Properties

Label 405.4.e.s.136.1
Level $405$
Weight $4$
Character 405.136
Analytic conductor $23.896$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.148347072.2
Defining polynomial: \( x^{6} + 29x^{4} + 223x^{2} + 243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.1
Root \(4.00586i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.4.e.s.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.76174 + 3.05142i) q^{2} +(-2.20744 - 3.82340i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-12.7162 + 22.0252i) q^{7} -12.6321 q^{8} +O(q^{10})\) \(q+(-1.76174 + 3.05142i) q^{2} +(-2.20744 - 3.82340i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-12.7162 + 22.0252i) q^{7} -12.6321 q^{8} -17.6174 q^{10} +(-35.6781 + 61.7962i) q^{11} +(25.6968 + 44.5081i) q^{13} +(-44.8053 - 77.6051i) q^{14} +(39.9139 - 69.1330i) q^{16} +33.3191 q^{17} +113.372 q^{19} +(11.0372 - 19.1170i) q^{20} +(-125.711 - 217.738i) q^{22} +(40.9884 + 70.9939i) q^{23} +(-12.5000 + 21.6506i) q^{25} -181.084 q^{26} +112.281 q^{28} +(-123.414 + 213.759i) q^{29} +(-111.340 - 192.846i) q^{31} +(90.1075 + 156.071i) q^{32} +(-58.6995 + 101.671i) q^{34} -127.162 q^{35} +22.3910 q^{37} +(-199.731 + 345.945i) q^{38} +(-31.5802 - 54.6985i) q^{40} +(-217.113 - 376.050i) q^{41} +(118.425 - 205.118i) q^{43} +315.029 q^{44} -288.843 q^{46} +(-53.9919 + 93.5166i) q^{47} +(-151.905 - 263.107i) q^{49} +(-44.0435 - 76.2855i) q^{50} +(113.448 - 196.498i) q^{52} +123.961 q^{53} -356.781 q^{55} +(160.632 - 278.223i) q^{56} +(-434.845 - 753.174i) q^{58} +(85.5454 + 148.169i) q^{59} +(39.7196 - 68.7963i) q^{61} +784.604 q^{62} +3.63945 q^{64} +(-128.484 + 222.540i) q^{65} +(305.753 + 529.580i) q^{67} +(-73.5500 - 127.392i) q^{68} +(224.027 - 388.026i) q^{70} -511.102 q^{71} -410.012 q^{73} +(-39.4471 + 68.3243i) q^{74} +(-250.262 - 433.466i) q^{76} +(-907.381 - 1571.63i) q^{77} +(396.798 - 687.275i) q^{79} +399.139 q^{80} +1529.98 q^{82} +(135.040 - 233.897i) q^{83} +(83.2977 + 144.276i) q^{85} +(417.267 + 722.727i) q^{86} +(450.688 - 780.614i) q^{88} -177.400 q^{89} -1307.06 q^{91} +(180.959 - 313.430i) q^{92} +(-190.239 - 329.504i) q^{94} +(283.430 + 490.914i) q^{95} +(440.930 - 763.714i) q^{97} +1070.47 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 5 q^{4} + 15 q^{5} + 25 q^{7} - 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 5 q^{4} + 15 q^{5} + 25 q^{7} - 54 q^{8} - 10 q^{10} - 58 q^{11} + 47 q^{13} - 159 q^{14} + 127 q^{16} + 68 q^{17} - 10 q^{19} + 25 q^{20} - 260 q^{22} + 51 q^{23} - 75 q^{25} + 506 q^{26} + 166 q^{28} - 350 q^{29} - 638 q^{31} - 245 q^{32} + 154 q^{34} + 250 q^{35} - 828 q^{37} - 397 q^{38} - 135 q^{40} - 179 q^{41} + 836 q^{43} + 664 q^{44} + 522 q^{46} - 235 q^{47} - 892 q^{49} - 25 q^{50} + 1335 q^{52} + 1010 q^{53} - 580 q^{55} - 15 q^{56} - 1876 q^{58} - 535 q^{59} + 104 q^{61} + 696 q^{62} - 606 q^{64} - 235 q^{65} + 40 q^{67} - 830 q^{68} + 795 q^{70} + 904 q^{71} - 1420 q^{73} - 1394 q^{74} - 849 q^{76} - 2148 q^{77} + 634 q^{79} + 1270 q^{80} + 1226 q^{82} - 1734 q^{83} + 170 q^{85} - 460 q^{86} + 768 q^{88} - 1704 q^{89} - 2458 q^{91} + 1839 q^{92} - 1751 q^{94} - 25 q^{95} + 76 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76174 + 3.05142i −0.622868 + 1.07884i 0.366080 + 0.930583i \(0.380700\pi\)
−0.988949 + 0.148257i \(0.952634\pi\)
\(3\) 0 0
\(4\) −2.20744 3.82340i −0.275930 0.477925i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −12.7162 + 22.0252i −0.686612 + 1.18925i 0.286315 + 0.958135i \(0.407570\pi\)
−0.972927 + 0.231111i \(0.925764\pi\)
\(8\) −12.6321 −0.558264
\(9\) 0 0
\(10\) −17.6174 −0.557111
\(11\) −35.6781 + 61.7962i −0.977940 + 1.69384i −0.308071 + 0.951363i \(0.599683\pi\)
−0.669870 + 0.742479i \(0.733650\pi\)
\(12\) 0 0
\(13\) 25.6968 + 44.5081i 0.548231 + 0.949563i 0.998396 + 0.0566179i \(0.0180317\pi\)
−0.450165 + 0.892945i \(0.648635\pi\)
\(14\) −44.8053 77.6051i −0.855338 1.48149i
\(15\) 0 0
\(16\) 39.9139 69.1330i 0.623655 1.08020i
\(17\) 33.3191 0.475357 0.237678 0.971344i \(-0.423614\pi\)
0.237678 + 0.971344i \(0.423614\pi\)
\(18\) 0 0
\(19\) 113.372 1.36891 0.684455 0.729055i \(-0.260040\pi\)
0.684455 + 0.729055i \(0.260040\pi\)
\(20\) 11.0372 19.1170i 0.123400 0.213735i
\(21\) 0 0
\(22\) −125.711 217.738i −1.21826 2.11008i
\(23\) 40.9884 + 70.9939i 0.371594 + 0.643620i 0.989811 0.142388i \(-0.0454780\pi\)
−0.618217 + 0.786008i \(0.712145\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −181.084 −1.36590
\(27\) 0 0
\(28\) 112.281 0.757828
\(29\) −123.414 + 213.759i −0.790253 + 1.36876i 0.135557 + 0.990770i \(0.456718\pi\)
−0.925810 + 0.377989i \(0.876616\pi\)
\(30\) 0 0
\(31\) −111.340 192.846i −0.645070 1.11729i −0.984285 0.176585i \(-0.943495\pi\)
0.339215 0.940709i \(-0.389838\pi\)
\(32\) 90.1075 + 156.071i 0.497779 + 0.862178i
\(33\) 0 0
\(34\) −58.6995 + 101.671i −0.296085 + 0.512834i
\(35\) −127.162 −0.614124
\(36\) 0 0
\(37\) 22.3910 0.0994880 0.0497440 0.998762i \(-0.484159\pi\)
0.0497440 + 0.998762i \(0.484159\pi\)
\(38\) −199.731 + 345.945i −0.852651 + 1.47683i
\(39\) 0 0
\(40\) −31.5802 54.6985i −0.124832 0.216215i
\(41\) −217.113 376.050i −0.827007 1.43242i −0.900375 0.435114i \(-0.856708\pi\)
0.0733680 0.997305i \(-0.476625\pi\)
\(42\) 0 0
\(43\) 118.425 205.118i 0.419991 0.727446i −0.575947 0.817487i \(-0.695367\pi\)
0.995938 + 0.0900414i \(0.0286999\pi\)
\(44\) 315.029 1.07937
\(45\) 0 0
\(46\) −288.843 −0.925817
\(47\) −53.9919 + 93.5166i −0.167564 + 0.290230i −0.937563 0.347816i \(-0.886924\pi\)
0.769999 + 0.638046i \(0.220257\pi\)
\(48\) 0 0
\(49\) −151.905 263.107i −0.442872 0.767077i
\(50\) −44.0435 76.2855i −0.124574 0.215768i
\(51\) 0 0
\(52\) 113.448 196.498i 0.302547 0.524027i
\(53\) 123.961 0.321272 0.160636 0.987014i \(-0.448646\pi\)
0.160636 + 0.987014i \(0.448646\pi\)
\(54\) 0 0
\(55\) −356.781 −0.874696
\(56\) 160.632 278.223i 0.383311 0.663913i
\(57\) 0 0
\(58\) −434.845 753.174i −0.984447 1.70511i
\(59\) 85.5454 + 148.169i 0.188764 + 0.326949i 0.944838 0.327537i \(-0.106219\pi\)
−0.756074 + 0.654486i \(0.772885\pi\)
\(60\) 0 0
\(61\) 39.7196 68.7963i 0.0833700 0.144401i −0.821325 0.570460i \(-0.806765\pi\)
0.904695 + 0.426059i \(0.140098\pi\)
\(62\) 784.604 1.60717
\(63\) 0 0
\(64\) 3.63945 0.00710830
\(65\) −128.484 + 222.540i −0.245176 + 0.424658i
\(66\) 0 0
\(67\) 305.753 + 529.580i 0.557517 + 0.965648i 0.997703 + 0.0677416i \(0.0215793\pi\)
−0.440186 + 0.897907i \(0.645087\pi\)
\(68\) −73.5500 127.392i −0.131165 0.227185i
\(69\) 0 0
\(70\) 224.027 388.026i 0.382519 0.662542i
\(71\) −511.102 −0.854318 −0.427159 0.904176i \(-0.640486\pi\)
−0.427159 + 0.904176i \(0.640486\pi\)
\(72\) 0 0
\(73\) −410.012 −0.657373 −0.328686 0.944439i \(-0.606606\pi\)
−0.328686 + 0.944439i \(0.606606\pi\)
\(74\) −39.4471 + 68.3243i −0.0619680 + 0.107332i
\(75\) 0 0
\(76\) −250.262 433.466i −0.377724 0.654236i
\(77\) −907.381 1571.63i −1.34293 2.32602i
\(78\) 0 0
\(79\) 396.798 687.275i 0.565105 0.978791i −0.431935 0.901905i \(-0.642169\pi\)
0.997040 0.0768858i \(-0.0244977\pi\)
\(80\) 399.139 0.557814
\(81\) 0 0
\(82\) 1529.98 2.06047
\(83\) 135.040 233.897i 0.178586 0.309319i −0.762811 0.646622i \(-0.776181\pi\)
0.941396 + 0.337302i \(0.109514\pi\)
\(84\) 0 0
\(85\) 83.2977 + 144.276i 0.106293 + 0.184105i
\(86\) 417.267 + 722.727i 0.523198 + 0.906206i
\(87\) 0 0
\(88\) 450.688 780.614i 0.545949 0.945611i
\(89\) −177.400 −0.211284 −0.105642 0.994404i \(-0.533690\pi\)
−0.105642 + 0.994404i \(0.533690\pi\)
\(90\) 0 0
\(91\) −1307.06 −1.50569
\(92\) 180.959 313.430i 0.205068 0.355188i
\(93\) 0 0
\(94\) −190.239 329.504i −0.208741 0.361550i
\(95\) 283.430 + 490.914i 0.306097 + 0.530176i
\(96\) 0 0
\(97\) 440.930 763.714i 0.461543 0.799416i −0.537495 0.843267i \(-0.680629\pi\)
0.999038 + 0.0438508i \(0.0139626\pi\)
\(98\) 1070.47 1.10340
\(99\) 0 0
\(100\) 110.372 0.110372
\(101\) 513.017 888.572i 0.505417 0.875408i −0.494563 0.869142i \(-0.664672\pi\)
0.999980 0.00626636i \(-0.00199466\pi\)
\(102\) 0 0
\(103\) 895.139 + 1550.43i 0.856317 + 1.48318i 0.875418 + 0.483367i \(0.160586\pi\)
−0.0191010 + 0.999818i \(0.506080\pi\)
\(104\) −324.603 562.229i −0.306057 0.530107i
\(105\) 0 0
\(106\) −218.387 + 378.258i −0.200110 + 0.346601i
\(107\) 2007.30 1.81358 0.906788 0.421587i \(-0.138527\pi\)
0.906788 + 0.421587i \(0.138527\pi\)
\(108\) 0 0
\(109\) −211.654 −0.185989 −0.0929945 0.995667i \(-0.529644\pi\)
−0.0929945 + 0.995667i \(0.529644\pi\)
\(110\) 628.554 1088.69i 0.544821 0.943657i
\(111\) 0 0
\(112\) 1015.11 + 1758.22i 0.856418 + 1.48336i
\(113\) 0.972457 + 1.68434i 0.000809567 + 0.00140221i 0.866430 0.499299i \(-0.166409\pi\)
−0.865620 + 0.500701i \(0.833076\pi\)
\(114\) 0 0
\(115\) −204.942 + 354.970i −0.166182 + 0.287836i
\(116\) 1089.71 0.872219
\(117\) 0 0
\(118\) −602.835 −0.470300
\(119\) −423.693 + 733.858i −0.326386 + 0.565316i
\(120\) 0 0
\(121\) −1880.35 3256.86i −1.41273 2.44693i
\(122\) 139.951 + 242.402i 0.103857 + 0.179886i
\(123\) 0 0
\(124\) −491.551 + 851.392i −0.355989 + 0.616590i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1178.02 −0.823089 −0.411544 0.911390i \(-0.635011\pi\)
−0.411544 + 0.911390i \(0.635011\pi\)
\(128\) −727.272 + 1259.67i −0.502206 + 0.869846i
\(129\) 0 0
\(130\) −452.709 784.116i −0.305425 0.529012i
\(131\) 260.609 + 451.388i 0.173813 + 0.301053i 0.939750 0.341863i \(-0.111058\pi\)
−0.765937 + 0.642916i \(0.777725\pi\)
\(132\) 0 0
\(133\) −1441.66 + 2497.03i −0.939910 + 1.62797i
\(134\) −2154.63 −1.38904
\(135\) 0 0
\(136\) −420.889 −0.265374
\(137\) −224.766 + 389.306i −0.140168 + 0.242778i −0.927560 0.373675i \(-0.878098\pi\)
0.787392 + 0.616453i \(0.211431\pi\)
\(138\) 0 0
\(139\) 1172.72 + 2031.22i 0.715605 + 1.23946i 0.962726 + 0.270480i \(0.0871823\pi\)
−0.247121 + 0.968985i \(0.579484\pi\)
\(140\) 280.704 + 486.193i 0.169456 + 0.293506i
\(141\) 0 0
\(142\) 900.427 1559.59i 0.532128 0.921673i
\(143\) −3667.24 −2.14455
\(144\) 0 0
\(145\) −1234.14 −0.706824
\(146\) 722.333 1251.12i 0.409457 0.709200i
\(147\) 0 0
\(148\) −49.4268 85.6098i −0.0274518 0.0475478i
\(149\) −634.691 1099.32i −0.348966 0.604427i 0.637100 0.770781i \(-0.280134\pi\)
−0.986066 + 0.166354i \(0.946800\pi\)
\(150\) 0 0
\(151\) −1079.16 + 1869.16i −0.581594 + 1.00735i 0.413697 + 0.910415i \(0.364237\pi\)
−0.995291 + 0.0969350i \(0.969096\pi\)
\(152\) −1432.12 −0.764213
\(153\) 0 0
\(154\) 6394.27 3.34588
\(155\) 556.698 964.228i 0.288484 0.499669i
\(156\) 0 0
\(157\) 1171.65 + 2029.36i 0.595593 + 1.03160i 0.993463 + 0.114156i \(0.0364164\pi\)
−0.397869 + 0.917442i \(0.630250\pi\)
\(158\) 1398.11 + 2421.60i 0.703972 + 1.21932i
\(159\) 0 0
\(160\) −450.538 + 780.354i −0.222613 + 0.385578i
\(161\) −2084.87 −1.02056
\(162\) 0 0
\(163\) 3399.94 1.63376 0.816882 0.576804i \(-0.195700\pi\)
0.816882 + 0.576804i \(0.195700\pi\)
\(164\) −958.528 + 1660.22i −0.456393 + 0.790496i
\(165\) 0 0
\(166\) 475.812 + 824.130i 0.222471 + 0.385331i
\(167\) −904.608 1566.83i −0.419166 0.726017i 0.576690 0.816963i \(-0.304344\pi\)
−0.995856 + 0.0909465i \(0.971011\pi\)
\(168\) 0 0
\(169\) −222.146 + 384.769i −0.101113 + 0.175134i
\(170\) −586.995 −0.264826
\(171\) 0 0
\(172\) −1045.66 −0.463553
\(173\) −663.704 + 1149.57i −0.291679 + 0.505203i −0.974207 0.225657i \(-0.927547\pi\)
0.682528 + 0.730860i \(0.260881\pi\)
\(174\) 0 0
\(175\) −317.906 550.629i −0.137322 0.237849i
\(176\) 2848.10 + 4933.06i 1.21980 + 2.11275i
\(177\) 0 0
\(178\) 312.531 541.320i 0.131602 0.227942i
\(179\) 448.734 0.187374 0.0936871 0.995602i \(-0.470135\pi\)
0.0936871 + 0.995602i \(0.470135\pi\)
\(180\) 0 0
\(181\) −3450.55 −1.41700 −0.708502 0.705709i \(-0.750629\pi\)
−0.708502 + 0.705709i \(0.750629\pi\)
\(182\) 2302.70 3988.40i 0.937845 1.62439i
\(183\) 0 0
\(184\) −517.768 896.800i −0.207448 0.359310i
\(185\) 55.9775 + 96.9559i 0.0222462 + 0.0385315i
\(186\) 0 0
\(187\) −1188.76 + 2058.99i −0.464870 + 0.805179i
\(188\) 476.736 0.184944
\(189\) 0 0
\(190\) −1997.31 −0.762634
\(191\) −796.047 + 1378.79i −0.301570 + 0.522335i −0.976492 0.215554i \(-0.930844\pi\)
0.674922 + 0.737890i \(0.264177\pi\)
\(192\) 0 0
\(193\) −221.650 383.908i −0.0826668 0.143183i 0.821728 0.569880i \(-0.193010\pi\)
−0.904395 + 0.426697i \(0.859677\pi\)
\(194\) 1553.61 + 2690.93i 0.574961 + 0.995862i
\(195\) 0 0
\(196\) −670.644 + 1161.59i −0.244404 + 0.423320i
\(197\) 208.992 0.0755839 0.0377919 0.999286i \(-0.487968\pi\)
0.0377919 + 0.999286i \(0.487968\pi\)
\(198\) 0 0
\(199\) −479.916 −0.170957 −0.0854783 0.996340i \(-0.527242\pi\)
−0.0854783 + 0.996340i \(0.527242\pi\)
\(200\) 157.901 273.492i 0.0558264 0.0966941i
\(201\) 0 0
\(202\) 1807.60 + 3130.86i 0.629617 + 1.09053i
\(203\) −3138.71 5436.41i −1.08519 1.87961i
\(204\) 0 0
\(205\) 1085.56 1880.25i 0.369849 0.640597i
\(206\) −6308.00 −2.13349
\(207\) 0 0
\(208\) 4102.63 1.36763
\(209\) −4044.89 + 7005.95i −1.33871 + 2.31872i
\(210\) 0 0
\(211\) 1316.07 + 2279.50i 0.429393 + 0.743731i 0.996819 0.0796934i \(-0.0253941\pi\)
−0.567426 + 0.823424i \(0.692061\pi\)
\(212\) −273.638 473.954i −0.0886486 0.153544i
\(213\) 0 0
\(214\) −3536.33 + 6125.10i −1.12962 + 1.95656i
\(215\) 1184.25 0.375651
\(216\) 0 0
\(217\) 5663.28 1.77165
\(218\) 372.879 645.846i 0.115847 0.200652i
\(219\) 0 0
\(220\) 787.573 + 1364.12i 0.241355 + 0.418040i
\(221\) 856.192 + 1482.97i 0.260605 + 0.451381i
\(222\) 0 0
\(223\) −1676.61 + 2903.97i −0.503471 + 0.872038i 0.496521 + 0.868025i \(0.334611\pi\)
−0.999992 + 0.00401278i \(0.998723\pi\)
\(224\) −4583.31 −1.36712
\(225\) 0 0
\(226\) −6.85286 −0.00201701
\(227\) 345.382 598.219i 0.100986 0.174913i −0.811105 0.584900i \(-0.801134\pi\)
0.912091 + 0.409988i \(0.134467\pi\)
\(228\) 0 0
\(229\) 334.066 + 578.619i 0.0964003 + 0.166970i 0.910192 0.414186i \(-0.135934\pi\)
−0.813792 + 0.581156i \(0.802600\pi\)
\(230\) −722.108 1250.73i −0.207019 0.358567i
\(231\) 0 0
\(232\) 1558.97 2700.21i 0.441170 0.764128i
\(233\) 940.537 0.264449 0.132225 0.991220i \(-0.457788\pi\)
0.132225 + 0.991220i \(0.457788\pi\)
\(234\) 0 0
\(235\) −539.919 −0.149874
\(236\) 377.673 654.149i 0.104171 0.180430i
\(237\) 0 0
\(238\) −1492.87 2585.73i −0.406591 0.704236i
\(239\) 553.702 + 959.039i 0.149858 + 0.259561i 0.931175 0.364573i \(-0.118785\pi\)
−0.781317 + 0.624134i \(0.785452\pi\)
\(240\) 0 0
\(241\) −614.431 + 1064.23i −0.164228 + 0.284451i −0.936381 0.350985i \(-0.885847\pi\)
0.772153 + 0.635437i \(0.219180\pi\)
\(242\) 13250.7 3.51979
\(243\) 0 0
\(244\) −350.715 −0.0920172
\(245\) 759.526 1315.54i 0.198058 0.343047i
\(246\) 0 0
\(247\) 2913.29 + 5045.96i 0.750478 + 1.29987i
\(248\) 1406.45 + 2436.04i 0.360119 + 0.623745i
\(249\) 0 0
\(250\) 220.217 381.427i 0.0557111 0.0964944i
\(251\) −738.480 −0.185707 −0.0928534 0.995680i \(-0.529599\pi\)
−0.0928534 + 0.995680i \(0.529599\pi\)
\(252\) 0 0
\(253\) −5849.54 −1.45359
\(254\) 2075.36 3594.63i 0.512676 0.887981i
\(255\) 0 0
\(256\) −2547.97 4413.21i −0.622062 1.07744i
\(257\) 3156.28 + 5466.84i 0.766084 + 1.32690i 0.939672 + 0.342078i \(0.111131\pi\)
−0.173588 + 0.984818i \(0.555536\pi\)
\(258\) 0 0
\(259\) −284.729 + 493.165i −0.0683097 + 0.118316i
\(260\) 1134.48 0.270606
\(261\) 0 0
\(262\) −1836.50 −0.433051
\(263\) 2996.81 5190.62i 0.702628 1.21699i −0.264913 0.964272i \(-0.585343\pi\)
0.967541 0.252715i \(-0.0813234\pi\)
\(264\) 0 0
\(265\) 309.903 + 536.768i 0.0718385 + 0.124428i
\(266\) −5079.66 8798.24i −1.17088 2.02802i
\(267\) 0 0
\(268\) 1349.86 2338.03i 0.307672 0.532903i
\(269\) 1749.70 0.396584 0.198292 0.980143i \(-0.436461\pi\)
0.198292 + 0.980143i \(0.436461\pi\)
\(270\) 0 0
\(271\) −1931.68 −0.432994 −0.216497 0.976283i \(-0.569463\pi\)
−0.216497 + 0.976283i \(0.569463\pi\)
\(272\) 1329.90 2303.45i 0.296459 0.513482i
\(273\) 0 0
\(274\) −791.957 1371.71i −0.174613 0.302438i
\(275\) −891.952 1544.91i −0.195588 0.338768i
\(276\) 0 0
\(277\) 1895.77 3283.58i 0.411213 0.712242i −0.583809 0.811891i \(-0.698438\pi\)
0.995023 + 0.0996484i \(0.0317718\pi\)
\(278\) −8264.13 −1.78291
\(279\) 0 0
\(280\) 1606.32 0.342843
\(281\) 2244.68 3887.90i 0.476536 0.825384i −0.523103 0.852269i \(-0.675226\pi\)
0.999639 + 0.0268857i \(0.00855902\pi\)
\(282\) 0 0
\(283\) −1566.93 2714.00i −0.329132 0.570073i 0.653208 0.757179i \(-0.273423\pi\)
−0.982340 + 0.187105i \(0.940089\pi\)
\(284\) 1128.23 + 1954.15i 0.235732 + 0.408300i
\(285\) 0 0
\(286\) 6460.72 11190.3i 1.33577 2.31362i
\(287\) 11043.4 2.27133
\(288\) 0 0
\(289\) −3802.84 −0.774036
\(290\) 2174.22 3765.87i 0.440258 0.762550i
\(291\) 0 0
\(292\) 905.077 + 1567.64i 0.181389 + 0.314175i
\(293\) 1398.75 + 2422.71i 0.278894 + 0.483058i 0.971110 0.238632i \(-0.0766990\pi\)
−0.692216 + 0.721690i \(0.743366\pi\)
\(294\) 0 0
\(295\) −427.727 + 740.845i −0.0844178 + 0.146216i
\(296\) −282.845 −0.0555406
\(297\) 0 0
\(298\) 4472.64 0.869439
\(299\) −2106.54 + 3648.63i −0.407438 + 0.705704i
\(300\) 0 0
\(301\) 3011.83 + 5216.65i 0.576742 + 0.998946i
\(302\) −3802.39 6585.93i −0.724513 1.25489i
\(303\) 0 0
\(304\) 4525.12 7837.73i 0.853728 1.47870i
\(305\) 397.196 0.0745684
\(306\) 0 0
\(307\) −6839.91 −1.27158 −0.635789 0.771863i \(-0.719325\pi\)
−0.635789 + 0.771863i \(0.719325\pi\)
\(308\) −4005.98 + 6938.57i −0.741111 + 1.28364i
\(309\) 0 0
\(310\) 1961.51 + 3397.44i 0.359375 + 0.622456i
\(311\) 1209.70 + 2095.27i 0.220566 + 0.382032i 0.954980 0.296670i \(-0.0958762\pi\)
−0.734414 + 0.678702i \(0.762543\pi\)
\(312\) 0 0
\(313\) −1951.59 + 3380.25i −0.352429 + 0.610425i −0.986674 0.162707i \(-0.947978\pi\)
0.634245 + 0.773132i \(0.281311\pi\)
\(314\) −8256.59 −1.48391
\(315\) 0 0
\(316\) −3503.64 −0.623718
\(317\) 4947.36 8569.09i 0.876567 1.51826i 0.0214825 0.999769i \(-0.493161\pi\)
0.855084 0.518489i \(-0.173505\pi\)
\(318\) 0 0
\(319\) −8806.32 15253.0i −1.54564 2.67713i
\(320\) 9.09863 + 15.7593i 0.00158946 + 0.00275303i
\(321\) 0 0
\(322\) 3673.00 6361.81i 0.635677 1.10102i
\(323\) 3777.44 0.650720
\(324\) 0 0
\(325\) −1284.84 −0.219292
\(326\) −5989.80 + 10374.6i −1.01762 + 1.76257i
\(327\) 0 0
\(328\) 2742.58 + 4750.29i 0.461688 + 0.799668i
\(329\) −1373.15 2378.36i −0.230103 0.398551i
\(330\) 0 0
\(331\) −2081.52 + 3605.30i −0.345651 + 0.598686i −0.985472 0.169839i \(-0.945675\pi\)
0.639820 + 0.768524i \(0.279009\pi\)
\(332\) −1192.38 −0.197109
\(333\) 0 0
\(334\) 6374.73 1.04434
\(335\) −1528.76 + 2647.90i −0.249329 + 0.431851i
\(336\) 0 0
\(337\) −4852.47 8404.72i −0.784364 1.35856i −0.929378 0.369129i \(-0.879656\pi\)
0.145014 0.989430i \(-0.453677\pi\)
\(338\) −782.727 1355.72i −0.125961 0.218170i
\(339\) 0 0
\(340\) 367.750 636.961i 0.0586589 0.101600i
\(341\) 15889.5 2.52336
\(342\) 0 0
\(343\) −996.691 −0.156899
\(344\) −1495.95 + 2591.06i −0.234466 + 0.406107i
\(345\) 0 0
\(346\) −2338.55 4050.48i −0.363355 0.629350i
\(347\) −2716.19 4704.58i −0.420210 0.727825i 0.575750 0.817626i \(-0.304710\pi\)
−0.995960 + 0.0898011i \(0.971377\pi\)
\(348\) 0 0
\(349\) −5285.97 + 9155.57i −0.810749 + 1.40426i 0.101592 + 0.994826i \(0.467607\pi\)
−0.912341 + 0.409432i \(0.865727\pi\)
\(350\) 2240.27 0.342135
\(351\) 0 0
\(352\) −12859.5 −1.94719
\(353\) −4821.49 + 8351.07i −0.726975 + 1.25916i 0.231181 + 0.972911i \(0.425741\pi\)
−0.958156 + 0.286247i \(0.907592\pi\)
\(354\) 0 0
\(355\) −1277.75 2213.13i −0.191031 0.330876i
\(356\) 391.599 + 678.270i 0.0582998 + 0.100978i
\(357\) 0 0
\(358\) −790.552 + 1369.28i −0.116709 + 0.202147i
\(359\) 3002.18 0.441362 0.220681 0.975346i \(-0.429172\pi\)
0.220681 + 0.975346i \(0.429172\pi\)
\(360\) 0 0
\(361\) 5994.17 0.873913
\(362\) 6078.97 10529.1i 0.882607 1.52872i
\(363\) 0 0
\(364\) 2885.27 + 4997.43i 0.415465 + 0.719606i
\(365\) −1025.03 1775.40i −0.146993 0.254599i
\(366\) 0 0
\(367\) 574.638 995.302i 0.0817326 0.141565i −0.822262 0.569110i \(-0.807288\pi\)
0.903994 + 0.427545i \(0.140621\pi\)
\(368\) 6544.03 0.926986
\(369\) 0 0
\(370\) −394.471 −0.0554258
\(371\) −1576.32 + 2730.27i −0.220589 + 0.382071i
\(372\) 0 0
\(373\) 256.607 + 444.456i 0.0356209 + 0.0616972i 0.883286 0.468834i \(-0.155326\pi\)
−0.847665 + 0.530531i \(0.821992\pi\)
\(374\) −4188.57 7254.81i −0.579106 1.00304i
\(375\) 0 0
\(376\) 682.029 1181.31i 0.0935451 0.162025i
\(377\) −12685.3 −1.73296
\(378\) 0 0
\(379\) 12560.0 1.70228 0.851138 0.524942i \(-0.175913\pi\)
0.851138 + 0.524942i \(0.175913\pi\)
\(380\) 1251.31 2167.33i 0.168923 0.292583i
\(381\) 0 0
\(382\) −2804.85 4858.15i −0.375677 0.650692i
\(383\) −136.995 237.282i −0.0182771 0.0316568i 0.856742 0.515745i \(-0.172485\pi\)
−0.875019 + 0.484088i \(0.839151\pi\)
\(384\) 0 0
\(385\) 4536.91 7858.15i 0.600577 1.04023i
\(386\) 1561.95 0.205962
\(387\) 0 0
\(388\) −3893.31 −0.509415
\(389\) −3423.21 + 5929.18i −0.446179 + 0.772805i −0.998134 0.0610691i \(-0.980549\pi\)
0.551954 + 0.833874i \(0.313882\pi\)
\(390\) 0 0
\(391\) 1365.69 + 2365.45i 0.176640 + 0.305949i
\(392\) 1918.88 + 3323.59i 0.247239 + 0.428231i
\(393\) 0 0
\(394\) −368.188 + 637.721i −0.0470788 + 0.0815429i
\(395\) 3967.98 0.505445
\(396\) 0 0
\(397\) −12117.5 −1.53189 −0.765943 0.642909i \(-0.777727\pi\)
−0.765943 + 0.642909i \(0.777727\pi\)
\(398\) 845.486 1464.43i 0.106483 0.184435i
\(399\) 0 0
\(400\) 997.848 + 1728.32i 0.124731 + 0.216041i
\(401\) −1508.40 2612.63i −0.187845 0.325358i 0.756686 0.653778i \(-0.226817\pi\)
−0.944532 + 0.328421i \(0.893484\pi\)
\(402\) 0 0
\(403\) 5722.13 9911.02i 0.707294 1.22507i
\(404\) −4529.82 −0.557839
\(405\) 0 0
\(406\) 22118.4 2.70373
\(407\) −798.868 + 1383.68i −0.0972933 + 0.168517i
\(408\) 0 0
\(409\) −3267.56 5659.59i −0.395038 0.684226i 0.598068 0.801445i \(-0.295935\pi\)
−0.993106 + 0.117219i \(0.962602\pi\)
\(410\) 3824.96 + 6625.02i 0.460735 + 0.798016i
\(411\) 0 0
\(412\) 3951.93 6844.95i 0.472568 0.818511i
\(413\) −4351.26 −0.518430
\(414\) 0 0
\(415\) 1350.40 0.159732
\(416\) −4630.94 + 8021.03i −0.545795 + 0.945344i
\(417\) 0 0
\(418\) −14252.1 24685.3i −1.66768 2.88851i
\(419\) 3574.22 + 6190.74i 0.416736 + 0.721807i 0.995609 0.0936102i \(-0.0298407\pi\)
−0.578873 + 0.815418i \(0.696507\pi\)
\(420\) 0 0
\(421\) −7400.77 + 12818.5i −0.856749 + 1.48393i 0.0182632 + 0.999833i \(0.494186\pi\)
−0.875013 + 0.484100i \(0.839147\pi\)
\(422\) −9274.28 −1.06982
\(423\) 0 0
\(424\) −1565.89 −0.179354
\(425\) −416.489 + 721.379i −0.0475357 + 0.0823342i
\(426\) 0 0
\(427\) 1010.17 + 1749.66i 0.114486 + 0.198295i
\(428\) −4430.99 7674.70i −0.500420 0.866754i
\(429\) 0 0
\(430\) −2086.33 + 3613.64i −0.233981 + 0.405268i
\(431\) −2284.19 −0.255280 −0.127640 0.991821i \(-0.540740\pi\)
−0.127640 + 0.991821i \(0.540740\pi\)
\(432\) 0 0
\(433\) 5529.26 0.613670 0.306835 0.951763i \(-0.400730\pi\)
0.306835 + 0.951763i \(0.400730\pi\)
\(434\) −9977.21 + 17281.0i −1.10351 + 1.91133i
\(435\) 0 0
\(436\) 467.214 + 809.239i 0.0513200 + 0.0888888i
\(437\) 4646.93 + 8048.71i 0.508679 + 0.881057i
\(438\) 0 0
\(439\) 5930.81 10272.5i 0.644788 1.11681i −0.339562 0.940584i \(-0.610279\pi\)
0.984350 0.176223i \(-0.0563878\pi\)
\(440\) 4506.88 0.488311
\(441\) 0 0
\(442\) −6033.55 −0.649291
\(443\) −7646.81 + 13244.7i −0.820115 + 1.42048i 0.0854817 + 0.996340i \(0.472757\pi\)
−0.905596 + 0.424141i \(0.860576\pi\)
\(444\) 0 0
\(445\) −443.499 768.162i −0.0472446 0.0818301i
\(446\) −5907.49 10232.1i −0.627193 1.08633i
\(447\) 0 0
\(448\) −46.2801 + 80.1595i −0.00488065 + 0.00845353i
\(449\) −12998.8 −1.36626 −0.683129 0.730297i \(-0.739381\pi\)
−0.683129 + 0.730297i \(0.739381\pi\)
\(450\) 0 0
\(451\) 30984.6 3.23506
\(452\) 4.29329 7.43619i 0.000446768 0.000773825i
\(453\) 0 0
\(454\) 1216.95 + 2107.81i 0.125802 + 0.217895i
\(455\) −3267.66 5659.75i −0.336682 0.583150i
\(456\) 0 0
\(457\) −7155.97 + 12394.5i −0.732477 + 1.26869i 0.223344 + 0.974740i \(0.428303\pi\)
−0.955821 + 0.293948i \(0.905031\pi\)
\(458\) −2354.14 −0.240179
\(459\) 0 0
\(460\) 1809.59 0.183419
\(461\) 2145.17 3715.54i 0.216725 0.375379i −0.737080 0.675806i \(-0.763796\pi\)
0.953805 + 0.300427i \(0.0971290\pi\)
\(462\) 0 0
\(463\) 7255.14 + 12566.3i 0.728240 + 1.26135i 0.957626 + 0.288013i \(0.0929947\pi\)
−0.229386 + 0.973335i \(0.573672\pi\)
\(464\) 9851.85 + 17063.9i 0.985691 + 1.70727i
\(465\) 0 0
\(466\) −1656.98 + 2869.97i −0.164717 + 0.285298i
\(467\) 7393.05 0.732569 0.366285 0.930503i \(-0.380630\pi\)
0.366285 + 0.930503i \(0.380630\pi\)
\(468\) 0 0
\(469\) −15552.1 −1.53119
\(470\) 951.195 1647.52i 0.0933518 0.161690i
\(471\) 0 0
\(472\) −1080.62 1871.68i −0.105380 0.182524i
\(473\) 8450.34 + 14636.4i 0.821452 + 1.42280i
\(474\) 0 0
\(475\) −1417.15 + 2454.57i −0.136891 + 0.237102i
\(476\) 3741.11 0.360239
\(477\) 0 0
\(478\) −3901.91 −0.373366
\(479\) 6754.93 11699.9i 0.644344 1.11604i −0.340109 0.940386i \(-0.610464\pi\)
0.984453 0.175650i \(-0.0562027\pi\)
\(480\) 0 0
\(481\) 575.376 + 996.580i 0.0545424 + 0.0944702i
\(482\) −2164.93 3749.77i −0.204585 0.354352i
\(483\) 0 0
\(484\) −8301.53 + 14378.7i −0.779632 + 1.35036i
\(485\) 4409.30 0.412817
\(486\) 0 0
\(487\) −11140.0 −1.03655 −0.518277 0.855213i \(-0.673427\pi\)
−0.518277 + 0.855213i \(0.673427\pi\)
\(488\) −501.740 + 869.040i −0.0465425 + 0.0806139i
\(489\) 0 0
\(490\) 2676.17 + 4635.26i 0.246729 + 0.427347i
\(491\) 1006.37 + 1743.09i 0.0924988 + 0.160213i 0.908562 0.417750i \(-0.137181\pi\)
−0.816063 + 0.577963i \(0.803848\pi\)
\(492\) 0 0
\(493\) −4112.03 + 7122.24i −0.375652 + 0.650648i
\(494\) −20529.8 −1.86980
\(495\) 0 0
\(496\) −17776.0 −1.60920
\(497\) 6499.29 11257.1i 0.586585 1.01600i
\(498\) 0 0
\(499\) −3676.49 6367.87i −0.329824 0.571272i 0.652653 0.757657i \(-0.273656\pi\)
−0.982477 + 0.186385i \(0.940323\pi\)
\(500\) 275.930 + 477.925i 0.0246800 + 0.0427469i
\(501\) 0 0
\(502\) 1301.01 2253.41i 0.115671 0.200348i
\(503\) −16898.3 −1.49793 −0.748965 0.662609i \(-0.769449\pi\)
−0.748965 + 0.662609i \(0.769449\pi\)
\(504\) 0 0
\(505\) 5130.17 0.452059
\(506\) 10305.4 17849.4i 0.905394 1.56819i
\(507\) 0 0
\(508\) 2600.41 + 4504.04i 0.227115 + 0.393375i
\(509\) −9679.31 16765.1i −0.842884 1.45992i −0.887446 0.460911i \(-0.847523\pi\)
0.0445620 0.999007i \(-0.485811\pi\)
\(510\) 0 0
\(511\) 5213.80 9030.57i 0.451360 0.781779i
\(512\) 6319.06 0.545440
\(513\) 0 0
\(514\) −22242.2 −1.90868
\(515\) −4475.69 + 7752.13i −0.382957 + 0.663300i
\(516\) 0 0
\(517\) −3852.65 6672.99i −0.327736 0.567655i
\(518\) −1003.24 1737.66i −0.0850959 0.147390i
\(519\) 0 0
\(520\) 1623.02 2811.15i 0.136873 0.237071i
\(521\) 146.772 0.0123420 0.00617100 0.999981i \(-0.498036\pi\)
0.00617100 + 0.999981i \(0.498036\pi\)
\(522\) 0 0
\(523\) −2872.03 −0.240125 −0.120062 0.992766i \(-0.538309\pi\)
−0.120062 + 0.992766i \(0.538309\pi\)
\(524\) 1150.56 1992.83i 0.0959205 0.166139i
\(525\) 0 0
\(526\) 10559.2 + 18289.0i 0.875289 + 1.51605i
\(527\) −3709.73 6425.44i −0.306638 0.531113i
\(528\) 0 0
\(529\) 2723.41 4717.08i 0.223836 0.387695i
\(530\) −2183.87 −0.178984
\(531\) 0 0
\(532\) 12729.5 1.03740
\(533\) 11158.2 19326.5i 0.906781 1.57059i
\(534\) 0 0
\(535\) 5018.24 + 8691.84i 0.405528 + 0.702395i
\(536\) −3862.29 6689.69i −0.311242 0.539087i
\(537\) 0 0
\(538\) −3082.51 + 5339.07i −0.247020 + 0.427851i
\(539\) 21678.7 1.73241
\(540\) 0 0
\(541\) −3810.28 −0.302804 −0.151402 0.988472i \(-0.548379\pi\)
−0.151402 + 0.988472i \(0.548379\pi\)
\(542\) 3403.12 5894.38i 0.269698 0.467131i
\(543\) 0 0
\(544\) 3002.30 + 5200.14i 0.236622 + 0.409842i
\(545\) −529.135 916.490i −0.0415884 0.0720332i
\(546\) 0 0
\(547\) −2972.79 + 5149.03i −0.232372 + 0.402480i −0.958506 0.285073i \(-0.907982\pi\)
0.726134 + 0.687554i \(0.241315\pi\)
\(548\) 1984.63 0.154707
\(549\) 0 0
\(550\) 6285.54 0.487303
\(551\) −13991.6 + 24234.2i −1.08178 + 1.87371i
\(552\) 0 0
\(553\) 10091.6 + 17479.1i 0.776016 + 1.34410i
\(554\) 6679.72 + 11569.6i 0.512264 + 0.887267i
\(555\) 0 0
\(556\) 5177.44 8967.59i 0.394914 0.684012i
\(557\) 10872.2 0.827059 0.413530 0.910491i \(-0.364296\pi\)
0.413530 + 0.910491i \(0.364296\pi\)
\(558\) 0 0
\(559\) 12172.5 0.921007
\(560\) −5075.55 + 8791.11i −0.383002 + 0.663379i
\(561\) 0 0
\(562\) 7909.08 + 13698.9i 0.593638 + 1.02821i
\(563\) 6787.54 + 11756.4i 0.508100 + 0.880056i 0.999956 + 0.00937903i \(0.00298548\pi\)
−0.491856 + 0.870677i \(0.663681\pi\)
\(564\) 0 0
\(565\) −4.86228 + 8.42172i −0.000362049 + 0.000627088i
\(566\) 11042.1 0.820024
\(567\) 0 0
\(568\) 6456.27 0.476935
\(569\) 10321.3 17877.0i 0.760442 1.31712i −0.182181 0.983265i \(-0.558316\pi\)
0.942623 0.333859i \(-0.108351\pi\)
\(570\) 0 0
\(571\) 1365.39 + 2364.92i 0.100069 + 0.173325i 0.911713 0.410828i \(-0.134760\pi\)
−0.811644 + 0.584153i \(0.801427\pi\)
\(572\) 8095.23 + 14021.3i 0.591745 + 1.02493i
\(573\) 0 0
\(574\) −19455.6 + 33698.1i −1.41474 + 2.45040i
\(575\) −2049.42 −0.148638
\(576\) 0 0
\(577\) 21953.4 1.58394 0.791970 0.610560i \(-0.209055\pi\)
0.791970 + 0.610560i \(0.209055\pi\)
\(578\) 6699.61 11604.1i 0.482123 0.835061i
\(579\) 0 0
\(580\) 2724.28 + 4718.60i 0.195034 + 0.337809i
\(581\) 3434.41 + 5948.57i 0.245238 + 0.424765i
\(582\) 0 0
\(583\) −4422.70 + 7660.34i −0.314185 + 0.544184i
\(584\) 5179.29 0.366988
\(585\) 0 0
\(586\) −9856.92 −0.694856
\(587\) 5527.67 9574.21i 0.388674 0.673203i −0.603598 0.797289i \(-0.706267\pi\)
0.992271 + 0.124086i \(0.0396000\pi\)
\(588\) 0 0
\(589\) −12622.8 21863.3i −0.883042 1.52947i
\(590\) −1507.09 2610.35i −0.105162 0.182147i
\(591\) 0 0
\(592\) 893.713 1547.96i 0.0620462 0.107467i
\(593\) −16538.0 −1.14525 −0.572625 0.819817i \(-0.694075\pi\)
−0.572625 + 0.819817i \(0.694075\pi\)
\(594\) 0 0
\(595\) −4236.93 −0.291928
\(596\) −2802.09 + 4853.36i −0.192581 + 0.333559i
\(597\) 0 0
\(598\) −7422.33 12855.8i −0.507561 0.879122i
\(599\) −3201.79 5545.67i −0.218400 0.378280i 0.735919 0.677070i \(-0.236750\pi\)
−0.954319 + 0.298790i \(0.903417\pi\)
\(600\) 0 0
\(601\) 7105.18 12306.5i 0.482240 0.835264i −0.517552 0.855652i \(-0.673157\pi\)
0.999792 + 0.0203874i \(0.00648995\pi\)
\(602\) −21224.3 −1.43694
\(603\) 0 0
\(604\) 9528.72 0.641917
\(605\) 9401.75 16284.3i 0.631794 1.09430i
\(606\) 0 0
\(607\) 4457.86 + 7721.24i 0.298087 + 0.516302i 0.975698 0.219118i \(-0.0703180\pi\)
−0.677611 + 0.735420i \(0.736985\pi\)
\(608\) 10215.7 + 17694.0i 0.681414 + 1.18024i
\(609\) 0 0
\(610\) −699.755 + 1212.01i −0.0464463 + 0.0804474i
\(611\) −5549.66 −0.367455
\(612\) 0 0
\(613\) −15372.5 −1.01287 −0.506436 0.862277i \(-0.669037\pi\)
−0.506436 + 0.862277i \(0.669037\pi\)
\(614\) 12050.1 20871.4i 0.792026 1.37183i
\(615\) 0 0
\(616\) 11462.1 + 19852.9i 0.749710 + 1.29854i
\(617\) 8663.73 + 15006.0i 0.565298 + 0.979124i 0.997022 + 0.0771187i \(0.0245721\pi\)
−0.431724 + 0.902006i \(0.642095\pi\)
\(618\) 0 0
\(619\) 14393.7 24930.6i 0.934621 1.61881i 0.159313 0.987228i \(-0.449072\pi\)
0.775308 0.631583i \(-0.217595\pi\)
\(620\) −4915.51 −0.318406
\(621\) 0 0
\(622\) −8524.73 −0.549535
\(623\) 2255.85 3907.25i 0.145070 0.251269i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −6876.38 11910.2i −0.439034 0.760429i
\(627\) 0 0
\(628\) 5172.72 8959.41i 0.328685 0.569298i
\(629\) 746.047 0.0472923
\(630\) 0 0
\(631\) 18091.0 1.14135 0.570675 0.821176i \(-0.306682\pi\)
0.570675 + 0.821176i \(0.306682\pi\)
\(632\) −5012.38 + 8681.70i −0.315478 + 0.546423i
\(633\) 0 0
\(634\) 17431.9 + 30193.0i 1.09197 + 1.89135i
\(635\) −2945.05 5100.97i −0.184048 0.318781i
\(636\) 0 0
\(637\) 7806.94 13522.0i 0.485592 0.841070i
\(638\) 62057.7 3.85092
\(639\) 0 0
\(640\) −7272.72 −0.449187
\(641\) 9788.76 16954.6i 0.603171 1.04472i −0.389167 0.921167i \(-0.627237\pi\)
0.992338 0.123556i \(-0.0394297\pi\)
\(642\) 0 0
\(643\) 14985.9 + 25956.3i 0.919106 + 1.59194i 0.800777 + 0.598963i \(0.204420\pi\)
0.118329 + 0.992974i \(0.462246\pi\)
\(644\) 4602.23 + 7971.30i 0.281605 + 0.487753i
\(645\) 0 0
\(646\) −6654.87 + 11526.6i −0.405313 + 0.702023i
\(647\) 3635.64 0.220915 0.110457 0.993881i \(-0.464768\pi\)
0.110457 + 0.993881i \(0.464768\pi\)
\(648\) 0 0
\(649\) −12208.4 −0.738399
\(650\) 2263.55 3920.58i 0.136590 0.236581i
\(651\) 0 0
\(652\) −7505.17 12999.3i −0.450805 0.780818i
\(653\) −9703.64 16807.2i −0.581520 1.00722i −0.995299 0.0968453i \(-0.969125\pi\)
0.413779 0.910377i \(-0.364209\pi\)
\(654\) 0 0
\(655\) −1303.04 + 2256.94i −0.0777315 + 0.134635i
\(656\) −34663.3 −2.06307
\(657\) 0 0
\(658\) 9676.49 0.573296
\(659\) −2813.93 + 4873.87i −0.166335 + 0.288101i −0.937129 0.348984i \(-0.886527\pi\)
0.770793 + 0.637085i \(0.219860\pi\)
\(660\) 0 0
\(661\) 8331.49 + 14430.6i 0.490253 + 0.849144i 0.999937 0.0112181i \(-0.00357089\pi\)
−0.509684 + 0.860362i \(0.670238\pi\)
\(662\) −7334.18 12703.2i −0.430591 0.745805i
\(663\) 0 0
\(664\) −1705.84 + 2954.60i −0.0996979 + 0.172682i
\(665\) −14416.6 −0.840681
\(666\) 0 0
\(667\) −20234.1 −1.17461
\(668\) −3993.74 + 6917.36i −0.231321 + 0.400660i
\(669\) 0 0
\(670\) −5386.57 9329.81i −0.310599 0.537973i
\(671\) 2834.24 + 4909.04i 0.163062 + 0.282431i
\(672\) 0 0
\(673\) 6319.38 10945.5i 0.361953 0.626921i −0.626329 0.779559i \(-0.715443\pi\)
0.988282 + 0.152638i \(0.0487768\pi\)
\(674\) 34195.1 1.95422
\(675\) 0 0
\(676\) 1961.50 0.111601
\(677\) −12658.0 + 21924.3i −0.718591 + 1.24464i 0.242967 + 0.970035i \(0.421879\pi\)
−0.961558 + 0.274602i \(0.911454\pi\)
\(678\) 0 0
\(679\) 11213.9 + 19423.1i 0.633802 + 1.09778i
\(680\) −1052.22 1822.50i −0.0593395 0.102779i
\(681\) 0 0
\(682\) −27993.2 + 48485.6i −1.57172 + 2.72230i
\(683\) −24818.4 −1.39041 −0.695204 0.718812i \(-0.744686\pi\)
−0.695204 + 0.718812i \(0.744686\pi\)
\(684\) 0 0
\(685\) −2247.66 −0.125370
\(686\) 1755.91 3041.32i 0.0977273 0.169269i
\(687\) 0 0
\(688\) −9453.60 16374.1i −0.523859 0.907351i
\(689\) 3185.40 + 5517.28i 0.176131 + 0.305068i
\(690\) 0 0
\(691\) −9978.98 + 17284.1i −0.549375 + 0.951546i 0.448942 + 0.893561i \(0.351801\pi\)
−0.998317 + 0.0579852i \(0.981532\pi\)
\(692\) 5860.35 0.321932
\(693\) 0 0
\(694\) 19140.9 1.04694
\(695\) −5863.62 + 10156.1i −0.320028 + 0.554305i
\(696\) 0 0
\(697\) −7233.99 12529.6i −0.393124 0.680910i
\(698\) −18625.0 32259.4i −1.00998 1.74934i
\(699\) 0 0
\(700\) −1403.52 + 2430.96i −0.0757828 + 0.131260i
\(701\) 5624.21 0.303029 0.151515 0.988455i \(-0.451585\pi\)
0.151515 + 0.988455i \(0.451585\pi\)
\(702\) 0 0
\(703\) 2538.51 0.136190
\(704\) −129.849 + 224.904i −0.00695149 + 0.0120403i
\(705\) 0 0
\(706\) −16988.4 29424.8i −0.905620 1.56858i
\(707\) 13047.3 + 22598.6i 0.694051 + 1.20213i
\(708\) 0 0
\(709\) 3857.72 6681.76i 0.204344 0.353933i −0.745580 0.666416i \(-0.767827\pi\)
0.949923 + 0.312483i \(0.101161\pi\)
\(710\) 9004.27 0.475950
\(711\) 0 0
\(712\) 2240.92 0.117952
\(713\) 9127.25 15808.9i 0.479408 0.830360i
\(714\) 0 0
\(715\) −9168.11 15879.6i −0.479535 0.830579i
\(716\) −990.555 1715.69i −0.0517022 0.0895508i
\(717\) 0 0
\(718\) −5289.05 + 9160.91i −0.274910 + 0.476159i
\(719\) −21647.8 −1.12285 −0.561424 0.827528i \(-0.689746\pi\)
−0.561424 + 0.827528i \(0.689746\pi\)
\(720\) 0 0
\(721\) −45531.2 −2.35183
\(722\) −10560.2 + 18290.7i −0.544333 + 0.942812i
\(723\) 0 0
\(724\) 7616.90 + 13192.9i 0.390994 + 0.677222i
\(725\) −3085.34 5343.97i −0.158051 0.273752i
\(726\) 0 0
\(727\) 1535.65 2659.82i 0.0783412 0.135691i −0.824193 0.566309i \(-0.808371\pi\)
0.902534 + 0.430618i \(0.141704\pi\)
\(728\) 16510.9 0.840570
\(729\) 0 0
\(730\) 7223.33 0.366229
\(731\) 3945.80 6834.33i 0.199645 0.345796i
\(732\) 0 0
\(733\) −7326.01 12689.0i −0.369157 0.639399i 0.620277 0.784383i \(-0.287020\pi\)
−0.989434 + 0.144984i \(0.953687\pi\)
\(734\) 2024.72 + 3506.92i 0.101817 + 0.176353i
\(735\) 0 0
\(736\) −7386.72 + 12794.2i −0.369943 + 0.640760i
\(737\) −43634.7 −2.18087
\(738\) 0 0
\(739\) 17610.9 0.876629 0.438314 0.898822i \(-0.355576\pi\)
0.438314 + 0.898822i \(0.355576\pi\)
\(740\) 247.134 428.049i 0.0122768 0.0212640i
\(741\) 0 0
\(742\) −5554.13 9620.04i −0.274796 0.475960i
\(743\) −8394.09 14539.0i −0.414468 0.717879i 0.580905 0.813972i \(-0.302699\pi\)
−0.995372 + 0.0960925i \(0.969366\pi\)
\(744\) 0 0
\(745\) 3173.46 5496.59i 0.156062 0.270308i
\(746\) −1808.30 −0.0887485
\(747\) 0 0
\(748\) 10496.5 0.513087
\(749\) −25525.2 + 44211.0i −1.24522 + 2.15679i
\(750\) 0 0
\(751\) −11757.1 20363.9i −0.571269 0.989467i −0.996436 0.0843523i \(-0.973118\pi\)
0.425167 0.905115i \(-0.360215\pi\)
\(752\) 4310.05 + 7465.23i 0.209005 + 0.362007i
\(753\) 0 0
\(754\) 22348.2 38708.2i 1.07941 1.86959i
\(755\) −10791.6 −0.520193
\(756\) 0 0
\(757\) 24817.4 1.19155 0.595775 0.803151i \(-0.296845\pi\)
0.595775 + 0.803151i \(0.296845\pi\)
\(758\) −22127.4 + 38325.8i −1.06029 + 1.83648i
\(759\) 0 0
\(760\) −3580.30 6201.26i −0.170883 0.295978i
\(761\) 16258.9 + 28161.2i 0.774485 + 1.34145i 0.935084 + 0.354427i \(0.115324\pi\)
−0.160599 + 0.987020i \(0.551342\pi\)
\(762\) 0 0
\(763\) 2691.44 4661.72i 0.127702 0.221187i
\(764\) 7028.91 0.332850
\(765\) 0 0
\(766\) 965.398 0.0455369
\(767\) −4396.48 + 7614.93i −0.206972 + 0.358486i
\(768\) 0 0
\(769\) −9028.92 15638.5i −0.423395 0.733342i 0.572874 0.819644i \(-0.305829\pi\)
−0.996269 + 0.0863014i \(0.972495\pi\)
\(770\) 15985.7 + 27688.0i 0.748161 + 1.29585i
\(771\) 0 0
\(772\) −978.557 + 1694.91i −0.0456205 + 0.0790171i
\(773\) −38147.2 −1.77498 −0.887491 0.460825i \(-0.847553\pi\)
−0.887491 + 0.460825i \(0.847553\pi\)
\(774\) 0 0
\(775\) 5566.98 0.258028
\(776\) −5569.86 + 9647.28i −0.257663 + 0.446285i
\(777\) 0 0
\(778\) −12061.6 20891.3i −0.555822 0.962712i
\(779\) −24614.5 42633.5i −1.13210 1.96085i
\(780\) 0 0
\(781\) 18235.1 31584.1i 0.835472 1.44708i
\(782\) −9623.98 −0.440093
\(783\) 0 0
\(784\) −24252.5 −1.10480
\(785\) −5858.27 + 10146.8i −0.266357 + 0.461345i
\(786\) 0 0