Properties

Label 144.2.k.b.37.3
Level $144$
Weight $2$
Character 144.37
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 37.3
Root \(0.500000 + 1.44392i\) of defining polynomial
Character \(\chi\) \(=\) 144.37
Dual form 144.2.k.b.109.3

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.167452 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 0.197977 0.980207i \(-0.436563\pi\)
−0.980207 + 0.197977i \(0.936563\pi\)
\(6\) 0 0
\(7\) 2.55765i 0.966700i −0.875427 0.483350i \(-0.839420\pi\)
0.875427 0.483350i \(-0.160580\pi\)
\(8\) −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 0.632091 0.774894i \(-0.282197\pi\)
−0.774894 + 0.632091i \(0.782197\pi\)
\(12\) 0 0
\(13\) 2.88784 2.88784i 0.800943 0.800943i −0.182300 0.983243i \(-0.558354\pi\)
0.983243 + 0.182300i \(0.0583543\pi\)
\(14\) −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 −0.0466864 + 0.998910i \(0.514866\pi\)
−0.998910 + 0.0466864i \(0.985134\pi\)
\(20\) 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 \(0.0952810\pi\)
−0.955533 + 0.294884i \(0.904719\pi\)
\(24\) 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 −0.360821 0.932635i \(-0.617504\pi\)
0.932635 + 0.360821i \(0.117504\pi\)
\(30\) 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 0.446235 0.894916i \(-0.352765\pi\)
−0.894916 + 0.446235i \(0.852765\pi\)
\(38\) 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 \(0.0196145\pi\)
−0.998102 + 0.0615818i \(0.980385\pi\)
\(42\) 0 0
\(43\) −0.389604 0.389604i −0.0594141 0.0594141i 0.676775 0.736190i \(-0.263377\pi\)
−0.736190 + 0.676775i \(0.763377\pi\)
\(44\) 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 0.861615 0.507562i \(-0.169453\pi\)
−0.507562 + 0.861615i \(0.669453\pi\)
\(54\) 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 0.397044 0.917800i \(-0.370036\pi\)
−0.917800 + 0.397044i \(0.870036\pi\)
\(60\) 0 0
\(61\) −4.38607 + 4.38607i −0.561579 + 0.561579i −0.929756 0.368177i \(-0.879982\pi\)
0.368177 + 0.929756i \(0.379982\pi\)
\(62\) 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 −0.824589 0.565733i \(-0.808593\pi\)
0.565733 + 0.824589i \(0.308593\pi\)
\(68\) −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 \(-0.901832\pi\)
0.952820 0.303537i \(-0.0981676\pi\)
\(72\) 0 0
\(73\) 14.7721i 1.72895i 0.502676 + 0.864475i \(0.332349\pi\)
−0.502676 + 0.864475i \(0.667651\pi\)
\(74\) −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 −0.741445 0.671013i \(-0.765859\pi\)
0.671013 + 0.741445i \(0.265859\pi\)
\(84\) 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 \(0.108673\pi\)
−0.942285 + 0.334813i \(0.891327\pi\)
\(90\) 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 0.225498 0.974244i \(-0.427599\pi\)
−0.974244 + 0.225498i \(0.927599\pi\)
\(102\) 0 0
\(103\) 3.33686i 0.328790i 0.986395 + 0.164395i \(0.0525672\pi\)
−0.986395 + 0.164395i \(0.947433\pi\)
\(104\) 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 0.874560 + 0.484918i \(0.161151\pi\)
0.484918 + 0.874560i \(0.338849\pi\)
\(108\) 0 0
\(109\) 2.76901 2.76901i 0.265224 0.265224i −0.561949 0.827172i \(-0.689948\pi\)
0.827172 + 0.561949i \(0.189948\pi\)
\(110\) 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 −0.522659 0.852542i \(-0.675060\pi\)
0.852542 + 0.522659i \(0.175060\pi\)
\(132\) 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 \(-0.930010\pi\)
0.975924 0.218112i \(-0.0699898\pi\)
\(138\) 0 0
\(139\) 11.7757 + 11.7757i 0.998800 + 0.998800i 0.999999 0.00119925i \(-0.000381735\pi\)
−0.00119925 + 0.999999i \(0.500382\pi\)
\(140\) 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 0.952467 0.304640i \(-0.0985363\pi\)
−0.304640 + 0.952467i \(0.598536\pi\)
\(150\) 0 0
\(151\) 14.6506i 1.19225i −0.802893 0.596123i \(-0.796707\pi\)
0.802893 0.596123i \(-0.203293\pi\)
\(152\) −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 −0.821607 0.570054i \(-0.806922\pi\)
0.570054 + 0.821607i \(0.306922\pi\)
\(158\) −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 −0.457852 0.889029i \(-0.651381\pi\)
0.889029 + 0.457852i \(0.151381\pi\)
\(164\) 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 \(0.285209\pi\)
−0.624730 + 0.780841i \(0.714791\pi\)
\(168\) 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 −0.852955 0.521985i \(-0.825192\pi\)
0.521985 + 0.852955i \(0.325192\pi\)
\(174\) 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 −0.00713130 0.999975i \(-0.502270\pi\)
0.999975 + 0.00713130i \(0.00226998\pi\)
\(180\) 0 0
\(181\) 6.34628 + 6.34628i 0.471715 + 0.471715i 0.902469 0.430754i \(-0.141752\pi\)
−0.430754 + 0.902469i \(0.641752\pi\)
\(182\) −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 0.661631 0.749830i \(-0.269865\pi\)
−0.749830 + 0.661631i \(0.769865\pi\)
\(198\) 0 0
\(199\) 0.993710i 0.0704422i −0.999380 0.0352211i \(-0.988786\pi\)
0.999380 0.0352211i \(-0.0112135\pi\)
\(200\) −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 −0.546588 0.837402i \(-0.684073\pi\)
0.837402 + 0.546588i \(0.184073\pi\)
\(212\) −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 −0.685492 0.728081i \(-0.740413\pi\)
0.728081 + 0.685492i \(0.240413\pi\)
\(228\) 0 0
\(229\) 5.34275 + 5.34275i 0.353059 + 0.353059i 0.861246 0.508188i \(-0.169684\pi\)
−0.508188 + 0.861246i \(0.669684\pi\)
\(230\) −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 \(-0.724793\pi\)
0.648954 0.760828i \(-0.275207\pi\)
\(234\) 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 0.944465 0.328611i \(-0.106581\pi\)
−0.328611 + 0.944465i \(0.606581\pi\)
\(252\) 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 \(0.375703\pi\)
−0.380643 + 0.924722i \(0.624297\pi\)
\(264\) 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 −0.303046 + 0.952976i \(0.598004\pi\)
−0.952976 + 0.303046i \(0.901996\pi\)
\(270\) 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 0.970289 0.241951i \(-0.0777872\pi\)
−0.241951 + 0.970289i \(0.577787\pi\)
\(278\) 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 \(-0.973710\pi\)
0.996591 0.0824993i \(-0.0262902\pi\)
\(282\) 0 0
\(283\) 4.48528 + 4.48528i 0.266622 + 0.266622i 0.827738 0.561115i \(-0.189628\pi\)
−0.561115 + 0.827738i \(0.689628\pi\)
\(284\) −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 0.904976 0.425463i \(-0.139889\pi\)
−0.425463 + 0.904976i \(0.639889\pi\)
\(294\) 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 −0.342738 0.939431i \(-0.611354\pi\)
0.939431 + 0.342738i \(0.111354\pi\)
\(308\) 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 \(-0.859415\pi\)
0.904043 0.427442i \(-0.140585\pi\)
\(312\) 0 0
\(313\) 23.0027i 1.30019i 0.759852 + 0.650096i \(0.225271\pi\)
−0.759852 + 0.650096i \(0.774729\pi\)
\(314\) 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 −0.491346 0.870964i \(-0.663495\pi\)
0.870964 + 0.491346i \(0.163495\pi\)
\(318\) 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 −0.996436 0.0843464i \(-0.973120\pi\)
−0.0843464 0.996436i \(-0.526880\pi\)
\(332\) 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 0.518317 0.855188i \(-0.326559\pi\)
−0.855188 + 0.518317i \(0.826559\pi\)
\(348\) 0 0
\(349\) −4.74255 + 4.74255i −0.253863 + 0.253863i −0.822552 0.568690i \(-0.807451\pi\)
0.568690 + 0.822552i \(0.307451\pi\)
\(350\) 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 \(-0.667102\pi\)
0.501184 0.865341i \(-0.332898\pi\)
\(360\) 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 0.131004 0.991382i \(-0.458180\pi\)
−0.991382 + 0.131004i \(0.958180\pi\)
\(374\) −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 0.878075 0.478523i \(-0.158828\pi\)
−0.478523 + 0.878075i \(0.658828\pi\)
\(380\) −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 0.971248 + 0.238069i \(0.0765143\pi\)
0.238069 + 0.971248i \(0.423486\pi\)
\(390\) 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 −0.916145 0.400847i \(-0.868716\pi\)
0.400847 + 0.916145i \(0.368716\pi\)
\(398\) −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 \(-0.907656\pi\)
0.958213 0.286055i \(-0.0923440\pi\)
\(410\) −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 −0.852442 0.522822i \(-0.824879\pi\)
0.522822 + 0.852442i \(0.324879\pi\)
\(420\) 0 0
\(421\) −17.2239 17.2239i −0.839443 0.839443i 0.149343 0.988785i \(-0.452284\pi\)
−0.988785 + 0.149343i \(0.952284\pi\)
\(422\) −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 \(-0.861090\pi\)
0.906280 0.422678i \(-0.138910\pi\)
\(440\) −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 0.227997 0.973662i \(-0.426782\pi\)
−0.973662 + 0.227997i \(0.926782\pi\)
\(444\) 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 \(0.132922\pi\)
−0.914070 + 0.405557i \(0.867078\pi\)
\(458\) 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 −0.666585 0.745429i \(-0.732245\pi\)
0.745429 + 0.666585i \(0.232245\pi\)
\(462\) 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 −0.189883 0.981807i \(-0.560811\pi\)
0.981807 + 0.189883i \(0.0608108\pi\)
\(468\) 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 \(0.102620\pi\)
−0.948480 + 0.316836i \(0.897380\pi\)
\(488\) −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 0.524772 0.851243i \(-0.324151\pi\)
−0.851243 + 0.524772i \(0.824151\pi\)
\(492\) 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 −0.646735 0.762715i \(-0.723866\pi\)
0.762715 + 0.646735i \(0.223866\pi\)
\(500\) 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 \(-0.654959\pi\)
0.467817 0.883825i \(-0.345041\pi\)
\(504\) 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 −0.995368 0.0961393i \(-0.969351\pi\)
0.0961393 + 0.995368i \(0.469351\pi\)
\(510\) 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 \(0.169516\pi\)
−0.861515 + 0.507732i \(0.830484\pi\)
\(522\) 0 0
\(523\) −5.78550 5.78550i −0.252982 0.252982i 0.569210 0.822192i \(-0.307249\pi\)
−0.822192 + 0.569210i \(0.807249\pi\)
\(524\) −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 −0.602457 0.798152i \(-0.705811\pi\)
0.798152 + 0.602457i \(0.205811\pi\)
\(542\) −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 −0.207689 + 0.978195i \(0.566594\pi\)
−0.978195 + 0.207689i \(0.933406\pi\)
\(548\) −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 −0.681767 0.731569i \(-0.738788\pi\)
0.731569 + 0.681767i \(0.238788\pi\)
\(558\) 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 0.240326 0.970692i \(-0.422746\pi\)
0.970692 0.240326i \(-0.0772544\pi\)
\(564\) 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 \(0.191493\pi\)
−0.824435 + 0.565957i \(0.808507\pi\)
\(570\) 0 0
\(571\) −14.8284 14.8284i −0.620550 0.620550i 0.325122 0.945672i \(-0.394595\pi\)
−0.945672 + 0.325122i \(0.894595\pi\)
\(572\) 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 0.934703 + 0.355429i \(0.115665\pi\)
0.355429 + 0.934703i \(0.384335\pi\)
\(588\) 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 \(0.148595\pi\)
−0.893002 + 0.450052i \(0.851405\pi\)
\(600\) 0 0
\(601\) 10.7721i 0.439405i 0.975567 + 0.219703i \(0.0705087\pi\)
−0.975567 + 0.219703i \(0.929491\pi\)
\(602\) 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 0.462389 0.886677i \(-0.346993\pi\)
−0.886677 + 0.462389i \(0.846993\pi\)
\(614\) −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 \(0.147630\pi\)
−0.894363 + 0.447343i \(0.852370\pi\)
\(618\) 0 0
\(619\) 11.6398 + 11.6398i 0.467843 + 0.467843i 0.901215 0.433372i \(-0.142676\pi\)
−0.433372 + 0.901215i \(0.642676\pi\)
\(620\) 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 \(0.0258138\pi\)
−0.996713 + 0.0810075i \(0.974186\pi\)
\(632\) 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 −0.837378 0.546625i \(-0.815912\pi\)
0.546625 + 0.837378i \(0.315912\pi\)
\(644\) −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 \(-0.926690\pi\)
0.973595 0.228280i \(-0.0733102\pi\)
\(648\) 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 −0.668324 0.743870i \(-0.732988\pi\)
0.743870 + 0.668324i \(0.232988\pi\)
\(654\) 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 −0.992371 0.123290i \(-0.960656\pi\)
0.123290 + 0.992371i \(0.460656\pi\)
\(660\) 0 0
\(661\) 10.7033 + 10.7033i 0.416311 + 0.416311i 0.883930 0.467619i \(-0.154888\pi\)
−0.467619 + 0.883930i \(0.654888\pi\)
\(662\) −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 −0.999505 0.0314484i \(-0.989988\pi\)
−0.0314484 0.999505i \(-0.510012\pi\)
\(678\) 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 0.415766 0.909472i \(-0.363513\pi\)
−0.909472 + 0.415766i \(0.863513\pi\)
\(684\) 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 −0.985202 0.171399i \(-0.945171\pi\)
0.171399 + 0.985202i \(0.445171\pi\)
\(692\) 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 −0.922493 0.386014i \(-0.873852\pi\)
0.386014 + 0.922493i \(0.373852\pi\)
\(702\) 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 −0.993192 0.116485i \(-0.962837\pi\)
−0.116485 0.993192i \(-0.537163\pi\)
\(710\) 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 \(0.124028\pi\)
−0.925044 + 0.379861i \(0.875972\pi\)
\(728\) 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 0.302536 0.953138i \(-0.402167\pi\)
0.953138 0.302536i \(-0.0978331\pi\)
\(734\) 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 −0.370855 0.928691i \(-0.620935\pi\)
0.928691 + 0.370855i \(0.120935\pi\)
\(740\) 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 \(-0.987301\pi\)
0.999204 0.0398839i \(-0.0126988\pi\)
\(744\) 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 0.371340 0.928497i \(-0.378899\pi\)
−0.928497 + 0.371340i \(0.878899\pi\)
\(758\) 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 \(-0.975198\pi\)
0.996966 0.0778375i \(-0.0248015\pi\)
\(762\) 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 0.951240 + 0.308450i \(0.0998104\pi\)
0.308450 + 0.951240i \(0.400190\pi\)
\(774\) 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 −0.131873 0.991267i \(-0.542099\pi\)
0.991267 + 0.131873i \(0.0420992\pi\)
\(788\) 1.82424 + 2.98862i