Properties

Label 684.3.b.a.683.9
Level $684$
Weight $3$
Character 684.683
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.b (of order \(2\), degree \(1\), minimal)

Newform invariants

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

Embedding invariants

Embedding label 683.9
Character \(\chi\) \(=\) 684.683
Dual form 684.3.b.a.683.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.88680 - 0.663313i) q^{2} +(3.12003 + 2.50308i) q^{4} +0.647124i q^{5} -4.63116i q^{7} +(-4.22656 - 6.79236i) q^{8} +O(q^{10})\) \(q+(-1.88680 - 0.663313i) q^{2} +(3.12003 + 2.50308i) q^{4} +0.647124i q^{5} -4.63116i q^{7} +(-4.22656 - 6.79236i) q^{8} +(0.429246 - 1.22099i) q^{10} -14.8893 q^{11} -22.0174i q^{13} +(-3.07191 + 8.73808i) q^{14} +(3.46921 + 15.6194i) q^{16} +18.9443i q^{17} +(1.76418 + 18.9179i) q^{19} +(-1.61980 + 2.01905i) q^{20} +(28.0932 + 9.87628i) q^{22} +13.7179 q^{23} +24.5812 q^{25} +(-14.6044 + 41.5424i) q^{26} +(11.5922 - 14.4494i) q^{28} -21.8371 q^{29} -19.3751 q^{31} +(3.81482 - 31.7718i) q^{32} +(12.5660 - 35.7442i) q^{34} +2.99694 q^{35} +31.3197i q^{37} +(9.21984 - 36.8645i) q^{38} +(4.39550 - 2.73511i) q^{40} -38.1704 q^{41} +32.1401i q^{43} +(-46.4552 - 37.2691i) q^{44} +(-25.8830 - 9.09926i) q^{46} -75.4122 q^{47} +27.5523 q^{49} +(-46.3799 - 16.3050i) q^{50} +(55.1112 - 68.6949i) q^{52} +60.7547 q^{53} -9.63524i q^{55} +(-31.4565 + 19.5739i) q^{56} +(41.2022 + 14.4848i) q^{58} +113.793i q^{59} -106.204 q^{61} +(36.5569 + 12.8517i) q^{62} +(-28.2724 + 57.4166i) q^{64} +14.2480 q^{65} -25.0449 q^{67} +(-47.4191 + 59.1069i) q^{68} +(-5.65462 - 1.98791i) q^{70} -67.2579i q^{71} +99.5142 q^{73} +(20.7747 - 59.0940i) q^{74} +(-41.8487 + 63.4404i) q^{76} +68.9549i q^{77} -84.4233 q^{79} +(-10.1077 + 2.24501i) q^{80} +(72.0199 + 25.3189i) q^{82} -92.6388 q^{83} -12.2593 q^{85} +(21.3189 - 60.6420i) q^{86} +(62.9306 + 101.134i) q^{88} +120.417 q^{89} -101.966 q^{91} +(42.8003 + 34.3370i) q^{92} +(142.288 + 50.0219i) q^{94} +(-12.2422 + 1.14164i) q^{95} +140.014i q^{97} +(-51.9858 - 18.2758i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 8 q^{4} - 56 q^{16} - 400 q^{25} - 464 q^{49} - 272 q^{58} - 352 q^{61} - 200 q^{64} + 480 q^{73} + 152 q^{76} + 32 q^{82} + 704 q^{85}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88680 0.663313i −0.943400 0.331656i
\(3\) 0 0
\(4\) 3.12003 + 2.50308i 0.780008 + 0.625769i
\(5\) 0.647124i 0.129425i 0.997904 + 0.0647124i \(0.0206130\pi\)
−0.997904 + 0.0647124i \(0.979387\pi\)
\(6\) 0 0
\(7\) 4.63116i 0.661595i −0.943702 0.330797i \(-0.892682\pi\)
0.943702 0.330797i \(-0.107318\pi\)
\(8\) −4.22656 6.79236i −0.528320 0.849046i
\(9\) 0 0
\(10\) 0.429246 1.22099i 0.0429246 0.122099i
\(11\) −14.8893 −1.35357 −0.676787 0.736179i \(-0.736628\pi\)
−0.676787 + 0.736179i \(0.736628\pi\)
\(12\) 0 0
\(13\) 22.0174i 1.69364i −0.531877 0.846822i \(-0.678513\pi\)
0.531877 0.846822i \(-0.321487\pi\)
\(14\) −3.07191 + 8.73808i −0.219422 + 0.624149i
\(15\) 0 0
\(16\) 3.46921 + 15.6194i 0.216826 + 0.976210i
\(17\) 18.9443i 1.11437i 0.830388 + 0.557186i \(0.188119\pi\)
−0.830388 + 0.557186i \(0.811881\pi\)
\(18\) 0 0
\(19\) 1.76418 + 18.9179i 0.0928516 + 0.995680i
\(20\) −1.61980 + 2.01905i −0.0809901 + 0.100952i
\(21\) 0 0
\(22\) 28.0932 + 9.87628i 1.27696 + 0.448922i
\(23\) 13.7179 0.596431 0.298215 0.954499i \(-0.403609\pi\)
0.298215 + 0.954499i \(0.403609\pi\)
\(24\) 0 0
\(25\) 24.5812 0.983249
\(26\) −14.6044 + 41.5424i −0.561707 + 1.59778i
\(27\) 0 0
\(28\) 11.5922 14.4494i 0.414006 0.516049i
\(29\) −21.8371 −0.753002 −0.376501 0.926416i \(-0.622873\pi\)
−0.376501 + 0.926416i \(0.622873\pi\)
\(30\) 0 0
\(31\) −19.3751 −0.625003 −0.312501 0.949917i \(-0.601167\pi\)
−0.312501 + 0.949917i \(0.601167\pi\)
\(32\) 3.81482 31.7718i 0.119213 0.992869i
\(33\) 0 0
\(34\) 12.5660 35.7442i 0.369589 1.05130i
\(35\) 2.99694 0.0856268
\(36\) 0 0
\(37\) 31.3197i 0.846478i 0.906018 + 0.423239i \(0.139107\pi\)
−0.906018 + 0.423239i \(0.860893\pi\)
\(38\) 9.21984 36.8645i 0.242627 0.970120i
\(39\) 0 0
\(40\) 4.39550 2.73511i 0.109888 0.0683777i
\(41\) −38.1704 −0.930985 −0.465492 0.885052i \(-0.654123\pi\)
−0.465492 + 0.885052i \(0.654123\pi\)
\(42\) 0 0
\(43\) 32.1401i 0.747444i 0.927541 + 0.373722i \(0.121919\pi\)
−0.927541 + 0.373722i \(0.878081\pi\)
\(44\) −46.4552 37.2691i −1.05580 0.847026i
\(45\) 0 0
\(46\) −25.8830 9.09926i −0.562673 0.197810i
\(47\) −75.4122 −1.60451 −0.802257 0.596978i \(-0.796368\pi\)
−0.802257 + 0.596978i \(0.796368\pi\)
\(48\) 0 0
\(49\) 27.5523 0.562292
\(50\) −46.3799 16.3050i −0.927598 0.326101i
\(51\) 0 0
\(52\) 55.1112 68.6949i 1.05983 1.32106i
\(53\) 60.7547 1.14632 0.573158 0.819445i \(-0.305718\pi\)
0.573158 + 0.819445i \(0.305718\pi\)
\(54\) 0 0
\(55\) 9.63524i 0.175186i
\(56\) −31.4565 + 19.5739i −0.561724 + 0.349533i
\(57\) 0 0
\(58\) 41.2022 + 14.4848i 0.710383 + 0.249738i
\(59\) 113.793i 1.92870i 0.264634 + 0.964349i \(0.414749\pi\)
−0.264634 + 0.964349i \(0.585251\pi\)
\(60\) 0 0
\(61\) −106.204 −1.74105 −0.870525 0.492125i \(-0.836220\pi\)
−0.870525 + 0.492125i \(0.836220\pi\)
\(62\) 36.5569 + 12.8517i 0.589628 + 0.207286i
\(63\) 0 0
\(64\) −28.2724 + 57.4166i −0.441757 + 0.897135i
\(65\) 14.2480 0.219199
\(66\) 0 0
\(67\) −25.0449 −0.373805 −0.186903 0.982378i \(-0.559845\pi\)
−0.186903 + 0.982378i \(0.559845\pi\)
\(68\) −47.4191 + 59.1069i −0.697340 + 0.869219i
\(69\) 0 0
\(70\) −5.65462 1.98791i −0.0807803 0.0283987i
\(71\) 67.2579i 0.947295i −0.880715 0.473647i \(-0.842937\pi\)
0.880715 0.473647i \(-0.157063\pi\)
\(72\) 0 0
\(73\) 99.5142 1.36321 0.681604 0.731721i \(-0.261283\pi\)
0.681604 + 0.731721i \(0.261283\pi\)
\(74\) 20.7747 59.0940i 0.280740 0.798567i
\(75\) 0 0
\(76\) −41.8487 + 63.4404i −0.550641 + 0.834742i
\(77\) 68.9549i 0.895518i
\(78\) 0 0
\(79\) −84.4233 −1.06865 −0.534324 0.845279i \(-0.679434\pi\)
−0.534324 + 0.845279i \(0.679434\pi\)
\(80\) −10.1077 + 2.24501i −0.126346 + 0.0280626i
\(81\) 0 0
\(82\) 72.0199 + 25.3189i 0.878291 + 0.308767i
\(83\) −92.6388 −1.11613 −0.558065 0.829797i \(-0.688456\pi\)
−0.558065 + 0.829797i \(0.688456\pi\)
\(84\) 0 0
\(85\) −12.2593 −0.144227
\(86\) 21.3189 60.6420i 0.247895 0.705139i
\(87\) 0 0
\(88\) 62.9306 + 101.134i 0.715120 + 1.14925i
\(89\) 120.417 1.35300 0.676499 0.736444i \(-0.263496\pi\)
0.676499 + 0.736444i \(0.263496\pi\)
\(90\) 0 0
\(91\) −101.966 −1.12051
\(92\) 42.8003 + 34.3370i 0.465221 + 0.373228i
\(93\) 0 0
\(94\) 142.288 + 50.0219i 1.51370 + 0.532147i
\(95\) −12.2422 + 1.14164i −0.128866 + 0.0120173i
\(96\) 0 0
\(97\) 140.014i 1.44345i 0.692182 + 0.721723i \(0.256650\pi\)
−0.692182 + 0.721723i \(0.743350\pi\)
\(98\) −51.9858 18.2758i −0.530467 0.186488i
\(99\) 0 0
\(100\) 76.6942 + 61.5287i 0.766942 + 0.615287i
\(101\) 34.2779i 0.339385i 0.985497 + 0.169692i \(0.0542774\pi\)
−0.985497 + 0.169692i \(0.945723\pi\)
\(102\) 0 0
\(103\) −185.830 −1.80418 −0.902088 0.431553i \(-0.857966\pi\)
−0.902088 + 0.431553i \(0.857966\pi\)
\(104\) −149.550 + 93.0576i −1.43798 + 0.894785i
\(105\) 0 0
\(106\) −114.632 40.2994i −1.08143 0.380183i
\(107\) 161.771i 1.51188i 0.654643 + 0.755938i \(0.272819\pi\)
−0.654643 + 0.755938i \(0.727181\pi\)
\(108\) 0 0
\(109\) 100.731i 0.924138i 0.886844 + 0.462069i \(0.152893\pi\)
−0.886844 + 0.462069i \(0.847107\pi\)
\(110\) −6.39118 + 18.1798i −0.0581016 + 0.165271i
\(111\) 0 0
\(112\) 72.3358 16.0665i 0.645856 0.143451i
\(113\) −5.03853 −0.0445887 −0.0222944 0.999751i \(-0.507097\pi\)
−0.0222944 + 0.999751i \(0.507097\pi\)
\(114\) 0 0
\(115\) 8.87719i 0.0771929i
\(116\) −68.1324 54.6599i −0.587348 0.471206i
\(117\) 0 0
\(118\) 75.4804 214.705i 0.639665 1.81953i
\(119\) 87.7343 0.737263
\(120\) 0 0
\(121\) 100.692 0.832165
\(122\) 200.386 + 70.4465i 1.64251 + 0.577430i
\(123\) 0 0
\(124\) −60.4509 48.4973i −0.487507 0.391107i
\(125\) 32.0852i 0.256682i
\(126\) 0 0
\(127\) 31.2889 0.246369 0.123185 0.992384i \(-0.460689\pi\)
0.123185 + 0.992384i \(0.460689\pi\)
\(128\) 91.4296 89.5803i 0.714294 0.699846i
\(129\) 0 0
\(130\) −26.8831 9.45085i −0.206793 0.0726989i
\(131\) 18.9095 0.144347 0.0721736 0.997392i \(-0.477006\pi\)
0.0721736 + 0.997392i \(0.477006\pi\)
\(132\) 0 0
\(133\) 87.6120 8.17021i 0.658737 0.0614301i
\(134\) 47.2548 + 16.6126i 0.352648 + 0.123975i
\(135\) 0 0
\(136\) 128.677 80.0693i 0.946153 0.588745i
\(137\) 140.158i 1.02305i 0.859269 + 0.511524i \(0.170919\pi\)
−0.859269 + 0.511524i \(0.829081\pi\)
\(138\) 0 0
\(139\) 155.210i 1.11662i 0.829633 + 0.558309i \(0.188550\pi\)
−0.829633 + 0.558309i \(0.811450\pi\)
\(140\) 9.35054 + 7.50156i 0.0667896 + 0.0535826i
\(141\) 0 0
\(142\) −44.6130 + 126.902i −0.314176 + 0.893678i
\(143\) 327.824i 2.29247i
\(144\) 0 0
\(145\) 14.1313i 0.0974572i
\(146\) −187.764 66.0091i −1.28605 0.452117i
\(147\) 0 0
\(148\) −78.3956 + 97.7184i −0.529700 + 0.660260i
\(149\) 204.301i 1.37115i −0.728002 0.685575i \(-0.759551\pi\)
0.728002 0.685575i \(-0.240449\pi\)
\(150\) 0 0
\(151\) −194.202 −1.28610 −0.643052 0.765823i \(-0.722332\pi\)
−0.643052 + 0.765823i \(0.722332\pi\)
\(152\) 121.041 91.9406i 0.796322 0.604872i
\(153\) 0 0
\(154\) 45.7386 130.104i 0.297004 0.844832i
\(155\) 12.5381i 0.0808909i
\(156\) 0 0
\(157\) −124.358 −0.792087 −0.396043 0.918232i \(-0.629617\pi\)
−0.396043 + 0.918232i \(0.629617\pi\)
\(158\) 159.290 + 55.9990i 1.00816 + 0.354424i
\(159\) 0 0
\(160\) 20.5603 + 2.46866i 0.128502 + 0.0154291i
\(161\) 63.5299i 0.394595i
\(162\) 0 0
\(163\) 194.930i 1.19589i −0.801538 0.597944i \(-0.795984\pi\)
0.801538 0.597944i \(-0.204016\pi\)
\(164\) −119.093 95.5434i −0.726176 0.582582i
\(165\) 0 0
\(166\) 174.791 + 61.4485i 1.05296 + 0.370171i
\(167\) 6.41401i 0.0384073i −0.999816 0.0192036i \(-0.993887\pi\)
0.999816 0.0192036i \(-0.00611308\pi\)
\(168\) 0 0
\(169\) −315.764 −1.86843
\(170\) 23.1309 + 8.13177i 0.136064 + 0.0478339i
\(171\) 0 0
\(172\) −80.4492 + 100.278i −0.467728 + 0.583013i
\(173\) −99.2301 −0.573585 −0.286792 0.957993i \(-0.592589\pi\)
−0.286792 + 0.957993i \(0.592589\pi\)
\(174\) 0 0
\(175\) 113.840i 0.650512i
\(176\) −51.6542 232.562i −0.293490 1.32137i
\(177\) 0 0
\(178\) −227.202 79.8740i −1.27642 0.448730i
\(179\) 127.149i 0.710330i −0.934804 0.355165i \(-0.884425\pi\)
0.934804 0.355165i \(-0.115575\pi\)
\(180\) 0 0
\(181\) 3.33163i 0.0184068i 0.999958 + 0.00920341i \(0.00292958\pi\)
−0.999958 + 0.00920341i \(0.997070\pi\)
\(182\) 192.389 + 67.6353i 1.05709 + 0.371623i
\(183\) 0 0
\(184\) −57.9795 93.1770i −0.315106 0.506397i
\(185\) −20.2677 −0.109555
\(186\) 0 0
\(187\) 282.068i 1.50839i
\(188\) −235.288 188.763i −1.25153 1.00406i
\(189\) 0 0
\(190\) 23.8559 + 5.96638i 0.125558 + 0.0314020i
\(191\) 99.7437 0.522219 0.261109 0.965309i \(-0.415912\pi\)
0.261109 + 0.965309i \(0.415912\pi\)
\(192\) 0 0
\(193\) 55.1904i 0.285961i −0.989726 0.142980i \(-0.954331\pi\)
0.989726 0.142980i \(-0.0456686\pi\)
\(194\) 92.8733 264.179i 0.478728 1.36175i
\(195\) 0 0
\(196\) 85.9642 + 68.9656i 0.438593 + 0.351865i
\(197\) 148.744i 0.755043i −0.926001 0.377522i \(-0.876776\pi\)
0.926001 0.377522i \(-0.123224\pi\)
\(198\) 0 0
\(199\) 119.642i 0.601216i 0.953748 + 0.300608i \(0.0971897\pi\)
−0.953748 + 0.300608i \(0.902810\pi\)
\(200\) −103.894 166.965i −0.519470 0.834823i
\(201\) 0 0
\(202\) 22.7369 64.6755i 0.112559 0.320176i
\(203\) 101.131i 0.498182i
\(204\) 0 0
\(205\) 24.7010i 0.120493i
\(206\) 350.624 + 123.263i 1.70206 + 0.598366i
\(207\) 0 0
\(208\) 343.897 76.3828i 1.65335 0.367225i
\(209\) −26.2674 281.675i −0.125682 1.34773i
\(210\) 0 0
\(211\) −273.915 −1.29817 −0.649087 0.760714i \(-0.724849\pi\)
−0.649087 + 0.760714i \(0.724849\pi\)
\(212\) 189.557 + 152.074i 0.894135 + 0.717329i
\(213\) 0 0
\(214\) 107.305 305.229i 0.501423 1.42630i
\(215\) −20.7986 −0.0967378
\(216\) 0 0
\(217\) 89.7292i 0.413498i
\(218\) 66.8162 190.059i 0.306496 0.871832i
\(219\) 0 0
\(220\) 24.1177 30.0623i 0.109626 0.136647i
\(221\) 417.104 1.88735
\(222\) 0 0
\(223\) 208.529 0.935108 0.467554 0.883965i \(-0.345135\pi\)
0.467554 + 0.883965i \(0.345135\pi\)
\(224\) −147.140 17.6670i −0.656877 0.0788707i
\(225\) 0 0
\(226\) 9.50669 + 3.34212i 0.0420650 + 0.0147881i
\(227\) 218.093i 0.960762i −0.877060 0.480381i \(-0.840498\pi\)
0.877060 0.480381i \(-0.159502\pi\)
\(228\) 0 0
\(229\) 104.878 0.457983 0.228991 0.973428i \(-0.426457\pi\)
0.228991 + 0.973428i \(0.426457\pi\)
\(230\) 5.88835 16.7495i 0.0256015 0.0728238i
\(231\) 0 0
\(232\) 92.2956 + 148.325i 0.397826 + 0.639333i
\(233\) 85.0991i 0.365232i 0.983184 + 0.182616i \(0.0584566\pi\)
−0.983184 + 0.182616i \(0.941543\pi\)
\(234\) 0 0
\(235\) 48.8010i 0.207664i
\(236\) −284.833 + 355.038i −1.20692 + 1.50440i
\(237\) 0 0
\(238\) −165.537 58.1952i −0.695534 0.244518i
\(239\) 208.984 0.874411 0.437205 0.899362i \(-0.355968\pi\)
0.437205 + 0.899362i \(0.355968\pi\)
\(240\) 0 0
\(241\) 291.886i 1.21115i −0.795790 0.605573i \(-0.792944\pi\)
0.795790 0.605573i \(-0.207056\pi\)
\(242\) −189.986 66.7902i −0.785064 0.275993i
\(243\) 0 0
\(244\) −331.360 265.837i −1.35803 1.08950i
\(245\) 17.8298i 0.0727746i
\(246\) 0 0
\(247\) 416.523 38.8426i 1.68633 0.157257i
\(248\) 81.8899 + 131.603i 0.330201 + 0.530656i
\(249\) 0 0
\(250\) 21.2825 60.5384i 0.0851301 0.242154i
\(251\) 234.938 0.936006 0.468003 0.883727i \(-0.344974\pi\)
0.468003 + 0.883727i \(0.344974\pi\)
\(252\) 0 0
\(253\) −204.250 −0.807313
\(254\) −59.0359 20.7543i −0.232425 0.0817099i
\(255\) 0 0
\(256\) −231.929 + 108.374i −0.905973 + 0.423335i
\(257\) 54.0528 0.210322 0.105161 0.994455i \(-0.466464\pi\)
0.105161 + 0.994455i \(0.466464\pi\)
\(258\) 0 0
\(259\) 145.047 0.560025
\(260\) 44.4541 + 35.6638i 0.170977 + 0.137168i
\(261\) 0 0
\(262\) −35.6784 12.5429i −0.136177 0.0478736i
\(263\) 482.093 1.83305 0.916526 0.399975i \(-0.130981\pi\)
0.916526 + 0.399975i \(0.130981\pi\)
\(264\) 0 0
\(265\) 39.3158i 0.148362i
\(266\) −170.726 42.6986i −0.641826 0.160521i
\(267\) 0 0
\(268\) −78.1411 62.6894i −0.291571 0.233916i
\(269\) −99.6712 −0.370525 −0.185262 0.982689i \(-0.559314\pi\)
−0.185262 + 0.982689i \(0.559314\pi\)
\(270\) 0 0
\(271\) 78.1924i 0.288533i −0.989539 0.144266i \(-0.953918\pi\)
0.989539 0.144266i \(-0.0460822\pi\)
\(272\) −295.898 + 65.7218i −1.08786 + 0.241624i
\(273\) 0 0
\(274\) 92.9684 264.450i 0.339301 0.965145i
\(275\) −365.998 −1.33090
\(276\) 0 0
\(277\) 87.8522 0.317156 0.158578 0.987346i \(-0.449309\pi\)
0.158578 + 0.987346i \(0.449309\pi\)
\(278\) 102.953 292.850i 0.370333 1.05342i
\(279\) 0 0
\(280\) −12.6667 20.3563i −0.0452383 0.0727010i
\(281\) −223.682 −0.796023 −0.398011 0.917380i \(-0.630300\pi\)
−0.398011 + 0.917380i \(0.630300\pi\)
\(282\) 0 0
\(283\) 427.937i 1.51214i 0.654488 + 0.756072i \(0.272884\pi\)
−0.654488 + 0.756072i \(0.727116\pi\)
\(284\) 168.352 209.847i 0.592788 0.738898i
\(285\) 0 0
\(286\) 217.450 618.538i 0.760313 2.16272i
\(287\) 176.773i 0.615935i
\(288\) 0 0
\(289\) −69.8875 −0.241825
\(290\) −9.37346 + 26.6629i −0.0323223 + 0.0919411i
\(291\) 0 0
\(292\) 310.488 + 249.092i 1.06331 + 0.853054i
\(293\) −264.532 −0.902841 −0.451420 0.892311i \(-0.649082\pi\)
−0.451420 + 0.892311i \(0.649082\pi\)
\(294\) 0 0
\(295\) −73.6383 −0.249621
\(296\) 212.735 132.374i 0.718698 0.447211i
\(297\) 0 0
\(298\) −135.516 + 385.476i −0.454751 + 1.29354i
\(299\) 302.032i 1.01014i
\(300\) 0 0
\(301\) 148.846 0.494505
\(302\) 366.420 + 128.816i 1.21331 + 0.426544i
\(303\) 0 0
\(304\) −289.366 + 93.1856i −0.951860 + 0.306532i
\(305\) 68.7272i 0.225335i
\(306\) 0 0
\(307\) −567.515 −1.84858 −0.924291 0.381689i \(-0.875343\pi\)
−0.924291 + 0.381689i \(0.875343\pi\)
\(308\) −172.599 + 215.141i −0.560388 + 0.698511i
\(309\) 0 0
\(310\) −8.31667 + 23.6569i −0.0268280 + 0.0763125i
\(311\) 121.048 0.389222 0.194611 0.980880i \(-0.437655\pi\)
0.194611 + 0.980880i \(0.437655\pi\)
\(312\) 0 0
\(313\) 109.296 0.349190 0.174595 0.984640i \(-0.444138\pi\)
0.174595 + 0.984640i \(0.444138\pi\)
\(314\) 234.638 + 82.4880i 0.747255 + 0.262701i
\(315\) 0 0
\(316\) −263.403 211.318i −0.833555 0.668728i
\(317\) −494.489 −1.55990 −0.779952 0.625840i \(-0.784756\pi\)
−0.779952 + 0.625840i \(0.784756\pi\)
\(318\) 0 0
\(319\) 325.139 1.01924
\(320\) −37.1557 18.2958i −0.116112 0.0571743i
\(321\) 0 0
\(322\) −42.1402 + 119.868i −0.130870 + 0.372261i
\(323\) −358.387 + 33.4212i −1.10956 + 0.103471i
\(324\) 0 0
\(325\) 541.214i 1.66527i
\(326\) −129.299 + 367.794i −0.396624 + 1.12820i
\(327\) 0 0
\(328\) 161.329 + 259.267i 0.491858 + 0.790449i
\(329\) 349.246i 1.06154i
\(330\) 0 0
\(331\) 488.208 1.47495 0.737475 0.675375i \(-0.236018\pi\)
0.737475 + 0.675375i \(0.236018\pi\)
\(332\) −289.036 231.882i −0.870590 0.698440i
\(333\) 0 0
\(334\) −4.25450 + 12.1020i −0.0127380 + 0.0362334i
\(335\) 16.2072i 0.0483797i
\(336\) 0 0
\(337\) 322.191i 0.956056i 0.878345 + 0.478028i \(0.158648\pi\)
−0.878345 + 0.478028i \(0.841352\pi\)
\(338\) 595.784 + 209.450i 1.76267 + 0.619676i
\(339\) 0 0
\(340\) −38.2495 30.6860i −0.112499 0.0902531i
\(341\) 288.482 0.845988
\(342\) 0 0
\(343\) 354.526i 1.03360i
\(344\) 218.307 135.842i 0.634614 0.394889i
\(345\) 0 0
\(346\) 187.227 + 65.8206i 0.541120 + 0.190233i
\(347\) −269.767 −0.777425 −0.388713 0.921359i \(-0.627080\pi\)
−0.388713 + 0.921359i \(0.627080\pi\)
\(348\) 0 0
\(349\) 248.416 0.711795 0.355897 0.934525i \(-0.384175\pi\)
0.355897 + 0.934525i \(0.384175\pi\)
\(350\) −75.5113 + 214.793i −0.215747 + 0.613694i
\(351\) 0 0
\(352\) −56.8000 + 473.061i −0.161364 + 1.34392i
\(353\) 318.157i 0.901294i −0.892702 0.450647i \(-0.851193\pi\)
0.892702 0.450647i \(-0.148807\pi\)
\(354\) 0 0
\(355\) 43.5242 0.122603
\(356\) 375.704 + 301.412i 1.05535 + 0.846664i
\(357\) 0 0
\(358\) −84.3395 + 239.905i −0.235585 + 0.670125i
\(359\) −203.903 −0.567976 −0.283988 0.958828i \(-0.591658\pi\)
−0.283988 + 0.958828i \(0.591658\pi\)
\(360\) 0 0
\(361\) −354.775 + 66.7492i −0.982757 + 0.184901i
\(362\) 2.20991 6.28613i 0.00610474 0.0173650i
\(363\) 0 0
\(364\) −318.137 255.229i −0.874003 0.701178i
\(365\) 64.3981i 0.176433i
\(366\) 0 0
\(367\) 411.595i 1.12151i −0.827981 0.560756i \(-0.810511\pi\)
0.827981 0.560756i \(-0.189489\pi\)
\(368\) 47.5903 + 214.265i 0.129321 + 0.582242i
\(369\) 0 0
\(370\) 38.2411 + 13.4438i 0.103354 + 0.0363347i
\(371\) 281.365i 0.758396i
\(372\) 0 0
\(373\) 455.722i 1.22177i 0.791718 + 0.610887i \(0.209187\pi\)
−0.791718 + 0.610887i \(0.790813\pi\)
\(374\) −187.099 + 532.206i −0.500266 + 1.42301i
\(375\) 0 0
\(376\) 318.734 + 512.227i 0.847697 + 1.36231i
\(377\) 480.795i 1.27532i
\(378\) 0 0
\(379\) 326.021 0.860213 0.430106 0.902778i \(-0.358476\pi\)
0.430106 + 0.902778i \(0.358476\pi\)
\(380\) −41.0538 27.0813i −0.108036 0.0712666i
\(381\) 0 0
\(382\) −188.197 66.1613i −0.492661 0.173197i
\(383\) 239.458i 0.625217i −0.949882 0.312609i \(-0.898797\pi\)
0.949882 0.312609i \(-0.101203\pi\)
\(384\) 0 0
\(385\) −44.6224 −0.115902
\(386\) −36.6085 + 104.133i −0.0948407 + 0.269776i
\(387\) 0 0
\(388\) −350.467 + 436.849i −0.903265 + 1.12590i
\(389\) 381.887i 0.981714i −0.871240 0.490857i \(-0.836684\pi\)
0.871240 0.490857i \(-0.163316\pi\)
\(390\) 0 0
\(391\) 259.876i 0.664646i
\(392\) −116.451 187.145i −0.297070 0.477412i
\(393\) 0 0
\(394\) −98.6635 + 280.649i −0.250415 + 0.712308i
\(395\) 54.6323i 0.138310i
\(396\) 0 0
\(397\) 67.7120 0.170559 0.0852796 0.996357i \(-0.472822\pi\)
0.0852796 + 0.996357i \(0.472822\pi\)
\(398\) 79.3601 225.741i 0.199397 0.567188i
\(399\) 0 0
\(400\) 85.2774 + 383.943i 0.213194 + 0.959858i
\(401\) 393.401 0.981050 0.490525 0.871427i \(-0.336805\pi\)
0.490525 + 0.871427i \(0.336805\pi\)
\(402\) 0 0
\(403\) 426.588i 1.05853i
\(404\) −85.8001 + 106.948i −0.212377 + 0.264723i
\(405\) 0 0
\(406\) 67.0815 190.814i 0.165225 0.469985i
\(407\) 466.329i 1.14577i
\(408\) 0 0
\(409\) 497.707i 1.21689i −0.793597 0.608443i \(-0.791794\pi\)
0.793597 0.608443i \(-0.208206\pi\)
\(410\) −16.3845 + 46.6058i −0.0399621 + 0.113673i
\(411\) 0 0
\(412\) −579.796 465.147i −1.40727 1.12900i
\(413\) 526.995 1.27602
\(414\) 0 0
\(415\) 59.9488i 0.144455i
\(416\) −699.531 83.9922i −1.68157 0.201904i
\(417\) 0 0
\(418\) −137.277 + 548.888i −0.328414 + 1.31313i
\(419\) 328.054 0.782946 0.391473 0.920190i \(-0.371966\pi\)
0.391473 + 0.920190i \(0.371966\pi\)
\(420\) 0 0
\(421\) 194.786i 0.462675i 0.972874 + 0.231338i \(0.0743102\pi\)
−0.972874 + 0.231338i \(0.925690\pi\)
\(422\) 516.822 + 181.691i 1.22470 + 0.430547i
\(423\) 0 0
\(424\) −256.783 412.668i −0.605621 0.973274i
\(425\) 465.675i 1.09571i
\(426\) 0 0
\(427\) 491.848i 1.15187i
\(428\) −404.925 + 504.730i −0.946085 + 1.17928i
\(429\) 0 0
\(430\) 39.2429 + 13.7960i 0.0912625 + 0.0320837i
\(431\) 314.574i 0.729870i 0.931033 + 0.364935i \(0.118909\pi\)
−0.931033 + 0.364935i \(0.881091\pi\)
\(432\) 0 0
\(433\) 234.253i 0.540999i −0.962720 0.270500i \(-0.912811\pi\)
0.962720 0.270500i \(-0.0871889\pi\)
\(434\) 59.5185 169.301i 0.137139 0.390095i
\(435\) 0 0
\(436\) −252.138 + 314.284i −0.578297 + 0.720836i
\(437\) 24.2009 + 259.514i 0.0553795 + 0.593854i
\(438\) 0 0
\(439\) −239.334 −0.545181 −0.272590 0.962130i \(-0.587880\pi\)
−0.272590 + 0.962130i \(0.587880\pi\)
\(440\) −65.4461 + 40.7239i −0.148741 + 0.0925543i
\(441\) 0 0
\(442\) −786.992 276.670i −1.78053 0.625951i
\(443\) −253.331 −0.571854 −0.285927 0.958251i \(-0.592301\pi\)
−0.285927 + 0.958251i \(0.592301\pi\)
\(444\) 0 0
\(445\) 77.9246i 0.175111i
\(446\) −393.453 138.320i −0.882181 0.310134i
\(447\) 0 0
\(448\) 265.906 + 130.934i 0.593540 + 0.292264i
\(449\) −352.503 −0.785085 −0.392543 0.919734i \(-0.628404\pi\)
−0.392543 + 0.919734i \(0.628404\pi\)
\(450\) 0 0
\(451\) 568.331 1.26016
\(452\) −15.7204 12.6118i −0.0347796 0.0279023i
\(453\) 0 0
\(454\) −144.664 + 411.498i −0.318643 + 0.906383i
\(455\) 65.9846i 0.145021i
\(456\) 0 0
\(457\) −33.8092 −0.0739807 −0.0369903 0.999316i \(-0.511777\pi\)
−0.0369903 + 0.999316i \(0.511777\pi\)
\(458\) −197.884 69.5670i −0.432061 0.151893i
\(459\) 0 0
\(460\) −22.2203 + 27.6971i −0.0483050 + 0.0602111i
\(461\) 159.193i 0.345321i −0.984981 0.172660i \(-0.944764\pi\)
0.984981 0.172660i \(-0.0552363\pi\)
\(462\) 0 0
\(463\) 383.183i 0.827610i 0.910366 + 0.413805i \(0.135800\pi\)
−0.910366 + 0.413805i \(0.864200\pi\)
\(464\) −75.7573 341.081i −0.163270 0.735089i
\(465\) 0 0
\(466\) 56.4473 160.565i 0.121132 0.344560i
\(467\) 136.387 0.292049 0.146025 0.989281i \(-0.453352\pi\)
0.146025 + 0.989281i \(0.453352\pi\)
\(468\) 0 0
\(469\) 115.987i 0.247308i
\(470\) −32.3703 + 92.0778i −0.0688731 + 0.195910i
\(471\) 0 0
\(472\) 772.925 480.953i 1.63755 1.01897i
\(473\) 478.544i 1.01172i
\(474\) 0 0
\(475\) 43.3657 + 465.026i 0.0912962 + 0.979002i
\(476\) 273.734 + 219.606i 0.575071 + 0.461356i
\(477\) 0 0
\(478\) −394.312 138.622i −0.824920 0.290004i
\(479\) −31.4695 −0.0656982 −0.0328491 0.999460i \(-0.510458\pi\)
−0.0328491 + 0.999460i \(0.510458\pi\)
\(480\) 0 0
\(481\) 689.577 1.43363
\(482\) −193.612 + 550.731i −0.401684 + 1.14260i
\(483\) 0 0
\(484\) 314.162 + 252.040i 0.649095 + 0.520743i
\(485\) −90.6067 −0.186818
\(486\) 0 0
\(487\) 707.449 1.45267 0.726333 0.687343i \(-0.241223\pi\)
0.726333 + 0.687343i \(0.241223\pi\)
\(488\) 448.877 + 721.376i 0.919830 + 1.47823i
\(489\) 0 0
\(490\) 11.8267 33.6412i 0.0241362 0.0686556i
\(491\) −549.851 −1.11986 −0.559930 0.828540i \(-0.689172\pi\)
−0.559930 + 0.828540i \(0.689172\pi\)
\(492\) 0 0
\(493\) 413.689i 0.839125i
\(494\) −811.660 202.997i −1.64304 0.410924i
\(495\) 0 0
\(496\) −67.2162 302.627i −0.135517 0.610134i
\(497\) −311.482 −0.626725
\(498\) 0 0
\(499\) 92.5348i 0.185440i −0.995692 0.0927202i \(-0.970444\pi\)
0.995692 0.0927202i \(-0.0295562\pi\)
\(500\) −80.3117 + 100.107i −0.160623 + 0.200214i
\(501\) 0 0
\(502\) −443.280 155.837i −0.883029 0.310432i
\(503\) −29.7026 −0.0590510 −0.0295255 0.999564i \(-0.509400\pi\)
−0.0295255 + 0.999564i \(0.509400\pi\)
\(504\) 0 0
\(505\) −22.1820 −0.0439248
\(506\) 385.380 + 135.482i 0.761620 + 0.267751i
\(507\) 0 0
\(508\) 97.6223 + 78.3185i 0.192170 + 0.154170i
\(509\) −573.572 −1.12686 −0.563431 0.826163i \(-0.690519\pi\)
−0.563431 + 0.826163i \(0.690519\pi\)
\(510\) 0 0
\(511\) 460.867i 0.901892i
\(512\) 509.490 50.6380i 0.995097 0.0989023i
\(513\) 0 0
\(514\) −101.987 35.8539i −0.198418 0.0697547i
\(515\) 120.255i 0.233505i
\(516\) 0 0
\(517\) 1122.84 2.17183
\(518\) −273.674 96.2112i −0.528328 0.185736i
\(519\) 0 0
\(520\) −60.2198 96.7774i −0.115807 0.186110i
\(521\) 546.984 1.04987 0.524937 0.851141i \(-0.324089\pi\)
0.524937 + 0.851141i \(0.324089\pi\)
\(522\) 0 0
\(523\) 144.876 0.277009 0.138504 0.990362i \(-0.455771\pi\)
0.138504 + 0.990362i \(0.455771\pi\)
\(524\) 58.9982 + 47.3319i 0.112592 + 0.0903280i
\(525\) 0 0
\(526\) −909.613 319.778i −1.72930 0.607943i
\(527\) 367.048i 0.696486i
\(528\) 0 0
\(529\) −340.819 −0.644271
\(530\) 26.0787 74.1811i 0.0492051 0.139964i
\(531\) 0 0
\(532\) 293.803 + 193.808i 0.552261 + 0.364301i
\(533\) 840.411i 1.57676i
\(534\) 0 0
\(535\) −104.686 −0.195674
\(536\) 105.854 + 170.114i 0.197489 + 0.317378i
\(537\) 0 0
\(538\) 188.060 + 66.1132i 0.349553 + 0.122887i
\(539\) −410.236 −0.761105
\(540\) 0 0
\(541\) −933.960 −1.72636 −0.863179 0.504898i \(-0.831530\pi\)
−0.863179 + 0.504898i \(0.831530\pi\)
\(542\) −51.8660 + 147.534i −0.0956938 + 0.272202i
\(543\) 0 0
\(544\) 601.895 + 72.2691i 1.10643 + 0.132848i
\(545\) −65.1855 −0.119606
\(546\) 0 0
\(547\) 670.814 1.22635 0.613176 0.789947i \(-0.289892\pi\)
0.613176 + 0.789947i \(0.289892\pi\)
\(548\) −350.826 + 437.297i −0.640193 + 0.797987i
\(549\) 0 0
\(550\) 690.565 + 242.771i 1.25557 + 0.441402i
\(551\) −38.5245 413.112i −0.0699175 0.749749i
\(552\) 0 0
\(553\) 390.978i 0.707013i
\(554\) −165.760 58.2735i −0.299205 0.105187i
\(555\) 0 0
\(556\) −388.502 + 484.260i −0.698745 + 0.870971i
\(557\) 29.7179i 0.0533535i 0.999644 + 0.0266767i \(0.00849248\pi\)
−0.999644 + 0.0266767i \(0.991508\pi\)
\(558\) 0 0
\(559\) 707.640 1.26590
\(560\) 10.3970 + 46.8103i 0.0185661 + 0.0835897i
\(561\) 0 0
\(562\) 422.044 + 148.371i 0.750968 + 0.264006i
\(563\) 909.252i 1.61501i −0.589859 0.807506i \(-0.700817\pi\)
0.589859 0.807506i \(-0.299183\pi\)
\(564\) 0 0
\(565\) 3.26055i 0.00577089i
\(566\) 283.856 807.432i 0.501512 1.42656i
\(567\) 0 0
\(568\) −456.840 + 284.269i −0.804296 + 0.500474i
\(569\) −808.539 −1.42098 −0.710491 0.703706i \(-0.751527\pi\)
−0.710491 + 0.703706i \(0.751527\pi\)
\(570\) 0 0
\(571\) 384.360i 0.673135i 0.941659 + 0.336567i \(0.109266\pi\)
−0.941659 + 0.336567i \(0.890734\pi\)
\(572\) −820.568 + 1022.82i −1.43456 + 1.78815i
\(573\) 0 0
\(574\) 117.256 333.536i 0.204279 0.581073i
\(575\) 337.203 0.586440
\(576\) 0 0
\(577\) −197.780 −0.342773 −0.171387 0.985204i \(-0.554825\pi\)
−0.171387 + 0.985204i \(0.554825\pi\)
\(578\) 131.864 + 46.3573i 0.228138 + 0.0802029i
\(579\) 0 0
\(580\) 35.3717 44.0901i 0.0609857 0.0760174i
\(581\) 429.025i 0.738426i
\(582\) 0 0
\(583\) −904.596 −1.55162
\(584\) −420.603 675.937i −0.720210 1.15743i
\(585\) 0 0
\(586\) 499.120 + 175.468i 0.851740 + 0.299433i
\(587\) −779.727 −1.32833 −0.664163 0.747588i \(-0.731212\pi\)
−0.664163 + 0.747588i \(0.731212\pi\)
\(588\) 0 0
\(589\) −34.1811 366.536i −0.0580325 0.622303i
\(590\) 138.941 + 48.8452i 0.235493 + 0.0827885i
\(591\) 0 0
\(592\) −489.193 + 108.655i −0.826340 + 0.183538i
\(593\) 118.684i 0.200142i 0.994980 + 0.100071i \(0.0319069\pi\)
−0.994980 + 0.100071i \(0.968093\pi\)
\(594\) 0 0
\(595\) 56.7750i 0.0954201i
\(596\) 511.382 637.427i 0.858024 1.06951i
\(597\) 0 0
\(598\) −200.342 + 569.874i −0.335020 + 0.952967i
\(599\) 278.133i 0.464329i −0.972677 0.232164i \(-0.925419\pi\)
0.972677 0.232164i \(-0.0745808\pi\)
\(600\) 0 0
\(601\) 769.770i 1.28082i 0.768035 + 0.640408i \(0.221235\pi\)
−0.768035 + 0.640408i \(0.778765\pi\)
\(602\) −280.843 98.7315i −0.466516 0.164006i
\(603\) 0 0
\(604\) −605.916 486.102i −1.00317 0.804804i
\(605\) 65.1602i 0.107703i
\(606\) 0 0
\(607\) 341.395 0.562430 0.281215 0.959645i \(-0.409263\pi\)
0.281215 + 0.959645i \(0.409263\pi\)
\(608\) 607.786 + 16.1172i 0.999649 + 0.0265086i
\(609\) 0 0
\(610\) −45.5876 + 129.674i −0.0747338 + 0.212581i
\(611\) 1660.38i 2.71748i
\(612\) 0 0
\(613\) 192.021 0.313247 0.156624 0.987658i \(-0.449939\pi\)
0.156624 + 0.987658i \(0.449939\pi\)
\(614\) 1070.79 + 376.440i 1.74395 + 0.613094i
\(615\) 0 0
\(616\) 468.367 291.442i 0.760336 0.473120i
\(617\) 607.759i 0.985023i −0.870306 0.492511i \(-0.836079\pi\)
0.870306 0.492511i \(-0.163921\pi\)
\(618\) 0 0
\(619\) 118.381i 0.191246i 0.995418 + 0.0956231i \(0.0304844\pi\)
−0.995418 + 0.0956231i \(0.969516\pi\)
\(620\) 31.3838 39.1192i 0.0506190 0.0630955i
\(621\) 0 0
\(622\) −228.394 80.2928i −0.367193 0.129088i
\(623\) 557.670i 0.895136i
\(624\) 0 0
\(625\) 593.768 0.950028
\(626\) −206.221 72.4977i −0.329426 0.115811i
\(627\) 0 0
\(628\) −388.000 311.277i −0.617834 0.495664i
\(629\) −593.330 −0.943291
\(630\) 0 0
\(631\) 1215.14i 1.92574i −0.269960 0.962871i \(-0.587011\pi\)
0.269960 0.962871i \(-0.412989\pi\)
\(632\) 356.820 + 573.434i 0.564588 + 0.907332i
\(633\) 0 0
\(634\) 933.003 + 328.001i 1.47161 + 0.517352i
\(635\) 20.2478i 0.0318863i
\(636\) 0 0
\(637\) 606.630i 0.952323i
\(638\) −613.473 215.669i −0.961556 0.338039i
\(639\) 0 0
\(640\) 57.9695 + 59.1663i 0.0905774 + 0.0924473i
\(641\) 507.836 0.792255 0.396128 0.918195i \(-0.370354\pi\)
0.396128 + 0.918195i \(0.370354\pi\)
\(642\) 0 0
\(643\) 517.738i 0.805191i 0.915378 + 0.402596i \(0.131892\pi\)
−0.915378 + 0.402596i \(0.868108\pi\)
\(644\) 159.020 198.215i 0.246926 0.307788i
\(645\) 0 0
\(646\) 698.374 + 174.664i 1.08107 + 0.270377i
\(647\) 174.389 0.269535 0.134768 0.990877i \(-0.456971\pi\)
0.134768 + 0.990877i \(0.456971\pi\)
\(648\) 0 0
\(649\) 1694.30i 2.61064i
\(650\) −358.994 + 1021.16i −0.552298 + 1.57102i
\(651\) 0 0
\(652\) 487.924 608.188i 0.748350 0.932803i
\(653\) 1222.16i 1.87161i 0.352513 + 0.935807i \(0.385327\pi\)
−0.352513 + 0.935807i \(0.614673\pi\)
\(654\) 0 0
\(655\) 12.2368i 0.0186821i
\(656\) −132.421 596.197i −0.201861 0.908837i
\(657\) 0 0
\(658\) 231.659 658.958i 0.352066 1.00146i
\(659\) 289.924i 0.439945i −0.975506 0.219973i \(-0.929403\pi\)
0.975506 0.219973i \(-0.0705968\pi\)
\(660\) 0 0
\(661\) 116.537i 0.176304i −0.996107 0.0881520i \(-0.971904\pi\)
0.996107 0.0881520i \(-0.0280961\pi\)
\(662\) −921.152 323.835i −1.39147 0.489176i
\(663\) 0 0
\(664\) 391.543 + 629.236i 0.589673 + 0.947645i
\(665\) 5.28714 + 56.6958i 0.00795058 + 0.0852569i
\(666\) 0 0
\(667\) −299.559 −0.449114
\(668\) 16.0548 20.0119i 0.0240341 0.0299580i
\(669\) 0 0
\(670\) −10.7504 + 30.5797i −0.0160454 + 0.0456414i
\(671\) 1581.31 2.35664
\(672\) 0 0
\(673\) 436.189i 0.648126i −0.946035 0.324063i \(-0.894951\pi\)
0.946035 0.324063i \(-0.105049\pi\)
\(674\) 213.713 607.910i 0.317082 0.901944i
\(675\) 0 0
\(676\) −985.195 790.382i −1.45739 1.16920i
\(677\) 384.501 0.567949 0.283974 0.958832i \(-0.408347\pi\)
0.283974 + 0.958832i \(0.408347\pi\)
\(678\) 0 0
\(679\) 648.429 0.954977
\(680\) 51.8148 + 83.2698i 0.0761982 + 0.122456i
\(681\) 0 0
\(682\) −544.308 191.354i −0.798105 0.280577i
\(683\) 670.786i 0.982116i 0.871127 + 0.491058i \(0.163390\pi\)
−0.871127 + 0.491058i \(0.836610\pi\)
\(684\) 0 0
\(685\) −90.6994 −0.132408
\(686\) −235.162 + 668.920i −0.342801 + 0.975103i
\(687\) 0 0
\(688\) −502.008 + 111.501i −0.729663 + 0.162065i
\(689\) 1337.66i 1.94145i
\(690\) 0 0
\(691\) 710.048i 1.02757i −0.857920 0.513783i \(-0.828244\pi\)
0.857920 0.513783i \(-0.171756\pi\)
\(692\) −309.601 248.381i −0.447401 0.358932i
\(693\) 0 0
\(694\) 508.996 + 178.940i 0.733423 + 0.257838i
\(695\) −100.440 −0.144518
\(696\) 0 0
\(697\) 723.112i 1.03746i
\(698\) −468.712 164.778i −0.671508 0.236071i
\(699\) 0 0
\(700\) 284.950 355.184i 0.407071 0.507405i
\(701\) 1318.94i 1.88152i −0.339078 0.940758i \(-0.610115\pi\)
0.339078 0.940758i \(-0.389885\pi\)
\(702\) 0 0
\(703\) −592.503 + 55.2535i −0.842821 + 0.0785968i
\(704\) 420.957 854.895i 0.597951 1.21434i
\(705\) 0 0
\(706\) −211.037 + 600.298i −0.298920 + 0.850281i
\(707\) 158.746 0.224535
\(708\) 0 0
\(709\) 352.865 0.497694 0.248847 0.968543i \(-0.419948\pi\)
0.248847 + 0.968543i \(0.419948\pi\)
\(710\) −82.1215 28.8702i −0.115664 0.0406622i
\(711\) 0 0
\(712\) −508.948 817.914i −0.714815 1.14876i
\(713\) −265.786 −0.372771
\(714\) 0 0
\(715\) −212.143 −0.296703
\(716\) 318.264 396.709i 0.444502 0.554063i
\(717\) 0 0
\(718\) 384.725 + 135.252i 0.535829 + 0.188373i
\(719\) 123.090 0.171196 0.0855979 0.996330i \(-0.472720\pi\)
0.0855979 + 0.996330i \(0.472720\pi\)
\(720\) 0 0
\(721\) 860.609i 1.19363i
\(722\) 713.666 + 109.384i 0.988457 + 0.151502i
\(723\) 0 0
\(724\) −8.33934 + 10.3948i −0.0115184 + 0.0143575i
\(725\) −536.782 −0.740389
\(726\) 0 0
\(727\) 668.993i 0.920211i 0.887864 + 0.460105i \(0.152188\pi\)
−0.887864 + 0.460105i \(0.847812\pi\)
\(728\) 430.965 + 692.590i 0.591985 + 0.951360i
\(729\) 0 0
\(730\) 42.7160 121.506i 0.0585151 0.166447i
\(731\) −608.873 −0.832931
\(732\) 0 0
\(733\) −954.382 −1.30202 −0.651011 0.759068i \(-0.725655\pi\)
−0.651011 + 0.759068i \(0.725655\pi\)
\(734\) −273.016 + 776.597i −0.371956 + 1.05803i
\(735\) 0 0
\(736\) 52.3313 435.842i 0.0711023 0.592177i
\(737\) 372.902 0.505973
\(738\) 0 0
\(739\) 387.814i 0.524782i 0.964962 + 0.262391i \(0.0845110\pi\)
−0.964962 + 0.262391i \(0.915489\pi\)
\(740\) −63.2359 50.7317i −0.0854540 0.0685563i
\(741\) 0 0
\(742\) −186.633 + 530.880i −0.251527 + 0.715471i
\(743\) 478.165i 0.643560i 0.946815 + 0.321780i \(0.104281\pi\)
−0.946815 + 0.321780i \(0.895719\pi\)
\(744\) 0 0
\(745\) 132.208 0.177461
\(746\) 302.286 859.856i 0.405209 1.15262i
\(747\) 0 0
\(748\) 706.038 880.062i 0.943902 1.17655i
\(749\) 749.186 1.00025
\(750\) 0 0
\(751\) −938.092 −1.24912 −0.624562 0.780975i \(-0.714723\pi\)
−0.624562 + 0.780975i \(0.714723\pi\)
\(752\) −261.621 1177.89i −0.347900 1.56634i
\(753\) 0 0
\(754\) 318.917 907.163i 0.422967 1.20313i
\(755\) 125.673i 0.166454i
\(756\) 0 0
\(757\) −710.155 −0.938117 −0.469059 0.883167i \(-0.655407\pi\)
−0.469059 + 0.883167i \(0.655407\pi\)
\(758\) −615.136 216.254i −0.811525 0.285295i
\(759\) 0 0
\(760\) 59.4970 + 78.3285i 0.0782855 + 0.103064i
\(761\) 1234.32i 1.62197i −0.585065 0.810986i \(-0.698931\pi\)
0.585065 0.810986i \(-0.301069\pi\)
\(762\) 0 0
\(763\) 466.502 0.611405
\(764\) 311.204 + 249.666i 0.407335 + 0.326788i
\(765\) 0 0
\(766\) −158.836 + 451.810i −0.207357 + 0.589830i
\(767\) 2505.43 3.26653
\(768\) 0 0
\(769\) −343.803 −0.447078 −0.223539 0.974695i \(-0.571761\pi\)
−0.223539 + 0.974695i \(0.571761\pi\)
\(770\) 84.1935 + 29.5986i 0.109342 + 0.0384397i
\(771\) 0 0
\(772\) 138.146 172.196i 0.178945 0.223052i
\(773\) −172.010 −0.222522 −0.111261 0.993791i \(-0.535489\pi\)
−0.111261 + 0.993791i \(0.535489\pi\)
\(774\) 0 0
\(775\) −476.263 −0.614533
\(776\) 951.029 591.779i 1.22555 0.762601i
\(777\) 0 0
\(778\) −253.310 + 720.544i −0.325592 + 0.926149i
\(779\) −67.3394 722.104i −0.0864434 0.926963i
\(780\) 0 0
\(781\) 1001.43i 1.28223i
\(782\) 172.379 490.335i 0.220434 0.627027i
\(783\) 0 0
\(784\) 95.5848 + 430.350i 0.121919 + 0.548916i
\(785\) 80.4748i 0.102516i
\(786\) 0 0
\(787\) −783.490 −0.995540 −0.497770 0.867309i \(-0.665848\pi\)
−0.497770 + 0.867309i \(0.665848\pi\)
\(788\) 372.317 464.085i 0.472483 0.588940i
\(789\) 0 0
\(790\) −36.2383 + 103.080i −0.0458713 + 0.130481i
\(791\) 23.3342i 0.0294997i
\(792\) 0 0
\(793\) 2338.33i 2.94872i