Properties

Label 144.3.m.c.91.3
Level $144$
Weight $3$
Character 144.91
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 91.3
Root \(-1.25564 - 1.55672i\) of defining polynomial
Character \(\chi\) \(=\) 144.91
Dual form 144.3.m.c.19.3

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 0.610337 0.792142i \(-0.291034\pi\)
−0.792142 + 0.610337i \(0.791034\pi\)
\(6\) 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 0.246980 0.969021i \(-0.420562\pi\)
0.969021 0.246980i \(-0.0794382\pi\)
\(12\) 0 0
\(13\) 8.32795 8.32795i 0.640612 0.640612i −0.310094 0.950706i \(-0.600361\pi\)
0.950706 + 0.310094i \(0.100361\pi\)
\(14\) 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 0.994459 0.105123i \(-0.0335236\pi\)
−0.105123 + 0.994459i \(0.533524\pi\)
\(20\) −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 −0.263209 + 0.964739i \(0.584781\pi\)
−0.964739 + 0.263209i \(0.915219\pi\)
\(30\) 0 0
\(31\) 45.5687i 1.46996i −0.678089 0.734980i \(-0.737192\pi\)
0.678089 0.734980i \(-0.262808\pi\)
\(32\) 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 0.830868 0.556470i \(-0.187844\pi\)
−0.556470 + 0.830868i \(0.687844\pi\)
\(38\) −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 \(-0.887150\pi\)
0.937811 0.347148i \(-0.112850\pi\)
\(42\) 0 0
\(43\) 22.7354 22.7354i 0.528730 0.528730i −0.391464 0.920194i \(-0.628031\pi\)
0.920194 + 0.391464i \(0.128031\pi\)
\(44\) −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 \(0.0365661\pi\)
−0.993409 + 0.114623i \(0.963434\pi\)
\(48\) 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 0.197097 0.980384i \(-0.436849\pi\)
−0.980384 + 0.197097i \(0.936849\pi\)
\(54\) 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 −0.505689 0.862716i \(-0.668762\pi\)
0.862716 + 0.505689i \(0.168762\pi\)
\(60\) 0 0
\(61\) −68.7531 + 68.7531i −1.12710 + 1.12710i −0.136453 + 0.990647i \(0.543570\pi\)
−0.990647 + 0.136453i \(0.956430\pi\)
\(62\) 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 0.999923 + 0.0123779i \(0.00394012\pi\)
0.0123779 + 0.999923i \(0.496060\pi\)
\(68\) −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 \(0.0407351\pi\)
−0.991823 + 0.127624i \(0.959265\pi\)
\(74\) −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 \(-0.987320\pi\)
0.999207 0.0398242i \(-0.0126798\pi\)
\(80\) 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 0.992296 0.123894i \(-0.0395382\pi\)
−0.123894 + 0.992296i \(0.539538\pi\)
\(84\) 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 \(0.0189902\pi\)
−0.998221 + 0.0596240i \(0.981010\pi\)
\(90\) 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 0.994912 0.100753i \(-0.0321251\pi\)
−0.100753 + 0.994912i \(0.532125\pi\)
\(102\) 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 −0.822892 0.568197i \(-0.807641\pi\)
0.568197 + 0.822892i \(0.307641\pi\)
\(108\) 0 0
\(109\) −132.413 + 132.413i −1.21480 + 1.21480i −0.245366 + 0.969430i \(0.578908\pi\)
−0.969430 + 0.245366i \(0.921092\pi\)
\(110\) 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 \(0.124103\pi\)
−0.924954 + 0.380078i \(0.875897\pi\)
\(128\) −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 0.883855 0.467762i \(-0.154939\pi\)
−0.467762 + 0.883855i \(0.654939\pi\)
\(132\) 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 \(-0.969828\pi\)
0.995511 0.0946471i \(-0.0301723\pi\)
\(138\) 0 0
\(139\) 3.64066 3.64066i 0.0261918 0.0261918i −0.693890 0.720081i \(-0.744104\pi\)
0.720081 + 0.693890i \(0.244104\pi\)
\(140\) 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 0.767899 0.640571i \(-0.221302\pi\)
−0.640571 + 0.767899i \(0.721302\pi\)
\(150\) 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 −0.368000 0.929826i \(-0.619957\pi\)
0.929826 + 0.368000i \(0.119957\pi\)
\(158\) 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 0.762431 0.647070i \(-0.224006\pi\)
−0.647070 + 0.762431i \(0.724006\pi\)
\(164\) −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 −0.106876 0.994272i \(-0.534085\pi\)
0.994272 + 0.106876i \(0.0340849\pi\)
\(174\) 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 0.271921 0.962320i \(-0.412341\pi\)
−0.962320 + 0.271921i \(0.912341\pi\)
\(180\) 0 0
\(181\) 122.965 + 122.965i 0.679364 + 0.679364i 0.959856 0.280493i \(-0.0904978\pi\)
−0.280493 + 0.959856i \(0.590498\pi\)
\(182\) −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 \(0.169553\pi\)
−0.861456 + 0.507832i \(0.830447\pi\)
\(192\) 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 0.629800 0.776758i \(-0.283137\pi\)
−0.776758 + 0.629800i \(0.783137\pi\)
\(198\) 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 0.724310 0.689474i \(-0.242158\pi\)
−0.689474 + 0.724310i \(0.742158\pi\)
\(212\) −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 \(-0.666869\pi\)
0.500549 0.865708i \(-0.333131\pi\)
\(224\) −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 0.808106 0.589037i \(-0.200493\pi\)
−0.589037 + 0.808106i \(0.700493\pi\)
\(228\) 0 0
\(229\) −191.870 191.870i −0.837861 0.837861i 0.150716 0.988577i \(-0.451842\pi\)
−0.988577 + 0.150716i \(0.951842\pi\)
\(230\) 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 \(-0.778605\pi\)
0.767712 0.640795i \(-0.221395\pi\)
\(234\) 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 \(0.173127\pi\)
−0.855700 + 0.517473i \(0.826873\pi\)
\(240\) 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 −0.952575 0.304303i \(-0.901576\pi\)
0.304303 + 0.952575i \(0.401576\pi\)
\(252\) 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 −0.709913 0.704289i \(-0.751266\pi\)
0.704289 + 0.709913i \(0.251266\pi\)
\(270\) 0 0
\(271\) 166.098i 0.612909i −0.951885 0.306454i \(-0.900857\pi\)
0.951885 0.306454i \(-0.0991427\pi\)
\(272\) −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 0.987062 + 0.160338i \(0.0512586\pi\)
0.160338 + 0.987062i \(0.448741\pi\)
\(278\) 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 \(0.254352\pi\)
−0.697374 + 0.716708i \(0.745648\pi\)
\(282\) 0 0
\(283\) −192.406 + 192.406i −0.679881 + 0.679881i −0.959973 0.280092i \(-0.909635\pi\)
0.280092 + 0.959973i \(0.409635\pi\)
\(284\) 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 0.823921 0.566704i \(-0.191782\pi\)
−0.566704 + 0.823921i \(0.691782\pi\)
\(294\) 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 0.501703 0.865040i \(-0.332707\pi\)
−0.865040 + 0.501703i \(0.832707\pi\)
\(308\) 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 \(0.284829\pi\)
−0.625661 + 0.780095i \(0.715171\pi\)
\(314\) 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 −0.984913 0.173050i \(-0.944638\pi\)
0.173050 + 0.984913i \(0.444638\pi\)
\(318\) 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 −0.868667 0.495396i \(-0.835023\pi\)
0.495396 + 0.868667i \(0.335023\pi\)
\(332\) 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 −0.506918 0.861994i \(-0.669215\pi\)
0.861994 + 0.506918i \(0.169215\pi\)
\(348\) 0 0
\(349\) 115.371 115.371i 0.330575 0.330575i −0.522230 0.852805i \(-0.674900\pi\)
0.852805 + 0.522230i \(0.174900\pi\)
\(350\) −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 \(-0.942717\pi\)
0.983851 0.178991i \(-0.0572832\pi\)
\(368\) −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 0.233062 0.972462i \(-0.425126\pi\)
−0.972462 + 0.233062i \(0.925126\pi\)
\(374\) 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 −0.724104 0.689691i \(-0.757747\pi\)
0.689691 + 0.724104i \(0.257747\pi\)
\(380\) −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 \(0.0509027\pi\)
−0.987241 + 0.159235i \(0.949097\pi\)
\(384\) 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 0.940222 0.340563i \(-0.110618\pi\)
−0.340563 + 0.940222i \(0.610618\pi\)
\(390\) 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 −0.804695 0.593689i \(-0.797671\pi\)
0.593689 + 0.804695i \(0.297671\pi\)
\(398\) 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 \(-0.814914\pi\)
0.835659 0.549248i \(-0.185086\pi\)
\(410\) −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 0.918118 0.396307i \(-0.129708\pi\)
−0.396307 + 0.918118i \(0.629708\pi\)
\(420\) 0 0
\(421\) −61.2101 61.2101i −0.145392 0.145392i 0.630664 0.776056i \(-0.282783\pi\)
−0.776056 + 0.630664i \(0.782783\pi\)
\(422\) −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 \(-0.802527\pi\)
0.813657 0.581345i \(-0.197473\pi\)
\(432\) 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 −0.958899 0.283746i \(-0.908423\pi\)
0.283746 + 0.958899i \(0.408423\pi\)
\(444\) 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 \(0.247514\pi\)
−0.712609 + 0.701562i \(0.752486\pi\)
\(458\) 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 −0.136631 0.990622i \(-0.543627\pi\)
0.990622 + 0.136631i \(0.0436273\pi\)
\(462\) 0 0
\(463\) 395.861i 0.854991i 0.904018 + 0.427495i \(0.140604\pi\)
−0.904018 + 0.427495i \(0.859396\pi\)
\(464\) 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 0.790502 0.612460i \(-0.209820\pi\)
−0.612460 + 0.790502i \(0.709820\pi\)
\(468\) 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 \(0.148183\pi\)
−0.893584 + 0.448896i \(0.851817\pi\)
\(480\) 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 −0.00379588 0.999993i \(-0.501208\pi\)
0.999993 + 0.00379588i \(0.00120827\pi\)
\(492\) 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 0.918170 0.396188i \(-0.129667\pi\)
−0.396188 + 0.918170i \(0.629667\pi\)
\(500\) 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 −0.161371 0.986894i \(-0.551592\pi\)
0.986894 + 0.161371i \(0.0515916\pi\)
\(510\) 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 \(0.124199\pi\)
−0.924839 + 0.380358i \(0.875801\pi\)
\(522\) 0 0
\(523\) 564.600 564.600i 1.07954 1.07954i 0.0829913 0.996550i \(-0.473553\pi\)
0.996550 0.0829913i \(-0.0264474\pi\)
\(524\) 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 −0.733899 0.679259i \(-0.762301\pi\)
0.679259 + 0.733899i \(0.262301\pi\)
\(542\) 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 0.568965 0.822362i \(-0.307344\pi\)
−0.822362 + 0.568965i \(0.807344\pi\)
\(548\) −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 −0.759277 0.650767i \(-0.774447\pi\)
0.650767 + 0.759277i \(0.274447\pi\)
\(558\) 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 0.428649 0.903471i \(-0.358990\pi\)
−0.903471 + 0.428649i \(0.858990\pi\)
\(564\) 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 \(-0.910518\pi\)
0.960746 0.277429i \(-0.0894825\pi\)
\(570\) 0 0
\(571\) −670.572 + 670.572i −1.17438 + 1.17438i −0.193228 + 0.981154i \(0.561896\pi\)
−0.981154 + 0.193228i \(0.938104\pi\)
\(572\) −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 −0.252064 0.967711i \(-0.581109\pi\)
0.967711 + 0.252064i \(0.0811093\pi\)
\(588\) 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 \(-0.897613\pi\)
0.948712 0.316140i \(-0.102387\pi\)
\(602\) −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 \(-0.952149\pi\)
0.988722 0.149763i \(-0.0478512\pi\)
\(608\) 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 0.750657 0.660693i \(-0.229737\pi\)
−0.660693 + 0.750657i \(0.729737\pi\)
\(614\) 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 \(0.155657\pi\)
−0.882798 + 0.469752i \(0.844343\pi\)
\(618\) 0 0
\(619\) 91.1070 91.1070i 0.147184 0.147184i −0.629675 0.776859i \(-0.716812\pi\)
0.776859 + 0.629675i \(0.216812\pi\)
\(620\) 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 0.844353 + 0.535787i \(0.179985\pi\)
0.535787 + 0.844353i \(0.320015\pi\)
\(644\) 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 −0.987028 0.160549i \(-0.948674\pi\)
0.160549 + 0.987028i \(0.448674\pi\)
\(654\) 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 0.0500862 0.998745i \(-0.484050\pi\)
−0.998745 + 0.0500862i \(0.984050\pi\)
\(660\) 0 0
\(661\) −326.893 326.893i −0.494544 0.494544i 0.415191 0.909734i \(-0.363715\pi\)
−0.909734 + 0.415191i \(0.863715\pi\)
\(662\) −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 0.794025 0.607885i \(-0.207982\pi\)
−0.607885 + 0.794025i \(0.707982\pi\)
\(678\) 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 −0.996315 0.0857647i \(-0.972667\pi\)
0.0857647 + 0.996315i \(0.472667\pi\)
\(684\) 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 0.352176 0.935934i \(-0.385442\pi\)
−0.935934 + 0.352176i \(0.885442\pi\)
\(692\) −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 −0.956697 0.291086i \(-0.905983\pi\)
0.291086 + 0.956697i \(0.405983\pi\)
\(702\) 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 0.984376 + 0.176081i \(0.0563422\pi\)
0.176081 + 0.984376i \(0.443658\pi\)
\(710\) −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 \(-0.835593\pi\)
0.869553 0.493840i \(-0.164407\pi\)
\(720\) 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 −0.769662 0.638452i \(-0.779575\pi\)
0.638452 + 0.769662i \(0.279575\pi\)
\(734\) 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 0.974757 + 0.223268i \(0.0716726\pi\)
0.223268 + 0.974757i \(0.428327\pi\)
\(740\) −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 \(-0.723400\pi\)
0.645618 0.763661i \(-0.276600\pi\)
\(752\) −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 0.963177 0.268869i \(-0.0866497\pi\)
−0.268869 + 0.963177i \(0.586650\pi\)
\(758\) −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 \(-0.826747\pi\)
0.855495 0.517810i \(-0.173253\pi\)
\(762\) 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 0.505743 0.862684i \(-0.331218\pi\)
−0.862684 + 0.505743i \(0.831218\pi\)
\(774\) 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
\(785\)