Properties

Label 225.4.h.d.181.6
Level $225$
Weight $4$
Character 225.181
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.6
Character \(\chi\) \(=\) 225.181
Dual form 225.4.h.d.46.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.626289 - 1.92752i) q^{2} +(3.14904 - 2.28791i) q^{4} +(-3.12321 - 10.7352i) q^{5} -16.4425 q^{7} +(-19.4994 - 14.1671i) q^{8} +O(q^{10})\) \(q+(-0.626289 - 1.92752i) q^{2} +(3.14904 - 2.28791i) q^{4} +(-3.12321 - 10.7352i) q^{5} -16.4425 q^{7} +(-19.4994 - 14.1671i) q^{8} +(-18.7364 + 12.7434i) q^{10} +(-1.41112 - 4.34299i) q^{11} +(-17.0513 + 52.4784i) q^{13} +(10.2977 + 31.6932i) q^{14} +(-5.47256 + 16.8428i) q^{16} +(-1.72699 - 1.25473i) q^{17} +(22.2151 + 16.1402i) q^{19} +(-34.3964 - 26.6601i) q^{20} +(-7.48743 + 5.43993i) q^{22} +(-30.4050 - 93.5770i) q^{23} +(-105.491 + 67.0569i) q^{25} +111.832 q^{26} +(-51.7780 + 37.6189i) q^{28} +(2.70250 - 1.96348i) q^{29} +(54.6052 + 39.6730i) q^{31} -156.928 q^{32} +(-1.33692 + 4.11462i) q^{34} +(51.3533 + 176.514i) q^{35} +(-56.4702 + 173.797i) q^{37} +(17.1975 - 52.9285i) q^{38} +(-91.1869 + 253.578i) q^{40} +(11.7884 - 36.2811i) q^{41} -252.976 q^{43} +(-14.3801 - 10.4477i) q^{44} +(-161.329 + 117.213i) q^{46} +(-35.6846 + 25.9263i) q^{47} -72.6451 q^{49} +(195.321 + 161.339i) q^{50} +(66.3708 + 204.268i) q^{52} +(-163.853 + 119.046i) q^{53} +(-42.2158 + 28.7128i) q^{55} +(320.618 + 232.943i) q^{56} +(-5.47720 - 3.97942i) q^{58} +(36.4118 - 112.064i) q^{59} +(-248.210 - 763.911i) q^{61} +(42.2718 - 130.099i) q^{62} +(142.063 + 437.225i) q^{64} +(616.623 + 19.1484i) q^{65} +(523.504 + 380.348i) q^{67} -8.30906 q^{68} +(308.072 - 209.533i) q^{70} +(-798.476 + 580.127i) q^{71} +(-256.874 - 790.578i) q^{73} +370.365 q^{74} +106.884 q^{76} +(23.2023 + 71.4095i) q^{77} +(822.092 - 597.285i) q^{79} +(197.904 + 6.14563i) q^{80} -77.3154 q^{82} +(-926.758 - 673.329i) q^{83} +(-8.07608 + 22.4584i) q^{85} +(158.436 + 487.616i) q^{86} +(-34.0117 + 104.677i) q^{88} +(-349.060 - 1074.29i) q^{89} +(280.365 - 862.874i) q^{91} +(-309.843 - 225.114i) q^{92} +(72.3224 + 52.5453i) q^{94} +(103.887 - 288.894i) q^{95} +(457.822 - 332.627i) q^{97} +(45.4968 + 140.025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.626289 1.92752i −0.221427 0.681481i −0.998635 0.0522374i \(-0.983365\pi\)
0.777208 0.629244i \(-0.216635\pi\)
\(3\) 0 0
\(4\) 3.14904 2.28791i 0.393630 0.285989i
\(5\) −3.12321 10.7352i −0.279349 0.960190i
\(6\) 0 0
\(7\) −16.4425 −0.887810 −0.443905 0.896074i \(-0.646407\pi\)
−0.443905 + 0.896074i \(0.646407\pi\)
\(8\) −19.4994 14.1671i −0.861759 0.626104i
\(9\) 0 0
\(10\) −18.7364 + 12.7434i −0.592496 + 0.402982i
\(11\) −1.41112 4.34299i −0.0386790 0.119042i 0.929853 0.367932i \(-0.119934\pi\)
−0.968532 + 0.248890i \(0.919934\pi\)
\(12\) 0 0
\(13\) −17.0513 + 52.4784i −0.363782 + 1.11961i 0.586958 + 0.809617i \(0.300325\pi\)
−0.950740 + 0.309989i \(0.899675\pi\)
\(14\) 10.2977 + 31.6932i 0.196585 + 0.605026i
\(15\) 0 0
\(16\) −5.47256 + 16.8428i −0.0855087 + 0.263169i
\(17\) −1.72699 1.25473i −0.0246386 0.0179010i 0.575398 0.817874i \(-0.304847\pi\)
−0.600036 + 0.799973i \(0.704847\pi\)
\(18\) 0 0
\(19\) 22.2151 + 16.1402i 0.268237 + 0.194885i 0.713770 0.700380i \(-0.246986\pi\)
−0.445534 + 0.895265i \(0.646986\pi\)
\(20\) −34.3964 26.6601i −0.384564 0.298069i
\(21\) 0 0
\(22\) −7.48743 + 5.43993i −0.0725602 + 0.0527181i
\(23\) −30.4050 93.5770i −0.275647 0.848354i −0.989047 0.147598i \(-0.952846\pi\)
0.713400 0.700757i \(-0.247154\pi\)
\(24\) 0 0
\(25\) −105.491 + 67.0569i −0.843929 + 0.536455i
\(26\) 111.832 0.843542
\(27\) 0 0
\(28\) −51.7780 + 37.6189i −0.349469 + 0.253904i
\(29\) 2.70250 1.96348i 0.0173049 0.0125728i −0.579099 0.815257i \(-0.696596\pi\)
0.596404 + 0.802684i \(0.296596\pi\)
\(30\) 0 0
\(31\) 54.6052 + 39.6730i 0.316367 + 0.229854i 0.734624 0.678475i \(-0.237359\pi\)
−0.418257 + 0.908329i \(0.637359\pi\)
\(32\) −156.928 −0.866914
\(33\) 0 0
\(34\) −1.33692 + 4.11462i −0.00674353 + 0.0207545i
\(35\) 51.3533 + 176.514i 0.248008 + 0.852466i
\(36\) 0 0
\(37\) −56.4702 + 173.797i −0.250909 + 0.772219i 0.743699 + 0.668515i \(0.233070\pi\)
−0.994608 + 0.103704i \(0.966930\pi\)
\(38\) 17.1975 52.9285i 0.0734159 0.225951i
\(39\) 0 0
\(40\) −91.1869 + 253.578i −0.360448 + 1.00235i
\(41\) 11.7884 36.2811i 0.0449035 0.138199i −0.926091 0.377300i \(-0.876853\pi\)
0.970995 + 0.239101i \(0.0768527\pi\)
\(42\) 0 0
\(43\) −252.976 −0.897173 −0.448586 0.893739i \(-0.648072\pi\)
−0.448586 + 0.893739i \(0.648072\pi\)
\(44\) −14.3801 10.4477i −0.0492699 0.0357967i
\(45\) 0 0
\(46\) −161.329 + 117.213i −0.517102 + 0.375697i
\(47\) −35.6846 + 25.9263i −0.110747 + 0.0804627i −0.641780 0.766888i \(-0.721804\pi\)
0.531033 + 0.847351i \(0.321804\pi\)
\(48\) 0 0
\(49\) −72.6451 −0.211793
\(50\) 195.321 + 161.339i 0.552452 + 0.456336i
\(51\) 0 0
\(52\) 66.3708 + 204.268i 0.177000 + 0.544749i
\(53\) −163.853 + 119.046i −0.424659 + 0.308533i −0.779510 0.626390i \(-0.784532\pi\)
0.354851 + 0.934923i \(0.384532\pi\)
\(54\) 0 0
\(55\) −42.2158 + 28.7128i −0.103498 + 0.0703934i
\(56\) 320.618 + 232.943i 0.765078 + 0.555862i
\(57\) 0 0
\(58\) −5.47720 3.97942i −0.0123999 0.00900903i
\(59\) 36.4118 112.064i 0.0803460 0.247280i −0.902813 0.430034i \(-0.858501\pi\)
0.983159 + 0.182755i \(0.0585014\pi\)
\(60\) 0 0
\(61\) −248.210 763.911i −0.520984 1.60342i −0.772123 0.635473i \(-0.780805\pi\)
0.251139 0.967951i \(-0.419195\pi\)
\(62\) 42.2718 130.099i 0.0865892 0.266494i
\(63\) 0 0
\(64\) 142.063 + 437.225i 0.277467 + 0.853954i
\(65\) 616.623 + 19.1484i 1.17666 + 0.0365395i
\(66\) 0 0
\(67\) 523.504 + 380.348i 0.954571 + 0.693536i 0.951884 0.306460i \(-0.0991446\pi\)
0.00268734 + 0.999996i \(0.499145\pi\)
\(68\) −8.30906 −0.0148180
\(69\) 0 0
\(70\) 308.072 209.533i 0.526024 0.357772i
\(71\) −798.476 + 580.127i −1.33467 + 0.969696i −0.335050 + 0.942200i \(0.608753\pi\)
−0.999622 + 0.0274953i \(0.991247\pi\)
\(72\) 0 0
\(73\) −256.874 790.578i −0.411847 1.26754i −0.915040 0.403362i \(-0.867842\pi\)
0.503193 0.864174i \(-0.332158\pi\)
\(74\) 370.365 0.581811
\(75\) 0 0
\(76\) 106.884 0.161321
\(77\) 23.2023 + 71.4095i 0.0343396 + 0.105687i
\(78\) 0 0
\(79\) 822.092 597.285i 1.17079 0.850630i 0.179689 0.983724i \(-0.442491\pi\)
0.991104 + 0.133093i \(0.0424909\pi\)
\(80\) 197.904 + 6.14563i 0.276579 + 0.00858878i
\(81\) 0 0
\(82\) −77.3154 −0.104123
\(83\) −926.758 673.329i −1.22560 0.890452i −0.229049 0.973415i \(-0.573562\pi\)
−0.996553 + 0.0829629i \(0.973562\pi\)
\(84\) 0 0
\(85\) −8.07608 + 22.4584i −0.0103056 + 0.0286583i
\(86\) 158.436 + 487.616i 0.198658 + 0.611406i
\(87\) 0 0
\(88\) −34.0117 + 104.677i −0.0412006 + 0.126802i
\(89\) −349.060 1074.29i −0.415733 1.27949i −0.911594 0.411093i \(-0.865147\pi\)
0.495861 0.868402i \(-0.334853\pi\)
\(90\) 0 0
\(91\) 280.365 862.874i 0.322969 0.993998i
\(92\) −309.843 225.114i −0.351123 0.255106i
\(93\) 0 0
\(94\) 72.3224 + 52.5453i 0.0793562 + 0.0576557i
\(95\) 103.887 288.894i 0.112195 0.311999i
\(96\) 0 0
\(97\) 457.822 332.627i 0.479224 0.348177i −0.321801 0.946807i \(-0.604288\pi\)
0.801025 + 0.598630i \(0.204288\pi\)
\(98\) 45.4968 + 140.025i 0.0468967 + 0.144333i
\(99\) 0 0
\(100\) −178.776 + 452.519i −0.178776 + 0.452519i
\(101\) −732.732 −0.721877 −0.360938 0.932590i \(-0.617544\pi\)
−0.360938 + 0.932590i \(0.617544\pi\)
\(102\) 0 0
\(103\) 148.901 108.183i 0.142443 0.103491i −0.514282 0.857621i \(-0.671941\pi\)
0.656725 + 0.754130i \(0.271941\pi\)
\(104\) 1075.96 781.728i 1.01448 0.737065i
\(105\) 0 0
\(106\) 332.083 + 241.272i 0.304290 + 0.221080i
\(107\) −1461.97 −1.32088 −0.660440 0.750879i \(-0.729630\pi\)
−0.660440 + 0.750879i \(0.729630\pi\)
\(108\) 0 0
\(109\) 551.250 1696.57i 0.484405 1.49085i −0.348435 0.937333i \(-0.613287\pi\)
0.832840 0.553514i \(-0.186713\pi\)
\(110\) 81.7838 + 63.3893i 0.0708889 + 0.0549448i
\(111\) 0 0
\(112\) 89.9823 276.937i 0.0759155 0.233644i
\(113\) 602.823 1855.30i 0.501848 1.54453i −0.304158 0.952622i \(-0.598375\pi\)
0.806006 0.591907i \(-0.201625\pi\)
\(114\) 0 0
\(115\) −909.611 + 618.666i −0.737580 + 0.501660i
\(116\) 4.01802 12.3662i 0.00321606 0.00989803i
\(117\) 0 0
\(118\) −238.810 −0.186307
\(119\) 28.3959 + 20.6308i 0.0218744 + 0.0158926i
\(120\) 0 0
\(121\) 1059.93 770.085i 0.796342 0.578576i
\(122\) −1317.00 + 956.859i −0.977343 + 0.710081i
\(123\) 0 0
\(124\) 262.722 0.190267
\(125\) 1049.34 + 923.040i 0.750849 + 0.660474i
\(126\) 0 0
\(127\) −286.464 881.645i −0.200154 0.616011i −0.999878 0.0156424i \(-0.995021\pi\)
0.799724 0.600368i \(-0.204979\pi\)
\(128\) −261.874 + 190.263i −0.180833 + 0.131383i
\(129\) 0 0
\(130\) −349.275 1200.55i −0.235642 0.809960i
\(131\) 2108.91 + 1532.21i 1.40654 + 1.02191i 0.993815 + 0.111050i \(0.0354213\pi\)
0.412720 + 0.910858i \(0.364579\pi\)
\(132\) 0 0
\(133\) −365.271 265.385i −0.238143 0.173021i
\(134\) 405.264 1247.27i 0.261265 0.804090i
\(135\) 0 0
\(136\) 15.8992 + 48.9328i 0.0100246 + 0.0308526i
\(137\) −902.756 + 2778.40i −0.562976 + 1.73266i 0.110915 + 0.993830i \(0.464622\pi\)
−0.673890 + 0.738831i \(0.735378\pi\)
\(138\) 0 0
\(139\) 308.366 + 949.054i 0.188167 + 0.579120i 0.999989 0.00478634i \(-0.00152355\pi\)
−0.811821 + 0.583906i \(0.801524\pi\)
\(140\) 565.562 + 438.358i 0.341420 + 0.264629i
\(141\) 0 0
\(142\) 1618.28 + 1175.75i 0.956361 + 0.694837i
\(143\) 251.974 0.147351
\(144\) 0 0
\(145\) −29.5190 22.8797i −0.0169063 0.0131038i
\(146\) −1362.98 + 990.261i −0.772608 + 0.561333i
\(147\) 0 0
\(148\) 219.806 + 676.494i 0.122081 + 0.375726i
\(149\) 2608.22 1.43405 0.717026 0.697046i \(-0.245503\pi\)
0.717026 + 0.697046i \(0.245503\pi\)
\(150\) 0 0
\(151\) −434.771 −0.234312 −0.117156 0.993114i \(-0.537378\pi\)
−0.117156 + 0.993114i \(0.537378\pi\)
\(152\) −204.520 629.448i −0.109137 0.335888i
\(153\) 0 0
\(154\) 123.112 89.4459i 0.0644197 0.0468036i
\(155\) 255.356 710.107i 0.132327 0.367982i
\(156\) 0 0
\(157\) −2183.01 −1.10970 −0.554851 0.831949i \(-0.687225\pi\)
−0.554851 + 0.831949i \(0.687225\pi\)
\(158\) −1666.15 1210.53i −0.838933 0.609521i
\(159\) 0 0
\(160\) 490.120 + 1684.66i 0.242171 + 0.832402i
\(161\) 499.933 + 1538.64i 0.244722 + 0.753178i
\(162\) 0 0
\(163\) 1.56141 4.80554i 0.000750303 0.00230920i −0.950681 0.310171i \(-0.899614\pi\)
0.951431 + 0.307862i \(0.0996136\pi\)
\(164\) −45.8856 141.221i −0.0218480 0.0672411i
\(165\) 0 0
\(166\) −717.437 + 2208.04i −0.335445 + 1.03239i
\(167\) −182.453 132.560i −0.0845428 0.0614239i 0.544711 0.838624i \(-0.316639\pi\)
−0.629254 + 0.777200i \(0.716639\pi\)
\(168\) 0 0
\(169\) −685.824 498.280i −0.312164 0.226800i
\(170\) 48.3470 + 1.50135i 0.0218120 + 0.000677343i
\(171\) 0 0
\(172\) −796.631 + 578.786i −0.353154 + 0.256582i
\(173\) −1021.65 3144.32i −0.448986 1.38184i −0.878052 0.478565i \(-0.841157\pi\)
0.429066 0.903273i \(-0.358843\pi\)
\(174\) 0 0
\(175\) 1734.53 1102.58i 0.749248 0.476270i
\(176\) 80.8705 0.0346355
\(177\) 0 0
\(178\) −1852.11 + 1345.64i −0.779897 + 0.566629i
\(179\) 1464.76 1064.21i 0.611627 0.444373i −0.238360 0.971177i \(-0.576610\pi\)
0.849987 + 0.526804i \(0.176610\pi\)
\(180\) 0 0
\(181\) −1447.42 1051.61i −0.594395 0.431854i 0.249490 0.968377i \(-0.419737\pi\)
−0.843885 + 0.536524i \(0.819737\pi\)
\(182\) −1838.80 −0.748905
\(183\) 0 0
\(184\) −732.838 + 2255.44i −0.293617 + 0.903661i
\(185\) 2042.13 + 63.4155i 0.811568 + 0.0252022i
\(186\) 0 0
\(187\) −3.01228 + 9.27085i −0.00117797 + 0.00362541i
\(188\) −53.0549 + 163.286i −0.0205821 + 0.0633451i
\(189\) 0 0
\(190\) −621.912 19.3126i −0.237464 0.00737414i
\(191\) −1406.35 + 4328.29i −0.532774 + 1.63971i 0.215637 + 0.976474i \(0.430817\pi\)
−0.748411 + 0.663235i \(0.769183\pi\)
\(192\) 0 0
\(193\) 3534.94 1.31840 0.659199 0.751969i \(-0.270895\pi\)
0.659199 + 0.751969i \(0.270895\pi\)
\(194\) −927.874 674.140i −0.343389 0.249487i
\(195\) 0 0
\(196\) −228.762 + 166.206i −0.0833682 + 0.0605706i
\(197\) −135.139 + 98.1842i −0.0488744 + 0.0355093i −0.611954 0.790893i \(-0.709616\pi\)
0.563080 + 0.826402i \(0.309616\pi\)
\(198\) 0 0
\(199\) −3173.44 −1.13045 −0.565224 0.824937i \(-0.691210\pi\)
−0.565224 + 0.824937i \(0.691210\pi\)
\(200\) 3007.01 + 186.938i 1.06314 + 0.0660925i
\(201\) 0 0
\(202\) 458.902 + 1412.36i 0.159843 + 0.491946i
\(203\) −44.4358 + 32.2845i −0.0153635 + 0.0111622i
\(204\) 0 0
\(205\) −426.304 13.2383i −0.145241 0.00451026i
\(206\) −301.779 219.256i −0.102068 0.0741566i
\(207\) 0 0
\(208\) −790.569 574.382i −0.263539 0.191472i
\(209\) 38.7485 119.256i 0.0128244 0.0394693i
\(210\) 0 0
\(211\) 842.745 + 2593.70i 0.274962 + 0.846245i 0.989229 + 0.146373i \(0.0467599\pi\)
−0.714268 + 0.699873i \(0.753240\pi\)
\(212\) −243.612 + 749.762i −0.0789215 + 0.242895i
\(213\) 0 0
\(214\) 915.617 + 2817.98i 0.292478 + 0.900154i
\(215\) 790.097 + 2715.76i 0.250624 + 0.861456i
\(216\) 0 0
\(217\) −897.844 652.322i −0.280874 0.204067i
\(218\) −3615.42 −1.12324
\(219\) 0 0
\(220\) −67.2469 + 187.004i −0.0206081 + 0.0573082i
\(221\) 95.2934 69.2347i 0.0290051 0.0210734i
\(222\) 0 0
\(223\) −11.6372 35.8157i −0.00349456 0.0107551i 0.949294 0.314390i \(-0.101800\pi\)
−0.952789 + 0.303634i \(0.901800\pi\)
\(224\) 2580.29 0.769655
\(225\) 0 0
\(226\) −3953.67 −1.16369
\(227\) −1025.04 3154.75i −0.299710 0.922413i −0.981598 0.190957i \(-0.938841\pi\)
0.681888 0.731456i \(-0.261159\pi\)
\(228\) 0 0
\(229\) −3988.04 + 2897.48i −1.15082 + 0.836118i −0.988589 0.150635i \(-0.951868\pi\)
−0.162228 + 0.986753i \(0.551868\pi\)
\(230\) 1762.17 + 1365.83i 0.505192 + 0.391566i
\(231\) 0 0
\(232\) −80.5141 −0.0227845
\(233\) −5.77631 4.19673i −0.00162411 0.00117999i 0.586973 0.809607i \(-0.300320\pi\)
−0.588597 + 0.808427i \(0.700320\pi\)
\(234\) 0 0
\(235\) 389.776 + 302.109i 0.108197 + 0.0838614i
\(236\) −141.730 436.201i −0.0390926 0.120315i
\(237\) 0 0
\(238\) 21.9823 67.6545i 0.00598698 0.0184260i
\(239\) −2227.98 6857.03i −0.602997 1.85583i −0.510015 0.860165i \(-0.670360\pi\)
−0.0929815 0.995668i \(-0.529640\pi\)
\(240\) 0 0
\(241\) −1061.81 + 3267.92i −0.283806 + 0.873465i 0.702948 + 0.711241i \(0.251867\pi\)
−0.986754 + 0.162224i \(0.948133\pi\)
\(242\) −2148.18 1560.74i −0.570620 0.414580i
\(243\) 0 0
\(244\) −2529.39 1837.71i −0.663637 0.482160i
\(245\) 226.886 + 779.863i 0.0591642 + 0.203362i
\(246\) 0 0
\(247\) −1225.81 + 890.601i −0.315774 + 0.229424i
\(248\) −502.715 1547.20i −0.128719 0.396158i
\(249\) 0 0
\(250\) 1121.99 2600.72i 0.283842 0.657936i
\(251\) 1687.00 0.424233 0.212117 0.977244i \(-0.431964\pi\)
0.212117 + 0.977244i \(0.431964\pi\)
\(252\) 0 0
\(253\) −363.499 + 264.097i −0.0903279 + 0.0656271i
\(254\) −1519.98 + 1104.33i −0.375480 + 0.272802i
\(255\) 0 0
\(256\) 3506.15 + 2547.37i 0.855993 + 0.621915i
\(257\) −2098.27 −0.509286 −0.254643 0.967035i \(-0.581958\pi\)
−0.254643 + 0.967035i \(0.581958\pi\)
\(258\) 0 0
\(259\) 928.509 2857.66i 0.222760 0.685584i
\(260\) 1985.58 1350.48i 0.473617 0.322128i
\(261\) 0 0
\(262\) 1632.58 5024.57i 0.384966 1.18480i
\(263\) 43.9940 135.400i 0.0103148 0.0317456i −0.945767 0.324847i \(-0.894687\pi\)
0.956081 + 0.293101i \(0.0946873\pi\)
\(264\) 0 0
\(265\) 1789.74 + 1387.19i 0.414878 + 0.321565i
\(266\) −282.770 + 870.275i −0.0651794 + 0.200601i
\(267\) 0 0
\(268\) 2518.74 0.574092
\(269\) −2534.35 1841.31i −0.574432 0.417349i 0.262281 0.964992i \(-0.415525\pi\)
−0.836712 + 0.547643i \(0.815525\pi\)
\(270\) 0 0
\(271\) 2812.49 2043.40i 0.630431 0.458035i −0.226118 0.974100i \(-0.572604\pi\)
0.856550 + 0.516065i \(0.172604\pi\)
\(272\) 30.5841 22.2207i 0.00681778 0.00495341i
\(273\) 0 0
\(274\) 5920.80 1.30543
\(275\) 440.088 + 363.521i 0.0965030 + 0.0797133i
\(276\) 0 0
\(277\) −1027.03 3160.87i −0.222774 0.685626i −0.998510 0.0545694i \(-0.982621\pi\)
0.775736 0.631057i \(-0.217379\pi\)
\(278\) 1636.19 1188.76i 0.352994 0.256465i
\(279\) 0 0
\(280\) 1499.34 4169.44i 0.320009 0.889899i
\(281\) −2319.48 1685.20i −0.492415 0.357760i 0.313698 0.949523i \(-0.398432\pi\)
−0.806112 + 0.591763i \(0.798432\pi\)
\(282\) 0 0
\(283\) 6659.26 + 4838.24i 1.39877 + 1.01627i 0.994838 + 0.101478i \(0.0323571\pi\)
0.403933 + 0.914789i \(0.367643\pi\)
\(284\) −1187.15 + 3653.69i −0.248045 + 0.763403i
\(285\) 0 0
\(286\) −157.809 485.686i −0.0326274 0.100417i
\(287\) −193.831 + 596.550i −0.0398658 + 0.122694i
\(288\) 0 0
\(289\) −1516.79 4668.21i −0.308730 0.950174i
\(290\) −25.6136 + 71.2277i −0.00518649 + 0.0144229i
\(291\) 0 0
\(292\) −2617.68 1901.86i −0.524617 0.381157i
\(293\) −2288.26 −0.456251 −0.228125 0.973632i \(-0.573260\pi\)
−0.228125 + 0.973632i \(0.573260\pi\)
\(294\) 0 0
\(295\) −1316.76 40.8901i −0.259880 0.00807022i
\(296\) 3563.34 2588.92i 0.699713 0.508371i
\(297\) 0 0
\(298\) −1633.50 5027.40i −0.317538 0.977280i
\(299\) 5429.21 1.05010
\(300\) 0 0
\(301\) 4159.55 0.796519
\(302\) 272.292 + 838.029i 0.0518830 + 0.159679i
\(303\) 0 0
\(304\) −393.420 + 285.836i −0.0742242 + 0.0539271i
\(305\) −7425.57 + 5050.45i −1.39405 + 0.948157i
\(306\) 0 0
\(307\) −2783.54 −0.517475 −0.258737 0.965948i \(-0.583306\pi\)
−0.258737 + 0.965948i \(0.583306\pi\)
\(308\) 236.444 + 171.786i 0.0437423 + 0.0317806i
\(309\) 0 0
\(310\) −1528.67 47.4709i −0.280073 0.00869731i
\(311\) 2462.79 + 7579.70i 0.449043 + 1.38201i 0.877989 + 0.478681i \(0.158885\pi\)
−0.428946 + 0.903330i \(0.641115\pi\)
\(312\) 0 0
\(313\) −1489.79 + 4585.11i −0.269035 + 0.828005i 0.721701 + 0.692205i \(0.243360\pi\)
−0.990736 + 0.135800i \(0.956640\pi\)
\(314\) 1367.20 + 4207.80i 0.245718 + 0.756242i
\(315\) 0 0
\(316\) 1222.27 3761.75i 0.217588 0.669668i
\(317\) 6986.98 + 5076.34i 1.23794 + 0.899418i 0.997460 0.0712347i \(-0.0226939\pi\)
0.240484 + 0.970653i \(0.422694\pi\)
\(318\) 0 0
\(319\) −12.3409 8.96622i −0.00216602 0.00157371i
\(320\) 4250.02 2890.63i 0.742448 0.504971i
\(321\) 0 0
\(322\) 2652.65 1927.26i 0.459088 0.333547i
\(323\) −18.1136 55.7478i −0.00312033 0.00960338i
\(324\) 0 0
\(325\) −1720.28 6679.41i −0.293612 1.14002i
\(326\) −10.2407 −0.00173981
\(327\) 0 0
\(328\) −743.866 + 540.450i −0.125223 + 0.0909797i
\(329\) 586.742 426.293i 0.0983226 0.0714356i
\(330\) 0 0
\(331\) 1556.01 + 1130.51i 0.258388 + 0.187730i 0.709436 0.704770i \(-0.248950\pi\)
−0.451048 + 0.892500i \(0.648950\pi\)
\(332\) −4458.92 −0.737093
\(333\) 0 0
\(334\) −141.244 + 434.703i −0.0231392 + 0.0712152i
\(335\) 2448.12 6807.86i 0.399269 1.11031i
\(336\) 0 0
\(337\) 721.800 2221.47i 0.116673 0.359084i −0.875619 0.483003i \(-0.839546\pi\)
0.992292 + 0.123919i \(0.0395462\pi\)
\(338\) −530.921 + 1634.01i −0.0854388 + 0.262953i
\(339\) 0 0
\(340\) 25.9509 + 89.1998i 0.00413937 + 0.0142280i
\(341\) 95.2447 293.133i 0.0151255 0.0465515i
\(342\) 0 0
\(343\) 6834.23 1.07584
\(344\) 4932.87 + 3583.94i 0.773147 + 0.561724i
\(345\) 0 0
\(346\) −5420.88 + 3938.50i −0.842279 + 0.611952i
\(347\) 5254.02 3817.27i 0.812826 0.590553i −0.101822 0.994803i \(-0.532467\pi\)
0.914649 + 0.404250i \(0.132467\pi\)
\(348\) 0 0
\(349\) 4713.73 0.722980 0.361490 0.932376i \(-0.382268\pi\)
0.361490 + 0.932376i \(0.382268\pi\)
\(350\) −3211.57 2652.81i −0.490473 0.405140i
\(351\) 0 0
\(352\) 221.445 + 681.537i 0.0335314 + 0.103199i
\(353\) 3185.69 2314.54i 0.480331 0.348981i −0.321123 0.947038i \(-0.604060\pi\)
0.801454 + 0.598056i \(0.204060\pi\)
\(354\) 0 0
\(355\) 8721.62 + 6759.98i 1.30393 + 1.01066i
\(356\) −3557.10 2584.38i −0.529567 0.384753i
\(357\) 0 0
\(358\) −2968.65 2156.85i −0.438262 0.318416i
\(359\) −2913.64 + 8967.26i −0.428345 + 1.31831i 0.471409 + 0.881915i \(0.343746\pi\)
−0.899754 + 0.436397i \(0.856254\pi\)
\(360\) 0 0
\(361\) −1886.54 5806.18i −0.275046 0.846506i
\(362\) −1120.50 + 3448.53i −0.162685 + 0.500693i
\(363\) 0 0
\(364\) −1091.30 3358.68i −0.157142 0.483633i
\(365\) −7684.78 + 5226.75i −1.10203 + 0.749536i
\(366\) 0 0
\(367\) 2067.94 + 1502.45i 0.294130 + 0.213698i 0.725057 0.688689i \(-0.241813\pi\)
−0.430927 + 0.902387i \(0.641813\pi\)
\(368\) 1742.49 0.246831
\(369\) 0 0
\(370\) −1156.73 3975.96i −0.162528 0.558649i
\(371\) 2694.14 1957.41i 0.377016 0.273918i
\(372\) 0 0
\(373\) −3360.65 10343.0i −0.466509 1.43577i −0.857074 0.515193i \(-0.827720\pi\)
0.390565 0.920575i \(-0.372280\pi\)
\(374\) 19.7563 0.00273148
\(375\) 0 0
\(376\) 1063.13 0.145816
\(377\) 56.9593 + 175.303i 0.00778131 + 0.0239484i
\(378\) 0 0
\(379\) −5989.27 + 4351.46i −0.811737 + 0.589761i −0.914334 0.404962i \(-0.867285\pi\)
0.102597 + 0.994723i \(0.467285\pi\)
\(380\) −333.820 1147.42i −0.0450648 0.154899i
\(381\) 0 0
\(382\) 9223.65 1.23540
\(383\) 5046.70 + 3666.64i 0.673301 + 0.489182i 0.871128 0.491055i \(-0.163389\pi\)
−0.197828 + 0.980237i \(0.563389\pi\)
\(384\) 0 0
\(385\) 694.132 472.110i 0.0918864 0.0624959i
\(386\) −2213.90 6813.67i −0.291928 0.898463i
\(387\) 0 0
\(388\) 680.678 2094.91i 0.0890624 0.274106i
\(389\) −2416.91 7438.49i −0.315019 0.969528i −0.975747 0.218903i \(-0.929752\pi\)
0.660728 0.750625i \(-0.270248\pi\)
\(390\) 0 0
\(391\) −64.9047 + 199.756i −0.00839481 + 0.0258366i
\(392\) 1416.53 + 1029.17i 0.182515 + 0.132605i
\(393\) 0 0
\(394\) 273.888 + 198.991i 0.0350210 + 0.0254443i
\(395\) −8979.57 6959.92i −1.14383 0.886560i
\(396\) 0 0
\(397\) −6541.82 + 4752.91i −0.827013 + 0.600860i −0.918713 0.394926i \(-0.870770\pi\)
0.0916994 + 0.995787i \(0.470770\pi\)
\(398\) 1987.49 + 6116.87i 0.250311 + 0.770379i
\(399\) 0 0
\(400\) −552.120 2143.74i −0.0690150 0.267967i
\(401\) −1345.64 −0.167576 −0.0837882 0.996484i \(-0.526702\pi\)
−0.0837882 + 0.996484i \(0.526702\pi\)
\(402\) 0 0
\(403\) −3013.06 + 2189.12i −0.372435 + 0.270590i
\(404\) −2307.40 + 1676.43i −0.284153 + 0.206449i
\(405\) 0 0
\(406\) 90.0587 + 65.4315i 0.0110087 + 0.00799830i
\(407\) 834.486 0.101631
\(408\) 0 0
\(409\) 917.900 2825.00i 0.110971 0.341534i −0.880114 0.474762i \(-0.842534\pi\)
0.991085 + 0.133228i \(0.0425342\pi\)
\(410\) 241.472 + 830.000i 0.0290865 + 0.0999776i
\(411\) 0 0
\(412\) 221.382 681.344i 0.0264726 0.0814743i
\(413\) −598.700 + 1842.61i −0.0713320 + 0.219537i
\(414\) 0 0
\(415\) −4333.90 + 12051.9i −0.512633 + 1.42556i
\(416\) 2675.82 8235.34i 0.315368 0.970603i
\(417\) 0 0
\(418\) −254.136 −0.0297373
\(419\) −12542.9 9112.94i −1.46243 1.06252i −0.982721 0.185095i \(-0.940741\pi\)
−0.479713 0.877425i \(-0.659259\pi\)
\(420\) 0 0
\(421\) −1956.11 + 1421.19i −0.226448 + 0.164524i −0.695225 0.718793i \(-0.744695\pi\)
0.468776 + 0.883317i \(0.344695\pi\)
\(422\) 4471.61 3248.81i 0.515816 0.374763i
\(423\) 0 0
\(424\) 4881.57 0.559127
\(425\) 266.320 + 16.5564i 0.0303962 + 0.00188965i
\(426\) 0 0
\(427\) 4081.18 + 12560.6i 0.462535 + 1.42354i
\(428\) −4603.81 + 3344.86i −0.519938 + 0.377757i
\(429\) 0 0
\(430\) 4739.85 3223.78i 0.531571 0.361545i
\(431\) −6422.91 4666.52i −0.717821 0.521527i 0.167866 0.985810i \(-0.446312\pi\)
−0.885687 + 0.464282i \(0.846312\pi\)
\(432\) 0 0
\(433\) 1146.40 + 832.906i 0.127234 + 0.0924409i 0.649582 0.760291i \(-0.274944\pi\)
−0.522348 + 0.852732i \(0.674944\pi\)
\(434\) −695.054 + 2139.15i −0.0768747 + 0.236596i
\(435\) 0 0
\(436\) −2145.70 6603.79i −0.235689 0.725377i
\(437\) 834.902 2569.57i 0.0913931 0.281279i
\(438\) 0 0
\(439\) 4154.10 + 12785.0i 0.451628 + 1.38997i 0.875049 + 0.484034i \(0.160829\pi\)
−0.423422 + 0.905933i \(0.639171\pi\)
\(440\) 1229.96 + 38.1948i 0.133264 + 0.00413833i
\(441\) 0 0
\(442\) −193.132 140.319i −0.0207836 0.0151002i
\(443\) 13347.6 1.43152 0.715759 0.698347i \(-0.246081\pi\)
0.715759 + 0.698347i \(0.246081\pi\)
\(444\) 0 0
\(445\) −10442.6 + 7102.49i −1.11242 + 0.756608i
\(446\) −61.7472 + 44.8619i −0.00655564 + 0.00476295i
\(447\) 0 0
\(448\) −2335.87 7189.05i −0.246338 0.758149i
\(449\) 3063.89 0.322035 0.161017 0.986952i \(-0.448522\pi\)
0.161017 + 0.986952i \(0.448522\pi\)
\(450\) 0 0
\(451\) −174.203 −0.0181883
\(452\) −2346.45 7221.62i −0.244176 0.751496i
\(453\) 0 0
\(454\) −5438.86 + 3951.57i −0.562243 + 0.408494i
\(455\) −10138.8 314.847i −1.04465 0.0324401i
\(456\) 0 0
\(457\) −185.070 −0.0189435 −0.00947177 0.999955i \(-0.503015\pi\)
−0.00947177 + 0.999955i \(0.503015\pi\)
\(458\) 8082.62 + 5872.37i 0.824620 + 0.599122i
\(459\) 0 0
\(460\) −1448.95 + 4029.31i −0.146864 + 0.408408i
\(461\) −2389.28 7353.45i −0.241388 0.742916i −0.996210 0.0869857i \(-0.972277\pi\)
0.754822 0.655930i \(-0.227723\pi\)
\(462\) 0 0
\(463\) −4560.19 + 14034.8i −0.457732 + 1.40875i 0.410165 + 0.912011i \(0.365471\pi\)
−0.867897 + 0.496744i \(0.834529\pi\)
\(464\) 18.2810 + 56.2630i 0.00182903 + 0.00562919i
\(465\) 0 0
\(466\) −4.47165 + 13.7623i −0.000444517 + 0.00136808i
\(467\) 11511.6 + 8363.69i 1.14067 + 0.828748i 0.987213 0.159407i \(-0.0509582\pi\)
0.153460 + 0.988155i \(0.450958\pi\)
\(468\) 0 0
\(469\) −8607.71 6253.87i −0.847478 0.615729i
\(470\) 338.209 940.509i 0.0331923 0.0923031i
\(471\) 0 0
\(472\) −2297.63 + 1669.33i −0.224062 + 0.162790i
\(473\) 356.980 + 1098.67i 0.0347018 + 0.106801i
\(474\) 0 0
\(475\) −3425.81 212.973i −0.330920 0.0205724i
\(476\) 136.621 0.0131555
\(477\) 0 0
\(478\) −11821.7 + 8588.96i −1.13120 + 0.821862i
\(479\) −13254.4 + 9629.85i −1.26431 + 0.918578i −0.998961 0.0455728i \(-0.985489\pi\)
−0.265354 + 0.964151i \(0.585489\pi\)
\(480\) 0 0
\(481\) −8157.72 5926.93i −0.773305 0.561839i
\(482\) 6963.98 0.658092
\(483\) 0 0
\(484\) 1575.88 4850.06i 0.147998 0.455490i
\(485\) −5000.71 3875.97i −0.468186 0.362884i
\(486\) 0 0
\(487\) −4049.02 + 12461.6i −0.376752 + 1.15952i 0.565536 + 0.824723i \(0.308669\pi\)
−0.942289 + 0.334801i \(0.891331\pi\)
\(488\) −5982.49 + 18412.2i −0.554948 + 1.70795i
\(489\) 0 0
\(490\) 1361.11 925.747i 0.125487 0.0853490i
\(491\) −570.719 + 1756.49i −0.0524566 + 0.161445i −0.973853 0.227180i \(-0.927050\pi\)
0.921396 + 0.388624i \(0.127050\pi\)
\(492\) 0 0
\(493\) −7.13082 −0.000651432
\(494\) 2484.36 + 1804.99i 0.226269 + 0.164394i
\(495\) 0 0
\(496\) −967.034 + 702.591i −0.0875426 + 0.0636034i
\(497\) 13128.9 9538.72i 1.18493 0.860906i
\(498\) 0 0
\(499\) 17773.8 1.59451 0.797257 0.603640i \(-0.206284\pi\)
0.797257 + 0.603640i \(0.206284\pi\)
\(500\) 5416.26 + 505.886i 0.484445 + 0.0452478i
\(501\) 0 0
\(502\) −1056.55 3251.73i −0.0939366 0.289107i
\(503\) 1358.97 987.353i 0.120465 0.0875227i −0.525922 0.850533i \(-0.676279\pi\)
0.646386 + 0.763010i \(0.276279\pi\)
\(504\) 0 0
\(505\) 2288.48 + 7866.06i 0.201655 + 0.693139i
\(506\) 736.708 + 535.249i 0.0647246 + 0.0470252i
\(507\) 0 0
\(508\) −2919.21 2120.93i −0.254959 0.185239i
\(509\) −5876.65 + 18086.5i −0.511744 + 1.57499i 0.277385 + 0.960759i \(0.410532\pi\)
−0.789129 + 0.614228i \(0.789468\pi\)
\(510\) 0 0
\(511\) 4223.65 + 12999.1i 0.365642 + 1.12533i
\(512\) 1914.02 5890.75i 0.165212 0.508470i
\(513\) 0 0
\(514\) 1314.12 + 4044.46i 0.112769 + 0.347069i
\(515\) −1626.42 1260.61i −0.139162 0.107862i
\(516\) 0 0
\(517\) 162.953 + 118.392i 0.0138620 + 0.0100714i
\(518\) −6089.71 −0.516538
\(519\) 0 0
\(520\) −11752.5 9109.16i −0.991117 0.768198i
\(521\) −1611.58 + 1170.88i −0.135517 + 0.0984592i −0.653479 0.756945i \(-0.726691\pi\)
0.517961 + 0.855404i \(0.326691\pi\)
\(522\) 0 0
\(523\) −3681.59 11330.8i −0.307810 0.947342i −0.978614 0.205707i \(-0.934051\pi\)
0.670803 0.741635i \(-0.265949\pi\)
\(524\) 10146.6 0.845909
\(525\) 0 0
\(526\) −288.538 −0.0239180
\(527\) −44.5235 137.029i −0.00368022 0.0113265i
\(528\) 0 0
\(529\) 2011.12 1461.17i 0.165293 0.120093i
\(530\) 1552.95 4318.54i 0.127275 0.353934i
\(531\) 0 0
\(532\) −1757.43 −0.143222
\(533\) 1702.96 + 1237.28i 0.138393 + 0.100549i
\(534\) 0 0
\(535\) 4566.05 + 15694.6i 0.368986 + 1.26829i
\(536\) −4819.57 14833.1i −0.388384 1.19532i
\(537\) 0 0
\(538\) −1961.93 + 6038.21i −0.157221 + 0.483876i
\(539\) 102.511 + 315.497i 0.00819196 + 0.0252123i
\(540\) 0 0
\(541\) 3650.27 11234.4i 0.290088 0.892798i −0.694740 0.719261i \(-0.744480\pi\)
0.984827 0.173537i \(-0.0555196\pi\)
\(542\) −5700.12 4141.38i −0.451736 0.328206i
\(543\) 0 0
\(544\) 271.013 + 196.902i 0.0213595 + 0.0155186i
\(545\) −19934.8 619.049i −1.56681 0.0486553i
\(546\) 0 0
\(547\) 6225.01 4522.74i 0.486586 0.353525i −0.317284 0.948331i \(-0.602771\pi\)
0.803870 + 0.594805i \(0.202771\pi\)
\(548\) 3513.92 + 10814.7i 0.273918 + 0.843033i
\(549\) 0 0
\(550\) 425.072 1075.95i 0.0329548 0.0834156i
\(551\) 91.7274 0.00709205
\(552\) 0 0
\(553\) −13517.2 + 9820.84i −1.03944 + 0.755198i
\(554\) −5449.43 + 3959.24i −0.417914 + 0.303632i
\(555\) 0 0
\(556\) 3142.41 + 2283.09i 0.239690 + 0.174145i
\(557\) 20699.8 1.57465 0.787324 0.616540i \(-0.211466\pi\)
0.787324 + 0.616540i \(0.211466\pi\)
\(558\) 0 0
\(559\) 4313.55 13275.8i 0.326375 1.00448i
\(560\) −3254.02 101.049i −0.245549 0.00762521i
\(561\) 0 0
\(562\) −1795.59 + 5526.26i −0.134773 + 0.414789i
\(563\) 5732.09 17641.6i 0.429092 1.32061i −0.469929 0.882704i \(-0.655721\pi\)
0.899021 0.437905i \(-0.144279\pi\)
\(564\) 0 0
\(565\) −21799.8 676.965i −1.62323 0.0504073i
\(566\) 5155.18 15866.0i 0.382841 1.17826i
\(567\) 0 0
\(568\) 23788.5 1.75730
\(569\) 131.419 + 95.4817i 0.00968257 + 0.00703480i 0.592616 0.805485i \(-0.298095\pi\)
−0.582933 + 0.812520i \(0.698095\pi\)
\(570\) 0 0
\(571\) 13305.3 9666.86i 0.975147 0.708486i 0.0185281 0.999828i \(-0.494102\pi\)
0.956619 + 0.291343i \(0.0941020\pi\)
\(572\) 793.478 576.495i 0.0580017 0.0421407i
\(573\) 0 0
\(574\) 1271.26 0.0924412
\(575\) 9482.44 + 7832.67i 0.687731 + 0.568078i
\(576\) 0 0
\(577\) −1917.80 5902.39i −0.138369 0.425857i 0.857729 0.514101i \(-0.171874\pi\)
−0.996099 + 0.0882441i \(0.971874\pi\)
\(578\) −8048.11 + 5847.29i −0.579165 + 0.420788i
\(579\) 0 0
\(580\) −145.303 4.51220i −0.0104024 0.000323032i
\(581\) 15238.2 + 11071.2i 1.08810 + 0.790552i
\(582\) 0 0
\(583\) 748.232 + 543.622i 0.0531537 + 0.0386184i
\(584\) −6191.33 + 19054.9i −0.438697 + 1.35017i
\(585\) 0 0
\(586\) 1433.11 + 4410.66i 0.101026 + 0.310926i
\(587\) −4296.85 + 13224.4i −0.302130 + 0.929860i 0.678603 + 0.734505i \(0.262586\pi\)
−0.980733 + 0.195354i \(0.937414\pi\)
\(588\) 0 0
\(589\) 572.729 + 1762.68i 0.0400660 + 0.123311i
\(590\) 745.854 + 2563.68i 0.0520446 + 0.178890i
\(591\) 0 0
\(592\) −2618.20 1902.23i −0.181769 0.132063i
\(593\) 11389.2 0.788698 0.394349 0.918961i \(-0.370970\pi\)
0.394349 + 0.918961i \(0.370970\pi\)
\(594\) 0 0
\(595\) 132.791 369.272i 0.00914939 0.0254431i
\(596\) 8213.40 5967.38i 0.564486 0.410123i
\(597\) 0 0
\(598\) −3400.26 10464.9i −0.232520 0.715622i
\(599\) −12576.2 −0.857844 −0.428922 0.903342i \(-0.641106\pi\)
−0.428922 + 0.903342i \(0.641106\pi\)
\(600\) 0 0
\(601\) 2154.43 0.146225 0.0731124 0.997324i \(-0.476707\pi\)
0.0731124 + 0.997324i \(0.476707\pi\)
\(602\) −2605.08 8017.61i −0.176371 0.542813i
\(603\) 0 0
\(604\) −1369.11 + 994.717i −0.0922323 + 0.0670107i
\(605\) −11577.4 8973.49i −0.778000 0.603015i
\(606\) 0 0
\(607\) 9937.94 0.664528 0.332264 0.943186i \(-0.392187\pi\)
0.332264 + 0.943186i \(0.392187\pi\)
\(608\) −3486.18 2532.86i −0.232538 0.168949i
\(609\) 0 0
\(610\) 14385.4 + 11149.9i 0.954832 + 0.740075i
\(611\) −752.106 2314.74i −0.0497986 0.153264i
\(612\) 0 0
\(613\) 3184.38 9800.52i 0.209814 0.645741i −0.789667 0.613535i \(-0.789747\pi\)
0.999481 0.0322059i \(-0.0102532\pi\)
\(614\) 1743.30 + 5365.32i 0.114583 + 0.352649i
\(615\) 0 0
\(616\) 559.236 1721.15i 0.0365783 0.112577i
\(617\) 13637.9 + 9908.50i 0.889854 + 0.646517i 0.935840 0.352425i \(-0.114643\pi\)
−0.0459856 + 0.998942i \(0.514643\pi\)
\(618\) 0 0
\(619\) −6572.78 4775.40i −0.426789 0.310080i 0.353575 0.935406i \(-0.384966\pi\)
−0.780364 + 0.625326i \(0.784966\pi\)
\(620\) −820.537 2820.39i −0.0531509 0.182693i
\(621\) 0 0
\(622\) 13067.6 9494.17i 0.842385 0.612028i
\(623\) 5739.40 + 17664.1i 0.369092 + 1.13595i
\(624\) 0 0
\(625\) 6631.74 14147.8i 0.424432 0.905460i
\(626\) 9770.92 0.623841
\(627\) 0 0
\(628\) −6874.40 + 4994.54i −0.436813 + 0.317363i
\(629\) 315.592 229.291i 0.0200055 0.0145348i
\(630\) 0 0
\(631\) −9984.59 7254.23i −0.629921 0.457665i 0.226452 0.974022i \(-0.427287\pi\)
−0.856373 + 0.516358i \(0.827287\pi\)
\(632\) −24492.1 −1.54152
\(633\) 0 0
\(634\) 5408.87 16646.8i 0.338823 1.04279i
\(635\) −8569.99 + 5828.83i −0.535574 + 0.364268i
\(636\) 0 0
\(637\) 1238.69 3812.30i 0.0770466 0.237125i
\(638\) −9.55357 + 29.4029i −0.000592836 + 0.00182456i
\(639\) 0 0
\(640\) 2860.41 + 2217.05i 0.176668 + 0.136932i
\(641\) 4664.84 14356.9i 0.287442 0.884654i −0.698215 0.715889i \(-0.746022\pi\)
0.985656 0.168766i \(-0.0539781\pi\)
\(642\) 0 0
\(643\) 21379.1 1.31121 0.655606 0.755103i \(-0.272413\pi\)
0.655606 + 0.755103i \(0.272413\pi\)
\(644\) 5094.58 + 3701.43i 0.311731 + 0.226486i
\(645\) 0 0
\(646\) −96.1107 + 69.8285i −0.00585360 + 0.00425289i
\(647\) 7903.05 5741.90i 0.480218 0.348899i −0.321192 0.947014i \(-0.604084\pi\)
0.801410 + 0.598115i \(0.204084\pi\)
\(648\) 0 0
\(649\) −538.074 −0.0325443
\(650\) −11797.3 + 7499.12i −0.711889 + 0.452522i
\(651\) 0 0
\(652\) −6.07770 18.7052i −0.000365063 0.00112355i
\(653\) 10418.9 7569.74i 0.624382 0.453640i −0.230068 0.973175i \(-0.573895\pi\)
0.854449 + 0.519535i \(0.173895\pi\)
\(654\) 0 0
\(655\) 9862.10 27425.1i 0.588312 1.63601i
\(656\) 546.562 + 397.100i 0.0325300 + 0.0236344i
\(657\) 0 0
\(658\) −1189.16 863.974i −0.0704532 0.0511873i
\(659\) 1499.44 4614.81i 0.0886343 0.272788i −0.896908 0.442217i \(-0.854192\pi\)
0.985542 + 0.169429i \(0.0541922\pi\)
\(660\) 0 0
\(661\) −2892.29 8901.56i −0.170192 0.523798i 0.829189 0.558968i \(-0.188803\pi\)
−0.999381 + 0.0351704i \(0.988803\pi\)
\(662\) 1204.57 3707.27i 0.0707202 0.217655i
\(663\) 0 0
\(664\) 8532.07 + 26259.0i 0.498657 + 1.53471i
\(665\) −1708.16 + 4750.13i −0.0996081 + 0.276996i
\(666\) 0 0
\(667\) −265.907 193.192i −0.0154362 0.0112151i
\(668\) −877.838 −0.0508452
\(669\) 0 0
\(670\) −14655.5 455.107i −0.845062 0.0262423i
\(671\) −2967.40 + 2155.95i −0.170723 + 0.124038i
\(672\) 0 0
\(673\) −8985.41 27654.2i −0.514654 1.58394i −0.783911 0.620873i \(-0.786778\pi\)
0.269257 0.963068i \(-0.413222\pi\)
\(674\) −4733.99 −0.270544
\(675\) 0 0
\(676\) −3299.71 −0.187740
\(677\) −1446.09 4450.60i −0.0820940 0.252659i 0.901582 0.432608i \(-0.142407\pi\)
−0.983676 + 0.179949i \(0.942407\pi\)
\(678\) 0 0
\(679\) −7527.72 + 5469.21i −0.425460 + 0.309115i
\(680\) 475.649 323.510i 0.0268240 0.0182442i
\(681\) 0 0
\(682\) −624.671 −0.0350731
\(683\) −13511.7 9816.80i −0.756968 0.549970i 0.141011 0.990008i \(-0.454965\pi\)
−0.897979 + 0.440038i \(0.854965\pi\)
\(684\) 0 0
\(685\) 32646.3 + 1013.79i 1.82095 + 0.0565472i
\(686\) −4280.21 13173.1i −0.238220 0.733166i
\(687\) 0 0
\(688\) 1384.42 4260.82i 0.0767161 0.236108i
\(689\) −3453.45 10628.6i −0.190952 0.587689i
\(690\) 0 0
\(691\) −3623.18 + 11151.0i −0.199468 + 0.613899i 0.800428 + 0.599429i \(0.204606\pi\)
−0.999895 + 0.0144691i \(0.995394\pi\)
\(692\) −10411.1 7564.14i −0.571925 0.415528i
\(693\) 0 0
\(694\) −10648.4 7736.52i −0.582432 0.423162i
\(695\) 9225.23 6274.48i 0.503501 0.342453i
\(696\) 0 0
\(697\) −65.8813 + 47.8656i −0.00358025 + 0.00260120i
\(698\) −2952.16 9085.80i −0.160087 0.492697i
\(699\) 0 0
\(700\) 2939.51 7440.54i 0.158719 0.401751i
\(701\) −19249.4 −1.03714 −0.518572 0.855034i \(-0.673536\pi\)
−0.518572 + 0.855034i \(0.673536\pi\)
\(702\) 0 0
\(703\) −4059.62 + 2949.49i −0.217797 + 0.158239i
\(704\) 1698.39 1233.95i 0.0909242 0.0660603i
\(705\) 0 0
\(706\) −6456.48 4690.90i −0.344182 0.250063i
\(707\) 12047.9 0.640890
\(708\) 0 0
\(709\) 1993.96 6136.79i 0.105620 0.325066i −0.884255 0.467004i \(-0.845333\pi\)
0.989876 + 0.141938i \(0.0453334\pi\)
\(710\) 7567.74 21044.8i 0.400017 1.11239i
\(711\) 0 0
\(712\) −8413.23 + 25893.3i −0.442836 + 1.36291i
\(713\) 2052.21 6316.05i 0.107792 0.331750i
\(714\) 0 0
\(715\) −786.969 2705.01i −0.0411622 0.141485i
\(716\) 2177.77 6702.48i 0.113669 0.349837i
\(717\) 0 0
\(718\) 19109.3 0.993251
\(719\) −17508.2 12720.5i −0.908132 0.659797i 0.0324096 0.999475i \(-0.489682\pi\)
−0.940542 + 0.339678i \(0.889682\pi\)
\(720\) 0 0
\(721\) −2448.30 + 1778.79i −0.126462 + 0.0918803i
\(722\) −10010.0 + 7272.70i −0.515975 + 0.374878i
\(723\) 0 0
\(724\) −6963.96 −0.357477
\(725\) −153.425 + 388.352i −0.00785939 + 0.0198938i
\(726\) 0 0
\(727\) −6051.62 18625.0i −0.308724 0.950155i −0.978261 0.207376i \(-0.933508\pi\)
0.669537 0.742778i \(-0.266492\pi\)
\(728\) −17691.4 + 12853.5i −0.900668 + 0.654374i
\(729\) 0 0
\(730\) 14887.6 + 11539.1i 0.754813 + 0.585043i
\(731\) 436.885 + 317.416i 0.0221050 + 0.0160603i
\(732\) 0 0
\(733\) 8314.98 + 6041.19i 0.418992 + 0.304415i 0.777232 0.629214i \(-0.216623\pi\)
−0.358240 + 0.933629i \(0.616623\pi\)
\(734\) 1600.87 4926.97i 0.0805029 0.247762i
\(735\) 0 0
\(736\) 4771.40 + 14684.9i 0.238962 + 0.735450i
\(737\) 913.119 2810.29i 0.0456380 0.140459i
\(738\) 0 0
\(739\) 8283.58 + 25494.2i 0.412336 + 1.26904i 0.914612 + 0.404333i \(0.132496\pi\)
−0.502276 + 0.864707i \(0.667504\pi\)
\(740\) 6575.83 4472.51i 0.326665 0.222179i
\(741\) 0 0
\(742\) −5460.26 3967.11i −0.270152 0.196277i
\(743\) 3369.02 0.166349 0.0831746 0.996535i \(-0.473494\pi\)
0.0831746 + 0.996535i \(0.473494\pi\)
\(744\) 0 0
\(745\) −8146.03 27999.9i −0.400601 1.37696i
\(746\) −17831.6 + 12955.5i −0.875151 + 0.635835i
\(747\) 0 0
\(748\) 11.7251 + 36.0861i 0.000573144 + 0.00176396i
\(749\) 24038.4 1.17269
\(750\) 0 0
\(751\) 6458.58 0.313817 0.156909 0.987613i \(-0.449847\pi\)
0.156909 + 0.987613i \(0.449847\pi\)
\(752\) −241.386 742.911i −0.0117054 0.0360255i
\(753\) 0 0
\(754\) 302.227 219.581i 0.0145974 0.0106056i
\(755\) 1357.88 + 4667.37i 0.0654548 + 0.224984i
\(756\) 0 0
\(757\) −5810.90 −0.278997 −0.139499 0.990222i \(-0.544549\pi\)
−0.139499 + 0.990222i \(0.544549\pi\)
\(758\) 12138.5 + 8819.17i 0.581651 + 0.422594i
\(759\) 0 0
\(760\) −6118.52 + 4161.47i −0.292029 + 0.198622i
\(761\) 10479.9 + 32253.9i 0.499208 + 1.53640i 0.810295 + 0.586023i \(0.199307\pi\)
−0.311087 + 0.950382i \(0.600693\pi\)
\(762\) 0 0
\(763\) −9063.92 + 27895.9i −0.430060 + 1.32359i
\(764\) 5474.11 + 16847.6i 0.259223 + 0.797806i
\(765\) 0 0
\(766\) 3906.83 12024.0i 0.184281 0.567160i
\(767\) 5260.07 + 3821.66i 0.247627 + 0.179912i
\(768\) 0 0
\(769\) −29641.8 21536.0i −1.39000 1.00990i −0.995865 0.0908440i \(-0.971044\pi\)
−0.394137 0.919052i \(-0.628956\pi\)
\(770\) −1344.73 1042.28i −0.0629359 0.0487806i
\(771\) 0 0
\(772\) 11131.7 8087.64i 0.518961 0.377047i
\(773\) 136.048 + 418.714i 0.00633030 + 0.0194827i 0.954172 0.299259i \(-0.0967396\pi\)
−0.947841 + 0.318742i \(0.896740\pi\)
\(774\) 0 0
\(775\) −8420.71 523.493i −0.390298 0.0242638i
\(776\) −13639.6 −0.630971
\(777\) 0 0
\(778\) −12824.1 + 9317.29i −0.590961 + 0.429359i
\(779\) 847.465 615.720i 0.0389777 0.0283189i
\(780\) 0 0
\(781\) 3646.23 + 2649.14i 0.167058 + 0.121375i
\(782\) 425.683 0.0194660
\(783\) 0 0
\(784\) 397.554 1223.55i 0.0181102 0.0557374i
\(785\) 6818.01 + 23435.2i 0.309994 + 1.06553i
\(786\) 0 0
\(787\) 7874.56