Properties

Label 684.3.s.a.445.2
Level $684$
Weight $3$
Character 684.445
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.s (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 445.2
Character \(\chi\) \(=\) 684.445
Dual form 684.3.s.a.601.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.99241 - 0.213197i) q^{3} +(2.77840 + 4.81232i) q^{5} +(0.506731 + 0.877684i) q^{7} +(8.90909 + 1.27595i) q^{9} +O(q^{10})\) \(q+(-2.99241 - 0.213197i) q^{3} +(2.77840 + 4.81232i) q^{5} +(0.506731 + 0.877684i) q^{7} +(8.90909 + 1.27595i) q^{9} +(-3.59027 - 6.21853i) q^{11} -21.0389i q^{13} +(-7.28814 - 14.9928i) q^{15} +(5.88580 - 10.1945i) q^{17} +(4.15216 + 18.5408i) q^{19} +(-1.32923 - 2.73443i) q^{21} -38.5635 q^{23} +(-2.93898 + 5.09046i) q^{25} +(-26.3877 - 5.71757i) q^{27} +(34.4637 + 19.8976i) q^{29} +(47.7320 + 27.5581i) q^{31} +(9.41780 + 19.3739i) q^{33} +(-2.81580 + 4.87711i) q^{35} -39.2580i q^{37} +(-4.48544 + 62.9572i) q^{39} +(1.00630 - 0.580990i) q^{41} +32.6087 q^{43} +(18.6127 + 46.4185i) q^{45} +(13.8579 - 24.0026i) q^{47} +(23.9864 - 41.5457i) q^{49} +(-19.7862 + 29.2514i) q^{51} +(32.1220 - 18.5456i) q^{53} +(19.9504 - 34.5551i) q^{55} +(-8.47215 - 56.3669i) q^{57} +(3.95707 - 2.28462i) q^{59} +(-15.6455 + 27.0989i) q^{61} +(3.39463 + 8.46593i) q^{63} +(101.246 - 58.4545i) q^{65} -41.2008i q^{67} +(115.398 + 8.22163i) q^{69} +(27.3414 + 15.7856i) q^{71} +(56.0237 - 97.0360i) q^{73} +(9.87992 - 14.6062i) q^{75} +(3.63860 - 6.30224i) q^{77} +1.05589i q^{79} +(77.7439 + 22.7351i) q^{81} +(76.0080 + 131.650i) q^{83} +65.4124 q^{85} +(-98.8875 - 66.8895i) q^{87} +(27.7627 - 16.0288i) q^{89} +(18.4655 - 10.6611i) q^{91} +(-136.959 - 92.6416i) q^{93} +(-77.6878 + 71.4951i) q^{95} +136.516i q^{97} +(-24.0515 - 59.9825i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - q^{7} + 4 q^{9} + O(q^{10}) \) \( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) −2.99241 0.213197i −0.997472 0.0710658i
\(4\) 0 0
\(5\) 2.77840 + 4.81232i 0.555679 + 0.962465i 0.997850 + 0.0655341i \(0.0208751\pi\)
−0.442171 + 0.896931i \(0.645792\pi\)
\(6\) 0 0
\(7\) 0.506731 + 0.877684i 0.0723901 + 0.125383i 0.899948 0.435996i \(-0.143604\pi\)
−0.827558 + 0.561380i \(0.810271\pi\)
\(8\) 0 0
\(9\) 8.90909 + 1.27595i 0.989899 + 0.141772i
\(10\) 0 0
\(11\) −3.59027 6.21853i −0.326388 0.565321i 0.655404 0.755278i \(-0.272498\pi\)
−0.981792 + 0.189958i \(0.939165\pi\)
\(12\) 0 0
\(13\) 21.0389i 1.61838i −0.587548 0.809189i \(-0.699907\pi\)
0.587548 0.809189i \(-0.300093\pi\)
\(14\) 0 0
\(15\) −7.28814 14.9928i −0.485876 0.999521i
\(16\) 0 0
\(17\) 5.88580 10.1945i 0.346224 0.599677i −0.639352 0.768914i \(-0.720797\pi\)
0.985575 + 0.169238i \(0.0541305\pi\)
\(18\) 0 0
\(19\) 4.15216 + 18.5408i 0.218535 + 0.975829i
\(20\) 0 0
\(21\) −1.32923 2.73443i −0.0632966 0.130211i
\(22\) 0 0
\(23\) −38.5635 −1.67667 −0.838336 0.545154i \(-0.816471\pi\)
−0.838336 + 0.545154i \(0.816471\pi\)
\(24\) 0 0
\(25\) −2.93898 + 5.09046i −0.117559 + 0.203618i
\(26\) 0 0
\(27\) −26.3877 5.71757i −0.977321 0.211762i
\(28\) 0 0
\(29\) 34.4637 + 19.8976i 1.18840 + 0.686124i 0.957943 0.286958i \(-0.0926439\pi\)
0.230459 + 0.973082i \(0.425977\pi\)
\(30\) 0 0
\(31\) 47.7320 + 27.5581i 1.53974 + 0.888971i 0.998853 + 0.0478768i \(0.0152455\pi\)
0.540889 + 0.841094i \(0.318088\pi\)
\(32\) 0 0
\(33\) 9.41780 + 19.3739i 0.285388 + 0.587086i
\(34\) 0 0
\(35\) −2.81580 + 4.87711i −0.0804514 + 0.139346i
\(36\) 0 0
\(37\) 39.2580i 1.06103i −0.847677 0.530513i \(-0.821999\pi\)
0.847677 0.530513i \(-0.178001\pi\)
\(38\) 0 0
\(39\) −4.48544 + 62.9572i −0.115011 + 1.61429i
\(40\) 0 0
\(41\) 1.00630 0.580990i 0.0245440 0.0141705i −0.487678 0.873024i \(-0.662156\pi\)
0.512222 + 0.858853i \(0.328823\pi\)
\(42\) 0 0
\(43\) 32.6087 0.758342 0.379171 0.925327i \(-0.376209\pi\)
0.379171 + 0.925327i \(0.376209\pi\)
\(44\) 0 0
\(45\) 18.6127 + 46.4185i 0.413616 + 1.03152i
\(46\) 0 0
\(47\) 13.8579 24.0026i 0.294850 0.510695i −0.680100 0.733119i \(-0.738064\pi\)
0.974950 + 0.222424i \(0.0713971\pi\)
\(48\) 0 0
\(49\) 23.9864 41.5457i 0.489519 0.847872i
\(50\) 0 0
\(51\) −19.7862 + 29.2514i −0.387965 + 0.573556i
\(52\) 0 0
\(53\) 32.1220 18.5456i 0.606075 0.349918i −0.165353 0.986235i \(-0.552876\pi\)
0.771428 + 0.636317i \(0.219543\pi\)
\(54\) 0 0
\(55\) 19.9504 34.5551i 0.362734 0.628274i
\(56\) 0 0
\(57\) −8.47215 56.3669i −0.148634 0.988892i
\(58\) 0 0
\(59\) 3.95707 2.28462i 0.0670691 0.0387223i −0.466090 0.884737i \(-0.654338\pi\)
0.533160 + 0.846015i \(0.321005\pi\)
\(60\) 0 0
\(61\) −15.6455 + 27.0989i −0.256484 + 0.444244i −0.965298 0.261152i \(-0.915897\pi\)
0.708813 + 0.705396i \(0.249231\pi\)
\(62\) 0 0
\(63\) 3.39463 + 8.46593i 0.0538831 + 0.134380i
\(64\) 0 0
\(65\) 101.246 58.4545i 1.55763 0.899300i
\(66\) 0 0
\(67\) 41.2008i 0.614937i −0.951558 0.307469i \(-0.900518\pi\)
0.951558 0.307469i \(-0.0994819\pi\)
\(68\) 0 0
\(69\) 115.398 + 8.22163i 1.67243 + 0.119154i
\(70\) 0 0
\(71\) 27.3414 + 15.7856i 0.385090 + 0.222332i 0.680030 0.733184i \(-0.261967\pi\)
−0.294941 + 0.955516i \(0.595300\pi\)
\(72\) 0 0
\(73\) 56.0237 97.0360i 0.767448 1.32926i −0.171494 0.985185i \(-0.554859\pi\)
0.938942 0.344075i \(-0.111807\pi\)
\(74\) 0 0
\(75\) 9.87992 14.6062i 0.131732 0.194749i
\(76\) 0 0
\(77\) 3.63860 6.30224i 0.0472546 0.0818473i
\(78\) 0 0
\(79\) 1.05589i 0.0133657i 0.999978 + 0.00668284i \(0.00212723\pi\)
−0.999978 + 0.00668284i \(0.997873\pi\)
\(80\) 0 0
\(81\) 77.7439 + 22.7351i 0.959801 + 0.280681i
\(82\) 0 0
\(83\) 76.0080 + 131.650i 0.915759 + 1.58614i 0.805787 + 0.592206i \(0.201743\pi\)
0.109972 + 0.993935i \(0.464924\pi\)
\(84\) 0 0
\(85\) 65.4124 0.769557
\(86\) 0 0
\(87\) −98.8875 66.8895i −1.13664 0.768844i
\(88\) 0 0
\(89\) 27.7627 16.0288i 0.311941 0.180099i −0.335854 0.941914i \(-0.609025\pi\)
0.647795 + 0.761815i \(0.275691\pi\)
\(90\) 0 0
\(91\) 18.4655 10.6611i 0.202918 0.117155i
\(92\) 0 0
\(93\) −136.959 92.6416i −1.47267 0.996146i
\(94\) 0 0
\(95\) −77.6878 + 71.4951i −0.817766 + 0.752580i
\(96\) 0 0
\(97\) 136.516i 1.40738i 0.710505 + 0.703692i \(0.248466\pi\)
−0.710505 + 0.703692i \(0.751534\pi\)
\(98\) 0 0
\(99\) −24.0515 59.9825i −0.242945 0.605883i
\(100\) 0 0
\(101\) −51.4168 + 89.0564i −0.509077 + 0.881747i 0.490868 + 0.871234i \(0.336680\pi\)
−0.999945 + 0.0105129i \(0.996654\pi\)
\(102\) 0 0
\(103\) 67.3695 + 38.8958i 0.654072 + 0.377629i 0.790015 0.613088i \(-0.210073\pi\)
−0.135942 + 0.990717i \(0.543406\pi\)
\(104\) 0 0
\(105\) 9.46583 13.9940i 0.0901507 0.133276i
\(106\) 0 0
\(107\) 109.565i 1.02397i −0.858994 0.511986i \(-0.828910\pi\)
0.858994 0.511986i \(-0.171090\pi\)
\(108\) 0 0
\(109\) −9.20585 5.31500i −0.0844574 0.0487615i 0.457177 0.889376i \(-0.348861\pi\)
−0.541634 + 0.840614i \(0.682194\pi\)
\(110\) 0 0
\(111\) −8.36970 + 117.476i −0.0754027 + 1.05834i
\(112\) 0 0
\(113\) 176.506 + 101.906i 1.56200 + 0.901823i 0.997054 + 0.0766977i \(0.0244376\pi\)
0.564949 + 0.825126i \(0.308896\pi\)
\(114\) 0 0
\(115\) −107.145 185.580i −0.931692 1.61374i
\(116\) 0 0
\(117\) 26.8446 187.438i 0.229441 1.60203i
\(118\) 0 0
\(119\) 11.9301 0.100253
\(120\) 0 0
\(121\) 34.7199 60.1367i 0.286942 0.496998i
\(122\) 0 0
\(123\) −3.13515 + 1.52402i −0.0254890 + 0.0123904i
\(124\) 0 0
\(125\) 106.257 0.850058
\(126\) 0 0
\(127\) 205.368 118.570i 1.61707 0.933618i 0.629403 0.777079i \(-0.283300\pi\)
0.987672 0.156539i \(-0.0500336\pi\)
\(128\) 0 0
\(129\) −97.5788 6.95209i −0.756424 0.0538922i
\(130\) 0 0
\(131\) −11.8754 20.5688i −0.0906521 0.157014i 0.817134 0.576448i \(-0.195562\pi\)
−0.907786 + 0.419434i \(0.862228\pi\)
\(132\) 0 0
\(133\) −14.1689 + 13.0395i −0.106533 + 0.0980411i
\(134\) 0 0
\(135\) −45.8006 142.872i −0.339264 1.05831i
\(136\) 0 0
\(137\) −85.3353 + 147.805i −0.622886 + 1.07887i 0.366060 + 0.930591i \(0.380707\pi\)
−0.988946 + 0.148278i \(0.952627\pi\)
\(138\) 0 0
\(139\) −183.477 −1.31998 −0.659989 0.751276i \(-0.729439\pi\)
−0.659989 + 0.751276i \(0.729439\pi\)
\(140\) 0 0
\(141\) −46.5860 + 68.8714i −0.330397 + 0.488450i
\(142\) 0 0
\(143\) −130.831 + 75.5354i −0.914903 + 0.528220i
\(144\) 0 0
\(145\) 221.134i 1.52506i
\(146\) 0 0
\(147\) −80.6348 + 119.208i −0.548536 + 0.810941i
\(148\) 0 0
\(149\) 41.3286 + 71.5832i 0.277373 + 0.480424i 0.970731 0.240169i \(-0.0772028\pi\)
−0.693358 + 0.720593i \(0.743869\pi\)
\(150\) 0 0
\(151\) 64.0926 37.0039i 0.424454 0.245059i −0.272527 0.962148i \(-0.587859\pi\)
0.696981 + 0.717089i \(0.254526\pi\)
\(152\) 0 0
\(153\) 65.4448 83.3138i 0.427744 0.544535i
\(154\) 0 0
\(155\) 306.269i 1.97593i
\(156\) 0 0
\(157\) −134.217 232.470i −0.854882 1.48070i −0.876754 0.480939i \(-0.840296\pi\)
0.0218718 0.999761i \(-0.493037\pi\)
\(158\) 0 0
\(159\) −100.076 + 48.6479i −0.629410 + 0.305962i
\(160\) 0 0
\(161\) −19.5413 33.8465i −0.121375 0.210227i
\(162\) 0 0
\(163\) −303.332 −1.86093 −0.930467 0.366376i \(-0.880599\pi\)
−0.930467 + 0.366376i \(0.880599\pi\)
\(164\) 0 0
\(165\) −67.0669 + 99.1498i −0.406466 + 0.600908i
\(166\) 0 0
\(167\) 42.9565i 0.257224i −0.991695 0.128612i \(-0.958948\pi\)
0.991695 0.128612i \(-0.0410522\pi\)
\(168\) 0 0
\(169\) −273.636 −1.61915
\(170\) 0 0
\(171\) 13.3349 + 170.479i 0.0779820 + 0.996955i
\(172\) 0 0
\(173\) 266.137i 1.53836i 0.639030 + 0.769182i \(0.279336\pi\)
−0.639030 + 0.769182i \(0.720664\pi\)
\(174\) 0 0
\(175\) −5.95709 −0.0340405
\(176\) 0 0
\(177\) −12.3283 + 5.99289i −0.0696513 + 0.0338581i
\(178\) 0 0
\(179\) 11.5293i 0.0644093i −0.999481 0.0322046i \(-0.989747\pi\)
0.999481 0.0322046i \(-0.0102528\pi\)
\(180\) 0 0
\(181\) 89.5762 51.7169i 0.494896 0.285729i −0.231707 0.972786i \(-0.574431\pi\)
0.726603 + 0.687057i \(0.241098\pi\)
\(182\) 0 0
\(183\) 52.5953 77.7554i 0.287406 0.424893i
\(184\) 0 0
\(185\) 188.922 109.074i 1.02120 0.589590i
\(186\) 0 0
\(187\) −84.5264 −0.452013
\(188\) 0 0
\(189\) −8.35324 26.0573i −0.0441970 0.137869i
\(190\) 0 0
\(191\) −66.7070 115.540i −0.349251 0.604921i 0.636865 0.770975i \(-0.280231\pi\)
−0.986117 + 0.166054i \(0.946897\pi\)
\(192\) 0 0
\(193\) 148.126 85.5204i 0.767491 0.443111i −0.0644881 0.997918i \(-0.520541\pi\)
0.831979 + 0.554808i \(0.187208\pi\)
\(194\) 0 0
\(195\) −315.433 + 153.335i −1.61760 + 0.786331i
\(196\) 0 0
\(197\) −78.2214 −0.397063 −0.198531 0.980095i \(-0.563617\pi\)
−0.198531 + 0.980095i \(0.563617\pi\)
\(198\) 0 0
\(199\) −60.1557 104.193i −0.302290 0.523582i 0.674364 0.738399i \(-0.264418\pi\)
−0.976654 + 0.214817i \(0.931084\pi\)
\(200\) 0 0
\(201\) −8.78390 + 123.290i −0.0437010 + 0.613382i
\(202\) 0 0
\(203\) 40.3309i 0.198675i
\(204\) 0 0
\(205\) 5.59183 + 3.22844i 0.0272772 + 0.0157485i
\(206\) 0 0
\(207\) −343.566 49.2051i −1.65974 0.237706i
\(208\) 0 0
\(209\) 100.389 92.3866i 0.480329 0.442041i
\(210\) 0 0
\(211\) −36.7654 + 21.2265i −0.174243 + 0.100599i −0.584585 0.811332i \(-0.698743\pi\)
0.410342 + 0.911932i \(0.365409\pi\)
\(212\) 0 0
\(213\) −78.4513 53.0660i −0.368316 0.249136i
\(214\) 0 0
\(215\) 90.5999 + 156.924i 0.421395 + 0.729877i
\(216\) 0 0
\(217\) 55.8582i 0.257411i
\(218\) 0 0
\(219\) −188.334 + 278.428i −0.859973 + 1.27136i
\(220\) 0 0
\(221\) −214.481 123.831i −0.970504 0.560321i
\(222\) 0 0
\(223\) 109.639i 0.491657i −0.969313 0.245828i \(-0.920940\pi\)
0.969313 0.245828i \(-0.0790600\pi\)
\(224\) 0 0
\(225\) −32.6788 + 41.6014i −0.145239 + 0.184895i
\(226\) 0 0
\(227\) 277.452 160.187i 1.22226 0.705671i 0.256859 0.966449i \(-0.417313\pi\)
0.965399 + 0.260778i \(0.0839792\pi\)
\(228\) 0 0
\(229\) 149.471 258.891i 0.652710 1.13053i −0.329753 0.944067i \(-0.606965\pi\)
0.982463 0.186459i \(-0.0597012\pi\)
\(230\) 0 0
\(231\) −12.2318 + 18.0832i −0.0529516 + 0.0782822i
\(232\) 0 0
\(233\) −171.378 + 296.835i −0.735527 + 1.27397i 0.218965 + 0.975733i \(0.429732\pi\)
−0.954492 + 0.298237i \(0.903601\pi\)
\(234\) 0 0
\(235\) 154.011 0.655368
\(236\) 0 0
\(237\) 0.225113 3.15966i 0.000949843 0.0133319i
\(238\) 0 0
\(239\) 155.648 269.589i 0.651245 1.12799i −0.331576 0.943428i \(-0.607580\pi\)
0.982821 0.184561i \(-0.0590863\pi\)
\(240\) 0 0
\(241\) −61.0923 35.2717i −0.253495 0.146355i 0.367868 0.929878i \(-0.380088\pi\)
−0.621364 + 0.783522i \(0.713421\pi\)
\(242\) 0 0
\(243\) −227.795 84.6077i −0.937428 0.348180i
\(244\) 0 0
\(245\) 266.575 1.08806
\(246\) 0 0
\(247\) 390.077 87.3570i 1.57926 0.353672i
\(248\) 0 0
\(249\) −199.380 410.155i −0.800723 1.64721i
\(250\) 0 0
\(251\) −204.111 353.530i −0.813190 1.40849i −0.910620 0.413244i \(-0.864396\pi\)
0.0974307 0.995242i \(-0.468938\pi\)
\(252\) 0 0
\(253\) 138.453 + 239.808i 0.547246 + 0.947858i
\(254\) 0 0
\(255\) −195.741 13.9458i −0.767612 0.0546892i
\(256\) 0 0
\(257\) 334.530i 1.30167i 0.759217 + 0.650837i \(0.225582\pi\)
−0.759217 + 0.650837i \(0.774418\pi\)
\(258\) 0 0
\(259\) 34.4561 19.8932i 0.133035 0.0768079i
\(260\) 0 0
\(261\) 281.652 + 221.244i 1.07913 + 0.847676i
\(262\) 0 0
\(263\) −89.0859 −0.338730 −0.169365 0.985553i \(-0.554172\pi\)
−0.169365 + 0.985553i \(0.554172\pi\)
\(264\) 0 0
\(265\) 178.495 + 103.054i 0.673567 + 0.388884i
\(266\) 0 0
\(267\) −86.4949 + 42.0460i −0.323951 + 0.157475i
\(268\) 0 0
\(269\) −253.828 146.548i −0.943599 0.544787i −0.0525125 0.998620i \(-0.516723\pi\)
−0.891087 + 0.453833i \(0.850056\pi\)
\(270\) 0 0
\(271\) 102.311 177.208i 0.377531 0.653903i −0.613171 0.789950i \(-0.710106\pi\)
0.990702 + 0.136047i \(0.0434398\pi\)
\(272\) 0 0
\(273\) −57.5294 + 27.9656i −0.210730 + 0.102438i
\(274\) 0 0
\(275\) 42.2069 0.153480
\(276\) 0 0
\(277\) −61.0472 105.737i −0.220387 0.381721i 0.734539 0.678567i \(-0.237399\pi\)
−0.954925 + 0.296846i \(0.904065\pi\)
\(278\) 0 0
\(279\) 390.086 + 306.421i 1.39816 + 1.09828i
\(280\) 0 0
\(281\) 19.8408 + 11.4551i 0.0706080 + 0.0407655i 0.534888 0.844923i \(-0.320354\pi\)
−0.464280 + 0.885688i \(0.653687\pi\)
\(282\) 0 0
\(283\) −10.4229 18.0530i −0.0368301 0.0637916i 0.847023 0.531557i \(-0.178393\pi\)
−0.883853 + 0.467765i \(0.845059\pi\)
\(284\) 0 0
\(285\) 247.717 197.380i 0.869181 0.692562i
\(286\) 0 0
\(287\) 1.01985 + 0.588812i 0.00355349 + 0.00205161i
\(288\) 0 0
\(289\) 75.2147 + 130.276i 0.260258 + 0.450781i
\(290\) 0 0
\(291\) 29.1049 408.513i 0.100017 1.40383i
\(292\) 0 0
\(293\) −359.465 207.537i −1.22684 0.708318i −0.260475 0.965481i \(-0.583879\pi\)
−0.966368 + 0.257162i \(0.917212\pi\)
\(294\) 0 0
\(295\) 21.9886 + 12.6952i 0.0745378 + 0.0430344i
\(296\) 0 0
\(297\) 59.1840 + 184.620i 0.199273 + 0.621617i
\(298\) 0 0
\(299\) 811.334i 2.71349i
\(300\) 0 0
\(301\) 16.5238 + 28.6201i 0.0548965 + 0.0950835i
\(302\) 0 0
\(303\) 172.847 255.532i 0.570452 0.843340i
\(304\) 0 0
\(305\) −173.878 −0.570092
\(306\) 0 0
\(307\) 20.0192 + 11.5581i 0.0652090 + 0.0376484i 0.532250 0.846587i \(-0.321347\pi\)
−0.467041 + 0.884236i \(0.654680\pi\)
\(308\) 0 0
\(309\) −193.305 130.755i −0.625582 0.423156i
\(310\) 0 0
\(311\) −269.387 + 466.593i −0.866197 + 1.50030i −0.000344138 1.00000i \(0.500110\pi\)
−0.865853 + 0.500298i \(0.833224\pi\)
\(312\) 0 0
\(313\) 243.055 420.984i 0.776535 1.34500i −0.157393 0.987536i \(-0.550309\pi\)
0.933928 0.357462i \(-0.116358\pi\)
\(314\) 0 0
\(315\) −31.3092 + 39.8578i −0.0993942 + 0.126533i
\(316\) 0 0
\(317\) −202.411 116.862i −0.638521 0.368650i 0.145524 0.989355i \(-0.453513\pi\)
−0.784045 + 0.620704i \(0.786847\pi\)
\(318\) 0 0
\(319\) 285.751i 0.895771i
\(320\) 0 0
\(321\) −23.3590 + 327.864i −0.0727694 + 1.02138i
\(322\) 0 0
\(323\) 213.453 + 66.7980i 0.660844 + 0.206805i
\(324\) 0 0
\(325\) 107.098 + 61.8330i 0.329532 + 0.190255i
\(326\) 0 0
\(327\) 26.4146 + 17.8674i 0.0807785 + 0.0546402i
\(328\) 0 0
\(329\) 28.0890 0.0853769
\(330\) 0 0
\(331\) −424.338 + 244.992i −1.28199 + 0.740156i −0.977212 0.212267i \(-0.931915\pi\)
−0.304777 + 0.952424i \(0.598582\pi\)
\(332\) 0 0
\(333\) 50.0912 349.753i 0.150424 1.05031i
\(334\) 0 0
\(335\) 198.272 114.472i 0.591855 0.341708i
\(336\) 0 0
\(337\) −269.298 + 155.479i −0.799102 + 0.461362i −0.843157 0.537667i \(-0.819306\pi\)
0.0440548 + 0.999029i \(0.485972\pi\)
\(338\) 0 0
\(339\) −506.454 342.576i −1.49397 1.01055i
\(340\) 0 0
\(341\) 395.764i 1.16060i
\(342\) 0 0
\(343\) 98.2783 0.286526
\(344\) 0 0
\(345\) 281.056 + 578.175i 0.814655 + 1.67587i
\(346\) 0 0
\(347\) 57.3941 + 99.4096i 0.165401 + 0.286483i 0.936798 0.349872i \(-0.113775\pi\)
−0.771397 + 0.636355i \(0.780442\pi\)
\(348\) 0 0
\(349\) 174.607 + 302.428i 0.500307 + 0.866557i 1.00000 0.000354398i \(0.000112809\pi\)
−0.499693 + 0.866203i \(0.666554\pi\)
\(350\) 0 0
\(351\) −120.291 + 555.168i −0.342711 + 1.58168i
\(352\) 0 0
\(353\) 2.50075 + 4.33142i 0.00708428 + 0.0122703i 0.869546 0.493852i \(-0.164412\pi\)
−0.862462 + 0.506123i \(0.831078\pi\)
\(354\) 0 0
\(355\) 175.434i 0.494181i
\(356\) 0 0
\(357\) −35.6997 2.54346i −0.0999992 0.00712454i
\(358\) 0 0
\(359\) −285.463 + 494.437i −0.795162 + 1.37726i 0.127574 + 0.991829i \(0.459281\pi\)
−0.922736 + 0.385432i \(0.874052\pi\)
\(360\) 0 0
\(361\) −326.519 + 153.968i −0.904485 + 0.426505i
\(362\) 0 0
\(363\) −116.717 + 172.552i −0.321536 + 0.475349i
\(364\) 0 0
\(365\) 622.625 1.70582
\(366\) 0 0
\(367\) 81.0373 140.361i 0.220810 0.382454i −0.734244 0.678885i \(-0.762463\pi\)
0.955054 + 0.296431i \(0.0957966\pi\)
\(368\) 0 0
\(369\) 9.70658 3.89210i 0.0263051 0.0105477i
\(370\) 0 0
\(371\) 32.5544 + 18.7953i 0.0877477 + 0.0506612i
\(372\) 0 0
\(373\) −532.169 307.248i −1.42673 0.823721i −0.429865 0.902893i \(-0.641439\pi\)
−0.996861 + 0.0791726i \(0.974772\pi\)
\(374\) 0 0
\(375\) −317.966 22.6538i −0.847909 0.0604101i
\(376\) 0 0
\(377\) 418.624 725.078i 1.11041 1.92328i
\(378\) 0 0
\(379\) 286.091i 0.754856i −0.926039 0.377428i \(-0.876809\pi\)
0.926039 0.377428i \(-0.123191\pi\)
\(380\) 0 0
\(381\) −639.826 + 311.025i −1.67933 + 0.816339i
\(382\) 0 0
\(383\) 400.992 231.513i 1.04698 0.604473i 0.125176 0.992135i \(-0.460051\pi\)
0.921802 + 0.387662i \(0.126717\pi\)
\(384\) 0 0
\(385\) 40.4379 0.105034
\(386\) 0 0
\(387\) 290.514 + 41.6071i 0.750682 + 0.107512i
\(388\) 0 0
\(389\) 96.7327 167.546i 0.248670 0.430709i −0.714487 0.699649i \(-0.753340\pi\)
0.963157 + 0.268939i \(0.0866732\pi\)
\(390\) 0 0
\(391\) −226.977 + 393.136i −0.580504 + 1.00546i
\(392\) 0 0
\(393\) 31.1510 + 64.0823i 0.0792646 + 0.163059i
\(394\) 0 0
\(395\) −5.08128 + 2.93368i −0.0128640 + 0.00742703i
\(396\) 0 0
\(397\) 6.35868 11.0136i 0.0160168 0.0277420i −0.857906 0.513807i \(-0.828235\pi\)
0.873923 + 0.486065i \(0.161568\pi\)
\(398\) 0 0
\(399\) 45.1792 35.9987i 0.113231 0.0902223i
\(400\) 0 0
\(401\) −30.3215 + 17.5061i −0.0756146 + 0.0436561i −0.537331 0.843372i \(-0.680567\pi\)
0.461716 + 0.887028i \(0.347234\pi\)
\(402\) 0 0
\(403\) 579.793 1004.23i 1.43869 2.49189i
\(404\) 0 0
\(405\) 106.595 + 437.296i 0.263197 + 1.07974i
\(406\) 0 0
\(407\) −244.127 + 140.947i −0.599820 + 0.346306i
\(408\) 0 0
\(409\) 109.295i 0.267225i −0.991034 0.133613i \(-0.957342\pi\)
0.991034 0.133613i \(-0.0426578\pi\)
\(410\) 0 0
\(411\) 286.870 424.101i 0.697982 1.03188i
\(412\) 0 0
\(413\) 4.01035 + 2.31537i 0.00971028 + 0.00560623i
\(414\) 0 0
\(415\) −422.361 + 731.550i −1.01774 + 1.76277i
\(416\) 0 0
\(417\) 549.039 + 39.1168i 1.31664 + 0.0938053i
\(418\) 0 0
\(419\) 251.614 435.809i 0.600512 1.04012i −0.392232 0.919866i \(-0.628297\pi\)
0.992744 0.120250i \(-0.0383697\pi\)
\(420\) 0 0
\(421\) 742.171i 1.76288i 0.472298 + 0.881439i \(0.343424\pi\)
−0.472298 + 0.881439i \(0.656576\pi\)
\(422\) 0 0
\(423\) 154.088 196.160i 0.364274 0.463735i
\(424\) 0 0
\(425\) 34.5965 + 59.9229i 0.0814035 + 0.140995i
\(426\) 0 0
\(427\) −31.7123 −0.0742677
\(428\) 0 0
\(429\) 407.605 198.140i 0.950128 0.461866i
\(430\) 0 0
\(431\) 112.449 64.9223i 0.260902 0.150632i −0.363844 0.931460i \(-0.618536\pi\)
0.624746 + 0.780828i \(0.285203\pi\)
\(432\) 0 0
\(433\) 476.929 275.355i 1.10145 0.635923i 0.164850 0.986319i \(-0.447286\pi\)
0.936602 + 0.350395i \(0.113953\pi\)
\(434\) 0 0
\(435\) 47.1452 661.724i 0.108380 1.52120i
\(436\) 0 0
\(437\) −160.122 714.996i −0.366411 1.63615i
\(438\) 0 0
\(439\) 419.239i 0.954987i 0.878635 + 0.477493i \(0.158455\pi\)
−0.878635 + 0.477493i \(0.841545\pi\)
\(440\) 0 0
\(441\) 266.708 339.529i 0.604780 0.769908i
\(442\) 0 0
\(443\) −254.848 + 441.409i −0.575277 + 0.996409i 0.420734 + 0.907184i \(0.361772\pi\)
−0.996011 + 0.0892254i \(0.971561\pi\)
\(444\) 0 0
\(445\) 154.272 + 89.0689i 0.346678 + 0.200155i
\(446\) 0 0
\(447\) −108.411 223.018i −0.242530 0.498922i
\(448\) 0 0
\(449\) 580.640i 1.29318i 0.762836 + 0.646592i \(0.223806\pi\)
−0.762836 + 0.646592i \(0.776194\pi\)
\(450\) 0 0
\(451\) −7.22581 4.17182i −0.0160218 0.00925016i
\(452\) 0 0
\(453\) −199.681 + 97.0666i −0.440796 + 0.214275i
\(454\) 0 0
\(455\) 102.609 + 59.2414i 0.225515 + 0.130201i
\(456\) 0 0
\(457\) 108.041 + 187.133i 0.236414 + 0.409481i 0.959683 0.281086i \(-0.0906946\pi\)
−0.723269 + 0.690567i \(0.757361\pi\)
\(458\) 0 0
\(459\) −213.600 + 235.357i −0.465360 + 0.512760i
\(460\) 0 0
\(461\) 259.030 0.561887 0.280943 0.959724i \(-0.409353\pi\)
0.280943 + 0.959724i \(0.409353\pi\)
\(462\) 0 0
\(463\) 65.8203 114.004i 0.142161 0.246229i −0.786149 0.618036i \(-0.787928\pi\)
0.928310 + 0.371807i \(0.121262\pi\)
\(464\) 0 0
\(465\) 65.2958 916.485i 0.140421 1.97093i
\(466\) 0 0
\(467\) −17.1989 −0.0368284 −0.0184142 0.999830i \(-0.505862\pi\)
−0.0184142 + 0.999830i \(0.505862\pi\)
\(468\) 0 0
\(469\) 36.1613 20.8777i 0.0771029 0.0445154i
\(470\) 0 0
\(471\) 352.070 + 724.261i 0.747494 + 1.53771i
\(472\) 0 0
\(473\) −117.074 202.778i −0.247514 0.428706i
\(474\) 0 0
\(475\) −106.584 33.3545i −0.224388 0.0702199i
\(476\) 0 0
\(477\) 309.841 124.239i 0.649562 0.260459i
\(478\) 0 0
\(479\) 24.1287 41.7922i 0.0503731 0.0872488i −0.839739 0.542990i \(-0.817292\pi\)
0.890113 + 0.455741i \(0.150626\pi\)
\(480\) 0 0
\(481\) −825.946 −1.71714
\(482\) 0 0
\(483\) 51.2597 + 105.449i 0.106128 + 0.218321i
\(484\) 0 0
\(485\) −656.960 + 379.296i −1.35456 + 0.782054i
\(486\) 0 0
\(487\) 43.8696i 0.0900813i 0.998985 + 0.0450407i \(0.0143417\pi\)
−0.998985 + 0.0450407i \(0.985658\pi\)
\(488\) 0 0
\(489\) 907.696 + 64.6697i 1.85623 + 0.132249i
\(490\) 0 0
\(491\) 108.425 + 187.797i 0.220824 + 0.382479i 0.955058 0.296417i \(-0.0957919\pi\)
−0.734234 + 0.678896i \(0.762459\pi\)
\(492\) 0 0
\(493\) 405.693 234.227i 0.822906 0.475105i
\(494\) 0 0
\(495\) 221.830 282.399i 0.448142 0.570502i
\(496\) 0 0
\(497\) 31.9961i 0.0643785i
\(498\) 0 0
\(499\) −116.985 202.625i −0.234440 0.406061i 0.724670 0.689096i \(-0.241992\pi\)
−0.959110 + 0.283035i \(0.908659\pi\)
\(500\) 0 0
\(501\) −9.15821 + 128.544i −0.0182799 + 0.256574i
\(502\) 0 0
\(503\) −166.750 288.820i −0.331511 0.574195i 0.651297 0.758823i \(-0.274225\pi\)
−0.982808 + 0.184628i \(0.940892\pi\)
\(504\) 0 0
\(505\) −571.425 −1.13153
\(506\) 0 0
\(507\) 818.833 + 58.3386i 1.61506 + 0.115066i
\(508\) 0 0
\(509\) 289.196i 0.568165i −0.958800 0.284082i \(-0.908311\pi\)
0.958800 0.284082i \(-0.0916889\pi\)
\(510\) 0 0
\(511\) 113.556 0.222223
\(512\) 0 0
\(513\) −3.55786 512.988i −0.00693540 0.999976i
\(514\) 0 0
\(515\) 432.272i 0.839362i
\(516\) 0 0
\(517\) −199.015 −0.384942
\(518\) 0 0
\(519\) 56.7397 796.392i 0.109325 1.53447i
\(520\) 0 0
\(521\) 188.549i 0.361898i −0.983493 0.180949i \(-0.942083\pi\)
0.983493 0.180949i \(-0.0579169\pi\)
\(522\) 0 0
\(523\) −143.038 + 82.5829i −0.273495 + 0.157902i −0.630475 0.776210i \(-0.717140\pi\)
0.356980 + 0.934112i \(0.383806\pi\)
\(524\) 0 0
\(525\) 17.8261 + 1.27004i 0.0339544 + 0.00241912i
\(526\) 0 0
\(527\) 561.882 324.403i 1.06619 0.615565i
\(528\) 0 0
\(529\) 958.141 1.81123
\(530\) 0 0
\(531\) 38.1690 15.3048i 0.0718814 0.0288227i
\(532\) 0 0
\(533\) −12.2234 21.1716i −0.0229332 0.0397215i
\(534\) 0 0
\(535\) 527.263 304.415i 0.985538 0.569000i
\(536\) 0 0
\(537\) −2.45801 + 34.5003i −0.00457730 + 0.0642464i
\(538\) 0 0
\(539\) −344.471 −0.639093
\(540\) 0 0
\(541\) −139.846 242.221i −0.258496 0.447728i 0.707343 0.706870i \(-0.249894\pi\)
−0.965839 + 0.259142i \(0.916560\pi\)
\(542\) 0 0
\(543\) −279.075 + 135.661i −0.513951 + 0.249836i
\(544\) 0 0
\(545\) 59.0687i 0.108383i
\(546\) 0 0
\(547\) 196.738 + 113.587i 0.359667 + 0.207654i 0.668935 0.743321i \(-0.266751\pi\)
−0.309268 + 0.950975i \(0.600084\pi\)
\(548\) 0 0
\(549\) −173.964 + 221.463i −0.316875 + 0.403394i
\(550\) 0 0
\(551\) −225.818 + 721.600i −0.409833 + 1.30962i
\(552\) 0 0
\(553\) −0.926736 + 0.535051i −0.00167583 + 0.000967543i
\(554\) 0 0
\(555\) −588.588 + 286.118i −1.06052 + 0.515527i
\(556\) 0 0
\(557\) 16.6374 + 28.8168i 0.0298696 + 0.0517357i 0.880574 0.473909i \(-0.157157\pi\)
−0.850704 + 0.525645i \(0.823824\pi\)
\(558\) 0 0
\(559\) 686.052i 1.22728i
\(560\) 0 0
\(561\) 252.938 + 18.0208i 0.450870 + 0.0321227i
\(562\) 0 0
\(563\) 533.191 + 307.838i 0.947054 + 0.546782i 0.892165 0.451710i \(-0.149186\pi\)
0.0548896 + 0.998492i \(0.482519\pi\)
\(564\) 0 0
\(565\) 1132.54i 2.00450i
\(566\) 0 0
\(567\) 19.4410 + 79.7552i 0.0342875 + 0.140662i
\(568\) 0 0
\(569\) 759.702 438.614i 1.33515 0.770851i 0.349069 0.937097i \(-0.386498\pi\)
0.986084 + 0.166246i \(0.0531646\pi\)
\(570\) 0 0
\(571\) −445.952 + 772.412i −0.781002 + 1.35274i 0.150356 + 0.988632i \(0.451958\pi\)
−0.931358 + 0.364104i \(0.881375\pi\)
\(572\) 0 0
\(573\) 174.982 + 359.965i 0.305379 + 0.628211i
\(574\) 0 0
\(575\) 113.337 196.306i 0.197108 0.341401i
\(576\) 0 0
\(577\) 940.378 1.62977 0.814886 0.579622i \(-0.196800\pi\)
0.814886 + 0.579622i \(0.196800\pi\)
\(578\) 0 0
\(579\) −461.486 + 224.333i −0.797040 + 0.387448i
\(580\) 0 0
\(581\) −77.0312 + 133.422i −0.132584 + 0.229642i
\(582\) 0 0
\(583\) −230.653 133.168i −0.395631 0.228418i
\(584\) 0 0
\(585\) 976.596 391.591i 1.66940 0.669387i
\(586\) 0 0
\(587\) −220.328 −0.375346 −0.187673 0.982232i \(-0.560095\pi\)
−0.187673 + 0.982232i \(0.560095\pi\)
\(588\) 0 0
\(589\) −312.757 + 999.413i −0.530996 + 1.69680i
\(590\) 0 0
\(591\) 234.071 + 16.6766i 0.396059 + 0.0282176i
\(592\) 0 0
\(593\) −511.277 885.558i −0.862188 1.49335i −0.869813 0.493382i \(-0.835760\pi\)
0.00762469 0.999971i \(-0.497573\pi\)
\(594\) 0 0
\(595\) 33.1465 + 57.4114i 0.0557084 + 0.0964897i
\(596\) 0 0
\(597\) 157.797 + 324.613i 0.264317 + 0.543741i
\(598\) 0 0
\(599\) 1135.87i 1.89627i −0.317867 0.948135i \(-0.602967\pi\)
0.317867 0.948135i \(-0.397033\pi\)
\(600\) 0 0
\(601\) −33.2557 + 19.2002i −0.0553339 + 0.0319470i −0.527412 0.849610i \(-0.676837\pi\)
0.472078 + 0.881557i \(0.343504\pi\)
\(602\) 0 0
\(603\) 52.5702 367.062i 0.0871810 0.608726i
\(604\) 0 0
\(605\) 385.863 0.637790
\(606\) 0 0
\(607\) 418.741 + 241.760i 0.689854 + 0.398287i 0.803557 0.595227i \(-0.202938\pi\)
−0.113703 + 0.993515i \(0.536271\pi\)
\(608\) 0 0
\(609\) 8.59845 120.687i 0.0141190 0.198172i
\(610\) 0 0
\(611\) −504.990 291.556i −0.826497 0.477178i
\(612\) 0 0
\(613\) −233.580 + 404.573i −0.381044 + 0.659988i −0.991212 0.132284i \(-0.957769\pi\)
0.610167 + 0.792272i \(0.291102\pi\)
\(614\) 0 0
\(615\) −16.0448 10.8530i −0.0260891 0.0176472i
\(616\) 0 0
\(617\) −412.288 −0.668214 −0.334107 0.942535i \(-0.608435\pi\)
−0.334107 + 0.942535i \(0.608435\pi\)
\(618\) 0 0
\(619\) −72.2457 125.133i −0.116714 0.202154i 0.801750 0.597660i \(-0.203903\pi\)
−0.918463 + 0.395506i \(0.870569\pi\)
\(620\) 0 0
\(621\) 1017.60 + 220.489i 1.63865 + 0.355055i
\(622\) 0 0
\(623\) 28.1365 + 16.2446i 0.0451629 + 0.0260748i
\(624\) 0 0
\(625\) 368.699 + 638.606i 0.589919 + 1.02177i
\(626\) 0 0
\(627\) −320.102 + 255.056i −0.510529 + 0.406789i
\(628\) 0 0
\(629\) −400.216 231.065i −0.636273 0.367352i
\(630\) 0 0
\(631\) 201.659 + 349.283i 0.319586 + 0.553539i 0.980402 0.197009i \(-0.0631228\pi\)
−0.660816 + 0.750548i \(0.729790\pi\)
\(632\) 0 0
\(633\) 114.543 55.6802i 0.180952 0.0879624i
\(634\) 0 0
\(635\) 1141.19 + 658.866i 1.79715 + 1.03758i
\(636\) 0 0
\(637\) −874.078 504.649i −1.37218 0.792228i
\(638\) 0 0
\(639\) 223.445 + 175.521i 0.349680 + 0.274681i
\(640\) 0 0
\(641\) 522.043i 0.814420i 0.913335 + 0.407210i \(0.133498\pi\)
−0.913335 + 0.407210i \(0.866502\pi\)
\(642\) 0 0
\(643\) 336.732 + 583.236i 0.523688 + 0.907055i 0.999620 + 0.0275725i \(0.00877770\pi\)
−0.475931 + 0.879482i \(0.657889\pi\)
\(644\) 0 0
\(645\) −237.657 488.896i −0.368460 0.757979i
\(646\) 0 0
\(647\) −26.2000 −0.0404946 −0.0202473 0.999795i \(-0.506445\pi\)
−0.0202473 + 0.999795i \(0.506445\pi\)
\(648\) 0 0
\(649\) −28.4139 16.4048i −0.0437811 0.0252770i
\(650\) 0 0
\(651\) 11.9088 167.151i 0.0182931 0.256760i
\(652\) 0 0
\(653\) 368.122 637.605i 0.563739 0.976424i −0.433427 0.901189i \(-0.642696\pi\)
0.997166 0.0752357i \(-0.0239709\pi\)
\(654\) 0 0
\(655\) 65.9893 114.297i 0.100747 0.174499i
\(656\) 0 0
\(657\) 622.934 793.019i 0.948149 1.20703i
\(658\) 0 0
\(659\) −265.997 153.573i −0.403637 0.233040i 0.284415 0.958701i \(-0.408201\pi\)
−0.688052 + 0.725661i \(0.741534\pi\)
\(660\) 0 0
\(661\) 527.085i 0.797406i 0.917080 + 0.398703i \(0.130540\pi\)
−0.917080 + 0.398703i \(0.869460\pi\)
\(662\) 0 0
\(663\) 615.417 + 416.280i 0.928231 + 0.627874i
\(664\) 0 0
\(665\) −102.117 31.9565i −0.153559 0.0480549i
\(666\) 0 0
\(667\) −1329.04 767.321i −1.99256 1.15041i
\(668\) 0 0
\(669\) −23.3749 + 328.087i −0.0349400 + 0.490414i
\(670\) 0 0
\(671\) 224.687 0.334853
\(672\) 0 0
\(673\) −317.808 + 183.486i −0.472226 + 0.272640i −0.717171 0.696897i \(-0.754563\pi\)
0.244945 + 0.969537i \(0.421230\pi\)
\(674\) 0 0
\(675\) 106.658 117.522i 0.158012 0.174106i
\(676\) 0 0
\(677\) −713.738 + 412.077i −1.05427 + 0.608681i −0.923841 0.382777i \(-0.874968\pi\)
−0.130425 + 0.991458i \(0.541634\pi\)
\(678\) 0 0
\(679\) −119.818 + 69.1770i −0.176463 + 0.101881i
\(680\) 0 0
\(681\) −864.404 + 420.195i −1.26932 + 0.617026i
\(682\) 0 0
\(683\) 21.9799i 0.0321813i −0.999871 0.0160907i \(-0.994878\pi\)
0.999871 0.0160907i \(-0.00512204\pi\)
\(684\) 0 0
\(685\) −948.382 −1.38450
\(686\) 0 0
\(687\) −502.473 + 742.841i −0.731401 + 1.08128i
\(688\) 0 0
\(689\) −390.180 675.812i −0.566299 0.980859i
\(690\) 0 0
\(691\) −435.220 753.824i −0.629841 1.09092i −0.987583 0.157097i \(-0.949787\pi\)
0.357742 0.933821i \(-0.383547\pi\)
\(692\) 0 0
\(693\) 40.4580 51.5046i 0.0583809 0.0743212i
\(694\) 0 0
\(695\) −509.772 882.950i −0.733484 1.27043i
\(696\) 0 0
\(697\) 13.6784i 0.0196246i
\(698\) 0 0
\(699\) 576.118 851.716i 0.824203 1.21848i
\(700\) 0 0
\(701\) −319.482 + 553.359i −0.455752 + 0.789385i −0.998731 0.0503611i \(-0.983963\pi\)
0.542980 + 0.839746i \(0.317296\pi\)
\(702\) 0 0
\(703\) 727.872 163.005i 1.03538 0.231871i
\(704\) 0 0
\(705\) −460.866 32.8348i −0.653711 0.0465742i
\(706\) 0 0
\(707\) −104.218 −0.147409
\(708\) 0 0
\(709\) −76.8217 + 133.059i −0.108352 + 0.187671i −0.915103 0.403221i \(-0.867891\pi\)
0.806751 + 0.590892i \(0.201224\pi\)
\(710\) 0 0
\(711\) −1.34726 + 9.40701i −0.00189488 + 0.0132307i
\(712\) 0 0
\(713\) −1840.71 1062.74i −2.58164 1.49051i
\(714\) 0 0
\(715\) −727.002 419.735i −1.01679 0.587041i
\(716\) 0 0
\(717\) −523.238 + 773.540i −0.729760 + 1.07886i
\(718\) 0 0
\(719\) −233.565 + 404.547i −0.324847 + 0.562652i −0.981481 0.191557i \(-0.938646\pi\)
0.656634 + 0.754209i \(0.271980\pi\)
\(720\) 0 0
\(721\) 78.8388i 0.109346i
\(722\) 0 0
\(723\) 175.294 + 118.572i 0.242453 + 0.164000i
\(724\) 0 0
\(725\) −202.576 + 116.957i −0.279415 + 0.161320i
\(726\) 0 0
\(727\) 72.8160 0.100160 0.0500798 0.998745i \(-0.484052\pi\)
0.0500798 + 0.998745i \(0.484052\pi\)
\(728\) 0 0
\(729\) 663.619 + 301.747i 0.910314 + 0.413919i
\(730\) 0 0
\(731\) 191.928 332.430i 0.262556 0.454760i
\(732\) 0 0
\(733\) 290.253 502.733i 0.395980 0.685857i −0.597246 0.802058i \(-0.703738\pi\)
0.993226 + 0.116201i \(0.0370716\pi\)
\(734\) 0 0
\(735\) −797.704 56.8332i −1.08531 0.0773241i
\(736\) 0 0
\(737\) −256.208 + 147.922i −0.347637 + 0.200708i
\(738\) 0 0
\(739\) −264.128 + 457.483i −0.357413 + 0.619058i −0.987528 0.157444i \(-0.949674\pi\)
0.630115 + 0.776502i \(0.283008\pi\)
\(740\) 0 0
\(741\) −1185.90 + 178.245i −1.60040 + 0.240546i
\(742\) 0 0
\(743\) 1175.93 678.922i 1.58267 0.913757i 0.588207 0.808711i \(-0.299834\pi\)
0.994467 0.105046i \(-0.0334991\pi\)
\(744\) 0 0
\(745\) −229.655 + 397.773i −0.308261 + 0.533924i
\(746\) 0 0
\(747\) 509.184 + 1269.86i 0.681638 + 1.69995i
\(748\) 0 0
\(749\) 96.1635 55.5200i 0.128389 0.0741255i
\(750\) 0 0
\(751\) 406.447i 0.541208i 0.962691 + 0.270604i \(0.0872235\pi\)
−0.962691 + 0.270604i \(0.912777\pi\)
\(752\) 0 0
\(753\) 535.412 + 1101.42i 0.711039 + 1.46271i
\(754\) 0 0
\(755\) 356.149 + 205.623i 0.471721 + 0.272348i
\(756\) 0 0
\(757\) −483.094 + 836.744i −0.638169 + 1.10534i 0.347665 + 0.937619i \(0.386975\pi\)
−0.985834 + 0.167723i \(0.946359\pi\)
\(758\) 0 0
\(759\) −363.183 747.123i −0.478502 0.984352i
\(760\) 0 0
\(761\) −283.140 + 490.413i −0.372064 + 0.644433i −0.989883 0.141887i \(-0.954683\pi\)
0.617819 + 0.786320i \(0.288016\pi\)
\(762\) 0 0
\(763\) 10.7731i 0.0141194i
\(764\) 0 0
\(765\) 582.765 + 83.4629i 0.761784 + 0.109102i
\(766\) 0 0
\(767\) −48.0659 83.2526i −0.0626674 0.108543i
\(768\) 0 0
\(769\) 667.484 0.867989 0.433995 0.900916i \(-0.357104\pi\)
0.433995 + 0.900916i \(0.357104\pi\)
\(770\) 0 0
\(771\) 71.3210 1001.05i 0.0925046 1.29838i
\(772\) 0 0
\(773\) −1071.10 + 618.401i −1.38564 + 0.800002i −0.992821 0.119613i \(-0.961835\pi\)
−0.392823 + 0.919614i \(0.628501\pi\)
\(774\) 0 0
\(775\) −280.567 + 161.985i −0.362022 + 0.209013i
\(776\) 0 0
\(777\) −107.348 + 52.1829i −0.138157 + 0.0671594i
\(778\) 0 0
\(779\) 14.9503 + 16.2453i 0.0191917 + 0.0208540i
\(780\) 0 0
\(781\) 226.698i 0.290266i
\(782\) 0 0
\(783\) −795.650 722.100i −1.01616 0.922222i
\(784\) 0 0
\(785\) 745.814 1291.79i 0.950081 1.64559i
\(786\) 0 0
\(787\) 261.714 + 151.101i 0.332547 + 0.191996i 0.656971 0.753916i \(-0.271837\pi\)
−0.324424 + 0.945912i \(0.605171\pi\)
\(788\) 0 0
\(789\) 266.582 + 18.9929i 0.337873 + 0.0240721i
\(790\) 0 0
\(791\) 206.556i 0.261132i
\(792\) 0 0
\(793\) 570.131 + 329.165i 0.718954 + 0.415088i
\(794\) 0 0
\(795\) −512.161 346.436i −0.644227 0.435768i
\(796\) 0 0
\(797\) −1026.26 592.512i −1.28766