Properties

Label 810.4.e.u.271.1
Level $810$
Weight $4$
Character 810.271
Analytic conductor $47.792$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 810.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(47.7915471046\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 810.271
Dual form 810.4.e.u.541.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.00000 - 12.1244i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.00000 - 12.1244i) q^{7} -8.00000 q^{8} +10.0000 q^{10} +(-3.00000 - 5.19615i) q^{11} +(-34.0000 + 58.8897i) q^{13} +(14.0000 - 24.2487i) q^{14} +(-8.00000 - 13.8564i) q^{16} +78.0000 q^{17} +44.0000 q^{19} +(10.0000 + 17.3205i) q^{20} +(6.00000 - 10.3923i) q^{22} +(-60.0000 + 103.923i) q^{23} +(-12.5000 - 21.6506i) q^{25} -136.000 q^{26} +56.0000 q^{28} +(-63.0000 - 109.119i) q^{29} +(122.000 - 211.310i) q^{31} +(16.0000 - 27.7128i) q^{32} +(78.0000 + 135.100i) q^{34} -70.0000 q^{35} -304.000 q^{37} +(44.0000 + 76.2102i) q^{38} +(-20.0000 + 34.6410i) q^{40} +(240.000 - 415.692i) q^{41} +(-52.0000 - 90.0666i) q^{43} +24.0000 q^{44} -240.000 q^{46} +(-300.000 - 519.615i) q^{47} +(73.5000 - 127.306i) q^{49} +(25.0000 - 43.3013i) q^{50} +(-136.000 - 235.559i) q^{52} -258.000 q^{53} -30.0000 q^{55} +(56.0000 + 96.9948i) q^{56} +(126.000 - 218.238i) q^{58} +(-267.000 + 462.458i) q^{59} +(-181.000 - 313.501i) q^{61} +488.000 q^{62} +64.0000 q^{64} +(170.000 + 294.449i) q^{65} +(134.000 - 232.095i) q^{67} +(-156.000 + 270.200i) q^{68} +(-70.0000 - 121.244i) q^{70} -972.000 q^{71} +470.000 q^{73} +(-304.000 - 526.543i) q^{74} +(-88.0000 + 152.420i) q^{76} +(-42.0000 + 72.7461i) q^{77} +(-622.000 - 1077.34i) q^{79} -80.0000 q^{80} +960.000 q^{82} +(-198.000 - 342.946i) q^{83} +(195.000 - 337.750i) q^{85} +(104.000 - 180.133i) q^{86} +(24.0000 + 41.5692i) q^{88} -972.000 q^{89} +952.000 q^{91} +(-240.000 - 415.692i) q^{92} +(600.000 - 1039.23i) q^{94} +(110.000 - 190.526i) q^{95} +(23.0000 + 39.8372i) q^{97} +294.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 4 q^{4} + 5 q^{5} - 14 q^{7} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 4 q^{4} + 5 q^{5} - 14 q^{7} - 16 q^{8} + 20 q^{10} - 6 q^{11} - 68 q^{13} + 28 q^{14} - 16 q^{16} + 156 q^{17} + 88 q^{19} + 20 q^{20} + 12 q^{22} - 120 q^{23} - 25 q^{25} - 272 q^{26} + 112 q^{28} - 126 q^{29} + 244 q^{31} + 32 q^{32} + 156 q^{34} - 140 q^{35} - 608 q^{37} + 88 q^{38} - 40 q^{40} + 480 q^{41} - 104 q^{43} + 48 q^{44} - 480 q^{46} - 600 q^{47} + 147 q^{49} + 50 q^{50} - 272 q^{52} - 516 q^{53} - 60 q^{55} + 112 q^{56} + 252 q^{58} - 534 q^{59} - 362 q^{61} + 976 q^{62} + 128 q^{64} + 340 q^{65} + 268 q^{67} - 312 q^{68} - 140 q^{70} - 1944 q^{71} + 940 q^{73} - 608 q^{74} - 176 q^{76} - 84 q^{77} - 1244 q^{79} - 160 q^{80} + 1920 q^{82} - 396 q^{83} + 390 q^{85} + 208 q^{86} + 48 q^{88} - 1944 q^{89} + 1904 q^{91} - 480 q^{92} + 1200 q^{94} + 220 q^{95} + 46 q^{97} + 588 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 0 0
\(7\) −7.00000 12.1244i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 10.0000 0.316228
\(11\) −3.00000 5.19615i −0.0822304 0.142427i 0.821977 0.569520i \(-0.192871\pi\)
−0.904208 + 0.427093i \(0.859538\pi\)
\(12\) 0 0
\(13\) −34.0000 + 58.8897i −0.725377 + 1.25639i 0.233441 + 0.972371i \(0.425001\pi\)
−0.958819 + 0.284019i \(0.908332\pi\)
\(14\) 14.0000 24.2487i 0.267261 0.462910i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 78.0000 1.11281 0.556405 0.830911i \(-0.312180\pi\)
0.556405 + 0.830911i \(0.312180\pi\)
\(18\) 0 0
\(19\) 44.0000 0.531279 0.265639 0.964072i \(-0.414417\pi\)
0.265639 + 0.964072i \(0.414417\pi\)
\(20\) 10.0000 + 17.3205i 0.111803 + 0.193649i
\(21\) 0 0
\(22\) 6.00000 10.3923i 0.0581456 0.100711i
\(23\) −60.0000 + 103.923i −0.543951 + 0.942150i 0.454721 + 0.890634i \(0.349739\pi\)
−0.998672 + 0.0515165i \(0.983595\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −136.000 −1.02584
\(27\) 0 0
\(28\) 56.0000 0.377964
\(29\) −63.0000 109.119i −0.403407 0.698722i 0.590728 0.806871i \(-0.298841\pi\)
−0.994135 + 0.108149i \(0.965507\pi\)
\(30\) 0 0
\(31\) 122.000 211.310i 0.706834 1.22427i −0.259192 0.965826i \(-0.583456\pi\)
0.966026 0.258446i \(-0.0832105\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 78.0000 + 135.100i 0.393438 + 0.681454i
\(35\) −70.0000 −0.338062
\(36\) 0 0
\(37\) −304.000 −1.35074 −0.675369 0.737480i \(-0.736016\pi\)
−0.675369 + 0.737480i \(0.736016\pi\)
\(38\) 44.0000 + 76.2102i 0.187835 + 0.325340i
\(39\) 0 0
\(40\) −20.0000 + 34.6410i −0.0790569 + 0.136931i
\(41\) 240.000 415.692i 0.914188 1.58342i 0.106102 0.994355i \(-0.466163\pi\)
0.808086 0.589065i \(-0.200504\pi\)
\(42\) 0 0
\(43\) −52.0000 90.0666i −0.184417 0.319419i 0.758963 0.651134i \(-0.225706\pi\)
−0.943380 + 0.331714i \(0.892373\pi\)
\(44\) 24.0000 0.0822304
\(45\) 0 0
\(46\) −240.000 −0.769262
\(47\) −300.000 519.615i −0.931053 1.61263i −0.781525 0.623874i \(-0.785558\pi\)
−0.149528 0.988757i \(-0.547775\pi\)
\(48\) 0 0
\(49\) 73.5000 127.306i 0.214286 0.371154i
\(50\) 25.0000 43.3013i 0.0707107 0.122474i
\(51\) 0 0
\(52\) −136.000 235.559i −0.362689 0.628195i
\(53\) −258.000 −0.668661 −0.334330 0.942456i \(-0.608510\pi\)
−0.334330 + 0.942456i \(0.608510\pi\)
\(54\) 0 0
\(55\) −30.0000 −0.0735491
\(56\) 56.0000 + 96.9948i 0.133631 + 0.231455i
\(57\) 0 0
\(58\) 126.000 218.238i 0.285252 0.494071i
\(59\) −267.000 + 462.458i −0.589160 + 1.02046i 0.405183 + 0.914236i \(0.367208\pi\)
−0.994343 + 0.106219i \(0.966125\pi\)
\(60\) 0 0
\(61\) −181.000 313.501i −0.379913 0.658028i 0.611136 0.791525i \(-0.290713\pi\)
−0.991049 + 0.133497i \(0.957379\pi\)
\(62\) 488.000 0.999614
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 170.000 + 294.449i 0.324399 + 0.561875i
\(66\) 0 0
\(67\) 134.000 232.095i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) −156.000 + 270.200i −0.278203 + 0.481861i
\(69\) 0 0
\(70\) −70.0000 121.244i −0.119523 0.207020i
\(71\) −972.000 −1.62472 −0.812360 0.583156i \(-0.801818\pi\)
−0.812360 + 0.583156i \(0.801818\pi\)
\(72\) 0 0
\(73\) 470.000 0.753553 0.376776 0.926304i \(-0.377033\pi\)
0.376776 + 0.926304i \(0.377033\pi\)
\(74\) −304.000 526.543i −0.477558 0.827154i
\(75\) 0 0
\(76\) −88.0000 + 152.420i −0.132820 + 0.230050i
\(77\) −42.0000 + 72.7461i −0.0621603 + 0.107665i
\(78\) 0 0
\(79\) −622.000 1077.34i −0.885829 1.53430i −0.844761 0.535144i \(-0.820257\pi\)
−0.0410678 0.999156i \(-0.513076\pi\)
\(80\) −80.0000 −0.111803
\(81\) 0 0
\(82\) 960.000 1.29286
\(83\) −198.000 342.946i −0.261847 0.453533i 0.704886 0.709321i \(-0.250998\pi\)
−0.966733 + 0.255788i \(0.917665\pi\)
\(84\) 0 0
\(85\) 195.000 337.750i 0.248832 0.430990i
\(86\) 104.000 180.133i 0.130402 0.225864i
\(87\) 0 0
\(88\) 24.0000 + 41.5692i 0.0290728 + 0.0503556i
\(89\) −972.000 −1.15766 −0.578830 0.815448i \(-0.696491\pi\)
−0.578830 + 0.815448i \(0.696491\pi\)
\(90\) 0 0
\(91\) 952.000 1.09667
\(92\) −240.000 415.692i −0.271975 0.471075i
\(93\) 0 0
\(94\) 600.000 1039.23i 0.658354 1.14030i
\(95\) 110.000 190.526i 0.118797 0.205763i
\(96\) 0 0
\(97\) 23.0000 + 39.8372i 0.0240752 + 0.0416995i 0.877812 0.479005i \(-0.159003\pi\)
−0.853737 + 0.520705i \(0.825669\pi\)
\(98\) 294.000 0.303046
\(99\) 0 0
\(100\) 100.000 0.100000
\(101\) 753.000 + 1304.23i 0.741845 + 1.28491i 0.951655 + 0.307170i \(0.0993821\pi\)
−0.209810 + 0.977742i \(0.567285\pi\)
\(102\) 0 0
\(103\) 737.000 1276.52i 0.705037 1.22116i −0.261642 0.965165i \(-0.584264\pi\)
0.966678 0.255994i \(-0.0824028\pi\)
\(104\) 272.000 471.118i 0.256460 0.444201i
\(105\) 0 0
\(106\) −258.000 446.869i −0.236407 0.409469i
\(107\) 924.000 0.834827 0.417413 0.908717i \(-0.362937\pi\)
0.417413 + 0.908717i \(0.362937\pi\)
\(108\) 0 0
\(109\) 698.000 0.613360 0.306680 0.951813i \(-0.400782\pi\)
0.306680 + 0.951813i \(0.400782\pi\)
\(110\) −30.0000 51.9615i −0.0260035 0.0450394i
\(111\) 0 0
\(112\) −112.000 + 193.990i −0.0944911 + 0.163663i
\(113\) 111.000 192.258i 0.0924071 0.160054i −0.816116 0.577888i \(-0.803877\pi\)
0.908523 + 0.417834i \(0.137211\pi\)
\(114\) 0 0
\(115\) 300.000 + 519.615i 0.243262 + 0.421342i
\(116\) 504.000 0.403407
\(117\) 0 0
\(118\) −1068.00 −0.833198
\(119\) −546.000 945.700i −0.420603 0.728505i
\(120\) 0 0
\(121\) 647.500 1121.50i 0.486476 0.842602i
\(122\) 362.000 627.002i 0.268639 0.465296i
\(123\) 0 0
\(124\) 488.000 + 845.241i 0.353417 + 0.612136i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1906.00 −1.33173 −0.665867 0.746071i \(-0.731938\pi\)
−0.665867 + 0.746071i \(0.731938\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −340.000 + 588.897i −0.229384 + 0.397305i
\(131\) −1437.00 + 2488.96i −0.958407 + 1.66001i −0.232034 + 0.972708i \(0.574538\pi\)
−0.726372 + 0.687301i \(0.758795\pi\)
\(132\) 0 0
\(133\) −308.000 533.472i −0.200804 0.347803i
\(134\) 536.000 0.345547
\(135\) 0 0
\(136\) −624.000 −0.393438
\(137\) 399.000 + 691.088i 0.248824 + 0.430976i 0.963200 0.268787i \(-0.0866226\pi\)
−0.714376 + 0.699762i \(0.753289\pi\)
\(138\) 0 0
\(139\) 350.000 606.218i 0.213573 0.369919i −0.739257 0.673423i \(-0.764823\pi\)
0.952830 + 0.303504i \(0.0981566\pi\)
\(140\) 140.000 242.487i 0.0845154 0.146385i
\(141\) 0 0
\(142\) −972.000 1683.55i −0.574426 0.994934i
\(143\) 408.000 0.238592
\(144\) 0 0
\(145\) −630.000 −0.360818
\(146\) 470.000 + 814.064i 0.266421 + 0.461455i
\(147\) 0 0
\(148\) 608.000 1053.09i 0.337684 0.584887i
\(149\) −57.0000 + 98.7269i −0.0313397 + 0.0542820i −0.881270 0.472613i \(-0.843311\pi\)
0.849930 + 0.526895i \(0.176644\pi\)
\(150\) 0 0
\(151\) −532.000 921.451i −0.286712 0.496600i 0.686311 0.727308i \(-0.259229\pi\)
−0.973023 + 0.230708i \(0.925896\pi\)
\(152\) −352.000 −0.187835
\(153\) 0 0
\(154\) −168.000 −0.0879080
\(155\) −610.000 1056.55i −0.316106 0.547511i
\(156\) 0 0
\(157\) 974.000 1687.02i 0.495119 0.857571i −0.504865 0.863198i \(-0.668458\pi\)
0.999984 + 0.00562710i \(0.00179117\pi\)
\(158\) 1244.00 2154.67i 0.626375 1.08491i
\(159\) 0 0
\(160\) −80.0000 138.564i −0.0395285 0.0684653i
\(161\) 1680.00 0.822376
\(162\) 0 0
\(163\) 2060.00 0.989887 0.494944 0.868925i \(-0.335189\pi\)
0.494944 + 0.868925i \(0.335189\pi\)
\(164\) 960.000 + 1662.77i 0.457094 + 0.791710i
\(165\) 0 0
\(166\) 396.000 685.892i 0.185154 0.320696i
\(167\) 624.000 1080.80i 0.289141 0.500807i −0.684464 0.729047i \(-0.739964\pi\)
0.973605 + 0.228240i \(0.0732970\pi\)
\(168\) 0 0
\(169\) −1213.50 2101.84i −0.552344 0.956688i
\(170\) 780.000 0.351902
\(171\) 0 0
\(172\) 416.000 0.184417
\(173\) 573.000 + 992.465i 0.251817 + 0.436160i 0.964026 0.265807i \(-0.0856385\pi\)
−0.712209 + 0.701968i \(0.752305\pi\)
\(174\) 0 0
\(175\) −175.000 + 303.109i −0.0755929 + 0.130931i
\(176\) −48.0000 + 83.1384i −0.0205576 + 0.0356068i
\(177\) 0 0
\(178\) −972.000 1683.55i −0.409295 0.708919i
\(179\) −1146.00 −0.478525 −0.239263 0.970955i \(-0.576906\pi\)
−0.239263 + 0.970955i \(0.576906\pi\)
\(180\) 0 0
\(181\) −118.000 −0.0484579 −0.0242289 0.999706i \(-0.507713\pi\)
−0.0242289 + 0.999706i \(0.507713\pi\)
\(182\) 952.000 + 1648.91i 0.387730 + 0.671569i
\(183\) 0 0
\(184\) 480.000 831.384i 0.192316 0.333100i
\(185\) −760.000 + 1316.36i −0.302034 + 0.523138i
\(186\) 0 0
\(187\) −234.000 405.300i −0.0915068 0.158494i
\(188\) 2400.00 0.931053
\(189\) 0 0
\(190\) 440.000 0.168005
\(191\) −846.000 1465.31i −0.320494 0.555112i 0.660096 0.751181i \(-0.270516\pi\)
−0.980590 + 0.196069i \(0.937182\pi\)
\(192\) 0 0
\(193\) −1675.00 + 2901.19i −0.624711 + 1.08203i 0.363886 + 0.931443i \(0.381450\pi\)
−0.988597 + 0.150587i \(0.951884\pi\)
\(194\) −46.0000 + 79.6743i −0.0170238 + 0.0294860i
\(195\) 0 0
\(196\) 294.000 + 509.223i 0.107143 + 0.185577i
\(197\) −3606.00 −1.30415 −0.652073 0.758156i \(-0.726101\pi\)
−0.652073 + 0.758156i \(0.726101\pi\)
\(198\) 0 0
\(199\) 2696.00 0.960374 0.480187 0.877166i \(-0.340569\pi\)
0.480187 + 0.877166i \(0.340569\pi\)
\(200\) 100.000 + 173.205i 0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) −1506.00 + 2608.47i −0.524563 + 0.908570i
\(203\) −882.000 + 1527.67i −0.304947 + 0.528184i
\(204\) 0 0
\(205\) −1200.00 2078.46i −0.408837 0.708127i
\(206\) 2948.00 0.997072
\(207\) 0 0
\(208\) 1088.00 0.362689
\(209\) −132.000 228.631i −0.0436872 0.0756685i
\(210\) 0 0
\(211\) 2.00000 3.46410i 0.000652539 0.00113023i −0.865699 0.500565i \(-0.833126\pi\)
0.866351 + 0.499435i \(0.166459\pi\)
\(212\) 516.000 893.738i 0.167165 0.289539i
\(213\) 0 0
\(214\) 924.000 + 1600.41i 0.295156 + 0.511225i
\(215\) −520.000 −0.164947
\(216\) 0 0
\(217\) −3416.00 −1.06863
\(218\) 698.000 + 1208.97i 0.216856 + 0.375605i
\(219\) 0 0
\(220\) 60.0000 103.923i 0.0183873 0.0318477i
\(221\) −2652.00 + 4593.40i −0.807207 + 1.39812i
\(222\) 0 0
\(223\) 581.000 + 1006.32i 0.174469 + 0.302190i 0.939977 0.341237i \(-0.110846\pi\)
−0.765508 + 0.643426i \(0.777512\pi\)
\(224\) −448.000 −0.133631
\(225\) 0 0
\(226\) 444.000 0.130683
\(227\) 1200.00 + 2078.46i 0.350867 + 0.607719i 0.986402 0.164353i \(-0.0525536\pi\)
−0.635535 + 0.772072i \(0.719220\pi\)
\(228\) 0 0
\(229\) 1157.00 2003.98i 0.333872 0.578283i −0.649395 0.760451i \(-0.724978\pi\)
0.983268 + 0.182167i \(0.0583113\pi\)
\(230\) −600.000 + 1039.23i −0.172012 + 0.297934i
\(231\) 0 0
\(232\) 504.000 + 872.954i 0.142626 + 0.247035i
\(233\) −18.0000 −0.00506103 −0.00253051 0.999997i \(-0.500805\pi\)
−0.00253051 + 0.999997i \(0.500805\pi\)
\(234\) 0 0
\(235\) −3000.00 −0.832759
\(236\) −1068.00 1849.83i −0.294580 0.510228i
\(237\) 0 0
\(238\) 1092.00 1891.40i 0.297411 0.515131i
\(239\) 2934.00 5081.84i 0.794078 1.37538i −0.129345 0.991600i \(-0.541287\pi\)
0.923423 0.383784i \(-0.125379\pi\)
\(240\) 0 0
\(241\) 2165.00 + 3749.89i 0.578672 + 1.00229i 0.995632 + 0.0933643i \(0.0297621\pi\)
−0.416960 + 0.908925i \(0.636905\pi\)
\(242\) 2590.00 0.687981
\(243\) 0 0
\(244\) 1448.00 0.379913
\(245\) −367.500 636.529i −0.0958315 0.165985i
\(246\) 0 0
\(247\) −1496.00 + 2591.15i −0.385377 + 0.667493i
\(248\) −976.000 + 1690.48i −0.249903 + 0.432846i
\(249\) 0 0
\(250\) −125.000 216.506i −0.0316228 0.0547723i
\(251\) 498.000 0.125233 0.0626165 0.998038i \(-0.480056\pi\)
0.0626165 + 0.998038i \(0.480056\pi\)
\(252\) 0 0
\(253\) 720.000 0.178917
\(254\) −1906.00 3301.29i −0.470839 0.815517i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −321.000 + 555.988i −0.0779122 + 0.134948i −0.902349 0.431006i \(-0.858159\pi\)
0.824437 + 0.565954i \(0.191492\pi\)
\(258\) 0 0
\(259\) 2128.00 + 3685.80i 0.510531 + 0.884265i
\(260\) −1360.00 −0.324399
\(261\) 0 0
\(262\) −5748.00 −1.35539
\(263\) 3984.00 + 6900.49i 0.934084 + 1.61788i 0.776260 + 0.630413i \(0.217114\pi\)
0.157823 + 0.987467i \(0.449552\pi\)
\(264\) 0 0
\(265\) −645.000 + 1117.17i −0.149517 + 0.258971i
\(266\) 616.000 1066.94i 0.141990 0.245934i
\(267\) 0 0
\(268\) 536.000 + 928.379i 0.122169 + 0.211604i
\(269\) −4218.00 −0.956045 −0.478022 0.878348i \(-0.658646\pi\)
−0.478022 + 0.878348i \(0.658646\pi\)
\(270\) 0 0
\(271\) 848.000 0.190082 0.0950412 0.995473i \(-0.469702\pi\)
0.0950412 + 0.995473i \(0.469702\pi\)
\(272\) −624.000 1080.80i −0.139101 0.240931i
\(273\) 0 0
\(274\) −798.000 + 1382.18i −0.175945 + 0.304746i
\(275\) −75.0000 + 129.904i −0.0164461 + 0.0284854i
\(276\) 0 0
\(277\) 752.000 + 1302.50i 0.163117 + 0.282526i 0.935985 0.352040i \(-0.114512\pi\)
−0.772868 + 0.634567i \(0.781179\pi\)
\(278\) 1400.00 0.302037
\(279\) 0 0
\(280\) 560.000 0.119523
\(281\) 654.000 + 1132.76i 0.138841 + 0.240480i 0.927058 0.374917i \(-0.122329\pi\)
−0.788217 + 0.615397i \(0.788996\pi\)
\(282\) 0 0
\(283\) 2966.00 5137.26i 0.623005 1.07908i −0.365918 0.930647i \(-0.619245\pi\)
0.988923 0.148429i \(-0.0474217\pi\)
\(284\) 1944.00 3367.11i 0.406180 0.703525i
\(285\) 0 0
\(286\) 408.000 + 706.677i 0.0843551 + 0.146107i
\(287\) −6720.00 −1.38212
\(288\) 0 0
\(289\) 1171.00 0.238347
\(290\) −630.000 1091.19i −0.127569 0.220955i
\(291\) 0 0
\(292\) −940.000 + 1628.13i −0.188388 + 0.326298i
\(293\) −2613.00 + 4525.85i −0.521000 + 0.902399i 0.478701 + 0.877978i \(0.341108\pi\)
−0.999702 + 0.0244213i \(0.992226\pi\)
\(294\) 0 0
\(295\) 1335.00 + 2312.29i 0.263480 + 0.456361i
\(296\) 2432.00 0.477558
\(297\) 0 0
\(298\) −228.000 −0.0443211
\(299\) −4080.00 7066.77i −0.789139 1.36683i
\(300\) 0 0
\(301\) −728.000 + 1260.93i −0.139406 + 0.241458i
\(302\) 1064.00 1842.90i 0.202736 0.351149i
\(303\) 0 0
\(304\) −352.000 609.682i −0.0664098 0.115025i
\(305\) −1810.00 −0.339804
\(306\) 0 0
\(307\) 4448.00 0.826908 0.413454 0.910525i \(-0.364322\pi\)
0.413454 + 0.910525i \(0.364322\pi\)
\(308\) −168.000 290.985i −0.0310802 0.0538324i
\(309\) 0 0
\(310\) 1220.00 2113.10i 0.223520 0.387149i
\(311\) 4566.00 7908.54i 0.832521 1.44197i −0.0635115 0.997981i \(-0.520230\pi\)
0.896033 0.443988i \(-0.146437\pi\)
\(312\) 0 0
\(313\) 1085.00 + 1879.28i 0.195936 + 0.339370i 0.947207 0.320623i \(-0.103892\pi\)
−0.751271 + 0.659994i \(0.770559\pi\)
\(314\) 3896.00 0.700204
\(315\) 0 0
\(316\) 4976.00 0.885829
\(317\) −3837.00 6645.88i −0.679834 1.17751i −0.975031 0.222071i \(-0.928718\pi\)
0.295197 0.955437i \(-0.404615\pi\)
\(318\) 0 0
\(319\) −378.000 + 654.715i −0.0663446 + 0.114912i
\(320\) 160.000 277.128i 0.0279508 0.0484123i
\(321\) 0 0
\(322\) 1680.00 + 2909.85i 0.290754 + 0.503600i
\(323\) 3432.00 0.591212
\(324\) 0 0
\(325\) 1700.00 0.290151
\(326\) 2060.00 + 3568.02i 0.349978 + 0.606180i
\(327\) 0 0
\(328\) −1920.00 + 3325.54i −0.323214 + 0.559823i
\(329\) −4200.00 + 7274.61i −0.703810 + 1.21903i
\(330\) 0 0
\(331\) −4798.00 8310.38i −0.796743 1.38000i −0.921726 0.387841i \(-0.873221\pi\)
0.124983 0.992159i \(-0.460112\pi\)
\(332\) 1584.00 0.261847
\(333\) 0 0
\(334\) 2496.00 0.408907
\(335\) −670.000 1160.47i −0.109272 0.189264i
\(336\) 0 0
\(337\) −6079.00 + 10529.1i −0.982624 + 1.70195i −0.330570 + 0.943781i \(0.607241\pi\)
−0.652053 + 0.758173i \(0.726092\pi\)
\(338\) 2427.00 4203.69i 0.390566 0.676481i
\(339\) 0 0
\(340\) 780.000 + 1351.00i 0.124416 + 0.215495i
\(341\) −1464.00 −0.232493
\(342\) 0 0
\(343\) −6860.00 −1.07990
\(344\) 416.000 + 720.533i 0.0652012 + 0.112932i
\(345\) 0 0
\(346\) −1146.00 + 1984.93i −0.178062 + 0.308412i
\(347\) −5160.00 + 8937.38i −0.798280 + 1.38266i 0.122455 + 0.992474i \(0.460923\pi\)
−0.920735 + 0.390188i \(0.872410\pi\)
\(348\) 0 0
\(349\) 1079.00 + 1868.88i 0.165494 + 0.286645i 0.936831 0.349783i \(-0.113745\pi\)
−0.771336 + 0.636428i \(0.780411\pi\)
\(350\) −700.000 −0.106904
\(351\) 0 0
\(352\) −192.000 −0.0290728
\(353\) 165.000 + 285.788i 0.0248784 + 0.0430906i 0.878197 0.478300i \(-0.158747\pi\)
−0.853318 + 0.521391i \(0.825413\pi\)
\(354\) 0 0
\(355\) −2430.00 + 4208.88i −0.363299 + 0.629252i
\(356\) 1944.00 3367.11i 0.289415 0.501282i
\(357\) 0 0
\(358\) −1146.00 1984.93i −0.169184 0.293036i
\(359\) −8664.00 −1.27373 −0.636864 0.770976i \(-0.719769\pi\)
−0.636864 + 0.770976i \(0.719769\pi\)
\(360\) 0 0
\(361\) −4923.00 −0.717743
\(362\) −118.000 204.382i −0.0171324 0.0296743i
\(363\) 0 0
\(364\) −1904.00 + 3297.82i −0.274167 + 0.474871i
\(365\) 1175.00 2035.16i 0.168499 0.291850i
\(366\) 0 0
\(367\) −1891.00 3275.31i −0.268963 0.465857i 0.699631 0.714504i \(-0.253348\pi\)
−0.968594 + 0.248647i \(0.920014\pi\)
\(368\) 1920.00 0.271975
\(369\) 0 0
\(370\) −3040.00 −0.427141
\(371\) 1806.00 + 3128.08i 0.252730 + 0.437741i
\(372\) 0 0
\(373\) −5638.00 + 9765.30i −0.782640 + 1.35557i 0.147759 + 0.989023i \(0.452794\pi\)
−0.930399 + 0.366548i \(0.880539\pi\)
\(374\) 468.000 810.600i 0.0647051 0.112073i
\(375\) 0 0
\(376\) 2400.00 + 4156.92i 0.329177 + 0.570151i
\(377\) 8568.00 1.17049
\(378\) 0 0
\(379\) 980.000 0.132821 0.0664106 0.997792i \(-0.478845\pi\)
0.0664106 + 0.997792i \(0.478845\pi\)
\(380\) 440.000 + 762.102i 0.0593987 + 0.102882i
\(381\) 0 0
\(382\) 1692.00 2930.63i 0.226624 0.392524i
\(383\) 2100.00 3637.31i 0.280170 0.485268i −0.691257 0.722609i \(-0.742943\pi\)
0.971426 + 0.237341i \(0.0762759\pi\)
\(384\) 0 0
\(385\) 210.000 + 363.731i 0.0277989 + 0.0481492i
\(386\) −6700.00 −0.883474
\(387\) 0 0
\(388\) −184.000 −0.0240752
\(389\) −6669.00 11551.0i −0.869233 1.50556i −0.862782 0.505577i \(-0.831280\pi\)
−0.00645168 0.999979i \(-0.502054\pi\)
\(390\) 0 0
\(391\) −4680.00 + 8106.00i −0.605314 + 1.04843i
\(392\) −588.000 + 1018.45i −0.0757614 + 0.131223i
\(393\) 0 0
\(394\) −3606.00 6245.78i −0.461085 0.798623i
\(395\) −6220.00 −0.792309
\(396\) 0 0
\(397\) −7192.00 −0.909209 −0.454605 0.890693i \(-0.650219\pi\)
−0.454605 + 0.890693i \(0.650219\pi\)
\(398\) 2696.00 + 4669.61i 0.339543 + 0.588106i
\(399\) 0 0
\(400\) −200.000 + 346.410i −0.0250000 + 0.0433013i
\(401\) 1158.00 2005.71i 0.144209 0.249777i −0.784869 0.619662i \(-0.787270\pi\)
0.929078 + 0.369885i \(0.120603\pi\)
\(402\) 0 0
\(403\) 8296.00 + 14369.1i 1.02544 + 1.77612i
\(404\) −6024.00 −0.741845
\(405\) 0 0
\(406\) −3528.00 −0.431260
\(407\) 912.000 + 1579.63i 0.111072 + 0.192382i
\(408\) 0 0
\(409\) 6179.00 10702.3i 0.747022 1.29388i −0.202222 0.979340i \(-0.564816\pi\)
0.949244 0.314540i \(-0.101850\pi\)
\(410\) 2400.00 4156.92i 0.289092 0.500721i
\(411\) 0 0
\(412\) 2948.00 + 5106.09i 0.352518 + 0.610580i
\(413\) 7476.00 0.890726
\(414\) 0 0
\(415\) −1980.00 −0.234203
\(416\) 1088.00 + 1884.47i 0.128230 + 0.222100i
\(417\) 0 0
\(418\) 264.000 457.261i 0.0308915 0.0535057i
\(419\) −1653.00 + 2863.08i −0.192731 + 0.333820i −0.946154 0.323716i \(-0.895068\pi\)
0.753423 + 0.657536i \(0.228401\pi\)
\(420\) 0 0
\(421\) 7253.00 + 12562.6i 0.839643 + 1.45430i 0.890194 + 0.455582i \(0.150569\pi\)
−0.0505509 + 0.998721i \(0.516098\pi\)
\(422\) 8.00000 0.000922829
\(423\) 0 0
\(424\) 2064.00 0.236407
\(425\) −975.000 1688.75i −0.111281 0.192744i
\(426\) 0 0
\(427\) −2534.00 + 4389.02i −0.287187 + 0.497422i
\(428\) −1848.00 + 3200.83i −0.208707 + 0.361491i
\(429\) 0 0
\(430\) −520.000 900.666i −0.0583177 0.101009i
\(431\) −6480.00 −0.724201 −0.362100 0.932139i \(-0.617940\pi\)
−0.362100 + 0.932139i \(0.617940\pi\)
\(432\) 0 0
\(433\) 11894.0 1.32007 0.660034 0.751236i \(-0.270542\pi\)
0.660034 + 0.751236i \(0.270542\pi\)
\(434\) −3416.00 5916.69i −0.377819 0.654401i
\(435\) 0 0
\(436\) −1396.00 + 2417.94i −0.153340 + 0.265593i
\(437\) −2640.00 + 4572.61i −0.288989 + 0.500544i
\(438\) 0 0
\(439\) 6344.00 + 10988.1i 0.689710 + 1.19461i 0.971932 + 0.235263i \(0.0755952\pi\)
−0.282222 + 0.959349i \(0.591071\pi\)
\(440\) 240.000 0.0260035
\(441\) 0 0
\(442\) −10608.0 −1.14156
\(443\) −2484.00 4302.41i −0.266407 0.461431i 0.701524 0.712646i \(-0.252503\pi\)
−0.967931 + 0.251215i \(0.919170\pi\)
\(444\) 0 0
\(445\) −2430.00 + 4208.88i −0.258861 + 0.448360i
\(446\) −1162.00 + 2012.64i −0.123368 + 0.213680i
\(447\) 0 0
\(448\) −448.000 775.959i −0.0472456 0.0818317i
\(449\) −11508.0 −1.20957 −0.604784 0.796389i \(-0.706741\pi\)
−0.604784 + 0.796389i \(0.706741\pi\)
\(450\) 0 0
\(451\) −2880.00 −0.300696
\(452\) 444.000 + 769.031i 0.0462035 + 0.0800269i
\(453\) 0 0
\(454\) −2400.00 + 4156.92i −0.248100 + 0.429722i
\(455\) 2380.00 4122.28i 0.245222 0.424737i
\(456\) 0 0
\(457\) −541.000 937.039i −0.0553762 0.0959144i 0.837008 0.547190i \(-0.184302\pi\)
−0.892385 + 0.451276i \(0.850969\pi\)
\(458\) 4628.00 0.472166
\(459\) 0 0
\(460\) −2400.00 −0.243262
\(461\) 5619.00 + 9732.39i 0.567685 + 0.983260i 0.996794 + 0.0800071i \(0.0254943\pi\)
−0.429109 + 0.903253i \(0.641172\pi\)
\(462\) 0 0
\(463\) 1151.00 1993.59i 0.115532 0.200108i −0.802460 0.596706i \(-0.796476\pi\)
0.917992 + 0.396598i \(0.129809\pi\)
\(464\) −1008.00 + 1745.91i −0.100852 + 0.174680i
\(465\) 0 0
\(466\) −18.0000 31.1769i −0.00178934 0.00309923i
\(467\) 15876.0 1.57313 0.786567 0.617505i \(-0.211856\pi\)
0.786567 + 0.617505i \(0.211856\pi\)
\(468\) 0 0
\(469\) −3752.00 −0.369406
\(470\) −3000.00 5196.15i −0.294425 0.509959i
\(471\) 0 0
\(472\) 2136.00 3699.66i 0.208300 0.360785i
\(473\) −312.000 + 540.400i −0.0303293 + 0.0525319i
\(474\) 0 0
\(475\) −550.000 952.628i −0.0531279 0.0920201i
\(476\) 4368.00 0.420603
\(477\) 0 0
\(478\) 11736.0 1.12300
\(479\) −2322.00 4021.82i −0.221492 0.383636i 0.733769 0.679399i \(-0.237759\pi\)
−0.955261 + 0.295763i \(0.904426\pi\)
\(480\) 0 0
\(481\) 10336.0 17902.5i 0.979794 1.69705i
\(482\) −4330.00 + 7499.78i −0.409183 + 0.708725i
\(483\) 0 0
\(484\) 2590.00 + 4486.01i 0.243238 + 0.421301i
\(485\) 230.000 0.0215335
\(486\) 0 0
\(487\) 2426.00 0.225734 0.112867 0.993610i \(-0.463997\pi\)
0.112867 + 0.993610i \(0.463997\pi\)
\(488\) 1448.00 + 2508.01i 0.134319 + 0.232648i
\(489\) 0 0
\(490\) 735.000 1273.06i 0.0677631 0.117369i
\(491\) −117.000 + 202.650i −0.0107538 + 0.0186262i −0.871352 0.490658i \(-0.836756\pi\)
0.860598 + 0.509284i \(0.170090\pi\)
\(492\) 0 0
\(493\) −4914.00 8511.30i −0.448916 0.777545i
\(494\) −5984.00 −0.545006
\(495\) 0 0
\(496\) −3904.00 −0.353417
\(497\) 6804.00 + 11784.9i 0.614087 + 1.06363i
\(498\) 0 0
\(499\) −7102.00 + 12301.0i −0.637133 + 1.10355i 0.348926 + 0.937150i \(0.386546\pi\)
−0.986059 + 0.166396i \(0.946787\pi\)
\(500\) 250.000 433.013i 0.0223607 0.0387298i
\(501\) 0 0
\(502\) 498.000 + 862.561i 0.0442765 + 0.0766892i
\(503\) 4920.00 0.436127 0.218064 0.975935i \(-0.430026\pi\)
0.218064 + 0.975935i \(0.430026\pi\)
\(504\) 0 0
\(505\) 7530.00 0.663526
\(506\) 720.000 + 1247.08i 0.0632567 + 0.109564i
\(507\) 0 0
\(508\) 3812.00 6602.58i 0.332933 0.576658i
\(509\) 2229.00 3860.74i 0.194104 0.336197i −0.752503 0.658589i \(-0.771154\pi\)
0.946606 + 0.322392i \(0.104487\pi\)
\(510\) 0 0
\(511\) −3290.00 5698.45i −0.284816 0.493316i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −1284.00 −0.110184
\(515\) −3685.00 6382.61i −0.315302 0.546119i
\(516\) 0 0
\(517\) −1800.00 + 3117.69i −0.153122 + 0.265215i
\(518\) −4256.00 + 7371.61i −0.361000 + 0.625270i
\(519\) 0 0
\(520\) −1360.00 2355.59i −0.114692 0.198653i
\(521\) 4212.00 0.354186 0.177093 0.984194i \(-0.443331\pi\)
0.177093 + 0.984194i \(0.443331\pi\)
\(522\) 0 0
\(523\) −11212.0 −0.937412 −0.468706 0.883354i \(-0.655280\pi\)
−0.468706 + 0.883354i \(0.655280\pi\)
\(524\) −5748.00 9955.83i −0.479203 0.830005i
\(525\) 0 0
\(526\) −7968.00 + 13801.0i −0.660497 + 1.14401i
\(527\) 9516.00 16482.2i 0.786572 1.36238i
\(528\) 0 0
\(529\) −1116.50 1933.83i −0.0917646 0.158941i
\(530\) −2580.00 −0.211449
\(531\) 0 0
\(532\) 2464.00 0.200804
\(533\) 16320.0 + 28267.1i 1.32626 + 2.29715i
\(534\) 0 0
\(535\) 2310.00 4001.04i 0.186673 0.323327i
\(536\) −1072.00 + 1856.76i −0.0863868 + 0.149626i
\(537\) 0 0
\(538\) −4218.00 7305.79i −0.338013 0.585455i
\(539\) −882.000 −0.0704832
\(540\) 0 0
\(541\) 14018.0 1.11401 0.557006 0.830508i \(-0.311950\pi\)
0.557006 + 0.830508i \(0.311950\pi\)
\(542\) 848.000 + 1468.78i 0.0672043 + 0.116401i
\(543\) 0 0
\(544\) 1248.00 2161.60i 0.0983595 0.170364i
\(545\) 1745.00 3022.43i 0.137152 0.237553i
\(546\) 0 0
\(547\) −9100.00 15761.7i −0.711312 1.23203i −0.964365 0.264577i \(-0.914768\pi\)
0.253052 0.967453i \(-0.418566\pi\)
\(548\) −3192.00 −0.248824
\(549\) 0 0
\(550\) −300.000 −0.0232583
\(551\) −2772.00 4801.24i −0.214322 0.371216i
\(552\) 0 0
\(553\) −8708.00 + 15082.7i −0.669624 + 1.15982i
\(554\) −1504.00 + 2605.00i −0.115341 + 0.199776i
\(555\) 0 0
\(556\) 1400.00 + 2424.87i 0.106786 + 0.184959i
\(557\) −11826.0 −0.899612 −0.449806 0.893126i \(-0.648507\pi\)
−0.449806 + 0.893126i \(0.648507\pi\)
\(558\) 0 0
\(559\) 7072.00 0.535087
\(560\) 560.000 + 969.948i 0.0422577 + 0.0731925i
\(561\) 0 0
\(562\) −1308.00 + 2265.52i −0.0981755 + 0.170045i
\(563\) 1476.00 2556.51i 0.110490 0.191375i −0.805478 0.592626i \(-0.798091\pi\)
0.915968 + 0.401251i \(0.131425\pi\)
\(564\) 0 0
\(565\) −555.000 961.288i −0.0413257 0.0715782i
\(566\) 11864.0 0.881062
\(567\) 0 0
\(568\) 7776.00 0.574426
\(569\) −1542.00 2670.82i −0.113610 0.196778i 0.803613 0.595152i \(-0.202908\pi\)
−0.917223 + 0.398374i \(0.869575\pi\)
\(570\) 0 0
\(571\) 2378.00 4118.82i 0.174284 0.301869i −0.765629 0.643282i \(-0.777572\pi\)
0.939913 + 0.341413i \(0.110906\pi\)
\(572\) −816.000 + 1413.35i −0.0596480 + 0.103313i
\(573\) 0 0
\(574\) −6720.00 11639.4i −0.488654 0.846374i
\(575\) 3000.00 0.217580
\(576\) 0 0
\(577\) −11014.0 −0.794660 −0.397330 0.917676i \(-0.630063\pi\)
−0.397330 + 0.917676i \(0.630063\pi\)
\(578\) 1171.00 + 2028.23i 0.0842685 + 0.145957i
\(579\) 0 0
\(580\) 1260.00 2182.38i 0.0902046 0.156239i
\(581\) −2772.00 + 4801.24i −0.197938 + 0.342839i
\(582\) 0 0
\(583\) 774.000 + 1340.61i 0.0549842 + 0.0952355i
\(584\) −3760.00 −0.266421
\(585\) 0 0
\(586\) −10452.0 −0.736806
\(587\) 426.000 + 737.854i 0.0299538 + 0.0518816i 0.880614 0.473835i \(-0.157131\pi\)
−0.850660 + 0.525716i \(0.823797\pi\)
\(588\) 0 0
\(589\) 5368.00 9297.65i 0.375526 0.650429i
\(590\) −2670.00 + 4624.58i −0.186309 + 0.322696i
\(591\) 0 0
\(592\) 2432.00 + 4212.35i 0.168842 + 0.292443i
\(593\) 15546.0 1.07656 0.538278 0.842767i \(-0.319075\pi\)
0.538278 + 0.842767i \(0.319075\pi\)
\(594\) 0 0
\(595\) −5460.00 −0.376199
\(596\) −228.000 394.908i −0.0156699 0.0271410i
\(597\) 0 0
\(598\) 8160.00 14133.5i 0.558005 0.966494i
\(599\) 4308.00 7461.67i 0.293857 0.508975i −0.680862 0.732412i \(-0.738395\pi\)
0.974718 + 0.223437i \(0.0717278\pi\)
\(600\) 0 0
\(601\) −8755.00 15164.1i −0.594216 1.02921i −0.993657 0.112454i \(-0.964129\pi\)
0.399441 0.916759i \(-0.369204\pi\)
\(602\) −2912.00 −0.197150
\(603\) 0 0
\(604\) 4256.00 0.286712
\(605\) −3237.50 5607.51i −0.217559 0.376823i
\(606\) 0 0
\(607\) 6947.00 12032.6i 0.464531 0.804590i −0.534650 0.845074i \(-0.679556\pi\)
0.999180 + 0.0404833i \(0.0128898\pi\)
\(608\) 704.000 1219.36i 0.0469588 0.0813351i
\(609\) 0 0
\(610\) −1810.00 3135.01i −0.120139 0.208087i
\(611\) 40800.0 2.70146
\(612\) 0 0
\(613\) −6496.00 −0.428011 −0.214006 0.976832i \(-0.568651\pi\)
−0.214006 + 0.976832i \(0.568651\pi\)
\(614\) 4448.00 + 7704.16i 0.292356 + 0.506376i
\(615\) 0 0
\(616\) 336.000 581.969i 0.0219770 0.0380653i
\(617\) 285.000 493.634i 0.0185959 0.0322090i −0.856578 0.516018i \(-0.827414\pi\)
0.875174 + 0.483809i \(0.160747\pi\)
\(618\) 0 0
\(619\) 1070.00 + 1853.29i 0.0694781 + 0.120340i 0.898672 0.438622i \(-0.144533\pi\)
−0.829194 + 0.558962i \(0.811200\pi\)
\(620\) 4880.00 0.316106
\(621\) 0 0
\(622\) 18264.0 1.17736
\(623\) 6804.00 + 11784.9i 0.437555 + 0.757867i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −2170.00 + 3758.55i −0.138547 + 0.239971i
\(627\) 0 0
\(628\) 3896.00 + 6748.07i 0.247559 + 0.428786i
\(629\) −23712.0 −1.50312
\(630\) 0 0
\(631\) 14660.0 0.924890 0.462445 0.886648i \(-0.346972\pi\)
0.462445 + 0.886648i \(0.346972\pi\)
\(632\) 4976.00 + 8618.68i 0.313188 + 0.542457i
\(633\) 0 0
\(634\) 7674.00 13291.8i 0.480715 0.832623i
\(635\) −4765.00 + 8253.22i −0.297785 + 0.515778i
\(636\) 0 0
\(637\) 4998.00 + 8656.79i 0.310876 + 0.538453i
\(638\) −1512.00 −0.0938255
\(639\) 0 0
\(640\) 640.000 0.0395285
\(641\) 228.000 + 394.908i 0.0140491 + 0.0243337i 0.872964 0.487784i \(-0.162195\pi\)
−0.858915 + 0.512118i \(0.828861\pi\)
\(642\) 0 0
\(643\) 11726.0 20310.0i 0.719173 1.24564i −0.242155 0.970238i \(-0.577854\pi\)
0.961328 0.275407i \(-0.0888125\pi\)
\(644\) −3360.00 + 5819.69i −0.205594 + 0.356099i
\(645\) 0 0
\(646\) 3432.00 + 5944.40i 0.209025 + 0.362042i
\(647\) 7224.00 0.438956 0.219478 0.975617i \(-0.429565\pi\)
0.219478 + 0.975617i \(0.429565\pi\)
\(648\) 0 0
\(649\) 3204.00 0.193787
\(650\) 1700.00 + 2944.49i 0.102584 + 0.177680i
\(651\) 0 0
\(652\) −4120.00 + 7136.05i −0.247472 + 0.428634i
\(653\) −9573.00 + 16580.9i −0.573691 + 0.993663i 0.422491 + 0.906367i \(0.361156\pi\)
−0.996182 + 0.0872955i \(0.972178\pi\)
\(654\) 0 0
\(655\) 7185.00 + 12444.8i 0.428612 + 0.742379i
\(656\) −7680.00 −0.457094
\(657\) 0 0
\(658\) −16800.0 −0.995338
\(659\) −13905.0 24084.2i −0.821945 1.42365i −0.904232 0.427042i \(-0.859556\pi\)
0.0822865 0.996609i \(-0.473778\pi\)
\(660\) 0 0
\(661\) 15299.0 26498.6i 0.900245 1.55927i 0.0730698 0.997327i \(-0.476720\pi\)
0.827175 0.561944i \(-0.189946\pi\)
\(662\) 9596.00 16620.8i 0.563382 0.975807i
\(663\) 0 0
\(664\) 1584.00 + 2743.57i 0.0925770 + 0.160348i
\(665\) −3080.00 −0.179605
\(666\) 0 0
\(667\) 15120.0 0.877734
\(668\) 2496.00 + 4323.20i 0.144571 + 0.250404i
\(669\) 0 0
\(670\) 1340.00 2320.95i 0.0772667 0.133830i
\(671\) −1086.00 + 1881.01i −0.0624807 + 0.108220i
\(672\) 0 0
\(673\) 1889.00 + 3271.84i 0.108196 + 0.187400i 0.915039 0.403365i \(-0.132159\pi\)
−0.806844 + 0.590765i \(0.798826\pi\)
\(674\) −24316.0 −1.38964
\(675\) 0 0
\(676\) 9708.00 0.552344
\(677\) 13599.0 + 23554.2i 0.772012 + 1.33716i 0.936459 + 0.350778i \(0.114083\pi\)
−0.164447 + 0.986386i \(0.552584\pi\)
\(678\) 0 0
\(679\) 322.000 557.720i 0.0181992 0.0315219i
\(680\) −1560.00 + 2702.00i −0.0879754 + 0.152378i
\(681\) 0 0
\(682\) −1464.00 2535.72i −0.0821986 0.142372i
\(683\) 32316.0 1.81045 0.905225 0.424933i \(-0.139702\pi\)
0.905225 + 0.424933i \(0.139702\pi\)
\(684\) 0 0
\(685\) 3990.00 0.222555
\(686\) −6860.00 11881.9i −0.381802 0.661300i
\(687\) 0 0
\(688\) −832.000 + 1441.07i −0.0461042 + 0.0798548i
\(689\) 8772.00 15193.5i 0.485031 0.840099i
\(690\) 0 0
\(691\) −14662.0 25395.3i −0.807191 1.39810i −0.914802 0.403902i \(-0.867654\pi\)
0.107611 0.994193i \(-0.465680\pi\)
\(692\) −4584.00 −0.251817
\(693\) 0 0
\(694\) −20640.0 −1.12894
\(695\) −1750.00 3031.09i −0.0955126 0.165433i
\(696\) 0 0
\(697\) 18720.0 32424.0i 1.01732 1.76205i
\(698\) −2158.00 + 3737.77i −0.117022 + 0.202688i
\(699\) 0 0
\(700\) −700.000 1212.44i −0.0377964 0.0654654i
\(701\) 22782.0 1.22748 0.613741 0.789508i \(-0.289664\pi\)
0.613741 + 0.789508i \(0.289664\pi\)
\(702\) 0 0
\(703\) −13376.0 −0.717618
\(704\) −192.000 332.554i −0.0102788 0.0178034i
\(705\) 0 0
\(706\) −330.000 + 571.577i −0.0175917 + 0.0304697i
\(707\) 10542.0 18259.3i 0.560782 0.971303i
\(708\) 0 0
\(709\) −13027.0 22563.4i −0.690041 1.19519i −0.971824 0.235708i \(-0.924259\pi\)
0.281783 0.959478i \(-0.409074\pi\)
\(710\) −9720.00 −0.513782
\(711\) 0 0
\(712\) 7776.00 0.409295
\(713\) 14640.0 + 25357.2i 0.768965 + 1.33189i
\(714\) 0 0
\(715\) 1020.00 1766.69i 0.0533508 0.0924063i
\(716\) 2292.00 3969.86i 0.119631 0.207208i
\(717\) 0 0
\(718\) −8664.00 15006.5i −0.450331 0.779996i
\(719\) −5976.00 −0.309968 −0.154984 0.987917i \(-0.549533\pi\)
−0.154984 + 0.987917i \(0.549533\pi\)
\(720\) 0 0
\(721\) −20636.0 −1.06592
\(722\) −4923.00 8526.89i −0.253761 0.439526i
\(723\) 0 0
\(724\) 236.000 408.764i 0.0121145 0.0209829i
\(725\) −1575.00 + 2727.98i −0.0806814 + 0.139744i
\(726\) 0 0
\(727\) 2555.00 + 4425.39i 0.130343 + 0.225762i 0.923809 0.382854i \(-0.125059\pi\)
−0.793466 + 0.608615i \(0.791725\pi\)
\(728\) −7616.00 −0.387730
\(729\) 0 0
\(730\) 4700.00 0.238294
\(731\) −4056.00 7025.20i −0.205221 0.355453i
\(732\) 0 0
\(733\) −8668.00 + 15013.4i −0.436780 + 0.756525i −0.997439 0.0715214i \(-0.977215\pi\)
0.560659 + 0.828047i \(0.310548\pi\)
\(734\) 3782.00 6550.62i 0.190186 0.329411i
\(735\) 0 0
\(736\) 1920.00 + 3325.54i 0.0961578 + 0.166550i
\(737\) −1608.00 −0.0803683
\(738\) 0 0
\(739\) −13660.0 −0.679961 −0.339981 0.940432i \(-0.610420\pi\)
−0.339981 + 0.940432i \(0.610420\pi\)
\(740\) −3040.00 5265.43i −0.151017 0.261569i
\(741\) 0 0
\(742\) −3612.00 + 6256.17i −0.178707 + 0.309530i
\(743\) −660.000 + 1143.15i −0.0325882 + 0.0564445i −0.881860 0.471512i \(-0.843708\pi\)
0.849271 + 0.527957i \(0.177042\pi\)
\(744\) 0 0
\(745\) 285.000 + 493.634i 0.0140156 + 0.0242757i
\(746\) −22552.0 −1.10682
\(747\) 0 0
\(748\) 1872.00 0.0915068
\(749\) −6468.00 11202.9i −0.315535 0.546522i
\(750\) 0 0
\(751\) −7930.00 + 13735.2i −0.385313 + 0.667381i −0.991813 0.127702i \(-0.959240\pi\)
0.606500 + 0.795084i \(0.292573\pi\)
\(752\) −4800.00 + 8313.84i −0.232763 + 0.403158i
\(753\) 0 0
\(754\) 8568.00 + 14840.2i 0.413830 + 0.716775i
\(755\) −5320.00 −0.256443
\(756\) 0 0
\(757\) 22160.0 1.06396 0.531981 0.846756i \(-0.321448\pi\)
0.531981 + 0.846756i \(0.321448\pi\)
\(758\) 980.000 + 1697.41i 0.0469594 + 0.0813360i
\(759\) 0 0
\(760\) −880.000 + 1524.20i −0.0420013 + 0.0727483i
\(761\) −6558.00 + 11358.8i −0.312388 + 0.541072i −0.978879 0.204441i \(-0.934462\pi\)
0.666491 + 0.745513i \(0.267796\pi\)
\(762\) 0 0
\(763\) −4886.00 8462.80i −0.231828 0.401539i
\(764\) 6768.00 0.320494
\(765\) 0 0
\(766\) 8400.00 0.396220
\(767\) −18156.0 31447.1i −0.854726 1.48043i
\(768\) 0 0
\(769\) −16423.0 + 28445.5i −0.770128 + 1.33390i 0.167364 + 0.985895i \(0.446474\pi\)
−0.937492 + 0.348006i \(0.886859\pi\)
\(770\) −420.000 + 727.461i −0.0196568 + 0.0340466i
\(771\) 0 0
\(772\) −6700.00 11604.7i −0.312355 0.541015i
\(773\) −11982.0 −0.557520 −0.278760 0.960361i \(-0.589923\pi\)
−0.278760 + 0.960361i \(0.589923\pi\)
\(774\) 0 0
\(775\) −6100.00 −0.282734
\(776\) −184.000 318.697i −0.00851188 0.0147430i
\(777\) 0 0
\(778\) 13338.0 23102.1i 0.614641 1.06459i
\(779\) 10560.0 18290.5i 0.485688 0.841237i
\(780\) 0 0
\(781\) 2916.00 + 5050.66i 0.133601 + 0.231404i
\(782\) −18720.0 −0.856043
\(783\) 0 0
\(784\) −2352.00 −0.107143
\(785\) −4870.00 8435.09i −0.221424