Properties

Label 1148.2.k.b.337.4
Level $1148$
Weight $2$
Character 1148.337
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
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.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 337.4
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.64273 - 1.64273i) q^{3} -1.39147i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.39713i q^{9} +O(q^{10})\) \(q+(-1.64273 - 1.64273i) q^{3} -1.39147i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.39713i q^{9} +(3.79701 + 3.79701i) q^{11} +(3.40984 + 3.40984i) q^{13} +(-2.28582 + 2.28582i) q^{15} +(-2.83732 + 2.83732i) q^{17} +(-5.63692 + 5.63692i) q^{19} +2.32317i q^{21} +2.68666 q^{23} +3.06380 q^{25} +(-0.990346 + 0.990346i) q^{27} +(-2.77861 - 2.77861i) q^{29} +2.87366 q^{31} -12.4749i q^{33} +(-0.983920 + 0.983920i) q^{35} +6.03663 q^{37} -11.2029i q^{39} +(5.64675 - 3.01897i) q^{41} +1.35884i q^{43} +3.33555 q^{45} +(-9.35772 + 9.35772i) q^{47} +1.00000i q^{49} +9.32190 q^{51} +(5.67130 + 5.67130i) q^{53} +(5.28344 - 5.28344i) q^{55} +18.5199 q^{57} +6.26308 q^{59} -8.87031i q^{61} +(1.69503 - 1.69503i) q^{63} +(4.74470 - 4.74470i) q^{65} +(3.51370 - 3.51370i) q^{67} +(-4.41346 - 4.41346i) q^{69} +(-1.21557 - 1.21557i) q^{71} +12.7207i q^{73} +(-5.03301 - 5.03301i) q^{75} -5.36978i q^{77} +(-6.61093 - 6.61093i) q^{79} +10.4451 q^{81} -3.94145 q^{83} +(3.94805 + 3.94805i) q^{85} +9.12901i q^{87} +(-0.812315 - 0.812315i) q^{89} -4.82225i q^{91} +(-4.72065 - 4.72065i) q^{93} +(7.84363 + 7.84363i) q^{95} +(-13.3552 + 13.3552i) q^{97} +(-9.10195 + 9.10195i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −1.64273 1.64273i −0.948432 0.948432i 0.0503025 0.998734i \(-0.483981\pi\)
−0.998734 + 0.0503025i \(0.983981\pi\)
\(4\) 0 0
\(5\) 1.39147i 0.622286i −0.950363 0.311143i \(-0.899288\pi\)
0.950363 0.311143i \(-0.100712\pi\)
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 0 0
\(9\) 2.39713i 0.799045i
\(10\) 0 0
\(11\) 3.79701 + 3.79701i 1.14484 + 1.14484i 0.987553 + 0.157289i \(0.0502756\pi\)
0.157289 + 0.987553i \(0.449724\pi\)
\(12\) 0 0
\(13\) 3.40984 + 3.40984i 0.945720 + 0.945720i 0.998601 0.0528807i \(-0.0168403\pi\)
−0.0528807 + 0.998601i \(0.516840\pi\)
\(14\) 0 0
\(15\) −2.28582 + 2.28582i −0.590195 + 0.590195i
\(16\) 0 0
\(17\) −2.83732 + 2.83732i −0.688150 + 0.688150i −0.961823 0.273673i \(-0.911762\pi\)
0.273673 + 0.961823i \(0.411762\pi\)
\(18\) 0 0
\(19\) −5.63692 + 5.63692i −1.29320 + 1.29320i −0.360401 + 0.932797i \(0.617360\pi\)
−0.932797 + 0.360401i \(0.882640\pi\)
\(20\) 0 0
\(21\) 2.32317i 0.506958i
\(22\) 0 0
\(23\) 2.68666 0.560208 0.280104 0.959970i \(-0.409631\pi\)
0.280104 + 0.959970i \(0.409631\pi\)
\(24\) 0 0
\(25\) 3.06380 0.612761
\(26\) 0 0
\(27\) −0.990346 + 0.990346i −0.190592 + 0.190592i
\(28\) 0 0
\(29\) −2.77861 2.77861i −0.515974 0.515974i 0.400377 0.916351i \(-0.368879\pi\)
−0.916351 + 0.400377i \(0.868879\pi\)
\(30\) 0 0
\(31\) 2.87366 0.516124 0.258062 0.966128i \(-0.416916\pi\)
0.258062 + 0.966128i \(0.416916\pi\)
\(32\) 0 0
\(33\) 12.4749i 2.17161i
\(34\) 0 0
\(35\) −0.983920 + 0.983920i −0.166313 + 0.166313i
\(36\) 0 0
\(37\) 6.03663 0.992416 0.496208 0.868204i \(-0.334725\pi\)
0.496208 + 0.868204i \(0.334725\pi\)
\(38\) 0 0
\(39\) 11.2029i 1.79390i
\(40\) 0 0
\(41\) 5.64675 3.01897i 0.881875 0.471484i
\(42\) 0 0
\(43\) 1.35884i 0.207221i 0.994618 + 0.103610i \(0.0330395\pi\)
−0.994618 + 0.103610i \(0.966961\pi\)
\(44\) 0 0
\(45\) 3.33555 0.497234
\(46\) 0 0
\(47\) −9.35772 + 9.35772i −1.36496 + 1.36496i −0.497498 + 0.867465i \(0.665748\pi\)
−0.867465 + 0.497498i \(0.834252\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 9.32190 1.30533
\(52\) 0 0
\(53\) 5.67130 + 5.67130i 0.779012 + 0.779012i 0.979663 0.200651i \(-0.0643056\pi\)
−0.200651 + 0.979663i \(0.564306\pi\)
\(54\) 0 0
\(55\) 5.28344 5.28344i 0.712419 0.712419i
\(56\) 0 0
\(57\) 18.5199 2.45302
\(58\) 0 0
\(59\) 6.26308 0.815384 0.407692 0.913119i \(-0.366334\pi\)
0.407692 + 0.913119i \(0.366334\pi\)
\(60\) 0 0
\(61\) 8.87031i 1.13573i −0.823123 0.567863i \(-0.807770\pi\)
0.823123 0.567863i \(-0.192230\pi\)
\(62\) 0 0
\(63\) 1.69503 1.69503i 0.213554 0.213554i
\(64\) 0 0
\(65\) 4.74470 4.74470i 0.588508 0.588508i
\(66\) 0 0
\(67\) 3.51370 3.51370i 0.429267 0.429267i −0.459112 0.888379i \(-0.651832\pi\)
0.888379 + 0.459112i \(0.151832\pi\)
\(68\) 0 0
\(69\) −4.41346 4.41346i −0.531318 0.531318i
\(70\) 0 0
\(71\) −1.21557 1.21557i −0.144262 0.144262i 0.631287 0.775549i \(-0.282527\pi\)
−0.775549 + 0.631287i \(0.782527\pi\)
\(72\) 0 0
\(73\) 12.7207i 1.48884i 0.667710 + 0.744421i \(0.267275\pi\)
−0.667710 + 0.744421i \(0.732725\pi\)
\(74\) 0 0
\(75\) −5.03301 5.03301i −0.581161 0.581161i
\(76\) 0 0
\(77\) 5.36978i 0.611944i
\(78\) 0 0
\(79\) −6.61093 6.61093i −0.743788 0.743788i 0.229517 0.973305i \(-0.426285\pi\)
−0.973305 + 0.229517i \(0.926285\pi\)
\(80\) 0 0
\(81\) 10.4451 1.16057
\(82\) 0 0
\(83\) −3.94145 −0.432631 −0.216315 0.976324i \(-0.569404\pi\)
−0.216315 + 0.976324i \(0.569404\pi\)
\(84\) 0 0
\(85\) 3.94805 + 3.94805i 0.428226 + 0.428226i
\(86\) 0 0
\(87\) 9.12901i 0.978732i
\(88\) 0 0
\(89\) −0.812315 0.812315i −0.0861052 0.0861052i 0.662742 0.748848i \(-0.269392\pi\)
−0.748848 + 0.662742i \(0.769392\pi\)
\(90\) 0 0
\(91\) 4.82225i 0.505509i
\(92\) 0 0
\(93\) −4.72065 4.72065i −0.489508 0.489508i
\(94\) 0 0
\(95\) 7.84363 + 7.84363i 0.804739 + 0.804739i
\(96\) 0 0
\(97\) −13.3552 + 13.3552i −1.35601 + 1.35601i −0.477240 + 0.878773i \(0.658363\pi\)
−0.878773 + 0.477240i \(0.841637\pi\)
\(98\) 0 0
\(99\) −9.10195 + 9.10195i −0.914780 + 0.914780i
\(100\) 0 0
\(101\) 7.66669 7.66669i 0.762864 0.762864i −0.213975 0.976839i \(-0.568641\pi\)
0.976839 + 0.213975i \(0.0686410\pi\)
\(102\) 0 0
\(103\) 7.71218i 0.759904i 0.925006 + 0.379952i \(0.124059\pi\)
−0.925006 + 0.379952i \(0.875941\pi\)
\(104\) 0 0
\(105\) 3.23263 0.315473
\(106\) 0 0
\(107\) 2.84612 0.275145 0.137572 0.990492i \(-0.456070\pi\)
0.137572 + 0.990492i \(0.456070\pi\)
\(108\) 0 0
\(109\) 11.1648 11.1648i 1.06940 1.06940i 0.0719931 0.997405i \(-0.477064\pi\)
0.997405 0.0719931i \(-0.0229359\pi\)
\(110\) 0 0
\(111\) −9.91657 9.91657i −0.941239 0.941239i
\(112\) 0 0
\(113\) 0.0526448 0.00495241 0.00247620 0.999997i \(-0.499212\pi\)
0.00247620 + 0.999997i \(0.499212\pi\)
\(114\) 0 0
\(115\) 3.73842i 0.348609i
\(116\) 0 0
\(117\) −8.17385 + 8.17385i −0.755673 + 0.755673i
\(118\) 0 0
\(119\) 4.01257 0.367832
\(120\) 0 0
\(121\) 17.8346i 1.62133i
\(122\) 0 0
\(123\) −14.2355 4.31674i −1.28357 0.389227i
\(124\) 0 0
\(125\) 11.2206i 1.00360i
\(126\) 0 0
\(127\) −12.1760 −1.08045 −0.540223 0.841522i \(-0.681660\pi\)
−0.540223 + 0.841522i \(0.681660\pi\)
\(128\) 0 0
\(129\) 2.23220 2.23220i 0.196535 0.196535i
\(130\) 0 0
\(131\) 1.19620i 0.104512i 0.998634 + 0.0522561i \(0.0166412\pi\)
−0.998634 + 0.0522561i \(0.983359\pi\)
\(132\) 0 0
\(133\) 7.97181 0.691244
\(134\) 0 0
\(135\) 1.37804 + 1.37804i 0.118603 + 0.118603i
\(136\) 0 0
\(137\) 6.88192 6.88192i 0.587962 0.587962i −0.349117 0.937079i \(-0.613518\pi\)
0.937079 + 0.349117i \(0.113518\pi\)
\(138\) 0 0
\(139\) 13.0070 1.10324 0.551620 0.834096i \(-0.314010\pi\)
0.551620 + 0.834096i \(0.314010\pi\)
\(140\) 0 0
\(141\) 30.7444 2.58915
\(142\) 0 0
\(143\) 25.8944i 2.16540i
\(144\) 0 0
\(145\) −3.86635 + 3.86635i −0.321083 + 0.321083i
\(146\) 0 0
\(147\) 1.64273 1.64273i 0.135490 0.135490i
\(148\) 0 0
\(149\) −2.07975 + 2.07975i −0.170380 + 0.170380i −0.787146 0.616767i \(-0.788442\pi\)
0.616767 + 0.787146i \(0.288442\pi\)
\(150\) 0 0
\(151\) 10.6935 + 10.6935i 0.870224 + 0.870224i 0.992497 0.122272i \(-0.0390181\pi\)
−0.122272 + 0.992497i \(0.539018\pi\)
\(152\) 0 0
\(153\) −6.80143 6.80143i −0.549863 0.549863i
\(154\) 0 0
\(155\) 3.99861i 0.321176i
\(156\) 0 0
\(157\) 11.8460 + 11.8460i 0.945413 + 0.945413i 0.998585 0.0531721i \(-0.0169332\pi\)
−0.0531721 + 0.998585i \(0.516933\pi\)
\(158\) 0 0
\(159\) 18.6328i 1.47768i
\(160\) 0 0
\(161\) −1.89976 1.89976i −0.149722 0.149722i
\(162\) 0 0
\(163\) −8.57541 −0.671678 −0.335839 0.941919i \(-0.609020\pi\)
−0.335839 + 0.941919i \(0.609020\pi\)
\(164\) 0 0
\(165\) −17.3585 −1.35136
\(166\) 0 0
\(167\) −11.6900 11.6900i −0.904603 0.904603i 0.0912274 0.995830i \(-0.470921\pi\)
−0.995830 + 0.0912274i \(0.970921\pi\)
\(168\) 0 0
\(169\) 10.2540i 0.788773i
\(170\) 0 0
\(171\) −13.5125 13.5125i −1.03332 1.03332i
\(172\) 0 0
\(173\) 13.1738i 1.00158i −0.865568 0.500791i \(-0.833042\pi\)
0.865568 0.500791i \(-0.166958\pi\)
\(174\) 0 0
\(175\) −2.16644 2.16644i −0.163767 0.163767i
\(176\) 0 0
\(177\) −10.2886 10.2886i −0.773336 0.773336i
\(178\) 0 0
\(179\) −12.9575 + 12.9575i −0.968487 + 0.968487i −0.999518 0.0310315i \(-0.990121\pi\)
0.0310315 + 0.999518i \(0.490121\pi\)
\(180\) 0 0
\(181\) −1.88580 + 1.88580i −0.140170 + 0.140170i −0.773710 0.633540i \(-0.781601\pi\)
0.633540 + 0.773710i \(0.281601\pi\)
\(182\) 0 0
\(183\) −14.5715 + 14.5715i −1.07716 + 1.07716i
\(184\) 0 0
\(185\) 8.39981i 0.617566i
\(186\) 0 0
\(187\) −21.5466 −1.57565
\(188\) 0 0
\(189\) 1.40056 0.101876
\(190\) 0 0
\(191\) −4.02417 + 4.02417i −0.291178 + 0.291178i −0.837546 0.546367i \(-0.816010\pi\)
0.546367 + 0.837546i \(0.316010\pi\)
\(192\) 0 0
\(193\) 12.5676 + 12.5676i 0.904637 + 0.904637i 0.995833 0.0911963i \(-0.0290691\pi\)
−0.0911963 + 0.995833i \(0.529069\pi\)
\(194\) 0 0
\(195\) −15.5886 −1.11632
\(196\) 0 0
\(197\) 0.835521i 0.0595284i 0.999557 + 0.0297642i \(0.00947565\pi\)
−0.999557 + 0.0297642i \(0.990524\pi\)
\(198\) 0 0
\(199\) 5.34776 5.34776i 0.379093 0.379093i −0.491682 0.870775i \(-0.663618\pi\)
0.870775 + 0.491682i \(0.163618\pi\)
\(200\) 0 0
\(201\) −11.5441 −0.814260
\(202\) 0 0
\(203\) 3.92954i 0.275800i
\(204\) 0 0
\(205\) −4.20082 7.85730i −0.293398 0.548778i
\(206\) 0 0
\(207\) 6.44029i 0.447631i
\(208\) 0 0
\(209\) −42.8069 −2.96102
\(210\) 0 0
\(211\) −9.90360 + 9.90360i −0.681792 + 0.681792i −0.960404 0.278612i \(-0.910126\pi\)
0.278612 + 0.960404i \(0.410126\pi\)
\(212\) 0 0
\(213\) 3.99372i 0.273645i
\(214\) 0 0
\(215\) 1.89078 0.128950
\(216\) 0 0
\(217\) −2.03198 2.03198i −0.137940 0.137940i
\(218\) 0 0
\(219\) 20.8967 20.8967i 1.41207 1.41207i
\(220\) 0 0
\(221\) −19.3496 −1.30160
\(222\) 0 0
\(223\) 18.8022 1.25909 0.629543 0.776965i \(-0.283242\pi\)
0.629543 + 0.776965i \(0.283242\pi\)
\(224\) 0 0
\(225\) 7.34435i 0.489623i
\(226\) 0 0
\(227\) 15.7584 15.7584i 1.04592 1.04592i 0.0470287 0.998894i \(-0.485025\pi\)
0.998894 0.0470287i \(-0.0149752\pi\)
\(228\) 0 0
\(229\) −19.5153 + 19.5153i −1.28961 + 1.28961i −0.354583 + 0.935024i \(0.615377\pi\)
−0.935024 + 0.354583i \(0.884623\pi\)
\(230\) 0 0
\(231\) −8.82112 + 8.82112i −0.580387 + 0.580387i
\(232\) 0 0
\(233\) 3.06475 + 3.06475i 0.200779 + 0.200779i 0.800334 0.599555i \(-0.204656\pi\)
−0.599555 + 0.800334i \(0.704656\pi\)
\(234\) 0 0
\(235\) 13.0210 + 13.0210i 0.849397 + 0.849397i
\(236\) 0 0
\(237\) 21.7200i 1.41086i
\(238\) 0 0
\(239\) 4.89582 + 4.89582i 0.316684 + 0.316684i 0.847492 0.530808i \(-0.178111\pi\)
−0.530808 + 0.847492i \(0.678111\pi\)
\(240\) 0 0
\(241\) 4.74927i 0.305928i −0.988232 0.152964i \(-0.951118\pi\)
0.988232 0.152964i \(-0.0488818\pi\)
\(242\) 0 0
\(243\) −14.1875 14.1875i −0.910131 0.910131i
\(244\) 0 0
\(245\) 1.39147 0.0888980
\(246\) 0 0
\(247\) −38.4420 −2.44601
\(248\) 0 0
\(249\) 6.47475 + 6.47475i 0.410321 + 0.410321i
\(250\) 0 0
\(251\) 9.44955i 0.596450i −0.954496 0.298225i \(-0.903605\pi\)
0.954496 0.298225i \(-0.0963947\pi\)
\(252\) 0 0
\(253\) 10.2013 + 10.2013i 0.641349 + 0.641349i
\(254\) 0 0
\(255\) 12.9712i 0.812286i
\(256\) 0 0
\(257\) −15.6853 15.6853i −0.978419 0.978419i 0.0213529 0.999772i \(-0.493203\pi\)
−0.999772 + 0.0213529i \(0.993203\pi\)
\(258\) 0 0
\(259\) −4.26854 4.26854i −0.265234 0.265234i
\(260\) 0 0
\(261\) 6.66069 6.66069i 0.412286 0.412286i
\(262\) 0 0
\(263\) −18.3551 + 18.3551i −1.13183 + 1.13183i −0.141953 + 0.989873i \(0.545338\pi\)
−0.989873 + 0.141953i \(0.954662\pi\)
\(264\) 0 0
\(265\) 7.89145 7.89145i 0.484768 0.484768i
\(266\) 0 0
\(267\) 2.66883i 0.163330i
\(268\) 0 0
\(269\) 29.5365 1.80087 0.900435 0.434991i \(-0.143248\pi\)
0.900435 + 0.434991i \(0.143248\pi\)
\(270\) 0 0
\(271\) 12.9241 0.785082 0.392541 0.919735i \(-0.371596\pi\)
0.392541 + 0.919735i \(0.371596\pi\)
\(272\) 0 0
\(273\) −7.92165 + 7.92165i −0.479440 + 0.479440i
\(274\) 0 0
\(275\) 11.6333 + 11.6333i 0.701514 + 0.701514i
\(276\) 0 0
\(277\) −28.1335 −1.69038 −0.845189 0.534468i \(-0.820512\pi\)
−0.845189 + 0.534468i \(0.820512\pi\)
\(278\) 0 0
\(279\) 6.88854i 0.412406i
\(280\) 0 0
\(281\) −9.16870 + 9.16870i −0.546959 + 0.546959i −0.925560 0.378601i \(-0.876405\pi\)
0.378601 + 0.925560i \(0.376405\pi\)
\(282\) 0 0
\(283\) −5.44352 −0.323584 −0.161792 0.986825i \(-0.551727\pi\)
−0.161792 + 0.986825i \(0.551727\pi\)
\(284\) 0 0
\(285\) 25.7699i 1.52648i
\(286\) 0 0
\(287\) −6.12759 1.85812i −0.361700 0.109681i
\(288\) 0 0
\(289\) 0.899270i 0.0528982i
\(290\) 0 0
\(291\) 43.8779 2.57217
\(292\) 0 0
\(293\) 12.7779 12.7779i 0.746493 0.746493i −0.227326 0.973819i \(-0.572998\pi\)
0.973819 + 0.227326i \(0.0729982\pi\)
\(294\) 0 0
\(295\) 8.71491i 0.507402i
\(296\) 0 0
\(297\) −7.52071 −0.436396
\(298\) 0 0
\(299\) 9.16109 + 9.16109i 0.529800 + 0.529800i
\(300\) 0 0
\(301\) 0.960843 0.960843i 0.0553820 0.0553820i
\(302\) 0 0
\(303\) −25.1886 −1.44705
\(304\) 0 0
\(305\) −12.3428 −0.706746
\(306\) 0 0
\(307\) 26.0196i 1.48502i 0.669836 + 0.742509i \(0.266365\pi\)
−0.669836 + 0.742509i \(0.733635\pi\)
\(308\) 0 0
\(309\) 12.6690 12.6690i 0.720717 0.720717i
\(310\) 0 0
\(311\) −3.91468 + 3.91468i −0.221981 + 0.221981i −0.809332 0.587351i \(-0.800171\pi\)
0.587351 + 0.809332i \(0.300171\pi\)
\(312\) 0 0
\(313\) 18.4030 18.4030i 1.04020 1.04020i 0.0410391 0.999158i \(-0.486933\pi\)
0.999158 0.0410391i \(-0.0130668\pi\)
\(314\) 0 0
\(315\) −2.35859 2.35859i −0.132891 0.132891i
\(316\) 0 0
\(317\) −7.37950 7.37950i −0.414474 0.414474i 0.468820 0.883294i \(-0.344679\pi\)
−0.883294 + 0.468820i \(0.844679\pi\)
\(318\) 0 0
\(319\) 21.1008i 1.18142i
\(320\) 0 0
\(321\) −4.67541 4.67541i −0.260956 0.260956i
\(322\) 0 0
\(323\) 31.9875i 1.77983i
\(324\) 0 0
\(325\) 10.4471 + 10.4471i 0.579500 + 0.579500i
\(326\) 0 0
\(327\) −36.6817 −2.02850
\(328\) 0 0
\(329\) 13.2338 0.729603
\(330\) 0 0
\(331\) −3.98460 3.98460i −0.219014 0.219014i 0.589069 0.808083i \(-0.299495\pi\)
−0.808083 + 0.589069i \(0.799495\pi\)
\(332\) 0 0
\(333\) 14.4706i 0.792985i
\(334\) 0 0
\(335\) −4.88922 4.88922i −0.267127 0.267127i
\(336\) 0 0
\(337\) 29.4260i 1.60294i 0.598037 + 0.801469i \(0.295948\pi\)
−0.598037 + 0.801469i \(0.704052\pi\)
\(338\) 0 0
\(339\) −0.0864813 0.0864813i −0.00469702 0.00469702i
\(340\) 0 0
\(341\) 10.9113 + 10.9113i 0.590880 + 0.590880i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 0 0
\(345\) −6.14121 + 6.14121i −0.330632 + 0.330632i
\(346\) 0 0
\(347\) 23.3854 23.3854i 1.25540 1.25540i 0.302128 0.953267i \(-0.402303\pi\)
0.953267 0.302128i \(-0.0976970\pi\)
\(348\) 0 0
\(349\) 12.8398i 0.687298i 0.939098 + 0.343649i \(0.111663\pi\)
−0.939098 + 0.343649i \(0.888337\pi\)
\(350\) 0 0
\(351\) −6.75385 −0.360494
\(352\) 0 0
\(353\) −26.4153 −1.40594 −0.702971 0.711218i \(-0.748144\pi\)
−0.702971 + 0.711218i \(0.748144\pi\)
\(354\) 0 0
\(355\) −1.69144 + 1.69144i −0.0897722 + 0.0897722i
\(356\) 0 0
\(357\) −6.59158 6.59158i −0.348863 0.348863i
\(358\) 0 0
\(359\) 21.3610 1.12739 0.563695 0.825983i \(-0.309379\pi\)
0.563695 + 0.825983i \(0.309379\pi\)
\(360\) 0 0
\(361\) 44.5498i 2.34473i
\(362\) 0 0
\(363\) 29.2974 29.2974i 1.53772 1.53772i
\(364\) 0 0
\(365\) 17.7005 0.926485
\(366\) 0 0
\(367\) 35.7700i 1.86718i 0.358348 + 0.933588i \(0.383340\pi\)
−0.358348 + 0.933588i \(0.616660\pi\)
\(368\) 0 0
\(369\) 7.23688 + 13.5360i 0.376737 + 0.704657i
\(370\) 0 0
\(371\) 8.02042i 0.416400i
\(372\) 0 0
\(373\) 2.33828 0.121072 0.0605358 0.998166i \(-0.480719\pi\)
0.0605358 + 0.998166i \(0.480719\pi\)
\(374\) 0 0
\(375\) −18.4324 + 18.4324i −0.951844 + 0.951844i
\(376\) 0 0
\(377\) 18.9492i 0.975934i
\(378\) 0 0
\(379\) 16.1375 0.828930 0.414465 0.910065i \(-0.363969\pi\)
0.414465 + 0.910065i \(0.363969\pi\)
\(380\) 0 0
\(381\) 20.0019 + 20.0019i 1.02473 + 1.02473i
\(382\) 0 0
\(383\) 14.2602 14.2602i 0.728663 0.728663i −0.241691 0.970353i \(-0.577702\pi\)
0.970353 + 0.241691i \(0.0777019\pi\)
\(384\) 0 0
\(385\) −7.47191 −0.380804
\(386\) 0 0
\(387\) −3.25731 −0.165579
\(388\) 0 0
\(389\) 0.673571i 0.0341514i 0.999854 + 0.0170757i \(0.00543563\pi\)
−0.999854 + 0.0170757i \(0.994564\pi\)
\(390\) 0 0
\(391\) −7.62291 + 7.62291i −0.385507 + 0.385507i
\(392\) 0 0
\(393\) 1.96503 1.96503i 0.0991226 0.0991226i
\(394\) 0 0
\(395\) −9.19893 + 9.19893i −0.462849 + 0.462849i
\(396\) 0 0
\(397\) 20.1287 + 20.1287i 1.01023 + 1.01023i 0.999947 + 0.0102814i \(0.00327272\pi\)
0.0102814 + 0.999947i \(0.496727\pi\)
\(398\) 0 0
\(399\) −13.0955 13.0955i −0.655597 0.655597i
\(400\) 0 0
\(401\) 26.1701i 1.30687i 0.756982 + 0.653436i \(0.226673\pi\)
−0.756982 + 0.653436i \(0.773327\pi\)
\(402\) 0 0
\(403\) 9.79871 + 9.79871i 0.488109 + 0.488109i
\(404\) 0 0
\(405\) 14.5341i 0.722207i
\(406\) 0 0
\(407\) 22.9212 + 22.9212i 1.13616 + 1.13616i
\(408\) 0 0
\(409\) −15.2193 −0.752545 −0.376273 0.926509i \(-0.622794\pi\)
−0.376273 + 0.926509i \(0.622794\pi\)
\(410\) 0 0
\(411\) −22.6103 −1.11528
\(412\) 0 0
\(413\) −4.42867 4.42867i −0.217921 0.217921i
\(414\) 0 0
\(415\) 5.48443i 0.269220i
\(416\) 0 0
\(417\) −21.3670 21.3670i −1.04635 1.04635i
\(418\) 0 0
\(419\) 27.8634i 1.36121i −0.732649 0.680607i \(-0.761716\pi\)
0.732649 0.680607i \(-0.238284\pi\)
\(420\) 0 0
\(421\) 10.2472 + 10.2472i 0.499420 + 0.499420i 0.911257 0.411838i \(-0.135113\pi\)
−0.411838 + 0.911257i \(0.635113\pi\)
\(422\) 0 0
\(423\) −22.4317 22.4317i −1.09067 1.09067i
\(424\) 0 0
\(425\) −8.69298 + 8.69298i −0.421671 + 0.421671i
\(426\) 0 0
\(427\) −6.27225 + 6.27225i −0.303536 + 0.303536i
\(428\) 0 0
\(429\) 42.5376 42.5376i 2.05373 2.05373i
\(430\) 0 0
\(431\) 16.0920i 0.775123i −0.921844 0.387562i \(-0.873317\pi\)
0.921844 0.387562i \(-0.126683\pi\)
\(432\) 0 0
\(433\) 19.8042 0.951728 0.475864 0.879519i \(-0.342135\pi\)
0.475864 + 0.879519i \(0.342135\pi\)
\(434\) 0 0
\(435\) 12.7028 0.609051
\(436\) 0 0
\(437\) −15.1445 + 15.1445i −0.724460 + 0.724460i
\(438\) 0 0
\(439\) −13.3291 13.3291i −0.636161 0.636161i 0.313445 0.949606i \(-0.398517\pi\)
−0.949606 + 0.313445i \(0.898517\pi\)
\(440\) 0 0
\(441\) −2.39713 −0.114149
\(442\) 0 0
\(443\) 31.6454i 1.50352i −0.659439 0.751758i \(-0.729206\pi\)
0.659439 0.751758i \(-0.270794\pi\)
\(444\) 0 0
\(445\) −1.13031 + 1.13031i −0.0535820 + 0.0535820i
\(446\) 0 0
\(447\) 6.83294 0.323187
\(448\) 0 0
\(449\) 25.1004i 1.18456i 0.805732 + 0.592280i \(0.201772\pi\)
−0.805732 + 0.592280i \(0.798228\pi\)
\(450\) 0 0
\(451\) 32.9039 + 9.97771i 1.54938 + 0.469832i
\(452\) 0 0
\(453\) 35.1331i 1.65070i
\(454\) 0 0
\(455\) −6.71002 −0.314571
\(456\) 0 0
\(457\) −14.2221 + 14.2221i −0.665281 + 0.665281i −0.956620 0.291339i \(-0.905899\pi\)
0.291339 + 0.956620i \(0.405899\pi\)
\(458\) 0 0
\(459\) 5.61985i 0.262312i
\(460\) 0 0
\(461\) 4.50977 0.210041 0.105020 0.994470i \(-0.466509\pi\)
0.105020 + 0.994470i \(0.466509\pi\)
\(462\) 0 0
\(463\) 10.3359 + 10.3359i 0.480349 + 0.480349i 0.905243 0.424894i \(-0.139689\pi\)
−0.424894 + 0.905243i \(0.639689\pi\)
\(464\) 0 0
\(465\) −6.56865 + 6.56865i −0.304614 + 0.304614i
\(466\) 0 0
\(467\) 4.22742 0.195622 0.0978109 0.995205i \(-0.468816\pi\)
0.0978109 + 0.995205i \(0.468816\pi\)
\(468\) 0 0
\(469\) −4.96912 −0.229453
\(470\) 0 0
\(471\) 38.9196i 1.79332i
\(472\) 0 0
\(473\) −5.15952 + 5.15952i −0.237235 + 0.237235i
\(474\) 0 0
\(475\) −17.2704 + 17.2704i −0.792421 + 0.792421i
\(476\) 0 0
\(477\) −13.5949 + 13.5949i −0.622466 + 0.622466i
\(478\) 0 0
\(479\) −0.0501173 0.0501173i −0.00228992 0.00228992i 0.705961 0.708251i \(-0.250515\pi\)
−0.708251 + 0.705961i \(0.750515\pi\)
\(480\) 0 0
\(481\) 20.5840 + 20.5840i 0.938548 + 0.938548i
\(482\) 0 0
\(483\) 6.24158i 0.284002i
\(484\) 0 0
\(485\) 18.5834 + 18.5834i 0.843827 + 0.843827i
\(486\) 0 0
\(487\) 9.41980i 0.426852i 0.976959 + 0.213426i \(0.0684622\pi\)
−0.976959 + 0.213426i \(0.931538\pi\)
\(488\) 0 0
\(489\) 14.0871 + 14.0871i 0.637041 + 0.637041i
\(490\) 0 0
\(491\) 26.6650 1.20338 0.601688 0.798731i \(-0.294495\pi\)
0.601688 + 0.798731i \(0.294495\pi\)
\(492\) 0 0
\(493\) 15.7676 0.710135
\(494\) 0 0
\(495\) 12.6651 + 12.6651i 0.569255 + 0.569255i
\(496\) 0 0
\(497\) 1.71908i 0.0771113i
\(498\) 0 0
\(499\) 8.25372 + 8.25372i 0.369487 + 0.369487i 0.867290 0.497803i \(-0.165860\pi\)
−0.497803 + 0.867290i \(0.665860\pi\)
\(500\) 0 0
\(501\) 38.4072i 1.71591i
\(502\) 0 0
\(503\) 9.14704 + 9.14704i 0.407847 + 0.407847i 0.880987 0.473140i \(-0.156880\pi\)
−0.473140 + 0.880987i \(0.656880\pi\)
\(504\) 0 0
\(505\) −10.6680 10.6680i −0.474720 0.474720i
\(506\) 0 0
\(507\) 16.8447 16.8447i 0.748097 0.748097i
\(508\) 0 0
\(509\) 28.9559 28.9559i 1.28345 1.28345i 0.344758 0.938691i \(-0.387961\pi\)
0.938691 0.344758i \(-0.112039\pi\)
\(510\) 0 0
\(511\) 8.99488 8.99488i 0.397910 0.397910i
\(512\) 0 0
\(513\) 11.1650i 0.492947i
\(514\) 0 0
\(515\) 10.7313 0.472877
\(516\) 0 0
\(517\) −71.0627 −3.12533
\(518\) 0 0
\(519\) −21.6410 + 21.6410i −0.949933 + 0.949933i
\(520\) 0 0
\(521\) −30.0372 30.0372i −1.31595 1.31595i −0.916948 0.399006i \(-0.869355\pi\)
−0.399006 0.916948i \(-0.630645\pi\)
\(522\) 0 0
\(523\) −6.87633 −0.300681 −0.150340 0.988634i \(-0.548037\pi\)
−0.150340 + 0.988634i \(0.548037\pi\)
\(524\) 0 0
\(525\) 7.11774i 0.310644i
\(526\) 0 0
\(527\) −8.15347 + 8.15347i −0.355171 + 0.355171i
\(528\) 0 0
\(529\) −15.7819 −0.686168
\(530\) 0 0
\(531\) 15.0135i 0.651528i
\(532\) 0 0
\(533\) 29.5488 + 8.96032i 1.27990 + 0.388114i
\(534\) 0 0
\(535\) 3.96030i 0.171219i
\(536\) 0 0
\(537\) 42.5713 1.83709
\(538\) 0 0
\(539\) −3.79701 + 3.79701i −0.163549 + 0.163549i
\(540\) 0 0
\(541\) 13.3066i 0.572096i −0.958215 0.286048i \(-0.907658\pi\)
0.958215 0.286048i \(-0.0923416\pi\)
\(542\) 0 0
\(543\) 6.19572 0.265884
\(544\) 0 0
\(545\) −15.5356 15.5356i −0.665471 0.665471i
\(546\) 0 0
\(547\) −5.31007 + 5.31007i −0.227042 + 0.227042i −0.811456 0.584414i \(-0.801325\pi\)
0.584414 + 0.811456i \(0.301325\pi\)
\(548\) 0 0
\(549\) 21.2633 0.907496
\(550\) 0 0
\(551\) 31.3256 1.33451
\(552\) 0 0
\(553\) 9.34927i 0.397571i
\(554\) 0 0
\(555\) −13.7986 + 13.7986i −0.585719 + 0.585719i
\(556\) 0 0
\(557\) −26.0301 + 26.0301i −1.10293 + 1.10293i −0.108876 + 0.994055i \(0.534725\pi\)
−0.994055 + 0.108876i \(0.965275\pi\)
\(558\) 0 0
\(559\) −4.63342 + 4.63342i −0.195973 + 0.195973i
\(560\) 0 0
\(561\) 35.3954 + 35.3954i 1.49439 + 1.49439i
\(562\) 0 0
\(563\) 1.57386 + 1.57386i 0.0663304 + 0.0663304i 0.739494 0.673163i \(-0.235065\pi\)
−0.673163 + 0.739494i \(0.735065\pi\)
\(564\) 0 0
\(565\) 0.0732538i 0.00308181i
\(566\) 0 0
\(567\) −7.38584 7.38584i −0.310176 0.310176i
\(568\) 0 0
\(569\) 20.3768i 0.854240i −0.904195 0.427120i \(-0.859528\pi\)
0.904195 0.427120i \(-0.140472\pi\)
\(570\) 0 0
\(571\) −28.2426 28.2426i −1.18191 1.18191i −0.979248 0.202666i \(-0.935039\pi\)
−0.202666 0.979248i \(-0.564961\pi\)
\(572\) 0 0
\(573\) 13.2212 0.552326
\(574\) 0 0
\(575\) 8.23140 0.343273
\(576\) 0 0
\(577\) −21.8765 21.8765i −0.910731 0.910731i 0.0855985 0.996330i \(-0.472720\pi\)
−0.996330 + 0.0855985i \(0.972720\pi\)
\(578\) 0 0
\(579\) 41.2904i 1.71597i
\(580\) 0 0
\(581\) 2.78703 + 2.78703i 0.115625 + 0.115625i
\(582\) 0 0
\(583\) 43.0679i 1.78369i
\(584\) 0 0
\(585\) 11.3737 + 11.3737i 0.470244 + 0.470244i
\(586\) 0 0
\(587\) 3.07961 + 3.07961i 0.127109 + 0.127109i 0.767799 0.640690i \(-0.221352\pi\)
−0.640690 + 0.767799i \(0.721352\pi\)
\(588\) 0 0
\(589\) −16.1986 + 16.1986i −0.667451 + 0.667451i
\(590\) 0 0
\(591\) 1.37254 1.37254i 0.0564587 0.0564587i
\(592\) 0 0
\(593\) −5.45050 + 5.45050i −0.223825 + 0.223825i −0.810107 0.586282i \(-0.800591\pi\)
0.586282 + 0.810107i \(0.300591\pi\)
\(594\) 0 0
\(595\) 5.58339i 0.228896i
\(596\) 0 0
\(597\) −17.5699 −0.719087
\(598\) 0 0
\(599\) −6.92947 −0.283131 −0.141565 0.989929i \(-0.545214\pi\)
−0.141565 + 0.989929i \(0.545214\pi\)
\(600\) 0 0
\(601\) 9.89809 9.89809i 0.403752 0.403752i −0.475801 0.879553i \(-0.657842\pi\)
0.879553 + 0.475801i \(0.157842\pi\)
\(602\) 0 0
\(603\) 8.42281 + 8.42281i 0.343003 + 0.343003i
\(604\) 0 0
\(605\) 24.8164 1.00893
\(606\) 0 0
\(607\) 14.3632i 0.582983i −0.956573 0.291492i \(-0.905848\pi\)
0.956573 0.291492i \(-0.0941516\pi\)
\(608\) 0 0
\(609\) 6.45518 6.45518i 0.261577 0.261577i
\(610\) 0 0
\(611\) −63.8167 −2.58175
\(612\) 0 0
\(613\) 21.5867i 0.871877i −0.899976 0.435938i \(-0.856417\pi\)
0.899976 0.435938i \(-0.143583\pi\)
\(614\) 0 0
\(615\) −6.00663 + 19.8083i −0.242210 + 0.798746i
\(616\) 0 0
\(617\) 44.0803i 1.77461i −0.461188 0.887303i \(-0.652577\pi\)
0.461188 0.887303i \(-0.347423\pi\)
\(618\) 0 0
\(619\) 2.56103 0.102936 0.0514682 0.998675i \(-0.483610\pi\)
0.0514682 + 0.998675i \(0.483610\pi\)
\(620\) 0 0
\(621\) −2.66072 + 2.66072i −0.106771 + 0.106771i
\(622\) 0 0
\(623\) 1.14879i 0.0460252i
\(624\) 0 0
\(625\) −0.294100 −0.0117640
\(626\) 0 0
\(627\) 70.3203 + 70.3203i 2.80832 + 2.80832i
\(628\) 0 0
\(629\) −17.1278 + 17.1278i −0.682932 + 0.682932i
\(630\) 0 0
\(631\) 1.71634 0.0683262 0.0341631 0.999416i \(-0.489123\pi\)
0.0341631 + 0.999416i \(0.489123\pi\)
\(632\) 0 0
\(633\) 32.5379 1.29327
\(634\) 0 0
\(635\) 16.9426i 0.672346i
\(636\) 0 0
\(637\) −3.40984 + 3.40984i −0.135103 + 0.135103i
\(638\) 0 0
\(639\) 2.91389 2.91389i 0.115272 0.115272i
\(640\) 0 0
\(641\) 7.78184 7.78184i 0.307364 0.307364i −0.536522 0.843886i \(-0.680262\pi\)
0.843886 + 0.536522i \(0.180262\pi\)
\(642\) 0 0
\(643\) −15.1384 15.1384i −0.597001 0.597001i 0.342512 0.939513i \(-0.388722\pi\)
−0.939513 + 0.342512i \(0.888722\pi\)
\(644\) 0 0
\(645\) −3.10605 3.10605i −0.122301 0.122301i
\(646\) 0 0
\(647\) 2.71048i 0.106560i 0.998580 + 0.0532799i \(0.0169676\pi\)
−0.998580 + 0.0532799i \(0.983032\pi\)
\(648\) 0 0
\(649\) 23.7810 + 23.7810i 0.933486 + 0.933486i
\(650\) 0 0
\(651\) 6.67600i 0.261653i
\(652\) 0 0
\(653\) −0.968876 0.968876i −0.0379150 0.0379150i 0.687895 0.725810i \(-0.258535\pi\)
−0.725810 + 0.687895i \(0.758535\pi\)
\(654\) 0 0
\(655\) 1.66447 0.0650364
\(656\) 0 0
\(657\) −30.4932 −1.18965
\(658\) 0 0
\(659\) 1.80935 + 1.80935i 0.0704822 + 0.0704822i 0.741469 0.670987i \(-0.234129\pi\)
−0.670987 + 0.741469i \(0.734129\pi\)
\(660\) 0 0
\(661\) 42.6971i 1.66072i 0.557224 + 0.830362i \(0.311867\pi\)
−0.557224 + 0.830362i \(0.688133\pi\)
\(662\) 0 0
\(663\) 31.7862 + 31.7862i 1.23447 + 1.23447i
\(664\) 0 0
\(665\) 11.0926i 0.430151i
\(666\) 0 0
\(667\) −7.46517 7.46517i −0.289053 0.289053i
\(668\) 0 0
\(669\) −30.8869 30.8869i −1.19416 1.19416i
\(670\) 0 0
\(671\) 33.6807 33.6807i 1.30023 1.30023i
\(672\) 0 0
\(673\) 21.5076 21.5076i 0.829058 0.829058i −0.158329 0.987386i \(-0.550611\pi\)
0.987386 + 0.158329i \(0.0506106\pi\)
\(674\) 0 0
\(675\) −3.03422 + 3.03422i −0.116787 + 0.116787i
\(676\) 0 0
\(677\) 17.1202i 0.657981i 0.944333 + 0.328991i \(0.106708\pi\)
−0.944333 + 0.328991i \(0.893292\pi\)
\(678\) 0 0
\(679\) 18.8871 0.724819
\(680\) 0 0
\(681\) −51.7737 −1.98397
\(682\) 0 0
\(683\) 6.88317 6.88317i 0.263377 0.263377i −0.563048 0.826425i \(-0.690371\pi\)
0.826425 + 0.563048i \(0.190371\pi\)
\(684\) 0 0
\(685\) −9.57601 9.57601i −0.365880 0.365880i
\(686\) 0 0
\(687\) 64.1168 2.44621
\(688\) 0 0
\(689\) 38.6764i 1.47346i
\(690\) 0 0
\(691\) 25.9965 25.9965i 0.988954 0.988954i −0.0109857 0.999940i \(-0.503497\pi\)
0.999940 + 0.0109857i \(0.00349692\pi\)
\(692\) 0 0
\(693\) 12.8721 0.488971
\(694\) 0 0
\(695\) 18.0989i 0.686531i
\(696\) 0 0
\(697\) −7.45584 + 24.5874i −0.282410 + 0.931314i
\(698\) 0 0
\(699\) 10.0691i 0.380850i
\(700\) 0 0
\(701\) −16.4487 −0.621260 −0.310630 0.950531i \(-0.600540\pi\)
−0.310630 + 0.950531i \(0.600540\pi\)
\(702\) 0 0
\(703\) −34.0280 + 34.0280i −1.28339 + 1.28339i
\(704\) 0 0
\(705\) 42.7801i 1.61119i
\(706\) 0 0
\(707\) −10.8423 −0.407768
\(708\) 0 0
\(709\) 4.86608 + 4.86608i 0.182750 + 0.182750i 0.792553 0.609803i \(-0.208752\pi\)
−0.609803 + 0.792553i \(0.708752\pi\)
\(710\) 0 0
\(711\) 15.8473 15.8473i 0.594320 0.594320i
\(712\) 0 0
\(713\) 7.72054 0.289136
\(714\) 0 0
\(715\) 36.0314 1.34750
\(716\) 0 0
\(717\) 16.0850i 0.600707i
\(718\) 0 0
\(719\) −2.94403 + 2.94403i −0.109794 + 0.109794i −0.759869 0.650076i \(-0.774737\pi\)
0.650076 + 0.759869i \(0.274737\pi\)
\(720\) 0 0
\(721\) 5.45333 5.45333i 0.203093 0.203093i
\(722\) 0 0
\(723\) −7.80178 + 7.80178i −0.290151 + 0.290151i
\(724\) 0 0
\(725\) −8.51310 8.51310i −0.316169 0.316169i
\(726\) 0 0
\(727\) −24.1263 24.1263i −0.894794 0.894794i 0.100176 0.994970i \(-0.468059\pi\)
−0.994970 + 0.100176i \(0.968059\pi\)
\(728\) 0 0
\(729\) 15.2772i 0.565822i
\(730\) 0 0
\(731\) −3.85545 3.85545i −0.142599 0.142599i
\(732\) 0 0
\(733\) 21.2740i 0.785772i −0.919587 0.392886i \(-0.871477\pi\)
0.919587 0.392886i \(-0.128523\pi\)
\(734\) 0 0
\(735\) −2.28582 2.28582i −0.0843136 0.0843136i
\(736\) 0 0
\(737\) 26.6831 0.982885
\(738\) 0 0
\(739\) 10.9835 0.404036 0.202018 0.979382i \(-0.435250\pi\)
0.202018 + 0.979382i \(0.435250\pi\)
\(740\) 0 0
\(741\) 63.1499 + 63.1499i 2.31987 + 2.31987i
\(742\) 0 0
\(743\) 15.4013i 0.565020i −0.959264 0.282510i \(-0.908833\pi\)
0.959264 0.282510i \(-0.0911671\pi\)
\(744\) 0 0
\(745\) 2.89391 + 2.89391i 0.106025 + 0.106025i
\(746\) 0 0
\(747\) 9.44819i 0.345691i
\(748\) 0 0
\(749\) −2.01251 2.01251i −0.0735355 0.0735355i
\(750\) 0 0
\(751\) 10.8862 + 10.8862i 0.397244 + 0.397244i 0.877260 0.480016i \(-0.159369\pi\)
−0.480016 + 0.877260i \(0.659369\pi\)
\(752\) 0 0
\(753\) −15.5231 + 15.5231i −0.565692 + 0.565692i
\(754\) 0 0
\(755\) 14.8797 14.8797i 0.541528 0.541528i
\(756\) 0 0
\(757\) 1.36164 1.36164i 0.0494898 0.0494898i −0.681929 0.731419i \(-0.738859\pi\)
0.731419 + 0.681929i \(0.238859\pi\)
\(758\) 0 0
\(759\) 33.5159i 1.21655i
\(760\) 0 0
\(761\) −47.1115 −1.70779 −0.853895 0.520445i \(-0.825766\pi\)
−0.853895 + 0.520445i \(0.825766\pi\)
\(762\) 0 0
\(763\) −15.7895 −0.571617
\(764\) 0 0
\(765\) −9.46401 + 9.46401i −0.342172 + 0.342172i
\(766\) 0 0
\(767\) 21.3561 + 21.3561i 0.771125 + 0.771125i
\(768\) 0 0
\(769\) −14.8813 −0.536634 −0.268317 0.963331i \(-0.586467\pi\)
−0.268317 + 0.963331i \(0.586467\pi\)
\(770\) 0 0
\(771\) 51.5333i 1.85593i
\(772\) 0 0
\(773\) −15.7968 + 15.7968i −0.568172 + 0.568172i −0.931616 0.363444i \(-0.881601\pi\)
0.363444 + 0.931616i \(0.381601\pi\)
\(774\) 0 0
\(775\) 8.80431 0.316260
\(776\) 0 0
\(777\) 14.0241i 0.503113i
\(778\) 0 0
\(779\) −14.8126 + 48.8480i −0.530716 + 1.75016i
\(780\) 0 0
\(781\) 9.23110i 0.330315i
\(782\) 0 0
\(783\) 5.50356 0.196681
\(784\) 0 0
\(785\) 16.4834 16.4834i 0.588317 0.588317i
\(786\) 0 0
\(787\) 11.3031i 0.402913i −0.979497 0.201457i \(-0.935433\pi\)
0.979497 0.201457i \(-0.0645675\pi\)
\(788\) 0 0
\(789\) 60.3052 2.14692
\(790\) 0 0
\(791\) −0.0372255 0.0372255i −0.00132359 0.00132359i
\(792\) 0 0
\(793\) 30.2463 30.2463i 1.07408 1.07408i
\(794\) 0 0
\(795\) −25.9271 −0.919539
\(796\) 0 0
\(797\) 52.5765 1.86235 0.931177 0.364568i \(-0.118783\pi\)
0.931177 + 0.364568i \(0.118783\pi\)
\(798\) 0 0
\(799\) 53.1016i 1.87860i
\(800\) 0 0
\(801\) 1.94723 1.94723i