 0.313337i \(-0.101447\pi\)
\(758\) −47.1964 47.1964i −0.0622644 0.0622644i
\(759\) 321.081i 0.423031i
\(760\) 0 0
\(761\) −322.758 −0.424124 −0.212062 0.977256i \(-0.568018\pi\)
−0.212062 + 0.977256i \(0.568018\pi\)
\(762\) 90.6255 90.6255i 0.118931 0.118931i
\(763\) 236.969 + 236.969i 0.310576 + 0.310576i
\(764\) 187.505i 0.245426i
\(765\) 0 0
\(766\) −4.77858 −0.00623835
\(767\) −221.655 + 221.655i −0.288990 + 0.288990i
\(768\) 237.316 + 237.316i 0.309005 + 0.309005i
\(769\) 692.402i 0.900393i −0.892930 0.450196i \(-0.851354\pi\)
0.892930 0.450196i \(-0.148646\pi\)
\(770\) 0 0
\(771\) −81.4143 −0.105596
\(772\) −996.444 + 996.444i −1.29073 + 1.29073i
\(773\) −375.226 375.226i −0.485415 0.485415i 0.421441 0.906856i \(-0.361525\pi\)
−0.906856 + 0.421441i \(0.861525\pi\)
\(774\) 35.7276i 0.0461596i
\(775\) 0 0
\(776\) −87.3281 −0.112536
\(777\) −51.0806 + 51.0806i −0.0657408 + 0.0657408i
\(778\) −120.314 120.314i −0.154646 0.154646i
\(779\) 6.06123i 0.00778078i
\(780\) 0 0
\(781\) −771.696 −0.988087
\(782\) 90.0704 90.0704i 0.115180 0.115180i
\(783\) 129.136 + 129.136i 0.164925 + 0.164925i
\(784\) 372.939i 0.475687i
\(785\) 0 0
\(786\) −58.4291