Properties

Label 144.2.k.b.109.3
Level $144$
Weight $2$
Character 144.109
Analytic conductor $1.150$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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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: 8.0.18939904.2
Defining polynomial: \(x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 109.3
Root \(0.500000 - 1.44392i\) of defining polynomial
Character \(\chi\) \(=\) 144.109
Dual form 144.2.k.b.37.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.167452 + 1.40426i) q^{2} +(-1.94392 + 0.470294i) q^{4} +(-1.74912 + 1.74912i) q^{5} +2.55765i q^{7} +(-0.985930 - 2.65103i) q^{8} +O(q^{10})\) \(q+(0.167452 + 1.40426i) q^{2} +(-1.94392 + 0.470294i) q^{4} +(-1.74912 + 1.74912i) q^{5} +2.55765i q^{7} +(-0.985930 - 2.65103i) q^{8} +(-2.74912 - 2.16333i) q^{10} +(-0.473626 + 0.473626i) q^{11} +(2.88784 + 2.88784i) q^{13} +(-3.59161 + 0.428283i) q^{14} +(3.55765 - 1.82843i) q^{16} +6.44549 q^{17} +(-4.55765 - 4.55765i) q^{19} +(2.57754 - 4.22274i) q^{20} +(-0.744406 - 0.585786i) q^{22} -2.82843i q^{23} -1.11882i q^{25} +(-3.57172 + 4.53887i) q^{26} +(-1.20285 - 4.97186i) q^{28} +(3.07931 + 3.07931i) q^{29} +6.55765 q^{31} +(3.16333 + 4.68971i) q^{32} +(1.07931 + 9.05117i) q^{34} +(-4.47363 - 4.47363i) q^{35} +(-2.72922 + 2.72922i) q^{37} +(5.63696 - 7.16333i) q^{38} +(6.36147 + 2.91245i) q^{40} -0.788632i q^{41} +(-0.389604 + 0.389604i) q^{43} +(0.697947 - 1.14343i) q^{44} +(3.97186 - 0.473626i) q^{46} -2.82843 q^{47} +0.458440 q^{49} +(1.57113 - 0.187349i) q^{50} +(-6.97186 - 4.25559i) q^{52} +(2.57754 - 2.57754i) q^{53} -1.65685i q^{55} +(6.78039 - 2.52166i) q^{56} +(-3.80853 + 4.83980i) q^{58} +(-4.00000 + 4.00000i) q^{59} +(-4.38607 - 4.38607i) q^{61} +(1.09809 + 9.20867i) q^{62} +(-6.05588 + 5.22746i) q^{64} -10.1023 q^{65} +(-2.11882 - 2.11882i) q^{67} +(-12.5295 + 3.03127i) q^{68} +(5.53304 - 7.03127i) q^{70} +5.11529i q^{71} -14.7721i q^{73} +(-4.28956 - 3.37553i) q^{74} +(11.0031 + 6.71627i) q^{76} +(-1.21137 - 1.21137i) q^{77} -6.32000 q^{79} +(-3.02461 + 9.42088i) q^{80} +(1.10745 - 0.132058i) q^{82} +(-0.641669 - 0.641669i) q^{83} +(-11.2739 + 11.2739i) q^{85} +(-0.612348 - 0.481868i) q^{86} +(1.72256 + 0.788632i) q^{88} -6.31724i q^{89} +(-7.38607 + 7.38607i) q^{91} +(1.33019 + 5.49824i) q^{92} +(-0.473626 - 3.97186i) q^{94} +15.9437 q^{95} +12.6533 q^{97} +(0.0767667 + 0.643772i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{4} + 12q^{8} + O(q^{10}) \) \( 8q - 4q^{4} + 12q^{8} - 8q^{10} + 8q^{11} - 12q^{14} - 8q^{19} - 16q^{20} - 20q^{26} + 8q^{28} + 16q^{29} + 24q^{31} - 24q^{35} - 16q^{37} + 8q^{38} + 16q^{40} - 8q^{43} + 40q^{44} - 8q^{46} - 8q^{49} + 36q^{50} - 16q^{52} - 16q^{53} - 16q^{58} - 32q^{59} + 16q^{61} + 12q^{62} + 8q^{64} + 16q^{65} - 16q^{67} - 32q^{68} + 32q^{70} - 52q^{74} + 8q^{76} - 16q^{77} - 24q^{79} - 8q^{80} + 40q^{82} + 40q^{83} - 16q^{85} + 16q^{86} + 32q^{88} - 8q^{91} + 16q^{92} + 8q^{94} + 48q^{95} + 40q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.167452 + 1.40426i 0.118406 + 0.992965i
\(3\) 0 0
\(4\) −1.94392 + 0.470294i −0.971960 + 0.235147i
\(5\) −1.74912 + 1.74912i −0.782229 + 0.782229i −0.980207 0.197977i \(-0.936563\pi\)
0.197977 + 0.980207i \(0.436563\pi\)
\(6\) 0 0
\(7\) 2.55765i 0.966700i 0.875427 + 0.483350i \(0.160580\pi\)
−0.875427 + 0.483350i \(0.839420\pi\)
\(8\) −0.985930 2.65103i −0.348579 0.937279i
\(9\) 0 0
\(10\) −2.74912 2.16333i −0.869347 0.684105i
\(11\) −0.473626 + 0.473626i −0.142804 + 0.142804i −0.774894 0.632091i \(-0.782197\pi\)
0.632091 + 0.774894i \(0.282197\pi\)
\(12\) 0 0
\(13\) 2.88784 + 2.88784i 0.800943 + 0.800943i 0.983243 0.182300i \(-0.0583543\pi\)
−0.182300 + 0.983243i \(0.558354\pi\)
\(14\) −3.59161 + 0.428283i −0.959899 + 0.114463i
\(15\) 0 0
\(16\) 3.55765 1.82843i 0.889412 0.457107i
\(17\) 6.44549 1.56326 0.781630 0.623742i \(-0.214389\pi\)
0.781630 + 0.623742i \(0.214389\pi\)
\(18\) 0 0
\(19\) −4.55765 4.55765i −1.04560 1.04560i −0.998910 0.0466864i \(-0.985134\pi\)
−0.0466864 0.998910i \(-0.514866\pi\)
\(20\) 2.57754 4.22274i 0.576357 0.944234i
\(21\) 0 0
\(22\) −0.744406 0.585786i −0.158708 0.124890i
\(23\) 2.82843i 0.589768i −0.955533 0.294884i \(-0.904719\pi\)
0.955533 0.294884i \(-0.0952810\pi\)
\(24\) 0 0
\(25\) 1.11882i 0.223765i
\(26\) −3.57172 + 4.53887i −0.700471 + 0.890145i
\(27\) 0 0
\(28\) −1.20285 4.97186i −0.227317 0.939593i
\(29\) 3.07931 + 3.07931i 0.571813 + 0.571813i 0.932635 0.360821i \(-0.117504\pi\)
−0.360821 + 0.932635i \(0.617504\pi\)
\(30\) 0 0
\(31\) 6.55765 1.17779 0.588894 0.808210i \(-0.299563\pi\)
0.588894 + 0.808210i \(0.299563\pi\)
\(32\) 3.16333 + 4.68971i 0.559203 + 0.829031i
\(33\) 0 0
\(34\) 1.07931 + 9.05117i 0.185100 + 1.55226i
\(35\) −4.47363 4.47363i −0.756181 0.756181i
\(36\) 0 0
\(37\) −2.72922 + 2.72922i −0.448681 + 0.448681i −0.894916 0.446235i \(-0.852765\pi\)
0.446235 + 0.894916i \(0.352765\pi\)
\(38\) 5.63696 7.16333i 0.914435 1.16205i
\(39\) 0 0
\(40\) 6.36147 + 2.91245i 1.00584 + 0.460499i
\(41\) 0.788632i 0.123164i −0.998102 0.0615818i \(-0.980385\pi\)
0.998102 0.0615818i \(-0.0196145\pi\)
\(42\) 0 0
\(43\) −0.389604 + 0.389604i −0.0594141 + 0.0594141i −0.736190 0.676775i \(-0.763377\pi\)
0.676775 + 0.736190i \(0.263377\pi\)
\(44\) 0.697947 1.14343i 0.105219 0.172379i
\(45\) 0 0
\(46\) 3.97186 0.473626i 0.585619 0.0698323i
\(47\) −2.82843 −0.412568 −0.206284 0.978492i \(-0.566137\pi\)
−0.206284 + 0.978492i \(0.566137\pi\)
\(48\) 0 0
\(49\) 0.458440 0.0654915
\(50\) 1.57113 0.187349i 0.222191 0.0264952i
\(51\) 0 0
\(52\) −6.97186 4.25559i −0.966823 0.590145i
\(53\) 2.57754 2.57754i 0.354053 0.354053i −0.507562 0.861615i \(-0.669453\pi\)
0.861615 + 0.507562i \(0.169453\pi\)
\(54\) 0 0
\(55\) 1.65685i 0.223410i
\(56\) 6.78039 2.52166i 0.906068 0.336971i
\(57\) 0 0
\(58\) −3.80853 + 4.83980i −0.500084 + 0.635497i
\(59\) −4.00000 + 4.00000i −0.520756 + 0.520756i −0.917800 0.397044i \(-0.870036\pi\)
0.397044 + 0.917800i \(0.370036\pi\)
\(60\) 0 0
\(61\) −4.38607 4.38607i −0.561579 0.561579i 0.368177 0.929756i \(-0.379982\pi\)
−0.929756 + 0.368177i \(0.879982\pi\)
\(62\) 1.09809 + 9.20867i 0.139458 + 1.16950i
\(63\) 0 0
\(64\) −6.05588 + 5.22746i −0.756985 + 0.653432i
\(65\) −10.1023 −1.25304
\(66\) 0 0
\(67\) −2.11882 2.11882i −0.258856 0.258856i 0.565733 0.824589i \(-0.308593\pi\)
−0.824589 + 0.565733i \(0.808593\pi\)
\(68\) −12.5295 + 3.03127i −1.51943 + 0.367596i
\(69\) 0 0
\(70\) 5.53304 7.03127i 0.661325 0.840398i
\(71\) 5.11529i 0.607074i 0.952820 + 0.303537i \(0.0981676\pi\)
−0.952820 + 0.303537i \(0.901832\pi\)
\(72\) 0 0
\(73\) 14.7721i 1.72895i −0.502676 0.864475i \(-0.667651\pi\)
0.502676 0.864475i \(-0.332349\pi\)
\(74\) −4.28956 3.37553i −0.498651 0.392398i
\(75\) 0 0
\(76\) 11.0031 + 6.71627i 1.26215 + 0.770409i
\(77\) −1.21137 1.21137i −0.138048 0.138048i
\(78\) 0 0
\(79\) −6.32000 −0.711055 −0.355528 0.934666i \(-0.615699\pi\)
−0.355528 + 0.934666i \(0.615699\pi\)
\(80\) −3.02461 + 9.42088i −0.338162 + 1.05329i
\(81\) 0 0
\(82\) 1.10745 0.132058i 0.122297 0.0145834i
\(83\) −0.641669 0.641669i −0.0704323 0.0704323i 0.671013 0.741445i \(-0.265859\pi\)
−0.741445 + 0.671013i \(0.765859\pi\)
\(84\) 0 0
\(85\) −11.2739 + 11.2739i −1.22283 + 1.22283i
\(86\) −0.612348 0.481868i −0.0660311 0.0519611i
\(87\) 0 0
\(88\) 1.72256 + 0.788632i 0.183625 + 0.0840685i
\(89\) 6.31724i 0.669626i −0.942285 0.334813i \(-0.891327\pi\)
0.942285 0.334813i \(-0.108673\pi\)
\(90\) 0 0
\(91\) −7.38607 + 7.38607i −0.774271 + 0.774271i
\(92\) 1.33019 + 5.49824i 0.138682 + 0.573231i
\(93\) 0 0
\(94\) −0.473626 3.97186i −0.0488508 0.409666i
\(95\) 15.9437 1.63579
\(96\) 0 0
\(97\) 12.6533 1.28475 0.642375 0.766390i \(-0.277949\pi\)
0.642375 + 0.766390i \(0.277949\pi\)
\(98\) 0.0767667 + 0.643772i 0.00775461 + 0.0650308i
\(99\) 0 0
\(100\) 0.526176 + 2.17490i 0.0526176 + 0.217490i
\(101\) −7.52480 + 7.52480i −0.748745 + 0.748745i −0.974244 0.225498i \(-0.927599\pi\)
0.225498 + 0.974244i \(0.427599\pi\)
\(102\) 0 0
\(103\) 3.33686i 0.328790i −0.986395 0.164395i \(-0.947433\pi\)
0.986395 0.164395i \(-0.0525672\pi\)
\(104\) 4.80853 10.5029i 0.471515 1.02990i
\(105\) 0 0
\(106\) 4.05117 + 3.18794i 0.393484 + 0.309640i
\(107\) 14.0625 14.0625i 1.35948 1.35948i 0.484918 0.874560i \(-0.338849\pi\)
0.874560 0.484918i \(-0.161151\pi\)
\(108\) 0 0
\(109\) 2.76901 + 2.76901i 0.265224 + 0.265224i 0.827172 0.561949i \(-0.189948\pi\)
−0.561949 + 0.827172i \(0.689948\pi\)
\(110\) 2.32666 0.277444i 0.221839 0.0264532i
\(111\) 0 0
\(112\) 4.67647 + 9.09921i 0.441885 + 0.859794i
\(113\) −2.23765 −0.210500 −0.105250 0.994446i \(-0.533564\pi\)
−0.105250 + 0.994446i \(0.533564\pi\)
\(114\) 0 0
\(115\) 4.94725 + 4.94725i 0.461334 + 0.461334i
\(116\) −7.43411 4.53775i −0.690240 0.421320i
\(117\) 0 0
\(118\) −6.28687 4.94725i −0.578753 0.455431i
\(119\) 16.4853i 1.51120i
\(120\) 0 0
\(121\) 10.5514i 0.959214i
\(122\) 5.42475 6.89367i 0.491134 0.624123i
\(123\) 0 0
\(124\) −12.7475 + 3.08402i −1.14476 + 0.276953i
\(125\) −6.78863 6.78863i −0.607194 0.607194i
\(126\) 0 0
\(127\) 12.2145 1.08386 0.541931 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(128\) −8.35480 7.62872i −0.738467 0.674290i
\(129\) 0 0
\(130\) −1.69166 14.1864i −0.148368 1.24423i
\(131\) 3.77568 + 3.77568i 0.329883 + 0.329883i 0.852542 0.522659i \(-0.175060\pi\)
−0.522659 + 0.852542i \(0.675060\pi\)
\(132\) 0 0
\(133\) 11.6569 11.6569i 1.01078 1.01078i
\(134\) 2.62059 3.33019i 0.226384 0.287685i
\(135\) 0 0
\(136\) −6.35480 17.0872i −0.544920 1.46521i
\(137\) 5.10587i 0.436224i 0.975924 + 0.218112i \(0.0699898\pi\)
−0.975924 + 0.218112i \(0.930010\pi\)
\(138\) 0 0
\(139\) 11.7757 11.7757i 0.998800 0.998800i −0.00119925 0.999999i \(-0.500382\pi\)
0.999999 + 0.00119925i \(0.000381735\pi\)
\(140\) 10.8003 + 6.59245i 0.912791 + 0.557164i
\(141\) 0 0
\(142\) −7.18323 + 0.856566i −0.602803 + 0.0718814i
\(143\) −2.73551 −0.228755
\(144\) 0 0
\(145\) −10.7721 −0.894578
\(146\) 20.7440 2.47363i 1.71679 0.204719i
\(147\) 0 0
\(148\) 4.02185 6.58892i 0.330594 0.541606i
\(149\) 7.90774 7.90774i 0.647827 0.647827i −0.304640 0.952467i \(-0.598536\pi\)
0.952467 + 0.304640i \(0.0985363\pi\)
\(150\) 0 0
\(151\) 14.6506i 1.19225i 0.802893 + 0.596123i \(0.203293\pi\)
−0.802893 + 0.596123i \(0.796707\pi\)
\(152\) −7.58892 + 16.5760i −0.615543 + 1.34449i
\(153\) 0 0
\(154\) 1.49824 1.90393i 0.120731 0.153423i
\(155\) −11.4701 + 11.4701i −0.921300 + 0.921300i
\(156\) 0 0
\(157\) −3.15196 3.15196i −0.251553 0.251553i 0.570054 0.821607i \(-0.306922\pi\)
−0.821607 + 0.570054i \(0.806922\pi\)
\(158\) −1.05830 8.87495i −0.0841935 0.706053i
\(159\) 0 0
\(160\) −13.7359 2.66981i −1.08592 0.211067i
\(161\) 7.23412 0.570128
\(162\) 0 0
\(163\) 5.50490 + 5.50490i 0.431177 + 0.431177i 0.889029 0.457852i \(-0.151381\pi\)
−0.457852 + 0.889029i \(0.651381\pi\)
\(164\) 0.370889 + 1.53304i 0.0289616 + 0.119710i
\(165\) 0 0
\(166\) 0.793624 1.00852i 0.0615972 0.0782765i
\(167\) 20.1814i 1.56168i −0.624730 0.780841i \(-0.714791\pi\)
0.624730 0.780841i \(-0.285209\pi\)
\(168\) 0 0
\(169\) 3.67923i 0.283018i
\(170\) −17.7194 13.9437i −1.35902 1.06943i
\(171\) 0 0
\(172\) 0.574131 0.940588i 0.0437771 0.0717191i
\(173\) −4.35322 4.35322i −0.330969 0.330969i 0.521985 0.852955i \(-0.325192\pi\)
−0.852955 + 0.521985i \(0.825192\pi\)
\(174\) 0 0
\(175\) 2.86156 0.216313
\(176\) −0.819003 + 2.55098i −0.0617347 + 0.192288i
\(177\) 0 0
\(178\) 8.87108 1.05783i 0.664915 0.0792880i
\(179\) 13.2833 + 13.2833i 0.992843 + 0.992843i 0.999975 0.00713130i \(-0.00226998\pi\)
−0.00713130 + 0.999975i \(0.502270\pi\)
\(180\) 0 0
\(181\) 6.34628 6.34628i 0.471715 0.471715i −0.430754 0.902469i \(-0.641752\pi\)
0.902469 + 0.430754i \(0.141752\pi\)
\(182\) −11.6088 9.13519i −0.860503 0.677145i
\(183\) 0 0
\(184\) −7.49824 + 2.78863i −0.552777 + 0.205581i
\(185\) 9.54745i 0.701943i
\(186\) 0 0
\(187\) −3.05275 + 3.05275i −0.223239 + 0.223239i
\(188\) 5.49824 1.33019i 0.401000 0.0970142i
\(189\) 0 0
\(190\) 2.66981 + 22.3892i 0.193688 + 1.62428i
\(191\) −5.60058 −0.405243 −0.202622 0.979257i \(-0.564946\pi\)
−0.202622 + 0.979257i \(0.564946\pi\)
\(192\) 0 0
\(193\) −19.4514 −1.40014 −0.700071 0.714074i \(-0.746848\pi\)
−0.700071 + 0.714074i \(0.746848\pi\)
\(194\) 2.11882 + 17.7686i 0.152123 + 1.27571i
\(195\) 0 0
\(196\) −0.891171 + 0.215602i −0.0636551 + 0.0154001i
\(197\) −1.23793 + 1.23793i −0.0881988 + 0.0881988i −0.749830 0.661631i \(-0.769865\pi\)
0.661631 + 0.749830i \(0.269865\pi\)
\(198\) 0 0
\(199\) 0.993710i 0.0704422i 0.999380 + 0.0352211i \(0.0112135\pi\)
−0.999380 + 0.0352211i \(0.988786\pi\)
\(200\) −2.96603 + 1.10308i −0.209730 + 0.0779997i
\(201\) 0 0
\(202\) −11.8268 9.30676i −0.832134 0.654822i
\(203\) −7.87579 + 7.87579i −0.552772 + 0.552772i
\(204\) 0 0
\(205\) 1.37941 + 1.37941i 0.0963422 + 0.0963422i
\(206\) 4.68583 0.558763i 0.326477 0.0389309i
\(207\) 0 0
\(208\) 15.5541 + 4.99371i 1.07848 + 0.346251i
\(209\) 4.31724 0.298630
\(210\) 0 0
\(211\) 4.22432 + 4.22432i 0.290814 + 0.290814i 0.837402 0.546588i \(-0.184073\pi\)
−0.546588 + 0.837402i \(0.684073\pi\)
\(212\) −3.79834 + 6.22274i −0.260871 + 0.427380i
\(213\) 0 0
\(214\) 22.1023 + 17.3927i 1.51088 + 1.18894i
\(215\) 1.36293i 0.0929509i
\(216\) 0 0
\(217\) 16.7721i 1.13857i
\(218\) −3.42475 + 4.35211i −0.231954 + 0.294762i
\(219\) 0 0
\(220\) 0.779208 + 3.22079i 0.0525342 + 0.217146i
\(221\) 18.6135 + 18.6135i 1.25208 + 1.25208i
\(222\) 0 0
\(223\) −23.7659 −1.59148 −0.795740 0.605639i \(-0.792918\pi\)
−0.795740 + 0.605639i \(0.792918\pi\)
\(224\) −11.9946 + 8.09069i −0.801424 + 0.540582i
\(225\) 0 0
\(226\) −0.374699 3.14225i −0.0249246 0.209019i
\(227\) 0.641669 + 0.641669i 0.0425891 + 0.0425891i 0.728081 0.685492i \(-0.240413\pi\)
−0.685492 + 0.728081i \(0.740413\pi\)
\(228\) 0 0
\(229\) 5.34275 5.34275i 0.353059 0.353059i −0.508188 0.861246i \(-0.669684\pi\)
0.861246 + 0.508188i \(0.169684\pi\)
\(230\) −6.11882 + 7.77568i −0.403463 + 0.512713i
\(231\) 0 0
\(232\) 5.12735 11.1993i 0.336627 0.735271i
\(233\) 23.2271i 1.52166i 0.648954 + 0.760828i \(0.275207\pi\)
−0.648954 + 0.760828i \(0.724793\pi\)
\(234\) 0 0
\(235\) 4.94725 4.94725i 0.322723 0.322723i
\(236\) 5.89450 9.65685i 0.383699 0.628608i
\(237\) 0 0
\(238\) −23.1497 + 2.76049i −1.50057 + 0.178936i
\(239\) −26.9213 −1.74140 −0.870698 0.491817i \(-0.836333\pi\)
−0.870698 + 0.491817i \(0.836333\pi\)
\(240\) 0 0
\(241\) −10.3494 −0.666664 −0.333332 0.942809i \(-0.608173\pi\)
−0.333332 + 0.942809i \(0.608173\pi\)
\(242\) −14.8169 + 1.76685i −0.952466 + 0.113577i
\(243\) 0 0
\(244\) 10.5889 + 6.46343i 0.677886 + 0.413779i
\(245\) −0.801866 + 0.801866i −0.0512293 + 0.0512293i
\(246\) 0 0
\(247\) 26.3235i 1.67492i
\(248\) −6.46538 17.3845i −0.410552 1.10392i
\(249\) 0 0
\(250\) 8.39627 10.6698i 0.531027 0.674818i
\(251\) 9.75696 9.75696i 0.615854 0.615854i −0.328611 0.944465i \(-0.606581\pi\)
0.944465 + 0.328611i \(0.106581\pi\)
\(252\) 0 0
\(253\) 1.33962 + 1.33962i 0.0842209 + 0.0842209i
\(254\) 2.04534 + 17.1524i 0.128336 + 1.07624i
\(255\) 0 0
\(256\) 9.31371 13.0098i 0.582107 0.813112i
\(257\) −16.9965 −1.06021 −0.530105 0.847932i \(-0.677848\pi\)
−0.530105 + 0.847932i \(0.677848\pi\)
\(258\) 0 0
\(259\) −6.98038 6.98038i −0.433740 0.433740i
\(260\) 19.6381 4.75107i 1.21791 0.294649i
\(261\) 0 0
\(262\) −4.66981 + 5.93430i −0.288502 + 0.366622i
\(263\) 29.9929i 1.84944i −0.380643 0.924722i \(-0.624297\pi\)
0.380643 0.924722i \(-0.375703\pi\)
\(264\) 0 0
\(265\) 9.01686i 0.553901i
\(266\) 18.3213 + 14.4173i 1.12335 + 0.883984i
\(267\) 0 0
\(268\) 5.11529 + 3.12235i 0.312466 + 0.190728i
\(269\) −20.6003 20.6003i −1.25602 1.25602i −0.952976 0.303046i \(-0.901996\pi\)
−0.303046 0.952976i \(-0.598004\pi\)
\(270\) 0 0
\(271\) −26.6506 −1.61891 −0.809453 0.587184i \(-0.800236\pi\)
−0.809453 + 0.587184i \(0.800236\pi\)
\(272\) 22.9308 11.7851i 1.39038 0.714577i
\(273\) 0 0
\(274\) −7.16999 + 0.854988i −0.433155 + 0.0516517i
\(275\) 0.529904 + 0.529904i 0.0319544 + 0.0319544i
\(276\) 0 0
\(277\) 12.1220 12.1220i 0.728338 0.728338i −0.241951 0.970289i \(-0.577787\pi\)
0.970289 + 0.241951i \(0.0777872\pi\)
\(278\) 18.5080 + 14.5643i 1.11004 + 0.873509i
\(279\) 0 0
\(280\) −7.44902 + 16.2704i −0.445164 + 0.972341i
\(281\) 2.76588i 0.164999i 0.996591 + 0.0824993i \(0.0262902\pi\)
−0.996591 + 0.0824993i \(0.973710\pi\)
\(282\) 0 0
\(283\) 4.48528 4.48528i 0.266622 0.266622i −0.561115 0.827738i \(-0.689628\pi\)
0.827738 + 0.561115i \(0.189628\pi\)
\(284\) −2.40569 9.94372i −0.142752 0.590051i
\(285\) 0 0
\(286\) −0.458067 3.84138i −0.0270860 0.227146i
\(287\) 2.01704 0.119062
\(288\) 0 0
\(289\) 24.5443 1.44378
\(290\) −1.80382 15.1270i −0.105924 0.888285i
\(291\) 0 0
\(292\) 6.94725 + 28.7159i 0.406557 + 1.68047i
\(293\) 8.20793 8.20793i 0.479512 0.479512i −0.425463 0.904976i \(-0.639889\pi\)
0.904976 + 0.425463i \(0.139889\pi\)
\(294\) 0 0
\(295\) 13.9929i 0.814700i
\(296\) 9.92606 + 4.54441i 0.576940 + 0.264139i
\(297\) 0 0
\(298\) 12.4287 + 9.78039i 0.719977 + 0.566563i
\(299\) 8.16804 8.16804i 0.472370 0.472370i
\(300\) 0 0
\(301\) −0.996470 0.996470i −0.0574356 0.0574356i
\(302\) −20.5733 + 2.45327i −1.18386 + 0.141170i
\(303\) 0 0
\(304\) −24.5478 7.88118i −1.40791 0.452016i
\(305\) 15.3435 0.878567
\(306\) 0 0
\(307\) 10.4549 + 10.4549i 0.596693 + 0.596693i 0.939431 0.342738i \(-0.111354\pi\)
−0.342738 + 0.939431i \(0.611354\pi\)
\(308\) 2.92450 + 1.78510i 0.166639 + 0.101716i
\(309\) 0 0
\(310\) −18.0277 14.1864i −1.02391 0.805731i
\(311\) 15.0761i 0.854885i 0.904043 + 0.427442i \(0.140585\pi\)
−0.904043 + 0.427442i \(0.859415\pi\)
\(312\) 0 0
\(313\) 23.0027i 1.30019i −0.759852 0.650096i \(-0.774729\pi\)
0.759852 0.650096i \(-0.225271\pi\)
\(314\) 3.89838 4.95398i 0.219998 0.279569i
\(315\) 0 0
\(316\) 12.2856 2.97226i 0.691117 0.167203i
\(317\) 6.75892 + 6.75892i 0.379618 + 0.379618i 0.870964 0.491346i \(-0.163495\pi\)
−0.491346 + 0.870964i \(0.663495\pi\)
\(318\) 0 0
\(319\) −2.91688 −0.163314
\(320\) 1.44902 19.7359i 0.0810025 1.10327i
\(321\) 0 0
\(322\) 1.21137 + 10.1586i 0.0675069 + 0.566118i
\(323\) −29.3763 29.3763i −1.63454 1.63454i
\(324\) 0 0
\(325\) 3.23099 3.23099i 0.179223 0.179223i
\(326\) −6.80853 + 8.65214i −0.377090 + 0.479198i
\(327\) 0 0
\(328\) −2.09069 + 0.777537i −0.115439 + 0.0429323i
\(329\) 7.23412i 0.398830i
\(330\) 0 0
\(331\) −19.6631 + 19.6631i −1.08078 + 1.08078i −0.0843464 + 0.996436i \(0.526880\pi\)
−0.996436 + 0.0843464i \(0.973120\pi\)
\(332\) 1.54913 + 0.945580i 0.0850193 + 0.0518954i
\(333\) 0 0
\(334\) 28.3400 3.37941i 1.55070 0.184913i
\(335\) 7.41215 0.404969
\(336\) 0 0
\(337\) 3.00980 0.163954 0.0819771 0.996634i \(-0.473877\pi\)
0.0819771 + 0.996634i \(0.473877\pi\)
\(338\) −5.16662 + 0.616095i −0.281027 + 0.0335111i
\(339\) 0 0
\(340\) 16.6135 27.2176i 0.900995 1.47608i
\(341\) −3.10587 + 3.10587i −0.168192 + 0.168192i
\(342\) 0 0
\(343\) 19.0761i 1.03001i
\(344\) 1.41697 + 0.648728i 0.0763981 + 0.0349771i
\(345\) 0 0
\(346\) 5.38412 6.84203i 0.289452 0.367830i
\(347\) −6.27521 + 6.27521i −0.336871 + 0.336871i −0.855188 0.518317i \(-0.826559\pi\)
0.518317 + 0.855188i \(0.326559\pi\)
\(348\) 0 0
\(349\) −4.74255 4.74255i −0.253863 0.253863i 0.568690 0.822552i \(-0.307451\pi\)
−0.822552 + 0.568690i \(0.807451\pi\)
\(350\) 0.479174 + 4.01839i 0.0256129 + 0.214792i
\(351\) 0 0
\(352\) −3.71940 0.722930i −0.198245 0.0385323i
\(353\) 8.75882 0.466185 0.233093 0.972455i \(-0.425116\pi\)
0.233093 + 0.972455i \(0.425116\pi\)
\(354\) 0 0
\(355\) −8.94725 8.94725i −0.474871 0.474871i
\(356\) 2.97096 + 12.2802i 0.157460 + 0.650849i
\(357\) 0 0
\(358\) −16.4290 + 20.8776i −0.868300 + 1.10342i
\(359\) 32.7917i 1.73068i 0.501184 + 0.865341i \(0.332898\pi\)
−0.501184 + 0.865341i \(0.667102\pi\)
\(360\) 0 0
\(361\) 22.5443i 1.18654i
\(362\) 9.97455 + 7.84916i 0.524251 + 0.412543i
\(363\) 0 0
\(364\) 10.8843 17.8316i 0.570493 0.934628i
\(365\) 25.8382 + 25.8382i 1.35243 + 1.35243i
\(366\) 0 0
\(367\) 20.6435 1.07758 0.538791 0.842439i \(-0.318881\pi\)
0.538791 + 0.842439i \(0.318881\pi\)
\(368\) −5.17157 10.0625i −0.269587 0.524546i
\(369\) 0 0
\(370\) 13.4072 1.59874i 0.697005 0.0831145i
\(371\) 6.59245 + 6.59245i 0.342263 + 0.342263i
\(372\) 0 0
\(373\) −16.6167 + 16.6167i −0.860378 + 0.860378i −0.991382 0.131004i \(-0.958180\pi\)
0.131004 + 0.991382i \(0.458180\pi\)
\(374\) −4.79806 3.77568i −0.248102 0.195236i
\(375\) 0 0
\(376\) 2.78863 + 7.49824i 0.143813 + 0.386692i
\(377\) 17.7851i 0.915979i
\(378\) 0 0
\(379\) 7.77844 7.77844i 0.399552 0.399552i −0.478523 0.878075i \(-0.658828\pi\)
0.878075 + 0.478523i \(0.158828\pi\)
\(380\) −30.9933 + 7.49824i −1.58992 + 0.384651i
\(381\) 0 0
\(382\) −0.937828 7.86469i −0.0479834 0.402393i
\(383\) 17.2037 0.879070 0.439535 0.898225i \(-0.355143\pi\)
0.439535 + 0.898225i \(0.355143\pi\)
\(384\) 0 0
\(385\) 4.23765 0.215971
\(386\) −3.25717 27.3149i −0.165786 1.39029i
\(387\) 0 0
\(388\) −24.5970 + 5.95078i −1.24873 + 0.302105i
\(389\) 23.8515 23.8515i 1.20932 1.20932i 0.238069 0.971248i \(-0.423486\pi\)
0.971248 0.238069i \(-0.0765143\pi\)
\(390\) 0 0
\(391\) 18.2306i 0.921961i
\(392\) −0.451990 1.21534i −0.0228290 0.0613838i
\(393\) 0 0
\(394\) −1.94567 1.53109i −0.0980216 0.0771350i
\(395\) 11.0544 11.0544i 0.556208 0.556208i
\(396\) 0 0
\(397\) −10.2673 10.2673i −0.515299 0.515299i 0.400847 0.916145i \(-0.368716\pi\)
−0.916145 + 0.400847i \(0.868716\pi\)
\(398\) −1.39543 + 0.166399i −0.0699467 + 0.00834081i
\(399\) 0 0
\(400\) −2.04569 3.98038i −0.102284 0.199019i
\(401\) −32.2274 −1.60936 −0.804681 0.593708i \(-0.797663\pi\)
−0.804681 + 0.593708i \(0.797663\pi\)
\(402\) 0 0
\(403\) 18.9374 + 18.9374i 0.943341 + 0.943341i
\(404\) 11.0887 18.1665i 0.551685 0.903815i
\(405\) 0 0
\(406\) −12.3785 9.74088i −0.614335 0.483432i
\(407\) 2.58526i 0.128146i
\(408\) 0 0
\(409\) 11.5702i 0.572110i 0.958213 + 0.286055i \(0.0923440\pi\)
−0.958213 + 0.286055i \(0.907656\pi\)
\(410\) −1.70607 + 2.16804i −0.0842569 + 0.107072i
\(411\) 0 0
\(412\) 1.56930 + 6.48658i 0.0773140 + 0.319571i
\(413\) −10.2306 10.2306i −0.503414 0.503414i
\(414\) 0 0
\(415\) 2.24471 0.110188
\(416\) −4.40792 + 22.6783i −0.216116 + 1.11190i
\(417\) 0 0
\(418\) 0.722930 + 6.06255i 0.0353597 + 0.296529i
\(419\) −6.74717 6.74717i −0.329621 0.329621i 0.522822 0.852442i \(-0.324879\pi\)
−0.852442 + 0.522822i \(0.824879\pi\)
\(420\) 0 0
\(421\) −17.2239 + 17.2239i −0.839443 + 0.839443i −0.988785 0.149343i \(-0.952284\pi\)
0.149343 + 0.988785i \(0.452284\pi\)
\(422\) −5.22470 + 6.63944i −0.254334 + 0.323203i
\(423\) 0 0
\(424\) −9.37442 4.29186i −0.455262 0.208431i
\(425\) 7.21137i 0.349803i
\(426\) 0 0
\(427\) 11.2180 11.2180i 0.542879 0.542879i
\(428\) −20.7229 + 33.9500i −1.00168 + 1.64103i
\(429\) 0 0
\(430\) 1.91391 0.228225i 0.0922970 0.0110060i
\(431\) −40.7088 −1.96087 −0.980437 0.196832i \(-0.936935\pi\)
−0.980437 + 0.196832i \(0.936935\pi\)
\(432\) 0 0
\(433\) 7.31371 0.351474 0.175737 0.984437i \(-0.443769\pi\)
0.175737 + 0.984437i \(0.443769\pi\)
\(434\) −23.5525 + 2.80853i −1.13056 + 0.134814i
\(435\) 0 0
\(436\) −6.68499 4.08049i −0.320153 0.195420i
\(437\) −12.8910 + 12.8910i −0.616659 + 0.616659i
\(438\) 0 0
\(439\) 17.7122i 0.845356i 0.906280 + 0.422678i \(0.138910\pi\)
−0.906280 + 0.422678i \(0.861090\pi\)
\(440\) −4.39236 + 1.63354i −0.209398 + 0.0778761i
\(441\) 0 0
\(442\) −23.0215 + 29.2552i −1.09502 + 1.39153i
\(443\) −15.6944 + 15.6944i −0.745664 + 0.745664i −0.973662 0.227997i \(-0.926782\pi\)
0.227997 + 0.973662i \(0.426782\pi\)
\(444\) 0 0
\(445\) 11.0496 + 11.0496i 0.523801 + 0.523801i
\(446\) −3.97964 33.3736i −0.188441 1.58028i
\(447\) 0 0
\(448\) −13.3700 15.4888i −0.631673 0.731778i
\(449\) 28.3400 1.33745 0.668723 0.743511i \(-0.266841\pi\)
0.668723 + 0.743511i \(0.266841\pi\)
\(450\) 0 0
\(451\) 0.373517 + 0.373517i 0.0175882 + 0.0175882i
\(452\) 4.34981 1.05235i 0.204598 0.0494985i
\(453\) 0 0
\(454\) −0.793624 + 1.00852i −0.0372466 + 0.0473323i
\(455\) 25.8382i 1.21131i
\(456\) 0 0
\(457\) 17.3396i 0.811113i −0.914070 0.405557i \(-0.867078\pi\)
0.914070 0.405557i \(-0.132922\pi\)
\(458\) 8.39729 + 6.60798i 0.392380 + 0.308771i
\(459\) 0 0
\(460\) −11.9437 7.29040i −0.556879 0.339917i
\(461\) 1.69284 + 1.69284i 0.0788434 + 0.0788434i 0.745429 0.666585i \(-0.232245\pi\)
−0.666585 + 0.745429i \(0.732245\pi\)
\(462\) 0 0
\(463\) 2.70238 0.125590 0.0627951 0.998026i \(-0.479999\pi\)
0.0627951 + 0.998026i \(0.479999\pi\)
\(464\) 16.5854 + 5.32480i 0.769957 + 0.247198i
\(465\) 0 0
\(466\) −32.6169 + 3.88942i −1.51095 + 0.180174i
\(467\) 17.1136 + 17.1136i 0.791924 + 0.791924i 0.981807 0.189883i \(-0.0608108\pi\)
−0.189883 + 0.981807i \(0.560811\pi\)
\(468\) 0 0
\(469\) 5.41921 5.41921i 0.250236 0.250236i
\(470\) 7.77568 + 6.11882i 0.358665 + 0.282240i
\(471\) 0 0
\(472\) 14.5478 + 6.66038i 0.669618 + 0.306569i
\(473\) 0.369053i 0.0169691i
\(474\) 0 0
\(475\) −5.09921 + 5.09921i −0.233968 + 0.233968i
\(476\) −7.75293 32.0461i −0.355355 1.46883i
\(477\) 0 0
\(478\) −4.50803 37.8047i −0.206193 1.72915i
\(479\) 22.2251 1.01549 0.507745 0.861508i \(-0.330479\pi\)
0.507745 + 0.861508i \(0.330479\pi\)
\(480\) 0 0
\(481\) −15.7631 −0.718735
\(482\) −1.73303 14.5333i −0.0789373 0.661974i
\(483\) 0 0
\(484\) −4.96224 20.5110i −0.225556 0.932318i
\(485\) −22.1322 + 22.1322i −1.00497 + 1.00497i
\(486\) 0 0
\(487\) 13.9839i 0.633672i −0.948480 0.316836i \(-0.897380\pi\)
0.948480 0.316836i \(-0.102620\pi\)
\(488\) −7.30324 + 15.9520i −0.330602 + 0.722111i
\(489\) 0 0
\(490\) −1.26031 0.991758i −0.0569348 0.0448031i
\(491\) −7.23412 + 7.23412i −0.326471 + 0.326471i −0.851243 0.524772i \(-0.824151\pi\)
0.524772 + 0.851243i \(0.324151\pi\)
\(492\) 0 0
\(493\) 19.8476 + 19.8476i 0.893893 + 0.893893i
\(494\) 36.9652 4.40792i 1.66314 0.198322i
\(495\) 0 0
\(496\) 23.3298 11.9902i 1.04754 0.538375i
\(497\) −13.0831 −0.586858
\(498\) 0 0
\(499\) 2.59078 + 2.59078i 0.115979 + 0.115979i 0.762715 0.646735i \(-0.223866\pi\)
−0.646735 + 0.762715i \(0.723866\pi\)
\(500\) 16.3892 + 10.0039i 0.732948 + 0.447388i
\(501\) 0 0
\(502\) 15.3352 + 12.0675i 0.684443 + 0.538601i
\(503\) 39.6443i 1.76765i 0.467817 + 0.883825i \(0.345041\pi\)
−0.467817 + 0.883825i \(0.654959\pi\)
\(504\) 0 0
\(505\) 26.3235i 1.17138i
\(506\) −1.65685 + 2.10550i −0.0736562 + 0.0936008i
\(507\) 0 0
\(508\) −23.7440 + 5.74441i −1.05347 + 0.254867i
\(509\) −20.2875 20.2875i −0.899229 0.899229i 0.0961393 0.995368i \(-0.469351\pi\)
−0.995368 + 0.0961393i \(0.969351\pi\)
\(510\) 0 0
\(511\) 37.7819 1.67137
\(512\) 19.8288 + 10.9004i 0.876317 + 0.481734i
\(513\) 0 0
\(514\) −2.84609 23.8675i −0.125536 1.05275i
\(515\) 5.83655 + 5.83655i 0.257189 + 0.257189i
\(516\) 0 0
\(517\) 1.33962 1.33962i 0.0589162 0.0589162i
\(518\) 8.63343 10.9712i 0.379331 0.482046i
\(519\) 0 0
\(520\) 9.96021 + 26.7816i 0.436784 + 1.17445i
\(521\) 23.1784i 1.01546i −0.861515 0.507732i \(-0.830484\pi\)
0.861515 0.507732i \(-0.169516\pi\)
\(522\) 0 0
\(523\) −5.78550 + 5.78550i −0.252982 + 0.252982i −0.822192 0.569210i \(-0.807249\pi\)
0.569210 + 0.822192i \(0.307249\pi\)
\(524\) −9.11529 5.56394i −0.398203 0.243062i
\(525\) 0 0
\(526\) 42.1180 5.02238i 1.83643 0.218986i
\(527\) 42.2672 1.84119
\(528\) 0 0
\(529\) 15.0000 0.652174
\(530\) −12.6621 + 1.50989i −0.550005 + 0.0655855i
\(531\) 0 0
\(532\) −17.1778 + 28.1421i −0.744754 + 1.22012i
\(533\) 2.27744 2.27744i 0.0986470 0.0986470i
\(534\) 0 0
\(535\) 49.1941i 2.12685i
\(536\) −3.52805 + 7.70607i −0.152388 + 0.332852i
\(537\) 0 0
\(538\) 25.4787 32.3778i 1.09847 1.39591i
\(539\) −0.217129 + 0.217129i −0.00935241 + 0.00935241i
\(540\) 0 0
\(541\) 4.55175 + 4.55175i 0.195695 + 0.195695i 0.798152 0.602457i \(-0.205811\pi\)
−0.602457 + 0.798152i \(0.705811\pi\)
\(542\) −4.46269 37.4245i −0.191689 1.60752i
\(543\) 0 0
\(544\) 20.3892 + 30.2274i 0.874180 + 1.29599i
\(545\) −9.68667 −0.414931
\(546\) 0 0
\(547\) −27.7355 27.7355i −1.18588 1.18588i −0.978195 0.207689i \(-0.933406\pi\)
−0.207689 0.978195i \(-0.566594\pi\)
\(548\) −2.40126 9.92540i −0.102577 0.423992i
\(549\) 0 0
\(550\) −0.655392 + 0.832859i −0.0279460 + 0.0355132i
\(551\) 28.0688i 1.19577i
\(552\) 0 0
\(553\) 16.1643i 0.687377i
\(554\) 19.0523 + 14.9926i 0.809454 + 0.636974i
\(555\) 0 0
\(556\) −17.3529 + 28.4290i −0.735929 + 1.20566i
\(557\) 1.17538 + 1.17538i 0.0498026 + 0.0498026i 0.731569 0.681767i \(-0.238788\pi\)
−0.681767 + 0.731569i \(0.738788\pi\)
\(558\) 0 0
\(559\) −2.25023 −0.0951745
\(560\) −24.0953 7.73588i −1.01821 0.326901i
\(561\) 0 0
\(562\) −3.88403 + 0.463152i −0.163838 + 0.0195369i
\(563\) 28.7346 + 28.7346i 1.21102 + 1.21102i 0.970692 + 0.240326i \(0.0772544\pi\)
0.240326 + 0.970692i \(0.422746\pi\)
\(564\) 0 0
\(565\) 3.91391 3.91391i 0.164659 0.164659i
\(566\) 7.04959 + 5.54745i 0.296316 + 0.233177i
\(567\) 0 0
\(568\) 13.5608 5.04332i 0.568998 0.211613i
\(569\) 27.0004i 1.13191i −0.824435 0.565957i \(-0.808507\pi\)
0.824435 0.565957i \(-0.191493\pi\)
\(570\) 0 0
\(571\) −14.8284 + 14.8284i −0.620550 + 0.620550i −0.945672 0.325122i \(-0.894595\pi\)
0.325122 + 0.945672i \(0.394595\pi\)
\(572\) 5.31761 1.28649i 0.222341 0.0537910i
\(573\) 0 0
\(574\) 0.337758 + 2.83246i 0.0140977 + 0.118225i
\(575\) −3.16451 −0.131969
\(576\) 0 0
\(577\) −37.6372 −1.56686 −0.783429 0.621481i \(-0.786531\pi\)
−0.783429 + 0.621481i \(0.786531\pi\)
\(578\) 4.10999 + 34.4667i 0.170953 + 1.43363i
\(579\) 0 0
\(580\) 20.9402 5.06608i 0.869494 0.210357i
\(581\) 1.64116 1.64116i 0.0680869 0.0680869i
\(582\) 0 0
\(583\) 2.44158i 0.101120i
\(584\) −39.1614 + 14.5643i −1.62051 + 0.602675i
\(585\) 0 0
\(586\) 12.9005 + 10.1517i 0.532917 + 0.419362i
\(587\) 31.2574 31.2574i 1.29013 1.29013i 0.355429 0.934703i \(-0.384335\pi\)
0.934703 0.355429i \(-0.115665\pi\)
\(588\) 0 0
\(589\) −29.8874 29.8874i −1.23149 1.23149i
\(590\) 19.6498 2.34315i 0.808969 0.0964658i
\(591\) 0 0
\(592\) −4.71942 + 14.6998i −0.193967 + 0.604157i
\(593\) 3.59611 0.147675 0.0738373 0.997270i \(-0.476475\pi\)
0.0738373 + 0.997270i \(0.476475\pi\)
\(594\) 0 0
\(595\) −28.8347 28.8347i −1.18211 1.18211i
\(596\) −11.6530 + 19.0910i −0.477327 + 0.781996i
\(597\) 0 0
\(598\) 12.8379 + 10.1023i 0.524979 + 0.413115i
\(599\) 22.0296i 0.900104i −0.893002 0.450052i \(-0.851405\pi\)
0.893002 0.450052i \(-0.148595\pi\)
\(600\) 0 0
\(601\) 10.7721i 0.439405i −0.975567 0.219703i \(-0.929491\pi\)
0.975567 0.219703i \(-0.0705087\pi\)
\(602\) 1.23245 1.56617i 0.0502308 0.0638323i
\(603\) 0 0
\(604\) −6.89007 28.4795i −0.280353 1.15882i
\(605\) −18.4556 18.4556i −0.750325 0.750325i
\(606\) 0 0
\(607\) 5.47453 0.222204 0.111102 0.993809i \(-0.464562\pi\)
0.111102 + 0.993809i \(0.464562\pi\)
\(608\) 6.95668 35.7914i 0.282130 1.45153i
\(609\) 0 0
\(610\) 2.56930 + 21.5464i 0.104028 + 0.872387i
\(611\) −8.16804 8.16804i −0.330444 0.330444i
\(612\) 0 0
\(613\) −10.5049 + 10.5049i −0.424289 + 0.424289i −0.886677 0.462389i \(-0.846993\pi\)
0.462389 + 0.886677i \(0.346993\pi\)
\(614\) −12.9308 + 16.4322i −0.521843 + 0.663148i
\(615\) 0 0
\(616\) −2.01704 + 4.40569i −0.0812690 + 0.177510i
\(617\) 22.2235i 0.894686i −0.894363 0.447343i \(-0.852370\pi\)
0.894363 0.447343i \(-0.147630\pi\)
\(618\) 0 0
\(619\) 11.6398 11.6398i 0.467843 0.467843i −0.433372 0.901215i \(-0.642676\pi\)
0.901215 + 0.433372i \(0.142676\pi\)
\(620\) 16.9026 27.6913i 0.678826 1.11211i
\(621\) 0 0
\(622\) −21.1708 + 2.52452i −0.848871 + 0.101224i
\(623\) 16.1573 0.647327
\(624\) 0 0
\(625\) 29.3424 1.17369
\(626\) 32.3019 3.85185i 1.29105 0.153951i
\(627\) 0 0
\(628\) 7.60949 + 4.64480i 0.303652 + 0.185348i
\(629\) −17.5912 + 17.5912i −0.701405 + 0.701405i
\(630\) 0 0
\(631\) 4.06977i 0.162015i −0.996713 0.0810075i \(-0.974186\pi\)
0.996713 0.0810075i \(-0.0258138\pi\)
\(632\) 6.23108 + 16.7545i 0.247859 + 0.666458i
\(633\) 0 0
\(634\) −8.35951 + 10.6231i −0.331999 + 0.421897i
\(635\) −21.3646 + 21.3646i −0.847828 + 0.847828i
\(636\) 0 0
\(637\) 1.32390 + 1.32390i 0.0524549 + 0.0524549i
\(638\) −0.488437 4.09607i −0.0193374 0.162165i
\(639\) 0 0
\(640\) 27.9570 1.27001i 1.10510 0.0502016i
\(641\) 8.41958 0.332553 0.166277 0.986079i \(-0.446826\pi\)
0.166277 + 0.986079i \(0.446826\pi\)
\(642\) 0 0
\(643\) −7.37275 7.37275i −0.290753 0.290753i 0.546625 0.837378i \(-0.315912\pi\)
−0.837378 + 0.546625i \(0.815912\pi\)
\(644\) −14.0625 + 3.40216i −0.554142 + 0.134064i
\(645\) 0 0
\(646\) 36.3329 46.1712i 1.42950 1.81658i
\(647\) 11.6132i 0.456560i 0.973595 + 0.228280i \(0.0733102\pi\)
−0.973595 + 0.228280i \(0.926690\pi\)
\(648\) 0 0
\(649\) 3.78901i 0.148731i
\(650\) 5.07819 + 3.99612i 0.199183 + 0.156741i
\(651\) 0 0
\(652\) −13.2900 8.11216i −0.520477 0.317697i
\(653\) 1.93049 + 1.93049i 0.0755458 + 0.0755458i 0.743870 0.668324i \(-0.232988\pi\)
−0.668324 + 0.743870i \(0.732988\pi\)
\(654\) 0 0
\(655\) −13.2082 −0.516088
\(656\) −1.44196 2.80568i −0.0562990 0.109543i
\(657\) 0 0
\(658\) 10.1586 1.21137i 0.396024 0.0472240i
\(659\) −22.3102 22.3102i −0.869081 0.869081i 0.123290 0.992371i \(-0.460656\pi\)
−0.992371 + 0.123290i \(0.960656\pi\)
\(660\) 0 0
\(661\) 10.7033 10.7033i 0.416311 0.416311i −0.467619 0.883930i \(-0.654888\pi\)
0.883930 + 0.467619i \(0.154888\pi\)
\(662\) −30.9049 24.3196i −1.20115 0.945208i
\(663\) 0 0
\(664\) −1.06844 + 2.33372i −0.0414635 + 0.0905660i
\(665\) 40.7784i 1.58132i
\(666\) 0 0
\(667\) 8.70960 8.70960i 0.337237 0.337237i
\(668\) 9.49118 + 39.2310i 0.367225 + 1.51789i
\(669\) 0 0
\(670\) 1.24118 + 10.4086i 0.0479509 + 0.402120i
\(671\) 4.15472 0.160391
\(672\) 0 0
\(673\) −20.6345 −0.795401 −0.397700 0.917515i \(-0.630192\pi\)
−0.397700 + 0.917515i \(0.630192\pi\)
\(674\) 0.503997 + 4.22655i 0.0194132 + 0.162801i
\(675\) 0 0
\(676\) −1.73032 7.15213i −0.0665508 0.275082i
\(677\) −26.8246 + 26.8246i −1.03095 + 1.03095i −0.0314484 + 0.999505i \(0.510012\pi\)
−0.999505 + 0.0314484i \(0.989988\pi\)
\(678\) 0 0
\(679\) 32.3627i 1.24197i
\(680\) 41.0027 + 18.7721i 1.57238 + 0.719879i
\(681\) 0 0
\(682\) −4.88155 3.84138i −0.186924 0.147094i
\(683\) −12.9026 + 12.9026i −0.493705 + 0.493705i −0.909472 0.415766i \(-0.863513\pi\)
0.415766 + 0.909472i \(0.363513\pi\)
\(684\) 0 0
\(685\) −8.93077 8.93077i −0.341227 0.341227i
\(686\) −26.7878 + 3.19432i −1.02276 + 0.121960i
\(687\) 0 0
\(688\) −0.673711 + 2.09844i −0.0256850 + 0.0800022i
\(689\) 14.8871 0.567152
\(690\) 0 0
\(691\) −21.3923 21.3923i −0.813803 0.813803i 0.171399 0.985202i \(-0.445171\pi\)
−0.985202 + 0.171399i \(0.945171\pi\)
\(692\) 10.5096 + 6.41502i 0.399515 + 0.243863i
\(693\) 0 0
\(694\) −9.86286 7.76126i −0.374389 0.294614i
\(695\) 41.1941i 1.56258i
\(696\) 0 0
\(697\) 5.08312i 0.192537i
\(698\) 5.86564 7.45394i 0.222018 0.282136i
\(699\) 0 0
\(700\) −5.56264 + 1.34577i −0.210248 + 0.0508655i
\(701\) −14.2040 14.2040i −0.536479 0.536479i 0.386014 0.922493i \(-0.373852\pi\)
−0.922493 + 0.386014i \(0.873852\pi\)
\(702\) 0 0
\(703\) 24.8776 0.938278
\(704\) 0.392364 5.34408i 0.0147878 0.201413i
\(705\) 0 0
\(706\) 1.46668 + 12.2997i 0.0551993 + 0.462906i
\(707\) −19.2458 19.2458i −0.723812 0.723812i
\(708\) 0 0
\(709\) −29.5474 + 29.5474i −1.10968 + 1.10968i −0.116485 + 0.993192i \(0.537163\pi\)
−0.993192 + 0.116485i \(0.962837\pi\)
\(710\) 11.0661 14.0625i 0.415302 0.527758i
\(711\) 0 0
\(712\) −16.7472 + 6.22836i −0.627627 + 0.233418i
\(713\) 18.5478i 0.694622i
\(714\) 0 0
\(715\) 4.78473 4.78473i 0.178939 0.178939i
\(716\) −32.0688 19.5747i −1.19847 0.731540i
\(717\) 0 0
\(718\) −46.0483 + 5.49104i −1.71851 + 0.204924i
\(719\) −28.3683 −1.05796 −0.528979 0.848635i \(-0.677425\pi\)
−0.528979 + 0.848635i \(0.677425\pi\)
\(720\) 0 0
\(721\) 8.53450 0.317841
\(722\) −31.6582 + 3.77509i −1.17819 + 0.140494i
\(723\) 0 0
\(724\) −9.35204 + 15.3213i −0.347566 + 0.569411i
\(725\) 3.44521 3.44521i 0.127952 0.127952i
\(726\) 0 0
\(727\) 20.4843i 0.759722i −0.925044 0.379861i \(-0.875972\pi\)
0.925044 0.379861i \(-0.124028\pi\)
\(728\) 26.8628 + 12.2985i 0.995603 + 0.455814i
\(729\) 0 0
\(730\) −31.9570 + 40.6104i −1.18278 + 1.50306i
\(731\) −2.51119 + 2.51119i −0.0928797 + 0.0928797i
\(732\) 0 0
\(733\) 33.9961 + 33.9961i 1.25567 + 1.25567i 0.953138 + 0.302536i \(0.0978331\pi\)
0.302536 + 0.953138i \(0.402167\pi\)
\(734\) 3.45680 + 28.9889i 0.127593 + 1.07000i
\(735\) 0 0
\(736\) 13.2645 8.94725i 0.488936 0.329800i
\(737\) 2.00706 0.0739310
\(738\) 0 0
\(739\) 15.1645 + 15.1645i 0.557836 + 0.557836i 0.928691 0.370855i \(-0.120935\pi\)
−0.370855 + 0.928691i \(0.620935\pi\)
\(740\) 4.49011 + 18.5595i 0.165060 + 0.682260i
\(741\) 0 0
\(742\) −8.15363 + 10.3615i −0.299329 + 0.380381i
\(743\) 2.17431i 0.0797677i 0.999204 + 0.0398839i \(0.0126988\pi\)
−0.999204 + 0.0398839i \(0.987301\pi\)
\(744\) 0 0
\(745\) 27.6631i 1.01350i
\(746\) −26.1167 20.5517i −0.956200 0.752451i
\(747\) 0 0
\(748\) 4.49861 7.36999i 0.164485 0.269473i
\(749\) 35.9670 + 35.9670i 1.31421 + 1.31421i
\(750\) 0 0
\(751\) 29.8980 1.09099 0.545497 0.838113i \(-0.316341\pi\)
0.545497 + 0.838113i \(0.316341\pi\)
\(752\) −10.0625 + 5.17157i −0.366943 + 0.188588i
\(753\) 0 0
\(754\) −24.9750 + 2.97815i −0.909536 + 0.108458i
\(755\) −25.6256 25.6256i −0.932610 0.932610i
\(756\) 0 0
\(757\) −15.3294 + 15.3294i −0.557157 + 0.557157i −0.928497 0.371340i \(-0.878899\pi\)
0.371340 + 0.928497i \(0.378899\pi\)
\(758\) 12.2255 + 9.62047i 0.444050 + 0.349431i
\(759\) 0 0
\(760\) −15.7194 42.2672i −0.570203 1.53319i
\(761\) 4.29449i 0.155675i 0.996966 + 0.0778375i \(0.0248015\pi\)
−0.996966 + 0.0778375i \(0.975198\pi\)
\(762\) 0 0
\(763\) −7.08216 + 7.08216i −0.256392 + 0.256392i
\(764\) 10.8871 2.63392i 0.393880 0.0952918i
\(765\) 0 0
\(766\) 2.88080 + 24.1586i 0.104088 + 0.872886i
\(767\) −23.1027 −0.834191
\(768\) 0 0
\(769\) 33.8819 1.22181 0.610907 0.791703i \(-0.290805\pi\)
0.610907 + 0.791703i \(0.290805\pi\)
\(770\) 0.709603 + 5.95078i 0.0255723 + 0.214451i
\(771\) 0 0
\(772\) 37.8119 9.14787i 1.36088 0.329239i
\(773\) 35.0230 35.0230i 1.25969 1.25969i 0.308450 0.951240i \(-0.400190\pi\)
0.951240 0.308450i \(-0.0998104\pi\)
\(774\) 0 0
\(775\) 7.33686i 0.263548i
\(776\) −12.4753 33.5443i −0.447837 1.20417i
\(777\) 0 0
\(778\) 37.4877 + 29.4998i 1.34400 + 1.05762i
\(779\) −3.59431 + 3.59431i −0.128779 + 0.128779i
\(780\) 0 0
\(781\) −2.42274 2.42274i −0.0866923 0.0866923i
\(782\) 25.6006 3.05275i 0.915475 0.109166i
\(783\) 0 0
\(784\) 1.63097 0.838225i 0.0582489 0.0299366i
\(785\) 11.0263 0.393545
\(786\) 0 0
\(787\) 24.1090 + 24.1090i 0.859393 + 0.859393i 0.991267 0.131873i \(-0.0420992\pi\)
−0.131873 + 0.991267i \(0.542099\pi\)
\(788\) 1.82424 2.98862i