Properties

Label 720.2.u.a.179.8
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 179.8
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.23687 + 0.685679i) q^{2} +(1.05969 - 1.69619i) q^{4} +(-0.419806 + 2.19631i) q^{5} -0.263783i q^{7} +(-0.147653 + 2.82457i) q^{8} +O(q^{10})\) \(q+(-1.23687 + 0.685679i) q^{2} +(1.05969 - 1.69619i) q^{4} +(-0.419806 + 2.19631i) q^{5} -0.263783i q^{7} +(-0.147653 + 2.82457i) q^{8} +(-0.986717 - 3.00440i) q^{10} +(-0.913594 + 0.913594i) q^{11} +(-1.49018 + 1.49018i) q^{13} +(0.180870 + 0.326265i) q^{14} +(-1.75412 - 3.59487i) q^{16} -2.90538 q^{17} +(-0.296217 + 0.296217i) q^{19} +(3.28049 + 3.03947i) q^{20} +(0.503563 - 1.75643i) q^{22} +3.14640 q^{23} +(-4.64753 - 1.84404i) q^{25} +(0.821369 - 2.86493i) q^{26} +(-0.447426 - 0.279528i) q^{28} +(-2.43765 + 2.43765i) q^{29} +2.53546i q^{31} +(4.63454 + 3.24361i) q^{32} +(3.59358 - 1.99216i) q^{34} +(0.579348 + 0.110738i) q^{35} +(-1.53556 - 1.53556i) q^{37} +(0.163272 - 0.569491i) q^{38} +(-6.14164 - 1.51006i) q^{40} -10.7792 q^{41} +(-4.51269 + 4.51269i) q^{43} +(0.581504 + 2.51775i) q^{44} +(-3.89169 + 2.15742i) q^{46} -6.67809i q^{47} +6.93042 q^{49} +(7.01280 - 0.905871i) q^{50} +(0.948500 + 4.10674i) q^{52} +(-2.95356 + 2.95356i) q^{53} +(-1.62300 - 2.39006i) q^{55} +(0.745073 + 0.0389483i) q^{56} +(1.34361 - 4.68649i) q^{58} +(-9.76773 + 9.76773i) q^{59} +(-1.02388 - 1.02388i) q^{61} +(-1.73851 - 3.13603i) q^{62} +(-7.95640 - 0.834111i) q^{64} +(-2.64730 - 3.89847i) q^{65} +(3.67191 + 3.67191i) q^{67} +(-3.07880 + 4.92808i) q^{68} +(-0.792508 + 0.260279i) q^{70} -7.85546i q^{71} -12.4323 q^{73} +(2.95219 + 0.846384i) q^{74} +(0.188543 + 0.816337i) q^{76} +(0.240990 + 0.240990i) q^{77} +10.7196i q^{79} +(8.63182 - 2.34344i) q^{80} +(13.3324 - 7.39107i) q^{82} +(3.50410 - 3.50410i) q^{83} +(1.21970 - 6.38111i) q^{85} +(2.48735 - 8.67586i) q^{86} +(-2.44561 - 2.71540i) q^{88} -13.2383 q^{89} +(0.393083 + 0.393083i) q^{91} +(3.33421 - 5.33690i) q^{92} +(4.57903 + 8.25992i) q^{94} +(-0.526229 - 0.774936i) q^{95} -11.1057i q^{97} +(-8.57202 + 4.75204i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23687 + 0.685679i −0.874598 + 0.484848i
\(3\) 0 0
\(4\) 1.05969 1.69619i 0.529844 0.848095i
\(5\) −0.419806 + 2.19631i −0.187743 + 0.982218i
\(6\) 0 0
\(7\) 0.263783i 0.0997006i −0.998757 0.0498503i \(-0.984126\pi\)
0.998757 0.0498503i \(-0.0158744\pi\)
\(8\) −0.147653 + 2.82457i −0.0522031 + 0.998636i
\(9\) 0 0
\(10\) −0.986717 3.00440i −0.312027 0.950073i
\(11\) −0.913594 + 0.913594i −0.275459 + 0.275459i −0.831293 0.555834i \(-0.812399\pi\)
0.555834 + 0.831293i \(0.312399\pi\)
\(12\) 0 0
\(13\) −1.49018 + 1.49018i −0.413300 + 0.413300i −0.882887 0.469586i \(-0.844403\pi\)
0.469586 + 0.882887i \(0.344403\pi\)
\(14\) 0.180870 + 0.326265i 0.0483397 + 0.0871979i
\(15\) 0 0
\(16\) −1.75412 3.59487i −0.438531 0.898716i
\(17\) −2.90538 −0.704659 −0.352329 0.935876i \(-0.614610\pi\)
−0.352329 + 0.935876i \(0.614610\pi\)
\(18\) 0 0
\(19\) −0.296217 + 0.296217i −0.0679568 + 0.0679568i −0.740268 0.672312i \(-0.765302\pi\)
0.672312 + 0.740268i \(0.265302\pi\)
\(20\) 3.28049 + 3.03947i 0.733540 + 0.679646i
\(21\) 0 0
\(22\) 0.503563 1.75643i 0.107360 0.374472i
\(23\) 3.14640 0.656070 0.328035 0.944666i \(-0.393614\pi\)
0.328035 + 0.944666i \(0.393614\pi\)
\(24\) 0 0
\(25\) −4.64753 1.84404i −0.929505 0.368809i
\(26\) 0.821369 2.86493i 0.161084 0.561860i
\(27\) 0 0
\(28\) −0.447426 0.279528i −0.0845556 0.0528258i
\(29\) −2.43765 + 2.43765i −0.452660 + 0.452660i −0.896236 0.443577i \(-0.853709\pi\)
0.443577 + 0.896236i \(0.353709\pi\)
\(30\) 0 0
\(31\) 2.53546i 0.455382i 0.973733 + 0.227691i \(0.0731177\pi\)
−0.973733 + 0.227691i \(0.926882\pi\)
\(32\) 4.63454 + 3.24361i 0.819279 + 0.573395i
\(33\) 0 0
\(34\) 3.59358 1.99216i 0.616293 0.341653i
\(35\) 0.579348 + 0.110738i 0.0979277 + 0.0187181i
\(36\) 0 0
\(37\) −1.53556 1.53556i −0.252444 0.252444i 0.569528 0.821972i \(-0.307126\pi\)
−0.821972 + 0.569528i \(0.807126\pi\)
\(38\) 0.163272 0.569491i 0.0264861 0.0923836i
\(39\) 0 0
\(40\) −6.14164 1.51006i −0.971078 0.238762i
\(41\) −10.7792 −1.68343 −0.841713 0.539925i \(-0.818453\pi\)
−0.841713 + 0.539925i \(0.818453\pi\)
\(42\) 0 0
\(43\) −4.51269 + 4.51269i −0.688178 + 0.688178i −0.961829 0.273651i \(-0.911769\pi\)
0.273651 + 0.961829i \(0.411769\pi\)
\(44\) 0.581504 + 2.51775i 0.0876651 + 0.379566i
\(45\) 0 0
\(46\) −3.89169 + 2.15742i −0.573798 + 0.318095i
\(47\) 6.67809i 0.974100i −0.873374 0.487050i \(-0.838073\pi\)
0.873374 0.487050i \(-0.161927\pi\)
\(48\) 0 0
\(49\) 6.93042 0.990060
\(50\) 7.01280 0.905871i 0.991760 0.128109i
\(51\) 0 0
\(52\) 0.948500 + 4.10674i 0.131533 + 0.569503i
\(53\) −2.95356 + 2.95356i −0.405703 + 0.405703i −0.880237 0.474534i \(-0.842617\pi\)
0.474534 + 0.880237i \(0.342617\pi\)
\(54\) 0 0
\(55\) −1.62300 2.39006i −0.218845 0.322276i
\(56\) 0.745073 + 0.0389483i 0.0995646 + 0.00520468i
\(57\) 0 0
\(58\) 1.34361 4.68649i 0.176424 0.615367i
\(59\) −9.76773 + 9.76773i −1.27165 + 1.27165i −0.326428 + 0.945222i \(0.605845\pi\)
−0.945222 + 0.326428i \(0.894155\pi\)
\(60\) 0 0
\(61\) −1.02388 1.02388i −0.131095 0.131095i 0.638515 0.769610i \(-0.279549\pi\)
−0.769610 + 0.638515i \(0.779549\pi\)
\(62\) −1.73851 3.13603i −0.220791 0.398277i
\(63\) 0 0
\(64\) −7.95640 0.834111i −0.994550 0.104264i
\(65\) −2.64730 3.89847i −0.328357 0.483545i
\(66\) 0 0
\(67\) 3.67191 + 3.67191i 0.448595 + 0.448595i 0.894887 0.446292i \(-0.147256\pi\)
−0.446292 + 0.894887i \(0.647256\pi\)
\(68\) −3.07880 + 4.92808i −0.373359 + 0.597618i
\(69\) 0 0
\(70\) −0.792508 + 0.260279i −0.0947228 + 0.0311093i
\(71\) 7.85546i 0.932272i −0.884713 0.466136i \(-0.845646\pi\)
0.884713 0.466136i \(-0.154354\pi\)
\(72\) 0 0
\(73\) −12.4323 −1.45509 −0.727543 0.686062i \(-0.759338\pi\)
−0.727543 + 0.686062i \(0.759338\pi\)
\(74\) 2.95219 + 0.846384i 0.343185 + 0.0983901i
\(75\) 0 0
\(76\) 0.188543 + 0.816337i 0.0216273 + 0.0936403i
\(77\) 0.240990 + 0.240990i 0.0274634 + 0.0274634i
\(78\) 0 0
\(79\) 10.7196i 1.20605i 0.797724 + 0.603023i \(0.206037\pi\)
−0.797724 + 0.603023i \(0.793963\pi\)
\(80\) 8.63182 2.34344i 0.965066 0.262005i
\(81\) 0 0
\(82\) 13.3324 7.39107i 1.47232 0.816207i
\(83\) 3.50410 3.50410i 0.384625 0.384625i −0.488140 0.872765i \(-0.662325\pi\)
0.872765 + 0.488140i \(0.162325\pi\)
\(84\) 0 0
\(85\) 1.21970 6.38111i 0.132295 0.692129i
\(86\) 2.48735 8.67586i 0.268217 0.935542i
\(87\) 0 0
\(88\) −2.44561 2.71540i −0.260703 0.289463i
\(89\) −13.2383 −1.40326 −0.701629 0.712542i \(-0.747544\pi\)
−0.701629 + 0.712542i \(0.747544\pi\)
\(90\) 0 0
\(91\) 0.393083 + 0.393083i 0.0412063 + 0.0412063i
\(92\) 3.33421 5.33690i 0.347615 0.556410i
\(93\) 0 0
\(94\) 4.57903 + 8.25992i 0.472291 + 0.851946i
\(95\) −0.526229 0.774936i −0.0539900 0.0795068i
\(96\) 0 0
\(97\) 11.1057i 1.12761i −0.825908 0.563804i \(-0.809337\pi\)
0.825908 0.563804i \(-0.190663\pi\)
\(98\) −8.57202 + 4.75204i −0.865905 + 0.480029i
\(99\) 0 0
\(100\) −8.05278 + 5.92898i −0.805278 + 0.592898i
\(101\) −0.625096 0.625096i −0.0621994 0.0621994i 0.675323 0.737522i \(-0.264004\pi\)
−0.737522 + 0.675323i \(0.764004\pi\)
\(102\) 0 0
\(103\) 7.47669i 0.736701i 0.929687 + 0.368350i \(0.120077\pi\)
−0.929687 + 0.368350i \(0.879923\pi\)
\(104\) −3.98908 4.42914i −0.391161 0.434312i
\(105\) 0 0
\(106\) 1.62797 5.67837i 0.158123 0.551532i
\(107\) −10.7929 10.7929i −1.04339 1.04339i −0.999015 0.0443705i \(-0.985872\pi\)
−0.0443705 0.999015i \(-0.514128\pi\)
\(108\) 0 0
\(109\) −0.260948 0.260948i −0.0249942 0.0249942i 0.694499 0.719493i \(-0.255626\pi\)
−0.719493 + 0.694499i \(0.755626\pi\)
\(110\) 3.64625 + 1.84334i 0.347657 + 0.175755i
\(111\) 0 0
\(112\) −0.948264 + 0.462707i −0.0896025 + 0.0437217i
\(113\) 3.88893 0.365839 0.182920 0.983128i \(-0.441445\pi\)
0.182920 + 0.983128i \(0.441445\pi\)
\(114\) 0 0
\(115\) −1.32088 + 6.91046i −0.123173 + 0.644404i
\(116\) 1.55157 + 6.71786i 0.144059 + 0.623738i
\(117\) 0 0
\(118\) 5.38387 18.7789i 0.495625 1.72874i
\(119\) 0.766390i 0.0702549i
\(120\) 0 0
\(121\) 9.33069i 0.848245i
\(122\) 1.96846 + 0.564353i 0.178216 + 0.0510942i
\(123\) 0 0
\(124\) 4.30063 + 2.68680i 0.386208 + 0.241282i
\(125\) 6.00115 9.43325i 0.536759 0.843736i
\(126\) 0 0
\(127\) 18.1176 1.60768 0.803840 0.594846i \(-0.202787\pi\)
0.803840 + 0.594846i \(0.202787\pi\)
\(128\) 10.4130 4.42385i 0.920384 0.391017i
\(129\) 0 0
\(130\) 5.94746 + 3.00670i 0.521627 + 0.263705i
\(131\) 14.0610 + 14.0610i 1.22851 + 1.22851i 0.964526 + 0.263988i \(0.0850378\pi\)
0.263988 + 0.964526i \(0.414962\pi\)
\(132\) 0 0
\(133\) 0.0781369 + 0.0781369i 0.00677533 + 0.00677533i
\(134\) −7.05942 2.02392i −0.609841 0.174840i
\(135\) 0 0
\(136\) 0.428988 8.20646i 0.0367854 0.703698i
\(137\) 10.3404i 0.883440i −0.897153 0.441720i \(-0.854368\pi\)
0.897153 0.441720i \(-0.145632\pi\)
\(138\) 0 0
\(139\) 11.8106 + 11.8106i 1.00176 + 1.00176i 0.999998 + 0.00176137i \(0.000560663\pi\)
0.00176137 + 0.999998i \(0.499439\pi\)
\(140\) 0.801760 0.865337i 0.0677611 0.0731344i
\(141\) 0 0
\(142\) 5.38633 + 9.71618i 0.452011 + 0.815363i
\(143\) 2.72283i 0.227695i
\(144\) 0 0
\(145\) −4.33048 6.37716i −0.359627 0.529594i
\(146\) 15.3771 8.52454i 1.27262 0.705496i
\(147\) 0 0
\(148\) −4.23181 + 0.977386i −0.347853 + 0.0803407i
\(149\) 5.72046 + 5.72046i 0.468639 + 0.468639i 0.901473 0.432835i \(-0.142487\pi\)
−0.432835 + 0.901473i \(0.642487\pi\)
\(150\) 0 0
\(151\) −14.9974 −1.22047 −0.610234 0.792221i \(-0.708925\pi\)
−0.610234 + 0.792221i \(0.708925\pi\)
\(152\) −0.792948 0.880422i −0.0643166 0.0714117i
\(153\) 0 0
\(154\) −0.463316 0.132831i −0.0373350 0.0107039i
\(155\) −5.56865 1.06440i −0.447285 0.0854948i
\(156\) 0 0
\(157\) 0.0261720 0.0261720i 0.00208875 0.00208875i −0.706062 0.708150i \(-0.749530\pi\)
0.708150 + 0.706062i \(0.249530\pi\)
\(158\) −7.35019 13.2587i −0.584750 1.05481i
\(159\) 0 0
\(160\) −9.06957 + 8.81719i −0.717013 + 0.697060i
\(161\) 0.829967i 0.0654106i
\(162\) 0 0
\(163\) 17.1126 + 17.1126i 1.34036 + 1.34036i 0.895700 + 0.444659i \(0.146675\pi\)
0.444659 + 0.895700i \(0.353325\pi\)
\(164\) −11.4226 + 18.2836i −0.891953 + 1.42771i
\(165\) 0 0
\(166\) −1.93142 + 6.73680i −0.149907 + 0.522877i
\(167\) 19.4611 1.50594 0.752971 0.658053i \(-0.228620\pi\)
0.752971 + 0.658053i \(0.228620\pi\)
\(168\) 0 0
\(169\) 8.55875i 0.658365i
\(170\) 2.86679 + 8.72892i 0.219873 + 0.669477i
\(171\) 0 0
\(172\) 2.87233 + 12.4364i 0.219013 + 0.948268i
\(173\) 11.3427 + 11.3427i 0.862367 + 0.862367i 0.991613 0.129245i \(-0.0412555\pi\)
−0.129245 + 0.991613i \(0.541256\pi\)
\(174\) 0 0
\(175\) −0.486428 + 1.22594i −0.0367705 + 0.0926722i
\(176\) 4.88680 + 1.68169i 0.368356 + 0.126762i
\(177\) 0 0
\(178\) 16.3741 9.07724i 1.22729 0.680368i
\(179\) 4.50621 + 4.50621i 0.336810 + 0.336810i 0.855165 0.518356i \(-0.173456\pi\)
−0.518356 + 0.855165i \(0.673456\pi\)
\(180\) 0 0
\(181\) 10.0971 10.0971i 0.750512 0.750512i −0.224062 0.974575i \(-0.571932\pi\)
0.974575 + 0.224062i \(0.0719320\pi\)
\(182\) −0.755721 0.216663i −0.0560178 0.0160601i
\(183\) 0 0
\(184\) −0.464575 + 8.88723i −0.0342489 + 0.655176i
\(185\) 4.01719 2.72792i 0.295350 0.200561i
\(186\) 0 0
\(187\) 2.65434 2.65434i 0.194104 0.194104i
\(188\) −11.3273 7.07669i −0.826129 0.516121i
\(189\) 0 0
\(190\) 1.18223 + 0.597670i 0.0857683 + 0.0433595i
\(191\) 23.8545 1.72605 0.863025 0.505161i \(-0.168567\pi\)
0.863025 + 0.505161i \(0.168567\pi\)
\(192\) 0 0
\(193\) 13.8585i 0.997560i 0.866729 + 0.498780i \(0.166218\pi\)
−0.866729 + 0.498780i \(0.833782\pi\)
\(194\) 7.61492 + 13.7362i 0.546719 + 0.986205i
\(195\) 0 0
\(196\) 7.34408 11.7553i 0.524577 0.839665i
\(197\) −11.9818 + 11.9818i −0.853664 + 0.853664i −0.990582 0.136918i \(-0.956280\pi\)
0.136918 + 0.990582i \(0.456280\pi\)
\(198\) 0 0
\(199\) −11.4336 −0.810507 −0.405253 0.914204i \(-0.632817\pi\)
−0.405253 + 0.914204i \(0.632817\pi\)
\(200\) 5.89485 12.8550i 0.416829 0.908985i
\(201\) 0 0
\(202\) 1.20178 + 0.344546i 0.0845567 + 0.0242422i
\(203\) 0.643010 + 0.643010i 0.0451304 + 0.0451304i
\(204\) 0 0
\(205\) 4.52517 23.6744i 0.316051 1.65349i
\(206\) −5.12661 9.24769i −0.357188 0.644317i
\(207\) 0 0
\(208\) 7.97093 + 2.74303i 0.552685 + 0.190195i
\(209\) 0.541243i 0.0374386i
\(210\) 0 0
\(211\) 6.45820 6.45820i 0.444601 0.444601i −0.448954 0.893555i \(-0.648203\pi\)
0.893555 + 0.448954i \(0.148203\pi\)
\(212\) 1.87995 + 8.13966i 0.129115 + 0.559034i
\(213\) 0 0
\(214\) 20.7498 + 5.94891i 1.41843 + 0.406659i
\(215\) −8.01679 11.8057i −0.546741 0.805142i
\(216\) 0 0
\(217\) 0.668811 0.0454019
\(218\) 0.501684 + 0.143832i 0.0339783 + 0.00974150i
\(219\) 0 0
\(220\) −5.77388 + 0.220194i −0.389275 + 0.0148455i
\(221\) 4.32953 4.32953i 0.291236 0.291236i
\(222\) 0 0
\(223\) −0.620487 −0.0415509 −0.0207754 0.999784i \(-0.506614\pi\)
−0.0207754 + 0.999784i \(0.506614\pi\)
\(224\) 0.855609 1.22251i 0.0571678 0.0816826i
\(225\) 0 0
\(226\) −4.81009 + 2.66656i −0.319962 + 0.177377i
\(227\) −10.0579 + 10.0579i −0.667564 + 0.667564i −0.957152 0.289588i \(-0.906482\pi\)
0.289588 + 0.957152i \(0.406482\pi\)
\(228\) 0 0
\(229\) 14.9831 14.9831i 0.990113 0.990113i −0.00983872 0.999952i \(-0.503132\pi\)
0.999952 + 0.00983872i \(0.00313181\pi\)
\(230\) −3.10461 9.45304i −0.204712 0.623315i
\(231\) 0 0
\(232\) −6.52538 7.24523i −0.428412 0.475673i
\(233\) 2.07914i 0.136209i 0.997678 + 0.0681046i \(0.0216952\pi\)
−0.997678 + 0.0681046i \(0.978305\pi\)
\(234\) 0 0
\(235\) 14.6671 + 2.80350i 0.956779 + 0.182880i
\(236\) 6.21718 + 26.9187i 0.404704 + 1.75226i
\(237\) 0 0
\(238\) −0.525498 0.947924i −0.0340630 0.0614448i
\(239\) −13.2816 −0.859113 −0.429557 0.903040i \(-0.641330\pi\)
−0.429557 + 0.903040i \(0.641330\pi\)
\(240\) 0 0
\(241\) −3.84064 −0.247397 −0.123699 0.992320i \(-0.539476\pi\)
−0.123699 + 0.992320i \(0.539476\pi\)
\(242\) −6.39786 11.5408i −0.411270 0.741873i
\(243\) 0 0
\(244\) −2.82170 + 0.651704i −0.180641 + 0.0417210i
\(245\) −2.90943 + 15.2213i −0.185877 + 0.972455i
\(246\) 0 0
\(247\) 0.882830i 0.0561731i
\(248\) −7.16159 0.374368i −0.454761 0.0237724i
\(249\) 0 0
\(250\) −0.954446 + 15.7826i −0.0603645 + 0.998176i
\(251\) 10.6627 10.6627i 0.673022 0.673022i −0.285389 0.958412i \(-0.592123\pi\)
0.958412 + 0.285389i \(0.0921229\pi\)
\(252\) 0 0
\(253\) −2.87453 + 2.87453i −0.180720 + 0.180720i
\(254\) −22.4091 + 12.4229i −1.40607 + 0.779481i
\(255\) 0 0
\(256\) −9.84611 + 12.6117i −0.615382 + 0.788229i
\(257\) −11.6239 −0.725081 −0.362540 0.931968i \(-0.618090\pi\)
−0.362540 + 0.931968i \(0.618090\pi\)
\(258\) 0 0
\(259\) −0.405054 + 0.405054i −0.0251688 + 0.0251688i
\(260\) −9.41785 + 0.359162i −0.584071 + 0.0222743i
\(261\) 0 0
\(262\) −27.0329 7.75027i −1.67010 0.478813i
\(263\) 29.3422 1.80932 0.904658 0.426138i \(-0.140126\pi\)
0.904658 + 0.426138i \(0.140126\pi\)
\(264\) 0 0
\(265\) −5.24701 7.72685i −0.322321 0.474657i
\(266\) −0.150222 0.0430682i −0.00921070 0.00264068i
\(267\) 0 0
\(268\) 10.1193 2.33718i 0.618137 0.142766i
\(269\) 8.91793 8.91793i 0.543736 0.543736i −0.380886 0.924622i \(-0.624381\pi\)
0.924622 + 0.380886i \(0.124381\pi\)
\(270\) 0 0
\(271\) 31.2790i 1.90007i −0.312150 0.950033i \(-0.601049\pi\)
0.312150 0.950033i \(-0.398951\pi\)
\(272\) 5.09640 + 10.4445i 0.309014 + 0.633288i
\(273\) 0 0
\(274\) 7.09020 + 12.7897i 0.428335 + 0.772655i
\(275\) 5.93066 2.56124i 0.357632 0.154449i
\(276\) 0 0
\(277\) −4.04579 4.04579i −0.243088 0.243088i 0.575038 0.818126i \(-0.304987\pi\)
−0.818126 + 0.575038i \(0.804987\pi\)
\(278\) −22.7064 6.50986i −1.36184 0.390436i
\(279\) 0 0
\(280\) −0.398329 + 1.62006i −0.0238047 + 0.0968170i
\(281\) −19.2114 −1.14606 −0.573029 0.819535i \(-0.694232\pi\)
−0.573029 + 0.819535i \(0.694232\pi\)
\(282\) 0 0
\(283\) −10.0809 + 10.0809i −0.599247 + 0.599247i −0.940112 0.340865i \(-0.889280\pi\)
0.340865 + 0.940112i \(0.389280\pi\)
\(284\) −13.3244 8.32434i −0.790655 0.493959i
\(285\) 0 0
\(286\) 1.86699 + 3.36778i 0.110397 + 0.199141i
\(287\) 2.84337i 0.167839i
\(288\) 0 0
\(289\) −8.55875 −0.503456
\(290\) 9.72892 + 4.91839i 0.571302 + 0.288818i
\(291\) 0 0
\(292\) −13.1743 + 21.0875i −0.770969 + 1.23405i
\(293\) −4.81368 + 4.81368i −0.281218 + 0.281218i −0.833595 0.552376i \(-0.813721\pi\)
0.552376 + 0.833595i \(0.313721\pi\)
\(294\) 0 0
\(295\) −17.3524 25.5535i −1.01029 1.48778i
\(296\) 4.56402 4.11056i 0.265278 0.238922i
\(297\) 0 0
\(298\) −10.9979 3.15306i −0.637089 0.182652i
\(299\) −4.68869 + 4.68869i −0.271154 + 0.271154i
\(300\) 0 0
\(301\) 1.19037 + 1.19037i 0.0686118 + 0.0686118i
\(302\) 18.5498 10.2834i 1.06742 0.591742i
\(303\) 0 0
\(304\) 1.58446 + 0.545259i 0.0908750 + 0.0312727i
\(305\) 2.67859 1.81893i 0.153376 0.104152i
\(306\) 0 0
\(307\) −17.1791 17.1791i −0.980465 0.980465i 0.0193480 0.999813i \(-0.493841\pi\)
−0.999813 + 0.0193480i \(0.993841\pi\)
\(308\) 0.664140 0.153391i 0.0378429 0.00874026i
\(309\) 0 0
\(310\) 7.61753 2.50178i 0.432647 0.142092i
\(311\) 16.6032i 0.941479i −0.882272 0.470740i \(-0.843987\pi\)
0.882272 0.470740i \(-0.156013\pi\)
\(312\) 0 0
\(313\) −10.8345 −0.612404 −0.306202 0.951967i \(-0.599058\pi\)
−0.306202 + 0.951967i \(0.599058\pi\)
\(314\) −0.0144257 + 0.0503169i −0.000814090 + 0.00283954i
\(315\) 0 0
\(316\) 18.1824 + 11.3594i 1.02284 + 0.639017i
\(317\) 15.3464 + 15.3464i 0.861942 + 0.861942i 0.991564 0.129621i \(-0.0413762\pi\)
−0.129621 + 0.991564i \(0.541376\pi\)
\(318\) 0 0
\(319\) 4.45404i 0.249378i
\(320\) 5.17211 17.1245i 0.289129 0.957290i
\(321\) 0 0
\(322\) 0.569091 + 1.02656i 0.0317142 + 0.0572080i
\(323\) 0.860623 0.860623i 0.0478863 0.0478863i
\(324\) 0 0
\(325\) 9.67358 4.17768i 0.536594 0.231736i
\(326\) −32.8997 9.43226i −1.82215 0.522405i
\(327\) 0 0
\(328\) 1.59158 30.4466i 0.0878801 1.68113i
\(329\) −1.76157 −0.0971183
\(330\) 0 0
\(331\) −6.23806 6.23806i −0.342875 0.342875i 0.514572 0.857447i \(-0.327951\pi\)
−0.857447 + 0.514572i \(0.827951\pi\)
\(332\) −2.23037 9.65687i −0.122407 0.529990i
\(333\) 0 0
\(334\) −24.0708 + 13.3440i −1.31709 + 0.730154i
\(335\) −9.60613 + 6.52315i −0.524839 + 0.356398i
\(336\) 0 0
\(337\) 8.87003i 0.483181i −0.970378 0.241591i \(-0.922331\pi\)
0.970378 0.241591i \(-0.0776691\pi\)
\(338\) −5.86856 10.5861i −0.319207 0.575805i
\(339\) 0 0
\(340\) −9.53108 8.83083i −0.516895 0.478919i
\(341\) −2.31638 2.31638i −0.125439 0.125439i
\(342\) 0 0
\(343\) 3.67461i 0.198410i
\(344\) −12.0801 13.4127i −0.651315 0.723165i
\(345\) 0 0
\(346\) −21.8068 6.25196i −1.17234 0.336107i
\(347\) 11.3990 + 11.3990i 0.611932 + 0.611932i 0.943449 0.331517i \(-0.107560\pi\)
−0.331517 + 0.943449i \(0.607560\pi\)
\(348\) 0 0
\(349\) −11.5358 11.5358i −0.617496 0.617496i 0.327393 0.944888i \(-0.393830\pi\)
−0.944888 + 0.327393i \(0.893830\pi\)
\(350\) −0.238953 1.84986i −0.0127726 0.0988790i
\(351\) 0 0
\(352\) −7.19743 + 1.27075i −0.383624 + 0.0677310i
\(353\) 20.5642 1.09452 0.547260 0.836963i \(-0.315671\pi\)
0.547260 + 0.836963i \(0.315671\pi\)
\(354\) 0 0
\(355\) 17.2530 + 3.29777i 0.915695 + 0.175027i
\(356\) −14.0285 + 22.4547i −0.743508 + 1.19010i
\(357\) 0 0
\(358\) −8.66339 2.48377i −0.457875 0.131271i
\(359\) 18.8141i 0.992972i −0.868045 0.496486i \(-0.834623\pi\)
0.868045 0.496486i \(-0.165377\pi\)
\(360\) 0 0
\(361\) 18.8245i 0.990764i
\(362\) −5.56542 + 19.4122i −0.292512 + 1.02028i
\(363\) 0 0
\(364\) 1.08329 0.250198i 0.0567798 0.0131139i
\(365\) 5.21914 27.3051i 0.273182 1.42921i
\(366\) 0 0
\(367\) −12.1654 −0.635031 −0.317515 0.948253i \(-0.602849\pi\)
−0.317515 + 0.948253i \(0.602849\pi\)
\(368\) −5.51917 11.3109i −0.287707 0.589621i
\(369\) 0 0
\(370\) −3.09826 + 6.12859i −0.161071 + 0.318610i
\(371\) 0.779099 + 0.779099i 0.0404488 + 0.0404488i
\(372\) 0 0
\(373\) 14.7424 + 14.7424i 0.763330 + 0.763330i 0.976923 0.213592i \(-0.0685164\pi\)
−0.213592 + 0.976923i \(0.568516\pi\)
\(374\) −1.46304 + 5.10309i −0.0756522 + 0.263875i
\(375\) 0 0
\(376\) 18.8627 + 0.986038i 0.972772 + 0.0508510i
\(377\) 7.26505i 0.374169i
\(378\) 0 0
\(379\) 1.59803 + 1.59803i 0.0820853 + 0.0820853i 0.746957 0.664872i \(-0.231514\pi\)
−0.664872 + 0.746957i \(0.731514\pi\)
\(380\) −1.87208 + 0.0713941i −0.0960356 + 0.00366244i
\(381\) 0 0
\(382\) −29.5049 + 16.3565i −1.50960 + 0.836873i
\(383\) 24.9035i 1.27251i 0.771479 + 0.636255i \(0.219517\pi\)
−0.771479 + 0.636255i \(0.780483\pi\)
\(384\) 0 0
\(385\) −0.630458 + 0.428120i −0.0321311 + 0.0218190i
\(386\) −9.50252 17.1412i −0.483665 0.872464i
\(387\) 0 0
\(388\) −18.8373 11.7685i −0.956319 0.597457i
\(389\) 11.9793 + 11.9793i 0.607375 + 0.607375i 0.942259 0.334884i \(-0.108697\pi\)
−0.334884 + 0.942259i \(0.608697\pi\)
\(390\) 0 0
\(391\) −9.14150 −0.462306
\(392\) −1.02329 + 19.5755i −0.0516842 + 0.988710i
\(393\) 0 0
\(394\) 6.60422 23.0355i 0.332716 1.16051i
\(395\) −23.5435 4.50014i −1.18460 0.226427i
\(396\) 0 0
\(397\) −16.0845 + 16.0845i −0.807258 + 0.807258i −0.984218 0.176960i \(-0.943374\pi\)
0.176960 + 0.984218i \(0.443374\pi\)
\(398\) 14.1419 7.83978i 0.708868 0.392973i
\(399\) 0 0
\(400\) 1.52324 + 19.9419i 0.0761618 + 0.997095i
\(401\) 3.56411i 0.177983i −0.996032 0.0889915i \(-0.971636\pi\)
0.996032 0.0889915i \(-0.0283644\pi\)
\(402\) 0 0
\(403\) −3.77828 3.77828i −0.188210 0.188210i
\(404\) −1.72269 + 0.397875i −0.0857069 + 0.0197950i
\(405\) 0 0
\(406\) −1.23622 0.354420i −0.0613524 0.0175896i
\(407\) 2.80575 0.139076
\(408\) 0 0
\(409\) 0.455458i 0.0225209i −0.999937 0.0112605i \(-0.996416\pi\)
0.999937 0.0112605i \(-0.00358439\pi\)
\(410\) 10.6360 + 32.3849i 0.525275 + 1.59938i
\(411\) 0 0
\(412\) 12.6819 + 7.92296i 0.624792 + 0.390336i
\(413\) 2.57656 + 2.57656i 0.126784 + 0.126784i
\(414\) 0 0
\(415\) 6.22503 + 9.16712i 0.305575 + 0.449996i
\(416\) −11.7398 + 2.07273i −0.575593 + 0.101624i
\(417\) 0 0
\(418\) 0.371119 + 0.669447i 0.0181520 + 0.0327437i
\(419\) 7.20612 + 7.20612i 0.352042 + 0.352042i 0.860869 0.508827i \(-0.169921\pi\)
−0.508827 + 0.860869i \(0.669921\pi\)
\(420\) 0 0
\(421\) −13.9138 + 13.9138i −0.678119 + 0.678119i −0.959574 0.281455i \(-0.909183\pi\)
0.281455 + 0.959574i \(0.409183\pi\)
\(422\) −3.55969 + 12.4162i −0.173283 + 0.604411i
\(423\) 0 0
\(424\) −7.90645 8.77865i −0.383971 0.426329i
\(425\) 13.5028 + 5.35766i 0.654984 + 0.259885i
\(426\) 0 0
\(427\) −0.270083 + 0.270083i −0.0130702 + 0.0130702i
\(428\) −29.7438 + 6.86968i −1.43772 + 0.332059i
\(429\) 0 0
\(430\) 18.0106 + 9.10515i 0.868550 + 0.439089i
\(431\) 20.2896 0.977314 0.488657 0.872476i \(-0.337487\pi\)
0.488657 + 0.872476i \(0.337487\pi\)
\(432\) 0 0
\(433\) 13.2049i 0.634587i 0.948327 + 0.317294i \(0.102774\pi\)
−0.948327 + 0.317294i \(0.897226\pi\)
\(434\) −0.827232 + 0.458590i −0.0397084 + 0.0220130i
\(435\) 0 0
\(436\) −0.719140 + 0.166094i −0.0344406 + 0.00795445i
\(437\) −0.932017 + 0.932017i −0.0445844 + 0.0445844i
\(438\) 0 0
\(439\) 4.81740 0.229922 0.114961 0.993370i \(-0.463326\pi\)
0.114961 + 0.993370i \(0.463326\pi\)
\(440\) 6.99054 4.23138i 0.333261 0.201723i
\(441\) 0 0
\(442\) −2.38639 + 8.32373i −0.113509 + 0.395920i
\(443\) 9.16428 + 9.16428i 0.435408 + 0.435408i 0.890463 0.455055i \(-0.150380\pi\)
−0.455055 + 0.890463i \(0.650380\pi\)
\(444\) 0 0
\(445\) 5.55752 29.0754i 0.263452 1.37831i
\(446\) 0.767461 0.425455i 0.0363403 0.0201459i
\(447\) 0 0
\(448\) −0.220024 + 2.09876i −0.0103952 + 0.0991572i
\(449\) 3.67981i 0.173661i 0.996223 + 0.0868305i \(0.0276739\pi\)
−0.996223 + 0.0868305i \(0.972326\pi\)
\(450\) 0 0
\(451\) 9.84780 9.84780i 0.463715 0.463715i
\(452\) 4.12105 6.59636i 0.193838 0.310267i
\(453\) 0 0
\(454\) 5.54379 19.3367i 0.260183 0.907517i
\(455\) −1.02835 + 0.698312i −0.0482098 + 0.0327374i
\(456\) 0 0
\(457\) 18.1968 0.851212 0.425606 0.904908i \(-0.360061\pi\)
0.425606 + 0.904908i \(0.360061\pi\)
\(458\) −8.25854 + 28.8058i −0.385896 + 1.34601i
\(459\) 0 0
\(460\) 10.3217 + 9.56340i 0.481254 + 0.445896i
\(461\) −20.4826 + 20.4826i −0.953971 + 0.953971i −0.998986 0.0450155i \(-0.985666\pi\)
0.0450155 + 0.998986i \(0.485666\pi\)
\(462\) 0 0
\(463\) −22.5416 −1.04760 −0.523799 0.851842i \(-0.675486\pi\)
−0.523799 + 0.851842i \(0.675486\pi\)
\(464\) 13.0389 + 4.48708i 0.605318 + 0.208308i
\(465\) 0 0
\(466\) −1.42562 2.57163i −0.0660408 0.119128i
\(467\) −26.2704 + 26.2704i −1.21565 + 1.21565i −0.246507 + 0.969141i \(0.579283\pi\)
−0.969141 + 0.246507i \(0.920717\pi\)
\(468\) 0 0
\(469\) 0.968587 0.968587i 0.0447252 0.0447252i
\(470\) −20.0636 + 6.58939i −0.925466 + 0.303946i
\(471\) 0 0
\(472\) −26.1474 29.0319i −1.20353 1.33630i
\(473\) 8.24552i 0.379130i
\(474\) 0 0
\(475\) 1.92291 0.830438i 0.0882292 0.0381031i
\(476\) 1.29994 + 0.812135i 0.0595828 + 0.0372241i
\(477\) 0 0
\(478\) 16.4276 9.10690i 0.751379 0.416540i
\(479\) 0.723719 0.0330676 0.0165338 0.999863i \(-0.494737\pi\)
0.0165338 + 0.999863i \(0.494737\pi\)
\(480\) 0 0
\(481\) 4.57651 0.208671
\(482\) 4.75036 2.63344i 0.216373 0.119950i
\(483\) 0 0
\(484\) 15.8266 + 9.88762i 0.719392 + 0.449437i
\(485\) 24.3914 + 4.66222i 1.10756 + 0.211701i
\(486\) 0 0
\(487\) 15.0222i 0.680719i 0.940295 + 0.340360i \(0.110549\pi\)
−0.940295 + 0.340360i \(0.889451\pi\)
\(488\) 3.04321 2.74085i 0.137760 0.124072i
\(489\) 0 0
\(490\) −6.83836 20.8217i −0.308926 0.940629i
\(491\) −3.04102 + 3.04102i −0.137239 + 0.137239i −0.772389 0.635150i \(-0.780938\pi\)
0.635150 + 0.772389i \(0.280938\pi\)
\(492\) 0 0
\(493\) 7.08230 7.08230i 0.318971 0.318971i
\(494\) 0.605338 + 1.09194i 0.0272355 + 0.0491289i
\(495\) 0 0
\(496\) 9.11464 4.44751i 0.409260 0.199699i
\(497\) −2.07214 −0.0929481
\(498\) 0 0
\(499\) 11.3545 11.3545i 0.508298 0.508298i −0.405706 0.914004i \(-0.632974\pi\)
0.914004 + 0.405706i \(0.132974\pi\)
\(500\) −9.64124 20.1754i −0.431170 0.902271i
\(501\) 0 0
\(502\) −5.87716 + 20.4995i −0.262310 + 0.914938i
\(503\) −24.8256 −1.10692 −0.553459 0.832876i \(-0.686692\pi\)
−0.553459 + 0.832876i \(0.686692\pi\)
\(504\) 0 0
\(505\) 1.63532 1.11048i 0.0727708 0.0494159i
\(506\) 1.58441 5.52643i 0.0704357 0.245680i
\(507\) 0 0
\(508\) 19.1990 30.7309i 0.851820 1.36347i
\(509\) 22.3544 22.3544i 0.990841 0.990841i −0.00911778 0.999958i \(-0.502902\pi\)
0.999958 + 0.00911778i \(0.00290232\pi\)
\(510\) 0 0
\(511\) 3.27942i 0.145073i
\(512\) 3.53079 22.3502i 0.156040 0.987751i
\(513\) 0 0
\(514\) 14.3773 7.97029i 0.634154 0.351554i
\(515\) −16.4211 3.13876i −0.723601 0.138310i
\(516\) 0 0
\(517\) 6.10106 + 6.10106i 0.268324 + 0.268324i
\(518\) 0.223262 0.778736i 0.00980955 0.0342157i
\(519\) 0 0
\(520\) 11.4024 6.90186i 0.500027 0.302667i
\(521\) −30.7334 −1.34646 −0.673228 0.739435i \(-0.735093\pi\)
−0.673228 + 0.739435i \(0.735093\pi\)
\(522\) 0 0
\(523\) −12.6215 + 12.6215i −0.551898 + 0.551898i −0.926988 0.375090i \(-0.877612\pi\)
0.375090 + 0.926988i \(0.377612\pi\)
\(524\) 38.7504 8.94984i 1.69282 0.390976i
\(525\) 0 0
\(526\) −36.2924 + 20.1193i −1.58242 + 0.877244i
\(527\) 7.36649i 0.320889i
\(528\) 0 0
\(529\) −13.1002 −0.569572
\(530\) 11.7880 + 5.95934i 0.512038 + 0.258857i
\(531\) 0 0
\(532\) 0.215336 0.0497343i 0.00933599 0.00215626i
\(533\) 16.0629 16.0629i 0.695761 0.695761i
\(534\) 0 0
\(535\) 28.2353 19.1735i 1.22072 0.828944i
\(536\) −10.9137 + 9.82940i −0.471402 + 0.424566i
\(537\) 0 0
\(538\) −4.91547 + 17.1451i −0.211921 + 0.739180i
\(539\) −6.33159 + 6.33159i −0.272721 + 0.272721i
\(540\) 0 0
\(541\) 18.0279 + 18.0279i 0.775081 + 0.775081i 0.978990 0.203909i \(-0.0653645\pi\)
−0.203909 + 0.978990i \(0.565365\pi\)
\(542\) 21.4474 + 38.6880i 0.921244 + 1.66179i
\(543\) 0 0
\(544\) −13.4651 9.42393i −0.577312 0.404048i
\(545\) 0.682668 0.463574i 0.0292423 0.0198573i
\(546\) 0 0
\(547\) −26.0749 26.0749i −1.11488 1.11488i −0.992480 0.122403i \(-0.960940\pi\)
−0.122403 0.992480i \(-0.539060\pi\)
\(548\) −17.5393 10.9576i −0.749241 0.468086i
\(549\) 0 0
\(550\) −5.57925 + 7.23445i −0.237900 + 0.308478i
\(551\) 1.44414i 0.0615226i
\(552\) 0 0
\(553\) 2.82764 0.120244
\(554\) 7.77823 + 2.23000i 0.330465 + 0.0947435i
\(555\) 0 0
\(556\) 32.5485 7.51745i 1.38036 0.318811i
\(557\) 23.2849 + 23.2849i 0.986612 + 0.986612i 0.999912 0.0132999i \(-0.00423361\pi\)
−0.0132999 + 0.999912i \(0.504234\pi\)
\(558\) 0 0
\(559\) 13.4494i 0.568849i
\(560\) −0.618161 2.27693i −0.0261221 0.0962177i
\(561\) 0 0
\(562\) 23.7620 13.1729i 1.00234 0.555664i
\(563\) −2.08207 + 2.08207i −0.0877489 + 0.0877489i −0.749619 0.661870i \(-0.769763\pi\)
0.661870 + 0.749619i \(0.269763\pi\)
\(564\) 0 0
\(565\) −1.63259 + 8.54127i −0.0686837 + 0.359334i
\(566\) 5.55648 19.3810i 0.233556 0.814644i
\(567\) 0 0
\(568\) 22.1883 + 1.15988i 0.931001 + 0.0486675i
\(569\) 22.4930 0.942957 0.471478 0.881878i \(-0.343721\pi\)
0.471478 + 0.881878i \(0.343721\pi\)
\(570\) 0 0
\(571\) −17.5867 17.5867i −0.735979 0.735979i 0.235818 0.971797i \(-0.424223\pi\)
−0.971797 + 0.235818i \(0.924223\pi\)
\(572\) −4.61844 2.88535i −0.193107 0.120643i
\(573\) 0 0
\(574\) −1.94964 3.51687i −0.0813763 0.146791i
\(575\) −14.6230 5.80211i −0.609821 0.241965i
\(576\) 0 0
\(577\) 24.8497i 1.03450i −0.855833 0.517252i \(-0.826955\pi\)
0.855833 0.517252i \(-0.173045\pi\)
\(578\) 10.5861 5.86856i 0.440322 0.244100i
\(579\) 0 0
\(580\) −15.4058 + 0.587521i −0.639693 + 0.0243955i
\(581\) −0.924321 0.924321i −0.0383473 0.0383473i
\(582\) 0 0
\(583\) 5.39671i 0.223509i
\(584\) 1.83566 35.1158i 0.0759600 1.45310i
\(585\) 0 0
\(586\) 2.65325 9.25454i 0.109605 0.382301i
\(587\) −22.8896 22.8896i −0.944753 0.944753i 0.0537988 0.998552i \(-0.482867\pi\)
−0.998552 + 0.0537988i \(0.982867\pi\)
\(588\) 0 0
\(589\) −0.751046 0.751046i −0.0309463 0.0309463i
\(590\) 38.9841 + 19.7081i 1.60495 + 0.811371i
\(591\) 0 0
\(592\) −2.82657 + 8.21368i −0.116171 + 0.337580i
\(593\) 13.3090 0.546536 0.273268 0.961938i \(-0.411895\pi\)
0.273268 + 0.961938i \(0.411895\pi\)
\(594\) 0 0
\(595\) −1.68323 0.321735i −0.0690056 0.0131899i
\(596\) 15.7649 3.64109i 0.645756 0.149145i
\(597\) 0 0
\(598\) 2.58436 9.01424i 0.105682 0.368620i
\(599\) 7.33982i 0.299897i −0.988694 0.149948i \(-0.952089\pi\)
0.988694 0.149948i \(-0.0479108\pi\)
\(600\) 0 0
\(601\) 27.4748i 1.12072i 0.828250 + 0.560359i \(0.189337\pi\)
−0.828250 + 0.560359i \(0.810663\pi\)
\(602\) −2.28854 0.656119i −0.0932740 0.0267414i
\(603\) 0 0
\(604\) −15.8925 + 25.4384i −0.646658 + 1.03507i
\(605\) −20.4931 3.91708i −0.833162 0.159252i
\(606\) 0 0
\(607\) 27.4473 1.11405 0.557026 0.830495i \(-0.311942\pi\)
0.557026 + 0.830495i \(0.311942\pi\)
\(608\) −2.33364 + 0.412017i −0.0946416 + 0.0167095i
\(609\) 0 0
\(610\) −2.06587 + 4.08643i −0.0836445 + 0.165455i
\(611\) 9.95153 + 9.95153i 0.402596 + 0.402596i
\(612\) 0 0
\(613\) 17.6219 + 17.6219i 0.711742 + 0.711742i 0.966899 0.255158i \(-0.0821274\pi\)
−0.255158 + 0.966899i \(0.582127\pi\)
\(614\) 33.0277 + 9.46896i 1.33289 + 0.382136i
\(615\) 0 0
\(616\) −0.716277 + 0.645111i −0.0288596 + 0.0259923i
\(617\) 41.8102i 1.68322i −0.540088 0.841608i \(-0.681609\pi\)
0.540088 0.841608i \(-0.318391\pi\)
\(618\) 0 0
\(619\) 1.39925 + 1.39925i 0.0562406 + 0.0562406i 0.734668 0.678427i \(-0.237338\pi\)
−0.678427 + 0.734668i \(0.737338\pi\)
\(620\) −7.70646 + 8.31756i −0.309499 + 0.334041i
\(621\) 0 0
\(622\) 11.3844 + 20.5359i 0.456475 + 0.823416i
\(623\) 3.49204i 0.139906i
\(624\) 0 0
\(625\) 18.1990 + 17.1405i 0.727960 + 0.685620i
\(626\) 13.4009 7.42901i 0.535607 0.296923i
\(627\) 0 0
\(628\) −0.0166585 0.0721267i −0.000664747 0.00287817i
\(629\) 4.46139 + 4.46139i 0.177887 + 0.177887i
\(630\) 0 0
\(631\) 33.0559 1.31593 0.657967 0.753047i \(-0.271417\pi\)
0.657967 + 0.753047i \(0.271417\pi\)
\(632\) −30.2782 1.58277i −1.20440 0.0629594i
\(633\) 0 0
\(634\) −29.5043 8.45880i −1.17176 0.335942i
\(635\) −7.60589 + 39.7919i −0.301830 + 1.57909i
\(636\) 0 0
\(637\) −10.3275 + 10.3275i −0.409192 + 0.409192i
\(638\) 3.05404 + 5.50906i 0.120911 + 0.218106i
\(639\) 0 0
\(640\) 5.34471 + 24.7272i 0.211268 + 0.977428i
\(641\) 8.31451i 0.328404i 0.986427 + 0.164202i \(0.0525048\pi\)
−0.986427 + 0.164202i \(0.947495\pi\)
\(642\) 0 0
\(643\) 17.1504 + 17.1504i 0.676344 + 0.676344i 0.959171 0.282827i \(-0.0912722\pi\)
−0.282827 + 0.959171i \(0.591272\pi\)
\(644\) −1.40778 0.879506i −0.0554744 0.0346574i
\(645\) 0 0
\(646\) −0.474366 + 1.65459i −0.0186637 + 0.0650989i
\(647\) −5.95293 −0.234034 −0.117017 0.993130i \(-0.537333\pi\)
−0.117017 + 0.993130i \(0.537333\pi\)
\(648\) 0 0
\(649\) 17.8475i 0.700575i
\(650\) −9.10040 + 11.8002i −0.356947 + 0.462843i
\(651\) 0 0
\(652\) 47.1601 10.8922i 1.84693 0.426571i
\(653\) −24.1739 24.1739i −0.945997 0.945997i 0.0526174 0.998615i \(-0.483244\pi\)
−0.998615 + 0.0526174i \(0.983244\pi\)
\(654\) 0 0
\(655\) −36.7851 + 24.9793i −1.43731 + 0.976024i
\(656\) 18.9080 + 38.7497i 0.738234 + 1.51292i
\(657\) 0 0
\(658\) 2.17883 1.20787i 0.0849395 0.0470877i
\(659\) −25.0108 25.0108i −0.974284 0.974284i 0.0253938 0.999678i \(-0.491916\pi\)
−0.999678 + 0.0253938i \(0.991916\pi\)
\(660\) 0 0
\(661\) −28.8800 + 28.8800i −1.12330 + 1.12330i −0.132061 + 0.991242i \(0.542159\pi\)
−0.991242 + 0.132061i \(0.957841\pi\)
\(662\) 11.9930 + 3.43835i 0.466120 + 0.133635i
\(663\) 0 0
\(664\) 9.38018 + 10.4150i 0.364022 + 0.404179i
\(665\) −0.204415 + 0.138810i −0.00792687 + 0.00538283i
\(666\) 0 0
\(667\) −7.66982 + 7.66982i −0.296977 + 0.296977i
\(668\) 20.6227 33.0097i 0.797915 1.27718i
\(669\) 0 0
\(670\) 7.40873 14.6550i 0.286224 0.566172i
\(671\) 1.87083 0.0722224
\(672\) 0 0
\(673\) 26.0623i 1.00463i 0.864685 + 0.502315i \(0.167518\pi\)
−0.864685 + 0.502315i \(0.832482\pi\)
\(674\) 6.08199 + 10.9711i 0.234270 + 0.422589i
\(675\) 0 0
\(676\) 14.5173 + 9.06961i 0.558357 + 0.348831i
\(677\) 9.70043 9.70043i 0.372818 0.372818i −0.495685 0.868503i \(-0.665083\pi\)
0.868503 + 0.495685i \(0.165083\pi\)
\(678\) 0 0
\(679\) −2.92948 −0.112423
\(680\) 17.8438 + 4.38731i 0.684279 + 0.168246i
\(681\) 0 0
\(682\) 4.45335 + 1.27677i 0.170528 + 0.0488899i
\(683\) −8.36855 8.36855i −0.320214 0.320214i 0.528635 0.848849i \(-0.322704\pi\)
−0.848849 + 0.528635i \(0.822704\pi\)
\(684\) 0 0
\(685\) 22.7107 + 4.34096i 0.867731 + 0.165860i
\(686\) 2.51960 + 4.54501i 0.0961988 + 0.173529i
\(687\) 0 0
\(688\) 24.1383 + 8.30670i 0.920264 + 0.316690i
\(689\) 8.80266i 0.335355i
\(690\) 0 0
\(691\) 16.7998 16.7998i 0.639095 0.639095i −0.311237 0.950332i \(-0.600743\pi\)
0.950332 + 0.311237i \(0.100743\pi\)
\(692\) 31.2590 7.21963i 1.18829 0.274449i
\(693\) 0 0
\(694\) −21.9152 6.28303i −0.831889 0.238501i
\(695\) −30.8978 + 20.9815i −1.17202 + 0.795873i
\(696\) 0 0
\(697\) 31.3177 1.18624
\(698\) 22.1781 + 6.35840i 0.839452 + 0.240669i
\(699\) 0 0
\(700\) 1.56396 + 2.12419i 0.0591122 + 0.0802867i
\(701\) −26.5344 + 26.5344i −1.00219 + 1.00219i −0.00219271 + 0.999998i \(0.500698\pi\)
−0.999998 + 0.00219271i \(0.999302\pi\)
\(702\) 0 0
\(703\) 0.909716 0.0343106
\(704\) 8.03095 6.50688i 0.302678 0.245237i
\(705\) 0 0
\(706\) −25.4352 + 14.1004i −0.957265 + 0.530676i
\(707\) −0.164890 + 0.164890i −0.00620131 + 0.00620131i
\(708\) 0 0
\(709\) −32.4351 + 32.4351i −1.21813 + 1.21813i −0.249840 + 0.968287i \(0.580378\pi\)
−0.968287 + 0.249840i \(0.919622\pi\)
\(710\) −23.6009 + 7.75112i −0.885727 + 0.290894i
\(711\) 0 0
\(712\) 1.95467 37.3925i 0.0732545 1.40135i
\(713\) 7.97758i 0.298763i
\(714\) 0 0
\(715\) 5.98017 + 1.14306i 0.223646 + 0.0427480i
\(716\) 12.4186 2.86821i 0.464103 0.107190i
\(717\) 0 0
\(718\) 12.9005 + 23.2706i 0.481441 + 0.868452i
\(719\) −8.81868 −0.328881 −0.164441 0.986387i \(-0.552582\pi\)
−0.164441 + 0.986387i \(0.552582\pi\)
\(720\) 0 0
\(721\) 1.97222 0.0734495
\(722\) −12.9076 23.2834i −0.480370 0.866520i
\(723\) 0 0
\(724\) −6.42683 27.8264i −0.238851 1.03416i
\(725\) 15.8242 6.83390i 0.587695 0.253805i
\(726\) 0 0
\(727\) 10.5815i 0.392448i 0.980559 + 0.196224i \(0.0628679\pi\)
−0.980559 + 0.196224i \(0.937132\pi\)
\(728\) −1.16833 + 1.05225i −0.0433012 + 0.0389990i
\(729\) 0 0
\(730\) 12.2671 + 37.3514i 0.454027 + 1.38244i
\(731\) 13.1111 13.1111i 0.484931 0.484931i
\(732\) 0 0
\(733\) −0.891694 + 0.891694i −0.0329355 + 0.0329355i −0.723383 0.690447i \(-0.757414\pi\)
0.690447 + 0.723383i \(0.257414\pi\)
\(734\) 15.0471 8.34159i 0.555397 0.307894i
\(735\) 0 0
\(736\) 14.5821 + 10.2057i 0.537505 + 0.376187i
\(737\) −6.70927 −0.247139
\(738\) 0 0
\(739\) −22.1859 + 22.1859i −0.816120 + 0.816120i −0.985543 0.169423i \(-0.945810\pi\)
0.169423 + 0.985543i \(0.445810\pi\)
\(740\) −0.370100 9.70467i −0.0136052 0.356751i
\(741\) 0 0
\(742\) −1.49786 0.429431i −0.0549880 0.0157649i
\(743\) 7.89487 0.289635 0.144817 0.989458i \(-0.453741\pi\)
0.144817 + 0.989458i \(0.453741\pi\)
\(744\) 0 0
\(745\) −14.9654 + 10.1624i −0.548289 + 0.372322i
\(746\) −28.3429 8.12583i −1.03771 0.297508i
\(747\) 0 0
\(748\) −1.68949 7.31504i −0.0617740 0.267464i
\(749\) −2.84697 + 2.84697i −0.104026 + 0.104026i
\(750\) 0 0
\(751\) 4.43117i 0.161696i −0.996726 0.0808478i \(-0.974237\pi\)
0.996726 0.0808478i \(-0.0257628\pi\)
\(752\) −24.0068 + 11.7142i −0.875439 + 0.427173i
\(753\) 0 0
\(754\) 4.98149 + 8.98591i 0.181415 + 0.327248i
\(755\) 6.29598 32.9388i 0.229134 1.19877i
\(756\) 0 0
\(757\) 22.8329 + 22.8329i 0.829876 + 0.829876i 0.987499 0.157623i \(-0.0503832\pi\)
−0.157623 + 0.987499i \(0.550383\pi\)
\(758\) −3.07229 0.880817i −0.111591 0.0319927i
\(759\) 0 0
\(760\) 2.26656 1.37195i 0.0822168 0.0497659i
\(761\) −18.3941 −0.666784 −0.333392 0.942788i \(-0.608193\pi\)
−0.333392 + 0.942788i \(0.608193\pi\)
\(762\) 0 0
\(763\) −0.0688335 + 0.0688335i −0.00249194 + 0.00249194i
\(764\) 25.2783 40.4617i 0.914537 1.46385i
\(765\) 0 0
\(766\) −17.0758 30.8024i −0.616975 1.11294i
\(767\) 29.1113i 1.05115i
\(768\) 0 0
\(769\) 12.2959 0.443402 0.221701 0.975115i \(-0.428839\pi\)
0.221701 + 0.975115i \(0.428839\pi\)
\(770\) 0.486241 0.961820i 0.0175229 0.0346616i
\(771\) 0 0
\(772\) 23.5067 + 14.6857i 0.846026 + 0.528551i
\(773\) 16.8697 16.8697i 0.606762 0.606762i −0.335337 0.942098i \(-0.608850\pi\)
0.942098 + 0.335337i \(0.108850\pi\)
\(774\) 0 0
\(775\) 4.67551 11.7836i 0.167949 0.423280i
\(776\) 31.3687 + 1.63978i 1.12607 + 0.0588647i
\(777\) 0 0
\(778\) −23.0308 6.60287i −0.825694 0.236724i
\(779\) 3.19298 3.19298i 0.114400 0.114400i
\(780\) 0 0
\(781\) 7.17670 + 7.17670i 0.256803 + 0.256803i
\(782\) 11.3068 6.26814i 0.404332 0.224148i
\(783\) 0 0
\(784\) −12.1568 24.9139i −0.434171 0.889783i
\(785\) 0.0464945 + 0.0684688i 0.00165946 + 0.00244376i
\(786\) 0 0
\(787\) −32.0462 32.0462i −1.14232 1.14232i −0.988024 0.154299i \(-0.950688\pi\)
−0.154299 0.988024i \(-0.549312\pi\)
\(788\) 7.62641 + 33.0203i 0.271680 + 1.17630i
\(789\) 0 0
\(790\) 32.2058 10.5772i 1.14583 0.376319i
\(791\) 1.02583i