Properties

Label 45.3.g.b.37.1
Level $45$
Weight $3$
Character 45.37
Analytic conductor $1.226$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 45.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.22616118962\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.1
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 45.37
Dual form 45.3.g.b.28.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.224745 - 0.224745i) q^{2} -3.89898i q^{4} +(4.67423 - 1.77526i) q^{5} +(3.44949 + 3.44949i) q^{7} +(-1.77526 + 1.77526i) q^{8} +O(q^{10})\) \(q+(-0.224745 - 0.224745i) q^{2} -3.89898i q^{4} +(4.67423 - 1.77526i) q^{5} +(3.44949 + 3.44949i) q^{7} +(-1.77526 + 1.77526i) q^{8} +(-1.44949 - 0.651531i) q^{10} -11.3485 q^{11} +(-5.55051 + 5.55051i) q^{13} -1.55051i q^{14} -14.7980 q^{16} +(17.3485 + 17.3485i) q^{17} +8.69694i q^{19} +(-6.92168 - 18.2247i) q^{20} +(2.55051 + 2.55051i) q^{22} +(-11.5505 + 11.5505i) q^{23} +(18.6969 - 16.5959i) q^{25} +2.49490 q^{26} +(13.4495 - 13.4495i) q^{28} -35.1464i q^{29} +10.6969 q^{31} +(10.4268 + 10.4268i) q^{32} -7.79796i q^{34} +(22.2474 + 10.0000i) q^{35} +(-6.04541 - 6.04541i) q^{37} +(1.95459 - 1.95459i) q^{38} +(-5.14643 + 11.4495i) q^{40} -0.696938 q^{41} +(-26.4949 + 26.4949i) q^{43} +44.2474i q^{44} +5.19184 q^{46} +(-44.2474 - 44.2474i) q^{47} -25.2020i q^{49} +(-7.93189 - 0.472194i) q^{50} +(21.6413 + 21.6413i) q^{52} +(0.696938 - 0.696938i) q^{53} +(-53.0454 + 20.1464i) q^{55} -12.2474 q^{56} +(-7.89898 + 7.89898i) q^{58} +39.9342i q^{59} +5.90918 q^{61} +(-2.40408 - 2.40408i) q^{62} +54.5051i q^{64} +(-16.0908 + 35.7980i) q^{65} +(-45.1010 - 45.1010i) q^{67} +(67.6413 - 67.6413i) q^{68} +(-2.75255 - 7.24745i) q^{70} +68.0000 q^{71} +(77.7878 - 77.7878i) q^{73} +2.71735i q^{74} +33.9092 q^{76} +(-39.1464 - 39.1464i) q^{77} -24.4949i q^{79} +(-69.1691 + 26.2702i) q^{80} +(0.156633 + 0.156633i) q^{82} +(-13.1464 + 13.1464i) q^{83} +(111.889 + 50.2929i) q^{85} +11.9092 q^{86} +(20.1464 - 20.1464i) q^{88} -82.1816i q^{89} -38.2929 q^{91} +(45.0352 + 45.0352i) q^{92} +19.8888i q^{94} +(15.4393 + 40.6515i) q^{95} +(-24.5959 - 24.5959i) q^{97} +(-5.66403 + 5.66403i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{5} + 4 q^{7} - 12 q^{8} + O(q^{10}) \) \( 4 q + 4 q^{2} + 4 q^{5} + 4 q^{7} - 12 q^{8} + 4 q^{10} - 16 q^{11} - 32 q^{13} - 20 q^{16} + 40 q^{17} + 36 q^{20} + 20 q^{22} - 56 q^{23} + 16 q^{25} - 88 q^{26} + 44 q^{28} - 16 q^{31} + 76 q^{32} + 40 q^{35} + 64 q^{37} + 96 q^{38} + 48 q^{40} + 56 q^{41} - 8 q^{43} - 136 q^{46} - 128 q^{47} - 164 q^{50} - 80 q^{52} - 56 q^{53} - 124 q^{55} - 12 q^{58} + 200 q^{61} - 88 q^{62} + 112 q^{65} - 200 q^{67} + 104 q^{68} - 60 q^{70} + 272 q^{71} + 76 q^{73} + 312 q^{76} - 88 q^{77} - 164 q^{80} + 128 q^{82} + 16 q^{83} + 232 q^{85} + 224 q^{86} + 12 q^{88} - 16 q^{91} - 104 q^{92} - 144 q^{95} - 20 q^{97} + 188 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.224745 0.224745i −0.112372 0.112372i 0.648685 0.761057i \(-0.275319\pi\)
−0.761057 + 0.648685i \(0.775319\pi\)
\(3\) 0 0
\(4\) 3.89898i 0.974745i
\(5\) 4.67423 1.77526i 0.934847 0.355051i
\(6\) 0 0
\(7\) 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
\(9\) 0 0
\(10\) −1.44949 0.651531i −0.144949 0.0651531i
\(11\) −11.3485 −1.03168 −0.515840 0.856685i \(-0.672520\pi\)
−0.515840 + 0.856685i \(0.672520\pi\)
\(12\) 0 0
\(13\) −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
\(15\) 0 0
\(16\) −14.7980 −0.924872
\(17\) 17.3485 + 17.3485i 1.02050 + 1.02050i 0.999785 + 0.0207127i \(0.00659354\pi\)
0.0207127 + 0.999785i \(0.493406\pi\)
\(18\) 0 0
\(19\) 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
\(21\) 0 0
\(22\) 2.55051 + 2.55051i 0.115932 + 0.115932i
\(23\) −11.5505 + 11.5505i −0.502196 + 0.502196i −0.912120 0.409924i \(-0.865555\pi\)
0.409924 + 0.912120i \(0.365555\pi\)
\(24\) 0 0
\(25\) 18.6969 16.5959i 0.747878 0.663837i
\(26\) 2.49490 0.0959576
\(27\) 0 0
\(28\) 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
\(33\) 0 0
\(34\) 7.79796i 0.229352i
\(35\) 22.2474 + 10.0000i 0.635641 + 0.285714i
\(36\) 0 0
\(37\) −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
\(39\) 0 0
\(40\) −5.14643 + 11.4495i −0.128661 + 0.286237i
\(41\) −0.696938 −0.0169985 −0.00849925 0.999964i \(-0.502705\pi\)
−0.00849925 + 0.999964i \(0.502705\pi\)
\(42\) 0 0
\(43\) −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
\(45\) 0 0
\(46\) 5.19184 0.112866
\(47\) −44.2474 44.2474i −0.941435 0.941435i 0.0569424 0.998377i \(-0.481865\pi\)
−0.998377 + 0.0569424i \(0.981865\pi\)
\(48\) 0 0
\(49\) 25.2020i 0.514327i
\(50\) −7.93189 0.472194i −0.158638 0.00944387i
\(51\) 0 0
\(52\) 21.6413 + 21.6413i 0.416179 + 0.416179i
\(53\) 0.696938 0.696938i 0.0131498 0.0131498i −0.700501 0.713651i \(-0.747040\pi\)
0.713651 + 0.700501i \(0.247040\pi\)
\(54\) 0 0
\(55\) −53.0454 + 20.1464i −0.964462 + 0.366299i
\(56\) −12.2474 −0.218704
\(57\) 0 0
\(58\) −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
\(63\) 0 0
\(64\) 54.5051i 0.851642i
\(65\) −16.0908 + 35.7980i −0.247551 + 0.550738i
\(66\) 0 0
\(67\) −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
\(69\) 0 0
\(70\) −2.75255 7.24745i −0.0393222 0.103535i
\(71\) 68.0000 0.957746 0.478873 0.877884i \(-0.341045\pi\)
0.478873 + 0.877884i \(0.341045\pi\)
\(72\) 0 0
\(73\) 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
\(75\) 0 0
\(76\) 33.9092 0.446173
\(77\) −39.1464 39.1464i −0.508395 0.508395i
\(78\) 0 0
\(79\) 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
\(81\) 0 0
\(82\) 0.156633 + 0.156633i 0.00191016 + 0.00191016i
\(83\) −13.1464 + 13.1464i −0.158391 + 0.158391i −0.781853 0.623463i \(-0.785725\pi\)
0.623463 + 0.781853i \(0.285725\pi\)
\(84\) 0 0
\(85\) 111.889 + 50.2929i 1.31634 + 0.591681i
\(86\) 11.9092 0.138479
\(87\) 0 0
\(88\) 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
\(93\) 0 0
\(94\) 19.8888i 0.211583i
\(95\) 15.4393 + 40.6515i 0.162519 + 0.427911i
\(96\) 0 0
\(97\) −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
\(99\) 0 0
\(100\) −64.7071 72.8990i −0.647071 0.728990i
\(101\) 105.621 1.04575 0.522876 0.852409i \(-0.324859\pi\)
0.522876 + 0.852409i \(0.324859\pi\)
\(102\) 0 0
\(103\) −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
\(105\) 0 0
\(106\) −0.313267 −0.00295535
\(107\) −68.7423 68.7423i −0.642452 0.642452i 0.308706 0.951158i \(-0.400104\pi\)
−0.951158 + 0.308706i \(0.900104\pi\)
\(108\) 0 0
\(109\) 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
\(111\) 0 0
\(112\) −51.0454 51.0454i −0.455763 0.455763i
\(113\) −97.6413 + 97.6413i −0.864083 + 0.864083i −0.991809 0.127727i \(-0.959232\pi\)
0.127727 + 0.991809i \(0.459232\pi\)
\(114\) 0 0
\(115\) −33.4847 + 74.4949i −0.291171 + 0.647782i
\(116\) −137.035 −1.18134
\(117\) 0 0
\(118\) 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 0
\(124\) 41.7071i 0.336348i
\(125\) 57.9319 110.765i 0.463455 0.886120i
\(126\) 0 0
\(127\) 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
\(129\) 0 0
\(130\) 11.6617 4.42908i 0.0897057 0.0340698i
\(131\) −106.136 −0.810200 −0.405100 0.914272i \(-0.632763\pi\)
−0.405100 + 0.914272i \(0.632763\pi\)
\(132\) 0 0
\(133\) −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 0.968923 + 0.247363i \(0.0795639\pi\)
0.247363 + 0.968923i \(0.420436\pi\)
\(138\) 0 0
\(139\) 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
\(141\) 0 0
\(142\) −15.2827 15.2827i −0.107624 0.107624i
\(143\) 62.9898 62.9898i 0.440488 0.440488i
\(144\) 0 0
\(145\) −62.3939 164.283i −0.430303 1.13298i
\(146\) −34.9648 −0.239485
\(147\) 0 0
\(148\) −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
\(153\) 0 0
\(154\) 17.5959i 0.114259i
\(155\) 50.0000 18.9898i 0.322581 0.122515i
\(156\) 0 0
\(157\) 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
\(159\) 0 0
\(160\) 67.2474 + 30.2270i 0.420297 + 0.188919i
\(161\) −79.6867 −0.494949
\(162\) 0 0
\(163\) 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
\(165\) 0 0
\(166\) 5.90918 0.0355975
\(167\) 45.0352 + 45.0352i 0.269672 + 0.269672i 0.828968 0.559296i \(-0.188929\pi\)
−0.559296 + 0.828968i \(0.688929\pi\)
\(168\) 0 0
\(169\) 107.384i 0.635406i
\(170\) −13.8434 36.4495i −0.0814316 0.214409i
\(171\) 0 0
\(172\) 103.303 + 103.303i 0.600599 + 0.600599i
\(173\) −146.631 + 146.631i −0.847579 + 0.847579i −0.989831 0.142252i \(-0.954566\pi\)
0.142252 + 0.989831i \(0.454566\pi\)
\(174\) 0 0
\(175\) 121.742 + 7.24745i 0.695671 + 0.0414140i
\(176\) 167.934 0.954171
\(177\) 0 0
\(178\) −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
\(183\) 0 0
\(184\) 41.0102i 0.222882i
\(185\) −38.9898 17.5255i −0.210756 0.0947325i
\(186\) 0 0
\(187\) −196.879 196.879i −1.05283 1.05283i
\(188\) −172.520 + 172.520i −0.917659 + 0.917659i
\(189\) 0 0
\(190\) 5.66632 12.6061i 0.0298228 0.0663480i
\(191\) −48.0908 −0.251784 −0.125892 0.992044i \(-0.540179\pi\)
−0.125892 + 0.992044i \(0.540179\pi\)
\(192\) 0 0
\(193\) −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
\(195\) 0 0
\(196\) −98.2622 −0.501338
\(197\) 96.6969 + 96.6969i 0.490847 + 0.490847i 0.908573 0.417726i \(-0.137173\pi\)
−0.417726 + 0.908573i \(0.637173\pi\)
\(198\) 0 0
\(199\) 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
\(201\) 0 0
\(202\) −23.7378 23.7378i −0.117514 0.117514i
\(203\) 121.237 121.237i 0.597228 0.597228i
\(204\) 0 0
\(205\) −3.25765 + 1.23724i −0.0158910 + 0.00603533i
\(206\) 40.1158 0.194737
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) 30.8990i 0.144388i
\(215\) −76.8082 + 170.879i −0.357247 + 0.794784i
\(216\) 0 0
\(217\) 36.8990 + 36.8990i 0.170041 + 0.170041i
\(218\) 15.4393 15.4393i 0.0708224 0.0708224i
\(219\) 0 0
\(220\) 78.5505 + 206.823i 0.357048 + 0.940104i
\(221\) −192.586 −0.871429
\(222\) 0 0
\(223\) 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
\(225\) 0 0
\(226\) 43.8888 0.194198
\(227\) −253.171 253.171i −1.11529 1.11529i −0.992423 0.122870i \(-0.960790\pi\)
−0.122870 0.992423i \(-0.539210\pi\)
\(228\) 0 0
\(229\) 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
\(231\) 0 0
\(232\) 62.3939 + 62.3939i 0.268939 + 0.268939i
\(233\) 205.712 205.712i 0.882883 0.882883i −0.110944 0.993827i \(-0.535387\pi\)
0.993827 + 0.110944i \(0.0353873\pi\)
\(234\) 0 0
\(235\) −285.373 128.272i −1.21436 0.545840i
\(236\) 155.703 0.659757
\(237\) 0 0
\(238\) 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
\(243\) 0 0
\(244\) 23.0398i 0.0944254i
\(245\) −44.7401 117.800i −0.182612 0.480817i
\(246\) 0 0
\(247\) −48.2724 48.2724i −0.195435 0.195435i
\(248\) −18.9898 + 18.9898i −0.0765718 + 0.0765718i
\(249\) 0 0
\(250\) −37.9138 + 11.8740i −0.151655 + 0.0474959i
\(251\) 331.258 1.31975 0.659876 0.751375i \(-0.270609\pi\)
0.659876 + 0.751375i \(0.270609\pi\)
\(252\) 0 0
\(253\) 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 0.639480 0.768808i \(-0.279150\pi\)
−0.768808 + 0.639480i \(0.779150\pi\)
\(258\) 0 0
\(259\) 41.7071i 0.161031i
\(260\) 139.576 + 62.7378i 0.536829 + 0.241299i
\(261\) 0 0
\(262\) 23.8536 + 23.8536i 0.0910442 + 0.0910442i
\(263\) 278.157 278.157i 1.05763 1.05763i 0.0593952 0.998235i \(-0.481083\pi\)
0.998235 0.0593952i \(-0.0189172\pi\)
\(264\) 0 0
\(265\) 2.02041 4.49490i 0.00762419 0.0169619i
\(266\) 13.4847 0.0506943
\(267\) 0 0
\(268\) −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
\(273\) 0 0
\(274\) 74.8990i 0.273354i
\(275\) −212.182 + 188.338i −0.771570 + 0.684866i
\(276\) 0 0
\(277\) 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
\(279\) 0 0
\(280\) −57.2474 + 21.7423i −0.204455 + 0.0776512i
\(281\) −343.303 −1.22172 −0.610860 0.791739i \(-0.709176\pi\)
−0.610860 + 0.791739i \(0.709176\pi\)
\(282\) 0 0
\(283\) 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
\(285\) 0 0
\(286\) −28.3133 −0.0989974
\(287\) −2.40408 2.40408i −0.00837659 0.00837659i
\(288\) 0 0
\(289\) 312.939i 1.08283i
\(290\) −22.8990 + 50.9444i −0.0789620 + 0.175670i
\(291\) 0 0
\(292\) −303.293 303.293i −1.03867 1.03867i
\(293\) −96.5653 + 96.5653i −0.329574 + 0.329574i −0.852425 0.522850i \(-0.824869\pi\)
0.522850 + 0.852425i \(0.324869\pi\)
\(294\) 0 0
\(295\) 70.8934 + 186.662i 0.240316 + 0.632752i
\(296\) 21.4643 0.0725145
\(297\) 0 0
\(298\) −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
\(303\) 0 0
\(304\) 128.697i 0.423345i
\(305\) 27.6209 10.4903i 0.0905604 0.0343945i
\(306\) 0 0
\(307\) −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
\(309\) 0 0
\(310\) −15.5051 6.96938i −0.0500165 0.0224819i
\(311\) 586.302 1.88522 0.942608 0.333902i \(-0.108365\pi\)
0.942608 + 0.333902i \(0.108365\pi\)
\(312\) 0 0
\(313\) −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
\(315\) 0 0
\(316\) −95.5051 −0.302231
\(317\) 108.783 + 108.783i 0.343165 + 0.343165i 0.857556 0.514391i \(-0.171982\pi\)
−0.514391 + 0.857556i \(0.671982\pi\)
\(318\) 0 0
\(319\) 398.858i 1.25034i
\(320\) 96.7605 + 254.770i 0.302376 + 0.796155i
\(321\) 0 0
\(322\) 17.9092 + 17.9092i 0.0556186 + 0.0556186i
\(323\) −150.879 + 150.879i −0.467116 + 0.467116i
\(324\) 0 0
\(325\) −11.6617 + 195.893i −0.0358823 + 0.602749i
\(326\) −58.7061 −0.180080
\(327\) 0 0
\(328\) 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
\(333\) 0 0
\(334\) 20.2429i 0.0606074i
\(335\) −290.879 130.747i −0.868294 0.390289i
\(336\) 0 0
\(337\) 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
\(339\) 0 0
\(340\) 196.091 436.252i 0.576738 1.28309i
\(341\) −121.394 −0.355994
\(342\) 0 0
\(343\) 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 0.899062 0.437822i \(-0.144250\pi\)
−0.437822 + 0.899062i \(0.644250\pi\)
\(348\) 0 0
\(349\) 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
\(351\) 0 0
\(352\) −118.328 118.328i −0.336159 0.336159i
\(353\) 22.5199 22.5199i 0.0637957 0.0637957i −0.674489 0.738285i \(-0.735636\pi\)
0.738285 + 0.674489i \(0.235636\pi\)
\(354\) 0 0
\(355\) 317.848 120.717i 0.895346 0.340049i
\(356\) −320.424 −0.900069
\(357\) 0 0
\(358\) −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
\(363\) 0 0
\(364\) 149.303i 0.410173i
\(365\) 225.505 501.691i 0.617822 1.37450i
\(366\) 0 0
\(367\) 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
\(369\) 0 0
\(370\) 4.82399 + 12.7015i 0.0130378 + 0.0343284i
\(371\) 4.80816 0.0129600
\(372\) 0 0
\(373\) 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
\(375\) 0 0
\(376\) 157.101 0.417822
\(377\) 195.081 + 195.081i 0.517455 + 0.517455i
\(378\) 0 0
\(379\) 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
\(381\) 0 0
\(382\) 10.8082 + 10.8082i 0.0282936 + 0.0282936i
\(383\) 10.6311 10.6311i 0.0277575 0.0277575i −0.693092 0.720849i \(-0.743752\pi\)
0.720849 + 0.693092i \(0.243752\pi\)
\(384\) 0 0
\(385\) −252.474 113.485i −0.655778 0.294765i
\(386\) 114.874 0.297601
\(387\) 0 0
\(388\) −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
\(393\) 0 0
\(394\) 43.4643i 0.110315i
\(395\) −43.4847 114.495i −0.110088 0.289860i
\(396\) 0 0
\(397\) 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
\(399\) 0 0
\(400\) −276.677 + 245.586i −0.691691 + 0.613964i
\(401\) −420.302 −1.04813 −0.524067 0.851677i \(-0.675586\pi\)
−0.524067 + 0.851677i \(0.675586\pi\)
\(402\) 0 0
\(403\) −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
\(408\) 0 0
\(409\) 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
\(411\) 0 0
\(412\) 347.974 + 347.974i 0.844597 + 0.844597i
\(413\) −137.753 + 137.753i −0.333541 + 0.333541i
\(414\) 0 0
\(415\) −38.1112 + 84.7878i −0.0918343 + 0.204308i
\(416\) −115.748 −0.278240
\(417\) 0 0
\(418\) −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
\(423\) 0 0
\(424\) 2.47449i 0.00583605i
\(425\) 612.277 + 36.4495i 1.44065 + 0.0857635i
\(426\) 0 0
\(427\) 20.3837 + 20.3837i 0.0477369 + 0.0477369i
\(428\) −268.025 + 268.025i −0.626227 + 0.626227i
\(429\) 0 0
\(430\) 55.6663 21.1418i 0.129457 0.0491671i
\(431\) −804.636 −1.86690 −0.933452 0.358702i \(-0.883219\pi\)
−0.933452 + 0.358702i \(0.883219\pi\)
\(432\) 0 0
\(433\) −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
\(435\) 0 0
\(436\) 267.848 0.614330
\(437\) −100.454 100.454i −0.229872 0.229872i
\(438\) 0 0
\(439\) 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
\(441\) 0 0
\(442\) 43.2827 + 43.2827i 0.0979246 + 0.0979246i
\(443\) −245.131 + 245.131i −0.553342 + 0.553342i −0.927404 0.374062i \(-0.877965\pi\)
0.374062 + 0.927404i \(0.377965\pi\)
\(444\) 0 0
\(445\) −145.893 384.136i −0.327850 0.863227i
\(446\) −75.2577 −0.168739
\(447\) 0 0
\(448\) −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
\(453\) 0 0
\(454\) 113.798i 0.250656i
\(455\) −178.990 + 67.9796i −0.393384 + 0.149406i
\(456\) 0 0
\(457\) −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
\(459\) 0 0
\(460\) 290.454 + 130.556i 0.631422 + 0.283818i
\(461\) 722.620 1.56751 0.783753 0.621073i \(-0.213303\pi\)
0.783753 + 0.621073i \(0.213303\pi\)
\(462\) 0 0
\(463\) −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
\(465\) 0 0
\(466\) −92.4653 −0.198423
\(467\) −415.258 415.258i −0.889203 0.889203i 0.105244 0.994446i \(-0.466438\pi\)
−0.994446 + 0.105244i \(0.966438\pi\)
\(468\) 0 0
\(469\) 311.151i 0.663435i
\(470\) 35.3076 + 92.9648i 0.0751227 + 0.197797i
\(471\) 0 0
\(472\) −70.8934 70.8934i −0.150198 0.150198i
\(473\) 300.677 300.677i 0.635680 0.635680i
\(474\) 0 0
\(475\) 144.334 + 162.606i 0.303860 + 0.342329i
\(476\) 466.656 0.980370
\(477\) 0 0
\(478\) 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
\(483\) 0 0
\(484\) 30.3643i 0.0627361i
\(485\) −158.631 71.3031i −0.327074 0.147017i
\(486\) 0 0
\(487\) −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
\(489\) 0 0
\(490\) −16.4199 + 36.5301i −0.0335100 + 0.0745512i
\(491\) 414.318 0.843825 0.421912 0.906637i \(-0.361359\pi\)
0.421912 + 0.906637i \(0.361359\pi\)
\(492\) 0 0
\(493\) 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
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) −74.4485 74.4485i −0.148304 0.148304i
\(503\) 9.59133 9.59133i 0.0190683 0.0190683i −0.697508 0.716577i \(-0.745708\pi\)
0.716577 + 0.697508i \(0.245708\pi\)
\(504\) 0 0
\(505\) 493.697 187.504i 0.977618 0.371295i
\(506\) −58.9194 −0.116441
\(507\) 0 0
\(508\) 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
\(513\) 0 0
\(514\) 14.9398i 0.0290658i
\(515\) −258.727 + 575.601i −0.502382 + 1.11767i
\(516\) 0 0
\(517\) 502.141 + 502.141i 0.971259 + 0.971259i
\(518\) −9.37347 + 9.37347i −0.0180955 + 0.0180955i
\(519\) 0 0
\(520\) −34.9852 92.1158i −0.0672792 0.177146i
\(521\) −321.605 −0.617284 −0.308642 0.951178i \(-0.599875\pi\)
−0.308642 + 0.951178i \(0.599875\pi\)
\(522\) 0 0
\(523\) −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
\(525\) 0 0
\(526\) −125.029 −0.237697
\(527\) 185.576 + 185.576i 0.352136 + 0.352136i
\(528\) 0 0
\(529\) 262.171i 0.495598i
\(530\) −1.46428 + 0.556128i −0.00276280 + 0.00104930i
\(531\) 0 0
\(532\) 116.969 + 116.969i 0.219867 + 0.219867i
\(533\) 3.86836 3.86836i 0.00725772 0.00725772i
\(534\) 0 0
\(535\) −443.353 199.283i −0.828697 0.372491i
\(536\) 160.132 0.298753
\(537\) 0 0
\(538\) 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
\(543\) 0 0
\(544\) 361.778i 0.665032i
\(545\) 121.955 + 321.106i 0.223770 + 0.589185i
\(546\) 0 0
\(547\) −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
\(549\) 0 0
\(550\) 90.0148 + 5.35867i 0.163663 + 0.00974304i
\(551\) 305.666 0.554748
\(552\) 0 0
\(553\) 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 0.584991 0.811040i \(-0.301098\pi\)
−0.811040 + 0.584991i \(0.801098\pi\)
\(558\) 0 0
\(559\) 294.120i 0.526155i
\(560\) −329.217 147.980i −0.587887 0.264249i
\(561\) 0 0
\(562\) 77.1556 + 77.1556i 0.137288 + 0.137288i
\(563\) 200.009 200.009i 0.355256 0.355256i −0.506805 0.862061i \(-0.669174\pi\)
0.862061 + 0.506805i \(0.169174\pi\)
\(564\) 0 0
\(565\) −283.060 + 629.737i −0.500992 + 1.11458i
\(566\) −0.535718 −0.000946498
\(567\) 0 0
\(568\) −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
\(573\) 0 0
\(574\) 1.08061i 0.00188260i
\(575\) −24.2679 + 407.650i −0.0422050 + 0.708957i
\(576\) 0 0
\(577\) −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
\(579\) 0 0
\(580\) −640.535 + 243.272i −1.10437 + 0.419435i
\(581\) −90.6969 −0.156105
\(582\) 0 0
\(583\) −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 −0.999112 0.0421437i \(-0.986581\pi\)
−0.0421437 0.999112i \(-0.513419\pi\)
\(588\) 0 0
\(589\) 93.0306i 0.157947i
\(590\) 26.0183 57.8842i 0.0440989 0.0981088i
\(591\) 0 0
\(592\) 89.4597 + 89.4597i 0.151114 + 0.151114i
\(593\) −524.742 + 524.742i −0.884894 + 0.884894i −0.994027 0.109133i \(-0.965193\pi\)
0.109133 + 0.994027i \(0.465193\pi\)
\(594\) 0 0
\(595\) 212.474 + 559.444i 0.357100 + 0.940242i
\(596\) −330.842 −0.555105
\(597\) 0 0
\(598\) −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
\(603\) 0 0
\(604\) 580.829i 0.961637i
\(605\) 36.4018 13.8252i 0.0601682 0.0228517i
\(606\) 0 0
\(607\) 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
\(609\) 0 0
\(610\) −8.56530 3.85002i −0.0140415 0.00631150i
\(611\) 491.192 0.803915
\(612\) 0 0
\(613\) −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
\(615\) 0 0
\(616\) 138.990 0.225633
\(617\) −546.752 546.752i −0.886145 0.886145i 0.108005 0.994150i \(-0.465554\pi\)
−0.994150 + 0.108005i \(0.965554\pi\)
\(618\) 0 0
\(619\) 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
\(621\) 0 0
\(622\) −131.768 131.768i −0.211846 0.211846i
\(623\) 283.485 283.485i 0.455032 0.455032i
\(624\) 0 0
\(625\) 74.1510 620.586i 0.118642 0.992937i
\(626\) 46.0158 0.0735077
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) 48.8969i 0.0771245i
\(635\) 1061.72 + 477.233i 1.67200 + 0.751547i
\(636\) 0 0
\(637\) 139.884 + 139.884i 0.219598 + 0.219598i
\(638\) 89.6413 89.6413i 0.140504 0.140504i
\(639\) 0 0
\(640\) 156.420 347.994i 0.244406 0.543741i
\(641\) −47.2122 −0.0736541 −0.0368270 0.999322i \(-0.511725\pi\)
−0.0368270 + 0.999322i \(0.511725\pi\)
\(642\) 0 0
\(643\) 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
\(645\) 0 0
\(646\) 67.8184 0.104982
\(647\) 281.287 + 281.287i 0.434756 + 0.434756i 0.890243 0.455487i \(-0.150535\pi\)
−0.455487 + 0.890243i \(0.650535\pi\)
\(648\) 0 0
\(649\) 453.192i 0.698293i
\(650\) 46.6469 41.4051i 0.0717645 0.0637002i
\(651\) 0 0
\(652\) −509.231 509.231i −0.781029 0.781029i
\(653\) −89.8230 + 89.8230i −0.137554 + 0.137554i −0.772531 0.634977i \(-0.781010\pi\)
0.634977 + 0.772531i \(0.281010\pi\)
\(654\) 0 0
\(655\) −496.106 + 188.419i −0.757413 + 0.287662i
\(656\) 10.3133 0.0157214
\(657\) 0 0
\(658\) −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
\(663\) 0 0
\(664\) 46.6765i 0.0702960i
\(665\) −86.9694 + 193.485i −0.130781 + 0.290954i
\(666\) 0 0
\(667\) 405.959 + 405.959i 0.608634 + 0.608634i
\(668\) 175.591 175.591i 0.262861 0.262861i
\(669\) 0 0
\(670\) 35.9888 + 94.7582i 0.0537146 + 0.141430i
\(671\) −67.0602 −0.0999407
\(672\) 0 0
\(673\) 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
\(675\) 0 0
\(676\) 418.687 0.619359
\(677\) 48.3883 + 48.3883i 0.0714745 + 0.0714745i 0.741940 0.670466i \(-0.233906\pi\)
−0.670466 + 0.741940i \(0.733906\pi\)
\(678\) 0 0
\(679\) 169.687i 0.249907i
\(680\) −287.914 + 109.348i −0.423403 + 0.160807i
\(681\) 0 0
\(682\) 27.2827 + 27.2827i 0.0400039 + 0.0400039i
\(683\) −213.410 + 213.410i −0.312459 + 0.312459i −0.845862 0.533402i \(-0.820913\pi\)
0.533402 + 0.845862i \(0.320913\pi\)
\(684\) 0 0
\(685\) 1074.69 + 483.060i 1.56888 + 0.705197i
\(686\) −115.051 −0.167713
\(687\) 0 0
\(688\) 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
\(693\) 0 0
\(694\) 71.9408i 0.103661i
\(695\) −339.378 893.580i −0.488314 1.28573i
\(696\) 0 0
\(697\) −12.0908 12.0908i −0.0173469 0.0173469i
\(698\) −66.9760 + 66.9760i −0.0959542 + 0.0959542i
\(699\) 0 0
\(700\) 28.2577 474.671i 0.0403681 0.678101i
\(701\) 745.680 1.06374 0.531869 0.846827i \(-0.321490\pi\)
0.531869 + 0.846827i \(0.321490\pi\)
\(702\) 0 0
\(703\) 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
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) 145.893 + 145.893i 0.204906 + 0.204906i
\(713\) −123.555 + 123.555i −0.173289 + 0.173289i
\(714\) 0 0
\(715\) 182.606 406.252i 0.255393 0.568185i
\(716\) −716.288 −1.00040
\(717\) 0 0
\(718\) −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
\(723\) 0 0
\(724\) 1116.17i 1.54167i
\(725\) −583.287 657.131i −0.804534 0.906387i
\(726\) 0 0
\(727\) −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
\(729\) 0 0
\(730\) −163.434 + 62.0714i −0.223882 + 0.0850294i
\(731\) −919.292 −1.25758
\(732\) 0 0
\(733\) −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
\(735\) 0 0
\(736\) −240.869 −0.327268
\(737\) 511.828 + 511.828i 0.694474 + 0.694474i
\(738\) 0 0
\(739\) 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
\(741\) 0 0
\(742\) −1.08061 1.08061i −0.00145635 0.00145635i
\(743\) −420.702 + 420.702i −0.566220 + 0.566220i −0.931067 0.364847i \(-0.881121\pi\)
0.364847 + 0.931067i \(0.381121\pi\)
\(744\) 0 0
\(745\) −150.637 396.626i −0.202197 0.532383i
\(746\) −38.7490 −0.0519424
\(747\) 0 0
\(748\) −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
\(753\) 0 0
\(754\) 87.6867i 0.116295i
\(755\) 696.318 264.459i 0.922275 0.350276i
\(756\) 0 0
\(757\) −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
\(759\) 0 0
\(760\) −99.5755 44.7582i −0.131020 0.0588923i
\(761\) 322.758 0.424124 0.212062 0.977256i \(-0.431982\pi\)
0.212062 + 0.977256i \(0.431982\pi\)
\(762\) 0 0
\(763\) −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
\(768\) 0 0
\(769\) 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
\(771\) 0 0
\(772\) 996.444 + 996.444i 1.29073 + 1.29073i
\(773\) −375.226 + 375.226i −0.485415 + 0.485415i −0.906856 0.421441i \(-0.861525\pi\)
0.421441 + 0.906856i \(0.361525\pi\)
\(774\) 0 0
\(775\) 200.000 177.526i 0.258065 0.229065i
\(776\) 87.3281 0.112536
\(777\) 0 0
\(778\) 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
\(783\) 0 0
\(784\) 372.939i 0.475687i
\(785\) 108.697 + 48.8582i 0.138467 + 0.0622397i
\(786\) 0 0
\(787\) 910.990 + 910.990i 1.15755 + 1.15755i 0.985001 + 0.172546i \(0.0551993\pi\)
0.172546 + 0.985001i \(0.444801\pi\)
\(788\) 377.019 377.019i 0.478451 0.478451i