Properties

Label 720.2.u.a.179.7
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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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 179.7
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.23687 + 0.685679i) q^{2} +(1.05969 - 1.69619i) q^{4} +(-2.19631 + 0.419806i) q^{5} +0.263783i q^{7} +(-0.147653 + 2.82457i) q^{8} +O(q^{10})\) \(q+(-1.23687 + 0.685679i) q^{2} +(1.05969 - 1.69619i) q^{4} +(-2.19631 + 0.419806i) q^{5} +0.263783i q^{7} +(-0.147653 + 2.82457i) q^{8} +(2.42869 - 2.02521i) q^{10} +(0.913594 - 0.913594i) q^{11} +(1.49018 - 1.49018i) q^{13} +(-0.180870 - 0.326265i) q^{14} +(-1.75412 - 3.59487i) q^{16} -2.90538 q^{17} +(-0.296217 + 0.296217i) q^{19} +(-1.61533 + 4.17022i) q^{20} +(-0.503563 + 1.75643i) q^{22} +3.14640 q^{23} +(4.64753 - 1.84404i) q^{25} +(-0.821369 + 2.86493i) q^{26} +(0.447426 + 0.279528i) q^{28} +(2.43765 - 2.43765i) q^{29} +2.53546i q^{31} +(4.63454 + 3.24361i) q^{32} +(3.59358 - 1.99216i) q^{34} +(-0.110738 - 0.579348i) q^{35} +(1.53556 + 1.53556i) q^{37} +(0.163272 - 0.569491i) q^{38} +(-0.861481 - 6.26561i) q^{40} +10.7792 q^{41} +(4.51269 - 4.51269i) q^{43} +(-0.581504 - 2.51775i) q^{44} +(-3.89169 + 2.15742i) q^{46} -6.67809i q^{47} +6.93042 q^{49} +(-4.48396 + 5.46755i) q^{50} +(-0.948500 - 4.10674i) q^{52} +(-2.95356 + 2.95356i) q^{53} +(-1.62300 + 2.39006i) q^{55} +(-0.745073 - 0.0389483i) q^{56} +(-1.34361 + 4.68649i) q^{58} +(9.76773 - 9.76773i) q^{59} +(-1.02388 - 1.02388i) q^{61} +(-1.73851 - 3.13603i) q^{62} +(-7.95640 - 0.834111i) q^{64} +(-2.64730 + 3.89847i) q^{65} +(-3.67191 - 3.67191i) q^{67} +(-3.07880 + 4.92808i) q^{68} +(0.534215 + 0.640647i) q^{70} +7.85546i q^{71} +12.4323 q^{73} +(-2.95219 - 0.846384i) q^{74} +(0.188543 + 0.816337i) q^{76} +(0.240990 + 0.240990i) q^{77} +10.7196i q^{79} +(5.36174 + 7.15904i) q^{80} +(-13.3324 + 7.39107i) q^{82} +(3.50410 - 3.50410i) q^{83} +(6.38111 - 1.21970i) q^{85} +(-2.48735 + 8.67586i) q^{86} +(2.44561 + 2.71540i) q^{88} +13.2383 q^{89} +(0.393083 + 0.393083i) q^{91} +(3.33421 - 5.33690i) q^{92} +(4.57903 + 8.25992i) q^{94} +(0.526229 - 0.774936i) q^{95} +11.1057i q^{97} +(-8.57202 + 4.75204i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

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
\(5\) −2.19631 + 0.419806i −0.982218 + 0.187743i
\(6\) 0 0
\(7\) 0.263783i 0.0997006i 0.998757 + 0.0498503i \(0.0158744\pi\)
−0.998757 + 0.0498503i \(0.984126\pi\)
\(8\) −0.147653 + 2.82457i −0.0522031 + 0.998636i
\(9\) 0 0
\(10\) 2.42869 2.02521i 0.768019 0.640427i
\(11\) 0.913594 0.913594i 0.275459 0.275459i −0.555834 0.831293i \(-0.687601\pi\)
0.831293 + 0.555834i \(0.187601\pi\)
\(12\) 0 0
\(13\) 1.49018 1.49018i 0.413300 0.413300i −0.469586 0.882887i \(-0.655597\pi\)
0.882887 + 0.469586i \(0.155597\pi\)
\(14\) −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 \(0.265302\pi\)
\(20\) −1.61533 + 4.17022i −0.361199 + 0.932489i
\(21\) 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 −0.443577 0.896236i \(-0.646291\pi\)
0.896236 + 0.443577i \(0.146291\pi\)
\(30\) 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
\(35\) −0.110738 0.579348i −0.0187181 0.0979277i
\(36\) 0 0
\(37\) 1.53556 + 1.53556i 0.252444 + 0.252444i 0.821972 0.569528i \(-0.192874\pi\)
−0.569528 + 0.821972i \(0.692874\pi\)
\(38\) 0.163272 0.569491i 0.0264861 0.0923836i
\(39\) 0 0
\(40\) −0.861481 6.26561i −0.136212 0.990680i
\(41\) 10.7792 1.68343 0.841713 0.539925i \(-0.181547\pi\)
0.841713 + 0.539925i \(0.181547\pi\)
\(42\) 0 0
\(43\) 4.51269 4.51269i 0.688178 0.688178i −0.273651 0.961829i \(-0.588231\pi\)
0.961829 + 0.273651i \(0.0882313\pi\)
\(44\) −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
\(50\) −4.48396 + 5.46755i −0.634127 + 0.773229i
\(51\) 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 \(-0.394155\pi\)
0.945222 0.326428i \(-0.105845\pi\)
\(60\) 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 0.446292 0.894887i \(-0.352744\pi\)
−0.894887 + 0.446292i \(0.852744\pi\)
\(68\) −3.07880 + 4.92808i −0.373359 + 0.597618i
\(69\) 0 0
\(70\) 0.534215 + 0.640647i 0.0638509 + 0.0765720i
\(71\) 7.85546i 0.932272i 0.884713 + 0.466136i \(0.154354\pi\)
−0.884713 + 0.466136i \(0.845646\pi\)
\(72\) 0 0
\(73\) 12.4323 1.45509 0.727543 0.686062i \(-0.240662\pi\)
0.727543 + 0.686062i \(0.240662\pi\)
\(74\) −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 \(0.793963\pi\)
\(80\) 5.36174 + 7.15904i 0.599460 + 0.800404i
\(81\) 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
\(85\) 6.38111 1.21970i 0.692129 0.132295i
\(86\) −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 \(-0.252456\pi\)
0.701629 + 0.712542i \(0.252456\pi\)
\(90\) 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 \(0.190663\pi\)
−0.825908 + 0.563804i \(0.809337\pi\)
\(98\) −8.57202 + 4.75204i −0.865905 + 0.480029i
\(99\) 0 0
\(100\) 1.79708 9.83720i 0.179708 0.983720i
\(101\) 0.625096 + 0.625096i 0.0621994 + 0.0621994i 0.737522 0.675323i \(-0.235996\pi\)
−0.675323 + 0.737522i \(0.735996\pi\)
\(102\) 0 0
\(103\) 7.47669i 0.736701i −0.929687 0.368350i \(-0.879923\pi\)
0.929687 0.368350i \(-0.120077\pi\)
\(104\) 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 \(0.755626\pi\)
\(110\) 0.368621 4.06905i 0.0351466 0.387969i
\(111\) 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
\(115\) −6.91046 + 1.32088i −0.644404 + 0.123173i
\(116\) −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
\(125\) −9.43325 + 6.00115i −0.843736 + 0.536759i
\(126\) 0 0
\(127\) −18.1176 −1.60768 −0.803840 0.594846i \(-0.797213\pi\)
−0.803840 + 0.594846i \(0.797213\pi\)
\(128\) 10.4130 4.42385i 0.920384 0.391017i
\(129\) 0 0
\(130\) 0.601262 6.63709i 0.0527342 0.582111i
\(131\) −14.0610 14.0610i −1.22851 1.22851i −0.964526 0.263988i \(-0.914962\pi\)
−0.263988 0.964526i \(-0.585038\pi\)
\(132\) 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 \(0.499439\pi\)
\(140\) −1.10003 0.426096i −0.0929697 0.0360117i
\(141\) 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 0.432835 0.901473i \(-0.357513\pi\)
−0.901473 + 0.432835i \(0.857513\pi\)
\(150\) 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
\(155\) −1.06440 5.56865i −0.0854948 0.447285i
\(156\) 0 0
\(157\) −0.0261720 + 0.0261720i −0.00208875 + 0.00208875i −0.708150 0.706062i \(-0.750470\pi\)
0.706062 + 0.708150i \(0.250470\pi\)
\(158\) −7.35019 13.2587i −0.584750 1.05481i
\(159\) 0 0
\(160\) −11.5406 5.17836i −0.912362 0.409385i
\(161\) 0.829967i 0.0654106i
\(162\) 0 0
\(163\) −17.1126 17.1126i −1.34036 1.34036i −0.895700 0.444659i \(-0.853325\pi\)
−0.444659 0.895700i \(-0.646675\pi\)
\(164\) 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
\(170\) −7.05628 + 5.88400i −0.541192 + 0.451282i
\(171\) 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 0.518356 0.855165i \(-0.326544\pi\)
−0.855165 + 0.518356i \(0.826544\pi\)
\(180\) 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
\(190\) −0.119519 + 1.31932i −0.00867080 + 0.0957134i
\(191\) −23.8545 −1.72605 −0.863025 0.505161i \(-0.831433\pi\)
−0.863025 + 0.505161i \(0.831433\pi\)
\(192\) 0 0
\(193\) 13.8585i 0.997560i −0.866729 0.498780i \(-0.833782\pi\)
0.866729 0.498780i \(-0.166218\pi\)
\(194\) −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 \(0.632817\pi\)
\(200\) 4.52242 + 13.3995i 0.319783 + 0.947491i
\(201\) 0 0
\(202\) −1.20178 0.344546i −0.0845567 0.0242422i
\(203\) 0.643010 + 0.643010i 0.0451304 + 0.0451304i
\(204\) 0 0
\(205\) −23.6744 + 4.52517i −1.65349 + 0.316051i
\(206\) 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
\(220\) 2.33413 + 5.28564i 0.157367 + 0.356358i
\(221\) −4.32953 + 4.32953i −0.291236 + 0.291236i
\(222\) 0 0
\(223\) 0.620487 0.0415509 0.0207754 0.999784i \(-0.493386\pi\)
0.0207754 + 0.999784i \(0.493386\pi\)
\(224\) −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 \(0.00313181\pi\)
\(230\) 7.64164 6.37211i 0.503875 0.420165i
\(231\) 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
\(235\) 2.80350 + 14.6671i 0.182880 + 0.956779i
\(236\) −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 \(-0.358670\pi\)
0.429557 + 0.903040i \(0.358670\pi\)
\(240\) 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
\(245\) −15.2213 + 2.90943i −0.972455 + 0.185877i
\(246\) 0 0
\(247\) 0.882830i 0.0561731i
\(248\) −7.16159 0.374368i −0.454761 0.0237724i
\(249\) 0 0
\(250\) 7.55283 13.8908i 0.477683 0.878532i
\(251\) −10.6627 + 10.6627i −0.673022 + 0.673022i −0.958412 0.285389i \(-0.907877\pi\)
0.285389 + 0.958412i \(0.407877\pi\)
\(252\) 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
\(260\) 3.80723 + 8.62148i 0.236115 + 0.534682i
\(261\) 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 −0.924622 0.380886i \(-0.875619\pi\)
0.380886 + 0.924622i \(0.375619\pi\)
\(270\) 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
\(275\) 2.56124 5.93066i 0.154449 0.357632i
\(276\) 0 0
\(277\) 4.04579 + 4.04579i 0.243088 + 0.243088i 0.818126 0.575038i \(-0.195013\pi\)
−0.575038 + 0.818126i \(0.695013\pi\)
\(278\) −22.7064 6.50986i −1.36184 0.390436i
\(279\) 0 0
\(280\) 1.65276 0.227244i 0.0987713 0.0135804i
\(281\) 19.2114 1.14606 0.573029 0.819535i \(-0.305768\pi\)
0.573029 + 0.819535i \(0.305768\pi\)
\(282\) 0 0
\(283\) 10.0809 10.0809i 0.599247 0.599247i −0.340865 0.940112i \(-0.610720\pi\)
0.940112 + 0.340865i \(0.110720\pi\)
\(284\) 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
\(290\) 0.983552 10.8570i 0.0577562 0.637547i
\(291\) 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 0.999813 0.0193480i \(-0.00615904\pi\)
−0.0193480 + 0.999813i \(0.506159\pi\)
\(308\) 0.664140 0.153391i 0.0378429 0.00874026i
\(309\) 0 0
\(310\) 5.13483 + 6.15785i 0.291639 + 0.349743i
\(311\) 16.6032i 0.941479i 0.882272 + 0.470740i \(0.156013\pi\)
−0.882272 + 0.470740i \(0.843987\pi\)
\(312\) 0 0
\(313\) 10.8345 0.612404 0.306202 0.951967i \(-0.400942\pi\)
0.306202 + 0.951967i \(0.400942\pi\)
\(314\) 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
\(320\) 17.8249 1.50818i 0.996440 0.0843098i
\(321\) 0 0
\(322\) −0.569091 1.02656i −0.0317142 0.0572080i
\(323\) 0.860623 0.860623i 0.0478863 0.0478863i
\(324\) 0 0
\(325\) 4.17768 9.67358i 0.231736 0.536594i
\(326\) 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 \(0.0776691\pi\)
−0.970378 + 0.241591i \(0.922331\pi\)
\(338\) −5.86856 10.5861i −0.319207 0.575805i
\(339\) 0 0
\(340\) 4.69315 12.1161i 0.254522 0.657087i
\(341\) 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 \(0.893830\pi\)
\(350\) −1.44225 1.18279i −0.0770914 0.0632228i
\(351\) 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
\(355\) −3.29777 17.2530i −0.175027 0.915695i
\(356\) 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 \(0.165377\pi\)
−0.868045 + 0.496486i \(0.834623\pi\)
\(360\) 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
\(365\) −27.3051 + 5.21914i −1.42921 + 0.273182i
\(366\) 0 0
\(367\) 12.1654 0.635031 0.317515 0.948253i \(-0.397151\pi\)
0.317515 + 0.948253i \(0.397151\pi\)
\(368\) −5.51917 11.3109i −0.287707 0.589621i
\(369\) 0 0
\(370\) 6.83922 + 0.619574i 0.355554 + 0.0322101i
\(371\) −0.779099 0.779099i −0.0404488 0.0404488i
\(372\) 0 0
\(373\) −14.7424 14.7424i −0.763330 0.763330i 0.213592 0.976923i \(-0.431484\pi\)
−0.976923 + 0.213592i \(0.931484\pi\)
\(374\) 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 \(0.731514\pi\)
\(380\) −0.756800 1.71378i −0.0388230 0.0879148i
\(381\) 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 0.334884 0.942259i \(-0.391303\pi\)
−0.942259 + 0.334884i \(0.891303\pi\)
\(390\) 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
\(395\) −4.50014 23.5435i −0.226427 1.18460i
\(396\) 0 0
\(397\) 16.0845 16.0845i 0.807258 0.807258i −0.176960 0.984218i \(-0.556626\pi\)
0.984218 + 0.176960i \(0.0566264\pi\)
\(398\) 14.1419 7.83978i 0.708868 0.392973i
\(399\) 0 0
\(400\) −14.7814 13.4725i −0.739071 0.673627i
\(401\) 3.56411i 0.177983i 0.996032 + 0.0889915i \(0.0283644\pi\)
−0.996032 + 0.0889915i \(0.971636\pi\)
\(402\) 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 \(-0.00358439\pi\)
\(410\) 26.1793 21.8301i 1.29290 1.07811i
\(411\) 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 0.508827 0.860869i \(-0.330079\pi\)
−0.860869 + 0.508827i \(0.830079\pi\)
\(420\) 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
\(430\) 1.82080 20.0990i 0.0878067 0.969262i
\(431\) −20.2896 −0.977314 −0.488657 0.872476i \(-0.662513\pi\)
−0.488657 + 0.872476i \(0.662513\pi\)
\(432\) 0 0
\(433\) 13.2049i 0.634587i −0.948327 0.317294i \(-0.897226\pi\)
0.948327 0.317294i \(-0.102774\pi\)
\(434\) 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 \(0.463326\pi\)
\(440\) −6.51126 4.93718i −0.310412 0.235371i
\(441\) 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
\(445\) −29.0754 + 5.55752i −1.37831 + 0.263452i
\(446\) −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 \(-0.972326\pi\)
0.996223 0.0868305i \(-0.0276739\pi\)
\(450\) 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 \(-0.639939\pi\)
−0.425606 + 0.904908i \(0.639939\pi\)
\(458\) −8.25854 + 28.8058i −0.385896 + 1.34601i
\(459\) 0 0
\(460\) −5.08248 + 13.1212i −0.236972 + 0.611778i
\(461\) 20.4826 20.4826i 0.953971 0.953971i −0.0450155 0.998986i \(-0.514334\pi\)
0.998986 + 0.0450155i \(0.0143337\pi\)
\(462\) 0 0
\(463\) 22.5416 1.04760 0.523799 0.851842i \(-0.324514\pi\)
0.523799 + 0.851842i \(0.324514\pi\)
\(464\) −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
\(470\) −13.5245 16.2190i −0.623839 0.748128i
\(471\) 0 0
\(472\) 26.1474 + 29.0319i 1.20353 + 1.33630i
\(473\) 8.24552i 0.379130i
\(474\) 0 0
\(475\) −0.830438 + 1.92291i −0.0381031 + 0.0882292i
\(476\) −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 \(-0.505263\pi\)
−0.0165338 + 0.999863i \(0.505263\pi\)
\(480\) 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
\(485\) −4.66222 24.3914i −0.211701 1.10756i
\(486\) 0 0
\(487\) 15.0222i 0.680719i −0.940295 0.340360i \(-0.889451\pi\)
0.940295 0.340360i \(-0.110549\pi\)
\(488\) 3.04321 2.74085i 0.137760 0.124072i
\(489\) 0 0
\(490\) 16.8318 14.0355i 0.760385 0.634061i
\(491\) 3.04102 3.04102i 0.137239 0.137239i −0.635150 0.772389i \(-0.719062\pi\)
0.772389 + 0.635150i \(0.219062\pi\)
\(492\) 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 \(0.132974\pi\)
\(500\) 0.182782 + 22.3599i 0.00817426 + 0.999967i
\(501\) 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 −0.999958 0.00911778i \(-0.997098\pi\)
0.00911778 + 0.999958i \(0.497098\pi\)
\(510\) 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
\(515\) 3.13876 + 16.4211i 0.138310 + 0.723601i
\(516\) 0 0
\(517\) −6.10106 6.10106i −0.268324 0.268324i
\(518\) 0.223262 0.778736i 0.00980955 0.0342157i
\(519\) 0 0
\(520\) −10.6206 8.05310i −0.465745 0.353152i
\(521\) 30.7334 1.34646 0.673228 0.739435i \(-0.264907\pi\)
0.673228 + 0.739435i \(0.264907\pi\)
\(522\) 0 0
\(523\) 12.6215 12.6215i 0.551898 0.551898i −0.375090 0.926988i \(-0.622388\pi\)
0.926988 + 0.375090i \(0.122388\pi\)
\(524\) −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
\(530\) −1.19172 + 13.1549i −0.0517648 + 0.571411i
\(531\) 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 \(0.0390600\pi\)
0.122403 + 0.992480i \(0.460940\pi\)
\(548\) −17.5393 10.9576i −0.749241 0.468086i
\(549\) 0 0
\(550\) 0.898608 + 9.09164i 0.0383168 + 0.387669i
\(551\) 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
\(560\) −1.88843 + 1.41433i −0.0798008 + 0.0597665i
\(561\) 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
\(565\) −8.54127 + 1.63259i −0.359334 + 0.0686837i
\(566\) −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 \(-0.656279\pi\)
−0.471478 + 0.881878i \(0.656279\pi\)
\(570\) 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 \(0.173045\pi\)
−0.855833 + 0.517252i \(0.826955\pi\)
\(578\) 10.5861 5.86856i 0.440322 0.244100i
\(579\) 0 0
\(580\) 6.22792 + 14.1031i 0.258600 + 0.585600i
\(581\) 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
\(590\) 3.94113 43.5045i 0.162254 1.79105i
\(591\) 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
\(595\) 0.321735 + 1.68323i 0.0131899 + 0.0690056i
\(596\) −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 \(0.0479108\pi\)
−0.988694 + 0.149948i \(0.952089\pi\)
\(600\) 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
\(605\) −3.91708 20.4931i −0.159252 0.833162i
\(606\) 0 0
\(607\) −27.4473 −1.11405 −0.557026 0.830495i \(-0.688058\pi\)
−0.557026 + 0.830495i \(0.688058\pi\)
\(608\) −2.33364 + 0.412017i −0.0946416 + 0.0167095i
\(609\) 0 0
\(610\) −4.56027 0.413121i −0.184640 0.0167268i
\(611\) −9.95153 9.95153i −0.402596 0.402596i
\(612\) 0 0
\(613\) −17.6219 17.6219i −0.711742 0.711742i 0.255158 0.966899i \(-0.417873\pi\)
−0.966899 + 0.255158i \(0.917873\pi\)
\(614\) −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 \(0.737338\pi\)
\(620\) −10.5734 4.09561i −0.424639 0.164483i
\(621\) 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
\(635\) 39.7919 7.60589i 1.57909 0.301830i
\(636\) 0 0
\(637\) 10.3275 10.3275i 0.409192 0.409192i
\(638\) 3.05404 + 5.50906i 0.120911 + 0.218106i
\(639\) 0 0
\(640\) −21.0129 + 14.0876i −0.830607 + 0.556859i
\(641\) 8.31451i 0.328404i −0.986427 0.164202i \(-0.947495\pi\)
0.986427 0.164202i \(-0.0525048\pi\)
\(642\) 0 0
\(643\) −17.1504 17.1504i −0.676344 0.676344i 0.282827 0.959171i \(-0.408728\pi\)
−0.959171 + 0.282827i \(0.908728\pi\)
\(644\) 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
\(650\) 1.46573 + 14.8295i 0.0574908 + 0.581661i
\(651\) 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 0.999678 0.0253938i \(-0.00808397\pi\)
−0.0253938 + 0.999678i \(0.508084\pi\)
\(660\) 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
\(670\) −16.3543 1.48156i −0.631822 0.0572376i
\(671\) −1.87083 −0.0722224
\(672\) 0 0
\(673\) 26.0623i 1.00463i −0.864685 0.502315i \(-0.832482\pi\)
0.864685 0.502315i \(-0.167518\pi\)
\(674\) −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
\(680\) 2.50293 + 18.2040i 0.0959830 + 0.698091i
\(681\) 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
\(685\) 4.34096 + 22.7107i 0.165860 + 0.867731i
\(686\) −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
\(700\) 2.59489 + 0.474038i 0.0980774 + 0.0179170i
\(701\) 26.5344 26.5344i 1.00219 1.00219i 0.00219271 0.999998i \(-0.499302\pi\)
0.999998 0.00219271i \(-0.000697963\pi\)
\(702\) 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 \(0.919622\pi\)
\(710\) 15.9089 + 19.0785i 0.597052 + 0.716003i
\(711\) 0 0
\(712\) −1.95467 + 37.3925i −0.0732545 + 1.40135i
\(713\) 7.97758i 0.298763i
\(714\) 0 0
\(715\) 1.14306 + 5.98017i 0.0427480 + 0.223646i
\(716\) −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 \(-0.447418\pi\)
0.164441 + 0.986387i \(0.447418\pi\)
\(720\) 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
\(725\) 6.83390 15.8242i 0.253805 0.587695i
\(726\) 0 0
\(727\) 10.5815i 0.392448i −0.980559 0.196224i \(-0.937132\pi\)
0.980559 0.196224i \(-0.0628679\pi\)
\(728\) −1.16833 + 1.05225i −0.0433012 + 0.0389990i
\(729\) 0 0
\(730\) 30.1941 25.1779i 1.11753 0.931876i
\(731\) −13.1111 + 13.1111i −0.484931 + 0.484931i
\(732\) 0 0
\(733\) 0.891694 0.891694i 0.0329355 0.0329355i −0.690447 0.723383i \(-0.742586\pi\)
0.723383 + 0.690447i \(0.242586\pi\)
\(734\) −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 \(0.445810\pi\)
\(740\) −8.88405 + 3.92318i −0.326584 + 0.144219i
\(741\) 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
\(755\) 32.9388 6.29598i 1.19877 0.229134i
\(756\) 0 0
\(757\) −22.8329 22.8329i −0.829876 0.829876i 0.157623 0.987499i \(-0.449617\pi\)
−0.987499 + 0.157623i \(0.949617\pi\)
\(758\) −3.07229 0.880817i −0.111591 0.0319927i
\(759\) 0 0
\(760\) 2.11116 + 1.60079i 0.0765799 + 0.0580669i
\(761\) 18.3941 0.666784 0.333392 0.942788i \(-0.391807\pi\)
0.333392 + 0.942788i \(0.391807\pi\)
\(762\) 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 \(0.428839\pi\)
\(770\) 1.07335 + 0.0972358i 0.0386807 + 0.00350414i
\(771\) 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 \(0.0493118\pi\)
0.154299 + 0.988024i \(0.450688\pi\)
\(788\) 7.62641 + 33.0203i 0.271680 + 1.17630i
\(789\) 0 0
\(790\) 21.7094 + 26.0345i 0.772384 + 0.926267i
\(791\) 1.02583i