Properties

Label 144.2.x.d.85.1
Level $144$
Weight $2$
Character 144.85
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 85.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 144.85
Dual form 144.2.x.d.61.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 - 0.366025i) q^{2} +1.73205i q^{3} +(1.73205 - 1.00000i) q^{4} +(0.500000 - 0.133975i) q^{5} +(0.633975 + 2.36603i) q^{6} +(-2.13397 + 1.23205i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(1.36603 - 0.366025i) q^{2} +1.73205i q^{3} +(1.73205 - 1.00000i) q^{4} +(0.500000 - 0.133975i) q^{5} +(0.633975 + 2.36603i) q^{6} +(-2.13397 + 1.23205i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +(0.633975 - 0.366025i) q^{10} +(0.133975 - 0.500000i) q^{11} +(1.73205 + 3.00000i) q^{12} +(-1.23205 - 4.59808i) q^{13} +(-2.46410 + 2.46410i) q^{14} +(0.232051 + 0.866025i) q^{15} +(2.00000 - 3.46410i) q^{16} +4.00000 q^{17} +(-4.09808 + 1.09808i) q^{18} +(-3.00000 + 3.00000i) q^{19} +(0.732051 - 0.732051i) q^{20} +(-2.13397 - 3.69615i) q^{21} -0.732051i 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} -5.19615i q^{27} +(-2.46410 + 4.26795i) q^{28} +(-3.23205 - 0.866025i) q^{29} +(0.633975 + 1.09808i) q^{30} +(0.598076 - 1.03590i) q^{31} +(1.46410 - 5.46410i) q^{32} +(0.866025 + 0.232051i) q^{33} +(5.46410 - 1.46410i) q^{34} +(-0.901924 + 0.901924i) q^{35} +(-5.19615 + 3.00000i) q^{36} +(-7.73205 - 7.73205i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(7.96410 - 2.13397i) q^{39} +(0.732051 - 1.26795i) q^{40} +(9.69615 + 5.59808i) q^{41} +(-4.26795 - 4.26795i) q^{42} +(-2.33013 + 8.69615i) q^{43} +(-0.267949 - 1.00000i) q^{44} +(-1.50000 + 0.401924i) q^{45} +(0.633975 + 0.169873i) q^{46} +(4.59808 + 7.96410i) q^{47} +(6.00000 + 3.46410i) q^{48} +(-0.464102 + 0.803848i) q^{49} +(-4.73205 + 4.73205i) q^{50} +6.92820i q^{51} +(-6.73205 - 6.73205i) q^{52} +(2.26795 + 2.26795i) q^{53} +(-1.90192 - 7.09808i) q^{54} -0.267949i q^{55} +(-1.80385 + 6.73205i) q^{56} +(-5.19615 - 5.19615i) q^{57} -4.73205 q^{58} +(5.59808 - 1.50000i) q^{59} +(1.26795 + 1.26795i) q^{60} +(14.4282 + 3.86603i) q^{61} +(0.437822 - 1.63397i) q^{62} +(6.40192 - 3.69615i) q^{63} -8.00000i q^{64} +(-1.23205 - 2.13397i) q^{65} +1.26795 q^{66} +(-0.330127 - 1.23205i) q^{67} +(6.92820 - 4.00000i) q^{68} +(-0.401924 + 0.696152i) q^{69} +(-0.901924 + 1.56218i) q^{70} -10.9282i q^{71} +(-6.00000 + 6.00000i) q^{72} -0.535898i q^{73} +(-13.3923 - 7.73205i) q^{74} +(-4.09808 - 7.09808i) q^{75} +(-2.19615 + 8.19615i) q^{76} +(0.330127 + 1.23205i) q^{77} +(10.0981 - 5.83013i) q^{78} +(0.866025 + 1.50000i) q^{79} +(0.535898 - 2.00000i) q^{80} +9.00000 q^{81} +(15.2942 + 4.09808i) q^{82} +(-11.7942 - 3.16025i) q^{83} +(-7.39230 - 4.26795i) q^{84} +(2.00000 - 0.535898i) q^{85} +12.7321i 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} +0.928203 q^{92} +(1.79423 + 1.03590i) q^{93} +(9.19615 + 9.19615i) q^{94} +(-1.09808 + 1.90192i) q^{95} +(9.46410 + 2.53590i) q^{96} +(-0.500000 - 0.866025i) q^{97} +(-0.339746 + 1.26795i) q^{98} +(-0.401924 + 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 2q^{5} + 6q^{6} - 12q^{7} + 8q^{8} - 12q^{9} + O(q^{10}) \) \( 4q + 2q^{2} + 2q^{5} + 6q^{6} - 12q^{7} + 8q^{8} - 12q^{9} + 6q^{10} + 4q^{11} + 2q^{13} + 4q^{14} - 6q^{15} + 8q^{16} + 16q^{17} - 6q^{18} - 12q^{19} - 4q^{20} - 12q^{21} + 12q^{23} - 6q^{25} - 10q^{26} + 4q^{28} - 6q^{29} + 6q^{30} - 8q^{31} - 8q^{32} + 8q^{34} - 14q^{35} - 24q^{37} - 12q^{38} + 18q^{39} - 4q^{40} + 18q^{41} - 24q^{42} + 8q^{43} - 8q^{44} - 6q^{45} + 6q^{46} + 8q^{47} + 24q^{48} + 12q^{49} - 12q^{50} - 20q^{52} + 16q^{53} - 18q^{54} - 28q^{56} - 12q^{58} + 12q^{59} + 12q^{60} + 30q^{61} + 26q^{62} + 36q^{63} + 2q^{65} + 12q^{66} + 16q^{67} - 12q^{69} - 14q^{70} - 24q^{72} - 12q^{74} - 6q^{75} + 12q^{76} - 16q^{77} + 30q^{78} + 16q^{80} + 36q^{81} + 30q^{82} - 16q^{83} + 12q^{84} + 8q^{85} + 6q^{87} + 4q^{88} - 18q^{90} + 2q^{91} - 24q^{92} - 24q^{93} + 16q^{94} + 6q^{95} + 24q^{96} - 2q^{97} - 36q^{98} - 12q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 0.366025i 0.965926 0.258819i
\(3\) 1.73205i 1.00000i
\(4\) 1.73205 1.00000i 0.866025 0.500000i
\(5\) 0.500000 0.133975i 0.223607 0.0599153i −0.145276 0.989391i \(-0.546407\pi\)
0.368883 + 0.929476i \(0.379740\pi\)
\(6\) 0.633975 + 2.36603i 0.258819 + 0.965926i
\(7\) −2.13397 + 1.23205i −0.806567 + 0.465671i −0.845762 0.533560i \(-0.820854\pi\)
0.0391956 + 0.999232i \(0.487520\pi\)
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) −3.00000 −1.00000
\(10\) 0.633975 0.366025i 0.200480 0.115747i
\(11\) 0.133975 0.500000i 0.0403949 0.150756i −0.942783 0.333408i \(-0.891801\pi\)
0.983178 + 0.182652i \(0.0584681\pi\)
\(12\) 1.73205 + 3.00000i 0.500000 + 0.866025i
\(13\) −1.23205 4.59808i −0.341709 1.27528i −0.896410 0.443227i \(-0.853834\pi\)
0.554700 0.832050i \(-0.312833\pi\)
\(14\) −2.46410 + 2.46410i −0.658559 + 0.658559i
\(15\) 0.232051 + 0.866025i 0.0599153 + 0.223607i
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) −4.09808 + 1.09808i −0.965926 + 0.258819i
\(19\) −3.00000 + 3.00000i −0.688247 + 0.688247i −0.961844 0.273597i \(-0.911786\pi\)
0.273597 + 0.961844i \(0.411786\pi\)
\(20\) 0.732051 0.732051i 0.163692 0.163692i
\(21\) −2.13397 3.69615i −0.465671 0.806567i
\(22\) 0.732051i 0.156074i
\(23\) 0.401924 + 0.232051i 0.0838069 + 0.0483859i 0.541318 0.840818i \(-0.317926\pi\)
−0.457511 + 0.889204i \(0.651259\pi\)
\(24\) 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
\(27\) 5.19615i 1.00000i
\(28\) −2.46410 + 4.26795i −0.465671 + 0.806567i
\(29\) −3.23205 0.866025i −0.600177 0.160817i −0.0540766 0.998537i \(-0.517222\pi\)
−0.546100 + 0.837720i \(0.683888\pi\)
\(30\) 0.633975 + 1.09808i 0.115747 + 0.200480i
\(31\) 0.598076 1.03590i 0.107418 0.186053i −0.807306 0.590133i \(-0.799075\pi\)
0.914723 + 0.404081i \(0.132408\pi\)
\(32\) 1.46410 5.46410i 0.258819 0.965926i
\(33\) 0.866025 + 0.232051i 0.150756 + 0.0403949i
\(34\) 5.46410 1.46410i 0.937086 0.251091i
\(35\) −0.901924 + 0.901924i −0.152453 + 0.152453i
\(36\) −5.19615 + 3.00000i −0.866025 + 0.500000i
\(37\) −7.73205 7.73205i −1.27114 1.27114i −0.945490 0.325651i \(-0.894416\pi\)
−0.325651 0.945490i \(-0.605584\pi\)
\(38\) −3.00000 + 5.19615i −0.486664 + 0.842927i
\(39\) 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 \(0.00532782\pi\)
0.514425 + 0.857536i \(0.328006\pi\)
\(42\) −4.26795 4.26795i −0.658559 0.658559i
\(43\) −2.33013 + 8.69615i −0.355341 + 1.32615i 0.524714 + 0.851279i \(0.324172\pi\)
−0.880055 + 0.474872i \(0.842494\pi\)
\(44\) −0.267949 1.00000i −0.0403949 0.150756i
\(45\) −1.50000 + 0.401924i −0.223607 + 0.0599153i
\(46\) 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 \(0.599328\pi\)
\(48\) 6.00000 + 3.46410i 0.866025 + 0.500000i
\(49\) −0.464102 + 0.803848i −0.0663002 + 0.114835i
\(50\) −4.73205 + 4.73205i −0.669213 + 0.669213i
\(51\) 6.92820i 0.970143i
\(52\) −6.73205 6.73205i −0.933567 0.933567i
\(53\) 2.26795 + 2.26795i 0.311527 + 0.311527i 0.845501 0.533974i \(-0.179302\pi\)
−0.533974 + 0.845501i \(0.679302\pi\)
\(54\) −1.90192 7.09808i −0.258819 0.965926i
\(55\) 0.267949i 0.0361303i
\(56\) −1.80385 + 6.73205i −0.241049 + 0.899608i
\(57\) −5.19615 5.19615i −0.688247 0.688247i
\(58\) −4.73205 −0.621349
\(59\) 5.59808 1.50000i 0.728807 0.195283i 0.124709 0.992193i \(-0.460200\pi\)
0.604098 + 0.796910i \(0.293533\pi\)
\(60\) 1.26795 + 1.26795i 0.163692 + 0.163692i
\(61\) 14.4282 + 3.86603i 1.84734 + 0.494994i 0.999385 0.0350707i \(-0.0111656\pi\)
0.847957 + 0.530065i \(0.177832\pi\)
\(62\) 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
\(66\) 1.26795 0.156074
\(67\) −0.330127 1.23205i −0.0403314 0.150519i 0.942824 0.333292i \(-0.108159\pi\)
−0.983155 + 0.182773i \(0.941493\pi\)
\(68\) 6.92820 4.00000i 0.840168 0.485071i
\(69\) −0.401924 + 0.696152i −0.0483859 + 0.0838069i
\(70\) −0.901924 + 1.56218i −0.107801 + 0.186716i
\(71\) 10.9282i 1.29694i −0.761241 0.648470i \(-0.775409\pi\)
0.761241 0.648470i \(-0.224591\pi\)
\(72\) −6.00000 + 6.00000i −0.707107 + 0.707107i
\(73\) 0.535898i 0.0627222i −0.999508 0.0313611i \(-0.990016\pi\)
0.999508 0.0313611i \(-0.00998418\pi\)
\(74\) −13.3923 7.73205i −1.55682 0.898833i
\(75\) −4.09808 7.09808i −0.473205 0.819615i
\(76\) −2.19615 + 8.19615i −0.251916 + 0.940163i
\(77\) 0.330127 + 1.23205i 0.0376215 + 0.140405i
\(78\) 10.0981 5.83013i 1.14338 0.660132i
\(79\) 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
\(83\) −11.7942 3.16025i −1.29458 0.346883i −0.455185 0.890397i \(-0.650427\pi\)
−0.839400 + 0.543514i \(0.817093\pi\)
\(84\) −7.39230 4.26795i −0.806567 0.465671i
\(85\) 2.00000 0.535898i 0.216930 0.0581263i
\(86\) 12.7321i 1.37293i
\(87\) 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 \(0.216285\pi\)
−0.777900 + 0.628388i \(0.783715\pi\)
\(90\) −1.90192 + 1.09808i −0.200480 + 0.115747i
\(91\) 8.29423 + 8.29423i 0.869471 + 0.869471i
\(92\) 0.928203 0.0967719
\(93\) 1.79423 + 1.03590i 0.186053 + 0.107418i
\(94\) 9.19615 + 9.19615i 0.948511 + 0.948511i
\(95\) −1.09808 + 1.90192i −0.112660 + 0.195133i
\(96\) 9.46410 + 2.53590i 0.965926 + 0.258819i
\(97\) −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
\(99\) −0.401924 + 1.50000i −0.0403949 + 0.150756i
\(100\) −4.73205 + 8.19615i −0.473205 + 0.819615i
\(101\) 0.500000 1.86603i 0.0497519 0.185676i −0.936578 0.350459i \(-0.886026\pi\)
0.986330 + 0.164783i \(0.0526922\pi\)
\(102\) 2.53590 + 9.46410i 0.251091 + 0.937086i
\(103\) 1.79423 + 1.03590i 0.176791 + 0.102070i 0.585784 0.810467i \(-0.300787\pi\)
−0.408993 + 0.912537i \(0.634120\pi\)
\(104\) −11.6603 6.73205i −1.14338 0.660132i
\(105\) −1.56218 1.56218i −0.152453 0.152453i
\(106\) 3.92820 + 2.26795i 0.381541 + 0.220283i
\(107\) −11.3923 11.3923i −1.10134 1.10134i −0.994250 0.107086i \(-0.965848\pi\)
−0.107086 0.994250i \(-0.534152\pi\)
\(108\) −5.19615 9.00000i −0.500000 0.866025i
\(109\) 1.73205 1.73205i 0.165900 0.165900i −0.619274 0.785175i \(-0.712573\pi\)
0.785175 + 0.619274i \(0.212573\pi\)
\(110\) −0.0980762 0.366025i −0.00935120 0.0348992i
\(111\) 13.3923 13.3923i 1.27114 1.27114i
\(112\) 9.85641i 0.931343i
\(113\) −2.76795 + 4.79423i −0.260387 + 0.451003i −0.966345 0.257251i \(-0.917183\pi\)
0.705958 + 0.708254i \(0.250517\pi\)
\(114\) −9.00000 5.19615i −0.842927 0.486664i
\(115\) 0.232051 + 0.0621778i 0.0216388 + 0.00579811i
\(116\) −6.46410 + 1.73205i −0.600177 + 0.160817i
\(117\) 3.69615 + 13.7942i 0.341709 + 1.27528i
\(118\) 7.09808 4.09808i 0.653431 0.377258i
\(119\) −8.53590 + 4.92820i −0.782485 + 0.451768i
\(120\) 2.19615 + 1.26795i 0.200480 + 0.115747i
\(121\) 9.29423 + 5.36603i 0.844930 + 0.487820i
\(122\) 21.1244 1.91251
\(123\) −9.69615 + 16.7942i −0.874273 + 1.51428i
\(124\) 2.39230i 0.214835i
\(125\) −3.56218 + 3.56218i −0.318611 + 0.318611i
\(126\) 7.39230 7.39230i 0.658559 0.658559i
\(127\) −20.3923 −1.80952 −0.904762 0.425917i \(-0.859952\pi\)
−0.904762 + 0.425917i \(0.859952\pi\)
\(128\) −2.92820 10.9282i −0.258819 0.965926i
\(129\) −15.0622 4.03590i −1.32615 0.355341i
\(130\) −2.46410 2.46410i −0.216116 0.216116i
\(131\) −3.13397 11.6962i −0.273817 1.02190i −0.956630 0.291305i \(-0.905911\pi\)
0.682814 0.730593i \(-0.260756\pi\)
\(132\) 1.73205 0.464102i 0.150756 0.0403949i
\(133\) 2.70577 10.0981i 0.234620 0.875614i
\(134\) −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 0.265096 0.964222i \(-0.414596\pi\)
0.967589 + 0.252531i \(0.0812631\pi\)
\(138\) −0.294229 + 1.09808i −0.0250464 + 0.0934745i
\(139\) 4.33013 1.16025i 0.367277 0.0984115i −0.0704603 0.997515i \(-0.522447\pi\)
0.437737 + 0.899103i \(0.355780\pi\)
\(140\) −0.660254 + 2.46410i −0.0558017 + 0.208255i
\(141\) −13.7942 + 7.96410i −1.16168 + 0.670698i
\(142\) −4.00000 14.9282i −0.335673 1.25275i
\(143\) −2.46410 −0.206059
\(144\) −6.00000 + 10.3923i −0.500000 + 0.866025i
\(145\) −1.73205 −0.143839
\(146\) −0.196152 0.732051i −0.0162337 0.0605850i
\(147\) −1.39230 0.803848i −0.114835 0.0663002i
\(148\) −21.1244 5.66025i −1.73641 0.465270i
\(149\) −14.6962 + 3.93782i −1.20396 + 0.322599i −0.804388 0.594105i \(-0.797507\pi\)
−0.399568 + 0.916704i \(0.630840\pi\)
\(150\) −8.19615 8.19615i −0.669213 0.669213i
\(151\) −6.06218 + 3.50000i −0.493333 + 0.284826i −0.725956 0.687741i \(-0.758602\pi\)
0.232623 + 0.972567i \(0.425269\pi\)
\(152\) 12.0000i 0.973329i
\(153\) −12.0000 −0.970143
\(154\) 0.901924 + 1.56218i 0.0726791 + 0.125884i
\(155\) 0.160254 0.598076i 0.0128719 0.0480386i
\(156\) 11.6603 11.6603i 0.933567 0.933567i
\(157\) −0.232051 0.866025i −0.0185197 0.0691164i 0.956048 0.293212i \(-0.0947240\pi\)
−0.974567 + 0.224095i \(0.928057\pi\)
\(158\) 1.73205 + 1.73205i 0.137795 + 0.137795i
\(159\) −3.92820 + 3.92820i −0.311527 + 0.311527i
\(160\) 2.92820i 0.231495i
\(161\) −1.14359 −0.0901278
\(162\) 12.2942 3.29423i 0.965926 0.258819i
\(163\) 11.9282 11.9282i 0.934289 0.934289i −0.0636813 0.997970i \(-0.520284\pi\)
0.997970 + 0.0636813i \(0.0202841\pi\)
\(164\) 22.3923 1.74855
\(165\) 0.464102 0.0361303
\(166\) −17.2679 −1.34025
\(167\) −8.25833 4.76795i −0.639049 0.368955i 0.145199 0.989402i \(-0.453618\pi\)
−0.784248 + 0.620447i \(0.786951\pi\)
\(168\) −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
\(173\) −8.96410 2.40192i −0.681528 0.182615i −0.0985859 0.995129i \(-0.531432\pi\)
−0.582942 + 0.812514i \(0.698099\pi\)
\(174\) 8.19615i 0.621349i
\(175\) 5.83013 10.0981i 0.440716 0.763343i
\(176\) −1.46410 1.46410i −0.110361 0.110361i
\(177\) 2.59808 + 9.69615i 0.195283 + 0.728807i
\(178\) 4.33975 + 16.1962i 0.325278 + 1.21395i
\(179\) 7.92820 7.92820i 0.592582 0.592582i −0.345746 0.938328i \(-0.612374\pi\)
0.938328 + 0.345746i \(0.112374\pi\)
\(180\) −2.19615 + 2.19615i −0.163692 + 0.163692i
\(181\) −4.26795 4.26795i −0.317234 0.317234i 0.530470 0.847704i \(-0.322016\pi\)
−0.847704 + 0.530470i \(0.822016\pi\)
\(182\) 14.3660 + 8.29423i 1.06488 + 0.614809i
\(183\) −6.69615 + 24.9904i −0.494994 + 1.84734i
\(184\) 1.26795 0.339746i 0.0934745 0.0250464i
\(185\) −4.90192 2.83013i −0.360397 0.208075i
\(186\) 2.83013 + 0.758330i 0.207515 + 0.0556035i
\(187\) 0.535898 2.00000i 0.0391888 0.146254i
\(188\) 15.9282 + 9.19615i 1.16168 + 0.670698i
\(189\) 6.40192 + 11.0885i 0.465671 + 0.806567i
\(190\) −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 \(0.674905\pi\)
\(192\) 13.8564 1.00000
\(193\) −1.23205 + 2.13397i −0.0886850 + 0.153607i −0.906956 0.421226i \(-0.861600\pi\)
0.818271 + 0.574833i \(0.194933\pi\)
\(194\) −1.00000 1.00000i −0.0717958 0.0717958i
\(195\) 3.69615 2.13397i 0.264687 0.152817i
\(196\) 1.85641i 0.132600i
\(197\) 10.4641 + 10.4641i 0.745536 + 0.745536i 0.973637 0.228101i \(-0.0732517\pi\)
−0.228101 + 0.973637i \(0.573252\pi\)
\(198\) 2.19615i 0.156074i
\(199\) 5.85641i 0.415150i −0.978219 0.207575i \(-0.933443\pi\)
0.978219 0.207575i \(-0.0665570\pi\)
\(200\) −3.46410 + 12.9282i −0.244949 + 0.914162i
\(201\) 2.13397 0.571797i 0.150519 0.0403314i
\(202\) 2.73205i 0.192226i
\(203\) 7.96410 2.13397i 0.558970 0.149776i
\(204\) 6.92820 + 12.0000i 0.485071 + 0.840168i
\(205\) 5.59808 + 1.50000i 0.390987 + 0.104765i
\(206\) 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
\(210\) −2.70577 1.56218i −0.186716 0.107801i
\(211\) −0.526279 1.96410i −0.0362306 0.135214i 0.945442 0.325791i \(-0.105631\pi\)
−0.981672 + 0.190577i \(0.938964\pi\)
\(212\) 6.19615 + 1.66025i 0.425553 + 0.114027i
\(213\) 18.9282 1.29694
\(214\) −19.7321 11.3923i −1.34886 0.778762i
\(215\) 4.66025i 0.317827i
\(216\) −10.3923 10.3923i −0.707107 0.707107i
\(217\) 2.94744i 0.200085i
\(218\) 1.73205 3.00000i 0.117309 0.203186i
\(219\) 0.928203 0.0627222
\(220\) −0.267949 0.464102i −0.0180651 0.0312897i
\(221\) −4.92820 18.3923i −0.331507 1.23720i
\(222\) 13.3923 23.1962i 0.898833 1.55682i
\(223\) −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
\(227\) 17.2583 + 4.62436i 1.14548 + 0.306929i 0.781151 0.624343i \(-0.214633\pi\)
0.364325 + 0.931272i \(0.381300\pi\)
\(228\) −14.1962 3.80385i −0.940163 0.251916i
\(229\) 9.42820 2.52628i 0.623033 0.166941i 0.0665269 0.997785i \(-0.478808\pi\)
0.556506 + 0.830843i \(0.312142\pi\)
\(230\) 0.339746 0.0224022
\(231\) −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 \(-0.729553\pi\)
0.660259 0.751038i \(-0.270447\pi\)
\(234\) 10.0981 + 17.4904i 0.660132 + 1.14338i
\(235\) 3.36603 + 3.36603i 0.219575 + 0.219575i
\(236\) 8.19615 8.19615i 0.533524 0.533524i
\(237\) −2.59808 + 1.50000i −0.168763 + 0.0974355i
\(238\) −9.85641 + 9.85641i −0.638896 + 0.638896i
\(239\) −5.59808 + 9.69615i −0.362109 + 0.627192i −0.988308 0.152472i \(-0.951277\pi\)
0.626198 + 0.779664i \(0.284610\pi\)
\(240\) 3.46410 + 0.928203i 0.223607 + 0.0599153i
\(241\) −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
\(243\) 15.5885i 1.00000i
\(244\) 28.8564 7.73205i 1.84734 0.494994i
\(245\) −0.124356 + 0.464102i −0.00794479 + 0.0296504i
\(246\) −7.09808 + 26.4904i −0.452557 + 1.68897i
\(247\) 17.4904 + 10.0981i 1.11289 + 0.642525i
\(248\) −0.875644 3.26795i −0.0556035 0.207515i
\(249\) 5.47372 20.4282i 0.346883 1.29458i
\(250\) −3.56218 + 6.16987i −0.225292 + 0.390217i
\(251\) 7.39230 + 7.39230i 0.466598 + 0.466598i 0.900811 0.434212i \(-0.142973\pi\)
−0.434212 + 0.900811i \(0.642973\pi\)
\(252\) 7.39230 12.8038i 0.465671 0.806567i
\(253\) 0.169873 0.169873i 0.0106798 0.0106798i
\(254\) −27.8564 + 7.46410i −1.74787 + 0.468339i
\(255\) 0.928203 + 3.46410i 0.0581263 + 0.216930i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −5.16025 + 8.93782i −0.321888 + 0.557526i −0.980878 0.194626i \(-0.937651\pi\)
0.658990 + 0.752152i \(0.270984\pi\)
\(258\) −22.0526 −1.37293
\(259\) 26.0263 + 6.97372i 1.61719 + 0.433326i
\(260\) −4.26795 2.46410i −0.264687 0.152817i
\(261\) 9.69615 + 2.59808i 0.600177 + 0.160817i
\(262\) −8.56218 14.8301i −0.528973 0.916208i
\(263\) 3.40192 1.96410i 0.209772 0.121112i −0.391434 0.920206i \(-0.628021\pi\)
0.601205 + 0.799095i \(0.294687\pi\)
\(264\) 2.19615 1.26795i 0.135164 0.0780369i
\(265\) 1.43782 + 0.830127i 0.0883247 + 0.0509943i
\(266\) 14.7846i 0.906503i
\(267\) −20.5359 −1.25678
\(268\) −1.80385 1.80385i −0.110188 0.110188i
\(269\) 7.73205 7.73205i 0.471431 0.471431i −0.430946 0.902378i \(-0.641820\pi\)
0.902378 + 0.430946i \(0.141820\pi\)
\(270\) −1.90192 3.29423i −0.115747 0.200480i
\(271\) −14.9282 −0.906824 −0.453412 0.891301i \(-0.649793\pi\)
−0.453412 + 0.891301i \(0.649793\pi\)
\(272\) 8.00000 13.8564i 0.485071 0.840168i
\(273\) −14.3660 + 14.3660i −0.869471 + 0.869471i
\(274\) 16.6603 16.6603i 1.00648 1.00648i
\(275\) 0.633975 + 2.36603i 0.0382301 + 0.142677i
\(276\) 1.60770i 0.0967719i
\(277\) −3.69615 + 13.7942i −0.222080 + 0.828815i 0.761473 + 0.648197i \(0.224477\pi\)
−0.983553 + 0.180618i \(0.942190\pi\)
\(278\) 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 0.100219 0.994965i \(-0.468046\pi\)
0.911775 + 0.410691i \(0.134712\pi\)
\(282\) −15.9282 + 15.9282i −0.948511 + 0.948511i
\(283\) −15.5263 + 4.16025i −0.922942 + 0.247301i −0.688842 0.724911i \(-0.741881\pi\)
−0.234099 + 0.972213i \(0.575214\pi\)
\(284\) −10.9282 18.9282i −0.648470 1.12318i
\(285\) −3.29423 1.90192i −0.195133 0.112660i
\(286\) −3.36603 + 0.901924i −0.199037 + 0.0533319i
\(287\) −27.5885 −1.62850
\(288\) −4.39230 + 16.3923i −0.258819 + 0.965926i
\(289\) −1.00000 −0.0588235
\(290\) −2.36603 + 0.633975i −0.138938 + 0.0372283i
\(291\) 1.50000 0.866025i 0.0879316 0.0507673i
\(292\) −0.535898 0.928203i −0.0313611 0.0543190i
\(293\) −14.4282 + 3.86603i −0.842905 + 0.225856i −0.654336 0.756204i \(-0.727052\pi\)
−0.188569 + 0.982060i \(0.560385\pi\)
\(294\) −2.19615 0.588457i −0.128082 0.0343195i
\(295\) 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
\(299\) 0.571797 2.13397i 0.0330679 0.123411i
\(300\) −14.1962 8.19615i −0.819615 0.473205i
\(301\) −5.74167 21.4282i −0.330944 1.23510i
\(302\) −7.00000 + 7.00000i −0.402805 + 0.402805i
\(303\) 3.23205 + 0.866025i 0.185676 + 0.0497519i
\(304\) 4.39230 + 16.3923i 0.251916 + 0.940163i
\(305\) 7.73205 0.442736
\(306\) −16.3923 + 4.39230i −0.937086 + 0.251091i
\(307\) −5.92820 + 5.92820i −0.338340 + 0.338340i −0.855742 0.517402i \(-0.826899\pi\)
0.517402 + 0.855742i \(0.326899\pi\)
\(308\) 1.80385 + 1.80385i 0.102784 + 0.102784i
\(309\) −1.79423 + 3.10770i −0.102070 + 0.176791i
\(310\) 0.875644i 0.0497333i
\(311\) 27.1865 + 15.6962i 1.54161 + 0.890047i 0.998738 + 0.0502299i \(0.0159954\pi\)
0.542869 + 0.839817i \(0.317338\pi\)
\(312\) 11.6603 20.1962i 0.660132 1.14338i
\(313\) −7.83975 + 4.52628i −0.443129 + 0.255840i −0.704924 0.709283i \(-0.749019\pi\)
0.261795 + 0.965123i \(0.415686\pi\)
\(314\) −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
\(317\) 2.03590 + 0.545517i 0.114347 + 0.0306393i 0.315539 0.948913i \(-0.397815\pi\)
−0.201192 + 0.979552i \(0.564481\pi\)
\(318\) −3.92820 + 6.80385i −0.220283 + 0.381541i
\(319\) −0.866025 + 1.50000i −0.0484881 + 0.0839839i
\(320\) −1.07180 4.00000i −0.0599153 0.223607i
\(321\) 19.7321 19.7321i 1.10134 1.10134i
\(322\) −1.56218 + 0.418584i −0.0870568 + 0.0233268i
\(323\) −12.0000 + 12.0000i −0.667698 + 0.667698i
\(324\) 15.5885 9.00000i 0.866025 0.500000i
\(325\) 15.9282 + 15.9282i 0.883538 + 0.883538i
\(326\) 11.9282 20.6603i 0.660642 1.14427i
\(327\) 3.00000 + 3.00000i 0.165900 + 0.165900i
\(328\) 30.5885 8.19615i 1.68897 0.452557i
\(329\) −19.6244 11.3301i −1.08193 0.624650i
\(330\) 0.633975 0.169873i 0.0348992 0.00935120i
\(331\) 7.06218 26.3564i 0.388172 1.44868i −0.444933 0.895564i \(-0.646772\pi\)
0.833105 0.553115i \(-0.186561\pi\)
\(332\) −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
\(336\) −17.0718 −0.931343
\(337\) 0.696152 1.20577i 0.0379218 0.0656826i −0.846442 0.532482i \(-0.821260\pi\)
0.884363 + 0.466799i \(0.154593\pi\)
\(338\) −9.66025 + 9.66025i −0.525449 + 0.525449i
\(339\) −8.30385 4.79423i −0.451003 0.260387i
\(340\) 2.92820 2.92820i 0.158804 0.158804i
\(341\) −0.437822 0.437822i −0.0237094 0.0237094i
\(342\) 9.00000 15.5885i 0.486664 0.842927i
\(343\) 19.5359i 1.05484i
\(344\) 12.7321 + 22.0526i 0.686466 + 1.18899i
\(345\) −0.107695 + 0.401924i −0.00579811 + 0.0216388i
\(346\) −13.1244 −0.705570
\(347\) 19.5263 5.23205i 1.04823 0.280871i 0.306707 0.951804i \(-0.400773\pi\)
0.741518 + 0.670933i \(0.234106\pi\)
\(348\) −3.00000 11.1962i −0.160817 0.600177i
\(349\) 7.96410 + 2.13397i 0.426309 + 0.114229i 0.465593 0.884999i \(-0.345841\pi\)
−0.0392843 + 0.999228i \(0.512508\pi\)
\(350\) 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 \(-0.467591\pi\)
\(354\) 7.09808 + 12.2942i 0.377258 + 0.653431i
\(355\) −1.46410 5.46410i −0.0777064 0.290004i
\(356\) 11.8564 + 20.5359i 0.628388 + 1.08840i
\(357\) −8.53590 14.7846i −0.451768 0.782485i
\(358\) 7.92820 13.7321i 0.419019 0.725761i
\(359\) 15.0718i 0.795459i 0.917503 + 0.397730i \(0.130202\pi\)
−0.917503 + 0.397730i \(0.869798\pi\)
\(360\) −2.19615 + 3.80385i −0.115747 + 0.200480i
\(361\) 1.00000i 0.0526316i
\(362\) −7.39230 4.26795i −0.388531 0.224318i
\(363\) −9.29423 + 16.0981i −0.487820 + 0.844930i
\(364\) 22.6603 + 6.07180i 1.18772 + 0.318249i
\(365\) −0.0717968 0.267949i −0.00375801 0.0140251i
\(366\) 36.5885i 1.91251i
\(367\) 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
\(371\) −7.63397 2.04552i −0.396336 0.106198i
\(372\) 4.14359 0.214835
\(373\) −13.4282 + 3.59808i −0.695286 + 0.186301i −0.589118 0.808047i \(-0.700525\pi\)
−0.106168 + 0.994348i \(0.533858\pi\)
\(374\) 2.92820i 0.151414i
\(375\) −6.16987 6.16987i −0.318611 0.318611i
\(376\) 25.1244 + 6.73205i 1.29569 + 0.347179i
\(377\) 15.9282i 0.820344i
\(378\) 12.8038 + 12.8038i 0.658559 + 0.658559i
\(379\) 15.5885 + 15.5885i 0.800725 + 0.800725i 0.983209 0.182484i \(-0.0584137\pi\)
−0.182484 + 0.983209i \(0.558414\pi\)
\(380\) 4.39230i 0.225320i
\(381\) 35.3205i 1.80952i
\(382\) 13.1962 + 13.1962i 0.675174 + 0.675174i
\(383\) 12.3301 21.3564i 0.630040 1.09126i −0.357503 0.933912i \(-0.616372\pi\)
0.987543 0.157349i \(-0.0502949\pi\)
\(384\) 18.9282 5.07180i 0.965926 0.258819i
\(385\) 0.330127 + 0.571797i 0.0168248 + 0.0291415i
\(386\) −0.901924 + 3.36603i −0.0459067 + 0.171326i
\(387\) 6.99038 26.0885i 0.355341 1.32615i
\(388\) −1.73205 1.00000i −0.0879316 0.0507673i
\(389\) −2.03590 + 7.59808i −0.103224 + 0.385238i −0.998138 0.0610019i \(-0.980570\pi\)
0.894914 + 0.446240i \(0.147237\pi\)
\(390\) 4.26795 4.26795i 0.216116 0.216116i
\(391\) 1.60770 + 0.928203i 0.0813046 + 0.0469413i
\(392\) 0.679492 + 2.53590i 0.0343195 + 0.128082i
\(393\) 20.2583 5.42820i 1.02190 0.273817i
\(394\) 18.1244 + 10.4641i 0.913092 + 0.527174i
\(395\) 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 −0.0582984 + 0.998299i \(0.518567\pi\)
−0.998299 + 0.0582984i \(0.981433\pi\)
\(398\) −2.14359 8.00000i −0.107449 0.401004i
\(399\) 17.4904 + 4.68653i 0.875614 + 0.234620i
\(400\) 18.9282i 0.946410i
\(401\) 1.16025 2.00962i 0.0579403 0.100356i −0.835600 0.549338i \(-0.814880\pi\)
0.893541 + 0.448982i \(0.148213\pi\)
\(402\) 2.70577 1.56218i 0.134952 0.0779143i
\(403\) −5.50000 1.47372i −0.273975 0.0734112i
\(404\) −1.00000 3.73205i −0.0497519 0.185676i
\(405\) 4.50000 1.20577i 0.223607 0.0599153i
\(406\) 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 0.381294 0.924454i \(-0.375479\pi\)
−0.609954 + 0.792437i \(0.708812\pi\)
\(410\) 8.19615 0.404779
\(411\) 14.4282 + 24.9904i 0.711691 + 1.23268i
\(412\) 4.14359 0.204140
\(413\) −10.0981 + 10.0981i −0.496894 + 0.496894i
\(414\) −1.90192 0.509619i −0.0934745 0.0250464i
\(415\) −6.32051 −0.310262
\(416\) −26.9282 −1.32026
\(417\) 2.00962 + 7.50000i 0.0984115 + 0.367277i
\(418\) 2.19615 + 2.19615i 0.107417 + 0.107417i
\(419\) −0.526279 1.96410i −0.0257104 0.0959526i 0.951878 0.306476i \(-0.0991499\pi\)
−0.977589 + 0.210523i \(0.932483\pi\)
\(420\) −4.26795 1.14359i −0.208255 0.0558017i
\(421\) −2.89230 + 10.7942i −0.140962 + 0.526079i 0.858940 + 0.512077i \(0.171124\pi\)
−0.999902 + 0.0140017i \(0.995543\pi\)
\(422\) −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
\(426\) 25.8564 6.92820i 1.25275 0.335673i
\(427\) −35.5526 + 9.52628i −1.72051 + 0.461009i
\(428\) −31.1244 8.33975i −1.50445 0.403117i
\(429\) 4.26795i 0.206059i
\(430\) 1.70577 + 6.36603i 0.0822596 + 0.306997i
\(431\) 31.3205 1.50866 0.754328 0.656498i \(-0.227963\pi\)
0.754328 + 0.656498i \(0.227963\pi\)
\(432\) −18.0000 10.3923i −0.866025 0.500000i
\(433\) 24.3923 1.17222 0.586110 0.810232i \(-0.300659\pi\)
0.586110 + 0.810232i \(0.300659\pi\)
\(434\) 1.07884 + 4.02628i 0.0517859 + 0.193268i
\(435\) 3.00000i 0.143839i
\(436\) 1.26795 4.73205i 0.0607238 0.226624i
\(437\) −1.90192 + 0.509619i −0.0909814 + 0.0243784i
\(438\) 1.26795 0.339746i 0.0605850 0.0162337i
\(439\) −18.0622 + 10.4282i −0.862061 + 0.497711i −0.864702 0.502286i \(-0.832493\pi\)
0.00264111 + 0.999997i \(0.499159\pi\)
\(440\) −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
\(443\) −4.33013 + 16.1603i −0.205731 + 0.767797i 0.783495 + 0.621398i \(0.213435\pi\)
−0.989226 + 0.146399i \(0.953232\pi\)
\(444\) 9.80385 36.5885i 0.465270 1.73641i
\(445\) 1.58846 + 5.92820i 0.0753001 + 0.281024i
\(446\) −15.5885 15.5885i −0.738135 0.738135i
\(447\) −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 \(0.494896\pi\)
\(450\) 14.1962 14.1962i 0.669213 0.669213i
\(451\) 4.09808 4.09808i 0.192971 0.192971i
\(452\) 11.0718i 0.520774i
\(453\) −6.06218 10.5000i −0.284826 0.493333i
\(454\) 25.2679 1.18588
\(455\) 5.25833 + 3.03590i 0.246514 + 0.142325i
\(456\) −20.7846 −0.973329
\(457\) −19.0359 + 10.9904i −0.890462 + 0.514108i −0.874094 0.485758i \(-0.838544\pi\)
−0.0163683 + 0.999866i \(0.505210\pi\)
\(458\) 11.9545 6.90192i 0.558596 0.322506i
\(459\) 20.7846i 0.970143i
\(460\) 0.464102 0.124356i 0.0216388 0.00579811i
\(461\) 2.23205 + 0.598076i 0.103957 + 0.0278552i 0.310423 0.950599i \(-0.399529\pi\)
−0.206466 + 0.978454i \(0.566196\pi\)
\(462\) −2.70577 + 1.56218i −0.125884 + 0.0726791i
\(463\) 3.33013 5.76795i 0.154764 0.268059i −0.778209 0.628005i \(-0.783872\pi\)
0.932973 + 0.359946i \(0.117205\pi\)
\(464\) −9.46410 + 9.46410i −0.439360 + 0.439360i
\(465\) 1.03590 + 0.277568i 0.0480386 + 0.0128719i
\(466\) −8.39230 31.3205i −0.388766 1.45089i
\(467\) −19.7846 + 19.7846i −0.915523 + 0.915523i −0.996700 0.0811771i \(-0.974132\pi\)
0.0811771 + 0.996700i \(0.474132\pi\)
\(468\) 20.1962 + 20.1962i 0.933567 + 0.933567i
\(469\) 2.22243 + 2.22243i 0.102622 + 0.102622i
\(470\) 5.83013 + 3.36603i 0.268924 + 0.155263i
\(471\) 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
\(474\) −3.00000 + 3.00000i −0.137795 + 0.137795i
\(475\) 5.19615 19.3923i 0.238416 0.889780i
\(476\) −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 \(0.823589\pi\)
\(480\) 5.07180 0.231495
\(481\) −26.0263 + 45.0788i −1.18670 + 2.05542i
\(482\) −12.4641 12.4641i −0.567724 0.567724i
\(483\) 1.98076i 0.0901278i
\(484\) 21.4641 0.975641
\(485\) −0.366025 0.366025i −0.0166204 0.0166204i
\(486\) 5.70577 + 21.2942i 0.258819 + 0.965926i
\(487\) 34.7846i 1.57624i −0.615521 0.788121i \(-0.711054\pi\)
0.615521 0.788121i \(-0.288946\pi\)
\(488\) 36.5885 21.1244i 1.65628 0.956255i
\(489\) 20.6603 + 20.6603i 0.934289 + 0.934289i
\(490\) 0.679492i 0.0306963i
\(491\) −1.86603 + 0.500000i −0.0842125 + 0.0225647i −0.300679 0.953725i \(-0.597213\pi\)
0.216467 + 0.976290i \(0.430547\pi\)
\(492\) 38.7846i 1.74855i
\(493\) −12.9282 3.46410i −0.582257 0.156015i
\(494\) 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
\(498\) 29.9090i 1.34025i
\(499\) 0.669873 + 2.50000i 0.0299876 + 0.111915i 0.979297 0.202427i \(-0.0648828\pi\)
−0.949310 + 0.314342i \(0.898216\pi\)
\(500\) −2.60770 + 9.73205i −0.116620 + 0.435231i
\(501\) 8.25833 14.3038i 0.368955 0.639049i
\(502\) 12.8038 + 7.39230i 0.571464 + 0.329935i
\(503\) 13.8564i 0.617827i 0.951090 + 0.308913i \(0.0999653\pi\)
−0.951090 + 0.308913i \(0.900035\pi\)
\(504\) 5.41154 20.1962i 0.241049 0.899608i
\(505\) 1.00000i 0.0444994i
\(506\) 0.169873 0.294229i 0.00755178 0.0130801i
\(507\) −8.36603 14.4904i −0.371548 0.643540i
\(508\) −35.3205 + 20.3923i −1.56709 + 0.904762i
\(509\) 5.69615 + 21.2583i 0.252478 + 0.942259i 0.969476 + 0.245185i \(0.0788486\pi\)
−0.716999 + 0.697074i \(0.754485\pi\)
\(510\) 2.53590 + 4.39230i 0.112291 + 0.194495i
\(511\) 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
\(515\) 1.03590 + 0.277568i 0.0456471 + 0.0122311i
\(516\) −30.1244 + 8.07180i −1.32615 + 0.355341i
\(517\) 4.59808 1.23205i 0.202223 0.0541855i
\(518\) 38.1051 1.67424
\(519\) 4.16025 15.5263i 0.182615 0.681528i
\(520\) −6.73205 1.80385i −0.295220 0.0791039i
\(521\) 14.1436i 0.619642i 0.950795 + 0.309821i \(0.100269\pi\)
−0.950795 + 0.309821i \(0.899731\pi\)
\(522\) 14.1962 0.621349
\(523\) −2.12436 2.12436i −0.0928916 0.0928916i 0.659134 0.752026i \(-0.270923\pi\)
−0.752026 + 0.659134i \(0.770923\pi\)
\(524\) −17.1244 17.1244i −0.748081 0.748081i
\(525\) 17.4904 + 10.0981i 0.763343 + 0.440716i
\(526\) 3.92820 3.92820i 0.171278 0.171278i
\(527\) 2.39230 4.14359i 0.104210 0.180498i
\(528\) 2.53590 2.53590i 0.110361 0.110361i
\(529\) −11.3923 19.7321i −0.495318 0.857915i
\(530\) 2.26795 + 0.607695i 0.0985134 + 0.0263966i
\(531\) −16.7942 + 4.50000i −0.728807 + 0.195283i
\(532\) −5.41154 20.1962i −0.234620 0.875614i
\(533\) 13.7942 51.4808i 0.597494 2.22988i
\(534\) −28.0526 + 7.51666i −1.21395 + 0.325278i
\(535\) −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
\(538\) 7.73205 13.3923i 0.333352 0.577383i
\(539\) 0.339746 + 0.339746i 0.0146339 + 0.0146339i
\(540\) −3.80385 3.80385i −0.163692 0.163692i
\(541\) −15.0000 + 15.0000i −0.644900 + 0.644900i −0.951756 0.306856i \(-0.900723\pi\)
0.306856 + 0.951756i \(0.400723\pi\)
\(542\) −20.3923 + 5.46410i −0.875924 + 0.234703i
\(543\) 7.39230 7.39230i 0.317234 0.317234i
\(544\) 5.85641 21.8564i 0.251091 0.937086i
\(545\) 0.633975 1.09808i 0.0271565 0.0470364i
\(546\) −14.3660 + 24.8827i −0.614809 + 1.06488i
\(547\) −28.2583 7.57180i −1.20824 0.323747i −0.402168 0.915566i \(-0.631743\pi\)
−0.806071 + 0.591819i \(0.798410\pi\)
\(548\) 16.6603 28.8564i 0.711691 1.23268i
\(549\) −43.2846 11.5981i −1.84734 0.494994i
\(550\) 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
\(554\) 20.1962i 0.858052i
\(555\) 4.90192 8.49038i 0.208075 0.360397i
\(556\) 6.33975 6.33975i 0.268865 0.268865i
\(557\) 27.9808 27.9808i 1.18558 1.18558i 0.207307 0.978276i \(-0.433530\pi\)
0.978276 0.207307i \(-0.0664699\pi\)
\(558\) −1.31347 + 4.90192i −0.0556035 + 0.207515i
\(559\) 42.8564 1.81263
\(560\) 1.32051 + 4.92820i 0.0558017 + 0.208255i
\(561\) 3.46410 + 0.928203i 0.146254 + 0.0391888i
\(562\) 19.5885 19.5885i 0.826289 0.826289i
\(563\) 7.86603 + 29.3564i 0.331513 + 1.23723i 0.907600 + 0.419836i \(0.137912\pi\)
−0.576086 + 0.817389i \(0.695421\pi\)
\(564\) −15.9282 + 27.5885i −0.670698 + 1.16168i
\(565\) −0.741670 + 2.76795i −0.0312023 + 0.116448i
\(566\) −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 −0.915919 0.401364i \(-0.868536\pi\)
−0.110368 + 0.993891i \(0.535203\pi\)
\(570\) −5.19615 1.39230i −0.217643 0.0583172i
\(571\) −5.40192 + 1.44744i −0.226063 + 0.0605735i −0.370073 0.929003i \(-0.620667\pi\)
0.144009 + 0.989576i \(0.454001\pi\)
\(572\) −4.26795 + 2.46410i −0.178452 + 0.103029i
\(573\) −19.7942 + 11.4282i −0.826916 + 0.477420i
\(574\) −37.6865 + 10.0981i −1.57301 + 0.421486i
\(575\) −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 \(0.218330\pi\)
\(578\) −1.36603 + 0.366025i −0.0568192 + 0.0152246i
\(579\) −3.69615 2.13397i −0.153607 0.0886850i
\(580\) −3.00000 + 1.73205i −0.124568 + 0.0719195i
\(581\) 29.0622 7.78719i 1.20570 0.323067i
\(582\) 1.73205 1.73205i 0.0717958 0.0717958i
\(583\) 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
\(587\) 0.794229 2.96410i 0.0327813 0.122342i −0.947596 0.319470i \(-0.896495\pi\)
0.980378 + 0.197129i \(0.0631617\pi\)
\(588\) −3.21539 −0.132600
\(589\) 1.31347 + 4.90192i 0.0541204 + 0.201980i
\(590\) 3.00000 3.00000i 0.123508 0.123508i
\(591\) −18.1244 + 18.1244i −0.745536 + 0.745536i
\(592\) −42.2487 + 11.3205i −1.73641 + 0.465270i
\(593\) 1.46410 0.0601234 0.0300617 0.999548i \(-0.490430\pi\)
0.0300617 + 0.999548i \(0.490430\pi\)
\(594\) −3.80385 −0.156074
\(595\) −3.60770 + 3.60770i −0.147901 + 0.147901i
\(596\) −21.5167 + 21.5167i −0.881357 + 0.881357i
\(597\) 10.1436 0.415150
\(598\) 3.12436i 0.127764i
\(599\) −30.3109 17.5000i −1.23847 0.715031i −0.269688 0.962948i \(-0.586921\pi\)
−0.968781 + 0.247917i \(0.920254\pi\)
\(600\) −22.3923 6.00000i −0.914162 0.244949i
\(601\) 30.2321 17.4545i 1.23319 0.711983i 0.265497 0.964112i \(-0.414464\pi\)
0.967694 + 0.252128i \(0.0811305\pi\)
\(602\) −15.6865 27.1699i −0.639335 1.10736i
\(603\) 0.990381 + 3.69615i 0.0403314 + 0.150519i
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) 5.36603 + 1.43782i 0.218160 + 0.0584558i
\(606\) 4.73205 0.192226
\(607\) −4.59808 + 7.96410i −0.186630 + 0.323253i −0.944125 0.329589i \(-0.893090\pi\)
0.757494 + 0.652842i \(0.226423\pi\)
\(608\) 12.0000 + 20.7846i 0.486664 + 0.842927i
\(609\) 3.69615 + 13.7942i 0.149776 + 0.558970i
\(610\) 10.5622 2.83013i 0.427650 0.114588i
\(611\) 30.9545 30.9545i 1.25228 1.25228i
\(612\) −20.7846 + 12.0000i −0.840168 + 0.485071i
\(613\) −7.58846 7.58846i −0.306495 0.306495i 0.537053 0.843548i \(-0.319537\pi\)
−0.843548 + 0.537053i \(0.819537\pi\)
\(614\) −5.92820 + 10.2679i −0.239243 + 0.414381i
\(615\) −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 0.653899 0.756582i \(-0.273132\pi\)
−0.328270 + 0.944584i \(0.606466\pi\)
\(618\) −1.31347 + 4.90192i −0.0528354 + 0.197184i
\(619\) 8.86603 33.0885i 0.356356 1.32994i −0.522414 0.852692i \(-0.674969\pi\)
0.878770 0.477246i \(-0.158365\pi\)
\(620\) −0.320508 1.19615i −0.0128719 0.0480386i
\(621\) 1.20577 2.08846i 0.0483859 0.0838069i
\(622\) 42.8827 + 11.4904i 1.71944 + 0.460722i
\(623\) −14.6077 25.3013i −0.585245 1.01367i
\(624\) 8.53590 31.8564i 0.341709 1.27528i
\(625\) 10.5263 18.2321i 0.421051 0.729282i
\(626\) −9.05256 + 9.05256i −0.361813 + 0.361813i
\(627\) −3.29423 + 1.90192i −0.131559 + 0.0759555i
\(628\) −1.26795 1.26795i −0.0505967 0.0505967i
\(629\) −30.9282 30.9282i −1.23319 1.23319i
\(630\) 2.70577 4.68653i 0.107801 0.186716i
\(631\) 32.2487i 1.28380i 0.766788 + 0.641900i \(0.221854\pi\)
−0.766788 + 0.641900i \(0.778146\pi\)
\(632\) 4.73205 + 1.26795i 0.188231 + 0.0504363i
\(633\) 3.40192 0.911543i 0.135214 0.0362306i
\(634\) 2.98076 0.118381
\(635\) −10.1962 + 2.73205i −0.404622 + 0.108418i
\(636\) −2.87564 + 10.7321i −0.114027 + 0.425553i
\(637\) 4.26795 + 1.14359i 0.169102 + 0.0453108i
\(638\) −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 \(0.760173\pi\)
\(642\) 19.7321 34.1769i 0.778762 1.34886i
\(643\) −0.277568 1.03590i −0.0109462 0.0408518i 0.960237 0.279187i \(-0.0900650\pi\)
−0.971183 + 0.238335i \(0.923398\pi\)
\(644\) −1.98076 + 1.14359i −0.0780530 + 0.0450639i
\(645\) −8.07180 −0.317827
\(646\) −12.0000 + 20.7846i −0.472134 + 0.817760i
\(647\) 46.3923i 1.82387i −0.410335 0.911935i \(-0.634588\pi\)
0.410335 0.911935i \(-0.365412\pi\)
\(648\) 18.0000 18.0000i 0.707107 0.707107i
\(649\) 3.00000i 0.117760i
\(650\) 27.5885 + 15.9282i 1.08211 + 0.624756i
\(651\) −5.10512 −0.200085
\(652\) 8.73205 32.5885i 0.341974 1.27626i
\(653\) 5.71539 + 21.3301i 0.223661 + 0.834712i 0.982937 + 0.183944i \(0.0588865\pi\)
−0.759276 + 0.650768i \(0.774447\pi\)
\(654\) 5.19615 + 3.00000i 0.203186 + 0.117309i
\(655\) −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
\(659\) 8.33013 + 2.23205i 0.324496 + 0.0869484i 0.417390 0.908728i \(-0.362945\pi\)
−0.0928939 + 0.995676i \(0.529612\pi\)
\(660\) 0.803848 0.464102i 0.0312897 0.0180651i
\(661\) −15.6962 + 4.20577i −0.610510 + 0.163586i −0.550810 0.834631i \(-0.685681\pi\)
−0.0596998 + 0.998216i \(0.519014\pi\)
\(662\) 38.5885i 1.49978i
\(663\) 31.8564 8.53590i 1.23720 0.331507i
\(664\) −29.9090 + 17.2679i −1.16069 + 0.670126i
\(665\) 5.41154i 0.209851i
\(666\) 40.1769 + 23.1962i 1.55682 + 0.898833i
\(667\) −1.09808 1.09808i −0.0425177 0.0425177i
\(668\) −19.0718 −0.737910
\(669\) 23.3827 13.5000i 0.904027 0.521940i
\(670\) −0.660254 0.660254i −0.0255078 0.0255078i
\(671\) 3.86603 6.69615i 0.149246 0.258502i
\(672\) −23.3205 + 6.24871i −0.899608 + 0.241049i
\(673\) 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
\(675\) 12.2942 + 21.2942i 0.473205 + 0.819615i
\(676\) −9.66025 + 16.7321i −0.371548 + 0.643540i
\(677\) −12.2321 + 45.6506i −0.470116 + 1.75450i 0.169229 + 0.985577i \(0.445872\pi\)
−0.639345 + 0.768920i \(0.720795\pi\)
\(678\) −13.0981 3.50962i −0.503029 0.134786i
\(679\) 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
\(682\) −0.758330 0.437822i −0.0290380 0.0167651i
\(683\) −5.39230 5.39230i −0.206331 0.206331i 0.596375 0.802706i \(-0.296607\pi\)
−0.802706 + 0.596375i \(0.796607\pi\)
\(684\) 6.58846 24.5885i 0.251916 0.940163i
\(685\) 6.09808 6.09808i 0.232996 0.232996i
\(686\) −7.15064 26.6865i −0.273013 1.01890i
\(687\) 4.37564 + 16.3301i 0.166941 + 0.623033i
\(688\) 25.4641 + 25.4641i 0.970810 + 0.970810i
\(689\) 7.63397 13.2224i 0.290831 0.503735i
\(690\) 0.588457i 0.0224022i
\(691\) −18.5263 4.96410i −0.704773 0.188843i −0.111405 0.993775i \(-0.535535\pi\)
−0.593367 + 0.804932i \(0.702202\pi\)
\(692\) −17.9282 + 4.80385i −0.681528 + 0.182615i
\(693\) −0.990381 3.69615i −0.0376215 0.140405i
\(694\) 24.7583 14.2942i 0.939813 0.542601i
\(695\) 2.00962 1.16025i 0.0762292 0.0440109i
\(696\) −8.19615 14.1962i −0.310674 0.538104i
\(697\) 38.7846 + 22.3923i 1.46907 + 0.848169i
\(698\) 11.6603 0.441347
\(699\) 39.7128 1.50208
\(700\) 23.3205i 0.881432i
\(701\) −21.0526 + 21.0526i −0.795144 + 0.795144i −0.982325 0.187181i \(-0.940065\pi\)
0.187181 + 0.982325i \(0.440065\pi\)
\(702\) −30.2942 + 17.4904i −1.14338 + 0.660132i
\(703\) 46.3923 1.74972
\(704\) −4.00000 1.07180i −0.150756 0.0403949i
\(705\) −5.83013 + 5.83013i −0.219575 + 0.219575i
\(706\) −30.4641 30.4641i −1.14653 1.14653i
\(707\) 1.23205 + 4.59808i 0.0463360 + 0.172928i
\(708\) 14.1962 + 14.1962i 0.533524 + 0.533524i
\(709\) 10.7487 40.1147i 0.403676 1.50654i −0.402808 0.915285i \(-0.631966\pi\)
0.806484 0.591256i \(-0.201368\pi\)
\(710\) −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
\(714\) −17.0718 17.0718i −0.638896 0.638896i
\(715\) −1.23205 + 0.330127i −0.0460761 + 0.0123461i
\(716\) 5.80385 21.6603i 0.216900 0.809482i
\(717\) −16.7942 9.69615i −0.627192 0.362109i
\(718\) 5.51666 + 20.5885i 0.205880 + 0.768354i
\(719\) 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
\(722\) 0.366025 + 1.36603i 0.0136221 + 0.0508382i
\(723\) 18.6962 10.7942i 0.695317 0.401442i
\(724\) −11.6603 3.12436i −0.433350 0.116116i
\(725\) 15.2942 4.09808i 0.568013 0.152199i
\(726\) −6.80385 + 25.3923i −0.252514 + 0.942397i
\(727\) 9.06218 5.23205i 0.336098 0.194046i −0.322447 0.946587i \(-0.604506\pi\)
0.658545 + 0.752541i \(0.271172\pi\)
\(728\) 33.1769 1.22962
\(729\) −27.0000 −1.00000
\(730\) −0.196152 0.339746i −0.00725993 0.0125746i
\(731\) −9.32051 + 34.7846i −0.344731 + 1.28656i
\(732\) 13.3923 + 49.9808i 0.494994 + 1.84734i
\(733\) −7.37564 27.5263i −0.272426 1.01671i −0.957547 0.288277i \(-0.906917\pi\)
0.685121 0.728429i \(-0.259749\pi\)
\(734\) 30.9090 + 30.9090i 1.14087 + 1.14087i
\(735\) −0.803848 0.215390i −0.0296504 0.00794479i
\(736\) 1.85641 1.85641i 0.0684280 0.0684280i
\(737\) −0.660254 −0.0243208
\(738\) −45.8827 12.2942i −1.68897 0.452557i
\(739\) −29.7321 + 29.7321i −1.09371 + 1.09371i −0.0985823 + 0.995129i \(0.531431\pi\)
−0.995129 + 0.0985823i \(0.968569\pi\)
\(740\) −11.3205 −0.416150
\(741\) −17.4904 + 30.2942i −0.642525 + 1.11289i
\(742\) −11.1769 −0.410317
\(743\) 25.1147 + 14.5000i 0.921370 + 0.531953i 0.884072 0.467351i \(-0.154791\pi\)
0.0372984 + 0.999304i \(0.488125\pi\)
\(744\) 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
\(747\) 35.3827 + 9.48076i 1.29458 + 0.346883i
\(748\) −1.07180 4.00000i −0.0391888 0.146254i
\(749\) 38.3468 + 10.2750i 1.40116 + 0.375440i
\(750\) −10.6865 6.16987i −0.390217 0.225292i
\(751\) 4.72243 8.17949i 0.172324 0.298474i −0.766908 0.641757i \(-0.778206\pi\)
0.939232 + 0.343283i \(0.111539\pi\)
\(752\) 36.7846 1.34140
\(753\) −12.8038 + 12.8038i −0.466598 + 0.466598i
\(754\) 5.83013 + 21.7583i 0.212321 + 0.792392i
\(755\) −2.56218 + 2.56218i −0.0932472 + 0.0932472i
\(756\) 22.1769 + 12.8038i 0.806567 + 0.465671i
\(757\) 8.46410 + 8.46410i 0.307633 + 0.307633i 0.843991 0.536358i \(-0.180200\pi\)
−0.536358 + 0.843991i \(0.680200\pi\)
\(758\) 27.0000 + 15.5885i 0.980684 + 0.566198i
\(759\) 0.294229 + 0.294229i 0.0106798 + 0.0106798i
\(760\) 1.60770 + 6.00000i 0.0583172 + 0.217643i
\(761\) −25.2846 14.5981i −0.916566 0.529180i −0.0340283 0.999421i \(-0.510834\pi\)
−0.882538 + 0.470241i \(0.844167\pi\)
\(762\) −12.9282 48.2487i −0.468339 1.74787i
\(763\) −1.56218 + 5.83013i −0.0565546 + 0.211065i
\(764\) 22.8564 + 13.1962i 0.826916 + 0.477420i
\(765\) −6.00000 + 1.60770i −0.216930 + 0.0581263i
\(766\) 9.02628 33.6865i 0.326133 1.21714i
\(767\) −13.7942 23.8923i −0.498081 0.862701i
\(768\) 24.0000 13.8564i 0.866025 0.500000i
\(769\) −3.50000 + 6.06218i −0.126213 + 0.218608i −0.922207 0.386698i \(-0.873616\pi\)
0.795993 + 0.605305i \(0.206949\pi\)
\(770\) 0.660254 + 0.660254i 0.0237939 + 0.0237939i
\(771\) −15.4808 8.93782i −0.557526 0.321888i