Properties

Label 48.2.j.a.37.2
Level $48$
Weight $2$
Character 48.37
Analytic conductor $0.383$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 48.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.383281929702\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.2
Root \(0.500000 + 1.44392i\) of defining polynomial
Character \(\chi\) \(=\) 48.37
Dual form 48.2.j.a.13.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.167452 + 1.40426i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.94392 - 0.470294i) q^{4} +(1.74912 + 1.74912i) q^{5} +(-0.874559 - 1.11137i) q^{6} -2.55765i q^{7} +(0.985930 - 2.65103i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.167452 + 1.40426i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.94392 - 0.470294i) q^{4} +(1.74912 + 1.74912i) q^{5} +(-0.874559 - 1.11137i) q^{6} -2.55765i q^{7} +(0.985930 - 2.65103i) q^{8} -1.00000i q^{9} +(-2.74912 + 2.16333i) q^{10} +(0.473626 + 0.473626i) q^{11} +(1.70711 - 1.04201i) q^{12} +(2.88784 - 2.88784i) q^{13} +(3.59161 + 0.428283i) q^{14} -2.47363 q^{15} +(3.55765 + 1.82843i) q^{16} -6.44549 q^{17} +(1.40426 + 0.167452i) q^{18} +(-4.55765 + 4.55765i) q^{19} +(-2.57754 - 4.22274i) q^{20} +(1.80853 + 1.80853i) q^{21} +(-0.744406 + 0.585786i) q^{22} -2.82843i q^{23} +(1.17740 + 2.57172i) q^{24} +1.11882i q^{25} +(3.57172 + 4.53887i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.20285 + 4.97186i) q^{28} +(-3.07931 + 3.07931i) q^{29} +(0.414214 - 3.47363i) q^{30} +6.55765 q^{31} +(-3.16333 + 4.68971i) q^{32} -0.669808 q^{33} +(1.07931 - 9.05117i) q^{34} +(4.47363 - 4.47363i) q^{35} +(-0.470294 + 1.94392i) q^{36} +(-2.72922 - 2.72922i) q^{37} +(-5.63696 - 7.16333i) q^{38} +4.08402i q^{39} +(6.36147 - 2.91245i) q^{40} -0.788632i q^{41} +(-2.84250 + 2.23681i) q^{42} +(-0.389604 - 0.389604i) q^{43} +(-0.697947 - 1.14343i) q^{44} +(1.74912 - 1.74912i) q^{45} +(3.97186 + 0.473626i) q^{46} +2.82843 q^{47} +(-3.80853 + 1.22274i) q^{48} +0.458440 q^{49} +(-1.57113 - 0.187349i) q^{50} +(4.55765 - 4.55765i) q^{51} +(-6.97186 + 4.25559i) q^{52} +(-2.57754 - 2.57754i) q^{53} +(-1.11137 + 0.874559i) q^{54} +1.65685i q^{55} +(-6.78039 - 2.52166i) q^{56} -6.44549i q^{57} +(-3.80853 - 4.83980i) q^{58} +(4.00000 + 4.00000i) q^{59} +(4.80853 + 1.16333i) q^{60} +(-4.38607 + 4.38607i) q^{61} +(-1.09809 + 9.20867i) q^{62} -2.55765 q^{63} +(-6.05588 - 5.22746i) q^{64} +10.1023 q^{65} +(0.112161 - 0.940588i) q^{66} +(-2.11882 + 2.11882i) q^{67} +(12.5295 + 3.03127i) q^{68} +(2.00000 + 2.00000i) q^{69} +(5.53304 + 7.03127i) q^{70} +5.11529i q^{71} +(-2.65103 - 0.985930i) q^{72} +14.7721i q^{73} +(4.28956 - 3.37553i) q^{74} +(-0.791128 - 0.791128i) q^{75} +(11.0031 - 6.71627i) q^{76} +(1.21137 - 1.21137i) q^{77} +(-5.73505 - 0.683878i) q^{78} -6.32000 q^{79} +(3.02461 + 9.42088i) q^{80} -1.00000 q^{81} +(1.10745 + 0.132058i) q^{82} +(0.641669 - 0.641669i) q^{83} +(-2.66510 - 4.36618i) q^{84} +(-11.2739 - 11.2739i) q^{85} +(0.612348 - 0.481868i) q^{86} -4.35480i q^{87} +(1.72256 - 0.788632i) q^{88} -6.31724i q^{89} +(2.16333 + 2.74912i) q^{90} +(-7.38607 - 7.38607i) q^{91} +(-1.33019 + 5.49824i) q^{92} +(-4.63696 + 4.63696i) q^{93} +(-0.473626 + 3.97186i) q^{94} -15.9437 q^{95} +(-1.07931 - 5.55294i) q^{96} +12.6533 q^{97} +(-0.0767667 + 0.643772i) q^{98} +(0.473626 - 0.473626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{4} - 12q^{8} + O(q^{10}) \) \( 8q - 4q^{4} - 12q^{8} - 8q^{10} - 8q^{11} + 8q^{12} + 12q^{14} - 8q^{15} + 4q^{18} - 8q^{19} + 16q^{20} + 4q^{24} + 20q^{26} + 8q^{28} - 16q^{29} - 8q^{30} + 24q^{31} + 24q^{35} - 4q^{36} - 16q^{37} - 8q^{38} + 16q^{40} - 20q^{42} - 8q^{43} - 40q^{44} - 8q^{46} - 16q^{48} - 8q^{49} - 36q^{50} + 8q^{51} - 16q^{52} + 16q^{53} + 4q^{54} - 16q^{58} + 32q^{59} + 24q^{60} + 16q^{61} - 12q^{62} + 8q^{63} + 8q^{64} - 16q^{65} + 24q^{66} - 16q^{67} + 32q^{68} + 16q^{69} + 32q^{70} - 4q^{72} + 52q^{74} + 16q^{75} + 8q^{76} + 16q^{77} - 12q^{78} - 24q^{79} + 8q^{80} - 8q^{81} + 40q^{82} - 40q^{83} - 24q^{84} - 16q^{85} - 16q^{86} + 32q^{88} - 8q^{90} - 8q^{91} - 16q^{92} + 8q^{94} - 48q^{95} - 40q^{98} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) −1.94392 0.470294i −0.971960 0.235147i
\(5\) 1.74912 + 1.74912i 0.782229 + 0.782229i 0.980207 0.197977i \(-0.0634373\pi\)
−0.197977 + 0.980207i \(0.563437\pi\)
\(6\) −0.874559 1.11137i −0.357037 0.453716i
\(7\) 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
\(9\) 1.00000i 0.333333i
\(10\) −2.74912 + 2.16333i −0.869347 + 0.684105i
\(11\) 0.473626 + 0.473626i 0.142804 + 0.142804i 0.774894 0.632091i \(-0.217803\pi\)
−0.632091 + 0.774894i \(0.717803\pi\)
\(12\) 1.70711 1.04201i 0.492799 0.300803i
\(13\) 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
\(15\) −2.47363 −0.638687
\(16\) 3.55765 + 1.82843i 0.889412 + 0.457107i
\(17\) −6.44549 −1.56326 −0.781630 0.623742i \(-0.785611\pi\)
−0.781630 + 0.623742i \(0.785611\pi\)
\(18\) 1.40426 + 0.167452i 0.330988 + 0.0394688i
\(19\) −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
\(21\) 1.80853 + 1.80853i 0.394654 + 0.394654i
\(22\) −0.744406 + 0.585786i −0.158708 + 0.124890i
\(23\) 2.82843i 0.589768i −0.955533 0.294884i \(-0.904719\pi\)
0.955533 0.294884i \(-0.0952810\pi\)
\(24\) 1.17740 + 2.57172i 0.240336 + 0.524950i
\(25\) 1.11882i 0.223765i
\(26\) 3.57172 + 4.53887i 0.700471 + 0.890145i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −1.20285 + 4.97186i −0.227317 + 0.939593i
\(29\) −3.07931 + 3.07931i −0.571813 + 0.571813i −0.932635 0.360821i \(-0.882496\pi\)
0.360821 + 0.932635i \(0.382496\pi\)
\(30\) 0.414214 3.47363i 0.0756247 0.634194i
\(31\) 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
\(33\) −0.669808 −0.116599
\(34\) 1.07931 9.05117i 0.185100 1.55226i
\(35\) 4.47363 4.47363i 0.756181 0.756181i
\(36\) −0.470294 + 1.94392i −0.0783823 + 0.323987i
\(37\) −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
\(39\) 4.08402i 0.653967i
\(40\) 6.36147 2.91245i 1.00584 0.460499i
\(41\) 0.788632i 0.123164i −0.998102 0.0615818i \(-0.980385\pi\)
0.998102 0.0615818i \(-0.0196145\pi\)
\(42\) −2.84250 + 2.23681i −0.438607 + 0.345148i
\(43\) −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
\(45\) 1.74912 1.74912i 0.260743 0.260743i
\(46\) 3.97186 + 0.473626i 0.585619 + 0.0698323i
\(47\) 2.82843 0.412568 0.206284 0.978492i \(-0.433863\pi\)
0.206284 + 0.978492i \(0.433863\pi\)
\(48\) −3.80853 + 1.22274i −0.549714 + 0.176488i
\(49\) 0.458440 0.0654915
\(50\) −1.57113 0.187349i −0.222191 0.0264952i
\(51\) 4.55765 4.55765i 0.638198 0.638198i
\(52\) −6.97186 + 4.25559i −0.966823 + 0.590145i
\(53\) −2.57754 2.57754i −0.354053 0.354053i 0.507562 0.861615i \(-0.330547\pi\)
−0.861615 + 0.507562i \(0.830547\pi\)
\(54\) −1.11137 + 0.874559i −0.151239 + 0.119012i
\(55\) 1.65685i 0.223410i
\(56\) −6.78039 2.52166i −0.906068 0.336971i
\(57\) 6.44549i 0.853726i
\(58\) −3.80853 4.83980i −0.500084 0.635497i
\(59\) 4.00000 + 4.00000i 0.520756 + 0.520756i 0.917800 0.397044i \(-0.129964\pi\)
−0.397044 + 0.917800i \(0.629964\pi\)
\(60\) 4.80853 + 1.16333i 0.620779 + 0.150185i
\(61\) −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
\(63\) −2.55765 −0.322233
\(64\) −6.05588 5.22746i −0.756985 0.653432i
\(65\) 10.1023 1.25304
\(66\) 0.112161 0.940588i 0.0138060 0.115778i
\(67\) −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
\(69\) 2.00000 + 2.00000i 0.240772 + 0.240772i
\(70\) 5.53304 + 7.03127i 0.661325 + 0.840398i
\(71\) 5.11529i 0.607074i 0.952820 + 0.303537i \(0.0981676\pi\)
−0.952820 + 0.303537i \(0.901832\pi\)
\(72\) −2.65103 0.985930i −0.312426 0.116193i
\(73\) 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
\(75\) −0.791128 0.791128i −0.0913516 0.0913516i
\(76\) 11.0031 6.71627i 1.26215 0.770409i
\(77\) 1.21137 1.21137i 0.138048 0.138048i
\(78\) −5.73505 0.683878i −0.649366 0.0774339i
\(79\) −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
\(81\) −1.00000 −0.111111
\(82\) 1.10745 + 0.132058i 0.122297 + 0.0145834i
\(83\) 0.641669 0.641669i 0.0704323 0.0704323i −0.671013 0.741445i \(-0.734141\pi\)
0.741445 + 0.671013i \(0.234141\pi\)
\(84\) −2.66510 4.36618i −0.290786 0.476389i
\(85\) −11.2739 11.2739i −1.22283 1.22283i
\(86\) 0.612348 0.481868i 0.0660311 0.0519611i
\(87\) 4.35480i 0.466884i
\(88\) 1.72256 0.788632i 0.183625 0.0840685i
\(89\) 6.31724i 0.669626i −0.942285 0.334813i \(-0.891327\pi\)
0.942285 0.334813i \(-0.108673\pi\)
\(90\) 2.16333 + 2.74912i 0.228035 + 0.289782i
\(91\) −7.38607 7.38607i −0.774271 0.774271i
\(92\) −1.33019 + 5.49824i −0.138682 + 0.573231i
\(93\) −4.63696 + 4.63696i −0.480830 + 0.480830i
\(94\) −0.473626 + 3.97186i −0.0488508 + 0.409666i
\(95\) −15.9437 −1.63579
\(96\) −1.07931 5.55294i −0.110157 0.566744i
\(97\) 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
\(99\) 0.473626 0.473626i 0.0476012 0.0476012i
\(100\) 0.526176 2.17490i 0.0526176 0.217490i
\(101\) 7.52480 + 7.52480i 0.748745 + 0.748745i 0.974244 0.225498i \(-0.0724010\pi\)
−0.225498 + 0.974244i \(0.572401\pi\)
\(102\) 5.63696 + 7.16333i 0.558142 + 0.709275i
\(103\) 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
\(105\) 6.32666i 0.617419i
\(106\) 4.05117 3.18794i 0.393484 0.309640i
\(107\) −14.0625 14.0625i −1.35948 1.35948i −0.874560 0.484918i \(-0.838849\pi\)
−0.484918 0.874560i \(-0.661151\pi\)
\(108\) −1.04201 1.70711i −0.100268 0.164266i
\(109\) 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
\(111\) 3.85970 0.366347
\(112\) 4.67647 9.09921i 0.441885 0.859794i
\(113\) 2.23765 0.210500 0.105250 0.994446i \(-0.466436\pi\)
0.105250 + 0.994446i \(0.466436\pi\)
\(114\) 9.05117 + 1.07931i 0.847720 + 0.101087i
\(115\) 4.94725 4.94725i 0.461334 0.461334i
\(116\) 7.43411 4.53775i 0.690240 0.421320i
\(117\) −2.88784 2.88784i −0.266981 0.266981i
\(118\) −6.28687 + 4.94725i −0.578753 + 0.455431i
\(119\) 16.4853i 1.51120i
\(120\) −2.43882 + 6.55765i −0.222633 + 0.598629i
\(121\) 10.5514i 0.959214i
\(122\) −5.42475 6.89367i −0.491134 0.624123i
\(123\) 0.557647 + 0.557647i 0.0502814 + 0.0502814i
\(124\) −12.7475 3.08402i −1.14476 0.276953i
\(125\) 6.78863 6.78863i 0.607194 0.607194i
\(126\) 0.428283 3.59161i 0.0381545 0.319966i
\(127\) 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
\(129\) 0.550984 0.0485114
\(130\) −1.69166 + 14.1864i −0.148368 + 1.24423i
\(131\) −3.77568 + 3.77568i −0.329883 + 0.329883i −0.852542 0.522659i \(-0.824940\pi\)
0.522659 + 0.852542i \(0.324940\pi\)
\(132\) 1.30205 + 0.315007i 0.113329 + 0.0274178i
\(133\) 11.6569 + 11.6569i 1.01078 + 1.01078i
\(134\) −2.62059 3.33019i −0.226384 0.287685i
\(135\) 2.47363i 0.212896i
\(136\) −6.35480 + 17.0872i −0.544920 + 1.46521i
\(137\) 5.10587i 0.436224i 0.975924 + 0.218112i \(0.0699898\pi\)
−0.975924 + 0.218112i \(0.930010\pi\)
\(138\) −3.14343 + 2.47363i −0.267587 + 0.210569i
\(139\) 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
\(141\) −2.00000 + 2.00000i −0.168430 + 0.168430i
\(142\) −7.18323 0.856566i −0.602803 0.0718814i
\(143\) 2.73551 0.228755
\(144\) 1.82843 3.55765i 0.152369 0.296471i
\(145\) −10.7721 −0.894578
\(146\) −20.7440 2.47363i −1.71679 0.204719i
\(147\) −0.324166 + 0.324166i −0.0267368 + 0.0267368i
\(148\) 4.02185 + 6.58892i 0.330594 + 0.541606i
\(149\) −7.90774 7.90774i −0.647827 0.647827i 0.304640 0.952467i \(-0.401464\pi\)
−0.952467 + 0.304640i \(0.901464\pi\)
\(150\) 1.24343 0.978478i 0.101526 0.0798924i
\(151\) 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
\(153\) 6.44549i 0.521087i
\(154\) 1.49824 + 1.90393i 0.120731 + 0.153423i
\(155\) 11.4701 + 11.4701i 0.921300 + 0.921300i
\(156\) 1.92069 7.93901i 0.153778 0.635629i
\(157\) −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
\(159\) 3.64520 0.289083
\(160\) −13.7359 + 2.66981i −1.08592 + 0.211067i
\(161\) −7.23412 −0.570128
\(162\) 0.167452 1.40426i 0.0131563 0.110329i
\(163\) 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
\(165\) −1.17157 1.17157i −0.0912068 0.0912068i
\(166\) 0.793624 + 1.00852i 0.0615972 + 0.0782765i
\(167\) 20.1814i 1.56168i −0.624730 0.780841i \(-0.714791\pi\)
0.624730 0.780841i \(-0.285209\pi\)
\(168\) 6.57754 3.01138i 0.507469 0.232333i
\(169\) 3.67923i 0.283018i
\(170\) 17.7194 13.9437i 1.35902 1.06943i
\(171\) 4.55765 + 4.55765i 0.348532 + 0.348532i
\(172\) 0.574131 + 0.940588i 0.0437771 + 0.0717191i
\(173\) 4.35322 4.35322i 0.330969 0.330969i −0.521985 0.852955i \(-0.674808\pi\)
0.852955 + 0.521985i \(0.174808\pi\)
\(174\) 6.11529 + 0.729220i 0.463599 + 0.0552820i
\(175\) 2.86156 0.216313
\(176\) 0.819003 + 2.55098i 0.0617347 + 0.192288i
\(177\) −5.65685 −0.425195
\(178\) 8.87108 + 1.05783i 0.664915 + 0.0792880i
\(179\) −13.2833 + 13.2833i −0.992843 + 0.992843i −0.999975 0.00713130i \(-0.997730\pi\)
0.00713130 + 0.999975i \(0.497730\pi\)
\(180\) −4.22274 + 2.57754i −0.314745 + 0.192119i
\(181\) 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
\(183\) 6.20285i 0.458528i
\(184\) −7.49824 2.78863i −0.552777 0.205581i
\(185\) 9.54745i 0.701943i
\(186\) −5.73505 7.28798i −0.420514 0.534381i
\(187\) −3.05275 3.05275i −0.223239 0.223239i
\(188\) −5.49824 1.33019i −0.401000 0.0970142i
\(189\) 1.80853 1.80853i 0.131551 0.131551i
\(190\) 2.66981 22.3892i 0.193688 1.62428i
\(191\) 5.60058 0.405243 0.202622 0.979257i \(-0.435054\pi\)
0.202622 + 0.979257i \(0.435054\pi\)
\(192\) 7.97852 0.585786i 0.575800 0.0422755i
\(193\) −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
\(195\) −7.14343 + 7.14343i −0.511552 + 0.511552i
\(196\) −0.891171 0.215602i −0.0636551 0.0154001i
\(197\) 1.23793 + 1.23793i 0.0881988 + 0.0881988i 0.749830 0.661631i \(-0.230135\pi\)
−0.661631 + 0.749830i \(0.730135\pi\)
\(198\) 0.585786 + 0.744406i 0.0416300 + 0.0529026i
\(199\) 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
\(201\) 2.99647i 0.211355i
\(202\) −11.8268 + 9.30676i −0.832134 + 0.654822i
\(203\) 7.87579 + 7.87579i 0.552772 + 0.552772i
\(204\) −11.0031 + 6.71627i −0.770373 + 0.470233i
\(205\) 1.37941 1.37941i 0.0963422 0.0963422i
\(206\) −4.68583 0.558763i −0.326477 0.0389309i
\(207\) −2.82843 −0.196589
\(208\) 15.5541 4.99371i 1.07848 0.346251i
\(209\) −4.31724 −0.298630
\(210\) −8.88431 1.05941i −0.613076 0.0731064i
\(211\) 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
\(213\) −3.61706 3.61706i −0.247837 0.247837i
\(214\) 22.1023 17.3927i 1.51088 1.18894i
\(215\) 1.36293i 0.0929509i
\(216\) 2.57172 1.17740i 0.174983 0.0801120i
\(217\) 16.7721i 1.13857i
\(218\) 3.42475 + 4.35211i 0.231954 + 0.294762i
\(219\) −10.4455 10.4455i −0.705841 0.705841i
\(220\) 0.779208 3.22079i 0.0525342 0.217146i
\(221\) −18.6135 + 18.6135i −1.25208 + 1.25208i
\(222\) −0.646314 + 5.42004i −0.0433778 + 0.363769i
\(223\) −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
\(225\) 1.11882 0.0745883
\(226\) −0.374699 + 3.14225i −0.0249246 + 0.209019i
\(227\) −0.641669 + 0.641669i −0.0425891 + 0.0425891i −0.728081 0.685492i \(-0.759587\pi\)
0.685492 + 0.728081i \(0.259587\pi\)
\(228\) −3.03127 + 12.5295i −0.200751 + 0.829787i
\(229\) 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
\(231\) 1.71313i 0.112716i
\(232\) 5.12735 + 11.1993i 0.336627 + 0.735271i
\(233\) 23.2271i 1.52166i 0.648954 + 0.760828i \(0.275207\pi\)
−0.648954 + 0.760828i \(0.724793\pi\)
\(234\) 4.53887 3.57172i 0.296715 0.233490i
\(235\) 4.94725 + 4.94725i 0.322723 + 0.322723i
\(236\) −5.89450 9.65685i −0.383699 0.628608i
\(237\) 4.46891 4.46891i 0.290287 0.290287i
\(238\) −23.1497 2.76049i −1.50057 0.178936i
\(239\) 26.9213 1.74140 0.870698 0.491817i \(-0.163667\pi\)
0.870698 + 0.491817i \(0.163667\pi\)
\(240\) −8.80029 4.52284i −0.568056 0.291948i
\(241\) −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
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 10.5889 6.46343i 0.677886 0.413779i
\(245\) 0.801866 + 0.801866i 0.0512293 + 0.0512293i
\(246\) −0.876464 + 0.689705i −0.0558813 + 0.0439740i
\(247\) 26.3235i 1.67492i
\(248\) 6.46538 17.3845i 0.410552 1.10392i
\(249\) 0.907457i 0.0575077i
\(250\) 8.39627 + 10.6698i 0.531027 + 0.674818i
\(251\) −9.75696 9.75696i −0.615854 0.615854i 0.328611 0.944465i \(-0.393419\pi\)
−0.944465 + 0.328611i \(0.893419\pi\)
\(252\) 4.97186 + 1.20285i 0.313198 + 0.0757722i
\(253\) 1.33962 1.33962i 0.0842209 0.0842209i
\(254\) −2.04534 + 17.1524i −0.128336 + 1.07624i
\(255\) 15.9437 0.998435
\(256\) 9.31371 + 13.0098i 0.582107 + 0.813112i
\(257\) 16.9965 1.06021 0.530105 0.847932i \(-0.322152\pi\)
0.530105 + 0.847932i \(0.322152\pi\)
\(258\) −0.0922633 + 0.773727i −0.00574406 + 0.0481701i
\(259\) −6.98038 + 6.98038i −0.433740 + 0.433740i
\(260\) −19.6381 4.75107i −1.21791 0.294649i
\(261\) 3.07931 + 3.07931i 0.190604 + 0.190604i
\(262\) −4.66981 5.93430i −0.288502 0.366622i
\(263\) 29.9929i 1.84944i −0.380643 0.924722i \(-0.624297\pi\)
0.380643 0.924722i \(-0.375703\pi\)
\(264\) −0.660384 + 1.77568i −0.0406438 + 0.109285i
\(265\) 9.01686i 0.553901i
\(266\) −18.3213 + 14.4173i −1.12335 + 0.883984i
\(267\) 4.46696 + 4.46696i 0.273374 + 0.273374i
\(268\) 5.11529 3.12235i 0.312466 0.190728i
\(269\) 20.6003 20.6003i 1.25602 1.25602i 0.303046 0.952976i \(-0.401996\pi\)
0.952976 0.303046i \(-0.0980037\pi\)
\(270\) −3.47363 0.414214i −0.211398 0.0252082i
\(271\) −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
\(273\) 10.4455 0.632190
\(274\) −7.16999 0.854988i −0.433155 0.0516517i
\(275\) −0.529904 + 0.529904i −0.0319544 + 0.0319544i
\(276\) −2.94725 4.82843i −0.177404 0.290637i
\(277\) 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
\(279\) 6.55765i 0.392596i
\(280\) −7.44902 16.2704i −0.445164 0.972341i
\(281\) 2.76588i 0.164999i 0.996591 + 0.0824993i \(0.0262902\pi\)
−0.996591 + 0.0824993i \(0.973710\pi\)
\(282\) −2.47363 3.14343i −0.147302 0.187189i
\(283\) 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
\(285\) 11.2739 11.2739i 0.667809 0.667809i
\(286\) −0.458067 + 3.84138i −0.0270860 + 0.227146i
\(287\) −2.01704 −0.119062
\(288\) 4.68971 + 3.16333i 0.276344 + 0.186401i
\(289\) 24.5443 1.44378
\(290\) 1.80382 15.1270i 0.105924 0.888285i
\(291\) −8.94725 + 8.94725i −0.524497 + 0.524497i
\(292\) 6.94725 28.7159i 0.406557 1.68047i
\(293\) −8.20793 8.20793i −0.479512 0.479512i 0.425463 0.904976i \(-0.360111\pi\)
−0.904976 + 0.425463i \(0.860111\pi\)
\(294\) −0.400933 0.509498i −0.0233829 0.0297145i
\(295\) 13.9929i 0.814700i
\(296\) −9.92606 + 4.54441i −0.576940 + 0.264139i
\(297\) 0.669808i 0.0388662i
\(298\) 12.4287 9.78039i 0.719977 0.566563i
\(299\) −8.16804 8.16804i −0.472370 0.472370i
\(300\) 1.16583 + 1.90995i 0.0673091 + 0.110271i
\(301\) −0.996470 + 0.996470i −0.0574356 + 0.0574356i
\(302\) 20.5733 + 2.45327i 1.18386 + 0.141170i
\(303\) −10.6417 −0.611348
\(304\) −24.5478 + 7.88118i −1.40791 + 0.452016i
\(305\) −15.3435 −0.878567
\(306\) −9.05117 1.07931i −0.517421 0.0617000i
\(307\) 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
\(309\) −2.35951 2.35951i −0.134228 0.134228i
\(310\) −18.0277 + 14.1864i −1.02391 + 0.805731i
\(311\) 15.0761i 0.854885i 0.904043 + 0.427442i \(0.140585\pi\)
−0.904043 + 0.427442i \(0.859415\pi\)
\(312\) 10.8268 + 4.02656i 0.612950 + 0.227959i
\(313\) 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
\(315\) −4.47363 4.47363i −0.252060 0.252060i
\(316\) 12.2856 + 2.97226i 0.691117 + 0.167203i
\(317\) −6.75892 + 6.75892i −0.379618 + 0.379618i −0.870964 0.491346i \(-0.836505\pi\)
0.491346 + 0.870964i \(0.336505\pi\)
\(318\) −0.610396 + 5.11882i −0.0342293 + 0.287049i
\(319\) −2.91688 −0.163314
\(320\) −1.44902 19.7359i −0.0810025 1.10327i
\(321\) 19.8874 1.11001
\(322\) 1.21137 10.1586i 0.0675069 0.566118i
\(323\) 29.3763 29.3763i 1.63454 1.63454i
\(324\) 1.94392 + 0.470294i 0.107996 + 0.0261274i
\(325\) 3.23099 + 3.23099i 0.179223 + 0.179223i
\(326\) 6.80853 + 8.65214i 0.377090 + 0.479198i
\(327\) 3.91598i 0.216554i
\(328\) −2.09069 0.777537i −0.115439 0.0429323i
\(329\) 7.23412i 0.398830i
\(330\) 1.84138 1.44902i 0.101365 0.0797657i
\(331\) −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
\(333\) −2.72922 + 2.72922i −0.149560 + 0.149560i
\(334\) 28.3400 + 3.37941i 1.55070 + 0.184913i
\(335\) −7.41215 −0.404969
\(336\) 3.12735 + 9.74088i 0.170611 + 0.531408i
\(337\) 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
\(339\) −1.58226 + 1.58226i −0.0859364 + 0.0859364i
\(340\) 16.6135 + 27.2176i 0.900995 + 1.47608i
\(341\) 3.10587 + 3.10587i 0.168192 + 0.168192i
\(342\) −7.16333 + 5.63696i −0.387349 + 0.304812i
\(343\) 19.0761i 1.03001i
\(344\) −1.41697 + 0.648728i −0.0763981 + 0.0349771i
\(345\) 6.99647i 0.376677i
\(346\) 5.38412 + 6.84203i 0.289452 + 0.367830i
\(347\) 6.27521 + 6.27521i 0.336871 + 0.336871i 0.855188 0.518317i \(-0.173441\pi\)
−0.518317 + 0.855188i \(0.673441\pi\)
\(348\) −2.04804 + 8.46538i −0.109786 + 0.453792i
\(349\) −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
\(351\) 4.08402 0.217989
\(352\) −3.71940 + 0.722930i −0.198245 + 0.0385323i
\(353\) −8.75882 −0.466185 −0.233093 0.972455i \(-0.574884\pi\)
−0.233093 + 0.972455i \(0.574884\pi\)
\(354\) 0.947252 7.94372i 0.0503459 0.422204i
\(355\) −8.94725 + 8.94725i −0.474871 + 0.474871i
\(356\) −2.97096 + 12.2802i −0.157460 + 0.650849i
\(357\) −11.6569 11.6569i −0.616946 0.616946i
\(358\) −16.4290 20.8776i −0.868300 1.10342i
\(359\) 32.7917i 1.73068i 0.501184 + 0.865341i \(0.332898\pi\)
−0.501184 + 0.865341i \(0.667102\pi\)
\(360\) −2.91245 6.36147i −0.153500 0.335279i
\(361\) 22.5443i 1.18654i
\(362\) −9.97455 + 7.84916i −0.524251 + 0.412543i
\(363\) 7.46094 + 7.46094i 0.391598 + 0.391598i
\(364\) 10.8843 + 17.8316i 0.570493 + 0.934628i
\(365\) −25.8382 + 25.8382i −1.35243 + 1.35243i
\(366\) 8.71044 + 1.03868i 0.455302 + 0.0542926i
\(367\) 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
\(369\) −0.788632 −0.0410546
\(370\) 13.4072 + 1.59874i 0.697005 + 0.0831145i
\(371\) −6.59245 + 6.59245i −0.342263 + 0.342263i
\(372\) 11.1946 6.83314i 0.580413 0.354282i
\(373\) −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
\(375\) 9.60058i 0.495772i
\(376\) 2.78863 7.49824i 0.143813 0.386692i
\(377\) 17.7851i 0.915979i
\(378\) 2.23681 + 2.84250i 0.115049 + 0.146202i
\(379\) 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
\(381\) −8.63696 + 8.63696i −0.442485 + 0.442485i
\(382\) −0.937828 + 7.86469i −0.0479834 + 0.402393i
\(383\) −17.2037 −0.879070 −0.439535 0.898225i \(-0.644857\pi\)
−0.439535 + 0.898225i \(0.644857\pi\)
\(384\) −0.513421 + 11.3021i −0.0262004 + 0.576755i
\(385\) 4.23765 0.215971
\(386\) 3.25717 27.3149i 0.165786 1.39029i
\(387\) −0.389604 + 0.389604i −0.0198047 + 0.0198047i
\(388\) −24.5970 5.95078i −1.24873 0.302105i
\(389\) −23.8515 23.8515i −1.20932 1.20932i −0.971248 0.238069i \(-0.923486\pi\)
−0.238069 0.971248i \(-0.576514\pi\)
\(390\) −8.83509 11.2275i −0.447382 0.568524i
\(391\) 18.2306i 0.921961i
\(392\) 0.451990 1.21534i 0.0228290 0.0613838i
\(393\) 5.33962i 0.269348i
\(394\) −1.94567 + 1.53109i −0.0980216 + 0.0771350i
\(395\) −11.0544 11.0544i −0.556208 0.556208i
\(396\) −1.14343 + 0.697947i −0.0574597 + 0.0350732i
\(397\) −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
\(399\) −16.4853 −0.825296
\(400\) −2.04569 + 3.98038i −0.102284 + 0.199019i
\(401\) 32.2274 1.60936 0.804681 0.593708i \(-0.202337\pi\)
0.804681 + 0.593708i \(0.202337\pi\)
\(402\) 4.20784 + 0.501765i 0.209868 + 0.0250258i
\(403\) 18.9374 18.9374i 0.943341 0.943341i
\(404\) −11.0887 18.1665i −0.551685 0.903815i
\(405\) −1.74912 1.74912i −0.0869143 0.0869143i
\(406\) −12.3785 + 9.74088i −0.614335 + 0.483432i
\(407\) 2.58526i 0.128146i
\(408\) −7.58892 16.5760i −0.375708 0.820633i
\(409\) 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
\(411\) −3.61040 3.61040i −0.178088 0.178088i
\(412\) 1.56930 6.48658i 0.0773140 0.319571i
\(413\) 10.2306 10.2306i 0.503414 0.503414i
\(414\) 0.473626 3.97186i 0.0232774 0.195206i
\(415\) 2.24471 0.110188
\(416\) 4.40792 + 22.6783i 0.216116 + 1.11190i
\(417\) −16.6533 −0.815517
\(418\) 0.722930 6.06255i 0.0353597 0.296529i
\(419\) 6.74717 6.74717i 0.329621 0.329621i −0.522822 0.852442i \(-0.675121\pi\)
0.852442 + 0.522822i \(0.175121\pi\)
\(420\) 2.97539 12.2985i 0.145184 0.600106i
\(421\) −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
\(423\) 2.82843i 0.137523i
\(424\) −9.37442 + 4.29186i −0.455262 + 0.208431i
\(425\) 7.21137i 0.349803i
\(426\) 5.68499 4.47363i 0.275439 0.216748i
\(427\) 11.2180 + 11.2180i 0.542879 + 0.542879i
\(428\) 20.7229 + 33.9500i 1.00168 + 1.64103i
\(429\) −1.93430 + 1.93430i −0.0933888 + 0.0933888i
\(430\) 1.91391 + 0.228225i 0.0922970 + 0.0110060i
\(431\) 40.7088 1.96087 0.980437 0.196832i \(-0.0630654\pi\)
0.980437 + 0.196832i \(0.0630654\pi\)
\(432\) 1.22274 + 3.80853i 0.0588293 + 0.183238i
\(433\) 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
\(435\) 7.61706 7.61706i 0.365210 0.365210i
\(436\) −6.68499 + 4.08049i −0.320153 + 0.195420i
\(437\) 12.8910 + 12.8910i 0.616659 + 0.616659i
\(438\) 16.4173 12.9191i 0.784451 0.617299i
\(439\) 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
\(441\) 0.458440i 0.0218305i
\(442\) −23.0215 29.2552i −1.09502 1.39153i
\(443\) 15.6944 + 15.6944i 0.745664 + 0.745664i 0.973662 0.227997i \(-0.0732178\pi\)
−0.227997 + 0.973662i \(0.573218\pi\)
\(444\) −7.50295 1.81519i −0.356074 0.0861453i
\(445\) 11.0496 11.0496i 0.523801 0.523801i
\(446\) 3.97964 33.3736i 0.188441 1.58028i
\(447\) 11.1832 0.528949
\(448\) −13.3700 + 15.4888i −0.631673 + 0.731778i
\(449\) −28.3400 −1.33745 −0.668723 0.743511i \(-0.733159\pi\)
−0.668723 + 0.743511i \(0.733159\pi\)
\(450\) −0.187349 + 1.57113i −0.00883173 + 0.0740636i
\(451\) 0.373517 0.373517i 0.0175882 0.0175882i
\(452\) −4.34981 1.05235i −0.204598 0.0494985i
\(453\) 10.3595 + 10.3595i 0.486732 + 0.486732i
\(454\) −0.793624 1.00852i −0.0372466 0.0473323i
\(455\) 25.8382i 1.21131i
\(456\) −17.0872 6.35480i −0.800179 0.297591i
\(457\) 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
\(459\) −4.55765 4.55765i −0.212733 0.212733i
\(460\) −11.9437 + 7.29040i −0.556879 + 0.339917i
\(461\) −1.69284 + 1.69284i −0.0788434 + 0.0788434i −0.745429 0.666585i \(-0.767755\pi\)
0.666585 + 0.745429i \(0.267755\pi\)
\(462\) −2.40569 0.286867i −0.111923 0.0133463i
\(463\) 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
\(465\) −16.2212 −0.752239
\(466\) −32.6169 3.88942i −1.51095 0.180174i
\(467\) −17.1136 + 17.1136i −0.791924 + 0.791924i −0.981807 0.189883i \(-0.939189\pi\)
0.189883 + 0.981807i \(0.439189\pi\)
\(468\) 4.25559 + 6.97186i 0.196715 + 0.322274i
\(469\) 5.41921 + 5.41921i 0.250236 + 0.250236i
\(470\) −7.77568 + 6.11882i −0.358665 + 0.282240i
\(471\) 4.45754i 0.205393i
\(472\) 14.5478 6.66038i 0.669618 0.306569i
\(473\) 0.369053i 0.0169691i
\(474\) 5.52721 + 7.02387i 0.253873 + 0.322617i
\(475\) −5.09921 5.09921i −0.233968 0.233968i
\(476\) 7.75293 32.0461i 0.355355 1.46883i
\(477\) −2.57754 + 2.57754i −0.118018 + 0.118018i
\(478\) −4.50803 + 37.8047i −0.206193 + 1.72915i
\(479\) −22.2251 −1.01549 −0.507745 0.861508i \(-0.669521\pi\)
−0.507745 + 0.861508i \(0.669521\pi\)
\(480\) 7.82490 11.6006i 0.357156 0.529491i
\(481\) −15.7631 −0.718735
\(482\) 1.73303 14.5333i 0.0789373 0.661974i
\(483\) 5.11529 5.11529i 0.232754 0.232754i
\(484\) −4.96224 + 20.5110i −0.225556 + 0.932318i
\(485\) 22.1322 + 22.1322i 1.00497 + 1.00497i
\(486\) 0.874559 + 1.11137i 0.0396708 + 0.0504128i
\(487\) 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
\(489\) 7.78510i 0.352055i
\(490\) −1.26031 + 0.991758i −0.0569348 + 0.0448031i
\(491\) 7.23412 + 7.23412i 0.326471 + 0.326471i 0.851243 0.524772i \(-0.175849\pi\)
−0.524772 + 0.851243i \(0.675849\pi\)
\(492\) −0.821763 1.34628i −0.0370480 0.0606950i
\(493\) 19.8476 19.8476i 0.893893 0.893893i
\(494\) −36.9652 4.40792i −1.66314 0.198322i
\(495\) 1.65685 0.0744701
\(496\) 23.3298 + 11.9902i 1.04754 + 0.538375i
\(497\) 13.0831 0.586858
\(498\) −1.27431 0.151955i −0.0571032 0.00680929i
\(499\) 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
\(501\) 14.2704 + 14.2704i 0.637554 + 0.637554i
\(502\) 15.3352 12.0675i 0.684443 0.538601i
\(503\) 39.6443i 1.76765i 0.467817 + 0.883825i \(0.345041\pi\)
−0.467817 + 0.883825i \(0.654959\pi\)
\(504\) −2.52166 + 6.78039i −0.112324 + 0.302023i
\(505\) 26.3235i 1.17138i
\(506\) 1.65685 + 2.10550i 0.0736562 + 0.0936008i
\(507\) 2.60161 + 2.60161i 0.115542 + 0.115542i
\(508\) −23.7440 5.74441i −1.05347 0.254867i
\(509\) 20.2875 20.2875i 0.899229 0.899229i −0.0961393 0.995368i \(-0.530649\pi\)
0.995368 + 0.0961393i \(0.0306494\pi\)
\(510\) −2.66981 + 22.3892i −0.118221 + 0.991411i
\(511\) 37.7819 1.67137
\(512\) −19.8288 + 10.9004i −0.876317 + 0.481734i
\(513\) −6.44549 −0.284575
\(514\) −2.84609 + 23.8675i −0.125536 + 1.05275i
\(515\) −5.83655 + 5.83655i −0.257189 + 0.257189i
\(516\) −1.07107 0.259124i −0.0471511 0.0114073i
\(517\) 1.33962 + 1.33962i 0.0589162 + 0.0589162i
\(518\) −8.63343 10.9712i −0.379331 0.482046i
\(519\) 6.15639i 0.270235i
\(520\) 9.96021 26.7816i 0.436784 1.17445i
\(521\) 23.1784i 1.01546i −0.861515 0.507732i \(-0.830484\pi\)
0.861515 0.507732i \(-0.169516\pi\)
\(522\) −4.83980 + 3.80853i −0.211832 + 0.166695i
\(523\) −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
\(525\) −2.02343 + 2.02343i −0.0883096 + 0.0883096i
\(526\) 42.1180 + 5.02238i 1.83643 + 0.218986i
\(527\) −42.2672 −1.84119
\(528\) −2.38294 1.22470i −0.103704 0.0532980i
\(529\) 15.0000 0.652174
\(530\) 12.6621 + 1.50989i 0.550005 + 0.0655855i
\(531\) 4.00000 4.00000i 0.173585 0.173585i
\(532\) −17.1778 28.1421i −0.744754 1.22012i
\(533\) −2.27744 2.27744i −0.0986470 0.0986470i
\(534\) −7.02080 + 5.52480i −0.303820 + 0.239081i
\(535\) 49.1941i 2.12685i
\(536\) 3.52805 + 7.70607i 0.152388 + 0.332852i
\(537\) 18.7855i 0.810653i
\(538\) 25.4787 + 32.3778i 1.09847 + 1.39591i
\(539\) 0.217129 + 0.217129i 0.00935241 + 0.00935241i
\(540\) 1.16333 4.80853i 0.0500618 0.206926i
\(541\) 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
\(543\) −8.97499 −0.385154
\(544\) 20.3892 30.2274i 0.874180 1.29599i
\(545\) 9.68667 0.414931
\(546\) −1.74912 + 14.6682i −0.0748553 + 0.627742i
\(547\) −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
\(549\) 4.38607 + 4.38607i 0.187193 + 0.187193i
\(550\) −0.655392 0.832859i −0.0279460 0.0355132i
\(551\) 28.0688i 1.19577i
\(552\) 7.27391 3.33019i 0.309598 0.141742i
\(553\) 16.1643i 0.687377i
\(554\) −19.0523 + 14.9926i −0.809454 + 0.636974i
\(555\) 6.75107 + 6.75107i 0.286567 + 0.286567i
\(556\) −17.3529 28.4290i −0.735929 1.20566i
\(557\) −1.17538 + 1.17538i −0.0498026 + 0.0498026i −0.731569 0.681767i \(-0.761212\pi\)
0.681767 + 0.731569i \(0.261212\pi\)
\(558\) 9.20867 + 1.09809i 0.389834 + 0.0464859i
\(559\) −2.25023 −0.0951745
\(560\) 24.0953 7.73588i 1.01821 0.326901i
\(561\) 4.31724 0.182274
\(562\) −3.88403 0.463152i −0.163838 0.0195369i
\(563\) −28.7346 + 28.7346i −1.21102 + 1.21102i −0.240326 + 0.970692i \(0.577254\pi\)
−0.970692 + 0.240326i \(0.922746\pi\)
\(564\) 4.82843 2.94725i 0.203313 0.124102i
\(565\) 3.91391 + 3.91391i 0.164659 + 0.164659i
\(566\) −7.04959 + 5.54745i −0.296316 + 0.233177i
\(567\) 2.55765i 0.107411i
\(568\) 13.5608 + 5.04332i 0.568998 + 0.211613i
\(569\) 27.0004i 1.13191i −0.824435 0.565957i \(-0.808507\pi\)
0.824435 0.565957i \(-0.191493\pi\)
\(570\) 13.9437 + 17.7194i 0.584038 + 0.742184i
\(571\) −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
\(573\) −3.96021 + 3.96021i −0.165440 + 0.165440i
\(574\) 0.337758 2.83246i 0.0140977 0.118225i
\(575\) 3.16451 0.131969
\(576\) −5.22746 + 6.05588i −0.217811 + 0.252328i
\(577\) −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
\(579\) 13.7542 13.7542i 0.571605 0.571605i
\(580\) 20.9402 + 5.06608i 0.869494 + 0.210357i
\(581\) −1.64116 1.64116i −0.0680869 0.0680869i
\(582\) −11.0661 14.0625i −0.458704 0.582911i
\(583\) 2.44158i 0.101120i
\(584\) 39.1614 + 14.5643i 1.62051 + 0.602675i
\(585\) 10.1023i 0.417680i
\(586\) 12.9005 10.1517i 0.532917 0.419362i
\(587\) −31.2574 31.2574i −1.29013 1.29013i −0.934703 0.355429i \(-0.884335\pi\)
−0.355429 0.934703i \(-0.615665\pi\)
\(588\) 0.782607 0.477700i 0.0322742 0.0197000i
\(589\) −29.8874 + 29.8874i −1.23149 + 1.23149i
\(590\) −19.6498 2.34315i −0.808969 0.0964658i
\(591\) −1.75070 −0.0720140
\(592\) −4.71942 14.6998i −0.193967 0.604157i
\(593\) −3.59611 −0.147675 −0.0738373 0.997270i \(-0.523525\pi\)
−0.0738373 + 0.997270i \(0.523525\pi\)
\(594\) −0.940588 0.112161i −0.0385928 0.00460201i
\(595\) −28.8347 + 28.8347i −1.18211 + 1.18211i
\(596\) 11.6530 + 19.0910i 0.477327 + 0.781996i
\(597\) 0.702659 + 0.702659i 0.0287579 + 0.0287579i
\(598\) 12.8379 10.1023i 0.524979 0.413115i
\(599\) 22.0296i 0.900104i −0.893002 0.450052i \(-0.851405\pi\)
0.893002 0.450052i \(-0.148595\pi\)
\(600\) −2.87730 + 1.31730i −0.117465 + 0.0537787i
\(601\) 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
\(603\) 2.11882 + 2.11882i 0.0862852 + 0.0862852i
\(604\) −6.89007 + 28.4795i −0.280353 + 1.15882i
\(605\) 18.4556 18.4556i 0.750325 0.750325i
\(606\) 1.78197 14.9437i 0.0723875 0.607047i
\(607\) 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
\(609\) −11.1380 −0.451336
\(610\) 2.56930 21.5464i 0.104028 0.872387i
\(611\) 8.16804 8.16804i 0.330444 0.330444i
\(612\) 3.03127 12.5295i 0.122532 0.506475i
\(613\) −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
\(615\) 1.95078i 0.0786631i
\(616\) −2.01704 4.40569i −0.0812690 0.177510i
\(617\) 22.2235i 0.894686i −0.894363 0.447343i \(-0.852370\pi\)
0.894363 0.447343i \(-0.147630\pi\)
\(618\) 3.70849 2.91828i 0.149177 0.117390i
\(619\) 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
\(621\) 2.00000 2.00000i 0.0802572 0.0802572i
\(622\) −21.1708 2.52452i −0.848871 0.101224i
\(623\) −16.1573 −0.647327
\(624\) −7.46734 + 14.5295i −0.298933 + 0.581646i
\(625\) 29.3424 1.17369
\(626\) −32.3019 3.85185i −1.29105 0.153951i
\(627\) 3.05275 3.05275i 0.121915 0.121915i
\(628\) 7.60949 4.64480i 0.303652 0.185348i
\(629\) 17.5912 + 17.5912i 0.701405 + 0.701405i
\(630\) 7.03127 5.53304i 0.280133 0.220442i
\(631\) 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
\(633\) 5.97409i 0.237449i
\(634\) −8.35951 10.6231i −0.331999 0.421897i
\(635\) 21.3646 + 21.3646i 0.847828 + 0.847828i
\(636\) −7.08597 1.71431i −0.280977 0.0679770i
\(637\) 1.32390 1.32390i 0.0524549 0.0524549i
\(638\) 0.488437 4.09607i 0.0193374 0.162165i
\(639\) 5.11529 0.202358
\(640\) 27.9570 + 1.27001i 1.10510 + 0.0502016i
\(641\) −8.41958 −0.332553 −0.166277 0.986079i \(-0.553174\pi\)
−0.166277 + 0.986079i \(0.553174\pi\)
\(642\) −3.33019 + 27.9272i −0.131432 + 1.10220i
\(643\) −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
\(645\) 0.963735 + 0.963735i 0.0379470 + 0.0379470i
\(646\) 36.3329 + 46.1712i 1.42950 + 1.81658i
\(647\) 11.6132i 0.456560i 0.973595 + 0.228280i \(0.0733102\pi\)
−0.973595 + 0.228280i \(0.926690\pi\)
\(648\) −0.985930 + 2.65103i −0.0387310 + 0.104142i
\(649\) 3.78901i 0.148731i
\(650\) −5.07819 + 3.99612i −0.199183 + 0.156741i
\(651\) 11.8597 + 11.8597i 0.464818 + 0.464818i
\(652\) −13.2900 + 8.11216i −0.520477 + 0.317697i
\(653\) −1.93049 + 1.93049i −0.0755458 + 0.0755458i −0.743870 0.668324i \(-0.767012\pi\)
0.668324 + 0.743870i \(0.267012\pi\)
\(654\) −5.49907 0.655738i −0.215031 0.0256414i
\(655\) −13.2082 −0.516088
\(656\) 1.44196 2.80568i 0.0562990 0.109543i
\(657\) 14.7721 0.576316
\(658\) 10.1586 + 1.21137i 0.396024 + 0.0472240i
\(659\) 22.3102 22.3102i 0.869081 0.869081i −0.123290 0.992371i \(-0.539344\pi\)
0.992371 + 0.123290i \(0.0393444\pi\)
\(660\) 1.72646 + 2.82843i 0.0672024 + 0.110096i
\(661\) 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
\(663\) 26.3235i 1.02232i
\(664\) −1.06844 2.33372i −0.0414635 0.0905660i
\(665\) 40.7784i 1.58132i
\(666\) −3.37553 4.28956i −0.130799 0.166217i
\(667\) 8.70960 + 8.70960i 0.337237 + 0.337237i
\(668\) −9.49118 + 39.2310i −0.367225 + 1.51789i
\(669\) 16.8050 16.8050i 0.649719 0.649719i
\(670\) 1.24118 10.4086i 0.0479509 0.402120i
\(671\) −4.15472 −0.160391
\(672\) −14.2025 + 2.76049i −0.547871 + 0.106488i
\(673\) −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
\(675\) −0.791128 + 0.791128i −0.0304505 + 0.0304505i
\(676\) −1.73032 + 7.15213i −0.0665508 + 0.275082i
\(677\) 26.8246 + 26.8246i 1.03095 + 1.03095i 0.999505 + 0.0314484i \(0.0100120\pi\)
0.0314484 + 0.999505i \(0.489988\pi\)
\(678\) −1.95696 2.48686i −0.0751564 0.0955073i
\(679\) 32.3627i 1.24197i
\(680\) −41.0027 + 18.7721i −1.57238 + 0.719879i
\(681\) 0.907457i 0.0347738i
\(682\) −4.88155 + 3.84138i −0.186924 + 0.147094i
\(683\) 12.9026 + 12.9026i 0.493705 + 0.493705i 0.909472 0.415766i \(-0.136487\pi\)
−0.415766 + 0.909472i \(0.636487\pi\)
\(684\) −6.71627 11.0031i −0.256803 0.420715i
\(685\) −8.93077 + 8.93077i −0.341227 + 0.341227i
\(686\) 26.7878 + 3.19432i 1.02276 + 0.121960i
\(687\) −7.55579 −0.288271
\(688\) −0.673711 2.09844i −0.0256850 0.0800022i
\(689\) −14.8871 −0.567152
\(690\) −9.82490 1.17157i −0.374027 0.0446010i
\(691\) −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
\(693\) −1.21137 1.21137i −0.0460161 0.0460161i
\(694\) −9.86286 + 7.76126i −0.374389 + 0.294614i
\(695\) 41.1941i 1.56258i
\(696\) −11.5447 4.29353i −0.437600 0.162746i
\(697\) 5.08312i 0.192537i
\(698\) −5.86564 7.45394i −0.222018 0.282136i
\(699\) −16.4240 16.4240i −0.621213 0.621213i
\(700\) −5.56264 1.34577i −0.210248 0.0508655i
\(701\) 14.2040 14.2040i 0.536479 0.536479i −0.386014 0.922493i \(-0.626148\pi\)
0.922493 + 0.386014i \(0.126148\pi\)
\(702\) −0.683878 + 5.73505i −0.0258113 + 0.216455i
\(703\) 24.8776 0.938278
\(704\) −0.392364 5.34408i −0.0147878 0.201413i
\(705\) −6.99647 −0.263502
\(706\) 1.46668 12.2997i 0.0551993 0.462906i
\(707\) 19.2458 19.2458i 0.723812 0.723812i
\(708\) 10.9965 + 2.66038i 0.413273 + 0.0999834i
\(709\) −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
\(711\) 6.32000i 0.237018i
\(712\) −16.7472 6.22836i −0.627627 0.233418i
\(713\) 18.5478i 0.694622i
\(714\) 18.3213 14.4173i 0.685656 0.539556i
\(715\) 4.78473 + 4.78473i 0.178939 + 0.178939i
\(716\) 32.0688 19.5747i 1.19847 0.731540i
\(717\) −19.0363 + 19.0363i −0.710922 + 0.710922i
\(718\) −46.0483 5.49104i −1.71851 0.204924i
\(719\) 28.3683 1.05796 0.528979 0.848635i \(-0.322575\pi\)
0.528979 + 0.848635i \(0.322575\pi\)
\(720\) 9.42088 3.02461i 0.351095 0.112721i
\(721\) 8.53450 0.317841
\(722\) 31.6582 + 3.77509i 1.17819 + 0.140494i
\(723\) 7.31814 7.31814i 0.272165 0.272165i
\(724\) −9.35204 15.3213i −0.347566 0.569411i
\(725\) −3.44521 3.44521i −0.127952 0.127952i
\(726\) −11.7265 + 9.22778i −0.435210 + 0.342475i
\(727\) 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
\(729\) 1.00000i 0.0370370i
\(730\) −31.9570 40.6104i −1.18278 1.50306i
\(731\) 2.51119 + 2.51119i 0.0928797 + 0.0928797i
\(732\) −2.91716 + 12.0578i −0.107821 + 0.445670i
\(733\) 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
\(735\) −1.13401 −0.0418286
\(736\) 13.2645 + 8.94725i 0.488936 + 0.329800i
\(737\) −2.00706 −0.0739310
\(738\) 0.132058 1.10745i 0.00486112 0.0407658i
\(739\) 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
\(741\) −18.6135 18.6135i −0.683785 0.683785i
\(742\) −8.15363 10.3615i −0.299329 0.380381i
\(743\) 2.17431i 0.0797677i 0.999204 + 0.0398839i \(0.0126988\pi\)
−0.999204 + 0.0398839i \(0.987301\pi\)
\(744\) 7.72098 + 16.8644i 0.283065 + 0.618279i
\(745\) 27.6631i 1.01350i
\(746\) 26.1167 20.5517i 0.956200 0.752451i
\(747\) −0.641669 0.641669i −0.0234774 0.0234774i
\(748\) 4.49861 + 7.36999i 0.164485 + 0.269473i
\(749\) −35.9670 + 35.9670i −1.31421 + 1.31421i
\(750\) −13.4818 1.60764i −0.492284 0.0587026i
\(751\) 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
\(753\) 13.7984 0.502843
\(754\) −24.9750 2.97815i −0.909536 0.108458i
\(755\) 25.6256 25.6256i 0.932610 0.932610i
\(756\) −4.36618 + 2.66510i −0.158796 + 0.0969286i
\(757\) −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
\(759\) 1.89450i 0.0687661i
\(760\) −15.7194 + 42.2672i −0.570203 + 1.53319i
\(761\) 4.29449i 0.155675i 0.996966 + 0.0778375i \(0.0248015\pi\)
−0.996966 + 0.0778375i \(0.975198\pi\)
\(762\) −10.6823 13.5749i −0.386979 0.491765i
\(763\) −7.08216 7.08216i −0.256392 0.256392i
\(764\) −10.8871 2.63392i −0.393880 0.0952918i
\(765\) −11.2739 + 11.2739i −0.407609 + 0.407609i
\(766\) 2.88080 24.1586i 0.104088 0.872886i
\(767\) 23.1027 0.834191
\(768\) −15.7851 2.61353i −0.569596 0.0943076i
\(769\) 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
\(771\) −12.0183 + 12.0183i −0.432829 + 0.432829i
\(772\) 37.8119 + 9.14787i 1.36088 + 0.329239i
\(773\) −35.0230 35.0230i −1.25969 1.25969i −0.951240 0.308450i \(-0.900190\pi\)
−0.308450 0.951240i \(-0.599810\pi\)
\(774\) −0.481868 0.612348i −0.0173204