Properties

Label 144.4.k.a.109.3
Level $144$
Weight $4$
Character 144.109
Analytic conductor $8.496$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 144.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.49627504083\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} - x^{8} + 6 x^{7} + 14 x^{6} - 80 x^{5} + 56 x^{4} + 96 x^{3} - 64 x^{2} - 512 x + 1024\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 109.3
Root \(-1.62580 + 1.16481i\) of defining polynomial
Character \(\chi\) \(=\) 144.109
Dual form 144.4.k.a.37.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.460984 - 2.79061i) q^{2} +(-7.57499 + 2.57285i) q^{4} +(-8.22587 + 8.22587i) q^{5} -2.67171i q^{7} +(10.6718 + 19.9528i) q^{8} +O(q^{10})\) \(q+(-0.460984 - 2.79061i) q^{2} +(-7.57499 + 2.57285i) q^{4} +(-8.22587 + 8.22587i) q^{5} -2.67171i q^{7} +(10.6718 + 19.9528i) q^{8} +(26.7472 + 19.1632i) q^{10} +(45.2213 - 45.2213i) q^{11} +(35.3968 + 35.3968i) q^{13} +(-7.45568 + 1.23161i) q^{14} +(50.7609 - 38.9786i) q^{16} +72.4991 q^{17} +(19.4427 + 19.4427i) q^{19} +(41.1470 - 83.4748i) q^{20} +(-147.041 - 105.349i) q^{22} +139.462i q^{23} -10.3299i q^{25} +(82.4612 - 115.096i) q^{26} +(6.87389 + 20.2381i) q^{28} +(-66.0434 - 66.0434i) q^{29} +188.682 q^{31} +(-132.174 - 123.685i) q^{32} +(-33.4209 - 202.317i) q^{34} +(21.9771 + 21.9771i) q^{35} +(-84.0653 + 84.0653i) q^{37} +(45.2941 - 63.2196i) q^{38} +(-251.914 - 76.3445i) q^{40} -104.629i q^{41} +(-31.4857 + 31.4857i) q^{43} +(-226.203 + 458.898i) q^{44} +(389.183 - 64.2896i) q^{46} +488.151 q^{47} +335.862 q^{49} +(-28.8266 + 4.76190i) q^{50} +(-359.201 - 177.060i) q^{52} +(-149.560 + 149.560i) q^{53} +743.968i q^{55} +(53.3080 - 28.5118i) q^{56} +(-153.856 + 214.746i) q^{58} +(-284.698 + 284.698i) q^{59} +(-228.069 - 228.069i) q^{61} +(-86.9792 - 526.537i) q^{62} +(-284.227 + 425.863i) q^{64} -582.338 q^{65} +(139.151 + 139.151i) q^{67} +(-549.180 + 186.529i) q^{68} +(51.1984 - 71.4606i) q^{70} +453.655i q^{71} -259.747i q^{73} +(273.346 + 195.841i) q^{74} +(-197.301 - 97.2550i) q^{76} +(-120.818 - 120.818i) q^{77} +323.190 q^{79} +(-96.9197 + 738.185i) q^{80} +(-291.979 + 48.2323i) q^{82} +(563.897 + 563.897i) q^{83} +(-596.368 + 596.368i) q^{85} +(102.379 + 73.3499i) q^{86} +(1384.88 + 419.700i) q^{88} -866.853i q^{89} +(94.5697 - 94.5697i) q^{91} +(-358.814 - 1056.42i) q^{92} +(-225.030 - 1362.24i) q^{94} -319.866 q^{95} -936.077 q^{97} +(-154.827 - 937.259i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} + 8q^{4} + 2q^{5} + 44q^{8} + O(q^{10}) \) \( 10q + 2q^{2} + 8q^{4} + 2q^{5} + 44q^{8} - 68q^{10} - 18q^{11} - 2q^{13} - 188q^{14} + 280q^{16} + 4q^{17} - 26q^{19} + 196q^{20} - 588q^{22} + 264q^{26} + 280q^{28} + 202q^{29} + 368q^{31} - 968q^{32} + 436q^{34} - 476q^{35} - 10q^{37} + 1232q^{38} - 1336q^{40} - 838q^{43} - 868q^{44} + 1132q^{46} + 944q^{47} + 94q^{49} - 726q^{50} - 236q^{52} + 378q^{53} + 488q^{56} + 8q^{58} - 1706q^{59} + 910q^{61} + 80q^{62} + 512q^{64} + 492q^{65} + 1942q^{67} + 880q^{68} + 160q^{70} + 452q^{74} - 1228q^{76} + 268q^{77} - 4416q^{79} + 2648q^{80} - 704q^{82} + 2562q^{83} - 12q^{85} - 3764q^{86} + 1528q^{88} + 3332q^{91} - 632q^{92} - 3248q^{94} - 6900q^{95} - 4q^{97} - 314q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.460984 2.79061i −0.162982 0.986629i
\(3\) 0 0
\(4\) −7.57499 + 2.57285i −0.946874 + 0.321606i
\(5\) −8.22587 + 8.22587i −0.735744 + 0.735744i −0.971751 0.236007i \(-0.924161\pi\)
0.236007 + 0.971751i \(0.424161\pi\)
\(6\) 0 0
\(7\) 2.67171i 0.144259i −0.997395 0.0721293i \(-0.977021\pi\)
0.997395 0.0721293i \(-0.0229794\pi\)
\(8\) 10.6718 + 19.9528i 0.471630 + 0.881797i
\(9\) 0 0
\(10\) 26.7472 + 19.1632i 0.845820 + 0.605993i
\(11\) 45.2213 45.2213i 1.23952 1.23952i 0.279323 0.960197i \(-0.409890\pi\)
0.960197 0.279323i \(-0.0901099\pi\)
\(12\) 0 0
\(13\) 35.3968 + 35.3968i 0.755176 + 0.755176i 0.975440 0.220264i \(-0.0706918\pi\)
−0.220264 + 0.975440i \(0.570692\pi\)
\(14\) −7.45568 + 1.23161i −0.142330 + 0.0235116i
\(15\) 0 0
\(16\) 50.7609 38.9786i 0.793139 0.609041i
\(17\) 72.4991 1.03433 0.517165 0.855886i \(-0.326987\pi\)
0.517165 + 0.855886i \(0.326987\pi\)
\(18\) 0 0
\(19\) 19.4427 + 19.4427i 0.234761 + 0.234761i 0.814676 0.579916i \(-0.196915\pi\)
−0.579916 + 0.814676i \(0.696915\pi\)
\(20\) 41.1470 83.4748i 0.460037 0.933277i
\(21\) 0 0
\(22\) −147.041 105.349i −1.42497 1.02093i
\(23\) 139.462i 1.26434i 0.774830 + 0.632170i \(0.217835\pi\)
−0.774830 + 0.632170i \(0.782165\pi\)
\(24\) 0 0
\(25\) 10.3299i 0.0826390i
\(26\) 82.4612 115.096i 0.621999 0.868159i
\(27\) 0 0
\(28\) 6.87389 + 20.2381i 0.0463944 + 0.136595i
\(29\) −66.0434 66.0434i −0.422895 0.422895i 0.463304 0.886199i \(-0.346664\pi\)
−0.886199 + 0.463304i \(0.846664\pi\)
\(30\) 0 0
\(31\) 188.682 1.09317 0.546584 0.837404i \(-0.315928\pi\)
0.546584 + 0.837404i \(0.315928\pi\)
\(32\) −132.174 123.685i −0.730165 0.683271i
\(33\) 0 0
\(34\) −33.4209 202.317i −0.168577 1.02050i
\(35\) 21.9771 + 21.9771i 0.106137 + 0.106137i
\(36\) 0 0
\(37\) −84.0653 + 84.0653i −0.373520 + 0.373520i −0.868758 0.495237i \(-0.835081\pi\)
0.495237 + 0.868758i \(0.335081\pi\)
\(38\) 45.2941 63.2196i 0.193360 0.269884i
\(39\) 0 0
\(40\) −251.914 76.3445i −0.995776 0.301778i
\(41\) 104.629i 0.398545i −0.979944 0.199272i \(-0.936142\pi\)
0.979944 0.199272i \(-0.0638578\pi\)
\(42\) 0 0
\(43\) −31.4857 + 31.4857i −0.111663 + 0.111663i −0.760731 0.649067i \(-0.775159\pi\)
0.649067 + 0.760731i \(0.275159\pi\)
\(44\) −226.203 + 458.898i −0.775032 + 1.57231i
\(45\) 0 0
\(46\) 389.183 64.2896i 1.24743 0.206065i
\(47\) 488.151 1.51498 0.757491 0.652846i \(-0.226425\pi\)
0.757491 + 0.652846i \(0.226425\pi\)
\(48\) 0 0
\(49\) 335.862 0.979189
\(50\) −28.8266 + 4.76190i −0.0815341 + 0.0134687i
\(51\) 0 0
\(52\) −359.201 177.060i −0.957926 0.472187i
\(53\) −149.560 + 149.560i −0.387617 + 0.387617i −0.873837 0.486220i \(-0.838376\pi\)
0.486220 + 0.873837i \(0.338376\pi\)
\(54\) 0 0
\(55\) 743.968i 1.82394i
\(56\) 53.3080 28.5118i 0.127207 0.0680366i
\(57\) 0 0
\(58\) −153.856 + 214.746i −0.348316 + 0.486165i
\(59\) −284.698 + 284.698i −0.628212 + 0.628212i −0.947618 0.319406i \(-0.896517\pi\)
0.319406 + 0.947618i \(0.396517\pi\)
\(60\) 0 0
\(61\) −228.069 228.069i −0.478709 0.478709i 0.426010 0.904719i \(-0.359919\pi\)
−0.904719 + 0.426010i \(0.859919\pi\)
\(62\) −86.9792 526.537i −0.178167 1.07855i
\(63\) 0 0
\(64\) −284.227 + 425.863i −0.555131 + 0.831763i
\(65\) −582.338 −1.11123
\(66\) 0 0
\(67\) 139.151 + 139.151i 0.253730 + 0.253730i 0.822498 0.568768i \(-0.192580\pi\)
−0.568768 + 0.822498i \(0.692580\pi\)
\(68\) −549.180 + 186.529i −0.979380 + 0.332647i
\(69\) 0 0
\(70\) 51.1984 71.4606i 0.0874197 0.122017i
\(71\) 453.655i 0.758294i 0.925336 + 0.379147i \(0.123783\pi\)
−0.925336 + 0.379147i \(0.876217\pi\)
\(72\) 0 0
\(73\) 259.747i 0.416454i −0.978081 0.208227i \(-0.933231\pi\)
0.978081 0.208227i \(-0.0667692\pi\)
\(74\) 273.346 + 195.841i 0.429403 + 0.307649i
\(75\) 0 0
\(76\) −197.301 97.2550i −0.297789 0.146788i
\(77\) −120.818 120.818i −0.178811 0.178811i
\(78\) 0 0
\(79\) 323.190 0.460275 0.230138 0.973158i \(-0.426082\pi\)
0.230138 + 0.973158i \(0.426082\pi\)
\(80\) −96.9197 + 738.185i −0.135449 + 1.03165i
\(81\) 0 0
\(82\) −291.979 + 48.2323i −0.393216 + 0.0649557i
\(83\) 563.897 + 563.897i 0.745732 + 0.745732i 0.973674 0.227943i \(-0.0732000\pi\)
−0.227943 + 0.973674i \(0.573200\pi\)
\(84\) 0 0
\(85\) −596.368 + 596.368i −0.761002 + 0.761002i
\(86\) 102.379 + 73.3499i 0.128369 + 0.0919711i
\(87\) 0 0
\(88\) 1384.88 + 419.700i 1.67760 + 0.508411i
\(89\) 866.853i 1.03243i −0.856459 0.516215i \(-0.827341\pi\)
0.856459 0.516215i \(-0.172659\pi\)
\(90\) 0 0
\(91\) 94.5697 94.5697i 0.108941 0.108941i
\(92\) −358.814 1056.42i −0.406619 1.19717i
\(93\) 0 0
\(94\) −225.030 1362.24i −0.246915 1.49472i
\(95\) −319.866 −0.345448
\(96\) 0 0
\(97\) −936.077 −0.979837 −0.489919 0.871768i \(-0.662974\pi\)
−0.489919 + 0.871768i \(0.662974\pi\)
\(98\) −154.827 937.259i −0.159591 0.966097i
\(99\) 0 0
\(100\) 26.5772 + 78.2487i 0.0265772 + 0.0782487i
\(101\) 1.58844 1.58844i 0.00156491 0.00156491i −0.706324 0.707889i \(-0.749648\pi\)
0.707889 + 0.706324i \(0.249648\pi\)
\(102\) 0 0
\(103\) 1388.28i 1.32807i −0.747700 0.664036i \(-0.768842\pi\)
0.747700 0.664036i \(-0.231158\pi\)
\(104\) −328.518 + 1084.01i −0.309749 + 1.02208i
\(105\) 0 0
\(106\) 486.310 + 348.420i 0.445609 + 0.319260i
\(107\) 821.526 821.526i 0.742243 0.742243i −0.230767 0.973009i \(-0.574123\pi\)
0.973009 + 0.230767i \(0.0741234\pi\)
\(108\) 0 0
\(109\) 532.797 + 532.797i 0.468190 + 0.468190i 0.901328 0.433138i \(-0.142594\pi\)
−0.433138 + 0.901328i \(0.642594\pi\)
\(110\) 2076.12 342.957i 1.79955 0.297270i
\(111\) 0 0
\(112\) −104.139 135.618i −0.0878593 0.114417i
\(113\) 67.2680 0.0560003 0.0280002 0.999608i \(-0.491086\pi\)
0.0280002 + 0.999608i \(0.491086\pi\)
\(114\) 0 0
\(115\) −1147.19 1147.19i −0.930230 0.930230i
\(116\) 670.198 + 330.359i 0.536434 + 0.264423i
\(117\) 0 0
\(118\) 925.722 + 663.240i 0.722200 + 0.517425i
\(119\) 193.696i 0.149211i
\(120\) 0 0
\(121\) 2758.92i 2.07282i
\(122\) −531.315 + 741.587i −0.394287 + 0.550329i
\(123\) 0 0
\(124\) −1429.26 + 485.449i −1.03509 + 0.351570i
\(125\) −943.262 943.262i −0.674943 0.674943i
\(126\) 0 0
\(127\) 1903.59 1.33005 0.665026 0.746820i \(-0.268421\pi\)
0.665026 + 0.746820i \(0.268421\pi\)
\(128\) 1319.44 + 596.851i 0.911118 + 0.412146i
\(129\) 0 0
\(130\) 268.448 + 1625.08i 0.181111 + 1.09638i
\(131\) −918.430 918.430i −0.612546 0.612546i 0.331062 0.943609i \(-0.392593\pi\)
−0.943609 + 0.331062i \(0.892593\pi\)
\(132\) 0 0
\(133\) 51.9451 51.9451i 0.0338662 0.0338662i
\(134\) 324.169 452.461i 0.208984 0.291691i
\(135\) 0 0
\(136\) 773.693 + 1446.56i 0.487821 + 0.912069i
\(137\) 477.234i 0.297612i −0.988866 0.148806i \(-0.952457\pi\)
0.988866 0.148806i \(-0.0475430\pi\)
\(138\) 0 0
\(139\) −1513.89 + 1513.89i −0.923788 + 0.923788i −0.997295 0.0735064i \(-0.976581\pi\)
0.0735064 + 0.997295i \(0.476581\pi\)
\(140\) −223.020 109.933i −0.134633 0.0663642i
\(141\) 0 0
\(142\) 1265.97 209.127i 0.748155 0.123589i
\(143\) 3201.37 1.87211
\(144\) 0 0
\(145\) 1086.53 0.622285
\(146\) −724.853 + 119.739i −0.410885 + 0.0678746i
\(147\) 0 0
\(148\) 420.507 853.081i 0.233550 0.473803i
\(149\) −375.353 + 375.353i −0.206377 + 0.206377i −0.802725 0.596349i \(-0.796618\pi\)
0.596349 + 0.802725i \(0.296618\pi\)
\(150\) 0 0
\(151\) 2997.52i 1.61546i 0.589553 + 0.807730i \(0.299304\pi\)
−0.589553 + 0.807730i \(0.700696\pi\)
\(152\) −180.448 + 595.423i −0.0962912 + 0.317731i
\(153\) 0 0
\(154\) −281.460 + 392.850i −0.147277 + 0.205564i
\(155\) −1552.07 + 1552.07i −0.804293 + 0.804293i
\(156\) 0 0
\(157\) −1509.01 1509.01i −0.767082 0.767082i 0.210510 0.977592i \(-0.432488\pi\)
−0.977592 + 0.210510i \(0.932488\pi\)
\(158\) −148.985 901.897i −0.0750167 0.454121i
\(159\) 0 0
\(160\) 2104.66 69.8265i 1.03993 0.0345017i
\(161\) 372.601 0.182392
\(162\) 0 0
\(163\) −1425.19 1425.19i −0.684844 0.684844i 0.276244 0.961088i \(-0.410910\pi\)
−0.961088 + 0.276244i \(0.910910\pi\)
\(164\) 269.195 + 792.565i 0.128174 + 0.377371i
\(165\) 0 0
\(166\) 1313.67 1833.56i 0.614219 0.857301i
\(167\) 792.415i 0.367179i 0.983003 + 0.183590i \(0.0587717\pi\)
−0.983003 + 0.183590i \(0.941228\pi\)
\(168\) 0 0
\(169\) 308.861i 0.140583i
\(170\) 1939.15 + 1389.31i 0.874857 + 0.626797i
\(171\) 0 0
\(172\) 157.496 319.512i 0.0698195 0.141643i
\(173\) 773.594 + 773.594i 0.339972 + 0.339972i 0.856357 0.516384i \(-0.172722\pi\)
−0.516384 + 0.856357i \(0.672722\pi\)
\(174\) 0 0
\(175\) −27.5984 −0.0119214
\(176\) 532.810 4058.13i 0.228194 1.73803i
\(177\) 0 0
\(178\) −2419.05 + 399.605i −1.01862 + 0.168268i
\(179\) −426.050 426.050i −0.177902 0.177902i 0.612539 0.790441i \(-0.290148\pi\)
−0.790441 + 0.612539i \(0.790148\pi\)
\(180\) 0 0
\(181\) −2618.06 + 2618.06i −1.07513 + 1.07513i −0.0781951 + 0.996938i \(0.524916\pi\)
−0.996938 + 0.0781951i \(0.975084\pi\)
\(182\) −307.502 220.312i −0.125239 0.0897286i
\(183\) 0 0
\(184\) −2782.65 + 1488.30i −1.11489 + 0.596300i
\(185\) 1383.02i 0.549631i
\(186\) 0 0
\(187\) 3278.50 3278.50i 1.28207 1.28207i
\(188\) −3697.74 + 1255.94i −1.43450 + 0.487227i
\(189\) 0 0
\(190\) 147.453 + 892.620i 0.0563019 + 0.340829i
\(191\) −3216.39 −1.21848 −0.609240 0.792986i \(-0.708525\pi\)
−0.609240 + 0.792986i \(0.708525\pi\)
\(192\) 0 0
\(193\) 2852.57 1.06390 0.531950 0.846776i \(-0.321459\pi\)
0.531950 + 0.846776i \(0.321459\pi\)
\(194\) 431.516 + 2612.22i 0.159696 + 0.966736i
\(195\) 0 0
\(196\) −2544.15 + 864.122i −0.927169 + 0.314913i
\(197\) −1609.02 + 1609.02i −0.581918 + 0.581918i −0.935430 0.353512i \(-0.884987\pi\)
0.353512 + 0.935430i \(0.384987\pi\)
\(198\) 0 0
\(199\) 747.136i 0.266146i 0.991106 + 0.133073i \(0.0424845\pi\)
−0.991106 + 0.133073i \(0.957516\pi\)
\(200\) 206.110 110.238i 0.0728708 0.0389750i
\(201\) 0 0
\(202\) −5.16496 3.70047i −0.00179904 0.00128893i
\(203\) −176.449 + 176.449i −0.0610062 + 0.0610062i
\(204\) 0 0
\(205\) 860.666 + 860.666i 0.293227 + 0.293227i
\(206\) −3874.15 + 639.975i −1.31032 + 0.216452i
\(207\) 0 0
\(208\) 3176.49 + 417.055i 1.05889 + 0.139027i
\(209\) 1758.44 0.581981
\(210\) 0 0
\(211\) −2227.13 2227.13i −0.726645 0.726645i 0.243305 0.969950i \(-0.421769\pi\)
−0.969950 + 0.243305i \(0.921769\pi\)
\(212\) 748.122 1517.72i 0.242364 0.491684i
\(213\) 0 0
\(214\) −2671.27 1913.85i −0.853290 0.611346i
\(215\) 517.995i 0.164311i
\(216\) 0 0
\(217\) 504.102i 0.157699i
\(218\) 1241.22 1732.44i 0.385623 0.538237i
\(219\) 0 0
\(220\) −1914.12 5635.55i −0.586590 1.72704i
\(221\) 2566.23 + 2566.23i 0.781102 + 0.781102i
\(222\) 0 0
\(223\) −358.053 −0.107520 −0.0537601 0.998554i \(-0.517121\pi\)
−0.0537601 + 0.998554i \(0.517121\pi\)
\(224\) −330.451 + 353.130i −0.0985677 + 0.105332i
\(225\) 0 0
\(226\) −31.0094 187.719i −0.00912706 0.0552516i
\(227\) −3455.40 3455.40i −1.01032 1.01032i −0.999946 0.0103741i \(-0.996698\pi\)
−0.0103741 0.999946i \(-0.503302\pi\)
\(228\) 0 0
\(229\) −1430.03 + 1430.03i −0.412659 + 0.412659i −0.882664 0.470005i \(-0.844252\pi\)
0.470005 + 0.882664i \(0.344252\pi\)
\(230\) −2672.53 + 3730.21i −0.766181 + 1.06940i
\(231\) 0 0
\(232\) 612.951 2022.55i 0.173458 0.572357i
\(233\) 926.479i 0.260496i 0.991481 + 0.130248i \(0.0415774\pi\)
−0.991481 + 0.130248i \(0.958423\pi\)
\(234\) 0 0
\(235\) −4015.47 + 4015.47i −1.11464 + 1.11464i
\(236\) 1424.10 2889.07i 0.392801 0.796875i
\(237\) 0 0
\(238\) −540.530 + 89.2908i −0.147216 + 0.0243187i
\(239\) 792.472 0.214480 0.107240 0.994233i \(-0.465799\pi\)
0.107240 + 0.994233i \(0.465799\pi\)
\(240\) 0 0
\(241\) 1449.01 0.387299 0.193650 0.981071i \(-0.437967\pi\)
0.193650 + 0.981071i \(0.437967\pi\)
\(242\) −7699.07 + 1271.82i −2.04510 + 0.337833i
\(243\) 0 0
\(244\) 2314.41 + 1140.83i 0.607233 + 0.299321i
\(245\) −2762.76 + 2762.76i −0.720433 + 0.720433i
\(246\) 0 0
\(247\) 1376.42i 0.354572i
\(248\) 2013.57 + 3764.73i 0.515571 + 0.963953i
\(249\) 0 0
\(250\) −2197.45 + 3067.10i −0.555915 + 0.775922i
\(251\) 3580.04 3580.04i 0.900280 0.900280i −0.0951802 0.995460i \(-0.530343\pi\)
0.995460 + 0.0951802i \(0.0303427\pi\)
\(252\) 0 0
\(253\) 6306.64 + 6306.64i 1.56717 + 1.56717i
\(254\) −877.525 5312.18i −0.216775 1.31227i
\(255\) 0 0
\(256\) 1057.34 3957.18i 0.258139 0.966108i
\(257\) 4708.87 1.14292 0.571461 0.820629i \(-0.306377\pi\)
0.571461 + 0.820629i \(0.306377\pi\)
\(258\) 0 0
\(259\) 224.598 + 224.598i 0.0538835 + 0.0538835i
\(260\) 4411.21 1498.27i 1.05220 0.357379i
\(261\) 0 0
\(262\) −2139.60 + 2986.36i −0.504522 + 0.704190i
\(263\) 2967.82i 0.695830i 0.937526 + 0.347915i \(0.113110\pi\)
−0.937526 + 0.347915i \(0.886890\pi\)
\(264\) 0 0
\(265\) 2460.53i 0.570374i
\(266\) −168.904 121.013i −0.0389330 0.0278938i
\(267\) 0 0
\(268\) −1412.08 696.050i −0.321852 0.158649i
\(269\) 663.633 + 663.633i 0.150418 + 0.150418i 0.778305 0.627887i \(-0.216080\pi\)
−0.627887 + 0.778305i \(0.716080\pi\)
\(270\) 0 0
\(271\) 8058.74 1.80640 0.903199 0.429223i \(-0.141212\pi\)
0.903199 + 0.429223i \(0.141212\pi\)
\(272\) 3680.12 2825.91i 0.820368 0.629949i
\(273\) 0 0
\(274\) −1331.77 + 219.997i −0.293633 + 0.0485055i
\(275\) −467.130 467.130i −0.102433 0.102433i
\(276\) 0 0
\(277\) 482.477 482.477i 0.104654 0.104654i −0.652841 0.757495i \(-0.726423\pi\)
0.757495 + 0.652841i \(0.226423\pi\)
\(278\) 4922.56 + 3526.80i 1.06200 + 0.760875i
\(279\) 0 0
\(280\) −203.970 + 673.039i −0.0435341 + 0.143649i
\(281\) 5899.10i 1.25235i 0.779682 + 0.626175i \(0.215381\pi\)
−0.779682 + 0.626175i \(0.784619\pi\)
\(282\) 0 0
\(283\) −679.897 + 679.897i −0.142812 + 0.142812i −0.774898 0.632086i \(-0.782199\pi\)
0.632086 + 0.774898i \(0.282199\pi\)
\(284\) −1167.18 3436.43i −0.243872 0.718009i
\(285\) 0 0
\(286\) −1475.78 8933.77i −0.305121 1.84708i
\(287\) −279.538 −0.0574935
\(288\) 0 0
\(289\) 343.118 0.0698388
\(290\) −500.872 3032.08i −0.101421 0.613965i
\(291\) 0 0
\(292\) 668.290 + 1967.58i 0.133934 + 0.394329i
\(293\) 3552.87 3552.87i 0.708398 0.708398i −0.257800 0.966198i \(-0.582998\pi\)
0.966198 + 0.257800i \(0.0829976\pi\)
\(294\) 0 0
\(295\) 4683.78i 0.924407i
\(296\) −2574.46 780.213i −0.505532 0.153206i
\(297\) 0 0
\(298\) 1220.49 + 874.432i 0.237253 + 0.169981i
\(299\) −4936.50 + 4936.50i −0.954799 + 0.954799i
\(300\) 0 0
\(301\) 84.1205 + 84.1205i 0.0161084 + 0.0161084i
\(302\) 8364.89 1381.81i 1.59386 0.263291i
\(303\) 0 0
\(304\) 1744.78 + 229.079i 0.329177 + 0.0432191i
\(305\) 3752.13 0.704415
\(306\) 0 0
\(307\) 2735.56 + 2735.56i 0.508556 + 0.508556i 0.914083 0.405527i \(-0.132912\pi\)
−0.405527 + 0.914083i \(0.632912\pi\)
\(308\) 1226.04 + 604.348i 0.226819 + 0.111805i
\(309\) 0 0
\(310\) 5046.70 + 3615.74i 0.924624 + 0.662453i
\(311\) 5796.70i 1.05692i −0.848960 0.528458i \(-0.822771\pi\)
0.848960 0.528458i \(-0.177229\pi\)
\(312\) 0 0
\(313\) 8362.62i 1.51017i 0.655627 + 0.755085i \(0.272404\pi\)
−0.655627 + 0.755085i \(0.727596\pi\)
\(314\) −3515.42 + 4906.67i −0.631804 + 0.881846i
\(315\) 0 0
\(316\) −2448.16 + 831.519i −0.435822 + 0.148027i
\(317\) 344.406 + 344.406i 0.0610214 + 0.0610214i 0.736959 0.675938i \(-0.236261\pi\)
−0.675938 + 0.736959i \(0.736261\pi\)
\(318\) 0 0
\(319\) −5973.13 −1.04837
\(320\) −1165.07 5841.11i −0.203530 1.02040i
\(321\) 0 0
\(322\) −171.763 1039.78i −0.0297266 0.179953i
\(323\) 1409.58 + 1409.58i 0.242820 + 0.242820i
\(324\) 0 0
\(325\) 365.644 365.644i 0.0624071 0.0624071i
\(326\) −3320.16 + 4634.14i −0.564069 + 0.787304i
\(327\) 0 0
\(328\) 2087.64 1116.58i 0.351435 0.187965i
\(329\) 1304.20i 0.218549i
\(330\) 0 0
\(331\) 2687.86 2687.86i 0.446339 0.446339i −0.447797 0.894135i \(-0.647791\pi\)
0.894135 + 0.447797i \(0.147791\pi\)
\(332\) −5722.33 2820.69i −0.945945 0.466282i
\(333\) 0 0
\(334\) 2211.32 365.290i 0.362270 0.0598437i
\(335\) −2289.27 −0.373361
\(336\) 0 0
\(337\) −1795.31 −0.290199 −0.145099 0.989417i \(-0.546350\pi\)
−0.145099 + 0.989417i \(0.546350\pi\)
\(338\) 861.910 142.380i 0.138703 0.0229125i
\(339\) 0 0
\(340\) 2983.12 6051.85i 0.475830 0.965316i
\(341\) 8532.42 8532.42i 1.35500 1.35500i
\(342\) 0 0
\(343\) 1813.72i 0.285515i
\(344\) −964.235 292.220i −0.151128 0.0458007i
\(345\) 0 0
\(346\) 1802.18 2515.41i 0.280017 0.390836i
\(347\) 1967.33 1967.33i 0.304357 0.304357i −0.538359 0.842716i \(-0.680955\pi\)
0.842716 + 0.538359i \(0.180955\pi\)
\(348\) 0 0
\(349\) −7363.37 7363.37i −1.12938 1.12938i −0.990279 0.139097i \(-0.955580\pi\)
−0.139097 0.990279i \(-0.544420\pi\)
\(350\) 12.7224 + 77.0163i 0.00194297 + 0.0117620i
\(351\) 0 0
\(352\) −11570.3 + 383.867i −1.75198 + 0.0581255i
\(353\) −10644.3 −1.60493 −0.802466 0.596698i \(-0.796479\pi\)
−0.802466 + 0.596698i \(0.796479\pi\)
\(354\) 0 0
\(355\) −3731.70 3731.70i −0.557911 0.557911i
\(356\) 2230.28 + 6566.40i 0.332036 + 0.977580i
\(357\) 0 0
\(358\) −992.537 + 1385.34i −0.146529 + 0.204518i
\(359\) 7459.42i 1.09664i −0.836269 0.548319i \(-0.815268\pi\)
0.836269 0.548319i \(-0.184732\pi\)
\(360\) 0 0
\(361\) 6102.96i 0.889775i
\(362\) 8512.87 + 6099.10i 1.23599 + 0.885530i
\(363\) 0 0
\(364\) −473.051 + 959.678i −0.0681170 + 0.138189i
\(365\) 2136.65 + 2136.65i 0.306403 + 0.306403i
\(366\) 0 0
\(367\) −6251.35 −0.889149 −0.444574 0.895742i \(-0.646645\pi\)
−0.444574 + 0.895742i \(0.646645\pi\)
\(368\) 5436.03 + 7079.21i 0.770034 + 1.00280i
\(369\) 0 0
\(370\) −3859.47 + 637.550i −0.542282 + 0.0895801i
\(371\) 399.582 + 399.582i 0.0559171 + 0.0559171i
\(372\) 0 0
\(373\) 8911.86 8911.86i 1.23710 1.23710i 0.275921 0.961180i \(-0.411017\pi\)
0.961180 0.275921i \(-0.0889827\pi\)
\(374\) −10660.3 7637.67i −1.47389 1.05598i
\(375\) 0 0
\(376\) 5209.43 + 9739.97i 0.714510 + 1.33591i
\(377\) 4675.45i 0.638721i
\(378\) 0 0
\(379\) 1184.03 1184.03i 0.160473 0.160473i −0.622303 0.782776i \(-0.713803\pi\)
0.782776 + 0.622303i \(0.213803\pi\)
\(380\) 2422.98 822.966i 0.327095 0.111098i
\(381\) 0 0
\(382\) 1482.70 + 8975.67i 0.198591 + 1.20219i
\(383\) 2880.38 0.384283 0.192142 0.981367i \(-0.438457\pi\)
0.192142 + 0.981367i \(0.438457\pi\)
\(384\) 0 0
\(385\) 1987.66 0.263119
\(386\) −1314.99 7960.42i −0.173397 1.04968i
\(387\) 0 0
\(388\) 7090.77 2408.38i 0.927782 0.315122i
\(389\) −9244.24 + 9244.24i −1.20489 + 1.20489i −0.232226 + 0.972662i \(0.574601\pi\)
−0.972662 + 0.232226i \(0.925399\pi\)
\(390\) 0 0
\(391\) 10110.9i 1.30774i
\(392\) 3584.24 + 6701.38i 0.461815 + 0.863446i
\(393\) 0 0
\(394\) 5231.87 + 3748.41i 0.668979 + 0.479295i
\(395\) −2658.52 + 2658.52i −0.338645 + 0.338645i
\(396\) 0 0
\(397\) −4257.80 4257.80i −0.538270 0.538270i 0.384751 0.923020i \(-0.374287\pi\)
−0.923020 + 0.384751i \(0.874287\pi\)
\(398\) 2084.96 344.417i 0.262587 0.0433771i
\(399\) 0 0
\(400\) −402.644 524.354i −0.0503305 0.0655442i
\(401\) −12722.6 −1.58437 −0.792187 0.610278i \(-0.791058\pi\)
−0.792187 + 0.610278i \(0.791058\pi\)
\(402\) 0 0
\(403\) 6678.72 + 6678.72i 0.825535 + 0.825535i
\(404\) −7.94560 + 16.1192i −0.000978486 + 0.00198505i
\(405\) 0 0
\(406\) 573.739 + 411.059i 0.0701335 + 0.0502476i
\(407\) 7603.08i 0.925972i
\(408\) 0 0
\(409\) 232.991i 0.0281678i 0.999901 + 0.0140839i \(0.00448320\pi\)
−0.999901 + 0.0140839i \(0.995517\pi\)
\(410\) 2005.03 2798.53i 0.241515 0.337097i
\(411\) 0 0
\(412\) 3571.84 + 10516.2i 0.427116 + 1.25752i
\(413\) 760.629 + 760.629i 0.0906250 + 0.0906250i
\(414\) 0 0
\(415\) −9277.08 −1.09734
\(416\) −300.471 9056.59i −0.0354129 1.06739i
\(417\) 0 0
\(418\) −810.614 4907.13i −0.0948527 0.574200i
\(419\) 6125.69 + 6125.69i 0.714223 + 0.714223i 0.967416 0.253193i \(-0.0814807\pi\)
−0.253193 + 0.967416i \(0.581481\pi\)
\(420\) 0 0
\(421\) −8308.44 + 8308.44i −0.961825 + 0.961825i −0.999298 0.0374725i \(-0.988069\pi\)
0.0374725 + 0.999298i \(0.488069\pi\)
\(422\) −5188.38 + 7241.73i −0.598499 + 0.835360i
\(423\) 0 0
\(424\) −4580.22 1388.07i −0.524611 0.158988i
\(425\) 748.907i 0.0854760i
\(426\) 0 0
\(427\) −609.333 + 609.333i −0.0690579 + 0.0690579i
\(428\) −4109.39 + 8336.72i −0.464100 + 0.941520i
\(429\) 0 0
\(430\) −1445.52 + 238.787i −0.162114 + 0.0267798i
\(431\) −8737.57 −0.976506 −0.488253 0.872702i \(-0.662366\pi\)
−0.488253 + 0.872702i \(0.662366\pi\)
\(432\) 0 0
\(433\) −11627.5 −1.29049 −0.645247 0.763974i \(-0.723245\pi\)
−0.645247 + 0.763974i \(0.723245\pi\)
\(434\) −1406.75 + 232.383i −0.155590 + 0.0257021i
\(435\) 0 0
\(436\) −5406.74 2665.13i −0.593890 0.292744i
\(437\) −2711.51 + 2711.51i −0.296817 + 0.296817i
\(438\) 0 0
\(439\) 17631.8i 1.91690i −0.285261 0.958450i \(-0.592080\pi\)
0.285261 0.958450i \(-0.407920\pi\)
\(440\) −14844.2 + 7939.45i −1.60834 + 0.860224i
\(441\) 0 0
\(442\) 5978.36 8344.34i 0.643352 0.897963i
\(443\) 4549.81 4549.81i 0.487964 0.487964i −0.419699 0.907663i \(-0.637864\pi\)
0.907663 + 0.419699i \(0.137864\pi\)
\(444\) 0 0
\(445\) 7130.62 + 7130.62i 0.759604 + 0.759604i
\(446\) 165.057 + 999.186i 0.0175239 + 0.106083i
\(447\) 0 0
\(448\) 1137.78 + 759.371i 0.119989 + 0.0800824i
\(449\) 12926.5 1.35867 0.679334 0.733830i \(-0.262269\pi\)
0.679334 + 0.733830i \(0.262269\pi\)
\(450\) 0 0
\(451\) −4731.46 4731.46i −0.494004 0.494004i
\(452\) −509.554 + 173.070i −0.0530252 + 0.0180101i
\(453\) 0 0
\(454\) −8049.78 + 11235.5i −0.832147 + 1.16148i
\(455\) 1555.84i 0.160305i
\(456\) 0 0
\(457\) 9320.32i 0.954018i 0.878898 + 0.477009i \(0.158279\pi\)
−0.878898 + 0.477009i \(0.841721\pi\)
\(458\) 4649.87 + 3331.43i 0.474398 + 0.339886i
\(459\) 0 0
\(460\) 11641.5 + 5738.43i 1.17998 + 0.581643i
\(461\) −12885.0 12885.0i −1.30177 1.30177i −0.927200 0.374566i \(-0.877792\pi\)
−0.374566 0.927200i \(-0.622208\pi\)
\(462\) 0 0
\(463\) 7038.37 0.706482 0.353241 0.935532i \(-0.385080\pi\)
0.353241 + 0.935532i \(0.385080\pi\)
\(464\) −5926.71 778.144i −0.592975 0.0778543i
\(465\) 0 0
\(466\) 2585.44 427.091i 0.257013 0.0424563i
\(467\) −6001.76 6001.76i −0.594707 0.594707i 0.344192 0.938899i \(-0.388153\pi\)
−0.938899 + 0.344192i \(0.888153\pi\)
\(468\) 0 0
\(469\) 371.769 371.769i 0.0366028 0.0366028i
\(470\) 13056.7 + 9354.53i 1.28140 + 0.918069i
\(471\) 0 0
\(472\) −8718.75 2642.29i −0.850239 0.257672i
\(473\) 2847.65i 0.276818i
\(474\) 0 0
\(475\) 200.840 200.840i 0.0194004 0.0194004i
\(476\) 498.351 + 1467.25i 0.0479872 + 0.141284i
\(477\) 0 0
\(478\) −365.317 2211.48i −0.0349565 0.211612i
\(479\) 587.317 0.0560234 0.0280117 0.999608i \(-0.491082\pi\)
0.0280117 + 0.999608i \(0.491082\pi\)
\(480\) 0 0
\(481\) −5951.28 −0.564148
\(482\) −667.971 4043.63i −0.0631229 0.382121i
\(483\) 0 0
\(484\) 7098.29 + 20898.8i 0.666631 + 1.96270i
\(485\) 7700.05 7700.05i 0.720910 0.720910i
\(486\) 0 0
\(487\) 8366.45i 0.778481i −0.921136 0.389240i \(-0.872738\pi\)
0.921136 0.389240i \(-0.127262\pi\)
\(488\) 2116.71 6984.51i 0.196351 0.647897i
\(489\) 0 0
\(490\) 8983.36 + 6436.19i 0.828218 + 0.593382i
\(491\) −1529.30 + 1529.30i −0.140563 + 0.140563i −0.773887 0.633324i \(-0.781690\pi\)
0.633324 + 0.773887i \(0.281690\pi\)
\(492\) 0 0
\(493\) −4788.09 4788.09i −0.437413 0.437413i
\(494\) 3841.04 634.505i 0.349831 0.0577889i
\(495\) 0 0
\(496\) 9577.65 7354.55i 0.867035 0.665784i
\(497\) 1212.03 0.109390
\(498\) 0 0
\(499\) 11364.5 + 11364.5i 1.01952 + 1.01952i 0.999806 + 0.0197191i \(0.00627718\pi\)
0.0197191 + 0.999806i \(0.493723\pi\)
\(500\) 9572.06 + 4718.33i 0.856151 + 0.422020i
\(501\) 0 0
\(502\) −11640.8 8340.15i −1.03497 0.741513i
\(503\) 12570.2i 1.11427i 0.830421 + 0.557137i \(0.188100\pi\)
−0.830421 + 0.557137i \(0.811900\pi\)
\(504\) 0 0
\(505\) 26.1326i 0.00230274i
\(506\) 14692.1 20506.6i 1.29080 1.80164i
\(507\) 0 0
\(508\) −14419.7 + 4897.66i −1.25939 + 0.427753i
\(509\) −11880.4 11880.4i −1.03456 1.03456i −0.999381 0.0351750i \(-0.988801\pi\)
−0.0351750 0.999381i \(-0.511199\pi\)
\(510\) 0 0
\(511\) −693.968 −0.0600770
\(512\) −11530.3 1126.42i −0.995262 0.0972291i
\(513\) 0 0
\(514\) −2170.71 13140.6i −0.186276 1.12764i
\(515\) 11419.8 + 11419.8i 0.977122 + 0.977122i
\(516\) 0 0
\(517\) 22074.8 22074.8i 1.87785 1.87785i
\(518\) 523.229 730.300i 0.0443810 0.0619451i
\(519\) 0 0
\(520\) −6214.57 11619.3i −0.524090 0.979882i
\(521\) 6612.98i 0.556085i 0.960569 + 0.278042i \(0.0896856\pi\)
−0.960569 + 0.278042i \(0.910314\pi\)
\(522\) 0 0
\(523\) 5129.30 5129.30i 0.428850 0.428850i −0.459387 0.888236i \(-0.651931\pi\)
0.888236 + 0.459387i \(0.151931\pi\)
\(524\) 9320.07 + 4594.11i 0.777003 + 0.383005i
\(525\) 0 0
\(526\) 8282.01 1368.11i 0.686526 0.113408i
\(527\) 13679.3 1.13070
\(528\) 0 0
\(529\) −7282.60 −0.598553
\(530\) −6866.38 + 1134.26i −0.562748 + 0.0929609i
\(531\) 0 0
\(532\) −259.837 + 527.130i −0.0211755 + 0.0429586i
\(533\) 3703.53 3703.53i 0.300972 0.300972i
\(534\) 0 0
\(535\) 13515.5i 1.09220i
\(536\) −1291.46 + 4261.42i −0.104072 + 0.343406i
\(537\) 0 0
\(538\) 1546.02 2157.86i 0.123891 0.172922i
\(539\) 15188.1 15188.1i 1.21372 1.21372i
\(540\) 0 0
\(541\) −10968.5 10968.5i −0.871672 0.871672i 0.120983 0.992655i \(-0.461395\pi\)
−0.992655 + 0.120983i \(0.961395\pi\)
\(542\) −3714.95 22488.8i −0.294411 1.78224i
\(543\) 0 0
\(544\) −9582.49 8967.07i −0.755231 0.706728i
\(545\) −8765.44 −0.688936
\(546\) 0 0
\(547\) 13088.8 + 13088.8i 1.02311 + 1.02311i 0.999727 + 0.0233784i \(0.00744226\pi\)
0.0233784 + 0.999727i \(0.492558\pi\)
\(548\) 1227.85 + 3615.04i 0.0957138 + 0.281801i
\(549\) 0 0
\(550\) −1088.24 + 1518.92i −0.0843684 + 0.117758i
\(551\) 2568.12i 0.198558i
\(552\) 0 0
\(553\) 863.469i 0.0663986i
\(554\) −1568.82 1123.99i −0.120312 0.0861981i
\(555\) 0 0
\(556\) 7572.70 15362.7i 0.577615 1.17181i
\(557\) −5049.87 5049.87i −0.384147 0.384147i 0.488447 0.872594i \(-0.337564\pi\)
−0.872594 + 0.488447i \(0.837564\pi\)
\(558\) 0 0
\(559\) −2228.98 −0.168651
\(560\) 1972.21 + 258.941i 0.148824 + 0.0195397i
\(561\) 0 0
\(562\) 16462.1 2719.39i 1.23561 0.204111i
\(563\) 3249.06 + 3249.06i 0.243217 + 0.243217i 0.818180 0.574962i \(-0.194983\pi\)
−0.574962 + 0.818180i \(0.694983\pi\)
\(564\) 0 0
\(565\) −553.338 + 553.338i −0.0412019 + 0.0412019i
\(566\) 2210.75 + 1583.90i 0.164178 + 0.117626i
\(567\) 0 0
\(568\) −9051.67 + 4841.29i −0.668661 + 0.357634i
\(569\) 2806.05i 0.206741i −0.994643 0.103371i \(-0.967037\pi\)
0.994643 0.103371i \(-0.0329628\pi\)
\(570\) 0 0
\(571\) −12038.8 + 12038.8i −0.882324 + 0.882324i −0.993770 0.111446i \(-0.964452\pi\)
0.111446 + 0.993770i \(0.464452\pi\)
\(572\) −24250.3 + 8236.64i −1.77265 + 0.602083i
\(573\) 0 0
\(574\) 128.863 + 780.082i 0.00937042 + 0.0567247i
\(575\) 1440.62 0.104484
\(576\) 0 0
\(577\) 7206.84 0.519973 0.259987 0.965612i \(-0.416282\pi\)
0.259987 + 0.965612i \(0.416282\pi\)
\(578\) −158.172 957.508i −0.0113825 0.0689050i
\(579\) 0 0
\(580\) −8230.45 + 2795.48i −0.589226 + 0.200131i
\(581\) 1506.57 1506.57i 0.107578 0.107578i
\(582\) 0 0
\(583\) 13526.6i 0.960918i
\(584\) 5182.68 2771.96i 0.367227 0.196412i
\(585\) 0 0
\(586\) −11552.5 8276.84i −0.814382 0.583470i
\(587\) −10377.0 + 10377.0i −0.729647 + 0.729647i −0.970549 0.240903i \(-0.922557\pi\)
0.240903 + 0.970549i \(0.422557\pi\)
\(588\) 0 0
\(589\) 3668.48 + 3668.48i 0.256633 + 0.256633i
\(590\) −13070.6 + 2159.14i −0.912047 + 0.150662i
\(591\) 0 0
\(592\) −990.483 + 7543.98i −0.0687645 + 0.523743i
\(593\) 4758.60 0.329531 0.164766 0.986333i \(-0.447313\pi\)
0.164766 + 0.986333i \(0.447313\pi\)
\(594\) 0 0
\(595\) 1593.32 + 1593.32i 0.109781 + 0.109781i
\(596\) 1877.57 3809.02i 0.129041 0.261785i
\(597\) 0 0
\(598\) 16051.5 + 11500.2i 1.09765 + 0.786417i
\(599\) 14256.4i 0.972455i −0.873832 0.486227i \(-0.838373\pi\)
0.873832 0.486227i \(-0.161627\pi\)
\(600\) 0 0
\(601\) 10385.2i 0.704862i 0.935838 + 0.352431i \(0.114645\pi\)
−0.935838 + 0.352431i \(0.885355\pi\)
\(602\) 195.969 273.526i 0.0132676 0.0185184i
\(603\) 0 0
\(604\) −7712.16 22706.2i −0.519542 1.52964i
\(605\) 22694.5 + 22694.5i 1.52506 + 1.52506i
\(606\) 0 0
\(607\) −16243.6 −1.08618 −0.543088 0.839676i \(-0.682745\pi\)
−0.543088 + 0.839676i \(0.682745\pi\)
\(608\) −165.042 4974.59i −0.0110088 0.331819i
\(609\) 0 0
\(610\) −1729.67 10470.7i −0.114807 0.694996i
\(611\) 17279.0 + 17279.0i 1.14408 + 1.14408i
\(612\) 0 0
\(613\) −500.502 + 500.502i −0.0329773 + 0.0329773i −0.723403 0.690426i \(-0.757423\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(614\) 6372.83 8894.92i 0.418870 0.584642i
\(615\) 0 0
\(616\) 1121.31 3699.99i 0.0733426 0.242008i
\(617\) 11575.9i 0.755316i −0.925945 0.377658i \(-0.876729\pi\)
0.925945 0.377658i \(-0.123271\pi\)
\(618\) 0 0
\(619\) 18356.1 18356.1i 1.19191 1.19191i 0.215380 0.976530i \(-0.430901\pi\)
0.976530 0.215380i \(-0.0690992\pi\)
\(620\) 7763.68 15750.2i 0.502898 1.02023i
\(621\) 0 0
\(622\) −16176.3 + 2672.18i −1.04278 + 0.172258i
\(623\) −2315.98 −0.148937
\(624\) 0 0
\(625\) 16809.5 1.07581
\(626\) 23336.8 3855.03i 1.48998 0.246131i
\(627\) 0 0
\(628\) 15313.2 + 7548.26i 0.973027 + 0.479631i
\(629\) −6094.66 + 6094.66i −0.386343 + 0.386343i
\(630\) 0 0
\(631\) 10224.8i 0.645079i −0.946556 0.322539i \(-0.895463\pi\)
0.946556 0.322539i \(-0.104537\pi\)
\(632\) 3449.01 + 6448.54i 0.217079 + 0.405869i
\(633\) 0 0
\(634\) 802.338 1119.87i 0.0502601 0.0701509i
\(635\) −15658.7 + 15658.7i −0.978578 + 0.978578i
\(636\) 0 0
\(637\) 11888.4 + 11888.4i 0.739461 + 0.739461i
\(638\) 2753.52 + 16668.7i 0.170866 + 1.03436i
\(639\) 0 0
\(640\) −15763.2 + 5943.92i −0.973584 + 0.367116i
\(641\) −19804.4 −1.22032 −0.610162 0.792277i \(-0.708896\pi\)
−0.610162 + 0.792277i \(0.708896\pi\)
\(642\) 0 0
\(643\) 15680.7 + 15680.7i 0.961723 + 0.961723i 0.999294 0.0375712i \(-0.0119621\pi\)
−0.0375712 + 0.999294i \(0.511962\pi\)
\(644\) −2822.45 + 958.646i −0.172702 + 0.0586583i
\(645\) 0 0
\(646\) 3283.78 4583.37i 0.199998 0.279149i
\(647\) 9232.26i 0.560985i 0.959856 + 0.280493i \(0.0904978\pi\)
−0.959856 + 0.280493i \(0.909502\pi\)
\(648\) 0 0
\(649\) 25748.8i 1.55736i
\(650\) −1188.93 851.814i −0.0717438 0.0514014i
\(651\) 0 0
\(652\) 14462.6 + 7129.00i 0.868710 + 0.428210i
\(653\) 19697.9 + 19697.9i 1.18046 + 1.18046i 0.979626 + 0.200833i \(0.0643648\pi\)
0.200833 + 0.979626i \(0.435635\pi\)
\(654\) 0 0
\(655\) 15109.8 0.901355
\(656\) −4078.30 5311.07i −0.242730 0.316101i
\(657\) 0 0
\(658\) −3639.50 + 601.213i −0.215627 + 0.0356196i
\(659\) −3888.06 3888.06i −0.229829 0.229829i 0.582792 0.812621i \(-0.301960\pi\)
−0.812621 + 0.582792i \(0.801960\pi\)
\(660\) 0 0
\(661\) −8110.20 + 8110.20i −0.477232 + 0.477232i −0.904245 0.427013i \(-0.859566\pi\)
0.427013 + 0.904245i \(0.359566\pi\)
\(662\) −8739.82 6261.70i −0.513116 0.367625i
\(663\) 0 0
\(664\) −5233.54 + 17269.1i −0.305875 + 1.00929i
\(665\) 854.587i 0.0498338i
\(666\) 0 0
\(667\) 9210.54 9210.54i 0.534683 0.534683i
\(668\) −2038.76 6002.54i −0.118087 0.347672i
\(669\) 0 0
\(670\) 1055.31 + 6388.45i 0.0608513 + 0.368369i
\(671\) −20627.1 −1.18674
\(672\) 0 0
\(673\) −28428.2 −1.62827 −0.814135 0.580676i \(-0.802788\pi\)
−0.814135 + 0.580676i \(0.802788\pi\)
\(674\) 827.610 + 5010.02i 0.0472972 + 0.286318i
\(675\) 0 0
\(676\) −794.652 2339.62i −0.0452124 0.133114i
\(677\) 16967.4 16967.4i 0.963235 0.963235i −0.0361128 0.999348i \(-0.511498\pi\)
0.999348 + 0.0361128i \(0.0114975\pi\)
\(678\) 0 0
\(679\) 2500.92i 0.141350i
\(680\) −18263.5 5534.91i −1.02996 0.312138i
\(681\) 0 0
\(682\) −27744.0 19877.3i −1.55773 1.11605i
\(683\) 9550.16 9550.16i 0.535032 0.535032i −0.387034 0.922066i \(-0.626500\pi\)
0.922066 + 0.387034i \(0.126500\pi\)
\(684\) 0 0
\(685\) 3925.66 + 3925.66i 0.218966 + 0.218966i
\(686\) −5061.38 + 836.095i −0.281697 + 0.0465339i
\(687\) 0 0
\(688\) −370.974 + 2825.51i −0.0205570 + 0.156572i
\(689\) −10587.9 −0.585439
\(690\) 0 0
\(691\) −20859.7 20859.7i −1.14839 1.14839i −0.986868 0.161527i \(-0.948358\pi\)
−0.161527 0.986868i \(-0.551642\pi\)
\(692\) −7850.30 3869.62i −0.431248 0.212574i
\(693\) 0 0
\(694\) −6396.96 4583.14i −0.349892 0.250683i
\(695\) 24906.1i 1.35934i
\(696\) 0 0
\(697\) 7585.52i 0.412227i
\(698\) −17153.9 + 23942.7i −0.930207 + 1.29834i
\(699\) 0 0
\(700\) 209.058 71.0065i 0.0112880 0.00383399i
\(701\) −23495.4 23495.4i −1.26592 1.26592i −0.948178 0.317740i \(-0.897076\pi\)
−0.317740 0.948178i \(-0.602924\pi\)
\(702\) 0 0
\(703\) −3268.91 −0.175376
\(704\) 6404.93 + 32111.1i 0.342890 + 1.71908i
\(705\) 0 0
\(706\) 4906.86 + 29704.2i 0.261575 + 1.58347i
\(707\) −4.24384 4.24384i −0.000225751 0.000225751i
\(708\) 0 0
\(709\) 4559.45 4559.45i 0.241515 0.241515i −0.575962 0.817477i \(-0.695372\pi\)
0.817477 + 0.575962i \(0.195372\pi\)
\(710\) −8693.47 + 12134.0i −0.459521 + 0.641380i
\(711\) 0 0
\(712\) 17296.1 9250.84i 0.910393 0.486924i
\(713\) 26313.9i 1.38214i
\(714\) 0 0
\(715\) −26334.1 + 26334.1i −1.37740 + 1.37740i
\(716\) 4323.49 + 2131.16i 0.225665 + 0.111236i
\(717\) 0 0
\(718\) −20816.3 + 3438.67i −1.08198 + 0.178733i
\(719\) 6494.67 0.336871 0.168436 0.985713i \(-0.446128\pi\)
0.168436 + 0.985713i \(0.446128\pi\)
\(720\) 0 0
\(721\) −3709.08 −0.191586
\(722\) −17031.0 + 2813.37i −0.877878 + 0.145018i
\(723\) 0 0
\(724\) 13095.9 26567.7i 0.672246 1.36378i
\(725\) −682.221 + 682.221i −0.0349476 + 0.0349476i
\(726\) 0 0
\(727\) 24866.4i 1.26856i −0.773103 0.634280i \(-0.781296\pi\)
0.773103 0.634280i \(-0.218704\pi\)
\(728\) 2896.15 + 877.704i 0.147443 + 0.0446839i
\(729\) 0 0
\(730\) 4977.59 6947.50i 0.252368 0.352245i
\(731\) −2282.68 + 2282.68i −0.115497 + 0.115497i
\(732\) 0 0
\(733\) −14914.3 14914.3i −0.751533 0.751533i 0.223232 0.974765i \(-0.428339\pi\)
−0.974765 + 0.223232i \(0.928339\pi\)
\(734\) 2881.77 + 17445.1i 0.144916 + 0.877260i
\(735\) 0 0
\(736\) 17249.4 18433.2i 0.863886 0.923176i
\(737\) 12585.1 0.629008
\(738\) 0 0
\(739\) 8451.86 + 8451.86i 0.420713 + 0.420713i 0.885449 0.464737i \(-0.153851\pi\)
−0.464737 + 0.885449i \(0.653851\pi\)
\(740\) 3558.30 + 10476.4i 0.176765 + 0.520431i
\(741\) 0 0
\(742\) 930.875 1299.28i 0.0460559 0.0642829i
\(743\) 5622.43i 0.277614i 0.990319 + 0.138807i \(0.0443267\pi\)
−0.990319 + 0.138807i \(0.955673\pi\)
\(744\) 0 0
\(745\) 6175.21i 0.303681i
\(746\) −28977.7 20761.3i −1.42219 1.01893i
\(747\) 0 0
\(748\) −16399.5 + 33269.7i −0.801638 + 1.62628i
\(749\) −2194.88 2194.88i −0.107075 0.107075i
\(750\) 0 0
\(751\) −32314.9 −1.57016 −0.785079 0.619396i \(-0.787378\pi\)
−0.785079 + 0.619396i \(0.787378\pi\)
\(752\) 24779.0 19027.4i 1.20159 0.922685i
\(753\) 0 0
\(754\) −13047.3 + 2155.30i −0.630181 + 0.104100i
\(755\) −24657.2 24657.2i −1.18857 1.18857i
\(756\) 0 0
\(757\) 12692.8 12692.8i 0.609418 0.609418i −0.333376 0.942794i \(-0.608188\pi\)
0.942794 + 0.333376i \(0.108188\pi\)
\(758\) −3849.97 2758.34i −0.184482 0.132173i
\(759\) 0 0
\(760\) −3413.53 6382.21i −0.162923 0.304615i
\(761\) 13108.2i 0.624404i 0.950016 + 0.312202i \(0.101067\pi\)
−0.950016 + 0.312202i \(0.898933\pi\)
\(762\) 0 0
\(763\) 1423.48 1423.48i 0.0675404 0.0675404i
\(764\) 24364.1 8275.27i 1.15375 0.391870i
\(765\) 0 0
\(766\) −1327.81 8038.01i −0.0626314 0.379145i
\(767\) −20154.8 −0.948822
\(768\) 0 0
\(769\) 23661.2 1.10955 0.554776 0.832000i \(-0.312804\pi\)
0.554776 + 0.832000i \(0.312804\pi\)
\(770\) −916.280 5546.79i −0.0428837 0.259601i
\(771\) 0 0
\(772\) −21608.2 + 7339.24i −1.00738 + 0.342157i
\(773\) −21370.5 + 21370.5i −0.994362 + 0.994362i −0.999984 0.00562228i \(-0.998210\pi\)
0.00562228 + 0.999984i \(0.498210\pi\)
\(774\) 0 0
\(775\) 1949.06i 0.0903384i
\(776\) −9989.59 18677.3i −0.462120 0.864018i
\(777\) 0 0
\(778\) 30058.5 + 21535.6i 1.38515 + 0.992402i
\(779\) 2034.27 2034.27i 0.0935627 0.0935627i
\(780\) 0 0
\(781\) 20514.8 + 20514.8i 0.939921 + 0.939921i
\(782\) 28215.4 4660.94i 1.29026 0.213139i
\(783\) 0 0
\(784\) 17048.7 13091.4i 0.776633 0.596366i
\(785\) 24825.8 1.12875
\(786\) 0 0