Properties

Label 144.4.k.a.37.3
Level $144$
Weight $4$
Character 144.37
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 37.3
Root \(-1.62580 - 1.16481i\) of defining polynomial
Character \(\chi\) \(=\) 144.37
Dual form 144.4.k.a.109.3

$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

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

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 0.236007 0.971751i \(-0.424161\pi\)
−0.971751 + 0.236007i \(0.924161\pi\)
\(6\) 0 0
\(7\) 2.67171i 0.144259i 0.997395 + 0.0721293i \(0.0229794\pi\)
−0.997395 + 0.0721293i \(0.977021\pi\)
\(8\) 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 0.960197 + 0.279323i \(0.0901099\pi\)
0.279323 + 0.960197i \(0.409890\pi\)
\(12\) 0 0
\(13\) 35.3968 35.3968i 0.755176 0.755176i −0.220264 0.975440i \(-0.570692\pi\)
0.975440 + 0.220264i \(0.0706918\pi\)
\(14\) −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 −0.579916 0.814676i \(-0.696915\pi\)
0.814676 + 0.579916i \(0.196915\pi\)
\(20\) 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 \(-0.782165\pi\)
0.774830 0.632170i \(-0.217835\pi\)
\(24\) 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 −0.886199 0.463304i \(-0.846664\pi\)
0.463304 + 0.886199i \(0.346664\pi\)
\(30\) 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 0.495237 0.868758i \(-0.335081\pi\)
−0.868758 + 0.495237i \(0.835081\pi\)
\(38\) 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 \(0.0638578\pi\)
−0.979944 + 0.199272i \(0.936142\pi\)
\(42\) 0 0
\(43\) −31.4857 31.4857i −0.111663 0.111663i 0.649067 0.760731i \(-0.275159\pi\)
−0.760731 + 0.649067i \(0.775159\pi\)
\(44\) −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 0.486220 0.873837i \(-0.338376\pi\)
−0.873837 + 0.486220i \(0.838376\pi\)
\(54\) 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 0.319406 0.947618i \(-0.396517\pi\)
−0.947618 + 0.319406i \(0.896517\pi\)
\(60\) 0 0
\(61\) −228.069 + 228.069i −0.478709 + 0.478709i −0.904719 0.426010i \(-0.859919\pi\)
0.426010 + 0.904719i \(0.359919\pi\)
\(62\) −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 −0.568768 0.822498i \(-0.692580\pi\)
0.822498 + 0.568768i \(0.192580\pi\)
\(68\) −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 \(-0.876217\pi\)
0.925336 0.379147i \(-0.123783\pi\)
\(72\) 0 0
\(73\) 259.747i 0.416454i 0.978081 + 0.208227i \(0.0667692\pi\)
−0.978081 + 0.208227i \(0.933231\pi\)
\(74\) 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 −0.227943 0.973674i \(-0.573200\pi\)
0.973674 + 0.227943i \(0.0732000\pi\)
\(84\) 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 \(0.172659\pi\)
−0.856459 + 0.516215i \(0.827341\pi\)
\(90\) 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 0.707889 0.706324i \(-0.249648\pi\)
−0.706324 + 0.707889i \(0.749648\pi\)
\(102\) 0 0
\(103\) 1388.28i 1.32807i 0.747700 + 0.664036i \(0.231158\pi\)
−0.747700 + 0.664036i \(0.768842\pi\)
\(104\) −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 0.973009 0.230767i \(-0.0741234\pi\)
−0.230767 + 0.973009i \(0.574123\pi\)
\(108\) 0 0
\(109\) 532.797 532.797i 0.468190 0.468190i −0.433138 0.901328i \(-0.642594\pi\)
0.901328 + 0.433138i \(0.142594\pi\)
\(110\) 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 −0.943609 0.331062i \(-0.892593\pi\)
0.331062 + 0.943609i \(0.392593\pi\)
\(132\) 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 \(0.0475430\pi\)
−0.988866 + 0.148806i \(0.952457\pi\)
\(138\) 0 0
\(139\) −1513.89 1513.89i −0.923788 0.923788i 0.0735064 0.997295i \(-0.476581\pi\)
−0.997295 + 0.0735064i \(0.976581\pi\)
\(140\) −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 0.596349 0.802725i \(-0.296618\pi\)
−0.802725 + 0.596349i \(0.796618\pi\)
\(150\) 0 0
\(151\) 2997.52i 1.61546i −0.589553 0.807730i \(-0.700696\pi\)
0.589553 0.807730i \(-0.299304\pi\)
\(152\) −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 −0.977592 0.210510i \(-0.932488\pi\)
0.210510 + 0.977592i \(0.432488\pi\)
\(158\) −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 −0.961088 0.276244i \(-0.910910\pi\)
0.276244 + 0.961088i \(0.410910\pi\)
\(164\) 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 \(-0.941228\pi\)
0.983003 0.183590i \(-0.0587717\pi\)
\(168\) 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 −0.516384 0.856357i \(-0.672722\pi\)
0.856357 + 0.516384i \(0.172722\pi\)
\(174\) 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 −0.790441 0.612539i \(-0.790148\pi\)
0.612539 + 0.790441i \(0.290148\pi\)
\(180\) 0 0
\(181\) −2618.06 2618.06i −1.07513 1.07513i −0.996938 0.0781951i \(-0.975084\pi\)
−0.0781951 0.996938i \(-0.524916\pi\)
\(182\) −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 0.353512 0.935430i \(-0.384987\pi\)
−0.935430 + 0.353512i \(0.884987\pi\)
\(198\) 0 0
\(199\) 747.136i 0.266146i −0.991106 0.133073i \(-0.957516\pi\)
0.991106 0.133073i \(-0.0424845\pi\)
\(200\) 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 −0.969950 0.243305i \(-0.921769\pi\)
0.243305 + 0.969950i \(0.421769\pi\)
\(212\) 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 −0.0103741 + 0.999946i \(0.503302\pi\)
−0.999946 + 0.0103741i \(0.996698\pi\)
\(228\) 0 0
\(229\) −1430.03 1430.03i −0.412659 0.412659i 0.470005 0.882664i \(-0.344252\pi\)
−0.882664 + 0.470005i \(0.844252\pi\)
\(230\) −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 \(-0.958423\pi\)
0.991481 0.130248i \(-0.0415774\pi\)
\(234\) 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 0.995460 0.0951802i \(-0.0303427\pi\)
−0.0951802 + 0.995460i \(0.530343\pi\)
\(252\) 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 \(-0.886890\pi\)
0.937526 0.347915i \(-0.113110\pi\)
\(264\) 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 −0.627887 0.778305i \(-0.716080\pi\)
0.778305 + 0.627887i \(0.216080\pi\)
\(270\) 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 0.757495 0.652841i \(-0.226423\pi\)
−0.652841 + 0.757495i \(0.726423\pi\)
\(278\) 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 \(-0.784619\pi\)
0.779682 0.626175i \(-0.215381\pi\)
\(282\) 0 0
\(283\) −679.897 679.897i −0.142812 0.142812i 0.632086 0.774898i \(-0.282199\pi\)
−0.774898 + 0.632086i \(0.782199\pi\)
\(284\) −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 0.966198 0.257800i \(-0.0829976\pi\)
−0.257800 + 0.966198i \(0.582998\pi\)
\(294\) 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 −0.405527 0.914083i \(-0.632912\pi\)
0.914083 + 0.405527i \(0.132912\pi\)
\(308\) 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 \(0.177229\pi\)
−0.848960 + 0.528458i \(0.822771\pi\)
\(312\) 0 0
\(313\) 8362.62i 1.51017i −0.655627 0.755085i \(-0.727596\pi\)
0.655627 0.755085i \(-0.272404\pi\)
\(314\) −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 −0.675938 0.736959i \(-0.736261\pi\)
0.736959 + 0.675938i \(0.236261\pi\)
\(318\) 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 0.894135 0.447797i \(-0.147791\pi\)
−0.447797 + 0.894135i \(0.647791\pi\)
\(332\) −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 0.842716 0.538359i \(-0.180955\pi\)
−0.538359 + 0.842716i \(0.680955\pi\)
\(348\) 0 0
\(349\) −7363.37 + 7363.37i −1.12938 + 1.12938i −0.139097 + 0.990279i \(0.544420\pi\)
−0.990279 + 0.139097i \(0.955580\pi\)
\(350\) 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 \(0.184732\pi\)
−0.836269 + 0.548319i \(0.815268\pi\)
\(360\) 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 0.961180 + 0.275921i \(0.0889827\pi\)
0.275921 + 0.961180i \(0.411017\pi\)
\(374\) −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 0.782776 0.622303i \(-0.213803\pi\)
−0.622303 + 0.782776i \(0.713803\pi\)
\(380\) 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 −0.972662 0.232226i \(-0.925399\pi\)
−0.232226 0.972662i \(-0.574601\pi\)
\(390\) 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 −0.923020 0.384751i \(-0.874287\pi\)
0.384751 + 0.923020i \(0.374287\pi\)
\(398\) 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 \(-0.995517\pi\)
0.999901 0.0140839i \(-0.00448320\pi\)
\(410\) 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 −0.253193 0.967416i \(-0.581481\pi\)
0.967416 + 0.253193i \(0.0814807\pi\)
\(420\) 0 0
\(421\) −8308.44 8308.44i −0.961825 0.961825i 0.0374725 0.999298i \(-0.488069\pi\)
−0.999298 + 0.0374725i \(0.988069\pi\)
\(422\) −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 \(0.407920\pi\)
−0.285261 + 0.958450i \(0.592080\pi\)
\(440\) −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 0.907663 0.419699i \(-0.137864\pi\)
−0.419699 + 0.907663i \(0.637864\pi\)
\(444\) 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 \(-0.841721\pi\)
0.878898 0.477009i \(-0.158279\pi\)
\(458\) 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 −0.374566 + 0.927200i \(0.622208\pi\)
−0.927200 + 0.374566i \(0.877792\pi\)
\(462\) 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 −0.938899 0.344192i \(-0.888153\pi\)
0.344192 + 0.938899i \(0.388153\pi\)
\(468\) 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 \(0.127262\pi\)
−0.921136 + 0.389240i \(0.872738\pi\)
\(488\) 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 0.633324 0.773887i \(-0.281690\pi\)
−0.773887 + 0.633324i \(0.781690\pi\)
\(492\) 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 0.0197191 0.999806i \(-0.493723\pi\)
0.999806 0.0197191i \(-0.00627718\pi\)
\(500\) 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 \(-0.811900\pi\)
0.830421 0.557137i \(-0.188100\pi\)
\(504\) 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 −0.0351750 + 0.999381i \(0.511199\pi\)
−0.999381 + 0.0351750i \(0.988801\pi\)
\(510\) 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 \(-0.910314\pi\)
0.960569 0.278042i \(-0.0896856\pi\)
\(522\) 0 0
\(523\) 5129.30 + 5129.30i 0.428850 + 0.428850i 0.888236 0.459387i \(-0.151931\pi\)
−0.459387 + 0.888236i \(0.651931\pi\)
\(524\) 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 −0.992655 0.120983i \(-0.961395\pi\)
0.120983 + 0.992655i \(0.461395\pi\)
\(542\) −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 0.0233784 0.999727i \(-0.492558\pi\)
0.999727 0.0233784i \(-0.00744226\pi\)
\(548\) 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 −0.872594 0.488447i \(-0.837564\pi\)
0.488447 + 0.872594i \(0.337564\pi\)
\(558\) 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 −0.574962 0.818180i \(-0.694983\pi\)
0.818180 + 0.574962i \(0.194983\pi\)
\(564\) 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 \(0.0329628\pi\)
−0.994643 + 0.103371i \(0.967037\pi\)
\(570\) 0 0
\(571\) −12038.8 12038.8i −0.882324 0.882324i 0.111446 0.993770i \(-0.464452\pi\)
−0.993770 + 0.111446i \(0.964452\pi\)
\(572\) −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 0.240903 0.970549i \(-0.422557\pi\)
−0.970549 + 0.240903i \(0.922557\pi\)
\(588\) 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 \(0.161627\pi\)
−0.873832 + 0.486227i \(0.838373\pi\)
\(600\) 0 0
\(601\) 10385.2i 0.704862i −0.935838 0.352431i \(-0.885355\pi\)
0.935838 0.352431i \(-0.114645\pi\)
\(602\) 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 0.690426 0.723403i \(-0.257423\pi\)
−0.723403 + 0.690426i \(0.757423\pi\)
\(614\) 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 \(0.123271\pi\)
−0.925945 + 0.377658i \(0.876729\pi\)
\(618\) 0 0
\(619\) 18356.1 + 18356.1i 1.19191 + 1.19191i 0.976530 + 0.215380i \(0.0690992\pi\)
0.215380 + 0.976530i \(0.430901\pi\)
\(620\) 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 \(0.104537\pi\)
−0.946556 + 0.322539i \(0.895463\pi\)
\(632\) 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 −0.0375712 0.999294i \(-0.511962\pi\)
0.999294 + 0.0375712i \(0.0119621\pi\)
\(644\) −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 \(-0.909502\pi\)
0.959856 0.280493i \(-0.0904978\pi\)
\(648\) 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 0.200833 0.979626i \(-0.435635\pi\)
0.979626 0.200833i \(-0.0643648\pi\)
\(654\) 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 −0.812621 0.582792i \(-0.801960\pi\)
0.582792 + 0.812621i \(0.301960\pi\)
\(660\) 0 0
\(661\) −8110.20 8110.20i −0.477232 0.477232i 0.427013 0.904245i \(-0.359566\pi\)
−0.904245 + 0.427013i \(0.859566\pi\)
\(662\) −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 0.999348 0.0361128i \(-0.0114975\pi\)
−0.0361128 + 0.999348i \(0.511498\pi\)
\(678\) 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 0.922066 0.387034i \(-0.126500\pi\)
−0.387034 + 0.922066i \(0.626500\pi\)
\(684\) 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 −0.161527 + 0.986868i \(0.551642\pi\)
−0.986868 + 0.161527i \(0.948358\pi\)
\(692\) −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 −0.317740 + 0.948178i \(0.602924\pi\)
−0.948178 + 0.317740i \(0.897076\pi\)
\(702\) 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 0.817477 0.575962i \(-0.195372\pi\)
−0.575962 + 0.817477i \(0.695372\pi\)
\(710\) −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 \(0.218704\pi\)
−0.773103 + 0.634280i \(0.781296\pi\)
\(728\) 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 −0.974765 0.223232i \(-0.928339\pi\)
0.223232 + 0.974765i \(0.428339\pi\)
\(734\) 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 −0.464737 0.885449i \(-0.653851\pi\)
0.885449 + 0.464737i \(0.153851\pi\)
\(740\) 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 \(-0.955673\pi\)
0.990319 0.138807i \(-0.0443267\pi\)
\(744\) 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 0.942794 0.333376i \(-0.108188\pi\)
−0.333376 + 0.942794i \(0.608188\pi\)
\(758\) −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 \(-0.898933\pi\)
0.950016 0.312202i \(-0.101067\pi\)
\(762\) 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 0.00562228 0.999984i \(-0.498210\pi\)
−0.999984 + 0.00562228i \(0.998210\pi\)
\(774\) 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