Properties

Label 144.2.k.c.37.4
Level $144$
Weight $2$
Character 144.37
Analytic conductor $1.150$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.629407744.1
Defining polynomial: \(x^{8} - 2 x^{6} + 2 x^{4} - 8 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.4
Root \(1.38255 + 0.297594i\) of defining polynomial
Character \(\chi\) \(=\) 144.37
Dual form 144.2.k.c.109.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.38255 + 0.297594i) q^{2} +(1.82288 + 0.822876i) q^{4} +(-0.595188 - 0.595188i) q^{5} +1.64575i q^{7} +(2.27533 + 1.68014i) q^{8} +O(q^{10})\) \(q+(1.38255 + 0.297594i) q^{2} +(1.82288 + 0.822876i) q^{4} +(-0.595188 - 0.595188i) q^{5} +1.64575i q^{7} +(2.27533 + 1.68014i) q^{8} +(-0.645751 - 1.00000i) q^{10} +(-3.36028 - 3.36028i) q^{11} +(2.64575 - 2.64575i) q^{13} +(-0.489766 + 2.27533i) q^{14} +(2.64575 + 3.00000i) q^{16} -5.53019 q^{17} +(-3.64575 + 3.64575i) q^{19} +(-0.595188 - 1.57472i) q^{20} +(-3.64575 - 5.64575i) q^{22} +4.33981i q^{23} -4.29150i q^{25} +(4.44524 - 2.87052i) q^{26} +(-1.35425 + 3.00000i) q^{28} +(6.12538 - 6.12538i) q^{29} -5.64575 q^{31} +(2.76510 + 4.93500i) q^{32} +(-7.64575 - 1.64575i) q^{34} +(0.979531 - 0.979531i) q^{35} +(-0.645751 - 0.645751i) q^{37} +(-6.12538 + 3.95547i) q^{38} +(-0.354249 - 2.35425i) q^{40} +7.91094i q^{41} +(-0.354249 - 0.354249i) q^{43} +(-3.36028 - 8.89047i) q^{44} +(-1.29150 + 6.00000i) q^{46} +9.10132 q^{47} +4.29150 q^{49} +(1.27713 - 5.93321i) q^{50} +(7.00000 - 2.64575i) q^{52} +(4.93500 + 4.93500i) q^{53} +4.00000i q^{55} +(-2.76510 + 3.74463i) q^{56} +(10.2915 - 6.64575i) q^{58} +(-4.33981 - 4.33981i) q^{59} +(-0.645751 + 0.645751i) q^{61} +(-7.80552 - 1.68014i) q^{62} +(2.35425 + 7.64575i) q^{64} -3.14944 q^{65} +(4.00000 - 4.00000i) q^{67} +(-10.0808 - 4.55066i) q^{68} +(1.64575 - 1.06275i) q^{70} +13.4411i q^{71} +3.29150i q^{73} +(-0.700610 - 1.08495i) q^{74} +(-9.64575 + 3.64575i) q^{76} +(5.53019 - 5.53019i) q^{77} +9.64575 q^{79} +(0.210845 - 3.36028i) q^{80} +(-2.35425 + 10.9373i) q^{82} +(3.36028 - 3.36028i) q^{83} +(3.29150 + 3.29150i) q^{85} +(-0.384343 - 0.595188i) q^{86} +(-2.00000 - 13.2915i) q^{88} +2.38075i q^{89} +(4.35425 + 4.35425i) q^{91} +(-3.57113 + 7.91094i) q^{92} +(12.5830 + 2.70850i) q^{94} +4.33981 q^{95} -10.5830 q^{97} +(5.93321 + 1.27713i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} + 16q^{10} - 8q^{19} - 8q^{22} - 32q^{28} - 24q^{31} - 40q^{34} + 16q^{37} - 24q^{40} - 24q^{43} + 32q^{46} - 8q^{49} + 56q^{52} + 40q^{58} + 16q^{61} + 40q^{64} + 32q^{67} - 8q^{70} - 56q^{76} + 56q^{79} - 40q^{82} - 16q^{85} - 16q^{88} + 56q^{91} + 16q^{94} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38255 + 0.297594i 0.977609 + 0.210431i
\(3\) 0 0
\(4\) 1.82288 + 0.822876i 0.911438 + 0.411438i
\(5\) −0.595188 0.595188i −0.266176 0.266176i 0.561381 0.827557i \(-0.310270\pi\)
−0.827557 + 0.561381i \(0.810270\pi\)
\(6\) 0 0
\(7\) 1.64575i 0.622036i 0.950404 + 0.311018i \(0.100670\pi\)
−0.950404 + 0.311018i \(0.899330\pi\)
\(8\) 2.27533 + 1.68014i 0.804450 + 0.594020i
\(9\) 0 0
\(10\) −0.645751 1.00000i −0.204204 0.316228i
\(11\) −3.36028 3.36028i −1.01316 1.01316i −0.999912 0.0132513i \(-0.995782\pi\)
−0.0132513 0.999912i \(-0.504218\pi\)
\(12\) 0 0
\(13\) 2.64575 2.64575i 0.733799 0.733799i −0.237571 0.971370i \(-0.576351\pi\)
0.971370 + 0.237571i \(0.0763512\pi\)
\(14\) −0.489766 + 2.27533i −0.130895 + 0.608107i
\(15\) 0 0
\(16\) 2.64575 + 3.00000i 0.661438 + 0.750000i
\(17\) −5.53019 −1.34127 −0.670634 0.741788i \(-0.733978\pi\)
−0.670634 + 0.741788i \(0.733978\pi\)
\(18\) 0 0
\(19\) −3.64575 + 3.64575i −0.836393 + 0.836393i −0.988382 0.151989i \(-0.951432\pi\)
0.151989 + 0.988382i \(0.451432\pi\)
\(20\) −0.595188 1.57472i −0.133088 0.352118i
\(21\) 0 0
\(22\) −3.64575 5.64575i −0.777277 1.20368i
\(23\) 4.33981i 0.904914i 0.891786 + 0.452457i \(0.149452\pi\)
−0.891786 + 0.452457i \(0.850548\pi\)
\(24\) 0 0
\(25\) 4.29150i 0.858301i
\(26\) 4.44524 2.87052i 0.871783 0.562955i
\(27\) 0 0
\(28\) −1.35425 + 3.00000i −0.255929 + 0.566947i
\(29\) 6.12538 6.12538i 1.13745 1.13745i 0.148549 0.988905i \(-0.452540\pi\)
0.988905 0.148549i \(-0.0474603\pi\)
\(30\) 0 0
\(31\) −5.64575 −1.01401 −0.507003 0.861944i \(-0.669247\pi\)
−0.507003 + 0.861944i \(0.669247\pi\)
\(32\) 2.76510 + 4.93500i 0.488804 + 0.872393i
\(33\) 0 0
\(34\) −7.64575 1.64575i −1.31124 0.282244i
\(35\) 0.979531 0.979531i 0.165571 0.165571i
\(36\) 0 0
\(37\) −0.645751 0.645751i −0.106161 0.106161i 0.652031 0.758192i \(-0.273917\pi\)
−0.758192 + 0.652031i \(0.773917\pi\)
\(38\) −6.12538 + 3.95547i −0.993668 + 0.641662i
\(39\) 0 0
\(40\) −0.354249 2.35425i −0.0560116 0.372239i
\(41\) 7.91094i 1.23548i 0.786382 + 0.617741i \(0.211952\pi\)
−0.786382 + 0.617741i \(0.788048\pi\)
\(42\) 0 0
\(43\) −0.354249 0.354249i −0.0540224 0.0540224i 0.679579 0.733602i \(-0.262162\pi\)
−0.733602 + 0.679579i \(0.762162\pi\)
\(44\) −3.36028 8.89047i −0.506582 1.34029i
\(45\) 0 0
\(46\) −1.29150 + 6.00000i −0.190422 + 0.884652i
\(47\) 9.10132 1.32756 0.663782 0.747926i \(-0.268950\pi\)
0.663782 + 0.747926i \(0.268950\pi\)
\(48\) 0 0
\(49\) 4.29150 0.613072
\(50\) 1.27713 5.93321i 0.180613 0.839082i
\(51\) 0 0
\(52\) 7.00000 2.64575i 0.970725 0.366900i
\(53\) 4.93500 + 4.93500i 0.677875 + 0.677875i 0.959519 0.281644i \(-0.0908798\pi\)
−0.281644 + 0.959519i \(0.590880\pi\)
\(54\) 0 0
\(55\) 4.00000i 0.539360i
\(56\) −2.76510 + 3.74463i −0.369501 + 0.500397i
\(57\) 0 0
\(58\) 10.2915 6.64575i 1.35134 0.872630i
\(59\) −4.33981 4.33981i −0.564996 0.564996i 0.365727 0.930722i \(-0.380821\pi\)
−0.930722 + 0.365727i \(0.880821\pi\)
\(60\) 0 0
\(61\) −0.645751 + 0.645751i −0.0826800 + 0.0826800i −0.747237 0.664557i \(-0.768620\pi\)
0.664557 + 0.747237i \(0.268620\pi\)
\(62\) −7.80552 1.68014i −0.991302 0.213378i
\(63\) 0 0
\(64\) 2.35425 + 7.64575i 0.294281 + 0.955719i
\(65\) −3.14944 −0.390640
\(66\) 0 0
\(67\) 4.00000 4.00000i 0.488678 0.488678i −0.419211 0.907889i \(-0.637693\pi\)
0.907889 + 0.419211i \(0.137693\pi\)
\(68\) −10.0808 4.55066i −1.22248 0.551848i
\(69\) 0 0
\(70\) 1.64575 1.06275i 0.196705 0.127022i
\(71\) 13.4411i 1.59517i 0.603207 + 0.797584i \(0.293889\pi\)
−0.603207 + 0.797584i \(0.706111\pi\)
\(72\) 0 0
\(73\) 3.29150i 0.385241i 0.981273 + 0.192621i \(0.0616987\pi\)
−0.981273 + 0.192621i \(0.938301\pi\)
\(74\) −0.700610 1.08495i −0.0814443 0.126123i
\(75\) 0 0
\(76\) −9.64575 + 3.64575i −1.10644 + 0.418196i
\(77\) 5.53019 5.53019i 0.630224 0.630224i
\(78\) 0 0
\(79\) 9.64575 1.08523 0.542616 0.839981i \(-0.317434\pi\)
0.542616 + 0.839981i \(0.317434\pi\)
\(80\) 0.210845 3.36028i 0.0235731 0.375691i
\(81\) 0 0
\(82\) −2.35425 + 10.9373i −0.259983 + 1.20782i
\(83\) 3.36028 3.36028i 0.368839 0.368839i −0.498215 0.867054i \(-0.666011\pi\)
0.867054 + 0.498215i \(0.166011\pi\)
\(84\) 0 0
\(85\) 3.29150 + 3.29150i 0.357014 + 0.357014i
\(86\) −0.384343 0.595188i −0.0414448 0.0641808i
\(87\) 0 0
\(88\) −2.00000 13.2915i −0.213201 1.41688i
\(89\) 2.38075i 0.252359i 0.992007 + 0.126180i \(0.0402716\pi\)
−0.992007 + 0.126180i \(0.959728\pi\)
\(90\) 0 0
\(91\) 4.35425 + 4.35425i 0.456449 + 0.456449i
\(92\) −3.57113 + 7.91094i −0.372316 + 0.824773i
\(93\) 0 0
\(94\) 12.5830 + 2.70850i 1.29784 + 0.279360i
\(95\) 4.33981 0.445256
\(96\) 0 0
\(97\) −10.5830 −1.07454 −0.537271 0.843410i \(-0.680545\pi\)
−0.537271 + 0.843410i \(0.680545\pi\)
\(98\) 5.93321 + 1.27713i 0.599344 + 0.129009i
\(99\) 0 0
\(100\) 3.53137 7.82288i 0.353137 0.782288i
\(101\) −0.595188 0.595188i −0.0592234 0.0592234i 0.676875 0.736098i \(-0.263334\pi\)
−0.736098 + 0.676875i \(0.763334\pi\)
\(102\) 0 0
\(103\) 16.9373i 1.66888i −0.551101 0.834439i \(-0.685792\pi\)
0.551101 0.834439i \(-0.314208\pi\)
\(104\) 10.4652 1.57472i 1.02620 0.154414i
\(105\) 0 0
\(106\) 5.35425 + 8.29150i 0.520051 + 0.805342i
\(107\) −2.38075 2.38075i −0.230156 0.230156i 0.582602 0.812758i \(-0.302035\pi\)
−0.812758 + 0.582602i \(0.802035\pi\)
\(108\) 0 0
\(109\) −6.64575 + 6.64575i −0.636548 + 0.636548i −0.949702 0.313155i \(-0.898614\pi\)
0.313155 + 0.949702i \(0.398614\pi\)
\(110\) −1.19038 + 5.53019i −0.113498 + 0.527283i
\(111\) 0 0
\(112\) −4.93725 + 4.35425i −0.466527 + 0.411438i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 2.58301 2.58301i 0.240866 0.240866i
\(116\) 16.2062 6.12538i 1.50471 0.568727i
\(117\) 0 0
\(118\) −4.70850 7.29150i −0.433452 0.671237i
\(119\) 9.10132i 0.834316i
\(120\) 0 0
\(121\) 11.5830i 1.05300i
\(122\) −1.08495 + 0.700610i −0.0982271 + 0.0634303i
\(123\) 0 0
\(124\) −10.2915 4.64575i −0.924204 0.417201i
\(125\) −5.53019 + 5.53019i −0.494635 + 0.494635i
\(126\) 0 0
\(127\) 0.937254 0.0831678 0.0415839 0.999135i \(-0.486760\pi\)
0.0415839 + 0.999135i \(0.486760\pi\)
\(128\) 0.979531 + 11.2712i 0.0865792 + 0.996245i
\(129\) 0 0
\(130\) −4.35425 0.937254i −0.381893 0.0822026i
\(131\) −6.72057 + 6.72057i −0.587179 + 0.587179i −0.936866 0.349688i \(-0.886288\pi\)
0.349688 + 0.936866i \(0.386288\pi\)
\(132\) 0 0
\(133\) −6.00000 6.00000i −0.520266 0.520266i
\(134\) 6.72057 4.33981i 0.580568 0.374903i
\(135\) 0 0
\(136\) −12.5830 9.29150i −1.07898 0.796740i
\(137\) 10.2917i 0.879279i −0.898174 0.439639i \(-0.855106\pi\)
0.898174 0.439639i \(-0.144894\pi\)
\(138\) 0 0
\(139\) −14.5830 14.5830i −1.23691 1.23691i −0.961256 0.275659i \(-0.911104\pi\)
−0.275659 0.961256i \(-0.588896\pi\)
\(140\) 2.59160 0.979531i 0.219030 0.0827855i
\(141\) 0 0
\(142\) −4.00000 + 18.5830i −0.335673 + 1.55945i
\(143\) −17.7809 −1.48692
\(144\) 0 0
\(145\) −7.29150 −0.605526
\(146\) −0.979531 + 4.55066i −0.0810666 + 0.376615i
\(147\) 0 0
\(148\) −0.645751 1.70850i −0.0530804 0.140438i
\(149\) −11.6556 11.6556i −0.954861 0.954861i 0.0441630 0.999024i \(-0.485938\pi\)
−0.999024 + 0.0441630i \(0.985938\pi\)
\(150\) 0 0
\(151\) 10.3542i 0.842617i 0.906917 + 0.421308i \(0.138429\pi\)
−0.906917 + 0.421308i \(0.861571\pi\)
\(152\) −14.4207 + 2.16991i −1.16967 + 0.176003i
\(153\) 0 0
\(154\) 9.29150 6.00000i 0.748731 0.483494i
\(155\) 3.36028 + 3.36028i 0.269904 + 0.269904i
\(156\) 0 0
\(157\) −6.64575 + 6.64575i −0.530389 + 0.530389i −0.920688 0.390299i \(-0.872372\pi\)
0.390299 + 0.920688i \(0.372372\pi\)
\(158\) 13.3357 + 2.87052i 1.06093 + 0.228366i
\(159\) 0 0
\(160\) 1.29150 4.58301i 0.102102 0.362318i
\(161\) −7.14226 −0.562889
\(162\) 0 0
\(163\) 11.6458 11.6458i 0.912166 0.912166i −0.0842767 0.996442i \(-0.526858\pi\)
0.996442 + 0.0842767i \(0.0268580\pi\)
\(164\) −6.50972 + 14.4207i −0.508324 + 1.12606i
\(165\) 0 0
\(166\) 5.64575 3.64575i 0.438195 0.282965i
\(167\) 17.7809i 1.37593i −0.725743 0.687965i \(-0.758504\pi\)
0.725743 0.687965i \(-0.241496\pi\)
\(168\) 0 0
\(169\) 1.00000i 0.0769231i
\(170\) 3.57113 + 5.53019i 0.273893 + 0.424146i
\(171\) 0 0
\(172\) −0.354249 0.937254i −0.0270112 0.0714649i
\(173\) −4.93500 + 4.93500i −0.375201 + 0.375201i −0.869367 0.494166i \(-0.835473\pi\)
0.494166 + 0.869367i \(0.335473\pi\)
\(174\) 0 0
\(175\) 7.06275 0.533893
\(176\) 1.19038 18.9713i 0.0897280 1.43002i
\(177\) 0 0
\(178\) −0.708497 + 3.29150i −0.0531041 + 0.246709i
\(179\) 2.38075 2.38075i 0.177946 0.177946i −0.612514 0.790460i \(-0.709842\pi\)
0.790460 + 0.612514i \(0.209842\pi\)
\(180\) 0 0
\(181\) −0.645751 0.645751i −0.0479983 0.0479983i 0.682700 0.730699i \(-0.260805\pi\)
−0.730699 + 0.682700i \(0.760805\pi\)
\(182\) 4.72416 + 7.31575i 0.350178 + 0.542280i
\(183\) 0 0
\(184\) −7.29150 + 9.87451i −0.537537 + 0.727958i
\(185\) 0.768687i 0.0565150i
\(186\) 0 0
\(187\) 18.5830 + 18.5830i 1.35892 + 1.35892i
\(188\) 16.5906 + 7.48925i 1.20999 + 0.546210i
\(189\) 0 0
\(190\) 6.00000 + 1.29150i 0.435286 + 0.0936954i
\(191\) −9.10132 −0.658548 −0.329274 0.944234i \(-0.606804\pi\)
−0.329274 + 0.944234i \(0.606804\pi\)
\(192\) 0 0
\(193\) 11.8745 0.854746 0.427373 0.904075i \(-0.359439\pi\)
0.427373 + 0.904075i \(0.359439\pi\)
\(194\) −14.6315 3.14944i −1.05048 0.226117i
\(195\) 0 0
\(196\) 7.82288 + 3.53137i 0.558777 + 0.252241i
\(197\) 8.50613 + 8.50613i 0.606037 + 0.606037i 0.941908 0.335871i \(-0.109031\pi\)
−0.335871 + 0.941908i \(0.609031\pi\)
\(198\) 0 0
\(199\) 13.6458i 0.967322i −0.875256 0.483661i \(-0.839307\pi\)
0.875256 0.483661i \(-0.160693\pi\)
\(200\) 7.21033 9.76458i 0.509847 0.690460i
\(201\) 0 0
\(202\) −0.645751 1.00000i −0.0454349 0.0703598i
\(203\) 10.0808 + 10.0808i 0.707537 + 0.707537i
\(204\) 0 0
\(205\) 4.70850 4.70850i 0.328856 0.328856i
\(206\) 5.04042 23.4166i 0.351183 1.63151i
\(207\) 0 0
\(208\) 14.9373 + 0.937254i 1.03571 + 0.0649869i
\(209\) 24.5015 1.69481
\(210\) 0 0
\(211\) −14.5830 + 14.5830i −1.00394 + 1.00394i −0.00394326 + 0.999992i \(0.501255\pi\)
−0.999992 + 0.00394326i \(0.998745\pi\)
\(212\) 4.93500 + 13.0568i 0.338937 + 0.896744i
\(213\) 0 0
\(214\) −2.58301 4.00000i −0.176571 0.273434i
\(215\) 0.421689i 0.0287590i
\(216\) 0 0
\(217\) 9.29150i 0.630748i
\(218\) −11.1658 + 7.21033i −0.756244 + 0.488345i
\(219\) 0 0
\(220\) −3.29150 + 7.29150i −0.221913 + 0.491593i
\(221\) −14.6315 + 14.6315i −0.984222 + 0.984222i
\(222\) 0 0
\(223\) −14.3542 −0.961232 −0.480616 0.876931i \(-0.659587\pi\)
−0.480616 + 0.876931i \(0.659587\pi\)
\(224\) −8.12179 + 4.55066i −0.542660 + 0.304054i
\(225\) 0 0
\(226\) 0 0
\(227\) 1.40122 1.40122i 0.0930023 0.0930023i −0.659075 0.752077i \(-0.729052\pi\)
0.752077 + 0.659075i \(0.229052\pi\)
\(228\) 0 0
\(229\) 17.9373 + 17.9373i 1.18533 + 1.18533i 0.978345 + 0.206982i \(0.0663643\pi\)
0.206982 + 0.978345i \(0.433636\pi\)
\(230\) 4.33981 2.80244i 0.286159 0.184787i
\(231\) 0 0
\(232\) 24.2288 3.64575i 1.59070 0.239355i
\(233\) 19.7400i 1.29321i −0.762825 0.646606i \(-0.776188\pi\)
0.762825 0.646606i \(-0.223812\pi\)
\(234\) 0 0
\(235\) −5.41699 5.41699i −0.353366 0.353366i
\(236\) −4.33981 11.4821i −0.282498 0.747419i
\(237\) 0 0
\(238\) 2.70850 12.5830i 0.175566 0.815635i
\(239\) 13.0194 0.842158 0.421079 0.907024i \(-0.361652\pi\)
0.421079 + 0.907024i \(0.361652\pi\)
\(240\) 0 0
\(241\) −1.29150 −0.0831930 −0.0415965 0.999134i \(-0.513244\pi\)
−0.0415965 + 0.999134i \(0.513244\pi\)
\(242\) −3.44703 + 16.0141i −0.221584 + 1.02942i
\(243\) 0 0
\(244\) −1.70850 + 0.645751i −0.109375 + 0.0413400i
\(245\) −2.55425 2.55425i −0.163185 0.163185i
\(246\) 0 0
\(247\) 19.2915i 1.22749i
\(248\) −12.8459 9.48566i −0.815718 0.602340i
\(249\) 0 0
\(250\) −9.29150 + 6.00000i −0.587646 + 0.379473i
\(251\) 18.7605 + 18.7605i 1.18415 + 1.18415i 0.978659 + 0.205492i \(0.0658795\pi\)
0.205492 + 0.978659i \(0.434121\pi\)
\(252\) 0 0
\(253\) 14.5830 14.5830i 0.916826 0.916826i
\(254\) 1.29580 + 0.278921i 0.0813056 + 0.0175011i
\(255\) 0 0
\(256\) −2.00000 + 15.8745i −0.125000 + 0.992157i
\(257\) 29.2630 1.82538 0.912688 0.408656i \(-0.134002\pi\)
0.912688 + 0.408656i \(0.134002\pi\)
\(258\) 0 0
\(259\) 1.06275 1.06275i 0.0660358 0.0660358i
\(260\) −5.74103 2.59160i −0.356044 0.160724i
\(261\) 0 0
\(262\) −11.2915 + 7.29150i −0.697591 + 0.450471i
\(263\) 8.67963i 0.535209i −0.963529 0.267604i \(-0.913768\pi\)
0.963529 0.267604i \(-0.0862320\pi\)
\(264\) 0 0
\(265\) 5.87451i 0.360868i
\(266\) −6.50972 10.0808i −0.399137 0.618097i
\(267\) 0 0
\(268\) 10.5830 4.00000i 0.646460 0.244339i
\(269\) −10.4652 + 10.4652i −0.638074 + 0.638074i −0.950080 0.312006i \(-0.898999\pi\)
0.312006 + 0.950080i \(0.398999\pi\)
\(270\) 0 0
\(271\) 6.35425 0.385993 0.192997 0.981199i \(-0.438179\pi\)
0.192997 + 0.981199i \(0.438179\pi\)
\(272\) −14.6315 16.5906i −0.887166 1.00595i
\(273\) 0 0
\(274\) 3.06275 14.2288i 0.185027 0.859591i
\(275\) −14.4207 + 14.4207i −0.869599 + 0.869599i
\(276\) 0 0
\(277\) −16.5203 16.5203i −0.992606 0.992606i 0.00736669 0.999973i \(-0.497655\pi\)
−0.999973 + 0.00736669i \(0.997655\pi\)
\(278\) −15.8219 24.5015i −0.948934 1.46950i
\(279\) 0 0
\(280\) 3.87451 0.583005i 0.231546 0.0348412i
\(281\) 2.38075i 0.142024i 0.997475 + 0.0710119i \(0.0226228\pi\)
−0.997475 + 0.0710119i \(0.977377\pi\)
\(282\) 0 0
\(283\) −2.58301 2.58301i −0.153544 0.153544i 0.626155 0.779699i \(-0.284628\pi\)
−0.779699 + 0.626155i \(0.784628\pi\)
\(284\) −11.0604 + 24.5015i −0.656313 + 1.45390i
\(285\) 0 0
\(286\) −24.5830 5.29150i −1.45362 0.312893i
\(287\) −13.0194 −0.768513
\(288\) 0 0
\(289\) 13.5830 0.799000
\(290\) −10.0808 2.16991i −0.591968 0.127421i
\(291\) 0 0
\(292\) −2.70850 + 6.00000i −0.158503 + 0.351123i
\(293\) −2.55425 2.55425i −0.149221 0.149221i 0.628549 0.777770i \(-0.283649\pi\)
−0.777770 + 0.628549i \(0.783649\pi\)
\(294\) 0 0
\(295\) 5.16601i 0.300777i
\(296\) −0.384343 2.55425i −0.0223395 0.148463i
\(297\) 0 0
\(298\) −12.6458 19.5830i −0.732549 1.13441i
\(299\) 11.4821 + 11.4821i 0.664025 + 0.664025i
\(300\) 0 0
\(301\) 0.583005 0.583005i 0.0336039 0.0336039i
\(302\) −3.08136 + 14.3152i −0.177312 + 0.823750i
\(303\) 0 0
\(304\) −20.5830 1.29150i −1.18052 0.0740728i
\(305\) 0.768687 0.0440149
\(306\) 0 0
\(307\) −20.0000 + 20.0000i −1.14146 + 1.14146i −0.153277 + 0.988183i \(0.548983\pi\)
−0.988183 + 0.153277i \(0.951017\pi\)
\(308\) 14.6315 5.53019i 0.833708 0.315112i
\(309\) 0 0
\(310\) 3.64575 + 5.64575i 0.207065 + 0.320657i
\(311\) 8.67963i 0.492177i −0.969247 0.246088i \(-0.920855\pi\)
0.969247 0.246088i \(-0.0791453\pi\)
\(312\) 0 0
\(313\) 9.29150i 0.525187i −0.964907 0.262593i \(-0.915422\pi\)
0.964907 0.262593i \(-0.0845778\pi\)
\(314\) −11.1658 + 7.21033i −0.630123 + 0.406903i
\(315\) 0 0
\(316\) 17.5830 + 7.93725i 0.989121 + 0.446505i
\(317\) 0.595188 0.595188i 0.0334291 0.0334291i −0.690195 0.723624i \(-0.742475\pi\)
0.723624 + 0.690195i \(0.242475\pi\)
\(318\) 0 0
\(319\) −41.1660 −2.30485
\(320\) 3.14944 5.95188i 0.176059 0.332720i
\(321\) 0 0
\(322\) −9.87451 2.12549i −0.550285 0.118449i
\(323\) 20.1617 20.1617i 1.12183 1.12183i
\(324\) 0 0
\(325\) −11.3542 11.3542i −0.629820 0.629820i
\(326\) 19.5665 12.6351i 1.08369 0.699793i
\(327\) 0 0
\(328\) −13.2915 + 18.0000i −0.733900 + 0.993884i
\(329\) 14.9785i 0.825792i
\(330\) 0 0
\(331\) −8.00000 8.00000i −0.439720 0.439720i 0.452198 0.891918i \(-0.350640\pi\)
−0.891918 + 0.452198i \(0.850640\pi\)
\(332\) 8.89047 3.36028i 0.487928 0.184419i
\(333\) 0 0
\(334\) 5.29150 24.5830i 0.289538 1.34512i
\(335\) −4.76150 −0.260149
\(336\) 0 0
\(337\) 4.70850 0.256488 0.128244 0.991743i \(-0.459066\pi\)
0.128244 + 0.991743i \(0.459066\pi\)
\(338\) 0.297594 1.38255i 0.0161870 0.0752007i
\(339\) 0 0
\(340\) 3.29150 + 8.70850i 0.178507 + 0.472285i
\(341\) 18.9713 + 18.9713i 1.02735 + 1.02735i
\(342\) 0 0
\(343\) 18.5830i 1.00339i
\(344\) −0.210845 1.40122i −0.0113680 0.0755487i
\(345\) 0 0
\(346\) −8.29150 + 5.35425i −0.445754 + 0.287846i
\(347\) −3.36028 3.36028i −0.180389 0.180389i 0.611136 0.791526i \(-0.290713\pi\)
−0.791526 + 0.611136i \(0.790713\pi\)
\(348\) 0 0
\(349\) 3.22876 3.22876i 0.172831 0.172831i −0.615391 0.788222i \(-0.711002\pi\)
0.788222 + 0.615391i \(0.211002\pi\)
\(350\) 9.76458 + 2.10183i 0.521939 + 0.112348i
\(351\) 0 0
\(352\) 7.29150 25.8745i 0.388638 1.37912i
\(353\) −7.14226 −0.380144 −0.190072 0.981770i \(-0.560872\pi\)
−0.190072 + 0.981770i \(0.560872\pi\)
\(354\) 0 0
\(355\) 8.00000 8.00000i 0.424596 0.424596i
\(356\) −1.95906 + 4.33981i −0.103830 + 0.230010i
\(357\) 0 0
\(358\) 4.00000 2.58301i 0.211407 0.136516i
\(359\) 4.76150i 0.251303i −0.992074 0.125651i \(-0.959898\pi\)
0.992074 0.125651i \(-0.0401020\pi\)
\(360\) 0 0
\(361\) 7.58301i 0.399106i
\(362\) −0.700610 1.08495i −0.0368233 0.0570239i
\(363\) 0 0
\(364\) 4.35425 + 11.5203i 0.228225 + 0.603826i
\(365\) 1.95906 1.95906i 0.102542 0.102542i
\(366\) 0 0
\(367\) 34.8118 1.81716 0.908580 0.417712i \(-0.137168\pi\)
0.908580 + 0.417712i \(0.137168\pi\)
\(368\) −13.0194 + 11.4821i −0.678685 + 0.598544i
\(369\) 0 0
\(370\) −0.228757 + 1.06275i −0.0118925 + 0.0552495i
\(371\) −8.12179 + 8.12179i −0.421662 + 0.421662i
\(372\) 0 0
\(373\) 11.9373 + 11.9373i 0.618088 + 0.618088i 0.945041 0.326953i \(-0.106022\pi\)
−0.326953 + 0.945041i \(0.606022\pi\)
\(374\) 20.1617 + 31.2221i 1.04254 + 1.61446i
\(375\) 0 0
\(376\) 20.7085 + 15.2915i 1.06796 + 0.788599i
\(377\) 32.4125i 1.66933i
\(378\) 0 0
\(379\) 8.35425 + 8.35425i 0.429129 + 0.429129i 0.888332 0.459203i \(-0.151865\pi\)
−0.459203 + 0.888332i \(0.651865\pi\)
\(380\) 7.91094 + 3.57113i 0.405823 + 0.183195i
\(381\) 0 0
\(382\) −12.5830 2.70850i −0.643803 0.138579i
\(383\) 9.10132 0.465056 0.232528 0.972590i \(-0.425300\pi\)
0.232528 + 0.972590i \(0.425300\pi\)
\(384\) 0 0
\(385\) −6.58301 −0.335501
\(386\) 16.4171 + 3.53378i 0.835607 + 0.179865i
\(387\) 0 0
\(388\) −19.2915 8.70850i −0.979378 0.442107i
\(389\) −20.7569 20.7569i −1.05242 1.05242i −0.998548 0.0538679i \(-0.982845\pi\)
−0.0538679 0.998548i \(-0.517155\pi\)
\(390\) 0 0
\(391\) 24.0000i 1.21373i
\(392\) 9.76458 + 7.21033i 0.493186 + 0.364177i
\(393\) 0 0
\(394\) 9.22876 + 14.2915i 0.464938 + 0.719996i
\(395\) −5.74103 5.74103i −0.288863 0.288863i
\(396\) 0 0
\(397\) 8.06275 8.06275i 0.404658 0.404658i −0.475213 0.879871i \(-0.657629\pi\)
0.879871 + 0.475213i \(0.157629\pi\)
\(398\) 4.06089 18.8659i 0.203554 0.945662i
\(399\) 0 0
\(400\) 12.8745 11.3542i 0.643725 0.567712i
\(401\) −16.5906 −0.828494 −0.414247 0.910165i \(-0.635955\pi\)
−0.414247 + 0.910165i \(0.635955\pi\)
\(402\) 0 0
\(403\) −14.9373 + 14.9373i −0.744078 + 0.744078i
\(404\) −0.595188 1.57472i −0.0296117 0.0783452i
\(405\) 0 0
\(406\) 10.9373 + 16.9373i 0.542807 + 0.840582i
\(407\) 4.33981i 0.215117i
\(408\) 0 0
\(409\) 25.1660i 1.24438i 0.782867 + 0.622190i \(0.213757\pi\)
−0.782867 + 0.622190i \(0.786243\pi\)
\(410\) 7.91094 5.10850i 0.390694 0.252291i
\(411\) 0 0
\(412\) 13.9373 30.8745i 0.686639 1.52108i
\(413\) 7.14226 7.14226i 0.351447 0.351447i
\(414\) 0 0
\(415\) −4.00000 −0.196352
\(416\) 20.3725 + 5.74103i 0.998846 + 0.281477i
\(417\) 0 0
\(418\) 33.8745 + 7.29150i 1.65686 + 0.356639i
\(419\) −18.7605 + 18.7605i −0.916509 + 0.916509i −0.996774 0.0802643i \(-0.974424\pi\)
0.0802643 + 0.996774i \(0.474424\pi\)
\(420\) 0 0
\(421\) 11.3542 + 11.3542i 0.553372 + 0.553372i 0.927412 0.374040i \(-0.122028\pi\)
−0.374040 + 0.927412i \(0.622028\pi\)
\(422\) −24.5015 + 15.8219i −1.19271 + 0.770197i
\(423\) 0 0
\(424\) 2.93725 + 19.5203i 0.142646 + 0.947988i
\(425\) 23.7328i 1.15121i
\(426\) 0 0
\(427\) −1.06275 1.06275i −0.0514299 0.0514299i
\(428\) −2.38075 6.29888i −0.115078 0.304468i
\(429\) 0 0
\(430\) −0.125492 + 0.583005i −0.00605177 + 0.0281150i
\(431\) −31.2221 −1.50391 −0.751957 0.659212i \(-0.770890\pi\)
−0.751957 + 0.659212i \(0.770890\pi\)
\(432\) 0 0
\(433\) −4.00000 −0.192228 −0.0961139 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) 2.76510 12.8459i 0.132729 0.616625i
\(435\) 0 0
\(436\) −17.5830 + 6.64575i −0.842073 + 0.318274i
\(437\) −15.8219 15.8219i −0.756863 0.756863i
\(438\) 0 0
\(439\) 0.479741i 0.0228968i 0.999934 + 0.0114484i \(0.00364422\pi\)
−0.999934 + 0.0114484i \(0.996356\pi\)
\(440\) −6.72057 + 9.10132i −0.320390 + 0.433888i
\(441\) 0 0
\(442\) −24.5830 + 15.8745i −1.16929 + 0.755073i
\(443\) −21.5629 21.5629i −1.02449 1.02449i −0.999693 0.0247926i \(-0.992107\pi\)
−0.0247926 0.999693i \(-0.507893\pi\)
\(444\) 0 0
\(445\) 1.41699 1.41699i 0.0671720 0.0671720i
\(446\) −19.8454 4.27174i −0.939708 0.202273i
\(447\) 0 0
\(448\) −12.5830 + 3.87451i −0.594491 + 0.183053i
\(449\) −9.44832 −0.445894 −0.222947 0.974831i \(-0.571568\pi\)
−0.222947 + 0.974831i \(0.571568\pi\)
\(450\) 0 0
\(451\) 26.5830 26.5830i 1.25174 1.25174i
\(452\) 0 0
\(453\) 0 0
\(454\) 2.35425 1.52026i 0.110490 0.0713493i
\(455\) 5.18319i 0.242992i
\(456\) 0 0
\(457\) 5.41699i 0.253396i −0.991941 0.126698i \(-0.959562\pi\)
0.991941 0.126698i \(-0.0404380\pi\)
\(458\) 19.4611 + 30.1371i 0.909357 + 1.40822i
\(459\) 0 0
\(460\) 6.83399 2.58301i 0.318636 0.120433i
\(461\) −8.50613 + 8.50613i −0.396170 + 0.396170i −0.876880 0.480710i \(-0.840379\pi\)
0.480710 + 0.876880i \(0.340379\pi\)
\(462\) 0 0
\(463\) 15.0627 0.700025 0.350013 0.936745i \(-0.386177\pi\)
0.350013 + 0.936745i \(0.386177\pi\)
\(464\) 34.5824 + 2.16991i 1.60545 + 0.100735i
\(465\) 0 0
\(466\) 5.87451 27.2915i 0.272131 1.26425i
\(467\) 25.4810 25.4810i 1.17912 1.17912i 0.199154 0.979968i \(-0.436181\pi\)
0.979968 0.199154i \(-0.0638194\pi\)
\(468\) 0 0
\(469\) 6.58301 + 6.58301i 0.303975 + 0.303975i
\(470\) −5.87719 9.10132i −0.271094 0.419812i
\(471\) 0 0
\(472\) −2.58301 17.1660i −0.118892 0.790130i
\(473\) 2.38075i 0.109467i
\(474\) 0 0
\(475\) 15.6458 + 15.6458i 0.717876 + 0.717876i
\(476\) 7.48925 16.5906i 0.343269 0.760428i
\(477\) 0 0
\(478\) 18.0000 + 3.87451i 0.823301 + 0.177216i
\(479\) 22.1208 1.01072 0.505362 0.862908i \(-0.331359\pi\)
0.505362 + 0.862908i \(0.331359\pi\)
\(480\) 0 0
\(481\) −3.41699 −0.155802
\(482\) −1.78556 0.384343i −0.0813302 0.0175064i
\(483\) 0 0
\(484\) −9.53137 + 21.1144i −0.433244 + 0.959744i
\(485\) 6.29888 + 6.29888i 0.286017 + 0.286017i
\(486\) 0 0
\(487\) 8.22876i 0.372881i −0.982466 0.186440i \(-0.940305\pi\)
0.982466 0.186440i \(-0.0596951\pi\)
\(488\) −2.55425 + 0.384343i −0.115625 + 0.0173984i
\(489\) 0 0
\(490\) −2.77124 4.29150i −0.125192 0.193870i
\(491\) −15.4002 15.4002i −0.695001 0.695001i 0.268327 0.963328i \(-0.413529\pi\)
−0.963328 + 0.268327i \(0.913529\pi\)
\(492\) 0 0
\(493\) −33.8745 + 33.8745i −1.52563 + 1.52563i
\(494\) −5.74103 + 26.6714i −0.258301 + 1.20000i
\(495\) 0 0
\(496\) −14.9373 16.9373i −0.670703 0.760505i
\(497\) −22.1208 −0.992252
\(498\) 0 0
\(499\) 10.5830 10.5830i 0.473760 0.473760i −0.429369 0.903129i \(-0.641264\pi\)
0.903129 + 0.429369i \(0.141264\pi\)
\(500\) −14.6315 + 5.53019i −0.654341 + 0.247318i
\(501\) 0 0
\(502\) 20.3542 + 31.5203i 0.908455 + 1.40682i
\(503\) 31.6438i 1.41093i 0.708747 + 0.705463i \(0.249261\pi\)
−0.708747 + 0.705463i \(0.750739\pi\)
\(504\) 0 0
\(505\) 0.708497i 0.0315277i
\(506\) 24.5015 15.8219i 1.08923 0.703369i
\(507\) 0 0
\(508\) 1.70850 + 0.771243i 0.0758023 + 0.0342184i
\(509\) 24.6750 24.6750i 1.09370 1.09370i 0.0985706 0.995130i \(-0.468573\pi\)
0.995130 0.0985706i \(-0.0314270\pi\)
\(510\) 0 0
\(511\) −5.41699 −0.239634
\(512\) −7.48925 + 21.3521i −0.330981 + 0.943637i
\(513\) 0 0
\(514\) 40.4575 + 8.70850i 1.78450 + 0.384115i
\(515\) −10.0808 + 10.0808i −0.444215 + 0.444215i
\(516\) 0 0
\(517\) −30.5830 30.5830i −1.34504 1.34504i
\(518\) 1.78556 1.15303i 0.0784532 0.0506612i
\(519\) 0 0
\(520\) −7.16601 5.29150i −0.314250 0.232048i
\(521\) 14.2098i 0.622543i −0.950321 0.311272i \(-0.899245\pi\)
0.950321 0.311272i \(-0.100755\pi\)
\(522\) 0 0
\(523\) −18.9373 18.9373i −0.828068 0.828068i 0.159181 0.987249i \(-0.449115\pi\)
−0.987249 + 0.159181i \(0.949115\pi\)
\(524\) −17.7809 + 6.72057i −0.776764 + 0.293589i
\(525\) 0 0
\(526\) 2.58301 12.0000i 0.112624 0.523225i
\(527\) 31.2221 1.36006
\(528\) 0 0
\(529\) 4.16601 0.181131
\(530\) 1.74822 8.12179i 0.0759377 0.352788i
\(531\) 0 0
\(532\) −6.00000 15.8745i −0.260133 0.688247i
\(533\) 20.9304 + 20.9304i 0.906596 + 0.906596i
\(534\) 0 0
\(535\) 2.83399i 0.122524i
\(536\) 15.8219 2.38075i 0.683401 0.102833i
\(537\) 0 0
\(538\) −17.5830 + 11.3542i −0.758057 + 0.489516i
\(539\) −14.4207 14.4207i −0.621142 0.621142i
\(540\) 0 0
\(541\) −28.5203 + 28.5203i −1.22618 + 1.22618i −0.260785 + 0.965397i \(0.583981\pi\)
−0.965397 + 0.260785i \(0.916019\pi\)
\(542\) 8.78505 + 1.89099i 0.377350 + 0.0812248i
\(543\) 0 0
\(544\) −15.2915 27.2915i −0.655618 1.17011i
\(545\) 7.91094 0.338868
\(546\) 0 0
\(547\) 14.9373 14.9373i 0.638671 0.638671i −0.311557 0.950228i \(-0.600850\pi\)
0.950228 + 0.311557i \(0.100850\pi\)
\(548\) 8.46878 18.7605i 0.361769 0.801408i
\(549\) 0 0
\(550\) −24.2288 + 15.6458i −1.03312 + 0.667137i
\(551\) 44.6632i 1.90272i
\(552\) 0 0
\(553\) 15.8745i 0.675053i
\(554\) −17.9237 27.7564i −0.761506 1.17926i
\(555\) 0 0
\(556\) −14.5830 38.5830i −0.618457 1.63628i
\(557\) 18.7978 18.7978i 0.796489 0.796489i −0.186051 0.982540i \(-0.559569\pi\)
0.982540 + 0.186051i \(0.0595689\pi\)
\(558\) 0 0
\(559\) −1.87451 −0.0792832
\(560\) 5.53019 + 0.346998i 0.233693 + 0.0146633i
\(561\) 0 0
\(562\) −0.708497 + 3.29150i −0.0298862 + 0.138844i
\(563\) 5.31935 5.31935i 0.224184 0.224184i −0.586074 0.810258i \(-0.699327\pi\)
0.810258 + 0.586074i \(0.199327\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −2.80244 4.33981i −0.117795 0.182416i
\(567\) 0 0
\(568\) −22.5830 + 30.5830i −0.947562 + 1.28323i
\(569\) 41.0921i 1.72267i 0.508038 + 0.861335i \(0.330371\pi\)
−0.508038 + 0.861335i \(0.669629\pi\)
\(570\) 0 0
\(571\) 4.00000 + 4.00000i 0.167395 + 0.167395i 0.785833 0.618438i \(-0.212234\pi\)
−0.618438 + 0.785833i \(0.712234\pi\)
\(572\) −32.4125 14.6315i −1.35523 0.611774i
\(573\) 0 0
\(574\) −18.0000 3.87451i −0.751305 0.161719i
\(575\) 18.6243 0.776688
\(576\) 0 0
\(577\) −39.0405 −1.62528 −0.812639 0.582767i \(-0.801970\pi\)
−0.812639 + 0.582767i \(0.801970\pi\)
\(578\) 18.7792 + 4.04222i 0.781110 + 0.168134i
\(579\) 0 0
\(580\) −13.2915 6.00000i −0.551900 0.249136i
\(581\) 5.53019 + 5.53019i 0.229431 + 0.229431i
\(582\) 0 0
\(583\) 33.1660i 1.37360i
\(584\) −5.53019 + 7.48925i −0.228841 + 0.309907i
\(585\) 0 0
\(586\) −2.77124 4.29150i −0.114479 0.177280i
\(587\) 4.76150 + 4.76150i 0.196528 + 0.196528i 0.798510 0.601982i \(-0.205622\pi\)
−0.601982 + 0.798510i \(0.705622\pi\)
\(588\) 0 0
\(589\) 20.5830 20.5830i 0.848108 0.848108i
\(590\) −1.53737 + 7.14226i −0.0632927 + 0.294042i
\(591\) 0 0
\(592\) 0.228757 3.64575i 0.00940184 0.149839i
\(593\) −22.1208 −0.908391 −0.454195 0.890902i \(-0.650073\pi\)
−0.454195 + 0.890902i \(0.650073\pi\)
\(594\) 0 0
\(595\) −5.41699 + 5.41699i −0.222075 + 0.222075i
\(596\) −11.6556 30.8377i −0.477431 1.26316i
\(597\) 0 0
\(598\) 12.4575 + 19.2915i 0.509426 + 0.788888i
\(599\) 13.8628i 0.566420i −0.959058 0.283210i \(-0.908601\pi\)
0.959058 0.283210i \(-0.0913993\pi\)
\(600\) 0 0
\(601\) 3.29150i 0.134263i 0.997744 + 0.0671316i \(0.0213847\pi\)
−0.997744 + 0.0671316i \(0.978615\pi\)
\(602\) 0.979531 0.632534i 0.0399227 0.0257801i
\(603\) 0 0
\(604\) −8.52026 + 18.8745i −0.346684 + 0.767993i
\(605\) 6.89407 6.89407i 0.280284 0.280284i
\(606\) 0 0
\(607\) 14.1033 0.572434 0.286217 0.958165i \(-0.407602\pi\)
0.286217 + 0.958165i \(0.407602\pi\)
\(608\) −28.0726 7.91094i −1.13850 0.320831i
\(609\) 0 0
\(610\) 1.06275 + 0.228757i 0.0430293 + 0.00926208i
\(611\) 24.0798 24.0798i 0.974165 0.974165i
\(612\) 0 0
\(613\) 26.6458 + 26.6458i 1.07621 + 1.07621i 0.996846 + 0.0793662i \(0.0252897\pi\)
0.0793662 + 0.996846i \(0.474710\pi\)
\(614\) −33.6028 + 21.6991i −1.35610 + 0.875703i
\(615\) 0 0
\(616\) 21.8745 3.29150i 0.881349 0.132618i
\(617\) 31.6438i 1.27393i 0.770893 + 0.636965i \(0.219810\pi\)
−0.770893 + 0.636965i \(0.780190\pi\)
\(618\) 0 0
\(619\) −21.1660 21.1660i −0.850734 0.850734i 0.139490 0.990224i \(-0.455454\pi\)
−0.990224 + 0.139490i \(0.955454\pi\)
\(620\) 3.36028 + 8.89047i 0.134952 + 0.357050i
\(621\) 0 0
\(622\) 2.58301 12.0000i 0.103569 0.481156i
\(623\) −3.91813 −0.156976
\(624\) 0 0
\(625\) −14.8745 −0.594980
\(626\) 2.76510 12.8459i 0.110515 0.513427i
\(627\) 0 0
\(628\) −17.5830 + 6.64575i −0.701638 + 0.265194i
\(629\) 3.57113 + 3.57113i 0.142390 + 0.142390i
\(630\) 0 0
\(631\) 8.22876i 0.327582i 0.986495 + 0.163791i \(0.0523722\pi\)
−0.986495 + 0.163791i \(0.947628\pi\)
\(632\) 21.9473 + 16.2062i 0.873015 + 0.644649i
\(633\) 0 0
\(634\) 1.00000 0.645751i 0.0397151 0.0256461i
\(635\) −0.557842 0.557842i −0.0221373 0.0221373i
\(636\) 0 0
\(637\) 11.3542 11.3542i 0.449872 0.449872i
\(638\) −56.9140 12.2508i −2.25325 0.485012i
\(639\) 0 0
\(640\) 6.12549 7.29150i 0.242131 0.288222i
\(641\) −16.5906 −0.655288 −0.327644 0.944801i \(-0.606255\pi\)
−0.327644 + 0.944801i \(0.606255\pi\)
\(642\) 0 0
\(643\) −3.64575 + 3.64575i −0.143774 + 0.143774i −0.775330 0.631556i \(-0.782417\pi\)
0.631556 + 0.775330i \(0.282417\pi\)
\(644\) −13.0194 5.87719i −0.513038 0.231594i
\(645\) 0 0
\(646\) 33.8745 21.8745i 1.33277 0.860641i
\(647\) 4.33981i 0.170616i 0.996355 + 0.0853079i \(0.0271874\pi\)
−0.996355 + 0.0853079i \(0.972813\pi\)
\(648\) 0 0
\(649\) 29.1660i 1.14487i
\(650\) −12.3188 19.0767i −0.483184 0.748252i
\(651\) 0 0
\(652\) 30.8118 11.6458i 1.20668 0.456083i
\(653\) 20.7569 20.7569i 0.812280 0.812280i −0.172696 0.984975i \(-0.555248\pi\)
0.984975 + 0.172696i \(0.0552477\pi\)
\(654\) 0 0
\(655\) 8.00000 0.312586
\(656\) −23.7328 + 20.9304i −0.926611 + 0.817194i
\(657\) 0 0
\(658\) −4.45751 + 20.7085i −0.173772 + 0.807301i
\(659\) −24.9232 + 24.9232i −0.970870 + 0.970870i −0.999588 0.0287175i \(-0.990858\pi\)
0.0287175 + 0.999588i \(0.490858\pi\)
\(660\) 0 0
\(661\) −2.77124 2.77124i −0.107789 0.107789i 0.651155 0.758944i \(-0.274285\pi\)
−0.758944 + 0.651155i \(0.774285\pi\)
\(662\) −8.67963 13.4411i −0.337343 0.522404i
\(663\) 0 0
\(664\) 13.2915 2.00000i 0.515810 0.0776151i
\(665\) 7.14226i 0.276965i
\(666\) 0 0
\(667\) 26.5830 + 26.5830i 1.02930 + 1.02930i
\(668\) 14.6315 32.4125i 0.566110 1.25408i
\(669\) 0 0
\(670\) −6.58301 1.41699i −0.254324 0.0547433i
\(671\) 4.33981 0.167537
\(672\) 0 0
\(673\) 20.0000 0.770943 0.385472 0.922720i \(-0.374039\pi\)
0.385472 + 0.922720i \(0.374039\pi\)
\(674\) 6.50972 + 1.40122i 0.250745 + 0.0539730i
\(675\) 0 0
\(676\) 0.822876 1.82288i 0.0316491 0.0701106i
\(677\) 14.0363 + 14.0363i 0.539460 + 0.539460i 0.923370 0.383911i \(-0.125423\pi\)
−0.383911 + 0.923370i \(0.625423\pi\)
\(678\) 0 0
\(679\) 17.4170i 0.668403i
\(680\) 1.95906 + 13.0194i 0.0751266 + 0.499273i
\(681\) 0 0
\(682\) 20.5830 + 31.8745i 0.788164 + 1.22054i
\(683\) 0.557842 + 0.557842i 0.0213452 + 0.0213452i 0.717699 0.696354i \(-0.245195\pi\)
−0.696354 + 0.717699i \(0.745195\pi\)
\(684\) 0 0
\(685\) −6.12549 + 6.12549i −0.234043 + 0.234043i
\(686\) −5.53019 + 25.6919i −0.211144 + 0.980921i
\(687\) 0 0
\(688\) 0.125492 2.00000i 0.00478434 0.0762493i
\(689\) 26.1136 0.994848
\(690\) 0 0
\(691\) −3.64575 + 3.64575i −0.138691 + 0.138691i −0.773044 0.634353i \(-0.781267\pi\)
0.634353 + 0.773044i \(0.281267\pi\)
\(692\) −13.0568 + 4.93500i −0.496345 + 0.187601i
\(693\) 0 0
\(694\) −3.64575 5.64575i −0.138391 0.214310i
\(695\) 17.3593i 0.658474i
\(696\) 0 0
\(697\) 43.7490i 1.65711i
\(698\) 5.42477 3.50305i 0.205330 0.132592i
\(699\) 0 0
\(700\) 12.8745 + 5.81176i 0.486611 + 0.219664i
\(701\) 4.16632 4.16632i 0.157360 0.157360i −0.624036 0.781396i \(-0.714508\pi\)
0.781396 + 0.624036i \(0.214508\pi\)
\(702\) 0 0
\(703\) 4.70850 0.177584
\(704\) 17.7809 33.6028i 0.670145 1.26645i
\(705\) 0 0
\(706\) −9.87451 2.12549i −0.371632 0.0799940i
\(707\) 0.979531 0.979531i 0.0368391 0.0368391i
\(708\) 0 0
\(709\) −8.77124 8.77124i −0.329411 0.329411i 0.522951 0.852362i \(-0.324831\pi\)
−0.852362 + 0.522951i \(0.824831\pi\)
\(710\) 13.4411 8.67963i 0.504437 0.325741i
\(711\) 0 0
\(712\) −4.00000 + 5.41699i −0.149906 + 0.203010i
\(713\) 24.5015i 0.917589i
\(714\) 0 0
\(715\) 10.5830 + 10.5830i 0.395782 + 0.395782i
\(716\) 6.29888 2.38075i 0.235400 0.0889729i
\(717\) 0 0
\(718\) 1.41699 6.58301i 0.0528818 0.245676i
\(719\) 40.3234 1.50381 0.751904 0.659272i \(-0.229135\pi\)
0.751904 + 0.659272i \(0.229135\pi\)
\(720\) 0 0
\(721\) 27.8745 1.03810
\(722\) 2.25666 10.4839i 0.0839841 0.390169i
\(723\) 0 0
\(724\) −0.645751 1.70850i −0.0239992 0.0634958i
\(725\) −26.2871 26.2871i −0.976278 0.976278i
\(726\) 0 0
\(727\) 33.3948i 1.23854i 0.785177 + 0.619272i \(0.212572\pi\)
−0.785177 + 0.619272i \(0.787428\pi\)
\(728\) 2.59160 + 17.2231i 0.0960510 + 0.638331i
\(729\) 0 0
\(730\) 3.29150 2.12549i 0.121824 0.0786680i
\(731\) 1.95906 + 1.95906i 0.0724586 + 0.0724586i
\(732\) 0 0
\(733\) −12.6458 + 12.6458i −0.467081 + 0.467081i −0.900968 0.433886i \(-0.857142\pi\)
0.433886 + 0.900968i \(0.357142\pi\)
\(734\) 48.1289 + 10.3598i 1.77647 + 0.382386i
\(735\) 0 0
\(736\) −21.4170 + 12.0000i −0.789441 + 0.442326i
\(737\) −26.8823 −0.990221
\(738\) 0 0
\(739\) −9.16601 + 9.16601i −0.337177 + 0.337177i −0.855304 0.518127i \(-0.826630\pi\)
0.518127 + 0.855304i \(0.326630\pi\)
\(740\) −0.632534 + 1.40122i −0.0232524 + 0.0515099i
\(741\) 0 0
\(742\) −13.6458 + 8.81176i −0.500951 + 0.323490i
\(743\) 22.5425i 0.827002i 0.910504 + 0.413501i \(0.135694\pi\)
−0.910504 + 0.413501i \(0.864306\pi\)
\(744\) 0 0
\(745\) 13.8745i 0.508323i
\(746\) 12.9514 + 20.0563i 0.474183 + 0.734312i
\(747\) 0 0
\(748\) 18.5830 + 49.1660i 0.679462 + 1.79769i
\(749\) 3.91813 3.91813i 0.143165 0.143165i
\(750\) 0 0
\(751\) 12.9373 0.472087 0.236044 0.971742i \(-0.424149\pi\)
0.236044 + 0.971742i \(0.424149\pi\)
\(752\) 24.0798 + 27.3040i 0.878101 + 0.995673i
\(753\) 0 0
\(754\) 9.64575 44.8118i 0.351278 1.63195i
\(755\) 6.16272 6.16272i 0.224284 0.224284i
\(756\) 0 0
\(757\) −7.22876 7.22876i −0.262734 0.262734i 0.563430 0.826164i \(-0.309481\pi\)
−0.826164 + 0.563430i \(0.809481\pi\)
\(758\) 9.06397 + 14.0363i 0.329218 + 0.509822i
\(759\) 0 0
\(760\) 9.87451 + 7.29150i 0.358186 + 0.264491i
\(761\) 7.91094i 0.286771i 0.989667 + 0.143386i \(0.0457989\pi\)
−0.989667 + 0.143386i \(0.954201\pi\)
\(762\) 0 0
\(763\) −10.9373 10.9373i −0.395955 0.395955i
\(764\) −16.5906 7.48925i −0.600226 0.270952i
\(765\) 0 0
\(766\) 12.5830 + 2.70850i 0.454642 + 0.0978620i
\(767\) −22.9641 −0.829187
\(768\) 0 0
\(769\) 17.2915 0.623548 0.311774 0.950156i \(-0.399077\pi\)
0.311774 + 0.950156i \(0.399077\pi\)
\(770\) −9.10132 1.95906i −0.327989 0.0705997i
\(771\) 0 0
\(772\) 21.6458 + 9.77124i 0.779048 + 0.351675i
\(773\) 21.5256 + 21.5256i 0.774221 + 0.774221i 0.978841 0.204620i \(-0.0655960\pi\)
−0.204620 + 0.978841i \(0.565596\pi\)
\(774\) 0 0
\(775\) 24.2288i 0.870323i
\(776\) −24.0798 17.7809i −0.864415 0.638299i
\(777\) 0 0
\(778\) −22.5203 34.8745i −0.807390 1.25031i
\(779\) −28.8413 28.8413i −1.03335 1.03335i
\(780\) 0 0
\(781\) 45.1660 45.1660i 1.61617 1.61617i
\(782\) 7.14226 33.1811i 0.255407 1.18656i
\(783\) 0 0
\(784\) 11.3542 + 12.8745i 0.405509 + 0.459804i
\(785\) 7.91094 0.282354
\(786\) 0 0
\(787\) 6.22876 6.22876i 0.222031 0.222031i −0.587322 0.809353i \(-0.699818\pi\)
0.809353 + 0.587322i \(0.199818\pi\)
\(788\) 8.50613 + 22.5051i 0.303018 + 0.801711i