Properties

Label 144.2.x.a.13.1
Level $144$
Weight $2$
Character 144.13
Analytic conductor $1.150$
Analytic rank $0$
Dimension $4$
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.x (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 13.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 144.13
Dual form 144.2.x.a.133.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} -1.73205 q^{3} -2.00000i q^{4} +(-0.133975 - 0.500000i) q^{5} +(1.73205 - 1.73205i) q^{6} +(2.13397 - 1.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} -1.73205 q^{3} -2.00000i q^{4} +(-0.133975 - 0.500000i) q^{5} +(1.73205 - 1.73205i) q^{6} +(2.13397 - 1.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(0.633975 + 0.366025i) q^{10} +(-0.500000 - 0.133975i) q^{11} +3.46410i q^{12} +(4.59808 - 1.23205i) q^{13} +(-0.901924 + 3.36603i) q^{14} +(0.232051 + 0.866025i) q^{15} -4.00000 q^{16} +4.00000 q^{17} +(-3.00000 + 3.00000i) q^{18} +(-3.00000 - 3.00000i) q^{19} +(-1.00000 + 0.267949i) q^{20} +(-3.69615 + 2.13397i) q^{21} +(0.633975 - 0.366025i) q^{22} +(-0.401924 - 0.232051i) q^{23} +(-3.46410 - 3.46410i) q^{24} +(4.09808 - 2.36603i) q^{25} +(-3.36603 + 5.83013i) q^{26} -5.19615 q^{27} +(-2.46410 - 4.26795i) q^{28} +(0.866025 - 3.23205i) q^{29} +(-1.09808 - 0.633975i) q^{30} +(0.598076 - 1.03590i) q^{31} +(4.00000 - 4.00000i) q^{32} +(0.866025 + 0.232051i) q^{33} +(-4.00000 + 4.00000i) q^{34} +(-0.901924 - 0.901924i) q^{35} -6.00000i q^{36} +(-7.73205 + 7.73205i) q^{37} +6.00000 q^{38} +(-7.96410 + 2.13397i) q^{39} +(0.732051 - 1.26795i) q^{40} +(-9.69615 - 5.59808i) q^{41} +(1.56218 - 5.83013i) q^{42} +(8.69615 + 2.33013i) q^{43} +(-0.267949 + 1.00000i) q^{44} +(-0.401924 - 1.50000i) q^{45} +(0.633975 - 0.169873i) q^{46} +(4.59808 + 7.96410i) q^{47} +6.92820 q^{48} +(-0.464102 + 0.803848i) q^{49} +(-1.73205 + 6.46410i) q^{50} -6.92820 q^{51} +(-2.46410 - 9.19615i) q^{52} +(2.26795 - 2.26795i) q^{53} +(5.19615 - 5.19615i) q^{54} +0.267949i q^{55} +(6.73205 + 1.80385i) q^{56} +(5.19615 + 5.19615i) q^{57} +(2.36603 + 4.09808i) q^{58} +(-1.50000 - 5.59808i) q^{59} +(1.73205 - 0.464102i) q^{60} +(-3.86603 + 14.4282i) q^{61} +(0.437822 + 1.63397i) q^{62} +(6.40192 - 3.69615i) q^{63} +8.00000i q^{64} +(-1.23205 - 2.13397i) q^{65} +(-1.09808 + 0.633975i) q^{66} +(1.23205 - 0.330127i) q^{67} -8.00000i q^{68} +(0.696152 + 0.401924i) q^{69} +1.80385 q^{70} +10.9282i q^{71} +(6.00000 + 6.00000i) q^{72} +0.535898i q^{73} -15.4641i q^{74} +(-7.09808 + 4.09808i) q^{75} +(-6.00000 + 6.00000i) q^{76} +(-1.23205 + 0.330127i) q^{77} +(5.83013 - 10.0981i) q^{78} +(0.866025 + 1.50000i) q^{79} +(0.535898 + 2.00000i) q^{80} +9.00000 q^{81} +(15.2942 - 4.09808i) q^{82} +(3.16025 - 11.7942i) q^{83} +(4.26795 + 7.39230i) q^{84} +(-0.535898 - 2.00000i) q^{85} +(-11.0263 + 6.36603i) q^{86} +(-1.50000 + 5.59808i) q^{87} +(-0.732051 - 1.26795i) q^{88} -11.8564i q^{89} +(1.90192 + 1.09808i) q^{90} +(8.29423 - 8.29423i) q^{91} +(-0.464102 + 0.803848i) q^{92} +(-1.03590 + 1.79423i) q^{93} +(-12.5622 - 3.36603i) q^{94} +(-1.09808 + 1.90192i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(-0.500000 - 0.866025i) q^{97} +(-0.339746 - 1.26795i) q^{98} +(-1.50000 - 0.401924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 4q^{5} + 12q^{7} + 8q^{8} + 12q^{9} + O(q^{10}) \) \( 4q - 4q^{2} - 4q^{5} + 12q^{7} + 8q^{8} + 12q^{9} + 6q^{10} - 2q^{11} + 8q^{13} - 14q^{14} - 6q^{15} - 16q^{16} + 16q^{17} - 12q^{18} - 12q^{19} - 4q^{20} + 6q^{21} + 6q^{22} - 12q^{23} + 6q^{25} - 10q^{26} + 4q^{28} + 6q^{30} - 8q^{31} + 16q^{32} - 16q^{34} - 14q^{35} - 24q^{37} + 24q^{38} - 18q^{39} - 4q^{40} - 18q^{41} - 18q^{42} + 14q^{43} - 8q^{44} - 12q^{45} + 6q^{46} + 8q^{47} + 12q^{49} + 4q^{52} + 16q^{53} + 20q^{56} + 6q^{58} - 6q^{59} - 12q^{61} + 26q^{62} + 36q^{63} + 2q^{65} + 6q^{66} - 2q^{67} - 18q^{69} + 28q^{70} + 24q^{72} - 18q^{75} - 24q^{76} + 2q^{77} + 6q^{78} + 16q^{80} + 36q^{81} + 30q^{82} - 22q^{83} + 24q^{84} - 16q^{85} - 6q^{86} - 6q^{87} + 4q^{88} + 18q^{90} + 2q^{91} + 12q^{92} - 18q^{93} - 26q^{94} + 6q^{95} - 2q^{97} - 36q^{98} - 6q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.707107 + 0.707107i
\(3\) −1.73205 −1.00000
\(4\) 2.00000i 1.00000i
\(5\) −0.133975 0.500000i −0.0599153 0.223607i 0.929476 0.368883i \(-0.120260\pi\)
−0.989391 + 0.145276i \(0.953593\pi\)
\(6\) 1.73205 1.73205i 0.707107 0.707107i
\(7\) 2.13397 1.23205i 0.806567 0.465671i −0.0391956 0.999232i \(-0.512480\pi\)
0.845762 + 0.533560i \(0.179146\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 3.00000 1.00000
\(10\) 0.633975 + 0.366025i 0.200480 + 0.115747i
\(11\) −0.500000 0.133975i −0.150756 0.0403949i 0.182652 0.983178i \(-0.441532\pi\)
−0.333408 + 0.942783i \(0.608199\pi\)
\(12\) 3.46410i 1.00000i
\(13\) 4.59808 1.23205i 1.27528 0.341709i 0.443227 0.896410i \(-0.353834\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) −0.901924 + 3.36603i −0.241049 + 0.899608i
\(15\) 0.232051 + 0.866025i 0.0599153 + 0.223607i
\(16\) −4.00000 −1.00000
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) −3.00000 + 3.00000i −0.707107 + 0.707107i
\(19\) −3.00000 3.00000i −0.688247 0.688247i 0.273597 0.961844i \(-0.411786\pi\)
−0.961844 + 0.273597i \(0.911786\pi\)
\(20\) −1.00000 + 0.267949i −0.223607 + 0.0599153i
\(21\) −3.69615 + 2.13397i −0.806567 + 0.465671i
\(22\) 0.633975 0.366025i 0.135164 0.0780369i
\(23\) −0.401924 0.232051i −0.0838069 0.0483859i 0.457511 0.889204i \(-0.348741\pi\)
−0.541318 + 0.840818i \(0.682074\pi\)
\(24\) −3.46410 3.46410i −0.707107 0.707107i
\(25\) 4.09808 2.36603i 0.819615 0.473205i
\(26\) −3.36603 + 5.83013i −0.660132 + 1.14338i
\(27\) −5.19615 −1.00000
\(28\) −2.46410 4.26795i −0.465671 0.806567i
\(29\) 0.866025 3.23205i 0.160817 0.600177i −0.837720 0.546100i \(-0.816112\pi\)
0.998537 0.0540766i \(-0.0172215\pi\)
\(30\) −1.09808 0.633975i −0.200480 0.115747i
\(31\) 0.598076 1.03590i 0.107418 0.186053i −0.807306 0.590133i \(-0.799075\pi\)
0.914723 + 0.404081i \(0.132408\pi\)
\(32\) 4.00000 4.00000i 0.707107 0.707107i
\(33\) 0.866025 + 0.232051i 0.150756 + 0.0403949i
\(34\) −4.00000 + 4.00000i −0.685994 + 0.685994i
\(35\) −0.901924 0.901924i −0.152453 0.152453i
\(36\) 6.00000i 1.00000i
\(37\) −7.73205 + 7.73205i −1.27114 + 1.27114i −0.325651 + 0.945490i \(0.605584\pi\)
−0.945490 + 0.325651i \(0.894416\pi\)
\(38\) 6.00000 0.973329
\(39\) −7.96410 + 2.13397i −1.27528 + 0.341709i
\(40\) 0.732051 1.26795i 0.115747 0.200480i
\(41\) −9.69615 5.59808i −1.51428 0.874273i −0.999860 0.0167371i \(-0.994672\pi\)
−0.514425 0.857536i \(-0.671994\pi\)
\(42\) 1.56218 5.83013i 0.241049 0.899608i
\(43\) 8.69615 + 2.33013i 1.32615 + 0.355341i 0.851279 0.524714i \(-0.175828\pi\)
0.474872 + 0.880055i \(0.342494\pi\)
\(44\) −0.267949 + 1.00000i −0.0403949 + 0.150756i
\(45\) −0.401924 1.50000i −0.0599153 0.223607i
\(46\) 0.633975 0.169873i 0.0934745 0.0250464i
\(47\) 4.59808 + 7.96410i 0.670698 + 1.16168i 0.977706 + 0.209977i \(0.0673388\pi\)
−0.307008 + 0.951707i \(0.599328\pi\)
\(48\) 6.92820 1.00000
\(49\) −0.464102 + 0.803848i −0.0663002 + 0.114835i
\(50\) −1.73205 + 6.46410i −0.244949 + 0.914162i
\(51\) −6.92820 −0.970143
\(52\) −2.46410 9.19615i −0.341709 1.27528i
\(53\) 2.26795 2.26795i 0.311527 0.311527i −0.533974 0.845501i \(-0.679302\pi\)
0.845501 + 0.533974i \(0.179302\pi\)
\(54\) 5.19615 5.19615i 0.707107 0.707107i
\(55\) 0.267949i 0.0361303i
\(56\) 6.73205 + 1.80385i 0.899608 + 0.241049i
\(57\) 5.19615 + 5.19615i 0.688247 + 0.688247i
\(58\) 2.36603 + 4.09808i 0.310674 + 0.538104i
\(59\) −1.50000 5.59808i −0.195283 0.728807i −0.992193 0.124709i \(-0.960200\pi\)
0.796910 0.604098i \(-0.206467\pi\)
\(60\) 1.73205 0.464102i 0.223607 0.0599153i
\(61\) −3.86603 + 14.4282i −0.494994 + 1.84734i 0.0350707 + 0.999385i \(0.488834\pi\)
−0.530065 + 0.847957i \(0.677832\pi\)
\(62\) 0.437822 + 1.63397i 0.0556035 + 0.207515i
\(63\) 6.40192 3.69615i 0.806567 0.465671i
\(64\) 8.00000i 1.00000i
\(65\) −1.23205 2.13397i −0.152817 0.264687i
\(66\) −1.09808 + 0.633975i −0.135164 + 0.0780369i
\(67\) 1.23205 0.330127i 0.150519 0.0403314i −0.182773 0.983155i \(-0.558507\pi\)
0.333292 + 0.942824i \(0.391841\pi\)
\(68\) 8.00000i 0.970143i
\(69\) 0.696152 + 0.401924i 0.0838069 + 0.0483859i
\(70\) 1.80385 0.215601
\(71\) 10.9282i 1.29694i 0.761241 + 0.648470i \(0.224591\pi\)
−0.761241 + 0.648470i \(0.775409\pi\)
\(72\) 6.00000 + 6.00000i 0.707107 + 0.707107i
\(73\) 0.535898i 0.0627222i 0.999508 + 0.0313611i \(0.00998418\pi\)
−0.999508 + 0.0313611i \(0.990016\pi\)
\(74\) 15.4641i 1.79767i
\(75\) −7.09808 + 4.09808i −0.819615 + 0.473205i
\(76\) −6.00000 + 6.00000i −0.688247 + 0.688247i
\(77\) −1.23205 + 0.330127i −0.140405 + 0.0376215i
\(78\) 5.83013 10.0981i 0.660132 1.14338i
\(79\) 0.866025 + 1.50000i 0.0974355 + 0.168763i 0.910622 0.413239i \(-0.135603\pi\)
−0.813187 + 0.582003i \(0.802269\pi\)
\(80\) 0.535898 + 2.00000i 0.0599153 + 0.223607i
\(81\) 9.00000 1.00000
\(82\) 15.2942 4.09808i 1.68897 0.452557i
\(83\) 3.16025 11.7942i 0.346883 1.29458i −0.543514 0.839400i \(-0.682907\pi\)
0.890397 0.455185i \(-0.150427\pi\)
\(84\) 4.26795 + 7.39230i 0.465671 + 0.806567i
\(85\) −0.535898 2.00000i −0.0581263 0.216930i
\(86\) −11.0263 + 6.36603i −1.18899 + 0.686466i
\(87\) −1.50000 + 5.59808i −0.160817 + 0.600177i
\(88\) −0.732051 1.26795i −0.0780369 0.135164i
\(89\) 11.8564i 1.25678i −0.777900 0.628388i \(-0.783715\pi\)
0.777900 0.628388i \(-0.216285\pi\)
\(90\) 1.90192 + 1.09808i 0.200480 + 0.115747i
\(91\) 8.29423 8.29423i 0.869471 0.869471i
\(92\) −0.464102 + 0.803848i −0.0483859 + 0.0838069i
\(93\) −1.03590 + 1.79423i −0.107418 + 0.186053i
\(94\) −12.5622 3.36603i −1.29569 0.347179i
\(95\) −1.09808 + 1.90192i −0.112660 + 0.195133i
\(96\) −6.92820 + 6.92820i −0.707107 + 0.707107i
\(97\) −0.500000 0.866025i −0.0507673 0.0879316i 0.839525 0.543321i \(-0.182833\pi\)
−0.890292 + 0.455389i \(0.849500\pi\)
\(98\) −0.339746 1.26795i −0.0343195 0.128082i
\(99\) −1.50000 0.401924i −0.150756 0.0403949i
\(100\) −4.73205 8.19615i −0.473205 0.819615i
\(101\) −1.86603 0.500000i −0.185676 0.0497519i 0.164783 0.986330i \(-0.447308\pi\)
−0.350459 + 0.936578i \(0.613974\pi\)
\(102\) 6.92820 6.92820i 0.685994 0.685994i
\(103\) −1.79423 1.03590i −0.176791 0.102070i 0.408993 0.912537i \(-0.365880\pi\)
−0.585784 + 0.810467i \(0.699213\pi\)
\(104\) 11.6603 + 6.73205i 1.14338 + 0.660132i
\(105\) 1.56218 + 1.56218i 0.152453 + 0.152453i
\(106\) 4.53590i 0.440565i
\(107\) −11.3923 + 11.3923i −1.10134 + 1.10134i −0.107086 + 0.994250i \(0.534152\pi\)
−0.994250 + 0.107086i \(0.965848\pi\)
\(108\) 10.3923i 1.00000i
\(109\) 1.73205 + 1.73205i 0.165900 + 0.165900i 0.785175 0.619274i \(-0.212573\pi\)
−0.619274 + 0.785175i \(0.712573\pi\)
\(110\) −0.267949 0.267949i −0.0255480 0.0255480i
\(111\) 13.3923 13.3923i 1.27114 1.27114i
\(112\) −8.53590 + 4.92820i −0.806567 + 0.465671i
\(113\) −2.76795 + 4.79423i −0.260387 + 0.451003i −0.966345 0.257251i \(-0.917183\pi\)
0.705958 + 0.708254i \(0.250517\pi\)
\(114\) −10.3923 −0.973329
\(115\) −0.0621778 + 0.232051i −0.00579811 + 0.0216388i
\(116\) −6.46410 1.73205i −0.600177 0.160817i
\(117\) 13.7942 3.69615i 1.27528 0.341709i
\(118\) 7.09808 + 4.09808i 0.653431 + 0.377258i
\(119\) 8.53590 4.92820i 0.782485 0.451768i
\(120\) −1.26795 + 2.19615i −0.115747 + 0.200480i
\(121\) −9.29423 5.36603i −0.844930 0.487820i
\(122\) −10.5622 18.2942i −0.956255 1.65628i
\(123\) 16.7942 + 9.69615i 1.51428 + 0.874273i
\(124\) −2.07180 1.19615i −0.186053 0.107418i
\(125\) −3.56218 3.56218i −0.318611 0.318611i
\(126\) −2.70577 + 10.0981i −0.241049 + 0.899608i
\(127\) −20.3923 −1.80952 −0.904762 0.425917i \(-0.859952\pi\)
−0.904762 + 0.425917i \(0.859952\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) −15.0622 4.03590i −1.32615 0.355341i
\(130\) 3.36603 + 0.901924i 0.295220 + 0.0791039i
\(131\) 11.6962 3.13397i 1.02190 0.273817i 0.291305 0.956630i \(-0.405911\pi\)
0.730593 + 0.682814i \(0.239244\pi\)
\(132\) 0.464102 1.73205i 0.0403949 0.150756i
\(133\) −10.0981 2.70577i −0.875614 0.234620i
\(134\) −0.901924 + 1.56218i −0.0779143 + 0.134952i
\(135\) 0.696152 + 2.59808i 0.0599153 + 0.223607i
\(136\) 8.00000 + 8.00000i 0.685994 + 0.685994i
\(137\) −14.4282 + 8.33013i −1.23268 + 0.711691i −0.967589 0.252531i \(-0.918737\pi\)
−0.265096 + 0.964222i \(0.585404\pi\)
\(138\) −1.09808 + 0.294229i −0.0934745 + 0.0250464i
\(139\) −1.16025 4.33013i −0.0984115 0.367277i 0.899103 0.437737i \(-0.144220\pi\)
−0.997515 + 0.0704603i \(0.977553\pi\)
\(140\) −1.80385 + 1.80385i −0.152453 + 0.152453i
\(141\) −7.96410 13.7942i −0.670698 1.16168i
\(142\) −10.9282 10.9282i −0.917074 0.917074i
\(143\) −2.46410 −0.206059
\(144\) −12.0000 −1.00000
\(145\) −1.73205 −0.143839
\(146\) −0.535898 0.535898i −0.0443513 0.0443513i
\(147\) 0.803848 1.39230i 0.0663002 0.114835i
\(148\) 15.4641 + 15.4641i 1.27114 + 1.27114i
\(149\) 3.93782 + 14.6962i 0.322599 + 1.20396i 0.916704 + 0.399568i \(0.130840\pi\)
−0.594105 + 0.804388i \(0.702493\pi\)
\(150\) 3.00000 11.1962i 0.244949 0.914162i
\(151\) 6.06218 3.50000i 0.493333 0.284826i −0.232623 0.972567i \(-0.574731\pi\)
0.725956 + 0.687741i \(0.241398\pi\)
\(152\) 12.0000i 0.973329i
\(153\) 12.0000 0.970143
\(154\) 0.901924 1.56218i 0.0726791 0.125884i
\(155\) −0.598076 0.160254i −0.0480386 0.0128719i
\(156\) 4.26795 + 15.9282i 0.341709 + 1.27528i
\(157\) 0.866025 0.232051i 0.0691164 0.0185197i −0.224095 0.974567i \(-0.571943\pi\)
0.293212 + 0.956048i \(0.405276\pi\)
\(158\) −2.36603 0.633975i −0.188231 0.0504363i
\(159\) −3.92820 + 3.92820i −0.311527 + 0.311527i
\(160\) −2.53590 1.46410i −0.200480 0.115747i
\(161\) −1.14359 −0.0901278
\(162\) −9.00000 + 9.00000i −0.707107 + 0.707107i
\(163\) 11.9282 + 11.9282i 0.934289 + 0.934289i 0.997970 0.0636813i \(-0.0202841\pi\)
−0.0636813 + 0.997970i \(0.520284\pi\)
\(164\) −11.1962 + 19.3923i −0.874273 + 1.51428i
\(165\) 0.464102i 0.0361303i
\(166\) 8.63397 + 14.9545i 0.670126 + 1.16069i
\(167\) 8.25833 + 4.76795i 0.639049 + 0.368955i 0.784248 0.620447i \(-0.213049\pi\)
−0.145199 + 0.989402i \(0.546382\pi\)
\(168\) −11.6603 3.12436i −0.899608 0.241049i
\(169\) 8.36603 4.83013i 0.643540 0.371548i
\(170\) 2.53590 + 1.46410i 0.194495 + 0.112291i
\(171\) −9.00000 9.00000i −0.688247 0.688247i
\(172\) 4.66025 17.3923i 0.355341 1.32615i
\(173\) 2.40192 8.96410i 0.182615 0.681528i −0.812514 0.582942i \(-0.801901\pi\)
0.995129 0.0985859i \(-0.0314319\pi\)
\(174\) −4.09808 7.09808i −0.310674 0.538104i
\(175\) 5.83013 10.0981i 0.440716 0.763343i
\(176\) 2.00000 + 0.535898i 0.150756 + 0.0403949i
\(177\) 2.59808 + 9.69615i 0.195283 + 0.728807i
\(178\) 11.8564 + 11.8564i 0.888675 + 0.888675i
\(179\) 7.92820 + 7.92820i 0.592582 + 0.592582i 0.938328 0.345746i \(-0.112374\pi\)
−0.345746 + 0.938328i \(0.612374\pi\)
\(180\) −3.00000 + 0.803848i −0.223607 + 0.0599153i
\(181\) −4.26795 + 4.26795i −0.317234 + 0.317234i −0.847704 0.530470i \(-0.822016\pi\)
0.530470 + 0.847704i \(0.322016\pi\)
\(182\) 16.5885i 1.22962i
\(183\) 6.69615 24.9904i 0.494994 1.84734i
\(184\) −0.339746 1.26795i −0.0250464 0.0934745i
\(185\) 4.90192 + 2.83013i 0.360397 + 0.208075i
\(186\) −0.758330 2.83013i −0.0556035 0.207515i
\(187\) −2.00000 0.535898i −0.146254 0.0391888i
\(188\) 15.9282 9.19615i 1.16168 0.670698i
\(189\) −11.0885 + 6.40192i −0.806567 + 0.465671i
\(190\) −0.803848 3.00000i −0.0583172 0.217643i
\(191\) 6.59808 + 11.4282i 0.477420 + 0.826916i 0.999665 0.0258797i \(-0.00823869\pi\)
−0.522245 + 0.852795i \(0.674905\pi\)
\(192\) 13.8564i 1.00000i
\(193\) −1.23205 + 2.13397i −0.0886850 + 0.153607i −0.906956 0.421226i \(-0.861600\pi\)
0.818271 + 0.574833i \(0.194933\pi\)
\(194\) 1.36603 + 0.366025i 0.0980749 + 0.0262791i
\(195\) 2.13397 + 3.69615i 0.152817 + 0.264687i
\(196\) 1.60770 + 0.928203i 0.114835 + 0.0663002i
\(197\) 10.4641 10.4641i 0.745536 0.745536i −0.228101 0.973637i \(-0.573252\pi\)
0.973637 + 0.228101i \(0.0732517\pi\)
\(198\) 1.90192 1.09808i 0.135164 0.0780369i
\(199\) 5.85641i 0.415150i 0.978219 + 0.207575i \(0.0665570\pi\)
−0.978219 + 0.207575i \(0.933443\pi\)
\(200\) 12.9282 + 3.46410i 0.914162 + 0.244949i
\(201\) −2.13397 + 0.571797i −0.150519 + 0.0403314i
\(202\) 2.36603 1.36603i 0.166473 0.0961132i
\(203\) −2.13397 7.96410i −0.149776 0.558970i
\(204\) 13.8564i 0.970143i
\(205\) −1.50000 + 5.59808i −0.104765 + 0.390987i
\(206\) 2.83013 0.758330i 0.197184 0.0528354i
\(207\) −1.20577 0.696152i −0.0838069 0.0483859i
\(208\) −18.3923 + 4.92820i −1.27528 + 0.341709i
\(209\) 1.09808 + 1.90192i 0.0759555 + 0.131559i
\(210\) −3.12436 −0.215601
\(211\) 1.96410 0.526279i 0.135214 0.0362306i −0.190577 0.981672i \(-0.561036\pi\)
0.325791 + 0.945442i \(0.394369\pi\)
\(212\) −4.53590 4.53590i −0.311527 0.311527i
\(213\) 18.9282i 1.29694i
\(214\) 22.7846i 1.55752i
\(215\) 4.66025i 0.317827i
\(216\) −10.3923 10.3923i −0.707107 0.707107i
\(217\) 2.94744i 0.200085i
\(218\) −3.46410 −0.234619
\(219\) 0.928203i 0.0627222i
\(220\) 0.535898 0.0361303
\(221\) 18.3923 4.92820i 1.23720 0.331507i
\(222\) 26.7846i 1.79767i
\(223\) −7.79423 13.5000i −0.521940 0.904027i −0.999674 0.0255224i \(-0.991875\pi\)
0.477734 0.878504i \(-0.341458\pi\)
\(224\) 3.60770 13.4641i 0.241049 0.899608i
\(225\) 12.2942 7.09808i 0.819615 0.473205i
\(226\) −2.02628 7.56218i −0.134786 0.503029i
\(227\) −4.62436 + 17.2583i −0.306929 + 1.14548i 0.624343 + 0.781151i \(0.285367\pi\)
−0.931272 + 0.364325i \(0.881300\pi\)
\(228\) 10.3923 10.3923i 0.688247 0.688247i
\(229\) −2.52628 9.42820i −0.166941 0.623033i −0.997785 0.0665269i \(-0.978808\pi\)
0.830843 0.556506i \(-0.187858\pi\)
\(230\) −0.169873 0.294229i −0.0112011 0.0194009i
\(231\) 2.13397 0.571797i 0.140405 0.0376215i
\(232\) 8.19615 4.73205i 0.538104 0.310674i
\(233\) 22.9282i 1.50208i 0.660259 + 0.751038i \(0.270447\pi\)
−0.660259 + 0.751038i \(0.729553\pi\)
\(234\) −10.0981 + 17.4904i −0.660132 + 1.14338i
\(235\) 3.36603 3.36603i 0.219575 0.219575i
\(236\) −11.1962 + 3.00000i −0.728807 + 0.195283i
\(237\) −1.50000 2.59808i −0.0974355 0.168763i
\(238\) −3.60770 + 13.4641i −0.233852 + 0.872748i
\(239\) −5.59808 + 9.69615i −0.362109 + 0.627192i −0.988308 0.152472i \(-0.951277\pi\)
0.626198 + 0.779664i \(0.284610\pi\)
\(240\) −0.928203 3.46410i −0.0599153 0.223607i
\(241\) −6.23205 10.7942i −0.401442 0.695317i 0.592458 0.805601i \(-0.298157\pi\)
−0.993900 + 0.110284i \(0.964824\pi\)
\(242\) 14.6603 3.92820i 0.942397 0.252514i
\(243\) −15.5885 −1.00000
\(244\) 28.8564 + 7.73205i 1.84734 + 0.494994i
\(245\) 0.464102 + 0.124356i 0.0296504 + 0.00794479i
\(246\) −26.4904 + 7.09808i −1.68897 + 0.452557i
\(247\) −17.4904 10.0981i −1.11289 0.642525i
\(248\) 3.26795 0.875644i 0.207515 0.0556035i
\(249\) −5.47372 + 20.4282i −0.346883 + 1.29458i
\(250\) 7.12436 0.450584
\(251\) 7.39230 7.39230i 0.466598 0.466598i −0.434212 0.900811i \(-0.642973\pi\)
0.900811 + 0.434212i \(0.142973\pi\)
\(252\) −7.39230 12.8038i −0.465671 0.806567i
\(253\) 0.169873 + 0.169873i 0.0106798 + 0.0106798i
\(254\) 20.3923 20.3923i 1.27953 1.27953i
\(255\) 0.928203 + 3.46410i 0.0581263 + 0.216930i
\(256\) 16.0000 1.00000
\(257\) −5.16025 + 8.93782i −0.321888 + 0.557526i −0.980878 0.194626i \(-0.937651\pi\)
0.658990 + 0.752152i \(0.270984\pi\)
\(258\) 19.0981 11.0263i 1.18899 0.686466i
\(259\) −6.97372 + 26.0263i −0.433326 + 1.61719i
\(260\) −4.26795 + 2.46410i −0.264687 + 0.152817i
\(261\) 2.59808 9.69615i 0.160817 0.600177i
\(262\) −8.56218 + 14.8301i −0.528973 + 0.916208i
\(263\) −3.40192 + 1.96410i −0.209772 + 0.121112i −0.601205 0.799095i \(-0.705313\pi\)
0.391434 + 0.920206i \(0.371979\pi\)
\(264\) 1.26795 + 2.19615i 0.0780369 + 0.135164i
\(265\) −1.43782 0.830127i −0.0883247 0.0509943i
\(266\) 12.8038 7.39230i 0.785054 0.453251i
\(267\) 20.5359i 1.25678i
\(268\) −0.660254 2.46410i −0.0403314 0.150519i
\(269\) 7.73205 + 7.73205i 0.471431 + 0.471431i 0.902378 0.430946i \(-0.141820\pi\)
−0.430946 + 0.902378i \(0.641820\pi\)
\(270\) −3.29423 1.90192i −0.200480 0.115747i
\(271\) −14.9282 −0.906824 −0.453412 0.891301i \(-0.649793\pi\)
−0.453412 + 0.891301i \(0.649793\pi\)
\(272\) −16.0000 −0.970143
\(273\) −14.3660 + 14.3660i −0.869471 + 0.869471i
\(274\) 6.09808 22.7583i 0.368398 1.37488i
\(275\) −2.36603 + 0.633975i −0.142677 + 0.0382301i
\(276\) 0.803848 1.39230i 0.0483859 0.0838069i
\(277\) 13.7942 + 3.69615i 0.828815 + 0.222080i 0.648197 0.761473i \(-0.275523\pi\)
0.180618 + 0.983553i \(0.442190\pi\)
\(278\) 5.49038 + 3.16987i 0.329291 + 0.190116i
\(279\) 1.79423 3.10770i 0.107418 0.186053i
\(280\) 3.60770i 0.215601i
\(281\) −16.9641 + 9.79423i −1.01199 + 0.584275i −0.911775 0.410691i \(-0.865288\pi\)
−0.100219 + 0.994965i \(0.531954\pi\)
\(282\) 21.7583 + 5.83013i 1.29569 + 0.347179i
\(283\) 4.16025 + 15.5263i 0.247301 + 0.922942i 0.972213 + 0.234099i \(0.0752141\pi\)
−0.724911 + 0.688842i \(0.758119\pi\)
\(284\) 21.8564 1.29694
\(285\) 1.90192 3.29423i 0.112660 0.195133i
\(286\) 2.46410 2.46410i 0.145705 0.145705i
\(287\) −27.5885 −1.62850
\(288\) 12.0000 12.0000i 0.707107 0.707107i
\(289\) −1.00000 −0.0588235
\(290\) 1.73205 1.73205i 0.101710 0.101710i
\(291\) 0.866025 + 1.50000i 0.0507673 + 0.0879316i
\(292\) 1.07180 0.0627222
\(293\) 3.86603 + 14.4282i 0.225856 + 0.842905i 0.982060 + 0.188569i \(0.0603849\pi\)
−0.756204 + 0.654336i \(0.772948\pi\)
\(294\) 0.588457 + 2.19615i 0.0343195 + 0.128082i
\(295\) −2.59808 + 1.50000i −0.151266 + 0.0873334i
\(296\) −30.9282 −1.79767
\(297\) 2.59808 + 0.696152i 0.150756 + 0.0403949i
\(298\) −18.6340 10.7583i −1.07944 0.623213i
\(299\) −2.13397 0.571797i −0.123411 0.0330679i
\(300\) 8.19615 + 14.1962i 0.473205 + 0.819615i
\(301\) 21.4282 5.74167i 1.23510 0.330944i
\(302\) −2.56218 + 9.56218i −0.147437 + 0.550242i
\(303\) 3.23205 + 0.866025i 0.185676 + 0.0497519i
\(304\) 12.0000 + 12.0000i 0.688247 + 0.688247i
\(305\) 7.73205 0.442736
\(306\) −12.0000 + 12.0000i −0.685994 + 0.685994i
\(307\) −5.92820 5.92820i −0.338340 0.338340i 0.517402 0.855742i \(-0.326899\pi\)
−0.855742 + 0.517402i \(0.826899\pi\)
\(308\) 0.660254 + 2.46410i 0.0376215 + 0.140405i
\(309\) 3.10770 + 1.79423i 0.176791 + 0.102070i
\(310\) 0.758330 0.437822i 0.0430703 0.0248666i
\(311\) −27.1865 15.6962i −1.54161 0.890047i −0.998738 0.0502299i \(-0.984005\pi\)
−0.542869 0.839817i \(-0.682662\pi\)
\(312\) −20.1962 11.6603i −1.14338 0.660132i
\(313\) 7.83975 4.52628i 0.443129 0.255840i −0.261795 0.965123i \(-0.584314\pi\)
0.704924 + 0.709283i \(0.250981\pi\)
\(314\) −0.633975 + 1.09808i −0.0357773 + 0.0619680i
\(315\) −2.70577 2.70577i −0.152453 0.152453i
\(316\) 3.00000 1.73205i 0.168763 0.0974355i
\(317\) −0.545517 + 2.03590i −0.0306393 + 0.114347i −0.979552 0.201192i \(-0.935519\pi\)
0.948913 + 0.315539i \(0.102185\pi\)
\(318\) 7.85641i 0.440565i
\(319\) −0.866025 + 1.50000i −0.0484881 + 0.0839839i
\(320\) 4.00000 1.07180i 0.223607 0.0599153i
\(321\) 19.7321 19.7321i 1.10134 1.10134i
\(322\) 1.14359 1.14359i 0.0637300 0.0637300i
\(323\) −12.0000 12.0000i −0.667698 0.667698i
\(324\) 18.0000i 1.00000i
\(325\) 15.9282 15.9282i 0.883538 0.883538i
\(326\) −23.8564 −1.32128
\(327\) −3.00000 3.00000i −0.165900 0.165900i
\(328\) −8.19615 30.5885i −0.452557 1.68897i
\(329\) 19.6244 + 11.3301i 1.08193 + 0.624650i
\(330\) 0.464102 + 0.464102i 0.0255480 + 0.0255480i
\(331\) −26.3564 7.06218i −1.44868 0.388172i −0.553115 0.833105i \(-0.686561\pi\)
−0.895564 + 0.444933i \(0.853228\pi\)
\(332\) −23.5885 6.32051i −1.29458 0.346883i
\(333\) −23.1962 + 23.1962i −1.27114 + 1.27114i
\(334\) −13.0263 + 3.49038i −0.712766 + 0.190985i
\(335\) −0.330127 0.571797i −0.0180368 0.0312406i
\(336\) 14.7846 8.53590i 0.806567 0.465671i
\(337\) 0.696152 1.20577i 0.0379218 0.0656826i −0.846442 0.532482i \(-0.821260\pi\)
0.884363 + 0.466799i \(0.154593\pi\)
\(338\) −3.53590 + 13.1962i −0.192328 + 0.717776i
\(339\) 4.79423 8.30385i 0.260387 0.451003i
\(340\) −4.00000 + 1.07180i −0.216930 + 0.0581263i
\(341\) −0.437822 + 0.437822i −0.0237094 + 0.0237094i
\(342\) 18.0000 0.973329
\(343\) 19.5359i 1.05484i
\(344\) 12.7321 + 22.0526i 0.686466 + 1.18899i
\(345\) 0.107695 0.401924i 0.00579811 0.0216388i
\(346\) 6.56218 + 11.3660i 0.352785 + 0.611041i
\(347\) −5.23205 19.5263i −0.280871 1.04823i −0.951804 0.306707i \(-0.900773\pi\)
0.670933 0.741518i \(-0.265894\pi\)
\(348\) 11.1962 + 3.00000i 0.600177 + 0.160817i
\(349\) −2.13397 + 7.96410i −0.114229 + 0.426309i −0.999228 0.0392843i \(-0.987492\pi\)
0.884999 + 0.465593i \(0.154159\pi\)
\(350\) 4.26795 + 15.9282i 0.228131 + 0.851398i
\(351\) −23.8923 + 6.40192i −1.27528 + 0.341709i
\(352\) −2.53590 + 1.46410i −0.135164 + 0.0780369i
\(353\) −15.2321 26.3827i −0.810720 1.40421i −0.912361 0.409387i \(-0.865742\pi\)
0.101640 0.994821i \(-0.467591\pi\)
\(354\) −12.2942 7.09808i −0.653431 0.377258i
\(355\) 5.46410 1.46410i 0.290004 0.0777064i
\(356\) −23.7128 −1.25678
\(357\) −14.7846 + 8.53590i −0.782485 + 0.451768i
\(358\) −15.8564 −0.838037
\(359\) 15.0718i 0.795459i −0.917503 0.397730i \(-0.869798\pi\)
0.917503 0.397730i \(-0.130202\pi\)
\(360\) 2.19615 3.80385i 0.115747 0.200480i
\(361\) 1.00000i 0.0526316i
\(362\) 8.53590i 0.448637i
\(363\) 16.0981 + 9.29423i 0.844930 + 0.487820i
\(364\) −16.5885 16.5885i −0.869471 0.869471i
\(365\) 0.267949 0.0717968i 0.0140251 0.00375801i
\(366\) 18.2942 + 31.6865i 0.956255 + 1.65628i
\(367\) 15.4545 + 26.7679i 0.806717 + 1.39728i 0.915125 + 0.403169i \(0.132091\pi\)
−0.108408 + 0.994106i \(0.534575\pi\)
\(368\) 1.60770 + 0.928203i 0.0838069 + 0.0483859i
\(369\) −29.0885 16.7942i −1.51428 0.874273i
\(370\) −7.73205 + 2.07180i −0.401970 + 0.107708i
\(371\) 2.04552 7.63397i 0.106198 0.396336i
\(372\) 3.58846 + 2.07180i 0.186053 + 0.107418i
\(373\) 3.59808 + 13.4282i 0.186301 + 0.695286i 0.994348 + 0.106168i \(0.0338581\pi\)
−0.808047 + 0.589118i \(0.799475\pi\)
\(374\) 2.53590 1.46410i 0.131128 0.0757069i
\(375\) 6.16987 + 6.16987i 0.318611 + 0.318611i
\(376\) −6.73205 + 25.1244i −0.347179 + 1.29569i
\(377\) 15.9282i 0.820344i
\(378\) 4.68653 17.4904i 0.241049 0.899608i
\(379\) 15.5885 15.5885i 0.800725 0.800725i −0.182484 0.983209i \(-0.558414\pi\)
0.983209 + 0.182484i \(0.0584137\pi\)
\(380\) 3.80385 + 2.19615i 0.195133 + 0.112660i
\(381\) 35.3205 1.80952
\(382\) −18.0263 4.83013i −0.922305 0.247131i
\(383\) 12.3301 21.3564i 0.630040 1.09126i −0.357503 0.933912i \(-0.616372\pi\)
0.987543 0.157349i \(-0.0502949\pi\)
\(384\) 13.8564 + 13.8564i 0.707107 + 0.707107i
\(385\) 0.330127 + 0.571797i 0.0168248 + 0.0291415i
\(386\) −0.901924 3.36603i −0.0459067 0.171326i
\(387\) 26.0885 + 6.99038i 1.32615 + 0.355341i
\(388\) −1.73205 + 1.00000i −0.0879316 + 0.0507673i
\(389\) 7.59808 + 2.03590i 0.385238 + 0.103224i 0.446240 0.894914i \(-0.352763\pi\)
−0.0610019 + 0.998138i \(0.519430\pi\)
\(390\) −5.83013 1.56218i −0.295220 0.0791039i
\(391\) −1.60770 0.928203i −0.0813046 0.0469413i
\(392\) −2.53590 + 0.679492i −0.128082 + 0.0343195i
\(393\) −20.2583 + 5.42820i −1.02190 + 0.273817i
\(394\) 20.9282i 1.05435i
\(395\) 0.633975 0.633975i 0.0318987 0.0318987i
\(396\) −0.803848 + 3.00000i −0.0403949 + 0.150756i
\(397\) −21.0526 21.0526i −1.05660 1.05660i −0.998299 0.0582984i \(-0.981433\pi\)
−0.0582984 0.998299i \(-0.518567\pi\)
\(398\) −5.85641 5.85641i −0.293555 0.293555i
\(399\) 17.4904 + 4.68653i 0.875614 + 0.234620i
\(400\) −16.3923 + 9.46410i −0.819615 + 0.473205i
\(401\) 1.16025 2.00962i 0.0579403 0.100356i −0.835600 0.549338i \(-0.814880\pi\)
0.893541 + 0.448982i \(0.148213\pi\)
\(402\) 1.56218 2.70577i 0.0779143 0.134952i
\(403\) 1.47372 5.50000i 0.0734112 0.273975i
\(404\) −1.00000 + 3.73205i −0.0497519 + 0.185676i
\(405\) −1.20577 4.50000i −0.0599153 0.223607i
\(406\) 10.0981 + 5.83013i 0.501159 + 0.289344i
\(407\) 4.90192 2.83013i 0.242979 0.140284i
\(408\) −13.8564 13.8564i −0.685994 0.685994i
\(409\) 4.62436 + 2.66987i 0.228660 + 0.132017i 0.609954 0.792437i \(-0.291188\pi\)
−0.381294 + 0.924454i \(0.624521\pi\)
\(410\) −4.09808 7.09808i −0.202390 0.350549i
\(411\) 24.9904 14.4282i 1.23268 0.711691i
\(412\) −2.07180 + 3.58846i −0.102070 + 0.176791i
\(413\) −10.0981 10.0981i −0.496894 0.496894i
\(414\) 1.90192 0.509619i 0.0934745 0.0250464i
\(415\) −6.32051 −0.310262
\(416\) 13.4641 23.3205i 0.660132 1.14338i
\(417\) 2.00962 + 7.50000i 0.0984115 + 0.367277i
\(418\) −3.00000 0.803848i −0.146735 0.0393175i
\(419\) 1.96410 0.526279i 0.0959526 0.0257104i −0.210523 0.977589i \(-0.567517\pi\)
0.306476 + 0.951878i \(0.400850\pi\)
\(420\) 3.12436 3.12436i 0.152453 0.152453i
\(421\) 10.7942 + 2.89230i 0.526079 + 0.140962i 0.512077 0.858940i \(-0.328876\pi\)
0.0140017 + 0.999902i \(0.495543\pi\)
\(422\) −1.43782 + 2.49038i −0.0699921 + 0.121230i
\(423\) 13.7942 + 23.8923i 0.670698 + 1.16168i
\(424\) 9.07180 0.440565
\(425\) 16.3923 9.46410i 0.795144 0.459076i
\(426\) 18.9282 + 18.9282i 0.917074 + 0.917074i
\(427\) 9.52628 + 35.5526i 0.461009 + 1.72051i
\(428\) 22.7846 + 22.7846i 1.10134 + 1.10134i
\(429\) 4.26795 0.206059
\(430\) 4.66025 + 4.66025i 0.224737 + 0.224737i
\(431\) 31.3205 1.50866 0.754328 0.656498i \(-0.227963\pi\)
0.754328 + 0.656498i \(0.227963\pi\)
\(432\) 20.7846 1.00000
\(433\) 24.3923 1.17222 0.586110 0.810232i \(-0.300659\pi\)
0.586110 + 0.810232i \(0.300659\pi\)
\(434\) 2.94744 + 2.94744i 0.141482 + 0.141482i
\(435\) 3.00000 0.143839
\(436\) 3.46410 3.46410i 0.165900 0.165900i
\(437\) 0.509619 + 1.90192i 0.0243784 + 0.0909814i
\(438\) 0.928203 + 0.928203i 0.0443513 + 0.0443513i
\(439\) 18.0622 10.4282i 0.862061 0.497711i −0.00264111 0.999997i \(-0.500841\pi\)
0.864702 + 0.502286i \(0.167507\pi\)
\(440\) −0.535898 + 0.535898i −0.0255480 + 0.0255480i
\(441\) −1.39230 + 2.41154i −0.0663002 + 0.114835i
\(442\) −13.4641 + 23.3205i −0.640422 + 1.10924i
\(443\) 16.1603 + 4.33013i 0.767797 + 0.205731i 0.621398 0.783495i \(-0.286565\pi\)
0.146399 + 0.989226i \(0.453232\pi\)
\(444\) −26.7846 26.7846i −1.27114 1.27114i
\(445\) −5.92820 + 1.58846i −0.281024 + 0.0753001i
\(446\) 21.2942 + 5.70577i 1.00831 + 0.270176i
\(447\) −6.82051 25.4545i −0.322599 1.20396i
\(448\) 9.85641 + 17.0718i 0.465671 + 0.806567i
\(449\) 0.679492 0.0320672 0.0160336 0.999871i \(-0.494896\pi\)
0.0160336 + 0.999871i \(0.494896\pi\)
\(450\) −5.19615 + 19.3923i −0.244949 + 0.914162i
\(451\) 4.09808 + 4.09808i 0.192971 + 0.192971i
\(452\) 9.58846 + 5.53590i 0.451003 + 0.260387i
\(453\) −10.5000 + 6.06218i −0.493333 + 0.284826i
\(454\) −12.6340 21.8827i −0.592942 1.02701i
\(455\) −5.25833 3.03590i −0.246514 0.142325i
\(456\) 20.7846i 0.973329i
\(457\) 19.0359 10.9904i 0.890462 0.514108i 0.0163683 0.999866i \(-0.494790\pi\)
0.874094 + 0.485758i \(0.161456\pi\)
\(458\) 11.9545 + 6.90192i 0.558596 + 0.322506i
\(459\) −20.7846 −0.970143
\(460\) 0.464102 + 0.124356i 0.0216388 + 0.00579811i
\(461\) −0.598076 + 2.23205i −0.0278552 + 0.103957i −0.978454 0.206466i \(-0.933804\pi\)
0.950599 + 0.310423i \(0.100471\pi\)
\(462\) −1.56218 + 2.70577i −0.0726791 + 0.125884i
\(463\) 3.33013 5.76795i 0.154764 0.268059i −0.778209 0.628005i \(-0.783872\pi\)
0.932973 + 0.359946i \(0.117205\pi\)
\(464\) −3.46410 + 12.9282i −0.160817 + 0.600177i
\(465\) 1.03590 + 0.277568i 0.0480386 + 0.0128719i
\(466\) −22.9282 22.9282i −1.06213 1.06213i
\(467\) −19.7846 19.7846i −0.915523 0.915523i 0.0811771 0.996700i \(-0.474132\pi\)
−0.996700 + 0.0811771i \(0.974132\pi\)
\(468\) −7.39230 27.5885i −0.341709 1.27528i
\(469\) 2.22243 2.22243i 0.102622 0.102622i
\(470\) 6.73205i 0.310526i
\(471\) −1.50000 + 0.401924i −0.0691164 + 0.0185197i
\(472\) 8.19615 14.1962i 0.377258 0.653431i
\(473\) −4.03590 2.33013i −0.185571 0.107139i
\(474\) 4.09808 + 1.09808i 0.188231 + 0.0504363i
\(475\) −19.3923 5.19615i −0.889780 0.238416i
\(476\) −9.85641 17.0718i −0.451768 0.782485i
\(477\) 6.80385 6.80385i 0.311527 0.311527i
\(478\) −4.09808 15.2942i −0.187442 0.699542i
\(479\) 0.669873 + 1.16025i 0.0306073 + 0.0530134i 0.880923 0.473259i \(-0.156923\pi\)
−0.850316 + 0.526272i \(0.823589\pi\)
\(480\) 4.39230 + 2.53590i 0.200480 + 0.115747i
\(481\) −26.0263 + 45.0788i −1.18670 + 2.05542i
\(482\) 17.0263 + 4.56218i 0.775526 + 0.207802i
\(483\) 1.98076 0.0901278
\(484\) −10.7321 + 18.5885i −0.487820 + 0.844930i
\(485\) −0.366025 + 0.366025i −0.0166204 + 0.0166204i
\(486\) 15.5885 15.5885i 0.707107 0.707107i
\(487\) 34.7846i 1.57624i 0.615521 + 0.788121i \(0.288946\pi\)
−0.615521 + 0.788121i \(0.711054\pi\)
\(488\) −36.5885 + 21.1244i −1.65628 + 0.956255i
\(489\) −20.6603 20.6603i −0.934289 0.934289i
\(490\) −0.588457 + 0.339746i −0.0265838 + 0.0153482i
\(491\) 0.500000 + 1.86603i 0.0225647 + 0.0842125i 0.976290 0.216467i \(-0.0694533\pi\)
−0.953725 + 0.300679i \(0.902787\pi\)
\(492\) 19.3923 33.5885i 0.874273 1.51428i
\(493\) 3.46410 12.9282i 0.156015 0.582257i
\(494\) 27.5885 7.39230i 1.24126 0.332596i
\(495\) 0.803848i 0.0361303i
\(496\) −2.39230 + 4.14359i −0.107418 + 0.186053i
\(497\) 13.4641 + 23.3205i 0.603947 + 1.04607i
\(498\) −14.9545 25.9019i −0.670126 1.16069i
\(499\) −2.50000 + 0.669873i −0.111915 + 0.0299876i −0.314342 0.949310i \(-0.601784\pi\)
0.202427 + 0.979297i \(0.435117\pi\)
\(500\) −7.12436 + 7.12436i −0.318611 + 0.318611i
\(501\) −14.3038 8.25833i −0.639049 0.368955i
\(502\) 14.7846i 0.659869i
\(503\) 13.8564i 0.617827i −0.951090 0.308913i \(-0.900035\pi\)
0.951090 0.308913i \(-0.0999653\pi\)
\(504\) 20.1962 + 5.41154i 0.899608 + 0.241049i
\(505\) 1.00000i 0.0444994i
\(506\) −0.339746 −0.0151036
\(507\) −14.4904 + 8.36603i −0.643540 + 0.371548i
\(508\) 40.7846i 1.80952i
\(509\) −21.2583 + 5.69615i −0.942259 + 0.252478i −0.697074 0.716999i \(-0.745515\pi\)
−0.245185 + 0.969476i \(0.578849\pi\)
\(510\) −4.39230 2.53590i −0.194495 0.112291i
\(511\) 0.660254 + 1.14359i 0.0292079 + 0.0505896i
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 15.5885 + 15.5885i 0.688247 + 0.688247i
\(514\) −3.77757 14.0981i −0.166621 0.621839i
\(515\) −0.277568 + 1.03590i −0.0122311 + 0.0456471i
\(516\) −8.07180 + 30.1244i −0.355341 + 1.32615i
\(517\) −1.23205 4.59808i −0.0541855 0.202223i
\(518\) −19.0526 33.0000i −0.837121 1.44994i
\(519\) −4.16025 + 15.5263i −0.182615 + 0.681528i
\(520\) 1.80385 6.73205i 0.0791039 0.295220i
\(521\) 14.1436i 0.619642i −0.950795 0.309821i \(-0.899731\pi\)
0.950795 0.309821i \(-0.100269\pi\)
\(522\) 7.09808 + 12.2942i 0.310674 + 0.538104i
\(523\) −2.12436 + 2.12436i −0.0928916 + 0.0928916i −0.752026 0.659134i \(-0.770923\pi\)
0.659134 + 0.752026i \(0.270923\pi\)
\(524\) −6.26795 23.3923i −0.273817 1.02190i
\(525\) −10.0981 + 17.4904i −0.440716 + 0.763343i
\(526\) 1.43782 5.36603i 0.0626920 0.233970i
\(527\) 2.39230 4.14359i 0.104210 0.180498i
\(528\) −3.46410 0.928203i −0.150756 0.0403949i
\(529\) −11.3923 19.7321i −0.495318 0.857915i
\(530\) 2.26795 0.607695i 0.0985134 0.0263966i
\(531\) −4.50000 16.7942i −0.195283 0.728807i
\(532\) −5.41154 + 20.1962i −0.234620 + 0.875614i
\(533\) −51.4808 13.7942i −2.22988 0.597494i
\(534\) −20.5359 20.5359i −0.888675 0.888675i
\(535\) 7.22243 + 4.16987i 0.312253 + 0.180279i
\(536\) 3.12436 + 1.80385i 0.134952 + 0.0779143i
\(537\) −13.7321 13.7321i −0.592582 0.592582i
\(538\) −15.4641 −0.666705
\(539\) 0.339746 0.339746i 0.0146339 0.0146339i
\(540\) 5.19615 1.39230i 0.223607 0.0599153i
\(541\) −15.0000 15.0000i −0.644900 0.644900i 0.306856 0.951756i \(-0.400723\pi\)
−0.951756 + 0.306856i \(0.900723\pi\)
\(542\) 14.9282 14.9282i 0.641221 0.641221i
\(543\) 7.39230 7.39230i 0.317234 0.317234i
\(544\) 16.0000 16.0000i 0.685994 0.685994i
\(545\) 0.633975 1.09808i 0.0271565 0.0470364i
\(546\) 28.7321i 1.22962i
\(547\) 7.57180 28.2583i 0.323747 1.20824i −0.591819 0.806071i \(-0.701590\pi\)
0.915566 0.402168i \(-0.131743\pi\)
\(548\) 16.6603 + 28.8564i 0.711691 + 1.23268i
\(549\) −11.5981 + 43.2846i −0.494994 + 1.84734i
\(550\) 1.73205 3.00000i 0.0738549 0.127920i
\(551\) −12.2942 + 7.09808i −0.523752 + 0.302388i
\(552\) 0.588457 + 2.19615i 0.0250464 + 0.0934745i
\(553\) 3.69615 + 2.13397i 0.157176 + 0.0907458i
\(554\) −17.4904 + 10.0981i −0.743095 + 0.429026i
\(555\) −8.49038 4.90192i −0.360397 0.208075i
\(556\) −8.66025 + 2.32051i −0.367277 + 0.0984115i
\(557\) 27.9808 + 27.9808i 1.18558 + 1.18558i 0.978276 + 0.207307i \(0.0664699\pi\)
0.207307 + 0.978276i \(0.433530\pi\)
\(558\) 1.31347 + 4.90192i 0.0556035 + 0.207515i
\(559\) 42.8564 1.81263
\(560\) 3.60770 + 3.60770i 0.152453 + 0.152453i
\(561\) 3.46410 + 0.928203i 0.146254 + 0.0391888i
\(562\) 7.16987 26.7583i 0.302443 1.12873i
\(563\) −29.3564 + 7.86603i −1.23723 + 0.331513i −0.817389 0.576086i \(-0.804579\pi\)
−0.419836 + 0.907600i \(0.637912\pi\)
\(564\) −27.5885 + 15.9282i −1.16168 + 0.670698i
\(565\) 2.76795 + 0.741670i 0.116448 + 0.0312023i
\(566\) −19.6865 11.3660i −0.827487 0.477750i
\(567\) 19.2058 11.0885i 0.806567 0.465671i
\(568\) −21.8564 + 21.8564i −0.917074 + 0.917074i
\(569\) 24.4808 14.1340i 1.02629 0.592527i 0.110368 0.993891i \(-0.464797\pi\)
0.915919 + 0.401364i \(0.131464\pi\)
\(570\) 1.39230 + 5.19615i 0.0583172 + 0.217643i
\(571\) 1.44744 + 5.40192i 0.0605735 + 0.226063i 0.989576 0.144009i \(-0.0459995\pi\)
−0.929003 + 0.370073i \(0.879333\pi\)
\(572\) 4.92820i 0.206059i
\(573\) −11.4282 19.7942i −0.477420 0.826916i
\(574\) 27.5885 27.5885i 1.15152 1.15152i
\(575\) −2.19615 −0.0915859
\(576\) 24.0000i 1.00000i
\(577\) 37.1769 1.54770 0.773848 0.633372i \(-0.218330\pi\)
0.773848 + 0.633372i \(0.218330\pi\)
\(578\) 1.00000 1.00000i 0.0415945 0.0415945i
\(579\) 2.13397 3.69615i 0.0886850 0.153607i
\(580\) 3.46410i 0.143839i
\(581\) −7.78719 29.0622i −0.323067 1.20570i
\(582\) −2.36603 0.633975i −0.0980749 0.0262791i
\(583\) −1.43782 + 0.830127i −0.0595485 + 0.0343803i
\(584\) −1.07180 + 1.07180i −0.0443513 + 0.0443513i
\(585\) −3.69615 6.40192i −0.152817 0.264687i
\(586\) −18.2942 10.5622i −0.755728 0.436320i
\(587\) −2.96410 0.794229i −0.122342 0.0327813i 0.197129 0.980378i \(-0.436838\pi\)
−0.319470 + 0.947596i \(0.603505\pi\)
\(588\) −2.78461 1.60770i −0.114835 0.0663002i
\(589\) −4.90192 + 1.31347i −0.201980 + 0.0541204i
\(590\) 1.09808 4.09808i 0.0452071 0.168715i
\(591\) −18.1244 + 18.1244i −0.745536 + 0.745536i
\(592\) 30.9282 30.9282i 1.27114 1.27114i
\(593\) 1.46410 0.0601234 0.0300617 0.999548i \(-0.490430\pi\)
0.0300617 + 0.999548i \(0.490430\pi\)
\(594\) −3.29423 + 1.90192i −0.135164 + 0.0780369i
\(595\) −3.60770 3.60770i −0.147901 0.147901i
\(596\) 29.3923 7.87564i 1.20396 0.322599i
\(597\) 10.1436i 0.415150i
\(598\) 2.70577 1.56218i 0.110647 0.0638822i
\(599\) 30.3109 + 17.5000i 1.23847 + 0.715031i 0.968781 0.247917i \(-0.0797461\pi\)
0.269688 + 0.962948i \(0.413079\pi\)
\(600\) −22.3923 6.00000i −0.914162 0.244949i
\(601\) −30.2321 + 17.4545i −1.23319 + 0.711983i −0.967694 0.252128i \(-0.918869\pi\)
−0.265497 + 0.964112i \(0.585536\pi\)
\(602\) −15.6865 + 27.1699i −0.639335 + 1.10736i
\(603\) 3.69615 0.990381i 0.150519 0.0403314i
\(604\) −7.00000 12.1244i −0.284826 0.493333i
\(605\) −1.43782 + 5.36603i −0.0584558 + 0.218160i
\(606\) −4.09808 + 2.36603i −0.166473 + 0.0961132i
\(607\) −4.59808 + 7.96410i −0.186630 + 0.323253i −0.944125 0.329589i \(-0.893090\pi\)
0.757494 + 0.652842i \(0.226423\pi\)
\(608\) −24.0000 −0.973329
\(609\) 3.69615 + 13.7942i 0.149776 + 0.558970i
\(610\) −7.73205 + 7.73205i −0.313062 + 0.313062i
\(611\) 30.9545 + 30.9545i 1.25228 + 1.25228i
\(612\) 24.0000i 0.970143i
\(613\) −7.58846 + 7.58846i −0.306495 + 0.306495i −0.843548 0.537053i \(-0.819537\pi\)
0.537053 + 0.843548i \(0.319537\pi\)
\(614\) 11.8564 0.478486
\(615\) 2.59808 9.69615i 0.104765 0.390987i
\(616\) −3.12436 1.80385i −0.125884 0.0726791i
\(617\) −8.08846 4.66987i −0.325629 0.188002i 0.328270 0.944584i \(-0.393534\pi\)
−0.653899 + 0.756582i \(0.726868\pi\)
\(618\) −4.90192 + 1.31347i −0.197184 + 0.0528354i
\(619\) −33.0885 8.86603i −1.32994 0.356356i −0.477246 0.878770i \(-0.658365\pi\)
−0.852692 + 0.522414i \(0.825031\pi\)
\(620\) −0.320508 + 1.19615i −0.0128719 + 0.0480386i
\(621\) 2.08846 + 1.20577i 0.0838069 + 0.0483859i
\(622\) 42.8827 11.4904i 1.71944 0.460722i
\(623\) −14.6077 25.3013i −0.585245 1.01367i
\(624\) 31.8564 8.53590i 1.27528 0.341709i
\(625\) 10.5263 18.2321i 0.421051 0.729282i
\(626\) −3.31347 + 12.3660i −0.132433 + 0.494246i
\(627\) −1.90192 3.29423i −0.0759555 0.131559i
\(628\) −0.464102 1.73205i −0.0185197 0.0691164i
\(629\) −30.9282 + 30.9282i −1.23319 + 1.23319i
\(630\) 5.41154 0.215601
\(631\) 32.2487i 1.28380i −0.766788 0.641900i \(-0.778146\pi\)
0.766788 0.641900i \(-0.221854\pi\)
\(632\) −1.26795 + 4.73205i −0.0504363 + 0.188231i
\(633\) −3.40192 + 0.911543i −0.135214 + 0.0362306i
\(634\) −1.49038 2.58142i −0.0591906 0.102521i
\(635\) 2.73205 + 10.1962i 0.108418 + 0.404622i
\(636\) 7.85641 + 7.85641i 0.311527 + 0.311527i
\(637\) −1.14359 + 4.26795i −0.0453108 + 0.169102i
\(638\) −0.633975 2.36603i −0.0250993 0.0936718i
\(639\) 32.7846i 1.29694i
\(640\) −2.92820 + 5.07180i −0.115747 + 0.200480i
\(641\) 5.76795 + 9.99038i 0.227820 + 0.394596i 0.957162 0.289553i \(-0.0935068\pi\)
−0.729342 + 0.684150i \(0.760173\pi\)
\(642\) 39.4641i 1.55752i
\(643\) 1.03590 0.277568i 0.0408518 0.0109462i −0.238335 0.971183i \(-0.576602\pi\)
0.279187 + 0.960237i \(0.409935\pi\)
\(644\) 2.28719i 0.0901278i
\(645\) 8.07180i 0.317827i
\(646\) 24.0000 0.944267
\(647\) 46.3923i 1.82387i 0.410335 + 0.911935i \(0.365412\pi\)
−0.410335 + 0.911935i \(0.634588\pi\)
\(648\) 18.0000 + 18.0000i 0.707107 + 0.707107i
\(649\) 3.00000i 0.117760i
\(650\) 31.8564i 1.24951i
\(651\) 5.10512i 0.200085i
\(652\) 23.8564 23.8564i 0.934289 0.934289i
\(653\) −21.3301 + 5.71539i −0.834712 + 0.223661i −0.650768 0.759276i \(-0.725553\pi\)
−0.183944 + 0.982937i \(0.558886\pi\)
\(654\) 6.00000 0.234619
\(655\) −3.13397 5.42820i −0.122455 0.212097i
\(656\) 38.7846 + 22.3923i 1.51428 + 0.874273i
\(657\) 1.60770i 0.0627222i
\(658\) −30.9545 + 8.29423i −1.20673 + 0.323343i
\(659\) −2.23205 + 8.33013i −0.0869484 + 0.324496i −0.995676 0.0928939i \(-0.970388\pi\)
0.908728 + 0.417390i \(0.137055\pi\)
\(660\) −0.928203 −0.0361303
\(661\) 4.20577 + 15.6962i 0.163586 + 0.610510i 0.998216 + 0.0596998i \(0.0190143\pi\)
−0.834631 + 0.550810i \(0.814319\pi\)
\(662\) 33.4186 19.2942i 1.29885 0.749891i
\(663\) −31.8564 + 8.53590i −1.23720 + 0.331507i
\(664\) 29.9090 17.2679i 1.16069 0.670126i
\(665\) 5.41154i 0.209851i
\(666\) 46.3923i 1.79767i
\(667\) −1.09808 + 1.09808i −0.0425177 + 0.0425177i
\(668\) 9.53590 16.5167i 0.368955 0.639049i
\(669\) 13.5000 + 23.3827i 0.521940 + 0.904027i
\(670\) 0.901924 + 0.241670i 0.0348444 + 0.00933652i
\(671\) 3.86603 6.69615i 0.149246 0.258502i
\(672\) −6.24871 + 23.3205i −0.241049 + 0.899608i
\(673\) 3.83975 + 6.65064i 0.148011 + 0.256363i 0.930492 0.366311i \(-0.119379\pi\)
−0.782481 + 0.622674i \(0.786046\pi\)
\(674\) 0.509619 + 1.90192i 0.0196298 + 0.0732594i
\(675\) −21.2942 + 12.2942i −0.819615 + 0.473205i
\(676\) −9.66025 16.7321i −0.371548 0.643540i
\(677\) 45.6506 + 12.2321i 1.75450 + 0.470116i 0.985577 0.169229i \(-0.0541279\pi\)
0.768920 + 0.639345i \(0.220795\pi\)
\(678\) 3.50962 + 13.0981i 0.134786 + 0.503029i
\(679\) −2.13397 1.23205i −0.0818944 0.0472818i
\(680\) 2.92820 5.07180i 0.112291 0.194495i
\(681\) 8.00962 29.8923i 0.306929 1.14548i
\(682\) 0.875644i 0.0335302i
\(683\) −5.39230 + 5.39230i −0.206331 + 0.206331i −0.802706 0.596375i \(-0.796607\pi\)
0.596375 + 0.802706i \(0.296607\pi\)
\(684\) −18.0000 + 18.0000i −0.688247 + 0.688247i
\(685\) 6.09808 + 6.09808i 0.232996 + 0.232996i
\(686\) −19.5359 19.5359i −0.745884 0.745884i
\(687\) 4.37564 + 16.3301i 0.166941 + 0.623033i
\(688\) −34.7846 9.32051i −1.32615 0.355341i
\(689\) 7.63397 13.2224i 0.290831 0.503735i
\(690\) 0.294229 + 0.509619i 0.0112011 + 0.0194009i
\(691\) 4.96410 18.5263i 0.188843 0.704773i −0.804932 0.593367i \(-0.797798\pi\)
0.993775 0.111405i \(-0.0355352\pi\)
\(692\) −17.9282 4.80385i −0.681528 0.182615i
\(693\) −3.69615 + 0.990381i −0.140405 + 0.0376215i
\(694\) 24.7583 + 14.2942i 0.939813 + 0.542601i
\(695\) −2.00962 + 1.16025i −0.0762292 + 0.0440109i
\(696\) −14.1962 + 8.19615i −0.538104 + 0.310674i
\(697\) −38.7846 22.3923i −1.46907 0.848169i
\(698\) −5.83013 10.0981i −0.220674 0.382218i
\(699\) 39.7128i 1.50208i
\(700\) −20.1962 11.6603i −0.763343 0.440716i
\(701\) −21.0526 21.0526i −0.795144 0.795144i 0.187181 0.982325i \(-0.440065\pi\)
−0.982325 + 0.187181i \(0.940065\pi\)
\(702\) 17.4904 30.2942i 0.660132 1.14338i
\(703\) 46.3923 1.74972
\(704\) 1.07180 4.00000i 0.0403949 0.150756i
\(705\) −5.83013 + 5.83013i −0.219575 + 0.219575i
\(706\) 41.6147 + 11.1506i 1.56619 + 0.419660i
\(707\) −4.59808 + 1.23205i −0.172928 + 0.0463360i
\(708\) 19.3923 5.19615i 0.728807 0.195283i
\(709\) −40.1147 10.7487i −1.50654 0.403676i −0.591256 0.806484i \(-0.701368\pi\)
−0.915285 + 0.402808i \(0.868034\pi\)
\(710\) −4.00000 + 6.92820i −0.150117 + 0.260011i
\(711\) 2.59808 + 4.50000i 0.0974355 + 0.168763i
\(712\) 23.7128 23.7128i 0.888675 0.888675i
\(713\) −0.480762 + 0.277568i −0.0180047 + 0.0103950i
\(714\) 6.24871 23.3205i 0.233852 0.872748i
\(715\) 0.330127 + 1.23205i 0.0123461 + 0.0460761i
\(716\) 15.8564 15.8564i 0.592582 0.592582i
\(717\) 9.69615 16.7942i 0.362109 0.627192i
\(718\) 15.0718 + 15.0718i 0.562474 + 0.562474i
\(719\) 23.3205 0.869708 0.434854 0.900501i \(-0.356800\pi\)
0.434854 + 0.900501i \(0.356800\pi\)
\(720\) 1.60770 + 6.00000i 0.0599153 + 0.223607i
\(721\) −5.10512 −0.190125
\(722\) 1.00000 + 1.00000i 0.0372161 + 0.0372161i
\(723\) 10.7942 + 18.6962i 0.401442 + 0.695317i
\(724\) 8.53590 + 8.53590i 0.317234 + 0.317234i
\(725\) −4.09808 15.2942i −0.152199 0.568013i
\(726\) −25.3923 + 6.80385i −0.942397 + 0.252514i
\(727\) −9.06218 + 5.23205i −0.336098 + 0.194046i −0.658545 0.752541i \(-0.728828\pi\)
0.322447 + 0.946587i \(0.395494\pi\)
\(728\) 33.1769 1.22962
\(729\) 27.0000 1.00000
\(730\) −0.196152 + 0.339746i −0.00725993 + 0.0125746i
\(731\) 34.7846 + 9.32051i 1.28656 + 0.344731i
\(732\) −49.9808 13.3923i −1.84734 0.494994i
\(733\) 27.5263 7.37564i 1.01671 0.272426i 0.288277 0.957547i \(-0.406917\pi\)
0.728429 + 0.685121i \(0.240251\pi\)
\(734\) −42.2224 11.3135i −1.55846 0.417588i
\(735\) −0.803848 0.215390i −0.0296504 0.00794479i
\(736\) −2.53590 + 0.679492i −0.0934745 + 0.0250464i
\(737\) −0.660254 −0.0243208
\(738\) 45.8827 12.2942i 1.68897 0.452557i
\(739\) −29.7321 29.7321i −1.09371 1.09371i −0.995129 0.0985823i \(-0.968569\pi\)
−0.0985823 0.995129i \(-0.531431\pi\)
\(740\) 5.66025 9.80385i 0.208075 0.360397i
\(741\) 30.2942 + 17.4904i 1.11289 + 0.642525i
\(742\) 5.58846 + 9.67949i 0.205159 + 0.355345i
\(743\) −25.1147 14.5000i −0.921370 0.531953i −0.0372984 0.999304i \(-0.511875\pi\)
−0.884072 + 0.467351i \(0.845209\pi\)
\(744\) −5.66025 + 1.51666i −0.207515 + 0.0556035i
\(745\) 6.82051 3.93782i 0.249884 0.144271i
\(746\) −17.0263 9.83013i −0.623376 0.359907i
\(747\) 9.48076 35.3827i 0.346883 1.29458i
\(748\) −1.07180 + 4.00000i −0.0391888 + 0.146254i
\(749\) −10.2750 + 38.3468i −0.375440 + 1.40116i
\(750\) −12.3397 −0.450584
\(751\) 4.72243 8.17949i 0.172324 0.298474i −0.766908 0.641757i \(-0.778206\pi\)
0.939232 + 0.343283i \(0.111539\pi\)
\(752\) −18.3923 31.8564i −0.670698 1.16168i
\(753\) −12.8038 + 12.8038i −0.466598 + 0.466598i
\(754\) 15.9282 + 15.9282i 0.580071 + 0.580071i
\(755\) −2.56218 2.56218i −0.0932472 0.0932472i
\(756\) 12.8038 + 22.1769i 0.465671 + 0.806567i
\(757\) 8.46410 8.46410i 0.307633 0.307633i −0.536358 0.843991i \(-0.680200\pi\)
0.843991 + 0.536358i \(0.180200\pi\)
\(758\) 31.1769i 1.13240i
\(759\) −0.294229 0.294229i −0.0106798 0.0106798i
\(760\) −6.00000 + 1.60770i −0.217643 + 0.0583172i
\(761\) 25.2846 + 14.5981i 0.916566 + 0.529180i 0.882538 0.470241i \(-0.155833\pi\)
0.0340283 + 0.999421i \(0.489166\pi\)
\(762\) −35.3205 + 35.3205i −1.27953 + 1.27953i
\(763\) 5.83013 + 1.56218i 0.211065 + 0.0565546i
\(764\) 22.8564 13.1962i 0.826916 0.477420i
\(765\) −1.60770 6.00000i −0.0581263 0.216930i
\(766\) 9.02628 + 33.6865i 0.326133 + 1.21714i
\(767\) −13.7942 23.8923i −0.498081 0.862701i
\(768\) −27.7128 −1.00000
\(769\) −3.50000 + 6.06218i −0.126213 + 0.218608i −0.922207 0.386698i \(-0.873616\pi\)
0.795993 + 0.605305i \(0.206949\pi\)
\(770\) −0.901924 0.241670i −0.0325031 0.00870917i
\(771\) 8.93782 15.4808i 0.321888 0.557526i
\(772\) 4.26795 + 2.46410i