Properties

Label 280.2.h.b.251.11
Level $280$
Weight $2$
Character 280.251
Analytic conductor $2.236$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - x^{15} - 2 x^{12} + 6 x^{11} - 12 x^{9} + 8 x^{8} - 24 x^{7} + 48 x^{5} - 32 x^{4} - 128 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.11
Root \(1.07046 + 0.924187i\) of defining polynomial
Character \(\chi\) \(=\) 280.251
Dual form 280.2.h.b.251.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.07046 - 0.924187i) q^{2} +2.99734i q^{3} +(0.291758 - 1.97860i) q^{4} +1.00000 q^{5} +(2.77010 + 3.20852i) q^{6} +(0.183359 + 2.63939i) q^{7} +(-1.51629 - 2.38765i) q^{8} -5.98405 q^{9} +O(q^{10})\) \(q+(1.07046 - 0.924187i) q^{2} +2.99734i q^{3} +(0.291758 - 1.97860i) q^{4} +1.00000 q^{5} +(2.77010 + 3.20852i) q^{6} +(0.183359 + 2.63939i) q^{7} +(-1.51629 - 2.38765i) q^{8} -5.98405 q^{9} +(1.07046 - 0.924187i) q^{10} +4.87706 q^{11} +(5.93055 + 0.874498i) q^{12} -2.42800 q^{13} +(2.63557 + 2.65590i) q^{14} +2.99734i q^{15} +(-3.82975 - 1.15455i) q^{16} +3.92955i q^{17} +(-6.40567 + 5.53038i) q^{18} -5.24043i q^{19} +(0.291758 - 1.97860i) q^{20} +(-7.91115 + 0.549588i) q^{21} +(5.22068 - 4.50731i) q^{22} -0.114122i q^{23} +(7.15660 - 4.54482i) q^{24} +1.00000 q^{25} +(-2.59907 + 2.24393i) q^{26} -8.94421i q^{27} +(5.27581 + 0.407269i) q^{28} -3.60881i q^{29} +(2.77010 + 3.20852i) q^{30} +4.62694 q^{31} +(-5.16661 + 2.30351i) q^{32} +14.6182i q^{33} +(3.63164 + 4.20642i) q^{34} +(0.183359 + 2.63939i) q^{35} +(-1.74589 + 11.8401i) q^{36} -7.83800i q^{37} +(-4.84313 - 5.60965i) q^{38} -7.27754i q^{39} +(-1.51629 - 2.38765i) q^{40} -10.4815i q^{41} +(-7.96063 + 7.89969i) q^{42} +2.76350 q^{43} +(1.42292 - 9.64977i) q^{44} -5.98405 q^{45} +(-0.105470 - 0.122163i) q^{46} -12.0817 q^{47} +(3.46057 - 11.4791i) q^{48} +(-6.93276 + 0.967910i) q^{49} +(1.07046 - 0.924187i) q^{50} -11.7782 q^{51} +(-0.708388 + 4.80405i) q^{52} +0.668088i q^{53} +(-8.26612 - 9.57439i) q^{54} +4.87706 q^{55} +(6.02392 - 4.43987i) q^{56} +15.7073 q^{57} +(-3.33521 - 3.86307i) q^{58} -1.37541i q^{59} +(5.93055 + 0.874498i) q^{60} -1.17808 q^{61} +(4.95294 - 4.27615i) q^{62} +(-1.09723 - 15.7942i) q^{63} +(-3.40175 + 7.24072i) q^{64} -2.42800 q^{65} +(13.5099 + 15.6482i) q^{66} +2.57766 q^{67} +(7.77504 + 1.14648i) q^{68} +0.342063 q^{69} +(2.63557 + 2.65590i) q^{70} +9.43699i q^{71} +(9.07353 + 14.2878i) q^{72} -5.62623i q^{73} +(-7.24377 - 8.39024i) q^{74} +2.99734i q^{75} +(-10.3687 - 1.52894i) q^{76} +(0.894251 + 12.8725i) q^{77} +(-6.72581 - 7.79030i) q^{78} +11.8804i q^{79} +(-3.82975 - 1.15455i) q^{80} +8.85669 q^{81} +(-9.68687 - 11.2200i) q^{82} -5.52348i q^{83} +(-1.22072 + 15.8134i) q^{84} +3.92955i q^{85} +(2.95821 - 2.55399i) q^{86} +10.8168 q^{87} +(-7.39501 - 11.6447i) q^{88} +6.21826i q^{89} +(-6.40567 + 5.53038i) q^{90} +(-0.445195 - 6.40844i) q^{91} +(-0.225803 - 0.0332961i) q^{92} +13.8685i q^{93} +(-12.9329 + 11.1657i) q^{94} -5.24043i q^{95} +(-6.90442 - 15.4861i) q^{96} +7.85094i q^{97} +(-6.52669 + 7.44327i) q^{98} -29.1845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + O(q^{10}) \) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + q^{10} - 4q^{11} + 14q^{12} - q^{14} + 9q^{16} - 15q^{18} + q^{20} - 4q^{21} + 6q^{22} + 22q^{24} + 16q^{25} - 20q^{26} + q^{28} - 16q^{31} - 19q^{32} - 14q^{34} + 15q^{36} - 30q^{38} + q^{40} + 44q^{42} - 4q^{43} - 20q^{44} - 16q^{45} + 6q^{46} - 34q^{48} - 8q^{49} + q^{50} - 40q^{51} - 38q^{52} + 26q^{54} - 4q^{55} + 33q^{56} - 16q^{57} + 18q^{58} + 14q^{60} - 8q^{61} + 28q^{62} + 28q^{63} - 23q^{64} + 46q^{66} + 20q^{67} + 12q^{68} - 40q^{69} - q^{70} - 13q^{72} - 28q^{74} + 34q^{76} - 4q^{77} - 6q^{78} + 9q^{80} + 24q^{81} - 16q^{82} - 42q^{84} - 24q^{86} + 72q^{87} - 44q^{88} - 15q^{90} - 32q^{91} - 30q^{92} - 58q^{94} - 30q^{96} + 5q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.07046 0.924187i 0.756928 0.653499i
\(3\) 2.99734i 1.73052i 0.501328 + 0.865258i \(0.332845\pi\)
−0.501328 + 0.865258i \(0.667155\pi\)
\(4\) 0.291758 1.97860i 0.145879 0.989302i
\(5\) 1.00000 0.447214
\(6\) 2.77010 + 3.20852i 1.13089 + 1.30987i
\(7\) 0.183359 + 2.63939i 0.0693031 + 0.997596i
\(8\) −1.51629 2.38765i −0.536088 0.844162i
\(9\) −5.98405 −1.99468
\(10\) 1.07046 0.924187i 0.338508 0.292253i
\(11\) 4.87706 1.47049 0.735244 0.677803i \(-0.237068\pi\)
0.735244 + 0.677803i \(0.237068\pi\)
\(12\) 5.93055 + 0.874498i 1.71200 + 0.252446i
\(13\) −2.42800 −0.673406 −0.336703 0.941611i \(-0.609312\pi\)
−0.336703 + 0.941611i \(0.609312\pi\)
\(14\) 2.63557 + 2.65590i 0.704385 + 0.709818i
\(15\) 2.99734i 0.773910i
\(16\) −3.82975 1.15455i −0.957439 0.288637i
\(17\) 3.92955i 0.953057i 0.879159 + 0.476528i \(0.158105\pi\)
−0.879159 + 0.476528i \(0.841895\pi\)
\(18\) −6.40567 + 5.53038i −1.50983 + 1.30352i
\(19\) 5.24043i 1.20224i −0.799160 0.601118i \(-0.794722\pi\)
0.799160 0.601118i \(-0.205278\pi\)
\(20\) 0.291758 1.97860i 0.0652391 0.442430i
\(21\) −7.91115 + 0.549588i −1.72635 + 0.119930i
\(22\) 5.22068 4.50731i 1.11305 0.960962i
\(23\) 0.114122i 0.0237961i −0.999929 0.0118981i \(-0.996213\pi\)
0.999929 0.0118981i \(-0.00378736\pi\)
\(24\) 7.15660 4.54482i 1.46084 0.927708i
\(25\) 1.00000 0.200000
\(26\) −2.59907 + 2.24393i −0.509720 + 0.440070i
\(27\) 8.94421i 1.72131i
\(28\) 5.27581 + 0.407269i 0.997034 + 0.0769665i
\(29\) 3.60881i 0.670139i −0.942193 0.335069i \(-0.891240\pi\)
0.942193 0.335069i \(-0.108760\pi\)
\(30\) 2.77010 + 3.20852i 0.505749 + 0.585794i
\(31\) 4.62694 0.831023 0.415511 0.909588i \(-0.363603\pi\)
0.415511 + 0.909588i \(0.363603\pi\)
\(32\) −5.16661 + 2.30351i −0.913336 + 0.407208i
\(33\) 14.6182i 2.54470i
\(34\) 3.63164 + 4.20642i 0.622821 + 0.721395i
\(35\) 0.183359 + 2.63939i 0.0309933 + 0.446138i
\(36\) −1.74589 + 11.8401i −0.290982 + 1.97334i
\(37\) 7.83800i 1.28856i −0.764790 0.644279i \(-0.777157\pi\)
0.764790 0.644279i \(-0.222843\pi\)
\(38\) −4.84313 5.60965i −0.785660 0.910006i
\(39\) 7.27754i 1.16534i
\(40\) −1.51629 2.38765i −0.239746 0.377521i
\(41\) 10.4815i 1.63694i −0.574552 0.818468i \(-0.694824\pi\)
0.574552 0.818468i \(-0.305176\pi\)
\(42\) −7.96063 + 7.89969i −1.22835 + 1.21895i
\(43\) 2.76350 0.421430 0.210715 0.977548i \(-0.432421\pi\)
0.210715 + 0.977548i \(0.432421\pi\)
\(44\) 1.42292 9.64977i 0.214513 1.45476i
\(45\) −5.98405 −0.892049
\(46\) −0.105470 0.122163i −0.0155507 0.0180119i
\(47\) −12.0817 −1.76229 −0.881145 0.472846i \(-0.843227\pi\)
−0.881145 + 0.472846i \(0.843227\pi\)
\(48\) 3.46057 11.4791i 0.499490 1.65686i
\(49\) −6.93276 + 0.967910i −0.990394 + 0.138273i
\(50\) 1.07046 0.924187i 0.151386 0.130700i
\(51\) −11.7782 −1.64928
\(52\) −0.708388 + 4.80405i −0.0982358 + 0.666202i
\(53\) 0.668088i 0.0917689i 0.998947 + 0.0458845i \(0.0146106\pi\)
−0.998947 + 0.0458845i \(0.985389\pi\)
\(54\) −8.26612 9.57439i −1.12488 1.30291i
\(55\) 4.87706 0.657622
\(56\) 6.02392 4.43987i 0.804980 0.593302i
\(57\) 15.7073 2.08049
\(58\) −3.33521 3.86307i −0.437935 0.507246i
\(59\) 1.37541i 0.179063i −0.995984 0.0895314i \(-0.971463\pi\)
0.995984 0.0895314i \(-0.0285369\pi\)
\(60\) 5.93055 + 0.874498i 0.765631 + 0.112897i
\(61\) −1.17808 −0.150837 −0.0754186 0.997152i \(-0.524029\pi\)
−0.0754186 + 0.997152i \(0.524029\pi\)
\(62\) 4.95294 4.27615i 0.629024 0.543072i
\(63\) −1.09723 15.7942i −0.138238 1.98989i
\(64\) −3.40175 + 7.24072i −0.425219 + 0.905090i
\(65\) −2.42800 −0.301156
\(66\) 13.5099 + 15.6482i 1.66296 + 1.92615i
\(67\) 2.57766 0.314911 0.157456 0.987526i \(-0.449671\pi\)
0.157456 + 0.987526i \(0.449671\pi\)
\(68\) 7.77504 + 1.14648i 0.942862 + 0.139031i
\(69\) 0.342063 0.0411795
\(70\) 2.63557 + 2.65590i 0.315010 + 0.317440i
\(71\) 9.43699i 1.11996i 0.828505 + 0.559982i \(0.189192\pi\)
−0.828505 + 0.559982i \(0.810808\pi\)
\(72\) 9.07353 + 14.2878i 1.06933 + 1.68384i
\(73\) 5.62623i 0.658500i −0.944243 0.329250i \(-0.893204\pi\)
0.944243 0.329250i \(-0.106796\pi\)
\(74\) −7.24377 8.39024i −0.842072 0.975346i
\(75\) 2.99734i 0.346103i
\(76\) −10.3687 1.52894i −1.18938 0.175381i
\(77\) 0.894251 + 12.8725i 0.101909 + 1.46695i
\(78\) −6.72581 7.79030i −0.761548 0.882078i
\(79\) 11.8804i 1.33665i 0.743872 + 0.668323i \(0.232987\pi\)
−0.743872 + 0.668323i \(0.767013\pi\)
\(80\) −3.82975 1.15455i −0.428180 0.129082i
\(81\) 8.85669 0.984077
\(82\) −9.68687 11.2200i −1.06974 1.23904i
\(83\) 5.52348i 0.606280i −0.952946 0.303140i \(-0.901965\pi\)
0.952946 0.303140i \(-0.0980350\pi\)
\(84\) −1.22072 + 15.8134i −0.133192 + 1.72538i
\(85\) 3.92955i 0.426220i
\(86\) 2.95821 2.55399i 0.318992 0.275404i
\(87\) 10.8168 1.15969
\(88\) −7.39501 11.6447i −0.788311 1.24133i
\(89\) 6.21826i 0.659135i 0.944132 + 0.329567i \(0.106903\pi\)
−0.944132 + 0.329567i \(0.893097\pi\)
\(90\) −6.40567 + 5.53038i −0.675217 + 0.582953i
\(91\) −0.445195 6.40844i −0.0466691 0.671787i
\(92\) −0.225803 0.0332961i −0.0235416 0.00347135i
\(93\) 13.8685i 1.43810i
\(94\) −12.9329 + 11.1657i −1.33393 + 1.15165i
\(95\) 5.24043i 0.537657i
\(96\) −6.90442 15.4861i −0.704679 1.58054i
\(97\) 7.85094i 0.797142i 0.917137 + 0.398571i \(0.130494\pi\)
−0.917137 + 0.398571i \(0.869506\pi\)
\(98\) −6.52669 + 7.44327i −0.659296 + 0.751884i
\(99\) −29.1845 −2.93316
\(100\) 0.291758 1.97860i 0.0291758 0.197860i
\(101\) −10.9057 −1.08516 −0.542580 0.840004i \(-0.682552\pi\)
−0.542580 + 0.840004i \(0.682552\pi\)
\(102\) −12.6081 + 10.8853i −1.24839 + 1.07780i
\(103\) 15.8202 1.55881 0.779403 0.626523i \(-0.215523\pi\)
0.779403 + 0.626523i \(0.215523\pi\)
\(104\) 3.68154 + 5.79722i 0.361005 + 0.568464i
\(105\) −7.91115 + 0.549588i −0.772049 + 0.0536343i
\(106\) 0.617438 + 0.715160i 0.0599709 + 0.0694624i
\(107\) 6.53444 0.631708 0.315854 0.948808i \(-0.397709\pi\)
0.315854 + 0.948808i \(0.397709\pi\)
\(108\) −17.6971 2.60954i −1.70290 0.251103i
\(109\) 10.9309i 1.04699i 0.852028 + 0.523496i \(0.175372\pi\)
−0.852028 + 0.523496i \(0.824628\pi\)
\(110\) 5.22068 4.50731i 0.497772 0.429755i
\(111\) 23.4931 2.22987
\(112\) 2.34508 10.3199i 0.221589 0.975140i
\(113\) 3.72004 0.349951 0.174976 0.984573i \(-0.444015\pi\)
0.174976 + 0.984573i \(0.444015\pi\)
\(114\) 16.8140 14.5165i 1.57478 1.35960i
\(115\) 0.114122i 0.0106419i
\(116\) −7.14040 1.05290i −0.662970 0.0977591i
\(117\) 14.5293 1.34323
\(118\) −1.27113 1.47232i −0.117017 0.135538i
\(119\) −10.3716 + 0.720518i −0.950766 + 0.0660498i
\(120\) 7.15660 4.54482i 0.653305 0.414884i
\(121\) 12.7857 1.16233
\(122\) −1.26108 + 1.08876i −0.114173 + 0.0985719i
\(123\) 31.4166 2.83274
\(124\) 1.34995 9.15488i 0.121229 0.822133i
\(125\) 1.00000 0.0894427
\(126\) −15.7714 15.8930i −1.40502 1.41586i
\(127\) 3.80326i 0.337485i 0.985660 + 0.168742i \(0.0539706\pi\)
−0.985660 + 0.168742i \(0.946029\pi\)
\(128\) 3.05035 + 10.8947i 0.269615 + 0.962968i
\(129\) 8.28315i 0.729291i
\(130\) −2.59907 + 2.24393i −0.227954 + 0.196805i
\(131\) 7.68109i 0.671100i 0.942022 + 0.335550i \(0.108922\pi\)
−0.942022 + 0.335550i \(0.891078\pi\)
\(132\) 28.9236 + 4.26497i 2.51748 + 0.371218i
\(133\) 13.8315 0.960878i 1.19935 0.0833187i
\(134\) 2.75927 2.38224i 0.238365 0.205794i
\(135\) 8.94421i 0.769795i
\(136\) 9.38241 5.95833i 0.804535 0.510922i
\(137\) −16.9739 −1.45018 −0.725090 0.688655i \(-0.758202\pi\)
−0.725090 + 0.688655i \(0.758202\pi\)
\(138\) 0.366164 0.316130i 0.0311699 0.0269108i
\(139\) 2.54598i 0.215947i 0.994154 + 0.107973i \(0.0344362\pi\)
−0.994154 + 0.107973i \(0.965564\pi\)
\(140\) 5.27581 + 0.407269i 0.445887 + 0.0344205i
\(141\) 36.2128i 3.04967i
\(142\) 8.72154 + 10.1019i 0.731895 + 0.847732i
\(143\) −11.8415 −0.990235
\(144\) 22.9174 + 6.90887i 1.90979 + 0.575739i
\(145\) 3.60881i 0.299695i
\(146\) −5.19969 6.02264i −0.430329 0.498437i
\(147\) −2.90116 20.7798i −0.239283 1.71389i
\(148\) −15.5083 2.28680i −1.27477 0.187974i
\(149\) 13.7925i 1.12992i −0.825118 0.564961i \(-0.808891\pi\)
0.825118 0.564961i \(-0.191109\pi\)
\(150\) 2.77010 + 3.20852i 0.226178 + 0.261975i
\(151\) 0.128374i 0.0104469i 0.999986 + 0.00522347i \(0.00166269\pi\)
−0.999986 + 0.00522347i \(0.998337\pi\)
\(152\) −12.5123 + 7.94599i −1.01488 + 0.644505i
\(153\) 23.5146i 1.90105i
\(154\) 12.8538 + 12.9530i 1.03579 + 1.04378i
\(155\) 4.62694 0.371645
\(156\) −14.3994 2.12328i −1.15287 0.169999i
\(157\) 13.1585 1.05017 0.525083 0.851051i \(-0.324034\pi\)
0.525083 + 0.851051i \(0.324034\pi\)
\(158\) 10.9797 + 12.7174i 0.873496 + 1.01174i
\(159\) −2.00249 −0.158808
\(160\) −5.16661 + 2.30351i −0.408456 + 0.182109i
\(161\) 0.301213 0.0209253i 0.0237389 0.00164914i
\(162\) 9.48071 8.18523i 0.744875 0.643093i
\(163\) 0.158264 0.0123962 0.00619809 0.999981i \(-0.498027\pi\)
0.00619809 + 0.999981i \(0.498027\pi\)
\(164\) −20.7388 3.05806i −1.61943 0.238795i
\(165\) 14.6182i 1.13802i
\(166\) −5.10472 5.91264i −0.396203 0.458910i
\(167\) −16.7105 −1.29310 −0.646550 0.762871i \(-0.723789\pi\)
−0.646550 + 0.762871i \(0.723789\pi\)
\(168\) 13.3078 + 18.0557i 1.02672 + 1.39303i
\(169\) −7.10482 −0.546524
\(170\) 3.63164 + 4.20642i 0.278534 + 0.322618i
\(171\) 31.3590i 2.39808i
\(172\) 0.806274 5.46788i 0.0614778 0.416922i
\(173\) 5.19433 0.394918 0.197459 0.980311i \(-0.436731\pi\)
0.197459 + 0.980311i \(0.436731\pi\)
\(174\) 11.5789 9.99676i 0.877798 0.757853i
\(175\) 0.183359 + 2.63939i 0.0138606 + 0.199519i
\(176\) −18.6779 5.63079i −1.40790 0.424437i
\(177\) 4.12256 0.309871
\(178\) 5.74684 + 6.65639i 0.430744 + 0.498917i
\(179\) −17.3274 −1.29511 −0.647555 0.762019i \(-0.724208\pi\)
−0.647555 + 0.762019i \(0.724208\pi\)
\(180\) −1.74589 + 11.8401i −0.130131 + 0.882507i
\(181\) 21.0585 1.56526 0.782631 0.622485i \(-0.213877\pi\)
0.782631 + 0.622485i \(0.213877\pi\)
\(182\) −6.39916 6.44852i −0.474337 0.477996i
\(183\) 3.53110i 0.261026i
\(184\) −0.272484 + 0.173042i −0.0200878 + 0.0127568i
\(185\) 7.83800i 0.576261i
\(186\) 12.8171 + 14.8456i 0.939795 + 1.08854i
\(187\) 19.1647i 1.40146i
\(188\) −3.52492 + 23.9048i −0.257081 + 1.74344i
\(189\) 23.6073 1.64000i 1.71718 0.119292i
\(190\) −4.84313 5.60965i −0.351358 0.406967i
\(191\) 8.43465i 0.610310i 0.952303 + 0.305155i \(0.0987083\pi\)
−0.952303 + 0.305155i \(0.901292\pi\)
\(192\) −21.7029 10.1962i −1.56627 0.735849i
\(193\) −25.6337 −1.84516 −0.922578 0.385811i \(-0.873922\pi\)
−0.922578 + 0.385811i \(0.873922\pi\)
\(194\) 7.25573 + 8.40410i 0.520931 + 0.603379i
\(195\) 7.27754i 0.521156i
\(196\) −0.107576 + 13.9996i −0.00768397 + 0.999970i
\(197\) 1.78729i 0.127339i −0.997971 0.0636697i \(-0.979720\pi\)
0.997971 0.0636697i \(-0.0202804\pi\)
\(198\) −31.2408 + 26.9720i −2.22019 + 1.91681i
\(199\) 22.3178 1.58206 0.791032 0.611774i \(-0.209544\pi\)
0.791032 + 0.611774i \(0.209544\pi\)
\(200\) −1.51629 2.38765i −0.107218 0.168832i
\(201\) 7.72612i 0.544958i
\(202\) −11.6741 + 10.0789i −0.821388 + 0.709151i
\(203\) 9.52505 0.661706i 0.668527 0.0464427i
\(204\) −3.43639 + 23.3044i −0.240595 + 1.63164i
\(205\) 10.4815i 0.732060i
\(206\) 16.9348 14.6208i 1.17990 1.01868i
\(207\) 0.682913i 0.0474657i
\(208\) 9.29864 + 2.80324i 0.644745 + 0.194370i
\(209\) 25.5579i 1.76787i
\(210\) −7.96063 + 7.89969i −0.549335 + 0.545130i
\(211\) 8.58471 0.590996 0.295498 0.955343i \(-0.404514\pi\)
0.295498 + 0.955343i \(0.404514\pi\)
\(212\) 1.32188 + 0.194920i 0.0907872 + 0.0133872i
\(213\) −28.2859 −1.93812
\(214\) 6.99484 6.03904i 0.478157 0.412820i
\(215\) 2.76350 0.188469
\(216\) −21.3556 + 13.5620i −1.45307 + 0.922776i
\(217\) 0.848389 + 12.2123i 0.0575924 + 0.829024i
\(218\) 10.1022 + 11.7011i 0.684207 + 0.792497i
\(219\) 16.8637 1.13954
\(220\) 1.42292 9.64977i 0.0959332 0.650587i
\(221\) 9.54096i 0.641794i
\(222\) 25.1484 21.7121i 1.68785 1.45722i
\(223\) −14.0359 −0.939916 −0.469958 0.882689i \(-0.655731\pi\)
−0.469958 + 0.882689i \(0.655731\pi\)
\(224\) −7.02721 13.2143i −0.469526 0.882919i
\(225\) −5.98405 −0.398937
\(226\) 3.98214 3.43801i 0.264888 0.228693i
\(227\) 29.9063i 1.98495i 0.122442 + 0.992476i \(0.460927\pi\)
−0.122442 + 0.992476i \(0.539073\pi\)
\(228\) 4.58274 31.0786i 0.303500 2.05823i
\(229\) −8.92103 −0.589518 −0.294759 0.955572i \(-0.595239\pi\)
−0.294759 + 0.955572i \(0.595239\pi\)
\(230\) −0.105470 0.122163i −0.00695450 0.00805518i
\(231\) −38.5831 + 2.68037i −2.53858 + 0.176356i
\(232\) −8.61657 + 5.47198i −0.565706 + 0.359253i
\(233\) 0.565155 0.0370245 0.0185123 0.999829i \(-0.494107\pi\)
0.0185123 + 0.999829i \(0.494107\pi\)
\(234\) 15.5530 13.4278i 1.01673 0.877800i
\(235\) −12.0817 −0.788120
\(236\) −2.72139 0.401286i −0.177147 0.0261215i
\(237\) −35.6095 −2.31309
\(238\) −10.4365 + 10.3566i −0.676497 + 0.671319i
\(239\) 8.51136i 0.550554i 0.961365 + 0.275277i \(0.0887695\pi\)
−0.961365 + 0.275277i \(0.911230\pi\)
\(240\) 3.46057 11.4791i 0.223379 0.740971i
\(241\) 2.17523i 0.140119i 0.997543 + 0.0700595i \(0.0223189\pi\)
−0.997543 + 0.0700595i \(0.977681\pi\)
\(242\) 13.6865 11.8163i 0.879803 0.759584i
\(243\) 0.286112i 0.0183541i
\(244\) −0.343713 + 2.33095i −0.0220040 + 0.149224i
\(245\) −6.93276 + 0.967910i −0.442918 + 0.0618375i
\(246\) 33.6302 29.0348i 2.14418 1.85119i
\(247\) 12.7238i 0.809593i
\(248\) −7.01576 11.0475i −0.445501 0.701518i
\(249\) 16.5557 1.04918
\(250\) 1.07046 0.924187i 0.0677017 0.0584507i
\(251\) 9.41690i 0.594390i −0.954817 0.297195i \(-0.903949\pi\)
0.954817 0.297195i \(-0.0960511\pi\)
\(252\) −31.5707 2.43712i −1.98877 0.153524i
\(253\) 0.556580i 0.0349919i
\(254\) 3.51492 + 4.07123i 0.220546 + 0.255452i
\(255\) −11.7782 −0.737580
\(256\) 13.3340 + 8.84327i 0.833378 + 0.552704i
\(257\) 4.44138i 0.277045i −0.990359 0.138523i \(-0.955765\pi\)
0.990359 0.138523i \(-0.0442354\pi\)
\(258\) 7.65518 + 8.86676i 0.476591 + 0.552021i
\(259\) 20.6875 1.43717i 1.28546 0.0893011i
\(260\) −0.708388 + 4.80405i −0.0439324 + 0.297935i
\(261\) 21.5953i 1.33671i
\(262\) 7.09876 + 8.22228i 0.438563 + 0.507974i
\(263\) 13.6247i 0.840132i 0.907493 + 0.420066i \(0.137993\pi\)
−0.907493 + 0.420066i \(0.862007\pi\)
\(264\) 34.9031 22.1654i 2.14814 1.36418i
\(265\) 0.668088i 0.0410403i
\(266\) 13.9180 13.8115i 0.853370 0.846837i
\(267\) −18.6383 −1.14064
\(268\) 0.752052 5.10017i 0.0459389 0.311542i
\(269\) −10.2713 −0.626253 −0.313127 0.949711i \(-0.601376\pi\)
−0.313127 + 0.949711i \(0.601376\pi\)
\(270\) −8.26612 9.57439i −0.503060 0.582679i
\(271\) −2.67264 −0.162352 −0.0811758 0.996700i \(-0.525868\pi\)
−0.0811758 + 0.996700i \(0.525868\pi\)
\(272\) 4.53686 15.0492i 0.275087 0.912494i
\(273\) 19.2083 1.33440i 1.16254 0.0807616i
\(274\) −18.1698 + 15.6871i −1.09768 + 0.947690i
\(275\) 4.87706 0.294098
\(276\) 0.0997996 0.676807i 0.00600723 0.0407390i
\(277\) 28.1383i 1.69067i −0.534239 0.845333i \(-0.679402\pi\)
0.534239 0.845333i \(-0.320598\pi\)
\(278\) 2.35296 + 2.72536i 0.141121 + 0.163456i
\(279\) −27.6878 −1.65763
\(280\) 6.02392 4.43987i 0.359998 0.265333i
\(281\) 0.466842 0.0278494 0.0139247 0.999903i \(-0.495567\pi\)
0.0139247 + 0.999903i \(0.495567\pi\)
\(282\) −33.4674 38.7643i −1.99295 2.30838i
\(283\) 10.8004i 0.642019i −0.947076 0.321009i \(-0.895978\pi\)
0.947076 0.321009i \(-0.104022\pi\)
\(284\) 18.6721 + 2.75332i 1.10798 + 0.163379i
\(285\) 15.7073 0.930423
\(286\) −12.6758 + 10.9437i −0.749536 + 0.647117i
\(287\) 27.6648 1.92188i 1.63300 0.113445i
\(288\) 30.9172 13.7843i 1.82181 0.812250i
\(289\) 1.55860 0.0916824
\(290\) −3.33521 3.86307i −0.195850 0.226848i
\(291\) −23.5319 −1.37947
\(292\) −11.1321 1.64150i −0.651456 0.0960613i
\(293\) 7.34532 0.429118 0.214559 0.976711i \(-0.431169\pi\)
0.214559 + 0.976711i \(0.431169\pi\)
\(294\) −22.3100 19.5627i −1.30115 1.14092i
\(295\) 1.37541i 0.0800793i
\(296\) −18.7144 + 11.8846i −1.08775 + 0.690781i
\(297\) 43.6214i 2.53117i
\(298\) −12.7468 14.7642i −0.738402 0.855269i
\(299\) 0.277089i 0.0160244i
\(300\) 5.93055 + 0.874498i 0.342401 + 0.0504892i
\(301\) 0.506712 + 7.29396i 0.0292064 + 0.420417i
\(302\) 0.118642 + 0.137419i 0.00682706 + 0.00790758i
\(303\) 32.6882i 1.87789i
\(304\) −6.05032 + 20.0696i −0.347010 + 1.15107i
\(305\) −1.17808 −0.0674564
\(306\) −21.7319 25.1714i −1.24233 1.43895i
\(307\) 5.08078i 0.289975i −0.989433 0.144988i \(-0.953686\pi\)
0.989433 0.144988i \(-0.0463142\pi\)
\(308\) 25.7304 + 1.98627i 1.46613 + 0.113178i
\(309\) 47.4184i 2.69754i
\(310\) 4.95294 4.27615i 0.281308 0.242869i
\(311\) −17.8319 −1.01116 −0.505578 0.862781i \(-0.668721\pi\)
−0.505578 + 0.862781i \(0.668721\pi\)
\(312\) −17.3762 + 11.0348i −0.983735 + 0.624724i
\(313\) 3.54008i 0.200097i 0.994983 + 0.100049i \(0.0318998\pi\)
−0.994983 + 0.100049i \(0.968100\pi\)
\(314\) 14.0857 12.1610i 0.794900 0.686282i
\(315\) −1.09723 15.7942i −0.0618218 0.889904i
\(316\) 23.5065 + 3.46619i 1.32235 + 0.194988i
\(317\) 4.86360i 0.273167i 0.990629 + 0.136583i \(0.0436122\pi\)
−0.990629 + 0.136583i \(0.956388\pi\)
\(318\) −2.14358 + 1.85067i −0.120206 + 0.103781i
\(319\) 17.6004i 0.985431i
\(320\) −3.40175 + 7.24072i −0.190164 + 0.404769i
\(321\) 19.5859i 1.09318i
\(322\) 0.303097 0.300777i 0.0168909 0.0167616i
\(323\) 20.5925 1.14580
\(324\) 2.58401 17.5239i 0.143556 0.973549i
\(325\) −2.42800 −0.134681
\(326\) 0.169415 0.146265i 0.00938301 0.00810088i
\(327\) −32.7637 −1.81183
\(328\) −25.0262 + 15.8930i −1.38184 + 0.877542i
\(329\) −2.21528 31.8882i −0.122132 1.75805i
\(330\) 13.5099 + 15.6482i 0.743698 + 0.861403i
\(331\) −9.38870 −0.516050 −0.258025 0.966138i \(-0.583072\pi\)
−0.258025 + 0.966138i \(0.583072\pi\)
\(332\) −10.9288 1.61152i −0.599794 0.0884435i
\(333\) 46.9030i 2.57027i
\(334\) −17.8879 + 15.4437i −0.978784 + 0.845040i
\(335\) 2.57766 0.140832
\(336\) 30.9323 + 7.02901i 1.68749 + 0.383464i
\(337\) 19.7551 1.07613 0.538064 0.842904i \(-0.319156\pi\)
0.538064 + 0.842904i \(0.319156\pi\)
\(338\) −7.60540 + 6.56618i −0.413679 + 0.357153i
\(339\) 11.1502i 0.605596i
\(340\) 7.77504 + 1.14648i 0.421661 + 0.0621765i
\(341\) 22.5658 1.22201
\(342\) 28.9815 + 33.5684i 1.56714 + 1.81517i
\(343\) −3.82587 18.1208i −0.206578 0.978430i
\(344\) −4.19026 6.59828i −0.225924 0.355755i
\(345\) 0.342063 0.0184161
\(346\) 5.56031 4.80053i 0.298924 0.258078i
\(347\) −29.8093 −1.60025 −0.800124 0.599835i \(-0.795233\pi\)
−0.800124 + 0.599835i \(0.795233\pi\)
\(348\) 3.15589 21.4022i 0.169174 1.14728i
\(349\) −15.6993 −0.840364 −0.420182 0.907440i \(-0.638034\pi\)
−0.420182 + 0.907440i \(0.638034\pi\)
\(350\) 2.63557 + 2.65590i 0.140877 + 0.141964i
\(351\) 21.7165i 1.15914i
\(352\) −25.1978 + 11.2344i −1.34305 + 0.598794i
\(353\) 10.2186i 0.543879i −0.962314 0.271939i \(-0.912335\pi\)
0.962314 0.271939i \(-0.0876651\pi\)
\(354\) 4.41303 3.81002i 0.234550 0.202500i
\(355\) 9.43699i 0.500863i
\(356\) 12.3035 + 1.81423i 0.652084 + 0.0961539i
\(357\) −2.15964 31.0873i −0.114300 1.64531i
\(358\) −18.5482 + 16.0137i −0.980304 + 0.846352i
\(359\) 23.4758i 1.23900i −0.784995 0.619502i \(-0.787334\pi\)
0.784995 0.619502i \(-0.212666\pi\)
\(360\) 9.07353 + 14.2878i 0.478217 + 0.753034i
\(361\) −8.46208 −0.445373
\(362\) 22.5422 19.4619i 1.18479 1.02290i
\(363\) 38.3230i 2.01144i
\(364\) −12.8097 0.988848i −0.671408 0.0518297i
\(365\) 5.62623i 0.294490i
\(366\) −3.26339 3.77989i −0.170580 0.197578i
\(367\) 21.5002 1.12230 0.561151 0.827714i \(-0.310359\pi\)
0.561151 + 0.827714i \(0.310359\pi\)
\(368\) −0.131759 + 0.437060i −0.00686844 + 0.0227833i
\(369\) 62.7218i 3.26517i
\(370\) −7.24377 8.39024i −0.376586 0.436188i
\(371\) −1.76334 + 0.122500i −0.0915483 + 0.00635987i
\(372\) 27.4403 + 4.04625i 1.42271 + 0.209788i
\(373\) 0.781051i 0.0404413i 0.999796 + 0.0202206i \(0.00643687\pi\)
−0.999796 + 0.0202206i \(0.993563\pi\)
\(374\) 17.7117 + 20.5149i 0.915851 + 1.06080i
\(375\) 2.99734i 0.154782i
\(376\) 18.3192 + 28.8468i 0.944742 + 1.48766i
\(377\) 8.76218i 0.451275i
\(378\) 23.7549 23.5731i 1.22182 1.21247i
\(379\) 4.53381 0.232886 0.116443 0.993197i \(-0.462851\pi\)
0.116443 + 0.993197i \(0.462851\pi\)
\(380\) −10.3687 1.52894i −0.531905 0.0784328i
\(381\) −11.3997 −0.584023
\(382\) 7.79519 + 9.02893i 0.398837 + 0.461960i
\(383\) −36.0555 −1.84235 −0.921176 0.389147i \(-0.872770\pi\)
−0.921176 + 0.389147i \(0.872770\pi\)
\(384\) −32.6552 + 9.14293i −1.66643 + 0.466573i
\(385\) 0.894251 + 12.8725i 0.0455752 + 0.656041i
\(386\) −27.4398 + 23.6903i −1.39665 + 1.20581i
\(387\) −16.5369 −0.840619
\(388\) 15.5339 + 2.29057i 0.788615 + 0.116286i
\(389\) 21.1691i 1.07332i −0.843800 0.536658i \(-0.819687\pi\)
0.843800 0.536658i \(-0.180313\pi\)
\(390\) −6.72581 7.79030i −0.340574 0.394477i
\(391\) 0.448449 0.0226791
\(392\) 12.8231 + 15.0854i 0.647663 + 0.761927i
\(393\) −23.0228 −1.16135
\(394\) −1.65179 1.91322i −0.0832161 0.0963867i
\(395\) 11.8804i 0.597766i
\(396\) −8.51482 + 57.7447i −0.427886 + 2.90178i
\(397\) 14.1445 0.709891 0.354946 0.934887i \(-0.384499\pi\)
0.354946 + 0.934887i \(0.384499\pi\)
\(398\) 23.8902 20.6258i 1.19751 1.03388i
\(399\) 2.88008 + 41.4578i 0.144184 + 2.07549i
\(400\) −3.82975 1.15455i −0.191488 0.0577274i
\(401\) 17.8168 0.889729 0.444865 0.895598i \(-0.353252\pi\)
0.444865 + 0.895598i \(0.353252\pi\)
\(402\) 7.14037 + 8.27048i 0.356130 + 0.412494i
\(403\) −11.2342 −0.559616
\(404\) −3.18183 + 21.5781i −0.158302 + 1.07355i
\(405\) 8.85669 0.440092
\(406\) 9.58462 9.51125i 0.475677 0.472035i
\(407\) 38.2264i 1.89481i
\(408\) 17.8591 + 28.1223i 0.884159 + 1.39226i
\(409\) 32.5292i 1.60846i −0.594315 0.804232i \(-0.702577\pi\)
0.594315 0.804232i \(-0.297423\pi\)
\(410\) −9.68687 11.2200i −0.478400 0.554117i
\(411\) 50.8766i 2.50956i
\(412\) 4.61566 31.3018i 0.227397 1.54213i
\(413\) 3.63024 0.252193i 0.178632 0.0124096i
\(414\) 0.631139 + 0.731029i 0.0310188 + 0.0359281i
\(415\) 5.52348i 0.271137i
\(416\) 12.5445 5.59293i 0.615046 0.274216i
\(417\) −7.63116 −0.373699
\(418\) −23.6202 27.3586i −1.15530 1.33815i
\(419\) 34.4793i 1.68443i 0.539146 + 0.842213i \(0.318747\pi\)
−0.539146 + 0.842213i \(0.681253\pi\)
\(420\) −1.22072 + 15.8134i −0.0595652 + 0.771614i
\(421\) 12.2635i 0.597688i 0.954302 + 0.298844i \(0.0966010\pi\)
−0.954302 + 0.298844i \(0.903399\pi\)
\(422\) 9.18957 7.93388i 0.447341 0.386215i
\(423\) 72.2972 3.51521
\(424\) 1.59516 1.01301i 0.0774679 0.0491962i
\(425\) 3.92955i 0.190611i
\(426\) −30.2788 + 26.1414i −1.46701 + 1.26656i
\(427\) −0.216011 3.10940i −0.0104535 0.150475i
\(428\) 1.90647 12.9291i 0.0921529 0.624950i
\(429\) 35.4930i 1.71362i
\(430\) 2.95821 2.55399i 0.142658 0.123164i
\(431\) 21.7718i 1.04871i −0.851499 0.524357i \(-0.824306\pi\)
0.851499 0.524357i \(-0.175694\pi\)
\(432\) −10.3265 + 34.2541i −0.496835 + 1.64805i
\(433\) 26.1597i 1.25715i 0.777747 + 0.628577i \(0.216362\pi\)
−0.777747 + 0.628577i \(0.783638\pi\)
\(434\) 12.1946 + 12.2887i 0.585360 + 0.589875i
\(435\) 10.8168 0.518627
\(436\) 21.6279 + 3.18918i 1.03579 + 0.152734i
\(437\) −0.598049 −0.0286086
\(438\) 18.0519 15.5852i 0.862553 0.744691i
\(439\) 29.5333 1.40955 0.704775 0.709431i \(-0.251048\pi\)
0.704775 + 0.709431i \(0.251048\pi\)
\(440\) −7.39501 11.6447i −0.352543 0.555140i
\(441\) 41.4860 5.79202i 1.97552 0.275811i
\(442\) −8.81763 10.2132i −0.419412 0.485792i
\(443\) −21.7915 −1.03535 −0.517673 0.855579i \(-0.673202\pi\)
−0.517673 + 0.855579i \(0.673202\pi\)
\(444\) 6.85431 46.4837i 0.325291 2.20602i
\(445\) 6.21826i 0.294774i
\(446\) −15.0249 + 12.9718i −0.711449 + 0.614234i
\(447\) 41.3407 1.95535
\(448\) −19.7348 7.65091i −0.932383 0.361471i
\(449\) −1.75711 −0.0829231 −0.0414615 0.999140i \(-0.513201\pi\)
−0.0414615 + 0.999140i \(0.513201\pi\)
\(450\) −6.40567 + 5.53038i −0.301966 + 0.260705i
\(451\) 51.1189i 2.40709i
\(452\) 1.08535 7.36048i 0.0510506 0.346208i
\(453\) −0.384781 −0.0180786
\(454\) 27.6390 + 32.0134i 1.29716 + 1.50246i
\(455\) −0.445195 6.40844i −0.0208711 0.300432i
\(456\) −23.8168 37.5037i −1.11532 1.75627i
\(457\) 3.78856 0.177221 0.0886106 0.996066i \(-0.471757\pi\)
0.0886106 + 0.996066i \(0.471757\pi\)
\(458\) −9.54958 + 8.24470i −0.446223 + 0.385249i
\(459\) 35.1468 1.64051
\(460\) −0.225803 0.0332961i −0.0105281 0.00155244i
\(461\) 32.3541 1.50688 0.753439 0.657517i \(-0.228393\pi\)
0.753439 + 0.657517i \(0.228393\pi\)
\(462\) −38.8244 + 38.5272i −1.80628 + 1.79245i
\(463\) 31.2530i 1.45245i −0.687456 0.726226i \(-0.741273\pi\)
0.687456 0.726226i \(-0.258727\pi\)
\(464\) −4.16654 + 13.8208i −0.193427 + 0.641617i
\(465\) 13.8685i 0.643137i
\(466\) 0.604974 0.522309i 0.0280249 0.0241955i
\(467\) 22.6800i 1.04950i 0.851255 + 0.524752i \(0.175842\pi\)
−0.851255 + 0.524752i \(0.824158\pi\)
\(468\) 4.23903 28.7477i 0.195949 1.32886i
\(469\) 0.472636 + 6.80344i 0.0218243 + 0.314154i
\(470\) −12.9329 + 11.1657i −0.596550 + 0.515035i
\(471\) 39.4406i 1.81733i
\(472\) −3.28399 + 2.08551i −0.151158 + 0.0959934i
\(473\) 13.4777 0.619708
\(474\) −38.1184 + 32.9098i −1.75084 + 1.51160i
\(475\) 5.24043i 0.240447i
\(476\) −1.60038 + 20.7316i −0.0733535 + 0.950230i
\(477\) 3.99787i 0.183050i
\(478\) 7.86608 + 9.11104i 0.359786 + 0.416729i
\(479\) 12.8639 0.587765 0.293883 0.955842i \(-0.405053\pi\)
0.293883 + 0.955842i \(0.405053\pi\)
\(480\) −6.90442 15.4861i −0.315142 0.706839i
\(481\) 19.0307i 0.867723i
\(482\) 2.01032 + 2.32849i 0.0915675 + 0.106060i
\(483\) 0.0627202 + 0.902838i 0.00285387 + 0.0410805i
\(484\) 3.73032 25.2978i 0.169560 1.14990i
\(485\) 7.85094i 0.356493i
\(486\) −0.264421 0.306271i −0.0119944 0.0138927i
\(487\) 20.3133i 0.920483i 0.887794 + 0.460241i \(0.152237\pi\)
−0.887794 + 0.460241i \(0.847763\pi\)
\(488\) 1.78630 + 2.81283i 0.0808620 + 0.127331i
\(489\) 0.474370i 0.0214518i
\(490\) −6.52669 + 7.44327i −0.294846 + 0.336253i
\(491\) 16.4582 0.742746 0.371373 0.928484i \(-0.378887\pi\)
0.371373 + 0.928484i \(0.378887\pi\)
\(492\) 9.16606 62.1611i 0.413238 2.80244i
\(493\) 14.1810 0.638680
\(494\) 11.7591 + 13.6202i 0.529068 + 0.612804i
\(495\) −29.1845 −1.31175
\(496\) −17.7200 5.34202i −0.795653 0.239864i
\(497\) −24.9079 + 1.73035i −1.11727 + 0.0776170i
\(498\) 17.7222 15.3006i 0.794151 0.685636i
\(499\) 18.7483 0.839291 0.419645 0.907688i \(-0.362154\pi\)
0.419645 + 0.907688i \(0.362154\pi\)
\(500\) 0.291758 1.97860i 0.0130478 0.0884859i
\(501\) 50.0872i 2.23773i
\(502\) −8.70298 10.0804i −0.388433 0.449910i
\(503\) 19.5629 0.872269 0.436134 0.899882i \(-0.356347\pi\)
0.436134 + 0.899882i \(0.356347\pi\)
\(504\) −36.0474 + 26.5684i −1.60568 + 1.18345i
\(505\) −10.9057 −0.485298
\(506\) −0.514384 0.595795i −0.0228672 0.0264863i
\(507\) 21.2956i 0.945769i
\(508\) 7.52515 + 1.10963i 0.333875 + 0.0492320i
\(509\) −19.9845 −0.885797 −0.442898 0.896572i \(-0.646050\pi\)
−0.442898 + 0.896572i \(0.646050\pi\)
\(510\) −12.6081 + 10.8853i −0.558295 + 0.482008i
\(511\) 14.8498 1.03162i 0.656917 0.0456361i
\(512\) 22.4464 2.85680i 0.991998 0.126254i
\(513\) −46.8715 −2.06943
\(514\) −4.10466 4.75430i −0.181049 0.209703i
\(515\) 15.8202 0.697119
\(516\) 16.3891 + 2.41668i 0.721489 + 0.106388i
\(517\) −58.9229 −2.59143
\(518\) 20.8169 20.6576i 0.914643 0.907641i
\(519\) 15.5692i 0.683411i
\(520\) 3.68154 + 5.79722i 0.161446 + 0.254225i
\(521\) 1.35111i 0.0591932i −0.999562 0.0295966i \(-0.990578\pi\)
0.999562 0.0295966i \(-0.00942226\pi\)
\(522\) 19.9581 + 23.1168i 0.873541 + 1.01180i
\(523\) 28.1452i 1.23071i −0.788252 0.615353i \(-0.789014\pi\)
0.788252 0.615353i \(-0.210986\pi\)
\(524\) 15.1978 + 2.24102i 0.663921 + 0.0978994i
\(525\) −7.91115 + 0.549588i −0.345271 + 0.0239860i
\(526\) 12.5917 + 14.5846i 0.549025 + 0.635919i
\(527\) 18.1818i 0.792012i
\(528\) 16.8774 55.9841i 0.734495 2.43640i
\(529\) 22.9870 0.999434
\(530\) 0.617438 + 0.715160i 0.0268198 + 0.0310645i
\(531\) 8.23051i 0.357174i
\(532\) 2.13426 27.6475i 0.0925320 1.19867i
\(533\) 25.4491i 1.10232i
\(534\) −19.9515 + 17.2252i −0.863384 + 0.745408i
\(535\) 6.53444 0.282508
\(536\) −3.90847 6.15455i −0.168820 0.265836i
\(537\) 51.9360i 2.24121i
\(538\) −10.9950 + 9.49262i −0.474028 + 0.409256i
\(539\) −33.8115 + 4.72055i −1.45636 + 0.203329i
\(540\) −17.6971 2.60954i −0.761560 0.112297i
\(541\) 0.0636523i 0.00273663i −0.999999 0.00136831i \(-0.999564\pi\)
0.999999 0.00136831i \(-0.000435548\pi\)
\(542\) −2.86095 + 2.47002i −0.122888 + 0.106096i
\(543\) 63.1194i 2.70871i
\(544\) −9.05179 20.3025i −0.388092 0.870461i
\(545\) 10.9309i 0.468229i
\(546\) 19.3284 19.1804i 0.827179 0.820847i
\(547\) 26.6632 1.14004 0.570018 0.821632i \(-0.306936\pi\)
0.570018 + 0.821632i \(0.306936\pi\)
\(548\) −4.95227 + 33.5847i −0.211551 + 1.43467i
\(549\) 7.04966 0.300872
\(550\) 5.22068 4.50731i 0.222611 0.192192i
\(551\) −18.9117 −0.805665
\(552\) −0.518665 0.816727i −0.0220759 0.0347622i
\(553\) −31.3569 + 2.17837i −1.33343 + 0.0926336i
\(554\) −26.0050 30.1208i −1.10485 1.27971i
\(555\) 23.4931 0.997228
\(556\) 5.03748 + 0.742809i 0.213637 + 0.0315021i
\(557\) 9.81678i 0.415950i 0.978134 + 0.207975i \(0.0666873\pi\)
−0.978134 + 0.207975i \(0.933313\pi\)
\(558\) −29.6386 + 25.5887i −1.25470 + 1.08326i
\(559\) −6.70978 −0.283794
\(560\) 2.34508 10.3199i 0.0990978 0.436096i
\(561\) −57.4430 −2.42525
\(562\) 0.499734 0.431449i 0.0210800 0.0181996i
\(563\) 30.8680i 1.30093i 0.759535 + 0.650466i \(0.225426\pi\)
−0.759535 + 0.650466i \(0.774574\pi\)
\(564\) −71.6509 10.5654i −3.01705 0.444883i
\(565\) 3.72004 0.156503
\(566\) −9.98161 11.5614i −0.419558 0.485962i
\(567\) 1.62395 + 23.3763i 0.0681995 + 0.981711i
\(568\) 22.5322 14.3092i 0.945432 0.600400i
\(569\) 30.9000 1.29540 0.647698 0.761897i \(-0.275732\pi\)
0.647698 + 0.761897i \(0.275732\pi\)
\(570\) 16.8140 14.5165i 0.704263 0.608030i
\(571\) −37.5033 −1.56946 −0.784732 0.619835i \(-0.787199\pi\)
−0.784732 + 0.619835i \(0.787199\pi\)
\(572\) −3.45485 + 23.4296i −0.144455 + 0.979642i
\(573\) −25.2815 −1.05615
\(574\) 27.8378 27.6247i 1.16193 1.15303i
\(575\) 0.114122i 0.00475922i
\(576\) 20.3563 43.3288i 0.848178 1.80537i
\(577\) 17.4216i 0.725272i 0.931931 + 0.362636i \(0.118123\pi\)
−0.931931 + 0.362636i \(0.881877\pi\)
\(578\) 1.66842 1.44044i 0.0693969 0.0599143i
\(579\) 76.8330i 3.19307i
\(580\) −7.14040 1.05290i −0.296489 0.0437192i
\(581\) 14.5786 1.01278i 0.604822 0.0420171i
\(582\) −25.1899 + 21.7479i −1.04416 + 0.901479i
\(583\) 3.25830i 0.134945i
\(584\) −13.4335 + 8.53097i −0.555881 + 0.353014i
\(585\) 14.5293 0.600711
\(586\) 7.86286 6.78845i 0.324812 0.280428i
\(587\) 12.4270i 0.512918i −0.966555 0.256459i \(-0.917444\pi\)
0.966555 0.256459i \(-0.0825558\pi\)
\(588\) −41.9615 0.322441i −1.73046 0.0132972i
\(589\) 24.2471i 0.999086i
\(590\) −1.27113 1.47232i −0.0523317 0.0606143i
\(591\) 5.35713 0.220363
\(592\) −9.04934 + 30.0176i −0.371926 + 1.23372i
\(593\) 13.7257i 0.563646i 0.959466 + 0.281823i \(0.0909391\pi\)
−0.959466 + 0.281823i \(0.909061\pi\)
\(594\) −40.3143 46.6948i −1.65412 1.91591i
\(595\) −10.3716 + 0.720518i −0.425195 + 0.0295384i
\(596\) −27.2898 4.02406i −1.11783 0.164832i
\(597\) 66.8940i 2.73779i
\(598\) 0.256082 + 0.296612i 0.0104720 + 0.0121293i
\(599\) 27.7947i 1.13566i 0.823146 + 0.567829i \(0.192217\pi\)
−0.823146 + 0.567829i \(0.807783\pi\)
\(600\) 7.15660 4.54482i 0.292167 0.185542i
\(601\) 38.9855i 1.59025i −0.606443 0.795127i \(-0.707404\pi\)
0.606443 0.795127i \(-0.292596\pi\)
\(602\) 7.28339 + 7.33957i 0.296849 + 0.299139i
\(603\) −15.4248 −0.628148
\(604\) 0.254002 + 0.0374542i 0.0103352 + 0.00152399i
\(605\) 12.7857 0.519811
\(606\) −30.2100 34.9913i −1.22720 1.42142i
\(607\) −11.7981 −0.478872 −0.239436 0.970912i \(-0.576962\pi\)
−0.239436 + 0.970912i \(0.576962\pi\)
\(608\) 12.0714 + 27.0752i 0.489560 + 1.09805i
\(609\) 1.98336 + 28.5498i 0.0803697 + 1.15690i
\(610\) −1.26108 + 1.08876i −0.0510597 + 0.0440827i
\(611\) 29.3342 1.18674
\(612\) −46.5262 6.86058i −1.88071 0.277323i
\(613\) 13.4628i 0.543756i −0.962332 0.271878i \(-0.912355\pi\)
0.962332 0.271878i \(-0.0876447\pi\)
\(614\) −4.69559 5.43876i −0.189498 0.219490i
\(615\) 31.4166 1.26684
\(616\) 29.3790 21.6535i 1.18371 0.872443i
\(617\) −15.2924 −0.615650 −0.307825 0.951443i \(-0.599601\pi\)
−0.307825 + 0.951443i \(0.599601\pi\)
\(618\) 43.8234 + 50.7594i 1.76284 + 2.04184i
\(619\) 3.76548i 0.151347i 0.997133 + 0.0756736i \(0.0241107\pi\)
−0.997133 + 0.0756736i \(0.975889\pi\)
\(620\) 1.34995 9.15488i 0.0542151 0.367669i
\(621\) −1.02073 −0.0409606
\(622\) −19.0883 + 16.4800i −0.765372 + 0.660789i
\(623\) −16.4124 + 1.14017i −0.657550 + 0.0456801i
\(624\) −8.40227 + 27.8712i −0.336360 + 1.11574i
\(625\) 1.00000 0.0400000
\(626\) 3.27169 + 3.78950i 0.130763 + 0.151459i
\(627\) 76.6056 3.05933
\(628\) 3.83911 26.0356i 0.153197 1.03893i
\(629\) 30.7998 1.22807
\(630\) −15.7714 15.8930i −0.628346 0.633193i
\(631\) 21.1777i 0.843070i −0.906812 0.421535i \(-0.861492\pi\)
0.906812 0.421535i \(-0.138508\pi\)
\(632\) 28.3662 18.0140i 1.12835 0.716560i
\(633\) 25.7313i 1.02273i
\(634\) 4.49487 + 5.20627i 0.178514 + 0.206768i
\(635\) 3.80326i 0.150928i
\(636\) −0.584241 + 3.96213i −0.0231667 + 0.157109i
\(637\) 16.8327 2.35009i 0.666937 0.0931138i
\(638\) −16.2660 18.8404i −0.643978 0.745900i
\(639\) 56.4714i 2.23397i
\(640\) 3.05035 + 10.8947i 0.120576 + 0.430652i
\(641\) 29.5569 1.16743 0.583713 0.811960i \(-0.301599\pi\)
0.583713 + 0.811960i \(0.301599\pi\)
\(642\) 18.1011 + 20.9659i 0.714392 + 0.827458i
\(643\) 19.8063i 0.781085i −0.920585 0.390543i \(-0.872287\pi\)
0.920585 0.390543i \(-0.127713\pi\)
\(644\) 0.0464784 0.602086i 0.00183150 0.0237255i
\(645\) 8.28315i 0.326149i
\(646\) 22.0434 19.0314i 0.867288 0.748779i
\(647\) 12.4755 0.490461 0.245231 0.969465i \(-0.421136\pi\)
0.245231 + 0.969465i \(0.421136\pi\)
\(648\) −13.4293 21.1467i −0.527552 0.830720i
\(649\) 6.70794i 0.263310i
\(650\) −2.59907 + 2.24393i −0.101944 + 0.0880140i
\(651\) −36.6044 + 2.54291i −1.43464 + 0.0996646i
\(652\) 0.0461747 0.313141i 0.00180834 0.0122636i
\(653\) 9.99757i 0.391235i −0.980680 0.195618i \(-0.937329\pi\)
0.980680 0.195618i \(-0.0626712\pi\)
\(654\) −35.0721 + 30.2797i −1.37143 + 1.18403i
\(655\) 7.68109i 0.300125i
\(656\) −12.1014 + 40.1416i −0.472480 + 1.56727i
\(657\) 33.6676i 1.31350i
\(658\) −31.8420 32.0876i −1.24133 1.25091i
\(659\) 27.2870 1.06295 0.531475 0.847074i \(-0.321638\pi\)
0.531475 + 0.847074i \(0.321638\pi\)
\(660\) 28.9236 + 4.26497i 1.12585 + 0.166014i
\(661\) −38.2384 −1.48730 −0.743650 0.668569i \(-0.766907\pi\)
−0.743650 + 0.668569i \(0.766907\pi\)
\(662\) −10.0502 + 8.67691i −0.390612 + 0.337238i
\(663\) 28.5975 1.11063
\(664\) −13.1881 + 8.37517i −0.511799 + 0.325020i
\(665\) 13.8315 0.960878i 0.536364 0.0372613i
\(666\) 43.3471 + 50.2076i 1.67967 + 1.94551i
\(667\) −0.411845 −0.0159467
\(668\) −4.87543 + 33.0636i −0.188636 + 1.27927i
\(669\) 42.0705i 1.62654i
\(670\) 2.75927 2.38224i 0.106600 0.0920338i
\(671\) −5.74554 −0.221804
\(672\) 39.6078 21.0630i 1.52790 0.812521i
\(673\) 8.47579 0.326718 0.163359 0.986567i \(-0.447767\pi\)
0.163359 + 0.986567i \(0.447767\pi\)
\(674\) 21.1470 18.2574i 0.814552 0.703249i
\(675\) 8.94421i 0.344263i
\(676\) −2.07289 + 14.0576i −0.0797264 + 0.540678i
\(677\) 23.2065 0.891897 0.445948 0.895059i \(-0.352866\pi\)
0.445948 + 0.895059i \(0.352866\pi\)
\(678\) 10.3049 + 11.9358i 0.395756 + 0.458393i
\(679\) −20.7217 + 1.43954i −0.795225 + 0.0552444i
\(680\) 9.38241 5.95833i 0.359799 0.228491i
\(681\) −89.6394 −3.43499
\(682\) 24.1558 20.8550i 0.924972 0.798581i
\(683\) −25.7680 −0.985986 −0.492993 0.870033i \(-0.664097\pi\)
−0.492993 + 0.870033i \(0.664097\pi\)
\(684\) 62.0470 + 9.14923i 2.37243 + 0.349830i
\(685\) −16.9739 −0.648540
\(686\) −20.8424 15.8617i −0.795767 0.605603i
\(687\) 26.7394i 1.02017i
\(688\) −10.5835 3.19059i −0.403493 0.121640i
\(689\) 1.62212i 0.0617978i
\(690\) 0.366164 0.316130i 0.0139396 0.0120349i
\(691\) 24.5498i 0.933917i 0.884279 + 0.466958i \(0.154650\pi\)
−0.884279 + 0.466958i \(0.845350\pi\)
\(692\) 1.51549 10.2775i 0.0576102 0.390693i
\(693\) −5.35124 77.0294i −0.203277 2.92610i
\(694\) −31.9096 + 27.5494i −1.21127 + 1.04576i
\(695\) 2.54598i 0.0965744i
\(696\) −16.4014 25.8268i −0.621693 0.978962i
\(697\) 41.1877 1.56009
\(698\) −16.8054 + 14.5091i −0.636095 + 0.549177i
\(699\) 1.69396i 0.0640715i
\(700\) 5.27581 + 0.407269i 0.199407 + 0.0153933i
\(701\) 2.33837i 0.0883188i −0.999024 0.0441594i \(-0.985939\pi\)
0.999024 0.0441594i \(-0.0140610\pi\)
\(702\) 20.0701 + 23.2466i 0.757498 + 0.877387i
\(703\) −41.0745 −1.54915
\(704\) −16.5905 + 35.3134i −0.625280 + 1.33092i
\(705\) 36.2128i 1.36385i
\(706\) −9.44386 10.9385i −0.355424 0.411677i
\(707\) −1.99966 28.7845i −0.0752049 1.08255i
\(708\) 1.20279 8.15693i 0.0452037 0.306556i
\(709\) 36.8318i 1.38325i 0.722257 + 0.691624i \(0.243105\pi\)
−0.722257 + 0.691624i \(0.756895\pi\)
\(710\) 8.72154 + 10.1019i 0.327314 + 0.379117i
\(711\) 71.0927i 2.66618i
\(712\) 14.8470 9.42867i 0.556417 0.353354i
\(713\) 0.528036i 0.0197751i
\(714\) −31.0423 31.2817i −1.16173 1.17069i
\(715\) −11.8415 −0.442847
\(716\) −5.05540 + 34.2840i −0.188929 + 1.28125i
\(717\) −25.5114 −0.952742
\(718\) −21.6960 25.1298i −0.809688 0.937837i
\(719\) 33.8925 1.26398 0.631989 0.774978i \(-0.282239\pi\)
0.631989 + 0.774978i \(0.282239\pi\)
\(720\) 22.9174 + 6.90887i 0.854082 + 0.257478i
\(721\) 2.90076 + 41.7556i 0.108030 + 1.55506i
\(722\) −9.05830 + 7.82055i −0.337115 + 0.291051i
\(723\) −6.51991 −0.242478
\(724\) 6.14397 41.6664i 0.228339 1.54852i
\(725\) 3.60881i 0.134028i
\(726\) 35.4176 + 41.0231i 1.31447 + 1.52251i
\(727\) −4.28102 −0.158774 −0.0793871 0.996844i \(-0.525296\pi\)
−0.0793871 + 0.996844i \(0.525296\pi\)
\(728\) −14.6261 + 10.7800i −0.542078 + 0.399533i
\(729\) 27.4276 1.01584
\(730\) −5.19969 6.02264i −0.192449 0.222908i
\(731\) 10.8593i 0.401647i
\(732\) −6.98664 1.03023i −0.258234 0.0380782i
\(733\) −38.0426 −1.40513 −0.702567 0.711618i \(-0.747963\pi\)
−0.702567 + 0.711618i \(0.747963\pi\)
\(734\) 23.0151 19.8702i 0.849501 0.733422i
\(735\) −2.90116 20.7798i −0.107011 0.766476i
\(736\) 0.262882 + 0.589624i 0.00968996 + 0.0217338i
\(737\) 12.5714 0.463073
\(738\) 57.9667 + 67.1411i 2.13378 + 2.47150i
\(739\) 9.93398 0.365427 0.182714 0.983166i \(-0.441512\pi\)
0.182714 + 0.983166i \(0.441512\pi\)
\(740\) −15.5083 2.28680i −0.570096 0.0840644i
\(741\) −38.1374 −1.40101
\(742\) −1.77437 + 1.76079i −0.0651393 + 0.0646406i
\(743\) 1.68905i 0.0619651i −0.999520 0.0309826i \(-0.990136\pi\)
0.999520 0.0309826i \(-0.00986363\pi\)
\(744\) 33.1132 21.0286i 1.21399 0.770947i
\(745\) 13.7925i 0.505316i
\(746\) 0.721837 + 0.836082i 0.0264283 + 0.0306111i
\(747\) 33.0527i 1.20934i
\(748\) 37.9193 + 5.59144i 1.38647 + 0.204443i
\(749\) 1.19815 + 17.2469i 0.0437793 + 0.630189i
\(750\) 2.77010 + 3.20852i 0.101150 + 0.117159i
\(751\) 36.9451i 1.34815i 0.738664 + 0.674073i \(0.235457\pi\)
−0.738664 + 0.674073i \(0.764543\pi\)
\(752\) 46.2698 + 13.9488i 1.68728 + 0.508662i
\(753\) 28.2257 1.02860
\(754\) 8.09789 + 9.37954i 0.294908 + 0.341583i
\(755\) 0.128374i 0.00467202i
\(756\) 3.64270 47.1879i 0.132484 1.71621i
\(757\) 45.8391i 1.66605i 0.553235 + 0.833025i \(0.313393\pi\)
−0.553235 + 0.833025i \(0.686607\pi\)
\(758\) 4.85325 4.19009i 0.176278 0.152191i
\(759\) 1.66826 0.0605540
\(760\) −12.5123 + 7.94599i −0.453869 + 0.288231i
\(761\) 19.9588i 0.723506i 0.932274 + 0.361753i \(0.117822\pi\)
−0.932274 + 0.361753i \(0.882178\pi\)
\(762\) −12.2029 + 10.5354i −0.442063 + 0.381658i
\(763\) −28.8509 + 2.00428i −1.04447 + 0.0725597i
\(764\) 16.6888 + 2.46088i 0.603781 + 0.0890314i
\(765\) 23.5146i 0.850174i
\(766\) −38.5959 + 33.3220i −1.39453 + 1.20397i
\(767\) 3.33949i 0.120582i
\(768\) −26.5063 + 39.9667i −0.956463 + 1.44217i
\(769\) 13.9529i 0.503153i −0.967837 0.251576i \(-0.919051\pi\)
0.967837 0.251576i \(-0.0809490\pi\)
\(770\) 12.8538 + 12.9530i 0.463219 + 0.466792i
\(771\) 13.3123 0.479431
\(772\) −7.47884 + 50.7190i −0.269169 + 1.82542i
\(773\) 33.8775 1.21849 0.609245 0.792982i \(-0.291473\pi\)
0.609245 + 0.792982i \(0.291473\pi\)
\(774\) −17.7021 + 15.2832i −0.636288 + 0.549344i
\(775\) 4.62694 0.166205
\(776\) 18.7453 11.9043i 0.672917 0.427338i
\(777\) 4.30767 + 62.0076i 0.154537 + 2.22451i
\(778\) −19.5642 22.6606i −0.701410 0.812422i
\(779\) −54.9276 −1.96798
\(780\) −14.3994