Properties

Label 1148.2.ba.a.113.20
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.20
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.97070i q^{3} +(-1.19128 - 3.66638i) q^{5} +(0.587785 + 0.809017i) q^{7} -5.82504 q^{9} +O(q^{10})\) \(q+2.97070i q^{3} +(-1.19128 - 3.66638i) q^{5} +(0.587785 + 0.809017i) q^{7} -5.82504 q^{9} +(4.98041 + 1.61823i) q^{11} +(-2.38697 + 3.28538i) q^{13} +(10.8917 - 3.53893i) q^{15} +(2.97903 + 0.967945i) q^{17} +(-3.36727 - 4.63465i) q^{19} +(-2.40334 + 1.74613i) q^{21} +(5.39996 + 3.92330i) q^{23} +(-7.97814 + 5.79646i) q^{25} -8.39233i q^{27} +(-1.02744 + 0.333834i) q^{29} +(-3.02483 + 9.30948i) q^{31} +(-4.80728 + 14.7953i) q^{33} +(2.26595 - 3.11881i) q^{35} +(2.04499 + 6.29382i) q^{37} +(-9.75986 - 7.09095i) q^{39} +(5.80494 - 2.70234i) q^{41} +(4.17317 + 3.03199i) q^{43} +(6.93925 + 21.3568i) q^{45} +(-6.87656 + 9.46477i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-2.87547 + 8.84979i) q^{51} +(-7.78264 + 2.52873i) q^{53} -20.1879i q^{55} +(13.7682 - 10.0031i) q^{57} +(-6.32287 - 4.59383i) q^{59} +(2.36896 - 1.72115i) q^{61} +(-3.42387 - 4.71255i) q^{63} +(14.8890 + 4.83773i) q^{65} +(5.27199 - 1.71297i) q^{67} +(-11.6549 + 16.0417i) q^{69} +(-1.52552 - 0.495673i) q^{71} -0.262695 q^{73} +(-17.2195 - 23.7006i) q^{75} +(1.61823 + 4.98041i) q^{77} +7.95510i q^{79} +7.45595 q^{81} +14.9661 q^{83} -12.0754i q^{85} +(-0.991720 - 3.05220i) q^{87} +(-8.00164 - 11.0133i) q^{89} -4.06095 q^{91} +(-27.6556 - 8.98586i) q^{93} +(-12.9811 + 17.8669i) q^{95} +(-3.97545 + 1.29170i) q^{97} +(-29.0111 - 9.42627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 2.97070i 1.71513i 0.514374 + 0.857566i \(0.328024\pi\)
−0.514374 + 0.857566i \(0.671976\pi\)
\(4\) 0 0
\(5\) −1.19128 3.66638i −0.532757 1.63966i −0.748447 0.663195i \(-0.769200\pi\)
0.215690 0.976462i \(-0.430800\pi\)
\(6\) 0 0
\(7\) 0.587785 + 0.809017i 0.222162 + 0.305780i
\(8\) 0 0
\(9\) −5.82504 −1.94168
\(10\) 0 0
\(11\) 4.98041 + 1.61823i 1.50165 + 0.487916i 0.940499 0.339798i \(-0.110359\pi\)
0.561151 + 0.827713i \(0.310359\pi\)
\(12\) 0 0
\(13\) −2.38697 + 3.28538i −0.662025 + 0.911199i −0.999546 0.0301185i \(-0.990412\pi\)
0.337521 + 0.941318i \(0.390412\pi\)
\(14\) 0 0
\(15\) 10.8917 3.53893i 2.81223 0.913749i
\(16\) 0 0
\(17\) 2.97903 + 0.967945i 0.722520 + 0.234761i 0.647116 0.762392i \(-0.275975\pi\)
0.0754047 + 0.997153i \(0.475975\pi\)
\(18\) 0 0
\(19\) −3.36727 4.63465i −0.772505 1.06326i −0.996070 0.0885733i \(-0.971769\pi\)
0.223564 0.974689i \(-0.428231\pi\)
\(20\) 0 0
\(21\) −2.40334 + 1.74613i −0.524453 + 0.381037i
\(22\) 0 0
\(23\) 5.39996 + 3.92330i 1.12597 + 0.818065i 0.985103 0.171963i \(-0.0550110\pi\)
0.140867 + 0.990029i \(0.455011\pi\)
\(24\) 0 0
\(25\) −7.97814 + 5.79646i −1.59563 + 1.15929i
\(26\) 0 0
\(27\) 8.39233i 1.61510i
\(28\) 0 0
\(29\) −1.02744 + 0.333834i −0.190790 + 0.0619915i −0.402854 0.915264i \(-0.631982\pi\)
0.212064 + 0.977256i \(0.431982\pi\)
\(30\) 0 0
\(31\) −3.02483 + 9.30948i −0.543276 + 1.67203i 0.181777 + 0.983340i \(0.441815\pi\)
−0.725053 + 0.688693i \(0.758185\pi\)
\(32\) 0 0
\(33\) −4.80728 + 14.7953i −0.836840 + 2.57553i
\(34\) 0 0
\(35\) 2.26595 3.11881i 0.383016 0.527176i
\(36\) 0 0
\(37\) 2.04499 + 6.29382i 0.336193 + 1.03470i 0.966131 + 0.258051i \(0.0830804\pi\)
−0.629938 + 0.776646i \(0.716920\pi\)
\(38\) 0 0
\(39\) −9.75986 7.09095i −1.56283 1.13546i
\(40\) 0 0
\(41\) 5.80494 2.70234i 0.906580 0.422034i
\(42\) 0 0
\(43\) 4.17317 + 3.03199i 0.636403 + 0.462374i 0.858613 0.512625i \(-0.171327\pi\)
−0.222210 + 0.974999i \(0.571327\pi\)
\(44\) 0 0
\(45\) 6.93925 + 21.3568i 1.03444 + 3.18369i
\(46\) 0 0
\(47\) −6.87656 + 9.46477i −1.00305 + 1.38058i −0.0796134 + 0.996826i \(0.525369\pi\)
−0.923436 + 0.383753i \(0.874631\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −2.87547 + 8.84979i −0.402646 + 1.23922i
\(52\) 0 0
\(53\) −7.78264 + 2.52873i −1.06903 + 0.347348i −0.790109 0.612967i \(-0.789976\pi\)
−0.278919 + 0.960315i \(0.589976\pi\)
\(54\) 0 0
\(55\) 20.1879i 2.72213i
\(56\) 0 0
\(57\) 13.7682 10.0031i 1.82364 1.32495i
\(58\) 0 0
\(59\) −6.32287 4.59383i −0.823167 0.598066i 0.0944509 0.995530i \(-0.469890\pi\)
−0.917618 + 0.397464i \(0.869890\pi\)
\(60\) 0 0
\(61\) 2.36896 1.72115i 0.303315 0.220371i −0.425708 0.904861i \(-0.639975\pi\)
0.729023 + 0.684490i \(0.239975\pi\)
\(62\) 0 0
\(63\) −3.42387 4.71255i −0.431367 0.593726i
\(64\) 0 0
\(65\) 14.8890 + 4.83773i 1.84675 + 0.600046i
\(66\) 0 0
\(67\) 5.27199 1.71297i 0.644077 0.209273i 0.0312761 0.999511i \(-0.490043\pi\)
0.612801 + 0.790238i \(0.290043\pi\)
\(68\) 0 0
\(69\) −11.6549 + 16.0417i −1.40309 + 1.93119i
\(70\) 0 0
\(71\) −1.52552 0.495673i −0.181046 0.0588255i 0.217091 0.976151i \(-0.430343\pi\)
−0.398137 + 0.917326i \(0.630343\pi\)
\(72\) 0 0
\(73\) −0.262695 −0.0307461 −0.0153730 0.999882i \(-0.504894\pi\)
−0.0153730 + 0.999882i \(0.504894\pi\)
\(74\) 0 0
\(75\) −17.2195 23.7006i −1.98834 2.73671i
\(76\) 0 0
\(77\) 1.61823 + 4.98041i 0.184415 + 0.567570i
\(78\) 0 0
\(79\) 7.95510i 0.895018i 0.894279 + 0.447509i \(0.147689\pi\)
−0.894279 + 0.447509i \(0.852311\pi\)
\(80\) 0 0
\(81\) 7.45595 0.828439
\(82\) 0 0
\(83\) 14.9661 1.64275 0.821373 0.570392i \(-0.193209\pi\)
0.821373 + 0.570392i \(0.193209\pi\)
\(84\) 0 0
\(85\) 12.0754i 1.30976i
\(86\) 0 0
\(87\) −0.991720 3.05220i −0.106324 0.327230i
\(88\) 0 0
\(89\) −8.00164 11.0133i −0.848172 1.16741i −0.984262 0.176713i \(-0.943454\pi\)
0.136090 0.990696i \(-0.456546\pi\)
\(90\) 0 0
\(91\) −4.06095 −0.425703
\(92\) 0 0
\(93\) −27.6556 8.98586i −2.86776 0.931791i
\(94\) 0 0
\(95\) −12.9811 + 17.8669i −1.33183 + 1.83310i
\(96\) 0 0
\(97\) −3.97545 + 1.29170i −0.403646 + 0.131153i −0.503802 0.863819i \(-0.668066\pi\)
0.100156 + 0.994972i \(0.468066\pi\)
\(98\) 0 0
\(99\) −29.0111 9.42627i −2.91572 0.947376i
\(100\) 0 0
\(101\) 4.58989 + 6.31745i 0.456711 + 0.628609i 0.973823 0.227309i \(-0.0729927\pi\)
−0.517111 + 0.855918i \(0.672993\pi\)
\(102\) 0 0
\(103\) 6.61588 4.80672i 0.651882 0.473620i −0.212030 0.977263i \(-0.568007\pi\)
0.863912 + 0.503643i \(0.168007\pi\)
\(104\) 0 0
\(105\) 9.26505 + 6.73145i 0.904176 + 0.656922i
\(106\) 0 0
\(107\) −10.1340 + 7.36280i −0.979693 + 0.711788i −0.957640 0.287968i \(-0.907020\pi\)
−0.0220528 + 0.999757i \(0.507020\pi\)
\(108\) 0 0
\(109\) 6.60432i 0.632579i −0.948663 0.316290i \(-0.897563\pi\)
0.948663 0.316290i \(-0.102437\pi\)
\(110\) 0 0
\(111\) −18.6970 + 6.07503i −1.77464 + 0.576616i
\(112\) 0 0
\(113\) −3.43262 + 10.5645i −0.322913 + 0.993825i 0.649460 + 0.760396i \(0.274995\pi\)
−0.972374 + 0.233430i \(0.925005\pi\)
\(114\) 0 0
\(115\) 7.95147 24.4721i 0.741478 2.28204i
\(116\) 0 0
\(117\) 13.9042 19.1374i 1.28544 1.76926i
\(118\) 0 0
\(119\) 0.967945 + 2.97903i 0.0887313 + 0.273087i
\(120\) 0 0
\(121\) 13.2866 + 9.65328i 1.20787 + 0.877571i
\(122\) 0 0
\(123\) 8.02782 + 17.2447i 0.723844 + 1.55490i
\(124\) 0 0
\(125\) 15.1622 + 11.0160i 1.35615 + 0.985299i
\(126\) 0 0
\(127\) −2.96625 9.12918i −0.263212 0.810083i −0.992100 0.125450i \(-0.959962\pi\)
0.728888 0.684633i \(-0.240038\pi\)
\(128\) 0 0
\(129\) −9.00712 + 12.3972i −0.793032 + 1.09152i
\(130\) 0 0
\(131\) −2.24859 + 6.92044i −0.196460 + 0.604641i 0.803497 + 0.595309i \(0.202970\pi\)
−0.999956 + 0.00933190i \(0.997030\pi\)
\(132\) 0 0
\(133\) 1.77028 5.44836i 0.153503 0.472433i
\(134\) 0 0
\(135\) −30.7695 + 9.99762i −2.64822 + 0.860458i
\(136\) 0 0
\(137\) 3.23696i 0.276552i 0.990394 + 0.138276i \(0.0441561\pi\)
−0.990394 + 0.138276i \(0.955844\pi\)
\(138\) 0 0
\(139\) 11.7339 8.52515i 0.995254 0.723094i 0.0341884 0.999415i \(-0.489115\pi\)
0.961065 + 0.276321i \(0.0891154\pi\)
\(140\) 0 0
\(141\) −28.1170 20.4282i −2.36788 1.72036i
\(142\) 0 0
\(143\) −17.2046 + 12.4999i −1.43872 + 1.04529i
\(144\) 0 0
\(145\) 2.44793 + 3.36929i 0.203289 + 0.279804i
\(146\) 0 0
\(147\) −2.82530 0.917996i −0.233027 0.0757150i
\(148\) 0 0
\(149\) 19.8381 6.44581i 1.62520 0.528061i 0.652043 0.758182i \(-0.273912\pi\)
0.973162 + 0.230121i \(0.0739123\pi\)
\(150\) 0 0
\(151\) 8.57436 11.8016i 0.697772 0.960401i −0.302203 0.953244i \(-0.597722\pi\)
0.999974 0.00715685i \(-0.00227812\pi\)
\(152\) 0 0
\(153\) −17.3529 5.63831i −1.40290 0.455831i
\(154\) 0 0
\(155\) 37.7356 3.03099
\(156\) 0 0
\(157\) −0.780720 1.07457i −0.0623083 0.0857600i 0.776726 0.629839i \(-0.216879\pi\)
−0.839034 + 0.544079i \(0.816879\pi\)
\(158\) 0 0
\(159\) −7.51210 23.1199i −0.595748 1.83352i
\(160\) 0 0
\(161\) 6.67472i 0.526042i
\(162\) 0 0
\(163\) 4.29344 0.336288 0.168144 0.985762i \(-0.446223\pi\)
0.168144 + 0.985762i \(0.446223\pi\)
\(164\) 0 0
\(165\) 59.9720 4.66882
\(166\) 0 0
\(167\) 6.99195i 0.541053i −0.962713 0.270526i \(-0.912802\pi\)
0.962713 0.270526i \(-0.0871978\pi\)
\(168\) 0 0
\(169\) −1.07887 3.32042i −0.0829901 0.255417i
\(170\) 0 0
\(171\) 19.6145 + 26.9970i 1.49996 + 2.06451i
\(172\) 0 0
\(173\) 9.14472 0.695260 0.347630 0.937632i \(-0.386987\pi\)
0.347630 + 0.937632i \(0.386987\pi\)
\(174\) 0 0
\(175\) −9.37887 3.04738i −0.708976 0.230360i
\(176\) 0 0
\(177\) 13.6469 18.7833i 1.02576 1.41184i
\(178\) 0 0
\(179\) 16.4623 5.34893i 1.23045 0.399798i 0.379573 0.925162i \(-0.376071\pi\)
0.850878 + 0.525364i \(0.176071\pi\)
\(180\) 0 0
\(181\) −19.6633 6.38900i −1.46156 0.474891i −0.533016 0.846105i \(-0.678942\pi\)
−0.928547 + 0.371214i \(0.878942\pi\)
\(182\) 0 0
\(183\) 5.11302 + 7.03747i 0.377965 + 0.520225i
\(184\) 0 0
\(185\) 20.6394 14.9954i 1.51744 1.10248i
\(186\) 0 0
\(187\) 13.2704 + 9.64152i 0.970429 + 0.705058i
\(188\) 0 0
\(189\) 6.78954 4.93289i 0.493866 0.358815i
\(190\) 0 0
\(191\) 16.7182i 1.20969i 0.796343 + 0.604845i \(0.206765\pi\)
−0.796343 + 0.604845i \(0.793235\pi\)
\(192\) 0 0
\(193\) 13.9528 4.53353i 1.00434 0.326331i 0.239743 0.970836i \(-0.422937\pi\)
0.764600 + 0.644505i \(0.222937\pi\)
\(194\) 0 0
\(195\) −14.3714 + 44.2307i −1.02916 + 3.16743i
\(196\) 0 0
\(197\) −3.11701 + 9.59316i −0.222077 + 0.683484i 0.776498 + 0.630120i \(0.216994\pi\)
−0.998575 + 0.0533639i \(0.983006\pi\)
\(198\) 0 0
\(199\) −1.51152 + 2.08043i −0.107149 + 0.147477i −0.859224 0.511600i \(-0.829053\pi\)
0.752075 + 0.659077i \(0.229053\pi\)
\(200\) 0 0
\(201\) 5.08873 + 15.6615i 0.358931 + 1.10468i
\(202\) 0 0
\(203\) −0.873989 0.634990i −0.0613420 0.0445676i
\(204\) 0 0
\(205\) −16.8231 18.0639i −1.17498 1.26164i
\(206\) 0 0
\(207\) −31.4550 22.8534i −2.18627 1.58842i
\(208\) 0 0
\(209\) −9.27045 28.5315i −0.641250 1.97357i
\(210\) 0 0
\(211\) 3.88236 5.34360i 0.267272 0.367869i −0.654194 0.756327i \(-0.726992\pi\)
0.921467 + 0.388458i \(0.126992\pi\)
\(212\) 0 0
\(213\) 1.47249 4.53187i 0.100894 0.310518i
\(214\) 0 0
\(215\) 6.14501 18.9124i 0.419086 1.28982i
\(216\) 0 0
\(217\) −9.30948 + 3.02483i −0.631969 + 0.205339i
\(218\) 0 0
\(219\) 0.780386i 0.0527336i
\(220\) 0 0
\(221\) −10.2909 + 7.47677i −0.692241 + 0.502942i
\(222\) 0 0
\(223\) 1.50009 + 1.08988i 0.100454 + 0.0729839i 0.636878 0.770964i \(-0.280225\pi\)
−0.536425 + 0.843948i \(0.680225\pi\)
\(224\) 0 0
\(225\) 46.4730 33.7646i 3.09820 2.25097i
\(226\) 0 0
\(227\) 5.44266 + 7.49118i 0.361242 + 0.497207i 0.950494 0.310742i \(-0.100578\pi\)
−0.589252 + 0.807949i \(0.700578\pi\)
\(228\) 0 0
\(229\) 4.53439 + 1.47331i 0.299641 + 0.0973592i 0.454979 0.890502i \(-0.349647\pi\)
−0.155338 + 0.987861i \(0.549647\pi\)
\(230\) 0 0
\(231\) −14.7953 + 4.80728i −0.973458 + 0.316296i
\(232\) 0 0
\(233\) −6.95886 + 9.57804i −0.455890 + 0.627479i −0.973650 0.228047i \(-0.926766\pi\)
0.517760 + 0.855526i \(0.326766\pi\)
\(234\) 0 0
\(235\) 42.8934 + 13.9369i 2.79806 + 0.909144i
\(236\) 0 0
\(237\) −23.6322 −1.53508
\(238\) 0 0
\(239\) 14.2989 + 19.6808i 0.924919 + 1.27304i 0.961809 + 0.273723i \(0.0882550\pi\)
−0.0368895 + 0.999319i \(0.511745\pi\)
\(240\) 0 0
\(241\) 1.22228 + 3.76179i 0.0787339 + 0.242318i 0.982674 0.185340i \(-0.0593387\pi\)
−0.903941 + 0.427658i \(0.859339\pi\)
\(242\) 0 0
\(243\) 3.02761i 0.194222i
\(244\) 0 0
\(245\) 3.85506 0.246291
\(246\) 0 0
\(247\) 23.2641 1.48026
\(248\) 0 0
\(249\) 44.4598i 2.81753i
\(250\) 0 0
\(251\) 1.77278 + 5.45604i 0.111897 + 0.344382i 0.991287 0.131719i \(-0.0420496\pi\)
−0.879390 + 0.476101i \(0.842050\pi\)
\(252\) 0 0
\(253\) 20.5452 + 28.2781i 1.29167 + 1.77783i
\(254\) 0 0
\(255\) 35.8722 2.24640
\(256\) 0 0
\(257\) −9.51315 3.09101i −0.593414 0.192812i −0.00311306 0.999995i \(-0.500991\pi\)
−0.590301 + 0.807183i \(0.700991\pi\)
\(258\) 0 0
\(259\) −3.88979 + 5.35384i −0.241700 + 0.332671i
\(260\) 0 0
\(261\) 5.98485 1.94460i 0.370453 0.120368i
\(262\) 0 0
\(263\) −14.1985 4.61338i −0.875518 0.284473i −0.163423 0.986556i \(-0.552253\pi\)
−0.712095 + 0.702083i \(0.752253\pi\)
\(264\) 0 0
\(265\) 18.5426 + 25.5217i 1.13906 + 1.56779i
\(266\) 0 0
\(267\) 32.7172 23.7704i 2.00226 1.45473i
\(268\) 0 0
\(269\) −4.23806 3.07913i −0.258399 0.187738i 0.451042 0.892503i \(-0.351052\pi\)
−0.709441 + 0.704765i \(0.751052\pi\)
\(270\) 0 0
\(271\) 1.71026 1.24258i 0.103891 0.0754811i −0.534627 0.845088i \(-0.679548\pi\)
0.638518 + 0.769607i \(0.279548\pi\)
\(272\) 0 0
\(273\) 12.0638i 0.730137i
\(274\) 0 0
\(275\) −49.1144 + 15.9582i −2.96171 + 0.962318i
\(276\) 0 0
\(277\) 3.63707 11.1938i 0.218530 0.672568i −0.780354 0.625338i \(-0.784961\pi\)
0.998884 0.0472291i \(-0.0150391\pi\)
\(278\) 0 0
\(279\) 17.6198 54.2281i 1.05487 3.24655i
\(280\) 0 0
\(281\) 1.80727 2.48749i 0.107813 0.148391i −0.751701 0.659504i \(-0.770766\pi\)
0.859514 + 0.511113i \(0.170766\pi\)
\(282\) 0 0
\(283\) −2.24964 6.92369i −0.133727 0.411570i 0.861663 0.507482i \(-0.169424\pi\)
−0.995390 + 0.0959112i \(0.969424\pi\)
\(284\) 0 0
\(285\) −53.0771 38.5628i −3.14402 2.28426i
\(286\) 0 0
\(287\) 5.59830 + 3.10791i 0.330457 + 0.183454i
\(288\) 0 0
\(289\) −5.81560 4.22528i −0.342094 0.248546i
\(290\) 0 0
\(291\) −3.83726 11.8099i −0.224944 0.692307i
\(292\) 0 0
\(293\) 2.72283 3.74766i 0.159070 0.218941i −0.722042 0.691850i \(-0.756796\pi\)
0.881111 + 0.472909i \(0.156796\pi\)
\(294\) 0 0
\(295\) −9.31044 + 28.6546i −0.542075 + 1.66834i
\(296\) 0 0
\(297\) 13.5807 41.7972i 0.788035 2.42532i
\(298\) 0 0
\(299\) −25.7791 + 8.37612i −1.49084 + 0.484404i
\(300\) 0 0
\(301\) 5.15833i 0.297321i
\(302\) 0 0
\(303\) −18.7672 + 13.6352i −1.07815 + 0.783321i
\(304\) 0 0
\(305\) −9.13251 6.63515i −0.522926 0.379928i
\(306\) 0 0
\(307\) −8.91405 + 6.47644i −0.508752 + 0.369630i −0.812350 0.583170i \(-0.801812\pi\)
0.303598 + 0.952800i \(0.401812\pi\)
\(308\) 0 0
\(309\) 14.2793 + 19.6538i 0.812321 + 1.11806i
\(310\) 0 0
\(311\) −32.2878 10.4909i −1.83087 0.594887i −0.999216 0.0395980i \(-0.987392\pi\)
−0.831658 0.555289i \(-0.812608\pi\)
\(312\) 0 0
\(313\) 8.62551 2.80260i 0.487543 0.158412i −0.0549222 0.998491i \(-0.517491\pi\)
0.542465 + 0.840078i \(0.317491\pi\)
\(314\) 0 0
\(315\) −13.1992 + 18.1672i −0.743693 + 1.02361i
\(316\) 0 0
\(317\) 14.8460 + 4.82376i 0.833834 + 0.270929i 0.694660 0.719339i \(-0.255555\pi\)
0.139175 + 0.990268i \(0.455555\pi\)
\(318\) 0 0
\(319\) −5.65727 −0.316747
\(320\) 0 0
\(321\) −21.8726 30.1051i −1.22081 1.68030i
\(322\) 0 0
\(323\) −5.54511 17.0661i −0.308538 0.949583i
\(324\) 0 0
\(325\) 40.0471i 2.22142i
\(326\) 0 0
\(327\) 19.6194 1.08496
\(328\) 0 0
\(329\) −11.6991 −0.644992
\(330\) 0 0
\(331\) 31.7320i 1.74415i −0.489373 0.872075i \(-0.662774\pi\)
0.489373 0.872075i \(-0.337226\pi\)
\(332\) 0 0
\(333\) −11.9121 36.6617i −0.652780 2.00905i
\(334\) 0 0
\(335\) −12.5608 17.2885i −0.686272 0.944573i
\(336\) 0 0
\(337\) 17.2822 0.941420 0.470710 0.882288i \(-0.343998\pi\)
0.470710 + 0.882288i \(0.343998\pi\)
\(338\) 0 0
\(339\) −31.3839 10.1973i −1.70454 0.553839i
\(340\) 0 0
\(341\) −30.1298 + 41.4701i −1.63162 + 2.24573i
\(342\) 0 0
\(343\) −0.951057 + 0.309017i −0.0513522 + 0.0166853i
\(344\) 0 0
\(345\) 72.6992 + 23.6214i 3.91399 + 1.27173i
\(346\) 0 0
\(347\) −10.5340 14.4988i −0.565493 0.778335i 0.426519 0.904479i \(-0.359740\pi\)
−0.992012 + 0.126144i \(0.959740\pi\)
\(348\) 0 0
\(349\) −19.6771 + 14.2962i −1.05329 + 0.765259i −0.972835 0.231499i \(-0.925637\pi\)
−0.0804541 + 0.996758i \(0.525637\pi\)
\(350\) 0 0
\(351\) 27.5720 + 20.0322i 1.47168 + 1.06924i
\(352\) 0 0
\(353\) 14.1620 10.2893i 0.753765 0.547643i −0.143226 0.989690i \(-0.545748\pi\)
0.896992 + 0.442047i \(0.145748\pi\)
\(354\) 0 0
\(355\) 6.18364i 0.328194i
\(356\) 0 0
\(357\) −8.84979 + 2.87547i −0.468380 + 0.152186i
\(358\) 0 0
\(359\) 9.06232 27.8910i 0.478291 1.47203i −0.363176 0.931720i \(-0.618308\pi\)
0.841467 0.540308i \(-0.181692\pi\)
\(360\) 0 0
\(361\) −4.27017 + 13.1422i −0.224746 + 0.691696i
\(362\) 0 0
\(363\) −28.6770 + 39.4705i −1.50515 + 2.07166i
\(364\) 0 0
\(365\) 0.312943 + 0.963140i 0.0163802 + 0.0504130i
\(366\) 0 0
\(367\) −18.2612 13.2676i −0.953229 0.692562i −0.00166078 0.999999i \(-0.500529\pi\)
−0.951568 + 0.307437i \(0.900529\pi\)
\(368\) 0 0
\(369\) −33.8140 + 15.7412i −1.76029 + 0.819454i
\(370\) 0 0
\(371\) −6.62031 4.80993i −0.343709 0.249719i
\(372\) 0 0
\(373\) −5.16355 15.8918i −0.267359 0.822845i −0.991141 0.132817i \(-0.957598\pi\)
0.723782 0.690029i \(-0.242402\pi\)
\(374\) 0 0
\(375\) −32.7251 + 45.0423i −1.68992 + 2.32597i
\(376\) 0 0
\(377\) 1.35568 4.17237i 0.0698213 0.214888i
\(378\) 0 0
\(379\) 0.0691676 0.212876i 0.00355290 0.0109347i −0.949264 0.314479i \(-0.898170\pi\)
0.952817 + 0.303545i \(0.0981701\pi\)
\(380\) 0 0
\(381\) 27.1200 8.81183i 1.38940 0.451444i
\(382\) 0 0
\(383\) 21.7968i 1.11376i −0.830592 0.556882i \(-0.811998\pi\)
0.830592 0.556882i \(-0.188002\pi\)
\(384\) 0 0
\(385\) 16.3323 11.8661i 0.832372 0.604754i
\(386\) 0 0
\(387\) −24.3089 17.6614i −1.23569 0.897782i
\(388\) 0 0
\(389\) 8.00647 5.81704i 0.405944 0.294936i −0.366014 0.930610i \(-0.619278\pi\)
0.771958 + 0.635674i \(0.219278\pi\)
\(390\) 0 0
\(391\) 12.2891 + 16.9145i 0.621486 + 0.855403i
\(392\) 0 0
\(393\) −20.5585 6.67987i −1.03704 0.336955i
\(394\) 0 0
\(395\) 29.1664 9.47675i 1.46752 0.476827i
\(396\) 0 0
\(397\) 5.19042 7.14399i 0.260499 0.358547i −0.658654 0.752446i \(-0.728874\pi\)
0.919154 + 0.393899i \(0.128874\pi\)
\(398\) 0 0
\(399\) 16.1854 + 5.25897i 0.810285 + 0.263278i
\(400\) 0 0
\(401\) 22.1463 1.10593 0.552966 0.833204i \(-0.313496\pi\)
0.552966 + 0.833204i \(0.313496\pi\)
\(402\) 0 0
\(403\) −23.3650 32.1591i −1.16389 1.60196i
\(404\) 0 0
\(405\) −8.88213 27.3364i −0.441357 1.35836i
\(406\) 0 0
\(407\) 34.6550i 1.71779i
\(408\) 0 0
\(409\) −15.5384 −0.768324 −0.384162 0.923266i \(-0.625510\pi\)
−0.384162 + 0.923266i \(0.625510\pi\)
\(410\) 0 0
\(411\) −9.61602 −0.474323
\(412\) 0 0
\(413\) 7.81549i 0.384575i
\(414\) 0 0
\(415\) −17.8288 54.8716i −0.875184 2.69354i
\(416\) 0 0
\(417\) 25.3256 + 34.8578i 1.24020 + 1.70699i
\(418\) 0 0
\(419\) 0.834711 0.0407783 0.0203892 0.999792i \(-0.493509\pi\)
0.0203892 + 0.999792i \(0.493509\pi\)
\(420\) 0 0
\(421\) −5.83545 1.89605i −0.284402 0.0924080i 0.163342 0.986570i \(-0.447773\pi\)
−0.447745 + 0.894162i \(0.647773\pi\)
\(422\) 0 0
\(423\) 40.0562 55.1327i 1.94760 2.68064i
\(424\) 0 0
\(425\) −29.3777 + 9.54541i −1.42503 + 0.463020i
\(426\) 0 0
\(427\) 2.78488 + 0.904863i 0.134770 + 0.0437894i
\(428\) 0 0
\(429\) −37.1333 51.1096i −1.79281 2.46759i
\(430\) 0 0
\(431\) −23.1608 + 16.8273i −1.11562 + 0.810542i −0.983539 0.180697i \(-0.942165\pi\)
−0.132077 + 0.991239i \(0.542165\pi\)
\(432\) 0 0
\(433\) 24.9993 + 18.1630i 1.20139 + 0.872859i 0.994420 0.105489i \(-0.0336407\pi\)
0.206967 + 0.978348i \(0.433641\pi\)
\(434\) 0 0
\(435\) −10.0091 + 7.27206i −0.479901 + 0.348668i
\(436\) 0 0
\(437\) 38.2378i 1.82916i
\(438\) 0 0
\(439\) −17.4652 + 5.67480i −0.833570 + 0.270843i −0.694548 0.719446i \(-0.744396\pi\)
−0.139022 + 0.990289i \(0.544396\pi\)
\(440\) 0 0
\(441\) 1.80004 5.53994i 0.0857160 0.263807i
\(442\) 0 0
\(443\) 2.24539 6.91059i 0.106681 0.328332i −0.883440 0.468544i \(-0.844779\pi\)
0.990121 + 0.140213i \(0.0447786\pi\)
\(444\) 0 0
\(445\) −30.8468 + 42.4570i −1.46228 + 2.01266i
\(446\) 0 0
\(447\) 19.1485 + 58.9331i 0.905695 + 2.78744i
\(448\) 0 0
\(449\) −9.33107 6.77942i −0.440361 0.319941i 0.345418 0.938449i \(-0.387737\pi\)
−0.785778 + 0.618508i \(0.787737\pi\)
\(450\) 0 0
\(451\) 33.2840 4.06498i 1.56728 0.191412i
\(452\) 0 0
\(453\) 35.0590 + 25.4718i 1.64721 + 1.19677i
\(454\) 0 0
\(455\) 4.83773 + 14.8890i 0.226796 + 0.698007i
\(456\) 0 0
\(457\) 15.1886 20.9053i 0.710493 0.977910i −0.289293 0.957241i \(-0.593420\pi\)
0.999786 0.0206697i \(-0.00657985\pi\)
\(458\) 0 0
\(459\) 8.12331 25.0010i 0.379164 1.16695i
\(460\) 0 0
\(461\) 11.6166 35.7521i 0.541037 1.66514i −0.189192 0.981940i \(-0.560587\pi\)
0.730230 0.683202i \(-0.239413\pi\)
\(462\) 0 0
\(463\) −34.6062 + 11.2442i −1.60829 + 0.522564i −0.969138 0.246519i \(-0.920713\pi\)
−0.639149 + 0.769083i \(0.720713\pi\)
\(464\) 0 0
\(465\) 112.101i 5.19856i
\(466\) 0 0
\(467\) 17.5964 12.7846i 0.814266 0.591599i −0.100798 0.994907i \(-0.532140\pi\)
0.915064 + 0.403308i \(0.132140\pi\)
\(468\) 0 0
\(469\) 4.48463 + 3.25827i 0.207081 + 0.150453i
\(470\) 0 0
\(471\) 3.19222 2.31928i 0.147090 0.106867i
\(472\) 0 0
\(473\) 15.8776 + 21.8537i 0.730055 + 1.00483i
\(474\) 0 0
\(475\) 53.7292 + 17.4577i 2.46526 + 0.801013i
\(476\) 0 0
\(477\) 45.3342 14.7300i 2.07571 0.674439i
\(478\) 0 0
\(479\) −18.1217 + 24.9423i −0.828001 + 1.13965i 0.160291 + 0.987070i \(0.448757\pi\)
−0.988292 + 0.152575i \(0.951243\pi\)
\(480\) 0 0
\(481\) −25.5589 8.30458i −1.16538 0.378656i
\(482\) 0 0
\(483\) −19.8286 −0.902231
\(484\) 0 0
\(485\) 9.47176 + 13.0368i 0.430091 + 0.591969i
\(486\) 0 0
\(487\) −5.44184 16.7483i −0.246593 0.758936i −0.995370 0.0961140i \(-0.969359\pi\)
0.748777 0.662822i \(-0.230641\pi\)
\(488\) 0 0
\(489\) 12.7545i 0.576779i
\(490\) 0 0
\(491\) 18.7779 0.847435 0.423717 0.905795i \(-0.360725\pi\)
0.423717 + 0.905795i \(0.360725\pi\)
\(492\) 0 0
\(493\) −3.38389 −0.152403
\(494\) 0 0
\(495\) 117.595i 5.28551i
\(496\) 0 0
\(497\) −0.495673 1.52552i −0.0222340 0.0684291i
\(498\) 0 0
\(499\) 5.70625 + 7.85398i 0.255447 + 0.351593i 0.917410 0.397944i \(-0.130276\pi\)
−0.661963 + 0.749537i \(0.730276\pi\)
\(500\) 0 0
\(501\) 20.7709 0.927977
\(502\) 0 0
\(503\) 27.6016 + 8.96830i 1.23069 + 0.399877i 0.850966 0.525221i \(-0.176017\pi\)
0.379729 + 0.925098i \(0.376017\pi\)
\(504\) 0 0
\(505\) 17.6943 24.3542i 0.787388 1.08375i
\(506\) 0 0
\(507\) 9.86397 3.20500i 0.438074 0.142339i
\(508\) 0 0
\(509\) 9.05328 + 2.94159i 0.401280 + 0.130384i 0.502702 0.864460i \(-0.332339\pi\)
−0.101422 + 0.994843i \(0.532339\pi\)
\(510\) 0 0
\(511\) −0.154408 0.212524i −0.00683061 0.00940153i
\(512\) 0 0
\(513\) −38.8956 + 28.2593i −1.71728 + 1.24768i
\(514\) 0 0
\(515\) −25.5046 18.5302i −1.12387 0.816538i
\(516\) 0 0
\(517\) −49.5643 + 36.0106i −2.17983 + 1.58374i
\(518\) 0 0
\(519\) 27.1662i 1.19246i
\(520\) 0 0
\(521\) −36.8958 + 11.9882i −1.61644 + 0.525212i −0.971097 0.238685i \(-0.923284\pi\)
−0.645339 + 0.763897i \(0.723284\pi\)
\(522\) 0 0
\(523\) 9.19704 28.3056i 0.402158 1.23772i −0.521086 0.853504i \(-0.674473\pi\)
0.923245 0.384213i \(-0.125527\pi\)
\(524\) 0 0
\(525\) 9.05284 27.8618i 0.395098 1.21599i
\(526\) 0 0
\(527\) −18.0221 + 24.8053i −0.785056 + 1.08054i
\(528\) 0 0
\(529\) 6.65991 + 20.4971i 0.289561 + 0.891178i
\(530\) 0 0
\(531\) 36.8309 + 26.7592i 1.59833 + 1.16125i
\(532\) 0 0
\(533\) −4.97802 + 25.5218i −0.215622 + 1.10547i
\(534\) 0 0
\(535\) 39.0673 + 28.3841i 1.68903 + 1.22715i
\(536\) 0 0
\(537\) 15.8900 + 48.9045i 0.685706 + 2.11039i
\(538\) 0 0
\(539\) −3.07806 + 4.23659i −0.132582 + 0.182483i
\(540\) 0 0
\(541\) −8.07530 + 24.8532i −0.347184 + 1.06852i 0.613220 + 0.789912i \(0.289874\pi\)
−0.960404 + 0.278611i \(0.910126\pi\)
\(542\) 0 0
\(543\) 18.9798 58.4138i 0.814501 2.50678i
\(544\) 0 0
\(545\) −24.2140 + 7.86760i −1.03721 + 0.337011i
\(546\) 0 0
\(547\) 36.3465i 1.55406i −0.629461 0.777032i \(-0.716724\pi\)
0.629461 0.777032i \(-0.283276\pi\)
\(548\) 0 0
\(549\) −13.7993 + 10.0258i −0.588940 + 0.427890i
\(550\) 0 0
\(551\) 5.00686 + 3.63770i 0.213300 + 0.154971i
\(552\) 0 0
\(553\) −6.43581 + 4.67589i −0.273678 + 0.198839i
\(554\) 0 0
\(555\) 44.5468 + 61.3134i 1.89091 + 2.60261i
\(556\) 0 0
\(557\) 12.9322 + 4.20192i 0.547955 + 0.178041i 0.569894 0.821718i \(-0.306984\pi\)
−0.0219396 + 0.999759i \(0.506984\pi\)
\(558\) 0 0
\(559\) −19.9224 + 6.47319i −0.842630 + 0.273787i
\(560\) 0 0
\(561\) −28.6420 + 39.4224i −1.20927 + 1.66441i
\(562\) 0 0
\(563\) −20.1820 6.55751i −0.850568 0.276366i −0.148884 0.988855i \(-0.547568\pi\)
−0.701684 + 0.712488i \(0.747568\pi\)
\(564\) 0 0
\(565\) 42.8228 1.80157
\(566\) 0 0
\(567\) 4.38250 + 6.03199i 0.184048 + 0.253320i
\(568\) 0 0
\(569\) 6.08577 + 18.7301i 0.255129 + 0.785206i 0.993804 + 0.111145i \(0.0354517\pi\)
−0.738675 + 0.674061i \(0.764548\pi\)
\(570\) 0 0
\(571\) 2.76007i 0.115505i −0.998331 0.0577526i \(-0.981607\pi\)
0.998331 0.0577526i \(-0.0183935\pi\)
\(572\) 0 0
\(573\) −49.6648 −2.07478
\(574\) 0 0
\(575\) −65.8229 −2.74501
\(576\) 0 0
\(577\) 3.43113i 0.142840i 0.997446 + 0.0714199i \(0.0227530\pi\)
−0.997446 + 0.0714199i \(0.977247\pi\)
\(578\) 0 0
\(579\) 13.4678 + 41.4495i 0.559701 + 1.72258i
\(580\) 0 0
\(581\) 8.79687 + 12.1078i 0.364955 + 0.502318i
\(582\) 0 0
\(583\) −42.8528 −1.77478
\(584\) 0 0
\(585\) −86.7290 28.1800i −3.58580 1.16510i
\(586\) 0 0
\(587\) 24.1938 33.2999i 0.998584 1.37443i 0.0723938 0.997376i \(-0.476936\pi\)
0.926190 0.377057i \(-0.123064\pi\)
\(588\) 0 0
\(589\) 53.3317 17.3285i 2.19749 0.714009i
\(590\) 0 0
\(591\) −28.4984 9.25968i −1.17227 0.380892i
\(592\) 0 0
\(593\) 7.50753 + 10.3332i 0.308297 + 0.424335i 0.934849 0.355045i \(-0.115534\pi\)
−0.626552 + 0.779380i \(0.715534\pi\)
\(594\) 0 0
\(595\) 9.76917 7.09771i 0.400497 0.290978i
\(596\) 0 0
\(597\) −6.18031 4.49026i −0.252943 0.183774i
\(598\) 0 0
\(599\) 17.0935 12.4192i 0.698423 0.507434i −0.180995 0.983484i \(-0.557932\pi\)
0.879418 + 0.476050i \(0.157932\pi\)
\(600\) 0 0
\(601\) 12.7699i 0.520894i −0.965488 0.260447i \(-0.916130\pi\)
0.965488 0.260447i \(-0.0838700\pi\)
\(602\) 0 0
\(603\) −30.7096 + 9.97814i −1.25059 + 0.406341i
\(604\) 0 0
\(605\) 19.5646 60.2136i 0.795413 2.44803i
\(606\) 0 0
\(607\) −6.51703 + 20.0574i −0.264518 + 0.814103i 0.727286 + 0.686334i \(0.240781\pi\)
−0.991804 + 0.127768i \(0.959219\pi\)
\(608\) 0 0
\(609\) 1.88636 2.59636i 0.0764393 0.105210i
\(610\) 0 0
\(611\) −14.6812 45.1842i −0.593939 1.82796i
\(612\) 0 0
\(613\) −8.14323 5.91640i −0.328902 0.238961i 0.411063 0.911607i \(-0.365158\pi\)
−0.739965 + 0.672646i \(0.765158\pi\)
\(614\) 0 0
\(615\) 53.6624 49.9764i 2.16388 2.01524i
\(616\) 0 0
\(617\) 10.0985 + 7.33697i 0.406549 + 0.295375i 0.772203 0.635375i \(-0.219155\pi\)
−0.365654 + 0.930751i \(0.619155\pi\)
\(618\) 0 0
\(619\) 2.01315 + 6.19583i 0.0809152 + 0.249031i 0.983328 0.181841i \(-0.0582058\pi\)
−0.902413 + 0.430873i \(0.858206\pi\)
\(620\) 0 0
\(621\) 32.9257 45.3183i 1.32126 1.81856i
\(622\) 0 0
\(623\) 4.20671 12.9469i 0.168538 0.518708i
\(624\) 0 0
\(625\) 7.08948 21.8192i 0.283579 0.872767i
\(626\) 0 0
\(627\) 84.7584 27.5397i 3.38493 1.09983i
\(628\) 0 0
\(629\) 20.7289i 0.826515i
\(630\) 0 0
\(631\) 6.63173 4.81823i 0.264005 0.191811i −0.447906 0.894081i \(-0.647830\pi\)
0.711911 + 0.702270i \(0.247830\pi\)
\(632\) 0 0
\(633\) 15.8742 + 11.5333i 0.630944 + 0.458408i
\(634\) 0 0
\(635\) −29.9374 + 21.7508i −1.18803 + 0.863155i
\(636\) 0 0
\(637\) −2.38697 3.28538i −0.0945750 0.130171i
\(638\) 0 0
\(639\) 8.88623 + 2.88731i 0.351534 + 0.114220i
\(640\) 0 0
\(641\) −11.2746 + 3.66334i −0.445321 + 0.144693i −0.523089 0.852278i \(-0.675220\pi\)
0.0777685 + 0.996971i \(0.475220\pi\)
\(642\) 0 0
\(643\) −11.2237 + 15.4480i −0.442618 + 0.609211i −0.970791 0.239925i \(-0.922877\pi\)
0.528173 + 0.849137i \(0.322877\pi\)
\(644\) 0 0
\(645\) 56.1830 + 18.2550i 2.21220 + 0.718789i
\(646\) 0 0
\(647\) 17.3516 0.682161 0.341081 0.940034i \(-0.389207\pi\)
0.341081 + 0.940034i \(0.389207\pi\)
\(648\) 0 0
\(649\) −24.0566 33.1110i −0.944303 1.29972i
\(650\) 0 0
\(651\) −8.98586 27.6556i −0.352184 1.08391i
\(652\) 0 0
\(653\) 1.75123i 0.0685311i −0.999413 0.0342656i \(-0.989091\pi\)
0.999413 0.0342656i \(-0.0109092\pi\)
\(654\) 0 0
\(655\) 28.0517 1.09607
\(656\) 0 0
\(657\) 1.53021 0.0596990
\(658\) 0 0
\(659\) 17.0302i 0.663404i −0.943384 0.331702i \(-0.892377\pi\)
0.943384 0.331702i \(-0.107623\pi\)
\(660\) 0 0
\(661\) −6.80064 20.9302i −0.264514 0.814091i −0.991805 0.127762i \(-0.959221\pi\)
0.727291 0.686330i \(-0.240779\pi\)
\(662\) 0 0
\(663\) −22.2112 30.5711i −0.862613 1.18728i
\(664\) 0 0
\(665\) −22.0847 −0.856408
\(666\) 0 0
\(667\) −6.85785 2.22825i −0.265537 0.0862782i
\(668\) 0 0
\(669\) −3.23771 + 4.45632i −0.125177 + 0.172291i
\(670\) 0 0
\(671\) 14.5836 4.73851i 0.562995 0.182928i
\(672\) 0 0
\(673\) −11.1012 3.60699i −0.427919 0.139039i 0.0871361 0.996196i \(-0.472228\pi\)
−0.515055 + 0.857157i \(0.672228\pi\)
\(674\) 0 0
\(675\) 48.6458 + 66.9552i 1.87238 + 2.57711i
\(676\) 0 0
\(677\) 0.239096 0.173713i 0.00918920 0.00667635i −0.583181 0.812342i \(-0.698192\pi\)
0.592370 + 0.805666i \(0.298192\pi\)
\(678\) 0 0
\(679\) −3.38172 2.45697i −0.129779 0.0942897i
\(680\) 0 0
\(681\) −22.2540 + 16.1685i −0.852776 + 0.619578i
\(682\) 0 0
\(683\) 19.9422i 0.763069i −0.924355 0.381534i \(-0.875396\pi\)
0.924355 0.381534i \(-0.124604\pi\)
\(684\) 0 0
\(685\) 11.8679 3.85613i 0.453451 0.147335i
\(686\) 0 0
\(687\) −4.37676 + 13.4703i −0.166984 + 0.513924i
\(688\) 0 0
\(689\) 10.2691 31.6049i 0.391220 1.20405i
\(690\) 0 0
\(691\) 6.94995 9.56579i 0.264389 0.363900i −0.656097 0.754677i \(-0.727794\pi\)
0.920485 + 0.390777i \(0.127794\pi\)
\(692\) 0 0
\(693\) −9.42627 29.0111i −0.358074 1.10204i
\(694\) 0 0
\(695\) −45.2348 32.8650i −1.71585 1.24664i
\(696\) 0 0
\(697\) 19.9088 2.43147i 0.754100 0.0920983i
\(698\) 0 0
\(699\) −28.4535 20.6727i −1.07621 0.781911i
\(700\) 0 0
\(701\) −9.12472 28.0830i −0.344636 1.06068i −0.961779 0.273829i \(-0.911710\pi\)
0.617143 0.786851i \(-0.288290\pi\)
\(702\) 0 0
\(703\) 22.2836 30.6708i 0.840443 1.15677i
\(704\) 0 0
\(705\) −41.4023 + 127.423i −1.55930 + 4.79904i
\(706\) 0 0
\(707\) −2.41305 + 7.42660i −0.0907521 + 0.279306i
\(708\) 0 0
\(709\) −20.9216 + 6.79783i −0.785726 + 0.255298i −0.674283 0.738473i \(-0.735547\pi\)
−0.111443 + 0.993771i \(0.535547\pi\)
\(710\) 0 0
\(711\) 46.3388i 1.73784i
\(712\) 0 0
\(713\) −52.8579 + 38.4035i −1.97954 + 1.43822i
\(714\) 0 0
\(715\) 66.3247 + 48.1877i 2.48040 + 1.80212i
\(716\) 0 0
\(717\) −58.4655 + 42.4777i −2.18344 + 1.58636i
\(718\) 0 0
\(719\) 23.3074 + 32.0800i 0.869221 + 1.19638i 0.979291 + 0.202456i \(0.0648925\pi\)
−0.110070 + 0.993924i \(0.535108\pi\)
\(720\) 0 0
\(721\) 7.77743 + 2.52704i 0.289647 + 0.0941119i
\(722\) 0 0
\(723\) −11.1751 + 3.63102i −0.415607 + 0.135039i
\(724\) 0 0
\(725\) 6.26197 8.61887i 0.232564 0.320097i
\(726\) 0 0
\(727\) −30.0540 9.76513i −1.11464 0.362169i −0.306921 0.951735i \(-0.599299\pi\)
−0.807720 + 0.589566i \(0.799299\pi\)
\(728\) 0 0
\(729\) 31.3620 1.16156
\(730\) 0 0
\(731\) 9.49720 + 13.0718i 0.351267 + 0.483477i
\(732\) 0 0
\(733\) 2.62554 + 8.08058i 0.0969765 + 0.298463i 0.987764 0.155958i \(-0.0498463\pi\)
−0.890787 + 0.454421i \(0.849846\pi\)
\(734\) 0 0
\(735\) 11.4522i 0.422422i
\(736\) 0 0
\(737\) 29.0287 1.06929
\(738\) 0 0
\(739\) 12.7252 0.468105 0.234052 0.972224i \(-0.424801\pi\)
0.234052 + 0.972224i \(0.424801\pi\)
\(740\) 0 0
\(741\) 69.1107i 2.53885i
\(742\) 0 0
\(743\) 9.98294 + 30.7243i 0.366239 + 1.12717i 0.949202 + 0.314668i \(0.101893\pi\)
−0.582963 + 0.812498i \(0.698107\pi\)
\(744\) 0 0
\(745\) −47.2656 65.0555i −1.73168 2.38345i
\(746\) 0 0
\(747\) −87.1782 −3.18968
\(748\) 0 0
\(749\) −11.9133 3.87085i −0.435301 0.141438i
\(750\) 0 0
\(751\) 9.71540 13.3721i 0.354520 0.487955i −0.594092 0.804397i \(-0.702488\pi\)
0.948612 + 0.316442i \(0.102488\pi\)
\(752\) 0 0
\(753\) −16.2083 + 5.26638i −0.590662 + 0.191918i
\(754\) 0 0
\(755\) −53.4837 17.3779i −1.94647 0.632447i
\(756\) 0 0
\(757\) −23.4310 32.2500i −0.851614 1.17215i −0.983505 0.180882i \(-0.942105\pi\)
0.131891 0.991264i \(-0.457895\pi\)
\(758\) 0 0
\(759\) −84.0055 + 61.0336i −3.04921 + 2.21538i
\(760\) 0 0
\(761\) 22.7363 + 16.5189i 0.824190 + 0.598809i 0.917910 0.396790i \(-0.129876\pi\)
−0.0937198 + 0.995599i \(0.529876\pi\)
\(762\) 0 0
\(763\) 5.34301 3.88192i 0.193430 0.140535i
\(764\) 0 0
\(765\) 70.3394i 2.54313i
\(766\) 0 0
\(767\) 30.1849 9.80768i 1.08991 0.354135i
\(768\) 0 0
\(769\) −9.07695 + 27.9360i −0.327323 + 1.00740i 0.643058 + 0.765818i \(0.277665\pi\)
−0.970381 + 0.241580i \(0.922335\pi\)
\(770\) 0 0
\(771\) 9.18245 28.2607i 0.330698 1.01778i
\(772\) 0 0
\(773\) 14.4361 19.8695i 0.519229 0.714658i −0.466212 0.884673i \(-0.654382\pi\)
0.985441 + 0.170015i \(0.0543817\pi\)
\(774\) 0 0
\(775\) −29.8295 91.8057i −1.07151 3.29776i
\(776\) 0 0
\(777\) −15.9046 11.5554i −0.570576 0.414547i
\(778\) 0 0
\(779\) −32.0712 17.8044i −1.14907 0.637909i
\(780\) 0 0
\(781\) −6.79562 4.93730i −0.243166 0.176671i
\(782\) 0 0
\(783\) 2.80165 + 8.62258i 0.100123 + 0.308146i
\(784\) 0 0
\(785\) −3.00973 + 4.14253i −0.107422 + 0.147853i
\(786\) 0 0
\(787\) −6.70583 + 20.6384i −0.239037 + 0.735680i 0.757523 + 0.652808i \(0.226409\pi\)
−0.996560 + 0.0828721i \(0.973591\pi\)
\(788\) 0 0
\(789\) 13.7049 42.1795i 0.487909 1.50163i
\(790\) 0 0
\(791\) −10.5645 + 3.43262i −0.375631 + 0.122050i
\(792\) 0 0
\(793\) 11.8913i 0.422271i
\(794\) 0 0
\(795\) −75.8173 + 55.0845i −2.68896 + 1.95364i
\(796\) 0 0
\(797\) 9.18455 + 6.67297i 0.325333 + 0.236369i 0.738448 0.674311i</