Properties

Label 810.4.e.a.541.1
Level $810$
Weight $4$
Character 810.541
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 541.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 810.541
Dual form 810.4.e.a.271.1

$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) 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 \(-0.807129\pi\)
0.904208 + 0.427093i \(0.140462\pi\)
\(12\) 0 0
\(13\) −34.0000 58.8897i −0.725377 1.25639i −0.958819 0.284019i \(-0.908332\pi\)
0.233441 0.972371i \(-0.425001\pi\)
\(14\) −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 \(-0.687820\pi\)
−0.556405 + 0.830911i \(0.687820\pi\)
\(18\) 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 0.998672 + 0.0515165i \(0.0164055\pi\)
−0.454721 + 0.890634i \(0.650261\pi\)
\(24\) 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 \(-0.701159\pi\)
0.994135 + 0.108149i \(0.0344925\pi\)
\(30\) 0 0
\(31\) 122.000 + 211.310i 0.706834 + 1.22427i 0.966026 + 0.258446i \(0.0832105\pi\)
−0.259192 + 0.965826i \(0.583456\pi\)
\(32\) −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 −0.808086 0.589065i \(-0.799496\pi\)
−0.106102 0.994355i \(-0.533837\pi\)
\(42\) 0 0
\(43\) −52.0000 + 90.0666i −0.184417 + 0.319419i −0.943380 0.331714i \(-0.892373\pi\)
0.758963 + 0.651134i \(0.225706\pi\)
\(44\) −24.0000 −0.0822304
\(45\) 0 0
\(46\) −240.000 −0.769262
\(47\) 300.000 519.615i 0.931053 1.61263i 0.149528 0.988757i \(-0.452225\pi\)
0.781525 0.623874i \(-0.214442\pi\)
\(48\) 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 \(-0.391490\pi\)
0.334330 + 0.942456i \(0.391490\pi\)
\(54\) 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 0.994343 + 0.106219i \(0.0338746\pi\)
−0.405183 + 0.914236i \(0.632792\pi\)
\(60\) 0 0
\(61\) −181.000 + 313.501i −0.379913 + 0.658028i −0.991049 0.133497i \(-0.957379\pi\)
0.611136 + 0.791525i \(0.290713\pi\)
\(62\) −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 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 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 \(-0.198182\pi\)
0.812360 + 0.583156i \(0.198182\pi\)
\(72\) 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 −0.0410678 + 0.999156i \(0.513076\pi\)
−0.844761 + 0.535144i \(0.820257\pi\)
\(80\) 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 \(-0.749002\pi\)
0.966733 + 0.255788i \(0.0823350\pi\)
\(84\) 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 \(-0.303509\pi\)
0.578830 + 0.815448i \(0.303509\pi\)
\(90\) 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 −0.853737 0.520705i \(-0.825669\pi\)
0.877812 + 0.479005i \(0.159003\pi\)
\(98\) −294.000 −0.303046
\(99\) 0 0
\(100\) 100.000 0.100000
\(101\) −753.000 + 1304.23i −0.741845 + 1.28491i 0.209810 + 0.977742i \(0.432715\pi\)
−0.951655 + 0.307170i \(0.900618\pi\)
\(102\) 0 0
\(103\) 737.000 + 1276.52i 0.705037 + 1.22116i 0.966678 + 0.255994i \(0.0824028\pi\)
−0.261642 + 0.965165i \(0.584264\pi\)
\(104\) −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 \(-0.637063\pi\)
−0.417413 + 0.908717i \(0.637063\pi\)
\(108\) 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 \(-0.196123\pi\)
−0.908523 + 0.417834i \(0.862789\pi\)
\(114\) 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 0.726372 + 0.687301i \(0.241205\pi\)
0.232034 + 0.972708i \(0.425462\pi\)
\(132\) 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 \(-0.913377\pi\)
0.714376 + 0.699762i \(0.246711\pi\)
\(138\) 0 0
\(139\) 350.000 + 606.218i 0.213573 + 0.369919i 0.952830 0.303504i \(-0.0981566\pi\)
−0.739257 + 0.673423i \(0.764823\pi\)
\(140\) −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 \(-0.156689\pi\)
−0.849930 + 0.526895i \(0.823356\pi\)
\(150\) 0 0
\(151\) −532.000 + 921.451i −0.286712 + 0.496600i −0.973023 0.230708i \(-0.925896\pi\)
0.686311 + 0.727308i \(0.259229\pi\)
\(152\) 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 0.999984 0.00562710i \(-0.00179117\pi\)
−0.504865 + 0.863198i \(0.668458\pi\)
\(158\) −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 \(-0.260036\pi\)
−0.973605 + 0.228240i \(0.926703\pi\)
\(168\) 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 \(-0.914362\pi\)
0.712209 + 0.701968i \(0.247695\pi\)
\(174\) 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 \(-0.423094\pi\)
0.239263 + 0.970955i \(0.423094\pi\)
\(180\) 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 \(-0.729484\pi\)
0.980590 + 0.196069i \(0.0628177\pi\)
\(192\) 0 0
\(193\) −1675.00 2901.19i −0.624711 1.08203i −0.988597 0.150587i \(-0.951884\pi\)
0.363886 0.931443i \(-0.381450\pi\)
\(194\) 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 \(-0.273899\pi\)
0.652073 + 0.758156i \(0.273899\pi\)
\(198\) 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 0.866351 0.499435i \(-0.166459\pi\)
−0.865699 + 0.500565i \(0.833126\pi\)
\(212\) −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 −0.765508 0.643426i \(-0.777512\pi\)
0.939977 + 0.341237i \(0.110846\pi\)
\(224\) 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 \(-0.947446\pi\)
0.635535 + 0.772072i \(0.280780\pi\)
\(228\) 0 0
\(229\) 1157.00 + 2003.98i 0.333872 + 0.578283i 0.983268 0.182167i \(-0.0583113\pi\)
−0.649395 + 0.760451i \(0.724978\pi\)
\(230\) 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 \(-0.499195\pi\)
0.00253051 + 0.999997i \(0.499195\pi\)
\(234\) 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 −0.923423 0.383784i \(-0.874621\pi\)
0.129345 0.991600i \(-0.458713\pi\)
\(240\) 0 0
\(241\) 2165.00 3749.89i 0.578672 1.00229i −0.416960 0.908925i \(-0.636905\pi\)
0.995632 0.0933643i \(-0.0297621\pi\)
\(242\) −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 \(-0.519944\pi\)
−0.0626165 + 0.998038i \(0.519944\pi\)
\(252\) 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 \(-0.141841\pi\)
−0.824437 + 0.565954i \(0.808508\pi\)
\(258\) 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 −0.157823 + 0.987467i \(0.550448\pi\)
−0.776260 + 0.630413i \(0.782886\pi\)
\(264\) 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 \(-0.341354\pi\)
0.478022 + 0.878348i \(0.341354\pi\)
\(270\) 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 −0.772868 0.634567i \(-0.781179\pi\)
0.935985 + 0.352040i \(0.114512\pi\)
\(278\) −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 \(-0.877671\pi\)
0.788217 + 0.615397i \(0.211004\pi\)
\(282\) 0 0
\(283\) 2966.00 + 5137.26i 0.623005 + 1.07908i 0.988923 + 0.148429i \(0.0474217\pi\)
−0.365918 + 0.930647i \(0.619245\pi\)
\(284\) −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 0.999702 + 0.0244213i \(0.00777430\pi\)
−0.478701 + 0.877978i \(0.658892\pi\)
\(294\) 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 −0.896033 0.443988i \(-0.853563\pi\)
0.0635115 0.997981i \(-0.479770\pi\)
\(312\) 0 0
\(313\) 1085.00 1879.28i 0.195936 0.339370i −0.751271 0.659994i \(-0.770559\pi\)
0.947207 + 0.320623i \(0.103892\pi\)
\(314\) −3896.00 −0.700204
\(315\) 0 0
\(316\) 4976.00 0.885829
\(317\) 3837.00 6645.88i 0.679834 1.17751i −0.295197 0.955437i \(-0.595385\pi\)
0.975031 0.222071i \(-0.0712815\pi\)
\(318\) 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 0.124983 + 0.992159i \(0.460112\pi\)
−0.921726 + 0.387841i \(0.873221\pi\)
\(332\) −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 −0.652053 0.758173i \(-0.726092\pi\)
−0.330570 0.943781i \(-0.607241\pi\)
\(338\) −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 0.920735 + 0.390188i \(0.127590\pi\)
−0.122455 + 0.992474i \(0.539077\pi\)
\(348\) 0 0
\(349\) 1079.00 1868.88i 0.165494 0.286645i −0.771336 0.636428i \(-0.780411\pi\)
0.936831 + 0.349783i \(0.113745\pi\)
\(350\) 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 \(-0.841253\pi\)
0.853318 + 0.521391i \(0.174587\pi\)
\(354\) 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 \(-0.280231\pi\)
0.636864 + 0.770976i \(0.280231\pi\)
\(360\) 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 −0.968594 0.248647i \(-0.920014\pi\)
0.699631 + 0.714504i \(0.253348\pi\)
\(368\) −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 −0.930399 0.366548i \(-0.880539\pi\)
0.147759 0.989023i \(-0.452794\pi\)
\(374\) −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 \(-0.257057\pi\)
−0.971426 + 0.237341i \(0.923724\pi\)
\(384\) 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 0.00645168 0.999979i \(-0.497946\pi\)
0.862782 0.505577i \(-0.168720\pi\)
\(390\) 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 \(-0.212730\pi\)
−0.929078 + 0.369885i \(0.879397\pi\)
\(402\) 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 0.949244 + 0.314540i \(0.101850\pi\)
−0.202222 + 0.979340i \(0.564816\pi\)
\(410\) −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 \(-0.104932\pi\)
−0.753423 + 0.657536i \(0.771599\pi\)
\(420\) 0 0
\(421\) 7253.00 12562.6i 0.839643 1.45430i −0.0505509 0.998721i \(-0.516098\pi\)
0.890194 0.455582i \(-0.150569\pi\)
\(422\) −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 \(-0.382060\pi\)
0.362100 + 0.932139i \(0.382060\pi\)
\(432\) 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 −0.282222 0.959349i \(-0.591071\pi\)
0.971932 0.235263i \(-0.0755952\pi\)
\(440\) −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 \(-0.747497\pi\)
0.967931 + 0.251215i \(0.0808301\pi\)
\(444\) 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 \(-0.293259\pi\)
0.604784 + 0.796389i \(0.293259\pi\)
\(450\) 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 −0.892385 0.451276i \(-0.850969\pi\)
0.837008 + 0.547190i \(0.184302\pi\)
\(458\) −4628.00 −0.472166
\(459\) 0 0
\(460\) −2400.00 −0.243262
\(461\) −5619.00 + 9732.39i −0.567685 + 0.983260i 0.429109 + 0.903253i \(0.358828\pi\)
−0.996794 + 0.0800071i \(0.974506\pi\)
\(462\) 0 0
\(463\) 1151.00 + 1993.59i 0.115532 + 0.200108i 0.917992 0.396598i \(-0.129809\pi\)
−0.802460 + 0.596706i \(0.796476\pi\)
\(464\) 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 \(-0.788144\pi\)
−0.786567 + 0.617505i \(0.788144\pi\)
\(468\) 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 \(-0.762241\pi\)
0.955261 + 0.295763i \(0.0955738\pi\)
\(480\) 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 \(-0.163244\pi\)
−0.860598 + 0.509284i \(0.829910\pi\)
\(492\) 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 −0.986059 0.166396i \(-0.946787\pi\)
0.348926 0.937150i \(-0.386546\pi\)
\(500\) −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 \(-0.569974\pi\)
−0.218064 + 0.975935i \(0.569974\pi\)
\(504\) 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 \(-0.228846\pi\)
−0.946606 + 0.322392i \(0.895513\pi\)
\(510\) 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 \(-0.556669\pi\)
−0.177093 + 0.984194i \(0.556669\pi\)
\(522\) 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 0.253052 + 0.967453i \(0.418566\pi\)
−0.964365 + 0.264577i \(0.914768\pi\)
\(548\) 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 \(-0.351493\pi\)
0.449806 + 0.893126i \(0.351493\pi\)
\(558\) 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 \(-0.201909\pi\)
−0.915968 + 0.401251i \(0.868575\pi\)
\(564\) 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 \(-0.797092\pi\)
0.917223 + 0.398374i \(0.130425\pi\)
\(570\) 0 0
\(571\) 2378.00 + 4118.82i 0.174284 + 0.301869i 0.939913 0.341413i \(-0.110906\pi\)
−0.765629 + 0.643282i \(0.777572\pi\)
\(572\) 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 \(-0.842869\pi\)
0.850660 + 0.525716i \(0.176203\pi\)
\(588\) 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 \(-0.680925\pi\)
−0.538278 + 0.842767i \(0.680925\pi\)
\(594\) 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 \(-0.261605\pi\)
−0.974718 + 0.223437i \(0.928272\pi\)
\(600\) 0 0
\(601\) −8755.00 + 15164.1i −0.594216 + 1.02921i 0.399441 + 0.916759i \(0.369204\pi\)
−0.993657 + 0.112454i \(0.964129\pi\)
\(602\) 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 0.999180 0.0404833i \(-0.0128898\pi\)
−0.534650 + 0.845074i \(0.679556\pi\)
\(608\) −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 \(-0.172586\pi\)
−0.875174 + 0.483809i \(0.839253\pi\)
\(618\) 0 0
\(619\) 1070.00 1853.29i 0.0694781 0.120340i −0.829194 0.558962i \(-0.811200\pi\)
0.898672 + 0.438622i \(0.144533\pi\)
\(620\) −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 \(-0.837805\pi\)
0.858915 + 0.512118i \(0.171139\pi\)
\(642\) 0 0
\(643\) 11726.0 + 20310.0i 0.719173 + 1.24564i 0.961328 + 0.275407i \(0.0888125\pi\)
−0.242155 + 0.970238i \(0.577854\pi\)
\(644\) 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 \(-0.570435\pi\)
−0.219478 + 0.975617i \(0.570435\pi\)
\(648\) 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 0.996182 + 0.0872955i \(0.0278224\pi\)
−0.422491 + 0.906367i \(0.638844\pi\)
\(654\) 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 −0.0822865 0.996609i \(-0.526222\pi\)
0.904232 0.427042i \(-0.140444\pi\)
\(660\) 0 0
\(661\) 15299.0 + 26498.6i 0.900245 + 1.55927i 0.827175 + 0.561944i \(0.189946\pi\)
0.0730698 + 0.997327i \(0.476720\pi\)
\(662\) −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 −0.806844 0.590765i \(-0.798826\pi\)
0.915039 + 0.403365i \(0.132159\pi\)
\(674\) 24316.0 1.38964
\(675\) 0 0
\(676\) 9708.00 0.552344
\(677\) −13599.0 + 23554.2i −0.772012 + 1.33716i 0.164447 + 0.986386i \(0.447416\pi\)
−0.936459 + 0.350778i \(0.885917\pi\)
\(678\) 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 \(-0.860298\pi\)
−0.905225 + 0.424933i \(0.860298\pi\)
\(684\) 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 0.107611 + 0.994193i \(0.465680\pi\)
−0.914802 + 0.403902i \(0.867654\pi\)
\(692\) 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 \(-0.710336\pi\)
−0.613741 + 0.789508i \(0.710336\pi\)
\(702\) 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 0.281783 + 0.959478i \(0.409074\pi\)
−0.971824 + 0.235708i \(0.924259\pi\)
\(710\) 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 \(-0.450467\pi\)
0.154984 + 0.987917i \(0.450467\pi\)
\(720\) 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 −0.793466 0.608615i \(-0.791725\pi\)
0.923809 + 0.382854i \(0.125059\pi\)
\(728\) 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 0.560659 0.828047i \(-0.310548\pi\)
−0.997439 + 0.0715214i \(0.977215\pi\)
\(734\) −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 \(-0.156292\pi\)
−0.849271 + 0.527957i \(0.822958\pi\)
\(744\) 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 0.606500 0.795084i \(-0.292573\pi\)
−0.991813 + 0.127702i \(0.959240\pi\)
\(752\) 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 \(-0.0655377\pi\)
−0.666491 + 0.745513i \(0.732204\pi\)
\(762\) 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 −0.937492 0.348006i \(-0.886859\pi\)
0.167364 0.985895i \(-0.446474\pi\)
\(770\) 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 \(-0.410077\pi\)
0.278760 + 0.960361i \(0.410077\pi\)
\(774\) 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 0.383517i