Properties

Label 15.3.f.a.7.2
Level $15$
Weight $3$
Character 15.7
Analytic conductor $0.409$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 15.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.408720396540\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.2
Root \(1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 15.7
Dual form 15.3.f.a.13.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.224745 + 0.224745i) q^{2} +(-1.22474 + 1.22474i) q^{3} -3.89898i q^{4} +(-4.67423 + 1.77526i) q^{5} -0.550510 q^{6} +(3.44949 + 3.44949i) q^{7} +(1.77526 - 1.77526i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(0.224745 + 0.224745i) q^{2} +(-1.22474 + 1.22474i) q^{3} -3.89898i q^{4} +(-4.67423 + 1.77526i) q^{5} -0.550510 q^{6} +(3.44949 + 3.44949i) q^{7} +(1.77526 - 1.77526i) q^{8} -3.00000i q^{9} +(-1.44949 - 0.651531i) q^{10} +11.3485 q^{11} +(4.77526 + 4.77526i) q^{12} +(-5.55051 + 5.55051i) q^{13} +1.55051i q^{14} +(3.55051 - 7.89898i) q^{15} -14.7980 q^{16} +(-17.3485 - 17.3485i) q^{17} +(0.674235 - 0.674235i) q^{18} +8.69694i q^{19} +(6.92168 + 18.2247i) q^{20} -8.44949 q^{21} +(2.55051 + 2.55051i) q^{22} +(11.5505 - 11.5505i) q^{23} +4.34847i q^{24} +(18.6969 - 16.5959i) q^{25} -2.49490 q^{26} +(3.67423 + 3.67423i) q^{27} +(13.4495 - 13.4495i) q^{28} +35.1464i q^{29} +(2.57321 - 0.977296i) q^{30} +10.6969 q^{31} +(-10.4268 - 10.4268i) q^{32} +(-13.8990 + 13.8990i) q^{33} -7.79796i q^{34} +(-22.2474 - 10.0000i) q^{35} -11.6969 q^{36} +(-6.04541 - 6.04541i) q^{37} +(-1.95459 + 1.95459i) q^{38} -13.5959i q^{39} +(-5.14643 + 11.4495i) q^{40} +0.696938 q^{41} +(-1.89898 - 1.89898i) q^{42} +(-26.4949 + 26.4949i) q^{43} -44.2474i q^{44} +(5.32577 + 14.0227i) q^{45} +5.19184 q^{46} +(44.2474 + 44.2474i) q^{47} +(18.1237 - 18.1237i) q^{48} -25.2020i q^{49} +(7.93189 + 0.472194i) q^{50} +42.4949 q^{51} +(21.6413 + 21.6413i) q^{52} +(-0.696938 + 0.696938i) q^{53} +1.65153i q^{54} +(-53.0454 + 20.1464i) q^{55} +12.2474 q^{56} +(-10.6515 - 10.6515i) q^{57} +(-7.89898 + 7.89898i) q^{58} -39.9342i q^{59} +(-30.7980 - 13.8434i) q^{60} +5.90918 q^{61} +(2.40408 + 2.40408i) q^{62} +(10.3485 - 10.3485i) q^{63} +54.5051i q^{64} +(16.0908 - 35.7980i) q^{65} -6.24745 q^{66} +(-45.1010 - 45.1010i) q^{67} +(-67.6413 + 67.6413i) q^{68} +28.2929i q^{69} +(-2.75255 - 7.24745i) q^{70} -68.0000 q^{71} +(-5.32577 - 5.32577i) q^{72} +(77.7878 - 77.7878i) q^{73} -2.71735i q^{74} +(-2.57321 + 43.2247i) q^{75} +33.9092 q^{76} +(39.1464 + 39.1464i) q^{77} +(3.05561 - 3.05561i) q^{78} -24.4949i q^{79} +(69.1691 - 26.2702i) q^{80} -9.00000 q^{81} +(0.156633 + 0.156633i) q^{82} +(13.1464 - 13.1464i) q^{83} +32.9444i q^{84} +(111.889 + 50.2929i) q^{85} -11.9092 q^{86} +(-43.0454 - 43.0454i) q^{87} +(20.1464 - 20.1464i) q^{88} +82.1816i q^{89} +(-1.95459 + 4.34847i) q^{90} -38.2929 q^{91} +(-45.0352 - 45.0352i) q^{92} +(-13.1010 + 13.1010i) q^{93} +19.8888i q^{94} +(-15.4393 - 40.6515i) q^{95} +25.5403 q^{96} +(-24.5959 - 24.5959i) q^{97} +(5.66403 - 5.66403i) q^{98} -34.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 4q^{5} - 12q^{6} + 4q^{7} + 12q^{8} + O(q^{10}) \) \( 4q - 4q^{2} - 4q^{5} - 12q^{6} + 4q^{7} + 12q^{8} + 4q^{10} + 16q^{11} + 24q^{12} - 32q^{13} + 24q^{15} - 20q^{16} - 40q^{17} - 12q^{18} - 36q^{20} - 24q^{21} + 20q^{22} + 56q^{23} + 16q^{25} + 88q^{26} + 44q^{28} - 24q^{30} - 16q^{31} - 76q^{32} - 36q^{33} - 40q^{35} + 12q^{36} + 64q^{37} - 96q^{38} + 48q^{40} - 56q^{41} + 12q^{42} - 8q^{43} + 36q^{45} - 136q^{46} + 128q^{47} + 48q^{48} + 164q^{50} + 72q^{51} - 80q^{52} + 56q^{53} - 124q^{55} - 72q^{57} - 12q^{58} - 84q^{60} + 200q^{61} + 88q^{62} + 12q^{63} - 112q^{65} + 24q^{66} - 200q^{67} - 104q^{68} - 60q^{70} - 272q^{71} - 36q^{72} + 76q^{73} + 24q^{75} + 312q^{76} + 88q^{77} + 120q^{78} + 164q^{80} - 36q^{81} + 128q^{82} - 16q^{83} + 232q^{85} - 224q^{86} - 84q^{87} + 12q^{88} - 96q^{90} - 16q^{91} + 104q^{92} - 72q^{93} + 144q^{95} - 84q^{96} - 20q^{97} - 188q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.224745 + 0.224745i 0.112372 + 0.112372i 0.761057 0.648685i \(-0.224681\pi\)
−0.648685 + 0.761057i \(0.724681\pi\)
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 3.89898i 0.974745i
\(5\) −4.67423 + 1.77526i −0.934847 + 0.355051i
\(6\) −0.550510 −0.0917517
\(7\) 3.44949 + 3.44949i 0.492784 + 0.492784i 0.909182 0.416398i \(-0.136708\pi\)
−0.416398 + 0.909182i \(0.636708\pi\)
\(8\) 1.77526 1.77526i 0.221907 0.221907i
\(9\) 3.00000i 0.333333i
\(10\) −1.44949 0.651531i −0.144949 0.0651531i
\(11\) 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 \(-0.847624\pi\)
0.460630 + 0.887592i \(0.347624\pi\)
\(14\) 1.55051i 0.110751i
\(15\) 3.55051 7.89898i 0.236701 0.526599i
\(16\) −14.7980 −0.924872
\(17\) −17.3485 17.3485i −1.02050 1.02050i −0.999785 0.0207127i \(-0.993406\pi\)
−0.0207127 0.999785i \(-0.506594\pi\)
\(18\) 0.674235 0.674235i 0.0374575 0.0374575i
\(19\) 8.69694i 0.457734i 0.973458 + 0.228867i \(0.0735020\pi\)
−0.973458 + 0.228867i \(0.926498\pi\)
\(20\) 6.92168 + 18.2247i 0.346084 + 0.911237i
\(21\) −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 \(-0.634445\pi\)
0.912120 + 0.409924i \(0.134445\pi\)
\(24\) 4.34847i 0.181186i
\(25\) 18.6969 16.5959i 0.747878 0.663837i
\(26\) −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 \(0.207216\pi\)
−0.795485 + 0.605973i \(0.792784\pi\)
\(30\) 2.57321 0.977296i 0.0857738 0.0325765i
\(31\) 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
\(35\) −22.2474 10.0000i −0.635641 0.285714i
\(36\) −11.6969 −0.324915
\(37\) −6.04541 6.04541i −0.163389 0.163389i 0.620677 0.784066i \(-0.286858\pi\)
−0.784066 + 0.620677i \(0.786858\pi\)
\(38\) −1.95459 + 1.95459i −0.0514366 + 0.0514366i
\(39\) 13.5959i 0.348613i
\(40\) −5.14643 + 11.4495i −0.128661 + 0.286237i
\(41\) 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 \(-0.893496\pi\)
0.328384 + 0.944544i \(0.393496\pi\)
\(44\) 44.2474i 1.00562i
\(45\) 5.32577 + 14.0227i 0.118350 + 0.311616i
\(46\) 5.19184 0.112866
\(47\) 44.2474 + 44.2474i 0.941435 + 0.941435i 0.998377 0.0569424i \(-0.0181351\pi\)
−0.0569424 + 0.998377i \(0.518135\pi\)
\(48\) 18.1237 18.1237i 0.377578 0.377578i
\(49\) 25.2020i 0.514327i
\(50\) 7.93189 + 0.472194i 0.158638 + 0.00944387i
\(51\) 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 \(-0.752960\pi\)
0.700501 + 0.713651i \(0.252960\pi\)
\(54\) 1.65153i 0.0305839i
\(55\) −53.0454 + 20.1464i −0.964462 + 0.366299i
\(56\) 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 \(-0.890106\pi\)
0.940993 0.338425i \(-0.109894\pi\)
\(60\) −30.7980 13.8434i −0.513299 0.230723i
\(61\) 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
\(65\) 16.0908 35.7980i 0.247551 0.550738i
\(66\) −6.24745 −0.0946583
\(67\) −45.1010 45.1010i −0.673150 0.673150i 0.285291 0.958441i \(-0.407910\pi\)
−0.958441 + 0.285291i \(0.907910\pi\)
\(68\) −67.6413 + 67.6413i −0.994725 + 0.994725i
\(69\) 28.2929i 0.410041i
\(70\) −2.75255 7.24745i −0.0393222 0.103535i
\(71\) −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 0.0678931 0.997693i \(-0.478372\pi\)
0.997693 0.0678931i \(-0.0216277\pi\)
\(74\) 2.71735i 0.0367209i
\(75\) −2.57321 + 43.2247i −0.0343095 + 0.576330i
\(76\) 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 \(-0.950452\pi\)
0.987910 0.155031i \(-0.0495477\pi\)
\(80\) 69.1691 26.2702i 0.864614 0.328377i
\(81\) −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 \(-0.714275\pi\)
0.781853 + 0.623463i \(0.214275\pi\)
\(84\) 32.9444i 0.392195i
\(85\) 111.889 + 50.2929i 1.31634 + 0.591681i
\(86\) −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 \(0.152758\pi\)
−0.887039 + 0.461695i \(0.847242\pi\)
\(90\) −1.95459 + 4.34847i −0.0217177 + 0.0483163i
\(91\) −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
\(95\) −15.4393 40.6515i −0.162519 0.427911i
\(96\) 25.5403 0.266045
\(97\) −24.5959 24.5959i −0.253566 0.253566i 0.568865 0.822431i \(-0.307383\pi\)
−0.822431 + 0.568865i \(0.807383\pi\)
\(98\) 5.66403 5.66403i 0.0577962 0.0577962i
\(99\) 34.0454i 0.343893i
\(100\) −64.7071 72.8990i −0.647071 0.728990i
\(101\) −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 \(-0.959914\pi\)
0.125601 + 0.992081i \(0.459914\pi\)
\(104\) 19.7071i 0.189492i
\(105\) 39.4949 15.0000i 0.376142 0.142857i
\(106\) −0.313267 −0.00295535
\(107\) 68.7423 + 68.7423i 0.642452 + 0.642452i 0.951158 0.308706i \(-0.0998958\pi\)
−0.308706 + 0.951158i \(0.599896\pi\)
\(108\) 14.3258 14.3258i 0.132646 0.132646i
\(109\) 68.6969i 0.630247i 0.949051 + 0.315124i \(0.102046\pi\)
−0.949051 + 0.315124i \(0.897954\pi\)
\(110\) −16.4495 7.39388i −0.149541 0.0672171i
\(111\) 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 \(-0.540768\pi\)
0.991809 + 0.127727i \(0.0407681\pi\)
\(114\) 4.78775i 0.0419978i
\(115\) −33.4847 + 74.4949i −0.291171 + 0.647782i
\(116\) 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
\(120\) −7.71964 20.3258i −0.0643304 0.169381i
\(121\) 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
\(125\) −57.9319 + 110.765i −0.463455 + 0.886120i
\(126\) 4.65153 0.0369169
\(127\) 164.621 + 164.621i 1.29623 + 1.29623i 0.930865 + 0.365362i \(0.119055\pi\)
0.365362 + 0.930865i \(0.380945\pi\)
\(128\) −53.9569 + 53.9569i −0.421538 + 0.421538i
\(129\) 64.8990i 0.503093i
\(130\) 11.6617 4.42908i 0.0897057 0.0340698i
\(131\) 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
\(135\) −23.6969 10.6515i −0.175533 0.0789002i
\(136\) −61.5959 −0.452911
\(137\) −166.631 166.631i −1.21629 1.21629i −0.968923 0.247363i \(-0.920436\pi\)
−0.247363 0.968923i \(-0.579564\pi\)
\(138\) −6.35867 + 6.35867i −0.0460774 + 0.0460774i
\(139\) 191.171i 1.37533i −0.726026 0.687667i \(-0.758635\pi\)
0.726026 0.687667i \(-0.241365\pi\)
\(140\) −38.9898 + 86.7423i −0.278499 + 0.619588i
\(141\) −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
\(145\) −62.3939 164.283i −0.430303 1.13298i
\(146\) 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 \(0.0919084\pi\)
−0.958604 + 0.284744i \(0.908092\pi\)
\(150\) −10.2929 + 9.13622i −0.0686190 + 0.0609082i
\(151\) 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
\(155\) −50.0000 + 18.9898i −0.322581 + 0.122515i
\(156\) −53.0102 −0.339809
\(157\) 16.8536 + 16.8536i 0.107348 + 0.107348i 0.758741 0.651393i \(-0.225815\pi\)
−0.651393 + 0.758741i \(0.725815\pi\)
\(158\) 5.50510 5.50510i 0.0348424 0.0348424i
\(159\) 1.70714i 0.0107368i
\(160\) 67.2474 + 30.2270i 0.420297 + 0.188919i
\(161\) 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 \(-0.558266\pi\)
0.983293 + 0.182029i \(0.0582664\pi\)
\(164\) 2.71735i 0.0165692i
\(165\) 40.2929 89.6413i 0.244199 0.543281i
\(166\) 5.90918 0.0355975
\(167\) −45.0352 45.0352i −0.269672 0.269672i 0.559296 0.828968i \(-0.311071\pi\)
−0.828968 + 0.559296i \(0.811071\pi\)
\(168\) −15.0000 + 15.0000i −0.0892857 + 0.0892857i
\(169\) 107.384i 0.635406i
\(170\) 13.8434 + 36.4495i 0.0814316 + 0.214409i
\(171\) 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 \(-0.545434\pi\)
0.989831 + 0.142252i \(0.0454343\pi\)
\(174\) 19.3485i 0.111198i
\(175\) 121.742 + 7.24745i 0.695671 + 0.0414140i
\(176\) −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 \(0.171526\pi\)
−0.858292 + 0.513161i \(0.828474\pi\)
\(180\) 54.6742 20.7650i 0.303746 0.115361i
\(181\) −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
\(185\) 38.9898 + 17.5255i 0.210756 + 0.0947325i
\(186\) −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
\(190\) 5.66632 12.6061i 0.0298228 0.0663480i
\(191\) 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 −0.413809 + 0.910364i \(0.635802\pi\)
−0.910364 + 0.413809i \(0.864198\pi\)
\(194\) 11.0556i 0.0569877i
\(195\) 24.1362 + 63.5505i 0.123776 + 0.325900i
\(196\) −98.2622 −0.501338
\(197\) −96.6969 96.6969i −0.490847 0.490847i 0.417726 0.908573i \(-0.362827\pi\)
−0.908573 + 0.417726i \(0.862827\pi\)
\(198\) 7.65153 7.65153i 0.0386441 0.0386441i
\(199\) 192.606i 0.967870i 0.875104 + 0.483935i \(0.160793\pi\)
−0.875104 + 0.483935i \(0.839207\pi\)
\(200\) 3.72985 62.6538i 0.0186492 0.313269i
\(201\) 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
\(205\) −3.25765 + 1.23724i −0.0158910 + 0.00603533i
\(206\) −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
\(210\) 12.2474 + 5.50510i 0.0583212 + 0.0262148i
\(211\) 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
\(215\) 76.8082 170.879i 0.357247 0.794784i
\(216\) 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
\(220\) 78.5505 + 206.823i 0.357048 + 0.940104i
\(221\) 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 \(-0.571855\pi\)
0.974629 + 0.223826i \(0.0718548\pi\)
\(224\) 71.9342i 0.321135i
\(225\) −49.7878 56.0908i −0.221279 0.249293i
\(226\) 43.8888 0.194198
\(227\) 253.171 + 253.171i 1.11529 + 1.11529i 0.992423 + 0.122870i \(0.0392098\pi\)
0.122870 + 0.992423i \(0.460790\pi\)
\(228\) −41.5301 + 41.5301i −0.182150 + 0.182150i
\(229\) 224.202i 0.979048i −0.871990 0.489524i \(-0.837171\pi\)
0.871990 0.489524i \(-0.162829\pi\)
\(230\) −24.2679 + 9.21683i −0.105512 + 0.0400732i
\(231\) −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 \(-0.964613\pi\)
0.110944 + 0.993827i \(0.464613\pi\)
\(234\) 7.48469i 0.0319859i
\(235\) −285.373 128.272i −1.21436 0.545840i
\(236\) −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 \(-0.742566\pi\)
0.690401 0.723427i \(-0.257434\pi\)
\(240\) −52.5403 + 116.889i −0.218918 + 0.487037i
\(241\) 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
\(245\) 44.7401 + 117.800i 0.182612 + 0.480817i
\(246\) −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
\(250\) −37.9138 + 11.8740i −0.151655 + 0.0474959i
\(251\) −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
\(255\) −198.631 + 75.4393i −0.778946 + 0.295840i
\(256\) 193.767 0.756904
\(257\) 33.2372 + 33.2372i 0.129328 + 0.129328i 0.768808 0.639480i \(-0.220850\pi\)
−0.639480 + 0.768808i \(0.720850\pi\)
\(258\) 14.5857 14.5857i 0.0565338 0.0565338i
\(259\) 41.7071i 0.161031i
\(260\) −139.576 62.7378i −0.536829 0.241299i
\(261\) 105.439 0.403982
\(262\) 23.8536 + 23.8536i 0.0910442 + 0.0910442i
\(263\) −278.157 + 278.157i −1.05763 + 1.05763i −0.0593952 + 0.998235i \(0.518917\pi\)
−0.998235 + 0.0593952i \(0.981083\pi\)
\(264\) 49.3485i 0.186926i
\(265\) 2.02041 4.49490i 0.00762419 0.0169619i
\(266\) −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 \(-0.637615\pi\)
0.418988 0.907992i \(-0.362385\pi\)
\(270\) −2.93189 7.71964i −0.0108588 0.0285913i
\(271\) 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
\(275\) 212.182 188.338i 0.771570 0.684866i
\(276\) 110.313 0.399686
\(277\) 101.510 + 101.510i 0.366461 + 0.366461i 0.866185 0.499724i \(-0.166565\pi\)
−0.499724 + 0.866185i \(0.666565\pi\)
\(278\) 42.9648 42.9648i 0.154550 0.154550i
\(279\) 32.0908i 0.115021i
\(280\) −57.2474 + 21.7423i −0.204455 + 0.0776512i
\(281\) 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 \(-0.749052\pi\)
0.709209 + 0.704998i \(0.249052\pi\)
\(284\) 265.131i 0.933558i
\(285\) 68.6969 + 30.8786i 0.241042 + 0.108346i
\(286\) −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
\(290\) 22.8990 50.9444i 0.0789620 0.175670i
\(291\) 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 \(-0.675131\pi\)
0.852425 + 0.522850i \(0.175131\pi\)
\(294\) 13.8740i 0.0471904i
\(295\) 70.8934 + 186.662i 0.240316 + 0.632752i
\(296\) −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
\(300\) 168.532 + 10.0329i 0.561775 + 0.0334430i
\(301\) −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
\(305\) −27.6209 + 10.4903i −0.0905604 + 0.0343945i
\(306\) −23.3939 −0.0764506
\(307\) −124.969 124.969i −0.407066 0.407066i 0.473648 0.880714i \(-0.342937\pi\)
−0.880714 + 0.473648i \(0.842937\pi\)
\(308\) 152.631 152.631i 0.495556 0.495556i
\(309\) 218.611i 0.707478i
\(310\) −15.5051 6.96938i −0.0500165 0.0224819i
\(311\) −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 \(-0.824290\pi\)
0.524400 + 0.851472i \(0.324290\pi\)
\(314\) 7.57551i 0.0241258i
\(315\) −30.0000 + 66.7423i −0.0952381 + 0.211880i
\(316\) −95.5051 −0.302231
\(317\) −108.783 108.783i −0.343165 0.343165i 0.514391 0.857556i \(-0.328018\pi\)
−0.857556 + 0.514391i \(0.828018\pi\)
\(318\) 0.383672 0.383672i 0.00120651 0.00120651i
\(319\) 398.858i 1.25034i
\(320\) −96.7605 254.770i −0.302376 0.796155i
\(321\) −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
\(325\) −11.6617 + 195.893i −0.0358823 + 0.602749i
\(326\) 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
\(330\) 29.2020 11.0908i 0.0884910 0.0336085i
\(331\) −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
\(335\) 290.879 + 130.747i 0.868294 + 0.390289i
\(336\) 125.035 0.372129
\(337\) 213.808 + 213.808i 0.634446 + 0.634446i 0.949180 0.314734i \(-0.101915\pi\)
−0.314734 + 0.949180i \(0.601915\pi\)
\(338\) −24.1339 + 24.1339i −0.0714022 + 0.0714022i
\(339\) 239.171i 0.705520i
\(340\) 196.091 436.252i 0.576738 1.28309i
\(341\) 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
\(345\) −50.2270 132.247i −0.145586 0.383326i
\(346\) 65.9092 0.190489
\(347\) −160.050 160.050i −0.461239 0.461239i 0.437822 0.899062i \(-0.355750\pi\)
−0.899062 + 0.437822i \(0.855750\pi\)
\(348\) −167.833 + 167.833i −0.482279 + 0.482279i
\(349\) 298.009i 0.853894i −0.904277 0.426947i \(-0.859589\pi\)
0.904277 0.426947i \(-0.140411\pi\)
\(350\) 25.7321 + 28.9898i 0.0735204 + 0.0828280i
\(351\) −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 \(-0.764364\pi\)
0.674489 + 0.738285i \(0.264364\pi\)
\(354\) 21.9842i 0.0621022i
\(355\) 317.848 120.717i 0.895346 0.340049i
\(356\) 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 \(0.0214167\pi\)
−0.997737 + 0.0672318i \(0.978583\pi\)
\(360\) 34.3485 + 15.4393i 0.0954124 + 0.0428869i
\(361\) 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
\(365\) −225.505 + 501.691i −0.617822 + 1.37450i
\(366\) −3.25307 −0.00888816
\(367\) 146.510 + 146.510i 0.399209 + 0.399209i 0.877954 0.478745i \(-0.158908\pi\)
−0.478745 + 0.877954i \(0.658908\pi\)
\(368\) −170.924 + 170.924i −0.464467 + 0.464467i
\(369\) 2.09082i 0.00566617i
\(370\) 4.82399 + 12.7015i 0.0130378 + 0.0343284i
\(371\) −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 \(-0.697746\pi\)
0.813159 + 0.582042i \(0.197746\pi\)
\(374\) 88.4949i 0.236617i
\(375\) −64.7071 206.611i −0.172552 0.550962i
\(376\) 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 \(-0.910645\pi\)
0.960857 0.277045i \(-0.0893551\pi\)
\(380\) −158.499 + 60.1975i −0.417104 + 0.158414i
\(381\) −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 \(-0.756248\pi\)
0.693092 + 0.720849i \(0.256248\pi\)
\(384\) 132.167i 0.344184i
\(385\) −252.474 113.485i −0.655778 0.294765i
\(386\) −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 \(-0.758448\pi\)
0.725621 0.688094i \(-0.241552\pi\)
\(390\) −8.85816 + 19.7071i −0.0227132 + 0.0505311i
\(391\) −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
\(395\) 43.4847 + 114.495i 0.110088 + 0.289860i
\(396\) −132.742 −0.335208
\(397\) 118.742 + 118.742i 0.299099 + 0.299099i 0.840661 0.541562i \(-0.182167\pi\)
−0.541562 + 0.840661i \(0.682167\pi\)
\(398\) −43.2872 + 43.2872i −0.108762 + 0.108762i
\(399\) 73.4847i 0.184172i
\(400\) −276.677 + 245.586i −0.691691 + 0.613964i
\(401\) 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
\(405\) 42.0681 15.9773i 0.103872 0.0394501i
\(406\) −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 \(-0.783170\pi\)
0.776823 0.629719i \(-0.216830\pi\)
\(410\) −1.01021 0.454077i −0.00246391 0.00110750i
\(411\) 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
\(415\) −38.1112 + 84.7878i −0.0918343 + 0.204308i
\(416\) 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 \(-0.966282\pi\)
0.994395 0.105730i \(-0.0337178\pi\)
\(420\) −58.4847 153.990i −0.139249 0.366642i
\(421\) −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
\(425\) −612.277 36.4495i −1.44065 0.0857635i
\(426\) 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
\(430\) 55.6663 21.1418i 0.129457 0.0491671i
\(431\) 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 \(-0.940411\pi\)
0.186113 + 0.982528i \(0.440411\pi\)
\(434\) 16.5857i 0.0382159i
\(435\) 277.621 + 124.788i 0.638209 + 0.286868i
\(436\) 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 \(0.164131\pi\)
−0.869981 + 0.493085i \(0.835869\pi\)
\(440\) −58.4041 + 129.934i −0.132737 + 0.295305i
\(441\) −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 \(-0.622035\pi\)
0.927404 + 0.374062i \(0.122035\pi\)
\(444\) 57.7367i 0.130038i
\(445\) −145.893 384.136i −0.327850 0.863227i
\(446\) 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 \(0.141467\pi\)
−0.902855 + 0.429945i \(0.858533\pi\)
\(450\) 1.41658 23.7957i 0.00314796 0.0528793i
\(451\) 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
\(455\) 178.990 67.9796i 0.393384 0.149406i
\(456\) −37.8184 −0.0829350
\(457\) −223.747 223.747i −0.489599 0.489599i 0.418580 0.908180i \(-0.362528\pi\)
−0.908180 + 0.418580i \(0.862528\pi\)
\(458\) 50.3883 50.3883i 0.110018 0.110018i
\(459\) 127.485i 0.277744i
\(460\) 290.454 + 130.556i 0.631422 + 0.283818i
\(461\) −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 \(-0.813472\pi\)
0.553029 + 0.833162i \(0.313472\pi\)
\(464\) 520.095i 1.12090i
\(465\) 37.9796 84.4949i 0.0816765 0.181709i
\(466\) −92.4653 −0.198423
\(467\) 415.258 + 415.258i 0.889203 + 0.889203i 0.994446 0.105244i \(-0.0335623\pi\)
−0.105244 + 0.994446i \(0.533562\pi\)
\(468\) 64.9240 64.9240i 0.138726 0.138726i
\(469\) 311.151i 0.663435i
\(470\) −35.3076 92.9648i −0.0751227 0.197797i
\(471\) −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
\(475\) 144.334 + 162.606i 0.303860 + 0.342329i
\(476\) −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 \(0.103118\pi\)
−0.947984 + 0.318318i \(0.896882\pi\)
\(480\) −119.381 + 45.3406i −0.248711 + 0.0944595i
\(481\) 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
\(485\) 158.631 + 71.3031i 0.327074 + 0.147017i
\(486\) 4.95459 0.0101946
\(487\) −429.318 429.318i −0.881556 0.881556i 0.112137 0.993693i \(-0.464231\pi\)
−0.993693 + 0.112137i \(0.964231\pi\)
\(488\) 10.4903 10.4903i 0.0214965 0.0214965i
\(489\) 319.918i 0.654230i
\(490\) −16.4199 + 36.5301i −0.0335100 + 0.0745512i
\(491\) −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
\(495\) 60.4393 + 159.136i 0.122100 + 0.321487i
\(496\) −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 \(0.120067\pi\)
−0.929699 + 0.368321i \(0.879933\pi\)
\(500\) 431.871 + 225.875i 0.863741 + 0.451750i
\(501\) 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 \(-0.754292\pi\)
0.697508 + 0.716577i \(0.254292\pi\)
\(504\) 36.7423i 0.0729015i
\(505\) 493.697 187.504i 0.977618 0.371295i
\(506\) 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 \(0.276640\pi\)
−0.645522 + 0.763742i \(0.723360\pi\)
\(510\) −61.5959 27.6867i −0.120776 0.0542877i
\(511\) 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
\(515\) 258.727 575.601i 0.502382 1.11767i
\(516\) −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
\(520\) −34.9852 92.1158i −0.0672792 0.177146i
\(521\) 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 −0.121030 + 0.992649i \(0.538620\pi\)
−0.992649 + 0.121030i \(0.961380\pi\)
\(524\) 413.823i 0.789738i
\(525\) −157.980 + 140.227i −0.300914 + 0.267099i
\(526\) −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
\(530\) 1.46428 0.556128i 0.00276280 0.00104930i
\(531\) −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
\(535\) −443.353 199.283i −0.828697 0.372491i
\(536\) −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
\(540\) −41.5301 + 92.3939i −0.0769076 + 0.171100i
\(541\) 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
\(545\) −121.955 321.106i −0.223770 0.589185i
\(546\) 21.0806 0.0386092
\(547\) −661.778 661.778i −1.20983 1.20983i −0.971081 0.238750i \(-0.923262\pi\)
−0.238750 0.971081i \(-0.576738\pi\)
\(548\) −649.691 + 649.691i −1.18557 + 1.18557i
\(549\) 17.7276i 0.0322906i
\(550\) 90.0148 + 5.35867i 0.163663 + 0.00974304i
\(551\) −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
\(555\) −69.2168 + 26.2883i −0.124715 + 0.0473663i
\(556\) −745.373 −1.34060
\(557\) 125.909 + 125.909i 0.226049 + 0.226049i 0.811040 0.584991i \(-0.198902\pi\)
−0.584991 + 0.811040i \(0.698902\pi\)
\(558\) 7.21225 7.21225i 0.0129252 0.0129252i
\(559\) 294.120i 0.526155i
\(560\) 329.217 + 147.980i 0.587887 + 0.264249i
\(561\) 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 \(-0.830826\pi\)
0.506805 + 0.862061i \(0.330826\pi\)
\(564\) 422.586i 0.749265i
\(565\) −283.060 + 629.737i −0.500992 + 1.11458i
\(566\) 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 \(-0.823280\pi\)
0.849804 0.527099i \(-0.176720\pi\)
\(570\) 8.49948 + 22.3791i 0.0149114 + 0.0392616i
\(571\) −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
\(575\) 24.2679 407.650i 0.0422050 0.708957i
\(576\) 163.515 0.283881
\(577\) −292.121 292.121i −0.506276 0.506276i 0.407105 0.913381i \(-0.366538\pi\)
−0.913381 + 0.407105i \(0.866538\pi\)
\(578\) −70.3314 + 70.3314i −0.121681 + 0.121681i
\(579\) 626.005i 1.08118i
\(580\) −640.535 + 243.272i −1.10437 + 0.419435i
\(581\) 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
\(585\) −107.394 48.2724i −0.183579 0.0825170i
\(586\) 43.4051 0.0740702
\(587\) 611.217 + 611.217i 1.04126 + 1.04126i 0.999112 + 0.0421437i \(0.0134187\pi\)
0.0421437 + 0.999112i \(0.486581\pi\)
\(588\) 120.346 120.346i 0.204670 0.204670i
\(589\) 93.0306i 0.157947i
\(590\) −26.0183 + 57.8842i −0.0440989 + 0.0981088i
\(591\) 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 \(-0.534807\pi\)
0.994027 + 0.109133i \(0.0348074\pi\)
\(594\) 18.7423i 0.0315528i
\(595\) 212.474 + 559.444i 0.357100 + 0.940242i
\(596\) 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 \(-0.900375\pi\)
0.951420 0.307895i \(-0.0996245\pi\)
\(600\) 72.1668 + 81.3031i 0.120278 + 0.135505i
\(601\) 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
\(605\) −36.4018 + 13.8252i −0.0601682 + 0.0228517i
\(606\) 58.1454 0.0959495
\(607\) 513.611 + 513.611i 0.846146 + 0.846146i 0.989650 0.143504i \(-0.0458369\pi\)
−0.143504 + 0.989650i \(0.545837\pi\)
\(608\) 90.6811 90.6811i 0.149147 0.149147i
\(609\) 296.969i 0.487634i
\(610\) −8.56530 3.85002i −0.0140415 0.00631150i
\(611\) −491.192 −0.803915
\(612\) 202.924 + 202.924i 0.331575 + 0.331575i
\(613\) −615.287 + 615.287i −1.00373 + 1.00373i −0.00373821 + 0.999993i \(0.501190\pi\)
−0.999993 + 0.00373821i \(0.998810\pi\)
\(614\) 56.1725i 0.0914861i
\(615\) 2.47449 5.50510i 0.00402356 0.00895139i
\(616\) 138.990 0.225633
\(617\) 546.752 + 546.752i 0.886145 + 0.886145i 0.994150 0.108005i \(-0.0344463\pi\)
−0.108005 + 0.994150i \(0.534446\pi\)
\(618\) 49.1316 49.1316i 0.0795010 0.0795010i
\(619\) 152.869i 0.246962i 0.992347 + 0.123481i \(0.0394058\pi\)
−0.992347 + 0.123481i \(0.960594\pi\)
\(620\) 74.0408 + 194.949i 0.119421 + 0.314434i
\(621\) 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
\(625\) 74.1510 620.586i 0.118642 0.992937i
\(626\) −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
\(630\) −21.7423 + 8.25765i −0.0345117 + 0.0131074i
\(631\) −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
\(635\) −1061.72 477.233i −1.67200 0.751547i
\(636\) −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
\(640\) 156.420 347.994i 0.244406 0.543741i
\(641\) 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 \(-0.581023\pi\)
0.967779 + 0.251803i \(0.0810234\pi\)
\(644\) 310.697i 0.482449i
\(645\) 115.212 + 303.353i 0.178624 + 0.470315i
\(646\) 67.8184 0.104982
\(647\) −281.287 281.287i −0.434756 0.434756i 0.455487 0.890243i \(-0.349465\pi\)
−0.890243 + 0.455487i \(0.849465\pi\)
\(648\) −15.9773 + 15.9773i −0.0246563 + 0.0246563i
\(649\) 453.192i 0.698293i
\(650\) −46.6469 + 41.4051i −0.0717645 + 0.0637002i
\(651\) −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 \(-0.718990\pi\)
0.772531 + 0.634977i \(0.218990\pi\)
\(654\) 37.8184i 0.0578263i
\(655\) −496.106 + 188.419i −0.757413 + 0.287662i
\(656\) −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 \(0.306228\pi\)
−0.571844 + 0.820362i \(0.693772\pi\)
\(660\) −349.510 157.101i −0.529560 0.238032i
\(661\) −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
\(665\) 86.9694 193.485i 0.130781 0.290954i
\(666\) −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
\(670\) 35.9888 + 94.7582i 0.0537146 + 0.141430i
\(671\) 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 \(-0.671174\pi\)
0.858859 + 0.512213i \(0.171174\pi\)
\(674\) 96.1046i 0.142588i
\(675\) 129.674 + 7.71964i 0.192110 + 0.0114365i
\(676\) 418.687 0.619359
\(677\) −48.3883 48.3883i −0.0714745 0.0714745i 0.670466 0.741940i \(-0.266094\pi\)
−0.741940 + 0.670466i \(0.766094\pi\)
\(678\) −53.7526 + 53.7526i −0.0792810 + 0.0792810i
\(679\) 169.687i 0.249907i
\(680\) 287.914 109.348i 0.423403 0.160807i
\(681\) −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 \(-0.679087\pi\)
0.845862 + 0.533402i \(0.179087\pi\)
\(684\) 101.728i 0.148724i
\(685\) 1074.69 + 483.060i 1.56888 + 0.705197i
\(686\) 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
\(690\) 18.4337 41.0102i 0.0267155 0.0594351i
\(691\) 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
\(695\) 339.378 + 893.580i 0.488314 + 1.28573i
\(696\) −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
\(700\) 28.2577 474.671i 0.0403681 0.678101i
\(701\) −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
\(705\) 506.611 192.409i 0.718597 0.272920i
\(706\) −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 \(0.169278\pi\)
−0.861895 + 0.507087i \(0.830722\pi\)
\(710\) 98.5653 + 44.3041i 0.138824 + 0.0624001i
\(711\) −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
\(715\) 182.606 406.252i 0.255393 0.568185i
\(716\) 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 \(-0.861710\pi\)
0.907101 0.420912i \(-0.138290\pi\)
\(720\) −78.8105 207.507i −0.109459 0.288205i
\(721\) −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
\(725\) 583.287 + 657.131i 0.804534 + 0.906387i
\(726\) −4.28724 −0.00590529
\(727\) −246.126 246.126i −0.338550 0.338550i 0.517271 0.855821i \(-0.326948\pi\)
−0.855821 + 0.517271i \(0.826948\pi\)
\(728\) −67.9796 + 67.9796i −0.0933786 + 0.0933786i
\(729\) 27.0000i 0.0370370i
\(730\) −163.434 + 62.0714i −0.223882 + 0.0850294i
\(731\) 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 \(-0.834118\pi\)
0.497865 + 0.867255i \(0.334118\pi\)
\(734\) 65.8546i 0.0897202i
\(735\) −199.070 89.4801i −0.270844 0.121742i
\(736\) −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 \(-0.886557\pi\)
0.937162 0.348895i \(-0.113443\pi\)
\(740\) 68.3316 152.020i 0.0923400 0.205433i
\(741\) 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 \(-0.618879\pi\)
0.931067 + 0.364847i \(0.118879\pi\)
\(744\) 46.5153i 0.0625206i
\(745\) −150.637 396.626i −0.202197 0.532383i
\(746\) 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
\(750\) 31.8921 60.9773i 0.0425228 0.0813031i
\(751\) −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
\(755\) −696.318 + 264.459i −0.922275 + 0.350276i
\(756\) 98.8332 0.130732
\(757\) −956.075 956.075i −1.26298 1.26298i −0.949642 0.313337i \(-0.898553\pi\)
−0.313337 0.949642i \(-0.601447\pi\)
\(758\) 47.1964 47.1964i 0.0622644 0.0622644i
\(759\) 321.081i 0.423031i
\(760\) −99.5755 44.7582i −0.131020 0.0588923i
\(761\) −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
\(765\) 150.879 335.666i 0.197227 0.438780i
\(766\) −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 \(0.148646\pi\)
−0.892930 + 0.450196i \(0.851354\pi\)
\(770\) −31.2372 82.2474i −0.0405678 0.106815i
\(771\) −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 \(-0.638475\pi\)
0.906856 + 0.421441i \(0.138475\pi\)
\(774\) 35.7276i 0.0461596i
\(775\) 200.000 177.526i 0.258065 0.229065i
\(776\)