Properties

Label 48.2.k.a.35.5
Level $48$
Weight $2$
Character 48.35
Analytic conductor $0.383$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(0.383281929702\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.163368480538624.2
Defining polynomial: \(x^{12} - 2 x^{10} - 2 x^{8} + 16 x^{6} - 8 x^{4} - 32 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 35.5
Root \(-1.27715 - 0.607364i\) of defining polynomial
Character \(\chi\) \(=\) 48.35
Dual form 48.2.k.a.11.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.607364 + 1.27715i) q^{2} +(0.0835731 - 1.73003i) q^{3} +(-1.26222 + 1.55139i) q^{4} +(0.431733 + 0.431733i) q^{5} +(2.26027 - 0.944024i) q^{6} -3.10278 q^{7} +(-2.74798 - 0.669785i) q^{8} +(-2.98603 - 0.289169i) q^{9} +O(q^{10})\) \(q+(0.607364 + 1.27715i) q^{2} +(0.0835731 - 1.73003i) q^{3} +(-1.26222 + 1.55139i) q^{4} +(0.431733 + 0.431733i) q^{5} +(2.26027 - 0.944024i) q^{6} -3.10278 q^{7} +(-2.74798 - 0.669785i) q^{8} +(-2.98603 - 0.289169i) q^{9} +(-0.289169 + 0.813607i) q^{10} +(2.98603 - 2.98603i) q^{11} +(2.57846 + 2.31334i) q^{12} +(2.10278 + 2.10278i) q^{13} +(-1.88451 - 3.96271i) q^{14} +(0.782994 - 0.710831i) q^{15} +(-0.813607 - 3.91638i) q^{16} +2.42945i q^{17} +(-1.44430 - 3.98924i) q^{18} +(-0.710831 + 0.710831i) q^{19} +(-1.21473 + 0.124844i) q^{20} +(-0.259309 + 5.36790i) q^{21} +(5.62721 + 2.00000i) q^{22} +5.97206i q^{23} +(-1.38841 + 4.69812i) q^{24} -4.62721i q^{25} +(-1.40841 + 3.96271i) q^{26} +(-0.749823 + 5.14177i) q^{27} +(3.91638 - 4.81361i) q^{28} +(2.86119 - 2.86119i) q^{29} +(1.38340 + 0.568267i) q^{30} +0.524438i q^{31} +(4.50765 - 3.41776i) q^{32} +(-4.91638 - 5.41549i) q^{33} +(-3.10278 + 1.47556i) q^{34} +(-1.33957 - 1.33957i) q^{35} +(4.21764 - 4.26750i) q^{36} +(1.52444 - 1.52444i) q^{37} +(-1.33957 - 0.476105i) q^{38} +(3.81361 - 3.46214i) q^{39} +(-0.897225 - 1.47556i) q^{40} +1.81568 q^{41} +(-7.01311 + 2.92909i) q^{42} +(0.710831 + 0.710831i) q^{43} +(0.863466 + 8.40152i) q^{44} +(-1.16432 - 1.41401i) q^{45} +(-7.62721 + 3.62721i) q^{46} -7.53805 q^{47} +(-6.84347 + 1.08026i) q^{48} +2.62721 q^{49} +(5.90964 - 2.81040i) q^{50} +(4.20304 + 0.203037i) q^{51} +(-5.91638 + 0.608056i) q^{52} +(-8.83325 - 8.83325i) q^{53} +(-7.02222 + 2.16529i) q^{54} +2.57834 q^{55} +(8.52636 + 2.07819i) q^{56} +(1.17036 + 1.28917i) q^{57} +(5.39194 + 1.91638i) q^{58} +(-0.0804722 + 0.0804722i) q^{59} +(0.114465 + 2.11195i) q^{60} +(-5.72999 - 5.72999i) q^{61} +(-0.669785 + 0.318525i) q^{62} +(9.26498 + 0.897225i) q^{63} +(7.10278 + 3.68111i) q^{64} +1.81568i q^{65} +(3.93035 - 9.56812i) q^{66} +(-0.391944 + 0.391944i) q^{67} +(-3.76903 - 3.06650i) q^{68} +(10.3319 + 0.499104i) q^{69} +(0.897225 - 2.52444i) q^{70} -5.01985i q^{71} +(8.01187 + 2.79463i) q^{72} +13.4600i q^{73} +(2.87282 + 1.02105i) q^{74} +(-8.00523 - 0.386711i) q^{75} +(-0.205550 - 2.00000i) q^{76} +(-9.26498 + 9.26498i) q^{77} +(6.73791 + 2.76777i) q^{78} +3.47556i q^{79} +(1.33957 - 2.04209i) q^{80} +(8.83276 + 1.72693i) q^{81} +(1.10278 + 2.31889i) q^{82} +(4.55202 + 4.55202i) q^{83} +(-8.00040 - 7.17776i) q^{84} +(-1.04888 + 1.04888i) q^{85} +(-0.476105 + 1.33957i) q^{86} +(-4.71083 - 5.18907i) q^{87} +(-10.2056 + 6.20555i) q^{88} +12.5579 q^{89} +(1.09874 - 2.34584i) q^{90} +(-6.52444 - 6.52444i) q^{91} +(-9.26498 - 7.53805i) q^{92} +(0.907295 + 0.0438289i) q^{93} +(-4.57834 - 9.62721i) q^{94} -0.613779 q^{95} +(-5.53613 - 8.08401i) q^{96} -8.67609 q^{97} +(1.59567 + 3.35534i) q^{98} +(-9.77985 + 8.05292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{3} - 4q^{4} - 8q^{6} - 8q^{7} + O(q^{10}) \) \( 12q - 2q^{3} - 4q^{4} - 8q^{6} - 8q^{7} - 8q^{12} - 4q^{13} + 16q^{16} + 4q^{18} - 12q^{19} - 8q^{21} + 16q^{22} + 24q^{24} + 10q^{27} - 8q^{28} + 28q^{30} - 4q^{33} - 8q^{34} + 20q^{36} - 4q^{37} + 20q^{39} - 40q^{40} - 24q^{42} + 12q^{43} - 12q^{45} - 40q^{46} - 48q^{48} - 20q^{49} + 24q^{51} - 16q^{52} - 52q^{54} + 24q^{55} + 32q^{58} - 16q^{60} + 12q^{61} + 56q^{64} + 28q^{66} + 28q^{67} + 4q^{69} + 40q^{70} + 40q^{72} - 34q^{75} + 56q^{76} + 60q^{78} - 4q^{81} - 16q^{82} + 16q^{84} + 32q^{85} - 60q^{87} - 64q^{88} - 16q^{90} - 56q^{91} + 28q^{93} - 48q^{94} - 56q^{96} - 8q^{97} - 52q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.607364 + 1.27715i 0.429471 + 0.903081i
\(3\) 0.0835731 1.73003i 0.0482510 0.998835i
\(4\) −1.26222 + 1.55139i −0.631109 + 0.775694i
\(5\) 0.431733 + 0.431733i 0.193077 + 0.193077i 0.797024 0.603947i \(-0.206406\pi\)
−0.603947 + 0.797024i \(0.706406\pi\)
\(6\) 2.26027 0.944024i 0.922751 0.385396i
\(7\) −3.10278 −1.17274 −0.586369 0.810044i \(-0.699443\pi\)
−0.586369 + 0.810044i \(0.699443\pi\)
\(8\) −2.74798 0.669785i −0.971557 0.236805i
\(9\) −2.98603 0.289169i −0.995344 0.0963895i
\(10\) −0.289169 + 0.813607i −0.0914431 + 0.257285i
\(11\) 2.98603 2.98603i 0.900322 0.900322i −0.0951415 0.995464i \(-0.530330\pi\)
0.995464 + 0.0951415i \(0.0303304\pi\)
\(12\) 2.57846 + 2.31334i 0.744339 + 0.667802i
\(13\) 2.10278 + 2.10278i 0.583205 + 0.583205i 0.935783 0.352578i \(-0.114695\pi\)
−0.352578 + 0.935783i \(0.614695\pi\)
\(14\) −1.88451 3.96271i −0.503657 1.05908i
\(15\) 0.782994 0.710831i 0.202168 0.183536i
\(16\) −0.813607 3.91638i −0.203402 0.979095i
\(17\) 2.42945i 0.589229i 0.955616 + 0.294615i \(0.0951913\pi\)
−0.955616 + 0.294615i \(0.904809\pi\)
\(18\) −1.44430 3.98924i −0.340424 0.940272i
\(19\) −0.710831 + 0.710831i −0.163076 + 0.163076i −0.783928 0.620852i \(-0.786787\pi\)
0.620852 + 0.783928i \(0.286787\pi\)
\(20\) −1.21473 + 0.124844i −0.271621 + 0.0279159i
\(21\) −0.259309 + 5.36790i −0.0565858 + 1.17137i
\(22\) 5.62721 + 2.00000i 1.19973 + 0.426401i
\(23\) 5.97206i 1.24526i 0.782516 + 0.622631i \(0.213936\pi\)
−0.782516 + 0.622631i \(0.786064\pi\)
\(24\) −1.38841 + 4.69812i −0.283408 + 0.959000i
\(25\) 4.62721i 0.925443i
\(26\) −1.40841 + 3.96271i −0.276212 + 0.777151i
\(27\) −0.749823 + 5.14177i −0.144304 + 0.989533i
\(28\) 3.91638 4.81361i 0.740127 0.909686i
\(29\) 2.86119 2.86119i 0.531309 0.531309i −0.389653 0.920962i \(-0.627405\pi\)
0.920962 + 0.389653i \(0.127405\pi\)
\(30\) 1.38340 + 0.568267i 0.252573 + 0.103751i
\(31\) 0.524438i 0.0941918i 0.998890 + 0.0470959i \(0.0149966\pi\)
−0.998890 + 0.0470959i \(0.985003\pi\)
\(32\) 4.50765 3.41776i 0.796847 0.604181i
\(33\) −4.91638 5.41549i −0.855832 0.942715i
\(34\) −3.10278 + 1.47556i −0.532122 + 0.253057i
\(35\) −1.33957 1.33957i −0.226429 0.226429i
\(36\) 4.21764 4.26750i 0.702940 0.711250i
\(37\) 1.52444 1.52444i 0.250616 0.250616i −0.570607 0.821223i \(-0.693292\pi\)
0.821223 + 0.570607i \(0.193292\pi\)
\(38\) −1.33957 0.476105i −0.217307 0.0772344i
\(39\) 3.81361 3.46214i 0.610666 0.554385i
\(40\) −0.897225 1.47556i −0.141864 0.233307i
\(41\) 1.81568 0.283561 0.141780 0.989898i \(-0.454717\pi\)
0.141780 + 0.989898i \(0.454717\pi\)
\(42\) −7.01311 + 2.92909i −1.08215 + 0.451969i
\(43\) 0.710831 + 0.710831i 0.108401 + 0.108401i 0.759227 0.650826i \(-0.225577\pi\)
−0.650826 + 0.759227i \(0.725577\pi\)
\(44\) 0.863466 + 8.40152i 0.130172 + 1.26658i
\(45\) −1.16432 1.41401i −0.173567 0.210788i
\(46\) −7.62721 + 3.62721i −1.12457 + 0.534803i
\(47\) −7.53805 −1.09954 −0.549769 0.835317i \(-0.685284\pi\)
−0.549769 + 0.835317i \(0.685284\pi\)
\(48\) −6.84347 + 1.08026i −0.987769 + 0.155922i
\(49\) 2.62721 0.375316
\(50\) 5.90964 2.81040i 0.835749 0.397451i
\(51\) 4.20304 + 0.203037i 0.588543 + 0.0284309i
\(52\) −5.91638 + 0.608056i −0.820455 + 0.0843223i
\(53\) −8.83325 8.83325i −1.21334 1.21334i −0.969921 0.243419i \(-0.921731\pi\)
−0.243419 0.969921i \(-0.578269\pi\)
\(54\) −7.02222 + 2.16529i −0.955603 + 0.294658i
\(55\) 2.57834 0.347663
\(56\) 8.52636 + 2.07819i 1.13938 + 0.277710i
\(57\) 1.17036 + 1.28917i 0.155017 + 0.170755i
\(58\) 5.39194 + 1.91638i 0.707997 + 0.251633i
\(59\) −0.0804722 + 0.0804722i −0.0104766 + 0.0104766i −0.712326 0.701849i \(-0.752358\pi\)
0.701849 + 0.712326i \(0.252358\pi\)
\(60\) 0.114465 + 2.11195i 0.0147774 + 0.272652i
\(61\) −5.72999 5.72999i −0.733650 0.733650i 0.237691 0.971341i \(-0.423609\pi\)
−0.971341 + 0.237691i \(0.923609\pi\)
\(62\) −0.669785 + 0.318525i −0.0850628 + 0.0404527i
\(63\) 9.26498 + 0.897225i 1.16728 + 0.113040i
\(64\) 7.10278 + 3.68111i 0.887847 + 0.460139i
\(65\) 1.81568i 0.225207i
\(66\) 3.93035 9.56812i 0.483793 1.17775i
\(67\) −0.391944 + 0.391944i −0.0478835 + 0.0478835i −0.730643 0.682760i \(-0.760780\pi\)
0.682760 + 0.730643i \(0.260780\pi\)
\(68\) −3.76903 3.06650i −0.457061 0.371868i
\(69\) 10.3319 + 0.499104i 1.24381 + 0.0600850i
\(70\) 0.897225 2.52444i 0.107239 0.301728i
\(71\) 5.01985i 0.595747i −0.954605 0.297873i \(-0.903723\pi\)
0.954605 0.297873i \(-0.0962774\pi\)
\(72\) 8.01187 + 2.79463i 0.944208 + 0.329350i
\(73\) 13.4600i 1.57537i 0.616078 + 0.787686i \(0.288721\pi\)
−0.616078 + 0.787686i \(0.711279\pi\)
\(74\) 2.87282 + 1.02105i 0.333959 + 0.118694i
\(75\) −8.00523 0.386711i −0.924365 0.0446535i
\(76\) −0.205550 2.00000i −0.0235782 0.229416i
\(77\) −9.26498 + 9.26498i −1.05584 + 1.05584i
\(78\) 6.73791 + 2.76777i 0.762918 + 0.313388i
\(79\) 3.47556i 0.391031i 0.980701 + 0.195516i \(0.0626380\pi\)
−0.980701 + 0.195516i \(0.937362\pi\)
\(80\) 1.33957 2.04209i 0.149769 0.228313i
\(81\) 8.83276 + 1.72693i 0.981418 + 0.191881i
\(82\) 1.10278 + 2.31889i 0.121781 + 0.256078i
\(83\) 4.55202 + 4.55202i 0.499649 + 0.499649i 0.911329 0.411680i \(-0.135058\pi\)
−0.411680 + 0.911329i \(0.635058\pi\)
\(84\) −8.00040 7.17776i −0.872915 0.783158i
\(85\) −1.04888 + 1.04888i −0.113767 + 0.113767i
\(86\) −0.476105 + 1.33957i −0.0513397 + 0.144450i
\(87\) −4.71083 5.18907i −0.505054 0.556326i
\(88\) −10.2056 + 6.20555i −1.08792 + 0.661514i
\(89\) 12.5579 1.33114 0.665568 0.746338i \(-0.268190\pi\)
0.665568 + 0.746338i \(0.268190\pi\)
\(90\) 1.09874 2.34584i 0.115817 0.247273i
\(91\) −6.52444 6.52444i −0.683947 0.683947i
\(92\) −9.26498 7.53805i −0.965941 0.785896i
\(93\) 0.907295 + 0.0438289i 0.0940821 + 0.00454485i
\(94\) −4.57834 9.62721i −0.472219 0.992971i
\(95\) −0.613779 −0.0629724
\(96\) −5.53613 8.08401i −0.565029 0.825071i
\(97\) −8.67609 −0.880923 −0.440462 0.897771i \(-0.645185\pi\)
−0.440462 + 0.897771i \(0.645185\pi\)
\(98\) 1.59567 + 3.35534i 0.161187 + 0.338941i
\(99\) −9.77985 + 8.05292i −0.982912 + 0.809348i
\(100\) 7.17860 + 5.84056i 0.717860 + 0.584056i
\(101\) 0.182046 + 0.182046i 0.0181142 + 0.0181142i 0.716106 0.697992i \(-0.245923\pi\)
−0.697992 + 0.716106i \(0.745923\pi\)
\(102\) 2.29346 + 5.49122i 0.227087 + 0.543712i
\(103\) 6.35720 0.626394 0.313197 0.949688i \(-0.398600\pi\)
0.313197 + 0.949688i \(0.398600\pi\)
\(104\) −4.36997 7.18679i −0.428511 0.704723i
\(105\) −2.42945 + 2.20555i −0.237090 + 0.215240i
\(106\) 5.91638 16.6464i 0.574650 1.61684i
\(107\) 1.64646 1.64646i 0.159169 0.159169i −0.623029 0.782199i \(-0.714098\pi\)
0.782199 + 0.623029i \(0.214098\pi\)
\(108\) −7.03043 7.65330i −0.676504 0.736439i
\(109\) 6.57331 + 6.57331i 0.629609 + 0.629609i 0.947970 0.318360i \(-0.103132\pi\)
−0.318360 + 0.947970i \(0.603132\pi\)
\(110\) 1.56599 + 3.29292i 0.149311 + 0.313968i
\(111\) −2.50993 2.76473i −0.238232 0.262417i
\(112\) 2.52444 + 12.1517i 0.238537 + 1.14822i
\(113\) 8.31277i 0.782000i 0.920391 + 0.391000i \(0.127871\pi\)
−0.920391 + 0.391000i \(0.872129\pi\)
\(114\) −0.935629 + 2.27771i −0.0876297 + 0.213327i
\(115\) −2.57834 + 2.57834i −0.240431 + 0.240431i
\(116\) 0.827365 + 8.05026i 0.0768189 + 0.747447i
\(117\) −5.67090 6.88701i −0.524274 0.636704i
\(118\) −0.151651 0.0538991i −0.0139606 0.00496182i
\(119\) 7.53805i 0.691012i
\(120\) −2.62776 + 1.42891i −0.239880 + 0.130441i
\(121\) 6.83276i 0.621160i
\(122\) 3.83786 10.7982i 0.347464 0.977626i
\(123\) 0.151742 3.14118i 0.0136821 0.283231i
\(124\) −0.813607 0.661956i −0.0730640 0.0594454i
\(125\) 4.15639 4.15639i 0.371759 0.371759i
\(126\) 4.48132 + 12.3777i 0.399228 + 1.10269i
\(127\) 15.7789i 1.40015i −0.714070 0.700074i \(-0.753150\pi\)
0.714070 0.700074i \(-0.246850\pi\)
\(128\) −0.387362 + 11.3071i −0.0342383 + 0.999414i
\(129\) 1.28917 1.17036i 0.113505 0.103044i
\(130\) −2.31889 + 1.10278i −0.203380 + 0.0967198i
\(131\) 0.0804722 + 0.0804722i 0.00703089 + 0.00703089i 0.710613 0.703583i \(-0.248417\pi\)
−0.703583 + 0.710613i \(0.748417\pi\)
\(132\) 14.6071 0.791685i 1.27138 0.0689073i
\(133\) 2.20555 2.20555i 0.191245 0.191245i
\(134\) −0.738623 0.262518i −0.0638073 0.0226781i
\(135\) −2.54359 + 1.89615i −0.218918 + 0.163194i
\(136\) 1.62721 6.67609i 0.139532 0.572470i
\(137\) −13.2604 −1.13291 −0.566457 0.824091i \(-0.691686\pi\)
−0.566457 + 0.824091i \(0.691686\pi\)
\(138\) 5.63777 + 13.4985i 0.479919 + 1.14907i
\(139\) 8.39194 + 8.39194i 0.711795 + 0.711795i 0.966911 0.255115i \(-0.0821134\pi\)
−0.255115 + 0.966911i \(0.582113\pi\)
\(140\) 3.76903 0.387362i 0.318541 0.0327380i
\(141\) −0.629978 + 13.0411i −0.0530537 + 1.09826i
\(142\) 6.41110 3.04888i 0.538008 0.255856i
\(143\) 12.5579 1.05014
\(144\) 1.29696 + 11.9297i 0.108080 + 0.994142i
\(145\) 2.47054 0.205167
\(146\) −17.1904 + 8.17510i −1.42269 + 0.676576i
\(147\) 0.219564 4.54517i 0.0181094 0.374879i
\(148\) 0.440820 + 4.28917i 0.0362351 + 0.352567i
\(149\) 5.79002 + 5.79002i 0.474337 + 0.474337i 0.903315 0.428978i \(-0.141126\pi\)
−0.428978 + 0.903315i \(0.641126\pi\)
\(150\) −4.36820 10.4587i −0.356662 0.853953i
\(151\) 9.94610 0.809402 0.404701 0.914449i \(-0.367376\pi\)
0.404701 + 0.914449i \(0.367376\pi\)
\(152\) 2.42945 1.47725i 0.197055 0.119820i
\(153\) 0.702522 7.25443i 0.0567955 0.586486i
\(154\) −17.4600 6.20555i −1.40696 0.500057i
\(155\) −0.226417 + 0.226417i −0.0181863 + 0.0181863i
\(156\) 0.557507 + 10.2864i 0.0446363 + 0.823568i
\(157\) −9.15165 9.15165i −0.730381 0.730381i 0.240314 0.970695i \(-0.422750\pi\)
−0.970695 + 0.240314i \(0.922750\pi\)
\(158\) −4.43881 + 2.11093i −0.353133 + 0.167937i
\(159\) −16.0200 + 14.5436i −1.27047 + 1.15338i
\(160\) 3.42166 + 0.470539i 0.270506 + 0.0371994i
\(161\) 18.5300i 1.46037i
\(162\) 3.15915 + 12.3296i 0.248206 + 0.968707i
\(163\) 15.7003 15.7003i 1.22974 1.22974i 0.265678 0.964062i \(-0.414404\pi\)
0.964062 0.265678i \(-0.0855959\pi\)
\(164\) −2.29178 + 2.81682i −0.178958 + 0.219956i
\(165\) 0.215480 4.46061i 0.0167751 0.347258i
\(166\) −3.04888 + 8.57834i −0.236639 + 0.665808i
\(167\) 19.1437i 1.48139i 0.671843 + 0.740694i \(0.265503\pi\)
−0.671843 + 0.740694i \(0.734497\pi\)
\(168\) 4.30792 14.5772i 0.332363 1.12466i
\(169\) 4.15667i 0.319744i
\(170\) −1.97662 0.702522i −0.151600 0.0538810i
\(171\) 2.32811 1.91701i 0.178035 0.146598i
\(172\) −2.00000 + 0.205550i −0.152499 + 0.0156730i
\(173\) 13.3281 13.3281i 1.01331 1.01331i 0.0134040 0.999910i \(-0.495733\pi\)
0.999910 0.0134040i \(-0.00426674\pi\)
\(174\) 3.76603 9.16808i 0.285502 0.695031i
\(175\) 14.3572i 1.08530i
\(176\) −14.1239 9.26498i −1.06463 0.698374i
\(177\) 0.132494 + 0.145945i 0.00995889 + 0.0109699i
\(178\) 7.62721 + 16.0383i 0.571684 + 1.20212i
\(179\) −9.18451 9.18451i −0.686483 0.686483i 0.274970 0.961453i \(-0.411332\pi\)
−0.961453 + 0.274970i \(0.911332\pi\)
\(180\) 3.66331 0.0215261i 0.273047 0.00160446i
\(181\) −16.5139 + 16.5139i −1.22747 + 1.22747i −0.262548 + 0.964919i \(0.584563\pi\)
−0.964919 + 0.262548i \(0.915437\pi\)
\(182\) 4.36997 12.2954i 0.323924 0.911395i
\(183\) −10.3919 + 9.43420i −0.768195 + 0.697396i
\(184\) 4.00000 16.4111i 0.294884 1.20984i
\(185\) 1.31630 0.0967764
\(186\) 0.495082 + 1.18537i 0.0363012 + 0.0869156i
\(187\) 7.25443 + 7.25443i 0.530496 + 0.530496i
\(188\) 9.51467 11.6944i 0.693929 0.852904i
\(189\) 2.32653 15.9537i 0.169230 1.16046i
\(190\) −0.372787 0.783887i −0.0270448 0.0568692i
\(191\) −3.17852 −0.229989 −0.114995 0.993366i \(-0.536685\pi\)
−0.114995 + 0.993366i \(0.536685\pi\)
\(192\) 6.96205 11.9804i 0.502443 0.864611i
\(193\) −11.4600 −0.824907 −0.412454 0.910979i \(-0.635328\pi\)
−0.412454 + 0.910979i \(0.635328\pi\)
\(194\) −5.26954 11.0807i −0.378331 0.795545i
\(195\) 3.14118 + 0.151742i 0.224944 + 0.0108664i
\(196\) −3.31612 + 4.07583i −0.236866 + 0.291130i
\(197\) 14.8053 + 14.8053i 1.05483 + 1.05483i 0.998407 + 0.0564281i \(0.0179712\pi\)
0.0564281 + 0.998407i \(0.482029\pi\)
\(198\) −16.2247 7.59928i −1.15304 0.540057i
\(199\) −24.4550 −1.73357 −0.866783 0.498686i \(-0.833816\pi\)
−0.866783 + 0.498686i \(0.833816\pi\)
\(200\) −3.09924 + 12.7155i −0.219149 + 0.899120i
\(201\) 0.645320 + 0.710831i 0.0455173 + 0.0501382i
\(202\) −0.121932 + 0.343068i −0.00857908 + 0.0241382i
\(203\) −8.87762 + 8.87762i −0.623087 + 0.623087i
\(204\) −5.62014 + 6.26426i −0.393489 + 0.438586i
\(205\) 0.783887 + 0.783887i 0.0547491 + 0.0547491i
\(206\) 3.86113 + 8.11909i 0.269018 + 0.565684i
\(207\) 1.72693 17.8328i 0.120030 1.23946i
\(208\) 6.52444 9.94610i 0.452388 0.689638i
\(209\) 4.24513i 0.293642i
\(210\) −4.29238 1.76320i −0.296202 0.121673i
\(211\) −6.18639 + 6.18639i −0.425889 + 0.425889i −0.887225 0.461336i \(-0.847370\pi\)
0.461336 + 0.887225i \(0.347370\pi\)
\(212\) 24.8533 2.55430i 1.70693 0.175430i
\(213\) −8.68451 0.419525i −0.595053 0.0287454i
\(214\) 3.10278 + 1.10278i 0.212101 + 0.0753842i
\(215\) 0.613779i 0.0418594i
\(216\) 5.50438 13.6272i 0.374526 0.927217i
\(217\) 1.62721i 0.110462i
\(218\) −4.40271 + 12.3875i −0.298189 + 0.838987i
\(219\) 23.2862 + 1.12489i 1.57354 + 0.0760132i
\(220\) −3.25443 + 4.00000i −0.219413 + 0.269680i
\(221\) −5.10860 + 5.10860i −0.343641 + 0.343641i
\(222\) 2.00653 4.88475i 0.134670 0.327843i
\(223\) 8.18996i 0.548441i 0.961667 + 0.274220i \(0.0884197\pi\)
−0.961667 + 0.274220i \(0.911580\pi\)
\(224\) −13.9862 + 10.6046i −0.934493 + 0.708547i
\(225\) −1.33804 + 13.8170i −0.0892030 + 0.921133i
\(226\) −10.6167 + 5.04888i −0.706209 + 0.335846i
\(227\) 9.91030 + 9.91030i 0.657770 + 0.657770i 0.954852 0.297082i \(-0.0960135\pi\)
−0.297082 + 0.954852i \(0.596014\pi\)
\(228\) −3.47725 + 0.188462i −0.230286 + 0.0124812i
\(229\) 7.15165 7.15165i 0.472594 0.472594i −0.430159 0.902753i \(-0.641542\pi\)
0.902753 + 0.430159i \(0.141542\pi\)
\(230\) −4.85891 1.72693i −0.320387 0.113871i
\(231\) 15.2544 + 16.8030i 1.00367 + 1.10556i
\(232\) −9.77886 + 5.94610i −0.642014 + 0.390381i
\(233\) −19.6431 −1.28686 −0.643432 0.765503i \(-0.722490\pi\)
−0.643432 + 0.765503i \(0.722490\pi\)
\(234\) 5.35144 11.4255i 0.349835 0.746908i
\(235\) −3.25443 3.25443i −0.212295 0.212295i
\(236\) −0.0232700 0.226417i −0.00151475 0.0147385i
\(237\) 6.01284 + 0.290464i 0.390576 + 0.0188676i
\(238\) 9.62721 4.57834i 0.624040 0.296770i
\(239\) 9.44247 0.610782 0.305391 0.952227i \(-0.401213\pi\)
0.305391 + 0.952227i \(0.401213\pi\)
\(240\) −3.42094 2.48817i −0.220820 0.160610i
\(241\) 16.6167 1.07037 0.535186 0.844734i \(-0.320241\pi\)
0.535186 + 0.844734i \(0.320241\pi\)
\(242\) 8.72646 4.14997i 0.560958 0.266770i
\(243\) 3.72583 15.1366i 0.239012 0.971017i
\(244\) 16.1219 1.65693i 1.03210 0.106074i
\(245\) 1.13425 + 1.13425i 0.0724649 + 0.0724649i
\(246\) 4.10392 1.71404i 0.261656 0.109283i
\(247\) −2.98944 −0.190213
\(248\) 0.351261 1.44114i 0.0223051 0.0915128i
\(249\) 8.25557 7.49472i 0.523176 0.474958i
\(250\) 7.83276 + 2.78389i 0.495387 + 0.176068i
\(251\) 2.03382 2.03382i 0.128374 0.128374i −0.640001 0.768374i \(-0.721066\pi\)
0.768374 + 0.640001i \(0.221066\pi\)
\(252\) −13.0864 + 13.2411i −0.824364 + 0.834110i
\(253\) 17.8328 + 17.8328i 1.12114 + 1.12114i
\(254\) 20.1520 9.58351i 1.26445 0.601323i
\(255\) 1.72693 + 1.90225i 0.108145 + 0.119123i
\(256\) −14.6761 + 6.37279i −0.917256 + 0.398299i
\(257\) 15.0761i 0.940421i −0.882554 0.470211i \(-0.844178\pi\)
0.882554 0.470211i \(-0.155822\pi\)
\(258\) 2.27771 + 0.935629i 0.141804 + 0.0582497i
\(259\) −4.72999 + 4.72999i −0.293907 + 0.293907i
\(260\) −2.81682 2.29178i −0.174692 0.142130i
\(261\) −9.37096 + 7.71623i −0.580048 + 0.477623i
\(262\) −0.0538991 + 0.151651i −0.00332990 + 0.00936903i
\(263\) 29.8138i 1.83840i −0.393796 0.919198i \(-0.628838\pi\)
0.393796 0.919198i \(-0.371162\pi\)
\(264\) 9.88290 + 18.1746i 0.608250 + 1.11857i
\(265\) 7.62721i 0.468536i
\(266\) 4.15639 + 1.47725i 0.254844 + 0.0905757i
\(267\) 1.04950 21.7256i 0.0642285 1.32958i
\(268\) −0.113338 1.10278i −0.00692321 0.0673627i
\(269\) −16.3713 + 16.3713i −0.998176 + 0.998176i −0.999998 0.00182258i \(-0.999420\pi\)
0.00182258 + 0.999998i \(0.499420\pi\)
\(270\) −3.96655 2.09690i −0.241397 0.127613i
\(271\) 13.3466i 0.810751i −0.914150 0.405375i \(-0.867141\pi\)
0.914150 0.405375i \(-0.132859\pi\)
\(272\) 9.51467 1.97662i 0.576912 0.119850i
\(273\) −11.8328 + 10.7422i −0.716151 + 0.650149i
\(274\) −8.05390 16.9355i −0.486554 1.02311i
\(275\) −13.8170 13.8170i −0.833197 0.833197i
\(276\) −13.8154 + 15.3988i −0.831588 + 0.926896i
\(277\) 10.6811 10.6811i 0.641766 0.641766i −0.309224 0.950989i \(-0.600069\pi\)
0.950989 + 0.309224i \(0.100069\pi\)
\(278\) −5.62080 + 15.8147i −0.337113 + 0.948504i
\(279\) 0.151651 1.56599i 0.00907911 0.0937533i
\(280\) 2.78389 + 4.57834i 0.166369 + 0.273608i
\(281\) −17.5943 −1.04959 −0.524794 0.851229i \(-0.675858\pi\)
−0.524794 + 0.851229i \(0.675858\pi\)
\(282\) −17.0380 + 7.11610i −1.01460 + 0.423758i
\(283\) −17.1758 17.1758i −1.02100 1.02100i −0.999775 0.0212224i \(-0.993244\pi\)
−0.0212224 0.999775i \(-0.506756\pi\)
\(284\) 7.78774 + 6.33615i 0.462117 + 0.375982i
\(285\) −0.0512954 + 1.06186i −0.00303848 + 0.0628990i
\(286\) 7.62721 + 16.0383i 0.451007 + 0.948365i
\(287\) −5.63363 −0.332543
\(288\) −14.4483 + 8.90208i −0.851373 + 0.524560i
\(289\) 11.0978 0.652809
\(290\) 1.50052 + 3.15525i 0.0881133 + 0.185282i
\(291\) −0.725088 + 15.0099i −0.0425054 + 0.879897i
\(292\) −20.8816 16.9894i −1.22201 0.994232i
\(293\) −3.72465 3.72465i −0.217597 0.217597i 0.589888 0.807485i \(-0.299172\pi\)
−0.807485 + 0.589888i \(0.799172\pi\)
\(294\) 5.93821 2.48015i 0.346323 0.144645i
\(295\) −0.0694851 −0.00404558
\(296\) −5.21017 + 3.16808i −0.302835 + 0.184141i
\(297\) 13.1145 + 17.5925i 0.760979 + 1.02082i
\(298\) −3.87807 + 10.9114i −0.224650 + 0.632078i
\(299\) −12.5579 + 12.5579i −0.726242 + 0.726242i
\(300\) 10.7043 11.9311i 0.618013 0.688843i
\(301\) −2.20555 2.20555i −0.127126 0.127126i
\(302\) 6.04090 + 12.7027i 0.347615 + 0.730956i
\(303\) 0.330160 0.299731i 0.0189672 0.0172191i
\(304\) 3.36222 + 2.20555i 0.192837 + 0.126497i
\(305\) 4.94765i 0.283302i
\(306\) 9.69167 3.50885i 0.554036 0.200588i
\(307\) −13.4408 + 13.4408i −0.767108 + 0.767108i −0.977596 0.210488i \(-0.932495\pi\)
0.210488 + 0.977596i \(0.432495\pi\)
\(308\) −2.67914 26.0680i −0.152658 1.48536i
\(309\) 0.531291 10.9982i 0.0302241 0.625664i
\(310\) −0.426686 0.151651i −0.0242341 0.00861320i
\(311\) 13.8320i 0.784341i −0.919893 0.392170i \(-0.871724\pi\)
0.919893 0.392170i \(-0.128276\pi\)
\(312\) −12.7986 + 6.95958i −0.724578 + 0.394008i
\(313\) 3.94056i 0.222734i 0.993779 + 0.111367i \(0.0355229\pi\)
−0.993779 + 0.111367i \(0.964477\pi\)
\(314\) 6.12964 17.2464i 0.345916 0.973271i
\(315\) 3.61264 + 4.38736i 0.203549 + 0.247200i
\(316\) −5.39194 4.38692i −0.303321 0.246784i
\(317\) 8.92199 8.92199i 0.501109 0.501109i −0.410673 0.911782i \(-0.634706\pi\)
0.911782 + 0.410673i \(0.134706\pi\)
\(318\) −28.3043 11.6267i −1.58723 0.651994i
\(319\) 17.0872i 0.956699i
\(320\) 1.47725 + 4.65576i 0.0825805 + 0.260265i
\(321\) −2.71083 2.98603i −0.151304 0.166664i
\(322\) 23.6655 11.2544i 1.31883 0.627185i
\(323\) −1.72693 1.72693i −0.0960891 0.0960891i
\(324\) −13.8280 + 11.5233i −0.768223 + 0.640182i
\(325\) 9.72999 9.72999i 0.539723 0.539723i
\(326\) 29.5874 + 10.5158i 1.63869 + 0.582417i
\(327\) 11.9214 10.8227i 0.659255 0.598497i
\(328\) −4.98944 1.21611i −0.275496 0.0671486i
\(329\) 23.3889 1.28947
\(330\) 5.82774 2.43401i 0.320806 0.133988i
\(331\) 9.44082 + 9.44082i 0.518914 + 0.518914i 0.917243 0.398328i \(-0.130410\pi\)
−0.398328 + 0.917243i \(0.630410\pi\)
\(332\) −12.8076 + 1.31630i −0.702908 + 0.0722414i
\(333\) −4.99284 + 4.11120i −0.273606 + 0.225292i
\(334\) −24.4494 + 11.6272i −1.33781 + 0.636213i
\(335\) −0.338430 −0.0184904
\(336\) 21.2337 3.35181i 1.15840 0.182856i
\(337\) 5.94056 0.323603 0.161801 0.986823i \(-0.448270\pi\)
0.161801 + 0.986823i \(0.448270\pi\)
\(338\) 5.30869 2.52461i 0.288755 0.137321i
\(339\) 14.3814 + 0.694724i 0.781089 + 0.0377322i
\(340\) −0.303302 2.95112i −0.0164489 0.160047i
\(341\) 1.56599 + 1.56599i 0.0848030 + 0.0848030i
\(342\) 3.86233 + 1.80902i 0.208851 + 0.0978208i
\(343\) 13.5678 0.732591
\(344\) −1.47725 2.42945i −0.0796477 0.130987i
\(345\) 4.24513 + 4.67609i 0.228550 + 0.251752i
\(346\) 25.1169 + 8.92694i 1.35029 + 0.479915i
\(347\) −4.09918 + 4.09918i −0.220056 + 0.220056i −0.808522 0.588466i \(-0.799732\pi\)
0.588466 + 0.808522i \(0.299732\pi\)
\(348\) 13.9964 0.758585i 0.750283 0.0406644i
\(349\) −8.10278 8.10278i −0.433732 0.433732i 0.456164 0.889896i \(-0.349223\pi\)
−0.889896 + 0.456164i \(0.849223\pi\)
\(350\) −18.3363 + 8.72004i −0.980116 + 0.466106i
\(351\) −12.3887 + 9.23527i −0.661259 + 0.492942i
\(352\) 3.25443 23.6655i 0.173461 1.26138i
\(353\) 29.2465i 1.55664i 0.627870 + 0.778318i \(0.283927\pi\)
−0.627870 + 0.778318i \(0.716073\pi\)
\(354\) −0.105921 + 0.257857i −0.00562965 + 0.0137049i
\(355\) 2.16724 2.16724i 0.115025 0.115025i
\(356\) −15.8508 + 19.4822i −0.840092 + 1.03255i
\(357\) −13.0411 0.629978i −0.690207 0.0333420i
\(358\) 6.15165 17.3083i 0.325125 0.914773i
\(359\) 21.3235i 1.12541i 0.826657 + 0.562706i \(0.190240\pi\)
−0.826657 + 0.562706i \(0.809760\pi\)
\(360\) 2.25246 + 4.66552i 0.118715 + 0.245895i
\(361\) 17.9894i 0.946812i
\(362\) −31.1206 11.0608i −1.63566 0.581340i
\(363\) −11.8209 0.571035i −0.620437 0.0299716i
\(364\) 18.3572 1.88666i 0.962179 0.0988880i
\(365\) −5.81112 + 5.81112i −0.304168 + 0.304168i
\(366\) −18.3606 7.54207i −0.959722 0.394230i
\(367\) 32.8277i 1.71359i 0.515654 + 0.856797i \(0.327549\pi\)
−0.515654 + 0.856797i \(0.672451\pi\)
\(368\) 23.3889 4.85891i 1.21923 0.253288i
\(369\) −5.42166 0.525036i −0.282240 0.0273323i
\(370\) 0.799473 + 1.68111i 0.0415626 + 0.0873969i
\(371\) 27.4076 + 27.4076i 1.42293 + 1.42293i
\(372\) −1.21320 + 1.35224i −0.0629015 + 0.0701106i
\(373\) 1.35720 1.35720i 0.0702732 0.0702732i −0.671097 0.741370i \(-0.734176\pi\)
0.741370 + 0.671097i \(0.234176\pi\)
\(374\) −4.85891 + 13.6711i −0.251248 + 0.706914i
\(375\) −6.84333 7.53805i −0.353388 0.389263i
\(376\) 20.7144 + 5.04888i 1.06826 + 0.260376i
\(377\) 12.0329 0.619724
\(378\) 21.7884 6.71840i 1.12067 0.345557i
\(379\) −17.3869 17.3869i −0.893106 0.893106i 0.101708 0.994814i \(-0.467569\pi\)
−0.994814 + 0.101708i \(0.967569\pi\)
\(380\) 0.774723 0.952209i 0.0397425 0.0488473i
\(381\) −27.2980 1.31869i −1.39852 0.0675585i
\(382\) −1.93051 4.05944i −0.0987737 0.207699i
\(383\) 32.9757 1.68498 0.842491 0.538711i \(-0.181088\pi\)
0.842491 + 0.538711i \(0.181088\pi\)
\(384\) 19.5292 + 1.61512i 0.996598 + 0.0824211i
\(385\) −8.00000 −0.407718
\(386\) −6.96037 14.6361i −0.354274 0.744958i
\(387\) −1.91701 2.32811i −0.0974473 0.118345i
\(388\) 10.9511 13.4600i 0.555959 0.683327i
\(389\) −3.97434 3.97434i −0.201507 0.201507i 0.599138 0.800645i \(-0.295510\pi\)
−0.800645 + 0.599138i \(0.795510\pi\)
\(390\) 1.71404 + 4.10392i 0.0867938 + 0.207810i
\(391\) −14.5089 −0.733744
\(392\) −7.21953 1.75967i −0.364641 0.0888767i
\(393\) 0.145945 0.132494i 0.00736195 0.00668346i
\(394\) −9.91638 + 27.9008i −0.499580 + 1.40562i
\(395\) −1.50052 + 1.50052i −0.0754991 + 0.0754991i
\(396\) −0.148883 25.3369i −0.00748164 1.27323i
\(397\) −15.9355 15.9355i −0.799782 0.799782i 0.183279 0.983061i \(-0.441329\pi\)
−0.983061 + 0.183279i \(0.941329\pi\)
\(398\) −14.8530 31.2326i −0.744516 1.56555i
\(399\) −3.63135 4.00000i −0.181795 0.200250i
\(400\) −18.1219 + 3.76473i −0.906097 + 0.188237i
\(401\) 29.7716i 1.48672i −0.668891 0.743361i \(-0.733231\pi\)
0.668891 0.743361i \(-0.266769\pi\)
\(402\) −0.515894 + 1.25590i −0.0257305 + 0.0626387i
\(403\) −1.10278 + 1.10278i −0.0549331 + 0.0549331i
\(404\) −0.512205 + 0.0526419i −0.0254832 + 0.00261903i
\(405\) 3.06782 + 4.55897i 0.152441 + 0.226537i
\(406\) −16.7300 5.94610i −0.830295 0.295100i
\(407\) 9.10404i 0.451270i
\(408\) −11.4139 3.37307i −0.565071 0.166992i
\(409\) 15.6655i 0.774610i 0.921952 + 0.387305i \(0.126594\pi\)
−0.921952 + 0.387305i \(0.873406\pi\)
\(410\) −0.525036 + 1.47725i −0.0259297 + 0.0729559i
\(411\) −1.10821 + 22.9410i −0.0546642 + 1.13159i
\(412\) −8.02418 + 9.86248i −0.395323 + 0.485890i
\(413\) 0.249687 0.249687i 0.0122863 0.0122863i
\(414\) 23.8240 8.62542i 1.17088 0.423916i
\(415\) 3.93051i 0.192941i
\(416\) 16.6654 + 2.29178i 0.817086 + 0.112364i
\(417\) 15.2197 13.8170i 0.745311 0.676621i
\(418\) −5.42166 + 2.57834i −0.265182 + 0.126111i
\(419\) −14.1554 14.1554i −0.691538 0.691538i 0.271032 0.962570i \(-0.412635\pi\)
−0.962570 + 0.271032i \(0.912635\pi\)
\(420\) −0.355160 6.55291i −0.0173300 0.319749i
\(421\) −7.35720 + 7.35720i −0.358568 + 0.358568i −0.863285 0.504717i \(-0.831597\pi\)
0.504717 + 0.863285i \(0.331597\pi\)
\(422\) −11.6583 4.14356i −0.567519 0.201705i
\(423\) 22.5089 + 2.17977i 1.09442 + 0.105984i
\(424\) 18.3572 + 30.1900i 0.891504 + 1.46615i
\(425\) 11.2416 0.545298
\(426\) −4.73886 11.3462i −0.229599 0.549726i
\(427\) 17.7789 + 17.7789i 0.860380 + 0.860380i
\(428\) 0.476105 + 4.63249i 0.0230134 + 0.223920i
\(429\) 1.04950 21.7256i 0.0506705 1.04892i
\(430\) −0.783887 + 0.372787i −0.0378024 + 0.0179774i
\(431\) −20.7097 −0.997553 −0.498776 0.866731i \(-0.666217\pi\)
−0.498776 + 0.866731i \(0.666217\pi\)
\(432\) 20.7472 1.24678i 0.998199 0.0599858i
\(433\) −23.4005 −1.12456 −0.562279 0.826948i \(-0.690075\pi\)
−0.562279 + 0.826948i \(0.690075\pi\)
\(434\) 2.07819 0.988310i 0.0997565 0.0474404i
\(435\) 0.206471 4.27411i 0.00989951 0.204928i
\(436\) −18.4947 + 1.90080i −0.885736 + 0.0910316i
\(437\) −4.24513 4.24513i −0.203072 0.203072i
\(438\) 12.7065 + 30.4232i 0.607142 + 1.45368i
\(439\) 20.2594 0.966931 0.483465 0.875363i \(-0.339378\pi\)
0.483465 + 0.875363i \(0.339378\pi\)
\(440\) −7.08522 1.72693i −0.337774 0.0823283i
\(441\) −7.84494 0.759707i −0.373569 0.0361765i
\(442\) −9.62721 3.42166i −0.457920 0.162752i
\(443\) −4.05264 + 4.05264i −0.192547 + 0.192547i −0.796796 0.604249i \(-0.793473\pi\)
0.604249 + 0.796796i \(0.293473\pi\)
\(444\) 7.45725 0.404173i 0.353905 0.0191812i
\(445\) 5.42166 + 5.42166i 0.257011 + 0.257011i
\(446\) −10.4598 + 4.97429i −0.495286 + 0.235539i
\(447\) 10.5008 9.53303i 0.496671 0.450897i
\(448\) −22.0383 11.4217i −1.04121 0.539623i
\(449\) 5.38394i 0.254084i 0.991897 + 0.127042i \(0.0405483\pi\)
−0.991897 + 0.127042i \(0.959452\pi\)
\(450\) −18.4590 + 6.68306i −0.870168 + 0.315043i
\(451\) 5.42166 5.42166i 0.255296 0.255296i
\(452\) −12.8963 10.4925i −0.606592 0.493528i
\(453\) 0.831227 17.2071i 0.0390544 0.808459i
\(454\) −6.63778 + 18.6761i −0.311526 + 0.876512i
\(455\) 5.63363i 0.264109i
\(456\) −2.35265 4.32650i −0.110173 0.202607i
\(457\) 28.0766i 1.31337i −0.754165 0.656685i \(-0.771958\pi\)
0.754165 0.656685i \(-0.228042\pi\)
\(458\) 13.4774 + 4.79007i 0.629756 + 0.223825i
\(459\) −12.4917 1.82166i −0.583062 0.0850279i
\(460\) −0.745574 7.25443i −0.0347626 0.338239i
\(461\) 22.7962 22.7962i 1.06172 1.06172i 0.0637594 0.997965i \(-0.479691\pi\)
0.997965 0.0637594i \(-0.0203090\pi\)
\(462\) −12.1950 + 29.6877i −0.567362 + 1.38120i
\(463\) 0.740035i 0.0343923i 0.999852 + 0.0171962i \(0.00547398\pi\)
−0.999852 + 0.0171962i \(0.994526\pi\)
\(464\) −13.5334 8.87762i −0.628272 0.412133i
\(465\) 0.372787 + 0.410632i 0.0172876 + 0.0190426i
\(466\) −11.9305 25.0872i −0.552670 1.16214i
\(467\) 9.73282 + 9.73282i 0.450381 + 0.450381i 0.895481 0.445100i \(-0.146832\pi\)
−0.445100 + 0.895481i \(0.646832\pi\)
\(468\) 17.8423 0.104844i 0.824762 0.00484641i
\(469\) 1.21611 1.21611i 0.0561549 0.0561549i
\(470\) 2.17977 6.13301i 0.100545 0.282895i
\(471\) −16.5975 + 15.0678i −0.764772 + 0.694289i
\(472\) 0.275035 0.167237i 0.0126595 0.00769770i
\(473\) 4.24513 0.195191
\(474\) 3.28101 + 7.85571i 0.150702 + 0.360825i
\(475\) 3.28917 + 3.28917i 0.150917 + 0.150917i
\(476\) 11.6944 + 9.51467i 0.536014 + 0.436104i
\(477\) 23.8221 + 28.9307i 1.09074 + 1.32464i
\(478\) 5.73501 + 12.0594i 0.262313 + 0.551586i
\(479\) −28.2478 −1.29067 −0.645337 0.763898i \(-0.723283\pi\)
−0.645337 + 0.763898i \(0.723283\pi\)
\(480\) 1.10001 5.88027i 0.0502082 0.268396i
\(481\) 6.41110 0.292321
\(482\) 10.0923 + 21.2219i 0.459694 + 0.966633i
\(483\) −32.0575 1.54861i −1.45866 0.0704641i
\(484\) 10.6003 + 8.62444i 0.481830 + 0.392020i
\(485\) −3.74576 3.74576i −0.170086 0.170086i
\(486\) 21.5947 4.43501i 0.979555 0.201176i
\(487\) 19.7094 0.893117 0.446559 0.894754i \(-0.352649\pi\)
0.446559 + 0.894754i \(0.352649\pi\)
\(488\) 11.9080 + 19.5837i 0.539051 + 0.886515i
\(489\) −25.8499 28.4741i −1.16897 1.28764i
\(490\) −0.759707 + 2.13752i −0.0343201 + 0.0965632i
\(491\) 29.4414 29.4414i 1.32867 1.32867i 0.422143 0.906529i \(-0.361278\pi\)
0.906529 0.422143i \(-0.138722\pi\)
\(492\) 4.68165 + 4.20027i 0.211065 + 0.189363i
\(493\) 6.95112 + 6.95112i 0.313063 + 0.313063i
\(494\) −1.81568 3.81796i −0.0816911 0.171778i
\(495\) −7.69899 0.745574i −0.346044 0.0335111i
\(496\) 2.05390 0.426686i 0.0922228 0.0191588i
\(497\) 15.5755i 0.698656i
\(498\) 14.5860 + 5.99158i 0.653615 + 0.268489i
\(499\) 4.43026 4.43026i 0.198326 0.198326i −0.600956 0.799282i \(-0.705213\pi\)
0.799282 + 0.600956i \(0.205213\pi\)
\(500\) 1.20190 + 11.6944i 0.0537504 + 0.522991i
\(501\) 33.1193 + 1.59990i 1.47966 + 0.0714784i
\(502\) 3.83276 + 1.36222i 0.171065 + 0.0607990i
\(503\) 27.6805i 1.23421i 0.786879 + 0.617107i \(0.211696\pi\)
−0.786879 + 0.617107i \(0.788304\pi\)
\(504\) −24.8590 8.67111i −1.10731 0.386242i
\(505\) 0.157190i 0.00699488i
\(506\) −11.9441 + 33.6061i −0.530981 + 1.49397i
\(507\) −7.19119 0.347386i −0.319372 0.0154280i
\(508\) 24.4791 + 19.9164i 1.08609 + 0.883647i
\(509\) −17.3235 + 17.3235i −0.767851 + 0.767851i −0.977728 0.209877i \(-0.932694\pi\)
0.209877 + 0.977728i \(0.432694\pi\)
\(510\) −1.38058 + 3.36091i −0.0611330 + 0.148823i
\(511\) 41.7633i 1.84750i
\(512\) −17.0527 14.8730i −0.753631 0.657298i
\(513\) −3.12193 4.18793i −0.137837 0.184902i
\(514\) 19.2544 9.15667i 0.849276 0.403884i
\(515\) 2.74461 + 2.74461i 0.120942 + 0.120942i
\(516\) 0.188462 + 3.47725i 0.00829659 + 0.153077i
\(517\) −22.5089 + 22.5089i −0.989938 + 0.989938i
\(518\) −8.91372 3.16808i −0.391646 0.139197i
\(519\) −21.9441 24.1719i −0.963240 1.06103i
\(520\) 1.21611 4.98944i 0.0533301 0.218801i
\(521\) 10.1284 0.443735 0.221868 0.975077i \(-0.428785\pi\)
0.221868 + 0.975077i \(0.428785\pi\)
\(522\) −15.5464 7.28156i −0.680445 0.318705i
\(523\) 1.45641 + 1.45641i 0.0636842 + 0.0636842i 0.738232 0.674547i \(-0.235661\pi\)
−0.674547 + 0.738232i \(0.735661\pi\)
\(524\) −0.226417 + 0.0232700i −0.00989108 + 0.00101656i
\(525\) 24.8384 + 1.19988i 1.08404 + 0.0523669i
\(526\) 38.0766 18.1078i 1.66022 0.789538i
\(527\) −1.27410 −0.0555006
\(528\) −17.2091 + 23.6605i −0.748930 + 1.02969i
\(529\) −12.6655 −0.550675
\(530\) 9.74109 4.63249i 0.423126 0.201223i
\(531\) 0.263563 0.217023i 0.0114376 0.00941798i
\(532\) 0.637776 + 6.20555i 0.0276511 + 0.269045i
\(533\) 3.81796 + 3.81796i 0.165374 + 0.165374i
\(534\) 28.3842 11.8550i 1.22831 0.513014i
\(535\) 1.42166 0.0614638
\(536\) 1.33957 0.814535i 0.0578606 0.0351825i
\(537\) −16.6571 + 15.1219i −0.718806 + 0.652560i
\(538\) −30.8519 10.9653i −1.33012 0.472746i
\(539\) 7.84494 7.84494i 0.337905 0.337905i
\(540\) 0.268914 6.33945i 0.0115722 0.272807i
\(541\) 5.18996 + 5.18996i 0.223134 + 0.223134i 0.809817 0.586683i \(-0.199566\pi\)
−0.586683 + 0.809817i \(0.699566\pi\)
\(542\) 17.0456 8.10626i 0.732173 0.348194i
\(543\) 27.1894 + 29.9497i 1.16681 + 1.28526i
\(544\) 8.30330 + 10.9511i 0.356001 + 0.469526i
\(545\) 5.67583i 0.243126i
\(546\) −20.9062 8.58776i −0.894703 0.367522i
\(547\) 12.6413 12.6413i 0.540505 0.540505i −0.383172 0.923677i \(-0.625168\pi\)
0.923677 + 0.383172i \(0.125168\pi\)
\(548\) 16.7376 20.5721i 0.714993 0.878795i
\(549\) 15.4530 + 18.7669i 0.659518 + 0.800950i
\(550\) 9.25443 26.0383i 0.394610 1.11028i
\(551\) 4.06764i 0.173287i
\(552\) −28.0575 8.29166i −1.19420 0.352916i
\(553\) 10.7839i 0.458578i
\(554\) 20.1287 + 7.15405i 0.855186 + 0.303947i
\(555\) 0.110007 2.27724i 0.00466955 0.0966636i
\(556\) −23.6116 + 2.42669i −1.00136 + 0.102914i
\(557\) −6.90317 + 6.90317i −0.292497 + 0.292497i −0.838066 0.545569i \(-0.816314\pi\)
0.545569 + 0.838066i \(0.316314\pi\)
\(558\) 2.09211 0.757443i 0.0885660 0.0320651i
\(559\) 2.98944i 0.126440i
\(560\) −4.15639 + 6.33615i −0.175639 + 0.267751i
\(561\) 13.1567 11.9441i 0.555475 0.504281i
\(562\) −10.6861 22.4705i −0.450767 0.947862i
\(563\) −18.3840 18.3840i −0.774794 0.774794i 0.204146 0.978940i \(-0.434558\pi\)
−0.978940 + 0.204146i \(0.934558\pi\)
\(564\) −19.4366 17.4380i −0.818428 0.734274i
\(565\) −3.58890 + 3.58890i −0.150986 + 0.150986i
\(566\) 11.5041 32.3681i 0.483554 1.36053i
\(567\) −27.4061 5.35828i −1.15095 0.225027i
\(568\) −3.36222 + 13.7944i −0.141076 + 0.578802i
\(569\) −43.5570 −1.82601 −0.913003 0.407953i \(-0.866243\pi\)
−0.913003 + 0.407953i \(0.866243\pi\)
\(570\) −1.38731 + 0.579422i −0.0581079 + 0.0242693i
\(571\) 7.00859 + 7.00859i 0.293301 + 0.293301i 0.838383 0.545082i \(-0.183502\pi\)
−0.545082 + 0.838383i \(0.683502\pi\)
\(572\) −15.8508 + 19.4822i −0.662756 + 0.814591i
\(573\) −0.265638 + 5.49894i −0.0110972 + 0.229721i
\(574\) −3.42166 7.19499i −0.142817 0.300313i
\(575\) 27.6340 1.15242
\(576\) −20.1446 13.0458i −0.839360 0.543576i
\(577\) 28.4494 1.18436 0.592182 0.805804i \(-0.298267\pi\)
0.592182 + 0.805804i \(0.298267\pi\)
\(578\) 6.74037 + 14.1735i 0.280362 + 0.589539i
\(579\) −0.957746 + 19.8261i −0.0398026 + 0.823946i
\(580\) −3.11836 + 3.83276i −0.129483 + 0.159147i
\(581\) −14.1239 14.1239i −0.585958 0.585958i
\(582\) −19.6103 + 8.19044i −0.812873 + 0.339504i
\(583\) −52.7527 −2.18479
\(584\) 9.01530 36.9877i 0.373056 1.53056i
\(585\) 0.525036 5.42166i 0.0217076 0.224158i
\(586\) 2.49472 7.01916i 0.103056 0.289959i
\(587\) 19.9011 19.9011i 0.821405 0.821405i −0.164904 0.986310i \(-0.552732\pi\)
0.986310 + 0.164904i \(0.0527315\pi\)
\(588\) 6.77418 + 6.07762i 0.279362 + 0.250637i
\(589\) −0.372787 0.372787i −0.0153604 0.0153604i
\(590\) −0.0422027 0.0887428i −0.00173746 0.00365348i
\(591\) 26.8510 24.3764i 1.10450 1.00271i
\(592\) −7.21057 4.72999i −0.296353 0.194401i
\(593\) 20.4344i 0.839140i 0.907723 + 0.419570i \(0.137819\pi\)
−0.907723 + 0.419570i \(0.862181\pi\)
\(594\) −14.5029 + 27.4342i −0.595063 + 1.12564i
\(595\) 3.25443 3.25443i 0.133418 0.133418i
\(596\) −16.2908 + 1.67429i −0.667298 + 0.0685816i
\(597\) −2.04378 + 42.3079i −0.0836462 + 1.73155i
\(598\) −23.6655 8.41110i −0.967755 0.343955i
\(599\) 32.6704i 1.33488i 0.744665 + 0.667438i \(0.232609\pi\)
−0.744665 + 0.667438i \(0.767391\pi\)
\(600\) 21.7392 + 6.42446i 0.887499 + 0.262278i
\(601\) 6.73553i 0.274748i 0.990519 + 0.137374i \(0.0438662\pi\)
−0.990519 + 0.137374i \(0.956134\pi\)
\(602\) 1.47725 4.15639i 0.0602080 0.169402i
\(603\) 1.28369 1.05702i 0.0522760 0.0430451i
\(604\) −12.5542 + 15.4303i −0.510821 + 0.627848i
\(605\) 2.94993 2.94993i 0.119932 0.119932i
\(606\) 0.583328 + 0.239617i 0.0236961 + 0.00973378i
\(607\) 21.2388i 0.862058i 0.902338 + 0.431029i \(0.141849\pi\)
−0.902338 + 0.431029i \(0.858151\pi\)
\(608\) −0.774723 + 5.63363i −0.0314192 + 0.228474i
\(609\) 14.6167 + 16.1005i 0.592297 + 0.652426i
\(610\) 6.31889 3.00502i 0.255844 0.121670i
\(611\) −15.8508 15.8508i −0.641256 0.641256i
\(612\) 10.3677 + 10.2466i 0.419089 + 0.414193i
\(613\) −9.62219 + 9.62219i −0.388637 + 0.388637i −0.874201 0.485564i \(-0.838614\pi\)
0.485564 + 0.874201i \(0.338614\pi\)
\(614\) −25.3294 9.00246i −1.02221 0.363310i
\(615\) 1.42166 1.29064i 0.0573270 0.0520436i
\(616\) 31.6655 19.2544i 1.27584 0.775783i
\(617\) 3.74576 0.150798 0.0753992 0.997153i \(-0.475977\pi\)
0.0753992 + 0.997153i \(0.475977\pi\)
\(618\) 14.3690 6.00135i 0.578005 0.241410i
\(619\) −13.0680 13.0680i −0.525249 0.525249i 0.393903 0.919152i \(-0.371124\pi\)
−0.919152 + 0.393903i \(0.871124\pi\)
\(620\) −0.0654727 0.637049i −0.00262945 0.0255845i
\(621\) −30.7070 4.47799i −1.23223 0.179696i
\(622\) 17.6655 8.40105i 0.708323 0.336852i
\(623\) −38.9643 −1.56107
\(624\) −16.6618 12.1187i −0.667007 0.485137i
\(625\) −19.5472 −0.781887
\(626\) −5.03268 + 2.39335i −0.201147 + 0.0956576i
\(627\) 7.34422 + 0.354779i 0.293300 + 0.0141685i
\(628\) 25.7491 2.64637i 1.02750 0.105602i
\(629\) 3.70355 + 3.70355i 0.147670 + 0.147670i
\(630\) −3.40913 + 7.27860i −0.135823 + 0.289986i
\(631\) −7.51388 −0.299123 −0.149561 0.988752i \(-0.547786\pi\)
−0.149561 + 0.988752i \(0.547786\pi\)
\(632\) 2.32788 9.55077i 0.0925981 0.379909i
\(633\) 10.1857 + 11.2197i 0.404843 + 0.445942i
\(634\) 16.8136 + 5.97582i 0.667754 + 0.237330i
\(635\) 6.81226 6.81226i 0.270336 0.270336i
\(636\) −2.34195 43.2105i −0.0928645 1.71341i
\(637\) 5.52444 + 5.52444i 0.218886 + 0.218886i
\(638\) 21.8229 10.3781i 0.863976 0.410874i
\(639\) −1.45158 + 14.9894i −0.0574238 + 0.592973i
\(640\) −5.04888 + 4.71440i −0.199574 + 0.186353i
\(641\) 27.7227i 1.09498i 0.836811 + 0.547491i \(0.184417\pi\)
−0.836811 + 0.547491i \(0.815583\pi\)
\(642\) 2.16715 5.27574i 0.0855304 0.208217i
\(643\) 19.7003 19.7003i 0.776903 0.776903i −0.202400 0.979303i \(-0.564874\pi\)
0.979303 + 0.202400i \(0.0648742\pi\)
\(644\) 28.7472 + 23.3889i 1.13280 + 0.921651i
\(645\) 1.06186 + 0.0512954i 0.0418106 + 0.00201976i
\(646\) 1.15667 3.25443i 0.0455087 0.128044i
\(647\) 5.29520i 0.208176i −0.994568 0.104088i \(-0.966808\pi\)
0.994568 0.104088i \(-0.0331923\pi\)
\(648\) −23.1156 10.6616i −0.908065 0.418828i
\(649\) 0.480585i 0.0188646i
\(650\) 18.3363 + 6.51700i 0.719208 + 0.255618i
\(651\) −2.81513 0.135991i −0.110334 0.00532992i
\(652\) 4.54002 + 44.1744i 0.177801 + 1.73000i
\(653\) 29.7039 29.7039i 1.16240 1.16240i 0.178457 0.983948i \(-0.442890\pi\)
0.983948 0.178457i \(-0.0571104\pi\)
\(654\) 21.0628 + 8.65210i 0.823622 + 0.338324i
\(655\) 0.0694851i 0.00271501i
\(656\) −1.47725 7.11088i −0.0576767 0.277633i
\(657\) 3.89220 40.1919i 0.151849 1.56804i
\(658\) 14.2056 + 29.8711i 0.553790 + 1.16450i
\(659\) 1.03268 + 1.03268i 0.0402276 + 0.0402276i 0.726934 0.686707i \(-0.240944\pi\)
−0.686707 + 0.726934i \(0.740944\pi\)
\(660\) 6.64815 + 5.96456i 0.258779 + 0.232170i
\(661\) 29.8277 29.8277i 1.16016 1.16016i 0.175725 0.984439i \(-0.443773\pi\)
0.984439 0.175725i \(-0.0562271\pi\)
\(662\) −6.32332 + 17.7913i −0.245763 + 0.691480i
\(663\) 8.41110 + 9.26498i 0.326660 + 0.359822i
\(664\) −9.45998 15.5577i −0.367118 0.603757i
\(665\) 1.90442 0.0738502
\(666\) −8.28308 3.87961i −0.320963 0.150332i
\(667\) 17.0872 + 17.0872i 0.661619 + 0.661619i
\(668\) −29.6994 24.1636i −1.14910 0.934918i
\(669\) 14.1689 + 0.684461i 0.547802 + 0.0264628i
\(670\) −0.205550 0.432226i −0.00794109 0.0166983i
\(671\) −34.2198 −1.32104
\(672\) 17.1774 + 25.0829i 0.662631 + 0.967593i
\(673\) −0.891685 −0.0343719 −0.0171860 0.999852i \(-0.505471\pi\)
−0.0171860 + 0.999852i \(0.505471\pi\)
\(674\) 3.60808 + 7.58698i 0.138978 + 0.292240i
\(675\) 23.7920 + 3.46959i 0.915756 + 0.133545i
\(676\) 6.44861 + 5.24663i 0.248024 + 0.201794i
\(677\) −8.13073 8.13073i −0.312489 0.312489i 0.533384 0.845873i \(-0.320920\pi\)
−0.845873 + 0.533384i \(0.820920\pi\)
\(678\) 7.84746 + 18.7891i 0.301380 + 0.721591i
\(679\) 26.9200 1.03309
\(680\) 3.58481 2.17977i 0.137471 0.0835902i
\(681\) 17.9734 16.3169i 0.688742 0.625266i
\(682\) −1.04888 + 2.95112i −0.0401635 + 0.113004i
\(683\) −14.5917 + 14.5917i −0.558337 + 0.558337i −0.928834 0.370497i \(-0.879187\pi\)
0.370497 + 0.928834i \(0.379187\pi\)
\(684\) 0.0354419 + 6.03150i 0.00135515 + 0.230620i
\(685\) −5.72496 5.72496i −0.218740 0.218740i
\(686\) 8.24057 + 17.3281i 0.314626 + 0.661589i
\(687\) −11.7749 12.9703i −0.449241 0.494847i
\(688\) 2.20555 3.36222i 0.0840858 0.128184i
\(689\) 37.1487i 1.41525i
\(690\) −3.39373 + 8.26175i −0.129197 + 0.314519i
\(691\) −11.2197 + 11.2197i −0.426817 + 0.426817i −0.887543 0.460726i \(-0.847589\pi\)
0.460726 + 0.887543i \(0.347589\pi\)
\(692\) 3.85406 + 37.4999i 0.146509 + 1.42553i
\(693\) 30.3447 24.9864i 1.15270 0.949154i
\(694\) −7.72496 2.74557i −0.293236 0.104221i
\(695\) 7.24616i 0.274863i
\(696\) 9.46970 + 17.4147i 0.358948 + 0.660102i
\(697\) 4.41110i 0.167082i
\(698\) 5.42712 15.2698i 0.205420 0.577970i
\(699\) −1.64164 + 33.9833i −0.0620924 + 1.28536i
\(700\) −22.2736 18.1219i −0.841862 0.684945i
\(701\) −14.7166 + 14.7166i −0.555837 + 0.555837i −0.928120 0.372282i \(-0.878575\pi\)
0.372282 + 0.928120i \(0.378575\pi\)
\(702\) −19.3193 10.2130i −0.729158 0.385466i
\(703\) 2.16724i 0.0817389i
\(704\) 32.2010 10.2172i 1.21362 0.385075i
\(705\) −5.90225 + 5.35828i −0.222292 + 0.201805i
\(706\) −37.3522 + 17.7633i −1.40577 + 0.668530i
\(707\) −0.564847 0.564847i −0.0212433 0.0212433i
\(708\) −0.393654 + 0.0213356i −0.0147944 + 0.000801839i
\(709\) −23.2978 + 23.2978i −0.874966 + 0.874966i −0.993009 0.118043i \(-0.962338\pi\)
0.118043 + 0.993009i \(0.462338\pi\)
\(710\) 4.08419 + 1.45158i 0.153277 + 0.0544770i
\(711\) 1.00502 10.3781i 0.0376913 0.389211i
\(712\) −34.5089 8.41110i −1.29327 0.315219i
\(713\) −3.13198 −0.117293
\(714\) −7.11610 17.0380i −0.266313 0.637632i
\(715\) 5.42166 + 5.42166i 0.202759 + 0.202759i
\(716\) 25.8416 2.65587i 0.965746 0.0992546i
\(717\) 0.789136 16.3358i 0.0294708 0.610071i
\(718\) −27.2333 + 12.9511i −1.01634 + 0.483332i
\(719\) 27.3421 1.01969 0.509844 0.860267i \(-0.329703\pi\)
0.509844 + 0.860267i \(0.329703\pi\)
\(720\) −4.59051 + 5.71039i −0.171078 + 0.212814i
\(721\) −19.7250 −0.734596
\(722\) −22.9752 + 10.9261i −0.855048 + 0.406628i
\(723\) 1.38871 28.7474i 0.0516465 1.06913i
\(724\) −4.77529 46.4635i −0.177472 1.72680i
\(725\) −13.2393 13.2393i −0.491696 0.491696i
\(726\) −6.45029 15.4439i −0.239393 0.573176i
\(727\) 24.1517 0.895735 0.447868 0.894100i \(-0.352184\pi\)
0.447868 + 0.894100i \(0.352184\pi\)
\(728\) 13.5590 + 22.2990i 0.502532 + 0.826456i
\(729\) −25.8755 7.71083i −0.958353 0.285586i
\(730\) −10.9511 3.89220i −0.405319 0.144057i
\(731\) −1.72693 + 1.72693i −0.0638729 + 0.0638729i
\(732\) −1.51919 28.0300i −0.0561508 1.03602i
\(733\) −6.00502 6.00502i −0.221801 0.221801i 0.587456 0.809256i \(-0.300130\pi\)
−0.809256 + 0.587456i \(0.800130\pi\)
\(734\) −41.9259 + 19.9384i −1.54751 + 0.735939i
\(735\) 2.05709 1.86751i 0.0758770 0.0688840i
\(736\) 20.4111 + 26.9200i 0.752363 + 0.992283i
\(737\) 2.34071i 0.0862212i
\(738\) −2.62237 7.24316i −0.0965308 0.266624i
\(739\) −10.9008 + 10.9008i −0.400992 + 0.400992i −0.878583 0.477590i \(-0.841510\pi\)
0.477590 + 0.878583i \(0.341510\pi\)
\(740\) −1.66146 + 2.04209i −0.0610765 + 0.0750688i
\(741\) −0.249837 + 5.17183i −0.00917798 + 0.189992i
\(742\) −18.3572 + 51.6499i −0.673914 + 1.89613i
\(743\) 1.29064i 0.0473490i −0.999720 0.0236745i \(-0.992463\pi\)
0.999720 0.0236745i \(-0.00753652\pi\)
\(744\) −2.46387 0.728134i −0.0903299 0.0266947i
\(745\) 4.99948i 0.183167i
\(746\) 2.55766 + 0.909033i 0.0936427 + 0.0332821i
\(747\) −12.2762 14.9088i −0.449162 0.545483i
\(748\) −20.4111 + 2.09775i −0.746304 + 0.0767014i
\(749\) −5.10860 + 5.10860i −0.186664 + 0.186664i
\(750\) 5.47083 13.3183i 0.199766 0.486315i
\(751\) 1.46552i 0.0534774i 0.999642 + 0.0267387i \(0.00851221\pi\)
−0.999642 + 0.0267387i \(0.991488\pi\)
\(752\) 6.13301 + 29.5219i 0.223648 + 1.07655i
\(753\) −3.34861 3.68855i −0.122030 0.134418i
\(754\) 7.30833 + 15.3678i 0.266154 + 0.559661i
\(755\) 4.29406 + 4.29406i 0.156277 + 0.156277i
\(756\) 21.8138 + 23.7465i 0.793362 + 0.863651i
\(757\) 4.71943 4.71943i 0.171530 0.171530i −0.616121 0.787651i \(-0.711297\pi\)
0.787651 + 0.616121i \(0.211297\pi\)
\(758\) 11.6455 32.7659i 0.422984 1.19011i
\(759\) 32.3416 29.3609i 1.17393 1.06573i
\(760\) 1.68665 + 0.411100i 0.0611813 + 0.0149122i
\(761\) 29.1578 1.05697 0.528485 0.848943i \(-0.322760\pi\)
0.528485 + 0.848943i \(0.322760\pi\)
\(762\) −14.8956 35.6645i −0.539612 1.29199i
\(763\) −20.3955 20.3955i −0.738367 0.738367i
\(764\) 4.01198 4.93111i 0.145148 0.178401i
\(765\) 3.43528 2.82867i 0.124203 0.102271i
\(766\) 20.0283 + 42.1149i 0.723651 + 1.52167i
\(767\) −0.338430 −0.0122200
\(768\) 9.79861 + 25.9227i 0.353577 + 0.935405i
\(769\) 20.8122 0.750505 0.375253 0.926923i \(-0.377556\pi\)
0.375253 + 0.926923i \(0.377556\pi\)
\(770\) −4.85891 10.2172i −0.175103 0.368202i
\(771\) −26.0822 1.25996i −0.939326 0.0453762i
\(772\) 14.4650 17.7789i 0.520607 0.639875i
\(773\) −26.6607 26.6607i −0.958918 0.958918i 0.0402703 0.999189i \(-0.487178\pi\)
−0.999189 +