Properties

Label 114.2.h.e.107.1
Level $114$
Weight $2$
Character 114.107
Analytic conductor $0.910$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.h (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.910294583043\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 114.107
Dual form 114.2.h.e.65.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.22474 - 0.707107i) q^{5} +(-1.72474 - 0.158919i) q^{6} -0.449490 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.22474 - 0.707107i) q^{5} +(-1.72474 - 0.158919i) q^{6} -0.449490 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +(-1.22474 - 0.707107i) q^{10} +3.14626i q^{11} +(0.724745 + 1.57313i) q^{12} +(-3.00000 - 1.73205i) q^{13} +(0.224745 + 0.389270i) q^{14} +(0.224745 - 2.43916i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.550510 - 0.317837i) q^{17} +(-1.94949 + 2.28024i) q^{18} +(3.17423 + 2.98735i) q^{19} +1.41421i q^{20} +(-0.449490 + 0.635674i) q^{21} +(2.72474 - 1.57313i) q^{22} +(6.12372 + 3.53553i) q^{23} +(1.00000 - 1.41421i) q^{24} +(-1.50000 + 2.59808i) q^{25} +3.46410i q^{26} +(-5.00000 - 1.41421i) q^{27} +(0.224745 - 0.389270i) q^{28} +(-1.22474 + 2.12132i) q^{29} +(-2.22474 + 1.02494i) q^{30} +4.24264i q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.44949 + 3.14626i) q^{33} +(-0.550510 - 0.317837i) q^{34} +(-0.550510 + 0.317837i) q^{35} +(2.94949 + 0.548188i) q^{36} -7.70674i q^{37} +(1.00000 - 4.24264i) q^{38} +(-5.44949 + 2.51059i) q^{39} +(1.22474 - 0.707107i) q^{40} +(1.50000 + 2.59808i) q^{41} +(0.775255 + 0.0714323i) q^{42} +(4.44949 + 7.70674i) q^{43} +(-2.72474 - 1.57313i) q^{44} +(-3.22474 - 2.75699i) q^{45} -7.07107i q^{46} +(-11.5732 - 6.68180i) q^{47} +(-1.72474 - 0.158919i) q^{48} -6.79796 q^{49} +3.00000 q^{50} +(0.101021 - 1.09638i) q^{51} +(3.00000 - 1.73205i) q^{52} +(5.44949 - 9.43879i) q^{53} +(1.27526 + 5.03723i) q^{54} +(2.22474 + 3.85337i) q^{55} -0.449490 q^{56} +(7.39898 - 1.50170i) q^{57} +2.44949 q^{58} +(-5.72474 - 9.91555i) q^{59} +(2.00000 + 1.41421i) q^{60} +(0.775255 - 1.34278i) q^{61} +(3.67423 - 2.12132i) q^{62} +(0.449490 + 1.27135i) q^{63} +1.00000 q^{64} -4.89898 q^{65} +(0.500000 - 5.42650i) q^{66} +(2.17423 + 1.25529i) q^{67} +0.635674i q^{68} +(11.1237 - 5.12472i) q^{69} +(0.550510 + 0.317837i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(-1.00000 - 2.82843i) q^{72} +(-4.39898 - 7.61926i) q^{73} +(-6.67423 + 3.85337i) q^{74} +(2.17423 + 4.71940i) q^{75} +(-4.17423 + 1.25529i) q^{76} -1.41421i q^{77} +(4.89898 + 3.46410i) q^{78} +(-7.34847 + 4.24264i) q^{79} +(-1.22474 - 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(1.50000 - 2.59808i) q^{82} +17.0027i q^{83} +(-0.325765 - 0.707107i) q^{84} +(0.449490 - 0.778539i) q^{85} +(4.44949 - 7.70674i) q^{86} +(1.77526 + 3.85337i) q^{87} +3.14626i q^{88} +(-3.55051 + 6.14966i) q^{89} +(-0.775255 + 4.17121i) q^{90} +(1.34847 + 0.778539i) q^{91} +(-6.12372 + 3.53553i) q^{92} +(6.00000 + 4.24264i) q^{93} +13.3636i q^{94} +(6.00000 + 1.41421i) q^{95} +(0.724745 + 1.57313i) q^{96} +(2.84847 - 1.64456i) q^{97} +(3.39898 + 5.88721i) q^{98} +(8.89898 - 3.14626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 4q^{3} - 2q^{4} - 2q^{6} + 8q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 4q^{3} - 2q^{4} - 2q^{6} + 8q^{7} + 4q^{8} - 4q^{9} - 2q^{12} - 12q^{13} - 4q^{14} - 4q^{15} - 2q^{16} + 12q^{17} + 2q^{18} - 2q^{19} + 8q^{21} + 6q^{22} + 4q^{24} - 6q^{25} - 20q^{27} - 4q^{28} - 4q^{30} - 2q^{32} + 8q^{33} - 12q^{34} - 12q^{35} + 2q^{36} + 4q^{38} - 12q^{39} + 6q^{41} + 8q^{42} + 8q^{43} - 6q^{44} - 8q^{45} - 12q^{47} - 2q^{48} + 12q^{49} + 12q^{50} + 20q^{51} + 12q^{52} + 12q^{53} + 10q^{54} + 4q^{55} + 8q^{56} + 10q^{57} - 18q^{59} + 8q^{60} + 8q^{61} - 8q^{63} + 4q^{64} + 2q^{66} - 6q^{67} + 20q^{69} + 12q^{70} - 12q^{71} - 4q^{72} + 2q^{73} - 12q^{74} - 6q^{75} - 2q^{76} - 28q^{81} + 6q^{82} - 16q^{84} - 8q^{85} + 8q^{86} + 12q^{87} - 24q^{89} - 8q^{90} - 24q^{91} + 24q^{93} + 24q^{95} - 2q^{96} - 18q^{97} - 6q^{98} + 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(97\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 1.00000 1.41421i 0.577350 0.816497i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.22474 0.707107i 0.547723 0.316228i −0.200480 0.979698i \(-0.564250\pi\)
0.748203 + 0.663470i \(0.230917\pi\)
\(6\) −1.72474 0.158919i −0.704124 0.0648783i
\(7\) −0.449490 −0.169891 −0.0849456 0.996386i \(-0.527072\pi\)
−0.0849456 + 0.996386i \(0.527072\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) −1.22474 0.707107i −0.387298 0.223607i
\(11\) 3.14626i 0.948634i 0.880354 + 0.474317i \(0.157305\pi\)
−0.880354 + 0.474317i \(0.842695\pi\)
\(12\) 0.724745 + 1.57313i 0.209216 + 0.454124i
\(13\) −3.00000 1.73205i −0.832050 0.480384i 0.0225039 0.999747i \(-0.492836\pi\)
−0.854554 + 0.519362i \(0.826170\pi\)
\(14\) 0.224745 + 0.389270i 0.0600656 + 0.104037i
\(15\) 0.224745 2.43916i 0.0580289 0.629788i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.550510 0.317837i 0.133518 0.0770869i −0.431753 0.901992i \(-0.642105\pi\)
0.565271 + 0.824905i \(0.308771\pi\)
\(18\) −1.94949 + 2.28024i −0.459499 + 0.537457i
\(19\) 3.17423 + 2.98735i 0.728219 + 0.685344i
\(20\) 1.41421i 0.316228i
\(21\) −0.449490 + 0.635674i −0.0980867 + 0.138716i
\(22\) 2.72474 1.57313i 0.580918 0.335393i
\(23\) 6.12372 + 3.53553i 1.27688 + 0.737210i 0.976274 0.216537i \(-0.0694763\pi\)
0.300610 + 0.953747i \(0.402810\pi\)
\(24\) 1.00000 1.41421i 0.204124 0.288675i
\(25\) −1.50000 + 2.59808i −0.300000 + 0.519615i
\(26\) 3.46410i 0.679366i
\(27\) −5.00000 1.41421i −0.962250 0.272166i
\(28\) 0.224745 0.389270i 0.0424728 0.0735650i
\(29\) −1.22474 + 2.12132i −0.227429 + 0.393919i −0.957046 0.289938i \(-0.906365\pi\)
0.729616 + 0.683857i \(0.239699\pi\)
\(30\) −2.22474 + 1.02494i −0.406181 + 0.187128i
\(31\) 4.24264i 0.762001i 0.924575 + 0.381000i \(0.124420\pi\)
−0.924575 + 0.381000i \(0.875580\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 4.44949 + 3.14626i 0.774557 + 0.547694i
\(34\) −0.550510 0.317837i −0.0944117 0.0545086i
\(35\) −0.550510 + 0.317837i −0.0930532 + 0.0537243i
\(36\) 2.94949 + 0.548188i 0.491582 + 0.0913647i
\(37\) 7.70674i 1.26698i −0.773751 0.633490i \(-0.781622\pi\)
0.773751 0.633490i \(-0.218378\pi\)
\(38\) 1.00000 4.24264i 0.162221 0.688247i
\(39\) −5.44949 + 2.51059i −0.872617 + 0.402016i
\(40\) 1.22474 0.707107i 0.193649 0.111803i
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0.775255 + 0.0714323i 0.119624 + 0.0110222i
\(43\) 4.44949 + 7.70674i 0.678541 + 1.17527i 0.975420 + 0.220352i \(0.0707207\pi\)
−0.296880 + 0.954915i \(0.595946\pi\)
\(44\) −2.72474 1.57313i −0.410771 0.237159i
\(45\) −3.22474 2.75699i −0.480717 0.410989i
\(46\) 7.07107i 1.04257i
\(47\) −11.5732 6.68180i −1.68813 0.974640i −0.955952 0.293524i \(-0.905172\pi\)
−0.732175 0.681117i \(-0.761495\pi\)
\(48\) −1.72474 0.158919i −0.248945 0.0229379i
\(49\) −6.79796 −0.971137
\(50\) 3.00000 0.424264
\(51\) 0.101021 1.09638i 0.0141457 0.153523i
\(52\) 3.00000 1.73205i 0.416025 0.240192i
\(53\) 5.44949 9.43879i 0.748545 1.29652i −0.199975 0.979801i \(-0.564086\pi\)
0.948520 0.316717i \(-0.102581\pi\)
\(54\) 1.27526 + 5.03723i 0.173540 + 0.685481i
\(55\) 2.22474 + 3.85337i 0.299985 + 0.519588i
\(56\) −0.449490 −0.0600656
\(57\) 7.39898 1.50170i 0.980019 0.198905i
\(58\) 2.44949 0.321634
\(59\) −5.72474 9.91555i −0.745298 1.29089i −0.950055 0.312082i \(-0.898974\pi\)
0.204757 0.978813i \(-0.434360\pi\)
\(60\) 2.00000 + 1.41421i 0.258199 + 0.182574i
\(61\) 0.775255 1.34278i 0.0992612 0.171926i −0.812118 0.583493i \(-0.801685\pi\)
0.911379 + 0.411568i \(0.135019\pi\)
\(62\) 3.67423 2.12132i 0.466628 0.269408i
\(63\) 0.449490 + 1.27135i 0.0566304 + 0.160175i
\(64\) 1.00000 0.125000
\(65\) −4.89898 −0.607644
\(66\) 0.500000 5.42650i 0.0615457 0.667956i
\(67\) 2.17423 + 1.25529i 0.265625 + 0.153359i 0.626898 0.779101i \(-0.284324\pi\)
−0.361273 + 0.932460i \(0.617658\pi\)
\(68\) 0.635674i 0.0770869i
\(69\) 11.1237 5.12472i 1.33914 0.616944i
\(70\) 0.550510 + 0.317837i 0.0657986 + 0.0379888i
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) −1.00000 2.82843i −0.117851 0.333333i
\(73\) −4.39898 7.61926i −0.514862 0.891766i −0.999851 0.0172466i \(-0.994510\pi\)
0.484990 0.874520i \(-0.338823\pi\)
\(74\) −6.67423 + 3.85337i −0.775864 + 0.447945i
\(75\) 2.17423 + 4.71940i 0.251059 + 0.544949i
\(76\) −4.17423 + 1.25529i −0.478818 + 0.143992i
\(77\) 1.41421i 0.161165i
\(78\) 4.89898 + 3.46410i 0.554700 + 0.392232i
\(79\) −7.34847 + 4.24264i −0.826767 + 0.477334i −0.852745 0.522328i \(-0.825064\pi\)
0.0259772 + 0.999663i \(0.491730\pi\)
\(80\) −1.22474 0.707107i −0.136931 0.0790569i
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) 17.0027i 1.86629i 0.359506 + 0.933143i \(0.382945\pi\)
−0.359506 + 0.933143i \(0.617055\pi\)
\(84\) −0.325765 0.707107i −0.0355439 0.0771517i
\(85\) 0.449490 0.778539i 0.0487540 0.0844444i
\(86\) 4.44949 7.70674i 0.479801 0.831039i
\(87\) 1.77526 + 3.85337i 0.190327 + 0.413125i
\(88\) 3.14626i 0.335393i
\(89\) −3.55051 + 6.14966i −0.376353 + 0.651863i −0.990529 0.137307i \(-0.956155\pi\)
0.614175 + 0.789170i \(0.289489\pi\)
\(90\) −0.775255 + 4.17121i −0.0817191 + 0.439684i
\(91\) 1.34847 + 0.778539i 0.141358 + 0.0816131i
\(92\) −6.12372 + 3.53553i −0.638442 + 0.368605i
\(93\) 6.00000 + 4.24264i 0.622171 + 0.439941i
\(94\) 13.3636i 1.37835i
\(95\) 6.00000 + 1.41421i 0.615587 + 0.145095i
\(96\) 0.724745 + 1.57313i 0.0739690 + 0.160557i
\(97\) 2.84847 1.64456i 0.289218 0.166980i −0.348371 0.937357i \(-0.613265\pi\)
0.637589 + 0.770377i \(0.279932\pi\)
\(98\) 3.39898 + 5.88721i 0.343349 + 0.594698i
\(99\) 8.89898 3.14626i 0.894381 0.316211i
\(100\) −1.50000 2.59808i −0.150000 0.259808i
\(101\) −8.57321 4.94975i −0.853067 0.492518i 0.00861771 0.999963i \(-0.497257\pi\)
−0.861684 + 0.507445i \(0.830590\pi\)
\(102\) −1.00000 + 0.460702i −0.0990148 + 0.0456163i
\(103\) 5.02118i 0.494752i −0.968920 0.247376i \(-0.920432\pi\)
0.968920 0.247376i \(-0.0795682\pi\)
\(104\) −3.00000 1.73205i −0.294174 0.169842i
\(105\) −0.101021 + 1.09638i −0.00985859 + 0.106995i
\(106\) −10.8990 −1.05860
\(107\) 4.89898 0.473602 0.236801 0.971558i \(-0.423901\pi\)
0.236801 + 0.971558i \(0.423901\pi\)
\(108\) 3.72474 3.62302i 0.358414 0.348625i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 2.22474 3.85337i 0.212121 0.367405i
\(111\) −10.8990 7.70674i −1.03449 0.731492i
\(112\) 0.224745 + 0.389270i 0.0212364 + 0.0367825i
\(113\) 18.7980 1.76836 0.884182 0.467143i \(-0.154717\pi\)
0.884182 + 0.467143i \(0.154717\pi\)
\(114\) −5.00000 5.65685i −0.468293 0.529813i
\(115\) 10.0000 0.932505
\(116\) −1.22474 2.12132i −0.113715 0.196960i
\(117\) −1.89898 + 10.2173i −0.175561 + 0.944593i
\(118\) −5.72474 + 9.91555i −0.527005 + 0.912800i
\(119\) −0.247449 + 0.142865i −0.0226836 + 0.0130964i
\(120\) 0.224745 2.43916i 0.0205163 0.222664i
\(121\) 1.10102 0.100093
\(122\) −1.55051 −0.140377
\(123\) 5.17423 + 0.476756i 0.466545 + 0.0429876i
\(124\) −3.67423 2.12132i −0.329956 0.190500i
\(125\) 11.3137i 1.01193i
\(126\) 0.876276 1.02494i 0.0780648 0.0913093i
\(127\) −9.00000 5.19615i −0.798621 0.461084i 0.0443678 0.999015i \(-0.485873\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 15.3485 + 1.41421i 1.35136 + 0.124515i
\(130\) 2.44949 + 4.24264i 0.214834 + 0.372104i
\(131\) −1.92679 + 1.11243i −0.168344 + 0.0971935i −0.581805 0.813328i \(-0.697653\pi\)
0.413461 + 0.910522i \(0.364320\pi\)
\(132\) −4.94949 + 2.28024i −0.430798 + 0.198469i
\(133\) −1.42679 1.34278i −0.123718 0.116434i
\(134\) 2.51059i 0.216882i
\(135\) −7.12372 + 1.80348i −0.613113 + 0.155219i
\(136\) 0.550510 0.317837i 0.0472059 0.0272543i
\(137\) −3.39898 1.96240i −0.290394 0.167659i 0.347725 0.937596i \(-0.386954\pi\)
−0.638120 + 0.769937i \(0.720288\pi\)
\(138\) −10.0000 7.07107i −0.851257 0.601929i
\(139\) 7.17423 12.4261i 0.608511 1.05397i −0.382975 0.923759i \(-0.625101\pi\)
0.991486 0.130213i \(-0.0415661\pi\)
\(140\) 0.635674i 0.0537243i
\(141\) −21.0227 + 9.68520i −1.77043 + 0.815641i
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) 5.44949 9.43879i 0.455709 0.789312i
\(144\) −1.94949 + 2.28024i −0.162457 + 0.190020i
\(145\) 3.46410i 0.287678i
\(146\) −4.39898 + 7.61926i −0.364062 + 0.630574i
\(147\) −6.79796 + 9.61377i −0.560686 + 0.792930i
\(148\) 6.67423 + 3.85337i 0.548619 + 0.316745i
\(149\) −1.77526 + 1.02494i −0.145435 + 0.0839667i −0.570952 0.820984i \(-0.693426\pi\)
0.425517 + 0.904950i \(0.360092\pi\)
\(150\) 3.00000 4.24264i 0.244949 0.346410i
\(151\) 9.61377i 0.782357i −0.920315 0.391179i \(-0.872067\pi\)
0.920315 0.391179i \(-0.127933\pi\)
\(152\) 3.17423 + 2.98735i 0.257464 + 0.242306i
\(153\) −1.44949 1.23924i −0.117184 0.100187i
\(154\) −1.22474 + 0.707107i −0.0986928 + 0.0569803i
\(155\) 3.00000 + 5.19615i 0.240966 + 0.417365i
\(156\) 0.550510 5.97469i 0.0440761 0.478358i
\(157\) −5.34847 9.26382i −0.426854 0.739333i 0.569737 0.821827i \(-0.307045\pi\)
−0.996592 + 0.0824935i \(0.973712\pi\)
\(158\) 7.34847 + 4.24264i 0.584613 + 0.337526i
\(159\) −7.89898 17.1455i −0.626430 1.35973i
\(160\) 1.41421i 0.111803i
\(161\) −2.75255 1.58919i −0.216931 0.125245i
\(162\) 8.39898 + 3.23375i 0.659886 + 0.254067i
\(163\) 18.3485 1.43716 0.718582 0.695443i \(-0.244792\pi\)
0.718582 + 0.695443i \(0.244792\pi\)
\(164\) −3.00000 −0.234261
\(165\) 7.67423 + 0.707107i 0.597438 + 0.0550482i
\(166\) 14.7247 8.50134i 1.14286 0.659832i
\(167\) 2.44949 4.24264i 0.189547 0.328305i −0.755552 0.655089i \(-0.772631\pi\)
0.945099 + 0.326783i \(0.105965\pi\)
\(168\) −0.449490 + 0.635674i −0.0346789 + 0.0490434i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) −0.898979 −0.0689486
\(171\) 5.27526 11.9654i 0.403409 0.915020i
\(172\) −8.89898 −0.678541
\(173\) −0.550510 0.953512i −0.0418545 0.0724942i 0.844339 0.535809i \(-0.179993\pi\)
−0.886194 + 0.463315i \(0.846660\pi\)
\(174\) 2.44949 3.46410i 0.185695 0.262613i
\(175\) 0.674235 1.16781i 0.0509673 0.0882780i
\(176\) 2.72474 1.57313i 0.205385 0.118579i
\(177\) −19.7474 1.81954i −1.48431 0.136765i
\(178\) 7.10102 0.532244
\(179\) 7.65153 0.571902 0.285951 0.958244i \(-0.407690\pi\)
0.285951 + 0.958244i \(0.407690\pi\)
\(180\) 4.00000 1.41421i 0.298142 0.105409i
\(181\) 18.6742 + 10.7816i 1.38804 + 0.801388i 0.993095 0.117314i \(-0.0374285\pi\)
0.394950 + 0.918703i \(0.370762\pi\)
\(182\) 1.55708i 0.115418i
\(183\) −1.12372 2.43916i −0.0830681 0.180308i
\(184\) 6.12372 + 3.53553i 0.451447 + 0.260643i
\(185\) −5.44949 9.43879i −0.400654 0.693954i
\(186\) 0.674235 7.31747i 0.0494373 0.536543i
\(187\) 1.00000 + 1.73205i 0.0731272 + 0.126660i
\(188\) 11.5732 6.68180i 0.844063 0.487320i
\(189\) 2.24745 + 0.635674i 0.163478 + 0.0462385i
\(190\) −1.77526 5.90326i −0.128791 0.428267i
\(191\) 8.19955i 0.593299i −0.954986 0.296649i \(-0.904131\pi\)
0.954986 0.296649i \(-0.0958693\pi\)
\(192\) 1.00000 1.41421i 0.0721688 0.102062i
\(193\) −22.3485 + 12.9029i −1.60868 + 0.928771i −0.619012 + 0.785382i \(0.712467\pi\)
−0.989666 + 0.143389i \(0.954200\pi\)
\(194\) −2.84847 1.64456i −0.204508 0.118073i
\(195\) −4.89898 + 6.92820i −0.350823 + 0.496139i
\(196\) 3.39898 5.88721i 0.242784 0.420515i
\(197\) 20.2918i 1.44573i 0.690989 + 0.722865i \(0.257175\pi\)
−0.690989 + 0.722865i \(0.742825\pi\)
\(198\) −7.17423 6.13361i −0.509851 0.435897i
\(199\) 1.44949 2.51059i 0.102752 0.177971i −0.810066 0.586339i \(-0.800569\pi\)
0.912817 + 0.408368i \(0.133902\pi\)
\(200\) −1.50000 + 2.59808i −0.106066 + 0.183712i
\(201\) 3.94949 1.81954i 0.278576 0.128340i
\(202\) 9.89949i 0.696526i
\(203\) 0.550510 0.953512i 0.0386382 0.0669234i
\(204\) 0.898979 + 0.635674i 0.0629412 + 0.0445061i
\(205\) 3.67423 + 2.12132i 0.256620 + 0.148159i
\(206\) −4.34847 + 2.51059i −0.302972 + 0.174921i
\(207\) 3.87628 20.8560i 0.269420 1.44960i
\(208\) 3.46410i 0.240192i
\(209\) −9.39898 + 9.98698i −0.650141 + 0.690814i
\(210\) 1.00000 0.460702i 0.0690066 0.0317914i
\(211\) −1.34847 + 0.778539i −0.0928325 + 0.0535968i −0.545698 0.837982i \(-0.683735\pi\)
0.452865 + 0.891579i \(0.350402\pi\)
\(212\) 5.44949 + 9.43879i 0.374272 + 0.648259i
\(213\) −10.3485 0.953512i −0.709065 0.0653335i
\(214\) −2.44949 4.24264i −0.167444 0.290021i
\(215\) 10.8990 + 6.29253i 0.743304 + 0.429147i
\(216\) −5.00000 1.41421i −0.340207 0.0962250i
\(217\) 1.90702i 0.129457i
\(218\) 0 0
\(219\) −15.1742 1.39816i −1.02538 0.0944789i
\(220\) −4.44949 −0.299985
\(221\) −2.20204 −0.148125
\(222\) −1.22474 + 13.2922i −0.0821995 + 0.892112i
\(223\) −15.6742 + 9.04952i −1.04962 + 0.606001i −0.922544 0.385892i \(-0.873894\pi\)
−0.127080 + 0.991892i \(0.540561\pi\)
\(224\) 0.224745 0.389270i 0.0150164 0.0260092i
\(225\) 8.84847 + 1.64456i 0.589898 + 0.109638i
\(226\) −9.39898 16.2795i −0.625211 1.08290i
\(227\) −0.550510 −0.0365386 −0.0182693 0.999833i \(-0.505816\pi\)
−0.0182693 + 0.999833i \(0.505816\pi\)
\(228\) −2.39898 + 7.15855i −0.158876 + 0.474087i
\(229\) 0.898979 0.0594062 0.0297031 0.999559i \(-0.490544\pi\)
0.0297031 + 0.999559i \(0.490544\pi\)
\(230\) −5.00000 8.66025i −0.329690 0.571040i
\(231\) −2.00000 1.41421i −0.131590 0.0930484i
\(232\) −1.22474 + 2.12132i −0.0804084 + 0.139272i
\(233\) 15.3990 8.89060i 1.00882 0.582443i 0.0979745 0.995189i \(-0.468764\pi\)
0.910846 + 0.412746i \(0.135430\pi\)
\(234\) 9.79796 3.46410i 0.640513 0.226455i
\(235\) −18.8990 −1.23283
\(236\) 11.4495 0.745298
\(237\) −1.34847 + 14.6349i −0.0875925 + 0.950642i
\(238\) 0.247449 + 0.142865i 0.0160397 + 0.00926054i
\(239\) 21.0703i 1.36293i 0.731852 + 0.681463i \(0.238656\pi\)
−0.731852 + 0.681463i \(0.761344\pi\)
\(240\) −2.22474 + 1.02494i −0.143607 + 0.0661599i
\(241\) −5.84847 3.37662i −0.376733 0.217507i 0.299663 0.954045i \(-0.403126\pi\)
−0.676396 + 0.736538i \(0.736459\pi\)
\(242\) −0.550510 0.953512i −0.0353881 0.0612941i
\(243\) 1.00000 + 15.5563i 0.0641500 + 0.997940i
\(244\) 0.775255 + 1.34278i 0.0496306 + 0.0859628i
\(245\) −8.32577 + 4.80688i −0.531914 + 0.307100i
\(246\) −2.17423 4.71940i −0.138624 0.300898i
\(247\) −4.34847 14.4600i −0.276686 0.920066i
\(248\) 4.24264i 0.269408i
\(249\) 24.0454 + 17.0027i 1.52382 + 1.07750i
\(250\) 9.79796 5.65685i 0.619677 0.357771i
\(251\) 3.27526 + 1.89097i 0.206732 + 0.119357i 0.599792 0.800156i \(-0.295250\pi\)
−0.393060 + 0.919513i \(0.628583\pi\)
\(252\) −1.32577 0.246405i −0.0835154 0.0155221i
\(253\) −11.1237 + 19.2669i −0.699343 + 1.21130i
\(254\) 10.3923i 0.652071i
\(255\) −0.651531 1.41421i −0.0408004 0.0885615i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.50000 12.9904i 0.467837 0.810318i −0.531487 0.847066i \(-0.678367\pi\)
0.999325 + 0.0367485i \(0.0117000\pi\)
\(258\) −6.44949 13.9993i −0.401528 0.871557i
\(259\) 3.46410i 0.215249i
\(260\) 2.44949 4.24264i 0.151911 0.263117i
\(261\) 7.22474 + 1.34278i 0.447200 + 0.0831161i
\(262\) 1.92679 + 1.11243i 0.119037 + 0.0687262i
\(263\) −7.77526 + 4.48905i −0.479443 + 0.276806i −0.720184 0.693783i \(-0.755943\pi\)
0.240741 + 0.970589i \(0.422609\pi\)
\(264\) 4.44949 + 3.14626i 0.273847 + 0.193639i
\(265\) 15.4135i 0.946843i
\(266\) −0.449490 + 1.90702i −0.0275600 + 0.116927i
\(267\) 5.14643 + 11.1708i 0.314956 + 0.683645i
\(268\) −2.17423 + 1.25529i −0.132813 + 0.0766793i
\(269\) −12.2474 21.2132i −0.746740 1.29339i −0.949377 0.314138i \(-0.898285\pi\)
0.202637 0.979254i \(-0.435049\pi\)
\(270\) 5.12372 + 5.26758i 0.311820 + 0.320575i
\(271\) 10.0227 + 17.3598i 0.608836 + 1.05453i 0.991433 + 0.130619i \(0.0416965\pi\)
−0.382597 + 0.923915i \(0.624970\pi\)
\(272\) −0.550510 0.317837i −0.0333796 0.0192717i
\(273\) 2.44949 1.12848i 0.148250 0.0682990i
\(274\) 3.92480i 0.237106i
\(275\) −8.17423 4.71940i −0.492925 0.284590i
\(276\) −1.12372 + 12.1958i −0.0676403 + 0.734100i
\(277\) 20.2474 1.21655 0.608276 0.793726i \(-0.291862\pi\)
0.608276 + 0.793726i \(0.291862\pi\)
\(278\) −14.3485 −0.860564
\(279\) 12.0000 4.24264i 0.718421 0.254000i
\(280\) −0.550510 + 0.317837i −0.0328993 + 0.0189944i
\(281\) −11.2980 + 19.5686i −0.673980 + 1.16737i 0.302786 + 0.953058i \(0.402083\pi\)
−0.976766 + 0.214309i \(0.931250\pi\)
\(282\) 18.8990 + 13.3636i 1.12542 + 0.795791i
\(283\) 4.72474 + 8.18350i 0.280857 + 0.486458i 0.971596 0.236646i \(-0.0760480\pi\)
−0.690739 + 0.723104i \(0.742715\pi\)
\(284\) 6.00000 0.356034
\(285\) 8.00000 7.07107i 0.473879 0.418854i
\(286\) −10.8990 −0.644470
\(287\) −0.674235 1.16781i −0.0397988 0.0689336i
\(288\) 2.94949 + 0.548188i 0.173800 + 0.0323023i
\(289\) −8.29796 + 14.3725i −0.488115 + 0.845440i
\(290\) 3.00000 1.73205i 0.176166 0.101710i
\(291\) 0.522704 5.67291i 0.0306414 0.332552i
\(292\) 8.79796 0.514862
\(293\) 19.3485 1.13035 0.565175 0.824971i \(-0.308809\pi\)
0.565175 + 0.824971i \(0.308809\pi\)
\(294\) 11.7247 + 1.08032i 0.683801 + 0.0630057i
\(295\) −14.0227 8.09601i −0.816433 0.471368i
\(296\) 7.70674i 0.447945i
\(297\) 4.44949 15.7313i 0.258186 0.912824i
\(298\) 1.77526 + 1.02494i 0.102838 + 0.0593734i
\(299\) −12.2474 21.2132i −0.708288 1.22679i
\(300\) −5.17423 0.476756i −0.298735 0.0275255i
\(301\) −2.00000 3.46410i −0.115278 0.199667i
\(302\) −8.32577 + 4.80688i −0.479094 + 0.276605i
\(303\) −15.5732 + 7.17461i −0.894658 + 0.412170i
\(304\) 1.00000 4.24264i 0.0573539 0.243332i
\(305\) 2.19275i 0.125557i
\(306\) −0.348469 + 1.87492i −0.0199207 + 0.107182i
\(307\) 18.5227 10.6941i 1.05715 0.610344i 0.132505 0.991182i \(-0.457698\pi\)
0.924642 + 0.380838i \(0.124365\pi\)
\(308\) 1.22474 + 0.707107i 0.0697863 + 0.0402911i
\(309\) −7.10102 5.02118i −0.403963 0.285645i
\(310\) 3.00000 5.19615i 0.170389 0.295122i
\(311\) 15.5563i 0.882120i −0.897478 0.441060i \(-0.854603\pi\)
0.897478 0.441060i \(-0.145397\pi\)
\(312\) −5.44949 + 2.51059i −0.308517 + 0.142134i
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) −5.34847 + 9.26382i −0.301832 + 0.522788i
\(315\) 1.44949 + 1.23924i 0.0816695 + 0.0698233i
\(316\) 8.48528i 0.477334i
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) −10.8990 + 15.4135i −0.611184 + 0.864345i
\(319\) −6.67423 3.85337i −0.373685 0.215747i
\(320\) 1.22474 0.707107i 0.0684653 0.0395285i
\(321\) 4.89898 6.92820i 0.273434 0.386695i
\(322\) 3.17837i 0.177124i
\(323\) 2.69694 + 0.635674i 0.150062 + 0.0353699i
\(324\) −1.39898 8.89060i −0.0777211 0.493922i
\(325\) 9.00000 5.19615i 0.499230 0.288231i
\(326\) −9.17423 15.8902i −0.508114 0.880079i
\(327\) 0 0
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) 5.20204 + 3.00340i 0.286798 + 0.165583i
\(330\) −3.22474 6.99964i −0.177516 0.385317i
\(331\) 23.2952i 1.28042i 0.768200 + 0.640210i \(0.221153\pi\)
−0.768200 + 0.640210i \(0.778847\pi\)
\(332\) −14.7247 8.50134i −0.808125 0.466571i
\(333\) −21.7980 + 7.70674i −1.19452 + 0.422327i
\(334\) −4.89898 −0.268060
\(335\) 3.55051 0.193985
\(336\) 0.775255 + 0.0714323i 0.0422936 + 0.00389695i
\(337\) −17.8485 + 10.3048i −0.972268 + 0.561339i −0.899927 0.436041i \(-0.856380\pi\)
−0.0723411 + 0.997380i \(0.523047\pi\)
\(338\) −0.500000 + 0.866025i −0.0271964 + 0.0471056i
\(339\) 18.7980 26.5843i 1.02096 1.44386i
\(340\) 0.449490 + 0.778539i 0.0243770 + 0.0422222i
\(341\) −13.3485 −0.722860
\(342\) −13.0000 + 1.41421i −0.702959 + 0.0764719i
\(343\) 6.20204 0.334879
\(344\) 4.44949 + 7.70674i 0.239900 + 0.415520i
\(345\) 10.0000 14.1421i 0.538382 0.761387i
\(346\) −0.550510 + 0.953512i −0.0295956 + 0.0512611i
\(347\) −3.27526 + 1.89097i −0.175825 + 0.101513i −0.585330 0.810795i \(-0.699035\pi\)
0.409505 + 0.912308i \(0.365702\pi\)
\(348\) −4.22474 0.389270i −0.226470 0.0208670i
\(349\) 32.4949 1.73941 0.869706 0.493570i \(-0.164308\pi\)
0.869706 + 0.493570i \(0.164308\pi\)
\(350\) −1.34847 −0.0720787
\(351\) 12.5505 + 12.9029i 0.669897 + 0.688706i
\(352\) −2.72474 1.57313i −0.145229 0.0838482i
\(353\) 24.9951i 1.33036i −0.746684 0.665179i \(-0.768355\pi\)
0.746684 0.665179i \(-0.231645\pi\)
\(354\) 8.29796 + 18.0116i 0.441032 + 0.957304i
\(355\) −7.34847 4.24264i −0.390016 0.225176i
\(356\) −3.55051 6.14966i −0.188177 0.325932i
\(357\) −0.0454077 + 0.492810i −0.00240323 + 0.0260823i
\(358\) −3.82577 6.62642i −0.202198 0.350217i
\(359\) −20.8207 + 12.0208i −1.09887 + 0.634434i −0.935925 0.352200i \(-0.885434\pi\)
−0.162948 + 0.986635i \(0.552100\pi\)
\(360\) −3.22474 2.75699i −0.169959 0.145306i
\(361\) 1.15153 + 18.9651i 0.0606069 + 0.998162i
\(362\) 21.5631i 1.13333i
\(363\) 1.10102 1.55708i 0.0577886 0.0817254i
\(364\) −1.34847 + 0.778539i −0.0706790 + 0.0408065i
\(365\) −10.7753 6.22110i −0.564003 0.325627i
\(366\) −1.55051 + 2.19275i −0.0810465 + 0.114617i
\(367\) 4.32577 7.49245i 0.225803 0.391102i −0.730757 0.682638i \(-0.760833\pi\)
0.956560 + 0.291535i \(0.0941661\pi\)
\(368\) 7.07107i 0.368605i
\(369\) 5.84847 6.84072i 0.304459 0.356113i
\(370\) −5.44949 + 9.43879i −0.283305 + 0.490699i
\(371\) −2.44949 + 4.24264i −0.127171 + 0.220267i
\(372\) −6.67423 + 3.07483i −0.346043 + 0.159423i
\(373\) 25.4558i 1.31805i −0.752119 0.659027i \(-0.770968\pi\)
0.752119 0.659027i \(-0.229032\pi\)
\(374\) 1.00000 1.73205i 0.0517088 0.0895622i
\(375\) 16.0000 + 11.3137i 0.826236 + 0.584237i
\(376\) −11.5732 6.68180i −0.596843 0.344587i
\(377\) 7.34847 4.24264i 0.378465 0.218507i
\(378\) −0.573214 2.26418i −0.0294830 0.116457i
\(379\) 1.55708i 0.0799817i 0.999200 + 0.0399909i \(0.0127329\pi\)
−0.999200 + 0.0399909i \(0.987267\pi\)
\(380\) −4.22474 + 4.48905i −0.216725 + 0.230283i
\(381\) −16.3485 + 7.53177i −0.837557 + 0.385864i
\(382\) −7.10102 + 4.09978i −0.363320 + 0.209763i
\(383\) −10.2247 17.7098i −0.522460 0.904927i −0.999659 0.0261318i \(-0.991681\pi\)
0.477198 0.878796i \(-0.341652\pi\)
\(384\) −1.72474 0.158919i −0.0880155 0.00810978i
\(385\) −1.00000 1.73205i −0.0509647 0.0882735i
\(386\) 22.3485 + 12.9029i 1.13751 + 0.656740i
\(387\) 17.3485 20.2918i 0.881872 1.03149i
\(388\) 3.28913i 0.166980i
\(389\) 13.1010 + 7.56388i 0.664248 + 0.383504i 0.793894 0.608057i \(-0.208051\pi\)
−0.129646 + 0.991560i \(0.541384\pi\)
\(390\) 8.44949 + 0.778539i 0.427857 + 0.0394229i
\(391\) 4.49490 0.227317
\(392\) −6.79796 −0.343349
\(393\) −0.353572 + 3.83732i −0.0178353 + 0.193567i
\(394\) 17.5732 10.1459i 0.885326 0.511143i
\(395\) −6.00000 + 10.3923i −0.301893 + 0.522894i
\(396\) −1.72474 + 9.27987i −0.0866717 + 0.466331i
\(397\) 2.67423 + 4.63191i 0.134216 + 0.232469i 0.925298 0.379242i \(-0.123815\pi\)
−0.791082 + 0.611711i \(0.790482\pi\)
\(398\) −2.89898 −0.145313
\(399\) −3.32577 + 0.674999i −0.166497 + 0.0337922i
\(400\) 3.00000 0.150000
\(401\) 3.39898 + 5.88721i 0.169737 + 0.293993i 0.938327 0.345748i \(-0.112375\pi\)
−0.768590 + 0.639741i \(0.779042\pi\)
\(402\) −3.55051 2.51059i −0.177083 0.125217i
\(403\) 7.34847 12.7279i 0.366053 0.634023i
\(404\) 8.57321 4.94975i 0.426533 0.246259i
\(405\) −4.57321 + 11.8780i −0.227245 + 0.590220i
\(406\) −1.10102 −0.0546427
\(407\) 24.2474 1.20190
\(408\) 0.101021 1.09638i 0.00500126 0.0542787i
\(409\) 3.15153 + 1.81954i 0.155833 + 0.0899703i 0.575889 0.817528i \(-0.304656\pi\)
−0.420056 + 0.907498i \(0.637989\pi\)
\(410\) 4.24264i 0.209529i
\(411\) −6.17423 + 2.84448i −0.304553 + 0.140308i
\(412\) 4.34847 + 2.51059i 0.214234 + 0.123688i
\(413\) 2.57321 + 4.45694i 0.126620 + 0.219312i
\(414\) −20.0000 + 7.07107i −0.982946 + 0.347524i
\(415\) 12.0227 + 20.8239i 0.590171 + 1.02221i
\(416\) 3.00000 1.73205i 0.147087 0.0849208i
\(417\) −10.3990 22.5720i −0.509240 1.10536i
\(418\) 13.3485 + 3.14626i 0.652895 + 0.153889i
\(419\) 24.5344i 1.19859i 0.800530 + 0.599293i \(0.204552\pi\)
−0.800530 + 0.599293i \(0.795448\pi\)
\(420\) −0.898979 0.635674i −0.0438657 0.0310177i
\(421\) −3.97730 + 2.29629i −0.193842 + 0.111914i −0.593780 0.804628i \(-0.702365\pi\)
0.399938 + 0.916542i \(0.369032\pi\)
\(422\) 1.34847 + 0.778539i 0.0656425 + 0.0378987i
\(423\) −7.32577 + 39.4158i −0.356191 + 1.91646i
\(424\) 5.44949 9.43879i 0.264651 0.458388i
\(425\) 1.90702i 0.0925042i
\(426\) 4.34847 + 9.43879i 0.210684 + 0.457311i
\(427\) −0.348469 + 0.603566i −0.0168636 + 0.0292086i
\(428\) −2.44949 + 4.24264i −0.118401 + 0.205076i
\(429\) −7.89898 17.1455i −0.381366 0.827794i
\(430\) 12.5851i 0.606905i
\(431\) −1.65153 + 2.86054i −0.0795514 + 0.137787i −0.903056 0.429522i \(-0.858682\pi\)
0.823505 + 0.567309i \(0.192015\pi\)
\(432\) 1.27526 + 5.03723i 0.0613557 + 0.242354i
\(433\) −17.6969 10.2173i −0.850461 0.491014i 0.0103456 0.999946i \(-0.496707\pi\)
−0.860806 + 0.508933i \(0.830040\pi\)
\(434\) −1.65153 + 0.953512i −0.0792760 + 0.0457700i
\(435\) 4.89898 + 3.46410i 0.234888 + 0.166091i
\(436\) 0 0
\(437\) 8.87628 + 29.5163i 0.424610 + 1.41196i
\(438\) 6.37628 + 13.8404i 0.304670 + 0.661318i
\(439\) −9.67423 + 5.58542i −0.461726 + 0.266578i −0.712770 0.701398i \(-0.752560\pi\)
0.251044 + 0.967976i \(0.419226\pi\)
\(440\) 2.22474 + 3.85337i 0.106061 + 0.183702i
\(441\) 6.79796 + 19.2275i 0.323712 + 0.915597i
\(442\) 1.10102 + 1.90702i 0.0523702 + 0.0907079i
\(443\) 16.3207 + 9.42274i 0.775418 + 0.447688i 0.834804 0.550547i \(-0.185581\pi\)
−0.0593859 + 0.998235i \(0.518914\pi\)
\(444\) 12.1237 5.58542i 0.575366 0.265072i
\(445\) 10.0424i 0.476053i
\(446\) 15.6742 + 9.04952i 0.742197 + 0.428507i
\(447\) −0.325765 + 3.53553i −0.0154082 + 0.167225i
\(448\) −0.449490 −0.0212364
\(449\) −30.7980 −1.45345 −0.726723 0.686931i \(-0.758958\pi\)
−0.726723 + 0.686931i \(0.758958\pi\)
\(450\) −3.00000 8.48528i −0.141421 0.400000i
\(451\) −8.17423 + 4.71940i −0.384910 + 0.222228i
\(452\) −9.39898 + 16.2795i −0.442091 + 0.765724i
\(453\) −13.5959 9.61377i −0.638792 0.451694i
\(454\) 0.275255 + 0.476756i 0.0129184 + 0.0223753i
\(455\) 2.20204 0.103233
\(456\) 7.39898 1.50170i 0.346489 0.0703235i
\(457\) −13.0000 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) −0.449490 0.778539i −0.0210033 0.0363787i
\(459\) −3.20204 + 0.810647i −0.149458 + 0.0378378i
\(460\) −5.00000 + 8.66025i −0.233126 + 0.403786i
\(461\) 33.2474 19.1954i 1.54849 0.894020i 0.550231 0.835013i \(-0.314540\pi\)
0.998258 0.0590072i \(-0.0187935\pi\)
\(462\) −0.224745 + 2.43916i −0.0104561 + 0.113480i
\(463\) −19.7980 −0.920089 −0.460045 0.887896i \(-0.652167\pi\)
−0.460045 + 0.887896i \(0.652167\pi\)
\(464\) 2.44949 0.113715
\(465\) 10.3485 + 0.953512i 0.479899 + 0.0442180i
\(466\) −15.3990 8.89060i −0.713344 0.411849i
\(467\) 12.6172i 0.583853i −0.956441 0.291926i \(-0.905704\pi\)
0.956441 0.291926i \(-0.0942962\pi\)
\(468\) −7.89898 6.75323i −0.365130 0.312168i
\(469\) −0.977296 0.564242i −0.0451273 0.0260543i
\(470\) 9.44949 + 16.3670i 0.435872 + 0.754953i
\(471\) −18.4495 1.69994i −0.850108 0.0783292i
\(472\) −5.72474 9.91555i −0.263503 0.456400i
\(473\) −24.2474 + 13.9993i −1.11490 + 0.643687i
\(474\) 13.3485 6.14966i 0.613115 0.282463i
\(475\) −12.5227 + 3.76588i −0.574581 + 0.172791i
\(476\) 0.285729i 0.0130964i
\(477\) −32.1464 5.97469i −1.47188 0.273562i
\(478\) 18.2474 10.5352i 0.834619 0.481867i
\(479\) −0.853572 0.492810i −0.0390007 0.0225171i 0.480373 0.877064i \(-0.340501\pi\)
−0.519374 + 0.854547i \(0.673835\pi\)
\(480\) 2.00000 + 1.41421i 0.0912871 + 0.0645497i
\(481\) −13.3485 + 23.1202i −0.608638 + 1.05419i
\(482\) 6.75323i 0.307601i
\(483\) −5.00000 + 2.30351i −0.227508 + 0.104813i
\(484\) −0.550510 + 0.953512i −0.0250232 + 0.0433414i
\(485\) 2.32577 4.02834i 0.105608 0.182918i
\(486\) 12.9722 8.64420i 0.588431 0.392109i
\(487\) 25.0273i 1.13409i 0.823686 + 0.567046i \(0.191914\pi\)
−0.823686 + 0.567046i \(0.808086\pi\)
\(488\) 0.775255 1.34278i 0.0350942 0.0607849i
\(489\) 18.3485 25.9487i 0.829746 1.17344i
\(490\) 8.32577 + 4.80688i 0.376120 + 0.217153i
\(491\) 13.8990 8.02458i 0.627252 0.362144i −0.152435 0.988314i \(-0.548711\pi\)
0.779687 + 0.626169i \(0.215378\pi\)
\(492\) −3.00000 + 4.24264i −0.135250 + 0.191273i
\(493\) 1.55708i 0.0701273i
\(494\) −10.3485 + 10.9959i −0.465600 + 0.494728i
\(495\) 8.67423 10.1459i 0.389878 0.456024i
\(496\) 3.67423 2.12132i 0.164978 0.0952501i
\(497\) 1.34847 + 2.33562i 0.0604871 + 0.104767i
\(498\) 2.70204 29.3253i 0.121081 1.31410i
\(499\) −3.72474 6.45145i −0.166742 0.288806i 0.770530 0.637403i \(-0.219992\pi\)
−0.937273 + 0.348597i \(0.886658\pi\)
\(500\) −9.79796 5.65685i −0.438178 0.252982i
\(501\) −3.55051 7.70674i −0.158625 0.344312i
\(502\) 3.78194i 0.168796i
\(503\) 13.4722 + 7.77817i 0.600695 + 0.346812i 0.769315 0.638870i \(-0.220598\pi\)
−0.168620 + 0.985681i \(0.553931\pi\)
\(504\) 0.449490 + 1.27135i 0.0200219 + 0.0566304i
\(505\) −14.0000 −0.622992
\(506\) 22.2474 0.989020
\(507\) −1.72474 0.158919i −0.0765986 0.00705782i
\(508\) 9.00000 5.19615i 0.399310 0.230542i
\(509\) −8.69694 + 15.0635i −0.385485 + 0.667680i −0.991836 0.127517i \(-0.959299\pi\)
0.606351 + 0.795197i \(0.292633\pi\)
\(510\) −0.898979 + 1.27135i −0.0398075 + 0.0562963i
\(511\) 1.97730 + 3.42478i 0.0874704 + 0.151503i
\(512\) 1.00000 0.0441942
\(513\) −11.6464 19.4258i −0.514202 0.857669i
\(514\) −15.0000 −0.661622
\(515\) −3.55051 6.14966i −0.156454 0.270987i
\(516\) −8.89898 + 12.5851i −0.391756 + 0.554026i
\(517\) 21.0227 36.4124i 0.924577 1.60142i
\(518\) 3.00000 1.73205i 0.131812 0.0761019i
\(519\) −1.89898 0.174973i −0.0833559 0.00768045i
\(520\) −4.89898 −0.214834
\(521\) 25.8990 1.13465 0.567327 0.823492i \(-0.307977\pi\)
0.567327 + 0.823492i \(0.307977\pi\)
\(522\) −2.44949 6.92820i −0.107211 0.303239i
\(523\) −5.69694 3.28913i −0.249110 0.143824i 0.370247 0.928933i \(-0.379273\pi\)
−0.619357 + 0.785110i \(0.712606\pi\)
\(524\) 2.22486i 0.0971935i
\(525\) −0.977296 2.12132i −0.0426527 0.0925820i
\(526\) 7.77526 + 4.48905i 0.339017 + 0.195732i
\(527\) 1.34847 + 2.33562i 0.0587402 + 0.101741i
\(528\) 0.500000 5.42650i 0.0217597 0.236158i
\(529\) 13.5000 + 23.3827i 0.586957 + 1.01664i
\(530\) −13.3485 + 7.70674i −0.579820 + 0.334759i
\(531\) −22.3207 + 26.1076i −0.968634 + 1.13297i
\(532\) 1.87628 0.564242i 0.0813469 0.0244630i
\(533\) 10.3923i 0.450141i
\(534\) 7.10102 10.0424i 0.307291 0.434575i
\(535\) 6.00000 3.46410i 0.259403 0.149766i
\(536\) 2.17423 + 1.25529i 0.0939126 + 0.0542205i
\(537\) 7.65153 10.8209i 0.330188 0.466956i
\(538\) −12.2474 + 21.2132i −0.528025 + 0.914566i
\(539\) 21.3882i 0.921254i
\(540\) 2.00000 7.07107i 0.0860663 0.304290i
\(541\) −5.34847 + 9.26382i −0.229949 + 0.398283i −0.957793 0.287460i \(-0.907189\pi\)
0.727844 + 0.685743i \(0.240522\pi\)
\(542\) 10.0227 17.3598i 0.430512 0.745669i
\(543\) 33.9217 15.6278i 1.45572 0.670652i
\(544\) 0.635674i 0.0272543i
\(545\) 0 0
\(546\) −2.20204 1.55708i −0.0942387 0.0666368i
\(547\) −32.3939 18.7026i −1.38506 0.799666i −0.392309 0.919834i \(-0.628323\pi\)
−0.992754 + 0.120168i \(0.961657\pi\)
\(548\) 3.39898 1.96240i 0.145197 0.0838296i
\(549\) −4.57321 0.849971i −0.195180 0.0362759i
\(550\) 9.43879i 0.402471i
\(551\) −10.2247 + 3.07483i −0.435589 + 0.130992i
\(552\) 11.1237 5.12472i 0.473457 0.218123i
\(553\) 3.30306 1.90702i 0.140460 0.0810949i
\(554\) −10.1237 17.5348i −0.430116 0.744982i
\(555\) −18.7980 1.73205i −0.797929 0.0735215i
\(556\) 7.17423 + 12.4261i 0.304255 + 0.526986i
\(557\) −0.247449 0.142865i −0.0104847 0.00605337i 0.494748 0.869036i \(-0.335260\pi\)
−0.505233 + 0.862983i \(0.668594\pi\)
\(558\) −9.67423 8.27098i −0.409543 0.350139i
\(559\) 30.8270i 1.30384i
\(560\) 0.550510 + 0.317837i 0.0232633 + 0.0134311i
\(561\) 3.44949 + 0.317837i 0.145638 + 0.0134191i
\(562\) 22.5959 0.953151
\(563\) −40.8434 −1.72134 −0.860671 0.509161i \(-0.829956\pi\)
−0.860671 + 0.509161i \(0.829956\pi\)
\(564\) 2.12372 23.0488i 0.0894249 0.970529i
\(565\) 23.0227 13.2922i 0.968572 0.559206i
\(566\) 4.72474 8.18350i 0.198596 0.343978i
\(567\) 3.14643 2.54270i 0.132138 0.106783i
\(568\) −3.00000 5.19615i −0.125877 0.218026i
\(569\) 34.2929 1.43763 0.718816 0.695201i \(-0.244685\pi\)
0.718816 + 0.695201i \(0.244685\pi\)
\(570\) −10.1237 3.39267i −0.424036 0.142103i
\(571\) 33.0454 1.38291 0.691454 0.722421i \(-0.256971\pi\)
0.691454 + 0.722421i \(0.256971\pi\)
\(572\) 5.44949 + 9.43879i 0.227855 + 0.394656i
\(573\) −11.5959 8.19955i −0.484426 0.342541i
\(574\) −0.674235 + 1.16781i −0.0281420 + 0.0487434i
\(575\) −18.3712 + 10.6066i −0.766131 + 0.442326i
\(576\) −1.00000 2.82843i −0.0416667 0.117851i
\(577\) 18.5959 0.774158 0.387079 0.922047i \(-0.373484\pi\)
0.387079 + 0.922047i \(0.373484\pi\)
\(578\) 16.5959 0.690299
\(579\) −4.10102 + 44.5084i −0.170433 + 1.84971i
\(580\) −3.00000 1.73205i −0.124568 0.0719195i
\(581\) 7.64253i 0.317065i
\(582\) −5.17423 + 2.38378i −0.214479 + 0.0988108i
\(583\) 29.6969 + 17.1455i 1.22992 + 0.710096i
\(584\) −4.39898 7.61926i −0.182031 0.315287i
\(585\) 4.89898 + 13.8564i 0.202548 + 0.572892i
\(586\) −9.67423 16.7563i −0.399639 0.692195i
\(587\) 13.8990 8.02458i 0.573672 0.331210i −0.184942 0.982749i \(-0.559210\pi\)
0.758615 + 0.651540i \(0.225877\pi\)
\(588\) −4.92679 10.6941i −0.203177 0.441017i
\(589\) −12.6742 + 13.4671i −0.522233 + 0.554904i
\(590\) 16.1920i 0.666615i
\(591\) 28.6969 + 20.2918i 1.18043 + 0.834693i
\(592\) −6.67423 + 3.85337i −0.274309 + 0.158373i
\(593\) −15.0959 8.71563i −0.619915 0.357908i 0.156921 0.987611i \(-0.449843\pi\)
−0.776836 + 0.629703i \(0.783177\pi\)
\(594\) −15.8485 + 4.01229i −0.650271 + 0.164626i
\(595\) −0.202041 + 0.349945i −0.00828287 + 0.0143464i
\(596\) 2.04989i 0.0839667i
\(597\) −2.10102 4.56048i −0.0859890 0.186648i
\(598\) −12.2474 + 21.2132i −0.500835 + 0.867472i
\(599\) 2.57321 4.45694i 0.105139 0.182106i −0.808656 0.588282i \(-0.799805\pi\)
0.913795 + 0.406176i \(0.133138\pi\)
\(600\) 2.17423 + 4.71940i 0.0887628 + 0.192669i
\(601\) 14.0314i 0.572352i −0.958177 0.286176i \(-0.907616\pi\)
0.958177 0.286176i \(-0.0923842\pi\)
\(602\) −2.00000 + 3.46410i −0.0815139 + 0.141186i
\(603\) 1.37628 7.40496i 0.0560463 0.301553i
\(604\) 8.32577 + 4.80688i 0.338771 + 0.195589i
\(605\) 1.34847 0.778539i 0.0548231 0.0316521i
\(606\) 14.0000 + 9.89949i 0.568711 + 0.402139i
\(607\) 11.5208i 0.467614i 0.972283 + 0.233807i \(0.0751185\pi\)
−0.972283 + 0.233807i \(0.924882\pi\)
\(608\) −4.17423 + 1.25529i −0.169288 + 0.0509089i
\(609\) −0.797959 1.73205i −0.0323349 0.0701862i
\(610\) −1.89898 + 1.09638i −0.0768874 + 0.0443910i
\(611\) 23.1464 + 40.0908i 0.936404 + 1.62190i
\(612\) 1.79796 0.635674i 0.0726782 0.0256956i
\(613\) −23.8990 41.3942i −0.965271 1.67190i −0.708886 0.705323i \(-0.750802\pi\)
−0.256385 0.966575i \(-0.582531\pi\)
\(614\) −18.5227 10.6941i −0.747515 0.431578i
\(615\) 6.67423 3.07483i 0.269131 0.123989i
\(616\) 1.41421i 0.0569803i
\(617\) −8.05051 4.64796i −0.324101 0.187120i 0.329118 0.944289i \(-0.393249\pi\)
−0.653219 + 0.757169i \(0.726582\pi\)
\(618\) −0.797959 + 8.66025i −0.0320986 + 0.348367i
\(619\) −30.6969 −1.23381 −0.616907 0.787036i \(-0.711615\pi\)
−0.616907 + 0.787036i \(0.711615\pi\)
\(620\) −6.00000 −0.240966
\(621\) −25.6186 26.3379i −1.02804 1.05690i
\(622\) −13.4722 + 7.77817i −0.540186 + 0.311876i
\(623\) 1.59592 2.76421i 0.0639391 0.110746i
\(624\) 4.89898 + 3.46410i 0.196116 + 0.138675i
\(625\) 0.500000 + 0.866025i 0.0200000 + 0.0346410i
\(626\) −19.0000 −0.759393
\(627\) 4.72474 + 23.2791i 0.188688 + 0.929680i
\(628\) 10.6969 0.426854
\(629\) −2.44949 4.24264i −0.0976676 0.169165i
\(630\) 0.348469 1.87492i 0.0138833 0.0746984i
\(631\) 17.1237 29.6592i 0.681685 1.18071i −0.292782 0.956179i \(-0.594581\pi\)
0.974466 0.224533i \(-0.0720857\pi\)
\(632\) −7.34847 + 4.24264i −0.292306 + 0.168763i
\(633\) −0.247449 + 2.68556i −0.00983520 + 0.106742i
\(634\) −6.00000 −0.238290
\(635\) −14.6969 −0.583230
\(636\) 18.7980 + 1.73205i 0.745388 + 0.0686803i
\(637\) 20.3939 + 11.7744i 0.808035 + 0.466519i
\(638\) 7.70674i 0.305113i
\(639\) −11.6969 + 13.6814i −0.462724 + 0.541229i
\(640\) −1.22474 0.707107i −0.0484123 0.0279508i
\(641\) 13.1969 + 22.8578i 0.521248 + 0.902828i 0.999695 + 0.0247111i \(0.00786658\pi\)
−0.478447 + 0.878116i \(0.658800\pi\)
\(642\) −8.44949 0.778539i −0.333475 0.0307265i
\(643\) −5.07321 8.78706i −0.200068 0.346528i 0.748482 0.663155i \(-0.230783\pi\)
−0.948550 + 0.316627i \(0.897450\pi\)
\(644\) 2.75255 1.58919i 0.108466 0.0626227i
\(645\) 19.7980 9.12096i 0.779544 0.359137i
\(646\) −0.797959 2.65345i −0.0313953 0.104399i
\(647\) 14.7778i 0.580976i −0.956879 0.290488i \(-0.906182\pi\)
0.956879 0.290488i \(-0.0938176\pi\)
\(648\) −7.00000 + 5.65685i −0.274986 + 0.222222i
\(649\) 31.1969 18.0116i 1.22459 0.707016i
\(650\) −9.00000 5.19615i −0.353009 0.203810i
\(651\) −2.69694 1.90702i −0.105701 0.0747421i
\(652\) −9.17423 + 15.8902i −0.359291 + 0.622310i
\(653\) 8.19955i 0.320873i −0.987046 0.160437i \(-0.948710\pi\)
0.987046 0.160437i \(-0.0512902\pi\)
\(654\) 0 0
\(655\) −1.57321 + 2.72489i −0.0614706 + 0.106470i
\(656\) 1.50000 2.59808i 0.0585652 0.101438i
\(657\) −17.1515 + 20.0614i −0.669145 + 0.782672i
\(658\) 6.00680i 0.234169i
\(659\) 12.0000 20.7846i 0.467454 0.809653i −0.531855 0.846836i \(-0.678505\pi\)
0.999309 + 0.0371821i \(0.0118382\pi\)
\(660\) −4.44949 + 6.29253i −0.173196 + 0.244936i
\(661\) 25.7196 + 14.8492i 1.00038 + 0.577569i 0.908360 0.418189i \(-0.137335\pi\)
0.0920180 + 0.995757i \(0.470668\pi\)
\(662\) 20.1742 11.6476i 0.784094 0.452697i
\(663\) −2.20204 + 3.11416i −0.0855202 + 0.120944i
\(664\) 17.0027i 0.659832i
\(665\) −2.69694 0.635674i −0.104583 0.0246504i
\(666\) 17.5732 + 15.0242i 0.680948 + 0.582177i
\(667\) −15.0000 + 8.66025i −0.580802 + 0.335326i
\(668\) 2.44949 + 4.24264i 0.0947736 + 0.164153i
\(669\) −2.87628 + 31.2162i −0.111203 + 1.20689i
\(670\) −1.77526 3.07483i −0.0685841 0.118791i
\(671\) 4.22474 + 2.43916i 0.163094 + 0.0941626i
\(672\) −0.325765 0.707107i −0.0125667 0.0272772i
\(673\) 3.46410i 0.133531i 0.997769 + 0.0667657i \(0.0212680\pi\)
−0.997769 + 0.0667657i \(0.978732\pi\)
\(674\) 17.8485 + 10.3048i 0.687497 + 0.396927i
\(675\) 11.1742 10.8691i 0.430096 0.418350i
\(676\) 1.00000 0.0384615
\(677\) 32.6969 1.25665 0.628323 0.777953i \(-0.283742\pi\)
0.628323 + 0.777953i \(0.283742\pi\)
\(678\) −32.4217 2.98735i −1.24515 0.114728i
\(679\) −1.28036 + 0.739215i −0.0491356 + 0.0283685i
\(680\) 0.449490 0.778539i 0.0172371 0.0298556i
\(681\) −0.550510 + 0.778539i −0.0210956 + 0.0298337i
\(682\) 6.67423 + 11.5601i 0.255570 + 0.442660i
\(683\) −17.3939 −0.665558 −0.332779 0.943005i \(-0.607986\pi\)
−0.332779 + 0.943005i \(0.607986\pi\)
\(684\) 7.72474 + 10.5512i 0.295363 + 0.403436i
\(685\) −5.55051 −0.212074
\(686\) −3.10102 5.37113i −0.118398 0.205071i
\(687\) 0.898979 1.27135i 0.0342982 0.0485050i
\(688\) 4.44949 7.70674i 0.169635 0.293817i
\(689\) −32.6969 + 18.8776i −1.24565 + 0.719179i
\(690\) −17.2474 1.58919i −0.656599 0.0604993i
\(691\) −40.0000 −1.52167 −0.760836 0.648944i \(-0.775211\pi\)
−0.760836 + 0.648944i \(0.775211\pi\)
\(692\) 1.10102 0.0418545
\(693\) −4.00000 + 1.41421i −0.151947 + 0.0537215i
\(694\) 3.27526 + 1.89097i 0.124327 + 0.0717802i
\(695\) 20.2918i 0.769712i
\(696\) 1.77526 + 3.85337i 0.0672909 + 0.146062i
\(697\) 1.65153 + 0.953512i 0.0625562 + 0.0361168i
\(698\) −16.2474 28.1414i −0.614975 1.06517i
\(699\) 2.82577 30.6681i 0.106880 1.15997i
\(700\) 0.674235 + 1.16781i 0.0254837 + 0.0441390i
\(701\) 8.57321 4.94975i 0.323806 0.186949i −0.329282 0.944232i \(-0.606807\pi\)
0.653088 + 0.757282i \(0.273473\pi\)
\(702\) 4.89898 17.3205i 0.184900 0.653720i
\(703\) 23.0227 24.4630i 0.868318 0.922640i
\(704\) 3.14626i 0.118579i
\(705\) −18.8990 + 26.7272i −0.711777 + 1.00660i
\(706\) −21.6464 + 12.4976i −0.814674 + 0.470352i
\(707\) 3.85357 + 2.22486i 0.144928 + 0.0836745i
\(708\) 11.4495 16.1920i 0.430298 0.608534i
\(709\) 8.67423 15.0242i 0.325768 0.564246i −0.655900 0.754848i \(-0.727711\pi\)
0.981667 + 0.190602i \(0.0610439\pi\)
\(710\) 8.48528i 0.318447i
\(711\) 19.3485 + 16.5420i 0.725624 + 0.620372i
\(712\) −3.55051 + 6.14966i −0.133061 + 0.230468i
\(713\) −15.0000 + 25.9808i −0.561754 + 0.972987i
\(714\) 0.449490 0.207081i 0.0168217 0.00774980i
\(715\) 15.4135i 0.576432i
\(716\) −3.82577 + 6.62642i −0.142976 + 0.247641i
\(717\) 29.7980 + 21.0703i 1.11283 + 0.786886i
\(718\) 20.8207 + 12.0208i 0.777020 + 0.448613i
\(719\) −26.1464 + 15.0956i −0.975097 + 0.562973i −0.900786 0.434262i \(-0.857009\pi\)
−0.0743109 + 0.997235i \(0.523676\pi\)
\(720\) −0.775255 + 4.17121i −0.0288921 + 0.155452i
\(721\) 2.25697i 0.0840539i
\(722\) 15.8485 10.4798i 0.589819 0.390017i
\(723\) −10.6237 + 4.89437i −0.395101 + 0.182024i
\(724\) −18.6742 + 10.7816i −0.694022 + 0.400694i
\(725\) −3.67423 6.36396i −0.136458 0.236352i
\(726\) −1.89898 0.174973i −0.0704777 0.00649384i
\(727\) −4.00000 6.92820i −0.148352 0.256953i 0.782267 0.622944i \(-0.214063\pi\)
−0.930618 + 0.365991i \(0.880730\pi\)
\(728\) 1.34847 + 0.778539i 0.0499776 + 0.0288546i
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 12.4422i 0.460506i
\(731\) 4.89898 + 2.82843i 0.181195 + 0.104613i
\(732\) 2.67423 + 0.246405i 0.0988426 + 0.00910739i
\(733\) −20.0454 −0.740394 −0.370197 0.928953i \(-0.620710\pi\)
−0.370197 + 0.928953i \(0.620710\pi\)
\(734\) −8.65153 −0.319334
\(735\) −1.52781 + 16.5813i −0.0563540 + 0.611610i
\(736\) −6.12372 + 3.53553i −0.225723 + 0.130322i
\(737\) −3.94949 + 6.84072i −0.145481 + 0.251981i
\(738\) −8.84847 1.64456i −0.325717 0.0605373i
\(739\) −12.1742 21.0864i −0.447836 0.775676i 0.550408 0.834895i \(-0.314472\pi\)
−0.998245 + 0.0592200i \(0.981139\pi\)
\(740\) 10.8990 0.400654
\(741\) −24.7980 8.31031i −0.910976 0.305287i
\(742\) 4.89898 0.179847
\(743\) 2.32577 + 4.02834i 0.0853241 + 0.147786i 0.905529 0.424284i \(-0.139474\pi\)
−0.820205 + 0.572069i \(0.806141\pi\)
\(744\) 6.00000 + 4.24264i 0.219971 + 0.155543i
\(745\) −1.44949 + 2.51059i −0.0531052 + 0.0919809i
\(746\) −22.0454 + 12.7279i −0.807140 + 0.466002i
\(747\) 48.0908 17.0027i 1.75955 0.622095i
\(748\) −2.00000 −0.0731272
\(749\) −2.20204 −0.0804608
\(750\) 1.79796 19.5133i 0.0656522 0.712524i
\(751\) 17.6969 + 10.2173i 0.645770 + 0.372836i 0.786834 0.617165i \(-0.211719\pi\)
−0.141063 + 0.990001i \(0.545052\pi\)
\(752\) 13.3636i 0.487320i
\(753\) 5.94949 2.74094i 0.216811 0.0998854i
\(754\) −7.34847 4.24264i −0.267615 0.154508i
\(755\) −6.79796 11.7744i −0.247403 0.428515i
\(756\) −1.67423 + 1.62851i −0.0608913 + 0.0592284i
\(757\) 19.6969 + 34.1161i 0.715897 + 1.23997i 0.962612 + 0.270883i \(0.0873155\pi\)
−0.246715 + 0.969088i \(0.579351\pi\)
\(758\) 1.34847 0.778539i 0.0489786 0.0282778i
\(759\) 16.1237 + 34.9982i 0.585254 + 1.27035i
\(760\) 6.00000 + 1.41421i 0.217643 + 0.0512989i
\(761\) 31.5734i 1.14453i −0.820067 0.572267i \(-0.806064\pi\)
0.820067 0.572267i \(-0.193936\pi\)
\(762\) 14.6969 + 10.3923i 0.532414 + 0.376473i
\(763\) 0 0
\(764\) 7.10102 + 4.09978i 0.256906 + 0.148325i
\(765\) −2.65153 0.492810i −0.0958663 0.0178176i
\(766\) −10.2247 + 17.7098i −0.369435 + 0.639880i
\(767\) 39.6622i 1.43212i
\(768\) 0.724745 + 1.57313i 0.0261520 + 0.0567655i
\(769\) −1.79796 + 3.11416i −0.0648361 + 0.112299i −0.896621 0.442798i \(-0.853986\pi\)
0.831785 + 0.555098i \(0.187319\pi\)
\(770\) −1.00000 + 1.73205i −0.0360375 + 0.0624188i
\(771\) −10.8712 23.5970i −0.391516 0.849825i
\(772\) 25.8058i 0.928771i
\(773\) 1.22474 2.12132i 0.0440510 0.0762986i −0.843159 0.537664i \(-0.819307\pi\)
0.887210