Properties

Label 405.4.e.t.271.2
Level $405$
Weight $4$
Character 405.271
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: 6.0.95327307.1
Defining polynomial: \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 85x^{2} - 68x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.2
Root \(0.500000 - 3.26212i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.t.136.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.129356 + 0.224051i) q^{2} +(3.96653 - 6.87024i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.25871 - 12.5725i) q^{7} +4.12208 q^{8} +O(q^{10})\) \(q+(0.129356 + 0.224051i) q^{2} +(3.96653 - 6.87024i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.25871 - 12.5725i) q^{7} +4.12208 q^{8} -1.29356 q^{10} +(24.6423 + 42.6817i) q^{11} +(-36.0900 + 62.5097i) q^{13} +(1.87792 - 3.25265i) q^{14} +(-31.1991 - 54.0383i) q^{16} +118.017 q^{17} +123.389 q^{19} +(19.8327 + 34.3512i) q^{20} +(-6.37526 + 11.0423i) q^{22} +(45.7442 - 79.2312i) q^{23} +(-12.5000 - 21.6506i) q^{25} -18.6739 q^{26} -115.168 q^{28} +(-87.2001 - 151.035i) q^{29} +(23.1478 - 40.0932i) q^{31} +(24.5599 - 42.5390i) q^{32} +(15.2662 + 26.4418i) q^{34} +72.5871 q^{35} +154.977 q^{37} +(15.9611 + 27.6455i) q^{38} +(-10.3052 + 17.8491i) q^{40} +(182.101 - 315.409i) q^{41} +(-62.8569 - 108.871i) q^{43} +390.978 q^{44} +23.6692 q^{46} +(110.762 + 191.845i) q^{47} +(66.1222 - 114.527i) q^{49} +(3.23390 - 5.60129i) q^{50} +(286.304 + 495.894i) q^{52} -13.6794 q^{53} -246.423 q^{55} +(-29.9210 - 51.8247i) q^{56} +(22.5597 - 39.0746i) q^{58} +(-119.543 + 207.055i) q^{59} +(27.2729 + 47.2380i) q^{61} +11.9772 q^{62} -486.477 q^{64} +(-180.450 - 312.549i) q^{65} +(38.0279 - 65.8662i) q^{67} +(468.118 - 810.804i) q^{68} +(9.38959 + 16.2633i) q^{70} +728.303 q^{71} -501.815 q^{73} +(20.0472 + 34.7227i) q^{74} +(489.427 - 847.712i) q^{76} +(357.742 - 619.628i) q^{77} +(-198.805 - 344.340i) q^{79} +311.991 q^{80} +94.2237 q^{82} +(684.731 + 1185.99i) q^{83} +(-295.042 + 511.028i) q^{85} +(16.2619 - 28.1664i) q^{86} +(101.577 + 175.937i) q^{88} +1468.13 q^{89} +1047.87 q^{91} +(-362.892 - 628.547i) q^{92} +(-28.6554 + 49.6326i) q^{94} +(-308.473 + 534.290i) q^{95} +(-167.512 - 290.139i) q^{97} +34.2133 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} - 23 q^{4} - 15 q^{5} - 44 q^{7} - 72 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} - 23 q^{4} - 15 q^{5} - 44 q^{7} - 72 q^{8} - 10 q^{10} - 38 q^{11} - 28 q^{13} + 108 q^{14} - 191 q^{16} - 38 q^{17} + 374 q^{19} - 115 q^{20} - 122 q^{22} + 81 q^{23} - 75 q^{25} + 832 q^{26} + 820 q^{28} - 160 q^{29} - 227 q^{31} + 569 q^{32} - 17 q^{34} + 440 q^{35} + 156 q^{37} + 757 q^{38} + 180 q^{40} + 338 q^{41} - 22 q^{43} + 3272 q^{44} - 2850 q^{46} + 472 q^{47} + 197 q^{49} + 25 q^{50} + 1566 q^{52} + 1042 q^{53} + 380 q^{55} + 1254 q^{56} + 2096 q^{58} - 140 q^{59} - 595 q^{61} + 2814 q^{62} - 1836 q^{64} - 140 q^{65} - 878 q^{67} + 3053 q^{68} + 540 q^{70} - 1204 q^{71} + 2588 q^{73} - 2878 q^{74} - 525 q^{76} - 288 q^{77} - 629 q^{79} + 1910 q^{80} - 3364 q^{82} + 1287 q^{83} + 95 q^{85} + 3730 q^{86} + 858 q^{88} + 4308 q^{89} - 880 q^{91} - 1959 q^{92} + 1108 q^{94} - 935 q^{95} - 1392 q^{97} - 5386 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.129356 + 0.224051i 0.0457343 + 0.0792142i 0.887986 0.459870i \(-0.152104\pi\)
−0.842252 + 0.539084i \(0.818771\pi\)
\(3\) 0 0
\(4\) 3.96653 6.87024i 0.495817 0.858780i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −7.25871 12.5725i −0.391934 0.678849i 0.600771 0.799421i \(-0.294860\pi\)
−0.992705 + 0.120572i \(0.961527\pi\)
\(8\) 4.12208 0.182172
\(9\) 0 0
\(10\) −1.29356 −0.0409060
\(11\) 24.6423 + 42.6817i 0.675448 + 1.16991i 0.976338 + 0.216251i \(0.0693829\pi\)
−0.300890 + 0.953659i \(0.597284\pi\)
\(12\) 0 0
\(13\) −36.0900 + 62.5097i −0.769967 + 1.33362i 0.167614 + 0.985853i \(0.446394\pi\)
−0.937580 + 0.347768i \(0.886940\pi\)
\(14\) 1.87792 3.25265i 0.0358496 0.0620934i
\(15\) 0 0
\(16\) −31.1991 54.0383i −0.487485 0.844349i
\(17\) 118.017 1.68372 0.841861 0.539694i \(-0.181460\pi\)
0.841861 + 0.539694i \(0.181460\pi\)
\(18\) 0 0
\(19\) 123.389 1.48986 0.744932 0.667141i \(-0.232482\pi\)
0.744932 + 0.667141i \(0.232482\pi\)
\(20\) 19.8327 + 34.3512i 0.221736 + 0.384058i
\(21\) 0 0
\(22\) −6.37526 + 11.0423i −0.0617823 + 0.107010i
\(23\) 45.7442 79.2312i 0.414709 0.718298i −0.580688 0.814126i \(-0.697217\pi\)
0.995398 + 0.0958280i \(0.0305499\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −18.6739 −0.140856
\(27\) 0 0
\(28\) −115.168 −0.777309
\(29\) −87.2001 151.035i −0.558367 0.967120i −0.997633 0.0687632i \(-0.978095\pi\)
0.439266 0.898357i \(-0.355239\pi\)
\(30\) 0 0
\(31\) 23.1478 40.0932i 0.134112 0.232289i −0.791146 0.611627i \(-0.790515\pi\)
0.925258 + 0.379339i \(0.123849\pi\)
\(32\) 24.5599 42.5390i 0.135676 0.234997i
\(33\) 0 0
\(34\) 15.2662 + 26.4418i 0.0770039 + 0.133375i
\(35\) 72.5871 0.350556
\(36\) 0 0
\(37\) 154.977 0.688595 0.344297 0.938861i \(-0.388117\pi\)
0.344297 + 0.938861i \(0.388117\pi\)
\(38\) 15.9611 + 27.6455i 0.0681379 + 0.118018i
\(39\) 0 0
\(40\) −10.3052 + 17.8491i −0.0407349 + 0.0705549i
\(41\) 182.101 315.409i 0.693645 1.20143i −0.276990 0.960873i \(-0.589337\pi\)
0.970635 0.240556i \(-0.0773296\pi\)
\(42\) 0 0
\(43\) −62.8569 108.871i −0.222921 0.386110i 0.732773 0.680473i \(-0.238226\pi\)
−0.955694 + 0.294363i \(0.904892\pi\)
\(44\) 390.978 1.33959
\(45\) 0 0
\(46\) 23.6692 0.0758658
\(47\) 110.762 + 191.845i 0.343750 + 0.595392i 0.985126 0.171835i \(-0.0549695\pi\)
−0.641376 + 0.767227i \(0.721636\pi\)
\(48\) 0 0
\(49\) 66.1222 114.527i 0.192776 0.333898i
\(50\) 3.23390 5.60129i 0.00914686 0.0158428i
\(51\) 0 0
\(52\) 286.304 + 495.894i 0.763525 + 1.32246i
\(53\) −13.6794 −0.0354530 −0.0177265 0.999843i \(-0.505643\pi\)
−0.0177265 + 0.999843i \(0.505643\pi\)
\(54\) 0 0
\(55\) −246.423 −0.604139
\(56\) −29.9210 51.8247i −0.0713993 0.123667i
\(57\) 0 0
\(58\) 22.5597 39.0746i 0.0510731 0.0884612i
\(59\) −119.543 + 207.055i −0.263784 + 0.456887i −0.967244 0.253848i \(-0.918304\pi\)
0.703461 + 0.710734i \(0.251637\pi\)
\(60\) 0 0
\(61\) 27.2729 + 47.2380i 0.0572448 + 0.0991509i 0.893228 0.449605i \(-0.148435\pi\)
−0.835983 + 0.548756i \(0.815102\pi\)
\(62\) 11.9772 0.0245341
\(63\) 0 0
\(64\) −486.477 −0.950150
\(65\) −180.450 312.549i −0.344339 0.596413i
\(66\) 0 0
\(67\) 38.0279 65.8662i 0.0693410 0.120102i −0.829270 0.558848i \(-0.811244\pi\)
0.898611 + 0.438745i \(0.144577\pi\)
\(68\) 468.118 810.804i 0.834818 1.44595i
\(69\) 0 0
\(70\) 9.38959 + 16.2633i 0.0160324 + 0.0277690i
\(71\) 728.303 1.21738 0.608688 0.793410i \(-0.291696\pi\)
0.608688 + 0.793410i \(0.291696\pi\)
\(72\) 0 0
\(73\) −501.815 −0.804562 −0.402281 0.915516i \(-0.631782\pi\)
−0.402281 + 0.915516i \(0.631782\pi\)
\(74\) 20.0472 + 34.7227i 0.0314924 + 0.0545464i
\(75\) 0 0
\(76\) 489.427 847.712i 0.738699 1.27946i
\(77\) 357.742 619.628i 0.529461 0.917054i
\(78\) 0 0
\(79\) −198.805 344.340i −0.283130 0.490396i 0.689024 0.724739i \(-0.258040\pi\)
−0.972154 + 0.234343i \(0.924706\pi\)
\(80\) 311.991 0.436020
\(81\) 0 0
\(82\) 94.2237 0.126894
\(83\) 684.731 + 1185.99i 0.905530 + 1.56842i 0.820205 + 0.572070i \(0.193859\pi\)
0.0853248 + 0.996353i \(0.472807\pi\)
\(84\) 0 0
\(85\) −295.042 + 511.028i −0.376492 + 0.652103i
\(86\) 16.2619 28.1664i 0.0203902 0.0353169i
\(87\) 0 0
\(88\) 101.577 + 175.937i 0.123048 + 0.213125i
\(89\) 1468.13 1.74856 0.874278 0.485425i \(-0.161335\pi\)
0.874278 + 0.485425i \(0.161335\pi\)
\(90\) 0 0
\(91\) 1047.87 1.20710
\(92\) −362.892 628.547i −0.411240 0.712288i
\(93\) 0 0
\(94\) −28.6554 + 49.6326i −0.0314423 + 0.0544597i
\(95\) −308.473 + 534.290i −0.333144 + 0.577022i
\(96\) 0 0
\(97\) −167.512 290.139i −0.175343 0.303702i 0.764937 0.644105i \(-0.222770\pi\)
−0.940280 + 0.340403i \(0.889437\pi\)
\(98\) 34.2133 0.0352659
\(99\) 0 0
\(100\) −198.327 −0.198327
\(101\) 603.043 + 1044.50i 0.594109 + 1.02903i 0.993672 + 0.112321i \(0.0358286\pi\)
−0.399563 + 0.916706i \(0.630838\pi\)
\(102\) 0 0
\(103\) −530.555 + 918.948i −0.507545 + 0.879093i 0.492417 + 0.870359i \(0.336113\pi\)
−0.999962 + 0.00873396i \(0.997220\pi\)
\(104\) −148.766 + 257.670i −0.140266 + 0.242948i
\(105\) 0 0
\(106\) −1.76951 3.06489i −0.00162142 0.00280838i
\(107\) −475.578 −0.429681 −0.214841 0.976649i \(-0.568923\pi\)
−0.214841 + 0.976649i \(0.568923\pi\)
\(108\) 0 0
\(109\) 1320.42 1.16030 0.580152 0.814508i \(-0.302993\pi\)
0.580152 + 0.814508i \(0.302993\pi\)
\(110\) −31.8763 55.2114i −0.0276299 0.0478563i
\(111\) 0 0
\(112\) −452.930 + 784.498i −0.382124 + 0.661858i
\(113\) 34.0875 59.0413i 0.0283777 0.0491517i −0.851488 0.524374i \(-0.824299\pi\)
0.879865 + 0.475223i \(0.157633\pi\)
\(114\) 0 0
\(115\) 228.721 + 396.156i 0.185464 + 0.321233i
\(116\) −1383.53 −1.10739
\(117\) 0 0
\(118\) −61.8547 −0.0482559
\(119\) −856.650 1483.76i −0.659907 1.14299i
\(120\) 0 0
\(121\) −548.983 + 950.867i −0.412459 + 0.714400i
\(122\) −7.05583 + 12.2211i −0.00523610 + 0.00906920i
\(123\) 0 0
\(124\) −183.633 318.062i −0.132990 0.230345i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −593.009 −0.414339 −0.207170 0.978305i \(-0.566425\pi\)
−0.207170 + 0.978305i \(0.566425\pi\)
\(128\) −259.408 449.308i −0.179130 0.310262i
\(129\) 0 0
\(130\) 46.6846 80.8602i 0.0314963 0.0545531i
\(131\) −169.469 + 293.528i −0.113027 + 0.195769i −0.916989 0.398912i \(-0.869388\pi\)
0.803962 + 0.594680i \(0.202721\pi\)
\(132\) 0 0
\(133\) −895.646 1551.30i −0.583927 1.01139i
\(134\) 19.6766 0.0126850
\(135\) 0 0
\(136\) 486.475 0.306727
\(137\) 405.721 + 702.729i 0.253015 + 0.438235i 0.964354 0.264614i \(-0.0852444\pi\)
−0.711339 + 0.702849i \(0.751911\pi\)
\(138\) 0 0
\(139\) 1553.06 2689.98i 0.947691 1.64145i 0.197420 0.980319i \(-0.436744\pi\)
0.750271 0.661130i \(-0.229923\pi\)
\(140\) 287.919 498.691i 0.173812 0.301050i
\(141\) 0 0
\(142\) 94.2105 + 163.177i 0.0556758 + 0.0964334i
\(143\) −3557.36 −2.08029
\(144\) 0 0
\(145\) 872.001 0.499419
\(146\) −64.9129 112.432i −0.0367961 0.0637327i
\(147\) 0 0
\(148\) 614.720 1064.73i 0.341417 0.591351i
\(149\) −1270.51 + 2200.58i −0.698550 + 1.20992i 0.270419 + 0.962743i \(0.412838\pi\)
−0.968969 + 0.247181i \(0.920496\pi\)
\(150\) 0 0
\(151\) 562.685 + 974.599i 0.303249 + 0.525243i 0.976870 0.213834i \(-0.0685952\pi\)
−0.673621 + 0.739077i \(0.735262\pi\)
\(152\) 508.620 0.271411
\(153\) 0 0
\(154\) 185.105 0.0968582
\(155\) 115.739 + 200.466i 0.0599767 + 0.103883i
\(156\) 0 0
\(157\) −1615.03 + 2797.31i −0.820975 + 1.42197i 0.0839811 + 0.996467i \(0.473236\pi\)
−0.904957 + 0.425504i \(0.860097\pi\)
\(158\) 51.4333 89.0850i 0.0258975 0.0448559i
\(159\) 0 0
\(160\) 122.800 + 212.695i 0.0606760 + 0.105094i
\(161\) −1328.17 −0.650154
\(162\) 0 0
\(163\) −694.054 −0.333512 −0.166756 0.985998i \(-0.553329\pi\)
−0.166756 + 0.985998i \(0.553329\pi\)
\(164\) −1444.62 2502.16i −0.687842 1.19138i
\(165\) 0 0
\(166\) −177.148 + 306.830i −0.0828275 + 0.143462i
\(167\) −1608.02 + 2785.17i −0.745103 + 1.29056i 0.205044 + 0.978753i \(0.434266\pi\)
−0.950147 + 0.311803i \(0.899067\pi\)
\(168\) 0 0
\(169\) −1506.48 2609.29i −0.685697 1.18766i
\(170\) −152.662 −0.0688744
\(171\) 0 0
\(172\) −997.296 −0.442111
\(173\) −148.773 257.683i −0.0653816 0.113244i 0.831482 0.555552i \(-0.187493\pi\)
−0.896863 + 0.442308i \(0.854160\pi\)
\(174\) 0 0
\(175\) −181.468 + 314.311i −0.0783867 + 0.135770i
\(176\) 1537.63 2663.26i 0.658542 1.14063i
\(177\) 0 0
\(178\) 189.912 + 328.937i 0.0799690 + 0.138510i
\(179\) −3450.12 −1.44064 −0.720320 0.693642i \(-0.756005\pi\)
−0.720320 + 0.693642i \(0.756005\pi\)
\(180\) 0 0
\(181\) −3089.75 −1.26883 −0.634417 0.772991i \(-0.718760\pi\)
−0.634417 + 0.772991i \(0.718760\pi\)
\(182\) 135.548 + 234.776i 0.0552060 + 0.0956197i
\(183\) 0 0
\(184\) 188.561 326.598i 0.0755484 0.130854i
\(185\) −387.442 + 671.069i −0.153974 + 0.266692i
\(186\) 0 0
\(187\) 2908.20 + 5037.15i 1.13727 + 1.96980i
\(188\) 1757.36 0.681748
\(189\) 0 0
\(190\) −159.611 −0.0609444
\(191\) −766.057 1326.85i −0.290209 0.502657i 0.683650 0.729810i \(-0.260392\pi\)
−0.973859 + 0.227153i \(0.927058\pi\)
\(192\) 0 0
\(193\) 2597.21 4498.50i 0.968660 1.67777i 0.269219 0.963079i \(-0.413235\pi\)
0.699442 0.714690i \(-0.253432\pi\)
\(194\) 43.3373 75.0625i 0.0160383 0.0277792i
\(195\) 0 0
\(196\) −524.552 908.550i −0.191163 0.331104i
\(197\) −2005.61 −0.725349 −0.362674 0.931916i \(-0.618136\pi\)
−0.362674 + 0.931916i \(0.618136\pi\)
\(198\) 0 0
\(199\) −2874.68 −1.02402 −0.512011 0.858979i \(-0.671099\pi\)
−0.512011 + 0.858979i \(0.671099\pi\)
\(200\) −51.5260 89.2457i −0.0182172 0.0315531i
\(201\) 0 0
\(202\) −156.015 + 270.225i −0.0543424 + 0.0941237i
\(203\) −1265.92 + 2192.64i −0.437686 + 0.758094i
\(204\) 0 0
\(205\) 910.506 + 1577.04i 0.310207 + 0.537295i
\(206\) −274.522 −0.0928488
\(207\) 0 0
\(208\) 4503.90 1.50139
\(209\) 3040.59 + 5266.45i 1.00632 + 1.74301i
\(210\) 0 0
\(211\) 1374.97 2381.52i 0.448610 0.777016i −0.549686 0.835372i \(-0.685253\pi\)
0.998296 + 0.0583560i \(0.0185858\pi\)
\(212\) −54.2598 + 93.9807i −0.0175782 + 0.0304463i
\(213\) 0 0
\(214\) −61.5190 106.554i −0.0196512 0.0340368i
\(215\) 628.569 0.199386
\(216\) 0 0
\(217\) −672.093 −0.210252
\(218\) 170.804 + 295.842i 0.0530657 + 0.0919125i
\(219\) 0 0
\(220\) −977.444 + 1692.98i −0.299542 + 0.518822i
\(221\) −4259.23 + 7377.20i −1.29641 + 2.24545i
\(222\) 0 0
\(223\) 391.864 + 678.728i 0.117673 + 0.203816i 0.918845 0.394618i \(-0.129123\pi\)
−0.801172 + 0.598434i \(0.795790\pi\)
\(224\) −713.093 −0.212703
\(225\) 0 0
\(226\) 17.6377 0.00519134
\(227\) 72.8326 + 126.150i 0.0212955 + 0.0368848i 0.876477 0.481444i \(-0.159888\pi\)
−0.855181 + 0.518329i \(0.826554\pi\)
\(228\) 0 0
\(229\) 1705.91 2954.72i 0.492270 0.852636i −0.507691 0.861539i \(-0.669501\pi\)
0.999960 + 0.00890324i \(0.00283403\pi\)
\(230\) −59.1729 + 102.490i −0.0169641 + 0.0293827i
\(231\) 0 0
\(232\) −359.446 622.578i −0.101719 0.176182i
\(233\) 134.977 0.0379511 0.0189756 0.999820i \(-0.493960\pi\)
0.0189756 + 0.999820i \(0.493960\pi\)
\(234\) 0 0
\(235\) −1107.62 −0.307459
\(236\) 948.347 + 1642.58i 0.261577 + 0.453064i
\(237\) 0 0
\(238\) 221.626 383.867i 0.0603608 0.104548i
\(239\) 1122.66 1944.51i 0.303845 0.526275i −0.673159 0.739498i \(-0.735063\pi\)
0.977003 + 0.213223i \(0.0683962\pi\)
\(240\) 0 0
\(241\) −2079.27 3601.40i −0.555757 0.962600i −0.997844 0.0656276i \(-0.979095\pi\)
0.442087 0.896972i \(-0.354238\pi\)
\(242\) −284.057 −0.0754542
\(243\) 0 0
\(244\) 432.715 0.113532
\(245\) 330.611 + 572.635i 0.0862121 + 0.149324i
\(246\) 0 0
\(247\) −4453.11 + 7713.02i −1.14714 + 1.98691i
\(248\) 95.4171 165.267i 0.0244314 0.0423165i
\(249\) 0 0
\(250\) 16.1695 + 28.0064i 0.00409060 + 0.00708513i
\(251\) 3946.14 0.992343 0.496171 0.868225i \(-0.334739\pi\)
0.496171 + 0.868225i \(0.334739\pi\)
\(252\) 0 0
\(253\) 4508.96 1.12046
\(254\) −76.7094 132.865i −0.0189495 0.0328215i
\(255\) 0 0
\(256\) −1878.80 + 3254.17i −0.458690 + 0.794475i
\(257\) 2847.92 4932.74i 0.691239 1.19726i −0.280193 0.959944i \(-0.590399\pi\)
0.971432 0.237317i \(-0.0762681\pi\)
\(258\) 0 0
\(259\) −1124.93 1948.44i −0.269883 0.467452i
\(260\) −2863.04 −0.682917
\(261\) 0 0
\(262\) −87.6873 −0.0206769
\(263\) −1407.03 2437.05i −0.329891 0.571387i 0.652599 0.757703i \(-0.273679\pi\)
−0.982490 + 0.186316i \(0.940345\pi\)
\(264\) 0 0
\(265\) 34.1985 59.2335i 0.00792753 0.0137309i
\(266\) 231.715 401.342i 0.0534110 0.0925106i
\(267\) 0 0
\(268\) −301.678 522.521i −0.0687608 0.119097i
\(269\) 200.985 0.0455548 0.0227774 0.999741i \(-0.492749\pi\)
0.0227774 + 0.999741i \(0.492749\pi\)
\(270\) 0 0
\(271\) −2406.05 −0.539326 −0.269663 0.962955i \(-0.586912\pi\)
−0.269663 + 0.962955i \(0.586912\pi\)
\(272\) −3682.01 6377.43i −0.820790 1.42165i
\(273\) 0 0
\(274\) −104.965 + 181.805i −0.0231429 + 0.0400847i
\(275\) 616.057 1067.04i 0.135090 0.233982i
\(276\) 0 0
\(277\) 4214.67 + 7300.02i 0.914205 + 1.58345i 0.808061 + 0.589098i \(0.200517\pi\)
0.106143 + 0.994351i \(0.466150\pi\)
\(278\) 803.593 0.173368
\(279\) 0 0
\(280\) 299.210 0.0638615
\(281\) −1987.13 3441.81i −0.421859 0.730681i 0.574263 0.818671i \(-0.305289\pi\)
−0.996121 + 0.0879906i \(0.971955\pi\)
\(282\) 0 0
\(283\) 1536.20 2660.78i 0.322678 0.558895i −0.658362 0.752702i \(-0.728750\pi\)
0.981040 + 0.193807i \(0.0620836\pi\)
\(284\) 2888.84 5003.62i 0.603595 1.04546i
\(285\) 0 0
\(286\) −460.166 797.031i −0.0951406 0.164788i
\(287\) −5287.28 −1.08745
\(288\) 0 0
\(289\) 9014.97 1.83492
\(290\) 112.799 + 195.373i 0.0228406 + 0.0395610i
\(291\) 0 0
\(292\) −1990.47 + 3447.59i −0.398915 + 0.690942i
\(293\) −1991.11 + 3448.70i −0.397002 + 0.687628i −0.993355 0.115095i \(-0.963283\pi\)
0.596352 + 0.802723i \(0.296616\pi\)
\(294\) 0 0
\(295\) −597.717 1035.28i −0.117968 0.204326i
\(296\) 638.826 0.125443
\(297\) 0 0
\(298\) −657.391 −0.127791
\(299\) 3301.81 + 5718.91i 0.638625 + 1.10613i
\(300\) 0 0
\(301\) −912.520 + 1580.53i −0.174740 + 0.302659i
\(302\) −145.574 + 252.141i −0.0277378 + 0.0480433i
\(303\) 0 0
\(304\) −3849.62 6667.74i −0.726286 1.25796i
\(305\) −272.729 −0.0512013
\(306\) 0 0
\(307\) −2996.06 −0.556984 −0.278492 0.960439i \(-0.589835\pi\)
−0.278492 + 0.960439i \(0.589835\pi\)
\(308\) −2837.99 4915.55i −0.525032 0.909381i
\(309\) 0 0
\(310\) −29.9431 + 51.8630i −0.00548598 + 0.00950200i
\(311\) 1539.97 2667.30i 0.280783 0.486331i −0.690795 0.723051i \(-0.742739\pi\)
0.971578 + 0.236720i \(0.0760724\pi\)
\(312\) 0 0
\(313\) −3976.82 6888.06i −0.718158 1.24389i −0.961729 0.274003i \(-0.911652\pi\)
0.243571 0.969883i \(-0.421681\pi\)
\(314\) −835.655 −0.150187
\(315\) 0 0
\(316\) −3154.26 −0.561523
\(317\) 3416.49 + 5917.53i 0.605328 + 1.04846i 0.991999 + 0.126242i \(0.0402915\pi\)
−0.386671 + 0.922218i \(0.626375\pi\)
\(318\) 0 0
\(319\) 4297.62 7443.69i 0.754296 1.30648i
\(320\) 1216.19 2106.51i 0.212460 0.367992i
\(321\) 0 0
\(322\) −171.808 297.580i −0.0297344 0.0515014i
\(323\) 14562.0 2.50852
\(324\) 0 0
\(325\) 1804.50 0.307987
\(326\) −89.7802 155.504i −0.0152530 0.0264189i
\(327\) 0 0
\(328\) 750.636 1300.14i 0.126363 0.218867i
\(329\) 1607.97 2785.09i 0.269454 0.466708i
\(330\) 0 0
\(331\) 1148.29 + 1988.89i 0.190682 + 0.330270i 0.945476 0.325691i \(-0.105597\pi\)
−0.754795 + 0.655961i \(0.772264\pi\)
\(332\) 10864.0 1.79591
\(333\) 0 0
\(334\) −832.028 −0.136307
\(335\) 190.139 + 329.331i 0.0310102 + 0.0537113i
\(336\) 0 0
\(337\) −3630.74 + 6288.63i −0.586881 + 1.01651i 0.407757 + 0.913091i \(0.366311\pi\)
−0.994638 + 0.103418i \(0.967022\pi\)
\(338\) 389.744 675.056i 0.0627198 0.108634i
\(339\) 0 0
\(340\) 2340.59 + 4054.02i 0.373342 + 0.646647i
\(341\) 2281.66 0.362342
\(342\) 0 0
\(343\) −6899.32 −1.08609
\(344\) −259.101 448.777i −0.0406099 0.0703384i
\(345\) 0 0
\(346\) 38.4894 66.6657i 0.00598036 0.0103583i
\(347\) −3712.61 + 6430.43i −0.574361 + 0.994822i 0.421750 + 0.906712i \(0.361416\pi\)
−0.996111 + 0.0881101i \(0.971917\pi\)
\(348\) 0 0
\(349\) 239.080 + 414.098i 0.0366695 + 0.0635134i 0.883778 0.467907i \(-0.154992\pi\)
−0.847108 + 0.531420i \(0.821658\pi\)
\(350\) −93.8959 −0.0143399
\(351\) 0 0
\(352\) 2420.85 0.366567
\(353\) 2496.54 + 4324.14i 0.376424 + 0.651985i 0.990539 0.137231i \(-0.0438204\pi\)
−0.614115 + 0.789216i \(0.710487\pi\)
\(354\) 0 0
\(355\) −1820.76 + 3153.64i −0.272213 + 0.471488i
\(356\) 5823.39 10086.4i 0.866964 1.50162i
\(357\) 0 0
\(358\) −446.295 773.006i −0.0658867 0.114119i
\(359\) −6873.09 −1.01044 −0.505219 0.862991i \(-0.668588\pi\)
−0.505219 + 0.862991i \(0.668588\pi\)
\(360\) 0 0
\(361\) 8365.87 1.21969
\(362\) −399.678 692.262i −0.0580293 0.100510i
\(363\) 0 0
\(364\) 4156.40 7199.10i 0.598502 1.03664i
\(365\) 1254.54 2172.92i 0.179906 0.311605i
\(366\) 0 0
\(367\) 4344.36 + 7524.65i 0.617912 + 1.07025i 0.989866 + 0.142004i \(0.0453545\pi\)
−0.371954 + 0.928251i \(0.621312\pi\)
\(368\) −5708.70 −0.808659
\(369\) 0 0
\(370\) −200.472 −0.0281677
\(371\) 99.2948 + 171.984i 0.0138952 + 0.0240672i
\(372\) 0 0
\(373\) −1747.27 + 3026.36i −0.242548 + 0.420105i −0.961439 0.275017i \(-0.911316\pi\)
0.718892 + 0.695122i \(0.244650\pi\)
\(374\) −752.388 + 1303.17i −0.104024 + 0.180175i
\(375\) 0 0
\(376\) 456.568 + 790.799i 0.0626216 + 0.108464i
\(377\) 12588.2 1.71970
\(378\) 0 0
\(379\) −5802.83 −0.786468 −0.393234 0.919438i \(-0.628644\pi\)
−0.393234 + 0.919438i \(0.628644\pi\)
\(380\) 2447.14 + 4238.56i 0.330356 + 0.572194i
\(381\) 0 0
\(382\) 198.189 343.273i 0.0265450 0.0459774i
\(383\) 1679.28 2908.60i 0.224040 0.388049i −0.731991 0.681314i \(-0.761409\pi\)
0.956031 + 0.293266i \(0.0947420\pi\)
\(384\) 0 0
\(385\) 1788.71 + 3098.14i 0.236782 + 0.410119i
\(386\) 1343.86 0.177204
\(387\) 0 0
\(388\) −2657.76 −0.347751
\(389\) −9.56850 16.5731i −0.00124715 0.00216013i 0.865401 0.501080i \(-0.167064\pi\)
−0.866648 + 0.498920i \(0.833730\pi\)
\(390\) 0 0
\(391\) 5398.58 9350.62i 0.698256 1.20941i
\(392\) 272.561 472.090i 0.0351184 0.0608268i
\(393\) 0 0
\(394\) −259.438 449.360i −0.0331733 0.0574579i
\(395\) 1988.05 0.253239
\(396\) 0 0
\(397\) −4348.59 −0.549747 −0.274873 0.961480i \(-0.588636\pi\)
−0.274873 + 0.961480i \(0.588636\pi\)
\(398\) −371.857 644.076i −0.0468330 0.0811171i
\(399\) 0 0
\(400\) −779.976 + 1350.96i −0.0974970 + 0.168870i
\(401\) −4250.81 + 7362.61i −0.529364 + 0.916886i 0.470049 + 0.882640i \(0.344236\pi\)
−0.999413 + 0.0342457i \(0.989097\pi\)
\(402\) 0 0
\(403\) 1670.81 + 2893.93i 0.206523 + 0.357709i
\(404\) 9567.96 1.17828
\(405\) 0 0
\(406\) −655.019 −0.0800690
\(407\) 3818.98 + 6614.66i 0.465110 + 0.805594i
\(408\) 0 0
\(409\) 1405.33 2434.11i 0.169900 0.294276i −0.768484 0.639869i \(-0.778989\pi\)
0.938385 + 0.345593i \(0.112322\pi\)
\(410\) −235.559 + 408.001i −0.0283742 + 0.0491456i
\(411\) 0 0
\(412\) 4208.93 + 7290.07i 0.503298 + 0.871738i
\(413\) 3470.93 0.413543
\(414\) 0 0
\(415\) −6847.31 −0.809930
\(416\) 1772.73 + 3070.47i 0.208931 + 0.361880i
\(417\) 0 0
\(418\) −786.638 + 1362.50i −0.0920471 + 0.159430i
\(419\) 8177.71 14164.2i 0.953478 1.65147i 0.215666 0.976467i \(-0.430808\pi\)
0.737812 0.675006i \(-0.235859\pi\)
\(420\) 0 0
\(421\) 2255.45 + 3906.55i 0.261102 + 0.452242i 0.966535 0.256535i \(-0.0825808\pi\)
−0.705433 + 0.708776i \(0.749248\pi\)
\(422\) 711.443 0.0820675
\(423\) 0 0
\(424\) −56.3876 −0.00645854
\(425\) −1475.21 2555.14i −0.168372 0.291629i
\(426\) 0 0
\(427\) 395.932 685.774i 0.0448723 0.0777212i
\(428\) −1886.40 + 3267.33i −0.213043 + 0.369001i
\(429\) 0 0
\(430\) 81.3093 + 140.832i 0.00911880 + 0.0157942i
\(431\) 5850.47 0.653845 0.326923 0.945051i \(-0.393988\pi\)
0.326923 + 0.945051i \(0.393988\pi\)
\(432\) 0 0
\(433\) −3836.82 −0.425833 −0.212916 0.977070i \(-0.568296\pi\)
−0.212916 + 0.977070i \(0.568296\pi\)
\(434\) −86.9394 150.583i −0.00961572 0.0166549i
\(435\) 0 0
\(436\) 5237.48 9071.59i 0.575298 0.996446i
\(437\) 5644.33 9776.27i 0.617860 1.07017i
\(438\) 0 0
\(439\) −8113.67 14053.3i −0.882106 1.52785i −0.848995 0.528400i \(-0.822792\pi\)
−0.0331103 0.999452i \(-0.510541\pi\)
\(440\) −1015.77 −0.110057
\(441\) 0 0
\(442\) −2203.83 −0.237162
\(443\) −3352.56 5806.81i −0.359560 0.622776i 0.628327 0.777949i \(-0.283740\pi\)
−0.987887 + 0.155173i \(0.950407\pi\)
\(444\) 0 0
\(445\) −3670.33 + 6357.19i −0.390989 + 0.677213i
\(446\) −101.380 + 175.595i −0.0107634 + 0.0186428i
\(447\) 0 0
\(448\) 3531.20 + 6116.21i 0.372396 + 0.645009i
\(449\) 213.100 0.0223982 0.0111991 0.999937i \(-0.496435\pi\)
0.0111991 + 0.999937i \(0.496435\pi\)
\(450\) 0 0
\(451\) 17949.6 1.87408
\(452\) −270.419 468.379i −0.0281403 0.0487404i
\(453\) 0 0
\(454\) −18.8427 + 32.6365i −0.00194787 + 0.00337381i
\(455\) −2619.67 + 4537.40i −0.269916 + 0.467509i
\(456\) 0 0
\(457\) −8231.03 14256.6i −0.842520 1.45929i −0.887758 0.460311i \(-0.847738\pi\)
0.0452381 0.998976i \(-0.485595\pi\)
\(458\) 882.680 0.0900545
\(459\) 0 0
\(460\) 3628.92 0.367824
\(461\) −781.029 1352.78i −0.0789071 0.136671i 0.823872 0.566777i \(-0.191810\pi\)
−0.902779 + 0.430105i \(0.858476\pi\)
\(462\) 0 0
\(463\) 2962.14 5130.57i 0.297326 0.514984i −0.678197 0.734880i \(-0.737238\pi\)
0.975523 + 0.219896i \(0.0705717\pi\)
\(464\) −5441.12 + 9424.30i −0.544392 + 0.942914i
\(465\) 0 0
\(466\) 17.4601 + 30.2417i 0.00173567 + 0.00300627i
\(467\) −17905.1 −1.77420 −0.887098 0.461582i \(-0.847282\pi\)
−0.887098 + 0.461582i \(0.847282\pi\)
\(468\) 0 0
\(469\) −1104.13 −0.108708
\(470\) −143.277 248.163i −0.0140614 0.0243551i
\(471\) 0 0
\(472\) −492.768 + 853.499i −0.0480540 + 0.0832320i
\(473\) 3097.87 5365.67i 0.301142 0.521594i
\(474\) 0 0
\(475\) −1542.36 2671.45i −0.148986 0.258052i
\(476\) −13591.7 −1.30877
\(477\) 0 0
\(478\) 580.893 0.0555846
\(479\) −4957.72 8587.02i −0.472910 0.819104i 0.526609 0.850107i \(-0.323463\pi\)
−0.999519 + 0.0310033i \(0.990130\pi\)
\(480\) 0 0
\(481\) −5593.11 + 9687.55i −0.530195 + 0.918324i
\(482\) 537.933 931.727i 0.0508344 0.0880477i
\(483\) 0 0
\(484\) 4355.12 + 7543.29i 0.409008 + 0.708423i
\(485\) 1675.12 0.156831
\(486\) 0 0
\(487\) 11910.8 1.10828 0.554138 0.832425i \(-0.313048\pi\)
0.554138 + 0.832425i \(0.313048\pi\)
\(488\) 112.421 + 194.719i 0.0104284 + 0.0180625i
\(489\) 0 0
\(490\) −85.5331 + 148.148i −0.00788570 + 0.0136584i
\(491\) −5531.88 + 9581.50i −0.508453 + 0.880666i 0.491499 + 0.870878i \(0.336449\pi\)
−0.999952 + 0.00978823i \(0.996884\pi\)
\(492\) 0 0
\(493\) −10291.1 17824.7i −0.940135 1.62836i
\(494\) −2304.15 −0.209856
\(495\) 0 0
\(496\) −2888.76 −0.261510
\(497\) −5286.54 9156.56i −0.477130 0.826414i
\(498\) 0 0
\(499\) −4673.62 + 8094.95i −0.419279 + 0.726212i −0.995867 0.0908227i \(-0.971050\pi\)
0.576588 + 0.817035i \(0.304384\pi\)
\(500\) 495.817 858.780i 0.0443472 0.0768116i
\(501\) 0 0
\(502\) 510.457 + 884.138i 0.0453841 + 0.0786076i
\(503\) −19474.2 −1.72627 −0.863135 0.504973i \(-0.831502\pi\)
−0.863135 + 0.504973i \(0.831502\pi\)
\(504\) 0 0
\(505\) −6030.43 −0.531387
\(506\) 583.262 + 1010.24i 0.0512434 + 0.0887562i
\(507\) 0 0
\(508\) −2352.19 + 4074.12i −0.205436 + 0.355826i
\(509\) −11082.0 + 19194.7i −0.965035 + 1.67149i −0.255514 + 0.966805i \(0.582245\pi\)
−0.709521 + 0.704684i \(0.751089\pi\)
\(510\) 0 0
\(511\) 3642.53 + 6309.05i 0.315335 + 0.546176i
\(512\) −5122.66 −0.442172
\(513\) 0 0
\(514\) 1473.58 0.126453
\(515\) −2652.77 4594.74i −0.226981 0.393142i
\(516\) 0 0
\(517\) −5458.83 + 9454.98i −0.464370 + 0.804312i
\(518\) 291.034 504.085i 0.0246859 0.0427572i
\(519\) 0 0
\(520\) −743.830 1288.35i −0.0627290 0.108650i
\(521\) −254.564 −0.0214062 −0.0107031 0.999943i \(-0.503407\pi\)
−0.0107031 + 0.999943i \(0.503407\pi\)
\(522\) 0 0
\(523\) 4049.92 0.338606 0.169303 0.985564i \(-0.445848\pi\)
0.169303 + 0.985564i \(0.445848\pi\)
\(524\) 1344.41 + 2328.58i 0.112081 + 0.194131i
\(525\) 0 0
\(526\) 364.016 630.495i 0.0301747 0.0522640i
\(527\) 2731.83 4731.67i 0.225807 0.391110i
\(528\) 0 0
\(529\) 1898.44 + 3288.20i 0.156032 + 0.270256i
\(530\) 17.6951 0.00145024
\(531\) 0 0
\(532\) −14210.4 −1.15808
\(533\) 13144.1 + 22766.2i 1.06817 + 1.85012i
\(534\) 0 0
\(535\) 1188.95 2059.31i 0.0960796 0.166415i
\(536\) 156.754 271.506i 0.0126320 0.0218792i
\(537\) 0 0
\(538\) 25.9986 + 45.0309i 0.00208342 + 0.00360859i
\(539\) 6517.60 0.520841
\(540\) 0 0
\(541\) −4085.88 −0.324705 −0.162353 0.986733i \(-0.551908\pi\)
−0.162353 + 0.986733i \(0.551908\pi\)
\(542\) −311.238 539.079i −0.0246657 0.0427222i
\(543\) 0 0
\(544\) 2898.48 5020.32i 0.228440 0.395670i
\(545\) −3301.05 + 5717.58i −0.259452 + 0.449384i
\(546\) 0 0
\(547\) 7696.10 + 13330.0i 0.601575 + 1.04196i 0.992583 + 0.121571i \(0.0387932\pi\)
−0.391008 + 0.920387i \(0.627873\pi\)
\(548\) 6437.22 0.501796
\(549\) 0 0
\(550\) 318.763 0.0247129
\(551\) −10759.5 18636.1i −0.831891 1.44088i
\(552\) 0 0
\(553\) −2886.13 + 4998.93i −0.221937 + 0.384405i
\(554\) −1090.39 + 1888.60i −0.0836211 + 0.144836i
\(555\) 0 0
\(556\) −12320.6 21339.8i −0.939762 1.62772i
\(557\) −10897.6 −0.828987 −0.414493 0.910052i \(-0.636041\pi\)
−0.414493 + 0.910052i \(0.636041\pi\)
\(558\) 0 0
\(559\) 9074.02 0.686566
\(560\) −2264.65 3922.49i −0.170891 0.295992i
\(561\) 0 0
\(562\) 514.095 890.439i 0.0385868 0.0668343i
\(563\) 775.845 1343.80i 0.0580781 0.100594i −0.835525 0.549453i \(-0.814836\pi\)
0.893603 + 0.448859i \(0.148169\pi\)
\(564\) 0 0
\(565\) 170.438 + 295.207i 0.0126909 + 0.0219813i
\(566\) 794.870 0.0590298
\(567\) 0 0
\(568\) 3002.12 0.221772
\(569\) 623.475 + 1079.89i 0.0459357 + 0.0795630i 0.888079 0.459691i \(-0.152040\pi\)
−0.842143 + 0.539254i \(0.818706\pi\)
\(570\) 0 0
\(571\) −2098.29 + 3634.34i −0.153784 + 0.266362i −0.932616 0.360871i \(-0.882479\pi\)
0.778832 + 0.627233i \(0.215813\pi\)
\(572\) −14110.4 + 24439.9i −1.03144 + 1.78651i
\(573\) 0 0
\(574\) −683.943 1184.62i −0.0497338 0.0861415i
\(575\) −2287.21 −0.165884
\(576\) 0 0
\(577\) 20585.1 1.48521 0.742607 0.669728i \(-0.233589\pi\)
0.742607 + 0.669728i \(0.233589\pi\)
\(578\) 1166.14 + 2019.82i 0.0839189 + 0.145352i
\(579\) 0 0
\(580\) 3458.82 5990.85i 0.247620 0.428891i
\(581\) 9940.53 17217.5i 0.709815 1.22944i
\(582\) 0 0
\(583\) −337.091 583.859i −0.0239466 0.0414768i
\(584\) −2068.52 −0.146569
\(585\) 0 0
\(586\) −1030.25 −0.0726265
\(587\) 2427.89 + 4205.23i 0.170715 + 0.295687i 0.938670 0.344817i \(-0.112059\pi\)
−0.767955 + 0.640504i \(0.778726\pi\)
\(588\) 0 0
\(589\) 2856.19 4947.06i 0.199808 0.346078i
\(590\) 154.637 267.839i 0.0107903 0.0186894i
\(591\) 0 0
\(592\) −4835.13 8374.68i −0.335680 0.581414i
\(593\) −23965.6 −1.65961 −0.829804 0.558055i \(-0.811548\pi\)
−0.829804 + 0.558055i \(0.811548\pi\)
\(594\) 0 0
\(595\) 8566.50 0.590239
\(596\) 10079.0 + 17457.4i 0.692706 + 1.19980i
\(597\) 0 0
\(598\) −854.220 + 1479.55i −0.0584141 + 0.101176i
\(599\) −7114.56 + 12322.8i −0.485297 + 0.840560i −0.999857 0.0168947i \(-0.994622\pi\)
0.514560 + 0.857454i \(0.327955\pi\)
\(600\) 0 0
\(601\) 4438.98 + 7688.55i 0.301281 + 0.521834i 0.976426 0.215851i \(-0.0692524\pi\)
−0.675145 + 0.737685i \(0.735919\pi\)
\(602\) −472.161 −0.0319665
\(603\) 0 0
\(604\) 8927.64 0.601424
\(605\) −2744.92 4754.33i −0.184457 0.319490i
\(606\) 0 0
\(607\) 5438.36 9419.51i 0.363651 0.629862i −0.624908 0.780699i \(-0.714863\pi\)
0.988559 + 0.150837i \(0.0481968\pi\)
\(608\) 3030.42 5248.85i 0.202138 0.350113i
\(609\) 0 0
\(610\) −35.2791 61.1053i −0.00234166 0.00405587i
\(611\) −15989.5 −1.05870
\(612\) 0 0
\(613\) −19544.8 −1.28778 −0.643890 0.765118i \(-0.722680\pi\)
−0.643890 + 0.765118i \(0.722680\pi\)
\(614\) −387.559 671.272i −0.0254733 0.0441210i
\(615\) 0 0
\(616\) 1474.64 2554.16i 0.0964530 0.167062i
\(617\) −2520.88 + 4366.29i −0.164484 + 0.284895i −0.936472 0.350742i \(-0.885929\pi\)
0.771988 + 0.635637i \(0.219263\pi\)
\(618\) 0 0
\(619\) 2604.03 + 4510.31i 0.169087 + 0.292867i 0.938099 0.346367i \(-0.112585\pi\)
−0.769012 + 0.639234i \(0.779252\pi\)
\(620\) 1836.33 0.118950
\(621\) 0 0
\(622\) 796.818 0.0513657
\(623\) −10656.7 18458.0i −0.685318 1.18701i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 1028.85 1782.03i 0.0656889 0.113777i
\(627\) 0 0
\(628\) 12812.1 + 22191.2i 0.814107 + 1.41007i
\(629\) 18289.9 1.15940
\(630\) 0 0
\(631\) −20284.6 −1.27974 −0.639872 0.768482i \(-0.721013\pi\)
−0.639872 + 0.768482i \(0.721013\pi\)
\(632\) −819.490 1419.40i −0.0515784 0.0893364i
\(633\) 0 0
\(634\) −883.888 + 1530.94i −0.0553686 + 0.0959012i
\(635\) 1482.52 2567.81i 0.0926491 0.160473i
\(636\) 0 0
\(637\) 4772.70 + 8266.56i 0.296862 + 0.514180i
\(638\) 2223.69 0.137989
\(639\) 0 0
\(640\) 2594.08 0.160219
\(641\) 10426.2 + 18058.7i 0.642449 + 1.11275i 0.984885 + 0.173212i \(0.0554147\pi\)
−0.342436 + 0.939541i \(0.611252\pi\)
\(642\) 0 0
\(643\) 1093.61 1894.19i 0.0670729 0.116174i −0.830539 0.556961i \(-0.811967\pi\)
0.897612 + 0.440787i \(0.145301\pi\)
\(644\) −5268.25 + 9124.88i −0.322357 + 0.558339i
\(645\) 0 0
\(646\) 1883.68 + 3262.63i 0.114725 + 0.198710i
\(647\) 17044.1 1.03566 0.517831 0.855483i \(-0.326740\pi\)
0.517831 + 0.855483i \(0.326740\pi\)
\(648\) 0 0
\(649\) −11783.3 −0.712688
\(650\) 233.423 + 404.301i 0.0140856 + 0.0243969i
\(651\) 0 0
\(652\) −2752.99 + 4768.32i −0.165361 + 0.286414i
\(653\) −4237.13 + 7338.93i −0.253923 + 0.439808i −0.964602 0.263708i \(-0.915054\pi\)
0.710679 + 0.703516i \(0.248388\pi\)
\(654\) 0 0
\(655\) −847.343 1467.64i −0.0505472 0.0875504i
\(656\) −22725.6 −1.35257
\(657\) 0 0
\(658\) 832.005 0.0492932
\(659\) −12780.1 22135.7i −0.755450 1.30848i −0.945151 0.326635i \(-0.894085\pi\)
0.189701 0.981842i \(-0.439248\pi\)
\(660\) 0 0
\(661\) −604.797 + 1047.54i −0.0355883 + 0.0616407i −0.883271 0.468863i \(-0.844664\pi\)
0.847683 + 0.530504i \(0.177997\pi\)
\(662\) −297.076 + 514.551i −0.0174414 + 0.0302093i
\(663\) 0 0
\(664\) 2822.52 + 4888.74i 0.164962 + 0.285723i
\(665\) 8956.46 0.522281
\(666\) 0 0
\(667\) −15955.6 −0.926241
\(668\) 12756.5 + 22094.9i 0.738869 + 1.27976i
\(669\) 0 0
\(670\) −49.1914 + 85.2020i −0.00283646 + 0.00491290i
\(671\) −1344.13 + 2328.10i −0.0773318 + 0.133943i
\(672\) 0 0
\(673\) 4349.11 + 7532.87i 0.249102 + 0.431457i 0.963277 0.268510i \(-0.0865312\pi\)
−0.714175 + 0.699967i \(0.753198\pi\)
\(674\) −1878.64 −0.107362
\(675\) 0 0
\(676\) −23902.0 −1.35992
\(677\) 4212.24 + 7295.82i 0.239128 + 0.414182i 0.960464 0.278403i \(-0.0898051\pi\)
−0.721336 + 0.692585i \(0.756472\pi\)
\(678\) 0 0
\(679\) −2431.84 + 4212.07i −0.137445 + 0.238062i
\(680\) −1216.19 + 2106.50i −0.0685863 + 0.118795i
\(681\) 0 0
\(682\) 295.147 + 511.209i 0.0165715 + 0.0287026i
\(683\) −17828.6 −0.998817 −0.499408 0.866367i \(-0.666449\pi\)
−0.499408 + 0.866367i \(0.666449\pi\)
\(684\) 0 0
\(685\) −4057.21 −0.226304
\(686\) −892.470 1545.80i −0.0496715 0.0860336i
\(687\) 0 0
\(688\) −3922.15 + 6793.37i −0.217341 + 0.376446i
\(689\) 493.689 855.095i 0.0272976 0.0472809i
\(690\) 0 0
\(691\) −7262.54 12579.1i −0.399826 0.692519i 0.593878 0.804555i \(-0.297596\pi\)
−0.993704 + 0.112036i \(0.964263\pi\)
\(692\) −2360.45 −0.129669
\(693\) 0 0
\(694\) −1921.00 −0.105072
\(695\) 7765.31 + 13449.9i 0.423820 + 0.734078i
\(696\) 0 0
\(697\) 21491.0 37223.5i 1.16791 2.02287i
\(698\) −61.8529 + 107.132i −0.00335411 + 0.00580949i
\(699\) 0 0
\(700\) 1439.60 + 2493.45i 0.0777309 + 0.134634i
\(701\) 18815.5 1.01377 0.506883 0.862015i \(-0.330798\pi\)
0.506883 + 0.862015i \(0.330798\pi\)
\(702\) 0 0
\(703\) 19122.4 1.02591
\(704\) −11987.9 20763.6i −0.641777 1.11159i
\(705\) 0 0
\(706\) −645.886 + 1118.71i −0.0344310 + 0.0596362i
\(707\) 8754.63 15163.5i 0.465703 0.806621i
\(708\) 0 0
\(709\) 6467.21 + 11201.5i 0.342569 + 0.593346i 0.984909 0.173073i \(-0.0553697\pi\)
−0.642340 + 0.766420i \(0.722036\pi\)
\(710\) −942.105 −0.0497980
\(711\) 0 0
\(712\) 6051.75 0.318538
\(713\) −2117.75 3668.06i −0.111235 0.192665i
\(714\) 0 0
\(715\) 8893.40 15403.8i 0.465167 0.805692i
\(716\) −13685.0 + 23703.2i −0.714293 + 1.23719i
\(717\) 0 0
\(718\) −889.076 1539.92i −0.0462117 0.0800411i
\(719\) −8471.10 −0.439386 −0.219693 0.975569i \(-0.570506\pi\)
−0.219693 + 0.975569i \(0.570506\pi\)
\(720\) 0 0
\(721\) 15404.6 0.795695
\(722\) 1082.18 + 1874.39i 0.0557818 + 0.0966169i
\(723\) 0 0
\(724\) −12255.6 + 21227.3i −0.629109 + 1.08965i
\(725\) −2180.00 + 3775.87i −0.111673 + 0.193424i
\(726\) 0 0
\(727\) −12184.7 21104.6i −0.621605 1.07665i −0.989187 0.146660i \(-0.953148\pi\)
0.367582 0.929991i \(-0.380186\pi\)
\(728\) 4319.40 0.219900
\(729\) 0 0
\(730\) 649.129 0.0329114
\(731\) −7418.17 12848.7i −0.375337 0.650102i
\(732\) 0 0
\(733\) 17705.9 30667.5i 0.892199 1.54533i 0.0549659 0.998488i \(-0.482495\pi\)
0.837233 0.546846i \(-0.184172\pi\)
\(734\) −1123.94 + 1946.72i −0.0565196 + 0.0978947i
\(735\) 0 0
\(736\) −2246.94 3891.82i −0.112532 0.194911i
\(737\) 3748.37 0.187345
\(738\) 0 0
\(739\) −24447.0 −1.21691 −0.608456 0.793588i \(-0.708211\pi\)
−0.608456 + 0.793588i \(0.708211\pi\)
\(740\) 3073.60 + 5323.63i 0.152686 + 0.264460i
\(741\) 0 0
\(742\) −25.6888 + 44.4943i −0.00127098 + 0.00220140i
\(743\) 12063.0 20893.7i 0.595623 1.03165i −0.397836 0.917457i \(-0.630239\pi\)
0.993459 0.114192i \(-0.0364280\pi\)
\(744\) 0 0
\(745\) −6352.53 11002.9i −0.312401 0.541094i
\(746\) −904.081 −0.0443710
\(747\) 0 0
\(748\) 46141.9 2.25550
\(749\) 3452.08 + 5979.19i 0.168406 + 0.291689i
\(750\) 0 0
\(751\) −5941.19 + 10290.4i −0.288678 + 0.500005i −0.973494 0.228711i \(-0.926549\pi\)
0.684816 + 0.728716i \(0.259882\pi\)
\(752\) 6911.31 11970.7i 0.335146 0.580490i
\(753\) 0 0
\(754\) 1628.36 + 2820.41i 0.0786491 + 0.136224i
\(755\) −5626.85 −0.271234
\(756\) 0 0
\(757\) −14601.3 −0.701049 −0.350525 0.936554i \(-0.613997\pi\)
−0.350525 + 0.936554i \(0.613997\pi\)
\(758\) −750.632 1300.13i −0.0359686 0.0622994i
\(759\) 0 0
\(760\) −1271.55 + 2202.39i −0.0606894 + 0.105117i
\(761\) 10148.2 17577.1i 0.483404 0.837281i −0.516414 0.856339i \(-0.672733\pi\)
0.999818 + 0.0190580i \(0.00606673\pi\)
\(762\) 0 0
\(763\) −9584.54 16600.9i −0.454762 0.787671i
\(764\) −12154.4 −0.575562
\(765\) 0 0
\(766\) 868.902 0.0409853
\(767\) −8628.65 14945.3i −0.406209 0.703575i
\(768\) 0 0
\(769\) −18161.0 + 31455.8i −0.851629 + 1.47506i 0.0281090 + 0.999605i \(0.491051\pi\)
−0.879738 + 0.475459i \(0.842282\pi\)
\(770\) −462.762 + 801.527i −0.0216582 + 0.0375130i
\(771\) 0 0
\(772\) −20603.9 35686.9i −0.960556 1.66373i
\(773\) 28930.9 1.34615 0.673073 0.739576i \(-0.264974\pi\)
0.673073 + 0.739576i \(0.264974\pi\)
\(774\) 0 0
\(775\) −1157.39 −0.0536448
\(776\) −690.497 1195.98i −0.0319425 0.0553261i
\(777\) 0 0
\(778\) 2.47549 4.28767i 0.000114075 0.000197584i
\(779\) 22469.3 38918.0i 1.03344 1.78996i
\(780\) 0 0
\(781\) 17947.0 + 31085.2i 0.822274 + 1.42422i
\(782\) 2793.36 0.127737
\(783\) 0 0
\(784\) −8251.80 −0.375902
\(785\) −8075.13 13986.5i