Properties

Label 684.3.m.a.353.9
Level $684$
Weight $3$
Character 684.353
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 353.9
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.38029 + 1.82598i) q^{3} +5.89395i q^{5} +(-0.351537 + 0.608880i) q^{7} +(2.33159 - 8.69274i) q^{9} +O(q^{10})\) \(q+(-2.38029 + 1.82598i) q^{3} +5.89395i q^{5} +(-0.351537 + 0.608880i) q^{7} +(2.33159 - 8.69274i) q^{9} +(15.3415 + 8.85744i) q^{11} +(7.81809 - 13.5413i) q^{13} +(-10.7622 - 14.0293i) q^{15} +(19.3842 + 11.1915i) q^{17} +(18.0937 - 5.79811i) q^{19} +(-0.275041 - 2.09121i) q^{21} +(2.81046 + 1.62262i) q^{23} -9.73867 q^{25} +(10.3229 + 24.9487i) q^{27} +7.47447i q^{29} +(4.28250 + 7.41751i) q^{31} +(-52.6909 + 6.93003i) q^{33} +(-3.58871 - 2.07194i) q^{35} -37.7752 q^{37} +(6.11685 + 46.5080i) q^{39} -52.3411i q^{41} +(-3.07286 - 5.32236i) q^{43} +(51.2346 + 13.7423i) q^{45} +71.9825i q^{47} +(24.2528 + 42.0072i) q^{49} +(-66.5755 + 8.75617i) q^{51} +(-20.4757 + 11.8217i) q^{53} +(-52.2053 + 90.4223i) q^{55} +(-32.4811 + 46.8399i) q^{57} -54.8968i q^{59} -69.6850 q^{61} +(4.47319 + 4.47548i) q^{63} +(79.8119 + 46.0794i) q^{65} +(51.2608 - 88.7864i) q^{67} +(-9.65260 + 1.26953i) q^{69} +(-7.22572 - 4.17177i) q^{71} +(-39.6816 + 68.7305i) q^{73} +(23.1809 - 17.7826i) q^{75} +(-10.7862 + 6.22743i) q^{77} +(58.3917 + 101.137i) q^{79} +(-70.1273 - 40.5359i) q^{81} +(86.3290 + 49.8421i) q^{83} +(-65.9620 + 114.250i) q^{85} +(-13.6482 - 17.7914i) q^{87} +(4.82896 - 2.78800i) q^{89} +(5.49669 + 9.52055i) q^{91} +(-23.7378 - 9.83609i) q^{93} +(34.1738 + 106.643i) q^{95} +(-52.8639 - 91.5630i) q^{97} +(112.766 - 112.708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.38029 + 1.82598i −0.793431 + 0.608660i
\(4\) 0 0
\(5\) 5.89395i 1.17879i 0.807845 + 0.589395i \(0.200634\pi\)
−0.807845 + 0.589395i \(0.799366\pi\)
\(6\) 0 0
\(7\) −0.351537 + 0.608880i −0.0502196 + 0.0869828i −0.890042 0.455878i \(-0.849325\pi\)
0.839823 + 0.542861i \(0.182659\pi\)
\(8\) 0 0
\(9\) 2.33159 8.69274i 0.259066 0.965860i
\(10\) 0 0
\(11\) 15.3415 + 8.85744i 1.39468 + 0.805222i 0.993829 0.110920i \(-0.0353796\pi\)
0.400856 + 0.916141i \(0.368713\pi\)
\(12\) 0 0
\(13\) 7.81809 13.5413i 0.601391 1.04164i −0.391219 0.920298i \(-0.627947\pi\)
0.992611 0.121343i \(-0.0387201\pi\)
\(14\) 0 0
\(15\) −10.7622 14.0293i −0.717483 0.935289i
\(16\) 0 0
\(17\) 19.3842 + 11.1915i 1.14025 + 0.658322i 0.946492 0.322728i \(-0.104600\pi\)
0.193755 + 0.981050i \(0.437933\pi\)
\(18\) 0 0
\(19\) 18.0937 5.79811i 0.952300 0.305164i
\(20\) 0 0
\(21\) −0.275041 2.09121i −0.0130972 0.0995815i
\(22\) 0 0
\(23\) 2.81046 + 1.62262i 0.122194 + 0.0705487i 0.559851 0.828593i \(-0.310858\pi\)
−0.437657 + 0.899142i \(0.644192\pi\)
\(24\) 0 0
\(25\) −9.73867 −0.389547
\(26\) 0 0
\(27\) 10.3229 + 24.9487i 0.382329 + 0.924026i
\(28\) 0 0
\(29\) 7.47447i 0.257740i 0.991661 + 0.128870i \(0.0411351\pi\)
−0.991661 + 0.128870i \(0.958865\pi\)
\(30\) 0 0
\(31\) 4.28250 + 7.41751i 0.138145 + 0.239275i 0.926795 0.375569i \(-0.122553\pi\)
−0.788649 + 0.614843i \(0.789219\pi\)
\(32\) 0 0
\(33\) −52.6909 + 6.93003i −1.59669 + 0.210001i
\(34\) 0 0
\(35\) −3.58871 2.07194i −0.102535 0.0591983i
\(36\) 0 0
\(37\) −37.7752 −1.02095 −0.510476 0.859892i \(-0.670531\pi\)
−0.510476 + 0.859892i \(0.670531\pi\)
\(38\) 0 0
\(39\) 6.11685 + 46.5080i 0.156842 + 1.19251i
\(40\) 0 0
\(41\) 52.3411i 1.27661i −0.769783 0.638306i \(-0.779636\pi\)
0.769783 0.638306i \(-0.220364\pi\)
\(42\) 0 0
\(43\) −3.07286 5.32236i −0.0714620 0.123776i 0.828080 0.560610i \(-0.189433\pi\)
−0.899542 + 0.436834i \(0.856100\pi\)
\(44\) 0 0
\(45\) 51.2346 + 13.7423i 1.13855 + 0.305384i
\(46\) 0 0
\(47\) 71.9825i 1.53154i 0.643113 + 0.765771i \(0.277642\pi\)
−0.643113 + 0.765771i \(0.722358\pi\)
\(48\) 0 0
\(49\) 24.2528 + 42.0072i 0.494956 + 0.857289i
\(50\) 0 0
\(51\) −66.5755 + 8.75617i −1.30540 + 0.171690i
\(52\) 0 0
\(53\) −20.4757 + 11.8217i −0.386334 + 0.223050i −0.680571 0.732682i \(-0.738268\pi\)
0.294236 + 0.955733i \(0.404935\pi\)
\(54\) 0 0
\(55\) −52.2053 + 90.4223i −0.949188 + 1.64404i
\(56\) 0 0
\(57\) −32.4811 + 46.8399i −0.569843 + 0.821753i
\(58\) 0 0
\(59\) 54.8968i 0.930454i −0.885192 0.465227i \(-0.845973\pi\)
0.885192 0.465227i \(-0.154027\pi\)
\(60\) 0 0
\(61\) −69.6850 −1.14238 −0.571189 0.820819i \(-0.693518\pi\)
−0.571189 + 0.820819i \(0.693518\pi\)
\(62\) 0 0
\(63\) 4.47319 + 4.47548i 0.0710030 + 0.0710393i
\(64\) 0 0
\(65\) 79.8119 + 46.0794i 1.22788 + 0.708915i
\(66\) 0 0
\(67\) 51.2608 88.7864i 0.765087 1.32517i −0.175114 0.984548i \(-0.556029\pi\)
0.940201 0.340621i \(-0.110637\pi\)
\(68\) 0 0
\(69\) −9.65260 + 1.26953i −0.139893 + 0.0183990i
\(70\) 0 0
\(71\) −7.22572 4.17177i −0.101771 0.0587573i 0.448251 0.893908i \(-0.352047\pi\)
−0.550021 + 0.835151i \(0.685380\pi\)
\(72\) 0 0
\(73\) −39.6816 + 68.7305i −0.543583 + 0.941513i 0.455112 + 0.890434i \(0.349599\pi\)
−0.998695 + 0.0510789i \(0.983734\pi\)
\(74\) 0 0
\(75\) 23.1809 17.7826i 0.309079 0.237102i
\(76\) 0 0
\(77\) −10.7862 + 6.22743i −0.140081 + 0.0808758i
\(78\) 0 0
\(79\) 58.3917 + 101.137i 0.739136 + 1.28022i 0.952885 + 0.303332i \(0.0980992\pi\)
−0.213749 + 0.976889i \(0.568567\pi\)
\(80\) 0 0
\(81\) −70.1273 40.5359i −0.865770 0.500443i
\(82\) 0 0
\(83\) 86.3290 + 49.8421i 1.04011 + 0.600507i 0.919864 0.392238i \(-0.128299\pi\)
0.120244 + 0.992744i \(0.461632\pi\)
\(84\) 0 0
\(85\) −65.9620 + 114.250i −0.776023 + 1.34411i
\(86\) 0 0
\(87\) −13.6482 17.7914i −0.156876 0.204499i
\(88\) 0 0
\(89\) 4.82896 2.78800i 0.0542580 0.0313259i −0.472626 0.881263i \(-0.656694\pi\)
0.526884 + 0.849937i \(0.323360\pi\)
\(90\) 0 0
\(91\) 5.49669 + 9.52055i 0.0604032 + 0.104621i
\(92\) 0 0
\(93\) −23.7378 9.83609i −0.255246 0.105764i
\(94\) 0 0
\(95\) 34.1738 + 106.643i 0.359724 + 1.12256i
\(96\) 0 0
\(97\) −52.8639 91.5630i −0.544989 0.943948i −0.998608 0.0527524i \(-0.983201\pi\)
0.453619 0.891196i \(-0.350133\pi\)
\(98\) 0 0
\(99\) 112.766 112.708i 1.13905 1.13846i
\(100\) 0 0
\(101\) 116.203i 1.15053i −0.817969 0.575263i \(-0.804900\pi\)
0.817969 0.575263i \(-0.195100\pi\)
\(102\) 0 0
\(103\) 42.8692 + 74.2516i 0.416205 + 0.720889i 0.995554 0.0941908i \(-0.0300264\pi\)
−0.579349 + 0.815080i \(0.696693\pi\)
\(104\) 0 0
\(105\) 12.3255 1.62108i 0.117386 0.0154389i
\(106\) 0 0
\(107\) 197.729i 1.84794i 0.382467 + 0.923969i \(0.375075\pi\)
−0.382467 + 0.923969i \(0.624925\pi\)
\(108\) 0 0
\(109\) −30.6364 + 53.0638i −0.281068 + 0.486824i −0.971648 0.236432i \(-0.924022\pi\)
0.690580 + 0.723256i \(0.257355\pi\)
\(110\) 0 0
\(111\) 89.9161 68.9768i 0.810055 0.621412i
\(112\) 0 0
\(113\) 14.7705 8.52775i 0.130712 0.0754668i −0.433218 0.901289i \(-0.642622\pi\)
0.563930 + 0.825822i \(0.309289\pi\)
\(114\) 0 0
\(115\) −9.56365 + 16.5647i −0.0831622 + 0.144041i
\(116\) 0 0
\(117\) −99.4826 99.5335i −0.850279 0.850713i
\(118\) 0 0
\(119\) −13.6285 + 7.86843i −0.114525 + 0.0661213i
\(120\) 0 0
\(121\) 96.4084 + 166.984i 0.796764 + 1.38004i
\(122\) 0 0
\(123\) 95.5737 + 124.587i 0.777022 + 1.01290i
\(124\) 0 0
\(125\) 89.9495i 0.719596i
\(126\) 0 0
\(127\) −13.0431 22.5913i −0.102702 0.177885i 0.810095 0.586298i \(-0.199415\pi\)
−0.912797 + 0.408414i \(0.866082\pi\)
\(128\) 0 0
\(129\) 17.0328 + 7.05778i 0.132038 + 0.0547115i
\(130\) 0 0
\(131\) 47.2412i 0.360619i −0.983610 0.180310i \(-0.942290\pi\)
0.983610 0.180310i \(-0.0577100\pi\)
\(132\) 0 0
\(133\) −2.83025 + 13.0551i −0.0212801 + 0.0981589i
\(134\) 0 0
\(135\) −147.046 + 60.8426i −1.08923 + 0.450686i
\(136\) 0 0
\(137\) 199.989i 1.45977i −0.683568 0.729887i \(-0.739573\pi\)
0.683568 0.729887i \(-0.260427\pi\)
\(138\) 0 0
\(139\) 26.1789 45.3431i 0.188337 0.326210i −0.756359 0.654157i \(-0.773024\pi\)
0.944696 + 0.327947i \(0.106357\pi\)
\(140\) 0 0
\(141\) −131.439 171.339i −0.932188 1.21517i
\(142\) 0 0
\(143\) 239.883 138.496i 1.67750 0.968507i
\(144\) 0 0
\(145\) −44.0542 −0.303822
\(146\) 0 0
\(147\) −134.433 55.7042i −0.914511 0.378940i
\(148\) 0 0
\(149\) 95.0740i 0.638081i −0.947741 0.319040i \(-0.896639\pi\)
0.947741 0.319040i \(-0.103361\pi\)
\(150\) 0 0
\(151\) −17.7076 + 30.6705i −0.117269 + 0.203116i −0.918684 0.394992i \(-0.870747\pi\)
0.801416 + 0.598108i \(0.204081\pi\)
\(152\) 0 0
\(153\) 142.481 142.408i 0.931245 0.930770i
\(154\) 0 0
\(155\) −43.7185 + 25.2409i −0.282055 + 0.162844i
\(156\) 0 0
\(157\) 52.3742 0.333593 0.166797 0.985991i \(-0.446658\pi\)
0.166797 + 0.985991i \(0.446658\pi\)
\(158\) 0 0
\(159\) 27.1521 65.5273i 0.170768 0.412121i
\(160\) 0 0
\(161\) −1.97596 + 1.14082i −0.0122731 + 0.00708585i
\(162\) 0 0
\(163\) −263.493 −1.61652 −0.808261 0.588824i \(-0.799591\pi\)
−0.808261 + 0.588824i \(0.799591\pi\)
\(164\) 0 0
\(165\) −40.8453 310.557i −0.247547 1.88217i
\(166\) 0 0
\(167\) −225.097 129.960i −1.34789 0.778202i −0.359936 0.932977i \(-0.617201\pi\)
−0.987950 + 0.154775i \(0.950535\pi\)
\(168\) 0 0
\(169\) −37.7450 65.3763i −0.223343 0.386842i
\(170\) 0 0
\(171\) −8.21430 170.803i −0.0480369 0.998846i
\(172\) 0 0
\(173\) 45.1264 26.0537i 0.260846 0.150600i −0.363874 0.931448i \(-0.618546\pi\)
0.624721 + 0.780848i \(0.285213\pi\)
\(174\) 0 0
\(175\) 3.42350 5.92968i 0.0195629 0.0338839i
\(176\) 0 0
\(177\) 100.240 + 130.670i 0.566330 + 0.738251i
\(178\) 0 0
\(179\) 173.576i 0.969697i 0.874598 + 0.484849i \(0.161125\pi\)
−0.874598 + 0.484849i \(0.838875\pi\)
\(180\) 0 0
\(181\) −116.587 201.934i −0.644125 1.11566i −0.984503 0.175369i \(-0.943888\pi\)
0.340378 0.940289i \(-0.389445\pi\)
\(182\) 0 0
\(183\) 165.871 127.243i 0.906398 0.695320i
\(184\) 0 0
\(185\) 222.645i 1.20349i
\(186\) 0 0
\(187\) 198.256 + 343.389i 1.06019 + 1.83630i
\(188\) 0 0
\(189\) −18.8196 2.48499i −0.0995748 0.0131481i
\(190\) 0 0
\(191\) 120.700 + 69.6861i 0.631936 + 0.364849i 0.781502 0.623903i \(-0.214454\pi\)
−0.149565 + 0.988752i \(0.547787\pi\)
\(192\) 0 0
\(193\) −95.5330 −0.494990 −0.247495 0.968889i \(-0.579607\pi\)
−0.247495 + 0.968889i \(0.579607\pi\)
\(194\) 0 0
\(195\) −274.116 + 36.0524i −1.40572 + 0.184884i
\(196\) 0 0
\(197\) 310.234i 1.57479i −0.616446 0.787397i \(-0.711428\pi\)
0.616446 0.787397i \(-0.288572\pi\)
\(198\) 0 0
\(199\) 119.255 + 206.556i 0.599271 + 1.03797i 0.992929 + 0.118711i \(0.0378761\pi\)
−0.393658 + 0.919257i \(0.628791\pi\)
\(200\) 0 0
\(201\) 40.1063 + 304.939i 0.199534 + 1.51711i
\(202\) 0 0
\(203\) −4.55106 2.62755i −0.0224190 0.0129436i
\(204\) 0 0
\(205\) 308.496 1.50486
\(206\) 0 0
\(207\) 20.6579 20.6473i 0.0997965 0.0997455i
\(208\) 0 0
\(209\) 328.941 + 71.3119i 1.57388 + 0.341205i
\(210\) 0 0
\(211\) −8.65754 −0.0410310 −0.0205155 0.999790i \(-0.506531\pi\)
−0.0205155 + 0.999790i \(0.506531\pi\)
\(212\) 0 0
\(213\) 24.8169 3.26398i 0.116511 0.0153238i
\(214\) 0 0
\(215\) 31.3697 18.1113i 0.145906 0.0842387i
\(216\) 0 0
\(217\) −6.02183 −0.0277504
\(218\) 0 0
\(219\) −31.0467 236.056i −0.141766 1.07788i
\(220\) 0 0
\(221\) 303.095 174.992i 1.37147 0.791818i
\(222\) 0 0
\(223\) 151.382 + 262.201i 0.678842 + 1.17579i 0.975330 + 0.220753i \(0.0708513\pi\)
−0.296488 + 0.955037i \(0.595815\pi\)
\(224\) 0 0
\(225\) −22.7066 + 84.6557i −0.100918 + 0.376248i
\(226\) 0 0
\(227\) 16.6155 + 9.59297i 0.0731961 + 0.0422598i 0.536151 0.844122i \(-0.319878\pi\)
−0.462955 + 0.886382i \(0.653211\pi\)
\(228\) 0 0
\(229\) −193.340 334.875i −0.844281 1.46234i −0.886245 0.463218i \(-0.846695\pi\)
0.0419640 0.999119i \(-0.486639\pi\)
\(230\) 0 0
\(231\) 14.3032 34.5186i 0.0619187 0.149431i
\(232\) 0 0
\(233\) 284.002 + 163.969i 1.21889 + 0.703728i 0.964681 0.263421i \(-0.0848508\pi\)
0.254211 + 0.967149i \(0.418184\pi\)
\(234\) 0 0
\(235\) −424.261 −1.80537
\(236\) 0 0
\(237\) −323.664 134.115i −1.36567 0.565885i
\(238\) 0 0
\(239\) 244.966 141.431i 1.02496 0.591762i 0.109425 0.993995i \(-0.465099\pi\)
0.915538 + 0.402233i \(0.131766\pi\)
\(240\) 0 0
\(241\) −237.088 −0.983767 −0.491884 0.870661i \(-0.663691\pi\)
−0.491884 + 0.870661i \(0.663691\pi\)
\(242\) 0 0
\(243\) 240.941 31.5639i 0.991528 0.129893i
\(244\) 0 0
\(245\) −247.588 + 142.945i −1.01056 + 0.583449i
\(246\) 0 0
\(247\) 62.9440 290.343i 0.254834 1.17548i
\(248\) 0 0
\(249\) −296.499 + 38.9963i −1.19076 + 0.156612i
\(250\) 0 0
\(251\) 85.5177 49.3737i 0.340708 0.196708i −0.319877 0.947459i \(-0.603642\pi\)
0.660585 + 0.750751i \(0.270308\pi\)
\(252\) 0 0
\(253\) 28.7445 + 49.7870i 0.113615 + 0.196787i
\(254\) 0 0
\(255\) −51.6085 392.393i −0.202386 1.53879i
\(256\) 0 0
\(257\) 129.972 + 75.0395i 0.505728 + 0.291982i 0.731076 0.682296i \(-0.239018\pi\)
−0.225348 + 0.974278i \(0.572352\pi\)
\(258\) 0 0
\(259\) 13.2794 23.0006i 0.0512717 0.0888053i
\(260\) 0 0
\(261\) 64.9736 + 17.4274i 0.248941 + 0.0667718i
\(262\) 0 0
\(263\) −303.157 + 175.028i −1.15269 + 0.665505i −0.949541 0.313643i \(-0.898451\pi\)
−0.203148 + 0.979148i \(0.565117\pi\)
\(264\) 0 0
\(265\) −69.6763 120.683i −0.262930 0.455407i
\(266\) 0 0
\(267\) −6.40351 + 15.4539i −0.0239832 + 0.0578796i
\(268\) 0 0
\(269\) 86.7627 + 50.0925i 0.322538 + 0.186217i 0.652523 0.757769i \(-0.273710\pi\)
−0.329985 + 0.943986i \(0.607044\pi\)
\(270\) 0 0
\(271\) 102.668 177.826i 0.378849 0.656186i −0.612046 0.790822i \(-0.709653\pi\)
0.990895 + 0.134636i \(0.0429865\pi\)
\(272\) 0 0
\(273\) −30.4681 12.6249i −0.111605 0.0462449i
\(274\) 0 0
\(275\) −149.406 86.2597i −0.543295 0.313672i
\(276\) 0 0
\(277\) −111.754 + 193.564i −0.403444 + 0.698786i −0.994139 0.108109i \(-0.965520\pi\)
0.590695 + 0.806895i \(0.298854\pi\)
\(278\) 0 0
\(279\) 74.4635 19.9320i 0.266894 0.0714410i
\(280\) 0 0
\(281\) 174.168i 0.619817i −0.950766 0.309908i \(-0.899702\pi\)
0.950766 0.309908i \(-0.100298\pi\)
\(282\) 0 0
\(283\) −421.632 −1.48987 −0.744933 0.667139i \(-0.767519\pi\)
−0.744933 + 0.667139i \(0.767519\pi\)
\(284\) 0 0
\(285\) −276.072 191.442i −0.968675 0.671726i
\(286\) 0 0
\(287\) 31.8694 + 18.3998i 0.111043 + 0.0641108i
\(288\) 0 0
\(289\) 105.998 + 183.594i 0.366775 + 0.635273i
\(290\) 0 0
\(291\) 293.024 + 121.418i 1.00695 + 0.417245i
\(292\) 0 0
\(293\) −411.502 + 237.581i −1.40444 + 0.810855i −0.994845 0.101411i \(-0.967664\pi\)
−0.409598 + 0.912266i \(0.634331\pi\)
\(294\) 0 0
\(295\) 323.559 1.09681
\(296\) 0 0
\(297\) −62.6127 + 474.186i −0.210817 + 1.59659i
\(298\) 0 0
\(299\) 43.9449 25.3716i 0.146973 0.0848548i
\(300\) 0 0
\(301\) 4.32090 0.0143552
\(302\) 0 0
\(303\) 212.184 + 276.597i 0.700279 + 0.912863i
\(304\) 0 0
\(305\) 410.720i 1.34662i
\(306\) 0 0
\(307\) 112.818 195.406i 0.367485 0.636503i −0.621687 0.783266i \(-0.713552\pi\)
0.989172 + 0.146763i \(0.0468856\pi\)
\(308\) 0 0
\(309\) −237.623 98.4623i −0.769007 0.318648i
\(310\) 0 0
\(311\) 239.811 138.455i 0.771095 0.445192i −0.0621700 0.998066i \(-0.519802\pi\)
0.833265 + 0.552874i \(0.186469\pi\)
\(312\) 0 0
\(313\) −506.860 −1.61936 −0.809681 0.586870i \(-0.800360\pi\)
−0.809681 + 0.586870i \(0.800360\pi\)
\(314\) 0 0
\(315\) −26.3783 + 26.3648i −0.0837405 + 0.0836977i
\(316\) 0 0
\(317\) 518.454i 1.63550i 0.575573 + 0.817750i \(0.304779\pi\)
−0.575573 + 0.817750i \(0.695221\pi\)
\(318\) 0 0
\(319\) −66.2047 + 114.670i −0.207538 + 0.359467i
\(320\) 0 0
\(321\) −361.050 470.654i −1.12477 1.46621i
\(322\) 0 0
\(323\) 415.621 + 90.1034i 1.28675 + 0.278958i
\(324\) 0 0
\(325\) −76.1378 + 131.875i −0.234270 + 0.405768i
\(326\) 0 0
\(327\) −23.9698 182.249i −0.0733022 0.557336i
\(328\) 0 0
\(329\) −43.8287 25.3045i −0.133218 0.0769134i
\(330\) 0 0
\(331\) 155.993 270.188i 0.471278 0.816278i −0.528182 0.849131i \(-0.677126\pi\)
0.999460 + 0.0328536i \(0.0104595\pi\)
\(332\) 0 0
\(333\) −88.0764 + 328.370i −0.264494 + 0.986096i
\(334\) 0 0
\(335\) 523.303 + 302.129i 1.56210 + 0.901877i
\(336\) 0 0
\(337\) 523.845 1.55444 0.777218 0.629232i \(-0.216630\pi\)
0.777218 + 0.629232i \(0.216630\pi\)
\(338\) 0 0
\(339\) −19.5866 + 47.2692i −0.0577776 + 0.139437i
\(340\) 0 0
\(341\) 151.728i 0.444950i
\(342\) 0 0
\(343\) −68.5537 −0.199865
\(344\) 0 0
\(345\) −7.48257 56.8920i −0.0216886 0.164904i
\(346\) 0 0
\(347\) 297.721i 0.857986i 0.903308 + 0.428993i \(0.141132\pi\)
−0.903308 + 0.428993i \(0.858868\pi\)
\(348\) 0 0
\(349\) −45.0994 + 78.1145i −0.129225 + 0.223824i −0.923376 0.383896i \(-0.874582\pi\)
0.794152 + 0.607720i \(0.207916\pi\)
\(350\) 0 0
\(351\) 418.544 + 55.2656i 1.19243 + 0.157452i
\(352\) 0 0
\(353\) 360.529 + 208.152i 1.02133 + 0.589665i 0.914489 0.404611i \(-0.132593\pi\)
0.106841 + 0.994276i \(0.465927\pi\)
\(354\) 0 0
\(355\) 24.5882 42.5880i 0.0692626 0.119966i
\(356\) 0 0
\(357\) 18.0723 43.6146i 0.0506226 0.122170i
\(358\) 0 0
\(359\) 53.4979 + 30.8870i 0.149019 + 0.0860362i 0.572656 0.819796i \(-0.305913\pi\)
−0.423636 + 0.905832i \(0.639247\pi\)
\(360\) 0 0
\(361\) 293.764 209.819i 0.813750 0.581215i
\(362\) 0 0
\(363\) −534.390 221.432i −1.47215 0.610005i
\(364\) 0 0
\(365\) −405.094 233.881i −1.10985 0.640770i
\(366\) 0 0
\(367\) −314.752 −0.857635 −0.428818 0.903391i \(-0.641070\pi\)
−0.428818 + 0.903391i \(0.641070\pi\)
\(368\) 0 0
\(369\) −454.987 122.038i −1.23303 0.330726i
\(370\) 0 0
\(371\) 16.6230i 0.0448060i
\(372\) 0 0
\(373\) 83.5260 + 144.671i 0.223930 + 0.387859i 0.955998 0.293373i \(-0.0947778\pi\)
−0.732068 + 0.681232i \(0.761445\pi\)
\(374\) 0 0
\(375\) −164.246 214.106i −0.437989 0.570950i
\(376\) 0 0
\(377\) 101.214 + 58.4361i 0.268473 + 0.155003i
\(378\) 0 0
\(379\) 61.9252 0.163391 0.0816955 0.996657i \(-0.473967\pi\)
0.0816955 + 0.996657i \(0.473967\pi\)
\(380\) 0 0
\(381\) 72.2978 + 29.9575i 0.189758 + 0.0786287i
\(382\) 0 0
\(383\) 612.419i 1.59900i −0.600663 0.799502i \(-0.705097\pi\)
0.600663 0.799502i \(-0.294903\pi\)
\(384\) 0 0
\(385\) −36.7042 63.5735i −0.0953356 0.165126i
\(386\) 0 0
\(387\) −53.4305 + 14.3020i −0.138063 + 0.0369561i
\(388\) 0 0
\(389\) 90.5540i 0.232787i −0.993203 0.116393i \(-0.962867\pi\)
0.993203 0.116393i \(-0.0371333\pi\)
\(390\) 0 0
\(391\) 36.3190 + 62.9064i 0.0928876 + 0.160886i
\(392\) 0 0
\(393\) 86.2614 + 112.448i 0.219495 + 0.286127i
\(394\) 0 0
\(395\) −596.099 + 344.158i −1.50911 + 0.871286i
\(396\) 0 0
\(397\) −23.3966 + 40.5241i −0.0589335 + 0.102076i −0.893987 0.448093i \(-0.852103\pi\)
0.835053 + 0.550169i \(0.185437\pi\)
\(398\) 0 0
\(399\) −17.1016 36.2430i −0.0428611 0.0908347i
\(400\) 0 0
\(401\) 157.389i 0.392491i −0.980555 0.196245i \(-0.937125\pi\)
0.980555 0.196245i \(-0.0628749\pi\)
\(402\) 0 0
\(403\) 133.924 0.332318
\(404\) 0 0
\(405\) 238.916 413.327i 0.589917 1.02056i
\(406\) 0 0
\(407\) −579.530 334.592i −1.42391 0.822092i
\(408\) 0 0
\(409\) 185.625 321.512i 0.453851 0.786094i −0.544770 0.838586i \(-0.683383\pi\)
0.998621 + 0.0524919i \(0.0167164\pi\)
\(410\) 0 0
\(411\) 365.176 + 476.032i 0.888506 + 1.15823i
\(412\) 0 0
\(413\) 33.4255 + 19.2982i 0.0809335 + 0.0467270i
\(414\) 0 0
\(415\) −293.767 + 508.819i −0.707872 + 1.22607i
\(416\) 0 0
\(417\) 20.4823 + 155.732i 0.0491181 + 0.373458i
\(418\) 0 0
\(419\) −587.569 + 339.233i −1.40231 + 0.809625i −0.994630 0.103499i \(-0.966996\pi\)
−0.407682 + 0.913124i \(0.633663\pi\)
\(420\) 0 0
\(421\) 254.605 + 440.988i 0.604761 + 1.04748i 0.992089 + 0.125535i \(0.0400648\pi\)
−0.387328 + 0.921942i \(0.626602\pi\)
\(422\) 0 0
\(423\) 625.725 + 167.834i 1.47925 + 0.396770i
\(424\) 0 0
\(425\) −188.776 108.990i −0.444180 0.256447i
\(426\) 0 0
\(427\) 24.4969 42.4298i 0.0573697 0.0993673i
\(428\) 0 0
\(429\) −318.100 + 767.684i −0.741492 + 1.78947i
\(430\) 0 0
\(431\) 399.240 230.501i 0.926311 0.534806i 0.0406683 0.999173i \(-0.487051\pi\)
0.885643 + 0.464367i \(0.153718\pi\)
\(432\) 0 0
\(433\) 369.211 + 639.492i 0.852681 + 1.47689i 0.878780 + 0.477227i \(0.158358\pi\)
−0.0260989 + 0.999659i \(0.508308\pi\)
\(434\) 0 0
\(435\) 104.862 80.4421i 0.241062 0.184924i
\(436\) 0 0
\(437\) 60.2598 + 13.0638i 0.137894 + 0.0298944i
\(438\) 0 0
\(439\) −259.366 449.236i −0.590812 1.02332i −0.994123 0.108253i \(-0.965474\pi\)
0.403312 0.915063i \(-0.367859\pi\)
\(440\) 0 0
\(441\) 421.705 112.880i 0.956247 0.255964i
\(442\) 0 0
\(443\) 147.886i 0.333828i −0.985971 0.166914i \(-0.946620\pi\)
0.985971 0.166914i \(-0.0533802\pi\)
\(444\) 0 0
\(445\) 16.4324 + 28.4617i 0.0369266 + 0.0639588i
\(446\) 0 0
\(447\) 173.603 + 226.304i 0.388374 + 0.506273i
\(448\) 0 0
\(449\) 134.495i 0.299543i 0.988721 + 0.149771i \(0.0478538\pi\)
−0.988721 + 0.149771i \(0.952146\pi\)
\(450\) 0 0
\(451\) 463.608 802.992i 1.02795 1.78047i
\(452\) 0 0
\(453\) −13.8544 105.339i −0.0305836 0.232535i
\(454\) 0 0
\(455\) −56.1137 + 32.3973i −0.123327 + 0.0712028i
\(456\) 0 0
\(457\) −144.575 + 250.411i −0.316356 + 0.547944i −0.979725 0.200348i \(-0.935793\pi\)
0.663369 + 0.748292i \(0.269126\pi\)
\(458\) 0 0
\(459\) −79.1118 + 599.139i −0.172357 + 1.30531i
\(460\) 0 0
\(461\) −397.301 + 229.382i −0.861824 + 0.497574i −0.864623 0.502422i \(-0.832443\pi\)
0.00279853 + 0.999996i \(0.499109\pi\)
\(462\) 0 0
\(463\) 21.5817 + 37.3807i 0.0466128 + 0.0807358i 0.888390 0.459089i \(-0.151824\pi\)
−0.841778 + 0.539824i \(0.818491\pi\)
\(464\) 0 0
\(465\) 57.9735 139.910i 0.124674 0.300881i
\(466\) 0 0
\(467\) 41.0873i 0.0879814i 0.999032 + 0.0439907i \(0.0140072\pi\)
−0.999032 + 0.0439907i \(0.985993\pi\)
\(468\) 0 0
\(469\) 36.0402 + 62.4234i 0.0768447 + 0.133099i
\(470\) 0 0
\(471\) −124.666 + 95.6342i −0.264683 + 0.203045i
\(472\) 0 0
\(473\) 108.871i 0.230171i
\(474\) 0 0
\(475\) −176.209 + 56.4659i −0.370966 + 0.118876i
\(476\) 0 0
\(477\) 55.0216 + 205.553i 0.115349 + 0.430930i
\(478\) 0 0
\(479\) 901.802i 1.88268i 0.337465 + 0.941338i \(0.390430\pi\)
−0.337465 + 0.941338i \(0.609570\pi\)
\(480\) 0 0
\(481\) −295.330 + 511.526i −0.613992 + 1.06346i
\(482\) 0 0
\(483\) 2.62025 6.32356i 0.00542495 0.0130923i
\(484\) 0 0
\(485\) 539.668 311.577i 1.11272 0.642428i
\(486\) 0 0
\(487\) 7.53975 0.0154820 0.00774102 0.999970i \(-0.497536\pi\)
0.00774102 + 0.999970i \(0.497536\pi\)
\(488\) 0 0
\(489\) 627.191 481.133i 1.28260 0.983913i
\(490\) 0 0
\(491\) 672.915i 1.37050i −0.728309 0.685249i \(-0.759693\pi\)
0.728309 0.685249i \(-0.240307\pi\)
\(492\) 0 0
\(493\) −83.6504 + 144.887i −0.169676 + 0.293888i
\(494\) 0 0
\(495\) 664.295 + 664.635i 1.34201 + 1.34270i
\(496\) 0 0
\(497\) 5.08021 2.93306i 0.0102218 0.00590153i
\(498\) 0 0
\(499\) 835.632 1.67461 0.837307 0.546733i \(-0.184129\pi\)
0.837307 + 0.546733i \(0.184129\pi\)
\(500\) 0 0
\(501\) 773.101 101.680i 1.54311 0.202954i
\(502\) 0 0
\(503\) −229.542 + 132.526i −0.456347 + 0.263472i −0.710507 0.703690i \(-0.751534\pi\)
0.254160 + 0.967162i \(0.418201\pi\)
\(504\) 0 0
\(505\) 684.895 1.35623
\(506\) 0 0
\(507\) 209.220 + 86.6931i 0.412663 + 0.170992i
\(508\) 0 0
\(509\) −44.0537 25.4344i −0.0865496 0.0499694i 0.456101 0.889928i \(-0.349246\pi\)
−0.542650 + 0.839959i \(0.682579\pi\)
\(510\) 0 0
\(511\) −27.8991 48.3226i −0.0545970 0.0945648i
\(512\) 0 0
\(513\) 331.435 + 391.561i 0.646071 + 0.763277i
\(514\) 0 0
\(515\) −437.635 + 252.669i −0.849777 + 0.490619i
\(516\) 0 0
\(517\) −637.580 + 1104.32i −1.23323 + 2.13602i
\(518\) 0 0
\(519\) −59.8405 + 144.415i −0.115300 + 0.278257i
\(520\) 0 0
\(521\) 775.621i 1.48872i −0.667781 0.744358i \(-0.732756\pi\)
0.667781 0.744358i \(-0.267244\pi\)
\(522\) 0 0
\(523\) −422.410 731.635i −0.807667 1.39892i −0.914476 0.404641i \(-0.867396\pi\)
0.106808 0.994280i \(-0.465937\pi\)
\(524\) 0 0
\(525\) 2.67854 + 20.3656i 0.00510198 + 0.0387917i
\(526\) 0 0
\(527\) 191.710i 0.363776i
\(528\) 0 0
\(529\) −259.234 449.007i −0.490046 0.848784i
\(530\) 0 0
\(531\) −477.203 127.997i −0.898688 0.241049i
\(532\) 0 0
\(533\) −708.767 409.207i −1.32977 0.767743i
\(534\) 0 0
\(535\) −1165.41 −2.17833
\(536\) 0 0
\(537\) −316.946 413.161i −0.590216 0.769388i
\(538\) 0 0
\(539\) 859.272i 1.59420i
\(540\) 0 0
\(541\) 451.156 + 781.425i 0.833929 + 1.44441i 0.894899 + 0.446268i \(0.147247\pi\)
−0.0609701 + 0.998140i \(0.519419\pi\)
\(542\) 0 0
\(543\) 646.238 + 267.777i 1.19012 + 0.493144i
\(544\) 0 0
\(545\) −312.755 180.569i −0.573863 0.331320i
\(546\) 0 0
\(547\) −184.656 −0.337580 −0.168790 0.985652i \(-0.553986\pi\)
−0.168790 + 0.985652i \(0.553986\pi\)
\(548\) 0 0
\(549\) −162.477 + 605.754i −0.295951 + 1.10338i
\(550\) 0 0
\(551\) 43.3378 + 135.241i 0.0786530 + 0.245446i
\(552\) 0 0
\(553\) −82.1074 −0.148476
\(554\) 0 0
\(555\) 406.546 + 529.961i 0.732515 + 0.954885i
\(556\) 0 0
\(557\) 218.277 126.022i 0.391880 0.226252i −0.291095 0.956694i \(-0.594019\pi\)
0.682974 + 0.730442i \(0.260686\pi\)
\(558\) 0 0
\(559\) −96.0957 −0.171906
\(560\) 0 0
\(561\) −1098.93 455.355i −1.95887 0.811685i
\(562\) 0 0
\(563\) −561.132 + 323.970i −0.996683 + 0.575435i −0.907265 0.420559i \(-0.861834\pi\)
−0.0894175 + 0.995994i \(0.528501\pi\)
\(564\) 0 0
\(565\) 50.2622 + 87.0566i 0.0889596 + 0.154083i
\(566\) 0 0
\(567\) 49.3338 28.4493i 0.0870085 0.0501751i
\(568\) 0 0
\(569\) −154.886 89.4234i −0.272207 0.157159i 0.357683 0.933843i \(-0.383567\pi\)
−0.629890 + 0.776684i \(0.716900\pi\)
\(570\) 0 0
\(571\) 291.759 + 505.342i 0.510962 + 0.885012i 0.999919 + 0.0127040i \(0.00404393\pi\)
−0.488958 + 0.872308i \(0.662623\pi\)
\(572\) 0 0
\(573\) −414.546 + 54.5222i −0.723467 + 0.0951521i
\(574\) 0 0
\(575\) −27.3702 15.8022i −0.0476003 0.0274821i
\(576\) 0 0
\(577\) 536.087 0.929094 0.464547 0.885549i \(-0.346217\pi\)
0.464547 + 0.885549i \(0.346217\pi\)
\(578\) 0 0
\(579\) 227.397 174.441i 0.392740 0.301280i
\(580\) 0 0
\(581\) −60.6957 + 35.0427i −0.104468 + 0.0603144i
\(582\) 0 0
\(583\) −418.839 −0.718420
\(584\) 0 0
\(585\) 586.645 586.346i 1.00281 1.00230i
\(586\) 0 0
\(587\) −382.920 + 221.079i −0.652334 + 0.376625i −0.789350 0.613944i \(-0.789582\pi\)
0.137016 + 0.990569i \(0.456249\pi\)
\(588\) 0 0
\(589\) 120.494 + 109.380i 0.204574 + 0.185704i
\(590\) 0 0
\(591\) 566.482 + 738.449i 0.958514 + 1.24949i
\(592\) 0 0
\(593\) −410.110 + 236.777i −0.691585 + 0.399287i −0.804205 0.594351i \(-0.797409\pi\)
0.112621 + 0.993638i \(0.464076\pi\)
\(594\) 0 0
\(595\) −46.3762 80.3259i −0.0779431 0.135001i
\(596\) 0 0
\(597\) −661.028 273.906i −1.10725 0.458804i
\(598\) 0 0
\(599\) 774.211 + 446.991i 1.29251 + 0.746228i 0.979098 0.203391i \(-0.0651961\pi\)
0.313407 + 0.949619i \(0.398529\pi\)
\(600\) 0 0
\(601\) 42.3132 73.2886i 0.0704047 0.121944i −0.828674 0.559731i \(-0.810904\pi\)
0.899079 + 0.437787i \(0.144238\pi\)
\(602\) 0 0
\(603\) −652.277 652.611i −1.08172 1.08227i
\(604\) 0 0
\(605\) −984.198 + 568.227i −1.62677 + 0.939218i
\(606\) 0 0
\(607\) −444.617 770.099i −0.732483 1.26870i −0.955819 0.293956i \(-0.905028\pi\)
0.223336 0.974741i \(-0.428305\pi\)
\(608\) 0 0
\(609\) 15.6307 2.05579i 0.0256662 0.00337568i
\(610\) 0 0
\(611\) 974.738 + 562.765i 1.59532 + 0.921056i
\(612\) 0 0
\(613\) 329.622 570.923i 0.537720 0.931359i −0.461306 0.887241i \(-0.652619\pi\)
0.999026 0.0441175i \(-0.0140476\pi\)
\(614\) 0 0
\(615\) −734.310 + 563.307i −1.19400 + 0.915946i
\(616\) 0 0
\(617\) −179.946 103.892i −0.291646 0.168382i 0.347038 0.937851i \(-0.387188\pi\)
−0.638684 + 0.769469i \(0.720521\pi\)
\(618\) 0 0
\(619\) 403.579 699.019i 0.651985 1.12927i −0.330656 0.943751i \(-0.607270\pi\)
0.982641 0.185520i \(-0.0593968\pi\)
\(620\) 0 0
\(621\) −11.4702 + 86.8675i −0.0184706 + 0.139883i
\(622\) 0 0
\(623\) 3.92034i 0.00629269i
\(624\) 0 0
\(625\) −773.625 −1.23780
\(626\) 0 0
\(627\) −913.191 + 430.897i −1.45645 + 0.687237i
\(628\) 0 0
\(629\) −732.242 422.760i −1.16414 0.672115i
\(630\) 0 0
\(631\) −496.871 860.606i −0.787435 1.36388i −0.927534 0.373740i \(-0.878075\pi\)
0.140099 0.990138i \(-0.455258\pi\)
\(632\) 0 0
\(633\) 20.6075 15.8085i 0.0325553 0.0249739i
\(634\) 0 0
\(635\) 133.152 76.8755i 0.209689 0.121064i
\(636\) 0 0
\(637\) 758.444 1.19065
\(638\) 0 0
\(639\) −53.1115 + 53.0844i −0.0831166 + 0.0830741i
\(640\) 0 0
\(641\) −751.727 + 434.010i −1.17274 + 0.677083i −0.954324 0.298773i \(-0.903423\pi\)
−0.218417 + 0.975855i \(0.570089\pi\)
\(642\) 0 0
\(643\) 209.372 0.325617 0.162808 0.986658i \(-0.447945\pi\)
0.162808 + 0.986658i \(0.447945\pi\)
\(644\) 0 0
\(645\) −41.5982 + 100.391i −0.0644934 + 0.155645i
\(646\) 0 0
\(647\) 570.098i 0.881140i 0.897718 + 0.440570i \(0.145224\pi\)
−0.897718 + 0.440570i \(0.854776\pi\)
\(648\) 0 0
\(649\) 486.245 842.201i 0.749221 1.29769i
\(650\) 0 0
\(651\) 14.3337 10.9957i 0.0220180 0.0168905i
\(652\) 0 0
\(653\) 343.712 198.442i 0.526358 0.303893i −0.213174 0.977014i \(-0.568380\pi\)
0.739532 + 0.673121i \(0.235047\pi\)
\(654\) 0 0
\(655\) 278.437 0.425095
\(656\) 0 0
\(657\) 504.935 + 505.193i 0.768546 + 0.768939i
\(658\) 0 0
\(659\) 395.517i 0.600178i −0.953911 0.300089i \(-0.902984\pi\)
0.953911 0.300089i \(-0.0970164\pi\)
\(660\) 0 0
\(661\) 209.238 362.411i 0.316548 0.548278i −0.663217 0.748427i \(-0.730809\pi\)
0.979765 + 0.200149i \(0.0641428\pi\)
\(662\) 0 0
\(663\) −401.923 + 969.977i −0.606218 + 1.46301i
\(664\) 0 0
\(665\) −76.9464 16.6814i −0.115709 0.0250848i
\(666\) 0 0
\(667\) −12.1282 + 21.0067i −0.0181833 + 0.0314943i
\(668\) 0 0
\(669\) −839.107 347.695i −1.25427 0.519724i
\(670\) 0 0
\(671\) −1069.08 617.231i −1.59326 0.919867i
\(672\) 0 0
\(673\) 197.751 342.514i 0.293835 0.508936i −0.680879 0.732396i \(-0.738402\pi\)
0.974713 + 0.223460i \(0.0717352\pi\)
\(674\) 0 0
\(675\) −100.531 242.967i −0.148935 0.359952i
\(676\) 0 0
\(677\) 592.263 + 341.943i 0.874835 + 0.505086i 0.868952 0.494896i \(-0.164794\pi\)
0.00588308 + 0.999983i \(0.498127\pi\)
\(678\) 0 0
\(679\) 74.3345 0.109476
\(680\) 0 0
\(681\) −57.0664 + 7.50551i −0.0837979 + 0.0110213i
\(682\) 0 0
\(683\) 692.506i 1.01392i −0.861970 0.506959i \(-0.830770\pi\)
0.861970 0.506959i \(-0.169230\pi\)
\(684\) 0 0
\(685\) 1178.73 1.72077
\(686\) 0 0
\(687\) 1071.68 + 444.066i 1.55994 + 0.646384i
\(688\) 0 0
\(689\) 369.691i 0.536562i
\(690\) 0 0
\(691\) 672.752 1165.24i 0.973591 1.68631i 0.289084 0.957304i \(-0.406649\pi\)
0.684507 0.729006i \(-0.260017\pi\)
\(692\) 0 0
\(693\) 28.9843 + 108.282i 0.0418244 + 0.156251i
\(694\) 0 0
\(695\) 267.250 + 154.297i 0.384533 + 0.222010i
\(696\) 0 0
\(697\) 585.773 1014.59i 0.840421 1.45565i
\(698\) 0 0
\(699\) −975.411 + 128.289i −1.39544 + 0.183531i
\(700\) 0 0
\(701\) −208.828 120.567i −0.297900 0.171993i 0.343599 0.939116i \(-0.388354\pi\)
−0.641499 + 0.767124i \(0.721687\pi\)
\(702\) 0 0
\(703\) −683.493 + 219.025i −0.972252 + 0.311557i
\(704\) 0 0
\(705\) 1009.87 774.693i 1.43243 1.09885i
\(706\) 0 0
\(707\) 70.7537 + 40.8497i 0.100076 + 0.0577789i
\(708\) 0 0
\(709\) 238.357 0.336187 0.168093 0.985771i \(-0.446239\pi\)
0.168093 + 0.985771i \(0.446239\pi\)
\(710\) 0 0
\(711\) 1015.31 271.773i 1.42800 0.382240i
\(712\) 0 0
\(713\) 27.7955i 0.0389839i
\(714\) 0 0
\(715\) 816.292 + 1413.86i 1.14167 + 1.97742i
\(716\) 0 0
\(717\) −324.841 + 783.951i −0.453055 + 1.09338i
\(718\) 0 0
\(719\) 101.612 + 58.6655i 0.141324 + 0.0815933i 0.568995 0.822341i \(-0.307332\pi\)
−0.427671 + 0.903934i \(0.640666\pi\)
\(720\) 0 0
\(721\) −60.2804 −0.0836066
\(722\) 0 0
\(723\) 564.339 432.918i 0.780551 0.598780i
\(724\) 0 0
\(725\) 72.7915i 0.100402i
\(726\) 0 0
\(727\) −123.015 213.068i −0.169209 0.293078i 0.768933 0.639329i \(-0.220788\pi\)
−0.938142 + 0.346251i \(0.887455\pi\)
\(728\) 0 0
\(729\) −515.876 + 515.085i −0.707649 + 0.706564i
\(730\) 0 0
\(731\) 137.559i 0.188180i
\(732\) 0 0
\(733\) −573.658 993.605i −0.782617 1.35553i −0.930412 0.366514i \(-0.880551\pi\)
0.147796 0.989018i \(-0.452782\pi\)
\(734\) 0 0
\(735\) 328.318 792.342i 0.446691 1.07802i
\(736\) 0 0
\(737\) 1572.84 908.079i 2.13411 1.23213i
\(738\) 0 0
\(739\) −331.543 + 574.249i −0.448637 + 0.777062i −0.998298 0.0583262i \(-0.981424\pi\)
0.549661 + 0.835388i \(0.314757\pi\)
\(740\) 0 0
\(741\) 380.335 + 806.036i 0.513273 + 1.08777i
\(742\) 0 0
\(743\) 895.276i 1.20495i 0.798139 + 0.602474i \(0.205818\pi\)
−0.798139 + 0.602474i \(0.794182\pi\)
\(744\) 0 0
\(745\) 560.362 0.752163
\(746\) 0 0
\(747\) 634.548 634.224i 0.849462 0.849028i
\(748\) 0 0
\(749\) −120.393 69.5092i −0.160739 0.0928027i
\(750\) 0 0
\(751\) 659.782 1142.78i 0.878538 1.52167i 0.0255919 0.999672i \(-0.491853\pi\)
0.852946 0.522000i \(-0.174814\pi\)
\(752\) 0 0
\(753\) −113.402 + 273.677i −0.150600 + 0.363449i
\(754\) 0 0
\(755\) −180.770 104.368i −0.239431 0.138236i
\(756\) 0 0
\(757\) 571.887 990.537i 0.755465 1.30850i −0.189678 0.981846i \(-0.560744\pi\)
0.945143 0.326657i \(-0.105922\pi\)
\(758\) 0 0
\(759\) −159.330 66.0207i −0.209922 0.0869838i
\(760\) 0 0
\(761\) 228.476 131.910i 0.300231 0.173338i −0.342316 0.939585i \(-0.611211\pi\)
0.642547 + 0.766247i \(0.277878\pi\)
\(762\) 0 0
\(763\) −21.5396 37.3078i −0.0282302 0.0488961i
\(764\) 0 0
\(765\) 839.344 + 839.774i 1.09718 + 1.09774i
\(766\) 0 0
\(767\) −743.375 429.188i −0.969198 0.559567i
\(768\) 0 0
\(769\) 197.800 342.599i 0.257217 0.445512i −0.708279 0.705933i \(-0.750528\pi\)
0.965495 + 0.260421i \(0.0838613\pi\)
\(770\) 0 0
\(771\) −446.393 + 58.7107i −0.578979 + 0.0761487i
\(772\) 0 0
\(773\) 1281.12 739.656i 1.65734 0.956864i 0.683400 0.730044i \(-0.260500\pi\)
0.973937 0.226820i \(-0.0728330\pi\)
\(774\) 0 0
\(775\) −41.7059 72.2367i −0.0538141 0.0932087i
\(776\) 0 0
\(777\) 10.3897 + 78.9960i 0.0133716 + 0.101668i
\(778\) 0 0
\(779\) −303.479 947.043i −0.389575 1.21572i
\(780\) 0 0
\(781\) −73.9024 128.003i −0.0946253 0.163896i
\(782\) 0 0
\(783\) −186.478 + 77.1582i −0.238159 + 0.0985417i
\(784\) 0 0
\(785\) 308.691i 0.393237i
\(786\) 0 0
\(787\) −454.543 787.291i −0.577564 1.00037i −0.995758 0.0920122i \(-0.970670\pi\)
0.418194 0.908358i \(-0.362663\pi\)
\(788\) 0 0
\(789\) 402.006 970.177i 0.509513 1.22963i
\(790\) 0 0
\(791\) 11.9913i 0.0151596i
\(792\) 0 0
\(793\) −544.804 + 943.628i −0.687016 + 1.18995i
\(794\) 0 0
\(795\) 386.215 + 160.033i 0.485805 + 0.201300i
\(796\) 0 0
\(797\)