Properties

Label 405.4.e.r.136.2
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: 6.0.95327307.1
Defining polynomial: \(x^{6} - 3 x^{5} + 20 x^{4} - 35 x^{3} + 85 x^{2} - 68 x + 16\)
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 136.2
Root \(0.500000 - 3.26212i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.4.e.r.271.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.129356 + 0.224051i) q^{2} +(3.96653 + 6.87024i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-7.25871 + 12.5725i) q^{7} -4.12208 q^{8} +O(q^{10})\) \(q+(-0.129356 + 0.224051i) q^{2} +(3.96653 + 6.87024i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-7.25871 + 12.5725i) q^{7} -4.12208 q^{8} -1.29356 q^{10} +(-24.6423 + 42.6817i) q^{11} +(-36.0900 - 62.5097i) q^{13} +(-1.87792 - 3.25265i) q^{14} +(-31.1991 + 54.0383i) q^{16} -118.017 q^{17} +123.389 q^{19} +(-19.8327 + 34.3512i) q^{20} +(-6.37526 - 11.0423i) q^{22} +(-45.7442 - 79.2312i) q^{23} +(-12.5000 + 21.6506i) q^{25} +18.6739 q^{26} -115.168 q^{28} +(87.2001 - 151.035i) q^{29} +(23.1478 + 40.0932i) q^{31} +(-24.5599 - 42.5390i) q^{32} +(15.2662 - 26.4418i) q^{34} -72.5871 q^{35} +154.977 q^{37} +(-15.9611 + 27.6455i) q^{38} +(-10.3052 - 17.8491i) q^{40} +(-182.101 - 315.409i) q^{41} +(-62.8569 + 108.871i) q^{43} -390.978 q^{44} +23.6692 q^{46} +(-110.762 + 191.845i) q^{47} +(66.1222 + 114.527i) q^{49} +(-3.23390 - 5.60129i) q^{50} +(286.304 - 495.894i) q^{52} +13.6794 q^{53} -246.423 q^{55} +(29.9210 - 51.8247i) q^{56} +(22.5597 + 39.0746i) q^{58} +(119.543 + 207.055i) q^{59} +(27.2729 - 47.2380i) q^{61} -11.9772 q^{62} -486.477 q^{64} +(180.450 - 312.549i) q^{65} +(38.0279 + 65.8662i) q^{67} +(-468.118 - 810.804i) q^{68} +(9.38959 - 16.2633i) q^{70} -728.303 q^{71} -501.815 q^{73} +(-20.0472 + 34.7227i) q^{74} +(489.427 + 847.712i) q^{76} +(-357.742 - 619.628i) q^{77} +(-198.805 + 344.340i) q^{79} -311.991 q^{80} +94.2237 q^{82} +(-684.731 + 1185.99i) q^{83} +(-295.042 - 511.028i) q^{85} +(-16.2619 - 28.1664i) q^{86} +(101.577 - 175.937i) q^{88} -1468.13 q^{89} +1047.87 q^{91} +(362.892 - 628.547i) q^{92} +(-28.6554 - 49.6326i) q^{94} +(308.473 + 534.290i) q^{95} +(-167.512 + 290.139i) q^{97} -34.2133 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8} + O(q^{10}) \) \( 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8} - 10 q^{10} + 38 q^{11} - 28 q^{13} - 108 q^{14} - 191 q^{16} + 38 q^{17} + 374 q^{19} + 115 q^{20} - 122 q^{22} - 81 q^{23} - 75 q^{25} - 832 q^{26} + 820 q^{28} + 160 q^{29} - 227 q^{31} - 569 q^{32} - 17 q^{34} - 440 q^{35} + 156 q^{37} - 757 q^{38} + 180 q^{40} - 338 q^{41} - 22 q^{43} - 3272 q^{44} - 2850 q^{46} - 472 q^{47} + 197 q^{49} - 25 q^{50} + 1566 q^{52} - 1042 q^{53} + 380 q^{55} - 1254 q^{56} + 2096 q^{58} + 140 q^{59} - 595 q^{61} - 2814 q^{62} - 1836 q^{64} + 140 q^{65} - 878 q^{67} - 3053 q^{68} + 540 q^{70} + 1204 q^{71} + 2588 q^{73} + 2878 q^{74} - 525 q^{76} + 288 q^{77} - 629 q^{79} - 1910 q^{80} - 3364 q^{82} - 1287 q^{83} + 95 q^{85} - 3730 q^{86} + 858 q^{88} - 4308 q^{89} - 880 q^{91} + 1959 q^{92} + 1108 q^{94} + 935 q^{95} - 1392 q^{97} + 5386 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.129356 + 0.224051i −0.0457343 + 0.0792142i −0.887986 0.459870i \(-0.847896\pi\)
0.842252 + 0.539084i \(0.181229\pi\)
\(3\) 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 −0.992705 0.120572i \(-0.961527\pi\)
0.600771 + 0.799421i \(0.294860\pi\)
\(8\) −4.12208 −0.182172
\(9\) 0 0
\(10\) −1.29356 −0.0409060
\(11\) −24.6423 + 42.6817i −0.675448 + 1.16991i 0.300890 + 0.953659i \(0.402716\pi\)
−0.976338 + 0.216251i \(0.930617\pi\)
\(12\) 0 0
\(13\) −36.0900 62.5097i −0.769967 1.33362i −0.937580 0.347768i \(-0.886940\pi\)
0.167614 0.985853i \(-0.446394\pi\)
\(14\) −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 \(-0.818540\pi\)
−0.841861 + 0.539694i \(0.818540\pi\)
\(18\) 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 \(-0.302783\pi\)
−0.995398 + 0.0958280i \(0.969450\pi\)
\(24\) 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 −0.439266 0.898357i \(-0.644761\pi\)
0.997633 0.0687632i \(-0.0219053\pi\)
\(30\) 0 0
\(31\) 23.1478 + 40.0932i 0.134112 + 0.232289i 0.925258 0.379339i \(-0.123849\pi\)
−0.791146 + 0.611627i \(0.790515\pi\)
\(32\) −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 −0.970635 0.240556i \(-0.922670\pi\)
0.276990 0.960873i \(-0.410663\pi\)
\(42\) 0 0
\(43\) −62.8569 + 108.871i −0.222921 + 0.386110i −0.955694 0.294363i \(-0.904892\pi\)
0.732773 + 0.680473i \(0.238226\pi\)
\(44\) −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 \(-0.945031\pi\)
0.641376 + 0.767227i \(0.278364\pi\)
\(48\) 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 \(-0.494357\pi\)
0.0177265 + 0.999843i \(0.494357\pi\)
\(54\) 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 \(-0.0816962\pi\)
−0.703461 + 0.710734i \(0.748363\pi\)
\(60\) 0 0
\(61\) 27.2729 47.2380i 0.0572448 0.0991509i −0.835983 0.548756i \(-0.815102\pi\)
0.893228 + 0.449605i \(0.148435\pi\)
\(62\) −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 0.898611 0.438745i \(-0.144577\pi\)
−0.829270 + 0.558848i \(0.811244\pi\)
\(68\) −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 \(-0.708304\pi\)
−0.608688 + 0.793410i \(0.708304\pi\)
\(72\) 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 −0.972154 0.234343i \(-0.924706\pi\)
0.689024 + 0.724739i \(0.258040\pi\)
\(80\) −311.991 −0.436020
\(81\) 0 0
\(82\) 94.2237 0.126894
\(83\) −684.731 + 1185.99i −0.905530 + 1.56842i −0.0853248 + 0.996353i \(0.527193\pi\)
−0.820205 + 0.572070i \(0.806141\pi\)
\(84\) 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 \(-0.838665\pi\)
−0.874278 + 0.485425i \(0.838665\pi\)
\(90\) 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 −0.940280 0.340403i \(-0.889437\pi\)
0.764937 + 0.644105i \(0.222770\pi\)
\(98\) −34.2133 −0.0352659
\(99\) 0 0
\(100\) −198.327 −0.198327
\(101\) −603.043 + 1044.50i −0.594109 + 1.02903i 0.399563 + 0.916706i \(0.369162\pi\)
−0.993672 + 0.112321i \(0.964171\pi\)
\(102\) 0 0
\(103\) −530.555 918.948i −0.507545 0.879093i −0.999962 0.00873396i \(-0.997220\pi\)
0.492417 0.870359i \(-0.336113\pi\)
\(104\) 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 \(-0.431077\pi\)
0.214841 + 0.976649i \(0.431077\pi\)
\(108\) 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 \(-0.175701\pi\)
−0.879865 + 0.475223i \(0.842367\pi\)
\(114\) 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 \(-0.130612\pi\)
−0.803962 + 0.594680i \(0.797279\pi\)
\(132\) 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 \(-0.914756\pi\)
0.711339 + 0.702849i \(0.248089\pi\)
\(138\) 0 0
\(139\) 1553.06 + 2689.98i 0.947691 + 1.64145i 0.750271 + 0.661130i \(0.229923\pi\)
0.197420 + 0.980319i \(0.436744\pi\)
\(140\) −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 0.968969 + 0.247181i \(0.0795043\pi\)
−0.270419 + 0.962743i \(0.587162\pi\)
\(150\) 0 0
\(151\) 562.685 974.599i 0.303249 0.525243i −0.673621 0.739077i \(-0.735262\pi\)
0.976870 + 0.213834i \(0.0685952\pi\)
\(152\) −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 −0.904957 0.425504i \(-0.860097\pi\)
0.0839811 0.996467i \(-0.473236\pi\)
\(158\) −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 0.950147 + 0.311803i \(0.100933\pi\)
−0.205044 + 0.978753i \(0.565734\pi\)
\(168\) 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 \(-0.812507\pi\)
0.896863 + 0.442308i \(0.145840\pi\)
\(174\) 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 \(-0.243995\pi\)
0.720320 + 0.693642i \(0.243995\pi\)
\(180\) 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 \(-0.739608\pi\)
0.973859 + 0.227153i \(0.0729418\pi\)
\(192\) 0 0
\(193\) 2597.21 + 4498.50i 0.968660 + 1.67777i 0.699442 + 0.714690i \(0.253432\pi\)
0.269219 + 0.963079i \(0.413235\pi\)
\(194\) −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 \(-0.381864\pi\)
0.362674 + 0.931916i \(0.381864\pi\)
\(198\) 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 0.998296 0.0583560i \(-0.0185858\pi\)
−0.549686 + 0.835372i \(0.685253\pi\)
\(212\) 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 −0.801172 0.598434i \(-0.795790\pi\)
0.918845 + 0.394618i \(0.129123\pi\)
\(224\) 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 \(-0.840112\pi\)
0.855181 + 0.518329i \(0.173446\pi\)
\(228\) 0 0
\(229\) 1705.91 + 2954.72i 0.492270 + 0.852636i 0.999960 0.00890324i \(-0.00283403\pi\)
−0.507691 + 0.861539i \(0.669501\pi\)
\(230\) 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 \(-0.506040\pi\)
−0.0189756 + 0.999820i \(0.506040\pi\)
\(234\) 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 \(-0.264937\pi\)
−0.977003 + 0.213223i \(0.931604\pi\)
\(240\) 0 0
\(241\) −2079.27 + 3601.40i −0.555757 + 0.962600i 0.442087 + 0.896972i \(0.354238\pi\)
−0.997844 + 0.0656276i \(0.979095\pi\)
\(242\) 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 \(-0.665261\pi\)
−0.496171 + 0.868225i \(0.665261\pi\)
\(252\) 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 −0.971432 0.237317i \(-0.923732\pi\)
0.280193 0.959944i \(-0.409601\pi\)
\(258\) 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 \(-0.726321\pi\)
0.982490 + 0.186316i \(0.0596548\pi\)
\(264\) 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 \(-0.507251\pi\)
−0.0227774 + 0.999741i \(0.507251\pi\)
\(270\) 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 0.106143 0.994351i \(-0.466150\pi\)
0.808061 0.589098i \(-0.200517\pi\)
\(278\) −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 \(-0.694711\pi\)
0.996121 + 0.0879906i \(0.0280445\pi\)
\(282\) 0 0
\(283\) 1536.20 + 2660.78i 0.322678 + 0.558895i 0.981040 0.193807i \(-0.0620836\pi\)
−0.658362 + 0.752702i \(0.728750\pi\)
\(284\) −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 \(-0.0367172\pi\)
−0.596352 + 0.802723i \(0.703384\pi\)
\(294\) 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 \(-0.257261\pi\)
−0.971578 + 0.236720i \(0.923928\pi\)
\(312\) 0 0
\(313\) −3976.82 + 6888.06i −0.718158 + 1.24389i 0.243571 + 0.969883i \(0.421681\pi\)
−0.961729 + 0.274003i \(0.911652\pi\)
\(314\) 835.655 0.150187
\(315\) 0 0
\(316\) −3154.26 −0.561523
\(317\) −3416.49 + 5917.53i −0.605328 + 1.04846i 0.386671 + 0.922218i \(0.373625\pi\)
−0.991999 + 0.126242i \(0.959708\pi\)
\(318\) 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 −0.754795 0.655961i \(-0.772264\pi\)
0.945476 + 0.325691i \(0.105597\pi\)
\(332\) −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 −0.994638 0.103418i \(-0.967022\pi\)
0.407757 0.913091i \(-0.366311\pi\)
\(338\) −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 0.996111 + 0.0881101i \(0.0280827\pi\)
−0.421750 + 0.906712i \(0.638584\pi\)
\(348\) 0 0
\(349\) 239.080 414.098i 0.0366695 0.0635134i −0.847108 0.531420i \(-0.821658\pi\)
0.883778 + 0.467907i \(0.154992\pi\)
\(350\) 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 \(-0.956180\pi\)
0.614115 + 0.789216i \(0.289513\pi\)
\(354\) 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 \(-0.331412\pi\)
0.505219 + 0.862991i \(0.331412\pi\)
\(360\) 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 −0.371954 0.928251i \(-0.621312\pi\)
0.989866 0.142004i \(-0.0453545\pi\)
\(368\) 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 0.718892 0.695122i \(-0.244650\pi\)
−0.961439 + 0.275017i \(0.911316\pi\)
\(374\) 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 \(-0.238591\pi\)
−0.956031 + 0.293266i \(0.905258\pi\)
\(384\) 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 \(-0.832936\pi\)
0.866648 + 0.498920i \(0.166270\pi\)
\(390\) 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 0.999413 + 0.0342457i \(0.0109029\pi\)
−0.470049 + 0.882640i \(0.655764\pi\)
\(402\) 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 0.938385 0.345593i \(-0.112322\pi\)
−0.768484 + 0.639869i \(0.778989\pi\)
\(410\) 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 −0.737812 0.675006i \(-0.764141\pi\)
−0.215666 0.976467i \(-0.569192\pi\)
\(420\) 0 0
\(421\) 2255.45 3906.55i 0.261102 0.452242i −0.705433 0.708776i \(-0.749248\pi\)
0.966535 + 0.256535i \(0.0825808\pi\)
\(422\) −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 \(-0.606012\pi\)
−0.326923 + 0.945051i \(0.606012\pi\)
\(432\) 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 −0.0331103 + 0.999452i \(0.510541\pi\)
−0.848995 + 0.528400i \(0.822792\pi\)
\(440\) 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 \(-0.716260\pi\)
0.987887 + 0.155173i \(0.0495934\pi\)
\(444\) 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 \(-0.503565\pi\)
−0.0111991 + 0.999937i \(0.503565\pi\)
\(450\) 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 0.0452381 + 0.998976i \(0.485595\pi\)
−0.887758 + 0.460311i \(0.847738\pi\)
\(458\) −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 \(-0.808190\pi\)
0.902779 + 0.430105i \(0.141524\pi\)
\(462\) 0 0
\(463\) 2962.14 + 5130.57i 0.297326 + 0.514984i 0.975523 0.219896i \(-0.0705717\pi\)
−0.678197 + 0.734880i \(0.737238\pi\)
\(464\) 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 \(-0.152718\pi\)
0.887098 + 0.461582i \(0.152718\pi\)
\(468\) 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 \(-0.676537\pi\)
0.999519 + 0.0310033i \(0.00987023\pi\)
\(480\) 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 0.999952 + 0.00978823i \(0.00311574\pi\)
−0.491499 + 0.870878i \(0.663551\pi\)
\(492\) 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 0.576588 0.817035i \(-0.304384\pi\)
−0.995867 + 0.0908227i \(0.971050\pi\)
\(500\) −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 \(-0.168498\pi\)
0.863135 + 0.504973i \(0.168498\pi\)
\(504\) 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 0.709521 + 0.704684i \(0.248911\pi\)
0.255514 + 0.966805i \(0.417755\pi\)
\(510\) 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 \(-0.496593\pi\)
0.0107031 + 0.999943i \(0.496593\pi\)
\(522\) 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 −0.391008 0.920387i \(-0.627873\pi\)
0.992583 0.121571i \(-0.0387932\pi\)
\(548\) −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 \(-0.363959\pi\)
0.414493 + 0.910052i \(0.363959\pi\)
\(558\) 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 \(-0.185164\pi\)
−0.893603 + 0.448859i \(0.851831\pi\)
\(564\) 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 \(-0.847960\pi\)
0.842143 + 0.539254i \(0.181294\pi\)
\(570\) 0 0
\(571\) −2098.29 3634.34i −0.153784 0.266362i 0.778832 0.627233i \(-0.215813\pi\)
−0.932616 + 0.360871i \(0.882479\pi\)
\(572\) 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 \(-0.887941\pi\)
0.767955 + 0.640504i \(0.221274\pi\)
\(588\) 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 \(-0.188452\pi\)
0.829804 + 0.558055i \(0.188452\pi\)
\(594\) 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 \(-0.00537802\pi\)
−0.514560 + 0.857454i \(0.672045\pi\)
\(600\) 0 0
\(601\) 4438.98 7688.55i 0.301281 0.521834i −0.675145 0.737685i \(-0.735919\pi\)
0.976426 + 0.215851i \(0.0692524\pi\)
\(602\) 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 0.988559 0.150837i \(-0.0481968\pi\)
−0.624908 + 0.780699i \(0.714863\pi\)
\(608\) −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 \(-0.114071\pi\)
−0.771988 + 0.635637i \(0.780737\pi\)
\(618\) 0 0
\(619\) 2604.03 4510.31i 0.169087 0.292867i −0.769012 0.639234i \(-0.779252\pi\)
0.938099 + 0.346367i \(0.112585\pi\)
\(620\) −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 0.342436 + 0.939541i \(0.388748\pi\)
−0.984885 + 0.173212i \(0.944585\pi\)
\(642\) 0 0
\(643\) 1093.61 + 1894.19i 0.0670729 + 0.116174i 0.897612 0.440787i \(-0.145301\pi\)
−0.830539 + 0.556961i \(0.811967\pi\)
\(644\) 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 \(-0.673260\pi\)
−0.517831 + 0.855483i \(0.673260\pi\)
\(648\) 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 \(-0.0849456\pi\)
−0.710679 + 0.703516i \(0.751612\pi\)
\(654\) 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 −0.189701 0.981842i \(-0.560752\pi\)
0.945151 0.326635i \(-0.105915\pi\)
\(660\) 0 0
\(661\) −604.797 1047.54i −0.0355883 0.0616407i 0.847683 0.530504i \(-0.177997\pi\)
−0.883271 + 0.468863i \(0.844664\pi\)
\(662\) 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 −0.714175 0.699967i \(-0.753198\pi\)
0.963277 + 0.268510i \(0.0865312\pi\)
\(674\) 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 \(-0.910195\pi\)
0.721336 + 0.692585i \(0.243528\pi\)
\(678\) 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 \(-0.333551\pi\)
0.499408 + 0.866367i \(0.333551\pi\)
\(684\) 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 −0.993704 0.112036i \(-0.964263\pi\)
0.593878 + 0.804555i \(0.297596\pi\)
\(692\) 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 \(-0.669202\pi\)
−0.506883 + 0.862015i \(0.669202\pi\)
\(702\) 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 −0.642340 0.766420i \(-0.722036\pi\)
0.984909 + 0.173073i \(0.0553697\pi\)
\(710\) 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 \(-0.429494\pi\)
0.219693 + 0.975569i \(0.429494\pi\)
\(720\) 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 0.367582 + 0.929991i \(0.380186\pi\)
−0.989187 + 0.146660i \(0.953148\pi\)
\(728\) −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 0.837233 + 0.546846i \(0.184172\pi\)
0.0549659 + 0.998488i \(0.482495\pi\)
\(734\) 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 −0.993459 0.114192i \(-0.963572\pi\)
0.397836 0.917457i \(-0.369761\pi\)
\(744\) 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 0.684816 0.728716i \(-0.259882\pi\)
−0.973494 + 0.228711i \(0.926549\pi\)
\(752\) −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 \(-0.327267\pi\)
−0.999818 + 0.0190580i \(0.993933\pi\)
\(762\) 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 −0.879738 0.475459i \(-0.842282\pi\)
0.0281090 0.999605i \(-0.491051\pi\)
\(770\) 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 \(-0.735026\pi\)
−0.673073 + 0.739576i \(0.735026\pi\)
\(774\) 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 0.367151 0.635925i
\(786\) 0 0