Properties

Label 405.4.e.w.271.5
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} - 20304 x^{3} + 10368 x^{2} + 124416 x + 746496 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.5
Root \(1.25636 - 1.25636i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.w.136.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.78729 + 3.09567i) q^{2} +(-2.38879 + 4.13751i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.07987 - 12.2627i) q^{7} +11.5188 q^{8} +O(q^{10})\) \(q+(1.78729 + 3.09567i) q^{2} +(-2.38879 + 4.13751i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.07987 - 12.2627i) q^{7} +11.5188 q^{8} -17.8729 q^{10} +(-31.8319 - 55.1345i) q^{11} +(5.19795 - 9.00312i) q^{13} +(25.3075 - 43.8339i) q^{14} +(39.6977 + 68.7584i) q^{16} +108.605 q^{17} +18.6145 q^{19} +(-11.9440 - 20.6876i) q^{20} +(113.786 - 197.082i) q^{22} +(64.4120 - 111.565i) q^{23} +(-12.5000 - 21.6506i) q^{25} +37.1609 q^{26} +67.6494 q^{28} +(-41.8248 - 72.4426i) q^{29} +(5.23638 - 9.06967i) q^{31} +(-95.8273 + 165.978i) q^{32} +(194.109 + 336.206i) q^{34} +70.7987 q^{35} -81.8885 q^{37} +(33.2695 + 57.6245i) q^{38} +(-28.7969 + 49.8777i) q^{40} +(153.726 - 266.262i) q^{41} +(111.220 + 192.638i) q^{43} +304.159 q^{44} +460.491 q^{46} +(-180.965 - 313.441i) q^{47} +(71.2509 - 123.410i) q^{49} +(44.6822 - 77.3918i) q^{50} +(24.8337 + 43.0132i) q^{52} +562.215 q^{53} +318.319 q^{55} +(-81.5513 - 141.251i) q^{56} +(149.506 - 258.952i) q^{58} +(-231.155 + 400.372i) q^{59} +(324.533 + 562.108i) q^{61} +37.4356 q^{62} -49.9208 q^{64} +(25.9898 + 45.0156i) q^{65} +(-127.090 + 220.126i) q^{67} +(-259.435 + 449.355i) q^{68} +(126.538 + 219.170i) q^{70} -1092.93 q^{71} +1034.52 q^{73} +(-146.358 - 253.500i) q^{74} +(-44.4663 + 77.0179i) q^{76} +(-450.731 + 780.690i) q^{77} +(-575.927 - 997.534i) q^{79} -396.977 q^{80} +1099.01 q^{82} +(-262.160 - 454.075i) q^{83} +(-271.513 + 470.274i) q^{85} +(-397.563 + 688.599i) q^{86} +(-366.664 - 635.081i) q^{88} +656.485 q^{89} -147.203 q^{91} +(307.734 + 533.010i) q^{92} +(646.874 - 1120.42i) q^{94} +(-46.5363 + 80.6033i) q^{95} +(-562.755 - 974.721i) q^{97} +509.383 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + 40 q^{10} - 88 q^{11} - 20 q^{13} - 180 q^{14} - 58 q^{16} + 248 q^{17} - 92 q^{19} - 170 q^{20} + 74 q^{22} - 210 q^{23} - 150 q^{25} + 8 q^{26} + 704 q^{28} - 296 q^{29} + 104 q^{31} - 722 q^{32} + 428 q^{34} + 400 q^{35} - 408 q^{37} + 20 q^{38} - 330 q^{40} - 344 q^{41} - 512 q^{43} + 1432 q^{44} - 372 q^{46} - 238 q^{47} - 68 q^{49} - 100 q^{50} + 468 q^{52} + 1700 q^{53} + 880 q^{55} - 2316 q^{56} - 890 q^{58} - 1840 q^{59} + 364 q^{61} + 2076 q^{62} - 1980 q^{64} - 100 q^{65} - 88 q^{67} - 236 q^{68} - 900 q^{70} + 2728 q^{71} + 1672 q^{73} - 1316 q^{74} + 2106 q^{76} - 840 q^{77} + 680 q^{79} + 580 q^{80} + 3484 q^{82} - 2148 q^{83} - 620 q^{85} - 2872 q^{86} - 1296 q^{88} + 6000 q^{89} - 6116 q^{91} - 1002 q^{92} + 3662 q^{94} + 230 q^{95} + 612 q^{97} + 3964 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.78729 + 3.09567i 0.631902 + 1.09449i 0.987163 + 0.159718i \(0.0510586\pi\)
−0.355261 + 0.934767i \(0.615608\pi\)
\(3\) 0 0
\(4\) −2.38879 + 4.13751i −0.298599 + 0.517189i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −7.07987 12.2627i −0.382277 0.662123i 0.609110 0.793086i \(-0.291527\pi\)
−0.991387 + 0.130962i \(0.958193\pi\)
\(8\) 11.5188 0.509062
\(9\) 0 0
\(10\) −17.8729 −0.565190
\(11\) −31.8319 55.1345i −0.872516 1.51124i −0.859385 0.511329i \(-0.829153\pi\)
−0.0131312 0.999914i \(-0.504180\pi\)
\(12\) 0 0
\(13\) 5.19795 9.00312i 0.110896 0.192078i −0.805236 0.592955i \(-0.797961\pi\)
0.916132 + 0.400877i \(0.131294\pi\)
\(14\) 25.3075 43.8339i 0.483123 0.836794i
\(15\) 0 0
\(16\) 39.6977 + 68.7584i 0.620276 + 1.07435i
\(17\) 108.605 1.54945 0.774724 0.632300i \(-0.217889\pi\)
0.774724 + 0.632300i \(0.217889\pi\)
\(18\) 0 0
\(19\) 18.6145 0.224761 0.112381 0.993665i \(-0.464152\pi\)
0.112381 + 0.993665i \(0.464152\pi\)
\(20\) −11.9440 20.6876i −0.133538 0.231294i
\(21\) 0 0
\(22\) 113.786 197.082i 1.10269 1.90991i
\(23\) 64.4120 111.565i 0.583949 1.01143i −0.411057 0.911610i \(-0.634840\pi\)
0.995006 0.0998192i \(-0.0318264\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 37.1609 0.280302
\(27\) 0 0
\(28\) 67.6494 0.456590
\(29\) −41.8248 72.4426i −0.267816 0.463871i 0.700481 0.713671i \(-0.252969\pi\)
−0.968298 + 0.249799i \(0.919635\pi\)
\(30\) 0 0
\(31\) 5.23638 9.06967i 0.0303381 0.0525471i −0.850458 0.526043i \(-0.823675\pi\)
0.880796 + 0.473496i \(0.157008\pi\)
\(32\) −95.8273 + 165.978i −0.529376 + 0.916906i
\(33\) 0 0
\(34\) 194.109 + 336.206i 0.979098 + 1.69585i
\(35\) 70.7987 0.341919
\(36\) 0 0
\(37\) −81.8885 −0.363848 −0.181924 0.983313i \(-0.558233\pi\)
−0.181924 + 0.983313i \(0.558233\pi\)
\(38\) 33.2695 + 57.6245i 0.142027 + 0.245998i
\(39\) 0 0
\(40\) −28.7969 + 49.8777i −0.113830 + 0.197159i
\(41\) 153.726 266.262i 0.585562 1.01422i −0.409244 0.912425i \(-0.634207\pi\)
0.994805 0.101797i \(-0.0324593\pi\)
\(42\) 0 0
\(43\) 111.220 + 192.638i 0.394438 + 0.683187i 0.993029 0.117868i \(-0.0376059\pi\)
−0.598591 + 0.801055i \(0.704273\pi\)
\(44\) 304.159 1.04213
\(45\) 0 0
\(46\) 460.491 1.47599
\(47\) −180.965 313.441i −0.561628 0.972768i −0.997355 0.0726889i \(-0.976842\pi\)
0.435727 0.900079i \(-0.356491\pi\)
\(48\) 0 0
\(49\) 71.2509 123.410i 0.207728 0.359796i
\(50\) 44.6822 77.3918i 0.126380 0.218897i
\(51\) 0 0
\(52\) 24.8337 + 43.0132i 0.0662271 + 0.114709i
\(53\) 562.215 1.45710 0.728548 0.684994i \(-0.240195\pi\)
0.728548 + 0.684994i \(0.240195\pi\)
\(54\) 0 0
\(55\) 318.319 0.780402
\(56\) −81.5513 141.251i −0.194603 0.337062i
\(57\) 0 0
\(58\) 149.506 258.952i 0.338467 0.586242i
\(59\) −231.155 + 400.372i −0.510065 + 0.883458i 0.489867 + 0.871797i \(0.337045\pi\)
−0.999932 + 0.0116608i \(0.996288\pi\)
\(60\) 0 0
\(61\) 324.533 + 562.108i 0.681184 + 1.17985i 0.974620 + 0.223867i \(0.0718682\pi\)
−0.293435 + 0.955979i \(0.594799\pi\)
\(62\) 37.4356 0.0766827
\(63\) 0 0
\(64\) −49.9208 −0.0975015
\(65\) 25.9898 + 45.0156i 0.0495944 + 0.0859000i
\(66\) 0 0
\(67\) −127.090 + 220.126i −0.231739 + 0.401384i −0.958320 0.285697i \(-0.907775\pi\)
0.726581 + 0.687081i \(0.241108\pi\)
\(68\) −259.435 + 449.355i −0.462664 + 0.801357i
\(69\) 0 0
\(70\) 126.538 + 219.170i 0.216059 + 0.374225i
\(71\) −1092.93 −1.82685 −0.913426 0.407006i \(-0.866573\pi\)
−0.913426 + 0.407006i \(0.866573\pi\)
\(72\) 0 0
\(73\) 1034.52 1.65865 0.829324 0.558769i \(-0.188726\pi\)
0.829324 + 0.558769i \(0.188726\pi\)
\(74\) −146.358 253.500i −0.229916 0.398227i
\(75\) 0 0
\(76\) −44.4663 + 77.0179i −0.0671136 + 0.116244i
\(77\) −450.731 + 780.690i −0.667086 + 1.15543i
\(78\) 0 0
\(79\) −575.927 997.534i −0.820213 1.42065i −0.905524 0.424296i \(-0.860522\pi\)
0.0853111 0.996354i \(-0.472812\pi\)
\(80\) −396.977 −0.554792
\(81\) 0 0
\(82\) 1099.01 1.48007
\(83\) −262.160 454.075i −0.346697 0.600496i 0.638964 0.769237i \(-0.279363\pi\)
−0.985660 + 0.168741i \(0.946030\pi\)
\(84\) 0 0
\(85\) −271.513 + 470.274i −0.346467 + 0.600099i
\(86\) −397.563 + 688.599i −0.498492 + 0.863414i
\(87\) 0 0
\(88\) −366.664 635.081i −0.444165 0.769316i
\(89\) 656.485 0.781879 0.390940 0.920416i \(-0.372150\pi\)
0.390940 + 0.920416i \(0.372150\pi\)
\(90\) 0 0
\(91\) −147.203 −0.169573
\(92\) 307.734 + 533.010i 0.348733 + 0.604024i
\(93\) 0 0
\(94\) 646.874 1120.42i 0.709787 1.22939i
\(95\) −46.5363 + 80.6033i −0.0502582 + 0.0870497i
\(96\) 0 0
\(97\) −562.755 974.721i −0.589063 1.02029i −0.994355 0.106100i \(-0.966163\pi\)
0.405292 0.914187i \(-0.367170\pi\)
\(98\) 509.383 0.525056
\(99\) 0 0
\(100\) 119.440 0.119440
\(101\) 190.162 + 329.371i 0.187345 + 0.324491i 0.944364 0.328902i \(-0.106678\pi\)
−0.757019 + 0.653393i \(0.773345\pi\)
\(102\) 0 0
\(103\) −382.139 + 661.884i −0.365566 + 0.633178i −0.988867 0.148804i \(-0.952458\pi\)
0.623301 + 0.781982i \(0.285791\pi\)
\(104\) 59.8740 103.705i 0.0564531 0.0977797i
\(105\) 0 0
\(106\) 1004.84 + 1740.43i 0.920742 + 1.59477i
\(107\) −816.083 −0.737325 −0.368662 0.929563i \(-0.620184\pi\)
−0.368662 + 0.929563i \(0.620184\pi\)
\(108\) 0 0
\(109\) 606.775 0.533198 0.266599 0.963808i \(-0.414100\pi\)
0.266599 + 0.963808i \(0.414100\pi\)
\(110\) 568.928 + 985.412i 0.493137 + 0.854139i
\(111\) 0 0
\(112\) 562.109 973.601i 0.474235 0.821399i
\(113\) 13.6613 23.6621i 0.0113730 0.0196986i −0.860283 0.509817i \(-0.829713\pi\)
0.871656 + 0.490118i \(0.163046\pi\)
\(114\) 0 0
\(115\) 322.060 + 557.824i 0.261150 + 0.452325i
\(116\) 399.643 0.319879
\(117\) 0 0
\(118\) −1652.56 −1.28924
\(119\) −768.910 1331.79i −0.592318 1.02593i
\(120\) 0 0
\(121\) −1361.04 + 2357.39i −1.02257 + 1.77114i
\(122\) −1160.07 + 2009.30i −0.860883 + 1.49109i
\(123\) 0 0
\(124\) 25.0172 + 43.3311i 0.0181179 + 0.0313810i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1206.22 −0.842794 −0.421397 0.906876i \(-0.638460\pi\)
−0.421397 + 0.906876i \(0.638460\pi\)
\(128\) 677.396 + 1173.28i 0.467765 + 0.810192i
\(129\) 0 0
\(130\) −92.9024 + 160.912i −0.0626775 + 0.108561i
\(131\) 766.002 1326.75i 0.510885 0.884878i −0.489036 0.872264i \(-0.662651\pi\)
0.999920 0.0126146i \(-0.00401547\pi\)
\(132\) 0 0
\(133\) −131.789 228.264i −0.0859212 0.148820i
\(134\) −908.585 −0.585745
\(135\) 0 0
\(136\) 1251.00 0.788765
\(137\) −1236.06 2140.92i −0.770830 1.33512i −0.937109 0.349038i \(-0.886509\pi\)
0.166279 0.986079i \(-0.446825\pi\)
\(138\) 0 0
\(139\) −6.06336 + 10.5020i −0.00369991 + 0.00640843i −0.867869 0.496792i \(-0.834511\pi\)
0.864170 + 0.503201i \(0.167844\pi\)
\(140\) −169.123 + 292.930i −0.102097 + 0.176837i
\(141\) 0 0
\(142\) −1953.37 3383.34i −1.15439 1.99946i
\(143\) −661.843 −0.387036
\(144\) 0 0
\(145\) 418.248 0.239542
\(146\) 1848.98 + 3202.53i 1.04810 + 1.81537i
\(147\) 0 0
\(148\) 195.615 338.815i 0.108645 0.188178i
\(149\) 1568.26 2716.30i 0.862258 1.49348i −0.00748582 0.999972i \(-0.502383\pi\)
0.869744 0.493503i \(-0.164284\pi\)
\(150\) 0 0
\(151\) 1350.04 + 2338.33i 0.727580 + 1.26020i 0.957903 + 0.287091i \(0.0926881\pi\)
−0.230324 + 0.973114i \(0.573979\pi\)
\(152\) 214.416 0.114418
\(153\) 0 0
\(154\) −3222.35 −1.68613
\(155\) 26.1819 + 45.3483i 0.0135676 + 0.0234998i
\(156\) 0 0
\(157\) −221.314 + 383.326i −0.112502 + 0.194858i −0.916778 0.399397i \(-0.869220\pi\)
0.804277 + 0.594255i \(0.202553\pi\)
\(158\) 2058.69 3565.76i 1.03659 1.79542i
\(159\) 0 0
\(160\) −479.136 829.889i −0.236744 0.410053i
\(161\) −1824.11 −0.892921
\(162\) 0 0
\(163\) −2116.29 −1.01694 −0.508469 0.861080i \(-0.669788\pi\)
−0.508469 + 0.861080i \(0.669788\pi\)
\(164\) 734.441 + 1272.09i 0.349696 + 0.605692i
\(165\) 0 0
\(166\) 937.111 1623.12i 0.438156 0.758909i
\(167\) −647.312 + 1121.18i −0.299943 + 0.519517i −0.976123 0.217220i \(-0.930301\pi\)
0.676180 + 0.736737i \(0.263634\pi\)
\(168\) 0 0
\(169\) 1044.46 + 1809.06i 0.475404 + 0.823424i
\(170\) −1941.09 −0.875732
\(171\) 0 0
\(172\) −1062.72 −0.471116
\(173\) −1461.09 2530.67i −0.642106 1.11216i −0.984962 0.172772i \(-0.944728\pi\)
0.342856 0.939388i \(-0.388606\pi\)
\(174\) 0 0
\(175\) −176.997 + 306.567i −0.0764554 + 0.132425i
\(176\) 2527.31 4377.42i 1.08240 1.87478i
\(177\) 0 0
\(178\) 1173.33 + 2032.26i 0.494071 + 0.855756i
\(179\) 3955.51 1.65167 0.825834 0.563913i \(-0.190705\pi\)
0.825834 + 0.563913i \(0.190705\pi\)
\(180\) 0 0
\(181\) −2694.00 −1.10632 −0.553159 0.833076i \(-0.686578\pi\)
−0.553159 + 0.833076i \(0.686578\pi\)
\(182\) −263.095 455.693i −0.107153 0.185595i
\(183\) 0 0
\(184\) 741.946 1285.09i 0.297266 0.514880i
\(185\) 204.721 354.588i 0.0813590 0.140918i
\(186\) 0 0
\(187\) −3457.11 5987.89i −1.35192 2.34159i
\(188\) 1729.15 0.670806
\(189\) 0 0
\(190\) −332.695 −0.127033
\(191\) 428.173 + 741.618i 0.162207 + 0.280951i 0.935660 0.352903i \(-0.114805\pi\)
−0.773453 + 0.633854i \(0.781472\pi\)
\(192\) 0 0
\(193\) 867.607 1502.74i 0.323584 0.560464i −0.657641 0.753332i \(-0.728446\pi\)
0.981225 + 0.192868i \(0.0617789\pi\)
\(194\) 2011.61 3484.21i 0.744460 1.28944i
\(195\) 0 0
\(196\) 340.407 + 589.602i 0.124055 + 0.214870i
\(197\) 2943.95 1.06471 0.532354 0.846522i \(-0.321308\pi\)
0.532354 + 0.846522i \(0.321308\pi\)
\(198\) 0 0
\(199\) −4172.06 −1.48618 −0.743088 0.669193i \(-0.766640\pi\)
−0.743088 + 0.669193i \(0.766640\pi\)
\(200\) −143.985 249.388i −0.0509062 0.0881721i
\(201\) 0 0
\(202\) −679.749 + 1177.36i −0.236767 + 0.410093i
\(203\) −592.228 + 1025.77i −0.204760 + 0.354655i
\(204\) 0 0
\(205\) 768.632 + 1331.31i 0.261871 + 0.453574i
\(206\) −2731.97 −0.924006
\(207\) 0 0
\(208\) 825.387 0.275146
\(209\) −592.536 1026.30i −0.196108 0.339669i
\(210\) 0 0
\(211\) −1925.52 + 3335.10i −0.628239 + 1.08814i 0.359666 + 0.933081i \(0.382891\pi\)
−0.987905 + 0.155060i \(0.950443\pi\)
\(212\) −1343.01 + 2326.17i −0.435088 + 0.753594i
\(213\) 0 0
\(214\) −1458.58 2526.33i −0.465917 0.806991i
\(215\) −1112.20 −0.352796
\(216\) 0 0
\(217\) −148.291 −0.0463902
\(218\) 1084.48 + 1878.38i 0.336928 + 0.583577i
\(219\) 0 0
\(220\) −760.398 + 1317.05i −0.233027 + 0.403615i
\(221\) 564.524 977.785i 0.171828 0.297615i
\(222\) 0 0
\(223\) −410.357 710.759i −0.123227 0.213435i 0.797812 0.602907i \(-0.205991\pi\)
−0.921038 + 0.389472i \(0.872658\pi\)
\(224\) 2713.78 0.809473
\(225\) 0 0
\(226\) 97.6667 0.0287464
\(227\) 2630.61 + 4556.36i 0.769163 + 1.33223i 0.938018 + 0.346588i \(0.112660\pi\)
−0.168855 + 0.985641i \(0.554007\pi\)
\(228\) 0 0
\(229\) −9.79945 + 16.9731i −0.00282780 + 0.00489789i −0.867436 0.497549i \(-0.834233\pi\)
0.864608 + 0.502447i \(0.167567\pi\)
\(230\) −1151.23 + 1993.98i −0.330042 + 0.571649i
\(231\) 0 0
\(232\) −481.770 834.449i −0.136335 0.236139i
\(233\) −3181.79 −0.894619 −0.447309 0.894379i \(-0.647618\pi\)
−0.447309 + 0.894379i \(0.647618\pi\)
\(234\) 0 0
\(235\) 1809.65 0.502335
\(236\) −1104.36 1912.81i −0.304610 0.527599i
\(237\) 0 0
\(238\) 2748.53 4760.59i 0.748574 1.29657i
\(239\) −817.052 + 1415.18i −0.221133 + 0.383013i −0.955152 0.296115i \(-0.904309\pi\)
0.734019 + 0.679128i \(0.237642\pi\)
\(240\) 0 0
\(241\) −707.355 1225.17i −0.189065 0.327471i 0.755874 0.654718i \(-0.227212\pi\)
−0.944939 + 0.327247i \(0.893879\pi\)
\(242\) −9730.28 −2.58465
\(243\) 0 0
\(244\) −3100.97 −0.813604
\(245\) 356.254 + 617.051i 0.0928990 + 0.160906i
\(246\) 0 0
\(247\) 96.7575 167.589i 0.0249252 0.0431718i
\(248\) 60.3166 104.471i 0.0154440 0.0267497i
\(249\) 0 0
\(250\) 223.411 + 386.959i 0.0565190 + 0.0978938i
\(251\) 5932.53 1.49186 0.745932 0.666022i \(-0.232005\pi\)
0.745932 + 0.666022i \(0.232005\pi\)
\(252\) 0 0
\(253\) −8201.42 −2.03802
\(254\) −2155.86 3734.07i −0.532563 0.922426i
\(255\) 0 0
\(256\) −2621.08 + 4539.85i −0.639913 + 1.10836i
\(257\) −3500.65 + 6063.30i −0.849666 + 1.47167i 0.0318400 + 0.999493i \(0.489863\pi\)
−0.881506 + 0.472172i \(0.843470\pi\)
\(258\) 0 0
\(259\) 579.760 + 1004.17i 0.139091 + 0.240913i
\(260\) −248.337 −0.0592353
\(261\) 0 0
\(262\) 5476.26 1.29132
\(263\) −1827.27 3164.93i −0.428420 0.742045i 0.568313 0.822812i \(-0.307596\pi\)
−0.996733 + 0.0807677i \(0.974263\pi\)
\(264\) 0 0
\(265\) −1405.54 + 2434.46i −0.325817 + 0.564331i
\(266\) 471.088 815.948i 0.108587 0.188079i
\(267\) 0 0
\(268\) −607.183 1051.67i −0.138394 0.239706i
\(269\) 2589.46 0.586922 0.293461 0.955971i \(-0.405193\pi\)
0.293461 + 0.955971i \(0.405193\pi\)
\(270\) 0 0
\(271\) 4854.10 1.08806 0.544032 0.839064i \(-0.316897\pi\)
0.544032 + 0.839064i \(0.316897\pi\)
\(272\) 4311.37 + 7467.52i 0.961086 + 1.66465i
\(273\) 0 0
\(274\) 4418.39 7652.87i 0.974177 1.68732i
\(275\) −795.798 + 1378.36i −0.174503 + 0.302249i
\(276\) 0 0
\(277\) 3757.58 + 6508.31i 0.815058 + 1.41172i 0.909287 + 0.416170i \(0.136628\pi\)
−0.0942291 + 0.995551i \(0.530039\pi\)
\(278\) −43.3478 −0.00935191
\(279\) 0 0
\(280\) 815.513 0.174058
\(281\) 1806.03 + 3128.14i 0.383412 + 0.664090i 0.991548 0.129744i \(-0.0414154\pi\)
−0.608135 + 0.793834i \(0.708082\pi\)
\(282\) 0 0
\(283\) −2583.45 + 4474.67i −0.542652 + 0.939900i 0.456099 + 0.889929i \(0.349246\pi\)
−0.998751 + 0.0499712i \(0.984087\pi\)
\(284\) 2610.77 4521.99i 0.545496 0.944827i
\(285\) 0 0
\(286\) −1182.90 2048.85i −0.244568 0.423605i
\(287\) −4353.45 −0.895387
\(288\) 0 0
\(289\) 6882.07 1.40079
\(290\) 747.529 + 1294.76i 0.151367 + 0.262175i
\(291\) 0 0
\(292\) −2471.25 + 4280.33i −0.495271 + 0.857834i
\(293\) 2113.18 3660.13i 0.421342 0.729785i −0.574729 0.818344i \(-0.694893\pi\)
0.996071 + 0.0885584i \(0.0282260\pi\)
\(294\) 0 0
\(295\) −1155.77 2001.86i −0.228108 0.395094i
\(296\) −943.255 −0.185221
\(297\) 0 0
\(298\) 11211.7 2.17945
\(299\) −669.621 1159.82i −0.129516 0.224328i
\(300\) 0 0
\(301\) 1574.84 2727.71i 0.301569 0.522333i
\(302\) −4825.81 + 8358.55i −0.919517 + 1.59265i
\(303\) 0 0
\(304\) 738.954 + 1279.91i 0.139414 + 0.241472i
\(305\) −3245.33 −0.609270
\(306\) 0 0
\(307\) 5734.25 1.06603 0.533015 0.846106i \(-0.321059\pi\)
0.533015 + 0.846106i \(0.321059\pi\)
\(308\) −2153.41 3729.81i −0.398383 0.690019i
\(309\) 0 0
\(310\) −93.5891 + 162.101i −0.0171468 + 0.0296991i
\(311\) −3310.19 + 5733.42i −0.603549 + 1.04538i 0.388730 + 0.921352i \(0.372914\pi\)
−0.992279 + 0.124026i \(0.960419\pi\)
\(312\) 0 0
\(313\) −46.7155 80.9136i −0.00843615 0.0146118i 0.861777 0.507288i \(-0.169352\pi\)
−0.870213 + 0.492676i \(0.836019\pi\)
\(314\) −1582.20 −0.284360
\(315\) 0 0
\(316\) 5503.08 0.979659
\(317\) −996.584 1726.13i −0.176573 0.305834i 0.764131 0.645061i \(-0.223168\pi\)
−0.940705 + 0.339227i \(0.889835\pi\)
\(318\) 0 0
\(319\) −2662.72 + 4611.97i −0.467348 + 0.809470i
\(320\) 124.802 216.163i 0.0218020 0.0377622i
\(321\) 0 0
\(322\) −3260.21 5646.86i −0.564238 0.977289i
\(323\) 2021.63 0.348256
\(324\) 0 0
\(325\) −259.898 −0.0443586
\(326\) −3782.42 6551.35i −0.642605 1.11302i
\(327\) 0 0
\(328\) 1770.74 3067.01i 0.298087 0.516302i
\(329\) −2562.42 + 4438.25i −0.429395 + 0.743734i
\(330\) 0 0
\(331\) 1194.59 + 2069.09i 0.198370 + 0.343587i 0.948000 0.318270i \(-0.103102\pi\)
−0.749630 + 0.661857i \(0.769769\pi\)
\(332\) 2504.99 0.414093
\(333\) 0 0
\(334\) −4627.73 −0.758138
\(335\) −635.450 1100.63i −0.103637 0.179504i
\(336\) 0 0
\(337\) −5142.75 + 8907.50i −0.831286 + 1.43983i 0.0657327 + 0.997837i \(0.479062\pi\)
−0.897019 + 0.441992i \(0.854272\pi\)
\(338\) −3733.51 + 6466.63i −0.600817 + 1.04065i
\(339\) 0 0
\(340\) −1297.18 2246.77i −0.206910 0.358378i
\(341\) −666.735 −0.105882
\(342\) 0 0
\(343\) −6874.58 −1.08219
\(344\) 1281.11 + 2218.95i 0.200794 + 0.347785i
\(345\) 0 0
\(346\) 5222.76 9046.09i 0.811495 1.40555i
\(347\) −2115.10 + 3663.47i −0.327218 + 0.566758i −0.981959 0.189095i \(-0.939445\pi\)
0.654741 + 0.755854i \(0.272778\pi\)
\(348\) 0 0
\(349\) 5605.46 + 9708.94i 0.859752 + 1.48913i 0.872166 + 0.489211i \(0.162715\pi\)
−0.0124138 + 0.999923i \(0.503952\pi\)
\(350\) −1265.38 −0.193249
\(351\) 0 0
\(352\) 12201.5 1.84756
\(353\) 5691.50 + 9857.98i 0.858154 + 1.48637i 0.873688 + 0.486486i \(0.161722\pi\)
−0.0155346 + 0.999879i \(0.504945\pi\)
\(354\) 0 0
\(355\) 2732.31 4732.51i 0.408496 0.707536i
\(356\) −1568.21 + 2716.21i −0.233468 + 0.404379i
\(357\) 0 0
\(358\) 7069.63 + 12245.0i 1.04369 + 1.80773i
\(359\) 8942.57 1.31468 0.657341 0.753593i \(-0.271681\pi\)
0.657341 + 0.753593i \(0.271681\pi\)
\(360\) 0 0
\(361\) −6512.50 −0.949482
\(362\) −4814.95 8339.74i −0.699084 1.21085i
\(363\) 0 0
\(364\) 351.638 609.055i 0.0506342 0.0877010i
\(365\) −2586.30 + 4479.60i −0.370885 + 0.642391i
\(366\) 0 0
\(367\) 222.085 + 384.662i 0.0315878 + 0.0547118i 0.881387 0.472395i \(-0.156610\pi\)
−0.849799 + 0.527106i \(0.823277\pi\)
\(368\) 10228.0 1.44884
\(369\) 0 0
\(370\) 1463.58 0.205643
\(371\) −3980.41 6894.27i −0.557015 0.964778i
\(372\) 0 0
\(373\) −1708.05 + 2958.42i −0.237103 + 0.410674i −0.959882 0.280405i \(-0.909531\pi\)
0.722779 + 0.691079i \(0.242864\pi\)
\(374\) 12357.7 21404.1i 1.70856 2.95931i
\(375\) 0 0
\(376\) −2084.50 3610.45i −0.285903 0.495199i
\(377\) −869.613 −0.118799
\(378\) 0 0
\(379\) 598.277 0.0810855 0.0405428 0.999178i \(-0.487091\pi\)
0.0405428 + 0.999178i \(0.487091\pi\)
\(380\) −222.331 385.089i −0.0300141 0.0519860i
\(381\) 0 0
\(382\) −1530.54 + 2650.97i −0.204998 + 0.355066i
\(383\) 4528.59 7843.74i 0.604178 1.04647i −0.388003 0.921658i \(-0.626835\pi\)
0.992181 0.124808i \(-0.0398316\pi\)
\(384\) 0 0
\(385\) −2253.66 3903.45i −0.298330 0.516723i
\(386\) 6202.65 0.817893
\(387\) 0 0
\(388\) 5377.22 0.703575
\(389\) −315.703 546.814i −0.0411485 0.0712714i 0.844718 0.535212i \(-0.179768\pi\)
−0.885866 + 0.463941i \(0.846435\pi\)
\(390\) 0 0
\(391\) 6995.47 12116.5i 0.904798 1.56716i
\(392\) 820.722 1421.53i 0.105747 0.183159i
\(393\) 0 0
\(394\) 5261.68 + 9113.49i 0.672791 + 1.16531i
\(395\) 5759.27 0.733620
\(396\) 0 0
\(397\) −4615.39 −0.583475 −0.291738 0.956498i \(-0.594233\pi\)
−0.291738 + 0.956498i \(0.594233\pi\)
\(398\) −7456.66 12915.3i −0.939118 1.62660i
\(399\) 0 0
\(400\) 992.442 1718.96i 0.124055 0.214870i
\(401\) −2345.60 + 4062.69i −0.292104 + 0.505938i −0.974307 0.225224i \(-0.927689\pi\)
0.682203 + 0.731163i \(0.261022\pi\)
\(402\) 0 0
\(403\) −54.4369 94.2874i −0.00672877 0.0116546i
\(404\) −1817.03 −0.223764
\(405\) 0 0
\(406\) −4233.93 −0.517552
\(407\) 2606.67 + 4514.88i 0.317464 + 0.549863i
\(408\) 0 0
\(409\) 7781.64 13478.2i 0.940776 1.62947i 0.176781 0.984250i \(-0.443432\pi\)
0.763995 0.645222i \(-0.223235\pi\)
\(410\) −2747.53 + 4758.86i −0.330953 + 0.573228i
\(411\) 0 0
\(412\) −1825.70 3162.21i −0.218315 0.378133i
\(413\) 6546.19 0.779944
\(414\) 0 0
\(415\) 2621.60 0.310095
\(416\) 996.212 + 1725.49i 0.117412 + 0.203363i
\(417\) 0 0
\(418\) 2118.06 3668.60i 0.247842 0.429275i
\(419\) −2139.22 + 3705.23i −0.249422 + 0.432011i −0.963365 0.268192i \(-0.913574\pi\)
0.713944 + 0.700203i \(0.246907\pi\)
\(420\) 0 0
\(421\) 48.8531 + 84.6161i 0.00565548 + 0.00979558i 0.868839 0.495094i \(-0.164866\pi\)
−0.863184 + 0.504890i \(0.831533\pi\)
\(422\) −13765.8 −1.58794
\(423\) 0 0
\(424\) 6476.02 0.741753
\(425\) −1357.56 2351.37i −0.154945 0.268372i
\(426\) 0 0
\(427\) 4595.31 7959.31i 0.520802 0.902056i
\(428\) 1949.45 3376.55i 0.220164 0.381336i
\(429\) 0 0
\(430\) −1987.82 3443.00i −0.222932 0.386130i
\(431\) 11932.9 1.33361 0.666806 0.745231i \(-0.267661\pi\)
0.666806 + 0.745231i \(0.267661\pi\)
\(432\) 0 0
\(433\) 6304.32 0.699691 0.349845 0.936807i \(-0.386234\pi\)
0.349845 + 0.936807i \(0.386234\pi\)
\(434\) −265.039 459.062i −0.0293141 0.0507734i
\(435\) 0 0
\(436\) −1449.46 + 2510.54i −0.159212 + 0.275764i
\(437\) 1199.00 2076.73i 0.131249 0.227330i
\(438\) 0 0
\(439\) 6461.34 + 11191.4i 0.702466 + 1.21671i 0.967598 + 0.252495i \(0.0812512\pi\)
−0.265132 + 0.964212i \(0.585415\pi\)
\(440\) 3666.64 0.397273
\(441\) 0 0
\(442\) 4035.87 0.434314
\(443\) 1912.21 + 3312.04i 0.205083 + 0.355214i 0.950159 0.311765i \(-0.100920\pi\)
−0.745076 + 0.666979i \(0.767587\pi\)
\(444\) 0 0
\(445\) −1641.21 + 2842.66i −0.174834 + 0.302821i
\(446\) 1466.85 2540.66i 0.155734 0.269740i
\(447\) 0 0
\(448\) 353.433 + 612.163i 0.0372726 + 0.0645580i
\(449\) −530.656 −0.0557756 −0.0278878 0.999611i \(-0.508878\pi\)
−0.0278878 + 0.999611i \(0.508878\pi\)
\(450\) 0 0
\(451\) −19573.6 −2.04365
\(452\) 65.2680 + 113.048i 0.00679193 + 0.0117640i
\(453\) 0 0
\(454\) −9403.32 + 16287.0i −0.972070 + 1.68367i
\(455\) 368.008 637.409i 0.0379176 0.0656752i
\(456\) 0 0
\(457\) 7796.80 + 13504.5i 0.798072 + 1.38230i 0.920870 + 0.389870i \(0.127480\pi\)
−0.122798 + 0.992432i \(0.539187\pi\)
\(458\) −70.0577 −0.00714756
\(459\) 0 0
\(460\) −3077.34 −0.311916
\(461\) 3637.30 + 6300.00i 0.367475 + 0.636486i 0.989170 0.146774i \(-0.0468889\pi\)
−0.621695 + 0.783260i \(0.713556\pi\)
\(462\) 0 0
\(463\) −1342.57 + 2325.40i −0.134761 + 0.233413i −0.925506 0.378732i \(-0.876360\pi\)
0.790745 + 0.612146i \(0.209693\pi\)
\(464\) 3320.69 5751.61i 0.332240 0.575456i
\(465\) 0 0
\(466\) −5686.78 9849.79i −0.565311 0.979147i
\(467\) −8844.77 −0.876418 −0.438209 0.898873i \(-0.644387\pi\)
−0.438209 + 0.898873i \(0.644387\pi\)
\(468\) 0 0
\(469\) 3599.12 0.354354
\(470\) 3234.37 + 5602.09i 0.317426 + 0.549799i
\(471\) 0 0
\(472\) −2662.62 + 4611.79i −0.259655 + 0.449735i
\(473\) 7080.67 12264.1i 0.688308 1.19218i
\(474\) 0 0
\(475\) −232.682 403.017i −0.0224761 0.0389298i
\(476\) 7347.07 0.707463
\(477\) 0 0
\(478\) −5841.23 −0.558936
\(479\) −6167.17 10681.9i −0.588278 1.01893i −0.994458 0.105134i \(-0.966473\pi\)
0.406180 0.913793i \(-0.366861\pi\)
\(480\) 0 0
\(481\) −425.653 + 737.252i −0.0403495 + 0.0698873i
\(482\) 2528.49 4379.48i 0.238941 0.413858i
\(483\) 0 0
\(484\) −6502.49 11262.6i −0.610677 1.05772i
\(485\) 5627.55 0.526874
\(486\) 0 0
\(487\) 3540.31 0.329419 0.164709 0.986342i \(-0.447331\pi\)
0.164709 + 0.986342i \(0.447331\pi\)
\(488\) 3738.22 + 6474.79i 0.346765 + 0.600615i
\(489\) 0 0
\(490\) −1273.46 + 2205.69i −0.117406 + 0.203353i
\(491\) −3855.63 + 6678.14i −0.354383 + 0.613809i −0.987012 0.160646i \(-0.948642\pi\)
0.632629 + 0.774455i \(0.281976\pi\)
\(492\) 0 0
\(493\) −4542.39 7867.64i −0.414967 0.718744i
\(494\) 691.734 0.0630012
\(495\) 0 0
\(496\) 831.488 0.0752720
\(497\) 7737.77 + 13402.2i 0.698363 + 1.20960i
\(498\) 0 0
\(499\) 6081.29 10533.1i 0.545563 0.944943i −0.453008 0.891506i \(-0.649649\pi\)
0.998571 0.0534365i \(-0.0170175\pi\)
\(500\) −298.599 + 517.189i −0.0267075 + 0.0462588i
\(501\) 0 0
\(502\) 10603.1 + 18365.2i 0.942711 + 1.63282i
\(503\) −8796.85 −0.779786 −0.389893 0.920860i \(-0.627488\pi\)
−0.389893 + 0.920860i \(0.627488\pi\)
\(504\) 0 0
\(505\) −1901.62 −0.167566
\(506\) −14658.3 25388.9i −1.28783 2.23058i
\(507\) 0 0
\(508\) 2881.41 4990.76i 0.251658 0.435884i
\(509\) 10974.1 19007.7i 0.955634 1.65521i 0.222722 0.974882i \(-0.428506\pi\)
0.732911 0.680324i \(-0.238161\pi\)
\(510\) 0 0
\(511\) −7324.26 12686.0i −0.634063 1.09823i
\(512\) −7900.20 −0.681919
\(513\) 0 0
\(514\) −25026.6 −2.14762
\(515\) −1910.69 3309.42i −0.163486 0.283166i
\(516\) 0 0
\(517\) −11520.9 + 19954.9i −0.980059 + 1.69751i
\(518\) −2072.40 + 3589.50i −0.175784 + 0.304466i
\(519\) 0 0
\(520\) 299.370 + 518.524i 0.0252466 + 0.0437284i
\(521\) −11232.4 −0.944531 −0.472265 0.881456i \(-0.656564\pi\)
−0.472265 + 0.881456i \(0.656564\pi\)
\(522\) 0 0
\(523\) −1962.88 −0.164112 −0.0820560 0.996628i \(-0.526149\pi\)
−0.0820560 + 0.996628i \(0.526149\pi\)
\(524\) 3659.64 + 6338.68i 0.305100 + 0.528448i
\(525\) 0 0
\(526\) 6531.72 11313.3i 0.541438 0.937798i
\(527\) 568.697 985.013i 0.0470073 0.0814190i
\(528\) 0 0
\(529\) −2214.30 3835.28i −0.181992 0.315220i
\(530\) −10048.4 −0.823537
\(531\) 0 0
\(532\) 1259.26 0.102624
\(533\) −1598.12 2768.03i −0.129873 0.224947i
\(534\) 0 0
\(535\) 2040.21 3533.74i 0.164871 0.285565i
\(536\) −1463.92 + 2535.58i −0.117970 + 0.204329i
\(537\) 0 0
\(538\) 4628.11 + 8016.11i 0.370877 + 0.642378i
\(539\) −9072.20 −0.724986
\(540\) 0 0
\(541\) 2816.86 0.223856 0.111928 0.993716i \(-0.464297\pi\)
0.111928 + 0.993716i \(0.464297\pi\)
\(542\) 8675.67 + 15026.7i 0.687549 + 1.19087i
\(543\) 0 0
\(544\) −10407.3 + 18026.0i −0.820240 + 1.42070i
\(545\) −1516.94 + 2627.41i −0.119227 + 0.206507i
\(546\) 0 0
\(547\) −2264.45 3922.15i −0.177004 0.306579i 0.763849 0.645395i \(-0.223307\pi\)
−0.940853 + 0.338815i \(0.889974\pi\)
\(548\) 11810.8 0.920676
\(549\) 0 0
\(550\) −5689.28 −0.441076
\(551\) −778.549 1348.49i −0.0601947 0.104260i
\(552\) 0 0
\(553\) −8154.97 + 14124.8i −0.627097 + 1.08616i
\(554\) −13431.7 + 23264.5i −1.03007 + 1.78414i
\(555\) 0 0
\(556\) −28.9682 50.1744i −0.00220958 0.00382710i
\(557\) −6267.47 −0.476771 −0.238385 0.971171i \(-0.576618\pi\)
−0.238385 + 0.971171i \(0.576618\pi\)
\(558\) 0 0
\(559\) 2312.46 0.174967
\(560\) 2810.54 + 4868.01i 0.212084 + 0.367341i
\(561\) 0 0
\(562\) −6455.80 + 11181.8i −0.484558 + 0.839279i
\(563\) −4897.00 + 8481.86i −0.366579 + 0.634934i −0.989028 0.147727i \(-0.952804\pi\)
0.622449 + 0.782660i \(0.286138\pi\)
\(564\) 0 0
\(565\) 68.3065 + 118.310i 0.00508615 + 0.00880948i
\(566\) −18469.5 −1.37161
\(567\) 0 0
\(568\) −12589.2 −0.929981
\(569\) 3799.94 + 6581.69i 0.279968 + 0.484919i 0.971376 0.237545i \(-0.0763428\pi\)
−0.691409 + 0.722464i \(0.743010\pi\)
\(570\) 0 0
\(571\) 6047.07 10473.8i 0.443191 0.767630i −0.554733 0.832028i \(-0.687180\pi\)
0.997924 + 0.0643988i \(0.0205130\pi\)
\(572\) 1581.01 2738.38i 0.115568 0.200170i
\(573\) 0 0
\(574\) −7780.87 13476.9i −0.565796 0.979988i
\(575\) −3220.60 −0.233580
\(576\) 0 0
\(577\) 3113.85 0.224665 0.112332 0.993671i \(-0.464168\pi\)
0.112332 + 0.993671i \(0.464168\pi\)
\(578\) 12300.2 + 21304.7i 0.885161 + 1.53314i
\(579\) 0 0
\(580\) −999.107 + 1730.50i −0.0715270 + 0.123888i
\(581\) −3712.12 + 6429.58i −0.265068 + 0.459112i
\(582\) 0 0
\(583\) −17896.4 30997.4i −1.27134 2.20203i
\(584\) 11916.4 0.844354
\(585\) 0 0
\(586\) 15107.4 1.06499
\(587\) 2973.96 + 5151.04i 0.209111 + 0.362191i 0.951435 0.307850i \(-0.0996096\pi\)
−0.742324 + 0.670042i \(0.766276\pi\)
\(588\) 0 0
\(589\) 97.4727 168.828i 0.00681883 0.0118106i
\(590\) 4131.40 7155.80i 0.288283 0.499321i
\(591\) 0 0
\(592\) −3250.79 5630.53i −0.225687 0.390901i
\(593\) −22153.0 −1.53409 −0.767043 0.641596i \(-0.778273\pi\)
−0.767043 + 0.641596i \(0.778273\pi\)
\(594\) 0 0
\(595\) 7689.10 0.529786
\(596\) 7492.47 + 12977.3i 0.514939 + 0.891901i
\(597\) 0 0
\(598\) 2393.61 4145.85i 0.163682 0.283506i
\(599\) −13438.2 + 23275.6i −0.916643 + 1.58767i −0.112164 + 0.993690i \(0.535778\pi\)
−0.804478 + 0.593982i \(0.797555\pi\)
\(600\) 0 0
\(601\) −12920.1 22378.2i −0.876907 1.51885i −0.854717 0.519094i \(-0.826269\pi\)
−0.0221904 0.999754i \(-0.507064\pi\)
\(602\) 11258.8 0.762249
\(603\) 0 0
\(604\) −12899.8 −0.869019
\(605\) −6805.20 11787.0i −0.457307 0.792079i
\(606\) 0 0
\(607\) 1384.37 2397.80i 0.0925697 0.160335i −0.816022 0.578021i \(-0.803825\pi\)
0.908592 + 0.417685i \(0.137159\pi\)
\(608\) −1783.78 + 3089.60i −0.118983 + 0.206085i
\(609\) 0 0
\(610\) −5800.35 10046.5i −0.384999 0.666837i
\(611\) −3762.60 −0.249130
\(612\) 0 0
\(613\) 10177.3 0.670563 0.335282 0.942118i \(-0.391169\pi\)
0.335282 + 0.942118i \(0.391169\pi\)
\(614\) 10248.8 + 17751.4i 0.673626 + 1.16675i
\(615\) 0 0
\(616\) −5191.87 + 8992.58i −0.339588 + 0.588184i
\(617\) 4208.61 7289.53i 0.274607 0.475633i −0.695429 0.718595i \(-0.744786\pi\)
0.970036 + 0.242962i \(0.0781190\pi\)
\(618\) 0 0
\(619\) 6640.13 + 11501.0i 0.431162 + 0.746795i 0.996974 0.0777399i \(-0.0247704\pi\)
−0.565812 + 0.824535i \(0.691437\pi\)
\(620\) −250.172 −0.0162051
\(621\) 0 0
\(622\) −23665.1 −1.52553
\(623\) −4647.83 8050.27i −0.298895 0.517700i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 166.988 289.232i 0.0106616 0.0184665i
\(627\) 0 0
\(628\) −1057.34 1831.37i −0.0671857 0.116369i
\(629\) −8893.52 −0.563764
\(630\) 0 0
\(631\) −14454.1 −0.911903 −0.455951 0.890005i \(-0.650701\pi\)
−0.455951 + 0.890005i \(0.650701\pi\)
\(632\) −6633.96 11490.4i −0.417539 0.723199i
\(633\) 0 0
\(634\) 3562.37 6170.20i 0.223154 0.386514i
\(635\) 3015.55 5223.09i 0.188455 0.326413i
\(636\) 0 0
\(637\) −740.717 1282.96i −0.0460727 0.0798002i
\(638\) −19036.2 −1.18127
\(639\) 0 0
\(640\) −6773.96 −0.418381
\(641\) 10532.5 + 18242.8i 0.648997 + 1.12410i 0.983363 + 0.181653i \(0.0581447\pi\)
−0.334366 + 0.942443i \(0.608522\pi\)
\(642\) 0 0
\(643\) 3564.41 6173.73i 0.218610 0.378644i −0.735773 0.677228i \(-0.763181\pi\)
0.954383 + 0.298584i \(0.0965143\pi\)
\(644\) 4357.43 7547.29i 0.266625 0.461809i
\(645\) 0 0
\(646\) 3613.24 + 6258.32i 0.220064 + 0.381161i
\(647\) −1364.92 −0.0829376 −0.0414688 0.999140i \(-0.513204\pi\)
−0.0414688 + 0.999140i \(0.513204\pi\)
\(648\) 0 0
\(649\) 29432.4 1.78016
\(650\) −464.512 804.558i −0.0280302 0.0485498i
\(651\) 0 0
\(652\) 5055.39 8756.18i 0.303657 0.525949i
\(653\) 6080.31 10531.4i 0.364381 0.631127i −0.624295 0.781188i \(-0.714614\pi\)
0.988677 + 0.150061i \(0.0479471\pi\)
\(654\) 0 0
\(655\) 3830.01 + 6633.77i 0.228475 + 0.395730i
\(656\) 24410.3 1.45284
\(657\) 0 0
\(658\) −18319.1 −1.08534
\(659\) −3084.28 5342.14i −0.182317 0.315782i 0.760352 0.649511i \(-0.225026\pi\)
−0.942669 + 0.333729i \(0.891693\pi\)
\(660\) 0 0
\(661\) −9068.85 + 15707.7i −0.533642 + 0.924295i 0.465586 + 0.885003i \(0.345844\pi\)
−0.999228 + 0.0392922i \(0.987490\pi\)
\(662\) −4270.15 + 7396.11i −0.250701 + 0.434226i
\(663\) 0 0
\(664\) −3019.76 5230.38i −0.176490 0.305690i
\(665\) 1317.89 0.0768502
\(666\) 0 0
\(667\) −10776.1 −0.625564
\(668\) −3092.59 5356.52i −0.179125 0.310254i
\(669\) 0 0
\(670\) 2271.46 3934.29i 0.130977 0.226858i
\(671\) 20661.0 35786.0i 1.18869 2.05887i
\(672\) 0 0
\(673\) 10851.1 + 18794.6i 0.621512 + 1.07649i 0.989204 + 0.146543i \(0.0468148\pi\)
−0.367692 + 0.929948i \(0.619852\pi\)
\(674\) −36766.3 −2.10116
\(675\) 0 0
\(676\) −9980.02 −0.567821
\(677\) −5235.29 9067.79i −0.297206 0.514776i 0.678290 0.734795i \(-0.262721\pi\)
−0.975496 + 0.220019i \(0.929388\pi\)
\(678\) 0 0
\(679\) −7968.47 + 13801.8i −0.450371 + 0.780065i
\(680\) −3127.49 + 5416.97i −0.176373 + 0.305487i
\(681\) 0 0
\(682\) −1191.65 2063.99i −0.0669070 0.115886i
\(683\) 15386.0 0.861974 0.430987 0.902358i \(-0.358166\pi\)
0.430987 + 0.902358i \(0.358166\pi\)
\(684\) 0 0
\(685\) 12360.6 0.689451
\(686\) −12286.8 21281.4i −0.683840 1.18445i
\(687\) 0 0
\(688\) −8830.33 + 15294.6i −0.489321 + 0.847529i
\(689\) 2922.37 5061.69i 0.161587 0.279876i
\(690\) 0 0
\(691\) −7595.57 13155.9i −0.418161 0.724276i 0.577594 0.816324i \(-0.303992\pi\)
−0.995755 + 0.0920487i \(0.970658\pi\)
\(692\) 13960.9 0.766929
\(693\) 0 0
\(694\) −15121.2 −0.827079
\(695\) −30.3168 52.5102i −0.00165465 0.00286594i
\(696\) 0 0
\(697\) 16695.5 28917.4i 0.907297 1.57148i
\(698\) −20037.1 + 34705.3i −1.08656 + 1.88197i
\(699\) 0 0
\(700\) −845.617 1464.65i −0.0456590 0.0790838i
\(701\) 5181.93 0.279199 0.139600 0.990208i \(-0.455418\pi\)
0.139600 + 0.990208i \(0.455418\pi\)
\(702\) 0 0
\(703\) −1524.32 −0.0817791
\(704\) 1589.07 + 2752.36i 0.0850717 + 0.147348i
\(705\) 0 0
\(706\) −20344.7 + 35238.1i −1.08454 + 1.87847i
\(707\) 2692.65 4663.80i 0.143235 0.248091i
\(708\) 0 0
\(709\) 4393.27 + 7609.36i 0.232712 + 0.403069i 0.958605 0.284739i \(-0.0919068\pi\)
−0.725893 + 0.687807i \(0.758573\pi\)
\(710\) 19533.7 1.03252
\(711\) 0 0
\(712\) 7561.89 0.398025
\(713\) −674.570 1168.39i −0.0354318 0.0613696i
\(714\) 0 0
\(715\) 1654.61 2865.86i 0.0865438 0.149898i
\(716\) −9448.89 + 16366.0i −0.493187 + 0.854224i
\(717\) 0 0
\(718\) 15983.0 + 27683.3i 0.830750 + 1.43890i
\(719\) 14433.0 0.748625 0.374312 0.927303i \(-0.377879\pi\)
0.374312 + 0.927303i \(0.377879\pi\)
\(720\) 0 0
\(721\) 10822.0 0.558989
\(722\) −11639.7 20160.6i −0.599979 1.03919i
\(723\) 0 0
\(724\) 6435.41 11146.5i 0.330345 0.572175i
\(725\) −1045.62 + 1811.07i −0.0535632 + 0.0927742i
\(726\) 0 0
\(727\) −13349.5 23121.9i −0.681023 1.17957i −0.974669 0.223653i \(-0.928202\pi\)
0.293646 0.955914i \(-0.405131\pi\)
\(728\) −1695.60 −0.0863230
\(729\) 0 0
\(730\) −18489.8 −0.937451
\(731\) 12079.0 + 20921.5i 0.611161 + 1.05856i
\(732\) 0 0
\(733\) 3866.92 6697.71i 0.194854 0.337497i −0.751999 0.659165i \(-0.770910\pi\)
0.946853 + 0.321668i \(0.104243\pi\)
\(734\) −793.859 + 1375.00i −0.0399208 + 0.0691449i
\(735\) 0 0
\(736\) 12344.8 + 21381.9i 0.618257 + 1.07085i
\(737\) 16182.1 0.808784
\(738\) 0 0
\(739\) 28142.2 1.40085 0.700426 0.713725i \(-0.252994\pi\)
0.700426 + 0.713725i \(0.252994\pi\)
\(740\) 978.074 + 1694.07i 0.0485874 + 0.0841559i
\(741\) 0 0
\(742\) 14228.3 24644.1i 0.703957 1.21929i
\(743\) 11384.6 19718.6i 0.562125 0.973629i −0.435186 0.900341i \(-0.643317\pi\)
0.997311 0.0732884i \(-0.0233493\pi\)
\(744\) 0 0
\(745\) 7841.28 + 13581.5i 0.385614 + 0.667902i
\(746\) −12211.1 −0.599302
\(747\) 0 0
\(748\) 33033.3 1.61473
\(749\) 5777.76 + 10007.4i 0.281862 + 0.488200i
\(750\) 0 0
\(751\) −254.918 + 441.531i −0.0123863 + 0.0214537i −0.872152 0.489235i \(-0.837276\pi\)
0.859766 + 0.510688i \(0.170609\pi\)
\(752\) 14367.8 24885.8i 0.696729 1.20677i
\(753\) 0 0
\(754\) −1554.25 2692.04i −0.0750695 0.130024i
\(755\) −13500.4 −0.650767
\(756\) 0 0
\(757\) −28105.6 −1.34943 −0.674713 0.738080i \(-0.735733\pi\)
−0.674713 + 0.738080i \(0.735733\pi\)
\(758\) 1069.29 + 1852.07i 0.0512381 + 0.0887469i
\(759\) 0 0
\(760\) −536.041 + 928.450i −0.0255845 + 0.0443137i
\(761\) 4347.82 7530.64i 0.207107 0.358720i −0.743695 0.668519i \(-0.766929\pi\)
0.950802 + 0.309799i \(0.100262\pi\)
\(762\) 0 0
\(763\) −4295.89 7440.70i −0.203829 0.353043i
\(764\) −4091.27 −0.193739
\(765\) 0 0
\(766\) 32375.5 1.52712
\(767\) 2403.06 + 4162.23i 0.113129 + 0.195945i
\(768\) 0 0
\(769\) −2730.93 + 4730.12i −0.128062 + 0.221811i −0.922926 0.384978i \(-0.874209\pi\)
0.794863 + 0.606788i \(0.207542\pi\)
\(770\) 8055.87 13953.2i 0.377030 0.653036i
\(771\) 0 0
\(772\) 4145.06 + 7179.46i 0.193244 + 0.334708i
\(773\) −37952.9 −1.76594 −0.882970 0.469430i \(-0.844459\pi\)
−0.882970 + 0.469430i \(0.844459\pi\)
\(774\) 0 0
\(775\) −261.819 −0.0121352
\(776\) −6482.24 11227.6i −0.299870 0.519390i
\(777\) 0 0
\(778\) 1128.50 1954.63i 0.0520037 0.0900730i
\(779\) 2861.55 4956.34i 0.131612 0.227958i
\(780\) 0 0
\(781\) 34789.9 + 60257.9i 1.59396 + 2.76082i
\(782\) 50011.7 2.28697
\(783\) 0 0
\(784\) 11314.0 0.515396