Properties

Label 144.3.m.c.19.3
Level $144$
Weight $3$
Character 144.19
Analytic conductor $3.924$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.3
Root \(-1.25564 + 1.55672i\) of defining polynomial
Character \(\chi\) \(=\) 144.19
Dual form 144.3.m.c.91.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.25564 - 1.55672i) q^{2} +(-0.846753 + 3.90935i) q^{4} +(-0.909023 + 0.909023i) q^{5} -0.654713 q^{7} +(7.14897 - 3.59057i) q^{8} +O(q^{10})\) \(q+(-1.25564 - 1.55672i) q^{2} +(-0.846753 + 3.90935i) q^{4} +(-0.909023 + 0.909023i) q^{5} -0.654713 q^{7} +(7.14897 - 3.59057i) q^{8} +(2.55650 + 0.273691i) q^{10} +(13.3760 + 13.3760i) q^{11} +(8.32795 + 8.32795i) q^{13} +(0.822082 + 1.01921i) q^{14} +(-14.5660 - 6.62050i) q^{16} +3.93529 q^{17} +(16.8974 - 16.8974i) q^{19} +(-2.78397 - 4.32340i) q^{20} +(4.02729 - 37.6181i) q^{22} +23.1787 q^{23} +23.3474i q^{25} +(2.50740 - 23.4212i) q^{26} +(0.554380 - 2.55950i) q^{28} +(-35.6105 - 35.6105i) q^{29} +45.5687i q^{31} +(7.98336 + 30.9882i) q^{32} +(-4.94130 - 6.12615i) q^{34} +(0.595149 - 0.595149i) q^{35} +(10.1527 - 10.1527i) q^{37} +(-47.5215 - 5.08752i) q^{38} +(-3.23467 + 9.76249i) q^{40} +28.4661i q^{41} +(22.7354 + 22.7354i) q^{43} +(-63.6176 + 40.9653i) q^{44} +(-29.1040 - 36.0827i) q^{46} -10.7746i q^{47} -48.5714 q^{49} +(36.3453 - 29.3158i) q^{50} +(-39.6086 + 25.5051i) q^{52} +(-41.5142 + 41.5142i) q^{53} -24.3182 q^{55} +(-4.68053 + 2.35079i) q^{56} +(-10.7217 + 100.149i) q^{58} +(21.0646 + 21.0646i) q^{59} +(-68.7531 - 68.7531i) q^{61} +(70.9377 - 57.2178i) q^{62} +(38.2157 - 51.3377i) q^{64} -15.1406 q^{65} +(67.8242 - 67.8242i) q^{67} +(-3.33222 + 15.3844i) q^{68} +(-1.67377 - 0.179189i) q^{70} -33.3094 q^{71} -18.6331i q^{73} +(-28.5531 - 3.05682i) q^{74} +(51.7499 + 80.3657i) q^{76} +(-8.75745 - 8.75745i) q^{77} +6.29222i q^{79} +(19.2590 - 7.22265i) q^{80} +(44.3137 - 35.7431i) q^{82} +(72.0774 - 72.0774i) q^{83} +(-3.57727 + 3.57727i) q^{85} +(6.84524 - 63.9400i) q^{86} +(143.652 + 47.5973i) q^{88} -10.6131i q^{89} +(-5.45242 - 5.45242i) q^{91} +(-19.6266 + 90.6135i) q^{92} +(-16.7730 + 13.5290i) q^{94} +30.7202i q^{95} +143.631 q^{97} +(60.9880 + 75.6120i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} + 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} + 12q^{8} - 56q^{10} - 32q^{11} + 44q^{14} + 32q^{16} - 32q^{19} - 80q^{20} + 32q^{22} + 128q^{23} + 100q^{26} - 120q^{28} - 32q^{29} - 160q^{32} + 96q^{34} - 96q^{35} - 96q^{37} - 168q^{38} + 48q^{40} + 160q^{43} - 88q^{44} + 136q^{46} + 112q^{49} + 236q^{50} - 48q^{52} + 160q^{53} - 256q^{55} + 224q^{56} + 144q^{58} + 128q^{59} - 32q^{61} + 276q^{62} - 408q^{64} + 32q^{65} + 320q^{67} + 448q^{68} - 384q^{70} - 512q^{71} - 348q^{74} + 72q^{76} - 224q^{77} - 552q^{80} - 40q^{82} + 160q^{83} + 160q^{85} - 528q^{86} + 480q^{88} - 480q^{91} - 496q^{92} + 312q^{94} + 440q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25564 1.55672i −0.627818 0.778360i
\(3\) 0 0
\(4\) −0.846753 + 3.90935i −0.211688 + 0.977337i
\(5\) −0.909023 + 0.909023i −0.181805 + 0.181805i −0.792142 0.610337i \(-0.791034\pi\)
0.610337 + 0.792142i \(0.291034\pi\)
\(6\) 0 0
\(7\) −0.654713 −0.0935305 −0.0467652 0.998906i \(-0.514891\pi\)
−0.0467652 + 0.998906i \(0.514891\pi\)
\(8\) 7.14897 3.59057i 0.893622 0.448821i
\(9\) 0 0
\(10\) 2.55650 + 0.273691i 0.255650 + 0.0273691i
\(11\) 13.3760 + 13.3760i 1.21600 + 1.21600i 0.969021 + 0.246980i \(0.0794382\pi\)
0.246980 + 0.969021i \(0.420562\pi\)
\(12\) 0 0
\(13\) 8.32795 + 8.32795i 0.640612 + 0.640612i 0.950706 0.310094i \(-0.100361\pi\)
−0.310094 + 0.950706i \(0.600361\pi\)
\(14\) 0.822082 + 1.01921i 0.0587202 + 0.0728004i
\(15\) 0 0
\(16\) −14.5660 6.62050i −0.910376 0.413781i
\(17\) 3.93529 0.231488 0.115744 0.993279i \(-0.463075\pi\)
0.115744 + 0.993279i \(0.463075\pi\)
\(18\) 0 0
\(19\) 16.8974 16.8974i 0.889336 0.889336i −0.105123 0.994459i \(-0.533524\pi\)
0.994459 + 0.105123i \(0.0335236\pi\)
\(20\) −2.78397 4.32340i −0.139198 0.216170i
\(21\) 0 0
\(22\) 4.02729 37.6181i 0.183059 1.70991i
\(23\) 23.1787 1.00777 0.503884 0.863771i \(-0.331904\pi\)
0.503884 + 0.863771i \(0.331904\pi\)
\(24\) 0 0
\(25\) 23.3474i 0.933894i
\(26\) 2.50740 23.4212i 0.0964386 0.900814i
\(27\) 0 0
\(28\) 0.554380 2.55950i 0.0197993 0.0914108i
\(29\) −35.6105 35.6105i −1.22795 1.22795i −0.964739 0.263209i \(-0.915219\pi\)
−0.263209 0.964739i \(-0.584781\pi\)
\(30\) 0 0
\(31\) 45.5687i 1.46996i 0.678089 + 0.734980i \(0.262808\pi\)
−0.678089 + 0.734980i \(0.737192\pi\)
\(32\) 7.98336 + 30.9882i 0.249480 + 0.968380i
\(33\) 0 0
\(34\) −4.94130 6.12615i −0.145332 0.180181i
\(35\) 0.595149 0.595149i 0.0170043 0.0170043i
\(36\) 0 0
\(37\) 10.1527 10.1527i 0.274398 0.274398i −0.556470 0.830868i \(-0.687844\pi\)
0.830868 + 0.556470i \(0.187844\pi\)
\(38\) −47.5215 5.08752i −1.25057 0.133882i
\(39\) 0 0
\(40\) −3.23467 + 9.76249i −0.0808669 + 0.244062i
\(41\) 28.4661i 0.694295i 0.937811 + 0.347148i \(0.112850\pi\)
−0.937811 + 0.347148i \(0.887150\pi\)
\(42\) 0 0
\(43\) 22.7354 + 22.7354i 0.528730 + 0.528730i 0.920194 0.391464i \(-0.128031\pi\)
−0.391464 + 0.920194i \(0.628031\pi\)
\(44\) −63.6176 + 40.9653i −1.44586 + 0.931030i
\(45\) 0 0
\(46\) −29.1040 36.0827i −0.632696 0.784407i
\(47\) 10.7746i 0.229247i −0.993409 0.114623i \(-0.963434\pi\)
0.993409 0.114623i \(-0.0365661\pi\)
\(48\) 0 0
\(49\) −48.5714 −0.991252
\(50\) 36.3453 29.3158i 0.726906 0.586316i
\(51\) 0 0
\(52\) −39.6086 + 25.5051i −0.761703 + 0.490484i
\(53\) −41.5142 + 41.5142i −0.783287 + 0.783287i −0.980384 0.197097i \(-0.936849\pi\)
0.197097 + 0.980384i \(0.436849\pi\)
\(54\) 0 0
\(55\) −24.3182 −0.442149
\(56\) −4.68053 + 2.35079i −0.0835809 + 0.0419784i
\(57\) 0 0
\(58\) −10.7217 + 100.149i −0.184857 + 1.72671i
\(59\) 21.0646 + 21.0646i 0.357027 + 0.357027i 0.862716 0.505689i \(-0.168762\pi\)
−0.505689 + 0.862716i \(0.668762\pi\)
\(60\) 0 0
\(61\) −68.7531 68.7531i −1.12710 1.12710i −0.990647 0.136453i \(-0.956430\pi\)
−0.136453 0.990647i \(-0.543570\pi\)
\(62\) 70.9377 57.2178i 1.14416 0.922867i
\(63\) 0 0
\(64\) 38.2157 51.3377i 0.597120 0.802152i
\(65\) −15.1406 −0.232932
\(66\) 0 0
\(67\) 67.8242 67.8242i 1.01230 1.01230i 0.0123779 0.999923i \(-0.496060\pi\)
0.999923 0.0123779i \(-0.00394012\pi\)
\(68\) −3.33222 + 15.3844i −0.0490033 + 0.226242i
\(69\) 0 0
\(70\) −1.67377 0.179189i −0.0239110 0.00255985i
\(71\) −33.3094 −0.469147 −0.234573 0.972098i \(-0.575369\pi\)
−0.234573 + 0.972098i \(0.575369\pi\)
\(72\) 0 0
\(73\) 18.6331i 0.255248i −0.991823 0.127624i \(-0.959265\pi\)
0.991823 0.127624i \(-0.0407351\pi\)
\(74\) −28.5531 3.05682i −0.385853 0.0413083i
\(75\) 0 0
\(76\) 51.7499 + 80.3657i 0.680920 + 1.05744i
\(77\) −8.75745 8.75745i −0.113733 0.113733i
\(78\) 0 0
\(79\) 6.29222i 0.0796483i 0.999207 + 0.0398242i \(0.0126798\pi\)
−0.999207 + 0.0398242i \(0.987320\pi\)
\(80\) 19.2590 7.22265i 0.240738 0.0902832i
\(81\) 0 0
\(82\) 44.3137 35.7431i 0.540411 0.435891i
\(83\) 72.0774 72.0774i 0.868402 0.868402i −0.123894 0.992296i \(-0.539538\pi\)
0.992296 + 0.123894i \(0.0395382\pi\)
\(84\) 0 0
\(85\) −3.57727 + 3.57727i −0.0420855 + 0.0420855i
\(86\) 6.84524 63.9400i 0.0795958 0.743489i
\(87\) 0 0
\(88\) 143.652 + 47.5973i 1.63241 + 0.540878i
\(89\) 10.6131i 0.119248i −0.998221 0.0596240i \(-0.981010\pi\)
0.998221 0.0596240i \(-0.0189902\pi\)
\(90\) 0 0
\(91\) −5.45242 5.45242i −0.0599167 0.0599167i
\(92\) −19.6266 + 90.6135i −0.213333 + 0.984930i
\(93\) 0 0
\(94\) −16.7730 + 13.5290i −0.178436 + 0.143925i
\(95\) 30.7202i 0.323371i
\(96\) 0 0
\(97\) 143.631 1.48073 0.740366 0.672204i \(-0.234652\pi\)
0.740366 + 0.672204i \(0.234652\pi\)
\(98\) 60.9880 + 75.6120i 0.622326 + 0.771551i
\(99\) 0 0
\(100\) −91.2730 19.7694i −0.912730 0.197694i
\(101\) 90.3100 90.3100i 0.894159 0.894159i −0.100753 0.994912i \(-0.532125\pi\)
0.994912 + 0.100753i \(0.0321251\pi\)
\(102\) 0 0
\(103\) −95.1656 −0.923938 −0.461969 0.886896i \(-0.652857\pi\)
−0.461969 + 0.886896i \(0.652857\pi\)
\(104\) 89.4384 + 29.6343i 0.859984 + 0.284945i
\(105\) 0 0
\(106\) 116.753 + 12.4992i 1.10144 + 0.117917i
\(107\) −27.2524 27.2524i −0.254695 0.254695i 0.568197 0.822892i \(-0.307641\pi\)
−0.822892 + 0.568197i \(0.807641\pi\)
\(108\) 0 0
\(109\) −132.413 132.413i −1.21480 1.21480i −0.969430 0.245366i \(-0.921092\pi\)
−0.245366 0.969430i \(-0.578908\pi\)
\(110\) 30.5348 + 37.8566i 0.277589 + 0.344151i
\(111\) 0 0
\(112\) 9.53657 + 4.33453i 0.0851479 + 0.0387012i
\(113\) −37.9551 −0.335886 −0.167943 0.985797i \(-0.553712\pi\)
−0.167943 + 0.985797i \(0.553712\pi\)
\(114\) 0 0
\(115\) −21.0699 + 21.0699i −0.183217 + 0.183217i
\(116\) 169.367 109.061i 1.46006 0.940177i
\(117\) 0 0
\(118\) 6.34219 59.2411i 0.0537474 0.502044i
\(119\) −2.57649 −0.0216512
\(120\) 0 0
\(121\) 236.835i 1.95731i
\(122\) −20.7004 + 193.358i −0.169675 + 1.58490i
\(123\) 0 0
\(124\) −178.144 38.5854i −1.43665 0.311173i
\(125\) −43.9488 43.9488i −0.351591 0.351591i
\(126\) 0 0
\(127\) 96.5399i 0.760157i −0.924954 0.380078i \(-0.875897\pi\)
0.924954 0.380078i \(-0.124103\pi\)
\(128\) −127.903 + 4.97043i −0.999246 + 0.0388315i
\(129\) 0 0
\(130\) 19.0111 + 23.5697i 0.146239 + 0.181305i
\(131\) 54.5082 54.5082i 0.416093 0.416093i −0.467762 0.883855i \(-0.654939\pi\)
0.883855 + 0.467762i \(0.154939\pi\)
\(132\) 0 0
\(133\) −11.0629 + 11.0629i −0.0831801 + 0.0831801i
\(134\) −190.746 20.4207i −1.42348 0.152393i
\(135\) 0 0
\(136\) 28.1333 14.1299i 0.206863 0.103897i
\(137\) 25.9333i 0.189294i 0.995511 + 0.0946471i \(0.0301723\pi\)
−0.995511 + 0.0946471i \(0.969828\pi\)
\(138\) 0 0
\(139\) 3.64066 + 3.64066i 0.0261918 + 0.0261918i 0.720081 0.693890i \(-0.244104\pi\)
−0.693890 + 0.720081i \(0.744104\pi\)
\(140\) 1.82270 + 2.83059i 0.0130193 + 0.0202185i
\(141\) 0 0
\(142\) 41.8245 + 51.8534i 0.294539 + 0.365165i
\(143\) 222.789i 1.55797i
\(144\) 0 0
\(145\) 64.7415 0.446493
\(146\) −29.0066 + 23.3964i −0.198675 + 0.160250i
\(147\) 0 0
\(148\) 31.0937 + 48.2874i 0.210093 + 0.326266i
\(149\) 18.9718 18.9718i 0.127328 0.127328i −0.640571 0.767899i \(-0.721302\pi\)
0.767899 + 0.640571i \(0.221302\pi\)
\(150\) 0 0
\(151\) −103.209 −0.683503 −0.341751 0.939790i \(-0.611020\pi\)
−0.341751 + 0.939790i \(0.611020\pi\)
\(152\) 60.1278 181.470i 0.395578 1.19388i
\(153\) 0 0
\(154\) −2.63672 + 24.6291i −0.0171216 + 0.159929i
\(155\) −41.4230 41.4230i −0.267245 0.267245i
\(156\) 0 0
\(157\) 88.2067 + 88.2067i 0.561826 + 0.561826i 0.929826 0.368000i \(-0.119957\pi\)
−0.368000 + 0.929826i \(0.619957\pi\)
\(158\) 9.79522 7.90074i 0.0619951 0.0500047i
\(159\) 0 0
\(160\) −35.4260 20.9119i −0.221412 0.130699i
\(161\) −15.1754 −0.0942571
\(162\) 0 0
\(163\) 18.8038 18.8038i 0.115361 0.115361i −0.647070 0.762431i \(-0.724006\pi\)
0.762431 + 0.647070i \(0.224006\pi\)
\(164\) −111.284 24.1037i −0.678561 0.146974i
\(165\) 0 0
\(166\) −202.707 21.7013i −1.22113 0.130731i
\(167\) −267.105 −1.59943 −0.799715 0.600380i \(-0.795016\pi\)
−0.799715 + 0.600380i \(0.795016\pi\)
\(168\) 0 0
\(169\) 30.2905i 0.179234i
\(170\) 10.0606 + 1.07706i 0.0591798 + 0.00633562i
\(171\) 0 0
\(172\) −108.132 + 69.6293i −0.628673 + 0.404822i
\(173\) 153.520 + 153.520i 0.887396 + 0.887396i 0.994272 0.106876i \(-0.0340849\pi\)
−0.106876 + 0.994272i \(0.534085\pi\)
\(174\) 0 0
\(175\) 15.2858i 0.0873476i
\(176\) −106.279 283.391i −0.603859 1.61018i
\(177\) 0 0
\(178\) −16.5216 + 13.3262i −0.0928179 + 0.0748661i
\(179\) −123.581 + 123.581i −0.690399 + 0.690399i −0.962320 0.271921i \(-0.912341\pi\)
0.271921 + 0.962320i \(0.412341\pi\)
\(180\) 0 0
\(181\) 122.965 122.965i 0.679364 0.679364i −0.280493 0.959856i \(-0.590498\pi\)
0.959856 + 0.280493i \(0.0904978\pi\)
\(182\) −1.64163 + 15.3341i −0.00901995 + 0.0842536i
\(183\) 0 0
\(184\) 165.704 83.2246i 0.900564 0.452307i
\(185\) 18.4581i 0.0997737i
\(186\) 0 0
\(187\) 52.6385 + 52.6385i 0.281489 + 0.281489i
\(188\) 42.1217 + 9.12342i 0.224051 + 0.0485288i
\(189\) 0 0
\(190\) 47.8228 38.5734i 0.251699 0.203018i
\(191\) 193.992i 1.01566i −0.861456 0.507832i \(-0.830447\pi\)
0.861456 0.507832i \(-0.169553\pi\)
\(192\) 0 0
\(193\) 141.555 0.733444 0.366722 0.930331i \(-0.380480\pi\)
0.366722 + 0.930331i \(0.380480\pi\)
\(194\) −180.348 223.593i −0.929631 1.15254i
\(195\) 0 0
\(196\) 41.1279 189.882i 0.209836 0.968788i
\(197\) −28.9507 + 28.9507i −0.146958 + 0.146958i −0.776758 0.629800i \(-0.783137\pi\)
0.629800 + 0.776758i \(0.283137\pi\)
\(198\) 0 0
\(199\) −27.6253 −0.138821 −0.0694104 0.997588i \(-0.522112\pi\)
−0.0694104 + 0.997588i \(0.522112\pi\)
\(200\) 83.8302 + 166.910i 0.419151 + 0.834548i
\(201\) 0 0
\(202\) −253.984 27.1908i −1.25735 0.134608i
\(203\) 23.3147 + 23.3147i 0.114851 + 0.114851i
\(204\) 0 0
\(205\) −25.8763 25.8763i −0.126226 0.126226i
\(206\) 119.493 + 148.146i 0.580065 + 0.719156i
\(207\) 0 0
\(208\) −66.1699 176.440i −0.318124 0.848271i
\(209\) 452.039 2.16287
\(210\) 0 0
\(211\) 7.35041 7.35041i 0.0348361 0.0348361i −0.689474 0.724310i \(-0.742158\pi\)
0.724310 + 0.689474i \(0.242158\pi\)
\(212\) −127.141 197.446i −0.599723 0.931348i
\(213\) 0 0
\(214\) −8.20523 + 76.6435i −0.0383422 + 0.358147i
\(215\) −41.3340 −0.192251
\(216\) 0 0
\(217\) 29.8345i 0.137486i
\(218\) −39.8673 + 372.392i −0.182877 + 1.70822i
\(219\) 0 0
\(220\) 20.5915 95.0683i 0.0935977 0.432129i
\(221\) 32.7729 + 32.7729i 0.148294 + 0.148294i
\(222\) 0 0
\(223\) 386.106i 1.73142i 0.500549 + 0.865708i \(0.333131\pi\)
−0.500549 + 0.865708i \(0.666869\pi\)
\(224\) −5.22681 20.2884i −0.0233340 0.0905730i
\(225\) 0 0
\(226\) 47.6579 + 59.0855i 0.210875 + 0.261440i
\(227\) 49.7286 49.7286i 0.219069 0.219069i −0.589037 0.808106i \(-0.700493\pi\)
0.808106 + 0.589037i \(0.200493\pi\)
\(228\) 0 0
\(229\) −191.870 + 191.870i −0.837861 + 0.837861i −0.988577 0.150716i \(-0.951842\pi\)
0.150716 + 0.988577i \(0.451842\pi\)
\(230\) 59.2562 + 6.34380i 0.257636 + 0.0275817i
\(231\) 0 0
\(232\) −382.440 126.717i −1.64845 0.546193i
\(233\) 298.610i 1.28159i 0.767712 + 0.640795i \(0.221395\pi\)
−0.767712 + 0.640795i \(0.778605\pi\)
\(234\) 0 0
\(235\) 9.79435 + 9.79435i 0.0416781 + 0.0416781i
\(236\) −100.185 + 64.5123i −0.424514 + 0.273357i
\(237\) 0 0
\(238\) 3.23514 + 4.01087i 0.0135930 + 0.0168524i
\(239\) 247.352i 1.03495i −0.855700 0.517473i \(-0.826873\pi\)
0.855700 0.517473i \(-0.173127\pi\)
\(240\) 0 0
\(241\) −220.337 −0.914260 −0.457130 0.889400i \(-0.651123\pi\)
−0.457130 + 0.889400i \(0.651123\pi\)
\(242\) 368.686 297.379i 1.52350 1.22884i
\(243\) 0 0
\(244\) 326.997 210.563i 1.34015 0.862963i
\(245\) 44.1525 44.1525i 0.180214 0.180214i
\(246\) 0 0
\(247\) 281.441 1.13944
\(248\) 163.618 + 325.770i 0.659748 + 1.31359i
\(249\) 0 0
\(250\) −13.2322 + 123.600i −0.0529290 + 0.494399i
\(251\) −162.716 162.716i −0.648272 0.648272i 0.304303 0.952575i \(-0.401576\pi\)
−0.952575 + 0.304303i \(0.901576\pi\)
\(252\) 0 0
\(253\) 310.038 + 310.038i 1.22545 + 1.22545i
\(254\) −150.286 + 121.219i −0.591675 + 0.477240i
\(255\) 0 0
\(256\) 168.338 + 192.869i 0.657570 + 0.753394i
\(257\) −101.165 −0.393637 −0.196819 0.980440i \(-0.563061\pi\)
−0.196819 + 0.980440i \(0.563061\pi\)
\(258\) 0 0
\(259\) −6.64713 + 6.64713i −0.0256646 + 0.0256646i
\(260\) 12.8203 59.1899i 0.0493090 0.227653i
\(261\) 0 0
\(262\) −153.296 16.4115i −0.585101 0.0626393i
\(263\) 323.635 1.23055 0.615276 0.788312i \(-0.289045\pi\)
0.615276 + 0.788312i \(0.289045\pi\)
\(264\) 0 0
\(265\) 75.4747i 0.284810i
\(266\) 31.1130 + 3.33087i 0.116966 + 0.0125220i
\(267\) 0 0
\(268\) 207.718 + 322.579i 0.775068 + 1.20365i
\(269\) −1.51275 1.51275i −0.00562361 0.00562361i 0.704289 0.709913i \(-0.251266\pi\)
−0.709913 + 0.704289i \(0.751266\pi\)
\(270\) 0 0
\(271\) 166.098i 0.612909i 0.951885 + 0.306454i \(0.0991427\pi\)
−0.951885 + 0.306454i \(0.900857\pi\)
\(272\) −57.3216 26.0536i −0.210741 0.0957854i
\(273\) 0 0
\(274\) 40.3709 32.5628i 0.147339 0.118842i
\(275\) −312.294 + 312.294i −1.13562 + 1.13562i
\(276\) 0 0
\(277\) 317.830 317.830i 1.14740 1.14740i 0.160338 0.987062i \(-0.448741\pi\)
0.987062 0.160338i \(-0.0512586\pi\)
\(278\) 1.09614 10.2388i 0.00394296 0.0368304i
\(279\) 0 0
\(280\) 2.11778 6.39163i 0.00756352 0.0228272i
\(281\) 402.790i 1.43342i −0.697374 0.716708i \(-0.745648\pi\)
0.697374 0.716708i \(-0.254352\pi\)
\(282\) 0 0
\(283\) −192.406 192.406i −0.679881 0.679881i 0.280092 0.959973i \(-0.409635\pi\)
−0.959973 + 0.280092i \(0.909635\pi\)
\(284\) 28.2048 130.218i 0.0993128 0.458515i
\(285\) 0 0
\(286\) 346.821 279.743i 1.21266 0.978121i
\(287\) 18.6371i 0.0649378i
\(288\) 0 0
\(289\) −273.513 −0.946413
\(290\) −81.2918 100.784i −0.280317 0.347532i
\(291\) 0 0
\(292\) 72.8434 + 15.7777i 0.249464 + 0.0540331i
\(293\) 75.3645 75.3645i 0.257217 0.257217i −0.566704 0.823921i \(-0.691782\pi\)
0.823921 + 0.566704i \(0.191782\pi\)
\(294\) 0 0
\(295\) −38.2964 −0.129818
\(296\) 36.1276 109.036i 0.122053 0.368364i
\(297\) 0 0
\(298\) −53.3556 5.71210i −0.179046 0.0191681i
\(299\) 193.031 + 193.031i 0.645588 + 0.645588i
\(300\) 0 0
\(301\) −14.8852 14.8852i −0.0494524 0.0494524i
\(302\) 129.593 + 160.667i 0.429116 + 0.532011i
\(303\) 0 0
\(304\) −357.997 + 134.258i −1.17762 + 0.441640i
\(305\) 124.996 0.409824
\(306\) 0 0
\(307\) −111.544 + 111.544i −0.363337 + 0.363337i −0.865040 0.501703i \(-0.832707\pi\)
0.501703 + 0.865040i \(0.332707\pi\)
\(308\) 41.6513 26.8205i 0.135232 0.0870797i
\(309\) 0 0
\(310\) −12.4718 + 116.496i −0.0402315 + 0.375794i
\(311\) 224.484 0.721813 0.360906 0.932602i \(-0.382467\pi\)
0.360906 + 0.932602i \(0.382467\pi\)
\(312\) 0 0
\(313\) 488.339i 1.56019i −0.625661 0.780095i \(-0.715171\pi\)
0.625661 0.780095i \(-0.284829\pi\)
\(314\) 26.5575 248.069i 0.0845781 0.790027i
\(315\) 0 0
\(316\) −24.5985 5.32795i −0.0778433 0.0168606i
\(317\) −257.361 257.361i −0.811863 0.811863i 0.173050 0.984913i \(-0.444638\pi\)
−0.984913 + 0.173050i \(0.944638\pi\)
\(318\) 0 0
\(319\) 952.652i 2.98637i
\(320\) 11.9282 + 81.4061i 0.0372757 + 0.254394i
\(321\) 0 0
\(322\) 19.0548 + 23.6238i 0.0591763 + 0.0733659i
\(323\) 66.4962 66.4962i 0.205871 0.205871i
\(324\) 0 0
\(325\) −194.436 + 194.436i −0.598263 + 0.598263i
\(326\) −52.8829 5.66150i −0.162218 0.0173666i
\(327\) 0 0
\(328\) 102.209 + 203.503i 0.311614 + 0.620437i
\(329\) 7.05427i 0.0214416i
\(330\) 0 0
\(331\) −123.553 123.553i −0.373271 0.373271i 0.495396 0.868667i \(-0.335023\pi\)
−0.868667 + 0.495396i \(0.835023\pi\)
\(332\) 220.744 + 342.807i 0.664891 + 1.03255i
\(333\) 0 0
\(334\) 335.387 + 415.807i 1.00415 + 1.24493i
\(335\) 123.307i 0.368082i
\(336\) 0 0
\(337\) −246.234 −0.730665 −0.365333 0.930877i \(-0.619045\pi\)
−0.365333 + 0.930877i \(0.619045\pi\)
\(338\) −47.1538 + 38.0339i −0.139508 + 0.112526i
\(339\) 0 0
\(340\) −10.9557 17.0139i −0.0322228 0.0500408i
\(341\) −609.528 + 609.528i −1.78747 + 1.78747i
\(342\) 0 0
\(343\) 63.8813 0.186243
\(344\) 244.168 + 80.9018i 0.709790 + 0.235180i
\(345\) 0 0
\(346\) 46.2221 431.752i 0.133590 1.24784i
\(347\) 123.212 + 123.212i 0.355076 + 0.355076i 0.861994 0.506918i \(-0.169215\pi\)
−0.506918 + 0.861994i \(0.669215\pi\)
\(348\) 0 0
\(349\) 115.371 + 115.371i 0.330575 + 0.330575i 0.852805 0.522230i \(-0.174900\pi\)
−0.522230 + 0.852805i \(0.674900\pi\)
\(350\) −23.7957 + 19.1934i −0.0679878 + 0.0548384i
\(351\) 0 0
\(352\) −307.712 + 521.283i −0.874183 + 1.48092i
\(353\) −650.544 −1.84290 −0.921451 0.388495i \(-0.872995\pi\)
−0.921451 + 0.388495i \(0.872995\pi\)
\(354\) 0 0
\(355\) 30.2790 30.2790i 0.0852930 0.0852930i
\(356\) 41.4902 + 8.98665i 0.116546 + 0.0252434i
\(357\) 0 0
\(358\) 347.555 + 37.2083i 0.970824 + 0.103934i
\(359\) −94.4878 −0.263197 −0.131599 0.991303i \(-0.542011\pi\)
−0.131599 + 0.991303i \(0.542011\pi\)
\(360\) 0 0
\(361\) 210.044i 0.581838i
\(362\) −345.821 37.0226i −0.955306 0.102272i
\(363\) 0 0
\(364\) 25.9323 16.6986i 0.0712425 0.0458752i
\(365\) 16.9379 + 16.9379i 0.0464053 + 0.0464053i
\(366\) 0 0
\(367\) 131.379i 0.357982i 0.983851 + 0.178991i \(0.0572832\pi\)
−0.983851 + 0.178991i \(0.942717\pi\)
\(368\) −337.621 153.455i −0.917449 0.416996i
\(369\) 0 0
\(370\) 28.7341 23.1767i 0.0776598 0.0626398i
\(371\) 27.1799 27.1799i 0.0732612 0.0732612i
\(372\) 0 0
\(373\) −275.796 + 275.796i −0.739400 + 0.739400i −0.972462 0.233062i \(-0.925126\pi\)
0.233062 + 0.972462i \(0.425126\pi\)
\(374\) 15.8486 148.038i 0.0423758 0.395824i
\(375\) 0 0
\(376\) −38.6869 77.0273i −0.102891 0.204860i
\(377\) 593.125i 1.57328i
\(378\) 0 0
\(379\) −13.0427 13.0427i −0.0344135 0.0344135i 0.689691 0.724104i \(-0.257747\pi\)
−0.724104 + 0.689691i \(0.757747\pi\)
\(380\) −120.096 26.0124i −0.316042 0.0684538i
\(381\) 0 0
\(382\) −301.991 + 243.583i −0.790553 + 0.637653i
\(383\) 121.974i 0.318470i −0.987241 0.159235i \(-0.949097\pi\)
0.987241 0.159235i \(-0.0509027\pi\)
\(384\) 0 0
\(385\) 15.9214 0.0413544
\(386\) −177.741 220.361i −0.460470 0.570883i
\(387\) 0 0
\(388\) −121.620 + 561.504i −0.313454 + 1.44717i
\(389\) 233.267 233.267i 0.599659 0.599659i −0.340563 0.940222i \(-0.610618\pi\)
0.940222 + 0.340563i \(0.110618\pi\)
\(390\) 0 0
\(391\) 91.2149 0.233286
\(392\) −347.235 + 174.399i −0.885804 + 0.444894i
\(393\) 0 0
\(394\) 81.4198 + 8.71657i 0.206649 + 0.0221233i
\(395\) −5.71977 5.71977i −0.0144804 0.0144804i
\(396\) 0 0
\(397\) −83.7693 83.7693i −0.211006 0.211006i 0.593689 0.804695i \(-0.297671\pi\)
−0.804695 + 0.593689i \(0.797671\pi\)
\(398\) 34.6874 + 43.0049i 0.0871542 + 0.108053i
\(399\) 0 0
\(400\) 154.571 340.078i 0.386428 0.850195i
\(401\) −589.134 −1.46916 −0.734581 0.678521i \(-0.762621\pi\)
−0.734581 + 0.678521i \(0.762621\pi\)
\(402\) 0 0
\(403\) −379.494 + 379.494i −0.941673 + 0.941673i
\(404\) 276.583 + 429.524i 0.684612 + 1.06318i
\(405\) 0 0
\(406\) 7.01965 65.5691i 0.0172898 0.161500i
\(407\) 271.606 0.667337
\(408\) 0 0
\(409\) 449.285i 1.09850i 0.835659 + 0.549248i \(0.185086\pi\)
−0.835659 + 0.549248i \(0.814914\pi\)
\(410\) −7.79092 + 72.7735i −0.0190023 + 0.177496i
\(411\) 0 0
\(412\) 80.5818 372.036i 0.195587 0.902999i
\(413\) −13.7913 13.7913i −0.0333929 0.0333929i
\(414\) 0 0
\(415\) 131.040i 0.315759i
\(416\) −191.583 + 324.553i −0.460536 + 0.780175i
\(417\) 0 0
\(418\) −567.597 703.698i −1.35789 1.68349i
\(419\) 218.639 218.639i 0.521811 0.521811i −0.396307 0.918118i \(-0.629708\pi\)
0.918118 + 0.396307i \(0.129708\pi\)
\(420\) 0 0
\(421\) −61.2101 + 61.2101i −0.145392 + 0.145392i −0.776056 0.630664i \(-0.782783\pi\)
0.630664 + 0.776056i \(0.282783\pi\)
\(422\) −20.6720 2.21308i −0.0489857 0.00524427i
\(423\) 0 0
\(424\) −147.725 + 445.844i −0.348407 + 1.05152i
\(425\) 91.8787i 0.216185i
\(426\) 0 0
\(427\) 45.0136 + 45.0136i 0.105418 + 0.105418i
\(428\) 129.615 83.4631i 0.302839 0.195007i
\(429\) 0 0
\(430\) 51.9004 + 64.3454i 0.120699 + 0.149640i
\(431\) 501.119i 1.16269i 0.813657 + 0.581345i \(0.197473\pi\)
−0.813657 + 0.581345i \(0.802527\pi\)
\(432\) 0 0
\(433\) 75.5505 0.174482 0.0872408 0.996187i \(-0.472195\pi\)
0.0872408 + 0.996187i \(0.472195\pi\)
\(434\) −46.4439 + 37.4612i −0.107014 + 0.0863162i
\(435\) 0 0
\(436\) 629.769 405.527i 1.44442 0.930108i
\(437\) 391.659 391.659i 0.896245 0.896245i
\(438\) 0 0
\(439\) 717.251 1.63383 0.816915 0.576758i \(-0.195682\pi\)
0.816915 + 0.576758i \(0.195682\pi\)
\(440\) −173.850 + 87.3160i −0.395114 + 0.198446i
\(441\) 0 0
\(442\) 9.86737 92.1692i 0.0223244 0.208528i
\(443\) −299.093 299.093i −0.675153 0.675153i 0.283746 0.958899i \(-0.408423\pi\)
−0.958899 + 0.283746i \(0.908423\pi\)
\(444\) 0 0
\(445\) 9.64753 + 9.64753i 0.0216798 + 0.0216798i
\(446\) 601.059 484.809i 1.34767 1.08702i
\(447\) 0 0
\(448\) −25.0203 + 33.6115i −0.0558489 + 0.0750257i
\(449\) 44.5560 0.0992339 0.0496170 0.998768i \(-0.484200\pi\)
0.0496170 + 0.998768i \(0.484200\pi\)
\(450\) 0 0
\(451\) −380.763 + 380.763i −0.844263 + 0.844263i
\(452\) 32.1386 148.380i 0.0711031 0.328274i
\(453\) 0 0
\(454\) −139.855 14.9725i −0.308050 0.0329790i
\(455\) 9.91275 0.0217863
\(456\) 0 0
\(457\) 641.227i 1.40312i −0.712609 0.701562i \(-0.752486\pi\)
0.712609 0.701562i \(-0.247514\pi\)
\(458\) 539.607 + 57.7689i 1.17818 + 0.126133i
\(459\) 0 0
\(460\) −64.5287 100.211i −0.140280 0.217850i
\(461\) 393.690 + 393.690i 0.853991 + 0.853991i 0.990622 0.136631i \(-0.0436273\pi\)
−0.136631 + 0.990622i \(0.543627\pi\)
\(462\) 0 0
\(463\) 395.861i 0.854991i −0.904018 0.427495i \(-0.859396\pi\)
0.904018 0.427495i \(-0.140604\pi\)
\(464\) 282.944 + 754.462i 0.609792 + 1.62600i
\(465\) 0 0
\(466\) 464.853 374.946i 0.997538 0.804606i
\(467\) 83.1457 83.1457i 0.178042 0.178042i −0.612460 0.790502i \(-0.709820\pi\)
0.790502 + 0.612460i \(0.209820\pi\)
\(468\) 0 0
\(469\) −44.4054 + 44.4054i −0.0946810 + 0.0946810i
\(470\) 2.94891 27.5452i 0.00627428 0.0586068i
\(471\) 0 0
\(472\) 226.224 + 74.9564i 0.479288 + 0.158806i
\(473\) 608.217i 1.28587i
\(474\) 0 0
\(475\) 394.509 + 394.509i 0.830546 + 0.830546i
\(476\) 2.18165 10.0724i 0.00458330 0.0211605i
\(477\) 0 0
\(478\) −385.058 + 310.584i −0.805560 + 0.649758i
\(479\) 430.043i 0.897793i −0.893584 0.448896i \(-0.851817\pi\)
0.893584 0.448896i \(-0.148183\pi\)
\(480\) 0 0
\(481\) 169.103 0.351565
\(482\) 276.663 + 343.003i 0.573989 + 0.711624i
\(483\) 0 0
\(484\) −925.871 200.541i −1.91296 0.414340i
\(485\) −130.564 + 130.564i −0.269204 + 0.269204i
\(486\) 0 0
\(487\) 573.790 1.17821 0.589107 0.808055i \(-0.299480\pi\)
0.589107 + 0.808055i \(0.299480\pi\)
\(488\) −738.376 244.652i −1.51307 0.501335i
\(489\) 0 0
\(490\) −124.172 13.2936i −0.253413 0.0271297i
\(491\) 489.133 + 489.133i 0.996197 + 0.996197i 0.999993 0.00379588i \(-0.00120827\pi\)
−0.00379588 + 0.999993i \(0.501208\pi\)
\(492\) 0 0
\(493\) −140.138 140.138i −0.284255 0.284255i
\(494\) −353.388 438.125i −0.715360 0.886893i
\(495\) 0 0
\(496\) 301.688 663.755i 0.608242 1.33822i
\(497\) 21.8081 0.0438795
\(498\) 0 0
\(499\) 260.469 260.469i 0.521982 0.521982i −0.396188 0.918170i \(-0.629667\pi\)
0.918170 + 0.396188i \(0.129667\pi\)
\(500\) 209.025 134.598i 0.418050 0.269195i
\(501\) 0 0
\(502\) −48.9911 + 457.616i −0.0975919 + 0.911586i
\(503\) 975.416 1.93920 0.969598 0.244701i \(-0.0786900\pi\)
0.969598 + 0.244701i \(0.0786900\pi\)
\(504\) 0 0
\(505\) 164.188i 0.325124i
\(506\) 93.3472 871.938i 0.184481 1.72320i
\(507\) 0 0
\(508\) 377.408 + 81.7454i 0.742929 + 0.160916i
\(509\) 420.191 + 420.191i 0.825523 + 0.825523i 0.986894 0.161371i \(-0.0515916\pi\)
−0.161371 + 0.986894i \(0.551592\pi\)
\(510\) 0 0
\(511\) 12.1994i 0.0238735i
\(512\) 88.8714 504.228i 0.173577 0.984820i
\(513\) 0 0
\(514\) 127.026 + 157.485i 0.247133 + 0.306391i
\(515\) 86.5077 86.5077i 0.167976 0.167976i
\(516\) 0 0
\(517\) 144.121 144.121i 0.278764 0.278764i
\(518\) 18.6941 + 2.00134i 0.0360890 + 0.00386359i
\(519\) 0 0
\(520\) −108.240 + 54.3633i −0.208153 + 0.104545i
\(521\) 396.333i 0.760716i −0.924839 0.380358i \(-0.875801\pi\)
0.924839 0.380358i \(-0.124199\pi\)
\(522\) 0 0
\(523\) 564.600 + 564.600i 1.07954 + 1.07954i 0.996550 + 0.0829913i \(0.0264474\pi\)
0.0829913 + 0.996550i \(0.473553\pi\)
\(524\) 166.937 + 259.246i 0.318581 + 0.494745i
\(525\) 0 0
\(526\) −406.368 503.809i −0.772563 0.957812i
\(527\) 179.326i 0.340278i
\(528\) 0 0
\(529\) 8.25115 0.0155976
\(530\) −117.493 + 94.7688i −0.221685 + 0.178809i
\(531\) 0 0
\(532\) −33.8813 52.6165i −0.0636867 0.0989032i
\(533\) −237.064 + 237.064i −0.444773 + 0.444773i
\(534\) 0 0
\(535\) 49.5461 0.0926095
\(536\) 241.346 728.401i 0.450273 1.35896i
\(537\) 0 0
\(538\) −0.455463 + 4.25439i −0.000846586 + 0.00790779i
\(539\) −649.691 649.691i −1.20536 1.20536i
\(540\) 0 0
\(541\) −29.5601 29.5601i −0.0546398 0.0546398i 0.679259 0.733899i \(-0.262301\pi\)
−0.733899 + 0.679259i \(0.762301\pi\)
\(542\) 258.568 208.559i 0.477064 0.384795i
\(543\) 0 0
\(544\) 31.4169 + 121.948i 0.0577516 + 0.224168i
\(545\) 240.733 0.441711
\(546\) 0 0
\(547\) −138.608 + 138.608i −0.253397 + 0.253397i −0.822362 0.568965i \(-0.807344\pi\)
0.568965 + 0.822362i \(0.307344\pi\)
\(548\) −101.382 21.9591i −0.185004 0.0400713i
\(549\) 0 0
\(550\) 878.283 + 94.0265i 1.59688 + 0.170957i
\(551\) −1203.45 −2.18412
\(552\) 0 0
\(553\) 4.11960i 0.00744955i
\(554\) −893.851 95.6932i −1.61345 0.172731i
\(555\) 0 0
\(556\) −17.3154 + 11.1499i −0.0311428 + 0.0200538i
\(557\) −60.4400 60.4400i −0.108510 0.108510i 0.650767 0.759277i \(-0.274447\pi\)
−0.759277 + 0.650767i \(0.774447\pi\)
\(558\) 0 0
\(559\) 378.678i 0.677421i
\(560\) −12.6091 + 4.72877i −0.0225163 + 0.00844423i
\(561\) 0 0
\(562\) −627.031 + 505.758i −1.11571 + 0.899924i
\(563\) −267.325 + 267.325i −0.474822 + 0.474822i −0.903471 0.428649i \(-0.858990\pi\)
0.428649 + 0.903471i \(0.358990\pi\)
\(564\) 0 0
\(565\) 34.5021 34.5021i 0.0610656 0.0610656i
\(566\) −57.9303 + 541.115i −0.102350 + 0.956034i
\(567\) 0 0
\(568\) −238.128 + 119.600i −0.419240 + 0.210563i
\(569\) 315.715i 0.554859i 0.960746 + 0.277429i \(0.0894825\pi\)
−0.960746 + 0.277429i \(0.910518\pi\)
\(570\) 0 0
\(571\) −670.572 670.572i −1.17438 1.17438i −0.981154 0.193228i \(-0.938104\pi\)
−0.193228 0.981154i \(-0.561896\pi\)
\(572\) −870.962 188.648i −1.52266 0.329803i
\(573\) 0 0
\(574\) −29.0128 + 23.4015i −0.0505449 + 0.0407691i
\(575\) 541.161i 0.941149i
\(576\) 0 0
\(577\) 413.628 0.716859 0.358430 0.933557i \(-0.383312\pi\)
0.358430 + 0.933557i \(0.383312\pi\)
\(578\) 343.434 + 425.784i 0.594176 + 0.736650i
\(579\) 0 0
\(580\) −54.8200 + 253.097i −0.0945173 + 0.436374i
\(581\) −47.1900 + 47.1900i −0.0812220 + 0.0812220i
\(582\) 0 0
\(583\) −1110.59 −1.90495
\(584\) −66.9035 133.208i −0.114561 0.228095i
\(585\) 0 0
\(586\) −211.952 22.6910i −0.361693 0.0387218i
\(587\) 420.085 + 420.085i 0.715647 + 0.715647i 0.967711 0.252064i \(-0.0811093\pi\)
−0.252064 + 0.967711i \(0.581109\pi\)
\(588\) 0 0
\(589\) 769.993 + 769.993i 1.30729 + 1.30729i
\(590\) 48.0863 + 59.6167i 0.0815023 + 0.101045i
\(591\) 0 0
\(592\) −215.101 + 80.6687i −0.363347 + 0.136265i
\(593\) 740.798 1.24924 0.624619 0.780930i \(-0.285254\pi\)
0.624619 + 0.780930i \(0.285254\pi\)
\(594\) 0 0
\(595\) 2.34209 2.34209i 0.00393628 0.00393628i
\(596\) 58.1031 + 90.2320i 0.0974885 + 0.151396i
\(597\) 0 0
\(598\) 58.1183 542.872i 0.0971878 0.907812i
\(599\) −435.161 −0.726479 −0.363240 0.931696i \(-0.618329\pi\)
−0.363240 + 0.931696i \(0.618329\pi\)
\(600\) 0 0
\(601\) 380.001i 0.632280i 0.948712 + 0.316140i \(0.102387\pi\)
−0.948712 + 0.316140i \(0.897613\pi\)
\(602\) −4.48167 + 41.8624i −0.00744463 + 0.0695388i
\(603\) 0 0
\(604\) 87.3924 403.480i 0.144689 0.668013i
\(605\) −215.288 215.288i −0.355849 0.355849i
\(606\) 0 0
\(607\) 181.813i 0.299527i 0.988722 + 0.149763i \(0.0478512\pi\)
−0.988722 + 0.149763i \(0.952149\pi\)
\(608\) 658.517 + 388.721i 1.08309 + 0.639344i
\(609\) 0 0
\(610\) −156.950 194.584i −0.257295 0.318990i
\(611\) 89.7303 89.7303i 0.146858 0.146858i
\(612\) 0 0
\(613\) 55.1479 55.1479i 0.0899640 0.0899640i −0.660693 0.750657i \(-0.729737\pi\)
0.750657 + 0.660693i \(0.229737\pi\)
\(614\) 313.703 + 33.5841i 0.510917 + 0.0546973i
\(615\) 0 0
\(616\) −94.0510 31.1626i −0.152680 0.0505886i
\(617\) 579.674i 0.939504i −0.882798 0.469752i \(-0.844343\pi\)
0.882798 0.469752i \(-0.155657\pi\)
\(618\) 0 0
\(619\) 91.1070 + 91.1070i 0.147184 + 0.147184i 0.776859 0.629675i \(-0.216812\pi\)
−0.629675 + 0.776859i \(0.716812\pi\)
\(620\) 197.012 126.862i 0.317761 0.204616i
\(621\) 0 0
\(622\) −281.870 349.458i −0.453167 0.561830i
\(623\) 6.94852i 0.0111533i
\(624\) 0 0
\(625\) −503.783 −0.806053
\(626\) −760.208 + 613.177i −1.21439 + 0.979516i
\(627\) 0 0
\(628\) −419.520 + 270.141i −0.668025 + 0.430162i
\(629\) 39.9540 39.9540i 0.0635199 0.0635199i
\(630\) 0 0
\(631\) −693.474 −1.09901 −0.549504 0.835491i \(-0.685183\pi\)
−0.549504 + 0.835491i \(0.685183\pi\)
\(632\) 22.5926 + 44.9829i 0.0357478 + 0.0711755i
\(633\) 0 0
\(634\) −77.4869 + 723.790i −0.122219 + 1.14162i
\(635\) 87.7570 + 87.7570i 0.138200 + 0.138200i
\(636\) 0 0
\(637\) −404.500 404.500i −0.635007 0.635007i
\(638\) −1483.01 + 1196.19i −2.32447 + 1.87490i
\(639\) 0 0
\(640\) 111.749 120.785i 0.174608 0.188727i
\(641\) 218.329 0.340607 0.170304 0.985392i \(-0.445525\pi\)
0.170304 + 0.985392i \(0.445525\pi\)
\(642\) 0 0
\(643\) 887.430 887.430i 1.38014 1.38014i 0.535787 0.844353i \(-0.320015\pi\)
0.844353 0.535787i \(-0.179985\pi\)
\(644\) 12.8498 59.3259i 0.0199531 0.0921210i
\(645\) 0 0
\(646\) −187.011 20.0209i −0.289491 0.0309921i
\(647\) 223.177 0.344941 0.172470 0.985015i \(-0.444825\pi\)
0.172470 + 0.985015i \(0.444825\pi\)
\(648\) 0 0
\(649\) 563.520i 0.868290i
\(650\) 546.822 + 58.5413i 0.841265 + 0.0900635i
\(651\) 0 0
\(652\) 57.5884 + 89.4327i 0.0883258 + 0.137167i
\(653\) −539.691 539.691i −0.826479 0.826479i 0.160549 0.987028i \(-0.448674\pi\)
−0.987028 + 0.160549i \(0.948674\pi\)
\(654\) 0 0
\(655\) 99.0983i 0.151295i
\(656\) 188.460 414.638i 0.287286 0.632070i
\(657\) 0 0
\(658\) 10.9815 8.85760i 0.0166892 0.0134614i
\(659\) −625.166 + 625.166i −0.948659 + 0.948659i −0.998745 0.0500862i \(-0.984050\pi\)
0.0500862 + 0.998745i \(0.484050\pi\)
\(660\) 0 0
\(661\) −326.893 + 326.893i −0.494544 + 0.494544i −0.909734 0.415191i \(-0.863715\pi\)
0.415191 + 0.909734i \(0.363715\pi\)
\(662\) −37.1996 + 347.474i −0.0561928 + 0.524886i
\(663\) 0 0
\(664\) 256.481 774.078i 0.386266 1.16578i
\(665\) 20.1129i 0.0302450i
\(666\) 0 0
\(667\) −825.404 825.404i −1.23749 1.23749i
\(668\) 226.172 1044.21i 0.338581 1.56318i
\(669\) 0 0
\(670\) 191.955 154.829i 0.286500 0.231089i
\(671\) 1839.28i 2.74111i
\(672\) 0 0
\(673\) 422.147 0.627262 0.313631 0.949545i \(-0.398455\pi\)
0.313631 + 0.949545i \(0.398455\pi\)
\(674\) 309.181 + 383.318i 0.458725 + 0.568720i
\(675\) 0 0
\(676\) 118.416 + 25.6486i 0.175172 + 0.0379417i
\(677\) 126.017 126.017i 0.186140 0.186140i −0.607885 0.794025i \(-0.707982\pi\)
0.794025 + 0.607885i \(0.207982\pi\)
\(678\) 0 0
\(679\) −94.0372 −0.138494
\(680\) −12.7294 + 38.4183i −0.0187197 + 0.0564974i
\(681\) 0 0
\(682\) 1714.21 + 183.518i 2.51350 + 0.269089i
\(683\) −621.906 621.906i −0.910551 0.910551i 0.0857647 0.996315i \(-0.472667\pi\)
−0.996315 + 0.0857647i \(0.972667\pi\)
\(684\) 0 0
\(685\) −23.5740 23.5740i −0.0344145 0.0344145i
\(686\) −80.2117 99.4452i −0.116927 0.144964i
\(687\) 0 0
\(688\) −180.644 481.684i −0.262564 0.700122i
\(689\) −691.456 −1.00357
\(690\) 0 0
\(691\) −403.376 + 403.376i −0.583758 + 0.583758i −0.935934 0.352176i \(-0.885442\pi\)
0.352176 + 0.935934i \(0.385442\pi\)
\(692\) −730.154 + 470.168i −1.05514 + 0.679434i
\(693\) 0 0
\(694\) 37.0969 346.515i 0.0534537 0.499301i
\(695\) −6.61889 −0.00952359
\(696\) 0 0
\(697\) 112.022i 0.160721i
\(698\) 34.7361 324.463i 0.0497652 0.464847i
\(699\) 0 0
\(700\) 59.7576 + 12.9433i 0.0853680 + 0.0184904i
\(701\) −466.593 466.593i −0.665611 0.665611i 0.291086 0.956697i \(-0.405983\pi\)
−0.956697 + 0.291086i \(0.905983\pi\)
\(702\) 0 0
\(703\) 343.109i 0.488065i
\(704\) 1197.87 175.521i 1.70152 0.249319i
\(705\) 0 0
\(706\) 816.847 + 1012.72i 1.15701 + 1.43444i
\(707\) −59.1272 + 59.1272i −0.0836311 + 0.0836311i
\(708\) 0 0
\(709\) 822.764 822.764i 1.16046 1.16046i 0.176081 0.984376i \(-0.443658\pi\)
0.984376 0.176081i \(-0.0563422\pi\)
\(710\) −85.1554 9.11650i −0.119937 0.0128401i
\(711\) 0 0
\(712\) −38.1069 75.8726i −0.0535210 0.106563i
\(713\) 1056.22i 1.48138i
\(714\) 0 0
\(715\) −202.521 202.521i −0.283246 0.283246i
\(716\) −378.480 587.766i −0.528603 0.820902i
\(717\) 0 0
\(718\) 118.642 + 147.091i 0.165240 + 0.204862i
\(719\) 710.142i 0.987681i 0.869553 + 0.493840i \(0.164407\pi\)
−0.869553 + 0.493840i \(0.835593\pi\)
\(720\) 0 0
\(721\) 62.3062 0.0864164
\(722\) −326.979 + 263.738i −0.452879 + 0.365289i
\(723\) 0 0
\(724\) 376.592 + 584.833i 0.520154 + 0.807781i
\(725\) 831.411 831.411i 1.14677 1.14677i
\(726\) 0 0
\(727\) −214.095 −0.294490 −0.147245 0.989100i \(-0.547041\pi\)
−0.147245 + 0.989100i \(0.547041\pi\)
\(728\) −58.5565 19.4019i −0.0804347 0.0266510i
\(729\) 0 0
\(730\) 5.09972 47.6355i 0.00698592 0.0652541i
\(731\) 89.4704 + 89.4704i 0.122395 + 0.122395i
\(732\) 0 0
\(733\) −96.1768 96.1768i −0.131210 0.131210i 0.638452 0.769662i \(-0.279575\pi\)
−0.769662 + 0.638452i \(0.779575\pi\)
\(734\) 204.521 164.965i 0.278638 0.224747i
\(735\) 0 0
\(736\) 185.044 + 718.265i 0.251418 + 0.975903i
\(737\) 1814.43 2.46192
\(738\) 0 0
\(739\) 885.341 885.341i 1.19803 1.19803i 0.223268 0.974757i \(-0.428327\pi\)
0.974757 0.223268i \(-0.0716726\pi\)
\(740\) −72.1593 15.6295i −0.0975125 0.0211209i
\(741\) 0 0
\(742\) −76.4396 8.18341i −0.103018 0.0110289i
\(743\) −906.258 −1.21973 −0.609864 0.792506i \(-0.708776\pi\)
−0.609864 + 0.792506i \(0.708776\pi\)
\(744\) 0 0
\(745\) 34.4917i 0.0462976i
\(746\) 775.637 + 83.0376i 1.03973 + 0.111310i
\(747\) 0 0
\(748\) −250.354 + 161.211i −0.334698 + 0.215522i
\(749\) 17.8425 + 17.8425i 0.0238218 + 0.0238218i
\(750\) 0 0
\(751\) 1147.02i 1.52732i 0.645618 + 0.763661i \(0.276600\pi\)
−0.645618 + 0.763661i \(0.723400\pi\)
\(752\) −71.3333 + 156.943i −0.0948581 + 0.208701i
\(753\) 0 0
\(754\) −923.329 + 744.749i −1.22457 + 0.987731i
\(755\) 93.8192 93.8192i 0.124264 0.124264i
\(756\) 0 0
\(757\) 525.591 525.591i 0.694308 0.694308i −0.268869 0.963177i \(-0.586650\pi\)
0.963177 + 0.268869i \(0.0866497\pi\)
\(758\) −3.92694 + 36.6808i −0.00518066 + 0.0483915i
\(759\) 0 0
\(760\) 110.303 + 219.618i 0.145135 + 0.288971i
\(761\) 788.107i 1.03562i 0.855495 + 0.517810i \(0.173253\pi\)
−0.855495 + 0.517810i \(0.826747\pi\)
\(762\) 0 0
\(763\) 86.6925 + 86.6925i 0.113621 + 0.113621i
\(764\) 758.382 + 164.263i 0.992647 + 0.215004i
\(765\) 0 0
\(766\) −189.879 + 153.155i −0.247884 + 0.199941i
\(767\) 350.850i 0.457431i
\(768\) 0 0
\(769\) −768.187 −0.998943 −0.499471 0.866330i \(-0.666472\pi\)
−0.499471 + 0.866330i \(0.666472\pi\)
\(770\) −19.9915 24.7852i −0.0259630 0.0321886i
\(771\) 0 0
\(772\) −119.862 + 553.387i −0.155261 + 0.716822i
\(773\) −275.915 + 275.915i −0.356941 + 0.356941i −0.862684 0.505743i \(-0.831218\pi\)
0.505743 + 0.862684i \(0.331218\pi\)
\(774\) 0 0
\(775\) −1063.91 −1.37279
\(776\) 1026.81 515.717i 1.32321 0.664583i
\(777\) 0 0
\(778\) −656.031 70.2328i −0.843227 0.0902735i
\(779\) 481.003 + 481.003i 0.617462 + 0.617462i
\(780\) 0 0
\(781\) −445.547 445.547i −0.570483 0.570483i
\(782\) −114.533 141.996i −0.146461 0.181581i
\(783\) 0 0
\(784\) 707.491 + 321.567i 0.902412 + 0.410162i
\(785\) −160.364 −0.204285
\(786\) 0 0
\(787\) 240.824 240.824i 0.306002 0.306002i −0.537354